Starts dribbling to schaum4.output (2009/2/17, 17:59:58).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate((p*x+q)/sqrt(a*x+b),x)
 

                               +-------+
        (2a p x + 6a q - 4b p)\|a x + b
   (1)  --------------------------------
                         2
                       3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R        (2a p x + 6a q - 4b p)\|a x + b
--R   (1)  --------------------------------
--R                         2
--R                       3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=(2*(a*p*x+3*a*q-2*b*p))/(3*a^2)*sqrt(a*x+b)
 

                               +-------+
        (2a p x + 6a q - 4b p)\|a x + b
   (2)  --------------------------------
                         2
                       3a
                                                     Type: Expression Integer
--R
--R                               +-------+
--R        (2a p x + 6a q - 4b p)\|a x + b
--R   (2)  --------------------------------
--R                         2
--R                       3a
--R                                                     Type: Expression Integer
--E

--S 3      14:113 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x)
 

   (1)
                                                          +--------------+
                      2  +-------+                        |             2
        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
    log(------------------------------------------------------------------)
                                      p x + q
   [-----------------------------------------------------------------------,
                                +--------------+
                                |             2
                               \|- a p q + b p
           +------------+
           |           2  +-------+
          \|a p q - b p  \|a x + b
    2atan(-------------------------)
                  a q - b p
    --------------------------------]
              +------------+
              |           2
             \|a p q - b p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                                                          +--------------+
--R                      2  +-------+                        |             2
--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R    log(------------------------------------------------------------------)
--R                                      p x + q
--R   [-----------------------------------------------------------------------,
--R                                +--------------+
--R                                |             2
--R                               \|- a p q + b p
--R           +------------+
--R           |           2  +-------+
--R          \|a p q - b p  \|a x + b
--R    2atan(-------------------------)
--R                  a q - b p
--R    --------------------------------]
--R              +------------+
--R              |           2
--R             \|a p q - b p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 5
aa1:=aa.1
 

   (2)
                                                         +--------------+
                     2  +-------+                        |             2
       (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
   log(------------------------------------------------------------------)
                                     p x + q
   -----------------------------------------------------------------------
                               +--------------+
                               |             2
                              \|- a p q + b p
                                                     Type: Expression Integer
--R
--R   (2)
--R                                                         +--------------+
--R                     2  +-------+                        |             2
--R       (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R   log(------------------------------------------------------------------)
--R                                     p x + q
--R   -----------------------------------------------------------------------
--R                               +--------------+
--R                               |             2
--R                              \|- a p q + b p
--R                                                     Type: Expression Integer
--E

--S 6
aa2:=aa.2
 

               +------------+
               |           2  +-------+
              \|a p q - b p  \|a x + b
        2atan(-------------------------)
                      a q - b p
   (3)  --------------------------------
                  +------------+
                  |           2
                 \|a p q - b p
                                                     Type: Expression Integer
--R
--R               +------------+
--R               |           2  +-------+
--R              \|a p q - b p  \|a x + b
--R        2atan(-------------------------)
--R                      a q - b p
--R   (3)  --------------------------------
--R                  +------------+
--R                  |           2
--R                 \|a p q - b p
--R                                                     Type: Expression Integer
--E

--S 7
bb1:=1/sqrt(b*p-a*q)*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
 

             +-----------+    +-----------+
            \|a p x + b p  - \|- a q + b p
        log(-------------------------------)
             +-----------+    +-----------+
            \|a p x + b p  + \|- a q + b p
   (4)  ------------------------------------
                    +-----------+
                   \|- a q + b p
                                                     Type: Expression Integer
--R
--R             +-----------+    +-----------+
--R            \|a p x + b p  - \|- a q + b p
--R        log(-------------------------------)
--R             +-----------+    +-----------+
--R            \|a p x + b p  + \|- a q + b p
--R   (4)  ------------------------------------
--R                    +-----------+
--R                   \|- a q + b p
--R                                                     Type: Expression Integer
--E

--S 8
bb2:=2/(sqrt(a*q-b*p)*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
 

               +-----------+
               |a p x + b p
        2atan( |----------- )
              \| a q - b p
   (5)  ---------------------
            +-+ +---------+
           \|p \|a q - b p
                                                     Type: Expression Integer
--R
--R               +-----------+
--R               |a p x + b p
--R        2atan( |----------- )
--R              \| a q - b p
--R   (5)  ---------------------
--R            +-+ +---------+
--R           \|p \|a q - b p
--R                                                     Type: Expression Integer
--E

--S 9
cc1:=aa1-bb1
 

   (6)
          +-----------+
         \|- a q + b p
      *
                                                             +--------------+
                         2  +-------+                        |             2
           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
       log(------------------------------------------------------------------)
                                         p x + q
     + 
          +--------------+     +-----------+    +-----------+
          |             2     \|a p x + b p  - \|- a q + b p
       - \|- a p q + b p  log(-------------------------------)
                               +-----------+    +-----------+
                              \|a p x + b p  + \|- a q + b p
  /
      +--------------+
      |             2  +-----------+
     \|- a p q + b p  \|- a q + b p
                                                     Type: Expression Integer
--R
--R   (6)
--R          +-----------+
--R         \|- a q + b p
--R      *
--R                                                             +--------------+
--R                         2  +-------+                        |             2
--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R       log(------------------------------------------------------------------)
--R                                         p x + q
--R     + 
--R          +--------------+     +-----------+    +-----------+
--R          |             2     \|a p x + b p  - \|- a q + b p
--R       - \|- a p q + b p  log(-------------------------------)
--R                               +-----------+    +-----------+
--R                              \|a p x + b p  + \|- a q + b p
--R  /
--R      +--------------+
--R      |             2  +-----------+
--R     \|- a p q + b p  \|- a q + b p
--R                                                     Type: Expression Integer
--E

--S 10
cc2:=aa1-bb2
 

   (7)
          +-+ +---------+
         \|p \|a q - b p
      *
                                                             +--------------+
                         2  +-------+                        |             2
           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
       log(------------------------------------------------------------------)
                                         p x + q
     + 
           +--------------+      +-----------+
           |             2       |a p x + b p
       - 2\|- a p q + b p  atan( |----------- )
                                \| a q - b p
  /
      +--------------+
      |             2  +-+ +---------+
     \|- a p q + b p  \|p \|a q - b p
                                                     Type: Expression Integer
--R
--R   (7)
--R          +-+ +---------+
--R         \|p \|a q - b p
--R      *
--R                                                             +--------------+
--R                         2  +-------+                        |             2
--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R       log(------------------------------------------------------------------)
--R                                         p x + q
--R     + 
--R           +--------------+      +-----------+
--R           |             2       |a p x + b p
--R       - 2\|- a p q + b p  atan( |----------- )
--R                                \| a q - b p
--R  /
--R      +--------------+
--R      |             2  +-+ +---------+
--R     \|- a p q + b p  \|p \|a q - b p
--R                                                     Type: Expression Integer
--E

--S 11
cc3:=aa2-bb1
 

   (8)
          +------------+     +-----------+    +-----------+
          |           2     \|a p x + b p  - \|- a q + b p
       - \|a p q - b p  log(-------------------------------)
                             +-----------+    +-----------+
                            \|a p x + b p  + \|- a q + b p
     + 
                            +------------+
                            |           2  +-------+
         +-----------+     \|a p q - b p  \|a x + b
       2\|- a q + b p atan(-------------------------)
                                   a q - b p
  /
                    +------------+
      +-----------+ |           2
     \|- a q + b p \|a p q - b p
                                                     Type: Expression Integer
--R
--R   (8)
--R          +------------+     +-----------+    +-----------+
--R          |           2     \|a p x + b p  - \|- a q + b p
--R       - \|a p q - b p  log(-------------------------------)
--R                             +-----------+    +-----------+
--R                            \|a p x + b p  + \|- a q + b p
--R     + 
--R                            +------------+
--R                            |           2  +-------+
--R         +-----------+     \|a p q - b p  \|a x + b
--R       2\|- a q + b p atan(-------------------------)
--R                                   a q - b p
--R  /
--R                    +------------+
--R      +-----------+ |           2
--R     \|- a q + b p \|a p q - b p
--R                                                     Type: Expression Integer
--E

--S 12     14:114 Axiom cannot simplify these answers
cc4:=aa2-bb2
 

   (9)
                              +------------+
                              |           2  +-------+
         +-+ +---------+     \|a p q - b p  \|a x + b
       2\|p \|a q - b p atan(-------------------------)
                                     a q - b p
     + 
           +------------+      +-----------+
           |           2       |a p x + b p
       - 2\|a p q - b p  atan( |----------- )
                              \| a q - b p
  /
                      +------------+
      +-+ +---------+ |           2
     \|p \|a q - b p \|a p q - b p
                                                     Type: Expression Integer
--R
--R   (9)
--R                              +------------+
--R                              |           2  +-------+
--R         +-+ +---------+     \|a p q - b p  \|a x + b
--R       2\|p \|a q - b p atan(-------------------------)
--R                                     a q - b p
--R     + 
--R           +------------+      +-----------+
--R           |           2       |a p x + b p
--R       - 2\|a p q - b p  atan( |----------- )
--R                              \| a q - b p
--R  /
--R                      +------------+
--R      +-+ +---------+ |           2
--R     \|p \|a q - b p \|a p q - b p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(sqrt(a*x+b)/(p*x+q),x)
 

   (1)
   [
                                +-----------+
                                |- a q + b p  +-------+
          +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
          |- a q + b p         \|     p
          |----------- log(-------------------------------------------------)
         \|     p                               p x + q
       + 
           +-------+
         2\|a x + b
    /
       p
     ,
         +---------+       +-------+
         |a q - b p       \|a x + b       +-------+
    - 2  |--------- atan(------------ + 2\|a x + b
        \|    p           +---------+
                          |a q - b p
                          |---------
                         \|    p
    -----------------------------------------------]
                           p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                                +-----------+
--R                                |- a q + b p  +-------+
--R          +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R          |- a q + b p         \|     p
--R          |----------- log(-------------------------------------------------)
--R         \|     p                               p x + q
--R       + 
--R           +-------+
--R         2\|a x + b
--R    /
--R       p
--R     ,
--R         +---------+       +-------+
--R         |a q - b p       \|a x + b       +-------+
--R    - 2  |--------- atan(------------ + 2\|a x + b
--R        \|    p           +---------+
--R                          |a q - b p
--R                          |---------
--R                         \|    p
--R    -----------------------------------------------]
--R                           p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 14
aa1:=aa.1
 

   (2)
                              +-----------+
                              |- a q + b p  +-------+
        +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
        |- a q + b p         \|     p
        |----------- log(-------------------------------------------------)
       \|     p                               p x + q
     + 
         +-------+
       2\|a x + b
  /
     p
                                                     Type: Expression Integer
--R
--R   (2)
--R                              +-----------+
--R                              |- a q + b p  +-------+
--R        +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R        |- a q + b p         \|     p
--R        |----------- log(-------------------------------------------------)
--R       \|     p                               p x + q
--R     + 
--R         +-------+
--R       2\|a x + b
--R  /
--R     p
--R                                                     Type: Expression Integer
--E

--S 15
aa2:=aa.2
 

             +---------+       +-------+
             |a q - b p       \|a x + b       +-------+
        - 2  |--------- atan(------------ + 2\|a x + b
            \|    p           +---------+
                              |a q - b p
                              |---------
                             \|    p
   (3)  -----------------------------------------------
                               p
                                                     Type: Expression Integer
--R
--R             +---------+       +-------+
--R             |a q - b p       \|a x + b       +-------+
--R        - 2  |--------- atan(------------ + 2\|a x + b
--R            \|    p           +---------+
--R                              |a q - b p
--R                              |---------
--R                             \|    p
--R   (3)  -----------------------------------------------
--R                               p
--R                                                     Type: Expression Integer
--E

--S 16
bb1:=(2*sqrt(a*x+b))/p+sqrt(b*p-a*q)/(p*sqrt(p))*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
 

                           +-----------+    +-----------+
         +-----------+    \|a p x + b p  - \|- a q + b p       +-+ +-------+
        \|- a q + b p log(-------------------------------) + 2\|p \|a x + b
                           +-----------+    +-----------+
                          \|a p x + b p  + \|- a q + b p
   (4)  --------------------------------------------------------------------
                                          +-+
                                        p\|p
                                                     Type: Expression Integer
--R
--R                           +-----------+    +-----------+
--R         +-----------+    \|a p x + b p  - \|- a q + b p       +-+ +-------+
--R        \|- a q + b p log(-------------------------------) + 2\|p \|a x + b
--R                           +-----------+    +-----------+
--R                          \|a p x + b p  + \|- a q + b p
--R   (4)  --------------------------------------------------------------------
--R                                          +-+
--R                                        p\|p
--R                                                     Type: Expression Integer
--E

--S 17
bb2:=(2*sqrt(a*x+b))/p-(2*sqrt(a*q-b*p))/(p*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
 

                             +-----------+
            +---------+      |a p x + b p       +-+ +-------+
        - 2\|a q - b p atan( |----------- ) + 2\|p \|a x + b
                            \| a q - b p
   (5)  -----------------------------------------------------
                                  +-+
                                p\|p
                                                     Type: Expression Integer
--R
--R                             +-----------+
--R            +---------+      |a p x + b p       +-+ +-------+
--R        - 2\|a q - b p atan( |----------- ) + 2\|p \|a x + b
--R                            \| a q - b p
--R   (5)  -----------------------------------------------------
--R                                  +-+
--R                                p\|p
--R                                                     Type: Expression Integer
--E

--S 18
cc1:=aa1-bb1
 

   (6)
                            +-----------+    +-----------+
          +-----------+    \|a p x + b p  - \|- a q + b p
       - \|- a q + b p log(-------------------------------)
                            +-----------+    +-----------+
                           \|a p x + b p  + \|- a q + b p
     + 
                                  +-----------+
                                  |- a q + b p  +-------+
        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
        |- a q + b p  +-+        \|     p
        |----------- \|p log(-------------------------------------------------)
       \|     p                                   p x + q
  /
       +-+
     p\|p
                                                     Type: Expression Integer
--R
--R   (6)
--R                            +-----------+    +-----------+
--R          +-----------+    \|a p x + b p  - \|- a q + b p
--R       - \|- a q + b p log(-------------------------------)
--R                            +-----------+    +-----------+
--R                           \|a p x + b p  + \|- a q + b p
--R     + 
--R                                  +-----------+
--R                                  |- a q + b p  +-------+
--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R        |- a q + b p  +-+        \|     p
--R        |----------- \|p log(-------------------------------------------------)
--R       \|     p                                   p x + q
--R  /
--R       +-+
--R     p\|p
--R                                                     Type: Expression Integer
--E

--S 19
cc2:=aa1-bb2
 

   (7)
                                  +-----------+
                                  |- a q + b p  +-------+
        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
        |- a q + b p  +-+        \|     p
        |----------- \|p log(-------------------------------------------------)
       \|     p                                   p x + q
     + 
                          +-----------+
         +---------+      |a p x + b p
       2\|a q - b p atan( |----------- )
                         \| a q - b p
  /
       +-+
     p\|p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                  +-----------+
--R                                  |- a q + b p  +-------+
--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R        |- a q + b p  +-+        \|     p
--R        |----------- \|p log(-------------------------------------------------)
--R       \|     p                                   p x + q
--R     + 
--R                          +-----------+
--R         +---------+      |a p x + b p
--R       2\|a q - b p atan( |----------- )
--R                         \| a q - b p
--R  /
--R       +-+
--R     p\|p
--R                                                     Type: Expression Integer
--E

--S 20
cc3:=aa2-bb1
 

   (8)
                            +-----------+    +-----------+
          +-----------+    \|a p x + b p  - \|- a q + b p
       - \|- a q + b p log(-------------------------------)
                            +-----------+    +-----------+
                           \|a p x + b p  + \|- a q + b p
     + 
               +---------+       +-------+
           +-+ |a q - b p       \|a x + b
       - 2\|p  |--------- atan(------------)
              \|    p           +---------+
                                |a q - b p
                                |---------
                               \|    p
  /
       +-+
     p\|p
                                                     Type: Expression Integer
--R
--R   (8)
--R                            +-----------+    +-----------+
--R          +-----------+    \|a p x + b p  - \|- a q + b p
--R       - \|- a q + b p log(-------------------------------)
--R                            +-----------+    +-----------+
--R                           \|a p x + b p  + \|- a q + b p
--R     + 
--R               +---------+       +-------+
--R           +-+ |a q - b p       \|a x + b
--R       - 2\|p  |--------- atan(------------)
--R              \|    p           +---------+
--R                                |a q - b p
--R                                |---------
--R                               \|    p
--R  /
--R       +-+
--R     p\|p
--R                                                     Type: Expression Integer
--E

--S 21     14:115 Axiom cannot simplify these answers
cc4:=aa2-bb2
 

   (9)
           +---------+       +-------+                        +-----------+
       +-+ |a q - b p       \|a x + b        +---------+      |a p x + b p
   - 2\|p  |--------- atan(------------) + 2\|a q - b p atan( |----------- )
          \|    p           +---------+                      \| a q - b p
                            |a q - b p
                            |---------
                           \|    p
   -------------------------------------------------------------------------
                                       +-+
                                     p\|p
                                                     Type: Expression Integer
--R
--R   (9)
--R           +---------+       +-------+                        +-----------+
--R       +-+ |a q - b p       \|a x + b        +---------+      |a p x + b p
--R   - 2\|p  |--------- atan(------------) + 2\|a q - b p atan( |----------- )
--R          \|    p           +---------+                      \| a q - b p
--R                            |a q - b p
--R                            |---------
--R                           \|    p
--R   -------------------------------------------------------------------------
--R                                       +-+
--R                                     p\|p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 22     14:116 Axiom cannot compute this integral
aa:=integrate((p*x+q)^n*sqrt(a*x+b),x)
 

           x
         ++            n +--------+
   (1)   |   (q + %L p) \|b + %L a d%L
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n +--------+
--I   (1)   |   (q + %L p) \|b + %L a d%L
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 23     14:117 Axiom cannot compute this integral
aa:=integrate(1/((p*x+q)^n*sqrt(a*x+b)),x)
 

           x
         ++             1
   (1)   |   ---------------------- d%L
        ++             n +--------+
             (q + %L p) \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             1
--I   (1)   |   ---------------------- d%L
--R        ++             n +--------+
--I             (q + %L p) \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 24     14:118 Axiom cannot compute this integral
aa:=integrate((p*x+q)^n/sqrt(a*x+b),x)
 

           x           n
         ++  (q + %L p)
   (1)   |   ----------- d%L
        ++    +--------+
             \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           n
--I         ++  (q + %L p)
--I   (1)   |   ----------- d%L
--R        ++    +--------+
--I             \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 25     14:119 Axiom cannot compute this integral
aa:=integrate(sqrt(a*x+b)/(p*x+q)^n,x)
 

           x  +--------+
         ++  \|b + %L a
   (1)   |   ----------- d%L
        ++             n
             (q + %L p)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +--------+
--I         ++  \|b + %L a
--I   (1)   |   ----------- d%L
--R        ++             n
--I             (q + %L p)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to danzwill2.output (2009/2/17, 17:44:36).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set break resume
 

--S 1 of 17
i1:= integrate(e^(1991*x),x)
 

          1991x log(e)
        %e
   (1)  --------------
          1991log(e)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          1991x log(e)
--R        %e
--R   (1)  --------------
--R          1991log(e)
--R                                          Type: Union(Expression Integer,...)
--E 1

--S 2 of 17
i2:= integrate((sin(x)-cos(x))^2,x)
 

              2
   (2)  cos(x)  + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R   (2)  cos(x)  + x
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 17
i3:= integrate(log(x),x)
 

   (3)  x log(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (3)  x log(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 17
i4:= integrate(1/(%pi*x),x)
 

        log(x)
   (4)  ------
          %pi
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        log(x)
--R   (4)  ------
--R          %pi
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 17
i5:= integrate(%e^(sin(x)^2)*%e^(cos(x)^2),x)
 

   (5)  x %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)  x %e
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 17
i6:= integrate(1/(x*log(x)),x)
 

   (6)  log(log(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (6)  log(log(x))
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 17
i7:= integrate(x/(x^4+1),x)
 

              2
        atan(x )
   (7)  --------
            2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R        atan(x )
--R   (7)  --------
--R            2
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 17
i8:= integrate((x+1)/(x^2+2*x+2)^(1/3),x)
 

          +-----------+2
         3| 2
        3\|x  + 2x + 2
   (8)  ----------------
                4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +-----------+2
--R         3| 2
--R        3\|x  + 2x + 2
--R   (8)  ----------------
--R                4
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 17
i9:= integrate(x*%e^x*sin(x),x)
 

            x                          x
        x %e sin(x) + (- x + 1)cos(x)%e
   (9)  --------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x                          x
--R        x %e sin(x) + (- x + 1)cos(x)%e
--R   (9)  --------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 17
i10:= integrate(%e^(%e^x+x),x)
 

             x
           %e  + x
         %e
   (10)  ---------
              x
            %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R           %e  + x
--R         %e
--R   (10)  ---------
--R              x
--R            %e
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 17
i11:= integrate(1/(sec(x)+tan(x)*sin(x)),x)
 

               (2cos(x) + 3)sin(x)             sin(x)
   (11)  atan(---------------------) - atan(-----------)
                    2                       2cos(x) + 2
              cos(x)  + 2cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               (2cos(x) + 3)sin(x)             sin(x)
--R   (11)  atan(---------------------) - atan(-----------)
--R                    2                       2cos(x) + 2
--R              cos(x)  + 2cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 17
i12:= integrate((%e^(5*x)+%e^(7*x))/(%e^x+%e^(-x)),x)
 

            x 6
         (%e )
   (12)  ------
            6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x 6
--R         (%e )
--R   (12)  ------
--R            6
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 17
i13:= integrate(sqrt(-1+2/(1+3*x)),x)
 

                  +--------+             +--------+
                  |- 3x + 1              |- 3x + 1
         - 2atan( |-------- ) + (3x + 1) |--------
                 \| 3x + 1              \| 3x + 1
   (13)  ------------------------------------------
                              3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +--------+             +--------+
--R                  |- 3x + 1              |- 3x + 1
--R         - 2atan( |-------- ) + (3x + 1) |--------
--R                 \| 3x + 1              \| 3x + 1
--R   (13)  ------------------------------------------
--R                              3
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 17
i14:= integrate(sinh(x)-cosh(x),x)
 

                 1
   (14)  -----------------
         sinh(x) + cosh(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 1
--R   (14)  -----------------
--R         sinh(x) + cosh(x)
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 17
i15:= integrate((sin(x)*%e^sec(x))/cos(x)^2,x)
 

              1
           ------
           cos(x)
   (15)  %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R           ------
--R           cos(x)
--R   (15)  %e
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 17
i16:= integrate((x^2+1)/(x^4-x^2+1),x)
 

               3
   (16)  atan(x ) + atan(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3
--R   (16)  atan(x ) + atan(x)
--R                                          Type: Union(Expression Integer,...)
--E 16

--S 17 of 17
i17:= integrate(1/(%pi*x^2+atan(x)+x^2*atan(x)+%pi),x)
 

                    2x   2               2x          2
         log(atan(------)  - 4%pi atan(------) + 4%pi )
                   2                    2
                  x  - 1               x  - 1
   (17)  ----------------------------------------------
                                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2x   2               2x          2
--R         log(atan(------)  - 4%pi atan(------) + 4%pi )
--R                   2                    2
--R                  x  - 1               x  - 1
--R   (17)  ----------------------------------------------
--R                                2
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 18
i18:= integrate(sec(x)^3,x)
 

   (18)
         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
                   cos(x) + 1                        cos(x) + 1
   --------------------------------------------------------------------------
                                           2
                                    2cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (18)
--R         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
--R   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
--R                   cos(x) + 1                        cos(x) + 1
--R   --------------------------------------------------------------------------
--R                                           2
--R                                    2cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 18
 
--S 19 of 19 
i19:= integrate(1/(x^2-10*x+26),x)
 

   (19)  atan(x - 5)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (19)  atan(x - 5)
--R                                          Type: Union(Expression Integer,...)
--E 19 

--S 20 of 20 
i20:= integrate(1/(x^2-11*x-26),x)
 

         - log(x + 2) + log(x - 13)
   (20)  --------------------------
                     15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - log(x + 2) + log(x - 13)
--R   (20)  --------------------------
--R                     15
--R                                          Type: Union(Expression Integer,...)
--E 20 

--S 21 of 21 
i21:= integrate(1/(12+13*cos(x)),x)
 

             sin(x) + 5cos(x) + 5        sin(x) - 5cos(x) - 5
         log(--------------------) - log(--------------------)
                  cos(x) + 1                  cos(x) + 1
   (21)  -----------------------------------------------------
                                   5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             sin(x) + 5cos(x) + 5        sin(x) - 5cos(x) - 5
--R         log(--------------------) - log(--------------------)
--R                  cos(x) + 1                  cos(x) + 1
--R   (21)  -----------------------------------------------------
--R                                   5
--R                                          Type: Union(Expression Integer,...)
--E 21 

--S 22 of 22 
i22:= integrate((x^3+1)/(x+1),x)
 

           3     2
         2x  - 3x  + 6x
   (22)  --------------
                6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           3     2
--R         2x  - 3x  + 6x
--R   (22)  --------------
--R                6
--R                                          Type: Union(Expression Integer,...)
--E 22 

--S 23 of 23 
i23:= integrate((1-4*x^4)^(-1/2)/(4*x)^(-1),x)
 

                  +---------+
                  |    4
                 \|- 4x  + 1  - 1
   (23)  - 2atan(----------------)
                          2
                        2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+
--R                  |    4
--R                 \|- 4x  + 1  - 1
--R   (23)  - 2atan(----------------)
--R                          2
--R                        2x
--R                                          Type: Union(Expression Integer,...)
--E 23 

--S 24 of 24 
i24:= integrate(%e^(1991),x)
 

             1991
   (24)  x %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             1991
--R   (24)  x %e
--R                                          Type: Union(Expression Integer,...)
--E 24 

--S 25 of 25 
i25:= integrate((log(x)+1)*x^x,x)
 

           x log(x)
   (25)  %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x log(x)
--R   (25)  %e
--R                                          Type: Union(Expression Integer,...)
--E 25 

--S 26 of 26 
i26:= integrate(cos(2*x)*sin(6*x),x)
 

                   4          2
         - 2cos(2x)  + cos(2x)
   (26)  ----------------------
                    4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   4          2
--R         - 2cos(2x)  + cos(2x)
--R   (26)  ----------------------
--R                    4
--R                                          Type: Union(Expression Integer,...)
--E 26 

--S 27 of 27 
i27:= integrate(1/(sqrt(x)*(1+sqrt(x))),x)
 

               +-+
   (27)  2log(\|x  + 1)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-+
--R   (27)  2log(\|x  + 1)
--R                                          Type: Union(Expression Integer,...)
--E 27 

--S 28 of 28 
i28:= integrate(e^(1/x)*x^(-3),x)
 

                         log(e)
                         ------
                            x
         (- log(e) + x)%e
   (28)  ----------------------
                        2
                x log(e)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         log(e)
--R                         ------
--R                            x
--R         (- log(e) + x)%e
--R   (28)  ----------------------
--R                        2
--R                x log(e)
--R                                          Type: Union(Expression Integer,...)
--E 28 

--S 29 of 29 
i29:= integrate(sqrt(csc(x)-sin(x)),x)
 

                         +--------------------------------+
                         |         - 16cos(x) + 16
   (29)  (- cos(x) - 1)  |--------------------------------
                        4|      3          2
                        \|cos(x)  + 3cos(x)  + 3cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         +--------------------------------+
--R                         |         - 16cos(x) + 16
--R   (29)  (- cos(x) - 1)  |--------------------------------
--R                        4|      3          2
--R                        \|cos(x)  + 3cos(x)  + 3cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 29 

--S 30 of 30 
i30:= integrate((x^2+1)/(x^3-x),x)
 

              2
   (30)  log(x  - 1) - log(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R   (30)  log(x  - 1) - log(x)
--R                                          Type: Union(Expression Integer,...)
--E 30 

--S 31 of 31 
i31:= integrate(42^x,x)
 

           x log(42)
         %e
   (31)  -----------
           log(42)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x log(42)
--R         %e
--R   (31)  -----------
--R           log(42)
--R                                          Type: Union(Expression Integer,...)
--E 31 

--S 32 of 32 
i32:= integrate(x^5*%e^x,x)
 

           5     4      3      2                x
   (32)  (x  - 5x  + 20x  - 60x  + 120x - 120)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           5     4      3      2                x
--R   (32)  (x  - 5x  + 20x  - 60x  + 120x - 120)%e
--R                                          Type: Union(Expression Integer,...)
--E 32 

--S 33 of 33 
i33:= integrate(x*%e^(x^2),x)
 

            2
           x
         %e
   (33)  ----
           2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2
--R           x
--R         %e
--R   (33)  ----
--R           2
--R                                          Type: Union(Expression Integer,...)
--E 33 

--S 34 of 34 
i34:= integrate(1/(x^2+1)^2,x)
 

           2
         (x  + 1)atan(x) + x
   (34)  -------------------
                 2
               2x  + 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2
--R         (x  + 1)atan(x) + x
--R   (34)  -------------------
--R                 2
--R               2x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 34 

--S 35 of 35 
i35:= integrate(1/(%e^x+%e^(-x)),x)
 

                x
   (35)  atan(%e )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                x
--R   (35)  atan(%e )
--R                                          Type: Union(Expression Integer,...)
--E 35 

--S 36 of 36 
i36:= integrate(tan(x)*log(abs(sec(x))),x)
 

              +-------+ 2
              |   1
         log( |------- )
              |      2
             \|cos(x)
   (36)  ----------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              +-------+ 2
--R              |   1
--R         log( |------- )
--R              |      2
--R             \|cos(x)
--R   (36)  ----------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 36 

--S 37 of 37 
i37:= integrate(cos(sin(x))*cos(x),x)
 

   (37)  sin(sin(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (37)  sin(sin(x))
--R                                          Type: Union(Expression Integer,...)
--E 37 

--S 38 of 38 
i38:= integrate(1/(x^2-9),x)
 

         - log(x + 3) + log(x - 3)
   (38)  -------------------------
                     6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - log(x + 3) + log(x - 3)
--R   (38)  -------------------------
--R                     6
--R                                          Type: Union(Expression Integer,...)
--E 38 

--S 39 of 39 
i39:= integrate(%pi/sqrt(16-%e^2),x)
 

             %pi x
   (39)  -------------
          +----------+
          |    2
         \|- %e  + 16
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             %pi x
--R   (39)  -------------
--R          +----------+
--R          |    2
--R         \|- %e  + 16
--R                                          Type: Union(Expression Integer,...)
--E 39 

--S 40 of 40 
i40:= integrate(sqrt(tan(x)),x)
 

   (40)
          +-+
         \|2
      *
                                                  +------+
                  +-+                 +-+      2  |sin(x)
         log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------  + 4cos(x)sin(x) + 1)
                                                 \|cos(x)
     + 
                              +------+
                              |sin(x)     +-+                +-+      2    +-+
                2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)  - \|2
        +-+                  \|cos(x)
       \|2 atan(--------------------------------------------------------------)
                               +------+
                             2 |sin(x)     +-+                +-+      2
                      2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)
                              \|cos(x)
     + 
       -
             +-+
            \|2
         *
                             +------+
                             |sin(x)      +-+                 +-+      2    +-+
               4cos(x)sin(x) |------  - 2\|2 cos(x)sin(x) + 2\|2 cos(x)  - \|2
                            \|cos(x)
          atan(----------------------------------------------------------------)
                           +------+
                         2 |sin(x)      +-+                 +-+      2    +-+
                  4cos(x)  |------  - 2\|2 cos(x)sin(x) - 2\|2 cos(x)  + \|2
                          \|cos(x)
     + 
                                 +------+
                                 |sin(x)     +-+                +-+      2
                   2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)
          +-+                   \|cos(x)
       - \|2 atan(---------------------------------------------------------)
                           +------+
                         2 |sin(x)     +-+                +-+      2    +-+
                  2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)  + \|2
                          \|cos(x)
  /
     4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (40)
--R          +-+
--R         \|2
--R      *
--R                                                  +------+
--R                  +-+                 +-+      2  |sin(x)
--R         log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------  + 4cos(x)sin(x) + 1)
--R                                                 \|cos(x)
--R     + 
--R                              +------+
--R                              |sin(x)     +-+                +-+      2    +-+
--R                2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)  - \|2
--R        +-+                  \|cos(x)
--R       \|2 atan(--------------------------------------------------------------)
--R                               +------+
--R                             2 |sin(x)     +-+                +-+      2
--R                      2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)
--R                              \|cos(x)
--R     + 
--R       -
--R             +-+
--R            \|2
--R         *
--R                             +------+
--R                             |sin(x)      +-+                 +-+      2    +-+
--R               4cos(x)sin(x) |------  - 2\|2 cos(x)sin(x) + 2\|2 cos(x)  - \|2
--R                            \|cos(x)
--R          atan(----------------------------------------------------------------)
--R                           +------+
--R                         2 |sin(x)      +-+                 +-+      2    +-+
--R                  4cos(x)  |------  - 2\|2 cos(x)sin(x) - 2\|2 cos(x)  + \|2
--R                          \|cos(x)
--R     + 
--R                                 +------+
--R                                 |sin(x)     +-+                +-+      2
--R                   2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)
--R          +-+                   \|cos(x)
--R       - \|2 atan(---------------------------------------------------------)
--R                           +------+
--R                         2 |sin(x)     +-+                +-+      2    +-+
--R                  2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)  + \|2
--R                          \|cos(x)
--R  /
--R     4
--R                                          Type: Union(Expression Integer,...)
--E 40 

--S 41 of 41 
i41:= integrate(sin(x)^(-1),x)
 

               sin(x)
   (41)  log(----------)
             cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               sin(x)
--R   (41)  log(----------)
--R             cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 41 

--S 42 of 42 
i42:= integrate((x^2-2*x+2)/(x^2+1),x)
 

                2
   (42)  - log(x  + 1) + atan(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R   (42)  - log(x  + 1) + atan(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 42 

--S 43 of 43 
i43:= integrate((sin(x)^2*cos(x)^2)/(1+cos(2*x)),x)
 

         - cos(x)sin(x) + x
   (43)  ------------------
                  4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - cos(x)sin(x) + x
--R   (43)  ------------------
--R                  4
--R                                          Type: Union(Expression Integer,...)
--E 43 

--S 44 of 44 
i44:= integrate(sqrt(x+x^2*sqrt(x)),x)
 

                       +----------+
            +-+     2  | 2 +-+
         (4\|x  + 4x )\|x \|x  + x
   (44)  --------------------------
                     9x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       +----------+
--R            +-+     2  | 2 +-+
--R         (4\|x  + 4x )\|x \|x  + x
--R   (44)  --------------------------
--R                     9x
--R                                          Type: Union(Expression Integer,...)
--E 44 

--S 45 of 45 
i45:= integrate(cos(4*x)*cos(2*x),x)
 

                  2
         (2cos(2x)  + 1)sin(2x)
   (45)  ----------------------
                    6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R         (2cos(2x)  + 1)sin(2x)
--R   (45)  ----------------------
--R                    6
--R                                          Type: Union(Expression Integer,...)
--E 45 

--S 46 of 46 
i46:= integrate(sqrt(x^3-1)/x,x)
 

                  +------+      +------+
                  | 3           | 3
         - 2atan(\|x  - 1 ) + 2\|x  - 1
   (46)  -------------------------------
                        3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +------+      +------+
--R                  | 3           | 3
--R         - 2atan(\|x  - 1 ) + 2\|x  - 1
--R   (46)  -------------------------------
--R                        3
--R                                          Type: Union(Expression Integer,...)
--E 46 

--S 47 of 47 
i47:= integrate((%e^x*(x-2))/x^3,x)
 

           x
         %e
   (47)  ---
           2
          x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         %e
--R   (47)  ---
--R           2
--R          x
--R                                          Type: Union(Expression Integer,...)
--E 47 

--S 48 of 48 
i48:= integrate(cot(x)/log(sin(x)),x)
 

   (48)  log(log(sin(x)))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (48)  log(log(sin(x)))
--R                                          Type: Union(Expression Integer,...)
--E 48 

--S 49 of 49 
i49:= integrate(x*sec(x)^2,x)
 

                          2                      2cos(x)
         - cos(x)log(----------) + cos(x)log(- ----------) + x sin(x)
                     cos(x) + 1                cos(x) + 1
   (49)  ------------------------------------------------------------
                                    cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2                      2cos(x)
--R         - cos(x)log(----------) + cos(x)log(- ----------) + x sin(x)
--R                     cos(x) + 1                cos(x) + 1
--R   (49)  ------------------------------------------------------------
--R                                    cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 49 

--S 50 of 50 
i50:= integrate(x*sec(x)*(x*tan(x)+2),x)
 

            2
           x
   (50)  ------
         cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2
--R           x
--R   (50)  ------
--R         cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 50 
)spool
 
Starts dribbling to kamke2.output (2009/2/17, 17:47:24).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 126
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 126
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 126
g:=operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

-------------------------------------------------------------------
--S 4 of 126
ode101 := x*D(y(x),x) + x*y(x)**2 - y(x)
 

          ,            2
   (4)  xy (x) + x y(x)  - y(x)

                                                     Type: Expression Integer
--R
--R          ,            2
--R   (4)  xy (x) + x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 126
yx:=solve(ode101,y,x)
 

         2
        x y(x) - 2x
   (5)  -----------
           2y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         2
--R        x y(x) - 2x
--R   (5)  -----------
--R           2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 126
ode101expr := x*D(yx,x) + x*yx**2 - yx
 

          2 ,        5     2     2     4         3
        4x y (x) + (x  + 2x )y(x)  - 4x y(x) + 4x

   (6)  ------------------------------------------
                               2
                          4y(x)
                                                     Type: Expression Integer
--R
--R          2 ,        5     2     2     4         3
--R        4x y (x) + (x  + 2x )y(x)  - 4x y(x) + 4x
--R
--R   (6)  ------------------------------------------
--R                               2
--R                          4y(x)
--R                                                     Type: Expression Integer
--E 6

-------------------------------------------------------------------
--S 7 of 126
ode102 := x*D(y(x),x) + x*y(x)**2 - y(x) - a*x**3
 

          ,            2             3
   (7)  xy (x) + x y(x)  - y(x) - a x

                                                     Type: Expression Integer
--R
--R          ,            2             3
--R   (7)  xy (x) + x y(x)  - y(x) - a x
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 126
yx:=solve(ode102,y,x)
 

                            +-+
               (2y(x) + 3x)\|a  + 3y(x) + 2a x
   (8)  ---------------------------------------------
                                                2 +-+
                        +-+                    x \|a
        ((6y(x) - 4a x)\|a  + 4a y(x) - 6a x)%e
                                          Type: Union(Expression Integer,...)
--R
--R                            +-+
--R               (2y(x) + 3x)\|a  + 3y(x) + 2a x
--R   (8)  ---------------------------------------------
--R                                                2 +-+
--R                        +-+                    x \|a
--R        ((6y(x) - 4a x)\|a  + 4a y(x) - 6a x)%e
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 126
ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3
 

   (9)
                   2         2           3       2  3  +-+
           ((- 144a  - 108a)x y(x) + (32a  + 216a )x )\|a
         + 
                 3       2  2            3       2  3
           (- 32a  - 216a )x y(x) + (144a  + 108a )x
      *
            2 +-+
           x \|a  ,
         %e      y (x)

     + 
                      3       2  3    3       4       3  4    2
               (- 144a  - 108a )x y(x)  + (96a  + 648a )x y(x)
             + 
                      4       3  5           5       4  6
               (- 432a  - 324a )x y(x) + (32a  + 216a )x
          *
              +-+
             \|a
         + 
                 4       3  3    3        4       3  4    2
           (- 32a  - 216a )x y(x)  + (432a  + 324a )x y(x)
         + 
                 5       4  5            5       4  6
           (- 96a  - 648a )x y(x) + (144a  + 108a )x
      *
             2 +-+ 2
            x \|a
         (%e      )
     + 
                       2         2      2            3
               ((- 144a  - 108a)x  - 16a  - 108a)y(x)
             + 
                    3       2  3        2              2
               ((32a  + 216a )x  + (216a  + 162a)x)y(x)
             + 
                     3       2  4         3       2  2              4       3  5
               ((144a  + 108a )x  + (- 16a  - 108a )x )y(x) + (- 32a  - 216a )x
             + 
                     3      2  3
               (- 72a  - 54a )x
          *
              +-+
             \|a
         + 
                  3       2  2      2           3
           ((- 32a  - 216a )x  - 72a  - 54a)y(x)
         + 
                 3       2  3       3       2       2
           ((144a  + 108a )x  + (48a  + 324a )x)y(x)
         + 
                4       3  4         3      2  2               4       3  5
           ((32a  + 216a )x  + (- 72a  - 54a )x )y(x) + (- 144a  - 108a )x
         + 
                 4       3  3
           (- 16a  - 108a )x
      *
            2 +-+
           x \|a
         %e
     + 
                           3      2        2    2         2        3
           (36a + 27)x y(x)  + (8a  + 54a)x y(x)  + (- 36a  - 27a)x y(x)
         + 
                3      2  4
           (- 8a  - 54a )x
      *
          +-+
         \|a
     + 
          2             3       2        2    2        3      2  3
       (8a  + 54a)x y(x)  + (36a  + 27a)x y(x)  + (- 8a  - 54a )x y(x)
     + 
             3      2  4
       (- 36a  - 27a )x
  /
                  2            3         3       2       2
             (144a  + 108a)y(x)  + (- 96a  - 648a )x y(x)
           + 
                  3       2  2             4       3  3
             (432a  + 324a )x y(x) + (- 32a  - 216a )x
        *
            +-+
           \|a
       + 
             3       2     3          3       2       2       4       3  2
         (32a  + 216a )y(x)  + (- 432a  - 324a )x y(x)  + (96a  + 648a )x y(x)
       + 
                4       3  3
         (- 144a  - 108a )x
    *
           2 +-+ 2
          x \|a
       (%e      )
                                                     Type: Expression Integer
--R
--R   (9)
--R                   2         2           3       2  3  +-+
--R           ((- 144a  - 108a)x y(x) + (32a  + 216a )x )\|a
--R         + 
--R                 3       2  2            3       2  3
--R           (- 32a  - 216a )x y(x) + (144a  + 108a )x
--R      *
--R            2 +-+
--R           x \|a  ,
--R         %e      y (x)
--R
--R     + 
--R                      3       2  3    3       4       3  4    2
--R               (- 144a  - 108a )x y(x)  + (96a  + 648a )x y(x)
--R             + 
--R                      4       3  5           5       4  6
--R               (- 432a  - 324a )x y(x) + (32a  + 216a )x
--R          *
--R              +-+
--R             \|a
--R         + 
--R                 4       3  3    3        4       3  4    2
--R           (- 32a  - 216a )x y(x)  + (432a  + 324a )x y(x)
--R         + 
--R                 5       4  5            5       4  6
--R           (- 96a  - 648a )x y(x) + (144a  + 108a )x
--R      *
--R             2 +-+ 2
--R            x \|a
--R         (%e      )
--R     + 
--R                       2         2      2            3
--R               ((- 144a  - 108a)x  - 16a  - 108a)y(x)
--R             + 
--R                    3       2  3        2              2
--R               ((32a  + 216a )x  + (216a  + 162a)x)y(x)
--R             + 
--R                     3       2  4         3       2  2              4       3  5
--R               ((144a  + 108a )x  + (- 16a  - 108a )x )y(x) + (- 32a  - 216a )x
--R             + 
--R                     3      2  3
--R               (- 72a  - 54a )x
--R          *
--R              +-+
--R             \|a
--R         + 
--R                  3       2  2      2           3
--R           ((- 32a  - 216a )x  - 72a  - 54a)y(x)
--R         + 
--R                 3       2  3       3       2       2
--R           ((144a  + 108a )x  + (48a  + 324a )x)y(x)
--R         + 
--R                4       3  4         3      2  2               4       3  5
--R           ((32a  + 216a )x  + (- 72a  - 54a )x )y(x) + (- 144a  - 108a )x
--R         + 
--R                 4       3  3
--R           (- 16a  - 108a )x
--R      *
--R            2 +-+
--R           x \|a
--R         %e
--R     + 
--R                           3      2        2    2         2        3
--R           (36a + 27)x y(x)  + (8a  + 54a)x y(x)  + (- 36a  - 27a)x y(x)
--R         + 
--R                3      2  4
--R           (- 8a  - 54a )x
--R      *
--R          +-+
--R         \|a
--R     + 
--R          2             3       2        2    2        3      2  3
--R       (8a  + 54a)x y(x)  + (36a  + 27a)x y(x)  + (- 8a  - 54a )x y(x)
--R     + 
--R             3      2  4
--R       (- 36a  - 27a )x
--R  /
--R                  2            3         3       2       2
--R             (144a  + 108a)y(x)  + (- 96a  - 648a )x y(x)
--R           + 
--R                  3       2  2             4       3  3
--R             (432a  + 324a )x y(x) + (- 32a  - 216a )x
--R        *
--R            +-+
--R           \|a
--R       + 
--R             3       2     3          3       2       2       4       3  2
--R         (32a  + 216a )y(x)  + (- 432a  - 324a )x y(x)  + (96a  + 648a )x y(x)
--R       + 
--R                4       3  3
--R         (- 144a  - 108a )x
--R    *
--R           2 +-+ 2
--R          x \|a
--R       (%e      )
--R                                                     Type: Expression Integer
--E 9

-------------------------------------------------------------------
--S 10 of 126
ode103 := x*D(y(x),x) + x*y(x)**2 - (2*x**2+1)*y(x) - x**3
 

           ,            2        2             3
   (10)  xy (x) + x y(x)  + (- 2x  - 1)y(x) - x

                                                     Type: Expression Integer
--R
--R           ,            2        2             3
--R   (10)  xy (x) + x y(x)  + (- 2x  - 1)y(x) - x
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 126
yx:=solve(ode103,y,x)
 

                   +-+              +-+
                (2\|2  + 3)y(x) + x\|2  + x
   (11)  -----------------------------------------
                                             2 +-+
             +-+                +-+         x \|2
         ((6\|2  + 8)y(x) - 14x\|2  - 20x)%e
                                          Type: Union(Expression Integer,...)
--R
--R                   +-+              +-+
--R                (2\|2  + 3)y(x) + x\|2  + x
--R   (11)  -----------------------------------------
--R                                             2 +-+
--R             +-+                +-+         x \|2
--R         ((6\|2  + 8)y(x) - 14x\|2  - 20x)%e
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 126
ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3
 

   (12)
                                                            2 +-+
               2 +-+        2             3 +-+        3   x \|2  ,
       ((- 792x \|2  - 1120x )y(x) + 1912x \|2  + 2704x )%e      y (x)

     + 
                  3 +-+        3     3         4 +-+        4     2
           (- 792x \|2  - 1120x )y(x)  + (5736x \|2  + 8112x )y(x)
         + 
                    5 +-+         5              6 +-+         6
           (- 13848x \|2  - 19584x )y(x) + 11144x \|2  + 15760x
      *
             2 +-+ 2
            x \|2
         (%e      )
     + 
                    2        +-+        2           3
           ((- 1352x  - 280)\|2  - 1912x  - 396)y(x)
         + 
                  3          +-+        3             2
           ((5968x  + 2028x)\|2  + 8440x  + 2868x)y(x)
         + 
                    4        2  +-+        4        2
           ((- 5176x  - 2984x )\|2  - 7320x  - 4220x )y(x)
         + 
                   5       3  +-+        5       3
           (- 3264x  - 676x )\|2  - 4616x  - 956x
      *
            2 +-+
           x \|2
         %e
     + 
            +-+            3          2 +-+       2     2
       (99x\|2  + 140x)y(x)  + (- 157x \|2  - 222x )y(x)
     + 
              3 +-+       3           4 +-+      4
       (- 181x \|2  - 256x )y(x) - 41x \|2  - 58x
  /
              +-+            3            +-+             2
         (792\|2  + 1120)y(x)  + (- 5736x\|2  - 8112x)y(x)
       + 
                2 +-+         2              3 +-+         3
         (13848x \|2  + 19584x )y(x) - 11144x \|2  - 15760x
    *
           2 +-+ 2
          x \|2
       (%e      )
                                                     Type: Expression Integer
--R
--R   (12)
--R                                                            2 +-+
--R               2 +-+        2             3 +-+        3   x \|2  ,
--R       ((- 792x \|2  - 1120x )y(x) + 1912x \|2  + 2704x )%e      y (x)
--R
--R     + 
--R                  3 +-+        3     3         4 +-+        4     2
--R           (- 792x \|2  - 1120x )y(x)  + (5736x \|2  + 8112x )y(x)
--R         + 
--R                    5 +-+         5              6 +-+         6
--R           (- 13848x \|2  - 19584x )y(x) + 11144x \|2  + 15760x
--R      *
--R             2 +-+ 2
--R            x \|2
--R         (%e      )
--R     + 
--R                    2        +-+        2           3
--R           ((- 1352x  - 280)\|2  - 1912x  - 396)y(x)
--R         + 
--R                  3          +-+        3             2
--R           ((5968x  + 2028x)\|2  + 8440x  + 2868x)y(x)
--R         + 
--R                    4        2  +-+        4        2
--R           ((- 5176x  - 2984x )\|2  - 7320x  - 4220x )y(x)
--R         + 
--R                   5       3  +-+        5       3
--R           (- 3264x  - 676x )\|2  - 4616x  - 956x
--R      *
--R            2 +-+
--R           x \|2
--R         %e
--R     + 
--R            +-+            3          2 +-+       2     2
--R       (99x\|2  + 140x)y(x)  + (- 157x \|2  - 222x )y(x)
--R     + 
--R              3 +-+       3           4 +-+      4
--R       (- 181x \|2  - 256x )y(x) - 41x \|2  - 58x
--R  /
--R              +-+            3            +-+             2
--R         (792\|2  + 1120)y(x)  + (- 5736x\|2  - 8112x)y(x)
--R       + 
--R                2 +-+         2              3 +-+         3
--R         (13848x \|2  + 19584x )y(x) - 11144x \|2  - 15760x
--R    *
--R           2 +-+ 2
--R          x \|2
--R       (%e      )
--R                                                     Type: Expression Integer
--E 12

-------------------------------------------------------------------
--S 13 of 126
ode106 := x*D(y(x),x) + x**a*y(x)**2 + (a-b)*y(x)/2 + x**b
 

            ,        b        2 a
         2xy (x) + 2x  + 2y(x) x  + (- b + a)y(x)

   (13)  ----------------------------------------
                             2
                                                     Type: Expression Integer
--R
--R            ,        b        2 a
--R         2xy (x) + 2x  + 2y(x) x  + (- b + a)y(x)
--R
--R   (13)  ----------------------------------------
--R                             2
--R                                                     Type: Expression Integer
--E 13

--S 14 of 126
yx:=solve(ode106,y,x)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 14

-------------------------------------------------------------------
--S 15 of 126
ode107 := x*D(y(x),x) + a*x**alpha*y(x)**2 + b*y(x) - c*x**beta
 

           ,         beta         2 alpha
   (15)  xy (x) - c x     + a y(x) x      + b y(x)

                                                     Type: Expression Integer
--R
--R           ,         beta         2 alpha
--R   (15)  xy (x) - c x     + a y(x) x      + b y(x)
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 126
yx:=solve(ode107,y,x)
 

   (16)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (16)  "failed"
--R                                                    Type: Union("failed",...)
--E 16

-------------------------------------------------------------------
--S 17 of 126
ode108 := x*D(y(x),x) - y(x)**2*log(x) + y(x)
 

           ,          2
   (17)  xy (x) - y(x) log(x) + y(x)

                                                     Type: Expression Integer
--R
--R           ,          2
--R   (17)  xy (x) - y(x) log(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 17
--S 18 of 126
yx:=solve(ode108,y,x)
 

         - y(x)log(x) - y(x) + 1
   (18)  -----------------------
                  x y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         - y(x)log(x) - y(x) + 1
--R   (18)  -----------------------
--R                  x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 126
ode108expr := x*D(yx,x) - yx**2*log(x) + yx
 

   (19)
          2 ,          2      3           2               2
       - x y (x) - y(x) log(x)  + (- 2y(x)  + 2y(x))log(x)

     + 
              2                            2
       (- y(x)  + 2y(x) - 1)log(x) - x y(x)
  /
      2    2
     x y(x)
                                                     Type: Expression Integer
--R
--R   (19)
--R          2 ,          2      3           2               2
--R       - x y (x) - y(x) log(x)  + (- 2y(x)  + 2y(x))log(x)
--R
--R     + 
--R              2                            2
--R       (- y(x)  + 2y(x) - 1)log(x) - x y(x)
--R  /
--R      2    2
--R     x y(x)
--R                                                     Type: Expression Integer
--E 19

-------------------------------------------------------------------
--S 20 of 126
ode109 := x*D(y(x),x) - y(x)*(2*y(x)*log(x)-1)
 

           ,           2
   (20)  xy (x) - 2y(x) log(x) + y(x)

                                                     Type: Expression Integer
--R
--R           ,           2
--R   (20)  xy (x) - 2y(x) log(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 126
yx:=solve(ode109,y,x)
 

         - 2y(x)log(x) - 2y(x) + 1
   (21)  -------------------------
                   x y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         - 2y(x)log(x) - 2y(x) + 1
--R   (21)  -------------------------
--R                   x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 21

--S 22 of 126
ode109expr := x*D(yx,x) - yx*(2*yx*log(x)-1)
 

   (22)
          2 ,           2      3            2               2
       - x y (x) - 8y(x) log(x)  + (- 16y(x)  + 8y(x))log(x)

     + 
               2                             2
       (- 8y(x)  + 8y(x) - 2)log(x) - 2x y(x)
  /
      2    2
     x y(x)
                                                     Type: Expression Integer
--R
--R   (22)
--R          2 ,           2      3            2               2
--R       - x y (x) - 8y(x) log(x)  + (- 16y(x)  + 8y(x))log(x)
--R
--R     + 
--R               2                             2
--R       (- 8y(x)  + 8y(x) - 2)log(x) - 2x y(x)
--R  /
--R      2    2
--R     x y(x)
--R                                                     Type: Expression Integer
--E 22

-------------------------------------------------------------------
--S 23 of 126
ode110 := x*D(y(x),x) + f(x)*(y(x)**2-x**2)
 

           ,              2    2
   (23)  xy (x) + f(x)y(x)  - x f(x)

                                                     Type: Expression Integer
--R
--R           ,              2    2
--R   (23)  xy (x) + f(x)y(x)  - x f(x)
--R
--R                                                     Type: Expression Integer
--E 23

--S 24 of 126
yx:=solve(ode110,y,x)
 

   (24)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (24)  "failed"
--R                                                    Type: Union("failed",...)
--E 24

-------------------------------------------------------------------
--S 25 of 126
ode111 := x*D(y(x),x) + y(x)**3 + 3*x*y(x)**2
 

           ,          3          2
   (25)  xy (x) + y(x)  + 3x y(x)

                                                     Type: Expression Integer
--R
--R           ,          3          2
--R   (25)  xy (x) + y(x)  + 3x y(x)
--R
--R                                                     Type: Expression Integer
--E 25


--S 26 of 126
yx:=solve(ode111,y,x)
 

   (26)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (26)  "failed"
--R                                                    Type: Union("failed",...)
--E 26

-------------------------------------------------------------------
--S 27 of 126
ode112 := x*D(y(x),x) - sqrt(y(x)**2 + x**2) - y(x)
 

                   +----------+
           ,       |    2    2
   (27)  xy (x) - \|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                   +----------+
--R           ,       |    2    2
--R   (27)  xy (x) - \|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 27


--S 28 of 126
yx:=solve(ode112,y,x)
 

   (28)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (28)  "failed"
--R                                                    Type: Union("failed",...)
--E 28

-------------------------------------------------------------------
--S 29 of 126
ode113 := x*D(y(x),x) + a*sqrt(y(x)**2 + x**2) - y(x)
 

                    +----------+
           ,        |    2    2
   (29)  xy (x) + a\|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                    +----------+
--R           ,        |    2    2
--R   (29)  xy (x) + a\|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 29

--S 30 of 126
yx:=solve(ode113,y,x)
 

   (30)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (30)  "failed"
--R                                                    Type: Union("failed",...)
--E 30

-------------------------------------------------------------------
--S 31 of 126
ode114 := x*D(y(x),x) - x*sqrt(y(x)**2 + x**2) - y(x)
 

                    +----------+
           ,        |    2    2
   (31)  xy (x) - x\|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                    +----------+
--R           ,        |    2    2
--R   (31)  xy (x) - x\|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 31

--S 32 of 126
yx:=solve(ode114,y,x)
 

   (32)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (32)  "failed"
--R                                                    Type: Union("failed",...)
--E 32

-------------------------------------------------------------------
--S 33 of 126
ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)**2 + x**2) - y(x)
 

                                  +----------+
           ,                   2  |    2    2
   (33)  xy (x) + (- x y(x) + x )\|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                                  +----------+
--R           ,                   2  |    2    2
--R   (33)  xy (x) + (- x y(x) + x )\|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 33

--S 34 of 126
yx:=solve(ode115,y,x)
 

   (34)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (34)  "failed"
--R                                                    Type: Union("failed",...)
--E 34

-------------------------------------------------------------------
--S 35 of 126
ode116 := x*D(y(x),x) - x*sqrt((y(x)**2 - x**2)*(y(x)**2-4*x**2)) - y(x)
 

                    +----------------------+
           ,        |    4     2    2     4
   (35)  xy (x) - x\|y(x)  - 5x y(x)  + 4x   - y(x)

                                                     Type: Expression Integer
--R
--R                    +----------------------+
--R           ,        |    4     2    2     4
--R   (35)  xy (x) - x\|y(x)  - 5x y(x)  + 4x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 35

--S 36 of 126
yx:=solve(ode116,y,x)
 

   (36)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

-------------------------------------------------------------------
--S 37 of 126
ode117 := x*D(y(x),x) - x*exp(y(x)/x) - y(x) - x
 

                      y(x)
                      ----
           ,            x
   (37)  xy (x) - x %e     - y(x) - x

                                                     Type: Expression Integer
--R
--R                      y(x)
--R                      ----
--R           ,            x
--R   (37)  xy (x) - x %e     - y(x) - x
--R
--R                                                     Type: Expression Integer
--E 37

--S 38 of 126
yx:=solve(ode117,y,x)
 

   (38)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (38)  "failed"
--R                                                    Type: Union("failed",...)
--E 38

-------------------------------------------------------------------
--S 39 of 126
ode118 := x*D(y(x),x) - y(x)*log(y(x))
 

           ,
   (39)  xy (x) - y(x)log(y(x))

                                                     Type: Expression Integer
--R
--R           ,
--R   (39)  xy (x) - y(x)log(y(x))
--R
--R                                                     Type: Expression Integer
--E 39

--S 40 of 126
yx:=solve(ode118,y,x)
 

               x
   (40)  - ---------
           log(y(x))
                                          Type: Union(Expression Integer,...)
--R
--R               x
--R   (40)  - ---------
--R           log(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 40

--S 41 of 126
ode118expr := x*D(yx,x) - yx*log(yx)
 

                                  x         2 ,
         x y(x)log(y(x))log(- ---------) + x y (x) - x y(x)log(y(x))
                              log(y(x))
   (41)  -----------------------------------------------------------
                                             2
                                y(x)log(y(x))
                                                     Type: Expression Integer
--R
--R                                  x         2 ,
--R         x y(x)log(y(x))log(- ---------) + x y (x) - x y(x)log(y(x))
--R                              log(y(x))
--R   (41)  -----------------------------------------------------------
--R                                             2
--R                                y(x)log(y(x))
--R                                                     Type: Expression Integer
--E 41

-------------------------------------------------------------------
--S 42 of 126
ode119 := x*D(y(x),x) - y(x)*(log(x*y(x))-1)
 

           ,
   (42)  xy (x) - y(x)log(x y(x)) + y(x)

                                                     Type: Expression Integer
--R
--R           ,
--R   (42)  xy (x) - y(x)log(x y(x)) + y(x)
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 126
yx:=solve(ode119,y,x)
 

   (43)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (43)  "failed"
--R                                                    Type: Union("failed",...)
--E 43

-------------------------------------------------------------------
--S 44 of 126
ode120 := x*D(y(x),x) - y(x)*(x*log(x**2/y(x))+2)
 

                              2
           ,                 x
   (44)  xy (x) - x y(x)log(----) - 2y(x)
                            y(x)
                                                     Type: Expression Integer
--R
--R                              2
--R           ,                 x
--R   (44)  xy (x) - x y(x)log(----) - 2y(x)
--R                            y(x)
--R                                                     Type: Expression Integer
--E 44

--S 45 of 126
yx:=solve(ode120,y,x)
 

   (45)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (45)  "failed"
--R                                                    Type: Union("failed",...)
--E 45

-------------------------------------------------------------------
--S 46 of 126
ode121 := x*D(y(x),x) + sin(y(x)-x)
 

           ,
   (46)  xy (x) + sin(y(x) - x)

                                                     Type: Expression Integer
--R
--R           ,
--R   (46)  xy (x) + sin(y(x) - x)
--R
--R                                                     Type: Expression Integer
--E 46

--S 47 of 126
yx:=solve(ode121,y,x)
 

   (47)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (47)  "failed"
--R                                                    Type: Union("failed",...)
--E 47

-------------------------------------------------------------------
--S 48 of 126
ode122 := x*D(y(x),x) + (sin(y(x))-3*x**2*cos(y(x)))*cos(y(x))
 

           ,                             2         2
   (48)  xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x))

                                                     Type: Expression Integer
--R
--R           ,                             2         2
--R   (48)  xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 48

--S 49 of 126
yx:=solve(ode122,y,x)
 

   (49)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (49)  "failed"
--R                                                    Type: Union("failed",...)
--E 49

-------------------------------------------------------------------
--S 50 of 126
ode123 := x*D(y(x),x) - x*sin(y(x)/x) - y(x)
 

           ,            y(x)
   (50)  xy (x) - x sin(----) - y(x)
                          x
                                                     Type: Expression Integer
--R
--R           ,            y(x)
--R   (50)  xy (x) - x sin(----) - y(x)
--R                          x
--R                                                     Type: Expression Integer
--E 50

--S 51 of 126
yx:=solve(ode123,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 51

-------------------------------------------------------------------
--S 52 of 126
ode124 := x*D(y(x),x) + x*cos(y(x)/x) - y(x) + x
 

           ,            y(x)
   (52)  xy (x) + x cos(----) - y(x) + x
                          x
                                                     Type: Expression Integer
--R
--R           ,            y(x)
--R   (52)  xy (x) + x cos(----) - y(x) + x
--R                          x
--R                                                     Type: Expression Integer
--E 52

--S 53 of 126
yx:=solve(ode124,y,x)
 

   (53)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (53)  "failed"
--R                                                    Type: Union("failed",...)
--E 53

-------------------------------------------------------------------
--S 54 of 126
ode125 := x*D(y(x),x) + x*tan(y(x)/x) - y(x)
 

           ,            y(x)
   (54)  xy (x) + x tan(----) - y(x)
                          x
                                                     Type: Expression Integer
--R
--R           ,            y(x)
--R   (54)  xy (x) + x tan(----) - y(x)
--R                          x
--R                                                     Type: Expression Integer
--E 54

--S 55 of 126
yx:=solve(ode125,y,x)
 

   (55)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (55)  "failed"
--R                                                    Type: Union("failed",...)
--E 55

-------------------------------------------------------------------
--S 56 of 126
ode126 := x*D(y(x),x) - y(x)*f(x*y(x))
 

           ,
   (56)  xy (x) - y(x)f(x y(x))

                                                     Type: Expression Integer
--R
--R           ,
--R   (56)  xy (x) - y(x)f(x y(x))
--R
--R                                                     Type: Expression Integer
--E 56

--S 57 of 126
yx:=solve(ode126,y,x)
 

   (57)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (57)  "failed"
--R                                                    Type: Union("failed",...)
--E 57

-------------------------------------------------------------------
--S 58 of 126
ode127 := x*D(y(x),x) - y(x)*f(x**a*y(x)**b)
 

                  a    b      ,
   (58)  - y(x)f(x y(x) ) + xy (x)

                                                     Type: Expression Integer
--R
--R                  a    b      ,
--R   (58)  - y(x)f(x y(x) ) + xy (x)
--R
--R                                                     Type: Expression Integer
--E 58
--S 59 of 126
yx:=solve(ode127,y,x)
 

   (59)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (59)  "failed"
--R                                                    Type: Union("failed",...)
--E 59

-------------------------------------------------------------------
--S 60 of 126
ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x**a*y(x))
 

           ,                 a
   (60)  xy (x) - f(x)g(y(x)x ) + a y(x)

                                                     Type: Expression Integer
--R
--R           ,                 a
--R   (60)  xy (x) - f(x)g(y(x)x ) + a y(x)
--R
--R                                                     Type: Expression Integer
--E 60
--S 61 of 126
yx:=solve(ode128,y,x)
 

   (61)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (61)  "failed"
--R                                                    Type: Union("failed",...)
--E 61

-------------------------------------------------------------------
--S 62 of 126
ode129 := (x+1)*D(y(x),x) + y(x)*(y(x)-x)
 

                 ,          2
   (62)  (x + 1)y (x) + y(x)  - x y(x)

                                                     Type: Expression Integer
--R
--R                 ,          2
--R   (62)  (x + 1)y (x) + y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 62
--S 63 of 126
yx:=solve(ode129,y,x)
 

                              x
                        - x ++            1
         (- x - 1)y(x)%e    |   --------------------- d%U  + 1
                           ++      2             - %U
                                (%U  + 2%U + 1)%e
   (63)  -----------------------------------------------------
                                         - x
                            (x + 1)y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              x
--R                        - x ++            1
--I         (- x - 1)y(x)%e    |   --------------------- d%U  + 1
--I                           ++      2             - %U
--I                                (%U  + 2%U + 1)%e
--R   (63)  -----------------------------------------------------
--R                                         - x
--R                            (x + 1)y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 63

-------------------------------------------------------------------
--S 64 of 126
ode130 := 2*x*D(y(x),x) - y(x) -2*x**3
 

            ,               3
   (64)  2xy (x) - y(x) - 2x

                                                     Type: Expression Integer
--R
--R            ,               3
--R   (64)  2xy (x) - y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 64
--S 65 of 126
ode130a:=solve(ode130,y,x)
 

                        3
                      2x           +-+
   (65)  [particular= ---,basis= [\|x ]]
                       5
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                        3
--R                      2x           +-+
--R   (65)  [particular= ---,basis= [\|x ]]
--R                       5
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 65

--S 66 of 126
yx:=ode130a.particular
 

           3
         2x
   (66)  ---
          5
                                                     Type: Expression Integer
--R
--R           3
--R         2x
--R   (66)  ---
--R          5
--R                                                     Type: Expression Integer
--E 66

--S 67 of 126
ode130expr := 2*x*D(yx,x) - yx -2*x**3
 

   (67)  0
                                                     Type: Expression Integer
--R
--R   (67)  0
--R                                                     Type: Expression Integer
--E 67

-------------------------------------------------------------------
--S 68 of 126
ode131 := (2*x+1)*D(y(x),x) - 4*exp(-y(x)) + 2
 

                  ,         - y(x)
   (68)  (2x + 1)y (x) - 4%e       + 2

                                                     Type: Expression Integer
--R
--R                  ,         - y(x)
--R   (68)  (2x + 1)y (x) - 4%e       + 2
--R
--R                                                     Type: Expression Integer
--E 68
--S 69 of 126
yx:=solve(ode131,y,x)
 

                 - y(x)            y(x)
   (69)  (- 4x %e       + 2x + 1)%e
                                          Type: Union(Expression Integer,...)
--R
--R                 - y(x)            y(x)
--R   (69)  (- 4x %e       + 2x + 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 69

--S 70 of 126
ode131expr := (2*x+1)*D(yx,x) - 4*exp(-yx) + 2
 

   (70)
                - y(x)            y(x)
          (4x %e       - 2x - 1)%e          2            y(x) ,
     - 4%e                             + (4x  + 4x + 1)%e    y (x)

   + 
                  - y(x)            y(x)
     ((- 8x - 4)%e       + 4x + 2)%e     + 2
                                                     Type: Expression Integer
--R
--R   (70)
--R                - y(x)            y(x)
--R          (4x %e       - 2x - 1)%e          2            y(x) ,
--R     - 4%e                             + (4x  + 4x + 1)%e    y (x)
--R
--R   + 
--R                  - y(x)            y(x)
--R     ((- 8x - 4)%e       + 4x + 2)%e     + 2
--R                                                     Type: Expression Integer
--E 70

-------------------------------------------------------------------
--S 71 of 126
ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)**4 - y(x)
 

            ,             4
   (71)  3xy (x) - 3x y(x) log(x) - y(x)

                                                     Type: Expression Integer
--R
--R            ,             4
--R   (71)  3xy (x) - 3x y(x) log(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 71
--S 72 of 126
yx:=solve(ode132,y,x)
 

             2    3           2    3
         - 6x y(x) log(x) + 3x y(x)  - 4x
   (72)  --------------------------------
                           3
                      4y(x)
                                          Type: Union(Expression Integer,...)
--R
--R             2    3           2    3
--R         - 6x y(x) log(x) + 3x y(x)  - 4x
--R   (72)  --------------------------------
--R                           3
--R                      4y(x)
--R                                          Type: Union(Expression Integer,...)
--E 72

--S 73 of 126
ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx
 

   (73)
            2    8 ,           9    12      5
       2304x y(x) y (x) - 3888x y(x)  log(x)

     + 
             9    12         8    9       4
       (7776x y(x)   - 10368x y(x) )log(x)
     + 
               9    12         8    9         7    6       3
       (- 5832x y(x)   + 15552x y(x)  - 10368x y(x) )log(x)
     + 
             9    12        8    9         7    6        6    3       2
       (1944x y(x)   - 7776x y(x)  + 10368x y(x)  - 4608x y(x) )log(x)
     + 
                  9        2     12        8    9        7    6        6    3
           (- 243x  - 1920x )y(x)   + 1296x y(x)  - 2592x y(x)  + 2304x y(x)
         + 
                 5
           - 768x
      *
         log(x)
     + 
             2    12            9
       - 192x y(x)   - 512x y(x)
  /
            12
     256y(x)
                                                     Type: Expression Integer
--R
--R   (73)
--R            2    8 ,           9    12      5
--R       2304x y(x) y (x) - 3888x y(x)  log(x)
--R
--R     + 
--R             9    12         8    9       4
--R       (7776x y(x)   - 10368x y(x) )log(x)
--R     + 
--R               9    12         8    9         7    6       3
--R       (- 5832x y(x)   + 15552x y(x)  - 10368x y(x) )log(x)
--R     + 
--R             9    12        8    9         7    6        6    3       2
--R       (1944x y(x)   - 7776x y(x)  + 10368x y(x)  - 4608x y(x) )log(x)
--R     + 
--R                  9        2     12        8    9        7    6        6    3
--R           (- 243x  - 1920x )y(x)   + 1296x y(x)  - 2592x y(x)  + 2304x y(x)
--R         + 
--R                 5
--R           - 768x
--R      *
--R         log(x)
--R     + 
--R             2    12            9
--R       - 192x y(x)   - 512x y(x)
--R  /
--R            12
--R     256y(x)
--R                                                     Type: Expression Integer
--E 73

-------------------------------------------------------------------
--S 74 of 126
ode133 := x**2*D(y(x),x) + y(x) - x
 

          2 ,
   (74)  x y (x) + y(x) - x

                                                     Type: Expression Integer
--R
--R          2 ,
--R   (74)  x y (x) + y(x) - x
--R
--R                                                     Type: Expression Integer
--E 74
--S 75 of 126
yx:=solve(ode133,y,x)
 

                        1                            1
                        -   x                        -
                        x ++     1                   x
   (75)  [particular= %e  |   ------- d%U ,basis= [%e ]]
                         ++         1
                                   --
                                   %U
                              %U %e
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                        1                            1
--R                        -   x                        -
--R                        x ++     1                   x
--I   (75)  [particular= %e  |   ------- d%U ,basis= [%e ]]
--R                         ++         1
--R                                   --
--I                                   %U
--I                              %U %e
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 75

-------------------------------------------------------------------
--S 76 of 126
ode134 := x**2*D(y(x),x) - y(x) + x**2*exp(x-1/x)
 

                        2
                       x  - 1
                       ------
          2 ,       2     x
   (76)  x y (x) + x %e       - y(x)

                                                     Type: Expression Integer
--R
--R                        2
--R                       x  - 1
--R                       ------
--R          2 ,       2     x
--R   (76)  x y (x) + x %e       - y(x)
--R
--R                                                     Type: Expression Integer
--E 76
--S 77 of 126
ode134a:=solve(ode134,y,x)
 

                           2
                          x  - 1             1
                          ------           - -
                             x               x
   (77)  [particular= - %e      ,basis= [%e   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                           2
--R                          x  - 1             1
--R                          ------           - -
--R                             x               x
--R   (77)  [particular= - %e      ,basis= [%e   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 77

--S 78 of 126
yx:=ode134a.particular
 

              2
             x  - 1
             ------
                x
   (78)  - %e
                                                     Type: Expression Integer
--R
--R              2
--R             x  - 1
--R             ------
--R                x
--R   (78)  - %e
--R                                                     Type: Expression Integer
--E 78

--S 79 of 126
ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x)
 

   (79)  0
                                                     Type: Expression Integer
--R
--R   (79)  0
--R                                                     Type: Expression Integer
--E 79

-------------------------------------------------------------------
--S 80 of 126
ode135 := x**2*D(y(x),x) - (x-1)*y(x)
 

          2 ,
   (80)  x y (x) + (- x + 1)y(x)

                                                     Type: Expression Integer
--R
--R          2 ,
--R   (80)  x y (x) + (- x + 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 80
--S 81 of 126
ode135a:=solve(ode135,y,x)
 

                                    1
                                    -
                                    x
   (81)  [particular= 0,basis= [x %e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                    1
--R                                    -
--R                                    x
--R   (81)  [particular= 0,basis= [x %e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 81

--S 82 of 126
yx:=ode135a.particular
 

   (82)  0
                                                     Type: Expression Integer
--R
--R   (82)  0
--R                                                     Type: Expression Integer
--E 82

--S 83 of 126
ode135expr := x**2*D(yx,x) - (x-1)*yx
 

   (83)  0
                                                     Type: Expression Integer
--R
--R   (83)  0
--R                                                     Type: Expression Integer
--E 83

-------------------------------------------------------------------
--S 84 of 126
ode136 := x**2*D(y(x),x) + y(x)**2 + x*y(x) + x**2
 

          2 ,          2             2
   (84)  x y (x) + y(x)  + x y(x) + x

                                                     Type: Expression Integer
--R
--R          2 ,          2             2
--R   (84)  x y (x) + y(x)  + x y(x) + x
--R
--R                                                     Type: Expression Integer
--E 84
--S 85 of 126
yx:=solve(ode136,y,x)
 

         (- y(x) - x)log(x) + x
   (85)  ----------------------
                y(x) + x
                                          Type: Union(Expression Integer,...)
--R
--R         (- y(x) - x)log(x) + x
--R   (85)  ----------------------
--R                y(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 126
ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2
 

   (86)
          3 ,           2              2       2
       - x y (x) + (y(x)  + 2x y(x) + x )log(x)

     + 
                2        2              3     2            2         2     3
       (- x y(x)  + (- 2x  - 2x)y(x) - x  - 2x )log(x) + (x  - x)y(x)  + 2x y(x)
     + 
        4    2
       x  + x
  /
         2              2
     y(x)  + 2x y(x) + x
                                                     Type: Expression Integer
--R
--R   (86)
--R          3 ,           2              2       2
--R       - x y (x) + (y(x)  + 2x y(x) + x )log(x)
--R
--R     + 
--R                2        2              3     2            2         2     3
--R       (- x y(x)  + (- 2x  - 2x)y(x) - x  - 2x )log(x) + (x  - x)y(x)  + 2x y(x)
--R     + 
--R        4    2
--R       x  + x
--R  /
--R         2              2
--R     y(x)  + 2x y(x) + x
--R                                                     Type: Expression Integer
--E 86

-------------------------------------------------------------------
--S 87 of 126
ode137 := x**2*D(y(x),x) - y(x)**2 - x*y(x)
 

          2 ,          2
   (87)  x y (x) - y(x)  - x y(x)

                                                     Type: Expression Integer
--R
--R          2 ,          2
--R   (87)  x y (x) - y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 87
--S 88 of 126
yx:=solve(ode137,y,x)
 

         y(x)log(x) + x
   (88)  --------------
              y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         y(x)log(x) + x
--R   (88)  --------------
--R              y(x)
--R                                          Type: Union(Expression Integer,...)
--E 88

--S 89 of 126
ode137expr := x**2*D(yx,x) - yx**2 - x*yx
 

            3 ,          2      2            2                          2    2
         - x y (x) - y(x) log(x)  + (- x y(x)  - 2x y(x))log(x) + x y(x)  - x

   (89)  ---------------------------------------------------------------------
                                             2
                                         y(x)
                                                     Type: Expression Integer
--R
--R            3 ,          2      2            2                          2    2
--R         - x y (x) - y(x) log(x)  + (- x y(x)  - 2x y(x))log(x) + x y(x)  - x
--R
--R   (89)  ---------------------------------------------------------------------
--R                                             2
--R                                         y(x)
--R                                                     Type: Expression Integer
--E 89

-------------------------------------------------------------------
--S 90 of 126
ode138 := x**2*D(y(x),x) - y(x)**2 - x*y(x) - x**2
 

          2 ,          2             2
   (90)  x y (x) - y(x)  - x y(x) - x

                                                     Type: Expression Integer
--R
--R          2 ,          2             2
--R   (90)  x y (x) - y(x)  - x y(x) - x
--R
--R                                                     Type: Expression Integer
--E 90

--S 91 of 126
yx:=solve(ode138,y,x)
 

                         +---+               +---+
                    (- 7\|- 1  + 9)y(x) + 9x\|- 1  + 7x
   (91)  --------------------------------------------------------
                                                      +---+
              +---+                 +---+         - 2\|- 1 log(x)
         ((18\|- 1  + 14)y(x) - 14x\|- 1  + 18x)%e
                                          Type: Union(Expression Integer,...)
--R
--R                         +---+               +---+
--R                    (- 7\|- 1  + 9)y(x) + 9x\|- 1  + 7x
--R   (91)  --------------------------------------------------------
--R                                                      +---+
--R              +---+                 +---+         - 2\|- 1 log(x)
--R         ((18\|- 1  + 14)y(x) - 14x\|- 1  + 18x)%e
--R                                          Type: Union(Expression Integer,...)
--E 91

--S 92 of 126
ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2
 

   (92)
                  3 +---+        3             4 +---+        4
         ((- 1188x \|- 1  + 2716x )y(x) - 2716x \|- 1  - 1188x )
      *
               +---+
           - 2\|- 1 log(x) ,
         %e               y (x)

     + 
                   2 +---+        2     3           3 +---+        3     2
           (- 1188x \|- 1  + 2716x )y(x)  + (- 8148x \|- 1  - 3564x )y(x)
         + 
                 4 +---+        4             5 +---+        5
           (3564x \|- 1  - 8148x )y(x) + 2716x \|- 1  + 1188x
      *
                +---+       2
            - 2\|- 1 log(x)
         (%e               )
     + 
                   +---+             3         2 +---+        2     2
           (- 170x\|- 1  - 3310x)y(x)  + (4498x \|- 1  - 2886x )y(x)
         + 
                 3 +---+        3             4 +---+       4
           (2546x \|- 1  - 2122x )y(x) + 3310x \|- 1  - 170x
      *
               +---+
           - 2\|- 1 log(x)
         %e
     + 
            +---+           3           +---+            2
       (297\|- 1  - 679)y(x)  + (- 679x\|- 1  - 297x)y(x)
     + 
            2 +---+       2            3 +---+       3
       (297x \|- 1  - 679x )y(x) - 679x \|- 1  - 297x
  /
               +---+            3          +---+             2
         (1188\|- 1  - 2716)y(x)  + (8148x\|- 1  + 3564x)y(x)
       + 
                 2 +---+        2             3 +---+        3
         (- 3564x \|- 1  + 8148x )y(x) - 2716x \|- 1  - 1188x
    *
              +---+       2
          - 2\|- 1 log(x)
       (%e               )
                                                     Type: Expression Integer
--R
--R   (92)
--R                  3 +---+        3             4 +---+        4
--R         ((- 1188x \|- 1  + 2716x )y(x) - 2716x \|- 1  - 1188x )
--R      *
--R               +---+
--R           - 2\|- 1 log(x) ,
--R         %e               y (x)
--R
--R     + 
--R                   2 +---+        2     3           3 +---+        3     2
--R           (- 1188x \|- 1  + 2716x )y(x)  + (- 8148x \|- 1  - 3564x )y(x)
--R         + 
--R                 4 +---+        4             5 +---+        5
--R           (3564x \|- 1  - 8148x )y(x) + 2716x \|- 1  + 1188x
--R      *
--R                +---+       2
--R            - 2\|- 1 log(x)
--R         (%e               )
--R     + 
--R                   +---+             3         2 +---+        2     2
--R           (- 170x\|- 1  - 3310x)y(x)  + (4498x \|- 1  - 2886x )y(x)
--R         + 
--R                 3 +---+        3             4 +---+       4
--R           (2546x \|- 1  - 2122x )y(x) + 3310x \|- 1  - 170x
--R      *
--R               +---+
--R           - 2\|- 1 log(x)
--R         %e
--R     + 
--R            +---+           3           +---+            2
--R       (297\|- 1  - 679)y(x)  + (- 679x\|- 1  - 297x)y(x)
--R     + 
--R            2 +---+       2            3 +---+       3
--R       (297x \|- 1  - 679x )y(x) - 679x \|- 1  - 297x
--R  /
--R               +---+            3          +---+             2
--R         (1188\|- 1  - 2716)y(x)  + (8148x\|- 1  + 3564x)y(x)
--R       + 
--R                 2 +---+        2             3 +---+        3
--R         (- 3564x \|- 1  + 8148x )y(x) - 2716x \|- 1  - 1188x
--R    *
--R              +---+       2
--R          - 2\|- 1 log(x)
--R       (%e               )
--R                                                     Type: Expression Integer
--E 92

-------------------------------------------------------------------
--S 93 of 126
ode139 := x**2*(D(y(x),x)+y(x)**2) + a*x**k - b*(b-1)
 

          2 ,         k    2    2    2
   (93)  x y (x) + a x  + x y(x)  - b  + b

                                                     Type: Expression Integer
--R
--R          2 ,         k    2    2    2
--R   (93)  x y (x) + a x  + x y(x)  - b  + b
--R
--R                                                     Type: Expression Integer
--E 93


--S 94 of 126
yx:=solve(ode139,y,x)
 

   (94)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (94)  "failed"
--R                                                    Type: Union("failed",...)
--E 94

-------------------------------------------------------------------
--S 95 of 126
ode140 := x**2*(D(y(x),x)+y(x)**2) + 4*x*y(x) + 2
 

          2 ,       2    2
   (95)  x y (x) + x y(x)  + 4x y(x) + 2

                                                     Type: Expression Integer
--R
--R          2 ,       2    2
--R   (95)  x y (x) + x y(x)  + 4x y(x) + 2
--R
--R                                                     Type: Expression Integer
--E 95
--S 96 of 126
yx:=solve(ode140,y,x)
 

              x y(x) + 2
   (96)  --------------------
           2
         (x  - x)y(x) + x - 2
                                          Type: Union(Expression Integer,...)
--R
--R              x y(x) + 2
--R   (96)  --------------------
--R           2
--R         (x  - x)y(x) + x - 2
--R                                          Type: Union(Expression Integer,...)
--E 96

--S 97 of 126
ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2
 

   (97)
      4 ,         4     3     2     2       3      2                2
   - x y (x) + (6x  - 8x  + 2x )y(x)  + (16x  - 28x  + 8x)y(x) + 12x  - 24x + 8

   ----------------------------------------------------------------------------
               4     3    2     2      3     2              2
             (x  - 2x  + x )y(x)  + (2x  - 6x  + 4x)y(x) + x  - 4x + 4
                                                     Type: Expression Integer
--R
--R   (97)
--R      4 ,         4     3     2     2       3      2                2
--R   - x y (x) + (6x  - 8x  + 2x )y(x)  + (16x  - 28x  + 8x)y(x) + 12x  - 24x + 8
--R
--R   ----------------------------------------------------------------------------
--R               4     3    2     2      3     2              2
--R             (x  - 2x  + x )y(x)  + (2x  - 6x  + 4x)y(x) + x  - 4x + 4
--R                                                     Type: Expression Integer
--E 97

-------------------------------------------------------------------
--S 98 of 126
ode141 := x**2*(D(y(x),x)+y(x)**2) + a*x*y(x) + b
 

          2 ,       2    2
   (98)  x y (x) + x y(x)  + a x y(x) + b

                                                     Type: Expression Integer
--R
--R          2 ,       2    2
--R   (98)  x y (x) + x y(x)  + a x y(x) + b
--R
--R                                                     Type: Expression Integer
--E 98


--S 99 of 126
yx:=solve(ode141,y,x)
 
                                                     2
   WARNING (genufact): No known algorithm to factor ?  + (a - 1)? + b
     , trying square-free.

   (99)
      +------------------+
      |        2
     \|- 4b + a  - 2a + 1  - 2x y(x) - a + 1
  /
                          +------------------+
                          |        2                   2
       ((2x y(x) + a - 1)\|- 4b + a  - 2a + 1  - 4b + a  - 2a + 1)
    *
                  +------------------+
                  |        2
         - log(x)\|- 4b + a  - 2a + 1
       %e
                                          Type: Union(Expression Integer,...)
--R                                                     2
--R   WARNING (genufact): No known algorithm to factor ?  + (a - 1)? + b
--R     , trying square-free.
--R
--R   (99)
--R      +------------------+
--R      |        2
--R     \|- 4b + a  - 2a + 1  - 2x y(x) - a + 1
--R  /
--R                          +------------------+
--R                          |        2                   2
--R       ((2x y(x) + a - 1)\|- 4b + a  - 2a + 1  - 4b + a  - 2a + 1)
--R    *
--R                  +------------------+
--R                  |        2
--R         - log(x)\|- 4b + a  - 2a + 1
--R       %e
--R                                          Type: Union(Expression Integer,...)
--E 99

--S 100 of 126
ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b
 

   (100)
                        2           4                       3     2           3
             ((- 8b + 2a  - 4a + 2)x y(x) + ((- 4a + 4)b + a  - 3a  + 3a - 1)x )
          *
              +------------------+
              |        2
             \|- 4b + a  - 2a + 1
         + 
               2        2                4     3     2           3
           (16b  + (- 8a  + 16a - 8)b + a  - 4a  + 6a  - 4a + 1)x
      *
                    +------------------+
                    |        2
           - log(x)\|- 4b + a  - 2a + 1  ,
         %e                             y (x)

     + 
                  2        2             3    3
               (8b  + (- 2a  + 4a - 2)b)x y(x)
             + 
                           2        3     2             2    2
               ((12a - 12)b  + (- 3a  + 9a  - 9a + 3)b)x y(x)
             + 
                          3       2             2
                     - 24b  + (18a  - 36a + 18)b
                   + 
                          4      3      2
                     (- 3a  + 12a  - 18a  + 12a - 3)b
              *
                 x y(x)
             + 
                            3      3      2            2
               (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b
             + 
                   5     4      3      2
               (- a  + 5a  - 10a  + 10a  - 5a + 1)b
          *
              +------------------+
              |        2
             \|- 4b + a  - 2a + 1
         + 
                   3       2             2        4      3      2              2
             (- 48b  + (24a  - 48a + 24)b  + (- 3a  + 12a  - 18a  + 12a - 3)b)x
          *
                 2
             y(x)
         + 
                            3       3      2             2
               (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b
             + 
                    5      4      3      2
               (- 3a  + 15a  - 30a  + 30a  - 15a + 3)b
          *
             x y(x)
         + 
              4         2             3      4      3      2            2
           16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b
         + 
               6     5      4      3      2
           (- a  + 6a  - 15a  + 20a  - 15a  + 6a - 1)b
      *
                     +------------------+ 2
                     |        2
            - log(x)\|- 4b + a  - 2a + 1
         (%e                             )
     + 
                         2           4    3
               (- 8b + 2a  - 4a + 2)x y(x)
             + 
                                 3     2           3    2
               ((- 16a + 4)b + 4a  - 9a  + 6a - 1)x y(x)
             + 
                    2        2                4     3     2       2
               (- 8b  + (- 6a  + 4a + 2)b + 2a  - 6a  + 6a  - 2a)x y(x)
             + 
                           2      3     2
               ((- 8a + 4)b  + (2a  - 5a  + 4a - 1)b)x
          *
              +------------------+
              |        2
             \|- 4b + a  - 2a + 1
         + 
                       3     2       4    3
           (- 8a b + 2a  - 4a  + 2a)x y(x)
         + 
               2         2                 4      3      2           3    2
           (16b  + (- 20a  + 28a - 8)b + 4a  - 13a  + 15a  - 7a + 1)x y(x)
         + 
                2         3      2             5     4      3     2       2
           (8a b  + (- 10a  + 20a  - 10a)b + 2a  - 8a  + 12a  - 8a  + 2a)x y(x)
         + 
               3         2            2      4     3     2
           (16b  + (- 12a  + 20a - 8)b  + (2a  - 7a  + 9a  - 5a + 1)b)x
      *
                    +------------------+
                    |        2
           - log(x)\|- 4b + a  - 2a + 1
         %e
     + 
               5    3              4    2            2           3
           - 2x y(x)  + (- 3a + 3)x y(x)  + (- 2b - a  + 2a - 1)x y(x)
         + 
                       2
           (- a + 1)b x
      *
          +------------------+
          |        2
         \|- 4b + a  - 2a + 1
     + 
                2           4    2                   3     2           3
       (- 4b + a  - 2a + 1)x y(x)  + ((- 4a + 4)b + a  - 3a  + 3a - 1)x y(x)
     + 
            2     2             2
       (- 4b  + (a  - 2a + 1)b)x
  /
                     2           3    3
             (8b - 2a  + 4a - 2)x y(x)
           + 
                              3     2           2    2
             ((12a - 12)b - 3a  + 9a  - 9a + 3)x y(x)
           + 
                   2       2                  4      3      2
             (- 24b  + (18a  - 36a + 18)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
           + 
                          2      3      2                5     4      3      2
             (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b - a  + 5a  - 10a  + 10a
           + 
             - 5a + 1
        *
            +------------------+
            |        2
           \|- 4b + a  - 2a + 1
       + 
               2       2                  4      3      2            2    2
         (- 48b  + (24a  - 48a + 24)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
       + 
                          2       3      2                  5      4      3
             (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b - 3a  + 15a  - 30a
           + 
                2
             30a  - 15a + 3
        *
           x y(x)
       + 
            3         2             2      4      3      2                6
         16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b - a
       + 
           5      4      3      2
         6a  - 15a  + 20a  - 15a  + 6a - 1
    *
                   +------------------+ 2
                   |        2
          - log(x)\|- 4b + a  - 2a + 1
       (%e                             )
                                                     Type: Expression Integer
--R
--R   (100)
--R                        2           4                       3     2           3
--R             ((- 8b + 2a  - 4a + 2)x y(x) + ((- 4a + 4)b + a  - 3a  + 3a - 1)x )
--R          *
--R              +------------------+
--R              |        2
--R             \|- 4b + a  - 2a + 1
--R         + 
--R               2        2                4     3     2           3
--R           (16b  + (- 8a  + 16a - 8)b + a  - 4a  + 6a  - 4a + 1)x
--R      *
--R                    +------------------+
--R                    |        2
--R           - log(x)\|- 4b + a  - 2a + 1  ,
--R         %e                             y (x)
--R
--R     + 
--R                  2        2             3    3
--R               (8b  + (- 2a  + 4a - 2)b)x y(x)
--R             + 
--R                           2        3     2             2    2
--R               ((12a - 12)b  + (- 3a  + 9a  - 9a + 3)b)x y(x)
--R             + 
--R                          3       2             2
--R                     - 24b  + (18a  - 36a + 18)b
--R                   + 
--R                          4      3      2
--R                     (- 3a  + 12a  - 18a  + 12a - 3)b
--R              *
--R                 x y(x)
--R             + 
--R                            3      3      2            2
--R               (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b
--R             + 
--R                   5     4      3      2
--R               (- a  + 5a  - 10a  + 10a  - 5a + 1)b
--R          *
--R              +------------------+
--R              |        2
--R             \|- 4b + a  - 2a + 1
--R         + 
--R                   3       2             2        4      3      2              2
--R             (- 48b  + (24a  - 48a + 24)b  + (- 3a  + 12a  - 18a  + 12a - 3)b)x
--R          *
--R                 2
--R             y(x)
--R         + 
--R                            3       3      2             2
--R               (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b
--R             + 
--R                    5      4      3      2
--R               (- 3a  + 15a  - 30a  + 30a  - 15a + 3)b
--R          *
--R             x y(x)
--R         + 
--R              4         2             3      4      3      2            2
--R           16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b
--R         + 
--R               6     5      4      3      2
--R           (- a  + 6a  - 15a  + 20a  - 15a  + 6a - 1)b
--R      *
--R                     +------------------+ 2
--R                     |        2
--R            - log(x)\|- 4b + a  - 2a + 1
--R         (%e                             )
--R     + 
--R                         2           4    3
--R               (- 8b + 2a  - 4a + 2)x y(x)
--R             + 
--R                                 3     2           3    2
--R               ((- 16a + 4)b + 4a  - 9a  + 6a - 1)x y(x)
--R             + 
--R                    2        2                4     3     2       2
--R               (- 8b  + (- 6a  + 4a + 2)b + 2a  - 6a  + 6a  - 2a)x y(x)
--R             + 
--R                           2      3     2
--R               ((- 8a + 4)b  + (2a  - 5a  + 4a - 1)b)x
--R          *
--R              +------------------+
--R              |        2
--R             \|- 4b + a  - 2a + 1
--R         + 
--R                       3     2       4    3
--R           (- 8a b + 2a  - 4a  + 2a)x y(x)
--R         + 
--R               2         2                 4      3      2           3    2
--R           (16b  + (- 20a  + 28a - 8)b + 4a  - 13a  + 15a  - 7a + 1)x y(x)
--R         + 
--R                2         3      2             5     4      3     2       2
--R           (8a b  + (- 10a  + 20a  - 10a)b + 2a  - 8a  + 12a  - 8a  + 2a)x y(x)
--R         + 
--R               3         2            2      4     3     2
--R           (16b  + (- 12a  + 20a - 8)b  + (2a  - 7a  + 9a  - 5a + 1)b)x
--R      *
--R                    +------------------+
--R                    |        2
--R           - log(x)\|- 4b + a  - 2a + 1
--R         %e
--R     + 
--R               5    3              4    2            2           3
--R           - 2x y(x)  + (- 3a + 3)x y(x)  + (- 2b - a  + 2a - 1)x y(x)
--R         + 
--R                       2
--R           (- a + 1)b x
--R      *
--R          +------------------+
--R          |        2
--R         \|- 4b + a  - 2a + 1
--R     + 
--R                2           4    2                   3     2           3
--R       (- 4b + a  - 2a + 1)x y(x)  + ((- 4a + 4)b + a  - 3a  + 3a - 1)x y(x)
--R     + 
--R            2     2             2
--R       (- 4b  + (a  - 2a + 1)b)x
--R  /
--R                     2           3    3
--R             (8b - 2a  + 4a - 2)x y(x)
--R           + 
--R                              3     2           2    2
--R             ((12a - 12)b - 3a  + 9a  - 9a + 3)x y(x)
--R           + 
--R                   2       2                  4      3      2
--R             (- 24b  + (18a  - 36a + 18)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
--R           + 
--R                          2      3      2                5     4      3      2
--R             (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b - a  + 5a  - 10a  + 10a
--R           + 
--R             - 5a + 1
--R        *
--R            +------------------+
--R            |        2
--R           \|- 4b + a  - 2a + 1
--R       + 
--R               2       2                  4      3      2            2    2
--R         (- 48b  + (24a  - 48a + 24)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
--R       + 
--R                          2       3      2                  5      4      3
--R             (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b - 3a  + 15a  - 30a
--R           + 
--R                2
--R             30a  - 15a + 3
--R        *
--R           x y(x)
--R       + 
--R            3         2             2      4      3      2                6
--R         16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b - a
--R       + 
--R           5      4      3      2
--R         6a  - 15a  + 20a  - 15a  + 6a - 1
--R    *
--R                   +------------------+ 2
--R                   |        2
--R          - log(x)\|- 4b + a  - 2a + 1
--R       (%e                             )
--R                                                     Type: Expression Integer
--E 100

-------------------------------------------------------------------
--S 101 of 126
ode142 := x**2*(D(y(x),x)-y(x)**2) - a*x**2*y(x) + a*x + 2
 

           2 ,       2    2      2
   (101)  x y (x) - x y(x)  - a x y(x) + a x + 2

                                                     Type: Expression Integer
--R
--R           2 ,       2    2      2
--R   (101)  x y (x) - x y(x)  - a x y(x) + a x + 2
--R
--R                                                     Type: Expression Integer
--E 101


--S 102 of 126
yx:=solve(ode142,y,x)
 

            2 3       2              3 3    2 2
          (a x  - 2a x  + 2x)y(x) + a x  - a x  + 2a x - 2
   (102)  ------------------------------------------------
                         3          3   - a x
                       (a x y(x) - a )%e
                                          Type: Union(Expression Integer,...)
--R
--R            2 3       2              3 3    2 2
--R          (a x  - 2a x  + 2x)y(x) + a x  - a x  + 2a x - 2
--R   (102)  ------------------------------------------------
--R                         3          3   - a x
--R                       (a x y(x) - a )%e
--R                                          Type: Union(Expression Integer,...)
--E 102

--S 103 of 126
ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2
 

   (103)
          6 6  - a x ,
       - a x %e     y (x)

     + 
          7 3     6 2     2        7 2     6          7      6    - a x 2
       ((a x  + 2a x )y(x)  + (- 2a x  - 4a x)y(x) + a x + 2a )(%e     )
     + 
              5 5     4 4     2      6 5     5 4     4 3          6 4     5 3
           (2a x  - 2a x )y(x)  + (2a x  - 4a x  + 4a x )y(x) - 3a x  + 2a x
         + 
               4 2
           - 2a x
      *
           - a x
         %e
     + 
           4 8     3 7     2 6       5     4     2
       (- a x  + 4a x  - 8a x  + 8a x  - 4x )y(x)
     + 
            5 8     4 7      3 6      2 5        4     3         6 8     5 7
       (- 2a x  + 6a x  - 12a x  + 16a x  - 16a x  + 8x )y(x) - a x  + 2a x
     + 
           4 6     3 5     2 4       3     2
       - 5a x  + 8a x  - 8a x  + 8a x  - 4x
  /
       6 2    2     6          6    - a x 2
     (a x y(x)  - 2a x y(x) + a )(%e     )
                                                     Type: Expression Integer
--R
--R   (103)
--R          6 6  - a x ,
--R       - a x %e     y (x)
--R
--R     + 
--R          7 3     6 2     2        7 2     6          7      6    - a x 2
--R       ((a x  + 2a x )y(x)  + (- 2a x  - 4a x)y(x) + a x + 2a )(%e     )
--R     + 
--R              5 5     4 4     2      6 5     5 4     4 3          6 4     5 3
--R           (2a x  - 2a x )y(x)  + (2a x  - 4a x  + 4a x )y(x) - 3a x  + 2a x
--R         + 
--R               4 2
--R           - 2a x
--R      *
--R           - a x
--R         %e
--R     + 
--R           4 8     3 7     2 6       5     4     2
--R       (- a x  + 4a x  - 8a x  + 8a x  - 4x )y(x)
--R     + 
--R            5 8     4 7      3 6      2 5        4     3         6 8     5 7
--R       (- 2a x  + 6a x  - 12a x  + 16a x  - 16a x  + 8x )y(x) - a x  + 2a x
--R     + 
--R           4 6     3 5     2 4       3     2
--R       - 5a x  + 8a x  - 8a x  + 8a x  - 4x
--R  /
--R       6 2    2     6          6    - a x 2
--R     (a x y(x)  - 2a x y(x) + a )(%e     )
--R                                                     Type: Expression Integer
--E 103

-------------------------------------------------------------------
--S 104 of 126
ode143 := x**2*(D(y(x),x)+a*y(x)**2) - b
 

           2 ,         2    2
   (104)  x y (x) + a x y(x)  - b

                                                     Type: Expression Integer
--R
--R           2 ,         2    2
--R   (104)  x y (x) + a x y(x)  - b
--R
--R                                                     Type: Expression Integer
--E 104


--S 105 of 126
yx:=solve(ode143,y,x)
 
                                                     2
   WARNING (genufact): No known algorithm to factor ?  - ? - a b
     , trying square-free.

                            +--------+     2
                          a\|4a b + 1  - 2a x y(x) + a
   (105)  ------------------------------------------------------------
                                                            +--------+
                           +--------+              - log(x)\|4a b + 1
          ((2a x y(x) - 1)\|4a b + 1  + 4a b + 1)%e
                                          Type: Union(Expression Integer,...)
--R                                                     2
--R   WARNING (genufact): No known algorithm to factor ?  - ? - a b
--R     , trying square-free.
--R
--R                            +--------+     2
--R                          a\|4a b + 1  - 2a x y(x) + a
--R   (105)  ------------------------------------------------------------
--R                                                            +--------+
--R                           +--------+              - log(x)\|4a b + 1
--R          ((2a x y(x) - 1)\|4a b + 1  + 4a b + 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 105

--S 106 of 126
ode143expr := x**2*(D(yx,x)+a*yx**2) - b
 

   (106)
                                  +--------+
            3      2  3  - log(x)\|4a b + 1  ,
       (- 8a b - 2a )x %e                   y (x)

     + 
                 2 2                     2      +--------+
           ((- 8a b  - 2a b)x y(x) + 4a b  + b)\|4a b + 1
         + 
                3 2     2   2    2      2 2                   2 3       2
           (- 8a b  - 2a b)x y(x)  + (8a b  + 2a b)x y(x) - 8a b  - 6a b  - b
      *
                     +--------+ 2
            - log(x)\|4a b + 1
         (%e                   )
     + 
                                                           +--------+
             4      3  3    2      3 2     2      - log(x)\|4a b + 1
       ((- 8a b - 2a )x y(x)  + (8a b  + 2a b)x)%e
     + 
            4 3        3 2  +--------+     5 4    2     4 3          4     3  2
       (- 2a x y(x) + a x )\|4a b + 1  + 2a x y(x)  - 2a x y(x) + (2a b + a )x
  /
             2                          +--------+      3      2  2    2
         ((8a b + 2a)x y(x) - 4a b - 1)\|4a b + 1  + (8a b + 2a )x y(x)
       + 
              2                  2 2
         (- 8a b - 2a)x y(x) + 8a b  + 6a b + 1
    *
                   +--------+ 2
          - log(x)\|4a b + 1
       (%e                   )
                                                     Type: Expression Integer
--R
--R   (106)
--R                                  +--------+
--R            3      2  3  - log(x)\|4a b + 1  ,
--R       (- 8a b - 2a )x %e                   y (x)
--R
--R     + 
--R                 2 2                     2      +--------+
--R           ((- 8a b  - 2a b)x y(x) + 4a b  + b)\|4a b + 1
--R         + 
--R                3 2     2   2    2      2 2                   2 3       2
--R           (- 8a b  - 2a b)x y(x)  + (8a b  + 2a b)x y(x) - 8a b  - 6a b  - b
--R      *
--R                     +--------+ 2
--R            - log(x)\|4a b + 1
--R         (%e                   )
--R     + 
--R                                                           +--------+
--R             4      3  3    2      3 2     2      - log(x)\|4a b + 1
--R       ((- 8a b - 2a )x y(x)  + (8a b  + 2a b)x)%e
--R     + 
--R            4 3        3 2  +--------+     5 4    2     4 3          4     3  2
--R       (- 2a x y(x) + a x )\|4a b + 1  + 2a x y(x)  - 2a x y(x) + (2a b + a )x
--R  /
--R             2                          +--------+      3      2  2    2
--R         ((8a b + 2a)x y(x) - 4a b - 1)\|4a b + 1  + (8a b + 2a )x y(x)
--R       + 
--R              2                  2 2
--R         (- 8a b - 2a)x y(x) + 8a b  + 6a b + 1
--R    *
--R                   +--------+ 2
--R          - log(x)\|4a b + 1
--R       (%e                   )
--R                                                     Type: Expression Integer
--E 106

-------------------------------------------------------------------
--S 107 of 126
ode144 := x**2*(D(y(x),x)+a*y(x)**2) + b*x**alpha + c
 

           2 ,         alpha      2    2
   (107)  x y (x) + b x      + a x y(x)  + c

                                                     Type: Expression Integer
--R
--R           2 ,         alpha      2    2
--R   (107)  x y (x) + b x      + a x y(x)  + c
--R
--R                                                     Type: Expression Integer
--E 107

--S 108 of 126
yx:=solve(ode144,y,x)
 

   (108)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (108)  "failed"
--R                                                    Type: Union("failed",...)
--E 108

-------------------------------------------------------------------
--S 109 of 126
ode145 := x**2*D(y(x),x) + a*y(x)**3 - a*x**2*y(x)**2
 

           2 ,            3      2    2
   (109)  x y (x) + a y(x)  - a x y(x)

                                                     Type: Expression Integer
--R
--R           2 ,            3      2    2
--R   (109)  x y (x) + a y(x)  - a x y(x)
--R
--R                                                     Type: Expression Integer
--E 109

--S 110 of 126
yx:=solve(ode145,y,x)
 

   (110)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (110)  "failed"
--R                                                    Type: Union("failed",...)
--E 110

-------------------------------------------------------------------
--S 111 of 126
ode146 := x**2*D(y(x),x) + x*y(x)**3 + a*y(x)**2
 

           2 ,            3         2
   (111)  x y (x) + x y(x)  + a y(x)

                                                     Type: Expression Integer
--R
--R           2 ,            3         2
--R   (111)  x y (x) + x y(x)  + a y(x)
--R
--R                                                     Type: Expression Integer
--E 111

--S 112 of 126
yx:=solve(ode146,y,x)
 

   (112)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (112)  "failed"
--R                                                    Type: Union("failed",...)
--E 112

-------------------------------------------------------------------
--S 113 of 126
ode147 := x**2*D(y(x),x) + a*x**2*y(x)**3 + b*y(x)**2
 

           2 ,         2    3         2
   (113)  x y (x) + a x y(x)  + b y(x)

                                                     Type: Expression Integer
--R
--R           2 ,         2    3         2
--R   (113)  x y (x) + a x y(x)  + b y(x)
--R
--R                                                     Type: Expression Integer
--E 113
--S 114 of 126
yx:=solve(ode147,y,x)
 

   (114)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (114)  "failed"
--R                                                    Type: Union("failed",...)
--E 114

-------------------------------------------------------------------
--S 115 of 126
ode148 := (x**2+1)*D(y(x),x) + x*y(x) - 1
 

            2      ,
   (115)  (x  + 1)y (x) + x y(x) - 1

                                                     Type: Expression Integer
--R
--R            2      ,
--R   (115)  (x  + 1)y (x) + x y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 115
--S 116 of 126
ode148a:=solve(ode148,y,x)
 

                              +------+
                              | 2
                         log(\|x  + 1  - x)             1
   (116)  [particular= - ------------------,basis= [---------]]
                               +------+              +------+
                               | 2                   | 2
                              \|x  + 1              \|x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                              +------+
--R                              | 2
--R                         log(\|x  + 1  - x)             1
--R   (116)  [particular= - ------------------,basis= [---------]]
--R                               +------+              +------+
--R                               | 2                   | 2
--R                              \|x  + 1              \|x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 116

--S 117 of 126
yx:=ode148a.particular
 

                 +------+
                 | 2
            log(\|x  + 1  - x)
   (117)  - ------------------
                  +------+
                  | 2
                 \|x  + 1
                                                     Type: Expression Integer
--R
--R                 +------+
--R                 | 2
--R            log(\|x  + 1  - x)
--R   (117)  - ------------------
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R                                                     Type: Expression Integer
--E 117

--S 118 of 126
ode148expr := (x**2+1)*D(yx,x) + x*yx - 1
 

   (118)  0
                                                     Type: Expression Integer
--R
--R   (118)  0
--R                                                     Type: Expression Integer
--E 118

-------------------------------------------------------------------
--S 119 of 126
ode149 := (x**2+1)*D(y(x),x) + x*y(x) - x*(x**2+1)
 

            2      ,                3
   (119)  (x  + 1)y (x) + x y(x) - x  - x

                                                     Type: Expression Integer
--R
--R            2      ,                3
--R   (119)  (x  + 1)y (x) + x y(x) - x  - x
--R
--R                                                     Type: Expression Integer
--E 119
--S 120 of 126
ode149a:=solve(ode149,y,x)
 

                        2
                       x  + 1             1
   (120)  [particular= ------,basis= [---------]]
                          3            +------+
                                       | 2
                                      \|x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                        2
--R                       x  + 1             1
--R   (120)  [particular= ------,basis= [---------]]
--R                          3            +------+
--R                                       | 2
--R                                      \|x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 120

--S 121 of 126
yx:=ode149a.particular
 

           2
          x  + 1
   (121)  ------
             3
                                                     Type: Expression Integer
--R
--R           2
--R          x  + 1
--R   (121)  ------
--R             3
--R                                                     Type: Expression Integer
--E 121

--S 122 of 126
ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1)
 

   (122)  0
                                                     Type: Expression Integer
--R
--R   (122)  0
--R                                                     Type: Expression Integer
--E 122

-------------------------------------------------------------------
--S 123 of 126
ode150 := (x**2+1)*D(y(x),x) + 2*x*y(x) - 2*x**2
 

            2      ,                  2
   (123)  (x  + 1)y (x) + 2x y(x) - 2x

                                                     Type: Expression Integer
--R
--R            2      ,                  2
--R   (123)  (x  + 1)y (x) + 2x y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 123

--S 124 of 126
ode150a:=solve(ode150,y,x)
 

                         3
                       2x  + 3            1
   (124)  [particular= -------,basis= [------]]
                         2              2
                       3x  + 3         x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                         3
--R                       2x  + 3            1
--R   (124)  [particular= -------,basis= [------]]
--R                         2              2
--R                       3x  + 3         x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 124

--S 125 of 126
yx:=ode150a.particular
 

            3
          2x  + 3
   (125)  -------
            2
          3x  + 3
                                                     Type: Expression Integer
--R
--R            3
--R          2x  + 3
--R   (125)  -------
--R            2
--R          3x  + 3
--R                                                     Type: Expression Integer
--E 125

--S 126 of 126
ode150expr := (x**2+1)*D(yx,x) + 2*x*yx - 2*x**2
 

   (126)  0
                                                     Type: Expression Integer
--R
--R   (126)  0
--R                                                     Type: Expression Integer
--E 126
)spool
 
Starts dribbling to mappkg1.output (2009/2/17, 17:54:2).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 26
power(q: FRAC INT, n: INT): FRAC INT == q**n
 
   Function declaration power : (Fraction Integer,Integer) -> Fraction 
      Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration power : (Fraction Integer,Integer) -> Fraction 
--R      Integer has been added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 26
power(2,3)
 
   Compiling function power with type (Fraction Integer,Integer) -> 
      Fraction Integer 

   (2)  8
                                                       Type: Fraction Integer
--R 
--R   Compiling function power with type (Fraction Integer,Integer) -> 
--R      Fraction Integer 
--R
--R   (2)  8
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 26
rewop := twist power
 

   (3)  theMap(MAPPKG3;twist;MM;5!0)
                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--R   (3)  theMap(MAPPKG3;twist;MM;5!0)
--R                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--E 3

--S 4 of 26
rewop(3, 2)
 

   (4)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (4)  8
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 26
square: FRAC INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 26
square:= curryRight(power, 2)
 

   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--R   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 6

--S 7 of 26
square 4
 

   (7)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (7)  16
--R                                                       Type: Fraction Integer
--E 7

--S 8 of 26
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
 

   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--R   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
--R              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--E 8

--S 9 of 26
squirrel(1/2, 1/3)
 

        1
   (9)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (9)  -
--R        4
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 26
sixteen := curry(square, 4/1)
 

   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                               Type: (() -> Fraction Integer)
--R 
--R
--R   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                               Type: (() -> Fraction Integer)
--E 10

--S 11 of 26
sixteen()
 

   (11)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  16
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 26
square2:=square*square
 

   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--R   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 12

--S 13 of 26
square2  3
 

   (13)  81
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  81
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 26
sc(x: FRAC INT): FRAC INT == x + 1
 
   Function declaration sc : Fraction Integer -> Fraction Integer has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration sc : Fraction Integer -> Fraction Integer has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 14

--S 15 of 26
incfns := [sc**i for i in 0..10]
 
   Compiling function sc with type Fraction Integer -> Fraction Integer
      

   (15)
   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0)]
                            Type: List (Fraction Integer -> Fraction Integer)
--R 
--R   Compiling function sc with type Fraction Integer -> Fraction Integer
--R      
--R
--R   (15)
--R   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--R    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--R    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--R    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--R    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--R    theMap(MAPPKG1;**;MNniM;6!0,0)]
--R                            Type: List (Fraction Integer -> Fraction Integer)
--E 15

--S 16 of 26
[f 4 for f in incfns]
 

   (16)  [4,5,6,7,8,9,10,11,12,13,14]
                                                  Type: List Fraction Integer
--R 
--R
--R   (16)  [4,5,6,7,8,9,10,11,12,13,14]
--R                                                  Type: List Fraction Integer
--E 16

--S 17 of 26
times(n:NNI, i:INT):INT == n*i
 
   Function declaration times : (NonNegativeInteger,Integer) -> Integer
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration times : (NonNegativeInteger,Integer) -> Integer
--R      has been added to workspace.
--R                                                                   Type: Void
--E 17

--S 18 of 26
r := recur(times)
 
   Compiling function times with type (NonNegativeInteger,Integer) -> 
      Integer 

   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
                              Type: ((NonNegativeInteger,Integer) -> Integer)
--R 
--R   Compiling function times with type (NonNegativeInteger,Integer) -> 
--R      Integer 
--R
--R   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
--R                              Type: ((NonNegativeInteger,Integer) -> Integer)
--E 18

--S 19 of 26
fact := curryRight(r, 1)
 

   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                        Type: (NonNegativeInteger -> Integer)
--R 
--R
--R   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                        Type: (NonNegativeInteger -> Integer)
--E 19

--S 20 of 26
fact 4
 

   (20)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  24
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 26
mto2ton(m, n) ==
  raiser := square**n
  raiser m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 26
mto2ton(3, 3)
 
   Compiling function mto2ton with type (PositiveInteger,
      PositiveInteger) -> Fraction Integer 

   (22)  6561
                                                       Type: Fraction Integer
--R 
--R   Compiling function mto2ton with type (PositiveInteger,
--R      PositiveInteger) -> Fraction Integer 
--R
--R   (22)  6561
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 26
shiftfib(r: List INT) : INT ==
  t := r.1
  r.1 := r.2
  r.2 := r.2 + t
  t
 
   Function declaration shiftfib : List Integer -> Integer has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration shiftfib : List Integer -> Integer has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 23

--S 24 of 26
fibinit: List INT := [0, 1]
 

   (24)  [0,1]
                                                           Type: List Integer
--R 
--R
--R   (24)  [0,1]
--R                                                           Type: List Integer
--E 24

--S 25 of 26
fibs := curry(shiftfib, fibinit)
 
   Compiling function shiftfib with type List Integer -> Integer 

   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                                        Type: (() -> Integer)
--R 
--R   Compiling function shiftfib with type List Integer -> Integer 
--R
--R   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                                        Type: (() -> Integer)
--E 25

--S 26 of 26
[fibs() for i in 0..30]
 

   (26)
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
    317811, 514229, 832040]
                                                           Type: List Integer
--R 
--R
--R   (26)
--R   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
--R    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
--R    317811, 514229, 832040]
--R                                                           Type: List Integer
--E 26
)spool 
 
Starts dribbling to is.output (2009/2/17, 17:46:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 5
f: INT -> INT
--R                                                                   Type: Void
--E 1

--S 2 of 5
 f n ==
   not empty?(u := Is(n, 2*m%)) => integer eval(m%, u)
   3 * n + 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

)set stream showall on
 
 
--S 3 of 5
g(n:INT):STREAM(INT) == generate(f, n)
 
   Function declaration g : Integer -> Stream Integer has been added to
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration g : Integer -> Stream Integer has been added to
--R      workspace.
--R                                                                   Type: Void
--E 3

--S 4 of 5
s := g 27
 
   There are 3 exposed and 0 unexposed library operations named 
      generate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op generate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      generate with argument type(s) 
                                 Variable f
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function g with type Integer -> Stream Integer 
   There are 3 exposed and 0 unexposed library operations named 
      generate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op generate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      generate with argument type(s) 
                                 Variable f
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   Compiling function f with type Integer -> Integer 
--R   Compiling function g with type Integer -> Stream Integer 
--R
--R   (3)  [27,82,41,124,62,31,94,47,142,71,...]
--R                                                         Type: Stream Integer
--E 4

--S 5 of 5
extend(s, 150)
 
   There are 11 exposed and 0 unexposed library operations named extend
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op extend
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      extend with argument type(s) 
                                 Variable s
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R
--R   (4)
--R   [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242,
--R    121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350,
--R    175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167,
--R    502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479,
--R    1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734,
--R    1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433,
--R    1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53,
--R    160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20,
--R    10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4,
--R    2, 7, 22, 11, 34, 17, 52, 26, ...]
--R                                                         Type: Stream Integer
--E 5
)spool 
 
Starts dribbling to void.output (2009/2/17, 18:1:35).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 4
a : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

)set message void on
 

--S 2  of 4
b : Fraction Integer
 

   (2)  "()"
                                                                   Type: Void
--R 
--R
--R   (2)  "()"
--R                                                                   Type: Void
--E 2

)set message void off
 

--S 3  of 4
3::Void
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
% :: PositiveInteger
 
 
Daly Bug
   Cannot convert from type Void to PositiveInteger for value
   "()"

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Void to PositiveInteger for value
--R   "()"
--R
--E 4
)spool 
 
Starts dribbling to seccsc.output (2009/2/17, 18:0:15).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
[[0.01,1.0000500,sec(0.01),sec(0.01)-1.0000500],_
[0.02,1.0002000,sec(0.02),sec(0.02)-1.0002000],_
[0.03,1.0004502,sec(0.03),sec(0.03)-1.0004502],_
[0.04,1.0008005,sec(0.04),sec(0.04)-1.0008005],_
[0.05,1.0012513,sec(0.05),sec(0.05)-1.0012513],_
[0.06,1.0018027,sec(0.06),sec(0.06)-1.0018027],_
[0.07,1.0024550,sec(0.07),sec(0.07)-1.0024550],_
[0.08,1.0032086,sec(0.08),sec(0.08)-1.0032086],_
[0.09,1.0040637,sec(0.09),sec(0.09)-1.0040637],_
[0.10,1.0050209,sec(0.10),sec(0.10)-1.0050209],_
[0.11,1.0060807,sec(0.11),sec(0.11)-1.0060807],_
[0.12,1.0072435,sec(0.12),sec(0.12)-1.0072435],_
[0.13,1.0085099,sec(0.13),sec(0.13)-1.0085099],_
[0.14,1.0098807,sec(0.14),sec(0.14)-1.0098807],_
[0.15,1.0113564,sec(0.15),sec(0.15)-1.0113564],_
[0.16,1.0129380,sec(0.16),sec(0.16)-1.0129380],_
[0.17,1.0146261,sec(0.17),sec(0.17)-1.0146261],_
[0.18,1.0164216,sec(0.18),sec(0.18)-1.0164216],_
[0.19,1.0183255,sec(0.19),sec(0.19)-1.0183255],_
[0.20,1.0203388,sec(0.20),sec(0.20)-1.0203388],_
[0.21,1.0224626,sec(0.21),sec(0.21)-1.0224626],_
[0.22,1.0246978,sec(0.22),sec(0.22)-1.0246978],_
[0.23,1.0270458,sec(0.23),sec(0.23)-1.0270458],_
[0.24,1.0295078,sec(0.24),sec(0.24)-1.0295078],_
[0.25,1.0320850,sec(0.25),sec(0.25)-1.0320850],_
[0.26,1.0347789,sec(0.26),sec(0.26)-1.0347789],_
[0.27,1.0375910,sec(0.27),sec(0.27)-1.0375910],_
[0.28,1.0405227,sec(0.28),sec(0.28)-1.0405227],_
[0.29,1.0435757,sec(0.29),sec(0.29)-1.0435757],_
[0.30,1.0467516,sec(0.30),sec(0.30)-1.0467516],_
[0.31,1.0500522,sec(0.31),sec(0.31)-1.0500522],_
[0.32,1.0534794,sec(0.32),sec(0.32)-1.0534794],_
[0.33,1.0570351,sec(0.33),sec(0.33)-1.0570351],_
[0.34,1.0607213,sec(0.34),sec(0.34)-1.0607213],_
[0.35,1.0645402,sec(0.35),sec(0.35)-1.0645402],_
[0.36,1.0684938,sec(0.36),sec(0.36)-1.0684938],_
[0.37,1.0725847,sec(0.37),sec(0.37)-1.0725847],_
[0.38,1.0768150,sec(0.38),sec(0.38)-1.0768150],_
[0.39,1.0811874,sec(0.39),sec(0.39)-1.0811874],_
[0.40,1.0857044,sec(0.40),sec(0.40)-1.0857044],_
[0.41,1.0903689,sec(0.41),sec(0.41)-1.0903689],_
[0.42,1.0951836,sec(0.42),sec(0.42)-1.0951836],_
[0.43,1.1001515,sec(0.43),sec(0.43)-1.1001515],_
[0.44,1.1052757,sec(0.44),sec(0.44)-1.1052757],_
[0.45,1.1105594,sec(0.45),sec(0.45)-1.1105594],_
[0.46,1.1160060,sec(0.46),sec(0.46)-1.1160060],_
[0.47,1.1216191,sec(0.47),sec(0.47)-1.1216191],_
[0.48,1.1274022,sec(0.48),sec(0.48)-1.1274022],_
[0.49,1.1333591,sec(0.49),sec(0.49)-1.1333591],_
[0.50,1.1394939,sec(0.50),sec(0.50)-1.1394939],_
[0.51,1.1458107,sec(0.51),sec(0.51)-1.1458107],_
[0.52,1.1523138,sec(0.52),sec(0.52)-1.1523138],_
[0.53,1.1590077,sec(0.53),sec(0.53)-1.1590077],_
[0.54,1.1658970,sec(0.54),sec(0.54)-1.1658970],_
[0.55,1.1729868,sec(0.55),sec(0.55)-1.1729868],_
[0.56,1.1802821,sec(0.56),sec(0.56)-1.1802821],_
[0.57,1.1877881,sec(0.57),sec(0.57)-1.1877881],_
[0.58,1.1955106,sec(0.58),sec(0.58)-1.1955106],_
[0.59,1.2034553,sec(0.59),sec(0.59)-1.2034553],_
[0.60,1.2116283,sec(0.60),sec(0.60)-1.2116283],_
[0.61,1.2200359,sec(0.61),sec(0.61)-1.2200359],_
[0.62,1.2286847,sec(0.62),sec(0.62)-1.2286847],_
[0.63,1.2375816,sec(0.63),sec(0.63)-1.2375816],_
[0.64,1.2467339,sec(0.64),sec(0.64)-1.2467339],_
[0.65,1.2561492,sec(0.65),sec(0.65)-1.2561492],_
[0.66,1.2658352,sec(0.66),sec(0.66)-1.2658352],_
[0.67,1.2758004,sec(0.67),sec(0.67)-1.2758004],_
[0.68,1.2860534,sec(0.68),sec(0.68)-1.2860534],_
[0.69,1.2966031,sec(0.69),sec(0.69)-1.2966031],_
[0.70,1.3074593,sec(0.70),sec(0.70)-1.3074593],_
[0.71,1.3186317,sec(0.71),sec(0.71)-1.3186317],_
[0.72,1.3301309,sec(0.72),sec(0.72)-1.3301309],_
[0.73,1.3419677,sec(0.73),sec(0.73)-1.3419677],_
[0.74,1.3541538,sec(0.74),sec(0.74)-1.3541538],_
[0.75,1.3667011,sec(0.75),sec(0.75)-1.3667011],_
[0.76,1.3796224,sec(0.76),sec(0.76)-1.3796224],_
[0.77,1.3929310,sec(0.77),sec(0.77)-1.3929310],_
[0.78,1.4066408,sec(0.78),sec(0.78)-1.4066408],_
[0.79,1.4207667,sec(0.79),sec(0.79)-1.4207667],_
[0.80,1.4353242,sec(0.80),sec(0.80)-1.4353242],_
[0.81,1.4503296,sec(0.81),sec(0.81)-1.4503296],_
[0.82,1.4658002,sec(0.82),sec(0.82)-1.4658002],_
[0.83,1.4817542,sec(0.83),sec(0.83)-1.4817542],_
[0.84,1.4982108,sec(0.84),sec(0.84)-1.4982108],_
[0.85,1.5151902,sec(0.85),sec(0.85)-1.5151902],_
[0.86,1.5327139,sec(0.86),sec(0.86)-1.5327139],_
[0.87,1.5508046,sec(0.87),sec(0.87)-1.5508046],_
[0.88,1.5694863,sec(0.88),sec(0.88)-1.5694863],_
[0.89,1.5887844,sec(0.89),sec(0.89)-1.5887844],_
[0.90,1.6087258,sec(0.90),sec(0.90)-1.6087258],_
[0.91,1.6293392,sec(0.91),sec(0.91)-1.6293392],_
[0.92,1.6506549,sec(0.92),sec(0.92)-1.6506549],_
[0.93,1.6727052,sec(0.93),sec(0.93)-1.6727052],_
[0.94,1.6955244,sec(0.94),sec(0.94)-1.6955244],_
[0.95,1.7191492,sec(0.95),sec(0.95)-1.7191492],_
[0.96,1.7436184,sec(0.96),sec(0.96)-1.7436184],_
[0.97,1.7689737,sec(0.97),sec(0.97)-1.7689737],_
[0.98,1.7952595,sec(0.98),sec(0.98)-1.7952595],_
[0.99,1.8225232,sec(0.99),sec(0.99)-1.8225232],_
[1.00,1.8508157,sec(1.00),sec(1.00)-1.8508157],_
[1.01,1.8801915,sec(1.01),sec(1.01)-1.8801915],_
[1.02,1.9107089,sec(1.02),sec(1.02)-1.9107089],_
[1.03,1.9424308,sec(1.03),sec(1.03)-1.9424308],_
[1.04,1.9754247,sec(1.04),sec(1.04)-1.9754247],_
[1.05,2.0097632,sec(1.05),sec(1.05)-2.0097632],_
[1.06,2.0455249,sec(1.06),sec(1.06)-2.0455249],_
[1.07,2.0827943,sec(1.07),sec(1.07)-2.0827943],_
[1.08,2.1216631,sec(1.08),sec(1.08)-2.1216631],_
[1.09,2.1622306,sec(1.09),sec(1.09)-2.1622306],_
[1.10,2.2046044,sec(1.10),sec(1.10)-2.2046044],_
[1.11,2.2489016,sec(1.11),sec(1.11)-2.2489016],_
[1.12,2.2952497,sec(1.12),sec(1.12)-2.2952497],_
[1.13,2.3437877,sec(1.13),sec(1.13)-2.3437877],_
[1.14,2.3946675,sec(1.14),sec(1.14)-2.3946675],_
[1.15,2.4480557,sec(1.15),sec(1.15)-2.4480557],_
[1.16,2.5041348,sec(1.16),sec(1.16)-2.5041348],_
[1.17,2.5631057,sec(1.17),sec(1.17)-2.5631057],_
[1.18,2.6251899,sec(1.18),sec(1.18)-2.6251899],_
[1.19,2.6906321,sec(1.19),sec(1.19)-2.6906321],_
[1.20,2.7597036,sec(1.20),sec(1.20)-2.7597036],_
[1.21,2.8327055,sec(1.21),sec(1.21)-2.8327055],_
[1.22,2.9099735,sec(1.22),sec(1.22)-2.9099735],_
[1.23,2.9918825,sec(1.23),sec(1.23)-2.9918825],_
[1.24,3.0788530,sec(1.24),sec(1.24)-3.0788530],_
[1.25,3.1713577,sec(1.25),sec(1.25)-3.1713577],_
[1.26,3.2699304,sec(1.26),sec(1.26)-3.2699304],_
[1.27,3.3751757,sec(1.27),sec(1.27)-3.3751757],_
[1.28,3.4877815,sec(1.28),sec(1.28)-3.4877815],_
[1.29,3.6085336,sec(1.29),sec(1.29)-3.6085336],_
[1.30,3.7383341,sec(1.30),sec(1.30)-3.7383341],_
[1.31,3.8782233,sec(1.31),sec(1.31)-3.8782233],_
[1.32,4.0294074,sec(1.32),sec(1.32)-4.0294074],_
[1.33,4.1932931,sec(1.33),sec(1.33)-4.1932931],_
[1.34,4.3715310,sec(1.34),sec(1.34)-4.3715310],_
[1.35,4.5660706,sec(1.35),sec(1.35)-4.5660706],_
[1.36,4.7792314,sec(1.36),sec(1.36)-4.7792314],_
[1.37,5.0137949,sec(1.37),sec(1.37)-5.0137949],_
[1.38,5.2731260,sec(1.38),sec(1.38)-5.2731260],_
[1.39,5.5613339,sec(1.39),sec(1.39)-5.5613339],_
[1.40,5.8834901,sec(1.40),sec(1.40)-5.8834901],_
[1.41,6.2459280,sec(1.41),sec(1.41)-6.2459280],_
[1.42,6.6566608,sec(1.42),sec(1.42)-6.6566608],_
[1.43,7.1259785,sec(1.43),sec(1.43)-7.1259785],_
[1.44,7.6673176,sec(1.44),sec(1.44)-7.6673176],_
[1.45,8.2985645,sec(1.45),sec(1.45)-8.2985645],_
[1.46,9.0440625,sec(1.46),sec(1.46)-9.0440625],_
[1.47,9.9378158,sec(1.47),sec(1.47)-9.9378158],_
[1.48,11.0288087,sec(1.48),sec(1.48)-11.0288087],_
[1.49,12.3902766,sec(1.49),sec(1.49)-12.3902766],_
[1.50,14.1368329,sec(1.50),sec(1.50)-14.1368329],_
[1.51,16.4584992,sec(1.51),sec(1.51)-16.4584992],_
[1.52,19.6949314,sec(1.52),sec(1.52)-19.6949314],_
[1.53,24.5188114,sec(1.53),sec(1.53)-24.5188114],_
[1.54,32.4765383,sec(1.54),sec(1.54)-32.4765383],_
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R    [0.55,1.1729868,1.1729867870 360221145,- 0.1296397788 55 E -7],
--R    [0.56,1.1802821,1.1802820508 263244778,- 0.4917367552 22 E -7],
--R    [0.57,1.1877881,1.1877881478 962049114,0.4789620491 14 E -7],
--R    [0.58,1.1955106,1.1955106424 672935752,0.4246729357 52 E -7],
--R    [0.59,1.2034553,1.2034553430 251038492,0.4302510384 92 E -7],
--R    [0.6,1.2116283,1.2116283145 123167046,0.1451231670 46 E -7],
--R    [0.61,1.2200359,1.2200358912 946465932,- 0.8705353406 83 E -8],
--R    [0.62,1.2286847,1.2286846909 558135602,- 0.9044186439 82 E -8],
--R    [0.63,1.2375816,1.2375816289 829659823,0.2898296598 23 E -7],
--R    [0.64,1.2467339,1.2467339344 091835044,0.3440918350 44 E -7],
--R    [0.65,1.2561492,1.2561491664 854909887,- 0.3351450901 13 E -7],
--R    [0.66,1.2658352,1.2658352324 611882698,0.3246118826 98 E -7],
--R    [0.67,1.2758004,1.2758004065 583108419,0.6558310841 9 E -8],
--R    [0.68,1.2860534,1.2860533502 337547427,- 0.4976624525 73 E -7],
--R    [0.69,1.2966031,1.2966031338 311052265,0.3383110522 65 E -7],
--R    [0.7,1.3074593,1.3074592597 335938699,- 0.4026640613 01 E -7],
--R    [0.71,1.3186317,1.3186316871 399746265,- 0.1286002537 35 E -7],
--R    [0.72,1.3301309,1.3301308585 965713491,- 0.4140342865 09 E -7],
--R    [0.73,1.3419677,1.3419677284 314378096,0.2843143780 96 E -7],
--R    [0.74,1.3541538,1.3541537932 506339213,- 0.6749366078 7 E -8],
--R    [0.75,1.3667011,1.3667011246 722261352,0.2467222613 52 E -7],
--R    [0.76,1.3796224,1.3796224044 909559952,0.4490955995 2 E -8],
--R    [0.77,1.392931,1.3929309624 858048639,- 0.3751419513 61 E -7],
--R    [0.78,1.4066408,1.4066408171 041612211,0.1710416122 11 E -7],
--R    [0.79,1.4207667,1.4207667192 802507471,0.1928025074 71 E -7],
--R    [0.8,1.4353242,1.4353241996 722398005,- 0.3277601995 E -9],
--R    [0.81,1.4503296,1.4503296196 323374816,0.1963233748 16 E -7],
--R    [0.82,1.4658002,1.4658002262 577216995,0.2625772169 95 E -7],
--R    [0.83,1.4817542,1.4817542119 076845659,0.1190768456 59 E -7],
--R    [0.84,1.4982108,1.4982107786 145889242,- 0.2138541107 58 E -7],
--R    [0.85,1.5151902,1.5151902078 636927634,0.7863692763 37 E -8],
--R    [0.86,1.5327139,1.5327139362 703728857,0.3627037288 57 E -7],
--R    [0.87,1.5508046,1.5508046377 436210518,0.3774362105 18 E -7],
--R    [0.88,1.5694863,1.5694863127 928890316,0.1279288903 16 E -7],
--R    [0.89,1.5887844,1.5887843857 125782891,- 0.1428742171 09 E -7],
--R    [0.9,1.6087258,1.6087258104 66049513,0.1046604951 3 E -7],
--R    [0.91,1.6293392,1.6293391861 905347268,- 0.1380946527 32 E -7],
--R    [0.92,1.6506549,1.6506548833 576031068,- 0.1664239689 32 E -7],
--R    [0.93,1.6727052,1.6727051817 530083925,- 0.1824699160 75 E -7],
--R    [0.94,1.6955244,1.6955244215 873528318,0.2158735283 18 E -7],
--R    [0.95,1.7191492,1.7191491692 180088055,- 0.3078199119 45 E -7],
--R    [0.96,1.7436184,1.7436183991 566481012,- 0.8433518988 E -9],
--R    [0.97,1.7689737,1.7689736942 596852048,- 0.5740314795 2 E -8],
--R    [0.98,1.7952595,1.7952594662 558616387,- 0.3374413836 13 E -7],
--R    [0.99,1.8225232,1.8225231990 619311821,- 0.9380688178 8 E -9],
--R    [1.0,1.8508157,1.8508157176 809256179,0.1768092561 79 E -7],
--R    [1.01,1.8801915,1.8801914858 76130416,- 0.1412386958 4 E -7],
--R    [1.02,1.9107089,1.9107089362 776886454,0.3627768864 54 E -7],
--R    [1.03,1.9424308,1.9424308371 197244332,0.3711972443 32 E -7],
--R    [1.04,1.9754247,1.9754247004 385756762,0.4385756762 E -9],
--R    [1.05,2.0097632,2.0097632373 047619814,0.3730476198 15 E -7],
--R    [1.06,2.0455249,2.0455248665 340933506,- 0.3346590664 94 E -7],
--R    [1.07,2.0827943,2.0827942843 529550117,- 0.1564704498 83 E -7],
--R    [1.08,2.1216631,2.1216631037 112423848,0.3711242384 8 E -8],
--R    [1.09,2.1622306,2.1622305733 829374458,- 0.2661706255 42 E -7],
--R    [1.1,2.2046044,2.2046043887 17359034,- 0.1128264096 6 E -7],
--R    [1.11,2.2489016,2.2489016079 636949635,0.7963694963 5 E -8],
--R    [1.12,2.2952497,2.2952496905 621863932,- 0.9437813606 7 E -8],
--R    [1.13,2.3437877,2.3437876767 70567607,- 0.2322943239 29 E -7],
--R    [1.14,2.3946675,2.3946675315 911689408,0.3159116894 08 E -7],
--R    [1.15,2.4480557,2.4480556803 301802962,- 0.1966981970 38 E -7],
--R    [1.16,2.5041348,2.5041347684 432143166,- 0.3155678568 34 E -7],
--R    [1.17,2.5631057,2.5631056848 391647153,- 0.1516083528 47 E -7],
--R    [1.18,2.6251899,2.6251898958 332672918,- 0.4166732708 2 E -8],
--R    [1.19,2.6906321,2.6906321468 544274307,0.4685442743 07 E -7],
--R    [1.2,2.7597036,2.7597036013 324064569,0.1332406457 E -8],
--R    [1.21,2.8327055,2.8327055015 843215452,0.1584321545 E -8],
--R    [1.22,2.9099735,2.9099734558 632119939,- 0.4413678800 61 E -7],
--R    [1.23,2.9918825,2.9918824801 830430638,- 0.1981695693 62 E -7],
--R    [1.24,3.078853,3.0788529546 387066657,- 0.4536129333 43 E -7],
--R    [1.25,3.1713577,3.1713576937 701033609,- 0.6229896639 1 E -8],
--R    [1.26,3.2699304,3.2699303818 839873852,- 0.1811601261 48 E -7],
--R    [1.27,3.3751757,3.3751756909 804379951,- 0.9019562004 9 E -8],
--R    [1.28,3.4877815,3.4877814863 175858326,- 0.1368241416 7 E -7],
--R    [1.29,3.6085336,3.6085336400 439333502,0.4004393335 02 E -7],
--R    [1.3,3.7383341,3.7383341270 754411719,0.2707544117 19 E -7],
--R    [1.31,3.8782233,3.8782232842 002831965,- 0.1579971680 35 E -7],
--R    [1.32,4.0294074,4.0294073944 135738582,- 0.5586426141 8 E -8],
--R    [1.33,4.1932931,4.1932931445 375416679,0.4453754166 79 E -7],
--R    [1.34,4.371531,4.3715310407 788541477,0.4077885414 77 E -7],
--R    [1.35,4.5660706,4.5660706221 959586487,0.2219595864 9 E -7],
--R    [1.36,4.7792314,4.7792313898 566530439,- 0.1014334695 6 E -7],
--R    [1.37,5.0137949,5.0137949303 632701112,0.3036327011 12 E -7],
--R    [1.38,5.273126,5.2731260096 064537537,0.9606453753 8 E -8],
--R    [1.39,5.5613339,5.5613338533 248644648,- 0.4667513553 52 E -7],
--R    [1.4,5.8834901,5.8834900848 27344827,- 0.1517265517 3 E -7],
--R    [1.41,6.245928,6.2459279846 284984955,- 0.1537150150 4 E -7],
--R    [1.42,6.6566608,6.6566608218 158868243,0.2181588682 4 E -7],
--R    [1.43,7.1259785,7.1259784562 869696006,- 0.4371303039 94 E -7],
--R    [1.44,7.6673176,7.6673176194 346817373,0.1943468173 7 E -7],
--R    [1.45,8.2985645,8.2985644666 089360285,- 0.3339106397 1 E -7],
--R    [1.46,9.0440625,9.0440625062 951398291,0.6295139829 E -8],
--R    [1.47,9.9378158,9.9378157688 028373544,- 0.3119716264 6 E -7],
--R    [1.48,11.0288087,11.0288086918 92599526,- 0.8107400473 9 E -8],
--R    [1.49,12.3902766,12.3902765961 36436494,- 0.3863563506 E -8],
--R    [1.5,14.1368329,14.1368329029 69903082,0.2969903082 E -8],
--R    [1.51,16.4584992,16.4584992338 68991507,0.3386899150 7 E -7],
--R    [1.52,19.6949314,19.6949314465 35659932,0.4653565993 2 E -7],
--R    [1.53,24.5188114,24.5188114348 30172969,0.3483017296 9 E -7],
--R    [1.54,32.4765383,32.4765382933 55461787,- 0.6644538213 E -8],
--R    [1.55,48.088881,48.0888810173 88679831,0.1738867983 E -7],
--R    [1.56,92.6258945,92.6258945325 36624847,0.3253662485 E -7],
--R    [1.57,1255.7659897,1255.7659896641 100942,- 0.358899058 E -7],
--R    [1.58,- 108.6538055,- 108.6538054739 3097269,0.2606902731 E -7],
--R    [1.59,- 52.0765718,- 52.0765717826 07291365,0.1739270863 E -7],
--R    [1.6,- 34.2471356,- 34.2471356100 18689204,- 0.100186892 E -7]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
[[0.01,100.0016667,csc(0.01),csc(0.01)-100.0016667],_
[0.02,50.0033335,csc(0.02),csc(0.02)-50.0033335],_
[0.03,33.3383339,csc(0.03),csc(0.03)-33.3383339],_
[0.04,25.0066679,csc(0.04),csc(0.04)-25.0066679],_
[0.05,20.0083358,csc(0.05),csc(0.05)-20.0083358],_
[0.06,16.6766709,csc(0.06),csc(0.06)-16.6766709],_
[0.07,14.2973876,csc(0.07),csc(0.07)-14.2973876],_
[0.08,12.5133432,csc(0.08),csc(0.08)-12.5133432],_
[0.09,11.1261253,csc(0.09),csc(0.09)-11.1261253],_
[0.10,10.0166861,csc(0.10),csc(0.10)-10.0166861],_
[0.11,9.1092683,csc(0.11),csc(0.11)-9.1092683],_
[0.12,8.3533670,csc(0.12),csc(0.12)-8.3533670],_
[0.13,7.7140172,csc(0.13),csc(0.13)-7.7140172],_
[0.14,7.1662439,csc(0.14),csc(0.14)-7.1662439],_
[0.15,6.6917324,csc(0.15),csc(0.15)-6.6917324],_
[0.16,6.2767465,csc(0.16),csc(0.16)-6.2767465],_
[0.17,5.9107821,csc(0.17),csc(0.17)-5.9107821],_
[0.18,5.5856693,csc(0.18),csc(0.18)-5.5856693],_
[0.19,5.2949584,csc(0.19),csc(0.19)-5.2949584],_
[0.20,5.0334895,csc(0.20),csc(0.20)-5.0334895],_
[0.21,4.7970857,csc(0.21),csc(0.21)-4.7970857],_
[0.22,4.5823293,csc(0.22),csc(0.22)-4.5823293],_
[0.23,4.3863973,csc(0.23),csc(0.23)-4.3863973],_
[0.24,4.2069371,csc(0.24),csc(0.24)-4.2069371],_
[0.25,4.0419725,csc(0.25),csc(0.25)-4.0419725],_
[0.26,3.8898314,csc(0.26),csc(0.26)-3.8898314],_
[0.27,3.7490894,csc(0.27),csc(0.27)-3.7490894],_
[0.28,3.6185256,csc(0.28),csc(0.28)-3.6185256],_
[0.29,3.4970877,csc(0.29),csc(0.29)-3.4970877],_
[0.30,3.3838634,csc(0.30),csc(0.30)-3.3838634],_
[0.31,3.2780583,csc(0.31),csc(0.31)-3.2780583],_
[0.32,3.1789774,csc(0.32),csc(0.32)-3.1789774],_
[0.33,3.0860099,csc(0.33),csc(0.33)-3.0860099],_
[0.34,2.9986168,csc(0.34),csc(0.34)-2.9986168],_
[0.35,2.9163208,csc(0.35),csc(0.35)-2.9163208],_
[0.36,2.8386975,csc(0.36),csc(0.36)-2.8386975],_
[0.37,2.7653687,csc(0.37),csc(0.37)-2.7653687],_
[0.38,2.6959957,csc(0.38),csc(0.38)-2.6959957],_
[0.39,2.6302748,csc(0.39),csc(0.39)-2.6302748],_
[0.40,2.5679325,csc(0.40),csc(0.40)-2.5679325],_
[0.41,2.5087220,csc(0.41),csc(0.41)-2.5087220],_
[0.42,2.4524203,csc(0.42),csc(0.42)-2.4524203],_
[0.43,2.3988248,csc(0.43),csc(0.43)-2.3988248],_
[0.44,2.3477515,csc(0.44),csc(0.44)-2.3477515],_
[0.45,2.2990327,csc(0.45),csc(0.45)-2.2990327],_
[0.46,2.2525155,csc(0.46),csc(0.46)-2.2525155],_
[0.47,2.2080598,csc(0.47),csc(0.47)-2.2080598],_
[0.48,2.1655372,csc(0.48),csc(0.48)-2.1655372],_
[0.49,2.1248300,csc(0.49),csc(0.49)-2.1248300],_
[0.50,2.0858296,csc(0.50),csc(0.50)-2.0858296],_
[0.51,2.0484363,csc(0.51),csc(0.51)-2.0484363],_
[0.52,2.0125578,csc(0.52),csc(0.52)-2.0125578],_
[0.53,1.9781089,csc(0.53),csc(0.53)-1.9781089],_
[0.54,1.9450107,csc(0.54),csc(0.54)-1.9450107],_
[0.55,1.9131900,csc(0.55),csc(0.55)-1.9131900],_
[0.56,1.8825790,csc(0.56),csc(0.56)-1.8825790],_
[0.57,1.8531145,csc(0.57),csc(0.57)-1.8531145],_
[0.58,1.8247378,csc(0.58),csc(0.58)-1.8247378],_
[0.59,1.7973941,csc(0.59),csc(0.59)-1.7973941],_
[0.60,1.7710322,csc(0.60),csc(0.60)-1.7710322],_
[0.61,1.7456045,csc(0.61),csc(0.61)-1.7456045],_
[0.62,1.7210662,csc(0.62),csc(0.62)-1.7210662],_
[0.63,1.6973757,csc(0.63),csc(0.63)-1.6973757],_
[0.64,1.6744937,csc(0.64),csc(0.64)-1.6744937],_
[0.65,1.6523834,csc(0.65),csc(0.65)-1.6523834],_
[0.66,1.6310105,csc(0.66),csc(0.66)-1.6310105],_
[0.67,1.6103423,csc(0.67),csc(0.67)-1.6103423],_
[0.68,1.5903484,csc(0.68),csc(0.68)-1.5903484],_
[0.69,1.5710001,csc(0.69),csc(0.69)-1.5710001],_
[0.70,1.5522703,csc(0.70),csc(0.70)-1.5522703],_
[0.71,1.5341335,csc(0.71),csc(0.71)-1.5341335],_
[0.72,1.5165654,csc(0.72),csc(0.72)-1.5165654],_
[0.73,1.4995435,csc(0.73),csc(0.73)-1.4995435],_
[0.74,1.4830460,csc(0.74),csc(0.74)-1.4830460],_
[0.75,1.4670527,csc(0.75),csc(0.75)-1.4670527],_
[0.76,1.4515443,csc(0.76),csc(0.76)-1.4515443],_
[0.77,1.4365025,csc(0.77),csc(0.77)-1.4365025],_
[0.78,1.4219099,csc(0.78),csc(0.78)-1.4219099],_
[0.79,1.4077503,csc(0.79),csc(0.79)-1.4077503],_
[0.80,1.3940078,csc(0.80),csc(0.80)-1.3940078],_
[0.81,1.3806678,csc(0.81),csc(0.81)-1.3806678],_
[0.82,1.3677162,csc(0.82),csc(0.82)-1.3677162],_
[0.83,1.3551396,csc(0.83),csc(0.83)-1.3551396],_
[0.84,1.3429252,csc(0.84),csc(0.84)-1.3429252],_
[0.85,1.3310609,csc(0.85),csc(0.85)-1.3310609],_
[0.86,1.3195353,csc(0.86),csc(0.86)-1.3195353],_
[0.87,1.3083372,csc(0.87),csc(0.87)-1.3083372],_
[0.88,1.2974563,csc(0.88),csc(0.88)-1.2974563],_
[0.89,1.2868825,csc(0.89),csc(0.89)-1.2868825],_
[0.90,1.2766062,csc(0.90),csc(0.90)-1.2766062],_
[0.91,1.2666184,csc(0.91),csc(0.91)-1.2666184],_
[0.92,1.2569105,csc(0.92),csc(0.92)-1.2569105],_
[0.93,1.2474740,csc(0.93),csc(0.93)-1.2474740],_
[0.94,1.2383010,csc(0.94),csc(0.94)-1.2383010],_
[0.95,1.2293840,csc(0.95),csc(0.95)-1.2293840],_
[0.96,1.2207157,csc(0.96),csc(0.96)-1.2207157],_
[0.97,1.2122891,csc(0.97),csc(0.97)-1.2122891],_
[0.98,1.2040977,csc(0.98),csc(0.98)-1.2040977],_
[0.99,1.1961351,csc(0.99),csc(0.99)-1.1961351],_
[1.00,1.1883951,csc(1.00),csc(1.00)-1.1883951],_
[1.01,1.1808720,csc(1.01),csc(1.01)-1.1808720],_
[1.02,1.1735601,csc(1.02),csc(1.02)-1.1735601],_
[1.03,1.1664542,csc(1.03),csc(1.03)-1.1664542],_
[1.04,1.1595490,csc(1.04),csc(1.04)-1.1595490],_
[1.05,1.1528398,csc(1.05),csc(1.05)-1.1528398],_
[1.06,1.1463217,csc(1.06),csc(1.06)-1.1463217],_
[1.07,1.1399902,csc(1.07),csc(1.07)-1.1399902],_
[1.08,1.1338411,csc(1.08),csc(1.08)-1.1338411],_
[1.09,1.1278701,csc(1.09),csc(1.09)-1.1278701],_
[1.10,1.1220733,csc(1.10),csc(1.10)-1.1220733],_
[1.11,1.1164469,csc(1.11),csc(1.11)-1.1164469],_
[1.12,1.1109871,csc(1.12),csc(1.12)-1.1109871],_
[1.13,1.1056905,csc(1.13),csc(1.13)-1.1056905],_
[1.14,1.1005537,csc(1.14),csc(1.14)-1.1005537],_
[1.15,1.0955735,csc(1.15),csc(1.15)-1.0955735],_
[1.16,1.0907467,csc(1.16),csc(1.16)-1.0907467],_
[1.17,1.0860704,csc(1.17),csc(1.17)-1.0860704],_
[1.18,1.0815417,csc(1.18),csc(1.18)-1.0815417],_
[1.19,1.0771579,csc(1.19),csc(1.19)-1.0771579],_
[1.20,1.0729164,csc(1.20),csc(1.20)-1.0729164],_
[1.21,1.0688146,csc(1.21),csc(1.21)-1.0688146],_
[1.22,1.0648501,csc(1.22),csc(1.22)-1.0648501],_
[1.23,1.0610206,csc(1.23),csc(1.23)-1.0610206],_
[1.24,1.0573239,csc(1.24),csc(1.24)-1.0573239],_
[1.25,1.0537579,csc(1.25),csc(1.25)-1.0537579],_
[1.26,1.0503205,csc(1.26),csc(1.26)-1.0503205],_
[1.27,1.0470098,csc(1.27),csc(1.27)-1.0470098],_
[1.28,1.0438241,csc(1.28),csc(1.28)-1.0438241],_
[1.29,1.0407614,csc(1.29),csc(1.29)-1.0407614],_
[1.30,1.0378200,csc(1.30),csc(1.30)-1.0378200],_
[1.31,1.0349985,csc(1.31),csc(1.31)-1.0349985],_
[1.32,1.0322953,csc(1.32),csc(1.32)-1.0322953],_
[1.33,1.0297088,csc(1.33),csc(1.33)-1.0297088],_
[1.34,1.0272377,csc(1.34),csc(1.34)-1.0272377],_
[1.35,1.0248807,csc(1.35),csc(1.35)-1.0248807],_
[1.36,1.0226365,csc(1.36),csc(1.36)-1.0226365],_
[1.37,1.0205039,csc(1.37),csc(1.37)-1.0205039],_
[1.38,1.0184818,csc(1.38),csc(1.38)-1.0184818],_
[1.39,1.0165693,csc(1.39),csc(1.39)-1.0165693],_
[1.40,1.0147651,csc(1.40),csc(1.40)-1.0147651],_
[1.41,1.0130685,csc(1.41),csc(1.41)-1.0130685],_
[1.42,1.0114785,csc(1.42),csc(1.42)-1.0114785],_
[1.43,1.0099943,csc(1.43),csc(1.43)-1.0099943],_
[1.44,1.0086152,csc(1.44),csc(1.44)-1.0086152],_
[1.45,1.0073405,csc(1.45),csc(1.45)-1.0073405],_
[1.46,1.0061695,csc(1.46),csc(1.46)-1.0061695],_
[1.47,1.0051015,csc(1.47),csc(1.47)-1.0051015],_
[1.48,1.0041362,csc(1.48),csc(1.48)-1.0041362],_
[1.49,1.0032729,csc(1.49),csc(1.49)-1.0032729],_
[1.50,1.0025113,csc(1.50),csc(1.50)-1.0025113],_
[1.51,1.0018509,csc(1.51),csc(1.51)-1.0018509],_
[1.52,1.0012915,csc(1.52),csc(1.52)-1.0012915],_
[1.53,1.0008327,csc(1.53),csc(1.53)-1.0008327],_
[1.54,1.0004744,csc(1.54),csc(1.54)-1.0004744],_
[1.55,1.0002163,csc(1.55),csc(1.55)-1.0002163],_
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[1.57,1.0000003,csc(1.57),csc(1.57)-1.0000003],_
[1.58,1.0000424,csc(1.58),csc(1.58)-1.0000424],_
[1.59,1.0001844,csc(1.59),csc(1.59)-1.0001844],_
[1.60,1.0004266,csc(1.60),csc(1.60)-1.0004266]]
 

   (2)
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    [1.13,1.1056905,1.1056905377 257534608,0.3772575346 08 E -7],
    [1.14,1.1005537,1.1005537483 206146725,0.4832061467 25 E -7],
    [1.15,1.0955735,1.0955735167 567859913,0.1675678599 13 E -7],
    [1.16,1.0907467,1.0907467376 934304007,0.3769343040 07 E -7],
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    [1.18,1.0815417,1.0815417448 948071115,0.4489480711 15 E -7],
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    [1.23,1.0610206,1.0610205637 991976338,- 0.3620080236 62 E -7],
    [1.24,1.0573239,1.0573238716 04949513,- 0.2839505048 7 E -7],
    [1.25,1.0537579,1.0537578582 454329877,- 0.4175456701 23 E -7],
    [1.26,1.0503205,1.0503204961 930909767,- 0.3806909023 3 E -8],
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    [1.28,1.0438241,1.0438240549 567728718,- 0.4504322712 82 E -7],
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    [1.3,1.03782,1.0378200456 748014427,0.4567480144 27 E -7],
    [1.31,1.0349985,1.0349985252 107504451,0.2521075044 51 E -7],
    [1.32,1.0322953,1.0322952536 591153897,- 0.4634088461 03 E -7],
    [1.33,1.0297088,1.0297087682 324287489,- 0.3176757125 11 E -7],
    [1.34,1.0272377,1.0272376778 151033218,- 0.2218489667 82 E -7],
    [1.35,1.0248807,1.0248806610 794017372,- 0.3892059826 28 E -7],
    [1.36,1.0226365,1.0226364647 10509886,- 0.3528949011 4 E -7],
    [1.37,1.0205039,1.0205039017 361575009,0.1736157500 9 E -8],
    [1.38,1.0184818,1.0184818499 565392157,0.4995653921 57 E -7],
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    [1.44,1.0086152,1.0086152401 902637594,0.4019026375 94 E -7],
    [1.45,1.0073405,1.0073404992 46207189,- 0.753792811 E -9],
    [1.46,1.0061695,1.0061694655 087995079,- 0.3449120049 21 E -7],
    [1.47,1.0051015,1.0051015438 747215132,0.4387472151 32 E -7],
    [1.48,1.0041362,1.0041361930 846981533,- 0.6915301846 7 E -8],
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    [1.5,1.0025113,1.0025113042 4672491,0.424672491 E -8],
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    [1.54,1.0004744,1.0004743943 377968613,- 0.5662203138 7 E -8],
    [1.55,1.0002163,1.0002162825 786817653,- 0.1742131823 47 E -7],
    [1.56,1.0000583,1.0000582831 667632601,- 0.1683323673 99 E -7],
    [1.57,1.0000003,1.0000003170 68265912,0.1706826591 2 E -7],
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    [1.59,1.0001844,1.0001844188 697576625,0.1886975766 25 E -7],
    [1.6,1.0004266,1.0004265788 504192126,- 0.2114958078 74 E -7]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,100.0016667,100.0016666861 1131614,- 0.1388868386 E -7],
--R    [0.02,50.0033335,50.0033334888 95450004,- 0.1110455 E -7],
--R    [0.03,33.3383339,33.3383338583 83159355,- 0.4161684064 5 E -7],
--R    [0.04,25.0066679,25.0066679113 21092611,0.1132109261 E -7],
--R    [0.05,20.0083358,20.0083357645 29760655,- 0.3547023934 5 E -7],
--R    [0.06,16.6766709,16.6766708682 61540425,- 0.3173845957 5 E -7],
--R    [0.07,14.2973876,14.2973876252 73006648,0.2527300664 8 E -7],
--R    [0.08,12.5133432,12.5133432956 11602375,0.9561160237 45 E -7],
--R    [0.09,11.1261253,11.1261252982 27770129,- 0.1772229871 E -8],
--R    [0.1,10.0166861,10.0166861316 34776649,0.3163477664 9 E -7],
--R    [0.11,9.1092683,9.1092683378 58666259,0.3785866625 9 E -7],
--R    [0.12,8.353367,8.3533669844 258284979,- 0.1557417150 2 E -7],
--R    [0.13,7.7140172,7.7140171546 756812171,- 0.4532431878 29 E -7],
--R    [0.14,7.1662439,7.1662439422 359760119,0.4223597601 19 E -7],
--R    [0.15,6.6917324,6.6917324477 182351442,0.4771823514 42 E -7],
--R    [0.16,6.2767465,6.2767465266 620801848,0.2666208018 5 E -7],
--R    [0.17,5.9107821,5.9107820970 378013996,- 0.29621986 E -8],
--R    [0.18,5.5856693,5.5856693442 568113649,0.4425681136 49 E -7],
--R    [0.19,5.2949584,5.2949584403 976760687,0.4039767606 87 E -7],
--R    [0.2,5.0334895,5.0334895476 723442024,0.4767234420 24 E -7],
--R    [0.21,4.7970857,4.7970856780 525825143,- 0.2194741748 6 E -7],
--R    [0.22,4.5823293,4.5823293184 602630424,0.1846026304 2 E -7],
--R    [0.23,4.3863973,4.3863973276 543190295,0.2765431903 E -7],
--R    [0.24,4.2069371,4.2069371089 029182611,0.8902918261 1 E -8],
--R    [0.25,4.0419725,4.0419725012 210710728,0.1221071073 E -8],
--R    [0.26,3.8898314,3.8898313880 215197583,- 0.1197848024 2 E -7],
--R    [0.27,3.7490894,3.7490893927 385091643,- 0.7261490835 7 E -8],
--R    [0.28,3.6185256,3.6185256396 812993389,0.3968129933 89 E -7],
--R    [0.29,3.4970877,3.4970876678 206681256,- 0.3217933187 44 E -7],
--R    [0.3,3.3838634,3.3838633618 241225849,- 0.3817587741 51 E -7],
--R    [0.31,3.2780583,3.2780583157 998724616,0.1579987246 16 E -7],
--R    [0.32,3.1789774,3.1789774413 44609289,0.4134460928 89 E -7],
--R    [0.33,3.0860099,3.0860099195 883096277,0.1958830962 77 E -7],
--R    [0.34,2.9986168,2.9986168087 661743229,0.8766174322 8 E -8],
--R    [0.35,2.9163208,2.9163207762 123651255,- 0.2378763487 45 E -7],
--R    [0.36,2.8386975,2.8386975416 936122006,0.4169361220 06 E -7],
--R    [0.37,2.7653687,2.7653687083 157807533,0.8315780753 3 E -8],
--R    [0.38,2.6959957,2.6959957253 979436817,0.2539794368 17 E -7],
--R    [0.39,2.6302748,2.6302747801 40398548,- 0.1985960145 2 E -7],
--R    [0.4,2.5679325,2.5679324555 477830703,- 0.4445221692 97 E -7],
--R    [0.41,2.508722,2.5087220237 8334365,0.2378334365 E -7],
--R    [0.42,2.4524203,2.4524202690 492617941,- 0.3095073820 59 E -7],
--R    [0.43,2.3988248,2.3988247537 912204017,- 0.4620877959 83 E -7],
--R    [0.44,2.3477515,2.3477514576 984533152,- 0.4230154668 48 E -7],
--R    [0.45,2.2990327,2.2990327315 089707901,0.3150897079 01 E -7],
--R    [0.46,2.2525155,2.2525155177 149280284,0.1771492802 84 E -7],
--R    [0.47,2.2080598,2.2080597984 171557468,- 0.1582844253 E -8],
--R    [0.48,2.1655372,2.1655372372 03038964,0.3720303896 4 E -7],
--R    [0.49,2.12483,2.1248299873 30230062,- 0.1266976993 8 E -7],
--R    [0.5,2.0858296,2.0858296429 334881858,0.4293348818 58 E -7],
--R    [0.51,2.0484363,2.0484363136 241303362,0.1362413033 6 E -7],
--R    [0.52,2.0125578,2.0125578058 716625444,0.5871662544 4 E -8],
--R    [0.53,1.9781089,1.9781088970 643983743,- 0.2935601625 7 E -8],
--R    [0.54,1.9450107,1.9450106902 35237839,- 0.9764762161 01 E -8],
--R    [0.55,1.91319,1.9131900391 862495448,0.3918624954 48 E -7],
--R    [0.56,1.882579,1.8825790352 123253874,0.3521232538 73 E -7],
--R    [0.57,1.8531145,1.8531145478 592311512,0.4785923115 12 E -7],
--R    [0.58,1.8247378,1.8247378131 947842124,0.1319478421 24 E -7],
--R    [0.59,1.7973941,1.7973940639 561336125,- 0.3604386638 75 E -7],
--R    [0.6,1.7710322,1.7710321966 877253734,- 0.3312274626 6 E -8],
--R    [0.61,1.7456045,1.7456044716 252507363,- 0.2837474926 37 E -7],
--R    [0.62,1.7210662,1.7210662416 285829803,0.4162858298 03 E -7],
--R    [0.63,1.6973757,1.6973757069 361725968,0.6936172596 8 E -8],
--R    [0.64,1.6744937,1.6744936929 168164811,- 0.7083183518 9 E -8],
--R    [0.65,1.6523834,1.6523834483 423011016,0.4834230110 16 E -7],
--R    [0.66,1.6310105,1.6310104620 046062096,- 0.3799539379 04 E -7],
--R    [0.67,1.6103423,1.6103422957 612188444,- 0.4238781155 6 E -8],
--R    [0.68,1.5903484,1.5903484323 175770922,0.3231757709 22 E -7],
--R    [0.69,1.5710001,1.5710001362 517238398,0.3625172383 98 E -7],
--R    [0.7,1.5522703,1.5522703269 57103912,0.2695710391 2 E -7],
--R    [0.71,1.5341335,1.5341334623 286338699,- 0.3767136613 01 E -7],
--R    [0.72,1.5165654,1.5165654321 477203357,0.3214772033 57 E -7],
--R    [0.73,1.4995435,1.4995434602 363547077,- 0.3976364529 23 E -7],
--R    [0.74,1.483046,1.4830460145 509444868,0.1455094448 68 E -7],
--R    [0.75,1.4670527,1.4670527244 75010117,0.2447501011 7 E -7],
--R    [0.76,1.4515443,1.4515443046 478685727,0.4647868572 7 E -8],
--R    [0.77,1.4365025,1.4365024847 353014963,- 0.1526469850 37 E -7],
--R    [0.78,1.4219099,1.4219099446 09135172,0.4460913517 2 E -7],
--R    [0.79,1.4077503,1.4077502544 566480148,- 0.4554335198 52 E -7],
--R    [0.8,1.3940078,1.3940078193 886361745,0.1938863617 45 E -7],
--R    [0.81,1.3806678,1.3806678281 575591498,0.2815755914 98 E -7],
--R    [0.82,1.3677162,1.3677162056 35104192,0.5635104192 E -8],
--R    [0.83,1.3551396,1.3551395687 323139549,- 0.3126768604 51 E -7],
--R    [0.84,1.3429252,1.3429251854 756057525,- 0.1452439424 75 E -7],
--R    [0.85,1.3310609,1.3310609369 789990246,0.3697899902 46 E -7],
--R    [0.86,1.3195353,1.3195352820 770317831,- 0.1792296821 69 E -7],
--R    [0.87,1.3083372,1.3083372244 045115315,0.2440451153 15 E -7],
--R    [0.88,1.2974563,1.2974562817 286954688,- 0.1827130453 12 E -7],
--R    [0.89,1.2868825,1.2868824573 569776297,- 0.4264302237 03 E -7],
--R    [0.9,1.2766062,1.2766062134 58895496,0.1345889549 6 E -7],
--R    [0.91,1.2666184,1.2666184461 554476329,0.4615544763 29 E -7],
--R    [0.92,1.2569105,1.2569104622 415061901,- 0.3775849380 99 E -7],
--R    [0.93,1.247474,1.2474739574 186627875,- 0.4258133721 25 E -7],
--R    [0.94,1.238301,1.2383009959 262950556,- 0.4073704944 4 E -8],
--R    [0.95,1.229384,1.2293839914 681003518,- 0.8531899648 15 E -8],
--R    [0.96,1.2207157,1.2207156893 399160175,- 0.1066008398 25 E -7],
--R    [0.97,1.2122891,1.2122891496 724233695,0.4967242336 95 E -7],
--R    [0.98,1.2040977,1.2040977317 093965936,0.3170939659 36 E -7],
--R    [0.99,1.1961351,1.1961350790 485799284,- 0.2095142007 16 E -7],
--R    [1.0,1.1883951,1.1883951057 781212163,0.5778121216 3 E -8],
--R    [1.01,1.180872,1.1808719834 468142375,- 0.1655318576 25 E -7],
--R    [1.02,1.1735601,1.1735601288 11257282,0.2881125728 2 E -7],
--R    [1.03,1.1664542,1.1664541923 074667313,- 0.7692533268 72 E -8],
--R    [1.04,1.159549,1.1595490471 9853279,0.4719853279 E -7],
--R    [1.05,1.1528398,1.1528397793 536064181,- 0.2064639358 19 E -7],
--R    [1.06,1.1463217,1.1463216776 16894679,- 0.2238310532 1 E -7],
--R    [1.07,1.1399902,1.1399902247 284454927,0.2472844549 27 E -7],
--R    [1.08,1.1338411,1.1338410887 613485139,- 0.1123865148 61 E -7],
--R    [1.09,1.1278701,1.1278701150 42590264,0.1504259026 4 E -7],
--R    [1.1,1.1220733,1.1220733185 272000494,0.1852720004 94 E -7],
--R    [1.11,1.1164469,1.1164468765 975278264,- 0.2340247217 36 E -7],
--R    [1.12,1.1109871,1.1109871222 615233658,0.2226152336 58 E -7],
--R    [1.13,1.1056905,1.1056905377 257534608,0.3772575346 08 E -7],
--R    [1.14,1.1005537,1.1005537483 206146725,0.4832061467 25 E -7],
--R    [1.15,1.0955735,1.0955735167 567859913,0.1675678599 13 E -7],
--R    [1.16,1.0907467,1.0907467376 934304007,0.3769343040 07 E -7],
--R    [1.17,1.0860704,1.0860704326 000071521,0.3260000715 21 E -7],
--R    [1.18,1.0815417,1.0815417448 948071115,0.4489480711 15 E -7],
--R    [1.19,1.0771579,1.0771579353 444804665,0.3534448046 65 E -7],
--R    [1.2,1.0729164,1.0729163777 098972287,- 0.2229010277 13 E -7],
--R    [1.21,1.0688146,1.0688145546 246734829,- 0.4537532651 71 E -7],
--R    [1.22,1.0648501,1.0648500536 936167054,- 0.4630638329 46 E -7],
--R    [1.23,1.0610206,1.0610205637 991976338,- 0.3620080236 62 E -7],
--R    [1.24,1.0573239,1.0573238716 04949513,- 0.2839505048 7 E -7],
--R    [1.25,1.0537579,1.0537578582 454329877,- 0.4175456701 23 E -7],
--R    [1.26,1.0503205,1.0503204961 930909767,- 0.3806909023 3 E -8],
--R    [1.27,1.0470098,1.0470098462 929566457,0.4629295664 57 E -7],
--R    [1.28,1.0438241,1.0438240549 567728718,- 0.4504322712 82 E -7],
--R    [1.29,1.0407614,1.0407613515 086368049,- 0.4849136319 51 E -7],
--R    [1.3,1.03782,1.0378200456 748014427,0.4567480144 27 E -7],
--R    [1.31,1.0349985,1.0349985252 107504451,0.2521075044 51 E -7],
--R    [1.32,1.0322953,1.0322952536 591153897,- 0.4634088461 03 E -7],
--R    [1.33,1.0297088,1.0297087682 324287489,- 0.3176757125 11 E -7],
--R    [1.34,1.0272377,1.0272376778 151033218,- 0.2218489667 82 E -7],
--R    [1.35,1.0248807,1.0248806610 794017372,- 0.3892059826 28 E -7],
--R    [1.36,1.0226365,1.0226364647 10509886,- 0.3528949011 4 E -7],
--R    [1.37,1.0205039,1.0205039017 361575009,0.1736157500 9 E -8],
--R    [1.38,1.0184818,1.0184818499 565392157,0.4995653921 57 E -7],
--R    [1.39,1.0165693,1.0165692504 705818114,- 0.4952941818 86 E -7],
--R    [1.4,1.0147651,1.0147651062 948794009,0.6294879400 9 E -8],
--R    [1.41,1.0130685,1.0130684810 718793105,- 0.1892812068 95 E -7],
--R    [1.42,1.0114785,1.0114784978 641485933,- 0.2135851406 7 E -8],
--R    [1.43,1.0099943,1.0099943380 317855887,0.3803178558 87 E -7],
--R    [1.44,1.0086152,1.0086152401 902637594,0.4019026375 94 E -7],
--R    [1.45,1.0073405,1.0073404992 46207189,- 0.753792811 E -9],
--R    [1.46,1.0061695,1.0061694655 087995079,- 0.3449120049 21 E -7],
--R    [1.47,1.0051015,1.0051015438 747215132,0.4387472151 32 E -7],
--R    [1.48,1.0041362,1.0041361930 846981533,- 0.6915301846 7 E -8],
--R    [1.49,1.0032729,1.0032729250 49913637,0.2504991363 7 E -7],
--R    [1.5,1.0025113,1.0025113042 4672491,0.424672491 E -8],
--R    [1.51,1.0018509,1.0018509471 78269319,0.4717826931 9 E -7],
--R    [1.52,1.0012915,1.0012915219 017225962,0.2190172259 62 E -7],
--R    [1.53,1.0008327,1.0008327476 201189712,0.4762011897 12 E -7],
--R    [1.54,1.0004744,1.0004743943 377968613,- 0.5662203138 7 E -8],
--R    [1.55,1.0002163,1.0002162825 786817653,- 0.1742131823 47 E -7],
--R    [1.56,1.0000583,1.0000582831 667632601,- 0.1683323673 99 E -7],
--R    [1.57,1.0000003,1.0000003170 68265912,0.1706826591 2 E -7],
--R    [1.58,1.0000424,1.0000423552 951549942,- 0.4470484500 58 E -7],
--R    [1.59,1.0001844,1.0001844188 697576625,0.1886975766 25 E -7],
--R    [1.6,1.0004266,1.0004265788 504192126,- 0.2114958078 74 E -7]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to mathml.output (2009/2/17, 17:55:1).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 21
(x+y)**2
 

         2           2
   (1)  y  + 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2           2
--R   (1)  y  + 2x y + x
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 21
coerce(%)$MMLFORM
 

   (2)
  "<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mro
  w><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0
  .3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><m
  n>2</mn></mrow></msup></mrow></mrow>"
                                                                 Type: String
--R 
--R
--R   (2)
--R  "<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mro
--R  w><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0
--R  .3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><m
--R  n>2</mn></mrow></msup></mrow></mrow>"
--R                                                                 Type: String
--E 2

--S 3 of 21
(x+y)**2
 

         2           2
   (3)  y  + 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2           2
--R   (3)  y  + 2x y + x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 21
display(coerce(%)$MMLFORM)$MMLFORM
 
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
</math>
                                                                   Type: Void
--R 
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
--R</math>
--R                                                                   Type: Void
--E 4

)set output mathml on
 

--S 5 of 21
(x+y)**2
 

         2           2
   (5)  y  + 2x y + x
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
</math>

                                                     Type: Polynomial Integer
--R 
--R
--R         2           2
--R   (5)  y  + 2x y + x
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
--R</math>
--R
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 21
integrate(x**x,x)
 

           x
         ++    %I
   (6)   |   %I  d%I
        ++
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
</math>

                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    %I
--R   (6)   |   %I  d%I
--R        ++
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
--R</math>
--R
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 21
integral(x**x,x)
 

           x
         ++    %I
   (7)   |   %I  d%I
        ++
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
</math>

                                                     Type: Expression Integer
--R 
--R
--R           x
--R         ++    %I
--R   (7)   |   %I  d%I
--R        ++
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 21
(5+sqrt 63 + sqrt 847)**(1/3)
 

         +----------+
        3|   +-+
   (8)  \|14\|7  + 5
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mroot><mrow><mrow><mrow><mrow><mrow><mn>14</mn></mrow><mspace width='0.3em'/><msqrt><mrow><mn>7</mn></mrow></msqrt></mrow><mo>+</mo><mn>5</mn></mrow></mrow></mrow><mn>3</mn></mroot></mrow>
</math>

                                                        Type: AlgebraicNumber
--R 
--R
--R         +----------+
--R        3|   +-+
--R   (8)  \|14\|7  + 5
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mroot><mrow><mrow><mrow><mrow><mrow><mn>14</mn></mrow><mspace width='0.3em'/><msqrt><mrow><mn>7</mn></mrow></msqrt></mrow><mo>+</mo><mn>5</mn></mrow></mrow></mrow><mn>3</mn></mroot></mrow>
--R</math>
--R
--R                                                        Type: AlgebraicNumber
--E 8

--S 9 of 21
set [1,2,3]
 

   (9)  {1,2,3}
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow>
</math>

                                                    Type: Set PositiveInteger
--R 
--R
--R   (9)  {1,2,3}
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow>
--R</math>
--R
--R                                                    Type: Set PositiveInteger
--E 9

--S 10 of 21
multiset [x rem 5 for x in primes(2,1000)]
 

   (10)  {0,40: 1,47: 2,42: 3,38: 4}
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>{</mo><mn>0</mn><mo>,</mo><mrow><mrow><mn>40</mn></mrow><mtext>: </mtext><mn>1</mn></mrow><mo>,</mo><mrow><mrow><mn>47</mn></mrow><mtext>: </mtext><mn>2</mn></mrow><mo>,</mo><mrow><mrow><mn>42</mn></mrow><mtext>: </mtext><mn>3</mn></mrow><mo>,</mo><mrow><mrow><mn>38</mn></mrow><mtext>: </mtext><mn>4</mn></mrow><mo>}</mo></mrow>
</math>

                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {0,40: 1,47: 2,42: 3,38: 4}
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>{</mo><mn>0</mn><mo>,</mo><mrow><mrow><mn>40</mn></mrow><mtext>: </mtext><mn>1</mn></mrow><mo>,</mo><mrow><mrow><mn>47</mn></mrow><mtext>: </mtext><mn>2</mn></mrow><mo>,</mo><mrow><mrow><mn>42</mn></mrow><mtext>: </mtext><mn>3</mn></mrow><mo>,</mo><mrow><mrow><mn>38</mn></mrow><mtext>: </mtext><mn>4</mn></mrow><mo>}</mo></mrow>
--R</math>
--R
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 21
series(sin(a*x),x=0)
 

                3        5        7          9            11
               a   3    a   5    a    7     a     9      a      11      12
   (11)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
                6      120      5040      362880      39916800
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><mi>a</mi><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>39916800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>12</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                3        5        7          9            11
--R               a   3    a   5    a    7     a     9      a      11      12
--R   (11)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R                6      120      5040      362880      39916800
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><mi>a</mi><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>39916800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>12</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11

--S 12 of 21
matrix [[xi+yj for i in 1..10] for j in 1..10]
 

   (12)
   [
     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ]
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>[</mo><mtable><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr></mtable><mo>]</mo></mrow>
</math>

                                              Type: Matrix Polynomial Integer
--R 
--R
--R   (12)
--R   [
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ]
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>[</mo><mtable><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr></mtable><mo>]</mo></mrow>
--R</math>
--R
--R                                              Type: Matrix Polynomial Integer
--E 12

--S 13 of 21
y:=operator 'y
 

   (13)  y
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mi>y</mi>
</math>

                                                          Type: BasicOperator
--R 
--R
--R   (13)  y
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mi>y</mi>
--R</math>
--R
--R                                                          Type: BasicOperator
--E 13

--S 14 of 21
D(y(x,z),[x,x,z,x])
 

   (14)  y        (x,z)
          ,1,1,2,1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<msub><mi>y</mi><mrow><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>(</mo><mi><mi>x</mi></mi><mo>,</mo><mi><mi>z</mi></mi><mo>)</mo>
</math>

                                                     Type: Expression Integer
--R 
--R
--R   (14)  y        (x,z)
--R          ,1,1,2,1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<msub><mi>y</mi><mrow><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>(</mo><mi><mi>x</mi></mi><mo>,</mo><mi><mi>z</mi></mi><mo>)</mo>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 14

)clear all
 
   All user variables and function definitions have been cleared.

--S 15 of 21
y:=operator 'y
 

   (1)  y
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mi>y</mi>
</math>

                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mi>y</mi>
--R</math>
--R
--R                                                          Type: BasicOperator
--E 15

--S 16 of 21
D(y x,x,2)
 

         ,,
   (2)  y  (x)

<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<msup><mi>y</mi><mrow><mo>&#x02032;</mo><mo>&#x02032;</mo></mrow></msup><mo>&#x02061;</mo><mo>(</mo><mi>x</mi><mo>)</mo>
</math>

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (2)  y  (x)
--R
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<msup><mi>y</mi><mrow><mo>&#x02032;</mo><mo>&#x02032;</mo></mrow></msup><mo>&#x02061;</mo><mo>(</mo><mi>x</mi><mo>)</mo>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 16

--S 17 of 21
x:=series 'x
 

   (3)  x
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mi>x</mi>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)  x
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mi>x</mi>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 17

--S 18 of 21
sin(1+x)
 

   (4)
                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
                           2           6          24          120
   + 
       sin(1)  6   cos(1)  7   sin(1)  8   cos(1)  9    sin(1)  10      11
     - ------ x  - ------ x  + ------ x  + ------ x  - ------- x   + O(x  )
         720        5040        40320      362880      3628800
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>40320</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (4)
--R                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
--R     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
--R                           2           6          24          120
--R   + 
--R       sin(1)  6   cos(1)  7   sin(1)  8   cos(1)  9    sin(1)  10      11
--R     - ------ x  - ------ x  + ------ x  + ------ x  - ------- x   + O(x  )
--R         720        5040        40320      362880      3628800
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>40320</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 18

)clear all
 
   All user variables and function definitions have been cleared.

--S 19 of 21
series(1/log(y),y=1)
 

   (1)
            - 1   1    1            1        2    19        3    3         4
     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
                  2   12           24            720            160
   + 
        863         5    275         6    33953         7     8183         8
     - ----- (y - 1)  + ----- (y - 1)  - ------- (y - 1)  + ------- (y - 1)
       60480            24192            3628800            1036800
   + 
        3250433         9            10
     - --------- (y - 1)  + O((y - 1)  )
       479001600
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup></mrow><mo>+</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>12</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>19</mn></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mrow><mn>160</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>863</mn></mrow></mrow><mrow><mrow><mn>60480</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>275</mn></mrow></mrow><mrow><mrow><mn>24192</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>33953</mn></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>8183</mn></mrow></mrow><mrow><mrow><mn>1036800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>3250433</mn></mrow></mrow><mrow><mrow><mn>479001600</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--R 
--R
--R   (1)
--R            - 1   1    1            1        2    19        3    3         4
--R     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
--R                  2   12           24            720            160
--R   + 
--R        863         5    275         6    33953         7     8183         8
--R     - ----- (y - 1)  + ----- (y - 1)  - ------- (y - 1)  + ------- (y - 1)
--R       60480            24192            3628800            1036800
--R   + 
--R        3250433         9            10
--R     - --------- (y - 1)  + O((y - 1)  )
--R       479001600
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup></mrow><mo>+</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>12</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>19</mn></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mrow><mn>160</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>863</mn></mrow></mrow><mrow><mrow><mn>60480</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>275</mn></mrow></mrow><mrow><mrow><mn>24192</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>33953</mn></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>8183</mn></mrow></mrow><mrow><mrow><mn>1036800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>3250433</mn></mrow></mrow><mrow><mrow><mn>479001600</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--E 19

)clear all
 
   All user variables and function definitions have been cleared.

--S 20 of 21
y:UTS(FLOAT,'z,0):=exp(z)
 

   (1)
                    2                            3
     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
   + 
                                4                               5
     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
   + 
                                 6                               7
     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 z  + 0.0000027557 3192239858 90653 z
   + 
                                   10      11
     0.2755731922 3985890653 E -6 z   + O(z  )
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mn>1.0</mn><mo>+</mo><mi>z</mi><mo>+</mo><mrow><mn>0.5</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.1666666666 6666666667</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0416666666 6666666666 7</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0083333333 3333333333 34</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0013888888 8888888888 89</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0001984126 9841269841 27</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000248015 8730158730 1587</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000027557 3192239858 90653</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.2755731922 3985890653 E -6</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--R 
--R
--R   (1)
--R                    2                            3
--R     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 z  + 0.0000027557 3192239858 90653 z
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 z   + O(z  )
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mn>1.0</mn><mo>+</mo><mi>z</mi><mo>+</mo><mrow><mn>0.5</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.1666666666 6666666667</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0416666666 6666666666 7</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0083333333 3333333333 34</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0013888888 8888888888 89</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0001984126 9841269841 27</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000248015 8730158730 1587</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000027557 3192239858 90653</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.2755731922 3985890653 E -6</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--E 20

--S 21 of 21
c:=continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (2)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mn>3</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>15</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>25</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow>
</math>

                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (2)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mn>3</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>15</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>25</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow>
--R</math>
--R
--R                                              Type: ContinuedFraction Integer
--E 21
)spool
 
Starts dribbling to complex.output (2009/2/17, 17:44:13).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from ComplexXmpPage

--S 1 of 16
a := complex(4/3,5/2)
 

        4   5
   (1)  - + - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (1)  - + - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 1

--S 2 of 16
b := complex(4/3,-5/2)
 

        4   5
   (2)  - - - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (2)  - - - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 2

--S 3 of 16
a + b
 

        8
   (3)  -
        3
                                               Type: Complex Fraction Integer
--R 
--R
--R        8
--R   (3)  -
--R        3
--R                                               Type: Complex Fraction Integer
--E 3

--S 4 of 16
a - b
 

   (4)  5%i
                                               Type: Complex Fraction Integer
--R 
--R
--R   (4)  5%i
--R                                               Type: Complex Fraction Integer
--E 4

--S 5 of 16
a * b
 

        289
   (5)  ---
         36
                                               Type: Complex Fraction Integer
--R 
--R
--R        289
--R   (5)  ---
--R         36
--R                                               Type: Complex Fraction Integer
--E 5

--S 6 of 16
a / b
 

          161   240
   (6)  - --- + --- %i
          289   289
                                               Type: Complex Fraction Integer
--R 
--R
--R          161   240
--R   (6)  - --- + --- %i
--R          289   289
--R                                               Type: Complex Fraction Integer
--E 6

--S 7 of 16
% :: Fraction Complex Integer
 

        - 15 + 8%i
   (7)  ----------
         15 + 8%i
                                               Type: Fraction Complex Integer
--R 
--R
--R        - 15 + 8%i
--R   (7)  ----------
--R         15 + 8%i
--R                                               Type: Fraction Complex Integer
--E 7

--S 8 of 16
3.4 + 6.7 * %i
 

   (8)  3.4 + 6.7 %i
                                                          Type: Complex Float
--R 
--R
--R   (8)  3.4 + 6.7 %i
--R                                                          Type: Complex Float
--E 8

--S 9 of 16
conjugate a
 

        4   5
   (9)  - - - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (9)  - - - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 9

--S 10 of 16
norm a
 

         289
   (10)  ---
          36
                                                       Type: Fraction Integer
--R 
--R
--R         289
--R   (10)  ---
--R          36
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 16
real a
 

         4
   (11)  -
         3
                                                       Type: Fraction Integer
--R 
--R
--R         4
--R   (11)  -
--R         3
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 16
imag a
 

         5
   (12)  -
         2
                                                       Type: Fraction Integer
--R 
--R
--R         5
--R   (12)  -
--R         2
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 16
gcd(13 - 13*%i,31 + 27*%i)
 

   (13)  5 + %i
                                                        Type: Complex Integer
--R 
--R
--R   (13)  5 + %i
--R                                                        Type: Complex Integer
--E 13

--S 14 of 16
lcm(13 - 13*%i,31 + 27*%i)
 

   (14)  143 - 39%i
                                                        Type: Complex Integer
--R 
--R
--R   (14)  143 - 39%i
--R                                                        Type: Complex Integer
--E 14

--S 15 of 16
factor(13 - 13*%i)
 

   (15)  - (1 + %i)(2 + 3%i)(3 + 2%i)
                                               Type: Factored Complex Integer
--R 
--R
--R   (15)  - (1 + %i)(2 + 3%i)(3 + 2%i)
--R                                               Type: Factored Complex Integer
--E 15

--S 16 of 16
factor complex(2,0)
 

                      2
   (16)  - %i (1 + %i)
                                               Type: Factored Complex Integer
--R 
--R
--R                      2
--R   (16)  - %i (1 + %i)
--R                                               Type: Factored Complex Integer
--E 16
)spool
 
Starts dribbling to macbug.output (2009/2/17, 17:52:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 5
macro ff(x) == x**2 + 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 5
ff z
 

         2
   (2)  z  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (2)  z  + 1
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 5
macro gg(x) == ff(2*x - 2/3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
gg(1/w)
 

           2
        13w  - 24w + 36
   (4)  ---------------
                2
              9w
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2
--R        13w  - 24w + 36
--R   (4)  ---------------
--R                2
--R              9w
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 5
macro ff(x) == gg(-x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
)spool 
 
Starts dribbling to lindep.output (2009/2/17, 17:52:30).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 10
v(i:INT):DIRPROD(5, FRAC INT) ==
   directProduct vector [i / (i + j) for j in 0..4]
 
   Function declaration v : Integer -> DirectProduct(5,Fraction Integer
      ) has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration v : Integer -> DirectProduct(5,Fraction Integer
--R      ) has been added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 10
V := vector [v i for i in 1..6]
 
   Compiling function v with type Integer -> DirectProduct(5,Fraction 
      Integer) 

   (2)
       1 1 1 1     2 1 2 1     3 3 1 3     4 2 4 1     5 5 5 5     6 3 2 3
   [[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-]]
       2 3 4 5     3 2 5 3     4 5 2 7     5 3 7 2     6 7 8 9     7 4 3 5
                               Type: Vector DirectProduct(5,Fraction Integer)
--R 
--R   Compiling function v with type Integer -> DirectProduct(5,Fraction 
--R      Integer) 
--R
--R   (2)
--R       1 1 1 1     2 1 2 1     3 3 1 3     4 2 4 1     5 5 5 5     6 3 2 3
--R   [[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-]]
--R       2 3 4 5     3 2 5 3     4 5 2 7     5 3 7 2     6 7 8 9     7 4 3 5
--R                               Type: Vector DirectProduct(5,Fraction Integer)
--E 2

--S 3 of 10
linearlyDependentOverZ? V
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 10
linearDependenceOverZ V
 

   (4)  [- 1,15,- 70,140,- 126,42]
                                              Type: Union(Vector Integer,...)
--R 
--R
--R   (4)  [- 1,15,- 70,140,- 126,42]
--R                                              Type: Union(Vector Integer,...)
--E 4

--S 5 of 10
solveLinearlyOverQ(delete(V, 2), V.2)
 

          1 14   28 42   14
   (5)  [--,--,- --,--,- --]
         15  3    3  5    5
                                     Type: Union(Vector Fraction Integer,...)
--R 
--R
--R          1 14   28 42   14
--R   (5)  [--,--,- --,--,- --]
--R         15  3    3  5    5
--R                                     Type: Union(Vector Fraction Integer,...)
--E 5

--S 6 of 10
w(i:INT):SQMATRIX(2, INT) ==
   squareMatrix matrix [[i, i + 1], [i - 1, -i]]
 
   Function declaration w : Integer -> SquareMatrix(2,Integer) has been
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration w : Integer -> SquareMatrix(2,Integer) has been
--R      added to workspace.
--R                                                                   Type: Void
--E 6

--S 7 of 10
W := vector [w i for i in 1..3]
 
   Compiling function w with type Integer -> SquareMatrix(2,Integer) 

         +1   2 + +2   3 + +3   4 +
   (7)  [|      |,|      |,|      |]
         +0  - 1+ +1  - 2+ +2  - 3+
                                         Type: Vector SquareMatrix(2,Integer)
--R 
--R   Compiling function w with type Integer -> SquareMatrix(2,Integer) 
--R
--R         +1   2 + +2   3 + +3   4 +
--R   (7)  [|      |,|      |,|      |]
--R         +0  - 1+ +1  - 2+ +2  - 3+
--R                                         Type: Vector SquareMatrix(2,Integer)
--E 7

--S 8 of 10
linearlyDependentOverZ? W
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 10
linearDependenceOverZ W
 

   (9)  [1,- 2,1]
                                              Type: Union(Vector Integer,...)
--R 
--R
--R   (9)  [1,- 2,1]
--R                                              Type: Union(Vector Integer,...)
--E 9

--S 10 of 10
solveLinearlyOverQ(delete(W, 2), W.2)
 

          1 1
   (10)  [-,-]
          2 2
                                     Type: Union(Vector Fraction Integer,...)
--R 
--R
--R          1 1
--R   (10)  [-,-]
--R          2 2
--R                                     Type: Union(Vector Fraction Integer,...)
--E 10
)spool 
 
Starts dribbling to atansqrt.output (2009/2/17, 17:43:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
z:=atan sqrt ((1-cos x)/(1+cos x))
 

              +------------+
              |- cos(x) + 1
   (1)  atan( |------------ )
             \| cos(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R              +------------+
--R              |- cos(x) + 1
--R   (1)  atan( |------------ )
--R             \| cos(x) + 1
--R                                                     Type: Expression Integer
--E 1
--S 2 of 3
integrate(differentiate(z,x),x)
 

        x
   (2)  -
        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        x
--R   (2)  -
--R        2
--R                                          Type: Union(Expression Integer,...)
--E 2
--S 3 of 3
rootSimp(normalize(z))
 

        x
   (3)  -
        2
                                                     Type: Expression Integer
--R 
--R
--R        x
--R   (3)  -
--R        2
--R                                                     Type: Expression Integer
--E 3
)spool
 
Starts dribbling to regset.output (2009/2/17, 17:57:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 34
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 34
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 34
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 34
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 34
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 34
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 34
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 34
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 34
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 34
T := REGSET(R,E,V,P)
 

   (10)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
--R  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
--R  ariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 34
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 34
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 34
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 34
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 34
zeroSetSplit(lp)$T
 

            5    4      2     3     8     5    3    2   4                2
   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R            5    4      2     3     8     5    3    2   4                2
--R   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 15

--S 16 of 34
lts := zeroSetSplit(lp,false)$T
 

   (16)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5          2     3         2
    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5          2     3         2
--R    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16

--S 17 of 34
[coHeight(ts) for ts in lts]
 

   (17)  [1,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (17)  [1,0,0]
--R                                                Type: List NonNegativeInteger
--E 17

--S 18 of 34
f1 := y**2*z+2*x*y*t-2*x-z
 

                          2
   (18)  (2t y - 2)x + z y  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                          2
--R   (18)  (2t y - 2)x + z y  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 18

--S 19 of 34
f2 :=   -x**3*z+ 4*x*y**2*z+ 4*x**2*y*t+ 2*y**3*t+ 4*x**2- 10*y**2+ 4*x*z- 10*y*t+ 2
 

              3              2        2              3      2
   (19)  - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R              3              2        2              3      2
--R   (19)  - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 19

--S 20 of 34
f3 :=  2*y*z*t+x*t**2-x-2*z
 

           2
   (20)  (t  - 1)x + 2t z y - 2z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           2
--R   (20)  (t  - 1)x + 2t z y - 2z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 20

--S 21 of 34
f4 :=   -x*z**3+ 4*y*z**2*t+ 4*x*z*t**2+ 2*y*t**3+ 4*x*z+ 4*z**2-10*y*t- 10*t**2+2
 

             3      2                2     3             2      2
   (21)  (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R             3      2                2     3             2      2
--R   (21)  (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 21

--S 22 of 34
lf := [f1, f2, f3, f4]
 

   (22)
                     2
   [(2t y - 2)x + z y  - z,
         3              2        2              3      2
    - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2,
      2
    (t  - 1)x + 2t z y - 2z,
        3      2                2     3             2      2
    (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (22)
--R                     2
--R   [(2t y - 2)x + z y  - z,
--R         3              2        2              3      2
--R    - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2,
--R      2
--R    (t  - 1)x + 2t z y - 2z,
--R        3      2                2     3             2      2
--R    (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 22

--S 23 of 34
zeroSetSplit(lf)$T
 

   (23)
      2      8      6       2                 3            2
   [{t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
       2      2     2
    {3t  + 1,z  - 7t  - 1,y + t,x + z},
      8      6      2         3            2
    {t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
      2      2
    {t  + 3,z  - 4,y + t,x - z}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (23)
--R      2      8      6       2                 3            2
--R   [{t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
--R       2      2     2
--R    {3t  + 1,z  - 7t  - 1,y + t,x + z},
--R      8      6      2         3            2
--R    {t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
--R      2      2
--R    {t  + 3,z  - 4,y + t,x - z}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 23

--S 24 of 34
lts2 := zeroSetSplit(lf,false)$T
 

   (24)
      8      6      2         3            2
   [{t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
      2      8      6       2                 3            2
    {t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
       2      2     2                     2      2
    {3t  + 1,z  - 7t  - 1,y + t,x + z}, {t  + 3,z  - 4,y + t,x - z}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (24)
--R      8      6      2         3            2
--R   [{t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
--R      2      8      6       2                 3            2
--R    {t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
--R       2      2     2                     2      2
--R    {3t  + 1,z  - 7t  - 1,y + t,x + z}, {t  + 3,z  - 4,y + t,x - z}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 24

--S 25 of 34
[coHeight(ts) for ts in lts2]
 

   (25)  [0,0,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (25)  [0,0,0,0]
--R                                                Type: List NonNegativeInteger
--E 25

--S 26 of 34
degrees := [degree(ts) for ts in lts2]
 

   (26)  [8,16,4,4]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (26)  [8,16,4,4]
--R                                                Type: List NonNegativeInteger
--E 26

--S 27 of 34
reduce(+,degrees)
 

   (27)  32
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  32
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 34
u : R := 2
 

   (28)  2
                                                                Type: Integer
--R 
--R
--R   (28)  2
--R                                                                Type: Integer
--E 28

--S 29 of 34
q1 := 2*(u-1)**2+ 2*(x-z*x+z**2)+ y**2*(x-1)**2- 2*u*x+ 2*y*t*(1-x)*(x-z)+ 2*u*z*t*(t-y)+ u**2*t**2*(1-2*z)+ 2*u*t**2*(z-x)+ 2*u*t*y*(z-1)+ 2*u*z*x*(y+1)+ (u**2-2*u)*z**2*t**2+ 2*u**2*z**2+ 4*u*(1-u)*z+ t**2*(z-x)**2
 

   (29)
       2           2  2        2                            2           2
     (y  - 2t y + t )x  + (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x
   + 
      2                      2       2          2
     y  + (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (29)
--R       2           2  2        2                            2           2
--R     (y  - 2t y + t )x  + (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x
--R   + 
--R      2                      2       2          2
--R     y  + (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 29

--S 30 of 34
q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+ u*y*(x+u-z*x-1)+ u*(u+1)*z**2*t
 

                                               2
   (30)  (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                                               2
--R   (30)  (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 30

--S 31 of 34
q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1)
 

                         2
   (31)  (- 2z - 2)x - 2z  + 8z - 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                         2
--R   (31)  (- 2z - 2)x - 2z  + 8z - 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 31

--S 32 of 34
q4 :=   u**2+4*(z-x**2)+3*y**2*(x-1)**2- 3*t**2*(z-x)**2 +3*u**2*t**2*(z-1)**2+u**2*z*(z-2)+6*u*t*y*(z+x+z*x-1)
 

   (32)
        2     2      2        2                      2        2
     (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y  + (12t z - 12t)y
   + 
        2      2         2            2
     (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (32)
--R        2     2      2        2                      2        2
--R     (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y  + (12t z - 12t)y
--R   + 
--R        2      2         2            2
--R     (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 32

--S 33 of 34
lq := [q1, q2, q3, q4]
 

   (33)
   [
         2           2  2
       (y  - 2t y + t )x
     + 
            2                            2           2          2
       (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x + y
     + 
                          2       2          2
       (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
     ,
                                          2                         2
    (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z, (- 2z - 2)x - 2z  + 8z - 2,

          2     2      2        2                      2        2
       (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y
     + 
                           2      2         2            2
       (12t z - 12t)y + (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
     ]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (33)
--R   [
--R         2           2  2
--R       (y  - 2t y + t )x
--R     + 
--R            2                            2           2          2
--R       (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x + y
--R     + 
--R                          2       2          2
--R       (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
--R     ,
--R                                          2                         2
--R    (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z, (- 2z - 2)x - 2z  + 8z - 2,
--R
--R          2     2      2        2                      2        2
--R       (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y
--R     + 
--R                           2      2         2            2
--R       (12t z - 12t)y + (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
--R     ]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 33

--S 34 of 34
zeroSetSplit(lq,true,true)$T
 
[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; {0}][2 <4,1>,<3,1> -> |7|; {0}][1 <3,1> -> |3|; {0}]G[2 <4,1>,<4,1> -> |8|; {0}]W[3 <5,1>,<4,1>,<3,2> -> |12|; {0}]GI[3 <4,2>,<4,1>,<3,2> -> |11|; {0}]GWw[3 <4,1>,<3,2>,<5,2> -> |12|; {0}][3 <3,2>,<3,2>,<5,2> -> |11|; {0}]GIwWWWw[4 <3,2>,<4,2>,<5,2>,<2,3> -> |14|; {0}][4 <2,2>,<4,2>,<5,2>,<2,3> -> |13|; {0}]Gwww[5 <3,2>,<3,2>,<4,2>,<5,2>,<2,3> -> |17|; {0}]Gwwwwww[8 <3,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}]Gwwwwww[8 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |31|; {0}][8 <3,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}][8 <2,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |29|; {0}][8 <1,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |28|; {0}][7 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |27|; {0}][6 <4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |23|; {0}][5 <4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |19|; {0}]GIGIWwww[6 <5,2>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |23|; {0}][6 <4,3>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |22|; {0}]GIGI[6 <3,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |21|; {0}][6 <2,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |20|; {0}]GGG[5 <4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |18|; {0}]GIGIWwwwW[6 <5,2>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |22|; {0}][6 <4,3>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |21|; {0}]GIwwWwWWWWWWWwWWWWwwwww[8 <4,2>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][8 <3,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}][8 <2,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |25|; {0}]Gwwwwwwwwwwwwwwwwwwww[9 <5,2>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |29|; {0}]GI[9 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |28|; {0}][9 <3,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][9 <2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}]GGwwwwwwwwwwwwWWwwwwwwww[11 <3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {0}][11 <2,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {0}][11 <1,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |31|; {0}]GGGwwwwwwwwwwwww[12 <2,3>,<2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {0}]GGwwwwwwwwwwwww[13 <3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}]Gwwwwwwwwwwwww[13 <2,3>,<3,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]GGGwwwwwwwwwwwww[15 <3,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {0}][14 <4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {0}]GIGGGGIGGI[14 <3,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GGG[14 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}][14 <1,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}]GGG[13 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]Gwwwwwwwwwwwww[15 <3,3>,<3,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]Gwwwwwwwwwwwww[15 <4,3>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |49|; {0}]GIGI[15 <3,4>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]G[14 <4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {0}][13 <3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]Gwwwwwwwwwwwww[13 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GIGGGGIGGI[13 <3,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]GGGGGGGG[13 <2,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}][13 <1,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}][13 <0,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}][12 <4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][11 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {1}][10 <3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |30|; {1}][10 <2,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |29|; {1}]GGGwwwwwwwwwwwww[11 <3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {1}]GGGwwwwwwwwwwwww[12 <4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}]Gwwwwwwwwwwwww[12 <3,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]GGwwwwwwwwwwwww[13 <5,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}]GIGGGGIGGIW[13 <4,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GGW[13 <3,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {1}]GGG[12 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]Gwwwwwwwwwwwww[12 <4,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]Gwwwwwwwwwwwww[13 <5,3>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {1}]GIGIW[13 <4,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {1}][13 <3,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}][13 <2,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GG[12 <5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {1}]GIGGGGIGGIW[12 <4,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]GGGGGGW[12 <3,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}][12 <2,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][12 <1,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |37|; {1}]GGG[11 <4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |36|; {1}][10 <5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {1}][9 <3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |27|; {1}]W[9 <2,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |26|; {1}][9 <1,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |25|; {1}][8 <3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |24|; {1}]W[8 <2,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}][8 <1,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][7 <4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]w[7 <3,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}][7 <2,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}][7 <1,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}][6 <2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}]GGwwwwww[7 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]GIW[7 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}]GG[6 <3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]Gwwwwww[7 <4,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}]GIW[7 <3,4>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][6 <4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}]GIW[6 <3,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]GGW[6 <2,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}][6 <1,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |16|; {1}]GGG[5 <3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |15|; {1}]GIW[5 <2,4>,<3,3>,<3,3>,<3,4>,<3,4> -> |14|; {1}]GG[4 <3,3>,<3,3>,<3,4>,<3,4> -> |12|; {1}][3 <3,3>,<3,4>,<3,4> -> |9|; {1}]W[3 <2,4>,<3,4>,<3,4> -> |8|; {1}][3 <1,4>,<3,4>,<3,4> -> |7|; {1}]G[2 <3,4>,<3,4> -> |6|; {1}]G[1 <3,4> -> |3|; {1}][1 <2,4> -> |2|; {1}][1 <1,4> -> |1|; {1}]
   *** QCMPACK Statistics ***
      Table     size:  36
      Entries reused:  255

   *** REGSETGCD: Gcd Statistics ***
      Table     size:  125
      Entries reused:  0

   *** REGSETGCD: Inv Set Statistics ***
      Table     size:  30
      Entries reused:  0

   (34)
   [
     {
                         24                   23                    22
         960725655771966t   + 386820897948702t   + 8906817198608181t
       + 
                          21                     20                    19
         2704966893949428t   + 37304033340228264t   + 7924782817170207t
       + 
                           18                     17                      16
         93126799040354990t   + 13101273653130910t   + 156146250424711858t
       + 
                           15                      14                     13
         16626490957259119t   + 190699288479805763t   + 24339173367625275t
       + 
                            12                     11                      10
         180532313014960135t   + 35288089030975378t   + 135054975747656285t
       + 
                           9                     8                     7
         34733736952488540t  + 75947600354493972t  + 19772555692457088t
       + 
                           6                    5                    4
         28871558573755428t  + 5576152439081664t  + 6321711820352976t
       + 
                       3                   2
       438314209312320t  + 581105748367008t  - 60254467992576t + 1449115951104
       ,

                                                                         23
             26604210869491302385515265737052082361668474181372891857784t
           + 
                                                                          22
             443104378424686086067294899528296664238693556855017735265295t
           + 
                                                                          21
             279078393286701234679141342358988327155321305829547090310242t
           + 
                                                                           20
             3390276361413232465107617176615543054620626391823613392185226t
           + 
                                                                          19
             941478179503540575554198645220352803719793196473813837434129t
           + 
                                                                            18
             11547855194679475242211696749673949352585747674184320988144390t
           + 
                                                                           17
             1343609566765597789881701656699413216467215660333356417241432t
           + 
                                                                            16
             23233813868147873503933551617175640859899102987800663566699334t
           + 
                                                                          15
             869574020537672336950845440508790740850931336484983573386433t
           + 
                                                                            14
             31561554305876934875419461486969926554241750065103460820476969t
           + 
                                                                           13
             1271400990287717487442065952547731879554823889855386072264931t
           + 
                                                                            12
             31945089913863736044802526964079540198337049550503295825160523t
           + 
                                                                           11
             3738735704288144509871371560232845884439102270778010470931960t
           + 
                                                                            10
             25293997512391412026144601435771131587561905532992045692885927t
           + 
                                                                           9
             5210239009846067123469262799870052773410471135950175008046524t
           + 
                                                                            8
             15083887986930297166259870568608270427403187606238713491129188t
           + 
                                                                           7
             3522087234692930126383686270775779553481769125670839075109000t
           + 
                                                                           6
             6079945200395681013086533792568886491101244247440034969288588t
           + 
                                                                           5
             1090634852433900888199913756247986023196987723469934933603680t
           + 
                                                                           4
             1405819430871907102294432537538335402102838994019667487458352t
           + 
                                                                         3
             88071527950320450072536671265507748878347828884933605202432t
           + 
                                                                          2
             135882489433640933229781177155977768016065765482378657129440t
           + 
             - 13957283442882262230559894607400314082516690749975646520320t
           + 
             334637692973189299277258325709308472592117112855749713920
        *
           z
       + 
                                                                    23
         8567175484043952879756725964506833932149637101090521164936t
       + 
                                                                      22
         149792392864201791845708374032728942498797519251667250945721t
       + 
                                                                     21
         77258371783645822157410861582159764138123003074190374021550t
       + 
                                                                       20
         1108862254126854214498918940708612211184560556764334742191654t
       + 
                                                                      19
         213250494460678865219774480106826053783815789621501732672327t
       + 
                                                                       18
         3668929075160666195729177894178343514501987898410131431699882t
       + 
                                                                      17
         171388906471001872879490124368748236314765459039567820048872t
       + 
                                                                       16
         7192430746914602166660233477331022483144921771645523139658986t
       + 
                                                                        15
         - 128798674689690072812879965633090291959663143108437362453385t
       + 
                                                                       14
         9553010858341425909306423132921134040856028790803526430270671t
       + 
                                                                       13
         - 13296096245675492874538687646300437824658458709144441096603t
       + 
                                                                       12
         9475806805814145326383085518325333106881690568644274964864413t
       + 
                                                                      11
         803234687925133458861659855664084927606298794799856265539336t
       + 
                                                                       10
         7338202759292865165994622349207516400662174302614595173333825t
       + 
                                                                       9
         1308004628480367351164369613111971668880538855640917200187108t
       + 
                                                                       8
         4268059455741255498880229598973705747098216067697754352634748t
       + 
                                                                      7
         892893526858514095791318775904093300103045601514470613580600t
       + 
                                                                       6
         1679152575460683956631925852181341501981598137465328797013652t
       + 
                                                                      5
         269757415767922980378967154143357835544113158280591408043936t
       + 
                                                                      4
         380951527864657529033580829801282724081345372680202920198224t
       + 
                                                                     3
         19785545294228495032998826937601341132725035339452913286656t
       + 
                                                                     2
         36477412057384782942366635303396637763303928174935079178528t
       + 
         - 3722212879279038648713080422224976273210890229485838670848t
       + 
         89079724853114348361230634484013862024728599906874105856
       ,
         3      2                  3       2
      (3z  - 11z  + 8z + 4)y + 2t z  + 4t z  - 5t z - t,
                  2
      (z + 1)x + z  - 4z + 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; {0}][2 <4,1>,<3,1> -> |7|; {0}][1 <3,1> -> |3|; {0}]G[2 <4,1>,<4,1> -> |8|; {0}]W[3 <5,1>,<4,1>,<3,2> -> |12|; {0}]GI[3 <4,2>,<4,1>,<3,2> -> |11|; {0}]GWw[3 <4,1>,<3,2>,<5,2> -> |12|; {0}][3 <3,2>,<3,2>,<5,2> -> |11|; {0}]GIwWWWw[4 <3,2>,<4,2>,<5,2>,<2,3> -> |14|; {0}][4 <2,2>,<4,2>,<5,2>,<2,3> -> |13|; {0}]Gwww[5 <3,2>,<3,2>,<4,2>,<5,2>,<2,3> -> |17|; {0}]Gwwwwww[8 <3,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}]Gwwwwww[8 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |31|; {0}][8 <3,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}][8 <2,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |29|; {0}][8 <1,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |28|; {0}][7 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |27|; {0}][6 <4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |23|; {0}][5 <4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |19|; {0}]GIGIWwww[6 <5,2>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |23|; {0}][6 <4,3>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |22|; {0}]GIGI[6 <3,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |21|; {0}][6 <2,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |20|; {0}]GGG[5 <4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |18|; {0}]GIGIWwwwW[6 <5,2>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |22|; {0}][6 <4,3>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |21|; {0}]GIwwWwWWWWWWWwWWWWwwwww[8 <4,2>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][8 <3,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}][8 <2,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |25|; {0}]Gwwwwwwwwwwwwwwwwwwww[9 <5,2>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |29|; {0}]GI[9 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |28|; {0}][9 <3,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][9 <2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}]GGwwwwwwwwwwwwWWwwwwwwww[11 <3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {0}][11 <2,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {0}][11 <1,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |31|; {0}]GGGwwwwwwwwwwwww[12 <2,3>,<2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {0}]GGwwwwwwwwwwwww[13 <3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}]Gwwwwwwwwwwwww[13 <2,3>,<3,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]GGGwwwwwwwwwwwww[15 <3,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {0}][14 <4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {0}]GIGGGGIGGI[14 <3,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GGG[14 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}][14 <1,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}]GGG[13 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]Gwwwwwwwwwwwww[15 <3,3>,<3,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]Gwwwwwwwwwwwww[15 <4,3>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |49|; {0}]GIGI[15 <3,4>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]G[14 <4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {0}][13 <3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]Gwwwwwwwwwwwww[13 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GIGGGGIGGI[13 <3,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]GGGGGGGG[13 <2,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}][13 <1,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}][13 <0,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}][12 <4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][11 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {1}][10 <3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |30|; {1}][10 <2,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |29|; {1}]GGGwwwwwwwwwwwww[11 <3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {1}]GGGwwwwwwwwwwwww[12 <4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}]Gwwwwwwwwwwwww[12 <3,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]GGwwwwwwwwwwwww[13 <5,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}]GIGGGGIGGIW[13 <4,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GGW[13 <3,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {1}]GGG[12 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]Gwwwwwwwwwwwww[12 <4,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]Gwwwwwwwwwwwww[13 <5,3>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {1}]GIGIW[13 <4,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {1}][13 <3,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}][13 <2,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GG[12 <5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {1}]GIGGGGIGGIW[12 <4,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]GGGGGGW[12 <3,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}][12 <2,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][12 <1,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |37|; {1}]GGG[11 <4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |36|; {1}][10 <5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {1}][9 <3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |27|; {1}]W[9 <2,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |26|; {1}][9 <1,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |25|; {1}][8 <3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |24|; {1}]W[8 <2,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}][8 <1,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][7 <4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]w[7 <3,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}][7 <2,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}][7 <1,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}][6 <2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}]GGwwwwww[7 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]GIW[7 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}]GG[6 <3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]Gwwwwww[7 <4,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}]GIW[7 <3,4>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][6 <4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}]GIW[6 <3,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]GGW[6 <2,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}][6 <1,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |16|; {1}]GGG[5 <3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |15|; {1}]GIW[5 <2,4>,<3,3>,<3,3>,<3,4>,<3,4> -> |14|; {1}]GG[4 <3,3>,<3,3>,<3,4>,<3,4> -> |12|; {1}][3 <3,3>,<3,4>,<3,4> -> |9|; {1}]W[3 <2,4>,<3,4>,<3,4> -> |8|; {1}][3 <1,4>,<3,4>,<3,4> -> |7|; {1}]G[2 <3,4>,<3,4> -> |6|; {1}]G[1 <3,4> -> |3|; {1}][1 <2,4> -> |2|; {1}][1 <1,4> -> |1|; {1}]
--R   *** QCMPACK Statistics ***
--R      Table     size:  36
--R      Entries reused:  255
--R
--R   *** REGSETGCD: Gcd Statistics ***
--R      Table     size:  125
--R      Entries reused:  0
--R
--R   *** REGSETGCD: Inv Set Statistics ***
--R      Table     size:  30
--R      Entries reused:  0
--R
--R   (34)
--R   [
--R     {
--R                         24                   23                    22
--R         960725655771966t   + 386820897948702t   + 8906817198608181t
--R       + 
--R                          21                     20                    19
--R         2704966893949428t   + 37304033340228264t   + 7924782817170207t
--R       + 
--R                           18                     17                      16
--R         93126799040354990t   + 13101273653130910t   + 156146250424711858t
--R       + 
--R                           15                      14                     13
--R         16626490957259119t   + 190699288479805763t   + 24339173367625275t
--R       + 
--R                            12                     11                      10
--R         180532313014960135t   + 35288089030975378t   + 135054975747656285t
--R       + 
--R                           9                     8                     7
--R         34733736952488540t  + 75947600354493972t  + 19772555692457088t
--R       + 
--R                           6                    5                    4
--R         28871558573755428t  + 5576152439081664t  + 6321711820352976t
--R       + 
--R                       3                   2
--R       438314209312320t  + 581105748367008t  - 60254467992576t + 1449115951104
--R       ,
--R
--R                                                                         23
--R             26604210869491302385515265737052082361668474181372891857784t
--R           + 
--R                                                                          22
--R             443104378424686086067294899528296664238693556855017735265295t
--R           + 
--R                                                                          21
--R             279078393286701234679141342358988327155321305829547090310242t
--R           + 
--R                                                                           20
--R             3390276361413232465107617176615543054620626391823613392185226t
--R           + 
--R                                                                          19
--R             941478179503540575554198645220352803719793196473813837434129t
--R           + 
--R                                                                            18
--R             11547855194679475242211696749673949352585747674184320988144390t
--R           + 
--R                                                                           17
--R             1343609566765597789881701656699413216467215660333356417241432t
--R           + 
--R                                                                            16
--R             23233813868147873503933551617175640859899102987800663566699334t
--R           + 
--R                                                                          15
--R             869574020537672336950845440508790740850931336484983573386433t
--R           + 
--R                                                                            14
--R             31561554305876934875419461486969926554241750065103460820476969t
--R           + 
--R                                                                           13
--R             1271400990287717487442065952547731879554823889855386072264931t
--R           + 
--R                                                                            12
--R             31945089913863736044802526964079540198337049550503295825160523t
--R           + 
--R                                                                           11
--R             3738735704288144509871371560232845884439102270778010470931960t
--R           + 
--R                                                                            10
--R             25293997512391412026144601435771131587561905532992045692885927t
--R           + 
--R                                                                           9
--R             5210239009846067123469262799870052773410471135950175008046524t
--R           + 
--R                                                                            8
--R             15083887986930297166259870568608270427403187606238713491129188t
--R           + 
--R                                                                           7
--R             3522087234692930126383686270775779553481769125670839075109000t
--R           + 
--R                                                                           6
--R             6079945200395681013086533792568886491101244247440034969288588t
--R           + 
--R                                                                           5
--R             1090634852433900888199913756247986023196987723469934933603680t
--R           + 
--R                                                                           4
--R             1405819430871907102294432537538335402102838994019667487458352t
--R           + 
--R                                                                         3
--R             88071527950320450072536671265507748878347828884933605202432t
--R           + 
--R                                                                          2
--R             135882489433640933229781177155977768016065765482378657129440t
--R           + 
--R             - 13957283442882262230559894607400314082516690749975646520320t
--R           + 
--R             334637692973189299277258325709308472592117112855749713920
--R        *
--R           z
--R       + 
--R                                                                    23
--R         8567175484043952879756725964506833932149637101090521164936t
--R       + 
--R                                                                      22
--R         149792392864201791845708374032728942498797519251667250945721t
--R       + 
--R                                                                     21
--R         77258371783645822157410861582159764138123003074190374021550t
--R       + 
--R                                                                       20
--R         1108862254126854214498918940708612211184560556764334742191654t
--R       + 
--R                                                                      19
--R         213250494460678865219774480106826053783815789621501732672327t
--R       + 
--R                                                                       18
--R         3668929075160666195729177894178343514501987898410131431699882t
--R       + 
--R                                                                      17
--R         171388906471001872879490124368748236314765459039567820048872t
--R       + 
--R                                                                       16
--R         7192430746914602166660233477331022483144921771645523139658986t
--R       + 
--R                                                                        15
--R         - 128798674689690072812879965633090291959663143108437362453385t
--R       + 
--R                                                                       14
--R         9553010858341425909306423132921134040856028790803526430270671t
--R       + 
--R                                                                       13
--R         - 13296096245675492874538687646300437824658458709144441096603t
--R       + 
--R                                                                       12
--R         9475806805814145326383085518325333106881690568644274964864413t
--R       + 
--R                                                                      11
--R         803234687925133458861659855664084927606298794799856265539336t
--R       + 
--R                                                                       10
--R         7338202759292865165994622349207516400662174302614595173333825t
--R       + 
--R                                                                       9
--R         1308004628480367351164369613111971668880538855640917200187108t
--R       + 
--R                                                                       8
--R         4268059455741255498880229598973705747098216067697754352634748t
--R       + 
--R                                                                      7
--R         892893526858514095791318775904093300103045601514470613580600t
--R       + 
--R                                                                       6
--R         1679152575460683956631925852181341501981598137465328797013652t
--R       + 
--R                                                                      5
--R         269757415767922980378967154143357835544113158280591408043936t
--R       + 
--R                                                                      4
--R         380951527864657529033580829801282724081345372680202920198224t
--R       + 
--R                                                                     3
--R         19785545294228495032998826937601341132725035339452913286656t
--R       + 
--R                                                                     2
--R         36477412057384782942366635303396637763303928174935079178528t
--R       + 
--R         - 3722212879279038648713080422224976273210890229485838670848t
--R       + 
--R         89079724853114348361230634484013862024728599906874105856
--R       ,
--R         3      2                  3       2
--R      (3z  - 11z  + 8z + 4)y + 2t z  + 4t z  - 5t z - t,
--R                  2
--R      (z + 1)x + z  - 4z + 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 34
)spool 
 
Starts dribbling to newlodo.output (2009/2/17, 17:55:31).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 55
RN:=FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 55
Dx: LODO2(RN, UP(x,RN))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 55
Dx := D()                  -- definition of an operator
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 55
a  := Dx  + 1
 

   (4)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 55
b  := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (5)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (5)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 55
p: UP(x,RN) := 4*x**2 + 2/3      -- something to work on
 

          2   2
   (6)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (6)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 55
a p                        -- application of an operator to a polynomial
 

          2        2
   (7)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (7)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 55
(a*b) p = a b p            -- multiplication is defined by this identity
 

          2         37    2         37
   (8)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (8)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 55
c := (1/9)*b*(a + b)**2    -- exponentiation follows from multiplication
 

         1  6    5  5   13  4   19  3   79  2    7     1
   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
        72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R         1  6    5  5   13  4   19  3   79  2    7     1
--R   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R        72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 55
(a**2 - 3/4*b + c) (p + 1) -- general application of operator expressions
 

           2   44     541
   (10)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (10)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 10

)clear all
 
   All user variables and function definitions have been cleared.

--S 11 of 55
RFZ := FRAC UP(x,INT)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 11

--S 12 of 55
(Dx, a, b): LODO1 RFZ
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 55
Dx := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 55
b := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 14

--S 15 of 55
a := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 55
p: RFZ := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 55
(a*b - b*a) p  -- operator multiplication is not commutative
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18 of 55
leftDivide(a,b)      -- result is the quotient/remainder pair
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 55
a - (b * %.quotient + %.remainder)
 

   (9)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (9)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 55
rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 20

--S 21 of 55
a - (%.quotient * b + %.remainder)
 

   (11)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (11)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 21

--S 22 of 55
e := leftGcd(a,b)
 

           2 2        1
   (12)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (12)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 22

--S 23 of 55
leftRemainder(a, e)    -- remainder from left division
 

   (13)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 23

--S 24 of 55
rightRemainder(a, e)    -- remainder from right division
 

               5
   (14)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (14)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 24

--S 25 of 55
f := rightLcm(a,b)
 

            3 3       2        2         7
   (15)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (15)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 25

--S 26 of 55
leftRemainder(f, b)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 26

--S 27 of 55
rightRemainder(f, b)  -- the remainder is non-zero
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 27

)clear all
 
   All user variables and function definitions have been cleared.

--S 44 of 55
PZ := UP(x,INT); Vect := DPMM(3, PZ, SQMATRIX(3,PZ), PZ);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 44

--S 45 of 55
Modo := LODO2(SQMATRIX(3,PZ), Vect);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 45

--S 46 of 55
p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect
 

           2          3
   (3)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (3)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 46

--S 47 of 55
m := [[x**2, 1, 0], [1, x**4, 0], [0, 0, 4*x**2]]::(SQMATRIX(3,PZ))
 

        + 2         +
        |x   1    0 |
        |           |
   (4)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (4)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 47

--S 48 of 55
q: Vect := m * p
 

           4    2        5     2        5     3
   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 48

--S 49 of 55
Dx:  Modo := D()
 

   (6)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (6)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 49

--S 50 of 55
a:   Modo := 1*Dx  + m
 

            + 2         +
            |x   1    0 |
            |           |
   (7)  D + |     4     |
            |1   x    0 |
            |           |
            |          2|
            +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R            + 2         +
--R            |x   1    0 |
--R            |           |
--R   (7)  D + |     4     |
--R            |1   x    0 |
--R            |           |
--R            |          2|
--R            +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 50

--S 51 of 55
b:   Modo := m*Dx  + 1
 

        + 2         +
        |x   1    0 |    +1  0  0+
        |           |    |       |
   (8)  |     4     |D + |0  1  0|
        |1   x    0 |    |       |
        |           |    +0  0  1+
        |          2|
        +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R        + 2         +
--R        |x   1    0 |    +1  0  0+
--R        |           |    |       |
--R   (8)  |     4     |D + |0  1  0|
--R        |1   x    0 |    |       |
--R        |           |    +0  0  1+
--R        |          2|
--R        +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 51

--S 52 of 55
a*b
 

   (9)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 52

--S 53 of 55
a p
 

            4    2        5     2        5     3      2
   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 53

--S 54 of 55
b p
 

            3     2       4         4     3     2
   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 54

--S 55 of 55
(a+b) (p + q)
 

   (12)
      6      5      4      3      2
   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
      9      8     6      5      4      3     2
    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
        7       6      5       4      3      2
    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (12)
--R      6      5      4      3      2
--R   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
--R      9      8     6      5      4      3     2
--R    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
--R        7       6      5       4      3      2
--R    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 55
)spool 
 
Starts dribbling to schaum32.output (2009/2/17, 17:59:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(sech(a*x),x)
 

        2atan(sinh(a x) + cosh(a x))
   (1)  ----------------------------
                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        2atan(sinh(a x) + cosh(a x))
--R   (1)  ----------------------------
--R                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=2/a*atan(%e^(a*x))
 

                a x
        2atan(%e   )
   (2)  ------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        2atan(%e   )
--R   (2)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                               a x
        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
   (3)  -------------------------------------------
                             a
                                                     Type: Expression Integer
--R
--R                                               a x
--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
--R   (3)  -------------------------------------------
--R                             a
--R                                                     Type: Expression Integer
--E

--S 4
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 5
dd:=atanrule cc
 

                   a x
               - %e    + %i           - sinh(a x) - cosh(a x) + %i
        %i log(------------) - %i log(----------------------------)
                  a x                  sinh(a x) + cosh(a x) + %i
                %e    + %i
   (5)  -----------------------------------------------------------
                                     a
                                             Type: Expression Complex Integer
--R
--R                   a x
--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
--R        %i log(------------) - %i log(----------------------------)
--R                  a x                  sinh(a x) + cosh(a x) + %i
--R                %e    + %i
--R   (5)  -----------------------------------------------------------
--R                                     a
--R                                             Type: Expression Complex Integer
--E

--S 6
ee:=expandLog dd
 

   (6)
       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
     + 
                  a x                  a x
       - %i log(%e    + %i) + %i log(%e    - %i)
  /
     a
                                             Type: Expression Complex Integer
--R
--R   (6)
--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
--R     + 
--R                  a x                  a x
--R       - %i log(%e    + %i) + %i log(%e    - %i)
--R  /
--R     a
--R                                             Type: Expression Complex Integer
--E

--S 7      14:626 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                             Type: Expression Complex Integer
--R
--R   (7)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(sech(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=tanh(a*x)/a
 

        tanh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        tanh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 10
cc:=aa-bb
 

                    2                                  2
        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
   (3)  ------------------------------------------------------------------
                         2                                      2
              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R                    2                                  2
--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
--R   (3)  ------------------------------------------------------------------
--R                         2                                      2
--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 11
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12
dd:=sinhsqrrule cc
 

                                                        2
        (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)tanh(a x) - 4
   (5)  -------------------------------------------------------------------
                                                                 2
              4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R                                                        2
--R        (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)tanh(a x) - 4
--R   (5)  -------------------------------------------------------------------
--R                                                                 2
--R              4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 13
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 14
ee:=coshsqrrule dd
 

        (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2
   (7)  -----------------------------------------------------
               2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R        (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2
--R   (7)  -----------------------------------------------------
--R               2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 15
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %O sinh(y + x) - %O sinh(y - x)
   (8)  %O cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %L sinh(y + x) - %L sinh(y - x)
--I   (8)  %L cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 16
ff:=sinhcoshrule ee
 

        (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2
   (9)  --------------------------------------------
               a sinh(2a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R        (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2
--R   (9)  --------------------------------------------
--R               a sinh(2a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 17     14:627 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

           1
   (10)  - -
           a
                                                     Type: Expression Integer
--R
--R           1
--R   (10)  - -
--R           a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 18
aa:=integrate(sech(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
      *
         atan(sinh(a x) + cosh(a x))
     + 
                3                      2              2
       sinh(a x)  + 3cosh(a x)sinh(a x)  + (3cosh(a x)  - 1)sinh(a x)
     + 
                3
       cosh(a x)  - cosh(a x)
  /
                  4                        3                2               2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
     + 
                  3                                       4               2
     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R                3                      2              2
--R       sinh(a x)  + 3cosh(a x)sinh(a x)  + (3cosh(a x)  - 1)sinh(a x)
--R     + 
--R                3
--R       cosh(a x)  - cosh(a x)
--R  /
--R                  4                        3                2               2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
--R     + 
--R                  3                                       4               2
--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 19
bb:=(sech(a*x)*tanh(a*x))/(2*a)+1/(2*a)*atan(sinh(a*x))
 

        atan(sinh(a x)) + sech(a x)tanh(a x)
   (2)  ------------------------------------
                         2a
                                                     Type: Expression Integer
--R
--R        atan(sinh(a x)) + sech(a x)tanh(a x)
--R   (2)  ------------------------------------
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 20     14:628 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                     4                      3               2              2
           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
         + 
                      3                                    4             2
           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
      *
         atan(sinh(a x) + cosh(a x))
     + 
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  - 4cosh(a x))sinh(a x) - cosh(a x)  - 2cosh(a x)  - 1
      *
         atan(sinh(a x))
     + 
                               4                               3
           - sech(a x)sinh(a x)  - 4cosh(a x)sech(a x)sinh(a x)
         + 
                        2                       2
           (- 6cosh(a x)  - 2)sech(a x)sinh(a x)
         + 
                        3
           (- 4cosh(a x)  - 4cosh(a x))sech(a x)sinh(a x)
         + 
                       4             2
           (- cosh(a x)  - 2cosh(a x)  - 1)sech(a x)
      *
         tanh(a x)
     + 
                 3                      2              2
       2sinh(a x)  + 6cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
     + 
                 3
       2cosh(a x)  - 2cosh(a x)
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
     + 
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     4                      3               2              2
--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
--R         + 
--R                      3                                    4             2
--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  - 4cosh(a x))sinh(a x) - cosh(a x)  - 2cosh(a x)  - 1
--R      *
--R         atan(sinh(a x))
--R     + 
--R                               4                               3
--R           - sech(a x)sinh(a x)  - 4cosh(a x)sech(a x)sinh(a x)
--R         + 
--R                        2                       2
--R           (- 6cosh(a x)  - 2)sech(a x)sinh(a x)
--R         + 
--R                        3
--R           (- 4cosh(a x)  - 4cosh(a x))sech(a x)sinh(a x)
--R         + 
--R                       4             2
--R           (- cosh(a x)  - 2cosh(a x)  - 1)sech(a x)
--R      *
--R         tanh(a x)
--R     + 
--R                 3                      2              2
--R       2sinh(a x)  + 6cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R     + 
--R                 3
--R       2cosh(a x)  - 2cosh(a x)
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
--R     + 
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 21
aa:=integrate(sech(a*x)^n*tanh(a*x),x)
 

   (1)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
  /
     a n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R  /
--R     a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22
bb:=-sech(a*x)^n/(n*a)
 

                   n
          sech(a x)
   (2)  - ----------
              a n
                                                     Type: Expression Integer
--R
--R                   n
--R          sech(a x)
--R   (2)  - ----------
--R              a n
--R                                                     Type: Expression Integer
--E

--S 23
cc:=aa-bb
 

   (3)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                n
       sech(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (3)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                n
--R       sech(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 24
sechrule:=rule(sech(x) == 1/cosh(x))
 

                      1
   (4)  sech(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (4)  sech(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25
dd:=sechrule cc
 

   (5)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
            1     n
       (---------)
        cosh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (5)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R            1     n
--R       (---------)
--R        cosh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 26
ee:=expandLog dd
 

   (6)
       sinh
                           2                                  2
            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
                              2                                  2
               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        cosh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (6)
--R       sinh
--R                           2                                  2
--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R                              2                                  2
--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        cosh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 27     14:629 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28
aa:=integrate(1/sech(a*x),x)
 

        sinh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sinh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29
bb:=sinh(a*x)/a
 

        sinh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        sinh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 30     14:630 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 31     14:631 Axiom cannot compute this integral
aa:=integrate(x*sech(a*x),x)
 

           x
         ++
   (1)   |   %T sech(%T a)d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O sech(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(x*sech(a*x)^2,x)
 

   (1)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                     2                                           2
       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                     2                                           2
--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 33
bb:=(x*tanh(a*x))/a-1/a^2*log(cosh(a*x))
 

        - log(cosh(a x)) + a x tanh(a x)
   (2)  --------------------------------
                        2
                       a
                                                     Type: Expression Integer
--R
--R        - log(cosh(a x)) + a x tanh(a x)
--R   (2)  --------------------------------
--R                        2
--R                       a
--R                                                     Type: Expression Integer
--E

--S 34
cc:=aa-bb
 

   (3)
                 2                                  2
       (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)log(cosh(a x))
     + 
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                         2                                          2
         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
      *
         tanh(a x)
     + 
                     2                                           2
       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2                                  2
--R       (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)log(cosh(a x))
--R     + 
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                         2                                          2
--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
--R      *
--R         tanh(a x)
--R     + 
--R                     2                                           2
--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 35
dd:=expandLog cc
 

   (4)
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                         2                                          2
         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
      *
         tanh(a x)
     + 
                                   2
       (- log(- 2) + 2a x)sinh(a x)  + (- 2log(- 2) + 4a x)cosh(a x)sinh(a x)
     + 
                                   2
       (- log(- 2) + 2a x)cosh(a x)  - log(- 2)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (4)
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                         2                                          2
--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
--R      *
--R         tanh(a x)
--R     + 
--R                                   2
--R       (- log(- 2) + 2a x)sinh(a x)  + (- 2log(- 2) + 4a x)cosh(a x)sinh(a x)
--R     + 
--R                                   2
--R       (- log(- 2) + 2a x)cosh(a x)  - log(- 2)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 36
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37
ee:=sinhsqrrule dd
 

   (6)
                                                       2
         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                                                                     2
         (- 4a x cosh(a x)sinh(a x) - a x cosh(2a x) - 2a x cosh(a x)  - a x)
      *
         tanh(a x)
     + 
       (- 4log(- 2) + 8a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
     + 
                                    2
       (- 2log(- 2) + 4a x)cosh(a x)  - log(- 2) - 2a x
  /
       2                      2               2         2    2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                       2
--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                                                                     2
--R         (- 4a x cosh(a x)sinh(a x) - a x cosh(2a x) - 2a x cosh(a x)  - a x)
--R      *
--R         tanh(a x)
--R     + 
--R       (- 4log(- 2) + 8a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
--R     + 
--R                                    2
--R       (- 2log(- 2) + 4a x)cosh(a x)  - log(- 2) - 2a x
--R  /
--R       2                      2               2         2    2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 38
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 39
ff:=coshsqrrule ee
 

   (8)
       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (- 2a x cosh(a x)sinh(a x) - a x cosh(2a x) - a x)tanh(a x)
     + 
       (- 2log(- 2) + 4a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
     + 
       - log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (- 2a x cosh(a x)sinh(a x) - a x cosh(2a x) - a x)tanh(a x)
--R     + 
--R       (- 2log(- 2) + 4a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
--R     + 
--R       - log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 40
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %U sinh(y + x) - %U sinh(y - x)
   (9)  %U cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %P sinh(y + x) - %P sinh(y - x)
--I   (9)  %P cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 41
gg:=sinhcoshrule ff
 

   (10)
       (sinh(2a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (- a x sinh(2a x) - a x cosh(2a x) - a x)tanh(a x)
     + 
       (- log(- 2) + 2a x)sinh(2a x) + (- log(- 2) + 2a x)cosh(2a x) - log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (sinh(2a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (- a x sinh(2a x) - a x cosh(2a x) - a x)tanh(a x)
--R     + 
--R       (- log(- 2) + 2a x)sinh(2a x) + (- log(- 2) + 2a x)cosh(2a x) - log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 42     14:632 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         log(- 1) - log(- 2)
   (11)  -------------------
                   2
                  a
                                                     Type: Expression Integer
--R
--R         log(- 1) - log(- 2)
--R   (11)  -------------------
--R                   2
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 43     14:633 Axiom cannot compute this integral
aa:=integrate(sech(a*x)/x,x)
 

           x
         ++  sech(%T a)
   (1)   |   ---------- d%T
        ++       %T
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sech(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 44
aa:=integrate(1/(q+p*sech(a*x)),x)
 

   (1)
   [
           p
        *
           log
                       2         2      2
                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                    + 
                       2         2                     2     2
                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
                 *
                     +---------+
                     |   2    2
                    \|- q  + p
                + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
             /
                             2                                             2
                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                + 
                  2p cosh(a x) + q
       + 
             +---------+
             |   2    2
         a x\|- q  + p
    /
           +---------+
           |   2    2
       a q\|- q  + p
     ,
                                              +-------+
                                              | 2    2         +-------+
              (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
    - 2p atan(-----------------------------------------) + a x\|q  - p
                                2    2
                               q  - p
    --------------------------------------------------------------------]
                                    +-------+
                                    | 2    2
                                a q\|q  - p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           p
--R        *
--R           log
--R                       2         2      2
--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                    + 
--R                       2         2                     2     2
--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
--R                 *
--R                     +---------+
--R                     |   2    2
--R                    \|- q  + p
--R                + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R             /
--R                             2                                             2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                + 
--R                  2p cosh(a x) + q
--R       + 
--R             +---------+
--R             |   2    2
--R         a x\|- q  + p
--R    /
--R           +---------+
--R           |   2    2
--R       a q\|- q  + p
--R     ,
--R                                              +-------+
--R                                              | 2    2         +-------+
--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
--R    - 2p atan(-----------------------------------------) + a x\|q  - p
--R                                2    2
--R                               q  - p
--R    --------------------------------------------------------------------]
--R                                    +-------+
--R                                    | 2    2
--R                                a q\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 45
t1:=integrate(1/(p+q*cosh(a*x)),x)
 

   (2)
   [
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
    /
         +---------+
         |   2    2
       a\|- q  + p
     ,
                                          +-------+
                                          | 2    2
          (q sinh(a x) + q cosh(a x) + p)\|q  - p
    2atan(-----------------------------------------)
                            2    2
                           q  - p
    ------------------------------------------------]
                         +-------+
                         | 2    2
                       a\|q  - p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R    /
--R         +---------+
--R         |   2    2
--R       a\|- q  + p
--R     ,
--R                                          +-------+
--R                                          | 2    2
--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R    2atan(-----------------------------------------)
--R                            2    2
--R                           q  - p
--R    ------------------------------------------------]
--R                         +-------+
--R                         | 2    2
--R                       a\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 46
bb1:=x/q-p/q*t1.1
 

   (3)
       -
            p
         *
            log
                        2         2      2
                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                     + 
                        2         2                     2     2
                       q cosh(a x)  + 2p q cosh(a x) - q  + 2p
                  *
                      +---------+
                      |   2    2
                     \|- q  + p
                 + 
                      3     2                 3     2                  2     3
                   (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
              /
                              2                                             2
                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                 + 
                   2p cosh(a x) + q
     + 
           +---------+
           |   2    2
       a x\|- q  + p
  /
         +---------+
         |   2    2
     a q\|- q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            p
--R         *
--R            log
--R                        2         2      2
--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                     + 
--R                        2         2                     2     2
--R                       q cosh(a x)  + 2p q cosh(a x) - q  + 2p
--R                  *
--R                      +---------+
--R                      |   2    2
--R                     \|- q  + p
--R                 + 
--R                      3     2                 3     2                  2     3
--R                   (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R              /
--R                              2                                             2
--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                 + 
--R                   2p cosh(a x) + q
--R     + 
--R           +---------+
--R           |   2    2
--R       a x\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 47
bb2:=x/q-p/q*t1.2
 

                                                  +-------+
                                                  | 2    2         +-------+
                  (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
        - 2p atan(-----------------------------------------) + a x\|q  - p
                                    2    2
                                   q  - p
   (4)  --------------------------------------------------------------------
                                        +-------+
                                        | 2    2
                                    a q\|q  - p
                                                     Type: Expression Integer
--R
--R                                                  +-------+
--R                                                  | 2    2         +-------+
--R                  (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
--R        - 2p atan(-----------------------------------------) + a x\|q  - p
--R                                    2    2
--R                                   q  - p
--R   (4)  --------------------------------------------------------------------
--R                                        +-------+
--R                                        | 2    2
--R                                    a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 48
cc1:=aa.1-bb1
 

   (5)
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
  /
         +---------+
         |   2    2
     a q\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R  /
--R         +---------+
--R         |   2    2
--R     a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 49
cc2:=aa.2-bb1
 

   (6)
           +-------+
           | 2    2
         p\|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                                                            +-------+
            +---------+                                     | 2    2
            |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       - 2p\|- q  + p  atan(-----------------------------------------)
                                              2    2
                                             q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R           +-------+
--R           | 2    2
--R         p\|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                                                            +-------+
--R            +---------+                                     | 2    2
--R            |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       - 2p\|- q  + p  atan(-----------------------------------------)
--R                                              2    2
--R                                             q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 50
cc3:=aa.1-bb2
 

   (7)
           +-------+
           | 2    2
         p\|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                                                          +-------+
          +---------+                                     | 2    2
          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       2p\|- q  + p  atan(-----------------------------------------)
                                            2    2
                                           q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R           +-------+
--R           | 2    2
--R         p\|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                                                          +-------+
--R          +---------+                                     | 2    2
--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       2p\|- q  + p  atan(-----------------------------------------)
--R                                            2    2
--R                                           q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 51     14:634 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 52     14:635 Axiom cannot compute this integral
aa:=integrate(sech(a*x)^n,x)
 

           x
         ++            n
   (1)   |   sech(%T a) d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   sech(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to dpol.output (2009/2/17, 17:44:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 18
odvar:=ODVAR Symbol
 

   (1)  OrderlyDifferentialVariable Symbol
                                                                 Type: Domain
--R 
--R
--R   (1)  OrderlyDifferentialVariable Symbol
--R                                                                 Type: Domain
--E 1

--S 2 of 18
[makeVariable('w,i)$odvar for i in 5..0 by -1]
 

   (2)  [w ,w ,w ,w ,w ,w]
          5  4  3  2  1
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (2)  [w ,w ,w ,w ,w ,w]
--R          5  4  3  2  1
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 2

--S 3 of 18
sort %
 

   (3)  [w,w ,w ,w ,w ,w ]
            1  2  3  4  5
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (3)  [w,w ,w ,w ,w ,w ]
--R            1  2  3  4  5
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 3

--S 4 of 18
dpol:=DSMP (FRAC INT, Symbol, odvar)
 

   (4)
  DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDiffe
  rentialVariable Symbol)
                                                                 Type: Domain
--R 
--R
--R   (4)
--R  DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDiffe
--R  rentialVariable Symbol)
--R                                                                 Type: Domain
--E 4

--S 5 of 18
w := makeVariable('w)$dpol
 

   (5)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
Type: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--R 
--R
--R   (5)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--RType: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--E 5

--S 6 of 18
z := makeVariable('z)$dpol
 

   (6)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
Type: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--R 
--R
--R   (6)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--RType: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--E 6

--S 7 of 18
(f,b):dpol
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 18
f:=w.4::dpol - w.1 * w.1 * z.3
 

               2
   (8)  w  - w  z
         4    1  3
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R               2
--R   (8)  w  - w  z
--R         4    1  3
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 8

--S 9 of 18
b:=(z.1::dpol)**3 * (z.2)**2 - w.2
 

          3  2
   (9)  z  z   - w
         1  2     2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R          3  2
--R   (9)  z  z   - w
--R         1  2     2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 9

--S 10 of 18
lb:=leader b
 

   (10)  z
          2
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (10)  z
--R          2
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 10

--S 11 of 18
sb:=separant b
 

            3
   (11)  2z  z
           1  2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            3
--R   (11)  2z  z
--R           1  2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 11

--S 12 of 18
bprime:= differentiate b
 

            3               2  3
   (12)  2z  z z  - w  + 3z  z
           1  2 3    3     1  2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            3               2  3
--R   (12)  2z  z z  - w  + 3z  z
--R           1  2 3    3     1  2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 12

--S 13 of 18
lbprime:= leader bprime
 

   (13)  z
          3
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (13)  z
--R          3
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 13

--S 14 of 18
pbf:=differentiate (f, lbprime)
 

             2
   (14)  - w
            1
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R             2
--R   (14)  - w
--R            1
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 14

--S 15 of 18
ftilde:=sb * f- pbf * bprime
 

            3         2        2  2  3
   (15)  2z  z w  - w  w  + 3w  z  z
           1  2 4    1  3     1  1  2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            3         2        2  2  3
--R   (15)  2z  z w  - w  w  + 3w  z  z
--R           1  2 4    1  3     1  1  2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 15

--S 16 of 18
ib:=initial b
 

           3
   (16)  z
          1
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R           3
--R   (16)  z
--R          1
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 16

--S 17 of 18
lcef:=leadingCoefficient univariate(ftilde, lb)
 

            2  2
   (17)  3w  z
           1  1
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            2  2
--R   (17)  3w  z
--R           1  1
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 17

--S 18 of 18
f0:=ib * ftilde - lcef * b * lb
 

            6         2  3        2  2
   (18)  2z  z w  - w  z  w  + 3w  z  w z
           1  2 4    1  1  3     1  1  2 2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            6         2  3        2  2
--R   (18)  2z  z w  - w  z  w  + 3w  z  w z
--R           1  2 4    1  1  3     1  1  2 2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 18
)spool
 
Starts dribbling to overload.output (2009/2/17, 17:55:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 28
cos(1.237)
 

   (1)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R
--R   (1)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 1


--S 2 of 28
cos(1.237/2)
 

   (2)  0.8147490934 6341557739
                                                                  Type: Float
--R 
--R
--R   (2)  0.8147490934 6341557739
--R                                                                  Type: Float
--E 2


--S 3 of 28
cos(2/3)
 

            2
   (3)  cos(-)
            3
                                                     Type: Expression Integer
--R 
--R
--R            2
--R   (3)  cos(-)
--R            3
--R                                                     Type: Expression Integer
--E 3


--S 4 of 28
cos(2/3::Float)
 

   (4)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (4)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 4

--S 5 of 28
cos((2/3)::Float)
 

   (5)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (5)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 5

--S 6 of 28
cos(2/3$Float)
 

   (6)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (6)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 6

--S 7 of 28
cos((2/3)$Float)
 

   (7)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (7)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 7

--S 8 of 28
cos(2/3@Float)
 

   (8)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (8)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 8

--S 9 of 28
cos((2/3)@Float)
 

   (9)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (9)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 9


--S 10 of 28
cos(2/3)::Float
 
 
Daly Bug
   Cannot convert from type Expression Integer to Float for value
       2
   cos(-)
       3

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Expression Integer to Float for value
--R       2
--R   cos(-)
--R       3
--R
--E 10


--S 11 of 28
cosf(x:Expression Integer):Expression Integer == 1+cos(x/2)
 
   Function declaration cosf : Expression Integer -> Expression Integer
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration cosf : Expression Integer -> Expression Integer
--R      has been added to workspace.
--R                                                                   Type: Void
--E 11


--S 12 of 28
cosf(2/3)
 
   Compiling function cosf with type Expression Integer -> Expression 
      Integer 

             1
   (11)  cos(-) + 1
             3
                                                     Type: Expression Integer
--R 
--R   Compiling function cosf with type Expression Integer -> Expression 
--R      Integer 
--R
--R             1
--R   (11)  cos(-) + 1
--R             3
--R                                                     Type: Expression Integer
--E 12

--S 13 of 28
cosf((2/3)::Float)
 
   Conversion failed in the compiled user function cosf .
 
Daly Bug
   Cannot convert from type Float to Expression Integer for value
   0.6666666666 6666666667

--R 
--R   Conversion failed in the compiled user function cosf .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Expression Integer for value
--R   0.6666666666 6666666667
--R
--E 13


--S 14 of 28
--draw(cosf(x),x=0..15)
--E 14


--S 15 of 28
cos(2/3)+1.2323
 

   (12)  2.0181872607 769480007
                                                       Type: Expression Float
--R 
--R
--R   (12)  2.0181872607 769480007
--R                                                       Type: Expression Float
--E 15


--S 16 of 28
3/4+%pi
 

         4%pi + 3
   (13)  --------
             4
                                                                     Type: Pi
--R 
--R
--R         4%pi + 3
--R   (13)  --------
--R             4
--R                                                                     Type: Pi
--E 16


--S 17 of 28
C:=Complex Expression Integer
 

   (14)  Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (14)  Complex Expression Integer
--R                                                                 Type: Domain
--E 17

--S 18 of 28
Q:=Quaternion C
 

   (15)  Quaternion Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (15)  Quaternion Complex Expression Integer
--R                                                                 Type: Domain
--E 18


--S 19 of 28
((x:Q)/(y:Q)):Q == x*inv(y)
 
   Function declaration ?/? : (Quaternion Complex Expression Integer,
      Quaternion Complex Expression Integer) -> Quaternion Complex 
      Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration ?/? : (Quaternion Complex Expression Integer,
--R      Quaternion Complex Expression Integer) -> Quaternion Complex 
--R      Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 19


--S 20 of 28
x:=15/6
 
   Compiling function / with type (Quaternion Complex Expression 
      Integer,Quaternion Complex Expression Integer) -> Quaternion 
      Complex Expression Integer 

         5
   (17)  -
         2
                                  Type: Quaternion Complex Expression Integer
--R 
--R   Compiling function / with type (Quaternion Complex Expression 
--R      Integer,Quaternion Complex Expression Integer) -> Quaternion 
--R      Complex Expression Integer 
--R
--R         5
--R   (17)  -
--R         2
--R                                  Type: Quaternion Complex Expression Integer
--E 20


--S 21 of 28
cos(x)
 

             5
   (18)  cos(-)
             2
                                                     Type: Expression Integer
--R 
--R
--R             5
--R   (18)  cos(-)
--R             2
--R                                                     Type: Expression Integer
--E 21


--S 22 of 28
cos(1.237)
 

   (19)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R
--R   (19)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 22


--S 23 of 28
cos(15.457/6)
 
   Conversion failed in the compiled user function / .
 
Daly Bug
   Cannot convert from type Float to Quaternion Complex Expression 
      Integer for value
   15.457

--R 
--R   Conversion failed in the compiled user function / .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Quaternion Complex Expression 
--R      Integer for value
--R   15.457
--R
--E 23


--S 24 of 28
c(y:Float):Float == cos(y)
 
   Function declaration c : Float -> Float has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration c : Float -> Float has been added to workspace.
--R                                                                   Type: Void
--E 24


--S 25 of 28
c(1.237)
 
   Compiling function c with type Float -> Float 

   (21)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R   Compiling function c with type Float -> Float 
--R
--R   (21)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 25


--S 26 of 28
c(x)
 

   (22)  - 0.8011436155 4693371483
                                                                  Type: Float
--R 
--R
--R   (22)  - 0.8011436155 4693371483
--R                                                                  Type: Float
--E 26


--S 27 of 28
c(1.237/2)
 
   Conversion failed in the compiled user function / .
 
Daly Bug
   Cannot convert from type Float to Quaternion Complex Expression 
      Integer for value
   1.237

--R 
--R   Conversion failed in the compiled user function / .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Quaternion Complex Expression 
--R      Integer for value
--R   1.237
--R
--E 27


--S 28 of 28
cos(2/3::Float)
 

             2
   (23)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (23)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 28

--S 29 of 28
cos((2/3)::Float)
 

   (24)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (24)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 29

--S 30 of 28
cos(2/3$Float)
 

             2
   (25)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (25)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 30

--S 31 of 28
cos((2/3)$Float)
 

   (26)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (26)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 31

--S 32 of 28
cos(2/3@Float)
 

             2
   (27)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (27)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 32

--S 33 of 28
cos((2/3)@Float)
 
 
Daly Bug
   An expression involving @ Float actually evaluated to one of type 
      Quaternion Complex Expression Integer . Perhaps you should use ::
      Float .
--R 
--R 
--RDaly Bug
--R   An expression involving @ Float actually evaluated to one of type 
--R      Quaternion Complex Expression Integer . Perhaps you should use ::
--R      Float .
--E 33


--S 34 of 28
c(2/3::Float)
 

   (28)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (28)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 34

--S 35 of 28
c((2/3)::Float)
 

   (29)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (29)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 35

--S 36 of 28
c(2/3$Float)
 

   (30)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (30)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 36

--S 37 of 28
c((2/3)$Float)
 

   (31)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (31)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 37

--S 38 of 28
c(2/3@Float)
 

   (32)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (32)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 38

--S 39 of 28
c((2/3)@Float)
 
 
Daly Bug
   An expression involving @ Float actually evaluated to one of type 
      Quaternion Complex Expression Integer . Perhaps you should use ::
      Float .
--R 
--R 
--RDaly Bug
--R   An expression involving @ Float actually evaluated to one of type 
--R      Quaternion Complex Expression Integer . Perhaps you should use ::
--R      Float .
--E 39


--S 40 of 28
c2(y) == cos(y)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 40

--S 41 of 28
c2(1.237)
 
   Compiling function c2 with type Float -> Float 

   (34)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R   Compiling function c2 with type Float -> Float 
--R
--R   (34)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 41

--S 42 of 28
c2(x)
 
   There are 2 exposed and 6 unexposed library operations named cos 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op cos
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named cos 
      with argument type(s) 
                    Quaternion Complex Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.

             5
   (35)  cos(-)
             2
                                                     Type: Expression Integer
--R 
--R   There are 2 exposed and 6 unexposed library operations named cos 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op cos
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named cos 
--R      with argument type(s) 
--R                    Quaternion Complex Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R
--R             5
--R   (35)  cos(-)
--R             2
--R                                                     Type: Expression Integer
--E 42


--S 43 of 28
c2(1.237/2)
 
   Conversion failed in the compiled user function / .
 
Daly Bug
   Cannot convert from type Float to Quaternion Complex Expression 
      Integer for value
   1.237

--R 
--R   Conversion failed in the compiled user function / .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Quaternion Complex Expression 
--R      Integer for value
--R   1.237
--R
--E 43


--S 44 of 28
c2(2/3::Float)
 

             2
   (36)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (36)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 44

--S 45 of 28
c2((2/3)::Float)
 

   (37)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (37)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 45

--S 46 of 28
c2(2/3$Float)
 

             2
   (38)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (38)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 46

--S 47 of 28
c2((2/3)$Float)
 

   (39)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (39)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 47

--S 48 of 28
c2(2/3@Float)
 

             2
   (40)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (40)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 48

--S 49 of 28
c2((2/3)@Float)
 
 
Daly Bug
   An expression involving @ Float actually evaluated to one of type 
      Quaternion Complex Expression Integer . Perhaps you should use ::
      Float .
--R 
--R 
--RDaly Bug
--R   An expression involving @ Float actually evaluated to one of type 
--R      Quaternion Complex Expression Integer . Perhaps you should use ::
--R      Float .
--E 49


--S 50 of 28
--draw(c(x),x=0..15)
--E 50


--S 51 of 28
--draw(cos(x),x=0..15)
--E 51

)spool 
 
Starts dribbling to reclos2.output (2009/2/17, 17:57:39).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 31
LR:=radicalSolve(p^3-p+1/10=0,p)
 

   (1)
                        +------------------+2
                        |    +-+    +-----+
            +---+       |- 3\|3  + \|- 373
       (- 3\|- 3  + 3)  |------------------  - 2
                       3|         +-+
                       \|      60\|3
   [p= -----------------------------------------,
                          +------------------+
                          |    +-+    +-----+
              +---+       |- 3\|3  + \|- 373
           (3\|- 3  + 3)  |------------------
                         3|         +-+
                         \|      60\|3
                        +------------------+2
                        |    +-+    +-----+
            +---+       |- 3\|3  + \|- 373
       (- 3\|- 3  - 3)  |------------------  + 2
                       3|         +-+
                       \|      60\|3
    p= -----------------------------------------,
                          +------------------+
                          |    +-+    +-----+
              +---+       |- 3\|3  + \|- 373
           (3\|- 3  - 3)  |------------------
                         3|         +-+
                         \|      60\|3
          +------------------+2
          |    +-+    +-----+
          |- 3\|3  + \|- 373
       3  |------------------  + 1
         3|         +-+
         \|      60\|3
    p= ---------------------------]
             +------------------+
             |    +-+    +-----+
             |- 3\|3  + \|- 373
          3  |------------------
            3|         +-+
            \|      60\|3
                                       Type: List Equation Expression Integer
--R
--R   (1)
--R                        +------------------+2
--R                        |    +-+    +-----+
--R            +---+       |- 3\|3  + \|- 373
--R       (- 3\|- 3  + 3)  |------------------  - 2
--R                       3|         +-+
--R                       \|      60\|3
--R   [p= -----------------------------------------,
--R                          +------------------+
--R                          |    +-+    +-----+
--R              +---+       |- 3\|3  + \|- 373
--R           (3\|- 3  + 3)  |------------------
--R                         3|         +-+
--R                         \|      60\|3
--R                        +------------------+2
--R                        |    +-+    +-----+
--R            +---+       |- 3\|3  + \|- 373
--R       (- 3\|- 3  - 3)  |------------------  + 2
--R                       3|         +-+
--R                       \|      60\|3
--R    p= -----------------------------------------,
--R                          +------------------+
--R                          |    +-+    +-----+
--R              +---+       |- 3\|3  + \|- 373
--R           (3\|- 3  - 3)  |------------------
--R                         3|         +-+
--R                         \|      60\|3
--R          +------------------+2
--R          |    +-+    +-----+
--R          |- 3\|3  + \|- 373
--R       3  |------------------  + 1
--R         3|         +-+
--R         \|      60\|3
--R    p= ---------------------------]
--R             +------------------+
--R             |    +-+    +-----+
--R             |- 3\|3  + \|- 373
--R          3  |------------------
--R            3|         +-+
--R            \|      60\|3
--R                                       Type: List Equation Expression Integer
--E 1

--S 2 of 31
t2:=map(eq +-> (rhs eq)::Complex Float,LR)
 

   (2)
   [0.1010312578 8101081769 - 0.6 E -20 %i, - 1.0466805318 046022612,
    0.9456492739 2359144347 + 0.3 E -20 %i]
                                                     Type: List Complex Float
--R
--R   (2)
--R   [0.1010312578 8101081769 - 0.6 E -20 %i, - 1.0466805318 046022612,
--R    0.9456492739 2359144347 + 0.3 E -20 %i]
--R                                                     Type: List Complex Float
--E 2

--S 3 of 31
t3:=reduce('+, map (eq +-> (rhs eq)::Complex Float, LR))
 

   (3)  0.3 E -20 - 0.2 E -20 %i
                                                          Type: Complex Float
--R
--R   (3)  0.3 E -20 - 0.2 E -20 %i
--R                                                          Type: Complex Float
--E 3

--S 4 of 31
t4:=reduce('*, map (eq +-> (rhs eq)::Complex Float, LR))
 

   (4)  - 0.0999999999 9999999999 8 + 0.5405624429 3105340769 E -20 %i
                                                          Type: Complex Float
--R
--R   (4)  - 0.0999999999 9999999999 8 + 0.5405624429 3105340769 E -20 %i
--R                                                          Type: Complex Float
--E 4

--S 5 of 31
t5:=map(eq +-> numeric real rhs eq, LR)
 

   (5)
   [- 0.9456492739 2359144347,- 0.1010312578 8101081769,1.0466805318 046022612]
                                                             Type: List Float
--R
--R   (5)
--R   [- 0.9456492739 2359144347,- 0.1010312578 8101081769,1.0466805318 046022612]
--R                                                             Type: List Float
--E 5

--S 6 of 31
t6:=map(eq +-> numeric imag rhs eq, LR)
 

   (6)  [0.4890347001 0975238235 E -21,- 0.4890347001 0975238235 E -21,0.0]
                                                             Type: List Float
--R
--R   (6)  [0.4890347001 0975238235 E -21,- 0.4890347001 0975238235 E -21,0.0]
--R                                                             Type: List Float
--E 6

--S 7 of 31
t7:=numeric(sqrt(3)::Complex EXPR INT)
 

   (7)  1.7320508075 688772935
                                                                  Type: Float
--R
--R   (7)  1.7320508075 688772935
--R                                                                  Type: Float
--E 7

--S 8 of 31
t8:=discriminant(p^3-p+1/10)
 

        373
   (8)  ---
        100
                                                       Type: Fraction Integer
--R
--R        373
--R   (8)  ---
--R        100
--R                                                       Type: Fraction Integer
--E 8

--S 9 of 31
t9:=select(p+->rhs(p)::AlgebraicNumber > 0, radicalSolve(p^3-p+1/10=0,p))
 

                             +------------------+2
                             |    +-+    +-----+
                 +---+       |- 3\|3  + \|- 373
            (- 3\|- 3  - 3)  |------------------  + 2
                            3|         +-+
                            \|      60\|3
   (9)  [p= -----------------------------------------]
                               +------------------+
                               |    +-+    +-----+
                   +---+       |- 3\|3  + \|- 373
                (3\|- 3  - 3)  |------------------
                              3|         +-+
                              \|      60\|3
                                       Type: List Equation Expression Integer
--R
--R                             +------------------+2
--R                             |    +-+    +-----+
--R                 +---+       |- 3\|3  + \|- 373
--R            (- 3\|- 3  - 3)  |------------------  + 2
--R                            3|         +-+
--R                            \|      60\|3
--R   (9)  [p= -----------------------------------------]
--R                               +------------------+
--R                               |    +-+    +-----+
--R                   +---+       |- 3\|3  + \|- 373
--R                (3\|- 3  - 3)  |------------------
--R                              3|         +-+
--R                              \|      60\|3
--R                                       Type: List Equation Expression Integer
--E 9

--S 10 of 31
t10:=complexNumeric rhs t9.1
 

   (10)  - 1.0466805318 046022612
                                                          Type: Complex Float
--R
--R   (10)  - 1.0466805318 046022612
--R                                                          Type: Complex Float
--E 10

--S 11 of 31
t11:=select(p+->rhs(p)::AN < 0, radicalSolve(p^2-p+1/10=0,p))
 

                +--+
             - \|15  + 5
   (11)  [p= -----------]
                  10
                                       Type: List Equation Expression Integer
--R
--R                +--+
--R             - \|15  + 5
--R   (11)  [p= -----------]
--R                  10
--R                                       Type: List Equation Expression Integer
--E 11

--S 12 of 31
t12:=p^3-p+1/10
 

          3        1
   (12)  p  - p + --
                  10
                                            Type: Polynomial Fraction Integer
--R
--R          3        1
--R   (12)  p  - p + --
--R                  10
--R                                            Type: Polynomial Fraction Integer
--E 12

--S 13 of 31
t13:=select(positive?,allRootsOf(t12)$RealClosure(Fraction Integer))
 

   (13)  [%B2,%B3]
                                      Type: List RealClosure Fraction Integer
--R
--I   (13)  [%B2,%B3]
--R                                      Type: List RealClosure Fraction Integer
--E 13

--S 14 of 31
t14:=approximate(t13.1,1/10^20)::Float
 

   (14)  0.1010312578 8101081769
                                                                  Type: Float
--R
--R   (14)  0.1010312578 8101081769
--R                                                                  Type: Float
--E 14

--S 15 of 31
t15:=eval(t12,p=t14)
 

   (15)  0.3 E -20
                                                       Type: Polynomial Float
--R
--R   (15)  0.3 E -20
--R                                                       Type: Polynomial Float
--E 15

--S 16 of 31
t16:=approximate(t13.2,1/10^20)::Float
 

   (16)  0.9456492739 2359144347
                                                                  Type: Float
--R
--R   (16)  0.9456492739 2359144347
--R                                                                  Type: Float
--E 16

--S 17 of 31
t17:=eval(t12,p=t16)
 

   (17)  0.1 E -20
                                                       Type: Polynomial Float
--R
--R   (17)  0.1 E -20
--R                                                       Type: Polynomial Float
--E 17

)clear all
 
   All user variables and function definitions have been cleared.
--S 18 of 31
t1:=(x^3+x^2-4*x-4)/(2*x^2+7*x-4)
 

         3    2
        x  + x  - 4x - 4
   (1)  ----------------
            2
          2x  + 7x - 4
                                            Type: Fraction Polynomial Integer
--R
--R         3    2
--R        x  + x  - 4x - 4
--R   (1)  ----------------
--R            2
--R          2x  + 7x - 4
--R                                            Type: Fraction Polynomial Integer
--E 18

--S 19 of 31
t2:=differentiate(t1,x)
 

           4      3     2
         2x  + 14x  + 3x  + 8x + 44
   (2)  ----------------------------
          4      3      2
        4x  + 28x  + 33x  - 56x + 16
                                            Type: Fraction Polynomial Integer
--R
--R           4      3     2
--R         2x  + 14x  + 3x  + 8x + 44
--R   (2)  ----------------------------
--R          4      3      2
--R        4x  + 28x  + 33x  - 56x + 16
--R                                            Type: Fraction Polynomial Integer
--E 19

--S 20 of 31
t3:=allRootsOf(numer t2)$RealClosure(Fraction Integer)
 

   (3)  [%B4,%B5]
                                      Type: List RealClosure Fraction Integer
--R
--I   (3)  [%B4,%B5]
--R                                      Type: List RealClosure Fraction Integer
--E 20

--S 21 of 31
t4:=approximate(t3.1,1/10^20)::Float
 

   (4)  - 6.7957899636 620037966
                                                                  Type: Float
--R
--R   (4)  - 6.7957899636 620037966
--R                                                                  Type: Float
--E 21

--S 22 of 31
t5:=eval(t2,x=t4)
 

   (5)  0.3908839188 6520300529 E -20
                                              Type: Fraction Polynomial Float
--R
--R   (5)  0.3908839188 6520300529 E -20
--R                                              Type: Fraction Polynomial Float
--E 22

--S 23 of 31
t6:=approximate(t3.2,1/10^20)::Float
 

   (6)  - 1.5241463459 294127043
                                                                  Type: Float
--R
--R   (6)  - 1.5241463459 294127043
--R                                                                  Type: Float
--E 23

--S 24 of 31
t7:=eval(t2,x=t6)
 

   (7)  - 0.2158472497 0513415786 E -20
                                              Type: Fraction Polynomial Float
--R
--R   (7)  - 0.2158472497 0513415786 E -20
--R                                              Type: Fraction Polynomial Float
--E 24

)clear all
 
   All user variables and function definitions have been cleared.

--S 25 of 31
t1:=(x^3+x^2-4*x-4)/(2*x^2+7*x-4)
 

         3    2
        x  + x  - 4x - 4
   (1)  ----------------
            2
          2x  + 7x - 4
                                            Type: Fraction Polynomial Integer
--R
--R         3    2
--R        x  + x  - 4x - 4
--R   (1)  ----------------
--R            2
--R          2x  + 7x - 4
--R                                            Type: Fraction Polynomial Integer
--E 25

--S 26 of 31
t2:=differentiate(t1,x)
 

           4      3     2
         2x  + 14x  + 3x  + 8x + 44
   (2)  ----------------------------
          4      3      2
        4x  + 28x  + 33x  - 56x + 16
                                            Type: Fraction Polynomial Integer
--R
--R           4      3     2
--R         2x  + 14x  + 3x  + 8x + 44
--R   (2)  ----------------------------
--R          4      3      2
--R        4x  + 28x  + 33x  - 56x + 16
--R                                            Type: Fraction Polynomial Integer
--E 26

--S 27 of 31
t3:=allRootsOf(numer t2)$RealClosure(Fraction Integer)
 

   (3)  [%B6,%B7]
                                      Type: List RealClosure Fraction Integer
--R
--I   (3)  [%B6,%B7]
--R                                      Type: List RealClosure Fraction Integer
--E 27

--S 28 of 31
t4:=radicalSolve(t2)
 

   (4)
   [
     x =
           -
                2
             *
                ROOT
                              +----------------+2      +----------------+
                             3|    +---+              3|    +---+
                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                      *
                          +---------------------------------------------------+
                          |  +----------------+2      +----------------+
                          | 3|    +---+              3|    +---+
                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                          |---------------------------------------------------
                          |                  +----------------+
                          |                 3|    +---+
                         \|                4\|324\|145  + 3969
                     + 
                             +----------------+
                            3|    +---+
                       - 333\|324\|145  + 3969
                  /
                         +----------------+
                        3|    +---+
                       4\|324\|145  + 3969
                    *
                        +---------------------------------------------------+
                        |  +----------------+2      +----------------+
                        | 3|    +---+              3|    +---+
                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                        |---------------------------------------------------
                        |                  +----------------+
                        |                 3|    +---+
                       \|                4\|324\|145  + 3969
         + 
             +---------------------------------------------------+
             |  +----------------+2      +----------------+
             | 3|    +---+              3|    +---+
             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           2 |---------------------------------------------------  - 7
             |                  +----------------+
             |                 3|    +---+
            \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
             2
          *
             ROOT
                           +----------------+2      +----------------+
                          3|    +---+              3|    +---+
                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                   *
                       +---------------------------------------------------+
                       |  +----------------+2      +----------------+
                       | 3|    +---+              3|    +---+
                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                       |---------------------------------------------------
                       |                  +----------------+
                       |                 3|    +---+
                      \|                4\|324\|145  + 3969
                  + 
                          +----------------+
                         3|    +---+
                    - 333\|324\|145  + 3969
               /
                      +----------------+
                     3|    +---+
                    4\|324\|145  + 3969
                 *
                     +---------------------------------------------------+
                     |  +----------------+2      +----------------+
                     | 3|    +---+              3|    +---+
                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                     |---------------------------------------------------
                     |                  +----------------+
                     |                 3|    +---+
                    \|                4\|324\|145  + 3969
         + 
             +---------------------------------------------------+
             |  +----------------+2      +----------------+
             | 3|    +---+              3|    +---+
             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           2 |---------------------------------------------------  - 7
             |                  +----------------+
             |                 3|    +---+
            \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
           -
                2
             *
                ROOT
                              +----------------+2      +----------------+
                             3|    +---+              3|    +---+
                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                      *
                          +---------------------------------------------------+
                          |  +----------------+2      +----------------+
                          | 3|    +---+              3|    +---+
                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                          |---------------------------------------------------
                          |                  +----------------+
                          |                 3|    +---+
                         \|                4\|324\|145  + 3969
                     + 
                           +----------------+
                          3|    +---+
                       333\|324\|145  + 3969
                  /
                         +----------------+
                        3|    +---+
                       4\|324\|145  + 3969
                    *
                        +---------------------------------------------------+
                        |  +----------------+2      +----------------+
                        | 3|    +---+              3|    +---+
                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                        |---------------------------------------------------
                        |                  +----------------+
                        |                 3|    +---+
                       \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
             2
          *
             ROOT
                           +----------------+2      +----------------+
                          3|    +---+              3|    +---+
                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                   *
                       +---------------------------------------------------+
                       |  +----------------+2      +----------------+
                       | 3|    +---+              3|    +---+
                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                       |---------------------------------------------------
                       |                  +----------------+
                       |                 3|    +---+
                      \|                4\|324\|145  + 3969
                  + 
                        +----------------+
                       3|    +---+
                    333\|324\|145  + 3969
               /
                      +----------------+
                     3|    +---+
                    4\|324\|145  + 3969
                 *
                     +---------------------------------------------------+
                     |  +----------------+2      +----------------+
                     | 3|    +---+              3|    +---+
                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                     |---------------------------------------------------
                     |                  +----------------+
                     |                 3|    +---+
                    \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ]
                                       Type: List Equation Expression Integer
--R
--R   (4)
--R   [
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                              +----------------+2      +----------------+
--R                             3|    +---+              3|    +---+
--R                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                      *
--R                          +---------------------------------------------------+
--R                          |  +----------------+2      +----------------+
--R                          | 3|    +---+              3|    +---+
--R                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                          |---------------------------------------------------
--R                          |                  +----------------+
--R                          |                 3|    +---+
--R                         \|                4\|324\|145  + 3969
--R                     + 
--R                             +----------------+
--R                            3|    +---+
--R                       - 333\|324\|145  + 3969
--R                  /
--R                         +----------------+
--R                        3|    +---+
--R                       4\|324\|145  + 3969
--R                    *
--R                        +---------------------------------------------------+
--R                        |  +----------------+2      +----------------+
--R                        | 3|    +---+              3|    +---+
--R                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                        |---------------------------------------------------
--R                        |                  +----------------+
--R                        |                 3|    +---+
--R                       \|                4\|324\|145  + 3969
--R         + 
--R             +---------------------------------------------------+
--R             |  +----------------+2      +----------------+
--R             | 3|    +---+              3|    +---+
--R             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           2 |---------------------------------------------------  - 7
--R             |                  +----------------+
--R             |                 3|    +---+
--R            \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                           +----------------+2      +----------------+
--R                          3|    +---+              3|    +---+
--R                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                   *
--R                       +---------------------------------------------------+
--R                       |  +----------------+2      +----------------+
--R                       | 3|    +---+              3|    +---+
--R                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                       |---------------------------------------------------
--R                       |                  +----------------+
--R                       |                 3|    +---+
--R                      \|                4\|324\|145  + 3969
--R                  + 
--R                          +----------------+
--R                         3|    +---+
--R                    - 333\|324\|145  + 3969
--R               /
--R                      +----------------+
--R                     3|    +---+
--R                    4\|324\|145  + 3969
--R                 *
--R                     +---------------------------------------------------+
--R                     |  +----------------+2      +----------------+
--R                     | 3|    +---+              3|    +---+
--R                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                     |---------------------------------------------------
--R                     |                  +----------------+
--R                     |                 3|    +---+
--R                    \|                4\|324\|145  + 3969
--R         + 
--R             +---------------------------------------------------+
--R             |  +----------------+2      +----------------+
--R             | 3|    +---+              3|    +---+
--R             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           2 |---------------------------------------------------  - 7
--R             |                  +----------------+
--R             |                 3|    +---+
--R            \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                              +----------------+2      +----------------+
--R                             3|    +---+              3|    +---+
--R                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                      *
--R                          +---------------------------------------------------+
--R                          |  +----------------+2      +----------------+
--R                          | 3|    +---+              3|    +---+
--R                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                          |---------------------------------------------------
--R                          |                  +----------------+
--R                          |                 3|    +---+
--R                         \|                4\|324\|145  + 3969
--R                     + 
--R                           +----------------+
--R                          3|    +---+
--R                       333\|324\|145  + 3969
--R                  /
--R                         +----------------+
--R                        3|    +---+
--R                       4\|324\|145  + 3969
--R                    *
--R                        +---------------------------------------------------+
--R                        |  +----------------+2      +----------------+
--R                        | 3|    +---+              3|    +---+
--R                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                        |---------------------------------------------------
--R                        |                  +----------------+
--R                        |                 3|    +---+
--R                       \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                           +----------------+2      +----------------+
--R                          3|    +---+              3|    +---+
--R                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                   *
--R                       +---------------------------------------------------+
--R                       |  +----------------+2      +----------------+
--R                       | 3|    +---+              3|    +---+
--R                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                       |---------------------------------------------------
--R                       |                  +----------------+
--R                       |                 3|    +---+
--R                      \|                4\|324\|145  + 3969
--R                  + 
--R                        +----------------+
--R                       3|    +---+
--R                    333\|324\|145  + 3969
--R               /
--R                      +----------------+
--R                     3|    +---+
--R                    4\|324\|145  + 3969
--R                 *
--R                     +---------------------------------------------------+
--R                     |  +----------------+2      +----------------+
--R                     | 3|    +---+              3|    +---+
--R                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                     |---------------------------------------------------
--R                     |                  +----------------+
--R                     |                 3|    +---+
--R                    \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ]
--R                                       Type: List Equation Expression Integer
--E 28

--S 29 of 31
bound?(x,s) == (a:=complexNumeric rhs x; imag a < 10^-digits() and real a >= left(mainCharacterization s)::Float and real a < right(mainCharacterization s)::Float)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 29

--S 30 of 31
t6:=[ (B:=select(x+->bound?(x,s),t4); #B=1 => B.1; error "failed") for s in t3 ]
 
   Compiling function bound? with type (Equation Expression Integer,
      RealClosure Fraction Integer) -> Boolean 

   (6)
   [
     x =
           -
                2
             *
                ROOT
                              +----------------+2      +----------------+
                             3|    +---+              3|    +---+
                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                      *
                          +---------------------------------------------------+
                          |  +----------------+2      +----------------+
                          | 3|    +---+              3|    +---+
                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                          |---------------------------------------------------
                          |                  +----------------+
                          |                 3|    +---+
                         \|                4\|324\|145  + 3969
                     + 
                           +----------------+
                          3|    +---+
                       333\|324\|145  + 3969
                  /
                         +----------------+
                        3|    +---+
                       4\|324\|145  + 3969
                    *
                        +---------------------------------------------------+
                        |  +----------------+2      +----------------+
                        | 3|    +---+              3|    +---+
                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                        |---------------------------------------------------
                        |                  +----------------+
                        |                 3|    +---+
                       \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
             2
          *
             ROOT
                           +----------------+2      +----------------+
                          3|    +---+              3|    +---+
                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                   *
                       +---------------------------------------------------+
                       |  +----------------+2      +----------------+
                       | 3|    +---+              3|    +---+
                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                       |---------------------------------------------------
                       |                  +----------------+
                       |                 3|    +---+
                      \|                4\|324\|145  + 3969
                  + 
                        +----------------+
                       3|    +---+
                    333\|324\|145  + 3969
               /
                      +----------------+
                     3|    +---+
                    4\|324\|145  + 3969
                 *
                     +---------------------------------------------------+
                     |  +----------------+2      +----------------+
                     | 3|    +---+              3|    +---+
                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                     |---------------------------------------------------
                     |                  +----------------+
                     |                 3|    +---+
                    \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ]
                                       Type: List Equation Expression Integer
--R   Compiling function bound? with type (Equation Expression Integer,
--R      RealClosure Fraction Integer) -> Boolean 
--R
--R   (6)
--R   [
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                              +----------------+2      +----------------+
--R                             3|    +---+              3|    +---+
--R                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                      *
--R                          +---------------------------------------------------+
--R                          |  +----------------+2      +----------------+
--R                          | 3|    +---+              3|    +---+
--R                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                          |---------------------------------------------------
--R                          |                  +----------------+
--R                          |                 3|    +---+
--R                         \|                4\|324\|145  + 3969
--R                     + 
--R                           +----------------+
--R                          3|    +---+
--R                       333\|324\|145  + 3969
--R                  /
--R                         +----------------+
--R                        3|    +---+
--R                       4\|324\|145  + 3969
--R                    *
--R                        +---------------------------------------------------+
--R                        |  +----------------+2      +----------------+
--R                        | 3|    +---+              3|    +---+
--R                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                        |---------------------------------------------------
--R                        |                  +----------------+
--R                        |                 3|    +---+
--R                       \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                           +----------------+2      +----------------+
--R                          3|    +---+              3|    +---+
--R                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                   *
--R                       +---------------------------------------------------+
--R                       |  +----------------+2      +----------------+
--R                       | 3|    +---+              3|    +---+
--R                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                       |---------------------------------------------------
--R                       |                  +----------------+
--R                       |                 3|    +---+
--R                      \|                4\|324\|145  + 3969
--R                  + 
--R                        +----------------+
--R                       3|    +---+
--R                    333\|324\|145  + 3969
--R               /
--R                      +----------------+
--R                     3|    +---+
--R                    4\|324\|145  + 3969
--R                 *
--R                     +---------------------------------------------------+
--R                     |  +----------------+2      +----------------+
--R                     | 3|    +---+              3|    +---+
--R                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                     |---------------------------------------------------
--R                     |                  +----------------+
--R                     |                 3|    +---+
--R                    \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ]
--R                                       Type: List Equation Expression Integer
--E 30

--S 31 of 31
t7:=map(x+->real complexNumeric rhs x,t6)
 

   (7)  [- 6.7957899636 620037966,- 1.5241463459 294127044]
                                                             Type: List Float
--R
--R   (7)  [- 6.7957899636 620037966,- 1.5241463459 294127044]
--R                                                             Type: List Float
--E 31

)spool 
 
Starts dribbling to opalg.output (2009/2/17, 17:55:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 9
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 9
L 5
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

        63  5   35  3   15
   (2)  -- x  - -- x  + -- x
         8       4       8
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R        63  5   35  3   15
--R   (2)  -- x  - -- x  + -- x
--R         8       4       8
--R                                            Type: Polynomial Fraction Integer
--E 2

--S 3 of 9
dx := operator("D")::OP(POLY FRAC INT)
 

   (3)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (3)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 3

--S 4 of 9
evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT)
 

   (4)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (4)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 4

--S 5 of 9
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 9
E 5
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                      2      2
   (6)  30 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                      2      2
--R   (6)  30 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 6

--S 7 of 9
[L i for i in 1..10]
 

   (7)
       3  2   1  5  3   3    35  4   15  2   3  63  5   35  3   15
   [x, - x  - -, - x  - - x, -- x  - -- x  + -, -- x  - -- x  + -- x,
       2      2  2      2     8       4      8   8       4       8
    231  6   315  4   105  2    5  429  7   693  5   315  3   35
    --- x  - --- x  + --- x  - --, --- x  - --- x  + --- x  - -- x,
     16       16       16      16   16       16       16      16
    6435  8   3003  6   3465  4   315  2    35
    ---- x  - ---- x  + ---- x  - --- x  + ---,
     128       32        64        32      128
    12155  9   6435  7   9009  5   1155  3   315
    ----- x  - ---- x  + ---- x  - ---- x  + --- x,
     128        32        64        32       128
    46189  10   109395  8   45045  6   15015  4   3465  2    63
    ----- x   - ------ x  + ----- x  - ----- x  + ---- x  - ---]
     256          256        128        128        256      256
                                       Type: List Polynomial Fraction Integer
--R 
--R
--R   (7)
--R       3  2   1  5  3   3    35  4   15  2   3  63  5   35  3   15
--R   [x, - x  - -, - x  - - x, -- x  - -- x  + -, -- x  - -- x  + -- x,
--R       2      2  2      2     8       4      8   8       4       8
--R    231  6   315  4   105  2    5  429  7   693  5   315  3   35
--R    --- x  - --- x  + --- x  - --, --- x  - --- x  + --- x  - -- x,
--R     16       16       16      16   16       16       16      16
--R    6435  8   3003  6   3465  4   315  2    35
--R    ---- x  - ---- x  + ---- x  - --- x  + ---,
--R     128       32        64        32      128
--R    12155  9   6435  7   9009  5   1155  3   315
--R    ----- x  - ---- x  + ---- x  - ---- x  + --- x,
--R     128        32        64        32       128
--R    46189  10   109395  8   45045  6   15015  4   3465  2    63
--R    ----- x   - ------ x  + ----- x  - ----- x  + ---- x  - ---]
--R     256          256        128        128        256      256
--R                                       Type: List Polynomial Fraction Integer
--E 7

--S 8 of 9
[E i for i in 1..10]
 

   (8)
                 2      2               2      2                2      2
   [2 - 2x D - (x  - 1)D , 6 - 2x D - (x  - 1)D , 12 - 2x D - (x  - 1)D ,
                  2      2                2      2                2      2
    20 - 2x D - (x  - 1)D , 30 - 2x D - (x  - 1)D , 42 - 2x D - (x  - 1)D ,
                  2      2                2      2                2      2
    56 - 2x D - (x  - 1)D , 72 - 2x D - (x  - 1)D , 90 - 2x D - (x  - 1)D ,
                   2      2
    110 - 2x D - (x  - 1)D ]
                              Type: List Operator Polynomial Fraction Integer
--R 
--R
--R   (8)
--R                 2      2               2      2                2      2
--R   [2 - 2x D - (x  - 1)D , 6 - 2x D - (x  - 1)D , 12 - 2x D - (x  - 1)D ,
--R                  2      2                2      2                2      2
--R    20 - 2x D - (x  - 1)D , 30 - 2x D - (x  - 1)D , 42 - 2x D - (x  - 1)D ,
--R                  2      2                2      2                2      2
--R    56 - 2x D - (x  - 1)D , 72 - 2x D - (x  - 1)D , 90 - 2x D - (x  - 1)D ,
--R                   2      2
--R    110 - 2x D - (x  - 1)D ]
--R                              Type: List Operator Polynomial Fraction Integer
--E 8

--S 9 of 9
[(E i)(L i) for i in 1..10]
 

   (9)  [0,0,0,0,0,0,0,0,0,0]
                                       Type: List Polynomial Fraction Integer
--R 
--R
--R   (9)  [0,0,0,0,0,0,0,0,0,0]
--R                                       Type: List Polynomial Fraction Integer
--E 9
)spool 
 
Starts dribbling to parabola.output (2009/2/17, 17:55:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1
draw(curve(t**2 + 2*t - 1,t**2 + t - 2),t = -4..3)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (1)  TwoDimensionalViewport: "t*t+2*t-1"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Compiling function %D with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (1)  TwoDimensionalViewport: "t*t+2*t-1"
--R                                                 Type: TwoDimensionalViewport
--E 1
)spool 
 
Starts dribbling to eqtbl.output (2009/2/17, 17:45:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 6
e: EqTable(List Integer, Integer) := table()
 

   (1)  table()
                                          Type: EqTable(List Integer,Integer)
--R 
--R
--R   (1)  table()
--R                                          Type: EqTable(List Integer,Integer)
--E 1

--S 2 of 6
l1 := [1,2,3]
 

   (2)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 6
l2 := [1,2,3]
 

   (3)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 3

--S 4 of 6
e.l1 := 111
 

   (4)  111
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  111
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 6
e.l2 := 222
 

   (5)  222
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  222
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 6
e.l1
 

   (6)  111
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  111
--R                                                        Type: PositiveInteger
--E 6
)spool
 
Starts dribbling to ifact.output (2009/2/17, 17:46:29).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 7
factor(3**17-1)
 

   (1)  2 1871 34511
                                                       Type: Factored Integer
--R 
--R
--R   (1)  2 1871 34511
--R                                                       Type: Factored Integer
--E 1

--S 2 of 7
factor(3**23-1)
 

   (2)  2 47 1001523179
                                                       Type: Factored Integer
--R 
--R
--R   (2)  2 47 1001523179
--R                                                       Type: Factored Integer
--E 2

--S 3 of 7
factor(3**31-1)
 

   (3)  2 683 102673 4404047
                                                       Type: Factored Integer
--R 
--R
--R   (3)  2 683 102673 4404047
--R                                                       Type: Factored Integer
--E 3

--S 4 of 7
factor(3**41-1)
 

   (4)  2 83 2526913 86950696619
                                                       Type: Factored Integer
--R 
--R
--R   (4)  2 83 2526913 86950696619
--R                                                       Type: Factored Integer
--E 4

--S 5 of 7
factor(3**53-1)
 

   (5)  2 107 24169 3747607031112307667
                                                       Type: Factored Integer
--R 
--R
--R   (5)  2 107 24169 3747607031112307667
--R                                                       Type: Factored Integer
--E 5

--S 6 of 7
factor(111111111111111111111111)
 

   (6)  3 7 11 13 37 73 101 137 9901 99990001
                                                       Type: Factored Integer
--R 
--R
--R   (6)  3 7 11 13 37 73 101 137 9901 99990001
--R                                                       Type: Factored Integer
--E 6

--S 7 of 7
factor(11111111111111111111111111111111111111111111111)
 

   (7)  35121409 316362908763458525001406154038726382279
                                                       Type: Factored Integer
--R 
--R
--R   (7)  35121409 316362908763458525001406154038726382279
--R                                                       Type: Factored Integer
--E 7
)spool 
 
Starts dribbling to derham.output (2009/2/17, 17:44:39).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 33
coefRing := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 33
lv : List Symbol := [x,y,z]
 

   (2)  [x,y,z]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z]
--R                                                            Type: List Symbol
--E 2

--S 3 of 33
der := DERHAM(coefRing,lv)
 

   (3)  DeRhamComplex(Integer,[x,y,z])
                                                                 Type: Domain
--R 
--R
--R   (3)  DeRhamComplex(Integer,[x,y,z])
--R                                                                 Type: Domain
--E 3

--S 4 of 33
R := Expression coefRing
 

   (4)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (4)  Expression Integer
--R                                                                 Type: Domain
--E 4

--S 5 of 33
f : R := x**2*y*z-5*x**3*y**2*z**5
 

            3 2 5    2
   (5)  - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3 2 5    2
--R   (5)  - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 5

--S 6 of 33
g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2
 

            2     3 2       2
   (6)  - 7z sin(x y ) + y z cos(z)
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2
--R   (6)  - 7z sin(x y ) + y z cos(z)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 33
h : R :=x*y*z-2*x**3*y*z**2
 

            3   2
   (7)  - 2x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3   2
--R   (7)  - 2x y z  + x y z
--R                                                     Type: Expression Integer
--E 7

--S 8 of 33
dx : der := generator(1)
 

   (8)  dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (8)  dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 8

--S 9 of 33
dy : der := generator(2)
 

   (9)  dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (9)  dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 9

--S 10 of 33
dz : der := generator(3)
 

   (10)  dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (10)  dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 10

--S 11 of 33
[dx,dy,dz] := [generator(i)$der for i in 1..3]
 

   (11)  [dx,dy,dz]
                                    Type: List DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (11)  [dx,dy,dz]
--R                                    Type: List DeRhamComplex(Integer,[x,y,z])
--E 11

--S 12 of 33
alpha : der := f*dx + g*dy + h*dz
 

   (12)
          3   2                   2     3 2       2
     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
   + 
          3 2 5    2
     (- 5x y z  + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (12)
--R          3   2                   2     3 2       2
--R     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
--R   + 
--R          3 2 5    2
--R     (- 5x y z  + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 12

--S 13 of 33
beta  : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy
 

   (13)  x dy + cos(tan(x y z) + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (13)  x dy + cos(tan(x y z) + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 13

--S 14 of 33
exteriorDifferential alpha;
 

                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 14

--S 15 of 33
exteriorDifferential %
 

   (15)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (15)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 15

--S 16 of 33
gamma := alpha * beta
 

   (16)
        4   2    2               3   2
     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
   + 
       2     3 2       2                                   4 2 5    3
   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (16)
--R        4   2    2               3   2
--R     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
--R   + 
--R       2     3 2       2                                   4 2 5    3
--R   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 16

--S 17 of 33
exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))
 

   (17)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (17)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 17

--S 18 of 33
a : BOP := operator('a)
 

   (18)  a
                                                          Type: BasicOperator
--R 
--R
--R   (18)  a
--R                                                          Type: BasicOperator
--E 18

--S 19 of 33
b : BOP := operator('b)
 

   (19)  b
                                                          Type: BasicOperator
--R 
--R
--R   (19)  b
--R                                                          Type: BasicOperator
--E 19

--S 20 of 33
c : BOP := operator('c)
 

   (20)  c
                                                          Type: BasicOperator
--R 
--R
--R   (20)  c
--R                                                          Type: BasicOperator
--E 20

--S 21 of 33
sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz
 

   (21)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (21)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 21

--S 22 of 33
theta  := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz
 

   (22)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (22)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 22

--S 23 of 33
totalDifferential(a(x,y,z))$der
 

   (23)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
          ,3             ,2             ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (23)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
--R          ,3             ,2             ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 23

--S 24 of 33
exteriorDifferential sigma
 

   (24)
     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
       ,2           ,3                  ,1           ,3
   + 
     (b  (x,y,z) - a  (x,y,z))dx dy
       ,1           ,2
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (24)
--R     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
--R       ,2           ,3                  ,1           ,3
--R   + 
--R     (b  (x,y,z) - a  (x,y,z))dx dy
--R       ,1           ,2
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 24

--S 25 of 33
exteriorDifferential theta
 

   (25)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
           ,1           ,2           ,3
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (25)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
--R           ,1           ,2           ,3
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 25

--S 26 of 33
one : der := 1
 

   (26)  1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (26)  1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 26

--S 27 of 33
g1 : der := a([x,t,y,u,v,z,e]) * one
 

   (27)  a(x,t,y,u,v,z,e)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (27)  a(x,t,y,u,v,z,e)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 27

--S 28 of 33
h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one
 

   (28)  a(x,y,x,t,x,z,y,r,u,x)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (28)  a(x,y,x,t,x,z,y,r,u,x)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 28

--S 29 of 33
exteriorDifferential g1
 

   (29)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
          ,6                     ,3                     ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (29)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
--R          ,6                     ,3                     ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 29

--S 30 of 33
exteriorDifferential h1
 

   (30)
     a  (x,y,x,t,x,z,y,r,u,x)dz
      ,6
   + 
     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
       ,7                         ,2
   + 
         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,10                         ,5
       + 
         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,3                         ,1
    *
       dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (30)
--R     a  (x,y,x,t,x,z,y,r,u,x)dz
--R      ,6
--R   + 
--R     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
--R       ,7                         ,2
--R   + 
--R         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,10                         ,5
--R       + 
--R         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,3                         ,1
--R    *
--R       dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 30

--S 31 of 33
coefficient(gamma, dx*dy)
 

            2     3 2       2                                   4 2 5    3
   (31)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2                                   4 2 5    3
--R   (31)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 31

--S 32 of 33
coefficient(gamma, one)
 

   (32)  0
                                                     Type: Expression Integer
--R 
--R
--R   (32)  0
--R                                                     Type: Expression Integer
--E 32

--S 33 of 33
coefficient(g1,one)
 

   (33)  a(x,t,y,u,v,z,e)
                                                     Type: Expression Integer
--R 
--R
--R   (33)  a(x,t,y,u,v,z,e)
--R                                                     Type: Expression Integer
--E 33
)spool
 
Starts dribbling to radff.output (2009/2/17, 17:57:27).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 27
P0 := UP(x, INT)
 

   (1)  UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 27
P1 := UP(y, FRAC P0)
 

   (2)  UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 2

--S 3 of 27
R := RADFF(INT, P0, P1, 1 - x**20, 20)
 

   (3)
  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
  mial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
                                                                 Type: Domain
--R 
--R
--R   (3)
--R  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
--R  mial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--R                                                                 Type: Domain
--E 3

--S 4 of 27
definingPolynomial()$R
 

         20    20
   (4)  y   + x   - 1
       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R         20    20
--R   (4)  y   + x   - 1
--R       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--E 4

--S 5 of 27
genus()$R
 

   (5)  171
                                                     Type: NonNegativeInteger
--R 
--R
--R   (5)  171
--R                                                     Type: NonNegativeInteger
--E 5

--S 6 of 27
rank()$R
 

   (6)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  20
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 27
numberOfComponents()$R
 

   (7)  1
                                                     Type: NonNegativeInteger
--R 
--R
--R   (7)  1
--R                                                     Type: NonNegativeInteger
--E 7

--S 8 of 27
integralBasisAtInfinity()$R
 

   (8)
       1     1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9   1   10
   [1, - y, -- y , -- y , -- y , -- y , -- y , -- y , -- y , -- y , --- y  ,
       x     2      3      4      5      6      7      8      9      10
            x      x      x      x      x      x      x      x      x
     1   11   1   12   1   13   1   14   1   15   1   16   1   17   1   18
    --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  ,
     11       12       13       14       15       16       17       18
    x        x        x        x        x        x        x        x
     1   19
    --- y  ]
     19
    x
Type: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--R 
--R
--R   (8)
--R       1     1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9   1   10
--R   [1, - y, -- y , -- y , -- y , -- y , -- y , -- y , -- y , -- y , --- y  ,
--R       x     2      3      4      5      6      7      8      9      10
--R            x      x      x      x      x      x      x      x      x
--R     1   11   1   12   1   13   1   14   1   15   1   16   1   17   1   18
--R    --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  ,
--R     11       12       13       14       15       16       17       18
--R    x        x        x        x        x        x        x        x
--R     1   19
--R    --- y  ]
--R     19
--R    x
--RType: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--E 8

--S 9 of 27
branchPoint?(0)$R
 

   (9)  false
                                                                Type: Boolean
--R 
--R
--R   (9)  false
--R                                                                Type: Boolean
--E 9

--S 10 of 27
branchPoint?(1)$R
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 27
y := generator()$R
 

   (11)  y
Type: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--R 
--R
--R   (11)  y
--RType: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--E 11

--S 12 of 27
norm y
 

          20
   (12)  x   - 1
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          20
--R   (12)  x   - 1
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 12

--S 13 of 27
trace y
 

   (13)  0
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)  0
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 27
R2 := RADFF(INT, P0, P1, 2 * x**2, 4)
 

   (14)
  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
  mial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
                                                                 Type: Domain
--R 
--R
--R   (14)
--R  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
--R  mial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R                                                                 Type: Domain
--E 14

--S 15 of 27
definingPolynomial()$R2
 

          4     2
   (15)  y  - 2x
       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R          4     2
--R   (15)  y  - 2x
--R       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--E 15

--S 16 of 27
rank()$R2
 

   (16)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  4
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 27
absolutelyIrreducible?()$R2
 

   (17)  false
                                                                Type: Boolean
--R 
--R
--R   (17)  false
--R                                                                Type: Boolean
--E 17

--S 18 of 27
numberOfComponents()$R2
 

   (18)  2
                                                     Type: NonNegativeInteger
--R 
--R
--R   (18)  2
--R                                                     Type: NonNegativeInteger
--E 18

--S 19 of 27
genus()$R2
 

   (19)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (19)  0
--R                                                     Type: NonNegativeInteger
--E 19

--S 20 of 27
integralBasis()$R2
 

              1  2 1  3
   (20)  [1,y,- y ,- y ]
              x    x
Type: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R 
--R
--R              1  2 1  3
--R   (20)  [1,y,- y ,- y ]
--R              x    x
--RType: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--E 20

--S 21 of 27
y := generator()$R2
 

   (21)  y
Type: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R 
--R
--R   (21)  y
--RType: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--E 21

--S 22 of 27
integralCoordinates(y**3)
 

   (22)  [num= [0,0,0,x],den= 1]
Type: Record(num: Vector UnivariatePolynomial(x,Integer),den: UnivariatePolynomial(x,Integer))
--R 
--R
--R   (22)  [num= [0,0,0,x],den= 1]
--RType: Record(num: Vector UnivariatePolynomial(x,Integer),den: UnivariatePolynomial(x,Integer))
--E 23

--S 24 of 27
integralRepresents(%.num, %.den)$R2
 

          3
   (23)  y
Type: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R 
--R
--R          3
--R   (23)  y
--RType: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--E 24

--S 25 of 27
norm y
 

             2
   (24)  - 2x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             2
--R   (24)  - 2x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 25

--S 26 of 27
trace y
 

   (25)  0
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (25)  0
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 26

--S 27 of 27
regularRepresentation y
 

         + 0   1  0  0+
         |            |
         | 0   0  1  0|
   (26)  |            |
         | 0   0  0  1|
         |            |
         |  2         |
         +2x   0  0  0+
                        Type: Matrix Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         + 0   1  0  0+
--R         |            |
--R         | 0   0  1  0|
--R   (26)  |            |
--R         | 0   0  0  1|
--R         |            |
--R         |  2         |
--R         +2x   0  0  0+
--R                        Type: Matrix Fraction UnivariatePolynomial(x,Integer)
--E 27
)spool 
 
Starts dribbling to list.output (2009/2/17, 17:52:32).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 33
[2, 4, 5, 6]
 

   (1)  [2,4,5,6]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [2,4,5,6]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 33
[1]
 

   (2)  [1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 33
list(1)
 

   (3)  [1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [1]
--R                                                   Type: List PositiveInteger
--E 3

--S 4 of 33
append([1,2,3],[5,6,7])
 

   (4)  [1,2,3,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [1,2,3,5,6,7]
--R                                                   Type: List PositiveInteger
--E 4

--S 5 of 33
cons(10,[9,8,7])
 

   (5)  [10,9,8,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [10,9,8,7]
--R                                                   Type: List PositiveInteger
--E 5

)clear all
 
   All user variables and function definitions have been cleared.

--S 6 of 33
empty? [x+1]
 

   (1)  false
                                                                Type: Boolean
--R 
--R
--R   (1)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 33
([] = nil)@Boolean
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 33
k := [4,3,7,3,8,5,9,2]
 

   (3)  [4,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [4,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 8

--S 9 of 33
first k
 

   (4)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 33
k.first
 

   (5)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  4
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 33
k.1
 

   (6)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 33
k(1)
 

   (7)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 33
n := #k
 

   (8)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  8
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 33
last k
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 33
k.last
 

   (10)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  2
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 33
k.(#k)
 

   (11)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  2
--R                                                        Type: PositiveInteger
--E 16

)clear all
 
   All user variables and function definitions have been cleared.

--S 17 of 33
k := [4,3,7,3,8,5,9,2]
 

   (1)  [4,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [4,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 17

--S 18 of 33
k.1 := 999
 

   (2)  999
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  999
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 33
k
 

   (3)  [999,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [999,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 19

--S 20 of 33
k := [1,2]
 

   (4)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [1,2]
--R                                                   Type: List PositiveInteger
--E 20

--S 21 of 33
m := cons(0,k)
 

   (5)  [0,1,2]
                                                           Type: List Integer
--R 
--R
--R   (5)  [0,1,2]
--R                                                           Type: List Integer
--E 21

--S 22 of 33
m.2 := 99
 

   (6)  99
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  99
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 33
m
 

   (7)  [0,99,2]
                                                           Type: List Integer
--R 
--R
--R   (7)  [0,99,2]
--R                                                           Type: List Integer
--E 23

--S 24 of 33
k
 

   (8)  [99,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (8)  [99,2]
--R                                                   Type: List PositiveInteger
--E 24

)clear all
 
   All user variables and function definitions have been cleared.

--S 25 of 33
k := [1,2,3]
 

   (1)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 25

--S 26 of 33
rest k
 

   (2)  [2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [2,3]
--R                                                   Type: List PositiveInteger
--E 26

--S 27 of 33
removeDuplicates [4,3,4,3,5,3,4]
 

   (3)  [4,3,5]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [4,3,5]
--R                                                   Type: List PositiveInteger
--E 27

--S 28 of 33
reverse [1,2,3,4,5,6]
 

   (4)  [6,5,4,3,2,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [6,5,4,3,2,1]
--R                                                   Type: List PositiveInteger
--E 28

--S 29 of 33
member?(1/2,[3/4,5/6,1/2])
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 33
member?(1/12,[3/4,5/6,1/2])
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 30

)clear all
 
   All user variables and function definitions have been cleared.

--S 31 of 33
[1..3,10,20..23]
 

   (1)  [1..3,10..10,20..23]
                                           Type: List Segment PositiveInteger
--R 
--R
--R   (1)  [1..3,10..10,20..23]
--R                                           Type: List Segment PositiveInteger
--E 31

--S 32 of 33
expand [1..3,10,20..23]
 

   (2)  [1,2,3,10,20,21,22,23]
                                                           Type: List Integer
--R 
--R
--R   (2)  [1,2,3,10,20,21,22,23]
--R                                                           Type: List Integer
--E 32

--S 33 of 33
expand [1..]
 

   (3)  [1,2,3,4,5,6,7,8,9,10,...]
                                                         Type: Stream Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                         Type: Stream Integer
--E 33
)spool 
 
Starts dribbling to pfr1.output (2009/2/17, 17:56:10).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 10
partialFraction(1,factorial 10)
 

        159   23   12   1
   (1)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                                                Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (1)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                                                Type: PartialFraction Integer
--E 1

--S 2 of 10
f := padicFraction(%)
 

        1    1    1    1    1    1    2    1    2   2    2   1
   (2)  - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
        2    4    5    6    7    8    2    3    4   5    2   7
            2    2    2    2    2    3    3    3        5
                                                Type: PartialFraction Integer
--R 
--R
--R        1    1    1    1    1    1    2    1    2   2    2   1
--R   (2)  - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
--R        2    4    5    6    7    8    2    3    4   5    2   7
--R            2    2    2    2    2    3    3    3        5
--R                                                Type: PartialFraction Integer
--E 2

--S 3 of 10
compactFraction(f)
 

        159   23   12   1
   (3)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                                                Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (3)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                                                Type: PartialFraction Integer
--E 3

--S 4 of 10
numberOfFractionalTerms(f)
 

   (4)  12
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  12
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 10
nthFractionalTerm(f,3)
 

         1
   (5)  --
         5
        2
                                                Type: PartialFraction Integer
--R 
--R
--R         1
--R   (5)  --
--R         5
--R        2
--R                                                Type: PartialFraction Integer
--E 5

--S 6 of 10
partialFraction(1,- 13 + 14 * %i)
 

             1         4
   (6)  - ------- + -------
          1 + 2%i   3 + 8%i
                                        Type: PartialFraction Complex Integer
--R 
--R
--R             1         4
--R   (6)  - ------- + -------
--R          1 + 2%i   3 + 8%i
--R                                        Type: PartialFraction Complex Integer
--E 6

--S 7 of 10
% :: Fraction Complex Integer
 

              %i
   (7)  - ---------
          14 + 13%i
                                               Type: Fraction Complex Integer
--R 
--R
--R              %i
--R   (7)  - ---------
--R          14 + 13%i
--R                                               Type: Fraction Complex Integer
--E 7

--S 8 of 10
u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])
 

                      2       3       4
   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
                      Type: Factored UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                      2       3       4
--R   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
--R                      Type: Factored UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 10
partialFraction(1,u)
 

   (9)
     1     1      7     17  2         139   607  3   10115  2   391     44179
    ---    - x + --   - -- x  - 12x - ---   --- x  + ----- x  + --- x + -----
    648    4     16      8             8    324       432        4       324
   ----- + -------- + ------------------- + ---------------------------------
   x + 1          2                3                            4
           (x + 2)          (x + 3)                      (x + 4)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (9)
--R     1     1      7     17  2         139   607  3   10115  2   391     44179
--R    ---    - x + --   - -- x  - 12x - ---   --- x  + ----- x  + --- x + -----
--R    648    4     16      8             8    324       432        4       324
--R   ----- + -------- + ------------------- + ---------------------------------
--R   x + 1          2                3                            4
--R           (x + 2)          (x + 3)                      (x + 4)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 10
padicFraction %
 

   (10)
       1       1         1        17        3          1       607       403
      ---      -        --        --        -          -       ---       ---
      648      4        16         8        4          2       324       432
     ----- + ----- - -------- - ----- + -------- - -------- + ----- + --------
     x + 1   x + 2          2   x + 3          2          3   x + 4          2
                     (x + 2)            (x + 3)    (x + 3)            (x + 4)
   + 
        13          1
        --         --
        36         12
     -------- + --------
            3          4
     (x + 4)    (x + 4)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (10)
--R       1       1         1        17        3          1       607       403
--R      ---      -        --        --        -          -       ---       ---
--R      648      4        16         8        4          2       324       432
--R     ----- + ----- - -------- - ----- + -------- - -------- + ----- + --------
--R     x + 1   x + 2          2   x + 3          2          3   x + 4          2
--R                     (x + 2)            (x + 3)    (x + 3)            (x + 4)
--R   + 
--R        13          1
--R        --         --
--R        36         12
--R     -------- + --------
--R            3          4
--R     (x + 4)    (x + 4)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 10
)spool 
 
Starts dribbling to sinhcosh.output (2009/2/17, 18:0:23).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
[[0.00,0.000000000,sinh(0.00),sinh(0.00)-0.000000000],_
[0.01,0.010000167,sinh(0.01),sinh(0.01)-0.010000167],_
[0.02,0.020001333,sinh(0.02),sinh(0.02)-0.020001333],_
[0.03,0.030004500,sinh(0.03),sinh(0.03)-0.030004500],_
[0.04,0.040010668,sinh(0.04),sinh(0.04)-0.040010668],_
[0.05,0.050020836,sinh(0.05),sinh(0.05)-0.050020836],_
[0.06,0.060036006,sinh(0.06),sinh(0.06)-0.060036006],_
[0.07,0.070057181,sinh(0.07),sinh(0.07)-0.070057181],_
[0.08,0.080085361,sinh(0.08),sinh(0.08)-0.080085361],_
[0.09,0.090121549,sinh(0.09),sinh(0.09)-0.090121549],_
[0.10,0.100166750,sinh(0.10),sinh(0.10)-0.100166750],_
[0.11,0.110221968,sinh(0.11),sinh(0.11)-0.110221968],_
[0.12,0.120288207,sinh(0.12),sinh(0.12)-0.120288207],_
[0.13,0.130366476,sinh(0.13),sinh(0.13)-0.130366476],_
[0.14,0.140457782,sinh(0.14),sinh(0.14)-0.140457782],_
[0.15,0.150563133,sinh(0.15),sinh(0.15)-0.150563133],_
[0.16,0.160683541,sinh(0.16),sinh(0.16)-0.160683541],_
[0.17,0.170820017,sinh(0.17),sinh(0.17)-0.170820017],_
[0.18,0.180973576,sinh(0.18),sinh(0.18)-0.180973576],_
[0.19,0.191145232,sinh(0.19),sinh(0.19)-0.191145232],_
[0.20,0.201336003,sinh(0.20),sinh(0.20)-0.201336003],_
[0.21,0.211546907,sinh(0.21),sinh(0.21)-0.211546907],_
[0.22,0.221778966,sinh(0.22),sinh(0.22)-0.221778966],_
[0.23,0.232033204,sinh(0.23),sinh(0.23)-0.232033204],_
[0.24,0.242310645,sinh(0.24),sinh(0.24)-0.242310645],_
[0.25,0.252612317,sinh(0.25),sinh(0.25)-0.252612317],_
[0.26,0.262939250,sinh(0.26),sinh(0.26)-0.262939250],_
[0.27,0.273292478,sinh(0.27),sinh(0.27)-0.273292478],_
[0.28,0.283673035,sinh(0.28),sinh(0.28)-0.283673035],_
[0.29,0.294081960,sinh(0.29),sinh(0.29)-0.294081960],_
[0.30,0.304520293,sinh(0.30),sinh(0.30)-0.304520293],_
[0.31,0.314989079,sinh(0.31),sinh(0.31)-0.314989079],_
[0.32,0.325489364,sinh(0.32),sinh(0.32)-0.325489364],_
[0.33,0.336022198,sinh(0.33),sinh(0.33)-0.336022198],_
[0.34,0.346588634,sinh(0.34),sinh(0.34)-0.346588634],_
[0.35,0.357189729,sinh(0.35),sinh(0.35)-0.357189729],_
[0.36,0.367826544,sinh(0.36),sinh(0.36)-0.367826544],_
[0.37,0.378500142,sinh(0.37),sinh(0.37)-0.378500142],_
[0.38,0.389211590,sinh(0.38),sinh(0.38)-0.389211590],_
[0.39,0.399961960,sinh(0.39),sinh(0.39)-0.399961960],_
[0.40,0.410752326,sinh(0.40),sinh(0.40)-0.410752326],_
[0.41,0.421583767,sinh(0.41),sinh(0.41)-0.421583767],_
[0.42,0.432457368,sinh(0.42),sinh(0.42)-0.432457368],_
[0.43,0.443374214,sinh(0.43),sinh(0.43)-0.443374214],_
[0.44,0.454335399,sinh(0.44),sinh(0.44)-0.454335399],_
[0.45,0.465342017,sinh(0.45),sinh(0.45)-0.465342017],_
[0.46,0.476395170,sinh(0.46),sinh(0.46)-0.476395170],_
[0.47,0.487495962,sinh(0.47),sinh(0.47)-0.487495962],_
[0.48,0.498645505,sinh(0.48),sinh(0.48)-0.498645505],_
[0.49,0.509844913,sinh(0.49),sinh(0.49)-0.509844913],_
[0.50,0.521095305,sinh(0.50),sinh(0.50)-0.521095305],_
[0.51,0.532397808,sinh(0.51),sinh(0.51)-0.532397808],_
[0.52,0.543753551,sinh(0.52),sinh(0.52)-0.543753551],_
[0.53,0.555163669,sinh(0.53),sinh(0.53)-0.555163669],_
[0.54,0.566629305,sinh(0.54),sinh(0.54)-0.566629305],_
[0.55,0.578151604,sinh(0.55),sinh(0.55)-0.578151604],_
[0.56,0.589731718,sinh(0.56),sinh(0.56)-0.589731718],_
[0.57,0.601370806,sinh(0.57),sinh(0.57)-0.601370806],_
[0.58,0.613070032,sinh(0.58),sinh(0.58)-0.613070032],_
[0.59,0.624830565,sinh(0.59),sinh(0.59)-0.624830565],_
[0.60,0.636653582,sinh(0.60),sinh(0.60)-0.636653582],_
[0.61,0.648540265,sinh(0.61),sinh(0.61)-0.648540265],_
[0.62,0.660491802,sinh(0.62),sinh(0.62)-0.660491802],_
[0.63,0.672509389,sinh(0.63),sinh(0.63)-0.672509389],_
[0.64,0.684594228,sinh(0.64),sinh(0.64)-0.684594228],_
[0.65,0.696747526,sinh(0.65),sinh(0.65)-0.696747526],_
[0.66,0.708970500,sinh(0.66),sinh(0.66)-0.708970500],_
[0.67,0.721264371,sinh(0.67),sinh(0.67)-0.721264371],_
[0.68,0.733630370,sinh(0.68),sinh(0.68)-0.733630370],_
[0.69,0.746069732,sinh(0.69),sinh(0.69)-0.746069732],_
[0.70,0.758583702,sinh(0.70),sinh(0.70)-0.758583702],_
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R    [1.13,1.386311622,1.3863116218 51229278,- 0.148770722 E -9],
--R    [1.14,1.403474672,1.4034746716 849259325,- 0.3150740675 E -9],
--R    [1.15,1.42077807,1.4207780701 553572045,0.1553572045 E -9],
--R    [1.16,1.438223548,1.4382235476 16789684,- 0.383210316 E -9],
--R    [1.17,1.455812849,1.4558128486 315074606,- 0.3684925394 E -9],
--R    [1.18,1.473547732,1.4735477321 442698057,0.1442698057 E -9],
--R    [1.19,1.491429972,1.4914299716 582071144,- 0.3417928856 E -9],
--R    [1.2,1.509461355,1.5094613554 121726964,0.4121726964 E -9],
--R    [1.21,1.527643687,1.5276436865 595681515,- 0.4404318485 E -9],
--R    [1.22,1.545978783,1.5459787833 486602124,0.3486602124 E -9],
--R    [1.23,1.564468479,1.5644684793 044070864,0.3044070864 E -9],
--R    [1.24,1.583114623,1.5831146234 118124797,0.4118124797 E -9],
--R    [1.25,1.60191908,1.6019190803 008256379,0.3008256379 E -9],
--R    [1.26,1.62088373,1.6208837304 328058954,0.4328058954 E -9],
--R    [1.27,1.64001047,1.6400104702 88570378,0.288570378 E -9],
--R    [1.28,1.659301213,1.6593012125 580436651,- 0.4419563349 E -9],
--R    [1.29,1.678757886,1.6787578863 315283762,0.3315283762 E -9],
--R    [1.3,1.698382437,1.6983824372 926158087,0.2926158087 E -9],
--R    [1.31,1.718176828,1.7181768279 127559182,- 0.872440818 E -10],
--R    [1.32,1.738143038,1.7381430376 475060993,- 0.3524939007 E -9],
--R    [1.33,1.758283063,1.7582830631 344783905,0.1344783905 E -9],
--R    [1.34,1.778598918,1.7785989183 930048997,0.3930048997 E -9],
--R    [1.35,1.799092635,1.7990926350 255414153,0.255414153 E -10],
--R    [1.36,1.819766262,1.8197662624 20829345,0.420829345 E -9],
--R    [1.37,1.840621868,1.8406218679 588362979,- 0.411637021 E -10],
--R    [1.38,1.861661537,1.8616615372 174958039,0.2174958039 E -9],
--R    [1.39,1.882887374,1.8828873741 812668452,0.1812668451 E -9],
--R    [1.4,1.904301501,1.9043015014 515340551,0.4515340551 E -9],
--R    [1.41,1.92590606,1.9259060604 588696261,0.4588696261 E -9],
--R    [1.42,1.947703212,1.9477032116 771781509,- 0.3228218491 E -9],
--R    [1.43,1.969695135,1.9696951348 397458135,- 0.1602541865 E -9],
--R    [1.44,1.991884029,1.9918840291 572155345,0.1572155345 E -9],
--R    [1.45,2.014272114,2.0142721135 375098676,- 0.4624901324 E -9],
--R    [1.46,2.036861627,2.0368616268 077236416,- 0.192276358 E -9],
--R    [1.47,2.059654828,2.0596548279 380085349,- 0.619914651 E -10],
--R    [1.48,2.082653996,2.0826539962 674719736,0.2674719736 E -9],
--R    [1.49,2.105861432,2.1058614317 321129415,- 0.2678870585 E -9],
--R    [1.5,2.129279455,2.1292794550 948174968,0.948174968 E -10],
--R    [1.51,2.152910408,2.1529104081 774369945,0.177436994 E -9],
--R    [1.52,2.176756654,2.1767566540 94972223,0.94972223 E -10],
--R    [1.53,2.200820577,2.2008205774 918868736,0.4918868736 E -9],
--R    [1.54,2.225104585,2.2251045847 805739743,- 0.219426026 E -9],
--R    [1.55,2.249611104,2.2496111043 819991339,0.3819991339 E -9],
--R    [1.56,2.274342587,2.2743425869 685446626,- 0.314553374 E -10],
--R    [1.57,2.299301506,2.2993015057 090788526,- 0.2909211474 E -9],
--R    [1.58,2.324490357,2.3244903565 162749255,- 0.4837250745 E -9],
--R    [1.59,2.349911658,2.3499116582 962043799,0.2962043799 E -9],
--R    [1.6,2.375567953,2.3755679532 002296976,0.200229698 E -9],
--R    [1.61,2.401461807,2.4014618068 79221598,- 0.120778402 E -9],
--R    [1.62,2.427595809,2.4275958087 401262638,- 0.2598737362 E -9],
--R    [1.63,2.453972572,2.4539725722 049081927,0.204908193 E -9],
--R    [1.64,2.480594735,2.4805947349 718945727,- 0.281054273 E -10],
--R    [1.65,2.507464959,2.5074649592 795473117,0.2795473117 E -9],
--R    [1.66,2.534585932,2.5345859321 726891034,0.172689103 E -9],
--R    [1.67,2.561960366,2.5619603657 712101481,- 0.228789852 E -9],
--R    [1.68,2.589590998,2.5895909975 412824018,- 0.4587175982 E -9],
--R    [1.69,2.617480591,2.6174805905 69108475,- 0.430891525 E -9],
--R    [1.7,2.645631934,2.6456319338 372325553,- 0.162767445 E -9],
--R    [1.71,2.674047843,2.6740478425 034409861,- 0.4965590139 E -9],
--R    [1.72,2.702731158,2.7027311581 822803909,0.182280391 E -9],
--R    [1.73,2.731684749,2.7316847492 292214966,0.229221497 E -9],
--R    [1.74,2.760911511,2.7609115110 274970701,0.274970701 E -10],
--R    [1.75,2.790414366,2.7904143662 776426551,0.2776426551 E -9],
--R    [1.76,2.820196265,2.8201962652 897690607,0.2897690607 E -9],
--R    [1.77,2.850260186,2.8502601862 785958316,0.2785958316 E -9],
--R    [1.78,2.880609136,2.8806091356 612752013,- 0.3387247987 E -9],
--R    [1.79,2.911246148,2.9112461483 580363133,0.3580363133 E -9],
--R    [1.8,2.942174288,2.9421742880 956797727,0.956797727 E -10],
--R    [1.81,2.973396648,2.9733966477 139528796,- 0.2860471204 E -9],
--R    [1.82,3.004916349,3.0049163494 748361809,0.4748361809 E -9],
--R    [1.83,3.036736545,3.0367365453 747722708,0.3747722708 E -9],
--R    [1.84,3.068860417,3.0688604174 598680611,0.4598680611 E -9],
--R    [1.85,3.101291178,3.1012911781 441020441,0.144102044 E -9],
--R    [1.86,3.134032071,3.1340320705 305683671,- 0.4694316329 E -9],
--R    [1.87,3.167086369,3.1670863687 357898447,- 0.2642101554 E -9],
--R    [1.88,3.200457378,3.2004573782 171323393,0.217132339 E -9],
--R    [1.89,3.234148436,3.2341484361 033532526,0.103353253 E -9],
--R    [1.9,3.268162912,3.2681629115 283171817,- 0.4716828183 E -9],
--R    [1.91,3.302504206,3.3025042059 679121137,- 0.320878863 E -10],
--R    [1.92,3.337175754,3.3371757535 801998489,- 0.4198001511 E -9],
--R    [1.93,3.372181022,3.3721810215 488346686,- 0.4511653313 E -9],
--R    [1.94,3.40752351,3.4075235104 297845903,0.4297845903 E -9],
--R    [1.95,3.443206754,3.4432067545 013898812,0.5013898812 E -9],
--R    [1.96,3.479234322,3.4792343221 177938377,0.117793838 E -9],
--R    [1.97,3.515609816,3.5156098160 657811731,0.657811731 E -10],
--R    [1.98,3.552336874,3.5523368739 25059699,- 0.74940301 E -10],
--R    [1.99,3.589419168,3.5894191684 320213268,0.4320213268 E -9],
--R    [2.0,3.626860408,3.6268604078 470187677,- 0.152981232 E -9]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
[[0.00,1.000000000,cosh(0.00),cosh(0.00)-1.000000000],_
[0.01,1.000050000,cosh(0.01),cosh(0.01)-1.000050000],_
[0.02,1.000200007,cosh(0.02),cosh(0.02)-1.000200007],_
[0.03,1.000450034,cosh(0.03),cosh(0.03)-1.000450034],_
[0.04,1.000800107,cosh(0.04),cosh(0.04)-1.000800107],_
[0.05,1.001250260,cosh(0.05),cosh(0.05)-1.001250260],_
[0.06,1.001800540,cosh(0.06),cosh(0.06)-1.001800540],_
[0.07,1.002451001,cosh(0.07),cosh(0.07)-1.002451001],_
[0.08,1.003201707,cosh(0.08),cosh(0.08)-1.003201707],_
[0.09,1.004052734,cosh(0.09),cosh(0.09)-1.004052734],_
[0.10,1.005004168,cosh(0.10),cosh(0.10)-1.005004168],_
[0.11,1.006056103,cosh(0.11),cosh(0.11)-1.006056103],_
[0.12,1.007208644,cosh(0.12),cosh(0.12)-1.007208644],_
[0.13,1.008461907,cosh(0.13),cosh(0.13)-1.008461907],_
[0.14,1.009816017,cosh(0.14),cosh(0.14)-1.009816017],_
[0.15,1.011271110,cosh(0.15),cosh(0.15)-1.011271110],_
[0.16,1.012827330,cosh(0.16),cosh(0.16)-1.012827330],_
[0.17,1.014484834,cosh(0.17),cosh(0.17)-1.014484834],_
[0.18,1.016243787,cosh(0.18),cosh(0.18)-1.016243787],_
[0.19,1.018104366,cosh(0.19),cosh(0.19)-1.018104366],_
[0.20,1.020066756,cosh(0.20),cosh(0.20)-1.020066756],_
[0.21,1.022131153,cosh(0.21),cosh(0.21)-1.022131153],_
[0.22,1.024297764,cosh(0.22),cosh(0.22)-1.024297764],_
[0.23,1.026566806,cosh(0.23),cosh(0.23)-1.026566806],_
[0.24,1.028938506,cosh(0.24),cosh(0.24)-1.028938506],_
[0.25,1.031413100,cosh(0.25),cosh(0.25)-1.031413100],_
[0.26,1.033990836,cosh(0.26),cosh(0.26)-1.033990836],_
[0.27,1.036671973,cosh(0.27),cosh(0.27)-1.036671973],_
[0.28,1.039456777,cosh(0.28),cosh(0.28)-1.039456777],_
[0.29,1.042345528,cosh(0.29),cosh(0.29)-1.042345528],_
[0.30,1.045338514,cosh(0.30),cosh(0.30)-1.045338514],_
[0.31,1.048436035,cosh(0.31),cosh(0.31)-1.048436035],_
[0.32,1.051638401,cosh(0.32),cosh(0.32)-1.051638401],_
[0.33,1.054945931,cosh(0.33),cosh(0.33)-1.054945931],_
[0.34,1.058358957,cosh(0.34),cosh(0.34)-1.058358957],_
[0.35,1.061877819,cosh(0.35),cosh(0.35)-1.061877819],_
[0.36,1.065502870,cosh(0.36),cosh(0.36)-1.065502870],_
[0.37,1.069234473,cosh(0.37),cosh(0.37)-1.069234473],_
[0.38,1.073072999,cosh(0.38),cosh(0.38)-1.073072999],_
[0.39,1.077018834,cosh(0.39),cosh(0.39)-1.077018834],_
[0.40,1.081072372,cosh(0.40),cosh(0.40)-1.081072372],_
[0.41,1.085234018,cosh(0.41),cosh(0.41)-1.085234018],_
[0.42,1.089504188,cosh(0.42),cosh(0.42)-1.089504188],_
[0.43,1.093883309,cosh(0.43),cosh(0.43)-1.093883309],_
[0.44,1.098371820,cosh(0.44),cosh(0.44)-1.098371820],_
[0.45,1.102970169,cosh(0.45),cosh(0.45)-1.102970169],_
[0.46,1.107678815,cosh(0.46),cosh(0.46)-1.107678815],_
[0.47,1.112498231,cosh(0.47),cosh(0.47)-1.112498231],_
[0.48,1.117428897,cosh(0.48),cosh(0.48)-1.117428897],_
[0.49,1.122471307,cosh(0.49),cosh(0.49)-1.122471307],_
[0.50,1.127625965,cosh(0.50),cosh(0.50)-1.127625965],_
[0.51,1.132893387,cosh(0.51),cosh(0.51)-1.132893387],_
[0.52,1.138274099,cosh(0.52),cosh(0.52)-1.138274099],_
[0.53,1.143768639,cosh(0.53),cosh(0.53)-1.143768639],_
[0.54,1.149377557,cosh(0.54),cosh(0.54)-1.149377557],_
[0.55,1.155101414,cosh(0.55),cosh(0.55)-1.155101414],_
[0.56,1.160940782,cosh(0.56),cosh(0.56)-1.160940782],_
[0.57,1.166896245,cosh(0.57),cosh(0.57)-1.166896245],_
[0.58,1.172968399,cosh(0.58),cosh(0.58)-1.172968399],_
[0.59,1.179157850,cosh(0.59),cosh(0.59)-1.179157850],_
[0.60,1.185465218,cosh(0.60),cosh(0.60)-1.185465218],_
[0.61,1.191891134,cosh(0.61),cosh(0.61)-1.191891134],_
[0.62,1.198436240,cosh(0.62),cosh(0.62)-1.198436240],_
[0.63,1.205101190,cosh(0.63),cosh(0.63)-1.205101190],_
[0.64,1.211886652,cosh(0.64),cosh(0.64)-1.211886652],_
[0.65,1.218793303,cosh(0.65),cosh(0.65)-1.218793303],_
[0.66,1.225821834,cosh(0.66),cosh(0.66)-1.225821834],_
[0.67,1.232972949,cosh(0.67),cosh(0.67)-1.232972949],_
[0.68,1.240247362,cosh(0.68),cosh(0.68)-1.240247362],_
[0.69,1.247645801,cosh(0.69),cosh(0.69)-1.247645801],_
[0.70,1.255169006,cosh(0.70),cosh(0.70)-1.255169006],_
[0.71,1.262817728,cosh(0.71),cosh(0.71)-1.262817728],_
[0.72,1.270592733,cosh(0.72),cosh(0.72)-1.270592733],_
[0.73,1.278494799,cosh(0.73),cosh(0.73)-1.278494799],_
[0.74,1.286524715,cosh(0.74),cosh(0.74)-1.286524715],_
[0.75,1.294683285,cosh(0.75),cosh(0.75)-1.294683285],_
[0.76,1.302971324,cosh(0.76),cosh(0.76)-1.302971324],_
[0.77,1.311389661,cosh(0.77),cosh(0.77)-1.311389661],_
[0.78,1.319939138,cosh(0.78),cosh(0.78)-1.319939138],_
[0.79,1.328620611,cosh(0.79),cosh(0.79)-1.328620611],_
[0.80,1.337434946,cosh(0.80),cosh(0.80)-1.337434946],_
[0.81,1.346383026,cosh(0.81),cosh(0.81)-1.346383026],_
[0.82,1.355465746,cosh(0.82),cosh(0.82)-1.355465746],_
[0.83,1.364684013,cosh(0.83),cosh(0.83)-1.364684013],_
[0.84,1.374038750,cosh(0.84),cosh(0.84)-1.374038750],_
[0.85,1.383530892,cosh(0.85),cosh(0.85)-1.383530892],_
[0.86,1.393161388,cosh(0.86),cosh(0.86)-1.393161388],_
[0.87,1.402931201,cosh(0.87),cosh(0.87)-1.402931201],_
[0.88,1.412841309,cosh(0.88),cosh(0.88)-1.412841309],_
[0.89,1.422892702,cosh(0.89),cosh(0.89)-1.422892702],_
[0.90,1.433086385,cosh(0.90),cosh(0.90)-1.433086385],_
[0.91,1.443423379,cosh(0.91),cosh(0.91)-1.443423379],_
[0.92,1.453904716,cosh(0.92),cosh(0.92)-1.453904716],_
[0.93,1.464531444,cosh(0.93),cosh(0.93)-1.464531444],_
[0.94,1.475304627,cosh(0.94),cosh(0.94)-1.475304627],_
[0.95,1.486225341,cosh(0.95),cosh(0.95)-1.486225341],_
[0.96,1.497294680,cosh(0.96),cosh(0.96)-1.497294680],_
[0.97,1.508513749,cosh(0.97),cosh(0.97)-1.508513749],_
[0.98,1.519883670,cosh(0.98),cosh(0.98)-1.519883670],_
[0.99,1.531405582,cosh(0.99),cosh(0.99)-1.531405582],_
[1.00,1.543080635,cosh(1.00),cosh(1.00)-1.543080635],_
[1.01,1.554909997,cosh(1.01),cosh(1.01)-1.554909997],_
[1.02,1.566894852,cosh(1.02),cosh(1.02)-1.566894852],_
[1.03,1.579036398,cosh(1.03),cosh(1.03)-1.579036398],_
[1.04,1.591335848,cosh(1.04),cosh(1.04)-1.591335848],_
[1.05,1.603794434,cosh(1.05),cosh(1.05)-1.603794434],_
[1.06,1.616413400,cosh(1.06),cosh(1.06)-1.616413400],_
[1.07,1.629194009,cosh(1.07),cosh(1.07)-1.629194009],_
[1.08,1.642137538,cosh(1.08),cosh(1.08)-1.642137538],_
[1.09,1.655245283,cosh(1.09),cosh(1.09)-1.655245283],_
[1.10,1.668518554,cosh(1.10),cosh(1.10)-1.668518554],_
[1.11,1.681958678,cosh(1.11),cosh(1.11)-1.681958678],_
[1.12,1.695566999,cosh(1.12),cosh(1.12)-1.695566999],_
[1.13,1.709344878,cosh(1.13),cosh(1.13)-1.709344878],_
[1.14,1.723293694,cosh(1.14),cosh(1.14)-1.723293694],_
[1.15,1.737414840,cosh(1.15),cosh(1.15)-1.737414840],_
[1.16,1.751709728,cosh(1.16),cosh(1.16)-1.751709728],_
[1.17,1.766179790,cosh(1.17),cosh(1.17)-1.766179790],_
[1.18,1.780826471,cosh(1.18),cosh(1.18)-1.780826471],_
[1.19,1.795651236,cosh(1.19),cosh(1.19)-1.795651236],_
[1.20,1.810655567,cosh(1.20),cosh(1.20)-1.810655567],_
[1.21,1.825840966,cosh(1.21),cosh(1.21)-1.825840966],_
[1.22,1.841208950,cosh(1.22),cosh(1.22)-1.841208950],_
[1.23,1.856761057,cosh(1.23),cosh(1.23)-1.856761057],_
[1.24,1.872498841,cosh(1.24),cosh(1.24)-1.872498841],_
[1.25,1.888423877,cosh(1.25),cosh(1.25)-1.888423877],_
[1.26,1.904537757,cosh(1.26),cosh(1.26)-1.904537757],_
[1.27,1.920842092,cosh(1.27),cosh(1.27)-1.920842092],_
[1.28,1.937338513,cosh(1.28),cosh(1.28)-1.937338513],_
[1.29,1.954028669,cosh(1.29),cosh(1.29)-1.954028669],_
[1.30,1.970914230,cosh(1.30),cosh(1.30)-1.970914230],_
[1.31,1.987996884,cosh(1.31),cosh(1.31)-1.987996884],_
[1.32,2.005278340,cosh(1.32),cosh(1.32)-2.005278340],_
[1.33,2.022760324,cosh(1.33),cosh(1.33)-2.022760324],_
[1.34,2.040444587,cosh(1.34),cosh(1.34)-2.040444587],_
[1.35,2.058332896,cosh(1.35),cosh(1.35)-2.058332896],_
[1.36,2.076427039,cosh(1.36),cosh(1.36)-2.076427039],_
[1.37,2.094728828,cosh(1.37),cosh(1.37)-2.094728828],_
[1.38,2.113240090,cosh(1.38),cosh(1.38)-2.113240090],_
[1.39,2.131962679,cosh(1.39),cosh(1.39)-2.131962679],_
[1.40,2.150898465,cosh(1.40),cosh(1.40)-2.150898465],_
[1.41,2.170049344,cosh(1.41),cosh(1.41)-2.170049344],_
[1.42,2.189417229,cosh(1.42),cosh(1.42)-2.189417229],_
[1.43,2.209004057,cosh(1.43),cosh(1.43)-2.209004057],_
[1.44,2.228811788,cosh(1.44),cosh(1.44)-2.228811788],_
[1.45,2.248842402,cosh(1.45),cosh(1.45)-2.248842402],_
[1.46,2.269097902,cosh(1.46),cosh(1.46)-2.269097902],_
[1.47,2.289580313,cosh(1.47),cosh(1.47)-2.289580313],_
[1.48,2.310291685,cosh(1.48),cosh(1.48)-2.310291685],_
[1.49,2.331234087,cosh(1.49),cosh(1.49)-2.331234087],_
[1.50,2.352409615,cosh(1.50),cosh(1.50)-2.352409615],_
[1.51,2.373820386,cosh(1.51),cosh(1.51)-2.373820386],_
[1.52,2.395468541,cosh(1.52),cosh(1.52)-2.395468541],_
[1.53,2.417356245,cosh(1.53),cosh(1.53)-2.417356245],_
[1.54,2.439485686,cosh(1.54),cosh(1.54)-2.439485686],_
[1.55,2.461859078,cosh(1.55),cosh(1.55)-2.461859078],_
[1.56,2.484478658,cosh(1.56),cosh(1.56)-2.484478658],_
[1.57,2.507346688,cosh(1.57),cosh(1.57)-2.507346688],_
[1.58,2.530465455,cosh(1.58),cosh(1.58)-2.530465455],_
[1.59,2.553837270,cosh(1.59),cosh(1.59)-2.553837270],_
[1.60,2.577464471,cosh(1.60),cosh(1.60)-2.577464471],_
[1.61,2.601349421,cosh(1.61),cosh(1.61)-2.601349421],_
[1.62,2.625494508,cosh(1.62),cosh(1.62)-2.625494508],_
[1.63,2.649902146,cosh(1.63),cosh(1.63)-2.649902146],_
[1.64,2.674574777,cosh(1.64),cosh(1.64)-2.674574777],_
[1.65,2.699514868,cosh(1.65),cosh(1.65)-2.699514868],_
[1.66,2.724724912,cosh(1.66),cosh(1.66)-2.724724912],_
[1.67,2.750207431,cosh(1.67),cosh(1.67)-2.750207431],_
[1.68,2.775964974,cosh(1.68),cosh(1.68)-2.775964974],_
[1.69,2.802000115,cosh(1.69),cosh(1.69)-2.802000115],_
[1.70,2.828315458,cosh(1.70),cosh(1.70)-2.828315458],_
[1.71,2.854913635,cosh(1.71),cosh(1.71)-2.854913635],_
[1.72,2.881797306,cosh(1.72),cosh(1.72)-2.881797306],_
[1.73,2.908969159,cosh(1.73),cosh(1.73)-2.908969159],_
[1.74,2.936431912,cosh(1.74),cosh(1.74)-2.936431912],_
[1.75,2.964188310,cosh(1.75),cosh(1.75)-2.964188310],_
[1.76,2.992241129,cosh(1.76),cosh(1.76)-2.992241129],_
[1.77,3.020593175,cosh(1.77),cosh(1.77)-3.020593175],_
[1.78,3.049247283,cosh(1.78),cosh(1.78)-3.049247283],_
[1.79,3.078206318,cosh(1.79),cosh(1.79)-3.078206318],_
[1.80,3.107473176,cosh(1.80),cosh(1.80)-3.107473176],_
[1.81,3.137050785,cosh(1.81),cosh(1.81)-3.137050785],_
[1.82,3.166942100,cosh(1.82),cosh(1.82)-3.166942100],_
[1.83,3.197150113,cosh(1.83),cosh(1.83)-3.197150113],_
[1.84,3.227677844,cosh(1.84),cosh(1.84)-3.227677844],_
[1.85,3.258528344,cosh(1.85),cosh(1.85)-3.258528344],_
[1.86,3.289704701,cosh(1.86),cosh(1.86)-3.289704701],_
[1.87,3.321210031,cosh(1.87),cosh(1.87)-3.321210031],_
[1.88,3.353047484,cosh(1.88),cosh(1.88)-3.353047484],_
[1.89,3.385220245,cosh(1.89),cosh(1.89)-3.385220245],_
[1.90,3.417731531,cosh(1.90),cosh(1.90)-3.417731531],_
[1.91,3.450584593,cosh(1.91),cosh(1.91)-3.450584593],_
[1.92,3.483782716,cosh(1.92),cosh(1.92)-3.483782716],_
[1.93,3.517329220,cosh(1.93),cosh(1.93)-3.517329220],_
[1.94,3.551227460,cosh(1.94),cosh(1.94)-3.551227460],_
[1.95,3.585480826,cosh(1.95),cosh(1.95)-3.585480826],_
[1.96,3.620092743,cosh(1.96),cosh(1.96)-3.620092743],_
[1.97,3.655066672,cosh(1.97),cosh(1.97)-3.655066672],_
[1.98,3.690406111,cosh(1.98),cosh(1.98)-3.690406111],_
[1.99,3.726114594,cosh(1.99),cosh(1.99)-3.726114594],_
[2.00,3.762195691,cosh(2.00),cosh(2.00)-3.762195691]]
 

   (2)
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    [1.71,2.854913635,2.8549136351 205630698,0.12056307 E -9],
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    [1.73,2.908969159,2.9089691591 990993011,0.199099301 E -9],
    [1.74,2.936431912,2.9364319116 444939418,- 0.3555060582 E -9],
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    [2.0,3.762195691,3.7621956910 836314596,0.836314596 E -10]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.0,1.0,1.0,0.0], [0.01,1.00005,1.0000500004 166680556,0.4166680556 E -9],
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--R    [1.82,3.1669421,3.1669421004 087169461,0.4087169461 E -9],
--R    [1.83,3.197150113,3.1971501131 499450329,0.149945033 E -9],
--R    [1.84,3.227677844,3.2276778435 667887561,- 0.4332112439 E -9],
--R    [1.85,3.258528344,3.2585283444 577296603,0.4577296603 E -9],
--R    [1.86,3.289704701,3.2897047008 98565676,- 0.101434324 E -9],
--R    [1.87,3.321210031,3.3212100305 509212704,- 0.4490787296 E -9],
--R    [1.88,3.353047484,3.3530474839 74016208,- 0.25983792 E -10],
--R    [1.89,3.385220245,3.3852202449 397240979,- 0.602759021 E -10],
--R    [1.9,3.417731531,3.4177315307 509522343,- 0.2490477656 E -9],
--R    [1.91,3.450584593,3.4505845925 633745687,- 0.4366254312 E -9],
--R    [1.92,3.483782716,3.4837827157 105499861,- 0.289450014 E -9],
--R    [1.93,3.51732922,3.5173292200 324583986,0.324583986 E -10],
--R    [1.94,3.55122746,3.5512274602 074875108,0.207487511 E -9],
--R    [1.95,3.585480826,3.5854808260 879034531,0.879034531 E -10],
--R    [1.96,3.620092743,3.6200927430 388388338,0.388388338 E -10],
--R    [1.97,3.655066672,3.6550666722 808321068,0.2808321068 E -9],
--R    [1.98,3.690406111,3.6904061112 359525095,0.2359525095 E -9],
--R    [1.99,3.726114594,3.7261145938 775451847,- 0.122454815 E -9],
--R    [2.0,3.762195691,3.7621956910 836314596,0.836314596 E -10]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to lodo2.output (2009/2/17, 17:52:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 26
Q  := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 26
PQ := UnivariatePolynomial('x, Q)
 

   (2)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 26
x: PQ := 'x
 

   (3)  x
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (3)  x
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 3

--S 4 of 26
Dx: LODO2(Q, PQ) := D()
 

   (4)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 26
a := Dx  + 1
 

   (5)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (5)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 26
b := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (6)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (6)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 6

--S 7 of 26
p := 4*x**2 + 2/3
 

          2   2
   (7)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (7)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 26
a p
 

          2        2
   (8)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (8)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 26
(a * b) p = a b p
 

          2         37    2         37
   (9)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (9)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 26
c := (1/9)*b*(a + b)**2
 

          1  6    5  5   13  4   19  3   79  2    7     1
   (10)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
         72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          1  6    5  5   13  4   19  3   79  2    7     1
--R   (10)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R         72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 10

--S 11 of 26
(a**2 - 3/4*b + c) (p + 1)
 

           2   44     541
   (11)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (11)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 11

)clear all
 
   All user variables and function definitions have been cleared.

--S 12 of 26
PZ   := UnivariatePolynomial(x,Integer)
 

   (1)  UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 12

--S 13 of 26
x:PZ := 'x
 

   (2)  x
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (2)  x
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 26
Mat  := SquareMatrix(3,PZ)
 

   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
                                                                 Type: Domain
--R 
--R
--R   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 14

--S 15 of 26
Vect := DPMM(3, PZ, Mat, PZ);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 15

--S 16 of 26
Modo := LODO2(Mat, Vect);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 16

--S 17 of 26
m:Mat := matrix [[x**2,1,0],[1,x**4,0],[0,0,4*x**2]]
 

        + 2         +
        |x   1    0 |
        |           |
   (6)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (6)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 17

--S 18 of 26
p:Vect := directProduct [3*x**2+1,2*x,7*x**3+2*x]
 

           2          3
   (7)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (7)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 26
q: Vect := m * p
 

           4    2        5     2        5     3
   (8)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (8)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 19

--S 20 of 26
Dx : Modo := D()
 

   (9)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 20

--S 21 of 26
a : Modo := Dx  + m
 

             + 2         +
             |x   1    0 |
             |           |
   (10)  D + |     4     |
             |1   x    0 |
             |           |
             |          2|
             +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R             + 2         +
--R             |x   1    0 |
--R             |           |
--R   (10)  D + |     4     |
--R             |1   x    0 |
--R             |           |
--R             |          2|
--R             +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 21

--S 22 of 26
b : Modo := m*Dx  + 1
 

         + 2         +
         |x   1    0 |    +1  0  0+
         |           |    |       |
   (11)  |     4     |D + |0  1  0|
         |1   x    0 |    |       |
         |           |    +0  0  1+
         |          2|
         +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R         + 2         +
--R         |x   1    0 |    +1  0  0+
--R         |           |    |       |
--R   (11)  |     4     |D + |0  1  0|
--R         |1   x    0 |    |       |
--R         |           |    +0  0  1+
--R         |          2|
--R         +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 22

--S 23 of 26
c := a*b
 

   (12)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (12)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 23

--S 24 of 26
a p
 

            4    2        5     2        5     3      2
   (13)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (13)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 24

--S 25 of 26
b p
 

            3     2       4         4     3     2
   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 25

--S 26 of 26
(a + b + c) (p + q)
 

   (15)
       8      7      6      5      4      3      2
   [10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x  + 40x + 17,
       12      9      8      7     6      5      4      3      2
    10x   + 10x  + 12x  + 92x  + 6x  + 32x  + 72x  + 28x  + 49x  + 32x + 19,
         8       7        6        5       4       3      2
    2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x  + 98x  + 18x + 4]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (15)
--R       8      7      6      5      4      3      2
--R   [10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x  + 40x + 17,
--R       12      9      8      7     6      5      4      3      2
--R    10x   + 10x  + 12x  + 92x  + 6x  + 32x  + 72x  + 28x  + 49x  + 32x + 19,
--R         8       7        6        5       4       3      2
--R    2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x  + 98x  + 18x + 4]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 26
)spool 
 
Starts dribbling to ei.output (2009/2/17, 17:45:23).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
digits 35
 

   (1)  20
                                                        Type: PositiveInteger

--S 1 of 20
gamma:=0.577215664901532860606512090082
 

   (2)  0.5772156649 0153286060 6512090082
                                                                  Type: Float
--R 
--R
--R   (2)  0.5772156649 0153286060 6512090082
--R                                                                  Type: Float
--E 1


--S 2 of 20
aChebyshev:=_
[0.191217322586055345391519326510E1,_
-0.420835505286848437550974986680E-01,_
 0.172281962728432678337118157835E-02,_
-0.991578217344456364559842322973E-04,_
 0.717609316802277505265590665592E-05,_
-0.615273314509512696827956791331E-06,_
 0.602485710656275831293999701610E-07,_
-0.657384884528830482295894189637E-08,_
 0.785316754183239981994810079871E-09,_
-0.101373028800387898554202774257E-09,_
 0.139977041322676860277823488623E-10,_
-0.205100837678381899618962318711E-11,_
 0.316838872600247781814907985818E-12,_
-0.513276008283918065415984751899E-13,_
 0.868093304076654934187433687383E-14,_
-0.152701504090308497198572355351E-14,_
 0.278468625164935739650105251453E-15,_
-0.524989043742176696808472933696E-16,_
 0.102071799124856129247455787226E-16,_
-0.204226467989971841308462421876E-17,_
 0.419706417272648474408827228562E-18,_
-0.884450817617281050816483737536E-19,_
 0.190827262959471741995060168262E-19,_
-0.420974622293519950336450865676E-20,_
 0.948390405819837327641500214512E-21,_
-0.217946786013667431994032574014E-21,_
 0.510393686907145094993452562741E-22,_
-0.121688311333441509089746779693E-22,_
 0.295128916644787519294773757144E-23,_
-0.727535376377284689714438950920E-24,_
 0.182163904862307396121667115976E-24,_
-0.462962996316331716612753482064E-25,_
 0.119353979097157791523052371292E-25,_
-0.311949328522014244931062147473E-26,_
 0.826141973453346642284170028518E-27,_
-0.221580337366098298302591177697E-27,_
 0.601603167165426389045303124429E-28,_
-0.165272509838212659649744302314E-28,_
 0.459223035877302702795636377166E-29,_
-0.129006276721326384737453212670E-29,_
 0.366271848103200259081177078922E-30]
 

   (3)
   [1.9121732258 6055345391 51932651, - 0.0420835505 2868484375 5097498668,
    0.0017228196 2728432678 3371181578 35,
    - 0.0000991578 2173444563 6455984232 2973,
    0.0000071760 9316802277 5052655906 65592,
    - 0.6152733145 0951269682 7956791331 E -6,
    0.6024857106 5627583129 399970161 E -7,
    - 0.6573848845 2883048229 5894189637 E -8,
    0.7853167541 8323998199 4810079871 E -9,
    - 0.1013730288 0038789855 4202774257 E -9,
    0.1399770413 2267686027 7823488623 E -10,
    - 0.2051008376 7838189961 8962318711 E -11,
    0.3168388726 0024778181 4907985818 E -12,
    - 0.5132760082 8391806541 5984751899 E -13,
    0.8680933040 7665493418 7433687383 E -14,
    - 0.1527015040 9030849719 8572355351 E -14,
    0.2784686251 6493573965 0105251453 E -15,
    - 0.5249890437 4217669680 8472933696 E -16,
    0.1020717991 2485612924 7455787226 E -16,
    - 0.2042264679 8997184130 8462421876 E -17,
    0.4197064172 7264847440 8827228562 E -18,
    - 0.8844508176 1728105081 6483737536 E -19,
    0.1908272629 5947174199 5060168262 E -19,
    - 0.4209746222 9351995033 6450865676 E -20,
    0.9483904058 1983732764 1500214512 E -21,
    - 0.2179467860 1366743199 4032574014 E -21,
    0.5103936869 0714509499 3452562741 E -22,
    - 0.1216883113 3344150908 9746779693 E -22,
    0.2951289166 4478751929 4773757144 E -23,
    - 0.7275353763 7728468971 443895092 E -24,
    0.1821639048 6230739612 1667115976 E -24,
    - 0.4629629963 1633171661 2753482064 E -25,
    0.1193539790 9715779152 3052371292 E -25,
    - 0.3119493285 2201424493 1062147473 E -26,
    0.8261419734 5334664228 4170028518 E -27,
    - 0.2215803373 6609829830 2591177697 E -27,
    0.6016031671 6542638904 5303124429 E -28,
    - 0.1652725098 3821265964 9744302314 E -28,
    0.4592230358 7730270279 5636377166 E -29,
    - 0.1290062767 2132638473 745321267 E -29,
    0.3662718481 0320025908 1177078922 E -30]
                                                             Type: List Float
--R 
--R
--R   (3)
--R   [1.9121732258 6055345391 51932651, - 0.0420835505 2868484375 5097498668,
--R    0.0017228196 2728432678 3371181578 35,
--R    - 0.0000991578 2173444563 6455984232 2973,
--R    0.0000071760 9316802277 5052655906 65592,
--R    - 0.6152733145 0951269682 7956791331 E -6,
--R    0.6024857106 5627583129 399970161 E -7,
--R    - 0.6573848845 2883048229 5894189637 E -8,
--R    0.7853167541 8323998199 4810079871 E -9,
--R    - 0.1013730288 0038789855 4202774257 E -9,
--R    0.1399770413 2267686027 7823488623 E -10,
--R    - 0.2051008376 7838189961 8962318711 E -11,
--R    0.3168388726 0024778181 4907985818 E -12,
--R    - 0.5132760082 8391806541 5984751899 E -13,
--R    0.8680933040 7665493418 7433687383 E -14,
--R    - 0.1527015040 9030849719 8572355351 E -14,
--R    0.2784686251 6493573965 0105251453 E -15,
--R    - 0.5249890437 4217669680 8472933696 E -16,
--R    0.1020717991 2485612924 7455787226 E -16,
--R    - 0.2042264679 8997184130 8462421876 E -17,
--R    0.4197064172 7264847440 8827228562 E -18,
--R    - 0.8844508176 1728105081 6483737536 E -19,
--R    0.1908272629 5947174199 5060168262 E -19,
--R    - 0.4209746222 9351995033 6450865676 E -20,
--R    0.9483904058 1983732764 1500214512 E -21,
--R    - 0.2179467860 1366743199 4032574014 E -21,
--R    0.5103936869 0714509499 3452562741 E -22,
--R    - 0.1216883113 3344150908 9746779693 E -22,
--R    0.2951289166 4478751929 4773757144 E -23,
--R    - 0.7275353763 7728468971 443895092 E -24,
--R    0.1821639048 6230739612 1667115976 E -24,
--R    - 0.4629629963 1633171661 2753482064 E -25,
--R    0.1193539790 9715779152 3052371292 E -25,
--R    - 0.3119493285 2201424493 1062147473 E -26,
--R    0.8261419734 5334664228 4170028518 E -27,
--R    - 0.2215803373 6609829830 2591177697 E -27,
--R    0.6016031671 6542638904 5303124429 E -28,
--R    - 0.1652725098 3821265964 9744302314 E -28,
--R    0.4592230358 7730270279 5636377166 E -29,
--R    - 0.1290062767 2132638473 745321267 E -29,
--R    0.3662718481 0320025908 1177078922 E -30]
--R                                                             Type: List Float
--E 2

--S 3 of 20
[[-160.,0.993826695674061273878797850088,_
 Ei1(-160.0),Ei1(-160.0)-0.993826695674061273878797850088],_
[-80.0,0.987801333094288773564522608410,_
 Ei1(-80.0),Ei1(-80.0)-0.987801333094288773564522608410],_
[-53.0-1.0/3.0,0.981916290143194439617735426105,_
 Ei1(-53.0-1.0/3.0),Ei1(-53.0-1.0/3.0)-0.981916290143194439617735426105],_
[-40.0,0.976164603185143050808000604060,_
 Ei1(-40.0),Ei1(-40.0)-0.976164603185143050808000604060],_
[-32.0,0.970539884074663920462584664361,_
 Ei1(-32.0),Ei1(-32.0)-0.970539884074663920462584664361],_
[-26.0-2.0/3.0,0.965036251123377035763536593528,_
 Ei1(-26.0-2.0/3.0),Ei1(-26.0-2.0/3.0)-0.965036251123377035763536593528],_
[-22.0-6.0/7.0,0.959648271079367276165478970820,_
 Ei1(-22.0-6.0/7.0),Ei1(-22.0-6.0/7.0)-0.959648271079367276165478970820],_
[-20.0,0.954370909919216833975195829433,_
 Ei1(-20.0),Ei1(-20.0)-0.954370909919216833975195829433],_
[-17.0-7.0/9.0,0.949199490779745744606445346803,_
 Ei1(-17.0-7.0/9.0),Ei1(-17.0-7.0/9.0)-0.949199490779745744606445346803],_
[-16.0,0.944129657736902978984149471583,_
 Ei1(-16.0),Ei1(-16.0)-0.944129657736902978984149471583],_
[-14.0-6.0/11.0,0.939157344419284241240422409988,_
 Ei1(-14.0-6.0/11.0),Ei1(-14.0-6.0/11.0)-0.939157344419284241240422409988],_
[-13.0-1.0/3.0,0.934278746653410464809375801650,_
 Ei1(-13.0-1.0/3.0),Ei1(-13.0-1.0/3.0)-0.934278746653410464809375801650],_
[-12.0-4.0/13.0,0.929490298497214037725319679042,_
 Ei1(-12.0-4.0/13.0),Ei1(-12.0-4.0/13.0)-0.929490298497214037725319679042],_
[-11.0-3.0/7.0,0.924788651140841696055993585492,_
 Ei1(-11.0-3.0/7.0),Ei1(-11.0-3.0/7.0)-0.924788651140841696055993585492],_
[-10.0-2.0/3.0,0.920170654249445676202148012149,_
 Ei1(-10.0-2.0/3.0),Ei1(-10.0-2.0/3.0)-0.920170654249445676202148012149],_
[-10.0,0.915633339397880818760698157666,_
 Ei1(-10.0),Ei1(-10.0)-0.915633339397880818760698157666]]
 

   (4)
   [[- 160.0,0.99382669567406123,0.99382669567406112,- 1.1102230246251565E-16],
    [- 80.0,0.98780133309428875,0.98780133309428875,0.0],
    [- 53.333333333333329,0.98191629014319437,0.98191629014319437,0.0],
    [- 40.0,0.97616460318514298,0.97616460318514298,0.0],
    [- 32.0,0.97053988407466385,0.97053988407466352,- 3.3306690738754696E-16],

     [- 26.666666666666664, 0.96503625112337699, 0.96503625112337688,
      - 1.1102230246251565E-16]
     ,
    [- 22.857142857142854,0.95964827107936723,0.95964827107936723,0.0],
    [- 20.0,0.9543709099192168,0.9543709099192168,0.0],
    [- 17.777777777777775,0.94919949077974564,0.94919949077974564,0.0],
    [- 16.0,0.94412965773690294,0.94412965773690283,- 1.1102230246251565E-16],

     [- 14.545454545454545, 0.93915734441928422, 0.939157344419284,
      - 2.2204460492503131E-16]
     ,

     [- 13.333333333333332, 0.93427874665341037, 0.93427874665341049,
      1.1102230246251565E-16]
     ,

     [- 12.307692307692307, 0.92949029849721398, 0.92949029849721376,
      - 2.2204460492503131E-16]
     ,
    [- 11.428571428571427,0.92478865114084163,0.92478865114084163,0.0],
    [- 10.666666666666666,0.92017065424944566,0.92017065424944566,0.0],
    [- 10.0,0.91563333939788072,0.91563333939788083,1.1102230246251565E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (4)
--R   [[- 160.,0.99382669567406123,0.99382669567406123,0.],
--R    [- 80.,0.98780133309428875,0.98780133309428886,1.1102230246251565E-16],
--R    [- 53.333333333333336,0.98191629014319448,0.98191629014319448,0.],
--R    [- 40.,0.97616460318514309,0.97616460318514309,0.],
--R    [- 32.,0.97053988407466396,0.97053988407466363,- 3.3306690738754696E-16],
--R    [- 26.666666666666668,0.96503625112337699,0.96503625112337699,0.],
--R
--R     [- 22.857142857142858, 0.95964827107936723, 0.95964827107936734,
--R      1.1102230246251565E-16]
--R     ,
--R    [- 20.,0.9543709099192168,0.95437090991921691,1.1102230246251565E-16],
--R    [- 17.777777777777779,0.94919949077974575,0.94919949077974575,0.],
--R    [- 16.,0.94412965773690294,0.94412965773690294,0.],
--R
--R     [- 14.545454545454545, 0.93915734441928422, 0.93915734441928411,
--R      - 1.1102230246251565E-16]
--R     ,
--R
--R     [- 13.333333333333334, 0.93427874665341049, 0.9342787466534106,
--R      1.1102230246251565E-16]
--R     ,
--R
--R     [- 12.307692307692308, 0.92949029849721398, 0.92949029849721387,
--R      - 1.1102230246251565E-16]
--R     ,
--R    [- 11.428571428571429,0.92478865114084174,0.92478865114084174,0.],
--R
--R     [- 10.666666666666666, 0.92017065424944566, 0.92017065424944577,
--R      1.1102230246251565E-16]
--R     ,
--R    [- 10.,0.91563333939788083,0.91563333939788094,1.1102230246251565E-16]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 3

--S 4 of 20
bChebyshev:=[_
 0.175755649606129373848762834691E1,_
-0.435854151773616611705001867964E-01,_
-0.797950713955842540133217027492E-02,_
-0.148437232730371213850970210001E-02,_
-0.280030198437751457486203954948E-03,_
-0.534864851286579323039177361553E-04,_
-0.103286724357355486610233266460E-04,_
-0.201408331300553687732226198639E-05,_
-0.396175843427386645822338443500E-06,_
-0.785387276709663163067607656069E-07,_
-0.156792598100746982624616270279E-07,_
-0.315005593937639988250007372851E-08,_
-0.636509682252420373040380263972E-09,_
-0.129288811328056318356593121259E-09,_
-0.263869099965925576132149942808E-10,_
-0.540895828704506873491922207896E-11,_
-0.111322278460108989997676692708E-11,_
-0.229962472607446246184338864145E-12,_
-0.476668238949519026223913482091E-13,_
-0.991175674733527094506246643371E-14,_
-0.206710358049570724000900805021E-14,_
-0.432277678338338505645764394579E-15,_
-0.906301479966501725514905603356E-16,_
-0.190466997958166139744015963342E-16,_
-0.401179232635027866346744227520E-17,_
-0.846777213001683223134166334685E-18,_
-0.179084273365869665555826492204E-18,_
-0.379449063817147824401106175166E-19,_
-0.805399923679827985260999654058E-20,_
-0.171233901123620129743228671244E-20,_
-0.364627405877496862086576562816E-21,_
-0.777596963889394794353098157647E-22,_
-0.166062849844840205662531950966E-22,_
-0.355117862578825093005927145352E-23,_
-0.760372268594135809295734653294E-24,_
-0.163007413725849002889638374755E-24,_
-0.349857520272863223507538497255E-25,_
-0.751717962789009882460645145143E-26,_
-0.161687744005272276298777317918E-26,_
-0.348127008572475691748202271565E-27,_
-0.750270777550246547010642233720E-28,_
-0.161845436449591026807612330206E-28,_
-0.349436677170516166749482836452E-29,_
-0.755103690612616785856037026797E-30]
 

   (5)
   [1.7575564960 6129373848 762834691, - 0.0435854151 7736166117 0500186796 4,
    - 0.0079795071 3955842540 1332170274 92,
    - 0.0014843723 2730371213 8509702100 01,
    - 0.0002800301 9843775145 7486203954 948,
    - 0.0000534864 8512865793 2303917736 1553,
    - 0.0000103286 7243573554 8661023326 646,
    - 0.0000020140 8331300553 6877322261 98639,
    - 0.3961758434 2738664582 23384435 E -6,
    - 0.7853872767 0966316306 7607656069 E -7,
    - 0.1567925981 0074698262 4616270279 E -7,
    - 0.3150055939 3763998825 0007372851 E -8,
    - 0.6365096822 5242037304 0380263972 E -9,
    - 0.1292888113 2805631835 6593121259 E -9,
    - 0.2638690999 6592557613 2149942808 E -10,
    - 0.5408958287 0450687349 1922207896 E -11,
    - 0.1113222784 6010898999 7676692708 E -11,
    - 0.2299624726 0744624618 4338864145 E -12,
    - 0.4766682389 4951902622 3913482091 E -13,
    - 0.9911756747 3352709450 6246643371 E -14,
    - 0.2067103580 4957072400 0900805021 E -14,
    - 0.4322776783 3833850564 5764394579 E -15,
    - 0.9063014799 6650172551 4905603356 E -16,
    - 0.1904669979 5816613974 4015963342 E -16,
    - 0.4011792326 3502786634 674422752 E -17,
    - 0.8467772130 0168322313 4166334685 E -18,
    - 0.1790842733 6586966555 5826492204 E -18,
    - 0.3794490638 1714782440 1106175166 E -19,
    - 0.8053999236 7982798526 0999654058 E -20,
    - 0.1712339011 2362012974 3228671244 E -20,
    - 0.3646274058 7749686208 6576562816 E -21,
    - 0.7775969638 8939479435 3098157647 E -22,
    - 0.1660628498 4484020566 2531950966 E -22,
    - 0.3551178625 7882509300 5927145352 E -23,
    - 0.7603722685 9413580929 5734653294 E -24,
    - 0.1630074137 2584900288 9638374755 E -24,
    - 0.3498575202 7286322350 7538497255 E -25,
    - 0.7517179627 8900988246 0645145143 E -26,
    - 0.1616877440 0527227629 8777317918 E -26,
    - 0.3481270085 7247569174 8202271565 E -27,
    - 0.7502707775 5024654701 064223372 E -28,
    - 0.1618454364 4959102680 7612330206 E -28,
    - 0.3494366771 7051616674 9482836452 E -29,
    - 0.7551036906 1261678585 6037026797 E -30]
                                                             Type: List Float
--R 
--R
--R   (5)
--R   [1.7575564960 6129373848 762834691, - 0.0435854151 7736166117 0500186796 4,
--R    - 0.0079795071 3955842540 1332170274 92,
--R    - 0.0014843723 2730371213 8509702100 01,
--R    - 0.0002800301 9843775145 7486203954 948,
--R    - 0.0000534864 8512865793 2303917736 1553,
--R    - 0.0000103286 7243573554 8661023326 646,
--R    - 0.0000020140 8331300553 6877322261 98639,
--R    - 0.3961758434 2738664582 23384435 E -6,
--R    - 0.7853872767 0966316306 7607656069 E -7,
--R    - 0.1567925981 0074698262 4616270279 E -7,
--R    - 0.3150055939 3763998825 0007372851 E -8,
--R    - 0.6365096822 5242037304 0380263972 E -9,
--R    - 0.1292888113 2805631835 6593121259 E -9,
--R    - 0.2638690999 6592557613 2149942808 E -10,
--R    - 0.5408958287 0450687349 1922207896 E -11,
--R    - 0.1113222784 6010898999 7676692708 E -11,
--R    - 0.2299624726 0744624618 4338864145 E -12,
--R    - 0.4766682389 4951902622 3913482091 E -13,
--R    - 0.9911756747 3352709450 6246643371 E -14,
--R    - 0.2067103580 4957072400 0900805021 E -14,
--R    - 0.4322776783 3833850564 5764394579 E -15,
--R    - 0.9063014799 6650172551 4905603356 E -16,
--R    - 0.1904669979 5816613974 4015963342 E -16,
--R    - 0.4011792326 3502786634 674422752 E -17,
--R    - 0.8467772130 0168322313 4166334685 E -18,
--R    - 0.1790842733 6586966555 5826492204 E -18,
--R    - 0.3794490638 1714782440 1106175166 E -19,
--R    - 0.8053999236 7982798526 0999654058 E -20,
--R    - 0.1712339011 2362012974 3228671244 E -20,
--R    - 0.3646274058 7749686208 6576562816 E -21,
--R    - 0.7775969638 8939479435 3098157647 E -22,
--R    - 0.1660628498 4484020566 2531950966 E -22,
--R    - 0.3551178625 7882509300 5927145352 E -23,
--R    - 0.7603722685 9413580929 5734653294 E -24,
--R    - 0.1630074137 2584900288 9638374755 E -24,
--R    - 0.3498575202 7286322350 7538497255 E -25,
--R    - 0.7517179627 8900988246 0645145143 E -26,
--R    - 0.1616877440 0527227629 8777317918 E -26,
--R    - 0.3481270085 7247569174 8202271565 E -27,
--R    - 0.7502707775 5024654701 064223372 E -28,
--R    - 0.1618454364 4959102680 7612330206 E -28,
--R    - 0.3494366771 7051616674 9482836452 E -29,
--R    - 0.7551036906 1261678585 6037026797 E -30]
--R                                                             Type: List Float
--E 4

--S 5 of 20
[[-10.000,0.915633339397880818760698157661,_
  Ei2(-10.000),Ei2(-10.000)-0.915633339397880818760698157661],_
[ -9.625,0.912844461467993418856575662217,_
  Ei2( -9.625),Ei2( -9.625)-0.912844461467993418856575662217],_
[ -9.250,0.909862751525424139378954274597,_
  Ei2( -9.250),Ei2( -9.250)-0.909862751525424139378954274597],_
[ -8.875,0.906667270654753880334995756418,_
  Ei2( -8.875),Ei2( -8.875)-0.906667270654753880334995756418],_
[ -8.500,0.903233901973207844144682926135,_
  Ei2( -8.500),Ei2( -8.500)-0.903233901973207844144682926135],_
[ -8.125,0.899534717688473836301415777697,_
  Ei2( -8.125),Ei2( -8.125)-0.899534717688473836301415777697],_
[ -7.750,0.895537187087539157179475513219,_
  Ei2( -7.750),Ei2( -7.750)-0.895537187087539157179475513219],_
[ -7.375,0.891203176321254316267087476258,_
  Ei2( -7.375),Ei2( -7.375)-0.891203176321254316267087476258],_
[ -7.000,0.886487672536429352893993846569,_
  Ei2( -7.000),Ei2( -7.000)-0.886487672536429352893993846569],_
[ -6.625,0.881337138468210200394305706270,_
  Ei2( -6.625),Ei2( -6.625)-0.881337138468210200394305706270],_
[ -6.250,0.875687364788465932276462155532,_
  Ei2( -6.250),Ei2( -6.250)-0.875687364788465932276462155532],_
[ -5.875,0.869460629454113410302047153364,_
  Ei2( -5.875),Ei2( -5.875)-0.869460629454113410302047153364],_
[ -5.500,0.862561884690701422090918986586,_
  Ei2( -5.500),Ei2( -5.500)-0.862561884690701422090918986586],_
[ -5.125,0.854873553890199542392425567234,_
  Ei2( -5.125),Ei2( -5.125)-0.854873553890199542392425567234],_
[ -4.750,0.846248299103587361171665798810,_
  Ei2( -4.750),Ei2( -4.750)-0.846248299103587361171665798810],_
[ -4.375,0.836498754556298741742152267582,_
  Ei2( -4.375),Ei2( -4.375)-0.836498754556298741742152267582],_
[ -4.000,0.825382599604223332408183035504,_
  Ei2( -4.000),Ei2( -4.000)-0.825382599604223332408183035504]]
 

   (6)
   [[- 10.0,0.91563333939788072,0.91563333939788083,1.1102230246251565E-16],
    [- 9.625,0.91284446146799336,0.91284446146799336,0.0],
    [- 9.25,0.90986275152542406,0.90986275152542395,- 1.1102230246251565E-16],
    [- 8.875,0.90666727065475383,0.90666727065475394,1.1102230246251565E-16],
    [- 8.5,0.90323390197320774,0.90323390197320796,2.2204460492503131E-16],
    [- 8.125,0.89953471768847382,0.89953471768847415,3.3306690738754696E-16],
    [- 7.75,0.89553718708753915,0.89553718708753927,1.1102230246251565E-16],
    [- 7.375,0.89120317632125423,0.89120317632125412,- 1.1102230246251565E-16],
    [- 7.0,0.88648767253642935,0.88648767253642924,- 1.1102230246251565E-16],
    [- 6.625,0.88133713846821016,0.88133713846821005,- 1.1102230246251565E-16],
    [- 6.25,0.87568736478846587,0.87568736478846598,1.1102230246251565E-16],
    [- 5.875,0.8694606294541134,0.86946062945411307,- 3.3306690738754696E-16],
    [- 5.5,0.86256188469070139,0.86256188469070139,0.0],
    [- 5.125,0.85487355389019948,0.85487355389019937,- 1.1102230246251565E-16],
    [- 4.75,0.84624829910358734,0.84624829910358745,1.1102230246251565E-16],
    [- 4.375,0.83649875455629874,0.83649875455629874,0.0],
    [- 4.0,0.82538259960422322,0.82538259960422322,0.0]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (6)
--R   [[- 10.,0.91563333939788083,0.91563333939788083,0.],
--R    [- 9.625,0.91284446146799347,0.91284446146799336,- 1.1102230246251565E-16],
--R    [- 9.25,0.90986275152542417,0.90986275152542395,- 2.2204460492503131E-16],
--R    [- 8.875,0.90666727065475383,0.90666727065475394,1.1102230246251565E-16],
--R    [- 8.5,0.90323390197320785,0.90323390197320796,1.1102230246251565E-16],
--R    [- 8.125,0.89953471768847382,0.89953471768847415,3.3306690738754696E-16],
--R    [- 7.75,0.89553718708753915,0.89553718708753927,1.1102230246251565E-16],
--R    [- 7.375,0.89120317632125434,0.89120317632125423,- 1.1102230246251565E-16],
--R    [- 7.,0.88648767253642935,0.88648767253642924,- 1.1102230246251565E-16],
--R    [- 6.625,0.88133713846821016,0.88133713846821005,- 1.1102230246251565E-16],
--R    [- 6.25,0.87568736478846598,0.87568736478846598,0.],
--R    [- 5.875,0.8694606294541134,0.86946062945411307,- 3.3306690738754696E-16],
--R    [- 5.5,0.86256188469070139,0.86256188469070139,0.],
--R    [- 5.125,0.85487355389019959,0.85487355389019937,- 2.2204460492503131E-16],
--R    [- 4.75,0.84624829910358734,0.84624829910358745,1.1102230246251565E-16],
--R    [- 4.375,0.83649875455629874,0.83649875455629874,0.],
--R    [- 4.,0.82538259960422333,0.82538259960422322,- 1.1102230246251565E-16]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 5

--S 6 of 20
cChebyshev:=[_
0.329370010376739129393905231421E1,_
0.167983505237130291565505796064E1,_
0.722043610567875435240299679644E0,_
0.260031236054809561713740181192E0,_
0.801049430817375022394742889237E-01,_
0.215140366397633375480552483005E-01,_
0.511620778993033120621968910894E-02,_
0.109093286100739135605066199014E-02,_
0.210741532023938916318348675226E-03,_
0.371990451665188857095940815956E-04,_
0.604349163712387875704767032866E-05,_
0.909295427396260952649596541772E-06,_
0.127380516065926478865567184969E-06,_
0.166918574841098907390896143814E-07,_
0.205441702640104792547612484551E-08,_
0.238358444446681765914052321417E-09,_
0.261538637888544296669068664148E-10,_
0.272185862285416706446550268995E-11,_
0.269375003198357929925326427442E-12,_
0.254122094670726355467884089307E-13,_
0.229013040686503709418510620516E-14,_
0.197546573907462299401057650412E-15,_
0.163402455192893174068635419984E-16,_
0.129823543707963760991961293204E-17,_
0.992258792507371059644632581302E-19,_
0.730625280672210329447230880087E-20,_
0.518967683460434512720780080019E-21,_
0.356040945409970681128043162227E-22,_
0.236197943257938642370187203948E-23,_
0.151683776772145297549624516819E-24,_
0.943908972224487442925310405245E-26,_
0.569722755950369211989581737831E-27,_
0.333833362779543303156597939562E-28,_
0.190062601281619148526680482237E-29]
 

   (7)
   [3.2937001037 6739129393 905231421, 1.6798350523 7130291565 505796064,
    0.7220436105 6787543524 0299679644, 0.2600312360 5480956171 3740181192,
    0.0801049430 8173750223 9474288923 7, 0.0215140366 3976333754 8055248300 5,
    0.0051162077 8993033120 6219689108 94,
    0.0010909328 6100739135 6050661990 14,
    0.0002107415 3202393891 6318348675 226,
    0.0000371990 4516651888 5709594081 5956,
    0.0000060434 9163712387 8757047670 32866,
    0.9092954273 9626095264 9596541772 E -6,
    0.1273805160 6592647886 5567184969 E -6,
    0.1669185748 4109890739 0896143814 E -7,
    0.2054417026 4010479254 7612484551 E -8,
    0.2383584444 4668176591 4052321417 E -9,
    0.2615386378 8854429666 9068664148 E -10,
    0.2721858622 8541670644 6550268995 E -11,
    0.2693750031 9835792992 5326427442 E -12,
    0.2541220946 7072635546 7884089307 E -13,
    0.2290130406 8650370941 8510620516 E -14,
    0.1975465739 0746229940 1057650412 E -15,
    0.1634024551 9289317406 8635419984 E -16,
    0.1298235437 0796376099 1961293204 E -17,
    0.9922587925 0737105964 4632581302 E -19,
    0.7306252806 7221032944 7230880087 E -20,
    0.5189676834 6043451272 0780080019 E -21,
    0.3560409454 0997068112 8043162227 E -22,
    0.2361979432 5793864237 0187203948 E -23,
    0.1516837767 7214529754 9624516819 E -24,
    0.9439089722 2448744292 5310405245 E -26,
    0.5697227559 5036921198 9581737831 E -27,
    0.3338333627 7954330315 6597939562 E -28,
    0.1900626012 8161914852 6680482237 E -29]
                                                             Type: List Float
--R 
--R
--R   (7)
--R   [3.2937001037 6739129393 905231421, 1.6798350523 7130291565 505796064,
--R    0.7220436105 6787543524 0299679644, 0.2600312360 5480956171 3740181192,
--R    0.0801049430 8173750223 9474288923 7, 0.0215140366 3976333754 8055248300 5,
--R    0.0051162077 8993033120 6219689108 94,
--R    0.0010909328 6100739135 6050661990 14,
--R    0.0002107415 3202393891 6318348675 226,
--R    0.0000371990 4516651888 5709594081 5956,
--R    0.0000060434 9163712387 8757047670 32866,
--R    0.9092954273 9626095264 9596541772 E -6,
--R    0.1273805160 6592647886 5567184969 E -6,
--R    0.1669185748 4109890739 0896143814 E -7,
--R    0.2054417026 4010479254 7612484551 E -8,
--R    0.2383584444 4668176591 4052321417 E -9,
--R    0.2615386378 8854429666 9068664148 E -10,
--R    0.2721858622 8541670644 6550268995 E -11,
--R    0.2693750031 9835792992 5326427442 E -12,
--R    0.2541220946 7072635546 7884089307 E -13,
--R    0.2290130406 8650370941 8510620516 E -14,
--R    0.1975465739 0746229940 1057650412 E -15,
--R    0.1634024551 9289317406 8635419984 E -16,
--R    0.1298235437 0796376099 1961293204 E -17,
--R    0.9922587925 0737105964 4632581302 E -19,
--R    0.7306252806 7221032944 7230880087 E -20,
--R    0.5189676834 6043451272 0780080019 E -21,
--R    0.3560409454 0997068112 8043162227 E -22,
--R    0.2361979432 5793864237 0187203948 E -23,
--R    0.1516837767 7214529754 9624516819 E -24,
--R    0.9439089722 2448744292 5310405245 E -26,
--R    0.5697227559 5036921198 9581737831 E -27,
--R    0.3338333627 7954330315 6597939562 E -28,
--R    0.1900626012 8161914852 6680482237 E -29]
--R                                                             Type: List Float
--E 6

--S 7 of 20
[[-4.0,0.491822344607818096479962798267,_
  Ei3(-4.0),Ei3(-4.0)-0.491822344607818096479962798267],_
[-3.5,0.524842506644128356918258753311,_
  Ei3(-3.5),Ei3(-3.5)-0.524842506644128356918258753311],_
[-3.0,0.562958778221279863138086024270,_
  Ei3(-3.0),Ei3(-3.0)-0.562958778221279863138086024270],_
[-2.5,0.607368525858383064514266925640,_
  Ei3(-2.5),Ei3(-2.5)-0.607368525858383064514266925640],_
[-2.0,0.659631678084769644795492023380,_
  Ei3(-2.0),Ei3(-2.0)-0.659631678084769644795492023380],_
[-1.5,0.721800236944219929657623030310,_
  Ei3(-1.5),Ei3(-1.5)-0.721800236944219929657623030310],_
[-1.0,0.796599599297053134283675865540,_
  Ei3(-1.0),Ei3(-1.0)-0.796599599297053134283675865540],_
[-0.5,0.887684158235496725872151815870,_
  Ei3(-0.5),Ei3(-0.5)-0.887684158235496725872151815870],_
[0.0,1.00000000000000000000000000000,_
  Ei3(0.0),Ei3(0.0)-1.00000000000000000000000000000],_
[0.5,1.14030284104317205746248768807,_
  Ei3(0.5),Ei3(0.5)-1.14030284104317205746248768807],_
[1.0,1.31790215145440389486000884424,_
  Ei3(1.0),Ei3(1.0)-1.31790215145440389486000884424],_
[1.5,1.54573645074673373024859074039,_
  Ei3(1.5),Ei3(1.5)-1.54573645074673373024859074039],_
[2.0,1.84193575527020599667788045934,_
  Ei3(2.0),Ei3(2.0)-1.84193575527020599667788045934],_
[2.5,2.23210379912116511445340506423,_
  Ei3(2.5),Ei3(2.5)-2.23210379912116511445340506423],_
[3.0,2.75266820568525800200219289740,_
  Ei3(3.0),Ei3(3.0)-2.75266820568525800200219289740],_
[3.5,3.45582153193012412437300898811,_
  Ei3(3.5),Ei3(3.5)-3.45582153193012412437300898811],_
[4.0,4.41684111100869913580118598668,_
  Ei3(4.0),Ei3(4.0)-4.41684111100869913580118598668]]
 

   (8)
   [[- 4.0,0.4918223446078181,0.49182234460781793,- 1.6653345369377348E-16],
    [- 3.5,0.52484250664412835,0.52484250664412813,- 2.2204460492503131E-16],
    [- 3.0,0.56295877822127982,0.56295877822127993,1.1102230246251565E-16],
    [- 2.5,0.60736852585838297,0.60736852585838319,2.2204460492503131E-16],
    [- 2.0,0.65963167808476963,0.65963167808476963,0.0],
    [- 1.5,0.72180023694421991,0.72180023694421991,0.0],
    [- 1.0,0.79659959929705304,0.79659959929705304,0.0],
    [- 0.5,0.88768415823549662,0.88768415823549662,0.0], [0.0,1.0,1.0,0.0],
    [0.5,1.1403028410431719,1.140302841043171,- 8.8817841970012523E-16],
    [1.0,1.3179021514544038,1.3179021514544034,- 4.4408920985006262E-16],
    [1.5,1.5457364507467337,1.545736450746733,- 6.6613381477509392E-16],
    [2.0,1.8419357552702058,1.8419357552702067,8.8817841970012523E-16],
    [2.5,2.2321037991211647,2.2321037991211643,- 4.4408920985006262E-16],
    [3.0,2.7526682056852576,2.7526682056852585,8.8817841970012523E-16],
    [3.5,3.4558215319301238,3.4558215319301233,- 4.4408920985006262E-16],
    [4.0,4.4168411110086989,4.4168411110086998,8.8817841970012523E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (8)
--R   [[- 4.,0.4918223446078181,0.49182234460781826,1.6653345369377348E-16],
--R    [- 3.5,0.52484250664412835,0.52484250664412835,0.],
--R    [- 3.,0.56295877822127982,0.56295877822128015,3.3306690738754696E-16],
--R    [- 2.5,0.60736852585838308,0.60736852585838341,3.3306690738754696E-16],
--R    [- 2.,0.65963167808476963,0.65963167808476975,1.1102230246251565E-16],
--R    [- 1.5,0.72180023694421991,0.72180023694422013,2.2204460492503131E-16],
--R    [- 1.,0.79659959929705315,0.79659959929705293,- 2.2204460492503131E-16],
--R    [- 0.5,0.88768415823549673,0.88768415823549696,2.2204460492503131E-16],
--R    [0.,1.,1.,0.],
--R    [0.5,1.1403028410431721,1.1403028410431715,- 6.6613381477509392E-16],
--R    [1.,1.3179021514544038,1.3179021514544034,- 4.4408920985006262E-16],
--R    [1.5,1.5457364507467337,1.5457364507467335,- 2.2204460492503131E-16],
--R    [2.,1.841935755270206,1.8419357552702071,1.1102230246251565E-15],
--R    [2.5,2.2321037991211652,2.2321037991211647,- 4.4408920985006262E-16],
--R    [3.,2.7526682056852581,2.7526682056852589,8.8817841970012523E-16],
--R    [3.5,3.4558215319301242,3.4558215319301238,- 4.4408920985006262E-16],
--R    [4.,4.4168411110086989,4.4168411110087007,1.7763568394002505E-15]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 7

--S 8 of 20
dChebyshev:=[_
 0.245513353878129528673420457043E1,_
-0.162438379130376524396002276856E0,_
 0.449575308093572641480785417193E-01,_
-0.674157867998922998848718835050E-02,_
-0.130669714280329428051599341387E-02,_
 0.138108314600072576020202089820E-02,_
-0.585022879015965798687368242394E-03,_
 0.174929934107891970038740976432E-03,_
-0.404728149905293035522869333800E-04,_
 0.721710241217099750035752600049E-05,_
-0.861277697019867752414815450193E-06,_
-0.251447529653225597779084739054E-09,_ -- E-06? or wrong place?
 0.379474713820149510814074505574E-07,_
-0.144211796952119806160265640172E-07,_
 0.393504929597610131087190848042E-08,_
-0.928468940106331753047289210353E-09,_
 0.203178956800654613366090995698E-09,_
-0.429249850499236831427918026902E-10,_
 0.899264717778123935268001544182E-11,_
-0.190086911841210975242396635722E-11,_
 0.409219891222373834526121178338E-12,_
-0.899925343729319019825435824585E-13,_
 0.201965467082426383354948543451E-13,_
-0.461293026138308207194950531726E-14,_
 0.106902307293863695668857256409E-14,_
-0.250703007057007295692572254042E-15,_
 0.593732250379155160706073763509E-16,_
-0.141773458243766252344732005648E-16,_
 0.340920375436080893426806402093E-17,_
-0.824829026950549379288702529656E-18,_
 0.200636971262144231398824095937E-18,_
-0.490385166796742224403498152027E-19,_
 0.120373448234833217166664609324E-19,_
-0.296628244714136825381453572575E-20,_
 0.733551238428807599242142328436E-21,_
-0.181992414290851127344263485604E-21,_
 0.452862937429576060217359526404E-22,_
-0.112998004375060961338906717853E-22,_
 0.282668125129011656923764408445E-23,_
-0.708771797716904961666732640699E-24,_
 0.178110452401870951534401530034E-24,_
-0.448500407661896357312006142358E-25,_
 0.113154029257547662245053090840E-25,_
-0.285995789977932163790414326136E-26,_
 0.724077580692267361758172726753E-27,_
-0.183613223412577898050666710105E-27,_
 0.466312873522730486582600122073E-28,_
-0.118595958891902887946724005478E-28,_
 0.302029059055671310731137614875E-29,_
-0.770165054816636606098827057102E-30]
 

   (9)
   [2.4551335387 8129528673 420457043, - 0.1624383791 3037652439 6002276856,
    0.0449575308 0935726414 8078541719 3,
    - 0.0067415786 7998922998 8487188350 5,
    - 0.0013066971 4280329428 0515993413 87,
    0.0013810831 4600072576 0202020898 2,
    - 0.0005850228 7901596579 8687368242 394,
    0.0001749299 3410789197 0038740976 432,
    - 0.0000404728 1499052930 3552286933 38,
    0.0000072171 0241217099 7500357526 00049,
    - 0.8612776970 1986775241 4815450193 E -6,
    - 0.2514475296 5322559777 9084739054 E -9,
    0.3794747138 2014951081 4074505574 E -7,
    - 0.1442117969 5211980616 0265640172 E -7,
    0.3935049295 9761013108 7190848042 E -8,
    - 0.9284689401 0633175304 7289210353 E -9,
    0.2031789568 0065461336 6090995698 E -9,
    - 0.4292498504 9923683142 7918026902 E -10,
    0.8992647177 7812393526 8001544182 E -11,
    - 0.1900869118 4121097524 2396635722 E -11,
    0.4092198912 2237383452 6121178338 E -12,
    - 0.8999253437 2931901982 5435824585 E -13,
    0.2019654670 8242638335 4948543451 E -13,
    - 0.4612930261 3830820719 4950531726 E -14,
    0.1069023072 9386369566 8857256409 E -14,
    - 0.2507030070 5700729569 2572254042 E -15,
    0.5937322503 7915516070 6073763509 E -16,
    - 0.1417734582 4376625234 4732005648 E -16,
    0.3409203754 3608089342 6806402093 E -17,
    - 0.8248290269 5054937928 8702529656 E -18,
    0.2006369712 6214423139 8824095937 E -18,
    - 0.4903851667 9674222440 3498152027 E -19,
    0.1203734482 3483321716 6664609324 E -19,
    - 0.2966282447 1413682538 1453572575 E -20,
    0.7335512384 2880759924 2142328436 E -21,
    - 0.1819924142 9085112734 4263485604 E -21,
    0.4528629374 2957606021 7359526404 E -22,
    - 0.1129980043 7506096133 8906717853 E -22,
    0.2826681251 2901165692 3764408445 E -23,
    - 0.7087717977 1690496166 6732640699 E -24,
    0.1781104524 0187095153 4401530034 E -24,
    - 0.4485004076 6189635731 2006142358 E -25,
    0.1131540292 5754766224 505309084 E -25,
    - 0.2859957899 7793216379 0414326136 E -26,
    0.7240775806 9226736175 8172726753 E -27,
    - 0.1836132234 1257789805 0666710105 E -27,
    0.4663128735 2273048658 2600122073 E -28,
    - 0.1185959588 9190288794 6724005478 E -28,
    0.3020290590 5567131073 1137614875 E -29,
    - 0.7701650548 1663660609 8827057102 E -30]
                                                             Type: List Float
--R 
--R
--R   (9)
--R   [2.4551335387 8129528673 420457043, - 0.1624383791 3037652439 6002276856,
--R    0.0449575308 0935726414 8078541719 3,
--R    - 0.0067415786 7998922998 8487188350 5,
--R    - 0.0013066971 4280329428 0515993413 87,
--R    0.0013810831 4600072576 0202020898 2,
--R    - 0.0005850228 7901596579 8687368242 394,
--R    0.0001749299 3410789197 0038740976 432,
--R    - 0.0000404728 1499052930 3552286933 38,
--R    0.0000072171 0241217099 7500357526 00049,
--R    - 0.8612776970 1986775241 4815450193 E -6,
--R    - 0.2514475296 5322559777 9084739054 E -9,
--R    0.3794747138 2014951081 4074505574 E -7,
--R    - 0.1442117969 5211980616 0265640172 E -7,
--R    0.3935049295 9761013108 7190848042 E -8,
--R    - 0.9284689401 0633175304 7289210353 E -9,
--R    0.2031789568 0065461336 6090995698 E -9,
--R    - 0.4292498504 9923683142 7918026902 E -10,
--R    0.8992647177 7812393526 8001544182 E -11,
--R    - 0.1900869118 4121097524 2396635722 E -11,
--R    0.4092198912 2237383452 6121178338 E -12,
--R    - 0.8999253437 2931901982 5435824585 E -13,
--R    0.2019654670 8242638335 4948543451 E -13,
--R    - 0.4612930261 3830820719 4950531726 E -14,
--R    0.1069023072 9386369566 8857256409 E -14,
--R    - 0.2507030070 5700729569 2572254042 E -15,
--R    0.5937322503 7915516070 6073763509 E -16,
--R    - 0.1417734582 4376625234 4732005648 E -16,
--R    0.3409203754 3608089342 6806402093 E -17,
--R    - 0.8248290269 5054937928 8702529656 E -18,
--R    0.2006369712 6214423139 8824095937 E -18,
--R    - 0.4903851667 9674222440 3498152027 E -19,
--R    0.1203734482 3483321716 6664609324 E -19,
--R    - 0.2966282447 1413682538 1453572575 E -20,
--R    0.7335512384 2880759924 2142328436 E -21,
--R    - 0.1819924142 9085112734 4263485604 E -21,
--R    0.4528629374 2957606021 7359526404 E -22,
--R    - 0.1129980043 7506096133 8906717853 E -22,
--R    0.2826681251 2901165692 3764408445 E -23,
--R    - 0.7087717977 1690496166 6732640699 E -24,
--R    0.1781104524 0187095153 4401530034 E -24,
--R    - 0.4485004076 6189635731 2006142358 E -25,
--R    0.1131540292 5754766224 505309084 E -25,
--R    - 0.2859957899 7793216379 0414326136 E -26,
--R    0.7240775806 9226736175 8172726753 E -27,
--R    - 0.1836132234 1257789805 0666710105 E -27,
--R    0.4663128735 2273048658 2600122073 E -28,
--R    - 0.1185959588 9190288794 6724005478 E -28,
--R    0.3020290590 5567131073 1137614875 E -29,
--R    - 0.7701650548 1663660609 8827057102 E -30]
--R                                                             Type: List Float
--E 8

--S 9 of 20
[[4.0,1.43820803145448278470968670330,_
  Ei4(4.0),Ei4(4.0)-1.43820803145448278470968670330],_
[4.5,1.39641902962974607100674523183,_
  Ei4(4.5), Ei4(4.5)-1.39641902962974607100674523183],_
[5.0,1.35383127745528597790189174047,_
  Ei4(5.0),Ei4(5.0)-1.35383127745528597790189174047],_
[5.5,1.31414356574211924541219816991,_
  Ei4(5.5),Ei4(5.5)-1.31414356574211924541219816991],_
[6.0,1.27888386048956161892314099578,_
  Ei4(6.0),Ei4(6.0)-1.27888386048956161892314099578],_
[6.5,1.24839115500170148640741941387,_
  Ei4(6.5),Ei4(6.5)-1.24839115500170148640741941387],_
[7.0,1.22240805236053105903656846622,_
  Ei4(7.0),Ei4(7.0)-1.22240805236053105903656846622],_
[7.5,1.20042149959963078643879158950,_
  Ei4(7.5),Ei4(7.5)-1.20042149959963078643879158950],_
[8.0,1.18184798698720797317739362644,_
  Ei4(8.0),Ei4(8.0)-1.18184798698720797317739362644],_
[8.5,1.16612652581174849439918142965,_
  Ei4(8.5),Ei4(8.5)-1.16612652581174849439918142965],_
[9.0,1.15275920870892481322396814952,_
  Ei4(9.0),Ei4(9.0)-1.15275920870892481322396814952],_
[9.5,1.14132347595262420155338560641,_
  Ei4(9.5),Ei4(9.5)-1.14132347595262420155338560641],_
[10.0,1.13147020473410778034051681355,_
  Ei4(10.0),Ei4(10.0)-1.13147020473410778034051681355],_
[10.5,1.12291557001776060642888630755,_
  Ei4(10.5),Ei4(10.5)-1.12291557001776060642888630755],_
[11.0,1.11543093899803844164779434229,_
  Ei4(11.0),Ei4(11.0)-1.11543093899803844164779434229],_
[11.5,1.10883292630507730586855234934,_
  Ei4(11.5),Ei4(11.5)-1.10883292630507730586855234934],_
[12.0,1.10297454490675907267241234953,_
  Ei4(12.0),Ei4(12.0)-1.10297454490675907267241234953]]
 

   (10)
   [[4.0,1.4382080314544827,1.4382080314544827,0.0],
    [4.5,1.3964190296297461,1.3964190296297465,4.4408920985006262E-16],
    [5.0,1.3538312774552859,1.3538312774552856,- 2.2204460492503131E-16],
    [5.5,1.3141435657421192,1.3141435657421192,0.0],
    [6.0,1.2788838604895616,1.2788838604895618,2.2204460492503131E-16],
    [6.5,1.2483911550017013,1.2483911550017011,- 2.2204460492503131E-16],
    [7.0,1.222408052360531,1.222408052360531,0.0],
    [7.5,1.2004214995996307,1.2004214995996305,- 2.2204460492503131E-16],
    [8.0,1.1818479869872078,1.1818479869872081,2.2204460492503131E-16],
    [8.5,1.1661265258117484,1.1661265258117477,- 6.6613381477509392E-16],
    [9.0,1.1527592087089247,1.1527592087089251,4.4408920985006262E-16],
    [9.5,1.1413234759526241,1.1413234759526236,- 4.4408920985006262E-16],
    [10.0,1.1314702047341076,1.1314702047341079,2.2204460492503131E-16],
    [10.5,1.1229155700177604,1.1229155700177604,0.0],
    [11.0,1.1154309389980384,1.115430938998039,6.6613381477509392E-16],
    [11.5,1.1088329263050771,1.1088329263050771,0.0],
    [12.0,1.1029745449067589,1.1029745449067592,2.2204460492503131E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (10)
--R   [[4.,1.4382080314544827,1.4382080314544827,0.],
--R    [4.5,1.3964190296297461,1.3964190296297465,4.4408920985006262E-16],
--R    [5.,1.3538312774552861,1.3538312774552856,- 4.4408920985006262E-16],
--R    [5.5,1.3141435657421192,1.314143565742119,- 2.2204460492503131E-16],
--R    [6.,1.2788838604895616,1.2788838604895618,2.2204460492503131E-16],
--R    [6.5,1.2483911550017015,1.2483911550017011,- 4.4408920985006262E-16],
--R    [7.,1.222408052360531,1.222408052360531,0.],
--R    [7.5,1.2004214995996307,1.2004214995996305,- 2.2204460492503131E-16],
--R    [8.,1.1818479869872081,1.1818479869872081,0.],
--R    [8.5,1.1661265258117486,1.1661265258117477,- 8.8817841970012523E-16],
--R    [9.,1.1527592087089249,1.1527592087089251,2.2204460492503131E-16],
--R    [9.5,1.1413234759526243,1.1413234759526236,- 6.6613381477509392E-16],
--R    [10.,1.1314702047341079,1.1314702047341079,0.],
--R    [10.5,1.1229155700177607,1.1229155700177604,- 2.2204460492503131E-16],
--R    [11.,1.1154309389980384,1.115430938998039,6.6613381477509392E-16],
--R    [11.5,1.1088329263050773,1.1088329263050771,- 2.2204460492503131E-16],
--R    [12.,1.1029745449067592,1.1029745449067592,0.]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 9

--S 10 of 20
eChebyshev:=[_
 0.211702864043698668329789991614E1,_
-0.320423727375485794990618303177E-01,_
 0.889173207735316835890182400335E-02,_
-0.250795280518929937088352442063E-02,_
 0.720278946595987548875760902487E-03,_
-0.210349005850113053423531441256E-03,_
 0.620573231827693216588857730842E-04,_
-0.182656674981670265449155689733E-04,_
 0.527065157528936375807788296811E-05,_ --? 7560 or 7580?
-0.145966654761994575323066719367E-05,_
 0.378171997358963671980484193981E-06,_
-0.884258128284071920077971589012E-07,_
 0.174174919853839361377350309156E-07,_
-0.231351774704369063506474480152E-08,_
-0.122860981918086238832104835230E-09,_
 0.234996623632286370478311381926E-09,_
-0.110071940102726287690738963049E-09,_
 0.384827515786120711149705563369E-10,_
-0.114844096749001589658439301603E-10,_
 0.305687629308852082630893626200E-11,_
-0.738827872928473566454163131431E-12,_
 0.163093309416594110564148013749E-12,_
-0.327698937331271249657111774748E-13,_
 0.589811434707131961711164283918E-14,_
-0.909970763595649204643554720718E-15,_
 0.104075238266955386585405697541E-15,_
-0.180981542605922793227163355935E-17,_
-0.377709884256394773369593494417E-17,_
 0.158033290102847957136759888420E-17,_
-0.468429175880882730648433752957E-18,_
 0.119951685259198093707533478542E-18,_
-0.282359474984186517679349931117E-19,_
 0.629373806564463522627520190349E-20,_
-0.135241024950479756305343973177E-20,_
 0.283710605385529141590980426210E-21,_
-0.586700742024638323531936371015E-22,_
 0.120524763609547311112449686917E-22,_
-0.247444661699884869728416011246E-23,_
 0.509996258583785008142986465688E-24,_
-0.105838257877542240887093294733E-24,_
 0.221527624507048278566429387155E-25,_
-0.467927875475696258671852546231E-26,_
 0.997287299060207704824269828079E-27,_
-0.214326794521678804591907805844E-27,_
 0.464065690883818114338414829515E-28,_
-0.101144734921151390948461800780E-28,_
 0.221721152271007711093046878345E-29,_
-0.488489046924378553224914645512E-30]
 

   (11)
   [2.1170286404 3698668329 789991614, - 0.0320423727 3754857949 9061830317 7,
    0.0088917320 7735316835 8901824003 35,
    - 0.0025079528 0518929937 0883524420 63,
    0.0007202789 4659598754 8875760902 487,
    - 0.0002103490 0585011305 3423531441 256,
    0.0000620573 2318276932 1658885773 0842,
    - 0.0000182656 6749816702 6544915568 9733,
    0.0000052706 5157528936 3758077882 96811,
    - 0.0000014596 6654761994 5753230667 19367,
    0.3781719973 5896367198 0484193981 E -6,
    - 0.8842581282 8407192007 7971589012 E -7,
    0.1741749198 5383936137 7350309156 E -7,
    - 0.2313517747 0436906350 6474480152 E -8,
    - 0.1228609819 1808623883 210483523 E -9,
    0.2349966236 3228637047 8311381926 E -9,
    - 0.1100719401 0272628769 0738963049 E -9,
    0.3848275157 8612071114 9705563369 E -10,
    - 0.1148440967 4900158965 8439301603 E -10,
    0.3056876293 0885208263 08936262 E -11,
    - 0.7388278729 2847356645 4163131431 E -12,
    0.1630933094 1659411056 4148013749 E -12,
    - 0.3276989373 3127124965 7111774748 E -13,
    0.5898114347 0713196171 1164283918 E -14,
    - 0.9099707635 9564920464 3554720718 E -15,
    0.1040752382 6695538658 5405697541 E -15,
    - 0.1809815426 0592279322 7163355935 E -17,
    - 0.3777098842 5639477336 9593494417 E -17,
    0.1580332901 0284795713 675988842 E -17,
    - 0.4684291758 8088273064 8433752957 E -18,
    0.1199516852 5919809370 7533478542 E -18,
    - 0.2823594749 8418651767 9349931117 E -19,
    0.6293738065 6446352262 7520190349 E -20,
    - 0.1352410249 5047975630 5343973177 E -20,
    0.2837106053 8552914159 098042621 E -21,
    - 0.5867007420 2463832353 1936371015 E -22,
    0.1205247636 0954731111 2449686917 E -22,
    - 0.2474446616 9988486972 8416011246 E -23,
    0.5099962585 8378500814 2986465688 E -24,
    - 0.1058382578 7754224088 7093294733 E -24,
    0.2215276245 0704827856 6429387155 E -25,
    - 0.4679278754 7569625867 1852546231 E -26,
    0.9972872990 6020770482 4269828079 E -27,
    - 0.2143267945 2167880459 1907805844 E -27,
    0.4640656908 8381811433 8414829515 E -28,
    - 0.1011447349 2115139094 846180078 E -28,
    0.2217211522 7100771109 3046878345 E -29,
    - 0.4884890469 2437855322 4914645512 E -30]
                                                             Type: List Float
--R 
--R
--R   (11)
--R   [2.1170286404 3698668329 789991614, - 0.0320423727 3754857949 9061830317 7,
--R    0.0088917320 7735316835 8901824003 35,
--R    - 0.0025079528 0518929937 0883524420 63,
--R    0.0007202789 4659598754 8875760902 487,
--R    - 0.0002103490 0585011305 3423531441 256,
--R    0.0000620573 2318276932 1658885773 0842,
--R    - 0.0000182656 6749816702 6544915568 9733,
--R    0.0000052706 5157528936 3758077882 96811,
--R    - 0.0000014596 6654761994 5753230667 19367,
--R    0.3781719973 5896367198 0484193981 E -6,
--R    - 0.8842581282 8407192007 7971589012 E -7,
--R    0.1741749198 5383936137 7350309156 E -7,
--R    - 0.2313517747 0436906350 6474480152 E -8,
--R    - 0.1228609819 1808623883 210483523 E -9,
--R    0.2349966236 3228637047 8311381926 E -9,
--R    - 0.1100719401 0272628769 0738963049 E -9,
--R    0.3848275157 8612071114 9705563369 E -10,
--R    - 0.1148440967 4900158965 8439301603 E -10,
--R    0.3056876293 0885208263 08936262 E -11,
--R    - 0.7388278729 2847356645 4163131431 E -12,
--R    0.1630933094 1659411056 4148013749 E -12,
--R    - 0.3276989373 3127124965 7111774748 E -13,
--R    0.5898114347 0713196171 1164283918 E -14,
--R    - 0.9099707635 9564920464 3554720718 E -15,
--R    0.1040752382 6695538658 5405697541 E -15,
--R    - 0.1809815426 0592279322 7163355935 E -17,
--R    - 0.3777098842 5639477336 9593494417 E -17,
--R    0.1580332901 0284795713 675988842 E -17,
--R    - 0.4684291758 8088273064 8433752957 E -18,
--R    0.1199516852 5919809370 7533478542 E -18,
--R    - 0.2823594749 8418651767 9349931117 E -19,
--R    0.6293738065 6446352262 7520190349 E -20,
--R    - 0.1352410249 5047975630 5343973177 E -20,
--R    0.2837106053 8552914159 098042621 E -21,
--R    - 0.5867007420 2463832353 1936371015 E -22,
--R    0.1205247636 0954731111 2449686917 E -22,
--R    - 0.2474446616 9988486972 8416011246 E -23,
--R    0.5099962585 8378500814 2986465688 E -24,
--R    - 0.1058382578 7754224088 7093294733 E -24,
--R    0.2215276245 0704827856 6429387155 E -25,
--R    - 0.4679278754 7569625867 1852546231 E -26,
--R    0.9972872990 6020770482 4269828079 E -27,
--R    - 0.2143267945 2167880459 1907805844 E -27,
--R    0.4640656908 8381811433 8414829515 E -28,
--R    - 0.1011447349 2115139094 846180078 E -28,
--R    0.2217211522 7100771109 3046878345 E -29,
--R    - 0.4884890469 2437855322 4914645512 E -30]
--R                                                             Type: List Float
--E 10

--S 11 of 20
[[12.00,1.10297454490675907267241234952,_
  Ei5(12.00),Ei5(12.00)-1.10297454490675907267241234952],_
[13.25,1.09084489821547569266468614954,_
  Ei5(13.25),Ei5(13.25)-1.09084489821547569266468614954],_
[14.50,1.08135139573519128506346643795,_
  Ei5(14.50),Ei5(14.50)-1.08135139573519128506346643795],_
[15.75,1.07370138419975723712157900374,_
  Ei5(15.75),Ei5(15.75)-1.07370138419975723712157900374],_
[17.00,1.06739369195853783129572196197,_
  Ei5(17.00),Ei5(17.00)-1.06739369195853783129572196197],_
[18.25,1.06209660862215024268372647556,_
  Ei5(18.25),Ei5(18.25)-1.06209660862215024268372647556],_
[19.50,1.05758134215872503195393949410,_
  Ei5(19.50),Ei5(19.50)-1.05758134215872503195393949410],_
[20.75,1.05368445128940944082102194964,_
  Ei5(20.75),Ei5(20.75)-1.05368445128940944082102194964],_
[22.00,1.05028571968518979411780664532,_
  Ei5(22.00),Ei5(22.00)-1.05028571968518979411780664532],_
[23.25,1.04729455170532485811492365591,_
  Ei5(23.25),Ei5(23.25)-1.04729455170532485811492365591],_
[24.50,1.04464126790464363689761075289,_
  Ei5(24.50),Ei5(24.50)-1.04464126790464363689761075289],_
[25.75,1.04227133720232023885710928048,_
  Ei5(25.75),Ei5(25.75)-1.04227133720232023885710928048],_
[27.00,1.04014143832301043813713899754,_
  Ei5(27.00),Ei5(27.00)-1.04014143832301043813713899754],_
[28.25,1.03821670036014587680056548394,_
  Ei5(28.25),Ei5(28.25)-1.03821670036014587680056548394],_
[29.50,1.03646872629241184575154685419,_
  Ei5(29.50),Ei5(29.50)-1.03646872629241184575154685419],_
[30.75,1.03487414989647969472990938990,_
  Ei5(30.75),Ei5(30.75)-1.03487414989647969472990938990],_
[32.00,1.03341356421624104943493552567,_
  Ei5(32.00),Ei5(32.00)-1.03341356421624104943493552567]]
 

   (12)
   [[12.0,1.1029745449067589,1.1029745449067585,- 4.4408920985006262E-16],
    [13.25,1.0908448982154755,1.090844898215475,- 4.4408920985006262E-16],
    [14.5,1.0813513957351912,1.0813513957351915,2.2204460492503131E-16],
    [15.75,1.0737013841997571,1.0737013841997574,2.2204460492503131E-16],
    [17.0,1.0673936919585376,1.0673936919585385,8.8817841970012523E-16],
    [18.25,1.0620966086221502,1.0620966086221502,0.0],
    [19.5,1.057581342158725,1.0575813421587252,2.2204460492503131E-16],
    [20.75,1.0536844512894092,1.0536844512894095,2.2204460492503131E-16],
    [22.0,1.0502857196851896,1.0502857196851898,2.2204460492503131E-16],
    [23.25,1.0472945517053247,1.0472945517053245,- 2.2204460492503131E-16],
    [24.5,1.0446412679046435,1.0446412679046437,2.2204460492503131E-16],
    [25.75,1.0422713372023202,1.04227133720232,- 2.2204460492503131E-16],
    [27.0,1.0401414383230103,1.0401414383230101,- 2.2204460492503131E-16],
    [28.25,1.0382167003601457,1.0382167003601459,2.2204460492503131E-16],
    [29.5,1.0364687262924117,1.0364687262924113,- 4.4408920985006262E-16],
    [30.75,1.0348741498964795,1.0348741498964795,0.0],
    [32.0,1.033413564216241,1.0334135642162412,2.2204460492503131E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (12)
--R   [[12.,1.1029745449067592,1.1029745449067585,- 6.6613381477509392E-16],
--R    [13.25,1.0908448982154757,1.090844898215475,- 6.6613381477509392E-16],
--R    [14.5,1.0813513957351912,1.0813513957351915,2.2204460492503131E-16],
--R    [15.75,1.0737013841997571,1.0737013841997574,2.2204460492503131E-16],
--R    [17.,1.0673936919585378,1.0673936919585385,6.6613381477509392E-16],
--R    [18.25,1.0620966086221502,1.0620966086221502,0.],
--R    [19.5,1.057581342158725,1.0575813421587252,2.2204460492503131E-16],
--R    [20.75,1.0536844512894095,1.0536844512894095,0.],
--R    [22.,1.0502857196851898,1.0502857196851898,0.],
--R    [23.25,1.0472945517053249,1.0472945517053245,- 4.4408920985006262E-16],
--R    [24.5,1.0446412679046437,1.0446412679046437,0.],
--R    [25.75,1.0422713372023202,1.04227133720232,- 2.2204460492503131E-16],
--R    [27.,1.0401414383230105,1.0401414383230101,- 4.4408920985006262E-16],
--R    [28.25,1.0382167003601459,1.0382167003601459,0.],
--R    [29.5,1.0364687262924119,1.0364687262924113,- 6.6613381477509392E-16],
--R    [30.75,1.0348741498964797,1.0348741498964795,- 2.2204460492503131E-16],
--R    [32.,1.033413564216241,1.0334135642162412,2.2204460492503131E-16]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 11


--S 12 of 20
fChebyshev:=[_
 0.203284394579616699087873844202E1,_
 0.166992045203136285147618434339E-01,_
 0.284528472436134680742489985325E-03,_
 0.756394435851620648948786693854E-05,_
 0.279897128945085915750484318090E-06,_
 0.135790182853453106952556392593E-07,_
 0.834359620204046925585610289412E-09,_
 0.637097172764024843827524337306E-10,_
 0.600724760881186123576083084850E-11,_
 0.702287617467977359075059216588E-12,_
 0.101830267370368769309667322152E-12,_
 0.176181290343088004040656741554E-13,_
 0.325082861423536069424072007647E-14,_
 0.507177002550581867881479300685E-15,_
 0.166517738704329429853520036957E-16,_
-0.316675389079751440072410018963E-16,_
-0.158840376366414151548423134074E-16,_
-0.417551325613801883089626455063E-17,_
-0.289234774970714188202868862358E-18,_
 0.280062590339660807289978777339E-18,_
 0.132293863953927089140532005364E-18,_
 0.180444744417730199585334811191E-19,_
-0.790538408652261656202021080364E-20,_
-0.443571136636957344718167314045E-20,_
-0.426410399497810261760579779746E-21,_
 0.392010176693714390725625388636E-21,_
 0.152737805134396364472804486402E-21,_
-0.102484952704949060786953149788E-22,_
-0.213490787477108937948904287231E-22,_
-0.323913947516023687614279789345E-23,_
 0.214218376229645970296249355934E-23,_
 0.823460941961899553169207838151E-24,_
-0.152465282962067210811495038147E-24,_
-0.137820828248824401290438126477E-24,_
 0.213131120142873706791513005998E-26,_
 0.201264965187132665859213006507E-25,_
 0.199553566205637402320607178286E-26,_
-0.279899581220179711426020884464E-26,_
-0.553451183050700250949784942560E-27,_
 0.388499542268455253129749000696E-27,_
 0.112130440723307012540043264712E-27,_
-0.556656828674459488057823816866E-28,_
-0.204548261246513576288865878722E-28,_
 0.845381406448938089437361193598E-29,_
 0.356575515120151526590791715785E-29,_
-0.138365242347797751810195772006E-29,_
-0.606214265320934505767865286306E-30]
 

   (13)
   [2.0328439457 9616699087 873844202, 0.0166992045 2031362851 4761843433 9,
    0.0002845284 7243613468 0742489985 325,
    0.0000075639 4435851620 6489487866 93854,
    0.2798971289 4508591575 048431809 E -6,
    0.1357901828 5345310695 2556392593 E -7,
    0.8343596202 0404692558 5610289412 E -9,
    0.6370971727 6402484382 7524337306 E -10,
    0.6007247608 8118612357 608308485 E -11,
    0.7022876174 6797735907 5059216588 E -12,
    0.1018302673 7036876930 9667322152 E -12,
    0.1761812903 4308800404 0656741554 E -13,
    0.3250828614 2353606942 4072007647 E -14,
    0.5071770025 5058186788 1479300685 E -15,
    0.1665177387 0432942985 3520036957 E -16,
    - 0.3166753890 7975144007 2410018963 E -16,
    - 0.1588403763 6641415154 8423134074 E -16,
    - 0.4175513256 1380188308 9626455063 E -17,
    - 0.2892347749 7071418820 2868862358 E -18,
    0.2800625903 3966080728 9978777339 E -18,
    0.1322938639 5392708914 0532005364 E -18,
    0.1804447444 1773019958 5334811191 E -19,
    - 0.7905384086 5226165620 2021080364 E -20,
    - 0.4435711366 3695734471 8167314045 E -20,
    - 0.4264103994 9781026176 0579779746 E -21,
    0.3920101766 9371439072 5625388636 E -21,
    0.1527378051 3439636447 2804486402 E -21,
    - 0.1024849527 0494906078 6953149788 E -22,
    - 0.2134907874 7710893794 8904287231 E -22,
    - 0.3239139475 1602368761 4279789345 E -23,
    0.2142183762 2964597029 6249355934 E -23,
    0.8234609419 6189955316 9207838151 E -24,
    - 0.1524652829 6206721081 1495038147 E -24,
    - 0.1378208282 4882440129 0438126477 E -24,
    0.2131311201 4287370679 1513005998 E -26,
    0.2012649651 8713266585 9213006507 E -25,
    0.1995535662 0563740232 0607178286 E -26,
    - 0.2798995812 2017971142 6020884464 E -26,
    - 0.5534511830 5070025094 978494256 E -27,
    0.3884995422 6845525312 9749000696 E -27,
    0.1121304407 2330701254 0043264712 E -27,
    - 0.5566568286 7445948805 7823816866 E -28,
    - 0.2045482612 4651357628 8865878722 E -28,
    0.8453814064 4893808943 7361193598 E -29,
    0.3565755151 2015152659 0791715785 E -29,
    - 0.1383652423 4779775181 0195772006 E -29,
    - 0.6062142653 2093450576 7865286306 E -30]
                                                             Type: List Float
--R 
--R
--R   (13)
--R   [2.0328439457 9616699087 873844202, 0.0166992045 2031362851 4761843433 9,
--R    0.0002845284 7243613468 0742489985 325,
--R    0.0000075639 4435851620 6489487866 93854,
--R    0.2798971289 4508591575 048431809 E -6,
--R    0.1357901828 5345310695 2556392593 E -7,
--R    0.8343596202 0404692558 5610289412 E -9,
--R    0.6370971727 6402484382 7524337306 E -10,
--R    0.6007247608 8118612357 608308485 E -11,
--R    0.7022876174 6797735907 5059216588 E -12,
--R    0.1018302673 7036876930 9667322152 E -12,
--R    0.1761812903 4308800404 0656741554 E -13,
--R    0.3250828614 2353606942 4072007647 E -14,
--R    0.5071770025 5058186788 1479300685 E -15,
--R    0.1665177387 0432942985 3520036957 E -16,
--R    - 0.3166753890 7975144007 2410018963 E -16,
--R    - 0.1588403763 6641415154 8423134074 E -16,
--R    - 0.4175513256 1380188308 9626455063 E -17,
--R    - 0.2892347749 7071418820 2868862358 E -18,
--R    0.2800625903 3966080728 9978777339 E -18,
--R    0.1322938639 5392708914 0532005364 E -18,
--R    0.1804447444 1773019958 5334811191 E -19,
--R    - 0.7905384086 5226165620 2021080364 E -20,
--R    - 0.4435711366 3695734471 8167314045 E -20,
--R    - 0.4264103994 9781026176 0579779746 E -21,
--R    0.3920101766 9371439072 5625388636 E -21,
--R    0.1527378051 3439636447 2804486402 E -21,
--R    - 0.1024849527 0494906078 6953149788 E -22,
--R    - 0.2134907874 7710893794 8904287231 E -22,
--R    - 0.3239139475 1602368761 4279789345 E -23,
--R    0.2142183762 2964597029 6249355934 E -23,
--R    0.8234609419 6189955316 9207838151 E -24,
--R    - 0.1524652829 6206721081 1495038147 E -24,
--R    - 0.1378208282 4882440129 0438126477 E -24,
--R    0.2131311201 4287370679 1513005998 E -26,
--R    0.2012649651 8713266585 9213006507 E -25,
--R    0.1995535662 0563740232 0607178286 E -26,
--R    - 0.2798995812 2017971142 6020884464 E -26,
--R    - 0.5534511830 5070025094 978494256 E -27,
--R    0.3884995422 6845525312 9749000696 E -27,
--R    0.1121304407 2330701254 0043264712 E -27,
--R    - 0.5566568286 7445948805 7823816866 E -28,
--R    - 0.2045482612 4651357628 8865878722 E -28,
--R    0.8453814064 4893808943 7361193598 E -29,
--R    0.3565755151 2015152659 0791715785 E -29,
--R    - 0.1383652423 4779775181 0195772006 E -29,
--R    - 0.6062142653 2093450576 7865286306 E -30]
--R                                                             Type: List Float
--E 12

--S 13 of 20
[[32,1.03341356421624104943493552567,_
  Ei6(32.0),Ei6(32.0)-1.03341356421624104943493552567],_
[34+2/15,1.03118521236465926355875784663,_
  Ei6(34.0+2/15),Ei6(34.0+2/15)-1.03118521236465926355875784663],_
[36+4/7,1.02897740410580800863378435059,_
  Ei6(36.0+4/7),Ei6(36.0+4/7)-1.02897740410580800863378435059],_
[39+5/13,1.02678968370902852450984510823,_
  Ei6(39.0+5/13),Ei6(39.0+5/13)-1.02678968370902852450984510823],_
[42+2/3,1.02462161468107839101187804247,_
  Ei6(42.0+2/3),Ei6(42.0+2/3)-1.02462161468107839101187804247],_
[46+6/11,1.02247277840542059591275364791,_
  Ei6(46.0+6/11),Ei6(46.0+6/11)-1.02247277840542059591275364791],_
[51+1/5,1.02034277293078377487217829808,_
  Ei6(51.0+1/5),Ei6(51.0+1/5)-1.02034277293078377487217829808],_
[56+8/9,1.01823121188483269682337017143,_
  Ei6(56.0+8/9),Ei6(56.0+8/9)-1.01823121188483269682337017143],_
[64,1.01613772349432532170357100831,_
  Ei6(64.0),Ei6(64.0)-1.01613772349432532170357100831],_
[73+1/7,1.01406194969697133145942329335,_
  Ei6(73.0+1/7),Ei6(73.0+1/7)-1.01406194969697133145942329335],_
[85+1/3,1.01200354533298848201864466702,_
  Ei6(85.0+1/3),Ei6(85.0+1/3)-1.01200354533298848201864466702],_
[102+2/5,1.00996217740644975574367545570,_
  Ei6(102.0+2/5),Ei6(102.0+2/5)-1.00996217740644975574367545570],_
[128,1.00793752440814018281776821694,_
  Ei6(128.0),Ei6(128.0)-1.00793752440814018281776821694],_
[170+2/3,1.00592927569292911294663030932,_
  Ei6(170.0+2/3),Ei6(170.0+2/3)-1.00592927569292911294663030932],_
[256,1.00393713090569862788009078297,_
  Ei6(256.0),Ei6(256.0)-1.00393713090569862788009078297],_
[512,1.00196079945071192531337468473,_
  Ei6(512.0),Ei6(512.0)-1.00196079945071192531337468473],_
[infinity(),1.00000000000000000000000000001,_
  Ei6(infinity()),Ei6(infinity())-1.00000000000000000000000000001]]
 

   (14)
   [[32.0,1.033413564216241,1.0334135642162412,2.2204460492503131E-16],

      512
     [---, 1.0311852123 6465926355 875784663, 1.0311852123646588,
       15
      - 4.4408920985006262E-16]
     ,
     256
    [---,1.0289774041 0580800863 378435059,1.028977404105808,0.0],
      7
     512
    [---,1.0267896837 0902852450 984510823,1.0267896837090285,0.0],
      13

      128
     [---, 1.0246216146 8107839101 187804247, 1.0246216146810787,
       3
      4.4408920985006262E-16]
     ,

      512
     [---, 1.0224727784 0542059591 275364791, 1.0224727784054206,
       11
      2.2204460492503131E-16]
     ,
     256
    [---,1.0203427729 3078377487 217829808,1.0203427729307837,0.0],
      5

      512
     [---, 1.0182312118 8483269682 337017143, 1.0182312118848329,
       9
      2.2204460492503131E-16]
     ,
    [64.0,1.0161377234943252,1.0161377234943252,0.0],
     512
    [---,1.0140619496 9697133145 942329335,1.0140619496969712,0.0],
      7

      256
     [---, 1.0120035453 3298848201 864466702, 1.0120035453329885,
       3
      2.2204460492503131E-16]
     ,

      512
     [---, 1.0099621774 0644975574 36754557, 1.0099621774064493,
       5
      - 2.2204460492503131E-16]
     ,
    [128.0,1.0079375244081401,1.0079375244081401,0.0],

      512
     [---, 1.0059292756 9292911294 663030932, 1.0059292756929286,
       3
      - 4.4408920985006262E-16]
     ,
    [256.0,1.0039371309056986,1.0039371309056981,- 4.4408920985006262E-16],
    [512.0,1.0019607994507118,1.0019607994507116,- 2.2204460492503131E-16],
    [infinity,1.0,1.0,0.0]]
                                                          Type: List List Any
--R 
--R
--R   (14)
--R   [[32.,1.033413564216241,1.0334135642162412,2.2204460492503131E-16],
--R
--R      512
--R     [---, 1.0311852123 6465926355 875784663, 1.0311852123646588,
--R       15
--R      - 4.4408920985006262E-16]
--R     ,
--R     256
--R    [---,1.0289774041 0580800863 378435059,1.028977404105808,0.],
--R      7
--R     512
--R    [---,1.0267896837 0902852450 984510823,1.0267896837090285,0.],
--R      13
--R
--R      128
--R     [---, 1.0246216146 8107839101 187804247, 1.0246216146810787,
--R       3
--R      2.2204460492503131E-16]
--R     ,
--R     512
--R    [---,1.0224727784 0542059591 275364791,1.0224727784054206,0.],
--R      11
--R     256
--R    [---,1.0203427729 3078377487 217829808,1.0203427729307837,0.],
--R      5
--R
--R      512
--R     [---, 1.0182312118 8483269682 337017143, 1.0182312118848329,
--R       9
--R      2.2204460492503131E-16]
--R     ,
--R    [64.,1.0161377234943254,1.0161377234943252,- 2.2204460492503131E-16],
--R
--R      512
--R     [---, 1.0140619496 9697133145 942329335, 1.0140619496969712,
--R       7
--R      - 2.2204460492503131E-16]
--R     ,
--R     256
--R    [---,1.0120035453 3298848201 864466702,1.0120035453329885,0.],
--R      3
--R
--R      512
--R     [---, 1.0099621774 0644975574 36754557, 1.0099621774064493,
--R       5
--R      - 4.4408920985006262E-16]
--R     ,
--R    [128.,1.0079375244081401,1.0079375244081401,0.],
--R
--R      512
--R     [---, 1.0059292756 9292911294 663030932, 1.0059292756929286,
--R       3
--R      - 4.4408920985006262E-16]
--R     ,
--R    [256.,1.0039371309056986,1.0039371309056981,- 4.4408920985006262E-16],
--R    [512.,1.001960799450712,1.0019607994507116,- 4.4408920985006262E-16],
--R    [infinity,1.,1.,0.]]
--R                                                          Type: List List Any
--E 13

--S 14 of 20
h(x:DFLOAT):DFLOAT==
  x=0.0::DFLOAT => 1.0 
  y:DFLOAT:=retract(Ei(x))
  (y-log(x)-gamma)/x
 
   Function declaration h : DoubleFloat -> DoubleFloat has been added 
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration h : DoubleFloat -> DoubleFloat has been added 
--R      to workspace.
--R                                                                   Type: Void
--E 14

--S 15 of 20
[[0.00,1.000000000,h(0.00),h(0.00)-1.000000000],_
 [0.01,1.002505566,h(0.01),h(0.01)-1.002505566],_
 [0.02,1.005022306,h(0.02),h(0.02)-1.005022306],_
 [0.03,1.007550283,h(0.03),h(0.03)-1.007550283],_
 [0.04,1.010089560,h(0.04),h(0.04)-1.010089560],_
 [0.05,1.012640202,h(0.05),h(0.05)-1.012640202],_
 [0.06,1.015202272,h(0.06),h(0.06)-1.015202272],_
 [0.07,1.017775836,h(0.07),h(0.07)-1.017775836],_
 [0.08,1.020360958,h(0.08),h(0.08)-1.020360958],_
 [0.09,1.022957705,h(0.09),h(0.09)-1.022957705],_
 [0.10,1.025566141,h(0.10),h(0.10)-1.025566141],_
 [0.11,1.028186335,h(0.11),h(0.11)-1.028186335],_
 [0.12,1.030818352,h(0.12),h(0.12)-1.030818352],_
 [0.13,1.033462259,h(0.13),h(0.13)-1.033462259],_
 [0.14,1.036118125,h(0.14),h(0.14)-1.036118125],_
 [0.15,1.038786018,h(0.15),h(0.15)-1.038786018],_
 [0.16,1.041466006,h(0.16),h(0.16)-1.041466006],_
 [0.17,1.044158158,h(0.17),h(0.17)-1.044158158],_
 [0.18,1.046862544,h(0.18),h(0.18)-1.046862544],_
 [0.19,1.049579234,h(0.19),h(0.19)-1.049579234],_
 [0.20,1.052308298,h(0.20),h(0.20)-1.052308298],_
 [0.21,1.055049807,h(0.21),h(0.21)-1.055049807],_
 [0.22,1.057803833,h(0.22),h(0.22)-1.057803833],_
 [0.23,1.060570446,h(0.23),h(0.23)-1.060570446],_
 [0.24,1.063349719,h(0.24),h(0.24)-1.063349719],_
 [0.25,1.066141726,h(0.25),h(0.25)-1.066141726],_
 [0.26,1.068946539,h(0.26),h(0.26)-1.068946539],_
 [0.27,1.071764232,h(0.27),h(0.27)-1.071764232],_
 [0.28,1.074594879,h(0.28),h(0.28)-1.074594879],_
 [0.29,1.077438555,h(0.29),h(0.29)-1.077438555],_
 [0.30,1.080295334,h(0.30),h(0.30)-1.080295334],_
 [0.31,1.083165293,h(0.31),h(0.31)-1.083165293],_
 [0.32,1.086048507,h(0.32),h(0.32)-1.086048507],_
 [0.33,1.088945053,h(0.33),h(0.33)-1.088945053],_
 [0.34,1.091855008,h(0.34),h(0.34)-1.091855008],_
 [0.35,1.094778451,h(0.35),h(0.35)-1.094778451],_
 [0.36,1.097715458,h(0.36),h(0.36)-1.097715458],_
 [0.37,1.100666108,h(0.37),h(0.37)-1.100666108],_
 [0.38,1.103630481,h(0.38),h(0.38)-1.103630481],_
 [0.39,1.106608656,h(0.39),h(0.39)-1.106608656],_
 [0.40,1.109600714,h(0.40),h(0.40)-1.109600714],_
 [0.41,1.112606735,h(0.41),h(0.41)-1.112606735],_
 [0.42,1.115626800,h(0.42),h(0.42)-1.115626800],_
 [0.43,1.118660991,h(0.43),h(0.43)-1.118660991],_
 [0.44,1.121709391,h(0.44),h(0.44)-1.121709391],_
 [0.45,1.124772082,h(0.45),h(0.45)-1.124772082],_
 [0.46,1.127849147,h(0.46),h(0.46)-1.127849147],_
 [0.47,1.130940671,h(0.47),h(0.47)-1.130940671],_
 [0.48,1.134046738,h(0.48),h(0.48)-1.134046738],_
 [0.49,1.137167432,h(0.49),h(0.49)-1.137167432],_
 [0.50,1.140302841,h(0.50),h(0.50)-1.140302841]]
 
   Compiling function h with type DoubleFloat -> DoubleFloat 

   (16)
   [[0.0,1.0,1.0,0.0],

     [0.0099999999999999985, 1.002505566, 1.0025055659888873,
      - 1.1112666342683042E-11]
     ,

     [0.019999999999999997, 1.0050223059999999, 1.0050223058229559,
      - 1.7704393506789984E-10]
     ,

     [0.029999999999999999, 1.0075502829999998, 1.0075502826056404,
      - 3.9435943399723783E-10]
     ,

     [0.039999999999999994, 1.0100895599999999, 1.0100895598460393,
      - 1.5396062202910343E-10]
     ,

     [0.049999999999999996, 1.0126402019999998, 1.0126402014616698,
      - 5.3833004720615918E-10]
     ,

     [0.059999999999999998, 1.0152022719999998, 1.0152022717813274,
      - 2.1867241351003486E-10]
     ,

     [0.069999999999999993, 1.017775836, 1.017775835547966,
      - 4.5203396581428024E-10]
     ,

     [0.079999999999999988, 1.0203609579999999, 1.020360957921568,
      - 7.8431927619249109E-11]
     ,

     [0.089999999999999997, 1.0229577049999998, 1.0229577044820883,
      - 5.1791149147106808E-10]
     ,

     [0.099999999999999992, 1.0255661409999999, 1.0255661412323613,
      2.3236146340366304E-10]
     ,

     [0.10999999999999999, 1.0281863349999998, 1.0281863346010789,
      - 3.9892089631621275E-10]
     ,
    [0.12,1.0308183519999998,1.0308183514457614,- 5.5423843292601305E-10],
    [0.12999999999999998,1.033462259,1.0334622590557518,5.5751847582996561E-11],

     [0.13999999999999999, 1.0361181249999998, 1.0361181251552547,
      1.5525492003121144E-10]
     ,

     [0.14999999999999999, 1.0387860179999999, 1.038786017906365,
      - 9.3634877629256152E-11]
     ,

     [0.15999999999999998, 1.0414660059999998, 1.0414660059121479,
      - 8.7851947938588637E-11]
     ,

     [0.16999999999999998, 1.0441581579999999, 1.0441581582197252,
      2.1972534902658936E-10]
     ,

     [0.17999999999999999, 1.0468625439999999, 1.0468625443233892,
      3.233893153264944E-10]
     ,

     [0.18999999999999997, 1.0495792339999999, 1.0495792341677361,
      1.6773626931865238E-10]
     ,

     [0.19999999999999998, 1.0523082979999998, 1.0523082981508358,
      1.5083601034859839E-10]
     ,

     [0.20999999999999999, 1.0550498069999998, 1.055049807127405,
      1.2740519750309431E-10]
     ,

     [0.21999999999999997, 1.0578038329999999, 1.0578038324120198,
      - 5.8798010904581588E-10]
     ,

     [0.22999999999999998, 1.0605704459999998, 1.0605704457823433,
      - 2.1765655944250284E-10]
     ,

     [0.23999999999999999, 1.0633497189999999, 1.0633497194823853,
      4.8238546490608769E-10]
     ,
    [0.25,1.0661417259999999,1.0661417262257755,2.2577562042158661E-10],

     [0.25999999999999995, 1.0689465389999999, 1.0689465391990725,
      1.9907253623330234E-10]
     ,

     [0.26999999999999996, 1.0717642319999998, 1.0717642320650855,
      6.5085714595625177E-11]
     ,

     [0.27999999999999997, 1.0745948789999999, 1.0745948789662334,
      - 3.3766545115554436E-11]
     ,

     [0.28999999999999998, 1.0774385549999999, 1.0774385545279166,
      - 4.7208326137138101E-10]
     ,

     [0.29999999999999999, 1.0802953339999999, 1.0802953338619237,
      - 1.3807621712658147E-10]
     ,
    [0.31,1.083165293,1.0831652925698589,- 4.3014103390248692E-10],

     [0.31999999999999995, 1.0860485069999999, 1.0860485067465933,
      - 2.5340662901385258E-10]
     ,

     [0.32999999999999996, 1.088945053, 1.0889450529837439,
      - 1.6256107571166467E-11]
     ,

     [0.33999999999999997, 1.0918550079999998, 1.0918550083731844,
      3.7318459433777207E-10]
     ,

     [0.34999999999999998, 1.0947784509999998, 1.0947784505105673,
      - 4.8943249453259341E-10]
     ,

     [0.35999999999999999, 1.0977154579999999, 1.0977154574988892,
      - 5.0111070848402051E-10]
     ,
    [0.37,1.100666108,1.1006661079520701,- 4.7929882285302483E-11],

     [0.37999999999999995, 1.1036304809999999, 1.1036304809985673,
      - 1.432631790976302E-12]
     ,

     [0.38999999999999996, 1.1066086559999999, 1.1066086562850106,
      2.8501068172204214E-10]
     ,

     [0.39999999999999997, 1.1096007139999999, 1.1096007139798676,
      - 2.0132340239342739E-11]
     ,

     [0.40999999999999998, 1.112606735, 1.1126067347771347,
      - 2.2286528178483422E-10]
     ,

     [0.41999999999999998, 1.1156267999999998, 1.1156267999000613,
      - 9.9938501918472866E-11]
     ,

     [0.42999999999999999, 1.1186609909999998, 1.1186609911048897,
      1.0488987456369614E-10]
     ,

     [0.43999999999999995, 1.1217093909999998, 1.1217093906846374,
      - 3.1536240285845452E-10]
     ,

     [0.44999999999999996, 1.1247720819999998, 1.1247720814728974,
      - 5.2710236175812497E-10]
     ,

     [0.45999999999999996, 1.1278491469999998, 1.1278491468476695,
      - 1.5233037053974385E-10]
     ,

     [0.46999999999999997, 1.1309406709999998, 1.1309406707352232,
      - 2.6477664505364373E-10]
     ,

     [0.47999999999999998, 1.1340467379999999, 1.1340467376139858,
      - 3.8601410956573545E-10]
     ,

     [0.48999999999999999, 1.1371674319999998, 1.1371674325184582,
      5.1845838733299843E-10]
     ,
    [0.5,1.1403028409999998,1.1403028410431713,4.3171466401759062E-11]]
                                                  Type: List List DoubleFloat
--R 
--R   Compiling function h with type DoubleFloat -> DoubleFloat 
--R
--R   (16)
--R   [[0.,1.,1.,0.],
--R    [1.0E-2,1.002505566,1.002505565988876,- 1.1123990617534218E-11],
--R    [2.0E-2,1.0050223060000001,1.0050223058229502,- 1.7704993027223281E-10],
--R
--R     [2.9999999999999999E-2, 1.007550283, 1.0075502826056368,
--R      - 3.9436320875552155E-10]
--R     ,
--R
--R     [4.0000000000000001E-2, 1.0100895599999999, 1.0100895598460362,
--R      - 1.5396373065357238E-10]
--R     ,
--R
--R     [5.0000000000000003E-2, 1.012640202, 1.0126402014616676,
--R      - 5.3833248969681335E-10]
--R     ,
--R
--R     [5.9999999999999998E-2, 1.015202272, 1.0152022717813329,
--R      - 2.1866708443951666E-10]
--R     ,
--R
--R     [7.0000000000000007E-2, 1.017775836, 1.0177758355479642,
--R      - 4.5203574217111964E-10]
--R     ,
--R
--R     [8.0000000000000002E-2, 1.0203609579999999, 1.0203609579215664,
--R      - 7.8433481931483584E-11]
--R     ,
--R
--R     [8.9999999999999997E-2, 1.0229577050000001, 1.0229577044820872,
--R      - 5.1791282373869763E-10]
--R     ,
--R
--R     [0.10000000000000001, 1.0255661410000001, 1.0255661412323602,
--R      2.3236013113603349E-10]
--R     ,
--R    [0.11,1.028186335,1.0281863346010778,- 3.989222285838423E-10],
--R    [0.12,1.030818352,1.0308183514457605,- 5.5423954314903767E-10],
--R    [0.13,1.033462259,1.0334622590557541,5.5754068029045811E-11],
--R    [0.14000000000000001,1.036118125,1.0361181251552536,1.5525358776358189E-10],
--R
--R     [0.14999999999999999, 1.0387860179999999, 1.0387860179063644,
--R      - 9.3635543763070928E-11]
--R     ,
--R    [0.16,1.0414660060000001,1.0414660059121499,- 8.7850171581749237E-11],
--R
--R     [0.17000000000000001, 1.0441581579999999, 1.0441581582197257,
--R      2.1972579311579921E-10]
--R     ,
--R
--R     [0.17999999999999999, 1.0468625439999999, 1.0468625443233892,
--R      3.233893153264944E-10]
--R     ,
--R    [0.19,1.0495792340000001,1.0495792341677359,1.6773582522944253E-10],
--R    [0.20000000000000001,1.052308298,1.0523082981508358,1.5083578830399347E-10],
--R
--R     [0.20999999999999999, 1.0550498070000001, 1.055049807127405,
--R      1.2740497545848939E-10]
--R     ,
--R    [0.22,1.0578038329999999,1.0578038324120198,- 5.8798010904581588E-10],
--R
--R     [0.23000000000000001, 1.0605704460000001, 1.0605704457823433,
--R      - 2.1765678148710776E-10]
--R     ,
--R
--R     [0.23999999999999999, 1.0633497190000001, 1.0633497194823853,
--R      4.8238524286148277E-10]
--R     ,
--R    [0.25,1.0661417259999999,1.0661417262257755,2.2577562042158661E-10],
--R
--R     [0.26000000000000001, 1.0689465389999999, 1.0689465391990731,
--R      1.9907320236711712E-10]
--R     ,
--R    [0.27000000000000002,1.071764232,1.0717642320650853,6.5085270506415327E-11],
--R
--R     [0.28000000000000003, 1.0745948789999999, 1.0745948789662336,
--R      - 3.3766323070949511E-11]
--R     ,
--R
--R     [0.28999999999999998, 1.0774385550000001, 1.0774385545279166,
--R      - 4.7208348341598594E-10]
--R     ,
--R
--R     [0.29999999999999999, 1.0802953340000001, 1.0802953338619241,
--R      - 1.3807599508197654E-10]
--R     ,
--R    [0.31,1.083165293,1.0831652925698594,- 4.3014058981327707E-10],
--R
--R     [0.32000000000000001, 1.0860485070000001, 1.0860485067465939,
--R      - 2.5340618492464273E-10]
--R     ,
--R
--R     [0.33000000000000002, 1.088945053, 1.0889450529837443,
--R      - 1.6255663481956617E-11]
--R     ,
--R    [0.34000000000000002,1.091855008,1.0918550083731842,3.7318415024856222E-10],
--R
--R     [0.34999999999999998, 1.094778451, 1.0947784505105673,
--R      - 4.8943271657719833E-10]
--R     ,
--R
--R     [0.35999999999999999, 1.0977154579999999, 1.0977154574988892,
--R      - 5.0111070848402051E-10]
--R     ,
--R    [0.37,1.100666108,1.1006661079520708,- 4.7929216151487708E-11],
--R    [0.38,1.1036304809999999,1.1036304809985678,- 1.4321877017664519E-12],
--R
--R     [0.39000000000000001, 1.1066086559999999, 1.1066086562850108,
--R      2.8501090376664706E-10]
--R     ,
--R
--R     [0.40000000000000002, 1.1096007139999999, 1.1096007139798676,
--R      - 2.0132340239342739E-11]
--R     ,
--R    [0.40999999999999998,1.112606735,1.1126067347771349,- 2.228650597402293E-10]
--R     ,
--R    [0.41999999999999998,1.1156268,1.1156267999000615,- 9.9938501918472866E-11],
--R    [0.42999999999999999,1.118660991,1.1186609911048895,1.0488943047448629E-10],
--R    [0.44,1.121709391,1.1217093906846374,- 3.1536262490305944E-10],
--R
--R     [0.45000000000000001, 1.124772082, 1.1247720814728976,
--R      - 5.2710236175812497E-10]
--R     ,
--R
--R     [0.46000000000000002, 1.1278491470000001, 1.1278491468476701,
--R      - 1.52329926450534E-10]
--R     ,
--R
--R     [0.46999999999999997, 1.1309406710000001, 1.1309406707352239,
--R      - 2.6477620096443388E-10]
--R     ,
--R
--R     [0.47999999999999998, 1.1340467380000001, 1.134046737613986,
--R      - 3.8601410956573545E-10]
--R     ,
--R    [0.48999999999999999,1.137167432,1.1371674325184589,5.1845883142220828E-10],
--R    [0.5,1.140302841,1.1403028410431715,4.3171466401759062E-11]]
--R                                                  Type: List List DoubleFloat
--E 15

--S 16 of 20
[[0.50,0.454219905,Ei(0.50),Ei(0.50)-0.454219905],_
 [0.51,0.487032167,Ei(0.51),Ei(0.51)-0.487032167],_
 [0.52,0.519530633,Ei(0.52),Ei(0.52)-0.519530633],_
 [0.53,0.551730445,Ei(0.53),Ei(0.53)-0.551730445],_
 [0.54,0.583645931,Ei(0.54),Ei(0.54)-0.583645931],_
 [0.55,0.615290657,Ei(0.55),Ei(0.55)-0.615290657],_
 [0.56,0.646677490,Ei(0.56),Ei(0.56)-0.646677490],_
 [0.57,0.677818642,Ei(0.57),Ei(0.57)-0.677818642],_
 [0.58,0.708725720,Ei(0.58),Ei(0.58)-0.708725720],_
 [0.59,0.739409764,Ei(0.59),Ei(0.59)-0.739409764],_
 [0.60,0.769881290,Ei(0.60),Ei(0.60)-0.769881290],_
 [0.61,0.800150320,Ei(0.61),Ei(0.61)-0.800150320],_
 [0.62,0.830226417,Ei(0.62),Ei(0.62)-0.830226417],_
 [0.63,0.860118716,Ei(0.63),Ei(0.63)-0.860118716],_
 [0.64,0.889835949,Ei(0.64),Ei(0.64)-0.889835949],_
 [0.65,0.919386468,Ei(0.65),Ei(0.65)-0.919386468],_
 [0.66,0.948778277,Ei(0.66),Ei(0.66)-0.948778277],_
 [0.67,0.978019042,Ei(0.67),Ei(0.67)-0.978019042],_
 [0.68,1.007116121,Ei(0.68),Ei(0.68)-1.007116121],_
 [0.69,1.036076576,Ei(0.69),Ei(0.69)-1.036076576],_
 [0.70,1.064907195,Ei(0.70),Ei(0.70)-1.064907195],_
 [0.71,1.093614501,Ei(0.71),Ei(0.71)-1.093614501],_
 [0.72,1.122204777,Ei(0.72),Ei(0.72)-1.122204777],_
 [0.73,1.150684069,Ei(0.73),Ei(0.73)-1.150684069],_
 [0.74,1.179058208,Ei(0.74),Ei(0.74)-1.179058208],_
 [0.75,1.207332816,Ei(0.75),Ei(0.75)-1.207332816],_
 [0.76,1.235513319,Ei(0.76),Ei(0.76)-1.235513319],_
 [0.77,1.263604960,Ei(0.77),Ei(0.77)-1.263604960],_
 [0.78,1.291612805,Ei(0.78),Ei(0.78)-1.291612805],_
 [0.79,1.319541753,Ei(0.79),Ei(0.79)-1.319541753],_
 [0.80,1.347396548,Ei(0.80),Ei(0.80)-1.347396548],_
 [0.81,1.375181783,Ei(0.81),Ei(0.81)-1.375181783],_
 [0.82,1.402901910,Ei(0.82),Ei(0.82)-1.402901910],_
 [0.83,1.430561245,Ei(0.83),Ei(0.83)-1.430561245],_
 [0.84,1.458163978,Ei(0.84),Ei(0.84)-1.458163978],_
 [0.85,1.485714176,Ei(0.85),Ei(0.85)-1.485714176],_
 [0.86,1.513215791,Ei(0.86),Ei(0.86)-1.513215791],_
 [0.87,1.540672664,Ei(0.87),Ei(0.87)-1.540672664],_
 [0.88,1.568088534,Ei(0.88),Ei(0.88)-1.568088534],_
 [0.89,1.595467036,Ei(0.89),Ei(0.89)-1.595467036],_
 [0.90,1.622811714,Ei(0.90),Ei(0.90)-1.622811714],_
 [0.91,1.650126019,Ei(0.91),Ei(0.91)-1.650126019],_
 [0.92,1.677413317,Ei(0.92),Ei(0.92)-1.677413317],_
 [0.93,1.704676891,Ei(0.93),Ei(0.93)-1.704676891],_
 [0.94,1.731919946,Ei(0.94),Ei(0.94)-1.731919946],_
 [0.95,1.759145612,Ei(0.95),Ei(0.95)-1.759145612],_
 [0.96,1.786356947,Ei(0.96),Ei(0.96)-1.786356947],_
 [0.97,1.813556941,Ei(0.97),Ei(0.97)-1.813556941],_
 [0.98,1.840748519,Ei(0.98),Ei(0.98)-1.840748519],_
 [0.99,1.867934543,Ei(0.99),Ei(0.99)-1.867934543],_
 [1.00,1.895117816,Ei(1.00),Ei(1.00)-1.895117816],_
 [1.01,1.922301085,Ei(1.01),Ei(1.01)-1.922301085],_
 [1.02,1.949487042,Ei(1.02),Ei(1.02)-1.949487042],_
 [1.03,1.976678325,Ei(1.03),Ei(1.03)-1.976678325],_
 [1.04,2.003877525,Ei(1.04),Ei(1.04)-2.003877525],_
 [1.05,2.031087184,Ei(1.05),Ei(1.05)-2.031087184],_
 [1.06,2.058309800,Ei(1.06),Ei(1.06)-2.058309800],_
 [1.07,2.085547825,Ei(1.07),Ei(1.07)-2.085547825],_
 [1.08,2.112803672,Ei(1.08),Ei(1.08)-2.112803672],_
 [1.09,2.140079712,Ei(1.09),Ei(1.09)-2.140079712],_
 [1.10,2.167378280,Ei(1.10),Ei(1.10)-2.167378280],_
 [1.11,2.194701672,Ei(1.11),Ei(1.11)-2.194701672],_
 [1.12,2.222052152,Ei(1.12),Ei(1.12)-2.222052152],_
 [1.13,2.249431949,Ei(1.13),Ei(1.13)-2.249431949],_
 [1.14,2.276843260,Ei(1.14),Ei(1.14)-2.276843260],_
 [1.15,2.304288252,Ei(1.15),Ei(1.15)-2.304288252],_
 [1.16,2.331769062,Ei(1.16),Ei(1.16)-2.331769062],_
 [1.17,2.359287800,Ei(1.17),Ei(1.17)-2.359287800],_
 [1.18,2.386846549,Ei(1.18),Ei(1.18)-2.386846549],_
 [1.19,2.414447367,Ei(1.19),Ei(1.19)-2.414447367],_
 [1.20,2.442092285,Ei(1.20),Ei(1.20)-2.442092285],_
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 [2.00,4.954234356,Ei(2.00),Ei(2.00)-4.954234356]]
 

   (17)
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     [1.5999999999999999, 3.6053199489999996, 3.605319949019469,
      1.9469315049036595E-11]
     ,

     [1.6099999999999999, 3.6363347189999997, 3.6363347191218365,
      1.2183676290078438E-10]
     ,

     [1.6199999999999999, 3.6674672209999999, 3.6674672206298218,
      - 3.7017811038708714E-10]
     ,

     [1.6299999999999999, 3.6987190989999998, 3.6987190986647662,
      - 3.3523361864240542E-10]
     ,

     [1.6399999999999999, 3.7300919989999999, 3.7300919990684158,
      6.8415939580290797E-11]
     ,

     [1.6499999999999999, 3.7615875689999996, 3.761587568694134,
      - 3.0586555510581093E-10]
     ,

     [1.6599999999999999, 3.7932074559999998, 3.7932074556923916,
      - 3.0760816116526257E-10]
     ,

     [1.6699999999999999, 3.8249533099999997, 3.824953309790788,
      - 2.0921175902799405E-10]
     ,

     [1.6799999999999999, 3.8568267829999998, 3.8568267825688234,
      - 4.3117642789525235E-10]
     ,

     [1.6899999999999999, 3.8888295279999996, 3.8888295277276343,
      - 2.723652414715616E-10]
     ,
    [1.7,3.9209632009999997,3.9209632013549034,3.5490366201429424E-10],
    [1.71,3.9532294619999999,3.9532294621851567,1.8515677879804571E-10],
    [1.72,3.9856299719999999,3.9856299718556261,- 1.4437384621146521E-10],
    [1.73,4.0181663949999997,4.0181663951578663,1.5786660867433966E-10],
    [1.74,4.0508403999999993,4.0508404002853169,2.8531754736604853E-10],
    [1.75,4.0836536589999994,4.0836536590769548,7.6955330996497651E-11],

     [1.7599999999999998, 4.1166078469999992, 4.1166078472572485,
      2.5724933294668517E-10]
     ,

     [1.7699999999999998, 4.1497046449999999, 4.1497046446724974,
      - 3.2750246958812568E-10]
     ,

     [1.7799999999999998, 4.1829457359999997, 4.1829457355238064,
      - 4.7619330700854334E-10]
     ,

     [1.7899999999999998, 4.2163328089999998, 4.21633280859675,
      - 4.0324987793383116E-10]
     ,
    [1.7999999999999998,4.249867557,4.2498675574879332,4.879332493601396E-10],

     [1.8099999999999998, 4.2835516809999996, 4.2835516808285554,
      - 1.7144419217629547E-10]
     ,

     [1.8199999999999998, 4.3173868829999993, 4.3173868825051116,
      - 4.9488768638639158E-10]
     ,

     [1.8299999999999998, 4.3513748719999992, 4.3513748718773675,
      - 1.2263168258641599E-10]
     ,

     [1.8399999999999999, 4.3855173639999991, 4.3855173639937197,
      - 6.2794214272798854E-12]
     ,

     [1.8499999999999999, 4.4198160799999995, 4.4198160798040753,
      - 1.9592416578007033E-10]
     ,

     [1.8599999999999999, 4.4542727459999991, 4.4542727463703331,
      3.7033398569974452E-10]
     ,

     [1.8699999999999999, 4.4888890969999995, 4.4888890970746296,
      7.4630079893722723E-11]
     ,

     [1.8799999999999999, 4.5236668719999997, 4.5236668718253901,
      - 1.7460966006410672E-10]
     ,

     [1.8899999999999999, 4.5586078169999995, 4.5586078172613478,
      2.6134827635360125E-10]
     ,

     [1.8999999999999999, 4.5937136869999993, 4.5937136869535857,
      - 4.6413539678269444E-11]
     ,

     [1.9099999999999999, 4.6289862419999999, 4.6289862416057295,
      - 3.9427039411066289E-10]
     ,

     [1.9199999999999999, 4.6644272489999992, 4.6644272492523706,
      2.5237145706569208E-10]
     ,

     [1.9299999999999999, 4.7000384849999994, 4.7000384854557842,
      4.5578474328067387E-10]
     ,

     [1.9399999999999999, 4.7358217339999999, 4.7358217335010906,
      - 4.9890935827079375E-10]
     ,
    [1.95,4.7717787849999995,4.7717787845898787,- 4.1012082618863133E-10],
    [1.96,4.8079114379999996,4.8079114380324137,3.241407142695607E-11],
    [1.97,4.8442215009999998,4.8442215014384953,4.3849546216279123E-10],
    [1.98,4.8807107909999994,4.880710790907032,- 9.2967411546851508E-11],
    [1.99,4.917381131,4.9173811312144435,2.1444357400923764E-10],
    [2.0,4.9542343559999997,4.9542343560018915,1.8918200339612667E-12]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (17)
--R   [[0.5,0.45421990499999998,0.45421990486317332,- 1.3682666111236585E-10],
--R
--R     [0.51000000000000001, 0.48703216700000002, 0.48703216680456007,
--R      - 1.9543994200788006E-10]
--R     ,
--R
--R     [0.52000000000000002, 0.51953063300000002, 0.51953063245569719,
--R      - 5.443028250340376E-10]
--R     ,
--R
--R     [0.53000000000000003, 0.55173044500000001, 0.55173044523266401,
--R      2.3266399917787339E-10]
--R     ,
--R
--R     [0.54000000000000004, 0.58364593099999995, 0.58364593072977955,
--R      - 2.7022040161028826E-10]
--R     ,
--R
--R     [0.55000000000000004, 0.61529065699999996, 0.61529065706218644,
--R      6.2186478189119043E-11]
--R     ,
--R
--R     [0.56000000000000005, 0.64667748999999997, 0.64667748977430584,
--R      - 2.2569413005157912E-10]
--R     ,
--R
--R     [0.56999999999999995, 0.67781864199999997, 0.67781864189137597,
--R      - 1.0862399868472039E-10]
--R     ,
--R
--R     [0.57999999999999996, 0.70872572, 0.70872571962101083,
--R      - 3.7898917337741977E-10]
--R     ,
--R
--R     [0.58999999999999997, 0.73940976400000002, 0.73940976415103654,
--R      1.510365166268457E-10]
--R     ,
--R
--R     [0.59999999999999998, 0.76988129000000005, 0.76988128993735938,
--R      - 6.2640670428493195E-11]
--R     ,
--R
--R     [0.60999999999999999, 0.80015031999999997, 0.80015031983004981,
--R      - 1.699501650520574E-10]
--R     ,
--R    [0.62,0.83022641699999999,0.83022641734618519,3.4618519162421535E-10],
--R    [0.63,0.86011871600000001,0.86011871636343917,3.6343916764991491E-10],
--R
--R     [0.64000000000000001, 0.88983594899999996, 0.88983594847818637,
--R      - 5.2181359233571811E-10]
--R     ,
--R
--R     [0.65000000000000002, 0.91938646800000001, 0.91938646824544334,
--R      2.4544333232512372E-10]
--R     ,
--R
--R     [0.66000000000000003, 0.94877827699999995, 0.94877827649472835,
--R      - 5.0527160233571067E-10]
--R     ,
--R
--R     [0.67000000000000004, 0.97801904200000001, 0.97801904189549682,
--R      - 1.045031838842192E-10]
--R     ,
--R
--R     [0.68000000000000005, 1.0071161209999999, 1.0071161209277915,
--R      - 7.2208461432410331E-11]
--R     ,
--R
--R     [0.68999999999999995, 1.0360765759999999, 1.0360765763978435,
--R      3.978435358931165E-10]
--R     ,
--R    [0.69999999999999996,1.064907195,1.0649071946242905,- 3.757094635403746E-10]
--R     ,
--R    [0.70999999999999996,1.093614501,1.0936145014081782,4.0817815794014223E-10],
--R
--R     [0.71999999999999997, 1.1222047770000001, 1.1222047768888612,
--R      - 1.111388758801013E-10]
--R     ,
--R    [0.72999999999999998,1.150684069,1.1506840693780345,3.780344925985446E-10],
--R
--R     [0.73999999999999999, 1.1790582080000001, 1.1790582082553465,
--R      2.5534641068247765E-10]
--R     ,
--R    [0.75,1.2073328160000001,1.2073328160012218,1.2216894162975223E-12],
--R
--R     [0.76000000000000001, 1.2355133190000001, 1.2355133194354742,
--R      4.3547410122357633E-10]
--R     ,
--R
--R     [0.77000000000000002, 1.2636049600000001, 1.2636049602240513,
--R      2.2405122201973882E-10]
--R     ,
--R
--R     [0.78000000000000003, 1.291612805, 1.2916128047105979,
--R      - 2.8940205787364448E-10]
--R     ,
--R    [0.79000000000000004,1.319541753,1.3195417531244753,1.2447531894110853E-10],
--R
--R     [0.80000000000000004, 1.3473965480000001, 1.3473965482123258,
--R      2.1232571256746269E-10]
--R     ,
--R
--R     [0.81000000000000005, 1.3751817829999999, 1.3751817833361941,
--R      3.361941836033111E-10]
--R     ,
--R    [0.81999999999999995,1.40290191,1.4029019100774811,7.7481132620960125E-11],
--R    [0.82999999999999996,1.430561245,1.4305612453827297,3.8272962576968439E-10],
--R    [0.83999999999999997,1.458163978,1.4581639782841678,2.8416780040174672E-10],
--R
--R     [0.84999999999999998, 1.4857141760000001, 1.4857141762252541,
--R      2.2525403764461771E-10]
--R     ,
--R
--R     [0.85999999999999999, 1.5132157909999999, 1.5132157910189581,
--R      1.8958168368499173E-11]
--R     ,
--R    [0.87,1.5406726639999999,1.5406726644642923,4.6429238231837644E-10],
--R    [0.88,1.5680885339999999,1.5680885336445423,- 3.5545766330358219E-10],
--R
--R     [0.89000000000000001, 1.5954670360000001, 1.5954670359288246,
--R      - 7.1175509930299086E-11]
--R     ,
--R
--R     [0.90000000000000002, 1.622811714, 1.6228117136968674,
--R      - 3.0313263010839364E-10]
--R     ,
--R
--R     [0.91000000000000003, 1.650126019, 1.6501260188054063,
--R      - 1.9459367450735954E-10]
--R     ,
--R
--R     [0.92000000000000004, 1.6774133170000001, 1.677413316813162,
--R      - 1.8683810054653804E-10]
--R     ,
--R
--R     [0.93000000000000005, 1.7046768910000001, 1.7046768909800791,
--R      - 1.9920953775454109E-11]
--R     ,
--R
--R     [0.93999999999999995, 1.7319199460000001, 1.7319199460553549,
--R      5.5354831829390605E-11]
--R     ,
--R
--R     [0.94999999999999996, 1.759145612, 1.7591456118676905,
--R      - 1.3230949669207348E-10]
--R     ,
--R
--R     [0.95999999999999996, 1.786356947, 1.7863569467301943,
--R      - 2.6980573331059077E-10]
--R     ,
--R
--R     [0.96999999999999997, 1.8135569410000001, 1.8135569406715355,
--R      - 3.2846458886126584E-10]
--R     ,
--R
--R     [0.97999999999999998, 1.8407485189999999, 1.8407485185040211,
--R      - 4.9597881357499318E-10]
--R     ,
--R
--R     [0.98999999999999999, 1.8679345430000001, 1.8679345427385856,
--R      - 2.6141444564586891E-10]
--R     ,
--R    [1.,1.895117816,1.8951178163559361,3.5593616942719564E-10],
--R    [1.01,1.922301085,1.9223010854424856,4.4248560371329404E-10],
--R    [1.02,1.9494870419999999,1.9494870416990668,- 3.0093305625200628E-10],
--R    [1.03,1.976678325,1.976678324829928,- 1.7007195651785878E-10],
--R    [1.04,2.003877525,2.0038775248189595,- 1.8104051591194548E-10],
--R    [1.05,2.031087184,2.0310871840996643,9.9664276831390453E-11],
--R    [1.0600000000000001,2.0583098,2.0583097996249284,- 3.7507152939042498E-10],
--R
--R     [1.0700000000000001, 2.0855478249999999, 2.085547824842283,
--R      - 1.5771695061062019E-10]
--R     ,
--R
--R     [1.0800000000000001, 2.1128036720000001, 2.1128036715799325,
--R      - 4.2006753631085303E-10]
--R     ,
--R
--R     [1.0900000000000001, 2.1400797119999999, 2.1400797118485424,
--R      - 1.5145751319778356E-10]
--R     ,
--R
--R     [1.1000000000000001, 2.1673782799999999, 2.1673782795634038,
--R      - 4.3659609261226251E-10]
--R     ,
--R
--R     [1.1100000000000001, 2.1947016719999999, 2.1947016721913277,
--R      1.9132784245812218E-10]
--R     ,
--R
--R     [1.1200000000000001, 2.2220521519999998, 2.2220521523263717,
--R      3.2637181845984742E-10]
--R     ,
--R
--R     [1.1299999999999999, 2.2494319489999999, 2.2494319491981756,
--R      1.9817569807401014E-10]
--R     ,
--R
--R     [1.1399999999999999, 2.2768432600000001, 2.2768432601165496,
--R      1.1654943676830953E-10]
--R     ,
--R
--R     [1.1499999999999999, 2.3042882520000001, 2.304288251855628,
--R      - 1.4437206985462581E-10]
--R     ,
--R
--R     [1.1599999999999999, 2.3317690619999998, 2.3317690619808027,
--R      - 1.9197088363398507E-11]
--R     ,
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--R     [1.1699999999999999, 2.3592878000000002, 2.3592878001213737,
--R      1.2137357785491076E-10]
--R     ,
--R
--R     [1.1799999999999999, 2.3868465489999999, 2.3868465491917359,
--R      1.9173596044197438E-10]
--R     ,
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--R     [1.1899999999999999, 2.4144473670000002, 2.4144473665637345,
--R      - 4.3626569024013406E-10]
--R     ,
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--R    [1.22,2.4975224420000002,2.497522442409561,4.095608296950104E-10],
--R    [1.23,2.5253116339999999,2.5253116343560089,3.5600900005761105E-10],
--R    [1.24,2.5531528360000002,2.5531528362393039,2.3930368797664414E-10],
--R    [1.25,2.5810479740000001,2.5810479743554762,3.5547609300579097E-10],
--R    [1.26,2.6089989560000002,2.6089989564882825,4.8828230347908175E-10],
--R    [1.27,2.6370076729999998,2.6370076727691485,- 2.308513380455679E-10],
--R    [1.28,2.6650759970000002,2.6650759965061086,- 4.9389159428869789E-10],
--R    [1.29,2.693205785,2.6932057849832494,- 1.6750600906334512E-11],
--R    [1.3,2.7213988800000002,2.7213988802320226,2.3202240129194251E-10],
--R
--R     [1.3100000000000001, 2.7496571099999998, 2.7496571097757787,
--R      - 2.2422108614250646E-10]
--R     ,
--R
--R     [1.3200000000000001, 2.7779822869999999, 2.777982287348725,
--R      3.4872504883765032E-10]
--R     ,
--R
--R     [1.3300000000000001, 2.8063762140000001, 2.8063762135905539,
--R      - 4.0944625467886908E-10]
--R     ,
--R
--R     [1.3400000000000001, 2.8348406769999999, 2.8348406767178056,
--R      - 2.8219426795317304E-10]
--R     ,
--R    [1.3500000000000001,2.863377453,2.8633774531730753,1.7307533184407475E-10],
--R
--R     [1.3600000000000001, 2.8919883080000002, 2.8919883082530298,
--R      2.5302959727468988E-10]
--R     ,
--R
--R     [1.3700000000000001, 2.9206749969999999, 2.9206749967162473,
--R      - 2.8375257699053691E-10]
--R     ,
--R
--R     [1.3799999999999999, 2.9494392629999999, 2.9494392633717355,
--R      3.7173553124603131E-10]
--R     ,
--R
--R     [1.3899999999999999, 2.9782828440000002, 2.9782828436490232,
--R      - 3.5097702522079999E-10]
--R     ,
--R
--R     [1.3999999999999999, 3.0072074639999999, 3.0072074641506457,
--R      1.5064571812217764E-10]
--R     ,
--R
--R     [1.4099999999999999, 3.0362148430000002, 3.0362148431877847,
--R      1.8778445465272853E-10]
--R     ,
--R    [1.4199999999999999,3.065306691,3.065306691299837,2.9983704408209633E-10],
--R
--R     [1.4299999999999999, 3.0944847119999999, 3.0944847117585681,
--R      - 2.4143176347024564E-10]
--R     ,
--R
--R     [1.4399999999999999, 3.1237506009999998, 3.1237506010575933,
--R      5.7593485536244771E-11]
--R     ,
--R    [1.45,3.1531060489999998,3.1531060493877443,3.8774450317191622E-10],
--R    [1.46,3.1825527409999999,3.1825527410990038,9.9003916176343409E-11],
--R    [1.47,3.2120923549999998,3.2120923551495331,1.4953327465150323E-10],
--R    [1.48,3.2417265660000001,3.2417265655423857,- 4.5761439082525612E-10],
--R    [1.49,3.2714570420000002,3.2714570417503985,- 2.4960167266385724E-10],
--R    [1.5,3.3012854489999999,3.3012854491297974,1.297975060765566E-10],
--R    [1.51,3.3312134489999998,3.3312134493229739,3.2297409191528459E-10],
--R    [1.52,3.3612427010000001,3.3612427006508958,- 3.4910430102286227E-10],
--R    [1.53,3.3913748579999998,3.3913748584955847,4.9558490644585618E-10],
--R    [1.54,3.4216115760000001,3.4216115756731122,- 3.2688785012169319E-10],
--R    [1.55,3.4519545030000001,3.4519545027974381,- 2.0256196719969921E-10],
--R
--R     [1.5600000000000001, 3.4824052889999999, 3.4824052886355643,
--R      - 3.6443559281451599E-10]
--R     ,
--R
--R     [1.5700000000000001, 3.5129655799999999, 3.5129655804542947,
--R      4.5429482398162691E-10]
--R     ,
--R
--R     [1.5800000000000001, 3.5436370240000001, 3.5436370243589819,
--R      3.5898173322834737E-10]
--R     ,
--R
--R     [1.5900000000000001, 3.5744212659999999, 3.5744212656246064,
--R      - 3.7539349406756628E-10]
--R     ,
--R
--R     [1.6000000000000001, 3.6053199490000001, 3.6053199490194707,
--R      1.9470647316666145E-11]
--R     ,
--R
--R     [1.6100000000000001, 3.6363347190000002, 3.6363347191218383,
--R      1.2183809516841393E-10]
--R     ,
--R
--R     [1.6200000000000001, 3.6674672209999999, 3.6674672206298222,
--R      - 3.7017766629787729E-10]
--R     ,
--R
--R     [1.6299999999999999, 3.6987190989999998, 3.6987190986647667,
--R      - 3.3523317455319557E-10]
--R     ,
--R
--R     [1.6399999999999999, 3.7300919989999999, 3.7300919990684158,
--R      6.8415939580290797E-11]
--R     ,
--R    [1.6499999999999999,3.761587569,3.7615875686941349,- 3.0586511101660108E-10]
--R     ,
--R
--R     [1.6599999999999999, 3.7932074560000002, 3.7932074556923925,
--R      - 3.0760771707605272E-10]
--R     ,
--R
--R     [1.6699999999999999, 3.8249533100000002, 3.824953309790788,
--R      - 2.092122031172039E-10]
--R     ,
--R
--R     [1.6799999999999999, 3.8568267829999998, 3.8568267825688243,
--R      - 4.3117553971683265E-10]
--R     ,
--R    [1.6899999999999999,3.888829528,3.8888295277276339,- 2.723661296499813E-10],
--R    [1.7,3.9209632010000002,3.9209632013549038,3.5490366201429424E-10],
--R    [1.71,3.9532294619999999,3.953229462185158,1.8515811106567526E-10],
--R    [1.72,3.9856299719999999,3.985629971855627,- 1.4437295803304551E-10],
--R    [1.73,4.0181663949999997,4.0181663951578672,1.5786749685275936E-10],
--R    [1.74,4.0508404000000002,4.0508404002853169,2.8531665918762883E-10],
--R    [1.75,4.0836536590000003,4.0836536590769557,7.6955330996497651E-11],
--R    [1.76,4.116607847,4.1166078472572494,2.5724933294668517E-10],
--R    [1.77,4.1497046449999999,4.1497046446724992,- 3.2750069323128628E-10],
--R    [1.78,4.1829457359999997,4.1829457355238073,- 4.7619241883012364E-10],
--R    [1.79,4.2163328089999998,4.2163328085967509,- 4.0324898975541146E-10],
--R    [1.8,4.249867557,4.2498675574879341,4.879341375385593E-10],
--R
--R     [1.8100000000000001, 4.2835516809999996, 4.2835516808285554,
--R      - 1.7144419217629547E-10]
--R     ,
--R
--R     [1.8200000000000001, 4.3173868830000002, 4.3173868825051116,
--R      - 4.9488857456481128E-10]
--R     ,
--R
--R     [1.8300000000000001, 4.3513748720000001, 4.3513748718773684,
--R      - 1.2263168258641599E-10]
--R     ,
--R    [1.8400000000000001,4.385517364,4.3855173639937215,- 6.2785332488601853E-12]
--R     ,
--R
--R     [1.8500000000000001, 4.4198160800000004, 4.4198160798040753,
--R      - 1.9592505395849003E-10]
--R     ,
--R    [1.8600000000000001,4.454272746,4.4542727463703349,3.7033487387816422E-10],
--R
--R     [1.8700000000000001, 4.4888890970000004, 4.4888890970746314,
--R      7.4630968072142423E-11]
--R     ,
--R
--R     [1.8799999999999999, 4.5236668719999997, 4.523666871825391,
--R      - 1.7460877188568702E-10]
--R     ,
--R
--R     [1.8899999999999999, 4.5586078170000004, 4.5586078172613478,
--R      2.6134738817518155E-10]
--R     ,
--R
--R     [1.8999999999999999, 4.5937136870000002, 4.5937136869535857,
--R      - 4.6414427856689144E-11]
--R     ,
--R
--R     [1.9099999999999999, 4.6289862419999999, 4.6289862416057304,
--R      - 3.9426950593224319E-10]
--R     ,
--R
--R     [1.9199999999999999, 4.6644272490000001, 4.6644272492523706,
--R      2.5237056888727238E-10]
--R     ,
--R
--R     [1.9299999999999999, 4.7000384850000003, 4.7000384854557851,
--R      4.5578474328067387E-10]
--R     ,
--R
--R     [1.9399999999999999, 4.7358217339999999, 4.7358217335010897,
--R      - 4.9891024644921345E-10]
--R     ,
--R    [1.95,4.7717787850000004,4.7717787845898787,- 4.1012171436705103E-10],
--R    [1.96,4.8079114379999996,4.8079114380324146,3.241495960537577E-11],
--R    [1.97,4.8442215009999998,4.8442215014384944,4.3849457398437153E-10],
--R    [1.98,4.8807107910000003,4.8807107909070337,- 9.2966523368431808E-11],
--R    [1.99,4.917381131,4.9173811312144435,2.1444357400923764E-10],
--R    [2.,4.9542343559999997,4.9542343560018924,1.8927082123809669E-12]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 16

--S 17 of 20
f(x)==x/10.0*exp(-x/10.0)*Ei(x/10.0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 20
[[2.0,1.340965420,f(2.0),f(2.0)-1.340965420],_
 [2.1,1.371486802,f(2.1),f(2.1)-1.371486802],_
 [2.2,1.397421992,f(2.2),f(2.2)-1.397421992],_
 [2.3,1.419171534,f(2.3),f(2.3)-1.419171534],_
 [2.4,1.437118315,f(2.4),f(2.4)-1.437118315],_
 [2.5,1.451625159,f(2.5),f(2.5)-1.451625159],_
 [2.6,1.463033397,f(2.6),f(2.6)-1.463033397],_
 [2.7,1.471662153,f(2.7),f(2.7)-1.471662153],_
 [2.8,1.477808187,f(2.8),f(2.8)-1.477808187],_
 [2.9,1.481746162,f(2.9),f(2.9)-1.481746162],_
 [3.0,1.483729204,f(3.0),f(3.0)-1.483729204],_
 [3.1,1.483989691,f(3.1),f(3.1)-1.483989691],_
 [3.2,1.482740191,f(3.2),f(3.2)-1.482740191],_
 [3.3,1.480174491,f(3.3),f(3.3)-1.480174491],_
 [3.4,1.476468706,f(3.4),f(3.4)-1.476468706],_
 [3.5,1.471782389,f(3.5),f(3.5)-1.471782389],_
 [3.6,1.466259659,f(3.6),f(3.6)-1.466259659],_
 [3.7,1.460030313,f(3.7),f(3.7)-1.460030313],_
 [3.8,1.453210902,f(3.8),f(3.8)-1.453210902],_
 [3.9,1.445905765,f(3.9),f(3.9)-1.445905765],_
 [4.0,1.438208032,f(4.0),f(4.0)-1.438208032],_
 [4.1,1.430200557,f(4.1),f(4.1)-1.430200557],_
 [4.2,1.421956813,f(4.2),f(4.2)-1.421956813],_
 [4.3,1.413541719,f(4.3),f(4.3)-1.413541719],_
 [4.4,1.405012424,f(4.4),f(4.4)-1.405012424],_
 [4.5,1.396419030,f(4.5),f(4.5)-1.396419030],_
 [4.6,1.387805263,f(4.6),f(4.6)-1.387805263],_
 [4.7,1.379209093,f(4.7),f(4.7)-1.379209093],_
 [4.8,1.370663313,f(4.8),f(4.8)-1.370663313],_
 [4.9,1.362196054,f(4.9),f(4.9)-1.362196054],_
 [5.0,1.353831278,f(5.0),f(5.0)-1.353831278],_
 [5.1,1.345589212,f(5.1),f(5.1)-1.345589212],_
 [5.2,1.337486755,f(5.2),f(5.2)-1.337486755],_
 [5.3,1.329537845,f(5.3),f(5.3)-1.329537845],_
 [5.4,1.321753788,f(5.4),f(5.4)-1.321753788],_
 [5.5,1.314143566,f(5.5),f(5.5)-1.314143566],_
 [5.6,1.306714107,f(5.6),f(5.6)-1.306714107],_
 [5.7,1.299470536,f(5.7),f(5.7)-1.299470536],_
 [5.8,1.292416395,f(5.8),f(5.8)-1.292416395],_
 [5.9,1.285553849,f(5.9),f(5.9)-1.285553849],_
 [6.0,1.278883860,f(6.0),f(6.0)-1.278883860],_
 [6.1,1.272406357,f(6.1),f(6.1)-1.272406357],_
 [6.2,1.266120373,f(6.2),f(6.2)-1.266120373],_
 [6.3,1.260024184,f(6.3),f(6.3)-1.260024184],_
 [6.4,1.254115417,f(6.4),f(6.4)-1.254115417],_
 [6.5,1.248391155,f(6.5),f(6.5)-1.248391155],_
 [6.6,1.242848032,f(6.6),f(6.6)-1.242848032],_
 [6.7,1.237482309,f(6.7),f(6.7)-1.237482309],_
 [6.8,1.232289952,f(6.8),f(6.8)-1.232289952],_
 [6.9,1.227266684,f(6.9),f(6.9)-1.227266684],_
 [7.0,1.222408053,f(7.0),f(7.0)-1.222408053],_
 [7.1,1.217709472,f(7.1),f(7.1)-1.217709472],_
 [7.2,1.213166264,f(7.2),f(7.2)-1.213166264],_
 [7.3,1.208773699,f(7.3),f(7.3)-1.208773699],_
 [7.4,1.204527026,f(7.4),f(7.4)-1.204527026],_
 [7.5,1.200421500,f(7.5),f(7.5)-1.200421500],_
 [7.6,1.196452401,f(7.6),f(7.6)-1.196452401],_
 [7.7,1.192615063,f(7.7),f(7.7)-1.192615063],_
 [7.8,1.188904881,f(7.8),f(7.8)-1.188904881],_
 [7.9,1.185317334,f(7.9),f(7.9)-1.185317334],_
 [8.0,1.181847987,f(8.0),f(8.0)-1.181847987],_
 [8.1,1.178492509,f(8.1),f(8.1)-1.178492509],_
 [8.2,1.175246676,f(8.2),f(8.2)-1.175246676],_
 [8.3,1.172106376,f(8.3),f(8.3)-1.172106376],_
 [8.4,1.169067617,f(8.4),f(8.4)-1.169067617],_
 [8.5,1.166126526,f(8.5),f(8.5)-1.166126526],_
 [8.6,1.163279354,f(8.6),f(8.6)-1.163279354],_
 [8.7,1.160522476,f(8.7),f(8.7)-1.160522476],_
 [8.8,1.157852390,f(8.8),f(8.8)-1.157852390],_
 [8.9,1.155265719,f(8.9),f(8.9)-1.155265719],_
 [9.0,1.152759209,f(9.0),f(9.0)-1.152759209],_
 [9.1,1.150329724,f(9.1),f(9.1)-1.150329724],_
 [9.2,1.147974251,f(9.2),f(9.2)-1.147974251],_
 [9.3,1.145689889,f(9.3),f(9.3)-1.145689889],_
 [9.4,1.143473855,f(9.4),f(9.4)-1.143473855],_
 [9.5,1.141323476,f(9.5),f(9.5)-1.141323476],_
 [9.6,1.139236185,f(9.6),f(9.6)-1.139236185],_
 [9.7,1.137209523,f(9.7),f(9.7)-1.137209523],_
 [9.8,1.135241130,f(9.8),f(9.8)-1.135241130],_
 [9.9,1.133328746,f(9.9),f(9.9)-1.133328746],_
 [10.0,1.131470205,f(10.0),f(10.0)-1.131470205]]
 
   Compiling function f with type Float -> OnePointCompletion 
      DoubleFloat 

   (19)
   [[2.0,1.3409654199999999,- 0.1345601329966275,- 1.4755255529966274],

     [2.0999999999999996, 1.3714868019999999, - 0.12968783850914051,
      - 1.5011746405091404]
     ,

     [2.1999999999999997, 1.3974219919999999, - 0.12432857913849613,
      - 1.521750571138496]
     ,
    [2.2999999999999998,1.419171534,- 0.11851397777493737,- 1.5376855117749373],
    [2.3999999999999999,1.437118315,- 0.11227320930676461,- 1.5493915243067646],
    [2.5,1.451625159,- 0.10563327984220375,- 1.5572584388422037],

     [2.5999999999999996, 1.4630333969999998, - 0.098619263183169548,
      - 1.5616526601831693]
     ,

     [2.6999999999999997, 1.4716621529999998, - 0.091254502584207656,
      - 1.5629166555842076]
     ,

     [2.7999999999999998, 1.4778081869999999, - 0.083560784069182589,
      - 1.5613689710691825]
     ,

     [2.8999999999999999, 1.4817461619999999, - 0.075558486253840151,
      - 1.55730464825384]
     ,
    [3.0,1.4837292039999999,- 0.067266710614573219,- 1.5509959146145731],

     [3.0999999999999996, 1.4839896909999999, - 0.058703395368669357,
      - 1.5426930863686692]
     ,
    [3.1999999999999997,1.482740191,- 0.049885415529372645,- 1.5326256065293726]
     ,

     [3.2999999999999998, 1.4801744909999999, - 0.040828671227296956,
      - 1.5210031622272968]
     ,

     [3.3999999999999999, 1.4764687059999999, - 0.031548166016793992,
      - 1.5080168720167939]
     ,
    [3.5,1.4717823889999999,- 0.02205807658873344,- 1.4938404655887334],

     [3.5999999999999996, 1.4662596589999999, - 0.012371815072632754,
      - 1.4786314740726327]
     ,

     [3.6999999999999997, 1.4600303129999999, - 0.0025020849182829184,
      - 1.4625323979182827]
     ,

     [3.7999999999999998, 1.4532109019999999, 0.0075390688098496616,
      - 1.4456718331901504]
     ,

     [3.8999999999999999, 1.4459057649999998, 0.017740214020573266,
      - 1.4281655509794264]
     ,
    [4.0,1.4382080319999999,0.028090490467135788,- 1.4101175415328642],

     [4.0999999999999996, 1.4302005569999998, 0.038579572390008407,
      - 1.3916209846099914]
     ,
    [4.1999999999999993,1.421956813,0.049197634492545085,- 1.3727591785074549],

     [4.2999999999999998, 1.4135417189999999, 0.059935320871702939,
      - 1.3536063981282971]
     ,

     [4.3999999999999995, 1.4050124239999999, 0.070783716577210207,
      - 1.3342287074227897]
     ,
    [4.5,1.3964190299999999,0.081734321515770508,- 1.3146847084842295],
    [4.5999999999999996,1.387805263,0.09277902645351857,- 1.2950262365464813],

     [4.6999999999999993, 1.3792090929999998, 0.10391009090110481,
      - 1.275299002098895]
     ,

     [4.7999999999999998, 1.3706633129999999, 0.11512012269240554,
      - 1.2555431903075944]
     ,
    [4.8999999999999995,1.362196054,0.12640205909067995,- 1.23579399490932],
    [5.0,1.3538312779999999,0.13774914927563492,- 1.2160821287243651],

     [5.0999999999999996, 1.3455892119999999, 0.149154938081803,
      - 1.196434273918197]
     ,

     [5.1999999999999993, 1.3374867549999998, 0.16061325087332839,
      - 1.1768735041266714]
     ,

     [5.2999999999999998, 1.3295378449999999, 0.17211817945300253,
      - 1.1574196655469975]
     ,

     [5.3999999999999995, 1.3217537879999999, 0.18366406891450346,
      - 1.1380897190854964]
     ,
    [5.5,1.3141435659999998,0.19524550535650231,- 1.1188980606434975],

     [5.5999999999999996, 1.3067141069999999, 0.20685730438580616,
      - 1.0998568026141937]
     ,

     [5.6999999999999993, 1.2994705359999998, 0.21849450034417647,
      - 1.0809760356558233]
     ,

     [5.7999999999999998, 1.2924163949999998, 0.23015233620004191,
      - 1.0622640587999579]
     ,

     [5.8999999999999995, 1.2855538489999998, 0.24182625405213545,
      - 1.0437275949478644]
     ,
    [6.0,1.2788838599999999,0.25351188619722098,- 1.0253719738027789],

     [6.0999999999999996, 1.2724063569999999, 0.26520504671863676,
      - 1.0072013102813631]
     ,

     [6.1999999999999993, 1.2661203729999999, 0.27690172355643172,
      - 0.98921864944356819]
     ,

     [6.2999999999999998, 1.2600241839999999, 0.28859807102347895,
      - 0.97142611297652093]
     ,
    [6.3999999999999995,1.254115417,0.30029040273517305,- 0.95382501426482691],
    [6.5,1.248391155,0.31197518492319359,- 0.93641597007680644],

     [6.5999999999999996, 1.2428480319999999, 0.32364903010640256,
      - 0.91919900189359738]
     ,

     [6.6999999999999993, 1.2374823089999998, 0.33530869109425587,
      - 0.90217361790574391]
     ,

     [6.7999999999999998, 1.2322899519999999, 0.34695105530018905,
      - 0.88533889669981081]
     ,

     [6.8999999999999995, 1.2272666839999999, 0.35857313934432239,
      - 0.86869354465567761]
     ,
    [7.0,1.2224080529999999,0.37017208392651257,- 0.85223596907348731],

     [7.0999999999999996, 1.2177094719999999, 0.38174514895231298,
      - 0.83596432304768697]
     ,

     [7.1999999999999993, 1.2131662639999998, 0.39328970889579107,
      - 0.81987655510420876]
     ,
    [7.2999999999999998,1.208773699,0.40480324838440257,- 0.80397045061559735],

     [7.3999999999999995, 1.2045270259999998, 0.41628335799226329,
      - 0.78824366800773649]
     ,
    [7.5,1.2004214999999998,0.42772773022919908,- 0.77269376977080073],

     [7.5999999999999996, 1.1964524009999999, 0.43913415571389086,
      - 0.75731824528610914]
     ,

     [7.6999999999999993, 1.1926150629999999, 0.45050051952030129,
      - 0.74211454347969852]
     ,

     [7.7999999999999998, 1.1889048809999998, 0.4618247976873473,
      - 0.7270800833126525]
     ,

     [7.8999999999999995, 1.1853173339999998, 0.47310505388250546,
      - 0.71221228011749438]
     ,
    [8.0,1.1818479869999998,0.48433943621069137,- 0.6975085507893084],

     [8.0999999999999996, 1.1784925089999998, 0.49552617416036338,
      - 0.68296633483963642]
     ,
    [8.1999999999999993,1.175246676,0.50666357567934217,- 0.66858310032065782],

     [8.2999999999999989, 1.1721063759999999, 0.51775002437336048,
      - 0.65435635162663941]
     ,

     [8.3999999999999986, 1.1690676169999998, 0.52878397682080924,
      - 0.64028364017919059]
     ,
    [8.5,1.166126526,0.53976395999758897,- 0.62636256600241103],

     [8.5999999999999996, 1.1632793539999999, 0.5506885688063663,
      - 0.61259078519363364]
     ,

     [8.6999999999999993, 1.1605224759999999, 0.56155646370489865,
      - 0.59896601229510127]
     ,
    [8.7999999999999989,1.15785239,0.57236636842843402,- 0.58548602157156593],
    [8.8999999999999986,1.155265719,0.58311706780150507,- 0.5721486511984949],
    [9.0,1.1527592089999998,0.59380740563471446,- 0.55895180336528538],

     [9.0999999999999996, 1.1503297239999999, 0.60443628270239658,
      - 0.54589344129760331]
     ,

     [9.1999999999999993, 1.1479742509999999, 0.61500265479727356,
      - 0.53297159620272638]
     ,

     [9.2999999999999989, 1.1456898889999998, 0.62550553085845118,
      - 0.52018435814154862]
     ,

     [9.3999999999999986, 1.1434738549999999, 0.63594397116933887,
      - 0.507529883830661]
     ,
    [9.5,1.1413234759999999,0.64631708562224488,- 0.49500639037775507],

     [9.5999999999999996, 1.1392361849999999, 0.6566240320466048,
      - 0.4826121529533951]
     ,

     [9.6999999999999993, 1.1372095229999999, 0.66686401459797284,
      - 0.47034550840202705]
     ,

     [9.7999999999999989, 1.1352411299999998, 0.67703628220505319,
      - 0.45820484779494663]
     ,

     [9.8999999999999986, 1.1333287459999999, 0.68714012707221583,
      - 0.44618861892778405]
     ,
    [10.0,1.1314702049999998,0.69717488323506571,- 0.43429532176493413]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R   Compiling function f with type Float -> OnePointCompletion 
--R      DoubleFloat 
--R
--R   (19)
--R   [[2.,1.3409654200000001,- 0.13456013299662745,- 1.4755255529966276],
--R
--R     [2.1000000000000001, 1.3714868019999999, - 0.12968783850914051,
--R      - 1.5011746405091404]
--R     ,
--R
--R     [2.2000000000000002, 1.3974219919999999, - 0.12432857913849607,
--R      - 1.521750571138496]
--R     ,
--R    [2.2999999999999998,1.419171534,- 0.11851397777493734,- 1.5376855117749373],
--R    [2.3999999999999999,1.437118315,- 0.1122732093067646,- 1.5493915243067646],
--R    [2.5,1.451625159,- 0.10563327984220373,- 1.5572584388422037],
--R
--R     [2.6000000000000001, 1.463033397, - 9.8619263183169451E-2,
--R      - 1.5616526601831695]
--R     ,
--R
--R     [2.7000000000000002, 1.471662153, - 9.1254502584207586E-2,
--R      - 1.5629166555842076]
--R     ,
--R
--R     [2.7999999999999998, 1.4778081869999999, - 8.3560784069182492E-2,
--R      - 1.5613689710691825]
--R     ,
--R
--R     [2.8999999999999999, 1.4817461620000001, - 7.5558486253840138E-2,
--R      - 1.5573046482538402]
--R     ,
--R    [3.,1.4837292040000001,- 6.7266710614573164E-2,- 1.5509959146145733],
--R
--R     [3.1000000000000001, 1.4839896910000001, - 5.8703395368669309E-2,
--R      - 1.5426930863686694]
--R     ,
--R
--R     [3.2000000000000002, 1.482740191, - 4.9885415529372513E-2,
--R      - 1.5326256065293724]
--R     ,
--R
--R     [3.2999999999999998, 1.4801744910000001, - 4.0828671227296824E-2,
--R      - 1.5210031622272968]
--R     ,
--R
--R     [3.3999999999999999, 1.4764687059999999, - 3.1548166016793916E-2,
--R      - 1.5080168720167939]
--R     ,
--R    [3.5,1.4717823889999999,- 2.2058076588733416E-2,- 1.4938404655887334],
--R
--R     [3.6000000000000001, 1.4662596590000001, - 1.2371815072632724E-2,
--R      - 1.4786314740726327]
--R     ,
--R
--R     [3.7000000000000002, 1.4600303130000001, - 2.5020849182828334E-3,
--R      - 1.4625323979182829]
--R     ,
--R
--R     [3.7999999999999998, 1.4532109019999999, 7.5390688098497787E-3,
--R      - 1.4456718331901501]
--R     ,
--R    [3.8999999999999999,1.445905765,1.774021402057336E-2,- 1.4281655509794267],
--R    [4.,1.4382080319999999,2.8090490467135878E-2,- 1.4101175415328639],
--R    [4.0999999999999996,1.430200557,3.8579572390008463E-2,- 1.3916209846099916],
--R    [4.2000000000000002,1.421956813,4.9197634492545148E-2,- 1.3727591785074549],
--R
--R     [4.2999999999999998, 1.4135417189999999, 5.9935320871702981E-2,
--R      - 1.3536063981282969]
--R     ,
--R
--R     [4.4000000000000004, 1.4050124239999999, 7.0783716577210318E-2,
--R      - 1.3342287074227897]
--R     ,
--R    [4.5,1.3964190299999999,8.1734321515770605E-2,- 1.3146847084842292],
--R    [4.5999999999999996,1.387805263,9.2779026453518668E-2,- 1.2950262365464813],
--R
--R     [4.7000000000000002, 1.3792090930000001, 0.10391009090110491,
--R      - 1.2752990020988952]
--R     ,
--R
--R     [4.7999999999999998, 1.3706633130000001, 0.11512012269240564,
--R      - 1.2555431903075944]
--R     ,
--R    [4.9000000000000004,1.362196054,0.12640205909068003,- 1.23579399490932],
--R    [5.,1.3538312779999999,0.13774914927563506,- 1.2160821287243648],
--R
--R     [5.0999999999999996, 1.3455892119999999, 0.14915493808180313,
--R      - 1.1964342739181968]
--R     ,
--R    [5.2000000000000002,1.337486755,0.16061325087332862,- 1.1768735041266714],
--R
--R     [5.2999999999999998, 1.3295378449999999, 0.17211817945300276,
--R      - 1.1574196655469973]
--R     ,
--R
--R     [5.4000000000000004, 1.3217537880000001, 0.1836640689145036,
--R      - 1.1380897190854964]
--R     ,
--R    [5.5,1.314143566,0.19524550535650245,- 1.1188980606434975],
--R
--R     [5.5999999999999996, 1.3067141069999999, 0.20685730438580638,
--R      - 1.0998568026141935]
--R     ,
--R
--R     [5.7000000000000002, 1.2994705360000001, 0.21849450034417656,
--R      - 1.0809760356558236]
--R     ,
--R
--R     [5.7999999999999998, 1.2924163950000001, 0.23015233620004197,
--R      - 1.0622640587999581]
--R     ,
--R    [5.9000000000000004,1.285553849,0.24182625405213551,- 1.0437275949478646],
--R    [6.,1.2788838600000001,0.25351188619722104,- 1.0253719738027791],
--R
--R     [6.0999999999999996, 1.2724063569999999, 0.26520504671863687,
--R      - 1.0072013102813631]
--R     ,
--R
--R     [6.2000000000000002, 1.2661203729999999, 0.27690172355643178,
--R      - 0.98921864944356819]
--R     ,
--R
--R     [6.2999999999999998, 1.2600241839999999, 0.28859807102347912,
--R      - 0.97142611297652082]
--R     ,
--R    [6.4000000000000004,1.254115417,0.30029040273517321,- 0.9538250142648268],
--R    [6.5,1.248391155,0.31197518492319382,- 0.93641597007680621],
--R
--R     [6.5999999999999996, 1.2428480319999999, 0.32364903010640295,
--R      - 0.91919900189359693]
--R     ,
--R    [6.7000000000000002,1.237482309,0.33530869109425609,- 0.90217361790574391],
--R
--R     [6.7999999999999998, 1.2322899519999999, 0.34695105530018927,
--R      - 0.88533889669981058]
--R     ,
--R
--R     [6.9000000000000004, 1.2272666839999999, 0.3585731393443225,
--R      - 0.86869354465567739]
--R     ,
--R    [7.,1.2224080530000001,0.37017208392651269,- 0.85223596907348742],
--R
--R     [7.0999999999999996, 1.2177094719999999, 0.38174514895231304,
--R      - 0.83596432304768686]
--R     ,
--R    [7.2000000000000002,1.213166264,0.39328970889579112,- 0.81987655510420887],
--R    [7.2999999999999998,1.208773699,0.40480324838440268,- 0.80397045061559735],
--R
--R     [7.4000000000000004, 1.2045270260000001, 0.4162833579922634,
--R      - 0.78824366800773671]
--R     ,
--R    [7.5,1.2004215,0.42772773022919919,- 0.77269376977080084],
--R
--R     [7.5999999999999996, 1.1964524009999999, 0.43913415571389103,
--R      - 0.75731824528610892]
--R     ,
--R
--R     [7.7000000000000002, 1.1926150630000001, 0.45050051952030151,
--R      - 0.74211454347969852]
--R     ,
--R    [7.7999999999999998,1.188904881,0.46182479768734747,- 0.7270800833126525],
--R
--R     [7.9000000000000004, 1.1853173340000001, 0.47310505388250573,
--R      - 0.71221228011749438]
--R     ,
--R    [8.,1.181847987,0.48433943621069148,- 0.69750855078930862],
--R    [8.0999999999999996,1.178492509,0.49552617416036354,- 0.68296633483963642],
--R    [8.1999999999999993,1.175246676,0.50666357567934228,- 0.66858310032065771],
--R
--R     [8.3000000000000007, 1.1721063759999999, 0.51775002437336082,
--R      - 0.65435635162663908]
--R     ,
--R
--R     [8.4000000000000004, 1.1690676170000001, 0.52878397682080924,
--R      - 0.64028364017919082]
--R     ,
--R    [8.5,1.166126526,0.53976395999758919,- 0.6263625660024108],
--R
--R     [8.5999999999999996, 1.1632793539999999, 0.5506885688063663,
--R      - 0.61259078519363364]
--R     ,
--R
--R     [8.6999999999999993, 1.1605224759999999, 0.56155646370489876,
--R      - 0.59896601229510116]
--R     ,
--R    [8.8000000000000007,1.15785239,0.57236636842843447,- 0.58548602157156548],
--R    [8.9000000000000004,1.155265719,0.58311706780150541,- 0.57214865119849456],
--R    [9.,1.1527592090000001,0.59380740563471446,- 0.5589518033652856],
--R
--R     [9.0999999999999996, 1.1503297240000001, 0.60443628270239691,
--R      - 0.5458934412976032]
--R     ,
--R
--R     [9.1999999999999993, 1.1479742509999999, 0.61500265479727367,
--R      - 0.53297159620272627]
--R     ,
--R    [9.3000000000000007,1.145689889,0.62550553085845151,- 0.52018435814154851],
--R
--R     [9.4000000000000004, 1.1434738550000001, 0.63594397116933887,
--R      - 0.50752988383066122]
--R     ,
--R    [9.5,1.1413234759999999,0.6463170856222451,- 0.49500639037775485],
--R
--R     [9.5999999999999996, 1.1392361849999999, 0.65662403204660502,
--R      - 0.48261215295339488]
--R     ,
--R
--R     [9.6999999999999993, 1.1372095230000001, 0.66686401459797295,
--R      - 0.47034550840202716]
--R     ,
--R    [9.8000000000000007,1.13524113,0.6770362822050533,- 0.45820484779494675],
--R
--R     [9.9000000000000004, 1.1333287460000001, 0.68714012707221583,
--R      - 0.44618861892778428]
--R     ,
--R    [10.,1.1314702050000001,0.69717488323506582,- 0.43429532176493424]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 18

--S 19 of 20
g(y)==(y=0 => 1 ; (x:DFLOAT:=y^-1) ; x*exp(-x)*Ei(x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 20
[[0.100,1.13147021,g(0.100),g(0.100)-1.13147021],_
 [0.095,1.12249671,g(0.095),g(0.095)-1.12249671],_
 [0.090,1.11389377,g(0.090),g(0.090)-1.11389377],_
 [0.085,1.10564739,g(0.085),g(0.085)-1.10564739],_
 [0.080,1.09773775,g(0.080),g(0.080)-1.09773775],_
 [0.075,1.09014087,g(0.075),g(0.075)-1.09014087],_
 [0.070,1.08283054,g(0.070),g(0.070)-1.08283054],_
 [0.065,1.07578038,g(0.065),g(0.065)-1.07578038],_
 [0.060,1.06896548,g(0.060),g(0.060)-1.06896548],_
 [0.055,1.06236365,g(0.055),g(0.055)-1.06236365],_
 [0.050,1.05595591,g(0.050),g(0.050)-1.05595591],_
 [0.045,1.04972640,g(0.045),g(0.045)-1.04972640],_
 [0.040,1.04366194,g(0.040),g(0.040)-1.04366194],_
 [0.035,1.03775135,g(0.035),g(0.035)-1.03775135],_
 [0.030,1.03198503,g(0.030),g(0.030)-1.03198503],_
 [0.025,1.02635451,g(0.025),g(0.025)-1.02635451],_
 [0.020,1.02085228,g(0.020),g(0.020)-1.02085228],_
 [0.015,1.01547157,g(0.015),g(0.015)-1.01547157],_
 [0.010,1.01020625,g(0.010),g(0.010)-1.01020625],_
 [0.005,1.00505077,g(0.005),g(0.005)-1.00505077],_
 [0.000,1.00000000,g(0.000),g(0.000)-1.00000000]]
 
   Compiling function g with type Float -> OnePointCompletion 
      DoubleFloat 

   (21)
   [
     [0.099999999999999992, 1.1314702099999998, 1.1314702047341079,
      - 5.2658919447168273E-9]
     ,

     [0.094999999999999987, 1.1224967099999998, 1.1224967463528541,
      3.6352854282384328E-8]
     ,

     [0.089999999999999997, 1.1138937699999998, 1.1138937808537757,
      1.0853775878061356E-8]
     ,

     [0.084999999999999992, 1.1056473899999999, 1.1056473901733923,
      1.733924115399077E-10]
     ,

     [0.079999999999999988, 1.0977377499999998, 1.0977377526473173,
      2.6473174763452789E-9]
     ,

     [0.074999999999999997, 1.0901408699999999, 1.0901408684282585,
      - 1.5717414036942046E-9]
     ,

     [0.069999999999999993, 1.0828305399999998, 1.0828305423224371,
      2.3224373535413179E-9]
     ,

     [0.064999999999999988, 1.0757803799999999, 1.0757803749062493,
      - 5.0937505324810672E-9]
     ,

     [0.059999999999999998, 1.0689654799999999, 1.0689654755715123,
      - 4.4284875766464893E-9]
     ,
    [0.054999999999999993,1.06236365,1.0623636462639567,- 3.7360432525446186E-9]
     ,
    [0.049999999999999996,1.05595591,1.0559559055929626,- 4.4070374016769165E-9]
     ,

     [0.044999999999999998, 1.0497263999999999, 1.0497264028491122,
      2.8491122794349621E-9]
     ,

     [0.039999999999999994, 1.0436619399999998, 1.0436619362666135,
      - 3.7333862668020856E-9]
     ,
    [0.034999999999999996,1.03775135,1.0377513519241477,1.924147730036907E-9],
    [0.029999999999999999,1.03198503,1.0319850279857541,- 2.0142458811989172E-9]
     ,
    [0.024999999999999998,1.02635451,1.026354511439006,1.4390060254498849E-9],

     [0.019999999999999997, 1.0208522799999999, 1.0208522777971993,
      - 2.2028006085861307E-9]
     ,

     [0.014999999999999999, 1.0154715699999999, 1.0154715653071829,
      - 4.692817023865814E-9]
     ,
    [0.0099999999999999985,1.01020625,1.0102062527748354,2.7748354725076751E-9],

     [0.0049999999999999992, 1.00505077, 1.0050507653866605,
      - 4.6133394882019729E-9]
     ,
    [0.0,1.0,1.0,0.0]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R   Compiling function g with type Float -> OnePointCompletion 
--R      DoubleFloat 
--R
--R   (21)
--R   [[0.10000000000000001,1.13147021,1.1314702047341079,- 5.2658921667614322E-9],
--R
--R     [9.5000000000000001E-2, 1.1224967100000001, 1.1224967463528539,
--R      3.6352853838295118E-8]
--R     ,
--R    [8.9999999999999997E-2,1.11389377,1.1138937808537757,1.0853775656016751E-8],
--R
--R     [8.5000000000000006E-2, 1.1056473899999999, 1.1056473901733923,
--R      1.733924115399077E-10]
--R     ,
--R
--R     [8.0000000000000002E-2, 1.0977377500000001, 1.0977377526473173,
--R      2.647317254300674E-9]
--R     ,
--R
--R     [7.4999999999999997E-2, 1.0901408699999999, 1.0901408684282585,
--R      - 1.5717414036942046E-9]
--R     ,
--R    [7.0000000000000007E-2,1.08283054,1.0828305423224371,2.3224371314967129E-9],
--R
--R     [6.5000000000000002E-2, 1.0757803800000001, 1.0757803749062493,
--R      - 5.0937507545256722E-9]
--R     ,
--R
--R     [5.9999999999999998E-2, 1.0689654799999999, 1.0689654755715123,
--R      - 4.4284875766464893E-9]
--R     ,
--R    [5.5E-2,1.06236365,1.0623636462639567,- 3.7360432525446186E-9],
--R
--R     [5.0000000000000003E-2, 1.05595591, 1.0559559055929626,
--R      - 4.4070374016769165E-9]
--R     ,
--R
--R     [4.4999999999999998E-2, 1.0497263999999999, 1.0497264028491122,
--R      2.8491122794349621E-9]
--R     ,
--R
--R     [4.0000000000000001E-2, 1.04366194, 1.0436619362666135,
--R      - 3.7333864888466906E-9]
--R     ,
--R    [3.5000000000000003E-2,1.03775135,1.0377513519241477,1.924147730036907E-9],
--R
--R     [2.9999999999999999E-2, 1.03198503, 1.0319850279857541,
--R      - 2.0142458811989172E-9]
--R     ,
--R    [2.5000000000000001E-2,1.02635451,1.026354511439006,1.4390060254498849E-9],
--R    [2.0E-2,1.0208522799999999,1.0208522777971993,- 2.2028006085861307E-9],
--R
--R     [1.4999999999999999E-2, 1.0154715700000001, 1.0154715653071829,
--R      - 4.6928172459104189E-9]
--R     ,
--R    [1.0E-2,1.01020625,1.0102062527748354,2.7748354725076751E-9],
--R
--R     [5.0000000000000001E-3, 1.00505077, 1.0050507653866605,
--R      - 4.6133394882019729E-9]
--R     ,
--R    [0.,1.,1.,0.]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 20

)spool 
 
Starts dribbling to schaum23.output (2009/2/17, 17:59:18).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(csc(a*x),x)
 

              sin(a x)
        log(------------)
            cos(a x) + 1
   (1)  -----------------
                a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)
--R        log(------------)
--R            cos(a x) + 1
--R   (1)  -----------------
--R                a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb1:=1/a*log(csc(a*x)-cot(a*x))
 

        log(csc(a x) - cot(a x))
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R        log(csc(a x) - cot(a x))
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 3
bb2:=1/a*log(tan((a*x)/2))
 

                a x
        log(tan(---))
                 2
   (3)  -------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---))
--R                 2
--R   (3)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 4
cc1:=aa-bb1
 

              sin(a x)
        log(------------) - log(csc(a x) - cot(a x))
            cos(a x) + 1
   (4)  --------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R              sin(a x)
--R        log(------------) - log(csc(a x) - cot(a x))
--R            cos(a x) + 1
--R   (4)  --------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 5
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (5)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (5)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 6
dd1:=cotrule cc1
 

              sin(a x)          csc(a x)sin(a x) - cos(a x)
        log(------------) - log(---------------------------)
            cos(a x) + 1                  sin(a x)
   (6)  ----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R              sin(a x)          csc(a x)sin(a x) - cos(a x)
--R        log(------------) - log(---------------------------)
--R            cos(a x) + 1                  sin(a x)
--R   (6)  ----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 7
cscrule:=rule(csc(a) == 1/sin(a))
 

                     1
   (7)  csc(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (7)  csc(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 8
ee1:=cscrule dd1
 

              sin(a x)          - cos(a x) + 1
        log(------------) - log(--------------)
            cos(a x) + 1           sin(a x)
   (8)  ---------------------------------------
                           a
                                                     Type: Expression Integer
--R
--R              sin(a x)          - cos(a x) + 1
--R        log(------------) - log(--------------)
--R            cos(a x) + 1           sin(a x)
--R   (8)  ---------------------------------------
--R                           a
--R                                                     Type: Expression Integer
--E

--S 9
ff1:=expandLog ee1
 

        2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1)
   (9)  -----------------------------------------------------------------
                                        a
                                                     Type: Expression Integer
--R
--R        2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1)
--R   (9)  -----------------------------------------------------------------
--R                                        a
--R                                                     Type: Expression Integer
--E

--S 10
gg1:=complexNormalize ff1
 

           2log(- 1)
   (10)  - ---------
               a
                                                     Type: Expression Integer
--R
--R           2log(- 1)
--R   (10)  - ---------
--R               a
--R                                                     Type: Expression Integer
--E

--S 11
cc2:=aa-bb2
 

                   a x           sin(a x)
         - log(tan(---)) + log(------------)
                    2          cos(a x) + 1
   (11)  -----------------------------------
                          a
                                                     Type: Expression Integer
--R
--R                   a x           sin(a x)
--R         - log(tan(---)) + log(------------)
--R                    2          cos(a x) + 1
--R   (11)  -----------------------------------
--R                          a
--R                                                     Type: Expression Integer
--E

--S 12
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                   sin(a)
   (12)  tan(a) == ------
                   cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sin(a)
--R   (12)  tan(a) == ------
--R                   cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 13
dd2:=tanrule cc2
 

                                     a x
                                 sin(---)
               sin(a x)               2
         log(------------) - log(--------)
             cos(a x) + 1            a x
                                 cos(---)
                                      2
   (13)  ---------------------------------
                         a
                                                     Type: Expression Integer
--R
--R                                     a x
--R                                 sin(---)
--R               sin(a x)               2
--R         log(------------) - log(--------)
--R             cos(a x) + 1            a x
--R                                 cos(---)
--R                                      2
--R   (13)  ---------------------------------
--R                         a
--R                                                     Type: Expression Integer
--E

--S 14
ee2:=expandLog dd2
 

                                 a x                                 a x
         log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
                                  2                                   2
   (14)  -----------------------------------------------------------------
                                         a
                                                     Type: Expression Integer
--R
--R                                 a x                                 a x
--R         log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
--R                                  2                                   2
--R   (14)  -----------------------------------------------------------------
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 15     14:461 Schaums and Axiom agree
ff2:=complexNormalize ee2
 

   (15)  0
                                                     Type: Expression Integer
--R
--R   (15)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(csc(a*x)^2,x)
 

           cos(a x)
   (1)  - ----------
          a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           cos(a x)
--R   (1)  - ----------
--R          a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17
bb:=-cot(a*x)/a
 

          cot(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cot(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 18
cc:=aa-bb
 

        cot(a x)sin(a x) - cos(a x)
   (3)  ---------------------------
                 a sin(a x)
                                                     Type: Expression Integer
--R
--R        cot(a x)sin(a x) - cos(a x)
--R   (3)  ---------------------------
--R                 a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 19
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20     14:462 Schaums and Axiom agree
dd:=cotrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 21
aa:=integrate(csc(a*x)^3,x)
 

                 2           sin(a x)
        (cos(a x)  - 1)log(------------) + cos(a x)
                           cos(a x) + 1
   (1)  -------------------------------------------
                                2
                     2a cos(a x)  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2           sin(a x)
--R        (cos(a x)  - 1)log(------------) + cos(a x)
--R                           cos(a x) + 1
--R   (1)  -------------------------------------------
--R                                2
--R                     2a cos(a x)  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22
bb:=-(csc(a*x)*cot(a*x))/(2*a)+1/(2*a)*log(tan((a*x)/2))
 

                a x
        log(tan(---)) - cot(a x)csc(a x)
                 2
   (2)  --------------------------------
                       2a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---)) - cot(a x)csc(a x)
--R                 2
--R   (2)  --------------------------------
--R                       2a
--R                                                     Type: Expression Integer
--E

--S 23
cc:=aa-bb
 

   (3)
                  2             a x              2           sin(a x)
       (- cos(a x)  + 1)log(tan(---)) + (cos(a x)  - 1)log(------------)
                                 2                         cos(a x) + 1
     + 
                2
       (cos(a x)  - 1)cot(a x)csc(a x) + cos(a x)
  /
                2
     2a cos(a x)  - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2             a x              2           sin(a x)
--R       (- cos(a x)  + 1)log(tan(---)) + (cos(a x)  - 1)log(------------)
--R                                 2                         cos(a x) + 1
--R     + 
--R                2
--R       (cos(a x)  - 1)cot(a x)csc(a x) + cos(a x)
--R  /
--R                2
--R     2a cos(a x)  - 2a
--R                                                     Type: Expression Integer
--E

--S 24
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25
dd:=cotrule cc
 

   (5)
                  2                     a x
       (- cos(a x)  + 1)sin(a x)log(tan(---))
                                         2
     + 
                2                   sin(a x)
       (cos(a x)  - 1)sin(a x)log(------------) + cos(a x)sin(a x)
                                  cos(a x) + 1
     + 
                3
       (cos(a x)  - cos(a x))csc(a x)
  /
                 2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                  2                     a x
--R       (- cos(a x)  + 1)sin(a x)log(tan(---))
--R                                         2
--R     + 
--R                2                   sin(a x)
--R       (cos(a x)  - 1)sin(a x)log(------------) + cos(a x)sin(a x)
--R                                  cos(a x) + 1
--R     + 
--R                3
--R       (cos(a x)  - cos(a x))csc(a x)
--R  /
--R                 2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 26
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (6)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (6)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27
ee:=tanrule dd
 

   (7)
                2                   sin(a x)
       (cos(a x)  - 1)sin(a x)log(------------)
                                  cos(a x) + 1
     + 
                                        a x
                                    sin(---)
                  2                      2
       (- cos(a x)  + 1)sin(a x)log(--------) + cos(a x)sin(a x)
                                        a x
                                    cos(---)
                                         2
     + 
                3
       (cos(a x)  - cos(a x))csc(a x)
  /
                 2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (7)
--R                2                   sin(a x)
--R       (cos(a x)  - 1)sin(a x)log(------------)
--R                                  cos(a x) + 1
--R     + 
--R                                        a x
--R                                    sin(---)
--R                  2                      2
--R       (- cos(a x)  + 1)sin(a x)log(--------) + cos(a x)sin(a x)
--R                                        a x
--R                                    cos(---)
--R                                         2
--R     + 
--R                3
--R       (cos(a x)  - cos(a x))csc(a x)
--R  /
--R                 2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 28
cscrule:=rule(csc(a) == 1/sin(a))
 

                     1
   (8)  csc(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (8)  csc(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29
ff:=cscrule ee
 

   (9)
                2             2      sin(a x)
       (cos(a x)  - 1)sin(a x) log(------------)
                                   cos(a x) + 1
     + 
                                         a x
                                     sin(---)
                  2             2         2                      2           3
       (- cos(a x)  + 1)sin(a x) log(--------) + cos(a x)sin(a x)  + cos(a x)
                                         a x
                                     cos(---)
                                          2
     + 
       - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (9)
--R                2             2      sin(a x)
--R       (cos(a x)  - 1)sin(a x) log(------------)
--R                                   cos(a x) + 1
--R     + 
--R                                         a x
--R                                     sin(---)
--R                  2             2         2                      2           3
--R       (- cos(a x)  + 1)sin(a x) log(--------) + cos(a x)sin(a x)  + cos(a x)
--R                                         a x
--R                                     cos(---)
--R                                          2
--R     + 
--R       - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 30
gg:=expandLog ff
 

   (10)
                2             2
       (cos(a x)  - 1)sin(a x) log(sin(a x))
     + 
                  2             2        a x
       (- cos(a x)  + 1)sin(a x) log(sin(---))
                                          2
     + 
                  2             2
       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1)
     + 
                2             2        a x                     2           3
       (cos(a x)  - 1)sin(a x) log(cos(---)) + cos(a x)sin(a x)  + cos(a x)
                                        2
     + 
       - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (10)
--R                2             2
--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
--R     + 
--R                  2             2        a x
--R       (- cos(a x)  + 1)sin(a x) log(sin(---))
--R                                          2
--R     + 
--R                  2             2
--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1)
--R     + 
--R                2             2        a x                     2           3
--R       (cos(a x)  - 1)sin(a x) log(cos(---)) + cos(a x)sin(a x)  + cos(a x)
--R                                        2
--R     + 
--R       - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 31     14:463 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (11)  0
                                                     Type: Expression Integer
--R
--R   (11)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(csc(a*x)^n*cot(a*x),x)
 

                          1
            n log(- -------------)
                            2
                    cos(a x)  - 1
            ----------------------
                       2
          %e
   (1)  - ------------------------
                     a n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          1
--R            n log(- -------------)
--R                            2
--R                    cos(a x)  - 1
--R            ----------------------
--R                       2
--R          %e
--R   (1)  - ------------------------
--R                     a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33
bb:=-csc(a*x)^n/(n*a)
 

                  n
          csc(a x)
   (2)  - ---------
             a n
                                                     Type: Expression Integer
--R
--R                  n
--R          csc(a x)
--R   (2)  - ---------
--R             a n
--R                                                     Type: Expression Integer
--E

--S 34
cc:=aa-bb
 

                          1
            n log(- -------------)
                            2
                    cos(a x)  - 1
            ----------------------
                       2                     n
        - %e                       + csc(a x)
   (3)  --------------------------------------
                          a n
                                                     Type: Expression Integer
--R
--R                          1
--R            n log(- -------------)
--R                            2
--R                    cos(a x)  - 1
--R            ----------------------
--R                       2                     n
--R        - %e                       + csc(a x)
--R   (3)  --------------------------------------
--R                          a n
--R                                                     Type: Expression Integer
--E

--S 35     14:464 Schaums and Axiom agree
normalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(1/csc(a*x),x)
 

          cos(a x)
   (1)  - --------
              a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          cos(a x)
--R   (1)  - --------
--R              a
--R                                          Type: Union(Expression Integer,...)
--E

--S 37
bb:=-cos(a*x)/a
 

          cos(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cos(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E 

--S 38     14:465 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39     14:466 Axiom cannot compute this integral
aa:=integrate(x*csc(a*x),x)
 

           x
         ++
   (1)   |   %P csc(%P a)d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %H csc(%H a)d%H
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 40     14:467 Axiom cannot compute this integral
aa:=integrate(csc(a*x)/x,x)
 

           x
         ++  csc(%P a)
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  csc(%H a)
--I   (1)   |   --------- d%H
--I        ++       %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 41
aa:=integrate(x*csc(a*x)^2,x)
 

                      sin(a x)                        2
        sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x)
                    cos(a x) + 1                cos(a x) + 1
   (1)  --------------------------------------------------------------------
                                      2
                                     a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      sin(a x)                        2
--R        sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x)
--R                    cos(a x) + 1                cos(a x) + 1
--R   (1)  --------------------------------------------------------------------
--R                                      2
--R                                     a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 42
bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))
 

        log(sin(a x)) - a x cot(a x)
   (2)  ----------------------------
                      2
                     a
                                                     Type: Expression Integer
--R
--R        log(sin(a x)) - a x cot(a x)
--R   (2)  ----------------------------
--R                      2
--R                     a
--R                                                     Type: Expression Integer
--E

--S 43
cc:=aa-bb
 

   (3)
                                               sin(a x)
       - sin(a x)log(sin(a x)) + sin(a x)log(------------)
                                             cos(a x) + 1
     + 
                           2
       - sin(a x)log(------------) + a x cot(a x)sin(a x) - a x cos(a x)
                     cos(a x) + 1
  /
      2
     a sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                               sin(a x)
--R       - sin(a x)log(sin(a x)) + sin(a x)log(------------)
--R                                             cos(a x) + 1
--R     + 
--R                           2
--R       - sin(a x)log(------------) + a x cot(a x)sin(a x) - a x cos(a x)
--R                     cos(a x) + 1
--R  /
--R      2
--R     a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 44
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 45
dd:=cotrule cc
 

                                sin(a x)                2
        - log(sin(a x)) + log(------------) - log(------------)
                              cos(a x) + 1        cos(a x) + 1
   (5)  -------------------------------------------------------
                                    2
                                   a
                                                     Type: Expression Integer
--R
--R                                sin(a x)                2
--R        - log(sin(a x)) + log(------------) - log(------------)
--R                              cos(a x) + 1        cos(a x) + 1
--R   (5)  -------------------------------------------------------
--R                                    2
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 46     14:468 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

          log(2)
   (6)  - ------
             2
            a
                                                     Type: Expression Integer
--R
--R          log(2)
--R   (6)  - ------
--R             2
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 47
aa:=integrate(1/(q+p*csc(a*x)),x)
 

   (1)
   [
           p
        *
           log
                                                          +-------+
                                    2    2             2  | 2    2
                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
                + 
                      2    3              3    2              3    2
                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
             /
                q sin(a x) + p
       + 
             +-------+
             | 2    2
         a x\|q  - p
    /
           +-------+
           | 2    2
       a q\|q  - p
     ,
                                          +---------+
                                          |   2    2         +---------+
            (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
    2p atan(-----------------------------------------) + a x\|- q  + p
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    --------------------------------------------------------------------]
                                   +---------+
                                   |   2    2
                               a q\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           p
--R        *
--R           log
--R                                                          +-------+
--R                                    2    2             2  | 2    2
--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R                + 
--R                      2    3              3    2              3    2
--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R             /
--R                q sin(a x) + p
--R       + 
--R             +-------+
--R             | 2    2
--R         a x\|q  - p
--R    /
--R           +-------+
--R           | 2    2
--R       a q\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2         +---------+
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
--R    2p atan(-----------------------------------------) + a x\|- q  + p
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    --------------------------------------------------------------------]
--R                                   +---------+
--R                                   |   2    2
--R                               a q\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 48
t1:=integrate(1/(p+q*sin(a*x)),x)
 

   (2)
   [
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
    /
         +-------+
         | 2    2
       a\|q  - p
     ,
                                          +---------+
                                          |   2    2
            (p sin(a x) + q cos(a x) + q)\|- q  + p
      2atan(-----------------------------------------)
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    - ------------------------------------------------]
                          +---------+
                          |   2    2
                        a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R    /
--R         +-------+
--R         | 2    2
--R       a\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
--R      2atan(-----------------------------------------)
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    - ------------------------------------------------]
--R                          +---------+
--R                          |   2    2
--R                        a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 49
bb1:=x/q-p/q*t1.1
 

   (3)
       -
            p
         *
            log
                                                           +-------+
                                     2    2             2  | 2    2
                   (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
                 + 
                         2    3                3    2              3    2
                   (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
              /
                 q sin(a x) + p
     + 
           +-------+
           | 2    2
       a x\|q  - p
  /
         +-------+
         | 2    2
     a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            p
--R         *
--R            log
--R                                                           +-------+
--R                                     2    2             2  | 2    2
--R                   (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R                 + 
--R                         2    3                3    2              3    2
--R                   (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R              /
--R                 q sin(a x) + p
--R     + 
--R           +-------+
--R           | 2    2
--R       a x\|q  - p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 50
bb2:=x/q-p/q*t1.2
 

                                              +---------+
                                              |   2    2         +---------+
                (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
        2p atan(-----------------------------------------) + a x\|- q  + p
                         2    2             2    2
                       (q  - p )cos(a x) + q  - p
   (4)  --------------------------------------------------------------------
                                       +---------+
                                       |   2    2
                                   a q\|- q  + p
                                                     Type: Expression Integer
--R
--R                                              +---------+
--R                                              |   2    2         +---------+
--R                (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
--R        2p atan(-----------------------------------------) + a x\|- q  + p
--R                         2    2             2    2
--R                       (q  - p )cos(a x) + q  - p
--R   (4)  --------------------------------------------------------------------
--R                                       +---------+
--R                                       |   2    2
--R                                   a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 51
cc1:=aa.1-bb1
 

   (5)
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
  /
         +-------+
         | 2    2
     a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 52
cc2:=aa.2-bb1
 

   (6)
           +---------+
           |   2    2
         p\|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                                                      +---------+
          +-------+                                   |   2    2
          | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       2p\|q  - p  atan(-----------------------------------------)
                                 2    2             2    2
                               (q  - p )cos(a x) + q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R           +---------+
--R           |   2    2
--R         p\|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                      +---------+
--R          +-------+                                   |   2    2
--R          | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       2p\|q  - p  atan(-----------------------------------------)
--R                                 2    2             2    2
--R                               (q  - p )cos(a x) + q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 53
cc3:=aa.1-bb2
 

   (7)
           +---------+
           |   2    2
         p\|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
                                                        +---------+
            +-------+                                   |   2    2
            | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       - 2p\|q  - p  atan(-----------------------------------------)
                                   2    2             2    2
                                 (q  - p )cos(a x) + q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R           +---------+
--R           |   2    2
--R         p\|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                        +---------+
--R            +-------+                                   |   2    2
--R            | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       - 2p\|q  - p  atan(-----------------------------------------)
--R                                   2    2             2    2
--R                                 (q  - p )cos(a x) + q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 54     14:469 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 55     14:470 Axiom cannot compute this integral
aa:=integrate(csc(a*x)^n,x)
 

           x
         ++           n
   (1)   |   csc(%P a) d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   csc(%H a) d%H
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to string.output (2009/2/17, 18:0:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 35
hello := "Hello, I'm AXIOM!"
 

   (1)  "Hello, I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (1)  "Hello, I'm AXIOM!"
--R                                                                 Type: String
--E 1

--S 2 of 35
said  := "Jane said, _"Look!_""
 

   (2)  "Jane said, "Look!""
                                                                 Type: String
--R 
--R
--R   (2)  "Jane said, "Look!""
--R                                                                 Type: String
--E 2

--S 3 of 35
saw   := "She saw exactly one underscore: __."
 

   (3)  "She saw exactly one underscore: _."
                                                                 Type: String
--R 
--R
--R   (3)  "She saw exactly one underscore: _."
--R                                                                 Type: String
--E 3

--S 4 of 35
gasp: String := new(32, char "x")
 

   (4)  "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
                                                                 Type: String
--R 
--R
--R   (4)  "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
--R                                                                 Type: String
--E 4

--S 5 of 35
#gasp
 

   (5)  32
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  32
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 35
hello.2
 

   (6)  e
                                                              Type: Character
--R 
--R
--R   (6)  e
--R                                                              Type: Character
--E 6

--S 7 of 35
hello 2
 

   (7)  e
                                                              Type: Character
--R 
--R
--R   (7)  e
--R                                                              Type: Character
--E 7

--S 8 of 35
hello(2)
 

   (8)  e
                                                              Type: Character
--R 
--R
--R   (8)  e
--R                                                              Type: Character
--E 8

--S 9 of 35
hullo := copy hello
 

   (9)  "Hello, I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (9)  "Hello, I'm AXIOM!"
--R                                                                 Type: String
--E 9

--S 10 of 35
hullo.2 := char "u"; [hello, hullo]
 

   (10)  ["Hello, I'm AXIOM!","Hullo, I'm AXIOM!"]
                                                            Type: List String
--R 
--R
--R   (10)  ["Hello, I'm AXIOM!","Hullo, I'm AXIOM!"]
--R                                                            Type: List String
--E 10

--S 11 of 35
saidsaw := concat ["alpha","---","omega"]
 

   (11)  "alpha---omega"
                                                                 Type: String
--R 
--R
--R   (11)  "alpha---omega"
--R                                                                 Type: String
--E 11

--S 12 of 35
concat("hello ","goodbye")
 

   (12)  "hello goodbye"
                                                                 Type: String
--R 
--R
--R   (12)  "hello goodbye"
--R                                                                 Type: String
--E 12

--S 13 of 35
"This " "is " "several " "strings " "concatenated."
 

   (13)  "This is several strings concatenated."
                                                                 Type: String
--R 
--R
--R   (13)  "This is several strings concatenated."
--R                                                                 Type: String
--E 13

--S 14 of 35
hello(1..5)
 

   (14)  "Hello"
                                                                 Type: String
--R 
--R
--R   (14)  "Hello"
--R                                                                 Type: String
--E 14

--S 15 of 35
hello(8..)
 

   (15)  "I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (15)  "I'm AXIOM!"
--R                                                                 Type: String
--E 15

--S 16 of 35
split(hello, char " ")
 

   (16)  ["Hello,","I'm","AXIOM!"]
                                                            Type: List String
--R 
--R
--R   (16)  ["Hello,","I'm","AXIOM!"]
--R                                                            Type: List String
--E 16

--S 17 of 35
other := complement alphanumeric();
 

                                                         Type: CharacterClass
--R 
--R
--R                                                         Type: CharacterClass
--E 17

--S 18 of 35
split(saidsaw, other)
 

   (18)  ["alpha","omega"]
                                                            Type: List String
--R 
--R
--R   (18)  ["alpha","omega"]
--R                                                            Type: List String
--E 18

--S 19 of 35
trim     ("## ++ relax ++ ##", char "#")
 

   (19)  " ++ relax ++ "
                                                                 Type: String
--R 
--R
--R   (19)  " ++ relax ++ "
--R                                                                 Type: String
--E 19

--S 20 of 35
trim     ("## ++ relax ++ ##", other)
 

   (20)  "relax"
                                                                 Type: String
--R 
--R
--R   (20)  "relax"
--R                                                                 Type: String
--E 20

--S 21 of 35
leftTrim ("## ++ relax ++ ##", other)
 

   (21)  "relax ++ ##"
                                                                 Type: String
--R 
--R
--R   (21)  "relax ++ ##"
--R                                                                 Type: String
--E 21

--S 22 of 35
rightTrim("## ++ relax ++ ##", other)
 

   (22)  "## ++ relax"
                                                                 Type: String
--R 
--R
--R   (22)  "## ++ relax"
--R                                                                 Type: String
--E 22

--S 23 of 35
upperCase hello
 

   (23)  "HELLO, I'M AXIOM!"
                                                                 Type: String
--R 
--R
--R   (23)  "HELLO, I'M AXIOM!"
--R                                                                 Type: String
--E 23

--S 24 of 35
lowerCase hello
 

   (24)  "hello, i'm axiom!"
                                                                 Type: String
--R 
--R
--R   (24)  "hello, i'm axiom!"
--R                                                                 Type: String
--E 24

--S 25 of 35
prefix?("He", "Hello")
 

   (25)  true
                                                                Type: Boolean
--R 
--R
--R   (25)  true
--R                                                                Type: Boolean
--E 25

--S 26 of 35
prefix?("Her", "Hello")
 

   (26)  false
                                                                Type: Boolean
--R 
--R
--R   (26)  false
--R                                                                Type: Boolean
--E 26

--S 27 of 35
suffix?("", "Hello")
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 35
suffix?("LO", "Hello")
 

   (28)  false
                                                                Type: Boolean
--R 
--R
--R   (28)  false
--R                                                                Type: Boolean
--E 28

--S 29 of 35
substring?("ll", "Hello", 3)
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 35
substring?("ll", "Hello", 4)
 

   (30)  false
                                                                Type: Boolean
--R 
--R
--R   (30)  false
--R                                                                Type: Boolean
--E 30

--S 31 of 35
n := position("nd", "underground",   1)
 

   (31)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (31)  2
--R                                                        Type: PositiveInteger
--E 31

--S 32 of 35
n := position("nd", "underground", n+1)
 

   (32)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (32)  10
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 35
n := position("nd", "underground", n+1)
 

   (33)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (33)  0
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 35
position(char "d", "underground", 1)
 

   (34)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (34)  3
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 35
position(hexDigit(), "underground", 1)
 

   (35)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  3
--R                                                        Type: PositiveInteger
--E 35
)spool 
 
Starts dribbling to schaum15.output (2009/2/17, 17:58:36).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(x^4+a^4),x)
 

   (1)
        +------+          +------+2            +------+
        |   1          8  |   1        4  +-+  |   1      2
        |------ log(16a   |------  + 4a x\|2   |------ + x )
       4|    12          4|    12             4|    12
       \|256a            \|256a               \|256a
     + 
          +------+          +------+2            +------+
          |   1          8  |   1        4  +-+  |   1      2
       -  |------ log(16a   |------  - 4a x\|2   |------ + x )
         4|    12          4|    12             4|    12
         \|256a            \|256a               \|256a
     + 
                              +------+                               +------+
                           4  |   1                               4  |   1
                         4a   |------                           4a   |------
        +------+             4|    12          +------+             4|    12
        |   1                \|256a            |   1                \|256a
     2  |------ atan(-------------------- - 2  |------ atan(--------------------)
       4|    12           +------+            4|    12           +------+
       \|256a          4  |   1       +-+     \|256a          4  |   1       +-+
                     4a   |------ - x\|2                    4a   |------ + x\|2
                         4|    12                               4|    12
                         \|256a                                 \|256a
  /
      +-+
     \|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R        +------+          +------+2            +------+
--R        |   1          8  |   1        4  +-+  |   1      2
--R        |------ log(16a   |------  + 4a x\|2   |------ + x )
--R       4|    12          4|    12             4|    12
--R       \|256a            \|256a               \|256a
--R     + 
--R          +------+          +------+2            +------+
--R          |   1          8  |   1        4  +-+  |   1      2
--R       -  |------ log(16a   |------  - 4a x\|2   |------ + x )
--R         4|    12          4|    12             4|    12
--R         \|256a            \|256a               \|256a
--R     + 
--R                              +------+                               +------+
--R                           4  |   1                               4  |   1
--R                         4a   |------                           4a   |------
--R        +------+             4|    12          +------+             4|    12
--R        |   1                \|256a            |   1                \|256a
--R     2  |------ atan(-------------------- - 2  |------ atan(--------------------)
--R       4|    12           +------+            4|    12           +------+
--R       \|256a          4  |   1       +-+     \|256a          4  |   1       +-+
--R                     4a   |------ - x\|2                    4a   |------ + x\|2
--R                         4|    12                               4|    12
--R                         \|256a                                 \|256a
--R  /
--R      +-+
--R     \|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/(4*a^3*sqrt(2))*log((x^2+a*x*sqrt(2)+a^2)/(x^2-a*x*sqrt(2)+a^2))-1/(2*a^3*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
 

                      +-+    2    2                  +-+
         +-+    - a x\|2  - x  - a       +-+     a x\|2
        \|2 log(-------------------) - 2\|2 atan(-------)
                     +-+    2    2                2    2
                 a x\|2  - x  - a                x  - a
   (2)  -------------------------------------------------
                                 3
                               8a
                                                     Type: Expression Integer
--R
--R                      +-+    2    2                  +-+
--R         +-+    - a x\|2  - x  - a       +-+     a x\|2
--R        \|2 log(-------------------) - 2\|2 atan(-------)
--R                     +-+    2    2                2    2
--R                 a x\|2  - x  - a                x  - a
--R   (2)  -------------------------------------------------
--R                                 3
--R                               8a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

   (3)
            +------+          +------+2            +------+
         3  |   1          8  |   1        4  +-+  |   1      2
       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
           4|    12          4|    12             4|    12
           \|256a            \|256a               \|256a
     + 
              +------+          +------+2            +------+
           3  |   1          8  |   1        4  +-+  |   1      2
       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
             4|    12          4|    12             4|    12
             \|256a            \|256a               \|256a
     + 
                                  +------+
                               4  |   1
                             4a   |------
            +------+             4|    12
         3  |   1                \|256a
       8a   |------ atan(--------------------)
           4|    12           +------+
           \|256a          4  |   1       +-+
                         4a   |------ - x\|2
                             4|    12
                             \|256a
     + 
                                    +------+
                                 4  |   1
                               4a   |------
              +------+             4|    12                 +-+    2    2
           3  |   1                \|256a             - a x\|2  - x  - a
       - 8a   |------ atan(-------------------- - log(-------------------)
             4|    12           +------+                   +-+    2    2
             \|256a          4  |   1       +-+        a x\|2  - x  - a
                           4a   |------ + x\|2
                               4|    12
                               \|256a
     + 
                 +-+
             a x\|2
       2atan(-------)
              2    2
             x  - a
  /
       3 +-+
     4a \|2
                                                     Type: Expression Integer
--R
--R   (3)
--R            +------+          +------+2            +------+
--R         3  |   1          8  |   1        4  +-+  |   1      2
--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
--R           4|    12          4|    12             4|    12
--R           \|256a            \|256a               \|256a
--R     + 
--R              +------+          +------+2            +------+
--R           3  |   1          8  |   1        4  +-+  |   1      2
--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
--R             4|    12          4|    12             4|    12
--R             \|256a            \|256a               \|256a
--R     + 
--R                                  +------+
--R                               4  |   1
--R                             4a   |------
--R            +------+             4|    12
--R         3  |   1                \|256a
--R       8a   |------ atan(--------------------)
--R           4|    12           +------+
--R           \|256a          4  |   1       +-+
--R                         4a   |------ - x\|2
--R                             4|    12
--R                             \|256a
--R     + 
--R                                    +------+
--R                                 4  |   1
--R                               4a   |------
--R              +------+             4|    12                 +-+    2    2
--R           3  |   1                \|256a             - a x\|2  - x  - a
--R       - 8a   |------ atan(-------------------- - log(-------------------)
--R             4|    12           +------+                   +-+    2    2
--R             \|256a          4  |   1       +-+        a x\|2  - x  - a
--R                           4a   |------ + x\|2
--R                               4|    12
--R                               \|256a
--R     + 
--R                 +-+
--R             a x\|2
--R       2atan(-------)
--R              2    2
--R             x  - a
--R  /
--R       3 +-+
--R     4a \|2
--R                                                     Type: Expression Integer
--E

--S 4
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 5
dd:=atanrule cc
 

   (5)
            +------+          +------+2            +------+
         3  |   1          8  |   1        4  +-+  |   1      2
       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
           4|    12          4|    12             4|    12
           \|256a            \|256a               \|256a
     + 
              +------+          +------+2            +------+
           3  |   1          8  |   1        4  +-+  |   1      2
       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
             4|    12          4|    12             4|    12
             \|256a            \|256a               \|256a
     + 
                                          +------+
                                       4  |   1          +-+
                           (- 4 + 4%i)a   |------ + %i x\|2
               +------+                  4|    12
            3  |   1                     \|256a
       4%i a   |------ log(---------------------------------)
              4|    12                   +------+
              \|256a                  4  |   1          +-+
                            (4 + 4%i)a   |------ + %i x\|2
                                        4|    12
                                        \|256a
     + 
                                            +------+
                                         4  |   1          +-+
                             (- 4 + 4%i)a   |------ - %i x\|2
                 +------+                  4|    12
              3  |   1                     \|256a
       - 4%i a   |------ log(---------------------------------)
                4|    12                   +------+
                \|256a                  4  |   1          +-+
                              (4 + 4%i)a   |------ - %i x\|2
                                          4|    12
                                          \|256a
     + 
                      +-+       2       2              +-+    2    2
                - a x\|2  + %i x  - %i a         - a x\|2  - x  - a
       - %i log(-------------------------) - log(-------------------)
                     +-+       2       2              +-+    2    2
                 a x\|2  + %i x  - %i a           a x\|2  - x  - a
  /
       3 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (5)
--R            +------+          +------+2            +------+
--R         3  |   1          8  |   1        4  +-+  |   1      2
--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
--R           4|    12          4|    12             4|    12
--R           \|256a            \|256a               \|256a
--R     + 
--R              +------+          +------+2            +------+
--R           3  |   1          8  |   1        4  +-+  |   1      2
--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
--R             4|    12          4|    12             4|    12
--R             \|256a            \|256a               \|256a
--R     + 
--R                                          +------+
--R                                       4  |   1          +-+
--R                           (- 4 + 4%i)a   |------ + %i x\|2
--R               +------+                  4|    12
--R            3  |   1                     \|256a
--R       4%i a   |------ log(---------------------------------)
--R              4|    12                   +------+
--R              \|256a                  4  |   1          +-+
--R                            (4 + 4%i)a   |------ + %i x\|2
--R                                        4|    12
--R                                        \|256a
--R     + 
--R                                            +------+
--R                                         4  |   1          +-+
--R                             (- 4 + 4%i)a   |------ - %i x\|2
--R                 +------+                  4|    12
--R              3  |   1                     \|256a
--R       - 4%i a   |------ log(---------------------------------)
--R                4|    12                   +------+
--R                \|256a                  4  |   1          +-+
--R                              (4 + 4%i)a   |------ - %i x\|2
--R                                          4|    12
--R                                          \|256a
--R     + 
--R                      +-+       2       2              +-+    2    2
--R                - a x\|2  + %i x  - %i a         - a x\|2  - x  - a
--R       - %i log(-------------------------) - log(-------------------)
--R                     +-+       2       2              +-+    2    2
--R                 a x\|2  + %i x  - %i a           a x\|2  - x  - a
--R  /
--R       3 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 6
ee:=rootSimp dd
 

   (6)
                                         +-+
               +-+    2    2           x\|2  + (1 + %i)a
       log(a x\|2  + x  + a ) + %i log(-----------------)
                                         +-+
                                       x\|2  + (1 - %i)a
     + 
                  +-+                               +-+       2       2
                x\|2  + (- 1 - %i)a           - a x\|2  + %i x  - %i a
       - %i log(-------------------) - %i log(-------------------------)
                  +-+                              +-+       2       2
                x\|2  + (- 1 + %i)a            a x\|2  + %i x  - %i a
     + 
                   +-+    2    2
             - a x\|2  - x  - a               +-+    2    2
       - log(-------------------) - log(- a x\|2  + x  + a )
                  +-+    2    2
              a x\|2  - x  - a
  /
       3 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (6)
--R                                         +-+
--R               +-+    2    2           x\|2  + (1 + %i)a
--R       log(a x\|2  + x  + a ) + %i log(-----------------)
--R                                         +-+
--R                                       x\|2  + (1 - %i)a
--R     + 
--R                  +-+                               +-+       2       2
--R                x\|2  + (- 1 - %i)a           - a x\|2  + %i x  - %i a
--R       - %i log(-------------------) - %i log(-------------------------)
--R                  +-+                              +-+       2       2
--R                x\|2  + (- 1 + %i)a            a x\|2  + %i x  - %i a
--R     + 
--R                   +-+    2    2
--R             - a x\|2  - x  - a               +-+    2    2
--R       - log(-------------------) - log(- a x\|2  + x  + a )
--R                  +-+    2    2
--R              a x\|2  - x  - a
--R  /
--R       3 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 7
ff:=expandLog ee
 

   (7)
                  +-+       2       2               +-+       2       2
       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
     + 
                +-+                         +-+
       %i log(x\|2  + (1 + %i)a) - %i log(x\|2  + (1 - %i)a)
     + 
                +-+                           +-+
       %i log(x\|2  + (- 1 + %i)a) - %i log(x\|2  + (- 1 - %i)a)
     + 
       (- 2 - %i)log(- 1)
  /
       3 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                  +-+       2       2               +-+       2       2
--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
--R     + 
--R                +-+                         +-+
--R       %i log(x\|2  + (1 + %i)a) - %i log(x\|2  + (1 - %i)a)
--R     + 
--R                +-+                           +-+
--R       %i log(x\|2  + (- 1 + %i)a) - %i log(x\|2  + (- 1 - %i)a)
--R     + 
--R       (- 2 - %i)log(- 1)
--R  /
--R       3 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 8
gg:=complexNormalize ff
 

               %i             %i
        %i log(--) - %i log(- --) + (- 2 - %i)log(- 1)
                2              2
   (8)  ----------------------------------------------
                              3 +-+
                            4a \|2
                                             Type: Expression Complex Integer
--R
--R               %i             %i
--R        %i log(--) - %i log(- --) + (- 2 - %i)log(- 1)
--R                2              2
--R   (8)  ----------------------------------------------
--R                              3 +-+
--R                            4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 9      14:311 Schaums and Axiom differ by a constant
hh:=expandLog gg
 

        %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1)
   (9)  ----------------------------------------------
                              3 +-+
                            4a \|2
                                             Type: Expression Complex Integer
--R
--R        %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1)
--R   (9)  ----------------------------------------------
--R                              3 +-+
--R                            4a \|2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(x/(x^4+a^4),x)
 

              2
             x
        atan(--)
              2
             a
   (1)  --------
             2
           2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R             x
--R        atan(--)
--R              2
--R             a
--R   (1)  --------
--R             2
--R           2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=1/(2*a^2)*atan(x^2/a^2)
 

              2
             x
        atan(--)
              2
             a
   (2)  --------
             2
           2a
                                                     Type: Expression Integer
--R
--R              2
--R             x
--R        atan(--)
--R              2
--R             a
--R   (2)  --------
--R             2
--R           2a
--R                                                     Type: Expression Integer
--E

--S 12     14:312 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(x^2/(x^4+a^4),x)
 

   (1)
          +-----+               +-----+3        +-----+2
          |  1          4  +-+  |  1         4  |  1       2
       -  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
         4|    4               4|    4         4|    4
         \|256a                \|256a          \|256a
     + 
        +-----+                 +-----+3        +-----+2
        |  1            4  +-+  |  1         4  |  1       2
        |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
       4|    4                 4|    4         4|    4
       \|256a                  \|256a          \|256a
     + 
                              +-----+3                               +-----+3
                           4  |  1                                4  |  1
                        64a   |-----                           64a   |-----
        +-----+              4|    4           +-----+              4|    4
        |  1                 \|256a            |  1                 \|256a
     2  |----- atan(--------------------- - 2  |----- atan(---------------------)
       4|    4            +-----+3            4|    4            +-----+3
       \|256a          4  |  1        +-+     \|256a          4  |  1        +-+
                    64a   |-----  - x\|2                   64a   |-----  + x\|2
                         4|    4                                4|    4
                         \|256a                                 \|256a
  /
      +-+
     \|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R          +-----+               +-----+3        +-----+2
--R          |  1          4  +-+  |  1         4  |  1       2
--R       -  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R         4|    4               4|    4         4|    4
--R         \|256a                \|256a          \|256a
--R     + 
--R        +-----+                 +-----+3        +-----+2
--R        |  1            4  +-+  |  1         4  |  1       2
--R        |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
--R       4|    4                 4|    4         4|    4
--R       \|256a                  \|256a          \|256a
--R     + 
--R                              +-----+3                               +-----+3
--R                           4  |  1                                4  |  1
--R                        64a   |-----                           64a   |-----
--R        +-----+              4|    4           +-----+              4|    4
--R        |  1                 \|256a            |  1                 \|256a
--R     2  |----- atan(--------------------- - 2  |----- atan(---------------------)
--R       4|    4            +-----+3            4|    4            +-----+3
--R       \|256a          4  |  1        +-+     \|256a          4  |  1        +-+
--R                    64a   |-----  - x\|2                   64a   |-----  + x\|2
--R                         4|    4                                4|    4
--R                         \|256a                                 \|256a
--R  /
--R      +-+
--R     \|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=1/(4*a*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))-1/(2*a*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
 

                      +-+    2    2                  +-+
         +-+    - a x\|2  + x  + a       +-+     a x\|2
        \|2 log(-------------------) - 2\|2 atan(-------)
                     +-+    2    2                2    2
                 a x\|2  + x  + a                x  - a
   (2)  -------------------------------------------------
                                8a
                                                     Type: Expression Integer
--R
--R                      +-+    2    2                  +-+
--R         +-+    - a x\|2  + x  + a       +-+     a x\|2
--R        \|2 log(-------------------) - 2\|2 atan(-------)
--R                     +-+    2    2                2    2
--R                 a x\|2  + x  + a                x  - a
--R   (2)  -------------------------------------------------
--R                                8a
--R                                                     Type: Expression Integer
--E

--S 15
cc:=aa-bb
 

   (3)
             +-----+               +-----+3        +-----+2
             |  1          4  +-+  |  1         4  |  1       2
       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
            4|    4               4|    4         4|    4
            \|256a                \|256a          \|256a
     + 
           +-----+                 +-----+3        +-----+2
           |  1            4  +-+  |  1         4  |  1       2
       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
          4|    4                 4|    4         4|    4
          \|256a                  \|256a          \|256a
     + 
                                 +-----+3
                              4  |  1
                           64a   |-----
           +-----+              4|    4
           |  1                 \|256a
       8a  |----- atan(---------------------)
          4|    4            +-----+3
          \|256a          4  |  1        +-+
                       64a   |-----  - x\|2
                            4|    4
                            \|256a
     + 
                                   +-----+3
                                4  |  1
                             64a   |-----
             +-----+              4|    4                  +-+    2    2
             |  1                 \|256a             - a x\|2  + x  + a
       - 8a  |----- atan(--------------------- - log(-------------------)
            4|    4            +-----+3                   +-+    2    2
            \|256a          4  |  1        +-+        a x\|2  + x  + a
                         64a   |-----  + x\|2
                              4|    4
                              \|256a
     + 
                 +-+
             a x\|2
       2atan(-------)
              2    2
             x  - a
  /
        +-+
     4a\|2
                                                     Type: Expression Integer
--R
--R   (3)
--R             +-----+               +-----+3        +-----+2
--R             |  1          4  +-+  |  1         4  |  1       2
--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R            4|    4               4|    4         4|    4
--R            \|256a                \|256a          \|256a
--R     + 
--R           +-----+                 +-----+3        +-----+2
--R           |  1            4  +-+  |  1         4  |  1       2
--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
--R          4|    4                 4|    4         4|    4
--R          \|256a                  \|256a          \|256a
--R     + 
--R                                 +-----+3
--R                              4  |  1
--R                           64a   |-----
--R           +-----+              4|    4
--R           |  1                 \|256a
--R       8a  |----- atan(---------------------)
--R          4|    4            +-----+3
--R          \|256a          4  |  1        +-+
--R                       64a   |-----  - x\|2
--R                            4|    4
--R                            \|256a
--R     + 
--R                                   +-----+3
--R                                4  |  1
--R                             64a   |-----
--R             +-----+              4|    4                  +-+    2    2
--R             |  1                 \|256a             - a x\|2  + x  + a
--R       - 8a  |----- atan(--------------------- - log(-------------------)
--R            4|    4            +-----+3                   +-+    2    2
--R            \|256a          4  |  1        +-+        a x\|2  + x  + a
--R                         64a   |-----  + x\|2
--R                              4|    4
--R                              \|256a
--R     + 
--R                 +-+
--R             a x\|2
--R       2atan(-------)
--R              2    2
--R             x  - a
--R  /
--R        +-+
--R     4a\|2
--R                                                     Type: Expression Integer
--E

--S 16
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 17
dd:=atanrule cc
 

   (5)
             +-----+               +-----+3        +-----+2
             |  1          4  +-+  |  1         4  |  1       2
       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
            4|    4               4|    4         4|    4
            \|256a                \|256a          \|256a
     + 
                                          +-----+3
                                       4  |  1           +-+
                         (- 64 + 64%i)a   |-----  + %i x\|2
              +-----+                    4|    4
              |  1                       \|256a
       4%i a  |----- log(-----------------------------------)
             4|    4                     +-----+3
             \|256a                   4  |  1           +-+
                          (64 + 64%i)a   |-----  + %i x\|2
                                        4|    4
                                        \|256a
     + 
                                            +-----+3
                                         4  |  1           +-+
                           (- 64 + 64%i)a   |-----  - %i x\|2
                +-----+                    4|    4
                |  1                       \|256a
       - 4%i a  |----- log(-----------------------------------)
               4|    4                     +-----+3
               \|256a                   4  |  1           +-+
                            (64 + 64%i)a   |-----  - %i x\|2
                                          4|    4
                                          \|256a
     + 
           +-----+                 +-----+3        +-----+2
           |  1            4  +-+  |  1         4  |  1       2
       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
          4|    4                 4|    4         4|    4
          \|256a                  \|256a          \|256a
     + 
                   +-+    2    2                 +-+       2       2
             - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
       - log(-------------------) - %i log(-------------------------)
                  +-+    2    2                 +-+       2       2
              a x\|2  + x  + a              a x\|2  + %i x  - %i a
  /
        +-+
     4a\|2
                                             Type: Expression Complex Integer
--R
--R   (5)
--R             +-----+               +-----+3        +-----+2
--R             |  1          4  +-+  |  1         4  |  1       2
--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R            4|    4               4|    4         4|    4
--R            \|256a                \|256a          \|256a
--R     + 
--R                                          +-----+3
--R                                       4  |  1           +-+
--R                         (- 64 + 64%i)a   |-----  + %i x\|2
--R              +-----+                    4|    4
--R              |  1                       \|256a
--R       4%i a  |----- log(-----------------------------------)
--R             4|    4                     +-----+3
--R             \|256a                   4  |  1           +-+
--R                          (64 + 64%i)a   |-----  + %i x\|2
--R                                        4|    4
--R                                        \|256a
--R     + 
--R                                            +-----+3
--R                                         4  |  1           +-+
--R                           (- 64 + 64%i)a   |-----  - %i x\|2
--R                +-----+                    4|    4
--R                |  1                       \|256a
--R       - 4%i a  |----- log(-----------------------------------)
--R               4|    4                     +-----+3
--R               \|256a                   4  |  1           +-+
--R                            (64 + 64%i)a   |-----  - %i x\|2
--R                                          4|    4
--R                                          \|256a
--R     + 
--R           +-----+                 +-----+3        +-----+2
--R           |  1            4  +-+  |  1         4  |  1       2
--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
--R          4|    4                 4|    4         4|    4
--R          \|256a                  \|256a          \|256a
--R     + 
--R                   +-+    2    2                 +-+       2       2
--R             - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
--R       - log(-------------------) - %i log(-------------------------)
--R                  +-+    2    2                 +-+       2       2
--R              a x\|2  + x  + a              a x\|2  + %i x  - %i a
--R  /
--R        +-+
--R     4a\|2
--R                                             Type: Expression Complex Integer
--E

--S 18
ee:=expandLog dd
 

   (6)
             +-----+               +-----+3        +-----+2
             |  1          4  +-+  |  1         4  |  1       2
       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
            4|    4               4|    4         4|    4
            \|256a                \|256a          \|256a
     + 
           +-----+               +-----+3        +-----+2
           |  1          4  +-+  |  1         4  |  1       2
       4a  |----- log(64a x\|2   |-----  - 16a   |-----  - x )
          4|    4               4|    4         4|    4
          \|256a                \|256a          \|256a
     + 
              +-----+                   +-----+3
              |  1                   4  |  1        +-+
       4%i a  |----- log((64 + 64%i)a   |-----  + x\|2 )
             4|    4                   4|    4
             \|256a                    \|256a
     + 
                +-----+                   +-----+3
                |  1                   4  |  1           +-+
       - 4%i a  |----- log((64 + 64%i)a   |-----  + %i x\|2 )
               4|    4                   4|    4
               \|256a                    \|256a
     + 
              +-----+                   +-----+3
              |  1                   4  |  1           +-+
       4%i a  |----- log((64 + 64%i)a   |-----  - %i x\|2 )
             4|    4                   4|    4
             \|256a                    \|256a
     + 
                +-----+                   +-----+3                       +-----+
                |  1                   4  |  1        +-+                |  1
       - 4%i a  |----- log((64 + 64%i)a   |-----  - x\|2  + 4a log(- 1)  |-----
               4|    4                   4|    4                        4|    4
               \|256a                    \|256a                         \|256a
     + 
               +-+    2    2               +-+       2       2
       log(a x\|2  + x  + a ) + %i log(a x\|2  + %i x  - %i a )
     + 
                    +-+       2       2            +-+    2    2
       - %i log(a x\|2  - %i x  + %i a ) - log(a x\|2  - x  - a )
     + 
       (- 1 - %i)log(- 1)
  /
        +-+
     4a\|2
                                             Type: Expression Complex Integer
--R
--R   (6)
--R             +-----+               +-----+3        +-----+2
--R             |  1          4  +-+  |  1         4  |  1       2
--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R            4|    4               4|    4         4|    4
--R            \|256a                \|256a          \|256a
--R     + 
--R           +-----+               +-----+3        +-----+2
--R           |  1          4  +-+  |  1         4  |  1       2
--R       4a  |----- log(64a x\|2   |-----  - 16a   |-----  - x )
--R          4|    4               4|    4         4|    4
--R          \|256a                \|256a          \|256a
--R     + 
--R              +-----+                   +-----+3
--R              |  1                   4  |  1        +-+
--R       4%i a  |----- log((64 + 64%i)a   |-----  + x\|2 )
--R             4|    4                   4|    4
--R             \|256a                    \|256a
--R     + 
--R                +-----+                   +-----+3
--R                |  1                   4  |  1           +-+
--R       - 4%i a  |----- log((64 + 64%i)a   |-----  + %i x\|2 )
--R               4|    4                   4|    4
--R               \|256a                    \|256a
--R     + 
--R              +-----+                   +-----+3
--R              |  1                   4  |  1           +-+
--R       4%i a  |----- log((64 + 64%i)a   |-----  - %i x\|2 )
--R             4|    4                   4|    4
--R             \|256a                    \|256a
--R     + 
--R                +-----+                   +-----+3                       +-----+
--R                |  1                   4  |  1        +-+                |  1
--R       - 4%i a  |----- log((64 + 64%i)a   |-----  - x\|2  + 4a log(- 1)  |-----
--R               4|    4                   4|    4                        4|    4
--R               \|256a                    \|256a                         \|256a
--R     + 
--R               +-+    2    2               +-+       2       2
--R       log(a x\|2  + x  + a ) + %i log(a x\|2  + %i x  - %i a )
--R     + 
--R                    +-+       2       2            +-+    2    2
--R       - %i log(a x\|2  - %i x  + %i a ) - log(a x\|2  - x  - a )
--R     + 
--R       (- 1 - %i)log(- 1)
--R  /
--R        +-+
--R     4a\|2
--R                                             Type: Expression Complex Integer
--E

--S 19
ff:=rootSimp ee
 

   (7)
                  +-+       2       2               +-+       2       2
       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
     + 
                +-+                            +-+
       %i log(x\|2  + (1 + %i)a) - %i log(%i x\|2  + (1 + %i)a)
     + 
                   +-+                           +-+
     %i log(- %i x\|2  + (1 + %i)a) - %i log(- x\|2  + (1 + %i)a) - %i log(- 1)
  /
        +-+
     4a\|2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                  +-+       2       2               +-+       2       2
--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
--R     + 
--R                +-+                            +-+
--R       %i log(x\|2  + (1 + %i)a) - %i log(%i x\|2  + (1 + %i)a)
--R     + 
--R                   +-+                           +-+
--R     %i log(- %i x\|2  + (1 + %i)a) - %i log(- x\|2  + (1 + %i)a) - %i log(- 1)
--R  /
--R        +-+
--R     4a\|2
--R                                             Type: Expression Complex Integer
--E

--S 20     14:313 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

        %i log(2) - %i log(- 1) - %i log(- 2)
   (8)  -------------------------------------
                           +-+
                        4a\|2
                                             Type: Expression Complex Integer
--R
--R        %i log(2) - %i log(- 1) - %i log(- 2)
--R   (8)  -------------------------------------
--R                           +-+
--R                        4a\|2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 21
aa:=integrate(x^3/(x^4+a^4),x)
 

             4    4
        log(x  + a )
   (1)  ------------
              4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4    4
--R        log(x  + a )
--R   (1)  ------------
--R              4
--R                                          Type: Union(Expression Integer,...)
--E

--S 22
bb:=1/4*log(x^4+a^4)
 

             4    4
        log(x  + a )
   (2)  ------------
              4
                                                     Type: Expression Integer
--R
--R             4    4
--R        log(x  + a )
--R   (2)  ------------
--R              4
--R                                                     Type: Expression Integer
--E 

--S 23     14:314 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 24
aa:=integrate(1/(x*(x^4+a^4)),x)
 

               4    4
        - log(x  + a ) + 4log(x)
   (1)  ------------------------
                     4
                   4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               4    4
--R        - log(x  + a ) + 4log(x)
--R   (1)  ------------------------
--R                     4
--R                   4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25
bb:=1/(4*a^4)*log(x^4/(x^4+a^4))
 

                4
               x
        log(-------)
             4    4
            x  + a
   (2)  ------------
               4
             4a
                                                     Type: Expression Integer
--R
--R                4
--R               x
--R        log(-------)
--R             4    4
--R            x  + a
--R   (2)  ------------
--R               4
--R             4a
--R                                                     Type: Expression Integer
--E

--S 26
cc:=aa-bb
 

                                           4
               4    4                     x
        - log(x  + a ) + 4log(x) - log(-------)
                                        4    4
                                       x  + a
   (3)  ---------------------------------------
                            4
                          4a
                                                     Type: Expression Integer
--R
--R                                           4
--R               4    4                     x
--R        - log(x  + a ) + 4log(x) - log(-------)
--R                                        4    4
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            4
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 27     14:315 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28
aa:=integrate(1/(x^2*(x^4+a^4)),x)
 

   (1)
            +------+                +------+3         +------+2
        4   |   1          16  +-+  |   1         12  |   1       2
       a x  |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
              +------+                  +------+3         +------+2
          4   |   1            16  +-+  |   1         12  |   1       2
       - a x  |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
             4|    20                  4|    20          4|    20
             \|256a                    \|256a            \|256a
     + 
                                       +------+3
                                   16  |   1
                                64a    |------
               +------+               4|    20
           4   |   1                  \|256a
       - 2a x  |------ atan(-----------------------)
              4|    20             +------+3
              \|256a           16  |   1        +-+
                            64a    |------  - x\|2
                                  4|    20
                                  \|256a
     + 
                                     +------+3
                                 16  |   1
                              64a    |------
             +------+               4|    20
         4   |   1                  \|256a           +-+
       2a x  |------ atan(----------------------- - \|2
            4|    20             +------+3
            \|256a           16  |   1        +-+
                          64a    |------  + x\|2
                                4|    20
                                \|256a
  /
      4  +-+
     a x\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +------+                +------+3         +------+2
--R        4   |   1          16  +-+  |   1         12  |   1       2
--R       a x  |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R              +------+                  +------+3         +------+2
--R          4   |   1            16  +-+  |   1         12  |   1       2
--R       - a x  |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
--R             4|    20                  4|    20          4|    20
--R             \|256a                    \|256a            \|256a
--R     + 
--R                                       +------+3
--R                                   16  |   1
--R                                64a    |------
--R               +------+               4|    20
--R           4   |   1                  \|256a
--R       - 2a x  |------ atan(-----------------------)
--R              4|    20             +------+3
--R              \|256a           16  |   1        +-+
--R                            64a    |------  - x\|2
--R                                  4|    20
--R                                  \|256a
--R     + 
--R                                     +------+3
--R                                 16  |   1
--R                              64a    |------
--R             +------+               4|    20
--R         4   |   1                  \|256a           +-+
--R       2a x  |------ atan(----------------------- - \|2
--R            4|    20             +------+3
--R            \|256a           16  |   1        +-+
--R                          64a    |------  + x\|2
--R                                4|    20
--R                                \|256a
--R  /
--R      4  +-+
--R     a x\|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29
bb:=-1/(a^4*x)-1/(4*a^5*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))+1/(2*a^5*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
 

                         +-+    2    2                   +-+
            +-+    - a x\|2  + x  + a        +-+     a x\|2
        - x\|2 log(-------------------) + 2x\|2 atan(-------) - 8a
                        +-+    2    2                 2    2
                    a x\|2  + x  + a                 x  - a
   (2)  ----------------------------------------------------------
                                     5
                                   8a x
                                                     Type: Expression Integer
--R
--R                         +-+    2    2                   +-+
--R            +-+    - a x\|2  + x  + a        +-+     a x\|2
--R        - x\|2 log(-------------------) + 2x\|2 atan(-------) - 8a
--R                        +-+    2    2                 2    2
--R                    a x\|2  + x  + a                 x  - a
--R   (2)  ----------------------------------------------------------
--R                                     5
--R                                   8a x
--R                                                     Type: Expression Integer
--E

--S 30
cc:=aa-bb
 

   (3)
            +------+                +------+3         +------+2
         5  |   1          16  +-+  |   1         12  |   1       2
       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
              +------+                  +------+3         +------+2
           5  |   1            16  +-+  |   1         12  |   1       2
       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
             4|    20                  4|    20          4|    20
             \|256a                    \|256a            \|256a
     + 
                                      +------+3
                                  16  |   1
                               64a    |------
              +------+               4|    20
           5  |   1                  \|256a
       - 8a   |------ atan(-----------------------)
             4|    20             +------+3
             \|256a           16  |   1        +-+
                           64a    |------  - x\|2
                                 4|    20
                                 \|256a
     + 
                                    +------+3
                                16  |   1
                             64a    |------
            +------+               4|    20                  +-+    2    2
         5  |   1                  \|256a              - a x\|2  + x  + a
       8a   |------ atan(----------------------- + log(-------------------)
           4|    20             +------+3                   +-+    2    2
           \|256a           16  |   1        +-+        a x\|2  + x  + a
                         64a    |------  + x\|2
                               4|    20
                               \|256a
     + 
                   +-+
               a x\|2
       - 2atan(-------)
                2    2
               x  - a
  /
       5 +-+
     4a \|2
                                                     Type: Expression Integer
--R
--R   (3)
--R            +------+                +------+3         +------+2
--R         5  |   1          16  +-+  |   1         12  |   1       2
--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R              +------+                  +------+3         +------+2
--R           5  |   1            16  +-+  |   1         12  |   1       2
--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
--R             4|    20                  4|    20          4|    20
--R             \|256a                    \|256a            \|256a
--R     + 
--R                                      +------+3
--R                                  16  |   1
--R                               64a    |------
--R              +------+               4|    20
--R           5  |   1                  \|256a
--R       - 8a   |------ atan(-----------------------)
--R             4|    20             +------+3
--R             \|256a           16  |   1        +-+
--R                           64a    |------  - x\|2
--R                                 4|    20
--R                                 \|256a
--R     + 
--R                                    +------+3
--R                                16  |   1
--R                             64a    |------
--R            +------+               4|    20                  +-+    2    2
--R         5  |   1                  \|256a              - a x\|2  + x  + a
--R       8a   |------ atan(----------------------- + log(-------------------)
--R           4|    20             +------+3                   +-+    2    2
--R           \|256a           16  |   1        +-+        a x\|2  + x  + a
--R                         64a    |------  + x\|2
--R                               4|    20
--R                               \|256a
--R     + 
--R                   +-+
--R               a x\|2
--R       - 2atan(-------)
--R                2    2
--R               x  - a
--R  /
--R       5 +-+
--R     4a \|2
--R                                                     Type: Expression Integer
--E

--S 31
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 32
dd:=atanrule cc
 

   (5)
            +------+                +------+3         +------+2
         5  |   1          16  +-+  |   1         12  |   1       2
       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
                                               +------+3
                                           16  |   1           +-+
                             (- 64 + 64%i)a    |------  + %i x\|2
                 +------+                     4|    20
              5  |   1                        \|256a
       - 4%i a   |------ log(-------------------------------------)
                4|    20                      +------+3
                \|256a                    16  |   1           +-+
                              (64 + 64%i)a    |------  + %i x\|2
                                             4|    20
                                             \|256a
     + 
                                             +------+3
                                         16  |   1           +-+
                           (- 64 + 64%i)a    |------  - %i x\|2
               +------+                     4|    20
            5  |   1                        \|256a
       4%i a   |------ log(-------------------------------------)
              4|    20                      +------+3
              \|256a                    16  |   1           +-+
                            (64 + 64%i)a    |------  - %i x\|2
                                           4|    20
                                           \|256a
     + 
              +------+                  +------+3         +------+2
           5  |   1            16  +-+  |   1         12  |   1       2
       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
             4|    20                  4|    20          4|    20
             \|256a                    \|256a            \|256a
     + 
                 +-+    2    2                 +-+       2       2
           - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
       log(-------------------) + %i log(-------------------------)
                +-+    2    2                 +-+       2       2
            a x\|2  + x  + a              a x\|2  + %i x  - %i a
  /
       5 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (5)
--R            +------+                +------+3         +------+2
--R         5  |   1          16  +-+  |   1         12  |   1       2
--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R                                               +------+3
--R                                           16  |   1           +-+
--R                             (- 64 + 64%i)a    |------  + %i x\|2
--R                 +------+                     4|    20
--R              5  |   1                        \|256a
--R       - 4%i a   |------ log(-------------------------------------)
--R                4|    20                      +------+3
--R                \|256a                    16  |   1           +-+
--R                              (64 + 64%i)a    |------  + %i x\|2
--R                                             4|    20
--R                                             \|256a
--R     + 
--R                                             +------+3
--R                                         16  |   1           +-+
--R                           (- 64 + 64%i)a    |------  - %i x\|2
--R               +------+                     4|    20
--R            5  |   1                        \|256a
--R       4%i a   |------ log(-------------------------------------)
--R              4|    20                      +------+3
--R              \|256a                    16  |   1           +-+
--R                            (64 + 64%i)a    |------  - %i x\|2
--R                                           4|    20
--R                                           \|256a
--R     + 
--R              +------+                  +------+3         +------+2
--R           5  |   1            16  +-+  |   1         12  |   1       2
--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
--R             4|    20                  4|    20          4|    20
--R             \|256a                    \|256a            \|256a
--R     + 
--R                 +-+    2    2                 +-+       2       2
--R           - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
--R       log(-------------------) + %i log(-------------------------)
--R                +-+    2    2                 +-+       2       2
--R            a x\|2  + x  + a              a x\|2  + %i x  - %i a
--R  /
--R       5 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 33
ee:=expandLog dd
 

   (6)
            +------+                +------+3         +------+2
         5  |   1          16  +-+  |   1         12  |   1       2
       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
              +------+                +------+3         +------+2
           5  |   1          16  +-+  |   1         12  |   1       2
       - 4a   |------ log(64a  x\|2   |------  - 16a    |------  - x )
             4|    20                4|    20          4|    20
             \|256a                  \|256a            \|256a
     + 
                 +------+                    +------+3
              5  |   1                   16  |   1        +-+
       - 4%i a   |------ log((64 + 64%i)a    |------  + x\|2 )
                4|    20                    4|    20
                \|256a                      \|256a
     + 
               +------+                    +------+3
            5  |   1                   16  |   1           +-+
       4%i a   |------ log((64 + 64%i)a    |------  + %i x\|2 )
              4|    20                    4|    20
              \|256a                      \|256a
     + 
                 +------+                    +------+3
              5  |   1                   16  |   1           +-+
       - 4%i a   |------ log((64 + 64%i)a    |------  - %i x\|2 )
                4|    20                    4|    20
                \|256a                      \|256a
     + 
               +------+                    +------+3
            5  |   1                   16  |   1        +-+
       4%i a   |------ log((64 + 64%i)a    |------  - x\|2 )
              4|    20                    4|    20
              \|256a                      \|256a
     + 
                      +------+
           5          |   1             +-+    2    2
       - 4a log(- 1)  |------ - log(a x\|2  + x  + a )
                     4|    20
                     \|256a
     + 
                    +-+       2       2               +-+       2       2
       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
     + 
               +-+    2    2
       log(a x\|2  - x  - a ) + (1 + %i)log(- 1)
  /
       5 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (6)
--R            +------+                +------+3         +------+2
--R         5  |   1          16  +-+  |   1         12  |   1       2
--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R              +------+                +------+3         +------+2
--R           5  |   1          16  +-+  |   1         12  |   1       2
--R       - 4a   |------ log(64a  x\|2   |------  - 16a    |------  - x )
--R             4|    20                4|    20          4|    20
--R             \|256a                  \|256a            \|256a
--R     + 
--R                 +------+                    +------+3
--R              5  |   1                   16  |   1        +-+
--R       - 4%i a   |------ log((64 + 64%i)a    |------  + x\|2 )
--R                4|    20                    4|    20
--R                \|256a                      \|256a
--R     + 
--R               +------+                    +------+3
--R            5  |   1                   16  |   1           +-+
--R       4%i a   |------ log((64 + 64%i)a    |------  + %i x\|2 )
--R              4|    20                    4|    20
--R              \|256a                      \|256a
--R     + 
--R                 +------+                    +------+3
--R              5  |   1                   16  |   1           +-+
--R       - 4%i a   |------ log((64 + 64%i)a    |------  - %i x\|2 )
--R                4|    20                    4|    20
--R                \|256a                      \|256a
--R     + 
--R               +------+                    +------+3
--R            5  |   1                   16  |   1        +-+
--R       4%i a   |------ log((64 + 64%i)a    |------  - x\|2 )
--R              4|    20                    4|    20
--R              \|256a                      \|256a
--R     + 
--R                      +------+
--R           5          |   1             +-+    2    2
--R       - 4a log(- 1)  |------ - log(a x\|2  + x  + a )
--R                     4|    20
--R                     \|256a
--R     + 
--R                    +-+       2       2               +-+       2       2
--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
--R     + 
--R               +-+    2    2
--R       log(a x\|2  - x  - a ) + (1 + %i)log(- 1)
--R  /
--R       5 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 34
ff:=rootSimp ee
 

   (7)
                    +-+       2       2               +-+       2       2
       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
     + 
                  +-+                            +-+
       - %i log(x\|2  + (1 + %i)a) + %i log(%i x\|2  + (1 + %i)a)
     + 
                       +-+                           +-+
       - %i log(- %i x\|2  + (1 + %i)a) + %i log(- x\|2  + (1 + %i)a)
     + 
       %i log(- 1)
  /
       5 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                    +-+       2       2               +-+       2       2
--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
--R     + 
--R                  +-+                            +-+
--R       - %i log(x\|2  + (1 + %i)a) + %i log(%i x\|2  + (1 + %i)a)
--R     + 
--R                       +-+                           +-+
--R       - %i log(- %i x\|2  + (1 + %i)a) + %i log(- x\|2  + (1 + %i)a)
--R     + 
--R       %i log(- 1)
--R  /
--R       5 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 35     14:316 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

        - %i log(2) + %i log(- 1) + %i log(- 2)
   (8)  ---------------------------------------
                          5 +-+
                        4a \|2
                                             Type: Expression Complex Integer
--R
--R        - %i log(2) + %i log(- 1) + %i log(- 2)
--R   (8)  ---------------------------------------
--R                          5 +-+
--R                        4a \|2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(1/(x^3*(x^4+a^4)),x)
 

                  2
           2     x      2
        - x atan(--) - a
                  2
                 a
   (1)  -----------------
                6 2
              2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R           2     x      2
--R        - x atan(--) - a
--R                  2
--R                 a
--R   (1)  -----------------
--R                6 2
--R              2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37
bb:=-1/(2*a^4*x^2)-1/(2*a^6)*atan(x^2/a^2)
 

                  2
           2     x      2
        - x atan(--) - a
                  2
                 a
   (2)  -----------------
                6 2
              2a x
                                                     Type: Expression Integer
--R
--R                  2
--R           2     x      2
--R        - x atan(--) - a
--R                  2
--R                 a
--R   (2)  -----------------
--R                6 2
--R              2a x
--R                                                     Type: Expression Integer
--E

--S 38     14:317 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(1/(x^4-a^4),x)
 

                                          x
        - log(x + a) + log(x - a) - 2atan(-)
                                          a
   (1)  ------------------------------------
                           3
                         4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          x
--R        - log(x + a) + log(x - a) - 2atan(-)
--R                                          a
--R   (1)  ------------------------------------
--R                           3
--R                         4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40
bb:=1/(4*a^3)*log((x-a)/(x+a))-1/(2*a^3)*atan(x/a)
 

            x - a          x
        log(-----) - 2atan(-)
            x + a          a
   (2)  ---------------------
                   3
                 4a
                                                     Type: Expression Integer
--R
--R            x - a          x
--R        log(-----) - 2atan(-)
--R            x + a          a
--R   (2)  ---------------------
--R                   3
--R                 4a
--R                                                     Type: Expression Integer
--E

--S 41
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                            3
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                            3
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 42     14:318 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 43
aa:=integrate(x/(x^4-a^4),x)
 

               2    2         2    2
        - log(x  + a ) + log(x  - a )
   (1)  -----------------------------
                       2
                     4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2         2    2
--R        - log(x  + a ) + log(x  - a )
--R   (1)  -----------------------------
--R                       2
--R                     4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 44
bb:=1/(4*a^2)*log((x^2-a^2)/(x^2+a^2))
 

             2    2
            x  - a
        log(-------)
             2    2
            x  + a
   (2)  ------------
               2
             4a
                                                     Type: Expression Integer
--R
--R             2    2
--R            x  - a
--R        log(-------)
--R             2    2
--R            x  + a
--R   (2)  ------------
--R               2
--R             4a
--R                                                     Type: Expression Integer
--E

--S 45
cc:=aa-bb
 

                                             2    2
               2    2         2    2        x  - a
        - log(x  + a ) + log(x  - a ) - log(-------)
                                             2    2
                                            x  + a
   (3)  --------------------------------------------
                               2
                             4a
                                                     Type: Expression Integer
--R
--R                                             2    2
--R               2    2         2    2        x  - a
--R        - log(x  + a ) + log(x  - a ) - log(-------)
--R                                             2    2
--R                                            x  + a
--R   (3)  --------------------------------------------
--R                               2
--R                             4a
--R                                                     Type: Expression Integer
--E

--S 46     14:319 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 47
aa:=integrate(x^2/(x^4-a^4),x)
 

                                          x
        - log(x + a) + log(x - a) + 2atan(-)
                                          a
   (1)  ------------------------------------
                         4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          x
--R        - log(x + a) + log(x - a) + 2atan(-)
--R                                          a
--R   (1)  ------------------------------------
--R                         4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 48
bb:=1/(4*a)*log((x-a)/(x+a))+1/(2*a)*atan(x/a)
 

            x - a          x
        log(-----) + 2atan(-)
            x + a          a
   (2)  ---------------------
                  4a
                                                     Type: Expression Integer
--R
--R            x - a          x
--R        log(-----) + 2atan(-)
--R            x + a          a
--R   (2)  ---------------------
--R                  4a
--R                                                     Type: Expression Integer
--E 

--S 49
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 50     14:320 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 51
aa:=integrate(x^3/(x^4-a^4),x)
 

             4    4
        log(x  - a )
   (1)  ------------
              4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4    4
--R        log(x  - a )
--R   (1)  ------------
--R              4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 52
bb:=1/4*log(x^4-a^4)
 

             4    4
        log(x  - a )
   (2)  ------------
              4
                                                     Type: Expression Integer
--R
--R             4    4
--R        log(x  - a )
--R   (2)  ------------
--R              4
--R                                                     Type: Expression Integer
--E

--S 53     14:321 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 54
aa:=integrate(1/(x*(x^4-a^4)),x)
 

             4    4
        log(x  - a ) - 4log(x)
   (1)  ----------------------
                    4
                  4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4    4
--R        log(x  - a ) - 4log(x)
--R   (1)  ----------------------
--R                    4
--R                  4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 55
bb:=1/(4*a^4)*log((x^4-a^4)/x^4)
 

             4    4
            x  - a
        log(-------)
                4
               x
   (2)  ------------
               4
             4a
                                                     Type: Expression Integer
--R
--R             4    4
--R            x  - a
--R        log(-------)
--R                4
--R               x
--R   (2)  ------------
--R               4
--R             4a
--R                                                     Type: Expression Integer
--E 

--S 56
cc:=aa-bb
 

                                      4    4
             4    4                  x  - a
        log(x  - a ) - 4log(x) - log(-------)
                                         4
                                        x
   (3)  -------------------------------------
                           4
                         4a
                                                     Type: Expression Integer
--R
--R                                      4    4
--R             4    4                  x  - a
--R        log(x  - a ) - 4log(x) - log(-------)
--R                                         4
--R                                        x
--R   (3)  -------------------------------------
--R                           4
--R                         4a
--R                                                     Type: Expression Integer
--E

--S 57     14:322 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 58
aa:=integrate(1/(x^2*(x^4-a^4)),x)
 

                                                x
        - x log(x + a) + x log(x - a) + 2x atan(-) + 4a
                                                a
   (1)  -----------------------------------------------
                                5
                              4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                x
--R        - x log(x + a) + x log(x - a) + 2x atan(-) + 4a
--R                                                a
--R   (1)  -----------------------------------------------
--R                                5
--R                              4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 59
bb:=1/(a^4*x)+1/(4*a^5)*log((x-a)/(x+a))+1/(2*a^5)*atan(x/a)
 

              x - a            x
        x log(-----) + 2x atan(-) + 4a
              x + a            a
   (2)  ------------------------------
                       5
                     4a x
                                                     Type: Expression Integer
--R
--R              x - a            x
--R        x log(-----) + 2x atan(-) + 4a
--R              x + a            a
--R   (2)  ------------------------------
--R                       5
--R                     4a x
--R                                                     Type: Expression Integer
--E

--S 60
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                            5
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                            5
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 61     14:323 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 62
aa:=integrate(1/(x^3*(x^4-a^4)),x)
 

           2     2    2     2     2    2      2
        - x log(x  + a ) + x log(x  - a ) + 2a
   (1)  ---------------------------------------
                           6 2
                         4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2     2     2    2      2
--R        - x log(x  + a ) + x log(x  - a ) + 2a
--R   (1)  ---------------------------------------
--R                           6 2
--R                         4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63
bb:=1/(2*a^4*x^2)+1/(4*a^6)*log((x^2-a^2)/(x^2+a^2))
 

               2    2
         2    x  - a       2
        x log(-------) + 2a
               2    2
              x  + a
   (2)  --------------------
                  6 2
                4a x
                                                     Type: Expression Integer
--R
--R               2    2
--R         2    x  - a       2
--R        x log(-------) + 2a
--R               2    2
--R              x  + a
--R   (2)  --------------------
--R                  6 2
--R                4a x
--R                                                     Type: Expression Integer
--E

--S 64
cc:=aa-bb
 

                                             2    2
               2    2         2    2        x  - a
        - log(x  + a ) + log(x  - a ) - log(-------)
                                             2    2
                                            x  + a
   (3)  --------------------------------------------
                               6
                             4a
                                                     Type: Expression Integer
--R
--R                                             2    2
--R               2    2         2    2        x  - a
--R        - log(x  + a ) + log(x  - a ) - log(-------)
--R                                             2    2
--R                                            x  + a
--R   (3)  --------------------------------------------
--R                               6
--R                             4a
--R                                                     Type: Expression Integer
--E

--S 65     14:324 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)spool
 
Starts dribbling to uniseg.output (2009/2/17, 18:1:34).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 9
pints  := 1..
 

   (1)  1..
                                       Type: UniversalSegment PositiveInteger
--R 
--R
--R   (1)  1..
--R                                       Type: UniversalSegment PositiveInteger
--E 1

--S 2 of 9
nevens := (0..) by -2
 

   (2)  0.. by - 2
                                    Type: UniversalSegment NonNegativeInteger
--R 
--R
--R   (2)  0.. by - 2
--R                                    Type: UniversalSegment NonNegativeInteger
--E 2

--S 3 of 9
useg: UniversalSegment(Integer) := 3..10
 

   (3)  3..10
                                               Type: UniversalSegment Integer
--R 
--R
--R   (3)  3..10
--R                                               Type: UniversalSegment Integer
--E 3

--S 4 of 9
hasHi pints
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 9
hasHi nevens
 

   (5)  false
                                                                Type: Boolean
--R 
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 9
hasHi useg
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 9
expand pints
 

   (7)  [1,2,3,4,5,6,7,8,9,10,...]
                                                         Type: Stream Integer
--R 
--R
--R   (7)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                         Type: Stream Integer
--E 7

--S 8 of 9
expand nevens
 

   (8)  [0,- 2,- 4,- 6,- 8,- 10,- 12,- 14,- 16,- 18,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [0,- 2,- 4,- 6,- 8,- 10,- 12,- 14,- 16,- 18,...]
--R                                                         Type: Stream Integer
--E 8

--S 9 of 9
expand [1, 3, 10..15, 100..]
 

   (9)  [1,3,10,11,12,13,14,15,100,101,...]
                                                         Type: Stream Integer
--R 
--R
--R   (9)  [1,3,10,11,12,13,14,15,100,101,...]
--R                                                         Type: Stream Integer
--E 9
)spool 
 
Starts dribbling to schaum6.output (2009/2/17, 18:0:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(x^2+a^2),x)
 

             x
        atan(-)
             a
   (1)  -------
           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R        atan(-)
--R             a
--R   (1)  -------
--R           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=(1/a)*atan(x/a)
 

             x
        atan(-)
             a
   (2)  -------
           a
                                                     Type: Expression Integer
--R
--R             x
--R        atan(-)
--R             a
--R   (2)  -------
--R           a
--R                                                     Type: Expression Integer
--E

--S 3      14:125 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x/(x^2+a^2),x)
 

             2    2
        log(x  + a )
   (1)  ------------
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R        log(x  + a )
--R   (1)  ------------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=(1/2)*log(x^2+a^2)
 

             2    2
        log(x  + a )
   (2)  ------------
              2
                                                     Type: Expression Integer
--R
--R             2    2
--R        log(x  + a )
--R   (2)  ------------
--R              2
--R                                                     Type: Expression Integer
--E

--S 6      14:126 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2/(x^2+a^2),x)
 

                 x
   (1)  - a atan(-) + x
                 a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 x
--R   (1)  - a atan(-) + x
--R                 a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=x-a*atan(x/a)
 

                 x
   (2)  - a atan(-) + x
                 a
                                                     Type: Expression Integer
--R
--R                 x
--R   (2)  - a atan(-) + x
--R                 a
--R                                                     Type: Expression Integer
--E

--S 9      14:127 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(x^3/(x^2+a^2),x)
 

           2     2    2     2
        - a log(x  + a ) + x
   (1)  ---------------------
                  2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2     2
--R        - a log(x  + a ) + x
--R   (1)  ---------------------
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=x^2/2-a^2/2*log(x^2+a^2)
 

           2     2    2     2
        - a log(x  + a ) + x
   (2)  ---------------------
                  2
                                                     Type: Expression Integer
--R
--R           2     2    2     2
--R        - a log(x  + a ) + x
--R   (2)  ---------------------
--R                  2
--R                                                     Type: Expression Integer
--E

--S 12     14:128 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(1/(x*(x^2+a^2)),x)
 

               2    2
        - log(x  + a ) + 2log(x)
   (1)  ------------------------
                     2
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R        - log(x  + a ) + 2log(x)
--R   (1)  ------------------------
--R                     2
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=1/(2*a^2)*log(x^2/(x^2+a^2))
 

                2
               x
        log(-------)
             2    2
            x  + a
   (2)  ------------
               2
             2a
                                                     Type: Expression Integer
--R
--R                2
--R               x
--R        log(-------)
--R             2    2
--R            x  + a
--R   (2)  ------------
--R               2
--R             2a
--R                                                     Type: Expression Integer
--E

--S 15
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  + a ) + 2log(x) - log(-------)
                                        2    2
                                       x  + a
   (3)  ---------------------------------------
                            2
                          2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  + a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            2
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 16
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 17
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  2
                2a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  2
--R                2a
--R                                                     Type: Expression Integer
--E

--S 18
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19     14:129 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(1/(x^2*(x^2+a^2)),x)
 

                 x
        - x atan(-) - a
                 a
   (1)  ---------------
               3
              a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 x
--R        - x atan(-) - a
--R                 a
--R   (1)  ---------------
--R               3
--R              a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21
bb:=-1/(a^2*x)-1/a^3*atan(x/a)
 

                 x
        - x atan(-) - a
                 a
   (2)  ---------------
               3
              a x
                                                     Type: Expression Integer
--R
--R                 x
--R        - x atan(-) - a
--R                 a
--R   (2)  ---------------
--R               3
--R              a x
--R                                                     Type: Expression Integer
--E

--S 22     14:130 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(1/(x^3*(x^2+a^2)),x)
 

         2     2    2      2          2
        x log(x  + a ) - 2x log(x) - a
   (1)  -------------------------------
                       4 2
                     2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         2     2    2      2          2
--R        x log(x  + a ) - 2x log(x) - a
--R   (1)  -------------------------------
--R                       4 2
--R                     2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=-1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2+a^2))
 

                    2
           2       x        2
        - x log(-------) - a
                 2    2
                x  + a
   (2)  ---------------------
                  4 2
                2a x
                                                     Type: Expression Integer
--R
--R                    2
--R           2       x        2
--R        - x log(-------) - a
--R                 2    2
--R                x  + a
--R   (2)  ---------------------
--R                  4 2
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 25
cc:=aa-bb
 

                                         2
             2    2                     x
        log(x  + a ) - 2log(x) + log(-------)
                                      2    2
                                     x  + a
   (3)  -------------------------------------
                           4
                         2a
                                                     Type: Expression Integer
--R
--R                                         2
--R             2    2                     x
--R        log(x  + a ) - 2log(x) + log(-------)
--R                                      2    2
--R                                     x  + a
--R   (3)  -------------------------------------
--R                           4
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 26
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27
dd:=divlog cc
 

             2
        log(x ) - 2log(x)
   (5)  -----------------
                 4
               2a
                                                     Type: Expression Integer
--R
--R             2
--R        log(x ) - 2log(x)
--R   (5)  -----------------
--R                 4
--R               2a
--R                                                     Type: Expression Integer
--E

--S 28
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29     14:131 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 30
aa:=integrate(1/((x^2+a^2)^2),x)
 

          2    2      x
        (x  + a )atan(-) + a x
                      a
   (1)  ----------------------
                3 2     5
              2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      x
--R        (x  + a )atan(-) + a x
--R                      a
--R   (1)  ----------------------
--R                3 2     5
--R              2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 31
bb:=x/(2*a^2*(x^2+a^2))+1/(2*a^3)*atan(x/a)
 

          2    2      x
        (x  + a )atan(-) + a x
                      a
   (2)  ----------------------
                3 2     5
              2a x  + 2a
                                                     Type: Expression Integer
--R
--R          2    2      x
--R        (x  + a )atan(-) + a x
--R                      a
--R   (2)  ----------------------
--R                3 2     5
--R              2a x  + 2a
--R                                                     Type: Expression Integer
--E

--S 32     14:132 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 33
aa:=integrate(x/((x^2+a^2)^2),x)
 

              1
   (1)  - ---------
            2     2
          2x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            2     2
--R          2x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34
bb:=-1/(2*(x^2+a^2))
 

              1
   (2)  - ---------
            2     2
          2x  + 2a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            2     2
--R          2x  + 2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 35     14:133 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(x^2/((x^2+a^2)^2),x)
 

          2    2      x
        (x  + a )atan(-) - a x
                      a
   (1)  ----------------------
                  2     3
              2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      x
--R        (x  + a )atan(-) - a x
--R                      a
--R   (1)  ----------------------
--R                  2     3
--R              2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37
bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a)
 

          2    2      x
        (x  + a )atan(-) - a x
                      a
   (2)  ----------------------
                  2     3
              2a x  + 2a
                                                     Type: Expression Integer
--R
--R          2    2      x
--R        (x  + a )atan(-) - a x
--R                      a
--R   (2)  ----------------------
--R                  2     3
--R              2a x  + 2a
--R                                                     Type: Expression Integer
--E

--S 38     14:134 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(x^3/((x^2+a^2)^2),x)
 

          2    2      2    2     2
        (x  + a )log(x  + a ) + a
   (1)  --------------------------
                   2     2
                 2x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      2    2     2
--R        (x  + a )log(x  + a ) + a
--R   (1)  --------------------------
--R                   2     2
--R                 2x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40
bb:=a^2/(2*(x^2+a^2))+1/2*log(x^2+a^2)
 

          2    2      2    2     2
        (x  + a )log(x  + a ) + a
   (2)  --------------------------
                   2     2
                 2x  + 2a
                                                     Type: Expression Integer
--R
--R          2    2      2    2     2
--R        (x  + a )log(x  + a ) + a
--R   (2)  --------------------------
--R                   2     2
--R                 2x  + 2a
--R                                                     Type: Expression Integer
--E

--S 41     14:135 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 42
aa:=integrate(1/(x*(x^2+a^2)^2),x)
 

            2    2      2    2       2     2           2
        (- x  - a )log(x  + a ) + (2x  + 2a )log(x) + a
   (1)  ------------------------------------------------
                             4 2     6
                           2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2      2    2       2     2           2
--R        (- x  - a )log(x  + a ) + (2x  + 2a )log(x) + a
--R   (1)  ------------------------------------------------
--R                             4 2     6
--R                           2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 43
bb:=1/(2*a^2*(x^2+a^2))+1/(2*a^4)*log(x^2/(x^2+a^2))
 

                         2
          2    2        x        2
        (x  + a )log(-------) + a
                      2    2
                     x  + a
   (2)  --------------------------
                  4 2     6
                2a x  + 2a
                                                     Type: Expression Integer
--R
--R                         2
--R          2    2        x        2
--R        (x  + a )log(-------) + a
--R                      2    2
--R                     x  + a
--R   (2)  --------------------------
--R                  4 2     6
--R                2a x  + 2a
--R                                                     Type: Expression Integer
--E

--S 44
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  + a ) + 2log(x) - log(-------)
                                        2    2
                                       x  + a
   (3)  ---------------------------------------
                            4
                          2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  + a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            4
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 45
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 46
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 47
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 48     14:136 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(1/(x^2*(x^2+a^2)^2),x)
 

             3     2       x        2     3
        (- 3x  - 3a x)atan(-) - 3a x  - 2a
                           a
   (1)  -----------------------------------
                      5 3     7
                    2a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R
--R             3     2       x        2     3
--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
--R                           a
--R   (1)  -----------------------------------
--R                      5 3     7
--R                    2a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E

--S 50
bb:=-1/(a^4*x)-x/(2*a^4*(x^2+a^2))-3/(2*a^5)*atan(x/a)
 

             3     2       x        2     3
        (- 3x  - 3a x)atan(-) - 3a x  - 2a
                           a
   (2)  -----------------------------------
                      5 3     7
                    2a x  + 2a x
                                                     Type: Expression Integer
--R
--R             3     2       x        2     3
--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
--R                           a
--R   (2)  -----------------------------------
--R                      5 3     7
--R                    2a x  + 2a x
--R                                                     Type: Expression Integer
--E

--S 51     14:137 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 52
aa:=integrate(1/(x^3*(x^2+a^2)^2),x)
 

           4     2 2      2    2         4     2 2            2 2    4
        (2x  + 2a x )log(x  + a ) + (- 4x  - 4a x )log(x) - 2a x  - a
   (1)  --------------------------------------------------------------
                                   6 4     8 2
                                 2a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           4     2 2      2    2         4     2 2            2 2    4
--R        (2x  + 2a x )log(x  + a ) + (- 4x  - 4a x )log(x) - 2a x  - a
--R   (1)  --------------------------------------------------------------
--R                                   6 4     8 2
--R                                 2a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53
bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2+a^2))-1/a^6*log(x^2/(x^2+a^2))
 

                               2
             4     2 2        x         2 2    4
        (- 2x  - 2a x )log(-------) - 2a x  - a
                            2    2
                           x  + a
   (2)  ----------------------------------------
                        6 4     8 2
                      2a x  + 2a x
                                                     Type: Expression Integer
--R
--R                               2
--R             4     2 2        x         2 2    4
--R        (- 2x  - 2a x )log(-------) - 2a x  - a
--R                            2    2
--R                           x  + a
--R   (2)  ----------------------------------------
--R                        6 4     8 2
--R                      2a x  + 2a x
--R                                                     Type: Expression Integer
--E

--S 54
cc:=aa-bb
 

                                         2
             2    2                     x
        log(x  + a ) - 2log(x) + log(-------)
                                      2    2
                                     x  + a
   (3)  -------------------------------------
                           6
                          a
                                                     Type: Expression Integer
--R
--R                                         2
--R             2    2                     x
--R        log(x  + a ) - 2log(x) + log(-------)
--R                                      2    2
--R                                     x  + a
--R   (3)  -------------------------------------
--R                           6
--R                          a
--R                                                     Type: Expression Integer
--E

--S 55
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 56
dd:=divlog cc
 

             2
        log(x ) - 2log(x)
   (5)  -----------------
                 6
                a
                                                     Type: Expression Integer
--R
--R             2
--R        log(x ) - 2log(x)
--R   (5)  -----------------
--R                 6
--R                a
--R                                                     Type: Expression Integer
--E

--S 57
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 58     14:138 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 59     14:139 Axiom cannot do this integral
aa:=integrate(1/((x^2+a^2)^n),x)
 

           x
         ++       1
   (1)   |   ----------- d%L
        ++     2     2 n
             (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 60
aa:=integrate(x/((x^2+a^2)^n),x)
 

                   2    2
                - x  - a
   (1)  ------------------------
                         2    2
                  n log(x  + a )
        (2n - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2    2
--R                - x  - a
--R   (1)  ------------------------
--R                         2    2
--R                  n log(x  + a )
--R        (2n - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 61
bb:=-1/(2*(n-1)*(x^2+a^2)^(n-1))
 

                     1
   (2)  - ----------------------
                    2    2 n - 1
          (2n - 2)(x  + a )
                                                     Type: Expression Integer
--R
--R                     1
--R   (2)  - ----------------------
--R                    2    2 n - 1
--R          (2n - 2)(x  + a )
--R                                                     Type: Expression Integer
--E

--S 62
cc:=aa-bb
 

                 2    2
          n log(x  + a )       2    2   2    2 n - 1
        %e               + (- x  - a )(x  + a )
   (3)  --------------------------------------------
                                          2    2
                     2    2 n - 1  n log(x  + a )
           (2n - 2)(x  + a )     %e
                                                     Type: Expression Integer
--R
--R                 2    2
--R          n log(x  + a )       2    2   2    2 n - 1
--R        %e               + (- x  - a )(x  + a )
--R   (3)  --------------------------------------------
--R                                          2    2
--R                     2    2 n - 1  n log(x  + a )
--R           (2n - 2)(x  + a )     %e
--R                                                     Type: Expression Integer
--E

--S 63
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 64
dd:=explog cc
 

          2    2 n       2    2   2    2 n - 1
        (x  + a )  + (- x  - a )(x  + a )
   (5)  --------------------------------------
                     2    2 n - 1  2    2 n
           (2n - 2)(x  + a )     (x  + a )
                                                     Type: Expression Integer
--R
--R          2    2 n       2    2   2    2 n - 1
--R        (x  + a )  + (- x  - a )(x  + a )
--R   (5)  --------------------------------------
--R                     2    2 n - 1  2    2 n
--R           (2n - 2)(x  + a )     (x  + a )
--R                                                     Type: Expression Integer
--E

--S 65     14:140 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 66     14:141 Axiom cannot do this integral
aa:=integrate(1/(x*(x^2+a^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++        2     2 n
             %L (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++        2     2 n
--I             %L (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 67     14:142 Axiom cannot do this integral
aa:=integrate(x^m/((x^2+a^2)^n),x)
 

           x       m
         ++      %L
   (1)   |   ----------- d%L
        ++     2     2 n
             (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %L
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 68     14:143 Axiom cannot do this integral
aa:=integrate(1/(x^m*(x^2+a^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++     m  2     2 n
             %L (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++     m  2     2 n
--I             %L (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to tbagg.output (2009/2/17, 18:1:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 7
R ==> Record(key: Symbol, entry: String)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 1

--S 2 of 7
T ==> AssociationList(Symbol, String)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 2

--S 3 of 7
t1:=construct([[x,"ix"]$R])$T
 

   (3)  table(x= "ix")
                                         Type: AssociationList(Symbol,String)
--R
--R   (3)  table(x= "ix")
--R                                         Type: AssociationList(Symbol,String)
--E 3

--S 4 of 7
t2:=construct([[y,"iy"]$R])$T
 

   (4)  table(y= "iy")
                                         Type: AssociationList(Symbol,String)
--R
--R   (4)  table(y= "iy")
--R                                         Type: AssociationList(Symbol,String)
--E 4

--S 5 of 7
(t1=t2)::Boolean
 

   (5)  false
                                                                Type: Boolean
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 7
t3:=construct([[y,"iy"]$R])$T
 

   (6)  table(y= "iy")
                                         Type: AssociationList(Symbol,String)
--R
--R   (6)  table(y= "iy")
--R                                         Type: AssociationList(Symbol,String)
--E 6

--S 7 of 7
(t3=t2)::Boolean
 

   (7)  true
                                                                Type: Boolean
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7
)spool 
 
Starts dribbling to file.output (2009/2/17, 17:46:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 12
ifile:File List Integer:=open("/tmp/jazz1","output")
 

   (1)  "/tmp/jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (1)  "/tmp/jazz1"
--R                                                      Type: File List Integer
--E 1

--S 2 of 12
write!(ifile, [-1,2,3])
 

   (2)  [- 1,2,3]
                                                           Type: List Integer
--R 
--R
--R   (2)  [- 1,2,3]
--R                                                           Type: List Integer
--E 2

--S 3 of 12
write!(ifile, [10,-10,0,111])
 

   (3)  [10,- 10,0,111]
                                                           Type: List Integer
--R 
--R
--R   (3)  [10,- 10,0,111]
--R                                                           Type: List Integer
--E 3

--S 4 of 12
write!(ifile, [7])
 

   (4)  [7]
                                                           Type: List Integer
--R 
--R
--R   (4)  [7]
--R                                                           Type: List Integer
--E 4

--S 5 of 12
reopen!(ifile, "input")
 

   (5)  "/tmp/jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (5)  "/tmp/jazz1"
--R                                                      Type: File List Integer
--E 5

--S 6 of 12
read! ifile
 

   (6)  [- 1,2,3]
                                                           Type: List Integer
--R 
--R
--R   (6)  [- 1,2,3]
--R                                                           Type: List Integer
--E 6

--S 7 of 12
read! ifile
 

   (7)  [10,- 10,0,111]
                                                           Type: List Integer
--R 
--R
--R   (7)  [10,- 10,0,111]
--R                                                           Type: List Integer
--E 7

--S 8 of 12
readIfCan! ifile
 

   (8)  [7]
                                                Type: Union(List Integer,...)
--R 
--R
--R   (8)  [7]
--R                                                Type: Union(List Integer,...)
--E 8

--S 9 of 12
readIfCan! ifile
 

   (9)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (9)  "failed"
--R                                                    Type: Union("failed",...)
--E 9

--S 10 of 12
iomode ifile
 

   (10)  "input"
                                                                 Type: String
--R 
--R
--R   (10)  "input"
--R                                                                 Type: String
--E 10

--S 11 of 12
name ifile
 

   (11)  "/tmp/jazz1"
                                                               Type: FileName
--R 
--R
--R   (11)  "/tmp/jazz1"
--R                                                               Type: FileName
--E 11

--S 12 of 12
close! ifile
 

   (12)  "/tmp/jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (12)  "/tmp/jazz1"
--R                                                      Type: File List Integer
--E 12
)spool 
 
Starts dribbling to kernel.output (2009/2/17, 17:48:9).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 19
x :: Expression Integer
 

   (1)  x
                                                     Type: Expression Integer
--R 
--R
--R   (1)  x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 19
kernel x
 

   (2)  x
                                              Type: Kernel Expression Integer
--R 
--R
--R   (2)  x
--R                                              Type: Kernel Expression Integer
--E 2

--S 3 of 19
sin(x) + cos(x)
 

   (3)  sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 19
kernels %
 

   (4)  [sin(x),cos(x)]
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (4)  [sin(x),cos(x)]
--R                                         Type: List Kernel Expression Integer
--E 4

--S 5 of 19
sin(x)**2 + sin(x) + cos(x)
 

              2
   (5)  sin(x)  + sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R              2
--R   (5)  sin(x)  + sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 19
kernels %
 

   (6)  [sin(x),cos(x)]
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (6)  [sin(x),cos(x)]
--R                                         Type: List Kernel Expression Integer
--E 6

--S 7 of 19
kernels(1 :: Expression Integer)
 

   (7)  []
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (7)  []
--R                                         Type: List Kernel Expression Integer
--E 7

--S 8 of 19
mainKernel(cos(x) + tan(x))
 

   (8)  tan(x)
                                   Type: Union(Kernel Expression Integer,...)
--R 
--R
--R   (8)  tan(x)
--R                                   Type: Union(Kernel Expression Integer,...)
--E 8

--S 9 of 19
height kernel x
 

   (9)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  1
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 19
height mainKernel(sin x)
 

   (10)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  2
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 19
height mainKernel(sin cos x)
 

   (11)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  3
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 19
height mainKernel(sin cos (tan x + sin x))
 

   (12)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 19
operator mainKernel(sin cos (tan x + sin x))
 

   (13)  sin
                                                          Type: BasicOperator
--R 
--R
--R   (13)  sin
--R                                                          Type: BasicOperator
--E 13

--S 14 of 19
name mainKernel(sin cos (tan x + sin x))
 

   (14)  sin
                                                                 Type: Symbol
--R 
--R
--R   (14)  sin
--R                                                                 Type: Symbol
--E 14

--S 15 of 19
f := operator 'f
 

   (15)  f
                                                          Type: BasicOperator
--R 
--R
--R   (15)  f
--R                                                          Type: BasicOperator
--E 15

--S 16 of 19
e := f(x, y, 10)
 

   (16)  f(x,y,10)
                                                     Type: Expression Integer
--R 
--R
--R   (16)  f(x,y,10)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 19
is?(e, f)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 19
is?(e, 'f)
 

   (18)  true
                                                                Type: Boolean
--R 
--R
--R   (18)  true
--R                                                                Type: Boolean
--E 18

--S 19 of 19
argument mainKernel e
 

   (19)  [x,y,10]
                                                Type: List Expression Integer
--R 
--R
--R   (19)  [x,y,10]
--R                                                Type: List Expression Integer
--E 19
)spool 
 
Starts dribbling to fname1.output (2009/2/17, 17:46:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 18
fn: FileName
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
fn := "/spad/src/input/fname.input"
 

   (2)  "/spad/src/input/fname.input"
                                                               Type: FileName
--R 
--R
--R   (2)  "/spad/src/input/fname.input"
--R                                                               Type: FileName
--E 2

--S 3 of 18
directory fn
 

   (3)  "/spad/src/input"
                                                                 Type: String
--R 
--R
--R   (3)  "/spad/src/input"
--R                                                                 Type: String
--E 3

--S 4 of 18
name fn
 

   (4)  "fname"
                                                                 Type: String
--R 
--R
--R   (4)  "fname"
--R                                                                 Type: String
--E 4

--S 5 of 18
extension fn
 

   (5)  "input"
                                                                 Type: String
--R 
--R
--R   (5)  "input"
--R                                                                 Type: String
--E 5

--S 6 of 18
fn := filename("/u/smwatt/work", "fname", "input")
 

   (6)  "/u/smwatt/work/fname.input"
                                                               Type: FileName
--R 
--R
--R   (6)  "/u/smwatt/work/fname.input"
--R                                                               Type: FileName
--E 6

--S 7 of 18
objdir := "/tmp"
 

   (7)  "/tmp"
                                                                 Type: String
--R 
--R
--R   (7)  "/tmp"
--R                                                                 Type: String
--E 7

--S 8 of 18
fn := filename(objdir, "table", "spad")
 

   (8)  "/tmp/table.spad"
                                                               Type: FileName
--R 
--R
--R   (8)  "/tmp/table.spad"
--R                                                               Type: FileName
--E 8

--S 9 of 18
fn := filename("", "letter", "")
 

   (9)  "letter"
                                                               Type: FileName
--R 
--R
--R   (9)  "letter"
--R                                                               Type: FileName
--E 9

--S 10 of 18
exists? "/etc/passwd"
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 18
readable? "/etc/passwd"
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 18
readable? "/etc/security/passwd"
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 18
readable? "/ect/passwd"
 

   (13)  false
                                                                Type: Boolean
--R 
--R
--R   (13)  false
--R                                                                Type: Boolean
--E 13

--S 14 of 18
writable? "/etc/passwd"
 

   (14)  false
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 18
writable? "/dev/null"
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 18
writable? "/etc/DoesNotExist"
 

   (16)  false
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 18
writable? "/tmp/DoesNotExist"
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 18
fn := new(objdir, "xxx", "yy")
 

   (18)  "NIL"
                                                               Type: FileName
--R 
--R
--I   (18)  "/tmp/xxx1420.yy"
--R                                                               Type: FileName
--E 18
)spool 
 
Starts dribbling to kamke1.output (2009/2/17, 17:46:58).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 120
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 120
f := operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 120
g := operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

--S 4 of 120
h := operator 'h
 

   (4)  h
                                                          Type: BasicOperator
--R
--R   (4)  h
--R                                                          Type: BasicOperator
--E 4

--S 5 of 120
ode51 := D(y(x),x) - (y(x)-f(x))*(y(x)-g(x))*(y(x)-(a*f(x)+b*g(x))/(a+b))*h(x)_
           - D(f(x),x)*(y(x)-g(x))/(f(x)-g(x)) _
           - D(g(x),x)*(y(x)-f(x))/(g(x)-f(x))
 

   (5)
                                     ,                                    ,
       ((b + a)g(x) + (- b - a)f(x))y (x) + ((- b - a)y(x) + (b + a)f(x))g (x)

     + 
                                     ,
       ((b + a)y(x) + (- b - a)g(x))f (x)

     + 
                                            3
       ((- b - a)g(x) + (b + a)f(x))h(x)y(x)
     + 
                    2                                     2         2
       ((2b + a)g(x)  + (- b + a)f(x)g(x) + (- b - 2a)f(x) )h(x)y(x)
     + 
                3                     2               2             3
       (- b g(x)  + (- b - 2a)f(x)g(x)  + (2b + a)f(x) g(x) + a f(x) )h(x)y(x)
     + 
                  3                2    2         3
       (b f(x)g(x)  + (- b + a)f(x) g(x)  - a f(x) g(x))h(x)
  /
     (b + a)g(x) + (- b - a)f(x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                     ,                                    ,
--R       ((b + a)g(x) + (- b - a)f(x))y (x) + ((- b - a)y(x) + (b + a)f(x))g (x)
--R
--R     + 
--R                                     ,
--R       ((b + a)y(x) + (- b - a)g(x))f (x)
--R
--R     + 
--R                                            3
--R       ((- b - a)g(x) + (b + a)f(x))h(x)y(x)
--R     + 
--R                    2                                     2         2
--R       ((2b + a)g(x)  + (- b + a)f(x)g(x) + (- b - 2a)f(x) )h(x)y(x)
--R     + 
--R                3                     2               2             3
--R       (- b g(x)  + (- b - 2a)f(x)g(x)  + (2b + a)f(x) g(x) + a f(x) )h(x)y(x)
--R     + 
--R                  3                2    2         3
--R       (b f(x)g(x)  + (- b + a)f(x) g(x)  - a f(x) g(x))h(x)
--R  /
--R     (b + a)g(x) + (- b - a)f(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 120
ode51a:=solve(ode51,y,x)
 

   (6)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (6)  "failed"
--R                                                    Type: Union("failed",...)
--E 6

--S 7 of 120
ode52 := D(y(x),x) - a*y(x)**n - b*x**(n/(1-n))
 

                                 n
                             - -----
         ,            n        n - 1
   (7)  y (x) - a y(x)  - b x

                                                     Type: Expression Integer
--R
--R                                 n
--R                             - -----
--R         ,            n        n - 1
--R   (7)  y (x) - a y(x)  - b x
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 120
ode52a:=solve(ode52,y,x)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8

--S 9 of 120
ode53 := D(y(x),x) - f(x)**(1-n)*D(g(x),x)*y(x)**n/(a*g(x)+b)**n _
           - D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x)
 

   (9)
                       n ,
       f(x)(a g(x) + b) y (x)

     + 
                - n + 1    n       2            n  ,                      n ,
     (- f(x)f(x)       y(x)  - f(x) (a g(x) + b) )g (x) - y(x)(a g(x) + b) f (x)

  /
                     n
     f(x)(a g(x) + b)
                                                     Type: Expression Integer
--R
--R   (9)
--R                       n ,
--R       f(x)(a g(x) + b) y (x)
--R
--R     + 
--R                - n + 1    n       2            n  ,                      n ,
--R     (- f(x)f(x)       y(x)  - f(x) (a g(x) + b) )g (x) - y(x)(a g(x) + b) f (x)
--R
--R  /
--R                     n
--R     f(x)(a g(x) + b)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 120
ode53a:=solve(ode53,y,x)
 

   (10)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (10)  "failed"
--R                                                    Type: Union("failed",...)
--E 10

--S 11 of 120
ode54 := D(y(x),x) - a**n*f(x)**(1-n)*D(g(x),x)*y(x)**n - _
          D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x)
 

              ,              n    - n + 1    n       2  ,           ,
         f(x)y (x) + (- f(x)a f(x)       y(x)  - f(x) )g (x) - y(x)f (x)

   (11)  ---------------------------------------------------------------
                                       f(x)
                                                     Type: Expression Integer
--R
--R              ,              n    - n + 1    n       2  ,           ,
--R         f(x)y (x) + (- f(x)a f(x)       y(x)  - f(x) )g (x) - y(x)f (x)
--R
--R   (11)  ---------------------------------------------------------------
--R                                       f(x)
--R                                                     Type: Expression Integer
--E 11

--S 12 of 120
ode54a:=solve(ode54,y,x)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 120
ode55 := D(y(x),x) - f(x)*y(x)**n - g(x)*y(x) - h(x)
 

          ,              n
   (13)  y (x) - f(x)y(x)  - g(x)y(x) - h(x)

                                                     Type: Expression Integer
--R
--R          ,              n
--R   (13)  y (x) - f(x)y(x)  - g(x)y(x) - h(x)
--R
--R                                                     Type: Expression Integer
--E 13

--S 14 of 120
ode55a:=solve(ode55,y,x)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 14

--S 15 of 120
ode56 := D(y(x),x) - f(x)*y(x)**a - g(x)*y(x)**b
 

          ,              b           a
   (15)  y (x) - g(x)y(x)  - f(x)y(x)

                                                     Type: Expression Integer
--R
--R          ,              b           a
--R   (15)  y (x) - g(x)y(x)  - f(x)y(x)
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 120
ode5a:=solve(ode56,y,x)
 

   (16)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (16)  "failed"
--R                                                    Type: Union("failed",...)
--E 16

--S 17 of 120
ode57 := D(y(x),x) - sqrt(abs(y(x)))
 

            +---------+    ,
   (17)  - \|abs(y(x))  + y (x)

                                                     Type: Expression Integer
--R
--R            +---------+    ,
--R   (17)  - \|abs(y(x))  + y (x)
--R
--R                                                     Type: Expression Integer
--E 17

--S 18 of 120
yx:=solve(ode57,y,x)
 

             +---------+
         - x\|abs(y(x))  + 2y(x)
   (18)  -----------------------
                  +----+
                 \|y(x)
                                          Type: Union(Expression Integer,...)
--R
--R             +---------+
--R         - x\|abs(y(x))  + 2y(x)
--R   (18)  -----------------------
--R                  +----+
--R                 \|y(x)
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 120
ode57expr := D(yx,x) - sqrt(abs(yx))
 

   (19)
                             +--------------------------+
                             |      +---------+
          +----+ +---------+ |    x\|abs(y(x))  - 2y(x)      ,    +---------+
       - \|y(x) \|abs(y(x))  |abs(---------------------)  + y (x)\|abs(y(x))
                             |            +----+
                            \|           \|y(x)
     + 
       - abs(y(x))
  /
      +----+ +---------+
     \|y(x) \|abs(y(x))
                                                     Type: Expression Integer
--R
--R   (19)
--R                             +--------------------------+
--R                             |      +---------+
--R          +----+ +---------+ |    x\|abs(y(x))  - 2y(x)      ,    +---------+
--R       - \|y(x) \|abs(y(x))  |abs(---------------------)  + y (x)\|abs(y(x))
--R                             |            +----+
--R                            \|           \|y(x)
--R     + 
--R       - abs(y(x))
--R  /
--R      +----+ +---------+
--R     \|y(x) \|abs(y(x))
--R                                                     Type: Expression Integer
--E 19

--S 20 of 120
ode58 := D(y(x),x) - a*sqrt(y(x)) - b*x
 

          ,        +----+
   (20)  y (x) - a\|y(x)  - b x

                                                     Type: Expression Integer
--R
--R          ,        +----+
--R   (20)  y (x) - a\|y(x)  - b x
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 120
ode58a:=solve(ode58,y,x)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--  this never finishes
--  ode59 := D(y(x),x) - a*sqrt(y(x)**2+1) - b
--

--S 22 of 120
ode60 := D(y(x),x) - sqrt(y(x)**2-1)/sqrt(x**2-1)
 

          +------+         +---------+
          | 2      ,       |    2
         \|x  - 1 y (x) - \|y(x)  - 1

   (22)  -----------------------------
                    +------+
                    | 2
                   \|x  - 1
                                                     Type: Expression Integer
--R
--R          +------+         +---------+
--R          | 2      ,       |    2
--R         \|x  - 1 y (x) - \|y(x)  - 1
--R
--R   (22)  -----------------------------
--R                    +------+
--R                    | 2
--R                   \|x  - 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 120
ode60a:=solve(ode60,y,x)
 

   (23)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (23)  "failed"
--R                                                    Type: Union("failed",...)
--E 23

--S 24 of 120
ode61 := D(y(x),x) - sqrt(x**2-1)/sqrt(y(x)**2-1)
 

          +---------+         +------+
          |    2      ,       | 2
         \|y(x)  - 1 y (x) - \|x  - 1

   (24)  -----------------------------
                   +---------+
                   |    2
                  \|y(x)  - 1
                                                     Type: Expression Integer
--R
--R          +---------+         +------+
--R          |    2      ,       | 2
--R         \|y(x)  - 1 y (x) - \|x  - 1
--R
--R   (24)  -----------------------------
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R                                                     Type: Expression Integer
--E 24

--S 25 of 120
yx:=solve(ode61,y,x)
 

   (25)
                    +------+                    +---------+
                    | 2             2           |    2
           (4x y(x)\|x  - 1  + (- 4x  + 2)y(x))\|y(x)  - 1
         + 
                             +------+
                     2       | 2           2         2     2
           (- 4x y(x)  + 2x)\|x  - 1  + (4x  - 2)y(x)  - 2x  + 1
      *
              +---------+
              |    2
         log(\|y(x)  - 1  - y(x))
     + 
                      +------+                      +------+
                      | 2           2               | 2
           (- 4x y(x)\|x  - 1  + (4x  - 2)y(x))log(\|x  - 1  - x)
         + 
                                  +------+
                     3     3      | 2           2         3
           (- 4x y(x)  + 4x y(x))\|x  - 1  + (4x  - 2)y(x)
         + 
                4     2
           (- 4x  + 2x  + 1)y(x)
      *
          +---------+
          |    2
         \|y(x)  - 1
     + 
                        +------+                                   +------+
                2       | 2             2         2     2          | 2
       ((4x y(x)  - 2x)\|x  - 1  + (- 4x  + 2)y(x)  + 2x  - 1)log(\|x  - 1  - x)
     + 
                                                +------+
               4        3          2     3      | 2             2         4
       (4x y(x)  + (- 4x  - 2x)y(x)  + 2x  - x)\|x  - 1  + (- 4x  + 2)y(x)
     + 
          4         2     4     2
       (4x  - 2)y(x)  - 2x  + 2x
  /
                +------+                    +---------+
                | 2             2           |    2
       (8x y(x)\|x  - 1  + (- 8x  + 4)y(x))\|y(x)  - 1
     + 
                         +------+
                 2       | 2           2         2     2
       (- 8x y(x)  + 4x)\|x  - 1  + (8x  - 4)y(x)  - 4x  + 2
                                          Type: Union(Expression Integer,...)
--R
--R   (25)
--R                    +------+                    +---------+
--R                    | 2             2           |    2
--R           (4x y(x)\|x  - 1  + (- 4x  + 2)y(x))\|y(x)  - 1
--R         + 
--R                             +------+
--R                     2       | 2           2         2     2
--R           (- 4x y(x)  + 2x)\|x  - 1  + (4x  - 2)y(x)  - 2x  + 1
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  - 1  - y(x))
--R     + 
--R                      +------+                      +------+
--R                      | 2           2               | 2
--R           (- 4x y(x)\|x  - 1  + (4x  - 2)y(x))log(\|x  - 1  - x)
--R         + 
--R                                  +------+
--R                     3     3      | 2           2         3
--R           (- 4x y(x)  + 4x y(x))\|x  - 1  + (4x  - 2)y(x)
--R         + 
--R                4     2
--R           (- 4x  + 2x  + 1)y(x)
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                        +------+                                   +------+
--R                2       | 2             2         2     2          | 2
--R       ((4x y(x)  - 2x)\|x  - 1  + (- 4x  + 2)y(x)  + 2x  - 1)log(\|x  - 1  - x)
--R     + 
--R                                                +------+
--R               4        3          2     3      | 2             2         4
--R       (4x y(x)  + (- 4x  - 2x)y(x)  + 2x  - x)\|x  - 1  + (- 4x  + 2)y(x)
--R     + 
--R          4         2     4     2
--R       (4x  - 2)y(x)  - 2x  + 2x
--R  /
--R                +------+                    +---------+
--R                | 2             2           |    2
--R       (8x y(x)\|x  - 1  + (- 8x  + 4)y(x))\|y(x)  - 1
--R     + 
--R                         +------+
--R                 2       | 2           2         2     2
--R       (- 8x y(x)  + 4x)\|x  - 1  + (8x  - 4)y(x)  - 4x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 25

--S 26 of 120
ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1)
 

   (26)
                             4      2         5       4      2          3
                       (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
                     + 
                             4      2
                       (- 32x  + 32x  - 4)y(x)
                  *
                      +------+
                      | 2
                     \|x  - 1
                 + 
                       5      3           5         5       3           3
                   (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
                 + 
                       5      3
                   (32x  - 48x  + 16x)y(x)
              *
                  +---------+
                  |    2
                 \|y(x)  - 1
             + 
                       4      2         6          4       2          4
                   (64x  - 64x  + 8)y(x)  + (- 128x  + 128x  - 16)y(x)
                 + 
                       4      2         2     4     2
                   (72x  - 72x  + 9)y(x)  - 8x  + 8x  - 1
              *
                  +------+
                  | 2
                 \|x  - 1
             + 
                     5      3           6        5       3           4
               (- 64x  + 96x  - 32x)y(x)  + (128x  - 192x  + 64x)y(x)
             + 
                     5       3           2     5      3
               (- 72x  + 108x  - 36x)y(x)  + 8x  - 12x  + 4x
          *
              ,
             y (x)

         + 
                       5      3           4         5      3           2     5
                   (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
                 + 
                        3
                   - 12x  + 4x
              *
                  +------+
                  | 2
                 \|x  - 1
             + 
                     6       4      2         4       6       4      2         2
               (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
             + 
                   6      4     2
               - 8x  + 16x  - 9x  + 1
          *
              +---------+
              |    2
             \|y(x)  - 1
         + 
                     5      3           5       5       3           3
               (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
             + 
                     5      3
               (- 32x  + 48x  - 16x)y(x)
          *
              +------+
              | 2
             \|x  - 1
         + 
               6       4      2         5         6       4       2          3
           (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
         + 
               6      4      2
           (32x  - 64x  + 36x  - 4)y(x)
      *
         ROOT
                                                                 +------+
                             3           3         3             | 2
                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                      + 
                              4      2         3       4      2
                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                   *
                       +---------+
                       |    2
                      \|y(x)  - 1
                  + 
                             3           4       3           2     3
                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                        4      2         4         4      2         2     4
                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
                  + 
                        2
                    - 8x  + 1
               *
                       +---------+        2
                       |    2
                  log(\|y(x)  - 1  - y(x))
              + 
                                                                      +------+
                                    3           3       3             | 2
                            ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
                          + 
                                 4       2          3         4      2
                            (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
                       *
                               +------+
                               | 2
                          log(\|x  - 1  - x)
                      + 
                                   3           5        5           3
                            (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
                          + 
                                  5      3
                            (- 64x  + 48x )y(x)
                       *
                           +------+
                           | 2
                          \|x  - 1
                      + 
                             4       2          5
                        (128x  - 128x  + 16)y(x)
                      + 
                               6      4      2          3
                        (- 128x  + 64x  + 64x  - 16)y(x)
                      + 
                            6      4      2
                        (64x  - 80x  + 16x  + 2)y(x)
                   *
                       +---------+
                       |    2
                      \|y(x)  - 1
                  + 
                                   3           4          3           2      3
                              (128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x
                            + 
                              - 8x
                       *
                           +------+
                           | 2
                          \|x  - 1
                      + 
                               4       2          4        4       2          2
                        (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
                      + 
                             4      2
                        - 16x  + 16x  - 2
                   *
                           +------+
                           | 2
                      log(\|x  - 1  - x)
                  + 
                             3           6          5      3           4
                        (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
                      + 
                             5      3           2      5      3
                        (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                           4       2          6        6       2          4
                    (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
                  + 
                           6       4         2      6      4     2
                    (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
               *
                       +---------+
                       |    2
                  log(\|y(x)  - 1  - y(x))
              + 
                                                                 +------+
                             3           3         3             | 2
                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                      + 
                              4      2         3       4      2
                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                   *
                           +------+     2
                           | 2
                      log(\|x  - 1  - x)
                  + 
                                 3           5          5           3
                            (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
                          + 
                                5      3
                            (64x  - 48x )y(x)
                       *
                           +------+
                           | 2
                          \|x  - 1
                      + 
                               4       2          5
                        (- 128x  + 128x  - 16)y(x)
                      + 
                             6      4      2          3
                        (128x  - 64x  - 64x  + 16)y(x)
                      + 
                              6      4      2
                        (- 64x  + 80x  - 16x  - 2)y(x)
                   *
                           +------+
                           | 2
                      log(\|x  - 1  - x)
                  + 
                            3           7          5      3           5
                        (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
                      + 
                            7      5       3            3
                        (64x  + 32x  - 320x  + 128x)y(x)
                      + 
                              7      5       3
                        (- 32x  + 32x  + 128x  - 66x)y(x)
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                          4      2         7        6      4      2          5
                    (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
                  + 
                          8       4       2          3
                    (- 64x  + 344x  - 280x  + 28)y(x)
                  + 
                        8      6       4       2
                    (32x  - 48x  - 116x  + 132x  - 16)y(x)
               *
                   +---------+
                   |    2
                  \|y(x)  - 1
              + 
                             3           4       3           2     3
                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                        4      2         4         4      2         2     4
                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
                  + 
                        2
                    - 8x  + 1
               *
                       +------+     2
                       | 2
                  log(\|x  - 1  - x)
              + 
                               3           6        5      3           4
                        (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
                      + 
                               5      3           2      5      3
                        (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                         4       2          6          6       2          4
                    (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
                  + 
                         6       4         2      6      4     2
                    (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
               *
                       +------+
                       | 2
                  log(\|x  - 1  - x)
              + 
                          3           8        5           6
                    (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
                  + 
                          7      5       3            4
                    (- 64x  - 96x  + 344x  - 116x)y(x)
                  + 
                        7      5       3            2     7      5      3
                    (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
               *
                   +------+
                   | 2
                  \|x  - 1
              + 
                    4      2         8          6      4      2          6
                (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
              + 
                    8      6       4       2          4
                (64x  + 64x  - 400x  + 272x  - 23)y(x)
              + 
                      8      6       4       2          2     8      6      4
                (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
              + 
                   2
                31x  - 4
           /
                                                                +------+
                          3            3          3             | 2
                    ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
                  + 
                           4       2          3        4       2
                    (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
               *
                   +---------+
                   |    2
                  \|y(x)  - 1
              + 
                          3            4        3            2      3
                  ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
               *
                   +------+
                   | 2
                  \|x  - 1
              + 
                     4       2          4          4       2          2      4
                (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
              + 
                     2
                - 32x  + 4
     + 
                   5      3           4         5      3           2     5
               (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
             + 
                    3
               - 12x  + 4x
          *
              +------+
              | 2
             \|x  - 1
         + 
                 6       4      2         4       6       4      2         2
           (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
         + 
               6      4     2
           - 8x  + 16x  - 9x  + 1
      *
          +---------+
          |    2
         \|y(x)  - 1
     + 
                 5      3           5       5       3           3
           (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
         + 
                 5      3
           (- 32x  + 48x  - 16x)y(x)
      *
          +------+
          | 2
         \|x  - 1
     + 
           6       4      2         5         6       4       2          3
       (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
     + 
           6      4      2
       (32x  - 64x  + 36x  - 4)y(x)
  /
                       4      2         4         4      2         2     4     2
                   (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
                 + 
                   1
            *
                +------+
                | 2
               \|x  - 1
           + 
                   5      3           4       5      3           2     5      3
             (- 64x  + 96x  - 32x)y(x)  + (64x  - 96x  + 32x)y(x)  - 8x  + 12x
           + 
             - 4x
        *
            +---------+
            |    2
           \|y(x)  - 1
       + 
                   4      2         5       4      2          3
             (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
           + 
                   4      2
             (- 32x  + 32x  - 4)y(x)
        *
            +------+
            | 2
           \|x  - 1
       + 
             5      3           5         5       3           3
         (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
       + 
             5      3
         (32x  - 48x  + 16x)y(x)
    *
       ROOT
                                                               +------+
                           3           3         3             | 2
                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                    + 
                            4      2         3       4      2
                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                 *
                     +---------+
                     |    2
                    \|y(x)  - 1
                + 
                                                                       +------+
                         3           4       3           2     3       | 2
                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
                + 
                      4      2         4         4      2         2     4     2
                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
                + 
                  1
             *
                     +---------+        2
                     |    2
                log(\|y(x)  - 1  - y(x))
            + 
                                                                    +------+
                                  3           3       3             | 2
                          ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
                        + 
                               4       2          3         4      2
                          (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
                     *
                             +------+
                             | 2
                        log(\|x  - 1  - x)
                    + 
                                 3           5        5           3
                          (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
                        + 
                                5      3
                          (- 64x  + 48x )y(x)
                     *
                         +------+
                         | 2
                        \|x  - 1
                    + 
                           4       2          5
                      (128x  - 128x  + 16)y(x)
                    + 
                             6      4      2          3
                      (- 128x  + 64x  + 64x  - 16)y(x)
                    + 
                          6      4      2
                      (64x  - 80x  + 16x  + 2)y(x)
                 *
                     +---------+
                     |    2
                    \|y(x)  - 1
                + 
                              3           4          3           2      3
                        ((128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x  - 8x)
                     *
                         +------+
                         | 2
                        \|x  - 1
                    + 
                             4       2          4        4       2          2
                      (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
                    + 
                           4      2
                      - 16x  + 16x  - 2
                 *
                         +------+
                         | 2
                    log(\|x  - 1  - x)
                + 
                           3           6          5      3           4
                      (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
                    + 
                           5      3           2      5      3
                      (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
                 *
                     +------+
                     | 2
                    \|x  - 1
                + 
                         4       2          6        6       2          4
                  (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
                + 
                         6       4         2      6      4     2
                  (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
             *
                     +---------+
                     |    2
                log(\|y(x)  - 1  - y(x))
            + 
                                                               +------+
                           3           3         3             | 2
                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                    + 
                            4      2         3       4      2
                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                 *
                         +------+     2
                         | 2
                    log(\|x  - 1  - x)
                + 
                               3           5          5           3
                          (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
                        + 
                              5      3
                          (64x  - 48x )y(x)
                     *
                         +------+
                         | 2
                        \|x  - 1
                    + 
                             4       2          5
                      (- 128x  + 128x  - 16)y(x)
                    + 
                           6      4      2          3
                      (128x  - 64x  - 64x  + 16)y(x)
                    + 
                            6      4      2
                      (- 64x  + 80x  - 16x  - 2)y(x)
                 *
                         +------+
                         | 2
                    log(\|x  - 1  - x)
                + 
                          3           7          5      3           5
                      (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
                    + 
                          7      5       3            3
                      (64x  + 32x  - 320x  + 128x)y(x)
                    + 
                            7      5       3
                      (- 32x  + 32x  + 128x  - 66x)y(x)
                 *
                     +------+
                     | 2
                    \|x  - 1
                + 
                        4      2         7        6      4      2          5
                  (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
                + 
                        8       4       2          3
                  (- 64x  + 344x  - 280x  + 28)y(x)
                + 
                      8      6       4       2
                  (32x  - 48x  - 116x  + 132x  - 16)y(x)
             *
                 +---------+
                 |    2
                \|y(x)  - 1
            + 
                                                                       +------+
                         3           4       3           2     3       | 2
                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
                + 
                      4      2         4         4      2         2     4     2
                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
                + 
                  1
             *
                     +------+     2
                     | 2
                log(\|x  - 1  - x)
            + 
                             3           6        5      3           4
                      (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
                    + 
                             5      3           2      5      3
                      (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
                 *
                     +------+
                     | 2
                    \|x  - 1
                + 
                       4       2          6          6       2          4
                  (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
                + 
                       6       4         2      6      4     2
                  (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
             *
                     +------+
                     | 2
                log(\|x  - 1  - x)
            + 
                        3           8        5           6
                  (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
                + 
                        7      5       3            4
                  (- 64x  - 96x  + 344x  - 116x)y(x)
                + 
                      7      5       3            2     7      5      3
                  (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
             *
                 +------+
                 | 2
                \|x  - 1
            + 
                  4      2         8          6      4      2          6
              (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
            + 
                  8      6       4       2          4
              (64x  + 64x  - 400x  + 272x  - 23)y(x)
            + 
                    8      6       4       2          2     8      6      4
              (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
            + 
                 2
              31x  - 4
         /
                                                              +------+
                        3            3          3             | 2
                  ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
                + 
                         4       2          3        4       2
                  (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
             *
                 +---------+
                 |    2
                \|y(x)  - 1
            + 
                        3            4        3            2      3
                ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
             *
                 +------+
                 | 2
                \|x  - 1
            + 
                   4       2          4          4       2          2      4
              (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
            + 
                   2
              - 32x  + 4
                                                     Type: Expression Integer
--R
--R   (26)
--R                             4      2         5       4      2          3
--R                       (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R                     + 
--R                             4      2
--R                       (- 32x  + 32x  - 4)y(x)
--R                  *
--R                      +------+
--R                      | 2
--R                     \|x  - 1
--R                 + 
--R                       5      3           5         5       3           3
--R                   (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R                 + 
--R                       5      3
--R                   (32x  - 48x  + 16x)y(x)
--R              *
--R                  +---------+
--R                  |    2
--R                 \|y(x)  - 1
--R             + 
--R                       4      2         6          4       2          4
--R                   (64x  - 64x  + 8)y(x)  + (- 128x  + 128x  - 16)y(x)
--R                 + 
--R                       4      2         2     4     2
--R                   (72x  - 72x  + 9)y(x)  - 8x  + 8x  - 1
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     5      3           6        5       3           4
--R               (- 64x  + 96x  - 32x)y(x)  + (128x  - 192x  + 64x)y(x)
--R             + 
--R                     5       3           2     5      3
--R               (- 72x  + 108x  - 36x)y(x)  + 8x  - 12x  + 4x
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                       5      3           4         5      3           2     5
--R                   (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R                 + 
--R                        3
--R                   - 12x  + 4x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     6       4      2         4       6       4      2         2
--R               (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R             + 
--R                   6      4     2
--R               - 8x  + 16x  - 9x  + 1
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  - 1
--R         + 
--R                     5      3           5       5       3           3
--R               (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R             + 
--R                     5      3
--R               (- 32x  + 48x  - 16x)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R               6       4      2         5         6       4       2          3
--R           (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R         + 
--R               6      4      2
--R           (32x  - 64x  + 36x  - 4)y(x)
--R      *
--R         ROOT
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +---------+        2
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                      +------+
--R                                    3           3       3             | 2
--R                            ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
--R                          + 
--R                                 4       2          3         4      2
--R                            (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
--R                       *
--R                               +------+
--R                               | 2
--R                          log(\|x  - 1  - x)
--R                      + 
--R                                   3           5        5           3
--R                            (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
--R                          + 
--R                                  5      3
--R                            (- 64x  + 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                             4       2          5
--R                        (128x  - 128x  + 16)y(x)
--R                      + 
--R                               6      4      2          3
--R                        (- 128x  + 64x  + 64x  - 16)y(x)
--R                      + 
--R                            6      4      2
--R                        (64x  - 80x  + 16x  + 2)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                                   3           4          3           2      3
--R                              (128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x
--R                            + 
--R                              - 8x
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          4        4       2          2
--R                        (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
--R                      + 
--R                             4      2
--R                        - 16x  + 16x  - 2
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                             3           6          5      3           4
--R                        (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
--R                      + 
--R                             5      3           2      5      3
--R                        (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                           4       2          6        6       2          4
--R                    (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
--R                  + 
--R                           6       4         2      6      4     2
--R                    (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
--R               *
--R                       +---------+
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                           +------+     2
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                                 3           5          5           3
--R                            (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
--R                          + 
--R                                5      3
--R                            (64x  - 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  + 128x  - 16)y(x)
--R                      + 
--R                             6      4      2          3
--R                        (128x  - 64x  - 64x  + 16)y(x)
--R                      + 
--R                              6      4      2
--R                        (- 64x  + 80x  - 16x  - 2)y(x)
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                            3           7          5      3           5
--R                        (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
--R                      + 
--R                            7      5       3            3
--R                        (64x  + 32x  - 320x  + 128x)y(x)
--R                      + 
--R                              7      5       3
--R                        (- 32x  + 32x  + 128x  - 66x)y(x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                          4      2         7        6      4      2          5
--R                    (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
--R                  + 
--R                          8       4       2          3
--R                    (- 64x  + 344x  - 280x  + 28)y(x)
--R                  + 
--R                        8      6       4       2
--R                    (32x  - 48x  - 116x  + 132x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +------+     2
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                               3           6        5      3           4
--R                        (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
--R                      + 
--R                               5      3           2      5      3
--R                        (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                         4       2          6          6       2          4
--R                    (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
--R                  + 
--R                         6       4         2      6      4     2
--R                    (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
--R               *
--R                       +------+
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                          3           8        5           6
--R                    (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
--R                  + 
--R                          7      5       3            4
--R                    (- 64x  - 96x  + 344x  - 116x)y(x)
--R                  + 
--R                        7      5       3            2     7      5      3
--R                    (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                    4      2         8          6      4      2          6
--R                (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
--R              + 
--R                    8      6       4       2          4
--R                (64x  + 64x  - 400x  + 272x  - 23)y(x)
--R              + 
--R                      8      6       4       2          2     8      6      4
--R                (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
--R              + 
--R                   2
--R                31x  - 4
--R           /
--R                                                                +------+
--R                          3            3          3             | 2
--R                    ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
--R                  + 
--R                           4       2          3        4       2
--R                    (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                          3            4        3            2      3
--R                  ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                     4       2          4          4       2          2      4
--R                (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
--R              + 
--R                     2
--R                - 32x  + 4
--R     + 
--R                   5      3           4         5      3           2     5
--R               (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R             + 
--R                    3
--R               - 12x  + 4x
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R                 6       4      2         4       6       4      2         2
--R           (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R         + 
--R               6      4     2
--R           - 8x  + 16x  - 9x  + 1
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                 5      3           5       5       3           3
--R           (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R         + 
--R                 5      3
--R           (- 32x  + 48x  - 16x)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  - 1
--R     + 
--R           6       4      2         5         6       4       2          3
--R       (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R     + 
--R           6      4      2
--R       (32x  - 64x  + 36x  - 4)y(x)
--R  /
--R                       4      2         4         4      2         2     4     2
--R                   (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
--R                 + 
--R                   1
--R            *
--R                +------+
--R                | 2
--R               \|x  - 1
--R           + 
--R                   5      3           4       5      3           2     5      3
--R             (- 64x  + 96x  - 32x)y(x)  + (64x  - 96x  + 32x)y(x)  - 8x  + 12x
--R           + 
--R             - 4x
--R        *
--R            +---------+
--R            |    2
--R           \|y(x)  - 1
--R       + 
--R                   4      2         5       4      2          3
--R             (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R           + 
--R                   4      2
--R             (- 32x  + 32x  - 4)y(x)
--R        *
--R            +------+
--R            | 2
--R           \|x  - 1
--R       + 
--R             5      3           5         5       3           3
--R         (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R       + 
--R             5      3
--R         (32x  - 48x  + 16x)y(x)
--R    *
--R       ROOT
--R                                                               +------+
--R                           3           3         3             | 2
--R                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                    + 
--R                            4      2         3       4      2
--R                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                 *
--R                     +---------+
--R                     |    2
--R                    \|y(x)  - 1
--R                + 
--R                                                                       +------+
--R                         3           4       3           2     3       | 2
--R                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
--R                + 
--R                      4      2         4         4      2         2     4     2
--R                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
--R                + 
--R                  1
--R             *
--R                     +---------+        2
--R                     |    2
--R                log(\|y(x)  - 1  - y(x))
--R            + 
--R                                                                    +------+
--R                                  3           3       3             | 2
--R                          ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
--R                        + 
--R                               4       2          3         4      2
--R                          (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
--R                     *
--R                             +------+
--R                             | 2
--R                        log(\|x  - 1  - x)
--R                    + 
--R                                 3           5        5           3
--R                          (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
--R                        + 
--R                                5      3
--R                          (- 64x  + 48x )y(x)
--R                     *
--R                         +------+
--R                         | 2
--R                        \|x  - 1
--R                    + 
--R                           4       2          5
--R                      (128x  - 128x  + 16)y(x)
--R                    + 
--R                             6      4      2          3
--R                      (- 128x  + 64x  + 64x  - 16)y(x)
--R                    + 
--R                          6      4      2
--R                      (64x  - 80x  + 16x  + 2)y(x)
--R                 *
--R                     +---------+
--R                     |    2
--R                    \|y(x)  - 1
--R                + 
--R                              3           4          3           2      3
--R                        ((128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x  - 8x)
--R                     *
--R                         +------+
--R                         | 2
--R                        \|x  - 1
--R                    + 
--R                             4       2          4        4       2          2
--R                      (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
--R                    + 
--R                           4      2
--R                      - 16x  + 16x  - 2
--R                 *
--R                         +------+
--R                         | 2
--R                    log(\|x  - 1  - x)
--R                + 
--R                           3           6          5      3           4
--R                      (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
--R                    + 
--R                           5      3           2      5      3
--R                      (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
--R                 *
--R                     +------+
--R                     | 2
--R                    \|x  - 1
--R                + 
--R                         4       2          6        6       2          4
--R                  (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
--R                + 
--R                         6       4         2      6      4     2
--R                  (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
--R             *
--R                     +---------+
--R                     |    2
--R                log(\|y(x)  - 1  - y(x))
--R            + 
--R                                                               +------+
--R                           3           3         3             | 2
--R                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                    + 
--R                            4      2         3       4      2
--R                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                 *
--R                         +------+     2
--R                         | 2
--R                    log(\|x  - 1  - x)
--R                + 
--R                               3           5          5           3
--R                          (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
--R                        + 
--R                              5      3
--R                          (64x  - 48x )y(x)
--R                     *
--R                         +------+
--R                         | 2
--R                        \|x  - 1
--R                    + 
--R                             4       2          5
--R                      (- 128x  + 128x  - 16)y(x)
--R                    + 
--R                           6      4      2          3
--R                      (128x  - 64x  - 64x  + 16)y(x)
--R                    + 
--R                            6      4      2
--R                      (- 64x  + 80x  - 16x  - 2)y(x)
--R                 *
--R                         +------+
--R                         | 2
--R                    log(\|x  - 1  - x)
--R                + 
--R                          3           7          5      3           5
--R                      (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
--R                    + 
--R                          7      5       3            3
--R                      (64x  + 32x  - 320x  + 128x)y(x)
--R                    + 
--R                            7      5       3
--R                      (- 32x  + 32x  + 128x  - 66x)y(x)
--R                 *
--R                     +------+
--R                     | 2
--R                    \|x  - 1
--R                + 
--R                        4      2         7        6      4      2          5
--R                  (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
--R                + 
--R                        8       4       2          3
--R                  (- 64x  + 344x  - 280x  + 28)y(x)
--R                + 
--R                      8      6       4       2
--R                  (32x  - 48x  - 116x  + 132x  - 16)y(x)
--R             *
--R                 +---------+
--R                 |    2
--R                \|y(x)  - 1
--R            + 
--R                                                                       +------+
--R                         3           4       3           2     3       | 2
--R                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
--R                + 
--R                      4      2         4         4      2         2     4     2
--R                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
--R                + 
--R                  1
--R             *
--R                     +------+     2
--R                     | 2
--R                log(\|x  - 1  - x)
--R            + 
--R                             3           6        5      3           4
--R                      (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
--R                    + 
--R                             5      3           2      5      3
--R                      (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
--R                 *
--R                     +------+
--R                     | 2
--R                    \|x  - 1
--R                + 
--R                       4       2          6          6       2          4
--R                  (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
--R                + 
--R                       6       4         2      6      4     2
--R                  (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
--R             *
--R                     +------+
--R                     | 2
--R                log(\|x  - 1  - x)
--R            + 
--R                        3           8        5           6
--R                  (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
--R                + 
--R                        7      5       3            4
--R                  (- 64x  - 96x  + 344x  - 116x)y(x)
--R                + 
--R                      7      5       3            2     7      5      3
--R                  (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
--R             *
--R                 +------+
--R                 | 2
--R                \|x  - 1
--R            + 
--R                  4      2         8          6      4      2          6
--R              (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
--R            + 
--R                  8      6       4       2          4
--R              (64x  + 64x  - 400x  + 272x  - 23)y(x)
--R            + 
--R                    8      6       4       2          2     8      6      4
--R              (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
--R            + 
--R                 2
--R              31x  - 4
--R         /
--R                                                              +------+
--R                        3            3          3             | 2
--R                  ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
--R                + 
--R                         4       2          3        4       2
--R                  (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
--R             *
--R                 +---------+
--R                 |    2
--R                \|y(x)  - 1
--R            + 
--R                        3            4        3            2      3
--R                ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
--R             *
--R                 +------+
--R                 | 2
--R                \|x  - 1
--R            + 
--R                   4       2          4          4       2          2      4
--R              (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
--R            + 
--R                   2
--R              - 32x  + 4
--R                                                     Type: Expression Integer
--E 26

--S 27 of 120
ode62 := D(y(x),x) - (y(x)-x**2*sqrt(x**2-y(x)**2))/_
                      (x*y(x)*sqrt(x**2-y(x)**2)+x)
 

                 +------------+                +------------+
                 |      2    2       ,       2 |      2    2
         (x y(x)\|- y(x)  + x   + x)y (x) + x \|- y(x)  + x   - y(x)

   (27)  -----------------------------------------------------------
                                 +------------+
                                 |      2    2
                          x y(x)\|- y(x)  + x   + x
                                                     Type: Expression Integer
--R
--R                 +------------+                +------------+
--R                 |      2    2       ,       2 |      2    2
--R         (x y(x)\|- y(x)  + x   + x)y (x) + x \|- y(x)  + x   - y(x)
--R
--R   (27)  -----------------------------------------------------------
--R                                 +------------+
--R                                 |      2    2
--R                          x y(x)\|- y(x)  + x   + x
--R                                                     Type: Expression Integer
--E 27

--S 28 of 120
ode62a:=solve(ode62,y,x)
 

   (28)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (28)  "failed"
--R                                                    Type: Union("failed",...)
--E 28

--S 29 of 120
ode63 := D(y(x),x) - (1+ y(x)**2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)**3)
 

                 +-----+ ,        +--------+               2
         (x + 1)\|x + 1 y (x)abs(\|y(x) + 1  + y(x)) - y(x)  - 1

   (29)  -------------------------------------------------------
                          +-----+     +--------+
                  (x + 1)\|x + 1 abs(\|y(x) + 1  + y(x))
                                                     Type: Expression Integer
--R
--R                 +-----+ ,        +--------+               2
--R         (x + 1)\|x + 1 y (x)abs(\|y(x) + 1  + y(x)) - y(x)  - 1
--R
--R   (29)  -------------------------------------------------------
--R                          +-----+     +--------+
--R                  (x + 1)\|x + 1 abs(\|y(x) + 1  + y(x))
--R                                                     Type: Expression Integer
--E 29

--S 30 of 120
ode63a:=solve(ode63,y,x)
 

   (30)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (30)  "failed"
--R                                                    Type: Union("failed",...)
--E 30

--S 31 of 120
ode64 := D(y(x),x) - sqrt((a*y(x)**2+b*y(x)+c)/(a*x**2+b*x+c))
 

                  +--------------------+
                  |      2
          ,       |a y(x)  + b y(x) + c
   (31)  y (x) -  |--------------------
                  |      2
                 \|   a x  + b x + c
                                                     Type: Expression Integer
--R
--R                  +--------------------+
--R                  |      2
--R          ,       |a y(x)  + b y(x) + c
--R   (31)  y (x) -  |--------------------
--R                  |      2
--R                 \|   a x  + b x + c
--R                                                     Type: Expression Integer
--E 31

--S 32 of 120
yx:=solve(ode64,y,x)
 

   (32)
       log
                                                +--------------------+
                                                |      2
                       2 2                  +-+ |a y(x)  + b y(x) + c
                    (2a x  + 2a b x + 2a c)\|a  |--------------------
                                                |      2
                                               \|   a x  + b x + c
                 *
                     +--------------------+
                     |      2
                    \|a y(x)  + b y(x) + c
                + 
                       3 3     2   2     2        2
                  (- 2a x  - 2a b x  - 2a c x)y(x)
                + 
                       2   3       2 2                     2   3           2
                  (- 2a b x  - 2a b x  - 2a b c x)y(x) - 2a c x  - 2a b c x
                + 
                        2
                  - 2a c x
             *
                 +-------------------------+
                 |        2               2
                \|a c y(x)  + b c y(x) + c
            + 
                      3 4    2   3     2   2                2    3     2
                  (- a x  - a b x  - 2a c x  - a b c x - a c  - a )y(x)
                + 
                      2   4      2 3           2    2         2    2
                  (- a b x  - a b x  - 2a b c x  - b c x - b c  - a b)y(x)
                + 
                     2   4          3       2 2      2     3    2
                  - a c x  - a b c x  - 2a c x  - b c x - c  - a c
             *
                     +--------------------+
                 +-+ |      2
                \|a \|a y(x)  + b y(x) + c
            + 
                     4 3     3   2     3        2
                  (2a x  + 2a b x  + 2a c x)y(x)
                + 
                     3   3     2 2 2     2               3   3     2     2
                  (2a b x  + 2a b x  + 2a b c x)y(x) + 2a c x  + 2a b c x
                + 
                    2 2
                  2a c x
             *
                 +--------------------+
                 |      2
                 |a y(x)  + b y(x) + c
                 |--------------------
                 |      2
                \|   a x  + b x + c
         /
                                        +--------------------+
                                        |      2
                   2 2                  |a y(x)  + b y(x) + c
                (2a x  + 2a b x + 2a c) |--------------------
                                        |      2
                                       \|   a x  + b x + c
             *
                 +-------------------------+
                 |        2               2
                \|a c y(x)  + b c y(x) + c
            + 
                3 4    2   3                2    3     2
              (a x  + a b x  - a b c x - a c  - a )y(x)
            + 
                2   4      2 3    2         2    2          2   4          3
              (a b x  + a b x  - b c x - b c  - a b)y(x) + a c x  + a b c x
            + 
                   2     3    2
              - b c x - c  - a c
     + 
       log
                                    +--------------------+
                 +-+ +-+            |      2                         +-+
              (2\|a \|c  - 2a y(x))\|a y(x)  + b y(x) + c  + 2a y(x)\|c
            + 
                        2                +-+
              (- 2a y(x)  - b y(x) - 2c)\|a
         /
                  +--------------------+
              +-+ |      2
            2\|c \|a y(x)  + b y(x) + c  - b y(x) - 2c
  /
      +-+
     \|a
                                          Type: Union(Expression Integer,...)
--R
--R   (32)
--R       log
--R                                                +--------------------+
--R                                                |      2
--R                       2 2                  +-+ |a y(x)  + b y(x) + c
--R                    (2a x  + 2a b x + 2a c)\|a  |--------------------
--R                                                |      2
--R                                               \|   a x  + b x + c
--R                 *
--R                     +--------------------+
--R                     |      2
--R                    \|a y(x)  + b y(x) + c
--R                + 
--R                       3 3     2   2     2        2
--R                  (- 2a x  - 2a b x  - 2a c x)y(x)
--R                + 
--R                       2   3       2 2                     2   3           2
--R                  (- 2a b x  - 2a b x  - 2a b c x)y(x) - 2a c x  - 2a b c x
--R                + 
--R                        2
--R                  - 2a c x
--R             *
--R                 +-------------------------+
--R                 |        2               2
--R                \|a c y(x)  + b c y(x) + c
--R            + 
--R                      3 4    2   3     2   2                2    3     2
--R                  (- a x  - a b x  - 2a c x  - a b c x - a c  - a )y(x)
--R                + 
--R                      2   4      2 3           2    2         2    2
--R                  (- a b x  - a b x  - 2a b c x  - b c x - b c  - a b)y(x)
--R                + 
--R                     2   4          3       2 2      2     3    2
--R                  - a c x  - a b c x  - 2a c x  - b c x - c  - a c
--R             *
--R                     +--------------------+
--R                 +-+ |      2
--R                \|a \|a y(x)  + b y(x) + c
--R            + 
--R                     4 3     3   2     3        2
--R                  (2a x  + 2a b x  + 2a c x)y(x)
--R                + 
--R                     3   3     2 2 2     2               3   3     2     2
--R                  (2a b x  + 2a b x  + 2a b c x)y(x) + 2a c x  + 2a b c x
--R                + 
--R                    2 2
--R                  2a c x
--R             *
--R                 +--------------------+
--R                 |      2
--R                 |a y(x)  + b y(x) + c
--R                 |--------------------
--R                 |      2
--R                \|   a x  + b x + c
--R         /
--R                                        +--------------------+
--R                                        |      2
--R                   2 2                  |a y(x)  + b y(x) + c
--R                (2a x  + 2a b x + 2a c) |--------------------
--R                                        |      2
--R                                       \|   a x  + b x + c
--R             *
--R                 +-------------------------+
--R                 |        2               2
--R                \|a c y(x)  + b c y(x) + c
--R            + 
--R                3 4    2   3                2    3     2
--R              (a x  + a b x  - a b c x - a c  - a )y(x)
--R            + 
--R                2   4      2 3    2         2    2          2   4          3
--R              (a b x  + a b x  - b c x - b c  - a b)y(x) + a c x  + a b c x
--R            + 
--R                   2     3    2
--R              - b c x - c  - a c
--R     + 
--R       log
--R                                    +--------------------+
--R                 +-+ +-+            |      2                         +-+
--R              (2\|a \|c  - 2a y(x))\|a y(x)  + b y(x) + c  + 2a y(x)\|c
--R            + 
--R                        2                +-+
--R              (- 2a y(x)  - b y(x) - 2c)\|a
--R         /
--R                  +--------------------+
--R              +-+ |      2
--R            2\|c \|a y(x)  + b y(x) + c  - b y(x) - 2c
--R  /
--R      +-+
--R     \|a
--R                                          Type: Union(Expression Integer,...)
--E 32

--S 33 of 120
ode64expr := D(yx,x) - sqrt((a*yx**2+b*yx+c)/(a*x**2+b*x+c));
 

                                                     Type: Expression Integer
--E 33

--S 34 of 120
ode65 := D(y(x),x) - sqrt((y(x)**3+1)/(x**3+1))
 

                  +---------+
                  |    3
          ,       |y(x)  + 1
   (34)  y (x) -  |---------
                  |   3
                 \|  x  + 1
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |    3
--R          ,       |y(x)  + 1
--R   (34)  y (x) -  |---------
--R                  |   3
--R                 \|  x  + 1
--R                                                     Type: Expression Integer
--E 34

--S 35 of 120
ode65a:=solve(ode65,y,x)
 

                 +---------+
                 |    3
                 |y(x)  + 1
                 |---------
            x    |   3                 y(x)
          ++    \| %S  + 1           ++          1
   (35)   |   - ------------ d%S  +  |      ---------- d%S
         ++      +---------+        ++       +-------+
                 |    3                      |  3
                \|y(x)  + 1                 \|%S  + 1
                                          Type: Union(Expression Integer,...)
--R
--R                 +---------+
--R                 |    3
--R                 |y(x)  + 1
--R                 |---------
--R            x    |   3                 y(x)
--I          ++    \| %P  + 1           ++          1
--I   (35)   |   - ------------ d%P  +  |      ---------- d%P
--R         ++      +---------+        ++       +-------+
--R                 |    3                      |  3
--I                \|y(x)  + 1                 \|%P  + 1
--R                                          Type: Union(Expression Integer,...)
--E 35

--S 36 of 120
ode66 := D(y(x),x) - sqrt(abs(y(x)*(1-y(x))*(1-a*y(x))))/_
               sqrt(abs(x*(1-x)*(1-a*x)))
 

   (36)
          +------------------------------------+
          |          3                2
       - \|abs(a y(x)  + (- a - 1)y(x)  + y(x))
     + 
        +---------------------------+
        |       3             2       ,
       \|abs(a x  + (- a - 1)x  + x) y (x)

  /
      +---------------------------+
      |       3             2
     \|abs(a x  + (- a - 1)x  + x)
                                                     Type: Expression Integer
--R
--R   (36)
--R          +------------------------------------+
--R          |          3                2
--R       - \|abs(a y(x)  + (- a - 1)y(x)  + y(x))
--R     + 
--R        +---------------------------+
--R        |       3             2       ,
--R       \|abs(a x  + (- a - 1)x  + x) y (x)
--R
--R  /
--R      +---------------------------+
--R      |       3             2
--R     \|abs(a x  + (- a - 1)x  + x)
--R                                                     Type: Expression Integer
--E 36

--S 37 of 120
ode66a:=solve(ode66,y,x)
 

   (37)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (37)  "failed"
--R                                                    Type: Union("failed",...)
--E 37

--S 38 of 120
ode67 := D(y(x),x) - sqrt(1-y(x)**4)/sqrt(1-x**4)
 

          +--------+         +-----------+
          |   4      ,       |      4
         \|- x  + 1 y (x) - \|- y(x)  + 1

   (38)  ---------------------------------
                     +--------+
                     |   4
                    \|- x  + 1
                                                     Type: Expression Integer
--R
--R          +--------+         +-----------+
--R          |   4      ,       |      4
--R         \|- x  + 1 y (x) - \|- y(x)  + 1
--R
--R   (38)  ---------------------------------
--R                     +--------+
--R                     |   4
--R                    \|- x  + 1
--R                                                     Type: Expression Integer
--E 38

--S 39 of 120
ode67a:=solve(ode67,y,x)
 

   (39)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (39)  "failed"
--R                                                    Type: Union("failed",...)
--E 39

--S 40 of 120
ode68 := D(y(x),x) - sqrt((a*y(x)**4+b*y(x)**2+1)/(a*x**4+b*x**2+1))
 

                  +---------------------+
                  |      4         2
          ,       |a y(x)  + b y(x)  + 1
   (40)  y (x) -  |---------------------
                  |      4      2
                 \|   a x  + b x  + 1
                                                     Type: Expression Integer
--R
--R                  +---------------------+
--R                  |      4         2
--R          ,       |a y(x)  + b y(x)  + 1
--R   (40)  y (x) -  |---------------------
--R                  |      4      2
--R                 \|   a x  + b x  + 1
--R                                                     Type: Expression Integer
--E 40

--S 41 of 120
ode68a:=solve(ode68,y,x)
 

   (41)
           +---------------------+
           |      4         2
           |a y(x)  + b y(x)  + 1
           |---------------------
      x    |     2      4                    y(x)
    ++    \|   %S b + %S a + 1             ++              1
    |   - ------------------------ d%S  +  |      ------------------ d%S
   ++      +---------------------+        ++       +---------------+
           |      4         2                      |  2      4
          \|a y(x)  + b y(x)  + 1                 \|%S b + %S a + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (41)
--R           +---------------------+
--R           |      4         2
--R           |a y(x)  + b y(x)  + 1
--R           |---------------------
--R      x    |     2      4                    y(x)
--I    ++    \|   %N b + %N a + 1             ++              1
--I    |   - ------------------------ d%N  +  |      ------------------ d%N
--R   ++      +---------------------+        ++       +---------------+
--R           |      4         2                      |  2      4
--I          \|a y(x)  + b y(x)  + 1                 \|%N b + %N a + 1
--R                                          Type: Union(Expression Integer,...)
--E 41

--S 42 of 120
ode69 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)*_
                           (a4*x**4+a3*x**3+a2*x**2+a1*x+a0))
 

   (42)
      ,
     y (x)

   + 
     -
        ROOT
                     4          3          2                       4
             (a4 b4 x  + a3 b4 x  + a2 b4 x  + a1 b4 x + a0 b4)y(x)
           + 
                     4          3          2                       3
             (a4 b3 x  + a3 b3 x  + a2 b3 x  + a1 b3 x + a0 b3)y(x)
           + 
                     4          3          2                       2
             (a4 b2 x  + a3 b2 x  + a2 b2 x  + a1 b2 x + a0 b2)y(x)
           + 
                     4          3          2                                 4
             (a4 b1 x  + a3 b1 x  + a2 b1 x  + a1 b1 x + a0 b1)y(x) + a4 b0 x
           + 
                    3          2
             a3 b0 x  + a2 b0 x  + a1 b0 x + a0 b0
                                                     Type: Expression Integer
--R 
--R
--R   (42)
--R      ,
--R     y (x)
--R
--R   + 
--R     -
--R        ROOT
--R                     4          3          2                       4
--R             (a4 b4 x  + a3 b4 x  + a2 b4 x  + a1 b4 x + a0 b4)y(x)
--R           + 
--R                     4          3          2                       3
--R             (a4 b3 x  + a3 b3 x  + a2 b3 x  + a1 b3 x + a0 b3)y(x)
--R           + 
--R                     4          3          2                       2
--R             (a4 b2 x  + a3 b2 x  + a2 b2 x  + a1 b2 x + a0 b2)y(x)
--R           + 
--R                     4          3          2                                 4
--R             (a4 b1 x  + a3 b1 x  + a2 b1 x  + a1 b1 x + a0 b1)y(x) + a4 b0 x
--R           + 
--R                    3          2
--R             a3 b0 x  + a2 b0 x  + a1 b0 x + a0 b0
--R                                                     Type: Expression Integer
--E 42

--S 43 of 120
ode69a:=solve(ode69,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   PFO::possibleOrder: more than 1 algebraic constant

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   PFO::possibleOrder: more than 1 algebraic constant
--R
--R   Continuing to read the file...
--R
--E 43

--S 44 of 120
ode70 := D(y(x),x) - sqrt((a4*x**4+a3*x**3+a2*x**2+a1*x+a0)/_
                        (b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0))
 

                  +---------------------------------------------+
                  |          4       3       2
          ,       |      a4 x  + a3 x  + a2 x  + a1 x + a0
   (43)  y (x) -  |---------------------------------------------
                  |       4          3          2
                 \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
                                                     Type: Expression Integer
--R
--R                  +---------------------------------------------+
--R                  |          4       3       2
--R          ,       |      a4 x  + a3 x  + a2 x  + a1 x + a0
--R   (43)  y (x) -  |---------------------------------------------
--R                  |       4          3          2
--R                 \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R                                                     Type: Expression Integer
--E 44

--S 45 of 120
ode70a:=solve(ode70,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   PFO::possibleOrder: more than 1 algebraic constant

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   PFO::possibleOrder: more than 1 algebraic constant
--R
--R   Continuing to read the file...
--R
--E 45

--S 46 of 120
ode71 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)/_
                       (a4*x**4+a3*x**3+a2*x**2+a1*x+a0))
 

                  +---------------------------------------------+
                  |       4          3          2
          ,       |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
   (44)  y (x) -  |---------------------------------------------
                  |          4       3       2
                 \|      a4 x  + a3 x  + a2 x  + a1 x + a0
                                                     Type: Expression Integer
--R
--R                  +---------------------------------------------+
--R                  |       4          3          2
--R          ,       |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R   (44)  y (x) -  |---------------------------------------------
--R                  |          4       3       2
--R                 \|      a4 x  + a3 x  + a2 x  + a1 x + a0
--R                                                     Type: Expression Integer
--E 46

--S 47 of 120
ode71a:=solve(ode71,y,x)
 

   (45)
             +---------------------------------------------+
             |       4          3          2
             |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
             |---------------------------------------------
        x    |        4       3       2
      ++    \|      %S a4 + %S a3 + %S a2 + %S a1 + a0
      |   - ------------------------------------------------ d%S
     ++      +---------------------------------------------+
             |       4          3          2
            \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
   + 
        y(x)
      ++                       1
      |      ------------------------------------- d%S
     ++       +----------------------------------+
              |  4       3       2
             \|%S b4 + %S b3 + %S b2 + %S b1 + b0
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (45)
--R             +---------------------------------------------+
--R             |       4          3          2
--R             |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R             |---------------------------------------------
--R        x    |        4       3       2
--I      ++    \|      %N a4 + %N a3 + %N a2 + %N a1 + a0
--I      |   - ------------------------------------------------ d%N
--R     ++      +---------------------------------------------+
--R             |       4          3          2
--R            \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R   + 
--R        y(x)
--R      ++                       1
--I      |      ------------------------------------- d%N
--R     ++       +----------------------------------+
--R              |  4       3       2
--I             \|%N b4 + %N b3 + %N b2 + %N b1 + b0
--R                                          Type: Union(Expression Integer,...)
--E 47

--S 48 of 120
R1:=operator 'R1
 

   (46)  R1
                                                          Type: BasicOperator
--R
--R   (46)  R1
--R                                                          Type: BasicOperator
--E 48

--S 49 of 120
R2:=operator 'R2
 

   (47)  R2
                                                          Type: BasicOperator
--R
--R   (47)  R2
--R                                                          Type: BasicOperator
--E 49

--S 50 of 120
ode72 := D(y(x),x) - R1(x,sqrt(a4*x**4+a3*x**3+a2*x**2+a1*x+a0))*_
             R2(y(x),sqrt(b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0))
 

   (48)
     -
                +---------------------------------+
                |    4       3       2
          R1(x,\|a4 x  + a3 x  + a2 x  + a1 x + a0 )
       *
                   +---------------------------------------------+
                   |       4          3          2
          R2(y(x),\|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0 )
   + 
      ,
     y (x)

                                                     Type: Expression Integer
--R
--R   (48)
--R     -
--R                +---------------------------------+
--R                |    4       3       2
--R          R1(x,\|a4 x  + a3 x  + a2 x  + a1 x + a0 )
--R       *
--R                   +---------------------------------------------+
--R                   |       4          3          2
--R          R2(y(x),\|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0 )
--R   + 
--R      ,
--R     y (x)
--R
--R                                                     Type: Expression Integer
--E 50

--S 51 of 120
ode72a:=solve(ode72,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 51

--S 52 of 120
ode73 := D(y(x),x) - ((a3*x**3+a2*x**2+a1*x+a0)/_
           (a3*y(x)**3+a2*y(x)**2+a1*y(x)+a0))**(2/3)
 

                  +----------------------------------+2
                  |         3       2
          ,       |     a3 x  + a2 x  + a1 x + a0
   (49)  y (x) -  |----------------------------------
                 3|       3          2
                 \|a3 y(x)  + a2 y(x)  + a1 y(x) + a0
                                                     Type: Expression Integer
--R
--R                  +----------------------------------+2
--R                  |         3       2
--R          ,       |     a3 x  + a2 x  + a1 x + a0
--R   (49)  y (x) -  |----------------------------------
--R                 3|       3          2
--R                 \|a3 y(x)  + a2 y(x)  + a1 y(x) + a0
--R                                                     Type: Expression Integer
--E 52


--S 53 of 120
ode74 := D(y(x),x) - f(x)*(y(x)-g(x))*sqrt((y(x)-a)*(y(x)-b))
 

                                         +---------------------------+
          ,                              |    2
   (50)  y (x) + (- f(x)y(x) + f(x)g(x))\|y(x)  + (- b - a)y(x) + a b

                                                     Type: Expression Integer
--R
--R                                         +---------------------------+
--R          ,                              |    2
--R   (50)  y (x) + (- f(x)y(x) + f(x)g(x))\|y(x)  + (- b - a)y(x) + a b
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 120
ode74a:=solve(ode74,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 54

--S 55 of 120
ode75 := D(y(x),x) - exp(x-y(x)) + exp(x)
 

          ,        - y(x) + x     x
   (52)  y (x) - %e           + %e

                                                     Type: Expression Integer
--R
--R          ,        - y(x) + x     x
--R   (52)  y (x) - %e           + %e
--R
--R                                                     Type: Expression Integer
--E 55

--S 56 of 120
ode75a:=solve(ode75,y,x)
 

   (53)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (53)  "failed"
--R                                                    Type: Union("failed",...)
--E 56

--S 57 of 120
ode76 := D(y(x),x) - a*cos(y(x)) + b
 

          ,
   (54)  y (x) - a cos(y(x)) + b

                                                     Type: Expression Integer
--R
--R          ,
--R   (54)  y (x) - a cos(y(x)) + b
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 120
yx:=solve(ode76,y,x)
 

   (55)
                                    +---------+              +---------+
               2    2               |   2    2               |   2    2
           (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
       log(-------------------------------------------------------------)
                                  a cos(y(x)) - b
     + 
         +---------+
         |   2    2
       x\|- b  + a
  /
      +---------+
      |   2    2
     \|- b  + a
                                          Type: Union(Expression Integer,...)
--R
--R   (55)
--R                                    +---------+              +---------+
--R               2    2               |   2    2               |   2    2
--R           (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
--R       log(-------------------------------------------------------------)
--R                                  a cos(y(x)) - b
--R     + 
--R         +---------+
--R         |   2    2
--R       x\|- b  + a
--R  /
--R      +---------+
--R      |   2    2
--R     \|- b  + a
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 120
ode76expr := D(yx,x) - a*cos(yx) + b
 

   (56)
                2 2    4                3    3
           ((- a b  + a )cos(y(x)) + a b  - a b)sin(y(x))
         + 
               +---------+                           +---------+
            2  |   2    2          2         2    3  |   2    2
           a b\|- b  + a  cos(y(x))  + (- a b  - a )\|- b  + a  cos(y(x))
         + 
               +---------+
            2  |   2    2
           a b\|- b  + a
      *
         cos
                log
                                            +---------+              +---------+
                       2    2               |   2    2               |   2    2
                   (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
                   -------------------------------------------------------------
                                          a cos(y(x)) - b
              + 
                  +---------+
                  |   2    2
                x\|- b  + a
           /
               +---------+
               |   2    2
              \|- b  + a
     + 
               +---------+
               |   2    2          2       2    2
           - a\|- b  + a  sin(y(x))  + (- b  + a )sin(y(x))
         + 
               +---------+               +---------+
               |   2    2          2     |   2    2
           - a\|- b  + a  cos(y(x))  + b\|- b  + a  cos(y(x))
      *
          ,
         y (x)

     + 
            3      2    3     3              4    3    2 2    2
       ((a b  + a b  - a b - a )cos(y(x)) - b  - b  + a b  + a b)sin(y(x))
     + 
                      +---------+
             2        |   2    2          2
       (- a b  - a b)\|- b  + a  cos(y(x))
     + 
                            +---------+                           +---------+
         3    2    2     2  |   2    2                   2        |   2    2
       (b  + b  + a b + a )\|- b  + a  cos(y(x)) + (- a b  - a b)\|- b  + a
  /
                                                        +---------+
            2    3              3    2                  |   2    2          2
       ((a b  - a )cos(y(x)) - b  + a b)sin(y(x)) - a b\|- b  + a  cos(y(x))
     + 
                 +---------+                +---------+
         2    2  |   2    2                 |   2    2
       (b  + a )\|- b  + a  cos(y(x)) - a b\|- b  + a
                                                     Type: Expression Integer
--R
--R   (56)
--R                2 2    4                3    3
--R           ((- a b  + a )cos(y(x)) + a b  - a b)sin(y(x))
--R         + 
--R               +---------+                           +---------+
--R            2  |   2    2          2         2    3  |   2    2
--R           a b\|- b  + a  cos(y(x))  + (- a b  - a )\|- b  + a  cos(y(x))
--R         + 
--R               +---------+
--R            2  |   2    2
--R           a b\|- b  + a
--R      *
--R         cos
--R                log
--R                                            +---------+              +---------+
--R                       2    2               |   2    2               |   2    2
--R                   (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
--R                   -------------------------------------------------------------
--R                                          a cos(y(x)) - b
--R              + 
--R                  +---------+
--R                  |   2    2
--R                x\|- b  + a
--R           /
--R               +---------+
--R               |   2    2
--R              \|- b  + a
--R     + 
--R               +---------+
--R               |   2    2          2       2    2
--R           - a\|- b  + a  sin(y(x))  + (- b  + a )sin(y(x))
--R         + 
--R               +---------+               +---------+
--R               |   2    2          2     |   2    2
--R           - a\|- b  + a  cos(y(x))  + b\|- b  + a  cos(y(x))
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R            3      2    3     3              4    3    2 2    2
--R       ((a b  + a b  - a b - a )cos(y(x)) - b  - b  + a b  + a b)sin(y(x))
--R     + 
--R                      +---------+
--R             2        |   2    2          2
--R       (- a b  - a b)\|- b  + a  cos(y(x))
--R     + 
--R                            +---------+                           +---------+
--R         3    2    2     2  |   2    2                   2        |   2    2
--R       (b  + b  + a b + a )\|- b  + a  cos(y(x)) + (- a b  - a b)\|- b  + a
--R  /
--R                                                        +---------+
--R            2    3              3    2                  |   2    2          2
--R       ((a b  - a )cos(y(x)) - b  + a b)sin(y(x)) - a b\|- b  + a  cos(y(x))
--R     + 
--R                 +---------+                +---------+
--R         2    2  |   2    2                 |   2    2
--R       (b  + a )\|- b  + a  cos(y(x)) - a b\|- b  + a
--R                                                     Type: Expression Integer
--E 59

--S 60 of 120
ode77 := D(y(x),x) - cos(a*y(x)+b*x)
 

          ,
   (57)  y (x) - cos(a y(x) + b x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (57)  y (x) - cos(a y(x) + b x)
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 120
ode77a:=solve(ode77,y,x)
 

   (58)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (58)  "failed"
--R                                                    Type: Union("failed",...)
--E 61

--S 62 of 120
ode78 := D(y(x),x) + a*sin(alpha*y(x)+beta*x) + b
 

          ,
   (59)  y (x) + a sin(alpha y(x) + beta x) + b

                                                     Type: Expression Integer
--R
--R          ,
--R   (59)  y (x) + a sin(alpha y(x) + beta x) + b
--R
--R                                                     Type: Expression Integer
--E 62

--S 63 of 120
ode78a:=solve(ode78,y,x)
 

   (60)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (60)  "failed"
--R                                                    Type: Union("failed",...)
--E 63

--S 64 of 120
ode79 := D(y(x),x) + f(x)*cos(a*y(x)) + g(x)*sin(a*y(x)) + h(x)
 

          ,
   (61)  y (x) + g(x)sin(a y(x)) + f(x)cos(a y(x)) + h(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (61)  y (x) + g(x)sin(a y(x)) + f(x)cos(a y(x)) + h(x)
--R
--R                                                     Type: Expression Integer
--E 64

--S 65 of 120
ode79a:=solve(ode79,y,x)
 

   (62)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (62)  "failed"
--R                                                    Type: Union("failed",...)
--E 65

--S 66 of 120
ode80 := D(y(x),x) + f(x)*sin(y(x)) + (1-D(f(x),x))*cos(y(x)) - D(f(x),x) - 1
 

          ,                        ,
   (63)  y (x) + (- cos(y(x)) - 1)f (x) + f(x)sin(y(x)) + cos(y(x)) - 1

                                                     Type: Expression Integer
--R
--R          ,                        ,
--R   (63)  y (x) + (- cos(y(x)) - 1)f (x) + f(x)sin(y(x)) + cos(y(x)) - 1
--R
--R                                                     Type: Expression Integer
--E 66

--S 67 of 120
ode80a:=solve(ode80,y,x)
 

   (64)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (64)  "failed"
--R                                                    Type: Union("failed",...)
--E 67

--S 68 of 120
ode81 := D(y(x),x) + 2*tan(y(x))*tan(x) - 1
 

          ,
   (65)  y (x) + 2tan(x)tan(y(x)) - 1

                                                     Type: Expression Integer
--R
--R          ,
--R   (65)  y (x) + 2tan(x)tan(y(x)) - 1
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 120
ode81a:=solve(ode81,y,x)
 

   (66)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (66)  "failed"
--R                                                    Type: Union("failed",...)
--E 69

--S 70 of 120
ode82 := D(y(x),x) - a*(1+tan(y(x))**2) + tan(y(x))*tan(x)
 

          ,                 2
   (67)  y (x) - a tan(y(x))  + tan(x)tan(y(x)) - a

                                                     Type: Expression Integer
--R
--R          ,                 2
--R   (67)  y (x) - a tan(y(x))  + tan(x)tan(y(x)) - a
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 120
ode82a:=solve(ode82,y,x)
 

   (68)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (68)  "failed"
--R                                                    Type: Union("failed",...)
--E 71

--S 72 of 120
ode83 := D(y(x),x) - tan(x*y(x))
 

          ,
   (69)  y (x) - tan(x y(x))

                                                     Type: Expression Integer
--R
--R          ,
--R   (69)  y (x) - tan(x y(x))
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 120
ode83a:=solve(ode83,y,x)
 

   (70)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (70)  "failed"
--R                                                    Type: Union("failed",...)
--E 73

--S 74 of 120
ode84 := D(y(x),x) - f(a*x + b*y(x))
 

          ,
   (71)  y (x) - f(b y(x) + a x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (71)  y (x) - f(b y(x) + a x)
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 120
ode84a:=solve(ode84,y,x)
 

   (72)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (72)  "failed"
--R                                                    Type: Union("failed",...)
--E 75

--S 76 of 120
ode85 := D(y(x),x) - x**(a-1)*y(x)**(1-b)*f(x**a/a + y(x)**b/b)
 

                                    b      a
            a - 1    - b + 1  a y(x)  + b x      ,
   (73)  - x     y(x)       f(--------------) + y (x)
                                    a b
                                                     Type: Expression Integer
--R
--R                                    b      a
--R            a - 1    - b + 1  a y(x)  + b x      ,
--R   (73)  - x     y(x)       f(--------------) + y (x)
--R                                    a b
--R                                                     Type: Expression Integer
--E 76

--S 77 of 120
ode85a:=solve(ode85,y,x)
 

   (74)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (74)  "failed"
--R                                                    Type: Union("failed",...)
--E 77

--S 78 of 120
ode86 := D(y(x),x) - (y(x)-x*f(x**2+a*y(x)**2))/(x+a*y(x)*f(x**2+a*y(x)**2))
 

                        2    2       ,                2    2
         (a y(x)f(a y(x)  + x ) + x)y (x) + x f(a y(x)  + x ) - y(x)

   (75)  -----------------------------------------------------------
                                        2    2
                          a y(x)f(a y(x)  + x ) + x
                                                     Type: Expression Integer
--R
--R                        2    2       ,                2    2
--R         (a y(x)f(a y(x)  + x ) + x)y (x) + x f(a y(x)  + x ) - y(x)
--R
--R   (75)  -----------------------------------------------------------
--R                                        2    2
--R                          a y(x)f(a y(x)  + x ) + x
--R                                                     Type: Expression Integer
--E 78

--S 79 of 120
ode86a:=solve(ode86,y,x)
 

   (76)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (76)  "failed"
--R                                                    Type: Union("failed",...)
--E 79

--S 80 of 120
ode87 := D(y(x),x) - (y(x)*a*f(x**c*y(x))+c*x**a*y(x)**b)/_
            (x*b*f(x**c*y(x))-x**a*y(x)**b)
 

           a    b              c   ,         a    b                c
         (x y(x)  - b x f(y(x)x ))y (x) + c x y(x)  + a y(x)f(y(x)x )

   (77)  ------------------------------------------------------------
                             a    b              c
                            x y(x)  - b x f(y(x)x )
                                                     Type: Expression Integer
--R
--R           a    b              c   ,         a    b                c
--R         (x y(x)  - b x f(y(x)x ))y (x) + c x y(x)  + a y(x)f(y(x)x )
--R
--R   (77)  ------------------------------------------------------------
--R                             a    b              c
--R                            x y(x)  - b x f(y(x)x )
--R                                                     Type: Expression Integer
--E 80

--S 81 of 120
ode87a:=solve(ode87,y,x)
 

   (78)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (78)  "failed"
--R                                                    Type: Union("failed",...)
--E 81

--S 82 of 120
ode88 := 2*D(y(x),x) - 3*y(x)**2 - 4*a*y(x) - b - c*exp(-2*a*x)
 

           ,          - 2a x        2
   (79)  2y (x) - c %e       - 3y(x)  - 4a y(x) - b

                                                     Type: Expression Integer
--R
--R           ,          - 2a x        2
--R   (79)  2y (x) - c %e       - 3y(x)  - 4a y(x) - b
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 120
ode88a:=solve(ode88,y,x)
 

   (80)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (80)  "failed"
--R                                                    Type: Union("failed",...)
--E 83

--S 84 of 120
ode89 := x*D(y(x),x) - sqrt(a**2 - x**2)
 

                   +---------+
           ,       |   2    2
   (81)  xy (x) - \|- x  + a

                                                     Type: Expression Integer
--R
--R                   +---------+
--R           ,       |   2    2
--R   (81)  xy (x) - \|- x  + a
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 120
ode89a:=solve(ode89,y,x)
 

   (82)
                                         +---------+
                   +---------+           |   2    2
                   |   2    2     2     \|- x  + a   - a     2
                (a\|- x  + a   - a )log(----------------) - x
                                                x
   [particular= ----------------------------------------------,basis= [1]]
                                +---------+
                                |   2    2
                               \|- x  + a   - a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (82)
--R                                         +---------+
--R                   +---------+           |   2    2
--R                   |   2    2     2     \|- x  + a   - a     2
--R                (a\|- x  + a   - a )log(----------------) - x
--R                                                x
--R   [particular= ----------------------------------------------,basis= [1]]
--R                                +---------+
--R                                |   2    2
--R                               \|- x  + a   - a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 85

--S 86 of 120
yx:=ode89a.particular
 

                                  +---------+
            +---------+           |   2    2
            |   2    2     2     \|- x  + a   - a     2
         (a\|- x  + a   - a )log(----------------) - x
                                         x
   (83)  ----------------------------------------------
                         +---------+
                         |   2    2
                        \|- x  + a   - a
                                                     Type: Expression Integer
--R
--R                                  +---------+
--R            +---------+           |   2    2
--R            |   2    2     2     \|- x  + a   - a     2
--R         (a\|- x  + a   - a )log(----------------) - x
--R                                         x
--R   (83)  ----------------------------------------------
--R                         +---------+
--R                         |   2    2
--R                        \|- x  + a   - a
--R                                                     Type: Expression Integer
--E 86

--S 87 of 120
ode89expr := x*D(yx,x) - sqrt(a**2 - x**2)
 

   (84)  0
                                                     Type: Expression Integer
--R
--R   (84)  0
--R                                                     Type: Expression Integer
--E 87

--S 88 of 120
ode90 := x*D(y(x),x) + y(x) - x*sin(x)
 

           ,
   (85)  xy (x) - x sin(x) + y(x)

                                                     Type: Expression Integer
--R
--R           ,
--R   (85)  xy (x) - x sin(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 88

--S 89 of 120
ode90a:=solve(ode90,y,x)
 

                      sin(x) - x cos(x)         1
   (86)  [particular= -----------------,basis= [-]]
                              x                 x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                      sin(x) - x cos(x)         1
--R   (86)  [particular= -----------------,basis= [-]]
--R                              x                 x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 89

--S 90 of 120
yx:=ode90a.particular
 

         sin(x) - x cos(x)
   (87)  -----------------
                 x
                                                     Type: Expression Integer
--R
--R         sin(x) - x cos(x)
--R   (87)  -----------------
--R                 x
--R                                                     Type: Expression Integer
--E 90

--S 91 of 120
ode90expr := x*D(yx,x) + yx - x*sin(x)
 

   (88)  0
                                                     Type: Expression Integer
--R
--R   (88)  0
--R                                                     Type: Expression Integer
--E 91

--S 92 of 120
ode91 := x*D(y(x),x) - y(x) - x/log(x)
 

                  ,
         x log(x)y (x) - y(x)log(x) - x

   (89)  ------------------------------
                     log(x)
                                                     Type: Expression Integer
--R
--R                  ,
--R         x log(x)y (x) - y(x)log(x) - x
--R
--R   (89)  ------------------------------
--R                     log(x)
--R                                                     Type: Expression Integer
--E 92

--S 93 of 120
ode91a:=solve(ode91,y,x)
 

   (90)  [particular= x log(log(x)),basis= [x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (90)  [particular= x log(log(x)),basis= [x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 93

--S 94 of 120
yx:=ode91a.particular
 

   (91)  x log(log(x))
                                                     Type: Expression Integer
--R
--R   (91)  x log(log(x))
--R                                                     Type: Expression Integer
--E 94

--S 95 of 120
ode91expr := x*D(yx,x) - yx - x/log(x)
 

   (92)  0
                                                     Type: Expression Integer
--R
--R   (92)  0
--R                                                     Type: Expression Integer
--E 95

--S 96 of 120
ode92 := x*D(y(x),x) - y(x) - x**2*sin(x)
 

           ,       2
   (93)  xy (x) - x sin(x) - y(x)

                                                     Type: Expression Integer
--R
--R           ,       2
--R   (93)  xy (x) - x sin(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 120
ode92a:=solve(ode92,y,x)
 

   (94)  [particular= - x cos(x),basis= [x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (94)  [particular= - x cos(x),basis= [x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 97

--S 98 of 120
yx:=ode92a.particular
 

   (95)  - x cos(x)
                                                     Type: Expression Integer
--R
--R   (95)  - x cos(x)
--R                                                     Type: Expression Integer
--E 98

--S 99 of 120
ode92expr := x*D(yx,x) - yx - x**2*sin(x)
 

   (96)  0
                                                     Type: Expression Integer
--R
--R   (96)  0
--R                                                     Type: Expression Integer
--E 99


--S 100 of 120
ode93 := x*D(y(x),x) - y(x) - x*cos(log(log(x)))/log(x)
 

                                         ,
         - x cos(log(log(x))) + x log(x)y (x) - y(x)log(x)

   (97)  -------------------------------------------------
                               log(x)
                                                     Type: Expression Integer
--R
--R                                         ,
--R         - x cos(log(log(x))) + x log(x)y (x) - y(x)log(x)
--R
--R   (97)  -------------------------------------------------
--R                               log(x)
--R                                                     Type: Expression Integer
--E 100

--S 101 of 120
ode93a:=solve(ode93,y,x)
 

   (98)  [particular= x sin(log(log(x))),basis= [x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (98)  [particular= x sin(log(log(x))),basis= [x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 101

--S 102 of 120
yx:=ode93a.particular
 

   (99)  x sin(log(log(x)))
                                                     Type: Expression Integer
--R
--R   (99)  x sin(log(log(x)))
--R                                                     Type: Expression Integer
--E 102

--S 103 of 120
ode93 := x*D(yx,x) - yx - x*cos(log(log(x)))/log(x)
 

   (100)  0
                                                     Type: Expression Integer
--R
--R   (100)  0
--R                                                     Type: Expression Integer
--E 103

--S 104 of 120
ode94 := x*D(y(x),x) +a*y(x) + b*x**n
 

            ,         n
   (101)  xy (x) + b x  + a y(x)

                                                     Type: Expression Integer
--R
--R            ,         n
--R   (101)  xy (x) + b x  + a y(x)
--R
--R                                                     Type: Expression Integer
--E 104

--S 105 of 120
ode94a:=solve(ode94,y,x)
 

                             n log(x)
                         b %e                   - a log(x)
   (102)  [particular= - ------------,basis= [%e          ]]
                             n + a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                             n log(x)
--R                         b %e                   - a log(x)
--R   (102)  [particular= - ------------,basis= [%e          ]]
--R                             n + a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 105

--S 106 of 120
yx:=ode94a.particular
 

                n log(x)
            b %e
   (103)  - ------------
                n + a
                                                     Type: Expression Integer
--R
--R                n log(x)
--R            b %e
--R   (103)  - ------------
--R                n + a
--R                                                     Type: Expression Integer
--E 106

--S 107 of 120
ode94expr := x*D(yx,x) +a*yx + b*x**n
 

                n log(x)      n
   (104)  - b %e         + b x
                                                     Type: Expression Integer
--R
--R                n log(x)      n
--R   (104)  - b %e         + b x
--R                                                     Type: Expression Integer
--E 107

--S 108 of 120
exprule := rule x^n == %e^(n*log(x))
 

           n      n log(x)
   (105)  x  == %e
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           n      n log(x)
--R   (105)  x  == %e
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 108

--S 109 of 120
exprule ode94expr
 

   (106)  0
                                                     Type: Expression Integer
--R
--R   (106)  0
--R                                                     Type: Expression Integer
--E 109

--S 110 of 120
ode95 := x*D(y(x),x) + y(x)**2 + x**2
 

            ,          2    2
   (107)  xy (x) + y(x)  + x

                                                     Type: Expression Integer
--R
--R            ,          2    2
--R   (107)  xy (x) + y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 110

--S 111 of 120
ode95a:=solve(ode95,y,x)
 

   (108)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (108)  "failed"
--R                                                    Type: Union("failed",...)
--E 111

--S 112 of 120
ode96 := x*D(y(x),x) - y(x)**2 + 1
 

            ,          2
   (109)  xy (x) - y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R            ,          2
--R   (109)  xy (x) - y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 112

--S 113 of 120
yx:=solve(ode96,y,x)
 

               - x y(x) - x
   (110)  ----------------------
           +--------+ +--------+
          \|y(x) - 1 \|y(x) + 1
                                          Type: Union(Expression Integer,...)
--R
--R               - x y(x) - x
--R   (110)  ----------------------
--R           +--------+ +--------+
--R          \|y(x) - 1 \|y(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 113

--S 114 of 120
ode96expr := x*D(yx,x) - yx**2 + 1
 

   (111)
    2 ,           2             2      +--------+ +--------+         2
   x y (x) + ((- x  + 1)y(x) - x  - 1)\|y(x) - 1 \|y(x) + 1  - x y(x)  + x

   -----------------------------------------------------------------------
                                  +--------+ +--------+
                       (y(x) - 1)\|y(x) - 1 \|y(x) + 1
                                                     Type: Expression Integer
--R
--R   (111)
--R    2 ,           2             2      +--------+ +--------+         2
--R   x y (x) + ((- x  + 1)y(x) - x  - 1)\|y(x) - 1 \|y(x) + 1  - x y(x)  + x
--R
--R   -----------------------------------------------------------------------
--R                                  +--------+ +--------+
--R                       (y(x) - 1)\|y(x) - 1 \|y(x) + 1
--R                                                     Type: Expression Integer
--E 114

--S 115 of 120
ode98 := x*D(y(x),x) + a*y(x)**2 - b*y(x) + c*x**(2*b)
 

            ,         2b         2
   (112)  xy (x) + c x   + a y(x)  - b y(x)

                                                     Type: Expression Integer
--R 
--R
--R            ,         2b         2
--R   (112)  xy (x) + c x   + a y(x)  - b y(x)
--R
--R                                                     Type: Expression Integer
--E 115

--S 116 of 120
ode98a:=solve(ode98,y,x)
 

   (113)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (113)  "failed"
--R                                                    Type: Union("failed",...)
--E 116

--S 117 of 120
ode99 := x*D(y(x),x) + a*y(x)**2 - b*y(x) - c*x**beta
 

            ,         beta         2
   (114)  xy (x) - c x     + a y(x)  - b y(x)

                                                     Type: Expression Integer
--R 
--R
--R            ,         beta         2
--R   (114)  xy (x) - c x     + a y(x)  - b y(x)
--R
--R                                                     Type: Expression Integer
--E 117

--S 118 of 120
ode99a:=solve(ode99,y,x)
 

   (115)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (115)  "failed"
--R                                                    Type: Union("failed",...)
--E 118

--S 119 of 120
ode100 := x*D(y(x),x) + x*y(x)**2 + a
 

            ,            2
   (116)  xy (x) + x y(x)  + a

                                                     Type: Expression Integer
--R 
--R
--R            ,            2
--R   (116)  xy (x) + x y(x)  + a
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 120
ode100a:=solve(ode100,y,x)
 

   (117)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (117)  "failed"
--R                                                    Type: Union("failed",...)
--E 120
)spool
 
Starts dribbling to exsum.output (2009/2/17, 17:45:56).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 13
sum(k * x**k,k = 1..n)
 

            2               n
        (n x  + (- n - 1)x)x  + x
   (1)  -------------------------
                2
               x  - 2x + 1
                                                     Type: Expression Integer
--R 
--R
--R            2               n
--R        (n x  + (- n - 1)x)x  + x
--R   (1)  -------------------------
--R                2
--R               x  - 2x + 1
--R                                                     Type: Expression Integer
--E 1

)clear all
 
   All user variables and function definitions have been cleared.

--S 2 of 13
limit( sum(1/(k * (k + 2)),k = 1..n) ,n = %plusInfinity)
 

        3
   (1)  -
        4
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R        3
--R   (1)  -
--R        4
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 2

)clear all
 
   All user variables and function definitions have been cleared.

--S 3 of 13
s := sum(k**2,k = a..b)
 

          3     2         3     2
        2b  + 3b  + b - 2a  + 3a  - a
   (1)  -----------------------------
                      6
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          3     2         3     2
--R        2b  + 3b  + b - 2a  + 3a  - a
--R   (1)  -----------------------------
--R                      6
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 13
eval(s,[a,b],[1,25])
 

   (2)  5525
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (2)  5525
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 13
reduce(+,[i**2 for i in 1..25])
 

   (3)  5525
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  5525
--R                                                        Type: PositiveInteger
--E 5

)clear all
 
   All user variables and function definitions have been cleared.

--S 6 of 13
sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))
 

   (1)
            3      2           3      2               2             2        2
       (128b  + 48b  + 4b - 54a  + 27a  - 3a)d + (192b  + 48b - 108a  + 36a)c
     + 
           2             2
       192b  + 48b - 108a  + 36a
  /
        2
     (2c  + 2)d
                                 Type: Union(Fraction Polynomial Integer,...)
--R 
--R
--R   (1)
--R            3      2           3      2               2             2        2
--R       (128b  + 48b  + 4b - 54a  + 27a  - 3a)d + (192b  + 48b - 108a  + 36a)c
--R     + 
--R           2             2
--R       192b  + 48b - 108a  + 36a
--R  /
--R        2
--R     (2c  + 2)d
--R                                 Type: Union(Fraction Polynomial Integer,...)
--E 6

)clear all
 
   All user variables and function definitions have been cleared.

--S 7 of 13
[i for i in 1..15]
 

   (1)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
--R                                                   Type: List PositiveInteger
--E 7

--S 8 of 13
reduce(+,[i for i in 1..15])
 

   (2)  120
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  120
--R                                                        Type: PositiveInteger
--E 8

)clear all
 
   All user variables and function definitions have been cleared.

--S 9 of 13
reduce(+,[1.0/factorial(n) for n in 0..20])
 

   (1)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (1)  2.7182818284 590452354
--R                                                                  Type: Float
--E 9

)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 13
[n**2 for n in 5..20]
 

   (1)  [25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400]
--R                                                   Type: List PositiveInteger
--E 10

--S 11 of 13
reduce(+,[n**2 for n in 5..20])
 

   (2)  2840
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  2840
--R                                                        Type: PositiveInteger
--E 11

)clear all
 
   All user variables and function definitions have been cleared.

--S 12 of 13
sum(k**3,k = 1..n)
 

         4     3    2
        n  + 2n  + n
   (1)  -------------
              4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         4     3    2
--R        n  + 2n  + n
--R   (1)  -------------
--R              4
--R                                            Type: Fraction Polynomial Integer
--E 12

--S 13 of 13
sum(k,k = 1..n) ** 2
 

         4     3    2
        n  + 2n  + n
   (2)  -------------
              4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         4     3    2
--R        n  + 2n  + n
--R   (2)  -------------
--R              4
--R                                            Type: Fraction Polynomial Integer
--E 13
)spool 
 
Starts dribbling to farray.output (2009/2/17, 17:45:57).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 16
flexibleArray [i for i in 1..6]
 

   (1)  [1,2,3,4,5,6]
                                          Type: FlexibleArray PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6]
--R                                          Type: FlexibleArray PositiveInteger
--E 1

--S 2 of 16
f : FARRAY INT := new(6,0)
 

   (2)  [0,0,0,0,0,0]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0]
--R                                                  Type: FlexibleArray Integer
--E 2

--S 3 of 16
for i in 1..6 repeat f.i := i; f
 

   (3)  [1,2,3,4,5,6]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6]
--R                                                  Type: FlexibleArray Integer
--E 3

--S 4 of 16
physicalLength f
 

   (4)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  6
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 16
concat!(f,11)
 

   (5)  [1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (5)  [1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 5

--S 6 of 16
physicalLength f
 

   (6)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  10
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 16
physicalLength!(f,15)
 

   (7)  [1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (7)  [1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 7

--S 8 of 16
concat!(f,f)
 

   (8)  [1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (8)  [1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 8

--S 9 of 16
insert!(22,f,1)
 

   (9)  [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (9)  [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 9

--S 10 of 16
g := f(10..)
 

   (10)  [2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (10)  [2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 10

--S 11 of 16
insert!(g,f,1)
 

   (11)  [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (11)  [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 11

--S 12 of 16
merge!(sort! f, sort! g)
 

   (12)  [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (12)  [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22]
--R                                                  Type: FlexibleArray Integer
--E 12

--S 13 of 16
removeDuplicates! f
 

   (13)  [1,2,3,4,5,6,11,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (13)  [1,2,3,4,5,6,11,22]
--R                                                  Type: FlexibleArray Integer
--E 13

--S 14 of 16
select!(i +-> even? i,f)
 

   (14)  [2,4,6,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (14)  [2,4,6,22]
--R                                                  Type: FlexibleArray Integer
--E 14

--S 15 of 16
physicalLength f
 

   (15)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  8
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 16
shrinkable(false)$FlexibleArray(Integer)
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16
)spool 
 
Starts dribbling to op.output (2009/2/17, 17:55:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 2
abs(x)
 

   (1)  abs(x)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  abs(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 2
eval(%,x=-3.4)
 

   (2)  3.4
                                                       Type: Expression Float
--R 
--R
--R   (2)  3.4
--R                                                       Type: Expression Float
--E 2
)spool 
 
Starts dribbling to triglim.output (2009/2/17, 18:1:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 6
limit(atan(1/sin(x)),x = 0)
 

                          %pi                 %pi
   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 1

--S 2 of 6
limit(atan(sqrt(1 - x**2)/x),x = 0)
 

                          %pi                 %pi
   (2)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (2)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 2

--S 3 of 6
limit(atan(-sin(x)/(cos(x) + a)),x = acos(-a))
 

                          %pi                 %pi
   (3)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (3)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 3

--S 4 of 6
limit(atan(sin(x)/(cos(x) + a)),x = acos(-a))
 

                        %pi                   %pi
   (4)  [leftHandLimit= ---,rightHandLimit= - ---]
                         2                     2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                        %pi                   %pi
--R   (4)  [leftHandLimit= ---,rightHandLimit= - ---]
--R                         2                     2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 4

--S 5 of 6
limit(atan(1/(cos(x) + a)),x = acos(-a))
 

                        %pi                   %pi
   (5)  [leftHandLimit= ---,rightHandLimit= - ---]
                         2                     2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                        %pi                   %pi
--R   (5)  [leftHandLimit= ---,rightHandLimit= - ---]
--R                         2                     2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 5

--S 6 of 6
limit(atan(1/(sin(x) + a)),x = asin(-a))
 

                          %pi                 %pi
   (6)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (6)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 6
)spool 
 
Starts dribbling to lodo3.output (2009/2/17, 17:52:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 16
Dx: LODO(EXPR INT, f +-> D(f, x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 16
Dx := D()
 

   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1403 envArg,SPADCALL(G1403,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R   (2)  D
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1405 envArg,SPADCALL(G1405,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 2

--S 3 of 16
Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1
 

                       3
         3    G     - x  + H
   (3)  D  + -- D + --------
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1403 envArg,SPADCALL(G1403,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R                       3
--R         3    G     - x  + H
--R   (3)  D  + -- D + --------
--R              2         3
--R             x         x
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1405 envArg,SPADCALL(G1405,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 3

--S 4 of 16
n == 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 16
phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 16
phi1 ==  Dop(phi) / exp x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 16
phi2 == phi1 *x**(n+3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 16
phi3 == retract(phi2)@(POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 16
pans == phi3 ::UP(x,POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 16
pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 16
leq == solve(pans1,[subscript(s,[i]) for i in 1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling function G1529 with type Integer -> Boolean 

   (12)
                           2                                3        2
         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
          0        0     0       0         0       0      0        0        0
   [[s = ---,s = ------------------,s = --------------------------------------]]
      1   3   2          18          3                    162
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--I   Compiling function G3350 with type Integer -> Boolean 
--R
--R   (12)
--R                           2                                3        2
--R         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
--R          0        0     0       0         0       0      0        0        0
--R   [[s = ---,s = ------------------,s = --------------------------------------]]
--R      1   3   2          18          3                    162
--R                         Type: List List Equation Fraction Polynomial Integer
--E 12

--S 13 of 16
n==4
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 13

--S 14 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (14)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 14

--S 15 of 16
n==7
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 15

--S 16 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ,

       s  =
        5
                               2         3          2
             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
                  0         0          0          0           0          0
           + 
                5        4          3          2
             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
              0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                   4          3           2                                6
             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
                 0          0           0            0            0      0
           + 
                  5          4           3           2
             90s G  + 2628s G  + 27864s G  + 90720s G
                0          0           0           0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                    3           2                            2
             (945s G  + 81648s G  + 2082996s G + 14171760s )H
                  0           0             0             0
           + 
                   5          4            3             2
             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
                 0          0            0             0              0
           + 
                7         6          5           4             3              2
             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
              0         0          0           0             0              0
           + 
             - 97977600s G
                        0
        /
           11022480
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (16)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ,
--R
--R       s  =
--R        5
--R                               2         3          2
--R             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
--R                  0         0          0          0           0          0
--R           + 
--R                5        4          3          2
--R             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
--R              0        0          0          0           0
--R        /
--R           29160
--R       ,
--R
--R       s  =
--R        6
--R                   3          2                        2
--R             405s H  + (405s G  + 18468s G + 174960s )H
--R                 0          0           0           0
--R           + 
--R                   4          3           2                                6
--R             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
--R                 0          0           0            0            0      0
--R           + 
--R                  5          4           3           2
--R             90s G  + 2628s G  + 27864s G  + 90720s G
--R                0          0           0           0
--R        /
--R           524880
--R       ,
--R
--R       s  =
--R        7
--R                                 3
--R             (2835s G + 91854s )H
--R                   0          0
--R           + 
--R                    3           2                            2
--R             (945s G  + 81648s G  + 2082996s G + 14171760s )H
--R                  0           0             0             0
--R           + 
--R                   5          4            3             2
--R             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
--R                 0          0            0             0              0
--R           + 
--R                7         6          5           4             3              2
--R             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
--R              0         0          0           0             0              0
--R           + 
--R             - 97977600s G
--R                        0
--R        /
--R           11022480
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 16
)spool 
 
Starts dribbling to array1.output (2009/2/17, 17:43:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 9
oneDimensionalArray [i**2 for i in 1..10]
 

   (1)  [1,4,9,16,25,36,49,64,81,100]
                                    Type: OneDimensionalArray PositiveInteger
--R 
--R
--R   (1)  [1,4,9,16,25,36,49,64,81,100]
--R                                    Type: OneDimensionalArray PositiveInteger
--E 1

--S 2 of 9
a : ARRAY1 INT := new(10,0)
 

   (2)  [0,0,0,0,0,0,0,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0,0,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 2

--S 3 of 9
for i in 1..10 repeat a.i := i; a
 

   (3)  [1,2,3,4,5,6,7,8,9,10]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10]
--R                                            Type: OneDimensionalArray Integer
--E 3

--S 4 of 9
map!(i +-> i ** 2,a); a
 

   (4)  [1,4,9,16,25,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (4)  [1,4,9,16,25,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 4

--S 5 of 9
reverse! a
 

   (5)  [100,81,64,49,36,25,16,9,4,1]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (5)  [100,81,64,49,36,25,16,9,4,1]
--R                                            Type: OneDimensionalArray Integer
--E 5

--S 6 of 9
swap!(a,4,5); a
 

   (6)  [100,81,64,36,49,25,16,9,4,1]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (6)  [100,81,64,36,49,25,16,9,4,1]
--R                                            Type: OneDimensionalArray Integer
--E 6

--S 7 of 9
sort! a
 

   (7)  [1,4,9,16,25,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (7)  [1,4,9,16,25,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 7

--S 8 of 9
b := a(6..10)
 

   (8)  [36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (8)  [36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 8

--S 9 of 9
copyInto!(a,b,1)
 

   (9)  [36,49,64,81,100,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (9)  [36,49,64,81,100,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 9
)spool
 
Starts dribbling to mpoly.output (2009/2/17, 17:55:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 10
m : MPOLY([x,y],INT) := (x**2 - x*y**3 +3*y)**2
 

         4     3 3     6       2     4      2
   (1)  x  - 2y x  + (y  + 6y)x  - 6y x + 9y
                                  Type: MultivariatePolynomial([x,y],Integer)
--R 
--R
--R         4     3 3     6       2     4      2
--R   (1)  x  - 2y x  + (y  + 6y)x  - 6y x + 9y
--R                                  Type: MultivariatePolynomial([x,y],Integer)
--E 1

--S 2 of 10
m :: MPOLY([y,x],INT)
 

         2 6       4     3 3     2     2     4
   (2)  x y  - 6x y  - 2x y  + 9y  + 6x y + x
                                  Type: MultivariatePolynomial([y,x],Integer)
--R 
--R
--R         2 6       4     3 3     2     2     4
--R   (2)  x y  - 6x y  - 2x y  + 9y  + 6x y + x
--R                                  Type: MultivariatePolynomial([y,x],Integer)
--E 2

--S 3 of 10
p : MPOLY([x,y],POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 10
p := (a**2*x - b*y**2 + 1)**2
 

         4 2        2   2     2      2 4       2
   (4)  a x  + (- 2a b y  + 2a )x + b y  - 2b y  + 1
                       Type: MultivariatePolynomial([x,y],Polynomial Integer)
--R 
--R
--R         4 2        2   2     2      2 4       2
--R   (4)  a x  + (- 2a b y  + 2a )x + b y  - 2b y  + 1
--R                       Type: MultivariatePolynomial([x,y],Polynomial Integer)
--E 4

--S 5 of 10
p :: POLY INT
 

         2 4        2          2    4 2     2
   (5)  b y  + (- 2a b x - 2b)y  + a x  + 2a x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2 4        2          2    4 2     2
--R   (5)  b y  + (- 2a b x - 2b)y  + a x  + 2a x + 1
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 10
% :: MPOLY([a,b],POLY INT)
 

         2 4          2        2    4 2     2
   (6)  x a  + (- 2x y b + 2x)a  + y b  - 2y b + 1
                       Type: MultivariatePolynomial([a,b],Polynomial Integer)
--R 
--R
--R         2 4          2        2    4 2     2
--R   (6)  x a  + (- 2x y b + 2x)a  + y b  - 2y b + 1
--R                       Type: MultivariatePolynomial([a,b],Polynomial Integer)
--E 6

--S 7 of 10
q : UP(x, FRAC MPOLY([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 10
q := (x**2 - x*(z+1)/y +2)**2
 

                             2    2
         4   - 2z - 2  3   4y  + z  + 2z + 1  2   - 4z - 4
   (8)  x  + -------- x  + ----------------- x  + -------- x + 4
                 y                  2                 y
                                   y
 Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer))
--R 
--R
--R                             2    2
--R         4   - 2z - 2  3   4y  + z  + 2z + 1  2   - 4z - 4
--R   (8)  x  + -------- x  + ----------------- x  + -------- x + 4
--R                 y                  2                 y
--R                                   y
--R Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer))
--E 8

--S 9 of 10
q :: UP(z, FRAC MPOLY([x,y],INT))
 

   (9)
    2            3     2             2 4       3      2      2            2
   x   2   - 2y x  + 2x  - 4y x     y x  - 2y x  + (4y  + 1)x  - 4y x + 4y
   -- z  + -------------------- z + ---------------------------------------
    2                2                                  2
   y                y                                  y
 Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer))
--R 
--R
--R   (9)
--R    2            3     2             2 4       3      2      2            2
--R   x   2   - 2y x  + 2x  - 4y x     y x  - 2y x  + (4y  + 1)x  - 4y x + 4y
--R   -- z  + -------------------- z + ---------------------------------------
--R    2                2                                  2
--R   y                y                                  y
--R Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer))
--E 9

--S 10 of 10
q :: MPOLY([x,z], FRAC UP(y,INT))
 

                                                2
          4      2     2  3     1  2    2     4y  + 1  2      4     4
   (10)  x  + (- - z - -)x  + (-- z  + -- z + -------)x  + (- - z - -)x + 4
                 y     y        2       2         2           y     y
                               y       y         y
 Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer))
--R 
--R
--R                                                2
--R          4      2     2  3     1  2    2     4y  + 1  2      4     4
--R   (10)  x  + (- - z - -)x  + (-- z  + -- z + -------)x  + (- - z - -)x + 4
--R                 y     y        2       2         2           y     y
--R                               y       y         y
--R Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer))
--E 10
)spool 
 
Starts dribbling to summation.output (2009/2/17, 18:0:53).
)set message test on
 
)set output mathml on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 5
summation(i^2,i=a..b)^(d-c)
 

         b      d - c
        --+    2
   (1)  >     i
        --+
        i= a
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>)</mo></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         b      d - c
--R        --+    2
--R   (1)  >     i
--R        --+
--R        i= a
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>)</mo></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 1
--S 2 of 5
summation(i^2^(d-c),i=a..b)
 

         b      d - c
        --+    2
   (2)  >     i
        --+
        i= a
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow></mrow></msup></mrow></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         b      d - c
--R        --+    2
--R   (2)  >     i
--R        --+
--R        i= a
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow></mrow></msup></mrow></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 2
--S 3 of 5
sum(operator(f) (i)+1,i=1..n)
 

         n
        --+
   (3)  >     f(i) + 1
        --+
        i= 1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         n
--R        --+
--R   (3)  >     f(i) + 1
--R        --+
--R        i= 1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 3
--S 4 of 5
sum(operator(f) (i),i=1..n)+1
 

         n
        --+
   (4)  >     f(i) + 1
        --+
        i= 1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo><mo>+</mo><mn>1</mn></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         n
--R        --+
--R   (4)  >     f(i) + 1
--R        --+
--R        i= 1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo><mo>+</mo><mn>1</mn></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 4
--S 5 of 5
sum(operator(f) (i)+1,i=1..n)^3
 

         n            3
        --+
   (5)  >     f(i) + 1
        --+
        i= 1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         n            3
--R        --+
--R   (5)  >     f(i) + 1
--R        --+
--R        i= 1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 5
)spool 
 
Starts dribbling to intdeq.output (2009/2/17, 17:46:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 7
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 7
deq := differentiate(y x, x, 2) + 2*w[0]*differentiate(y x, x) + w[0]**2*y x
 

         ,,          ,        2
   (2)  y  (x) + 2w y (x) + w  y(x)
                   0         0
                                                     Type: Expression Integer
--R 
--R
--R         ,,          ,        2
--R   (2)  y  (x) + 2w y (x) + w  y(x)
--R                   0         0
--R                                                     Type: Expression Integer
--E 2

--S 3 of 7
sol:= solve(deq = sin (w*x), y, x=0,[0,0])
 

                                                      - w x
            2     2               3     2                0
        (- w  + w  )sin(w x) + ((w  + w  w)x + 2w w)%e      - 2w w cos(w x)
                 0                     0         0              0
   (3)  -------------------------------------------------------------------
                                  4      2 2     4
                                 w  + 2w  w  + w
                                        0       0
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                      - w x
--R            2     2               3     2                0
--R        (- w  + w  )sin(w x) + ((w  + w  w)x + 2w w)%e      - 2w w cos(w x)
--R                 0                     0         0              0
--R   (3)  -------------------------------------------------------------------
--R                                  4      2 2     4
--R                                 w  + 2w  w  + w
--R                                        0       0
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 7
work:= sol *sin(w*x)
 

   (4)
           2     2         2
       (- w  + w  )sin(w x)
                0
     + 
                               - w x
           3     2                0
       (((w  + w  w)x + 2w w)%e      - 2w w cos(w x))sin(w x)
                0         0              0
  /
      4      2 2     4
     w  + 2w  w  + w
            0       0
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R           2     2         2
--R       (- w  + w  )sin(w x)
--R                0
--R     + 
--R                               - w x
--R           3     2                0
--R       (((w  + w  w)x + 2w w)%e      - 2w w cos(w x))sin(w x)
--R                0         0              0
--R  /
--R      4      2 2     4
--R     w  + 2w  w  + w
--R            0       0
--R                                                     Type: Expression Integer
--E 4

--S 5 of 7
integrate(work,x)
 

   (5)
                                                - w x
                  4      3 2       4      2 2      0      4     4
         (((- 2w w  - 2w  w )x + 2w  - 6w  w )%e      + (w  - w  )cos(w x))
                0       0                0                     0
      *
         sin(w x)
     + 
                                            - w x
             5      2 3         3              0         3      3          2
       ((- 2w  - 2w  w )x - 8w w )cos(w x)%e      + (2w w  + 2w  w)cos(w x)
                   0          0                        0       0
     + 
           5     4
       (- w  + w  w)x
                0
  /
       7      2 5      4 3      6
     2w  + 6w  w  + 6w  w  + 2w  w
             0        0        0
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)
--R                                                - w x
--R                  4      3 2       4      2 2      0      4     4
--R         (((- 2w w  - 2w  w )x + 2w  - 6w  w )%e      + (w  - w  )cos(w x))
--R                0       0                0                     0
--R      *
--R         sin(w x)
--R     + 
--R                                            - w x
--R             5      2 3         3              0         3      3          2
--R       ((- 2w  - 2w  w )x - 8w w )cos(w x)%e      + (2w w  + 2w  w)cos(w x)
--R                   0          0                        0       0
--R     + 
--R           5     4
--R       (- w  + w  w)x
--R                0
--R  /
--R       7      2 5      4 3      6
--R     2w  + 6w  w  + 6w  w  + 2w  w
--R             0        0        0
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 7
D(%,x)-work
 

          2     2         2     2     2         2    2     2
        (w  - w  )sin(w x)  + (w  - w  )cos(w x)  - w  + w
               0                     0                    0
   (6)  ----------------------------------------------------
                           4      2 2      4
                         2w  + 4w  w  + 2w
                                 0        0
                                                     Type: Expression Integer
--R 
--R
--R          2     2         2     2     2         2    2     2
--R        (w  - w  )sin(w x)  + (w  - w  )cos(w x)  - w  + w
--R               0                     0                    0
--R   (6)  ----------------------------------------------------
--R                           4      2 2      4
--R                         2w  + 4w  w  + 2w
--R                                 0        0
--R                                                     Type: Expression Integer
--E 6

--S 7 of 7
simplify %
 

   (7)  0
                                                     Type: Expression Integer
--R 
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E 7
)spool 
 
Starts dribbling to poly1.output (2009/2/17, 17:56:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 46
x + 1
 

   (1)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  x + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 46
z - 2.3
 

   (2)  z - 2.3
                                                       Type: Polynomial Float
--R 
--R
--R   (2)  z - 2.3
--R                                                       Type: Polynomial Float
--E 2

--S 3 of 46
y**2 - z + 3/4
 

               2   3
   (3)  - z + y  + -
                   4
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2   3
--R   (3)  - z + y  + -
--R                   4
--R                                            Type: Polynomial Fraction Integer
--E 3

--S 4 of 46
y **2 + x*y + y
 

         2
   (4)  y  + (x + 1)y
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (4)  y  + (x + 1)y
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 46
% :: DMP([y,x],INT)
 

         2
   (5)  y  + y x + y
                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--R 
--R
--R         2
--R   (5)  y  + y x + y
--R                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--E 5

--S 6 of 46
p := (y-1)**2 * x * z
 

            2
   (6)  (x y  - 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (6)  (x y  - 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 46
q := (y-1) * x * (z+5)
 

   (7)  (x y - x)z + 5x y - 5x
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  (x y - x)z + 5x y - 5x
--R                                                     Type: Polynomial Integer
--E 7

--S 8 of 46
factor(q)
 

   (8)  x(y - 1)(z + 5)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (8)  x(y - 1)(z + 5)
--R                                            Type: Factored Polynomial Integer
--E 8

--S 9 of 46
p - q**2
 

   (9)
         2 2     2     2  2          2      2       2             2
     (- x y  + 2x y - x )z  + ((- 10x  + x)y  + (20x  - 2x)y - 10x  + x)z
   + 
          2 2      2       2
     - 25x y  + 50x y - 25x
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)
--R         2 2     2     2  2          2      2       2             2
--R     (- x y  + 2x y - x )z  + ((- 10x  + x)y  + (20x  - 2x)y - 10x  + x)z
--R   + 
--R          2 2      2       2
--R     - 25x y  + 50x y - 25x
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 46
gcd(p,q)
 

   (10)  x y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)  x y - x
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 46
factor %
 

   (11)  x(y - 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (11)  x(y - 1)
--R                                            Type: Factored Polynomial Integer
--E 11

--S 12 of 46
lcm(p,q)
 

             2             2        2
   (12)  (x y  - 2x y + x)z  + (5x y  - 10x y + 5x)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2             2        2
--R   (12)  (x y  - 2x y + x)z  + (5x y  - 10x y + 5x)z
--R                                                     Type: Polynomial Integer
--E 12

--S 13 of 46
content p
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 46
resultant(p,q,z)
 

           2 3      2 2      2      2
   (14)  5x y  - 15x y  + 15x y - 5x
                                                     Type: Polynomial Integer
--R 
--R
--R           2 3      2 2      2      2
--R   (14)  5x y  - 15x y  + 15x y - 5x
--R                                                     Type: Polynomial Integer
--E 14

--S 15 of 46
resultant(p,q,x)
 

   (15)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  0
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 46
mainVariable p
 

   (16)  z
                                                      Type: Union(Symbol,...)
--R 
--R
--R   (16)  z
--R                                                      Type: Union(Symbol,...)
--E 16

--S 17 of 46
mainVariable(1 :: POLY INT)
 

   (17)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (17)  "failed"
--R                                                    Type: Union("failed",...)
--E 17

--S 18 of 46
ground? p
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 46
ground?(1 :: POLY INT)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19

--S 20 of 46
variables p
 

   (20)  [z,y,x]
                                                            Type: List Symbol
--R 
--R
--R   (20)  [z,y,x]
--R                                                            Type: List Symbol
--E 20

--S 21 of 46
degree(p,x)
 

   (21)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  1
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 46
degree(p,y)
 

   (22)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  2
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 46
degree(p,z)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 46
degree(p,[x,y,z])
 

   (24)  [1,2,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (24)  [1,2,1]
--R                                                Type: List NonNegativeInteger
--E 24

--S 25 of 46
minimumDegree(p,z)
 

   (25)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  1
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 46
totalDegree p
 

   (26)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  4
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 46
leadingMonomial p
 

            2
   (27)  x y z
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (27)  x y z
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 46
reductum p
 

   (28)  (- 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R   (28)  (- 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 28

--S 29 of 46
p - leadingMonomial p - reductum p
 

   (29)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (29)  0
--R                                                     Type: Polynomial Integer
--E 29

--S 30 of 46
leadingCoefficient p
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 46
p
 

             2
   (31)  (x y  - 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (31)  (x y  - 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 46
eval(p,x,w)
 

             2
   (32)  (w y  - 2w y + w)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (32)  (w y  - 2w y + w)z
--R                                                     Type: Polynomial Integer
--E 32

--S 33 of 46
eval(p,x,1)
 

           2
   (33)  (y  - 2y + 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (33)  (y  - 2y + 1)z
--R                                                     Type: Polynomial Integer
--E 33

--S 34 of 46
eval(p,x,y**2 - 1)
 

           4     3
   (34)  (y  - 2y  + 2y - 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           4     3
--R   (34)  (y  - 2y  + 2y - 1)z
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 46
D(p,x)
 

           2
   (35)  (y  - 2y + 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (35)  (y  - 2y + 1)z
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 46
D(p,y)
 

   (36)  (2x y - 2x)z
                                                     Type: Polynomial Integer
--R 
--R
--R   (36)  (2x y - 2x)z
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 46
D(p,z)
 

            2
   (37)  x y  - 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (37)  x y  - 2x y + x
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 46
integrate(p,y)
 

          1    3      2
   (38)  (- x y  - x y  + x y)z
          3
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1    3      2
--R   (38)  (- x y  - x y  + x y)z
--R          3
--R                                            Type: Polynomial Fraction Integer
--E 38

--S 39 of 46
qr := monicDivide(p,x+1,x)
 

                      2                           2
   (39)  [quotient= (y  - 2y + 1)z,remainder= (- y  + 2y - 1)z]
     Type: Record(quotient: Polynomial Integer,remainder: Polynomial Integer)
--R 
--R
--R                      2                           2
--R   (39)  [quotient= (y  - 2y + 1)z,remainder= (- y  + 2y - 1)z]
--R     Type: Record(quotient: Polynomial Integer,remainder: Polynomial Integer)
--E 39

--S 40 of 46
qr.remainder
 

             2
   (40)  (- y  + 2y - 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (40)  (- y  + 2y - 1)z
--R                                                     Type: Polynomial Integer
--E 40

--S 41 of 46
p - ((x+1) * qr.quotient + qr.remainder)
 

   (41)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (41)  0
--R                                                     Type: Polynomial Integer
--E 41

--S 42 of 46
p/q
 

         (y - 1)z
   (42)  --------
           z + 5
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         (y - 1)z
--R   (42)  --------
--R           z + 5
--R                                            Type: Fraction Polynomial Integer
--E 42

--S 43 of 46
(2/3) * x**2 - y + 4/5
 

               2  2   4
   (43)  - y + - x  + -
               3      5
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2  2   4
--R   (43)  - y + - x  + -
--R               3      5
--R                                            Type: Polynomial Fraction Integer
--E 43

--S 44 of 46
% :: FRAC POLY INT
 

                    2
         - 15y + 10x  + 12
   (44)  -----------------
                 15
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                    2
--R         - 15y + 10x  + 12
--R   (44)  -----------------
--R                 15
--R                                            Type: Fraction Polynomial Integer
--E 44

--S 45 of 46
% :: POLY FRAC INT
 

               2  2   4
   (45)  - y + - x  + -
               3      5
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2  2   4
--R   (45)  - y + - x  + -
--R               3      5
--R                                            Type: Polynomial Fraction Integer
--E 45

--S 46 of 46
map(numeric,%)
 

                                            2
   (46)  - 1.0 y + 0.6666666666 6666666667 x  + 0.8
                                                       Type: Polynomial Float
--R 
--R
--R                                            2
--R   (46)  - 1.0 y + 0.6666666666 6666666667 x  + 0.8
--R                                                       Type: Polynomial Float
--E 46
)spool 
 
Starts dribbling to fib.output (2009/2/17, 17:46:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 4
fib(n | n=0)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 4
fib(n | n=1)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
fib(n | n>1)==fib(n-1)+fib(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
fibs == [fib i for i in 0..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
)spool 
 
Starts dribbling to grpthry.output (2009/2/17, 17:46:20).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 68
x : PERM INT := [[1,3,5],[7,11,9]]
 

   (1)  (1 3 5)(7 11 9)
                                                    Type: Permutation Integer
--R 
--R
--R   (1)  (1 3 5)(7 11 9)
--R                                                    Type: Permutation Integer
--E 1

--S 2 of 68
y : PERM INT := [[3,5,7,9]]
 

   (2)  (3 5 7 9)
                                                    Type: Permutation Integer
--R 
--R
--R   (2)  (3 5 7 9)
--R                                                    Type: Permutation Integer
--E 2

--S 3 of 68
z : PERM INT := [1,3,11]
 

   (3)  (1 3 11)
                                                    Type: Permutation Integer
--R 
--R
--R   (3)  (1 3 11)
--R                                                    Type: Permutation Integer
--E 3

--S 4 of 68
g1 : PERMGRP INT := [ x , y ]
 

   (4)  <(1 3 5)(7 11 9),(3 5 7 9)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (4)  <(1 3 5)(7 11 9),(3 5 7 9)>
--R                                               Type: PermutationGroup Integer
--E 4

--S 5 of 68
g2 : PERMGRP INT := [ x , z ]
 

   (5)  <(1 3 5)(7 11 9),(1 3 11)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (5)  <(1 3 5)(7 11 9),(1 3 11)>
--R                                               Type: PermutationGroup Integer
--E 5

--S 6 of 68
g3 : PERMGRP INT := [ y , z ]
 

   (6)  <(3 5 7 9),(1 3 11)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (6)  <(3 5 7 9),(1 3 11)>
--R                                               Type: PermutationGroup Integer
--E 6

--S 7 of 68
order g1
 

   (7)  720
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  720
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 68
degree g3
 

   (8)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  6
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 68
movedPoints g2
 

   (9)  {1,3,5,7,9,11}
                                                            Type: Set Integer
--R 
--R
--R   (9)  {1,3,5,7,9,11}
--R                                                            Type: Set Integer
--E 9

--S 10 of 68
orbit (g1, 3)
 

   (10)  {1,3,5,7,9,11}
                                                            Type: Set Integer
--R 
--R
--R   (10)  {1,3,5,7,9,11}
--R                                                            Type: Set Integer
--E 10

--S 11 of 68
orbits g3
 

   (11)  {{1,3,5,7,9,11}}
                                                        Type: Set Set Integer
--R 
--R
--R   (11)  {{1,3,5,7,9,11}}
--R                                                        Type: Set Set Integer
--E 11

--S 12 of 68
member? ( y , g2 )
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 68
)sh PERMGRP
 
 PermutationGroup S: SetCategory  is a domain constructor
 Abbreviation for PermutationGroup is PERMGRP 
 This constructor is exposed in this frame.
 Issue )edit permgrps.spad.pamphlet to see algebra source code for PERMGRP 

------------------------------- Operations --------------------------------
 ?<? : (%,%) -> Boolean                ?<=? : (%,%) -> Boolean
 ?=? : (%,%) -> Boolean                base : % -> List S
 coerce : List Permutation S -> %      coerce : % -> List Permutation S
 coerce : % -> OutputForm              degree : % -> NonNegativeInteger
 hash : % -> SingleInteger             latex : % -> String
 movedPoints : % -> Set S              orbit : (%,List S) -> Set List S
 orbit : (%,Set S) -> Set Set S        orbit : (%,S) -> Set S
 orbits : % -> Set Set S               order : % -> NonNegativeInteger
 random : % -> Permutation S           ?~=? : (%,%) -> Boolean
 ?.? : (%,NonNegativeInteger) -> Permutation S
 generators : % -> List Permutation S
 initializeGroupForWordProblem : (%,Integer,Integer) -> Void
 initializeGroupForWordProblem : % -> Void
 member? : (Permutation S,%) -> Boolean
 permutationGroup : List Permutation S -> %
 random : (%,Integer) -> Permutation S
 strongGenerators : % -> List Permutation S
 wordInGenerators : (Permutation S,%) -> List NonNegativeInteger
 wordInStrongGenerators : (Permutation S,%) -> List NonNegativeInteger
 wordsForStrongGenerators : % -> List List NonNegativeInteger

--R 
--R PermutationGroup S: SetCategory  is a domain constructor
--R Abbreviation for PermutationGroup is PERMGRP 
--R This constructor is exposed in this frame.
--R Issue )edit permgrps.spad.pamphlet to see algebra source code for PERMGRP 
--R
--R------------------------------- Operations --------------------------------
--R ?<? : (%,%) -> Boolean                ?<=? : (%,%) -> Boolean
--R ?=? : (%,%) -> Boolean                base : % -> List S
--R coerce : List Permutation S -> %      coerce : % -> List Permutation S
--R coerce : % -> OutputForm              degree : % -> NonNegativeInteger
--R hash : % -> SingleInteger             latex : % -> String
--R movedPoints : % -> Set S              orbit : (%,List S) -> Set List S
--R orbit : (%,Set S) -> Set Set S        orbit : (%,S) -> Set S
--R orbits : % -> Set Set S               order : % -> NonNegativeInteger
--R random : % -> Permutation S           ?~=? : (%,%) -> Boolean
--R ?.? : (%,NonNegativeInteger) -> Permutation S
--R generators : % -> List Permutation S
--R initializeGroupForWordProblem : (%,Integer,Integer) -> Void
--R initializeGroupForWordProblem : % -> Void
--R member? : (Permutation S,%) -> Boolean
--R permutationGroup : List Permutation S -> %
--R random : (%,Integer) -> Permutation S
--R strongGenerators : % -> List Permutation S
--R wordInGenerators : (Permutation S,%) -> List NonNegativeInteger
--R wordInStrongGenerators : (Permutation S,%) -> List NonNegativeInteger
--R wordsForStrongGenerators : % -> List List NonNegativeInteger
--R
--E 13

)clear all
 
   All user variables and function definitions have been cleared.

--S 14 of 68
ptn9 := partitions 9
 

   (1)
   [[9],[8,1],[7,2],[7,1,1],[6,3],[6,2,1],[6,1,1,1],[5,4],[5,3,1],[5,2,2],...]
                                                    Type: Stream List Integer
--R 
--R
--R   (1)
--R   [[9],[8,1],[7,2],[7,1,1],[6,3],[6,2,1],[6,1,1,1],[5,4],[5,3,1],[5,2,2],...]
--R                                                    Type: Stream List Integer
--E 14

--S 15 of 68
map(dimensionOfIrreducibleRepresentation, ptn9)
 

   (2)  [1,8,27,28,48,105,56,42,162,120,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (2)  [1,8,27,28,48,105,56,42,162,120,...]
--R                                              Type: Stream NonNegativeInteger
--E 15

--S 16 of 68
yt := listYoungTableaus [4,2]
 

   (3)
    +0  2  4  5+  +0  2  3  5+  +0  2  3  4+  +0  1  4  5+  +0  1  3  5+
   [|          |, |          |, |          |, |          |, |          |,
    +1  3  0  0+  +1  4  0  0+  +1  5  0  0+  +2  3  0  0+  +2  4  0  0+
    +0  1  3  4+  +0  1  2  5+  +0  1  2  4+  +0  1  2  3+
    |          |, |          |, |          |, |          |]
    +2  5  0  0+  +3  4  0  0+  +3  5  0  0+  +4  5  0  0+
                                                    Type: List Matrix Integer
--R 
--R
--R   (3)
--R    +0  2  4  5+  +0  2  3  5+  +0  2  3  4+  +0  1  4  5+  +0  1  3  5+
--R   [|          |, |          |, |          |, |          |, |          |,
--R    +1  3  0  0+  +1  4  0  0+  +1  5  0  0+  +2  3  0  0+  +2  4  0  0+
--R    +0  1  3  4+  +0  1  2  5+  +0  1  2  4+  +0  1  2  3+
--R    |          |, |          |, |          |, |          |]
--R    +2  5  0  0+  +3  4  0  0+  +3  5  0  0+  +4  5  0  0+
--R                                                    Type: List Matrix Integer
--E 16

--S 17 of 68
r1 := irreducibleRepresentation([4,2],[1,2,4,5,3,6])
 

        + 0   - 1  - 1   0    0    0    0    0    1 +
        |                                           |
        |- 1   0    0    0    0    0    0    0    0 |
        |                                           |
        | 1    1    1    0    0    0    0    0    0 |
        |                                           |
        | 0    1    0    0    0    0    0    0   - 1|
        |                                           |
   (4)  | 0    0    0    0    0    0    1    0    0 |
        |                                           |
        | 0    0    0    0    1    0    0    0    0 |
        |                                           |
        | 1    0    0    0    0    0   - 1  - 1   0 |
        |                                           |
        |- 1  - 1  - 1  - 1  - 1  - 1   0    0    0 |
        |                                           |
        + 0    0    0    1    0    0    0    0    0 +
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   - 1  - 1   0    0    0    0    0    1 +
--R        |                                           |
--R        |- 1   0    0    0    0    0    0    0    0 |
--R        |                                           |
--R        | 1    1    1    0    0    0    0    0    0 |
--R        |                                           |
--R        | 0    1    0    0    0    0    0    0   - 1|
--R        |                                           |
--R   (4)  | 0    0    0    0    0    0    1    0    0 |
--R        |                                           |
--R        | 0    0    0    0    1    0    0    0    0 |
--R        |                                           |
--R        | 1    0    0    0    0    0   - 1  - 1   0 |
--R        |                                           |
--R        |- 1  - 1  - 1  - 1  - 1  - 1   0    0    0 |
--R        |                                           |
--R        + 0    0    0    1    0    0    0    0    0 +
--R                                                         Type: Matrix Integer
--E 17

--S 18 of 68
r2 := irreducibleRepresentation([4,2],[3,2,1,5,6,4])
 

        + 0    0   - 1   0    0    0    0   - 1   0 +
        |                                           |
        | 1    0    1    0   - 1   0   - 1   0    0 |
        |                                           |
        | 0    0    0    0    1    0    0    0    0 |
        |                                           |
        | 0    0    0    0    0    0    0    1    0 |
        |                                           |
   (5)  |- 1   0    0   - 1   0    0    0    0    0 |
        |                                           |
        | 0    0    0    0    0    0    1    0    0 |
        |                                           |
        | 0    0   - 1   0    0   - 1   0   - 1  - 1|
        |                                           |
        | 0    0    0    0    0    0    0    0    1 |
        |                                           |
        + 0   - 1   0    0   - 1   0   - 1   0    0 +
                                                         Type: Matrix Integer
--R 
--R
--R        + 0    0   - 1   0    0    0    0   - 1   0 +
--R        |                                           |
--R        | 1    0    1    0   - 1   0   - 1   0    0 |
--R        |                                           |
--R        | 0    0    0    0    1    0    0    0    0 |
--R        |                                           |
--R        | 0    0    0    0    0    0    0    1    0 |
--R        |                                           |
--R   (5)  |- 1   0    0   - 1   0    0    0    0    0 |
--R        |                                           |
--R        | 0    0    0    0    0    0    1    0    0 |
--R        |                                           |
--R        | 0    0   - 1   0    0   - 1   0   - 1  - 1|
--R        |                                           |
--R        | 0    0    0    0    0    0    0    0    1 |
--R        |                                           |
--R        + 0   - 1   0    0   - 1   0   - 1   0    0 +
--R                                                         Type: Matrix Integer
--E 18

--S 19 of 68
r3 := irreducibleRepresentation([4,2],[4,2,1,3,6,5])
 

        +0   0    0   0   1    0    1    0    1 +
        |                                       |
        |0   0    0   0   0    1    0    1    0 |
        |                                       |
        |0   0    0   1   0    0    0    0    0 |
        |                                       |
        |0  - 1   0   0  - 1   0   - 1   0    0 |
        |                                       |
   (6)  |0   0   - 1  0   0   - 1   0   - 1  - 1|
        |                                       |
        |1   1    1   0   0    0    0    0    0 |
        |                                       |
        |0   0    0   0   0    0    0    0    1 |
        |                                       |
        |0   0    0   0   1    0    0    0    0 |
        |                                       |
        +0   0    0   0   0    1    0    0    0 +
                                                         Type: Matrix Integer
--R 
--R
--R        +0   0    0   0   1    0    1    0    1 +
--R        |                                       |
--R        |0   0    0   0   0    1    0    1    0 |
--R        |                                       |
--R        |0   0    0   1   0    0    0    0    0 |
--R        |                                       |
--R        |0  - 1   0   0  - 1   0   - 1   0    0 |
--R        |                                       |
--R   (6)  |0   0   - 1  0   0   - 1   0   - 1  - 1|
--R        |                                       |
--R        |1   1    1   0   0    0    0    0    0 |
--R        |                                       |
--R        |0   0    0   0   0    0    0    0    1 |
--R        |                                       |
--R        |0   0    0   0   1    0    0    0    0 |
--R        |                                       |
--R        +0   0    0   0   0    1    0    0    0 +
--R                                                         Type: Matrix Integer
--E 19

--S 20 of 68
(r3 = r1*r2) :: Boolean
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 20

--S 21 of 68
irreducibleRepresentation [4,4,1]
 

   (8)
   [
   [
     [- 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 0, - 1,
      0, - 1, - 1, - 1, 0, 1, 1, 0, 0, 0, 0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 1, 0,
      1, 1, 0, - 1, - 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1, 0, 1,
      0, 0, 1, 1, 0, 0, - 1, 0, - 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1,
      - 1, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, - 1,
      - 1, - 1, 0, 0, 1, 0, 0, 0, 0, 0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 1, 1, 0, 0, 0,
      0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 1, 0,
      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1,
      0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0,
      - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
      0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
      0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, - 1]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, - 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 1]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
     ]
     ]
                                                    Type: List Matrix Integer
--R 
--R
--R   (8)
--R   [
--R   [
--R     [- 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 0, - 1,
--R      0, - 1, - 1, - 1, 0, 1, 1, 0, 0, 0, 0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 1, 0,
--R      1, 1, 0, - 1, - 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1, 0, 1,
--R      0, 0, 1, 1, 0, 0, - 1, 0, - 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1,
--R      - 1, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      - 1, - 1, 0, 0, 1, 0, 0, 0, 0, 0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 1, 1, 0, 0, 0,
--R      0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 1, 0,
--R      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1,
--R      0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0,
--R      - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
--R      0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
--R      0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
--R      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
--R      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, - 1]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, - 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 1]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
--R     ,
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
--R     ,
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
--R     ]
--R     ,
--R
--R   [
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--R      0, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0,
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--R      0, 0, 0, 0, - 1, - 1, 0, - 2, - 1, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 1,
--R      1, 0]
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--R
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--R
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--R      0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0]
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--R      - 1, - 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]
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--R      0, 0, 0, 0, 0]
--R     ,
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--R      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0]
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--R     ,
--R
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--R
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--R      1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]
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--R      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
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--R      0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
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--R      0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]
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--R     ,
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--R      0, 0, 0, - 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
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--R      - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
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--R     [- 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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--R      0, 0, 0, 0, - 1, - 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
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--R      - 1, - 1, 0, - 1, - 1, 0, 0, 0, 0, - 1, - 1, - 1, - 1, 0, - 1, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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--R      0, - 1, - 1, - 1, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0]
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--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
--R     ]
--R     ]
--R                                                    Type: List Matrix Integer
--E 21

)clear all
 
   All user variables and function definitions have been cleared.

--S 22 of 68
permutationRepresentation [2,3,1,4,6,5,11,10,7,8,9]
 

        +0  0  1  0  0  0  0  0  0  0  0+
        |                               |
        |1  0  0  0  0  0  0  0  0  0  0|
        |                               |
        |0  1  0  0  0  0  0  0  0  0  0|
        |                               |
        |0  0  0  1  0  0  0  0  0  0  0|
        |                               |
        |0  0  0  0  0  1  0  0  0  0  0|
        |                               |
   (1)  |0  0  0  0  1  0  0  0  0  0  0|
        |                               |
        |0  0  0  0  0  0  0  0  1  0  0|
        |                               |
        |0  0  0  0  0  0  0  0  0  1  0|
        |                               |
        |0  0  0  0  0  0  0  0  0  0  1|
        |                               |
        |0  0  0  0  0  0  0  1  0  0  0|
        |                               |
        +0  0  0  0  0  0  1  0  0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  0  1  0  0  0  0  0  0  0  0+
--R        |                               |
--R        |1  0  0  0  0  0  0  0  0  0  0|
--R        |                               |
--R        |0  1  0  0  0  0  0  0  0  0  0|
--R        |                               |
--R        |0  0  0  1  0  0  0  0  0  0  0|
--R        |                               |
--R        |0  0  0  0  0  1  0  0  0  0  0|
--R        |                               |
--R   (1)  |0  0  0  0  1  0  0  0  0  0  0|
--R        |                               |
--R        |0  0  0  0  0  0  0  0  1  0  0|
--R        |                               |
--R        |0  0  0  0  0  0  0  0  0  1  0|
--R        |                               |
--R        |0  0  0  0  0  0  0  0  0  0  1|
--R        |                               |
--R        |0  0  0  0  0  0  0  1  0  0  0|
--R        |                               |
--R        +0  0  0  0  0  0  1  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 68
gm2 := createGenericMatrix 2
 

        +x     x   +
        | 1,1   1,2|
   (2)  |          |
        |x     x   |
        + 2,1   2,2+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x     x   +
--R        | 1,1   1,2|
--R   (2)  |          |
--R        |x     x   |
--R        + 2,1   2,2+
--R                                              Type: Matrix Polynomial Integer
--E 23

--S 24 of 68
symmetricTensors (gm2,2)
 

        +      2          2                       +
        |  x          x             x   x         |
        |   1,1        1,2           1,1 1,2      |
        |                                         |
   (3)  |      2          2                       |
        |  x          x             x   x         |
        |   2,1        2,2           2,1 2,2      |
        |                                         |
        |2x   x     2x   x     x   x    + x   x   |
        +  1,1 2,1    1,2 2,2   1,1 2,2    1,2 2,1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +      2          2                       +
--R        |  x          x             x   x         |
--R        |   1,1        1,2           1,1 1,2      |
--R        |                                         |
--R   (3)  |      2          2                       |
--R        |  x          x             x   x         |
--R        |   2,1        2,2           2,1 2,2      |
--R        |                                         |
--R        |2x   x     2x   x     x   x    + x   x   |
--R        +  1,1 2,1    1,2 2,2   1,1 2,2    1,2 2,1+
--R                                              Type: Matrix Polynomial Integer
--E 24

--S 25 of 68
gm3 := createGenericMatrix 3
 

        +x     x     x   +
        | 1,1   1,2   1,3|
        |                |
   (4)  |x     x     x   |
        | 2,1   2,2   2,3|
        |                |
        |x     x     x   |
        + 3,1   3,2   3,3+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x     x     x   +
--R        | 1,1   1,2   1,3|
--R        |                |
--R   (4)  |x     x     x   |
--R        | 2,1   2,2   2,3|
--R        |                |
--R        |x     x     x   |
--R        + 3,1   3,2   3,3+
--R                                              Type: Matrix Polynomial Integer
--E 25

--S 26 of 68
antisymmetricTensors (gm3,2)
 

        +x   x    - x   x     x   x    - x   x     x   x    - x   x   +
        | 1,1 2,2    1,2 2,1   1,1 2,3    1,3 2,1   1,2 2,3    1,3 2,2|
        |                                                             |
   (5)  |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
        | 1,1 3,2    1,2 3,1   1,1 3,3    1,3 3,1   1,2 3,3    1,3 3,2|
        |                                                             |
        |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
        + 2,1 3,2    2,2 3,1   2,1 3,3    2,3 3,1   2,2 3,3    2,3 3,2+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x   x    - x   x     x   x    - x   x     x   x    - x   x   +
--R        | 1,1 2,2    1,2 2,1   1,1 2,3    1,3 2,1   1,2 2,3    1,3 2,2|
--R        |                                                             |
--R   (5)  |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
--R        | 1,1 3,2    1,2 3,1   1,1 3,3    1,3 3,1   1,2 3,3    1,3 3,2|
--R        |                                                             |
--R        |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
--R        + 2,1 3,2    2,2 3,1   2,1 3,3    2,3 3,1   2,2 3,3    2,3 3,2+
--R                                              Type: Matrix Polynomial Integer
--E 26

--S 27 of 68
tensorProduct(gm2,gm2)
 

        +     2                             2  +
        | x        x   x     x   x      x      |
        |  1,1      1,1 1,2   1,1 1,2    1,2   |
        |                                      |
        |x   x     x   x     x   x     x   x   |
        | 1,1 2,1   1,1 2,2   1,2 2,1   1,2 2,2|
   (6)  |                                      |
        |x   x     x   x     x   x     x   x   |
        | 1,1 2,1   1,2 2,1   1,1 2,2   1,2 2,2|
        |                                      |
        |     2                             2  |
        | x        x   x     x   x      x      |
        +  2,1      2,1 2,2   2,1 2,2    2,2   +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +     2                             2  +
--R        | x        x   x     x   x      x      |
--R        |  1,1      1,1 1,2   1,1 1,2    1,2   |
--R        |                                      |
--R        |x   x     x   x     x   x     x   x   |
--R        | 1,1 2,1   1,1 2,2   1,2 2,1   1,2 2,2|
--R   (6)  |                                      |
--R        |x   x     x   x     x   x     x   x   |
--R        | 1,1 2,1   1,2 2,1   1,1 2,2   1,2 2,2|
--R        |                                      |
--R        |     2                             2  |
--R        | x        x   x     x   x      x      |
--R        +  2,1      2,1 2,2   2,1 2,2    2,2   +
--R                                              Type: Matrix Polynomial Integer
--E 27

--S 28 of 68
)sh REP1
 
 RepresentationPackage1 R: Ring  is a package constructor
 Abbreviation for RepresentationPackage1 is REP1 
 This constructor is exposed in this frame.
 Issue )edit rep1.spad.pamphlet to see algebra source code for REP1 

------------------------------- Operations --------------------------------
 antisymmetricTensors : (Matrix R,PositiveInteger) -> Matrix R if R has commutative *
 antisymmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R if R has commutative *
 createGenericMatrix : NonNegativeInteger -> Matrix Polynomial R
 permutationRepresentation : (Permutation Integer,Integer) -> Matrix Integer
 permutationRepresentation : List Integer -> Matrix Integer
 permutationRepresentation : (List Permutation Integer,Integer) -> List Matrix Integer
 permutationRepresentation : List List Integer -> List Matrix Integer
 symmetricTensors : (Matrix R,PositiveInteger) -> Matrix R
 symmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R
 tensorProduct : (Matrix R,Matrix R) -> Matrix R
 tensorProduct : (List Matrix R,List Matrix R) -> List Matrix R
 tensorProduct : Matrix R -> Matrix R
 tensorProduct : List Matrix R -> List Matrix R

--R 
--R RepresentationPackage1 R: Ring  is a package constructor
--R Abbreviation for RepresentationPackage1 is REP1 
--R This constructor is exposed in this frame.
--I Issue )edit /research/research/s2/mnt/fedora5/../../src/algebra/REP1.spad to see algebra source code for REP1 
--R
--R------------------------------- Operations --------------------------------
--R antisymmetricTensors : (Matrix R,PositiveInteger) -> Matrix R if R has commutative *
--R antisymmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R if R has commutative *
--R createGenericMatrix : NonNegativeInteger -> Matrix Polynomial R
--R permutationRepresentation : (Permutation Integer,Integer) -> Matrix Integer
--R permutationRepresentation : List Integer -> Matrix Integer
--R permutationRepresentation : (List Permutation Integer,Integer) -> List Matrix Integer
--R permutationRepresentation : List List Integer -> List Matrix Integer
--R symmetricTensors : (Matrix R,PositiveInteger) -> Matrix R
--R symmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R
--R tensorProduct : (Matrix R,Matrix R) -> Matrix R
--R tensorProduct : (List Matrix R,List Matrix R) -> List Matrix R
--R tensorProduct : Matrix R -> Matrix R
--R tensorProduct : List Matrix R -> List Matrix R
--R
--E 28

)clear all
 
   All user variables and function definitions have been cleared.

--S 29 of 68
r0 := irreducibleRepresentation [2,2,2,1,1];
 

                                                    Type: List Matrix Integer
--R 
--R
--R                                                    Type: List Matrix Integer
--E 29

--S 30 of 68
r28 := meatAxe (r0::(LIST MATRIX PF 2))
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (2)
   [
      +0  1  1  1  1  1  1  0  0  1  1  1  0  0+
      |                                        |
      |1  0  1  1  1  0  0  1  1  1  0  0  1  1|
      |                                        |
      |1  1  0  1  0  1  0  0  1  0  1  0  0  1|
      |                                        |
      |1  1  1  0  0  0  1  1  0  0  0  1  1  0|
      |                                        |
      |1  1  0  0  0  1  1  1  1  1  1  1  1  1|
      |                                        |
      |1  0  1  0  1  0  1  0  1  1  1  1  0  1|
      |                                        |
      |1  0  0  1  1  1  0  1  0  1  1  1  1  0|
     [|                                        |,
      |0  1  1  0  1  1  0  1  0  1  1  0  0  0|
      |                                        |
      |0  1  0  1  1  0  1  0  1  1  0  1  0  0|
      |                                        |
      |1  1  0  0  1  0  0  0  0  0  0  0  0  0|
      |                                        |
      |1  0  1  0  0  1  0  0  0  0  0  0  0  0|
      |                                        |
      |1  0  0  1  0  0  1  0  0  0  0  0  0  0|
      |                                        |
      |0  1  1  0  0  0  0  1  0  0  0  0  0  0|
      |                                        |
      +0  1  0  1  0  0  0  0  1  0  0  0  0  0+
      +1  1  1  1  0  0  0  0  0  0  0  0  0  0+
      |                                        |
      |1  1  1  0  0  0  1  0  0  1  1  0  0  0|
      |                                        |
      |1  1  1  0  0  0  0  0  1  1  0  0  1  0|
      |                                        |
      |1  1  1  0  0  0  0  1  1  0  1  0  1  0|
      |                                        |
      |1  1  1  0  0  0  0  1  0  1  1  1  1  0|
      |                                        |
      |1  1  1  0  0  1  0  0  0  1  1  0  1  1|
      |                                        |
      |1  1  1  0  1  0  0  0  0  1  1  0  0  1|
      |                                        |]
      |1  1  0  0  0  0  0  0  0  0  1  1  1  1|
      |                                        |
      |1  0  1  0  0  0  0  0  0  1  0  1  0  1|
      |                                        |
      |0  0  0  1  0  0  1  0  0  1  1  1  1  0|
      |                                        |
      |0  0  0  1  0  0  0  0  1  1  1  0  1  1|
      |                                        |
      |0  0  0  1  0  0  0  1  1  1  1  0  0  1|
      |                                        |
      |0  0  0  0  0  0  1  0  1  0  1  1  1  1|
      |                                        |
      +0  0  0  0  0  0  1  1  1  1  0  1  0  1+
     ,

      +1  0  0  0  0  0  0  0  1  1  1  1  1  1+
      |                                        |
      |0  1  0  0  0  0  0  0  1  1  1  0  0  0|
      |                                        |
      |0  0  1  0  0  1  1  0  1  0  0  1  0  0|
      |                                        |
      |0  0  0  1  0  1  0  1  0  1  0  0  1  0|
      |                                        |
      |0  0  0  0  1  0  1  1  1  1  0  0  0  1|
      |                                        |
      |0  0  0  0  0  1  1  1  1  1  0  1  1  0|
      |                                        |
      |0  0  0  0  0  1  1  1  1  0  1  1  0  1|
     [|                                        |,
      |0  0  0  0  0  1  1  1  0  1  1  0  1  1|
      |                                        |
      |0  0  0  0  0  1  1  0  1  1  1  1  0  0|
      |                                        |
      |0  0  0  0  0  1  0  1  1  1  1  0  1  0|
      |                                        |
      |0  0  0  0  0  0  1  1  1  1  1  1  1  0|
      |                                        |
      |0  0  0  0  0  0  0  0  0  0  0  0  1  1|
      |                                        |
      |0  0  0  0  0  0  0  0  0  0  0  1  0  1|
      |                                        |
      +0  0  0  0  0  0  0  0  0  0  0  0  0  1+
      +0  0  1  1  1  1  1  0  1  0  0  0  0  0+
      |                                        |
      |0  0  1  0  0  0  0  0  0  0  0  0  1  1|
      |                                        |
      |0  0  0  0  0  0  0  1  0  1  0  0  1  0|
      |                                        |
      |0  0  0  0  0  0  0  1  0  0  1  0  0  1|
      |                                        |
      |0  0  1  0  0  0  0  0  0  1  1  0  1  1|
      |                                        |
      |0  0  0  0  0  0  0  1  1  0  0  1  0  0|
      |                                        |
      |0  0  0  0  0  0  1  0  0  1  0  1  0  0|
      |                                        |]
      |1  1  0  0  0  1  0  0  0  0  1  1  0  0|
      |                                        |
      |0  0  1  1  0  0  1  0  1  0  0  0  1  0|
      |                                        |
      |1  0  1  0  1  1  0  0  1  0  0  0  0  1|
      |                                        |
      |1  0  1  1  1  0  0  0  1  0  0  0  1  1|
      |                                        |
      |0  0  1  1  0  0  1  1  1  1  0  1  1  0|
      |                                        |
      |0  1  1  0  1  1  0  1  1  0  1  1  0  1|
      |                                        |
      +0  1  1  1  1  0  0  0  1  1  1  1  1  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (2)
--R   [
--R      +0  1  1  1  1  1  1  0  0  1  1  1  0  0+
--R      |                                        |
--R      |1  0  1  1  1  0  0  1  1  1  0  0  1  1|
--R      |                                        |
--R      |1  1  0  1  0  1  0  0  1  0  1  0  0  1|
--R      |                                        |
--R      |1  1  1  0  0  0  1  1  0  0  0  1  1  0|
--R      |                                        |
--R      |1  1  0  0  0  1  1  1  1  1  1  1  1  1|
--R      |                                        |
--R      |1  0  1  0  1  0  1  0  1  1  1  1  0  1|
--R      |                                        |
--R      |1  0  0  1  1  1  0  1  0  1  1  1  1  0|
--R     [|                                        |,
--R      |0  1  1  0  1  1  0  1  0  1  1  0  0  0|
--R      |                                        |
--R      |0  1  0  1  1  0  1  0  1  1  0  1  0  0|
--R      |                                        |
--R      |1  1  0  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |1  0  1  0  0  1  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |1  0  0  1  0  0  1  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  1  1  0  0  0  0  1  0  0  0  0  0  0|
--R      |                                        |
--R      +0  1  0  1  0  0  0  0  1  0  0  0  0  0+
--R      +1  1  1  1  0  0  0  0  0  0  0  0  0  0+
--R      |                                        |
--R      |1  1  1  0  0  0  1  0  0  1  1  0  0  0|
--R      |                                        |
--R      |1  1  1  0  0  0  0  0  1  1  0  0  1  0|
--R      |                                        |
--R      |1  1  1  0  0  0  0  1  1  0  1  0  1  0|
--R      |                                        |
--R      |1  1  1  0  0  0  0  1  0  1  1  1  1  0|
--R      |                                        |
--R      |1  1  1  0  0  1  0  0  0  1  1  0  1  1|
--R      |                                        |
--R      |1  1  1  0  1  0  0  0  0  1  1  0  0  1|
--R      |                                        |]
--R      |1  1  0  0  0  0  0  0  0  0  1  1  1  1|
--R      |                                        |
--R      |1  0  1  0  0  0  0  0  0  1  0  1  0  1|
--R      |                                        |
--R      |0  0  0  1  0  0  1  0  0  1  1  1  1  0|
--R      |                                        |
--R      |0  0  0  1  0  0  0  0  1  1  1  0  1  1|
--R      |                                        |
--R      |0  0  0  1  0  0  0  1  1  1  1  0  0  1|
--R      |                                        |
--R      |0  0  0  0  0  0  1  0  1  0  1  1  1  1|
--R      |                                        |
--R      +0  0  0  0  0  0  1  1  1  1  0  1  0  1+
--R     ,
--R
--R      +1  0  0  0  0  0  0  0  1  1  1  1  1  1+
--R      |                                        |
--R      |0  1  0  0  0  0  0  0  1  1  1  0  0  0|
--R      |                                        |
--R      |0  0  1  0  0  1  1  0  1  0  0  1  0  0|
--R      |                                        |
--R      |0  0  0  1  0  1  0  1  0  1  0  0  1  0|
--R      |                                        |
--R      |0  0  0  0  1  0  1  1  1  1  0  0  0  1|
--R      |                                        |
--R      |0  0  0  0  0  1  1  1  1  1  0  1  1  0|
--R      |                                        |
--R      |0  0  0  0  0  1  1  1  1  0  1  1  0  1|
--R     [|                                        |,
--R      |0  0  0  0  0  1  1  1  0  1  1  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  1  1  0  1  1  1  1  0  0|
--R      |                                        |
--R      |0  0  0  0  0  1  0  1  1  1  1  0  1  0|
--R      |                                        |
--R      |0  0  0  0  0  0  1  1  1  1  1  1  1  0|
--R      |                                        |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R      |                                        |
--R      +0  0  0  0  0  0  0  0  0  0  0  0  0  1+
--R      +0  0  1  1  1  1  1  0  1  0  0  0  0  0+
--R      |                                        |
--R      |0  0  1  0  0  0  0  0  0  0  0  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  0  1  0  0  1  0|
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  0  0  1  0  0  1|
--R      |                                        |
--R      |0  0  1  0  0  0  0  0  0  1  1  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  1  0  0  1  0  0|
--R      |                                        |
--R      |0  0  0  0  0  0  1  0  0  1  0  1  0  0|
--R      |                                        |]
--R      |1  1  0  0  0  1  0  0  0  0  1  1  0  0|
--R      |                                        |
--R      |0  0  1  1  0  0  1  0  1  0  0  0  1  0|
--R      |                                        |
--R      |1  0  1  0  1  1  0  0  1  0  0  0  0  1|
--R      |                                        |
--R      |1  0  1  1  1  0  0  0  1  0  0  0  1  1|
--R      |                                        |
--R      |0  0  1  1  0  0  1  1  1  1  0  1  1  0|
--R      |                                        |
--R      |0  1  1  0  1  1  0  1  1  0  1  1  0  1|
--R      |                                        |
--R      +0  1  1  1  1  0  0  0  1  1  1  1  1  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 30

--S 31 of 68
areEquivalent? (r28.1, r28.2)
 
   Dimensions of kernels differ

   Representations are not equivalent.

   (3)  [0]
                                                    Type: Matrix PrimeField 2
--R 
--R   Dimensions of kernels differ
--R
--R   Representations are not equivalent.
--R
--R   (3)  [0]
--R                                                    Type: Matrix PrimeField 2
--E 31

--S 32 of 68
meatAxe r28.2
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is irreducible, but we don't know
       whether it is absolutely irreducible

   (4)
   [
      +1  0  0  0  0  0  0  0  0  0  0  0  0  0+
      |                                        |
      |0  1  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  1  0  0  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  0  1  0  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  0  0  1  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  1  1  0  1  1  1  1  1  0  0  0  0|
      |                                        |
      |0  0  1  0  1  1  1  1  1  0  1  0  0  0|
     [|                                        |,
      |0  0  0  1  1  1  1  1  0  1  1  0  0  0|
      |                                        |
      |1  1  1  0  1  1  1  0  1  1  1  0  0  0|
      |                                        |
      |1  1  0  1  1  1  0  1  1  1  1  0  0  0|
      |                                        |
      |1  1  0  0  0  0  1  1  1  1  1  0  0  0|
      |                                        |
      |1  0  1  0  0  1  1  0  1  0  1  0  1  0|
      |                                        |
      |1  0  0  1  0  1  0  1  0  1  1  1  0  0|
      |                                        |
      +1  0  0  0  1  0  1  1  0  0  0  1  1  1+
      +0  0  0  0  0  0  0  1  0  1  1  0  0  0+
      |                                        |
      |0  0  0  0  0  0  0  1  0  0  0  0  1  1|
      |                                        |
      |1  1  0  0  1  0  0  0  1  1  1  1  1  1|
      |                                        |
      |1  0  0  0  0  0  0  0  1  0  1  1  0  1|
      |                                        |
      |1  0  0  0  0  0  0  0  0  1  1  0  1  1|
      |                                        |
      |1  0  0  0  0  0  0  1  0  1  0  0  1  0|
      |                                        |
      |1  0  0  0  0  0  1  0  1  0  0  1  0  0|
      |                                        |]
      |0  0  1  1  0  1  0  0  0  0  0  1  1  0|
      |                                        |
      |1  0  0  0  0  1  0  0  1  1  1  1  1  1|
      |                                        |
      |0  0  1  0  1  0  1  0  0  0  0  1  0  1|
      |                                        |
      |0  0  0  1  1  0  0  1  0  0  0  0  1  1|
      |                                        |
      |0  0  0  0  0  1  1  1  0  0  0  1  1  1|
      |                                        |
      |0  1  1  0  1  0  0  0  1  0  1  1  0  1|
      |                                        |
      +0  1  0  1  1  0  0  0  0  1  1  0  1  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is irreducible, but we don't know
--R       whether it is absolutely irreducible
--R
--R   (4)
--R   [
--R      +1  0  0  0  0  0  0  0  0  0  0  0  0  0+
--R      |                                        |
--R      |0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  1  1  0  1  1  1  1  1  0  0  0  0|
--R      |                                        |
--R      |0  0  1  0  1  1  1  1  1  0  1  0  0  0|
--R     [|                                        |,
--R      |0  0  0  1  1  1  1  1  0  1  1  0  0  0|
--R      |                                        |
--R      |1  1  1  0  1  1  1  0  1  1  1  0  0  0|
--R      |                                        |
--R      |1  1  0  1  1  1  0  1  1  1  1  0  0  0|
--R      |                                        |
--R      |1  1  0  0  0  0  1  1  1  1  1  0  0  0|
--R      |                                        |
--R      |1  0  1  0  0  1  1  0  1  0  1  0  1  0|
--R      |                                        |
--R      |1  0  0  1  0  1  0  1  0  1  1  1  0  0|
--R      |                                        |
--R      +1  0  0  0  1  0  1  1  0  0  0  1  1  1+
--R      +0  0  0  0  0  0  0  1  0  1  1  0  0  0+
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  0  0  0  0  1  1|
--R      |                                        |
--R      |1  1  0  0  1  0  0  0  1  1  1  1  1  1|
--R      |                                        |
--R      |1  0  0  0  0  0  0  0  1  0  1  1  0  1|
--R      |                                        |
--R      |1  0  0  0  0  0  0  0  0  1  1  0  1  1|
--R      |                                        |
--R      |1  0  0  0  0  0  0  1  0  1  0  0  1  0|
--R      |                                        |
--R      |1  0  0  0  0  0  1  0  1  0  0  1  0  0|
--R      |                                        |]
--R      |0  0  1  1  0  1  0  0  0  0  0  1  1  0|
--R      |                                        |
--R      |1  0  0  0  0  1  0  0  1  1  1  1  1  1|
--R      |                                        |
--R      |0  0  1  0  1  0  1  0  0  0  0  1  0  1|
--R      |                                        |
--R      |0  0  0  1  1  0  0  1  0  0  0  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  1  1  1  0  0  0  1  1  1|
--R      |                                        |
--R      |0  1  1  0  1  0  0  0  1  0  1  1  0  1|
--R      |                                        |
--R      +0  1  0  1  1  0  0  0  0  1  1  0  1  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 32

--S 33 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? r28.2
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (5)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 33

--S 34 of 68
ma := meatAxe r28.1
 
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (6)
     +0  0  0  0  1  0  1  1+ +1  1  1  1  1  1  0  0+
     |                      | |                      |
     |0  0  0  0  0  1  0  1| |1  0  0  1  1  0  1  0|
     |                      | |                      |
     |0  0  0  0  0  0  1  1| |0  0  1  1  0  0  1  0|
     |                      | |                      |
     |0  0  0  0  0  0  0  1| |1  1  0  1  1  1  1  1|
   [[|                      |,|                      |],
     |1  0  1  0  0  0  0  0| |1  1  1  1  0  0  1  0|
     |                      | |                      |
     |0  1  0  1  0  0  0  0| |1  0  0  1  1  1  1  1|
     |                      | |                      |
     |0  0  1  1  0  0  0  0| |0  1  1  0  1  0  1  1|
     |                      | |                      |
     +0  0  0  1  0  0  0  0+ +1  0  0  1  0  1  0  1+
     +0  1  1  0  0  1+ +1  1  0  0  0  0+
     |                | |                |
     |1  0  1  0  0  1| |1  0  1  1  0  0|
     |                | |                |
     |1  1  0  0  0  1| |1  0  0  1  0  1|
    [|                |,|                |]]
     |0  0  0  1  0  0| |1  0  1  1  1  0|
     |                | |                |
     |0  0  0  0  1  0| |1  0  0  0  1  1|
     |                | |                |
     +1  1  1  0  0  0+ +0  1  1  1  0  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (6)
--R     +0  0  0  0  1  0  1  1+ +1  1  1  1  1  1  0  0+
--R     |                      | |                      |
--R     |0  0  0  0  0  1  0  1| |1  0  0  1  1  0  1  0|
--R     |                      | |                      |
--R     |0  0  0  0  0  0  1  1| |0  0  1  1  0  0  1  0|
--R     |                      | |                      |
--R     |0  0  0  0  0  0  0  1| |1  1  0  1  1  1  1  1|
--R   [[|                      |,|                      |],
--R     |1  0  1  0  0  0  0  0| |1  1  1  1  0  0  1  0|
--R     |                      | |                      |
--R     |0  1  0  1  0  0  0  0| |1  0  0  1  1  1  1  1|
--R     |                      | |                      |
--R     |0  0  1  1  0  0  0  0| |0  1  1  0  1  0  1  1|
--R     |                      | |                      |
--R     +0  0  0  1  0  0  0  0+ +1  0  0  1  0  1  0  1+
--R     +0  1  1  0  0  1+ +1  1  0  0  0  0+
--R     |                | |                |
--R     |1  0  1  0  0  1| |1  0  1  1  0  0|
--R     |                | |                |
--R     |1  1  0  0  0  1| |1  0  0  1  0  1|
--R    [|                |,|                |]]
--R     |0  0  0  1  0  0| |1  0  1  1  1  0|
--R     |                | |                |
--R     |0  0  0  0  1  0| |1  0  0  0  1  1|
--R     |                | |                |
--R     +1  1  1  0  0  0+ +0  1  1  1  0  1+
--R                                          Type: List List Matrix PrimeField 2
--E 34

--S 35 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? ma.1
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (7)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 35

--S 36 of 68
isAbsolutelyIrreducible? ma.2
 
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (8)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 36

)clear all
 
   All user variables and function definitions have been cleared.

--S 37 of 68
px : PERM PF 29 := cycles [[1,3,5],[7,11,9]]
 

   (1)  (1 3 5)(7 11 9)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (1)  (1 3 5)(7 11 9)
--R                                              Type: Permutation PrimeField 29
--E 37

--S 38 of 68
py : PERM PF 29 := cycles [[3,5,7,9]]
 

   (2)  (3 5 7 9)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (2)  (3 5 7 9)
--R                                              Type: Permutation PrimeField 29
--E 38

--S 39 of 68
pz : PERM PF 29 := cycle [1,3,11]
 

   (3)  (1 3 11)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (3)  (1 3 11)
--R                                              Type: Permutation PrimeField 29
--E 39

--S 40 of 68
px * pz
 

   (4)  (1 5)(3 9 7 11)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (4)  (1 5)(3 9 7 11)
--R                                              Type: Permutation PrimeField 29
--E 40

--S 41 of 68
py ** 3
 

   (5)  (3 9 7 5)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (5)  (3 9 7 5)
--R                                              Type: Permutation PrimeField 29
--E 41

--S 42 of 68
inv px
 

   (6)  (1 5 3)(7 9 11)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (6)  (1 5 3)(7 9 11)
--R                                              Type: Permutation PrimeField 29
--E 42

--S 43 of 68
order px
 

   (7)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  3
--R                                                        Type: PositiveInteger
--E 43

--S 44 of 68
movedPoints py
 

   (8)  {3,5,7,9}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (8)  {3,5,7,9}
--R                                                      Type: Set PrimeField 29
--E 44

--S 45 of 68
orbit ( pz , 3 )
 

   (9)  {3,11,1}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (9)  {3,11,1}
--R                                                      Type: Set PrimeField 29
--E 45

--S 46 of 68
eval ( py , 7 )
 

   (10)  9
                                                          Type: PrimeField 29
--R 
--R
--R   (10)  9
--R                                                          Type: PrimeField 29
--E 46

--S 47 of 68
)sh PERM
 
 Permutation S: SetCategory  is a domain constructor
 Abbreviation for Permutation is PERM 
 This constructor is exposed in this frame.
 Issue )edit perm.spad.pamphlet to see algebra source code for PERM 

------------------------------- Operations --------------------------------
 ?*? : (%,%) -> %                      ?**? : (%,Integer) -> %
 ?**? : (%,PositiveInteger) -> %       ?/? : (%,%) -> %
 ?<? : (%,%) -> Boolean                ?=? : (%,%) -> Boolean
 1 : () -> %                           ?^? : (%,Integer) -> %
 ?^? : (%,PositiveInteger) -> %        coerce : List S -> %
 coerce : List List S -> %             coerce : % -> OutputForm
 coerceImages : List S -> %            commutator : (%,%) -> %
 conjugate : (%,%) -> %                cycle : List S -> %
 cyclePartition : % -> Partition       cycles : List List S -> %
 degree : % -> NonNegativeInteger      ?.? : (%,S) -> S
 eval : (%,S) -> S                     even? : % -> Boolean
 hash : % -> SingleInteger             inv : % -> %
 latex : % -> String                   movedPoints : % -> Set S
 odd? : % -> Boolean                   one? : % -> Boolean
 orbit : (%,S) -> Set S                order : % -> NonNegativeInteger
 recip : % -> Union(%,"failed")        sample : () -> %
 sign : % -> Integer                   sort : List % -> List %
 ?~=? : (%,%) -> Boolean              
 ?**? : (%,NonNegativeInteger) -> %
 ?<=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
 ?>? : (%,%) -> Boolean if S has FINITE or S has ORDSET
 ?>=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
 ?^? : (%,NonNegativeInteger) -> %
 coerceListOfPairs : List List S -> %
 coercePreimagesImages : List List S -> %
 fixedPoints : % -> Set S if S has FINITE
 listRepresentation : % -> Record(preimage: List S,image: List S)
 max : (%,%) -> % if S has FINITE or S has ORDSET
 min : (%,%) -> % if S has FINITE or S has ORDSET
 numberOfCycles : % -> NonNegativeInteger

--R 
--R Permutation S: SetCategory  is a domain constructor
--R Abbreviation for Permutation is PERM 
--R This constructor is exposed in this frame.
--I Issue )edit /research/research/s2/mnt/fedora5/../../src/algebra/PERM.spad to see algebra source code for PERM 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (%,%) -> %                      ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> %       ?/? : (%,%) -> %
--R ?<? : (%,%) -> Boolean                ?=? : (%,%) -> Boolean
--R 1 : () -> %                           ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> %        coerce : List S -> %
--R coerce : List List S -> %             coerce : % -> OutputForm
--R coerceImages : List S -> %            commutator : (%,%) -> %
--R conjugate : (%,%) -> %                cycle : List S -> %
--R cyclePartition : % -> Partition       cycles : List List S -> %
--R degree : % -> NonNegativeInteger      ?.? : (%,S) -> S
--R eval : (%,S) -> S                     even? : % -> Boolean
--R hash : % -> SingleInteger             inv : % -> %
--R latex : % -> String                   movedPoints : % -> Set S
--R odd? : % -> Boolean                   one? : % -> Boolean
--R orbit : (%,S) -> Set S                order : % -> NonNegativeInteger
--R recip : % -> Union(%,"failed")        sample : () -> %
--R sign : % -> Integer                   sort : List % -> List %
--R ?~=? : (%,%) -> Boolean              
--R ?**? : (%,NonNegativeInteger) -> %
--R ?<=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
--R ?>? : (%,%) -> Boolean if S has FINITE or S has ORDSET
--R ?>=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
--R ?^? : (%,NonNegativeInteger) -> %
--R coerceListOfPairs : List List S -> %
--R coercePreimagesImages : List List S -> %
--R fixedPoints : % -> Set S if S has FINITE
--R listRepresentation : % -> Record(preimage: List S,image: List S)
--R max : (%,%) -> % if S has FINITE or S has ORDSET
--R min : (%,%) -> % if S has FINITE or S has ORDSET
--R numberOfCycles : % -> NonNegativeInteger
--R
--E 47

)clear all
 
   All user variables and function definitions have been cleared.

--S 48 of 68
genA6 : List PERM INT := [cycle [1,2,3],cycle [2,3,4,5,6]]
 

   (1)  [(1 2 3),(2 3 4 5 6)]
                                               Type: List Permutation Integer
--R 
--R
--R   (1)  [(1 2 3),(2 3 4 5 6)]
--R                                               Type: List Permutation Integer
--E 48

--S 49 of 68
pRA6 := permutationRepresentation (genA6,6)
 

         +0  0  1  0  0  0+ +1  0  0  0  0  0+
         |                | |                |
         |1  0  0  0  0  0| |0  0  0  0  0  1|
         |                | |                |
         |0  1  0  0  0  0| |0  1  0  0  0  0|
   (2)  [|                |,|                |]
         |0  0  0  1  0  0| |0  0  1  0  0  0|
         |                | |                |
         |0  0  0  0  1  0| |0  0  0  1  0  0|
         |                | |                |
         +0  0  0  0  0  1+ +0  0  0  0  1  0+
                                                    Type: List Matrix Integer
--R 
--R
--R         +0  0  1  0  0  0+ +1  0  0  0  0  0+
--R         |                | |                |
--R         |1  0  0  0  0  0| |0  0  0  0  0  1|
--R         |                | |                |
--R         |0  1  0  0  0  0| |0  1  0  0  0  0|
--R   (2)  [|                |,|                |]
--R         |0  0  0  1  0  0| |0  0  1  0  0  0|
--R         |                | |                |
--R         |0  0  0  0  1  0| |0  0  0  1  0  0|
--R         |                | |                |
--R         +0  0  0  0  0  1+ +0  0  0  0  1  0+
--R                                                    Type: List Matrix Integer
--E 49

--S 50 of 68
sp0 := meatAxe (pRA6::(List Matrix PF 2))
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

          +0  0  1  0  0+ +1  0  0  0  0+
          |             | |             |
          |1  0  0  0  0| |1  1  1  1  1|
          |             | |             |
   (3)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
          |             | |             |
          |0  0  0  1  0| |0  0  1  0  0|
          |             | |             |
          +0  0  0  0  1+ +0  0  0  1  0+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R          +0  0  1  0  0+ +1  0  0  0  0+
--R          |             | |             |
--R          |1  0  0  0  0| |1  1  1  1  1|
--R          |             | |             |
--R   (3)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
--R          |             | |             |
--R          |0  0  0  1  0| |0  0  1  0  0|
--R          |             | |             |
--R          +0  0  0  0  1+ +0  0  0  1  0+
--R                                          Type: List List Matrix PrimeField 2
--E 50

--S 51 of 68
sp1 := meatAxe sp0.1
 
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices
     Representation is not irreducible and it will be split:

                    +0  1  0  0+ +0  1  1  1+
                    |          | |          |
                    |0  0  1  0| |1  1  0  1|
   (4)  [[[1],[1]],[|          |,|          |]]
                    |1  0  0  0| |1  1  1  0|
                    |          | |          |
                    +0  0  0  1+ +1  1  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R     Representation is not irreducible and it will be split:
--R
--R                    +0  1  0  0+ +0  1  1  1+
--R                    |          | |          |
--R                    |0  0  1  0| |1  1  0  1|
--R   (4)  [[[1],[1]],[|          |,|          |]]
--R                    |1  0  0  0| |1  1  1  0|
--R                    |          | |          |
--R                    +0  0  0  1+ +1  1  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 51

--S 52 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp1.2
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (5)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--I   (5)  true
--R                                                                Type: Boolean
--E 52

--S 53 of 68
d2211 := irreducibleRepresentation ([2,2,1,1],genA6)
 

   (6)
    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
    |                                     | |                                 |
    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
    |                                     | |                                 |
    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
    |                                     | |                                 |
   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
    |                                     | |                                 |
    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
    |                                     | |                                 |
    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
    |                                     | |                                 |
    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
                                                    Type: List Matrix Integer
--R 
--R
--R   (6)
--R    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
--R    |                                     | |                                 |
--R    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
--R    |                                     | |                                 |
--R   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
--R    |                                     | |                                 |
--R    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
--R                                                    Type: List Matrix Integer
--E 53

--S 54 of 68
d2211m2 := (d2211::(List Matrix PF 2)); sp2 := meatAxe d2211m2
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

                                      +1  0  0  0  0+ +1  1  1  0  0+
          +1  0  1  1+ +0  0  1  0+   |             | |             |
          |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
          |0  1  0  1| |1  1  1  1|   |             | |             |
   (7)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
          |1  1  0  0| |1  0  1  1|   |             | |             |
          |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
          +0  1  0  0+ +0  1  0  1+   |             | |             |
                                      +0  1  1  1  0+ +1  0  0  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R                                      +1  0  0  0  0+ +1  1  1  0  0+
--R          +1  0  1  1+ +0  0  1  0+   |             | |             |
--R          |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
--R          |0  1  0  1| |1  1  1  1|   |             | |             |
--R   (7)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
--R          |1  1  0  0| |1  0  1  1|   |             | |             |
--R          |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
--R          +0  1  0  0+ +0  1  0  1+   |             | |             |
--R                                      +0  1  1  1  0+ +1  0  0  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 54

--S 55 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp2.1
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (8)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 55

--S 56 of 68 random generation, FAILURE OK.
areEquivalent? (sp2.1, sp1.2)
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     There is no isomorphism, as the only possible one
       fails to do the necessary base change

   Representations are not equivalent.

   (9)  [0]
                                                    Type: Matrix PrimeField 2
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Dimensions of kernels differ
--R
--R   Representations are not equivalent.
--R
--R   (9)  [0]
--R                                                    Type: Matrix PrimeField 2
--E 56

--S 57 of 68
dA6d16 := tensorProduct(sp2.1,sp1.2); meatAxe dA6d16
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is irreducible, but we don't know
       whether it is absolutely irreducible

   (10)
   [
      +0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0+
      |                                              |
      |1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
      |                                              |
      |0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
      |                                              |
      |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0|
      |                                              |
      |0  0  0  0  1  0  0  0  1  0  0  0  1  0  0  0|
      |                                              |
      |0  0  0  0  0  1  0  0  0  1  0  0  0  1  0  0|
      |                                              |
      |0  0  0  0  0  0  0  1  0  0  0  1  0  0  0  1|
     [|                                              |,
      |0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      +0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0+
      +0  0  0  0  0  1  1  1  0  1  1  1  0  0  0  0+
      |                                              |
      |0  0  0  0  1  1  1  1  1  1  1  1  0  0  0  0|
      |                                              |
      |0  0  0  0  1  0  1  1  1  0  1  1  0  0  0  0|
      |                                              |
      |0  0  0  0  1  1  0  1  1  1  0  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
      |                                              |
      |0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1|
      |                                              |
      |0  0  0  0  1  0  1  1  0  0  0  0  1  0  1  1|
      |                                              |
      |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
      |                                              |]
      |0  1  1  1  0  1  1  1  0  1  1  1  0  0  0  0|
      |                                              |
      |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
      |                                              |
      |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
      |                                              |
      |1  1  0  1  1  1  0  1  1  1  0  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
      |                                              |
      |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
      |                                              |
      |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
      |                                              |
      +0  0  0  0  1  1  0  1  1  1  0  1  1  1  0  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is irreducible, but we don't know
--R       whether it is absolutely irreducible
--R
--R   (10)
--R   [
--R      +0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0+
--R      |                                              |
--R      |1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R      |                                              |
--R      |0  0  0  0  1  0  0  0  1  0  0  0  1  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  0  0  0  1  0  0  0  1  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  1  0  0  0  1  0  0  0  1|
--R     [|                                              |,
--R      |0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      +0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0+
--R      +0  0  0  0  0  1  1  1  0  1  1  1  0  0  0  0+
--R      |                                              |
--R      |0  0  0  0  1  1  1  1  1  1  1  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  0  1  1  1  0  1  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  1  0  1  1  1  0  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  0  1  1  0  0  0  0  1  0  1  1|
--R      |                                              |
--R      |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
--R      |                                              |]
--R      |0  1  1  1  0  1  1  1  0  1  1  1  0  0  0  0|
--R      |                                              |
--R      |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R      |                                              |
--R      |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R      |                                              |
--R      |1  1  0  1  1  1  0  1  1  1  0  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R      |                                              |
--R      +0  0  0  0  1  1  0  1  1  1  0  1  1  1  0  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 57

--S 58 of 68
isAbsolutelyIrreducible? dA6d16
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   We have not found a one-dimensional kernel so far,
     as we do a random search you could try again

   (11)  false
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   We have not found a one-dimensional kernel so far,
--R     as we do a random search you could try again
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 58

--S 59 of 68
sp3 := meatAxe (dA6d16 :: (List Matrix FF(2,2)))
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (12)
   [
      +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
      |                                                              |
      |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
      |                                                              |
      |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
      |                                                              |
      |  0       %A    %A + 1    %A      0       1       1       0   |
     [|                                                              |,
      |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
      |                                                              |
      |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
      |                                                              |
      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
      |                                                              |
      +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
      +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
      |                                                          |
      |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
      |                                                          |
      |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
      |                                                          |
      |  %A      1       0       %A    %A    0       1       %A  |
      |                                                          |]
      |  1       1       0     %A + 1  0     1       1       0   |
      |                                                          |
      |  1       %A      1       0     1     0       0       %A  |
      |                                                          |
      |%A + 1    0       1       1     0     %A    %A + 1    1   |
      |                                                          |
      +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
     ,

      +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
      |                                                              |
      |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
      |                                                              |
      |  1       1       %A      %A      1       %A      1     %A + 1|
      |                                                              |
      |  1       0       1     %A + 1  %A + 1    0       %A      1   |
     [|                                                              |,
      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
      |                                                              |
      |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
      |                                                              |
      |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
      |                                                              |
      +  %A      0     %A + 1    0       1       0       1       %A  +
      +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
      |                                                          |
      |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
      |                                                          |
      |  %A    0     1       0     %A + 1    0     %A + 1    1   |
      |                                                          |
      |  1     1   %A + 1    %A      %A      %A      1       0   |
      |                                                          |]
      |  1     %A    0       1       1       %A      1       0   |
      |                                                          |
      |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
      |                                                          |
      |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
      |                                                          |
      +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
     ]
                                      Type: List List Matrix FiniteField(2,2)
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (12)
--R   [
--R      +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
--R      |                                                              |
--R      |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
--R      |                                                              |
--R      |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
--R      |                                                              |
--R      |  0       %A    %A + 1    %A      0       1       1       0   |
--R     [|                                                              |,
--R      |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
--R      |                                                              |
--R      |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
--R      |                                                              |
--R      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R      |                                                              |
--R      +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
--R      +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
--R      |                                                          |
--R      |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
--R      |                                                          |
--R      |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
--R      |                                                          |
--R      |  %A      1       0       %A    %A    0       1       %A  |
--R      |                                                          |]
--R      |  1       1       0     %A + 1  0     1       1       0   |
--R      |                                                          |
--R      |  1       %A      1       0     1     0       0       %A  |
--R      |                                                          |
--R      |%A + 1    0       1       1     0     %A    %A + 1    1   |
--R      |                                                          |
--R      +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
--R     ,
--R
--R      +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
--R      |                                                              |
--R      |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
--R      |                                                              |
--R      |  1       1       %A      %A      1       %A      1     %A + 1|
--R      |                                                              |
--R      |  1       0       1     %A + 1  %A + 1    0       %A      1   |
--R     [|                                                              |,
--R      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R      |                                                              |
--R      |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
--R      |                                                              |
--R      |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
--R      |                                                              |
--R      +  %A      0     %A + 1    0       1       0       1       %A  +
--R      +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
--R      |                                                          |
--R      |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
--R      |                                                          |
--R      |  %A    0     1       0     %A + 1    0     %A + 1    1   |
--R      |                                                          |
--R      |  1     1   %A + 1    %A      %A      %A      1       0   |
--R      |                                                          |]
--R      |  1     %A    0       1       1       %A      1       0   |
--R      |                                                          |
--R      |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
--R      |                                                          |
--R      |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
--R      |                                                          |
--R      +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
--R     ]
--R                                      Type: List List Matrix FiniteField(2,2)
--E 59

--S 60 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp3.1
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (13)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 60

--S 61 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp3.2
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (14)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 61

--S 62 of 68 random generation, FAILURE OK.
areEquivalent? (sp3.1,sp3.2)
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     There is no isomorphism, as the only possible one
       fails to do the necessary base change

   Representations are not equivalent.

   (15)  [0]
                                                Type: Matrix FiniteField(2,2)
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     There is no isomorphism, as the only possible one
--R       fails to do the necessary base change
--R
--R   Representations are not equivalent.
--R
--R   (15)  [0]
--R                                                Type: Matrix FiniteField(2,2)
--E 62

--S 63 of 68
sp0.2
 

   (16)  [[1],[1]]
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (16)  [[1],[1]]
--R                                               Type: List Matrix PrimeField 2
--E 63

--S 64 of 68
sp1.2
 

          +0  1  0  0+ +0  1  1  1+
          |          | |          |
          |0  0  1  0| |1  1  0  1|
   (17)  [|          |,|          |]
          |1  0  0  0| |1  1  1  0|
          |          | |          |
          +0  0  0  1+ +1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +0  1  0  0+ +0  1  1  1+
--R          |          | |          |
--R          |0  0  1  0| |1  1  0  1|
--R   (17)  [|          |,|          |]
--R          |1  0  0  0| |1  1  1  0|
--R          |          | |          |
--R          +0  0  0  1+ +1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 64

--S 65 of 68
sp2.1
 

          +1  0  1  1+ +0  0  1  0+
          |          | |          |
          |0  1  0  1| |1  1  1  1|
   (18)  [|          |,|          |]
          |1  1  0  0| |1  0  1  1|
          |          | |          |
          +0  1  0  0+ +0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  1  1+ +0  0  1  0+
--R          |          | |          |
--R          |0  1  0  1| |1  1  1  1|
--R   (18)  [|          |,|          |]
--R          |1  1  0  0| |1  0  1  1|
--R          |          | |          |
--R          +0  1  0  0+ +0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 65

--S 66 of 68
sp3.1
 

   (19)
    +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
    |                                                              |
    |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
    |                                                              |
    |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
    |                                                              |
    |  0       %A    %A + 1    %A      0       1       1       0   |
   [|                                                              |,
    |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
    |                                                              |
    |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
    |                                                              |
    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
    |                                                              |
    +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
    +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
    |                                                          |
    |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
    |                                                          |
    |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
    |                                                          |
    |  %A      1       0       %A    %A    0       1       %A  |
    |                                                          |]
    |  1       1       0     %A + 1  0     1       1       0   |
    |                                                          |
    |  1       %A      1       0     1     0       0       %A  |
    |                                                          |
    |%A + 1    0       1       1     0     %A    %A + 1    1   |
    |                                                          |
    +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (19)
--R    +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
--R    |                                                              |
--R    |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
--R    |                                                              |
--R    |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
--R    |                                                              |
--R    |  0       %A    %A + 1    %A      0       1       1       0   |
--R   [|                                                              |,
--R    |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
--R    |                                                              |
--R    |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
--R    |                                                              |
--R    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R    |                                                              |
--R    +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
--R    +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
--R    |                                                          |
--R    |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
--R    |                                                          |
--R    |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
--R    |                                                          |
--R    |  %A      1       0       %A    %A    0       1       %A  |
--R    |                                                          |]
--R    |  1       1       0     %A + 1  0     1       1       0   |
--R    |                                                          |
--R    |  1       %A      1       0     1     0       0       %A  |
--R    |                                                          |
--R    |%A + 1    0       1       1     0     %A    %A + 1    1   |
--R    |                                                          |
--R    +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
--R                                           Type: List Matrix FiniteField(2,2)
--E 66

--S 67 of 68
sp3.2
 

   (20)
    +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
    |                                                              |
    |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
    |                                                              |
    |  1       1       %A      %A      1       %A      1     %A + 1|
    |                                                              |
    |  1       0       1     %A + 1  %A + 1    0       %A      1   |
   [|                                                              |,
    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
    |                                                              |
    |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
    |                                                              |
    |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
    |                                                              |
    +  %A      0     %A + 1    0       1       0       1       %A  +
    +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
    |                                                          |
    |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
    |                                                          |
    |  %A    0     1       0     %A + 1    0     %A + 1    1   |
    |                                                          |
    |  1     1   %A + 1    %A      %A      %A      1       0   |
    |                                                          |]
    |  1     %A    0       1       1       %A      1       0   |
    |                                                          |
    |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
    |                                                          |
    |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
    |                                                          |
    +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (20)
--R    +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
--R    |                                                              |
--R    |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
--R    |                                                              |
--R    |  1       1       %A      %A      1       %A      1     %A + 1|
--R    |                                                              |
--R    |  1       0       1     %A + 1  %A + 1    0       %A      1   |
--R   [|                                                              |,
--R    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R    |                                                              |
--R    |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
--R    |                                                              |
--R    |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
--R    |                                                              |
--R    +  %A      0     %A + 1    0       1       0       1       %A  +
--R    +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
--R    |                                                          |
--R    |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
--R    |                                                          |
--R    |  %A    0     1       0     %A + 1    0     %A + 1    1   |
--R    |                                                          |
--R    |  1     1   %A + 1    %A      %A      %A      1       0   |
--R    |                                                          |]
--R    |  1     %A    0       1       1       %A      1       0   |
--R    |                                                          |
--R    |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
--R    |                                                          |
--R    |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
--R    |                                                          |
--R    +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
--R                                           Type: List Matrix FiniteField(2,2)
--E 67

--S 68 of 68
dA6d16
 

   (21)
    +0  1  0  0  0  0  0  0  0  1  0  0  0  1  0  0+
    |                                              |
    |0  0  1  0  0  0  0  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  0  0  0  0  0  0  0  1  0  0  0  1  0  0  0|
    |                                              |
    |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  1|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  1  0  0|
    |                                              |
    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |0  0  0  0  1  0  0  0  0  0  0  0  1  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  1|
   [|                                              |,
    |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    +0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0+
    +0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0+
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  1  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  1  1  0  0  0  0|
    |                                              |
    |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
    |                                              |
    |1  1  0  1  1  1  0  1  1  1  0  1  1  1  0  1|
    |                                              |
    |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |]
    |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
    |                                              |
    |1  1  0  1  0  0  0  0  1  1  0  1  1  1  0  1|
    |                                              |
    |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
    |                                              |
    |1  1  1  1  0  0  0  0  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
    |                                              |
    |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
    |                                              |
    |0  0  0  0  1  1  1  0  0  0  0  0  1  1  1  0|
    |                                              |
    +0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (21)
--R    +0  1  0  0  0  0  0  0  0  1  0  0  0  1  0  0+
--R    |                                              |
--R    |0  0  1  0  0  0  0  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  0  0  0  0  0  0  0  1  0  0  0  1  0  0  0|
--R    |                                              |
--R    |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  1  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |0  0  0  0  1  0  0  0  0  0  0  0  1  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  1|
--R   [|                                              |,
--R    |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0+
--R    +0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  1  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
--R    |                                              |
--R    |1  1  0  1  1  1  0  1  1  1  0  1  1  1  0  1|
--R    |                                              |
--R    |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |]
--R    |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
--R    |                                              |
--R    |1  1  0  1  0  0  0  0  1  1  0  1  1  1  0  1|
--R    |                                              |
--R    |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
--R    |                                              |
--R    |1  1  1  1  0  0  0  0  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
--R    |                                              |
--R    |0  0  0  0  1  1  1  0  0  0  0  0  1  1  1  0|
--R    |                                              |
--R    +0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 68
)spool 
 
Starts dribbling to operator.output (2009/2/17, 17:55:52).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 6
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
dx := operator("D") :: OP(POLY FRAC INT)
 

   (2)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (2)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 2

--S 3 of 6
evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT)
 

   (3)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (3)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 3

--S 4 of 6
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 6
L 15
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

   (5)
     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
       2048          2048           2048           2048          2048
   + 
       2909907  5   255255  3   6435
     - ------- x  + ------ x  - ---- x
         2048        2048       2048
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R   (5)
--R     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
--R     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       2909907  5   255255  3   6435
--R     - ------- x  + ------ x  - ---- x
--R         2048        2048       2048
--R                                            Type: Polynomial Fraction Integer
--E 5

--S 6 of 6
E 15
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                       2      2
   (6)  240 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                       2      2
--R   (6)  240 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 6
)spool 
 
Starts dribbling to mfinfact.output (2009/2/17, 17:55:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 13
p:POLY PF 7 :=6*x +6*y +6*z +x^49+y^49+z^49
 

         49         49         49
   (1)  z   + 6z + y   + 6y + x   + 6x
                                                Type: Polynomial PrimeField 7
--R 
--R
--R         49         49         49
--R   (1)  z   + 6z + y   + 6y + x   + 6x
--R                                                Type: Polynomial PrimeField 7
--E 1

--S 2 of 13
factor p
 

   (2)
     (z + y + x + 1)(z + y + x + 2)(z + y + x + 3)(z + y + x + 4)(z + y + x + 5)
  *
     (z + y + x + 6)(z + y + x)
  *
       2                     2                2
     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 4)
  *
       2                     2                2
     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 6)
  *
       2                     2                2
     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 2)
  *
       2                     2                2
     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 1)
  *
       2                     2                2
     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 6)
  *
       2                     2                2
     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 1)
  *
       2                     2                2
     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 6)
  *
       2                     2                2
     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 2)
  *
       2                     2                2
     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 4)
  *
       2                     2                2
     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 6)
  *
       2                 2           2
     (z  + (2y + 2x)z + y  + 2x y + x  + 1)
  *
     2                 2           2       2                 2           2
   (z  + (2y + 2x)z + y  + 2x y + x  + 2)(z  + (2y + 2x)z + y  + 2x y + x  + 4)
                                       Type: Factored Polynomial PrimeField 7
--R 
--R
--R   (2)
--R     (z + y + x + 1)(z + y + x + 2)(z + y + x + 3)(z + y + x + 4)(z + y + x + 5)
--R  *
--R     (z + y + x + 6)(z + y + x)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 4)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 6)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 2)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 1)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 6)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 1)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 6)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 2)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 4)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 6)
--R  *
--R       2                 2           2
--R     (z  + (2y + 2x)z + y  + 2x y + x  + 1)
--R  *
--R     2                 2           2       2                 2           2
--R   (z  + (2y + 2x)z + y  + 2x y + x  + 2)(z  + (2y + 2x)z + y  + 2x y + x  + 4)
--R                                       Type: Factored Polynomial PrimeField 7
--E 2

--S 3 of 13
p:POLY PF 7:=(x+3*y+z)*(w*x+y)*(x*y+w**3)
 

   (3)
         2       2    3      4          3             2     3  2
     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
   + 
         3      4    3        4 2
     (w x  + (3w  + w )x)y + w x
                                                Type: Polynomial PrimeField 7
--R 
--R
--R   (3)
--R         2       2    3      4          3             2     3  2
--R     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
--R   + 
--R         3      4    3        4 2
--R     (w x  + (3w  + w )x)y + w x
--R                                                Type: Polynomial PrimeField 7
--E 3

--S 4 of 13
factor p
 

                         3
   (4)  (y + w x)(x y + w )(z + 3y + x)
                                       Type: Factored Polynomial PrimeField 7
--R 
--R
--R                         3
--R   (4)  (y + w x)(x y + w )(z + 3y + x)
--R                                       Type: Factored Polynomial PrimeField 7
--E 4

--S 5 of 13
pp:=p**2
 

   (5)
            2 4        3     3   3     2 4     4 2    6  2      5 3     7
           x y  + (2w x  + 2w x)y  + (w x  + 4w x  + w )y  + (2w x  + 2w x)y
         + 
            8 2
           w x
    *
        2
       z
   + 
           2 5             3     3   4       2       4      4     3  2     6  3
         6x y  + ((5w + 2)x  + 5w x)y  + ((6w  + 4w)x  + (3w  + 4w )x  + 6w )y
       + 
            2 5      5    4  3      7     6    2      5 4      8     7  2
         (2w x  + (5w  + w )x  + (5w  + 2w )x)y  + (4w x  + (6w  + 4w )x )y
       + 
           8 3
         2w x
    *
       z
   + 
       2 6             3     3   5       2           4     4     3  2     6  4
     2x y  + ((4w + 6)x  + 4w x)y  + ((2w  + 5w + 1)x  + (w  + 5w )x  + 2w )y
   + 
         2       5      5     4     3  3      7     6    3
     ((6w  + 2w)x  + (4w  + 3w  + 2w )x  + (4w  + 6w )x)y
   + 
       2 6      5     4  4      8     7    6  2  2      5 5      8     7  3
     (w x  + (5w  + 4w )x  + (2w  + 5w  + w )x )y  + (2w x  + (6w  + 2w )x )y
   + 
      8 4
     w x
                                                Type: Polynomial PrimeField 7
--R 
--R
--R   (5)
--R            2 4        3     3   3     2 4     4 2    6  2      5 3     7
--R           x y  + (2w x  + 2w x)y  + (w x  + 4w x  + w )y  + (2w x  + 2w x)y
--R         + 
--R            8 2
--R           w x
--R    *
--R        2
--R       z
--R   + 
--R           2 5             3     3   4       2       4      4     3  2     6  3
--R         6x y  + ((5w + 2)x  + 5w x)y  + ((6w  + 4w)x  + (3w  + 4w )x  + 6w )y
--R       + 
--R            2 5      5    4  3      7     6    2      5 4      8     7  2
--R         (2w x  + (5w  + w )x  + (5w  + 2w )x)y  + (4w x  + (6w  + 4w )x )y
--R       + 
--R           8 3
--R         2w x
--R    *
--R       z
--R   + 
--R       2 6             3     3   5       2           4     4     3  2     6  4
--R     2x y  + ((4w + 6)x  + 4w x)y  + ((2w  + 5w + 1)x  + (w  + 5w )x  + 2w )y
--R   + 
--R         2       5      5     4     3  3      7     6    3
--R     ((6w  + 2w)x  + (4w  + 3w  + 2w )x  + (4w  + 6w )x)y
--R   + 
--R       2 6      5     4  4      8     7    6  2  2      5 5      8     7  3
--R     (w x  + (5w  + 4w )x  + (2w  + 5w  + w )x )y  + (2w x  + (6w  + 2w )x )y
--R   + 
--R      8 4
--R     w x
--R                                                Type: Polynomial PrimeField 7
--E 5

--S 6 of 13
gcd(p,differentiate(p,x))
 

   (6)  1
                                                Type: Polynomial PrimeField 7
--R 
--R
--R   (6)  1
--R                                                Type: Polynomial PrimeField 7
--E 6

--S 7 of 13
p23:POLY PF 23:=(x+3*y+z)*(w*x+y)*(x*y+w**3)
 

   (7)
         2       2    3      4          3             2     3  2
     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
   + 
         3      4    3        4 2
     (w x  + (3w  + w )x)y + w x
                                               Type: Polynomial PrimeField 23
--R 
--R
--R   (7)
--R         2       2    3      4          3             2     3  2
--R     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
--R   + 
--R         3      4    3        4 2
--R     (w x  + (3w  + w )x)y + w x
--R                                               Type: Polynomial PrimeField 23
--E 7

--S 8 of 13
factor(p23)
 

                         3
   (8)  (y + w x)(x y + w )(z + 3y + x)
                                      Type: Factored Polynomial PrimeField 23
--R 
--R
--R                         3
--R   (8)  (y + w x)(x y + w )(z + 3y + x)
--R                                      Type: Factored Polynomial PrimeField 23
--E 8

--S 9 of 13
q: POLY PF 2 := y**4 + y**3 + x**4 + x**2
 

         4    3    4    2
   (9)  y  + y  + x  + x
                                                Type: Polynomial PrimeField 2
--R 
--R
--R         4    3    4    2
--R   (9)  y  + y  + x  + x
--R                                                Type: Polynomial PrimeField 2
--E 9

--S 10 of 13
factor q
 

          4    3    4    2
   (10)  y  + y  + x  + x
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R          4    3    4    2
--R   (10)  y  + y  + x  + x
--R                                       Type: Factored Polynomial PrimeField 2
--E 10

--S 11 of 13
factor(q*(q+1))
 

           4    3    4    2       4    3    4    2
   (11)  (y  + y  + x  + x  + 1)(y  + y  + x  + x )
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R           4    3    4    2       4    3    4    2
--R   (11)  (y  + y  + x  + x  + 1)(y  + y  + x  + x )
--R                                       Type: Factored Polynomial PrimeField 2
--E 11

--S 12 of 13
q:=x**2*y**2+z
 

              2 2
   (12)  z + x y
                                                Type: Polynomial PrimeField 2
--R 
--R
--R              2 2
--R   (12)  z + x y
--R                                                Type: Polynomial PrimeField 2
--E 12

--S 13 of 13
factor(q*(1+q))
 

               2 2           2 2
   (13)  (z + x y  + 1)(z + x y )
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R               2 2           2 2
--R   (13)  (z + x y  + 1)(z + x y )
--R                                       Type: Factored Polynomial PrimeField 2
--E 13
)spool 
 
Starts dribbling to cycles1.output (2009/2/17, 17:44:25).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from CycleIndicatorsXmpPage

)expose EVALCYC
 
   EvaluateCycleIndicators is now explicitly exposed in frame initial 
 
--S 1 of 46
complete 1
 

   (1)  (1)
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (1)  (1)
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 1

--S 2 of 46
complete 2
 

        1       1   2
   (2)  - (2) + - (1 )
        2       2
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1   2
--R   (2)  - (2) + - (1 )
--R        2       2
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 2

--S 3 of 46
complete 3
 

        1       1         1   3
   (3)  - (3) + - (2 1) + - (1 )
        3       2         6
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1         1   3
--R   (3)  - (3) + - (2 1) + - (1 )
--R        3       2         6
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 3

--S 4 of 46
complete 7
 

   (4)
     1       1          1          1     2     1         1            1     3
     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
      1      5      1    7
     --- (2 1 ) + ---- (1 )
     240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (4)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R      1      5      1    7
--R     --- (2 1 ) + ---- (1 )
--R     240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 4

--S 5 of 46
elementary 7
 

   (5)
     1       1          1          1     2     1         1            1     3
     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
        1      5      1    7
     - --- (2 1 ) + ---- (1 )
       240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (5)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R        1      5      1    7
--R     - --- (2 1 ) + ---- (1 )
--R       240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 5

--S 6 of 46
alternating 7
 

   (6)
     2       1     2    1           1   2      1     2     1     4     1   2 3
     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
     7       5          4           9         12          36          24
   + 
       1    7
     ---- (1 )
     2520
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (6)
--R     2       1     2    1           1   2      1     2     1     4     1   2 3
--R     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
--R     7       5          4           9         12          36          24
--R   + 
--R       1    7
--R     ---- (1 )
--R     2520
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 6

--S 7 of 46
cyclic 7
 

        6       1   7
   (7)  - (7) + - (1 )
        7       7
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        6       1   7
--R   (7)  - (7) + - (1 )
--R        7       7
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 7

--S 8 of 46
dihedral 7
 

        3       1   3      1   7
   (8)  - (7) + - (2 1) + -- (1 )
        7       2         14
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        3       1   3      1   7
--R   (8)  - (7) + - (2 1) + -- (1 )
--R        7       2         14
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 8

--S 9 of 46
graphs 5
 

   (9)
   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
   6           5        4         6         8          12          120
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (9)
--R   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
--R   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
--R   6           5        4         6         8          12          120
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 9

--S 10 of 46
cap(complete 2**2, complete 2*complete 1**2)
 

   (10)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (10)  4
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 46
cap(elementary 2**2, complete 2*complete 1**2)
 

   (11)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  2
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 46
cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)
 

   (12)  24
                                                       Type: Fraction Integer
--R 
--R
--R   (12)  24
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 46
cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)
 

   (13)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  8
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 46
cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)
 

   (14)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (14)  8
--R                                                       Type: Fraction Integer
--E 14

--S 15 of 46
eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))
 

   (15)  1500
                                                       Type: Fraction Integer
--R 
--R
--R   (15)  1500
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 46
square:=dihedral 4
 

         1       3   2    1     2    1   4
   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
         4       8        4          8
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1       3   2    1     2    1   4
--R   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
--R         4       8        4          8
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 16

--S 17 of 46
cap(complete 2**2,square)
 

   (17)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  2
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 46
cap(complete 3*complete 2**2,dihedral 7)
 

   (18)  18
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  18
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 46
cap(graphs 5,complete 7*complete 3)
 

   (19)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (19)  4
--R                                                       Type: Fraction Integer
--E 19

--S 20 of 46
s(x) == powerSum(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 46
cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)
 
   Compiling function s with type PositiveInteger -> 
      SymmetricPolynomial Fraction Integer 

         1   2    1   2 2    3   4     1   8
   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
         4        3          8        24
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R   Compiling function s with type PositiveInteger -> 
--R      SymmetricPolynomial Fraction Integer 
--R
--R         1   2    1   2 2    3   4     1   8
--R   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
--R         4        3          8        24
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 21

--S 22 of 46
cap(complete 4**2,cube)
 

   (22)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  7
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))
 

   (23)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (23)  7
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))
 

   (24)  17
                                                       Type: Fraction Integer
--R 
--R
--R   (24)  17
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))
 

   (25)  10
                                                       Type: Fraction Integer
--R 
--R
--R   (25)  10
--R                                                       Type: Fraction Integer
--E 25

--S 26 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))
 

   (26)  23
                                                       Type: Fraction Integer
--R 
--R
--R   (26)  23
--R                                                       Type: Fraction Integer
--E 26

--S 27 of 46
x: ULS(FRAC INT,'x,0) := 'x
 

   (27)  x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (27)  x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 27

--S 28 of 46
ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 46
Integers: INT -> ULS(FRAC INT, 'x, 0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 46
ZeroOrOne n == 1+x**n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 46
ZeroOrOne 5
 
   Compiling function ZeroOrOne with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5
   (31)  1 + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function ZeroOrOne with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5
--R   (31)  1 + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 31

--S 32 of 46
Integers n == 1/(1-x**n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 46
Integers 5
 
   Compiling function Integers with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5    10      11
   (33)  1 + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function Integers with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5    10      11
--R   (33)  1 + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 33

--S 34 of 46
eval(ZeroOrOne, graphs 5)
 

                   2     3     4     5     6     7     8    9    10      11
   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6     7     8    9    10      11
--R   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 34

--S 35 of 46
eval(ZeroOrOne,dihedral 8)
 

                   2     3     4     5     6    7    8
   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 35

--S 36 of 46
eval(Integers,complete 4)
 

   (36)
             2     3     4     5     6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (36)
--R             2     3     4     5     6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 36

--S 37 of 46
eval(Integers,elementary 4)
 

   (37)
      6    7     8     9     10     11     12      13      14      15      16
     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
   + 
        17
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (37)
--R      6    7     8     9     10     11     12      13      14      15      16
--R     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
--R   + 
--R        17
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 37

--S 38 of 46
eval(ZeroOrOne,cube)
 

                   2     3     4     5     6    7    8
   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 38

--S 39 of 46
eval(Integers,cube)
 

   (39)
               2     3      4      5      6       7       8       9       10
     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (39)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 39

--S 40 of 46
eval(Integers,graphs 5)
 

   (40)
               2     3      4      5      6       7       8       9       10
     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (40)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 40

--S 41 of 46
eval(ZeroOrOne ,graphs 15)
 

   (41)
               2     3      4      5      6       7       8        9        10
     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (41)
--R               2     3      4      5      6       7       8        9        10
--R     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 41

--S 42 of 46
cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)
 

   (42)  49958972383320
                                                       Type: Fraction Integer
--R 
--R
--R   (42)  49958972383320
--R                                                       Type: Fraction Integer
--E 42

--S 43 of 46
sf3221:= SFunction [3,2,2,1]
 

   (43)
      1          1     2     1   2     1            1     4     1   2
     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
     12         12          16        12           24          36
   + 
      1   2 2     1     2      1       3     1     5     1    4     1   3 2
     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
     36          24           36            72          192        48
   + 
      1   2 4     1      6     1    8
     -- (2 1 ) - --- (2 1 ) + --- (1 )
     96          144          576
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (43)
--R      1          1     2     1   2     1            1     4     1   2
--R     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
--R     12         12          16        12           24          36
--R   + 
--R      1   2 2     1     2      1       3     1     5     1    4     1   3 2
--R     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
--R     36          24           36            72          192        48
--R   + 
--R      1   2 4     1      6     1    8
--R     -- (2 1 ) - --- (2 1 ) + --- (1 )
--R     96          144          576
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 43

--S 44 of 46
cap(sf3221,complete 2**4)
 

   (44)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (44)  3
--R                                                       Type: Fraction Integer
--E 44

--S 45 of 46
cap(sf3221, powerSum 1**8)
 

   (45)  70
                                                       Type: Fraction Integer
--R 
--R
--R   (45)  70
--R                                                       Type: Fraction Integer
--E 45

--S 46 of 46
eval(Integers, sf3221)
 

   (46)
      9     10     11      12      13      14      15       16       17       18
     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
   + 
         19      20
     432x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (46)
--R      9     10     11      12      13      14      15       16       17       18
--R     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
--R   + 
--R         19      20
--R     432x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 46
)spool
 
Starts dribbling to tutchap1.output (2009/2/17, 18:1:19).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 19
1+1
 

   (1)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 19
123^45
 

   (2)
  1111040818513195628591079058717645191855915321226802182362907319986611100124_
   2743283966127048043
                                                        Type: PositiveInteger
--R 
--R
--R   (2)
--R  1111040818513195628591079058717645191855915321226802182362907319986611100124_
--R   2743283966127048043
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 19
2^(3+4)
 

   (3)  128
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  128
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 19
4/3
 

        4
   (4)  -
        3
                                                       Type: Fraction Integer
--R 
--R
--R        4
--R   (4)  -
--R        3
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 19
2/2
 

   (5)  1
                                                       Type: Fraction Integer
--R 
--R
--R   (5)  1
--R                                                       Type: Fraction Integer
--E 5

--S 6 of 19
a := 2
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 19
b := a
 

   (7)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  2
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 19
a := 3
 

   (8)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  3
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 19
b
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 19
i : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 19
i := 2/3
 
 
Daly Bug
   Cannot convert right-hand side of assignment
   2
   -
   3

      to an object of the type Integer of the left-hand side.
--R 
--R 
--RDaly Bug
--R   Cannot convert right-hand side of assignment
--R   2
--R   -
--R   3
--R
--R      to an object of the type Integer of the left-hand side.
--E 11

--S 12 of 19
i := 4/2
 

   (11)  2
                                                                Type: Integer
--R 
--R
--R   (11)  2
--R                                                                Type: Integer
--E 12

--S 13 of 19
c : PositiveInteger := 3
 

   (12)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  3
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 19
(j, k, l) : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 19
)display names
 

Names of User-Defined Objects in the Workspace:

%    a    b    c    i    j    k    l    

Names of System-Defined Objects in the Workspace:

%e                %i                %infinity         %minusInfinity    
%pi               %plusInfinity     SF                
--R 
--R
--RNames of User-Defined Objects in the Workspace:
--R
--R%    a    b    c    i    j    k    l    
--R
--RNames of System-Defined Objects in the Workspace:
--R
--R%e                %i                %infinity         %minusInfinity    
--R%pi               %plusInfinity     SF                
--E 15

)clear properties c i
 

--S 16  of 19
%%(1)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 19
1 + %%(-3)
 

   (15)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  4
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 19
1 _
  +_
  2
 

   (16)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  3
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 19
7 * 8 -- In the next chapter we shall move beyond elementary arithmetic.
 

   (17)  56
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  56
--R                                                        Type: PositiveInteger
--E 19
)spool 
 
Starts dribbling to algaggr.output (2009/2/17, 17:43:43).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 28
l := [1,4,2,-6,0,3,5,4,2,3]
 

   (1)  [1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 1

--S 2 of 28
m := list 555555
 

   (2)  [555555]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [555555]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 28
concat(5,l)
 

   (3)  [5,1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (3)  [5,1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 3

--S 4 of 28
concat(m,l)
 

   (4)  [555555,1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (4)  [555555,1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 4

--S 5 of 28
removeDuplicates l
 

   (5)  [1,4,2,- 6,0,3,5]
                                                           Type: List Integer
--R 
--R
--R   (5)  [1,4,2,- 6,0,3,5]
--R                                                           Type: List Integer
--E 5

--S 6 of 28
first l
 

   (6)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  1
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 28
rest l
 

   (7)  [4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (7)  [4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 7

--S 8 of 28
last l
 

   (8)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  3
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 28
#l
 

   (9)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  10
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 28
l
 

   (10)  [1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (10)  [1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 10

--S 11 of 28
first(l,3)
 

   (11)  [1,4,2]
                                                           Type: List Integer
--R 
--R
--R   (11)  [1,4,2]
--R                                                           Type: List Integer
--E 11

--S 12 of 28
rest(l,3)
 

   (12)  [- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (12)  [- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 12

--S 13 of 28
l.1
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 28
l.2
 

   (14)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  4
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 28
l.(#l)
 

   (15)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  3
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 28
l.1 := 1000000000
 

   (16)  1000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  1000000000
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 28
l
 

   (17)  [1000000000,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (17)  [1000000000,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 17

--S 18 of 28
insert(10,l,4)
 

   (18)  [1000000000,4,2,10,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (18)  [1000000000,4,2,10,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 18

--S 19 of 28
insert(2,l,1)
 

   (19)  [2,1000000000,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (19)  [2,1000000000,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 19

--S 20 of 28
position(-6,l)
 

   (20)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  4
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 28
reverse l
 

   (21)  [3,2,4,5,3,0,- 6,2,4,1000000000]
                                                           Type: List Integer
--R 
--R
--R   (21)  [3,2,4,5,3,0,- 6,2,4,1000000000]
--R                                                           Type: List Integer
--E 21

--S 22 of 28
l
 

   (22)  [1000000000,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (22)  [1000000000,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 22

--S 23 of 28
m := [4,2,3,6,5,7,-9,1,2,3,2]
 

   (23)  [4,2,3,6,5,7,- 9,1,2,3,2]
                                                           Type: List Integer
--R 
--R
--R   (23)  [4,2,3,6,5,7,- 9,1,2,3,2]
--R                                                           Type: List Integer
--E 23

--S 24 of 28
sl:SET(INT) := brace l
 

   (24)  {- 6,0,2,3,4,5,1000000000}
                                                            Type: Set Integer
--R 
--R
--R   (24)  {- 6,0,2,3,4,5,1000000000}
--R                                                            Type: Set Integer
--E 24

--S 25 of 28
sm:SET(INT) := brace m
 

   (25)  {- 9,1,2,3,4,5,6,7}
                                                            Type: Set Integer
--R 
--R
--R   (25)  {- 9,1,2,3,4,5,6,7}
--R                                                            Type: Set Integer
--E 25

--S 26 of 28
difference(sl, sm)
 

   (26)  {- 6,0,1000000000}
                                                            Type: Set Integer
--R 
--R
--R   (26)  {- 6,0,1000000000}
--R                                                            Type: Set Integer
--E 26

--S 27 of 28
intersect(sl,sm)
 

   (27)  {2,3,4,5}
                                                            Type: Set Integer
--R 
--R
--R   (27)  {2,3,4,5}
--R                                                            Type: Set Integer
--E 27

--S 28 of 28
union(sl,sm)
 

   (28)  {- 9,- 6,0,1,2,3,4,5,6,7,1000000000}
                                                            Type: Set Integer
--R 
--R
--R   (28)  {- 9,- 6,0,1,2,3,4,5,6,7,1000000000}
--R                                                            Type: Set Integer
--E 28
)spool 
 
Starts dribbling to lodo1.output (2009/2/17, 17:52:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 20
RFZ := Fraction UnivariatePolynomial('x, Integer)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 20
x : RFZ := 'x
 

   (2)  x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (2)  x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 2

--S 3 of 20
Dx : LODO1 RFZ := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 3

--S 4 of 20
b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 4

--S 5 of 20
a : LODO1 RFZ := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 5

--S 6 of 20
p := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 6

--S 7 of 20
(a*b - b*a) p
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 20
ld := leftDivide(a,b)
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 8

--S 9 of 20
a = b * ld.quotient + ld.remainder
 

           3 3       2        2         7     3 3       2        2         7
   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
                                        x                                  x
Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7     3 3       2        2         7
--R   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                        x                                  x
--RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 9

--S 10 of 20
rd := rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 10

--S 11 of 20
a = rd.quotient * b + rd.remainder
 

            3 3       2        2         7     3 3       2        2         7
   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
                                         x                                  x
Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7     3 3       2        2         7
--R   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                         x                                  x
--RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 11

--S 12 of 20
rightQuotient(a,b)
 

   (12)  5x D + 7
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (12)  5x D + 7
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 12

--S 13 of 20
rightRemainder(a,b)
 

               5
   (13)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (13)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 20
leftExactQuotient(a,b)
 

   (14)  5x D + 7
Type: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...)
--R 
--R
--R   (14)  5x D + 7
--RType: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...)
--E 14

--S 15 of 20
e := leftGcd(a,b)
 

           2 2        1
   (15)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (15)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 20
leftRemainder(a, e)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 20
rightRemainder(a, e)
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18 of 20
f := rightLcm(a,b)
 

            3 3       2        2         7
   (18)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (18)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 18

--S 19 of 20
rightRemainder(f, b)
 

               5
   (19)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (19)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 20
leftRemainder(f, b)
 

   (20)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (20)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 20
)spool 
 
Starts dribbling to schaum26.output (2009/2/17, 17:59:29).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(log(x),x)
 

   (1)  x log(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  x log(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=x*log(x)-x
 

   (2)  x log(x) - x
                                                     Type: Expression Integer
--R
--R   (2)  x log(x) - x
--R                                                     Type: Expression Integer
--E

--S 3      14:525 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*log(x),x)
 

          2          2
        2x log(x) - x
   (1)  --------------
               4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2          2
--R        2x log(x) - x
--R   (1)  --------------
--R               4
--R                                          Type: Union(Expression Integer,...)
--E

--S 5
bb:=x^2/2*(log(x)-1/2)
 

          2          2
        2x log(x) - x
   (2)  --------------
               4
                                                     Type: Expression Integer
--R
--R          2          2
--R        2x log(x) - x
--R   (2)  --------------
--R               4
--R                                                     Type: Expression Integer
--E 

--S 6      14:526 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^m*log(x),x)
 

                               m log(x)
        ((m + 1)x log(x) - x)%e
   (1)  -------------------------------
                   2
                  m  + 2m + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               m log(x)
--R        ((m + 1)x log(x) - x)%e
--R   (1)  -------------------------------
--R                   2
--R                  m  + 2m + 1
--R                                          Type: Union(Expression Integer,...)
--E

--S 8
bb:=x^(m+1)/(m+1)*(log(x)-1/(m+1))
 

                            m + 1
        ((m + 1)log(x) - 1)x
   (2)  -------------------------
                2
               m  + 2m + 1
                                                     Type: Expression Integer
--R
--R                            m + 1
--R        ((m + 1)log(x) - 1)x
--R   (2)  -------------------------
--R                2
--R               m  + 2m + 1
--R                                                     Type: Expression Integer
--E

--S 9
cc:=aa-bb
 

                               m log(x)                         m + 1
        ((m + 1)x log(x) - x)%e         + ((- m - 1)log(x) + 1)x
   (3)  -------------------------------------------------------------
                                  2
                                 m  + 2m + 1
                                                     Type: Expression Integer
--R
--R                               m log(x)                         m + 1
--R        ((m + 1)x log(x) - x)%e         + ((- m - 1)log(x) + 1)x
--R   (3)  -------------------------------------------------------------
--R                                  2
--R                                 m  + 2m + 1
--R                                                     Type: Expression Integer
--E

--S 10
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 11
dd:=explog cc
 

                              m + 1                         m
        ((- m - 1)log(x) + 1)x      + ((m + 1)x log(x) - x)x
   (5)  -----------------------------------------------------
                              2
                             m  + 2m + 1
                                                     Type: Expression Integer
--R
--R                              m + 1                         m
--R        ((- m - 1)log(x) + 1)x      + ((m + 1)x log(x) - x)x
--R   (5)  -----------------------------------------------------
--R                              2
--R                             m  + 2m + 1
--R                                                     Type: Expression Integer
--E

--S 12     14:527 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(log(x)/x,x)
 

              2
        log(x)
   (1)  -------
           2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R        log(x)
--R   (1)  -------
--R           2
--R                                          Type: Union(Expression Integer,...)
--E

--S 14
bb:=1/2*log(x)^2
 

              2
        log(x)
   (2)  -------
           2
                                                     Type: Expression Integer
--R
--R              2
--R        log(x)
--R   (2)  -------
--R           2
--R                                                     Type: Expression Integer
--E 

--S 15     14:528 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(log(x)/x^2,x)
 

        - log(x) - 1
   (1)  ------------
              x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(x) - 1
--R   (1)  ------------
--R              x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17
bb:=-log(x)/x-1/x
 

        - log(x) - 1
   (2)  ------------
              x
                                                     Type: Expression Integer
--R
--R        - log(x) - 1
--R   (2)  ------------
--R              x
--R                                                     Type: Expression Integer
--E

--S 18     14:529 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19
aa:=integrate(log(x)^2,x)
 

                2
   (1)  x log(x)  - 2x log(x) + 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R   (1)  x log(x)  - 2x log(x) + 2x
--R                                          Type: Union(Expression Integer,...)
--E

--S 20
bb:=x*log(x)^2-2*x*log(x)+2*x
 

                2
   (2)  x log(x)  - 2x log(x) + 2x
                                                     Type: Expression Integer
--R
--R                2
--R   (2)  x log(x)  - 2x log(x) + 2x
--R                                                     Type: Expression Integer
--E 

--S 21     14:530 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 22
aa:=integrate(log(x)^n/x,x)
 

                n log(log(x))
        log(x)%e
   (1)  ---------------------
                n + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                n log(log(x))
--R        log(x)%e
--R   (1)  ---------------------
--R                n + 1
--R                                          Type: Union(Expression Integer,...)
--E

--S 23
bb:=log(x)^(n+1)/(n+1)
 

              n + 1
        log(x)
   (2)  -----------
           n + 1
                                                     Type: Expression Integer
--R
--R              n + 1
--R        log(x)
--R   (2)  -----------
--R           n + 1
--R                                                     Type: Expression Integer
--E 

--S 24
cc:=aa-bb
 

                n log(log(x))         n + 1
        log(x)%e              - log(x)
   (3)  -----------------------------------
                       n + 1
                                                     Type: Expression Integer
--R
--R                n log(log(x))         n + 1
--R        log(x)%e              - log(x)
--R   (3)  -----------------------------------
--R                       n + 1
--R                                                     Type: Expression Integer
--E

--S 25
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26
dd:=explog cc
 

                n + 1               n
        - log(x)      + log(x)log(x)
   (5)  -----------------------------
                    n + 1
                                                     Type: Expression Integer
--R
--R                n + 1               n
--R        - log(x)      + log(x)log(x)
--R   (5)  -----------------------------
--R                    n + 1
--R                                                     Type: Expression Integer
--E

--S 27     14:531 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28
aa:=integrate(1/(x*log(x)),x)
 

   (1)  log(log(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  log(log(x))
--R                                          Type: Union(Expression Integer,...)
--E

--S 29
bb:=log(log(x))
 

   (2)  log(log(x))
                                                     Type: Expression Integer
--R
--R   (2)  log(log(x))
--R                                                     Type: Expression Integer
--E

--S 30     14:532 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 31     14:533 Schaums and Axiom agree by definition
aa:=integrate(1/log(x),x)
 

   (1)  li(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  li(x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 32     14:534 Axiom cannot compute this integral
aa:=integrate(x^m/log(x),x)
 

           x     m
         ++    %J
   (1)   |   ------- d%J
        ++   log(%J)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x     m
--I         ++    %I
--I   (1)   |   ------- d%I
--I        ++   log(%I)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 33     14:535 Axiom cannot compute this integral
aa:=integrate(log(x)^n,x)
 

           x
         ++         n
   (1)   |   log(%J) d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         n
--I   (1)   |   log(%I) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 34     14:536 Axiom cannot compute this integral
aa:=integrate(x^m*log(x)^n,x)
 

           x
         ++    m       n
   (1)   |   %J log(%J) d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    m       n
--I   (1)   |   %I log(%I) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 35
aa:=integrate(log(x^2+a^2),x)
 

               2    2            x
   (1)  x log(x  + a ) + 2a atan(-) - 2x
                                 a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2            x
--R   (1)  x log(x  + a ) + 2a atan(-) - 2x
--R                                 a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36
bb:=x*log(x^2+a^2)-2*x+2*a*atan(x/a)
 

               2    2            x
   (2)  x log(x  + a ) + 2a atan(-) - 2x
                                 a
                                                     Type: Expression Integer
--R
--R               2    2            x
--R   (2)  x log(x  + a ) + 2a atan(-) - 2x
--R                                 a
--R                                                     Type: Expression Integer
--E

--S 37     14:537 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 38
aa:=integrate(log(x^2-a^2),x)
 

               2    2
   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 39
bb:=x*log(x^2-a^2)-2*x+a*log((x+a)/(x-a))
 

               2    2          x + a
   (2)  x log(x  - a ) + a log(-----) - 2x
                               x - a
                                                     Type: Expression Integer
--R
--R               2    2          x + a
--R   (2)  x log(x  - a ) + a log(-----) - 2x
--R                               x - a
--R                                                     Type: Expression Integer
--E

--S 40
cc:=aa-bb
 

                                            x + a
   (3)  a log(x + a) - a log(x - a) - a log(-----)
                                            x - a
                                                     Type: Expression Integer
--R
--R                                            x + a
--R   (3)  a log(x + a) - a log(x - a) - a log(-----)
--R                                            x - a
--R                                                     Type: Expression Integer
--E

--S 41     14:538 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 42
aa:=integrate(x^m*log(x^2+a^2),x)
 

           x
         ++       2     2   m
   (1)   |   log(a  + %J )%J d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       2     2   m
--I   (1)   |   log(a  + %I )%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 43     14:539 Axiom cannot compute this integral
aa:=integrate(x^m*log(x^2-a^2),x)
 

           x
         ++         2     2   m
   (1)   |   log(- a  + %J )%J d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         2     2   m
--I   (1)   |   log(- a  + %I )%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to quat.output (2009/2/17, 17:56:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 25
q := quatern(2/11,-8,3/4,1)
 

         2        3
   (1)  -- - 8i + - j + k
        11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         2        3
--R   (1)  -- - 8i + - j + k
--R        11        4
--R                                            Type: Quaternion Fraction Integer
--E 1

--S 2  of 25
real q
 

         2
   (2)  --
        11
                                                       Type: Fraction Integer
--R 
--R
--R         2
--R   (2)  --
--R        11
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 25
imagI q
 

   (3)  - 8
                                                       Type: Fraction Integer
--R 
--R
--R   (3)  - 8
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 25
imagJ q
 

        3
   (4)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (4)  -
--R        4
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 25
imagK q
 

   (5)  1
                                                       Type: Fraction Integer
--R 
--R
--R   (5)  1
--R                                                       Type: Fraction Integer
--E 5

--S 6 of 25
inv q
 

          352     15488      484       1936
   (6)  ------ + ------ i - ----- j - ------ k
        126993   126993     42331     126993
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          352     15488      484       1936
--R   (6)  ------ + ------ i - ----- j - ------ k
--R        126993   126993     42331     126993
--R                                            Type: Quaternion Fraction Integer
--E 6
 
--S 7 of 25
q**6
 

          2029490709319345   48251690851     144755072553     48251690851
   (7)  - ---------------- - ----------- i + ------------ j + ----------- k
             7256313856        1288408         41229056         10307264
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2029490709319345   48251690851     144755072553     48251690851
--R   (7)  - ---------------- - ----------- i + ------------ j + ----------- k
--R             7256313856        1288408         41229056         10307264
--R                                            Type: Quaternion Fraction Integer
--E 7

--S 8 of 25
r := quatern(-2,3,23/9,-89)
 

                   23
   (8)  - 2 + 3i + -- j - 89k
                    9
                                            Type: Quaternion Fraction Integer
--R 
--R
--R                   23
--R   (8)  - 2 + 3i + -- j - 89k
--R                    9
--R                                            Type: Quaternion Fraction Integer
--E 8

--S 9 of 25
q + r
 

          20        119
   (9)  - -- - 5i + --- j - 88k
          11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          20        119
--R   (9)  - -- - 5i + --- j - 88k
--R          11         36
--R                                            Type: Quaternion Fraction Integer
--E 9

--S 10 of 25
q - r
 

         24         65
   (10)  -- - 11i - -- j + 90k
         11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         24         65
--R   (10)  -- - 11i - -- j + 90k
--R         11         36
--R                                            Type: Quaternion Fraction Integer
--E 10

--S 11 of 25
q * r
 

         14615   20893     140587     16187
   (11)  ----- - ----- i - ------ j - ----- k
          132     396        198       396
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         14615   20893     140587     16187
--R   (11)  ----- - ----- i - ------ j - ----- k
--R          132     396        198       396
--R                                            Type: Quaternion Fraction Integer
--E 11

--S 12 of 25
r * q
 

         14615   33997     140177     1787
   (12)  ----- + ----- i + ------ j + ---- k
          132     396        198       396
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         14615   33997     140177     1787
--R   (12)  ----- + ----- i + ------ j + ---- k
--R          132     396        198       396
--R                                            Type: Quaternion Fraction Integer
--E 12

--S 13  of 25
i := quatern(0,1,0,0)
 

   (13)  i
                                                     Type: Quaternion Integer
--R 
--R
--R   (13)  i
--R                                                     Type: Quaternion Integer
--E 13

--S 14 of 25
j := quatern(0,0,1,0)
 

   (14)  j
                                                     Type: Quaternion Integer
--R 
--R
--R   (14)  j
--R                                                     Type: Quaternion Integer
--E 14

--S 15 of 25
k := quatern(0,0,0,1)
 

   (15)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (15)  k
--R                                                     Type: Quaternion Integer
--E 15

--S 16  of 25
i*i
 

   (16)  - 1
                                                     Type: Quaternion Integer
--R 
--R
--R   (16)  - 1
--R                                                     Type: Quaternion Integer
--E 16

--S 17 of 25
j*j
 

   (17)  - 1
                                                     Type: Quaternion Integer
--R 
--R
--R   (17)  - 1
--R                                                     Type: Quaternion Integer
--E 17

--S 18 of 25
k*k
 

   (18)  - 1
                                                     Type: Quaternion Integer
--R 
--R
--R   (18)  - 1
--R                                                     Type: Quaternion Integer
--E 18

--S 19 of 25
i*j
 

   (19)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (19)  k
--R                                                     Type: Quaternion Integer
--E 19

--S 20 of 25
j*k
 

   (20)  i
                                                     Type: Quaternion Integer
--R 
--R
--R   (20)  i
--R                                                     Type: Quaternion Integer
--E 20

--S 21 of 25
k*i
 

   (21)  j
                                                     Type: Quaternion Integer
--R 
--R
--R   (21)  j
--R                                                     Type: Quaternion Integer
--E 21

--S 22 of 25
q * i
 

              2         3
   (22)  8 + -- i + j - - k
             11         4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R              2         3
--R   (22)  8 + -- i + j - - k
--R             11         4
--R                                            Type: Quaternion Fraction Integer
--E 22

--S 23 of 25
norm q
 

         126993
   (23)  ------
          1936
                                                       Type: Fraction Integer
--R 
--R
--R         126993
--R   (23)  ------
--R          1936
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 25
conjugate q
 

          2        3
   (24)  -- + 8i - - j - k
         11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2        3
--R   (24)  -- + 8i - - j - k
--R         11        4
--R                                            Type: Quaternion Fraction Integer
--E 24

--S 25 of 25
q * %
 

         126993
   (25)  ------
          1936
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         126993
--R   (25)  ------
--R          1936
--R                                            Type: Quaternion Fraction Integer
--E 25
)spool 
 
Starts dribbling to arrows.output (2009/2/17, 17:43:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 3
arrowAngle:=%pi-%pi/10.0@SF
 

   (1)  2.8274333882308138
                                                            Type: DoubleFloat
--R 
--R
--R   (1)  2.8274333882308138
--R                                                            Type: DoubleFloat
--E 1

--S 2 of 3
arrowScale:=0.2@SF
 

   (2)  0.20000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  0.20000000000000001
--R                                                            Type: DoubleFloat
--E 2

--S 3 of 3
makeArrow(p1,p2) ==
    delta    :=p2 -p1
    len      := arrowScale * length delta
    theta := atan(delta.1, delta.2)
    c1:= len*cos(theta+arrowAngle)
    s1:= len*sin(theta+arrowAngle)
    c2:= len*cos(theta-arrowAngle)
    s2:= len*sin(theta-arrowAngle)
    z:= p2.3*(1-arrowScale)
    p3:=point[p2.1+c1,p2.2+s1,z,p2.4]
    p4:=point[p2.1+c2,p2.2+s2,z,p2.4]
    [[p1,p2,p3],[p2,p4]]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3
)spool
 
Starts dribbling to schaum29.output (2009/2/17, 17:59:39).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(sinh(a*x)*cosh(a*x),x)
 

                 2            2
        sinh(a x)  + cosh(a x)
   (1)  -----------------------
                   4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2            2
--R        sinh(a x)  + cosh(a x)
--R   (1)  -----------------------
--R                   4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=sinh(a*x)^2/(2*a)
 

                 2
        sinh(a x)
   (2)  ----------
            2a
                                                     Type: Expression Integer
--R
--R                 2
--R        sinh(a x)
--R   (2)  ----------
--R            2a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                   2            2
        - sinh(a x)  + cosh(a x)
   (3)  -------------------------
                    4a
                                                     Type: Expression Integer
--R
--R                   2            2
--R        - sinh(a x)  + cosh(a x)
--R   (3)  -------------------------
--R                    4a
--R                                                     Type: Expression Integer
--E

--S 4
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5
dd:=sinhsqrrule cc
 

                                 2
        - cosh(2a x) + 2cosh(a x)  + 1
   (5)  ------------------------------
                      8a
                                                     Type: Expression Integer
--R
--R                                 2
--R        - cosh(2a x) + 2cosh(a x)  + 1
--R   (5)  ------------------------------
--R                      8a
--R                                                     Type: Expression Integer
--E

--S 6
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 7      14:590 Schaums and Axiom differ by a constant
ee:=coshsqrrule dd
 

         1
   (7)  --
        4a
                                                     Type: Expression Integer
--R
--R         1
--R   (7)  --
--R        4a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(sinh(p*x)*cosh(q*x),x)
 

        - q sinh(p x)sinh(q x) + p cosh(p x)cosh(q x)
   (1)  ---------------------------------------------
           2    2          2       2    2          2
         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - q sinh(p x)sinh(q x) + p cosh(p x)cosh(q x)
--R   (1)  ---------------------------------------------
--R           2    2          2       2    2          2
--R         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=(cosh(p+q)*x)/(2*(p+q))+(cosh(p-q)*x)/(2*(p-q))
 

        (q - p)x cosh(q + p) + (- q - p)x cosh(q - p)
   (2)  ---------------------------------------------
                            2     2
                          2q  - 2p
                                                     Type: Expression Integer
--R
--R        (q - p)x cosh(q + p) + (- q - p)x cosh(q - p)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 10     14:591 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       - 2q sinh(p x)sinh(q x)
     + 
                                                               2
       ((- q + p)x cosh(q + p) + (q + p)x cosh(q - p))sinh(p x)
     + 
       2p cosh(p x)cosh(q x)
     + 
                                                               2
       ((q - p)x cosh(q + p) + (- q - p)x cosh(q - p))cosh(p x)
  /
        2     2          2        2     2          2
     (2q  - 2p )sinh(p x)  + (- 2q  + 2p )cosh(p x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - 2q sinh(p x)sinh(q x)
--R     + 
--R                                                               2
--R       ((- q + p)x cosh(q + p) + (q + p)x cosh(q - p))sinh(p x)
--R     + 
--R       2p cosh(p x)cosh(q x)
--R     + 
--R                                                               2
--R       ((q - p)x cosh(q + p) + (- q - p)x cosh(q - p))cosh(p x)
--R  /
--R        2     2          2        2     2          2
--R     (2q  - 2p )sinh(p x)  + (- 2q  + 2p )cosh(p x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 11
aa:=integrate(sinh(a*x)^n*cosh(a*x),x)
 

        - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
   (1)  -------------------------------------------------------------------
                                      2                       2
                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
--R   (1)  -------------------------------------------------------------------
--R                                      2                       2
--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12
bb:=sinh(a*x)/((n+1)*a)
 

        sinh(a x)
   (2)  ---------
         a n + a
                                                     Type: Expression Integer
--R
--R        sinh(a x)
--R   (2)  ---------
--R         a n + a
--R                                                     Type: Expression Integer
--E

--S 13     14:592 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
     + 
                  3            2
       - sinh(a x)  + cosh(a x) sinh(a x)
  /
                       2                       2
     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
--R     + 
--R                  3            2
--R       - sinh(a x)  + cosh(a x) sinh(a x)
--R  /
--R                       2                       2
--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 14
aa:=integrate(cosh(a*x)^n*sinh(a*x),x)
 

        - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
   (1)  -------------------------------------------------------------------
                                      2                       2
                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
--R   (1)  -------------------------------------------------------------------
--R                                      2                       2
--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 15
bb:=cosh(a*x)^(n+1)/((n+1)*a)
 

                 n + 1
        cosh(a x)
   (2)  --------------
            a n + a
                                                     Type: Expression Integer
--R
--R                 n + 1
--R        cosh(a x)
--R   (2)  --------------
--R            a n + a
--R                                                     Type: Expression Integer
--E

--S 16     14:593 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
     + 
                   2            2          n + 1
       (- sinh(a x)  + cosh(a x) )cosh(a x)
  /
                       2                       2
     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
--R     + 
--R                   2            2          n + 1
--R       (- sinh(a x)  + cosh(a x) )cosh(a x)
--R  /
--R                       2                       2
--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 17
aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
 

                          3            3
        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
   (1)  -----------------------------------------------
                               8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          3            3
--R        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
--R   (1)  -----------------------------------------------
--R                               8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 18
bb:=sinh(4*a*x)/(32*a)-x/8
 

        sinh(4a x) - 4a x
   (2)  -----------------
               32a
                                                     Type: Expression Integer
--R
--R        sinh(4a x) - 4a x
--R   (2)  -----------------
--R               32a
--R                                                     Type: Expression Integer
--E

--S 19     14:594 Schaums and Axiom agree
cc:=complexNormalize(aa-bb)
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x)
 

                      2cosh(a x)                     2sinh(a x)
        - log(- ---------------------) + log(- ---------------------)
                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   (1)  -------------------------------------------------------------
                                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2cosh(a x)                     2sinh(a x)
--R        - log(- ---------------------) + log(- ---------------------)
--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   (1)  -------------------------------------------------------------
--R                                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21
bb:=1/a*log(tanh(a*x))
 

        log(tanh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(tanh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 22
cc:=aa-bb
 

   (3)
                                      2cosh(a x)
       - log(tanh(a x)) - log(- ---------------------)
                                sinh(a x) - cosh(a x)
     + 
                   2sinh(a x)
       log(- ---------------------)
             sinh(a x) - cosh(a x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      2cosh(a x)
--R       - log(tanh(a x)) - log(- ---------------------)
--R                                sinh(a x) - cosh(a x)
--R     + 
--R                   2sinh(a x)
--R       log(- ---------------------)
--R             sinh(a x) - cosh(a x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 23
dd:=expandLog cc
 

        - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x))
   (4)  --------------------------------------------------
                                 a
                                                     Type: Expression Integer
--R
--R        - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x))
--R   (4)  --------------------------------------------------
--R                                 a
--R                                                     Type: Expression Integer
--E

--S 24
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (5)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (5)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25
ee:=tanhrule dd
 

                             sinh(a x)
        log(sinh(a x)) - log(---------) - log(cosh(a x))
                             cosh(a x)
   (6)  ------------------------------------------------
                                a
                                                     Type: Expression Integer
--R
--R                             sinh(a x)
--R        log(sinh(a x)) - log(---------) - log(cosh(a x))
--R                             cosh(a x)
--R   (6)  ------------------------------------------------
--R                                a
--R                                                     Type: Expression Integer
--E

--S 26     14:595 Schaums and Axiom agree
ff:=expandLog ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)),x)
 

   (1)
                      2                                   2
         (- 2sinh(a x)  - 4cosh(a x)sinh(a x) - 2cosh(a x)  + 2)
      *
         atan(sinh(a x) + cosh(a x))
     + 
       - 2sinh(a x) - 2cosh(a x)
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                      2                                   2
--R         (- 2sinh(a x)  - 4cosh(a x)sinh(a x) - 2cosh(a x)  + 2)
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R       - 2sinh(a x) - 2cosh(a x)
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28
bb:=-1/a*atan(sinh(a*x)-csch(a*x))/a
 

          atan(sinh(a x) - csch(a x))
   (2)  - ---------------------------
                        2
                       a
                                                     Type: Expression Integer
--R
--R          atan(sinh(a x) - csch(a x))
--R   (2)  - ---------------------------
--R                        2
--R                       a
--R                                                     Type: Expression Integer
--E

--S 29     14:596 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                        2                                       2
         (- 2a sinh(a x)  - 4a cosh(a x)sinh(a x) - 2a cosh(a x)  + 2a)
      *
         atan(sinh(a x) + cosh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
         atan(sinh(a x) - csch(a x))
     + 
       - 2a sinh(a x) - 2a cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                        2                                       2
--R         (- 2a sinh(a x)  - 4a cosh(a x)sinh(a x) - 2a cosh(a x)  + 2a)
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R         atan(sinh(a x) - csch(a x))
--R     + 
--R       - 2a sinh(a x) - 2a cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 30
aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x)
 

   (1)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
       2sinh(a x) + 2cosh(a x)
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       2sinh(a x) + 2cosh(a x)
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 31
bb:=sech(a*x)/a+1/a*log(tanh((a*x)/2))
 

                 a x
        log(tanh(---)) + sech(a x)
                  2
   (2)  --------------------------
                     a
                                                     Type: Expression Integer
--R
--R                 a x
--R        log(tanh(---)) + sech(a x)
--R                  2
--R   (2)  --------------------------
--R                     a
--R                                                     Type: Expression Integer
--E

--S 32
cc:=aa-bb
 

   (3)
                   2                                  2              a x
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(tanh(---))
                                                                      2
     + 
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                           2
       - sech(a x)sinh(a x)  + (- 2cosh(a x)sech(a x) + 2)sinh(a x)
     + 
                   2
       (- cosh(a x)  - 1)sech(a x) + 2cosh(a x)
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2              a x
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(tanh(---))
--R                                                                      2
--R     + 
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                           2
--R       - sech(a x)sinh(a x)  + (- 2cosh(a x)sech(a x) + 2)sinh(a x)
--R     + 
--R                   2
--R       (- cosh(a x)  - 1)sech(a x) + 2cosh(a x)
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 33
sechrule:=rule(sech(x) == 1/cosh(x))
 

                      1
   (4)  sech(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (4)  sech(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34
dd:=sechrule cc
 

   (5)
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
                  a x
         log(tanh(---))
                   2
     + 
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                            2             2                     3
         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                  2            2
       - sinh(a x)  + cosh(a x)  - 1
  /
                         2               2                       3
     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                            2             2                     3
--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  2            2
--R       - sinh(a x)  + cosh(a x)  - 1
--R  /
--R                         2               2                       3
--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 35
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (6)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (6)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36
ee:=tanhrule dd
 

   (7)
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                            2             2                     3
         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
                  a x
             sinh(---)
                   2
         log(---------)
                  a x
             cosh(---)
                   2
     + 
                  2            2
       - sinh(a x)  + cosh(a x)  - 1
  /
                         2               2                       3
     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (7)
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                            2             2                     3
--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R                  a x
--R             sinh(---)
--R                   2
--R         log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R     + 
--R                  2            2
--R       - sinh(a x)  + cosh(a x)  - 1
--R  /
--R                         2               2                       3
--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 37
coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
 

               3    cosh(3x) - 3cosh(x)
   (8)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) - 3cosh(x)
--R   (8)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38
ff:=coshcuberule ee
 

   (9)
                                  2             2
             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
           + 
             - cosh(a x)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                             2             2
         (4cosh(a x)sinh(a x)  + 8cosh(a x) sinh(a x) + cosh(3a x) + cosh(a x))
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                  2             2
             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
           + 
             - cosh(a x)
      *
                  a x
             sinh(---)
                   2
         log(---------)
                  a x
             cosh(---)
                   2
     + 
                   2             2
       - 4sinh(a x)  + 4cosh(a x)  - 4
  /
                            2               2
       4a cosh(a x)sinh(a x)  + 8a cosh(a x) sinh(a x) + a cosh(3a x)
     + 
       a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (9)
--R                                  2             2
--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
--R           + 
--R             - cosh(a x)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                             2             2
--R         (4cosh(a x)sinh(a x)  + 8cosh(a x) sinh(a x) + cosh(3a x) + cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                  2             2
--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
--R           + 
--R             - cosh(a x)
--R      *
--R                  a x
--R             sinh(---)
--R                   2
--R         log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R     + 
--R                   2             2
--R       - 4sinh(a x)  + 4cosh(a x)  - 4
--R  /
--R                            2               2
--R       4a cosh(a x)sinh(a x)  + 8a cosh(a x) sinh(a x) + a cosh(3a x)
--R     + 
--R       a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 39
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

                2    cosh(2x) + 1
   (10)  cosh(x)  == ------------
                           2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                2    cosh(2x) + 1
--R   (10)  cosh(x)  == ------------
--R                           2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 40
gg:=coshsqrrule ff
 

   (11)
                                2
           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
         + 
           - cosh(a x)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                              2
           4cosh(a x)sinh(a x)  + (4cosh(2a x) + 4)sinh(a x) + cosh(3a x)
         + 
           cosh(a x)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                2
           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
         + 
           - cosh(a x)
      *
                  a x
             sinh(---)
                   2
         log(---------)
                  a x
             cosh(---)
                   2
     + 
                   2
       - 4sinh(a x)  + 2cosh(2a x) - 2
  /
                            2
       4a cosh(a x)sinh(a x)  + (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x)
     + 
       a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (11)
--R                                2
--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
--R         + 
--R           - cosh(a x)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                              2
--R           4cosh(a x)sinh(a x)  + (4cosh(2a x) + 4)sinh(a x) + cosh(3a x)
--R         + 
--R           cosh(a x)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                2
--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
--R         + 
--R           - cosh(a x)
--R      *
--R                  a x
--R             sinh(---)
--R                   2
--R         log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R     + 
--R                   2
--R       - 4sinh(a x)  + 2cosh(2a x) - 2
--R  /
--R                            2
--R       4a cosh(a x)sinh(a x)  + (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x)
--R     + 
--R       a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 41
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

                2    cosh(2x) - 1
   (12)  sinh(x)  == ------------
                           2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                2    cosh(2x) - 1
--R   (12)  sinh(x)  == ------------
--R                           2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 42
hh:=sinhsqrrule gg
 

   (13)
       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
     + 
                  a x
             sinh(---)
                   2
       - log(---------)
                  a x
             cosh(---)
                   2
  /
     a
                                                     Type: Expression Integer
--R
--R   (13)
--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  a x
--R             sinh(---)
--R                   2
--R       - log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 43
ii:=expandLog hh
 

   (14)
       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
     + 
                  a x              a x
       - log(sinh(---)) + log(cosh(---))
                   2                2
  /
     a
                                                     Type: Expression Integer
--R
--R   (14)
--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  a x              a x
--R       - log(sinh(---)) + log(cosh(---))
--R                   2                2
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 44     14:597 Schaums and Axiom agree
jj:=complexNormalize ii
 

   (15)  0
                                                     Type: Expression Integer
--R
--R   (15)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 45
aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x)
 

   (1)
   -
        4
     /
                     4                        3               2         2
          a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
        + 
                      3                       4
          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R   -
--R        4
--R     /
--R                     4                        3               2         2
--R          a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
--R        + 
--R                      3                       4
--R          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 46
bb:=-(2*coth(2*a*x))/a
 

          2coth(2a x)
   (2)  - -----------
               a
                                                     Type: Expression Integer
--R
--R          2coth(2a x)
--R   (2)  - -----------
--R               a
--R                                                     Type: Expression Integer
--E

--S 47     14:598 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                           4                                3
       2coth(2a x)sinh(a x)  + 8cosh(a x)coth(2a x)sinh(a x)
     + 
                  2                   2             3
       12cosh(a x) coth(2a x)sinh(a x)  + 8cosh(a x) coth(2a x)sinh(a x)
     + 
                  4
       (2cosh(a x)  - 2)coth(2a x) - 4
  /
                  4                        3               2         2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
     + 
                   3                       4
       4a cosh(a x) sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                           4                                3
--R       2coth(2a x)sinh(a x)  + 8cosh(a x)coth(2a x)sinh(a x)
--R     + 
--R                  2                   2             3
--R       12cosh(a x) coth(2a x)sinh(a x)  + 8cosh(a x) coth(2a x)sinh(a x)
--R     + 
--R                  4
--R       (2cosh(a x)  - 2)coth(2a x) - 4
--R  /
--R                  4                        3               2         2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
--R     + 
--R                   3                       4
--R       4a cosh(a x) sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 48
aa:=integrate(sinh(a*x)^2/cosh(a*x),x)
 

   (1)
                                                                         2
       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x)) + sinh(a x)
     + 
                                      2
       2cosh(a x)sinh(a x) + cosh(a x)  - 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                         2
--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x)) + sinh(a x)
--R     + 
--R                                      2
--R       2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49
bb:=sinh(a*x)/a-1/a*atan(sinh(a*x))
 

        - atan(sinh(a x)) + sinh(a x)
   (2)  -----------------------------
                      a
                                                     Type: Expression Integer
--R
--R        - atan(sinh(a x)) + sinh(a x)
--R   (2)  -----------------------------
--R                      a
--R                                                     Type: Expression Integer
--E

--S 50     14:599 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x))
     + 
                                                           2            2
       (2sinh(a x) + 2cosh(a x))atan(sinh(a x)) - sinh(a x)  + cosh(a x)  - 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x))
--R     + 
--R                                                           2            2
--R       (2sinh(a x) + 2cosh(a x))atan(sinh(a x)) - sinh(a x)  + cosh(a x)  - 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 51
aa:=integrate(cosh(a*x)^2/sinh(a*x),x)
 

   (1)
       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
     + 
                                                                          2
       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
     + 
                                      2
       2cosh(a x)sinh(a x) + cosh(a x)  + 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                                                          2
--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
--R     + 
--R                                      2
--R       2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 52
bb:=cosh(a*x)/a+1/a*log(tanh((a*x)/2))
 

                 a x
        log(tanh(---)) + cosh(a x)
                  2
   (2)  --------------------------
                     a
                                                     Type: Expression Integer
--R
--R                 a x
--R        log(tanh(---)) + cosh(a x)
--R                  2
--R   (2)  --------------------------
--R                     a
--R                                                     Type: Expression Integer
--E

--S 53     14:600 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                                           a x
       (- 2sinh(a x) - 2cosh(a x))log(tanh(---))
                                            2
     + 
       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
     + 
                                                                          2
       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
     + 
                  2
       - cosh(a x)  + 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           a x
--R       (- 2sinh(a x) - 2cosh(a x))log(tanh(---))
--R                                            2
--R     + 
--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                                                          2
--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
--R     + 
--R                  2
--R       - cosh(a x)  + 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 54
aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x)
 

   (1)
                     2cosh(a x)                - 2sinh(a x) - 2
       - log(- ---------------------) + log(---------------------)
               sinh(a x) - cosh(a x)        sinh(a x) - cosh(a x)
     + 
       2atan(sinh(a x) + cosh(a x))
  /
     2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     2cosh(a x)                - 2sinh(a x) - 2
--R       - log(- ---------------------) + log(---------------------)
--R               sinh(a x) - cosh(a x)        sinh(a x) - cosh(a x)
--R     + 
--R       2atan(sinh(a x) + cosh(a x))
--R  /
--R     2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 55
bb:=1/(2*a)*log((1+sinh(a*x))/cosh(a*x))+1/a*atan(%e^(a*x))
 

            sinh(a x) + 1            a x
        log(-------------) + 2atan(%e   )
              cosh(a x)
   (2)  ---------------------------------
                        2a
                                                     Type: Expression Integer
--R
--R            sinh(a x) + 1            a x
--R        log(-------------) + 2atan(%e   )
--R              cosh(a x)
--R   (2)  ---------------------------------
--R                        2a
--R                                                     Type: Expression Integer
--E

--S 56
cc:=aa-bb
 

   (3)
             sinh(a x) + 1                2cosh(a x)
       - log(-------------) - log(- ---------------------)
               cosh(a x)            sinh(a x) - cosh(a x)
     + 
              - 2sinh(a x) - 2                                             a x
       log(---------------------) + 2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
           sinh(a x) - cosh(a x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R             sinh(a x) + 1                2cosh(a x)
--R       - log(-------------) - log(- ---------------------)
--R               cosh(a x)            sinh(a x) - cosh(a x)
--R     + 
--R              - 2sinh(a x) - 2                                             a x
--R       log(---------------------) + 2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
--R           sinh(a x) - cosh(a x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 57
dd:=expandLog cc
 

                                             a x
        atan(sinh(a x) + cosh(a x)) - atan(%e   )
   (4)  -----------------------------------------
                            a
                                                     Type: Expression Integer
--R
--R                                             a x
--R        atan(sinh(a x) + cosh(a x)) - atan(%e   )
--R   (4)  -----------------------------------------
--R                            a
--R                                                     Type: Expression Integer
--E

--S 58
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (5)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (5)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 59
ee:=atanrule dd
 

                   a x
               - %e    + %i           - sinh(a x) - cosh(a x) + %i
        %i log(------------) - %i log(----------------------------)
                  a x                  sinh(a x) + cosh(a x) + %i
                %e    + %i
   (6)  -----------------------------------------------------------
                                     2a
                                             Type: Expression Complex Integer
--R
--R                   a x
--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
--R        %i log(------------) - %i log(----------------------------)
--R                  a x                  sinh(a x) + cosh(a x) + %i
--R                %e    + %i
--R   (6)  -----------------------------------------------------------
--R                                     2a
--R                                             Type: Expression Complex Integer
--E

--S 60
ff:=expandLog ee
 

   (7)
       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
     + 
                  a x                  a x
       - %i log(%e    + %i) + %i log(%e    - %i)
  /
     2a
                                             Type: Expression Complex Integer
--R
--R   (7)
--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
--R     + 
--R                  a x                  a x
--R       - %i log(%e    + %i) + %i log(%e    - %i)
--R  /
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 61     14:601 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 62
aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x)
 

   (1)
                      2                                          2
           - sinh(a x)  + (- 2cosh(a x) - 2)sinh(a x) - cosh(a x)  - 2cosh(a x)
         + 
           - 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                   2                                        2
         (sinh(a x)  + (2cosh(a x) + 2)sinh(a x) + cosh(a x)  + 2cosh(a x) + 1)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
       2sinh(a x) + 2cosh(a x)
  /
                   2                                              2
       2a sinh(a x)  + (4a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
     + 
       4a cosh(a x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                      2                                          2
--R           - sinh(a x)  + (- 2cosh(a x) - 2)sinh(a x) - cosh(a x)  - 2cosh(a x)
--R         + 
--R           - 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                   2                                        2
--R         (sinh(a x)  + (2cosh(a x) + 2)sinh(a x) + cosh(a x)  + 2cosh(a x) + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       2sinh(a x) + 2cosh(a x)
--R  /
--R                   2                                              2
--R       2a sinh(a x)  + (4a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R       4a cosh(a x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63
bb:=1/(2*a)*log(tanh((a*x)/2))+1/(2*a*(cosh(a*x)+1))
 

                                a x
        (cosh(a x) + 1)log(tanh(---)) + 1
                                 2
   (2)  ---------------------------------
                2a cosh(a x) + 2a
                                                     Type: Expression Integer
--R
--R                                a x
--R        (cosh(a x) + 1)log(tanh(---)) + 1
--R                                 2
--R   (2)  ---------------------------------
--R                2a cosh(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 64
cc:=aa-bb
 

   (3)
                                     2
           (- cosh(a x) - 1)sinh(a x)
         + 
                        2                                       3             2
           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
         + 
           - 3cosh(a x) - 1
      *
                  a x
         log(tanh(---))
                   2
     + 
                                     2
           (- cosh(a x) - 1)sinh(a x)
         + 
                        2                                       3             2
           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
         + 
           - 3cosh(a x) - 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                   2              2
           (cosh(a x) + 1)sinh(a x)  + (2cosh(a x)  + 4cosh(a x) + 2)sinh(a x)
         + 
                    3             2
           cosh(a x)  + 3cosh(a x)  + 3cosh(a x) + 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                  2            2
       - sinh(a x)  + cosh(a x)  - 1
  /
                                   2
       (2a cosh(a x) + 2a)sinh(a x)
     + 
                    2                                             3
       (4a cosh(a x)  + 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
     + 
                   2
       6a cosh(a x)  + 6a cosh(a x) + 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                     2
--R           (- cosh(a x) - 1)sinh(a x)
--R         + 
--R                        2                                       3             2
--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
--R         + 
--R           - 3cosh(a x) - 1
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                     2
--R           (- cosh(a x) - 1)sinh(a x)
--R         + 
--R                        2                                       3             2
--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
--R         + 
--R           - 3cosh(a x) - 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                   2              2
--R           (cosh(a x) + 1)sinh(a x)  + (2cosh(a x)  + 4cosh(a x) + 2)sinh(a x)
--R         + 
--R                    3             2
--R           cosh(a x)  + 3cosh(a x)  + 3cosh(a x) + 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  2            2
--R       - sinh(a x)  + cosh(a x)  - 1
--R  /
--R                                   2
--R       (2a cosh(a x) + 2a)sinh(a x)
--R     + 
--R                    2                                             3
--R       (4a cosh(a x)  + 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R                   2
--R       6a cosh(a x)  + 6a cosh(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 65
coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
 

               3    cosh(3x) - 3cosh(x)
   (4)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) - 3cosh(x)
--R   (4)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 66
dd:=coshcuberule cc
 

   (5)
                                      2
           (- 4cosh(a x) - 4)sinh(a x)
         + 
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                        2
           - 12cosh(a x)  - 9cosh(a x) - 4
      *
                  a x
         log(tanh(---))
                   2
     + 
                                      2
           (- 4cosh(a x) - 4)sinh(a x)
         + 
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                        2
           - 12cosh(a x)  - 9cosh(a x) - 4
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                    2              2
           (4cosh(a x) + 4)sinh(a x)  + (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x)
         + 
                                   2
           cosh(3a x) + 12cosh(a x)  + 9cosh(a x) + 4
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                   2             2
       - 4sinh(a x)  + 4cosh(a x)  - 4
  /
                                   2
       (8a cosh(a x) + 8a)sinh(a x)
     + 
                     2
       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                    2
       24a cosh(a x)  + 18a cosh(a x) + 8a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                      2
--R           (- 4cosh(a x) - 4)sinh(a x)
--R         + 
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                        2
--R           - 12cosh(a x)  - 9cosh(a x) - 4
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                      2
--R           (- 4cosh(a x) - 4)sinh(a x)
--R         + 
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                        2
--R           - 12cosh(a x)  - 9cosh(a x) - 4
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                    2              2
--R           (4cosh(a x) + 4)sinh(a x)  + (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x)
--R         + 
--R                                   2
--R           cosh(3a x) + 12cosh(a x)  + 9cosh(a x) + 4
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                   2             2
--R       - 4sinh(a x)  + 4cosh(a x)  - 4
--R  /
--R                                   2
--R       (8a cosh(a x) + 8a)sinh(a x)
--R     + 
--R                     2
--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                    2
--R       24a cosh(a x)  + 18a cosh(a x) + 8a
--R                                                     Type: Expression Integer
--E

--S 67
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 68
ee:=sinhsqrrule dd
 

   (7)
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                                                     2
           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
      *
                  a x
         log(tanh(---))
                   2
     + 
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                                                     2
           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      2
           (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
         + 
                                                   2
           (2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  + 7cosh(a x) + 2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                 2
       - 2cosh(2a x) + 4cosh(a x)  - 2
  /
                     2
       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                                                    2
       (4a cosh(a x) + 4a)cosh(2a x) + 24a cosh(a x)  + 14a cosh(a x) + 4a
                                                     Type: Expression Integer
--R
--R   (7)
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                                                     2
--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                                                     2
--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      2
--R           (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
--R         + 
--R                                                   2
--R           (2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  + 7cosh(a x) + 2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                 2
--R       - 2cosh(2a x) + 4cosh(a x)  - 2
--R  /
--R                     2
--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                                                    2
--R       (4a cosh(a x) + 4a)cosh(2a x) + 24a cosh(a x)  + 14a cosh(a x) + 4a
--R                                                     Type: Expression Integer
--E

--S 69
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (8)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (8)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 70
ff:=coshsqrrule ee
 

   (9)
                  a x
       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
                   2
     + 
       log(sinh(a x) + cosh(a x) - 1)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (9)
--R                  a x
--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
--R                   2
--R     + 
--R       log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 71     14:602 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (10)  0
                                                     Type: Expression Integer
--R
--R   (10)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 72
aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x)
 

   (1)
                   2                                        2
         (sinh(a x)  + (2cosh(a x) - 2)sinh(a x) + cosh(a x)  - 2cosh(a x) + 1)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      2                                          2
           - sinh(a x)  + (- 2cosh(a x) + 2)sinh(a x) - cosh(a x)  + 2cosh(a x)
         + 
           - 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
       - 2sinh(a x) - 2cosh(a x)
  /
                   2                                              2
       2a sinh(a x)  + (4a cosh(a x) - 4a)sinh(a x) + 2a cosh(a x)
     + 
       - 4a cosh(a x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   2                                        2
--R         (sinh(a x)  + (2cosh(a x) - 2)sinh(a x) + cosh(a x)  - 2cosh(a x) + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      2                                          2
--R           - sinh(a x)  + (- 2cosh(a x) + 2)sinh(a x) - cosh(a x)  + 2cosh(a x)
--R         + 
--R           - 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       - 2sinh(a x) - 2cosh(a x)
--R  /
--R                   2                                              2
--R       2a sinh(a x)  + (4a cosh(a x) - 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R       - 4a cosh(a x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 73
bb:=-1/(2*a)*log(tanh((a*x)/2))-1/(2*a*(cosh(a*x)-1))
 

                                  a x
        (- cosh(a x) + 1)log(tanh(---)) - 1
                                   2
   (2)  -----------------------------------
                 2a cosh(a x) - 2a
                                                     Type: Expression Integer
--R
--R                                  a x
--R        (- cosh(a x) + 1)log(tanh(---)) - 1
--R                                   2
--R   (2)  -----------------------------------
--R                 2a cosh(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 74
cc:=aa-bb
 

   (3)
                                   2              2
           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
         + 
                    3             2
           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
      *
                  a x
         log(tanh(---))
                   2
     + 
                                   2              2
           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
         + 
                    3             2
           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                     2
           (- cosh(a x) + 1)sinh(a x)
         + 
                        2                                       3             2
           (- 2cosh(a x)  + 4cosh(a x) - 2)sinh(a x) - cosh(a x)  + 3cosh(a x)
         + 
           - 3cosh(a x) + 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                2            2
       sinh(a x)  - cosh(a x)  + 1
  /
                                   2
       (2a cosh(a x) - 2a)sinh(a x)
     + 
                    2                                             3
       (4a cosh(a x)  - 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
     + 
                     2
       - 6a cosh(a x)  + 6a cosh(a x) - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                   2              2
--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
--R         + 
--R                    3             2
--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                   2              2
--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
--R         + 
--R                    3             2
--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                     2
--R           (- cosh(a x) + 1)sinh(a x)
--R         + 
--R                        2                                       3             2
--R           (- 2cosh(a x)  + 4cosh(a x) - 2)sinh(a x) - cosh(a x)  + 3cosh(a x)
--R         + 
--R           - 3cosh(a x) + 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                2            2
--R       sinh(a x)  - cosh(a x)  + 1
--R  /
--R                                   2
--R       (2a cosh(a x) - 2a)sinh(a x)
--R     + 
--R                    2                                             3
--R       (4a cosh(a x)  - 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R                     2
--R       - 6a cosh(a x)  + 6a cosh(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 75
coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
 

               3    cosh(3x) - 3cosh(x)
   (4)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) - 3cosh(x)
--R   (4)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 76
dd:=coshcuberule cc
 

   (5)
                                    2              2
           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
         + 
                                   2
           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
      *
                  a x
         log(tanh(---))
                   2
     + 
                                    2              2
           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
         + 
                                   2
           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                      2
           (- 4cosh(a x) + 4)sinh(a x)
         + 
                        2
           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                      2
           12cosh(a x)  - 9cosh(a x) + 4
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                 2             2
       4sinh(a x)  - 4cosh(a x)  + 4
  /
                                   2
       (8a cosh(a x) - 8a)sinh(a x)
     + 
                     2
       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                      2
       - 24a cosh(a x)  + 18a cosh(a x) - 8a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                    2              2
--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
--R         + 
--R                                   2
--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                    2              2
--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
--R         + 
--R                                   2
--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                      2
--R           (- 4cosh(a x) + 4)sinh(a x)
--R         + 
--R                        2
--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                      2
--R           12cosh(a x)  - 9cosh(a x) + 4
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                 2             2
--R       4sinh(a x)  - 4cosh(a x)  + 4
--R  /
--R                                   2
--R       (8a cosh(a x) - 8a)sinh(a x)
--R     + 
--R                     2
--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                      2
--R       - 24a cosh(a x)  + 18a cosh(a x) - 8a
--R                                                     Type: Expression Integer
--E

--S 77
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 78
ee:=sinhsqrrule dd
 

   (7)
                      2
           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
         + 
                                                   2
           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
      *
                  a x
         log(tanh(---))
                   2
     + 
                      2
           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
         + 
                                                   2
           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                        2
           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                                                     2
           (- 2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  - 7cosh(a x) + 2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                               2
       2cosh(2a x) - 4cosh(a x)  + 2
  /
                     2
       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                                                    2
       (4a cosh(a x) - 4a)cosh(2a x) - 24a cosh(a x)  + 14a cosh(a x) - 4a
                                                     Type: Expression Integer
--R
--R   (7)
--R                      2
--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
--R         + 
--R                                                   2
--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                      2
--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
--R         + 
--R                                                   2
--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                        2
--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                                                     2
--R           (- 2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  - 7cosh(a x) + 2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                               2
--R       2cosh(2a x) - 4cosh(a x)  + 2
--R  /
--R                     2
--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                                                    2
--R       (4a cosh(a x) - 4a)cosh(2a x) - 24a cosh(a x)  + 14a cosh(a x) - 4a
--R                                                     Type: Expression Integer
--E

--S 79
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (8)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (8)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 80
ff:=coshsqrrule ee
 

   (9)
                a x
       log(tanh(---)) + log(sinh(a x) + cosh(a x) + 1)
                 2
     + 
       - log(sinh(a x) + cosh(a x) - 1)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (9)
--R                a x
--R       log(tanh(---)) + log(sinh(a x) + cosh(a x) + 1)
--R                 2
--R     + 
--R       - log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 81     14:603 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (10)  0
                                                     Type: Expression Integer
--R
--R   (10)  0
--R                                                     Type: Expression Integer
--E

)spool
 
Starts dribbling to calculus2.output (2009/2/17, 17:44:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input for page FormalDerivativePage

--S 1 of 112
differentiate(f, x)
 

   (1)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  0
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 112
f := operator f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 112
x := operator x
 

   (3)  x
                                                          Type: BasicOperator
--R 
--R
--R   (3)  x
--R                                                          Type: BasicOperator
--E 3

--S 4 of 112
y := operator y
 

   (4)  y
                                                          Type: BasicOperator
--R 
--R
--R   (4)  y
--R                                                          Type: BasicOperator
--E 4

--S 5 of 112
a := f(x z, y z, z**2) + x y(z+1)
 

                                   2
   (5)  x(y(z + 1)) + f(x(z),y(z),z )
                                                     Type: Expression Integer
--R 
--R
--R                                   2
--R   (5)  x(y(z + 1)) + f(x(z),y(z),z )
--R                                                     Type: Expression Integer
--E 5

--S 6 of 112
dadz := differentiate(a, z)
 

   (6)
                      2     ,                  2     ,                  2
     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
        ,3                       ,2                       ,1
   + 
      ,           ,
     x (y(z + 1))y (z + 1)

                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                      2     ,                  2     ,                  2
--R     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
--R        ,3                       ,2                       ,1
--R   + 
--R      ,           ,
--R     x (y(z + 1))y (z + 1)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 112
eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

   (7)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 112
eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

            z             2
   (8)  f(%e ,log(z + 1),z ) + z + 2
                                                     Type: Expression Integer
--R 
--R
--R            z             2
--R   (8)  f(%e ,log(z + 1),z ) + z + 2
--R                                                     Type: Expression Integer
--E 8

--S 9 of 112
differentiate(%, z)
 

   (9)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (9)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 9

-- Input for page SeriesArithmeticPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 112
x := series x
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 10

--S 11 of 112
num := 3 + x
 

   (2)  3 + x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)  3 + x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11

--S 12 of 112
den := 1 + 7 * x
 

   (3)  1 + 7x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)  1 + 7x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 12

--S 13 of 112
num / den
 

   (4)
                   2       3        4         5          6           7
     3 - 20x + 140x  - 980x  + 6860x  - 48020x  + 336140x  - 2352980x
   + 
              8             9             10      11
     16470860x  - 115296020x  + 807072140x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (4)
--R                   2       3        4         5          6           7
--R     3 - 20x + 140x  - 980x  + 6860x  - 48020x  + 336140x  - 2352980x
--R   + 
--R              8             9             10      11
--R     16470860x  - 115296020x  + 807072140x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 13

--S 14 of 112
base := 1 / (1 - x)
 

                 2    3    4    5    6    7    8    9    10      11
   (5)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (5)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 14

--S 15 of 112
expon := x * base
 

             2    3    4    5    6    7    8    9    10    11      12
   (6)  x + x  + x  + x  + x  + x  + x  + x  + x  + x   + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             2    3    4    5    6    7    8    9    10    11      12
--R   (6)  x + x  + x  + x  + x  + x  + x  + x  + x  + x   + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 15

--S 16 of 112
base ** expon
 

   (7)
          2   3  3   7  4   43  5   649  6   241  7   3706  8   85763  9
     1 + x  + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
              2      3      12      120       30       315       5040
   + 
     245339  10      11
     ------ x   + O(x  )
      10080
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (7)
--R          2   3  3   7  4   43  5   649  6   241  7   3706  8   85763  9
--R     1 + x  + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R              2      3      12      120       30       315       5040
--R   + 
--R     245339  10      11
--R     ------ x   + O(x  )
--R      10080
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 16

-- Input for page SeriesConversionPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 17 of 112
f := sin(a*x)
 

   (1)  sin(a x)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  sin(a x)
--R                                                     Type: Expression Integer
--E 17

--S 18 of 112
series(f,x = 0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (2)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (2)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 18

--S 19 of 112
g := y / (exp(y) - 1)
 

           y
   (3)  -------
          y
        %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R           y
--R   (3)  -------
--R          y
--R        %e  - 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 112
series(g)
 

   (4)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - y + -- y  - --- y  + ----- y  - ------- y  + -------- y   + O(y  )
       2     12      720      30240      1209600      47900160
                        Type: UnivariatePuiseuxSeries(Expression Integer,y,0)
--R 
--R
--R   (4)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - y + -- y  - --- y  + ----- y  - ------- y  + -------- y   + O(y  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,y,0)
--E 20

--S 21 of 112
h := sin(3*x)
 

   (5)  sin(3x)
                                                     Type: Expression Integer
--R 
--R
--R   (5)  sin(3x)
--R                                                     Type: Expression Integer
--E 21

--S 22 of 112
series(h,x,x = %pi/12)
 

   (6)
                %pi               %pi 2              %pi 3               %pi 4
     sin(3)(x - ---) + sin(6)(x - ---)  + sin(9)(x - ---)  + sin(12)(x - ---)
                 12                12                 12                  12
   + 
                 %pi 5               %pi 6               %pi 7
     sin(15)(x - ---)  + sin(18)(x - ---)  + sin(21)(x - ---)
                  12                  12                  12
   + 
                 %pi 8               %pi 9               %pi 10
     sin(24)(x - ---)  + sin(27)(x - ---)  + sin(30)(x - ---)
                  12                  12                  12
   + 
                 %pi 11          %pi 12
     sin(33)(x - ---)   + O((x - ---)  )
                  12              12
                    Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/12)
--R 
--R
--R   (6)
--R                %pi               %pi 2              %pi 3               %pi 4
--R     sin(3)(x - ---) + sin(6)(x - ---)  + sin(9)(x - ---)  + sin(12)(x - ---)
--R                 12                12                 12                  12
--R   + 
--R                 %pi 5               %pi 6               %pi 7
--R     sin(15)(x - ---)  + sin(18)(x - ---)  + sin(21)(x - ---)
--R                  12                  12                  12
--R   + 
--R                 %pi 8               %pi 9               %pi 10
--R     sin(24)(x - ---)  + sin(27)(x - ---)  + sin(30)(x - ---)
--R                  12                  12                  12
--R   + 
--R                 %pi 11          %pi 12
--R     sin(33)(x - ---)   + O((x - ---)  )
--R                  12              12
--R                    Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/12)
--E 22

--S 23 of 112
series(sqrt(tan(a*x)),x = 0)
 

             1           5             9
             -    2 +-+  -      4 +-+  -
         +-+ 2   a \|a   2   19a \|a   2      6
   (7)  \|a x  + ------ x  + -------- x  + O(x )
                    6           360
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1           5             9
--R             -    2 +-+  -      4 +-+  -
--R         +-+ 2   a \|a   2   19a \|a   2      6
--R   (7)  \|a x  + ------ x  + -------- x  + O(x )
--R                    6           360
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 23

--S 24 of 112
series(sec(x) ** 2,x = %pi/2)
 

   (8)
          %pi - 2   1    1      %pi 2    2       %pi 4    1       %pi 6
     (x - ---)    + - + -- (x - ---)  + --- (x - ---)  + --- (x - ---)
           2        3   15       2      189       2      675       2
   + 
       2        %pi 8          %pi 9
     ----- (x - ---)  + O((x - ---) )
     10395       2              2
                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--R 
--R
--R   (8)
--R          %pi - 2   1    1      %pi 2    2       %pi 4    1       %pi 6
--R     (x - ---)    + - + -- (x - ---)  + --- (x - ---)  + --- (x - ---)
--R           2        3   15       2      189       2      675       2
--R   + 
--R       2        %pi 8          %pi 9
--R     ----- (x - ---)  + O((x - ---) )
--R     10395       2              2
--R                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--E 24

--S 25 of 112
bern := t * exp(t*x) / (exp(t) - 1)
 

            t x
        t %e
   (9)  -------
          t
        %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R            t x
--R        t %e
--R   (9)  -------
--R          t
--R        %e  - 1
--R                                                     Type: Expression Integer
--E 25

--S 26 of 112
series(bern,t = 0)
 

   (10)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
     ---------------------- t  + --------------------- t
               720                        720
   + 
        6       5       4      2            7      6      5     3
     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
     ------------------------------- t  + --------------------------- t
                  30240                              30240
   + 
        8       7       6      4      2
     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
     -------------------------------------- t
                     1209600
   + 
        9      8      7      5      3
     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
     ------------------------------------- t
                    3628800
   + 
        10       9       8       6       4      2
     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
     ------------------------------------------------ t   + O(t  )
                         239500800
                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--R 
--R
--R   (10)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
--R     ---------------------- t  + --------------------- t
--R               720                        720
--R   + 
--R        6       5       4      2            7      6      5     3
--R     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
--R     ------------------------------- t  + --------------------------- t
--R                  30240                              30240
--R   + 
--R        8       7       6      4      2
--R     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
--R     -------------------------------------- t
--R                     1209600
--R   + 
--R        9      8      7      5      3
--R     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
--R     ------------------------------------- t
--R                    3628800
--R   + 
--R        10       9       8       6       4      2
--R     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
--R     ------------------------------------------------ t   + O(t  )
--R                         239500800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 26

-- Input for page SeriesDifferentialEquationPage
)clear all
 
   All user variables and function definitions have been cleared.

)set streams calculate 7
 
 
--S 27 of 112
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 27

--S 28 of 112
eq := differentiate(y(x), x, 3) - sin(differentiate(y(x), x, 2)) * exp(y(x)) = cos(x)
 

         ,,,        y(x)     ,,
   (2)  y   (x) - %e    sin(y  (x))= cos(x)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,,        y(x)     ,,
--R   (2)  y   (x) - %e    sin(y  (x))= cos(x)
--R
--R                                            Type: Equation Expression Integer
--E 28

--S 29 of 112
seriesSolve(eq, y, x = 0, [1, 0, 0])
 
   Compiling function %B with type List UnivariateTaylorSeries(
      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
      Integer,x,0) 

   (3)
                          2            3              4      2
         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
         6      24        120           720                 5040
   + 
        8
     O(x )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--I   Compiling function %B with type List UnivariateTaylorSeries(
--R      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,0) 
--R
--R   (3)
--R                          2            3              4      2
--R         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
--R     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
--R         6      24        120           720                 5040
--R   + 
--R        8
--R     O(x )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 29

--S 30 of 112
x := operator 'x
 
   Compiled code for %B has been cleared.

   (4)  x
                                                          Type: BasicOperator
--R 
--I   Compiled code for %B has been cleared.
--R
--R   (4)  x
--R                                                          Type: BasicOperator
--E 30

--S 31 of 112
eq1 := differentiate(x(t), t) = 1 + x(t)**2
 

         ,         2
   (5)  x (t)= x(t)  + 1

                                            Type: Equation Expression Integer
--R 
--R
--R         ,         2
--R   (5)  x (t)= x(t)  + 1
--R
--R                                            Type: Equation Expression Integer
--E 31

--S 32 of 112
eq2 := differentiate(y(t), t) = x(t) * y(t)
 

         ,
   (6)  y (t)= x(t)y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,
--R   (6)  y (t)= x(t)y(t)
--R
--R                                            Type: Equation Expression Integer
--E 32

--S 33 of 112
seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])
 
   Compiling function %D with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 
   Compiling function %E with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 

             1  3    2  5    17  7      8      1  2    5  4    61  6      8
   (7)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
             3      15      315                2      24      720
                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--I   Compiling function %D with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--I   Compiling function %E with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R
--R             1  3    2  5    17  7      8      1  2    5  4    61  6      8
--R   (7)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
--R             3      15      315                2      24      720
--R                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--E 33

-- Input for page LaplacePage
)clear all
 
   All user variables and function definitions have been cleared.

--S 34 of 112
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
 

   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
--R                                                     Type: Expression Integer
--E 34

--S 35 of 112
laplace(%, t, s)
 

             3
           4a
   (2)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R             3
--R           4a
--R   (2)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 35

--S 36 of 112
laplace((exp(a*t) - exp(b*t))/t, t, s)
 

   (3)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 36

--S 37 of 112
laplace(2/t * (1 - cos(a*t)), t, s)
 

             2    2
   (4)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R             2    2
--R   (4)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 37

--S 38 of 112
laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
 

                    1
   (5)  ------------------------
           2             3    2
        b s  + 2a b s + b  + a b
                                                     Type: Expression Integer
--R 
--R
--R                    1
--R   (5)  ------------------------
--R           2             3    2
--R        b s  + 2a b s + b  + a b
--R                                                     Type: Expression Integer
--E 38

--S 39 of 112
laplace((cos(a*t) - cos(b*t))/t, t, s)
 

             2    2         2    2
        log(s  + b ) - log(s  + a )
   (6)  ---------------------------
                     2
                                                     Type: Expression Integer
--R 
--R
--R             2    2         2    2
--R        log(s  + b ) - log(s  + a )
--R   (6)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 39

--S 40 of 112
laplace(exp(a*t+b)*Ei(c*t), t, s)
 

          b    s + c - a
        %e log(---------)
                   c
   (7)  -----------------
              s - a
                                                     Type: Expression Integer
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (7)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 40

--S 41 of 112
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
 

               2    2
              s  + b             d
        a log(-------) + 2c atan(-)
                  2              s
                 b
   (8)  ---------------------------
                     2s
                                                     Type: Expression Integer
--R
--R               2    2
--R              s  + b             d
--R        a log(-------) + 2c atan(-)
--R                  2              s
--R                 b
--R   (8)  ---------------------------
--R                     2s
--R                                                     Type: Expression Integer
--E 41

--S 42 of 112
laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
 

                                    2
          4     2 2    4           t           3
        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
   (9)  ----------------------------------------
                      4     2 2    4
                     s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                                    2
--R          4     2 2    4           t           3
--R        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
--R   (9)  ----------------------------------------
--R                      4     2 2    4
--R                     s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 42

-- Input for page SeriesCoefficientPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 43 of 112
x := series(x)
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 43

--S 44 of 112
y := exp(x) * sin(x)
 

             2   1  3    1  5    1  6    1   7      9
   (2)  x + x  + - x  - -- x  - -- x  - --- x  + O(x )
                 3      30      90      630
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             2   1  3    1  5    1  6    1   7      9
--R   (2)  x + x  + - x  - -- x  - -- x  - --- x  + O(x )
--R                 3      30      90      630
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 44

--S 45 of 112
coefficient(y,6)
 

           1
   (3)  - --
          90
                                                     Type: Expression Integer
--R 
--R
--R           1
--R   (3)  - --
--R          90
--R                                                     Type: Expression Integer
--E 45

--S 46 of 112
coefficient(y,15)
 

               1
   (4)  - -----------
          10216206000
                                                     Type: Expression Integer
--R 
--R
--R               1
--R   (4)  - -----------
--R          10216206000
--R                                                     Type: Expression Integer
--E 46

--S 47 of 112
y
 

   (5)
          2   1  3    1  5    1  6    1   7     1    9      1    10
     x + x  + - x  - -- x  - -- x  - --- x  + ----- x  + ------ x
              3      30      90      630      22680      113400
   + 
        1     11       1     13       1      14        1       15      16
     ------- x   - -------- x   - --------- x   - ----------- x   + O(x  )
     1247400       97297200       681080400       10216206000
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (5)
--R          2   1  3    1  5    1  6    1   7     1    9      1    10
--R     x + x  + - x  - -- x  - -- x  - --- x  + ----- x  + ------ x
--R              3      30      90      630      22680      113400
--R   + 
--R        1     11       1     13       1      14        1       15      16
--R     ------- x   - -------- x   - --------- x   - ----------- x   + O(x  )
--R     1247400       97297200       681080400       10216206000
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 47

-- Input for page SymbolicIntegrationPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 48 of 112
f := (x**2+2*x+1) / (x**6+6*x**5+15*x**4+20*x**3+15*x**2+6*x+2)
 

                       2
                      x  + 2x + 1
   (1)  --------------------------------------
         6     5      4      3      2
        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                       2
--R                      x  + 2x + 1
--R   (1)  --------------------------------------
--R         6     5      4      3      2
--R        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
--R                                            Type: Fraction Polynomial Integer
--E 48

--S 49 of 112
integrate(f, x)
 

              3     2
        atan(x  + 3x  + 3x + 1)
   (2)  -----------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2
--R        atan(x  + 3x  + 3x + 1)
--R   (2)  -----------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 112
g := log(1 + sqrt(a * x + b)) / x
 

             +-------+
        log(\|a x + b  + 1)
   (3)  -------------------
                 x
                                                     Type: Expression Integer
--R 
--R
--R             +-------+
--R        log(\|a x + b  + 1)
--R   (3)  -------------------
--R                 x
--R                                                     Type: Expression Integer
--E 50

--S 51 of 112
integrate(g, x)
 

           x      +--------+
         ++  log(\|b + %J a  + 1)
   (4)   |   -------------------- d%J
        ++            %J
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x      +--------+
--I         ++  log(\|b + %G a  + 1)
--I   (4)   |   -------------------- d%G
--I        ++            %G
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 112
integrate(1/(x**2 - 2),x)
 

              2      +-+
            (x  + 2)\|2  - 4x
        log(-----------------)
                   2
                  x  - 2
   (5)  ----------------------
                   +-+
                 2\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2      +-+
--R            (x  + 2)\|2  - 4x
--R        log(-----------------)
--R                   2
--R                  x  - 2
--R   (5)  ----------------------
--R                   +-+
--R                 2\|2
--R                                          Type: Union(Expression Integer,...)
--E 52

--S 53 of 112
integrate(1/(x**2 + 2),x)
 

               +-+
             x\|2
        atan(-----)
               2
   (6)  -----------
             +-+
            \|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-+
--R             x\|2
--R        atan(-----)
--R               2
--R   (6)  -----------
--R             +-+
--R            \|2
--R                                          Type: Union(Expression Integer,...)
--E 53

--S 54 of 112
h := x**2 / (x**4 - a**2)
 

            2
           x
   (7)  -------
         4    2
        x  - a
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            2
--R           x
--R   (7)  -------
--R         4    2
--R        x  - a
--R                                            Type: Fraction Polynomial Integer
--E 54

--S 55 of 112
integrate(h, x)
 

   (8)
          2      +-+                   +-+
        (x  + a)\|a  - 2a x          x\|a
    log(-------------------) + 2atan(-----)
                2                      a
               x  - a
   [---------------------------------------,
                       +-+
                     4\|a
          2      +---+                   +---+
        (x  - a)\|- a  + 2a x          x\|- a
    log(---------------------) - 2atan(-------)
                 2                        a
                x  + a
    -------------------------------------------]
                        +---+
                      4\|- a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (8)
--R          2      +-+                   +-+
--R        (x  + a)\|a  - 2a x          x\|a
--R    log(-------------------) + 2atan(-----)
--R                2                      a
--R               x  - a
--R   [---------------------------------------,
--R                       +-+
--R                     4\|a
--R          2      +---+                   +---+
--R        (x  - a)\|- a  + 2a x          x\|- a
--R    log(---------------------) - 2atan(-------)
--R                 2                        a
--R                x  + a
--R    -------------------------------------------]
--R                        +---+
--R                      4\|- a
--R                                     Type: Union(List Expression Integer,...)
--E 55

--S 56 of 112
complexIntegrate(h, x)
 

   (9)
          +--+       +--+         +----+       +----+
          | 1        | 1          |   1        |   1
       -  |-- log(2a |--  + x) +  |- -- log(2a |- --  + x)
         \|4a       \|4a         \|  4a       \|  4a
     + 
          +----+         +----+         +--+         +--+
          |   1          |   1          | 1          | 1
       -  |- -- log(- 2a |- --  + x) +  |-- log(- 2a |--  + x)
         \|  4a         \|  4a         \|4a         \|4a
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (9)
--R          +--+       +--+         +----+       +----+
--R          | 1        | 1          |   1        |   1
--R       -  |-- log(2a |--  + x) +  |- -- log(2a |- --  + x)
--R         \|4a       \|4a         \|  4a       \|  4a
--R     + 
--R          +----+         +----+         +--+         +--+
--R          |   1          |   1          | 1          | 1
--R       -  |- -- log(- 2a |- --  + x) +  |-- log(- 2a |--  + x)
--R         \|  4a         \|  4a         \|4a         \|4a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 56

--S 57 of 112
expandLog %
 

   (10)
          +--+       +--+         +--+       +--+
          | 1        | 1          | 1        | 1
       -  |-- log(2a |--  + x) +  |-- log(2a |--  - x)
         \|4a       \|4a         \|4a       \|4a
     + 
        +----+       +----+         +----+       +----+                 +--+
        |   1        |   1          |   1        |   1                  | 1
        |- -- log(2a |- --  + x) -  |- -- log(2a |- --  - x) + log(- 1) |--
       \|  4a       \|  4a         \|  4a       \|  4a                 \|4a
     + 
                  +----+
                  |   1
       - log(- 1) |- --
                 \|  4a
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (10)
--R          +--+       +--+         +--+       +--+
--R          | 1        | 1          | 1        | 1
--R       -  |-- log(2a |--  + x) +  |-- log(2a |--  - x)
--R         \|4a       \|4a         \|4a       \|4a
--R     + 
--R        +----+       +----+         +----+       +----+                 +--+
--R        |   1        |   1          |   1        |   1                  | 1
--R        |- -- log(2a |- --  + x) -  |- -- log(2a |- --  - x) + log(- 1) |--
--R       \|  4a       \|  4a         \|  4a       \|  4a                 \|4a
--R     + 
--R                  +----+
--R                  |   1
--R       - log(- 1) |- --
--R                 \|  4a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 57

--S 58 of 112
rootSimp %
 

   (11)
                 +---+                    +-+                    +---+
        +-+    x\|- a  + a     +---+    x\|a  + a     +-+    - x\|- a  + a
       \|a log(-----------) - \|- a log(---------) - \|a log(-------------)
                   +---+                    +-+                   +---+
                  \|- a                    \|a                   \|- a
     + 
                     +-+
        +---+    - x\|a  + a             +-+            +---+
       \|- a log(-----------) - log(- 1)\|a  + log(- 1)\|- a
                      +-+
                     \|a
  /
       +---+ +-+
     4\|- a \|a
                                                     Type: Expression Integer
--R 
--R
--R   (11)
--R                 +---+                    +-+                    +---+
--R        +-+    x\|- a  + a     +---+    x\|a  + a     +-+    - x\|- a  + a
--R       \|a log(-----------) - \|- a log(---------) - \|a log(-------------)
--R                   +---+                    +-+                   +---+
--R                  \|- a                    \|a                   \|- a
--R     + 
--R                     +-+
--R        +---+    - x\|a  + a             +-+            +---+
--R       \|- a log(-----------) - log(- 1)\|a  + log(- 1)\|- a
--R                      +-+
--R                     \|a
--R  /
--R       +---+ +-+
--R     4\|- a \|a
--R                                                     Type: Expression Integer
--E 58

--S 59 of 112
ratForm %
 
   There are no library operations named ratForm 
      Use HyperDoc Browse or issue
                              )what op ratForm
      to learn if there is any operation containing " ratForm " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      ratForm with argument type(s) 
                             Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named ratForm 
--R      Use HyperDoc Browse or issue
--R                              )what op ratForm
--R      to learn if there is any operation containing " ratForm " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      ratForm with argument type(s) 
--R                             Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 59

-- Input for page DerivativePage
)clear all
 
   All user variables and function definitions have been cleared.

--S 60 of 112
f := exp exp x
 

            x
          %e
   (1)  %e
                                                     Type: Expression Integer
--R 
--R
--R            x
--R          %e
--R   (1)  %e
--R                                                     Type: Expression Integer
--E 60

--S 61 of 112
differentiate(f, x)
 

               x
          x  %e
   (2)  %e %e
                                                     Type: Expression Integer
--R 
--R
--R               x
--R          x  %e
--R   (2)  %e %e
--R                                                     Type: Expression Integer
--E 61

--S 62 of 112
differentiate(f, x, 4)
 

                                              x
            x 4       x 3       x 2     x   %e
   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
                                                     Type: Expression Integer
--R 
--R
--R                                              x
--R            x 4       x 3       x 2     x   %e
--R   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
--R                                                     Type: Expression Integer
--E 62

--S 63 of 112
g := sin(x**2 + y)
 

                 2
   (4)  sin(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (4)  sin(y + x )
--R                                                     Type: Expression Integer
--E 63

--S 64 of 112
differentiate(g, y)
 

                 2
   (5)  cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (5)  cos(y + x )
--R                                                     Type: Expression Integer
--E 64

--S 65 of 112
differentiate(g, [y, y, x, x])
 

          2         2              2
   (6)  4x sin(y + x ) - 2cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R          2         2              2
--R   (6)  4x sin(y + x ) - 2cos(y + x )
--R                                                     Type: Expression Integer
--E 65

-- Input for page SeriesFormulaPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 66 of 112
taylor(n +-> 1/factorial(n),x = 0)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (1)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
                2      6      24      120      720      5040
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (1)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
--R                2      6      24      120      720      5040
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 66

--S 67 of 112
taylor(n +-> (-1)**(n-1)/n,x = 1,1..)
 

   (2)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7            8
     - (x - 1)  + O((x - 1) )
     7
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (2)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7            8
--R     - (x - 1)  + O((x - 1) )
--R     7
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 67

--S 68 of 112
taylor(n +-> (-1)**(n-1)/n,x = 1,1..7)
 

   (3)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7
     - (x - 1)
     7
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (3)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7
--R     - (x - 1)
--R     7
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 68

--S 69 of 112
laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..)
 

   (4)
            - 1   1   1           1        2   1        3   1        4
     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
                  2   3           4            5            6
   + 
     1        5   1        6            7
     - (x - 1)  - - (x - 1)  + O((x - 1) )
     7            8
                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--R 
--R
--R   (4)
--R            - 1   1   1           1        2   1        3   1        4
--R     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
--R                  2   3           4            5            6
--R   + 
--R     1        5   1        6            7
--R     - (x - 1)  - - (x - 1)  + O((x - 1) )
--R     7            8
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--E 69

--S 70 of 112
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)
 

            1  3    1   5     1   7      9
   (5)  x - - x  + --- x  - ---- x  + O(x )
            6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      9
--R   (5)  x - - x  + --- x  - ---- x  + O(x )
--R            6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 70

--S 71 of 112
puiseux(j +-> j**2,x = 8,-4/3..,1/2)
 

                    4               5              1
                  - -             - -            - -
        16          3   25          6   1          3            0
   (6)  -- (x - 8)    + -- (x - 8)    + - (x - 8)    + O((x - 8) )
         9              36              9
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                    4               5              1
--R                  - -             - -            - -
--R        16          3   25          6   1          3            0
--R   (6)  -- (x - 8)    + -- (x - 8)    + - (x - 8)    + O((x - 8) )
--R         9              36              9
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 71

--S 72 of 112
series(n +-> 1/factorial(n),x = 0)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (7)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
                2      6      24      120      720      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (7)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
--R                2      6      24      120      720      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 72

--S 73 of 112
series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..)
 

   (8)
            - 1   1   1           1        2   1        3   1        4
     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
                  2   3           4            5            6
   + 
     1        5   1        6            7
     - (x - 1)  - - (x - 1)  + O((x - 1) )
     7            8
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (8)
--R            - 1   1   1           1        2   1        3   1        4
--R     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
--R                  2   3           4            5            6
--R   + 
--R     1        5   1        6            7
--R     - (x - 1)  - - (x - 1)  + O((x - 1) )
--R     7            8
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 73

--S 74 of 112
series(i +-> (-1)**((i - 1)/2)/factorial(i),x = 0,1..,2)
 

            1  3    1   5     1   7      9
   (9)  x - - x  + --- x  - ---- x  + O(x )
            6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      9
--R   (9)  x - - x  + --- x  - ---- x  + O(x )
--R            6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 74

-- Input for page SeriesCreationPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 75 of 112
x := series x
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 75

--S 76 of 112
1/(1 - x - x**2)
 

                  2     3     4     5      6      7      8
   (2)  1 + x + 2x  + 3x  + 5x  + 8x  + 13x  + 21x  + O(x )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                  2     3     4     5      6      7      8
--R   (2)  1 + x + 2x  + 3x  + 5x  + 8x  + 13x  + 21x  + O(x )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 76

--S 77 of 112
sin(x)
 

            1  3    1   5     1   7      9
   (3)  x - - x  + --- x  - ---- x  + O(x )
            6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      9
--R   (3)  x - - x  + --- x  - ---- x  + O(x )
--R            6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 77

--S 78 of 112
sin(1 + x)
 

   (4)
                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
                           2           6          24          120
   + 
       sin(1)  6   cos(1)  7      8
     - ------ x  - ------ x  + O(x )
         720        5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (4)
--R                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
--R     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
--R                           2           6          24          120
--R   + 
--R       sin(1)  6   cos(1)  7      8
--R     - ------ x  - ------ x  + O(x )
--R         720        5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 78

--S 79 of 112
sin(a * x)
 

               3        5        7
              a   3    a   5    a    7      9
   (5)  a x - -- x  + --- x  - ---- x  + O(x )
               6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7
--R              a   3    a   5    a    7      9
--R   (5)  a x - -- x  + --- x  - ---- x  + O(x )
--R               6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 79

--S 80 of 112
series(1/log(y),y = 1)
 

   (6)
            - 1   1    1            1        2    19        3    3         4
     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
                  2   12           24            720            160
   + 
        863         5    275         6            7
     - ----- (y - 1)  + ----- (y - 1)  + O((y - 1) )
       60480            24192
                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--R 
--R
--R   (6)
--R            - 1   1    1            1        2    19        3    3         4
--R     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
--R                  2   12           24            720            160
--R   + 
--R        863         5    275         6            7
--R     - ----- (y - 1)  + ----- (y - 1)  + O((y - 1) )
--R       60480            24192
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--E 80

--S 81 of 112
f : UTS(FLOAT,z,0) := exp(z)
 

   (7)
                    2                            3
     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
   + 
                                4                               5
     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
   + 
                                 6                               7      8
     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z  + O(z )
                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--R 
--R
--R   (7)
--R                    2                            3
--R     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
--R   + 
--R                                 6                               7      8
--R     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z  + O(z )
--R                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--E 81

--S 82 of 112
series(1/factorial(n),n,w = 0)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (8)  1 + w + - w  + - w  + -- w  + --- w  + --- w  + ---- w  + O(w )
                2      6      24      120      720      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,w,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (8)  1 + w + - w  + - w  + -- w  + --- w  + --- w  + ---- w  + O(w )
--R                2      6      24      120      720      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,w,0)
--E 82

-- Input for page SeriesFunctionPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 83 of 112
x := series x
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 83

--S 84 of 112
rat := x**2 / (1 - 6*x + x**2)
 

   (2)
    2     3      4       5        6        7         8          9      10
   x  + 6x  + 35x  + 204x  + 1189x  + 6930x  + 40391x  + 235416x  + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R    2     3      4       5        6        7         8          9      10
--R   x  + 6x  + 35x  + 204x  + 1189x  + 6930x  + 40391x  + 235416x  + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 84

--S 85 of 112
sin(rat)
 

   (3)
    2     3      4       5   7133  6        7   80711  8          9      10
   x  + 6x  + 35x  + 204x  + ---- x  + 6927x  + ----- x  + 235068x  + O(x  )
                               6                  2
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)
--R    2     3      4       5   7133  6        7   80711  8          9      10
--R   x  + 6x  + 35x  + 204x  + ---- x  + 6927x  + ----- x  + 235068x  + O(x  )
--R                               6                  2
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 85

--S 86 of 112
y : UTS(FRAC INT,y,0) := y
 

   (4)  y
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R   (4)  y
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 86

--S 87 of 112
exp(y)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (5)  1 + y + - y  + - y  + -- y  + --- y  + --- y  + ---- y  + O(y )
                2      6      24      120      720      5040
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (5)  1 + y + - y  + - y  + -- y  + --- y  + --- y  + ---- y  + O(y )
--R                2      6      24      120      720      5040
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 87

--S 88 of 112
tan(y**2)
 

         2   1  6      8
   (6)  y  + - y  + O(y )
             3
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R         2   1  6      8
--R   (6)  y  + - y  + O(y )
--R             3
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 88

--S 89 of 112
cos(y + y**5)
 

            1  2    1  4   721  6      8
   (7)  1 - - y  + -- y  - --- y  + O(y )
            2      24      720
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R            1  2    1  4   721  6      8
--R   (7)  1 - - y  + -- y  - --- y  + O(y )
--R            2      24      720
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 89

--S 90 of 112
log(1 + sin(y))
 

            1  2   1  3    1  4    1  5    1  6    61   7      8
   (8)  y - - y  + - y  - -- y  + -- y  - -- y  + ---- y  + O(y )
            2      6      12      24      45      5040
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R            1  2   1  3    1  4    1  5    1  6    61   7      8
--R   (8)  y - - y  + - y  - -- y  + -- y  - -- y  + ---- y  + O(y )
--R            2      6      12      24      45      5040
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 90

--S 91 of 112
z : UTS(EXPR INT,z,0) := z
 

   (9)  z
                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--R 
--R
--R   (9)  z
--R                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--E 91

--S 92 of 112
exp(2 + tan(z))
 

   (10)
                    2        2         2          2          2           2
       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
     %e  + %e z + --- z  + --- z  + ---- z  + ----- z  + ----- z  + ------ z
                   2        2         8        120        240         720
   + 
        8
     O(z )
                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--R 
--R
--R   (10)
--R                    2        2         2          2          2           2
--R       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
--R     %e  + %e z + --- z  + --- z  + ---- z  + ----- z  + ----- z  + ------ z
--R                   2        2         8        120        240         720
--R   + 
--R        8
--R     O(z )
--R                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--E 92

--S 93 of 112
w := taylor w
 

   (11)  w
                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--R 
--R
--R   (11)  w
--R                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--E 93

--S 94 of 112
exp(2 + tan(w))
 

   (12)
                    2        2         2          2          2           2
       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
     %e  + %e w + --- w  + --- w  + ---- w  + ----- w  + ----- w  + ------ w
                   2        2         8        120        240         720
   + 
        8
     O(w )
                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--R 
--R
--R   (12)
--R                    2        2         2          2          2           2
--R       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
--R     %e  + %e w + --- w  + --- w  + ---- w  + ----- w  + ----- w  + ------ w
--R                   2        2         8        120        240         720
--R   + 
--R        8
--R     O(w )
--R                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--E 94

-- Input for page LimitPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 95 of 112
f := sin(a*x) / tan(b*x)
 

        sin(a x)
   (1)  --------
        tan(b x)
                                                     Type: Expression Integer
--R 
--R
--R        sin(a x)
--R   (1)  --------
--R        tan(b x)
--R                                                     Type: Expression Integer
--E 95

--S 96 of 112
limit(f,x=0)
 

        a
   (2)  -
        b
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        a
--R   (2)  -
--R        b
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 96

--S 97 of 112
g := csc(a*x) / csch(b*x)
 

         csc(a x)
   (3)  ---------
        csch(b x)
                                                     Type: Expression Integer
--R 
--R
--R         csc(a x)
--R   (3)  ---------
--R        csch(b x)
--R                                                     Type: Expression Integer
--E 97

--S 98 of 112
limit(g,x=0)
 

        b
   (4)  -
        a
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        b
--R   (4)  -
--R        a
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 98

--S 99 of 112
h := (1 + k/x)**x
 

         x + k x
   (5)  (-----)
           x
                                                     Type: Expression Integer
--R 
--R
--R         x + k x
--R   (5)  (-----)
--R           x
--R                                                     Type: Expression Integer
--E 99

--S 100 of 112
limit(h,x=%plusInfinity)
 

          k
   (6)  %e
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R          k
--R   (6)  %e
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 100

-- Input for page SeriesBernoulliPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 101 of 112
reduce(+,[m**4 for m in 1..10])
 

   (1)  25333
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  25333
--R                                                        Type: PositiveInteger
--E 101

--S 102 of 112
sum4 := sum(m**4, m = 1..k)
 

          5      4      3
        6k  + 15k  + 10k  - k
   (2)  ---------------------
                  30
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          5      4      3
--R        6k  + 15k  + 10k  - k
--R   (2)  ---------------------
--R                  30
--R                                            Type: Fraction Polynomial Integer
--E 102

--S 103 of 112
eval(sum4, k = 10)
 

   (3)  25333
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (3)  25333
--R                                            Type: Fraction Polynomial Integer
--E 103

--S 104 of 112
f := t*exp(x*t) / (exp(t) - 1)
 

            t x
        t %e
   (4)  -------
          t
        %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R            t x
--R        t %e
--R   (4)  -------
--R          t
--R        %e  - 1
--R                                                     Type: Expression Integer
--E 104

)set streams calculate 5
 
 
--S 105 of 112
ff := taylor(f,t = 0)
 

   (5)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5      6
     ---------------------- t  + --------------------- t  + O(t )
               720                        720
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (5)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5      6
--R     ---------------------- t  + --------------------- t  + O(t )
--R               720                        720
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 105

--S 106 of 112
factorial(6) * coefficient(ff,6)
 

           6       5       4      2
        42x  - 126x  + 105x  - 21x  + 1
   (6)  -------------------------------
                       42
                                                     Type: Expression Integer
--R 
--R
--R           6       5       4      2
--R        42x  - 126x  + 105x  - 21x  + 1
--R   (6)  -------------------------------
--R                       42
--R                                                     Type: Expression Integer
--E 106

--S 107 of 112
g := eval(f, x = x + 1) - f
 

            t x + t       t x
        t %e        - t %e
   (7)  ---------------------
                 t
               %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R            t x + t       t x
--R        t %e        - t %e
--R   (7)  ---------------------
--R                 t
--R               %e  - 1
--R                                                     Type: Expression Integer
--E 107

--S 108 of 112
normalize(g)
 

            t x
   (8)  t %e
                                                     Type: Expression Integer
--R 
--R
--R            t x
--R   (8)  t %e
--R                                                     Type: Expression Integer
--E 108

--S 109 of 112
taylor(g,t = 0)
 

                    2       3       4
               2   x   3   x   4   x   5      6
   (9)  t + x t  + -- t  + -- t  + -- t  + O(t )
                    2       6      24
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R                    2       3       4
--R               2   x   3   x   4   x   5      6
--R   (9)  t + x t  + -- t  + -- t  + -- t  + O(t )
--R                    2       6      24
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 109

--S 110 of 112
B5 := factorial(5) * coefficient(ff,5)
 

           5      4      3
         6x  - 15x  + 10x  - x
   (10)  ---------------------
                   6
                                                     Type: Expression Integer
--R 
--R
--R           5      4      3
--R         6x  - 15x  + 10x  - x
--R   (10)  ---------------------
--R                   6
--R                                                     Type: Expression Integer
--E 110

--S 111 of 112
1/5 * (eval(B5, x = k + 1) - eval(B5, x = 1))
 

           5      4      3
         6k  + 15k  + 10k  - k
   (11)  ---------------------
                   30
                                                     Type: Expression Integer
--R 
--R
--R           5      4      3
--R         6k  + 15k  + 10k  - k
--R   (11)  ---------------------
--R                   30
--R                                                     Type: Expression Integer
--E 111

--S 112 of 112
sum4
 

           5      4      3
         6k  + 15k  + 10k  - k
   (12)  ---------------------
                   30
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           5      4      3
--R         6k  + 15k  + 10k  - k
--R   (12)  ---------------------
--R                   30
--R                                            Type: Fraction Polynomial Integer
--E 112
)spool
 
Starts dribbling to cycles.output (2009/2/17, 17:44:22).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.


)clear all
 
   All user variables and function definitions have been cleared.

)expose EVALCYC
 
   EvaluateCycleIndicators is now explicitly exposed in frame initial 

--S 1 of 46
complete 1
 

   (1)  (1)
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (1)  (1)
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 1

--S 2 of 46
complete 2
 

        1       1   2
   (2)  - (2) + - (1 )
        2       2
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1   2
--R   (2)  - (2) + - (1 )
--R        2       2
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 2

--S 3 of 46
complete 3
 

        1       1         1   3
   (3)  - (3) + - (2 1) + - (1 )
        3       2         6
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1         1   3
--R   (3)  - (3) + - (2 1) + - (1 )
--R        3       2         6
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 3

--S 4 of 46
complete 7
 

   (4)
     1       1          1          1     2     1         1            1     3
     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
      1      5      1    7
     --- (2 1 ) + ---- (1 )
     240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (4)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R      1      5      1    7
--R     --- (2 1 ) + ---- (1 )
--R     240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 4

--S 5 of 46
elementary 7
 

   (5)
     1       1          1          1     2     1         1            1     3
     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
        1      5      1    7
     - --- (2 1 ) + ---- (1 )
       240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (5)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R        1      5      1    7
--R     - --- (2 1 ) + ---- (1 )
--R       240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 5

--S 6 of 46
alternating 7
 

   (6)
     2       1     2    1           1   2      1     2     1     4     1   2 3
     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
     7       5          4           9         12          36          24
   + 
       1    7
     ---- (1 )
     2520
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (6)
--R     2       1     2    1           1   2      1     2     1     4     1   2 3
--R     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
--R     7       5          4           9         12          36          24
--R   + 
--R       1    7
--R     ---- (1 )
--R     2520
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 6

--S 7 of 46
cyclic 7
 

        6       1   7
   (7)  - (7) + - (1 )
        7       7
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        6       1   7
--R   (7)  - (7) + - (1 )
--R        7       7
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 7

--S 8 of 46
dihedral 7
 

        3       1   3      1   7
   (8)  - (7) + - (2 1) + -- (1 )
        7       2         14
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        3       1   3      1   7
--R   (8)  - (7) + - (2 1) + -- (1 )
--R        7       2         14
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 8

--S 9 of 46
graphs 5
 

   (9)
   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
   6           5        4         6         8          12          120
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (9)
--R   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
--R   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
--R   6           5        4         6         8          12          120
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 9

--S 10 of 46
cap(complete 2**2,complete 2*complete 1**2)
 

   (10)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (10)  4
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 46
cap(elementary 2**2,complete 2*complete 1**2)
 

   (11)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  2
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 46
cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)
 

   (12)  24
                                                       Type: Fraction Integer
--R 
--R
--R   (12)  24
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 46
cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)
 

   (13)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  8
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 46
cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)
 

   (14)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (14)  8
--R                                                       Type: Fraction Integer
--E 14

--S 15 of 46
eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))
 

   (15)  1500
                                                       Type: Fraction Integer
--R 
--R
--R   (15)  1500
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 46
square:=dihedral 4
 

         1       3   2    1     2    1   4
   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
         4       8        4          8
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1       3   2    1     2    1   4
--R   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
--R         4       8        4          8
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 16

--S 17 of 46
cap(complete 2**2,square)
 

   (17)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  2
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 46
cap(complete 3*complete 2**2,dihedral 7)
 

   (18)  18
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  18
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 46
cap(graphs 5,complete 7*complete 3)
 

   (19)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (19)  4
--R                                                       Type: Fraction Integer
--E 19

--S 20 of 46
macro s == powerSum
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 46
cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)
 

         1   2    1   2 2    3   4     1   8
   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
         4        3          8        24
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1   2    1   2 2    3   4     1   8
--R   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
--R         4        3          8        24
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 21

--S 22 of 46
cap(complete 4**2,cube)
 

   (22)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  7
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))
 

   (23)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (23)  7
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))
 

   (24)  17
                                                       Type: Fraction Integer
--R 
--R
--R   (24)  17
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))
 

   (25)  10
                                                       Type: Fraction Integer
--R 
--R
--R   (25)  10
--R                                                       Type: Fraction Integer
--E 25

--S 26 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))
 

   (26)  23
                                                       Type: Fraction Integer
--R 
--R
--R   (26)  23
--R                                                       Type: Fraction Integer
--E 26

--S 27 of 46
x:ULS(FRAC INT,'x,0):=x
 

   (27)  x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (27)  x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 27

--S 28 of 46
ZeroOrOne:INT->ULS(FRAC INT,'x,0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 46
Integers:INT->ULS(FRAC INT,'x,0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 46
ZeroOrOne n == 1+x**n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E

--S 31 of 46
ZeroOrOne 5
 
   Compiling function ZeroOrOne with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5
   (31)  1 + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function ZeroOrOne with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5
--R   (31)  1 + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 31

--S 32 of 46
Integers n == 1/(1-x**n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 46
Integers 5
 
   Compiling function Integers with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5    10      11
   (33)  1 + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function Integers with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5    10      11
--R   (33)  1 + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 33

--S 34 of 46
eval(ZeroOrOne,graphs 5)
 

                   2     3     4     5     6     7     8    9    10      11
   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6     7     8    9    10      11
--R   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 34

--S 35 of 46
eval(ZeroOrOne,dihedral 8)
 

                   2     3     4     5     6    7    8
   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 35

--S 36 of 46
eval(Integers,complete 4)
 

   (36)
             2     3     4     5     6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (36)
--R             2     3     4     5     6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 36

--S 37 of 46
eval(Integers,elementary 4)
 

   (37)
      6    7     8     9     10     11     12      13      14      15      16
     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
   + 
        17
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (37)
--R      6    7     8     9     10     11     12      13      14      15      16
--R     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
--R   + 
--R        17
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 37

--S 38 of 46
eval(ZeroOrOne,cube)
 

                   2     3     4     5     6    7    8
   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 38

--S 39 of 46
eval(Integers,cube)
 

   (39)
               2     3      4      5      6       7       8       9       10
     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (39)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 39

--S 40 of 46
eval(Integers,graphs 5)
 

   (40)
               2     3      4      5      6       7       8       9       10
     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (40)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 40

--S 41 of 46
eval(ZeroOrOne ,graphs 15)
 

   (41)
               2     3      4      5      6       7       8        9        10
     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (41)
--R               2     3      4      5      6       7       8        9        10
--R     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 41

--S 42 of 46
cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)
 

   (42)  49958972383320
                                                       Type: Fraction Integer
--R 
--R
--R   (42)  49958972383320
--R                                                       Type: Fraction Integer
--E 42

--S 43 of 46
sf3221:= SFunction [3,2,2,1]
 

   (43)
      1          1     2     1   2     1            1     4     1   2
     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
     12         12          16        12           24          36
   + 
      1   2 2     1     2      1       3     1     5     1    4     1   3 2
     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
     36          24           36            72          192        48
   + 
      1   2 4     1      6     1    8
     -- (2 1 ) - --- (2 1 ) + --- (1 )
     96          144          576
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (43)
--R      1          1     2     1   2     1            1     4     1   2
--R     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
--R     12         12          16        12           24          36
--R   + 
--R      1   2 2     1     2      1       3     1     5     1    4     1   3 2
--R     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
--R     36          24           36            72          192        48
--R   + 
--R      1   2 4     1      6     1    8
--R     -- (2 1 ) - --- (2 1 ) + --- (1 )
--R     96          144          576
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 43

--S 44 of 46
cap(sf3221,complete 2**4)
 

   (44)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (44)  3
--R                                                       Type: Fraction Integer
--E 44

--S 45 of 46
cap(sf3221,powerSum 1**8)
 

   (45)  70
                                                       Type: Fraction Integer
--R 
--R
--R   (45)  70
--R                                                       Type: Fraction Integer
--E 45

--S 46 of 46
eval(Integers,sf3221)
 

   (46)
      9     10     11      12      13      14      15       16       17       18
     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
   + 
         19      20
     432x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (46)
--R      9     10     11      12      13      14      15       16       17       18
--R     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
--R   + 
--R         19      20
--R     432x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 46
)spool
 
Starts dribbling to pfaffian.output (2009/2/17, 17:56:9).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 26
B0 n == matrix [[(if i=j+1 and odd? j then -1 else _
                   if i=j-1 and odd? i then 1 else 0) _
                     for j in 1..n] for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1
--S 2 of 26
B0 1
 
   Compiling function B0 with type PositiveInteger -> Matrix Integer 

   (2)  [0]
                                                         Type: Matrix Integer
--R 
--R   Compiling function B0 with type PositiveInteger -> Matrix Integer 
--R
--R   (2)  [0]
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 26
B0 2
 

        + 0   1+
   (3)  |      |
        +- 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1+
--R   (3)  |      |
--R        +- 1  0+
--R                                                         Type: Matrix Integer
--E 3

--S 4 of 26
B0 3
 

        + 0   1  0+
        |         |
   (4)  |- 1  0  0|
        |         |
        + 0   0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1  0+
--R        |         |
--R   (4)  |- 1  0  0|
--R        |         |
--R        + 0   0  0+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 26
B0 4
 

        + 0   1   0   0+
        |              |
        |- 1  0   0   0|
   (5)  |              |
        | 0   0   0   1|
        |              |
        + 0   0  - 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0+
--R        |              |
--R        |- 1  0   0   0|
--R   (5)  |              |
--R        | 0   0   0   1|
--R        |              |
--R        + 0   0  - 1  0+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 26
B0 5
 

        + 0   1   0   0  0+
        |                 |
        |- 1  0   0   0  0|
        |                 |
   (6)  | 0   0   0   1  0|
        |                 |
        | 0   0  - 1  0  0|
        |                 |
        + 0   0   0   0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0  0+
--R        |                 |
--R        |- 1  0   0   0  0|
--R        |                 |
--R   (6)  | 0   0   0   1  0|
--R        |                 |
--R        | 0   0  - 1  0  0|
--R        |                 |
--R        + 0   0   0   0  0+
--R                                                         Type: Matrix Integer
--E 6

--S 7 of 26
B0 6
 

        + 0   1   0   0   0   0+
        |                      |
        |- 1  0   0   0   0   0|
        |                      |
        | 0   0   0   1   0   0|
   (7)  |                      |
        | 0   0  - 1  0   0   0|
        |                      |
        | 0   0   0   0   0   1|
        |                      |
        + 0   0   0   0  - 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0   0   0+
--R        |                      |
--R        |- 1  0   0   0   0   0|
--R        |                      |
--R        | 0   0   0   1   0   0|
--R   (7)  |                      |
--R        | 0   0  - 1  0   0   0|
--R        |                      |
--R        | 0   0   0   0   0   1|
--R        |                      |
--R        + 0   0   0   0  - 1  0+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 26
B0 7
 

        + 0   1   0   0   0   0  0+
        |                         |
        |- 1  0   0   0   0   0  0|
        |                         |
        | 0   0   0   1   0   0  0|
        |                         |
   (8)  | 0   0  - 1  0   0   0  0|
        |                         |
        | 0   0   0   0   0   1  0|
        |                         |
        | 0   0   0   0  - 1  0  0|
        |                         |
        + 0   0   0   0   0   0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0   0   0  0+
--R        |                         |
--R        |- 1  0   0   0   0   0  0|
--R        |                         |
--R        | 0   0   0   1   0   0  0|
--R        |                         |
--R   (8)  | 0   0  - 1  0   0   0  0|
--R        |                         |
--R        | 0   0   0   0   0   1  0|
--R        |                         |
--R        | 0   0   0   0  - 1  0  0|
--R        |                         |
--R        + 0   0   0   0   0   0  0+
--R                                                         Type: Matrix Integer
--E 8

--S 9 of 26
B0 8
 

        + 0   1   0   0   0   0   0   0+
        |                              |
        |- 1  0   0   0   0   0   0   0|
        |                              |
        | 0   0   0   1   0   0   0   0|
        |                              |
        | 0   0  - 1  0   0   0   0   0|
   (9)  |                              |
        | 0   0   0   0   0   1   0   0|
        |                              |
        | 0   0   0   0  - 1  0   0   0|
        |                              |
        | 0   0   0   0   0   0   0   1|
        |                              |
        + 0   0   0   0   0   0  - 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0   0   0   0   0+
--R        |                              |
--R        |- 1  0   0   0   0   0   0   0|
--R        |                              |
--R        | 0   0   0   1   0   0   0   0|
--R        |                              |
--R        | 0   0  - 1  0   0   0   0   0|
--R   (9)  |                              |
--R        | 0   0   0   0   0   1   0   0|
--R        |                              |
--R        | 0   0   0   0  - 1  0   0   0|
--R        |                              |
--R        | 0   0   0   0   0   0   0   1|
--R        |                              |
--R        + 0   0   0   0   0   0  - 1  0+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 26
PfChar(lambda, A) ==
    n := nrows A
    odd? n => 0
    (n = 2) => lambda^2 + A.(1,2)
    M := subMatrix(A, 3, n, 3, n)
    r := subMatrix(A, 1, 1, 3, n)
    s := subMatrix(A, 3, n, 2, 2)

    p := PfChar(lambda, M)
    d := degree(p, lambda)

    B := B0(n-2)
    C := r*B
    g := [(C*s).(1,1), A.(1,2), 1]
    if d >= 4 then 
        B := M*B
        for i in 4..d by 2 repeat
            C := C*B
            g := cons((C*s).(1,1), g)
    g := reverse! g

    res := 0
    for i in 0..d by 2 for j in 2..d+2 repeat
        c := coefficient(p, lambda, i)
        for e in first(g, j) for k in 2..-d by -2 repeat
            res := res +  c * e * lambda^(k+i)

    res
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 26
pfaffian A == eval(PfChar(l, A), l=0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 26
m:Matrix(Integer):=[[0,15],[-15,0]]
 

         + 0    15+
   (12)  |        |
         +- 15  0 +
                                                         Type: Matrix Integer
--R 
--R
--R         + 0    15+
--R   (12)  |        |
--R         +- 15  0 +
--R                                                         Type: Matrix Integer
--E 12

--S 13 of 26
pfaffian m
 
   Compiling function B0 with type Integer -> Matrix Integer 
   The type of the local variable res has changed in the computation.
   We will attempt to interpret the code.
   Cannot compile map: PfChar 
   We will attempt to interpret the code.

   (13)  15
                                                     Type: Polynomial Integer
--R 
--R   Compiling function B0 with type Integer -> Matrix Integer 
--R   The type of the local variable res has changed in the computation.
--R   We will attempt to interpret the code.
--R   Cannot compile map: PfChar 
--R   We will attempt to interpret the code.
--R
--R   (13)  15
--R                                                     Type: Polynomial Integer
--E 13

--S 14 of 26
m1:Matrix(Polynomial(Integer)):=[[0,a,b,c],[-a,0,d,e],[-b,-d,0,f],[-c,-e,-f,0]]
 

         + 0    a    b   c+
         |                |
         |- a   0    d   e|
   (14)  |                |
         |- b  - d   0   f|
         |                |
         +- c  - e  - f  0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         + 0    a    b   c+
--R         |                |
--R         |- a   0    d   e|
--R   (14)  |                |
--R         |- b  - d   0   f|
--R         |                |
--R         +- c  - e  - f  0+
--R                                              Type: Matrix Polynomial Integer
--E 14

--S 15 of 26
pfaffian m1
 

   (15)  a f - b e + c d
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  a f - b e + c d
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 26
(a,b,c,d,e,f):=(3,5,7,11,13,17)
 

   (16)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  17
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 26
m1
 

         + 0    a    b   c+
         |                |
         |- a   0    d   e|
   (17)  |                |
         |- b  - d   0   f|
         |                |
         +- c  - e  - f  0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         + 0    a    b   c+
--R         |                |
--R         |- a   0    d   e|
--R   (17)  |                |
--R         |- b  - d   0   f|
--R         |                |
--R         +- c  - e  - f  0+
--R                                              Type: Matrix Polynomial Integer
--E 17

--S 18 of 26
a*f-b*e+d*c
 

   (18)  63
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  63
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 26
n:=pfaffian m1
 

   (19)  a f - b e + c d
                                                     Type: Polynomial Integer
--R 
--R
--R   (19)  a f - b e + c d
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 26
eval(n,['a,'b,'c,'d,'e,'f]::List(Symbol),[a,b,c,d,e,f])
 

   (20)  63
                                                     Type: Polynomial Integer
--R 
--R
--R   (20)  63
--R                                                     Type: Polynomial Integer
--E 20


)clear properties z
 
)clear properties d
 
)clear properties v
 

--S 21 of 26
z:SQMATRIX(2,INT):=[[0,0],[0,0]]
 

         +0  0+
   (21)  |    |
         +0  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +0  0+
--R   (21)  |    |
--R         +0  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 21

--S 22 of 26
d:SQMATRIX(2,INT):=[[0,1],[-1,0]]
 

         + 0   1+
   (22)  |      |
         +- 1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         + 0   1+
--R   (22)  |      |
--R         +- 1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 22

--S 23 of 26
v:SQMATRIX(4,SQMATRIX(2,INT)):=[[z,d,d,d],[-d,z,d,d],[-d,-d,z,d],[-d,-d,-d,z]]
 

         + +0  0+   + 0   1+  + 0   1+  + 0   1++
         | |    |   |      |  |      |  |      ||
         | +0  0+   +- 1  0+  +- 1  0+  +- 1  0+|
         |                                      |
         |+0  - 1+   +0  0+   + 0   1+  + 0   1+|
         ||      |   |    |   |      |  |      ||
         |+1   0 +   +0  0+   +- 1  0+  +- 1  0+|
   (23)  |                                      |
         |+0  - 1+  +0  - 1+   +0  0+   + 0   1+|
         ||      |  |      |   |    |   |      ||
         |+1   0 +  +1   0 +   +0  0+   +- 1  0+|
         |                                      |
         |+0  - 1+  +0  - 1+  +0  - 1+   +0  0+ |
         ||      |  |      |  |      |   |    | |
         ++1   0 +  +1   0 +  +1   0 +   +0  0+ +
                                Type: SquareMatrix(4,SquareMatrix(2,Integer))
--R 
--R
--R         + +0  0+   + 0   1+  + 0   1+  + 0   1++
--R         | |    |   |      |  |      |  |      ||
--R         | +0  0+   +- 1  0+  +- 1  0+  +- 1  0+|
--R         |                                      |
--R         |+0  - 1+   +0  0+   + 0   1+  + 0   1+|
--R         ||      |   |    |   |      |  |      ||
--R         |+1   0 +   +0  0+   +- 1  0+  +- 1  0+|
--R   (23)  |                                      |
--R         |+0  - 1+  +0  - 1+   +0  0+   + 0   1+|
--R         ||      |  |      |   |    |   |      ||
--R         |+1   0 +  +1   0 +   +0  0+   +- 1  0+|
--R         |                                      |
--R         |+0  - 1+  +0  - 1+  +0  - 1+   +0  0+ |
--R         ||      |  |      |  |      |   |    | |
--R         ++1   0 +  +1   0 +  +1   0 +   +0  0+ +
--R                                Type: SquareMatrix(4,SquareMatrix(2,Integer))
--E 23

--S 24 of 26
pfaffian v
 
   There are 1 exposed and 0 unexposed library operations named 
      subMatrix having 5 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op subMatrix
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      subMatrix with argument type(s) 
                   SquareMatrix(4,SquareMatrix(2,Integer))
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      subMatrix having 5 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op subMatrix
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      subMatrix with argument type(s) 
--R                   SquareMatrix(4,SquareMatrix(2,Integer))
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24

--S 25 of 26
mypf(m) ==
 nr:= nrows m
 odd? nr => 0
-- not zero? (nr mod 2)
 not square? m => 0
 not antisymmetric? m => 0
 nr = 2 => m.(1,2)
 nr = 4 => m.(1,2)*m.(3,4)-m.(1,3)*m.(2,4)+m.(2,3)*m.(1,4)
 0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 26
antisymmetric(seq,n) == 
  m:= matrix [[(if i<j then (seq.(j-i)) _
                 else if i>j then -(seq.(i-j))    
                  else 0) for j in 1..n] for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

)spool 
 
Starts dribbling to scope.output (2009/2/17, 18:0:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
showbug1():Void ==
 for i in 1..1 repeat
  z:="I'm OK"
  print(z)
  showbug2()
  print(z)
 
   Function declaration showbug1 : () -> Void has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration showbug1 : () -> Void has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 3
showbug2():Void ==
 for i in 1..1 repeat
  z:="I'm nasty"
 
   Function declaration showbug2 : () -> Void has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration showbug2 : () -> Void has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 2
-- used to print:
-- I'm OK
-- I'm nasty

--S 3 of 3
showbug1()
 
   Compiling function showbug2 with type () -> Void 
   Compiling function showbug1 with type () -> Void 
   "I'm OK"
   "I'm OK"
                                                                   Type: Void
--R 
--R   Compiling function showbug2 with type () -> Void 
--R   Compiling function showbug1 with type () -> Void 
--R   "I'm OK"
--R   "I'm OK"
--R                                                                   Type: Void
--E 3
)spool 
 
Starts dribbling to matrix.output (2009/2/17, 17:55:2).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 42
mat : MATRIX FRAC INT := matrix [[1/(i + j) for i in 1..5] for j in 1..5]
 

        +1  1  1  1  1 +
        |-  -  -  -  - |
        |2  3  4  5  6 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |3  4  5  6  7 |
        |              |
        |1  1  1  1  1 |
   (1)  |-  -  -  -  - |
        |4  5  6  7  8 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |5  6  7  8  9 |
        |              |
        |1  1  1  1   1|
        |-  -  -  -  --|
        +6  7  8  9  10+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +1  1  1  1  1 +
--R        |-  -  -  -  - |
--R        |2  3  4  5  6 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |3  4  5  6  7 |
--R        |              |
--R        |1  1  1  1  1 |
--R   (1)  |-  -  -  -  - |
--R        |4  5  6  7  8 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |5  6  7  8  9 |
--R        |              |
--R        |1  1  1  1   1|
--R        |-  -  -  -  --|
--R        +6  7  8  9  10+
--R                                                Type: Matrix Fraction Integer
--E 1

--S 2 of 42
matinv := inverse mat
 

        +  450     - 4200    12600    - 15120     6300  +
        |                                               |
        |- 4200    44100    - 141120   176400   - 75600 |
        |                                               |
   (2)  | 12600   - 141120   470400   - 604800   264600 |
        |                                               |
        |- 15120   176400   - 604800   793800   - 352800|
        |                                               |
        + 6300    - 75600    264600   - 352800   158760 +
                                     Type: Union(Matrix Fraction Integer,...)
--R 
--R
--R        +  450     - 4200    12600    - 15120     6300  +
--R        |                                               |
--R        |- 4200    44100    - 141120   176400   - 75600 |
--R        |                                               |
--R   (2)  | 12600   - 141120   470400   - 604800   264600 |
--R        |                                               |
--R        |- 15120   176400   - 604800   793800   - 352800|
--R        |                                               |
--R        + 6300    - 75600    264600   - 352800   158760 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 2

--S 3 of 42
mat * matinv
 

        +1  0  0  0  0+
        |             |
        |0  1  0  0  0|
        |             |
   (3)  |0  0  1  0  0|
        |             |
        |0  0  0  1  0|
        |             |
        +0  0  0  0  1+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +1  0  0  0  0+
--R        |             |
--R        |0  1  0  0  0|
--R        |             |
--R   (3)  |0  0  1  0  0|
--R        |             |
--R        |0  0  0  1  0|
--R        |             |
--R        +0  0  0  0  1+
--R                                                Type: Matrix Fraction Integer
--E 3

--S 4 of 42
mat1 : IMATRIX(FRAC INT,-3,47) := _
   matrix [[1/(i + j) for i in 1..5] for j in 1..5]
 

        +1  1  1  1  1 +
        |-  -  -  -  - |
        |2  3  4  5  6 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |3  4  5  6  7 |
        |              |
        |1  1  1  1  1 |
   (4)  |-  -  -  -  - |
        |4  5  6  7  8 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |5  6  7  8  9 |
        |              |
        |1  1  1  1   1|
        |-  -  -  -  --|
        +6  7  8  9  10+
                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--R 
--R
--R        +1  1  1  1  1 +
--R        |-  -  -  -  - |
--R        |2  3  4  5  6 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |3  4  5  6  7 |
--R        |              |
--R        |1  1  1  1  1 |
--R   (4)  |-  -  -  -  - |
--R        |4  5  6  7  8 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |5  6  7  8  9 |
--R        |              |
--R        |1  1  1  1   1|
--R        |-  -  -  -  --|
--R        +6  7  8  9  10+
--R                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--E 4

--S 5 of 42
mat1inv := inverse mat1
 

        +  450     - 4200    12600    - 15120     6300  +
        |                                               |
        |- 4200    44100    - 141120   176400   - 75600 |
        |                                               |
   (5)  | 12600   - 141120   470400   - 604800   264600 |
        |                                               |
        |- 15120   176400   - 604800   793800   - 352800|
        |                                               |
        + 6300    - 75600    264600   - 352800   158760 +
                       Type: Union(IndexedMatrix(Fraction Integer,-3,47),...)
--R 
--R
--R        +  450     - 4200    12600    - 15120     6300  +
--R        |                                               |
--R        |- 4200    44100    - 141120   176400   - 75600 |
--R        |                                               |
--R   (5)  | 12600   - 141120   470400   - 604800   264600 |
--R        |                                               |
--R        |- 15120   176400   - 604800   793800   - 352800|
--R        |                                               |
--R        + 6300    - 75600    264600   - 352800   158760 +
--R                       Type: Union(IndexedMatrix(Fraction Integer,-3,47),...)
--E 5

--S 6 of 42
mat1 * mat1inv
 

        +1  0  0  0  0+
        |             |
        |0  1  0  0  0|
        |             |
   (6)  |0  0  1  0  0|
        |             |
        |0  0  0  1  0|
        |             |
        +0  0  0  0  1+
                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--R 
--R
--R        +1  0  0  0  0+
--R        |             |
--R        |0  1  0  0  0|
--R        |             |
--R   (6)  |0  0  1  0  0|
--R        |             |
--R        |0  0  0  1  0|
--R        |             |
--R        +0  0  0  0  1+
--R                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--E 6
 
--S 7 of 42
mat2 : MATRIX INT := matrix [[j**i for i in 0..4] for j in 1..5]
 

        +1  1  1    1    1 +
        |                  |
        |1  2  4    8   16 |
        |                  |
   (7)  |1  3  9   27   81 |
        |                  |
        |1  4  16  64   256|
        |                  |
        +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  1  1    1    1 +
--R        |                  |
--R        |1  2  4    8   16 |
--R        |                  |
--R   (7)  |1  3  9   27   81 |
--R        |                  |
--R        |1  4  16  64   256|
--R        |                  |
--R        +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 42
rowEchelon  mat2
 

        +1  0  0  0  0 +
        |              |
        |0  1  1  1  1 |
        |              |
   (8)  |0  0  2  0  2 |
        |              |
        |0  0  0  6  12|
        |              |
        +0  0  0  0  24+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  0  0  0  0 +
--R        |              |
--R        |0  1  1  1  1 |
--R        |              |
--R   (8)  |0  0  2  0  2 |
--R        |              |
--R        |0  0  0  6  12|
--R        |              |
--R        +0  0  0  0  24+
--R                                                         Type: Matrix Integer
--E 8

--S 9 of 42
determinant mat2
 

   (9)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  288
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 42
minordet    mat2
 

   (10)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  288
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 42
mat3 : IMATRIX(INT,13,-7) := _
   matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (11)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                           Type: IndexedMatrix(Integer,13,-7)
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (11)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                           Type: IndexedMatrix(Integer,13,-7)
--E 11

--S 12 of 42
rowEchelon  mat3
 

         +1  0  0  0  0 +
         |              |
         |0  1  1  1  1 |
         |              |
   (12)  |0  0  2  0  2 |
         |              |
         |0  0  0  6  12|
         |              |
         +0  0  0  0  24+
                                           Type: IndexedMatrix(Integer,13,-7)
--R 
--R
--R         +1  0  0  0  0 +
--R         |              |
--R         |0  1  1  1  1 |
--R         |              |
--R   (12)  |0  0  2  0  2 |
--R         |              |
--R         |0  0  0  6  12|
--R         |              |
--R         +0  0  0  0  24+
--R                                           Type: IndexedMatrix(Integer,13,-7)
--E 12

--S 13 of 42
determinant mat3
 

   (13)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  288
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 42
minordet    mat3
 

   (14)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  288
--R                                                        Type: PositiveInteger
--E 14

--S 15  of 42
mat4 : MATRIX FRAC INT := matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (15)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (15)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                Type: Matrix Fraction Integer
--E 15

--S 16 of 42
rowEchelon  mat4
 

         +1  0  0  0  0+
         |             |
         |0  1  0  0  0|
         |             |
   (16)  |0  0  1  0  0|
         |             |
         |0  0  0  1  0|
         |             |
         +0  0  0  0  1+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  0  0  0  0+
--R         |             |
--R         |0  1  0  0  0|
--R         |             |
--R   (16)  |0  0  1  0  0|
--R         |             |
--R         |0  0  0  1  0|
--R         |             |
--R         +0  0  0  0  1+
--R                                                Type: Matrix Fraction Integer
--E 16

--S 17 of 42
determinant mat4
 

   (17)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  288
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 42
minordet    mat4
 

   (18)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  288
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 42
mat5 : IMATRIX(FRAC INT,-113,37) := _
   matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (19)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                Type: IndexedMatrix(Fraction Integer,-113,37)
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (19)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                Type: IndexedMatrix(Fraction Integer,-113,37)
--E 19

--S 20 of 42
rowEchelon  mat5
 

         +1  0  0  0  0+
         |             |
         |0  1  0  0  0|
         |             |
   (20)  |0  0  1  0  0|
         |             |
         |0  0  0  1  0|
         |             |
         +0  0  0  0  1+
                                Type: IndexedMatrix(Fraction Integer,-113,37)
--R 
--R
--R         +1  0  0  0  0+
--R         |             |
--R         |0  1  0  0  0|
--R         |             |
--R   (20)  |0  0  1  0  0|
--R         |             |
--R         |0  0  0  1  0|
--R         |             |
--R         +0  0  0  0  1+
--R                                Type: IndexedMatrix(Fraction Integer,-113,37)
--E 20

--S 21 of 42
determinant mat5
 

   (21)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (21)  288
--R                                                       Type: Fraction Integer
--E 21

--S 22 of 42
minordet    mat5
 

   (22)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  288
--R                                                       Type: Fraction Integer
--E 22
 
--S 23 of 42
mat6 : MATRIX INT := matrix [[1,2,3],[4,5,6],[7,8,9]]
 

         +1  2  3+
         |       |
   (23)  |4  5  6|
         |       |
         +7  8  9+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (23)  |4  5  6|
--R         |       |
--R         +7  8  9+
--R                                                         Type: Matrix Integer
--E 23

--S 24 of 42
rowEchelon mat6
 

         +1  2  3+
         |       |
   (24)  |0  3  6|
         |       |
         +0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (24)  |0  3  6|
--R         |       |
--R         +0  0  0+
--R                                                         Type: Matrix Integer
--E 24

--S 25 of 42
rank       mat6
 

   (25)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  2
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 42
nullity    mat6
 

   (26)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  1
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 42
nullSpace  mat6
 

   (27)  [[1,- 2,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (27)  [[1,- 2,1]]
--R                                                    Type: List Vector Integer
--E 27
 
--S 28 of 42
mat7 : IMATRIX(FRAC INT,163,61657) := matrix [[1,2,3],[4,5,6],[7,8,9]]
 

         +1  2  3+
         |       |
   (28)  |4  5  6|
         |       |
         +7  8  9+
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (28)  |4  5  6|
--R         |       |
--R         +7  8  9+
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 28

--S 29 of 42
rowEchelon mat7
 

         +1  0  - 1+
         |         |
   (29)  |0  1   2 |
         |         |
         +0  0   0 +
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         +1  0  - 1+
--R         |         |
--R   (29)  |0  1   2 |
--R         |         |
--R         +0  0   0 +
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 29

--S 30 of 42
rank       mat7
 

   (30)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  2
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 42
nullity    mat7
 

   (31)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (31)  1
--R                                                        Type: PositiveInteger
--E 31

--S 32 of 42
nullSpace  mat7
 

   (32)  [[1,- 2,1]]
                               Type: List IndexedVector(Fraction Integer,163)
--R 
--R
--R   (32)  [[1,- 2,1]]
--R                               Type: List IndexedVector(Fraction Integer,163)
--E 32

--S 33 of 42
mat8 : MATRIX INT := _
 matrix [[1,-2,13,0,5,-47],[-4,15,0,16,-2,1],[-7,0,8,-11,9,0]]
 

         + 1   - 2  13   0     5   - 47+
         |                             |
   (33)  |- 4  15   0    16   - 2   1  |
         |                             |
         +- 7   0   8   - 11   9    0  +
                                                         Type: Matrix Integer
--R 
--R
--R         + 1   - 2  13   0     5   - 47+
--R         |                             |
--R   (33)  |- 4  15   0    16   - 2   1  |
--R         |                             |
--R         +- 7   0   8   - 11   9    0  +
--R                                                         Type: Matrix Integer
--E 33

--S 34 of 42
rowEchelon mat8
 

         +1  5  65   16  23  - 234+
         |                        |
   (34)  |0  7  52   16  18  - 187|
         |                        |
         +0  0  203  21  80  - 703+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  5  65   16  23  - 234+
--R         |                        |
--R   (34)  |0  7  52   16  18  - 187|
--R         |                        |
--R         +0  0  203  21  80  - 703+
--R                                                         Type: Matrix Integer
--E 34

--S 35 of 42
rank       mat8
 

   (35)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  3
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 42
nullity    mat8
 

   (36)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (36)  3
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 42
nullSpace  mat8
 

   (37)
   [[- 49,- 44,- 3,29,0,0],[1187,506,- 560,0,1421,0],[5624,1405,4921,0,0,1421]]
                                                    Type: List Vector Integer
--R 
--R
--R   (37)
--R   [[- 49,- 44,- 3,29,0,0],[1187,506,- 560,0,1421,0],[5624,1405,4921,0,0,1421]]
--R                                                    Type: List Vector Integer
--E 37
 
--S 38 of 42
mat9 : IMATRIX(FRAC INT,163,61657) := _
 matrix [[1,-2,13,0,5,-47],[-4,15,0,16,-2,1],[-7,0,8,-11,9,0]]
 

         + 1   - 2  13   0     5   - 47+
         |                             |
   (38)  |- 4  15   0    16   - 2   1  |
         |                             |
         +- 7   0   8   - 11   9    0  +
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         + 1   - 2  13   0     5   - 47+
--R         |                             |
--R   (38)  |- 4  15   0    16   - 2   1  |
--R         |                             |
--R         +- 7   0   8   - 11   9    0  +
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 38

--S 39 of 42
rowEchelon mat9
 

         +         49    1187    5624+
         |1  0  0  --  - ----  - ----|
         |         29    1421    1421|
         |                           |
         |         44     506    1405|
   (39)  |0  1  0  --  - ----  - ----|
         |         29    1421    1421|
         |                           |
         |          3    80      703 |
         |0  0  1  --   ---    - --- |
         +         29   203      203 +
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         +         49    1187    5624+
--R         |1  0  0  --  - ----  - ----|
--R         |         29    1421    1421|
--R         |                           |
--R         |         44     506    1405|
--R   (39)  |0  1  0  --  - ----  - ----|
--R         |         29    1421    1421|
--R         |                           |
--R         |          3    80      703 |
--R         |0  0  1  --   ---    - --- |
--R         +         29   203      203 +
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 39

--S 40 of 42
rank       mat9
 

   (40)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (40)  3
--R                                                        Type: PositiveInteger
--E 40

--S 41 of 42
nullity    mat9
 

   (41)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (41)  3
--R                                                        Type: PositiveInteger
--E 41

--S 42 of 42
nullSpace  mat9
 

   (42)
       49   44    3         1187  506    80         5624 1405 703
   [[- --,- --,- --,1,0,0],[----,----,- ---,0,1,0],[----,----,---,0,0,1]]
       29   29   29         1421 1421   203         1421 1421 203
                               Type: List IndexedVector(Fraction Integer,163)
--R 
--R
--R   (42)
--R       49   44    3         1187  506    80         5624 1405 703
--R   [[- --,- --,- --,1,0,0],[----,----,- ---,0,1,0],[----,----,---,0,0,1]]
--R       29   29   29         1421 1421   203         1421 1421 203
--R                               Type: List IndexedVector(Fraction Integer,163)
--E 42
)spool 
 
Starts dribbling to float2.output (2009/2/17, 17:46:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 41
f := 2.0/3
 

   (1)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (1)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 1

--S 2 of 41
log exp f
 

   (2)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (2)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 2

--S 3 of 41
asin sin f
 

   (3)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (3)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 3

--S 4 of 41
acos cos f
 

   (4)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (4)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 4

--S 5 of 41
atan tan f
 

   (5)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (5)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 5

--S 6 of 41
asinh sinh f
 

   (6)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (6)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 6

--S 7 of 41
acosh cosh f
 

   (7)  0.6666666666 6666666666
                                                                  Type: Float
--R 
--R
--R   (7)  0.6666666666 6666666666
--R                                                                  Type: Float
--E 7

--S 8 of 41
atanh tanh f
 

   (8)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (8)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 8

--S 9 of 41
sqrt(f**2)
 

   (9)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (9)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 9

--S 10 of 41
4*atan(1.0)-%pi
 

   (10)  0.0
                                                                  Type: Float
--R 
--R
--R   (10)  0.0
--R                                                                  Type: Float
--E 10

--S 11 of 41
log exp1()
 

   (11)  1.0
                                                                  Type: Float
--R 
--R
--R   (11)  1.0
--R                                                                  Type: Float
--E 11

--S 12 of 41
exp log2()
 

   (12)  2.0
                                                                  Type: Float
--R 
--R
--R   (12)  2.0
--R                                                                  Type: Float
--E 12

--S 13 of 41
exp log10()
 

   (13)  10.0
                                                                  Type: Float
--R 
--R
--R   (13)  10.0
--R                                                                  Type: Float
--E 13
 
--S 14 of 41
f := 100.0/7
 

   (14)  14.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (14)  14.2857142857 14285714
--R                                                                  Type: Float
--E 14

--S 15 of 41
exp log f
 

   (15)  14.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (15)  14.2857142857 14285714
--R                                                                  Type: Float
--E 15

--S 16 of 41
sqrt(f**2)
 

   (16)  14.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (16)  14.2857142857 14285714
--R                                                                  Type: Float
--E 16

--S 17 of 41
sin(f)**2+cos(f)**2
 

   (17)  1.0
                                                                  Type: Float
--R 
--R
--R   (17)  1.0
--R                                                                  Type: Float
--E 17

--S 18 of 41
sinh(f)**2-cosh(f)**2
 

   (18)  - 1.0
                                                                  Type: Float
--R 
--R
--R   (18)  - 1.0
--R                                                                  Type: Float
--E 18

--S 19 of 41
truncate f
 

   (19)  14.0
                                                                  Type: Float
--R 
--R
--R   (19)  14.0
--R                                                                  Type: Float
--E 19

--S 20 of 41
round f
 

   (20)  14.0
                                                                  Type: Float
--R 
--R
--R   (20)  14.0
--R                                                                  Type: Float
--E 20

--S 21 of 41
fractionPart f
 

   (21)  0.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (21)  0.2857142857 14285714
--R                                                                  Type: Float
--E 21

--S 22 of 41
ceiling f
 

   (22)  15.0
                                                                  Type: Float
--R 
--R
--R   (22)  15.0
--R                                                                  Type: Float
--E 22

--S 23 of 41
floor f
 

   (23)  14.0
                                                                  Type: Float
--R 
--R
--R   (23)  14.0
--R                                                                  Type: Float
--E 23

--S 24 of 41
wholePart f
 

   (24)  14
                                                        Type: PositiveInteger
--R 
--R
--R   (24)  14
--R                                                        Type: PositiveInteger
--E 24
 
--S 25 of 41
digits 50
 

   (25)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  20
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 41
f := 1.0/3
 

   (26)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (26)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 26

--S 27 of 41
exp log f
 

   (27)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (27)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 27

--S 28 of 41
asin sin f
 

   (28)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (28)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 28

--S 29 of 41
acos cos f
 

   (29)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (29)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 29

--S 30 of 41
atan tan f
 

   (30)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (30)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 30

--S 31 of 41
asinh sinh f
 

   (31)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (31)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 31

--S 32 of 41
acosh cosh f
 

   (32)  0.3333333333 3333333333 3333333333 3333333333 3333333334
                                                                  Type: Float
--R 
--R
--R   (32)  0.3333333333 3333333333 3333333333 3333333333 3333333334
--R                                                                  Type: Float
--E 32

--S 33 of 41
atanh tanh f
 

   (33)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (33)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 33

--S 34 of 41
log exp1()
 

   (34)  1.0
                                                                  Type: Float
--R 
--R
--R   (34)  1.0
--R                                                                  Type: Float
--E 34

--S 35 of 41
sin numeric %pi
 

   (35)  - 0.6356225157 7200746034 5144300600 8220509036 2417341559 E -50
                                                                  Type: Float
--R 
--R
--R   (35)  - 0.6356225157 7200746034 5144300600 8220509036 2417341559 E -50
--R                                                                  Type: Float
--E 35

--S 36 of 41
exp log2()
 

   (36)  2.0
                                                                  Type: Float
--R 
--R
--R   (36)  2.0
--R                                                                  Type: Float
--E 36

--S 37 of 41
exp log10()
 

   (37)  10.0
                                                                  Type: Float
--R 
--R
--R   (37)  10.0
--R                                                                  Type: Float
--E 37

--S 38 of 41
f := 1024.0
 

   (38)  1024.0
                                                                  Type: Float
--R 
--R
--R   (38)  1024.0
--R                                                                  Type: Float
--E 38

--S 39 of 41
log2 f
 

   (39)  10.0
                                                                  Type: Float
--R 
--R
--R   (39)  10.0
--R                                                                  Type: Float
--E 39

--S 40 of 41
f := 1000.0
 

   (40)  1000.0
                                                                  Type: Float
--R 
--R
--R   (40)  1000.0
--R                                                                  Type: Float
--E 40

--S 41 of 41
log10 f
 

   (41)  3.0
                                                                  Type: Float
--R 
--R
--R   (41)  3.0
--R                                                                  Type: Float
--E 41
)spool 
 
Starts dribbling to chtheorem.output (2009/2/17, 17:44:9).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
D:=FFP(PF 2,x^4+x+1)
 

   (1)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
                                                                 Type: Domain
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +   3                                          3       +
        | %A  + 1           0            %A + 1      %A  + 1   |
        |                                                      |
        |     2       3     2                          3       |
        |   %A      %A  + %A  + %A + 1   %A + 1      %A  + 1   |
   (2)  |                                                      |
        |                3                2         3     2    |
        |    0         %A  + %A + 1     %A  + %A  %A  + %A  + 1|
        |                                                      |
        |  3     2                        2                    |
        +%A  + %A           1           %A  + 1         0      +
         Type: Matrix FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
p:=characteristicPolynomial(M,y)
 

         4     2 2
   (3)  y  + %A y  + y + %A + 1
     Type: Polynomial FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
SM:=SquareMatrix(4,D)
 

   (4)
   SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
                                                                 Type: Domain
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

             +  2               +
             |%A    0    0    0 |
             |                  |         +%A + 1    0       0       0   +
             |       2          |         |                              |
         4   | 0   %A    0    0 | 2       |  0     %A + 1    0       0   |
   (5)  y  + |                  |y  + y + |                              |
             |            2     |         |  0       0     %A + 1    0   |
             | 0    0   %A    0 |         |                              |
             |                  |         +  0       0       0     %A + 1+
             |                 2|
             + 0    0    0   %A +
Type: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
sm:=squareMatrix(M)$SM
 

        +   3                                          3       +
        | %A  + 1           0            %A + 1      %A  + 1   |
        |                                                      |
        |     2       3     2                          3       |
        |   %A      %A  + %A  + %A + 1   %A + 1      %A  + 1   |
   (6)  |                                                      |
        |                3                2         3     2    |
        |    0         %A  + %A + 1     %A  + %A  %A  + %A  + 1|
        |                                                      |
        |  3     2                        2                    |
        +%A  + %A           1           %A  + 1         0      +
Type: SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))

--S 1 of 4
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
Type: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--RType: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--E 1

)clear all
 
   All user variables and function definitions have been cleared.

D:=INT
 

   (1)  Integer
                                                                 Type: Domain
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +33896160  62655076  47582200  50295771+
        |                                      |
        |51600199  63914084  20224500  13679048|
   (2)  |                                      |
        |33831145  63444111  57097933  58618369|
        |                                      |
        +31150599  54006310  29733569  20919750+
                                                         Type: Matrix Integer
p:=characteristicPolynomial(M,y)
 

   (3)
      4             3                   2
     y  - 175827927y  + 817513371501548y  + 7762444549665525341460y
   + 
     100067543295422644360923557411
                                                     Type: Polynomial Integer
SM:=SquareMatrix(4,D)
 

   (4)  SquareMatrix(4,Integer)
                                                                 Type: Domain
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

   (5)
          +- 175827927       0            0            0     +
          |                                                  |
      4   |     0       - 175827927       0            0     | 3
     y  + |                                                  |y
          |     0            0       - 175827927       0     |
          |                                                  |
          +     0            0            0       - 175827927+
   + 
     +817513371501548         0                0                0       +
     |                                                                  |
     |       0         817513371501548         0                0       | 2
     |                                                                  |y
     |       0                0         817513371501548         0       |
     |                                                                  |
     +       0                0                0         817513371501548+
   + 
   [[7762444549665525341460,0,0,0], [0,7762444549665525341460,0,0],
    [0,0,7762444549665525341460,0], [0,0,0,7762444549665525341460]]
    *
       y
   + 
   [[100067543295422644360923557411,0,0,0],
    [0,100067543295422644360923557411,0,0],
    [0,0,100067543295422644360923557411,0],
    [0,0,0,100067543295422644360923557411]]
                                     Type: Polynomial SquareMatrix(4,Integer)
sm:=squareMatrix(M)$SM
 

        +33896160  62655076  47582200  50295771+
        |                                      |
        |51600199  63914084  20224500  13679048|
   (6)  |                                      |
        |33831145  63444111  57097933  58618369|
        |                                      |
        +31150599  54006310  29733569  20919750+
                                                Type: SquareMatrix(4,Integer)

--S 2 of 4
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                     Type: Polynomial SquareMatrix(4,Integer)
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                     Type: Polynomial SquareMatrix(4,Integer)
--E 2

)clear all
 
   All user variables and function definitions have been cleared.

D:=PF 7
 

   (1)  PrimeField 7
                                                                 Type: Domain
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +0  4  0  5+
        |          |
        |3  5  2  4|
   (2)  |          |
        |3  0  0  2|
        |          |
        +0  1  1  1+
                                                    Type: Matrix PrimeField 7
p:=characteristicPolynomial(M,y)
 

         4    3    2
   (3)  y  + y  + y  + 6y + 3
                                                Type: Polynomial PrimeField 7
SM:=SquareMatrix(4,D)
 

   (4)  SquareMatrix(4,PrimeField 7)
                                                                 Type: Domain
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

                       +6  0  0  0+    +3  0  0  0+
                       |          |    |          |
         4    3    2   |0  6  0  0|    |0  3  0  0|
   (5)  y  + y  + y  + |          |y + |          |
                       |0  0  6  0|    |0  0  3  0|
                       |          |    |          |
                       +0  0  0  6+    +0  0  0  3+
                                Type: Polynomial SquareMatrix(4,PrimeField 7)
sm:=squareMatrix(M)$SM
 

        +0  4  0  5+
        |          |
        |3  5  2  4|
   (6)  |          |
        |3  0  0  2|
        |          |
        +0  1  1  1+
                                           Type: SquareMatrix(4,PrimeField 7)

--S 3 of 4
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                Type: Polynomial SquareMatrix(4,PrimeField 7)
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                Type: Polynomial SquareMatrix(4,PrimeField 7)
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

D:=FF(2,4)
 

   (1)  FiniteField(2,4)
                                                                 Type: Domain
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +  3     2            3                 2         3     +
        |%A  + %A  + %A     %A  + 1           %A        %A  + %A|
        |                                                       |
        |                  3     2              2         2     |
        |      0         %A  + %A  + %A       %A        %A  + %A|
   (2)  |                                                       |
        |     3               2            3     2          2   |
        |   %A  + 1         %A  + 1      %A  + %A  + 1    %A    |
        |                                                       |
        |     2            3     2         3              3     |
        +   %A  + %A     %A  + %A  + %A  %A  + %A + 1   %A  + %A+
                                                Type: Matrix FiniteField(2,4)
p:=characteristicPolynomial(M,y)
 

         4      2           3     2 2      3            2
   (3)  y  + (%A  + %A + 1)y  + %A y  + (%A  + %A)y + %A  + %A + 1
                                            Type: Polynomial FiniteField(2,4)
SM:=SquareMatrix(4,D)
 

   (4)  SquareMatrix(4,FiniteField(2,4))
                                                                 Type: Domain
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

   (5)
          +  2                                                   +
          |%A  + %A + 1       0             0             0      |
          |                                                      |
          |                2                                     |
      4   |     0        %A  + %A + 1       0             0      | 3
     y  + |                                                      |y
          |                              2                       |
          |     0             0        %A  + %A + 1       0      |
          |                                                      |
          |                                            2         |
          +     0             0             0        %A  + %A + 1+
   + 
     +  2               +     +  3                                   +
     |%A    0    0    0 |     |%A  + %A     0         0         0    |
     |                  |     |                                      |
     |       2          |     |            3                         |
     | 0   %A    0    0 | 2   |   0      %A  + %A     0         0    |
     |                  |y  + |                                      |y
     |            2     |     |                      3               |
     | 0    0   %A    0 |     |   0         0      %A  + %A     0    |
     |                  |     |                                      |
     |                 2|     |                                3     |
     + 0    0    0   %A +     +   0         0         0      %A  + %A+
   + 
     +  2                                                   +
     |%A  + %A + 1       0             0             0      |
     |                                                      |
     |                2                                     |
     |     0        %A  + %A + 1       0             0      |
     |                                                      |
     |                              2                       |
     |     0             0        %A  + %A + 1       0      |
     |                                                      |
     |                                            2         |
     +     0             0             0        %A  + %A + 1+
                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
sm:=squareMatrix(M)$SM
 

        +  3     2            3                 2         3     +
        |%A  + %A  + %A     %A  + 1           %A        %A  + %A|
        |                                                       |
        |                  3     2              2         2     |
        |      0         %A  + %A  + %A       %A        %A  + %A|
   (6)  |                                                       |
        |     3               2            3     2          2   |
        |   %A  + 1         %A  + 1      %A  + %A  + 1    %A    |
        |                                                       |
        |     2            3     2         3              3     |
        +   %A  + %A     %A  + %A  + %A  %A  + %A + 1   %A  + %A+
                                       Type: SquareMatrix(4,FiniteField(2,4))

--S 4 of 4
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
--E 4
)spool 
 
Starts dribbling to besselk.output (2009/2/17, 17:43:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 4
D(besselK(a,x),x)
 

        - besselK(a + 1,x) - besselK(a - 1,x)
   (1)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R
--R        - besselK(a + 1,x) - besselK(a - 1,x)
--R   (1)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E 1

--S 2 of 4
D(besselK(a,x),a)
 

   (2)  besselK  (a,x)
               ,1
                                                     Type: Expression Integer
--R
--R   (2)  besselK  (a,x)
--R               ,1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 4
integrate(D(besselK(a,x),a),a)
 

   (3)  besselK(a,x)
                                          Type: Union(Expression Integer,...)
--R
--R   (3)  besselK(a,x)
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 4
limit(D(besselK(a,x),a),a=1/2)
 

   (4)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (4)  "failed"
--R                                                    Type: Union("failed",...)
--E 4

--S 5
stegun(x)== %e^x * besselK(1,x)
 
                                                                   Type: Void
--E 5

--S 6
[[0.1, 10.890182683 , stegun(0.1),  stegun(0.1)- 10.890182683 ],_
 [0.2,  5.833386037 , stegun(0.2),  stegun(0.2)-  5.833386037 ],_
 [0.3,  4.125157762 , stegun(0.3),  stegun(0.3)-  4.125157762 ],_
 [0.4,  3.258673880 , stegun(0.4),  stegun(0.4)-  3.258673880 ],_
 [0.5,  2.7310097082, stegun(0.5),  stegun(0.5)-  2.7310097082],_
 [0.6,  2.3739200376, stegun(0.6),  stegun(0.6)-  2.3739200376],_
 [0.7,  2.1150113128, stegun(0.7),  stegun(0.7)-  2.1150113128],_
 [0.8,  1.9179302990, stegun(0.8),  stegun(0.8)-  1.9179302990],_
 [0.9,  1.7623882197, stegun(0.9),  stegun(0.9)-  1.7623882197],_
 [1.0,  1.6361534863, stegun(1.0),  stegun(1.0)-  1.6361534863],_
 [1.1,  1.5314037541, stegun(1.1),  stegun(1.1)-  1.5314037541],_
 [1.2,  1.4428975522, stegun(1.2),  stegun(1.2)-  1.4428975522],_
 [1.3,  1.3669872841, stegun(1.3),  stegun(1.3)-  1.3669872841],_
 [1.4,  1.3010537400, stegun(1.4),  stegun(1.4)-  1.3010537400],_
 [1.5,  1.2431658736, stegun(1.5),  stegun(1.5)-  1.2431658736],_
 [1.6,  1.1918675654, stegun(1.6),  stegun(1.6)-  1.1918675654],_
 [1.7,  1.1460392462, stegun(1.7),  stegun(1.7)-  1.1460392462],_
 [1.8,  1.1048053726, stegun(1.8),  stegun(1.8)-  1.1048053726],_
 [1.9,  1.0674709298, stegun(1.9),  stegun(1.9)-  1.0674709298],_
 [2.0,  1.0334768471, stegun(2.0),  stegun(2.0)-  1.0334768471],_
 [2.1,  1.0023680527, stegun(2.1),  stegun(2.1)-  1.0023680527],_
 [2.2,  0.9737701679, stegun(2.2),  stegun(2.2)-  0.9737701679],_
 [2.3,  0.9473722250, stegun(2.3),  stegun(2.3)-  0.9473722250],_
 [2.4,  0.9229136650, stegun(2.4),  stegun(2.4)-  0.9229136650],_
 [2.5,  0.9001744239, stegun(2.5),  stegun(2.5)-  0.9001744239],_
 [2.6,  0.8789672806, stegun(2.6),  stegun(2.6)-  0.8789672806],_
 [2.7,  0.8591318867, stegun(2.7),  stegun(2.7)-  0.8591318867],_
 [2.8,  0.8405300604, stegun(2.8),  stegun(2.8)-  0.8405300604],_
 [2.9,  0.8230420403, stegun(2.9),  stegun(2.9)-  0.8230420403],_
 [3.0,  0.8065634800, stegun(3.0),  stegun(3.0)-  0.8065634800],_
 [3.1,  0.7910030157, stegun(3.1),  stegun(3.1)-  0.7910030157],_
 [3.2,  0.7762802824, stegun(3.2),  stegun(3.2)-  0.7762802824],_
 [3.3,  0.7623242864, stegun(3.3),  stegun(3.3)-  0.7623242864],_
 [3.4,  0.7490720613, stegun(3.4),  stegun(3.4)-  0.7490720613],_
 [3.5,  0.7364675480, stegun(3.5),  stegun(3.5)-  0.7364675480],_
 [3.6,  0.7244606608, stegun(3.6),  stegun(3.6)-  0.7244606608],_
 [3.7,  0.7130065010, stegun(3.7),  stegun(3.7)-  0.7130065010],_
 [3.8,  0.7020646931, stegun(3.8),  stegun(3.8)-  0.7020646931],_
 [3.9,  0.6915988206, stegun(3.9),  stegun(3.9)-  0.6915988206],_
 [4.0,  0.6815759452, stegun(4.0),  stegun(4.0)-  0.6815759452],_
 [4.1,  0.6719661952, stegun(4.1),  stegun(4.1)-  0.6719661952],_
 [4.2,  0.6627424110, stegun(4.2),  stegun(4.2)-  0.6627424110],_
 [4.3,  0.6538798395, stegun(4.3),  stegun(4.3)-  0.6538798395],_
 [4.4,  0.6453558689, stegun(4.4),  stegun(4.4)-  0.6453558689],_
 [4.5,  0.6371497988, stegun(4.5),  stegun(4.5)-  0.6371497988],_
 [4.6,  0.6292426383, stegun(4.6),  stegun(4.6)-  0.6292426383],_
 [4.7,  0.6216169312, stegun(4.7),  stegun(4.7)-  0.6216169312],_
 [4.8,  0.6142566003, stegun(4.8),  stegun(4.8)-  0.6142566003],_
 [4.9,  0.6071468131, stegun(4.9),  stegun(4.9)-  0.6071468131],_
 [5.0,  0.6002738587, stegun(5.0),  stegun(5.0)-  0.6002738587],_
 [5.1,  0.5936250463, stegun(5.1),  stegun(5.1)-  0.5936250463],_
 [5.2,  0.5871886062, stegun(5.2),  stegun(5.2)-  0.5871886062],_
 [5.3,  0.5809536085, stegun(5.3),  stegun(5.3)-  0.5809536085],_
 [5.4,  0.5749098871, stegun(5.4),  stegun(5.4)-  0.5749098871],_
 [5.5,  0.5690479741, stegun(5.5),  stegun(5.5)-  0.5690479741],_
 [5.6,  0.5633590393, stegun(5.6),  stegun(5.6)-  0.5633590393],_
 [5.7,  0.5578348348, stegun(5.7),  stegun(5.7)-  0.5578348348],_
 [5.8,  0.5524676495, stegun(5.8),  stegun(5.8)-  0.5524676495],_
 [5.9,  0.5472502639, stegun(5.9),  stegun(5.9)-  0.5472502639],_
 [6.0,  0.5421759104, stegun(6.0),  stegun(6.0)-  0.5421759104],_
 [6.1,  0.5372382386, stegun(6.1),  stegun(6.1)-  0.5372382386],_
 [6.2,  0.5324312833, stegun(6.2),  stegun(6.2)-  0.5324312833],_
 [6.3,  0.5277494344, stegun(6.3),  stegun(6.3)-  0.5277494344],_
 [6.4,  0.5231874101, stegun(6.4),  stegun(6.4)-  0.5231874101],_
 [6.5,  0.5187402336, stegun(6.5),  stegun(6.5)-  0.5187402336],_
 [6.6,  0.5144032108, stegun(6.6),  stegun(6.6)-  0.5144032108],_
 [6.7,  0.5101719097, stegun(6.7),  stegun(6.7)-  0.5101719097],_
 [6.8,  0.5060421421, stegun(6.8),  stegun(6.8)-  0.5060421421],_
 [6.9,  0.5020099471, stegun(6.9),  stegun(6.9)-  0.5020099471],_
 [7.0,  0.4980715749, stegun(7.0),  stegun(7.0)-  0.4980715749],_
 [7.1,  0.4942234737, stegun(7.1),  stegun(7.1)-  0.4942234737],_
 [7.2,  0.4904622755, stegun(7.2),  stegun(7.2)-  0.4904622755],_
 [7.3,  0.4867847842, stegun(7.3),  stegun(7.3)-  0.4867847842],_
 [7.4,  0.4831879648, stegun(7.4),  stegun(7.4)-  0.4831879648],_
 [7.5,  0.4796689336, stegun(7.5),  stegun(7.5)-  0.4796689336],_
 [7.6,  0.4762249486, stegun(7.6),  stegun(7.6)-  0.4762249486],_
 [7.7,  0.4728533995, stegun(7.7),  stegun(7.7)-  0.4728533995],_
 [7.8,  0.4695518010, stegun(7.8),  stegun(7.8)-  0.4695518010],_
 [7.9,  0.4663177847, stegun(7.9),  stegun(7.9)-  0.4663177847],_
 [8.0,  0.4631490928, stegun(8.0),  stegun(8.0)-  0.4631490928],_
 [8.1,  0.4600435709, stegun(8.1),  stegun(8.1)-  0.4600435709],_
 [8.2,  0.4569991615, stegun(8.2),  stegun(8.2)-  0.4569991615],_
 [8.3,  0.4540139001, stegun(8.3),  stegun(8.3)-  0.4540139001],_
 [8.4,  0.4510859089, stegun(8.4),  stegun(8.4)-  0.4510859089],_
 [8.5,  0.4482133915, stegun(8.5),  stegun(8.5)-  0.4482133915],_
 [8.6,  0.4453946295, stegun(8.6),  stegun(8.6)-  0.4453946295],_
 [8.7,  0.4426279775, stegun(8.7),  stegun(8.7)-  0.4426279775],_
 [8.8,  0.4399118594, stegun(8.8),  stegun(8.8)-  0.4399118594],_
 [8.9,  0.4372447648, stegun(8.9),  stegun(8.9)-  0.4372447648],_
 [9.0,  0.4346252454, stegun(9.0),  stegun(9.0)-  0.4346252454],_
 [9.1,  0.4320519116, stegun(9.1),  stegun(9.1)-  0.4320519116],_
 [9.2,  0.4295234301, stegun(9.2),  stegun(9.2)-  0.4295234301],_
 [9.3,  0.4270385204, stegun(9.3),  stegun(9.3)-  0.4270385204],_
 [9.4,  0.4245959520, stegun(9.4),  stegun(9.4)-  0.4245959520],_
 [9.5,  0.4221945430, stegun(9.5),  stegun(9.5)-  0.4221945430],_
 [9.6,  0.4198331565, stegun(9.6),  stegun(9.6)-  0.4198331565],_
 [9.7,  0.4175106989, stegun(9.7),  stegun(9.7)-  0.4175106989],_
 [9.8,  0.4152261179, stegun(9.8),  stegun(9.8)-  0.4152261179],_
 [9.9,  0.4129784003, stegun(9.9),  stegun(9.9)-  0.4129784003],_
 [10.0, 0.4107665704, stegun(10.0), stegun(10.0)- 0.4107665704]]
 
   Compiling function stegun with type Float -> Expression DoubleFloat 

   (6)
   [
     [0.099999999999999992, 10.890182682999999, 10.88992710127167,
      - 2.5558172832873538E-4]
     ,

     [0.19999999999999998, 5.8333860369999995, 5.8328122792663946,
      - 5.7375773360490712E-4]
     ,

     [0.29999999999999999, 4.1251577619999997, 4.1241472973297775,
      - 0.0010104646702222553]
     ,

     [0.39999999999999997, 3.2586738799999999, 3.2572055571493528,
      - 0.0014683228506471302]
     ,
    [0.5,2.7310097081999998,2.728881727367293,- 0.0021279808327068217],

     [0.59999999999999998, 2.3739200375999996, 2.3707164910612106,
      - 0.0032035465387889595]
     ,

     [0.69999999999999996, 2.1150113127999997, 2.1099362963276089,
      - 0.0050750164723907254]
     ,

     [0.79999999999999993, 1.9179302989999998, 1.9138347551422896,
      - 0.0040955438577101599]
     ,

     [0.89999999999999991, 1.7623882196999998, 1.7561789858304857,
      - 0.0062092338695141081]
     ,
    [1.0,1.6361534862999998,1.6334132069714467,- 0.0027402793285531413],

     [1.0999999999999999, 1.5314037540999998, 1.5137174937902307,
      - 0.017686260309769164]
     ,
    [1.2,1.4428975521999998,1.4203823995789373,- 0.022515152621062517],

     [1.2999999999999998, 1.3669872840999999, 1.3577503968154736,
      - 0.0092368872845263184]
     ,
    [1.3999999999999999,1.30105374,1.2685869247870485,- 0.032466815212951472],
    [1.5,1.2431658736,1.2105344846775452,- 0.032631388922454763],

     [1.5999999999999999, 1.1918675653999999, 1.1426767992405249,
      - 0.049190766159475041]
     ,
    [1.7,1.1460392462,1.1252670696207718,- 0.020772176579228141],

     [1.7999999999999998, 1.1048053725999998, 1.0177061184786962,
      - 0.087099254121303593]
     ,

     [1.8999999999999999, 1.0674709297999998, 1.0818323969910089,
      0.014361467191009059]
     ,
    [2.0,1.0334768471,1.060221137653407,0.026744290553406991],

     [2.0999999999999996, 1.0023680526999998, 1.0030399201807692,
      6.7186748076930591E-4]
     ,

     [2.1999999999999997, 0.97377016789999993, 1.4578276979566176,
      0.48405753005661767]
     ,

     [2.2999999999999998, 0.94737222499999996, 1.0634016822774299,
      0.11602945727742997]
     ,

     [2.3999999999999999, 0.92291366499999994, - 0.69872493136311642,
      - 1.6216385963631164]
     ,
    [2.5,0.90017442389999991,0.9835767884784371,0.083402364578437194],

     [2.5999999999999996, 0.87896728059999996, - 0.65688918383531703,
      - 1.535856464435317]
     ,

     [2.6999999999999997, 0.85913188669999996, - 2.2034398589008513,
      - 3.0625717456008514]
     ,

     [2.7999999999999998, 0.84053006039999989, - 2.3178907159103681,
      - 3.158420776310368]
     ,

     [2.8999999999999999, 0.82304204029999994, - 0.057747266105284176,
      - 0.88078930640528408]
     ,
    [3.0,0.80656348,- 11.438102720921068,- 12.244666200921067],

     [3.0999999999999996, 0.79100301569999998, 0.63289796803639442,
      - 0.15810504766360556]
     ,

     [3.1999999999999997, 0.77628028239999991, - 5.0663510653348052,
      - 5.8426313477348053]
     ,

     [3.2999999999999998, 0.76232428639999994, 0.042086120372451082,
      - 0.72023816602754887]
     ,

     [3.3999999999999999, 0.74907206129999993, - 0.061480701607031521,
      - 0.81055276290703149]
     ,
    [3.5,0.73646754799999992,- 6.7094259752588394,- 7.4458935232588397],

     [3.5999999999999996, 0.72446066079999993, - 38.575757169733002,
      - 39.300217830533001]
     ,

     [3.6999999999999997, 0.71300650099999996, - 2.4396034857810616,
      - 3.1526099867810613]
     ,

     [3.7999999999999998, 0.70206469309999997, 162.17924169109853,
      161.47717699799853]
     ,
    [3.8999999999999999,0.6915988206,12.326919505818488,11.635320685218488],
    [4.0,0.68157594519999998,136.27766334482624,135.59608739962624],

     [4.0999999999999996, 0.67196619519999989, - 196.31999722858816,
      - 196.99196342378818]
     ,

     [4.1999999999999993, 0.66274241099999998, 22.072400295416326,
      21.409657884416326]
     ,

     [4.2999999999999998, 0.65387983949999995, 309.77140002333903,
      309.11752018383902]
     ,

     [4.3999999999999995, 0.64535586889999996, 401.37367560809884,
      400.72831973919881]
     ,
    [4.5,0.63714979879999989,- 1509.6498824303562,- 1510.2870322291562],

     [4.5999999999999996, 0.62924263829999993, 300.50770660983937,
      299.87846397153936]
     ,

     [4.6999999999999993, 0.62161693119999994, 2945.5420363366243,
      2944.9204194054241]
     ,
    [4.7999999999999998,0.61425660029999996,4394.556044942723,4393.941788342423]
     ,

     [4.8999999999999995, 0.60714681309999996, - 4339.233295417388,
      - 4339.8404422304884]
     ,
    [5.0,0.60027385869999994,5328.6371311364028,5328.0368572777024],

     [5.0999999999999996, 0.5936250462999999, - 9875.7479433440876,
      - 9876.3415683903877]
     ,

     [5.1999999999999993, 0.58718860619999991, - 8722.8679811836228,
      - 8723.4551697898223]
     ,
    [5.2999999999999998,0.5809536085,3680.8528847670209,3680.2719311585211],

     [5.3999999999999995, 0.57490988709999991, - 19563.253284971233,
      - 19563.828194858332]
     ,
    [5.5,0.56904797409999996,27244.680190073832,27244.111142099733],

     [5.5999999999999996, 0.56335903929999998, 20956.868015735046,
      20956.304656695746]
     ,

     [5.6999999999999993, 0.55783483479999996, 41769.261917959157,
      41768.704083124358]
     ,

     [5.7999999999999998, 0.55246764949999994, - 61974.281213682625,
      - 61974.833681332122]
     ,

     [5.8999999999999995, 0.54725026389999998, 9571.4187934101992,
      9570.8715431462988]
     ,
    [6.0,0.54217591039999991,- 157382.98786093417,- 157383.53003684458],

     [6.0999999999999996, 0.53723823859999997, - 312787.26301847462,
      - 312787.80025671324]
     ,

     [6.1999999999999993, 0.53243128329999989, 244094.82460346271,
      244094.29217217941]
     ,

     [6.2999999999999998, 0.52774943439999999, - 242974.23942178453,
      - 242974.76717121893]
     ,

     [6.3999999999999995, 0.52318741009999992, 10262.909344751393,
      10262.386157341294]
     ,
    [6.5,0.51874023359999999,638280.0358961497,638279.51715591608],

     [6.5999999999999996, 0.51440321079999995, - 660662.7245848946,
      - 660663.23898810544]
     ,

     [6.6999999999999993, 0.51017190969999993, - 1821351.9277524189,
      - 1821352.4379243285]
     ,

     [6.7999999999999998, 0.50604214209999998, 1216555.668229098,
      1216555.1621869558]
     ,

     [6.8999999999999995, 0.50200994709999991, - 321190.74046772829,
      - 321191.24247767538]
     ,
    [7.0,0.49807157489999998,5407415.5469123255,5407415.0488407509],

     [7.0999999999999996, 0.49422347369999997, - 1.1833094868498195E7,
      - 1.1833095362721669E7]
     ,

     [7.1999999999999993, 0.49046227549999999, - 2086149.3072533312,
      - 2086149.7977156066]
     ,

     [7.2999999999999998, 0.48678478419999999, - 1797793.9761193111,
      - 1797794.4629040952]
     ,

     [7.3999999999999995, 0.48318796479999998, 4726506.2223073263,
      4726505.7391193612]
     ,
    [7.5,0.47966893359999996,- 3.9170920028673656E7,- 3.9170920508342586E7],

     [7.5999999999999996, 0.47622494859999998, - 2.292795394564034E7,
      - 2.2927954421865288E7]
     ,

     [7.6999999999999993, 0.47285339949999999, - 7.0213887611150801E7,
      - 7.0213888084004194E7]
     ,

     [7.7999999999999998, 0.46955180099999999, - 6.5792033508865409E7,
      - 6.579203397841721E7]
     ,

     [7.8999999999999995, 0.46631778469999996, - 3.6015283818809509E7,
      - 3.6015284285127297E7]
     ,
    [8.0,0.4631490928,4.7509555772277519E7,4.7509555309128426E7],

     [8.0999999999999996, 0.46004357089999998, - 2.4988514624740157E8,
      - 2.4988514670744514E8]
     ,

     [8.1999999999999993, 0.45699916149999997, 3.4655837124493146E8,
      3.4655837078793228E8]
     ,

     [8.2999999999999989, 0.45401390009999998, 4596746.1759276781,
      4596745.7219137782]
     ,
    [8.3999999999999986,0.4510859089,9.7993410885967597E7,9.7993410434881687E7],
    [8.5,0.44821339149999995,6.4860265842222035E8,6.4860265797400701E8],

     [8.5999999999999996, 0.44539462949999997, - 6.7392001635723794E8,
      - 6.7392001680263257E8]
     ,

     [8.6999999999999993, 0.44262797749999999, 3.0856408264647895E8,
      3.0856408220385098E8]
     ,

     [8.7999999999999989, 0.43991185939999999, 1.1965970108807921E9,
      1.1965970104408803E9]
     ,

     [8.8999999999999986, 0.43724476479999996, 5.9493298680874109E8,
      5.9493298637149632E8]
     ,
    [9.0,0.43462524539999997,1.7356653810645356E9,1.7356653806299105E9],

     [9.0999999999999996, 0.43205191159999995, 2.2362183271137366E9,
      2.2362183266816845E9]
     ,

     [9.1999999999999993, 0.42952343009999999, 6.0831216051095903E8,
      6.0831216008143556E8]
     ,

     [9.2999999999999989, 0.42703852039999995, - 8.328858353308898E9,
      - 8.3288583537359362E9]
     ,

     [9.3999999999999986, 0.424595952, - 1.2762232919346815E10,
      - 1.2762232919771412E10]
     ,
    [9.5,0.42219454299999998,- 3.2819105414042206E10,- 3.2819105414464401E10],

     [9.5999999999999996, 0.41983315649999997, - 2.6100656628516556E10,
      - 2.610065662893639E10]
     ,

     [9.6999999999999993, 0.41751069889999998, 5.9418099437315308E10,
      5.9418099436897797E10]
     ,

     [9.7999999999999989, 0.41522611789999997, 7.9048783049232651E10,
      7.9048783048817429E10]
     ,

     [9.8999999999999986, 0.41297840029999999, - 2.2853429623297096E10,
      - 2.2853429623710075E10]
     ,
    [10.0,0.41076657039999998,4.3443891534627167E10,4.34438915342164E10]]
                                       Type: List List Expression DoubleFloat
--E 6

)spool 
 
Starts dribbling to intef.output (2009/2/17, 17:46:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 16
(a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x)
 

                        a x + b
   (1)  --------------------------------------
         2        2         2          2 3
        b x log(x)  + 2a b x log(x) + a x  + x
                                                     Type: Expression Integer
--R 
--R
--R                        a x + b
--R   (1)  --------------------------------------
--R         2        2         2          2 3
--R        b x log(x)  + 2a b x log(x) + a x  + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 16
integrate(%,x)
 

   (2)  atan(b log(x) + a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)  atan(b log(x) + a x)
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 16
((exp(x)-x**2+2*x)/(x**2*(exp(x)+x)**2))*exp((x**2-1)/x+1/(exp(x)+x))
 

                           2       x    3
                         (x  - 1)%e  + x
                         ----------------
                                x    2
           x    2           x %e  + x
        (%e  - x  + 2x)%e
   (3)  ---------------------------------
               2   x 2     3  x    4
              x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R                           2       x    3
--R                         (x  - 1)%e  + x
--R                         ----------------
--R                                x    2
--R           x    2           x %e  + x
--R        (%e  - x  + 2x)%e
--R   (3)  ---------------------------------
--R               2   x 2     3  x    4
--R              x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 3

--S 4 of 16
integrate(%,x)
 

            2       x    3
          (x  - 1)%e  + x
          ----------------
                 x    2
             x %e  + x
        %e
   (4)  ------------------
                  x
                %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2       x    3
--R          (x  - 1)%e  + x
--R          ----------------
--R                 x    2
--R             x %e  + x
--R        %e
--R   (4)  ------------------
--R                  x
--R                %e
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 16
sin(x)/x
 

        sin(x)
   (5)  ------
           x
                                                     Type: Expression Integer
--R 
--R
--R        sin(x)
--R   (5)  ------
--R           x
--R                                                     Type: Expression Integer
--E 5

--S 6 of 16
integrate(%,x)
 

   (6)  Si(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (6)  Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 16
x * cot x
 

   (7)  x cot(x)
                                                     Type: Expression Integer
--R 
--R
--R   (7)  x cot(x)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 16
integrate(%,x)
 

           x
         ++
   (8)   |   %J cot(%J)d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--R   (8)   |   %J cot(%J)d%J
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 16
(2 * log(x)**2 - log x - x**2) / (log(x)**3 - x**2 * log x)
 

               2             2
        2log(x)  - log(x) - x
   (9)  ----------------------
                3    2
          log(x)  - x log(x)
                                                     Type: Expression Integer
--R 
--R
--R               2             2
--R        2log(x)  - log(x) - x
--R   (9)  ----------------------
--R                3    2
--R          log(x)  - x log(x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 16
integrate(%,x)
 

         log(log(x) + x) - log(log(x) - x) + 2li(x)
   (10)  ------------------------------------------
                              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         log(log(x) + x) - log(log(x) - x) + 2li(x)
--R   (10)  ------------------------------------------
--R                              2
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 16
cos(a * x) / (1 + cos(a * x))
 

           cos(a x)
   (11)  ------------
         cos(a x) + 1
                                                     Type: Expression Integer
--R 
--R
--R           cos(a x)
--R   (11)  ------------
--R         cos(a x) + 1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 16
integrate(%,x)
 

         - sin(a x) + a x cos(a x) + a x
   (12)  -------------------------------
                  a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - sin(a x) + a x cos(a x) + a x
--R   (12)  -------------------------------
--R                  a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 16
cos(3*x)*sin(2*x)
 

   (13)  cos(3x)sin(2x)
                                                     Type: Expression Integer
--R 
--R
--R   (13)  cos(3x)sin(2x)
--R                                                     Type: Expression Integer
--E 13

--S 14 of 16
integrate(%,x)
 

                  5           3
         - 8cos(x)  + 10cos(x)
   (14)  ----------------------
                    5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  5           3
--R         - 8cos(x)  + 10cos(x)
--R   (14)  ----------------------
--R                    5
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 16
cosh(a*x)*sinh(a*x)
 

   (15)  cosh(a x)sinh(a x)
                                                     Type: Expression Integer
--R 
--R
--R   (15)  cosh(a x)sinh(a x)
--R                                                     Type: Expression Integer
--E 15

--S 16 of 16
integrate(%,x)
 

                  2            2
         sinh(a x)  + cosh(a x)
   (16)  -----------------------
                    4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2            2
--R         sinh(a x)  + cosh(a x)
--R   (16)  -----------------------
--R                    4a
--R                                          Type: Union(Expression Integer,...)
--E 16
)spool 
 
Starts dribbling to skew.output (2009/2/17, 18:0:27).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 36
lv:List Symbol := [x,y,z]
 

   (1)  [x,y,z]
                                                            Type: List Symbol
--R 
--R
--R   (1)  [x,y,z]
--R                                                            Type: List Symbol
--E 1

--S 2 of 36
macro coefRing == Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 36
R := Expression coefRing
 

   (3)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (3)  Expression Integer
--R                                                                 Type: Domain
--E 3

--S 4 of 36
der := DERHAM(coefRing,lv)
 

   (4)  DeRhamComplex(Integer,[x,y,z])
                                                                 Type: Domain
--R 
--R
--R   (4)  DeRhamComplex(Integer,[x,y,z])
--R                                                                 Type: Domain
--E 4


--S 5 of 36
f:R:=x**2*y*z-5*x**3*y**2*z**5
 

            3 2 5    2
   (5)  - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3 2 5    2
--R   (5)  - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 5

--S 6 of 36
g:R:=z**2*y*cos(z)-7*sin(x**3*y**2)*z**2
 

            2     3 2       2
   (6)  - 7z sin(x y ) + y z cos(z)
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2
--R   (6)  - 7z sin(x y ) + y z cos(z)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 36
h:R:=x*y*z-2*x**3*y*z**2
 

            3   2
   (7)  - 2x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3   2
--R   (7)  - 2x y z  + x y z
--R                                                     Type: Expression Integer
--E 7


--S 8 of 36
dx :der := generator(1)
 

   (8)  dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (8)  dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 8

--S 9 of 36
dy :der := generator(2)
 

   (9)  dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (9)  dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 9

--S 10 of 36
dz :der := generator(3)
 

   (10)  dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (10)  dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 10

--S 11 of 36
[dx,dy,dz] := [generator(i)$der for i in 1..3]
 

   (11)  [dx,dy,dz]
                                    Type: List DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (11)  [dx,dy,dz]
--R                                    Type: List DeRhamComplex(Integer,[x,y,z])
--E 11

--S 12 of 36
alpha:der := f*dx + g*dy + h*dz
 

   (12)
          3   2                   2     3 2       2
     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
   + 
          3 2 5    2
     (- 5x y z  + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (12)
--R          3   2                   2     3 2       2
--R     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
--R   + 
--R          3 2 5    2
--R     (- 5x y z  + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 12

--S 13 of 36
beta:der  := cos(tan(x*y*z)+x*y*z)*dx + x*dy 
 

   (13)  x dy + cos(tan(x y z) + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (13)  x dy + cos(tan(x y z) + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 13

--S 14 of 36
exteriorDifferential alpha
 

   (14)
         2                  3 2                    3 2
     (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)dy dz
   + 
         3 2 4     2   2          2
     (25x y z  - 6x y z  + y z - x y)dx dz
   + 
           2 2 2     3 2       3   5    2
     (- 21x y z cos(x y ) + 10x y z  - x z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (14)
--R         2                  3 2                    3 2
--R     (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)dy dz
--R   + 
--R         3 2 4     2   2          2
--R     (25x y z  - 6x y z  + y z - x y)dx dz
--R   + 
--R           2 2 2     3 2       3   5    2
--R     (- 21x y z cos(x y ) + 10x y z  - x z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 14

--S 15 of 36
exteriorDifferential %
 

   (15)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (15)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 15

--S 16 of 36
macro exD == exteriorDifferential
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 36
gamma := alpha * beta
 

   (17)
        4   2    2               3   2
     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
   + 
       2     3 2       2                                   4 2 5    3
   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (17)
--R        4   2    2               3   2
--R     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
--R   + 
--R       2     3 2       2                                   4 2 5    3
--R   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 17

--S 18 of 36
delta := exD gamma
 

   (18)
                    2     3 2       2 2           4   3    2   2           2
           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
         + 
                    2     3 2        2 2           4   3     2   2
           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
      *
         sin(tan(x y z) + x y z)
     + 
             2                  3 2                    3 2
         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
      *
         cos(tan(x y z) + x y z)
     + 
            4 2 4     3   2             3
       - 25x y z  + 8x y z  - 2x y z + x y
  *
     dx dy dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (18)
--R                    2     3 2       2 2           4   3    2   2           2
--R           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
--R         + 
--R                    2     3 2        2 2           4   3     2   2
--R           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
--R      *
--R         sin(tan(x y z) + x y z)
--R     + 
--R             2                  3 2                    3 2
--R         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
--R      *
--R         cos(tan(x y z) + x y z)
--R     + 
--R            4 2 4     3   2             3
--R       - 25x y z  + 8x y z  - 2x y z + x y
--R  *
--R     dx dy dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 18

--S 19 of 36
epsilon := exD(alpha)*beta - alpha * exD(beta)
 

   (19)
                    2     3 2       2 2           4   3    2   2           2
           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
         + 
                    2     3 2        2 2           4   3     2   2
           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
      *
         sin(tan(x y z) + x y z)
     + 
             2                  3 2                    3 2
         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
      *
         cos(tan(x y z) + x y z)
     + 
            4 2 4     3   2             3
       - 25x y z  + 8x y z  - 2x y z + x y
  *
     dx dy dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (19)
--R                    2     3 2       2 2           4   3    2   2           2
--R           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
--R         + 
--R                    2     3 2        2 2           4   3     2   2
--R           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
--R      *
--R         sin(tan(x y z) + x y z)
--R     + 
--R             2                  3 2                    3 2
--R         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
--R      *
--R         cos(tan(x y z) + x y z)
--R     + 
--R            4 2 4     3   2             3
--R       - 25x y z  + 8x y z  - 2x y z + x y
--R  *
--R     dx dy dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 19

--S 20 of 36
delta - epsilon 
 

   (20)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (20)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 20

--S 21 of 36
a:BOP := operator('a)
 

   (21)  a
                                                          Type: BasicOperator
--R 
--R
--R   (21)  a
--R                                                          Type: BasicOperator
--E 21

--S 22 of 36
b:BOP := operator('b)
 

   (22)  b
                                                          Type: BasicOperator
--R 
--R
--R   (22)  b
--R                                                          Type: BasicOperator
--E 22

--S 23 of 36
c:BOP := operator('c)
 

   (23)  c
                                                          Type: BasicOperator
--R 
--R
--R   (23)  c
--R                                                          Type: BasicOperator
--E 23

--S 24 of 36
alpha := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz
 

   (24)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (24)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 24

--S 25 of 36
beta  := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz
 

   (25)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (25)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 25

--S 26 of 36
totalDifferential(a(x,y,z))$der
 

   (26)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
          ,3             ,2             ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (26)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
--R          ,3             ,2             ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 26

--S 27 of 36
exD alpha
 

   (27)
     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
       ,2           ,3                  ,1           ,3
   + 
     (b  (x,y,z) - a  (x,y,z))dx dy
       ,1           ,2
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (27)
--R     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
--R       ,2           ,3                  ,1           ,3
--R   + 
--R     (b  (x,y,z) - a  (x,y,z))dx dy
--R       ,1           ,2
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 27

--S 28 of 36
exD beta
 

   (28)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
           ,1           ,2           ,3
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (28)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
--R           ,1           ,2           ,3
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 28

--S 29 of 36
id:der := 1
 

   (29)  1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (29)  1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 29

--S 30 of 36
g1:der := a([x,t,y,u,v,z,e]) * id
 

   (30)  a(x,t,y,u,v,z,e)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (30)  a(x,t,y,u,v,z,e)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 30

--S 31 of 36
h1:der := a([x,y,x,t,x,z,y,r,u,x]) * id
 

   (31)  a(x,y,x,t,x,z,y,r,u,x)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (31)  a(x,y,x,t,x,z,y,r,u,x)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 31

--S 32 of 36
exD g1
 

   (32)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
          ,6                     ,3                     ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (32)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
--R          ,6                     ,3                     ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 32

--S 33 of 36
exD h1
 

   (33)
     a  (x,y,x,t,x,z,y,r,u,x)dz
      ,6
   + 
     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
       ,7                         ,2
   + 
         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,10                         ,5
       + 
         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,3                         ,1
    *
       dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (33)
--R     a  (x,y,x,t,x,z,y,r,u,x)dz
--R      ,6
--R   + 
--R     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
--R       ,7                         ,2
--R   + 
--R         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,10                         ,5
--R       + 
--R         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,3                         ,1
--R    *
--R       dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 33

--S 34 of 36
coefficient(gamma, dx*dy)
 

            2     3 2       2                                   4 2 5    3
   (34)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2                                   4 2 5    3
--R   (34)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 34

--S 35 of 36
coefficient(gamma, id)
 

   (35)  0
                                                     Type: Expression Integer
--R 
--R
--R   (35)  0
--R                                                     Type: Expression Integer
--E 35

--S 36 of 36
coefficient(g1,id)
 

   (36)  a(x,t,y,u,v,z,e)
                                                     Type: Expression Integer
--R 
--R
--R   (36)  a(x,t,y,u,v,z,e)
--R                                                     Type: Expression Integer
--E 36
)spool 
 
Starts dribbling to leg.output (2009/2/17, 17:48:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 4
p(n | n=0) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 4
p(n | n=1) == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
p(n | n>1) == ((2*n-1)*x*p(n-1)-(n-1)*p(n-2))/n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
p 3
 
   Compiling function p with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function p as a recurrence relation.

        5  3   3
   (4)  - x  - - x
        2      2
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function p with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function p as a recurrence relation.
--R
--R        5  3   3
--R   (4)  - x  - - x
--R        2      2
--R                                            Type: Polynomial Fraction Integer
--E 4
)spool 
 
Starts dribbling to sincos.output (2009/2/17, 18:0:20).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 2
[[0.01,0.00999983333416666468254,sin(0.01),sin(0.01)-(0.00999983333416666468254)],_
[0.02,0.01999866669333307936649,sin(0.02),sin(0.02)-(0.01999866669333307936649)],_
[0.03,0.02999550020249566076853,sin(0.03),sin(0.03)-(0.02999550020249566076853)],_
[0.04,0.03998933418663415945255,sin(0.04),sin(0.04)-(0.03998933418663415945255)],_
[0.05,0.04997916927067832879487,sin(0.05),sin(0.05)-(0.04997916927067832879487)],_
[0.06,0.05996400647944459919909,sin(0.06),sin(0.06)-(0.05996400647944459919909)],_
[0.07,0.06994284733753276397655,sin(0.07),sin(0.07)-(0.06994284733753276397655)],_
[0.08,0.07991469396917268730688,sin(0.08),sin(0.08)-(0.07991469396917268730688)],_
[0.09,0.08987854919801104969125,sin(0.09),sin(0.09)-(0.08987854919801104969125)],_
[0.10,0.09983341664682815230681,sin(0.10),sin(0.10)-(0.09983341664682815230681)],_
[0.11,0.10977830083717480866495,sin(0.11),sin(0.11)-(0.10977830083717480866495)],_
[0.12,0.11971220728891935996735,sin(0.12),sin(0.12)-(0.11971220728891935996735)],_
[0.13,0.12963414261969485954121,sin(0.13),sin(0.13)-(0.12963414261969485954121)],_
[0.14,0.13954311464423648171799,sin(0.14),sin(0.14)-(0.13954311464423648171799)],_
[0.15,0.14943813247359922149773,sin(0.15),sin(0.15)-(0.14943813247359922149773)],_
[0.16,0.15931820661424596331146,sin(0.16),sin(0.16)-(0.15931820661424596331146)],_
[0.17,0.16918234906699601015762,sin(0.17),sin(0.17)-(0.16918234906699601015762)],_
[0.18,0.17902957342582417834180,sin(0.18),sin(0.18)-(0.17902957342582417834180)],_
[0.19,0.18885889497650057799285,sin(0.19),sin(0.19)-(0.18885889497650057799285)],_
[0.20,0.19866933079506121545941,sin(0.20),sin(0.20)-(0.19866933079506121545941)],_
[0.21,0.20845989984609957060871,sin(0.21),sin(0.21)-(0.20845989984609957060871)],_
[0.22,0.21822962308086931995179,sin(0.22),sin(0.22)-(0.21822962308086931995179)],_
[0.23,0.22797752353518839540462,sin(0.23),sin(0.23)-(0.22797752353518839540462)],_
[0.24,0.23770262642713458836079,sin(0.24),sin(0.24)-(0.23770262642713458836079)],_
[0.25,0.24740395925452292959685,sin(0.25),sin(0.25)-(0.24740395925452292959685)],_
[0.26,0.25708055189215509735339,sin(0.26),sin(0.26)-(0.25708055189215509735339)],_
[0.27,0.26673143668883112873229,sin(0.27),sin(0.27)-(0.26673143668883112873229)],_
[0.28,0.27635564856411373331967,sin(0.28),sin(0.28)-(0.27635564856411373331967)],_
[0.29,0.28595222510483553268394,sin(0.29),sin(0.29)-(0.28595222510483553268394)],_
[0.30,0.29552020666133957510532,sin(0.30),sin(0.30)-(0.29552020666133957510532)],_
[0.31,0.30505863644344350156564,sin(0.31),sin(0.31)-(0.30505863644344350156564)],_
[0.32,0.31456656061611776666176,sin(0.32),sin(0.32)-(0.31456656061611776666176)],_
[0.33,0.32404302839486834670020,sin(0.33),sin(0.33)-(0.32404302839486834670020)],_
[0.34,0.33348709214081439678177,sin(0.34),sin(0.34)-(0.33348709214081439678177)],_
[0.35,0.34289780745545134918963,sin(0.35),sin(0.35)-(0.34289780745545134918963)],_
[0.36,0.35227423327508997684991,sin(0.36),sin(0.36)-(0.35227423327508997684991)],_
[0.37,0.36161543196496197803729,sin(0.37),sin(0.37)-(0.36161543196496197803729)],_
[0.38,0.37092046941298267184549,sin(0.38),sin(0.38)-(0.37092046941298267184549)],_
[0.39,0.38018841512316142823118,sin(0.39),sin(0.39)-(0.38018841512316142823118)],_
[0.40,0.38941834230865049166631,sin(0.40),sin(0.40)-(0.38941834230865049166631)],_
[0.41,0.39860932798442289359380,sin(0.41),sin(0.41)-(0.39860932798442289359380)],_
[0.42,0.40776045305957018597279,sin(0.42),sin(0.42)-(0.40776045305957018597279)],_
[0.43,0.41687080242921076621692,sin(0.43),sin(0.43)-(0.41687080242921076621692)],_
[0.44,0.42593946506599960276972,sin(0.44),sin(0.44)-(0.42593946506599960276972)],_
[0.45,0.43496553411123021042084,sin(0.45),sin(0.45)-(0.43496553411123021042084)],_
[0.46,0.44394810696551976524151,sin(0.46),sin(0.46)-(0.44394810696551976524151)],_
[0.47,0.45288628537906829070327,sin(0.47),sin(0.47)-(0.45288628537906829070327)],_
[0.48,0.46177917554148288913664,sin(0.48),sin(0.48)-(0.46177917554148288913664)],_
[0.49,0.47062588817115803618136,sin(0.49),sin(0.49)-(0.47062588817115803618136)],_
[0.50,0.47942553860420300027329,sin(0.50),sin(0.50)-(0.47942553860420300027329)],_
[0.51,0.48817724688290749450013,sin(0.51),sin(0.51)-(0.48817724688290749450013)],_
[0.52,0.49688013784373671433446,sin(0.52),sin(0.52)-(0.49688013784373671433446)],_
[0.53,0.50553334120484696181366,sin(0.53),sin(0.53)-(0.50553334120484696181366)],_
[0.54,0.51413599165311310467728,sin(0.54),sin(0.54)-(0.51413599165311310467728)],_
[0.55,0.52268722893065916778838,sin(0.55),sin(0.55)-(0.52268722893065916778838)],_
[0.56,0.53118619792088340385187,sin(0.56),sin(0.56)-(0.53118619792088340385187)],_
[0.57,0.53963204873396924099446,sin(0.57),sin(0.57)-(0.53963204873396924099446)],_
[0.58,0.54802393679187355618270,sin(0.58),sin(0.58)-(0.54802393679187355618270)],_
[0.59,0.55636102291278377572254,sin(0.59),sin(0.59)-(0.55636102291278377572254)],_
[0.60,0.56464247339503535720095,sin(0.60),sin(0.60)-(0.56464247339503535720095)],_
[0.61,0.57286746010048126119098,sin(0.61),sin(0.61)-(0.57286746010048126119098)],_
[0.62,0.58103516053730507584296,sin(0.62),sin(0.62)-(0.58103516053730507584296)],_
[0.63,0.58914475794226951311811,sin(0.63),sin(0.63)-(0.58914475794226951311811)],_
[0.64,0.59719544136239205188355,sin(0.64),sin(0.64)-(0.59719544136239205188355)],_
[0.65,0.60518640573603956037252,sin(0.65),sin(0.65)-(0.60518640573603956037252)],_
[0.66,0.61311685197343378861515,sin(0.66),sin(0.66)-(0.61311685197343378861515)],_
[0.67,0.62098598703655968035744,sin(0.67),sin(0.67)-(0.62098598703655968035744)],_
[0.68,0.62879302401846851370418,sin(0.68),sin(0.68)-(0.62879302401846851370418)],_
[0.69,0.63653718222196794023743,sin(0.69),sin(0.69)-(0.63653718222196794023743)],_
[0.70,0.64421768723769105367261,sin(0.70),sin(0.70)-(0.64421768723769105367261)],_
[0.71,0.65183377102153668121013,sin(0.71),sin(0.71)-(0.65183377102153668121013)],_
[0.72,0.65938467197147315361800,sin(0.72),sin(0.72)-(0.65938467197147315361800)],_
[0.73,0.66686963500369787373259,sin(0.73),sin(0.73)-(0.66686963500369787373259)],_
[0.74,0.67428791162814506748388,sin(0.74),sin(0.74)-(0.67428791162814506748388)],_
[0.75,0.68163876002333416673324,sin(0.75),sin(0.75)-(0.68163876002333416673324)],_
[0.76,0.68892144511055133914776,sin(0.76),sin(0.76)-(0.68892144511055133914776)],_
[0.77,0.69613523862735674701988,sin(0.77),sin(0.77)-(0.69613523862735674701988)],_
[0.78,0.70327941920041018436790,sin(0.78),sin(0.78)-(0.70327941920041018436790)],_
[0.79,0.71035327241760780981403,sin(0.79),sin(0.79)-(0.71035327241760780981403)],_
[0.80,0.71735609089952276162718,sin(0.80),sin(0.80)-(0.71735609089952276162718)],_
[0.81,0.72428717437014251092818,sin(0.81),sin(0.81)-(0.72428717437014251092818)],_
[0.82,0.73114582972689587938131,sin(0.82),sin(0.82)-(0.73114582972689587938131)],_
[0.83,0.73793137110996271872858,sin(0.83),sin(0.83)-(0.73793137110996271872858)],_
[0.84,0.74464311997085932125657,sin(0.84),sin(0.84)-(0.74464311997085932125657)],_
[0.85,0.75128040514029270271207,sin(0.85),sin(0.85)-(0.75128040514029270271207)],_
[0.86,0.75784256289527697229459,sin(0.86),sin(0.86)-(0.75784256289527697229459)],_
[0.87,0.76432893702550507814480,sin(0.87),sin(0.87)-(0.76432893702550507814480)],_
[0.88,0.77073887889896929120965,sin(0.88),sin(0.88)-(0.77073887889896929120965)],_
[0.89,0.77707174752682386549033,sin(0.89),sin(0.89)-(0.77707174752682386549033)],_
[0.90,0.78332690962748338846138,sin(0.90),sin(0.90)-(0.78332690962748338846138)],_
[0.91,0.78950373968995041187896,sin(0.91),sin(0.91)-(0.78950373968995041187896)],_
[0.92,0.79560162003636603026828,sin(0.92),sin(0.92)-(0.79560162003636603026828)],_
[0.93,0.80161994088377715208432,sin(0.93),sin(0.93)-(0.80161994088377715208432)],_
[0.94,0.80755810040511428687022,sin(0.94),sin(0.94)-(0.80755810040511428687022)],_
[0.95,0.81341550478937375068542,sin(0.95),sin(0.95)-(0.81341550478937375068542)],_
[0.96,0.81919156830099827163322,sin(0.96),sin(0.96)-(0.81919156830099827163322)],_
[0.97,0.82488571333845005747662,sin(0.97),sin(0.97)-(0.82488571333845005747662)],_
[0.98,0.83049737049197046808453,sin(0.98),sin(0.98)-(0.83049737049197046808453)],_
[0.99,0.83602597860052051678926,sin(0.99),sin(0.99)-(0.83602597860052051678926)],_
[1.00,0.84147098480789650665250,sin(1.00),sin(1.00)-(0.84147098480789650665250)],_
[1.01,0.84683184461801519012310,sin(1.01),sin(1.01)-(0.84683184461801519012310)],_
[1.02,0.85210802194936292361655,sin(1.02),sin(1.02)-(0.85210802194936292361655)],_
[1.03,0.85729898918860337214627,sin(1.03),sin(1.03)-(0.85729898918860337214627)],_
[1.04,0.86240422724333840328079,sin(1.04),sin(1.04)-(0.86240422724333840328079)],_
[1.05,0.86742322559401689438141,sin(1.05),sin(1.05)-(0.86742322559401689438141)],_
[1.06,0.87235548234498626228295,sin(1.06),sin(1.06)-(0.87235548234498626228295)],_
[1.07,0.87720050427468161030706,sin(1.07),sin(1.07)-(0.87720050427468161030706)],_
[1.08,0.88195780688494747373533,sin(1.08),sin(1.08)-(0.88195780688494747373533)],_
[1.09,0.88662691444948723160860,sin(1.09),sin(1.09)-(0.88662691444948723160860)],_
[1.10,0.89120736006143533995180,sin(1.10),sin(1.10)-(0.89120736006143533995180)],_
[1.11,0.89569868568004762924063,sin(1.11),sin(1.11)-(0.89569868568004762924063)],_
[1.12,0.90010044217650499711910,sin(1.12),sin(1.12)-(0.90010044217650499711910)],_
[1.13,0.90441218937882591603708,sin(1.13),sin(1.13)-(0.90441218937882591603708)],_
[1.14,0.90863349611588326459422,sin(1.14),sin(1.14)-(0.90863349611588326459422)],_
[1.15,0.91276394026052108094403,sin(1.15),sin(1.15)-(0.91276394026052108094403)],_
[1.16,0.91680310877176692661866,sin(1.16),sin(1.16)-(0.91680310877176692661866)],_
[1.17,0.92075059773613563957301,sin(1.17),sin(1.17)-(0.92075059773613563957301)],_
[1.18,0.92460601240802034610754,sin(1.18),sin(1.18)-(0.92460601240802034610754)],_
[1.19,0.92836896724916669260202,sin(1.19),sin(1.19)-(0.92836896724916669260202)],_
[1.20,0.93203908596722634967013,sin(1.20),sin(1.20)-(0.93203908596722634967013)],_
[1.21,0.93561600155338593341646,sin(1.21),sin(1.21)-(0.93561600155338593341646)],_
[1.22,0.93909935631906758093524,sin(1.22),sin(1.22)-(0.93909935631906758093524)],_
[1.23,0.94248880193169751002382,sin(1.23),sin(1.23)-(0.94248880193169751002382)],_
[1.24,0.94578399944953898628471,sin(1.24),sin(1.24)-(0.94578399944953898628471)],_
[1.25,0.94898461935558621434849,sin(1.25),sin(1.25)-(0.94898461935558621434849)],_
[1.26,0.95209034159051576385682,sin(1.26),sin(1.26)-(0.95209034159051576385682)],_
[1.27,0.95510085558469223509018,sin(1.27),sin(1.27)-(0.95510085558469223509018)],_
[1.28,0.95801586028922496370075,sin(1.28),sin(1.28)-(0.95801586028922496370075)],_
[1.29,0.96083506420607265890556,sin(1.29),sin(1.29)-(0.96083506420607265890556)],_
[1.30,0.96355818541719296470135,sin(1.30),sin(1.30)-(0.96355818541719296470135)],_
[1.31,0.96618495161273402916926,sin(1.31),sin(1.31)-(0.96618495161273402916926)],_
[1.32,0.96871510011826526273590,sin(1.32),sin(1.32)-(0.96871510011826526273590)],_
[1.33,0.97114837792104456233768,sin(1.33),sin(1.33)-(0.97114837792104456233768)],_
[1.34,0.97348454169531937478787,sin(1.34),sin(1.34)-(0.97348454169531937478787)],_
[1.35,0.97572335782665906926111,sin(1.35),sin(1.35)-(0.97572335782665906926111)],_
[1.36,0.97786460243531618567849,sin(1.36),sin(1.36)-(0.97786460243531618567849)],_
[1.37,0.97990806139861422288769,sin(1.37),sin(1.37)-(0.97990806139861422288769)],_
[1.38,0.98185353037235972787813,sin(1.38),sin(1.38)-(0.98185353037235972787813)],_
[1.39,0.98370081481127654484004,sin(1.39),sin(1.39)-(0.98370081481127654484004)],_
[1.40,0.98544972998846018065947,sin(1.40),sin(1.40)-(0.98544972998846018065947)],_
[1.41,0.98710010101385034142909,sin(1.41),sin(1.41)-(0.98710010101385034142909)],_
[1.42,0.98865176285171979273627,sin(1.42),sin(1.42)-(0.98865176285171979273627)],_
[1.43,0.99010456033717779485729,sin(1.43),sin(1.43)-(0.99010456033717779485729)],_
[1.44,0.99145834819168646252760,sin(1.44),sin(1.44)-(0.99145834819168646252760)],_
[1.45,0.99271299103758849766535,sin(1.45),sin(1.45)-(0.99271299103758849766535)],_
[1.46,0.99386836341164484228683,sin(1.46),sin(1.46)-(0.99386836341164484228683)],_
[1.47,0.99492434977758089785993,sin(1.47),sin(1.47)-(0.99492434977758089785993)],_
[1.48,0.99588084453764005648408,sin(1.48),sin(1.48)-(0.99588084453764005648408)],_
[1.49,0.99673775204314338855320,sin(1.49),sin(1.49)-(0.99673775204314338855320)],_
[1.50,0.99749498660405443094172,sin(1.50),sin(1.50)-(0.99749498660405443094172)],_
[1.51,0.99815247249754811924274,sin(1.51),sin(1.51)-(0.99815247249754811924274)],_
[1.52,0.99871014397558300717231,sin(1.52),sin(1.52)-(0.99871014397558300717231)],_
[1.53,0.99916794527147601592427,sin(1.53),sin(1.53)-(0.99916794527147601592427)],_
[1.54,0.99952583060547905600596,sin(1.54),sin(1.54)-(0.99952583060547905600596)],_
[1.55,0.99978376418935696389761,sin(1.55),sin(1.55)-(0.99978376418935696389761)],_
[1.56,0.99994172022996629574517,sin(1.56),sin(1.56)-(0.99994172022996629574517)],_
[1.57,0.99999968293183462021053,sin(1.57),sin(1.57)-(0.99999968293183462021053)],_
[1.58,0.99995764649874005255179,sin(1.58),sin(1.58)-(0.99995764649874005255179)],_
[1.59,0.99981561513429087198158,sin(1.59),sin(1.59)-(0.99981561513429087198158)],_
[1.60,0.99957360304150516434211,sin(1.60),sin(1.60)-(0.99957360304150516434211)]]
 

   (1)
   [[0.01,0.0099998333 3416666468 26,0.0099998333 3416666468 26,0.0],
    [0.02,0.0199986666 9333307936 7,0.0199986666 9333307936 7,0.0],
    [0.03,0.0299955002 0249566076 9,0.0299955002 0249566076 9,0.0],
    [0.04,0.0399893341 8663415945 2,0.0399893341 8663415945 2,0.0],
    [0.05,0.0499791692 7067832879 5,0.0499791692 7067832879 5,0.0],
    [0.06,0.0599640064 7944459919 9,0.0599640064 7944459919 9,0.0],
    [0.07,0.0699428473 3753276397 7,0.0699428473 3753276397 6,- 0.4 E -21],
    [0.08,0.0799146939 6917268730 7,0.0799146939 6917268730 7,0.0],
    [0.09,0.0898785491 9801104969 1,0.0898785491 9801104969 1,0.0],
    [0.1,0.0998334166 4682815230 7,0.0998334166 4682815230 7,0.0],
    [0.11,0.1097783008 3717480867,0.1097783008 3717480866,- 0.4 E -21],
    [0.12,0.1197122072 8891935997,0.1197122072 8891935997,0.4 E -21],
    [0.13,0.1296341426 1969485954,0.1296341426 1969485954,- 0.8 E -21],
    [0.14,0.1395431146 4423648172,0.1395431146 4423648172,0.0],
    [0.15,0.1494381324 735992215,0.1494381324 735992215,0.0],
    [0.16,0.1593182066 1424596331,0.1593182066 1424596331,0.0],
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R    [0.86,0.7578425628 952769723,0.7578425628 952769723,0.0],
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--R    [1.06,0.8723554823 4498626228,0.8723554823 4498626228,0.0],
--R    [1.07,0.8772005042 7468161031,0.8772005042 7468161031,0.0],
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--R    [1.12,0.9001004421 7650499712,0.9001004421 7650499712,0.0],
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--R    [1.15,0.9127639402 6052108094,0.9127639402 6052108094,0.0],
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--R    [1.17,0.9207505977 3613563957,0.9207505977 3613563958,0.3 E -20],
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--R    [1.19,0.9283689672 491666926,0.9283689672 491666926,0.0],
--R    [1.2,0.9320390859 6722634967,0.9320390859 6722634967,0.3 E -20],
--R    [1.21,0.9356160015 5338593342,0.9356160015 5338593342,0.0],
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--R    [1.28,0.9580158602 892249637,0.9580158602 892249637,0.0],
--R    [1.29,0.9608350642 0607265891,0.9608350642 0607265891,0.0],
--R    [1.3,0.9635581854 171929647,0.9635581854 171929647,- 0.3 E -20],
--R    [1.31,0.9661849516 1273402917,0.9661849516 1273402917,0.0],
--R    [1.32,0.9687151001 1826526273,0.9687151001 1826526273,0.0],
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--R    [1.35,0.9757233578 2665906926,0.9757233578 2665906926,0.0],
--R    [1.36,0.9778646024 3531618568,0.9778646024 3531618568,0.0],
--R    [1.37,0.9799080613 9861422289,0.9799080613 9861422289,0.0],
--R    [1.38,0.9818535303 7235972788,0.9818535303 7235972788,0.0],
--R    [1.39,0.9837008148 1127654484,0.9837008148 1127654484,0.0],
--R    [1.4,0.9854497299 8846018066,0.9854497299 8846018066,0.0],
--R    [1.41,0.9871001010 1385034143,0.9871001010 1385034143,0.0],
--R    [1.42,0.9886517628 5171979274,0.9886517628 5171979274,0.0],
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--R    [1.45,0.9927129910 3758849767,0.9927129910 3758849767,0.0],
--R    [1.46,0.9938683634 1164484229,0.9938683634 1164484229,0.0],
--R    [1.47,0.9949243497 7758089786,0.9949243497 7758089786,0.0],
--R    [1.48,0.9958808445 3764005648,0.9958808445 3764005648,0.0],
--R    [1.49,0.9967377520 4314338855,0.9967377520 4314338855,0.0],
--R    [1.5,0.9974949866 0405443094,0.9974949866 0405443094,0.0],
--R    [1.51,0.9981524724 9754811924,0.9981524724 9754811924,0.0],
--R    [1.52,0.9987101439 7558300717,0.9987101439 7558300717,0.0],
--R    [1.53,0.9991679452 7147601592,0.9991679452 7147601592,0.0],
--R    [1.54,0.9995258306 0547905601,0.9995258306 0547905601,0.0],
--R    [1.55,0.9997837641 893569639,0.9997837641 893569639,0.0],
--R    [1.56,0.9999417202 2996629574,0.9999417202 2996629574,0.0],
--R    [1.57,0.9999996829 3183462021,0.9999996829 3183462021,0.0],
--R    [1.58,0.9999576464 9874005255,0.9999576464 9874005255,0.0],
--R    [1.59,0.9998156151 3429087198,0.9998156151 3429087198,0.0],
--R    [1.6,0.9995736030 4150516434,0.9995736030 4150516434,0.0]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
[[0.01,0.99995000041666527778026,cos(0.01),cos(0.01)-(0.99995000041666527778026)],_
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   (2)
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    [1.53,0.0407850112 4159105868 9,0.0407850112 4159105868 8,- 0.1 E -20],
    [1.54,0.0307914590 8246615762 2,0.0307914590 8246615762 3,0.8 E -21],
    [1.55,0.0207948278 0309247364 4,0.0207948278 0309247364 7,0.3 E -20],
    [1.56,0.0107961170 5826744582 4,0.0107961170 5826744582 2,- 0.2 E -20],
    [1.57,0.0007963267 1073332548 541,0.0007963267 1073332548 514,- 0.3 E -21],
    [1.58,- 0.0092035432 6880826480 54,- 0.0092035432 6880826480 38,0.2 E -20],
    [1.59,- 0.0192024929 0169256809 5,- 0.0192024929 0169256809 8,- 0.3 E -20],
    [1.6,- 0.0291995223 0128872620 6,- 0.0291995223 0128872620 7,- 0.1 E -20]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,0.9999500004 1666527778,0.9999500004 1666527778,0.0],
--R    [0.02,0.9998000066 6657777841,0.9998000066 6657777841,0.0],
--R    [0.03,0.9995500337 4898751627,0.9995500337 4898751627,0.0],
--R    [0.04,0.9992001066 6097794031,0.9992001066 6097794031,0.0],
--R    [0.05,0.9987502603 9496624656,0.9987502603 9496624656,0.0],
--R    [0.06,0.9982005399 3520416555,0.9982005399 3520416555,0.0],
--R    [0.07,0.9975510002 5327957462,0.9975510002 5327957462,0.0],
--R    [0.08,0.9968017063 0261938498,0.9968017063 0261938498,0.0],
--R    [0.09,0.9959527330 1199425309,0.9959527330 1199425309,0.0],
--R    [0.1,0.9950041652 7802576609,0.9950041652 7802576609,0.0],
--R    [0.11,0.9939560979 5669685036,0.9939560979 5669685036,0.0],
--R    [0.12,0.9928086358 5386625225,0.9928086358 5386625225,0.0],
--R    [0.13,0.9915618937 1478803959,0.9915618937 1478803959,0.0],
--R    [0.14,0.9902159962 126371719,0.9902159962 126371719,0.0],
--R    [0.15,0.9887710779 3604228674,0.9887710779 3604228674,0.0],
--R    [0.16,0.9872272833 7562694904,0.9872272833 7562694904,0.0],
--R    [0.17,0.9855847669 0956070917,0.9855847669 0956070917,0.0],
--R    [0.18,0.9838436927 8812141459,0.9838436927 8812141459,0.0],
--R    [0.19,0.9820042351 1727031897,0.9820042351 1727031897,0.0],
--R    [0.2,0.9800665778 4124163112,0.9800665778 4124163112,0.0],
--R    [0.21,0.9780309147 2414824492,0.9780309147 2414824492,0.0],
--R    [0.22,0.9758974493 3060548941,0.9758974493 3060548941,0.0],
--R    [0.23,0.9736663950 0537483697,0.9736663950 0537483697,0.0],
--R    [0.24,0.9713379748 5202960493,0.9713379748 5202960493,0.0],
--R    [0.25,0.9689124217 1064478414,0.9689124217 1064478414,0.0],
--R    [0.26,0.9663899781 3451322556,0.9663899781 3451322556,0.0],
--R    [0.27,0.9637708963 6589051302,0.9637708963 6589051302,0.0],
--R    [0.28,0.9610554383 1077094792,0.9610554383 1077094792,0.0],
--R    [0.29,0.9582438755 1269716807,0.9582438755 1269716807,0.0],
--R    [0.3,0.9553364891 2560601964,0.9553364891 2560601964,0.0],
--R    [0.31,0.9523335698 8571339784,0.9523335698 8571339784,0.0],
--R    [0.32,0.9492354180 8244086758,0.9492354180 8244086758,0.0],
--R    [0.33,0.9460423435 2838697153,0.9460423435 2838697153,0.0],
--R    [0.34,0.9427546655 283462285,0.9427546655 283462285,0.0],
--R    [0.35,0.9393727128 4737892004,0.9393727128 4737892004,0.0],
--R    [0.36,0.9358968236 7793485835,0.9358968236 7793485835,0.0],
--R    [0.37,0.9323273456 060344232,0.9323273456 060344232,0.0],
--R    [0.38,0.9286646355 7651024949,0.9286646355 7651024949,0.0],
--R    [0.39,0.9249090598 5731304145,0.9249090598 5731304145,0.0],
--R    [0.4,0.9210609940 028850828,0.9210609940 028850828,0.0],
--R    [0.41,0.9171208228 1660510548,0.9171208228 1660510548,0.0],
--R    [0.42,0.9130889403 1230827244,0.9130889403 1230827244,0.0],
--R    [0.43,0.9089657496 7488512248,0.9089657496 7488512248,0.0],
--R    [0.44,0.9047516632 1996341716,0.9047516632 1996341717,0.3 E -20],
--R    [0.45,0.9004471023 5267692167,0.9004471023 5267692167,0.0],
--R    [0.46,0.8960524975 2552524254,0.8960524975 2552524254,0.0],
--R    [0.47,0.8915682881 9532893645,0.8915682881 9532893645,0.0],
--R    [0.48,0.8869949227 792841944,0.8869949227 792841944,0.0],
--R    [0.49,0.8823328586 101214957,0.8823328586 101214957,0.0],
--R    [0.5,0.8775825618 9037271612,0.8775825618 9037271612,0.0],
--R    [0.51,0.8727445076 457512631,0.8727445076 457512631,0.0],
--R    [0.52,0.8678191796 7764990039,0.8678191796 7764990039,0.0],
--R    [0.53,0.8628070705 1476101181,0.8628070705 1476101181,0.0],
--R    [0.54,0.8577086813 6382414254,0.8577086813 6382414254,0.0],
--R    [0.55,0.8525245220 595057428,0.8525245220 595057428,0.0],
--R    [0.56,0.8472551110 1341612609,0.8472551110 1341612609,0.0],
--R    [0.57,0.8419009751 6226874013,0.8419009751 6226874013,0.0],
--R    [0.58,0.8364626499 1518693466,0.8364626499 1518693466,0.0],
--R    [0.59,0.8309406791 0016349525,0.8309406791 0016349525,0.0],
--R    [0.6,0.8253356149 0967829724,0.8253356149 0967829724,0.0],
--R    [0.61,0.8196480178 454795179,0.8196480178 454795179,0.0],
--R    [0.62,0.8138784566 6253392868,0.8138784566 6253392868,0.0],
--R    [0.63,0.8080275083 1215187252,0.8080275083 1215187253,0.3 E -20],
--R    [0.64,0.8020957578 8429261359,0.8020957578 8429261358,- 0.3 E -20],
--R    [0.65,0.7960837985 4905582892,0.7960837985 4905582892,0.0],
--R    [0.66,0.7899922314 9736509279,0.7899922314 9736509279,0.0],
--R    [0.67,0.7838216658 808492853,0.7838216658 808492853,0.0],
--R    [0.68,0.7775727187 5092793718,0.7775727187 5092793718,0.0],
--R    [0.69,0.7712460149 9710660197,0.7712460149 9710660197,0.0],
--R    [0.7,0.7648421872 8448842626,0.7648421872 8448842626,0.0],
--R    [0.71,0.7583618759 9050816654,0.7583618759 9050816654,- 0.3 E -20],
--R    [0.72,0.7518057291 4089497945,0.7518057291 4089497945,0.0],
--R    [0.73,0.7451744023 4487038879,0.7451744023 4487038879,0.0],
--R    [0.74,0.7384685587 2958790979,0.7384685587 2958790979,0.3 E -20],
--R    [0.75,0.7316888688 7382088631,0.7316888688 7382088631,0.0],
--R    [0.76,0.7248360107 4090517234,0.7248360107 4090517234,0.0],
--R    [0.77,0.7179106696 1094336337,0.7179106696 1094336337,0.0],
--R    [0.78,0.7109135380 1227735722,0.7109135380 1227735722,0.0],
--R    [0.79,0.7038453156 5223609691,0.7038453156 5223609691,0.0],
--R    [0.8,0.6967067093 4716542092,0.6967067093 4716542092,- 0.3 E -20],
--R    [0.81,0.6894984329 5174701755,0.6894984329 5174701755,0.0],
--R    [0.82,0.6822212072 8761355167,0.6822212072 8761355167,0.0],
--R    [0.83,0.6748757600 7126710211,0.6748757600 7126710211,0.3 E -20],
--R    [0.84,0.6674628258 4130811792,0.6674628258 4130811792,0.0],
--R    [0.85,0.6599831458 8498217039,0.6599831458 8498217039,0.0],
--R    [0.86,0.6524374681 6405184627,0.6524374681 6405184627,0.0],
--R    [0.87,0.6448265472 4000119478,0.6448265472 4000119478,- 0.3 E -20],
--R    [0.88,0.6371511441 9858020802,0.6371511441 9858020802,0.0],
--R    [0.89,0.6294120265 736968802,0.6294120265 736968802,0.0],
--R    [0.9,0.6216099682 7066445648,0.6216099682 7066445648,0.0],
--R    [0.91,0.6137457494 8881154652,0.6137457494 8881154652,0.0],
--R    [0.92,0.6058201566 434628418,0.6058201566 434628418,0.0],
--R    [0.93,0.5978339822 872982385,0.5978339822 872982385,0.0],
--R    [0.94,0.5897880250 3109822996,0.5897880250 3109822996,- 0.3 E -20],
--R    [0.95,0.5816830894 6388349417,0.5816830894 6388349417,0.0],
--R    [0.96,0.5735199860 7245666213,0.5735199860 7245666212,- 0.3 E -20],
--R    [0.97,0.5652995311 6035431304,0.5652995311 6035431304,0.0],
--R    [0.98,0.5570225467 6621730088,0.5570225467 6621730087,- 0.3 E -20],
--R    [0.99,0.5486898605 8158757534,0.5486898605 8158757535,0.3 E -20],
--R    [1.0,0.5403023058 681397174,0.5403023058 681397174,0.0],
--R    [1.01,0.5318607213 7435546621,0.5318607213 7435546621,0.0],
--R    [1.02,0.5233659512 5164956989,0.5233659512 5164956989,- 0.3 E -20],
--R    [1.03,0.5148188449 6995534753,0.5148188449 6995534753,0.0],
--R    [1.04,0.5062202572 3277840374,0.5062202572 3277840374,0.0],
--R    [1.05,0.4975710478 9172699029,0.4975710478 9172699029,0.3 E -20],
--R    [1.06,0.4888720818 6052756192,0.4888720818 6052756192,- 0.2 E -20],
--R    [1.07,0.4801242290 2853412436,0.4801242290 2853412437,0.2 E -20],
--R    [1.08,0.4713283641 7374002391,0.4713283641 7374002391,0.0],
--R    [1.09,0.4624853668 7530087703,0.4624853668 7530087702,- 0.3 E -20],
--R    [1.1,0.4535961214 2557738777,0.4535961214 2557738777,- 0.2 E -20],
--R    [1.11,0.4446615167 4170684864,0.4446615167 4170684864,0.0],
--R    [1.12,0.4356824462 7671216761,0.4356824462 7671216762,0.2 E -20],
--R    [1.13,0.4266598079 3015731037,0.4266598079 3015731037,- 0.3 E -20],
--R    [1.14,0.4175945039 5835809217,0.4175945039 5835809217,0.0],
--R    [1.15,0.4084874408 8415729815,0.4084874408 8415729815,0.0],
--R    [1.16,0.3993395294 0627315445,0.3993395294 0627315445,0.3 E -20],
--R    [1.17,0.3901516843 0823021533,0.3901516843 0823021533,- 0.2 E -20],
--R    [1.18,0.3809248243 6688177303,0.3809248243 6688177303,0.0],
--R    [1.19,0.3716598722 6053293807,0.3716598722 6053293807,0.2 E -20],
--R    [1.2,0.3623577544 7667357764,0.3623577544 7667357763,- 0.3 E -20],
--R    [1.21,0.3530194012 193303387,0.3530194012 193303387,- 0.2 E -20],
--R    [1.22,0.3436457463 1604702048,0.3436457463 1604702048,0.0],
--R    [1.23,0.3342377271 2450259824,0.3342377271 2450259824,0.2 E -20],
--R    [1.24,0.3247962844 3877623658,0.3247962844 3877623657,- 0.3 E -20],
--R    [1.25,0.3153223623 9526866545,0.3153223623 9526866545,0.0],
--R    [1.26,0.3058169083 7828932689,0.3058169083 7828932689,0.2 E -20],
--R    [1.27,0.2962808729 2531873355,0.2962808729 2531873355,- 0.3 E -20],
--R    [1.28,0.2867152096 3195551278,0.2867152096 3195551278,- 0.2 E -20],
--R    [1.29,0.2771208750 5655764139,0.2771208750 5655764139,0.0],
--R    [1.3,0.2674988286 24587407,0.2674988286 24587407,0.2 E -20],
--R    [1.31,0.2578500325 3266966134,0.2578500325 3266966134,- 0.3 E -20],
--R    [1.32,0.2481754516 5237295957,0.2481754516 5237295957,0.0],
--R    [1.33,0.2384760534 3372320752,0.2384760534 3372320752,0.8 E -21],
--R    [1.34,0.2287528078 0845946523,0.2287528078 0845946523,- 0.3 E -20],
--R    [1.35,0.2190066870 9304158142,0.2190066870 9304158142,- 0.2 E -20],
--R    [1.36,0.2092386658 9141935768,0.2092386658 9141935768,0.0],
--R    [1.37,0.1994497209 9757296569,0.1994497209 9757296569,0.2 E -20],
--R    [1.38,0.1896408312 9783436321,0.1896408312 9783436321,- 0.3 E -20],
--R    [1.39,0.1798129776 729994766,0.1798129776 729994766,- 0.8 E -21],
--R    [1.4,0.1699671429 0024093862,0.1699671429 0024093862,0.8 E -21],
--R    [1.41,0.1601043115 5483119016,0.1601043115 5483119017,0.3 E -20],
--R    [1.42,0.1502254699 1168577349,0.1502254699 1168577349,- 0.2 E -20],
--R    [1.43,0.1403316058 4673666253,0.1403316058 4673666253,0.0],
--R    [1.44,0.1304237087 3814549298,0.1304237087 3814549298,0.2 E -20],
--R    [1.45,0.1205027693 6736657053,0.1205027693 6736657053,- 0.3 E -20],
--R    [1.46,0.1105697798 2006955117,0.1105697798 2006955117,- 0.8 E -21],
--R    [1.47,0.1006257333 8693170091,0.1006257333 8693170091,0.8 E -21],
--R    [1.48,0.0906716244 6430965577 6,0.0906716244 6430965577 9,0.3 E -20],
--R    [1.49,0.0807084484 5480061486 8,0.0807084484 5480061486 6,- 0.2 E -20],
--R    [1.5,0.0707372016 6770291008 8,0.0707372016 6770291008 8,0.0],
--R    [1.51,0.0607588812 1938590658 2,0.0607588812 1938590658 3,0.2 E -20],
--R    [1.52,0.0507744849 3357919672 6,0.0507744849 3357919672 3,- 0.3 E -20],
--R    [1.53,0.0407850112 4159105868 9,0.0407850112 4159105868 8,- 0.1 E -20],
--R    [1.54,0.0307914590 8246615762 2,0.0307914590 8246615762 3,0.8 E -21],
--R    [1.55,0.0207948278 0309247364 4,0.0207948278 0309247364 7,0.3 E -20],
--R    [1.56,0.0107961170 5826744582 4,0.0107961170 5826744582 2,- 0.2 E -20],
--R    [1.57,0.0007963267 1073332548 541,0.0007963267 1073332548 514,- 0.3 E -21],
--R    [1.58,- 0.0092035432 6880826480 54,- 0.0092035432 6880826480 38,0.2 E -20],
--R    [1.59,- 0.0192024929 0169256809 5,- 0.0192024929 0169256809 8,- 0.3 E -20],
--R    [1.6,- 0.0291995223 0128872620 6,- 0.0291995223 0128872620 7,- 0.1 E -20]]
--R                                                        Type: List List Float
--E 2
 
)spool 
 
Starts dribbling to tanatan.output (2009/2/17, 18:0:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 9
eq:=2*tan(x)+2*tan(2*x)
 

   (1)  2tan(2x) + 2tan(x)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  2tan(2x) + 2tan(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 9
thesols:=solve(eq,x)
 

                 2%pi      2%pi    %pi      %pi
   (2)  [x= 0,x= ----,x= - ----,x= ---,x= - ---]
                   3         3      3        3
                                       Type: List Equation Expression Integer
--R 
--R
--R                 2%pi      2%pi    %pi      %pi
--R   (2)  [x= 0,x= ----,x= - ----,x= ---,x= - ---]
--R                   3         3      3        3
--R                                       Type: List Equation Expression Integer
--E 2

--S 3 of 9
theproofs:=[eval(eq,i) for i in thesols]
 

   (3)  [0,0,0,0,0]
                                                Type: List Expression Integer
--R 
--R
--R   (3)  [0,0,0,0,0]
--R                                                Type: List Expression Integer
--E 3

--S 4 of 9
thetowers:=[tower i for i in theproofs];
 

                                    Type: List List Kernel Expression Integer
--R 
--R
--R                                    Type: List List Kernel Expression Integer
--E 4

--S 5 of 9
thesubs:LIST Record (a:LIST KERNEL EXPR INT ,b:LIST EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 9
thetans:LIST LIST Record(i:INT,k:KERNEL EXPR INT,z:List Equation EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 9
thetans:=_
 [[construct(j,i.j,Is(argument(i.j).1,n * atan(y))) for j in 1..#i_
      |is?(i.j,tan) and is?(argument(i.j).1,n * atan(y))] _
          for i in thetowers] ;
 

Type: List List Record(i: Integer,k: Kernel Expression Integer,z: List Equation Expression Integer)
--R 
--R
--RType: List List Record(i: Integer,k: Kernel Expression Integer,z: List Equation Expression Integer)
--E 7

--S 8 of 9
thesubs:=_
  [construct([j.k for j in thetans.i],_
             [tanNa(rhs(j.z.2),rhs(j.z.1) ::INT)$TangentExpansions(EXPR INT)_
                        for j in thetans.i]) _
            for i in 1..#theproofs];
 

Type: List Record(a: List Kernel Expression Integer,b: List Expression Integer)
--R 
--R
--RType: List Record(a: List Kernel Expression Integer,b: List Expression Integer)
--E 8

--S 9 of 9
thezeros:=[eval(i,j.a,j.b) for i in theproofs for j in thesubs]
 

   (9)  [0,0,0,0,0]
                                                Type: List Expression Integer
--R 
--R
--R   (9)  [0,0,0,0,0]
--R                                                Type: List Expression Integer
--E 9
)spool 
 
Starts dribbling to divisor.output (2009/2/17, 17:44:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 18
P0 := UP(x, FRAC INT)
 

   (1)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 18
P1 := UP(y, FRAC P0)
 

   (2)
   UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer))
                                                                 Type: Domain
--R 
--R
--R   (2)
--R   UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer))
--R                                                                 Type: Domain
--E 2

--S 3 of 18
R := RADFF(FRAC INT, P0, P1, 1 + x**8, 2)
 

   (3)
  RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer
  ),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x
  **8+1,2)
                                                                 Type: Domain
--R 
--R
--R   (3)
--R  RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer
--R  ),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x
--R  **8+1,2)
--R                                                                 Type: Domain
--E 3

--S 4 of 18
genus()$R
 

   (4)  3
                                                     Type: NonNegativeInteger
--R 
--R
--R   (4)  3
--R                                                     Type: NonNegativeInteger
--E 4

--S 5 of 18
fd := FDIV(FRAC INT, P0, P1, R)
 

   (5)
  FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),Univa
  riatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalF
  unctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),Univar
  iatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
  )
                                                                 Type: Domain
--R 
--R
--R   (5)
--R  FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),Univa
--R  riatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalF
--R  unctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),Univar
--R  iatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R  )
--R                                                                 Type: Domain
--E 5

--S 6 of 18
d1 := divisor(0, 1)$fd
 

   (6)  (x,y - 1)
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R   (6)  (x,y - 1)
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 6

--S 7 of 18
d2 := divisor(0, -1)$fd
 

   (7)  (x,y + 1)
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R   (7)  (x,y + 1)
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 7

--S 8 of 18
d  := d1 - d2
 

        1     2         8
   (8)  - (- x ,- 2y + x  + 2)
        x
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R        1     2         8
--R   (8)  - (- x ,- 2y + x  + 2)
--R        x
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 8

--S 9 of 18
d  := reduce d
 

        1     2         8
   (9)  - (- x ,- 2y + x  + 2)
        x
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R        1     2         8
--R   (9)  - (- x ,- 2y + x  + 2)
--R        x
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 9

--S 10 of 18
generator d
 

   (10)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (10)  "failed"
--R                                                    Type: Union("failed",...)
--E 10

--S 11 of 18
generator reduce(2 * d)
 

   (11)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (11)  "failed"
--R                                                    Type: Union("failed",...)
--E 11

--S 12 of 18
generator reduce(3 * d)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 18
generator reduce(4 * d)
 

            1      1
   (13)  - -- y + --
            4      4
           x      x
Type: Union(RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2),...)
--R 
--R
--R            1      1
--R   (13)  - -- y + --
--R            4      4
--R           x      x
--RType: Union(RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2),...)
--E 13

--S 14 of 18
lSpaceBasis d1
 

   (14)  [- 1]
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R   (14)  [- 1]
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 14

--S 15 of 18
lSpaceBasis(2 * d1)
 

   (15)  [- 1]
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R   (15)  [- 1]
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 15

--S 16 of 18
lSpaceBasis(3 * d1)
 

   (16)  [- 1]
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R   (16)  [- 1]
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 16

--S 17 of 18
lSpaceBasis(4 * d1)
 

           1      1
   (17)  [-- y + --,- 1]
           4      4
          x      x
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R           1      1
--R   (17)  [-- y + --,- 1]
--R           4      4
--R          x      x
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 17

--S 18 of 18
lSpaceBasis(5 * d1)
 

           1      1  1      1
   (18)  [-- y + --,-- y + --,- 1]
           5      5  4      4
          x      x  x      x
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R           1      1  1      1
--R   (18)  [-- y + --,-- y + --,- 1]
--R           5      5  4      4
--R          x      x  x      x
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 18
)spool
 
Starts dribbling to lodof.output (2009/2/17, 17:52:45).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 16
)expose LODOF 
 
   LinearOrdinaryDifferentialOperatorFactorizer is now explicitly 
      exposed in frame initial 
--R 
--R   LinearOrdinaryDifferentialOperatorFactorizer is now explicitly 
--R      exposed in frame initial 
--E 1

--S 2 of 16
P := UP(t, AN)
 

   (1)  UnivariatePolynomial(t,AlgebraicNumber)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(t,AlgebraicNumber)
--R                                                                 Type: Domain
--E 2

--S 3 of 16
Q := FRAC P
 

   (2)  Fraction UnivariatePolynomial(t,AlgebraicNumber)
                                                                 Type: Domain
--R 
--R
--R   (2)  Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R                                                                 Type: Domain
--E 3

--S 4 of 16
L := LODO1 Q
 

   (3)
  LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,Algebraic
  Number)
                                                                 Type: Domain
--R 
--R
--R   (3)
--R  LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,Algebraic
--R  Number)
--R                                                                 Type: Domain
--E 4

--S 5 of 16
d := D()$L
 

   (4)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (4)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 5

--S 6 of 16
t := t::P::Q
 

   (5)  t
                       Type: Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (5)  t
--R                       Type: Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 6

--S 7 of 16
op := d**2 + t * d + 1
 

         2
   (6)  D  + t D + 1
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R         2
--R   (6)  D  + t D + 1
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 7

--S 8 of 16
factor op
 

   (7)  [D,D + t]
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (7)  [D,D + t]
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 8

--S 9 of 16
op := 2*t**3 * d**2 + 3*t**2 * d - 2
 

          3 2     2
   (8)  2t D  + 3t D - 2
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R          3 2     2
--R   (8)  2t D  + 3t D - 2
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 9

--S 10 of 16
factor op
 

           3 2     2
   (9)  [2t D  + 3t D - 2]
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           3 2     2
--R   (9)  [2t D  + 3t D - 2]
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 10

--S 11 of 16
op := 2*t**3 * d**3 - (2*t**4 - 9*t**2) * d**2 - (3*t**3 - 6*t + 2) * d + 2*t
 

           3 3        4     2  2        3
   (10)  2t D  + (- 2t  + 9t )D  + (- 3t  + 6t - 2)D + 2t
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           3 3        4     2  2        3
--R   (10)  2t D  + (- 2t  + 9t )D  + (- 3t  + 6t - 2)D + 2t
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 11

--S 12 of 16
factor op
 

                      3 2        4     2       5      3
   (11)  [- D + t,- 2t D  + (- 8t  - 3t )D - 8t  - 10t  + 2]
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R                      3 2        4     2       5      3
--R   (11)  [- D + t,- 2t D  + (- 8t  - 3t )D - 8t  - 10t  + 2]
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 12

--S 13 of 16
op := (t**9 + t**3) * d**3 + 18 * t**8 * d**2 - 90 * t * d - 30 * (11*t**6-3)
 

           9    3  3      8 2               6
   (12)  (t  + t )D  + 18t D  - 90t D - 330t  + 90
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           9    3  3      8 2               6
--R   (12)  (t  + t )D  + 18t D  - 90t D - 330t  + 90
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 13

--S 14 of 16
factor op
 

   (13)
                                                          +--+      6    +--+
      9    3         +--+      8       +--+      2      (\|91  + 6)t  + \|91
   [(t  + t )D + (- \|91  + 7)t  + (- \|91  + 1)t , D + ---------------------,
                                                                 7
                                                                t  + t
          6
        5t  - 1
    D + -------]
          7
         t  + t
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (13)
--R                                                          +--+      6    +--+
--R      9    3         +--+      8       +--+      2      (\|91  + 6)t  + \|91
--R   [(t  + t )D + (- \|91  + 7)t  + (- \|91  + 1)t , D + ---------------------,
--R                                                                 7
--R                                                                t  + t
--R          6
--R        5t  - 1
--R    D + -------]
--R          7
--R         t  + t
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 14

--S 15 of 16
op := d**3 + 2 * d**2 + 5 / t * d + 7 / t**2
 

          3     2   5      7
   (14)  D  + 2D  + - D + --
                    t      2
                          t
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R          3     2   5      7
--R   (14)  D  + 2D  + - D + --
--R                    t      2
--R                          t
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 15

--S 16 of 16
factor op
 

           3     2   5      7
   (15)  [D  + 2D  + - D + --]
                     t      2
                           t
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           3     2   5      7
--R   (15)  [D  + 2D  + - D + --]
--R                     t      2
--R                           t
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 16
)spool 
 
Starts dribbling to schaum24.output (2009/2/17, 17:59:20).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(asin(x/a),x)
 

                    +---------+
                    |   2    2       +---------+
                 2x\|- x  + a        |   2    2
        - x atan(--------------) + 2\|- x  + a
                      2    2
                    2x  - a
   (1)  ----------------------------------------
                            2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +---------+
--R                    |   2    2       +---------+
--R                 2x\|- x  + a        |   2    2
--R        - x atan(--------------) + 2\|- x  + a
--R                      2    2
--R                    2x  - a
--R   (1)  ----------------------------------------
--R                            2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=s+asin(x/a)+sqrt(a^2-x^2)
 

         +---------+
         |   2    2         x
   (2)  \|- x  + a   + asin(-) + s
                            a
                                                     Type: Expression Integer
--R
--R         +---------+
--R         |   2    2         x
--R   (2)  \|- x  + a   + asin(-) + s
--R                            a
--R                                                     Type: Expression Integer
--E

--S 3      14:471 Axiom cannot simplify this expression
cc:=aa-bb
 

                    +---------+
                    |   2    2
                 2x\|- x  + a            x
        - x atan(--------------) - 2asin(-) - 2s
                      2    2             a
                    2x  - a
   (3)  ----------------------------------------
                            2
                                                     Type: Expression Integer
--R
--R                    +---------+
--R                    |   2    2
--R                 2x\|- x  + a            x
--R        - x atan(--------------) - 2asin(-) - 2s
--R                      2    2             a
--R                    2x  - a
--R   (3)  ----------------------------------------
--R                            2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*asin(x/a),x)
 

                            +---------+
                            |   2    2        +---------+
             2    2      2x\|- x  + a         |   2    2
        (- 2x  + a )atan(--------------) + 2x\|- x  + a
                              2    2
                            2x  - a
   (1)  -------------------------------------------------
                                8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            +---------+
--R                            |   2    2        +---------+
--R             2    2      2x\|- x  + a         |   2    2
--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
--R                              2    2
--R                            2x  - a
--R   (1)  -------------------------------------------------
--R                                8
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
 

          +---------+
          |   2    2       2    2      x
        x\|- x  + a   + (2x  - a )asin(-)
                                       a
   (2)  ---------------------------------
                        4
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2       2    2      x
--R        x\|- x  + a   + (2x  - a )asin(-)
--R                                       a
--R   (2)  ---------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E

--S 6
cc:=aa-bb
 

                            +---------+
                            |   2    2
             2    2      2x\|- x  + a           2     2      x
        (- 2x  + a )atan(--------------) + (- 4x  + 2a )asin(-)
                              2    2                         a
                            2x  - a
   (3)  -------------------------------------------------------
                                   8
                                                     Type: Expression Integer
--R
--R                            +---------+
--R                            |   2    2
--R             2    2      2x\|- x  + a           2     2      x
--R        (- 2x  + a )atan(--------------) + (- 4x  + 2a )asin(-)
--R                              2    2                         a
--R                            2x  - a
--R   (3)  -------------------------------------------------------
--R                                   8
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.
--S 7
t1:=x*asin(x/a)
 

               x
   (1)  x asin(-)
               a
                                                     Type: Expression Integer
--R
--R               x
--R   (1)  x asin(-)
--R               a
--R                                                     Type: Expression Integer
--E
--S 8
t2:=integrate(t1,x)
 

                            +---------+
                            |   2    2        +---------+
             2    2      2x\|- x  + a         |   2    2
        (- 2x  + a )atan(--------------) + 2x\|- x  + a
                              2    2
                            2x  - a
   (2)  -------------------------------------------------
                                8
                                          Type: Union(Expression Integer,...)
--R
--R                            +---------+
--R                            |   2    2        +---------+
--R             2    2      2x\|- x  + a         |   2    2
--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
--R                              2    2
--R                            2x  - a
--R   (2)  -------------------------------------------------
--R                                8
--R                                          Type: Union(Expression Integer,...)
--E
--S 9
t3:=D(t2,x)
 

                    +---------+
                    |   2    2
                 2x\|- x  + a
          x atan(--------------)
                      2    2
                    2x  - a
   (3)  - ----------------------
                     2
                                                     Type: Expression Integer
--R
--R                    +---------+
--R                    |   2    2
--R                 2x\|- x  + a
--R          x atan(--------------)
--R                      2    2
--R                    2x  - a
--R   (3)  - ----------------------
--R                     2
--R                                                     Type: Expression Integer
--E
--S 10
t4:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
 

          +---------+
          |   2    2       2    2      x
        x\|- x  + a   + (2x  - a )asin(-)
                                       a
   (4)  ---------------------------------
                        4
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2       2    2      x
--R        x\|- x  + a   + (2x  - a )asin(-)
--R                                       a
--R   (4)  ---------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E
--S 11
t5:=D(t4,x)
 

   (5)
                                           +---------+
                 +---------+               |   2    2               +---------+
              x  |   2    2        2    3  |- x  + a        2    2  |   2    2
   (4a x asin(-)\|- x  + a   - 2a x  + a ) |---------  + (2x  - a )\|- x  + a
              a                            |     2
                                          \|    a
   ----------------------------------------------------------------------------
                                           +---------+
                               +---------+ |   2    2
                               |   2    2  |- x  + a
                            4a\|- x  + a   |---------
                                           |     2
                                          \|    a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                           +---------+
--R                 +---------+               |   2    2               +---------+
--R              x  |   2    2        2    3  |- x  + a        2    2  |   2    2
--R   (4a x asin(-)\|- x  + a   - 2a x  + a ) |---------  + (2x  - a )\|- x  + a
--R              a                            |     2
--R                                          \|    a
--R   ----------------------------------------------------------------------------
--R                                           +---------+
--R                               +---------+ |   2    2
--R                               |   2    2  |- x  + a
--R                            4a\|- x  + a   |---------
--R                                           |     2
--R                                          \|    a
--R                                                     Type: Expression Integer
--E
--S 12
f:=makeFloatFunction(t1,x,a)
 
   Compiling function %V with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 

   (6)  theMap(MKBCFUNC;binaryFunction;SM;2!0,0)
                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--I   Compiling function %BF with type (DoubleFloat,DoubleFloat) -> 
--R      DoubleFloat 
--R
--I   (6)  theMap(MKBCFUNC;binaryFunction;SM;2!0,120)
--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--E
--S 13
axiom:=makeFloatFunction(t3,x,a)
 
   Compiling function %X with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 

   (7)  theMap(MKBCFUNC;binaryFunction;SM;2!0,0)
                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--I   Compiling function %BJ with type (DoubleFloat,DoubleFloat) -> 
--R      DoubleFloat 
--R
--I   (7)  theMap(MKBCFUNC;binaryFunction;SM;2!0,996)
--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--E
--S 14
schaums:=makeFloatFunction(t5,x,a)
 
   Compiling function %Y with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 

   (8)  theMap(MKBCFUNC;binaryFunction;SM;2!0,0)
                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--I   Compiling function %BK with type (DoubleFloat,DoubleFloat) -> 
--R      DoubleFloat 
--R
--I   (8)  theMap(MKBCFUNC;binaryFunction;SM;2!0,62)
--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--E
--S 15     14:472 Schaums and Axiom agree (modulo branch cuts)
[ [f(i::Float,i::Float+1.0::Float)::Float,axiom(i::Float,i::Float+1.0::Float)::Float,schaums(i::Float,i::Float+1.0::Float)::Float] for i in 1..4]
 

   (9)
   [[0.5235987755 9829892668,0.5235987755 9829892668,0.5235987755 9829881566],
    [1.4594553124 539326738,1.4594553124 539326738,1.4594553124 539324518],
    [2.5441862369 444430136,- 2.1682027434 402466604,2.5441862369 444430136],
    [3.7091808720 064496363,- 2.5740044351 731374839,3.7091808720 064500804]]
                                                        Type: List List Float
--R
--R   (9)
--R   [[0.5235987755 9829892668,0.5235987755 9829892668,0.5235987755 9829881566],
--R    [1.4594553124 539326738,1.4594553124 539326738,1.4594553124 539324518],
--R    [2.5441862369 444430136,- 2.1682027434 402466604,2.5441862369 444430136],
--R    [3.7091808720 064496363,- 2.5740044351 731374839,3.7091808720 064500804]]
--R                                                        Type: List List Float
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(x^2*asin(x/a),x)
 

                     +---------+
                     |   2    2                 +---------+
            3     2x\|- x  + a         2     2  |   2    2
        - 3x atan(--------------) + (2x  + 4a )\|- x  + a
                       2    2
                     2x  - a
   (1)  ---------------------------------------------------
                                 18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +---------+
--R                     |   2    2                 +---------+
--R            3     2x\|- x  + a         2     2  |   2    2
--R        - 3x atan(--------------) + (2x  + 4a )\|- x  + a
--R                       2    2
--R                     2x  - a
--R   (1)  ---------------------------------------------------
--R                                 18
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17
bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9
 

                   +---------+
          2     2  |   2    2      3     x
        (x  + 2a )\|- x  + a   + 3x asin(-)
                                         a
   (2)  -----------------------------------
                         9
                                                     Type: Expression Integer
--R
--R                   +---------+
--R          2     2  |   2    2      3     x
--R        (x  + 2a )\|- x  + a   + 3x asin(-)
--R                                         a
--R   (2)  -----------------------------------
--R                         9
--R                                                     Type: Expression Integer
--E

--S 18     14:473 Axiom cannot simplify this expression
cc:=aa-bb
 

                    +---------+
                    |   2    2
           3     2x\|- x  + a        3     x
        - x atan(--------------) - 2x asin(-)
                      2    2               a
                    2x  - a
   (3)  -------------------------------------
                          6
                                                     Type: Expression Integer
--R
--R                    +---------+
--R                    |   2    2
--R           3     2x\|- x  + a        3     x
--R        - x atan(--------------) - 2x asin(-)
--R                      2    2               a
--R                    2x  - a
--R   (3)  -------------------------------------
--R                          6
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19     14:474 Axiom cannot compute this integral
aa:=integrate(asin(x/a)/x,x)
 

                  %K
           x asin(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x asin(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(asin(x/a)/x^2,x)
 

   (1)
                                                                   +---------+
            +---------+               +---------+                  |   2    2
            |   2    2                |   2    2                2x\|- x  + a
   - x log(\|- x  + a   + a) + x log(\|- x  + a   - a) + a atan(--------------)
                                                                     2    2
                                                                   2x  - a
   ----------------------------------------------------------------------------
                                       2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                   +---------+
--R            +---------+               +---------+                  |   2    2
--R            |   2    2                |   2    2                2x\|- x  + a
--R   - x log(\|- x  + a   + a) + x log(\|- x  + a   - a) + a atan(--------------)
--R                                                                     2    2
--R                                                                   2x  - a
--R   ----------------------------------------------------------------------------
--R                                       2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21
bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x)
 

                 +---------+
                 |   2    2
                \|- x  + a   + a           x
        - x log(----------------) - a asin(-)
                        x                  a
   (2)  -------------------------------------
                         a x
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   + a           x
--R        - x log(----------------) - a asin(-)
--R                        x                  a
--R   (2)  -------------------------------------
--R                         a x
--R                                                     Type: Expression Integer
--E

--S 22     14:475 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                +---------+               +---------+
                |   2    2                |   2    2
       - x log(\|- x  + a   + a) + x log(\|- x  + a   - a)
     + 
               +---------+                  +---------+
               |   2    2                   |   2    2
              \|- x  + a   + a           2x\|- x  + a              x
       2x log(----------------) + a atan(--------------) + 2a asin(-)
                      x                       2    2               a
                                            2x  - a
  /
     2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                +---------+               +---------+
--R                |   2    2                |   2    2
--R       - x log(\|- x  + a   + a) + x log(\|- x  + a   - a)
--R     + 
--R               +---------+                  +---------+
--R               |   2    2                   |   2    2
--R              \|- x  + a   + a           2x\|- x  + a              x
--R       2x log(----------------) + a atan(--------------) + 2a asin(-)
--R                      x                       2    2               a
--R                                            2x  - a
--R  /
--R     2a x
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(asin(x/a)^2,x)
 

                  +---------+ 2                        +---------+
                  |   2    2        +---------+        |   2    2
               2x\|- x  + a         |   2    2      2x\|- x  + a
        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
                    2    2                               2    2
                  2x  - a                              2x  - a
   (1)  ----------------------------------------------------------------
                                        4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+ 2                        +---------+
--R                  |   2    2        +---------+        |   2    2
--R               2x\|- x  + a         |   2    2      2x\|- x  + a
--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
--R                    2    2                               2    2
--R                  2x  - a                              2x  - a
--R   (1)  ----------------------------------------------------------------
--R                                        4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a)
 

                 +---------+
              x  |   2    2           x 2
   (2)  2asin(-)\|- x  + a   + x asin(-)  - 2x
              a                       a
                                                     Type: Expression Integer
--R
--R                 +---------+
--R              x  |   2    2           x 2
--R   (2)  2asin(-)\|- x  + a   + x asin(-)  - 2x
--R              a                       a
--R                                                     Type: Expression Integer
--E

--S 25     14:476 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                 +---------+ 2                        +---------+
                 |   2    2        +---------+        |   2    2
              2x\|- x  + a         |   2    2      2x\|- x  + a
       x atan(--------------)  - 4\|- x  + a  atan(--------------)
                   2    2                               2    2
                 2x  - a                              2x  - a
     + 
                  +---------+
               x  |   2    2            x 2
       - 8asin(-)\|- x  + a   - 4x asin(-)
               a                        a
  /
     4
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +---------+ 2                        +---------+
--R                 |   2    2        +---------+        |   2    2
--R              2x\|- x  + a         |   2    2      2x\|- x  + a
--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
--R                   2    2                               2    2
--R                 2x  - a                              2x  - a
--R     + 
--R                  +---------+
--R               x  |   2    2            x 2
--R       - 8asin(-)\|- x  + a   - 4x asin(-)
--R               a                        a
--R  /
--R     4
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 26
aa:=integrate(acos(x/a),x)
 

                  +---------+
                  |   2    2       +---------+
               2x\|- x  + a        |   2    2
        x atan(--------------) - 2\|- x  + a
                    2    2
                  2x  - a
   (1)  --------------------------------------
                           2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+
--R                  |   2    2       +---------+
--R               2x\|- x  + a        |   2    2
--R        x atan(--------------) - 2\|- x  + a
--R                    2    2
--R                  2x  - a
--R   (1)  --------------------------------------
--R                           2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27
bb:=x*acos(x/a)-sqrt(a^2-x^2)
 

           +---------+
           |   2    2           x
   (2)  - \|- x  + a   + x acos(-)
                                a
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2           x
--R   (2)  - \|- x  + a   + x acos(-)
--R                                a
--R                                                     Type: Expression Integer
--E

--S 28     14:477 Axiom cannot simplify this expression
cc:=aa-bb
 

                  +---------+
                  |   2    2
               2x\|- x  + a              x
        x atan(--------------) - 2x acos(-)
                    2    2               a
                  2x  - a
   (3)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2
--R               2x\|- x  + a              x
--R        x atan(--------------) - 2x acos(-)
--R                    2    2               a
--R                  2x  - a
--R   (3)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(x*acos(x/a),x)
 

                          +---------+
                          |   2    2        +---------+
           2    2      2x\|- x  + a         |   2    2
        (2x  - a )atan(--------------) - 2x\|- x  + a
                            2    2
                          2x  - a
   (1)  -----------------------------------------------
                               8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +---------+
--R                          |   2    2        +---------+
--R           2    2      2x\|- x  + a         |   2    2
--R        (2x  - a )atan(--------------) - 2x\|- x  + a
--R                            2    2
--R                          2x  - a
--R   (1)  -----------------------------------------------
--R                               8
--R                                          Type: Union(Expression Integer,...)
--E

--S 30
bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4
 

            +---------+
            |   2    2       2    2      x
        - x\|- x  + a   + (2x  - a )acos(-)
                                         a
   (2)  -----------------------------------
                         4
                                                     Type: Expression Integer
--R
--R            +---------+
--R            |   2    2       2    2      x
--R        - x\|- x  + a   + (2x  - a )acos(-)
--R                                         a
--R   (2)  -----------------------------------
--R                         4
--R                                                     Type: Expression Integer
--E

--S 31     14:478 Axiom cannot simplify this expression
cc:=aa-bb
 

                          +---------+
                          |   2    2
           2    2      2x\|- x  + a           2     2      x
        (2x  - a )atan(--------------) + (- 4x  + 2a )acos(-)
                            2    2                         a
                          2x  - a
   (3)  -----------------------------------------------------
                                  8
                                                     Type: Expression Integer
--R
--R                          +---------+
--R                          |   2    2
--R           2    2      2x\|- x  + a           2     2      x
--R        (2x  - a )atan(--------------) + (- 4x  + 2a )acos(-)
--R                            2    2                         a
--R                          2x  - a
--R   (3)  -----------------------------------------------------
--R                                  8
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(x^2*acos(x/a),x)
 

                   +---------+
                   |   2    2                   +---------+
          3     2x\|- x  + a           2     2  |   2    2
        3x atan(--------------) + (- 2x  - 4a )\|- x  + a
                     2    2
                   2x  - a
   (1)  ---------------------------------------------------
                                 18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +---------+
--R                   |   2    2                   +---------+
--R          3     2x\|- x  + a           2     2  |   2    2
--R        3x atan(--------------) + (- 2x  - 4a )\|- x  + a
--R                     2    2
--R                   2x  - a
--R   (1)  ---------------------------------------------------
--R                                 18
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33
bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9
 

                     +---------+
            2     2  |   2    2      3     x
        (- x  - 2a )\|- x  + a   + 3x acos(-)
                                           a
   (2)  -------------------------------------
                          9
                                                     Type: Expression Integer
--R
--R                     +---------+
--R            2     2  |   2    2      3     x
--R        (- x  - 2a )\|- x  + a   + 3x acos(-)
--R                                           a
--R   (2)  -------------------------------------
--R                          9
--R                                                     Type: Expression Integer
--E

--S 34     14:479 Axiom cannot simplify this expression
cc:=aa-bb
 

                  +---------+
                  |   2    2
         3     2x\|- x  + a        3     x
        x atan(--------------) - 2x acos(-)
                    2    2               a
                  2x  - a
   (3)  -----------------------------------
                         6
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2
--R         3     2x\|- x  + a        3     x
--R        x atan(--------------) - 2x acos(-)
--R                    2    2               a
--R                  2x  - a
--R   (3)  -----------------------------------
--R                         6
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 35     14:480 Axiom cannot compute this integral
aa:=integrate(acos(x/a)/x,x)
 

                  %K
           x acos(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x acos(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(acos(x/a)/x^2,x)
 

   (1)
                                                                 +---------+
          +---------+               +---------+                  |   2    2
          |   2    2                |   2    2                2x\|- x  + a
   x log(\|- x  + a   + a) - x log(\|- x  + a   - a) - a atan(--------------)
                                                                   2    2
                                                                 2x  - a
   --------------------------------------------------------------------------
                                      2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                 +---------+
--R          +---------+               +---------+                  |   2    2
--R          |   2    2                |   2    2                2x\|- x  + a
--R   x log(\|- x  + a   + a) - x log(\|- x  + a   - a) - a atan(--------------)
--R                                                                   2    2
--R                                                                 2x  - a
--R   --------------------------------------------------------------------------
--R                                      2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37
bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x)
 

               +---------+
               |   2    2
              \|- x  + a   + a           x
        x log(----------------) - a acos(-)
                      x                  a
   (2)  -----------------------------------
                        a x
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   + a           x
--R        x log(----------------) - a acos(-)
--R                      x                  a
--R   (2)  -----------------------------------
--R                        a x
--R                                                     Type: Expression Integer
--E

--S 38     14:481 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
              +---------+               +---------+
              |   2    2                |   2    2
       x log(\|- x  + a   + a) - x log(\|- x  + a   - a)
     + 
                 +---------+                  +---------+
                 |   2    2                   |   2    2
                \|- x  + a   + a           2x\|- x  + a              x
       - 2x log(----------------) - a atan(--------------) + 2a acos(-)
                        x                       2    2               a
                                              2x  - a
  /
     2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R              +---------+               +---------+
--R              |   2    2                |   2    2
--R       x log(\|- x  + a   + a) - x log(\|- x  + a   - a)
--R     + 
--R                 +---------+                  +---------+
--R                 |   2    2                   |   2    2
--R                \|- x  + a   + a           2x\|- x  + a              x
--R       - 2x log(----------------) - a atan(--------------) + 2a acos(-)
--R                        x                       2    2               a
--R                                              2x  - a
--R  /
--R     2a x
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(acos(x/a)^2,x)
 

                  +---------+ 2                        +---------+
                  |   2    2        +---------+        |   2    2
               2x\|- x  + a         |   2    2      2x\|- x  + a
        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
                    2    2                               2    2
                  2x  - a                              2x  - a
   (1)  ----------------------------------------------------------------
                                        4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+ 2                        +---------+
--R                  |   2    2        +---------+        |   2    2
--R               2x\|- x  + a         |   2    2      2x\|- x  + a
--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
--R                    2    2                               2    2
--R                  2x  - a                              2x  - a
--R   (1)  ----------------------------------------------------------------
--R                                        4
--R                                          Type: Union(Expression Integer,...)
--E

--S 40
bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a)
 

                   +---------+
                x  |   2    2           x 2
   (2)  - 2acos(-)\|- x  + a   + x acos(-)  - 2x
                a                       a
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                x  |   2    2           x 2
--R   (2)  - 2acos(-)\|- x  + a   + x acos(-)  - 2x
--R                a                       a
--R                                                     Type: Expression Integer
--E

--S 41     14:482 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                 +---------+ 2                        +---------+
                 |   2    2        +---------+        |   2    2
              2x\|- x  + a         |   2    2      2x\|- x  + a
       x atan(--------------)  - 4\|- x  + a  atan(--------------)
                   2    2                               2    2
                 2x  - a                              2x  - a
     + 
                +---------+
             x  |   2    2            x 2
       8acos(-)\|- x  + a   - 4x acos(-)
             a                        a
  /
     4
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +---------+ 2                        +---------+
--R                 |   2    2        +---------+        |   2    2
--R              2x\|- x  + a         |   2    2      2x\|- x  + a
--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
--R                   2    2                               2    2
--R                 2x  - a                              2x  - a
--R     + 
--R                +---------+
--R             x  |   2    2            x 2
--R       8acos(-)\|- x  + a   - 4x acos(-)
--R             a                        a
--R  /
--R     4
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 42
aa:=integrate(atan(x/a),x)
 

                 2    2             2a x
        - a log(x  + a ) - x atan(-------)
                                   2    2
                                  x  - a
   (1)  ----------------------------------
                         2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2             2a x
--R        - a log(x  + a ) - x atan(-------)
--R                                   2    2
--R                                  x  - a
--R   (1)  ----------------------------------
--R                         2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 43
bb:=x*atan(x/a)-a/2*log(x^2+a^2)
 

                 2    2            x
        - a log(x  + a ) + 2x atan(-)
                                   a
   (2)  -----------------------------
                      2
                                                     Type: Expression Integer
--R
--R                 2    2            x
--R        - a log(x  + a ) + 2x atan(-)
--R                                   a
--R   (2)  -----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 44
cc:=aa-bb
 

                  x             2a x
        - 2x atan(-) - x atan(-------)
                  a            2    2
                              x  - a
   (3)  ------------------------------
                       2
                                                     Type: Expression Integer
--R
--R                  x             2a x
--R        - 2x atan(-) - x atan(-------)
--R                  a            2    2
--R                              x  - a
--R   (3)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E

--S 45
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 46
dd:=atanrule cc
 

                  2              2
                 x  + 2%i a x - a               - x + %i a
        %i x log(-----------------) + 2%i x log(----------)
                  2              2               x + %i a
                 x  - 2%i a x - a
   (5)  ---------------------------------------------------
                                 4
                                             Type: Expression Complex Integer
--R
--R                  2              2
--R                 x  + 2%i a x - a               - x + %i a
--R        %i x log(-----------------) + 2%i x log(----------)
--R                  2              2               x + %i a
--R                 x  - 2%i a x - a
--R   (5)  ---------------------------------------------------
--R                                 4
--R                                             Type: Expression Complex Integer
--E

--S 47     14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
ee:=expandLog dd
 

        %i x log(- 1)
   (6)  -------------
              2
                                             Type: Expression Complex Integer
--R
--R        %i x log(- 1)
--R   (6)  -------------
--R              2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 48     14:484 Axiom cannot compute this integral
aa:=integrate(x*tan(x/a),x)
 

           x
         ++         %K
   (1)   |   %K tan(--)d%K
        ++           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++         %H
--I   (1)   |   %H tan(--)d%H
--R        ++           a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(x^2*atan(x/a),x)
 

         3     2    2     3       2a x        2
        a log(x  + a ) - x atan(-------) - a x
                                 2    2
                                x  - a
   (1)  ---------------------------------------
                           6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         3     2    2     3       2a x        2
--R        a log(x  + a ) - x atan(-------) - a x
--R                                 2    2
--R                                x  - a
--R   (1)  ---------------------------------------
--R                           6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50
bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2)
 

         3     2    2      3     x       2
        a log(x  + a ) + 3x atan(-) - a x
                                 a
   (2)  ----------------------------------
                         6
                                                     Type: Expression Integer
--R
--R         3     2    2      3     x       2
--R        a log(x  + a ) + 3x atan(-) - a x
--R                                 a
--R   (2)  ----------------------------------
--R                         6
--R                                                     Type: Expression Integer
--E

--S 51     14:485 Axiom cannot simplify this expression
cc:=aa-bb
 

            3     x     3       2a x
        - 3x atan(-) - x atan(-------)
                  a            2    2
                              x  - a
   (3)  ------------------------------
                       6
                                                     Type: Expression Integer
--R
--R            3     x     3       2a x
--R        - 3x atan(-) - x atan(-------)
--R                  a            2    2
--R                              x  - a
--R   (3)  ------------------------------
--R                       6
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 52     14:486 Axiom cannot compute this integral
aa:=integrate(atan(x/a)/x,x)
 

                  %K
           x atan(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x atan(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 53
aa:=integrate(atan(x/a)/x^2,x)
 

                 2    2                         2a x
        - x log(x  + a ) + 2x log(x) + a atan(-------)
                                               2    2
                                              x  - a
   (1)  ----------------------------------------------
                             2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2                         2a x
--R        - x log(x  + a ) + 2x log(x) + a atan(-------)
--R                                               2    2
--R                                              x  - a
--R   (1)  ----------------------------------------------
--R                             2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54
bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2)
 

                 2    2
                x  + a             x
        - x log(-------) - 2a atan(-)
                    2              a
                   x
   (2)  -----------------------------
                     2a x
                                                     Type: Expression Integer
--R
--R                 2    2
--R                x  + a             x
--R        - x log(-------) - 2a atan(-)
--R                    2              a
--R                   x
--R   (2)  -----------------------------
--R                     2a x
--R                                                     Type: Expression Integer
--E

--S 55
cc:=aa-bb
 

   (3)
                                         2    2
            2    2                      x  + a             x             2a x
   - x log(x  + a ) + 2x log(x) + x log(-------) + 2a atan(-) + a atan(-------)
                                            2              a            2    2
                                           x                           x  - a
   ----------------------------------------------------------------------------
                                       2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                         2    2
--R            2    2                      x  + a             x             2a x
--R   - x log(x  + a ) + 2x log(x) + x log(-------) + 2a atan(-) + a atan(-------)
--R                                            2              a            2    2
--R                                           x                           x  - a
--R   ----------------------------------------------------------------------------
--R                                       2a x
--R                                                     Type: Expression Integer
--E

--S 56
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 57
dd:=atanrule cc
 

   (5)
                                                 2              2
                 2    2                         x  + 2%i a x - a
       - 2x log(x  + a ) + 4x log(x) - %i a log(-----------------)
                                                 2              2
                                                x  - 2%i a x - a
     + 
               2    2
              x  + a               - x + %i a
       2x log(-------) - 2%i a log(----------)
                  2                 x + %i a
                 x
  /
     4a x
                                             Type: Expression Complex Integer
--R
--R   (5)
--R                                                 2              2
--R                 2    2                         x  + 2%i a x - a
--R       - 2x log(x  + a ) + 4x log(x) - %i a log(-----------------)
--R                                                 2              2
--R                                                x  - 2%i a x - a
--R     + 
--R               2    2
--R              x  + a               - x + %i a
--R       2x log(-------) - 2%i a log(----------)
--R                  2                 x + %i a
--R                 x
--R  /
--R     4a x
--R                                             Type: Expression Complex Integer
--E

--S 58     14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
ee:=expandLog dd
 

          %i log(- 1)
   (6)  - -----------
               2x
                                             Type: Expression Complex Integer
--R
--R          %i log(- 1)
--R   (6)  - -----------
--R               2x
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 59
aa:=integrate(acot(x/a),x)
 

               2    2             2a x
        a log(x  + a ) + x atan(-------)
                                 2    2
                                x  - a
   (1)  --------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2             2a x
--R        a log(x  + a ) + x atan(-------)
--R                                 2    2
--R                                x  - a
--R   (1)  --------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E

--S 60
bb:=x*acot(x/a)+a/2*log(x^2+a^2)
 

               2    2            x
        a log(x  + a ) + 2x acot(-)
                                 a
   (2)  ---------------------------
                     2
                                                     Type: Expression Integer
--R
--R               2    2            x
--R        a log(x  + a ) + 2x acot(-)
--R                                 a
--R   (2)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 

--S 61
cc:=aa-bb
 

                 2a x             x
        x atan(-------) - 2x acot(-)
                2    2            a
               x  - a
   (3)  ----------------------------
                      2
                                                     Type: Expression Integer
--R
--R                 2a x             x
--R        x atan(-------) - 2x acot(-)
--R                2    2            a
--R               x  - a
--R   (3)  ----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 62
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 63
dd:=atanrule cc
 

                    2              2
                   x  + 2%i a x - a             x
        - %i x log(-----------------) - 4x acot(-)
                    2              2            a
                   x  - 2%i a x - a
   (5)  ------------------------------------------
                             4
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R                   x  + 2%i a x - a             x
--R        - %i x log(-----------------) - 4x acot(-)
--R                    2              2            a
--R                   x  - 2%i a x - a
--R   (5)  ------------------------------------------
--R                             4
--R                                             Type: Expression Complex Integer
--E

--S 64
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (6)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (6)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 65
ee:=acotrule dd
 

                    2              2
                   x  + 2%i a x - a               x + %i a
        - %i x log(-----------------) + 2%i x log(--------)
                    2              2              x - %i a
                   x  - 2%i a x - a
   (7)  ---------------------------------------------------
                                 4
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R                   x  + 2%i a x - a               x + %i a
--R        - %i x log(-----------------) + 2%i x log(--------)
--R                    2              2              x - %i a
--R                   x  - 2%i a x - a
--R   (7)  ---------------------------------------------------
--R                                 4
--R                                             Type: Expression Complex Integer
--E

--S 66     14:488 Axiom and Schaums agree
ff:=expandLog %
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 67
aa:=integrate(x*acot(x/a),x)
 

          2    2        2a x
        (x  + a )atan(-------) + 2a x
                       2    2
                      x  - a
   (1)  -----------------------------
                      4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2        2a x
--R        (x  + a )atan(-------) + 2a x
--R                       2    2
--R                      x  - a
--R   (1)  -----------------------------
--R                      4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68
bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2
 

          2    2      x
        (x  + a )acot(-) + a x
                      a
   (2)  ----------------------
                   2
                                                     Type: Expression Integer
--R
--R          2    2      x
--R        (x  + a )acot(-) + a x
--R                      a
--R   (2)  ----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 69
cc:=aa-bb
 

          2    2        2a x          2     2      x
        (x  + a )atan(-------) + (- 2x  - 2a )acot(-)
                       2    2                      a
                      x  - a
   (3)  ---------------------------------------------
                              4
                                                     Type: Expression Integer
--R
--R          2    2        2a x          2     2      x
--R        (x  + a )atan(-------) + (- 2x  - 2a )acot(-)
--R                       2    2                      a
--R                      x  - a
--R   (3)  ---------------------------------------------
--R                              4
--R                                                     Type: Expression Integer
--E

--S 70
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (4)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (4)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 71
dd:=acotrule cc
 

             2       2     x + %i a      2    2        2a x
        (%i x  + %i a )log(--------) + (x  + a )atan(-------)
                           x - %i a                   2    2
                                                     x  - a
   (5)  -----------------------------------------------------
                                  4
                                             Type: Expression Complex Integer
--R
--R             2       2     x + %i a      2    2        2a x
--R        (%i x  + %i a )log(--------) + (x  + a )atan(-------)
--R                           x - %i a                   2    2
--R                                                     x  - a
--R   (5)  -----------------------------------------------------
--R                                  4
--R                                             Type: Expression Complex Integer
--E

--S 72
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 73
ee:=atanrule dd
 

   (7)
                         2              2
          2       2     x  + 2%i a x - a           2        2     x + %i a
   (- %i x  - %i a )log(-----------------) + (2%i x  + 2%i a )log(--------)
                         2              2                         x - %i a
                        x  - 2%i a x - a
   ------------------------------------------------------------------------
                                       8
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                         2              2
--R          2       2     x  + 2%i a x - a           2        2     x + %i a
--R   (- %i x  - %i a )log(-----------------) + (2%i x  + 2%i a )log(--------)
--R                         2              2                         x - %i a
--R                        x  - 2%i a x - a
--R   ------------------------------------------------------------------------
--R                                       8
--R                                             Type: Expression Complex Integer
--E

--S 74     14:489 Axiom and Schaums agree
ff:=expandLog ee
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 75
aa:=integrate(x^2*acot(x/a),x)
 

           3     2    2     3       2a x        2
        - a log(x  + a ) + x atan(-------) + a x
                                   2    2
                                  x  - a
   (1)  -----------------------------------------
                            6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           3     2    2     3       2a x        2
--R        - a log(x  + a ) + x atan(-------) + a x
--R                                   2    2
--R                                  x  - a
--R   (1)  -----------------------------------------
--R                            6
--R                                          Type: Union(Expression Integer,...)
--E

--S 76
bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2)
 

           3     2    2      3     x       2
        - a log(x  + a ) + 2x acot(-) + a x
                                   a
   (2)  ------------------------------------
                          6
                                                     Type: Expression Integer
--R
--R           3     2    2      3     x       2
--R        - a log(x  + a ) + 2x acot(-) + a x
--R                                   a
--R   (2)  ------------------------------------
--R                          6
--R                                                     Type: Expression Integer
--E 

--S 77
cc:=aa-bb
 

         3       2a x       3     x
        x atan(-------) - 2x acot(-)
                2    2            a
               x  - a
   (3)  ----------------------------
                      6
                                                     Type: Expression Integer
--R
--R         3       2a x       3     x
--R        x atan(-------) - 2x acot(-)
--R                2    2            a
--R               x  - a
--R   (3)  ----------------------------
--R                      6
--R                                                     Type: Expression Integer
--E

--S 78
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 79
dd:=atanrule cc
 

                    2              2
              3    x  + 2%i a x - a       3     x
        - %i x log(-----------------) - 4x acot(-)
                    2              2            a
                   x  - 2%i a x - a
   (5)  ------------------------------------------
                            12
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R              3    x  + 2%i a x - a       3     x
--R        - %i x log(-----------------) - 4x acot(-)
--R                    2              2            a
--R                   x  - 2%i a x - a
--R   (5)  ------------------------------------------
--R                            12
--R                                             Type: Expression Complex Integer
--E

--S 80
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (6)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (6)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 81
ee:=acotrule dd
 

                    2              2
              3    x  + 2%i a x - a          3    x + %i a
        - %i x log(-----------------) + 2%i x log(--------)
                    2              2              x - %i a
                   x  - 2%i a x - a
   (7)  ---------------------------------------------------
                                 12
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R              3    x  + 2%i a x - a          3    x + %i a
--R        - %i x log(-----------------) + 2%i x log(--------)
--R                    2              2              x - %i a
--R                   x  - 2%i a x - a
--R   (7)  ---------------------------------------------------
--R                                 12
--R                                             Type: Expression Complex Integer
--E

--S 82     14:490 Axiom and Schaums agree
ff:=expandLog ee
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 83     14:491 Axiom cannot compute this integral
aa:=integrate(acot(x/a)/x,x)
 

                  %K
           x acot(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x acot(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 84
aa:=integrate(acot(x/a)/x^2,x)
 

               2    2                         2a x
        x log(x  + a ) - 2x log(x) - a atan(-------)
                                             2    2
                                            x  - a
   (1)  --------------------------------------------
                            2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2                         2a x
--R        x log(x  + a ) - 2x log(x) - a atan(-------)
--R                                             2    2
--R                                            x  - a
--R   (1)  --------------------------------------------
--R                            2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 85
bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2)
 

               2    2
              x  + a             x
        x log(-------) - 2a acot(-)
                  2              a
                 x
   (2)  ---------------------------
                    2a x
                                                     Type: Expression Integer
--R
--R               2    2
--R              x  + a             x
--R        x log(-------) - 2a acot(-)
--R                  2              a
--R                 x
--R   (2)  ---------------------------
--R                    2a x
--R                                                     Type: Expression Integer
--E

--S 86
cc:=aa-bb
 

   (3)
                                       2    2
          2    2                      x  + a              2a x             x
   x log(x  + a ) - 2x log(x) - x log(-------) - a atan(-------) + 2a acot(-)
                                          2              2    2            a
                                         x              x  - a
   --------------------------------------------------------------------------
                                      2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                       2    2
--R          2    2                      x  + a              2a x             x
--R   x log(x  + a ) - 2x log(x) - x log(-------) - a atan(-------) + 2a acot(-)
--R                                          2              2    2            a
--R                                         x              x  - a
--R   --------------------------------------------------------------------------
--R                                      2a x
--R                                                     Type: Expression Integer
--E

--S 87
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (4)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (4)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 88
dd:=acotrule cc
 

   (5)
                                                                2    2
              2    2                         x + %i a          x  + a
       x log(x  + a ) - 2x log(x) - %i a log(--------) - x log(-------)
                                             x - %i a              2
                                                                  x
     + 
                  2a x
       - a atan(-------)
                 2    2
                x  - a
  /
     2a x
                                             Type: Expression Complex Integer
--R
--R   (5)
--R                                                                2    2
--R              2    2                         x + %i a          x  + a
--R       x log(x  + a ) - 2x log(x) - %i a log(--------) - x log(-------)
--R                                             x - %i a              2
--R                                                                  x
--R     + 
--R                  2a x
--R       - a atan(-------)
--R                 2    2
--R                x  - a
--R  /
--R     2a x
--R                                             Type: Expression Complex Integer
--E

--S 89
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 90
ee:=atanrule dd
 

   (7)
                                               2              2
               2    2                         x  + 2%i a x - a
       2x log(x  + a ) - 4x log(x) + %i a log(-----------------)
                                               2              2
                                              x  - 2%i a x - a
     + 
                                       2    2
                   x + %i a           x  + a
       - 2%i a log(--------) - 2x log(-------)
                   x - %i a               2
                                         x
  /
     4a x
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                                               2              2
--R               2    2                         x  + 2%i a x - a
--R       2x log(x  + a ) - 4x log(x) + %i a log(-----------------)
--R                                               2              2
--R                                              x  - 2%i a x - a
--R     + 
--R                                       2    2
--R                   x + %i a           x  + a
--R       - 2%i a log(--------) - 2x log(-------)
--R                   x - %i a               2
--R                                         x
--R  /
--R     4a x
--R                                             Type: Expression Complex Integer
--E

--S 91     14:492 Schaums and Axiom agree
ff:=expandLog ee
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 92
aa:=integrate(asec(x/a),x)
 

   (1)
                          +---------+              +---------+
                      +-+ |   2    2               |   2    2
           +-+     2x\|2 \|- x  + a             2a\|- x  + a
       - a\|2 atan(------------------) + x atan(--------------)
                          2     2                      2
                        3x  - 2a                      x
     + 
                       x
       - 2a atan(------------)
                  +---------+
                  |   2    2
                 \|- x  + a
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                          +---------+              +---------+
--R                      +-+ |   2    2               |   2    2
--R           +-+     2x\|2 \|- x  + a             2a\|- x  + a
--R       - a\|2 atan(------------------) + x atan(--------------)
--R                          2     2                      2
--R                        3x  - 2a                      x
--R     + 
--R                       x
--R       - 2a atan(------------)
--R                  +---------+
--R                  |   2    2
--R                 \|- x  + a
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 93
bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2))
 

                 +-------+
                 | 2    2                x
   (2)  - a log(\|x  - a   + x) + x asec(-)
                                         a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2                x
--R   (2)  - a log(\|x  - a   + x) + x asec(-)
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 94
bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2))
 

               +-------+
               | 2    2                x
   (3)  a log(\|x  - a   + x) + x asec(-)
                                       a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2                x
--R   (3)  a log(\|x  - a   + x) + x asec(-)
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 95
cc1:=aa-bb1
 

   (4)
                                                 +---------+
               +-------+                     +-+ |   2    2
               | 2    2           +-+     2x\|2 \|- x  + a
       2a log(\|x  - a   + x) - a\|2 atan(------------------)
                                                 2     2
                                               3x  - 2a
     + 
                 +---------+
                 |   2    2
              2a\|- x  + a                    x                 x
       x atan(--------------) - 2a atan(------------) - 2x asec(-)
                     2                   +---------+            a
                    x                    |   2    2
                                        \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                 +---------+
--R               +-------+                     +-+ |   2    2
--R               | 2    2           +-+     2x\|2 \|- x  + a
--R       2a log(\|x  - a   + x) - a\|2 atan(------------------)
--R                                                 2     2
--R                                               3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2
--R              2a\|- x  + a                    x                 x
--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
--R                     2                   +---------+            a
--R                    x                    |   2    2
--R                                        \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 96     14:493 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                                   +---------+
                 +-------+                     +-+ |   2    2
                 | 2    2           +-+     2x\|2 \|- x  + a
       - 2a log(\|x  - a   + x) - a\|2 atan(------------------)
                                                   2     2
                                                 3x  - 2a
     + 
                 +---------+
                 |   2    2
              2a\|- x  + a                    x                 x
       x atan(--------------) - 2a atan(------------) - 2x asec(-)
                     2                   +---------+            a
                    x                    |   2    2
                                        \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                   +---------+
--R                 +-------+                     +-+ |   2    2
--R                 | 2    2           +-+     2x\|2 \|- x  + a
--R       - 2a log(\|x  - a   + x) - a\|2 atan(------------------)
--R                                                   2     2
--R                                                 3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2
--R              2a\|- x  + a                    x                 x
--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
--R                     2                   +---------+            a
--R                    x                    |   2    2
--R                                        \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 97
aa:=integrate(x*asec(x/a),x)
 

                          +---------+
                          |   2    2        +---------+
          2     2      2a\|- x  + a         |   2    2
        (x  - 2a )atan(--------------) + 2a\|- x  + a
                              2
                             x
   (1)  -----------------------------------------------
                               4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +---------+
--R                          |   2    2        +---------+
--R          2     2      2a\|- x  + a         |   2    2
--R        (x  - 2a )atan(--------------) + 2a\|- x  + a
--R                              2
--R                             x
--R   (1)  -----------------------------------------------
--R                               4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 98
bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2
 

            +-------+
            | 2    2     2     x
        - a\|x  - a   + x asec(-)
                               a
   (2)  -------------------------
                    2
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2     x
--R        - a\|x  - a   + x asec(-)
--R                               a
--R   (2)  -------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 99
bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2
 

          +-------+
          | 2    2     2     x
        a\|x  - a   + x asec(-)
                             a
   (3)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2     x
--R        a\|x  - a   + x asec(-)
--R                             a
--R   (3)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 100
cc1:=aa-bb1
 

   (4)
                     +---------+
                     |   2    2        +-------+      +---------+
     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (x  - 2a )atan(--------------) + 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
                         2                                                  a
                        x
   ---------------------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R   (4)
--R                     +---------+
--R                     |   2    2        +-------+      +---------+
--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (x  - 2a )atan(--------------) + 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
--R                         2                                                  a
--R                        x
--R   ---------------------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 101    14:494 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                     +---------+
                     |   2    2        +-------+      +---------+
     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (x  - 2a )atan(--------------) - 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
                         2                                                  a
                        x
   ---------------------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R   (5)
--R                     +---------+
--R                     |   2    2        +-------+      +---------+
--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (x  - 2a )atan(--------------) - 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
--R                         2                                                  a
--R                        x
--R   ---------------------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 102
aa:=integrate(x^2*asec(x/a),x)
 

   (1)
                            +---------+              +---------+
                        +-+ |   2    2               |   2    2
           3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
       - 2a \|2 atan(------------------) + x atan(--------------)
                            2     2                      2
                          3x  - 2a                      x
     + 
                                     +---------+
           3           x             |   2    2
       - 5a atan(------------) + a x\|- x  + a
                  +---------+
                  |   2    2
                 \|- x  + a
  /
     6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                            +---------+              +---------+
--R                        +-+ |   2    2               |   2    2
--R           3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
--R       - 2a \|2 atan(------------------) + x atan(--------------)
--R                            2     2                      2
--R                          3x  - 2a                      x
--R     + 
--R                                     +---------+
--R           3           x             |   2    2
--R       - 5a atan(------------) + a x\|- x  + a
--R                  +---------+
--R                  |   2    2
--R                 \|- x  + a
--R  /
--R     6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103
bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 

                 +-------+            +-------+
           3     | 2    2             | 2    2      3     x
        - a log(\|x  - a   + x) - a x\|x  - a   + 2x asec(-)
                                                          a
   (2)  ----------------------------------------------------
                                  6
                                                     Type: Expression Integer
--R
--R                 +-------+            +-------+
--R           3     | 2    2             | 2    2      3     x
--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x asec(-)
--R                                                          a
--R   (2)  ----------------------------------------------------
--R                                  6
--R                                                     Type: Expression Integer
--E

--S 104
bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 

               +-------+            +-------+
         3     | 2    2             | 2    2      3     x
        a log(\|x  - a   + x) + a x\|x  - a   + 2x asec(-)
                                                        a
   (3)  --------------------------------------------------
                                 6
                                                     Type: Expression Integer
--R
--R               +-------+            +-------+
--R         3     | 2    2             | 2    2      3     x
--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x asec(-)
--R                                                        a
--R   (3)  --------------------------------------------------
--R                                 6
--R                                                     Type: Expression Integer
--E

--S 105
cc1:=aa-bb1
 

   (4)
                                                  +---------+
              +-------+                       +-+ |   2    2
        3     | 2    2           3 +-+     2x\|2 \|- x  + a
       a log(\|x  - a   + x) - 2a \|2 atan(------------------)
                                                  2     2
                                                3x  - 2a
     + 
                 +---------+
                 |   2    2                                 +-------+
        3     2a\|- x  + a        3           x             | 2    2
       x atan(--------------) - 5a atan(------------) + a x\|x  - a
                     2                   +---------+
                    x                    |   2    2
                                        \|- x  + a
     + 
           +---------+
           |   2    2      3     x
       a x\|- x  + a   - 2x asec(-)
                                 a
  /
     6
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                  +---------+
--R              +-------+                       +-+ |   2    2
--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       a log(\|x  - a   + x) - 2a \|2 atan(------------------)
--R                                                  2     2
--R                                                3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2                                 +-------+
--R        3     2a\|- x  + a        3           x             | 2    2
--R       x atan(--------------) - 5a atan(------------) + a x\|x  - a
--R                     2                   +---------+
--R                    x                    |   2    2
--R                                        \|- x  + a
--R     + 
--R           +---------+
--R           |   2    2      3     x
--R       a x\|- x  + a   - 2x asec(-)
--R                                 a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E

--S 106     14:495 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                                    +---------+
                +-------+                       +-+ |   2    2
          3     | 2    2           3 +-+     2x\|2 \|- x  + a
       - a log(\|x  - a   + x) - 2a \|2 atan(------------------)
                                                    2     2
                                                  3x  - 2a
     + 
                 +---------+
                 |   2    2                                 +-------+
        3     2a\|- x  + a        3           x             | 2    2
       x atan(--------------) - 5a atan(------------) - a x\|x  - a
                     2                   +---------+
                    x                    |   2    2
                                        \|- x  + a
     + 
           +---------+
           |   2    2      3     x
       a x\|- x  + a   - 2x asec(-)
                                 a
  /
     6
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                    +---------+
--R                +-------+                       +-+ |   2    2
--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       - a log(\|x  - a   + x) - 2a \|2 atan(------------------)
--R                                                    2     2
--R                                                  3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2                                 +-------+
--R        3     2a\|- x  + a        3           x             | 2    2
--R       x atan(--------------) - 5a atan(------------) - a x\|x  - a
--R                     2                   +---------+
--R                    x                    |   2    2
--R                                        \|- x  + a
--R     + 
--R           +---------+
--R           |   2    2      3     x
--R       a x\|- x  + a   - 2x asec(-)
--R                                 a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 107    14:496 Axiom cannot compute this integral
aa:=integrate(asec(x/a)/x,x)
 

                  %K
           x asec(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x asec(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 108
aa:=integrate(asec(x/a)/x^2,x)
 

                      +---------+                 +---------+
                  +-+ |   2    2                  |   2    2
               2x\|2 \|- x  + a        +-+     2a\|- x  + a
        x atan(------------------) - a\|2 atan(--------------)
                      2     2                         2
                    3x  - 2a                         x
   (1)  ------------------------------------------------------
                                    +-+
                               2a x\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      +---------+                 +---------+
--R                  +-+ |   2    2                  |   2    2
--R               2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R        x atan(------------------) - a\|2 atan(--------------)
--R                      2     2                         2
--R                    3x  - 2a                         x
--R   (1)  ------------------------------------------------------
--R                                    +-+
--R                               2a x\|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 109
bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x)
 

         +-------+
         | 2    2           x
        \|x  - a   - a asec(-)
                            a
   (2)  ----------------------
                  a x
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2           x
--R        \|x  - a   - a asec(-)
--R                            a
--R   (2)  ----------------------
--R                  a x
--R                                                     Type: Expression Integer
--E

--S 110
bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x)
 

           +-------+
           | 2    2           x
        - \|x  - a   - a asec(-)
                              a
   (3)  ------------------------
                   a x
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2           x
--R        - \|x  - a   - a asec(-)
--R                              a
--R   (3)  ------------------------
--R                   a x
--R                                                     Type: Expression Integer
--E

--S 111
cc1:=aa-bb1
 

   (4)
                     +---------+                 +---------+
                 +-+ |   2    2                  |   2    2           +-------+
              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
       x atan(------------------) - a\|2 atan(--------------) - 2\|2 \|x  - a
                     2     2                         2
                   3x  - 2a                         x
     + 
          +-+     x
       2a\|2 asec(-)
                  a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (4)
--R                     +---------+                 +---------+
--R                 +-+ |   2    2                  |   2    2           +-------+
--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
--R       x atan(------------------) - a\|2 atan(--------------) - 2\|2 \|x  - a
--R                     2     2                         2
--R                   3x  - 2a                         x
--R     + 
--R          +-+     x
--R       2a\|2 asec(-)
--R                  a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E

--S 112    14:497 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                     +---------+                 +---------+
                 +-+ |   2    2                  |   2    2           +-------+
              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
       x atan(------------------) - a\|2 atan(--------------) + 2\|2 \|x  - a
                     2     2                         2
                   3x  - 2a                         x
     + 
          +-+     x
       2a\|2 asec(-)
                  a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (5)
--R                     +---------+                 +---------+
--R                 +-+ |   2    2                  |   2    2           +-------+
--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
--R       x atan(------------------) - a\|2 atan(--------------) + 2\|2 \|x  - a
--R                     2     2                         2
--R                   3x  - 2a                         x
--R     + 
--R          +-+     x
--R       2a\|2 asec(-)
--R                  a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 113
aa:=integrate(acsc(x/a),x)
 

   (1)
                        +---------+              +---------+
                    +-+ |   2    2               |   2    2
         +-+     2x\|2 \|- x  + a             2a\|- x  + a
       a\|2 atan(------------------) - x atan(--------------)
                        2     2                      2
                      3x  - 2a                      x
     + 
                     x
       2a atan(------------)
                +---------+
                |   2    2
               \|- x  + a
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                        +---------+              +---------+
--R                    +-+ |   2    2               |   2    2
--R         +-+     2x\|2 \|- x  + a             2a\|- x  + a
--R       a\|2 atan(------------------) - x atan(--------------)
--R                        2     2                      2
--R                      3x  - 2a                      x
--R     + 
--R                     x
--R       2a atan(------------)
--R                +---------+
--R                |   2    2
--R               \|- x  + a
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 114
bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2))
 

               +-------+
               | 2    2                x
   (2)  a log(\|x  - a   + x) + x acsc(-)
                                       a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2                x
--R   (2)  a log(\|x  - a   + x) + x acsc(-)
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 115
bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2))
 

                 +-------+
                 | 2    2                x
   (3)  - a log(\|x  - a   + x) + x acsc(-)
                                         a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2                x
--R   (3)  - a log(\|x  - a   + x) + x acsc(-)
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 116
cc1:=aa-bb1
 

   (4)
                                                   +---------+
                 +-------+                     +-+ |   2    2
                 | 2    2           +-+     2x\|2 \|- x  + a
       - 2a log(\|x  - a   + x) + a\|2 atan(------------------)
                                                   2     2
                                                 3x  - 2a
     + 
                   +---------+
                   |   2    2
                2a\|- x  + a                    x                 x
       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
                       2                   +---------+            a
                      x                    |   2    2
                                          \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                   +---------+
--R                 +-------+                     +-+ |   2    2
--R                 | 2    2           +-+     2x\|2 \|- x  + a
--R       - 2a log(\|x  - a   + x) + a\|2 atan(------------------)
--R                                                   2     2
--R                                                 3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2
--R                2a\|- x  + a                    x                 x
--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
--R                       2                   +---------+            a
--R                      x                    |   2    2
--R                                          \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 117    14:498 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                                 +---------+
               +-------+                     +-+ |   2    2
               | 2    2           +-+     2x\|2 \|- x  + a
       2a log(\|x  - a   + x) + a\|2 atan(------------------)
                                                 2     2
                                               3x  - 2a
     + 
                   +---------+
                   |   2    2
                2a\|- x  + a                    x                 x
       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
                       2                   +---------+            a
                      x                    |   2    2
                                          \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                 +---------+
--R               +-------+                     +-+ |   2    2
--R               | 2    2           +-+     2x\|2 \|- x  + a
--R       2a log(\|x  - a   + x) + a\|2 atan(------------------)
--R                                                 2     2
--R                                               3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2
--R                2a\|- x  + a                    x                 x
--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
--R                       2                   +---------+            a
--R                      x                    |   2    2
--R                                          \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 118
aa:=integrate(x*acsc(x/a),x)
 

                            +---------+
                            |   2    2        +---------+
            2     2      2a\|- x  + a         |   2    2
        (- x  + 2a )atan(--------------) - 2a\|- x  + a
                                2
                               x
   (1)  -------------------------------------------------
                                4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            +---------+
--R                            |   2    2        +---------+
--R            2     2      2a\|- x  + a         |   2    2
--R        (- x  + 2a )atan(--------------) - 2a\|- x  + a
--R                                2
--R                               x
--R   (1)  -------------------------------------------------
--R                                4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 119
bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2
 

          +-------+
          | 2    2     2     x
        a\|x  - a   + x acsc(-)
                             a
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2     x
--R        a\|x  - a   + x acsc(-)
--R                             a
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 120
bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2
 

            +-------+
            | 2    2     2     x
        - a\|x  - a   + x acsc(-)
                               a
   (3)  -------------------------
                    2
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2     x
--R        - a\|x  - a   + x acsc(-)
--R                               a
--R   (3)  -------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 121
cc1:=aa-bb1
 

   (4)
                       +---------+
                       |   2    2        +-------+      +---------+
       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (- x  + 2a )atan(--------------) - 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
                           2                                                  a
                          x
   -----------------------------------------------------------------------------
                                         4
                                                     Type: Expression Integer
--R
--R   (4)
--R                       +---------+
--R                       |   2    2        +-------+      +---------+
--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (- x  + 2a )atan(--------------) - 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
--R                           2                                                  a
--R                          x
--R   -----------------------------------------------------------------------------
--R                                         4
--R                                                     Type: Expression Integer
--E

--S 122    14:499 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                       +---------+
                       |   2    2        +-------+      +---------+
       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (- x  + 2a )atan(--------------) + 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
                           2                                                  a
                          x
   -----------------------------------------------------------------------------
                                         4
                                                     Type: Expression Integer
--R
--R   (5)
--R                       +---------+
--R                       |   2    2        +-------+      +---------+
--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (- x  + 2a )atan(--------------) + 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
--R                           2                                                  a
--R                          x
--R   -----------------------------------------------------------------------------
--R                                         4
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 123
aa:=integrate(x^2*acsc(x/a),x)
 

   (1)
                          +---------+              +---------+
                      +-+ |   2    2               |   2    2
         3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
       2a \|2 atan(------------------) - x atan(--------------)
                          2     2                      2
                        3x  - 2a                      x
     + 
                                   +---------+
         3           x             |   2    2
       5a atan(------------) - a x\|- x  + a
                +---------+
                |   2    2
               \|- x  + a
  /
     6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                          +---------+              +---------+
--R                      +-+ |   2    2               |   2    2
--R         3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
--R       2a \|2 atan(------------------) - x atan(--------------)
--R                          2     2                      2
--R                        3x  - 2a                      x
--R     + 
--R                                   +---------+
--R         3           x             |   2    2
--R       5a atan(------------) - a x\|- x  + a
--R                +---------+
--R                |   2    2
--R               \|- x  + a
--R  /
--R     6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 124
bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 

               +-------+            +-------+
         3     | 2    2             | 2    2      3     x
        a log(\|x  - a   + x) + a x\|x  - a   + 2x acsc(-)
                                                        a
   (2)  --------------------------------------------------
                                 6
                                                     Type: Expression Integer
--R
--R               +-------+            +-------+
--R         3     | 2    2             | 2    2      3     x
--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x acsc(-)
--R                                                        a
--R   (2)  --------------------------------------------------
--R                                 6
--R                                                     Type: Expression Integer
--E

--S 125
bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 

                 +-------+            +-------+
           3     | 2    2             | 2    2      3     x
        - a log(\|x  - a   + x) - a x\|x  - a   + 2x acsc(-)
                                                          a
   (3)  ----------------------------------------------------
                                  6
                                                     Type: Expression Integer
--R
--R                 +-------+            +-------+
--R           3     | 2    2             | 2    2      3     x
--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x acsc(-)
--R                                                          a
--R   (3)  ----------------------------------------------------
--R                                  6
--R                                                     Type: Expression Integer
--E

--S 126
cc1:=aa-bb1
 

   (4)
                                                    +---------+
                +-------+                       +-+ |   2    2
          3     | 2    2           3 +-+     2x\|2 \|- x  + a
       - a log(\|x  - a   + x) + 2a \|2 atan(------------------)
                                                    2     2
                                                  3x  - 2a
     + 
                   +---------+
                   |   2    2                                 +-------+
          3     2a\|- x  + a        3           x             | 2    2
       - x atan(--------------) + 5a atan(------------) - a x\|x  - a
                       2                   +---------+
                      x                    |   2    2
                                          \|- x  + a
     + 
             +---------+
             |   2    2      3     x
       - a x\|- x  + a   - 2x acsc(-)
                                   a
  /
     6
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                    +---------+
--R                +-------+                       +-+ |   2    2
--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       - a log(\|x  - a   + x) + 2a \|2 atan(------------------)
--R                                                    2     2
--R                                                  3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2                                 +-------+
--R          3     2a\|- x  + a        3           x             | 2    2
--R       - x atan(--------------) + 5a atan(------------) - a x\|x  - a
--R                       2                   +---------+
--R                      x                    |   2    2
--R                                          \|- x  + a
--R     + 
--R             +---------+
--R             |   2    2      3     x
--R       - a x\|- x  + a   - 2x acsc(-)
--R                                   a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E

--S 127    14:500 Axiom cannot simplify this expression
cc2:=aa-bb2
 

   (5)
                                                  +---------+
              +-------+                       +-+ |   2    2
        3     | 2    2           3 +-+     2x\|2 \|- x  + a
       a log(\|x  - a   + x) + 2a \|2 atan(------------------)
                                                  2     2
                                                3x  - 2a
     + 
                   +---------+
                   |   2    2                                 +-------+
          3     2a\|- x  + a        3           x             | 2    2
       - x atan(--------------) + 5a atan(------------) + a x\|x  - a
                       2                   +---------+
                      x                    |   2    2
                                          \|- x  + a
     + 
             +---------+
             |   2    2      3     x
       - a x\|- x  + a   - 2x acsc(-)
                                   a
  /
     6
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                  +---------+
--R              +-------+                       +-+ |   2    2
--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       a log(\|x  - a   + x) + 2a \|2 atan(------------------)
--R                                                  2     2
--R                                                3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2                                 +-------+
--R          3     2a\|- x  + a        3           x             | 2    2
--R       - x atan(--------------) + 5a atan(------------) + a x\|x  - a
--R                       2                   +---------+
--R                      x                    |   2    2
--R                                          \|- x  + a
--R     + 
--R             +---------+
--R             |   2    2      3     x
--R       - a x\|- x  + a   - 2x acsc(-)
--R                                   a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 128    14:501 Axiom cannot compute this integral
aa:=integrate(acsc(x/a)/x,x)
 

                  %K
           x acsc(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x acsc(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 129
aa:=integrate(acsc(x/a)/x^2,x)
 

                        +---------+                 +---------+
                    +-+ |   2    2                  |   2    2
                 2x\|2 \|- x  + a        +-+     2a\|- x  + a
        - x atan(------------------) + a\|2 atan(--------------)
                        2     2                         2
                      3x  - 2a                         x
   (1)  --------------------------------------------------------
                                     +-+
                                2a x\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        +---------+                 +---------+
--R                    +-+ |   2    2                  |   2    2
--R                 2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R        - x atan(------------------) + a\|2 atan(--------------)
--R                        2     2                         2
--R                      3x  - 2a                         x
--R   (1)  --------------------------------------------------------
--R                                     +-+
--R                                2a x\|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 130
bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x)
 

           +-------+
           | 2    2           x
        - \|x  - a   - a acsc(-)
                              a
   (2)  ------------------------
                   a x
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2           x
--R        - \|x  - a   - a acsc(-)
--R                              a
--R   (2)  ------------------------
--R                   a x
--R                                                     Type: Expression Integer
--E

--S 131
bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x)
 

         +-------+
         | 2    2           x
        \|x  - a   - a acsc(-)
                            a
   (3)  ----------------------
                  a x
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2           x
--R        \|x  - a   - a acsc(-)
--R                            a
--R   (3)  ----------------------
--R                  a x
--R                                                     Type: Expression Integer
--E

--S 132
cc1:=aa-bb1
 

   (4)
                       +---------+                 +---------+
                   +-+ |   2    2                  |   2    2
                2x\|2 \|- x  + a        +-+     2a\|- x  + a
       - x atan(------------------) + a\|2 atan(--------------)
                       2     2                         2
                     3x  - 2a                         x
     + 
             +-------+
         +-+ | 2    2       +-+     x
       2\|2 \|x  - a   + 2a\|2 acsc(-)
                                    a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (4)
--R                       +---------+                 +---------+
--R                   +-+ |   2    2                  |   2    2
--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R       - x atan(------------------) + a\|2 atan(--------------)
--R                       2     2                         2
--R                     3x  - 2a                         x
--R     + 
--R             +-------+
--R         +-+ | 2    2       +-+     x
--R       2\|2 \|x  - a   + 2a\|2 acsc(-)
--R                                    a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E

--S 133    14:502 Axiom cannot simplify this expression
cc2:=aa-bb2
 

   (5)
                       +---------+                 +---------+
                   +-+ |   2    2                  |   2    2
                2x\|2 \|- x  + a        +-+     2a\|- x  + a
       - x atan(------------------) + a\|2 atan(--------------)
                       2     2                         2
                     3x  - 2a                         x
     + 
               +-------+
           +-+ | 2    2       +-+     x
       - 2\|2 \|x  - a   + 2a\|2 acsc(-)
                                      a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (5)
--R                       +---------+                 +---------+
--R                   +-+ |   2    2                  |   2    2
--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R       - x atan(------------------) + a\|2 atan(--------------)
--R                       2     2                         2
--R                     3x  - 2a                         x
--R     + 
--R               +-------+
--R           +-+ | 2    2       +-+     x
--R       - 2\|2 \|x  - a   + 2a\|2 acsc(-)
--R                                      a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 134    14:503 Axiom cannot compute this integral
aa:=integrate(x^m*asin(x/a),x)
 

           x
         ++       %K   m
   (1)   |   asin(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   asin(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 135    14:504 Axiom cannot compute this integral
aa:=integrate(x^m*acos(x/a),x)
 

           x
         ++       %K   m
   (1)   |   acos(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   acos(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 136
aa:=integrate(x*m*atan(x/a),x)
 

              2    2         2a x
        (- m x  - a m)atan(-------) - 2a m x
                            2    2
                           x  - a
   (1)  ------------------------------------
                          4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2    2         2a x
--R        (- m x  - a m)atan(-------) - 2a m x
--R                            2    2
--R                           x  - a
--R   (1)  ------------------------------------
--R                          4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 137
t1:=integrate(x^(m+1)/(x^2+a^2),x)
 

           x    m + 1
         ++   %K
   (2)   |   -------- d%K
        ++    2     2
             a  + %K
                                          Type: Union(Expression Integer,...)
--E

--S 138
bb:=D(aa,x)
 

                     2a x
          m x atan(-------)
                    2    2
                   x  - a
   (3)  - -----------------
                  2
                                                     Type: Expression Integer
--R
--R                     2a x
--R          m x atan(-------)
--R                    2    2
--R                   x  - a
--R   (3)  - -----------------
--R                  2
--R                                                     Type: Expression Integer
--E
--S 139
aa1:=x*m*atan(x/a)
 

                 x
   (4)  m x atan(-)
                 a
                                                     Type: Expression Integer
--R
--R                 x
--R   (4)  m x atan(-)
--R                 a
--R                                                     Type: Expression Integer
--E
--S 140
dd:=aa1-bb
 

                  x               2a x
        2m x atan(-) + m x atan(-------)
                  a              2    2
                                x  - a
   (5)  --------------------------------
                        2
                                                     Type: Expression Integer
--R
--R                  x               2a x
--R        2m x atan(-) + m x atan(-------)
--R                  a              2    2
--R                                x  - a
--R   (5)  --------------------------------
--R                        2
--R                                                     Type: Expression Integer
--E
--S 141
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E
--S 142
ee:=atanrule dd
 

                      2              2
                     x  + 2%i a x - a                 - x + %i a
        - %i m x log(-----------------) - 2%i m x log(----------)
                      2              2                 x + %i a
                     x  - 2%i a x - a
   (7)  ---------------------------------------------------------
                                    4
                                             Type: Expression Complex Integer
--R
--R                      2              2
--R                     x  + 2%i a x - a                 - x + %i a
--R        - %i m x log(-----------------) - 2%i m x log(----------)
--R                      2              2                 x + %i a
--R                     x  - 2%i a x - a
--R   (7)  ---------------------------------------------------------
--R                                    4
--R                                             Type: Expression Complex Integer
--E
--S 143    14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
ff:=expandLog ee
 

          %i m x log(- 1)
   (8)  - ---------------
                 2
                                             Type: Expression Complex Integer
--R
--R          %i m x log(- 1)
--R   (8)  - ---------------
--R                 2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 144    14:506 Axiom cannot compute this integral
aa:=integrate(x^m*acot(x/a),x)
 

           x
         ++       %K   m
   (1)   |   acot(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   acot(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 145    14:507 Axiom cannot compute this integral
aa:=integrate(x^m*asec(x/a),x)
 

           x
         ++       %K   m
   (1)   |   asec(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   asec(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 146    14:508 Axiom cannot compute this integral
aa:=integrate(x^m*acsc(x/a),x)
 

           x
         ++       %K   m
   (1)   |   acsc(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   acsc(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to tanhcoth.output (2009/2/17, 18:0:58).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
[[0.00,0.00000000,tanh(0.00),tanh(0.00)-0.00000000],_
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[1.99,0.96331422,tanh(1.99),tanh(1.99)-0.96331422],_
[2.00,0.96402758,tanh(2.00),tanh(2.00)-0.96402758]]
 

   (1)
   [[0.0,0.0,0.0,0.0],
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    [0.03,0.029991,0.0299910032 3882014458 6,0.3238820144 586 E -8],
    [0.04,0.03997868,0.0399786803 1116357051,0.3111635705 1 E -9],
    [0.05,0.04995838,0.0499583749 5787997219 8,- 0.5042120027 802 E -8],
    [0.06,0.0599281,0.0599281035 2914350154 2,0.3529143501 54 E -8],
    [0.07,0.06988589,0.0698858903 1642898589,0.3164289858 9 E -9],
    [0.08,0.07982977,0.0798297691 1113136183 9,- 0.8888686381 61 E -9],
    [0.09,0.08975779,0.0897577847 4716010803 6,- 0.5252839891 96 E -8],
    [0.1,0.099668,0.0996679946 2495581711 9,- 0.5375044182 88 E -8],
    [0.11,0.10955847,0.1095584702 1442952908,0.2144295290 8 E -9],
    [0.12,0.1194273,0.1194272985 3438588961,- 0.1465614110 39 E -8],
    [0.13,0.12927258,0.1292725836 0605833328,0.3606058333 28 E -8],
    [0.14,0.13909245,0.1390924478 784580318,- 0.2121541968 2 E -8],
    [0.15,0.14888503,0.1488850336 233179743,0.3623317974 3 E -8],
    [0.16,0.1586485,0.1586485042 9749891877,0.4297498918 77 E -8],
    [0.17,0.16838105,0.1683810458 7081470823,- 0.4129185291 77 E -8],
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R                                                        Type: List List Float
--E 1
--S 2 of 2
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   (2)
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    [2.0,1.0373147,1.0373147207 275480959,0.2072754809 59 E -7]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,100.0033333,100.0033333111 1132275,0.3111113227 5 E -6],
--R    [0.02,50.0066665,50.0066664888 95661105,- 0.111043389 E -7],
--R    [0.03,33.3433327,33.3433327333 84757277,0.3338475727 7 E -7],
--R    [0.04,25.0133319,25.0133319113 27796018,0.1132779602 E -7],
--R    [0.05,20.0166639,20.0166638895 50099248,- 0.1044990075 E -7],
--R    [0.06,16.6866619,16.6866618683 11788711,- 0.3168821128 9 E -7],
--R    [0.07,14.30904,14.3090400003 80691777,0.380691777 E -9],
--R    [0.08,12.5266553,12.5266552958 19479794,- 0.4180520206 E -8],
--R    [0.09,11.1410949,11.1410949235 98139558,0.2359813955 8 E -7],
--R    [0.1,10.0333111,10.0333111322 5398961,0.3225398961 E -7],
--R    [0.11,9.1275462,9.1275462138 41655179,0.1384165517 9 E -7],
--R    [0.12,8.373295,8.3732949859 20466106,- 0.1407953389 4 E -7],
--R    [0.13,7.7355923,7.7355922818 667577388,- 0.1813324226 1 E -7],
--R    [0.14,7.1894629,7.1894629453 485603813,0.4534856038 12 E -7],
--R    [0.15,6.7165918,6.7165918270 201652046,0.2702016520 5 E -7],
--R    [0.16,6.3032425,6.3032425324 653055781,0.3246530557 81 E -7],
--R    [0.17,5.9389107,5.9389107296 982815716,0.2969828157 2 E -7],
--R    [0.18,5.6154264,5.6154263541 72649833,- 0.4582735016 7 E -7],
--R    [0.19,5.3263393,5.3263393280 051508097,0.2800515081 E -7],
--R    [0.2,5.0664896,5.0664895634 394727136,- 0.3656052728 64 E -7],
--R    [0.21,4.8316998,4.8316998224 69838787,0.2246983878 7 E -7],
--R    [0.22,4.6185523,4.6185523420 28042354,0.4202804235 4 E -7],
--R    [0.23,4.4242237,4.4242237308 667251076,0.3086672510 75 E -7],
--R    [0.24,4.2463611,4.2463611422 274259979,0.4222742599 79 E -7],
--R    [0.25,4.0829882,4.0829881650 735965683,- 0.3492640343 17 E -7],
--R    [0.26,3.9324324,3.9324324327 36408036,0.3273640803 6 E -7],
--R    [0.27,3.7932693,3.7932693185 329284388,0.1853292843 88 E -7],
--R    [0.28,3.6642777,3.6642776966 135092065,- 0.3386490793 5 E -8],
--R    [0.29,3.5444049,3.5444048557 416074988,- 0.4425839250 12 E -7],
--R    [0.3,3.4327384,3.4327384303 217415894,0.3032174158 94 E -7],
--R    [0.31,3.3284838,3.3284837641 356108564,- 0.3586438914 36 E -7],
--R    [0.32,3.2309455,3.2309455183 814022485,0.1838140224 85 E -7],
--R    [0.33,3.1395126,3.1395126237 094799327,0.2370947993 27 E -7],
--R    [0.34,3.0536459,3.0536458877 845481399,- 0.1221545186 E -7],
--R    [0.35,2.9728677,2.9728677272 689265964,0.2726892659 64 E -7],
--R    [0.36,2.8967536,2.8967536111 449900164,0.1114499001 6 E -7],
--R    [0.37,2.8249249,2.8249248916 098377328,- 0.8390162267 1 E -8],
--R    [0.38,2.7570428,2.7570427669 367181087,- 0.3306328189 13 E -7],
--R    [0.39,2.6928032,2.6928031731 296236301,- 0.2687037636 99 E -7],
--R    [0.4,2.6319324,2.6319324418 321883572,0.4183218835 72 E -7],
--R    [0.41,2.5741836,2.5741835936 66919577,- 0.6333080423 E -8],
--R    [0.42,2.5193332,2.5193331610 996456868,- 0.3890035431 32 E -7],
--R    [0.43,2.4671785,2.4671784546 273392718,- 0.4537266072 82 E -7],
--R    [0.44,2.4175352,2.4175352017 605355925,0.1760535592 E -8],
--R    [0.45,2.3702355,2.3702355008 100157433,0.8100157433 E -9],
--R    [0.46,2.325126,2.3251260415 726980245,0.4157269802 45 E -7],
--R    [0.47,2.2820666,2.2820665531 657326625,- 0.4683426733 75 E -7],
--R    [0.48,2.2409284,2.2409284458 829619758,0.4588296197 58 E -7],
--R    [0.49,2.2015936,2.2015936193 562076931,0.1935620769 3 E -7],
--R    [0.5,2.1639534,2.1639534137 386528488,0.1373865284 9 E -7],
--R    [0.51,2.1279077,2.1279076842 79778673,- 0.1572022132 7 E -7],
--R    [0.52,2.093364,2.0933639826 813995967,- 0.1731860040 33 E -7],
--R    [0.53,2.0602368,2.0602368311 315780091,0.3113157800 91 E -7],
--R    [0.54,2.0284471,2.0284470770 025658705,- 0.2299743412 95 E -7],
--R    [0.55,1.9979213,1.9979213179 463896248,0.1794638962 48 E -7],
--R    [0.56,1.9685914,1.9685913885 883209462,- 0.1141167905 38 E -7],
--R    [0.57,1.9403939,1.9403939012 535294422,0.1253529442 2 E -8],
--R    [0.58,1.9132698,1.9132698342 056208124,0.3420562081 24 E -7],
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--R    [0.62,1.8144604,1.8144604306 416324911,0.3064163249 11 E -7],
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--R    [0.67,1.7094605,1.7094604947 361744339,- 0.5263825566 1 E -8],
--R    [0.68,1.6905616,1.6905616412 966267409,0.4129662674 09 E -7],
--R    [0.69,1.6722911,1.6722911378 028518669,0.3780285186 7 E -7],
--R    [0.7,1.6546216,1.6546216358 026294047,0.3580262940 47 E -7],
--R    [0.71,1.6375273,1.6375273242 106478561,0.2421064785 61 E -7],
--R    [0.72,1.6209838,1.6209838226 402554549,0.2264025545 49 E -7],
--R    [0.73,1.6049681,1.6049680835 025519782,- 0.1649744802 18 E -7],
--R    [0.74,1.5894583,1.5894583020 434418638,0.2043441863 8 E -8],
--R    [0.75,1.5744338,1.5744338335 777364887,0.3357773648 87 E -7],
--R    [0.76,1.5598751,1.5598751172 573846082,0.1725738460 82 E -7],
--R    [0.77,1.5457636,1.5457636057 797852649,0.5779785264 9 E -8],
--R    [0.78,1.5320817,1.5320817005 030656562,0.5030656562 E -9],
--R    [0.79,1.5188127,1.5188126914 891934625,- 0.8510806537 49 E -8],
--R    [0.8,1.5059407,1.5059407020 437066212,0.2043706621 2 E -8],
--R    [0.81,1.4934506,1.4934506373 634333213,0.3736343332 13 E -7],
--R    [0.82,1.4813281,1.4813281369 414902969,0.3694149029 69 E -7],
--R    [0.83,1.4695595,1.4695595304 126515262,0.3041265152 62 E -7],
--R    [0.84,1.4581318,1.4581317965 523616189,- 0.3447638381 1 E -8],
--R    [0.85,1.4470325,1.4470325251 696546055,0.2516965460 55 E -7],
--R    [0.86,1.4362499,1.4362498816 584011227,- 0.1834159887 73 E -7],
--R    [0.87,1.4257726,1.4257725739 929697346,- 0.2600703026 54 E -7],
--R    [0.88,1.4155898,1.4155898219 738353763,0.2197383537 63 E -7],
--R    [0.89,1.4056913,1.4056913285 461485888,0.2854614858 88 E -7],
--R    [0.9,1.3960673,1.3960672530 300118351,- 0.4696998816 49 E -7],
--R    [0.91,1.3867082,1.3867081861 153858453,- 0.1388461415 47 E -7],
--R    [0.92,1.3776051,1.3776051264 873387552,0.2648733875 52 E -7],
--R    [0.93,1.3687495,1.3687494589 589029032,- 0.4104109709 68 E -7],
--R    [0.94,1.3601329,1.3601329339 992502041,0.3399925020 41 E -7],
--R    [0.95,1.3517476,1.3517476485 543534541,0.4855435345 41 E -7],
--R    [0.96,1.343586,1.3435860280 658708165,0.2806587081 65 E -7],
--R    [0.97,1.3356408,1.3356408096 017654982,0.9601765498 2 E -8],
--R    [0.98,1.327905,1.3279050260 192333791,0.2601923337 91 E -7],
--R    [0.99,1.320372,1.3203719910 869302267,- 0.8913069773 26 E -8],
--R    [1.0,1.3130353,1.3130352854 993313036,- 0.1450066869 64 E -7],
--R    [1.01,1.3058887,1.3058887437 213768521,0.4372137685 21 E -7],
--R    [1.02,1.2989264,1.2989264416 064081471,0.4160640814 71 E -7],
--R    [1.03,1.2921427,1.2921426847 348261269,- 0.1526517387 31 E -7],
--R    [1.04,1.285532,1.2855319974 249487926,- 0.2575051207 4 E -8],
--R    [1.05,1.2790891,1.2790891123 712411139,0.1237124111 39 E -7],
--R    [1.06,1.272809,1.2728089608 684747719,- 0.3913152522 81 E -7],
--R    [1.07,1.2666867,1.2666866635 834740719,- 0.3641652592 81 E -7],
--R    [1.08,1.2607175,1.2607175218 389451031,0.2183894510 31 E -7],
--R    [1.09,1.254897,1.2548970093 764914129,0.9376491412 86 E -8],
--R    [1.1,1.2492208,1.2492207645 683124166,- 0.3543168758 34 E -7],
--R    [1.11,1.2436846,1.2436845830 492796933,- 0.1695072030 67 E -7],
--R    [1.12,1.2382844,1.2382844107 43108546,0.1074310854 6 E -7],
--R    [1.13,1.2330163,1.2330163372 582033675,0.3725820336 75 E -7],
--R    [1.14,1.2278766,1.2278765896 304695801,- 0.1036953041 99 E -7],
--R    [1.15,1.2228615,1.2228615263 919649847,0.2639196498 47 E -7],
--R    [1.16,1.2179676,1.2179676319 457208259,0.3194572082 59 E -7],
--R    [1.17,1.2131915,1.2131915112 284082387,0.1122840823 87 E -7],
--R    [1.18,1.2085299,1.2085298846 437684793,- 0.1535623152 07 E -7],
--R    [1.19,1.2039796,1.2039795832 508740941,- 0.1674912590 59 E -7],
--R    [1.2,1.1995375,1.1995375441 923507667,0.4419235076 67 E -7],
--R    [1.21,1.1952008,1.1952008063 486731313,0.6348673131 3 E -8],
--R    [1.22,1.1909665,1.1909665062 055588292,0.6205558829 2 E -8],
--R    [1.23,1.1868319,1.1868318739 22329409,- 0.2607767059 1 E -7],
--R    [1.24,1.1827942,1.1827942295 898897106,0.2958988971 06 E -7],
--R    [1.25,1.178851,1.1788509796 677040268,- 0.2033229597 32 E -7],
--R    [1.26,1.1749996,1.1749996135 898220841,0.1358982208 41 E -7],
--R    [1.27,1.1712377,1.1712377005 306348077,0.5306348077 E -9],
--R    [1.28,1.1675629,1.1675628863 216226741,- 0.1367837732 59 E -7],
--R    [1.29,1.1639729,1.1639728905 10901625,- 0.9489098374 98 E -8],
--R    [1.3,1.1604655,1.1604655035 578761464,0.3557876146 4 E -8],
--R    [1.31,1.1570386,1.1570385841 557790704,- 0.1584422092 96 E -7],
--R    [1.32,1.1536901,1.1536900566 75315566,- 0.4332468443 4 E -7],
--R    [1.33,1.1504179,1.1504179087 23037052,0.8723037051 99 E -8],
--R    [1.34,1.1472202,1.1472201888 084516077,- 0.1119154839 23 E -7],
--R    [1.35,1.144095,1.1440950041 142329045,0.4114232904 5 E -8],
--R    [1.36,1.1410405,1.1410405183 642215979,0.1836422159 79 E -7],
--R    [1.37,1.138055,1.1380549497 842232286,- 0.5021577677 14 E -7],
--R    [1.38,1.1351366,1.1351365691 508965597,- 0.3084910344 03 E -7],
--R    [1.39,1.1322837,1.1322836979 242973771,- 0.2075702622 9 E -8],
--R    [1.4,1.1294947,1.1294947064 598964505,0.6459896450 5 E -8],
--R    [1.41,1.126768,1.1267680122 961278243,0.1229612782 43 E -7],
--R    [1.42,1.1241021,1.1241020785 137460187,- 0.2148625398 13 E -7],
--R    [1.43,1.1214954,1.1214954121 634791355,0.1216347913 55 E -7],
--R    [1.44,1.1189466,1.1189465627 586602379,- 0.3724133976 21 E -7],
--R    [1.45,1.1164541,1.1164541208 297026222,0.2082970262 22 E -7],
--R    [1.46,1.1140167,1.1140167165 374565427,0.1653745654 27 E -7],
--R    [1.47,1.111633,1.1116330183 426463597,0.1834264635 97 E -7],
--R    [1.48,1.1093017,1.1093017317 287386746,0.3172873867 46 E -7],
--R    [1.49,1.1070216,1.1070215979 757344389,- 0.2024265561 1 E -8],
--R    [1.5,1.1047914,1.1047913929 825119039,- 0.7017488096 1 E -8],
--R    [1.51,1.1026099,1.1026099261 354731665,0.2613547316 65 E -7],
--R    [1.52,1.100476,1.1004760392 213654987,0.3922136549 87 E -7],
--R    [1.53,1.0983886,1.0983886053 822601088,0.5382260108 8 E -8],
--R    [1.54,1.0963465,1.0963465281 107759211,0.2811077592 11 E -7],
--R    [1.55,1.0943487,1.0943487402 837348018,0.4028373480 18 E -7],
--R    [1.56,1.0923942,1.0923942032 325277949,0.3232527794 9 E -8],
--R    [1.57,1.0904819,1.0904819058 485597183,0.5848559718 3 E -8],
--R    [1.58,1.0886109,1.0886108637 222222566,- 0.3627777774 34 E -7],
--R    [1.59,1.0867801,1.0867801183 139237769,0.1831392377 69 E -7],
--R    [1.6,1.0849887,1.0849887361 557777925,0.3615577779 25 E -7],
--R    [1.61,1.0832358,1.0832358080 826215661,0.8082621566 08 E -8],
--R    [1.62,1.0815204,1.0815204484 911020471,0.4849110204 71 E -7],
--R    [1.63,1.0798418,1.0798417946 256284042,- 0.5374371595 8 E -8],
--R    [1.64,1.078199,1.0781990058 90049072,0.5890049072 E -8],
--R    [1.65,1.0765913,1.0765912631 839666847,- 0.3681603331 53 E -7],
--R    [1.66,1.0750178,1.0750177682 626567093,- 0.3173734329 07 E -7],
--R    [1.67,1.0734777,1.0734777431 19605205,0.4311960520 5 E -7],
--R    [1.68,1.0719704,1.0719704293 907280832,0.2939072808 32 E -7],
--R    [1.69,1.0704951,1.0704950877 793786871,- 0.1222062131 29 E -7],
--R    [1.7,1.069051,1.0690509975 012925984,- 0.2498707401 6 E -8],
--R    [1.71,1.0676375,1.0676374557 486584477,- 0.4425134155 23 E -7],
--R    [1.72,1.0662538,1.0662537771 725412807,- 0.2282745871 93 E -7],
--R    [1.73,1.0648993,1.0648992933 829208457,- 0.6617079154 3 E -8],
--R    [1.74,1.0635734,1.0635733524 656411166,- 0.4753435888 34 E -7],
--R    [1.75,1.0622753,1.0622753185 155995724,0.1851559957 24 E -7],
--R    [1.76,1.0610046,1.0610045711 855353057,- 0.2881446469 43 E -7],
--R    [1.77,1.0597605,1.0597605052 49804028,0.5249804028 E -8],
--R    [1.78,1.0585425,1.0585425301 825555676,0.3018255556 76 E -7],
--R    [1.79,1.0573501,1.0573500697 497555933,- 0.3025024440 67 E -7],
--R    [1.8,1.0561826,1.0561825616 145181279,- 0.3838548187 21 E -7],
--R    [1.81,1.0550395,1.0550394569 552390051,- 0.4304476099 49 E -7],
--R    [1.82,1.0539202,1.0539202200 960428446,0.2009604284 46 E -7],
--R    [1.83,1.0528243,1.0528243281 490774395,0.2814907743 95 E -7],
--R    [1.84,1.0517513,1.0517512706 682097163,- 0.2933179028 37 E -7],
--R    [1.85,1.0507005,1.0507005493 136967107,0.4931369671 07 E -7],
--R    [1.86,1.0496717,1.0496716775 274233515,- 0.2247257664 85 E -7],
--R    [1.87,1.0486642,1.0486641802 183162995,- 0.1978168370 05 E -7],
--R    [1.88,1.0476776,1.0476775934 575597155,- 0.6542440284 5 E -8],
--R    [1.89,1.0467115,1.0467114641 832546561,- 0.3581674534 39 E -7],
--R    [1.9,1.0457653,1.0457653499 141788749,0.4991417887 49 E -7],
--R    [1.91,1.0448388,1.0448388184 72318166,0.1847231816 6 E -7],
--R    [1.92,1.0439314,1.0439314477 1385408,0.4771385408 E -7],
--R    [1.93,1.0430428,1.0430428252 683058841,0.2526830588 41 E -7],
--R    [1.94,1.0421725,1.0421725482 855370847,0.4828553708 47 E -7],
--R    [1.95,1.0413202,1.0413202231 90348688,0.2319034868 8 E -7],
--R    [1.96,1.0404855,1.0404854654 443926981,- 0.3455560730 19 E -7],
--R    [1.97,1.0396679,1.0396678993 151501465,- 0.6848498535 E -9],
--R    [1.98,1.0388672,1.0388671576 517282541,- 0.4234827174 59 E -7],
--R    [1.99,1.0380829,1.0380828816 672411665,- 0.1833275883 35 E -7],
--R    [2.0,1.0373147,1.0373147207 275480959,0.2072754809 59 E -7]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to exlap.output (2009/2/17, 17:45:46).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
laplace(2/t * (1 - cos(a*t)), t, s)
 

             2    2
   (1)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R             2    2
--R   (1)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 6
laplace((exp(a*t) - exp(b*t))/t, t, s)
 

   (2)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
laplace(exp(a*t+b)*Ei(c*t), t, s)
 

          b    s + c - a
        %e log(---------)
                   c
   (3)  -----------------
              s - a
                                                     Type: Expression Integer
--R 
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (3)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 6
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
 

               2    2
              s  + b             d
        a log(-------) + 2c atan(-)
                  2              s
                 b
   (1)  ---------------------------
                     2s
                                                     Type: Expression Integer
--R 
--R
--R               2    2
--R              s  + b             d
--R        a log(-------) + 2c atan(-)
--R                  2              s
--R                 b
--R   (1)  ---------------------------
--R                     2s
--R                                                     Type: Expression Integer
--E 4

)clear all
 
   All user variables and function definitions have been cleared.

--S 5 of 6
laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s)
 

             3
           4a
   (1)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R             3
--R           4a
--R   (1)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 5

)clear all
 
   All user variables and function definitions have been cleared.

--S 6 of 6
laplace(t**4 * exp(-a*t) / factorial(4), t, s)
 

                            1
   (1)  ----------------------------------------
         5       4      2 3      3 2     4     5
        s  + 5a s  + 10a s  + 10a s  + 5a s + a
                                                     Type: Expression Integer
--R 
--R
--R                            1
--R   (1)  ----------------------------------------
--R         5       4      2 3      3 2     4     5
--R        s  + 5a s  + 10a s  + 10a s  + 5a s + a
--R                                                     Type: Expression Integer
--E 6
)spool 
 
Starts dribbling to intg0.output (2009/2/17, 17:46:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 25
y := sqrt(a * x + b)
 

         +-------+
   (1)  \|a x + b
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R   (1)  \|a x + b
--R                                                     Type: Expression Integer
--E 1

--S 2 of 25
integrate(y,x)
 

                    +-------+
        (2a x + 2b)\|a x + b
   (2)  ---------------------
                  3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-------+
--R        (2a x + 2b)\|a x + b
--R   (2)  ---------------------
--R                  3a
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 25
t1:=x * y
 

          +-------+
   (3)  x\|a x + b
                                                     Type: Expression Integer
--R 
--R
--R          +-------+
--R   (3)  x\|a x + b
--R                                                     Type: Expression Integer
--E 3

--S 4 of 25
integrate(t1,x)
 

           2 2              2  +-------+
        (6a x  + 2a b x - 4b )\|a x + b
   (4)  --------------------------------
                         2
                      15a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2              2  +-------+
--R        (6a x  + 2a b x - 4b )\|a x + b
--R   (4)  --------------------------------
--R                         2
--R                      15a
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 25
z := sqrt(a**2 - x**2)
 

         +---------+
         |   2    2
   (5)  \|- x  + a
                                                     Type: Expression Integer
--R 
--R
--R         +---------+
--R         |   2    2
--R   (5)  \|- x  + a
--R                                                     Type: Expression Integer
--E 5

--S 6 of 25
t2:=1 / z
 

              1
   (6)  ------------
         +---------+
         |   2    2
        \|- x  + a
                                                     Type: Expression Integer
--R 
--R
--R              1
--R   (6)  ------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a
--R                                                     Type: Expression Integer
--E 6

--S 7 of 25
integrate(t2,x)
 

                 +---------+
                 |   2    2
                \|- x  + a   - a
   (7)  - 2atan(----------------)
                        x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   - a
--R   (7)  - 2atan(----------------)
--R                        x
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 25
t3:=x**2 * z
 

           +---------+
         2 |   2    2
   (8)  x \|- x  + a
                                                     Type: Expression Integer
--R 
--R
--R           +---------+
--R         2 |   2    2
--R   (8)  x \|- x  + a
--R                                                     Type: Expression Integer
--E 8

--S 9 of 25
integrate(t3,x)
 

   (9)
                           +---------+
               5 2      7  |   2    2      4 4      6 2      8
         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                    +---------+
        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
  /
                     +---------+
           2      3  |   2    2      4      2 2      4
     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (9)
--R                           +---------+
--R               5 2      7  |   2    2      4 4      6 2      8
--R         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                    +---------+
--R        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
--R     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
--R  /
--R                     +---------+
--R           2      3  |   2    2      4      2 2      4
--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 25
t4:=x**3 / (a+b*x)**(1/3)
 

              3
             x
   (10)  ----------
         3+-------+
         \|b x + a
                                                     Type: Expression Integer
--R 
--R
--R              3
--R             x
--R   (10)  ----------
--R         3+-------+
--R         \|b x + a
--R                                                     Type: Expression Integer
--E 10

--S 11 of 25
integrate(t4,x)
 

              3 3         2 2       2          3 3+-------+2
         (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
   (11)  ---------------------------------------------------
                                    4
                                440b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3 3         2 2       2          3 3+-------+2
--R         (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
--R   (11)  ---------------------------------------------------
--R                                    4
--R                                440b
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 25
t5:=1 / (x**3 * (a+b*x)**(1/3))
 

               1
   (12)  ------------
          3 3+-------+
         x  \|b x + a
                                                     Type: Expression Integer
--R 
--R
--R               1
--R   (12)  ------------
--R          3 3+-------+
--R         x  \|b x + a
--R                                                     Type: Expression Integer
--E 12

--S 13 of 25
integrate(t5,x)
 

   (13)
           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
     + 
         2 2 +-+    3+-+2 3+-------+
       4b x \|3 log(\|a   \|b x + a - a)
     + 
                  +-+3+-+2 3+-------+    +-+
        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
                             3a
  /
        2 2 +-+3+-+
     18a x \|3 \|a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (13)
--R           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
--R       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
--R     + 
--R         2 2 +-+    3+-+2 3+-------+
--R       4b x \|3 log(\|a   \|b x + a - a)
--R     + 
--R                  +-+3+-+2 3+-------+    +-+
--R        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
--R     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
--R                             3a
--R  /
--R        2 2 +-+3+-+
--R     18a x \|3 \|a
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 25
t6:=x / (y + y**2) + log(y + 1)
 

           +-------+                +-------+
         (\|a x + b  + a x + b)log(\|a x + b  + 1) + x
   (14)  ---------------------------------------------
                       +-------+
                      \|a x + b  + a x + b
                                                     Type: Expression Integer
--R 
--R
--R           +-------+                +-------+
--R         (\|a x + b  + a x + b)log(\|a x + b  + 1) + x
--R   (14)  ---------------------------------------------
--R                       +-------+
--R                      \|a x + b  + a x + b
--R                                                     Type: Expression Integer
--E 14

--S 15 of 25
integrate(t6,x)
 

   (15)
          2                            +-------+                 +-------+
       (2a x + (2a - 4)b - 2a + 4)log(\|a x + b  + 1) + (2a - 4)\|a x + b
     + 
           2
       (- a  + 2a)x
  /
       2
     2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (15)
--R          2                            +-------+                 +-------+
--R       (2a x + (2a - 4)b - 2a + 4)log(\|a x + b  + 1) + (2a - 4)\|a x + b
--R     + 
--R           2
--R       (- a  + 2a)x
--R  /
--R       2
--R     2a
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 25
t7:=(2 + 1/sqrt(x)) * cos(x + sqrt x)
 

            +-+          +-+
         (2\|x  + 1)cos(\|x  + x)
   (16)  ------------------------
                    +-+
                   \|x
                                                     Type: Expression Integer
--R 
--R
--R            +-+          +-+
--R         (2\|x  + 1)cos(\|x  + x)
--R   (16)  ------------------------
--R                    +-+
--R                   \|x
--R                                                     Type: Expression Integer
--E 16

--S 17 of 25
integrate(t7,x)
 

               +-+
   (17)  2sin(\|x  + x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-+
--R   (17)  2sin(\|x  + x)
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 25
t8:=log(1 + y) / x
 

              +-------+
         log(\|a x + b  + 1)
   (18)  -------------------
                  x
                                                     Type: Expression Integer
--R 
--R
--R              +-------+
--R         log(\|a x + b  + 1)
--R   (18)  -------------------
--R                  x
--R                                                     Type: Expression Integer
--E 18

--S 19 of 25
integrate(t8,x)
 

            x      +--------+
          ++  log(\|b + %N a  + 1)
   (19)   |   -------------------- d%N
         ++            %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x      +--------+
--I          ++  log(\|b + %K a  + 1)
--I   (19)   |   -------------------- d%K
--I         ++            %K
--R                                          Type: Union(Expression Integer,...)
--E 19

--S 20 of 25
t9:=(sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b))))
 

                   +-----+          +-----+
             sinh(\|x + b  + 1) + 2\|x + b
   (20)  --------------------------------------
          +-----+      +-----+          +-----+
         \|x + b cosh(\|x + b  + 1) + x\|x + b
                                                     Type: Expression Integer
--R 
--R
--R                   +-----+          +-----+
--R             sinh(\|x + b  + 1) + 2\|x + b
--R   (20)  --------------------------------------
--R          +-----+      +-----+          +-----+
--R         \|x + b cosh(\|x + b  + 1) + x\|x + b
--R                                                     Type: Expression Integer
--E 20

--S 21 of 25
integrate(t9,x)
 

                              +-----+
                     - 2cosh(\|x + b  + 1) - 2x            +-----+
   (21)  2log(---------------------------------------) - 2\|x + b
                    +-----+              +-----+
              sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              +-----+
--R                     - 2cosh(\|x + b  + 1) - 2x            +-----+
--R   (21)  2log(---------------------------------------) - 2\|x + b
--R                    +-----+              +-----+
--R              sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
--R                                          Type: Union(Expression Integer,...)
--E 21

--S 22 of 25
t10:=tan(atan(x)/2)
 

             atan(x)
   (22)  tan(-------)
                2
                                                     Type: Expression Integer
--R 
--R
--R             atan(x)
--R   (22)  tan(-------)
--R                2
--R                                                     Type: Expression Integer
--E 22

--S 23 of 25
integrate(t10,x)
 

   (23)
           +------+          +------+
           | 2               | 2
       (- \|x  + 1  + x)log(\|x  + 1  - x + 1)
     + 
         +------+          +------+                           +------+
         | 2               | 2                                | 2
       (\|x  + 1  - x)log(\|x  + 1  - x - 1) + (- log(x) - x)\|x  + 1
     + 
                   2
       x log(x) + x  + 1
  /
      +------+
      | 2
     \|x  + 1  - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (23)
--R           +------+          +------+
--R           | 2               | 2
--R       (- \|x  + 1  + x)log(\|x  + 1  - x + 1)
--R     + 
--R         +------+          +------+                           +------+
--R         | 2               | 2                                | 2
--R       (\|x  + 1  - x)log(\|x  + 1  - x - 1) + (- log(x) - x)\|x  + 1
--R     + 
--R                   2
--R       x log(x) + x  + 1
--R  /
--R      +------+
--R      | 2
--R     \|x  + 1  - x
--R                                          Type: Union(Expression Integer,...)
--E 23

--S 24 of 25
t11:=tan(atan(x)/3)
 

             atan(x)
   (24)  tan(-------)
                3
                                                     Type: Expression Integer
--R 
--R
--R             atan(x)
--R   (24)  tan(-------)
--R                3
--R                                                     Type: Expression Integer
--E 24

--S 25 of 25
integrate(t11,x)
 

                   atan(x) 2             atan(x) 2           atan(x)
         8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
                      3                     3                   3
   (25)  ------------------------------------------------------------
                                      18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   atan(x) 2             atan(x) 2           atan(x)
--R         8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
--R                      3                     3                   3
--R   (25)  ------------------------------------------------------------
--R                                      18
--R                                          Type: Union(Expression Integer,...)
--E 25
)spool 
 
Starts dribbling to typetower.output (2009/2/17, 18:1:33).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 17
F:=PrimeField 3
 

   (1)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 3
--R                                                                 Type: Domain
--E 1

--S 2 of 17
P:=UnivariatePolynomial(x,F)
 

   (2)  UnivariatePolynomial(x,PrimeField 3)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,PrimeField 3)
--R                                                                 Type: Domain
--E 2

--S 3 of 17
S:=SquareMatrix(2,P)
 

   (3)  SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
                                                                 Type: Domain
--R 
--R
--R   (3)  SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--R                                                                 Type: Domain
--E 3

--S 4 of 17
R:=UnivariatePolynomial(z,S)
 

   (4)
   UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
                                                                 Type: Domain
--R 
--R
--R   (4)
--R   UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R                                                                 Type: Domain
--E 4


--S 5 of 17
s1:S:=matrix [[2*x+1,x^2-1],[0,x-1]]
 

        +         2    +
   (5)  |2x + 1  x  + 2|
        |              |
        +  0     x + 2 +
                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--R 
--R
--R        +         2    +
--R   (5)  |2x + 1  x  + 2|
--R        |              |
--R        +  0     x + 2 +
--R                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--E 5

--S 6 of 17
s2:=transpose s1
 

        +2x + 1    0  +
   (6)  |             |
        | 2           |
        +x  + 2  x + 2+
                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--R 
--R
--R        +2x + 1    0  +
--R   (6)  |             |
--R        | 2           |
--R        +x  + 2  x + 2+
--R                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--E 6


--S 7 of 17
r:R:=z^2+s1*z+s2
 

         2   +         2    +    +2x + 1    0  +
   (7)  z  + |2x + 1  x  + 2|z + |             |
             |              |    | 2           |
             +  0     x + 2 +    +x  + 2  x + 2+
Type: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R 
--R
--R         2   +         2    +    +2x + 1    0  +
--R   (7)  z  + |2x + 1  x  + 2|z + |             |
--R             |              |    | 2           |
--R             +  0     x + 2 +    +x  + 2  x + 2+
--RType: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--E 7

--S 8 of 17
r+2*r
 

   (8)  0
Type: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R 
--R
--R   (8)  0
--RType: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--E 8


--S 9 of 17
degree r
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9


--S 10 of 17
r2:=r*r
 

   (10)
                               + 2             +     + 4              +
      4   +         2    + 3   |x  + 2x    0   | 2   |x  + 2x     0   |
     z  + |x + 2  2x  + 1|z  + |               |z  + |                |z
          |              |     |  2       2    |     |          4     |
          +  0    2x + 1 +     +2x  + 1  x  + 2+     +   0     x  + 2x+
   + 
     + 2                    +
     |x  + x + 1      0     |
     |                      |
     |             2        |
     +    0       x  + x + 1+
Type: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R 
--R
--R   (10)
--R                               + 2             +     + 4              +
--R      4   +         2    + 3   |x  + 2x    0   | 2   |x  + 2x     0   |
--R     z  + |x + 2  2x  + 1|z  + |               |z  + |                |z
--R          |              |     |  2       2    |     |          4     |
--R          +  0    2x + 1 +     +2x  + 1  x  + 2+     +   0     x  + 2x+
--R   + 
--R     + 2                    +
--R     |x  + x + 1      0     |
--R     |                      |
--R     |             2        |
--R     +    0       x  + x + 1+
--RType: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--E 10


--S 11 of 17
gcd(r2,r)
 
   There are 4 exposed and 3 unexposed library operations named gcd 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op gcd
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named gcd 
      with argument type(s) 
UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 4 exposed and 3 unexposed library operations named gcd 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op gcd
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named gcd 
--R      with argument type(s) 
--RUnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--RUnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11


--S 12 of 17
p1:=s1(1,1)
 

   (11)  2x + 1
                                   Type: UnivariatePolynomial(x,PrimeField 3)
--R 
--R
--R   (11)  2x + 1
--R                                   Type: UnivariatePolynomial(x,PrimeField 3)
--E 12

--S 13 of 17
ps:=s1(1,2)
 

          2
   (12)  x  + 2
                                   Type: UnivariatePolynomial(x,PrimeField 3)
--R 
--R
--R          2
--R   (12)  x  + 2
--R                                   Type: UnivariatePolynomial(x,PrimeField 3)
--E 13

--S 14 of 17
gcd(p1,p2)
 

   (13)  1
          Type: UnivariatePolynomial(p2,UnivariatePolynomial(x,PrimeField 3))
--R 
--R
--R   (13)  1
--R          Type: UnivariatePolynomial(p2,UnivariatePolynomial(x,PrimeField 3))
--E 14


--S 15 of 17
q1:UP(x,INT):=2*x+1
 

   (14)  2x + 1
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (14)  2x + 1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 17
q2:UP(x,INT):=x^2+2
 

          2
   (15)  x  + 2
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R          2
--R   (15)  x  + 2
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 17
gcd(q1,q2)
 

   (16)  1
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 17


)spool 
 
Starts dribbling to fr1.output (2009/2/17, 17:46:9).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 1

--S 2 of 38
unit(g)
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 38
numberOfFactors(g)
 

   (3)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  3
--R                                                        Type: PositiveInteger
--E 4

--S 4 of 38
[nthFactor(g,i) for i in 1..numberOfFactors(g)]
 

   (4)  [2,7,11]
                                                           Type: List Integer
--R 
--R
--R   (4)  [2,7,11]
--R                                                           Type: List Integer
--E 4

--S 5 of 38
[nthExponent(g,i) for i in 1..numberOfFactors(g)]
 

   (5)  [3,2,1]
                                                           Type: List Integer
--R 
--R
--R   (5)  [3,2,1]
--R                                                           Type: List Integer
--E 5

--S 6 of 38
[nthFlag(g,i) for i in 1..numberOfFactors(g)]
 

   (6)  ["prime","prime","prime"]
                               Type: List Union("nil","sqfr","irred","prime")
--R 
--R
--R   (6)  ["prime","prime","prime"]
--R                               Type: List Union("nil","sqfr","irred","prime")
--E 6

--S 7 of 38
factorList(g)
 

   (7)
   [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2],
    [flg= "prime",fctr= 11,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--R 
--R
--R   (7)
--R   [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2],
--R    [flg= "prime",fctr= 11,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--E 7

--S 8 of 38
factors(g)
 

   (8)
   [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]]
                         Type: List Record(factor: Integer,exponent: Integer)
--R 
--R
--R   (8)
--R   [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]]
--R                         Type: List Record(factor: Integer,exponent: Integer)
--E 8

--S 9 of 38
first(%).factor
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9

)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 10

--S 11 of 38
expand(g)
 

   (2)  4312
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  4312
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 38
reduce(*,[t.factor for t in factors(g)])
 

   (3)  154
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  154
--R                                                        Type: PositiveInteger
--E 12

)clear all
 
   All user variables and function definitions have been cleared.

--S 13 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 13

--S 14 of 38
f := factor(246960)
 

         4 2   3
   (2)  2 3 5 7
                                                       Type: Factored Integer
--R 
--R
--R         4 2   3
--R   (2)  2 3 5 7
--R                                                       Type: Factored Integer
--E 14

--S 15 of 38
f * g
 

         7 2   5
   (3)  2 3 5 7 11
                                                       Type: Factored Integer
--R 
--R
--R         7 2   5
--R   (3)  2 3 5 7 11
--R                                                       Type: Factored Integer
--E 15

--S 16 of 38
f**500
 

         2000 1000 500 1500
   (4)  2    3    5   7
                                                       Type: Factored Integer
--R 
--R
--R         2000 1000 500 1500
--R   (4)  2    3    5   7
--R                                                       Type: Factored Integer
--E 16

--S 17 of 38
gcd(f,g)
 

         3 2
   (5)  2 7
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (5)  2 7
--R                                                       Type: Factored Integer
--E 17

--S 18 of 38
lcm(f,g)
 

         4 2   3
   (6)  2 3 5 7 11
                                                       Type: Factored Integer
--R 
--R
--R         4 2   3
--R   (6)  2 3 5 7 11
--R                                                       Type: Factored Integer
--E 18

--S 19 of 38
f + g
 

         3 2
   (7)  2 7 641
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (7)  2 7 641
--R                                                       Type: Factored Integer
--E 19

--S 20 of 38
f - g
 

         3 2
   (8)  2 7 619
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (8)  2 7 619
--R                                                       Type: Factored Integer
--E 20

--S 21 of 38
zero?(factor(0))
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 21

--S 22 of 38
zero?(g)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 22

--S 23 of 38
one?(factor(1))
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 23

--S 24 of 38
one?(f)
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 24

--S 25 of 38
0$Factored(Integer)
 

   (13)  0
                                                       Type: Factored Integer
--R 
--R
--R   (13)  0
--R                                                       Type: Factored Integer
--E 25

--S 26 of 38
1$Factored(Integer)
 

   (14)  1
                                                       Type: Factored Integer
--R 
--R
--R   (14)  1
--R                                                       Type: Factored Integer
--E 26

)clear all
 
   All user variables and function definitions have been cleared.

--S 27 of 38
nilFactor(24,2)
 

          2
   (1)  24
                                                       Type: Factored Integer
--R 
--R
--R          2
--R   (1)  24
--R                                                       Type: Factored Integer
--E 27

--S 28 of 38
nthFlag(%,1)
 

   (2)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (2)  "nil"
--R                                                       Type: Union("nil",...)
--E 28

--S 29 of 38
sqfrFactor(30,2)
 

          2
   (3)  30
                                                       Type: Factored Integer
--R 
--R
--R          2
--R   (3)  30
--R                                                       Type: Factored Integer
--E 29

--S 30 of 38
irreducibleFactor(13,10)
 

          10
   (4)  13
                                                       Type: Factored Integer
--R 
--R
--R          10
--R   (4)  13
--R                                                       Type: Factored Integer
--E 30

--S 31 of 38
primeFactor(11,5)
 

          5
   (5)  11
                                                       Type: Factored Integer
--R 
--R
--R          5
--R   (5)  11
--R                                                       Type: Factored Integer
--E 31

--S 32 of 38
h := factor(-720)
 

           4 2
   (6)  - 2 3 5
                                                       Type: Factored Integer
--R 
--R
--R           4 2
--R   (6)  - 2 3 5
--R                                                       Type: Factored Integer
--E 32

--S 33 of 38
h - makeFR(unit(h),factorList(h))
 

   (7)  0
                                                       Type: Factored Integer
--R 
--R
--R   (7)  0
--R                                                       Type: Factored Integer
--E 33

)clear all
 
   All user variables and function definitions have been cleared.

--S 34 of 38
p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63
 

           2            2      2                  2
   (1)  (4x  - 12x + 9)y  + (4x  - 12x + 9)y + 28x  - 84x + 63
                                                     Type: Polynomial Integer
--R 
--R
--R           2            2      2                  2
--R   (1)  (4x  - 12x + 9)y  + (4x  - 12x + 9)y + 28x  - 84x + 63
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 38
fp := factor(p)
 

                2  2
   (2)  (2x - 3) (y  + y + 7)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                2  2
--R   (2)  (2x - 3) (y  + y + 7)
--R                                            Type: Factored Polynomial Integer
--E 35

--S 36 of 38
D(p,x)
 

                  2
   (3)  (8x - 12)y  + (8x - 12)y + 56x - 84
                                                     Type: Polynomial Integer
--R 
--R
--R                  2
--R   (3)  (8x - 12)y  + (8x - 12)y + 56x - 84
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 38
D(fp,x)
 

                   2
   (4)  4(2x - 3)(y  + y + 7)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                   2
--R   (4)  4(2x - 3)(y  + y + 7)
--R                                            Type: Factored Polynomial Integer
--E 37

--S 38 of 38
numberOfFactors(%)
 

   (5)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  3
--R                                                        Type: PositiveInteger
--E 38
)spool 
 
Starts dribbling to tsetcatvermeer.output (2009/2/17, 18:1:18).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 21
ls : List Symbol := [w,v,u,y,x];
 

                                                            Type: List Symbol
--R 
--R
--R                                                            Type: List Symbol
--E 1

--S 2 of 21
V := OVAR(ls);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 2

--S 3 of 21
R := Integer;
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 3

--S 4 of 21
E := IndexedExponents V;
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 4

--S 5 of 21
P := NSMP(R, V);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 5

--S 6 of 21
LP := List(P);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 6

--S 7 of 21
x: P := 'x;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 7

--S 8 of 21
y: P := 'y;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 8

--S 9 of 21
u: P := 'u;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 9

--S 10 of 21
v: P := 'v;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 10

--S 11 of 21
w: P := 'w;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 11

--S 12 of 21
p1 := (x - u) ** 2 + (y - v) ** 2 - 1 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 12

--S 13 of 21
p2 := v ** 2 - u ** 3 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 13

--S 14 of 21
p3 := 2 * v * (x - u) + 3 * u ** 2 * (y - v) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 14

--S 15 of 21
f1 := (3 * w * u ** 2 - 1) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 15

--S 16 of 21
f2 := (2 * w * v - 1) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 16

--S 17 of 21
p4 := f1 * f2 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 17

--S 18 of 21
lp := [p1,p2,p3,p4] ;
 

Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 18

--S 19 of 21
T := REGSET(R,E,V,P)
 

   (19)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x]
  ,OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,Orde
  redVariableList [w,v,u,y,x]))
                                                                 Type: Domain
--R 
--R
--R   (19)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x]
--R  ,OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,Orde
--R  redVariableList [w,v,u,y,x]))
--R                                                                 Type: Domain
--E 19

--S 20 of 21
zeroSetSplit(lp)$T
 

   (20)
   [
     {
             6           3       2                 4
         729y  + (- 1458x  + 729x  - 4158x - 1685)y
       + 
              6        5        4        3       2                2       8
         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
       + 
             7        6        5        4        3        2
         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
       ,

                  4           3       2                  2        6        5
             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
           + 
                     4        3        2
             - 10125x  - 4800x  + 2501x  + 4968x - 1587
        *
           u
       + 
               3       2  2       6        5        4       3        2
         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
       ,
         2                   2                    2  2           2
      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--R 
--R
--R   (20)
--R   [
--R     {
--R             6           3       2                 4
--R         729y  + (- 1458x  + 729x  - 4158x - 1685)y
--R       + 
--R              6        5        4        3       2                2       8
--R         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
--R       + 
--R             7        6        5        4        3        2
--R         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
--R           + 
--R                     4        3        2
--R             - 10125x  - 4800x  + 2501x  + 4968x - 1587
--R        *
--R           u
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
--R       ,
--R         2                   2                    2  2           2
--R      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--E 20

--S 21 of 21
zeroSetSplit(lp,false)$T
 

   (21)
   [
     {
             6           3       2                 4
         729y  + (- 1458x  + 729x  - 4158x - 1685)y
       + 
              6        5        4        3       2                2       8
         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
       + 
             7        6        5        4        3        2
         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
       ,

                  4           3       2                  2        6        5
             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
           + 
                     4        3        2
             - 10125x  - 4800x  + 2501x  + 4968x - 1587
        *
           u
       + 
               3       2  2       6        5        4       3        2
         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
       ,
         2                   2                    2  2           2
      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
     ,

         4     3      2                               2
     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
        2          2
      6v  - 2u - 3x  + 2x + 3, 2v w - 1}
     ,

            6         5         4          3         2
     {59049x  + 91854x  - 45198x  + 145152x  + 63549x  + 60922x + 21420,

                            5                  4                  3
             31484448266904x  - 18316865522574x  + 23676995746098x
           + 
                           2
             6657857188965x  + 8904703998546x + 3890631403260
        *
            2
           y
       + 
                        5                  4                  3
         94262810316408x  - 82887296576616x  + 89801831438784x
       + 
                        2
         28141734167208x  + 38070359425432x + 16003865949120
       ,
           2             2         2       3      2                    3     2
      (243x  + 36x + 85)u  + (- 81y  - 162x  + 36x  + 154x + 72)u - 72x  + 4x ,
         2                   2                    2  2           2
      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
     ,

         4     3      2                               2
     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
        2          2             2
      6v  - 2u - 3x  + 2x + 3, 3u w - 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--R 
--R
--R   (21)
--R   [
--R     {
--R             6           3       2                 4
--R         729y  + (- 1458x  + 729x  - 4158x - 1685)y
--R       + 
--R              6        5        4        3       2                2       8
--R         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
--R       + 
--R             7        6        5        4        3        2
--R         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
--R           + 
--R                     4        3        2
--R             - 10125x  - 4800x  + 2501x  + 4968x - 1587
--R        *
--R           u
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
--R       ,
--R         2                   2                    2  2           2
--R      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
--R     ,
--R
--R         4     3      2                               2
--R     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
--R        2          2
--R      6v  - 2u - 3x  + 2x + 3, 2v w - 1}
--R     ,
--R
--R            6         5         4          3         2
--R     {59049x  + 91854x  - 45198x  + 145152x  + 63549x  + 60922x + 21420,
--R
--R                            5                  4                  3
--R             31484448266904x  - 18316865522574x  + 23676995746098x
--R           + 
--R                           2
--R             6657857188965x  + 8904703998546x + 3890631403260
--R        *
--R            2
--R           y
--R       + 
--R                        5                  4                  3
--R         94262810316408x  - 82887296576616x  + 89801831438784x
--R       + 
--R                        2
--R         28141734167208x  + 38070359425432x + 16003865949120
--R       ,
--R           2             2         2       3      2                    3     2
--R      (243x  + 36x + 85)u  + (- 81y  - 162x  + 36x  + 154x + 72)u - 72x  + 4x ,
--R         2                   2                    2  2           2
--R      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
--R     ,
--R
--R         4     3      2                               2
--R     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
--R        2          2             2
--R      6v  - 2u - 3x  + 2x + 3, 3u w - 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--E 21
)spool 
 
Starts dribbling to intlf.output (2009/2/17, 17:46:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 2
exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1)
 

                            2
                         - x
                 erf(x)%e
   (1)  ------------------------------
              3         2
        erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R                            2
--R                         - x
--R                 erf(x)%e
--R   (1)  ------------------------------
--R              3         2
--R        erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 2
integrate(%, x)
 

                     +---+    erf(x) - 1      +---+
        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
                              erf(x) + 1
   (2)  -------------------------------------------
                        8erf(x) - 8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +---+    erf(x) - 1      +---+
--R        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
--R                              erf(x) + 1
--R   (2)  -------------------------------------------
--R                        8erf(x) - 8
--R                                          Type: Union(Expression Integer,...)
--E 2
)spool 
 
Starts dribbling to elemnum.output (2009/2/17, 17:45:31).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set break resume
 

--S 1  of 50
x := 0.7::Float
 

   (1)  0.7
                                                                  Type: Float
--R 
--R
--R   (1)  0.7
--R                                                                  Type: Float
--E 1

--S 2 of 50
[exp log x]
 

   (2)  [0.7]
                                                             Type: List Float
--R 
--R
--R   (2)  [0.7]
--R                                                             Type: List Float
--E 2

--S 3 of 50
[log exp x]
 

   (3)  [0.7]
                                                             Type: List Float
--R 
--R
--R   (3)  [0.7]
--R                                                             Type: List Float
--E 3

--S 4 of 50
[sin asin x,  cos acos x,  tan atan x,  cot acot x]
 

   (4)  [0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (4)  [0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 4

--S 5 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (5)  [0.7,0.7,0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (5)  [0.7,0.7,0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 5

--S 6 of 50
[sinh asinh x,             tanh atanh x,             csch acsch x,sech asech x]
 

   (6)  [0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (6)  [0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 6

--S 7 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (7)  [0.7,0.7,0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (7)  [0.7,0.7,0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 7

--should give errors:
--acsc  x
--asec  x 
--acosh x
--acoth x

--S 8 of 50
x := 1.1::Float
 

   (8)  1.1
                                                                  Type: Float
--R 
--R
--R   (8)  1.1
--R                                                                  Type: Float
--E 8

--S 9 of 50
[exp log x]
 

   (9)  [1.1]
                                                             Type: List Float
--R 
--R
--R   (9)  [1.1]
--R                                                             Type: List Float
--E 9

--S 10 of 50
[log exp x]
 

   (10)  [1.1]
                                                             Type: List Float
--R 
--R
--R   (10)  [1.1]
--R                                                             Type: List Float
--E 10

--S 11 of 50
[                          tan atan x,  cot acot x, csc acsc x,   sec asec x  ]
 

   (11)  [1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (11)  [1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 11

--S 12 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (12)  [1.1,1.1,1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (12)  [1.1,1.1,1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 12

--S 13 of 50
[sinh asinh x,cosh acosh x,             coth acoth x,csch acsch x             ]
 

   (13)  [1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (13)  [1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 13

--S 14 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (14)  [1.1,1.1,1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (14)  [1.1,1.1,1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 14

--should give errors: 
--asin x
--acos x
--atanh x
--asech x

--S 15 of 50
x := 0.7::DoubleFloat
 

   (15)  0.69999999999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (15)  0.69999999999999996
--R                                                            Type: DoubleFloat
--E 15

--S 16 of 50
[exp log x]
 

   (16)  [0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (16)  [0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 16

--S 17 of 50
[log exp x]
 

   (17)  [0.70000000000000007]
                                                       Type: List DoubleFloat
--R 
--R
--R   (17)  [0.70000000000000007]
--R                                                       Type: List DoubleFloat
--E 17

--S 18 of 50
[sin asin x,  cos acos x,  tan atan x,  cot acot x]
 

   (18)
   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,
    0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (18)
--R   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,
--R    0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 18

--S 19 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (19)
   [0.69999999999999996, 0.69999999999999996, 0.69999999999999996,
    0.69999999999999996, 0.69999999999999996, 0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (19)
--R   [0.69999999999999996, 0.69999999999999996, 0.69999999999999996,
--R    0.69999999999999996, 0.69999999999999996, 0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 19

--S 20 of 50
[sinh asinh x,             tanh atanh x,             csch acsch x,sech asech x]
 

   (20)
   [0.69999999999999996, 0.69999999999999996, 0.69999999999999984,
    0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (20)
--R   [0.69999999999999996, 0.69999999999999996, 0.69999999999999984,
--R    0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 20

--S 21 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (21)
   [0.70000000000000007, 0.70000000000000018, 0.70000000000000029,
    0.70000000000000029, 0.70000000000000007, 0.70000000000000018]
                                                       Type: List DoubleFloat
--R 
--R
--R   (21)
--R   [0.70000000000000007, 0.70000000000000018, 0.70000000000000029,
--R    0.70000000000000029, 0.70000000000000007, 0.70000000000000018]
--R                                                       Type: List DoubleFloat
--E 21

--should give errors: 
--acsc  x
--asec  x 
--acosh x
--acoth x

--S 22 of 50
x := 1.1::DoubleFloat
 

   (22)  1.0999999999999999
                                                            Type: DoubleFloat
--R 
--R
--R   (22)  1.1000000000000001
--R                                                            Type: DoubleFloat
--E 22

--S 23 of 50
[exp log x]
 

   (23)  [1.0999999999999999]
                                                       Type: List DoubleFloat
--R 
--R
--R   (23)  [1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 23

--S 24 of 50
[log exp x]
 

   (24)  [1.0999999999999999]
                                                       Type: List DoubleFloat
--R 
--R
--R   (24)  [1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 24

--S 25 of 50
[                          tan atan x,  cot acot x, csc acsc x,   sec asec x  ]
 

   (25)
   [1.0999999999999999,1.0999999999999999,1.0999999999999999,1.0999999999999999]
                                                       Type: List DoubleFloat
--R 
--R
--R   (25)
--R   [1.1000000000000001,1.0999999999999999,1.1000000000000001,1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 25

--S 26 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (26)
   [1.0999999999999999, 1.0999999999999999, 1.0999999999999999,
    1.0999999999999999, 1.0999999999999999, 1.0999999999999999]
                                                       Type: List DoubleFloat
--R 
--R
--R   (26)
--R   [1.1000000000000003, 1.1000000000000001, 1.1000000000000001,
--R    1.1000000000000001, 1.0999999999999999, 1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 26

--S 27 of 50
[sinh asinh x,cosh acosh x,             coth acoth x,csch acsch x             ]
 

   (27)
   [1.0999999999999999,1.0999999999999996,1.1000000000000001,1.1000000000000001]
                                                       Type: List DoubleFloat
--R 
--R
--R   (27)
--R   [1.1000000000000001,1.1000000000000001,1.1000000000000001,1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 27

--S 28 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (28)
   [1.0999999999999999, 1.0999999999999999, 1.1000000000000001,
    1.1000000000000001, 1.0999999999999999, 1.0999999999999999]
                                                       Type: List DoubleFloat
--R 
--R
--R   (28)
--R   [1.1000000000000001, 1.0999999999999999, 1.1000000000000001,
--R    1.1000000000000003, 1.1000000000000001, 1.0999999999999999]
--R                                                       Type: List DoubleFloat
--E 28

--should give errors: 
--asin x
--acos x
--atanh x
--asech x

--S 29 of 50
qtest(a,b,n) ==
   m1 := if n = 1 or n = 4 then 0 else  1
   s1 := if n = 1 or n = 4 then 1 else -1
   s2 := if n = 1 or n = 2 then 1 else -1
   x := complex(s1*a, s2*b)
   [x- exp   log x, _
    x- sin   asin  x, x-    cos   acos  x, x- tan   atan  x , _
    x- csc   acsc  x, x-    sec   asec  x, x- cot   acot  x , _
    x- sinh  asinh x, x-    cosh  acosh x, x- tanh  atanh x , _
    x- csch  acsch x, x-    sech  asech x, x- coth  acoth x , _
    x- log   exp   x, _
    x- asin  sin   x, x- s1*acos  cos   x, x- atan  tan  x , _
    x- acsc  csc   x, x- s1*asec  sec   x, x- acot  cot  x + m1*%pi, _
    x- asinh sinh  x, x- s1*acosh cosh  x, x- atanh tanh x , _
    x- acsch csch  x, x- s1*asech sech  x, x- acoth coth x ]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 50
qerr(l) ==
    reduce(+, [norm v for v in l])/#l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 50
sa := 0.7::DoubleFloat
 

   (31)  0.69999999999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (31)  0.69999999999999996
--R                                                            Type: DoubleFloat
--E 31

--S 32 of 50
sb := 1.1::DoubleFloat
 

   (32)  1.0999999999999999
                                                            Type: DoubleFloat
--R 
--R
--R   (32)  1.1000000000000001
--R                                                            Type: DoubleFloat
--E 32

--S 33 of 50
ba := 0.7::Float
 

   (33)  0.7
                                                                  Type: Float
--R 
--R
--R   (33)  0.7
--R                                                                  Type: Float
--E 33

--S 34 of 50
bb := 1.1::Float
 

   (34)  1.1
                                                                  Type: Float
--R 
--R
--R   (34)  1.1
--R                                                                  Type: Float
--E 34

--S 35 of 50
qtest(sa, sb, 1)
 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 

   (35)
   [- 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16%i, - 1.1102230246251565E-16,
    1.1102230246251565E-16, 2.2204460492503131E-16,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    2.2204460492503131E-16, - 1.1102230246251565E-16,
    1.1102230246251565E-16 + 4.4408920985006262E-16%i,
    1.1102230246251565E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16, - 3.3306690738754696E-16,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i, 1.1102230246251565E-16,
    - 1.1102230246251565E-16, - 3.3306690738754696E-16,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16, - 3.3306690738754696E-16,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16%i]
                                               Type: List Complex DoubleFloat
--R 
--R   Compiling function qtest with type (DoubleFloat,DoubleFloat,
--R      PositiveInteger) -> List Complex DoubleFloat 
--R
--R   (35)
--R   [1.1102230246251565E-16, 2.2204460492503131E-16 - 4.4408920985006262E-16 %i,
--R    - 2.2204460492503131E-16,
--R    - 4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
--R    4.4408920985006262E-16, - 1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16 - 2.2204460492503131E-16 %i, 0.,
--R    - 6.6613381477509392E-16 %i, - 1.1102230246251565E-16,
--R    - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
--R    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
--R    - 3.3306690738754696E-16,
--R    - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
--R    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
--R    - 5.5511151231257827E-16, - 2.2204460492503131E-16,
--R    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.,
--R    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
--R                                               Type: List Complex DoubleFloat
--E 35

--S 36 of 50
qerr %
 
   Compiling function qerr with type List Complex DoubleFloat -> 
      DoubleFloat 

   (36)  9.434093758352245E-32
                                                            Type: DoubleFloat
--R 
--R   Compiling function qerr with type List Complex DoubleFloat -> 
--R      DoubleFloat 
--R
--R   (36)  1.2373359150401687E-31
--R                                                            Type: DoubleFloat
--E 36

--S 37 of 50
qtest(ba, bb, 1)
 
   Compiling function qtest with type (Float,Float,PositiveInteger) -> 
      List Complex Float 

   (37)
   [- 0.3 E -20, 0.7 E -20, 0.7 E -20, 0.7 E -20 + 0.7 E -20 %i,
    - 0.7 E -20 %i, - 0.1 E -19, 0.3 E -20 - 0.7 E -20 %i,
    - 0.3 E -20 - 0.7 E -20 %i, 0.0, - 0.3 E -20, 0.1 E -19 %i,
    0.3 E -19 + 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19, - 0.3 E -20,
    - 0.7 E -20 - 0.1 E -19 %i, 0.2 E -19, - 0.2 E -19 - 0.7 E -20 %i,
    0.1 E -19 - 0.1 E -19 %i, - 0.7 E -20, - 0.7 E -20 - 0.7 E -20 %i, 0.0,
    - 0.7 E -20, 0.0, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R   Compiling function qtest with type (Float,Float,PositiveInteger) -> 
--R      List Complex Float 
--R
--R   (37)
--R   [- 0.3 E -20, 0.7 E -20, 0.7 E -20, 0.7 E -20 + 0.7 E -20 %i,
--R    - 0.7 E -20 %i, - 0.1 E -19, 0.3 E -20 - 0.7 E -20 %i,
--R    - 0.3 E -20 - 0.7 E -20 %i, 0.0, - 0.3 E -20, 0.1 E -19 %i,
--R    0.3 E -19 + 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19, - 0.3 E -20,
--R    - 0.7 E -20 - 0.1 E -19 %i, 0.2 E -19, - 0.2 E -19 - 0.7 E -20 %i,
--R    0.1 E -19 - 0.1 E -19 %i, - 0.7 E -20, - 0.7 E -20 - 0.7 E -20 %i, 0.0,
--R    - 0.7 E -20, 0.0, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 37

--S 38 of 50
qerr %
 
   Compiling function qerr with type List Complex Float -> Float 

   (38)  0.1355456601 9472741322 E -39
                                                                  Type: Float
--R 
--R   Compiling function qerr with type List Complex Float -> Float 
--R
--R   (38)  0.1355456601 9472741322 E -39
--R                                                                  Type: Float
--E 38

--S 39 of 50
qtest(sa, sb, 2)
 

   (39)
   [- 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16%i, - 4.4408920985006262E-16,
    - 1.1102230246251565E-16, - 2.2204460492503131E-16,
    1.1102230246251565E-16 - 4.4408920985006262E-16%i,
    6.6613381477509392E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    4.4408920985006262E-16 - 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16,
    5.5511151231257827E-16 - 6.6613381477509392E-16%i,
    - 1.1102230246251565E-16 - 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16, 0.0,
    - 3.3306690738754696E-16 - 4.4408920985006262E-16%i, 0.0,
    3.3306690738754696E-16,
    - 3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16%i, 0.0, 0.0, 3.3306690738754696E-16,
    - 4.4408920985006262E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i, 3.3306690738754696E-16,
    2.2204460492503131E-16]
                                               Type: List Complex DoubleFloat
--R 
--R
--R   (39)
--R   [- 1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 - 4.4408920985006262E-16 %i,
--R    - 3.3306690738754696E-16,
--R    4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
--R    - 4.4408920985006262E-16,
--R    1.1102230246251565E-16 - 2.2204460492503131E-16 %i,
--R    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
--R    - 1.1102230246251565E-16,
--R    4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
--R    - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    - 1.1102230246251565E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i, 0.,
--R    4.4408920985006262E-16 - 4.4408920985006262E-16 %i, 0.,
--R    3.3306690738754696E-16, 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
--R    0., 8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
--R    3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i]
--R                                               Type: List Complex DoubleFloat
--E 39

--S 40 of 50
qerr %
 

   (40)  1.5075587010834239E-31
                                                            Type: DoubleFloat
--R 
--R
--R   (40)  1.3985214365396544E-31
--R                                                            Type: DoubleFloat
--E 40

--S 41 of 50
qtest(ba, bb, 2)
 

   (41)
   [0.3 E -20, - 0.7 E -20, - 0.3 E -20, - 0.7 E -20 + 0.7 E -20 %i,
    - 0.7 E -20 %i, - 0.3 E -20, - 0.7 E -20 %i, 0.1 E -19 + 0.1 E -19 %i,
    - 0.3 E -20, 0.0, 0.2 E -19 - 0.1 E -19 %i, - 0.2 E -19 + 0.7 E -20 %i,
    - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20, 0.7 E -20 - 0.1 E -19 %i,
    - 0.2 E -19, 0.2 E -19 - 0.7 E -20 %i, - 0.1 E -19 - 0.1 E -19 %i,
    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, 0.0,
    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R
--R   (41)
--R   [0.3 E -20, - 0.7 E -20, - 0.3 E -20, - 0.7 E -20 + 0.7 E -20 %i,
--R    - 0.7 E -20 %i, - 0.3 E -20, - 0.7 E -20 %i, 0.1 E -19 + 0.1 E -19 %i,
--R    - 0.3 E -20, 0.0, 0.2 E -19 - 0.1 E -19 %i, - 0.2 E -19 + 0.7 E -20 %i,
--R    - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20, 0.7 E -20 - 0.1 E -19 %i,
--R    - 0.2 E -19, 0.2 E -19 - 0.7 E -20 %i, - 0.1 E -19 - 0.1 E -19 %i,
--R    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, 0.0,
--R    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 41

--S 42 of 50
qerr %
 

   (42)  0.1351041433 8627553239 E -39
                                                                  Type: Float
--R 
--R
--R   (42)  0.1351041433 8627553239 E -39
--R                                                                  Type: Float
--E 42

--S 43 of 50
qtest(sa, sb, 3)
 

   (43)
   [- 1.1102230246251565E-16 + 2.2204460492503131E-16%i, 0.0,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16%i,
    4.4408920985006262E-16, 2.2204460492503131E-16,
    - 4.4408920985006262E-16 + 2.2204460492503131E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    4.4408920985006262E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16,
    5.5511151231257827E-16 + 6.6613381477509392E-16%i,
    - 1.1102230246251565E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16, 0.0, 0.0, 2.2204460492503131E-16,
    - 2.2204460492503131E-16, 0.0,
    - 3.3306690738754696E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16%i, 0.0, 3.3306690738754696E-16,
    4.4408920985006262E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i, 3.3306690738754696E-16,
    2.2204460492503131E-16]
                                               Type: List Complex DoubleFloat
--R 
--R
--R   (43)
--R   [- 1.1102230246251565E-16, 0.,
--R    - 2.2204460492503131E-16 + 4.4408920985006262E-16 %i,
--R    - 2.2204460492503131E-16, 1.1102230246251565E-16, - 4.4408920985006262E-16,
--R    - 1.1102230246251565E-16, - 1.1102230246251565E-16,
--R    4.4408920985006262E-16 + 2.2204460492503131E-16 %i,
--R    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    - 1.1102230246251565E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 0., 0.,
--R    - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 %i, 0.,
--R    - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
--R    8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
--R    3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i]
--R                                               Type: List Complex DoubleFloat
--E 43

--S 44 of 50
qerr %
 

   (44)  1.3274101770545873E-31
                                                            Type: DoubleFloat
--R 
--R
--R   (44)  1.0002983834232781E-31
--R                                                            Type: DoubleFloat
--E 44

--S 45 of 50
qtest(ba, bb, 3)
 

   (45)
   [0.3 E -20, - 0.3 E -20, - 0.7 E -20, - 0.3 E -20 - 0.7 E -20 %i,
    - 0.3 E -20, 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i,
    0.1 E -19 - 0.1 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19 + 0.1 E -19 %i,
    - 0.2 E -19 - 0.7 E -20 %i, - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20,
    - 0.3 E -20 + 0.1 E -19 %i, - 0.1 E -19 + 0.7 E -20 %i,
    0.3 E -20 + 0.7 E -20 %i, 0.1 E -19 %i, 0.3 E -20 + 0.7 E -20 %i,
    0.7 E -20 + 0.7 E -20 %i, 0.0, 0.3 E -20 + 0.7 E -20 %i,
    0.7 E -20 + 0.7 E -20 %i, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R
--R   (45)
--R   [0.3 E -20, - 0.3 E -20, - 0.7 E -20, - 0.3 E -20 - 0.7 E -20 %i,
--R    - 0.3 E -20, 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i,
--R    0.1 E -19 - 0.1 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19 + 0.1 E -19 %i,
--R    - 0.2 E -19 - 0.7 E -20 %i, - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20,
--R    - 0.3 E -20 + 0.1 E -19 %i, - 0.1 E -19 + 0.7 E -20 %i,
--R    0.3 E -20 + 0.7 E -20 %i, 0.1 E -19 %i, 0.3 E -20 + 0.7 E -20 %i,
--R    0.7 E -20 + 0.7 E -20 %i, 0.0, 0.3 E -20 + 0.7 E -20 %i,
--R    0.7 E -20 + 0.7 E -20 %i, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 45

--S 46 of 50
qerr %
 

   (46)  0.1258322904 0878603507 E -39
                                                                  Type: Float
--R 
--R
--R   (46)  0.1258322904 0878603507 E -39
--R                                                                  Type: Float
--E 46

--S 47 of 50
qtest(sa, sb, 4)
 

   (47)
   [- 1.1102230246251565E-16 + 2.2204460492503131E-16%i, 0.0,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    - 4.4408920985006262E-16, - 2.2204460492503131E-16, 2.2204460492503131E-16,
    - 4.4408920985006262E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16%i,
    - 2.2204460492503131E-16 + 4.4408920985006262E-16%i,
    2.2204460492503131E-16, - 1.1102230246251565E-16,
    1.1102230246251565E-16 - 4.4408920985006262E-16%i,
    1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16, 0.0, 0.0, 2.2204460492503131E-16, 0.0,
    2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16, - 3.3306690738754696E-16,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16, - 3.3306690738754696E-16,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i]
                                               Type: List Complex DoubleFloat
--R 
--R
--R   (47)
--R   [1.1102230246251565E-16, 0.,
--R    3.3306690738754696E-16 + 4.4408920985006262E-16 %i, 2.2204460492503131E-16,
--R    - 1.1102230246251565E-16,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16 + 2.2204460492503131E-16 %i, 0.,
--R    6.6613381477509392E-16 %i, - 1.1102230246251565E-16, 0., 0.,
--R    2.2204460492503131E-16 %i, 0., 0., - 6.6613381477509392E-16,
--R    - 2.2204460492503131E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
--R    0., - 1.1102230246251565E-16, - 1.1102230246251565E-16]
--R                                               Type: List Complex DoubleFloat
--E 47

--S 48 of 50
qerr %
 

   (48)  7.3481634801236077E-32
                                                            Type: DoubleFloat
--R 
--R
--R   (48)  7.3007559738002298E-32
--R                                                            Type: DoubleFloat
--E 48

--S 49 of 50
qtest(ba, bb, 4)
 

   (49)
   [- 0.3 E -20, 0.3 E -20, 0.7 E -20, 0.3 E -20 - 0.7 E -20 %i, 0.3 E -20,
    - 0.3 E -20, 0.0, - 0.3 E -20 + 0.7 E -20 %i, 0.0, - 0.3 E -20,
    - 0.1 E -19 %i, 0.3 E -19 - 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19,
    - 0.3 E -20, 0.3 E -20 + 0.1 E -19 %i, 0.1 E -19 + 0.7 E -20 %i,
    - 0.3 E -20 + 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i, - 0.7 E -20,
    - 0.7 E -20 + 0.7 E -20 %i, 0.0, - 0.7 E -20, 0.0, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R
--R   (49)
--R   [- 0.3 E -20, 0.3 E -20, 0.7 E -20, 0.3 E -20 - 0.7 E -20 %i, 0.3 E -20,
--R    - 0.3 E -20, 0.0, - 0.3 E -20 + 0.7 E -20 %i, 0.0, - 0.3 E -20,
--R    - 0.1 E -19 %i, 0.3 E -19 - 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19,
--R    - 0.3 E -20, 0.3 E -20 + 0.1 E -19 %i, 0.1 E -19 + 0.7 E -20 %i,
--R    - 0.3 E -20 + 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i, - 0.7 E -20,
--R    - 0.7 E -20 + 0.7 E -20 %i, 0.0, - 0.7 E -20, 0.0, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 49

--S 50 of 50
qerr %
 

   (50)  0.1125867861 5522961033 E -39
                                                                  Type: Float
--R 
--R
--R   (50)  0.1125867861 5522961033 E -39
--R                                                                  Type: Float
--E 50
)spool
 
Starts dribbling to table.output (2009/2/17, 18:0:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 18
t: Table(Polynomial Integer, String) := table()
 

   (1)  table()
                                       Type: Table(Polynomial Integer,String)
--R 
--R
--R   (1)  table()
--R                                       Type: Table(Polynomial Integer,String)
--E 1

--S 2 of 18
setelt(t, x**2 - 1, "Easy to factor")
 

   (2)  "Easy to factor"
                                                                 Type: String
--R 
--R
--R   (2)  "Easy to factor"
--R                                                                 Type: String
--E 2

--S 3 of 18
t(x**3 + 1) := "Harder to factor"
 

   (3)  "Harder to factor"
                                                                 Type: String
--R 
--R
--R   (3)  "Harder to factor"
--R                                                                 Type: String
--E 3

--S 4 of 18
t(x)        := "The easiest to factor"
 

   (4)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (4)  "The easiest to factor"
--R                                                                 Type: String
--E 4

--S 5 of 18
elt(t, x)
 

   (5)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (5)  "The easiest to factor"
--R                                                                 Type: String
--E 5

--S 6 of 18
t.x
 

   (6)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (6)  "The easiest to factor"
--R                                                                 Type: String
--E 6

--S 7 of 18
t x
 

   (7)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (7)  "The easiest to factor"
--R                                                                 Type: String
--E 7

--S 8 of 18
t.(x**2 - 1)
 

   (8)  "Easy to factor"
                                                                 Type: String
--R 
--R
--R   (8)  "Easy to factor"
--R                                                                 Type: String
--E 8

--S 9 of 18
t (x**3 + 1)
 

   (9)  "Harder to factor"
                                                                 Type: String
--R 
--R
--R   (9)  "Harder to factor"
--R                                                                 Type: String
--E 9

--S 10 of 18
keys t
 

             3      2
   (10)  [x,x  + 1,x  - 1]
                                                Type: List Polynomial Integer
--R 
--R
--R             3      2
--R   (10)  [x,x  + 1,x  - 1]
--R                                                Type: List Polynomial Integer
--E 10

--S 11 of 18
search(x, t)
 

   (11)  "The easiest to factor"
                                                      Type: Union(String,...)
--R 
--R
--R   (11)  "The easiest to factor"
--R                                                      Type: Union(String,...)
--E 11

--S 12 of 18
search(x**2, t)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 18
search(x**2, t) case "failed"
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 18
remove!(x**2-1, t)
 

   (14)  "Easy to factor"
                                                      Type: Union(String,...)
--R 
--R
--R   (14)  "Easy to factor"
--R                                                      Type: Union(String,...)
--E 14

--S 15 of 18
remove!(x-1, t)
 

   (15)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (15)  "failed"
--R                                                    Type: Union("failed",...)
--E 15

--S 16 of 18
#t
 

   (16)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 18
members t
 

   (17)  ["The easiest to factor","Harder to factor"]
                                                            Type: List String
--R 
--R
--R   (17)  ["The easiest to factor","Harder to factor"]
--R                                                            Type: List String
--E 17

--S 18 of 18
count(s: String +-> prefix?("Hard", s), t)
 

   (18)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  1
--R                                                        Type: PositiveInteger
--E 18
)spool 
 
Starts dribbling to none.output (2009/2/17, 17:55:33).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
[]
 

   (1)  []
                                                              Type: List None
--R 
--R
--R   (1)  []
--R                                                              Type: List None
--E 1

--S 2 of 3
[] :: List Float
 

   (2)  []
                                                             Type: List Float
--R 
--R
--R   (2)  []
--R                                                             Type: List Float
--E 2

--S 3 of 3
[]$List(NonNegativeInteger)
 

   (3)  []
                                                Type: List NonNegativeInteger
--R 
--R
--R   (3)  []
--R                                                Type: List NonNegativeInteger
--E 3
)spool 
 
Starts dribbling to equation2.output (2009/2/17, 17:45:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 27
solve([3*x**3 + y + 1,y - 1],[x,y])
 

            3
   (1)  [[3x  + 2= 0,y= 1]]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R            3
--R   (1)  [[3x  + 2= 0,y= 1]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 1

--S 2 of 27
solve([x**3 + x - y**2 + 4,x*y + 2],[x,y],"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                           List Polynomial Integer
                       List OrderedVariableList [x,y]
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                           List Polynomial Integer
--R                       List OrderedVariableList [x,y]
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 2

--S 3 of 27
solve([x = y**2-19,y = z**2+x+3,z = 3*x],[x,y,z])
 

                    2
             z    3z  + z + 9   4     3      2
   (2)  [[x= -,y= -----------,9z  + 6z  + 55z  + 15z - 90= 0]]
             3         3
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R                    2
--R             z    3z  + z + 9   4     3      2
--R   (2)  [[x= -,y= -----------,9z  + 6z  + 55z  + 15z - 90= 0]]
--R             3         3
--R                         Type: List List Equation Fraction Polynomial Integer
--E 3

--S 4 of 27
solve([3*x + 2*y - z,x - 1/2*y + 1/3*z,4/5*x - 2/3*y - z])
 

   (3)  [[z= 0,y= 0,x= 0]]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R   (3)  [[z= 0,y= 0,x= 0]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 4

--S 5 of 27
solve([x**2*y - 1,x*y**2 - 2],[x,y],.01)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                           List Polynomial Integer
                       List OrderedVariableList [x,y]
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                           List Polynomial Integer
--R                       List OrderedVariableList [x,y]
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5

--S 6 of 27
solve([x**2/a = 1,a**2 - a*x = 0],[x,a],.001)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                  List Equation Fraction Polynomial Integer
                       List OrderedVariableList [x,a]
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                  List Equation Fraction Polynomial Integer
--R                       List OrderedVariableList [x,a]
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6

--S 7 of 27
solve([x**2/a + a + y**3 - 1,a*y + a + 1],[x,y])
 

           2 2    4     3     2                - a - 1
   (4)  [[a x  + a  - 2a  - 3a  - 3a - 1= 0,y= -------]]
                                                  a
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R           2 2    4     3     2                - a - 1
--R   (4)  [[a x  + a  - 2a  - 3a  - 3a - 1= 0,y= -------]]
--R                                                  a
--R                         Type: List List Equation Fraction Polynomial Integer
--E 7

)clear all
 
   All user variables and function definitions have been cleared.

--S 8 of 27
solve(x**3 + 1 = 0,x)
 

                 2
   (1)  [x= - 1,x  - x + 1= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R                 2
--R   (1)  [x= - 1,x  - x + 1= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 8

--S 9 of 27
solve(x**3*y + x*y + 1,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9

--S 10 of 27
solve(3*x + 1/4*y = 1,x)
 

            - y + 4
   (2)  [x= -------]
               12
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R            - y + 4
--R   (2)  [x= -------]
--R               12
--R                              Type: List Equation Fraction Polynomial Integer
--E 10

--S 11 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                              Fraction Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                              Fraction Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11

--S 12 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12

--S 13 of 27
solve(x**3 - sqrt(2))
 

          3    +-+
   (3)  [x  - \|2 = 0]
                      Type: List Equation Fraction Polynomial AlgebraicNumber
--R 
--R
--R          3    +-+
--R   (3)  [x  - \|2 = 0]
--R                      Type: List Equation Fraction Polynomial AlgebraicNumber
--E 13

--S 14 of 27
solve(x**3/a + x/a + 1,x)
 

          3
   (4)  [x  + x + a= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R          3
--R   (4)  [x  + x + a= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 14

)clear all
 
   All user variables and function definitions have been cleared.

--S 15 of 27
solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                    Equation Fraction Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                    Equation Fraction Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15

--S 16 of 27
solve(x**3 + 1 = 0,x)
 

                 2
   (1)  [x= - 1,x  - x + 1= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R                 2
--R   (1)  [x= - 1,x  - x + 1= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 16

--S 17 of 27
solve(x**3*y + x*y + 1,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17

--S 18 of 27
solve(3*x + 1/4*y = 1,x)
 

            - y + 4
   (2)  [x= -------]
               12
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R            - y + 4
--R   (2)  [x= -------]
--R               12
--R                              Type: List Equation Fraction Polynomial Integer
--E 18

--S 19 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                              Fraction Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                              Fraction Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 19

--S 20 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20

--S 21 of 27
solve(x**3 - sqrt(2))
 

          3    +-+
   (3)  [x  - \|2 = 0]
                      Type: List Equation Fraction Polynomial AlgebraicNumber
--R 
--R
--R          3    +-+
--R   (3)  [x  - \|2 = 0]
--R                      Type: List Equation Fraction Polynomial AlgebraicNumber
--E 21

--S 22 of 27
solve(x**3/a + x/a + 1,x)
 

          3
   (4)  [x  + x + a= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R          3
--R   (4)  [x  + x + a= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 22

--S 23 of 27
solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                    Equation Fraction Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                    Equation Fraction Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23

)clear all
 
   All user variables and function definitions have been cleared.

--S 24  of 27
solve([[1,1,1],[3,-2,1],[1,2,2]],[8,0,17])
 

   (1)  [particular= [- 1,2,7],basis= [[0,0,0]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (1)  [particular= [- 1,2,7],basis= [[0,0,0]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 24

--S 25 of 27
solve([[1,2,3],[2,3,4],[3,4,5]],[2,2,2])
 

   (2)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (2)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 25

--S 26 of 27
solve([[1,2,3],[2,3,4],[3,4,5]],[2,3,2])
 

   (3)  [particular= "failed",basis= [[1,- 2,1]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (3)  [particular= "failed",basis= [[1,- 2,1]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 26

--S 27 of 27
solve([[1,2,3],[2,3,4],[3,4,5]])
 

   (4)  solve
             [1,2,3],[2,3,4],[3,4,5]
                                                                 Type: Symbol
--R 
--R
--R   (4)  solve
--R             [1,2,3],[2,3,4],[3,4,5]
--R                                                                 Type: Symbol
--E 27
)spool
 
Starts dribbling to ffdemo.output (2009/2/17, 17:45:57).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 350
p:=4817
 

   (1)  4817
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  4817
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 350
F:=PrimeField p
 

   (2)  PrimeField 4817
                                                                 Type: Domain
--R 
--R
--R   (2)  PrimeField 4817
--R                                                                 Type: Domain
--E 2

--S 3 of 350
size()$F
 

   (3)  4817
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  4817
--R                                                     Type: NonNegativeInteger
--E

--S 4 of 350
a:=index(size()$F quo 3)$F
 

   (4)  1605
                                                        Type: PrimeField 4817
--R 
--R
--R   (4)  1605
--R                                                        Type: PrimeField 4817
--E 4

--S 5 of 350
b:=index(size()$F quo 7)$F
 

   (5)  688
                                                        Type: PrimeField 4817
--R 
--R
--R   (5)  688
--R                                                        Type: PrimeField 4817
--E 5

--S 6 of 350
a+b
 

   (6)  2293
                                                        Type: PrimeField 4817
--R 
--R
--R   (6)  2293
--R                                                        Type: PrimeField 4817
--E 6

--S 7 of 350
a-b
 

   (7)  917
                                                        Type: PrimeField 4817
--R 
--R
--R   (7)  917
--R                                                        Type: PrimeField 4817
--E 7

--S 8 of 350
a*b
 

   (8)  1147
                                                        Type: PrimeField 4817
--R 
--R
--R   (8)  1147
--R                                                        Type: PrimeField 4817
--E 8

--S 9 of 350
a/b
 

   (9)  3216
                                                        Type: PrimeField 4817
--R 
--R
--R   (9)  3216
--R                                                        Type: PrimeField 4817
--E 9

--S 10 of 350
a**1234
 

   (10)  2068
                                                        Type: PrimeField 4817
--R 
--R
--R   (10)  2068
--R                                                        Type: PrimeField 4817
--E 10

--S 11 of 350
a**(-1)
 

   (11)  2407
                                                        Type: PrimeField 4817
--R 
--R
--R   (11)  2407
--R                                                        Type: PrimeField 4817
--E 11

--S 12 of 350
g := generator()$F
 

   (12)  1
                                                        Type: PrimeField 4817
--R 
--R
--R   (12)  1
--R                                                        Type: PrimeField 4817
--E 12

--S 13 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (13)  0
                                                        Type: PrimeField 4817
--R 
--R
--R   (13)  0
--R                                                        Type: PrimeField 4817
--E 13

--S 14 of 350
order(a)
 

   (14)  688
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  688
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 350
g:=primitiveElement()$F
 

   (15)  3
                                                        Type: PrimeField 4817
--R 
--R
--R   (15)  3
--R                                                        Type: PrimeField 4817
--E 15

--S 16 of 350
discreteLog(a)
 

   (16)  987
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  987
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 350
g**% - a
 

   (17)  0
                                                        Type: PrimeField 4817
--R 
--R
--R   (17)  0
--R                                                        Type: PrimeField 4817
--E 17

--S 18 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (18)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (18)  "failed"
--R                                                    Type: Union("failed",...)
--E 18

--S 19 of 350
extensionDegree()$F
 

   (19)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  1
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 350
degree(a)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 350
normalElement()$F
 

   (21)  1
                                                        Type: PrimeField 4817
--R 
--R
--R   (21)  1
--R                                                        Type: PrimeField 4817
--E 21

--S 22 of 350
definingPolynomial()$F
 

   (22)  ? + 4816
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (22)  ? + 4816
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 22

--S 23 of 350
minimalPolynomial(a)
 

   (23)  ? + 3212
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (23)  ? + 3212
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 23

--S 24 of 350
Frobenius(a)
 

   (24)  1605
                                                        Type: PrimeField 4817
--R 
--R
--R   (24)  1605
--R                                                        Type: PrimeField 4817
--E 24

--S 25 of 350
linearAssociatedOrder(a)
 

   (25)  ? + 4816
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (25)  ? + 4816
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 25

--S 26 of 350
linearAssociatedLog(a)
 

   (26)  1605
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (26)  1605
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 26

--S 27 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28 of 350
p:=7
 

   (28)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  7
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 350
P:=PrimeField p
 

   (29)  PrimeField 7
                                                                 Type: Domain
--R 
--R
--R   (29)  PrimeField 7
--R                                                                 Type: Domain
--E 29

--S 30 of 350
d:=6
 

   (30)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  6
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 350
f:=createIrreduciblePoly(d)$FFPOLY(P)
 

          6
   (31)  ?  + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6
--R   (31)  ?  + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 31

--S 32 of 350
F:=FFP(P,f)
 

   (32)  FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
                                                                 Type: Domain
--R 
--R
--R   (32)  FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R                                                                 Type: Domain
--E 32

--S 33 of 350
size()$F
 

   (33)  117649
                                                     Type: NonNegativeInteger
--R 
--R
--R   (33)  117649
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 350
a:=index(size()$F quo 3)$F
 

            5      4      3      2
   (34)  2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (34)  2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 34

--S 35 of 350
b:=index(size()$F quo 7)$F
 

           5
   (35)  %A
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R           5
--R   (35)  %A
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 35

--S 36 of 350
a+b
 

            5      4      3      2
   (36)  3%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (36)  3%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 36

--S 37 of 350
a-b
 

           5      4      3      2
   (37)  %A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R           5      4      3      2
--R   (37)  %A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 37

--S 38 of 350
a*b
 

            5      4      3      2
   (38)  2%A  + 3%A  + 3%A  + 3%A  + 3%A + 3
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (38)  2%A  + 3%A  + 3%A  + 3%A  + 3%A + 3
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 38

--S 39 of 350
a/b
 

            5      4      3      2
   (39)  6%A  + 6%A  + 6%A  + 6%A  + 6%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (39)  6%A  + 6%A  + 6%A  + 6%A  + 6%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 39

--S 40 of 350
a**1234
 

            5     4      3
   (40)  5%A  + %A  + 3%A  + 3%A + 4
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5     4      3
--R   (40)  5%A  + %A  + 3%A  + 3%A + 4
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 40

--S 41 of 350
a**(-1)
 

   (41)  %A + 6
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (41)  %A + 6
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 41

--S 42 of 350
g := generator()$F
 

   (42)  %A
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (42)  %A
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 42

--S 43 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (43)  0
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (43)  0
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 43

--S 44 of 350
order(a)
 

   (44)  117648
                                                        Type: PositiveInteger
--R 
--R
--R   (44)  117648
--R                                                        Type: PositiveInteger
--E 44

--S 45 of 350
g:=primitiveElement()$F
 

   (45)  %A + 1
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (45)  %A + 1
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 45

--S 46 of 350
discreteLog(a)
 

   (46)  58481
                                                        Type: PositiveInteger
--R 
--R
--R   (46)  58481
--R                                                        Type: PositiveInteger
--E 46

--S 47 of 350
g**% - a
 

   (47)  0
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (47)  0
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 47

--S 48 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (48)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (48)  "failed"
--R                                                    Type: Union("failed",...)
--E 48

--S 49 of 350
extensionDegree()$F
 

   (49)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (49)  6
--R                                                        Type: PositiveInteger
--E 49

--S 50 of 350
degree(a)
 

   (50)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (50)  6
--R                                                        Type: PositiveInteger
--E 50

--S 51 of 350
normalElement()$F
 

            5      4      3      2
   (51)  5%A  + 3%A  + 3%A  + 5%A  + %A + 5
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (51)  5%A  + 3%A  + 3%A  + 5%A  + %A + 5
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 51

--S 52 of 350
definingPolynomial()$F
 

          6
   (52)  ?  + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6
--R   (52)  ?  + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 52

--S 53 of 350
minimalPolynomial(a)
 

          6     5     4     3     2
   (53)  ?  + 2?  + 5?  + 2?  + 5?  + 2? + 5
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6     5     4     3     2
--R   (53)  ?  + 2?  + 5?  + 2?  + 5?  + 2? + 5
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 53

--S 54 of 350
Frobenius(a)
 

            5      4      3     2
   (54)  6%A  + 4%A  + 5%A  + %A  + 3%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3     2
--R   (54)  6%A  + 4%A  + 5%A  + %A  + 3%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 54

--S 55 of 350
linearAssociatedOrder(a)
 

          6
   (55)  ?  + 6
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6
--R   (55)  ?  + 6
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 55

--S 56 of 350
linearAssociatedLog(a)
 

           5     4     3     2
   (56)  2?  + 3?  + 3?  + 3?  + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R           5     4     3     2
--R   (56)  2?  + 3?  + 3?  + 3?  + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 56

--S 57 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   Compiling function G1513 with type Integer -> Boolean 
   Compiling function G1527 with type NonNegativeInteger -> Boolean 
   5
   5
      3
   2%A  + 2
      3
   6%A  + 6
      4      2
   5%A  + 5%A  + 5
      4      2
   4%A  + 4%A  + 4
      5      4      3      2
   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
      5      4      3      2
   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                                                                   Type: Void
--R 
--I   Compiling function G1515 with type Integer -> Boolean 
--I   Compiling function G1679 with type NonNegativeInteger -> Boolean 
--R   5
--R   5
--R      3
--R   2%A  + 2
--R      3
--R   6%A  + 6
--R      4      2
--R   5%A  + 5%A  + 5
--R      4      2
--R   4%A  + 4%A  + 4
--R      5      4      3      2
--R   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R      5      4      3      2
--R   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                                                                   Type: Void
--E 57

--S 58 of 350
f:=createNormalPoly(d)$FFPOLY(P)
 

          6     5
   (58)  ?  + 6?  + 2? + 4
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6     5
--R   (58)  ?  + 6?  + 2? + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 58

--S 59 of 350
F:=FFNBP(P,f)
 

   (59)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
                                                                 Type: Domain
--R 
--R
--R   (59)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R                                                                 Type: Domain
--E 59

--S 60 of 350
size()$F
 

   (60)  117649
                                                     Type: NonNegativeInteger
--R 
--R
--R   (60)  117649
--R                                                     Type: NonNegativeInteger
--E 60

--S 61 of 350
a:=index(size()$F quo 3)$F
 

             5       4       3       2
            q       q       q       q       q
   (61)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (61)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 61

--S 62 of 350
b:=index(size()$F quo 7)$F
 

            5
           q
   (62)  %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R            5
--R           q
--R   (62)  %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 62

--S 63 of 350
a+b
 

             5       4       3       2
            q       q       q       q       q
   (63)  3%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (63)  3%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 63

--S 64 of 350
a-b
 

            5       4       3       2
           q       q       q       q       q
   (64)  %B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R            5       4       3       2
--R           q       q       q       q       q
--R   (64)  %B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 64

--S 65 of 350
a*b
 

             5
            q
   (65)  2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5
--R            q
--R   (65)  2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 65

--S 66 of 350
a/b
 

             4       3       2
            q       q       q      q
   (66)  3%B   + 2%B   + 4%B   + %B  + 3%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             4       3       2
--R            q       q       q      q
--R   (66)  3%B   + 2%B   + 4%B   + %B  + 3%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 66

--S 67 of 350
a**1234
 

             5       4       3       2
            q       q       q       q       q
   (67)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (67)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 67

--S 68 of 350
a**(-1)
 

             5       4       3       2
            q       q       q       q       q
   (68)  4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (68)  4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 68

--S 69 of 350
g := generator()$F
 

   (69)  %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (69)  %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 69

--S 70 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (70)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (70)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 70

--S 71 of 350
order(a)
 

   (71)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (71)  3
--R                                                        Type: PositiveInteger
--E 71

--S 72 of 350
g:=primitiveElement()$F
 

            2
           q
   (72)  %B   + %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R            2
--R           q
--R   (72)  %B   + %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 72

--S 73 of 350
discreteLog(a)
 

   (73)  39216
                                                        Type: PositiveInteger
--R 
--R
--R   (73)  39216
--R                                                        Type: PositiveInteger
--E 73

--S 74 of 350
g**% - a
 

   (74)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (74)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 74

--S 75 of 350
discreteLog(b,a)
 

   (75)  9804
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (75)  9804
--R                                          Type: Union(NonNegativeInteger,...)
--E 75

--S 76 of 350
extensionDegree()$F
 

   (76)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (76)  6
--R                                                        Type: PositiveInteger
--E 76

--S 77 of 350
degree(a)
 

   (77)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (77)  1
--R                                                        Type: PositiveInteger
--E 77

--S 78 of 350
normalElement()$F
 

   (78)  %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (78)  %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 78

--S 79 of 350
definingPolynomial()$F
 

          6     5
   (79)  ?  + 6?  + 2? + 4
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6     5
--R   (79)  ?  + 6?  + 2? + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 79

--S 80 of 350
minimalPolynomial(a)
 

   (80)  ? + 5
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R   (80)  ? + 5
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 80

--S 81 of 350
Frobenius(a)
 

             5       4       3       2
            q       q       q       q       q
   (81)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (81)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 81

--S 82 of 350
linearAssociatedOrder(a)
 

   (82)  ? + 6
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R   (82)  ? + 6
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 82

--S 83 of 350
linearAssociatedLog(a)
 

           5     4     3     2
   (83)  2?  + 2?  + 2?  + 2?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R           5     4     3     2
--R   (83)  2?  + 2?  + 2?  + 2?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 83

--S 84 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
      5      4      3      2
     q      q      q      q      q
   %B   + %B   + %B   + %B   + %B  + %B
       5       4       3       2
      q       q       q       q       q
   5%B   + 5%B   + 5%B   + 5%B   + 5%B  + 5%B
      5      4      3      2
     q      q      q      q      q
   %B   + %B   + %B   + %B   + %B  + %B
       5       4       3       2
      q       q       q       q       q
   6%B   + 6%B   + 6%B   + 6%B   + 6%B  + 6%B
       5       4       3       2
      q       q       q       q       q
   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
       5       4       3       2
      q       q       q       q       q
   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
       5       4       3       2
      q       q       q       q       q
   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
       5       4       3       2
      q       q       q       q       q
   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
                                                                   Type: Void
--R 
--R      5      4      3      2
--R     q      q      q      q      q
--R   %B   + %B   + %B   + %B   + %B  + %B
--R       5       4       3       2
--R      q       q       q       q       q
--R   5%B   + 5%B   + 5%B   + 5%B   + 5%B  + 5%B
--R      5      4      3      2
--R     q      q      q      q      q
--R   %B   + %B   + %B   + %B   + %B  + %B
--R       5       4       3       2
--R      q       q       q       q       q
--R   6%B   + 6%B   + 6%B   + 6%B   + 6%B  + 6%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--R                                                                   Type: Void
--E 84

--S 85 of 350
p:=5
 

   (85)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (85)  5
--R                                                        Type: PositiveInteger
--E 85

--S 86 of 350
P:=PrimeField p
 

   (86)  PrimeField 5
                                                                 Type: Domain
--R 
--R
--R   (86)  PrimeField 5
--R                                                                 Type: Domain
--E 86

--S 87 of 350
d:=4
 

   (87)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (87)  4
--R                                                        Type: PositiveInteger
--E 87

--S 88 of 350
f:=createPrimitivePoly(d)$FFPOLY(P)
 

          4    2
   (88)  ?  + ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R          4    2
--R   (88)  ?  + ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 88

--S 89 of 350
F:=FFCGP(P,f)
 

   (89)
   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
                                                                 Type: Domain
--R 
--R
--R   (89)
--R   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R                                                                 Type: Domain
--E 89

--S 90 of 350
size()$F
 

   (90)  625
                                                     Type: NonNegativeInteger
--R 
--R
--R   (90)  625
--R                                                     Type: NonNegativeInteger
--E 90

--S 91 of 350
a:=index(size()$F quo 3)$F
 

           207
   (91)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           207
--R   (91)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 91

--S 92 of 350
b:=index(size()$F quo 7)$F
 

           88
   (92)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           88
--R   (92)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 92

--S 93 of 350
a+b
 

           70
   (93)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           70
--R   (93)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 93

--S 94 of 350
a-b
 

           237
   (94)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           237
--R   (94)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 94

--S 95 of 350
a*b
 

           295
   (95)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           295
--R   (95)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 95

--S 96 of 350
a/b
 

           119
   (96)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           119
--R   (96)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 96

--S 97 of 350
a**1234
 

           222
   (97)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           222
--R   (97)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 97

--S 98 of 350
a**(-1)
 

           417
   (98)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           417
--R   (98)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 98

--S 99 of 350
g := generator()$F
 

           1
   (99)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           1
--R   (99)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 99

--S 100 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (100)  0
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R   (100)  0
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 100

--S 101 of 350
order(a)
 

   (101)  208
                                                        Type: PositiveInteger
--R 
--R
--R   (101)  208
--R                                                        Type: PositiveInteger
--E 101

--S 102 of 350
g:=primitiveElement()$F
 

            1
   (102)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R            1
--R   (102)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 102

--S 103 of 350
discreteLog(a)
 

   (103)  207
                                                        Type: PositiveInteger
--R 
--R
--R   (103)  207
--R                                                        Type: PositiveInteger
--E 103

--S 104 of 350
g**% - a
 

   (104)  0
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R   (104)  0
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 104

--S 105 of 350
discreteLog(b,a)
 

   (105)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (105)  "failed"
--R                                                    Type: Union("failed",...)
--E 105

--S 106 of 350
extensionDegree()$F
 

   (106)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (106)  4
--R                                                        Type: PositiveInteger
--E 106

--S 107 of 350
degree(a)
 

   (107)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (107)  4
--R                                                        Type: PositiveInteger
--E 107

--S 108 of 350
normalElement()$F
 

            3
   (108)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R            3
--R   (108)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 108

--S 109 of 350
definingPolynomial()$F
 

           4    2
   (109)  ?  + ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R           4    2
--R   (109)  ?  + ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 109

--S 110 of 350
minimalPolynomial(a)
 

           4    3    2
   (110)  ?  + ?  + ?  + 3? + 3
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R           4    3    2
--R   (110)  ?  + ?  + ?  + 3? + 3
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 110

--S 111 of 350
Frobenius(a)
 

            411
   (111)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R            411
--R   (111)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 111

--S 112 of 350
linearAssociatedOrder(a)
 

           4
   (112)  ?  + 4
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R           4
--R   (112)  ?  + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 112

--S 113 of 350
linearAssociatedLog(a)
 

            3
   (113)  3?  + 4? + 4
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R            3
--R   (113)  3?  + 4? + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 113

--S 114 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
     468
   %C
     312
   %C
     390
   %C
     416
   %C
     207
   %C
     207
   %C
                                                                   Type: Void
--R 
--R     468
--R   %C
--R     312
--R   %C
--R     390
--R   %C
--R     416
--R   %C
--R     207
--R   %C
--R     207
--R   %C
--R                                                                   Type: Void
--E 114

--S 115 of 350
p:=3
 

   (115)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (115)  3
--R                                                        Type: PositiveInteger
--E 115

--S 116 of 350
P:=PrimeField p
 

   (116)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (116)  PrimeField 3
--R                                                                 Type: Domain
--E 116

--S 117 of 350
d1:=2
 

   (117)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (117)  2
--R                                                        Type: PositiveInteger
--E 117

--S 118 of 350
d2:=3
 

   (118)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (118)  3
--R                                                        Type: PositiveInteger
--E 118

--S 119 of 350
f1:=createIrreduciblePoly(d1)$FFPOLY(P)
 

           2
   (119)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (119)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 119

--S 120 of 350
F1:=FFP(P,f1)
 

   (120)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (120)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R                                                                 Type: Domain
--E 120

--S 121 of 350
f2:=createIrreduciblePoly(d2)$FFPOLY(F1)
 

           3
   (121)  ?  + ? + %D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (121)  ?  + ? + %D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 121

--S 122 of 350
F:=FFP(F1,f2)
 

   (122)
  FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 
  3,?*?+1),?**3+?+D)
                                                                 Type: Domain
--R 
--R
--R   (122)
--R  FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 
--R  3,?*?+1),?**3+?+D)
--R                                                                 Type: Domain
--E 122

--S 123 of 350
size()$F
 

   (123)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (123)  729
--R                                                     Type: NonNegativeInteger
--E 123

--S 124 of 350
a:=index(size()$F quo 3)$F
 

               2
   (124)  %D %E
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R               2
--R   (124)  %D %E
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 124

--S 125 of 350
b:=index(size()$F quo 7)$F
 

            2
   (125)  %E  + 2%E + %D + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R            2
--R   (125)  %E  + 2%E + %D + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 125

--S 126 of 350
a+b
 

                    2
   (126)  (%D + 1)%E  + 2%E + %D + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                    2
--R   (126)  (%D + 1)%E  + 2%E + %D + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 126

--S 127 of 350
a-b
 

                    2
   (127)  (%D + 2)%E  + %E + 2%D + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                    2
--R   (127)  (%D + 2)%E  + %E + 2%D + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 127

--S 128 of 350
a*b
 

                    2
   (128)  (%D + 2)%E  + (%D + 1)%E + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                    2
--R   (128)  (%D + 2)%E  + (%D + 1)%E + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 128

--S 129 of 350
a/b
 

                2
   (129)  2%D %E  + 2%D + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                2
--R   (129)  2%D %E  + 2%D + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 129

--S 130 of 350
a**1234
 

             2
   (130)  2%E  + %D %E + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R             2
--R   (130)  2%E  + %D %E + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 130

--S 131 of 350
a**(-1)
 

               2
   (131)  %D %E  + %E + %D
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R               2
--R   (131)  %D %E  + %E + %D
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 131

--S 132 of 350
g := generator()$F
 

   (132)  %E
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (132)  %E
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 132

--S 133 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (133)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (133)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 133

--S 134 of 350
order(a)
 

   (134)  52
                                                        Type: PositiveInteger
--R 
--R
--R   (134)  52
--R                                                        Type: PositiveInteger
--E 134

--S 135 of 350
g:=primitiveElement()$F
 

   (135)  %E + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (135)  %E + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 135

--S 136 of 350
discreteLog(a)
 

   (136)  462
                                                        Type: PositiveInteger
--R 
--R
--R   (136)  462
--R                                                        Type: PositiveInteger
--E 136

--S 137 of 350
g**% - a
 

   (137)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (137)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 137

--S 138 of 350
discreteLog(b,a)
 

   (138)  154
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (138)  154
--R                                          Type: Union(NonNegativeInteger,...)
--E 138

--S 139 of 350
extensionDegree()$F
 

   (139)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (139)  3
--R                                                        Type: PositiveInteger
--E 139

--S 140 of 350
degree(a)
 

   (140)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (140)  3
--R                                                        Type: PositiveInteger
--E 140

--S 141 of 350
normalElement()$F
 

            2
   (141)  %E  + %E
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R            2
--R   (141)  %E  + %E
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 141

--S 142 of 350
definingPolynomial()$F
 

           3
   (142)  ?  + ? + %D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (142)  ?  + ? + %D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 142

--S 143 of 350
minimalPolynomial(a)
 

           3        2
   (143)  ?  + 2%D ?  + 2? + 2%D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3        2
--R   (143)  ?  + 2%D ?  + 2? + 2%D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 143

--S 144 of 350
Frobenius(a)
 

               2
   (144)  %D %E  + 2%E + 2%D
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R               2
--R   (144)  %D %E  + 2%E + 2%D
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 144

--S 145 of 350
linearAssociatedOrder(a)
 

           3
   (145)  ?  + 2
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (145)  ?  + 2
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 145

--S 146 of 350
linearAssociatedLog(a)
 

                    2
   (146)  (2%D + 2)?  + (2%D + 1)?
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R                    2
--R   (146)  (2%D + 2)?  + (2%D + 1)?
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 146

--S 147 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   %D
   %D
        2
   %D %E
        2
   %D %E
                                                                   Type: Void
--R 
--R   %D
--R   %D
--R        2
--R   %D %E
--R        2
--R   %D %E
--R                                                                   Type: Void
--E 147

--S 148 of 350
f1:=createNormalPoly(d1)$FFPOLY(P)
 

           2
   (148)  ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (148)  ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 148

--S 149 of 350
F1:=FFNBP(P,f1)
 

   (149)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
                                                                 Type: Domain
--R 
--R
--R   (149)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R                                                                 Type: Domain
--E 149

--S 150 of 350
f2:=createIrreduciblePoly(d2)$FFPOLY(F1)
 

           3
   (150)  ?  + ? + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3
--R   (150)  ?  + ? + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 150

--S 151 of 350
F:=FFP(F1,f2)
 

   (151)
  FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(
  PrimeField 3,?*?+2*?+2),?**3+?+F)
                                                                 Type: Domain
--R 
--R
--R   (151)
--R  FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(
--R  PrimeField 3,?*?+2*?+2),?**3+?+F)
--R                                                                 Type: Domain
--E 151 of 350

--S 152 of 250
size()$F
 

   (152)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (152)  729
--R                                                     Type: NonNegativeInteger
--E 152

--S 153 of 350
a:=index(size()$F quo 3)$F
 

            q  2
   (153)  %F %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2
--R   (153)  %F %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 153

--S 154 of 350
b:=index(size()$F quo 7)$F
 

               2              q
   (154)  %F %G  + 2%F %G + %F  + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R               2              q
--R   (154)  %F %G  + 2%F %G + %F  + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 154

--S 155 of 350
a+b
 

            2              q
   (155)  %G  + 2%F %G + %F  + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            2              q
--R   (155)  %G  + 2%F %G + %F  + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 155

--S 156 of 350
a-b
 

             q         2              q
   (156)  (%F  + 2%F)%G  + %F %G + 2%F  + %F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R             q         2              q
--R   (156)  (%F  + 2%F)%G  + %F %G + 2%F  + %F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 156

--S 157 of 350
a*b
 

            q  2      q
   (157)  %F %G  + 2%F %G + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2      q
--R   (157)  %F %G  + 2%F %G + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 157

--S 158 of 350
a/b
 

            2
   (158)  %G  + %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            2
--R   (158)  %G  + %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 158

--S 159 of 350
a**1234
 

            q  2             q
   (159)  %F %G  + %F %G + %F  + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2             q
--R   (159)  %F %G  + %F %G + %F  + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 159

--S 160 of 350
a**(-1)
 

            q  2          q
   (160)  %F %G  + %G + %F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2          q
--R   (160)  %F %G  + %G + %F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 160

--S 161 of 350
g := generator()$F
 

   (161)  %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (161)  %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 161

--S 162 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (162)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (162)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 162

--S 163 of 350
order(a)
 

   (163)  728
                                                        Type: PositiveInteger
--R 
--R
--R   (163)  728
--R                                                        Type: PositiveInteger
--E 163

--S 164 of 350
g:=primitiveElement()$F
 

   (164)  %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (164)  %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 164

--S 165 of 350
discreteLog(a)
 

   (165)  639
                                                        Type: PositiveInteger
--R 
--R
--R   (165)  639
--R                                                        Type: PositiveInteger
--E 165

--S 166 of 350
g**% - a
 

   (166)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (166)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 166

--S 167 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (167)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (167)  "failed"
--R                                                    Type: Union("failed",...)
--E 167

--S 168 of 350
extensionDegree()$F
 

   (168)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (168)  3
--R                                                        Type: PositiveInteger
--E 168

--S 169 of 350
degree(a)
 

   (169)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (169)  3
--R                                                        Type: PositiveInteger
--E 169

--S 170 of 350
normalElement()$F
 

            2
   (170)  %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            2
--R   (170)  %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 170

--S 171 of 350
definingPolynomial()$F
 

           3
   (171)  ?  + ? + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3
--R   (171)  ?  + ? + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 171

--S 172 of 350
minimalPolynomial(a)
 

           3      q 2       q             q
   (172)  ?  + 2%F ?  + (2%F  + %F)? + 2%F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q 2       q             q
--R   (172)  ?  + 2%F ?  + (2%F  + %F)? + 2%F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 172

--S 173 of 350
Frobenius(a)
 

            q  2               q
   (173)  %F %G  + 2%F %G + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2               q
--R   (173)  %F %G  + 2%F %G + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 173

--S 174 of 350
linearAssociatedOrder(a)
 

           3      q
   (174)  ?  + 2%F  + 2%F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q
--R   (174)  ?  + 2%F  + 2%F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 174

--S 175 of 350
linearAssociatedLog(a)
 

            q
   (175)  %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R            q
--R   (175)  %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 175

--S 176 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
     q
   %F
     q
   %F
     q  2
   %F %G
     q  2
   %F %G
                                                                   Type: Void
--R 
--R     q
--R   %F
--R     q
--R   %F
--R     q  2
--R   %F %G
--R     q  2
--R   %F %G
--R                                                                   Type: Void
--E 176

--S 177 of 350
f1:=createPrimitivePoly(d1)$FFPOLY(P)
 

           2
   (177)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (177)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 177

--S 178 of 350
F1:=FFCGP(P,f1)
 

   (178)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
                                                                 Type: Domain
--R 
--R
--R   (178)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R                                                                 Type: Domain
--E 178

--S 179 of 350
f2:=createIrreduciblePoly(d2)$FFPOLY(F1)
 

           3         1
   (179)  ?  + ? + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3         1
--R   (179)  ?  + ? + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 179

--S 180 of 350
F:=FFP(F1,f2)
 

   (180)
  FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(
  PrimeField 3,?*?+?+2),?**3+?+H**1)
                                                                 Type: Domain
--R 
--R
--R   (180)
--R  FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(
--R  PrimeField 3,?*?+?+2),?**3+?+H**1)
--R                                                                 Type: Domain
--E 180

--S 181 of 350
size()$F
 

   (181)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (181)  729
--R                                                     Type: NonNegativeInteger
--E 181

--S 192 of 350
a:=index(size()$F quo 3)$F
 

            2  2
   (182)  %H %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2  2
--R   (182)  %H %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 182

--S 183 of 350
b:=index(size()$F quo 7)$F
 

            2     1       4
   (183)  %I  + %H %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2     1       4
--R   (183)  %I  + %H %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 183

--S 184 of 350
a+b
 

            3  2     1       4
   (184)  %H %I  + %H %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            3  2     1       4
--R   (184)  %H %I  + %H %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 184

--S 185 of 350
a-b
 

            5  2     5
   (185)  %H %I  + %H %I + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            5  2     5
--R   (185)  %H %I  + %H %I + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 185

--S 186 of 350
a*b
 

            2  2     3
   (186)  %H %I  + %H %I + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2  2     3
--R   (186)  %H %I  + %H %I + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 186

--S 187 of 350
a/b
 

            1  2     6
   (187)  %H %I  + %H %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            1  2     6
--R   (187)  %H %I  + %H %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 187

--S 188 of 350
a**1234
 

            5  2     7
   (188)  %H %I  + %H %I + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            5  2     7
--R   (188)  %H %I  + %H %I + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 188

--S 189 of 350
a**(-1)
 

            4  2     1       4
   (189)  %H %I  + %H %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            4  2     1       4
--R   (189)  %H %I  + %H %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 189

--S 190 of 350
g := generator()$F
 

   (190)  %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (190)  %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 190

--S 191 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (191)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (191)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 191

--S 192 of 350
order(a)
 

   (192)  91
                                                        Type: PositiveInteger
--R 
--R
--R   (192)  91
--R                                                        Type: PositiveInteger
--E 192

--S 193 of 350
g:=primitiveElement()$F
 

   (193)  %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (193)  %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 193

--S 194 of 350
discreteLog(a)
 

   (194)  184
                                                        Type: PositiveInteger
--R 
--R
--R   (194)  184
--R                                                        Type: PositiveInteger
--E 194

--S 195 of 350
g**% - a
 

   (195)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (195)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 195

--S 196 of 350
discreteLog(b,a)
 

   (196)  352
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (196)  352
--R                                          Type: Union(NonNegativeInteger,...)
--E 196

--S 197 of 350
extensionDegree()$F
 

   (197)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (197)  3
--R                                                        Type: PositiveInteger
--E 197

--S 198 of 350
degree(a)
 

   (198)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (198)  3
--R                                                        Type: PositiveInteger
--E 198

--S 199 of 350
normalElement()$F
 

            2
   (199)  %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2
--R   (199)  %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 199

--S 200 of 350
definingPolynomial()$F
 

           3         1
   (200)  ?  + ? + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3         1
--R   (200)  ?  + ? + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 200

--S 201 of 350
minimalPolynomial(a)
 

           3     6 2     4      4
   (201)  ?  + %H ?  + %H ? + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     6 2     4      4
--R   (201)  ?  + %H ?  + %H ? + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 201

--S 202 of 350
Frobenius(a)
 

            2  2          6
   (202)  %H %I  + %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2  2          6
--R   (202)  %H %I  + %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 202

--S 203 of 350
linearAssociatedOrder(a)
 

           3     4
   (203)  ?  + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4
--R   (203)  ?  + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 203

--S 204 of 350
linearAssociatedLog(a)
 

            2
   (204)  %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R            2
--R   (204)  %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 204

--S 205 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   1
     2
   %H
     2  2
   %H %I
     2  2
   %H %I
                                                                   Type: Void
--R 
--R   1
--R     2
--R   %H
--R     2  2
--R   %H %I
--R     2  2
--R   %H %I
--R                                                                   Type: Void
--E 205

--S 206 of 350
f1:=createIrreduciblePoly(d1)$FFPOLY(P)
 

           2
   (206)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (206)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 206

--S 207 of 350
F1:=FFP(P,f1)
 

   (207)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (207)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R                                                                 Type: Domain
--E 207

--S 208 of 350
f2:=createNormalPoly(d2)$FFPOLY(F1)
 

           3     2
   (208)  ?  + 2?  + 1
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3     2
--R   (208)  ?  + 2?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 208

--S 209 of 350
F:=FFNBP(F1,f2)
 

   (209)
  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(
  PrimeField 3,?*?+1),?**3+2*?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (209)
--R  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(
--R  PrimeField 3,?*?+1),?**3+2*?*?+1)
--R                                                                 Type: Domain
--E 209

--S 210 of 350
size()$F
 

   (210)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (210)  729
--R                                                     Type: NonNegativeInteger
--E 210

--S 211 of 350
a:=index(size()$F quo 3)$F
 

                2
               q
   (211)  %D %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                2
--R               q
--R   (211)  %D %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 211

--S 212 of 350
b:=index(size()$F quo 7)$F
 

             2
            q       q
   (212)  %J   + 2%J  + (%D + 2)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R             2
--R            q       q
--R   (212)  %J   + 2%J  + (%D + 2)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 212

--S 213 of 350
a+b
 

                     2
                    q       q
   (213)  (%D + 1)%J   + 2%J  + (%D + 2)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                     2
--R                    q       q
--R   (213)  (%D + 1)%J   + 2%J  + (%D + 2)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 213

--S 214 of 350
a-b
 

                     2
                    q      q
   (214)  (%D + 2)%J   + %J  + (2%D + 1)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                     2
--R                    q      q
--R   (214)  (%D + 2)%J   + %J  + (2%D + 1)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 214

--S 215 of 350
a*b
 

                     2
                    q         q
   (215)  (%D + 2)%J   + %D %J  + (2%D + 1)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                     2
--R                    q         q
--R   (215)  (%D + 2)%J   + %D %J  + (2%D + 1)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 215

--S 216 of 350
a/b
 

              2
             q         q
   (216)  2%J   + %D %J  + 2%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R              2
--R             q         q
--R   (216)  2%J   + %D %J  + 2%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 216

--S 217 of 350
a**1234
 

            q
   (217)  %J  + 2%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R            q
--R   (217)  %J  + 2%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 217

--S 218 of 350
a**(-1)
 

                q
   (218)  2%D %J  + %D %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                q
--R   (218)  2%D %J  + %D %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 218

--S 219 of 350
g := generator()$F
 

   (219)  %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (219)  %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 219

--S 220 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (220)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (220)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 220

--S 221 of 350
order(a)
 

   (221)  52
                                                        Type: PositiveInteger
--R 
--R
--R   (221)  52
--R                                                        Type: PositiveInteger
--E 221

--S 222 of 350
g:=primitiveElement()$F
 

                    q
   (222)  (%D + 1)%J  + 2%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                    q
--R   (222)  (%D + 1)%J  + 2%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 222

--S 223 of 350
discreteLog(a)
 

   (223)  462
                                                        Type: PositiveInteger
--R 
--R
--R   (223)  462
--R                                                        Type: PositiveInteger
--E 223

--S 224 of 350
g**% - a
 

   (224)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (224)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 224

--S 225 of 350
discreteLog(b,a)
 

   (225)  70
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (225)  70
--R                                          Type: Union(NonNegativeInteger,...)
--E 225

--S 226 of 350
extensionDegree()$F
 

   (226)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (226)  3
--R                                                        Type: PositiveInteger
--E 226

--S 227 of 350
degree(a)
 

   (227)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (227)  3
--R                                                        Type: PositiveInteger
--E 227

--S 228 of 350
normalElement()$F
 

   (228)  %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (228)  %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 228

--S 229 of 350
definingPolynomial()$F
 

           3     2
   (229)  ?  + 2?  + 1
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3     2
--R   (229)  ?  + 2?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 229

--S 230 of 350
minimalPolynomial(a)
 

           3        2
   (230)  ?  + 2%D ?  + 2%D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3        2
--R   (230)  ?  + 2%D ?  + 2%D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 230

--S 231 of 350
Frobenius(a)
 

   (231)  %D %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (231)  %D %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 231

--S 232 of 350
linearAssociatedOrder(a)
 

           3
   (232)  ?  + 2
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (232)  ?  + 2
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 232

--S 233 of 350
linearAssociatedLog(a)
 

              2
   (233)  %D ?
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R              2
--R   (233)  %D ?
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 233

--S 234 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
         2
        q         q
   %D %J   + %D %J  + %D %J
         2
        q         q
   %D %J   + %D %J  + %D %J
         2
        q
   %D %J
         2
        q
   %D %J
                                                                   Type: Void
--R 
--R         2
--R        q         q
--R   %D %J   + %D %J  + %D %J
--R         2
--R        q         q
--R   %D %J   + %D %J  + %D %J
--R         2
--R        q
--R   %D %J
--R         2
--R        q
--R   %D %J
--R                                                                   Type: Void
--E 234

--S 235 of 350
f1:=createNormalPoly(d1)$FFPOLY(P)
 

           2
   (235)  ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (235)  ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 235

--S 236 of 350
F1:=FFNBP(P,f1)
 

   (236)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
                                                                 Type: Domain
--R 
--R
--R   (236)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R                                                                 Type: Domain
--E 236

--S 237 of 350
f2:=createNormalPoly(d2)$FFPOLY(F1)
 

           3       q        2     q
   (237)  ?  + (2%F  + 2%F)?  + %F  + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3       q        2     q
--R   (237)  ?  + (2%F  + 2%F)?  + %F  + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 237

--S 238 of 350
F:=FFNBP(F1,f2)
 

   (238)
  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionBy
  Polynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
                                                                 Type: Domain
--R 
--R
--R   (238)
--R  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionBy
--R  Polynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R                                                                 Type: Domain
--E 238

--S 239 of 350
size()$F
 

   (239)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (239)  729
--R                                                     Type: NonNegativeInteger
--E 239

--S 240 of 350
a:=index(size()$F quo 3)$F
 

                2
            q  q
   (240)  %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                2
--R            q  q
--R   (240)  %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 240

--S 241 of 350
b:=index(size()$F quo 7)$F
 

                2
               q          q      q
   (241)  %F %K   + 2%F %K  + (%F  + 2%F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                2
--R               q          q      q
--R   (241)  %F %K   + 2%F %K  + (%F  + 2%F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 241

--S 242 of 350
a+b
 

             2
            q          q      q
   (242)  %K   + 2%F %K  + (%F  + 2%F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R             2
--R            q          q      q
--R   (242)  %K   + 2%F %K  + (%F  + 2%F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 242

--S 243 of 350
a-b
 

                        2
             q         q         q       q
   (243)  (%F  + 2%F)%K   + %F %K  + (2%F  + %F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                        2
--R             q         q         q       q
--R   (243)  (%F  + 2%F)%K   + %F %K  + (2%F  + %F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 243

--S 244 of 350
a*b
 

                2
            q  q        q         q      q
   (244)  %F %K   + (2%F  + 2%F)%K  + 2%F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                2
--R            q  q        q         q      q
--R   (244)  %F %K   + (2%F  + 2%F)%K  + 2%F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 244

--S 245 of 350
a/b
 

                         2
              q         q       q         q       q
   (245)  (2%F  + 2%F)%K   + (%F  + 2%F)%K  + (2%F  + 2%F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                         2
--R              q         q       q         q       q
--R   (245)  (2%F  + 2%F)%K   + (%F  + 2%F)%K  + (2%F  + 2%F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 245

--S 246 of 350
a**1234
 

             q         q       q
   (246)  (%F  + 2%F)%K  + (2%F  + %F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R             q         q       q
--R   (246)  (%F  + 2%F)%K  + (2%F  + %F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 246

--S 247 of 350
a**(-1)
 

                q
   (247)  2%F %K  + %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                q
--R   (247)  2%F %K  + %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 247

--S 248 of 350
g := generator()$F
 

   (248)  %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (248)  %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 248

--S 249 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (249)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (249)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 249

--S 250 of 350
order(a)
 

   (250)  104
                                                        Type: PositiveInteger
--R 
--R
--R   (250)  104
--R                                                        Type: PositiveInteger
--E 250

--S 251 of 350
g:=primitiveElement()$F
 

               q     q
   (251)  %F %K  + %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R               q     q
--R   (251)  %F %K  + %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 251

--S 252 of 350
discreteLog(a)
 

   (252)  343
                                                        Type: PositiveInteger
--R 
--R
--R   (252)  343
--R                                                        Type: PositiveInteger
--E 252

--S 253 of 350
g**% - a
 

   (253)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (253)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 253

--S 254 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (254)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (254)  "failed"
--R                                                    Type: Union("failed",...)
--E 254

--S 255 of 350
extensionDegree()$F
 

   (255)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (255)  3
--R                                                        Type: PositiveInteger
--E 255

--S 256 of 350
degree(a)
 

   (256)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (256)  3
--R                                                        Type: PositiveInteger
--E 256

--S 257 of 350
normalElement()$F
 

   (257)  %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (257)  %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 257

--S 258 of 350
definingPolynomial()$F
 

           3       q        2     q
   (258)  ?  + (2%F  + 2%F)?  + %F  + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3       q        2     q
--R   (258)  ?  + (2%F  + 2%F)?  + %F  + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 258

--S 259 of 350
minimalPolynomial(a)
 

           3      q 2
   (259)  ?  + 2%F ?  + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q 2
--R   (259)  ?  + 2%F ?  + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 259

--S 260 of 350
Frobenius(a)
 

            q
   (260)  %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R            q
--R   (260)  %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 260

--S 261 of 350
linearAssociatedOrder(a)
 

           3      q
   (261)  ?  + 2%F  + 2%F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q
--R   (261)  ?  + 2%F  + 2%F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 261

--S 262 of 350
linearAssociatedLog(a)
 

            q 2
   (262)  %F ?
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R            q 2
--R   (262)  %F ?
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 262

--S 263 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
          2
         q          q
   2%F %K   + 2%F %K  + 2%F %K
         2
     q  q      q  q     q
   %F %K   + %F %K  + %F %K
         2
     q  q
   %F %K
         2
     q  q
   %F %K
                                                                   Type: Void
--R 
--R          2
--R         q          q
--R   2%F %K   + 2%F %K  + 2%F %K
--R         2
--R     q  q      q  q     q
--R   %F %K   + %F %K  + %F %K
--R         2
--R     q  q
--R   %F %K
--R         2
--R     q  q
--R   %F %K
--R                                                                   Type: Void
--E 263

--S 264 of 350
f1:=createPrimitivePoly(d1)$FFPOLY(P)
 

           2
   (264)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (264)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 264

--S 265 of 350
F1:=FFCGP(P,f1)
 

   (265)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
                                                                 Type: Domain
--R 
--R
--R   (265)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R                                                                 Type: Domain
--E 265

--S 266 of 350
f2:=createNormalPoly(d2)$FFPOLY(F1)
 

           3     4 2
   (266)  ?  + %H ?  + 1
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4 2
--R   (266)  ?  + %H ?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 266

--S 267 of 350
F:=FFNBP(F1,f2)
 

   (267)
  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionBy
  Polynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (267)
--R  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionBy
--R  Polynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R                                                                 Type: Domain
--E 267

--S 268 of 350
size()$F
 

   (268)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (268)  729
--R                                                     Type: NonNegativeInteger
--E 268

--S 269 of 350
a:=index(size()$F quo 3)$F
 

                2
            2  q
   (269)  %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            2  q
--R   (269)  %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 269

--S 270 of 350
b:=index(size()$F quo 7)$F
 

             2
            q      1  q     4
   (270)  %L   + %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R             2
--R            q      1  q     4
--R   (270)  %L   + %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 270

--S 271 of 350
a+b
 

                2
            3  q      1  q     4
   (271)  %H %L   + %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            3  q      1  q     4
--R   (271)  %H %L   + %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 271

--S 272 of 350
a-b
 

                2
            5  q      5  q
   (272)  %H %L   + %H %L  + %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            5  q      5  q
--R   (272)  %H %L   + %H %L  + %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 272

--S 273 of 350
a*b
 

                2
            7  q      q     6
   (273)  %H %L   + %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            7  q      q     6
--R   (273)  %H %L   + %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 273

--S 274 of 350
a/b
 

                2
            2  q      5  q     6
   (274)  %H %L   + %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            2  q      5  q     6
--R   (274)  %H %L   + %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 274

--S 275 of 350
a**1234
 

            q     4
   (275)  %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            q     4
--R   (275)  %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 275

--S 276 of 350
a**(-1)
 

            6  q     2
   (276)  %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            6  q     2
--R   (276)  %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 276

--S 277 of 350
g := generator()$F
 

   (277)  %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (277)  %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 277

--S 278 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (278)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (278)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 278

--S 279 of 350
order(a)
 

   (279)  52
                                                        Type: PositiveInteger
--R 
--R
--R   (279)  52
--R                                                        Type: PositiveInteger
--E 279

--S 280 of 350
g:=primitiveElement()$F
 

            1  q     2
   (280)  %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            1  q     2
--R   (280)  %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 280

--S 281 of 350
discreteLog(a)
 

   (281)  98
                                                        Type: PositiveInteger
--R 
--R
--R   (281)  98
--R                                                        Type: PositiveInteger
--E 281

--S 282 of 350
g**% - a
 

   (282)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (282)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 282

--S 283 of 350
discreteLog(b,a)
 

   (283)  574
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (283)  574
--R                                          Type: Union(NonNegativeInteger,...)
--E 283

--S 284 of 350
extensionDegree()$F
 

   (284)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (284)  3
--R                                                        Type: PositiveInteger
--E 284

--S 285 of 350
degree(a)
 

   (285)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (285)  3
--R                                                        Type: PositiveInteger
--E 285

--S 286 of 350
normalElement()$F
 

   (286)  %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (286)  %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 286

--S 287 of 350
definingPolynomial()$F
 

           3     4 2
   (287)  ?  + %H ?  + 1
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4 2
--R   (287)  ?  + %H ?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 287

--S 288 of 350
minimalPolynomial(a)
 

           3     6 2     6
   (288)  ?  + %H ?  + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     6 2     6
--R   (288)  ?  + %H ?  + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 288

--S 289 of 350
Frobenius(a)
 

            2
   (289)  %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            2
--R   (289)  %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 289

--S 290 of 350
linearAssociatedOrder(a)
 

           3     4
   (290)  ?  + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4
--R   (290)  ?  + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 290 of 350

--S 291 of 350
linearAssociatedLog(a)
 

            2 2
   (291)  %H ?
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R            2 2
--R   (291)  %H ?
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 291

--S 292 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
         2
     2  q      2  q     2
   %H %L   + %H %L  + %H %L
         2
     2  q      2  q     2
   %H %L   + %H %L  + %H %L
         2
     2  q
   %H %L
         2
     2  q
   %H %L
                                                                   Type: Void
--R 
--R         2
--R     2  q      2  q     2
--R   %H %L   + %H %L  + %H %L
--R         2
--R     2  q      2  q     2
--R   %H %L   + %H %L  + %H %L
--R         2
--R     2  q
--R   %H %L
--R         2
--R     2  q
--R   %H %L
--R                                                                   Type: Void
--E 292

--S 293 of 350
P3:= PF 3
 

   (293)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (293)  PrimeField 3
--R                                                                 Type: Domain
--E 293

--S 294 of 350
fi:=createIrreduciblePoly(6)$FFPOLY(P3)
 

           6
   (294)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           6
--R   (294)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 294

--S 295 of 350
fn:=createNormalPoly(6)$FFPOLY(P3)
 

           6     5    3
   (295)  ?  + 2?  + ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           6     5    3
--R   (295)  ?  + 2?  + ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 295

--S 296 of 350
fp:=createPrimitivePoly(3)$FFPOLY(P3)
 

           3
   (296)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           3
--R   (296)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 296

--S 297 of 350
F:=FFP(P3,fn)
 

   (297)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (297)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 297

--S 298 of 350
N:=FFNBP(P3,fn)
 

   (298)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (298)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 298

--S 299 of 350
a:=index(size()$F quo 3)$F
 

            5
   (299)  %M
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            5
--R   (299)  %M
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 299

--S 300 of 350
b:=index(size()$F quo 7)$F
 

            4      2
   (300)  %M  + 2%M  + %M + 2
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            4      2
--R   (300)  %M  + 2%M  + %M + 2
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 300

--S 301 of 350
an:=coerce(a)$FFHOM(F,P3,N)
 

             4      3
            q      q      q
   (301)  %N   + %N   + %N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R             4      3
--R            q      q      q
--R   (301)  %N   + %N   + %N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 301

--S 302 of 350
bn:=coerce(b)$FFHOM(F,P3,N)
 

             3      2
            q      q       q
   (302)  %N   + %N   + 2%N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R             3      2
--R            q      q       q
--R   (302)  %N   + %N   + 2%N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 302

--S 303 of 350
cn := an*bn
 

              5       4      3
             q       q      q      q
   (303)  2%N   + 2%N   + %N   + %N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5       4      3
--R             q       q      q      q
--R   (303)  2%N   + 2%N   + %N   + %N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 303

--S 304 of 350
coerce(cn)$FFHOM(F,P3,N)
 

            5      3      2
   (304)  %M  + 2%M  + 2%M
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            5      3      2
--R   (304)  %M  + 2%M  + 2%M
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 304

--S 305 of 350
c:=a*b
 

            5      3      2
   (305)  %M  + 2%M  + 2%M
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            5      3      2
--R   (305)  %M  + 2%M  + 2%M
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 305

--S 306 of 350
F:=FFP(P3,fi)
 

   (306)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
                                                                 Type: Domain
--R 
--R
--R   (306)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R                                                                 Type: Domain
--E 306

--S 307 of 350
N:=FFNBP(P3,fn)
 

   (307)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (307)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 307

--S 308 of 350
a:=index(size()$F quo 3)$F
 

            5
   (308)  %O
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R            5
--R   (308)  %O
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 308

--S 309 of 350
b:=index(size()$F quo 7)$F
 

            4      2
   (309)  %O  + 2%O  + %O + 2
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R            4      2
--R   (309)  %O  + 2%O  + %O + 2
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 309

--S 310 of 350
an:=coerce(a)$FFHOM(F,P3,N)
 

              5      4       3      2
             q      q       q      q      q
   (310)  2%N   + %N   + 2%N   + %N   + %N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5      4       3      2
--R             q      q       q      q      q
--R   (310)  2%N   + %N   + 2%N   + %N   + %N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 310

--S 311 of 350
bn:=coerce(b)$FFHOM(F,P3,N)
 

              3      2
             q      q
   (311)  2%N   + %N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              3      2
--R             q      q
--R   (311)  2%N   + %N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 311

--S 312 of 350
cn := an*bn
 

              5      4      3      2
             q      q      q      q      q
   (312)  2%N   + %N   + %N   + %N   + %N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5      4      3      2
--R             q      q      q      q      q
--R   (312)  2%N   + %N   + %N   + %N   + %N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 312

--S 313 of 350
coerce(cn)$FFHOM(F,P3,N)
 

             5      4     3     2
   (313)  2%O  + 2%O  + %O  + %O  + %O + 1
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R             5      4     3     2
--R   (313)  2%O  + 2%O  + %O  + %O  + %O + 1
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 313

--S 314 of 350
c:=a*b
 

             5      4     3     2
   (314)  2%O  + 2%O  + %O  + %O  + %O + 1
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R             5      4     3     2
--R   (314)  2%O  + 2%O  + %O  + %O  + %O + 1
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 314

--S 315 of 350
C:=FFCGP(P3,fp)
 

   (315)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
                                                                 Type: Domain
--R 
--R
--R   (315)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R                                                                 Type: Domain
--E 315

--S 316 of 350
N:=FFNBP(P3,fn)
 

   (316)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (316)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 316

--S 317 of 350
a:=index(size()$C quo 3)$C
 

            8
   (317)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            8
--R   (317)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 317

--S 318 of 350
b:=index(size()$C quo 7)$C
 

            2
   (318)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            2
--R   (318)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 318

--S 319 of 350
an:=coerce(a)$FFHOM(C,P3,N)
 

              4       3
             q       q       q
   (319)  2%N   + 2%N   + 2%N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              4       3
--R             q       q       q
--R   (319)  2%N   + 2%N   + 2%N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 319

--S 320 of 350
bn:=coerce(b)$FFHOM(C,P3,N)
 

              5       2
             q       q
   (320)  2%N   + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5       2
--R             q       q
--R   (320)  2%N   + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 320

--S 321 of 350
cn := an+bn
 

              5       4       3       2
             q       q       q       q       q
   (321)  2%N   + 2%N   + 2%N   + 2%N   + 2%N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5       4       3       2
--R             q       q       q       q       q
--R   (321)  2%N   + 2%N   + 2%N   + 2%N   + 2%N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 321

--S 322 of 350
coerce(cn)$FFHOM(C,P3,N)
 

            13
   (322)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            13
--R   (322)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 322

--S 323 of 350
c:=a+b
 

            13
   (323)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            13
--R   (323)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 323

--S 324 of 350
f:=createPrimitiveNormalPoly(5)$FFPOLY(P3)
 

           5     4
   (324)  ?  + 2?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           5     4
--R   (324)  ?  + 2?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 324

--S 325 of 350
FP:=FFP(P3,f)
 

   (325)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
                                                                 Type: Domain
--R 
--R
--R   (325)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R                                                                 Type: Domain
--E 325

--S 326 of 350
Fc:=FFCGP(P3,f)  -- FC is a domain abbreviation
 

   (326)
   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
                                                                 Type: Domain
--R 
--R
--R   (326)
--R   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R                                                                 Type: Domain
--E 326

--S 328 of 350
FN:=FFNBP(P3,f)
 

   (327)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
                                                                 Type: Domain
--R 
--R
--R   (327)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R                                                                 Type: Domain
--E 327

--S 328 of 350
ap:=index(size()$FP quo 3)$FP
 

            4
   (328)  %Q
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4
--R   (328)  %Q
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 328

--S 329 of 350
ac:=coerce(ap)$FFHOM(Fc,P3,FP)
 

            4
   (329)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4
--R   (329)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 329

--S 330 of 350
an:=coerce(ap)$FFHOM(FN,P3,FP)
 

              3       2
             q       q       q
   (330)  2%S   + 2%S   + 2%S  + %S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R              3       2
--R             q       q       q
--R   (330)  2%S   + 2%S   + 2%S  + %S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 330

--S 331 of 350
bp:=index(size()$FP quo 7)$FP
 

            3
   (331)  %Q  + 2%Q + 1
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            3
--R   (331)  %Q  + 2%Q + 1
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 331

--S 332 of 350
bc:=coerce(bp)$FFHOM(Fc,P3,FP)
 

            133
   (332)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            133
--R   (332)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 332

--S 333 of 350
bn:=coerce(bp)$FFHOM(FN,P3,FP)
 

             4      3      2
            q      q      q       q
   (333)  %S   + %S   + %S   + 2%S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4      3      2
--R            q      q      q       q
--R   (333)  %S   + %S   + %S   + 2%S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 333

--S 334 of 350
ac+bc
 

            187
   (334)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (334)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 334

--S 335 of 350
an*bn
 

             4      2
            q      q      q
   (335)  %S   + %S   + %S  + 2%S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4      2
--R            q      q      q
--R   (335)  %S   + %S   + %S  + 2%S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 335

--S 336 of 350
ap+bp
 

            4     3
   (336)  %Q  + %Q  + 2%Q + 1
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4     3
--R   (336)  %Q  + %Q  + 2%Q + 1
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 336

--S 337 of 350
an+bn
 

             4
            q      q
   (337)  %S   + %S  + %S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4
--R            q      q
--R   (337)  %S   + %S  + %S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 337

--S 338 of 350
ac+bc
 

            187
   (338)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (338)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 338

--S 339 of 350
ap*bp
 

            4      2
   (339)  %Q  + 2%Q  + 2%Q
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4      2
--R   (339)  %Q  + 2%Q  + 2%Q
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 339

--S 340 of 350
an*bn
 

             4      2
            q      q      q
   (340)  %S   + %S   + %S  + 2%S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4      2
--R            q      q      q
--R   (340)  %S   + %S   + %S  + 2%S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 340

--S 341 of 350
ac*bc
 

            137
   (341)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            137
--R   (341)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 341

--S 342 of 350
discreteLog(ap)
 

   (342)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (342)  4
--R                                                        Type: PositiveInteger
--E 342

--S 343 of 350
discreteLog(an)
 

   (343)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (343)  4
--R                                                        Type: PositiveInteger
--E 343

--S 344 of 350
discreteLog(ac)
 

   (344)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (344)  4
--R                                                        Type: PositiveInteger
--E 344

--S 345 of 350
ap**1234567
 

             4     2
   (345)  2%Q  + %Q  + %Q
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4     2
--R   (345)  2%Q  + %Q  + %Q
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 345

--S 346 of 350
an**1234567
 

              4       2
             q       q       q
   (346)  2%S   + 2%S   + 2%S  + %S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R              4       2
--R             q       q       q
--R   (346)  2%S   + 2%S   + 2%S  + %S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 346

--S 347 of 350
ac**1234567
 

            16
   (347)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            16
--R   (347)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 347

--S 348 of 350
ap+bc
 

            187
   (348)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (348)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 348

--S 349 of 350
an+bc
 

            187
   (349)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (349)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 349

--S 350 of 350
an+bp
 

            4     3
   (350)  %Q  + %Q  + 2%Q + 1
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4     3
--R   (350)  %Q  + %Q  + 2%Q + 1
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 350
)spool 
 
Starts dribbling to float1.output (2009/2/17, 17:46:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 37
1.234
 

   (1)  1.234
                                                                  Type: Float
--R 
--R
--R   (1)  1.234
--R                                                                  Type: Float
--E 1

--S 2 of 37
1.234E2
 

   (2)  123.4
                                                                  Type: Float
--R 
--R
--R   (2)  123.4
--R                                                                  Type: Float
--E 2

--S 3 of 37
sqrt(1.2 + 2.3 / 3.4 ** 4.5)
 

   (3)  1.0996972790 671286226
                                                                  Type: Float
--R 
--R
--R   (3)  1.0996972790 671286226
--R                                                                  Type: Float
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 37
i := 3 :: Float
 

   (1)  3.0
                                                                  Type: Float
--R 
--R
--R   (1)  3.0
--R                                                                  Type: Float
--E 4

--S 5 of 37
i :: Integer
 

   (2)  3
                                                                Type: Integer
--R 
--R
--R   (2)  3
--R                                                                Type: Integer
--E 5

--S 6 of 37
i :: Fraction Integer
 

   (3)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (3)  3
--R                                                       Type: Fraction Integer
--E 6

--S 7 of 37
r := 3/7 :: Float
 

   (4)  0.4285714285 7142857143
                                                                  Type: Float
--R 
--R
--R   (4)  0.4285714285 7142857143
--R                                                                  Type: Float
--E 7

--S 8 of 37
r :: Fraction Integer
 

        3
   (5)  -
        7
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (5)  -
--R        7
--R                                                       Type: Fraction Integer
--E 8

--S 9 of 37
r :: Integer
 
 
Daly Bug
   Cannot convert from type Float to Integer for value
   0.4285714285 7142857143

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Float to Integer for value
--R   0.4285714285 7142857143
--R
--E 9

--S 10 of 37
truncate 3.6
 

   (6)  3.0
                                                                  Type: Float
--R 
--R
--R   (6)  3.0
--R                                                                  Type: Float
--E 10

--S 11 of 37
round 3.6
 

   (7)  4.0
                                                                  Type: Float
--R 
--R
--R   (7)  4.0
--R                                                                  Type: Float
--E 11

--S 21 of 37
truncate(-3.6)
 

   (8)  - 3.0
                                                                  Type: Float
--R 
--R
--R   (8)  - 3.0
--R                                                                  Type: Float
--E 12

--S 13 of 37
round(-3.6)
 

   (9)  - 4.0
                                                                  Type: Float
--R 
--R
--R   (9)  - 4.0
--R                                                                  Type: Float
--E 13

--S 14 of 37
fractionPart 3.6
 

   (10)  0.6
                                                                  Type: Float
--R 
--R
--R   (10)  0.6
--R                                                                  Type: Float
--E 14

--S 15 of 37
digits 40
 

   (11)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  20
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 37
sqrt 0.2
 

   (12)  0.4472135954 9995793928 1834733746 2552470881
                                                                  Type: Float
--R 
--R
--R   (12)  0.4472135954 9995793928 1834733746 2552470881
--R                                                                  Type: Float
--E 16

--S 17 of 37
pi()$Float
 

   (13)  3.1415926535 8979323846 2643383279 502884197
                                                                  Type: Float
--R 
--R
--R   (13)  3.1415926535 8979323846 2643383279 502884197
--R                                                                  Type: Float
--E 17

--S 18 of 37
digits 500
 

   (14)  40
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  40
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 37
pi()$Float
 

   (15)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (15)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 19

--S 20 of 37
digits 20
 

   (16)  500
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  500
--R                                                        Type: PositiveInteger
--E 20

)clear all
 
   All user variables and function definitions have been cleared.

--S 21 of 37
outputSpacing 0; x := sqrt 0.2
 

   (1)  0.44721359549995793928
                                                                  Type: Float
--R 
--R
--R   (1)  0.44721359549995793928
--R                                                                  Type: Float
--E 21

--S 22 of 37
outputSpacing 5; x
 

   (2)  0.44721 35954 99957 93928
                                                                  Type: Float
--R 
--R
--R   (2)  0.44721 35954 99957 93928
--R                                                                  Type: Float
--E 22

--S 23 of 37
y := x/10**10
 

   (3)  0.44721 35954 99957 93928 E -10
                                                                  Type: Float
--R 
--R
--R   (3)  0.44721 35954 99957 93928 E -10
--R                                                                  Type: Float
--E 23

--S 24 of 37
outputFloating(); x
 

   (4)  0.44721 35954 99957 93928 E 0
                                                                  Type: Float
--R 
--R
--R   (4)  0.44721 35954 99957 93928 E 0
--R                                                                  Type: Float
--E 24

--S 25 of 37
outputFixed(); y
 

   (5)  0.00000 00000 44721 35954 99957 93928
                                                                  Type: Float
--R 
--R
--R   (5)  0.00000 00000 44721 35954 99957 93928
--R                                                                  Type: Float
--E 25

--S 26 of 37
outputFloating 2; y
 

   (6)  0.45 E -10
                                                                  Type: Float
--R 
--R
--R   (6)  0.45 E -10
--R                                                                  Type: Float
--E 26

--S 27 of 37
outputFixed 2; x
 

   (7)  0.45
                                                                  Type: Float
--R 
--R
--R   (7)  0.45
--R                                                                  Type: Float
--E 27

--S 28 of 37
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

)clear all
 
   All user variables and function definitions have been cleared.

--S 29 of 37
a: Matrix Fraction Integer := matrix [[1/(i+j+1) for j in 0..9] for i in 0..9]
 

        +    1   1   1   1   1   1   1   1    1+
        |1   -   -   -   -   -   -   -   -   --|
        |    2   3   4   5   6   7   8   9   10|
        |                                      |
        |1   1   1   1   1   1   1   1    1   1|
        |-   -   -   -   -   -   -   -   --  --|
        |2   3   4   5   6   7   8   9   10  11|
        |                                      |
        |1   1   1   1   1   1   1    1   1   1|
        |-   -   -   -   -   -   -   --  --  --|
        |3   4   5   6   7   8   9   10  11  12|
        |                                      |
        |1   1   1   1   1   1    1   1   1   1|
        |-   -   -   -   -   -   --  --  --  --|
        |4   5   6   7   8   9   10  11  12  13|
        |                                      |
        |1   1   1   1   1    1   1   1   1   1|
        |-   -   -   -   -   --  --  --  --  --|
        |5   6   7   8   9   10  11  12  13  14|
   (1)  |                                      |
        |1   1   1   1    1   1   1   1   1   1|
        |-   -   -   -   --  --  --  --  --  --|
        |6   7   8   9   10  11  12  13  14  15|
        |                                      |
        |1   1   1    1   1   1   1   1   1   1|
        |-   -   -   --  --  --  --  --  --  --|
        |7   8   9   10  11  12  13  14  15  16|
        |                                      |
        |1   1    1   1   1   1   1   1   1   1|
        |-   -   --  --  --  --  --  --  --  --|
        |8   9   10  11  12  13  14  15  16  17|
        |                                      |
        |1    1   1   1   1   1   1   1   1   1|
        |-   --  --  --  --  --  --  --  --  --|
        |9   10  11  12  13  14  15  16  17  18|
        |                                      |
        | 1   1   1   1   1   1   1   1   1   1|
        |--  --  --  --  --  --  --  --  --  --|
        +10  11  12  13  14  15  16  17  18  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +    1   1   1   1   1   1   1   1    1+
--R        |1   -   -   -   -   -   -   -   -   --|
--R        |    2   3   4   5   6   7   8   9   10|
--R        |                                      |
--R        |1   1   1   1   1   1   1   1    1   1|
--R        |-   -   -   -   -   -   -   -   --  --|
--R        |2   3   4   5   6   7   8   9   10  11|
--R        |                                      |
--R        |1   1   1   1   1   1   1    1   1   1|
--R        |-   -   -   -   -   -   -   --  --  --|
--R        |3   4   5   6   7   8   9   10  11  12|
--R        |                                      |
--R        |1   1   1   1   1   1    1   1   1   1|
--R        |-   -   -   -   -   -   --  --  --  --|
--R        |4   5   6   7   8   9   10  11  12  13|
--R        |                                      |
--R        |1   1   1   1   1    1   1   1   1   1|
--R        |-   -   -   -   -   --  --  --  --  --|
--R        |5   6   7   8   9   10  11  12  13  14|
--R   (1)  |                                      |
--R        |1   1   1   1    1   1   1   1   1   1|
--R        |-   -   -   -   --  --  --  --  --  --|
--R        |6   7   8   9   10  11  12  13  14  15|
--R        |                                      |
--R        |1   1   1    1   1   1   1   1   1   1|
--R        |-   -   -   --  --  --  --  --  --  --|
--R        |7   8   9   10  11  12  13  14  15  16|
--R        |                                      |
--R        |1   1    1   1   1   1   1   1   1   1|
--R        |-   -   --  --  --  --  --  --  --  --|
--R        |8   9   10  11  12  13  14  15  16  17|
--R        |                                      |
--R        |1    1   1   1   1   1   1   1   1   1|
--R        |-   --  --  --  --  --  --  --  --  --|
--R        |9   10  11  12  13  14  15  16  17  18|
--R        |                                      |
--R        | 1   1   1   1   1   1   1   1   1   1|
--R        |--  --  --  --  --  --  --  --  --  --|
--R        +10  11  12  13  14  15  16  17  18  19+
--R                                                Type: Matrix Fraction Integer
--E 29

--S 30 of 37
d:= determinant a
 

                                  1
   (2)  -----------------------------------------------------
        46206893947914691316295628839036278726983680000000000
                                                       Type: Fraction Integer
--R 
--R
--R                                  1
--R   (2)  -----------------------------------------------------
--R        46206893947914691316295628839036278726983680000000000
--R                                                       Type: Fraction Integer
--E 30

--S 31 of 37
d :: Float
 

   (3)  0.21641 79226 43149 18691 E -52
                                                                  Type: Float
--R 
--R
--R   (3)  0.21641 79226 43149 18691 E -52
--R                                                                  Type: Float
--E 31

--S 32 of 37
b: Matrix DoubleFloat := matrix [[1/(i+j+1$DoubleFloat) for j in 0..9] for i in 0..9];
 

                                                     Type: Matrix DoubleFloat
--R 
--R
--R                                                     Type: Matrix DoubleFloat
--E 32

--S 33 of 37
determinant b
 

   (5)  2.1643677945721411E-53
                                                            Type: DoubleFloat
--R 
--R
--R   (5)  2.1643677945721411E-53
--R                                                            Type: DoubleFloat
--E 33

--S 34 of 37
digits 40
 

   (6)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  20
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 37
c: Matrix Float := matrix [[1/(i+j+1$Float) for j in 0..9] for i in 0..9];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 35

--S 36 of 37
determinant c
 

   (8)  0.21641 79226 43149 18690 60594 98362 26174 36159 E -52
                                                                  Type: Float
--R 
--R
--R   (8)  0.21641 79226 43149 18690 60594 98362 26174 36159 E -52
--R                                                                  Type: Float
--E 36

--S 37 of 37
digits 20
 

   (9)  40
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  40
--R                                                        Type: PositiveInteger
--E 37
)spool 
 
Starts dribbling to test.output (2009/2/17, 18:1:0).
)set message test on
 
)set message auto off
 
)set break resume
 

)clear all
 
   All user variables and function definitions have been cleared.

--S 1
eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F
 

           2                   2
   (1)  C y  + (B x + E)y + A x  + D x + F
                                                     Type: Polynomial Integer
--R 
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 1

--S 2
eq2:= eval(eq1,[x= xdot*cos(t) - ydot*sin(t), y=xdot*sin(t) + ydot*cos(t)])
 

   (2)
            2                       2       2
     (A ydot  - B xdot ydot + C xdot )sin(t)
   + 
               2                              2
     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
   + 
            2                       2       2
     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R            2                       2       2
--R     (A ydot  - B xdot ydot + C xdot )sin(t)
--R   + 
--R               2                              2
--R     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
--R   + 
--R            2                       2       2
--R     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
--R                                                     Type: Expression Integer
--E 2

)clear all
 
   All user variables and function definitions have been cleared.

--S 3
taylor exp x
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4
s := %
 

   (2)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5
s::(UTS(EXPR FLOAT, x, 0))
 

   (3)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--R 
--R
--R   (3)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--E 5

--S 6
s::(UTS(FLOAT, x, 0))
 

   (4)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--R 
--R
--R   (4)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--E 6

--S 7
eval(s,1)
 

             5 8 65 163 1957 685 109601 98641
   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
             2 3 24  60  720 252  40320 36288
                                              Type: Stream Expression Integer
--R 
--R
--R             5 8 65 163 1957 685 109601 98641
--R   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
--R             2 3 24  60  720 252  40320 36288
--R                                              Type: Stream Expression Integer
--E 7

--S 8
%::(Stream Float)
 

   (6)
   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
    2.7182787698 412698413, 2.7182815255 731922399, ...]
                                                           Type: Stream Float
--R 
--R
--R   (6)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                           Type: Stream Float
--E 8

)clear all
 
   All user variables and function definitions have been cleared.

--S 9
s := series(sin(a*x),x=0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 9

--S 10
eval(s, 1.0)
 

   (2)
                                          3
   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
                               3
    - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                      9                               7
       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
     + 
                                   5                            3
       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
     ,
    ...]
                                                Type: Stream Expression Float
--R 
--R
--R   (2)
--R                                          3
--R   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
--R                               3
--R    - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                      9                               7
--R       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
--R     + 
--R                                   5                            3
--R       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
--R     ,
--R    ...]
--R                                                Type: Stream Expression Float
--E 10

--S 11
s - a*x
 

   (3)
        3        5        7          9            11              13
       a   3    a   5    a    7     a     9      a      11       a       13
     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
        6      120      5040      362880      39916800       6227020800
   + 
        14
     O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)
--R        3        5        7          9            11              13
--R       a   3    a   5    a    7     a     9      a      11       a       13
--R     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
--R        6      120      5040      362880      39916800       6227020800
--R   + 
--R        14
--R     O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11


--S 12
eval(s, 1.0)
 

   (4)
                                          3
   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
                               3
    - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                      9                               7
       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
     + 
                                   5                            3
       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
     ,
    ...]
                                                Type: Stream Expression Float
--R 
--R
--R   (4)
--R                                          3
--R   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
--R                               3
--R    - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                      9                               7
--R       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
--R     + 
--R                                   5                            3
--R       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
--R     ,
--R    ...]
--R                                                Type: Stream Expression Float
--E 12

)clear all
 
   All user variables and function definitions have been cleared.

--S 13
v := vector [1,2,3]
 

   (1)  [1,2,3]
                                                 Type: Vector PositiveInteger
--R 
--R
--R   (1)  [1,2,3]
--R                                                 Type: Vector PositiveInteger
--E 13

--S 14
(1/2)*v
 

         1   3
   (2)  [-,1,-]
         2   2
                                                Type: Vector Fraction Integer
--R 
--R
--R         1   3
--R   (2)  [-,1,-]
--R         2   2
--R                                                Type: Vector Fraction Integer
--E 14

--S 15
eval(x**2, x=1/2)
 

        1
   (3)  -
        4
                                            Type: Polynomial Fraction Integer
--R 
--R
--R        1
--R   (3)  -
--R        4
--R                                            Type: Polynomial Fraction Integer
--E 15

--S 16
eval(x**2, x=0.5)
 

   (4)  0.25
                                                       Type: Polynomial Float
--R 
--R
--R   (4)  0.25
--R                                                       Type: Polynomial Float
--E 16

--S 17
eval(3**x, x=0.5)
 

   (5)  1.7320508075 688772935
                                                       Type: Expression Float
--R 
--R
--R   (5)  1.7320508075 688772935
--R                                                       Type: Expression Float
--E 17

)clear all
 
   All user variables and function definitions have been cleared.

--S 18
f(x) == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19
f(x,y) == x+y
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20
f 3
 
   Compiling function f with type PositiveInteger -> PositiveInteger 

   (3)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (3)  4
--R                                                        Type: PositiveInteger
--E 20

--S 21
f(3,4)
 
   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
      PositiveInteger 

   (4)  7
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
--R      PositiveInteger 
--R
--R   (4)  7
--R                                                        Type: PositiveInteger
--E 21

--S 22
f(5)
 

   (5)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  6
--R                                                        Type: PositiveInteger
--E 22

--S 23
f(1,x)
 
   Compiling function f with type (PositiveInteger,Variable x) -> 
      Polynomial Integer 

   (6)  x + 1
                                                     Type: Polynomial Integer
--R 
--R   Compiling function f with type (PositiveInteger,Variable x) -> 
--R      Polynomial Integer 
--R
--R   (6)  x + 1
--R                                                     Type: Polynomial Integer
--E 23

)clear all
 
   All user variables and function definitions have been cleared.

--S 24
series(n +-> bernoulli(n)/factorial(n), t=0)
 

   (1)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--R 
--R
--R   (1)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 24

)clear all
 
   All user variables and function definitions have been cleared.

--S 25
l := [1,2,-1]
 

   (1)  [1,2,- 1]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,- 1]
--R                                                           Type: List Integer
--E 25

--S 26
f : INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

--S 27
f x == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28
map(f, l)
 
   Compiling function f with type Integer -> Fraction Integer 

   (4)  [1,2,- 1]
                                                  Type: List Fraction Integer
--R 
--R   Compiling function f with type Integer -> Fraction Integer 
--R
--R   (4)  [1,2,- 1]
--R                                                  Type: List Fraction Integer
--E 28

)clear all
 
   All user variables and function definitions have been cleared.

--S 29
f: INT -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30
f x == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31
u g == g 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32
u f
 
   Compiling function u with type (Integer -> Integer) -> Integer 
   Compiling function f with type Integer -> Integer 

   (4)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function u with type (Integer -> Integer) -> Integer 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 32

)clear all
 
   All user variables and function definitions have been cleared.

--S 33
groebner [x**2 - y, y**3+1]
 

              2  6
   (1)  [y - x ,x  + 1]
                                                Type: List Polynomial Integer
--R 
--R
--R              2  6
--R   (1)  [y - x ,x  + 1]
--R                                                Type: List Polynomial Integer
--E 33

)clear all
 
   All user variables and function definitions have been cleared.

--S 34
factor x
 

   (1)  x
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (1)  x
--R                                            Type: Factored Polynomial Integer
--E 34

--draw(x, x=-1..1)

)clear all
 
   All user variables and function definitions have been cleared.

--S 35
{}$(List INT)
 
 
Daly Bug
   The function SEQ is not implemented in List Integer .
--R 
--RDaly Bug
--R   The function SEQ is not implemented in List Integer .
--E 35

--S 36
brace []  -- {}
 

   (1)  {}
                                                               Type: Set None
--R
--R   (1)  {}
--R                                                               Type: Set None
--E 36

--S 37
brace [1] -- {1}
 

   (2)  {1}
                                                    Type: Set PositiveInteger
--R
--R   (2)  {1}
--R                                                    Type: Set PositiveInteger
--E 37

--S 38
union(brace [], brace [1,2])   -- union({}, {1,2})
 

   (3)  {1,2}
                                                    Type: Set PositiveInteger
--R
--R   (3)  {1,2}
--R                                                    Type: Set PositiveInteger
--E 38

)clear all
 
   All user variables and function definitions have been cleared.

)set mes test off
 

--S 39
map(variable, [x,y])
 

   (1)  [x,y]
                         Type: List Union(OrderedVariableList [x,y],"failed")
--R 
--R
--R   (1)  [x,y]
--R                         Type: List Union(OrderedVariableList [x,y],"failed")
--E 39

)set mes test on
 

)clear all
 
   All user variables and function definitions have been cleared.

)set fun recur off
 

--S 40
p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 40

--S 41
pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 41

--S 42
pp(-1,x) -- should be 1/(x-1)
 
   Compiling function p with type (Integer,Polynomial Integer) -> 
      Polynomial Integer 
   Compiling function p with type (Integer,Variable x) -> Polynomial 
      Integer 
   Compiling function pp with type (Integer,Variable x) -> Fraction 
      Polynomial Fraction Integer 

          1
   (3)  -----
        x - 1
                                   Type: Fraction Polynomial Fraction Integer
--R 
--R   Compiling function p with type (Integer,Polynomial Integer) -> 
--R      Polynomial Integer 
--R   Compiling function p with type (Integer,Variable x) -> Polynomial 
--R      Integer 
--R   Compiling function pp with type (Integer,Variable x) -> Fraction 
--R      Polynomial Fraction Integer 
--R
--R          1
--R   (3)  -----
--R        x - 1
--R                                   Type: Fraction Polynomial Fraction Integer
--E 42

)clear all
 
   All user variables and function definitions have been cleared.

--S 43
f n ==
  for i in 1..n repeat
    j:=2*i
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 43

--S 44
g n ==
    j:=2*n
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 44

--S 45
g 3
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 45

--S 46
f 3
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0+
   |    |
   +0  1+
   +1  0  0  0+
   |          |
   |0  1  0  0|
   |          |
   |0  0  1  0|
   |          |
   +0  0  0  1+
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0+
--R   |    |
--R   +0  1+
--R   +1  0  0  0+
--R   |          |
--R   |0  1  0  0|
--R   |          |
--R   |0  0  1  0|
--R   |          |
--R   +0  0  0  1+
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 46

)clear all
 
   All user variables and function definitions have been cleared.

--S 47
mp(x,l) ==
  l is [a,:b] =>
    a*x**(#b)+ mp(x,b)
  0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 47

--S 48
mp(x, [1,3,4, 2])
 
   Compiling function mp with type (Variable x,List PositiveInteger)
       -> Polynomial Integer 

         3     2
   (2)  x  + 3x  + 4x + 2
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List PositiveInteger)
--R       -> Polynomial Integer 
--R
--R         3     2
--R   (2)  x  + 3x  + 4x + 2
--R                                                     Type: Polynomial Integer
--E 48

--S 49
mp(x, [1,2,-3, 4])
 
   Compiling function mp with type (Variable x,List Integer) -> 
      Polynomial Integer 

         3     2
   (3)  x  + 2x  - 3x + 4
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List Integer) -> 
--R      Polynomial Integer 
--R
--R         3     2
--R   (3)  x  + 2x  - 3x + 4
--R                                                     Type: Polynomial Integer
--E 49

)clear all
 
   All user variables and function definitions have been cleared.

--S 50
f1 n ==
  if n=0 then 1 else if n=1 then 1 else f1(n-1)+f1(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 50

--S 51
f2 n ==
  m:=n
  if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 51

--S 52
f3 n ==
  n=0 => 1
  n=1 => 1
  f3(n-1)+f3(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 52

--S 53
f4 n ==
  m:=n
  n=0 => 1
  n=1 => 1
  m:=n
  f4(n-1)+f4(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 53

--S 54
f5 n == if n=0 or n=1 then 1 else f5(n-1)+f5(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 54

--S 55
[f1 3,f2 3, f3 3,f4 3,f5 3]
 
   Compiling function f1 with type Integer -> PositiveInteger 
   Compiling function f2 with type Integer -> PositiveInteger 
   Compiling function f3 with type Integer -> PositiveInteger 
   Compiling function f4 with type Integer -> PositiveInteger 
   Compiling function f5 with type Integer -> PositiveInteger 

   (6)  [3,3,3,3,3]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function f1 with type Integer -> PositiveInteger 
--R   Compiling function f2 with type Integer -> PositiveInteger 
--R   Compiling function f3 with type Integer -> PositiveInteger 
--R   Compiling function f4 with type Integer -> PositiveInteger 
--R   Compiling function f5 with type Integer -> PositiveInteger 
--R
--R   (6)  [3,3,3,3,3]
--R                                                   Type: List PositiveInteger
--E 55

)clear all
 
   All user variables and function definitions have been cleared.

--S 56
g: GDMP([x,y], INT, DIRPROD(2, NNI)) := x**2 + y
 

         2
   (1)  x  + y
Type: GeneralDistributedMultivariatePolynomial([x,y],Integer,DirectProduct(2,NonNegativeInteger))
--R 
--R
--R         2
--R   (1)  x  + y
--RType: GeneralDistributedMultivariatePolynomial([x,y],Integer,DirectProduct(2,NonNegativeInteger))
--E 56

)clear all
 
   All user variables and function definitions have been cleared.

--S 57
i := INT
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 57

--S 58
i has Algebra(i)
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 58

)clear all
 
   All user variables and function definitions have been cleared.

--S 59
f x == if x<0 then return x else x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 59

--S 60
f 2 -- should be 3
 
   Compiling function f with type PositiveInteger -> PositiveInteger 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 60

--S 61
f(-2) -- should be -2
 
   Compiling function f with type Integer -> Integer 

   (3)  - 2
                                                                Type: Integer
--R 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (3)  - 2
--R                                                                Type: Integer
--E 61

)clear all
 
   All user variables and function definitions have been cleared.

--S 62
m = [[1,2],[2,3]]  -- Should return type EQ POLY SQMATRIX(2, INT)
 

           +1  2+
   (1)  m= |    |
           +2  3+
                            Type: Equation Polynomial SquareMatrix(2,Integer)
--R 
--R
--R           +1  2+
--R   (1)  m= |    |
--R           +2  3+
--R                            Type: Equation Polynomial SquareMatrix(2,Integer)
--E 62

--S 63
[1, "asd"]   -- Should be of type List Any
 

   (2)  [1,"asd"]
                                                               Type: List Any
--R 
--R
--R   (2)  [1,"asd"]
--R                                                               Type: List Any
--E 63

)set mes test off
 

--S 64
1+"asd"  -- These should both fail in the same way
 
   There are 12 exposed and 5 unexposed library operations named + 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op +
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named + 
      with argument type(s) 
                               PositiveInteger
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 12 exposed and 5 unexposed library operations named + 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                                )display op +
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named + 
--R      with argument type(s) 
--R                               PositiveInteger
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 64

--S 65
1/"asd"
 
   There are 13 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                               PositiveInteger
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 13 exposed and 12 unexposed library operations named / 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                                )display op /
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named / 
--R      with argument type(s) 
--R                               PositiveInteger
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 65

)set mes test on
 

)clear all
 
   All user variables and function definitions have been cleared.

--S 66
t := MPOLY([x,y], INT)
 

   (1)  MultivariatePolynomial([x,y],Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  MultivariatePolynomial([x,y],Integer)
--R                                                                 Type: Domain
--E 66

--S 67
)show t
 
 MultivariatePolynomial([x,y],Integer) is a domain constructor.
 Abbreviation for MultivariatePolynomial is MPOLY 
 This constructor is exposed in this frame.
 Issue )edit multpoly.spad.pamphlet to see algebra source code for MPOLY 

------------------------------- Operations --------------------------------

 ?*? : (Fraction Integer,%) -> %       ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?*? : (%,Fraction Integer) -> %
 ?*? : (%,Integer) -> %                ?*? : (%,%) -> %
 ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
 ?-? : (%,%) -> %                      -? : % -> %
 ?/? : (%,Integer) -> %                ?<? : (%,%) -> Boolean
 ?<=? : (%,%) -> Boolean               ?=? : (%,%) -> Boolean
 ?>? : (%,%) -> Boolean                ?>=? : (%,%) -> Boolean
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        associates? : (%,%) -> Boolean
 coefficients : % -> List Integer      coerce : % -> OutputForm
 coerce : Fraction Integer -> %        coerce : Integer -> %
 coerce : % -> %                       content : % -> Integer
 convert : % -> InputForm              convert : % -> Pattern Float
 convert : % -> Pattern Integer        eval : (%,Equation %) -> %
 eval : (%,List Equation %) -> %       eval : (%,List %,List %) -> %
 eval : (%,%,%) -> %                   factor : % -> Factored %
 gcd : List % -> %                     gcd : (%,%) -> %
 ground : % -> Integer                 ground? : % -> Boolean
 hash : % -> SingleInteger             latex : % -> String
 lcm : List % -> %                     lcm : (%,%) -> %
 leadingCoefficient : % -> Integer     leadingMonomial : % -> %
 max : (%,%) -> %                      min : (%,%) -> %
 monomial? : % -> Boolean              monomials : % -> List %
 one? : % -> Boolean                   prime? : % -> Boolean
 primitiveMonomials : % -> List %      primitivePart : % -> %
 recip : % -> Union(%,"failed")        reductum : % -> %
 retract : % -> Fraction Integer       retract : % -> Integer
 sample : () -> %                      squareFree : % -> Factored %
 squareFreePart : % -> %               unit? : % -> Boolean
 unitCanonical : % -> %                zero? : % -> Boolean
 ?~=? : (%,%) -> Boolean              
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,NonNegativeInteger) -> %
 D : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 D : (%,List OrderedVariableList [x,y]) -> %
 D : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 D : (%,OrderedVariableList [x,y]) -> %
 ?^? : (%,NonNegativeInteger) -> %
 binomThmExpt : (%,%,NonNegativeInteger) -> %
 characteristic : () -> NonNegativeInteger
 charthRoot : % -> Union(%,"failed")
 coefficient : (%,IndexedExponents OrderedVariableList [x,y]) -> Integer
 coefficient : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 coefficient : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 coerce : OrderedVariableList [x,y] -> %
 conditionP : Matrix % -> Union(Vector %,"failed")
 content : (%,OrderedVariableList [x,y]) -> %
 degree : % -> IndexedExponents OrderedVariableList [x,y]
 degree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
 degree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
 differentiate : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 differentiate : (%,List OrderedVariableList [x,y]) -> %
 differentiate : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 differentiate : (%,OrderedVariableList [x,y]) -> %
 discriminant : (%,OrderedVariableList [x,y]) -> %
 eval : (%,List OrderedVariableList [x,y],List Integer) -> %
 eval : (%,List OrderedVariableList [x,y],List %) -> %
 eval : (%,OrderedVariableList [x,y],Integer) -> %
 eval : (%,OrderedVariableList [x,y],%) -> %
 exquo : (%,Integer) -> Union(%,"failed")
 exquo : (%,%) -> Union(%,"failed")
 factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
 factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
 gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
 isExpt : % -> Union(Record(var: OrderedVariableList [x,y],exponent: NonNegativeInteger),"failed")
 isPlus : % -> Union(List %,"failed")
 isTimes : % -> Union(List %,"failed")
 mainVariable : % -> Union(OrderedVariableList [x,y],"failed")
 map : ((Integer -> Integer),%) -> %
 mapExponents : ((IndexedExponents OrderedVariableList [x,y] -> IndexedExponents OrderedVariableList [x,y]),%) -> %
 minimumDegree : % -> IndexedExponents OrderedVariableList [x,y]
 minimumDegree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
 minimumDegree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
 monicDivide : (%,%,OrderedVariableList [x,y]) -> Record(quotient: %,remainder: %)
 monomial : (Integer,IndexedExponents OrderedVariableList [x,y]) -> %
 monomial : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 monomial : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 multivariate : (SparseUnivariatePolynomial Integer,OrderedVariableList [x,y]) -> %
 multivariate : (SparseUnivariatePolynomial %,OrderedVariableList [x,y]) -> %
 numberOfMonomials : % -> NonNegativeInteger
 patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
 patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
 pomopo! : (%,Integer,IndexedExponents OrderedVariableList [x,y],%) -> %
 primitivePart : (%,OrderedVariableList [x,y]) -> %
 reducedSystem : Matrix % -> Matrix Integer
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer)
 resultant : (%,%,OrderedVariableList [x,y]) -> %
 retract : % -> OrderedVariableList [x,y]
 retractIfCan : % -> Union(Fraction Integer,"failed")
 retractIfCan : % -> Union(Integer,"failed")
 retractIfCan : % -> Union(OrderedVariableList [x,y],"failed")
 solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed")
 squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
 subtractIfCan : (%,%) -> Union(%,"failed")
 totalDegree : (%,List OrderedVariableList [x,y]) -> NonNegativeInteger
 totalDegree : % -> NonNegativeInteger
 unitNormal : % -> Record(unit: %,canonical: %,associate: %)
 univariate : % -> SparseUnivariatePolynomial Integer
 univariate : (%,OrderedVariableList [x,y]) -> SparseUnivariatePolynomial %
 variables : % -> List OrderedVariableList [x,y]


--R 
--R MultivariatePolynomial([x,y],Integer) is a domain constructor.
--R Abbreviation for MultivariatePolynomial is MPOLY 
--R This constructor is exposed in this frame.
--R Issue )edit multpoly.spad.pamphlet to see algebra source code for MPOLY 
--R
--R------------------------------- Operations --------------------------------
--R
--R ?*? : (Fraction Integer,%) -> %       ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> %        ?*? : (%,Fraction Integer) -> %
--R ?*? : (%,Integer) -> %                ?*? : (%,%) -> %
--R ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
--R ?-? : (%,%) -> %                      -? : % -> %
--R ?/? : (%,Integer) -> %                ?<? : (%,%) -> Boolean
--R ?<=? : (%,%) -> Boolean               ?=? : (%,%) -> Boolean
--R ?>? : (%,%) -> Boolean                ?>=? : (%,%) -> Boolean
--R 1 : () -> %                           0 : () -> %
--R ?^? : (%,PositiveInteger) -> %        associates? : (%,%) -> Boolean
--R coefficients : % -> List Integer      coerce : % -> OutputForm
--R coerce : Fraction Integer -> %        coerce : Integer -> %
--R coerce : % -> %                       content : % -> Integer
--R convert : % -> InputForm              convert : % -> Pattern Float
--R convert : % -> Pattern Integer        eval : (%,Equation %) -> %
--R eval : (%,List Equation %) -> %       eval : (%,List %,List %) -> %
--R eval : (%,%,%) -> %                   factor : % -> Factored %
--R gcd : List % -> %                     gcd : (%,%) -> %
--R ground : % -> Integer                 ground? : % -> Boolean
--R hash : % -> SingleInteger             latex : % -> String
--R lcm : List % -> %                     lcm : (%,%) -> %
--R leadingCoefficient : % -> Integer     leadingMonomial : % -> %
--R max : (%,%) -> %                      min : (%,%) -> %
--R monomial? : % -> Boolean              monomials : % -> List %
--R one? : % -> Boolean                   prime? : % -> Boolean
--R primitiveMonomials : % -> List %      primitivePart : % -> %
--R recip : % -> Union(%,"failed")        reductum : % -> %
--R retract : % -> Fraction Integer       retract : % -> Integer
--R sample : () -> %                      squareFree : % -> Factored %
--R squareFreePart : % -> %               unit? : % -> Boolean
--R unitCanonical : % -> %                zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean              
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R D : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R D : (%,List OrderedVariableList [x,y]) -> %
--R D : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R D : (%,OrderedVariableList [x,y]) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R binomThmExpt : (%,%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed")
--R coefficient : (%,IndexedExponents OrderedVariableList [x,y]) -> Integer
--R coefficient : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R coefficient : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R coerce : OrderedVariableList [x,y] -> %
--R conditionP : Matrix % -> Union(Vector %,"failed")
--R content : (%,OrderedVariableList [x,y]) -> %
--R degree : % -> IndexedExponents OrderedVariableList [x,y]
--R degree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
--R degree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
--R differentiate : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R differentiate : (%,List OrderedVariableList [x,y]) -> %
--R differentiate : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R differentiate : (%,OrderedVariableList [x,y]) -> %
--R discriminant : (%,OrderedVariableList [x,y]) -> %
--R eval : (%,List OrderedVariableList [x,y],List Integer) -> %
--R eval : (%,List OrderedVariableList [x,y],List %) -> %
--R eval : (%,OrderedVariableList [x,y],Integer) -> %
--R eval : (%,OrderedVariableList [x,y],%) -> %
--R exquo : (%,Integer) -> Union(%,"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
--R isExpt : % -> Union(Record(var: OrderedVariableList [x,y],exponent: NonNegativeInteger),"failed")
--R isPlus : % -> Union(List %,"failed")
--R isTimes : % -> Union(List %,"failed")
--R mainVariable : % -> Union(OrderedVariableList [x,y],"failed")
--R map : ((Integer -> Integer),%) -> %
--R mapExponents : ((IndexedExponents OrderedVariableList [x,y] -> IndexedExponents OrderedVariableList [x,y]),%) -> %
--R minimumDegree : % -> IndexedExponents OrderedVariableList [x,y]
--R minimumDegree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
--R minimumDegree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
--R monicDivide : (%,%,OrderedVariableList [x,y]) -> Record(quotient: %,remainder: %)
--R monomial : (Integer,IndexedExponents OrderedVariableList [x,y]) -> %
--R monomial : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R monomial : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R multivariate : (SparseUnivariatePolynomial Integer,OrderedVariableList [x,y]) -> %
--R multivariate : (SparseUnivariatePolynomial %,OrderedVariableList [x,y]) -> %
--R numberOfMonomials : % -> NonNegativeInteger
--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
--R pomopo! : (%,Integer,IndexedExponents OrderedVariableList [x,y],%) -> %
--R primitivePart : (%,OrderedVariableList [x,y]) -> %
--R reducedSystem : Matrix % -> Matrix Integer
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer)
--R resultant : (%,%,OrderedVariableList [x,y]) -> %
--R retract : % -> OrderedVariableList [x,y]
--R retractIfCan : % -> Union(Fraction Integer,"failed")
--R retractIfCan : % -> Union(Integer,"failed")
--R retractIfCan : % -> Union(OrderedVariableList [x,y],"failed")
--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed")
--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R totalDegree : (%,List OrderedVariableList [x,y]) -> NonNegativeInteger
--R totalDegree : % -> NonNegativeInteger
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R univariate : % -> SparseUnivariatePolynomial Integer
--R univariate : (%,OrderedVariableList [x,y]) -> SparseUnivariatePolynomial %
--R variables : % -> List OrderedVariableList [x,y]
--R
--R
--E 67

)clear all
 
   All user variables and function definitions have been cleared.

--S 68
)set fun cache all
 
   In general, interpreter functions will cache all values.
--R 
--R   In general, interpreter functions will cache all values.
--E 68

--S 69
u == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 69

--S 70
u
 
   Compiling body of rule u to compute value of type PositiveInteger 
   u will cache all previously computed values.

   (2)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule u to compute value of type PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 70

--S 71
)set fun cache 0
 
 In general, functions will cache no returned values.
--R 
--R In general, functions will cache no returned values.
--E 71

)clear all
 
   All user variables and function definitions have been cleared.

--S 72
factorp: (UP(x,INT),PositiveInteger,PositiveInteger) -> List(UP(x,INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 72

--S 73
factorp(poly,p,e) ==
   ppoly:UP(x,PF p):=poly
   pl := [rec.factor for rec in factors factor ppoly]
   facl:=pl::List(UP(x,INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 73

--S 74
factorp(x**2+x+5,7,1)
 
   Cannot compile the declaration for ppoly because its (possible 
      partial) type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   Compiling function factorp with type (UnivariatePolynomial(x,Integer
      ),PositiveInteger,PositiveInteger) -> List UnivariatePolynomial(x
      ,Integer) 

   (3)  [x + 2,x + 6]
                                   Type: List UnivariatePolynomial(x,Integer)
--R 
--R   Cannot compile the declaration for ppoly because its (possible 
--R      partial) type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function factorp with type (UnivariatePolynomial(x,Integer
--R      ),PositiveInteger,PositiveInteger) -> List UnivariatePolynomial(x
--R      ,Integer) 
--R
--R   (3)  [x + 2,x + 6]
--R                                   Type: List UnivariatePolynomial(x,Integer)
--E 74

)clear all
 
   All user variables and function definitions have been cleared.

--S 75
b:= 1..10
 

   (1)  1..10
                                                Type: Segment PositiveInteger
--R 
--R
--R   (1)  1..10
--R                                                Type: Segment PositiveInteger
--E 75

--S 76
for i in b by 2 repeat output i
 
   1
   3
   5
   7
   9
                                                                   Type: Void
--R 
--R   1
--R   3
--R   5
--R   7
--R   9
--R                                                                   Type: Void
--E 76

)clear all
 
   All user variables and function definitions have been cleared.

--S 77
macro RN == FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 77

--S 78
a51:=x+y+z+t+u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 78

--S 79
a52:=x*y+y*z+z*t+x*u+t*u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 79

--S 80
a53:=x*y*z+y*z*t+x*y*u+x*t*u+z*t*u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 80

--S 81
a54:=x*y*z*t+x*y*z*u+x*y*t*u+x*z*t*u+y*z*t*u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 81

--S 82
a55:=x*y*z*t*u-1;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 82

--S 83
arnborg5: List HDMP([x,y,z,t,u],RN):=[a51,a52,a53,a54,a55];
 

Type: List HomogeneousDistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--R 
--R
--RType: List HomogeneousDistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--E 83

--S 84
arnborg5l: List DMP([x,y,z,t,u],RN):=[a51,a52,a53,a54,a55];
 

   Type: List DistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--R 
--R
--R   Type: List DistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--E 84

)clear all
 
   All user variables and function definitions have been cleared.

--S 85
factorp(poly,p,e) ==
   [rec.factor for rec in factors factor (poly::UP(x, PF p))]::List UP(x, INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 85

--S 86
factorp(x**2+x+5,7,1)
 
   Cannot compile conversion for types involving local variables. In 
      particular, could not compile the expression involving :: UP(x,PF
      #2) 
   AXIOM will attempt to step through and interpret the code.

   (2)  [x + 2,x + 6]
                                   Type: List UnivariatePolynomial(x,Integer)
--R 
--R   Cannot compile conversion for types involving local variables. In 
--R      particular, could not compile the expression involving :: UP(x,PF
--R      #2) 
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (2)  [x + 2,x + 6]
--R                                   Type: List UnivariatePolynomial(x,Integer)
--E 86

)clear all
 
   All user variables and function definitions have been cleared.

--S 87
f (x) ==
  y: PF x := 1
  x = 3 => return x
  x = 4 => return(-x)
  (x+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 87

--S 88
f 3
 
   Cannot compile the declaration for y because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.

   (2)  3
                                                        Type: PositiveInteger
--R 
--R   Cannot compile the declaration for y because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 88

)clear all
 
   All user variables and function definitions have been cleared.

--S 89
f (x) ==
  x = 3 => return x
  x = 4 => return(-x)
  return (x+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 89

--S 90
f 3
 
   Compiling function f with type PositiveInteger -> Integer 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> Integer 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 90

)clear all
 
   All user variables and function definitions have been cleared.

--S 91
s:SQMATRIX(2, INT) := matrix [[1,2],[2,3]]
 

        +1  2+
   (1)  |    |
        +2  3+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (1)  |    |
--R        +2  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 91

--S 92
s::SQMATRIX(2, FRAC INT)
 

        +1  2+
   (2)  |    |
        +2  3+
                                       Type: SquareMatrix(2,Fraction Integer)
--R 
--R
--R        +1  2+
--R   (2)  |    |
--R        +2  3+
--R                                       Type: SquareMatrix(2,Fraction Integer)
--E 92

)clear all
 
   All user variables and function definitions have been cleared.

--S 93
Mat := SquareMatrix(2, Polynomial Integer)
 

   (1)  SquareMatrix(2,Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  SquareMatrix(2,Polynomial Integer)
--R                                                                 Type: Domain
--E 93

--S 94
s:Mat := matrix [[ 2*x + 1, x], [x, 1]]
 

        +2x + 1  x+
   (2)  |         |
        +  x     1+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +2x + 1  x+
--R   (2)  |         |
--R        +  x     1+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 94

--S 95
s**3
 

        +   3      2             3     2     +
        |12x  + 15x  + 6x + 1  5x  + 6x  + 3x|
   (3)  |                                    |
        |     3     2            3     2     |
        +   5x  + 6x  + 3x     2x  + 3x  + 1 +
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +   3      2             3     2     +
--R        |12x  + 15x  + 6x + 1  5x  + 6x  + 3x|
--R   (3)  |                                    |
--R        |     3     2            3     2     |
--R        +   5x  + 6x  + 3x     2x  + 3x  + 1 +
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 95

--S 96
%::Polynomial(?)
 

        +12  5+ 3   +15  6+ 2   +6  3+    +1  0+
   (4)  |     |x  + |     |x  + |    |x + |    |
        +5   2+     +6   3+     +3  0+    +0  1+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R 
--R
--R        +12  5+ 3   +15  6+ 2   +6  3+    +1  0+
--R   (4)  |     |x  + |     |x  + |    |x + |    |
--R        +5   2+     +6   3+     +3  0+    +0  1+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 96

)clear all
 
   All user variables and function definitions have been cleared.

--S 97
-2**2  -- Should return -4
 

   (1)  - 4
                                                                Type: Integer
--R 
--R
--R   (1)  - 4
--R                                                                Type: Integer
--E 97

)clear all
 
   All user variables and function definitions have been cleared.

--S 98
f: DMP([x,y], INT) := x**2-y**2
 

         2    2
   (1)  x  - y
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R         2    2
--R   (1)  x  - y
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 98

--S 99
coefficient(f, degree f)
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 99

)clear all
 
   All user variables and function definitions have been cleared.

--S 100
x+1::EXPR INT
 

   (1)  x + 1
                                                     Type: Expression Integer
--R 
--R
--R   (1)  x + 1
--R                                                     Type: Expression Integer
--E 100

--S 101
%::POLY INT
 

   (2)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  x + 1
--R                                                     Type: Polynomial Integer
--E 101

)clear all
 
   All user variables and function definitions have been cleared.

--S 102
solve([[1,2],[2,3]],[-2,3])
 

   (1)  [particular= [12,- 7],basis= [[0,0]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (1)  [particular= [12,- 7],basis= [[0,0]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 102

)clear all
 
   All user variables and function definitions have been cleared.

--S 103
eval(m**2, m=[[1,2],[2,3]])
 

        +5  8 +
   (1)  |     |
        +8  13+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R 
--R
--R        +5  8 +
--R   (1)  |     |
--R        +8  13+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 103

)clear all
 
   All user variables and function definitions have been cleared.

)set mes test off
 

--S 104
r: Ring
 
 
   Ring is a category, not a domain, and declarations require domains.
--R 
--R 
--R   Ring is a category, not a domain, and declarations require domains.
--E 104

--S 105
w: RF INT
 
 
   RationalFunction Integer is a package, not a domain, and 
      declarations require domains.
--R 
--R 
--R   RationalFunction Integer is a package, not a domain, and 
--R      declarations require domains.
--E 105

)set mes test on
 

)clear all
 
   All user variables and function definitions have been cleared.

--S 106
r:Record(a: INT) := [1]
 

   (1)  [a= 1]
                                                     Type: Record(a: Integer)
--R 
--R
--R   (1)  [a= 1]
--R                                                     Type: Record(a: Integer)
--E 106

)clear all
 
   All user variables and function definitions have been cleared.

--S 107
p: POLY FLOAT := (x-1)**30
 

   (1)
      30         29          28           27            26             25
     x   - 30.0 x   + 435.0 x   - 4060.0 x   + 27405.0 x   - 142506.0 x
   + 
               24              23              22               21
     593775.0 x   - 2035800.0 x   + 5852925.0 x   - 14307150.0 x
   + 
                 20               19               18                 17
     30045015.0 x   - 54627300.0 x   + 86493225.0 x   - 1 19759850.0 x
   + 
                   16                 15                 14                 13
     1 45422675.0 x   - 1 55117520.0 x   + 1 45422675.0 x   - 1 19759850.0 x
   + 
                 12               11               10               9
     86493225.0 x   - 54627300.0 x   + 30045015.0 x   - 14307150.0 x
   + 
                8              7             6             5            4
     5852925.0 x  - 2035800.0 x  + 593775.0 x  - 142506.0 x  + 27405.0 x
   + 
               3          2
     - 4060.0 x  + 435.0 x  - 30.0 x + 1.0
                                                       Type: Polynomial Float
--R 
--R
--R   (1)
--R      30         29          28           27            26             25
--R     x   - 30.0 x   + 435.0 x   - 4060.0 x   + 27405.0 x   - 142506.0 x
--R   + 
--R               24              23              22               21
--R     593775.0 x   - 2035800.0 x   + 5852925.0 x   - 14307150.0 x
--R   + 
--R                 20               19               18                 17
--R     30045015.0 x   - 54627300.0 x   + 86493225.0 x   - 1 19759850.0 x
--R   + 
--R                   16                 15                 14                 13
--R     1 45422675.0 x   - 1 55117520.0 x   + 1 45422675.0 x   - 1 19759850.0 x
--R   + 
--R                 12               11               10               9
--R     86493225.0 x   - 54627300.0 x   + 30045015.0 x   - 14307150.0 x
--R   + 
--R                8              7             6             5            4
--R     5852925.0 x  - 2035800.0 x  + 593775.0 x  - 142506.0 x  + 27405.0 x
--R   + 
--R               3          2
--R     - 4060.0 x  + 435.0 x  - 30.0 x + 1.0
--R                                                       Type: Polynomial Float
--E 107

--draw(p, x=-1..1)

)clear all
 
   All user variables and function definitions have been cleared.

--S 108
sayBranch x == _
 if x case INT then output "Integer Branch" _
 else if x case STRING then output "String Branch" _
 else if x case FLOAT then output "Float Branch" _
 else output "don't know"
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 108

--S 109
x:Union(INT,STRING,FLOAT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 109

--S 110
x:=3
 

   (3)  3
                                                     Type: Union(Integer,...)
--R 
--R
--R   (3)  3
--R                                                     Type: Union(Integer,...)
--E 110

--S 111
sayBranch(x)
 
 
Daly Bug
   case is only used for Unions and the object on the left-hand side 
      does not belong to a union.
--R 
--R 
--RDaly Bug
--R   case is only used for Unions and the object on the left-hand side 
--R      does not belong to a union.
--E 111

)clear all
 
   All user variables and function definitions have been cleared.

--S 112
RFI := FRAC POLY INT
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 112

--S 113
g:DMP([x,y], RFI) := a**2*x**2/b**2 - c**2*y**2/d**2
 

         2       2
        a   2   c   2
   (2)  -- x  - -- y
         2       2
        b       d
   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R         2       2
--R        a   2   c   2
--R   (2)  -- x  - -- y
--R         2       2
--R        b       d
--R   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 113

--S 114
factor g
 

         2
        a       b c        b c
   (3)  -- (x - --- y)(x + --- y)
         2      a d        a d
        b
Type: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R         2
--R        a       b c        b c
--R   (3)  -- (x - --- y)(x + --- y)
--R         2      a d        a d
--R        b
--RType: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 114

)clear all
 
   All user variables and function definitions have been cleared.

--S 115
f(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+v
 
   Function declaration f : (DoubleFloat,DoubleFloat) -> DoubleFloat 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : (DoubleFloat,DoubleFloat) -> DoubleFloat 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 115

--S 116
g(u:DoubleFloat, v:DoubleFloat):DoubleFloat == sin(u+v)
 
   Function declaration g : (DoubleFloat,DoubleFloat) -> DoubleFloat 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration g : (DoubleFloat,DoubleFloat) -> DoubleFloat 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 116

--S 117
h(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+cos(v)
 
   Function declaration h : (DoubleFloat,DoubleFloat) -> DoubleFloat 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration h : (DoubleFloat,DoubleFloat) -> DoubleFloat 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 117

--draw(surface(f,g,h), 0..4, 0..2*%pi)

)clear all
 
   All user variables and function definitions have been cleared.

)set mes test off
 

--S 118
(1+1)$Ring
 
 
   The right-hand side of the $ operator must be a package or domain 
      name, but Ring is a category.
--R 
--R 
--R   The right-hand side of the $ operator must be a package or domain 
--R      name, but Ring is a category.
--E 118

)set mes test on
 

)clear all
 
   All user variables and function definitions have been cleared.

--S 119
s := series(sin(a*x), x=0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 119

--S 120
s - a*x
 

   (2)
        3        5        7          9            11              13
       a   3    a   5    a    7     a     9      a      11       a       13
     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
        6      120      5040      362880      39916800       6227020800
   + 
        14
     O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R        3        5        7          9            11              13
--R       a   3    a   5    a    7     a     9      a      11       a       13
--R     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
--R        6      120      5040      362880      39916800       6227020800
--R   + 
--R        14
--R     O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 120

--S 121
s - sin(a*x)
 

           21
   (3)  O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R           21
--R   (3)  O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 121

)clear all
 
   All user variables and function definitions have been cleared.

--S 122
sin %i
 

   (1)  sin(%i)
                                             Type: Expression Complex Integer
--R 
--R
--R   (1)  sin(%i)
--R                                             Type: Expression Complex Integer
--E 122

--S 123
sin sqrt 2
 

             +-+
   (2)  sin(\|2 )
                                                     Type: Expression Integer
--R 
--R
--R             +-+
--R   (2)  sin(\|2 )
--R                                                     Type: Expression Integer
--E 123

--S 124
%i*sqrt(2)
 

           +-+
   (3)  %i\|2
                                             Type: Expression Complex Integer
--R 
--R
--R           +-+
--R   (3)  %i\|2
--R                                             Type: Expression Complex Integer
--E 124

--S 125
sin(%i*sqrt 2)
 

               +-+
   (4)  sin(%i\|2 )
                                             Type: Expression Complex Integer
--R 
--R
--R               +-+
--R   (4)  sin(%i\|2 )
--R                                             Type: Expression Complex Integer
--E 125

--S 126
%i * sin(x)
 

   (5)  %i sin(x)
                                             Type: Expression Complex Integer
--R 
--R
--R   (5)  %i sin(x)
--R                                             Type: Expression Complex Integer
--E 126

--S 127
sin(x/sqrt(2))
 

              +-+
            x\|2
   (6)  sin(-----)
              2
                                                     Type: Expression Integer
--R 
--R
--R              +-+
--R            x\|2
--R   (6)  sin(-----)
--R              2
--R                                                     Type: Expression Integer
--E 127

)clear all
 
   All user variables and function definitions have been cleared.

)set msg test off
 
   No option begins with msg .

--S 128
primaryDecomp xx
 
   There are 1 exposed and 0 unexposed library operations named 
      primaryDecomp having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                          )display op primaryDecomp
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      primaryDecomp with argument type(s) 
                                 Variable xx
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      primaryDecomp having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                          )display op primaryDecomp
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      primaryDecomp with argument type(s) 
--R                                 Variable xx
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 128

)set msg test on
 
   No option begins with msg .

)clear all
 
   All user variables and function definitions have been cleared.

--S 129
f l ==
  reduce((x,y) +-> l.1 + x + y, l)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 129

--S 130
f [10,2,53]
 
   Compiling function f with type List PositiveInteger -> 
      PositiveInteger 

   (2)  85
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type List PositiveInteger -> 
--R      PositiveInteger 
--R
--R   (2)  85
--R                                                        Type: PositiveInteger
--E 130

--S 131
g l ==
  (x:INT):INT +-> l.x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 131

--S 132
w := g [23,1,341,12] ;
 
   Compiling function g with type List PositiveInteger -> (Integer -> 
      Integer) 

                                                   Type: (Integer -> Integer)
--R 
--R   Compiling function g with type List PositiveInteger -> (Integer -> 
--R      Integer) 
--R
--R                                                   Type: (Integer -> Integer)
--E 132

--S 133
w(1) + w(3)
 

   (5)  364
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  364
--R                                                        Type: PositiveInteger
--E 133

--S 134
w(-1) 
 
 
Daly Bug
   >> Error detected within library code:
   index out of range

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   index out of range
--R
--R   Continuing to read the file...
--R
--E 134

)clear all
 
   All user variables and function definitions have been cleared.

--S 135
a := 2/3
 

        2
   (1)  -
        3
                                                       Type: Fraction Integer
--R 
--R
--R        2
--R   (1)  -
--R        3
--R                                                       Type: Fraction Integer
--E 135

)set mes test off
 

--S 136
a::PF 3
 
 
   Division by zero on conversion to GaloisField.
--R 
--R 
--R   Division by zero on conversion to GaloisField.
--E 136

)set mes test on
 

--S 137
b := x+1
 

   (2)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  x + 1
--R                                                     Type: Polynomial Integer
--E 137

--S 138
b:: EXPR FLOAT
 

   (3)  x + 1.0
                                                       Type: Expression Float
--R 
--R
--R   (3)  x + 1.0
--R                                                       Type: Expression Float
--E 138

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 139
symbol(s:Symbol,i:Integer):Symbol ==
  st0:String:= convert(i)
  st0:= concat(string(s),st0)
  st0::Symbol
 
   Function declaration symbol : (Symbol,Integer) -> Symbol has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration symbol : (Symbol,Integer) -> Symbol has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 139

--S 140
f(a,b) == symbol(a,b)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 140

--S 141
f('abc,3)
 
   Compiling function symbol with type (Symbol,Integer) -> Symbol 
   Compiling function f with type (Variable abc,PositiveInteger) -> 
      Symbol 

   (3)  abc3
                                                                 Type: Symbol
--R 
--R   Compiling function symbol with type (Symbol,Integer) -> Symbol 
--R   Compiling function f with type (Variable abc,PositiveInteger) -> 
--R      Symbol 
--R
--R   (3)  abc3
--R                                                                 Type: Symbol
--E 141

)clear all
 
   All user variables and function definitions have been cleared.

--S 142
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 412

--S 143
y := f(x)
 

   (2)  f(x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  f(x)
--R                                                     Type: Expression Integer
--E 143

--S 144
foo(u) == sin(u)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 144

--S 145
eval(y, 'f, foo)
 
   There are 2 exposed and 6 unexposed library operations named sin 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op sin
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Compiling function foo with type Expression Integer -> Expression 
      Integer 

   (4)  sin(x)
                                                     Type: Expression Integer
--R 
--R   There are 2 exposed and 6 unexposed library operations named sin 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op sin
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Compiling function foo with type Expression Integer -> Expression 
--R      Integer 
--R
--R   (4)  sin(x)
--R                                                     Type: Expression Integer
--E 145

)clear all
 
   All user variables and function definitions have been cleared.

--S 146
init()$(PF 3)
 

   (1)  0
                                                           Type: PrimeField 3
--R 
--R
--R   (1)  0
--R                                                           Type: PrimeField 3
--E 146

)clear all
 
   All user variables and function definitions have been cleared.

--draw((x,y) +-> x**2 - y**2, -1..1, -1..1)

)clear all
 
   All user variables and function definitions have been cleared.

--S 147
dmp := DMP([u1,u2,u3],Fraction INT)
 

   (1)  DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
--R                                                                 Type: Domain
--E 147

--S 148
p : dmp := 2*u1**4*u2*u3
 

           4
   (2)  2u1 u2 u3
         Type: DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
--R 
--R
--R           4
--R   (2)  2u1 u2 u3
--R         Type: DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
--E 148

--S 149
e1 := degree p
 

   (3)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (3)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 149

--S 150
e2 : DirectProduct(3,NonNegativeInteger) := e1
 

   (4)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (4)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 150

--S 151
sup(e1,e1)
 

   (5)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (5)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 151


--S 152
sup(e1,e1)$DirectProduct(3,NonNegativeInteger)
 

   (6)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (6)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 152

)clear all
 
   All user variables and function definitions have been cleared.

--S 153
sum:=0
 

   (1)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (1)  0
--R                                                     Type: NonNegativeInteger
--E 153

--S 154
m:=matrix [[1,2],[3,4]]
 

        +1  2+
   (2)  |    |
        +3  4+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2+
--R   (2)  |    |
--R        +3  4+
--R                                                         Type: Matrix Integer
--E 154

--S 155
lastcol:=ncols(m)
 

   (3)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  2
--R                                                        Type: PositiveInteger
--E 155

--S 156
for r in 1..nrows(m) repeat
 -- interpreter having a value for "row" would cause it to hide
 -- the system function
 Row:=row(m,r)
 for c in 1..lastcol repeat
  sum:=sum+Row.c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 156

--S 157
sum
 

   (5)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  10
--R                                                        Type: PositiveInteger
--E 157

)clear all
 
   All user variables and function definitions have been cleared.

--S 158
splitPoly(f,var) ==
   map(g +-> multivariate(g,var),monomials univariate(f,var))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 158

--S 159
g:=sin(x)+cos(x)
 

   (2)  sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 159

--S 160
k:=kernels(g).1
 

   (3)  sin(x)
                                              Type: Kernel Expression Integer
--R 
--R
--R   (3)  sin(x)
--R                                              Type: Kernel Expression Integer
--E 160

)set mes test off
 

--S 161
splitPoly([g],k) -- this is an incorrect call
 
   There are 4 exposed and 1 unexposed library operations named 
      univariate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op univariate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      univariate with argument type(s) 
                           List Expression Integer
                          Kernel Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   There are 4 exposed and 1 unexposed library operations named 
      univariate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op univariate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named 
      univariate with argument type(s) 
                           List Expression Integer
                          Kernel Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 4 exposed and 1 unexposed library operations named 
--R      univariate having 2 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                           )display op univariate
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      univariate with argument type(s) 
--R                           List Expression Integer
--R                          Kernel Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   There are 4 exposed and 1 unexposed library operations named 
--R      univariate having 2 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                           )display op univariate
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named 
--R      univariate with argument type(s) 
--R                           List Expression Integer
--R                          Kernel Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 161

)set mes test on
 

--S 162
splitPoly(numer g,k) -- this is a correct call
 
   Compiling function splitPoly with type (SparseMultivariatePolynomial
      (Integer,Kernel Expression Integer),Kernel Expression Integer)
       -> List SparseMultivariatePolynomial(Integer,Kernel Expression 
      Integer) 

   (4)  [sin(x),cos(x)]
   Type: List SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R   Compiling function splitPoly with type (SparseMultivariatePolynomial
--R      (Integer,Kernel Expression Integer),Kernel Expression Integer)
--R       -> List SparseMultivariatePolynomial(Integer,Kernel Expression 
--R      Integer) 
--R
--R   (4)  [sin(x),cos(x)]
--R   Type: List SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 162

)clear all
 
   All user variables and function definitions have been cleared.

--S 163
f x ==
  g := (y:DoubleFloat):DoubleFloat +-> y+x
  output(y+1)
  g(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 163

--S 164
f 3
 
   Compiling function f with type PositiveInteger -> DoubleFloat 
   y + 1

   (2)  6.0
                                                            Type: DoubleFloat
--R 
--R   Compiling function f with type PositiveInteger -> DoubleFloat 
--R   y + 1
--R
--R   (2)  6.
--R                                                            Type: DoubleFloat
--E 164

)clear all
 
   All user variables and function definitions have been cleared.

--S 165
f x == 1/factorial(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 165

--S 166
series(f, x=0)
 
   Compiling function f with type Integer -> Expression Integer 

   (2)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R   Compiling function f with type Integer -> Expression Integer 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 166

)clear all
 
   All user variables and function definitions have been cleared.

--S 167
node_a == i1+i2+i3-i5+i6=0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 167

--S 168
node_b == -i2-i3+i4-i6=0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 168

--S 169
i1 == va/r1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 169

--S 170
i2 == (va-vb)/r2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 170

--S 171
i3 == (va-vb)/r3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 171

--S 172
i4 == vb/r4
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 172

--S 173
node_a
 
   Compiling body of rule i1 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule i2 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule i3 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule nodea to compute value of type Equation 
      Fraction Polynomial Integer 

        (- r1 r3 - r1 r2)vb + ((r2 + r1)r3 + r1 r2)va + (i6 - i5)r1 r2 r3
   (7)  -----------------------------------------------------------------= 0
                                     r1 r2 r3
                                   Type: Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule i1 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule i2 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule i3 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule nodea to compute value of type Equation 
--R      Fraction Polynomial Integer 
--R
--R        (- r1 r3 - r1 r2)vb + ((r2 + r1)r3 + r1 r2)va + (i6 - i5)r1 r2 r3
--R   (7)  -----------------------------------------------------------------= 0
--R                                     r1 r2 r3
--R                                   Type: Equation Fraction Polynomial Integer
--E 173

--S 174
node_b
 
   Compiling body of rule i4 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule nodeb to compute value of type Equation 
      Fraction Polynomial Integer 

        ((r3 + r2)r4 + r2 r3)vb + (- r3 - r2)r4 va - i6 r2 r3 r4
   (8)  --------------------------------------------------------= 0
                                r2 r3 r4
                                   Type: Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule i4 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule nodeb to compute value of type Equation 
--R      Fraction Polynomial Integer 
--R
--R        ((r3 + r2)r4 + r2 r3)vb + (- r3 - r2)r4 va - i6 r2 r3 r4
--R   (8)  --------------------------------------------------------= 0
--R                                r2 r3 r4
--R                                   Type: Equation Fraction Polynomial Integer
--E 174

--S 175
ans == solve([node_a,node_b],[va,vb]) -- (*)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 175

--S 176
x1 == rhs(ans.1.1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 176

--S 177
x2 == rhs(ans.1.2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 177

--S 178
x1       -- (**)
 
   Compiling body of rule ans to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling body of rule x1 to compute value of type Fraction 
      Polynomial Integer 

         (i5 r1 r3 + i5 r1 r2)r4 + (- i6 + i5)r1 r2 r3
   (12)  ---------------------------------------------
               (r3 + r2)r4 + (r2 + r1)r3 + r1 r2
                                            Type: Fraction Polynomial Integer
--R 
--R   Compiling body of rule ans to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R   Compiling body of rule x1 to compute value of type Fraction 
--R      Polynomial Integer 
--R
--R         (i5 r1 r3 + i5 r1 r2)r4 + (- i6 + i5)r1 r2 r3
--R   (12)  ---------------------------------------------
--R               (r3 + r2)r4 + (r2 + r1)r3 + r1 r2
--R                                            Type: Fraction Polynomial Integer
--E 178

--S 179
r1 == 2  -- (***)
 
   Compiled code for i1 has been cleared.
   Compiled code for nodea has been cleared.
   Compiled code for ans has been cleared.
   Compiled code for x1 has been cleared.
                                                                   Type: Void
--R 
--R   Compiled code for i1 has been cleared.
--R   Compiled code for nodea has been cleared.
--R   Compiled code for ans has been cleared.
--R   Compiled code for x1 has been cleared.
--R                                                                   Type: Void
--E 179

--S 180
x1       -- (****)
 
   Compiling body of rule r1 to compute value of type PositiveInteger 
   Compiling body of rule i1 to compute value of type Polynomial 
      Fraction Integer 
   Compiling body of rule nodea to compute value of type Equation 
      Fraction Polynomial Integer 
   Compiling body of rule ans to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling body of rule x1 to compute value of type Fraction 
      Polynomial Integer 

         (2i5 r3 + 2i5 r2)r4 + (- 2i6 + 2i5)r2 r3
   (14)  ----------------------------------------
              (r3 + r2)r4 + (r2 + 2)r3 + 2r2
                                            Type: Fraction Polynomial Integer
--R 
--R   Compiling body of rule r1 to compute value of type PositiveInteger 
--R   Compiling body of rule i1 to compute value of type Polynomial 
--R      Fraction Integer 
--R   Compiling body of rule nodea to compute value of type Equation 
--R      Fraction Polynomial Integer 
--R   Compiling body of rule ans to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R   Compiling body of rule x1 to compute value of type Fraction 
--R      Polynomial Integer 
--R
--R         (2i5 r3 + 2i5 r2)r4 + (- 2i6 + 2i5)r2 r3
--R   (14)  ----------------------------------------
--R              (r3 + r2)r4 + (r2 + 2)r3 + 2r2
--R                                            Type: Fraction Polynomial Integer
--E 180

)clear all
 
   All user variables and function definitions have been cleared.

--S 181
"asd" "sdfsdf" "dfgdfg"
 

   (1)  "asdsdfsdfdfgdfg"
                                                                 Type: String
--R 
--R
--R   (1)  "asdsdfsdfdfgdfg"
--R                                                                 Type: String
--E 181

)clear all
 
   All user variables and function definitions have been cleared.

--S 182
s := 3.4
 

   (1)  3.4
                                                                  Type: Float
--R 
--R
--R   (1)  3.4
--R                                                                  Type: Float
--E 182

--S 183
while s > 1.0 repeat (s := 1/2; print s)
 
   1
   -
   2
                                                                   Type: Void
--R 
--R   1
--R   -
--R   2
--R                                                                   Type: Void
--E 183

--S 184
s
 

        1
   (3)  -
        2
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (3)  -
--R        2
--R                                                       Type: Fraction Integer
--E 184

)clear all
 
   All user variables and function definitions have been cleared.

--S 185
f x ==
  free s
  s := x
  while s > 1.0 repeat (s := 1/2; print s)
  s
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 185

--S 186
f(3.4)
 
   Compiling function f with type Float -> Float 
   Compiled code for f has been cleared.
   0.5

   (2)  0.5
                                                                  Type: Float
--R 
--R   Compiling function f with type Float -> Float 
--R   Compiled code for f has been cleared.
--R   0.5
--R
--R   (2)  0.5
--R                                                                  Type: Float
--E 186

)clear all
 
   All user variables and function definitions have been cleared.

--S 187
t x ==
  if x = 1 then (1; return [x])
  return [2]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 187

--S 188
t 1
 
   Compiling function t with type PositiveInteger -> List 
      PositiveInteger 

   (2)  [1]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function t with type PositiveInteger -> List 
--R      PositiveInteger 
--R
--R   (2)  [1]
--R                                                   Type: List PositiveInteger
--E 188
)spool 
 
Starts dribbling to dfloat.output (2009/2/17, 17:44:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 10
2.71828
 

   (1)  2.71828
                                                                  Type: Float
--R 
--R
--R   (1)  2.71828
--R                                                                  Type: Float
--E 1

--S 2 of 10
2.71828@DoubleFloat
 

   (2)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  2.71828
--R                                                            Type: DoubleFloat
--E 2

--S 3 of 10
2.71828 :: DoubleFloat
 

   (3)  2.7182799999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (3)  2.71828
--R                                                            Type: DoubleFloat
--E 3

--S 4 of 10
eApprox : DoubleFloat := 2.71828
 

   (4)  2.7182799999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (4)  2.71828
--R                                                            Type: DoubleFloat
--E 4

--S 5 of 10
avg : List DoubleFloat -> DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
avg l ==
  empty? l => 0 :: DoubleFloat
  reduce(_+,l) / #l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
avg []
 
   Compiling function avg with type List DoubleFloat -> DoubleFloat 

   (7)  0.0
                                                            Type: DoubleFloat
--R 
--R   Compiling function avg with type List DoubleFloat -> DoubleFloat 
--R
--R   (7)  0.
--R                                                            Type: DoubleFloat
--E 7

--S 8 of 10
avg [3.4,9.7,-6.8]
 

   (8)  2.1000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (8)  2.1000000000000001
--R                                                            Type: DoubleFloat
--E 8

--S 9 of 10
cos(3.1415926)$DoubleFloat
 

   (9)  - 0.99999999999999856
                                                            Type: DoubleFloat
--R 
--R
--R   (9)  - 0.99999999999999856
--R                                                            Type: DoubleFloat
--E 9

--S 10 of 10
cos(3.1415926 :: DoubleFloat)
 

   (10)  - 0.99999999999999856
                                                            Type: DoubleFloat
--R 
--R
--R   (10)  - 0.99999999999999856
--R                                                            Type: DoubleFloat
--E 10
)spool
 
Starts dribbling to char.output (2009/2/17, 17:44:9).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from CharacterXmpPage

--S 1 of 13
chars := [char "a", char "A", char "X", char "8", char "+"]
 

   (1)  [a,A,X,8,+]
                                                         Type: List Character
--R 
--R
--R   (1)  [a,A,X,8,+]
--R                                                         Type: List Character
--E 1

--S 2 of 13
space()
 

   (2)
                                                              Type: Character
--R 
--R
--R   (2)
--R                                                              Type: Character
--E 2

--S 3 of 13
quote()
 

   (3)  "
                                                              Type: Character
--R 
--R
--R   (3)  "
--R                                                              Type: Character
--E 3

--S 4 of 13
escape()
 

   (4)  _
                                                              Type: Character
--R 
--R
--R   (4)  _
--R                                                              Type: Character
--E 4

--S 5 of 13
[ord c for c in chars]
 

   (5)  [97,65,88,56,43]
                                                           Type: List Integer
--R 
--R
--R   (5)  [97,65,88,56,43]
--R                                                           Type: List Integer
--E 5

--S 6 of 13
[upperCase c for c in chars]
 

   (6)  [A,A,X,8,+]
                                                         Type: List Character
--R 
--R
--R   (6)  [A,A,X,8,+]
--R                                                         Type: List Character
--E 6

--S 7 of 13
[lowerCase c for c in chars]
 

   (7)  [a,a,x,8,+]
                                                         Type: List Character
--R 
--R
--R   (7)  [a,a,x,8,+]
--R                                                         Type: List Character
--E 7

--S 8 of 13
[alphabetic? c for c in chars]
 

   (8)  [true,true,true,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,true,true,false,false]
--R                                                           Type: List Boolean
--E 8

--S 9 of 13
[upperCase? c for c in chars]
 

   (9)  [false,true,true,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [false,true,true,false,false]
--R                                                           Type: List Boolean
--E 9

--S 10 of 13
[lowerCase? c for c in chars]
 

   (10)  [true,false,false,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (10)  [true,false,false,false,false]
--R                                                           Type: List Boolean
--E 10

--S 11 of 13
[digit? c for c in chars]
 

   (11)  [false,false,false,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (11)  [false,false,false,true,false]
--R                                                           Type: List Boolean
--E 11

--S 12 of 13
[hexDigit? c for c in chars]
 

   (12)  [true,true,false,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (12)  [true,true,false,true,false]
--R                                                           Type: List Boolean
--E 12

--S 13 of 13
[alphanumeric? c for c in chars]
 

   (13)  [true,true,true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (13)  [true,true,true,true,false]
--R                                                           Type: List Boolean
--E 13
)spool
 
Starts dribbling to pascal1.output (2009/2/17, 17:56:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 7
)set fun cache all
 
   In general, interpreter functions will cache all values.
--R 
--R   In general, interpreter functions will cache all values.
--E 1

--S 2 of 7
p(m,n | m = 1) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 7
p(m,n | m = n) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 7
p(i,n | 1 < i and i < n) == p(i-1,n-1)+p(i,n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 7
p(2,3)
 
   Compiling function p with type (Integer,Integer) -> PositiveInteger 
   p will cache all previously computed values.

   (4)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling function p with type (Integer,Integer) -> PositiveInteger 
--R   p will cache all previously computed values.
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 7
pr(n) == [p(i,n) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 7
l := [center blankSeparate [p(i,n)::OUTFORM for i in 1..n] for n in 1..10] ;
 

                                                        Type: List OutputForm
--R 
--R
--R                                                        Type: List OutputForm
--E 7
)spool 
 
Starts dribbling to expexpan.output (2009/2/17, 17:45:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 18
xxp f == exprToXXP(f,true)$FS2EXPXP(INT,EXPR INT,x,0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
f1 := (a**2 + 1) * exp(1/x**3 + 2/x**2) - exp(b) * exp(1/x**3 + 3/x**2)
 

            3x + 1                2x + 1
            ------                ------
               3                     3
              x     b     2         x
   (2)  - %e      %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R            3x + 1                2x + 1
--R            ------                ------
--R               3                     3
--R              x     b     2         x
--R   (2)  - %e      %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 2

--S 3 of 18
x1 := xxp f1
 
   Compiling function xxp with type Expression Integer -> Union(
      %expansion: ExponentialExpansion(Integer,Expression Integer,x,0),
      %problem: Record(func: String,prob: String)) 

                - 3     - 2              - 3     - 2
            b  x    + 3x        2       x    + 2x
   (3)  - %e %e             + (a  + 1)%e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R   Compiling function xxp with type Expression Integer -> Union(
--R      %expansion: ExponentialExpansion(Integer,Expression Integer,x,0),
--R      %problem: Record(func: String,prob: String)) 
--R
--R                - 3     - 2              - 3     - 2
--R            b  x    + 3x        2       x    + 2x
--R   (3)  - %e %e             + (a  + 1)%e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 3

--S 4 of 18
limitPlus x1   -- %minusInfinity
 

   (4)  - infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)  - infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 18
f2 := (a**2 + 1) * exp(1/x**3 + 2/x**2) - exp(b) * exp(-1/x**3 + 3/x**2)
 

            3x - 1                2x + 1
            ------                ------
               3                     3
              x     b     2         x
   (5)  - %e      %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R            3x - 1                2x + 1
--R            ------                ------
--R               3                     3
--R              x     b     2         x
--R   (5)  - %e      %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 5

--S 6 of 18
x2 := xxp f2
 

                   - 3     - 2           - 3     - 2
          2       x    + 2x        b  - x    + 3x
   (6)  (a  + 1)%e             - %e %e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R                   - 3     - 2           - 3     - 2
--R          2       x    + 2x        b  - x    + 3x
--R   (6)  (a  + 1)%e             - %e %e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 6

--S 7 of 18
limitPlus x2   -- %plusInfinity
 

   (7)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (7)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 7

--S 8 of 18
f3 := (a**2 + 1) * exp(1/x**3) - exp(b) * exp(c/x**2)
 

             c                 1
            --                --
             2                 3
            x   b     2       x
   (8)  - %e  %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R             c                 1
--R            --                --
--R             2                 3
--R            x   b     2       x
--R   (8)  - %e  %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 8

--S 9 of 18
x3 := xxp f3
 

                   - 3           - 2
          2       x        b  c x
   (9)  (a  + 1)%e     - %e %e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R                   - 3           - 2
--R          2       x        b  c x
--R   (9)  (a  + 1)%e     - %e %e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 9

--S 10 of 18
limitPlus x3   -- %plusInfinity
 

   (10)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (10)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 10

--S 11 of 18
f4 := (a**2 + 1) * exp(-1/x**3) - exp(b) * exp(c/x**2)
 

              c                   1
             --                - --
              2                   3
             x   b     2         x
   (11)  - %e  %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R              c                   1
--R             --                - --
--R              2                   3
--R             x   b     2         x
--R   (11)  - %e  %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 11

--S 12 of 18
x4 := xxp f4
 

                      - 3           - 2
           2       - x        b  c x
   (12)  (a  + 1)%e       - %e %e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R                      - 3           - 2
--R           2       - x        b  c x
--R   (12)  (a  + 1)%e       - %e %e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 12

--S 13 of 18
limitPlus x4   -- "failed"
 

   (13)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (13)  "failed"
--R                                                    Type: Union("failed",...)
--E 13

--S 14 of 18
p5 := tan(x) * exp(1/x**2) - tan(x) * exp(1/x**2 - 1/x) + sin(x) * exp(1/x)
 

             1     - x + 1
            --     -------            1
             2         2              -
            x         x               x
   (14)  (%e   - %e       )tan(x) + %e sin(x)
                                                     Type: Expression Integer
--R 
--R
--R             1     - x + 1
--R            --     -------            1
--R             2         2              -
--R            x         x               x
--R   (14)  (%e   - %e       )tan(x) + %e sin(x)
--R                                                     Type: Expression Integer
--E 14

--S 15 of 18
q5 := -4 * exp(-1/x**2 - 1/x) + sin(x) * exp(-1/x**2 + 1/x)
 

           x - 1            - x - 1
           -----            -------
              2                 2
             x                 x
   (15)  %e     sin(x) - 4%e
                                                     Type: Expression Integer
--R 
--R
--R           x - 1            - x - 1
--R           -----            -------
--R              2                 2
--R             x                 x
--R   (15)  %e     sin(x) - 4%e
--R                                                     Type: Expression Integer
--E 15

--S 16 of 18
f5 := p5 / q5
 

             1     - x + 1
            --     -------            1
             2         2              -
            x         x               x
         (%e   - %e       )tan(x) + %e sin(x)
   (16)  ------------------------------------
                x - 1            - x - 1
                -----            -------
                   2                 2
                  x                 x
              %e     sin(x) - 4%e
                                                     Type: Expression Integer
--R 
--R
--R             1     - x + 1
--R            --     -------            1
--R             2         2              -
--R            x         x               x
--R         (%e   - %e       )tan(x) + %e sin(x)
--R   (16)  ------------------------------------
--R                x - 1            - x - 1
--R                -----            -------
--R                   2                 2
--R                  x                 x
--R              %e     sin(x) - 4%e
--R                                                     Type: Expression Integer
--E 16

--S 17 of 18
x5 := xxp f5
 

   (17)
                1  3    1   5     1   7      1    9       1     11      12
         (- x + - x  - --- x  + ---- x  - ------ x  + -------- x   + O(x  ))
                6      120      5040      362880      39916800
      *
            - 2    - 1
           x    - x
         %e
     + 
                                                                           - 2
            1  3    1   5     1   7      1    9       1     11      12    x
       (x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  ))%e
            6      120      5040      362880      39916800
     + 
                                                                     - 1
            2  3    2  5    4   7     2   9      4    11      12    x
       (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))%e
            3      15      315      2835      155925
  /
              2  3    2  5    4   7     2   9      4    11      12
         (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))
              3      15      315      2835      155925
      *
              - 2    - 1
           - x    + x
         %e
     + 
                                                                      - 2    - 1
              2   1  4    1   6     1    8      1    10      11    - x    - x
     (- 4 + 2x  - - x  + --- x  - ----- x  + ------ x   + O(x  ))%e
                  6      180      10080      907200
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R   (17)
--R                1  3    1   5     1   7      1    9       1     11      12
--R         (- x + - x  - --- x  + ---- x  - ------ x  + -------- x   + O(x  ))
--R                6      120      5040      362880      39916800
--R      *
--R            - 2    - 1
--R           x    - x
--R         %e
--R     + 
--R                                                                           - 2
--R            1  3    1   5     1   7      1    9       1     11      12    x
--R       (x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  ))%e
--R            6      120      5040      362880      39916800
--R     + 
--R                                                                     - 1
--R            2  3    2  5    4   7     2   9      4    11      12    x
--R       (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))%e
--R            3      15      315      2835      155925
--R  /
--R              2  3    2  5    4   7     2   9      4    11      12
--R         (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))
--R              3      15      315      2835      155925
--R      *
--R              - 2    - 1
--R           - x    + x
--R         %e
--R     + 
--R                                                                      - 2    - 1
--R              2   1  4    1   6     1    8      1    10      11    - x    - x
--R     (- 4 + 2x  - - x  + --- x  - ----- x  + ------ x   + O(x  ))%e
--R                  6      180      10080      907200
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 17

--S 18 of 18
limitPlus x5   -- %plusInfinity
 

   (18)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (18)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 18
)spool 
 
Starts dribbling to conformal.output (2009/2/17, 17:44:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 18
C := Complex DoubleFloat                -- Complex Numbers
 

   (1)  Complex DoubleFloat
                                                                 Type: Domain
--R 
--R
--R   (1)  Complex DoubleFloat
--R                                                                 Type: Domain
--E 1

--S 2 of 18
S := Segment DoubleFloat                -- Draw ranges
 

   (2)  Segment DoubleFloat
                                                                 Type: Domain
--R 
--R
--R   (2)  Segment DoubleFloat
--R                                                                 Type: Domain
--E 2

--S 3 of 18
R3 := POINT DoubleFloat                         -- points in 3-space
 

   (3)  Point DoubleFloat
                                                                 Type: Domain
--R 
--R
--R   (3)  Point DoubleFloat
--R                                                                 Type: Domain
--E 3
--S 4 of 18
conformalDraw: (C -> C, S, S, PI, PI, String) -> VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 18
conformalDraw(f, rRange, tRange, rSteps, tSteps, coord) ==
  transformC :=
    coord = "polar" => polar2Complex
    cartesian2Complex
  cm := makeConformalMap(f, transformC)
  sp := createThreeSpace()
  adaptGrid(sp, cm, rRange, tRange, rSteps, tSteps)
  makeViewport3D(sp, "Conformal Map")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
--S 6 of 18
riemannConformalDraw: (C -> C, S, S, PI, PI, String) -> VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 18
riemannConformalDraw(f, rRange, tRange, rSteps, tSteps, coord) ==
  transformC :=
    coord = "polar" => polar2Complex
    cartesian2Complex
  sp := createThreeSpace()
  cm := makeRiemannConformalMap(f, transformC)
  adaptGrid(sp, cm, rRange, tRange, rSteps, tSteps)
  -- add an invisible point at the north pole for scaling
  curve(sp, [point [0,0,2.0@DoubleFloat,0], point [0,0, 2.0@DoubleFloat,0]])
  makeViewport3D(sp, "Conformal Map on the Riemann Sphere")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
--S 8 of 18
adaptGrid(sp, f, uRange, vRange,  uSteps, vSteps) ==
  delU := (hi(uRange) - lo(uRange))/uSteps
  delV := (hi(vRange) - lo(vRange))/vSteps
  uSteps := uSteps + 1; vSteps := vSteps + 1
  u := lo uRange
  -- draw the coodinate lines in the v direction
  for i in 1..uSteps repeat
    -- create a curve 'c' which fixes the current value of 'u'
    c := curryLeft(f,u)
    cf := (t:DoubleFloat):DoubleFloat +-> 0
    -- draw the 'v' coordinate line
    makeObject(c, vRange::Segment Float, colorFunction == cf, space == sp, _
               tubeRadius == 0.02,  tubePoints == 6)
    u := u + delU
  v := lo vRange
  -- draw the coodinate lines in the u direction
  for i in 1..vSteps repeat
    -- create a curve 'c' which fixes the current value of 'v'
    c := curryRight(f,v)
    cf := (t:DoubleFloat):DoubleFloat +-> 1
    -- draw the 'u' coordinate line
    makeObject(c, uRange::Segment Float, colorFunction == cf, space == sp, _
               tubeRadius == 0.02,  tubePoints == 6)
    v := v + delV
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8
--S 9 of 18
riemannTransform(z) ==
  r := sqrt norm z
  cosTheta := (real z)/r
  sinTheta := (imag z)/r
  cp := 4*r/(4+r**2)
  sp := sqrt(1-cp*cp)
  if r>2 then sp := -sp
  point [cosTheta*cp, sinTheta*cp, -sp + 1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9
--S 10 of 18
cartesian2Complex(r:DoubleFloat, i:DoubleFloat):C == complex(r, i)
 
   Function declaration cartesian2Complex : (DoubleFloat,DoubleFloat)
       -> Complex DoubleFloat has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration cartesian2Complex : (DoubleFloat,DoubleFloat)
--R       -> Complex DoubleFloat has been added to workspace.
--R                                                                   Type: Void
--E 10
--S 11 of 18
polar2Complex(r:DoubleFloat, th:DoubleFloat):C == complex(r*cos(th), r*sin(th))
 
   Function declaration polar2Complex : (DoubleFloat,DoubleFloat) -> 
      Complex DoubleFloat has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration polar2Complex : (DoubleFloat,DoubleFloat) -> 
--R      Complex DoubleFloat has been added to workspace.
--R                                                                   Type: Void
--E 11
--S 12 of 18
makeConformalMap(f, transformC) ==
  (u:DoubleFloat,v:DoubleFloat):R3 +->
    z := f transformC(u, v)
    point [real z, imag z, 0.0@DoubleFloat]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12
--S 13 of 18
makeRiemannConformalMap(f, transformC) ==
  (u:DoubleFloat, v:DoubleFloat):R3 +-> riemannTransform f transformC(u, v)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13
--S 14 of 18
riemannSphereDraw: (S, S, PI, PI, String) -> VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 18
riemannSphereDraw(rRange, tRange, rSteps, tSteps, coord) ==
  transformC :=
    coord = "polar" => polar2Complex
    cartesian2Complex
  grid := (u:DoubleFloat , v:DoubleFloat): R3 +->
    z1 := transformC(u, v)
    point [real z1, imag z1, 0]
  sp := createThreeSpace()
  adaptGrid(sp, grid, rRange, tRange, rSteps, tSteps)
  connectingLines(sp, grid, rRange, tRange, rSteps, tSteps)
  makeObject(riemannSphere, 0..2*%pi, 0..%pi, space == sp)
  f := (z:C):C +-> z
  cm := makeRiemannConformalMap(f, transformC)
  adaptGrid(sp, cm, rRange, tRange, rSteps, tSteps)
  makeViewport3D(sp, "Riemann Sphere")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15
--S 16 of 18
connectingLines(sp, f, uRange, vRange, uSteps, vSteps) ==
  delU := (hi(uRange) - lo(uRange))/uSteps
  delV := (hi(vRange) - lo(vRange))/vSteps
  uSteps := uSteps + 1; vSteps := vSteps + 1
  u := lo uRange
  -- for each grid point
  for i in 1..uSteps repeat
    v := lo vRange
    for j in 1..vSteps repeat
      p1 := f(u,v)
      p2 := riemannTransform complex(p1.1, p1.2)
      fun := lineFromTo(p1,p2)
      cf := (t:DoubleFloat):DoubleFloat +-> 3
      makeObject(fun, 0..1, space == sp, tubePoints == 4, tubeRadius == 0.01,
                 colorFunction == cf)
      v := v + delV
    u := u + delU
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 18
riemannSphere(u,v) ==
  sv := sin(v)
  0.99@DoubleFloat*(point [cos(u)*sv, sin(u)*sv, cos(v),0.0@DoubleFloat]) +
    point [0.0@DoubleFloat, 0.0@DoubleFloat, 1.0@DoubleFloat, 4.0@DoubleFloat]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17
--S 18 of 18
lineFromTo(p1, p2) ==
  d := p2 - p1
  (t:DoubleFloat):Point DoubleFloat +-> p1 + t*d
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18
)spool
 
Starts dribbling to sqrt3.output (2009/2/17, 18:0:43).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 23
t1:=(sqrt(3)-3)*(sqrt(3)+1)/6
 

           +-+
          \|3
   (1)  - ----
            3
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (1)  - ----
--R            3
--R                                                        Type: AlgebraicNumber
--E 1

--S 2 of 23
tt1:=-1/sqrt(3)
 

           +-+
          \|3
   (2)  - ----
            3
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (2)  - ----
--R            3
--R                                                        Type: AlgebraicNumber
--E 2

--S 3 of 23
t2:=sqrt(3)/6
 

         +-+
        \|3
   (3)  ----
          6
                                                        Type: AlgebraicNumber
--R 
--R
--R         +-+
--R        \|3
--R   (3)  ----
--R          6
--R                                                        Type: AlgebraicNumber
--E 3

--S 4 of 23
t1+t2
 

           +-+
          \|3
   (4)  - ----
            6
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (4)  - ----
--R            6
--R                                                        Type: AlgebraicNumber
--E 4

--S 5 of 23
tt1+t2
 

           +-+
          \|3
   (5)  - ----
            6
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (5)  - ----
--R            6
--R                                                        Type: AlgebraicNumber
--E 5

--S 6 of 23
RAN ==> RECLOS FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 23
x1:=(sqrt(3)$RAN-3)*(sqrt(3)$RAN+1)/6
 

         1  +-+   1  +-+   1  +-+   1
   (7)  (- \|3  - -)\|3  + - \|3  - -
         6        2        6        2
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         1  +-+   1  +-+   1  +-+   1
--R   (7)  (- \|3  - -)\|3  + - \|3  - -
--R         6        2        6        2
--R                                           Type: RealClosure Fraction Integer
--E 7

--S 8 of 23
xx1:=-1/sqrt(3)$RAN
 

          1  +-+
   (8)  - - \|3
          3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          1  +-+
--R   (8)  - - \|3
--R          3
--R                                           Type: RealClosure Fraction Integer
--E 8

--S 9 of 23
(x1=xx1)@Boolean
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 23
s3:=sqrt(3)$RAN
 

          +-+
   (10)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (10)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 10

--S 11 of 23
(s3-3)*(s3+1)/6
 

           1  +-+
   (11)  - - \|3
           3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           1  +-+
--R   (11)  - - \|3
--R           3
--R                                           Type: RealClosure Fraction Integer
--E 11

--S 12 of 23
f3:=sqrt(3,5)$RAN
 

         5+-+
   (12)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         5+-+
--R   (12)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 23
f25:=sqrt(1/25,5)$RAN
 

          +--+
          | 1
   (13)  5|--
         \|25
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          | 1
--R   (13)  5|--
--R         \|25
--R                                           Type: RealClosure Fraction Integer
--E 13

--S 14 of 23
f32:=sqrt(32/5,5)$RAN
 

          +--+
          |32
   (14)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |32
--R   (14)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 14

--S 15 of 23
f27:=sqrt(27/5,5)$RAN
 

          +--+
          |27
   (15)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |27
--R   (15)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 23
expr1:=sqrt(f32-f27,3)
 

          +---------------+
          |   +--+    +--+
          |   |27     |32
   (16)  3|- 5|--  + 5|--
         \|  \| 5    \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +---------------+
--R          |   +--+    +--+
--R          |   |27     |32
--R   (16)  3|- 5|--  + 5|--
--R         \|  \| 5    \| 5
--R                                           Type: RealClosure Fraction Integer
--E 16

--S 17 of 23
expr2:=(1+f3-f3^2)
 

           5+-+2   5+-+
   (17)  - \|3   + \|3  + 1
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           5+-+2   5+-+
--R   (17)  - \|3   + \|3  + 1
--R                                           Type: RealClosure Fraction Integer
--E 17

--S 18 of 23
expr1-f25*expr2
 

   (18)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (18)  0
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 23
s:=sqrt(190)$RAN+sqrt(1751)$RAN-sqrt(208)$RAN-sqrt(1698)$RAN
 

            +----+    +---+    +----+    +---+
   (19)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (19)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 19

--S 20 of 23
approximate(s,10^-15)::Float
 

   (20)  - 0.2341060678 6455900874 E -10
                                                                  Type: Float
--R 
--R
--R   (20)  - 0.2341060678 6455900874 E -10
--R                                                                  Type: Float
--E 20

--S 21 of 23
t:=sqrt(190)+sqrt(1751)-sqrt(208)-sqrt(1698)
 

          +----+    +----+    +---+     +--+
   (21)  \|1751  - \|1698  + \|190  - 4\|13
                                                        Type: AlgebraicNumber
--R 
--R
--R          +----+    +----+    +---+     +--+
--R   (21)  \|1751  - \|1698  + \|190  - 4\|13
--R                                                        Type: AlgebraicNumber
--E 21

--S 22 of 23
digits(30)
 

   (22)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  20
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 23
numeric t - approximate(s,10^-30)::Float
 

   (23)  - 0.5522026336 5 E -29
                                                                  Type: Float
--R 
--R
--R   (23)  - 0.5522026336 5 E -29
--R                                                                  Type: Float
--E 23

)spool 
 
Starts dribbling to assign.output (2009/2/17, 17:43:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- This file shows the difference between assignments and rewrite
-- rules.
--S 1  of 11
a := 1
 

   (1)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 11
b := a         -- the value of b is now 1
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 11
b              -- see, told you
 

   (3)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 11
a := 2         -- what is the value of b?
 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 11
b              -- it is the value it had AT ASSIGNMENT
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6  of 11
c == 1         -- c is a rule
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 11
c              -- it will evaluate to 1
 
   Compiling body of rule c to compute value of type PositiveInteger 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule c to compute value of type PositiveInteger 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 11
d == c         -- d is a rule that will evaluate to c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 11
d
 
   Compiling body of rule d to compute value of type PositiveInteger 

   (9)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule d to compute value of type PositiveInteger 
--R
--R   (9)  1
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 11
c == 2         -- we have changed the rule for c
 
   Compiled code for c has been cleared.
   Compiled code for d has been cleared.
   1 old definition(s) deleted for function or rule c 
                                                                   Type: Void
--R 
--R   Compiled code for c has been cleared.
--R   Compiled code for d has been cleared.
--R   1 old definition(s) deleted for function or rule c 
--R                                                                   Type: Void
--E 10

--S 11 of 11
d              -- and so the ultimate value computed from d will change
 
   Compiling body of rule c to compute value of type PositiveInteger 
   Compiling body of rule d to compute value of type PositiveInteger 

   (11)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule c to compute value of type PositiveInteger 
--R   Compiling body of rule d to compute value of type PositiveInteger 
--R
--R   (11)  2
--R                                                        Type: PositiveInteger
--E 11
)spool
 
Starts dribbling to numbers.output (2009/2/17, 17:55:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 76
x := factorial(200)
 

   (1)
  7886578673647905035523632139321850622951359776871732632947425332443594499634_
   033429203042840119846239041772121389196388302576427902426371050619266249528_
   299311134628572707633172373969889439224456214516642402540332918641312274282_
   948532775242424075739032403212574055795686602260319041703240623517008587961_
   78922222789623703897374720000000000000000000000000000000000000000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (1)
--R  7886578673647905035523632139321850622951359776871732632947425332443594499634_
--R   033429203042840119846239041772121389196388302576427902426371050619266249528_
--R   299311134628572707633172373969889439224456214516642402540332918641312274282_
--R   948532775242424075739032403212574055795686602260319041703240623517008587961_
--R   78922222789623703897374720000000000000000000000000000000000000000000000000
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 76
y := 2**90 - 1
 

   (2)  1237940039285380274899124223
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1237940039285380274899124223
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 76
x + y
 

   (3)
  7886578673647905035523632139321850622951359776871732632947425332443594499634_
   033429203042840119846239041772121389196388302576427902426371050619266249528_
   299311134628572707633172373969889439224456214516642402540332918641312274282_
   948532775242424075739032403212574055795686602260319041703240623517008587961_
   78922222789623703897374720000000000000000000001237940039285380274899124223
                                                        Type: PositiveInteger
--R 
--R
--R   (3)
--R  7886578673647905035523632139321850622951359776871732632947425332443594499634_
--R   033429203042840119846239041772121389196388302576427902426371050619266249528_
--R   299311134628572707633172373969889439224456214516642402540332918641312274282_
--R   948532775242424075739032403212574055795686602260319041703240623517008587961_
--R   78922222789623703897374720000000000000000000001237940039285380274899124223
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 76
x - y
 

   (4)
  7886578673647905035523632139321850622951359776871732632947425332443594499634_
   033429203042840119846239041772121389196388302576427902426371050619266249528_
   299311134628572707633172373969889439224456214516642402540332918641312274282_
   948532775242424075739032403212574055795686602260319041703240623517008587961_
   78922222789623703897374719999999999999999999998762059960714619725100875777
                                                        Type: PositiveInteger
--R 
--R
--R   (4)
--R  7886578673647905035523632139321850622951359776871732632947425332443594499634_
--R   033429203042840119846239041772121389196388302576427902426371050619266249528_
--R   299311134628572707633172373969889439224456214516642402540332918641312274282_
--R   948532775242424075739032403212574055795686602260319041703240623517008587961_
--R   78922222789623703897374719999999999999999999998762059960714619725100875777
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 76
x * y
 

   (5)
  9763111513082929821843631196609502257766429667654140423707949648813338983407_
   032918809235547978281276568726017975734913119466356078732929100728088106228_
   471338396755093151069532609217447970141651251638848591388190535247585868963_
   019469887899504821090561806743717655381133973032509524956986554360537566475_
   497856969235918273095211823926950507033823968598425600000000000000000000000_
   00000000000000000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (5)
--R  9763111513082929821843631196609502257766429667654140423707949648813338983407_
--R   032918809235547978281276568726017975734913119466356078732929100728088106228_
--R   471338396755093151069532609217447970141651251638848591388190535247585868963_
--R   019469887899504821090561806743717655381133973032509524956986554360537566475_
--R   497856969235918273095211823926950507033823968598425600000000000000000000000_
--R   00000000000000000000000000
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 76
factor(x)
 

   (6)
      197 97 49 32  19  16  11  10  8  6  6  5  4  4  4  3  3  3  2  2  2  2  2
     2   3  5  7  11  13  17  19  23 29 31 37 41 43 47 53 59 61 67 71 73 79 83
  *
       2  2
     89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181
  *
     191 193 197 199
                                                       Type: Factored Integer
--R 
--R
--R   (6)
--R      197 97 49 32  19  16  11  10  8  6  6  5  4  4  4  3  3  3  2  2  2  2  2
--R     2   3  5  7  11  13  17  19  23 29 31 37 41 43 47 53 59 61 67 71 73 79 83
--R  *
--R       2  2
--R     89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181
--R  *
--R     191 193 197 199
--R                                                       Type: Factored Integer
--E 6

--S 7 of 76
factor(y)
 

         3
   (7)  3 7 11 19 31 73 151 331 631 23311 18837001
                                                       Type: Factored Integer
--R 
--R
--R         3
--R   (7)  3 7 11 19 31 73 151 331 631 23311 18837001
--R                                                       Type: Factored Integer
--E 7

)clear all
 
   All user variables and function definitions have been cleared.

--S 8 of 76
sqrt(2.0)
 

   (1)  1.4142135623 730950488
                                                                  Type: Float
--R 
--R
--R   (1)  1.4142135623 730950488
--R                                                                  Type: Float
--E 8

--S 9 of 76
numeric %pi
 

   (2)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 897932385
--R                                                                  Type: Float
--E 9

--S 10 of 76
exp(1.0)
 

   (3)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (3)  2.7182818284 590452354
--R                                                                  Type: Float
--E 10

--S 11 of 76
exp(sqrt(163.0) * %pi)
 

   (4)  26253741 2640768743.97
                                                                  Type: Float
--R 
--R
--R   (4)  26253741 2640768743.97
--R                                                                  Type: Float
--E 11

--S 12 of 76
sin(%pi/6.)
 

   (5)  0.5
                                                                  Type: Float
--R 
--R
--R   (5)  0.5
--R                                                                  Type: Float
--E 12

)clear all
 
   All user variables and function definitions have been cleared.

--S 13 of 76
1/4 - 1/5
 

         1
   (1)  --
        20
                                                       Type: Fraction Integer
--R 
--R
--R         1
--R   (1)  --
--R        20
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 76
f := (x**2 + 1)/(x - 1)
 

         2
        x  + 1
   (2)  ------
         x - 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 1
--R   (2)  ------
--R         x - 1
--R                                            Type: Fraction Polynomial Integer
--E 14

--S 15 of 76
g := (x**2 - 3*x + 2)/(x + 2)
 

         2
        x  - 3x + 2
   (3)  -----------
           x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  - 3x + 2
--R   (3)  -----------
--R           x + 2
--R                                            Type: Fraction Polynomial Integer
--E 15

--S 16 of 76
f * g
 

         3     2
        x  - 2x  + x - 2
   (4)  ----------------
              x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         3     2
--R        x  - 2x  + x - 2
--R   (4)  ----------------
--R              x + 2
--R                                            Type: Fraction Polynomial Integer
--E 16

)clear all
 
   All user variables and function definitions have been cleared.

--S 17 of 76
numeric(%pi, 500)
 

   (1)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (1)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 17

--S 18 of 76
digits 500
 

   (2)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  20
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 76
numeric %pi
 

   (3)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (3)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 19

)clear all
 
   All user variables and function definitions have been cleared.

--S 20 of 76
F7 := PF 7
 

   (1)  PrimeField 7
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 7
--R                                                                 Type: Domain
--E 20

--S 21 of 76
F49 := FF(7,2)
 

   (2)  FiniteField(7,2)
                                                                 Type: Domain
--R 
--R
--R   (2)  FiniteField(7,2)
--R                                                                 Type: Domain
--E 21

--S 22 of 76
definingPolynomial()$F49
 

         2
   (3)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R         2
--R   (3)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 22

--S 23 of 76
e := random()$F49
 

   (4)  %A + 3
                                                       Type: FiniteField(7,2)
--R 
--R
--I   (4)  4%A + 3
--R                                                       Type: FiniteField(7,2)
--E 23

--S 24 of 76
norm e
 

   (5)  3
                                                           Type: PrimeField 7
--R 
--R
--I   (5)  4
--R                                                           Type: PrimeField 7
--E 24

--S 25 of 76
trace e
 

   (6)  6
                                                           Type: PrimeField 7
--R 
--R
--I   (6)  6
--R                                                           Type: PrimeField 7
--E 25

--S 26 of 76
order e
 

   (7)  48
                                                        Type: PositiveInteger
--R 
--R
--I   (7)  24
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 76
allElts := [index(i)$F49 for i in 1..48]
 

   (8)
   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
    6%A + 5, 6%A + 6]
                                                  Type: List FiniteField(7,2)
--R 
--R
--R   (8)
--R   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
--R    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
--R    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
--R    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
--R    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
--R    6%A + 5, 6%A + 6]
--R                                                  Type: List FiniteField(7,2)
--E 27

--S 28 of 76
reduce(+,allElts)
 

   (9)  0
                                                       Type: FiniteField(7,2)
--R 
--R
--R   (9)  0
--R                                                       Type: FiniteField(7,2)
--E 28

--S 29 of 76
[order e for e in allElts]
 

   (10)
   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
    48, 4, 24, 48, 48, 48, 48, 24]
                                                   Type: List PositiveInteger
--R 
--R
--R   (10)
--R   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
--R    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
--R    48, 4, 24, 48, 48, 48, 48, 24]
--R                                                   Type: List PositiveInteger
--E 29

--S 30 of 76
u:UP(x, F7) := x**2 + 1
 

          2
   (11)  x  + 1
                                   Type: UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R          2
--R   (11)  x  + 1
--R                                   Type: UnivariatePolynomial(x,PrimeField 7)
--E 30

--S 31 of 76
factor u
 

          2
   (12)  x  + 1
                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R          2
--R   (12)  x  + 1
--R                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--E 31

--S 32 of 76
u2:UP(x, F49) := u
 

          2
   (13)  x  + 1
                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R          2
--R   (13)  x  + 1
--R                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--E 32

--S 33 of 76
factor u2
 

   (14)  (x + %A)(x + 6%A)
                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R   (14)  (x + %A)(x + 6%A)
--R                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--E 33

)clear all
 
   All user variables and function definitions have been cleared.
--S 34 of 76
f: NNI -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 76
f(n) == 2**n - 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 35

--S 36 of 76
factor f(7)
 
   Compiling function f with type NonNegativeInteger -> Integer 

   (3)  127
                                                       Type: Factored Integer
--R 
--R   Compiling function f with type NonNegativeInteger -> Integer 
--R
--R   (3)  127
--R                                                       Type: Factored Integer
--E 36

--S 37 of 76
ints := [n for n in 1..]
 

   (4)  [1,2,3,4,5,6,7,8,9,10,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (4)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                 Type: Stream PositiveInteger
--E 37

--S 28 of 76
primes := [x for x in ints | prime? x]
 

   (5)  [2,3,5,7,11,13,17,19,23,29,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (5)  [2,3,5,7,11,13,17,19,23,29,...]
--R                                                 Type: Stream PositiveInteger
--E 38

--S 39 of 76
primes.25
 

   (6)  97
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  97
--R                                                        Type: PositiveInteger
--E 39

--S 40 of 76
numbers := [f(n) for n in primes]
 

   (7)  [3,7,31,127,2047,8191,131071,524287,8388607,536870911,...]
                                                         Type: Stream Integer
--R 
--R
--R   (7)  [3,7,31,127,2047,8191,131071,524287,8388607,536870911,...]
--R                                                         Type: Stream Integer
--E 40

--S 41 of 76
factors := [factor n for n in numbers]
 

   (8)  [3,7,31,127,23 89,8191,131071,524287,47 178481,233 1103 2089,...]
                                                Type: Stream Factored Integer
--R 
--R
--R   (8)  [3,7,31,127,23 89,8191,131071,524287,47 178481,233 1103 2089,...]
--R                                                Type: Stream Factored Integer
--E 41

--S 42 of 76
nums := [x for x in numbers | not prime? x]
 

   (9)
   [2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207,
    140737488355327, 9007199254740991, 576460752303423487,
    147573952589676412927, ...]
                                                         Type: Stream Integer
--R 
--R
--R   (9)
--R   [2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207,
--R    140737488355327, 9007199254740991, 576460752303423487,
--R    147573952589676412927, ...]
--R                                                         Type: Stream Integer
--E 42

)clear all
 
   All user variables and function definitions have been cleared.

--S 43 of 76
numbers := [n**2 - n + 41 for n in 0..40]
 

   (1)
   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
                                                           Type: List Integer
--R 
--R
--R   (1)
--R   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
--R    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
--R    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
--R                                                           Type: List Integer
--E 43

--S 44 of 76
[factor n for n in numbers]
 

   (2)
   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
                                                  Type: List Factored Integer
--R 
--R
--R   (2)
--R   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
--R    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
--R    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
--R                                                  Type: List Factored Integer
--E 44

)clear all
 
   All user variables and function definitions have been cleared.

--S 45 of 76
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 45

--S 46 of 76
differentiate(f x,x,7)
 

         (vii)
   (2)  f     (x)

                                                     Type: Expression Integer
--R 
--R
--R         (vii)
--R   (2)  f     (x)
--R
--R                                                     Type: Expression Integer
--E 46

--S 47 of 76
a := roman(1978 - 1965)
 

   (3)  XIII
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XIII
--R                                                           Type: RomanNumeral
--E 47

--S 48 of 76
x : UTS(ROMAN,'x,0) := x
 

   (4)  x
                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--R 
--R
--R   (4)  x
--R                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--E 48

--S 49 of 76
recip(1 - x - x**2)
 

   (5)
                 2        3      4         5         6        7          8
     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
   + 
         9           10      11
     LV x  + LXXXIX x   + O(x  )
                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--R 
--R
--R   (5)
--R                 2        3      4         5         6        7          8
--R     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
--R   + 
--R         9           10      11
--R     LV x  + LXXXIX x   + O(x  )
--R                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--E 49

--S 50 of 76
m : MATRIX FRAC ROMAN
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 50

--S 51 of 76
m := matrix [[1/(i + j) for i in 1..3] for j in 1..3]
 

        + I    I    I+
        |--   ---  --|
        |II   III  IV|
        |            |
        | I    I   I |
   (7)  |---  --   - |
        |III  IV   V |
        |            |
        | I    I    I|
        |--    -   --|
        +IV    V   VI+
                                           Type: Matrix Fraction RomanNumeral
--R 
--R
--R        + I    I    I+
--R        |--   ---  --|
--R        |II   III  IV|
--R        |            |
--R        | I    I   I |
--R   (7)  |---  --   - |
--R        |III  IV   V |
--R        |            |
--R        | I    I    I|
--R        |--    -   --|
--R        +IV    V   VI+
--R                                           Type: Matrix Fraction RomanNumeral
--E 51

--S 52 of 76
inverse m
 

        +LXXII   - CCXL    CLXXX +
        |                        |
   (8)  |- CCXL    CM     - DCCXX|
        |                        |
        +CLXXX   - DCCXX    DC   +
                                Type: Union(Matrix Fraction RomanNumeral,...)
--R 
--R
--R        +LXXII   - CCXL    CLXXX +
--R        |                        |
--R   (8)  |- CCXL    CM     - DCCXX|
--R        |                        |
--R        +CLXXX   - DCCXX    DC   +
--R                                Type: Union(Matrix Fraction RomanNumeral,...)
--E 52

--S 53 of 76
y := factorial 20
 

   (9)  2432902008176640000
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2432902008176640000
--R                                                        Type: PositiveInteger
--E 53

--S 54 of 76
roman y
 

   (10)
  ((((((((((((((((I))))))))))))))))((((((((((((((((I)))))))))))))))) ((((((((((
  (((((I)))))))))))))))(((((((((((((((I)))))))))))))))(((((((((((((((I)))))))))
  ))))))(((((((((((((((I))))))))))))))) ((((((((((((((I))))))))))))))((((((((((
  ((((I))))))))))))))((((((((((((((I)))))))))))))) (((((((((((((I)))))))))))))(
  ((((((((((((I))))))))))))) ((((((((((((I))))))))))))((((((((((((I))))))))))))
  ((((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((
  ((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((((
  ((((((((I)))))))))))) ((((((((((I))))))))))((((((((((I)))))))))) (((((((I))))
  )))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I))))))
  )(((((((I)))))))(((((((I))))))) ((((((I)))))) (((((I)))))(((((I)))))(((((I)))
  ))(((((I)))))(((((I)))))(((((I)))))(((((I))))) ((((I))))((((I))))((((I))))(((
  (I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))((I)
  )((I))((I))
                                                           Type: RomanNumeral
--R 
--R
--R   (10)
--R  ((((((((((((((((I))))))))))))))))((((((((((((((((I)))))))))))))))) ((((((((((
--R  (((((I)))))))))))))))(((((((((((((((I)))))))))))))))(((((((((((((((I)))))))))
--R  ))))))(((((((((((((((I))))))))))))))) ((((((((((((((I))))))))))))))((((((((((
--R  ((((I))))))))))))))((((((((((((((I)))))))))))))) (((((((((((((I)))))))))))))(
--R  ((((((((((((I))))))))))))) ((((((((((((I))))))))))))((((((((((((I))))))))))))
--R  ((((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((
--R  ((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((((
--R  ((((((((I)))))))))))) ((((((((((I))))))))))((((((((((I)))))))))) (((((((I))))
--R  )))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I))))))
--R  )(((((((I)))))))(((((((I))))))) ((((((I)))))) (((((I)))))(((((I)))))(((((I)))
--R  ))(((((I)))))(((((I)))))(((((I)))))(((((I))))) ((((I))))((((I))))((((I))))(((
--R  (I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))((I)
--R  )((I))((I))
--R                                                           Type: RomanNumeral
--E 54

)clear all
 
   All user variables and function definitions have been cleared.

--S 55 of 76
f: NNI -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 55

--S 56 of 76
f(n) == 2**(2**n) + 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 56

--S 57 of 76
factor f(1)
 
   Compiling function f with type NonNegativeInteger -> Integer 

   (3)  5
                                                       Type: Factored Integer
--R 
--R   Compiling function f with type NonNegativeInteger -> Integer 
--R
--R   (3)  5
--R                                                       Type: Factored Integer
--E 57

--S 58 of 76
factor f(2)
 

   (4)  17
                                                       Type: Factored Integer
--R 
--R
--R   (4)  17
--R                                                       Type: Factored Integer
--E 58

--S 59 of 76
for n in 1..6 repeat output factor f(n)
 
   5
   17
   257
   65537
   641 6700417
   274177 67280421310721
                                                                   Type: Void
--R 
--R   5
--R   17
--R   257
--R   65537
--R   641 6700417
--R   274177 67280421310721
--R                                                                   Type: Void
--E 59

)clear all
 
   All user variables and function definitions have been cleared.

--S 60 of 76
exp(%pi * sqrt(163.0))
 

   (1)
  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 3733699086 27
  07537410 3782106479 1011860731 2951181346 1860645041 9308388794 9753864044 90
  57287144 7719681485 2322432039 1164782914 8864228272 0131178317 0650104522 26
  87801444 8417703469 6946335570 7681723887 6810009237 0653951938 6506362757 65
  78885582 2394811427 6912100830 8866511072 8471062346 5811298183 0124591328 36
  10006498 2665923651 7261788308 6371078645 2195528154 2746651096 1100147250 20
  97904639 3817787125 7500980365 7792230643 1216511310 8738059929 8242335584 94
  56123995 65
                                                                  Type: Float
--R 
--R
--R   (1)
--R  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 3733699086 27
--R  07537410 3782106479 1011860731 2951181346 1860645041 9308388794 9753864044 90
--R  57287144 7719681485 2322432039 1164782914 8864228272 0131178317 0650104522 26
--R  87801444 8417703469 6946335570 7681723887 6810009237 0653951938 6506362757 65
--R  78885582 2394811427 6912100830 8866511072 8471062346 5811298183 0124591328 36
--R  10006498 2665923651 7261788308 6371078645 2195528154 2746651096 1100147250 20
--R  97904639 3817787125 7500980365 7792230643 1216511310 8738059929 8242335584 94
--R  56123995 65
--R                                                                  Type: Float
--E 60

--S 61 of 76
digits 40
 

   (2)  500
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  500
--R                                                        Type: PositiveInteger
--E 61

--S 62 of 76
x := exp(%pi * sqrt(163.0))
 

   (3)  26253741 2640768743.9999999999 9925007259 76
                                                                  Type: Float
--R 
--R
--R   (3)  26253741 2640768743.9999999999 9925007259 76
--R                                                                  Type: Float
--E 62

--S 63 of 76
numeric(1/3, 5)
 

   (4)  0.33333
                                                                  Type: Float
--R 
--R
--R   (4)  0.33333
--R                                                                  Type: Float
--E 63

--S 64 of 76
numeric(1/3, 60)
 

   (5)  0.3333333333 3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (5)  0.3333333333 3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 64

--S 65 of 76
numeric(1/3)
 

   (6)  0.3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (6)  0.3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 65

)clear all
 
   All user variables and function definitions have been cleared.

--S 66 of 76
61657 ** 10 / 999983 ** 12
 

   (1)
               794006207119672937688869745365148806136551203249
   ------------------------------------------------------------------------
   999796019072919181341770495558788771223957844095225846167460930641229761
                                                       Type: Fraction Integer
--R 
--R
--R   (1)
--R               794006207119672937688869745365148806136551203249
--R   ------------------------------------------------------------------------
--R   999796019072919181341770495558788771223957844095225846167460930641229761
--R                                                       Type: Fraction Integer
--E 66

--S 67 of 76
x := 104348/33215
 

        104348
   (2)  ------
         33215
                                                       Type: Fraction Integer
--R 
--R
--R        104348
--R   (2)  ------
--R         33215
--R                                                       Type: Fraction Integer
--E 67

--S 68 of 76
numeric x
 

   (3)  3.1415926539 2142104470 8715941592 653921421
                                                                  Type: Float
--R 
--R
--R   (3)  3.1415926539 2142104470 8715941592 653921421
--R                                                                  Type: Float
--E 68

--S 69 of 76
numer(x)
 

   (4)  104348
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  104348
--R                                                        Type: PositiveInteger
--E 69

--S 70 of 76
denom(x)
 

   (5)  33215
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  33215
--R                                                        Type: PositiveInteger
--E 70

--S 71 of 76
factor(numer x) / factor(denom x)
 

         2
        2 19 1373
   (6)  ---------
        5 7 13 73
                                              Type: Fraction Factored Integer
--R 
--R
--R         2
--R        2 19 1373
--R   (6)  ---------
--R        5 7 13 73
--R                                              Type: Fraction Factored Integer
--E 71

)clear all
 
   All user variables and function definitions have been cleared.

--S 72 of 76
x := 2/7 :: DECIMAL
 

          ______
   (1)  0.285714
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (1)  0.285714
--R                                                       Type: DecimalExpansion
--E 72

--S 73 of 76
y := 13/17 :: DECIMAL
 

          ________________
   (2)  0.7647058823529411
                                                       Type: DecimalExpansion
--R 
--R
--R          ________________
--R   (2)  0.7647058823529411
--R                                                       Type: DecimalExpansion
--E 73

--S 74 of 76
x - y
 

            ________________________________________________
   (3)  - 0.478991596638655462184873949579831932773109243697
                                                       Type: DecimalExpansion
--R 
--R
--R            ________________________________________________
--R   (3)  - 0.478991596638655462184873949579831932773109243697
--R                                                       Type: DecimalExpansion
--E 74

--S 75 of 76
x + y
 

          ________________________________________________
   (4)  1.050420168067226890756302521008403361344537815126
                                                       Type: DecimalExpansion
--R 
--R
--R          ________________________________________________
--R   (4)  1.050420168067226890756302521008403361344537815126
--R                                                       Type: DecimalExpansion
--E 75

--S 76 of 76
x * y
 

          ________________________________________________
   (5)  0.218487394957983193277310924369747899159663865546
                                                       Type: DecimalExpansion
--R 
--R
--R          ________________________________________________
--R   (5)  0.218487394957983193277310924369747899159663865546
--R                                                       Type: DecimalExpansion
--E 76
)spool 
 
Starts dribbling to matbug.output (2009/2/17, 17:55:1).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 12
msq := Matrix SquareMatrix(2,POLY INT)
 

   (1)  Matrix SquareMatrix(2,Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Matrix SquareMatrix(2,Polynomial Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 12
m : msq := zero(2,2)
 

        ++0  0+  +0  0++
        ||    |  |    ||
        |+0  0+  +0  0+|
   (2)  |              |
        |+0  0+  +0  0+|
        ||    |  |    ||
        ++0  0+  +0  0++
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        ++0  0+  +0  0++
--R        ||    |  |    ||
--R        |+0  0+  +0  0+|
--R   (2)  |              |
--R        |+0  0+  +0  0+|
--R        ||    |  |    ||
--R        ++0  0+  +0  0++
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 2

--S 3 of 12
m(1,1) := matrix([[1,2],[a,b]])
 

        +1  2+
   (3)  |    |
        +a  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +1  2+
--R   (3)  |    |
--R        +a  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 3

--S 4 of 12
m(1,2) := matrix([[a,b],[2,b]])
 

        +a  b+
   (4)  |    |
        +2  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +a  b+
--R   (4)  |    |
--R        +2  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 4

--S 5 of 12
m(2,2) := matrix([[1,2],[2,b]])
 

        +1  2+
   (5)  |    |
        +2  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +1  2+
--R   (5)  |    |
--R        +2  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 5

--S 6 of 12
m
 

        ++1  2+  +a  b++
        ||    |  |    ||
        |+a  b+  +2  b+|
   (6)  |              |
        |+0  0+  +1  2+|
        ||    |  |    ||
        ++0  0+  +2  b++
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        ++1  2+  +a  b++
--R        ||    |  |    ||
--R        |+a  b+  +2  b+|
--R   (6)  |              |
--R        |+0  0+  +1  2+|
--R        ||    |  |    ||
--R        ++0  0+  +2  b++
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 6

--S 7 of 12
m*m
 

        +                    +              2           ++
        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
        ||                |  |                          ||
        ||          2     |  |      2        2          ||
   (7)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
        |                                                |
        |      +0  0+              +  5     2b + 2+      |
        |      |    |              |              |      |
        |      +0  0+              |         2    |      |
        +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +                    +              2           ++
--R        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R        ||                |  |                          ||
--R        ||          2     |  |      2        2          ||
--R   (7)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R        |                                                |
--R        |      +0  0+              +  5     2b + 2+      |
--R        |      |    |              |              |      |
--R        |      +0  0+              |         2    |      |
--R        +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 7

--S 8 of 12
m**2
 

        +                    +              2           ++
        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
        ||                |  |                          ||
        ||          2     |  |      2        2          ||
   (8)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
        |                                                |
        |      +0  0+              +  5     2b + 2+      |
        |      |    |              |              |      |
        |      +0  0+              |         2    |      |
        +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +                    +              2           ++
--R        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R        ||                |  |                          ||
--R        ||          2     |  |      2        2          ||
--R   (8)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R        |                                                |
--R        |      +0  0+              +  5     2b + 2+      |
--R        |      |    |              |              |      |
--R        |      +0  0+              |         2    |      |
--R        +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 8

--S 9 of 12
m**3
 

        +matrix1  matrix2+
   (9)  |                |
        +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +matrix1  matrix2+
--R   (9)  |                |
--R        +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 9

--S 10 of 12
(m*m)*m
 

         +matrix1  matrix2+
   (10)  |                |
         +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R         +matrix1  matrix2+
--R   (10)  |                |
--R         +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 10

--S 11 of 12
mm:=m*m
 

         +                    +              2           ++
         |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
         ||                |  |                          ||
         ||          2     |  |      2        2          ||
   (11)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
         |                                                |
         |      +0  0+              +  5     2b + 2+      |
         |      |    |              |              |      |
         |      +0  0+              |         2    |      |
         +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R         +                    +              2           ++
--R         |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R         ||                |  |                          ||
--R         ||          2     |  |      2        2          ||
--R   (11)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R         |                                                |
--R         |      +0  0+              +  5     2b + 2+      |
--R         |      |    |              |              |      |
--R         |      +0  0+              |         2    |      |
--R         +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 11

--S 12 of 12
mm*m
 

         +matrix1  matrix2+
   (12)  |                |
         +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R         +matrix1  matrix2+
--R   (12)  |                |
--R         +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 12
)spool 
 
Starts dribbling to herm.output (2009/2/17, 17:46:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 29
)lib $TEST_AXIOMXL/herm
 
   )library cannot find the file herm.
--R 
--R   )library cannot find the file herm.
--E 1

--S 2 of 29
h0 := pHS([] :: List INT)
 
   There are no library operations named pHS 
      Use HyperDoc Browse or issue
                                )what op pHS
      to learn if there is any operation containing " pHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named pHS 
      with argument type(s) 
                                List Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named pHS 
--R      Use HyperDoc Browse or issue
--R                                )what op pHS
--R      to learn if there is any operation containing " pHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named pHS 
--R      with argument type(s) 
--R                                List Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 2

--       []

--S 3 of 29
h1 := pHS [1]
 

   (1)  pHS
           1
                                                                 Type: Symbol
--R 
--R
--R   (1)  pHS
--R           1
--R                                                                 Type: Symbol
--E 3
--       [1]

--S 4 of 29
h2 := pHS [1,2]
 

   (2)  pHS
           1,2
                                                                 Type: Symbol
--R 
--R
--R   (2)  pHS
--R           1,2
--R                                                                 Type: Symbol
--E 4
--       [1,2]

--S 5 of 29
h3 := pHS [1,2,3]
 

   (3)  pHS
           1,2,3
                                                                 Type: Symbol
--R 
--R
--R   (3)  pHS
--R           1,2,3
--R                                                                 Type: Symbol
--E 5
--       [1,2,3]

--S 6 of 29
h4 := pHS [1,2,3,4]
 

   (4)  pHS
           1,2,3,4
                                                                 Type: Symbol
--R 
--R
--R   (4)  pHS
--R           1,2,3,4
--R                                                                 Type: Symbol
--E 6
--       [1,2,3,4]

--S 7 of 29
h5 := pHS [1,2,3,4,5]
 

   (5)  pHS
           1,2,3,4,5
                                                                 Type: Symbol
--R 
--R
--R   (5)  pHS
--R           1,2,3,4,5
--R                                                                 Type: Symbol
--E 7
--       [1,2,3,4,5]

--S 8 of 29
f0 := expand h0
 

   (6)  h0
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  h0
--R                                                     Type: Polynomial Integer
--E 8
--       []

--S 9 of 29
f1 := expand h1
 

   (7)  pHS
           1
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  pHS
--R           1
--R                                                     Type: Polynomial Integer
--E 9
--       [1]

--S 10 of 29
f2 := expand h2
 

   (8)  pHS
           1,2
                                                     Type: Polynomial Integer
--R 
--R
--R   (8)  pHS
--R           1,2
--R                                                     Type: Polynomial Integer
--E 10
--       [1,2]

--S 11 of 29
f3 := expand h3
 

   (9)  pHS
           1,2,3
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)  pHS
--R           1,2,3
--R                                                     Type: Polynomial Integer
--E 11
--       [1,2 + 3%i,2 - 3%i]

--S 12 of 29
f4 := expand h4
 

   (10)  pHS
            1,2,3,4
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)  pHS
--R            1,2,3,4
--R                                                     Type: Polynomial Integer
--E 12
--       [1,2 + 4%i,3,2 - 4%i]

--S 13 of 29
f5 := expand h5
 

   (11)  pHS
            1,2,3,4,5
                                                     Type: Polynomial Integer
--R 
--R
--R   (11)  pHS
--R            1,2,3,4,5
--R                                                     Type: Polynomial Integer
--E 13
--       [1,2 + 5%i,3 + 4%i,3 - 4%i,2 - 5%i]

--S 14 of 29
packHS f0
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 14
--       []

--S 15 of 29
packHS f1
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15
--       [1]

--S 16 of 29
packHS f2
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16
--       [1,2]

--S 17 of 29
packHS f3
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       [1,2,3]

--S 18 of 29
packHS f4
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18
--       [1,2,3,4]

--S 19 of 29
packHS f5
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 19
--       [1,2,3,4,5]

--S 20 of 29
packHS vector[%i,3,3,3]
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                           Vector Complex Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                           Vector Complex Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
-- Error signalled from user code:
--    The argument of packHS is not Hermitian - the first element must
--    be real.

--S 21 of 29
packHS vector [1, 3, 5, 7]
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                           Vector PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                           Vector PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21
-- Error signalled from user code:
--    The argument of packHS is not Hermitian - elements 2 and 4 are 
--    not conjugate.

--S 22 of 29
packHS [1, 3, %i, 3]
 

   (12)  packHS
               1,3,%i,3
                                                                 Type: Symbol
--R 
--R
--R   (12)  packHS
--R               1,3,%i,3
--R                                                                 Type: Symbol
--E 22
-- Error signalled from user code:
--    The argument of packHS is not Hermitian - element 3 must be real
--    to be self-conjugate.

--S 23 of 29
conjHerm h0
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                 Variable h0
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                 Variable h0
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23
--       []

--S 24 of 29
conjHerm h1
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24
--       [1]

--S 25 of 29
conjHerm h2
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25
--       [1,2]

--S 26 of 29
conjHerm h3
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 26
--       [1,2,- 3]

--S 27 of 29
conjHerm h4
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 27
--       [1,2,3,- 4]

--S 28 of 29
conjHerm h5
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 28
--       [1,2,3,- 4,- 5]

--S 29 of 29
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 29
)spool 
 
Starts dribbling to bouquet.output (2009/2/17, 17:43:59).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 4
arrowScale := 0.2@DFLOAT
 

   (1)  0.20000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (1)  0.20000000000000001
--R                                                            Type: DoubleFloat
--E 1
--S 2 of 4
arrowAngle := %pi-%pi/10.0@DFLOAT
 

   (2)  2.8274333882308138
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  2.8274333882308138
--R                                                            Type: DoubleFloat
--E 2
--S 3 of 4
makeArrow(p1, p2) ==
  delta := p2 - p1
  len := arrowScale * length delta
  theta := atan(delta.1, delta.2)
  c1 := len * cos(theta + arrowAngle) 
  s1 := len * sin(theta + arrowAngle)
  c2 := len * cos(theta - arrowAngle) 
  s2 := len * sin(theta - arrowAngle)
  z  := p2.3*(1 - arrowScale)
  p3 := point [p2.1 + c1, p2.2 + s1, z, p2.4]
  p4 := point [p2.1 + c2, p2.2 + s2, z, p2.4]
  [[p1, p2, p3], [p2, p4]]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
drawBouquet(n,title) ==
  angle := 0.0@DFLOAT
  sp := create3Space()$ThreeSpace(DFLOAT)
  for i in 0..n-1 repeat
    start := point [0.0@DFLOAT,0.0@DFLOAT,0.0@DFLOAT,angle] 
    end   := point [cos angle, sin angle, 1.0@DFLOAT, angle]
    arrow := makeArrow(start, end)
    for a in arrow repeat curve(sp,a)
    angle := angle + 2*%pi/n
  makeViewport3D(sp,title)$VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
)spool
 
Starts dribbling to padic.output (2009/2/17, 17:55:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 20
root2 : PADIC 7 := sqrt(2,3)
 

   (1)
              2      3    4      5    6      7      8      9      10      11
   3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (1)
--R              2      3    4      5    6      7      8      9      10      11
--R   3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 1

--S 2 of 20
extend(root2,20)
 

   (2)
                2      3    4      5    6      7      8      9      10      11
     3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + 2 7
   + 
      12    13      15    16    17      18      19    20      21
     7   + 7   + 2 7   + 7   + 7   + 4 7   + 6 7   + 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (2)
--R                2      3    4      5    6      7      8      9      10      11
--R     3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + 2 7
--R   + 
--R      12    13      15    16    17      18      19    20      21
--R     7   + 7   + 2 7   + 7   + 7   + 4 7   + 6 7   + 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 2

--S 3 of 20
broot2 : BPADIC 7 := sqrt(2,3)
 

                   2    3      4      5    6      7      8      11
   (3)  3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                   2    3      4      5    6      7      8      11
--R   (3)  3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 3

--S 4 of 20
extend(broot2,20)
 

   (4)
                2    3      4      5    6      7      8      11    12    13
     3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + 3 7   + 7   + 7
   + 
        15    16    17      18      20      21
     2 7   + 7   + 7   - 3 7   + 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R   (4)
--R                2    3      4      5    6      7      8      11    12    13
--R     3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + 3 7   + 7   + 7
--R   + 
--R        15    16    17      18      20      21
--R     2 7   + 7   + 7   - 3 7   + 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 4

--S 5 of 20
xx : SUP INT := monomial(1,1)
 

   (5)  ?
                                     Type: SparseUnivariatePolynomial Integer
--R 
--R
--R   (5)  ?
--R                                     Type: SparseUnivariatePolynomial Integer
--E 5

--S 6 of 20
pp := xx^6 - 1
 

         6
   (6)  ?  - 1
                                     Type: SparseUnivariatePolynomial Integer
--R 
--R
--R         6
--R   (6)  ?  - 1
--R                                     Type: SparseUnivariatePolynomial Integer
--E 6

--S 7 of 20
r1 : PADIC 7 := root(pp,1)
 

               11
   (7)  1 + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R               11
--R   (7)  1 + O(7  )
--R                                                         Type: PAdicInteger 7
--E 7

--S 8 of 20
r2 : PADIC 7 := root(pp,2)
 

   (8)
                2      3      5      6      7      8      9      10      11
   2 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (8)
--R                2      3      5      6      7      8      9      10      11
--R   2 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 8

--S 9 of 20
r3 : PADIC 7 := root(pp,3)
 

   (9)
                2      3      5      6      7      8      9      10      11
   3 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (9)
--R                2      3      5      6      7      8      9      10      11
--R   3 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 9

--S 10 of 20
r4 : PADIC 7 := root(pp,4)
 

                      3      4      5      7      8      9      10      11
   (10)  4 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R                      3      4      5      7      8      9      10      11
--R   (10)  4 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 10

--S 11 of 20
r5 : PADIC 7 := root(pp,5)
 

                      3      4      5      7      8      9      10      11
   (11)  5 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R                      3      4      5      7      8      9      10      11
--R   (11)  5 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 11

--S 12 of 20
r6 : PADIC 7 := root(pp,6)
 

   (12)
                  2      3      4      5      6      7      8      9      10
     6 + 6 7 + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7
   + 
        11
     O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (12)
--R                  2      3      4      5      6      7      8      9      10
--R     6 + 6 7 + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7
--R   + 
--R        11
--R     O(7  )
--R                                                         Type: PAdicInteger 7
--E 12

--S 13 of 20
(x - r1) * (x - r2) * (x - r3) * (x - r4) * (x - r5) * (x - r6)
 

   (13)
      6      12  5      12  4      12  3      12  2      12                  2
     x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x + 6 + 6 7 + 6 7
   + 
        3      4      5      6      7      8      9      10      11
     6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7   + O(7  )
                                              Type: Polynomial PAdicInteger 7
--R 
--R
--R   (13)
--R      6      12  5      12  4      12  3      12  2      12                  2
--R     x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x + 6 + 6 7 + 6 7
--R   + 
--R        3      4      5      6      7      8      9      10      11
--R     6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7   + O(7  )
--R                                              Type: Polynomial PAdicInteger 7
--E 13

--S 14 of 20
rr1 : BPADIC 7 := root(pp,1)
 

                11
   (14)  1 + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                11
--R   (14)  1 + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 14

--S 15 of 20
rr2 : BPADIC 7 := root(pp,2)
 

                      3    4      5    6      7      8      9      10      11
   (15)  2 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                      3    4      5    6      7      8      9      10      11
--R   (15)  2 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 15

--S 16 of 20
rr3 : BPADIC 7 := root(pp,3)
 

                      3    4      5    6      7      8      9      10      11
   (16)  3 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                      3    4      5    6      7      8      9      10      11
--R   (16)  3 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 16

--S 17 of 20
rr4 : BPADIC 7 := root(pp,4)
 

   (17)
                  3    4      5    6      7      8      9      10      11
   - 3 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R   (17)
--R                  3    4      5    6      7      8      9      10      11
--R   - 3 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 17

--S 18 of 20
rr5 : BPADIC 7 := root(pp,5)
 

   (18)
                  3    4      5    6      7      8      9      10      11
   - 2 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R   (18)
--R                  3    4      5    6      7      8      9      10      11
--R   - 2 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 18

--S 19 of 20
rr6 : BPADIC 7 := root(pp,6)
 

                  11
   (19)  - 1 + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                  11
--R   (19)  - 1 + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 19

--S 20 of 20
(x - rr1) * (x - rr2) * (x - rr3) * (x - rr4) * (x - rr5) * (x - rr6)
 

          6      12  5      12  4      12  3      12  2      12            11
   (20)  x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x - 1 + O(7  )
                                      Type: Polynomial BalancedPAdicInteger 7
--R 
--R
--R          6      12  5      12  4      12  3      12  2      12            11
--R   (20)  x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x - 1 + O(7  )
--R                                      Type: Polynomial BalancedPAdicInteger 7
--E 20
)spool 
 
Starts dribbling to dhmatrix.output (2009/2/17, 17:44:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 16
t1:=DHMATRIX(DoubleFloat)
 

   (1)  DenavitHartenbergMatrix DoubleFloat
                                                                 Type: Domain
--R
--R   (1)  DenavitHartenbergMatrix DoubleFloat
--R                                                                 Type: Domain
--E 1

--S 2 of 16
t2:=identity()$t1
 

        +1.0  0.0  0.0  0.0+
        |                  |
        |0.0  1.0  0.0  0.0|
   (2)  |                  |
        |0.0  0.0  1.0  0.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                    Type: DenavitHartenbergMatrix DoubleFloat
--R
--R        +1.  0.  0.  0.+
--R        |              |
--R        |0.  1.  0.  0.|
--R   (2)  |              |
--R        |0.  0.  1.  0.|
--R        |              |
--R        +0.  0.  0.  1.+
--R                                    Type: DenavitHartenbergMatrix DoubleFloat
--E 2

--S 3 of 16
t3:=rotatex(30)
 

        +1   0     0    0+
        |                |
        |    +-+         |
        |   \|3     1    |
        |0  ----  - -   0|
        |     2     2    |
   (3)  |                |
        |          +-+   |
        |    1    \|3    |
        |0   -    ----  0|
        |    2      2    |
        |                |
        +0   0     0    1+
                             Type: DenavitHartenbergMatrix Expression Integer
--R
--R        +1   0     0    0+
--R        |                |
--R        |    +-+         |
--R        |   \|3     1    |
--R        |0  ----  - -   0|
--R        |     2     2    |
--R   (3)  |                |
--R        |          +-+   |
--R        |    1    \|3    |
--R        |0   -    ----  0|
--R        |    2      2    |
--R        |                |
--R        +0   0     0    1+
--R                             Type: DenavitHartenbergMatrix Expression Integer
--E 3

--S 4 of 16
t4:=rotatey(30)
 

        + +-+            +
        |\|3       1     |
        |----  0   -    0|
        |  2       2     |
        |                |
        | 0    1   0    0|
   (4)  |                |
        |          +-+   |
        |  1      \|3    |
        |- -   0  ----  0|
        |  2        2    |
        |                |
        + 0    0   0    1+
                             Type: DenavitHartenbergMatrix Expression Integer
--R
--R        + +-+            +
--R        |\|3       1     |
--R        |----  0   -    0|
--R        |  2       2     |
--R        |                |
--R        | 0    1   0    0|
--R   (4)  |                |
--R        |          +-+   |
--R        |  1      \|3    |
--R        |- -   0  ----  0|
--R        |  2        2    |
--R        |                |
--R        + 0    0   0    1+
--R                             Type: DenavitHartenbergMatrix Expression Integer
--E 4

--S 5 of 16
t5:=rotatez(30)
 

        + +-+            +
        |\|3     1       |
        |----  - -   0  0|
        |  2     2       |
        |                |
        |       +-+      |
   (5)  | 1    \|3       |
        | -    ----  0  0|
        | 2      2       |
        |                |
        | 0     0    1  0|
        |                |
        + 0     0    0  1+
                             Type: DenavitHartenbergMatrix Expression Integer
--R
--R        + +-+            +
--R        |\|3     1       |
--R        |----  - -   0  0|
--R        |  2     2       |
--R        |                |
--R        |       +-+      |
--R   (5)  | 1    \|3       |
--R        | -    ----  0  0|
--R        | 2      2       |
--R        |                |
--R        | 0     0    1  0|
--R        |                |
--R        + 0     0    0  1+
--R                             Type: DenavitHartenbergMatrix Expression Integer
--E 5

--S 6 of 16
t6:=scale(0.5,0.5,0.5)
 

        +0.5  0.0  0.0  0.0+
        |                  |
        |0.0  0.5  0.0  0.0|
   (6)  |                  |
        |0.0  0.0  0.5  0.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                          Type: DenavitHartenbergMatrix Float
--R
--R        +0.5  0.0  0.0  0.0+
--R        |                  |
--R        |0.0  0.5  0.0  0.0|
--R   (6)  |                  |
--R        |0.0  0.0  0.5  0.0|
--R        |                  |
--R        +0.0  0.0  0.0  1.0+
--R                                          Type: DenavitHartenbergMatrix Float
--E 6

--S 7 of 16
t7:=translate(2.0,2.0,2.0)
 

        +1.0  0.0  0.0  2.0+
        |                  |
        |0.0  1.0  0.0  2.0|
   (7)  |                  |
        |0.0  0.0  1.0  2.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                          Type: DenavitHartenbergMatrix Float
--R
--R        +1.0  0.0  0.0  2.0+
--R        |                  |
--R        |0.0  1.0  0.0  2.0|
--R   (7)  |                  |
--R        |0.0  0.0  1.0  2.0|
--R        |                  |
--R        +0.0  0.0  0.0  1.0+
--R                                          Type: DenavitHartenbergMatrix Float
--E 7

--S 8 of 16
t8:Point(DoubleFloat):=[4.0,0.0,0.0]$List(DoubleFloat)
 

   (8)  [4.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R
--R   (8)  [4.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 8

--S 9 of 16
t9:=translate(4.0,0.0,0.0)
 

        +1.0  0.0  0.0  4.0+
        |                  |
        |0.0  1.0  0.0  0.0|
   (9)  |                  |
        |0.0  0.0  1.0  0.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                          Type: DenavitHartenbergMatrix Float
--R
--R        +1.0  0.0  0.0  4.0+
--R        |                  |
--R        |0.0  1.0  0.0  0.0|
--R   (9)  |                  |
--R        |0.0  0.0  1.0  0.0|
--R        |                  |
--R        +0.0  0.0  0.0  1.0+
--R                                          Type: DenavitHartenbergMatrix Float
--E 9

--S 10 of 16
t10:=t9*t8
 

   (10)  [8.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R
--R   (10)  [8.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 10

--S 11 of 16
t11:=rotatez(90)*t10
 

   (11)  [0.0,8.0,0.0]
                                           Type: Point Expression DoubleFloat
--R
--R   (11)  [0.,8.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 11

--S 12 of 16
t12:=scale(0.0,0.5,0.0)*t11
 

   (12)  [0.0,4.0,0.0]
                                           Type: Point Expression DoubleFloat
--R
--R   (12)  [0.,4.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 12

--S 13 of 16
t13:=rotatex(90)*t12
 

   (13)  [0.0,0.0,4.0]
                                           Type: Point Expression DoubleFloat
--R
--R   (13)  [0.,0.,4.]
--R                                           Type: Point Expression DoubleFloat
--E 13

--S 14 of 16
t14:=rotatey(90)*t13
 

   (14)  [4.0,0.0,0.0]
                                           Type: Point Expression DoubleFloat
--R
--R   (14)  [4.,0.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 14

--S 15 of 16
t15:=rotatey(90)*rotatex(90)*scale(0.0,0.5,0.0)*_
     rotatez(90)*translate(4.0,0.0,0.0)
 

         +0.5  0.0  0.0  2.0+
         |                  |
         |0.0  0.0  0.0  0.0|
   (15)  |                  |
         |0.0  0.0  0.0  0.0|
         |                  |
         +0.0  0.0  0.0  1.0+
                               Type: DenavitHartenbergMatrix Expression Float
--R
--R         +0.5  0.0  0.0  2.0+
--R         |                  |
--R         |0.0  0.0  0.0  0.0|
--R   (15)  |                  |
--R         |0.0  0.0  0.0  0.0|
--R         |                  |
--R         +0.0  0.0  0.0  1.0+
--R                               Type: DenavitHartenbergMatrix Expression Float
--E 15

--S 16 of 16
t16:=t15*t8
 

   (16)  [4.0,0.0,0.0]
                                           Type: Point Expression DoubleFloat
--R
--R   (16)  [4.,0.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 16

)spool 
 
Starts dribbling to bug103.output (2009/2/17, 17:44:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 1
solve(z=z,z)
 

   (1)  [0= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R   (1)  [0= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 1
)spool 
 
Starts dribbling to schaum9.output (2009/2/17, 18:0:10).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(sqrt(x^2+a^2)),x)
 

               +-------+
               | 2    2
   (1)  - log(\|x  + a   - x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+
--R               | 2    2
--R   (1)  - log(\|x  + a   - x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=log(x+sqrt(x^2+a^2))
 

             +-------+
             | 2    2
   (2)  log(\|x  + a   + x)
                                                     Type: Expression Integer
--R
--R             +-------+
--R             | 2    2
--R   (2)  log(\|x  + a   + x)
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
--R                                                     Type: Expression Integer
--E

--S 4      14:182 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

               2
   (4)  - log(a )
                                                     Type: Expression Integer
--R
--R               2
--R   (4)  - log(a )
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 5
aa:=integrate(x/(sqrt(x^2+a^2)),x)
 

            +-------+
            | 2    2     2    2
        - x\|x  + a   + x  + a
   (1)  -----------------------
              +-------+
              | 2    2
             \|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +-------+
--R            | 2    2     2    2
--R        - x\|x  + a   + x  + a
--R   (1)  -----------------------
--R              +-------+
--R              | 2    2
--R             \|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 6
bb:=sqrt(x^2+a^2)
 

         +-------+
         | 2    2
   (2)  \|x  + a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2
--R   (2)  \|x  + a
--R                                                     Type: Expression Integer
--E

--S 7      14:183 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(x^2/sqrt(x^2+a^2),x)
 

   (1)
             +-------+                   +-------+
          2  | 2    2      2 2    4      | 2    2
       (2a x\|x  + a   - 2a x  - a )log(\|x  + a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  - a x)\|x  + a   + 2x  + 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  + a   - 4x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R             +-------+                   +-------+
--R          2  | 2    2      2 2    4      | 2    2
--R       (2a x\|x  + a   - 2a x  - a )log(\|x  + a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  - a x)\|x  + a   + 2x  + 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  + a   - 4x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2))
 

                 +-------+          +-------+
           2     | 2    2           | 2    2
        - a log(\|x  + a   + x) + x\|x  + a
   (2)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R
--R                 +-------+          +-------+
--R           2     | 2    2           | 2    2
--R        - a log(\|x  + a   + x) + x\|x  + a
--R   (2)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E

--S 10
cc:=aa-bb
 

               +-------+               +-------+
         2     | 2    2          2     | 2    2
        a log(\|x  + a   + x) + a log(\|x  + a   - x)
   (3)  ---------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         2     | 2    2          2     | 2    2
--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
--R   (3)  ---------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 11
logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
 

   (4)  c log(b) + c log(a) + %H == c log(a b) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (4)  c log(b) + c log(a) + %K == c log(a b) + %K
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12     14:184 Schaums and Axiom differ by a constant
dd:=logmul1 cc
 

         2     2
        a log(a )
   (5)  ---------
            2
                                                     Type: Expression Integer
--R
--R         2     2
--R        a log(a )
--R   (5)  ---------
--R            2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(x^3/sqrt(x^2+a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2     6
        (- 4x  + 5a x  + 6a x)\|x  + a   + 4x  - 3a x  - 9a x  - 2a
   (1)  ------------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  + 3a )\|x  + a   - 12x  - 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2     6
--R        (- 4x  + 5a x  + 6a x)\|x  + a   + 4x  - 3a x  - 9a x  - 2a
--R   (1)  ------------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2)
 

                   +-------+
          2     2  | 2    2
        (x  - 2a )\|x  + a
   (2)  --------------------
                  3
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2
--R        (x  - 2a )\|x  + a
--R   (2)  --------------------
--R                  3
--R                                                     Type: Expression Integer
--E

--S 15     14:185 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
 

               +-------+                 +-------+
               | 2    2                  | 2    2
        - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
   (1)  ---------------------------------------------------
                                 a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+                 +-------+
--R               | 2    2                  | 2    2
--R        - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R   (1)  ---------------------------------------------------
--R                                 a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17
bb:=-1/a*log((a+sqrt(x^2+a^2))/x)
 

               +-------+
               | 2    2
              \|x  + a   + a
          log(--------------)
                     x
   (2)  - -------------------
                   a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  + a   + a
--R          log(--------------)
--R                     x
--R   (2)  - -------------------
--R                   a
--R                                                     Type: Expression Integer
--E

--S 18
cc:=aa-bb
 

   (3)
                                                              +-------+
          +-------+                 +-------+                 | 2    2
          | 2    2                  | 2    2                 \|x  + a   + a
   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
                                                                    x
   -------------------------------------------------------------------------
                                       a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                              +-------+
--R          +-------+                 +-------+                 | 2    2
--R          | 2    2                  | 2    2                 \|x  + a   + a
--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
--R                                                                    x
--R   -------------------------------------------------------------------------
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 19
dd:=expandLog cc
 

   (4)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 20     14:186 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 21
aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
 

                  1
   (1)  - ----------------
            +-------+
            | 2    2     2
          x\|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  1
--R   (1)  - ----------------
--R            +-------+
--R            | 2    2     2
--R          x\|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22
bb:=-sqrt(x^2+a^2)/(a^2*x)
 

           +-------+
           | 2    2
          \|x  + a
   (2)  - ----------
               2
              a x
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2
--R          \|x  + a
--R   (2)  - ----------
--R               2
--R              a x
--R                                                     Type: Expression Integer
--E

--S 23     14:187 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           1
   (3)  - --
           2
          a
                                                     Type: Expression Integer
--R
--R           1
--R   (3)  - --
--R           2
--R          a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 24
aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
 

   (1)
            +-------+                   +-------+
          3 | 2    2      4    2 2      | 2    2
       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x + a)
     + 
              +-------+                   +-------+
            3 | 2    2      4    2 2      | 2    2
       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x - a)
     + 
                    +-------+
            2    3  | 2    2        3     3
       (2a x  + a )\|x  + a   - 2a x  - 2a x
  /
           +-------+
       3 3 | 2    2      3 4     5 2
     4a x \|x  + a   - 4a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +-------+                   +-------+
--R          3 | 2    2      4    2 2      | 2    2
--R       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x + a)
--R     + 
--R              +-------+                   +-------+
--R            3 | 2    2      4    2 2      | 2    2
--R       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x - a)
--R     + 
--R                    +-------+
--R            2    3  | 2    2        3     3
--R       (2a x  + a )\|x  + a   - 2a x  - 2a x
--R  /
--R           +-------+
--R       3 3 | 2    2      3 4     5 2
--R     4a x \|x  + a   - 4a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25
bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x)
 

               +-------+
               | 2    2           +-------+
         2    \|x  + a   + a      | 2    2
        x log(--------------) - a\|x  + a
                     x
   (2)  -----------------------------------
                         3 2
                       2a x
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2           +-------+
--R         2    \|x  + a   + a      | 2    2
--R        x log(--------------) - a\|x  + a
--R                     x
--R   (2)  -----------------------------------
--R                         3 2
--R                       2a x
--R                                                     Type: Expression Integer
--E

--S 26
cc:=aa-bb
 

   (3)
                                                            +-------+
        +-------+                 +-------+                 | 2    2
        | 2    2                  | 2    2                 \|x  + a   + a
   log(\|x  + a   - x + a) - log(\|x  + a   - x - a) - log(--------------)
                                                                  x
   -----------------------------------------------------------------------
                                       3
                                     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                            +-------+
--R        +-------+                 +-------+                 | 2    2
--R        | 2    2                  | 2    2                 \|x  + a   + a
--R   log(\|x  + a   - x + a) - log(\|x  + a   - x - a) - log(--------------)
--R                                                                  x
--R   -----------------------------------------------------------------------
--R                                       3
--R                                     2a
--R                                                     Type: Expression Integer
--E

--S 27
dd:=expandLog cc
 

   (4)
              +-------+             +-------+                 +-------+
              | 2    2              | 2    2                  | 2    2
       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
     + 
       log(x)
  /
       3
     2a
                                                     Type: Expression Integer
--R
--R   (4)
--R              +-------+             +-------+                 +-------+
--R              | 2    2              | 2    2                  | 2    2
--R       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
--R     + 
--R       log(x)
--R  /
--R       3
--R     2a
--R                                                     Type: Expression Integer
--E

--S 28     14:188 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        log(- 1)
   (5)  --------
             3
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R             3
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(sqrt(x^2+a^2),x)
 

   (1)
               +-------+                   +-------+
            2  | 2    2      2 2    4      | 2    2
       (- 2a x\|x  + a   + 2a x  + a )log(\|x  + a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  - a x)\|x  + a   + 2x  + 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  + a   - 4x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               +-------+                   +-------+
--R            2  | 2    2      2 2    4      | 2    2
--R       (- 2a x\|x  + a   + 2a x  + a )log(\|x  + a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  - a x)\|x  + a   + 2x  + 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  + a   - 4x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2))
 

               +-------+          +-------+
         2     | 2    2           | 2    2
        a log(\|x  + a   + x) + x\|x  + a
   (2)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R               +-------+          +-------+
--R         2     | 2    2           | 2    2
--R        a log(\|x  + a   + x) + x\|x  + a
--R   (2)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

                 +-------+               +-------+
           2     | 2    2          2     | 2    2
        - a log(\|x  + a   + x) - a log(\|x  + a   - x)
   (3)  -----------------------------------------------
                               2
                                                     Type: Expression Integer
--R
--R                 +-------+               +-------+
--R           2     | 2    2          2     | 2    2
--R        - a log(\|x  + a   + x) - a log(\|x  + a   - x)
--R   (3)  -----------------------------------------------
--R                               2
--R                                                     Type: Expression Integer
--E

--S 32     14:189 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           2     2
          a log(a )
   (4)  - ---------
              2
                                                     Type: Expression Integer
--R
--R           2     2
--R          a log(a )
--R   (4)  - ---------
--R              2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 33
aa:=integrate(x*sqrt(x^2+a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2    6
        (- 4x  - 7a x  - 3a x)\|x  + a   + 4x  + 9a x  + 6a x  + a
   (1)  -----------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  + 3a )\|x  + a   - 12x  - 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2    6
--R        (- 4x  - 7a x  - 3a x)\|x  + a   + 4x  + 9a x  + 6a x  + a
--R   (1)  -----------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34
bb:=(x^2+a^2)^(3/2)/3
 

                  +-------+
          2    2  | 2    2
        (x  + a )\|x  + a
   (2)  -------------------
                 3
                                                     Type: Expression Integer
--R
--R                  +-------+
--R          2    2  | 2    2
--R        (x  + a )\|x  + a
--R   (2)  -------------------
--R                 3
--R                                                     Type: Expression Integer
--E

--S 35     14:190 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(x^2*sqrt(x^2+a^2),x)
 

   (1)
                       +-------+                           +-------+
           4 3     6   | 2    2      4 4     6 2    8      | 2    2
       ((8a x  + 4a x)\|x  + a   - 8a x  - 8a x  - a )log(\|x  + a   - x)
     + 
                                      +-------+
           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
     (- 16x  - 24a x  - 10a x  - a x)\|x  + a   + 16x  + 32a x  + 20a x  + 4a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       +-------+                           +-------+
--R           4 3     6   | 2    2      4 4     6 2    8      | 2    2
--R       ((8a x  + 4a x)\|x  + a   - 8a x  - 8a x  - a )log(\|x  + a   - x)
--R     + 
--R                                      +-------+
--R           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
--R     (- 16x  - 24a x  - 10a x  - a x)\|x  + a   + 16x  + 32a x  + 20a x  + 4a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37
bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2))
 

                 +-------+                    +-------+
           4     | 2    2            3    2   | 2    2
        - a log(\|x  + a   + x) + (2x  + a x)\|x  + a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                 +-------+                    +-------+
--R           4     | 2    2            3    2   | 2    2
--R        - a log(\|x  + a   + x) + (2x  + a x)\|x  + a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 38
cc:=aa-bb
 

               +-------+               +-------+
         4     | 2    2          4     | 2    2
        a log(\|x  + a   + x) + a log(\|x  + a   - x)
   (3)  ---------------------------------------------
                              8
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         4     | 2    2          4     | 2    2
--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
--R   (3)  ---------------------------------------------
--R                              8
--R                                                     Type: Expression Integer
--E

--S 39     14:191 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

         4     2
        a log(a )
   (4)  ---------
            8
                                                     Type: Expression Integer
--R
--R         4     2
--R        a log(a )
--R   (4)  ---------
--R            8
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 40
aa:=integrate(x^3*sqrt(x^2+a^2),x)
 

   (1)
                                                  +-------+
             9      2 7     4 5      6 3      8   | 2    2       10       2 8
       (- 48x  - 76a x  - 3a x  + 35a x  + 10a x)\|x  + a   + 48x   + 100a x
     + 
          4 6      6 4      8 2     10
       35a x  - 40a x  - 25a x  - 2a
  /
                              +-------+
          4       2 2      4  | 2    2        5       2 3      4
     (240x  + 180a x  + 15a )\|x  + a   - 240x  - 300a x  - 75a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7     4 5      6 3      8   | 2    2       10       2 8
--R       (- 48x  - 76a x  - 3a x  + 35a x  + 10a x)\|x  + a   + 48x   + 100a x
--R     + 
--R          4 6      6 4      8 2     10
--R       35a x  - 40a x  - 25a x  - 2a
--R  /
--R                              +-------+
--R          4       2 2      4  | 2    2        5       2 3      4
--R     (240x  + 180a x  + 15a )\|x  + a   - 240x  - 300a x  - 75a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 41
bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3
 

                           +-------+
           4    2 2     4  | 2    2
        (3x  + a x  - 2a )\|x  + a
   (2)  ----------------------------
                     15
                                                     Type: Expression Integer
--R
--R                           +-------+
--R           4    2 2     4  | 2    2
--R        (3x  + a x  - 2a )\|x  + a
--R   (2)  ----------------------------
--R                     15
--R                                                     Type: Expression Integer
--E

--S 42     14:192 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 43
aa:=integrate(sqrt(x^2+a^2)/x,x)
 

   (1)
            +-------+            +-------+
            | 2    2             | 2    2
       (- a\|x  + a   + a x)log(\|x  + a   - x + a)
     + 
          +-------+            +-------+              +-------+
          | 2    2             | 2    2               | 2    2     2    2
       (a\|x  + a   - a x)log(\|x  + a   - x - a) - x\|x  + a   + x  + a
  /
      +-------+
      | 2    2
     \|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +-------+            +-------+
--R            | 2    2             | 2    2
--R       (- a\|x  + a   + a x)log(\|x  + a   - x + a)
--R     + 
--R          +-------+            +-------+              +-------+
--R          | 2    2             | 2    2               | 2    2     2    2
--R       (a\|x  + a   - a x)log(\|x  + a   - x - a) - x\|x  + a   + x  + a
--R  /
--R      +-------+
--R      | 2    2
--R     \|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 44
bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2          +-------+
                \|x  + a   + a     | 2    2
   (2)  - a log(--------------) + \|x  + a
                       x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2          +-------+
--R                \|x  + a   + a     | 2    2
--R   (2)  - a log(--------------) + \|x  + a
--R                       x
--R                                                     Type: Expression Integer
--E

--S 45
cc:=aa-bb
 

   (3)
              +-------+                   +-------+
              | 2    2                    | 2    2
     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
   + 
            +-------+
            | 2    2
           \|x  + a   + a
     a log(--------------)
                  x
                                                     Type: Expression Integer
--R
--R   (3)
--R              +-------+                   +-------+
--R              | 2    2                    | 2    2
--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
--R   + 
--R            +-------+
--R            | 2    2
--R           \|x  + a   + a
--R     a log(--------------)
--R                  x
--R                                                     Type: Expression Integer
--E

--S 46
dd:=expandLog cc
 

   (4)
            +-------+               +-------+
            | 2    2                | 2    2
     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
   + 
            +-------+
            | 2    2
     a log(\|x  + a   - x - a) - a log(x)
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+               +-------+
--R            | 2    2                | 2    2
--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
--R   + 
--R            +-------+
--R            | 2    2
--R     a log(\|x  + a   - x - a) - a log(x)
--R                                                     Type: Expression Integer
--E

--S 47     14:193 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

   (5)  - a log(- 1)
                                                     Type: Expression Integer
--R
--R   (5)  - a log(- 1)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 48
aa:=integrate(sqrt(x^2+a^2)/x^2,x)
 

             +-------+           +-------+
             | 2    2     2      | 2    2          2
        (- x\|x  + a   + x )log(\|x  + a   - x) - a
   (1)  --------------------------------------------
                        +-------+
                        | 2    2     2
                      x\|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+           +-------+
--R             | 2    2     2      | 2    2          2
--R        (- x\|x  + a   + x )log(\|x  + a   - x) - a
--R   (1)  --------------------------------------------
--R                        +-------+
--R                        | 2    2     2
--R                      x\|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49
bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2))
 

               +-------+         +-------+
               | 2    2          | 2    2
        x log(\|x  + a   + x) - \|x  + a
   (2)  ----------------------------------
                         x
                                                     Type: Expression Integer
--R
--R               +-------+         +-------+
--R               | 2    2          | 2    2
--R        x log(\|x  + a   + x) - \|x  + a
--R   (2)  ----------------------------------
--R                         x
--R                                                     Type: Expression Integer
--E

--S 50
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 51     14:194 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

               2
   (4)  - log(a ) - 1
                                                     Type: Expression Integer
--R
--R               2
--R   (4)  - log(a ) - 1
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 52
aa:=integrate(sqrt(x^2+a^2)/x^3,x)
 

   (1)
              +-------+                   +-------+
            3 | 2    2      4    2 2      | 2    2
       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x + a)
     + 
            +-------+                   +-------+
          3 | 2    2      4    2 2      | 2    2
       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x - a)
     + 
                    +-------+
            2    3  | 2    2        3     3
       (2a x  + a )\|x  + a   - 2a x  - 2a x
  /
           +-------+
         3 | 2    2        4     3 2
     4a x \|x  + a   - 4a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R              +-------+                   +-------+
--R            3 | 2    2      4    2 2      | 2    2
--R       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x + a)
--R     + 
--R            +-------+                   +-------+
--R          3 | 2    2      4    2 2      | 2    2
--R       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x - a)
--R     + 
--R                    +-------+
--R            2    3  | 2    2        3     3
--R       (2a x  + a )\|x  + a   - 2a x  - 2a x
--R  /
--R           +-------+
--R         3 | 2    2        4     3 2
--R     4a x \|x  + a   - 4a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53
bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2           +-------+
           2    \|x  + a   + a      | 2    2
        - x log(--------------) - a\|x  + a
                       x
   (2)  -------------------------------------
                            2
                        2a x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2           +-------+
--R           2    \|x  + a   + a      | 2    2
--R        - x log(--------------) - a\|x  + a
--R                       x
--R   (2)  -------------------------------------
--R                            2
--R                        2a x
--R                                                     Type: Expression Integer
--E

--S 54
cc:=aa-bb
 

   (3)
                                                              +-------+
          +-------+                 +-------+                 | 2    2
          | 2    2                  | 2    2                 \|x  + a   + a
   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
                                                                    x
   -------------------------------------------------------------------------
                                       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                              +-------+
--R          +-------+                 +-------+                 | 2    2
--R          | 2    2                  | 2    2                 \|x  + a   + a
--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
--R                                                                    x
--R   -------------------------------------------------------------------------
--R                                       2a
--R                                                     Type: Expression Integer
--E

--S 55
dd:=expandLog cc
 

   (4)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 56     14:195 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R             2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 57
aa:=integrate(1/(x^2+a^2)^(3/2),x)
 

                    1
   (1)  - ---------------------
            +-------+
            | 2    2     2    2
          x\|x  + a   - x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    1
--R   (1)  - ---------------------
--R            +-------+
--R            | 2    2     2    2
--R          x\|x  + a   - x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 58
bb:=x/(a^2*sqrt(x^2+a^2))
 

              x
   (2)  ------------
           +-------+
         2 | 2    2
        a \|x  + a
                                                     Type: Expression Integer
--R
--R              x
--R   (2)  ------------
--R           +-------+
--R         2 | 2    2
--R        a \|x  + a
--R                                                     Type: Expression Integer
--E

--S 59     14:196 Schaums and Axiom differ by a constant
cc:=aa-bb
 

         1
   (3)  --
         2
        a
                                                     Type: Expression Integer
--R
--R         1
--R   (3)  --
--R         2
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 60
aa:=integrate(x/(x^2+a^2)^(3/2),x)
 

             +-------+
             | 2    2
            \|x  + a   - x
   (1)  ---------------------
          +-------+
          | 2    2     2    2
        x\|x  + a   - x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+
--R             | 2    2
--R            \|x  + a   - x
--R   (1)  ---------------------
--R          +-------+
--R          | 2    2     2    2
--R        x\|x  + a   - x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 61
bb:=-1/sqrt(x^2+a^2)
 

               1
   (2)  - ----------
           +-------+
           | 2    2
          \|x  + a
                                                     Type: Expression Integer
--R
--R               1
--R   (2)  - ----------
--R           +-------+
--R           | 2    2
--R          \|x  + a
--R                                                     Type: Expression Integer
--E

--S 62     14:197 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 63
aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
 

             +-------+                +-------+
             | 2    2     2    2      | 2    2          2
        (- x\|x  + a   + x  + a )log(\|x  + a   - x) + a
   (1)  -------------------------------------------------
                        +-------+
                        | 2    2     2    2
                      x\|x  + a   - x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+                +-------+
--R             | 2    2     2    2      | 2    2          2
--R        (- x\|x  + a   + x  + a )log(\|x  + a   - x) + a
--R   (1)  -------------------------------------------------
--R                        +-------+
--R                        | 2    2     2    2
--R                      x\|x  + a   - x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 64
bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2))
 

         +-------+     +-------+
         | 2    2      | 2    2
        \|x  + a  log(\|x  + a   + x) - x
   (2)  ---------------------------------
                     +-------+
                     | 2    2
                    \|x  + a
                                                     Type: Expression Integer
--R
--R         +-------+     +-------+
--R         | 2    2      | 2    2
--R        \|x  + a  log(\|x  + a   + x) - x
--R   (2)  ---------------------------------
--R                     +-------+
--R                     | 2    2
--R                    \|x  + a
--R                                                     Type: Expression Integer
--E

--S 65
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 66     14:198 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

               2
   (4)  - log(a ) - 1
                                                     Type: Expression Integer
--R
--R               2
--R   (4)  - log(a ) - 1
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 67
aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
 

                       +-------+
             3     2   | 2    2      4     2 2     4
        (- 2x  - 4a x)\|x  + a   + 2x  + 5a x  + 2a
   (1)  --------------------------------------------
                         +-------+
                 2    2  | 2    2      3     2
              (2x  + a )\|x  + a   - 2x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       +-------+
--R             3     2   | 2    2      4     2 2     4
--R        (- 2x  - 4a x)\|x  + a   + 2x  + 5a x  + 2a
--R   (1)  --------------------------------------------
--R                         +-------+
--R                 2    2  | 2    2      3     2
--R              (2x  + a )\|x  + a   - 2x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68
bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2)
 

          2     2
         x  + 2a
   (2)  ----------
         +-------+
         | 2    2
        \|x  + a
                                                     Type: Expression Integer
--R
--R          2     2
--R         x  + 2a
--R   (2)  ----------
--R         +-------+
--R         | 2    2
--R        \|x  + a
--R                                                     Type: Expression Integer
--E

--S 69     14:199 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 70
aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
 

   (1)
            +-------+                +-------+
            | 2    2     2    2      | 2    2
       (- x\|x  + a   + x  + a )log(\|x  + a   - x + a)
     + 
          +-------+                +-------+              +-------+
          | 2    2     2    2      | 2    2               | 2    2
       (x\|x  + a   - x  - a )log(\|x  + a   - x - a) - a\|x  + a   + a x
  /
         +-------+
      3  | 2    2     3 2    5
     a x\|x  + a   - a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +-------+                +-------+
--R            | 2    2     2    2      | 2    2
--R       (- x\|x  + a   + x  + a )log(\|x  + a   - x + a)
--R     + 
--R          +-------+                +-------+              +-------+
--R          | 2    2     2    2      | 2    2               | 2    2
--R       (x\|x  + a   - x  - a )log(\|x  + a   - x - a) - a\|x  + a   + a x
--R  /
--R         +-------+
--R      3  | 2    2     3 2    5
--R     a x\|x  + a   - a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 71
bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x)
 

                         +-------+
           +-------+     | 2    2
           | 2    2     \|x  + a   + a
        - \|x  + a  log(--------------) + a
                               x
   (2)  -----------------------------------
                       +-------+
                     3 | 2    2
                    a \|x  + a
                                                     Type: Expression Integer
--R
--R                         +-------+
--R           +-------+     | 2    2
--R           | 2    2     \|x  + a   + a
--R        - \|x  + a  log(--------------) + a
--R                               x
--R   (2)  -----------------------------------
--R                       +-------+
--R                     3 | 2    2
--R                    a \|x  + a
--R                                                     Type: Expression Integer
--E

--S 72
cc:=aa-bb
 

   (3)
                                                              +-------+
          +-------+                 +-------+                 | 2    2
          | 2    2                  | 2    2                 \|x  + a   + a
   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
                                                                    x
   -------------------------------------------------------------------------
                                        3
                                       a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                              +-------+
--R          +-------+                 +-------+                 | 2    2
--R          | 2    2                  | 2    2                 \|x  + a   + a
--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
--R                                                                    x
--R   -------------------------------------------------------------------------
--R                                        3
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 73
dd:=expandLog cc
 

   (4)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
      3
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R      3
--R     a
--R                                                     Type: Expression Integer
--E

--S 74     14:200 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
              3
             a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R              3
--R             a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 75
aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
 

                           1
   (1)  - -----------------------------------
                      +-------+
             3    2   | 2    2      4     2 2
          (2x  + a x)\|x  + a   - 2x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           1
--R   (1)  - -----------------------------------
--R                      +-------+
--R             3    2   | 2    2      4     2 2
--R          (2x  + a x)\|x  + a   - 2x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 76
bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2))
 

              2    2
          - 2x  - a
   (2)  -------------
            +-------+
         4  | 2    2
        a x\|x  + a
                                                     Type: Expression Integer
--R
--R              2    2
--R          - 2x  - a
--R   (2)  -------------
--R            +-------+
--R         4  | 2    2
--R        a x\|x  + a
--R                                                     Type: Expression Integer
--E

--S 77     14:201 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           2
   (3)  - --
           4
          a
                                                     Type: Expression Integer
--R
--R           2
--R   (3)  - --
--R           4
--R          a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 78
aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
 

   (1)
                       +-------+                              +-------+
            5     2 3  | 2    2       6      2 4     4 2      | 2    2
       ((12x  + 9a x )\|x  + a   - 12x  - 15a x  - 3a x )log(\|x  + a   - x + a)
     + 
                           +-------+
                5     2 3  | 2    2       6      2 4     4 2
         ((- 12x  - 9a x )\|x  + a   + 12x  + 15a x  + 3a x )
      *
              +-------+
              | 2    2
         log(\|x  + a   - x - a)
     + 
                             +-------+
             4     3 2    5  | 2    2         5      3 3     5
       (12a x  + 7a x  + a )\|x  + a   - 12a x  - 13a x  - 3a x
  /
                     +-------+
        5 5     7 3  | 2    2      5 6      7 4     9 2
     (8a x  + 6a x )\|x  + a   - 8a x  - 10a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       +-------+                              +-------+
--R            5     2 3  | 2    2       6      2 4     4 2      | 2    2
--R       ((12x  + 9a x )\|x  + a   - 12x  - 15a x  - 3a x )log(\|x  + a   - x + a)
--R     + 
--R                           +-------+
--R                5     2 3  | 2    2       6      2 4     4 2
--R         ((- 12x  - 9a x )\|x  + a   + 12x  + 15a x  + 3a x )
--R      *
--R              +-------+
--R              | 2    2
--R         log(\|x  + a   - x - a)
--R     + 
--R                             +-------+
--R             4     3 2    5  | 2    2         5      3 3     5
--R       (12a x  + 7a x  + a )\|x  + a   - 12a x  - 13a x  - 3a x
--R  /
--R                     +-------+
--R        5 5     7 3  | 2    2      5 6      7 4     9 2
--R     (8a x  + 6a x )\|x  + a   - 8a x  - 10a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 79
bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x^2+a^2))/x)
 

                          +-------+
            +-------+     | 2    2
          2 | 2    2     \|x  + a   + a        2    3
        3x \|x  + a  log(--------------) - 3a x  - a
                                x
   (2)  ---------------------------------------------
                             +-------+
                         5 2 | 2    2
                       2a x \|x  + a
                                                     Type: Expression Integer
--R
--R                          +-------+
--R            +-------+     | 2    2
--R          2 | 2    2     \|x  + a   + a        2    3
--R        3x \|x  + a  log(--------------) - 3a x  - a
--R                                x
--R   (2)  ---------------------------------------------
--R                             +-------+
--R                         5 2 | 2    2
--R                       2a x \|x  + a
--R                                                     Type: Expression Integer
--E

--S 80
cc:=aa-bb
 

   (3)
                                                               +-------+
         +-------+                  +-------+                  | 2    2
         | 2    2                   | 2    2                  \|x  + a   + a
   3log(\|x  + a   - x + a) - 3log(\|x  + a   - x - a) - 3log(--------------)
                                                                     x
   --------------------------------------------------------------------------
                                         5
                                       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                               +-------+
--R         +-------+                  +-------+                  | 2    2
--R         | 2    2                   | 2    2                  \|x  + a   + a
--R   3log(\|x  + a   - x + a) - 3log(\|x  + a   - x - a) - 3log(--------------)
--R                                                                     x
--R   --------------------------------------------------------------------------
--R                                         5
--R                                       2a
--R                                                     Type: Expression Integer
--E

--S 81
dd:=expandLog cc
 

   (4)
               +-------+              +-------+
               | 2    2               | 2    2
       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
     + 
               +-------+
               | 2    2
       - 3log(\|x  + a   - x - a) + 3log(x)
  /
       5
     2a
                                                     Type: Expression Integer
--R
--R   (4)
--R               +-------+              +-------+
--R               | 2    2               | 2    2
--R       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
--R     + 
--R               +-------+
--R               | 2    2
--R       - 3log(\|x  + a   - x - a) + 3log(x)
--R  /
--R       5
--R     2a
--R                                                     Type: Expression Integer
--E

--S 82     14:202 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        3log(- 1)
   (5)  ---------
             5
           2a
                                                     Type: Expression Integer
--R
--R        3log(- 1)
--R   (5)  ---------
--R             5
--R           2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 83
aa:=integrate((x^2+a^2)^(3/2),x)
 

   (1)
                           +-------+                              +-------+
              4 3      6   | 2    2       4 4      6 2     8      | 2    2
       ((- 24a x  - 12a x)\|x  + a   + 24a x  + 24a x  + 3a )log(\|x  + a   - x)
     + 
                                         +-------+
             7      2 5      4 3     6   | 2    2       8      2 6      4 4
       (- 16x  - 56a x  - 42a x  - 5a x)\|x  + a   + 16x  + 64a x  + 68a x
     + 
          6 2
       20a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                           +-------+                              +-------+
--R              4 3      6   | 2    2       4 4      6 2     8      | 2    2
--R       ((- 24a x  - 12a x)\|x  + a   + 24a x  + 24a x  + 3a )log(\|x  + a   - x)
--R     + 
--R                                         +-------+
--R             7      2 5      4 3     6   | 2    2       8      2 6      4 4
--R       (- 16x  - 56a x  - 42a x  - 5a x)\|x  + a   + 16x  + 64a x  + 68a x
--R     + 
--R          6 2
--R       20a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84
bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2))
 

                +-------+                     +-------+
          4     | 2    2            3     2   | 2    2
        3a log(\|x  + a   + x) + (2x  + 5a x)\|x  + a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                +-------+                     +-------+
--R          4     | 2    2            3     2   | 2    2
--R        3a log(\|x  + a   + x) + (2x  + 5a x)\|x  + a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 85
cc:=aa-bb
 

                  +-------+                +-------+
            4     | 2    2           4     | 2    2
        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x)
   (3)  -------------------------------------------------
                                8
                                                     Type: Expression Integer
--R
--R                  +-------+                +-------+
--R            4     | 2    2           4     | 2    2
--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x)
--R   (3)  -------------------------------------------------
--R                                8
--R                                                     Type: Expression Integer
--E

--S 86     14:203 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

            4     2
          3a log(a )
   (4)  - ----------
               8
                                                     Type: Expression Integer
--R
--R            4     2
--R          3a log(a )
--R   (4)  - ----------
--R               8
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 87
aa:=integrate(x*(x^2+a^2)^(3/2),x)
 

   (1)
                                                  +-------+
             9      2 7      4 5      6 3     8   | 2    2       10      2 8
       (- 16x  - 52a x  - 61a x  - 30a x  - 5a x)\|x  + a   + 16x   + 60a x
     + 
          4 6      6 4      8 2    10
       85a x  + 55a x  + 15a x  + a
  /
                           +-------+
         4      2 2     4  | 2    2       5       2 3      4
     (80x  + 60a x  + 5a )\|x  + a   - 80x  - 100a x  - 25a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7      4 5      6 3     8   | 2    2       10      2 8
--R       (- 16x  - 52a x  - 61a x  - 30a x  - 5a x)\|x  + a   + 16x   + 60a x
--R     + 
--R          4 6      6 4      8 2    10
--R       85a x  + 55a x  + 15a x  + a
--R  /
--R                           +-------+
--R         4      2 2     4  | 2    2       5       2 3      4
--R     (80x  + 60a x  + 5a )\|x  + a   - 80x  - 100a x  - 25a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 88
bb:=(x^2+a^2)^(5/2)/5
 

                          +-------+
          4     2 2    4  | 2    2
        (x  + 2a x  + a )\|x  + a
   (2)  ---------------------------
                     5
                                                     Type: Expression Integer
--R
--R                          +-------+
--R          4     2 2    4  | 2    2
--R        (x  + 2a x  + a )\|x  + a
--R   (2)  ---------------------------
--R                     5
--R                                                     Type: Expression Integer
--E

--S 89     14:204 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 90
aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
 

   (1)
                                      +-------+
               6 5      8 3      10   | 2    2       6 6       8 4      10 2
           (96a x  + 96a x  + 18a  x)\|x  + a   - 96a x  - 144a x  - 54a  x
         + 
               12
           - 3a
      *
              +-------+
              | 2    2
         log(\|x  + a   - x)
     + 
                                                                 +-------+
              11       2 9       4 7       6 5      8 3     10   | 2    2
       (- 256x   - 832a x  - 912a x  - 404a x  - 68a x  - 3a  x)\|x  + a
     + 
           12       2 10        4 8       6 6       8 4      10 2
       256x   + 960a x   + 1296a x  + 772a x  + 198a x  + 18a  x
  /
                                  +-------+
           5        2 3       4   | 2    2         6        2 4       4 2      6
     (1536x  + 1536a x  + 288a x)\|x  + a   - 1536x  - 2304a x  - 864a x  - 48a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                      +-------+
--R               6 5      8 3      10   | 2    2       6 6       8 4      10 2
--R           (96a x  + 96a x  + 18a  x)\|x  + a   - 96a x  - 144a x  - 54a  x
--R         + 
--R               12
--R           - 3a
--R      *
--R              +-------+
--R              | 2    2
--R         log(\|x  + a   - x)
--R     + 
--R                                                                 +-------+
--R              11       2 9       4 7       6 5      8 3     10   | 2    2
--R       (- 256x   - 832a x  - 912a x  - 404a x  - 68a x  - 3a  x)\|x  + a
--R     + 
--R           12       2 10        4 8       6 6       8 4      10 2
--R       256x   + 960a x   + 1296a x  + 772a x  + 198a x  + 18a  x
--R  /
--R                                  +-------+
--R           5        2 3       4   | 2    2         6        2 4       4 2      6
--R     (1536x  + 1536a x  + 288a x)\|x  + a   - 1536x  - 2304a x  - 864a x  - 48a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91
bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^6/16*log(x+sqrt(x^2+a^2))
 

                  +-------+                              +-------+
            6     | 2    2            5      2 3     4   | 2    2
        - 3a log(\|x  + a   + x) + (8x  + 14a x  + 3a x)\|x  + a
   (2)  ----------------------------------------------------------
                                    48
                                                     Type: Expression Integer
--R
--R                  +-------+                              +-------+
--R            6     | 2    2            5      2 3     4   | 2    2
--R        - 3a log(\|x  + a   + x) + (8x  + 14a x  + 3a x)\|x  + a
--R   (2)  ----------------------------------------------------------
--R                                    48
--R                                                     Type: Expression Integer
--E

--S 92
cc:=aa-bb
 

               +-------+               +-------+
         6     | 2    2          6     | 2    2
        a log(\|x  + a   + x) + a log(\|x  + a   - x)
   (3)  ---------------------------------------------
                              16
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         6     | 2    2          6     | 2    2
--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
--R   (3)  ---------------------------------------------
--R                              16
--R                                                     Type: Expression Integer
--E

--S 93     14:205 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

         6     2
        a log(a )
   (4)  ---------
            16
                                                     Type: Expression Integer
--R
--R         6     2
--R        a log(a )
--R   (4)  ---------
--R            16
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 94
aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
 

   (1)
                   13        2 11        4 9       6 7       8 5       10 3
             - 320x   - 1072a x   - 1240a x  - 467a x  + 112a x  + 105a  x
           + 
                12
             14a  x
      *
          +-------+
          | 2    2
         \|x  + a
     + 
           14        2 12        4 10       6 8      8 6       10 4      12 2
       320x   + 1232a x   + 1736a x   + 973a x  + 21a x  - 175a  x  - 49a  x
     + 
           14
       - 2a
  /
                                            +-------+
             6        2 4       4 2      6  | 2    2         7        2 5
       (2240x  + 2800a x  + 840a x  + 35a )\|x  + a   - 2240x  - 3920a x
     + 
              4 3       6
       - 1960a x  - 245a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   13        2 11        4 9       6 7       8 5       10 3
--R             - 320x   - 1072a x   - 1240a x  - 467a x  + 112a x  + 105a  x
--R           + 
--R                12
--R             14a  x
--R      *
--R          +-------+
--R          | 2    2
--R         \|x  + a
--R     + 
--R           14        2 12        4 10       6 8      8 6       10 4      12 2
--R       320x   + 1232a x   + 1736a x   + 973a x  + 21a x  - 175a  x  - 49a  x
--R     + 
--R           14
--R       - 2a
--R  /
--R                                            +-------+
--R             6        2 4       4 2      6  | 2    2         7        2 5
--R       (2240x  + 2800a x  + 840a x  + 35a )\|x  + a   - 2240x  - 3920a x
--R     + 
--R              4 3       6
--R       - 1960a x  - 245a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 95
bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5
 

                                   +-------+
           6     2 4    4 2     6  | 2    2
        (5x  + 8a x  + a x  - 2a )\|x  + a
   (2)  ------------------------------------
                         35
                                                     Type: Expression Integer
--R
--R                                   +-------+
--R           6     2 4    4 2     6  | 2    2
--R        (5x  + 8a x  + a x  - 2a )\|x  + a
--R   (2)  ------------------------------------
--R                         35
--R                                                     Type: Expression Integer
--E

--S 96     14:206 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 97
aa:=integrate((x^2+a^2)^(3/2)/x,x)
 

   (1)
                         +-------+                      +-------+
              3 2     5  | 2    2       3 3     5       | 2    2
       ((- 12a x  - 3a )\|x  + a   + 12a x  + 9a x)log(\|x  + a   - x + a)
     + 
                       +-------+                      +-------+
            3 2     5  | 2    2       3 3     5       | 2    2
       ((12a x  + 3a )\|x  + a   - 12a x  - 9a x)log(\|x  + a   - x - a)
     + 
                                +-------+
            5      2 3      4   | 2    2      6      2 4      4 2     6
       (- 4x  - 19a x  - 12a x)\|x  + a   + 4x  + 21a x  + 21a x  + 4a
  /
                  +-------+
         2     2  | 2    2       3     2
     (12x  + 3a )\|x  + a   - 12x  - 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                         +-------+                      +-------+
--R              3 2     5  | 2    2       3 3     5       | 2    2
--R       ((- 12a x  - 3a )\|x  + a   + 12a x  + 9a x)log(\|x  + a   - x + a)
--R     + 
--R                       +-------+                      +-------+
--R            3 2     5  | 2    2       3 3     5       | 2    2
--R       ((12a x  + 3a )\|x  + a   - 12a x  - 9a x)log(\|x  + a   - x - a)
--R     + 
--R                                +-------+
--R            5      2 3      4   | 2    2      6      2 4      4 2     6
--R       (- 4x  - 19a x  - 12a x)\|x  + a   + 4x  + 21a x  + 21a x  + 4a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3     2
--R     (12x  + 3a )\|x  + a   - 12x  - 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 98
bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x)
 

                  +-------+
                  | 2    2                    +-------+
            3    \|x  + a   + a      2     2  | 2    2
        - 3a log(--------------) + (x  + 4a )\|x  + a
                        x
   (2)  -----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                  +-------+
--R                  | 2    2                    +-------+
--R            3    \|x  + a   + a      2     2  | 2    2
--R        - 3a log(--------------) + (x  + 4a )\|x  + a
--R                        x
--R   (2)  -----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 99
cc:=aa-bb
 

   (3)
              +-------+                   +-------+
        3     | 2    2              3     | 2    2
     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
   + 
            +-------+
            | 2    2
      3    \|x  + a   + a
     a log(--------------)
                  x
                                                     Type: Expression Integer
--R
--R   (3)
--R              +-------+                   +-------+
--R        3     | 2    2              3     | 2    2
--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
--R   + 
--R            +-------+
--R            | 2    2
--R      3    \|x  + a   + a
--R     a log(--------------)
--R                  x
--R                                                     Type: Expression Integer
--E

--S 100
dd:=expandLog cc
 

   (4)
            +-------+               +-------+
      3     | 2    2          3     | 2    2
     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
   + 
            +-------+
      3     | 2    2              3
     a log(\|x  + a   - x - a) - a log(x)
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+               +-------+
--R      3     | 2    2          3     | 2    2
--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
--R   + 
--R            +-------+
--R      3     | 2    2              3
--R     a log(\|x  + a   - x - a) - a log(x)
--R                                                     Type: Expression Integer
--E

--S 101    14:207 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

           3
   (5)  - a log(- 1)
                                                     Type: Expression Integer
--R
--R           3
--R   (5)  - a log(- 1)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 102
aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
 

   (1)
                          +-------+                       +-------+
              2 3     4   | 2    2       2 4     4 2      | 2    2
       ((- 12a x  - 3a x)\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x)
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2     6
       (- 4x  - 3a x  + 4a x)\|x  + a   + 4x  + 5a x  - 3a x  - 2a
  /
                  +-------+
        3     2   | 2    2      4     2 2
     (8x  + 2a x)\|x  + a   - 8x  - 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                          +-------+                       +-------+
--R              2 3     4   | 2    2       2 4     4 2      | 2    2
--R       ((- 12a x  - 3a x)\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x)
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (- 4x  - 3a x  + 4a x)\|x  + a   + 4x  + 5a x  - 3a x  - 2a
--R  /
--R                  +-------+
--R        3     2   | 2    2      4     2 2
--R     (8x  + 2a x)\|x  + a   - 8x  - 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103
bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2))
 

                  +-------+                   +-------+
          2       | 2    2           2     2  | 2    2
        3a x log(\|x  + a   + x) + (x  - 2a )\|x  + a
   (2)  -----------------------------------------------
                               2x
                                                     Type: Expression Integer
--R
--R                  +-------+                   +-------+
--R          2       | 2    2           2     2  | 2    2
--R        3a x log(\|x  + a   + x) + (x  - 2a )\|x  + a
--R   (2)  -----------------------------------------------
--R                               2x
--R                                                     Type: Expression Integer
--E

--S 104
cc:=aa-bb
 

                  +-------+                +-------+
            2     | 2    2           2     | 2    2           2
        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x) - 2a
   (3)  -------------------------------------------------------
                                   2
                                                     Type: Expression Integer
--R
--R                  +-------+                +-------+
--R            2     | 2    2           2     | 2    2           2
--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x) - 2a
--R   (3)  -------------------------------------------------------
--R                                   2
--R                                                     Type: Expression Integer
--E

--S 105    14:208 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

            2     2      2
        - 3a log(a ) - 2a
   (4)  ------------------
                 2
                                                     Type: Expression Integer
--R
--R            2     2      2
--R        - 3a log(a ) - 2a
--R   (4)  ------------------
--R                 2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 106
aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
 

   (1)
                           +-------+                       +-------+
                4     3 2  | 2    2         5     3 3      | 2    2
       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
     + 
                         +-------+                       +-------+
              4     3 2  | 2    2         5     3 3      | 2    2
       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2    6
       (- 8x  - 2a x  + 3a x)\|x  + a   + 8x  + 6a x  - 3a x  - a
  /
                   +-------+
        4     2 2  | 2    2      5     2 3
     (8x  + 2a x )\|x  + a   - 8x  - 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +-------+                       +-------+
--R                4     3 2  | 2    2         5     3 3      | 2    2
--R       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
--R     + 
--R                         +-------+                       +-------+
--R              4     3 2  | 2    2         5     3 3      | 2    2
--R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2    6
--R       (- 8x  - 2a x  + 3a x)\|x  + a   + 8x  + 6a x  - 3a x  - a
--R  /
--R                   +-------+
--R        4     2 2  | 2    2      5     2 3
--R     (8x  + 2a x )\|x  + a   - 8x  - 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 107
bb:=-(x^2+a^2)^(3/2)/(2*x^2)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x)
 

                    +-------+
                    | 2    2                    +-------+
              2    \|x  + a   + a       2    2  | 2    2
        - 3a x log(--------------) + (2x  - a )\|x  + a
                          x
   (2)  -------------------------------------------------
                                 2
                               2x
                                                     Type: Expression Integer
--R
--R                    +-------+
--R                    | 2    2                    +-------+
--R              2    \|x  + a   + a       2    2  | 2    2
--R        - 3a x log(--------------) + (2x  - a )\|x  + a
--R                          x
--R   (2)  -------------------------------------------------
--R                                 2
--R                               2x
--R                                                     Type: Expression Integer
--E

--S 108
cc:=aa-bb
 

   (3)
                 +-------+                    +-------+
                 | 2    2                     | 2    2
       - 3a log(\|x  + a   - x + a) + 3a log(\|x  + a   - x - a)
     + 
               +-------+
               | 2    2
              \|x  + a   + a
       3a log(--------------)
                     x
  /
     2
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +-------+                    +-------+
--R                 | 2    2                     | 2    2
--R       - 3a log(\|x  + a   - x + a) + 3a log(\|x  + a   - x - a)
--R     + 
--R               +-------+
--R               | 2    2
--R              \|x  + a   + a
--R       3a log(--------------)
--R                     x
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 109
dd:=expandLog cc
 

   (4)
               +-------+                +-------+
               | 2    2                 | 2    2
       3a log(\|x  + a   + a) - 3a log(\|x  + a   - x + a)
     + 
               +-------+
               | 2    2
       3a log(\|x  + a   - x - a) - 3a log(x)
  /
     2
                                                     Type: Expression Integer
--R
--R   (4)
--R               +-------+                +-------+
--R               | 2    2                 | 2    2
--R       3a log(\|x  + a   + a) - 3a log(\|x  + a   - x + a)
--R     + 
--R               +-------+
--R               | 2    2
--R       3a log(\|x  + a   - x - a) - 3a log(x)
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 110    14:209 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          3a log(- 1)
   (5)  - -----------
               2
                                                     Type: Expression Integer
--R
--R          3a log(- 1)
--R   (5)  - -----------
--R               2
--R                                                     Type: Expression Integer
--E

)spool
 
Starts dribbling to arith.output (2009/2/17, 17:43:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 25
234+108
 

   (1)  342
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  342
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 25
234*108
 

   (2)  25272
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  25272
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 25
234**108
 

   (3)
  7504341690759264167679309791024278941530727955934090653805060111651544673126_
   088300475695723868519539237537191538150810021660251720209488577129906170829_
   305169117495939513626114577980010503744097313250953950814884553019803764362_
   781777309157631769660459319296
                                                        Type: PositiveInteger
--R 
--R
--R   (3)
--R  7504341690759264167679309791024278941530727955934090653805060111651544673126_
--R   088300475695723868519539237537191538150810021660251720209488577129906170829_
--R   305169117495939513626114577980010503744097313250953950814884553019803764362_
--R   781777309157631769660459319296
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 25
factor %
 

         108 216  108
   (4)  2   3   13
                                                       Type: Factored Integer
--R 
--R
--R         108 216  108
--R   (4)  2   3   13
--R                                                       Type: Factored Integer
--E 4

--S 5 of 25
z := 1/2
 

        1
   (5)  -
        2
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (5)  -
--R        2
--R                                                       Type: Fraction Integer
--E 5

--S 6 of 25
v := (z + 1) ** 10
 

        59049
   (6)  -----
         1024
                                                       Type: Fraction Integer
--R 
--R
--R        59049
--R   (6)  -----
--R         1024
--R                                                       Type: Fraction Integer
--E 6

--S 7 of 25
1024 * %
 

   (7)  59049
                                                       Type: Fraction Integer
--R 
--R
--R   (7)  59049
--R                                                       Type: Fraction Integer
--E 7

--S 8 of 25
u := (x+1)**6
 

         6     5      4      3      2
   (8)  x  + 6x  + 15x  + 20x  + 15x  + 6x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         6     5      4      3      2
--R   (8)  x  + 6x  + 15x  + 20x  + 15x  + 6x + 1
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 25
differentiate(u,x)
 

          5      4      3      2
   (9)  6x  + 30x  + 60x  + 60x  + 30x + 6
                                                     Type: Polynomial Integer
--R 
--R
--R          5      4      3      2
--R   (9)  6x  + 30x  + 60x  + 60x  + 30x + 6
--R                                                     Type: Polynomial Integer
--E 9

-- factor %
)clear all
 
   All user variables and function definitions have been cleared.
 
-- compute Fibonacci numbers
--S 10 of 25
fib(n | n = 0)  == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 25
fib(n | n = 1)  == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 25
fib(n | n > 1)  == fib(n-1) + fib(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 25
fib 5
 
   Compiling function fib with type Integer -> PositiveInteger 
   Compiling function fib as a recurrence relation.

   (4)  8
                                                        Type: PositiveInteger
--R 
--R   Compiling function fib with type Integer -> PositiveInteger 
--R   Compiling function fib as a recurrence relation.
--R
--R   (4)  8
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 25
fib 20
 

   (5)  10946
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  10946
--R                                                        Type: PositiveInteger
--E 14

)clear all
 
   All user variables and function definitions have been cleared.

-- compute Legendre polynomials
--S 15 of 25
leg(n | n = 0)  == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 25
leg(n | n = 1)  == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 25
leg(n | n > 1)  == ((2*n-1)*x*leg(n-1)-(n-1)*leg(n-2))/n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 25
leg 3
 
   Compiling function leg with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function leg as a recurrence relation.

        5  3   3
   (4)  - x  - - x
        2      2
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function leg with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function leg as a recurrence relation.
--R
--R        5  3   3
--R   (4)  - x  - - x
--R        2      2
--R                                            Type: Polynomial Fraction Integer
--E 18

--S 19 of 25
leg 14
 

   (5)
     5014575  14   16900975  12   22309287  10   14549535  8   4849845  6
     ------- x   - -------- x   + -------- x   - -------- x  + ------- x
       2048          2048           2048           2048          2048
   + 
       765765  4   45045  2    429
     - ------ x  + ----- x  - ----
        2048        2048      2048
                                            Type: Polynomial Fraction Integer
--R 
--R
--R   (5)
--R     5014575  14   16900975  12   22309287  10   14549535  8   4849845  6
--R     ------- x   - -------- x   + -------- x   - -------- x  + ------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       765765  4   45045  2    429
--R     - ------ x  + ----- x  - ----
--R        2048        2048      2048
--R                                            Type: Polynomial Fraction Integer
--E 19

-- look at it as a polynomial with rational number coefficients
--% :: POLY FRAC INT
)clear all
 
   All user variables and function definitions have been cleared.
 
-- several flavors of computing factorial
--S 20 of 25
fac1(n | n=1)   == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 25
fac1(n | n > 1) == n*fac1(n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 25
fac2 n == if n = 1 then 1 else n*fac2(n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 25
fac3 n == reduce(*,[1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 25
fac1 10
 
   Compiling function fac1 with type Integer -> Integer 
   Compiling function fac1 as a recurrence relation.

   (5)  3628800
                                                        Type: PositiveInteger
--R 
--R   Compiling function fac1 with type Integer -> Integer 
--R   Compiling function fac1 as a recurrence relation.
--R
--R   (5)  3628800
--R                                                        Type: PositiveInteger
--E 24

--S 25 of 25
fac2 10
 
   Compiling function fac2 with type Integer -> Integer 
   Compiling function fac2 as a recurrence relation.

   (6)  3628800
                                                        Type: PositiveInteger
--R 
--R   Compiling function fac2 with type Integer -> Integer 
--R   Compiling function fac2 as a recurrence relation.
--R
--R   (6)  3628800
--R                                                        Type: PositiveInteger
--E 25
)spool
 
Starts dribbling to decimal.output (2009/2/17, 17:44:37).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from DecimalExpansionXmpPage

--S 1 of 7
r := decimal(22/7)
 

          ______
   (1)  3.142857
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (1)  3.142857
--R                                                       Type: DecimalExpansion
--E 1

--S 2 of 7
r + decimal(6/7)
 

   (2)  4
                                                       Type: DecimalExpansion
--R 
--R
--R   (2)  4
--R                                                       Type: DecimalExpansion
--E 2

--S 3 of 7
[decimal(1/i) for i in 350..354] 
 

   (3)
        ______    ______         __    ________________________________
   [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983,
       __________________________________________________________
    0.00282485875706214689265536723163841807909604519774011299435]
                                                  Type: List DecimalExpansion
--R 
--R
--R   (3)
--R        ______    ______         __    ________________________________
--R   [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983,
--R       __________________________________________________________
--R    0.00282485875706214689265536723163841807909604519774011299435]
--R                                                  Type: List DecimalExpansion
--E 3

--S 4 of 7
decimal(1/2049) 
 

   (4)
   0.
     OVERBAR
        00048804294777940458760370912640312347486578818936066373840897999023914
          104441190824792581747193753050268423621278672523182040019521717911176
          183504148365056124938994631527574426549536359199609565641776476329917
          032698877501220107369448511469009272816007808687164470473401659346022
          449975597852611029770619814543679843826256710590531966813079551
                                                       Type: DecimalExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        00048804294777940458760370912640312347486578818936066373840897999023914
--R          104441190824792581747193753050268423621278672523182040019521717911176
--R          183504148365056124938994631527574426549536359199609565641776476329917
--R          032698877501220107369448511469009272816007808687164470473401659346022
--R          449975597852611029770619814543679843826256710590531966813079551
--R                                                       Type: DecimalExpansion
--E 4

--S 5 of 7
p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9)
 

             2     _      _
   (5)  0.25x  + 0.6x + 0.4
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R             2     _      _
--R   (5)  0.25x  + 0.6x + 0.4
--R                                            Type: Polynomial DecimalExpansion
--E 5

--S 6 of 7
q := differentiate(p, x)
 

                 _
   (6)  0.5x + 0.6
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R                 _
--R   (6)  0.5x + 0.6
--R                                            Type: Polynomial DecimalExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              _
   (7)  x + 1.3
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R              _
--R   (7)  x + 1.3
--R                                            Type: Polynomial DecimalExpansion
--E 7
)spool
 
Starts dribbling to nepip.output (2009/2/17, 17:55:31).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 27
outputGeneral 5
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 27
mA1 := matrix [[ 0.5 ,   1.5 ,   6.6 ,   4.8],  _
               [ 1.5 ,   6.5 ,  16.2 ,   8.6],  _
               [ 6.6 ,  16.2 ,  37.6 ,   9.8],  _
               [ 4.8 ,   8.6 ,   9.8 , -17.1]];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 2

--S 3 of 27
mB1 := matrix[[ 1 ,  3 ,   4 ,  1],  _
              [ 3 , 13 ,  16 , 11],  _
              [ 4 , 16 ,  24 , 18],  _
              [ 1 , 11 ,  18 , 27]];
 

                                                         Type: Matrix Integer
--R 
--R
--R                                                         Type: Matrix Integer
--E 3

--S 4 of 27
mA2 := matrix [[ 3.9 ,  12.5 , -34.5 ,  -0.5],  _
               [ 4.3 ,  21.5 , -47.5 ,   7.5],  _
               [ 4.3 ,  21.5 , -43.5 ,   3.5],  _
               [ 4.4 ,  26.0 , -46.0 ,   6.0]];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 4

--S 5 of 27
mB2 := matrix[[ 1 , 2 , -3 , 1],  _
              [ 1 , 3 , -5 , 4],  _
              [ 1 , 3 , -4 , 3],  _
              [ 1 , 3 , -4 , 4]];
 

                                                         Type: Matrix Integer
--R 
--R
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 27 used to work?
nagEigenvalues(mA1,mB1) :: List Float
 
   There are no library operations named nagEigenvalues 
      Use HyperDoc Browse or issue
                           )what op nagEigenvalues
      to learn if there is any operation containing " nagEigenvalues " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvalues with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvalues 
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvalues with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6
--       [- 3.0,- 1.0,2.0,4.0]

--S 7 of 27
vv1 := nagEigenvectors(mA1,mB1);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 7

--S 8 of 27 used to work?
(vv1.eigenvalues) :: List Float
 
   There are no library operations named vv1 
      Use HyperDoc Browse or issue
                                )what op vv1
      to learn if there is any operation containing " vv1 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv1 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv1 
--R      Use HyperDoc Browse or issue
--R                                )what op vv1
--R      to learn if there is any operation containing " vv1 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv1 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 8
--       [- 3.0,- 1.0,2.0,4.0]

--S 9 of 27 used to work?
(vv1.eigenvectors) :: List Vector Complex Float
 
   There are no library operations named vv1 
      Use HyperDoc Browse or issue
                                )what op vv1
      to learn if there is any operation containing " vv1 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv1 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv1 
--R      Use HyperDoc Browse or issue
--R                                )what op vv1
--R      to learn if there is any operation containing " vv1 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv1 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9
-- [[- 4.35,0.05,1.0,- 0.5], [- 2.05,0.15,0.5,- 0.5], [- 3.95,0.85,0.5,- 0.5],
--  [2.65,0.05,- 1.0,0.5]]

--S 10 of 27
nagEigenvalues(mA2,mB2)
 
   There are no library operations named nagEigenvalues 
      Use HyperDoc Browse or issue
                           )what op nagEigenvalues
      to learn if there is any operation containing " nagEigenvalues " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvalues with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvalues 
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvalues with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 10

--S 11 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Matrix Integer to List Complex Float for 
      value
   +1  2  - 3  1+
   |            |
   |1  3  - 5  4|
   |            |
   |1  3  - 4  3|
   |            |
   +1  3  - 4  4+

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Matrix Integer to List Complex Float for 
--R      value
--R   +1  2  - 3  1+
--R   |            |
--R   |1  3  - 5  4|
--R   |            |
--R   |1  3  - 4  3|
--R   |            |
--R   +1  3  - 4  4+
--R
--E 11
--       [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]

--S 12 of 27
vv2 := nagEigenvectors(mA2,mB2);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12

--S 13 of 27
vv2.eigenvalues
 
   There are no library operations named vv2 
      Use HyperDoc Browse or issue
                                )what op vv2
      to learn if there is any operation containing " vv2 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2
--R      to learn if there is any operation containing " vv2 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 13


--S 14 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Matrix Integer to List Complex Float for 
      value
   +1  2  - 3  1+
   |            |
   |1  3  - 5  4|
   |            |
   |1  3  - 4  3|
   |            |
   +1  3  - 4  4+

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Matrix Integer to List Complex Float for 
--R      value
--R   +1  2  - 3  1+
--R   |            |
--R   |1  3  - 5  4|
--R   |            |
--R   |1  3  - 4  3|
--R   |            |
--R   +1  3  - 4  4+
--R
--E 14
--       [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]

--S 15 of 27 used to work?
vv2.eigenvectors :: List Vector Complex Float
 
   There are no library operations named vv2 
      Use HyperDoc Browse or issue
                                )what op vv2
      to learn if there is any operation containing " vv2 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2
--R      to learn if there is any operation containing " vv2 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15

-- [[0.99606,0.0056917,0.062609,0.062609],
--
--   [0.94491, 0.18898 + 0.26077 E -14 %i, 0.11339 - 0.15119 %i,
--    0.11339 - 0.15119 %i]
--   ,
--
--   [0.94491, 0.18898 - 0.26077 E -14 %i, 0.11339 + 0.15119 %i,
--    0.11339 + 0.15119 %i]
--   ,
--  [0.98752,0.010972,- 0.032917,0.15361]]

-- The same call with eps=0.0001:
--S 16 of 27
vv2a := nagEigenvectors(mA2,mB2,0.0001);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16

--S 17 of 27 used to work?
vv2a.eigenvalues :: List Complex Float
 
   There are no library operations named vv2a 
      Use HyperDoc Browse or issue
                                )what op vv2a
      to learn if there is any operation containing " vv2a " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2a 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2a 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2a
--R      to learn if there is any operation containing " vv2a " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2a 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       [1.9989,3.0003 + 3.9994 %i,3.0003 - 3.9994 %i,4.0]

--S 18 of 27
vv2a.eigenvectors :: List Vector Complex Float
 
   There are no library operations named vv2a 
      Use HyperDoc Browse or issue
                                )what op vv2a
      to learn if there is any operation containing " vv2a " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2a 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2a 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2a
--R      to learn if there is any operation containing " vv2a " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2a 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18
-- [[0.99605,0.0057355,0.062656,0.062656],
--
--   [0.94491, 0.18899 - 0.000048882 %i, 0.11336 - 0.15119 %i,
--    0.11336 - 0.15119 %i]
--   ,
--
--   [0.94491, 0.18899 + 0.000048882 %i, 0.11336 + 0.15119 %i,
--    0.11336 + 0.15119 %i]
--   ,
--  [0.98751,0.011031,- 0.032912,0.15367]]

--S 19 of 27
mB1(1,1) := -1;
 

                                                                Type: Integer
--R 
--R
--R                                                                Type: Integer
--E 19

--S 20 of 27
nagEigenvalues(mA1,mB1)
 
   There are no library operations named nagEigenvalues 
      Use HyperDoc Browse or issue
                           )what op nagEigenvalues
      to learn if there is any operation containing " nagEigenvalues " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvalues with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvalues 
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvalues with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20

--S 21 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Integer to List Complex Float for value
   - 1

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Integer to List Complex Float for value
--R   - 1
--R
--E 21
--       [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]

--S 22 of 27
vv3 := nagEigenvectors(mA1,mB1);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 22

--S 23 of 27
vv3.eigenvalues
 
   There are no library operations named vv3 
      Use HyperDoc Browse or issue
                                )what op vv3
      to learn if there is any operation containing " vv3 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv3 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv3 
--R      Use HyperDoc Browse or issue
--R                                )what op vv3
--R      to learn if there is any operation containing " vv3 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv3 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23


--S 24 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Integer to List Complex Float for value
   - 1

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Integer to List Complex Float for value
--R   - 1
--R
--E 24
--       [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]

--S 25 of 27 used to work?
vv3.eigenvectors :: List Vector Complex Float
 
   There are no library operations named vv3 
      Use HyperDoc Browse or issue
                                )what op vv3
      to learn if there is any operation containing " vv3 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv3 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv3 
--R      Use HyperDoc Browse or issue
--R                                )what op vv3
--R      to learn if there is any operation containing " vv3 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv3 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25
--  [[- 0.034577,0.63045,- 0.75202,0.1892],
--   [0.17876,- 0.73845,0.047413,0.64845],
--
--    [0.80838, - 0.00095133 + 0.47557 %i, - 0.20354 - 0.21737 %i,
--     0.15404 + 0.089179 %i]
--    ,
--
--    [0.80838, - 0.00095133 - 0.47557 %i, - 0.20354 + 0.21737 %i,
--     0.15404 - 0.089179 %i]
--   ]

--S 26 of 27
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

--S 27 of 27
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 27
)spool 
 
Starts dribbling to op1.output (2009/2/17, 17:55:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 21
R := SQMATRIX(2, INT)
 

   (1)  SquareMatrix(2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  SquareMatrix(2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 21
t := operator("tilde") :: OP(R)
 

   (2)  tilde
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R   (2)  tilde
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 2

--S 3 of 21
)set expose add constructor Operator
 
   Operator is now explicitly exposed in frame initial 
--R 
--R   Operator is now explicitly exposed in frame initial 
--E 3

--S 4 of 21
evaluate(t, m +-> transpose m)
 

   (3)  tilde
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R   (3)  tilde
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 4

--S 5 of 21
s : R := matrix [[0, 1], [1, 0]]
 

        +0  1+
   (4)  |    |
        +1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  1+
--R   (4)  |    |
--R        +1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 5

--S 6 of 21
rho := t * s
 

             +0  1+
   (5)  tilde|    |
             +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R             +0  1+
--R   (5)  tilde|    |
--R             +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 6

--S 7 of 21
z := rho**4 - 1
 

                   +0  1+     +0  1+     +0  1+     +0  1+
   (6)  - 1 + tilde|    |tilde|    |tilde|    |tilde|    |
                   +1  0+     +1  0+     +1  0+     +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R                   +0  1+     +0  1+     +0  1+     +0  1+
--R   (6)  - 1 + tilde|    |tilde|    |tilde|    |tilde|    |
--R                   +1  0+     +1  0+     +1  0+     +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 7

--S 8 of 21
m:R := matrix [[1, 2], [3, 4]]
 

        +1  2+
   (7)  |    |
        +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 21
z m
 

        +0  0+
   (8)  |    |
        +0  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  0+
--R   (8)  |    |
--R        +0  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 9

--S 10 of 21
rho m
 

        +3  1+
   (9)  |    |
        +4  2+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +3  1+
--R   (9)  |    |
--R        +4  2+
--R                                                Type: SquareMatrix(2,Integer)
--E 10

--S 11 of 21
rho rho m
 

         +4  3+
   (10)  |    |
         +2  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +4  3+
--R   (10)  |    |
--R         +2  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 11

--S 12 of 21
(rho**3) m
 

         +2  4+
   (11)  |    |
         +1  3+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +2  4+
--R   (11)  |    |
--R         +1  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 12

--S 13 of 21
b := t * s - s * t
 

           +0  1+             +0  1+
   (12)  - |    |tilde + tilde|    |
           +1  0+             +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R           +0  1+             +0  1+
--R   (12)  - |    |tilde + tilde|    |
--R           +1  0+             +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 13

--S 14 of 21
b m
 

         +1  - 3+
   (13)  |      |
         +3  - 1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +1  - 3+
--R   (13)  |      |
--R         +3  - 1+
--R                                                Type: SquareMatrix(2,Integer)
--E 14

--S 15 of 21
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 21
dx := operator("D") :: OP(POLY FRAC INT)
 

   (15)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (15)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 16

--S 17 of 21
evaluate(dx, p +-> D(p, 'x))
 

   (16)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (16)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 17

--S 18 of 21
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 21
L 15
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

   (18)
     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
       2048          2048           2048           2048          2048
   + 
       2909907  5   255255  3   6435
     - ------- x  + ------ x  - ---- x
         2048        2048       2048
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R   (18)
--R     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
--R     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       2909907  5   255255  3   6435
--R     - ------- x  + ------ x  - ---- x
--R         2048        2048       2048
--R                                            Type: Polynomial Fraction Integer
--E 18

--S 20 of 21
E 15
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                        2      2
   (19)  240 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                        2      2
--R   (19)  240 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 20

--S 21 of 21
(E 15)(L 15)
 

   (20)  0
                                            Type: Polynomial Fraction Integer
--R 
--R
--R   (20)  0
--R                                            Type: Polynomial Fraction Integer
--E 21
)spool 
 
Starts dribbling to kuipers.output (2009/2/17, 17:48:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 30
R1:=matrix([[cos a, sin a, 0],[-sin a, cos a, 0],[0, 0, 1]])
 

        + cos(a)   sin(a)  0+
        |                   |
   (1)  |- sin(a)  cos(a)  0|
        |                   |
        +   0        0     1+
                                              Type: Matrix Expression Integer
--R 
--R
--R        + cos(a)   sin(a)  0+
--R        |                   |
--R   (1)  |- sin(a)  cos(a)  0|
--R        |                   |
--R        +   0        0     1+
--R                                              Type: Matrix Expression Integer
--E 1

--S 2 of 30
R2:=matrix([[cos b, 0, -sin b],[0, 1, 0],[sin b, 0, cos b]])
 

        +cos(b)  0  - sin(b)+
        |                   |
   (2)  |  0     1     0    |
        |                   |
        +sin(b)  0   cos(b) +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +cos(b)  0  - sin(b)+
--R        |                   |
--R   (2)  |  0     1     0    |
--R        |                   |
--R        +sin(b)  0   cos(b) +
--R                                              Type: Matrix Expression Integer
--E 2

--S 3 of 30
R:=R2*R1
 

        +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
        |                                    |
   (3)  |  - sin(a)       cos(a)        0    |
        |                                    |
        +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
--R        |                                    |
--R   (3)  |  - sin(a)       cos(a)        0    |
--R        |                                    |
--R        +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
--R                                              Type: Matrix Expression Integer
--E 3

--S 4 of 30
V:=matrix([[x1],[y1],[z1]])
 

        +x1+
        |  |
   (4)  |y1|
        |  |
        +z1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x1+
--R        |  |
--R   (4)  |y1|
--R        |  |
--R        +z1+
--R                                              Type: Matrix Polynomial Integer
--E 4

--S 5 of 30
E:=R*V=V
 

        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b)+  +x1+
        |                                               |  |  |
   (5)  |            - x1 sin(a) + y1 cos(a)            |= |y1|
        |                                               |  |  |
        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b)   +  +z1+
                                     Type: Equation Matrix Expression Integer
--R 
--R
--R        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b)+  +x1+
--R        |                                               |  |  |
--R   (5)  |            - x1 sin(a) + y1 cos(a)            |= |y1|
--R        |                                               |  |  |
--R        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b)   +  +z1+
--R                                     Type: Equation Matrix Expression Integer
--E 5

--S 6 of 30
F:=lhs(E)-rhs(E)
 

        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+
        |                                                    |
   (6)  |            - x1 sin(a) + y1 cos(a) - y1            |
        |                                                    |
        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+
--R        |                                                    |
--R   (6)  |            - x1 sin(a) + y1 cos(a) - y1            |
--R        |                                                    |
--R        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +
--R                                              Type: Matrix Expression Integer
--E 6

--S 7 of 30
G:=F=matrix([[0],[0],[0]])
 

        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+  +0+
        |                                                    |  | |
   (7)  |            - x1 sin(a) + y1 cos(a) - y1            |= |0|
        |                                                    |  | |
        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +  +0+
                                     Type: Equation Matrix Expression Integer
--R 
--R
--R        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+  +0+
--R        |                                                    |  | |
--R   (7)  |            - x1 sin(a) + y1 cos(a) - y1            |= |0|
--R        |                                                    |  | |
--R        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +  +0+
--R                                     Type: Equation Matrix Expression Integer
--E 7

--S 8 of 30
H:=elt(F,2,1)
 

   (8)  - x1 sin(a) + y1 cos(a) - y1
                                                     Type: Expression Integer
--R 
--R
--R   (8)  - x1 sin(a) + y1 cos(a) - y1
--R                                                     Type: Expression Integer
--E 8

--S 9 of 30
x1:=k
 

   (9)  k
                                                             Type: Variable k
--R 
--R
--R   (9)  k
--R                                                             Type: Variable k
--E 9

--S 10 of 30
J:=subst(H,'x1=k)
 

   (10)  - k sin(a) + y1 cos(a) - y1
                                                     Type: Expression Integer
--R 
--R
--R   (10)  - k sin(a) + y1 cos(a) - y1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 30
L:=solve(J,y1)
 

               k sin(a)
   (11)  [y1= ----------]
              cos(a) - 1
                                       Type: List Equation Expression Integer
--R 
--R
--R               k sin(a)
--R   (11)  [y1= ----------]
--R              cos(a) - 1
--R                                       Type: List Equation Expression Integer
--E 11

--S 12 of 30
y1:=rhs(first(solve(J,y1)))
 

          k sin(a)
   (12)  ----------
         cos(a) - 1
                                                     Type: Expression Integer
--R 
--R
--R          k sin(a)
--R   (12)  ----------
--R         cos(a) - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 30
H1:=elt(F,3,1)
 

   (13)  (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1
                                                     Type: Expression Integer
--R 
--R
--R   (13)  (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 30
J1:=subst(H1,['x1=x1, 'y1=y1])
 

   (14)
                2           2
       (k sin(a)  + k cos(a)  - k cos(a))sin(b) + (z1 cos(a) - z1)cos(b)
     + 
       - z1 cos(a) + z1
  /
     cos(a) - 1
                                                     Type: Expression Integer
--R 
--R
--R   (14)
--R                2           2
--R       (k sin(a)  + k cos(a)  - k cos(a))sin(b) + (z1 cos(a) - z1)cos(b)
--R     + 
--R       - z1 cos(a) + z1
--R  /
--R     cos(a) - 1
--R                                                     Type: Expression Integer
--E 14

--S 15 of 30
z1:=simplify(rhs(first(solve(J1,z1))))
 

          k sin(b)
   (15)  ----------
         cos(b) - 1
                                                     Type: Expression Integer
--R 
--R
--R          k sin(b)
--R   (15)  ----------
--R         cos(b) - 1
--R                                                     Type: Expression Integer
--E 15

--S 16 of 30
[x1,y1,z1]
 

             k sin(a)   k sin(b)
   (16)  [k,----------,----------]
            cos(a) - 1 cos(b) - 1
                                                Type: List Expression Integer
--R 
--R
--R             k sin(a)   k sin(b)
--R   (16)  [k,----------,----------]
--R            cos(a) - 1 cos(b) - 1
--R                                                Type: List Expression Integer
--E 16

--S 17 of 30
y1:=eval(y1,[k=-1])
 

             sin(a)
   (17)  - ----------
           cos(a) - 1
                                                     Type: Expression Integer
--R 
--R
--R             sin(a)
--R   (17)  - ----------
--R           cos(a) - 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 30
z1:=eval(z1,[k=-1])
 

             sin(b)
   (18)  - ----------
           cos(b) - 1
                                                     Type: Expression Integer
--R 
--R
--R             sin(b)
--R   (18)  - ----------
--R           cos(b) - 1
--R                                                     Type: Expression Integer
--E 18

--S 19 of 30
[x1,y1,z1]
 

                sin(a)       sin(b)
   (19)  [k,- ----------,- ----------]
              cos(a) - 1   cos(b) - 1
                                                Type: List Expression Integer
--R 
--R
--R                sin(a)       sin(b)
--R   (19)  [k,- ----------,- ----------]
--R              cos(a) - 1   cos(b) - 1
--R                                                Type: List Expression Integer
--E 19

--S 20 of 30
RSQ:SQMATRIX(3,EXPR(INT)):=R
 

         +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
         |                                    |
   (20)  |  - sin(a)       cos(a)        0    |
         |                                    |
         +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
                                     Type: SquareMatrix(3,Expression Integer)
--R 
--R
--R         +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
--R         |                                    |
--R   (20)  |  - sin(a)       cos(a)        0    |
--R         |                                    |
--R         +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
--R                                     Type: SquareMatrix(3,Expression Integer)
--E 20

--S 21 of 30
TR:=trace(RSQ)
 

   (21)  (cos(a) + 1)cos(b) + cos(a)
                                                     Type: Expression Integer
--R 
--R
--R   (21)  (cos(a) + 1)cos(b) + cos(a)
--R                                                     Type: Expression Integer
--E 21

--S 22 of 30
TREQ:=TR=1+2*cos(c)
 

   (22)  (cos(a) + 1)cos(b) + cos(a)= 2cos(c) + 1
                                            Type: Equation Expression Integer
--R 
--R
--R   (22)  (cos(a) + 1)cos(b) + cos(a)= 2cos(c) + 1
--R                                            Type: Equation Expression Integer
--E 22

--S 23 of 30
c:=rhs(first(solve(TREQ,c)))
 

              (cos(a) + 1)cos(b) + cos(a) - 1
   (23)  acos(-------------------------------)
                             2
                                                     Type: Expression Integer
--R 
--R
--R              (cos(a) + 1)cos(b) + cos(a) - 1
--R   (23)  acos(-------------------------------)
--R                             2
--R                                                     Type: Expression Integer
--E 23

--S 24 of 30
x1v:=eval(x1,k=-1)
 

   (24)  - 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (24)  - 1
--R                                                     Type: Polynomial Integer
--E 24

--S 25 of 30
y1v:=numeric(eval(y1,[a=%pi/6]))
 

   (25)  3.7320508075 688772936
                                                                  Type: Float
--R 
--R
--R   (25)  3.7320508075 688772936
--R                                                                  Type: Float
--E 25

--S 26 of 30
z1v:=numeric(eval(z1,[k=-1,b=%pi/3]))
 

   (26)  1.7320508075 688772935
                                                                  Type: Float
--R 
--R
--R   (26)  1.7320508075 688772935
--R                                                                  Type: Float
--E 26

--S 27 of 30
[x1v, y1v, z1v]
 

   (27)  [- 1.0,3.7320508075 688772936,1.7320508075 688772935]
                                                  Type: List Polynomial Float
--R 
--R
--R   (27)  [- 1.0,3.7320508075 688772936,1.7320508075 688772935]
--R                                                  Type: List Polynomial Float
--E 27

--S 28 of 30
c1v:=numeric(eval(c,[a=%pi/6,b=%pi/3]))
 

   (28)  1.1598041770 494147762
                                                                  Type: Float
--R 
--R
--R   (28)  1.1598041770 494147762
--R                                                                  Type: Float
--E 28

--S 29 of 30
c1v*180/%pi
 

   (29)  66.4518844065 75160021
                                                                  Type: Float
--R 
--R
--R   (29)  66.4518844065 75160021
--R                                                                  Type: Float
--E 29

--S 30 of 30
rv:=eval(R,[a=%pi/6,b=%pi/3])
 

         + +-+           +-++
         |\|3    1      \|3 |
         |----   -    - ----|
         |  4    4        2 |
         |                  |
         |       +-+        |
   (30)  |  1   \|3         |
         |- -   ----    0   |
         |  2     2         |
         |                  |
         |       +-+        |
         | 3    \|3     1   |
         | -    ----    -   |
         + 4      4     2   +
                                              Type: Matrix Expression Integer
--R 
--R
--R         + +-+           +-++
--R         |\|3    1      \|3 |
--R         |----   -    - ----|
--R         |  4    4        2 |
--R         |                  |
--R         |       +-+        |
--R   (30)  |  1   \|3         |
--R         |- -   ----    0   |
--R         |  2     2         |
--R         |                  |
--R         |       +-+        |
--R         | 3    \|3     1   |
--R         | -    ----    -   |
--R         + 4      4     2   +
--R                                              Type: Matrix Expression Integer
--E 30
)spool 
 
Starts dribbling to exlimit.output (2009/2/17, 17:45:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 13
limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)
 

          1
   (1)  - -
          2
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R          1
--R   (1)  - -
--R          2
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 1

)clear all
 
   All user variables and function definitions have been cleared.

--S 2 of 13
complexLimit((2 + z)/(1 - z),z = %infinity)
 

   (1)  - 1
                         Type: OnePointCompletion Fraction Polynomial Integer
--R 
--R
--R   (1)  - 1
--R                         Type: OnePointCompletion Fraction Polynomial Integer
--E 2

--S 3 of 13
limit(sin(x)/x,x = %plusInfinity)
 

   (2)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (2)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 3

--S 4 of 13
complexLimit(sin(x)/x,x = %infinity)
 

   (3)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (3)  "failed"
--R                                                    Type: Union("failed",...)
--E 4

)clear all
 
   All user variables and function definitions have been cleared.

--S 5 of 13
limit(x * log(x),x = 0,"right")
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 13
limit(x * log(x),x = 0)
 

   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 6

)clear all
 
   All user variables and function definitions have been cleared.

--S 7 of 13
limit(sqrt(y**2)/y,y = 0)
 

   (1)  [leftHandLimit= - 1,rightHandLimit= 1]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (1)  [leftHandLimit= - 1,rightHandLimit= 1]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 7

--S 8 of 13
limit(sqrt(1 - cos(t))/t,t = 0)
 

                            1                    1
   (2)  [leftHandLimit= - ----,rightHandLimit= ----]
                           +-+                  +-+
                          \|2                  \|2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                            1                    1
--R   (2)  [leftHandLimit= - ----,rightHandLimit= ----]
--R                           +-+                  +-+
--R                          \|2                  \|2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 8

)clear all
 
   All user variables and function definitions have been cleared.

--S 9 of 13
limit(sqrt(3*x**2 + 1)/(5*x),x = %plusInfinity)
 

         +-+
        \|3
   (1)  ----
          5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         +-+
--R        \|3
--R   (1)  ----
--R          5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 9

--S 10 of 13
limit(sqrt(3*x**2 + 1)/(5*x),x = %minusInfinity)
 

           +-+
          \|3
   (2)  - ----
            5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R           +-+
--R          \|3
--R   (2)  - ----
--R            5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 10

)clear all
 
   All user variables and function definitions have been cleared.

--S 11 of 13
limit(sinh(a*x)/tan(b*x),x = 0)
 

        a
   (1)  -
        b
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        a
--R   (1)  -
--R        b
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 11

)clear all
 
   All user variables and function definitions have been cleared.

--S 12 of 13
limit(z * sin(1/z),z = 0)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 12

--S 13 of 13
complexLimit(z * sin(1/z),z = 0)
 

   (2)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (2)  "failed"
--R                                                    Type: Union("failed",...)
--E 13
)spool 
 
Starts dribbling to biquat.output (2009/2/17, 17:43:57).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 

--S 1 of 43
C:=Complex Expression Integer
 

   (1)  Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Complex Expression Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 43
Q:=Quaternion C
 

   (2)  Quaternion Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (2)  Quaternion Complex Expression Integer
--R                                                                 Type: Domain
--E 2

--S 3 of 43
q:Q:=quatern(q0,q1,q2,q3)
 

   (3)  q0 + q1 i + q2 j + q3 k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (3)  q0 + q1 i + q2 j + q3 k
--R                                  Type: Quaternion Complex Expression Integer
--E 3


--S 4 of 43
qlist(l:List C):Q==quatern(1.1,1.2,1.3,1.4)
 
   Function declaration qlist : List Complex Expression Integer -> 
      Quaternion Complex Expression Integer has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration qlist : List Complex Expression Integer -> 
--R      Quaternion Complex Expression Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 4


--S 5 of 43
listq(x:Q):List C == [real x, imagI x, imagJ x, imagK x]
 
   Function declaration listq : Quaternion Complex Expression Integer
       -> List Complex Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration listq : Quaternion Complex Expression Integer
--R       -> List Complex Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 5


--S 6 of 43
matrixq(x:Q):Matrix C == matrix _
             [[real x + %i*imagI(x), imagJ x + %i*imagK(x)],_
             [-imagJ(x) + %i*imagK(x), real x - %i*imagI(x)]]
 
   Function declaration matrixq : Quaternion Complex Expression Integer
       -> Matrix Complex Expression Integer has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration matrixq : Quaternion Complex Expression Integer
--R       -> Matrix Complex Expression Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 6


--S 7 of 43
sig0:=quatern(1,0,0,0)::Q
 

   (7)  1
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (7)  1
--R                                  Type: Quaternion Complex Expression Integer
--E 7

--S 8 of 43
sig1:=%i*quatern(0,0,0,1)::Q
 

   (8)  %i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (8)  %i k
--R                                  Type: Quaternion Complex Expression Integer
--E 8

--S 9 of 43
sig2:=%i*quatern(0,0,1,0)::Q
 

   (9)  %i j
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (9)  %i j
--R                                  Type: Quaternion Complex Expression Integer
--E 9

--S 10 of 43
sig3:=-%i*quatern(0,1,0,0)::Q
 

   (10)  - %i i
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (10)  - %i i
--R                                  Type: Quaternion Complex Expression Integer
--E 10


--S 11 of 43
siglist(x:Q):List C == [real x, -imagK(x)*%i, -imagJ(x)*%i, %i*imagI(x)]
 
   Function declaration siglist : Quaternion Complex Expression Integer
       -> List Complex Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration siglist : Quaternion Complex Expression Integer
--R       -> List Complex Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 11


--S 12 of 43
D(q:Q,x:Symbol,y:Symbol,z:Symbol):Q==sig1*D(q,x)+sig2*D(q,y)+sig3*D(q,z)
 
   Function declaration D : (Quaternion Complex Expression Integer,
      Symbol,Symbol,Symbol) -> Quaternion Complex Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration D : (Quaternion Complex Expression Integer,
--R      Symbol,Symbol,Symbol) -> Quaternion Complex Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 12


--S 13 of 43
Ft:=operator 'Ft
 

   (13)  Ft
                                                          Type: BasicOperator
--R 
--R
--R   (13)  Ft
--R                                                          Type: BasicOperator
--E 13

--S 14 of 43
Fx:=operator 'Fx
 

   (14)  Fx
                                                          Type: BasicOperator
--R 
--R
--R   (14)  Fx
--R                                                          Type: BasicOperator
--E 14

--S 15 of 43
Fy:=operator 'Fy
 

   (15)  Fy
                                                          Type: BasicOperator
--R 
--R
--R   (15)  Fy
--R                                                          Type: BasicOperator
--E 15

--S 16 of 43
Fz:=operator 'Fz
 

   (16)  Fz
                                                          Type: BasicOperator
--R 
--R
--R   (16)  Fz
--R                                                          Type: BasicOperator
--E 16


--S 17 of 43
F:Q:=Ft(x,y,z)*sig0+Fx(x,y,z)*sig1+Fy(x,y,z)*sig2+Fz(x,y,z)*sig3
 

   (17)  Ft(x,y,z) - Fz(x,y,z)%i i + Fy(x,y,z)%i j + Fx(x,y,z)%i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (17)  Ft(x,y,z) - Fz(x,y,z)%i i + Fy(x,y,z)%i j + Fx(x,y,z)%i k
--R                                  Type: Quaternion Complex Expression Integer
--E 17


--S 18 of 43
siglist(D(F,x,y,z))
 
   Compiling function D with type (Quaternion Complex Expression 
      Integer,Symbol,Symbol,Symbol) -> Quaternion Complex Expression 
      Integer 
   Compiling function siglist with type Quaternion Complex Expression 
      Integer -> List Complex Expression Integer 

   (18)
   [Fz  (x,y,z) + Fy  (x,y,z) + Fx  (x,y,z),
      ,3            ,2            ,1
    Ft  (x,y,z) + (Fz  (x,y,z) - Fy  (x,y,z))%i,
      ,1             ,2            ,3
    Ft  (x,y,z) + (- Fz  (x,y,z) + Fx  (x,y,z))%i,
      ,2               ,1            ,3
    Ft  (x,y,z) + (Fy  (x,y,z) - Fx  (x,y,z))%i]
      ,3             ,1            ,2
                                        Type: List Complex Expression Integer
--R 
--R   Compiling function D with type (Quaternion Complex Expression 
--R      Integer,Symbol,Symbol,Symbol) -> Quaternion Complex Expression 
--R      Integer 
--R   Compiling function siglist with type Quaternion Complex Expression 
--R      Integer -> List Complex Expression Integer 
--R
--R   (18)
--R   [Fz  (x,y,z) + Fy  (x,y,z) + Fx  (x,y,z),
--R      ,3            ,2            ,1
--R    Ft  (x,y,z) + (Fz  (x,y,z) - Fy  (x,y,z))%i,
--R      ,1             ,2            ,3
--R    Ft  (x,y,z) + (- Fz  (x,y,z) + Fx  (x,y,z))%i,
--R      ,2               ,1            ,3
--R    Ft  (x,y,z) + (Fy  (x,y,z) - Fx  (x,y,z))%i]
--R      ,3             ,1            ,2
--R                                        Type: List Complex Expression Integer
--E 18


--S 19 of 43
rot(theta:Expression Integer,q:Q):Q==cos(theta/2)-%i::Q*q*sin(theta/2)
 
   Function declaration rot : (Expression Integer,Quaternion Complex 
      Expression Integer) -> Quaternion Complex Expression Integer has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration rot : (Expression Integer,Quaternion Complex 
--R      Expression Integer) -> Quaternion Complex Expression Integer has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 19


--S 20 of 43
((x:Q)/(y:Q)):Q == x*inv(y)
 
   Function declaration ?/? : (Quaternion Complex Expression Integer,
      Quaternion Complex Expression Integer) -> Quaternion Complex 
      Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration ?/? : (Quaternion Complex Expression Integer,
--R      Quaternion Complex Expression Integer) -> Quaternion Complex 
--R      Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 20

--S 21 of 43
abs(q:Q):C == sqrt((q*conjugate(q))::C)
 
   Function declaration abs : Quaternion Complex Expression Integer -> 
      Complex Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration abs : Quaternion Complex Expression Integer -> 
--R      Complex Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 21

--S 22 of 43
exp(q:Q):Q == (_
  q-conjugate(q)=0 => exp( (q+conjugate(q))::C/2)$C * sig0; _
  exp( (q+conjugate(q))::C/2)$C * (sig0*cos(abs(q)) +_
  (q-conjugate(q))/abs(q-conjugate(q))*sin(abs(q))) )
 
   Function declaration exp : Quaternion Complex Expression Integer -> 
      Quaternion Complex Expression Integer has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration exp : Quaternion Complex Expression Integer -> 
--R      Quaternion Complex Expression Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 22


--S 23 of 43
qx:=sig1
 

   (23)  %i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (23)  %i k
--R                                  Type: Quaternion Complex Expression Integer
--E 23

--S 24 of 43
mm:=siglist(rot(2,qx))
 
   Compiling function / with type (Quaternion Complex Expression 
      Integer,Quaternion Complex Expression Integer) -> Quaternion 
      Complex Expression Integer 
   There are 2 exposed and 6 unexposed library operations named cos 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op cos
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named cos 
      with argument type(s) 
                    Quaternion Complex Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function rot with type (Expression Integer,Quaternion 
      Complex Expression Integer) -> Quaternion Complex Expression 
      Integer 

   (24)
                2         3                  3          2
    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
   [-------------------------------- + ----------------------------- %i,
                  2          2                     2          2
           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
                  2         3                    3            2
    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
    ---------------------------------- + --------------------------------- %i,
                   2          2                        2          2
            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
    0, 0]
                                        Type: List Complex Expression Integer
--R 
--R   Compiling function / with type (Quaternion Complex Expression 
--R      Integer,Quaternion Complex Expression Integer) -> Quaternion 
--R      Complex Expression Integer 
--R   There are 2 exposed and 6 unexposed library operations named cos 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op cos
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named cos 
--R      with argument type(s) 
--R                    Quaternion Complex Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function rot with type (Expression Integer,Quaternion 
--R      Complex Expression Integer) -> Quaternion Complex Expression 
--R      Integer 
--R
--R   (24)
--R                2         3                  3          2
--R    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
--R   [-------------------------------- + ----------------------------- %i,
--R                  2          2                     2          2
--R           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
--R                  2         3                    3            2
--R    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
--R    ---------------------------------- + --------------------------------- %i,
--R                   2          2                        2          2
--R            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
--R    0, 0]
--R                                        Type: List Complex Expression Integer
--E 24

--S 25 of 43
nn:=siglist(exp(-%i::Q*qx))
 
   There are 2 exposed and 7 unexposed library operations named exp 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op exp
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named exp 
      with argument type(s) 
                    Quaternion Complex Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function exp with type Quaternion Complex Expression 
      Integer -> Quaternion Complex Expression Integer 
   Compiling function abs with type Quaternion Complex Expression 
      Integer -> Complex Expression Integer 

   (25)
                2         3                  3          2
    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
   [-------------------------------- + ----------------------------- %i,
                  2          2                     2          2
           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
                  2         3                    3            2
    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
    ---------------------------------- + --------------------------------- %i,
                   2          2                        2          2
            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
    0, 0]
                                        Type: List Complex Expression Integer
--R 
--R   There are 2 exposed and 7 unexposed library operations named exp 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op exp
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named exp 
--R      with argument type(s) 
--R                    Quaternion Complex Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function exp with type Quaternion Complex Expression 
--R      Integer -> Quaternion Complex Expression Integer 
--R   Compiling function abs with type Quaternion Complex Expression 
--R      Integer -> Complex Expression Integer 
--R
--R   (25)
--R                2         3                  3          2
--R    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
--R   [-------------------------------- + ----------------------------- %i,
--R                  2          2                     2          2
--R           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
--R                  2         3                    3            2
--R    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
--R    ---------------------------------- + --------------------------------- %i,
--R                   2          2                        2          2
--R            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
--R    0, 0]
--R                                        Type: List Complex Expression Integer
--E 25

--S 26 of 43
(mm=nn)@Boolean
 

   (26)  true
                                                                Type: Boolean
--R 
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26


--S 27 of 43
qnv:=q1*sig1+q2*sig2+sqrt(1-q1^2-q2^2)*sig3
 

            +---------------+
            |    2     2
   (27)  - \|- q2  - q1  + 1 %i i + q2 %i j + q1 %i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R            +---------------+
--R            |    2     2
--R   (27)  - \|- q2  - q1  + 1 %i i + q2 %i j + q1 %i k
--R                                  Type: Quaternion Complex Expression Integer
--E 27


--S 28 of 43
theta:=_\theta
 

   (28)  \theta
                                                        Type: Variable \theta
--R 
--R
--R   (28)  \theta
--R                                                        Type: Variable \theta
--E 28

--S 29 of 43
testqeq:=map(simplify,siglist(rot(theta,qnv)-exp((-theta/2)*%i*qnv)))_
         ::List Expression Complex Integer
 

   (29)
           +-------+
           |      2
          \|\theta          \theta
   [- cos(----------) + cos(------),
               2               2
                        +-------+
          +-------+     |      2
          |      2     \|\theta                       \theta
    %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
                            2                            2
    ---------------------------------------------------------,
                              \theta
                        +-------+
          +-------+     |      2
          |      2     \|\theta                       \theta
    %i q2\|\theta  sin(----------) - %i \theta q2 sin(------)
                            2                            2
    ---------------------------------------------------------,
                              \theta

                                            +-------+
            +---------------+ +-------+     |      2
            |    2     2      |      2     \|\theta
         %i\|- q2  - q1  + 1 \|\theta  sin(----------)
                                                2
       + 
                                 +---------------+
                         \theta  |    2     2
         - %i \theta sin(------)\|- q2  - q1  + 1
                            2
    /
       \theta
     ]
                                        Type: List Expression Complex Integer
--R 
--R
--R   (29)
--R           +-------+
--R           |      2
--R          \|\theta          \theta
--R   [- cos(----------) + cos(------),
--R               2               2
--R                        +-------+
--R          +-------+     |      2
--R          |      2     \|\theta                       \theta
--R    %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
--R                            2                            2
--R    ---------------------------------------------------------,
--R                              \theta
--R                        +-------+
--R          +-------+     |      2
--R          |      2     \|\theta                       \theta
--R    %i q2\|\theta  sin(----------) - %i \theta q2 sin(------)
--R                            2                            2
--R    ---------------------------------------------------------,
--R                              \theta
--R
--R                                            +-------+
--R            +---------------+ +-------+     |      2
--R            |    2     2      |      2     \|\theta
--R         %i\|- q2  - q1  + 1 \|\theta  sin(----------)
--R                                                2
--R       + 
--R                                 +---------------+
--R                         \theta  |    2     2
--R         - %i \theta sin(------)\|- q2  - q1  + 1
--R                            2
--R    /
--R       \theta
--R     ]
--R                                        Type: List Expression Complex Integer
--E 29


--S 30 of 43
posthetaRule:=rule sqrt(theta^2)==theta
 

          +------+
          |     2
   (30)  \|theta   == theta
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R          +------+
--R          |     2
--R   (30)  \|theta   == theta
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 30


--S 31 of 43
map(x+->posthetaRule(x), [0,sqrt(theta^2),0,sqrt(theta^2)])
 

   (31)  [0,\theta,0,\theta]
                                                Type: List Expression Integer
--R 
--R
--R   (31)  [0,\theta,0,\theta]
--R                                                Type: List Expression Integer
--E 31


--S 32 of 43
posthetaRule testqeq.1
 
   There are no library operations named posthetaRule 
      Use HyperDoc Browse or issue
                            )what op posthetaRule
      to learn if there is any operation containing " posthetaRule " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      posthetaRule with argument type(s) 
                         Expression Complex Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named posthetaRule 
--R      Use HyperDoc Browse or issue
--R                            )what op posthetaRule
--R      to learn if there is any operation containing " posthetaRule " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      posthetaRule with argument type(s) 
--R                         Expression Complex Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 32


--S 33 of 43
[posthetaRule (testqeq.i::Expression Integer) for i in 1..1]
 

   (32)  [0]
                                                Type: List Expression Integer
--R 
--R
--R   (32)  [0]
--R                                                Type: List Expression Integer
--E 33


--S 34 of 43
[posthetaRule (testqeq.i::Expression Integer) for i in 1..4]
 
 
Daly Bug
   Cannot convert from type Expression Complex Integer to Expression 
      Integer for value
                       +-------+
         +-------+     |      2
         |      2     \|\theta                       \theta
   %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
                           2                            2
   ---------------------------------------------------------
                             \theta

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Expression Complex Integer to Expression 
--R      Integer for value
--R                       +-------+
--R         +-------+     |      2
--R         |      2     \|\theta                       \theta
--R   %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
--R                           2                            2
--R   ---------------------------------------------------------
--R                             \theta
--R
--E 34


--S 35 of 43
)show RewriteRule
 
 RewriteRule(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base))  is a domain constructor
 Abbreviation for RewriteRule is RULE 
 This constructor is exposed in this frame.
 Issue )edit rule.spad.pamphlet to see algebra source code for RULE 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                coerce : Equation F -> %
 coerce : % -> OutputForm              elt : (%,F,PositiveInteger) -> F
 ?.? : (%,F) -> F                      hash : % -> SingleInteger
 latex : % -> String                   lhs : % -> F
 pattern : % -> Pattern Base           retract : % -> Equation F
 rhs : % -> F                          rule : (F,F,List Symbol) -> %
 rule : (F,F) -> %                     ?~=? : (%,%) -> Boolean
 quotedOperators : % -> List Symbol
 retractIfCan : % -> Union(Equation F,"failed")
 suchThat : (%,List Symbol,(List F -> Boolean)) -> %

--R 
--R RewriteRule(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base))  is a domain constructor
--R Abbreviation for RewriteRule is RULE 
--R This constructor is exposed in this frame.
--R Issue )edit rule.spad.pamphlet to see algebra source code for RULE 
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean                coerce : Equation F -> %
--R coerce : % -> OutputForm              elt : (%,F,PositiveInteger) -> F
--R ?.? : (%,F) -> F                      hash : % -> SingleInteger
--R latex : % -> String                   lhs : % -> F
--R pattern : % -> Pattern Base           retract : % -> Equation F
--R rhs : % -> F                          rule : (F,F,List Symbol) -> %
--R rule : (F,F) -> %                     ?~=? : (%,%) -> Boolean
--R quotedOperators : % -> List Symbol
--R retractIfCan : % -> Union(Equation F,"failed")
--R suchThat : (%,List Symbol,(List F -> Boolean)) -> %
--R
--E 35


--S 36 of 43
Complex Integer has PatternMatchable Integer
 

   (33)  true
                                                                Type: Boolean
--R 
--R
--R   (33)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 43
Expression Complex Integer has FunctionSpace Complex Integer
 

   (34)  true
                                                                Type: Boolean
--R 
--R
--R   (34)  true
--R                                                                Type: Boolean
--E 37

--S 38 of 43
Expression Complex Integer has PatternMatchable Integer
 

   (35)  true
                                                                Type: Boolean
--R 
--R
--R   (35)  true
--R                                                                Type: Boolean
--E 38


--S 39 of 43
posxRule:=(rule sqrt('theta^2)==theta)$RewriteRule(Integer,Complex Integer,_
            Expression Complex Integer)
 

          +------+
          |     2
   (36)  \|theta   == theta
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R 
--R
--R          +------+
--R          |     2
--R   (36)  \|theta   == theta
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 39

--S 40 of 43
map(x+->posxRule x, testqeq)
 

   (37)  [0,0,0,0]
                                        Type: List Expression Complex Integer
--R 
--R
--R   (37)  [0,0,0,0]
--R                                        Type: List Expression Complex Integer
--E 40


--S 41 of 43
test (sqrt(x)^2=x)
 

   (38)  true
                                                                Type: Boolean
--R 
--R
--R   (38)  true
--R                                                                Type: Boolean
--E 41


--S 42 of 43
test (sqrt(sqrt(x)^2)=sqrt(x))
 

   (39)  true
                                                                Type: Boolean
--R 
--R
--R   (39)  true
--R                                                                Type: Boolean
--E 42


--S 43 of 43
eval(eval(testqeq,theta=sqrt(beta)),sqrt(beta)=theta)
 

   (40)  [0,0,0,0]
                                        Type: List Expression Complex Integer
--R 
--R
--R   (40)  [0,0,0,0]
--R                                        Type: List Expression Complex Integer
--E 43

)spool 
 
Starts dribbling to schaum25.output (2009/2/17, 17:59:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(%e^(a*x),x)
 

          a x
        %e
   (1)  -----
          a
                                          Type: Union(Expression Integer,...)
--R
--R          a x
--R        %e
--R   (1)  -----
--R          a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=%e^(a*x)/a
 

          a x
        %e
   (2)  -----
          a
                                                     Type: Expression Integer
--R
--R          a x
--R        %e
--R   (2)  -----
--R          a
--R                                                     Type: Expression Integer
--E

--S 3      14:509 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*%e^(a*x),x)
 

                   a x
        (a x - 1)%e
   (1)  --------------
               2
              a
                                          Type: Union(Expression Integer,...)
--R
--R                   a x
--R        (a x - 1)%e
--R   (1)  --------------
--R               2
--R              a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=%e^(a*x)/a*(x-1/a)
 

                   a x
        (a x - 1)%e
   (2)  --------------
               2
              a
                                                     Type: Expression Integer
--R
--R                   a x
--R        (a x - 1)%e
--R   (2)  --------------
--R               2
--R              a
--R                                                     Type: Expression Integer
--E

--S 6      14:510 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2*%e^(a*x),x)
 

          2 2              a x
        (a x  - 2a x + 2)%e
   (1)  ----------------------
                   3
                  a
                                          Type: Union(Expression Integer,...)
--R
--R          2 2              a x
--R        (a x  - 2a x + 2)%e
--R   (1)  ----------------------
--R                   3
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=%e^(a*x)/a*(x^2-(2*x)/a+2/a^2)
 

          2 2              a x
        (a x  - 2a x + 2)%e
   (2)  ----------------------
                   3
                  a
                                                     Type: Expression Integer
--R
--R          2 2              a x
--R        (a x  - 2a x + 2)%e
--R   (2)  ----------------------
--R                   3
--R                  a
--R                                                     Type: Expression Integer
--E

--S 9      14:511 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10     14:512 Axiom cannot compute this integral
aa:=integrate(x^n*%e^(a*x),x)
 

           x
         ++    %I a  n
   (1)   |   %e    %I d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++    %I a  n
--I   (1)   |   %e    %I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 11     14:513 Schaums and Axiom agree by definition
aa:=integrate(%e^(a*x)/x,x)
 

   (1)  Ei(a x)
                                          Type: Union(Expression Integer,...)
--R
--R   (1)  Ei(a x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 12     14:514 Axiom cannot compute this integral
aa:=integrate(%e^(a*x)/x^n,x)
 

           x   %I a
         ++  %e
   (1)   |   ------ d%I
        ++       n
               %I
                                          Type: Union(Expression Integer,...)
--R
--I           x   %I a
--R         ++  %e
--I   (1)   |   ------ d%I
--R        ++       n
--I               %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(1/(p+q*%e^(a*x)),x)
 

                  a x
        - log(q %e    + p) + a x
   (1)  ------------------------
                   a p
                                          Type: Union(Expression Integer,...)
--R
--R                  a x
--R        - log(q %e    + p) + a x
--R   (1)  ------------------------
--R                   a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=x/p-1/(a*p)*log(p+q*%e^(a*x))
 

                  a x
        - log(q %e    + p) + a x
   (2)  ------------------------
                   a p
                                                     Type: Expression Integer
--R
--R                  a x
--R        - log(q %e    + p) + a x
--R   (2)  ------------------------
--R                   a p
--R                                                     Type: Expression Integer
--E

--S 15     14:515 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(1/(p+q*%e^(a*x))^2,x)
 

               a x             a x                a x
        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
   (1)  ---------------------------------------------------------
                               2    a x      3
                            a p q %e    + a p
                                          Type: Union(Expression Integer,...)
--R
--R               a x             a x                a x
--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
--R   (1)  ---------------------------------------------------------
--R                               2    a x      3
--R                            a p q %e    + a p
--R                                          Type: Union(Expression Integer,...)
--E

--S 17
bb:=x/p^2+1/(a*p*(p+q*%e^(a*x)))-1/(a*p^2)*log(p+q*%e^(a*x))
 

               a x             a x                a x
        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
   (2)  ---------------------------------------------------------
                               2    a x      3
                            a p q %e    + a p
                                                     Type: Expression Integer
--R
--R               a x             a x                a x
--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
--R   (2)  ---------------------------------------------------------
--R                               2    a x      3
--R                            a p q %e    + a p
--R                                                     Type: Expression Integer
--E

--S 18     14:516 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19
aa:=integrate(1/(p*%e^(a*x)+q*%e^-(a*x)),x)
 

                   a x 2      +-----+          a x
             (p (%e   )  - q)\|- p q  + 2p q %e            a x +---+
         log(-------------------------------------)      %e   \|p q
                              a x 2                 atan(-----------)
                         p (%e   )  + q                       q
   (1)  [------------------------------------------,-----------------]
                            +-----+                        +---+
                         2a\|- p q                       a\|p q
                                     Type: Union(List Expression Integer,...)
--R
--R                   a x 2      +-----+          a x
--R             (p (%e   )  - q)\|- p q  + 2p q %e            a x +---+
--R         log(-------------------------------------)      %e   \|p q
--R                              a x 2                 atan(-----------)
--R                         p (%e   )  + q                       q
--R   (1)  [------------------------------------------,-----------------]
--R                            +-----+                        +---+
--R                         2a\|- p q                       a\|p q
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 20
bb1:=1/(a*sqrt(p*q))*atan(sqrt(p/q)*%e^(a*x))
 

                   +-+
               a x |p
        atan(%e    |- )
                  \|q
   (2)  ---------------
              +---+
            a\|p q
                                                     Type: Expression Integer
--R
--R                   +-+
--R               a x |p
--R        atan(%e    |- )
--R                  \|q
--R   (2)  ---------------
--R              +---+
--R            a\|p q
--R                                                     Type: Expression Integer
--E

--S 21
bb2:=1/(2*a*sqrt(-p*q))*log((%e^(a*x)-sqrt(-q/p))/(%e^(a*x)+sqrt(-q/p)))
 

               +---+
               |  q      a x
            -  |- -  + %e
              \|  p
        log(----------------)
              +---+
              |  q      a x
              |- -  + %e
             \|  p
   (3)  ---------------------
                 +-----+
              2a\|- p q
                                                     Type: Expression Integer
--R
--R               +---+
--R               |  q      a x
--R            -  |- -  + %e
--R              \|  p
--R        log(----------------)
--R              +---+
--R              |  q      a x
--R              |- -  + %e
--R             \|  p
--R   (3)  ---------------------
--R                 +-----+
--R              2a\|- p q
--R                                                     Type: Expression Integer
--E

--S 22
cc1:=aa.1-bb1
 

   (4)
                   a x 2      +-----+          a x                        +-+
    +---+    (p (%e   )  - q)\|- p q  + 2p q %e         +-----+       a x |p
   \|p q log(-------------------------------------) - 2\|- p q atan(%e    |- )
                              a x 2                                      \|q
                         p (%e   )  + q
   ---------------------------------------------------------------------------
                                    +-----+ +---+
                                 2a\|- p q \|p q
                                                     Type: Expression Integer
--R
--R   (4)
--R                   a x 2      +-----+          a x                        +-+
--R    +---+    (p (%e   )  - q)\|- p q  + 2p q %e         +-----+       a x |p
--R   \|p q log(-------------------------------------) - 2\|- p q atan(%e    |- )
--R                              a x 2                                      \|q
--R                         p (%e   )  + q
--R   ---------------------------------------------------------------------------
--R                                    +-----+ +---+
--R                                 2a\|- p q \|p q
--R                                                     Type: Expression Integer
--E

--S 23
cc2:=aa.2-bb1
 

               a x +---+               +-+
             %e   \|p q            a x |p
        atan(-----------) - atan(%e    |- )
                  q                   \|q
   (5)  -----------------------------------
                        +---+
                      a\|p q
                                                     Type: Expression Integer
--R
--R               a x +---+               +-+
--R             %e   \|p q            a x |p
--R        atan(-----------) - atan(%e    |- )
--R                  q                   \|q
--R   (5)  -----------------------------------
--R                        +---+
--R                      a\|p q
--R                                                     Type: Expression Integer
--E

--S 24
cc3:=aa.1-bb2
 

                                                            +---+
                                                            |  q      a x
                  a x 2      +-----+          a x        -  |- -  + %e
            (p (%e   )  - q)\|- p q  + 2p q %e             \|  p
        log(-------------------------------------) - log(----------------)
                             a x 2                         +---+
                        p (%e   )  + q                     |  q      a x
                                                           |- -  + %e
                                                          \|  p
   (6)  ------------------------------------------------------------------
                                       +-----+
                                    2a\|- p q
                                                     Type: Expression Integer
--R
--R                                                            +---+
--R                                                            |  q      a x
--R                  a x 2      +-----+          a x        -  |- -  + %e
--R            (p (%e   )  - q)\|- p q  + 2p q %e             \|  p
--R        log(-------------------------------------) - log(----------------)
--R                             a x 2                         +---+
--R                        p (%e   )  + q                     |  q      a x
--R                                                           |- -  + %e
--R                                                          \|  p
--R   (6)  ------------------------------------------------------------------
--R                                       +-----+
--R                                    2a\|- p q
--R                                                     Type: Expression Integer
--E

--S 25     14:517 Axiom cannot simplify these expressions
cc4:=aa.2-bb2
 

                       +---+
                       |  q      a x
                    -  |- -  + %e                       a x +---+
           +---+      \|  p               +-----+     %e   \|p q
        - \|p q log(----------------) + 2\|- p q atan(-----------)
                      +---+                                q
                      |  q      a x
                      |- -  + %e
                     \|  p
   (7)  ----------------------------------------------------------
                                +-----+ +---+
                             2a\|- p q \|p q
                                                     Type: Expression Integer
--R
--R                       +---+
--R                       |  q      a x
--R                    -  |- -  + %e                       a x +---+
--R           +---+      \|  p               +-----+     %e   \|p q
--R        - \|p q log(----------------) + 2\|- p q atan(-----------)
--R                      +---+                                q
--R                      |  q      a x
--R                      |- -  + %e
--R                     \|  p
--R   (7)  ----------------------------------------------------------
--R                                +-----+ +---+
--R                             2a\|- p q \|p q
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 26
aa:=integrate(%e^(a*x)*sin(b*x),x)
 

            a x                       a x
        a %e   sin(b x) - b cos(b x)%e
   (1)  ---------------------------------
                      2    2
                     b  + a
                                          Type: Union(Expression Integer,...)
--R
--R            a x                       a x
--R        a %e   sin(b x) - b cos(b x)%e
--R   (1)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27
bb:=((%e^(a*x))*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)
 

            a x                       a x
        a %e   sin(b x) - b cos(b x)%e
   (2)  ---------------------------------
                      2    2
                     b  + a
                                                     Type: Expression Integer
--R
--R            a x                       a x
--R        a %e   sin(b x) - b cos(b x)%e
--R   (2)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                                     Type: Expression Integer
--E

--S 28     14:518 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(%e^(a*x)*cos(b*x),x)
 

            a x                       a x
        b %e   sin(b x) + a cos(b x)%e
   (1)  ---------------------------------
                      2    2
                     b  + a
                                          Type: Union(Expression Integer,...)
--R
--R            a x                       a x
--R        b %e   sin(b x) + a cos(b x)%e
--R   (1)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=((%e^(a*x))*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)
 

            a x                       a x
        b %e   sin(b x) + a cos(b x)%e
   (2)  ---------------------------------
                      2    2
                     b  + a
                                                     Type: Expression Integer
--R
--R            a x                       a x
--R        b %e   sin(b x) + a cos(b x)%e
--R   (2)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                                     Type: Expression Integer
--E

--S 31     14:519 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(x*%e^(a*x)*sin(b*x),x)
 

   (1)
        2    3      2    2   a x                3    2                     a x
   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
   ---------------------------------------------------------------------------
                                  4     2 2    4
                                 b  + 2a b  + a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R        2    3      2    2   a x                3    2                     a x
--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
--R   ---------------------------------------------------------------------------
--R                                  4     2 2    4
--R                                 b  + 2a b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33
bb:=(x*%e^(a*x)*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*sin(b*x)-2*a*b*cos(b*x)))/(a^2+b^2)^2
 

   (2)
        2    3      2    2   a x                3    2                     a x
   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
   ---------------------------------------------------------------------------
                                  4     2 2    4
                                 b  + 2a b  + a
                                                     Type: Expression Integer
--R
--R   (2)
--R        2    3      2    2   a x                3    2                     a x
--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
--R   ---------------------------------------------------------------------------
--R                                  4     2 2    4
--R                                 b  + 2a b  + a
--R                                                     Type: Expression Integer
--E

--S 34     14:520 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 35
aa:=integrate(x*%e^(a*x)*cos(b*x),x)
 

   (1)
      3    2             a x                2    3      2    2           a x
   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
   -------------------------------------------------------------------------
                                 4     2 2    4
                                b  + 2a b  + a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R      3    2             a x                2    3      2    2           a x
--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
--R   -------------------------------------------------------------------------
--R                                 4     2 2    4
--R                                b  + 2a b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36
bb:=(x*%e^(a*x)*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*cos(b*x)+2*a*b*sin(b*x)))/(a^2+b^2)^2
 

   (2)
      3    2             a x                2    3      2    2           a x
   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
   -------------------------------------------------------------------------
                                 4     2 2    4
                                b  + 2a b  + a
                                                     Type: Expression Integer
--R
--R   (2)
--R      3    2             a x                2    3      2    2           a x
--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
--R   -------------------------------------------------------------------------
--R                                 4     2 2    4
--R                                b  + 2a b  + a
--R                                                     Type: Expression Integer
--E

--S 37     14:521 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 38     14:522 Schaums and Axiom agree by definition
aa:=integrate(%e^(a*x)*log(x),x)
 

          a x
        %e   log(x) - Ei(a x)
   (1)  ---------------------
                  a
                                          Type: Union(Expression Integer,...)
--R
--R          a x
--R        %e   log(x) - Ei(a x)
--R   (1)  ---------------------
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 39     14:523 Axiom cannot compute this integral
aa:=integrate(%e^(a*x)*sin(b*x)^n,x)
 

           x
         ++    %I a         n
   (1)   |   %e    sin(%I b) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++    %I a         n
--I   (1)   |   %e    sin(%I b) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 40     14:524 Axiom cannot compute this integral
aa:=integrate(%e^(a*x)*cos(b*x)^n,x)
 

           x
         ++    %I a         n
   (1)   |   %e    cos(%I b) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++    %I a         n
--I   (1)   |   %e    cos(%I b) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to fr.output (2009/2/17, 17:46:6).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 55
(x,y,z,w): FR INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 55
x := 2**8 * 78**7 * 111**3 * 74534
 

         16 10  7  3
   (2)  2  3  13 37 83 449
                                                       Type: Factored Integer
--R 
--R
--R         16 10  7  3
--R   (2)  2  3  13 37 83 449
--R                                                       Type: Factored Integer
--E 2

--S 3 of 55
y := 2**4 * 45**3 * 162**6 * 774325
 

         10 30 5
   (3)  2  3  5 47 659
                                                       Type: Factored Integer
--R 
--R
--R         10 30 5
--R   (3)  2  3  5 47 659
--R                                                       Type: Factored Integer
--E 3

--S 4 of 55
z1 := factorial 50
 

   (4)  30414093201713378043612608166064768844377641568960512000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  30414093201713378043612608166064768844377641568960512000000000000
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 55
z := z1 :: (FR INT)
 

         47 22 12 8  4  3  2  2  2
   (5)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
                                                       Type: Factored Integer
--R 
--R
--R         47 22 12 8  4  3  2  2  2
--R   (5)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
--R                                                       Type: Factored Integer
--E 5

--S 6 of 55
nthFactor(z,1)
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 55
nthFlag(z,1)
 

   (7)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (7)  "prime"
--R                                                     Type: Union("prime",...)
--E 7

--S 8 of 55
nthExponent(z,1)
 

   (8)  47
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  47
--R                                                        Type: PositiveInteger
--E 8


--S 9 of 55
factorList z
 

   (9)
   [[flg= "prime",fctr= 2,xpnt= 47], [flg= "prime",fctr= 3,xpnt= 22],
    [flg= "prime",fctr= 5,xpnt= 12], [flg= "prime",fctr= 7,xpnt= 8],
    [flg= "prime",fctr= 11,xpnt= 4], [flg= "prime",fctr= 13,xpnt= 3],
    [flg= "prime",fctr= 17,xpnt= 2], [flg= "prime",fctr= 19,xpnt= 2],
    [flg= "prime",fctr= 23,xpnt= 2], [flg= "prime",fctr= 29,xpnt= 1],
    [flg= "prime",fctr= 31,xpnt= 1], [flg= "prime",fctr= 37,xpnt= 1],
    [flg= "prime",fctr= 41,xpnt= 1], [flg= "prime",fctr= 43,xpnt= 1],
    [flg= "prime",fctr= 47,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--R 
--R
--R   (9)
--R   [[flg= "prime",fctr= 2,xpnt= 47], [flg= "prime",fctr= 3,xpnt= 22],
--R    [flg= "prime",fctr= 5,xpnt= 12], [flg= "prime",fctr= 7,xpnt= 8],
--R    [flg= "prime",fctr= 11,xpnt= 4], [flg= "prime",fctr= 13,xpnt= 3],
--R    [flg= "prime",fctr= 17,xpnt= 2], [flg= "prime",fctr= 19,xpnt= 2],
--R    [flg= "prime",fctr= 23,xpnt= 2], [flg= "prime",fctr= 29,xpnt= 1],
--R    [flg= "prime",fctr= 31,xpnt= 1], [flg= "prime",fctr= 37,xpnt= 1],
--R    [flg= "prime",fctr= 41,xpnt= 1], [flg= "prime",fctr= 43,xpnt= 1],
--R    [flg= "prime",fctr= 47,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--E 9

--S 10 of 55
r:=reduce(*,[(nthFactor(z,i) :: (FR INT)) for i in 1..(numberOfFactors z)])
 

   (10)  2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
                                                       Type: Factored Integer
--R 
--R
--R   (10)  2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
--R                                                       Type: Factored Integer
--E 10

--S 11 of 55
exquo(z,r)
 

          46 21 11 7  3  2
   (11)  2  3  5  7 11 13 17 19 23
                                            Type: Union(Factored Integer,...)
--R 
--R
--R          46 21 11 7  3  2
--R   (11)  2  3  5  7 11 13 17 19 23
--R                                            Type: Union(Factored Integer,...)
--E 11

--S 12 of 55
x*y
 

          26 40 5  7  3
   (12)  2  3  5 13 37 47 83 449 659
                                                       Type: Factored Integer
--R 
--R
--R          26 40 5  7  3
--R   (12)  2  3  5 13 37 47 83 449 659
--R                                                       Type: Factored Integer
--E 12

--S 13 of 55
y*x
 

          26 40 5  7  3
   (13)  2  3  5 13 37 47 83 449 659
                                                       Type: Factored Integer
--R 
--R
--R          26 40 5  7  3
--R   (13)  2  3  5 13 37 47 83 449 659
--R                                                       Type: Factored Integer
--E 13

--S 14 of 55
(x*y = y*x) :: BOOLEAN
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 55
gcd(x,z)
 

          16 10  3
   (15)  2  3  13 37
                                                       Type: Factored Integer
--R 
--R
--R          16 10  3
--R   (15)  2  3  13 37
--R                                                       Type: Factored Integer
--E 15

--S 16 of 55
x+y
 

          10 10
   (16)  2  3  1109 3557 2007307818601
                                                       Type: Factored Integer
--R 
--R
--R          10 10
--R   (16)  2  3  1109 3557 2007307818601
--R                                                       Type: Factored Integer
--E 16

--S 17 of 55
expand(x+y)
 

   (17)  478786494447911114328204288
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  478786494447911114328204288
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 55
f := x/y
 

          6  7  3
         2 13 37 83 449
   (18)  --------------
            20 5
           3  5 47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R          6  7  3
--R         2 13 37 83 449
--R   (18)  --------------
--R            20 5
--R           3  5 47 659
--R                                              Type: Fraction Factored Integer
--E 18

--S 19 of 55
g := (x ** 9) / y
 

          134 60  63  27  9   9
         2   3  13  37  83 449
   (19)  ----------------------
                 5
                5 47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R          134 60  63  27  9   9
--R         2   3  13  37  83 449
--R   (19)  ----------------------
--R                 5
--R                5 47 659
--R                                              Type: Fraction Factored Integer
--E 19

--S 20 of 55
f * g
 

          140 40  70  30  10   10
         2   3  13  37  83  449
   (20)  ------------------------
                 10  2   2
                5  47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R          140 40  70  30  10   10
--R         2   3  13  37  83  449
--R   (20)  ------------------------
--R                 10  2   2
--R                5  47 659
--R                                              Type: Fraction Factored Integer
--E 20

--S 21 of 55
(f * g) / (g * primeFactor(2,200)) 
 

             7  3
           13 37 83 449
   (21)  ---------------
          194 20 5
         2   3  5 47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R             7  3
--R           13 37 83 449
--R   (21)  ---------------
--R          194 20 5
--R         2   3  5 47 659
--R                                              Type: Fraction Factored Integer
--E 21

--S 22 of 55
(f * g) / (g * primeFactor(2,200)) * z
 

          2 7 8  4  10  2  2  2        4
         3 5 7 11 13  17 19 23 29 31 37 41 43 83 449
   (22)  -------------------------------------------
                            147
                           2   659
                                              Type: Fraction Factored Integer
--R 
--R
--R          2 7 8  4  10  2  2  2        4
--R         3 5 7 11 13  17 19 23 29 31 37 41 43 83 449
--R   (22)  -------------------------------------------
--R                            147
--R                           2   659
--R                                              Type: Fraction Factored Integer
--E 22 
 

)clear all
 
   All user variables and function definitions have been cleared.
--S 23  of 55
(u,v,w): FR POLY INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23
 
--S 24 of 55
u := (x**4 - y**4) :: POLY INT
 

                          2    2
   (2)  - (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                          2    2
--R   (2)  - (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 24

--S 25 of 55
v := primeFactor(x-y,2) * primeFactor(x+y,2) * primeFactor(x**2 + y**2,1)
 

               2       2  2    2
   (3)  (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2       2  2    2
--R   (3)  (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 25

--S 26 of 55
w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * primeFactor(x-y,2)
 

               2           2
   (4)  (y - x) (y + x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2           2
--R   (4)  (y - x) (y + x + 1)
--R                                            Type: Factored Polynomial Integer
--E 26

--S 27 of 55
unit w
 

   (5)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)  1
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 55
l := factorList u
 

   (6)
   [[flg= "prime",fctr= y - x,xpnt= 1], [flg= "prime",fctr= y + x,xpnt= 1],
                         2    2
    [flg= "prime",fctr= y  + x ,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--R 
--R
--R   (6)
--R   [[flg= "prime",fctr= y - x,xpnt= 1], [flg= "prime",fctr= y + x,xpnt= 1],
--R                         2    2
--R    [flg= "prime",fctr= y  + x ,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--E 28

--S 29 of 55
factorList v
 

   (7)
   [[flg= "prime",fctr= y - x,xpnt= 2], [flg= "prime",fctr= y + x,xpnt= 2],
                         2    2
    [flg= "prime",fctr= y  + x ,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--R 
--R
--R   (7)
--R   [[flg= "prime",fctr= y - x,xpnt= 2], [flg= "prime",fctr= y + x,xpnt= 2],
--R                         2    2
--R    [flg= "prime",fctr= y  + x ,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--E 29

--S 30 of 55
factorList w
 

   (8)
   [[flg= "prime",fctr= y - x,xpnt= 2],[flg= "prime",fctr= y + x + 1,xpnt= 2]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--R 
--R
--R   (8)
--R   [[flg= "prime",fctr= y - x,xpnt= 2],[flg= "prime",fctr= y + x + 1,xpnt= 2]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--E 30

--S 31 of 55
l.1.fctr
 

   (9)  y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)  y - x
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 55
l.1.xpnt
 

   (10)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  1
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 55
nthFactor(u,1)
 

   (11)  y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (11)  y - x
--R                                                     Type: Polynomial Integer
--E 33

--S 34 of 55
nthFactor(u,2)
 

   (12)  y + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (12)  y + x
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 55
nthFactor(u,3)
 

          2    2
   (13)  y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R          2    2
--R   (13)  y  + x
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 55
nthExponent(u,3)
 

   (14)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  1
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 55
nthFlag(u,3)
 

   (15)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (15)  "prime"
--R                                                     Type: Union("prime",...)
--E 37

--S 38 of 55
nthFactor(u,4)
 

   (16)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (16)  1
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 55
s:=reduce(*,[(nthFactor(v,i) :: FR POLY INT) for i in 1..(numberOfFactors v)])
 

                         2    2
   (17)  (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2
--R   (17)  (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 39

--S 40 of 55
exquo(v,s)
 

   (18)  (y - x)(y + x)
                                 Type: Union(Factored Polynomial Integer,...)
--R 
--R
--R   (18)  (y - x)(y + x)
--R                                 Type: Union(Factored Polynomial Integer,...)
--E 40

--S 41 of 55
gcd(u,v)
 

                         2    2
   (19)  (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2
--R   (19)  (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 41

--S 42 of 55
u + v
 

                         2    2       2    2
   (20)  (y - x)(y + x)(y  - x  - 1)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2       2    2
--R   (20)  (y - x)(y + x)(y  - x  - 1)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 42

--S 43 of 55
lcm(v,w)
 

                2       2           2  2    2
   (21)  (y - x) (y + x) (y + x + 1) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                2       2           2  2    2
--R   (21)  (y - x) (y + x) (y + x + 1) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 43

--S 44 of 55
u * v * w
 

                  5       3           2  2    2 2
   (22)  - (y - x) (y + x) (y + x + 1) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  5       3           2  2    2 2
--R   (22)  - (y - x) (y + x) (y + x + 1) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 44

--S 45 of 55
expand(u * v * w)
 

   (23)
        14     13      2           12      2       11       4     3  10
     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
   + 
        4     3  9        6     5     4  8        6     5  7      8     7  6
     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
   + 
        8     7  5     10     9     8  4      10     9  3        12     11  2
     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
   + 
          12     11      14     13    12
     (- 2x   - 2x  )y + x   + 2x   + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (23)
--R        14     13      2           12      2       11       4     3  10
--R     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
--R   + 
--R        4     3  9        6     5     4  8        6     5  7      8     7  6
--R     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
--R   + 
--R        8     7  5     10     9     8  4      10     9  3        12     11  2
--R     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
--R   + 
--R          12     11      14     13    12
--R     (- 2x   - 2x  )y + x   + 2x   + x
--R                                                     Type: Polynomial Integer
--E 45

--S 46 of 55
u/w
 

                      2    2
             (y + x)(y  + x )
   (24)  - -------------------
                             2
           (y - x)(y + x + 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                      2    2
--R             (y + x)(y  + x )
--R   (24)  - -------------------
--R                             2
--R           (y - x)(y + x + 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 46

--S 47 of 55
w/(u*v)
 

                             2
                  (y + x + 1)
   (25)  - -------------------------
                         3  2    2 2
           (y - x)(y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                             2
--R                  (y + x + 1)
--R   (25)  - -------------------------
--R                         3  2    2 2
--R           (y - x)(y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 47

--S 48 of 55
w/(u*v) * u/w
 

                     1
   (26)  -------------------------
                2       2  2    2
         (y - x) (y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                     1
--R   (26)  -------------------------
--R                2       2  2    2
--R         (y - x) (y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 48

--S 49 of 55
w/(u*v) + u/w
 

   (27)
   -
           10       9     2 8      3 7      4 6      5 5       6      4
          y   + 4x y  + 9x y  + 16x y  + 22x y  + 24x y  + (22x  + 1)y
        + 
              7           3      8     2            2
          (16x  + 4x + 4)y  + (9x  + 6x  + 12x + 6)y
        + 
             9     3      2                10    4     3     2
          (4x  + 4x  + 12x  + 12x + 4)y + x   + x  + 4x  + 6x  + 4x + 1
     /
                      3           2  2    2 2
        (y - x)(y + x) (y + x + 1) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R   (27)
--R   -
--R           10       9     2 8      3 7      4 6      5 5       6      4
--R          y   + 4x y  + 9x y  + 16x y  + 22x y  + 24x y  + (22x  + 1)y
--R        + 
--R              7           3      8     2            2
--R          (16x  + 4x + 4)y  + (9x  + 6x  + 12x + 6)y
--R        + 
--R             9     3      2                10    4     3     2
--R          (4x  + 4x  + 12x  + 12x + 4)y + x   + x  + 4x  + 6x  + 4x + 1
--R     /
--R                      3           2  2    2 2
--R        (y - x)(y + x) (y + x + 1) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 49

--S 50 of 55
differentiate(w,x)
 

   (28)  - 2(2x + 1)(y - x)(y + x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (28)  - 2(2x + 1)(y - x)(y + x + 1)
--R                                            Type: Factored Polynomial Integer
--E 50

--S 51 of 55
differentiate(w,y)
 

   (29)  2(y - x)(y + x + 1)(2y + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (29)  2(y - x)(y + x + 1)(2y + 1)
--R                                            Type: Factored Polynomial Integer
--E 51

--S 52 of 55
associates?(x,-x)
 

   (30)  true
                                                                Type: Boolean
--R 
--R
--R   (30)  true
--R                                                                Type: Boolean
--E 52

--S 53 of 55
characteristic()$FR POLY INT
 

   (31)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (31)  0
--R                                                     Type: NonNegativeInteger
--E 53

--S 54 of 55
1$FR POLY INT
 

   (32)  1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (32)  1
--R                                            Type: Factored Polynomial Integer
--E 54

--S 55 of 55
0$FR POLY INT
 

   (33)  0
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (33)  0
--R                                            Type: Factored Polynomial Integer
--E 55
)spool 
 
Starts dribbling to clif.output (2009/2/17, 17:44:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from ugxCliffordComplexPage
--S 1 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
m := matrix [[-1]]
 

   (2)  [- 1]
                                                         Type: Matrix Integer
--R 
--R
--R   (2)  [- 1]
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 36
C := CliffordAlgebra(1, K, quadraticForm m)
 

   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 3

--S 4 of 36
i: C := e(1)
 

   (4)  e
         1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 4

--S 5 of 36
x := a + b * i
 

   (5)  a + b e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  a + b e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 5

--S 6 of 36
y := c + d * i
 

   (6)  c + d e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  c + d e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 6

--S 7 of 36
x * y
 

   (7)  - b d + a c + (a d + b c)e
                                  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  - b d + a c + (a d + b c)e
--R                                  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 7

-- Input generated from ugxCliffordQuaternPage

)clear all
 
   All user variables and function definitions have been cleared.

--S 8 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 8

--S 9 of 36
m := matrix [[-1,0],[0,-1]]
 

        +- 1   0 +
   (2)  |        |
        + 0   - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 1   0 +
--R   (2)  |        |
--R        + 0   - 1+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 36
H  := CliffordAlgebra(2, K, quadraticForm m)
 

   (3)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 10

--S 11 of 36
i: H  := e(1)
 

   (4)  e
         1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 11

--S 12 of 36
j: H  := e(2)
 

   (5)  e
         2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  e
--R         2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 12

--S 13 of 36
k: H  := i * j
 

   (6)  e e
         1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  e e
--R         1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 13

--S 14 of 36
x := a + b * i + c * j + d * k
 

   (7)  a + b e  + c e  + d e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  a + b e  + c e  + d e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 14

--S 15 of 36
y := e + f * i + g * j + h * k
 

   (8)  e + f e  + g e  + h e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (8)  e + f e  + g e  + h e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 15

--S 16 of 36
x + y
 

   (9)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
                        1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (9)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                        1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 16

--S 17 of 36
x * y
 

   (10)
     - d h - c g - b f + a e + (c h - d g + a f + b e)e
                                                       1
   + 
     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
                               2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (10)
--R     - d h - c g - b f + a e + (c h - d g + a f + b e)e
--R                                                       1
--R   + 
--R     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
--R                               2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 17

--S 18 of 36
y * x
 

   (11)
     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
                                                         1
   + 
     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (11)
--R     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
--R                                                         1
--R   + 
--R     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 18

-- Input generated from ugxCliffordExteriorPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 19 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 19

--S 20 of 36
Ext := CliffordAlgebra(3, K, quadraticForm 0)
 

   (2)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (2)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 20

--S 21 of 36
i: Ext := e(1)
 

   (3)  e
         1
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (3)  e
--R         1
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 21

--S 22 of 36
j: Ext := e(2)
 

   (4)  e
         2
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         2
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 22

--S 23 of 36
k: Ext := e(3)
 

   (5)  e
         3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  e
--R         3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 23

--S 24 of 36
x := x1*i + x2*j + x3*k
 

   (6)  x1 e  + x2 e  + x3 e
            1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  x1 e  + x2 e  + x3 e
--R            1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 24

--S 25 of 36
y := y1*i + y2*j + y3*k
 

   (7)  y1 e  + y2 e  + y3 e
            1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  y1 e  + y2 e  + y3 e
--R            1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 25

--S 26 of 36
x + y
 

   (8)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
                  1             2             3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (8)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
--R                  1             2             3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 26

--S 27 of 36
x * y + y * x
 

   (9)  0
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (9)  0
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 27

--S 28 of 36
dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 36
dual2(x*y)
 
   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) 

   (11)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
                         1                     2                   3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) 
--R
--R   (11)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
--R                         1                     2                   3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 29

-- Input generated from ugxCliffordDiracPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 30 of 36
K := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 30

--S 31 of 36
g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]
 

        +1   0    0    0 +
        |                |
        |0  - 1   0    0 |
   (2)  |                |
        |0   0   - 1   0 |
        |                |
        +0   0    0   - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +1   0    0    0 +
--R        |                |
--R        |0  - 1   0    0 |
--R   (2)  |                |
--R        |0   0   - 1   0 |
--R        |                |
--R        +0   0    0   - 1+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 36
D := CliffordAlgebra(4,K, quadraticForm g)
 

   (3)  CliffordAlgebra(4,Fraction Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(4,Fraction Integer,MATRIX)
--R                                                                 Type: Domain
--E 32

--S 33 of 36
gam := [e(i)$D for i in 1..4]
 

   (4)  [e ,e ,e ,e ]
          1  2  3  4
                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (4)  [e ,e ,e ,e ]
--R          1  2  3  4
--R                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 33

--S 34 of 36
m := 1; n:= 2; r := 3; s := 4;
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 36
lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4])
 

   (6)  - 4e e e e
            1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (6)  - 4e e e e
--R            1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 35

--S 36 of 36
rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)
 

   (7)  - 4e e e e
            1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (7)  - 4e e e e
--R            1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 36
)spool
 
Starts dribbling to galois.output (2009/2/17, 17:46:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 28
p := x**5 - 5*x + 12
 

         5
   (1)  x  - 5x + 12
                                                     Type: Polynomial Integer
--R 
--R
--R         5
--R   (1)  x  - 5x + 12
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 28
q := resultant(eval(p,x,y),-eval(p,x,y-x),y)
 

   (2)
      25      21        17         15        13           11          9
     x   - 50x   - 2375x   + 90000x   - 5000x   + 2700000x   + 250000x
   + 
              7            5
     18000000x  + 64000000x
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)
--R      25      21        17         15        13           11          9
--R     x   - 50x   - 2375x   + 90000x   - 5000x   + 2700000x   + 250000x
--R   + 
--R              7            5
--R     18000000x  + 64000000x
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 28
q1 := exquo(q, x**5)
 

   (3)
      20      16        12         10        8           6          4
     x   - 50x   - 2375x   + 90000x   - 5000x  + 2700000x  + 250000x
   + 
              2
     18000000x  + 64000000
                                          Type: Union(Polynomial Integer,...)
--R 
--R
--R   (3)
--R      20      16        12         10        8           6          4
--R     x   - 50x   - 2375x   + 90000x   - 5000x  + 2700000x  + 250000x
--R   + 
--R              2
--R     18000000x  + 64000000
--R                                          Type: Union(Polynomial Integer,...)
--E 3

--S 4 of 28
factoredQ := factor q1
 

   (4)
       10      8      6        4        2
     (x   - 10x  - 75x  + 1500x  - 5500x  + 16000)
  *
       10      8       6       4        2
     (x   + 10x  + 125x  + 500x  + 2500x  + 4000)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (4)
--R       10      8      6        4        2
--R     (x   - 10x  - 75x  + 1500x  - 5500x  + 16000)
--R  *
--R       10      8       6       4        2
--R     (x   + 10x  + 125x  + 500x  + 2500x  + 4000)
--R                                            Type: Factored Polynomial Integer
--E 4

--S 5 of 28
r := nthFactor(factoredQ,1)
 

         10      8      6        4        2
   (5)  x   - 10x  - 75x  + 1500x  - 5500x  + 16000
                                                     Type: Polynomial Integer
--R 
--R
--R         10      8      6        4        2
--R   (5)  x   - 10x  - 75x  + 1500x  - 5500x  + 16000
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 28
beta := rootOf(eval(r,x,b))
 

   (6)  b
                                                        Type: AlgebraicNumber
--R 
--R
--R   (6)  b
--R                                                        Type: AlgebraicNumber
--E 6

--S 7 of 28
p := p::UP(x,INT)::UP(x,AN)
 

         5
   (7)  x  - 5x + 12
                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R         5
--R   (7)  x  - 5x + 12
--R                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--E 7

--S 8 of 28
algFactors := factor(p,[beta])
 

   (8)
       x
     + 
                9       8       7        6         5        4          3
           - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
         + 
                    2
           - 327000b  - 405200b + 2062400
      /
         1339200
  *
               8       6        4         2
          - 17b  + 156b  + 2979b  - 25410b  - 14080
     (x + -----------------------------------------)
                            66960
  *
              8        6         4          2
          143b  - 2100b  - 10485b  + 290550b  - 334800b - 960800
     (x + ------------------------------------------------------)
                                  669600
  *
              8        6         4          2
          143b  - 2100b  - 10485b  + 290550b  + 334800b - 960800
     (x + ------------------------------------------------------)
                                  669600
  *
       x
     + 
              9       8       7        6         5        4          3
           85b  - 116b  - 780b  + 2640b  - 14895b  - 8820b  + 127050b
         + 
                    2
           - 327000b  + 405200b + 2062400
      /
         1339200
                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R   (8)
--R       x
--R     + 
--R                9       8       7        6         5        4          3
--R           - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
--R         + 
--R                    2
--R           - 327000b  - 405200b + 2062400
--R      /
--R         1339200
--R  *
--R               8       6        4         2
--R          - 17b  + 156b  + 2979b  - 25410b  - 14080
--R     (x + -----------------------------------------)
--R                            66960
--R  *
--R              8        6         4          2
--R          143b  - 2100b  - 10485b  + 290550b  - 334800b - 960800
--R     (x + ------------------------------------------------------)
--R                                  669600
--R  *
--R              8        6         4          2
--R          143b  - 2100b  - 10485b  + 290550b  + 334800b - 960800
--R     (x + ------------------------------------------------------)
--R                                  669600
--R  *
--R       x
--R     + 
--R              9       8       7        6         5        4          3
--R           85b  - 116b  - 780b  + 2640b  - 14895b  - 8820b  + 127050b
--R         + 
--R                    2
--R           - 327000b  + 405200b + 2062400
--R      /
--R         1339200
--R                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--E 8

--S 9 of 28
factor(p)
 

         5
   (9)  x  - 5x + 12
                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R         5
--R   (9)  x  - 5x + 12
--R                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--E 9

--S 10 of 28
factor1 := nthFactor(algFactors,1)
 

   (10)
     x
   + 
              9       8       7        6         5        4          3
         - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
       + 
                  2
         - 327000b  - 405200b + 2062400
    /
       1339200
                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R   (10)
--R     x
--R   + 
--R              9       8       7        6         5        4          3
--R         - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
--R       + 
--R                  2
--R         - 327000b  - 405200b + 2062400
--R    /
--R       1339200
--R                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--E 10

--S 11 of 28
root1 := -coefficient(factor1,0)
 

   (11)
          9       8       7        6         5        4          3          2
       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
     + 
       405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (11)
--R          9       8       7        6         5        4          3          2
--R       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
--R     + 
--R       405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 11

--S 12 of 28
roots := [-coefficient(nthFactor(algFactors,i),0) for i in 1..5]
 

   (12)
   [
            9       8       7        6         5        4          3          2
         85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
       + 
         405200b - 2062400
    /
       1339200
     ,
       8       6        4         2
    17b  - 156b  - 2979b  + 25410b  + 14080
    ---------------------------------------,
                     66960
          8        6         4          2
    - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
    --------------------------------------------------------,
                             669600
          8        6         4          2
    - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
    --------------------------------------------------------,
                             669600

              9       8       7        6         5        4          3
         - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b
       + 
                2
         327000b  - 405200b - 2062400
    /
       1339200
     ]
                                                   Type: List AlgebraicNumber
--R 
--R
--R   (12)
--R   [
--R            9       8       7        6         5        4          3          2
--R         85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
--R       + 
--R         405200b - 2062400
--R    /
--R       1339200
--R     ,
--R       8       6        4         2
--R    17b  - 156b  - 2979b  + 25410b  + 14080
--R    ---------------------------------------,
--R                     66960
--R          8        6         4          2
--R    - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
--R    --------------------------------------------------------,
--R                             669600
--R          8        6         4          2
--R    - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
--R    --------------------------------------------------------,
--R                             669600
--R
--R              9       8       7        6         5        4          3
--R         - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b
--R       + 
--R                2
--R         327000b  - 405200b - 2062400
--R    /
--R       1339200
--R     ]
--R                                                   Type: List AlgebraicNumber
--E 12

--S 13 of 28
(a1,a2,a3,a4,a5) := (roots.1,roots.2,roots.3,roots.4,roots.5)
 

   (13)
            9       8       7        6         5        4          3          2
       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
     + 
       - 405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (13)
--R            9       8       7        6         5        4          3          2
--R       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
--R     + 
--R       - 405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 13

--S 14 of 28
eval(r,x,a1 - a2)
 

   (14)  0
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (14)  0
--R                                             Type: Polynomial AlgebraicNumber
--E 14

--S 15 of 28
eval(r,x,a1 - a3)
 

   (15)
             9         8          7          6           5           4
       47905b  + 66920b  - 536100b  - 980400b  - 3345075b  - 5787000b
     + 
                3             2
       75572250b  + 161688000b  - 184600000b - 710912000
  /
     4464
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (15)
--R             9         8          7          6           5           4
--R       47905b  + 66920b  - 536100b  - 980400b  - 3345075b  - 5787000b
--R     + 
--R                3             2
--R       75572250b  + 161688000b  - 184600000b - 710912000
--R  /
--R     4464
--R                                             Type: Polynomial AlgebraicNumber
--E 15

--S 16 of 28
eval(r,x,a1 - a4)
 

   (16)  0
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (16)  0
--R                                             Type: Polynomial AlgebraicNumber
--E 16

--S 17 of 28
eval(r,x,a1 - a5)
 

             8        6         4          2
         405b  + 3450b  - 19875b  - 198000b  - 588000
   (17)  --------------------------------------------
                              31
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R             8        6         4          2
--R         405b  + 3450b  - 19875b  - 198000b  - 588000
--R   (17)  --------------------------------------------
--R                              31
--R                                             Type: Polynomial AlgebraicNumber
--E 17

--S 18 of 28
bb := a1 - a4
 

   (18)
          9       8       7        6         5         4          3          2
       85b  + 402b  - 780b  - 6840b  - 14895b  - 12150b  + 127050b  + 908100b
     + 
       1074800b - 3984000
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (18)
--R          9       8       7        6         5         4          3          2
--R       85b  + 402b  - 780b  - 6840b  - 14895b  - 12150b  + 127050b  + 908100b
--R     + 
--R       1074800b - 3984000
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 18

--S 19 of 28
aa1 := subst(a1,beta = bb)
 

               8        6         4          2
         - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
   (19)  --------------------------------------------------------
                                  669600
                                                        Type: AlgebraicNumber
--R 
--R
--R               8        6         4          2
--R         - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
--R   (19)  --------------------------------------------------------
--R                                  669600
--R                                                        Type: AlgebraicNumber
--E 19

--S 20 of 28
aa2 := subst(a2,beta = bb)
 

   (20)
            9       8       7        6         5        4          3          2
       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
     + 
       - 405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (20)
--R            9       8       7        6         5        4          3          2
--R       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
--R     + 
--R       - 405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 20

--S 21 of 28
aa3 := subst(a3,beta = bb)
 

   (21)
          9       8       7        6         5        4          3          2
       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
     + 
       405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (21)
--R          9       8       7        6         5        4          3          2
--R       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
--R     + 
--R       405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 21

--S 22 of 28
aa4 := subst(a4,beta = bb)
 

               8        6         4          2
         - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
   (22)  --------------------------------------------------------
                                  669600
                                                        Type: AlgebraicNumber
--R 
--R
--R               8        6         4          2
--R         - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
--R   (22)  --------------------------------------------------------
--R                                  669600
--R                                                        Type: AlgebraicNumber
--E 22

--S 23 of 28
aa5 := subst(a5,beta = bb)
 

            8       6        4         2
         17b  - 156b  - 2979b  + 25410b  + 14080
   (23)  ---------------------------------------
                          66960
                                                        Type: AlgebraicNumber
--R 
--R
--R            8       6        4         2
--R         17b  - 156b  - 2979b  + 25410b  + 14080
--R   (23)  ---------------------------------------
--R                          66960
--R                                                        Type: AlgebraicNumber
--E 23

--S 24 of 28
(aa1 = a1) :: Boolean
 

   (24)  false
                                                                Type: Boolean
--R 
--R
--R   (24)  false
--R                                                                Type: Boolean
--E 24

--S 25 of 28
(aa1 = a2) :: Boolean
 

   (25)  false
                                                                Type: Boolean
--R 
--R
--R   (25)  false
--R                                                                Type: Boolean
--E 25

--S 26 of 28
(aa1 = a3) :: Boolean
 

   (26)  true
                                                                Type: Boolean
--R 
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26

--S 27 of 28
(aa1 = a4) :: Boolean
 

   (27)  false
                                                                Type: Boolean
--R 
--R
--R   (27)  false
--R                                                                Type: Boolean
--E 27

--S 28 of 28
(aa1 = a5) :: Boolean
 

   (28)  false
                                                                Type: Boolean
--R 
--R
--R   (28)  false
--R                                                                Type: Boolean
--E 28
)spool 
 
Starts dribbling to gbf.output (2009/2/17, 17:46:16).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 3
mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [[0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  x  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  y|
        |            3   |
        |                |
   (1)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  x  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  y  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  x  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  y|
--R        |            3   |
--R        |                |
--R   (1)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  x  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  y  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 1

--S 2 of 3
eq := determinant mfzn
 

   (2)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (2)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 2

--S 3 of 3
groebnerFactorize [eq, eval(eq, [x,y,z], [y,z,x]), eval(eq, [x,y,z], [z,x,y])]
 

   (3)
   [
                  22           22     22     121
     [x y + x z - -- x + y z - -- y - -- z + ---,
                   3            3      3      3
         2   22       25        2   22       25     22  2   388     250
      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
              3        9             3        9      3       9       27
       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
              3        9       3         9         27      9       27       81
     ,
             21994  2   21994     4427     463
    [x + y - -----,y  - ----- y + ----,z - ---],
              5625       5625      675      87
      2   1       11     5     265        2   38     265
    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
          2        2     6      18             3      9
         25     11     11        11     11     11        5     5     5
    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
          9      3      3         3      3      3        3     3     3
         19     5     5
    [x - --,y + -,z + -]]
          3     3     3
  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (3)
--R   [
--R                  22           22     22     121
--R     [x y + x z - -- x + y z - -- y - -- z + ---,
--R                   3            3      3      3
--R         2   22       25        2   22       25     22  2   388     250
--R      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
--R              3        9             3        9      3       9       27
--R       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
--R              3        9       3         9         27      9       27       81
--R     ,
--R             21994  2   21994     4427     463
--R    [x + y - -----,y  - ----- y + ----,z - ---],
--R              5625       5625      675      87
--R      2   1       11     5     265        2   38     265
--R    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
--R          2        2     6      18             3      9
--R         25     11     11        11     11     11        5     5     5
--R    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
--R          9      3      3         3      3      3        3     3     3
--R         19     5     5
--R    [x - --,y + -,z + -]]
--R          3     3     3
--R  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 3
)spool 
 
Starts dribbling to ode.output (2009/2/17, 17:55:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
)set break resume
 
--S 1 of 11
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 11
deqx:= differentiate(y x,x,2)+differentiate(y x,x) +y x
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 11
solve(deqx,y,x) --OK
 

                                             x     x
                                     +-+   - -   - -      +-+
                                   x\|3      2     2    x\|3
   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             x     x
--R                                     +-+   - -   - -      +-+
--R                                   x\|3      2     2    x\|3
--R   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 3

--S 4 of 11
solve(deqx,y,x=0,[1]) --OK
 

                      x
              +-+   - -
            x\|3      2
   (4)  cos(-----)%e
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      x
--R              +-+   - -
--R            x\|3      2
--R   (4)  cos(-----)%e
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 11
deqt:= differentiate(y t,t,2)+differentiate(y t,t) +y t
 

         ,,       ,
   (5)  y  (t) + y (t) + y(t)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (5)  y  (t) + y (t) + y(t)
--R
--R                                                     Type: Expression Integer
--E 5

--S 6 of 11
solve(deqt,y,t) --OK
 

                                             t     t
                                     +-+   - -   - -      +-+
                                   t\|3      2     2    t\|3
   (6)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             t     t
--R                                     +-+   - -   - -      +-+
--R                                   t\|3      2     2    t\|3
--R   (6)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 6

--S 7 of 11
solve(deqt,y,t=0,[1]) -- BUG!
 

                      t
              +-+   - -
            t\|3      2
   (7)  cos(-----)%e
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      t
--R              +-+   - -
--R            t\|3      2
--R   (7)  cos(-----)%e
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 11
deqz:= differentiate(y z,z,2)+differentiate(y z,z) +y z
 

         ,,       ,
   (8)  y  (z) + y (z) + y(z)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (8)  y  (z) + y (z) + y(z)
--R
--R                                                     Type: Expression Integer
--E 8

--S 9 of 11
solve(deqz,y,z) --OK
 

                                             z     z
                                     +-+   - -   - -      +-+
                                   z\|3      2     2    z\|3
   (9)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             z     z
--R                                     +-+   - -   - -      +-+
--R                                   z\|3      2     2    z\|3
--R   (9)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 9

--S 10 of 11
solve(deqz,y,z=0,[1]) -- BUG!
 

                       z
               +-+   - -
             z\|3      2
   (10)  cos(-----)%e
               2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       z
--R               +-+   - -
--R             z\|3      2
--R   (10)  cos(-----)%e
--R               2
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 11 needs fixing
solve(deqt,y,x=0,[1])
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseODE: equation has order 0
--R
--R   Continuing to read the file...
--R
--E 11
)spool 
 
Starts dribbling to bug6357.output (2009/2/17, 17:44:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- The original author assumed (roughly) that sqrt(1/x)=1/sqrt(x),
-- which is wrong (for example,
-- sqrt(-1/2) = %i/sqrt(2) != 1/(%i*sqrt(2)) = -%i/sqrt(2)
--S 1 of 2
sqrt(-1/2)
 

         +---+
        \|- 1
   (1)  ------
          +-+
         \|2
                                                        Type: AlgebraicNumber
--R 
--R
--R         +---+
--R        \|- 1
--R   (1)  ------
--R          +-+
--R         \|2
--R                                                        Type: AlgebraicNumber
--E 1

--S 2 of 2
sqrt(-1/abs(x))-1/sqrt(-abs(x))
 

                    +--------+
         +--------+ |     1
        \|- abs(x)  |- ------  - 1
                   \|  abs(x)
   (2)  --------------------------
                 +--------+
                \|- abs(x)
                                                     Type: Expression Integer
--R 
--R
--R                    +--------+
--R         +--------+ |     1
--R        \|- abs(x)  |- ------  - 1
--R                   \|  abs(x)
--R   (2)  --------------------------
--R                 +--------+
--R                \|- abs(x)
--R                                                     Type: Expression Integer
--E 2
)spool
 
Starts dribbling to knot2.output (2009/2/17, 17:48:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 8
f(x:SF):SF == x
 
   Function declaration f : DoubleFloat -> DoubleFloat has been added 
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : DoubleFloat -> DoubleFloat has been added 
--R      to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 8
[p,q] := [3,5]
 

   (2)  [3,5]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [3,5]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 8
PQ    := p/q
 

        3
   (3)  -
        5
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (3)  -
--R        5
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 8
l := lcm(p, q) quo p
 

   (4)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  5
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 8
maxRange := (odd? l => l * %pi; 2 * l * %pi)  
 

   (5)  5%pi
                                                                     Type: Pi
--R 
--R
--R   (5)  5%pi
--R                                                                     Type: Pi
--E 5

--S 6 of 8
theRange := 0..maxRange
 

   (6)  0..(5%pi)
                                                             Type: Segment Pi
--R 
--R
--R   (6)  0..(5%pi)
--R                                                             Type: Segment Pi
--E 6

--S 7 of 8
v:=draw(curve(sin t * cos(PQ*t),cos t * cos(PQ*t),cos t * sin(PQ*t)), _
        t=theRange, tubeRadius==0.1)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Compiling function %F with type DoubleFloat -> DoubleFloat 
   Transmitting data...

   (7)  ThreeDimensionalViewport: "DCOS((3*t)/5)*DSIN(t)"
                                               Type: ThreeDimensionalViewport
--R 
--I   Compiling function %B with type DoubleFloat -> DoubleFloat 
--I   Compiling function %D with type DoubleFloat -> DoubleFloat 
--I   Compiling function %F with type DoubleFloat -> DoubleFloat 
--R   Transmitting data...
--R
--R   (7)  ThreeDimensionalViewport: "DCOS((3*t)/5)*DSIN(t)"
--R                                               Type: ThreeDimensionalViewport
--E 7

--S 8 of 8
close(v)
 
 
Daly Bug
   >> Error detected within library code:
   This viewport has already been closed!

(8) -> Starts dribbling to ideal.output (2009/2/17, 17:46:29).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 18
(n,m) : List DMP([x,y],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
m := [x**2+y**2-1]
 

          2    2
   (2)  [x  + y  - 1]
         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R          2    2
--R   (2)  [x  + y  - 1]
--R         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 2

--S 3 of 18
n := [x**2-y**2]
 

          2    2
   (3)  [x  - y ]
         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R          2    2
--R   (3)  [x  - y ]
--R         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 3

--S 4 of 18
id := ideal m + ideal n
 

          2   1  2   1
   (4)  [x  - -,y  - -]
              2      2
Type: PolynomialIdeals(Fraction Integer,DirectProduct(2,NonNegativeInteger),OrderedVariableList [x,y],DistributedMultivariatePolynomial([x,y],Fraction Integer))
--R 
--R
--R          2   1  2   1
--R   (4)  [x  - -,y  - -]
--R              2      2
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(2,NonNegativeInteger),OrderedVariableList [x,y],DistributedMultivariatePolynomial([x,y],Fraction Integer))
--E 4

--S 5 of 18
zeroDim? id
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5

--S 6 of 18
zeroDim?(ideal m)
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 18
dimension ideal m
 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 18
(f,g):DMP([x,y],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 18
f := x**2-1
 

         2
   (9)  x  - 1
              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R         2
--R   (9)  x  - 1
--R              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 9

--S 10 of 18
g := x*(x**2-1)
 

          3
   (10)  x  - x
              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R          3
--R   (10)  x  - x
--R              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 10

--S 11 of 18
relationsIdeal [f,g]
 

              2     3     2          2          3
   (11)  [- %B  + %A  + %A ] | [%A= x  - 1,%B= x  - x]
Type: SuchThat(List Polynomial Fraction Integer,List Equation Polynomial Fraction Integer)
--R 
--R
--R              2     3     2          2          3
--R   (11)  [- %B  + %A  + %A ] | [%A= x  - 1,%B= x  - x]
--RType: SuchThat(List Polynomial Fraction Integer,List Equation Polynomial Fraction Integer)
--E 11

--S 12 of 18
l: List DMP([x,y,z],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 18
l:=[x**2+2*y**2,x*z**2-y*z,z**2-4]
 

           2     2    2        2
   (13)  [x  + 2y ,x z  - y z,z  - 4]
       Type: List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R           2     2    2        2
--R   (13)  [x  + 2y ,x z  - y z,z  - 4]
--R       Type: List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 13

--S 14 of 18
ld:=primaryDecomp ideal l
 

               1    2             1    2
   (14)  [[x + - y,y ,z + 2],[x - - y,y ,z - 2]]
               2                  2
Type: List PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               1    2             1    2
--R   (14)  [[x + - y,y ,z + 2],[x - - y,y ,z - 2]]
--R               2                  2
--RType: List PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 14

--S 15 of 18
reduce(intersect,ld)
 

              1      2  2
   (15)  [x - - y z,y ,z  - 4]
              4
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R              1      2  2
--R   (15)  [x - - y z,y ,z  - 4]
--R              4
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 15

--S 16 of 18
reduce(intersect,[radical ld.i for i in 1..2])
 

               2
   (16)  [x,y,z  - 4]
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               2
--R   (16)  [x,y,z  - 4]
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 16

--S 17 of 18
radical ideal l
 

               2
   (17)  [x,y,z  - 4]
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               2
--R   (17)  [x,y,z  - 4]
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 17

--S 18 of 18
quotient(ideal l,y)
 

               2
   (18)  [x,y,z  - 4]
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               2
--R   (18)  [x,y,z  - 4]
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 18
)spool 
 
Starts dribbling to lode.output (2009/2/17, 17:52:33).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 15
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 15
deq := differentiate(y x, x, 2) + differentiate(y x, x) + y x
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 15
solve(deq, y, x).basis
 

                       x     x
               +-+   - -   - -      +-+
             x\|3      2     2    x\|3
   (3)  [cos(-----)%e   ,%e   sin(-----)]
               2                    2
                                                Type: List Expression Integer
--R 
--R
--R                       x     x
--R               +-+   - -   - -      +-+
--R             x\|3      2     2    x\|3
--R   (3)  [cos(-----)%e   ,%e   sin(-----)]
--R               2                    2
--R                                                Type: List Expression Integer
--E 3

--S 4 of 15
deq := differentiate(y x, x, 2) + y x
 

         ,,
   (4)  y  (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (4)  y  (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 15
solve(deq, y, x = 0, [1, 1])
 

   (5)  sin(x) + cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)  sin(x) + cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 15
solve(deq = sin x, y, x)
 

                       x cos(x)
   (6)  [particular= - --------,basis= [cos(x),sin(x)]]
                           2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                       x cos(x)
--R   (6)  [particular= - --------,basis= [cos(x),sin(x)]]
--R                           2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 6

--S 7 of 15
deq := x**3 * differentiate(y x, x, 3) + x**2 * differentiate(y x, x, 2) - _
2 * x * differentiate(y x, x) + 2 * y x = 2 * x**4
 

         3 ,,,       2 ,,         ,               4
   (7)  x y   (x) + x y  (x) - 2xy (x) + 2y(x)= 2x

                                            Type: Equation Expression Integer
--R 
--R
--R         3 ,,,       2 ,,         ,               4
--R   (7)  x y   (x) + x y  (x) - 2xy (x) + 2y(x)= 2x
--R
--R                                            Type: Equation Expression Integer
--E 7

--S 8 of 15
solve(deq, y, x)
 

   (8)
                 5      3      2               3     2      3      3     2
                x  - 10x  + 20x  + 4         2x  - 3x  + 1 x  - 1 x  - 3x  - 1
   [particular= --------------------,basis= [-------------,------,------------]]
                         15x                       x          x         x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (8)
--R                 5      3      2               3     2      3      3     2
--R                x  - 10x  + 20x  + 4         2x  - 3x  + 1 x  - 1 x  - 3x  - 1
--R   [particular= --------------------,basis= [-------------,------,------------]]
--R                         15x                       x          x         x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 8

--S 9 of 15
solve(deq, y, x = 1, [b, 0, a])
 

          5                      3                    2
        2x  + (- 10b + 10a - 10)x  + (30b - 15a + 10)x  + 10b + 5a - 2
   (9)  --------------------------------------------------------------
                                      30x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          5                      3                    2
--R        2x  + (- 10b + 10a - 10)x  + (30b - 15a + 10)x  + 10b + 5a - 2
--R   (9)  --------------------------------------------------------------
--R                                      30x
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 15
deq := (x**9 + x**3) * differentiate(y x, x, 3) + _
18 * x**8 * differentiate(y x, x,2) - 90 * x * differentiate(y x, x) - _
30 * (11*x**6-3) * y x
 

           9    3  ,,,         8 ,,          ,             6
   (10)  (x  + x )y   (x) + 18x y  (x) - 90xy (x) + (- 330x  + 90)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           9    3  ,,,         8 ,,          ,             6
--R   (10)  (x  + x )y   (x) + 18x y  (x) - 90xy (x) + (- 330x  + 90)y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 15
solve(deq, y, x).basis
 

                        +--+            +--+
                     - \|91 log(x)     \|91 log(x)
             x   x %e              x %e
   (11)  [------,-----------------,---------------]
           6            6                6
          x  + 1       x  + 1           x  + 1
                                                Type: List Expression Integer
--R 
--R
--R                        +--+            +--+
--R                     - \|91 log(x)     \|91 log(x)
--R             x   x %e              x %e
--R   (11)  [------,-----------------,---------------]
--R           6            6                6
--R          x  + 1       x  + 1           x  + 1
--R                                                Type: List Expression Integer
--E 11

--S 12 of 15
deq := (2*x+2)* differentiate(y x, x, 3) + 3* differentiate(y x, x, 2) + _
(2*x**2+2*x)* differentiate(y x,x) - sqrt(x+1) * y x = 2 * x**2 + x - 1
 

   (12)
            ,,,        ,,         2       ,           +-----+    2
   (2x + 2)y   (x) + 3y  (x) + (2x  + 2x)y (x) - y(x)\|x + 1 = 2x  + x - 1

                                            Type: Equation Expression Integer
--R 
--R
--R   (12)
--R            ,,,        ,,         2       ,           +-----+    2
--R   (2x + 2)y   (x) + 3y  (x) + (2x  + 2x)y (x) - y(x)\|x + 1 = 2x  + x - 1
--R
--R                                            Type: Equation Expression Integer
--E 12

--S 13 of 15
solve(deq, y, x).particular
 

          +-----+
   (13)  \|x + 1  + x
                                                     Type: Expression Integer
--R 
--R
--R          +-----+
--R   (13)  \|x + 1  + x
--R                                                     Type: Expression Integer
--E 13

--S 14 of 15
deq := 2*x**3*differentiate(y x,x,2) + 3*x**2*differentiate(y x,x) - 2*y x
 

           3 ,,        2 ,
   (14)  2x y  (x) + 3x y (x) - 2y(x)

                                                     Type: Expression Integer
--R 
--R
--R           3 ,,        2 ,
--R   (14)  2x y  (x) + 3x y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 15
solve(deq,y,x).basis
 

                2      2
            - ----   ----
               +-+    +-+
              \|x    \|x
   (15)  [%e      ,%e    ]
                                                Type: List Expression Integer
--R 
--R
--R                2      2
--R            - ----   ----
--R               +-+    +-+
--R              \|x    \|x
--R   (15)  [%e      ,%e    ]
--R                                                Type: List Expression Integer
--E 15
)spool 
 
Starts dribbling to pat.output (2009/2/17, 17:56:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 21
rule square(x) == x*x
 
   There are no library operations named square 
      Use HyperDoc Browse or issue
                               )what op square
      to learn if there is any operation containing " square " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      square with argument type(s) 
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named square 
--R      Use HyperDoc Browse or issue
--R                               )what op square
--R      to learn if there is any operation containing " square " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      square with argument type(s) 
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 1

--S 2 of 21
fact(n | n > 0) == n * fact(n - 1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 21
fact(0) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 21
f('A) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 21
f(0) == 0 otherwise
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 21
binary(true) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 21
binary(false) == 0
 
   1 old definition(s) deleted for function or rule binary 
                                                                   Type: Void
--R 
--R   1 old definition(s) deleted for function or rule binary 
--R                                                                   Type: Void
--E 7

--S 8 of 21
sinValues == rules
  sin(%pi) == 0
  sin(%pi/4) == sqrt(2)/2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 21
integrate(log(1 + tan(x)),x,0,%pi/4) == %pi/8*log(2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 21
powerOf(x,x) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 21
powerOf(x,x**n) == n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 21
powerOf(x,y) == 0 otherwise
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 21
powerOf(x,x**n%) == n%
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 21
powerOf(x,y) == 0 otherwise
 
   1 old definition(s) deleted for function or rule powerOf 
                                                                   Type: Void
--R 
--R   1 old definition(s) deleted for function or rule powerOf 
--R                                                                   Type: Void
--E 14

--S 15 of 21
linearExponent?(exp(%a*x+%b | freeOf?(%a,x) and freeOf?(%b,x)),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 21
linearExponent?(exp(a) | freeOf?(a,x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 21
linearExponent?(u,x) == false
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 21
linearExponent?(exp(x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 21
linearExponent?(exp(a*x) | freeOf?(a,x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 21
linearExponent?(exp(x+b) | freeOf?(b,x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 21
linearExponent?(exp(a*x+b,x) | freeOf?(a,x) and freeOf?(b,x)) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21
)spool 
 
Starts dribbling to gonshor.output (2009/2/17, 17:46:19).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 98
R := FRAC POLY INT
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 98
(c100, c101, _
c200, c201, c202, c211, _
c300, c301, c302, c303, c311, c312, c322) : R
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 98
c100 :=  1 ;     c101 := -1 ;
 

                                            Type: Fraction Polynomial Integer
--R 
--R
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 98
c200 :=  0 ;     c201 :=  1 ;     c202 := -1 ;
                 c211 :=  2 ;
 

                                            Type: Fraction Polynomial Integer
--R 
--R
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 98
c300 :=  1 ;     c301 :=  0 ;     c302 := -1 ;     c303 :=  1 ;
                 c311 :=  1 ;     c312 :=  0 ;
                                  c322 :=  2 ;
 

                                            Type: Fraction Polynomial Integer
--R 
--R
--R                                            Type: Fraction Polynomial Integer
--E 5

--S 6 of 98
gonshor : List SquareMatrix(4,R) :=
  [matrix [ [1, 0, 0, 0], [0, 0, 0, 0],_
            [0, 0, 0, 0], [0, 0, 0, 0] ],_
   matrix [ [c100, c101, 0, 0], [c101, 0, 0, 0],_
            [0, 0, 0, 0], [0, 0, 0, 0] ],_
   matrix [ [c200, c201, c202, 0], [c201, c211, 0, 0],_
            [c202, 0, 0, 0], [0, 0, 0, 0] ],_
   matrix [ [c300, c301, c302, c303], [c301, c311, c312, 0],_
            [c302, c312, c322, 0], [c303, 0, 0, 0] ] ] ;
 

                       Type: List SquareMatrix(4,Fraction Polynomial Integer)
--R 
--R
--R                       Type: List SquareMatrix(4,Fraction Polynomial Integer)
--E 6

--S 7 of 98
basisSymbols : List Symbol := [subscript(e,[i]) for i in 0..3]
 

   (7)  [e ,e ,e ,e ]
          0  1  2  3
                                                            Type: List Symbol
--R 
--R
--R   (7)  [e ,e ,e ,e ]
--R          0  1  2  3
--R                                                            Type: List Symbol
--E 7

--S 8 of 98
GonshorGenetic := ALGSC(R, 4, basisSymbols, gonshor)
 

   (8)
  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
                                                                 Type: Domain
--R 
--R
--R   (8)
--R  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
--R  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R                                                                 Type: Domain
--E 8

--S 9 of 98
commutative?()$GonshorGenetic
 
   algebra is commutative

   (9)  true
                                                                Type: Boolean
--R 
--R   algebra is commutative
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 98
associative?()$GonshorGenetic
 
   algebra is not associative

   (10)  false
                                                                Type: Boolean
--R 
--R   algebra is not associative
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 98
e0 : GonshorGenetic := [1, 0, 0, 0] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 11

--S 12 of 98
e1 : GonshorGenetic := [0, 1, 0, 0] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 12

--S 13 of 98
e2 : GonshorGenetic := [0, 0, 1, 0] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 13

--S 14 of 98
e3 : GonshorGenetic := [0, 0, 0, 1] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 14

--S 15 of 98
x  : GonshorGenetic := x0*e0 + x1*e1 + x2*e2 + x3*e3
 

   (15)  x3 e  + x2 e  + x1 e  + x0 e
             3       2       1       0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (15)  x3 e  + x2 e  + x1 e  + x0 e
--R             3       2       1       0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 15

--S 16 of 98
Lx := leftRegularRepresentation x
 

         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
         |                                      |
         |0     - x0     2x1 + x0        x1     |
   (16)  |                                      |
         |0       0        - x0       2x2 - x0  |
         |                                      |
         +0       0          0           x0     +
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
--R         |                                      |
--R         |0     - x0     2x1 + x0        x1     |
--R   (16)  |                                      |
--R         |0       0        - x0       2x2 - x0  |
--R         |                                      |
--R         +0       0          0           x0     +
--R                                     Type: Matrix Fraction Polynomial Integer
--E 16

--S 17 of 98
p := characteristicPolynomial(Lx,Y)
 

           4     2  2    4
   (17)  x0  - 2Y x0  + Y
                                                     Type: Polynomial Integer
--R 
--R
--R           4     2  2    4
--R   (17)  x0  - 2Y x0  + Y
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 98
leftMinimalPolynomial x
 

          5      2 3     4
   (18)  ?  - 2x0 ?  + x0 ?
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--R
--R          5      2 3     4
--R   (18)  ?  - 2x0 ?  + x0 ?
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 18

)clear prop A a b c r s
 
 
--S 19 of 98
A := GonshorGenetic
 

   (19)
  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
                                                                 Type: Domain
--R 
--R
--R   (19)
--R  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
--R  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R                                                                 Type: Domain
--E 19

--S 20 of 98
a := x
 

   (20)  x3 e  + x2 e  + x1 e  + x0 e
             3       2       1       0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (20)  x3 e  + x2 e  + x1 e  + x0 e
--R             3       2       1       0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 20

--S 21 of 98
b := (1/4)*e1 + (1/5)*e2 + (3/20)*e3 + (2/5)*e0
 

          3      1      1      2
   (21)  -- e  + - e  + - e  + - e
         20  3   5  2   4  1   5  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          3      1      1      2
--R   (21)  -- e  + - e  + - e  + - e
--R         20  3   5  2   4  1   5  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 21

--S 22 of 98
c := (1/3)*e1 + (1/7)*e2 + (8/21)*e3 + (1/7)*e0
 

          8      1      1      1
   (22)  -- e  + - e  + - e  + - e
         21  3   7  2   3  1   7  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          8      1      1      1
--R   (22)  -- e  + - e  + - e  + - e
--R         21  3   7  2   3  1   7  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 22

--S 23 of 98
r  : R := r
 

   (23)  r
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (23)  r
--R                                            Type: Fraction Polynomial Integer
--E 23

--S 24 of 98
s  : R := s
 

   (24)  s
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (24)  s
--R                                            Type: Fraction Polynomial Integer
--E 24

--S 25 of 98
b*c
 

         2      1       47       2
   (25)  - e  + - e  - --- e  + -- e
         7  3   4  2   420  1   35  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         2      1       47       2
--R   (25)  - e  + - e  - --- e  + -- e
--R         7  3   4  2   420  1   35  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 25

--S 26 of 98
(b*c)*b
 

          893       277       4       4
   (26)  ---- e  - ---- e  + -- e  + --- e
         8400  3   1400  2   75  1   175  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          893       277       4       4
--R   (26)  ---- e  - ---- e  + -- e  + --- e
--R         8400  3   1400  2   75  1   175  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 26

--S 27 of 98
b*(c*b)
 

          893       277       4       4
   (27)  ---- e  - ---- e  + -- e  + --- e
         8400  3   1400  2   75  1   175  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          893       277       4       4
--R   (27)  ---- e  - ---- e  + -- e  + --- e
--R         8400  3   1400  2   75  1   175  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 27


)clear prop AP
 
--S 28  of 98
AP := ALGPKG(R,A)
 

   (28)
  AlgebraPackage(Fraction Polynomial Integer,AlgebraGivenByStructuralConstants(
  Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX
  ,MATRIX]))
                                                                 Type: Domain
--R 
--R
--R   (28)
--R  AlgebraPackage(Fraction Polynomial Integer,AlgebraGivenByStructuralConstants(
--R  Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX
--R  ,MATRIX]))
--R                                                                 Type: Domain
--E 28

--S 29 of 98
r*a
 

   (29)  r x3 e  + r x2 e  + r x1 e  + r x0 e
               3         2         1         0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (29)  r x3 e  + r x2 e  + r x1 e  + r x0 e
--R               3         2         1         0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 29

--S 30 of 98
a*r
 

   (30)  r x3 e  + r x2 e  + r x1 e  + r x0 e
               3         2         1         0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (30)  r x3 e  + r x2 e  + r x1 e  + r x0 e
--R               3         2         1         0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 30

--S 31 of 98
a*b
 

         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      2x0
   (31)  --------------- e  + ----------------- e  + ----------- e  + --- e
                20        3           20         2        20      1    5   0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      2x0
--R   (31)  --------------- e  + ----------------- e  + ----------- e  + --- e
--R                20        3           20         2        20      1    5   0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 31

--S 32 of 98
b*c
 

         2      1       47       2
   (32)  - e  + - e  - --- e  + -- e
         7  3   4  2   420  1   35  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         2      1       47       2
--R   (32)  - e  + - e  - --- e  + -- e
--R         7  3   4  2   420  1   35  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 32

--S 33 of 98
12 * c
 

         32      12            12
   (33)  -- e  + -- e  + 4e  + -- e
          7  3    7  2     1    7  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         32      12            12
--R   (33)  -- e  + -- e  + 4e  + -- e
--R          7  3    7  2     1    7  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 32

--S 34 of 98
(-3) * a
 

   (34)  - 3x3 e  - 3x2 e  - 3x1 e  - 3x0 e
                3        2        1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (34)  - 3x3 e  - 3x2 e  - 3x1 e  - 3x0 e
--R                3        2        1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 34

--S 35 of 98
d  :=  a ** 12
 

   (35)
             11        10  2         9  2        10         11           8  4
         12x0  x3 + 4x0  x2  + (144x0 x1  + 144x0  x1 - 68x0  )x2 + 248x0 x1
       + 
                9  3       10  2        11         12
         - 784x0 x1  - 86x0  x1  + 204x0  x1 - 24x0
    *
       e
        3
   + 
         11         10  2       11            11       12        12
     (4x0  x2 - 92x0  x1  + 28x0  x1)e  + (4x0  x1 - x0  )e  + x0  e
                                      2                    1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (35)
--R             11        10  2         9  2        10         11           8  4
--R         12x0  x3 + 4x0  x2  + (144x0 x1  + 144x0  x1 - 68x0  )x2 + 248x0 x1
--R       + 
--R                9  3       10  2        11         12
--R         - 784x0 x1  - 86x0  x1  + 204x0  x1 - 24x0
--R    *
--R       e
--R        3
--R   + 
--R         11         10  2       11            11       12        12
--R     (4x0  x2 - 92x0  x1  + 28x0  x1)e  + (4x0  x1 - x0  )e  + x0  e
--R                                      2                    1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 35

--S 36 of 98
-d
 

   (36)
               11        10  2           9  2        10         11
         - 12x0  x3 - 4x0  x2  + (- 144x0 x1  - 144x0  x1 + 68x0  )x2
       + 
                8  4        9  3       10  2        11         12
         - 248x0 x1  + 784x0 x1  + 86x0  x1  - 204x0  x1 + 24x0
    *
       e
        3
   + 
           11         10  2       11              11       12        12
     (- 4x0  x2 + 92x0  x1  - 28x0  x1)e  + (- 4x0  x1 + x0  )e  - x0  e
                                        2                      1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (36)
--R               11        10  2           9  2        10         11
--R         - 12x0  x3 - 4x0  x2  + (- 144x0 x1  - 144x0  x1 + 68x0  )x2
--R       + 
--R                8  4        9  3       10  2        11         12
--R         - 248x0 x1  + 784x0 x1  + 86x0  x1  - 204x0  x1 + 24x0
--R    *
--R       e
--R        3
--R   + 
--R           11         10  2       11              11       12        12
--R     (- 4x0  x2 + 92x0  x1  - 28x0  x1)e  + (- 4x0  x1 + x0  )e  - x0  e
--R                                        2                      1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 36

--S 37 of 98
a + b
 

         20x3 + 3      5x2 + 1      4x1 + 1      5x0 + 2
   (37)  -------- e  + ------- e  + ------- e  + ------- e
            20     3      5     2      4     1      5     0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         20x3 + 3      5x2 + 1      4x1 + 1      5x0 + 2
--R   (37)  -------- e  + ------- e  + ------- e  + ------- e
--R            20     3      5     2      4     1      5     0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 37

--S 38 of 98
d-c
 

   (38)
                11         10  2          9  2         10           11
           252x0  x3 + 84x0  x2  + (3024x0 x1  + 3024x0  x1 - 1428x0  )x2
         + 
                 8  4          9  3         10  2         11          12
           5208x0 x1  - 16464x0 x1  - 1806x0  x1  + 4284x0  x1 - 504x0   - 8
      /
         21
    *
       e
        3
   + 
         11          10  2        11                11        12
     28x0  x2 - 644x0  x1  + 196x0  x1 - 1      12x0  x1 - 3x0   - 1
     ------------------------------------- e  + -------------------- e
                       7                    2             3           1
   + 
        12
     7x0   - 1
     --------- e
         7      0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (38)
--R                11         10  2          9  2         10           11
--R           252x0  x3 + 84x0  x2  + (3024x0 x1  + 3024x0  x1 - 1428x0  )x2
--R         + 
--R                 8  4          9  3         10  2         11          12
--R           5208x0 x1  - 16464x0 x1  - 1806x0  x1  + 4284x0  x1 - 504x0   - 8
--R      /
--R         21
--R    *
--R       e
--R        3
--R   + 
--R         11          10  2        11                11        12
--R     28x0  x2 - 644x0  x1  + 196x0  x1 - 1      12x0  x1 - 3x0   - 1
--R     ------------------------------------- e  + -------------------- e
--R                       7                    2             3           1
--R   + 
--R        12
--R     7x0   - 1
--R     --------- e
--R         7      0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 38

--S 39 of 98
(a*(a*a) = leftPower(a,3)) :: Boolean
 

   (39)  true
                                                                Type: Boolean
--R 
--R
--R   (39)  true
--R                                                                Type: Boolean
--E 39

--S 40 of 98
(a ** 11 =  (a**8 * a**2) * a) :: Boolean
 

   (40)  true
                                                                Type: Boolean
--R 
--R
--R   (40)  true
--R                                                                Type: Boolean
--E 40

--S 41 of 98
(a ** 11 =  a**8 * (a**2 * a)) :: Boolean
 

   (41)  false
                                                                Type: Boolean
--R 
--R
--R   (41)  false
--R                                                                Type: Boolean
--E 41

--S 42 of 98
zero := 0$A
 

   (42)  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (42)  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 42

--S 43 of 98
zero : A := 0
 

   (43)  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (43)  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 43

--S 44 of 98
alternative?()$A
 
   algebra is not left alternative

   (44)  false
                                                                Type: Boolean
--R 
--R   algebra is not left alternative
--R
--R   (44)  false
--R                                                                Type: Boolean
--E 44

--S 45 of 98
antiCommutative?()$A
 
   algebra is not anti-commutative

   (45)  false
                                                                Type: Boolean
--R 
--R   algebra is not anti-commutative
--R
--R   (45)  false
--R                                                                Type: Boolean
--E 45

--S 46 of 98
associative?()$A
 
   algebra is not associative

   (46)  false
                                                                Type: Boolean
--R 
--R   algebra is not associative
--R
--R   (46)  false
--R                                                                Type: Boolean
--E 46

--S 47 of 98
commutative?()$A
 
   algebra is commutative

   (47)  true
                                                                Type: Boolean
--R 
--R   algebra is commutative
--R
--R   (47)  true
--R                                                                Type: Boolean
--E 47

--S 48 of 98
commutator(a,b)
 

   (48)  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (48)  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 48

--S 49 of 98
antiCommutator(a,b)
 

         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      4x0
   (49)  --------------- e  + ----------------- e  + ----------- e  + --- e
                10        3           10         2        10      1    5   0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      4x0
--R   (49)  --------------- e  + ----------------- e  + ----------- e  + --- e
--R                10        3           10         2        10      1    5   0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 49

--S 50 of 98
associator(a,b,c)
 

         - 21x2 + 6x1 + 7x0      12x2 - 30x1 + 58x0      12x1 - 28x0
   (50)  ------------------ e  + ------------------ e  + ----------- e
                 42          3           105         2       105      1
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         - 21x2 + 6x1 + 7x0      12x2 - 30x1 + 58x0      12x1 - 28x0
--R   (50)  ------------------ e  + ------------------ e  + ----------- e
--R                 42          3           105         2       105      1
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 50

--S 51 of 98
basis()$A
 

   (51)  [e ,e ,e ,e ]
           0  1  2  3
Type: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (51)  [e ,e ,e ,e ]
--R           0  1  2  3
--RType: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 51

--S 52 of 98
n := rank()$A
 

   (52)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (52)  4
--R                                                        Type: PositiveInteger
--E 52

--S 53 of 98
v : Vector R := [i for i in 1..n]
 

   (53)  [1,2,3,4]
                                     Type: Vector Fraction Polynomial Integer
--R 
--R
--R   (53)  [1,2,3,4]
--R                                     Type: Vector Fraction Polynomial Integer
--E 53

--S 54 of 98
g : A := represents  v
 

   (54)  4e  + 3e  + 2e  + e
           3     2     1    0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (54)  4e  + 3e  + 2e  + e
--R           3     2     1    0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 54

--S 55 of 98
coordinates a
 

   (55)  [x0,x1,x2,x3]
                                     Type: Vector Fraction Polynomial Integer
--R 
--R
--R   (55)  [x0,x1,x2,x3]
--R                                     Type: Vector Fraction Polynomial Integer
--E 55

--S 56 of 98
coordinates [a,b]
 

         +x0  x1  x2  x3+
         |              |
   (56)  |2   1   1    3|
         |-   -   -   --|
         +5   4   5   20+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  x1  x2  x3+
--R         |              |
--R   (56)  |2   1   1    3|
--R         |-   -   -   --|
--R         +5   4   5   20+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 56

--S 57 of 98
a.3
 

   (57)  x2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (57)  x2
--R                                            Type: Fraction Polynomial Integer
--E 57

--S 58 of 98
flexible?()$A
 
   algebra is flexible

   (58)  true
                                                                Type: Boolean
--R 
--R   algebra is flexible
--R
--R   (58)  true
--R                                                                Type: Boolean
--E 58

--S 59 of 98
leftAlternative?()$A
 
   algebra is not left alternative

   (59)  false
                                                                Type: Boolean
--R 
--R   algebra is not left alternative
--R
--R   (59)  false
--R                                                                Type: Boolean
--E 59

--S 60 of 98
rightAlternative?()$A
 
   algebra is not right alternative

   (60)  false
                                                                Type: Boolean
--R 
--R   algebra is not right alternative
--R
--R   (60)  false
--R                                                                Type: Boolean
--E 60

--S 61 of 98
sB := someBasis()$A
 

   (61)  [e ,e ,e ,e ]
           0  1  2  3
Type: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (61)  [e ,e ,e ,e ]
--R           0  1  2  3
--RType: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 61

--S 62 of 98
zero? a
 

   (62)  false
                                                                Type: Boolean
--R 
--R
--R   (62)  false
--R                                                                Type: Boolean
--E 62

--S 63 of 98
associatorDependence()$A
 

   (63)  [[1,1,1,0,0,0],[0,1,0,1,0,0],[1,0,0,0,1,0],[- 1,- 1,0,0,0,1]]
                                Type: List Vector Fraction Polynomial Integer
--R 
--R
--R   (63)  [[1,1,1,0,0,0],[0,1,0,1,0,0],[1,0,0,0,1,0],[- 1,- 1,0,0,0,1]]
--R                                Type: List Vector Fraction Polynomial Integer
--E 63

--S 64 of 98
jacobiIdentity?()$A
 
   Jacobi identity does not hold

   (64)  false
                                                                Type: Boolean
--R 
--R   Jacobi identity does not hold
--R
--R   (64)  false
--R                                                                Type: Boolean
--E 64

--S 65 of 98
jordanAlgebra?()$A
 
   algebra is commutative
   this is not a Jordan algebra

   (65)  false
                                                                Type: Boolean
--R 
--R   algebra is commutative
--R   this is not a Jordan algebra
--R
--R   (65)  false
--R                                                                Type: Boolean
--E 65

--S 66 of 98
jordanAdmissible?()$A
 
   algebra is not Jordan admissible

   (66)  false
                                                                Type: Boolean
--R 
--R   algebra is not Jordan admissible
--R
--R   (66)  false
--R                                                                Type: Boolean
--E 66

--S 67 of 98
lieAdmissible?()$A
 
   algebra is Lie admissible

   (67)  true
                                                                Type: Boolean
--R 
--R   algebra is Lie admissible
--R
--R   (67)  true
--R                                                                Type: Boolean
--E 67

--S 68 of 98
b2 := [reduce(+,[sB.i for i in 1..k]) for k in 1..n]
 

   (68)  [e ,e  + e ,e  + e  + e ,e  + e  + e  + e ]
           0  1    0  2    1    0  3    2    1    0
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (68)  [e ,e  + e ,e  + e  + e ,e  + e  + e  + e ]
--R           0  1    0  2    1    0  3    2    1    0
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 68

--S 69 of 98
coordinates  (a ,b2 :: Vector A)
 

   (69)  [- x1 + x0,- x2 + x1,- x3 + x2,x3]
                                     Type: Vector Fraction Polynomial Integer
--R 
--R
--R   (69)  [- x1 + x0,- x2 + x1,- x3 + x2,x3]
--R                                     Type: Vector Fraction Polynomial Integer
--E 69

--S 70 of 98
coordinates  ([a,b] ,bb := (b2 :: Vector A))
 

         +- x1 + x0  - x2 + x1  - x3 + x2  x3+
         |                                   |
   (70)  |    3          1          1       3|
         |   --         --         --      --|
         +   20         20         20      20+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +- x1 + x0  - x2 + x1  - x3 + x2  x3+
--R         |                                   |
--R   (70)  |    3          1          1       3|
--R         |   --         --         --      --|
--R         +   20         20         20      20+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 70

--S 71 of 98
leftMinimalPolynomial a
 

          5      2 3     4
   (71)  ?  - 2x0 ?  + x0 ?
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--R
--R          5      2 3     4
--R   (71)  ?  - 2x0 ?  + x0 ?
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 71

--S 72 of 98
leftPower (a,10)
 

   (72)
          9        8  2          7  2      8        9          8  2      10
     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
                                                                             3
   + 
           9         8  2      9        10            9       10        10
     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
                                            2                     1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (72)
--R          9        8  2          7  2      8        9          8  2      10
--R     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
--R                                                                             3
--R   + 
--R           9         8  2      9        10            9       10        10
--R     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
--R                                            2                     1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 72

--S 73 of 98
rightPower(a,10)
 

   (73)
          9        8  2          7  2      8        9          8  2      10
     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
                                                                             3
   + 
           9         8  2      9        10            9       10        10
     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
                                            2                     1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (73)
--R          9        8  2          7  2      8        9          8  2      10
--R     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
--R                                                                             3
--R   + 
--R           9         8  2      9        10            9       10        10
--R     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
--R                                            2                     1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 73

--S 74 of 98
leftRegularRepresentation a
 

         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
         |                                      |
         |0     - x0     2x1 + x0        x1     |
   (74)  |                                      |
         |0       0        - x0       2x2 - x0  |
         |                                      |
         +0       0          0           x0     +
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
--R         |                                      |
--R         |0     - x0     2x1 + x0        x1     |
--R   (74)  |                                      |
--R         |0       0        - x0       2x2 - x0  |
--R         |                                      |
--R         +0       0          0           x0     +
--R                                     Type: Matrix Fraction Polynomial Integer
--E 74

--S 75 of 98
leftRegularRepresentation (a,bb)
 

         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
         |                                                                |
         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
   (75)  |                                                                |
         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
         |                                                                |
         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
--R         |                                                                |
--R         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
--R   (75)  |                                                                |
--R         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
--R         |                                                                |
--R         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 75

--S 76 of 98
leftUnit()$A
 
   this algebra has no left unit

   (76)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   this algebra has no left unit
--R
--R   (76)  "failed"
--R                                                    Type: Union("failed",...)
--E 76

--S 77 of 98
represents (v,bb)
 

   (77)  4e  + 7e  + 9e  + 10e
           3     2     1      0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (77)  4e  + 7e  + 9e  + 10e
--R           3     2     1      0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 77

--S 78 of 98
rightMinimalPolynomial a
 

          5      2 3     4
   (78)  ?  - 2x0 ?  + x0 ?
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--R
--R          5      2 3     4
--R   (78)  ?  - 2x0 ?  + x0 ?
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 78

--S 79 of 98
rightRegularRepresentation a
 

         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
         |                                      |
         |0     - x0     2x1 + x0        x1     |
   (79)  |                                      |
         |0       0        - x0       2x2 - x0  |
         |                                      |
         +0       0          0           x0     +
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
--R         |                                      |
--R         |0     - x0     2x1 + x0        x1     |
--R   (79)  |                                      |
--R         |0       0        - x0       2x2 - x0  |
--R         |                                      |
--R         +0       0          0           x0     +
--R                                     Type: Matrix Fraction Polynomial Integer
--E 79

--S 80 of 98
rightRegularRepresentation (a,bb)
 

         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
         |                                                                |
         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
   (80)  |                                                                |
         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
         |                                                                |
         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
--R         |                                                                |
--R         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
--R   (80)  |                                                                |
--R         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
--R         |                                                                |
--R         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 80

--S 81 of 98
rightUnit()$A
 
   this algebra has no right unit

   (81)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   this algebra has no right unit
--R
--R   (81)  "failed"
--R                                                    Type: Union("failed",...)
--E 81

--S 82 of 98
structuralConstants()$A
 

          +1  0  0  0+ + 1   - 1  0  0+ + 0   1  - 1  0+ + 1   0  - 1  1+
          |          | |              | |              | |              |
          |0  0  0  0| |- 1   0   0  0| | 1   2   0   0| | 0   1   0   0|
   (82)  [|          |,|              |,|              |,|              |]
          |0  0  0  0| | 0    0   0  0| |- 1  0   0   0| |- 1  0   2   0|
          |          | |              | |              | |              |
          +0  0  0  0+ + 0    0   0  0+ + 0   0   0   0+ + 1   0   0   0+
                              Type: Vector Matrix Fraction Polynomial Integer
--R 
--R
--R          +1  0  0  0+ + 1   - 1  0  0+ + 0   1  - 1  0+ + 1   0  - 1  1+
--R          |          | |              | |              | |              |
--R          |0  0  0  0| |- 1   0   0  0| | 1   2   0   0| | 0   1   0   0|
--R   (82)  [|          |,|              |,|              |,|              |]
--R          |0  0  0  0| | 0    0   0  0| |- 1  0   0   0| |- 1  0   2   0|
--R          |          | |              | |              | |              |
--R          +0  0  0  0+ + 0    0   0  0+ + 0   0   0   0+ + 1   0   0   0+
--R                              Type: Vector Matrix Fraction Polynomial Integer
--E 82

--S 83 of 98
structuralConstants(bb)
 

          +0  1  1  1+ + 1   - 1   0    0 + +- 1  0   0   - 1+ +1  1  0  1+
          |          | |                  | |                | |          |
          |1  2  2  2| |- 1  - 5  - 4  - 4| | 0   2   2    1 | |1  2  1  2|
   (83)  [|          |,|                  |,|                |,|          |]
          |1  2  2  2| | 0   - 4  - 3  - 3| | 0   2   0   - 1| |0  1  2  3|
          |          | |                  | |                | |          |
          +1  2  2  2+ + 0   - 4  - 3  - 3+ +- 1  1  - 1  - 2+ +1  2  3  4+
                              Type: Vector Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  1  1  1+ + 1   - 1   0    0 + +- 1  0   0   - 1+ +1  1  0  1+
--R          |          | |                  | |                | |          |
--R          |1  2  2  2| |- 1  - 5  - 4  - 4| | 0   2   2    1 | |1  2  1  2|
--R   (83)  [|          |,|                  |,|                |,|          |]
--R          |1  2  2  2| | 0   - 4  - 3  - 3| | 0   2   0   - 1| |0  1  2  3|
--R          |          | |                  | |                | |          |
--R          +1  2  2  2+ + 0   - 4  - 3  - 3+ +- 1  1  - 1  - 2+ +1  2  3  4+
--R                              Type: Vector Matrix Fraction Polynomial Integer
--E 83

--S 84 of 98
unit()$A
 
   this algebra has no unit

   (84)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   this algebra has no unit
--R
--R   (84)  "failed"
--R                                                    Type: Union("failed",...)
--E 84

--S 85 of 98
biRank  a
 

   (85)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (85)  4
--R                                                        Type: PositiveInteger
--E 85

--S 86 of 98
leftRank a
 

   (86)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (86)  4
--R                                                        Type: PositiveInteger
--E 86

--S 87 of 98
doubleRank a
 

   (87)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (87)  4
--R                                                        Type: PositiveInteger
--E 87

--S 88 of 98
rightRank a
 

   (88)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (88)  4
--R                                                        Type: PositiveInteger
--E 88

--S 89 of 98
weakBiRank a
 

   (89)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (89)  4
--R                                                        Type: PositiveInteger
--E 89

--S 90 of 98
basisOfCenter()$AP
 

   (90)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (90)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 90

--S 91 of 98
basisOfLeftNucleus()$AP
 

   (91)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (91)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 91

--S 92 of 98
basisOfNucleus()$AP
 

   (92)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (92)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 92

--S 93 of 98
basisOfRightNucleus()$AP
 

   (93)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (93)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 93

--S 94 of 98
basisOfCentroid()$AP
 

          +0  0  0  0+ +1  0  0  0+
          |          | |          |
          |0  0  0  0| |0  1  0  0|
   (94)  [|          |,|          |]
          |0  0  0  0| |0  0  1  0|
          |          | |          |
          +1  0  0  0+ +0  0  0  1+
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  0  0  0+ +1  0  0  0+
--R          |          | |          |
--R          |0  0  0  0| |0  1  0  0|
--R   (94)  [|          |,|          |]
--R          |0  0  0  0| |0  0  1  0|
--R          |          | |          |
--R          +1  0  0  0+ +0  0  0  1+
--R                                Type: List Matrix Fraction Polynomial Integer
--E 94

--S 95 of 98
basisOfCommutingElements()$AP
 

   (95)  [e ,e ,e ,e ]
           3  2  1  0
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (95)  [e ,e ,e ,e ]
--R           3  2  1  0
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 95

--S 96 of 98
basisOfLeftNucloid()$AP
 

          +0  0  0  0+ +1  0  0  0+
          |          | |          |
          |0  0  0  0| |0  1  0  0|
   (96)  [|          |,|          |]
          |0  0  0  0| |0  0  1  0|
          |          | |          |
          +1  0  0  0+ +0  0  0  1+
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  0  0  0+ +1  0  0  0+
--R          |          | |          |
--R          |0  0  0  0| |0  1  0  0|
--R   (96)  [|          |,|          |]
--R          |0  0  0  0| |0  0  1  0|
--R          |          | |          |
--R          +1  0  0  0+ +0  0  0  1+
--R                                Type: List Matrix Fraction Polynomial Integer
--E 96

--S 97 of 98
basisOfMiddleNucleus()$AP
 

   (97)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (97)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 97

--S 98 of 98
basisOfRightNucloid()$AP
 

          +0  0  0  0+ +1  0  0  0+
          |          | |          |
          |0  0  0  0| |0  1  0  0|
   (98)  [|          |,|          |]
          |0  0  0  0| |0  0  1  0|
          |          | |          |
          +1  0  0  0+ +0  0  0  1+
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  0  0  0+ +1  0  0  0+
--R          |          | |          |
--R          |0  0  0  0| |0  1  0  0|
--R   (98)  [|          |,|          |]
--R          |0  0  0  0| |0  0  1  0|
--R          |          | |          |
--R          +1  0  0  0+ +0  0  0  1+
--R                                Type: List Matrix Fraction Polynomial Integer
--E 98
)spool 
 
Starts dribbling to algbrbf.output (2009/2/17, 17:43:43).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 13
digits 20
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 13
p := numeric %pi
 

   (2)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 897932385
--R                                                                  Type: Float
--E 2

--S 3 of 13
a := 163.0
 

   (3)  163.0
                                                                  Type: Float
--R 
--R
--R   (3)  163.0
--R                                                                  Type: Float
--E 3

--S 4 of 13
b := sqrt a
 

   (4)  12.7671453348 03704662
                                                                  Type: Float
--R 
--R
--R   (4)  12.7671453348 03704662
--R                                                                  Type: Float
--E 4

--S 5 of 13
exp(p * b)
 

   (5)  26253741 2640768743.97
                                                                  Type: Float
--R 
--R
--R   (5)  26253741 2640768743.97
--R                                                                  Type: Float
--E 5

--S 6 of 13
digits 60
 

   (6)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  20
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 13
p := numeric %pi
 

   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
                                                                  Type: Float
--R 
--R
--R   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
--R                                                                  Type: Float
--E 7

--S 8 of 13
a := 163.0
 

   (8)  163.0
                                                                  Type: Float
--R 
--R
--R   (8)  163.0
--R                                                                  Type: Float
--E 8

--S 9 of 13
b := sqrt a
 

   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
                                                                  Type: Float
--R 
--R
--R   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
--R                                                                  Type: Float
--E 9

--S 10 of 13
exp(p * b)
 

   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
                                                                  Type: Float
--R 
--R
--R   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
--R                                                                  Type: Float
--E 10

--S 11 of 13
c := cos(p/12)
 

   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
                                                                  Type: Float
--R 
--R
--R   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
--R                                                                  Type: Float
--E 11

--S 12 of 13
16*c**4 - 16*c**2 + 1
 

   (12)  0.0
                                                                  Type: Float
--R 
--R
--R   (12)  0.0
--R                                                                  Type: Float
--E 12

--S 13 of 13
numeric(%pi, 500)
 

   (13)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (13)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 13
)spool
 
Starts dribbling to mset.output (2009/2/17, 17:55:15).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 17
macro I == Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 17
macro symdif == symmetricDifference
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 17
s:Multiset I
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 17
t:Multiset I
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 17
t1:Multiset I
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 17
s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10]
 

   (6)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (6)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                                       Type: Multiset Integer
--E 6

--S 7 of 17
t := multiset [2,2,2,9]
 

   (7)  {3: 2,9}
                                                       Type: Multiset Integer
--R 
--R
--R   (7)  {3: 2,9}
--R                                                       Type: Multiset Integer
--E 7

--S 8 of 17
union(s,t)
 

   (8)  {1,5: 2,3: 3,4: 4,2: 5,6,7,9,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (8)  {1,5: 2,3: 3,4: 4,2: 5,6,7,9,10}
--R                                                       Type: Multiset Integer
--E 8

--S 9 of 17
union(s,s)
 

   (9)  {2: 1,4: 2,6: 3,8: 4,4: 5,2: 6,2: 7,2: 10}
                                                       Type: Multiset Integer
--R 
--R
--R   (9)  {2: 1,4: 2,6: 3,8: 4,4: 5,2: 6,2: 7,2: 10}
--R                                                       Type: Multiset Integer
--E 9

--S 10 of 17
intersect(s,t)
 

   (10)  {5: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {5: 2}
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 17
difference(s,t)
 

   (11)  {1,3: 3,4: 4,2: 5,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (11)  {1,3: 3,4: 4,2: 5,6,7,10}
--R                                                       Type: Multiset Integer
--E 11

--S 12 of 17
symdif(s,t)
 

   (12)  {1,3: 3,4: 4,2: 5,6,7,9,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (12)  {1,3: 3,4: 4,2: 5,6,7,9,10}
--R                                                       Type: Multiset Integer
--E 12

--S 13 of 17
symdif(s,s)
 

   (13)  {}
                                                       Type: Multiset Integer
--R 
--R
--R   (13)  {}
--R                                                       Type: Multiset Integer
--E 13

--S 14 of 17
t1 := multiset [2,2]
 

   (14)  {2: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (14)  {2: 2}
--R                                                       Type: Multiset Integer
--E 14

--S 15 of 17
[t1 < t, t1 < s, t1 <= t, t1 <= s]
 

   (15)  [true,true,true,true]
                                                           Type: List Boolean
--R 
--R
--R   (15)  [true,true,true,true]
--R                                                           Type: List Boolean
--E 15

--S 16 of 17
t1 := multiset [2,2,2]
 

   (16)  {3: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (16)  {3: 2}
--R                                                       Type: Multiset Integer
--E 16

--S 17 of 17
[t1 < t, t1 < s, t1 <= t, t1 <= s]
 

   (17)  [true,false,true,true]
                                                           Type: List Boolean
--R 
--R
--R   (17)  [true,false,true,true]
--R                                                           Type: List Boolean
--E 17
)spool 
 
Starts dribbling to symbol.output (2009/2/17, 18:0:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 24
X: Symbol := 'x
 

   (1)  x
                                                                 Type: Symbol
--R 
--R
--R   (1)  x
--R                                                                 Type: Symbol
--E 1

--S 2 of 24
XX: Symbol := x
 

   (2)  x
                                                                 Type: Symbol
--R 
--R
--R   (2)  x
--R                                                                 Type: Symbol
--E 2

--S 3 of 24
A := 'a
 

   (3)  a
                                                             Type: Variable a
--R 
--R
--R   (3)  a
--R                                                             Type: Variable a
--E 3

--S 4 of 24
B := b
 

   (4)  b
                                                             Type: Variable b
--R 
--R
--R   (4)  b
--R                                                             Type: Variable b
--E 4

--S 5 of 24
x**2 + 1
 

         2
   (5)  x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (5)  x  + 1
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 24
"Hello"::Symbol
 

   (6)  Hello
                                                                 Type: Symbol
--R 
--R
--R   (6)  Hello
--R                                                                 Type: Symbol
--E 6

--S 7 of 24
new()$Symbol
 

   (7)  %A
                                                                 Type: Symbol
--R 
--R
--R   (7)  %A
--R                                                                 Type: Symbol
--E 7

--S 8 of 24
new()$Symbol
 

   (8)  %B
                                                                 Type: Symbol
--R 
--R
--R   (8)  %B
--R                                                                 Type: Symbol
--E 8

--S 9 of 24
new("xyz")$Symbol
 

   (9)  %xyz0
                                                                 Type: Symbol
--R 
--R
--R   (9)  %xyz0
--R                                                                 Type: Symbol
--E 9

--S 10 of 24
X[i,j]
 

   (10)  x
          i,j
                                                                 Type: Symbol
--R 
--R
--R   (10)  x
--R          i,j
--R                                                                 Type: Symbol
--E 10

--S 11 of 24
U := subscript(u, [1,2,1,2])
 

   (11)  u
          1,2,1,2
                                                                 Type: Symbol
--R 
--R
--R   (11)  u
--R          1,2,1,2
--R                                                                 Type: Symbol
--E 11

--S 12 of 24
V := superscript(v, [n])
 

          n
   (12)  v
                                                                 Type: Symbol
--R 
--R
--R          n
--R   (12)  v
--R                                                                 Type: Symbol
--E 12

--S 13 of 24
P := argscript(p, [t])
 

   (13)  p(t)
                                                                 Type: Symbol
--R 
--R
--R   (13)  p(t)
--R                                                                 Type: Symbol
--E 13

--S 14 of 24
scripted? U
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 24
scripted? X
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 24
string X
 

   (16)  "x"
                                                                 Type: String
--R 
--R
--R   (16)  "x"
--R                                                                 Type: String
--E 16

--S 17 of 24
name U
 

   (17)  u
                                                                 Type: Symbol
--R 
--R
--R   (17)  u
--R                                                                 Type: Symbol
--E 17

--S 18 of 24
scripts U
 

   (18)  [sub= [1,2,1,2],sup= [],presup= [],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (18)  [sub= [1,2,1,2],sup= [],presup= [],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 18

--S 19 of 24
name X
 

   (19)  x
                                                                 Type: Symbol
--R 
--R
--R   (19)  x
--R                                                                 Type: Symbol
--E 19

--S 20 of 24
scripts X
 

   (20)  [sub= [],sup= [],presup= [],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (20)  [sub= [],sup= [],presup= [],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 20

--S 21 of 24
M := script(Mammoth, [[i,j],[k,l],[0,1],[2],[u,v,w]])
 

         0,1       k,l
   (21)     Mammoth   (u,v,w)
           2       i,j
                                                                 Type: Symbol
--R 
--R
--R         0,1       k,l
--R   (21)     Mammoth   (u,v,w)
--R           2       i,j
--R                                                                 Type: Symbol
--E 21

--S 22 of 24
scripts M
 

   (22)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [2],args= [u,v,w]]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (22)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [2],args= [u,v,w]]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 22

--S 23 of 24
N := script(Nut, [[i,j],[k,l],[0,1]])
 

         0,1   k,l
   (23)     Nut
               i,j
                                                                 Type: Symbol
--R 
--R
--R         0,1   k,l
--R   (23)     Nut
--R               i,j
--R                                                                 Type: Symbol
--E 23

--S 24 of 24
scripts N
 

   (24)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (24)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 24
)spool 
 
Starts dribbling to matrix1.output (2009/2/17, 17:55:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 38
m : Matrix(Integer) := new(3,3,0)
 

        +0  0  0+
        |       |
   (1)  |0  0  0|
        |       |
        +0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  0  0+
--R        |       |
--R   (1)  |0  0  0|
--R        |       |
--R        +0  0  0+
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 38
setelt(m,2,3,5)
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 38
m(1,2) := 10
 

   (3)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  10
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 38
m
 

        +0  10  0+
        |        |
   (4)  |0  0   5|
        |        |
        +0  0   0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  10  0+
--R        |        |
--R   (4)  |0  0   5|
--R        |        |
--R        +0  0   0+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 38
matrix [[1,2,3,4],[0,9,8,7]]
 

        +1  2  3  4+
   (5)  |          |
        +0  9  8  7+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2  3  4+
--R   (5)  |          |
--R        +0  9  8  7+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 38
dm := diagonalMatrix [1,x**2,x**3,x**4,x**5]
 

        +1  0   0   0   0 +
        |                 |
        |    2            |
        |0  x   0   0   0 |
        |                 |
        |        3        |
   (6)  |0  0   x   0   0 |
        |                 |
        |            4    |
        |0  0   0   x   0 |
        |                 |
        |                5|
        +0  0   0   0   x +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  0   0   0   0 +
--R        |                 |
--R        |    2            |
--R        |0  x   0   0   0 |
--R        |                 |
--R        |        3        |
--R   (6)  |0  0   x   0   0 |
--R        |                 |
--R        |            4    |
--R        |0  0   0   x   0 |
--R        |                 |
--R        |                5|
--R        +0  0   0   0   x +
--R                                              Type: Matrix Polynomial Integer
--E 6

--S 7 of 38
setRow!(dm,5,vector [1,1,1,1,1])
 

        +1  0   0   0   0+
        |                |
        |    2           |
        |0  x   0   0   0|
        |                |
   (7)  |        3       |
        |0  0   x   0   0|
        |                |
        |            4   |
        |0  0   0   x   0|
        |                |
        +1  1   1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  0   0   0   0+
--R        |                |
--R        |    2           |
--R        |0  x   0   0   0|
--R        |                |
--R   (7)  |        3       |
--R        |0  0   x   0   0|
--R        |                |
--R        |            4   |
--R        |0  0   0   x   0|
--R        |                |
--R        +1  1   1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 7

--S 8 of 38
setColumn!(dm,2,vector [y,y,y,y,y])
 

        +1  y  0   0   0+
        |               |
        |0  y  0   0   0|
        |               |
        |       3       |
   (8)  |0  y  x   0   0|
        |               |
        |           4   |
        |0  y  0   x   0|
        |               |
        +1  y  1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  y  0   0   0+
--R        |               |
--R        |0  y  0   0   0|
--R        |               |
--R        |       3       |
--R   (8)  |0  y  x   0   0|
--R        |               |
--R        |           4   |
--R        |0  y  0   x   0|
--R        |               |
--R        +1  y  1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 8

--S 9 of 38
cdm := copy(dm)
 

        +1  y  0   0   0+
        |               |
        |0  y  0   0   0|
        |               |
        |       3       |
   (9)  |0  y  x   0   0|
        |               |
        |           4   |
        |0  y  0   x   0|
        |               |
        +1  y  1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  y  0   0   0+
--R        |               |
--R        |0  y  0   0   0|
--R        |               |
--R        |       3       |
--R   (9)  |0  y  x   0   0|
--R        |               |
--R        |           4   |
--R        |0  y  0   x   0|
--R        |               |
--R        +1  y  1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 9

--S 10 of 38
setelt(dm,4,1,1-x**7)
 

            7
   (10)  - x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R            7
--R   (10)  - x  + 1
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 38
[dm,cdm]
 

          +   1      y  0   0   0+ +1  y  0   0   0+
          |                      | |               |
          |   0      y  0   0   0| |0  y  0   0   0|
          |                      | |               |
          |              3       | |       3       |
   (11)  [|   0      y  x   0   0|,|0  y  x   0   0|]
          |                      | |               |
          |   7              4   | |           4   |
          |- x  + 1  y  0   x   0| |0  y  0   x   0|
          |                      | |               |
          +   1      y  1   1   1+ +1  y  1   1   1+
                                         Type: List Matrix Polynomial Integer
--R 
--R
--R          +   1      y  0   0   0+ +1  y  0   0   0+
--R          |                      | |               |
--R          |   0      y  0   0   0| |0  y  0   0   0|
--R          |                      | |               |
--R          |              3       | |       3       |
--R   (11)  [|   0      y  x   0   0|,|0  y  x   0   0|]
--R          |                      | |               |
--R          |   7              4   | |           4   |
--R          |- x  + 1  y  0   x   0| |0  y  0   x   0|
--R          |                      | |               |
--R          +   1      y  1   1   1+ +1  y  1   1   1+
--R                                         Type: List Matrix Polynomial Integer
--E 11

--S 12 of 38
subMatrix(dm,2,3,2,4)
 

         +y  0   0+
   (12)  |        |
         |    3   |
         +y  x   0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +y  0   0+
--R   (12)  |        |
--R         |    3   |
--R         +y  x   0+
--R                                              Type: Matrix Polynomial Integer
--E 12

--S 13 of 38
d := diagonalMatrix [1.2,-1.3,1.4,-1.5]
 

         +1.2   0.0   0.0   0.0 +
         |                      |
         |0.0  - 1.3  0.0   0.0 |
   (13)  |                      |
         |0.0   0.0   1.4   0.0 |
         |                      |
         +0.0   0.0   0.0  - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2   0.0   0.0   0.0 +
--R         |                      |
--R         |0.0  - 1.3  0.0   0.0 |
--R   (13)  |                      |
--R         |0.0   0.0   1.4   0.0 |
--R         |                      |
--R         +0.0   0.0   0.0  - 1.5+
--R                                                           Type: Matrix Float
--E 13

--S 14 of 38
e := matrix [[6.7,9.11],[-31.33,67.19]]
 

         +  6.7    9.11 +
   (14)  |              |
         +- 31.33  67.19+
                                                           Type: Matrix Float
--R 
--R
--R         +  6.7    9.11 +
--R   (14)  |              |
--R         +- 31.33  67.19+
--R                                                           Type: Matrix Float
--E 14

--S 15 of 38
setsubMatrix!(d,1,2,e)
 

         +1.2    6.7    9.11    0.0 +
         |                          |
         |0.0  - 31.33  67.19   0.0 |
   (15)  |                          |
         |0.0    0.0     1.4    0.0 |
         |                          |
         +0.0    0.0     0.0   - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2    6.7    9.11    0.0 +
--R         |                          |
--R         |0.0  - 31.33  67.19   0.0 |
--R   (15)  |                          |
--R         |0.0    0.0     1.4    0.0 |
--R         |                          |
--R         +0.0    0.0     0.0   - 1.5+
--R                                                           Type: Matrix Float
--E 15

--S 16 of 38
d
 

         +1.2    6.7    9.11    0.0 +
         |                          |
         |0.0  - 31.33  67.19   0.0 |
   (16)  |                          |
         |0.0    0.0     1.4    0.0 |
         |                          |
         +0.0    0.0     0.0   - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2    6.7    9.11    0.0 +
--R         |                          |
--R         |0.0  - 31.33  67.19   0.0 |
--R   (16)  |                          |
--R         |0.0    0.0     1.4    0.0 |
--R         |                          |
--R         +0.0    0.0     0.0   - 1.5+
--R                                                           Type: Matrix Float
--E 16

--S 17 of 38
a := matrix [[1/2,1/3,1/4],[1/5,1/6,1/7]]
 

         +1  1  1+
         |-  -  -|
         |2  3  4|
   (17)  |       |
         |1  1  1|
         |-  -  -|
         +5  6  7+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1+
--R         |-  -  -|
--R         |2  3  4|
--R   (17)  |       |
--R         |1  1  1|
--R         |-  -  -|
--R         +5  6  7+
--R                                                Type: Matrix Fraction Integer
--E 17

--S 18 of 38
b := matrix [[3/5,3/7,3/11],[3/13,3/17,3/19]]
 

         +3   3    3+
         |-   -   --|
         |5   7   11|
   (18)  |          |
         | 3   3   3|
         |--  --  --|
         +13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +3   3    3+
--R         |-   -   --|
--R         |5   7   11|
--R   (18)  |          |
--R         | 3   3   3|
--R         |--  --  --|
--R         +13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 18

--S 19 of 38
horizConcat(a,b)
 

         +1  1  1  3   3    3+
         |-  -  -  -   -   --|
         |2  3  4  5   7   11|
   (19)  |                   |
         |1  1  1   3   3   3|
         |-  -  -  --  --  --|
         +5  6  7  13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1  3   3    3+
--R         |-  -  -  -   -   --|
--R         |2  3  4  5   7   11|
--R   (19)  |                   |
--R         |1  1  1   3   3   3|
--R         |-  -  -  --  --  --|
--R         +5  6  7  13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 19

--S 20 of 38
vab := vertConcat(a,b)
 

         +1   1   1 +
         |-   -   - |
         |2   3   4 |
         |          |
         |1   1   1 |
         |-   -   - |
         |5   6   7 |
   (20)  |          |
         |3   3    3|
         |-   -   --|
         |5   7   11|
         |          |
         | 3   3   3|
         |--  --  --|
         +13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1   1   1 +
--R         |-   -   - |
--R         |2   3   4 |
--R         |          |
--R         |1   1   1 |
--R         |-   -   - |
--R         |5   6   7 |
--R   (20)  |          |
--R         |3   3    3|
--R         |-   -   --|
--R         |5   7   11|
--R         |          |
--R         | 3   3   3|
--R         |--  --  --|
--R         +13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 20

--S 21 of 38
transpose vab
 

         +1  1  3    3+
         |-  -  -   --|
         |2  5  5   13|
         |            |
         |1  1  3    3|
   (21)  |-  -  -   --|
         |3  6  7   17|
         |            |
         |1  1   3   3|
         |-  -  --  --|
         +4  7  11  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  3    3+
--R         |-  -  -   --|
--R         |2  5  5   13|
--R         |            |
--R         |1  1  3    3|
--R   (21)  |-  -  -   --|
--R         |3  6  7   17|
--R         |            |
--R         |1  1   3   3|
--R         |-  -  --  --|
--R         +4  7  11  19+
--R                                                Type: Matrix Fraction Integer
--E 21

)clear all
 
   All user variables and function definitions have been cleared.

--S 22 of 38
m := matrix [[1,2],[3,4]]
 

        +1  2+
   (1)  |    |
        +3  4+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2+
--R   (1)  |    |
--R        +3  4+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 38
4 * m * (-5)
 

        +- 20  - 40+
   (2)  |          |
        +- 60  - 80+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 20  - 40+
--R   (2)  |          |
--R        +- 60  - 80+
--R                                                         Type: Matrix Integer
--E 23

--S 24 of 38
n := matrix([[1,0,-2],[-3,5,1]])
 

        + 1   0  - 2+
   (3)  |           |
        +- 3  5   1 +
                                                         Type: Matrix Integer
--R 
--R
--R        + 1   0  - 2+
--R   (3)  |           |
--R        +- 3  5   1 +
--R                                                         Type: Matrix Integer
--E 24

--S 25 of 38
m * n
 

        +- 5  10   0 +
   (4)  |            |
        +- 9  20  - 2+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 5  10   0 +
--R   (4)  |            |
--R        +- 9  20  - 2+
--R                                                         Type: Matrix Integer
--E 25

--S 26 of 38
vec := column(n,3)
 

   (5)  [- 2,1]
                                                         Type: Vector Integer
--R 
--R
--R   (5)  [- 2,1]
--R                                                         Type: Vector Integer
--E 26

--S 27 of 38
vec * m
 

   (6)  [1,0]
                                                         Type: Vector Integer
--R 
--R
--R   (6)  [1,0]
--R                                                         Type: Vector Integer
--E 27

--S 28 of 38
m * vec
 

   (7)  [0,- 2]
                                                         Type: Vector Integer
--R 
--R
--R   (7)  [0,- 2]
--R                                                         Type: Vector Integer
--E 28

--S 29 of 38
hilb := matrix([[1/(i + j) for i in 1..3] for j in 1..3])
 

        +1  1  1+
        |-  -  -|
        |2  3  4|
        |       |
        |1  1  1|
   (8)  |-  -  -|
        |3  4  5|
        |       |
        |1  1  1|
        |-  -  -|
        +4  5  6+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +1  1  1+
--R        |-  -  -|
--R        |2  3  4|
--R        |       |
--R        |1  1  1|
--R   (8)  |-  -  -|
--R        |3  4  5|
--R        |       |
--R        |1  1  1|
--R        |-  -  -|
--R        +4  5  6+
--R                                                Type: Matrix Fraction Integer
--E 29

--S 30 of 38
inverse(hilb)
 

        + 72    - 240   180 +
        |                   |
   (9)  |- 240   900   - 720|
        |                   |
        + 180   - 720   600 +
                                     Type: Union(Matrix Fraction Integer,...)
--R 
--R
--R        + 72    - 240   180 +
--R        |                   |
--R   (9)  |- 240   900   - 720|
--R        |                   |
--R        + 180   - 720   600 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 30

--S 31 of 38
mm := matrix([[1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16]])
 

         +1   2   3   4 +
         |              |
         |5   6   7   8 |
   (10)  |              |
         |9   10  11  12|
         |              |
         +13  14  15  16+
                                                         Type: Matrix Integer
--R 
--R
--R         +1   2   3   4 +
--R         |              |
--R         |5   6   7   8 |
--R   (10)  |              |
--R         |9   10  11  12|
--R         |              |
--R         +13  14  15  16+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 38
inverse(mm)
 

   (11)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (11)  "failed"
--R                                                    Type: Union("failed",...)
--E 32

--S 33 of 38
determinant(mm)
 

   (12)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (12)  0
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 38
trace(mm)
 

   (13)  34
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  34
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 38
rank(mm)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 38
nullity(mm)
 

   (15)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  2
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 38
nullSpace(mm)
 

   (16)  [[1,- 2,1,0],[2,- 3,0,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (16)  [[1,- 2,1,0],[2,- 3,0,1]]
--R                                                    Type: List Vector Integer
--E 37

--S 38 of 38
rowEchelon(mm)
 

         +1  2  3  4 +
         |           |
         |0  4  8  12|
   (17)  |           |
         |0  0  0  0 |
         |           |
         +0  0  0  0 +
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3  4 +
--R         |           |
--R         |0  4  8  12|
--R   (17)  |           |
--R         |0  0  0  0 |
--R         |           |
--R         +0  0  0  0 +
--R                                                         Type: Matrix Integer
--E 38
)spool 
 
Starts dribbling to kafile.output (2009/2/17, 17:46:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 5
ey: KeyedAccessFile(Integer) := open("/tmp/editor.year", "output")
 

   (1)  "/tmp/editor.year"
                                                Type: KeyedAccessFile Integer
--R 
--R
--R   (1)  "/tmp/editor.year"
--R                                                Type: KeyedAccessFile Integer
--E 1

--S 2 of 5
ey."Char"     := 1986
 

   (2)  1986
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1986
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 5
ey."Caviness" := 1985
 

   (3)  1985
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1985
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 5
ey."Fitch"    := 1984
 

   (4)  1984
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  1984
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 5
ey."Char"
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "/tmp/editor.year"

(5) -> Starts dribbling to schaum3.output (2009/2/17, 17:59:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/((a*x+b)*(p*x+q)),x)
 

        - log(p x + q) + log(a x + b)
   (1)  -----------------------------
                  a q - b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(p x + q) + log(a x + b)
--R   (1)  -----------------------------
--R                  a q - b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b))
 

              p x + q
          log(-------)
              a x + b
   (2)  - ------------
            a q - b p
                                                     Type: Expression Integer
--R 
--R
--R              p x + q
--R          log(-------)
--R              a x + b
--R   (2)  - ------------
--R            a q - b p
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                            p x + q
        - log(p x + q) + log(a x + b) + log(-------)
                                            a x + b
   (3)  --------------------------------------------
                          a q - b p
                                                     Type: Expression Integer
--R 
--R
--R                                            p x + q
--R        - log(p x + q) + log(a x + b) + log(-------)
--R                                            a x + b
--R   (3)  --------------------------------------------
--R                          a q - b p
--R                                                     Type: Expression Integer
--E

--S 4
logdiv:=rule(log(a)-log(b) == log(a/b))
 

                                      a
   (4)  - log(b) + log(a) + %G == log(-) + %G
                                      b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                      a
--I   (4)  - log(b) + log(a) + %I == log(-) + %I
--R                                      b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5
dd:=logdiv cc
 

                              1
        log(a x + b) + log(-------)
                           a x + b
   (5)  ---------------------------
                 a q - b p
                                                     Type: Expression Integer
--R
--R                              1
--R        log(a x + b) + log(-------)
--R                           a x + b
--R   (5)  ---------------------------
--R                 a q - b p
--R                                                     Type: Expression Integer
--E

--S 6
logmul:=rule(log(a)+log(b) == log(a*b))
 

   (6)  log(b) + log(a) + %H == log(a b) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(b) + log(a) + %J == log(a b) + %J
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 7      14:105 Schaums and Axiom agree
ee:=logmul dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(x/((a*x+b)*(p*x+q)),x)
 

        a q log(p x + q) - b p log(a x + b)
   (1)  -----------------------------------
                    2           2
                   a p q - a b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a q log(p x + q) - b p log(a x + b)
--R   (1)  -----------------------------------
--R                    2           2
--R                   a p q - a b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q))
 

        a q log(p x + q) - b p log(a x + b)
   (2)  -----------------------------------
                    2           2
                   a p q - a b p
                                                     Type: Expression Integer
--R 
--R
--R        a q log(p x + q) - b p log(a x + b)
--R   (2)  -----------------------------------
--R                    2           2
--R                   a p q - a b p
--R                                                     Type: Expression Integer
--E

--S 10     14:106 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 11
aa:=integrate(1/((a*x+b)^2*(p*x+q)),x)
 

        (a p x + b p)log(p x + q) + (- a p x - b p)log(a x + b) - a q + b p
   (1)  -------------------------------------------------------------------
                 3 2     2           2 2      2   2       2       3 2
               (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        (a p x + b p)log(p x + q) + (- a p x - b p)log(a x + b) - a q + b p
--R   (1)  -------------------------------------------------------------------
--R                 3 2     2           2 2      2   2       2       3 2
--R               (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12
bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b)))
 

                                  p x + q
                 (a p x + b p)log(-------) - a q + b p
                                  a x + b
   (2)  ------------------------------------------------------
          3 2     2           2 2      2   2       2       3 2
        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
                                                     Type: Expression Integer
--R 
--R
--R                                  p x + q
--R                 (a p x + b p)log(-------) - a q + b p
--R                                  a x + b
--R   (2)  ------------------------------------------------------
--R          3 2     2           2 2      2   2       2       3 2
--R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
--R                                                     Type: Expression Integer
--E

--S 13
cc:=aa-bb
 

                                                p x + q
        p log(p x + q) - p log(a x + b) - p log(-------)
                                                a x + b
   (3)  ------------------------------------------------
                      2 2               2 2
                     a q  - 2a b p q + b p
                                                     Type: Expression Integer
--R 
--R
--R                                                p x + q
--R        p log(p x + q) - p log(a x + b) - p log(-------)
--R                                                a x + b
--R   (3)  ------------------------------------------------
--R                      2 2               2 2
--R                     a q  - 2a b p q + b p
--R                                                     Type: Expression Integer
--E

--S 14
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 15     14:107 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(x/((a*x+b)^2*(p*x+q)),x)
 

   (1)
       2                             2                                    2
   (- a q x - a b q)log(p x + q) + (a q x + a b q)log(a x + b) + a b q - b p
   -------------------------------------------------------------------------
              4 2     3         2 2 2      3   2     2 2         3 2
            (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       2                             2                                    2
--R   (- a q x - a b q)log(p x + q) + (a q x + a b q)log(a x + b) + a b q - b p
--R   -------------------------------------------------------------------------
--R              4 2     3         2 2 2      3   2     2 2         3 2
--R            (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17
bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b)))
 

                  2                a x + b             2
                (a q x + a b q)log(-------) + a b q - b p
                                   p x + q
   (2)  --------------------------------------------------------
          4 2     3         2 2 2      3   2     2 2         3 2
        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
                                                     Type: Expression Integer
--R 
--R
--R                  2                a x + b             2
--R                (a q x + a b q)log(-------) + a b q - b p
--R                                   p x + q
--R   (2)  --------------------------------------------------------
--R          4 2     3         2 2 2      3   2     2 2         3 2
--R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
--R                                                     Type: Expression Integer
--E

--S 18
cc:=aa-bb
 

                                                  a x + b
        - q log(p x + q) + q log(a x + b) - q log(-------)
                                                  p x + q
   (3)  --------------------------------------------------
                       2 2               2 2
                      a q  - 2a b p q + b p
                                                     Type: Expression Integer
--R 
--R
--R                                                  a x + b
--R        - q log(p x + q) + q log(a x + b) - q log(-------)
--R                                                  p x + q
--R   (3)  --------------------------------------------------
--R                       2 2               2 2
--R                      a q  - 2a b p q + b p
--R                                                     Type: Expression Integer
--E

--S 19
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20     14:108 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 21
aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x)
 

   (1)
         3 2     2   2
       (a q x + a b q )log(p x + q)
     + 
             2           2 2         2       3 2                   2       3 2
       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
  /
       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R         3 2     2   2
--R       (a q x + a b q )log(p x + q)
--R     + 
--R             2           2 2         2       3 2                   2       3 2
--R       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
--R  /
--R       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
--R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22
bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_
     1/(b*p-a*q)^2*(q^2/p*log(p*x+q)+((b*(b*p-2*a*q))/a^2)*log(a*x+b))
 

   (2)
         3 2     2   2
       (a q x + a b q )log(p x + q)
     + 
             2           2 2         2       3 2                   2       3 2
       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
  /
       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R         3 2     2   2
--R       (a q x + a b q )log(p x + q)
--R     + 
--R             2           2 2         2       3 2                   2       3 2
--R       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
--R  /
--R       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
--R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
--R                                                     Type: Expression Integer
--E

--S 23     14:109 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 24     14:110 Axiom cannot do this integral
aa:=integrate(1/((a*x+b)^m*(p*x+q)^n),x)
 

           x
         ++             1
   (1)   |   ---------------------- d%N
        ++             m          n
             (b + %N a) (q + %N p)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             1
--I   (1)   |   ---------------------- d%L
--R        ++             m          n
--I             (b + %L a) (q + %L p)
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 25
aa:=integrate((a*x+b)/(p*x+q),x)
 

        (- a q + b p)log(p x + q) + a p x
   (1)  ---------------------------------
                         2
                        p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        (- a q + b p)log(p x + q) + a p x
--R   (1)  ---------------------------------
--R                         2
--R                        p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 26
bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q)
 

        (- a q + b p)log(p x + q) + a p x
   (2)  ---------------------------------
                         2
                        p
                                                     Type: Expression Integer
--R 
--R
--R        (- a q + b p)log(p x + q) + a p x
--R   (2)  ---------------------------------
--R                         2
--R                        p
--R                                                     Type: Expression Integer
--E

--S 27     14:111 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28     14:112 Axiom cannot do this integral
aa:=integrate((a*x+b)^m/(p*x+q)^n,x)
 

           x           m
         ++  (b + %N a)
   (1)   |   ----------- d%N
        ++             n
             (q + %N p)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           m
--I         ++  (b + %L a)
--I   (1)   |   ----------- d%L
--R        ++             n
--I             (q + %L p)
--R                                          Type: Union(Expression Integer,...)
--E
)spool
 
Starts dribbling to robidoux.output (2009/2/17, 17:57:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 15
X1:=operator 'X1
 

   (1)  X1
                                                          Type: BasicOperator
--R 
--R
--R   (1)  X1
--R                                                          Type: BasicOperator
--E 1

--S 2 of 15
deq1:=D(X1 t,t)=(1+ cos t /(2+sin t)) * X1 t
 

          ,     X1(t)sin(t) + X1(t)cos(t) + 2X1(t)
   (2)  X1 (t)= ----------------------------------
                            sin(t) + 2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,     X1(t)sin(t) + X1(t)cos(t) + 2X1(t)
--R   (2)  X1 (t)= ----------------------------------
--R                            sin(t) + 2
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 15
solve(deq1,X1,t)
 

                                 t            t
   (3)  [particular= 0,basis= [%e sin(t) + 2%e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                 t            t
--R   (3)  [particular= 0,basis= [%e sin(t) + 2%e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 3

--S 4 of 15
C1*%.basis.1
 

             t               t
   (4)  C1 %e sin(t) + 2C1 %e
                                                     Type: Expression Integer
--R 
--R
--R             t               t
--R   (4)  C1 %e sin(t) + 2C1 %e
--R                                                     Type: Expression Integer
--E 4

--S 5 of 15
function(%,'x1,'t)
 

   (5)  x1
                                                                 Type: Symbol
--R 
--R
--R   (5)  x1
--R                                                                 Type: Symbol
--E 5

--S 6 of 15
x1
 

   (6)  x1 t == C1 exp(t)sin(t) + 2C1 exp(t)
                                                      Type: FunctionCalled x1
--R 
--R
--R   (6)  x1 t == C1 exp(t)sin(t) + 2C1 exp(t)
--R                                                      Type: FunctionCalled x1
--E 6

--S 7 of 15
X2:=operator 'X2
 

   (7)  X2
                                                          Type: BasicOperator
--R 
--R
--R   (7)  X2
--R                                                          Type: BasicOperator
--E 7

--S 8 of 15
deq2:=D(X2 t,t)=x1 t - X2 t
 
   Compiling function x1 with type Variable t -> Expression Integer 

          ,          t               t
   (8)  X2 (t)= C1 %e sin(t) + 2C1 %e  - X2(t)

                                            Type: Equation Expression Integer
--R 
--R   Compiling function x1 with type Variable t -> Expression Integer 
--R
--R          ,          t               t
--R   (8)  X2 (t)= C1 %e sin(t) + 2C1 %e  - X2(t)
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 15
solve(deq2,X2,t)
 

   (9)
                      - t   t 2                              - t   t 2
                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
   [particular= ------------------------------------------------------,
                                           5
              - t
    basis= [%e   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (9)
--R                      - t   t 2                              - t   t 2
--R                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
--R   [particular= ------------------------------------------------------,
--R                                           5
--R              - t
--R    basis= [%e   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 9

--S 10 of 15
%.particular
 

               - t   t 2                              - t   t 2
         2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
   (10)  ------------------------------------------------------
                                    5
                                                     Type: Expression Integer
--R 
--R
--R               - t   t 2                              - t   t 2
--R         2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
--R   (10)  ------------------------------------------------------
--R                                    5
--R                                                     Type: Expression Integer
--E 10

--S 11 of 15
simplify %
 

               t                              t
         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e
   (11)  --------------------------------------
                            5
                                                     Type: Expression Integer
--R 
--R
--R               t                              t
--R         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e
--R   (11)  --------------------------------------
--R                            5
--R                                                     Type: Expression Integer
--E 11

--S 12 of 15
%+C2*%%(-3).basis.1
 

               t                              t         - t
         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
   (12)  --------------------------------------------------
                                  5
                                                     Type: Expression Integer
--R 
--R
--R               t                              t         - t
--R         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
--R   (12)  --------------------------------------------------
--R                                  5
--R                                                     Type: Expression Integer
--E 12

--S 13 of 15
function(%,'x2,'t)
 

   (13)  x2
                                                                 Type: Symbol
--R 
--R
--R   (13)  x2
--R                                                                 Type: Symbol
--E 13

--S 14 of 15
x2
 

                 2C1 exp(t)sin(t) + (- C1 cos(t) + 5C1)exp(t) + 5C2 exp(- t)
   (14)  x2 t == -----------------------------------------------------------
                                              5
                                                      Type: FunctionCalled x2
--R 
--R
--R                 2C1 exp(t)sin(t) + (- C1 cos(t) + 5C1)exp(t) + 5C2 exp(- t)
--R   (14)  x2 t == -----------------------------------------------------------
--R                                              5
--R                                                      Type: FunctionCalled x2
--E 14

--S 15 of 15
x1 t
 

              t               t
   (15)  C1 %e sin(t) + 2C1 %e
                                                     Type: Expression Integer
--R 
--R
--R              t               t
--R   (15)  C1 %e sin(t) + 2C1 %e
--R                                                     Type: Expression Integer
--E 15
)spool 
 
Starts dribbling to intrf.output (2009/2/17, 17:46:52).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 14
x + y/x
 

             2
        y + x
   (1)  ------
           x
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             2
--R        y + x
--R   (1)  ------
--R           x
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 14
integrate(%,x)
 

                     2
        2y log(x) + x
   (2)  --------------
               2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R        2y log(x) + x
--R   (2)  --------------
--R               2
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 14
(x+1)**2/((x+1)**6+1)
 

                       2
                      x  + 2x + 1
   (3)  --------------------------------------
         6     5      4      3      2
        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                       2
--R                      x  + 2x + 1
--R   (3)  --------------------------------------
--R         6     5      4      3      2
--R        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 14
integrate(%,x)
 

              3     2
        atan(x  + 3x  + 3x + 1)
   (4)  -----------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2
--R        atan(x  + 3x  + 3x + 1)
--R   (4)  -----------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 14
(2*x**2+4)**4/(x**2-2)**5
 

            8       6       4       2
         16x  + 128x  + 384x  + 512x  + 256
   (5)  ------------------------------------
         10      8      6      4      2
        x   - 10x  + 40x  - 80x  + 80x  - 32
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            8       6       4       2
--R         16x  + 128x  + 384x  + 512x  + 256
--R   (5)  ------------------------------------
--R         10      8      6      4      2
--R        x   - 10x  + 40x  - 80x  + 80x  - 32
--R                                            Type: Fraction Polynomial Integer
--E 5

--S 6 of 14
integrate(%,x)
 

   (6)
                                                   +-+    2
          8      6      4      2       +-+    - 2x\|2  + x  + 2       7      5
       (3x  - 24x  + 72x  - 96x  + 48)\|2 log(-----------------) - 20x  - 24x
                                                     2
                                                    x  - 2
     + 
            3
       - 48x  - 160x
  /
       8      6      4      2
     2x  - 16x  + 48x  - 64x  + 32
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (6)
--R                                                   +-+    2
--R          8      6      4      2       +-+    - 2x\|2  + x  + 2       7      5
--R       (3x  - 24x  + 72x  - 96x  + 48)\|2 log(-----------------) - 20x  - 24x
--R                                                     2
--R                                                    x  - 2
--R     + 
--R            3
--R       - 48x  - 160x
--R  /
--R       8      6      4      2
--R     2x  - 16x  + 48x  - 64x  + 32
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 14
x**5/(x**4+x**2+1)**2
 

                    5
                   x
   (7)  ------------------------
         8     6     4     2
        x  + 2x  + 3x  + 2x  + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                    5
--R                   x
--R   (7)  ------------------------
--R         8     6     4     2
--R        x  + 2x  + 3x  + 2x  + 1
--R                                            Type: Fraction Polynomial Integer
--E 7

--S 8 of 14
integrate(%,x)
 

                               2      +-+
           4     2          (2x  + 1)\|3         2      +-+
        (4x  + 4x  + 4)atan(-------------) + (- x  + 1)\|3
                                  3
   (8)  ---------------------------------------------------
                           4     2      +-+
                        (6x  + 6x  + 6)\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               2      +-+
--R           4     2          (2x  + 1)\|3         2      +-+
--R        (4x  + 4x  + 4)atan(-------------) + (- x  + 1)\|3
--R                                  3
--R   (8)  ---------------------------------------------------
--R                           4     2      +-+
--R                        (6x  + 6x  + 6)\|3
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 14
1/(x**2 + a)
 

           1
   (9)  ------
         2
        x  + a
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           1
--R   (9)  ------
--R         2
--R        x  + a
--R                                            Type: Fraction Polynomial Integer
--E 9

--S 10 of 14
integrate(%,x)
 

                2      +---+
              (x  - a)\|- a  + 2a x         +-+
          log(---------------------)      x\|a
                       2             atan(-----)
                      x  + a                a
   (10)  [--------------------------,-----------]
                      +---+               +-+
                    2\|- a               \|a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                2      +---+
--R              (x  - a)\|- a  + 2a x         +-+
--R          log(---------------------)      x\|a
--R                       2             atan(-----)
--R                      x  + a                a
--R   (10)  [--------------------------,-----------]
--R                      +---+               +-+
--R                    2\|- a               \|a
--R                                     Type: Union(List Expression Integer,...)
--E 10

--S 11 of 14
x**2/(x**4-a**2)
 

             2
            x
   (11)  -------
          4    2
         x  - a
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             2
--R            x
--R   (11)  -------
--R          4    2
--R         x  - a
--R                                            Type: Fraction Polynomial Integer
--E 11

--S 12 of 14
integrate(%,x)
 

   (12)
          2      +-+                   +-+
        (x  + a)\|a  - 2a x          x\|a
    log(-------------------) + 2atan(-----)
                2                      a
               x  - a
   [---------------------------------------,
                       +-+
                     4\|a
          2      +---+                   +---+
        (x  - a)\|- a  + 2a x          x\|- a
    log(---------------------) - 2atan(-------)
                 2                        a
                x  + a
    -------------------------------------------]
                        +---+
                      4\|- a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (12)
--R          2      +-+                   +-+
--R        (x  + a)\|a  - 2a x          x\|a
--R    log(-------------------) + 2atan(-----)
--R                2                      a
--R               x  - a
--R   [---------------------------------------,
--R                       +-+
--R                     4\|a
--R          2      +---+                   +---+
--R        (x  - a)\|- a  + 2a x          x\|- a
--R    log(---------------------) - 2atan(-------)
--R                 2                        a
--R                x  + a
--R    -------------------------------------------]
--R                        +---+
--R                      4\|- a
--R                                     Type: Union(List Expression Integer,...)
--E 12

--S 13 of 14
x/(1-x**3)
 

              x
   (13)  - ------
            3
           x  - 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R              x
--R   (13)  - ------
--R            3
--R           x  - 1
--R                                            Type: Fraction Polynomial Integer
--E 13

--S 14 of 14
integrate(%,x)
 

                                                                +-+
          +-+     2              +-+                   (2x + 1)\|3
         \|3 log(x  + x + 1) - 2\|3 log(x - 1) - 6atan(------------)
                                                             3
   (14)  -----------------------------------------------------------
                                      +-+
                                    6\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                +-+
--R          +-+     2              +-+                   (2x + 1)\|3
--R         \|3 log(x  + x + 1) - 2\|3 log(x - 1) - 6atan(------------)
--R                                                             3
--R   (14)  -----------------------------------------------------------
--R                                      +-+
--R                                    6\|3
--R                                          Type: Union(Expression Integer,...)
--E 14
)spool 
 
Starts dribbling to intheory.output (2009/2/17, 17:46:43).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 22
div144 := divisors(144)
 

   (1)  [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144]
--R                                                           Type: List Integer
--E 1

--S 2 of 22
#(div144)
 

   (2)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  15
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 22
reduce(+,div144)
 

   (3)  403
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  403
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 22
numberOfDivisors(144)
 

   (4)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  15
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 22
sumOfDivisors(144)
 

   (5)  403
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  403
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 22
f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 22
f1(200)
 
   Compiling function f1 with type PositiveInteger -> Integer 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling function f1 with type PositiveInteger -> Integer 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 22
f1(846)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 22
f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 22
f2(200)
 
   Compiling function f2 with type PositiveInteger -> Integer 

   (10)  200
                                                        Type: PositiveInteger
--R 
--R   Compiling function f2 with type PositiveInteger -> Integer 
--R
--R   (10)  200
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 22
f2(846)
 

   (11)  846
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  846
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 22
fibonacci(25)
 

   (12)  75025
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  75025
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 22
[fibonacci(n) for n in 1..15]
 

   (13)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
                                                           Type: List Integer
--R 
--R
--R   (13)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
--R                                                           Type: List Integer
--E 13

--S 14 of 22
fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 22
fib(25)
 
   Compiling function fib with type PositiveInteger -> Integer 

   (15)  75025
                                                        Type: PositiveInteger
--R 
--R   Compiling function fib with type PositiveInteger -> Integer 
--R
--R   (15)  75025
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 22
[fib(n) for n in 1..15]
 

   (16)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
                                                           Type: List Integer
--R 
--R
--R   (16)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
--R                                                           Type: List Integer
--E 16

--S 17 of 22
legendre(3,5)
 

   (17)  - 1
                                                                Type: Integer
--R 
--R
--R   (17)  - 1
--R                                                                Type: Integer
--E 17

--S 18 of 22
legendre(23,691)
 

   (18)  - 1
                                                                Type: Integer
--R 
--R
--R   (18)  - 1
--R                                                                Type: Integer
--E 18

--S 19 of 22
h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 22
h(-163)
 
   Compiling function h with type Integer -> Integer 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling function h with type Integer -> Integer 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 22
h(-499)
 

   (21)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  3
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 22
h(-1832)
 

   (22)  26
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  26
--R                                                        Type: PositiveInteger
--E 22
)spool 
 
Starts dribbling to kamke5.output (2009/2/17, 17:48:3).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 130
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 130
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 130
f0:=operator 'f0
 

   (3)  f0
                                                          Type: BasicOperator
--R 
--R
--R   (3)  f0
--R                                                          Type: BasicOperator
--E 3

--S 4 of 130
f1:=operator 'f1
 

   (4)  f1
                                                          Type: BasicOperator
--R 
--R
--R   (4)  f1
--R                                                          Type: BasicOperator
--E 4

--S 5 of 130
f2:=operator 'f2
 

   (5)  f2
                                                          Type: BasicOperator
--R 
--R
--R   (5)  f2
--R                                                          Type: BasicOperator
--E 5

--S 6 of 130
f3:=operator 'f3
 

   (6)  f3
                                                          Type: BasicOperator
--R 
--R
--R   (6)  f3
--R                                                          Type: BasicOperator
--E 6

--S 7 of 130
g:=operator 'g
 

   (7)  g
                                                          Type: BasicOperator
--R 
--R
--R   (7)  g
--R                                                          Type: BasicOperator
--E 7

--S 8 of 130
g0:=operator 'g0
 

   (8)  g0
                                                          Type: BasicOperator
--R 
--R
--R   (8)  g0
--R                                                          Type: BasicOperator
--E 8

--S 9 of 130
g1:=operator 'g1
 

   (9)  g1
                                                          Type: BasicOperator
--R 
--R
--R   (9)  g1
--R                                                          Type: BasicOperator
--E 9

--S 10 of 130
h:=operator 'h
 

   (10)  h
                                                          Type: BasicOperator
--R 
--R
--R   (10)  h
--R                                                          Type: BasicOperator
--E 10

--S 11 of 130
ode251 := (x**2*y(x)-1)*D(y(x),x)+x*y(x)**2-1
 

           2          ,            2
   (11)  (x y(x) - 1)y (x) + x y(x)  - 1

                                                     Type: Expression Integer
--R 
--R
--R           2          ,            2
--R   (11)  (x y(x) - 1)y (x) + x y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 11

--S 12 of 130
yx:=solve(ode251,y,x)
 

          2    2
         x y(x)  - 2y(x) - 2x
   (12)  --------------------
                   2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2
--R         x y(x)  - 2y(x) - 2x
--R   (12)  --------------------
--R                   2
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 130
ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1
 

   (13)
          6    3     4    2     5         3      ,        5    4     3    3
       (2x y(x)  - 6x y(x)  - 4x y(x) + 4x  + 4)y (x) + 3x y(x)  - 8x y(x)

     + 
            4    2      2         3
       - 10x y(x)  + 12x y(x) + 8x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R          6    3     4    2     5         3      ,        5    4     3    3
--R       (2x y(x)  - 6x y(x)  - 4x y(x) + 4x  + 4)y (x) + 3x y(x)  - 8x y(x)
--R
--R     + 
--R            4    2      2         3
--R       - 10x y(x)  + 12x y(x) + 8x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 13

--S 14 of 130
ode252 := (x**2*y(x)-1)*D(y(x),x)-(x*y(x)**2-1)
 

           2          ,            2
   (14)  (x y(x) - 1)y (x) - x y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R           2          ,            2
--R   (14)  (x y(x) - 1)y (x) - x y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 130
solve(ode252,y,x)
 

   (15)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (15)  "failed"
--R                                                    Type: Union("failed",...)
--E 15

--S 16 of 130
ode253 := (x**2*y(x)-1)*D(y(x),x)+8*(x*y(x)**2-1)
 

           2          ,             2
   (16)  (x y(x) - 1)y (x) + 8x y(x)  - 8

                                                     Type: Expression Integer
--R 
--R
--R           2          ,             2
--R   (16)  (x y(x) - 1)y (x) + 8x y(x)  - 8
--R
--R                                                     Type: Expression Integer
--E 16

--S 17 of 130
solve(ode253,y,x)
 

   (17)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (17)  "failed"
--R                                                    Type: Union("failed",...)
--E 17

--S 18 of 130
ode254 := x*(x*y(x)-2)*D(y(x),x)+x**2*y(x)**3+x*y(x)**2-2*y(x)
 

           2           ,       2    3         2
   (18)  (x y(x) - 2x)y (x) + x y(x)  + x y(x)  - 2y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2           ,       2    3         2
--R   (18)  (x y(x) - 2x)y (x) + x y(x)  + x y(x)  - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 130
solve(ode254,y,x)
 

   (19)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (19)  "failed"
--R                                                    Type: Union("failed",...)
--E 19

--S 20 of 130
ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)**2-y(x)
 

           2           ,            2
   (20)  (x y(x) - 3x)y (x) + x y(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2           ,            2
--R   (20)  (x y(x) - 3x)y (x) + x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 130
solve(ode255,y,x)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--S 22 of 130
ode256 := x**2*(y(x)-1)*D(y(x),x)+(x-1)*y(x)
 

           2        2  ,
   (22)  (x y(x) - x )y (x) + (x - 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2        2  ,
--R   (22)  (x y(x) - x )y (x) + (x - 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 22

--S 23 of 130
solve(ode256,y,x)
 

   (23)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (23)  "failed"
--R                                                    Type: Union("failed",...)
--E 23

--S 24 of 130
ode257 := x*(x*y(x)+x**4-1)*D(y(x),x)-y(x)*(x*y(x)-x**4-1)
 

           2        5      ,            2     4
   (24)  (x y(x) + x  - x)y (x) - x y(x)  + (x  + 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2        5      ,            2     4
--R   (24)  (x y(x) + x  - x)y (x) - x y(x)  + (x  + 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 24

--S 25 of 130
solve(ode257,y,x)
 

   (25)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (25)  "failed"
--R                                                    Type: Union("failed",...)
--E 25

--S 26 of 130
ode258 := 2*x**2*y(x)*D(y(x),x)+y(x)**2-2*x**3-x**2
 

           2     ,          2     3    2
   (26)  2x y(x)y (x) + y(x)  - 2x  - x

                                                     Type: Expression Integer
--R 
--R
--R           2     ,          2     3    2
--R   (26)  2x y(x)y (x) + y(x)  - 2x  - x
--R
--R                                                     Type: Expression Integer
--E 26

--S 27 of 130
yx:=solve(ode258,y,x)
 

                         1
                       - -
              2    2     x
   (27)  (y(x)  - x )%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         1
--R                       - -
--R              2    2     x
--R   (27)  (y(x)  - x )%e
--R                                          Type: Union(Expression Integer,...)
--E 27

--S 28 of 130
ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2
 

   (28)
                              1 2
                            - -
        2    3     4          x   ,
     (4x y(x)  - 4x y(x))(%e   ) y (x)

   + 
                                                   1 2
                                                 - -
           4        3     2     2     5     4      x       3    2
     (3y(x)  + (- 4x  - 6x )y(x)  + 4x  + 3x )(%e   )  - 2x  - x
                                                     Type: Expression Integer
--R 
--R
--R   (28)
--R                              1 2
--R                            - -
--R        2    3     4          x   ,
--R     (4x y(x)  - 4x y(x))(%e   ) y (x)
--R
--R   + 
--R                                                   1 2
--R                                                 - -
--R           4        3     2     2     5     4      x       3    2
--R     (3y(x)  + (- 4x  - 6x )y(x)  + 4x  + 3x )(%e   )  - 2x  - x
--R                                                     Type: Expression Integer
--E 28

--S 29 of 130
ode259 := 2*x**2*y(x)*D(y(x),x)-y(x)**2-x**2*exp(x-1/x)
 

                             2
                            x  - 1
                            ------
           2     ,       2     x         2
   (29)  2x y(x)y (x) - x %e       - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                             2
--R                            x  - 1
--R                            ------
--R           2     ,       2     x         2
--R   (29)  2x y(x)y (x) - x %e       - y(x)
--R
--R                                                     Type: Expression Integer
--E 29

--S 30 of 130
yx:=solve(ode259,y,x)
 

                 2
             1  x  - 1          1
             -  ------          -
             x     x         2  x
   (30)  - %e %e       + y(x) %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2
--R             1  x  - 1          1
--R             -  ------          -
--R             x     x         2  x
--R   (30)  - %e %e       + y(x) %e
--R                                          Type: Union(Expression Integer,...)
--E 30

--S 31 of 130
ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x)
 

   (31)
                        2
                  1 2  x  - 1              1 2
                  -    ------              -
          2       x       x       2    3   x    ,
     (- 4x y(x)(%e ) %e       + 4x y(x) (%e ) )y (x)

   + 
                        2     2                                   2
                 1 2   x  - 1                         1 2        x  - 1
                 -     ------                         -          ------
        2        x        x             2         2   x      2      x
     (2x  - 1)(%e ) (%e      )  + ((- 2x  + 4)y(x) (%e )  - x )%e
   + 
                1 2
                -
            4   x
     - 3y(x) (%e )
                                                     Type: Expression Integer
--R 
--R
--R   (31)
--R                        2
--R                  1 2  x  - 1              1 2
--R                  -    ------              -
--R          2       x       x       2    3   x    ,
--R     (- 4x y(x)(%e ) %e       + 4x y(x) (%e ) )y (x)
--R
--R   + 
--R                        2     2                                   2
--R                 1 2   x  - 1                         1 2        x  - 1
--R                 -     ------                         -          ------
--R        2        x        x             2         2   x      2      x
--R     (2x  - 1)(%e ) (%e      )  + ((- 2x  + 4)y(x) (%e )  - x )%e
--R   + 
--R                1 2
--R                -
--R            4   x
--R     - 3y(x) (%e )
--R                                                     Type: Expression Integer
--E 31

--S 32 of 130
ode260 := (2*x**2*y(x)+x)*D(y(x),x)-x**2*y(x)**3+2*x*y(x)**2+y(x)
 

            2          ,       2    3          2
   (32)  (2x y(x) + x)y (x) - x y(x)  + 2x y(x)  + y(x)

                                                     Type: Expression Integer
--R 
--R
--R            2          ,       2    3          2
--R   (32)  (2x y(x) + x)y (x) - x y(x)  + 2x y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 32

--S 33 of 130
solve(ode260,y,x)
 

   (33)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (33)  "failed"
--R                                                    Type: Union("failed",...)
--E 33

--S 34 of 130
ode261 := (2*x**2*y(x)-x)*D(y(x),x)-2*x*y(x)**2-y(x)
 

            2          ,             2
   (34)  (2x y(x) - x)y (x) - 2x y(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R            2          ,             2
--R   (34)  (2x y(x) - x)y (x) - 2x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 34

--S 35 of 130
solve(ode261,y,x)
 

   (35)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (35)  "failed"
--R                                                    Type: Union("failed",...)
--E 35

--S 36 of 130
ode262 := (2*x**2*y(x)-x**3)*D(y(x),x)+y(x)**3-4*x*y(x)**2+2*x**3
 

            2        3  ,          3          2     3
   (36)  (2x y(x) - x )y (x) + y(x)  - 4x y(x)  + 2x

                                                     Type: Expression Integer
--R 
--R
--R            2        3  ,          3          2     3
--R   (36)  (2x y(x) - x )y (x) + y(x)  - 4x y(x)  + 2x
--R
--R                                                     Type: Expression Integer
--E 36

--S 37 of 130
solve(ode262,y,x)
 

   (37)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (37)  "failed"
--R                                                    Type: Union("failed",...)
--E 37

--S 38 of 130
ode263 := 2*x**3+y(x)*D(y(x),x)+3*x**2*y(x)**2+7
 

              ,        2    2     3
   (38)  y(x)y (x) + 3x y(x)  + 2x  + 7

                                                     Type: Expression Integer
--R 
--R
--R              ,        2    2     3
--R   (38)  y(x)y (x) + 3x y(x)  + 2x  + 7
--R
--R                                                     Type: Expression Integer
--E 38

--S 39 of 130
solve(ode263,y,x)
 

            x                            3
          ++      2    2      3       2%K
   (39)   |   (3%K y(x)  + 2%K  + 7)%e    d%K
         ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x                            3
--I          ++      2    2      3       2%K
--I   (39)   |   (3%K y(x)  + 2%K  + 7)%e    d%K
--R         ++
--R                                          Type: Union(Expression Integer,...)
--E 39

--S 40 of 130
ode264 := 2*x*(x**3*y(x)+1)*D(y(x),x)+(3*x**3*y(x)-1)*y(x)
 

            4           ,        3    2
   (40)  (2x y(x) + 2x)y (x) + 3x y(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R            4           ,        3    2
--R   (40)  (2x y(x) + 2x)y (x) + 3x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 40

--S 41 of 130
solve(ode264,y,x)
 

   (41)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (41)  "failed"
--R                                                    Type: Union("failed",...)
--E 41

--S 42 of 130
ode265 := (x**(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)**2*x**(n-1)_
            *(x**(n**2)*y(x)**2-1)
 

   (42)
            2                                            2
           n  + n      ,         2              2 n - 1 n
     (y(x)x       - 1)y (x) + (2n  + 4n + 2)y(x) x     x

   + 
          2           n - 1
     (- 2n  - 4n - 2)x
                                                     Type: Expression Integer
--R 
--R
--R   (42)
--R            2                                            2
--R           n  + n      ,         2              2 n - 1 n
--R     (y(x)x       - 1)y (x) + (2n  + 4n + 2)y(x) x     x
--R
--R   + 
--R          2           n - 1
--R     (- 2n  - 4n - 2)x
--R                                                     Type: Expression Integer
--E 42

--S 43 of 130
solve(ode265,y,x)
 

   (43)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (43)  "failed"
--R                                                    Type: Union("failed",...)
--E 43

--S 44 of 130
ode266 := (y(x)-x)*sqrt(x**2+1)*D(y(x),x)-a*sqrt((y(x)**2+1)**3)
 

                    +------+          +---------------------------+
                    | 2      ,        |    6        4        2
   (44)  (y(x) - x)\|x  + 1 y (x) - a\|y(x)  + 3y(x)  + 3y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R                    +------+          +---------------------------+
--R                    | 2      ,        |    6        4        2
--R   (44)  (y(x) - x)\|x  + 1 y (x) - a\|y(x)  + 3y(x)  + 3y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 44

--S 45 of 130
solve(ode266,y,x)
 

   (45)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (45)  "failed"
--R                                                    Type: Union("failed",...)
--E 45

--S 46 of 130
ode267 := y(x)*D(y(x),x)*sin(x)**2+y(x)**2*cos(x)*sin(x)-1
 

                   2 ,          2
   (46)  y(x)sin(x) y (x) + y(x) cos(x)sin(x) - 1

                                                     Type: Expression Integer
--R 
--R
--R                   2 ,          2
--R   (46)  y(x)sin(x) y (x) + y(x) cos(x)sin(x) - 1
--R
--R                                                     Type: Expression Integer
--E 46

--S 47 of 130
yx:=solve(ode267,y,x)
 

             2      2
         y(x) sin(x)  - 2x
   (47)  -----------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2      2
--R         y(x) sin(x)  - 2x
--R   (47)  -----------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 47

--S 48 of 130
ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1
 

   (48)
             3      6                4  ,           4            5
       (2y(x) sin(x)  - 4x y(x)sin(x) )y (x) + 3y(x) cos(x)sin(x)

     + 
            2      4          2            3            2     2
     - 2y(x) sin(x)  - 8x y(x) cos(x)sin(x)  + 4x sin(x)  + 4x cos(x)sin(x) - 4
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (48)
--R             3      6                4  ,           4            5
--R       (2y(x) sin(x)  - 4x y(x)sin(x) )y (x) + 3y(x) cos(x)sin(x)
--R
--R     + 
--R            2      4          2            3            2     2
--R     - 2y(x) sin(x)  - 8x y(x) cos(x)sin(x)  + 4x sin(x)  + 4x cos(x)sin(x) - 4
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 48

--S 49 of 130
ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)**2+h(x)
 

                  ,              2
   (49)  f(x)y(x)y (x) + g(x)y(x)  + h(x)

                                                     Type: Expression Integer
--R 
--R
--R                  ,              2
--R   (49)  f(x)y(x)y (x) + g(x)y(x)  + h(x)
--R
--R                                                     Type: Expression Integer
--E 49

--S 50 of 130
solve(ode268,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 50

--S 51 of 130
ode269 := (g1(x)*y(x)+g0(x))*D(y(x),x)-f1(x)*y(x)-_
              f2(x)*y(x)**2-f3(x)*y(x)**3-f0(x)
 

   (50)
                       ,               3            2
   (g1(x)y(x) + g0(x))y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)

                                                     Type: Expression Integer
--R 
--R
--R   (50)
--R                       ,               3            2
--R   (g1(x)y(x) + g0(x))y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)
--R
--R                                                     Type: Expression Integer
--E 51

--S 52 of 130
solve(ode269,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 52

--S 53 of 130
ode270 := (y(x)**2-x)*D(y(x),x)-y(x)+x**2
 

              2      ,              2
   (52)  (y(x)  - x)y (x) - y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              2      ,              2
--R   (52)  (y(x)  - x)y (x) - y(x) + x
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 130
yx:=solve(ode270,y,x)
 

             3              3
         y(x)  - 3x y(x) + x
   (53)  --------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3              3
--R         y(x)  - 3x y(x) + x
--R   (53)  --------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 54

--S 55 of 130
ode270expr := (yx**2-x)*D(yx,x)-yx+x**2
 

   (54)
               8          6     3    5      2    4     4    3
           y(x)  - 7x y(x)  + 2x y(x)  + 15x y(x)  - 8x y(x)
         + 
             6     3          2     5        7     2
           (x  - 9x  - 9x)y(x)  + 6x y(x) - x  + 9x
      *
          ,
         y (x)

     + 
             7    2    6          5     3    4      5     2         3
       - y(x)  + x y(x)  + 6x y(x)  - 8x y(x)  + (2x  - 9x  - 3)y(x)
     + 
          4    2        6               8      3     2
       15x y(x)  + (- 7x  + 18x)y(x) + x  - 12x  + 9x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (54)
--R               8          6     3    5      2    4     4    3
--R           y(x)  - 7x y(x)  + 2x y(x)  + 15x y(x)  - 8x y(x)
--R         + 
--R             6     3          2     5        7     2
--R           (x  - 9x  - 9x)y(x)  + 6x y(x) - x  + 9x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             7    2    6          5     3    4      5     2         3
--R       - y(x)  + x y(x)  + 6x y(x)  - 8x y(x)  + (2x  - 9x  - 3)y(x)
--R     + 
--R          4    2        6               8      3     2
--R       15x y(x)  + (- 7x  + 18x)y(x) + x  - 12x  + 9x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 55

--S 56 of 130
ode271 := (y(x)**2+x**2)*D(y(x),x)+2*x*(y(x)+2*x)
 

              2    2  ,                  2
   (55)  (y(x)  + x )y (x) + 2x y(x) + 4x

                                                     Type: Expression Integer
--R 
--R
--R              2    2  ,                  2
--R   (55)  (y(x)  + x )y (x) + 2x y(x) + 4x
--R
--R                                                     Type: Expression Integer
--E 56

--S 57 of 130
yx:=solve(ode271,y,x)
 

             3     2         3
         y(x)  + 3x y(x) + 4x
   (56)  ---------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3     2         3
--R         y(x)  + 3x y(x) + 4x
--R   (56)  ---------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 57

--S 58 of 130
ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x)
 

   (57)
               8     2    6     3    5      4    4      5    3
           y(x)  + 7x y(x)  + 8x y(x)  + 15x y(x)  + 32x y(x)
         + 
               6     2     2      7          8     4
           (25x  + 9x )y(x)  + 24x y(x) + 16x  + 9x
      *
          ,
         y (x)

     + 
              7     2    6      3    5      4    4       5          3
       2x y(x)  + 4x y(x)  + 12x y(x)  + 40x y(x)  + (50x  + 6x)y(x)
     + 
          6    2        7      3           8      4      2
       84x y(x)  + (128x  + 36x )y(x) + 64x  + 60x  + 36x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (57)
--R               8     2    6     3    5      4    4      5    3
--R           y(x)  + 7x y(x)  + 8x y(x)  + 15x y(x)  + 32x y(x)
--R         + 
--R               6     2     2      7          8     4
--R           (25x  + 9x )y(x)  + 24x y(x) + 16x  + 9x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R              7     2    6      3    5      4    4       5          3
--R       2x y(x)  + 4x y(x)  + 12x y(x)  + 40x y(x)  + (50x  + 6x)y(x)
--R     + 
--R          6    2        7      3           8      4      2
--R       84x y(x)  + (128x  + 36x )y(x) + 64x  + 60x  + 36x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 58

--S 59 of 130
ode272 := (y(x)**2+x**2)*D(y(x),x)-y(x)**2
 

              2    2  ,          2
   (58)  (y(x)  + x )y (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2  ,          2
--R   (58)  (y(x)  + x )y (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 59

--S 60 of 130
solve(ode272,y,x)
 

   (59)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (59)  "failed"
--R                                                    Type: Union("failed",...)
--E 60

--S 61 of 130
ode273 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)
 

              2    2      ,
   (60)  (y(x)  + x  + a)y (x) + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2      ,
--R   (60)  (y(x)  + x  + a)y (x) + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 61

--S 62 of 130
yx:=solve(ode273,y,x)
 

             3      2
         y(x)  + (3x  + 3a)y(x)
   (61)  ----------------------
                    3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3      2
--R         y(x)  + (3x  + 3a)y(x)
--R   (61)  ----------------------
--R                    3
--R                                          Type: Union(Expression Integer,...)
--E 62

--S 63 of 130
ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx
 

   (62)
               8      2          6       4        2      2     4
           y(x)  + (7x  + 7a)y(x)  + (15x  + 30a x  + 15a )y(x)
         + 
              6        4       2      2     3          2     4        2     2
           (9x  + 27a x  + (27a  + 9)x  + 9a  + 9a)y(x)  + 9x  + 18a x  + 9a
      *
          ,
         y (x)

     + 
              7       3             5       5        3       2           3
       2x y(x)  + (12x  + 12a x)y(x)  + (18x  + 36a x  + (18a  + 6)x)y(x)
     + 
           3
       (36x  + 36a x)y(x)
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (62)
--R               8      2          6       4        2      2     4
--R           y(x)  + (7x  + 7a)y(x)  + (15x  + 30a x  + 15a )y(x)
--R         + 
--R              6        4       2      2     3          2     4        2     2
--R           (9x  + 27a x  + (27a  + 9)x  + 9a  + 9a)y(x)  + 9x  + 18a x  + 9a
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R              7       3             5       5        3       2           3
--R       2x y(x)  + (12x  + 12a x)y(x)  + (18x  + 36a x  + (18a  + 6)x)y(x)
--R     + 
--R           3
--R       (36x  + 36a x)y(x)
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 63

--S 64 of 130
ode274 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)+x**2+b
 

              2    2      ,                 2
   (63)  (y(x)  + x  + a)y (x) + 2x y(x) + x  + b

                                                     Type: Expression Integer
--R 
--R
--R              2    2      ,                 2
--R   (63)  (y(x)  + x  + a)y (x) + 2x y(x) + x  + b
--R
--R                                                     Type: Expression Integer
--E 64

--S 65 of 130
yx:=solve(ode274,y,x)
 

             3      2              3
         y(x)  + (3x  + 3a)y(x) + x  + 3b x
   (64)  ----------------------------------
                          3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3      2              3
--R         y(x)  + (3x  + 3a)y(x) + x  + 3b x
--R   (64)  ----------------------------------
--R                          3
--R                                          Type: Union(Expression Integer,...)
--E 65

--S 66 of 130
ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b
 

   (65)
               8      2          6      3            5
           y(x)  + (7x  + 7a)y(x)  + (2x  + 6b x)y(x)
         + 
               4        2      2     4      5              3               3
           (15x  + 30a x  + 15a )y(x)  + (8x  + (24b + 8a)x  + 24a b x)y(x)
         + 
               6              4      2      2      2     3          2
           (10x  + (6b + 27a)x  + (9b  + 27a  + 9)x  + 9a  + 9a)y(x)
         + 
              7               5              2  3      2            8
           (6x  + (18b + 12a)x  + (36a b + 6a )x  + 18a b x)y(x) + x
         + 
                    6      2             4        2        2     2
           (6b + a)x  + (9b  + 6a b + 9)x  + (9a b  + 18a)x  + 9a
      *
          ,
         y (x)

     + 
              7     2         6       3             5
       2x y(x)  + (x  + b)y(x)  + (12x  + 12a x)y(x)
     + 
           4              2            4
       (10x  + (18b + 6a)x  + 6a b)y(x)
     + 
           5              3      2      2           3
       (20x  + (8b + 36a)x  + (6b  + 18a  + 6)x)y(x)
     + 
           6               4              2  2     2      2
       (21x  + (45b + 30a)x  + (54a b + 9a )x  + 9a b)y(x)
     + 
          7              5       2               3         2                 8
       (8x  + (36b + 6a)x  + (36b  + 24a b + 36)x  + (18a b  + 36a)x)y(x) + x
     + 
           6       2       4      3                 2
       7b x  + (15b  + 15)x  + (9b  + 27b + 9a + 9)x  + (9a + 9)b
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (65)
--R               8      2          6      3            5
--R           y(x)  + (7x  + 7a)y(x)  + (2x  + 6b x)y(x)
--R         + 
--R               4        2      2     4      5              3               3
--R           (15x  + 30a x  + 15a )y(x)  + (8x  + (24b + 8a)x  + 24a b x)y(x)
--R         + 
--R               6              4      2      2      2     3          2
--R           (10x  + (6b + 27a)x  + (9b  + 27a  + 9)x  + 9a  + 9a)y(x)
--R         + 
--R              7               5              2  3      2            8
--R           (6x  + (18b + 12a)x  + (36a b + 6a )x  + 18a b x)y(x) + x
--R         + 
--R                    6      2             4        2        2     2
--R           (6b + a)x  + (9b  + 6a b + 9)x  + (9a b  + 18a)x  + 9a
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R              7     2         6       3             5
--R       2x y(x)  + (x  + b)y(x)  + (12x  + 12a x)y(x)
--R     + 
--R           4              2            4
--R       (10x  + (18b + 6a)x  + 6a b)y(x)
--R     + 
--R           5              3      2      2           3
--R       (20x  + (8b + 36a)x  + (6b  + 18a  + 6)x)y(x)
--R     + 
--R           6               4              2  2     2      2
--R       (21x  + (45b + 30a)x  + (54a b + 9a )x  + 9a b)y(x)
--R     + 
--R          7              5       2               3         2                 8
--R       (8x  + (36b + 6a)x  + (36b  + 24a b + 36)x  + (18a b  + 36a)x)y(x) + x
--R     + 
--R           6       2       4      3                 2
--R       7b x  + (15b  + 15)x  + (9b  + 27b + 9a + 9)x  + (9a + 9)b
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 66

--S 67 of 130
ode275 := (y(x)**2+x**2+x)*D(y(x),x)-y(x)
 

              2    2      ,
   (66)  (y(x)  + x  + x)y (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2      ,
--R   (66)  (y(x)  + x  + x)y (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 67

--S 68 of 130
solve(ode275,y,x)
 

   (67)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (67)  "failed"
--R                                                    Type: Union("failed",...)
--E 68

--S 69 of 130
ode276 := (y(x)**2-x**2)*D(y(x),x)+2*x*y(x)
 

              2    2  ,
   (68)  (y(x)  - x )y (x) + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2  ,
--R   (68)  (y(x)  - x )y (x) + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 69

--S 70 of 130
yx:=solve(ode276,y,x)
 

             2    2
         y(x)  + x
   (69)  ----------
            y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R         y(x)  + x
--R   (69)  ----------
--R            y(x)
--R                                          Type: Union(Expression Integer,...)
--E 70

--S 71 of 130
ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx
 

              6    6  ,             5     3    3     5
         (y(x)  - x )y (x) + 4x y(x)  + 4x y(x)  + 2x y(x)

   (70)  -------------------------------------------------
                                   4
                               y(x)
                                                     Type: Expression Integer
--R 
--R
--R              6    6  ,             5     3    3     5
--R         (y(x)  - x )y (x) + 4x y(x)  + 4x y(x)  + 2x y(x)
--R
--R   (70)  -------------------------------------------------
--R                                   4
--R                               y(x)
--R                                                     Type: Expression Integer
--E 71

--S 72 of 130
ode277 := (y(x)**2+x**4)*D(y(x),x)-4*x**3*y(x)
 

              2    4  ,        3
   (71)  (y(x)  + x )y (x) - 4x y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    4  ,        3
--R   (71)  (y(x)  + x )y (x) - 4x y(x)
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 130
yx:=solve(ode277,y,x)
 

             2    4
         y(x)  - x
   (72)  ----------
            y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    4
--R         y(x)  - x
--R   (72)  ----------
--R            y(x)
--R                                          Type: Union(Expression Integer,...)
--E 73

--S 74 of 130
ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx
 

              6    12  ,        3    5     7    3     11
         (y(x)  + x  )y (x) - 8x y(x)  + 8x y(x)  - 4x  y(x)

   (73)  ---------------------------------------------------
                                    4
                                y(x)
                                                     Type: Expression Integer
--R 
--R
--R              6    12  ,        3    5     7    3     11
--R         (y(x)  + x  )y (x) - 8x y(x)  + 8x y(x)  - 4x  y(x)
--R
--R   (73)  ---------------------------------------------------
--R                                    4
--R                                y(x)
--R                                                     Type: Expression Integer
--E 74

--S 75 of 130
ode278 := (y(x)**2+4*sin(x))*D(y(x),x)-cos(x)
 

                        2  ,
   (74)  (4sin(x) + y(x) )y (x) - cos(x)

                                                     Type: Expression Integer
--R 
--R
--R                        2  ,
--R   (74)  (4sin(x) + y(x) )y (x) - cos(x)
--R
--R                                                     Type: Expression Integer
--E 75

--S 76 of 130
yx:=solve(ode278,y,x)
 

                            2               - 4y(x)
         (- 32sin(x) - 8y(x)  - 4y(x) - 1)%e
   (75)  ------------------------------------------
                             32
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            2               - 4y(x)
--R         (- 32sin(x) - 8y(x)  - 4y(x) - 1)%e
--R   (75)  ------------------------------------------
--R                             32
--R                                          Type: Union(Expression Integer,...)
--E 76

--S 77 of 130
ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x)
 

   (76)
                         3            2                        2
               4096sin(x)  + (3072y(x)  + 1024y(x) + 256)sin(x)
             + 
                       4          3          2                             6
               (768y(x)  + 512y(x)  + 192y(x)  + 32y(x) + 4)sin(x) + 64y(x)
             + 
                     5         4        3       2
               64y(x)  + 32y(x)  + 8y(x)  + y(x)
          *
                - 4y(x) 3
             (%e       )
         + 
                       2           2         - 4y(x)
           (16384sin(x)  + 4096y(x) sin(x))%e
      *
          ,
         y (x)

     + 
                             2             2
           - 1024cos(x)sin(x)  + (- 512y(x)  - 256y(x) - 64)cos(x)sin(x)
         + 
                    4         3         2
           (- 64y(x)  - 64y(x)  - 32y(x)  - 8y(x) - 1)cos(x)
      *
            - 4y(x) 3
         (%e       )
     + 
                           - 4y(x)
       - 4096cos(x)sin(x)%e        - 1024cos(x)
  /
     1024
                                                     Type: Expression Integer
--R 
--R
--R   (76)
--R                         3            2                        2
--R               4096sin(x)  + (3072y(x)  + 1024y(x) + 256)sin(x)
--R             + 
--R                       4          3          2                             6
--R               (768y(x)  + 512y(x)  + 192y(x)  + 32y(x) + 4)sin(x) + 64y(x)
--R             + 
--R                     5         4        3       2
--R               64y(x)  + 32y(x)  + 8y(x)  + y(x)
--R          *
--R                - 4y(x) 3
--R             (%e       )
--R         + 
--R                       2           2         - 4y(x)
--R           (16384sin(x)  + 4096y(x) sin(x))%e
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                             2             2
--R           - 1024cos(x)sin(x)  + (- 512y(x)  - 256y(x) - 64)cos(x)sin(x)
--R         + 
--R                    4         3         2
--R           (- 64y(x)  - 64y(x)  - 32y(x)  - 8y(x) - 1)cos(x)
--R      *
--R            - 4y(x) 3
--R         (%e       )
--R     + 
--R                           - 4y(x)
--R       - 4096cos(x)sin(x)%e        - 1024cos(x)
--R  /
--R     1024
--R                                                     Type: Expression Integer
--E 77

--S 78 of 130
ode279 := (y(x)**2+2*y(x)+x)*D(y(x),x)+(y(x)+x)**2*y(x)**2+y(x)*(y(x)+1)
 

              2              ,          4          3     2         2
   (77)  (y(x)  + 2y(x) + x)y (x) + y(x)  + 2x y(x)  + (x  + 1)y(x)  + y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2              ,          4          3     2         2
--R   (77)  (y(x)  + 2y(x) + x)y (x) + y(x)  + 2x y(x)  + (x  + 1)y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 78

--S 79 of 130
solve(ode279,y,x)
 

   (78)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (78)  "failed"
--R                                                    Type: Union("failed",...)
--E 79

--S 80 of 130
ode280 := (y(x)+x)**2*D(y(x),x)-a**2
 

              2              2  ,       2
   (79)  (y(x)  + 2x y(x) + x )y (x) - a

                                                     Type: Expression Integer
--R 
--R
--R              2              2  ,       2
--R   (79)  (y(x)  + 2x y(x) + x )y (x) - a
--R
--R                                                     Type: Expression Integer
--E 80

--S 81 of 130
solve(ode280,y,x)
 

   (80)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (80)  "failed"
--R                                                    Type: Union("failed",...)
--E 81

--S 82 of 130
ode281 := (y(x)**2+2*x*y(x)-x**2)*D(y(x),x)-_
            y(x)**2+2*x*y(x)+x**2
 

              2              2  ,          2              2
   (81)  (y(x)  + 2x y(x) - x )y (x) - y(x)  + 2x y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              2              2  ,          2              2
--R   (81)  (y(x)  + 2x y(x) - x )y (x) - y(x)  + 2x y(x) + x
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 130
solve(ode281,y,x)
 

   (82)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (82)  "failed"
--R                                                    Type: Union("failed",...)
--E 83

--S 84 of 130
ode282 := (y(x)+3*x-1)**2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3)
 

   (83)
          2                    2           ,           2
     (y(x)  + (6x - 2)y(x) + 9x  - 6x + 1)y (x) - 8y(x)  + (- 12x + 10)y(x) + 6x

   + 
     - 3
                                                     Type: Expression Integer
--R 
--R
--R   (83)
--R          2                    2           ,           2
--R     (y(x)  + (6x - 2)y(x) + 9x  - 6x + 1)y (x) - 8y(x)  + (- 12x + 10)y(x) + 6x
--R
--R   + 
--R     - 3
--R                                                     Type: Expression Integer
--E 84

--S 85 of 130
solve(ode282,y,x)
 

   (84)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (84)  "failed"
--R                                                    Type: Union("failed",...)
--E 85

--S 86 of 130
ode283 := 3*(y(x)**2-x**2)*D(y(x),x)+2*y(x)**3-6*x*(x+1)*y(x)-3*exp(x)
 

               2     2  ,         x        3        2
   (85)  (3y(x)  - 3x )y (x) - 3%e  + 2y(x)  + (- 6x  - 6x)y(x)

                                                     Type: Expression Integer
--R 
--R
--R               2     2  ,         x        3        2
--R   (85)  (3y(x)  - 3x )y (x) - 3%e  + 2y(x)  + (- 6x  - 6x)y(x)
--R
--R                                                     Type: Expression Integer
--E 86

--S 87 of 130
yx:=solve(ode283,y,x)
 

              x 3        3     2        x 2
   (86)  - (%e )  + (y(x)  - 3x y(x))(%e )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              x 3        3     2        x 2
--R   (86)  - (%e )  + (y(x)  - 3x y(x))(%e )
--R                                          Type: Union(Expression Integer,...)
--E 87

--S 88 of 130
ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x)
 

   (87)
               2     2    x 8            5      2    3      4        x 7
         (9y(x)  - 9x )(%e )  + (- 18y(x)  + 72x y(x)  - 54x y(x))(%e )
       + 
               8      2    6       4    4      6    2    x 6
         (9y(x)  - 63x y(x)  + 135x y(x)  - 81x y(x) )(%e )
       + 
              2    2     4    x 2
         (- 9x y(x)  + 9x )(%e )
    *
        ,
       y (x)

   + 
            x 9          3         2               x 8
     - 11(%e )  + (30y(x)  + (- 90x  - 18x)y(x))(%e )
   + 
              6        2           4          4       3     2    x 7
     (- 27y(x)  + (162x  + 36x)y(x)  + (- 243x  - 108x )y(x) )(%e )
   + 
              9         2           7        4       3     5
         8y(x)  + (- 72x  - 18x)y(x)  + (216x  + 108x )y(x)
       + 
                6       5     3
         (- 216x  - 162x )y(x)
    *
          x 6
       (%e )
   + 
         2         x 3          2          3       4      3         x 2      x
     (15x  + 6x)(%e )  + ((- 12x  - 6x)y(x)  + (36x  + 36x )y(x))(%e )  - 3%e
                                                     Type: Expression Integer
--R 
--R
--R   (87)
--R               2     2    x 8            5      2    3      4        x 7
--R         (9y(x)  - 9x )(%e )  + (- 18y(x)  + 72x y(x)  - 54x y(x))(%e )
--R       + 
--R               8      2    6       4    4      6    2    x 6
--R         (9y(x)  - 63x y(x)  + 135x y(x)  - 81x y(x) )(%e )
--R       + 
--R              2    2     4    x 2
--R         (- 9x y(x)  + 9x )(%e )
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R            x 9          3         2               x 8
--R     - 11(%e )  + (30y(x)  + (- 90x  - 18x)y(x))(%e )
--R   + 
--R              6        2           4          4       3     2    x 7
--R     (- 27y(x)  + (162x  + 36x)y(x)  + (- 243x  - 108x )y(x) )(%e )
--R   + 
--R              9         2           7        4       3     5
--R         8y(x)  + (- 72x  - 18x)y(x)  + (216x  + 108x )y(x)
--R       + 
--R                6       5     3
--R         (- 216x  - 162x )y(x)
--R    *
--R          x 6
--R       (%e )
--R   + 
--R         2         x 3          2          3       4      3         x 2      x
--R     (15x  + 6x)(%e )  + ((- 12x  - 6x)y(x)  + (36x  + 36x )y(x))(%e )  - 3%e
--R                                                     Type: Expression Integer
--E 88

--S 89 of 130
ode284 := (4*y(x)**2+x**2)*D(y(x),x)-x*y(x)
 

               2    2  ,
   (88)  (4y(x)  + x )y (x) - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R               2    2  ,
--R   (88)  (4y(x)  + x )y (x) - x y(x)
--R
--R                                                     Type: Expression Integer
--E 89

--S 90 of 130
yx:=solve(ode284,y,x)
 

              2             2
         8y(x) log(y(x)) - x
   (89)  --------------------
                     2
                2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2             2
--R         8y(x) log(y(x)) - x
--R   (89)  --------------------
--R                     2
--R                2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 90

--S 91 of 130
ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx
 

   (90)
                   6       2    4          2
           (512y(x)  + 128x y(x) )log(y(x))
         + 
                  2    4      4    2               2    6     4    4     4    2
           (- 128x y(x)  - 32x y(x) )log(y(x)) + 8x y(x)  + 2x y(x)  + 8x y(x)
         + 
             6
           2x
      *
          ,
         y (x)

     + 
                  5         2             7      3    3              3    5
       - 128x y(x) log(y(x))  + (- 8x y(x)  + 32x y(x) )log(y(x)) - x y(x)
     + 
           5
       - 2x y(x)
  /
          7
     2y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (90)
--R                   6       2    4          2
--R           (512y(x)  + 128x y(x) )log(y(x))
--R         + 
--R                  2    4      4    2               2    6     4    4     4    2
--R           (- 128x y(x)  - 32x y(x) )log(y(x)) + 8x y(x)  + 2x y(x)  + 8x y(x)
--R         + 
--R             6
--R           2x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                  5         2             7      3    3              3    5
--R       - 128x y(x) log(y(x))  + (- 8x y(x)  + 32x y(x) )log(y(x)) - x y(x)
--R     + 
--R           5
--R       - 2x y(x)
--R  /
--R          7
--R     2y(x)
--R                                                     Type: Expression Integer
--E 91

--S 92 of 130
ode285 := (4*y(x)**2+2*x*y(x)+3*x**2)*D(y(x),x)+y(x)**2+6*x*y(x)+2*x**2
 

               2               2  ,          2               2
   (91)  (4y(x)  + 2x y(x) + 3x )y (x) + y(x)  + 6x y(x) + 2x

                                                     Type: Expression Integer
--R 
--R
--R               2               2  ,          2               2
--R   (91)  (4y(x)  + 2x y(x) + 3x )y (x) + y(x)  + 6x y(x) + 2x
--R
--R                                                     Type: Expression Integer
--E 92

--S 93 of 130
yx:=solve(ode285,y,x)
 

              3          2     2         3
         4y(x)  + 3x y(x)  + 9x y(x) + 2x
   (92)  ---------------------------------
                         3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3          2     2         3
--R         4y(x)  + 3x y(x)  + 9x y(x) + 2x
--R   (92)  ---------------------------------
--R                         3
--R                                          Type: Union(Expression Integer,...)
--E 93

--S 94 of 130
ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2
 

   (93)
                  8            7        2    6         3           5
           256y(x)  + 512x y(x)  + 1680x y(x)  + (2056x  + 96x)y(x)
         + 
                 4       2     4         5       3     3
           (3020x  + 120x )y(x)  + (2160x  + 324x )y(x)
         + 
                 6       4       2     2        7       5      3           8
           (1468x  + 210x  + 108x )y(x)  + (464x  + 186x  + 54x )y(x) + 48x
         + 
              6      4
           36x  + 81x
      *
          ,
         y (x)

     + 
             8            7         2          6         3           5
       64y(x)  + 480x y(x)  + (1028x  + 16)y(x)  + (2416x  + 48x)y(x)
     + 
             4       2     4         5       3           3
       (2700x  + 243x )y(x)  + (2936x  + 280x  + 72x)y(x)
     + 
             6       4      2     2        7       5       3           8      6
       (1624x  + 465x  + 81x )y(x)  + (384x  + 216x  + 324x )y(x) + 32x  + 28x
     + 
          4      2
       90x  + 18x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (93)
--R                  8            7        2    6         3           5
--R           256y(x)  + 512x y(x)  + 1680x y(x)  + (2056x  + 96x)y(x)
--R         + 
--R                 4       2     4         5       3     3
--R           (3020x  + 120x )y(x)  + (2160x  + 324x )y(x)
--R         + 
--R                 6       4       2     2        7       5      3           8
--R           (1468x  + 210x  + 108x )y(x)  + (464x  + 186x  + 54x )y(x) + 48x
--R         + 
--R              6      4
--R           36x  + 81x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             8            7         2          6         3           5
--R       64y(x)  + 480x y(x)  + (1028x  + 16)y(x)  + (2416x  + 48x)y(x)
--R     + 
--R             4       2     4         5       3           3
--R       (2700x  + 243x )y(x)  + (2936x  + 280x  + 72x)y(x)
--R     + 
--R             6       4      2     2        7       5       3           8      6
--R       (1624x  + 465x  + 81x )y(x)  + (384x  + 216x  + 324x )y(x) + 32x  + 28x
--R     + 
--R          4      2
--R       90x  + 18x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 94

--S 95 of 130
ode286 := (2*y(x)-3*x+1)**2*D(y(x),x)-(3*y(x)-2*x-4)**2
 

   (94)
           2                       2           ,           2
     (4y(x)  + (- 12x + 4)y(x) + 9x  - 6x + 1)y (x) - 9y(x)  + (12x + 24)y(x)

   + 
         2
     - 4x  - 16x - 16
                                                     Type: Expression Integer
--R 
--R
--R   (94)
--R           2                       2           ,           2
--R     (4y(x)  + (- 12x + 4)y(x) + 9x  - 6x + 1)y (x) - 9y(x)  + (12x + 24)y(x)
--R
--R   + 
--R         2
--R     - 4x  - 16x - 16
--R                                                     Type: Expression Integer
--E 95

--S 96 of 130
solve(ode286,y,x)
 

   (95)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (95)  "failed"
--R                                                    Type: Union("failed",...)
--E 96

--S 97 of 130
ode287 := (2*y(x)-4*x+1)**2*D(y(x),x)-(y(x)-2*x)**2
 

   (96)
         2                        2           ,          2               2
   (4y(x)  + (- 16x + 4)y(x) + 16x  - 8x + 1)y (x) - y(x)  + 4x y(x) - 4x

                                                     Type: Expression Integer
--R 
--R
--R   (96)
--R         2                        2           ,          2               2
--R   (4y(x)  + (- 16x + 4)y(x) + 16x  - 8x + 1)y (x) - y(x)  + 4x y(x) - 4x
--R
--R                                                     Type: Expression Integer
--E 97

--S 98 of 130
solve(ode287,y,x)
 

   (97)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (97)  "failed"
--R                                                    Type: Union("failed",...)
--E 98

--S 99 of 130
ode288 := (6*y(x)**2-3*x**2*y(x)+1)*D(y(x),x)-3*x*y(x)**2+x
 

               2     2          ,             2
   (98)  (6y(x)  - 3x y(x) + 1)y (x) - 3x y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R               2     2          ,             2
--R   (98)  (6y(x)  - 3x y(x) + 1)y (x) - 3x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 99

--S 100 of 130
yx:=solve(ode288,y,x)
 

              3     2    2            2
         4y(x)  - 3x y(x)  + 2y(x) + x
   (99)  ------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2    2            2
--R         4y(x)  - 3x y(x)  + 2y(x) + x
--R   (99)  ------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 100

--S 101 of 130
ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x
 

   (100)
                  8        2    7        4           6          6       2     5
           576y(x)  - 1152x y(x)  + (756x  + 672)y(x)  + (- 162x  - 720x )y(x)
         + 
               4           4       6      2     3         4          2
           (90x  + 240)y(x)  + (54x  - 48x )y(x)  + (- 54x  + 48)y(x)  + 4
      *
          ,
         y (x)

     + 
                  8       3    7          5            6      3    5
       - 288x y(x)  + 432x y(x)  + (- 162x  - 240x)y(x)  + 72x y(x)
     + 
           5           4      3    3     5
       (81x  - 24x)y(x)  - 72x y(x)  - 3x  + 8x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (100)
--R                  8        2    7        4           6          6       2     5
--R           576y(x)  - 1152x y(x)  + (756x  + 672)y(x)  + (- 162x  - 720x )y(x)
--R         + 
--R               4           4       6      2     3         4          2
--R           (90x  + 240)y(x)  + (54x  - 48x )y(x)  + (- 54x  + 48)y(x)  + 4
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                  8       3    7          5            6      3    5
--R       - 288x y(x)  + 432x y(x)  + (- 162x  - 240x)y(x)  + 72x y(x)
--R     + 
--R           5           4      3    3     5
--R       (81x  - 24x)y(x)  - 72x y(x)  - 3x  + 8x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 101

--S 102 of 130
ode289 := (6*y(x)-x)**2*D(y(x),x)-6*y(x)**2+2*x*y(x)+a
 

                 2               2  ,           2
   (101)  (36y(x)  - 12x y(x) + x )y (x) - 6y(x)  + 2x y(x) + a

                                                     Type: Expression Integer
--R 
--R
--R                 2               2  ,           2
--R   (101)  (36y(x)  - 12x y(x) + x )y (x) - 6y(x)  + 2x y(x) + a
--R
--R                                                     Type: Expression Integer
--E 102

--S 103 of 130
yx:=solve(ode289,y,x)
 

                3          2    2
   (102)  12y(x)  - 6x y(x)  + x y(x) + a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3          2    2
--R   (102)  12y(x)  - 6x y(x)  + x y(x) + a x
--R                                          Type: Union(Expression Integer,...)
--E 103

--S 104 of 130
ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a
 

   (103)
                   8               7          2    6
         186624y(x)  - 248832x y(x)  + 145152x y(x)
       + 
                  3                        5
         (- 46656x  + (31104a - 5184)x)y(x)
       + 
               4                     2     4          5                  3     3
         (8640x  + (- 25920a + 4320)x )y(x)  + (- 864x  + (8640a - 1440)x )y(x)
       + 
             6                   4         2              2     2
         (36x  + (- 1296a + 216)x  + (1296a  - 432a + 36)x )y(x)
       + 
                     5          2              3            2            4
         ((72a - 12)x  + (- 432a  + 144a - 12)x )y(x) + (36a  - 12a + 1)x
    *
        ,
       y (x)

   + 
                8              7            2                   6
     - 31104y(x)  + 41472x y(x)  + (- 23328x  + 5184a - 864)y(x)
   + 
           3                          5           4                  2     4
     (6912x  + (- 10368a + 1728)x)y(x)  + (- 1080x  + (6480a - 1080)x )y(x)
   + 
         5                   3        2                   3
     (72x  + (- 1728a + 288)x  + (864a  - 288a + 24)x)y(x)
   + 
                  4          2              2     2        2            3
     ((180a - 30)x  + (- 648a  + 216a - 18)x )y(x)  + (144a  - 48a + 4)x y(x)
   + 
         3      2       2
     (36a  - 18a  + 3a)x  + a
                                                     Type: Expression Integer
--R 
--R
--R   (103)
--R                   8               7          2    6
--R         186624y(x)  - 248832x y(x)  + 145152x y(x)
--R       + 
--R                  3                        5
--R         (- 46656x  + (31104a - 5184)x)y(x)
--R       + 
--R               4                     2     4          5                  3     3
--R         (8640x  + (- 25920a + 4320)x )y(x)  + (- 864x  + (8640a - 1440)x )y(x)
--R       + 
--R             6                   4         2              2     2
--R         (36x  + (- 1296a + 216)x  + (1296a  - 432a + 36)x )y(x)
--R       + 
--R                     5          2              3            2            4
--R         ((72a - 12)x  + (- 432a  + 144a - 12)x )y(x) + (36a  - 12a + 1)x
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R                8              7            2                   6
--R     - 31104y(x)  + 41472x y(x)  + (- 23328x  + 5184a - 864)y(x)
--R   + 
--R           3                          5           4                  2     4
--R     (6912x  + (- 10368a + 1728)x)y(x)  + (- 1080x  + (6480a - 1080)x )y(x)
--R   + 
--R         5                   3        2                   3
--R     (72x  + (- 1728a + 288)x  + (864a  - 288a + 24)x)y(x)
--R   + 
--R                  4          2              2     2        2            3
--R     ((180a - 30)x  + (- 648a  + 216a - 18)x )y(x)  + (144a  - 48a + 4)x y(x)
--R   + 
--R         3      2       2
--R     (36a  - 18a  + 3a)x  + a
--R                                                     Type: Expression Integer
--E 104

--S 105 of 130
ode290 := (a*y(x)**2+2*b*x*y(x)+c*x**2)*D(y(x),x)+b*y(x)**2+2*c*x*y(x)+d*x**2
 

                 2                  2  ,            2                  2
   (104)  (a y(x)  + 2b x y(x) + c x )y (x) + b y(x)  + 2c x y(x) + d x

                                                     Type: Expression Integer
--R 
--R
--R                 2                  2  ,            2                  2
--R   (104)  (a y(x)  + 2b x y(x) + c x )y (x) + b y(x)  + 2c x y(x) + d x
--R
--R                                                     Type: Expression Integer
--E 105

--S 106 of 130
yx:=solve(ode290,y,x)
 

                3            2       2          3
          a y(x)  + 3b x y(x)  + 3c x y(x) + d x
   (105)  ---------------------------------------
                             3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3            2       2          3
--R          a y(x)  + 3b x y(x)  + 3c x y(x) + d x
--R   (105)  ---------------------------------------
--R                             3
--R                                          Type: Union(Expression Integer,...)
--E 106

--S 107 of 130
ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2
 

   (106)
            4    8     3        7      3       2 2  2    6
           a y(x)  + 8a b x y(x)  + (7a c + 21a b )x y(x)
         + 
               3       2           3  3     2        5
           ((2a d + 36a b c + 18a b )x  + 6a b x)y(x)
         + 
                2         2 2        2   4        2 2     4
           ((10a b d + 15a c  + 45a b c)x  + 30a b x )y(x)
         + 
                2         2            2  5                 3  3     3
           (((8a c + 12a b )d + 36a b c )x  + (24a b c + 36b )x )y(x)
         + 
              2 2                   3  6                2   4         2     2
           ((a d  + 18a b c d + 9a c )x  + (6a b d + 54b c)x  + 9a c x )y(x)
         + 
                   2       2   7       2         2  5          3             2 8
           ((2a b d  + 6a c d)x  + (12b d + 18b c )x  + 18b c x )y(x) + a c d x
         + 
                   6     2 4
           6b c d x  + 9c x
      *
          ,
         y (x)

     + 
        3      8      3      2 2       7
       a b y(x)  + (2a c + 6a b )x y(x)
     + 
          3       2          3  2    2      6
       ((a d + 18a b c + 9a b )x  + a b)y(x)
     + 
           2         2 2        2   3        2      5
       ((8a b d + 12a c  + 36a b c)x  + 12a b x)y(x)
     + 
             2         2            2  4                 3  2     4
       (((10a c + 15a b )d + 45a b c )x  + (18a b c + 27b )x )y(x)
     + 
           2 2                    3  5                2   3              3
       ((2a d  + 36a b c d + 18a c )x  + (8a b d + 72b c)x  + 6a c x)y(x)
     + 
               2        2   6       2         2  4          2     2
       ((7a b d  + 21a c d)x  + (30b d + 45b c )x  + 27b c x )y(x)
     + 
            2 7            5      2 3           3 8       2 6          4       2
     (8a c d x  + 36b c d x  + 36c x )y(x) + a d x  + 7b d x  + 15c d x  + 9d x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (106)
--R            4    8     3        7      3       2 2  2    6
--R           a y(x)  + 8a b x y(x)  + (7a c + 21a b )x y(x)
--R         + 
--R               3       2           3  3     2        5
--R           ((2a d + 36a b c + 18a b )x  + 6a b x)y(x)
--R         + 
--R                2         2 2        2   4        2 2     4
--R           ((10a b d + 15a c  + 45a b c)x  + 30a b x )y(x)
--R         + 
--R                2         2            2  5                 3  3     3
--R           (((8a c + 12a b )d + 36a b c )x  + (24a b c + 36b )x )y(x)
--R         + 
--R              2 2                   3  6                2   4         2     2
--R           ((a d  + 18a b c d + 9a c )x  + (6a b d + 54b c)x  + 9a c x )y(x)
--R         + 
--R                   2       2   7       2         2  5          3             2 8
--R           ((2a b d  + 6a c d)x  + (12b d + 18b c )x  + 18b c x )y(x) + a c d x
--R         + 
--R                   6     2 4
--R           6b c d x  + 9c x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R        3      8      3      2 2       7
--R       a b y(x)  + (2a c + 6a b )x y(x)
--R     + 
--R          3       2          3  2    2      6
--R       ((a d + 18a b c + 9a b )x  + a b)y(x)
--R     + 
--R           2         2 2        2   3        2      5
--R       ((8a b d + 12a c  + 36a b c)x  + 12a b x)y(x)
--R     + 
--R             2         2            2  4                 3  2     4
--R       (((10a c + 15a b )d + 45a b c )x  + (18a b c + 27b )x )y(x)
--R     + 
--R           2 2                    3  5                2   3              3
--R       ((2a d  + 36a b c d + 18a c )x  + (8a b d + 72b c)x  + 6a c x)y(x)
--R     + 
--R               2        2   6       2         2  4          2     2
--R       ((7a b d  + 21a c d)x  + (30b d + 45b c )x  + 27b c x )y(x)
--R     + 
--R            2 7            5      2 3           3 8       2 6          4       2
--R     (8a c d x  + 36b c d x  + 36c x )y(x) + a d x  + 7b d x  + 15c d x  + 9d x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 107

--S 108 of 130
ode291 := (b*(beta*y(x)+alpha*x)**2-beta*(b*y(x)+a*x))*D(y(x),x)+_
              a*(beta*y(x)+alpha*x)**2-alpha*(b*y(x)+a*x)
 

   (107)
              2    2                                         2   2
       (b beta y(x)  + (2alpha b beta x - b beta)y(x) + alpha b x  - a beta x)
    *
        ,
       y (x)

   + 
           2    2                                            2 2
     a beta y(x)  + (2a alpha beta x - alpha b)y(x) + a alpha x  - a alpha x
                                                     Type: Expression Integer
--R 
--R
--R   (107)
--R              2    2                                         2   2
--R       (b beta y(x)  + (2alpha b beta x - b beta)y(x) + alpha b x  - a beta x)
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R           2    2                                            2 2
--R     a beta y(x)  + (2a alpha beta x - alpha b)y(x) + a alpha x  - a alpha x
--R                                                     Type: Expression Integer
--E 108

--S 109 of 130
solve(ode291,y,x)
 

   (108)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (108)  "failed"
--R                                                    Type: Union("failed",...)
--E 109

--S 110 of 130
ode292 := (a*y(x)+b*x+c)**2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)**2
 

   (109)
       2    2                          2 2             2  ,           2    2
     (a y(x)  + (2a b x + 2a c)y(x) + b x  + 2b c x + c )y (x) + alpha y(x)

   + 
                                              2 2                        2
     (2alpha beta x + 2alpha gamma)y(x) + beta x  + 2beta gamma x + gamma
                                                     Type: Expression Integer
--R 
--R
--R   (109)
--R       2    2                          2 2             2  ,           2    2
--R     (a y(x)  + (2a b x + 2a c)y(x) + b x  + 2b c x + c )y (x) + alpha y(x)
--R
--R   + 
--R                                              2 2                        2
--R     (2alpha beta x + 2alpha gamma)y(x) + beta x  + 2beta gamma x + gamma
--R                                                     Type: Expression Integer
--E 110

--S 111 of 130
solve(ode292,y,x)
 

   (110)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (110)  "failed"
--R                                                    Type: Union("failed",...)
--E 111

--S 112 of 130
ode293 := x*(y(x)**2-3*x)*D(y(x),x)+2*y(x)**3-5*x*y(x)
 

                 2     2  ,           3
   (111)  (x y(x)  - 3x )y (x) + 2y(x)  - 5x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 2     2  ,           3
--R   (111)  (x y(x)  - 3x )y (x) + 2y(x)  - 5x y(x)
--R
--R                                                     Type: Expression Integer
--E 112

--S 113 of 130
solve(ode293,y,x)
 

   (112)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (112)  "failed"
--R                                                    Type: Union("failed",...)
--E 113

--S 114 of 130
ode294 := x*(y(x)**2+x**2-a)*D(y(x),x)-y(x)*(y(x)**2+x**2+a)
 

                 2    3        ,          3       2
   (113)  (x y(x)  + x  - a x)y (x) - y(x)  + (- x  - a)y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 2    3        ,          3       2
--R   (113)  (x y(x)  + x  - a x)y (x) - y(x)  + (- x  - a)y(x)
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 130
solve(ode294,y,x)
 

   (114)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (114)  "failed"
--R                                                    Type: Union("failed",...)
--E 115

--S 116 of 130
ode295 := x*(y(x)**2+x*y(x)-x**2)*D(y(x),x)-y(x)**3+x*y(x)**2+x**2*y(x)
 

                 2    2        3  ,          3         2    2
   (115)  (x y(x)  + x y(x) - x )y (x) - y(x)  + x y(x)  + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 2    2        3  ,          3         2    2
--R   (115)  (x y(x)  + x y(x) - x )y (x) - y(x)  + x y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 116

--S 117 of 130
solve(ode295,y,x)
 

   (116)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (116)  "failed"
--R                                                    Type: Union("failed",...)
--E 117

--S 118 of 130
ode296 := x*(y(x)**2+x**2*y(x)+x**2)*D(y(x),x)-2*y(x)**3-2*x**2*y(x)**2+x**4
 

                 2    3        3  ,           3     2    2    4
   (117)  (x y(x)  + x y(x) + x )y (x) - 2y(x)  - 2x y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R                 2    3        3  ,           3     2    2    4
--R   (117)  (x y(x)  + x y(x) + x )y (x) - 2y(x)  - 2x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 118

--S 119 of 130
solve(ode296,y,x)
 

   (118)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (118)  "failed"
--R                                                    Type: Union("failed",...)
--E 119

--S 120 of 130
ode297 := 2*x*(y(x)**2+5*x**2)*D(y(x),x)+y(x)**3-x**2*y(x)
 

                  2      3  ,          3    2
   (119)  (2x y(x)  + 10x )y (x) + y(x)  - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                  2      3  ,          3    2
--R   (119)  (2x y(x)  + 10x )y (x) + y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 130
solve(ode297,y,x)
 

   (120)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (120)  "failed"
--R                                                    Type: Union("failed",...)
--E 121

--S 122 of 130
ode298 := 3*x*y(x)**2*D(y(x),x)+y(x)**3-2*x
 

                 2 ,          3
   (121)  3x y(x) y (x) + y(x)  - 2x

                                                     Type: Expression Integer
--R 
--R
--R                 2 ,          3
--R   (121)  3x y(x) y (x) + y(x)  - 2x
--R
--R                                                     Type: Expression Integer
--E 122

--S 123 of 130
yx:=solve(ode298,y,x)
 

                3    2
   (122)  x y(x)  - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3    2
--R   (122)  x y(x)  - x
--R                                          Type: Union(Expression Integer,...)
--E 123

--S 124 of 130
ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x
 

   (123)
        4    8      5    5     6    2  ,        3    9      4    6      5    3
     (9x y(x)  - 18x y(x)  + 9x y(x) )y (x) + 4x y(x)  - 15x y(x)  + 18x y(x)

   + 
         6
     - 7x  - 2x
                                                     Type: Expression Integer
--R 
--R
--R   (123)
--R        4    8      5    5     6    2  ,        3    9      4    6      5    3
--R     (9x y(x)  - 18x y(x)  + 9x y(x) )y (x) + 4x y(x)  - 15x y(x)  + 18x y(x)
--R
--R   + 
--R         6
--R     - 7x  - 2x
--R                                                     Type: Expression Integer
--E 124

--S 125 of 130
ode299 := (3*x*y(x)**2-x**2)*D(y(x),x)+y(x)**3-2*x*y(x)
 

                  2    2  ,          3
   (124)  (3x y(x)  - x )y (x) + y(x)  - 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                  2    2  ,          3
--R   (124)  (3x y(x)  - x )y (x) + y(x)  - 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 125

--S 126 of 130
yx:=solve(ode299,y,x)
 

                3    2
   (125)  x y(x)  - x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3    2
--R   (125)  x y(x)  - x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 126

--S 127 of 130
ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx
 

   (126)
        4    8      5    6      6    4        7     3     2    4  ,
     (9x y(x)  - 21x y(x)  + 15x y(x)  + (- 3x  - 3x )y(x)  + x )y (x)

   + 
       3    9      4    7      5    5        6     2     3     3
     4x y(x)  - 15x y(x)  + 18x y(x)  + (- 7x  - 3x )y(x)  + 4x y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (126)
--R        4    8      5    6      6    4        7     3     2    4  ,
--R     (9x y(x)  - 21x y(x)  + 15x y(x)  + (- 3x  - 3x )y(x)  + x )y (x)
--R
--R   + 
--R       3    9      4    7      5    5        6     2     3     3
--R     4x y(x)  - 15x y(x)  + 18x y(x)  + (- 7x  - 3x )y(x)  + 4x y(x)
--R                                                     Type: Expression Integer
--E 127

--S 128 of 130
ode300 := 6*x*y(x)**2*D(y(x),x)+2*y(x)**3+x
 

                 2 ,           3
   (127)  6x y(x) y (x) + 2y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R                 2 ,           3
--R   (127)  6x y(x) y (x) + 2y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 128

--S 129 of 130
yx:=solve(ode300,y,x)
 

                 3    2
          4x y(x)  + x
   (128)  -------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 3    2
--R          4x y(x)  + x
--R   (128)  -------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 129

--S 130 of 130
ode300expr := 6*x*yx**2*D(yx,x)+2*yx**3+x
 

   (129)
            4    8       5    5      6    2  ,          3    9       4    6
       (576x y(x)  + 288x y(x)  + 36x y(x) )y (x) + 256x y(x)  + 240x y(x)

     + 
          5    3     6
       72x y(x)  + 7x  + 4x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (129)
--R            4    8       5    5      6    2  ,          3    9       4    6
--R       (576x y(x)  + 288x y(x)  + 36x y(x) )y (x) + 256x y(x)  + 240x y(x)
--R
--R     + 
--R          5    3     6
--R       72x y(x)  + 7x  + 4x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 130

)spool
 
Starts dribbling to newton.output (2009/2/17, 17:55:32).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 5
newtonStep(f) ==
  fun  := complexNumericFunction f
  deriv := complexDerivativeFunction(f,1)
  (b:Complex DoubleFloat):Complex DoubleFloat +->
    b - fun(b)/deriv(b)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 5
complexFunPack := MakeUnaryCompiledFunction(EXPR INT, Complex DoubleFloat, Complex DoubleFloat)
 

   (2)
  MakeUnaryCompiledFunction(Expression Integer,Complex DoubleFloat,Complex Doub
  leFloat)
                                                                 Type: Domain
--R 
--R
--R   (2)
--R  MakeUnaryCompiledFunction(Expression Integer,Complex DoubleFloat,Complex Doub
--R  leFloat)
--R                                                                 Type: Domain
--E 2

--S 3 of 5
complexNumericFunction x ==
  v := theVariable x
  compiledFunction(x, v)$complexFunPack
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
complexDerivativeFunction(x,n) ==
  v := theVariable x
  df := differentiate(x,v,n)
  compiledFunction(df, v)$complexFunPack
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
theVariable x ==
  vl := variables x
  nv := # vl
  nv > 1 => error "Expression is not univariate."
  nv = 0 => 'x
  first vl
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
)spool 
 
Starts dribbling to bbtree.output (2009/2/17, 17:43:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 10
lm := [3,5,7,11]
 

   (1)  [3,5,7,11]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [3,5,7,11]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 10
modTree(12,lm)
 

   (2)  [0,2,5,1]
                                                           Type: List Integer
--R 
--R
--R   (2)  [0,2,5,1]
--R                                                           Type: List Integer
--E 2

--S 3 of 10
t := balancedBinaryTree(#lm, 0)
 

   (3)  [[0,0,0],0,[0,0,0]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (3)  [[0,0,0],0,[0,0,0]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 3

--S 4 of 10
setleaves!(t,lm)
 

   (4)  [[3,0,5],0,[7,0,11]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (4)  [[3,0,5],0,[7,0,11]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 4

--S 5 of 10
mapUp!(t,_*)
 

   (5)  1155
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1155
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
t
 

   (6)  [[3,15,5],1155,[7,77,11]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (6)  [[3,15,5],1155,[7,77,11]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 6

--S 7 of 10
mapDown!(t,12,_rem)
 

   (7)  [[0,12,2],12,[5,12,1]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (7)  [[0,12,2],12,[5,12,1]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 7

--S 8 of 10
leaves %
 

   (8)  [0,2,5,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (8)  [0,2,5,1]
--R                                                Type: List NonNegativeInteger
--E 8

--S 9 of 10
squares := [x**2 rem m for x in % for m in lm]
 

   (9)  [0,4,4,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (9)  [0,4,4,1]
--R                                                Type: List NonNegativeInteger
--E 9

--S 10 of 10
chineseRemainder(%,lm)
 

   (10)  144
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  144
--R                                                        Type: PositiveInteger
--E 10
)spool
 
Starts dribbling to bugs.output (2009/2/17, 17:44:1).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- File of Currently active and recently fixed interpreter bugs

--- eval a polynomial with EXPR substitution values
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 44 
eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F
 

           2                   2
   (1)  C y  + (B x + E)y + A x  + D x + F
                                                     Type: Polynomial Integer
--R 
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 44 
eq2:= eval(eq1,[x= xdot*cos(t) - ydot*sin(t), y=xdot*sin(t) + ydot*cos(t)])
 

   (2)
            2                       2       2
     (A ydot  - B xdot ydot + C xdot )sin(t)
   + 
               2                              2
     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
   + 
            2                       2       2
     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R            2                       2       2
--R     (A ydot  - B xdot ydot + C xdot )sin(t)
--R   + 
--R               2                              2
--R     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
--R   + 
--R            2                       2       2
--R     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
--R                                                     Type: Expression Integer
--E 2

-- UTS coercions.  Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 3 of 44 
taylor exp x
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 44 
s := %
 

   (2)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 44 
s::(UTS(EXPR FLOAT, x, 0))
 

   (3)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--R 
--R
--R   (3)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--E 5

--S 6 of 44 
s::(UTS(FLOAT, x, 0))
 

   (4)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--R 
--R
--R   (4)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--E 6

--S 7 of 44 
eval(s,1)
 

             5 8 65 163 1957 685 109601 98641
   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
             2 3 24  60  720 252  40320 36288
                                              Type: Stream Expression Integer
--R 
--R
--R             5 8 65 163 1957 685 109601 98641
--R   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
--R             2 3 24  60  720 252  40320 36288
--R                                              Type: Stream Expression Integer
--E 7

--S 8 of 44 
%::(Stream Float)
 

   (6)
   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
    2.7182787698 412698413, 2.7182815255 731922399, ...]
                                                           Type: Stream Float
--R 
--R
--R   (6)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                           Type: Stream Float
--E 8

-- overloading interpreter maps on arity
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 9 of 44 
f(x) == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 44 
f(x,y) == x+y
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 44 
f 3
 
   Compiling function f with type PositiveInteger -> PositiveInteger 

   (3)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (3)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 44 
f(3,4)
 
   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
      PositiveInteger 

   (4)  7
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
--R      PositiveInteger 
--R
--R   (4)  7
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 44 
f(5)
 

   (5)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  6
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 44 
f(1,x)
 
   Compiling function f with type (PositiveInteger,Variable x) -> 
      Polynomial Integer 

   (6)  x + 1
                                                     Type: Polynomial Integer
--R 
--R   Compiling function f with type (PositiveInteger,Variable x) -> 
--R      Polynomial Integer 
--R
--R   (6)  x + 1
--R                                                     Type: Polynomial Integer
--E 14

-- targetted function requiring a coercion
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 15 of 44 
series(n +-> bernoulli(n)/factorial(n), t=0)
 

   (1)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--R 
--R
--R   (1)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 15

-- in-homogeneous list mapping
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 16 of 44 
l := [1,2,-1]
 

   (1)  [1,2,- 1]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,- 1]
--R                                                           Type: List Integer
--E 16

--S 17 of 44 
f : INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 44 
f x == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 44 
map(f, l)
 
   Compiling function f with type Integer -> Fraction Integer 

   (4)  [1,2,- 1]
                                                  Type: List Fraction Integer
--R 
--R   Compiling function f with type Integer -> Fraction Integer 
--R
--R   (4)  [1,2,- 1]
--R                                                  Type: List Fraction Integer
--E 19

-- Function args to interpreter functions
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 20 of 44 
f: INT -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 44 
f x == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 44 
u g == g 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 44 
u f
 
   Compiling function u with type (Integer -> Integer) -> Integer 
   Compiling function f with type Integer -> Integer 

   (4)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function u with type (Integer -> Integer) -> Integer 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 23

-- category modemap requiring a field to be constructed
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 24 of 44 
groebner [x**2 - y, y**3+1]
 

              2  6
   (1)  [y - x ,x  + 1]
                                                Type: List Polynomial Integer
--R 
--R
--R              2  6
--R   (1)  [y - x ,x  + 1]
--R                                                Type: List Polynomial Integer
--E 24

-- operations requiring polynomials, passed variables
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.

--S 25 of 44 
factor x
 

   (1)  x
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (1)  x
--R                                            Type: Factored Polynomial Integer
--E 25

-- bracket parsing and empty-set types
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 26 of 44 
{}$(List INT)
 
 
Daly Bug
   The function SEQ is not implemented in List Integer .
--R 
--R 
--RDaly Bug
--R   The function SEQ is not implemented in List Integer .
--E 26

--S 27 of 44 
{1}
 

   (1)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 27

-- Shouldn't work, but no longer bombs the interpreter
--- Fixed by SCM, verified on 10/30/90

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 28 of 44 
map(variable, [x,y])
 

   (1)  [x,y]
                         Type: List Union(OrderedVariableList [x,y],"failed")
--R 
--R
--R   (1)  [x,y]
--R                         Type: List Union(OrderedVariableList [x,y],"failed")
--E 28

-- Recursive map type analysis bug
--- Fixed by SCM, verified on 10/30/90
)set fun recur off
 
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 29 of 44 
p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 44 
pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 44 
pp(-1,x) -- should be 1/(x-1)
 
   Compiling function p with type (Integer,Polynomial Integer) -> 
      Polynomial Integer 
   Compiling function p with type (Integer,Variable x) -> Polynomial 
      Integer 
   Compiling function pp with type (Integer,Variable x) -> Fraction 
      Polynomial Fraction Integer 

          1
   (3)  -----
        x - 1
                                   Type: Fraction Polynomial Fraction Integer
--R 
--R   Compiling function p with type (Integer,Polynomial Integer) -> 
--R      Polynomial Integer 
--R   Compiling function p with type (Integer,Variable x) -> Polynomial 
--R      Integer 
--R   Compiling function pp with type (Integer,Variable x) -> Fraction 
--R      Polynomial Fraction Integer 
--R
--R          1
--R   (3)  -----
--R        x - 1
--R                                   Type: Fraction Polynomial Fraction Integer
--E 31

-- interpret-code mode for iterators is broken

)clear all
 
   All user variables and function definitions have been cleared.

--S 32 of 44 
f n ==
  for i in 1..n repeat
    j:=2*i
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 44 
g n ==
    j:=2*n
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 44 
g 3 -- Should work
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 34

--S 35 of 44 
f 3 -- Bombs
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0+
   |    |
   +0  1+
   +1  0  0  0+
   |          |
   |0  1  0  0|
   |          |
   |0  0  1  0|
   |          |
   +0  0  0  1+
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0+
--R   |    |
--R   +0  1+
--R   +1  0  0  0+
--R   |          |
--R   |0  1  0  0|
--R   |          |
--R   |0  0  1  0|
--R   |          |
--R   +0  0  0  1+
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 35

-- Test interpreter list destructuring

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 36 of 44 
mp(x,l) ==
  l is [a,:b] =>
    a*x**(#b)+ mp(x,b)
  0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 44 
mp(x, [1,3,4, 2])
 
   Compiling function mp with type (Variable x,List PositiveInteger)
       -> Polynomial Integer 

         3     2
   (2)  x  + 3x  + 4x + 2
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List PositiveInteger)
--R       -> Polynomial Integer 
--R
--R         3     2
--R   (2)  x  + 3x  + 4x + 2
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 44 
mp(x, [1,2,-3, 4])
 
   Compiling function mp with type (Variable x,List Integer) -> 
      Polynomial Integer 

         3     2
   (3)  x  + 2x  - 3x + 4
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List Integer) -> 
--R      Polynomial Integer 
--R
--R         3     2
--R   (3)  x  + 2x  - 3x + 4
--R                                                     Type: Polynomial Integer
--E 38

-- Tests compilation of recursive functions

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 39 of 44 
f1 n ==
  if n=0 then 1 else if n=1 then 1 else f1(n-1)+f1(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 39

--S 40  of 44 
f2 n ==
  m:=n
  if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 40

--S 41  of 44 
f3 n ==
  n=0 => 1
  n=1 => 1
  f3(n-1)+f3(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 41

--S 42 of 44 
f4 n ==
  m:=n
  n=0 => 1
  n=1 => 1
  m:=n
  f4(n-1)+f4(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 42

--S 43 of 44 
f5 n == if n=0 or n=1 then 1 else f5(n-1)+f5(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 43

--S 44 of 44 
[f1 3,f2 3, f3 3,f4 3,f5 3]
 
   Compiling function f1 with type Integer -> PositiveInteger 
   Compiling function f2 with type Integer -> PositiveInteger 
   Compiling function f3 with type Integer -> PositiveInteger 
   Compiling function f4 with type Integer -> PositiveInteger 
   Compiling function f5 with type Integer -> PositiveInteger 

   (6)  [3,3,3,3,3]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function f1 with type Integer -> PositiveInteger 
--R   Compiling function f2 with type Integer -> PositiveInteger 
--R   Compiling function f3 with type Integer -> PositiveInteger 
--R   Compiling function f4 with type Integer -> PositiveInteger 
--R   Compiling function f5 with type Integer -> PositiveInteger 
--R
--R   (6)  [3,3,3,3,3]
--R                                                   Type: List PositiveInteger
--E 44
)spool
 
Starts dribbling to kamke0.output (2009/2/17, 17:46:55).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 134
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 134
f := operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 134
g := operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

--S 4 of 134
ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2)
 

         +---------------------------------+
         |    4       3       2              ,
        \|a4 x  + a3 x  + a2 x  + a1 x + a0 y (x) - 1

   (4)  ---------------------------------------------
              +---------------------------------+
              |    4       3       2
             \|a4 x  + a3 x  + a2 x  + a1 x + a0
                                                     Type: Expression Integer
--R 
--R
--R         +---------------------------------+
--R         |    4       3       2              ,
--R        \|a4 x  + a3 x  + a2 x  + a1 x + a0 y (x) - 1
--R
--R   (4)  ---------------------------------------------
--R              +---------------------------------+
--R              |    4       3       2
--R             \|a4 x  + a3 x  + a2 x  + a1 x + a0
--R                                                     Type: Expression Integer
--E 4

--S 5 of 134
ode1a:=solve(ode1,y,x)
 

   (5)
                   x
                 ++                    1
   [particular=  |   ------------------------------------- d%N ,basis= [1]]
                ++    +----------------------------------+
                      |  4       3       2
                     \|%N a4 + %N a3 + %N a2 + %N a1 + a0
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (5)
--R                   x
--R                 ++                    1
--I   [particular=  |   ------------------------------------- d%N ,basis= [1]]
--R                ++    +----------------------------------+
--R                      |  4       3       2
--I                     \|%N a4 + %N a3 + %N a2 + %N a1 + a0
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 5

--S 6 of 134
ode2 := D(y(x),x) + a*y(x) - c*exp(b*x)
 

         ,          b x
   (6)  y (x) - c %e    + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,          b x
--R   (6)  y (x) - c %e    + a y(x)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 134
ode2a:=solve(ode2,y,x)
 

                         b x
                     c %e              - a x
   (7)  [particular= -------,basis= [%e     ]]
                      b + a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                         b x
--R                     c %e              - a x
--R   (7)  [particular= -------,basis= [%e     ]]
--R                      b + a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 7

--S 8 of 134
yx:=ode2a.particular
 

            b x
        c %e
   (8)  -------
         b + a
                                                     Type: Expression Integer
--R
--R            b x
--R        c %e
--R   (8)  -------
--R         b + a
--R                                                     Type: Expression Integer
--E 8

--S 9 of 134
ode2expr:=D(yx,x) + a*yx -c*exp(b*x)
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E 9

--S 10 of 134
ode3 := D(y(x),x) + a*y(x) - b*sin(c*x)
 

          ,
   (10)  y (x) - b sin(c x) + a y(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (10)  y (x) - b sin(c x) + a y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 134
ode3a:=solve(ode3,y,x)
 

                      a b sin(c x) - b c cos(c x)           - a x
   (11)  [particular= ---------------------------,basis= [%e     ]]
                                 2    2
                                c  + a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                      a b sin(c x) - b c cos(c x)           - a x
--R   (11)  [particular= ---------------------------,basis= [%e     ]]
--R                                 2    2
--R                                c  + a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 11

--S 12 of 134
yx:=ode3a.particular
 

         a b sin(c x) - b c cos(c x)
   (12)  ---------------------------
                    2    2
                   c  + a
                                                     Type: Expression Integer
--R
--R         a b sin(c x) - b c cos(c x)
--R   (12)  ---------------------------
--R                    2    2
--R                   c  + a
--R                                                     Type: Expression Integer
--E 12

--S 13 of 134
ode3expr:=D(yx,x) + a*yx - b*sin(c*x)
 

   (13)  0
                                                     Type: Expression Integer
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 134
ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2)
 

                        2
          ,          - x
   (14)  y (x) - x %e     + 2x y(x)

                                                     Type: Expression Integer
--R
--R                        2
--R          ,          - x
--R   (14)  y (x) - x %e     + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 134
ode4a:=solve(ode4,y,x)
 

                             2
                       2  - x               2
                      x %e               - x
   (15)  [particular= --------,basis= [%e    ]]
                          2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                             2
--R                       2  - x               2
--R                      x %e               - x
--R   (15)  [particular= --------,basis= [%e    ]]
--R                          2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 15

--S 16 of 134
yx:=ode4a.particular
 

                2
          2  - x
         x %e
   (16)  --------
             2
                                                     Type: Expression Integer
--R
--R                2
--R          2  - x
--R         x %e
--R   (16)  --------
--R             2
--R                                                     Type: Expression Integer
--E 16

--S 17 of 134
ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2)
 

   (17)  0
                                                     Type: Expression Integer
--R
--R   (17)  0
--R                                                     Type: Expression Integer
--E 17

--S 18 of 134
ode5 := D(y(x),x) + y(x)*cos(x) - exp(2*x)
 

          ,        2x
   (18)  y (x) - %e   + y(x)cos(x)

                                                     Type: Expression Integer
--R
--R          ,        2x
--R   (18)  y (x) - %e   + y(x)cos(x)
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 134
ode5a:=solve(ode5,y,x)
 

                                   x      2%N
                        - sin(x) ++     %e                      - sin(x)
   (19)  [particular= %e         |   ----------- d%N ,basis= [%e        ]]
                                ++     - sin(%N)
                                     %e
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--I                                   x      2%H
--R                        - sin(x) ++     %e                      - sin(x)
--I   (19)  [particular= %e         |   ----------- d%H ,basis= [%e        ]]
--I                                ++     - sin(%H)
--R                                     %e
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 19

--S 20 of 134
ode6 := D(y(x),x) + y(x)*cos(x) - sin(2*x)/2
 

           ,
         2y (x) - sin(2x) + 2y(x)cos(x)

   (20)  ------------------------------
                        2
                                                     Type: Expression Integer
--R
--R           ,
--R         2y (x) - sin(2x) + 2y(x)cos(x)
--R
--R   (20)  ------------------------------
--R                        2
--R                                                     Type: Expression Integer
--E 20

--S 21 of 134
ode6a:=solve(ode6,y,x)
 

                                           - sin(x)
   (21)  [particular= sin(x) - 1,basis= [%e        ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                           - sin(x)
--R   (21)  [particular= sin(x) - 1,basis= [%e        ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 21

--S 22 of 134
yx:=ode6a.particular
 

   (22)  sin(x) - 1
                                                     Type: Expression Integer
--R
--R   (22)  sin(x) - 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 134
ode6expr:=D(yx,x) + yx*cos(x) - sin(2*x)/2
 

         - sin(2x) + 2cos(x)sin(x)
   (23)  -------------------------
                     2
                                                     Type: Expression Integer
--R
--R         - sin(2x) + 2cos(x)sin(x)
--R   (23)  -------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 23

--S 24 of 134
sin2rule := rule 2*cos(x)*sin(x) == sin(2*x)
 

   (24)  2%BJ cos(x)sin(x) == %BJ sin(2x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (24)  2%Y cos(x)sin(x) == %Y sin(2x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 24

--S 25 of 134
sin2rule ode6expr
 

   (25)  0
                                                     Type: Expression Integer
--R
--R   (25)  0
--R                                                     Type: Expression Integer
--E 25

--S 26 of 134
ode7 := D(y(x),x) + y(x)*cos(x) - exp(-sin(x))
 

          ,        - sin(x)
   (26)  y (x) - %e         + y(x)cos(x)

                                                     Type: Expression Integer
--R
--R          ,        - sin(x)
--R   (26)  y (x) - %e         + y(x)cos(x)
--R
--R                                                     Type: Expression Integer
--E 26

--S 27 of 134
ode7a:=solve(ode7,y,x)
 

                          - sin(x)           - sin(x)
   (27)  [particular= x %e        ,basis= [%e        ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                          - sin(x)           - sin(x)
--R   (27)  [particular= x %e        ,basis= [%e        ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 27

--S 28 of 134
yx:=ode7a.particular
 

             - sin(x)
   (28)  x %e
                                                     Type: Expression Integer
--R
--R             - sin(x)
--R   (28)  x %e
--R                                                     Type: Expression Integer
--E 28

--S 29 of 134
ode7expr := D(yx,x) + yx*cos(x) - exp(-sin(x))
 

   (29)  0
                                                     Type: Expression Integer
--R
--R   (29)  0
--R                                                     Type: Expression Integer
--E 29

--S 30 of 134
ode8 := D(y(x),x) + y(x)*tan(x) - sin(2*x)
 

          ,
   (30)  y (x) + y(x)tan(x) - sin(2x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (30)  y (x) + y(x)tan(x) - sin(2x)
--R
--R                                                     Type: Expression Integer
--E 30

--S 31 of 134
ode8a:=solve(ode8,y,x)
 

   (31)
                                        +-------+
                          2             |   1
                (- 2cos(x)  + 2cos(x))  |-------
                                       4|      4
                                       \|cos(x)                 1
   [particular= --------------------------------,basis= [--------------]]
                          +-----------+                   +-----------+
                          |      2                        |      2
                         \|tan(x)  + 1                   \|tan(x)  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (31)
--R                                        +-------+
--R                          2             |   1
--R                (- 2cos(x)  + 2cos(x))  |-------
--R                                       4|      4
--R                                       \|cos(x)                 1
--R   [particular= --------------------------------,basis= [--------------]]
--R                          +-----------+                   +-----------+
--R                          |      2                        |      2
--R                         \|tan(x)  + 1                   \|tan(x)  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 31

--S 32 of 134
yx:=ode8a.particular
 

                                 +-------+
                   2             |   1
         (- 2cos(x)  + 2cos(x))  |-------
                                4|      4
                                \|cos(x)
   (32)  --------------------------------
                   +-----------+
                   |      2
                  \|tan(x)  + 1
                                                     Type: Expression Integer
--R
--R                                 +-------+
--R                   2             |   1
--R         (- 2cos(x)  + 2cos(x))  |-------
--R                                4|      4
--R                                \|cos(x)
--R   (32)  --------------------------------
--R                   +-----------+
--R                   |      2
--R                  \|tan(x)  + 1
--R                                                     Type: Expression Integer
--E 32

--S 33 of 134
ode8expr:=D(yx,x) + yx*tan(x) - sin(2*x)
 

                           +-------+3 +-----------+
                 3         |   1      |      2
         - cos(x) sin(2x)  |-------  \|tan(x)  + 1 + 2sin(x)
                          4|      4
                          \|cos(x)
   (33)  ---------------------------------------------------
                            +-------+3 +-----------+
                         3  |   1      |      2
                   cos(x)   |-------  \|tan(x)  + 1
                           4|      4
                           \|cos(x)
                                                     Type: Expression Integer
--R
--R                           +-------+3 +-----------+
--R                 3         |   1      |      2
--R         - cos(x) sin(2x)  |-------  \|tan(x)  + 1 + 2sin(x)
--R                          4|      4
--R                          \|cos(x)
--R   (33)  ---------------------------------------------------
--R                            +-------+3 +-----------+
--R                         3  |   1      |      2
--R                   cos(x)   |-------  \|tan(x)  + 1
--R                           4|      4
--R                           \|cos(x)
--R                                                     Type: Expression Integer
--E 33

--S 34 of 134
ode9 := D(y(x),x) - (sin(log(x)) + cos(log(x)) +a)*y(x)
 

          ,
   (34)  y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (34)  y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x)
--R
--R                                                     Type: Expression Integer
--E 34

--S 35 of 134
ode9a:=solve(ode9,y,x)
 

                                  x sin(log(x)) + a x
   (35)  [particular= 0,basis= [%e                   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                  x sin(log(x)) + a x
--R   (35)  [particular= 0,basis= [%e                   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 35

--S 36 of 134
yx:=ode9a.particular
 

   (36)  0
                                                     Type: Expression Integer
--R
--R   (36)  0
--R                                                     Type: Expression Integer
--E 36

--S 37 of 134
ode9expr:=D(yx,x) - (sin(log(x)) + cos(log(x)) +a)*yx
 

   (37)  0
                                                     Type: Expression Integer
--R
--R   (37)  0
--R                                                     Type: Expression Integer
--E 37

--S 38 of 134
ode10 := D(y(x),x) + D(f(x),x)*y(x) - f(x)*D(f(x),x)
 

          ,                    ,
   (38)  y (x) + (y(x) - f(x))f (x)

                                                     Type: Expression Integer
--R
--R          ,                    ,
--R   (38)  y (x) + (y(x) - f(x))f (x)
--R
--R                                                     Type: Expression Integer
--E 38

--S 39 of 134
ode10a:=solve(ode10,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 39

--S 40 of 134
ode11 := D(y(x),x)  + f(x)*y(x) - g(x)
 

          ,
   (39)  y (x) + f(x)y(x) - g(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (39)  y (x) + f(x)y(x) - g(x)
--R
--R                                                     Type: Expression Integer
--E 40

--S 41 of 134
ode11a:=solve(ode11,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 41

--S 42 of 134
ode12 := D(y(x),x) + y(x)**2 - 1
 

          ,          2
   (40)  y (x) + y(x)  - 1

                                                     Type: Expression Integer
--R
--R          ,          2
--R   (40)  y (x) + y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 134
yx:=solve(ode12,y,x)
 

         - log(y(x) + 1) + log(y(x) - 1) + 2x
   (41)  ------------------------------------
                           2
                                          Type: Union(Expression Integer,...)
--R
--R         - log(y(x) + 1) + log(y(x) - 1) + 2x
--R   (41)  ------------------------------------
--R                           2
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 134
ode12expr:=D(yx,x) + yx**2 - 1
 

   (42)
         ,           2                  2
       4y (x) + (y(x)  - 1)log(y(x) + 1)

     + 
                2                            2
       ((- 2y(x)  + 2)log(y(x) - 1) - 4x y(x)  + 4x)log(y(x) + 1)
     + 
          2                  2           2                        2    2     2
     (y(x)  - 1)log(y(x) - 1)  + (4x y(x)  - 4x)log(y(x) - 1) + 4x y(x)  - 4x
  /
          2
     4y(x)  - 4
                                                     Type: Expression Integer
--R
--R   (42)
--R         ,           2                  2
--R       4y (x) + (y(x)  - 1)log(y(x) + 1)
--R
--R     + 
--R                2                            2
--R       ((- 2y(x)  + 2)log(y(x) - 1) - 4x y(x)  + 4x)log(y(x) + 1)
--R     + 
--R          2                  2           2                        2    2     2
--R     (y(x)  - 1)log(y(x) - 1)  + (4x y(x)  - 4x)log(y(x) - 1) + 4x y(x)  - 4x
--R  /
--R          2
--R     4y(x)  - 4
--R                                                     Type: Expression Integer
--E 44

--S 45 of 134
ode13 := D(y(x),x) + y(x)**2 - a*x - b
 

          ,          2
   (43)  y (x) + y(x)  - a x - b

                                                     Type: Expression Integer
--R
--R          ,          2
--R   (43)  y (x) + y(x)  - a x - b
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 134
ode13a:=solve(ode13,y,x)
 

   (44)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (44)  "failed"
--R                                                    Type: Union("failed",...)
--E 46

--S 47 of 134
ode14 := D(y(x),x) + y(x)**2 + a*x**m
 

          ,         m       2
   (45)  y (x) + a x  + y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,         m       2
--R   (45)  y (x) + a x  + y(x)
--R
--R                                                     Type: Expression Integer
--E 47

--S 48 of 134
ode14a:=solve(ode14,y,x)
 

   (46)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (46)  "failed"
--R                                                    Type: Union("failed",...)
--E 48

--S 49 of 134
ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1
 

          ,          2     2        4
   (47)  y (x) + y(x)  - 2x y(x) + x  - 2x - 1

                                                     Type: Expression Integer
--R 
--R
--R          ,          2     2        4
--R   (47)  y (x) + y(x)  - 2x y(x) + x  - 2x - 1
--R
--R                                                     Type: Expression Integer
--E 49

--S 50 of 134
yx:=solve(ode15,y,x)
 

                     2
             y(x) - x  + 1
   (48)  ---------------------
                    2       2x
         (2y(x) - 2x  - 2)%e
                                          Type: Union(Expression Integer,...)
--R
--R                     2
--R             y(x) - x  + 1
--R   (48)  ---------------------
--R                    2       2x
--R         (2y(x) - 2x  - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 50

--S 51 of 134
ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1
 

   (49)
            2x ,
       - 4%e  y (x)

     + 
              4              2        6     4      3     2                    8
           (4x  - 8x - 4)y(x)  + (- 8x  - 8x  + 16x  + 8x  + 16x + 8)y(x) + 4x
         + 
             6     5      3     2
           8x  - 8x  - 16x  - 8x  - 8x - 4
      *
            2x 2
         (%e  )
     + 
             2         2      4     2          6     4     2            2x
       ((- 4x  - 4)y(x)  + (8x  + 8x )y(x) - 4x  - 4x  + 4x  + 8x + 4)%e
     + 
           2        2             4     2
       y(x)  + (- 2x  + 2)y(x) + x  - 2x  + 1
  /
           2        2              4     2        2x 2
     (4y(x)  + (- 8x  - 8)y(x) + 4x  + 8x  + 4)(%e  )
                                                     Type: Expression Integer
--R
--R   (49)
--R            2x ,
--R       - 4%e  y (x)
--R
--R     + 
--R              4              2        6     4      3     2                    8
--R           (4x  - 8x - 4)y(x)  + (- 8x  - 8x  + 16x  + 8x  + 16x + 8)y(x) + 4x
--R         + 
--R             6     5      3     2
--R           8x  - 8x  - 16x  - 8x  - 8x - 4
--R      *
--R            2x 2
--R         (%e  )
--R     + 
--R             2         2      4     2          6     4     2            2x
--R       ((- 4x  - 4)y(x)  + (8x  + 8x )y(x) - 4x  - 4x  + 4x  + 8x + 4)%e
--R     + 
--R           2        2             4     2
--R       y(x)  + (- 2x  + 2)y(x) + x  - 2x  + 1
--R  /
--R           2        2              4     2        2x 2
--R     (4y(x)  + (- 8x  - 8)y(x) + 4x  + 8x  + 4)(%e  )
--R                                                     Type: Expression Integer
--E 51

--S 52 of 134
ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x)
 

          ,          2
   (50)  y (x) + y(x)  + x f(x)y(x) - f(x)

                                                     Type: Expression Integer
--R
--R          ,          2
--R   (50)  y (x) + y(x)  + x f(x)y(x) - f(x)
--R
--R                                                     Type: Expression Integer
--E 52

--S 53 of 134
ode16a:=solve(ode16,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 53

--S 54 of 134
ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4 
 

          ,          2
   (52)  y (x) - y(x)  - 3y(x) + 4

                                                     Type: Expression Integer
--R 
--R
--R          ,          2
--R   (52)  y (x) - y(x)  - 3y(x) + 4
--R
--R                                                     Type: Expression Integer
--E 54

--S 55 of 134
yx:=solve(ode17,y,x)
 

         - log(y(x) + 4) + log(y(x) - 1) - 5x
   (53)  ------------------------------------
                           5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - log(y(x) + 4) + log(y(x) - 1) - 5x
--R   (53)  ------------------------------------
--R                           5
--R                                          Type: Union(Expression Integer,...)
--E 55

--S 56 of 134
ode17expr:=D(yx,x) - yx**2 -3*yx + 4 
 

   (54)
          ,             2                          2
       25y (x) + (- y(x)  - 3y(x) + 4)log(y(x) + 4)

     + 
                 2                                             2
           (2y(x)  + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x)
         + 
           (- 30x + 45)y(x) + 40x - 60
      *
         log(y(x) + 4)
     + 
              2                          2
       (- y(x)  - 3y(x) + 4)log(y(x) - 1)
     + 
                      2
       ((10x - 15)y(x)  + (30x - 45)y(x) - 40x + 60)log(y(x) - 1)
     + 
           2                2         2                         2
     (- 25x  + 75x + 75)y(x)  + (- 75x  + 225x + 225)y(x) + 100x  - 300x - 300
  /
           2
     25y(x)  + 75y(x) - 100
                                                     Type: Expression Integer
--R
--R   (54)
--R          ,             2                          2
--R       25y (x) + (- y(x)  - 3y(x) + 4)log(y(x) + 4)
--R
--R     + 
--R                 2                                             2
--R           (2y(x)  + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x)
--R         + 
--R           (- 30x + 45)y(x) + 40x - 60
--R      *
--R         log(y(x) + 4)
--R     + 
--R              2                          2
--R       (- y(x)  - 3y(x) + 4)log(y(x) - 1)
--R     + 
--R                      2
--R       ((10x - 15)y(x)  + (30x - 45)y(x) - 40x + 60)log(y(x) - 1)
--R     + 
--R           2                2         2                         2
--R     (- 25x  + 75x + 75)y(x)  + (- 75x  + 225x + 225)y(x) + 100x  - 300x - 300
--R  /
--R           2
--R     25y(x)  + 75y(x) - 100
--R                                                     Type: Expression Integer
--E 56

--S 57 of 134
ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1 
 

          ,          2
   (55)  y (x) - y(x)  - x y(x) - x + 1

                                                     Type: Expression Integer
--R 
--R
--R          ,          2
--R   (55)  y (x) - y(x)  - x y(x) - x + 1
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 134
yx:=solve(ode18,y,x)
 

                          2
                       - x  + 4x
                       ---------   x
                           2     ++          1
         (- y(x) - 1)%e          |   - ------------- d%N  + 1
                                ++           2
                                         - %N  + 4%N
                                         -----------
                                              2
                                       %e
   (56)  ----------------------------------------------------
                                        2
                                     - x  + 4x
                                     ---------
                                         2
                         (y(x) + 1)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2
--R                       - x  + 4x
--R                       ---------   x
--R                           2     ++          1
--I         (- y(x) - 1)%e          |   - ------------- d%N  + 1
--R                                ++           2
--I                                         - %N  + 4%N
--R                                         -----------
--R                                              2
--R                                       %e
--R   (56)  ----------------------------------------------------
--R                                        2
--R                                     - x  + 4x
--R                                     ---------
--R                                         2
--R                         (y(x) + 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 134
ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 
 

   (57)
                                  2      2
                               - x  + 4x
                               ---------     x                     2
              2                    2       ++          1
       (- y(x)  - 2y(x) - 1)(%e         )  |   - ------------- d%N
                                          ++           2
                                                   - %N  + 4%N
                                                   -----------
                                                        2
                                                 %e
     + 
                                       2      2                   2
                                    - x  + 4x                  - x  + 4x
                                    ---------                  ---------
                 2                      2                          2
         ((x y(x)  + 2x y(x) + x)(%e         )  + (2y(x) + 2)%e         )
      *
            x
          ++          1
          |   - ------------- d%N
         ++           2
                  - %N  + 4%N
                  -----------
                       2
                %e
     + 
              2
           - x  + 4x
           ---------
               2     ,
       - %e         y (x)

     + 
                                                      2      2
                                                   - x  + 4x
                                                   ---------
                     2                                 2
       ((- x + 1)y(x)  + (- 2x + 2)y(x) - x + 1)(%e         )
     + 
                       2
                    - x  + 4x
                    ---------
            2           2
       (y(x)  - 1)%e          - 1
  /
                              2      2
                           - x  + 4x
                           ---------
          2                    2
     (y(x)  + 2y(x) + 1)(%e         )
                                                     Type: Expression Integer
--R   (57)
--R                                  2      2
--R                               - x  + 4x
--R                               ---------     x                     2
--R              2                    2       ++          1
--I       (- y(x)  - 2y(x) - 1)(%e         )  |   - ------------- d%H
--R                                          ++           2
--I                                                   - %H  + 4%H
--R                                                   -----------
--R                                                        2
--R                                                 %e
--R     + 
--R                                       2      2                   2
--R                                    - x  + 4x                  - x  + 4x
--R                                    ---------                  ---------
--R                 2                      2                          2
--R         ((x y(x)  + 2x y(x) + x)(%e         )  + (2y(x) + 2)%e         )
--R      *
--R            x
--R          ++          1
--I          |   - ------------- d%H
--R         ++           2
--I                  - %H  + 4%H
--R                  -----------
--R                       2
--R                %e
--R     + 
--R              2
--R           - x  + 4x
--R           ---------
--R               2     ,
--R       - %e         y (x)
--R
--R     + 
--R                                                      2      2
--R                                                   - x  + 4x
--R                                                   ---------
--R                     2                                 2
--R       ((- x + 1)y(x)  + (- 2x + 2)y(x) - x + 1)(%e         )
--R     + 
--R                       2
--R                    - x  + 4x
--R                    ---------
--R            2           2
--R       (y(x)  - 1)%e          - 1
--R  /
--R                              2      2
--R                           - x  + 4x
--R                           ---------
--R          2                    2
--R     (y(x)  + 2y(x) + 1)(%e         )
--R                                                     Type: Expression Integer
--E 59

--S 60 of 134
ode19 := D(y(x),x) - (y(x) + x)**2
 

          ,          2              2
   (58)  y (x) - y(x)  - 2x y(x) - x

                                                     Type: Expression Integer
--R 
--R
--R          ,          2              2
--R   (58)  y (x) - y(x)  - 2x y(x) - x
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 134
yx:=solve(ode19,y,x)
 

                             +---+
                   - y(x) + \|- 1  - x
   (59)  --------------------------------------
                                          +---+
            +---+          +---+       2x\|- 1
         (2\|- 1 y(x) + 2x\|- 1  - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             +---+
--R                   - y(x) + \|- 1  - x
--R   (59)  --------------------------------------
--R                                          +---+
--R            +---+          +---+       2x\|- 1
--R         (2\|- 1 y(x) + 2x\|- 1  - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 134
ode19expr := D(yx,x) - (yx + x)**2
 

   (60)
               +---+
            2x\|- 1  ,
       - 4%e        y (x)

     + 
              2    2        2 +---+     3          3 +---+     4     2
         (- 4x y(x)  + (- 8x \|- 1  - 8x )y(x) - 8x \|- 1  - 4x  + 4x )
      *
               +---+ 2
            2x\|- 1
         (%e        )
     + 
                 +---+         2        2 +---+                  3       +---+
           (- 4x\|- 1  + 4)y(x)  + (- 8x \|- 1  + 8x)y(x) + (- 4x  - 4x)\|- 1
         + 
             2
           4x
      *
              +---+
           2x\|- 1
         %e
     + 
           2        +---+                +---+    2
       y(x)  + (- 2\|- 1  + 2x)y(x) - 2x\|- 1  + x  - 1
  /
                                                             +---+ 2
           2      +---+                +---+     2        2x\|- 1
     (4y(x)  + (8\|- 1  + 8x)y(x) + 8x\|- 1  + 4x  - 4)(%e        )
                                                     Type: Expression Integer
--R
--R   (60)
--R               +---+
--R            2x\|- 1  ,
--R       - 4%e        y (x)
--R
--R     + 
--R              2    2        2 +---+     3          3 +---+     4     2
--R         (- 4x y(x)  + (- 8x \|- 1  - 8x )y(x) - 8x \|- 1  - 4x  + 4x )
--R      *
--R               +---+ 2
--R            2x\|- 1
--R         (%e        )
--R     + 
--R                 +---+         2        2 +---+                  3       +---+
--R           (- 4x\|- 1  + 4)y(x)  + (- 8x \|- 1  + 8x)y(x) + (- 4x  - 4x)\|- 1
--R         + 
--R             2
--R           4x
--R      *
--R              +---+
--R           2x\|- 1
--R         %e
--R     + 
--R           2        +---+                +---+    2
--R       y(x)  + (- 2\|- 1  + 2x)y(x) - 2x\|- 1  + x  - 1
--R  /
--R                                                             +---+ 2
--R           2      +---+                +---+     2        2x\|- 1
--R     (4y(x)  + (8\|- 1  + 8x)y(x) + 8x\|- 1  + 4x  - 4)(%e        )
--R                                                     Type: Expression Integer
--E 62

--S 63 of 134
ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x 
 

          ,          2     2
   (61)  y (x) - y(x)  + (x  + 1)y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R          ,          2     2
--R   (61)  y (x) - y(x)  + (x  + 1)y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 63

--S 64 of 134
yx:=solve(ode20,y,x)
 

                               3
                            - x  - 3x
                            ---------   x
                    2           3     ++          1
         (- y(x) + x  + 1)%e          |   - ------------- d%N  + 1
                                     ++           3
                                              - %N  - 3%N
                                              -----------
                                                   3
                                            %e
   (62)  ---------------------------------------------------------
                                             3
                                          - x  - 3x
                                          ---------
                                  2           3
                         (y(x) - x  - 1)%e
                                          Type: Union(Expression Integer,...)
--R
--R                               3
--R                            - x  - 3x
--R                            ---------   x
--R                    2           3     ++          1
--I         (- y(x) + x  + 1)%e          |   - ------------- d%H  + 1
--R                                     ++           3
--I                                              - %H  - 3%H
--R                                              -----------
--R                                                   3
--R                                            %e
--R   (62)  ---------------------------------------------------------
--R                                             3
--R                                          - x  - 3x
--R                                          ---------
--R                                  2           3
--R                         (y(x) - x  - 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 64

--S 65 of 134
ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x 
 

   (63)
                                                       3      2
                                                    - x  - 3x
                                                    ---------
                2      2             4     2            3
         (- y(x)  + (2x  + 2)y(x) - x  - 2x  - 1)(%e         )
      *
            x                     2
          ++          1
          |   - ------------- d%N
         ++           3
                  - %N  - 3%N
                  -----------
                       3
                %e
     + 
                  2         2      4     2             6     4     2
             ((- x  - 1)y(x)  + (2x  + 4x  + 2)y(x) - x  - 3x  - 3x  - 1)
          *
                   3      2
                - x  - 3x
                ---------
                    3
             (%e         )
         + 
                                 3
                              - x  - 3x
                              ---------
                      2           3
           (2y(x) - 2x  - 2)%e
      *
            x
          ++          1
          |   - ------------- d%N
         ++           3
                  - %N  - 3%N
                  -----------
                       3
                %e
     + 
              3
           - x  - 3x
           ---------
               3     ,
       - %e         y (x)

     + 
                                                           3      2
                                                        - x  - 3x
                                                        ---------
                 2      3               5     3             3
       (- 2x y(x)  + (4x  + 4x)y(x) - 2x  - 4x  - 2x)(%e         )
     + 
                                       3
                                    - x  - 3x
                                    ---------
            2    4     2                3
       (y(x)  - x  - 2x  + 2x - 1)%e          - 1
  /
                                                   3      2
                                                - x  - 3x
                                                ---------
          2        2             4     2            3
     (y(x)  + (- 2x  - 2)y(x) + x  + 2x  + 1)(%e         )
                                                     Type: Expression Integer
--R
--R   (63)
--R                                                       3      2
--R                                                    - x  - 3x
--R                                                    ---------
--R                2      2             4     2            3
--R         (- y(x)  + (2x  + 2)y(x) - x  - 2x  - 1)(%e         )
--R      *
--R            x                     2
--R          ++          1
--I          |   - ------------- d%H
--R         ++           3
--I                  - %H  - 3%H
--R                  -----------
--R                       3
--R                %e
--R     + 
--R                  2         2      4     2             6     4     2
--R             ((- x  - 1)y(x)  + (2x  + 4x  + 2)y(x) - x  - 3x  - 3x  - 1)
--R          *
--R                   3      2
--R                - x  - 3x
--R                ---------
--R                    3
--R             (%e         )
--R         + 
--R                                 3
--R                              - x  - 3x
--R                              ---------
--R                      2           3
--R           (2y(x) - 2x  - 2)%e
--R      *
--R            x
--R          ++          1
--I          |   - ------------- d%H
--R         ++           3
--I                  - %H  - 3%H
--R                  -----------
--R                       3
--R                %e
--R     + 
--R              3
--R           - x  - 3x
--R           ---------
--R               3     ,
--R       - %e         y (x)
--R
--R     + 
--R                                                           3      2
--R                                                        - x  - 3x
--R                                                        ---------
--R                 2      3               5     3             3
--R       (- 2x y(x)  + (4x  + 4x)y(x) - 2x  - 4x  - 2x)(%e         )
--R     + 
--R                                       3
--R                                    - x  - 3x
--R                                    ---------
--R            2    4     2                3
--R       (y(x)  - x  - 2x  + 2x - 1)%e          - 1
--R  /
--R                                                   3      2
--R                                                - x  - 3x
--R                                                ---------
--R          2        2             4     2            3
--R     (y(x)  + (- 2x  - 2)y(x) + x  + 2x  + 1)(%e         )
--R                                                     Type: Expression Integer
--E 65

--S 66 of 134
ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x) 
 

          ,                                2
   (64)  y (x) + y(x)sin(x) - cos(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,                                2
--R   (64)  y (x) + y(x)sin(x) - cos(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 66

--S 67 of 134
ode21a:=solve(ode21,y,x)
 

   (65)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (65)  "failed"
--R                                                    Type: Union("failed",...)
--E 67

--S 68 of 134
ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x) 
 

          ,                                  2
   (66)  y (x) - y(x)sin(2x) - cos(2x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,                                  2
--R   (66)  y (x) - y(x)sin(2x) - cos(2x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 134
ode22a:=solve(ode22,y,x)
 

   (67)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (67)  "failed"
--R                                                    Type: Union("failed",...)
--E 69

--S 70 of 134
ode23 := D(y(x),x) + a*y(x)**2 - b
 

          ,            2
   (68)  y (x) + a y(x)  - b

                                                     Type: Expression Integer
--R 
--R
--R          ,            2
--R   (68)  y (x) + a y(x)  - b
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 134
yx:=solve(ode23,y,x)
 

                    2      +---+
             (a y(x)  + b)\|a b  - 2a b y(x)       +---+
         log(-------------------------------) + 2x\|a b
                             2
                       a y(x)  - b
   (69)  -----------------------------------------------
                               +---+
                             2\|a b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2      +---+
--R             (a y(x)  + b)\|a b  - 2a b y(x)       +---+
--R         log(-------------------------------) + 2x\|a b
--R                             2
--R                       a y(x)  - b
--R   (69)  -----------------------------------------------
--R                               +---+
--R                             2\|a b
--R                                          Type: Union(Expression Integer,...)
--E 71

--S 72 of 134
ode23expr := D(yx,x) + a*yx**2 - b
 

   (70)
                                         2      +---+             2
          ,             2         (a y(x)  + b)\|a b  - 2a b y(x)
       4by (x) + (a y(x)  - b)log(-------------------------------)
                                                  2
                                            a y(x)  - b
     + 
                                           2      +---+
                 2         +---+    (a y(x)  + b)\|a b  - 2a b y(x)
       (4a x y(x)  - 4b x)\|a b log(-------------------------------)
                                                    2
                                              a y(x)  - b
     + 
          2   2       2            2       2 2     3     2
       (4a b x  - 4a b  + 4a b)y(x)  - 4a b x  + 4b  - 4b
  /
              2     2
     4a b y(x)  - 4b
                                                     Type: Expression Integer
--R
--R   (70)
--R                                         2      +---+             2
--R          ,             2         (a y(x)  + b)\|a b  - 2a b y(x)
--R       4by (x) + (a y(x)  - b)log(-------------------------------)
--R                                                  2
--R                                            a y(x)  - b
--R     + 
--R                                           2      +---+
--R                 2         +---+    (a y(x)  + b)\|a b  - 2a b y(x)
--R       (4a x y(x)  - 4b x)\|a b log(-------------------------------)
--R                                                    2
--R                                              a y(x)  - b
--R     + 
--R          2   2       2            2       2 2     3     2
--R       (4a b x  - 4a b  + 4a b)y(x)  - 4a b x  + 4b  - 4b
--R  /
--R              2     2
--R     4a b y(x)  - 4b
--R                                                     Type: Expression Integer
--E 72

--S 73 of 134
ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu
 

          ,         nu         2
   (71)  y (x) - b x   + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,         nu         2
--R   (71)  y (x) - b x   + a y(x)
--R
--R                                                     Type: Expression Integer
--E 73

--S 74 of 134
ode24a:=solve(ode24,y,x)
 

   (72)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (72)  "failed"
--R                                                    Type: Union("failed",...)
--E 74

--S 75 of 134
ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1)
 

          ,         2nu      nu - 1         2
   (73)  y (x) - b x    - c x       + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,         2nu      nu - 1         2
--R   (73)  y (x) - b x    - c x       + a y(x)
--R
--R                                                     Type: Expression Integer
--E 75

--S 76 of 134
ode25expr:=solve(ode25,y,x)
 

   (74)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (74)  "failed"
--R                                                    Type: Union("failed",...)
--E 76

--S 77 of 134
ode26 := D(y(x),x) - (A*y(x) - a)*(B*y(x) - b)
 

          ,              2
   (75)  y (x) - A B y(x)  + (A b + B a)y(x) - a b

                                                     Type: Expression Integer
--R 
--R
--R          ,              2
--R   (75)  y (x) - A B y(x)  + (A b + B a)y(x) - a b
--R
--R                                                     Type: Expression Integer
--E 77

--S 78 of 134
yx:=solve(ode26,y,x)
 

         log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x
   (76)  --------------------------------------------------
                              A b - B a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x
--R   (76)  --------------------------------------------------
--R                              A b - B a
--R                                          Type: Union(Expression Integer,...)
--E 78

--S 79 of 134
ode26expr := D(yx,x) - (A*yx - a)*(B*yx - b)
 

   (77)
         2 2               2 2  ,
       (A b  - 2A B a b + B a )y (x)

     + 
           2 2    2     2         2                                2
       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(B y(x) - b)
     + 
              2 2    2        2          2
           (2A B y(x)  + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a)
         + 
               3 2      2 3       3   2      3 2     2
           ((2A B b - 2A B a)x + A B b  - A B a )y(x)
         + 
                 3   2       3 2      3 3    2     2      2 2     3 3
           ((- 2A B b  + 2A B a )x - A b  - A B a b  + A B a b + B a )y(x)
         + 
              2     2       2 2       2   3    2 3
           (2A B a b  - 2A B a b)x + A a b  - B a b
      *
         log(B y(x) - b)
     + 
           2 2    2     2         2                                2
       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(A y(x) - a)
     + 
                 3 2      2 3       3   2      3 2     2
           ((- 2A B b + 2A B a)x - A B b  + A B a )y(x)
         + 
               3   2       3 2      3 3    2     2      2 2     3 3
           ((2A B b  - 2A B a )x + A b  + A B a b  - A B a b - B a )y(x)
         + 
                2     2       2 2       2   3    2 3
           (- 2A B a b  + 2A B a b)x - A a b  + B a b
      *
         log(A y(x) - a)
     + 
               4 2 2     3 3       2 4 2  2
           (- A B b  + 2A B a b - A B a )x
         + 
               4   3    3 2   2    2 3 2       4 3      3     3
           (- A B b  + A B a b  + A B a b - A B a )x - A B a b
         + 
              2 2 2    3   2         3 3     2 2         3 2
           (2A B a  - A B)b  + (- A B a  + 2A B a)b - A B a
      *
             2
         y(x)
     + 
             4   3    3 2   2    2 3 2       4 3  2     4 4     2 2 2 2    4 4
           (A B b  - A B a b  - A B a b + A B a )x  + (A b  - 2A B a b  + B a )x
         + 
            3   4       2   2    3  3         2 3    2     2     3 4      2 2
           A a b  + (- A B a  + A )b  + (- A B a  - A B a)b  + (B a  - A B a )b
         + 
            3 3
           B a
      *
         y(x)
     + 
           3     3     2 2 2 2      3 3   2
       (- A B a b  + 2A B a b  - A B a b)x
     + 
           3   4    2   2 3      2 3 2    3 4       2 2 4          3    2   3
       (- A a b  + A B a b  + A B a b  - B a b)x - A a b  + (2A B a  - A a)b
     + 
           2 4         2  2    2 3
       (- B a  + 2A B a )b  - B a b
  /
         3   2     2 2         3 2     2
       (A B b  - 2A B a b + A B a )y(x)
     + 
           3 3    2     2      2 2     3 3         2   3         2 2    2 3
       (- A b  + A B a b  + A B a b - B a )y(x) + A a b  - 2A B a b  + B a b
                                                     Type: Expression Integer
--R
--R   (77)
--R         2 2               2 2  ,
--R       (A b  - 2A B a b + B a )y (x)
--R
--R     + 
--R           2 2    2     2         2                                2
--R       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(B y(x) - b)
--R     + 
--R              2 2    2        2          2
--R           (2A B y(x)  + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a)
--R         + 
--R               3 2      2 3       3   2      3 2     2
--R           ((2A B b - 2A B a)x + A B b  - A B a )y(x)
--R         + 
--R                 3   2       3 2      3 3    2     2      2 2     3 3
--R           ((- 2A B b  + 2A B a )x - A b  - A B a b  + A B a b + B a )y(x)
--R         + 
--R              2     2       2 2       2   3    2 3
--R           (2A B a b  - 2A B a b)x + A a b  - B a b
--R      *
--R         log(B y(x) - b)
--R     + 
--R           2 2    2     2         2                                2
--R       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(A y(x) - a)
--R     + 
--R                 3 2      2 3       3   2      3 2     2
--R           ((- 2A B b + 2A B a)x - A B b  + A B a )y(x)
--R         + 
--R               3   2       3 2      3 3    2     2      2 2     3 3
--R           ((2A B b  - 2A B a )x + A b  + A B a b  - A B a b - B a )y(x)
--R         + 
--R                2     2       2 2       2   3    2 3
--R           (- 2A B a b  + 2A B a b)x - A a b  + B a b
--R      *
--R         log(A y(x) - a)
--R     + 
--R               4 2 2     3 3       2 4 2  2
--R           (- A B b  + 2A B a b - A B a )x
--R         + 
--R               4   3    3 2   2    2 3 2       4 3      3     3
--R           (- A B b  + A B a b  + A B a b - A B a )x - A B a b
--R         + 
--R              2 2 2    3   2         3 3     2 2         3 2
--R           (2A B a  - A B)b  + (- A B a  + 2A B a)b - A B a
--R      *
--R             2
--R         y(x)
--R     + 
--R             4   3    3 2   2    2 3 2       4 3  2     4 4     2 2 2 2    4 4
--R           (A B b  - A B a b  - A B a b + A B a )x  + (A b  - 2A B a b  + B a )x
--R         + 
--R            3   4       2   2    3  3         2 3    2     2     3 4      2 2
--R           A a b  + (- A B a  + A )b  + (- A B a  - A B a)b  + (B a  - A B a )b
--R         + 
--R            3 3
--R           B a
--R      *
--R         y(x)
--R     + 
--R           3     3     2 2 2 2      3 3   2
--R       (- A B a b  + 2A B a b  - A B a b)x
--R     + 
--R           3   4    2   2 3      2 3 2    3 4       2 2 4          3    2   3
--R       (- A a b  + A B a b  + A B a b  - B a b)x - A a b  + (2A B a  - A a)b
--R     + 
--R           2 4         2  2    2 3
--R       (- B a  + 2A B a )b  - B a b
--R  /
--R         3   2     2 2         3 2     2
--R       (A B b  - 2A B a b + A B a )y(x)
--R     + 
--R           3 3    2     2      2 2     3 3         2   3         2 2    2 3
--R       (- A b  + A B a b  + A B a b - B a )y(x) + A a b  - 2A B a b  + B a b
--R                                                     Type: Expression Integer
--E 79

--S 80 of 134
ode27 := D(y(x),x) + a*y(x)*(y(x)-x) - 1
 

          ,            2
   (78)  y (x) + a y(x)  - a x y(x) - 1

                                                     Type: Expression Integer
--R 
--R
--R          ,            2
--R   (78)  y (x) + a y(x)  - a x y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 80

--S 81 of 134
ode27a:=solve(ode27,y,x)
 

                          2
                       a x
                       ----   x
                         2  ++     a
         (- y(x) + x)%e     |   ------ d%N  + 1
                           ++       2
                                  %N a
                                  ----
                                    2
                                %e
   (79)  --------------------------------------
                                   2
                                a x
                                ----
                                  2
                    (y(x) - x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2
--R                       a x
--R                       ----   x
--R                         2  ++     a
--I         (- y(x) + x)%e     |   ------ d%N  + 1
--R                           ++       2
--I                                  %N a
--R                                  ----
--R                                    2
--R                                %e
--R   (79)  --------------------------------------
--R                                   2
--R                                a x
--R                                ----
--R                                  2
--R                    (y(x) - x)%e
--R                                          Type: Union(Expression Integer,...)
--E 81

--S 82 of 134
ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x 
 

          ,            2    3
   (80)  y (x) + x y(x)  - x y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R          ,            2    3
--R   (80)  y (x) + x y(x)  - x y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 134
ode28a:=solve(ode28,y,x)
 

                         4
                        x
                        --   x
                    2    4 ++    %N
         (- y(x) + x )%e   |   ----- d%N  + 1
                          ++       4
                                 %N
                                 ---
                                  4
                               %e
   (81)  ------------------------------------
                                  4
                                 x
                                 --
                             2    4
                    (y(x) - x )%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         4
--R                        x
--R                        --   x
--I                    2    4 ++    %N
--I         (- y(x) + x )%e   |   ----- d%N  + 1
--R                          ++       4
--I                                 %N
--R                                 ---
--R                                  4
--R                               %e
--R   (81)  ------------------------------------
--R                                  4
--R                                 x
--R                                 --
--R                             2    4
--R                    (y(x) - x )%e
--R                                          Type: Union(Expression Integer,...)
--E 83

--S 84 of 134
ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x) 
 

          ,            2
   (82)  y (x) - x y(x)  - 3x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,            2
--R   (82)  y (x) - x y(x)  - 3x y(x)
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 134
yx:=solve(ode29,y,x)
 

                                           2
         - 2log(y(x) + 3) + 2log(y(x)) - 3x
   (83)  -----------------------------------
                          6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                           2
--R         - 2log(y(x) + 3) + 2log(y(x)) - 3x
--R   (83)  -----------------------------------
--R                          6
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 134
ode29expr := D(yx,x) - x*yx**2 - 3*x*yx 
 

   (84)
          ,                2                         2
       36y (x) + (- 4x y(x)  - 12x y(x))log(y(x) + 3)

     + 
                   2                              3           2
           (8x y(x)  + 24x y(x))log(y(x)) + (- 12x  + 36x)y(x)
         + 
                 3
           (- 36x  + 108x)y(x)
      *
         log(y(x) + 3)
     + 
                 2                     2
       (- 4x y(x)  - 12x y(x))log(y(x))
     + 
            3           2       3
       ((12x  - 36x)y(x)  + (36x  - 108x)y(x))log(y(x))
     + 
            5      3           2         5       3
       (- 9x  + 54x  - 36x)y(x)  + (- 27x  + 162x  - 108x)y(x)
  /
           2
     36y(x)  + 108y(x)
                                                     Type: Expression Integer
--R
--R   (84)
--R          ,                2                         2
--R       36y (x) + (- 4x y(x)  - 12x y(x))log(y(x) + 3)
--R
--R     + 
--R                   2                              3           2
--R           (8x y(x)  + 24x y(x))log(y(x)) + (- 12x  + 36x)y(x)
--R         + 
--R                 3
--R           (- 36x  + 108x)y(x)
--R      *
--R         log(y(x) + 3)
--R     + 
--R                 2                     2
--R       (- 4x y(x)  - 12x y(x))log(y(x))
--R     + 
--R            3           2       3
--R       ((12x  - 36x)y(x)  + (36x  - 108x)y(x))log(y(x))
--R     + 
--R            5      3           2         5       3
--R       (- 9x  + 54x  - 36x)y(x)  + (- 27x  + 162x  - 108x)y(x)
--R  /
--R           2
--R     36y(x)  + 108y(x)
--R                                                     Type: Expression Integer
--E 86

--S 87 of 134
ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a
 

          ,       a       2 - a - 1
   (85)  y (x) - x  + y(x) x

                                                     Type: Expression Integer
--R 
--R
--R          ,       a       2 - a - 1
--R   (85)  y (x) - x  + y(x) x
--R
--R                                                     Type: Expression Integer
--E 87

--S 88 of 134
ode30a:=solve(ode30,y,x)
 

   (86)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (86)  "failed"
--R                                                    Type: Union("failed",...)
--E 88

--S 89 of 134
ode31 := D(y(x),x) - a*x**n*(y(x)**2+1) 
 

          ,               2      n
   (87)  y (x) + (- a y(x)  - a)x

                                                     Type: Expression Integer
--R 
--R
--R          ,               2      n
--R   (87)  y (x) + (- a y(x)  - a)x
--R
--R                                                     Type: Expression Integer
--E 89

--S 90 of 134
yx:=solve(ode31,y,x)
 

                 n log(x)
         - a x %e         + (n + 1)atan(y(x))
   (88)  ------------------------------------
                         n + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 n log(x)
--R         - a x %e         + (n + 1)atan(y(x))
--R   (88)  ------------------------------------
--R                         n + 1
--R                                          Type: Union(Expression Integer,...)
--E 90

--S 91 of 134
ode31expr := D(yx,x) - a*x**n*(yx**2+1) 
 

   (89)
         2           ,          3 2    2    3 2  n   n log(x) 2
       (n  + 2n + 1)y (x) + (- a x y(x)  - a x )x (%e        )

     + 
               2      2       2      2      2    n
           ((2a n + 2a )x y(x)  + (2a n + 2a )x)x atan(y(x))
         + 
                 2                2      2
           (- a n  - 2a n - a)y(x)  - a n  - 2a n - a
      *
           n log(x)
         %e
     + 
              2                2      2             n          2
       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x atan(y(x))
     + 
              2                2      2             n
       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x
  /
       2              2    2
     (n  + 2n + 1)y(x)  + n  + 2n + 1
                                                     Type: Expression Integer
--R
--R   (89)
--R         2           ,          3 2    2    3 2  n   n log(x) 2
--R       (n  + 2n + 1)y (x) + (- a x y(x)  - a x )x (%e        )
--R
--R     + 
--R               2      2       2      2      2    n
--R           ((2a n + 2a )x y(x)  + (2a n + 2a )x)x atan(y(x))
--R         + 
--R                 2                2      2
--R           (- a n  - 2a n - a)y(x)  - a n  - 2a n - a
--R      *
--R           n log(x)
--R         %e
--R     + 
--R              2                2      2             n          2
--R       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x atan(y(x))
--R     + 
--R              2                2      2             n
--R       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x
--R  /
--R       2              2    2
--R     (n  + 2n + 1)y(x)  + n  + 2n + 1
--R                                                     Type: Expression Integer
--E 91

--S 92 of 134
ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2
 

               2 ,           2      2
         cos(x) y (x) + (y(x) cos(x)  - 2)sin(x)

   (90)  ---------------------------------------
                               2
                         cos(x)
                                                     Type: Expression Integer
--R 
--R
--R               2 ,           2      2
--R         cos(x) y (x) + (y(x) cos(x)  - 2)sin(x)
--R
--R   (90)  ---------------------------------------
--R                               2
--R                         cos(x)
--R                                                     Type: Expression Integer
--E 92

--S 93 of 134
yx:=solve(ode32,y,x)
 

   (91)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (91)  "failed"
--R                                                    Type: Union("failed",...)
--E 93

--S 94 of 134
ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x)
 

                  ,           ,              2 ,
         f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x)

   (92)  ------------------------------------------
                          f(x)g(x)
                                                     Type: Expression Integer
--R
--R                  ,           ,              2 ,
--R         f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x)
--R
--R   (92)  ------------------------------------------
--R                          f(x)g(x)
--R                                                     Type: Expression Integer
--E 94

--S 95 of 134
ode33a:=solve(ode33,y,x)
 

   (93)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (93)  "failed"
--R                                                    Type: Union("failed",...)
--E 95

--S 96 of 134
ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x) 
 

          ,              2
   (94)  y (x) + f(x)y(x)  + g(x)y(x)

                                                     Type: Expression Integer
--R
--R          ,              2
--R   (94)  y (x) + f(x)y(x)  + g(x)y(x)
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 134
ode34a:=solve(ode34,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 97

--S 98 of 134
ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b) 
 

          ,              2
   (95)  y (x) + f(x)y(x)  + 2a f(x)y(x) + b f(x)

                                                     Type: Expression Integer
--R
--R          ,              2
--R   (95)  y (x) + f(x)y(x)  + 2a f(x)y(x) + b f(x)
--R
--R                                                     Type: Expression Integer
--E 98

--S 99 of 134
yx:=solve(ode35,y,x)
 

   (96)
         +--------+   x
         |       2  ++
       2\|- b + a   |   f(%N)d%N
                   ++
     + 
                                     +--------+
              2                   2  |       2            2                 3
         (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
     log(--------------------------------------------------------------------)
                                      2
                                  y(x)  + 2a y(x) + b
  /
       +--------+
       |       2
     2\|- b + a
                                          Type: Union(Expression Integer,...)
--R
--R   (96)
--R         +--------+   x
--R         |       2  ++
--I       2\|- b + a   |   f(%H)d%H
--R                   ++
--R     + 
--R                                     +--------+
--R              2                   2  |       2            2                 3
--R         (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
--R     log(--------------------------------------------------------------------)
--R                                      2
--R                                  y(x)  + 2a y(x) + b
--R  /
--R       +--------+
--R       |       2
--R     2\|- b + a
--R                                          Type: Union(Expression Integer,...)
--E 99

--S 100 of 134
ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) 
 

   (97)
                  2         2             3               2     2
         ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
      *
          +--------+   x          2
          |       2  ++
         \|- b + a   |   f(%N)d%N
                    ++
     + 
                      2         2             3               2     2
             ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
          *
             log
                                                +--------+
                         2                   2  |       2            2
                    (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x)
                  + 
                             3
                    2a b - 2a
               /
                      2
                  y(x)  + 2a y(x) + b
         + 
                           3         2       2       4
                 (8a b - 8a )f(x)y(x)  + (16a b - 16a )f(x)y(x)
               + 
                      2     3
                 (8a b  - 8a b)f(x)
          *
              +--------+
              |       2
             \|- b + a
      *
            x
          ++
          |   f(%N)d%N
         ++
     + 
                  +--------+
               2  |       2  ,
       (4b - 4a )\|- b + a  y (x)

     + 
                                              +--------+
                    2                         |       2
         (- f(x)y(x)  - 2a f(x)y(x) - b f(x))\|- b + a
      *
           log
                                              +--------+
                       2                   2  |       2            2
                  (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b
                + 
                      3
                  - 2a
             /
                    2
                y(x)  + 2a y(x) + b
        **
           2
     + 
                    3         2      2      4                 2     3
         ((4a b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4a b  - 4a b)f(x))
      *
                                       +--------+
                2                   2  |       2            2                 3
           (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
       log(--------------------------------------------------------------------)
                                        2
                                    y(x)  + 2a y(x) + b
     + 
              2        2           2         2
           (4b  + (- 4a  + 4)b - 4a )f(x)y(x)
         + 
                2        3            3
           (8a b  + (- 8a  + 8a)b - 8a )f(x)y(x)
         + 
              3        2      2     2
           (4b  + (- 4a  + 4)b  - 4a b)f(x)
      *
          +--------+
          |       2
         \|- b + a
  /
                                                       +--------+
              2     2             3          2     2   |       2
     ((4b - 4a )y(x)  + (8a b - 8a )y(x) + 4b  - 4a b)\|- b + a
                                                     Type: Expression Integer
--R
--R   (97)
--R                  2         2             3               2     2
--R         ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
--R      *
--R          +--------+   x          2
--R          |       2  ++
--I         \|- b + a   |   f(%H)d%H
--R                    ++
--R     + 
--R                      2         2             3               2     2
--R             ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
--R          *
--R             log
--R                                                +--------+
--R                         2                   2  |       2            2
--R                    (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x)
--R                  + 
--R                             3
--R                    2a b - 2a
--R               /
--R                      2
--R                  y(x)  + 2a y(x) + b
--R         + 
--R                           3         2       2       4
--R                 (8a b - 8a )f(x)y(x)  + (16a b - 16a )f(x)y(x)
--R               + 
--R                      2     3
--R                 (8a b  - 8a b)f(x)
--R          *
--R              +--------+
--R              |       2
--R             \|- b + a
--R      *
--R            x
--R          ++
--I          |   f(%H)d%H
--R         ++
--R     + 
--R                  +--------+
--R               2  |       2  ,
--R       (4b - 4a )\|- b + a  y (x)
--R
--R     + 
--R                                              +--------+
--R                    2                         |       2
--R         (- f(x)y(x)  - 2a f(x)y(x) - b f(x))\|- b + a
--R      *
--R           log
--R                                              +--------+
--R                       2                   2  |       2            2
--R                  (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b
--R                + 
--R                      3
--R                  - 2a
--R             /
--R                    2
--R                y(x)  + 2a y(x) + b
--R        **
--R           2
--R     + 
--R                    3         2      2      4                 2     3
--R         ((4a b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4a b  - 4a b)f(x))
--R      *
--R                                       +--------+
--R                2                   2  |       2            2                 3
--R           (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
--R       log(--------------------------------------------------------------------)
--R                                        2
--R                                    y(x)  + 2a y(x) + b
--R     + 
--R              2        2           2         2
--R           (4b  + (- 4a  + 4)b - 4a )f(x)y(x)
--R         + 
--R                2        3            3
--R           (8a b  + (- 8a  + 8a)b - 8a )f(x)y(x)
--R         + 
--R              3        2      2     2
--R           (4b  + (- 4a  + 4)b  - 4a b)f(x)
--R      *
--R          +--------+
--R          |       2
--R         \|- b + a
--R  /
--R                                                       +--------+
--R              2     2             3          2     2   |       2
--R     ((4b - 4a )y(x)  + (8a b - 8a )y(x) + 4b  - 4a b)\|- b + a
--R                                                     Type: Expression Integer
--E 100

--S 101 of 134
ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2 
 

          ,          3           2
   (98)  y (x) + y(x)  + a x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,          3           2
--R   (98)  y (x) + y(x)  + a x y(x)
--R
--R                                                     Type: Expression Integer
--E 101

--S 102 of 134
ode36a:=solve(ode36,y,x)
 

   (99)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (99)  "failed"
--R                                                    Type: Union("failed",...)
--E 102

--S 103 of 134
ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2
 

           ,            2  x       3
   (100)  y (x) - a y(x) %e  - y(x)

                                                     Type: Expression Integer
--R
--R           ,            2  x       3
--R   (100)  y (x) - a y(x) %e  - y(x)
--R
--R                                                     Type: Expression Integer
--E 103

--S 104 of 134
ode37a:=solve(ode37,y,x)
 

   (101)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (101)  "failed"
--R                                                    Type: Union("failed",...)
--E 104

--S 105 of 134
ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2)
 

           ,          +-+         3
   (102)  y (x) - b x\|x  - a y(x)

                                                     Type: Expression Integer
--R
--R           ,          +-+         3
--R   (102)  y (x) - b x\|x  - a y(x)
--R
--R                                                     Type: Expression Integer
--E 105

--S 106 of 134
ode38a:=solve(ode38,y,x)
 

   (103)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (103)  "failed"
--R                                                    Type: Union("failed",...)
--E 106

--S 107 of 134
ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0
 

           ,             3          2
   (104)  y (x) - a3 y(x)  - a2 y(x)  - a1 y(x) - a0

                                                     Type: Expression Integer
--R
--R           ,             3          2
--R   (104)  y (x) - a3 y(x)  - a2 y(x)  - a1 y(x) - a0
--R
--R                                                     Type: Expression Integer
--E 107

--S 108 of 134
yx:=solve(ode39,y,x)
 

   (105)
           ROOT
                           2  2                     3             3      2  2
                    (- 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2  + 3a1 a2 )
                 *
                         2
                    %%CR0
                + 
                               2
                  12a1 a3 - 4a2
             /
                    2  2                      3            3     2  2
                27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
         + 
           - %%CR0
      *
         log
                           2     3          2  2           2         4   2
                      162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
                    + 
                                 3       3  2            5      2  4
                      (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
                 *
                    %%CR0
                + 
                      2  3                       3   2           3      2  2
                  81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3
             *
                ROOT
                                 2  2                     3             3
                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
                         + 
                              2  2
                           3a1 a2
                      *
                              2
                         %%CR0
                     + 
                                    2
                       12a1 a3 - 4a2
                  /
                         2  2                      3            3     2  2
                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
            + 
                       2     3          2  2           2         4   2
                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
                + 
                             3       3  2            5      2  4
                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
             *
                     2
                %%CR0
            + 
                          2  3                     3   2
                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
                  + 
                              3      2  2
                    (- 12a0 a2  + 3a1 a2 )a3
             *
                %%CR0
            + 
                      3             2      3                         2   2
              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
            + 
                    2
              2a1 a2 a3
     + 
           -
              ROOT
                                 2  2                     3             3
                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
                         + 
                              2  2
                           3a1 a2
                    *
                            2
                       %%CR0
                   + 
                                  2
                     12a1 a3 - 4a2
                /
                       2  2                      3            3     2  2
                   27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
         + 
           - %%CR0
      *
         log
                             2     3        2  2           2         4   2
                      - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
                    + 
                                   3       3  2            5      2  4
                      (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
                 *
                    %%CR0
                + 
                      2  3                     3   2             3      2  2
                - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3  + (- 12a0 a2  + 3a1 a2 )a3
             *
                ROOT
                                 2  2                     3             3
                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
                         + 
                              2  2
                           3a1 a2
                      *
                              2
                         %%CR0
                     + 
                                    2
                       12a1 a3 - 4a2
                  /
                         2  2                      3            3     2  2
                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
            + 
                       2     3          2  2           2         4   2
                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
                + 
                             3       3  2            5      2  4
                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
             *
                     2
                %%CR0
            + 
                          2  3                     3   2
                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
                  + 
                              3      2  2
                    (- 12a0 a2  + 3a1 a2 )a3
             *
                %%CR0
            + 
                      3             2      3                         2   2
              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
            + 
                    2
              2a1 a2 a3
     + 
         2%%CR0
      *
         log
                         2     3        2  2           2         4   2
                  - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
                + 
                               3       3  2            5      2  4
                  (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
             *
                     2
                %%CR0
            + 
                     2  3                       3   2           3      2  2
                (81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3)
             *
                %%CR0
            + 
                      3            2      3                        2   2
              (27a0 a3  - 9a1 a2 a3  + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3
            + 
                       2        4
              - 11a1 a2 a3 + 2a2
     + 
       - 2x
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (105)
--R           ROOT
--R                           2  2                     3             3      2  2
--R                    (- 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2  + 3a1 a2 )
--R                 *
--R                         2
--I                    %%CK0
--R                + 
--R                               2
--R                  12a1 a3 - 4a2
--R             /
--R                    2  2                      3            3     2  2
--R                27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R         + 
--I           - %%CK0
--R      *
--R         log
--R                           2     3          2  2           2         4   2
--R                      162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
--R                    + 
--R                                 3       3  2            5      2  4
--R                      (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
--R                 *
--I                    %%CK0
--R                + 
--R                      2  3                       3   2           3      2  2
--R                  81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3
--R             *
--R                ROOT
--R                                 2  2                     3             3
--R                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
--R                         + 
--R                              2  2
--R                           3a1 a2
--R                      *
--R                              2
--I                         %%CK0
--R                     + 
--R                                    2
--R                       12a1 a3 - 4a2
--R                  /
--R                         2  2                      3            3     2  2
--R                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R            + 
--R                       2     3          2  2           2         4   2
--R                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
--R                + 
--R                             3       3  2            5      2  4
--R                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
--R             *
--R                     2
--I                %%CK0
--R            + 
--R                          2  3                     3   2
--R                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
--R                  + 
--R                              3      2  2
--R                    (- 12a0 a2  + 3a1 a2 )a3
--R             *
--I                %%CK0
--R            + 
--R                      3             2      3                         2   2
--R              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
--R            + 
--R                    2
--R              2a1 a2 a3
--R     + 
--R           -
--R              ROOT
--R                                 2  2                     3             3
--R                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
--R                         + 
--R                              2  2
--R                           3a1 a2
--R                    *
--R                            2
--I                       %%CK0
--R                   + 
--R                                  2
--R                     12a1 a3 - 4a2
--R                /
--R                       2  2                      3            3     2  2
--R                   27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R         + 
--I           - %%CK0
--R      *
--R         log
--R                             2     3        2  2           2         4   2
--R                      - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
--R                    + 
--R                                   3       3  2            5      2  4
--R                      (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
--R                 *
--I                    %%CK0
--R                + 
--R                      2  3                     3   2             3      2  2
--R                - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3  + (- 12a0 a2  + 3a1 a2 )a3
--R             *
--R                ROOT
--R                                 2  2                     3             3
--R                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
--R                         + 
--R                              2  2
--R                           3a1 a2
--R                      *
--R                              2
--I                         %%CK0
--R                     + 
--R                                    2
--R                       12a1 a3 - 4a2
--R                  /
--R                         2  2                      3            3     2  2
--R                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R            + 
--R                       2     3          2  2           2         4   2
--R                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
--R                + 
--R                             3       3  2            5      2  4
--R                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
--R             *
--R                     2
--I                %%CK0
--R            + 
--R                          2  3                     3   2
--R                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
--R                  + 
--R                              3      2  2
--R                    (- 12a0 a2  + 3a1 a2 )a3
--R             *
--I                %%CK0
--R            + 
--R                      3             2      3                         2   2
--R              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
--R            + 
--R                    2
--R              2a1 a2 a3
--R     + 
--I         2%%CK0
--R      *
--R         log
--R                         2     3        2  2           2         4   2
--R                  - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
--R                + 
--R                               3       3  2            5      2  4
--R                  (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
--R             *
--R                     2
--I                %%CK0
--R            + 
--R                     2  3                       3   2           3      2  2
--R                (81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3)
--R             *
--I                %%CK0
--R            + 
--R                      3            2      3                        2   2
--R              (27a0 a3  - 9a1 a2 a3  + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3
--R            + 
--R                       2        4
--R              - 11a1 a2 a3 + 2a2
--R     + 
--R       - 2x
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 108

--S 109 of 134
ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2
 

           ,             3            2
   (106)  y (x) + 3a y(x)  + 6a x y(x)

                                                     Type: Expression Integer
--R
--R           ,             3            2
--R   (106)  y (x) + 3a y(x)  + 6a x y(x)
--R
--R                                                     Type: Expression Integer
--E 109

--S 110 of 134
ode40a:=solve(ode40,y,x)
 

   (107)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (107)  "failed"
--R                                                    Type: Union("failed",...)
--E 110

--S 111 of 134
ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2
 

           ,              3         2
   (108)  y (x) + a x y(x)  + b y(x)

                                                     Type: Expression Integer
--R
--R           ,              3         2
--R   (108)  y (x) + a x y(x)  + b y(x)
--R
--R                                                     Type: Expression Integer
--E 111

--S 112 of 134
ode41a:=solve(ode41,y,x)
 

   (109)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (109)  "failed"
--R                                                    Type: Union("failed",...)
--E 112

--S 113 of 134
ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2
 

           ,          2          3                2
   (110)  y (x) + (- x  - 2x)y(x)  + (- x - 3)y(x)

                                                     Type: Expression Integer
--R
--R           ,          2          3                2
--R   (110)  y (x) + (- x  - 2x)y(x)  + (- x - 3)y(x)
--R
--R                                                     Type: Expression Integer
--E 113

--S 114 of 134
ode42a:=solve(ode42,y,x)
 

   (111)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (111)  "failed"
--R                                                    Type: Union("failed",...)
--E 114

--S 115 of 134
ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2
 

           ,           2     2          3          2
   (112)  y (x) + (3a x  + 4a x + b)y(x)  + 3x y(x)

                                                     Type: Expression Integer
--R
--R           ,           2     2          3          2
--R   (112)  y (x) + (3a x  + 4a x + b)y(x)  + 3x y(x)
--R
--R                                                     Type: Expression Integer
--E 115

--S 116 of 134
ode43a:=solve(ode43,y,x)
 

   (113)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (113)  "failed"
--R                                                    Type: Union("failed",...)
--E 116

--S 117 of 134
ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x)
 

           ,          3    3
   (114)  y (x) + 2a x y(x)  + 2x y(x)

                                                     Type: Expression Integer
--R
--R           ,          3    3
--R   (114)  y (x) + 2a x y(x)  + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 117

--S 118 of 134
yx:=solve(ode44,y,x)
 

               2         2
          (2a x  + a)y(x)  + 2
   (115)  --------------------
                         2
                    2  2x
               2y(x) %e
                                          Type: Union(Expression Integer,...)
--R
--R               2         2
--R          (2a x  + a)y(x)  + 2
--R   (115)  --------------------
--R                         2
--R                    2  2x
--R               2y(x) %e
--R                                          Type: Union(Expression Integer,...)
--E 118

--S 119 of 134
ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx
 

   (116)
                    2 2                                               2 2
              3   2x    ,              3            6          4    2x
       - 8y(x) (%e   ) y (x) + ((- 8a x  + 4a x)y(x)  - 8x y(x) )(%e   )

     + 
          4 9      4 7     4 5    4 3     6       3 7      3 5     3 3     4
       (8a x  + 12a x  + 6a x  + a x )y(x)  + (24a x  + 24a x  + 6a x )y(x)
     + 
           2 5      2 3     2       3
       (24a x  + 12a x )y(x)  + 8a x
  /
                2 3
          6   2x
     4y(x) (%e   )
                                                     Type: Expression Integer
--R
--R   (116)
--R                    2 2                                               2 2
--R              3   2x    ,              3            6          4    2x
--R       - 8y(x) (%e   ) y (x) + ((- 8a x  + 4a x)y(x)  - 8x y(x) )(%e   )
--R
--R     + 
--R          4 9      4 7     4 5    4 3     6       3 7      3 5     3 3     4
--R       (8a x  + 12a x  + 6a x  + a x )y(x)  + (24a x  + 24a x  + 6a x )y(x)
--R     + 
--R           2 5      2 3     2       3
--R       (24a x  + 12a x )y(x)  + 8a x
--R  /
--R                2 3
--R          6   2x
--R     4y(x) (%e   )
--R                                                     Type: Expression Integer
--E 119

--S 120 of 134
ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2
 

           ,         2 3     2      3          2
   (117)  y (x) + (2a x  - 2b x)y(x)  + 3b y(x)

                                                     Type: Expression Integer
--R
--R           ,         2 3     2      3          2
--R   (117)  y (x) + (2a x  - 2b x)y(x)  + 3b y(x)
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 134
ode45a:=solve(ode45,y,x)
 

   (118)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (118)  "failed"
--R                                                    Type: Union("failed",...)
--E 121

--S 122 of 134
ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _
              -x**(-2*a) + a*x**(-a-1)
 

           ,          3 a        - a      - a - 1    - 2a        2
   (119)  y (x) - y(x) x  - y(x)x    + a x        - x     + 3y(x)

                                                     Type: Expression Integer
--R
--R           ,          3 a        - a      - a - 1    - 2a        2
--R   (119)  y (x) - y(x) x  - y(x)x    + a x        - x     + 3y(x)
--R
--R                                                     Type: Expression Integer
--E 122

--S 123 of 134
ode46a:=solve(ode46,y,x)
 

   (120)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (120)  "failed"
--R                                                    Type: Union("failed",...)
--E 123

--S 124 of 134
ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2
 

           ,            3 n           3       2
   (121)  y (x) - a y(x) x  + a x y(x)  - y(x)

                                                     Type: Expression Integer
--R
--R           ,            3 n           3       2
--R   (121)  y (x) - a y(x) x  + a x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 124

--S 125 of 134
ode47a:=solve(ode47,y,x)
 

   (122)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (122)  "failed"
--R                                                    Type: Union("failed",...)
--E 125

--S 126 of 134
ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2
 

           ,            3 n           3         2
   (123)  y (x) - a y(x) x  - b x y(x)  - c y(x)

                                                     Type: Expression Integer
--R
--R           ,            3 n           3         2
--R   (123)  y (x) - a y(x) x  - b x y(x)  - c y(x)
--R
--R                                                     Type: Expression Integer
--E 126

--S 127 of 134
ode48a:=solve(ode48,y,x)
 

   (124)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (124)  "failed"
--R                                                    Type: Union("failed",...)
--E 127

--S 128 of 134
ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _
          (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1)
 
   There are no library operations named phi 
      Use HyperDoc Browse or issue
                                )what op phi
      to learn if there is any operation containing " phi " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named phi 
      with argument type(s) 
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named phi 
--R      Use HyperDoc Browse or issue
--R                                )what op phi
--R      to learn if there is any operation containing " phi " in its 
--R      name.
--R 
--R   Cannot find a definition or applicable library operation named phi 
--R      with argument type(s) 
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 128

--S 129 of 134
f1 := operator 'f1
 

   (125)  f1
                                                          Type: BasicOperator
--R
--R   (125)  f1
--R                                                          Type: BasicOperator
--E 129

--S 130 of 134
f2 := operator 'f2
 

   (126)  f2
                                                          Type: BasicOperator
--R
--R   (126)  f2
--R                                                          Type: BasicOperator
--E 130

--S 131 of 134
f3 := operator 'f3
 

   (127)  f3
                                                          Type: BasicOperator
--R
--R   (127)  f3
--R                                                          Type: BasicOperator
--E 131

--S 132 of 134
f0 := operator 'f0
 

   (128)  f0
                                                          Type: BasicOperator
--R
--R   (128)  f0
--R                                                          Type: BasicOperator
--E 132

--S 133 of 134
ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x)
 

           ,               3            2
   (129)  y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)

                                                     Type: Expression Integer
--R
--R           ,               3            2
--R   (129)  y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)
--R
--R                                                     Type: Expression Integer
--E 133

--S 134 of 134
ode50a:=solve(ode50,y,x)
 

   (130)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (130)  "failed"
--R                                                    Type: Union("failed",...)
--E 134

)spool
 
Starts dribbling to schaum10.output (2009/2/17, 17:57:59).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(sqrt(x^2-a^2)),x)
 

               +-------+
               | 2    2
   (1)  - log(\|x  - a   - x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+
--R               | 2    2
--R   (1)  - log(\|x  - a   - x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=log(x+sqrt(x^2-a^2))
 

             +-------+
             | 2    2
   (2)  log(\|x  - a   + x)
                                                     Type: Expression Integer
--R
--R             +-------+
--R             | 2    2
--R   (2)  log(\|x  - a   + x)
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x)
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x)
--R                                                     Type: Expression Integer
--E

--S 4
logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
 

   (4)  c log(b) + c log(a) + %H == c log(a b) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (4)  c log(b) + c log(a) + %I == c log(a b) + %I
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5      14:210 Schaums and Axiom differ by a constant
dd:=logmul1 cc
 

                 2
   (5)  - log(- a )
                                                     Type: Expression Integer
--R
--R                 2
--R   (5)  - log(- a )
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 6
aa:=integrate(x/(sqrt(x^2-a^2)),x)
 

            +-------+
            | 2    2     2    2
        - x\|x  - a   + x  - a
   (1)  -----------------------
              +-------+
              | 2    2
             \|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +-------+
--R            | 2    2     2    2
--R        - x\|x  - a   + x  - a
--R   (1)  -----------------------
--R              +-------+
--R              | 2    2
--R             \|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7
bb:=sqrt(x^2-a^2)
 

         +-------+
         | 2    2
   (2)  \|x  - a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2
--R   (2)  \|x  - a
--R                                                     Type: Expression Integer
--E

--S 8      14:xxx Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 9
aa:=integrate(x^2/sqrt(x^2-a^2),x)
 

   (1)
               +-------+                   +-------+
            2  | 2    2      2 2    4      | 2    2
       (- 2a x\|x  - a   + 2a x  - a )log(\|x  - a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  + a x)\|x  - a   + 2x  - 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  - a   - 4x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               +-------+                   +-------+
--R            2  | 2    2      2 2    4      | 2    2
--R       (- 2a x\|x  - a   + 2a x  - a )log(\|x  - a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  + a x)\|x  - a   + 2x  - 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  - a   - 4x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 10
bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2))
 

               +-------+          +-------+
         2     | 2    2           | 2    2
        a log(\|x  - a   + x) + x\|x  - a
   (2)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R               +-------+          +-------+
--R         2     | 2    2           | 2    2
--R        a log(\|x  - a   + x) + x\|x  - a
--R   (2)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 11     
cc:=aa-bb
 

                 +-------+               +-------+
           2     | 2    2          2     | 2    2
        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
   (3)  -----------------------------------------------
                               2
                                                     Type: Expression Integer
--R
--R                 +-------+               +-------+
--R           2     | 2    2          2     | 2    2
--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
--R   (3)  -----------------------------------------------
--R                               2
--R                                                     Type: Expression Integer
--E

--S 12     14:211 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           2       2
          a log(- a )
   (4)  - -----------
               2
                                                     Type: Expression Integer
--R
--R           2       2
--R          a log(- a )
--R   (4)  - -----------
--R               2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(x^3/sqrt(x^2-a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2     6
        (- 4x  - 5a x  + 6a x)\|x  - a   + 4x  + 3a x  - 9a x  + 2a
   (1)  ------------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  - 3a )\|x  - a   - 12x  + 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2     6
--R        (- 4x  - 5a x  + 6a x)\|x  - a   + 4x  + 3a x  - 9a x  + 2a
--R   (1)  ------------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2)
 

                   +-------+
          2     2  | 2    2
        (x  + 2a )\|x  - a
   (2)  --------------------
                  3
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2
--R        (x  + 2a )\|x  - a
--R   (2)  --------------------
--R                  3
--R                                                     Type: Expression Integer
--E

--S 15     14:212 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
 

               +-------+
               | 2    2
              \|x  - a   - x
        2atan(--------------)
                     a
   (1)  ---------------------
                  a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x
--R        2atan(--------------)
--R                     a
--R   (1)  ---------------------
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17
bb:=1/a*asec(x/a)
 

             x
        asec(-)
             a
   (2)  -------
           a
                                                     Type: Expression Integer
--R
--R             x
--R        asec(-)
--R             a
--R   (2)  -------
--R           a
--R                                                     Type: Expression Integer
--E

--S 18
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  - a   - x         x
        2atan(--------------) - asec(-)
                     a               a
   (3)  -------------------------------
                       a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x         x
--R        2atan(--------------) - asec(-)
--R                     a               a
--R   (3)  -------------------------------
--R                       a
--R                                                     Type: Expression Integer
--E

--S 19
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (4)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (4)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 20
dd:=asecrule cc
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a           +-------+
                    |    2                     | 2    2
                   \|   x                     \|x  - a   - x
        - 2%i log(------------------) + 4atan(--------------) - %pi
                           x                         a
   (5)  -----------------------------------------------------------
                                     2a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a           +-------+
--R                    |    2                     | 2    2
--R                   \|   x                     \|x  - a   - x
--R        - 2%i log(------------------) + 4atan(--------------) - %pi
--R                           x                         a
--R   (5)  -----------------------------------------------------------
--R                                     2a
--R                                             Type: Expression Complex Integer
--E

--S 21
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 22
ee:=atanrule dd
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a               +-------+
                    |    2                         | 2    2
                   \|   x                       - \|x  - a   + x + %i a
        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
                           x                      +-------+
                                                  | 2    2
                                                 \|x  - a   - x + %i a
   (7)  ----------------------------------------------------------------------
                                          2a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a               +-------+
--R                    |    2                         | 2    2
--R                   \|   x                       - \|x  - a   + x + %i a
--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
--R                           x                      +-------+
--R                                                  | 2    2
--R                                                 \|x  - a   - x + %i a
--R   (7)  ----------------------------------------------------------------------
--R                                          2a
--R                                             Type: Expression Complex Integer
--E

--S 23
ff:=expandLog ee
 

   (8)
                +-------+                        +-------+
                | 2    2                         | 2    2
       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
                   |    2
                  \|   x
  /
     2a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                +-------+                        +-------+
--R                | 2    2                         | 2    2
--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R                   |    2
--R                  \|   x
--R  /
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 24
gg:=rootSimp ff
 

   (9)
                  +-------+                    +-------+
                  | 2    2                     | 2    2
       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
  /
     2a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                    +-------+
--R                  | 2    2                     | 2    2
--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R  /
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 25     14:213 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

           %pi
   (10)  - ---
            2a
                                             Type: Expression Complex Integer
--R
--R           %pi
--R   (10)  - ---
--R            2a
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 26
aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
 

                  1
   (1)  - ----------------
            +-------+
            | 2    2     2
          x\|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  1
--R   (1)  - ----------------
--R            +-------+
--R            | 2    2     2
--R          x\|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27
bb:=sqrt(x^2-a^2)/(a^2*x)
 

         +-------+
         | 2    2
        \|x  - a
   (2)  ----------
             2
            a x
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2
--R        \|x  - a
--R   (2)  ----------
--R             2
--R            a x
--R                                                     Type: Expression Integer
--E

--S 28     14:214 Schaums and Axiom differ by a constant
cc:=aa-bb
 

         1
   (3)  --
         2
        a
                                                     Type: Expression Integer
--R
--R         1
--R   (3)  --
--R         2
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
 

   (1)
                                          +-------+
            +-------+                     | 2    2
          3 | 2    2      4     2 2      \|x  - a   - x
       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
                                                a
     + 
                      +-------+
              2    3  | 2    2        3     3
       (- 2a x  + a )\|x  - a   + 2a x  - 2a x
  /
           +-------+
       3 3 | 2    2      3 4     5 2
     4a x \|x  - a   - 4a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                          +-------+
--R            +-------+                     | 2    2
--R          3 | 2    2      4     2 2      \|x  - a   - x
--R       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
--R                                                a
--R     + 
--R                      +-------+
--R              2    3  | 2    2        3     3
--R       (- 2a x  + a )\|x  - a   + 2a x  - 2a x
--R  /
--R           +-------+
--R       3 3 | 2    2      3 4     5 2
--R     4a x \|x  - a   - 4a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a)
 

          +-------+
          | 2    2     2     x
        a\|x  - a   + x asec(-)
                             a
   (2)  -----------------------
                   3 2
                 2a x
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2     x
--R        a\|x  - a   + x asec(-)
--R                             a
--R   (2)  -----------------------
--R                   3 2
--R                 2a x
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  - a   - x         x
        2atan(--------------) - asec(-)
                     a               a
   (3)  -------------------------------
                        3
                      2a
                                                     Type: Expression Integer
--R 
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x         x
--R        2atan(--------------) - asec(-)
--R                     a               a
--R   (3)  -------------------------------
--R                        3
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 32
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 33
dd:=atanrule cc
 

                    +-------+
                    | 2    2
                 - \|x  - a   + x + %i a         x
        - %i log(-----------------------) - asec(-)
                   +-------+                     a
                   | 2    2
                  \|x  - a   - x + %i a
   (5)  -------------------------------------------
                              3
                            2a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                 - \|x  - a   + x + %i a         x
--R        - %i log(-----------------------) - asec(-)
--R                   +-------+                     a
--R                   | 2    2
--R                  \|x  - a   - x + %i a
--R   (5)  -------------------------------------------
--R                              3
--R                            2a
--R                                             Type: Expression Complex Integer
--E

--S 34
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 35
ee:=asecrule dd
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a               +-------+
                    |    2                         | 2    2
                   \|   x                       - \|x  - a   + x + %i a
        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
                           x                      +-------+
                                                  | 2    2
                                                 \|x  - a   - x + %i a
   (7)  ----------------------------------------------------------------------
                                            3
                                          4a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a               +-------+
--R                    |    2                         | 2    2
--R                   \|   x                       - \|x  - a   + x + %i a
--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
--R                           x                      +-------+
--R                                                  | 2    2
--R                                                 \|x  - a   - x + %i a
--R   (7)  ----------------------------------------------------------------------
--R                                            3
--R                                          4a
--R                                             Type: Expression Complex Integer
--E

--S 36
ff:=expandLog ee
 

   (8)
                +-------+                        +-------+
                | 2    2                         | 2    2
       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
                   |    2
                  \|   x
  /
       3
     4a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                +-------+                        +-------+
--R                | 2    2                         | 2    2
--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R                   |    2
--R                  \|   x
--R  /
--R       3
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 37
gg:=rootSimp ff
 

   (9)
                  +-------+                    +-------+
                  | 2    2                     | 2    2
       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
  /
       3
     4a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                    +-------+
--R                  | 2    2                     | 2    2
--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R  /
--R       3
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 38     14:215 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

           %pi
   (10)  - ---
             3
           4a
                                             Type: Expression Complex Integer
--R
--R           %pi
--R   (10)  - ---
--R             3
--R           4a
--R                                             Type: Expression Complex Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(sqrt(x^2-a^2),x)
 

   (1)
             +-------+                   +-------+
          2  | 2    2      2 2    4      | 2    2
       (2a x\|x  - a   - 2a x  + a )log(\|x  - a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  + a x)\|x  - a   + 2x  - 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  - a   - 4x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R             +-------+                   +-------+
--R          2  | 2    2      2 2    4      | 2    2
--R       (2a x\|x  - a   - 2a x  + a )log(\|x  - a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  + a x)\|x  - a   + 2x  - 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  - a   - 4x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40
bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2))
 

                 +-------+          +-------+
           2     | 2    2           | 2    2
        - a log(\|x  - a   + x) + x\|x  - a
   (2)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R
--R                 +-------+          +-------+
--R           2     | 2    2           | 2    2
--R        - a log(\|x  - a   + x) + x\|x  - a
--R   (2)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E

--S 41
cc:=aa-bb
 

               +-------+               +-------+
         2     | 2    2          2     | 2    2
        a log(\|x  - a   + x) + a log(\|x  - a   - x)
   (3)  ---------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         2     | 2    2          2     | 2    2
--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
--R   (3)  ---------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 42     14:216 Schaums and Axiom differ by a constant 
dd:=complexNormalize cc
 

         2       2
        a log(- a )
   (4)  -----------
             2
                                                     Type: Expression Integer
--R
--R         2       2
--R        a log(- a )
--R   (4)  -----------
--R             2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 43
aa:=integrate(x*sqrt(x^2-a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2    6
        (- 4x  + 7a x  - 3a x)\|x  - a   + 4x  - 9a x  + 6a x  - a
   (1)  -----------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  - 3a )\|x  - a   - 12x  + 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2    6
--R        (- 4x  + 7a x  - 3a x)\|x  - a   + 4x  - 9a x  + 6a x  - a
--R   (1)  -----------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
--R                                          Type: Union(Expression Integer,...)
--E

--S 44
bb:=(x^2-a^2)^(3/2)/3
 

                  +-------+
          2    2  | 2    2
        (x  - a )\|x  - a
   (2)  -------------------
                 3
                                                     Type: Expression Integer
--R
--R                  +-------+
--R          2    2  | 2    2
--R        (x  - a )\|x  - a
--R   (2)  -------------------
--R                 3
--R                                                     Type: Expression Integer
--E

--S 45     14:217 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 46
aa:=integrate(x^2*sqrt(x^2-a^2),x)
 

   (1)
                       +-------+                           +-------+
           4 3     6   | 2    2      4 4     6 2    8      | 2    2
       ((8a x  - 4a x)\|x  - a   - 8a x  + 8a x  - a )log(\|x  - a   - x)
     + 
                                      +-------+
           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
     (- 16x  + 24a x  - 10a x  + a x)\|x  - a   + 16x  - 32a x  + 20a x  - 4a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       +-------+                           +-------+
--R           4 3     6   | 2    2      4 4     6 2    8      | 2    2
--R       ((8a x  - 4a x)\|x  - a   - 8a x  + 8a x  - a )log(\|x  - a   - x)
--R     + 
--R                                      +-------+
--R           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
--R     (- 16x  + 24a x  - 10a x  + a x)\|x  - a   + 16x  - 32a x  + 20a x  - 4a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 47
bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2))
 

                 +-------+                    +-------+
           4     | 2    2            3    2   | 2    2
        - a log(\|x  - a   + x) + (2x  - a x)\|x  - a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                 +-------+                    +-------+
--R           4     | 2    2            3    2   | 2    2
--R        - a log(\|x  - a   + x) + (2x  - a x)\|x  - a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 48     
cc:=aa-bb
 

               +-------+               +-------+
         4     | 2    2          4     | 2    2
        a log(\|x  - a   + x) + a log(\|x  - a   - x)
   (3)  ---------------------------------------------
                              8
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         4     | 2    2          4     | 2    2
--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
--R   (3)  ---------------------------------------------
--R                              8
--R                                                     Type: Expression Integer
--E

--S 49     14:218 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

         4       2
        a log(- a )
   (4)  -----------
             8
                                                     Type: Expression Integer
--R
--R         4       2
--R        a log(- a )
--R   (4)  -----------
--R             8
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 50
aa:=integrate(x^3*sqrt(x^2-a^2),x)
 

   (1)
                                                  +-------+
             9      2 7     4 5      6 3      8   | 2    2       10       2 8
       (- 48x  + 76a x  - 3a x  - 35a x  + 10a x)\|x  - a   + 48x   - 100a x
     + 
          4 6      6 4      8 2     10
       35a x  + 40a x  - 25a x  + 2a
  /
                              +-------+
          4       2 2      4  | 2    2        5       2 3      4
     (240x  - 180a x  + 15a )\|x  - a   - 240x  + 300a x  - 75a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7     4 5      6 3      8   | 2    2       10       2 8
--R       (- 48x  + 76a x  - 3a x  - 35a x  + 10a x)\|x  - a   + 48x   - 100a x
--R     + 
--R          4 6      6 4      8 2     10
--R       35a x  + 40a x  - 25a x  + 2a
--R  /
--R                              +-------+
--R          4       2 2      4  | 2    2        5       2 3      4
--R     (240x  - 180a x  + 15a )\|x  - a   - 240x  + 300a x  - 75a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 51
bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3
 

                           +-------+
           4    2 2     4  | 2    2
        (3x  - a x  - 2a )\|x  - a
   (2)  ----------------------------
                     15
                                                     Type: Expression Integer
--R
--R                           +-------+
--R           4    2 2     4  | 2    2
--R        (3x  - a x  - 2a )\|x  - a
--R   (2)  ----------------------------
--R                     15
--R                                                     Type: Expression Integer
--E

--S 52     14:219 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 53
aa:=integrate(sqrt(x^2-a^2)/x,x)
 

                                     +-------+
              +-------+              | 2    2           +-------+
              | 2    2              \|x  - a   - x      | 2    2     2    2
        (- 2a\|x  - a   + 2a x)atan(--------------) - x\|x  - a   + x  - a
                                           a
   (1)  -------------------------------------------------------------------
                                    +-------+
                                    | 2    2
                                   \|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     +-------+
--R              +-------+              | 2    2           +-------+
--R              | 2    2              \|x  - a   - x      | 2    2     2    2
--R        (- 2a\|x  - a   + 2a x)atan(--------------) - x\|x  - a   + x  - a
--R                                           a
--R   (1)  -------------------------------------------------------------------
--R                                    +-------+
--R                                    | 2    2
--R                                   \|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54
bb:=sqrt(x^2-a^2)-a*asec(x/a)
 

         +-------+
         | 2    2           x
   (2)  \|x  - a   - a asec(-)
                            a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2           x
--R   (2)  \|x  - a   - a asec(-)
--R                            a
--R                                                     Type: Expression Integer
--E

--S 55
cc:=aa-bb
 

                   +-------+
                   | 2    2
                  \|x  - a   - x           x
   (3)  - 2a atan(--------------) + a asec(-)
                         a                 a
                                                     Type: Expression Integer
--R
--R                   +-------+
--R                   | 2    2
--R                  \|x  - a   - x           x
--R   (3)  - 2a atan(--------------) + a asec(-)
--R                         a                 a
--R                                                     Type: Expression Integer
--E

--S 56
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 57
dd:=atanrule cc
 

                    +-------+
                    | 2    2
                 - \|x  - a   + x + %i a           x
   (5)  %i a log(-----------------------) + a asec(-)
                   +-------+                       a
                   | 2    2
                  \|x  - a   - x + %i a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                 - \|x  - a   + x + %i a           x
--R   (5)  %i a log(-----------------------) + a asec(-)
--R                   +-------+                       a
--R                   | 2    2
--R                  \|x  - a   - x + %i a
--R                                             Type: Expression Complex Integer
--E

--S 58
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 59
ee:=asecrule dd
 

   (7)
               +-------+
               | 2    2
               |x  - a
             x |-------  + %i a                 +-------+
               |    2                           | 2    2
              \|   x                         - \|x  - a   + x + %i a
   2%i a log(------------------) + 2%i a log(-----------------------) + a %pi
                      x                        +-------+
                                               | 2    2
                                              \|x  - a   - x + %i a
   --------------------------------------------------------------------------
                                        2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R               +-------+
--R               | 2    2
--R               |x  - a
--R             x |-------  + %i a                 +-------+
--R               |    2                           | 2    2
--R              \|   x                         - \|x  - a   + x + %i a
--R   2%i a log(------------------) + 2%i a log(-----------------------) + a %pi
--R                      x                        +-------+
--R                                               | 2    2
--R                                              \|x  - a   - x + %i a
--R   --------------------------------------------------------------------------
--R                                        2
--R                                             Type: Expression Complex Integer
--E

--S 60
ff:=expandLog ee
 

   (8)
                    +-------+                          +-------+
                    | 2    2                           | 2    2
       - 2%i a log(\|x  - a   - x + %i a) + 2%i a log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       2%i a log(x |-------  + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
                   |    2
                  \|   x
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +-------+                          +-------+
--R                    | 2    2                           | 2    2
--R       - 2%i a log(\|x  - a   - x + %i a) + 2%i a log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       2%i a log(x |-------  + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
--R                   |    2
--R                  \|   x
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 61
gg:=rootSimp ff
 

   (9)
                  +-------+                      +-------+
                  | 2    2                       | 2    2
       2%i a log(\|x  - a   + %i a) - 2%i a log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       2%i a log(\|x  - a   - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                      +-------+
--R                  | 2    2                       | 2    2
--R       2%i a log(\|x  - a   + %i a) - 2%i a log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       2%i a log(\|x  - a   - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 62     14:220 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         a %pi
   (10)  -----
           2
                                             Type: Expression Complex Integer
--R
--R         a %pi
--R   (10)  -----
--R           2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 63
aa:=integrate(sqrt(x^2-a^2)/x^2,x)
 

             +-------+           +-------+
             | 2    2     2      | 2    2          2
        (- x\|x  - a   + x )log(\|x  - a   - x) + a
   (1)  --------------------------------------------
                        +-------+
                        | 2    2     2
                      x\|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+           +-------+
--R             | 2    2     2      | 2    2          2
--R        (- x\|x  - a   + x )log(\|x  - a   - x) + a
--R   (1)  --------------------------------------------
--R                        +-------+
--R                        | 2    2     2
--R                      x\|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 64
bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2))
 

               +-------+         +-------+
               | 2    2          | 2    2
        x log(\|x  - a   + x) - \|x  - a
   (2)  ----------------------------------
                         x
                                                     Type: Expression Integer
--R
--R               +-------+         +-------+
--R               | 2    2          | 2    2
--R        x log(\|x  - a   + x) - \|x  - a
--R   (2)  ----------------------------------
--R                         x
--R                                                     Type: Expression Integer
--E

--S 65
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 66     14:221 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

                 2
   (4)  - log(- a ) - 1
                                                     Type: Expression Integer
--R
--R                 2
--R   (4)  - log(- a ) - 1
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 67
aa:=integrate(sqrt(x^2-a^2)/x^3,x)
 

   (1)
                                          +-------+
            +-------+                     | 2    2
          3 | 2    2      4     2 2      \|x  - a   - x
       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
                                                a
     + 
                    +-------+
            2    3  | 2    2        3     3
       (2a x  - a )\|x  - a   - 2a x  + 2a x
  /
           +-------+
         3 | 2    2        4     3 2
     4a x \|x  - a   - 4a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                          +-------+
--R            +-------+                     | 2    2
--R          3 | 2    2      4     2 2      \|x  - a   - x
--R       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
--R                                                a
--R     + 
--R                    +-------+
--R            2    3  | 2    2        3     3
--R       (2a x  - a )\|x  - a   - 2a x  + 2a x
--R  /
--R           +-------+
--R         3 | 2    2        4     3 2
--R     4a x \|x  - a   - 4a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68
bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a)
 

            +-------+
            | 2    2     2     x
        - a\|x  - a   + x asec(-)
                               a
   (2)  -------------------------
                      2
                  2a x
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2     x
--R        - a\|x  - a   + x asec(-)
--R                               a
--R   (2)  -------------------------
--R                      2
--R                  2a x
--R                                                     Type: Expression Integer
--E

--S 69
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  - a   - x         x
        2atan(--------------) - asec(-)
                     a               a
   (3)  -------------------------------
                       2a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x         x
--R        2atan(--------------) - asec(-)
--R                     a               a
--R   (3)  -------------------------------
--R                       2a
--R                                                     Type: Expression Integer
--E

--S 70
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (4)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (4)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 71
dd:=asecrule cc
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a           +-------+
                    |    2                     | 2    2
                   \|   x                     \|x  - a   - x
        - 2%i log(------------------) + 4atan(--------------) - %pi
                           x                         a
   (5)  -----------------------------------------------------------
                                     4a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a           +-------+
--R                    |    2                     | 2    2
--R                   \|   x                     \|x  - a   - x
--R        - 2%i log(------------------) + 4atan(--------------) - %pi
--R                           x                         a
--R   (5)  -----------------------------------------------------------
--R                                     4a
--R                                             Type: Expression Complex Integer
--E

--S 72
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 73
ee:=atanrule dd
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a               +-------+
                    |    2                         | 2    2
                   \|   x                       - \|x  - a   + x + %i a
        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
                           x                      +-------+
                                                  | 2    2
                                                 \|x  - a   - x + %i a
   (7)  ----------------------------------------------------------------------
                                          4a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a               +-------+
--R                    |    2                         | 2    2
--R                   \|   x                       - \|x  - a   + x + %i a
--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
--R                           x                      +-------+
--R                                                  | 2    2
--R                                                 \|x  - a   - x + %i a
--R   (7)  ----------------------------------------------------------------------
--R                                          4a
--R                                             Type: Expression Complex Integer
--E

--S 74
ff:=expandLog ee
 

   (8)
                +-------+                        +-------+
                | 2    2                         | 2    2
       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
                   |    2
                  \|   x
  /
     4a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                +-------+                        +-------+
--R                | 2    2                         | 2    2
--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R                   |    2
--R                  \|   x
--R  /
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 75
gg:=rootSimp ff
 

   (9)
                  +-------+                    +-------+
                  | 2    2                     | 2    2
       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
  /
     4a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                    +-------+
--R                  | 2    2                     | 2    2
--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R  /
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 76     14:222 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

           %pi
   (10)  - ---
            4a
                                             Type: Expression Complex Integer
--R
--R           %pi
--R   (10)  - ---
--R            4a
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 77
aa:=integrate(1/(x^2-a^2)^(3/2),x)
 

                    1
   (1)  - ---------------------
            +-------+
            | 2    2     2    2
          x\|x  - a   - x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    1
--R   (1)  - ---------------------
--R            +-------+
--R            | 2    2     2    2
--R          x\|x  - a   - x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 78
bb:=-x/(a^2*sqrt(x^2-a^2))
 

                x
   (2)  - ------------
             +-------+
           2 | 2    2
          a \|x  - a
                                                     Type: Expression Integer
--R
--R                x
--R   (2)  - ------------
--R             +-------+
--R           2 | 2    2
--R          a \|x  - a
--R                                                     Type: Expression Integer
--E

--S 79     14:223 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           1
   (3)  - --
           2
          a
                                                     Type: Expression Integer
--R
--R           1
--R   (3)  - --
--R           2
--R          a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 80
aa:=integrate(x/(x^2-a^2)^(3/2),x)
 

             +-------+
             | 2    2
            \|x  - a   - x
   (1)  ---------------------
          +-------+
          | 2    2     2    2
        x\|x  - a   - x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+
--R             | 2    2
--R            \|x  - a   - x
--R   (1)  ---------------------
--R          +-------+
--R          | 2    2     2    2
--R        x\|x  - a   - x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 81
bb:=-1/sqrt(x^2-a^2)
 

               1
   (2)  - ----------
           +-------+
           | 2    2
          \|x  - a
                                                     Type: Expression Integer
--R
--R               1
--R   (2)  - ----------
--R           +-------+
--R           | 2    2
--R          \|x  - a
--R                                                     Type: Expression Integer
--E

--S 82     14:224 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 83
aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
 

             +-------+                +-------+
             | 2    2     2    2      | 2    2          2
        (- x\|x  - a   + x  - a )log(\|x  - a   - x) - a
   (1)  -------------------------------------------------
                        +-------+
                        | 2    2     2    2
                      x\|x  - a   - x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+                +-------+
--R             | 2    2     2    2      | 2    2          2
--R        (- x\|x  - a   + x  - a )log(\|x  - a   - x) - a
--R   (1)  -------------------------------------------------
--R                        +-------+
--R                        | 2    2     2    2
--R                      x\|x  - a   - x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84
bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2))
 

         +-------+     +-------+
         | 2    2      | 2    2
        \|x  - a  log(\|x  - a   + x) - x
   (2)  ---------------------------------
                     +-------+
                     | 2    2
                    \|x  - a
                                                     Type: Expression Integer
--R
--R         +-------+     +-------+
--R         | 2    2      | 2    2
--R        \|x  - a  log(\|x  - a   + x) - x
--R   (2)  ---------------------------------
--R                     +-------+
--R                     | 2    2
--R                    \|x  - a
--R                                                     Type: Expression Integer
--E

--S 85     
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 86     14:225 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

                 2
   (4)  - log(- a ) - 1
                                                     Type: Expression Integer
--R
--R                 2
--R   (4)  - log(- a ) - 1
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 87
aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
 

                       +-------+
             3     2   | 2    2      4     2 2     4
        (- 2x  + 4a x)\|x  - a   + 2x  - 5a x  + 2a
   (1)  --------------------------------------------
                         +-------+
                 2    2  | 2    2      3     2
              (2x  - a )\|x  - a   - 2x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       +-------+
--R             3     2   | 2    2      4     2 2     4
--R        (- 2x  + 4a x)\|x  - a   + 2x  - 5a x  + 2a
--R   (1)  --------------------------------------------
--R                         +-------+
--R                 2    2  | 2    2      3     2
--R              (2x  - a )\|x  - a   - 2x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 88
bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2)
 

          2     2
         x  - 2a
   (2)  ----------
         +-------+
         | 2    2
        \|x  - a
                                                     Type: Expression Integer
--R
--R          2     2
--R         x  - 2a
--R   (2)  ----------
--R         +-------+
--R         | 2    2
--R        \|x  - a
--R                                                     Type: Expression Integer
--E

--S 89     14:226 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 90
aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
 

                                          +-------+
              +-------+                   | 2    2           +-------+
              | 2    2      2     2      \|x  - a   - x      | 2    2
        (- 2x\|x  - a   + 2x  - 2a )atan(--------------) + a\|x  - a   - a x
                                                a
   (1)  --------------------------------------------------------------------
                                  +-------+
                               3  | 2    2     3 2    5
                              a x\|x  - a   - a x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          +-------+
--R              +-------+                   | 2    2           +-------+
--R              | 2    2      2     2      \|x  - a   - x      | 2    2
--R        (- 2x\|x  - a   + 2x  - 2a )atan(--------------) + a\|x  - a   - a x
--R                                                a
--R   (1)  --------------------------------------------------------------------
--R                                  +-------+
--R                               3  | 2    2     3 2    5
--R                              a x\|x  - a   - a x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91
bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a)
 

                  +-------+
               x  | 2    2
        - asec(-)\|x  - a   - a
               a
   (2)  -----------------------
                 +-------+
               3 | 2    2
              a \|x  - a
                                                     Type: Expression Integer
--R
--R                  +-------+
--R               x  | 2    2
--R        - asec(-)\|x  - a   - a
--R               a
--R   (2)  -----------------------
--R                 +-------+
--R               3 | 2    2
--R              a \|x  - a
--R                                                     Type: Expression Integer
--E

--S 92
cc:=aa-bb
 

                 +-------+
                 | 2    2
                \|x  - a   - x         x
        - 2atan(--------------) + asec(-)
                       a               a
   (3)  ---------------------------------
                         3
                        a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  - a   - x         x
--R        - 2atan(--------------) + asec(-)
--R                       a               a
--R   (3)  ---------------------------------
--R                         3
--R                        a
--R                                                     Type: Expression Integer
--E

--S 93
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 94
dd:=atanrule cc
 

                  +-------+
                  | 2    2
               - \|x  - a   + x + %i a         x
        %i log(-----------------------) + asec(-)
                 +-------+                     a
                 | 2    2
                \|x  - a   - x + %i a
   (5)  -----------------------------------------
                             3
                            a
                                             Type: Expression Complex Integer
--R
--R                  +-------+
--R                  | 2    2
--R               - \|x  - a   + x + %i a         x
--R        %i log(-----------------------) + asec(-)
--R                 +-------+                     a
--R                 | 2    2
--R                \|x  - a   - x + %i a
--R   (5)  -----------------------------------------
--R                             3
--R                            a
--R                                             Type: Expression Complex Integer
--E

--S 95
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 96
ee:=asecrule dd
 

                  +-------+
                  | 2    2
                  |x  - a
                x |-------  + %i a               +-------+
                  |    2                         | 2    2
                 \|   x                       - \|x  - a   + x + %i a
        2%i log(------------------) + 2%i log(-----------------------) + %pi
                         x                      +-------+
                                                | 2    2
                                               \|x  - a   - x + %i a
   (7)  --------------------------------------------------------------------
                                           3
                                         2a
                                             Type: Expression Complex Integer
--R
--R                  +-------+
--R                  | 2    2
--R                  |x  - a
--R                x |-------  + %i a               +-------+
--R                  |    2                         | 2    2
--R                 \|   x                       - \|x  - a   + x + %i a
--R        2%i log(------------------) + 2%i log(-----------------------) + %pi
--R                         x                      +-------+
--R                                                | 2    2
--R                                               \|x  - a   - x + %i a
--R   (7)  --------------------------------------------------------------------
--R                                           3
--R                                         2a
--R                                             Type: Expression Complex Integer
--E

--S 97
ff:=expandLog ee
 

   (8)
                  +-------+                        +-------+
                  | 2    2                         | 2    2
       - 2%i log(\|x  - a   - x + %i a) + 2%i log(\|x  - a   - x - %i a)
     + 
                 +-------+
                 | 2    2
                 |x  - a
       2%i log(x |-------  + %i a) - 2%i log(x) + 2%i log(- 1) + %pi
                 |    2
                \|   x
  /
       3
     2a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                  +-------+                        +-------+
--R                  | 2    2                         | 2    2
--R       - 2%i log(\|x  - a   - x + %i a) + 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                 +-------+
--R                 | 2    2
--R                 |x  - a
--R       2%i log(x |-------  + %i a) - 2%i log(x) + 2%i log(- 1) + %pi
--R                 |    2
--R                \|   x
--R  /
--R       3
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 98
gg:=rootSimp ff
 

   (9)
                +-------+                    +-------+
                | 2    2                     | 2    2
       2%i log(\|x  - a   + %i a) - 2%i log(\|x  - a   - x + %i a)
     + 
                +-------+
                | 2    2
       2%i log(\|x  - a   - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi
  /
       3
     2a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                +-------+                    +-------+
--R                | 2    2                     | 2    2
--R       2%i log(\|x  - a   + %i a) - 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                +-------+
--R                | 2    2
--R       2%i log(\|x  - a   - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi
--R  /
--R       3
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 99     14:227 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         %pi
   (10)  ---
           3
         2a
                                             Type: Expression Complex Integer
--R
--R         %pi
--R   (10)  ---
--R           3
--R         2a
--R                                             Type: Expression Complex Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 100
aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
 

                           1
   (1)  - -----------------------------------
                      +-------+
             3    2   | 2    2      4     2 2
          (2x  - a x)\|x  - a   - 2x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           1
--R   (1)  - -----------------------------------
--R                      +-------+
--R             3    2   | 2    2      4     2 2
--R          (2x  - a x)\|x  - a   - 2x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 101
bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2))
 

              2    2
          - 2x  + a
   (2)  -------------
            +-------+
         4  | 2    2
        a x\|x  - a
                                                     Type: Expression Integer
--R
--R              2    2
--R          - 2x  + a
--R   (2)  -------------
--R            +-------+
--R         4  | 2    2
--R        a x\|x  - a
--R                                                     Type: Expression Integer
--E

--S 102    14:228 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           2
   (3)  - --
           4
          a
                                                     Type: Expression Integer
--R
--R           2
--R   (3)  - --
--R           4
--R          a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 103
aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
 

   (1)
                                                                  +-------+
                          +-------+                               | 2    2
              5      2 3  | 2    2       6      2 4     4 2      \|x  - a   - x
       ((- 24x  + 18a x )\|x  - a   + 24x  - 30a x  + 6a x )atan(--------------)
                                                                        a
     + 
                             +-------+
             4     3 2    5  | 2    2         5      3 3     5
       (12a x  - 7a x  + a )\|x  - a   - 12a x  + 13a x  - 3a x
  /
                     +-------+
        5 5     7 3  | 2    2      5 6      7 4     9 2
     (8a x  - 6a x )\|x  - a   - 8a x  + 10a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                  +-------+
--R                          +-------+                               | 2    2
--R              5      2 3  | 2    2       6      2 4     4 2      \|x  - a   - x
--R       ((- 24x  + 18a x )\|x  - a   + 24x  - 30a x  + 6a x )atan(--------------)
--R                                                                        a
--R     + 
--R                             +-------+
--R             4     3 2    5  | 2    2         5      3 3     5
--R       (12a x  - 7a x  + a )\|x  - a   - 12a x  + 13a x  - 3a x
--R  /
--R                     +-------+
--R        5 5     7 3  | 2    2      5 6      7 4     9 2
--R     (8a x  - 6a x )\|x  - a   - 8a x  + 10a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 104
bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a)
 

                     +-------+
            2     x  | 2    2        2    3
        - 3x asec(-)\|x  - a   - 3a x  + a
                  a
   (2)  -----------------------------------
                        +-------+
                    5 2 | 2    2
                  2a x \|x  - a
                                                     Type: Expression Integer
--R
--R                     +-------+
--R            2     x  | 2    2        2    3
--R        - 3x asec(-)\|x  - a   - 3a x  + a
--R                  a
--R   (2)  -----------------------------------
--R                        +-------+
--R                    5 2 | 2    2
--R                  2a x \|x  - a
--R                                                     Type: Expression Integer
--E

--S 105
cc:=aa-bb
 

                 +-------+
                 | 2    2
                \|x  - a   - x          x
        - 6atan(--------------) + 3asec(-)
                       a                a
   (3)  ----------------------------------
                          5
                        2a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  - a   - x          x
--R        - 6atan(--------------) + 3asec(-)
--R                       a                a
--R   (3)  ----------------------------------
--R                          5
--R                        2a
--R                                                     Type: Expression Integer
--E

--S 106
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 107
dd:=atanrule cc
 

                   +-------+
                   | 2    2
                - \|x  - a   + x + %i a          x
        3%i log(-----------------------) + 3asec(-)
                  +-------+                      a
                  | 2    2
                 \|x  - a   - x + %i a
   (5)  -------------------------------------------
                              5
                            2a
                                             Type: Expression Complex Integer
--R
--R                   +-------+
--R                   | 2    2
--R                - \|x  - a   + x + %i a          x
--R        3%i log(-----------------------) + 3asec(-)
--R                  +-------+                      a
--R                  | 2    2
--R                 \|x  - a   - x + %i a
--R   (5)  -------------------------------------------
--R                              5
--R                            2a
--R                                             Type: Expression Complex Integer
--E

--S 108
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 109
ee:=asecrule dd
 

                  +-------+
                  | 2    2
                  |x  - a
                x |-------  + %i a               +-------+
                  |    2                         | 2    2
                 \|   x                       - \|x  - a   + x + %i a
        6%i log(------------------) + 6%i log(-----------------------) + 3%pi
                         x                      +-------+
                                                | 2    2
                                               \|x  - a   - x + %i a
   (7)  ---------------------------------------------------------------------
                                           5
                                         4a
                                             Type: Expression Complex Integer
--R
--R                  +-------+
--R                  | 2    2
--R                  |x  - a
--R                x |-------  + %i a               +-------+
--R                  |    2                         | 2    2
--R                 \|   x                       - \|x  - a   + x + %i a
--R        6%i log(------------------) + 6%i log(-----------------------) + 3%pi
--R                         x                      +-------+
--R                                                | 2    2
--R                                               \|x  - a   - x + %i a
--R   (7)  ---------------------------------------------------------------------
--R                                           5
--R                                         4a
--R                                             Type: Expression Complex Integer
--E

--S 110
ff:=expandLog ee
 

   (8)
                  +-------+                        +-------+
                  | 2    2                         | 2    2
       - 6%i log(\|x  - a   - x + %i a) + 6%i log(\|x  - a   - x - %i a)
     + 
                 +-------+
                 | 2    2
                 |x  - a
       6%i log(x |-------  + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
                 |    2
                \|   x
  /
       5
     4a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                  +-------+                        +-------+
--R                  | 2    2                         | 2    2
--R       - 6%i log(\|x  - a   - x + %i a) + 6%i log(\|x  - a   - x - %i a)
--R     + 
--R                 +-------+
--R                 | 2    2
--R                 |x  - a
--R       6%i log(x |-------  + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
--R                 |    2
--R                \|   x
--R  /
--R       5
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 111
gg:=rootSimp ff
 

   (9)
                +-------+                    +-------+
                | 2    2                     | 2    2
       6%i log(\|x  - a   + %i a) - 6%i log(\|x  - a   - x + %i a)
     + 
                +-------+
                | 2    2
       6%i log(\|x  - a   - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
  /
       5
     4a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                +-------+                    +-------+
--R                | 2    2                     | 2    2
--R       6%i log(\|x  - a   + %i a) - 6%i log(\|x  - a   - x + %i a)
--R     + 
--R                +-------+
--R                | 2    2
--R       6%i log(\|x  - a   - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
--R  /
--R       5
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 112    14:229 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         3%pi
   (10)  ----
            5
          4a
                                             Type: Expression Complex Integer
--R
--R         3%pi
--R   (10)  ----
--R            5
--R          4a
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 113
aa:=integrate((x^2-a^2)^(3/2),x)
 

   (1)
                           +-------+                              +-------+
              4 3      6   | 2    2       4 4      6 2     8      | 2    2
       ((- 24a x  + 12a x)\|x  - a   + 24a x  - 24a x  + 3a )log(\|x  - a   - x)
     + 
                                         +-------+
             7      2 5      4 3     6   | 2    2       8      2 6      4 4
       (- 16x  + 56a x  - 42a x  + 5a x)\|x  - a   + 16x  - 64a x  + 68a x
     + 
            6 2
       - 20a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +-------+                              +-------+
--R              4 3      6   | 2    2       4 4      6 2     8      | 2    2
--R       ((- 24a x  + 12a x)\|x  - a   + 24a x  - 24a x  + 3a )log(\|x  - a   - x)
--R     + 
--R                                         +-------+
--R             7      2 5      4 3     6   | 2    2       8      2 6      4 4
--R       (- 16x  + 56a x  - 42a x  + 5a x)\|x  - a   + 16x  - 64a x  + 68a x
--R     + 
--R            6 2
--R       - 20a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 114
bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2))
 

                +-------+                     +-------+
          4     | 2    2            3     2   | 2    2
        3a log(\|x  - a   + x) + (2x  - 5a x)\|x  - a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                +-------+                     +-------+
--R          4     | 2    2            3     2   | 2    2
--R        3a log(\|x  - a   + x) + (2x  - 5a x)\|x  - a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 115
cc:=aa-bb
 

                  +-------+                +-------+
            4     | 2    2           4     | 2    2
        - 3a log(\|x  - a   + x) - 3a log(\|x  - a   - x)
   (3)  -------------------------------------------------
                                8
                                                     Type: Expression Integer
--R
--R                  +-------+                +-------+
--R            4     | 2    2           4     | 2    2
--R        - 3a log(\|x  - a   + x) - 3a log(\|x  - a   - x)
--R   (3)  -------------------------------------------------
--R                                8
--R                                                     Type: Expression Integer
--E

--S 116    14:230 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

            4       2
          3a log(- a )
   (4)  - ------------
                8
                                                     Type: Expression Integer
--R
--R            4       2
--R          3a log(- a )
--R   (4)  - ------------
--R                8
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 117
aa:=integrate(x*(x^2-a^2)^(3/2),x)
 

   (1)
                                                  +-------+
             9      2 7      4 5      6 3     8   | 2    2       10      2 8
       (- 16x  + 52a x  - 61a x  + 30a x  - 5a x)\|x  - a   + 16x   - 60a x
     + 
          4 6      6 4      8 2    10
       85a x  - 55a x  + 15a x  - a
  /
                           +-------+
         4      2 2     4  | 2    2       5       2 3      4
     (80x  - 60a x  + 5a )\|x  - a   - 80x  + 100a x  - 25a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7      4 5      6 3     8   | 2    2       10      2 8
--R       (- 16x  + 52a x  - 61a x  + 30a x  - 5a x)\|x  - a   + 16x   - 60a x
--R     + 
--R          4 6      6 4      8 2    10
--R       85a x  - 55a x  + 15a x  - a
--R  /
--R                           +-------+
--R         4      2 2     4  | 2    2       5       2 3      4
--R     (80x  - 60a x  + 5a )\|x  - a   - 80x  + 100a x  - 25a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 118
bb:=(x^2-a^2)^(5/2)/5
 

                          +-------+
          4     2 2    4  | 2    2
        (x  - 2a x  + a )\|x  - a
   (2)  ---------------------------
                     5
                                                     Type: Expression Integer
--R
--R                          +-------+
--R          4     2 2    4  | 2    2
--R        (x  - 2a x  + a )\|x  - a
--R   (2)  ---------------------------
--R                     5
--R                                                     Type: Expression Integer
--E

--S 119    14:231 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 120
aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
 

   (1)
                                        +-------+
                 6 5      8 3      10   | 2    2       6 6       8 4      10 2
           (- 96a x  + 96a x  - 18a  x)\|x  - a   + 96a x  - 144a x  + 54a  x
         + 
               12
           - 3a
      *
              +-------+
              | 2    2
         log(\|x  - a   - x)
     + 
                                                                 +-------+
              11       2 9       4 7       6 5      8 3     10   | 2    2
       (- 256x   + 832a x  - 912a x  + 404a x  - 68a x  + 3a  x)\|x  - a
     + 
           12       2 10        4 8       6 6       8 4      10 2
       256x   - 960a x   + 1296a x  - 772a x  + 198a x  - 18a  x
  /
                                  +-------+
           5        2 3       4   | 2    2         6        2 4       4 2      6
     (1536x  - 1536a x  + 288a x)\|x  - a   - 1536x  + 2304a x  - 864a x  + 48a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                        +-------+
--R                 6 5      8 3      10   | 2    2       6 6       8 4      10 2
--R           (- 96a x  + 96a x  - 18a  x)\|x  - a   + 96a x  - 144a x  + 54a  x
--R         + 
--R               12
--R           - 3a
--R      *
--R              +-------+
--R              | 2    2
--R         log(\|x  - a   - x)
--R     + 
--R                                                                 +-------+
--R              11       2 9       4 7       6 5      8 3     10   | 2    2
--R       (- 256x   + 832a x  - 912a x  + 404a x  - 68a x  + 3a  x)\|x  - a
--R     + 
--R           12       2 10        4 8       6 6       8 4      10 2
--R       256x   - 960a x   + 1296a x  - 772a x  + 198a x  - 18a  x
--R  /
--R                                  +-------+
--R           5        2 3       4   | 2    2         6        2 4       4 2      6
--R     (1536x  - 1536a x  + 288a x)\|x  - a   - 1536x  + 2304a x  - 864a x  + 48a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 121
bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2))
 

                +-------+                              +-------+
          6     | 2    2            5      2 3     4   | 2    2
        3a log(\|x  - a   + x) + (8x  - 14a x  + 3a x)\|x  - a
   (2)  --------------------------------------------------------
                                   48
                                                     Type: Expression Integer
--R
--R                +-------+                              +-------+
--R          6     | 2    2            5      2 3     4   | 2    2
--R        3a log(\|x  - a   + x) + (8x  - 14a x  + 3a x)\|x  - a
--R   (2)  --------------------------------------------------------
--R                                   48
--R                                                     Type: Expression Integer
--E

--S 122
cc:=aa-bb
 

                 +-------+               +-------+
           6     | 2    2          6     | 2    2
        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
   (3)  -----------------------------------------------
                               16
                                                     Type: Expression Integer
--R
--R                 +-------+               +-------+
--R           6     | 2    2          6     | 2    2
--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
--R   (3)  -----------------------------------------------
--R                               16
--R                                                     Type: Expression Integer
--E

--S 123    14:232 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           6       2
          a log(- a )
   (4)  - -----------
               16
                                                     Type: Expression Integer
--R
--R           6       2
--R          a log(- a )
--R   (4)  - -----------
--R               16
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 124
aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
 

   (1)
                   13        2 11        4 9       6 7       8 5       10 3
             - 320x   + 1072a x   - 1240a x  + 467a x  + 112a x  - 105a  x
           + 
                12
             14a  x
      *
          +-------+
          | 2    2
         \|x  - a
     + 
           14        2 12        4 10       6 8      8 6       10 4      12 2
       320x   - 1232a x   + 1736a x   - 973a x  + 21a x  + 175a  x  - 49a  x
     + 
         14
       2a
  /
                                            +-------+
             6        2 4       4 2      6  | 2    2         7        2 5
       (2240x  - 2800a x  + 840a x  - 35a )\|x  - a   - 2240x  + 3920a x
     + 
              4 3       6
       - 1960a x  + 245a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   13        2 11        4 9       6 7       8 5       10 3
--R             - 320x   + 1072a x   - 1240a x  + 467a x  + 112a x  - 105a  x
--R           + 
--R                12
--R             14a  x
--R      *
--R          +-------+
--R          | 2    2
--R         \|x  - a
--R     + 
--R           14        2 12        4 10       6 8      8 6       10 4      12 2
--R       320x   - 1232a x   + 1736a x   - 973a x  + 21a x  + 175a  x  - 49a  x
--R     + 
--R         14
--R       2a
--R  /
--R                                            +-------+
--R             6        2 4       4 2      6  | 2    2         7        2 5
--R       (2240x  - 2800a x  + 840a x  - 35a )\|x  - a   - 2240x  + 3920a x
--R     + 
--R              4 3       6
--R       - 1960a x  + 245a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 125
bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5
 

                                   +-------+
           6     2 4    4 2     6  | 2    2
        (5x  - 8a x  + a x  + 2a )\|x  - a
   (2)  ------------------------------------
                         35
                                                     Type: Expression Integer
--R
--R                                   +-------+
--R           6     2 4    4 2     6  | 2    2
--R        (5x  - 8a x  + a x  + 2a )\|x  - a
--R   (2)  ------------------------------------
--R                         35
--R                                                     Type: Expression Integer
--E

--S 126    14:233 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 127
aa:=integrate((x^2-a^2)^(3/2)/x,x)
 

   (1)
                                                        +-------+
                       +-------+                        | 2    2
            3 2     5  | 2    2       3 3      5       \|x  - a   - x
       ((24a x  - 6a )\|x  - a   - 24a x  + 18a x)atan(--------------)
                                                              a
     + 
                                +-------+
            5      2 3      4   | 2    2      6      2 4      4 2     6
       (- 4x  + 19a x  - 12a x)\|x  - a   + 4x  - 21a x  + 21a x  - 4a
  /
                  +-------+
         2     2  | 2    2       3     2
     (12x  - 3a )\|x  - a   - 12x  + 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                        +-------+
--R                       +-------+                        | 2    2
--R            3 2     5  | 2    2       3 3      5       \|x  - a   - x
--R       ((24a x  - 6a )\|x  - a   - 24a x  + 18a x)atan(--------------)
--R                                                              a
--R     + 
--R                                +-------+
--R            5      2 3      4   | 2    2      6      2 4      4 2     6
--R       (- 4x  + 19a x  - 12a x)\|x  - a   + 4x  - 21a x  + 21a x  - 4a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3     2
--R     (12x  - 3a )\|x  - a   - 12x  + 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 128
bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a)
 

                   +-------+
          2     2  | 2    2      3     x
        (x  - 4a )\|x  - a   + 3a asec(-)
                                       a
   (2)  ---------------------------------
                        3
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2      3     x
--R        (x  - 4a )\|x  - a   + 3a asec(-)
--R                                       a
--R   (2)  ---------------------------------
--R                        3
--R                                                     Type: Expression Integer
--E

--S 129
cc:=aa-bb
 

                 +-------+
                 | 2    2
          3     \|x  - a   - x     3     x
   (3)  2a atan(--------------) - a asec(-)
                       a                 a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R          3     \|x  - a   - x     3     x
--R   (3)  2a atan(--------------) - a asec(-)
--R                       a                 a
--R                                                     Type: Expression Integer
--E

--S 130
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (4)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (4)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 131
dd:=asecrule cc
 

                      +-------+
                      | 2    2
                      |x  - a
                    x |-------  + %i a             +-------+
                      |    2                       | 2    2
               3     \|   x                 3     \|x  - a   - x     3
        - 2%i a log(------------------) + 4a atan(--------------) - a %pi
                             x                           a
   (5)  -----------------------------------------------------------------
                                        2
                                             Type: Expression Complex Integer
--R
--R                      +-------+
--R                      | 2    2
--R                      |x  - a
--R                    x |-------  + %i a             +-------+
--R                      |    2                       | 2    2
--R               3     \|   x                 3     \|x  - a   - x     3
--R        - 2%i a log(------------------) + 4a atan(--------------) - a %pi
--R                             x                           a
--R   (5)  -----------------------------------------------------------------
--R                                        2
--R                                             Type: Expression Complex Integer
--E

--S 132
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 133
ee:=atanrule dd
 

   (7)
                 +-------+
                 | 2    2
                 |x  - a
               x |-------  + %i a                 +-------+
                 |    2                           | 2    2
          3     \|   x                    3    - \|x  - a   + x + %i a     3
   - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi
                        x                        +-------+
                                                 | 2    2
                                                \|x  - a   - x + %i a
   ----------------------------------------------------------------------------
                                         2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                 +-------+
--R                 | 2    2
--R                 |x  - a
--R               x |-------  + %i a                 +-------+
--R                 |    2                           | 2    2
--R          3     \|   x                    3    - \|x  - a   + x + %i a     3
--R   - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi
--R                        x                        +-------+
--R                                                 | 2    2
--R                                                \|x  - a   - x + %i a
--R   ----------------------------------------------------------------------------
--R                                         2
--R                                             Type: Expression Complex Integer
--E

--S 134
ff:=expandLog ee
 

   (8)
                  +-------+                          +-------+
            3     | 2    2                     3     | 2    2
       2%i a log(\|x  - a   - x + %i a) - 2%i a log(\|x  - a   - x - %i a)
     + 
                     +-------+
                     | 2    2
              3      |x  - a                  3              3            3
       - 2%i a log(x |-------  + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
                     |    2
                    \|   x
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                  +-------+                          +-------+
--R            3     | 2    2                     3     | 2    2
--R       2%i a log(\|x  - a   - x + %i a) - 2%i a log(\|x  - a   - x - %i a)
--R     + 
--R                     +-------+
--R                     | 2    2
--R              3      |x  - a                  3              3            3
--R       - 2%i a log(x |-------  + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
--R                     |    2
--R                    \|   x
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 135
gg:=rootSimp ff
 

   (9)
                    +-------+                      +-------+
              3     | 2    2                 3     | 2    2
       - 2%i a log(\|x  - a   + %i a) + 2%i a log(\|x  - a   - x + %i a)
     + 
                  +-------+
            3     | 2    2                     3              3            3
     - 2%i a log(\|x  - a   - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                    +-------+                      +-------+
--R              3     | 2    2                 3     | 2    2
--R       - 2%i a log(\|x  - a   + %i a) + 2%i a log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R            3     | 2    2                     3              3            3
--R     - 2%i a log(\|x  - a   - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 136    14:234 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

            3
           a %pi
   (10)  - -----
             2
                                             Type: Expression Complex Integer
--R
--R            3
--R           a %pi
--R   (10)  - -----
--R             2
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 137
aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
 

   (1)
                        +-------+                       +-------+
            2 3     4   | 2    2       2 4     4 2      | 2    2
       ((12a x  - 3a x)\|x  - a   - 12a x  + 9a x )log(\|x  - a   - x)
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2     6
       (- 4x  + 3a x  + 4a x)\|x  - a   + 4x  - 5a x  - 3a x  + 2a
  /
                  +-------+
        3     2   | 2    2      4     2 2
     (8x  - 2a x)\|x  - a   - 8x  + 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                        +-------+                       +-------+
--R            2 3     4   | 2    2       2 4     4 2      | 2    2
--R       ((12a x  - 3a x)\|x  - a   - 12a x  + 9a x )log(\|x  - a   - x)
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (- 4x  + 3a x  + 4a x)\|x  - a   + 4x  - 5a x  - 3a x  + 2a
--R  /
--R                  +-------+
--R        3     2   | 2    2      4     2 2
--R     (8x  - 2a x)\|x  - a   - 8x  + 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 138
bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2))
 

                    +-------+                   +-------+
            2       | 2    2           2     2  | 2    2
        - 3a x log(\|x  - a   + x) + (x  + 2a )\|x  - a
   (2)  -------------------------------------------------
                                2x
                                                     Type: Expression Integer
--R
--R                    +-------+                   +-------+
--R            2       | 2    2           2     2  | 2    2
--R        - 3a x log(\|x  - a   + x) + (x  + 2a )\|x  - a
--R   (2)  -------------------------------------------------
--R                                2x
--R                                                     Type: Expression Integer
--E

--S 139
cc:=aa-bb
 

                +-------+                +-------+
          2     | 2    2           2     | 2    2           2
        3a log(\|x  - a   + x) + 3a log(\|x  - a   - x) + 2a
   (3)  -----------------------------------------------------
                                  2
                                                     Type: Expression Integer
--R
--R                +-------+                +-------+
--R          2     | 2    2           2     | 2    2           2
--R        3a log(\|x  - a   + x) + 3a log(\|x  - a   - x) + 2a
--R   (3)  -----------------------------------------------------
--R                                  2
--R                                                     Type: Expression Integer
--E

--S 140    14:235 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

          2       2      2
        3a log(- a ) + 2a
   (4)  ------------------
                 2
                                                     Type: Expression Integer
--R
--R          2       2      2
--R        3a log(- a ) + 2a
--R   (4)  ------------------
--R                 2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 141
aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
 

   (1)
                                                             +-------+
                           +-------+                         | 2    2
                4     3 2  | 2    2         5      3 3      \|x  - a   - x
       ((- 24a x  + 6a x )\|x  - a   + 24a x  - 18a x )atan(--------------)
                                                                   a
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2    6
       (- 8x  + 2a x  + 3a x)\|x  - a   + 8x  - 6a x  - 3a x  + a
  /
                   +-------+
        4     2 2  | 2    2      5     2 3
     (8x  - 2a x )\|x  - a   - 8x  + 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                             +-------+
--R                           +-------+                         | 2    2
--R                4     3 2  | 2    2         5      3 3      \|x  - a   - x
--R       ((- 24a x  + 6a x )\|x  - a   + 24a x  - 18a x )atan(--------------)
--R                                                                   a
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2    6
--R       (- 8x  + 2a x  + 3a x)\|x  - a   + 8x  - 6a x  - 3a x  + a
--R  /
--R                   +-------+
--R        4     2 2  | 2    2      5     2 3
--R     (8x  - 2a x )\|x  - a   - 8x  + 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 142
bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a)
 

                   +-------+
           2    2  | 2    2        2     x
        (2x  + a )\|x  - a   - 3a x asec(-)
                                         a
   (2)  -----------------------------------
                          2
                        2x
                                                     Type: Expression Integer
--R
--R                   +-------+
--R           2    2  | 2    2        2     x
--R        (2x  + a )\|x  - a   - 3a x asec(-)
--R                                         a
--R   (2)  -----------------------------------
--R                          2
--R                        2x
--R                                                     Type: Expression Integer
--E

--S 143
cc:=aa-bb
 

                   +-------+
                   | 2    2
                  \|x  - a   - x            x
        - 6a atan(--------------) + 3a asec(-)
                         a                  a
   (3)  --------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                   +-------+
--R                   | 2    2
--R                  \|x  - a   - x            x
--R        - 6a atan(--------------) + 3a asec(-)
--R                         a                  a
--R   (3)  --------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 144
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 145
dd:=atanrule cc
 

                     +-------+
                     | 2    2
                  - \|x  - a   + x + %i a            x
        3%i a log(-----------------------) + 3a asec(-)
                    +-------+                        a
                    | 2    2
                   \|x  - a   - x + %i a
   (5)  -----------------------------------------------
                               2
                                             Type: Expression Complex Integer
--R
--R                     +-------+
--R                     | 2    2
--R                  - \|x  - a   + x + %i a            x
--R        3%i a log(-----------------------) + 3a asec(-)
--R                    +-------+                        a
--R                    | 2    2
--R                   \|x  - a   - x + %i a
--R   (5)  -----------------------------------------------
--R                               2
--R                                             Type: Expression Complex Integer
--E

--S 146
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 147
ee:=asecrule dd
 

   (7)
               +-------+
               | 2    2
               |x  - a
             x |-------  + %i a                 +-------+
               |    2                           | 2    2
              \|   x                         - \|x  - a   + x + %i a
   6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi
                      x                        +-------+
                                               | 2    2
                                              \|x  - a   - x + %i a
   ---------------------------------------------------------------------------
                                        4
                                             Type: Expression Complex Integer
--R
--R   (7)
--R               +-------+
--R               | 2    2
--R               |x  - a
--R             x |-------  + %i a                 +-------+
--R               |    2                           | 2    2
--R              \|   x                         - \|x  - a   + x + %i a
--R   6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi
--R                      x                        +-------+
--R                                               | 2    2
--R                                              \|x  - a   - x + %i a
--R   ---------------------------------------------------------------------------
--R                                        4
--R                                             Type: Expression Complex Integer
--E

--S 148
ff:=expandLog ee
 

   (8)
                    +-------+                          +-------+
                    | 2    2                           | 2    2
       - 6%i a log(\|x  - a   - x + %i a) + 6%i a log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       6%i a log(x |-------  + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
                   |    2
                  \|   x
  /
     4
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +-------+                          +-------+
--R                    | 2    2                           | 2    2
--R       - 6%i a log(\|x  - a   - x + %i a) + 6%i a log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       6%i a log(x |-------  + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
--R                   |    2
--R                  \|   x
--R  /
--R     4
--R                                             Type: Expression Complex Integer
--E

--S 149
gg:=rootSimp ff
 

   (9)
                  +-------+                      +-------+
                  | 2    2                       | 2    2
       6%i a log(\|x  - a   + %i a) - 6%i a log(\|x  - a   - x + %i a)
     + 
                +-------+
                | 2    2
     6%i a log(\|x  - a   - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
  /
     4
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                      +-------+
--R                  | 2    2                       | 2    2
--R       6%i a log(\|x  - a   + %i a) - 6%i a log(\|x  - a   - x + %i a)
--R     + 
--R                +-------+
--R                | 2    2
--R     6%i a log(\|x  - a   - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
--R  /
--R     4
--R                                             Type: Expression Complex Integer
--E

--S 150    14:236 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         3a %pi
   (10)  ------
            4
                                             Type: Expression Complex Integer
--R
--R         3a %pi
--R   (10)  ------
--R            4
--R                                             Type: Expression Complex Integer
--E

)spool
 
Starts dribbling to mapleok.output (2009/2/17, 17:52:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set break resume
 
--S 1 of 224
in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 

            +-+
        %pi\|3
   (1)  -------
           3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            +-+
--R        %pi\|3
--R   (1)  -------
--R           3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 1

--S 2 of 224
in101a:=integrate((sqrt(z)^%i)^%i, z= 0..1,"noPole")
 

   (2)  2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (2)  2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 2

--S 3 of 224
in108a:=integrate(sqrt((1 + cos(z))*(1 + sin(z))),z=0..%plusInfinity,"noPole")
 

   (3)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (3)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 3

--S 4 of 224
in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole")
 

   (4)
              +-+              +-+                 +-+
       3log(2\|2  + 3) + 2log(\|2  + 1) - 3log(- 2\|2  + 3)
     + 
                     +-+       +-+      +-+
        +-+    (- 32\|2  - 30)\|5  + 48\|2  + 102           +-+
       \|5 log(----------------------------------) - log(4)\|5
                              +-+
                            2\|2  + 3
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)
--R              +-+              +-+                 +-+
--R       3log(2\|2  + 3) + 2log(\|2  + 1) - 3log(- 2\|2  + 3)
--R     + 
--R                     +-+       +-+      +-+
--R        +-+    (- 32\|2  - 30)\|5  + 48\|2  + 102           +-+
--R       \|5 log(----------------------------------) - log(4)\|5
--R                              +-+
--R                            2\|2  + 3
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 224
in120a:=integrate(1/(1+1/z^6), z=0..%plusInfinity)
 

   (5)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (5)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 224
in1030a:=integrate(%i*z/(%i*z+1), z= 0..%plusInfinity,"noPole")
 

   (6)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (6)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 6

--S 7 of 224
in1066a:=integrate(acoth(z)*real(z), z= 0..1,"noPole")
 

        1
   (7)  -
        2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R        1
--R   (7)  -
--R        2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 7

--S 8 of 224
in1067a:=integrate(acoth(z)*z^(1/2), z= 0..1,"noPole")
 

        - 2log(2) - %pi + 8
   (8)  -------------------
                 6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R        - 2log(2) - %pi + 8
--R   (8)  -------------------
--R                 6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 8

--S 9 of 224
in1076a:=integrate(sin(z)*(1-cos(z)/(1-sin(z)^2)^(1/2))^2, z= 0..1,"noPole")
 

   (9)  - 4cos(1) + 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (9)  - 4cos(1) + 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 9

--S 10 of 224
in1084a:=integrate(atan(sin(z))+atan(1/sin(z)), z= 0..1,"noPole")
 

           %pi
   (10)  - ---
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           %pi
--R   (10)  - ---
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 10

--S 11 of 224
in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole")
 

   (11)
               +--------+              +-------+
               |2%pi - 1               |%pi - 1
       - 2log( |--------  + 1) + 2log( |-------  + 1)
              \|  2%pi                \|  %pi
     + 
                    +-------+                          +--------+
                    |%pi - 1                           |2%pi - 1
             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
                   \|  %pi                            \|  2%pi
       - log(---------------------------) + log(----------------------------)
                         %pi                                2%pi
     + 
            +--------+        +-------+
            |2%pi - 1         |%pi - 1
       8%pi |--------  - 4%pi |-------
           \|  2%pi          \|  %pi
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (11)
--R               +--------+              +-------+
--R               |2%pi - 1               |%pi - 1
--R       - 2log( |--------  + 1) + 2log( |-------  + 1)
--R              \|  2%pi                \|  %pi
--R     + 
--R                    +-------+                          +--------+
--R                    |%pi - 1                           |2%pi - 1
--R             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
--R                   \|  %pi                            \|  2%pi
--R       - log(---------------------------) + log(----------------------------)
--R                         %pi                                2%pi
--R     + 
--R            +--------+        +-------+
--R            |2%pi - 1         |%pi - 1
--R       8%pi |--------  - 4%pi |-------
--R           \|  2%pi          \|  %pi
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 11

--S 12 of 224
in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*%i*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole")
 

   (12)  - infinity
   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--R 
--R
--R   (12)  - infinity
--R   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--E 12

--S 13 of 224
in1118:=integrate(acot(z), z= 0..1/2*%i)
 

         1     3    1     1
   (13)  - log(-) - - log(-)
         2     4    8     9
   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--R 
--R
--R         1     3    1     1
--R   (13)  - log(-) - - log(-)
--R         2     4    8     9
--R   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--E 13

--S 14 of 224
in1120a:=integrate((z^2)^(1/2), z= 1..2,"noPole")
 

         3
   (14)  -
         2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         3
--R   (14)  -
--R         2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 14

--S 15 of 224
in1130a:=integrate(3^log(z), z= -%i..%i,"noPole")
 

              log(%i)log(3)        log(- %i)log(3)
         %i %e              + %i %e
   (15)  -----------------------------------------
                         log(3) + 1
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              log(%i)log(3)        log(- %i)log(3)
--R         %i %e              + %i %e
--R   (15)  -----------------------------------------
--R                         log(3) + 1
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 15

--S 16 of 224
in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i)
 

   (16)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (16)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 16

--S 17 of 224
in1150a:=integrate(1/z^(1/2), z= -%i..%i,"noPole")
 

           +--+     +----+
   (17)  2\|%i  - 2\|- %i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R           +--+     +----+
--R   (17)  2\|%i  - 2\|- %i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 17

--S 18 of 224
in1161a:=integrate(hermiteH(1, z), z= -%i..%i)
 

   (18)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (18)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 18

--S 19 of 224
in1160:=integrate(hermiteH(2, z), z= -%i..%i)
 

           20%i
   (19)  - ----
             3
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R           20%i
--R   (19)  - ----
--R             3
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 19

--S 20 of 224
in1162:=integrate(laguerreL(1, z), z= -%i..%i)
 

   (20)  2%i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (20)  2%i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 20

--S 21 of 224
in1163:=integrate(legendreP(3, z), z= -%i..%i)
 

   (21)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (21)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 21

--S 22 of 224
in1164:=integrate(legendreP(2, z), z= -%i..%i)
 

   (22)  - 2%i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (22)  - 2%i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 22

--S 23 of 224
in1167a:=integrate((z^2)^(1/6), z= -3..-1,"noPole")
 

            3+---+    3+---+
         - 3\|- 1  + 9\|- 3
   (23)  -------------------
                  4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            3+---+    3+---+
--R         - 3\|- 1  + 9\|- 3
--R   (23)  -------------------
--R                  4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 23

--S 24 of 224
in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
 

   (24)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (24)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 24

--S 25 of 224
in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,"noPole")
 

   (25)
         3
      *
         log
               999999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99998000000000000000000000000000000000000000000000000000000000_
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             *
                3+--+2
                \|10
            + 
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             *
                3+--+
                \|10
            + 
              -
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     + 
       -
            12
         *
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                *
                   3+--+2
                   \|10
               + 
                 1
     + 
            +-+
         12\|3
      *
         atan
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               *
                  3+--+2
                  \|10
              + 
                - 1
           /
               +-+
              \|3
     + 
            +-+
       2%pi\|3
  /
     24
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (25)
--R         3
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--R               999999999999999999999999999999999999999999999999999999999999999_
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--R                3+--+2
--R                \|10
--R            + 
--R               300000000000000000000000000000000000000000000000000000000000000_
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--R             *
--R                3+--+
--R                \|10
--R            + 
--R              -
--R                19999999999999999999999999999999999999999999999999999999999999_
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--R       -
--R            12
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--R                  100000000000000000000000000000000000000000000000000000000000_
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--R                   00000000000
--R                *
--R                   3+--+2
--R                   \|10
--R               + 
--R                 1
--R     + 
--R            +-+
--R         12\|3
--R      *
--R         atan
--R                 2000000000000000000000000000000000000000000000000000000000000_
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--R               *
--R                  3+--+2
--R                  \|10
--R              + 
--R                - 1
--R           /
--R               +-+
--R              \|3
--R     + 
--R            +-+
--R       2%pi\|3
--R  /
--R     24
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 25

--S 26 of 224
in1183a:=integrate(csc(z), z= 1-%i..1+%i,"noPole")
 

   (26)
                            2                                      2
                 sin(1 + %i)                            sin(1 - %i)
   log(-------------------------------) - log(-------------------------------)
                  2                                      2
       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
   ---------------------------------------------------------------------------
                                        2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (26)
--R                            2                                      2
--R                 sin(1 + %i)                            sin(1 - %i)
--R   log(-------------------------------) - log(-------------------------------)
--R                  2                                      2
--R       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
--R   ---------------------------------------------------------------------------
--R                                        2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 26

--S 27 of 224
in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 

   (27)
         ROOT
                 +-----------------------------------------+
                 |         2                          2          +-+
                \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                              +-+            +-+             +-+           +-+
                      ((24576\|2 %%CC0 - 768\|2 )%%CC1 - 768\|2 %%CC0 - 48\|2 )
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                                             2               2
                    (196608%%CC0 - 6144)%%CC1  + (196608%%CC0  + 384)%%CC1
                  + 
                               2
                    - 6144%%CC0  + 384%%CC0 + 48
               *
                  ROOT
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                60\|2
           /
               +-+
              \|2
     + 
       -
            ROOT
                    +-----------------------------------------+
                    |         2                          2          +-+
                   \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                         ((24576%%CC0 - 768)%%CC1 - 768%%CC0 - 48)
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                              +-+             +-+      2
                       (98304\|2 %%CC0 - 3072\|2 )%%CC1
                     + 
                              +-+     2       +-+              +-+     2
                       (98304\|2 %%CC0  + 192\|2 )%%CC1 - 3072\|2 %%CC0
                     + 
                           +-+           +-+
                       192\|2 %%CC0 + 24\|2
                  *
                     ROOT
                             +-----------------------------------------+
                             |         2                          2
                            \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 42\|2
              /
                  +-+
                 \|2
     + 
       -
            ROOT
                      +-----------------------------------------+
                      |         2                          2          +-+
                   - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                                    +-+            +-+             +-+
                             (24576\|2 %%CC0 - 768\|2 )%%CC1 - 768\|2 %%CC0
                           + 
                                  +-+
                             - 48\|2
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                                                  2
                       (- 196608%%CC0 + 6144)%%CC1
                     + 
                                     2                        2
                       (- 196608%%CC0  - 384)%%CC1 + 6144%%CC0  - 384%%CC0 - 48
                  *
                     ROOT
                               +-----------------------------------------+
                               |         2                          2
                            - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 60\|2
              /
                  +-+
                 \|2
     + 
         ROOT
                   +-----------------------------------------+
                   |         2                          2          +-+
                - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                      ((24576%%CC0 - 768)%%CC1 - 768%%CC0 - 48)
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                             +-+             +-+      2
                    (- 98304\|2 %%CC0 + 3072\|2 )%%CC1
                  + 
                             +-+     2       +-+              +-+     2
                    (- 98304\|2 %%CC0  - 192\|2 )%%CC1 + 3072\|2 %%CC0
                  + 
                          +-+           +-+
                    - 192\|2 %%CC0 - 24\|2
               *
                  ROOT
                            +-----------------------------------------+
                            |         2                          2
                         - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                42\|2
           /
               +-+
              \|2
     + 
       -
            ROOT
                      +-----------------------------------------+
                      |         2                          2          +-+
                   - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                         ((- 24576%%CC0 + 768)%%CC1 + 768%%CC0 + 48)
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                              +-+             +-+      2
                       (98304\|2 %%CC0 - 3072\|2 )%%CC1
                     + 
                              +-+     2       +-+              +-+     2
                       (98304\|2 %%CC0  + 192\|2 )%%CC1 - 3072\|2 %%CC0
                     + 
                           +-+           +-+
                       192\|2 %%CC0 + 24\|2
                  *
                     ROOT
                               +-----------------------------------------+
                               |         2                          2
                            - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 42\|2
              /
                  +-+
                 \|2
     + 
         ROOT
                   +-----------------------------------------+
                   |         2                          2          +-+
                - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                                   +-+            +-+             +-+
                          (- 24576\|2 %%CC0 + 768\|2 )%%CC1 + 768\|2 %%CC0
                        + 
                             +-+
                          48\|2
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                                             2               2
                    (196608%%CC0 - 6144)%%CC1  + (196608%%CC0  + 384)%%CC1
                  + 
                               2
                    - 6144%%CC0  + 384%%CC0 + 48
               *
                  ROOT
                            +-----------------------------------------+
                            |         2                          2
                         - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                60\|2
           /
               +-+
              \|2
     + 
         ROOT
                 +-----------------------------------------+
                 |         2                          2          +-+
                \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                      ((- 24576%%CC0 + 768)%%CC1 + 768%%CC0 + 48)
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                             +-+             +-+      2
                    (- 98304\|2 %%CC0 + 3072\|2 )%%CC1
                  + 
                             +-+     2       +-+              +-+     2
                    (- 98304\|2 %%CC0  - 192\|2 )%%CC1 + 3072\|2 %%CC0
                  + 
                          +-+           +-+
                    - 192\|2 %%CC0 - 24\|2
               *
                  ROOT
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                42\|2
           /
               +-+
              \|2
     + 
       -
            ROOT
                    +-----------------------------------------+
                    |         2                          2          +-+
                   \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                                    +-+            +-+             +-+
                           (- 24576\|2 %%CC0 + 768\|2 )%%CC1 + 768\|2 %%CC0
                         + 
                              +-+
                           48\|2
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                                                  2
                       (- 196608%%CC0 + 6144)%%CC1
                     + 
                                     2                        2
                       (- 196608%%CC0  - 384)%%CC1 + 6144%%CC0  - 384%%CC0 - 48
                  *
                     ROOT
                             +-----------------------------------------+
                             |         2                          2
                            \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 60\|2
              /
                  +-+
                 \|2
     + 
       -
             +------+
            \|4%%CC1
         *
            log
                            +-+             +-+      2
                     (98304\|2 %%CC0 - 3072\|2 )%%CC1
                   + 
                            +-+     2       +-+               +-+     3
                     (98304\|2 %%CC0  + 192\|2 )%%CC1 + 98304\|2 %%CC0
                   + 
                         +-+           +-+
                     768\|2 %%CC0 - 36\|2
                *
                    +------+
                   \|4%%CC1
               + 
                                         2              2
                 (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1
               + 
                           3
                 12288%%CC0  + 96%%CC0 + 18
     + 
          +------+
         \|4%%CC1
      *
         log
                                          2              2
                  (98304%%CC0 - 3072)%%CC1  + (98304%%CC0  + 192)%%CC1
                + 
                            3
                  98304%%CC0  + 768%%CC0 - 36
             *
                 +------+
                \|4%%CC1
            + 
                                      2              2                        3
              (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1 + 12288%%CC0
            + 
              96%%CC0 + 9
     + 
       -
             +------+
            \|4%%CC1
         *
            log
                                               2                2
                     (- 98304%%CC0 + 3072)%%CC1  + (- 98304%%CC0  - 192)%%CC1
                   + 
                                 3
                     - 98304%%CC0  - 768%%CC0 + 36
                *
                    +------+
                   \|4%%CC1
               + 
                                         2              2
                 (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1
               + 
                           3
                 12288%%CC0  + 96%%CC0 + 9
     + 
          +------+
         \|4%%CC1
      *
         log
                           +-+             +-+      2
                  (- 98304\|2 %%CC0 + 3072\|2 )%%CC1
                + 
                           +-+     2       +-+               +-+     3
                  (- 98304\|2 %%CC0  - 192\|2 )%%CC1 - 98304\|2 %%CC0
                + 
                        +-+           +-+
                  - 768\|2 %%CC0 + 36\|2
             *
                 +------+
                \|4%%CC1
            + 
                                      2              2                        3
              (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1 + 12288%%CC0
            + 
              96%%CC0 + 18
     + 
          +------+
         \|4%%CC0
      *
         log
                       +-+     3        +-+     2       +-+           +-+
                (98304\|2 %%CC0  + 3072\|2 %%CC0  + 576\|2 %%CC0 - 60\|2 )
             *
                 +------+
                \|4%%CC0
            + 
                          3            2
              - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 30
     + 
       -
             +------+
            \|4%%CC0
         *
            log
                            3            2                  +------+
                 (98304%%CC0  + 3072%%CC0  + 576%%CC0 - 60)\|4%%CC0
               + 
                             3            2
                 - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 21
     + 
          +------+
         \|4%%CC0
      *
         log
                           3            2                  +------+
              (- 98304%%CC0  - 3072%%CC0  - 576%%CC0 + 60)\|4%%CC0
            + 
                          3            2
              - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 21
     + 
       -
             +------+
            \|4%%CC0
         *
            log
                            +-+     3        +-+     2       +-+           +-+
                   (- 98304\|2 %%CC0  - 3072\|2 %%CC0  - 576\|2 %%CC0 + 60\|2 )
                *
                    +------+
                   \|4%%CC0
               + 
                             3            2
                 - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 30
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (27)
--R         ROOT
--R                 +-----------------------------------------+
--R                 |         2                          2          +-+
--I                \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--R                              +-+            +-+             +-+           +-+
--I                      ((24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0 - 48\|2 )
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                                             2               2
--I                    (196608%%BQ0 - 6144)%%BQ1  + (196608%%BQ0  + 384)%%BQ1
--R                  + 
--R                               2
--I                    - 6144%%BQ0  + 384%%BQ0 + 48
--R               *
--R                  ROOT
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                60\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R            ROOT
--R                    +-----------------------------------------+
--R                    |         2                          2          +-+
--I                   \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--I                         ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48)
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                              +-+             +-+      2
--I                       (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
--R                     + 
--R                              +-+     2       +-+              +-+     2
--I                       (98304\|2 %%BQ0  + 192\|2 )%%BQ1 - 3072\|2 %%BQ0
--R                     + 
--R                           +-+           +-+
--I                       192\|2 %%BQ0 + 24\|2
--R                  *
--R                     ROOT
--R                             +-----------------------------------------+
--R                             |         2                          2
--I                            \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 42\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R       -
--R            ROOT
--R                      +-----------------------------------------+
--R                      |         2                          2          +-+
--I                   - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--R                                    +-+            +-+             +-+
--I                             (24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0
--R                           + 
--R                                  +-+
--R                             - 48\|2
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                                                  2
--I                       (- 196608%%BQ0 + 6144)%%BQ1
--R                     + 
--R                                     2                        2
--I                       (- 196608%%BQ0  - 384)%%BQ1 + 6144%%BQ0  - 384%%BQ0 - 48
--R                  *
--R                     ROOT
--R                               +-----------------------------------------+
--R                               |         2                          2
--I                            - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 60\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R         ROOT
--R                   +-----------------------------------------+
--R                   |         2                          2          +-+
--I                - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--I                      ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48)
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                             +-+             +-+      2
--I                    (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
--R                  + 
--R                             +-+     2       +-+              +-+     2
--I                    (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 + 3072\|2 %%BQ0
--R                  + 
--R                          +-+           +-+
--I                    - 192\|2 %%BQ0 - 24\|2
--R               *
--R                  ROOT
--R                            +-----------------------------------------+
--R                            |         2                          2
--I                         - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                42\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R            ROOT
--R                      +-----------------------------------------+
--R                      |         2                          2          +-+
--I                   - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--I                         ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48)
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                              +-+             +-+      2
--I                       (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
--R                     + 
--R                              +-+     2       +-+              +-+     2
--I                       (98304\|2 %%BQ0  + 192\|2 )%%BQ1 - 3072\|2 %%BQ0
--R                     + 
--R                           +-+           +-+
--I                       192\|2 %%BQ0 + 24\|2
--R                  *
--R                     ROOT
--R                               +-----------------------------------------+
--R                               |         2                          2
--I                            - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 42\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R         ROOT
--R                   +-----------------------------------------+
--R                   |         2                          2          +-+
--I                - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--R                                   +-+            +-+             +-+
--I                          (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0
--R                        + 
--R                             +-+
--R                          48\|2
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                                             2               2
--I                    (196608%%BQ0 - 6144)%%BQ1  + (196608%%BQ0  + 384)%%BQ1
--R                  + 
--R                               2
--I                    - 6144%%BQ0  + 384%%BQ0 + 48
--R               *
--R                  ROOT
--R                            +-----------------------------------------+
--R                            |         2                          2
--I                         - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                60\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R         ROOT
--R                 +-----------------------------------------+
--R                 |         2                          2          +-+
--I                \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--I                      ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48)
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                             +-+             +-+      2
--I                    (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
--R                  + 
--R                             +-+     2       +-+              +-+     2
--I                    (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 + 3072\|2 %%BQ0
--R                  + 
--R                          +-+           +-+
--I                    - 192\|2 %%BQ0 - 24\|2
--R               *
--R                  ROOT
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                42\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R            ROOT
--R                    +-----------------------------------------+
--R                    |         2                          2          +-+
--I                   \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--R                                    +-+            +-+             +-+
--I                           (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0
--R                         + 
--R                              +-+
--R                           48\|2
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                                                  2
--I                       (- 196608%%BQ0 + 6144)%%BQ1
--R                     + 
--R                                     2                        2
--I                       (- 196608%%BQ0  - 384)%%BQ1 + 6144%%BQ0  - 384%%BQ0 - 48
--R                  *
--R                     ROOT
--R                             +-----------------------------------------+
--R                             |         2                          2
--I                            \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 60\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ1
--R         *
--R            log
--R                            +-+             +-+      2
--I                     (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
--R                   + 
--R                            +-+     2       +-+               +-+     3
--I                     (98304\|2 %%BQ0  + 192\|2 )%%BQ1 + 98304\|2 %%BQ0
--R                   + 
--R                         +-+           +-+
--I                     768\|2 %%BQ0 - 36\|2
--R                *
--R                    +------+
--I                   \|4%%BQ1
--R               + 
--R                                         2              2
--I                 (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1
--R               + 
--R                           3
--I                 12288%%BQ0  + 96%%BQ0 + 18
--R     + 
--R          +------+
--I         \|4%%BQ1
--R      *
--R         log
--R                                          2              2
--I                  (98304%%BQ0 - 3072)%%BQ1  + (98304%%BQ0  + 192)%%BQ1
--R                + 
--R                            3
--I                  98304%%BQ0  + 768%%BQ0 - 36
--R             *
--R                 +------+
--I                \|4%%BQ1
--R            + 
--R                                      2              2                        3
--I              (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1 + 12288%%BQ0
--R            + 
--I              96%%BQ0 + 9
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ1
--R         *
--R            log
--R                                               2                2
--I                     (- 98304%%BQ0 + 3072)%%BQ1  + (- 98304%%BQ0  - 192)%%BQ1
--R                   + 
--R                                 3
--I                     - 98304%%BQ0  - 768%%BQ0 + 36
--R                *
--R                    +------+
--I                   \|4%%BQ1
--R               + 
--R                                         2              2
--I                 (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1
--R               + 
--R                           3
--I                 12288%%BQ0  + 96%%BQ0 + 9
--R     + 
--R          +------+
--I         \|4%%BQ1
--R      *
--R         log
--R                           +-+             +-+      2
--I                  (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
--R                + 
--R                           +-+     2       +-+               +-+     3
--I                  (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 - 98304\|2 %%BQ0
--R                + 
--R                        +-+           +-+
--I                  - 768\|2 %%BQ0 + 36\|2
--R             *
--R                 +------+
--I                \|4%%BQ1
--R            + 
--R                                      2              2                        3
--I              (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1 + 12288%%BQ0
--R            + 
--I              96%%BQ0 + 18
--R     + 
--R          +------+
--I         \|4%%BQ0
--R      *
--R         log
--R                       +-+     3        +-+     2       +-+           +-+
--I                (98304\|2 %%BQ0  + 3072\|2 %%BQ0  + 576\|2 %%BQ0 - 60\|2 )
--R             *
--R                 +------+
--I                \|4%%BQ0
--R            + 
--R                          3            2
--I              - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 30
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ0
--R         *
--R            log
--R                            3            2                  +------+
--I                 (98304%%BQ0  + 3072%%BQ0  + 576%%BQ0 - 60)\|4%%BQ0
--R               + 
--R                             3            2
--I                 - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 21
--R     + 
--R          +------+
--I         \|4%%BQ0
--R      *
--R         log
--R                           3            2                  +------+
--I              (- 98304%%BQ0  - 3072%%BQ0  - 576%%BQ0 + 60)\|4%%BQ0
--R            + 
--R                          3            2
--I              - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 21
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ0
--R         *
--R            log
--R                            +-+     3        +-+     2       +-+           +-+
--I                   (- 98304\|2 %%BQ0  - 3072\|2 %%BQ0  - 576\|2 %%BQ0 + 60\|2 )
--R                *
--R                    +------+
--I                   \|4%%BQ0
--R               + 
--R                             3            2
--I                 - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 30
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 27

--S 28 of 224
in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole")
 

   (28)
             +-+      4+-+    %pi
         (17\|2  - 24)\|2 cos(---)
                               8
      *
         log
                   %pi 4     +-+4+-+3    %pi 3
              2sin(---)  + 2\|2 \|2  sin(---)
                    8                     8
            + 
                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
              (4cos(---)  - 2\|2 \|2  cos(---) + 4\|2  )sin(---)
                     8                     8                 8
            + 
                 +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
              (2\|2 \|2  cos(---)  - 4\|2  cos(---) + 2\|2 \|2 )sin(---)
                              8                 8                    8
            + 
                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
              2cos(---)  - 2\|2 \|2  cos(---)  + 4\|2  cos(---)
                    8                     8                 8
            + 
                  +-+4+-+    %pi
              - 2\|2 \|2 cos(---) + 1
                              8
     + 
               +-+      4+-+    %pi
         (- 17\|2  + 24)\|2 cos(---)
                                 8
      *
         log
                   %pi 4    4+-+3    %pi 3
              2sin(---)  + 4\|2  sin(---)
                    8                 8
            + 
                      %pi 2        +-+     4+-+3    %pi         +-+      4+-+2
                (4cos(---)  + (- 4\|2  + 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
                       8                             8
             *
                    %pi 2
                sin(---)
                     8
            + 
                   4+-+3    %pi 2        +-+     4+-+2    %pi
                  4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
                             8                             8
                + 
                       +-+      4+-+
                  (- 8\|2  + 16)\|2
             *
                    %pi
                sin(---)
                     8
            + 
                   %pi 4        +-+     4+-+3    %pi 3
              2cos(---)  + (- 4\|2  + 4)\|2  cos(---)
                    8                             8
            + 
                    +-+      4+-+2    %pi 2         +-+      4+-+    %pi
              (- 12\|2  + 20)\|2  cos(---)  + (- 24\|2  + 32)\|2 cos(---)
                                       8                              8
            + 
                   +-+
              - 16\|2  + 24
     + 
             +-+      4+-+    %pi
         (17\|2  - 24)\|2 cos(---)
                               8
      *
         log
                   %pi 4    4+-+3    %pi 3
              2sin(---)  - 4\|2  sin(---)
                    8                 8
            + 
                      %pi 2      +-+     4+-+3    %pi         +-+      4+-+2
                (4cos(---)  + (4\|2  - 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
                       8                           8
             *
                    %pi 2
                sin(---)
                     8
            + 
                     4+-+3    %pi 2        +-+     4+-+2    %pi
                  - 4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
                               8                             8
                + 
                     +-+      4+-+
                  (8\|2  - 16)\|2
             *
                    %pi
                sin(---)
                     8
            + 
                   %pi 4      +-+     4+-+3    %pi 3
              2cos(---)  + (4\|2  - 4)\|2  cos(---)
                    8                           8
            + 
                    +-+      4+-+2    %pi 2       +-+      4+-+    %pi       +-+
              (- 12\|2  + 20)\|2  cos(---)  + (24\|2  - 32)\|2 cos(---) - 16\|2
                                       8                            8
            + 
              24
     + 
               +-+      4+-+    %pi
         (- 17\|2  + 24)\|2 cos(---)
                                 8
      *
         log
                   %pi 4     +-+4+-+3    %pi 3
              2sin(---)  - 2\|2 \|2  sin(---)
                    8                     8
            + 
                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
              (4cos(---)  + 2\|2 \|2  cos(---) + 4\|2  )sin(---)
                     8                     8                 8
            + 
                   +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
              (- 2\|2 \|2  cos(---)  - 4\|2  cos(---) - 2\|2 \|2 )sin(---)
                                8                 8                    8
            + 
                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
              2cos(---)  + 2\|2 \|2  cos(---)  + 4\|2  cos(---)
                    8                     8                 8
            + 
                +-+4+-+    %pi
              2\|2 \|2 cos(---) + 1
                            8
     + 
                                       4+-+    %pi    4+-+    %pi     +-+
                                       \|2 sin(---) - \|2 cos(---) + \|2
           +-+      4+-+    %pi                 8              8
       (68\|2  - 96)\|2 sin(---)atan(--------------------------------------)
                             8       4+-+    %pi    4+-+    %pi     +-+
                                     \|2 sin(---) + \|2 cos(---) - \|2  + 2
                                              8              8
     + 
                                       4+-+    %pi    4+-+    %pi     +-+
                                       \|2 sin(---) - \|2 cos(---) + \|2
             +-+      4+-+    %pi               8              8
       (- 68\|2  + 96)\|2 sin(---)atan(----------------------------------)
                               8           4+-+    %pi    4+-+    %pi
                                           \|2 sin(---) + \|2 cos(---)
                                                    8              8
     + 
                                     4+-+    %pi    4+-+    %pi     +-+
                                     \|2 sin(---) - \|2 cos(---) - \|2
           +-+      4+-+    %pi               8              8
       (68\|2  - 96)\|2 sin(---)atan(----------------------------------)
                             8           4+-+    %pi    4+-+    %pi
                                         \|2 sin(---) + \|2 cos(---)
                                                  8              8
     + 
                                         4+-+    %pi    4+-+    %pi     +-+
                                         \|2 sin(---) - \|2 cos(---) - \|2
             +-+      4+-+    %pi                 8              8
       (- 68\|2  + 96)\|2 sin(---)atan(--------------------------------------)
                               8       4+-+    %pi    4+-+    %pi     +-+
                                       \|2 sin(---) + \|2 cos(---) + \|2  - 2
                                                8              8
     + 
             +-+
       - 136\|2  + 192
  /
         +-+
     384\|2  - 544
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (28)
--R             +-+      4+-+    %pi
--R         (17\|2  - 24)\|2 cos(---)
--R                               8
--R      *
--R         log
--R                   %pi 4     +-+4+-+3    %pi 3
--R              2sin(---)  + 2\|2 \|2  sin(---)
--R                    8                     8
--R            + 
--R                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
--R              (4cos(---)  - 2\|2 \|2  cos(---) + 4\|2  )sin(---)
--R                     8                     8                 8
--R            + 
--R                 +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
--R              (2\|2 \|2  cos(---)  - 4\|2  cos(---) + 2\|2 \|2 )sin(---)
--R                              8                 8                    8
--R            + 
--R                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
--R              2cos(---)  - 2\|2 \|2  cos(---)  + 4\|2  cos(---)
--R                    8                     8                 8
--R            + 
--R                  +-+4+-+    %pi
--R              - 2\|2 \|2 cos(---) + 1
--R                              8
--R     + 
--R               +-+      4+-+    %pi
--R         (- 17\|2  + 24)\|2 cos(---)
--R                                 8
--R      *
--R         log
--R                   %pi 4    4+-+3    %pi 3
--R              2sin(---)  + 4\|2  sin(---)
--R                    8                 8
--R            + 
--R                      %pi 2        +-+     4+-+3    %pi         +-+      4+-+2
--R                (4cos(---)  + (- 4\|2  + 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
--R                       8                             8
--R             *
--R                    %pi 2
--R                sin(---)
--R                     8
--R            + 
--R                   4+-+3    %pi 2        +-+     4+-+2    %pi
--R                  4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
--R                             8                             8
--R                + 
--R                       +-+      4+-+
--R                  (- 8\|2  + 16)\|2
--R             *
--R                    %pi
--R                sin(---)
--R                     8
--R            + 
--R                   %pi 4        +-+     4+-+3    %pi 3
--R              2cos(---)  + (- 4\|2  + 4)\|2  cos(---)
--R                    8                             8
--R            + 
--R                    +-+      4+-+2    %pi 2         +-+      4+-+    %pi
--R              (- 12\|2  + 20)\|2  cos(---)  + (- 24\|2  + 32)\|2 cos(---)
--R                                       8                              8
--R            + 
--R                   +-+
--R              - 16\|2  + 24
--R     + 
--R             +-+      4+-+    %pi
--R         (17\|2  - 24)\|2 cos(---)
--R                               8
--R      *
--R         log
--R                   %pi 4    4+-+3    %pi 3
--R              2sin(---)  - 4\|2  sin(---)
--R                    8                 8
--R            + 
--R                      %pi 2      +-+     4+-+3    %pi         +-+      4+-+2
--R                (4cos(---)  + (4\|2  - 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
--R                       8                           8
--R             *
--R                    %pi 2
--R                sin(---)
--R                     8
--R            + 
--R                     4+-+3    %pi 2        +-+     4+-+2    %pi
--R                  - 4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
--R                               8                             8
--R                + 
--R                     +-+      4+-+
--R                  (8\|2  - 16)\|2
--R             *
--R                    %pi
--R                sin(---)
--R                     8
--R            + 
--R                   %pi 4      +-+     4+-+3    %pi 3
--R              2cos(---)  + (4\|2  - 4)\|2  cos(---)
--R                    8                           8
--R            + 
--R                    +-+      4+-+2    %pi 2       +-+      4+-+    %pi       +-+
--R              (- 12\|2  + 20)\|2  cos(---)  + (24\|2  - 32)\|2 cos(---) - 16\|2
--R                                       8                            8
--R            + 
--R              24
--R     + 
--R               +-+      4+-+    %pi
--R         (- 17\|2  + 24)\|2 cos(---)
--R                                 8
--R      *
--R         log
--R                   %pi 4     +-+4+-+3    %pi 3
--R              2sin(---)  - 2\|2 \|2  sin(---)
--R                    8                     8
--R            + 
--R                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
--R              (4cos(---)  + 2\|2 \|2  cos(---) + 4\|2  )sin(---)
--R                     8                     8                 8
--R            + 
--R                   +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
--R              (- 2\|2 \|2  cos(---)  - 4\|2  cos(---) - 2\|2 \|2 )sin(---)
--R                                8                 8                    8
--R            + 
--R                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
--R              2cos(---)  + 2\|2 \|2  cos(---)  + 4\|2  cos(---)
--R                    8                     8                 8
--R            + 
--R                +-+4+-+    %pi
--R              2\|2 \|2 cos(---) + 1
--R                            8
--R     + 
--R                                       4+-+    %pi    4+-+    %pi     +-+
--R                                       \|2 sin(---) - \|2 cos(---) + \|2
--R           +-+      4+-+    %pi                 8              8
--R       (68\|2  - 96)\|2 sin(---)atan(--------------------------------------)
--R                             8       4+-+    %pi    4+-+    %pi     +-+
--R                                     \|2 sin(---) + \|2 cos(---) - \|2  + 2
--R                                              8              8
--R     + 
--R                                       4+-+    %pi    4+-+    %pi     +-+
--R                                       \|2 sin(---) - \|2 cos(---) + \|2
--R             +-+      4+-+    %pi               8              8
--R       (- 68\|2  + 96)\|2 sin(---)atan(----------------------------------)
--R                               8           4+-+    %pi    4+-+    %pi
--R                                           \|2 sin(---) + \|2 cos(---)
--R                                                    8              8
--R     + 
--R                                     4+-+    %pi    4+-+    %pi     +-+
--R                                     \|2 sin(---) - \|2 cos(---) - \|2
--R           +-+      4+-+    %pi               8              8
--R       (68\|2  - 96)\|2 sin(---)atan(----------------------------------)
--R                             8           4+-+    %pi    4+-+    %pi
--R                                         \|2 sin(---) + \|2 cos(---)
--R                                                  8              8
--R     + 
--R                                         4+-+    %pi    4+-+    %pi     +-+
--R                                         \|2 sin(---) - \|2 cos(---) - \|2
--R             +-+      4+-+    %pi                 8              8
--R       (- 68\|2  + 96)\|2 sin(---)atan(--------------------------------------)
--R                               8       4+-+    %pi    4+-+    %pi     +-+
--R                                       \|2 sin(---) + \|2 cos(---) + \|2  - 2
--R                                                8              8
--R     + 
--R             +-+
--R       - 136\|2  + 192
--R  /
--R         +-+
--R     384\|2  - 544
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 28

--S 29 of 224
in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole")
 

   (29)
                                                                   +------+
                     3                             4            2  |sin(1)
           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
                                                                  \|cos(1)
         + 
                                       4           2      +-+
           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                                                                   +------+
                     3                             4            2  |sin(1)
           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
                                                                  \|cos(1)
         + 
                                       4           2      +-+
           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                                                                     +------+
                      3                              4            2  |sin(1)
           ((384cos(1)  + 96cos(1))sin(1) - 384cos(1)  + 480cos(1) ) |------
                                                                    \|cos(1)
         + 
                                         4            2       +-+
           (- 192cos(1)sin(1) + 384cos(1)  - 384cos(1)  - 12)\|2
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
                                                                      \|cos(1)
         + 
                                       4            2       +-+
           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
                                                                      \|cos(1)
         + 
                                       4            2       +-+
           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                          3                               5
               (- 96cos(1)  - 24cos(1))log(4) - 1024cos(1)
             + 
                                   3
               (96%pi + 1024)cos(1)  + (24%pi + 32)cos(1)
          *
             sin(1)
         + 
                    4            2                               4
           (96cos(1)  - 120cos(1) )log(4) + (- 96%pi - 512)cos(1)
         + 
                               2
           (120%pi + 512)cos(1)
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                        5            3
             (48cos(1)log(4) + 512cos(1)  - 384cos(1)  + (- 48%pi - 128)cos(1))
          *
             sin(1)
         + 
                      4           2                       6
           (- 96cos(1)  + 96cos(1)  + 3)log(4) - 512cos(1)
         + 
                               4                        2
           (96%pi + 1152)cos(1)  + (- 96%pi - 640)cos(1)  - 3%pi
      *
          +-+
         \|2
  /
                     3                                4             2  +-+
         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                      4             2
       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (29)
--R                                                                   +------+
--R                     3                             4            2  |sin(1)
--R           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                       4           2      +-+
--R           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                                                                   +------+
--R                     3                             4            2  |sin(1)
--R           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                       4           2      +-+
--R           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                                                                     +------+
--R                      3                              4            2  |sin(1)
--R           ((384cos(1)  + 96cos(1))sin(1) - 384cos(1)  + 480cos(1) ) |------
--R                                                                    \|cos(1)
--R         + 
--R                                         4            2       +-+
--R           (- 192cos(1)sin(1) + 384cos(1)  - 384cos(1)  - 12)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                       4            2       +-+
--R           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                       4            2       +-+
--R           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                          3                               5
--R               (- 96cos(1)  - 24cos(1))log(4) - 1024cos(1)
--R             + 
--R                                   3
--R               (96%pi + 1024)cos(1)  + (24%pi + 32)cos(1)
--R          *
--R             sin(1)
--R         + 
--R                    4            2                               4
--R           (96cos(1)  - 120cos(1) )log(4) + (- 96%pi - 512)cos(1)
--R         + 
--R                               2
--R           (120%pi + 512)cos(1)
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                        5            3
--R             (48cos(1)log(4) + 512cos(1)  - 384cos(1)  + (- 48%pi - 128)cos(1))
--R          *
--R             sin(1)
--R         + 
--R                      4           2                       6
--R           (- 96cos(1)  + 96cos(1)  + 3)log(4) - 512cos(1)
--R         + 
--R                               4                        2
--R           (96%pi + 1152)cos(1)  + (- 96%pi - 640)cos(1)  - 3%pi
--R      *
--R          +-+
--R         \|2
--R  /
--R                     3                                4             2  +-+
--R         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                      4             2
--R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 29

--S 30 of 224
in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole")
 

   (30)
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                                                                     +------+
                      3                              4            2  |sin(1)
           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
                                                                    \|cos(1)
         + 
                                        4            2      +-+
           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                       3                                       3
             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
          *
             sin(1)
         + 
                      4           2                    6
           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
         + 
                                 4                     2
           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                        5            3
           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
         + 
                    4           2                       6                      4
           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
         + 
                                2
           (- 32%pi - 128)cos(1)  - %pi
      *
          +-+
         \|2
  /
                     3                                4             2  +-+
         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                      4             2
       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (30)
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                                                                     +------+
--R                      3                              4            2  |sin(1)
--R           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
--R                                                                    \|cos(1)
--R         + 
--R                                        4            2      +-+
--R           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                       3                                       3
--R             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
--R          *
--R             sin(1)
--R         + 
--R                      4           2                    6
--R           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
--R         + 
--R                                 4                     2
--R           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                        5            3
--R           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
--R         + 
--R                    4           2                       6                      4
--R           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
--R         + 
--R                                2
--R           (- 32%pi - 128)cos(1)  - %pi
--R      *
--R          +-+
--R         \|2
--R  /
--R                     3                                4             2  +-+
--R         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                      4             2
--R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 30

--S 31 of 224
in1193a:=integrate(-sin(z)^2*cot(z-1), z= 0..1,"noPole")
 

   (31)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (31)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 31

--S 32 of 224
in1207:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1)
 

   (32)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (32)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 32

--S 33 of 224
in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (33)
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                                                                     +------+
                      3                              4            2  |sin(1)
           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
                                                                    \|cos(1)
         + 
                                        4            2      +-+
           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                       3                                       3
             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
          *
             sin(1)
         + 
                      4           2                    6
           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
         + 
                                 4                     2
           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                        5            3
           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
         + 
                    4           2                       6                      4
           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
         + 
                                2
           (- 32%pi - 128)cos(1)  - %pi
      *
          +-+
         \|2
  /
                     3                                4             2  +-+
         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                      4             2
       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (33)
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                                                                     +------+
--R                      3                              4            2  |sin(1)
--R           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
--R                                                                    \|cos(1)
--R         + 
--R                                        4            2      +-+
--R           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                       3                                       3
--R             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
--R          *
--R             sin(1)
--R         + 
--R                      4           2                    6
--R           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
--R         + 
--R                                 4                     2
--R           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                        5            3
--R           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
--R         + 
--R                    4           2                       6                      4
--R           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
--R         + 
--R                                2
--R           (- 32%pi - 128)cos(1)  - %pi
--R      *
--R          +-+
--R         \|2
--R  /
--R                     3                                4             2  +-+
--R         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                      4             2
--R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 33

--S 34 of 224
in1210a:=integrate(-sin(z)*cos(z)*cot(z-1), z= 0..1,"noPole")
 

   (34)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (34)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 34

--S 35 of 224
in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole")
 

   (35)
              1 2    1 2
         4cos(-) sin(-)
              2      2
      *
         log
                     1 4        1 2    1 2       1 4       2
                (sin(-)  - 2cos(-) sin(-)  + cos(-) )sin(1)
                     2          2      2         2
              + 
                      1           1 3        1 3          1
                (4cos(-)cos(1)sin(-)  - 4cos(-) cos(1)sin(-))sin(1)
                      2           2          2            2
              + 
                     1 2      2    1 2
                4cos(-) cos(1) sin(-)
                     2             2
           /
                  1 4      2        1 4             1 4
              cos(-) cos(1)  + 2cos(-) cos(1) + cos(-)
                  2                 2               2
     + 
                                1 2
                            sin(-)
              1 2    1 2        2
       - 4cos(-) sin(-) log(-------)
              2      2          1 2
                            cos(-)
                                2
     + 
                                                                2
              1 4        1 2    1 2       1 4            4cos(1)
       (- sin(-)  - 2cos(-) sin(-)  - cos(-) )log(---------------------)
              2          2      2         2             2
                                                  cos(1)  + 2cos(1) + 1
     + 
            1 4        1 2    1 2       1 4               4
       (sin(-)  - 2cos(-) sin(-)  + cos(-) )log(---------------------)
            2          2      2         2             2
                                                cos(1)  + 2cos(1) + 1
     + 
              1     1 3        1 3    1
       - 4cos(-)sin(-)  + 4cos(-) sin(-)
              2     2          2      2
  /
          1 4        1 4
     2sin(-)  - 2cos(-)
          2          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (35)
--R              1 2    1 2
--R         4cos(-) sin(-)
--R              2      2
--R      *
--R         log
--R                     1 4        1 2    1 2       1 4       2
--R                (sin(-)  - 2cos(-) sin(-)  + cos(-) )sin(1)
--R                     2          2      2         2
--R              + 
--R                      1           1 3        1 3          1
--R                (4cos(-)cos(1)sin(-)  - 4cos(-) cos(1)sin(-))sin(1)
--R                      2           2          2            2
--R              + 
--R                     1 2      2    1 2
--R                4cos(-) cos(1) sin(-)
--R                     2             2
--R           /
--R                  1 4      2        1 4             1 4
--R              cos(-) cos(1)  + 2cos(-) cos(1) + cos(-)
--R                  2                 2               2
--R     + 
--R                                1 2
--R                            sin(-)
--R              1 2    1 2        2
--R       - 4cos(-) sin(-) log(-------)
--R              2      2          1 2
--R                            cos(-)
--R                                2
--R     + 
--R                                                                2
--R              1 4        1 2    1 2       1 4            4cos(1)
--R       (- sin(-)  - 2cos(-) sin(-)  - cos(-) )log(---------------------)
--R              2          2      2         2             2
--R                                                  cos(1)  + 2cos(1) + 1
--R     + 
--R            1 4        1 2    1 2       1 4               4
--R       (sin(-)  - 2cos(-) sin(-)  + cos(-) )log(---------------------)
--R            2          2      2         2             2
--R                                                cos(1)  + 2cos(1) + 1
--R     + 
--R              1     1 3        1 3    1
--R       - 4cos(-)sin(-)  + 4cos(-) sin(-)
--R              2     2          2      2
--R  /
--R          1 4        1 4
--R     2sin(-)  - 2cos(-)
--R          2          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 35

--S 36 of 224
in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (36)
                  +------+
                  |sin(1)                        +-+
         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
                 \|cos(1)
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                  +------+
                  |sin(1)                        +-+
         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
                 \|cos(1)
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                    +------+
                    |sin(1)                        +-+
         (- 8cos(1) |------  + (4sin(1) + 4cos(1))\|2 )
                   \|cos(1)
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                  +------+
                  |sin(1)                          +-+
         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
                 \|cos(1)
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                  +------+
                  |sin(1)                          +-+
         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
                 \|cos(1)
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                                                          +------+
                                                          |sin(1)
       (- 32sin(1) - 2cos(1)log(4) + (- 2%pi - 32)cos(1)) |------
                                                         \|cos(1)
     + 
                                                               +-+
       ((log(4) + %pi + 32)sin(1) + cos(1)log(4) + %pi cos(1))\|2
  /
                  +------+
              +-+ |sin(1)
     16cos(1)\|2  |------  - 16sin(1) - 16cos(1)
                 \|cos(1)
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (36)
--R                  +------+
--R                  |sin(1)                        +-+
--R         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                  +------+
--R                  |sin(1)                        +-+
--R         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                    +------+
--R                    |sin(1)                        +-+
--R         (- 8cos(1) |------  + (4sin(1) + 4cos(1))\|2 )
--R                   \|cos(1)
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                  +------+
--R                  |sin(1)                          +-+
--R         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                  +------+
--R                  |sin(1)                          +-+
--R         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                                                          +------+
--R                                                          |sin(1)
--R       (- 32sin(1) - 2cos(1)log(4) + (- 2%pi - 32)cos(1)) |------
--R                                                         \|cos(1)
--R     + 
--R                                                               +-+
--R       ((log(4) + %pi + 32)sin(1) + cos(1)log(4) + %pi cos(1))\|2
--R  /
--R                  +------+
--R              +-+ |sin(1)
--R     16cos(1)\|2  |------  - 16sin(1) - 16cos(1)
--R                 \|cos(1)
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 36

--S 37 of 224
in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole")
 

   (37)
           +-+
         2\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                               +------+
                               |sin(1)                            2      +-+
                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
         +-+                  \|cos(1)
       4\|2 atan(-----------------------------------------------------------)
                               +------+
                             2 |sin(1)                            2  +-+
                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                              \|cos(1)
     + 
       -
              +-+
            4\|2
         *
                               +------+
                               |sin(1)                              2      +-+
                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                              \|cos(1)
            atan(-------------------------------------------------------------)
                             +------+
                           2 |sin(1)                              2      +-+
                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                            \|cos(1)
     + 
                                 +------+
                                 |sin(1)                            2  +-+
                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
           +-+                  \|cos(1)
       - 4\|2 atan(-------------------------------------------------------)
                             +------+
                           2 |sin(1)                            2      +-+
                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                            \|cos(1)
     + 
           +-+
       %pi\|2
  /
     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (37)
--R           +-+
--R         2\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                               +------+
--R                               |sin(1)                            2      +-+
--R                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R         +-+                  \|cos(1)
--R       4\|2 atan(-----------------------------------------------------------)
--R                               +------+
--R                             2 |sin(1)                            2  +-+
--R                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                              \|cos(1)
--R     + 
--R       -
--R              +-+
--R            4\|2
--R         *
--R                               +------+
--R                               |sin(1)                              2      +-+
--R                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                              \|cos(1)
--R            atan(-------------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                              2      +-+
--R                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R                                 +------+
--R                                 |sin(1)                            2  +-+
--R                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R           +-+                  \|cos(1)
--R       - 4\|2 atan(-------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                            2      +-+
--R                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R           +-+
--R       %pi\|2
--R  /
--R     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 37

--S 38 of 224
in1a:=integrate(log(abs(z^2-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 

   (38)  1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (38)  1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 38

--S 39 of 224
in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole")
 

   (39)
              %pi
         6cos(---)
               9
      *
         log
                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
                  2sin(---)  + 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
                        9                9       9            9        9
                + 
                    +-+    %pi 3    %pi 3           %pi 4          %pi 2
                  8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
                            9        9               9              9
                + 
                     +-+    %pi 5      +-+    %pi      %pi         %pi 6
                  (4\|3 cos(---)  + 4a\|3 cos(---))sin(---) - 2cos(---)
                             9                 9        9           9
                + 
                           %pi 2
                  - 2a cos(---)
                            9
             *
                 +-+
                \|a
            + 
                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
                   9            9        9             9              9
            + 
                 +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
              4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
                         9       9             9               9         9
            + 
                   +-+    %pi 3    %pi        %pi 8          %pi 4    2
              - 4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
                           9        9          9              9
     + 
              +-+    %pi         %pi
         (- 3\|3 sin(---) - 3cos(---))
                      9           9
      *
         log
                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
                  2sin(---)  - 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
                        9                9       9            9        9
                + 
                      +-+    %pi 3    %pi 3           %pi 4          %pi 2
                  - 8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
                              9        9               9              9
                + 
                       +-+    %pi 5      +-+    %pi      %pi         %pi 6
                  (- 4\|3 cos(---)  - 4a\|3 cos(---))sin(---) - 2cos(---)
                               9                 9        9           9
                + 
                           %pi 2
                  - 2a cos(---)
                            9
             *
                 +-+
                \|a
            + 
                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
                   9            9        9             9              9
            + 
                   +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
              - 4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
                           9       9             9               9         9
            + 
                 +-+    %pi 3    %pi        %pi 8          %pi 4    2
              4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
                         9        9          9              9
     + 
                5 +-+    10               +-+
       6a log(2a \|a  + a   + a) - 12log(\|a  + 1)
     + 
                       +-+    2
       3log((- 2a - 2)\|a  + a  + 3a + 1)
     + 
            +-+    %pi         %pi
         (3\|3 sin(---) - 3cos(---))
                    9           9
      *
         log
                         %pi 6        %pi 2    %pi 4
                  - 4sin(---)  - 4cos(---) sin(---)
                          9            9        9
                + 
                        %pi 4          %pi 2        %pi 6          %pi 2
                  (4cos(---)  - 4a)sin(---)  + 4cos(---)  + 4a cos(---)
                         9              9            9              9
             *
                 +-+
                \|a
            + 
                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 6a)sin(---)
                   9            9        9             9              9
            + 
                  %pi 6          %pi 2     %pi 2       %pi 8          %pi 4    2
            (4cos(---)  - 4a cos(---) )sin(---)  + cos(---)  + 6a cos(---)  + a
                   9              9         9           9              9
     + 
                %pi       +-+    %pi
         (12sin(---) - 12\|3 cos(---))
                 9                9
      *
               +-+    %pi 2        %pi     %pi     +-+    %pi 2
              \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
                       9            9       9              9
         atan(-------------------------------------------------)
                    %pi 2     +-+    %pi     %pi        %pi 2
                sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
                     9                9       9          9
     + 
                   +-+ +-+    +-+
         +-+     2\|3 \|a  - \|3
       6\|3 atan(----------------)
                    +-+
                  2\|a  - 2a + 1
     + 
                       +-+    %pi 2        %pi     %pi     +-+    %pi 2
                      \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
             %pi               9            9       9              9
       24sin(---)atan(-------------------------------------------------)
              9             %pi 2     +-+    %pi     %pi        %pi 2
                        sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
                             9                9       9          9
     + 
                                                %pi     %pi
                                           2cos(---)sin(---)
              %pi       +-+    %pi               9       9
       (12sin(---) + 12\|3 cos(---))atan(---------------------)
               9                9            %pi 2       %pi 2
                                         sin(---)  - cos(---)
                                              9           9
     + 
                  %pi       +-+    %pi
         (- 12sin(---) + 12\|3 cos(---))
                   9                9
      *
                 +-+    %pi 2        %pi     %pi     +-+    %pi 2
                \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
                         9            9       9              9
         atan(-----------------------------------------------------)
                +-+       %pi 2     +-+    %pi     %pi        %pi 2
              2\|a  + sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
                           9                9       9          9
     + 
                           +-+    %pi 2        %pi     %pi     +-+    %pi 2
                          \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
               %pi                 9            9       9              9
       - 24sin(---)atan(-----------------------------------------------------)
                9         +-+       %pi 2     +-+    %pi     %pi        %pi 2
                        2\|a  + sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
                                     9                9       9          9
     + 
                                                    %pi     %pi
                                               2cos(---)sin(---)
              %pi       +-+    %pi                   9       9
       (12sin(---) + 12\|3 cos(---))atan(----------------------------)
               9                9         +-+       %pi 2       %pi 2
                                         \|a  - sin(---)  + cos(---)
                                                     9           9
     + 
            +-+
       2%pi\|3  - 60a
  /
     12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (39)
--R              %pi
--R         6cos(---)
--R               9
--R      *
--R         log
--R                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
--R                  2sin(---)  + 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
--R                        9                9       9            9        9
--R                + 
--R                    +-+    %pi 3    %pi 3           %pi 4          %pi 2
--R                  8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
--R                            9        9               9              9
--R                + 
--R                     +-+    %pi 5      +-+    %pi      %pi         %pi 6
--R                  (4\|3 cos(---)  + 4a\|3 cos(---))sin(---) - 2cos(---)
--R                             9                 9        9           9
--R                + 
--R                           %pi 2
--R                  - 2a cos(---)
--R                            9
--R             *
--R                 +-+
--R                \|a
--R            + 
--R                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
--R              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
--R                   9            9        9             9              9
--R            + 
--R                 +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
--R              4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
--R                         9       9             9               9         9
--R            + 
--R                   +-+    %pi 3    %pi        %pi 8          %pi 4    2
--R              - 4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
--R                           9        9          9              9
--R     + 
--R              +-+    %pi         %pi
--R         (- 3\|3 sin(---) - 3cos(---))
--R                      9           9
--R      *
--R         log
--R                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
--R                  2sin(---)  - 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
--R                        9                9       9            9        9
--R                + 
--R                      +-+    %pi 3    %pi 3           %pi 4          %pi 2
--R                  - 8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
--R                              9        9               9              9
--R                + 
--R                       +-+    %pi 5      +-+    %pi      %pi         %pi 6
--R                  (- 4\|3 cos(---)  - 4a\|3 cos(---))sin(---) - 2cos(---)
--R                               9                 9        9           9
--R                + 
--R                           %pi 2
--R                  - 2a cos(---)
--R                            9
--R             *
--R                 +-+
--R                \|a
--R            + 
--R                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
--R              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
--R                   9            9        9             9              9
--R            + 
--R                   +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
--R              - 4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
--R                           9       9             9               9         9
--R            + 
--R                 +-+    %pi 3    %pi        %pi 8          %pi 4    2
--R              4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
--R                         9        9          9              9
--R     + 
--R                5 +-+    10               +-+
--R       6a log(2a \|a  + a   + a) - 12log(\|a  + 1)
--R     + 
--R                       +-+    2
--R       3log((- 2a - 2)\|a  + a  + 3a + 1)
--R     + 
--R            +-+    %pi         %pi
--R         (3\|3 sin(---) - 3cos(---))
--R                    9           9
--R      *
--R         log
--R                         %pi 6        %pi 2    %pi 4
--R                  - 4sin(---)  - 4cos(---) sin(---)
--R                          9            9        9
--R                + 
--R                        %pi 4          %pi 2        %pi 6          %pi 2
--R                  (4cos(---)  - 4a)sin(---)  + 4cos(---)  + 4a cos(---)
--R                         9              9            9              9
--R             *
--R                 +-+
--R                \|a
--R            + 
--R                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
--R              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 6a)sin(---)
--R                   9            9        9             9              9
--R            + 
--R                  %pi 6          %pi 2     %pi 2       %pi 8          %pi 4    2
--R            (4cos(---)  - 4a cos(---) )sin(---)  + cos(---)  + 6a cos(---)  + a
--R                   9              9         9           9              9
--R     + 
--R                %pi       +-+    %pi
--R         (12sin(---) - 12\|3 cos(---))
--R                 9                9
--R      *
--R               +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R              \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
--R                       9            9       9              9
--R         atan(-------------------------------------------------)
--R                    %pi 2     +-+    %pi     %pi        %pi 2
--R                sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
--R                     9                9       9          9
--R     + 
--R                   +-+ +-+    +-+
--R         +-+     2\|3 \|a  - \|3
--R       6\|3 atan(----------------)
--R                    +-+
--R                  2\|a  - 2a + 1
--R     + 
--R                       +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R                      \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
--R             %pi               9            9       9              9
--R       24sin(---)atan(-------------------------------------------------)
--R              9             %pi 2     +-+    %pi     %pi        %pi 2
--R                        sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
--R                             9                9       9          9
--R     + 
--R                                                %pi     %pi
--R                                           2cos(---)sin(---)
--R              %pi       +-+    %pi               9       9
--R       (12sin(---) + 12\|3 cos(---))atan(---------------------)
--R               9                9            %pi 2       %pi 2
--R                                         sin(---)  - cos(---)
--R                                              9           9
--R     + 
--R                  %pi       +-+    %pi
--R         (- 12sin(---) + 12\|3 cos(---))
--R                   9                9
--R      *
--R                 +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R                \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
--R                         9            9       9              9
--R         atan(-----------------------------------------------------)
--R                +-+       %pi 2     +-+    %pi     %pi        %pi 2
--R              2\|a  + sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
--R                           9                9       9          9
--R     + 
--R                           +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R                          \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
--R               %pi                 9            9       9              9
--R       - 24sin(---)atan(-----------------------------------------------------)
--R                9         +-+       %pi 2     +-+    %pi     %pi        %pi 2
--R                        2\|a  + sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
--R                                     9                9       9          9
--R     + 
--R                                                    %pi     %pi
--R                                               2cos(---)sin(---)
--R              %pi       +-+    %pi                   9       9
--R       (12sin(---) + 12\|3 cos(---))atan(----------------------------)
--R               9                9         +-+       %pi 2       %pi 2
--R                                         \|a  - sin(---)  + cos(---)
--R                                                     9           9
--R     + 
--R            +-+
--R       2%pi\|3  - 60a
--R  /
--R     12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 39

--S 40 of 224
in20a:=integrate(log(sin(z)^2+cos(z)^2), z= 0..1,"noPole")
 

   (40)  0
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (40)  0
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 40

--S 41 of 224
in126a:=integrate(atan(1/cot(z)), z= 0..2*%pi,"noPole")
 

             2
   (41)  2%pi
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R             2
--R   (41)  2%pi
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 41

--S 42 of 224
in128a:=integrate(atan(sqrt(1-cos(z)^2)/(1+cos(z))), z= 0..1,"noPole")
 

         1
   (42)  -
         4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         1
--R   (42)  -
--R         4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 42

--S 43 of 224
in134a:=integrate(log(exp(z)), z= -%i..%i)
 

   (43)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (43)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 43

--S 44 of 224
in1221a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole")
 

         log(4)
   (44)  ------
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(4)
--R   (44)  ------
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 44

--S 45 of 224
in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (45)
           +-+
         2\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                               +------+
                               |sin(1)                            2      +-+
                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
         +-+                  \|cos(1)
       4\|2 atan(-----------------------------------------------------------)
                               +------+
                             2 |sin(1)                            2  +-+
                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                              \|cos(1)
     + 
       -
              +-+
            4\|2
         *
                               +------+
                               |sin(1)                              2      +-+
                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                              \|cos(1)
            atan(-------------------------------------------------------------)
                             +------+
                           2 |sin(1)                              2      +-+
                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                            \|cos(1)
     + 
                                 +------+
                                 |sin(1)                            2  +-+
                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
           +-+                  \|cos(1)
       - 4\|2 atan(-------------------------------------------------------)
                             +------+
                           2 |sin(1)                            2      +-+
                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                            \|cos(1)
     + 
           +-+
       %pi\|2
  /
     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (45)
--R           +-+
--R         2\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                               +------+
--R                               |sin(1)                            2      +-+
--R                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R         +-+                  \|cos(1)
--R       4\|2 atan(-----------------------------------------------------------)
--R                               +------+
--R                             2 |sin(1)                            2  +-+
--R                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                              \|cos(1)
--R     + 
--R       -
--R              +-+
--R            4\|2
--R         *
--R                               +------+
--R                               |sin(1)                              2      +-+
--R                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                              \|cos(1)
--R            atan(-------------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                              2      +-+
--R                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R                                 +------+
--R                                 |sin(1)                            2  +-+
--R                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R           +-+                  \|cos(1)
--R       - 4\|2 atan(-------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                            2      +-+
--R                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R           +-+
--R       %pi\|2
--R  /
--R     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 45

--S 46 of 224
in1241a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole")
 

         log(4)
   (46)  ------
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(4)
--R   (46)  ------
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 46

--S 47 of 224
in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (47)
           +-+
         2\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                               +------+
                               |sin(1)                            2      +-+
                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
         +-+                  \|cos(1)
       4\|2 atan(-----------------------------------------------------------)
                               +------+
                             2 |sin(1)                            2  +-+
                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                              \|cos(1)
     + 
       -
              +-+
            4\|2
         *
                               +------+
                               |sin(1)                              2      +-+
                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                              \|cos(1)
            atan(-------------------------------------------------------------)
                             +------+
                           2 |sin(1)                              2      +-+
                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                            \|cos(1)
     + 
                                 +------+
                                 |sin(1)                            2  +-+
                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
           +-+                  \|cos(1)
       - 4\|2 atan(-------------------------------------------------------)
                             +------+
                           2 |sin(1)                            2      +-+
                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                            \|cos(1)
     + 
           +-+
       %pi\|2
  /
     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (47)
--R           +-+
--R         2\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                               +------+
--R                               |sin(1)                            2      +-+
--R                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R         +-+                  \|cos(1)
--R       4\|2 atan(-----------------------------------------------------------)
--R                               +------+
--R                             2 |sin(1)                            2  +-+
--R                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                              \|cos(1)
--R     + 
--R       -
--R              +-+
--R            4\|2
--R         *
--R                               +------+
--R                               |sin(1)                              2      +-+
--R                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                              \|cos(1)
--R            atan(-------------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                              2      +-+
--R                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R                                 +------+
--R                                 |sin(1)                            2  +-+
--R                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R           +-+                  \|cos(1)
--R       - 4\|2 atan(-------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                            2      +-+
--R                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R           +-+
--R       %pi\|2
--R  /
--R     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 47

--S 48 of 224
in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole")
 

   (48)
                  2         2
         (- sin(1)  + cos(1)  + 2cos(1) + 1)
      *
         log
                              2                                   2
                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
               *
                   +-+
                  \|3
              + 
                      2                                     2
              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
           /
                     2
              4sin(1)  - 4sin(1) + 1
     + 
                2         2
         (sin(1)  - cos(1)  - 2cos(1) - 1)
      *
         log
                              2                                     2
                    - 12sin(1)  + (- 42cos(1) - 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
               *
                   +-+
                  \|3
              + 
                        2                                   2
                21sin(1)  + (72cos(1) + 84)sin(1) + 63cos(1)  + 144cos(1) + 84
           /
                     2
              4sin(1)  + 4sin(1) + 1
     + 
                             +-+
       (- 4cos(1) - 4)sin(1)\|3
  /
             2          2                +-+
     (3sin(1)  - 3cos(1)  - 6cos(1) - 3)\|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (48)
--R                  2         2
--R         (- sin(1)  + cos(1)  + 2cos(1) + 1)
--R      *
--R         log
--R                              2                                   2
--R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R               *
--R                   +-+
--R                  \|3
--R              + 
--R                      2                                     2
--R              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R           /
--R                     2
--R              4sin(1)  - 4sin(1) + 1
--R     + 
--R                2         2
--R         (sin(1)  - cos(1)  - 2cos(1) - 1)
--R      *
--R         log
--R                              2                                     2
--R                    - 12sin(1)  + (- 42cos(1) - 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R               *
--R                   +-+
--R                  \|3
--R              + 
--R                        2                                   2
--R                21sin(1)  + (72cos(1) + 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R           /
--R                     2
--R              4sin(1)  + 4sin(1) + 1
--R     + 
--R                             +-+
--R       (- 4cos(1) - 4)sin(1)\|3
--R  /
--R             2          2                +-+
--R     (3sin(1)  - 3cos(1)  - 6cos(1) - 3)\|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 48

--S 49 of 224
in1273a:=integrate((1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole")
 

   (49)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (49)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 49

--S 50 of 224
in1274a:=integrate(1/(1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole")
 

   (50)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (50)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 50

--S 51 of 224
in1284a:=integrate(log(1+2^(1/2)/z^(1/4)-1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (51)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (51)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 51

--S 52 of 224
in1314a:=integrate(log(1-z)*atanh(z^(1/2)), z= 0..1,"noPole")
 

         log(16) - 6
   (52)  -----------
              2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(16) - 6
--R   (52)  -----------
--R              2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 52

--S 53 of 224
in1359a:=integrate((%i*z)^(1/2)*(-%i*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole")
 

   (53)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (53)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 53

--S 54 of 224
in1376a:=integrate(z*acoth(z^(1/2)), z= 0..1,"noPole")
 

         2
   (54)  -
         3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         2
--R   (54)  -
--R         3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 54

--S 55 of 224
in1377a:=integrate(z*acoth(1-z), z= 0..1,"noPole")
 

         log(4) - 1
   (55)  ----------
              2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(4) - 1
--R   (55)  ----------
--R              2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 55

--S 56 of 224
in1378a:=integrate(z*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole")
 

         - 3log(4) + 5
   (56)  -------------
               3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         - 3log(4) + 5
--R   (56)  -------------
--R               3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 56

--S 57 of 224
in1392a:=integrate(acoth(z^(1/2)), z= 0..1,"noPole")
 

   (57)  1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (57)  1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 57

--S 58 of 224
in1397a:=integrate(1/(-1+z^(1/2))^(1/2), z= 1..2,"noPole")
 

                     +--------+
            +-+      | +-+
         (4\|2  + 8)\|\|2  - 1
   (58)  ----------------------
                    3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                     +--------+
--R            +-+      | +-+
--R         (4\|2  + 8)\|\|2  - 1
--R   (58)  ----------------------
--R                    3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 58

--S 59 of 224
in1398a:=integrate(acoth(1/z), z= 1..2,"noPole")
 

         3log(9) - 2log(4)
   (59)  -----------------
                 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         3log(9) - 2log(4)
--R   (59)  -----------------
--R                 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 59

--S 60 of 224
in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole")
 

                 +-+
             - 2\|2  - 3      +-+
         log(-----------) + 4\|2  - 4
                +-+
              2\|2  - 3
   (60)  ----------------------------
                       4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 +-+
--R             - 2\|2  - 3      +-+
--R         log(-----------) + 4\|2  - 4
--R                +-+
--R              2\|2  - 3
--R   (60)  ----------------------------
--R                       4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 60

--S 61 of 224
in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole")
 

   (61)
         4+-+    %pi
         \|2 cos(---)
                  8
      *
         log
                   %pi 4     +-+4+-+3    %pi 3         %pi 2     4+-+2     %pi 2
              2sin(---)  + 4\|2 \|2  sin(---)  + (4cos(---)  + 12\|2  )sin(---)
                    8                     8             8                   8
            + 
                 +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
              (4\|2 \|2  cos(---)  + 8\|2 \|2 )sin(---) + 2cos(---)
                              8                     8           8
            + 
               4+-+2    %pi 2
              4\|2  cos(---)  + 4
                         8
     + 
       -
            4+-+    %pi
            \|2 cos(---)
                     8
         *
            log
                      %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
                 2sin(---)  + 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
                       8                 8             8                  8
               + 
                   4+-+3    %pi 2    4+-+     %pi         %pi 4
                 (4\|2  cos(---)  + 4\|2 )sin(---) + 2cos(---)
                             8                 8           8
               + 
                  4+-+2    %pi 2
                 2\|2  cos(---)  + 1
                            8
     + 
         4+-+    %pi
         \|2 cos(---)
                  8
      *
         log
                   %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
              2sin(---)  - 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
                    8                 8             8                  8
            + 
                  4+-+3    %pi 2    4+-+     %pi         %pi 4    4+-+2    %pi 2
              (- 4\|2  cos(---)  - 4\|2 )sin(---) + 2cos(---)  + 2\|2  cos(---)
                            8                 8           8                 8
            + 
              1
     + 
       -
            4+-+    %pi
            \|2 cos(---)
                     8
         *
            log
                      %pi 4     +-+4+-+3    %pi 3
                 2sin(---)  - 4\|2 \|2  sin(---)
                       8                     8
               + 
                       %pi 2     4+-+2     %pi 2
                 (4cos(---)  + 12\|2  )sin(---)
                        8                   8
               + 
                      +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
                 (- 4\|2 \|2  cos(---)  - 8\|2 \|2 )sin(---) + 2cos(---)
                                   8                     8           8
               + 
                  4+-+2    %pi 2
                 4\|2  cos(---)  + 4
                            8
     + 
                               4+-+    %pi
                               \|2 cos(---)
          4+-+    %pi                   8
       - 4\|2 sin(---)atan(-------------------)
                   8       4+-+    %pi     +-+
                           \|2 sin(---) - \|2
                                    8
     + 
                           4+-+    %pi                           4+-+    %pi
                           \|2 cos(---)                          \|2 cos(---)
        4+-+    %pi                 8         4+-+    %pi                 8
       4\|2 sin(---)atan(----------------) - 4\|2 sin(---)atan(----------------)
                 8       4+-+    %pi                   8       4+-+    %pi
                         \|2 sin(---) - 1                      \|2 sin(---) + 1
                                  8                                     8
     + 
                             4+-+    %pi
                             \|2 cos(---)
        4+-+    %pi                   8
       4\|2 sin(---)atan(-------------------)
                 8       4+-+    %pi     +-+
                         \|2 sin(---) + \|2
                                  8
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (61)
--R         4+-+    %pi
--R         \|2 cos(---)
--R                  8
--R      *
--R         log
--R                   %pi 4     +-+4+-+3    %pi 3         %pi 2     4+-+2     %pi 2
--R              2sin(---)  + 4\|2 \|2  sin(---)  + (4cos(---)  + 12\|2  )sin(---)
--R                    8                     8             8                   8
--R            + 
--R                 +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
--R              (4\|2 \|2  cos(---)  + 8\|2 \|2 )sin(---) + 2cos(---)
--R                              8                     8           8
--R            + 
--R               4+-+2    %pi 2
--R              4\|2  cos(---)  + 4
--R                         8
--R     + 
--R       -
--R            4+-+    %pi
--R            \|2 cos(---)
--R                     8
--R         *
--R            log
--R                      %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
--R                 2sin(---)  + 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
--R                       8                 8             8                  8
--R               + 
--R                   4+-+3    %pi 2    4+-+     %pi         %pi 4
--R                 (4\|2  cos(---)  + 4\|2 )sin(---) + 2cos(---)
--R                             8                 8           8
--R               + 
--R                  4+-+2    %pi 2
--R                 2\|2  cos(---)  + 1
--R                            8
--R     + 
--R         4+-+    %pi
--R         \|2 cos(---)
--R                  8
--R      *
--R         log
--R                   %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
--R              2sin(---)  - 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
--R                    8                 8             8                  8
--R            + 
--R                  4+-+3    %pi 2    4+-+     %pi         %pi 4    4+-+2    %pi 2
--R              (- 4\|2  cos(---)  - 4\|2 )sin(---) + 2cos(---)  + 2\|2  cos(---)
--R                            8                 8           8                 8
--R            + 
--R              1
--R     + 
--R       -
--R            4+-+    %pi
--R            \|2 cos(---)
--R                     8
--R         *
--R            log
--R                      %pi 4     +-+4+-+3    %pi 3
--R                 2sin(---)  - 4\|2 \|2  sin(---)
--R                       8                     8
--R               + 
--R                       %pi 2     4+-+2     %pi 2
--R                 (4cos(---)  + 12\|2  )sin(---)
--R                        8                   8
--R               + 
--R                      +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
--R                 (- 4\|2 \|2  cos(---)  - 8\|2 \|2 )sin(---) + 2cos(---)
--R                                   8                     8           8
--R               + 
--R                  4+-+2    %pi 2
--R                 4\|2  cos(---)  + 4
--R                            8
--R     + 
--R                               4+-+    %pi
--R                               \|2 cos(---)
--R          4+-+    %pi                   8
--R       - 4\|2 sin(---)atan(-------------------)
--R                   8       4+-+    %pi     +-+
--R                           \|2 sin(---) - \|2
--R                                    8
--R     + 
--R                           4+-+    %pi                           4+-+    %pi
--R                           \|2 cos(---)                          \|2 cos(---)
--R        4+-+    %pi                 8         4+-+    %pi                 8
--R       4\|2 sin(---)atan(----------------) - 4\|2 sin(---)atan(----------------)
--R                 8       4+-+    %pi                   8       4+-+    %pi
--R                         \|2 sin(---) - 1                      \|2 sin(---) + 1
--R                                  8                                     8
--R     + 
--R                             4+-+    %pi
--R                             \|2 cos(---)
--R        4+-+    %pi                   8
--R       4\|2 sin(---)atan(-------------------)
--R                 8       4+-+    %pi     +-+
--R                         \|2 sin(---) + \|2
--R                                  8
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 61

--S 62 of 224
in144:=integrate(1, z= %i*infinity..%plusInfinity)
 

   (62)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (62)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 62

--S 63 of 224
in146a:=integrate(csc(z), z= 1-%i..1+%i,"noPole")
 

   (63)
                            2                                      2
                 sin(1 + %i)                            sin(1 - %i)
   log(-------------------------------) - log(-------------------------------)
                  2                                      2
       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
   ---------------------------------------------------------------------------
                                        2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (63)
--R                            2                                      2
--R                 sin(1 + %i)                            sin(1 - %i)
--R   log(-------------------------------) - log(-------------------------------)
--R                  2                                      2
--R       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
--R   ---------------------------------------------------------------------------
--R                                        2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 63

--S 64 of 224
in148:=integrate(min(1,z), z= 0..2)
 

   (64)  2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (64)  2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 64

--S 65 of 224
in156a:=integrate(z^(2/3), z= 1..10,"noPole")
 

           3+--+2
         30\|10   - 3
   (65)  ------------
               5
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           3+--+2
--R         30\|10   - 3
--R   (65)  ------------
--R               5
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 65

--S 66 of 224
in1425a:=integrate(-(z^2+%i*z+3)/(z^2+%i*z+2), z= 0..%plusInfinity,"noPole")
 

   (66)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (66)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 66

--S 67 of 224
in1426a:=integrate(-%i/(1+%i*z^3)*z^3, z= 0..%plusInfinity,"noPole")
 

   (67)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (67)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 67

--S 68 of 224
in1428a:=integrate(-%i/(1+%i*z)*z, z= 0..%plusInfinity,"noPole")
 

   (68)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (68)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 68

--S 69 of 224
in1432:=integrate(-(z+%i)*(-1+1/(z+%i)), z= 0..%plusInfinity)
 

   (69)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (69)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 69

--S 70 of 224
in1434a:=integrate(-(1+(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (70)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (70)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 70

--S 71 of 224
in1440a:=integrate((1-(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (71)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (71)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 71

--S 72 of 224
in1460:=integrate(z^2+%i*z+3, z= 0..%plusInfinity)
 

   (72)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (72)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 72

--S 73 of 224
in1464a:=integrate(1+1/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (73)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (73)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 73

--S 74 of 224
in2045:=integrate(atan(1/tan(z)), z= 0..2*%pi,"noPole")
 

               2
   (74)  - 3%pi
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R               2
--R   (74)  - 3%pi
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 74

--S 75 of 224
in1502a:=integrate(log(z)^2*log(-z), z= 0..%plusInfinity,"noPole")
 

   (75)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (75)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 75

--S 76 of 224
in1512a:=integrate(log(z)*(1/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole")
 

   (76)  [ + infinity, + infinity]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (76)  [ + infinity, + infinity]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 76

--S 77 of 224
in1513a:=integrate(log(z)*(1/(z+%i))^(1/2), z= 1..%plusInfinity,"noPole")
 

   (77)  [ + infinity, + infinity]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (77)  [ + infinity, + infinity]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 77

--S 78 of 224
in1514a:=integrate(log(z)/(%i/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole")
 

   (78)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (78)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 78

--S 79 of 224
in161:=integrate((-z^2)^(1/3), z)
 

            +----+
           3|   2
         3z\|- z
   (79)  ---------
             5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +----+
--R           3|   2
--R         3z\|- z
--R   (79)  ---------
--R             5
--R                                          Type: Union(Expression Integer,...)
--E 79

--S 80 of 224
in179:=integrate(1/(1+(3*z+1)^2), z)
 

         atan(3z + 1)
   (80)  ------------
               3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         atan(3z + 1)
--R   (80)  ------------
--R               3
--R                                          Type: Union(Expression Integer,...)
--E 80

--S 81 of 224
in1636a:=integrate(-z/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (81)
   [ + infinity,

                               +------+                           +----+
           +---------+        \|1 - %i        +---------+       2\|- %i
         3\|- 4 + 4%i log(- ------------) - 3\|- 4 + 4%i atan(------------)
                             +---------+                       +---------+
                            \|- 4 + 4%i                       \|- 4 + 4%i
       + 
                     +------+             +----+
         (- 8 + 2%i)\|1 - %i  + (6 - 2%i)\|- %i
    /
       3
     ]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (81)
--R   [ + infinity,
--R
--R                               +------+                           +----+
--R           +---------+        \|1 - %i        +---------+       2\|- %i
--R         3\|- 4 + 4%i log(- ------------) - 3\|- 4 + 4%i atan(------------)
--R                             +---------+                       +---------+
--R                            \|- 4 + 4%i                       \|- 4 + 4%i
--R       + 
--R                     +------+             +----+
--R         (- 8 + 2%i)\|1 - %i  + (6 - 2%i)\|- %i
--R    /
--R       3
--R     ]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 81

--S 82 of 224
in1639a:=integrate(-z/(z-1)/(1-%i*z^2)^(1/2), z= 0..1,"noPole")
 

   (82)
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  + 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                        +------+         +-+               +----+ +------+
                    (16\|1 - %i  - 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
                  + 
                                  +----+
                    (- 16 + 16%i)\|- %i
               *
                   +------------------------+
                   |          +-+     +----+
                   |(1 + 3%i)\|2  + 2\|- %i
                   |------------------------
                   |           +-+
                  \|          \|2
              + 
                      +------+              +-+               +----+ +------+
                (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  + 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                                                 +------------------------+
                                                 |          +-+     +----+
                                +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
                   ((16 - 16%i)\|2  + 32\|- %i ) |------------------------
                                                 |           +-+
                                                \|          \|2
                 + 
                               +-+               +----+
                   (32 - 32%i)\|2  + (32 + 32%i)\|- %i
              /
                  +-+
                 \|2
     + 
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  - 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                        +------+         +-+                 +----+ +------+
                    (16\|1 - %i  - 16%i)\|2  + (- 48 + 16%i)\|- %i \|1 - %i
                  + 
                                +----+
                    (16 - 16%i)\|- %i
               *
                   +------------------------+
                   |          +-+     +----+
                   |(1 + 3%i)\|2  - 2\|- %i
                   |------------------------
                   |           +-+
                  \|          \|2
              + 
                      +------+              +-+                 +----+ +------+
                (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  - 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                                                 +------------------------+
                                                 |          +-+     +----+
                                +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
                   ((16 - 16%i)\|2  - 32\|- %i ) |------------------------
                                                 |           +-+
                                                \|          \|2
                 + 
                               +-+                 +----+
                   (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
              /
                  +-+
                 \|2
     + 
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  - 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                                                +------------------------+
                                                |          +-+     +----+
                               +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
                ((- 16 + 16%i)\|2  + 32\|- %i ) |------------------------
                                                |           +-+
                                               \|          \|2
              + 
                            +-+                 +----+
                (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  - 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                             +------+         +-+               +----+ +------+
                       (- 16\|1 - %i  + 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
                     + 
                                     +----+
                       (- 16 + 16%i)\|- %i
                  *
                      +------------------------+
                      |          +-+     +----+
                      |(1 + 3%i)\|2  - 2\|- %i
                      |------------------------
                      |           +-+
                     \|          \|2
                 + 
                       +------+              +-+                 +----+ +------+
                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
              /
                  +-+
                 \|2
     + 
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  + 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                                                +------------------------+
                                                |          +-+     +----+
                               +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
                ((- 16 + 16%i)\|2  - 32\|- %i ) |------------------------
                                                |           +-+
                                               \|          \|2
              + 
                            +-+               +----+
                (32 - 32%i)\|2  + (32 + 32%i)\|- %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  + 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                             +------+         +-+
                       (- 16\|1 - %i  + 16%i)\|2
                     + 
                                     +----+ +------+               +----+
                       (- 48 + 16%i)\|- %i \|1 - %i  + (16 - 16%i)\|- %i
                  *
                      +------------------------+
                      |          +-+     +----+
                      |(1 + 3%i)\|2  + 2\|- %i
                      |------------------------
                      |           +-+
                     \|          \|2
                 + 
                       +------+              +-+               +----+ +------+
                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
              /
                  +-+
                 \|2
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (82)
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  + 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                        +------+         +-+               +----+ +------+
--R                    (16\|1 - %i  - 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
--R                  + 
--R                                  +----+
--R                    (- 16 + 16%i)\|- %i
--R               *
--R                   +------------------------+
--R                   |          +-+     +----+
--R                   |(1 + 3%i)\|2  + 2\|- %i
--R                   |------------------------
--R                   |           +-+
--R                  \|          \|2
--R              + 
--R                      +------+              +-+               +----+ +------+
--R                (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  + 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                                                 +------------------------+
--R                                                 |          +-+     +----+
--R                                +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
--R                   ((16 - 16%i)\|2  + 32\|- %i ) |------------------------
--R                                                 |           +-+
--R                                                \|          \|2
--R                 + 
--R                               +-+               +----+
--R                   (32 - 32%i)\|2  + (32 + 32%i)\|- %i
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  - 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                        +------+         +-+                 +----+ +------+
--R                    (16\|1 - %i  - 16%i)\|2  + (- 48 + 16%i)\|- %i \|1 - %i
--R                  + 
--R                                +----+
--R                    (16 - 16%i)\|- %i
--R               *
--R                   +------------------------+
--R                   |          +-+     +----+
--R                   |(1 + 3%i)\|2  - 2\|- %i
--R                   |------------------------
--R                   |           +-+
--R                  \|          \|2
--R              + 
--R                      +------+              +-+                 +----+ +------+
--R                (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  - 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                                                 +------------------------+
--R                                                 |          +-+     +----+
--R                                +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
--R                   ((16 - 16%i)\|2  - 32\|- %i ) |------------------------
--R                                                 |           +-+
--R                                                \|          \|2
--R                 + 
--R                               +-+                 +----+
--R                   (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  - 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                                                +------------------------+
--R                                                |          +-+     +----+
--R                               +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
--R                ((- 16 + 16%i)\|2  + 32\|- %i ) |------------------------
--R                                                |           +-+
--R                                               \|          \|2
--R              + 
--R                            +-+                 +----+
--R                (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  - 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                             +------+         +-+               +----+ +------+
--R                       (- 16\|1 - %i  + 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
--R                     + 
--R                                     +----+
--R                       (- 16 + 16%i)\|- %i
--R                  *
--R                      +------------------------+
--R                      |          +-+     +----+
--R                      |(1 + 3%i)\|2  - 2\|- %i
--R                      |------------------------
--R                      |           +-+
--R                     \|          \|2
--R                 + 
--R                       +------+              +-+                 +----+ +------+
--R                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  + 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                                                +------------------------+
--R                                                |          +-+     +----+
--R                               +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
--R                ((- 16 + 16%i)\|2  - 32\|- %i ) |------------------------
--R                                                |           +-+
--R                                               \|          \|2
--R              + 
--R                            +-+               +----+
--R                (32 - 32%i)\|2  + (32 + 32%i)\|- %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  + 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                             +------+         +-+
--R                       (- 16\|1 - %i  + 16%i)\|2
--R                     + 
--R                                     +----+ +------+               +----+
--R                       (- 48 + 16%i)\|- %i \|1 - %i  + (16 - 16%i)\|- %i
--R                  *
--R                      +------------------------+
--R                      |          +-+     +----+
--R                      |(1 + 3%i)\|2  + 2\|- %i
--R                      |------------------------
--R                      |           +-+
--R                     \|          \|2
--R                 + 
--R                       +------+              +-+               +----+ +------+
--R                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
--R              /
--R                  +-+
--R                 \|2
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 82

--S 83 of 224
in1712a:=integrate(-log(-z)*(-%i*z)^(1/2), z= 0..1,"noPole")
 

           +----+
         4\|- %i
   (83)  --------
             9
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R           +----+
--R         4\|- %i
--R   (83)  --------
--R             9
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 83

--S 84 of 224
in1720a:=integrate(-z^2/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (84)
            +------+              +------+
            |   1                 |   1    +------+
       - %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
           \|1 + %i              \|1 + %i
     + 
        +------+              +------+
        |  %i                 |  %i    +------+
        |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
       \|1 + %i              \|1 + %i
     + 
          +------+                     +------+
          |   1                 +----+ |   1
       %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
         \|1 + %i                     \|1 + %i
     + 
          +------+              +------+
          |  %i                 |  %i    +----+
       -  |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
         \|1 + %i              \|1 + %i
     + 
        +------+                +------+
        |  %i                   |  %i    +----+
        |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
       \|1 + %i                \|1 + %i
     + 
            +------+                       +------+
            |   1                   +----+ |   1
       - %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
           \|1 + %i                       \|1 + %i
     + 
          +------+                +------+
          |  %i                   |  %i    +------+
       -  |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
         \|1 + %i                \|1 + %i
     + 
        +------+                +------+
        |   1                   |   1    +------+            +------+     +----+
     %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i) - 8\|1 - %i  + 8\|- %i
       \|1 + %i                \|1 + %i
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (84)
--R            +------+              +------+
--R            |   1                 |   1    +------+
--R       - %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
--R           \|1 + %i              \|1 + %i
--R     + 
--R        +------+              +------+
--R        |  %i                 |  %i    +------+
--R        |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
--R       \|1 + %i              \|1 + %i
--R     + 
--R          +------+                     +------+
--R          |   1                 +----+ |   1
--R       %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
--R         \|1 + %i                     \|1 + %i
--R     + 
--R          +------+              +------+
--R          |  %i                 |  %i    +----+
--R       -  |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
--R         \|1 + %i              \|1 + %i
--R     + 
--R        +------+                +------+
--R        |  %i                   |  %i    +----+
--R        |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
--R       \|1 + %i                \|1 + %i
--R     + 
--R            +------+                       +------+
--R            |   1                   +----+ |   1
--R       - %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
--R           \|1 + %i                       \|1 + %i
--R     + 
--R          +------+                +------+
--R          |  %i                   |  %i    +------+
--R       -  |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
--R         \|1 + %i                \|1 + %i
--R     + 
--R        +------+                +------+
--R        |   1                   |   1    +------+            +------+     +----+
--R     %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i) - 8\|1 - %i  + 8\|- %i
--R       \|1 + %i                \|1 + %i
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 84

--S 85 of 224
in1721a:=integrate(-z^2/(z^2-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (85)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (85)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 85

--S 86 of 224
in1723a:=integrate(-z^2/(z^2-1)*(1+%i/z)^(1/2), z= 0..1,"noPole")
 

   (86)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (86)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 86

--S 87 of 224
in1731:=integrate(-log(1-z^2)*atanh(z), z= 0..1)
 

                 2
         - log(4)  + 4log(4)
   (87)  -------------------
                  4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 2
--R         - log(4)  + 4log(4)
--R   (87)  -------------------
--R                  4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 87

--S 88 of 224
in1793a:=integrate((1-z^(1/2))^(1/2)*acoth(z^(1/2)), z= 0..1,"noPole")
 

             +-+       +-+
         - 2\|2 log(12\|2  + 17) + 16
   (88)  ----------------------------
                      15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R             +-+       +-+
--R         - 2\|2 log(12\|2  + 17) + 16
--R   (88)  ----------------------------
--R                      15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 88

--S 89 of 224
in1794a:=integrate((1-z^(1/2))^(1/2)*acoth(1-z^(1/2)), z= 0..1,"noPole")
 

         - 4log(2) - 8%pi + 32
   (89)  ---------------------
                   15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         - 4log(2) - 8%pi + 32
--R   (89)  ---------------------
--R                   15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 89

--S 90 of 224
in1796a:=integrate((1+(1-z)^(1/2))^(1/2), z= 0..1,"noPole")
 

           +-+
         8\|2  + 8
   (90)  ---------
             15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           +-+
--R         8\|2  + 8
--R   (90)  ---------
--R             15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 90

--S 91 of 224
in184:=integrate(exp(%i*z), z= %i..2*%i)
 

              2
         %i %e  - %i %e
   (91)  --------------
                  2
             %e %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              2
--R         %i %e  - %i %e
--R   (91)  --------------
--R                  2
--R             %e %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 91

--S 92 of 224
in184a:=integrate(exp(%i*z), z= %i..2*%i)
 

              2
         %i %e  - %i %e
   (92)  --------------
                  2
             %e %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              2
--R         %i %e  - %i %e
--R   (92)  --------------
--R                  2
--R             %e %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 92

--S 93 of 224
in187a:=integrate(2^log(z), z= -%i..%i,"noPole")
 

              log(%i)log(2)        log(- %i)log(2)
         %i %e              + %i %e
   (93)  -----------------------------------------
                         log(2) + 1
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              log(%i)log(2)        log(- %i)log(2)
--R         %i %e              + %i %e
--R   (93)  -----------------------------------------
--R                         log(2) + 1
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 93

--S 94 of 224
in187a:=integrate(2^log(z), z= -%i..%i,"noPole")
 

              log(%i)log(2)        log(- %i)log(2)
         %i %e              + %i %e
   (94)  -----------------------------------------
                         log(2) + 1
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              log(%i)log(2)        log(- %i)log(2)
--R         %i %e              + %i %e
--R   (94)  -----------------------------------------
--R                         log(2) + 1
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 94

--S 95 of 224
in194a:=integrate(sqrt(z^2), z= 1..2,"noPole")
 

         3
   (95)  -
         2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         3
--R   (95)  -
--R         2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 95

--S 96 of 224
in1854a:=integrate(1/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (96)
   [ + infinity,

                              +------+                          +----+
          +---------+        \|1 - %i       +---------+       2\|- %i
       - \|- 4 + 4%i log(- ------------) + \|- 4 + 4%i atan(------------)
                            +---------+                      +---------+
                           \|- 4 + 4%i                      \|- 4 + 4%i
     + 
         +------+     +----+
       2\|1 - %i  - 2\|- %i
     ]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (96)
--R   [ + infinity,
--R
--R                              +------+                          +----+
--R          +---------+        \|1 - %i       +---------+       2\|- %i
--R       - \|- 4 + 4%i log(- ------------) + \|- 4 + 4%i atan(------------)
--R                            +---------+                      +---------+
--R                           \|- 4 + 4%i                      \|- 4 + 4%i
--R     + 
--R         +------+     +----+
--R       2\|1 - %i  - 2\|- %i
--R     ]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 96

--S 97 of 224
in1856a:=integrate(1/(z-1)/(1-%i*z)^(1/2), z= 0..1,"noPole")
 

   (97)
   [ + infinity,
                                +------+
       +---------+           %i\|1 - %i          +---------+        1 + %i
    - \|- 2 - 2%i log(- --------------------) + \|- 2 - 2%i atan(------------)]
                                 +---------+                      +---------+
                        (1 + %i)\|- 2 - 2%i                      \|- 2 - 2%i
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (97)
--R   [ + infinity,
--R                                +------+
--R       +---------+           %i\|1 - %i          +---------+        1 + %i
--R    - \|- 2 - 2%i log(- --------------------) + \|- 2 - 2%i atan(------------)]
--R                                 +---------+                      +---------+
--R                        (1 + %i)\|- 2 - 2%i                      \|- 2 - 2%i
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 97

--S 98 of 224
in1863a:=integrate(1/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (98)
          +------+              +------+
          |   1                 |   1    +------+
       %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
         \|1 + %i              \|1 + %i
     + 
          +------+              +------+
          |  %i                 |  %i    +------+
       -  |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
         \|1 + %i              \|1 + %i
     + 
            +------+                     +------+
            |   1                 +----+ |   1
       - %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
           \|1 + %i                     \|1 + %i
     + 
        +------+              +------+
        |  %i                 |  %i    +----+
        |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
       \|1 + %i              \|1 + %i
     + 
          +------+                +------+
          |  %i                   |  %i    +----+
       -  |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
         \|1 + %i                \|1 + %i
     + 
          +------+                       +------+
          |   1                   +----+ |   1
       %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
         \|1 + %i                       \|1 + %i
     + 
        +------+                +------+
        |  %i                   |  %i    +------+
        |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
       \|1 + %i                \|1 + %i
     + 
            +------+                +------+
            |   1                   |   1    +------+
       - %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i)
           \|1 + %i                \|1 + %i
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (98)
--R          +------+              +------+
--R          |   1                 |   1    +------+
--R       %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
--R         \|1 + %i              \|1 + %i
--R     + 
--R          +------+              +------+
--R          |  %i                 |  %i    +------+
--R       -  |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
--R         \|1 + %i              \|1 + %i
--R     + 
--R            +------+                     +------+
--R            |   1                 +----+ |   1
--R       - %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
--R           \|1 + %i                     \|1 + %i
--R     + 
--R        +------+              +------+
--R        |  %i                 |  %i    +----+
--R        |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
--R       \|1 + %i              \|1 + %i
--R     + 
--R          +------+                +------+
--R          |  %i                   |  %i    +----+
--R       -  |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
--R         \|1 + %i                \|1 + %i
--R     + 
--R          +------+                       +------+
--R          |   1                   +----+ |   1
--R       %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
--R         \|1 + %i                       \|1 + %i
--R     + 
--R        +------+                +------+
--R        |  %i                   |  %i    +------+
--R        |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
--R       \|1 + %i                \|1 + %i
--R     + 
--R            +------+                +------+
--R            |   1                   |   1    +------+
--R       - %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i)
--R           \|1 + %i                \|1 + %i
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 98

--S 99 of 224
in1864a:=integrate(1/(z^2-1)*((1+z)/(z-1))^(1/3), z= 0..1,"noPole")
 

   (99)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (99)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 99

--S 100 of 224
in1866a:=integrate(1/(z^2-1)*(1-%i/z)^(1/2), z= 0..1,"noPole")
 

   (100)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (100)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 100

--S 101 of 224
in1870a:=integrate(1/(z^2-1)/(1+(%i*z)^(1/2))^(1/2), z= 0..1,"noPole")
 

   (101)
       -
             +-------------------+
             |    +---------+
             |    |  +-+
             |    |3\|2  + 4
             |4%i |---------  + 1
             |    |     +-+
            \|   \|  16\|2
         *
            log
                                    +---------+
                                    |  +-+                 +---------+
                          +-+       |3\|2  + 4        +-+  | +--+
                     ((48\|2  - 64) |---------  - 4%i\|2 )\|\|%i  + 1
                                    |     +-+
                                   \|  16\|2
                  *
                      +-------------------+
                      |    +---------+
                      |    |  +-+
                      |    |3\|2  + 4
                      |4%i |---------  + 1
                      |    |     +-+
                     \|   \|  16\|2
                 + 
                                       +---------+
                                       |  +-+
                           +-+         |3\|2  + 4       +--+      +-+
                   (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                       |     +-+
                                      \|  16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |    +---------+
          |    |  +-+
          |    |3\|2  + 4
          |4%i |---------  + 1
          |    |     +-+
         \|   \|  16\|2
      *
         log
                                                      +-------------------+
                               +---------+            |    +---------+
                               |  +-+                 |    |  +-+
                     +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
                ((48\|2  - 64) |---------  - 4%i\|2 ) |4%i |---------  + 1
                               |     +-+              |    |     +-+
                              \|  16\|2              \|   \|  16\|2
              + 
                                    +---------+
                                    |  +-+
                        +-+         |3\|2  + 4      +-+
                (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
                                    |     +-+
                                   \|  16\|2
           /
               +-+
              \|2
     + 
       -
             +-------------------+
             |  +-----------+
             |  |    +-+
             |  |- 3\|2  + 4
             |4 |-----------  + 1
             |  |      +-+
            \| \|   16\|2
         *
            log
                                        +-----------+
                                        |    +-+                 +---------+
                            +-+         |- 3\|2  + 4        +-+  | +--+
                     ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
                                        |      +-+
                                       \|   16\|2
                  *
                      +-------------------+
                      |  +-----------+
                      |  |    +-+
                      |  |- 3\|2  + 4
                      |4 |-----------  + 1
                      |  |      +-+
                     \| \|   16\|2
                 + 
                                   +-----------+
                                   |    +-+
                         +-+       |- 3\|2  + 4       +--+      +-+
                   (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
                                   |      +-+
                                  \|   16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |  +-----------+
          |  |    +-+
          |  |- 3\|2  + 4
          |4 |-----------  + 1
          |  |      +-+
         \| \|   16\|2
      *
         log
                                     +-----------+
                                     |    +-+
                         +-+         |- 3\|2  + 4        +-+
                  ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )
                                     |      +-+
                                    \|   16\|2
               *
                   +-------------------+
                   |  +-----------+
                   |  |    +-+
                   |  |- 3\|2  + 4
                   |4 |-----------  + 1
                   |  |      +-+
                  \| \|   16\|2
              + 
                                +-----------+
                                |    +-+
                      +-+       |- 3\|2  + 4      +-+
                (- 16\|2  - 16) |-----------  + 8\|2  + 4
                                |      +-+
                               \|   16\|2
           /
               +-+
              \|2
     + 
          +---------------------+
          |    +-----------+
          |    |    +-+
          |    |- 3\|2  + 4
          |- 4 |-----------  + 1
          |    |      +-+
         \|   \|   16\|2
      *
         log
                                     +-----------+
                                     |    +-+                 +---------+
                         +-+         |- 3\|2  + 4        +-+  | +--+
                  ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
                                     |      +-+
                                    \|   16\|2
               *
                   +---------------------+
                   |    +-----------+
                   |    |    +-+
                   |    |- 3\|2  + 4
                   |- 4 |-----------  + 1
                   |    |      +-+
                  \|   \|   16\|2
              + 
                              +-----------+
                              |    +-+
                    +-+       |- 3\|2  + 4       +--+      +-+
                (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
                              |      +-+
                             \|   16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |    +-----------+
             |    |    +-+
             |    |- 3\|2  + 4
             |- 4 |-----------  + 1
             |    |      +-+
            \|   \|   16\|2
         *
            log
                                        +-----------+
                                        |    +-+
                            +-+         |- 3\|2  + 4        +-+
                     ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )
                                        |      +-+
                                       \|   16\|2
                  *
                      +---------------------+
                      |    +-----------+
                      |    |    +-+
                      |    |- 3\|2  + 4
                      |- 4 |-----------  + 1
                      |    |      +-+
                     \|   \|   16\|2
                 + 
                                 +-----------+
                                 |    +-+
                       +-+       |- 3\|2  + 4      +-+
                   (16\|2  + 16) |-----------  + 8\|2  + 4
                                 |      +-+
                                \|   16\|2
              /
                  +-+
                 \|2
     + 
          +---------------------+
          |      +---------+
          |      |  +-+
          |      |3\|2  + 4
          |- 4%i |---------  + 1
          |      |     +-+
         \|     \|  16\|2
      *
         log
                                 +---------+
                                 |  +-+                 +---------+
                       +-+       |3\|2  + 4        +-+  | +--+
                  ((48\|2  - 64) |---------  + 4%i\|2 )\|\|%i  + 1
                                 |     +-+
                                \|  16\|2
               *
                   +---------------------+
                   |      +---------+
                   |      |  +-+
                   |      |3\|2  + 4
                   |- 4%i |---------  + 1
                   |      |     +-+
                  \|     \|  16\|2
              + 
                                  +---------+
                                  |  +-+
                      +-+         |3\|2  + 4       +--+      +-+
                (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                  |     +-+
                                 \|  16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |      +---------+
             |      |  +-+
             |      |3\|2  + 4
             |- 4%i |---------  + 1
             |      |     +-+
            \|     \|  16\|2
         *
            log
                                                         +---------------------+
                                  +---------+            |      +---------+
                                  |  +-+                 |      |  +-+
                        +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
                   ((48\|2  - 64) |---------  + 4%i\|2 ) |- 4%i |---------  + 1
                                  |     +-+              |      |     +-+
                                 \|  16\|2              \|     \|  16\|2
                 + 
                                     +---------+
                                     |  +-+
                         +-+         |3\|2  + 4      +-+
                   (16%i\|2  - 16%i) |---------  + 8\|2  - 4
                                     |     +-+
                                    \|  16\|2
              /
                  +-+
                 \|2
     + 
          +---------------------+
          |      +---------+
          |      |  +-+
          |      |3\|2  + 4
          |- 4%i |---------  + 1
          |      |     +-+
         \|     \|  16\|2
      *
         log
                                                        +---------------------+
                                 +---------+            |      +---------+
                                 |  +-+                 |      |  +-+
                       +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
                ((- 48\|2  + 64) |---------  - 4%i\|2 ) |- 4%i |---------  + 1
                                 |     +-+              |      |     +-+
                                \|  16\|2              \|     \|  16\|2
              + 
                                  +---------+
                                  |  +-+
                      +-+         |3\|2  + 4      +-+
                (16%i\|2  - 16%i) |---------  + 8\|2  - 4
                                  |     +-+
                                 \|  16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |      +---------+
             |      |  +-+
             |      |3\|2  + 4
             |- 4%i |---------  + 1
             |      |     +-+
            \|     \|  16\|2
         *
            log
                                      +---------+
                                      |  +-+                 +---------+
                            +-+       |3\|2  + 4        +-+  | +--+
                     ((- 48\|2  + 64) |---------  - 4%i\|2 )\|\|%i  + 1
                                      |     +-+
                                     \|  16\|2
                  *
                      +---------------------+
                      |      +---------+
                      |      |  +-+
                      |      |3\|2  + 4
                      |- 4%i |---------  + 1
                      |      |     +-+
                     \|     \|  16\|2
                 + 
                                     +---------+
                                     |  +-+
                         +-+         |3\|2  + 4       +--+      +-+
                   (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                     |     +-+
                                    \|  16\|2
              /
                  +-+
                 \|2
     + 
          +---------------------+
          |    +-----------+
          |    |    +-+
          |    |- 3\|2  + 4
          |- 4 |-----------  + 1
          |    |      +-+
         \|   \|   16\|2
      *
         log
                                       +-----------+
                                       |    +-+
                           +-+         |- 3\|2  + 4        +-+
                  ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )
                                       |      +-+
                                      \|   16\|2
               *
                   +---------------------+
                   |    +-----------+
                   |    |    +-+
                   |    |- 3\|2  + 4
                   |- 4 |-----------  + 1
                   |    |      +-+
                  \|   \|   16\|2
              + 
                              +-----------+
                              |    +-+
                    +-+       |- 3\|2  + 4      +-+
                (16\|2  + 16) |-----------  + 8\|2  + 4
                              |      +-+
                             \|   16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |    +-----------+
             |    |    +-+
             |    |- 3\|2  + 4
             |- 4 |-----------  + 1
             |    |      +-+
            \|   \|   16\|2
         *
            log
                                          +-----------+
                                          |    +-+                 +---------+
                              +-+         |- 3\|2  + 4        +-+  | +--+
                     ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
                                          |      +-+
                                         \|   16\|2
                  *
                      +---------------------+
                      |    +-----------+
                      |    |    +-+
                      |    |- 3\|2  + 4
                      |- 4 |-----------  + 1
                      |    |      +-+
                     \|   \|   16\|2
                 + 
                                 +-----------+
                                 |    +-+
                       +-+       |- 3\|2  + 4       +--+      +-+
                   (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
                                 |      +-+
                                \|   16\|2
              /
                  +-+
                 \|2
     + 
       -
             +-------------------+
             |  +-----------+
             |  |    +-+
             |  |- 3\|2  + 4
             |4 |-----------  + 1
             |  |      +-+
            \| \|   16\|2
         *
            log
                                          +-----------+
                                          |    +-+
                              +-+         |- 3\|2  + 4        +-+
                     ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )
                                          |      +-+
                                         \|   16\|2
                  *
                      +-------------------+
                      |  +-----------+
                      |  |    +-+
                      |  |- 3\|2  + 4
                      |4 |-----------  + 1
                      |  |      +-+
                     \| \|   16\|2
                 + 
                                   +-----------+
                                   |    +-+
                         +-+       |- 3\|2  + 4      +-+
                   (- 16\|2  - 16) |-----------  + 8\|2  + 4
                                   |      +-+
                                  \|   16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |  +-----------+
          |  |    +-+
          |  |- 3\|2  + 4
          |4 |-----------  + 1
          |  |      +-+
         \| \|   16\|2
      *
         log
                                       +-----------+
                                       |    +-+                 +---------+
                           +-+         |- 3\|2  + 4        +-+  | +--+
                  ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
                                       |      +-+
                                      \|   16\|2
               *
                   +-------------------+
                   |  +-----------+
                   |  |    +-+
                   |  |- 3\|2  + 4
                   |4 |-----------  + 1
                   |  |      +-+
                  \| \|   16\|2
              + 
                                +-----------+
                                |    +-+
                      +-+       |- 3\|2  + 4       +--+      +-+
                (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
                                |      +-+
                               \|   16\|2
           /
               +-+
              \|2
     + 
       -
             +-------------------+
             |    +---------+
             |    |  +-+
             |    |3\|2  + 4
             |4%i |---------  + 1
             |    |     +-+
            \|   \|  16\|2
         *
            log
                                                           +-------------------+
                                    +---------+            |    +---------+
                                    |  +-+                 |    |  +-+
                          +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
                   ((- 48\|2  + 64) |---------  + 4%i\|2 ) |4%i |---------  + 1
                                    |     +-+              |    |     +-+
                                   \|  16\|2              \|   \|  16\|2
                 + 
                                       +---------+
                                       |  +-+
                           +-+         |3\|2  + 4      +-+
                   (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
                                       |     +-+
                                      \|  16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |    +---------+
          |    |  +-+
          |    |3\|2  + 4
          |4%i |---------  + 1
          |    |     +-+
         \|   \|  16\|2
      *
         log
                                   +---------+
                                   |  +-+                 +---------+
                         +-+       |3\|2  + 4        +-+  | +--+
                  ((- 48\|2  + 64) |---------  + 4%i\|2 )\|\|%i  + 1
                                   |     +-+
                                  \|  16\|2
               *
                   +-------------------+
                   |    +---------+
                   |    |  +-+
                   |    |3\|2  + 4
                   |4%i |---------  + 1
                   |    |     +-+
                  \|   \|  16\|2
              + 
                                    +---------+
                                    |  +-+
                        +-+         |3\|2  + 4       +--+      +-+
                (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                    |     +-+
                                   \|  16\|2
           /
               +-+
              \|2
  /
       +-+
     4\|2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (101)
--R       -
--R             +-------------------+
--R             |    +---------+
--R             |    |  +-+
--R             |    |3\|2  + 4
--R             |4%i |---------  + 1
--R             |    |     +-+
--R            \|   \|  16\|2
--R         *
--R            log
--R                                    +---------+
--R                                    |  +-+                 +---------+
--R                          +-+       |3\|2  + 4        +-+  | +--+
--R                     ((48\|2  - 64) |---------  - 4%i\|2 )\|\|%i  + 1
--R                                    |     +-+
--R                                   \|  16\|2
--R                  *
--R                      +-------------------+
--R                      |    +---------+
--R                      |    |  +-+
--R                      |    |3\|2  + 4
--R                      |4%i |---------  + 1
--R                      |    |     +-+
--R                     \|   \|  16\|2
--R                 + 
--R                                       +---------+
--R                                       |  +-+
--R                           +-+         |3\|2  + 4       +--+      +-+
--R                   (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                       |     +-+
--R                                      \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |    +---------+
--R          |    |  +-+
--R          |    |3\|2  + 4
--R          |4%i |---------  + 1
--R          |    |     +-+
--R         \|   \|  16\|2
--R      *
--R         log
--R                                                      +-------------------+
--R                               +---------+            |    +---------+
--R                               |  +-+                 |    |  +-+
--R                     +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
--R                ((48\|2  - 64) |---------  - 4%i\|2 ) |4%i |---------  + 1
--R                               |     +-+              |    |     +-+
--R                              \|  16\|2              \|   \|  16\|2
--R              + 
--R                                    +---------+
--R                                    |  +-+
--R                        +-+         |3\|2  + 4      +-+
--R                (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
--R                                    |     +-+
--R                                   \|  16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +-------------------+
--R             |  +-----------+
--R             |  |    +-+
--R             |  |- 3\|2  + 4
--R             |4 |-----------  + 1
--R             |  |      +-+
--R            \| \|   16\|2
--R         *
--R            log
--R                                        +-----------+
--R                                        |    +-+                 +---------+
--R                            +-+         |- 3\|2  + 4        +-+  | +--+
--R                     ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
--R                                        |      +-+
--R                                       \|   16\|2
--R                  *
--R                      +-------------------+
--R                      |  +-----------+
--R                      |  |    +-+
--R                      |  |- 3\|2  + 4
--R                      |4 |-----------  + 1
--R                      |  |      +-+
--R                     \| \|   16\|2
--R                 + 
--R                                   +-----------+
--R                                   |    +-+
--R                         +-+       |- 3\|2  + 4       +--+      +-+
--R                   (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                                   |      +-+
--R                                  \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |  +-----------+
--R          |  |    +-+
--R          |  |- 3\|2  + 4
--R          |4 |-----------  + 1
--R          |  |      +-+
--R         \| \|   16\|2
--R      *
--R         log
--R                                     +-----------+
--R                                     |    +-+
--R                         +-+         |- 3\|2  + 4        +-+
--R                  ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )
--R                                     |      +-+
--R                                    \|   16\|2
--R               *
--R                   +-------------------+
--R                   |  +-----------+
--R                   |  |    +-+
--R                   |  |- 3\|2  + 4
--R                   |4 |-----------  + 1
--R                   |  |      +-+
--R                  \| \|   16\|2
--R              + 
--R                                +-----------+
--R                                |    +-+
--R                      +-+       |- 3\|2  + 4      +-+
--R                (- 16\|2  - 16) |-----------  + 8\|2  + 4
--R                                |      +-+
--R                               \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R          +---------------------+
--R          |    +-----------+
--R          |    |    +-+
--R          |    |- 3\|2  + 4
--R          |- 4 |-----------  + 1
--R          |    |      +-+
--R         \|   \|   16\|2
--R      *
--R         log
--R                                     +-----------+
--R                                     |    +-+                 +---------+
--R                         +-+         |- 3\|2  + 4        +-+  | +--+
--R                  ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
--R                                     |      +-+
--R                                    \|   16\|2
--R               *
--R                   +---------------------+
--R                   |    +-----------+
--R                   |    |    +-+
--R                   |    |- 3\|2  + 4
--R                   |- 4 |-----------  + 1
--R                   |    |      +-+
--R                  \|   \|   16\|2
--R              + 
--R                              +-----------+
--R                              |    +-+
--R                    +-+       |- 3\|2  + 4       +--+      +-+
--R                (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                              |      +-+
--R                             \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |    +-----------+
--R             |    |    +-+
--R             |    |- 3\|2  + 4
--R             |- 4 |-----------  + 1
--R             |    |      +-+
--R            \|   \|   16\|2
--R         *
--R            log
--R                                        +-----------+
--R                                        |    +-+
--R                            +-+         |- 3\|2  + 4        +-+
--R                     ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )
--R                                        |      +-+
--R                                       \|   16\|2
--R                  *
--R                      +---------------------+
--R                      |    +-----------+
--R                      |    |    +-+
--R                      |    |- 3\|2  + 4
--R                      |- 4 |-----------  + 1
--R                      |    |      +-+
--R                     \|   \|   16\|2
--R                 + 
--R                                 +-----------+
--R                                 |    +-+
--R                       +-+       |- 3\|2  + 4      +-+
--R                   (16\|2  + 16) |-----------  + 8\|2  + 4
--R                                 |      +-+
--R                                \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +---------------------+
--R          |      +---------+
--R          |      |  +-+
--R          |      |3\|2  + 4
--R          |- 4%i |---------  + 1
--R          |      |     +-+
--R         \|     \|  16\|2
--R      *
--R         log
--R                                 +---------+
--R                                 |  +-+                 +---------+
--R                       +-+       |3\|2  + 4        +-+  | +--+
--R                  ((48\|2  - 64) |---------  + 4%i\|2 )\|\|%i  + 1
--R                                 |     +-+
--R                                \|  16\|2
--R               *
--R                   +---------------------+
--R                   |      +---------+
--R                   |      |  +-+
--R                   |      |3\|2  + 4
--R                   |- 4%i |---------  + 1
--R                   |      |     +-+
--R                  \|     \|  16\|2
--R              + 
--R                                  +---------+
--R                                  |  +-+
--R                      +-+         |3\|2  + 4       +--+      +-+
--R                (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                  |     +-+
--R                                 \|  16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |      +---------+
--R             |      |  +-+
--R             |      |3\|2  + 4
--R             |- 4%i |---------  + 1
--R             |      |     +-+
--R            \|     \|  16\|2
--R         *
--R            log
--R                                                         +---------------------+
--R                                  +---------+            |      +---------+
--R                                  |  +-+                 |      |  +-+
--R                        +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
--R                   ((48\|2  - 64) |---------  + 4%i\|2 ) |- 4%i |---------  + 1
--R                                  |     +-+              |      |     +-+
--R                                 \|  16\|2              \|     \|  16\|2
--R                 + 
--R                                     +---------+
--R                                     |  +-+
--R                         +-+         |3\|2  + 4      +-+
--R                   (16%i\|2  - 16%i) |---------  + 8\|2  - 4
--R                                     |     +-+
--R                                    \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +---------------------+
--R          |      +---------+
--R          |      |  +-+
--R          |      |3\|2  + 4
--R          |- 4%i |---------  + 1
--R          |      |     +-+
--R         \|     \|  16\|2
--R      *
--R         log
--R                                                        +---------------------+
--R                                 +---------+            |      +---------+
--R                                 |  +-+                 |      |  +-+
--R                       +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
--R                ((- 48\|2  + 64) |---------  - 4%i\|2 ) |- 4%i |---------  + 1
--R                                 |     +-+              |      |     +-+
--R                                \|  16\|2              \|     \|  16\|2
--R              + 
--R                                  +---------+
--R                                  |  +-+
--R                      +-+         |3\|2  + 4      +-+
--R                (16%i\|2  - 16%i) |---------  + 8\|2  - 4
--R                                  |     +-+
--R                                 \|  16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |      +---------+
--R             |      |  +-+
--R             |      |3\|2  + 4
--R             |- 4%i |---------  + 1
--R             |      |     +-+
--R            \|     \|  16\|2
--R         *
--R            log
--R                                      +---------+
--R                                      |  +-+                 +---------+
--R                            +-+       |3\|2  + 4        +-+  | +--+
--R                     ((- 48\|2  + 64) |---------  - 4%i\|2 )\|\|%i  + 1
--R                                      |     +-+
--R                                     \|  16\|2
--R                  *
--R                      +---------------------+
--R                      |      +---------+
--R                      |      |  +-+
--R                      |      |3\|2  + 4
--R                      |- 4%i |---------  + 1
--R                      |      |     +-+
--R                     \|     \|  16\|2
--R                 + 
--R                                     +---------+
--R                                     |  +-+
--R                         +-+         |3\|2  + 4       +--+      +-+
--R                   (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                     |     +-+
--R                                    \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +---------------------+
--R          |    +-----------+
--R          |    |    +-+
--R          |    |- 3\|2  + 4
--R          |- 4 |-----------  + 1
--R          |    |      +-+
--R         \|   \|   16\|2
--R      *
--R         log
--R                                       +-----------+
--R                                       |    +-+
--R                           +-+         |- 3\|2  + 4        +-+
--R                  ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )
--R                                       |      +-+
--R                                      \|   16\|2
--R               *
--R                   +---------------------+
--R                   |    +-----------+
--R                   |    |    +-+
--R                   |    |- 3\|2  + 4
--R                   |- 4 |-----------  + 1
--R                   |    |      +-+
--R                  \|   \|   16\|2
--R              + 
--R                              +-----------+
--R                              |    +-+
--R                    +-+       |- 3\|2  + 4      +-+
--R                (16\|2  + 16) |-----------  + 8\|2  + 4
--R                              |      +-+
--R                             \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |    +-----------+
--R             |    |    +-+
--R             |    |- 3\|2  + 4
--R             |- 4 |-----------  + 1
--R             |    |      +-+
--R            \|   \|   16\|2
--R         *
--R            log
--R                                          +-----------+
--R                                          |    +-+                 +---------+
--R                              +-+         |- 3\|2  + 4        +-+  | +--+
--R                     ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
--R                                          |      +-+
--R                                         \|   16\|2
--R                  *
--R                      +---------------------+
--R                      |    +-----------+
--R                      |    |    +-+
--R                      |    |- 3\|2  + 4
--R                      |- 4 |-----------  + 1
--R                      |    |      +-+
--R                     \|   \|   16\|2
--R                 + 
--R                                 +-----------+
--R                                 |    +-+
--R                       +-+       |- 3\|2  + 4       +--+      +-+
--R                   (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                                 |      +-+
--R                                \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R       -
--R             +-------------------+
--R             |  +-----------+
--R             |  |    +-+
--R             |  |- 3\|2  + 4
--R             |4 |-----------  + 1
--R             |  |      +-+
--R            \| \|   16\|2
--R         *
--R            log
--R                                          +-----------+
--R                                          |    +-+
--R                              +-+         |- 3\|2  + 4        +-+
--R                     ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )
--R                                          |      +-+
--R                                         \|   16\|2
--R                  *
--R                      +-------------------+
--R                      |  +-----------+
--R                      |  |    +-+
--R                      |  |- 3\|2  + 4
--R                      |4 |-----------  + 1
--R                      |  |      +-+
--R                     \| \|   16\|2
--R                 + 
--R                                   +-----------+
--R                                   |    +-+
--R                         +-+       |- 3\|2  + 4      +-+
--R                   (- 16\|2  - 16) |-----------  + 8\|2  + 4
--R                                   |      +-+
--R                                  \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |  +-----------+
--R          |  |    +-+
--R          |  |- 3\|2  + 4
--R          |4 |-----------  + 1
--R          |  |      +-+
--R         \| \|   16\|2
--R      *
--R         log
--R                                       +-----------+
--R                                       |    +-+                 +---------+
--R                           +-+         |- 3\|2  + 4        +-+  | +--+
--R                  ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
--R                                       |      +-+
--R                                      \|   16\|2
--R               *
--R                   +-------------------+
--R                   |  +-----------+
--R                   |  |    +-+
--R                   |  |- 3\|2  + 4
--R                   |4 |-----------  + 1
--R                   |  |      +-+
--R                  \| \|   16\|2
--R              + 
--R                                +-----------+
--R                                |    +-+
--R                      +-+       |- 3\|2  + 4       +--+      +-+
--R                (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                                |      +-+
--R                               \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +-------------------+
--R             |    +---------+
--R             |    |  +-+
--R             |    |3\|2  + 4
--R             |4%i |---------  + 1
--R             |    |     +-+
--R            \|   \|  16\|2
--R         *
--R            log
--R                                                           +-------------------+
--R                                    +---------+            |    +---------+
--R                                    |  +-+                 |    |  +-+
--R                          +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
--R                   ((- 48\|2  + 64) |---------  + 4%i\|2 ) |4%i |---------  + 1
--R                                    |     +-+              |    |     +-+
--R                                   \|  16\|2              \|   \|  16\|2
--R                 + 
--R                                       +---------+
--R                                       |  +-+
--R                           +-+         |3\|2  + 4      +-+
--R                   (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
--R                                       |     +-+
--R                                      \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |    +---------+
--R          |    |  +-+
--R          |    |3\|2  + 4
--R          |4%i |---------  + 1
--R          |    |     +-+
--R         \|   \|  16\|2
--R      *
--R         log
--R                                   +---------+
--R                                   |  +-+                 +---------+
--R                         +-+       |3\|2  + 4        +-+  | +--+
--R                  ((- 48\|2  + 64) |---------  + 4%i\|2 )\|\|%i  + 1
--R                                   |     +-+
--R                                  \|  16\|2
--R               *
--R                   +-------------------+
--R                   |    +---------+
--R                   |    |  +-+
--R                   |    |3\|2  + 4
--R                   |4%i |---------  + 1
--R                   |    |     +-+
--R                  \|   \|  16\|2
--R              + 
--R                                    +---------+
--R                                    |  +-+
--R                        +-+         |3\|2  + 4       +--+      +-+
--R                (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                    |     +-+
--R                                   \|  16\|2
--R           /
--R               +-+
--R              \|2
--R  /
--R       +-+
--R     4\|2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 101

--S 102 of 224
in1872a:=integrate(1/(z^2-1)/(%i/(z+%i))^(1/2), z= 0..1,"noPole")
 

   (102)
                              +------+
        +------+              |  %i    +------+
       \|1 + %i log((2 + 2%i) |------ \|1 + %i  + 2%i)
                             \|1 + %i
     + 
          +------+              +------+
       - \|1 + %i log((2 + 2%i)\|1 + %i  + 1 + 3%i)
     + 
                              +------+
        +------+              |  %i    +------+
       \|1 - %i log((2 - 2%i) |------ \|1 - %i  - 2 + 2%i)
                             \|1 + %i
     + 
          +------+              +------+
       - \|1 - %i log((2 - 2%i)\|1 - %i  - 1 + 3%i)
     + 
        +------+                +------+
       \|1 - %i log((- 2 + 2%i)\|1 - %i  - 1 + 3%i)
     + 
                                  +------+
          +------+                |  %i    +------+
       - \|1 - %i log((- 2 + 2%i) |------ \|1 - %i  - 2 + 2%i)
                                 \|1 + %i
     + 
        +------+                +------+
       \|1 + %i log((- 2 - 2%i)\|1 + %i  + 1 + 3%i)
     + 
                                  +------+
          +------+                |  %i    +------+
       - \|1 + %i log((- 2 - 2%i) |------ \|1 + %i  + 2%i)
                                 \|1 + %i
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (102)
--R                              +------+
--R        +------+              |  %i    +------+
--R       \|1 + %i log((2 + 2%i) |------ \|1 + %i  + 2%i)
--R                             \|1 + %i
--R     + 
--R          +------+              +------+
--R       - \|1 + %i log((2 + 2%i)\|1 + %i  + 1 + 3%i)
--R     + 
--R                              +------+
--R        +------+              |  %i    +------+
--R       \|1 - %i log((2 - 2%i) |------ \|1 - %i  - 2 + 2%i)
--R                             \|1 + %i
--R     + 
--R          +------+              +------+
--R       - \|1 - %i log((2 - 2%i)\|1 - %i  - 1 + 3%i)
--R     + 
--R        +------+                +------+
--R       \|1 - %i log((- 2 + 2%i)\|1 - %i  - 1 + 3%i)
--R     + 
--R                                  +------+
--R          +------+                |  %i    +------+
--R       - \|1 - %i log((- 2 + 2%i) |------ \|1 - %i  - 2 + 2%i)
--R                                 \|1 + %i
--R     + 
--R        +------+                +------+
--R       \|1 + %i log((- 2 - 2%i)\|1 + %i  + 1 + 3%i)
--R     + 
--R                                  +------+
--R          +------+                |  %i    +------+
--R       - \|1 + %i log((- 2 - 2%i) |------ \|1 + %i  + 2%i)
--R                                 \|1 + %i
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 102

--S 103 of 224
in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole")
 

   (103)
           +-+     4+-+    %pi
         (\|2  - 1)\|2 cos(---)
                            8
      *
              4+-+2    %pi 2     4+-+3    4+-+     %pi     4+-+2
         log(4\|2  sin(---)  + (4\|2   + 4\|2 )sin(---) + 2\|2   + 3)
                        8                           8
     + 
             +-+     4+-+    %pi
         (- \|2  + 1)\|2 cos(---)
                              8
      *
              4+-+2    %pi 2       4+-+3    4+-+     %pi     4+-+2
         log(4\|2  sin(---)  + (- 4\|2   - 4\|2 )sin(---) + 2\|2   + 3)
                        8                             8
     + 
             +-+     4+-+    %pi
         (- \|2  + 1)\|2 cos(---)
                              8
      *
         log
               4+-+2    %pi 2
              4\|2  sin(---)
                         8
            + 
                    +-+     4+-+2    %pi     4+-+3        +-+      4+-+     %pi
              ((- 8\|2  + 8)\|2  cos(---) + 4\|2   + (- 8\|2  + 16)\|2 )sin(---)
                                      8                                      8
            + 
                   +-+      4+-+2    %pi 2
              (- 8\|2  + 12)\|2  cos(---)
                                      8
            + 
                    +-+     4+-+3         +-+      4+-+     %pi
              ((- 4\|2  + 4)\|2   + (- 24\|2  + 32)\|2 )cos(---)
                                                             8
            + 
                   +-+     4+-+2      +-+
              (- 4\|2  + 8)\|2   - 16\|2  + 26
     + 
           +-+     4+-+    %pi
         (\|2  - 1)\|2 cos(---)
                            8
      *
         log
               4+-+2    %pi 2
              4\|2  sin(---)
                         8
            + 
                    +-+     4+-+2    %pi     4+-+3      +-+      4+-+     %pi
              ((- 8\|2  + 8)\|2  cos(---) - 4\|2   + (8\|2  - 16)\|2 )sin(---)
                                      8                                    8
            + 
                   +-+      4+-+2    %pi 2
              (- 8\|2  + 12)\|2  cos(---)
                                      8
            + 
                  +-+     4+-+3       +-+      4+-+     %pi
              ((4\|2  - 4)\|2   + (24\|2  - 32)\|2 )cos(---)
                                                         8
            + 
                   +-+     4+-+2      +-+
              (- 4\|2  + 8)\|2   - 16\|2  + 26
     + 
                                       4+-+    %pi
                                       \|2 sin(---) + 1
          +-+     4+-+    %pi                   8
       (4\|2  - 4)\|2 sin(---)atan(-----------------------)
                           8       4+-+    %pi     +-+
                                   \|2 cos(---) - \|2  + 1
                                            8
     + 
                                     4+-+    %pi
                                     \|2 sin(---) + 1
            +-+     4+-+    %pi               8
       (- 4\|2  + 4)\|2 sin(---)atan(----------------)
                             8         4+-+    %pi
                                       \|2 cos(---)
                                                8
     + 
                                   4+-+    %pi
                                   \|2 sin(---) - 1
          +-+     4+-+    %pi               8
       (4\|2  - 4)\|2 sin(---)atan(----------------)
                           8         4+-+    %pi
                                     \|2 cos(---)
                                              8
     + 
                                         4+-+    %pi
                                         \|2 sin(---) - 1
            +-+     4+-+    %pi                   8                 +-+
       (- 4\|2  + 4)\|2 sin(---)atan(-----------------------) + %pi\|2  - 2%pi
                             8       4+-+    %pi     +-+
                                     \|2 cos(---) + \|2  - 1
                                              8
  /
       +-+
     2\|2  - 2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (103)
--R           +-+     4+-+    %pi
--R         (\|2  - 1)\|2 cos(---)
--R                            8
--R      *
--R              4+-+2    %pi 2     4+-+3    4+-+     %pi     4+-+2
--R         log(4\|2  sin(---)  + (4\|2   + 4\|2 )sin(---) + 2\|2   + 3)
--R                        8                           8
--R     + 
--R             +-+     4+-+    %pi
--R         (- \|2  + 1)\|2 cos(---)
--R                              8
--R      *
--R              4+-+2    %pi 2       4+-+3    4+-+     %pi     4+-+2
--R         log(4\|2  sin(---)  + (- 4\|2   - 4\|2 )sin(---) + 2\|2   + 3)
--R                        8                             8
--R     + 
--R             +-+     4+-+    %pi
--R         (- \|2  + 1)\|2 cos(---)
--R                              8
--R      *
--R         log
--R               4+-+2    %pi 2
--R              4\|2  sin(---)
--R                         8
--R            + 
--R                    +-+     4+-+2    %pi     4+-+3        +-+      4+-+     %pi
--R              ((- 8\|2  + 8)\|2  cos(---) + 4\|2   + (- 8\|2  + 16)\|2 )sin(---)
--R                                      8                                      8
--R            + 
--R                   +-+      4+-+2    %pi 2
--R              (- 8\|2  + 12)\|2  cos(---)
--R                                      8
--R            + 
--R                    +-+     4+-+3         +-+      4+-+     %pi
--R              ((- 4\|2  + 4)\|2   + (- 24\|2  + 32)\|2 )cos(---)
--R                                                             8
--R            + 
--R                   +-+     4+-+2      +-+
--R              (- 4\|2  + 8)\|2   - 16\|2  + 26
--R     + 
--R           +-+     4+-+    %pi
--R         (\|2  - 1)\|2 cos(---)
--R                            8
--R      *
--R         log
--R               4+-+2    %pi 2
--R              4\|2  sin(---)
--R                         8
--R            + 
--R                    +-+     4+-+2    %pi     4+-+3      +-+      4+-+     %pi
--R              ((- 8\|2  + 8)\|2  cos(---) - 4\|2   + (8\|2  - 16)\|2 )sin(---)
--R                                      8                                    8
--R            + 
--R                   +-+      4+-+2    %pi 2
--R              (- 8\|2  + 12)\|2  cos(---)
--R                                      8
--R            + 
--R                  +-+     4+-+3       +-+      4+-+     %pi
--R              ((4\|2  - 4)\|2   + (24\|2  - 32)\|2 )cos(---)
--R                                                         8
--R            + 
--R                   +-+     4+-+2      +-+
--R              (- 4\|2  + 8)\|2   - 16\|2  + 26
--R     + 
--R                                       4+-+    %pi
--R                                       \|2 sin(---) + 1
--R          +-+     4+-+    %pi                   8
--R       (4\|2  - 4)\|2 sin(---)atan(-----------------------)
--R                           8       4+-+    %pi     +-+
--R                                   \|2 cos(---) - \|2  + 1
--R                                            8
--R     + 
--R                                     4+-+    %pi
--R                                     \|2 sin(---) + 1
--R            +-+     4+-+    %pi               8
--R       (- 4\|2  + 4)\|2 sin(---)atan(----------------)
--R                             8         4+-+    %pi
--R                                       \|2 cos(---)
--R                                                8
--R     + 
--R                                   4+-+    %pi
--R                                   \|2 sin(---) - 1
--R          +-+     4+-+    %pi               8
--R       (4\|2  - 4)\|2 sin(---)atan(----------------)
--R                           8         4+-+    %pi
--R                                     \|2 cos(---)
--R                                              8
--R     + 
--R                                         4+-+    %pi
--R                                         \|2 sin(---) - 1
--R            +-+     4+-+    %pi                   8                 +-+
--R       (- 4\|2  + 4)\|2 sin(---)atan(-----------------------) + %pi\|2  - 2%pi
--R                             8       4+-+    %pi     +-+
--R                                     \|2 cos(---) + \|2  - 1
--R                                              8
--R  /
--R       +-+
--R     2\|2  - 2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 103

--S 104 of 224
in1945a:=integrate(acoth((1-z)/(1+z)), z= 0..1,"noPole")
 

          1
   (104)  -
          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (104)  -
--R          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 104

--S 105 of 224
in1946a:=integrate(acoth((1-z)/(1+z))*z, z= 0..1,"noPole")
 

          1
   (105)  -
          8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (105)  -
--R          8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 105

--S 106 of 224
in1947a:=integrate(acoth((1-z)/(1+z))*z^(1/2), z= 0..1,"noPole")
 

          2
   (106)  -
          9
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          2
--R   (106)  -
--R          9
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 106

--S 107 of 224
in1950a:=integrate(acoth((1-z)/(1+z))/(1-z)^(1/2), z= 0..1,"noPole")
 

          - log(4) - 2log(2) + 4
   (107)  ----------------------
                     2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - log(4) - 2log(2) + 4
--R   (107)  ----------------------
--R                     2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 107

--S 108 of 224
in1952a:=integrate(acoth((1-z)/(1+z))*(%i*z)^(1/2), z= 0..1,"noPole")
 

            +--+
          2\|%i
   (108)  ------
             9
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R            +--+
--R          2\|%i
--R   (108)  ------
--R             9
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 108

--S 109 of 224
in1954a:=integrate(acoth((1-z)/(1+z))/(%i*z)^(1/2), z= 0..1,"noPole")
 

                +--+
   (109)  - 2%i\|%i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                +--+
--R   (109)  - 2%i\|%i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 109

--S 110 of 224
in202a:=integrate(acsc(z), z= 0..1/2,"noPole")
 

                        +-+ +-+
              +-+     2\|2 \|3             +-+
          - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi
                          5
   (110)  --------------------------------------------
                               12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                        +-+ +-+
--R              +-+     2\|2 \|3             +-+
--R          - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi
--R                          5
--R   (110)  --------------------------------------------
--R                               12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 110

--S 111 of 224
in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole")
 

   (111)
               +--------+              +-------+
               |2%pi - 1               |%pi - 1
       - 2log( |--------  + 1) + 2log( |-------  + 1)
              \|  2%pi                \|  %pi
     + 
                    +-------+                          +--------+
                    |%pi - 1                           |2%pi - 1
             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
                   \|  %pi                            \|  2%pi
       - log(---------------------------) + log(----------------------------)
                         %pi                                2%pi
     + 
            +--------+        +-------+
            |2%pi - 1         |%pi - 1
       8%pi |--------  - 4%pi |-------
           \|  2%pi          \|  %pi
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (111)
--R               +--------+              +-------+
--R               |2%pi - 1               |%pi - 1
--R       - 2log( |--------  + 1) + 2log( |-------  + 1)
--R              \|  2%pi                \|  %pi
--R     + 
--R                    +-------+                          +--------+
--R                    |%pi - 1                           |2%pi - 1
--R             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
--R                   \|  %pi                            \|  2%pi
--R       - log(---------------------------) + log(----------------------------)
--R                         %pi                                2%pi
--R     + 
--R            +--------+        +-------+
--R            |2%pi - 1         |%pi - 1
--R       8%pi |--------  - 4%pi |-------
--R           \|  2%pi          \|  %pi
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 111

--S 112 of 224
in211:=integrate(acos(sin(2*z))*cos(z), z= 0..4*%pi/3)
 

                +-+
          13%pi\|3  + 36
   (112)  --------------
                12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+
--R          13%pi\|3  + 36
--R   (112)  --------------
--R                12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 112

--S 113 of 224
in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole")
 

   (113)
                                      3+---+2    3+---+
         3+---+2    3+---+            \|- 1   + 2\|- 1  + 1    3+---+2    3+---+
   - log(\|- 1   + 2\|- 1  + 1) + log(---------------------) - \|- 1   + 2\|- 1
                                             3+---+2
                                             \|- 1
   -----------------------------------------------------------------------------
                                         2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (113)
--R                                      3+---+2    3+---+
--R         3+---+2    3+---+            \|- 1   + 2\|- 1  + 1    3+---+2    3+---+
--R   - log(\|- 1   + 2\|- 1  + 1) + log(---------------------) - \|- 1   + 2\|- 1
--R                                             3+---+2
--R                                             \|- 1
--R   -----------------------------------------------------------------------------
--R                                         2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 113

--S 114 of 224
in216a:=integrate(1/(1/z-1)^(1/3), z= 0..1,"noPole")
 

           2%pi
   (114)  -----
            +-+
          3\|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           2%pi
--R   (114)  -----
--R            +-+
--R          3\|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 114

--S 115 of 224
in2023a:=integrate((1-z)/(-1+z^(1/2)), z= 1..2,"noPole")
 

              +-+
          - 4\|2  - 1
   (115)  -----------
               3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R              +-+
--R          - 4\|2  - 1
--R   (115)  -----------
--R               3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 115

--S 116 of 224
in2024a:=integrate(log(1-1/z)+csc(z-1), z= 0..1,"noPole")
 

   (116)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (116)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 116

--S 117 of 224
in2032a:=integrate(acoth(z)/z^(1/2), z= 0..1,"noPole")
 

          - 2log(2) + %pi
   (117)  ---------------
                 2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - 2log(2) + %pi
--R   (117)  ---------------
--R                 2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 117

--S 118 of 224
in2040a:=integrate(log(1-1/z^4)+cot(z), z= -1..1,"noPole")
 

   (118)  log(16) + log(4) + %pi
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (118)  log(16) + log(4) + %pi
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 118

--S 119 of 224
in2050a:=integrate(-csc(z-1)-1/z^(1/3), z= -1..1,"noPole")
 

   (119)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (119)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 119

--S 120 of 224
in2051a:=integrate((z^2+%i*z-1)^(1/2)*z, z= -1..1,"noPole")
 

   (120)
                    +----+                  +--+                   +----+
           (12132%i\|- %i  + 8550 + 8460%i)\|%i  + (8550 - 8460%i)\|- %i
         + 
           - 11925%i
      *
                       +----+
         log((8 - 4%i)\|- %i  + 3 - 8%i)
     + 
                      +----+                  +--+                     +----+
           (- 12132%i\|- %i  - 8550 - 8460%i)\|%i  + (- 8550 + 8460%i)\|- %i
         + 
           11925%i
      *
                         +--+
         log((- 8 - 4%i)\|%i  + 3 + 8%i)
     + 
               +----+                  +--+                   +----+
       (- 7360\|- %i  - 5116 + 5576%i)\|%i  + (5116 + 5576%i)\|- %i  + 7760
  /
               +----+                    +--+                       +----+
       (129408\|- %i  + 90240 - 91200%i)\|%i  + (- 90240 - 91200%i)\|- %i
     + 
       - 127200
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (120)
--R                    +----+                  +--+                   +----+
--R           (12132%i\|- %i  + 8550 + 8460%i)\|%i  + (8550 - 8460%i)\|- %i
--R         + 
--R           - 11925%i
--R      *
--R                       +----+
--R         log((8 - 4%i)\|- %i  + 3 - 8%i)
--R     + 
--R                      +----+                  +--+                     +----+
--R           (- 12132%i\|- %i  - 8550 - 8460%i)\|%i  + (- 8550 + 8460%i)\|- %i
--R         + 
--R           11925%i
--R      *
--R                         +--+
--R         log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R     + 
--R               +----+                  +--+                   +----+
--R       (- 7360\|- %i  - 5116 + 5576%i)\|%i  + (5116 + 5576%i)\|- %i  + 7760
--R  /
--R               +----+                    +--+                       +----+
--R       (129408\|- %i  + 90240 - 91200%i)\|%i  + (- 90240 - 91200%i)\|- %i
--R     + 
--R       - 127200
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 120

--S 121 of 224
in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole")
 

   (121)
                      4            3            2
       - log(4infinity  - 8infinity  + 8infinity  - 4infinity + 1)
     + 
                                  2infinity - 1
       (- 4infinity + 2)atan(----------------------) - %pi
                                      2
                             2infinity  - 2infinity
  /
     8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (121)
--R                      4            3            2
--R       - log(4infinity  - 8infinity  + 8infinity  - 4infinity + 1)
--R     + 
--R                                  2infinity - 1
--R       (- 4infinity + 2)atan(----------------------) - %pi
--R                                      2
--R                             2infinity  - 2infinity
--R  /
--R     8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 121

--S 122 of 224
in2054:=integrate(atan(1/z^(1/2))+1, z= -1..1)
 

   (122)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (122)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 122

--S 123 of 224
in2056a:=integrate(z^(1/2)-acoth(1-z), z= 0..1,"noPole")
 

          - 3log(4) + 4
   (123)  -------------
                6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - 3log(4) + 4
--R   (123)  -------------
--R                6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 123

--S 124 of 224
in2058a:=integrate((z^2+%i*z-3)^(1/2)+z, z= -1..1,"noPole")
 

   (124)
                  +--------+               +--------+
           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
         + 
                          +--------+
           (- 88 + 924%i)\|- 2 - %i  + 979
      *
                       +--------+
         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                +--------+               +--------+                +--------+
           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
         + 
           - 979
      *
                         +--------+
         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                 +--------+                 +--------+
       (- 1280%i\|- 2 - %i  - 2312 - 356%i)\|- 2 + %i
     + 
                        +--------+
       (- 2312 + 356%i)\|- 2 - %i  + 3360%i
  /
             +--------+                 +--------+                  +--------+
       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
     + 
       - 1424
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (124)
--R                  +--------+               +--------+
--R           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
--R         + 
--R                          +--------+
--R           (- 88 + 924%i)\|- 2 - %i  + 979
--R      *
--R                       +--------+
--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                +--------+               +--------+                +--------+
--R           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
--R         + 
--R           - 979
--R      *
--R                         +--------+
--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                 +--------+                 +--------+
--R       (- 1280%i\|- 2 - %i  - 2312 - 356%i)\|- 2 + %i
--R     + 
--R                        +--------+
--R       (- 2312 + 356%i)\|- 2 - %i  + 3360%i
--R  /
--R             +--------+                 +--------+                  +--------+
--R       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
--R     + 
--R       - 1424
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 124

--S 125 of 224
in2068a:=integrate(1/(%i*z)^(1/2)-csch(z), z= 0..1,"noPole")
 

   (125)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (125)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 125

--S 126 of 224
in2071a:=integrate(1/(3+z)^3*acoth(z), z= -1..1,"noPole")
 

          - 3log(16) + 3log(4) - 2
   (126)  ------------------------
                     128
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - 3log(16) + 3log(4) - 2
--R   (126)  ------------------------
--R                     128
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 126

--S 127 of 224
in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole")
 

   (127)
                                         3+---+2
         13467752003249079711273325865856\|- 1
       + 
                                           3+---+
         - 27601768453337700619258203429120\|- 1
       + 
         30944953633416008247597858726912
    *
         3+---+
         \|- 1
       %e
   + 
     - 9746099248106233432776547720320%e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (127)
--R                                         3+---+2
--R         13467752003249079711273325865856\|- 1
--R       + 
--R                                           3+---+
--R         - 27601768453337700619258203429120\|- 1
--R       + 
--R         30944953633416008247597858726912
--R    *
--R         3+---+
--R         \|- 1
--R       %e
--R   + 
--R     - 9746099248106233432776547720320%e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 127

--S 128 of 224
in2094a:=integrate(asinh(z)-acoth(z), z= -1..1,"noPole")
 

                +-+                +-+
          log(2\|2  + 3) + log(- 2\|2  + 3)
   (128)  ---------------------------------
                          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+                +-+
--R          log(2\|2  + 3) + log(- 2\|2  + 3)
--R   (128)  ---------------------------------
--R                          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 128

--S 129 of 224
in2096a:=integrate(log(z)^2, z= %minusInfinity..%plusInfinity,"noPole")
 

   (129)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (129)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 129

--S 130 of 224
in2098a:=integrate(1/z^(1/3)-z^2/(z-1)^2, z= -1..1,"noPole")
 

   (130)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (130)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 130

--S 131 of 224
in2105a:=integrate(-1/(z^2-%i*z+2)^(1/2)/z, z= 0..1,"noPole")
 

   (131)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (131)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 131

--S 132 of 224
in2106a:=integrate(acos(z)+acoth(1-z), z= 0..1,"noPole")
 

          log(4) + 2
   (132)  ----------
               2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(4) + 2
--R   (132)  ----------
--R               2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 132

--S 133 of 224
in2112a:=integrate(-cot(z-1)+log(1-1/z^4), z= -1..1,"noPole")
 

   (133)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (133)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 133

--S 134 of 224
in2115a:=integrate(-z/(z-1)+log(1-z^(1/3)), z= -1..1,"noPole")
 

   (134)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (134)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 134

--S 135 of 224
in2120a:=integrate(-z+1/(z^2+%i*z-3)^(1/2), z= -1..1,"noPole")
 

   (135)
                 +--------+                              +--------+
   log((8 - 4%i)\|- 2 - %i  - 5 - 8%i) - log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
   ---------------------------------------------------------------------------
                                        2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (135)
--R                 +--------+                              +--------+
--R   log((8 - 4%i)\|- 2 - %i  - 5 - 8%i) - log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R   ---------------------------------------------------------------------------
--R                                        2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 135

--S 136 of 224
in25:=integrate(cos(z), z= %i..a)
 

   (136)  sin(a) - sin(%i)
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (136)  sin(a) - sin(%i)
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 136

--S 137 of 224
in25a:=integrate(cos(z), z= %i..a)
 

   (137)  sin(a) - sin(%i)
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (137)  sin(a) - sin(%i)
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 137

--S 138 of 224
in25b:=integrate(exp(%i*z), z= %i..%i*infinity)
 

                    - infinity
          - %i %e %e           + %i
   (138)  -------------------------
                      %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                    - infinity
--R          - %i %e %e           + %i
--R   (138)  -------------------------
--R                      %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 138

--S 139 of 224
in25c:=integrate(exp(%i*z), z= %i..%i*infinity)
 

                    - infinity
          - %i %e %e           + %i
   (139)  -------------------------
                      %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                    - infinity
--R          - %i %e %e           + %i
--R   (139)  -------------------------
--R                      %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 139

--S 140 of 224
in28a:=integrate(1/z, z=1..z,"noPole")
 

               2
          log(z )
   (140)  -------
             2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R               2
--R          log(z )
--R   (140)  -------
--R             2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 140

--S 141 of 224
in30:=integrate(sin(3*asin(1/(1+z^2))), z= 0..%plusInfinity)
 

          3%pi
   (141)  ----
            4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          3%pi
--R   (141)  ----
--R            4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 141

--S 142 of 224
in32:=integrate(exp(-z), z= 0..%plusInfinity)
 

   (142)  1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (142)  1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 142

--S 143 of 224
in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 

   (143)
       log
                              2                                   2
                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
             *
                 +-+
                \|3
            + 
                      2                                     2
              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
         /
                   2
            4sin(1)  - 4sin(1) + 1
     + 
                   +-+
       - log(- 168\|3  + 291)
  /
      +-+
     \|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (143)
--R       log
--R                              2                                   2
--R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R             *
--R                 +-+
--R                \|3
--R            + 
--R                      2                                     2
--R              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R         /
--R                   2
--R            4sin(1)  - 4sin(1) + 1
--R     + 
--R                   +-+
--R       - log(- 168\|3  + 291)
--R  /
--R      +-+
--R     \|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 143

--S 144 of 224
in37:=integrate(atan(tan(1/z)), z= 0..1)
 

   (144)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (144)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 144

--S 145 of 224
in40:=integrate(atan(tan(z)), z= 0..%plusInfinity)
 

   (145)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (145)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 145

--S 146 of 224
in2157a:=integrate(acoth(z)-1/(1+z^(1/2)), z= 0..1,"noPole")
 

          log(4) + 10log(2) - 8
   (146)  ---------------------
                    4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(4) + 10log(2) - 8
--R   (146)  ---------------------
--R                    4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 146

--S 147 of 224
in2158a:=integrate(2*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole")
 

   (147)  2log(4) - 2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (147)  2log(4) - 2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 147

--S 148 of 224
in2168a:=integrate(-csch(z-1)-(1+%i*z)^(1/2), z= 0..1,"noPole")
 

   (148)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (148)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 148

--S 149 of 224
in2185a:=integrate(csch(z)+(z^2-%i*z+1)^(1/2), z= 0..1,"noPole")
 

   (149)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (149)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 149

--S 150 of 224
in2195a:=integrate(1-acoth(1-(1-z)^(1/2)), z= -1..1,"noPole")
 

   (150)
         +-+            +-+                 +-+          +-+
   2log(\|2 ) - log(- 2\|2  + 3) + 3log(- 4\|2  + 6) + 4\|2  - 4log(4) + 8
   -----------------------------------------------------------------------
                                      4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (150)
--R         +-+            +-+                 +-+          +-+
--R   2log(\|2 ) - log(- 2\|2  + 3) + 3log(- 4\|2  + 6) + 4\|2  - 4log(4) + 8
--R   -----------------------------------------------------------------------
--R                                      4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 150

--S 151 of 224
in2201a:=integrate(acoth(z)+%pi-asec(z-1), z= 0..1,"noPole")
 

                +-+
          - %pi\|2  + log(4) + 2%pi
   (151)  -------------------------
                      2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+
--R          - %pi\|2  + log(4) + 2%pi
--R   (151)  -------------------------
--R                      2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 151

--S 152 of 224
in221:=integrate(log(z+sqrt(z^2-1)), z)
 

             +------+           +------+          +------+
             | 2         2      | 2               | 2         2
          (z\|z  - 1  - z )log(\|z  - 1  + z) + z\|z  - 1  - z  + 1
   (152)  ---------------------------------------------------------
                                 +------+
                                 | 2
                                \|z  - 1  - z
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +------+           +------+          +------+
--R             | 2         2      | 2               | 2         2
--R          (z\|z  - 1  - z )log(\|z  - 1  + z) + z\|z  - 1  - z  + 1
--R   (152)  ---------------------------------------------------------
--R                                 +------+
--R                                 | 2
--R                                \|z  - 1  - z
--R                                          Type: Union(Expression Integer,...)
--E 152

--S 153 of 224
in227a:=integrate(atan(sin(z))+atan(1/(sin(z))), z= 0..1,"noPole")
 

            %pi
   (153)  - ---
             2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            %pi
--R   (153)  - ---
--R             2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 153

--S 154 of 224
in237a:=integrate(sin(z)*(1-cos(z)/sqrt(1-sin(z)^2))^2, z= 0..1,"noPole")
 

   (154)  - 4cos(1) + 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (154)  - 4cos(1) + 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 154

--S 155 of 224
in2221:=integrate((z-%i)*(-1+1/(z-%i)), z= 0..%plusInfinity)
 

   (155)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (155)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 155

--S 156 of 224
in2243a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..1,"noPole")
 

   (156)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (156)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 156

--S 157 of 224
in2254a:=integrate(cosh(z^(1/2))-acoth(1-z), z= 0..1,"noPole")
 

          - %e log(4) + 4%e - 4
   (157)  ---------------------
                   2%e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - %e log(4) + 4%e - 4
--R   (157)  ---------------------
--R                   2%e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 157

--S 158 of 224
in2270a:=integrate(log(z)*log(1/z)*(%i*z)^(1/3), z= -1..1,"noPole")
 

              3+--+     3+----+
          - 27\|%i  - 27\|- %i
   (158)  ---------------------
                    32
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              3+--+     3+----+
--R          - 27\|%i  - 27\|- %i
--R   (158)  ---------------------
--R                    32
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 158

--S 159 of 224
in2274a:=integrate(acoth(1-z)-acosh(1/z), z= -1..1,"noPole")
 

          3log(9) - 4%pi
   (159)  --------------
                 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          3log(9) - 4%pi
--R   (159)  --------------
--R                 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 159

--S 160 of 224
in2275a:=integrate((z^2+%i*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole")
 

   (160)
                       +--------+                          +--------+
           (- 51691200\|- 2 - %i  - 26455440 + 73601880%i)\|- 2 + %i
         + 
                                   +--------+
           (26455440 + 73601880%i)\|- 2 - %i  + 118339815
      *
                       +--------+
         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                     +--------+                          +--------+
           (51691200\|- 2 - %i  + 26455440 - 73601880%i)\|- 2 + %i
         + 
                                     +--------+
           (- 26455440 - 73601880%i)\|- 2 - %i  - 118339815
      *
                         +--------+
         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                      +--------+                           +--------+
       (- 123056128%i\|- 2 - %i  - 167267016 - 40872532%i)\|- 2 + %i
     + 
                                  +--------+
       (- 167267016 + 40872532%i)\|- 2 - %i  + 236452160%i
  /
                 +--------+                          +--------+
       (21872640\|- 2 - %i  + 11194368 - 31143936%i)\|- 2 + %i
     + 
                                 +--------+
       (- 11194368 - 31143936%i)\|- 2 - %i  - 50074368
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (160)
--R                       +--------+                          +--------+
--R           (- 51691200\|- 2 - %i  - 26455440 + 73601880%i)\|- 2 + %i
--R         + 
--R                                   +--------+
--R           (26455440 + 73601880%i)\|- 2 - %i  + 118339815
--R      *
--R                       +--------+
--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                     +--------+                          +--------+
--R           (51691200\|- 2 - %i  + 26455440 - 73601880%i)\|- 2 + %i
--R         + 
--R                                     +--------+
--R           (- 26455440 - 73601880%i)\|- 2 - %i  - 118339815
--R      *
--R                         +--------+
--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                      +--------+                           +--------+
--R       (- 123056128%i\|- 2 - %i  - 167267016 - 40872532%i)\|- 2 + %i
--R     + 
--R                                  +--------+
--R       (- 167267016 + 40872532%i)\|- 2 - %i  + 236452160%i
--R  /
--R                 +--------+                          +--------+
--R       (21872640\|- 2 - %i  + 11194368 - 31143936%i)\|- 2 + %i
--R     + 
--R                                 +--------+
--R       (- 11194368 - 31143936%i)\|- 2 - %i  - 50074368
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 160

--S 161 of 224
in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole")
 

   (161)
                3+---+2          3+---+                3+---+
       (- 918750\|- 1   + 1200000\|- 1  + 2100000)atan(\|- 1  + 1)
     + 
                               3+---+2                              3+---+
       (918750atan(2) - 466984)\|- 1   + (- 1200000atan(2) - 364526)\|- 1
     + 
       - 2100000atan(2) + 96142
  /
          3+---+2        3+---+
     30625\|- 1   - 40000\|- 1  - 70000
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (161)
--R                3+---+2          3+---+                3+---+
--R       (- 918750\|- 1   + 1200000\|- 1  + 2100000)atan(\|- 1  + 1)
--R     + 
--R                               3+---+2                              3+---+
--R       (918750atan(2) - 466984)\|- 1   + (- 1200000atan(2) - 364526)\|- 1
--R     + 
--R       - 2100000atan(2) + 96142
--R  /
--R          3+---+2        3+---+
--R     30625\|- 1   - 40000\|- 1  - 70000
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 161

--S 162 of 224
in2278a:=integrate(acoth(1-z)+log(abs(z-1)/z), z= 0..1,"noPole")
 

          log(4)
   (162)  ------
             2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(4)
--R   (162)  ------
--R             2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 162

--S 163 of 224
in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole")
 

   (163)
                                                                     +-+
               +-+               +-+               +-+            - \|3  - 2
       2log(12\|3  + 21) + log(6\|3  + 12) - log(2\|3  + 4) + log(----------)
                                                                    +-+
                                                                   \|3  - 2
     + 
       log(16) - 2log(4)
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (163)
--R                                                                     +-+
--R               +-+               +-+               +-+            - \|3  - 2
--R       2log(12\|3  + 21) + log(6\|3  + 12) - log(2\|3  + 4) + log(----------)
--R                                                                    +-+
--R                                                                   \|3  - 2
--R     + 
--R       log(16) - 2log(4)
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 163

--S 164 of 224
in2311a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..%pi,"noPole")
 

   (164)
              %pi - 1 2      %pi - 1               %pi - 1 2      %pi - 1
       log((%e       )  + 2%e        + 1) - log((%e       )  - 2%e        + 1)
     + 
                              2                    2
             +------+       %e  + 2%e + 1        %e  - 2%e + 1
       - 4%i\|%i %pi  - log(-------------) + log(-------------)
                                   2                    2
                                 %e                   %e
  /
     2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (164)
--R              %pi - 1 2      %pi - 1               %pi - 1 2      %pi - 1
--R       log((%e       )  + 2%e        + 1) - log((%e       )  - 2%e        + 1)
--R     + 
--R                              2                    2
--R             +------+       %e  + 2%e + 1        %e  - 2%e + 1
--R       - 4%i\|%i %pi  - log(-------------) + log(-------------)
--R                                   2                    2
--R                                 %e                   %e
--R  /
--R     2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 164

--S 165 of 224
in2312:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1)
 

   (165)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (165)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 165

--S 166 of 224
in2312a:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole")
 

                          +----+                              +--+
          - log((8 - 4%i)\|- %i  + 3 - 8%i) + log((- 8 - 4%i)\|%i  + 3 + 8%i)
   (166)  -------------------------------------------------------------------
                                           2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                          +----+                              +--+
--R          - log((8 - 4%i)\|- %i  + 3 - 8%i) + log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R   (166)  -------------------------------------------------------------------
--R                                           2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 166

--S 167 of 224
in2324a:=integrate(cosh(z^(1/2)-1)+acoth(1-z), z= 0..1,"noPole")
 

                         2
          %e log(4) + 2%e  - 4%e + 2
   (167)  --------------------------
                      2%e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                         2
--R          %e log(4) + 2%e  - 4%e + 2
--R   (167)  --------------------------
--R                      2%e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 167

--S 168 of 224
in2330a:=integrate(exp(-z)+1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole")
 

   (168)
                        +----+                                 +--+
       %e log((8 - 4%i)\|- %i  + 3 - 8%i) - %e log((- 8 - 4%i)\|%i  + 3 + 8%i)
     + 
          2
       2%e  - 2
  /
     2%e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (168)
--R                        +----+                                 +--+
--R       %e log((8 - 4%i)\|- %i  + 3 - 8%i) - %e log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R     + 
--R          2
--R       2%e  - 2
--R  /
--R     2%e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 168

--S 169 of 224
in2332a:=integrate(acoth(z^(1/2))*(1-z^(1/2)), z= 0..1,"noPole")
 

          log(16) - log(4) - 10log(2) + 8
   (169)  -------------------------------
                         12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(16) - log(4) - 10log(2) + 8
--R   (169)  -------------------------------
--R                         12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 169

--S 170 of 224
in2333a:=integrate(acoth(z)+1/(z^2+z+2)^(1/2), z= 0..1,"noPole")
 

                  +-+
          log(- 4\|2  + 9) + log(4)
   (170)  -------------------------
                      2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                  +-+
--R          log(- 4\|2  + 9) + log(4)
--R   (170)  -------------------------
--R                      2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 170

--S 171 of 224
in2360a:=integrate(1/(1-%i*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole")
 

   (171)  [ + infinity, + infinity]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (171)  [ + infinity, + infinity]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 171

--S 172 of 224
in2367a:=integrate(log(1-z^2)-1/(%i/(z-%i))^(1/2), z= -1..1,"noPole")
 

   (172)
                                         %i           %i
             (6log(4) + 3log(2%i) - 3log(--) - 3log(- --) + 3log(- 2%i) - 24)
                                          2            2
          *
              +--------+
              |    %i
              |- ------
             \|  1 + %i
         + 
           - 4 - 4%i
      *
          +------+
          |   1
          |------
         \|1 + %i
     + 
                 +--------+
                 |    %i
       (4 + 4%i) |- ------
                \|  1 + %i
  /
        +--------+ +------+
        |    %i    |   1
     6  |- ------  |------
       \|  1 + %i \|1 + %i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (172)
--R                                         %i           %i
--R             (6log(4) + 3log(2%i) - 3log(--) - 3log(- --) + 3log(- 2%i) - 24)
--R                                          2            2
--R          *
--R              +--------+
--R              |    %i
--R              |- ------
--R             \|  1 + %i
--R         + 
--R           - 4 - 4%i
--R      *
--R          +------+
--R          |   1
--R          |------
--R         \|1 + %i
--R     + 
--R                 +--------+
--R                 |    %i
--R       (4 + 4%i) |- ------
--R                \|  1 + %i
--R  /
--R        +--------+ +------+
--R        |    %i    |   1
--R     6  |- ------  |------
--R       \|  1 + %i \|1 + %i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 172

--S 173 of 224
in2375a:=integrate(acoth(1-z^(1/2))+1/z^(1/3), z= 0..1,"noPole")
 

          2log(4) + 1
   (173)  -----------
               2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          2log(4) + 1
--R   (173)  -----------
--R               2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 173

--S 174 of 224
in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole")
 

   (174)
           +-+
         3\|5
      *
         log
                      +-+      3+--------+2
                (- 12\|5  - 36)\|infinity
              + 
                      +-+                  3+--------+                     +-+
                (- 16\|5  - 4infinity - 32)\|infinity  + (- 8infinity - 6)\|5
              + 
                - 8infinity - 14
           /
              3+--------+2                   3+--------+
              \|infinity   + (- infinity + 2)\|infinity  - 2infinity - 1
     + 
         (3infinity + 6)
      *
               3+--------+2                 3+--------+
         log(- \|infinity   + (infinity - 2)\|infinity  + 2infinity + 1)
     + 
        3+--------+2     3+--------+     +-+      +-+
       3\|infinity   - 18\|infinity  - 3\|5 log(6\|5  + 14) - 4infinity
  /
     6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (174)
--R           +-+
--R         3\|5
--R      *
--R         log
--R                      +-+      3+--------+2
--R                (- 12\|5  - 36)\|infinity
--R              + 
--R                      +-+                  3+--------+                     +-+
--R                (- 16\|5  - 4infinity - 32)\|infinity  + (- 8infinity - 6)\|5
--R              + 
--R                - 8infinity - 14
--R           /
--R              3+--------+2                   3+--------+
--R              \|infinity   + (- infinity + 2)\|infinity  - 2infinity - 1
--R     + 
--R         (3infinity + 6)
--R      *
--R               3+--------+2                 3+--------+
--R         log(- \|infinity   + (infinity - 2)\|infinity  + 2infinity + 1)
--R     + 
--R        3+--------+2     3+--------+     +-+      +-+
--R       3\|infinity   - 18\|infinity  - 3\|5 log(6\|5  + 14) - 4infinity
--R  /
--R     6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 174

--S 175 of 224
in2378a:=integrate((z^2+%i*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole")
 

   (175)
                  +--------+               +--------+
           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
         + 
                          +--------+
           (- 88 + 924%i)\|- 2 - %i  + 979
      *
                       +--------+
         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                +--------+               +--------+                +--------+
           (640\|- 2 - %i  - 64 - 672%i)\|- 2 + %i  + (64 - 672%i)\|- 2 - %i
         + 
           - 712
      *
                2 4       2 2
             (%e )  + 2(%e )  + 1
         log(--------------------)
                       2 4
                    (%e )
     + 
                +--------+               +--------+                +--------+
           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
         + 
           - 979
      *
                         +--------+
         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                                         +--------+
           (- 640log(4) + 2560 - 1280%i)\|- 2 - %i  + (64 + 672%i)log(4) - 2568
         + 
           - 3044%i
      *
          +--------+
         \|- 2 + %i
     + 
                                              +--------+
       ((- 64 + 672%i)log(4) - 2056 - 2332%i)\|- 2 - %i  + 712log(4) - 2848
     + 
       3360%i
  /
             +--------+                 +--------+                  +--------+
       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
     + 
       - 1424
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (175)
--R                  +--------+               +--------+
--R           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
--R         + 
--R                          +--------+
--R           (- 88 + 924%i)\|- 2 - %i  + 979
--R      *
--R                       +--------+
--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                +--------+               +--------+                +--------+
--R           (640\|- 2 - %i  - 64 - 672%i)\|- 2 + %i  + (64 - 672%i)\|- 2 - %i
--R         + 
--R           - 712
--R      *
--R                2 4       2 2
--R             (%e )  + 2(%e )  + 1
--R         log(--------------------)
--R                       2 4
--R                    (%e )
--R     + 
--R                +--------+               +--------+                +--------+
--R           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
--R         + 
--R           - 979
--R      *
--R                         +--------+
--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                                         +--------+
--R           (- 640log(4) + 2560 - 1280%i)\|- 2 - %i  + (64 + 672%i)log(4) - 2568
--R         + 
--R           - 3044%i
--R      *
--R          +--------+
--R         \|- 2 + %i
--R     + 
--R                                              +--------+
--R       ((- 64 + 672%i)log(4) - 2056 - 2332%i)\|- 2 - %i  + 712log(4) - 2848
--R     + 
--R       3360%i
--R  /
--R             +--------+                 +--------+                  +--------+
--R       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
--R     + 
--R       - 1424
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 175

--S 176 of 224
in2386a:=integrate(acoth(1-z)-(z^2-z+2)^(1/2), z= 0..1,"noPole")
 

                   +-+                 +-+          +-+
          - 7log(4\|2  + 9) + 7log(- 4\|2  + 9) - 8\|2  + 8log(4)
   (176)  -------------------------------------------------------
                                     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                   +-+                 +-+          +-+
--R          - 7log(4\|2  + 9) + 7log(- 4\|2  + 9) - 8\|2  + 8log(4)
--R   (176)  -------------------------------------------------------
--R                                     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 176

--S 177 of 224
in2390a:=integrate((z^2-%i*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole")
 

   (177)
                   2%i +--------+                  2%i  +--------+
           (- 560%e   \|- 1 - %i  + (168 - 476%i)%e   )\|- 1 + %i
         + 
                            2%i +--------+        2%i
           (- 168 - 476%i)%e   \|- 1 - %i  + 455%e
      *
                       +--------+
         log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
     + 
                 2%i +--------+                    2%i  +--------+
           (560%e   \|- 1 - %i  + (- 168 + 476%i)%e   )\|- 1 + %i
         + 
                          2%i +--------+        2%i
           (168 + 476%i)%e   \|- 1 - %i  - 455%e
      *
                         +--------+
         log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i)
     + 
                       2%i 2            2%i          +--------+
           (- 640%i (%e   )  + 1280%i %e    + 640%i)\|- 1 - %i
         + 
                           2%i 2                     2%i
           (544 + 192%i)(%e   )  + (- 1480 - 580%i)%e    - 544 - 192%i
      *
          +--------+
         \|- 1 + %i
     + 
                        2%i 2                     2%i                +--------+
       ((544 - 192%i)(%e   )  + (- 1480 + 580%i)%e    - 544 + 192%i)\|- 1 - %i
     + 
                2%i 2            2%i
       520%i (%e   )  - 1824%i %e    - 520%i
  /
              2%i +--------+                     2%i  +--------+
       (1280%e   \|- 1 - %i  + (- 384 + 1088%i)%e   )\|- 1 + %i
     + 
                       2%i +--------+         2%i
       (384 + 1088%i)%e   \|- 1 - %i  - 1040%e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (177)
--R                   2%i +--------+                  2%i  +--------+
--R           (- 560%e   \|- 1 - %i  + (168 - 476%i)%e   )\|- 1 + %i
--R         + 
--R                            2%i +--------+        2%i
--R           (- 168 - 476%i)%e   \|- 1 - %i  + 455%e
--R      *
--R                       +--------+
--R         log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
--R     + 
--R                 2%i +--------+                    2%i  +--------+
--R           (560%e   \|- 1 - %i  + (- 168 + 476%i)%e   )\|- 1 + %i
--R         + 
--R                          2%i +--------+        2%i
--R           (168 + 476%i)%e   \|- 1 - %i  - 455%e
--R      *
--R                         +--------+
--R         log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i)
--R     + 
--R                       2%i 2            2%i          +--------+
--R           (- 640%i (%e   )  + 1280%i %e    + 640%i)\|- 1 - %i
--R         + 
--R                           2%i 2                     2%i
--R           (544 + 192%i)(%e   )  + (- 1480 - 580%i)%e    - 544 - 192%i
--R      *
--R          +--------+
--R         \|- 1 + %i
--R     + 
--R                        2%i 2                     2%i                +--------+
--R       ((544 - 192%i)(%e   )  + (- 1480 + 580%i)%e    - 544 + 192%i)\|- 1 - %i
--R     + 
--R                2%i 2            2%i
--R       520%i (%e   )  - 1824%i %e    - 520%i
--R  /
--R              2%i +--------+                     2%i  +--------+
--R       (1280%e   \|- 1 - %i  + (- 384 + 1088%i)%e   )\|- 1 + %i
--R     + 
--R                       2%i +--------+         2%i
--R       (384 + 1088%i)%e   \|- 1 - %i  - 1040%e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 177

--S 178 of 224
in2392a:=integrate(1/sec(z-1)+acoth(1-z^(1/2)), z= 0..1,"noPole")
 

   (178)  sin(1) + log(4) - 1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (178)  sin(1) + log(4) - 1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 178

--S 179 of 224
in2404a:=integrate(1/(1+%i*z^2)^(1/2)+acoth(z), z= -1..1,"noPole")
 

   (179)
   [
            +-----+
           \|- 4%i
        *
           log
                             +-----+             +------+               +-----+
                  ((4 - 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i  + (- 8 + 8%i)\|- 4%i
                + 
                  - 20%i
             /
                  +------+
                2\|1 + %i  - 2 - %i
       + 
         -
               +-----+
              \|- 4%i
           *
              log
                                  +-----+             +------+
                     ((- 4 + 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i
                   + 
                               +-----+
                     (8 - 8%i)\|- 4%i  - 20%i
                /
                     +------+
                   2\|1 + %i  - 2 - %i
    /
       4
     ,
                      +------+
        +---+     2%i\|1 + %i  - 2%i
    - 2\|4%i atan(------------------)]
                         +---+
                        \|4%i
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (179)
--R   [
--R            +-----+
--R           \|- 4%i
--R        *
--R           log
--R                             +-----+             +------+               +-----+
--R                  ((4 - 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i  + (- 8 + 8%i)\|- 4%i
--R                + 
--R                  - 20%i
--R             /
--R                  +------+
--R                2\|1 + %i  - 2 - %i
--R       + 
--R         -
--R               +-----+
--R              \|- 4%i
--R           *
--R              log
--R                                  +-----+             +------+
--R                     ((- 4 + 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i
--R                   + 
--R                               +-----+
--R                     (8 - 8%i)\|- 4%i  - 20%i
--R                /
--R                     +------+
--R                   2\|1 + %i  - 2 - %i
--R    /
--R       4
--R     ,
--R                      +------+
--R        +---+     2%i\|1 + %i  - 2%i
--R    - 2\|4%i atan(------------------)]
--R                         +---+
--R                        \|4%i
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 179

--S 180 of 224
in2409a:=integrate(tan(z)+1/(%i/(z+%i))^(1/2), z= 0..1/2*%pi,"noPole")
 

   (180)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (180)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 180

--S 181 of 224
in248a:=integrate(log(z^%i)^2, z= 0..1,"noPole")
 

   (181)  - 2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (181)  - 2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 181

--S 182 of 224
in248b:=integrate(log(z^%i)^2, z= 0..1,"noPole")
 

   (182)  - 2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (182)  - 2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 182

--S 183 of 224
in249a:=integrate((sin(z)/(cos(z)-1))^(1/3), z= 0..%pi,"noPole")
 

                 3+-+           3+-+         +-+
          3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3
   (183)  --------------------------------------
                            24
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 3+-+           3+-+         +-+
--R          3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3
--R   (183)  --------------------------------------
--R                            24
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 183

--S 184 of 224
in251a:=integrate((-1)^z*exp(-z)*sin(z), z= 0..%plusInfinity,"noPole")
 

               2
          - %pi  + 2
   (184)  ----------
              4
           %pi  + 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R               2
--R          - %pi  + 2
--R   (184)  ----------
--R              4
--R           %pi  + 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 184

--S 185 of 224
in2434a:=integrate(acoth(z^(1/2))+log(abs(z-1)), z= 0..1,"noPole")
 

          log(16) + log(4) - 6log(2)
   (185)  --------------------------
                       4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(16) + log(4) - 6log(2)
--R   (185)  --------------------------
--R                       4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 185

--S 186 of 224
in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole")
 

   (186)
                                        3+---+2    3+---+
           3+---+2    3+---+            \|- 1   - 2\|- 1  + 1
       log(\|- 1   - 2\|- 1  + 1) + log(---------------------) + 4atan(%e)
                                               3+---+2
                                               \|- 1
     + 
                1    3+---+2    3+---+
       - 4atan(--) + \|- 1   + 2\|- 1  - 3
               %e
  /
     2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (186)
--R                                        3+---+2    3+---+
--R           3+---+2    3+---+            \|- 1   - 2\|- 1  + 1
--R       log(\|- 1   - 2\|- 1  + 1) + log(---------------------) + 4atan(%e)
--R                                               3+---+2
--R                                               \|- 1
--R     + 
--R                1    3+---+2    3+---+
--R       - 4atan(--) + \|- 1   + 2\|- 1  - 3
--R               %e
--R  /
--R     2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 186

--S 187 of 224
in2462a:=integrate(log((1+(1-z)^(1/2))/z)+csch(z), z= -1..0,"noPole")
 

   (187)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (187)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 187

--S 188 of 224
in2469a:=integrate(1/(2+z)^2+1/(z^2-%i*z-2)^(1/2), z= -1..1,"noPole")
 

   (188)
                      +--------+
       3log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
     + 
                          +--------+
       - 3log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i) + 4
  /
     6
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (188)
--R                      +--------+
--R       3log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
--R     + 
--R                          +--------+
--R       - 3log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i) + 4
--R  /
--R     6
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 188

--S 189 of 224
in2484a:=integrate(log(1-z^2)+sinh(z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (189)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (189)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 189

--S 190 of 224
in2485a:=integrate(log(1-z^(1/2))-acoth(z^(1/2)), z= 0..1,"noPole")
 

          - log(16) + log(4) + 2log(2) - 10
   (190)  ---------------------------------
                          4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - log(16) + log(4) + 2log(2) - 10
--R   (190)  ---------------------------------
--R                          4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 190

--S 191 of 224
in2521a:=integrate(acoth(z^(1/2))+cos(z^(1/2)-1), z= 0..1,"noPole")
 

   (191)  - 2cos(1) + 3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (191)  - 2cos(1) + 3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 191

--S 192 of 224
in2524a:=integrate(log(abs(1+1/z^(1/3)))+log(1+1/z), z= -1..0,"noPole")
 

   (192)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (192)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 192

--S 193 of 224
in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole")
 

   (193)
                                          3+---+2    3+---+
              3+---+2   3+---+            \|- 1   - 2\|- 1  + 1    3+---+2
       - log(3\|- 1   + \|- 1  - 1) + log(---------------------) + \|- 1
                                                 3+---+2
                                                 \|- 1
     + 
        3+---+
       2\|- 1  - log(4)
  /
     2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (193)
--R                                          3+---+2    3+---+
--R              3+---+2   3+---+            \|- 1   - 2\|- 1  + 1    3+---+2
--R       - log(3\|- 1   + \|- 1  - 1) + log(---------------------) + \|- 1
--R                                                 3+---+2
--R                                                 \|- 1
--R     + 
--R        3+---+
--R       2\|- 1  - log(4)
--R  /
--R     2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 193

--S 194 of 224
in2566a:=integrate(log(1+(1-z)^(1/2))+acoth(1-z), z= -1..1,"noPole")
 

                +-+          +-+
          4log(\|2  + 1) + 4\|2  + 3log(9) - 4
   (194)  ------------------------------------
                            4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+          +-+
--R          4log(\|2  + 1) + 4\|2  + 3log(9) - 4
--R   (194)  ------------------------------------
--R                            4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 194

--S 195 of 224
in2586a:=integrate(acoth(z^(1/2))+atan(z^(1/2)), z= 0..1,"noPole")
 

          log(16) - log(4) - 2log(2) + 2%pi
   (195)  ---------------------------------
                          4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(16) - log(4) - 2log(2) + 2%pi
--R   (195)  ---------------------------------
--R                          4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 195

--S 196 of 224
in2591a:=integrate(log(z)/(1-z^(1/2))^3-log(z)*log(-z), z= 0..1,"noPole")
 

   (196)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (196)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 196

--S 197 of 224
in2598a:=integrate(exp(-z^(1/2))+acoth(1-z^(1/2)), z= 0..1,"noPole")
 

          %e log(4) + %e - 4
   (197)  ------------------
                  %e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          %e log(4) + %e - 4
--R   (197)  ------------------
--R                  %e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 197

--S 198 of 224
in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole")
 

   (198)
             6+-+2                6+-+3                6+-+3         6+-+4
       18log(\|2   + 1) + 3log(- 2\|2   + 3) - 6log(- 4\|2   + 6) + 3\|2
     + 
          6+-+3    6+-+2
       - 6\|2   - 6\|2   - 12log(2) + 7
  /
     6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (198)
--R             6+-+2                6+-+3                6+-+3         6+-+4
--R       18log(\|2   + 1) + 3log(- 2\|2   + 3) - 6log(- 4\|2   + 6) + 3\|2
--R     + 
--R          6+-+3    6+-+2
--R       - 6\|2   - 6\|2   - 12log(2) + 7
--R  /
--R     6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 198

--S 199 of 224
in271a:=integrate(1/sqrt((z^2-1)*(z^2-1)), z= 2..%plusInfinity,"noPole")
 

          log(9)
   (199)  ------
             4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(9)
--R   (199)  ------
--R             4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 199

--S 200 of 224
in275c:=integrate(sqrt(z), z= -%i..%i,"noPole")
 

              +--+       +----+
          2%i\|%i  + 2%i\|- %i
   (200)  ---------------------
                    3
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              +--+       +----+
--R          2%i\|%i  + 2%i\|- %i
--R   (200)  ---------------------
--R                    3
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 200

--S 201 of 224
in275a:=integrate(1/(1+z), z= -%i..%i,"noPole")
 

          log(2%i) - log(- 2%i)
   (201)  ---------------------
                    2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R          log(2%i) - log(- 2%i)
--R   (201)  ---------------------
--R                    2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 201

--S 202 of 224
in275b:=integrate(1/(1+z), z= -%i..%i,"noPole")
 

          log(2%i) - log(- 2%i)
   (202)  ---------------------
                    2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R          log(2%i) - log(- 2%i)
--R   (202)  ---------------------
--R                    2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 202

--S 203 of 224
in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole")
 

   (203)
           +-+
         3\|5
      *
         log
                                +--------+2                   +--------+
                      +-+      3| +-+               +-+      3| +-+          +-+
                (- 12\|5  - 36)\|\|5  - 2   + (- 20\|5  - 24)\|\|5  - 2  + 2\|5
              + 
                - 38
           /
               +--------+2                +--------+
              3| +-+             +-+     3| +-+          +-+
              \|\|5  - 2   + (- \|5  + 4)\|\|5  - 2  - 2\|5  + 3
     + 
                   +--------+2              +--------+
         +-+      3| +-+           +-+     3| +-+          +-+
       3\|5 log(- \|\|5  - 2   + (\|5  - 4)\|\|5  - 2  + 2\|5  - 3)
     + 
         +--------+2      +--------+
        3| +-+           3| +-+          +-+      +-+           +-+
       3\|\|5  - 2   - 18\|\|5  - 2  - 3\|5 log(6\|5  + 14) - 4\|5  + 8
  /
     6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (203)
--R           +-+
--R         3\|5
--R      *
--R         log
--R                                +--------+2                   +--------+
--R                      +-+      3| +-+               +-+      3| +-+          +-+
--R                (- 12\|5  - 36)\|\|5  - 2   + (- 20\|5  - 24)\|\|5  - 2  + 2\|5
--R              + 
--R                - 38
--R           /
--R               +--------+2                +--------+
--R              3| +-+             +-+     3| +-+          +-+
--R              \|\|5  - 2   + (- \|5  + 4)\|\|5  - 2  - 2\|5  + 3
--R     + 
--R                   +--------+2              +--------+
--R         +-+      3| +-+           +-+     3| +-+          +-+
--R       3\|5 log(- \|\|5  - 2   + (\|5  - 4)\|\|5  - 2  + 2\|5  - 3)
--R     + 
--R         +--------+2      +--------+
--R        3| +-+           3| +-+          +-+      +-+           +-+
--R       3\|\|5  - 2   - 18\|\|5  - 2  - 3\|5 log(6\|5  + 14) - 4\|5  + 8
--R  /
--R     6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 203

--S 204 of 224
in2634a:=integrate(1/(z^2+%i*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole")
 

   (204)
                     +----+                              +--+
       log((8 - 4%i)\|- %i  + 3 - 8%i) - log((- 8 - 4%i)\|%i  + 3 + 8%i)
     + 
       2log(4) - 4
  /
     2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (204)
--R                     +----+                              +--+
--R       log((8 - 4%i)\|- %i  + 3 - 8%i) - log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R     + 
--R       2log(4) - 4
--R  /
--R     2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 204

--S 205 of 224
in2656a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole")
 

   (205)
            +-+            +-+                 +-+          +-+
   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
   ----------------------------------------------------------------------
                                      4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (205)
--R            +-+            +-+                 +-+          +-+
--R   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
--R   ----------------------------------------------------------------------
--R                                      4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 205

--S 206 of 224
in2676a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole")
 

   (206)
            +-+            +-+                 +-+          +-+
   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
   ----------------------------------------------------------------------
                                      4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (206)
--R            +-+            +-+                 +-+          +-+
--R   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
--R   ----------------------------------------------------------------------
--R                                      4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 206

--S 207 of 224
in2664aa:=integrate(atanh(1/z)+(1+z^2)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (207)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (207)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 207

--S 208 of 224
in2681a:=integrate((z^2-%i*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole")
 

   (208)
                  +--------+               +--------+                +--------+
           (- 880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
         + 
           979
      *
                       +--------+
         log((8 + 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                +--------+               +--------+                  +--------+
           (880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i  + (- 88 + 924%i)\|- 2 - %i
         + 
           - 979
      *
                         +--------+
         log((- 8 + 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                                   - 4 + 3%i                      +--------+
           (320log(25) - 640%i log(---------) + 2560%pi + 1280%i)\|- 2 - %i
                                    4 + 3%i
         + 
                                                 - 4 + 3%i
           (32 + 336%i)log(25) + (672 - 64%i)log(---------) + (256 + 2688%i)%pi
                                                  4 + 3%i
         + 
           - 2312 - 356%i
      *
          +--------+
         \|- 2 + %i
     + 
                                                   - 4 + 3%i
           (- 32 + 336%i)log(25) + (672 + 64%i)log(---------)
                                                    4 + 3%i
         + 
           (- 256 + 2688%i)%pi - 2312 + 356%i
      *
          +--------+
         \|- 2 - %i
     + 
                                - 4 + 3%i
       - 356log(25) + 712%i log(---------) - 2848%pi - 3360%i
                                 4 + 3%i
  /
             +--------+                 +--------+                    +--------+
       (1280\|- 2 - %i  + 128 + 1344%i)\|- 2 + %i  + (- 128 + 1344%i)\|- 2 - %i
     + 
       - 1424
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (208)
--R                  +--------+               +--------+                +--------+
--R           (- 880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
--R         + 
--R           979
--R      *
--R                       +--------+
--R         log((8 + 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                +--------+               +--------+                  +--------+
--R           (880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i  + (- 88 + 924%i)\|- 2 - %i
--R         + 
--R           - 979
--R      *
--R                         +--------+
--R         log((- 8 + 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                                   - 4 + 3%i                      +--------+
--R           (320log(25) - 640%i log(---------) + 2560%pi + 1280%i)\|- 2 - %i
--R                                    4 + 3%i
--R         + 
--R                                                 - 4 + 3%i
--R           (32 + 336%i)log(25) + (672 - 64%i)log(---------) + (256 + 2688%i)%pi
--R                                                  4 + 3%i
--R         + 
--R           - 2312 - 356%i
--R      *
--R          +--------+
--R         \|- 2 + %i
--R     + 
--R                                                   - 4 + 3%i
--R           (- 32 + 336%i)log(25) + (672 + 64%i)log(---------)
--R                                                    4 + 3%i
--R         + 
--R           (- 256 + 2688%i)%pi - 2312 + 356%i
--R      *
--R          +--------+
--R         \|- 2 - %i
--R     + 
--R                                - 4 + 3%i
--R       - 356log(25) + 712%i log(---------) - 2848%pi - 3360%i
--R                                 4 + 3%i
--R  /
--R             +--------+                 +--------+                    +--------+
--R       (1280\|- 2 - %i  + 128 + 1344%i)\|- 2 + %i  + (- 128 + 1344%i)\|- 2 - %i
--R     + 
--R       - 1424
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 208

--S 209 of 224
in2720a:=integrate(acoth(1-(1-z)^(1/2))+atan(z-1), z= 0..1,"noPole")
 

          5log(4) - %pi - 4
   (209)  -----------------
                  4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          5log(4) - %pi - 4
--R   (209)  -----------------
--R                  4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 209

--S 210 of 224
in2724a:=integrate(log(1-1/z^3)-(1+1/z^2)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (210)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (210)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 210

--S 211 of 224
in2732:=integrate(atan(1/3*3^(1/2)*(2*z-1)), z= 0..%plusInfinity)
 

   (211)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (211)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 211

--S 212 of 224
in2783a:=integrate(1/z^(1/3)+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (212)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (212)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 212

--S 213 of 224
in285:=integrate(sqrt(1+sqrt(z-1)), z)
 

                                 +------------+
             +-----+             | +-----+
          (4\|z - 1  + 12z - 20)\|\|z - 1  + 1
   (213)  -------------------------------------
                            15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 +------------+
--R             +-----+             | +-----+
--R          (4\|z - 1  + 12z - 20)\|\|z - 1  + 1
--R   (213)  -------------------------------------
--R                            15
--R                                          Type: Union(Expression Integer,...)
--E 213

--S 214 of 224
in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z)
 

                                  +-------------+
             +------+             | +------+
             | 2          2       | | 2
          (2\|z  - 1  + 6z  - 10)\|\|z  - 1  + 1
   (214)  ---------------------------------------
                             15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                  +-------------+
--R             +------+             | +------+
--R             | 2          2       | | 2
--R          (2\|z  - 1  + 6z  - 10)\|\|z  - 1  + 1
--R   (214)  ---------------------------------------
--R                             15
--R                                          Type: Union(Expression Integer,...)
--E 214

--S 215 of 224
in295ba:=integrate(z*sqrt(1+sqrt(z^2-1)), z= 1..sqrt(2),"noPole")
 

            +-+
          4\|2  + 4
   (215)  ---------
              15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            +-+
--R          4\|2  + 4
--R   (215)  ---------
--R              15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 215

--S 216 of 224
integrate(1/sqrt(20+x^2+y^2), x = -5..5,"noPole")
 

                 +-------+                       +-------+
                 | 2          2                  | 2          2
          log(10\|y  + 45  + y  + 70) - log(- 10\|y  + 45  + y  + 70)
   (216)  -----------------------------------------------------------
                                       2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 +-------+                       +-------+
--R                 | 2          2                  | 2          2
--R          log(10\|y  + 45  + y  + 70) - log(- 10\|y  + 45  + y  + 70)
--R   (216)  -----------------------------------------------------------
--R                                       2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 216

--S 217 of 224
in291:=integrate(cos(2*atan(z-sqrt(2)))-sin(2*atan(z-sqrt(2))), z = 0..%plusInfinity)
 

   (217)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (217)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 217

--S 218 of 224
in2992a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..%plusInfinity,"noPole")
 

   (218)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (218)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 218

--S 219 of 224
in2997a:=integrate(log(1+1/z^3)-log(abs(1+z)), z= %minusInfinity..%plusInfinity,"noPole")
 

   (219)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (219)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 219

--S 220 of 224
in3008a:=integrate(exp(-z^(1/3))+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (220)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (220)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 220

--S 221 of 224
in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole")
 

   (221)
       log
                     +-+           - n 8          +-+          - n 6
              (- 816\|2  + 1154)(%e   )  + (- 560\|2  + 792)(%e   )
            + 
                     +-+          - n 4         +-+         - n 2
              (- 144\|2  + 204)(%e   )  + (- 16\|2  + 24)(%e   )  + 2
         /
               - n 8        - n 6        - n 4        - n 2
            (%e   )  + 12(%e   )  + 38(%e   )  + 12(%e   )  + 1
     + 
                  +-+
       - log(- 24\|2  + 34)
  /
        +-+
     4n\|2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (221)
--R       log
--R                     +-+           - n 8          +-+          - n 6
--R              (- 816\|2  + 1154)(%e   )  + (- 560\|2  + 792)(%e   )
--R            + 
--R                     +-+          - n 4         +-+         - n 2
--R              (- 144\|2  + 204)(%e   )  + (- 16\|2  + 24)(%e   )  + 2
--R         /
--R               - n 8        - n 6        - n 4        - n 2
--R            (%e   )  + 12(%e   )  + 38(%e   )  + 12(%e   )  + 1
--R     + 
--R                  +-+
--R       - log(- 24\|2  + 34)
--R  /
--R        +-+
--R     4n\|2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 221

--S 222 of 224
in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 

   (222)
       log
                              2                                   2
                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
             *
                 +-+
                \|3
            + 
                      2                                     2
              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
         /
                   2
            4sin(1)  - 4sin(1) + 1
     + 
                   +-+
       - log(- 168\|3  + 291)
  /
      +-+
     \|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (222)
--R       log
--R                              2                                   2
--R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R             *
--R                 +-+
--R                \|3
--R            + 
--R                      2                                     2
--R              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R         /
--R                   2
--R            4sin(1)  - 4sin(1) + 1
--R     + 
--R                   +-+
--R       - log(- 168\|3  + 291)
--R  /
--R      +-+
--R     \|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 222

--S 223 of 224
in317:=integrate((cos(z)^a)^(1/a), z= 0..%pi)
 

   (223)  0
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (223)  0
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 223

--S 224 of 224
in319a:=integrate(exp(-z)*atan(sin(z)/(1+cos(z))), z=0..%plusInfinity,"noPole")
 

          1
   (224)  -
          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (224)  -
--R          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 224
)spool 
 
Starts dribbling to scherk.output (2009/2/17, 18:0:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 7
(xOffset, yOffset):DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 7
drawScherk(m,n) ==
  free xOffset, yOffset
  space := create3Space()$ThreeSpace(DoubleFloat)
  for i in 0..m-1 repeat
    xOffset := i*%pi
    for j in 0 .. n-1 repeat
      rem(i+j, 2) = 0 => 'iter
      yOffset := j*%pi
      drawOneScherk(space)
  makeViewport3D(space, "Scherk's Minimal Surface")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 7
scherk1(u,v) ==
  x := cos(u)/exp(v)
  point [xOffset + acos(x), yOffset + u, v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 7
scherk2(u,v) ==
  x := cos(u)/exp(v)
  point [xOffset - acos(x), yOffset + u, v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 7
scherk3(u,v) ==
  x := exp(v) * cos(u)
  point [xOffset + u, yOffset + acos(x), v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 7
scherk4(u,v) ==
  x := exp(v) * cos(u)
  point [xOffset + u, yOffset - acos(x), v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 7
drawOneScherk(s) ==
  makeObject(scherk1, -%pi/2..%pi/2, 0..%pi/2,  space == s, _
             var1Steps == 28, var2Steps == 28)
  makeObject(scherk2, -%pi/2..%pi/2, 0..%pi/2,  space == s, _
             var1Steps == 28, var2Steps == 28)
  makeObject(scherk3, -%pi/2..%pi/2, -%pi/2..0, space == s, _
             var1Steps == 28, var2Steps == 28)
  makeObject(scherk4, -%pi/2..%pi/2, -%pi/2..0, space == s, _
             var1Steps == 28, var2Steps == 28)
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
)spool 
 
Starts dribbling to fnla.output (2009/2/17, 17:46:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 7
fnl := FNLA(4,4,INT)
 

   (1)  FreeNilpotentLie(4,4,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  FreeNilpotentLie(4,4,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 7
dimension()$fnl
 

   (2)  90
                                                     Type: NonNegativeInteger
--R 
--R
--R   (2)  90
--R                                                     Type: NonNegativeInteger
--E 2
 
--S 3 of 7
x:fnl := generator(1)
 

   (3)  e
         1
                                          Type: FreeNilpotentLie(4,4,Integer)
--R 
--R
--R   (3)  e
--R         1
--R                                          Type: FreeNilpotentLie(4,4,Integer)
--E 3

--S 4 of 7
y:fnl := generator(17)
 

   (4)  e
         17
                                          Type: FreeNilpotentLie(4,4,Integer)
--R 
--R
--R   (4)  e
--R         17
--R                                          Type: FreeNilpotentLie(4,4,Integer)
--E 4

--S 5 of 7
z:=x*y
 

   (5)  2e   - e   + e
          78    45    38
                                          Type: FreeNilpotentLie(4,4,Integer)
--R 
--R
--R   (5)  2e   - e   + e
--R          78    45    38
--R                                          Type: FreeNilpotentLie(4,4,Integer)
--E 5

--S 6 of 7
deepExpand z
 

   (6)  2[[e ,e ],[e ,e ]] - [e ,[e ,[e ,e ]]] + [e ,[e ,[e ,e ]]]
            1  2    2  3       3   2   1  2        2   2   1  3
                                                             Type: OutputForm
--R 
--R
--R   (6)  2[[e ,e ],[e ,e ]] - [e ,[e ,[e ,e ]]] + [e ,[e ,[e ,e ]]]
--R            1  2    2  3       3   2   1  2        2   2   1  3
--R                                                             Type: OutputForm
--E 6

--S 7 of 7
shallowExpand z
 

   (7)  2[e ,e ] - [e ,e  ] + [e ,e  ]
           5  8      3  14      2  15
                                                             Type: OutputForm
--R 
--R
--R   (7)  2[e ,e ] - [e ,e  ] + [e ,e  ]
--R           5  8      3  14      2  15
--R                                                             Type: OutputForm
--E 7
)spool 
 
Starts dribbling to strtbl.output (2009/2/17, 18:0:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
t: StringTable(Integer) := table()
 

   (1)  table()
                                                    Type: StringTable Integer
--R 
--R
--R   (1)  table()
--R                                                    Type: StringTable Integer
--E 1

--S 2 of 3
for s in split("My name is Ian Watt.",char " ")
  repeat
    t.s := #s
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 3
for key in keys t repeat output [key, t.key]
 
   ["Watt.",5]
   ["Ian",3]
   ["is",2]
   ["name",4]
   ["My",2]
                                                                   Type: Void
--R 
--R   ["Watt.",5]
--R   ["Ian",3]
--R   ["is",2]
--R   ["name",4]
--R   ["My",2]
--R                                                                   Type: Void
--E 3
)spool 
 
Starts dribbling to lword.output (2009/2/17, 17:52:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 22
a:Symbol :='a
 

   (1)  a
                                                                 Type: Symbol
--R 
--R
--R   (1)  a
--R                                                                 Type: Symbol
--E 1

--S 2 of 22
b:Symbol :='b
 

   (2)  b
                                                                 Type: Symbol
--R 
--R
--R   (2)  b
--R                                                                 Type: Symbol
--E 2

--S 3 of 22
c:Symbol :='c
 

   (3)  c
                                                                 Type: Symbol
--R 
--R
--R   (3)  c
--R                                                                 Type: Symbol
--E 3

--S 4 of 22
lword:= LyndonWord(Symbol)
 

   (4)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 22
magma := Magma(Symbol)
 

   (5)  Magma Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  Magma Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 22
word   := OrderedFreeMonoid(Symbol)
 

   (6)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (6)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 6

--S 7 of 22
LyndonWordsList1([a,b,c],3)$lword
 

   (7)
   [[[a],[b],[c]], [[a b],[a c],[b c]],
       2     2       2                      2    2       2
    [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]]
                             Type: OneDimensionalArray List LyndonWord Symbol
--R 
--R
--R   (7)
--R   [[[a],[b],[c]], [[a b],[a c],[b c]],
--R       2     2       2                      2    2       2
--R    [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]]
--R                             Type: OneDimensionalArray List LyndonWord Symbol
--E 7

--S 8 of 22
LyndonWordsList([a,b,c],3)$lword
 

   (8)
                                          2      2        2
   [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b],
        2     2        2
    [a c ], [b c], [b c ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (8)
--R                                          2      2        2
--R   [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b],
--R        2     2        2
--R    [a c ], [b c], [b c ]]
--R                                                 Type: List LyndonWord Symbol
--E 8

--S 9 of 22
lw := LyndonWordsList([a,b],5)$lword
 

   (9)
                       2        2     3      2 2       3     4      3 2
   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
      2          2 3           2       4
    [a b a b], [a b ], [a b a b ], [a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (9)
--R                       2        2     3      2 2       3     4      3 2
--R   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
--R      2          2 3           2       4
--R    [a b a b], [a b ], [a b a b ], [a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 9

--S 10 of 22
w1 : word := lw.4 :: word
 

          2
   (10)  a b
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R          2
--R   (10)  a b
--R                                               Type: OrderedFreeMonoid Symbol
--E 10

--S 11 of 22
w2 : word := lw.5 :: word
 

            2
   (11)  a b
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R            2
--R   (11)  a b
--R                                               Type: OrderedFreeMonoid Symbol
--E 11

--S 12 of 22
factor(a::word)$lword
 

   (12)  [[a]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (12)  [[a]]
--R                                                 Type: List LyndonWord Symbol
--E 12

--S 13 of 22
factor(w1*w2)$lword
 

            2     2
   (13)  [[a b a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R            2     2
--R   (13)  [[a b a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 13

--S 14 of 22
factor(w2*w2)$lword
 

              2      2
   (14)  [[a b ],[a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R              2      2
--R   (14)  [[a b ],[a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 14

--S 15 of 22
factor(w2*w1)$lword
 

              2    2
   (15)  [[a b ],[a b]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R              2    2
--R   (15)  [[a b ],[a b]]
--R                                                 Type: List LyndonWord Symbol
--E 15

--S 16 of 22
lyndon?(w1)$lword
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 22
lyndon?(w1*w2)$lword
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 22
lyndon?(w2*w1)$lword
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 22
lyndonIfCan(w1)$lword
 

           2
   (19)  [a b]
                                           Type: Union(LyndonWord Symbol,...)
--R 
--R
--R           2
--R   (19)  [a b]
--R                                           Type: Union(LyndonWord Symbol,...)
--E 19

--S 20 of 22
lyndonIfCan(w2*w1)$lword
 

   (20)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (20)  "failed"
--R                                                    Type: Union("failed",...)
--E 20

--S 21 of 22
lyndon(w1)$lword
 

           2
   (21)  [a b]
                                                      Type: LyndonWord Symbol
--R 
--R
--R           2
--R   (21)  [a b]
--R                                                      Type: LyndonWord Symbol
--E 21

--S 22 of 22
lyndon(w1*w2)$lword
 

           2     2
   (22)  [a b a b ]
                                                      Type: LyndonWord Symbol
--R 
--R
--R           2     2
--R   (22)  [a b a b ]
--R                                                      Type: LyndonWord Symbol
--E 22
)spool 
 
Starts dribbling to calculus.output (2009/2/17, 17:44:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input for page FormalDerivativePage

--S 1 of 24
differentiate(f, x)
 

   (1)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  0
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 24
f := operator f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 24
x := operator x
 

   (3)  x
                                                          Type: BasicOperator
--R 
--R
--R   (3)  x
--R                                                          Type: BasicOperator
--E 3

--S 4 of 24
y := operator y
 

   (4)  y
                                                          Type: BasicOperator
--R 
--R
--R   (4)  y
--R                                                          Type: BasicOperator
--E 4

--S 5 of 24
a := f(x z, y z, z**2) + x y(z+1)
 

                                   2
   (5)  x(y(z + 1)) + f(x(z),y(z),z )
                                                     Type: Expression Integer
--R 
--R
--R                                   2
--R   (5)  x(y(z + 1)) + f(x(z),y(z),z )
--R                                                     Type: Expression Integer
--E 5

--S 6 of 24
dadz := differentiate(a, z)
 

   (6)
                      2     ,                  2     ,                  2
     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
        ,3                       ,2                       ,1
   + 
      ,           ,
     x (y(z + 1))y (z + 1)

                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                      2     ,                  2     ,                  2
--R     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
--R        ,3                       ,2                       ,1
--R   + 
--R      ,           ,
--R     x (y(z + 1))y (z + 1)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 24
eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

   (7)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 24
eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

            z             2
   (8)  f(%e ,log(z + 1),z ) + z + 2
                                                     Type: Expression Integer
--R 
--R
--R            z             2
--R   (8)  f(%e ,log(z + 1),z ) + z + 2
--R                                                     Type: Expression Integer
--E 8

--S 9 of 24
differentiate(%, z)
 

   (9)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (9)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 9

-- Input for page LaplacePage
)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 24
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
 

   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
--R                                                     Type: Expression Integer
--E 10

--S 11 of 24
laplace(%, t, s)
 

             3
           4a
   (2)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R             3
--R           4a
--R   (2)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 11

--S 12 of 24
laplace((exp(a*t) - exp(b*t))/t, t, s)
 

   (3)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 12

--S 13 of 24
laplace(2/t * (1 - cos(a*t)), t, s)
 

             2    2
   (4)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R             2    2
--R   (4)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 13

--S 14 of 24
laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
 

                    1
   (5)  ------------------------
           2             3    2
        b s  + 2a b s + b  + a b
                                                     Type: Expression Integer
--R 
--R
--R                    1
--R   (5)  ------------------------
--R           2             3    2
--R        b s  + 2a b s + b  + a b
--R                                                     Type: Expression Integer
--E 14

--S 15 of 24
laplace((cos(a*t) - cos(b*t))/t, t, s)
 

             2    2         2    2
        log(s  + b ) - log(s  + a )
   (6)  ---------------------------
                     2
                                                     Type: Expression Integer
--R 
--R
--R             2    2         2    2
--R        log(s  + b ) - log(s  + a )
--R   (6)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 15

--S 16 of 24
laplace(exp(a*t+b)*Ei(c*t), t, s)
 

          b    s + c - a
        %e log(---------)
                   c
   (7)  -----------------
              s - a
                                                     Type: Expression Integer
--R 
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (7)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 16

--S 17 of 24
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
 

               2    2
              s  + b             d
        a log(-------) + 2c atan(-)
                  2              s
                 b
   (8)  ---------------------------
                     2s
                                                     Type: Expression Integer
--R 
--R
--R               2    2
--R              s  + b             d
--R        a log(-------) + 2c atan(-)
--R                  2              s
--R                 b
--R   (8)  ---------------------------
--R                     2s
--R                                                     Type: Expression Integer
--E 17

--S 18 of 24
laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
 

                                    2
          4     2 2    4           t           3
        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
   (9)  ----------------------------------------
                      4     2 2    4
                     s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                                    2
--R          4     2 2    4           t           3
--R        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
--R   (9)  ----------------------------------------
--R                      4     2 2    4
--R                     s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 18

-- Input for page DerivativePage
)clear all
 
   All user variables and function definitions have been cleared.

--S 19 of 24
f := exp exp x
 

            x
          %e
   (1)  %e
                                                     Type: Expression Integer
--R 
--R
--R            x
--R          %e
--R   (1)  %e
--R                                                     Type: Expression Integer
--E 19

--S 20 of 24
differentiate(f, x)
 

               x
          x  %e
   (2)  %e %e
                                                     Type: Expression Integer
--R 
--R
--R               x
--R          x  %e
--R   (2)  %e %e
--R                                                     Type: Expression Integer
--E 20

--S 21 of 24
differentiate(f, x, 4)
 

                                              x
            x 4       x 3       x 2     x   %e
   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
                                                     Type: Expression Integer
--R 
--R
--R                                              x
--R            x 4       x 3       x 2     x   %e
--R   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
--R                                                     Type: Expression Integer
--E 21

--S 22 of 24
g := sin(x**2 + y)
 

                 2
   (4)  sin(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (4)  sin(y + x )
--R                                                     Type: Expression Integer
--E 22

--S 23 of 24
differentiate(g, y)
 

                 2
   (5)  cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (5)  cos(y + x )
--R                                                     Type: Expression Integer
--E 23

--S 24 of 24
differentiate(g, [y, y, x, x])
 

          2         2              2
   (6)  4x sin(y + x ) - 2cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R          2         2              2
--R   (6)  4x sin(y + x ) - 2cos(y + x )
--R                                                     Type: Expression Integer
--E 24
 
)spool
 
Starts dribbling to gamma.output (2009/2/17, 17:46:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 12
[[1.000,1.0000000000,Gamma(1.000),Gamma(1.000)-1.0000000000],_
 [1.005,0.9971385354,Gamma(1.005),Gamma(1.005)-0.9971385354],_
 [1.010,0.9943258512,Gamma(1.010),Gamma(1.010)-0.9943258512],_
 [1.015,0.9915612888,Gamma(1.015),Gamma(1.015)-0.9915612888],_
 [1.020,0.9888442033,Gamma(1.020),Gamma(1.020)-0.9888442033],_
 [1.025,0.9861739633,Gamma(1.025),Gamma(1.025)-0.9861739633],_
 [1.030,0.9835499506,Gamma(1.030),Gamma(1.030)-0.9835499506],_
 [1.035,0.9809715606,Gamma(1.035),Gamma(1.035)-0.9809715606],_
 [1.040,0.9784382009,Gamma(1.040),Gamma(1.040)-0.9784382009],_
 [1.045,0.9759492919,Gamma(1.045),Gamma(1.045)-0.9759492919],_
 [1.050,0.9735042656,Gamma(1.050),Gamma(1.050)-0.9735042656],_
 [1.055,0.9711025663,Gamma(1.055),Gamma(1.055)-0.9711025663],_
 [1.060,0.9687436495,Gamma(1.060),Gamma(1.060)-0.9687436495],_
 [1.065,0.9664269823,Gamma(1.065),Gamma(1.065)-0.9664269823],_
 [1.070,0.9641520425,Gamma(1.070),Gamma(1.070)-0.9641520425],_
 [1.075,0.9619183189,Gamma(1.075),Gamma(1.075)-0.9619183189],_
 [1.080,0.9597253107,Gamma(1.080),Gamma(1.080)-0.9597253107],_
 [1.085,0.9575725273,Gamma(1.085),Gamma(1.085)-0.9575725273],_
 [1.090,0.9554594882,Gamma(1.090),Gamma(1.090)-0.9554594882],_
 [1.095,0.9533857227,Gamma(1.095),Gamma(1.095)-0.9533857227],_
 [1.100,0.9513507699,Gamma(1.100),Gamma(1.100)-0.9513507699],_
 [1.105,0.9493541778,Gamma(1.105),Gamma(1.105)-0.9493541778],_
 [1.110,0.9473955040,Gamma(1.110),Gamma(1.110)-0.9473955040],_
 [1.115,0.9454743149,Gamma(1.115),Gamma(1.115)-0.9454743149],_
 [1.120,0.9435901856,Gamma(1.120),Gamma(1.120)-0.9435901856],_
 [1.125,0.9417426997,Gamma(1.125),Gamma(1.125)-0.9417426997],_
 [1.130,0.9399314497,Gamma(1.130),Gamma(1.130)-0.9399314497],_
 [1.135,0.9381560356,Gamma(1.135),Gamma(1.135)-0.9381560356],_
 [1.140,0.9364160657,Gamma(1.140),Gamma(1.140)-0.9364160657],_
 [1.145,0.9347111562,Gamma(1.145),Gamma(1.145)-0.9347111562],_
 [1.150,0.9330409311,Gamma(1.150),Gamma(1.150)-0.9330409311],_
 [1.155,0.9314050217,Gamma(1.155),Gamma(1.155)-0.9314050217],_
 [1.160,0.9298030666,Gamma(1.160),Gamma(1.160)-0.9298030666],_
 [1.165,0.9282347120,Gamma(1.165),Gamma(1.165)-0.9282347120],_
 [1.170,0.9266996106,Gamma(1.170),Gamma(1.170)-0.9266996106],_
 [1.175,0.9251974225,Gamma(1.175),Gamma(1.175)-0.9251974225],_
 [1.180,0.9237278143,Gamma(1.180),Gamma(1.180)-0.9237278143],_
 [1.185,0.9222904591,Gamma(1.185),Gamma(1.185)-0.9222904591],_
 [1.190,0.9208850371,Gamma(1.190),Gamma(1.190)-0.9208850371],_
 [1.195,0.9195112341,Gamma(1.195),Gamma(1.195)-0.9195112341],_
 [1.200,0.9181687424,Gamma(1.200),Gamma(1.200)-0.9181687424],_
 [1.205,0.9168572606,Gamma(1.205),Gamma(1.205)-0.9168572606],_
 [1.210,0.9155764930,Gamma(1.210),Gamma(1.210)-0.9155764930],_
 [1.215,0.9143261500,Gamma(1.215),Gamma(1.215)-0.9143261500],_
 [1.220,0.9131059475,Gamma(1.220),Gamma(1.220)-0.9131059475],_
 [1.225,0.9119156071,Gamma(1.225),Gamma(1.225)-0.9119156071],_
 [1.230,0.9107548564,Gamma(1.230),Gamma(1.230)-0.9107548564],_
 [1.235,0.9096234274,Gamma(1.235),Gamma(1.235)-0.9096234274],_
 [1.240,0.9085210583,Gamma(1.240),Gamma(1.240)-0.9085210583],_
 [1.245,0.9074474922,Gamma(1.245),Gamma(1.245)-0.9074474922],_
 [1.250,0.9064024771,Gamma(1.250),Gamma(1.250)-0.9064024771],_
 [1.255,0.9053857663,Gamma(1.255),Gamma(1.255)-0.9053857663],_
 [1.260,0.9043971178,Gamma(1.260),Gamma(1.260)-0.9043971178],_
 [1.265,0.9034362946,Gamma(1.265),Gamma(1.265)-0.9034362946],_
 [1.270,0.9025030645,Gamma(1.270),Gamma(1.270)-0.9025030645],_
 [1.275,0.9015971994,Gamma(1.275),Gamma(1.275)-0.9015971994],_
 [1.280,0.9007184765,Gamma(1.280),Gamma(1.280)-0.9007184765],_
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   (1)
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     [1.9449999999999998, 0.97797978609999991, 0.97797978608168101,
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     [1.9749999999999999, 0.98968654619999996, 0.98968654619855945,
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     [1.9949999999999999, 0.99789636429999995, 0.99789636418206029,
      - 1.1793965803974515E-10]
     ]
                                                  Type: List List DoubleFloat
--R 
--R
--R   (1)
--R   [[1.,1.,1.,0.],
--R
--R     [1.0049999999999999, 0.99713853539999997, 0.99713853525101781,
--R      - 1.4898215994207931E-10]
--R     ,
--R    [1.01,0.99432585120000005,0.99432585119150585,- 8.4942053391046102E-12],
--R
--R     [1.0149999999999999, 0.99156128880000005, 0.99156128884897066,
--R      4.8970605348586105E-11]
--R     ,
--R    [1.02,0.9888442033,0.98884420326391309,- 3.6086911237021013E-11],
--R
--R     [1.0249999999999999, 0.98617396329999996, 0.98617396314825367,
--R      - 1.5174628220648856E-10]
--R     ,
--R    [1.03,0.98354995059999994,0.98354995055382399,- 4.6175951950999661E-11],
--R
--R     [1.0349999999999999, 0.98097156060000001, 0.98097156055058576,
--R      - 4.9414250469226317E-11]
--R     ,
--R    [1.04,0.9784382009,0.97843820091424472,1.4244716517453071E-11],
--R
--R     [1.0449999999999999, 0.97594929190000002, 0.97594929182295154,
--R      - 7.7048478708263701E-11]
--R     ,
--R    [1.05,0.97350426560000003,0.97350426556277558,- 3.7224445748051949E-11],
--R
--R     [1.0549999999999999, 0.97110256630000003, 0.97110256624166991,
--R      - 5.8330118513083562E-11]
--R     ,
--R
--R     [1.0600000000000001, 0.96874364950000003, 0.9687436495116386,
--R      1.1638578989447979E-11]
--R     ,
--R
--R     [1.0649999999999999, 0.96642698230000001, 0.96642698229884005,
--R      - 1.1599610161283636E-12]
--R     ,
--R
--R     [1.0700000000000001, 0.96415204249999997, 0.96415204254136644,
--R      4.1366465808323483E-11]
--R     ,
--R    [1.075,0.96191831890000001,0.96191831893444502,3.4445002405902869E-11],
--R
--R     [1.0800000000000001, 0.9597253107, 0.95972531068282241,
--R      - 1.7177592681605347E-11]
--R     ,
--R    [1.085,0.95757252729999998,0.957572527260101,- 3.9898973014373951E-11],
--R
--R     [1.0900000000000001, 0.95545948820000004, 0.95545948817480109,
--R      - 2.5198954034522103E-11]
--R     ,
--R    [1.095,0.95338572269999999,0.95338572274293298,4.2932990496069579E-11],
--R
--R     [1.1000000000000001, 0.9513507699, 0.95135076986687306,
--R      - 3.3126945631067883E-11]
--R     ,
--R    [1.105,0.94935417779999998,0.94935417782034381,2.0343837725533831E-11],
--R
--R     [1.1100000000000001, 0.94739550400000005, 0.94739550403930195,
--R      3.9301895071730542E-11]
--R     ,
--R    [1.115,0.9454743149,0.94547431491855183,1.8551826741486366E-11],
--R
--R     [1.1200000000000001, 0.94359018559999996, 0.9435901856139034,
--R      1.3903433959683298E-11]
--R     ,
--R    [1.125,0.94174269970000002,0.94174269984970138,1.4970136241743148E-10],
--R
--R     [1.1299999999999999, 0.93993144969999998, 0.93993144973155829,
--R      3.1558311519575E-11]
--R     ,
--R    [1.135,0.93815603560000005,0.93815603556413329,- 3.5866754011237845E-11],
--R
--R     [1.1399999999999999, 0.93641606570000002, 0.9364160656737992,
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--R
--R     [1.9199999999999999, 0.96877430899999994, 0.96877430902597383,
--R      2.5973889705710462E-11]
--R     ,
--R    [1.925,0.97057571340000004,0.97057571340755988,7.5598416415800784E-12],
--R
--R     [1.9299999999999999, 0.97239691780000004, 0.97239691778336623,
--R      - 1.6633805444143945E-11]
--R     ,
--R
--R     [1.9350000000000001, 0.9742379672, 0.97423796711012756,
--R      - 8.9872442821103959E-11]
--R     ,
--R
--R     [1.9399999999999999, 0.97609890749999995, 0.97609890747260597,
--R      - 2.73939759765085E-11]
--R     ,
--R
--R     [1.9450000000000001, 0.97797978610000003, 0.97797978608168112,
--R      - 1.8318901950920008E-11]
--R     ,
--R    [1.95,0.97988065130000002,0.97988065127258051,- 2.7419511106074879E-11],
--R    [1.9550000000000001,0.9818015524,0.98180155250325418,1.032541829815159E-10],
--R    [1.96,0.98374254039999998,0.98374254035288666,- 4.711331325069068E-11],
--R
--R     [1.9650000000000001, 0.98570366639999996, 0.98570366652054964,
--R      1.2054968134833643E-10]
--R     ,
--R    [1.97,0.98768498380000003,0.98768498382399139,2.399136445063732E-11],
--R
--R     [1.9750000000000001, 0.98968654619999996, 0.98968654619855956,
--R      - 1.4404033521486781E-12]
--R     ,
--R    [1.98,0.99170840869999999,0.99170840869626087,- 3.7391201246350647E-12],
--R
--R     [1.9850000000000001, 0.99375062739999998, 0.99375062748495313,
--R      8.4953155621292353E-11]
--R     ,
--R    [1.99,0.99581325980000002,0.995813259847667,4.7666981473071246E-11],
--R
--R     [1.9950000000000001, 0.99789636429999995, 0.99789636418206007,
--R      - 1.1793988008435008E-10]
--R     ]
--R                                                  Type: List List DoubleFloat
--E 1

--S 2 of 12
Psi(x:DFLOAT):DFLOAT==polygamma(0,x)
 
   Function declaration Psi : DoubleFloat -> DoubleFloat has been added
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration Psi : DoubleFloat -> DoubleFloat has been added
--R      to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 12
[[1.000, -0.5772156649, Psi(1.000), Psi(1.000)- -0.5772156649],_
 [1.005, -0.5690209113, Psi(1.005), Psi(1.005)- -0.5690209113],_
 [1.010, -0.5608854579, Psi(1.010), Psi(1.010)- -0.5608854579],_
 [1.015, -0.5528085156, Psi(1.015), Psi(1.015)- -0.5528085156],_
 [1.020, -0.5447893105, Psi(1.020), Psi(1.020)- -0.5447893105],_
 [1.025, -0.5368270828, Psi(1.025), Psi(1.025)- -0.5368270828],_
 [1.030, -0.5289210873, Psi(1.030), Psi(1.030)- -0.5289210873],_
 [1.035, -0.5210705921, Psi(1.035), Psi(1.035)- -0.5210705921],_
 [1.040, -0.5132748789, Psi(1.040), Psi(1.040)- -0.5132748789],_
 [1.045, -0.5055332428, Psi(1.045), Psi(1.045)- -0.5055332428],_
 [1.050, -0.4978449913, Psi(1.050), Psi(1.050)- -0.4978449913],_
 [1.055, -0.4902094448, Psi(1.055), Psi(1.055)- -0.4902094448],_
 [1.060, -0.4826259358, Psi(1.060), Psi(1.060)- -0.4826259358],_
 [1.065, -0.4750938088, Psi(1.065), Psi(1.065)- -0.4750938088],_
 [1.070, -0.4676124199, Psi(1.070), Psi(1.070)- -0.4676124199],_
 [1.075, -0.4601811367, Psi(1.075), Psi(1.075)- -0.4601811367],_
 [1.080, -0.4527993380, Psi(1.080), Psi(1.080)- -0.4527993380],_
 [1.085, -0.4454664135, Psi(1.085), Psi(1.085)- -0.4454664135],_
 [1.090, -0.4381817635, Psi(1.090), Psi(1.090)- -0.4381817635],_
 [1.095, -0.4309447988, Psi(1.095), Psi(1.095)- -0.4309447988],_
 [1.100, -0.4237549404, Psi(1.100), Psi(1.100)- -0.4237549404],_
 [1.105, -0.4166116193, Psi(1.105), Psi(1.105)- -0.4166116193],_
 [1.110, -0.4095142761, Psi(1.110), Psi(1.110)- -0.4095142761],_
 [1.115, -0.4024623611, Psi(1.115), Psi(1.115)- -0.4024623611],_
 [1.120, -0.3954553339, Psi(1.120), Psi(1.120)- -0.3954553339],_
 [1.125, -0.3884926633, Psi(1.125), Psi(1.125)- -0.3884926633],_
 [1.130, -0.3815738268, Psi(1.130), Psi(1.130)- -0.3815738268],_
 [1.135, -0.3746983110, Psi(1.135), Psi(1.135)- -0.3746983110],_
 [1.140, -0.3678656106, Psi(1.140), Psi(1.140)- -0.3678656106],_
 [1.145, -0.3610752291, Psi(1.145), Psi(1.145)- -0.3610752291],_
 [1.150, -0.3543266780, Psi(1.150), Psi(1.150)- -0.3543266780],_
 [1.155, -0.3476194768, Psi(1.155), Psi(1.155)- -0.3476194768],_
 [1.160, -0.3409531528, Psi(1.160), Psi(1.160)- -0.3409531528],_
 [1.165, -0.3343272413, Psi(1.165), Psi(1.165)- -0.3343272413],_
 [1.170, -0.3277412847, Psi(1.170), Psi(1.170)- -0.3277412847],_
 [1.175, -0.3211948332, Psi(1.175), Psi(1.175)- -0.3211948332],_
 [1.180, -0.3146874438, Psi(1.180), Psi(1.180)- -0.3146874438],_
 [1.185, -0.3082186809, Psi(1.185), Psi(1.185)- -0.3082186809],_
 [1.190, -0.3017881156, Psi(1.190), Psi(1.190)- -0.3017881156],_
 [1.195, -0.2953953259, Psi(1.195), Psi(1.195)- -0.2953953259],_
 [1.200, -0.2890398966, Psi(1.200), Psi(1.200)- -0.2890398966],_
 [1.205, -0.2827214187, Psi(1.205), Psi(1.205)- -0.2827214187],_
 [1.210, -0.2764394897, Psi(1.210), Psi(1.210)- -0.2764394897],_
 [1.215, -0.2701937135, Psi(1.215), Psi(1.215)- -0.2701937135],_
 [1.220, -0.2639837000, Psi(1.220), Psi(1.220)- -0.2639837000],_
 [1.225, -0.2578090652, Psi(1.225), Psi(1.225)- -0.2578090652],_
 [1.230, -0.2516694307, Psi(1.230), Psi(1.230)- -0.2516694307],_
 [1.235, -0.2455644243, Psi(1.235), Psi(1.235)- -0.2455644243],_
 [1.240, -0.2394936791, Psi(1.240), Psi(1.240)- -0.2394936791],_
 [1.245, -0.2334568341, Psi(1.245), Psi(1.245)- -0.2334568341],_
 [1.250, -0.2274535334, Psi(1.250), Psi(1.250)- -0.2274535334],_
 [1.255, -0.2214834266, Psi(1.255), Psi(1.255)- -0.2214834266],_
 [1.260, -0.2155461686, Psi(1.260), Psi(1.260)- -0.2155461686],_
 [1.265, -0.2096414193, Psi(1.265), Psi(1.265)- -0.2096414193],_
 [1.270, -0.2037688437, Psi(1.270), Psi(1.270)- -0.2037688437],_
 [1.275, -0.1979281118, Psi(1.275), Psi(1.275)- -0.1979281118],_
 [1.280, -0.1921188983, Psi(1.280), Psi(1.280)- -0.1921188983],_
 [1.285, -0.1863408828, Psi(1.285), Psi(1.285)- -0.1863408828],_
 [1.290, -0.1805937494, Psi(1.290), Psi(1.290)- -0.1805937494],_
 [1.295, -0.1748771870, Psi(1.295), Psi(1.295)- -0.1748771870],_
 [1.300, -0.1691908889, Psi(1.300), Psi(1.300)- -0.1691908889],_
 [1.305, -0.1635345526, Psi(1.305), Psi(1.305)- -0.1635345526],_
 [1.310, -0.1579078803, Psi(1.310), Psi(1.310)- -0.1579078803],_
 [1.315, -0.1523105782, Psi(1.315), Psi(1.315)- -0.1523105782],_
 [1.320, -0.1467423568, Psi(1.320), Psi(1.320)- -0.1467423568],_
 [1.325, -0.1412029305, Psi(1.325), Psi(1.325)- -0.1412029305],_
 [1.330, -0.1356920180, Psi(1.330), Psi(1.330)- -0.1356920180],_
 [1.335, -0.1302093416, Psi(1.335), Psi(1.335)- -0.1302093416],_
 [1.340, -0.1247546279, Psi(1.340), Psi(1.340)- -0.1247546279],_
 [1.345, -0.1193276069, Psi(1.345), Psi(1.345)- -0.1193276069],_
 [1.350, -0.1139280127, Psi(1.350), Psi(1.350)- -0.1139280127],_
 [1.355, -0.1085555827, Psi(1.355), Psi(1.355)- -0.1085555827],_
 [1.360, -0.1032100582, Psi(1.360), Psi(1.360)- -0.1032100582],_
 [1.365, -0.0978911840, Psi(1.365), Psi(1.365)- -0.0978911840],_
 [1.370, -0.0925987082, Psi(1.370), Psi(1.370)- -0.0925987082],_
 [1.375, -0.0873323825, Psi(1.375), Psi(1.375)- -0.0873323825],_
 [1.380, -0.0820919619, Psi(1.380), Psi(1.380)- -0.0820919619],_
 [1.385, -0.0768772046, Psi(1.385), Psi(1.385)- -0.0768772046],_
 [1.390, -0.0716878723, Psi(1.390), Psi(1.390)- -0.0716878723],_
 [1.395, -0.0665237297, Psi(1.395), Psi(1.395)- -0.0665237297],_
 [1.400, -0.0613845446, Psi(1.400), Psi(1.400)- -0.0613845446],_
 [1.405, -0.0562700879, Psi(1.405), Psi(1.405)- -0.0562700879],_
 [1.410, -0.0511801337, Psi(1.410), Psi(1.410)- -0.0511801337],_
 [1.415, -0.0461144589, Psi(1.415), Psi(1.415)- -0.0461144589],_
 [1.420, -0.0410728433, Psi(1.420), Psi(1.420)- -0.0410728433],_
 [1.425, -0.0360550697, Psi(1.425), Psi(1.425)- -0.0360550697],_
 [1.430, -0.0310609237, Psi(1.430), Psi(1.430)- -0.0310609237],_
 [1.435, -0.0260901935, Psi(1.435), Psi(1.435)- -0.0260901935],_
 [1.440, -0.0211426703, Psi(1.440), Psi(1.440)- -0.0211426703],_
 [1.445, -0.0162181479, Psi(1.445), Psi(1.445)- -0.0162181479],_
 [1.450, -0.0113164226, Psi(1.450), Psi(1.450)- -0.0113164226],_
 [1.455, -0.0064372934, Psi(1.455), Psi(1.455)- -0.0064372934],_
 [1.460, -0.0015805620, Psi(1.460), Psi(1.460)- -0.0015805620],_
 [1.465,  0.0032539677, Psi(1.465), Psi(1.465)-  0.0032539677],_
 [1.470,  0.0080664890, Psi(1.470), Psi(1.470)-  0.0080664890],_
 [1.475,  0.0128571930, Psi(1.475), Psi(1.475)-  0.0128571930],_
 [1.480,  0.0176262684, Psi(1.480), Psi(1.480)-  0.0176262684],_
 [1.485,  0.0223739013, Psi(1.485), Psi(1.485)-  0.0223739013],_
 [1.490,  0.0271002758, Psi(1.490), Psi(1.490)-  0.0271002758],_
 [1.495,  0.0318055736, Psi(1.495), Psi(1.495)-  0.0318055736],_
 [1.500,  0.0364899740, Psi(1.500), Psi(1.500)-  0.0364899740],_
 [1.505,  0.0411536543, Psi(1.505), Psi(1.505)-  0.0411536543],_
 [1.510,  0.0457967896, Psi(1.510), Psi(1.510)-  0.0457967896],_
 [1.515,  0.0504195527, Psi(1.515), Psi(1.515)-  0.0504195527],_
 [1.520,  0.0550221146, Psi(1.520), Psi(1.520)-  0.0550221146],_
 [1.525,  0.0596046439, Psi(1.525), Psi(1.525)-  0.0596046439],_
 [1.530,  0.0641673074, Psi(1.530), Psi(1.530)-  0.0641673074],_
 [1.535,  0.0687102697, Psi(1.535), Psi(1.535)-  0.0687102697],_
 [1.540,  0.0732336936, Psi(1.540), Psi(1.540)-  0.0732336936],_
 [1.545,  0.0777377300, Psi(1.545), Psi(1.545)-  0.0777377300],_
 [1.550,  0.0822225675, Psi(1.550), Psi(1.550)-  0.0822225675],_
 [1.555,  0.0866883334, Psi(1.555), Psi(1.555)-  0.0866883334],_
 [1.560,  0.0911351925, Psi(1.560), Psi(1.560)-  0.0911351925],_
 [1.565,  0.0955632984, Psi(1.565), Psi(1.565)-  0.0955632984],_
 [1.570,  0.0999728024, Psi(1.570), Psi(1.570)-  0.0999728024],_
 [1.575,  0.1043638544, Psi(1.575), Psi(1.575)-  0.1043638544],_
 [1.580,  0.1087366023, Psi(1.580), Psi(1.580)-  0.1087366023],_
 [1.585,  0.1130911923, Psi(1.585), Psi(1.585)-  0.1130911923],_
 [1.590,  0.1174277690, Psi(1.590), Psi(1.590)-  0.1174277690],_
 [1.595,  0.1217464754, Psi(1.595), Psi(1.595)-  0.1217464754],_
 [1.600,  0.1260474528, Psi(1.600), Psi(1.600)-  0.1260474528],_
 [1.605,  0.1303308407, Psi(1.605), Psi(1.605)-  0.1303308407],_
 [1.610,  0.1345967772, Psi(1.610), Psi(1.610)-  0.1345967772],_
 [1.615,  0.1388453988, Psi(1.615), Psi(1.615)-  0.1388453988],_
 [1.620,  0.1430768404, Psi(1.620), Psi(1.620)-  0.1430768404],_
 [1.625,  0.1472912354, Psi(1.625), Psi(1.625)-  0.1472912354],_
 [1.630,  0.1514887158, Psi(1.630), Psi(1.630)-  0.1514887158],_
 [1.635,  0.1556694120, Psi(1.635), Psi(1.635)-  0.1556694120],_
 [1.640,  0.1598334529, Psi(1.640), Psi(1.640)-  0.1598334529],_
 [1.645,  0.1639809660, Psi(1.645), Psi(1.645)-  0.1639809660],_
 [1.650,  0.1681120776, Psi(1.650), Psi(1.650)-  0.1681120776],_
 [1.655,  0.1722269122, Psi(1.655), Psi(1.655)-  0.1722269122],_
 [1.660,  0.1763255933, Psi(1.660), Psi(1.660)-  0.1763255933],_
 [1.665,  0.1804082427, Psi(1.665), Psi(1.665)-  0.1804082427],_
 [1.670,  0.1844749813, Psi(1.670), Psi(1.670)-  0.1844749813],_
 [1.675,  0.1885259282, Psi(1.675), Psi(1.675)-  0.1885259282],_
 [1.680,  0.1925612015, Psi(1.680), Psi(1.680)-  0.1925612015],_
 [1.685,  0.1965809180, Psi(1.685), Psi(1.685)-  0.1965809180],_
 [1.690,  0.2005851931, Psi(1.690), Psi(1.690)-  0.2005851931],_
 [1.695,  0.2045741410, Psi(1.695), Psi(1.695)-  0.2045741410],_
 [1.700,  0.2085478749, Psi(1.700), Psi(1.700)-  0.2085478749],_
 [1.705,  0.2125065064, Psi(1.705), Psi(1.705)-  0.2125065064],_
 [1.710,  0.2164501462, Psi(1.710), Psi(1.710)-  0.2164501462],_
 [1.715,  0.2203789037, Psi(1.715), Psi(1.715)-  0.2203789037],_
 [1.720,  0.2242928871, Psi(1.720), Psi(1.720)-  0.2242928871],_
 [1.725,  0.2281922037, Psi(1.725), Psi(1.725)-  0.2281922037],_
 [1.730,  0.2320769593, Psi(1.730), Psi(1.730)-  0.2320769593],_
 [1.735,  0.2359472589, Psi(1.735), Psi(1.735)-  0.2359472589],_
 [1.740,  0.2398032061, Psi(1.740), Psi(1.740)-  0.2398032061],_
 [1.745,  0.2436449038, Psi(1.745), Psi(1.745)-  0.2436449038],_
 [1.750,  0.2474724535, Psi(1.750), Psi(1.750)-  0.2474724535],_
 [1.755,  0.2512859559, Psi(1.755), Psi(1.755)-  0.2512859559],_
 [1.760,  0.2550855103, Psi(1.760), Psi(1.760)-  0.2550855103],_
 [1.765,  0.2588712154, Psi(1.765), Psi(1.765)-  0.2588712154],_
 [1.770,  0.2626431686, Psi(1.770), Psi(1.770)-  0.2626431686],_
 [1.775,  0.2664014664, Psi(1.775), Psi(1.775)-  0.2664014664],_
 [1.780,  0.2701462043, Psi(1.780), Psi(1.780)-  0.2701462043],_
 [1.785,  0.2738774769, Psi(1.785), Psi(1.785)-  0.2738774769],_
 [1.790,  0.2775953776, Psi(1.790), Psi(1.790)-  0.2775953776],_
 [1.795,  0.2812999992, Psi(1.795), Psi(1.795)-  0.2812999992],_
 [1.800,  0.2849914333, Psi(1.800), Psi(1.800)-  0.2849914333],_
 [1.805,  0.2886697707, Psi(1.805), Psi(1.805)-  0.2886697707],_
 [1.810,  0.2923351012, Psi(1.810), Psi(1.810)-  0.2923351012],_
 [1.815,  0.2959875138, Psi(1.815), Psi(1.815)-  0.2959875138],_
 [1.820,  0.2996270966, Psi(1.820), Psi(1.820)-  0.2996270966],_
 [1.825,  0.3032539367, Psi(1.825), Psi(1.825)-  0.3032539367],_
 [1.830,  0.3068681205, Psi(1.830), Psi(1.830)-  0.3068681205],_
 [1.835,  0.3104697335, Psi(1.835), Psi(1.835)-  0.3104697335],_
 [1.840,  0.3140588602, Psi(1.840), Psi(1.840)-  0.3140588602],_
 [1.845,  0.3176355846, Psi(1.845), Psi(1.845)-  0.3176355846],_
 [1.850,  0.3211999895, Psi(1.850), Psi(1.850)-  0.3211999895],_
 [1.855,  0.3247521572, Psi(1.855), Psi(1.855)-  0.3247521572],_
 [1.860,  0.3282921691, Psi(1.860), Psi(1.860)-  0.3282921691],_
 [1.865,  0.3318201056, Psi(1.865), Psi(1.865)-  0.3318201056],_
 [1.870,  0.3353360467, Psi(1.870), Psi(1.870)-  0.3353360467],_
 [1.875,  0.3388400713, Psi(1.875), Psi(1.875)-  0.3388400713],_
 [1.880,  0.3423322577, Psi(1.880), Psi(1.880)-  0.3423322577],_
 [1.885,  0.3458126835, Psi(1.885), Psi(1.885)-  0.3458126835],_
 [1.890,  0.3492814255, Psi(1.890), Psi(1.890)-  0.3492814255],_
 [1.895,  0.3527385596, Psi(1.895), Psi(1.895)-  0.3527385596],_
 [1.900,  0.3561841612, Psi(1.900), Psi(1.900)-  0.3561841612],_
 [1.905,  0.3596183049, Psi(1.905), Psi(1.905)-  0.3596183049],_
 [1.910,  0.3630410646, Psi(1.910), Psi(1.910)-  0.3630410646],_
 [1.915,  0.3664525136, Psi(1.915), Psi(1.915)-  0.3664525136],_
 [1.920,  0.3698527244, Psi(1.920), Psi(1.920)-  0.3698527244],_
 [1.925,  0.3732417688, Psi(1.925), Psi(1.925)-  0.3732417688],_
 [1.930,  0.3766197179, Psi(1.930), Psi(1.930)-  0.3766197179],_
 [1.935,  0.3799866424, Psi(1.935), Psi(1.935)-  0.3799866424],_
 [1.940,  0.3833426119, Psi(1.940), Psi(1.940)-  0.3833426119],_
 [1.945,  0.3866876959, Psi(1.945), Psi(1.945)-  0.3866876959],_
 [1.950,  0.3900219627, Psi(1.950), Psi(1.950)-  0.3900219627],_
 [1.955,  0.3933454805, Psi(1.955), Psi(1.955)-  0.3933454805],_
 [1.960,  0.3966583163, Psi(1.960), Psi(1.960)-  0.3966583163],_
 [1.965,  0.3999605371, Psi(1.965), Psi(1.965)-  0.3999605371],_
 [1.970,  0.4032522088, Psi(1.970), Psi(1.970)-  0.4032522088],_
 [1.975,  0.4065333970, Psi(1.975), Psi(1.975)-  0.4065333970],_
 [1.980,  0.4098041664, Psi(1.980), Psi(1.980)-  0.4098041664],_
 [1.985,  0.4130645816, Psi(1.985), Psi(1.985)-  0.4130645816],_
 [1.990,  0.4163147060, Psi(1.990), Psi(1.990)-  0.4163147060],_
 [1.995,  0.4195546030, Psi(1.995), Psi(1.995)-  0.4195546030],_
 [2.000,  0.4227843351, Psi(2.000), Psi(2.000)-  0.4227843351]]
 
   Internal Error
   The function polygamma with signature hashcode is missing from 
      domain DoubleFloat 

(3) -> Starts dribbling to ovar.output (2009/2/17, 17:55:52).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 5
ls:List Symbol:=['x,'a,'z]
 

   (1)  [x,a,z]
                                                            Type: List Symbol
--R 
--R
--R   (1)  [x,a,z]
--R                                                            Type: List Symbol
--E 1

--S 2 of 5
Z:=OVAR ls
 

   (2)  OrderedVariableList [x,a,z]
                                                                 Type: Domain
--R 
--R
--R   (2)  OrderedVariableList [x,a,z]
--R                                                                 Type: Domain
--E 2

--S 3 of 5
size()$Z
 

   (3)  3
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  3
--R                                                     Type: NonNegativeInteger
--E 3

--S 4 of 5
lv:=[index(i::PI)$Z for i in 1..size()$Z]
 
   Compiling function G1407 with type Integer -> Boolean 
   Compiling function G1421 with type NonNegativeInteger -> Boolean 

   (4)  [x,a,z]
                                       Type: List OrderedVariableList [x,a,z]
--R 
--I   Compiling function G1409 with type Integer -> Boolean 
--I   Compiling function G1573 with type NonNegativeInteger -> Boolean 
--R
--R   (4)  [x,a,z]
--R                                       Type: List OrderedVariableList [x,a,z]
--E 4

--S 5 of 5
sorted?(>,lv)
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5
)spool 
 
Starts dribbling to schaum20.output (2009/2/17, 17:59:13).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(tan(a*x),x)
 

                    2
        log(tan(a x)  + 1)
   (1)  ------------------
                2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2
--R        log(tan(a x)  + 1)
--R   (1)  ------------------
--R                2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb1:=-1/a*log(cos(a*x))
 

          log(cos(a x))
   (2)  - -------------
                a
                                                     Type: Expression Integer
--R
--R          log(cos(a x))
--R   (2)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 3
bb2:=1/a*log(sec(a*x))
 

        log(sec(a x))
   (3)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(sec(a x))
--R   (3)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 4
cc1:=aa-bb1
 

                    2
        log(tan(a x)  + 1) + 2log(cos(a x))
   (4)  -----------------------------------
                         2a
                                                     Type: Expression Integer
--R
--R                    2
--R        log(tan(a x)  + 1) + 2log(cos(a x))
--R   (4)  -----------------------------------
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 5
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (5)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (5)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 6
dd1:=tanrule cc1
 

                    2           2
            sin(a x)  + cos(a x)
        log(---------------------) + 2log(cos(a x))
                          2
                  cos(a x)
   (6)  -------------------------------------------
                             2a
                                                     Type: Expression Integer
--R
--R                    2           2
--R            sin(a x)  + cos(a x)
--R        log(---------------------) + 2log(cos(a x))
--R                          2
--R                  cos(a x)
--R   (6)  -------------------------------------------
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 7
ee1:=expandLog dd1
 

                    2           2
        log(sin(a x)  + cos(a x) )
   (7)  --------------------------
                    2a
                                                     Type: Expression Integer
--R
--R                    2           2
--R        log(sin(a x)  + cos(a x) )
--R   (7)  --------------------------
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 8
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (8)  sin(a)  + cos(a)  + %K == %K + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (8)  sin(a)  + cos(a)  + %K == %K + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 9      14:429 Schaums and Axiom agree
ff1:=sincossqrrule ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(tan(a*x)^2,x)
 

        tan(a x) - a x
   (1)  --------------
               a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        tan(a x) - a x
--R   (1)  --------------
--R               a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=tan(a*x)/a-x
 

        tan(a x) - a x
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        tan(a x) - a x
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 12     14:430 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(tan(a*x)^3,x)
 

                      2                2
        - log(tan(a x)  + 1) + tan(a x)
   (1)  --------------------------------
                       2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2                2
--R        - log(tan(a x)  + 1) + tan(a x)
--R   (1)  --------------------------------
--R                       2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=tan(a*x)^2/(2*a)+1/a*log(cos(a*x))
 

                                 2
        2log(cos(a x)) + tan(a x)
   (2)  --------------------------
                    2a
                                                     Type: Expression Integer
--R
--R                                 2
--R        2log(cos(a x)) + tan(a x)
--R   (2)  --------------------------
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 15
cc:=aa-bb
 

                      2
        - log(tan(a x)  + 1) - 2log(cos(a x))
   (3)  -------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                      2
--R        - log(tan(a x)  + 1) - 2log(cos(a x))
--R   (3)  -------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 16
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 17
dd:=tanrule cc
 

                      2           2
              sin(a x)  + cos(a x)
        - log(---------------------) - 2log(cos(a x))
                            2
                    cos(a x)
   (5)  ---------------------------------------------
                              2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R              sin(a x)  + cos(a x)
--R        - log(---------------------) - 2log(cos(a x))
--R                            2
--R                    cos(a x)
--R   (5)  ---------------------------------------------
--R                              2a
--R                                                     Type: Expression Integer
--E

--S 18
ee:=expandLog dd
 

                      2           2
          log(sin(a x)  + cos(a x) )
   (6)  - --------------------------
                      2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R          log(sin(a x)  + cos(a x) )
--R   (6)  - --------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 19
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (7)  sin(a)  + cos(a)  + %L == %L + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (7)  sin(a)  + cos(a)  + %L == %L + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20     14:431 Schaums and Axiom agree
ff:=sincossqrrule ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 21
aa:=integrate(tan(a*x)^n*sec(a*x)^2,x)
 

                        sin(a x)
                  n log(--------)
                        cos(a x)
        sin(a x)%e
   (1)  -------------------------
            (a n + a)cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        sin(a x)
--R                  n log(--------)
--R                        cos(a x)
--R        sin(a x)%e
--R   (1)  -------------------------
--R            (a n + a)cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22
bb:=tan(a*x)^(n+1)/((n+1)*a)
 

                n + 1
        tan(a x)
   (2)  -------------
           a n + a
                                                     Type: Expression Integer
--R
--R                n + 1
--R        tan(a x)
--R   (2)  -------------
--R           a n + a
--R                                                     Type: Expression Integer
--E

--S 23
cc:=aa-bb
 

                        sin(a x)
                  n log(--------)
                        cos(a x)                    n + 1
        sin(a x)%e                - cos(a x)tan(a x)
   (3)  -------------------------------------------------
                        (a n + a)cos(a x)
                                                     Type: Expression Integer
--R
--R                        sin(a x)
--R                  n log(--------)
--R                        cos(a x)                    n + 1
--R        sin(a x)%e                - cos(a x)tan(a x)
--R   (3)  -------------------------------------------------
--R                        (a n + a)cos(a x)
--R                                                     Type: Expression Integer
--E

--S 24
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25
dd:=explog cc
 

                          n + 1            sin(a x) n
        - cos(a x)tan(a x)      + sin(a x)(--------)
                                           cos(a x)
   (5)  ---------------------------------------------
                      (a n + a)cos(a x)
                                                     Type: Expression Integer
--R
--R                          n + 1            sin(a x) n
--R        - cos(a x)tan(a x)      + sin(a x)(--------)
--R                                           cos(a x)
--R   (5)  ---------------------------------------------
--R                      (a n + a)cos(a x)
--R                                                     Type: Expression Integer
--E

--S 26
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (6)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (6)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27
ee:=tanrule dd
 

                   sin(a x) n + 1            sin(a x) n
        - cos(a x)(--------)      + sin(a x)(--------)
                   cos(a x)                  cos(a x)
   (7)  -----------------------------------------------
                       (a n + a)cos(a x)
                                                     Type: Expression Integer
--R
--R                   sin(a x) n + 1            sin(a x) n
--R        - cos(a x)(--------)      + sin(a x)(--------)
--R                   cos(a x)                  cos(a x)
--R   (7)  -----------------------------------------------
--R                       (a n + a)cos(a x)
--R                                                     Type: Expression Integer
--E

--S 28     14:432 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(sec(a*x)^2/tan(a*x),x)
 

              sin(a x)              2cos(a x)
        log(------------) - log(- ------------)
            cos(a x) + 1          cos(a x) + 1
   (1)  ---------------------------------------
                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)              2cos(a x)
--R        log(------------) - log(- ------------)
--R            cos(a x) + 1          cos(a x) + 1
--R   (1)  ---------------------------------------
--R                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=1/a*log(tan(a*x))
 

        log(tan(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(tan(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

                                sin(a x)              2cos(a x)
        - log(tan(a x)) + log(------------) - log(- ------------)
                              cos(a x) + 1          cos(a x) + 1
   (3)  ---------------------------------------------------------
                                    a
                                                     Type: Expression Integer
--R
--R                                sin(a x)              2cos(a x)
--R        - log(tan(a x)) + log(------------) - log(- ------------)
--R                              cos(a x) + 1          cos(a x) + 1
--R   (3)  ---------------------------------------------------------
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 32
dd:=expandLog cc
 

        - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2)
   (4)  ----------------------------------------------------------
                                     a
                                                     Type: Expression Integer
--R
--R        - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2)
--R   (4)  ----------------------------------------------------------
--R                                     a
--R                                                     Type: Expression Integer
--E

--S 33     14:433 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 2)
   (5)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 2)
--R   (5)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 34
aa:=integrate(1/tan(a*x),x)
 

                      2
        - log(tan(a x)  + 1) + 2log(tan(a x))
   (1)  -------------------------------------
                          2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2
--R        - log(tan(a x)  + 1) + 2log(tan(a x))
--R   (1)  -------------------------------------
--R                          2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 35
bb:=1/a*log(sin(a*x))
 

        log(sin(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(sin(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 36
cc:=aa-bb
 

                      2
        - log(tan(a x)  + 1) + 2log(tan(a x)) - 2log(sin(a x))
   (3)  ------------------------------------------------------
                                  2a
                                                     Type: Expression Integer
--R
--R                      2
--R        - log(tan(a x)  + 1) + 2log(tan(a x)) - 2log(sin(a x))
--R   (3)  ------------------------------------------------------
--R                                  2a
--R                                                     Type: Expression Integer
--E

--S 37
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 38     14:435 Axiom cannot compute this integral
aa:=integrate(x*tan(a*x),x)
 

           x
         ++
   (1)   |   %T tan(%T a)d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %I tan(%I a)d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 39     14:436 Axiom cannot compute this integral
aa:=integrate(tan(a*x)/x,x)
 

           x
         ++  tan(%T a)
   (1)   |   --------- d%T
        ++       %T
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  tan(%I a)
--I   (1)   |   --------- d%I
--I        ++       %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 40
aa:=integrate(x*tan(a*x)^2,x)
 

                      2                         2 2
        - log(tan(a x)  + 1) + 2a x tan(a x) - a x
   (1)  -------------------------------------------
                              2
                            2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2                         2 2
--R        - log(tan(a x)  + 1) + 2a x tan(a x) - a x
--R   (1)  -------------------------------------------
--R                              2
--R                            2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 41
bb:=(x*tan(a*x))/a+1/a^2*log(cos(a*x))-x^2/2
 

                                          2 2
        2log(cos(a x)) + 2a x tan(a x) - a x
   (2)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                                          2 2
--R        2log(cos(a x)) + 2a x tan(a x) - a x
--R   (2)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 42
cc:=aa-bb
 

                      2
        - log(tan(a x)  + 1) - 2log(cos(a x))
   (3)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                      2
--R        - log(tan(a x)  + 1) - 2log(cos(a x))
--R   (3)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 43
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 44
dd:=tanrule cc
 

                      2           2
              sin(a x)  + cos(a x)
        - log(---------------------) - 2log(cos(a x))
                            2
                    cos(a x)
   (5)  ---------------------------------------------
                               2
                             2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R              sin(a x)  + cos(a x)
--R        - log(---------------------) - 2log(cos(a x))
--R                            2
--R                    cos(a x)
--R   (5)  ---------------------------------------------
--R                               2
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 45
ee:=expandLog dd
 

                      2           2
          log(sin(a x)  + cos(a x) )
   (6)  - --------------------------
                        2
                      2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R          log(sin(a x)  + cos(a x) )
--R   (6)  - --------------------------
--R                        2
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 46
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (7)  sin(a)  + cos(a)  + %BB == %BB + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (7)  sin(a)  + cos(a)  + %R == %R + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 47     14:437 Schaums and Axiom agree
ff:=sincossqrrule ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 48
aa:=integrate(1/(p+q*tan(a*x)),x)
 

                        2
        - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p) + 2a p x
   (1)  --------------------------------------------------------
                                  2       2
                              2a q  + 2a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2
--R        - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p) + 2a p x
--R   (1)  --------------------------------------------------------
--R                                  2       2
--R                              2a q  + 2a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49
bb:=(p*x)/(p^2+q^2)+q/(a*(p^2+q^2))*log(q*sin(a*x)+p*cos(a*x))
 

        q log(q sin(a x) + p cos(a x)) + a p x
   (2)  --------------------------------------
                         2      2
                      a q  + a p
                                                     Type: Expression Integer
--R
--R        q log(q sin(a x) + p cos(a x)) + a p x
--R   (2)  --------------------------------------
--R                         2      2
--R                      a q  + a p
--R                                                     Type: Expression Integer
--E

--S 50
cc:=aa-bb
 

   (3)
                       2
       - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p)
     + 
       - 2q log(q sin(a x) + p cos(a x))
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                       2
--R       - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p)
--R     + 
--R       - 2q log(q sin(a x) + p cos(a x))
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 51
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 52
dd:=tanrule cc
 

   (5)
                       2           2
               sin(a x)  + cos(a x)
       - q log(---------------------) - 2q log(q sin(a x) + p cos(a x))
                             2
                     cos(a x)
     + 
              q sin(a x) + p cos(a x)
       2q log(-----------------------)
                      cos(a x)
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (5)
--R                       2           2
--R               sin(a x)  + cos(a x)
--R       - q log(---------------------) - 2q log(q sin(a x) + p cos(a x))
--R                             2
--R                     cos(a x)
--R     + 
--R              q sin(a x) + p cos(a x)
--R       2q log(-----------------------)
--R                      cos(a x)
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 53
ee:=expandLog dd
 

                        2           2
          q log(sin(a x)  + cos(a x) )
   (6)  - ----------------------------
                      2       2
                  2a q  + 2a p
                                                     Type: Expression Integer
--R
--R                        2           2
--R          q log(sin(a x)  + cos(a x) )
--R   (6)  - ----------------------------
--R                      2       2
--R                  2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 54
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (7)  sin(a)  + cos(a)  + %BC == %BC + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (7)  sin(a)  + cos(a)  + %S == %S + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 55     14:438 Schaums and Axiom agree
ff:=sincossqrrule ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 56     14:439 Axiom cannot compute this integral
aa:=integrate(tan(a*x)^n,x)
 

           x
         ++           n
   (1)   |   tan(%T a) d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   tan(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to space3.output (2009/2/17, 18:0:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 1

--S 2 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 2

--S 3 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 3

--S 4 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 4

--S 5 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 5

--S 6 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 6

--S 7 of 185
closedCurve(space,[[1,1,1],[1,0,0],[0,0,0],[0,1,1]])
 

   (7)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 7

--S 8 of 185
cspace := closedCurve([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (8)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 8

--S 9 of 185
closedCurve cspace
 

   (9)  [[1.0,1.0,1.0],[1.0,0.0,0.0],[0.0,0.0,0.0],[0.0,1.0,1.0]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (9)  [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 9

)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 10

--S 11 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 11

--S 12 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 12

--S 13 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 13

--S 14 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 14

--S 15 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 15

--S 16 of 185
closedCurve? space
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 185
curve(space,[p0,p1,p2,p3])
 

   (8)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 17

--S 18 of 185
point(space,p0)
 

   (9)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 18

--S 19 of 185
components(space)
 

   (10)
   [3-Space with 1 component,3-Space with 1 component,3-Space with 1 component]
                                            Type: List ThreeSpace DoubleFloat
--R 
--R
--R   (10)
--R   [3-Space with 1 component,3-Space with 1 component,3-Space with 1 component]
--R                                            Type: List ThreeSpace DoubleFloat
--E 19

--S 20 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (11)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 20

--S 21 of 185
curve(space1,[p0,p1,p2,p3])
 

   (12)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (12)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 21

--S 22 of 185
point(space1,p0)
 

   (13)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 22

--S 23 of 185
space2 := point(p0)$(ThreeSpace DoubleFloat)
 

   (14)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (14)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 23

--S 24 of 185
space3 := curve[p0,p1,p2]$(ThreeSpace DoubleFloat)
 

   (15)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 24

--S 25 of 185
composite [space1,space2,space3]
 

   (16)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 25

--S 26 of 185
curve(space,[p0,p1,p2,p3])
 

   (17)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (17)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 26

--S 27 of 185
point(space,p0)
 

   (18)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (18)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 27

--S 28 of 185
point(space,p1)
 

   (19)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (19)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 28

--S 29 of 185
closedCurve(space,[p0,p1,p2])
 

   (20)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (20)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 29

--S 30 of 185
composite [space1,space2,space3]
 

   (21)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (21)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 30

--S 31 of 185
composites(space)
 

   (22)  []
                                            Type: List ThreeSpace DoubleFloat
--R 
--R
--R   (22)  []
--R                                            Type: List ThreeSpace DoubleFloat
--E 31

--S 32 of 185
curve(space,[p0,p1,p2,p3])
 

   (23)  3-Space with 8 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (23)  3-Space with 8 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 32

--S 33 of 185
point(space,p0)
 

   (24)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (24)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 33

--S 34 of 185
space4 := copy space
 

   (25)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (25)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 34

--S 35 of 185
curve(space,[p0,p1,p2])
 

   (26)  3-Space with 10 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (26)  3-Space with 10 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 35

--S 36 of 185
point(space,p0)
 

   (27)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (27)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 36

--S 37 of 185
sub := subspace(space)
 

   (28)  3-Space with depth of 3 and 11 components
                                                Type: SubSpace(3,DoubleFloat)
--R 
--R
--R   (28)  3-Space with depth of 3 and 11 components
--R                                                Type: SubSpace(3,DoubleFloat)
--E 37

--S 38 of 185
spNew := create3Space(sub)$(ThreeSpace DoubleFloat)
 

   (29)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (29)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 38

--S 39 of 185
curve(space,[p0,p1,p2,p3])
 

   (30)  3-Space with 12 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (30)  3-Space with 12 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 39

--S 40 of 185
curve(space,[[1,1,1],[1,0,0],[0,0,0],[0,1,1]])
 

   (31)  3-Space with 13 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (31)  3-Space with 13 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 40

--S 41 of 185
cspace := curve([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (32)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (32)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 41

--S 42 of 185
curve cspace
 

   (33)  [[1.0,1.0,1.0],[1.0,0.0,0.0],[0.0,0.0,0.0],[0.0,1.0,1.0]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (33)  [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 42

)clear all
 
   All user variables and function definitions have been cleared.

--S 43 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 43

--S 44 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 44

--S 45 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 45

--S 46 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 46

--S 47 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 47

--S 48 of 185
curve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 48

--S 49 of 185
curve? space
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 49

)clear all
 
   All user variables and function definitions have been cleared.

--S 50 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 50

--S 51 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 51

--S 52 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 52

--S 53 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 53

--S 54 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 54

--S 55 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 55

--S 56 of 185
curve(space,[p0,p1,p2,p3])
 

   (7)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 56

--S 57 of 185
point(space,p0)
 

   (8)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 57

--S 58 of 185
point(space,p3)
 

   (9)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 58

--S 59 of 185
polygon(space,[p0,p1,p3])
 

   (10)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 59

--S 60 of 185
polygon(space,[p0,p2,p3])
 

   (11)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 60

--S 61 of 185
lllip(space)
 

   (12)  [[[1,2,3,4]],[[5,6,7,8]],[[9]],[[10]],[[11],[12,13]],[[14],[15,16]]]
                                      Type: List List List NonNegativeInteger
--R 
--R
--R   (12)  [[[1,2,3,4]],[[5,6,7,8]],[[9]],[[10]],[[11],[12,13]],[[14],[15,16]]]
--R                                      Type: List List List NonNegativeInteger
--E 61

--S 62 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (13)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 62

--S 63 of 185
curve(space,[p0,p1,p2,p3])
 

   (14)  3-Space with 8 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (14)  3-Space with 8 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 63

--S 64 of 185
point(space,p0)
 

   (15)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 64

--S 65 of 185
polygon(space,[p0,p1,p3])
 

   (16)  3-Space with 10 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 10 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 65

--S 66 of 185
llprop(space)
 

   (17)
   [[Component is closed, not solid], [Component is not closed, not solid],
    [Component is not closed, not solid], [Component is not closed, not solid],
    [Component is not closed, not solid,Component is not closed, not solid],
    [Component is not closed, not solid,Component is not closed, not solid],
    [Component is closed, not solid], [Component is not closed, not solid],
    [Component is not closed, not solid],
    [Component is not closed, not solid,Component is not closed, not solid]]
                                    Type: List List SubSpaceComponentProperty
--R 
--R
--R   (17)
--R   [[Component is closed, not solid], [Component is not closed, not solid],
--R    [Component is not closed, not solid], [Component is not closed, not solid],
--R    [Component is not closed, not solid,Component is not closed, not solid],
--R    [Component is not closed, not solid,Component is not closed, not solid],
--R    [Component is closed, not solid], [Component is not closed, not solid],
--R    [Component is not closed, not solid],
--R    [Component is not closed, not solid,Component is not closed, not solid]]
--R                                    Type: List List SubSpaceComponentProperty
--E 66

--S 67 of 185
lprop(space)
 

   (18)
   [Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid]
                                         Type: List SubSpaceComponentProperty
--R 
--R
--R   (18)
--R   [Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid]
--R                                         Type: List SubSpaceComponentProperty
--E 67

--S 68 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (19)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (19)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 68

--S 69 of 185
curve(space,[p0,p1,p2,p3])
 

   (20)  3-Space with 12 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (20)  3-Space with 12 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 69

--S 70 of 185
point(space,p0)
 

   (21)  3-Space with 13 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (21)  3-Space with 13 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 70

--S 71 of 185
polygon(space,[p0,p1,p3])
 

   (22)  3-Space with 14 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (22)  3-Space with 14 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 71

--S 72 of 185
lp(space)
 

   (23)
   [[1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,0.0,0.0], [0.0,1.0,1.0], [1.0,1.0,1.0],
    [1.0,0.0,0.0], [0.0,0.0,0.0], [0.0,1.0,1.0], [1.0,1.0,1.0], [0.0,1.0,1.0],
    [1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,1.0,1.0], [1.0,1.0,1.0], [0.0,0.0,0.0],
    [0.0,1.0,1.0], [1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,0.0,0.0], [0.0,1.0,1.0],
    [1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,0.0,0.0], [0.0,1.0,1.0], [1.0,1.0,1.0],
    [1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,1.0,1.0], [1.0,1.0,1.0], [1.0,0.0,0.0],
    [0.0,0.0,0.0], [0.0,1.0,1.0], [1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,0.0,0.0],
    [0.0,1.0,1.0], [1.0,1.0,1.0], [1.0,1.0,1.0], [1.0,0.0,0.0], [0.0,1.0,1.0]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (23)
--R   [[1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,1.,1.], [1.,1.,1.], [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.],
--R    [1.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.],
--R    [1.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 72

--S 73 of 185
enterPointData(space,[p0,p1,p2,p3])
 

   (24)  44
                                                        Type: PositiveInteger
--R 
--R
--R   (24)  44
--R                                                        Type: PositiveInteger
--E 73

)clear all
 
   All user variables and function definitions have been cleared.

--S 74 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 74

--S 75 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 75

--S 76 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 76

--S 77 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 77

--S 78 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 78

--S 79 of 185
curve(space1,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 79

--S 80 of 185
space2 := copy space1
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 80

--S 81 of 185
point(space1,p3)
 

   (8)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 81

--S 82 of 185
space3 := copy space1
 

   (9)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 82

--S 83 of 185
curve(space3,[p0,p1,p2])
 

   (10)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 83

--S 84 of 185
newSpace1 := merge [space1,space2,space3]
 

   (11)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 84

--S 85 of 185
newSpace2 := merge(space2,space3)
 

   (12)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (12)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 85

--S 86 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (13)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 86

--S 87 of 185
prop := new()$SubSpaceComponentProperty()
 

   (14)  Component is not closed, not solid
                                              Type: SubSpaceComponentProperty
--R 
--R
--R   (14)  Component is not closed, not solid
--R                                              Type: SubSpaceComponentProperty
--E 87

--S 88 of 185
lprop := [prop, prop, prop]
 

   (15)
   [Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid]
                                         Type: List SubSpaceComponentProperty
--R 
--R
--R   (15)
--R   [Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid]
--R                                         Type: List SubSpaceComponentProperty
--E 88

--S 89 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],lprop,prop)
 

   (16)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 89

--S 90 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],lprop,prop)
 

   (17)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (17)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 90

--S 91 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],closed?(prop),closed?(prop))
 

   (18)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (18)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 91

--S 92 of 185
b := close(prop,true)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 92

--S 93 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],b,b)
 

   (20)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (20)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 93

--S 94 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],closed?(prop),closed?(prop))
 

   (21)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (21)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 94

--S 95 of 185
mesh(space,[[[1,1,1],[1,0,0],[0,0,0]],[[1,0,0],[0,0,0],[0,1,1]],[[1,1,1],[0,0,0],[0,1,1]]],closed?(prop),closed?(prop))
 

   (22)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (22)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 95

--S 96 of 185
mesh(space,[[[1,1,1],[1,0,0],[0,0,0]],[[1,0,0],[0,0,0],[0,1,1]],[[1,1,1],[0,0,0],[0,1,1]]],b,b)
 

   (23)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (23)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 96

)clear all
 
   All user variables and function definitions have been cleared.

--S 97 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (1)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (1)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 97

--S 98 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (2)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 98

--S 99 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (3)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 99

--S 100 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (4)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 100

--S 101 of 185
space := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (5)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (5)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 101

--S 102 of 185
space1 := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],false,false)$(ThreeSpace DoubleFloat)
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 102

)clear all
 
   All user variables and function definitions have been cleared.

--S 103 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (1)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (1)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 103

--S 104 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (2)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 104

--S 105 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (3)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 105

--S 106 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (4)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 106

--S 107 of 185
space := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (5)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (5)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 107

--S 108 of 185
mesh(space)
 

   (6)
   [[[1.0,1.0,1.0],[0.0,0.0,0.0],[0.0,1.0,1.0]],
    [[1.0,0.0,0.0],[0.0,0.0,0.0],[0.0,1.0,1.0]],
    [[1.0,1.0,1.0],[1.0,0.0,0.0],[0.0,0.0,0.0]]]
                                            Type: List List Point DoubleFloat
--R 
--R
--R   (6)
--R   [[[1.,1.,1.],[0.,0.,0.],[0.,1.,1.]], [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]],
--R    [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.]]]
--R                                            Type: List List Point DoubleFloat
--E 108

--S 109 of 185
s := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 109

--S 110 of 185
mesh(s)
 

   (8)
   [[[1.0,1.0,1.0],[0.0,0.0,0.0],[0.0,1.0,1.0]],
    [[1.0,0.0,0.0],[0.0,0.0,0.0],[0.0,1.0,1.0]],
    [[1.0,1.0,1.0],[1.0,0.0,0.0],[0.0,0.0,0.0]]]
                                            Type: List List Point DoubleFloat
--R 
--R
--R   (8)
--R   [[[1.,1.,1.],[0.,0.,0.],[0.,1.,1.]], [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]],
--R    [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.]]]
--R                                            Type: List List Point DoubleFloat
--E 110

--S 111 of 185
space2 := create3Space()$(ThreeSpace DoubleFloat)
 

   (9)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 111

--S 112 of 185
curve(space2,[p0,p1,p2,p3])
 

   (10)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 112

--S 113 of 185
mesh?(space2)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 113

--S 114 of 185
s1 := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (12)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (12)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 114

--S 115 of 185
mesh?(s1)
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 115

--S 116 of 185
i := enterPointData(space2,[p0,p1,p2,p3])::NNI
 

   (14)  8
                                                     Type: NonNegativeInteger
--R 
--R
--R   (14)  8
--R                                                     Type: NonNegativeInteger
--E 116

--S 117 of 185
modifyPointData(space2,i,p2)
 

   (15)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 117

--S 118 of 185
point(space2,p0)
 

   (16)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 118

--S 119 of 185
curve(space2,[p0,p1,p2,p3])
 

   (17)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (17)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 119

--S 120 of 185
numberOfComponents(space2)
 

   (18)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  3
--R                                                        Type: PositiveInteger
--E 120

)clear all
 
   All user variables and function definitions have been cleared.

--S 121 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 121

--S 122 of 185
numberOfComposites(space1)
 

   (2)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (2)  0
--R                                                     Type: NonNegativeInteger
--E 122

--S 123 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (3)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 123

--S 124 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (4)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 124

--S 125 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (5)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 125

--S 126 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (6)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (6)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 126

--S 127 of 185
curve(space1,[p0,p1,p2,p3])
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 127

--S 128 of 185
point(space1,p0)
 

   (8)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 128

--S 129 of 185
space2 := point(p0)$(ThreeSpace DoubleFloat)
 

   (9)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 129

--S 130 of 185
space3 := curve [p0,p1,p2]$(ThreeSpace DoubleFloat)
 

   (10)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 130

--S 131 of 185
s := composite [space1,space2,space3]
 

   (11)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 131

--S 132 of 185
numberOfComposites(s)
 

   (12)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  1
--R                                                        Type: PositiveInteger
--E 132

--S 133 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (13)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 133

--S 134 of 185
point(space,p0)
 

   (14)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (14)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 134

--S 135 of 185
curve(space,[p0,p1,p2,p3])
 

   (15)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 135

--S 136 of 185
closedCurve(space,[p0,p1,p2])
 

   (16)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 136

--S 137 of 185
objects space
 

   (17)  [points= 1,curves= 2,polygons= 0,constructs= 0]
Type: Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger)
--R 
--R
--R   (17)  [points= 1,curves= 2,polygons= 0,constructs= 0]
--RType: Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger)
--E 137

)clear all
 
   All user variables and function definitions have been cleared.

--S 138 of 185
s := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 138

--S 139 of 185
p := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 139

--S 140 of 185
point(s,p)
 

   (3)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (3)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 140

--S 141 of 185
point(s,[1,1,1])
 

   (4)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (4)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 141

--S 142 of 185
p0 := point [1,0,0]$(Point DoubleFloat)
 

   (5)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 142

--S 143 of 185
point(s,p)
 

   (6)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 143

--S 144 of 185
i := enterPointData(s,[p0])::NNI
 

   (7)  4
                                                     Type: NonNegativeInteger
--R 
--R
--R   (7)  4
--R                                                     Type: NonNegativeInteger
--E 144

--S 145 of 185
point(s,i)
 

   (8)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 145

--S 146 of 185
p := point [1,1,1]$(Point DoubleFloat)
 

   (9)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (9)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 146

--S 147 of 185
space := point(p)$(ThreeSpace DoubleFloat)
 

   (10)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 147

)clear all
 
   All user variables and function definitions have been cleared.

--S 148 of 185
s := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 148

--S 149 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 149

--S 150 of 185
curve(s,[p0,p0])
 

   (3)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (3)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 150

--S 151 of 185
space1 := point(p0)$(ThreeSpace DoubleFloat)
 

   (4)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (4)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 151

--S 152 of 185
point(space1)
 

   (5)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 152

)clear all
 
   All user variables and function definitions have been cleared.

--S 153 of 185
s := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 153

--S 154 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 154

--S 155 of 185
curve(s,[p0,p0,p0])
 

   (3)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (3)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 155

--S 156 of 185
point? s
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 156

--S 157 of 185
space := point(p0)$(ThreeSpace DoubleFloat)
 

   (5)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (5)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 157

--S 158 of 185
point? space
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 158

)clear all
 
   All user variables and function definitions have been cleared.

--S 159 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 159

--S 160 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 160

--S 161 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 161

--S 162 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 162

--S 163 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 163

--S 164 of 185
polygon(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 164

--S 165 of 185
polygon(space,[[1,1,1],[0,0,-1],[1,0,1]])
 

   (7)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 165

--S 166 of 185
s := polygon([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (8)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 166

)clear all
 
   All user variables and function definitions have been cleared.

--S 167 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 167

--S 168 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 168

--S 169 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 169

--S 170 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 170

--S 171 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 171

--S 172 of 185
curve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 172

--S 173 of 185
s := polygon([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 173

--S 174 of 185
polygon s
 

   (8)  [[1.0,0.0,0.0],[0.0,0.0,0.0],[0.0,1.0,1.0]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (8)  [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 174

)clear all
 
   All user variables and function definitions have been cleared.

--S 175 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 175

--S 176 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 176

--S 177 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 177

--S 178 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.0,0.0,0.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 178

--S 179 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.0,1.0,1.0]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 179

--S 180 of 185
curve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 180

--S 181 of 185
polygon? space
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 181

--S 182 of 185
s := polygon([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (8)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 182

--S 183 of 185
polygon s
 

   (9)  [[1.0,0.0,0.0],[0.0,0.0,0.0],[0.0,1.0,1.0]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (9)  [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 183

--S 184 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (10)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 184

--S 185 of 185
sub := subspace(space1)
 

   (11)  3-Space with depth of 3 and 0 components
                                                Type: SubSpace(3,DoubleFloat)
--R 
--R
--R   (11)  3-Space with depth of 3 and 0 components
--R                                                Type: SubSpace(3,DoubleFloat)
--E 185
)spool 
 
Starts dribbling to odpol.output (2009/2/17, 17:55:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 36
dpol:= ODPOL(FRAC INT)
 

   (1)  OrderlyDifferentialPolynomial Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  OrderlyDifferentialPolynomial Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
w := makeVariable('w)$dpol
 

   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 2

--S 3 of 36
z := makeVariable('z)$dpol
 

   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 3

--S 4 of 36
w.5
 

   (4)  w
         5
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (4)  w
--R         5
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 4

--S 5 of 36
w 0
 

   (5)  w
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (5)  w
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 5

--S 6 of 36
[z.i for i in 1..5]
 

   (6)  [z ,z ,z ,z ,z ]
          1  2  3  4  5
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (6)  [z ,z ,z ,z ,z ]
--R          1  2  3  4  5
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 6

--S 7 of 36
f:= w.4 - w.1 * w.1 * z.3
 

               2
   (7)  w  - w  z
         4    1  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R               2
--R   (7)  w  - w  z
--R         4    1  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 7

--S 8 of 36
g:=(z.1)**3 * (z.2)**2 - w.2
 

          3  2
   (8)  z  z   - w
         1  2     2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R          3  2
--R   (8)  z  z   - w
--R         1  2     2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 8

--S 9 of 36
D(f)
 

               2
   (9)  w  - w  z  - 2w w z
         5    1  4     1 2 3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R               2
--R   (9)  w  - w  z  - 2w w z
--R         5    1  4     1 2 3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 9

--S 10 of 36
D(f,4)
 

   (10)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (10)
--R            2                               2
--R     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
--R      8    1  7     1 2 6         1 3      2   5     1 3 5
--R   + 
--R                                         2
--R     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
--R          1 4      2 3  4     2 3 4     3  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 10

--S 11 of 36
df:=makeVariable(f)$dpol
 

   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 11

--S 12 of 36
df.4
 

   (12)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (12)
--R            2                               2
--R     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
--R      8    1  7     1 2 6         1 3      2   5     1 3 5
--R   + 
--R                                         2
--R     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
--R          1 4      2 3  4     2 3 4     3  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 12

--S 13 of 36
order(g)
 

   (13)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  2
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 36
order(g, 'w)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 36
differentialVariables(g)
 

   (15)  [z,w]
                                                            Type: List Symbol
--R 
--R
--R   (15)  [z,w]
--R                                                            Type: List Symbol
--E 15

--S 16 of 36
degree(g)
 

           2  3
   (16)  z  z
          2  1
                    Type: IndexedExponents OrderlyDifferentialVariable Symbol
--R 
--R
--R           2  3
--R   (16)  z  z
--R          2  1
--R                    Type: IndexedExponents OrderlyDifferentialVariable Symbol
--E 16

--S 17 of 36
degree(g, 'w)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 36
weights(g)
 

   (18)  [7,2]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (18)  [7,2]
--R                                                Type: List NonNegativeInteger
--E 18

--S 19 of 36
weights(g,'w)
 

   (19)  [2]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (19)  [2]
--R                                                Type: List NonNegativeInteger
--E 19

--S 20 of 36
weight(g)
 

   (20)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  7
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 36
isobaric?(g)
 

   (21)  false
                                                                Type: Boolean
--R 
--R
--R   (21)  false
--R                                                                Type: Boolean
--E 21

--S 22 of 36
eval(g,['w::Symbol],[f])
 

                  2                           2        3  2
   (22)  - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
            6    1  5     1 2 4      1 3     2   3    1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R                  2                           2        3  2
--R   (22)  - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
--R            6    1  5     1 2 4      1 3     2   3    1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 22

--S 23 of 36
eval(g,variables(w.0),[f])
 

           3  2
   (23)  z  z   - w
          1  2     2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R           3  2
--R   (23)  z  z   - w
--R          1  2     2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 23

--S 24 of 36
monomials(g)
 

            3  2
   (24)  [z  z  ,- w ]
           1  2     2
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3  2
--R   (24)  [z  z  ,- w ]
--R           1  2     2
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 24

--S 25 of 36
variables(g)
 

   (25)  [z ,w ,z ]
           2  2  1
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (25)  [z ,w ,z ]
--R           2  2  1
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 25

--S 26 of 36
gcd(f,g)
 

   (26)  1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (26)  1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 26

--S 27 of 36
groebner([f,g])
 

                 2     3  2
   (27)  [w  - w  z ,z  z   - w ]
           4    1  3  1  2     2
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R                 2     3  2
--R   (27)  [w  - w  z ,z  z   - w ]
--R           4    1  3  1  2     2
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 27

--S 28 of 36
lg:=leader(g)
 

   (28)  z
          2
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (28)  z
--R          2
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 28

--S 29 of 36
sg:=separant(g)
 

            3
   (29)  2z  z
           1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3
--R   (29)  2z  z
--R           1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 29

--S 30 of 36
ig:=initial(g)
 

           3
   (30)  z
          1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R           3
--R   (30)  z
--R          1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 30

--S 31 of 36
g1 := D g
 

            3               2  3
   (31)  2z  z z  - w  + 3z  z
           1  2 3    3     1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3               2  3
--R   (31)  2z  z z  - w  + 3z  z
--R           1  2 3    3     1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 31

--S 32 of 36
lg1:= leader g1
 

   (32)  z
          3
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (32)  z
--R          3
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 32

--S 33 of 36
pdf:=D(f, lg1)
 

             2
   (33)  - w
            1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R             2
--R   (33)  - w
--R            1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 33

--S 34 of 36
prf:=sg * f- pdf * g1
 

            3         2        2  2  3
   (34)  2z  z w  - w  w  + 3w  z  z
           1  2 4    1  3     1  1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3         2        2  2  3
--R   (34)  2z  z w  - w  w  + 3w  z  z
--R           1  2 4    1  3     1  1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 34

--S 35 of 36
lcf:=leadingCoefficient univariate(prf, lg)
 

            2  2
   (35)  3w  z
           1  1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            2  2
--R   (35)  3w  z
--R           1  1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 35

--S 36 of 36
ig * prf - lcf * g * lg
 

            6         2  3        2  2
   (36)  2z  z w  - w  z  w  + 3w  z  w z
           1  2 4    1  1  3     1  1  2 2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            6         2  3        2  2
--R   (36)  2z  z w  - w  z  w  + 3w  z  w z
--R           1  2 4    1  1  3     1  1  2 2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 36
)spool 
 
Starts dribbling to series2.output (2009/2/17, 18:0:18).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 38
f1 := taylor(1 - x**2,x = 0)
 

             2
   (1)  1 - x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R             2
--R   (1)  1 - x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 38
asin f1
 

   (2)
   %pi     1   2     1    4      1    6      5     8       7     10      11
   --- - ---- x  - ----- x  - ------ x  - ------- x  - -------- x   + O(x  )
    2     +-+        +-+         +-+          +-+           +-+
         \|2       8\|2       32\|2       512\|2       2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R   %pi     1   2     1    4      1    6      5     8       7     10      11
--R   --- - ---- x  - ----- x  - ------ x  - ------- x  - -------- x   + O(x  )
--R    2     +-+        +-+         +-+          +-+           +-+
--R         \|2       8\|2       32\|2       512\|2       2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 2

--S 3 of 38
sin %
 

            1  4    1  6    7   8     5   10      11
   (3)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
            4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  4    1  6    7   8     5   10      11
--R   (3)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
--R            4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 38
acos f1
 

          1   2     1    4      1    6      5     8       7     10      11
   (4)  ---- x  + ----- x  + ------ x  + ------- x  + -------- x   + O(x  )
         +-+        +-+         +-+          +-+           +-+
        \|2       8\|2       32\|2       512\|2       2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R          1   2     1    4      1    6      5     8       7     10      11
--R   (4)  ---- x  + ----- x  + ------ x  + ------- x  + -------- x   + O(x  )
--R         +-+        +-+         +-+          +-+           +-+
--R        \|2       8\|2       32\|2       512\|2       2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 38
cos %
 

            1  4    1  6    7   8     5   10      11
   (5)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
            4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  4    1  6    7   8     5   10      11
--R   (5)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
--R            4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 5

--S 6 of 38
f2 := taylor(1 + x**2,x = 0)
 

             2
   (6)  1 + x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R             2
--R   (6)  1 + x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 6

--S 7 of 38
acsc f2
 

   (7)
   %pi     1   2     5    4     43    6     177    8      2867    10      11
   --- - ---- x  + ----- x  - ------ x  + ------- x  - --------- x   + O(x  )
    2     +-+        +-+         +-+          +-+            +-+
         \|2       8\|2       96\|2       512\|2       10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (7)
--R   %pi     1   2     5    4     43    6     177    8      2867    10      11
--R   --- - ---- x  + ----- x  - ------ x  + ------- x  - --------- x   + O(x  )
--R    2     +-+        +-+         +-+          +-+            +-+
--R         \|2       8\|2       96\|2       512\|2       10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 7

--S 8 of 38
csc %
 

            1  4    5  6   287  8   1361  10      11
   (8)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
            4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  4    5  6   287  8   1361  10      11
--R   (8)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
--R            4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 8

--S 9 of 38
asec f2
 

          1   2     5    4     43    6     177    8      2867    10      11
   (9)  ---- x  - ----- x  + ------ x  - ------- x  + --------- x   + O(x  )
         +-+        +-+         +-+          +-+            +-+
        \|2       8\|2       96\|2       512\|2       10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R          1   2     5    4     43    6     177    8      2867    10      11
--R   (9)  ---- x  - ----- x  + ------ x  - ------- x  + --------- x   + O(x  )
--R         +-+        +-+         +-+          +-+            +-+
--R        \|2       8\|2       96\|2       512\|2       10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 9

--S 10 of 38
sec %
 

             1  4    5  6   287  8   1361  10      11
   (10)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
             4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R             1  4    5  6   287  8   1361  10      11
--R   (10)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
--R             4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 10

--S 11 of 38
f3 := taylor(1 - (x - a)**2,x = a)
 

                    2
   (11)  1 - (x - a)
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R                    2
--R   (11)  1 - (x - a)
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 11

--S 12 of 38
asin f3
 

   (12)
     %pi     1         2     1          4      1          6      5           8
     --- - ---- (x - a)  - ----- (x - a)  - ------ (x - a)  - ------- (x - a)
      2     +-+              +-+               +-+                +-+
           \|2             8\|2             32\|2             512\|2
   + 
           7           10            11
     - -------- (x - a)   + O((x - a)  )
            +-+
       2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (12)
--R     %pi     1         2     1          4      1          6      5           8
--R     --- - ---- (x - a)  - ----- (x - a)  - ------ (x - a)  - ------- (x - a)
--R      2     +-+              +-+               +-+                +-+
--R           \|2             8\|2             32\|2             512\|2
--R   + 
--R           7           10            11
--R     - -------- (x - a)   + O((x - a)  )
--R            +-+
--R       2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 12

--S 13 of 38
sin %
 

   (13)
       1        4    1        6    7         8     5         10            11
   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (13)
--R       1        4    1        6    7         8     5         10            11
--R   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 13

--S 14 of 38
acos f3
 

   (14)
       1         2     1          4      1          6      5           8
     ---- (x - a)  + ----- (x - a)  + ------ (x - a)  + ------- (x - a)
      +-+              +-+               +-+                +-+
     \|2             8\|2             32\|2             512\|2
   + 
         7           10            11
     -------- (x - a)   + O((x - a)  )
          +-+
     2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (14)
--R       1         2     1          4      1          6      5           8
--R     ---- (x - a)  + ----- (x - a)  + ------ (x - a)  + ------- (x - a)
--R      +-+              +-+               +-+                +-+
--R     \|2             8\|2             32\|2             512\|2
--R   + 
--R         7           10            11
--R     -------- (x - a)   + O((x - a)  )
--R          +-+
--R     2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 14

--S 15 of 38
cos %
 

   (15)
       1        4    1        6    7         8     5         10            11
   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (15)
--R       1        4    1        6    7         8     5         10            11
--R   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 15

--S 16 of 38
f4 := taylor(1 + (x - a)**2,x = a)
 

                    2
   (16)  1 + (x - a)
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R                    2
--R   (16)  1 + (x - a)
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 16

--S 17 of 38
acsc f4
 

   (17)
     %pi     1         2     5          4     43          6     177          8
     --- - ---- (x - a)  + ----- (x - a)  - ------ (x - a)  + ------- (x - a)
      2     +-+              +-+               +-+                +-+
           \|2             8\|2             96\|2             512\|2
   + 
          2867          10            11
     - --------- (x - a)   + O((x - a)  )
             +-+
       10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (17)
--R     %pi     1         2     5          4     43          6     177          8
--R     --- - ---- (x - a)  + ----- (x - a)  - ------ (x - a)  + ------- (x - a)
--R      2     +-+              +-+               +-+                +-+
--R           \|2             8\|2             96\|2             512\|2
--R   + 
--R          2867          10            11
--R     - --------- (x - a)   + O((x - a)  )
--R             +-+
--R       10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 17

--S 18 of 38
csc %
 

   (18)
       1        4    5        6   287        8   1361        10            11
   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (18)
--R       1        4    5        6   287        8   1361        10            11
--R   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 18

--S 19 of 38
asec f4
 

   (19)
       1         2     5          4     43          6     177          8
     ---- (x - a)  - ----- (x - a)  + ------ (x - a)  - ------- (x - a)
      +-+              +-+               +-+                +-+
     \|2             8\|2             96\|2             512\|2
   + 
        2867          10            11
     --------- (x - a)   + O((x - a)  )
           +-+
     10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (19)
--R       1         2     5          4     43          6     177          8
--R     ---- (x - a)  - ----- (x - a)  + ------ (x - a)  - ------- (x - a)
--R      +-+              +-+               +-+                +-+
--R     \|2             8\|2             96\|2             512\|2
--R   + 
--R        2867          10            11
--R     --------- (x - a)   + O((x - a)  )
--R           +-+
--R     10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 19

--S 20 of 38
sec %
 

   (20)
       1        4    5        6   287        8   1361        10            11
   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (20)
--R       1        4    5        6   287        8   1361        10            11
--R   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 20

--S 21 of 38
f5 := taylor(%i + x**2,x = 0)
 

               2
   (21)  %i + x
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--R 
--R
--R               2
--R   (21)  %i + x
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--E 21

--S 22 of 38
asinh f5
 

   (22)
                             +---+             +---+
          +---+         - %i\|2%i  + 4  2    9\|2%i  + 4 + 16%i   4
     log(\|2%i  + %i) + -------------- x  + -------------------- x
                           +---+               +---+
                         4\|2%i  + 4%i      64\|2%i  + 64 + 32%i
   + 
                       +---+
       (- 239 + 106%i)\|2%i  - 312 - 96%i   6
     ------------------------------------- x
                     +---+
     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
   + 
                          +---+
       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i   8
     -------------------------------------------- x
                        +---+
     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
   + 
                                 +---+
         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i     10      11
     ------------------------------------------------------------ x   + O(x  )
                                +---+
     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--R 
--R
--R   (22)
--R                             +---+             +---+
--R          +---+         - %i\|2%i  + 4  2    9\|2%i  + 4 + 16%i   4
--R     log(\|2%i  + %i) + -------------- x  + -------------------- x
--R                           +---+               +---+
--R                         4\|2%i  + 4%i      64\|2%i  + 64 + 32%i
--R   + 
--R                       +---+
--R       (- 239 + 106%i)\|2%i  - 312 - 96%i   6
--R     ------------------------------------- x
--R                     +---+
--R     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
--R   + 
--R                          +---+
--R       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i   8
--R     -------------------------------------------- x
--R                        +---+
--R     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
--R   + 
--R                                 +---+
--R         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i     10      11
--R     ------------------------------------------------------------ x   + O(x  )
--R                                +---+
--R     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--E 22

--S 23 of 38
map(normalize,sinh %)
 

   (23)
        +---+                     +---+
     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6  2
     ----------------- + ------------------ x
         +---+              +---+
        \|2%i  + %i       8\|2%i  + 8 + 4%i
   + 
                   +---+
         (8 + 3%i)\|2%i  + 18%i      4
     ------------------------------ x
                 +---+
     (64 + 96%i)\|2%i  - 32 + 192%i
   + 
                      +---+
       (118 + 1355%i)\|2%i  - 1216 + 1456%i    6
     ---------------------------------------- x
                      +---+
     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
   + 
                                       +---+
       (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i   8
     ---------------------------------------------------------------------- x
                                     +---+
     (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
   + 
                                                                      +---+
           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
         + 
           17079087293650217758937952 + 6236244540731754948247086%i
      /
                                                                         +---+
           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
         + 
           - 367150215832379728071180288 + 1001034013523215543416922112%i
    *
        10
       x
   + 
        11
     O(x  )
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--R 
--R
--R   (23)
--R        +---+                     +---+
--R     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6  2
--R     ----------------- + ------------------ x
--R         +---+              +---+
--R        \|2%i  + %i       8\|2%i  + 8 + 4%i
--R   + 
--R                   +---+
--R         (8 + 3%i)\|2%i  + 18%i      4
--R     ------------------------------ x
--R                 +---+
--R     (64 + 96%i)\|2%i  - 32 + 192%i
--R   + 
--R                      +---+
--R       (118 + 1355%i)\|2%i  - 1216 + 1456%i    6
--R     ---------------------------------------- x
--R                      +---+
--R     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
--R   + 
--R                                       +---+
--R       (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i   8
--R     ---------------------------------------------------------------------- x
--R                                     +---+
--R     (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
--R   + 
--R                                                                      +---+
--R           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
--R         + 
--R           17079087293650217758937952 + 6236244540731754948247086%i
--R      /
--R                                                                         +---+
--R           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
--R         + 
--R           - 367150215832379728071180288 + 1001034013523215543416922112%i
--R    *
--R        10
--R       x
--R   + 
--R        11
--R     O(x  )
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--E 23

--S 24 of 38
acosh f1
 

   (24)
                          +---+              +---+
          +---+        - \|- 2  - 4  2   - 9\|- 2  - 12  4
     log(\|- 2  + 1) + ------------ x  + -------------- x
                          +---+              +---+
                        4\|- 2  + 4       64\|- 2  - 32
   + 
          +---+                    +---+
      133\|- 2  - 152   6     2237\|- 2  - 3760   8
     ----------------- x  + -------------------- x
          +---+                    +---+
     1536\|- 2  + 2688      114688\|- 2  + 34816
   + 
              +---+
       140517\|- 2  - 342216    10      11
     ------------------------- x   + O(x  )
              +---+
     18841600\|- 2  - 13475840
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (24)
--R                          +---+              +---+
--R          +---+        - \|- 2  - 4  2   - 9\|- 2  - 12  4
--R     log(\|- 2  + 1) + ------------ x  + -------------- x
--R                          +---+              +---+
--R                        4\|- 2  + 4       64\|- 2  - 32
--R   + 
--R          +---+                    +---+
--R      133\|- 2  - 152   6     2237\|- 2  - 3760   8
--R     ----------------- x  + -------------------- x
--R          +---+                    +---+
--R     1536\|- 2  + 2688      114688\|- 2  + 34816
--R   + 
--R              +---+
--R       140517\|- 2  - 342216    10      11
--R     ------------------------- x   + O(x  )
--R              +---+
--R     18841600\|- 2  - 13475840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 24

--S 25 of 38
map(normalize,cosh %)
 

   (25)
        +---+         +---+              +---+                 +---+
       \|- 2      - 3\|- 2  + 6  2    11\|- 2  + 14  4   - 453\|- 2  + 240  6
     ---------- + ------------- x  + -------------- x  + ----------------- x
      +---+          +---+              +---+                 +---+
     \|- 2  + 1    8\|- 2  - 4       32\|- 2  - 160      7168\|- 2  + 2176
   + 
                +---+
     - 22730863\|- 2  + 116622452  8
     ---------------------------- x
               +---+
     670183424\|- 2  - 3124590592
   + 
                        +---+
       2255055395845397\|- 2  - 186126275620338262    10      11
     ----------------------------------------------- x   + O(x  )
                         +---+
     2942149446728507392\|- 2  + 7713476525184163840
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (25)
--R        +---+         +---+              +---+                 +---+
--R       \|- 2      - 3\|- 2  + 6  2    11\|- 2  + 14  4   - 453\|- 2  + 240  6
--R     ---------- + ------------- x  + -------------- x  + ----------------- x
--R      +---+          +---+              +---+                 +---+
--R     \|- 2  + 1    8\|- 2  - 4       32\|- 2  - 160      7168\|- 2  + 2176
--R   + 
--R                +---+
--R     - 22730863\|- 2  + 116622452  8
--R     ---------------------------- x
--R               +---+
--R     670183424\|- 2  - 3124590592
--R   + 
--R                        +---+
--R       2255055395845397\|- 2  - 186126275620338262    10      11
--R     ----------------------------------------------- x   + O(x  )
--R                         +---+
--R     2942149446728507392\|- 2  + 7713476525184163840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 25

--S 26 of 38
asech f2
 

   (26)
                           +---+             +---+
          +---+        - 3\|- 2  - 4  2   31\|- 2  - 12  4
     log(\|- 2  + 1) + ------------- x  + ------------- x
                          +---+              +---+
                        4\|- 2  + 4       64\|- 2  - 32
   + 
           +---+                   +---+
     - 481\|- 2  - 904  6    28397\|- 2  + 9296   8
     ----------------- x  + -------------------- x
          +---+                    +---+
     1536\|- 2  + 2688      114688\|- 2  + 34816
   + 
                +---+
     - 15819247\|- 2  + 48750368  10      11
     --------------------------- x   + O(x  )
               +---+
      77987840\|- 2  - 245063680
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (26)
--R                           +---+             +---+
--R          +---+        - 3\|- 2  - 4  2   31\|- 2  - 12  4
--R     log(\|- 2  + 1) + ------------- x  + ------------- x
--R                          +---+              +---+
--R                        4\|- 2  + 4       64\|- 2  - 32
--R   + 
--R           +---+                   +---+
--R     - 481\|- 2  - 904  6    28397\|- 2  + 9296   8
--R     ----------------- x  + -------------------- x
--R          +---+                    +---+
--R     1536\|- 2  + 2688      114688\|- 2  + 34816
--R   + 
--R                +---+
--R     - 15819247\|- 2  + 48750368  10      11
--R     --------------------------- x   + O(x  )
--R               +---+
--R      77987840\|- 2  - 245063680
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 26

--S 27 of 38
sech %
 

   (27)
                                 +---+               +---+
               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))  2
     --------------------- + ----------------------------------- x
               +---+            +---+               +---+      2
     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
   + 
               +---+               +---+      2
           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
         + 
                 +---+                +---+                +---+
           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                 +---+               +---+      2
           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
      /
             +---+                +---+      3
         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
    *
        4
       x
   + 
                  +---+                   +---+      3
           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
         + 
                    +---+                    +---+                +---+      2
           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                    +---+                   +---+      2          +---+
           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                  +---+                   +---+      3
           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
      /
                +---+                    +---+      4
         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
    *
        6
       x
   + 
                            +---+                             +---+      4
           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
         + 
                                 +---+                             +---+
             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
          *
                       +---+      3
             sinh(log(\|- 2  + 1))
         + 
                              +---+                             +---+      2
             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
          *
                       +---+      2
             sinh(log(\|- 2  + 1))
         + 
                               +---+                             +---+      3
             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
          *
                       +---+
             sinh(log(\|- 2  + 1))
         + 
                              +---+                           +---+      4
           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
      /
                           +---+                            +---+      5
         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
    *
        8
       x
   + 
                                                              +---+
               - 12221152405486797005988545574943642796394656\|- 2
             + 
               37637519606679038130877931502289421788636480
          *
                       +---+      5
             sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               17253119387520025009474512785116571944492864\|- 2
             + 
               - 108013651440447643426633659223764934754997824
          *
                       +---+                +---+      4
             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               15685216146928883301596685922653051925359412\|- 2
             + 
               67214446812749454239537980137157117493694568
          *
                       +---+      2          +---+      3
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                              +---+
               - 26995359328188426534667967009323500335310964\|- 2
             + 
               55273964842367651019386962337683658570477492
          *
                       +---+      3          +---+      2
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               - 386525745609157558466191079238605101103613\|- 2
             + 
               - 65032045559085732400544188402961111578157364
          *
                       +---+      4          +---+
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                           +---+
               7027759893774203888781041210243035688470658\|- 2
             + 
               12868136868984040775294141040070021247885438
          *
                       +---+      5
             cosh(log(\|- 2  + 1))
      /
                                                          +---+
             18629821302375761537774756048822860358942720\|- 2
           + 
             94473907670457185816258586943170775874920448
        *
                     +---+      6
           cosh(log(\|- 2  + 1))
    *
        10
       x
   + 
        11
     O(x  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (27)
--R                                 +---+               +---+
--R               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))  2
--R     --------------------- + ----------------------------------- x
--R               +---+            +---+               +---+      2
--R     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
--R   + 
--R               +---+               +---+      2
--R           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+                +---+                +---+
--R           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+               +---+      2
--R           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
--R      /
--R             +---+                +---+      3
--R         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
--R    *
--R        4
--R       x
--R   + 
--R                  +---+                   +---+      3
--R           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                    +---+                +---+      2
--R           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                   +---+      2          +---+
--R           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                  +---+                   +---+      3
--R           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
--R      /
--R                +---+                    +---+      4
--R         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
--R    *
--R        6
--R       x
--R   + 
--R                            +---+                             +---+      4
--R           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
--R         + 
--R                                 +---+                             +---+
--R             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      3
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                             +---+      2
--R             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      2
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                               +---+                             +---+      3
--R             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                           +---+      4
--R           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
--R      /
--R                           +---+                            +---+      5
--R         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
--R    *
--R        8
--R       x
--R   + 
--R                                                              +---+
--R               - 12221152405486797005988545574943642796394656\|- 2
--R             + 
--R               37637519606679038130877931502289421788636480
--R          *
--R                       +---+      5
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               17253119387520025009474512785116571944492864\|- 2
--R             + 
--R               - 108013651440447643426633659223764934754997824
--R          *
--R                       +---+                +---+      4
--R             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               15685216146928883301596685922653051925359412\|- 2
--R             + 
--R               67214446812749454239537980137157117493694568
--R          *
--R                       +---+      2          +---+      3
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                              +---+
--R               - 26995359328188426534667967009323500335310964\|- 2
--R             + 
--R               55273964842367651019386962337683658570477492
--R          *
--R                       +---+      3          +---+      2
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               - 386525745609157558466191079238605101103613\|- 2
--R             + 
--R               - 65032045559085732400544188402961111578157364
--R          *
--R                       +---+      4          +---+
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                           +---+
--R               7027759893774203888781041210243035688470658\|- 2
--R             + 
--R               12868136868984040775294141040070021247885438
--R          *
--R                       +---+      5
--R             cosh(log(\|- 2  + 1))
--R      /
--R                                                          +---+
--R             18629821302375761537774756048822860358942720\|- 2
--R           + 
--R             94473907670457185816258586943170775874920448
--R        *
--R                     +---+      6
--R           cosh(log(\|- 2  + 1))
--R    *
--R        10
--R       x
--R   + 
--R        11
--R     O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 27

--S 28 of 38
acsch f1
 

   (28)
                       +-+             +-+               +-+
          +-+         \|2  + 2  2    9\|2  + 12  4   221\|2  + 312  6
     log(\|2  + 1) + --------- x  + ----------- x  + ------------- x
                       +-+             +-+               +-+
                     2\|2  + 2      16\|2  + 24      576\|2  + 816
   + 
           +-+                        +-+
     14425\|2  + 20400  8   124515259\|2  + 176091168  10      11
     ----------------- x  + ------------------------- x   + O(x  )
           +-+                        +-+
     52224\|2  + 73856      602664960\|2  + 852296960
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (28)
--R                       +-+             +-+               +-+
--R          +-+         \|2  + 2  2    9\|2  + 12  4   221\|2  + 312  6
--R     log(\|2  + 1) + --------- x  + ----------- x  + ------------- x
--R                       +-+             +-+               +-+
--R                     2\|2  + 2      16\|2  + 24      576\|2  + 816
--R   + 
--R           +-+                        +-+
--R     14425\|2  + 20400  8   124515259\|2  + 176091168  10      11
--R     ----------------- x  + ------------------------- x   + O(x  )
--R           +-+                        +-+
--R     52224\|2  + 73856      602664960\|2  + 852296960
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 28

--S 29 of 38
map(normalize,csch %)
 

              2      11
   (29)  1 - x  + O(x  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R              2      11
--R   (29)  1 - x  + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 29

--S 30 of 38
f6 := taylor(%i + (x - a)**2,x = a)
 

                     2
   (30)  %i + (x - a)
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--R 
--R
--R                     2
--R   (30)  %i + (x - a)
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--E 30

--S 31 of 38
asinh f6
 

   (31)
                             +---+                   +---+
          +---+         - %i\|2%i  + 4        2    9\|2%i  + 4 + 16%i         4
     log(\|2%i  + %i) + -------------- (x - a)  + -------------------- (x - a)
                           +---+                     +---+
                         4\|2%i  + 4%i            64\|2%i  + 64 + 32%i
   + 
                       +---+
       (- 239 + 106%i)\|2%i  - 312 - 96%i         6
     ------------------------------------- (x - a)
                     +---+
     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
   + 
                          +---+
       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i         8
     -------------------------------------------- (x - a)
                        +---+
     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
   + 
                                 +---+
         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i           10
     ------------------------------------------------------------ (x - a)
                                +---+
     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
   + 
              11
     O((x - a)  )
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--R 
--R
--R   (31)
--R                             +---+                   +---+
--R          +---+         - %i\|2%i  + 4        2    9\|2%i  + 4 + 16%i         4
--R     log(\|2%i  + %i) + -------------- (x - a)  + -------------------- (x - a)
--R                           +---+                     +---+
--R                         4\|2%i  + 4%i            64\|2%i  + 64 + 32%i
--R   + 
--R                       +---+
--R       (- 239 + 106%i)\|2%i  - 312 - 96%i         6
--R     ------------------------------------- (x - a)
--R                     +---+
--R     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
--R   + 
--R                          +---+
--R       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i         8
--R     -------------------------------------------- (x - a)
--R                        +---+
--R     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
--R   + 
--R                                 +---+
--R         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i           10
--R     ------------------------------------------------------------ (x - a)
--R                                +---+
--R     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
--R   + 
--R              11
--R     O((x - a)  )
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--E 31

--S 32 of 38
map(normalize,sinh %)
 

   (32)
        +---+                     +---+
     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6        2
     ----------------- + ------------------ (x - a)
         +---+              +---+
        \|2%i  + %i       8\|2%i  + 8 + 4%i
   + 
                   +---+
         (8 + 3%i)\|2%i  + 18%i            4
     ------------------------------ (x - a)
                 +---+
     (64 + 96%i)\|2%i  - 32 + 192%i
   + 
                      +---+
       (118 + 1355%i)\|2%i  - 1216 + 1456%i          6
     ---------------------------------------- (x - a)
                      +---+
     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
   + 
                                         +---+
         (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i
       ----------------------------------------------------------------------
                                       +---+
       (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
    *
              8
       (x - a)
   + 
                                                                      +---+
           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
         + 
           17079087293650217758937952 + 6236244540731754948247086%i
      /
                                                                         +---+
           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
         + 
           - 367150215832379728071180288 + 1001034013523215543416922112%i
    *
              10
       (x - a)
   + 
              11
     O((x - a)  )
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--R 
--R
--R   (32)
--R        +---+                     +---+
--R     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6        2
--R     ----------------- + ------------------ (x - a)
--R         +---+              +---+
--R        \|2%i  + %i       8\|2%i  + 8 + 4%i
--R   + 
--R                   +---+
--R         (8 + 3%i)\|2%i  + 18%i            4
--R     ------------------------------ (x - a)
--R                 +---+
--R     (64 + 96%i)\|2%i  - 32 + 192%i
--R   + 
--R                      +---+
--R       (118 + 1355%i)\|2%i  - 1216 + 1456%i          6
--R     ---------------------------------------- (x - a)
--R                      +---+
--R     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
--R   + 
--R                                         +---+
--R         (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i
--R       ----------------------------------------------------------------------
--R                                       +---+
--R       (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
--R    *
--R              8
--R       (x - a)
--R   + 
--R                                                                      +---+
--R           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
--R         + 
--R           17079087293650217758937952 + 6236244540731754948247086%i
--R      /
--R                                                                         +---+
--R           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
--R         + 
--R           - 367150215832379728071180288 + 1001034013523215543416922112%i
--R    *
--R              10
--R       (x - a)
--R   + 
--R              11
--R     O((x - a)  )
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--E 32

--S 33 of 38
acosh f3
 

   (33)
                          +---+                    +---+
          +---+        - \|- 2  - 4        2   - 9\|- 2  - 12        4
     log(\|- 2  + 1) + ------------ (x - a)  + -------------- (x - a)
                          +---+                    +---+
                        4\|- 2  + 4             64\|- 2  - 32
   + 
          +---+                          +---+
      133\|- 2  - 152         6     2237\|- 2  - 3760         8
     ----------------- (x - a)  + -------------------- (x - a)
          +---+                          +---+
     1536\|- 2  + 2688            114688\|- 2  + 34816
   + 
              +---+
       140517\|- 2  - 342216          10            11
     ------------------------- (x - a)   + O((x - a)  )
              +---+
     18841600\|- 2  - 13475840
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (33)
--R                          +---+                    +---+
--R          +---+        - \|- 2  - 4        2   - 9\|- 2  - 12        4
--R     log(\|- 2  + 1) + ------------ (x - a)  + -------------- (x - a)
--R                          +---+                    +---+
--R                        4\|- 2  + 4             64\|- 2  - 32
--R   + 
--R          +---+                          +---+
--R      133\|- 2  - 152         6     2237\|- 2  - 3760         8
--R     ----------------- (x - a)  + -------------------- (x - a)
--R          +---+                          +---+
--R     1536\|- 2  + 2688            114688\|- 2  + 34816
--R   + 
--R              +---+
--R       140517\|- 2  - 342216          10            11
--R     ------------------------- (x - a)   + O((x - a)  )
--R              +---+
--R     18841600\|- 2  - 13475840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 33

--S 34 of 38
map(normalize,cosh %)
 

   (34)
        +---+         +---+                    +---+
       \|- 2      - 3\|- 2  + 6        2    11\|- 2  + 14        4
     ---------- + ------------- (x - a)  + -------------- (x - a)
      +---+          +---+                    +---+
     \|- 2  + 1    8\|- 2  - 4             32\|- 2  - 160
   + 
           +---+                             +---+
     - 453\|- 2  + 240        6   - 22730863\|- 2  + 116622452        8
     ----------------- (x - a)  + ---------------------------- (x - a)
          +---+                             +---+
     7168\|- 2  + 2176            670183424\|- 2  - 3124590592
   + 
                        +---+
       2255055395845397\|- 2  - 186126275620338262          10            11
     ----------------------------------------------- (x - a)   + O((x - a)  )
                         +---+
     2942149446728507392\|- 2  + 7713476525184163840
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (34)
--R        +---+         +---+                    +---+
--R       \|- 2      - 3\|- 2  + 6        2    11\|- 2  + 14        4
--R     ---------- + ------------- (x - a)  + -------------- (x - a)
--R      +---+          +---+                    +---+
--R     \|- 2  + 1    8\|- 2  - 4             32\|- 2  - 160
--R   + 
--R           +---+                             +---+
--R     - 453\|- 2  + 240        6   - 22730863\|- 2  + 116622452        8
--R     ----------------- (x - a)  + ---------------------------- (x - a)
--R          +---+                             +---+
--R     7168\|- 2  + 2176            670183424\|- 2  - 3124590592
--R   + 
--R                        +---+
--R       2255055395845397\|- 2  - 186126275620338262          10            11
--R     ----------------------------------------------- (x - a)   + O((x - a)  )
--R                         +---+
--R     2942149446728507392\|- 2  + 7713476525184163840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 34

--S 35 of 38
asech f4
 

   (35)
                           +---+                   +---+
          +---+        - 3\|- 2  - 4        2   31\|- 2  - 12        4
     log(\|- 2  + 1) + ------------- (x - a)  + ------------- (x - a)
                          +---+                    +---+
                        4\|- 2  + 4             64\|- 2  - 32
   + 
           +---+                         +---+
     - 481\|- 2  - 904        6    28397\|- 2  + 9296         8
     ----------------- (x - a)  + -------------------- (x - a)
          +---+                          +---+
     1536\|- 2  + 2688            114688\|- 2  + 34816
   + 
                +---+
     - 15819247\|- 2  + 48750368        10            11
     --------------------------- (x - a)   + O((x - a)  )
               +---+
      77987840\|- 2  - 245063680
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (35)
--R                           +---+                   +---+
--R          +---+        - 3\|- 2  - 4        2   31\|- 2  - 12        4
--R     log(\|- 2  + 1) + ------------- (x - a)  + ------------- (x - a)
--R                          +---+                    +---+
--R                        4\|- 2  + 4             64\|- 2  - 32
--R   + 
--R           +---+                         +---+
--R     - 481\|- 2  - 904        6    28397\|- 2  + 9296         8
--R     ----------------- (x - a)  + -------------------- (x - a)
--R          +---+                          +---+
--R     1536\|- 2  + 2688            114688\|- 2  + 34816
--R   + 
--R                +---+
--R     - 15819247\|- 2  + 48750368        10            11
--R     --------------------------- (x - a)   + O((x - a)  )
--R               +---+
--R      77987840\|- 2  - 245063680
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 35

--S 36 of 38
sech %
 

   (36)
                                 +---+               +---+
               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))        2
     --------------------- + ----------------------------------- (x - a)
               +---+            +---+               +---+      2
     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
   + 
               +---+               +---+      2
           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
         + 
                 +---+                +---+                +---+
           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                 +---+               +---+      2
           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
      /
             +---+                +---+      3
         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
    *
              4
       (x - a)
   + 
                  +---+                   +---+      3
           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
         + 
                    +---+                    +---+                +---+      2
           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                    +---+                   +---+      2          +---+
           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                  +---+                   +---+      3
           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
      /
                +---+                    +---+      4
         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
    *
              6
       (x - a)
   + 
                            +---+                             +---+      4
           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
         + 
                                 +---+                             +---+
             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
          *
                       +---+      3
             sinh(log(\|- 2  + 1))
         + 
                              +---+                             +---+      2
             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
          *
                       +---+      2
             sinh(log(\|- 2  + 1))
         + 
                               +---+                             +---+      3
             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
          *
                       +---+
             sinh(log(\|- 2  + 1))
         + 
                              +---+                           +---+      4
           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
      /
                           +---+                            +---+      5
         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
    *
              8
       (x - a)
   + 
                                                              +---+
               - 12221152405486797005988545574943642796394656\|- 2
             + 
               37637519606679038130877931502289421788636480
          *
                       +---+      5
             sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               17253119387520025009474512785116571944492864\|- 2
             + 
               - 108013651440447643426633659223764934754997824
          *
                       +---+                +---+      4
             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               15685216146928883301596685922653051925359412\|- 2
             + 
               67214446812749454239537980137157117493694568
          *
                       +---+      2          +---+      3
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                              +---+
               - 26995359328188426534667967009323500335310964\|- 2
             + 
               55273964842367651019386962337683658570477492
          *
                       +---+      3          +---+      2
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               - 386525745609157558466191079238605101103613\|- 2
             + 
               - 65032045559085732400544188402961111578157364
          *
                       +---+      4          +---+
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                           +---+
               7027759893774203888781041210243035688470658\|- 2
             + 
               12868136868984040775294141040070021247885438
          *
                       +---+      5
             cosh(log(\|- 2  + 1))
      /
                                                          +---+
             18629821302375761537774756048822860358942720\|- 2
           + 
             94473907670457185816258586943170775874920448
        *
                     +---+      6
           cosh(log(\|- 2  + 1))
    *
              10
       (x - a)
   + 
              11
     O((x - a)  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (36)
--R                                 +---+               +---+
--R               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))        2
--R     --------------------- + ----------------------------------- (x - a)
--R               +---+            +---+               +---+      2
--R     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
--R   + 
--R               +---+               +---+      2
--R           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+                +---+                +---+
--R           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+               +---+      2
--R           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
--R      /
--R             +---+                +---+      3
--R         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
--R    *
--R              4
--R       (x - a)
--R   + 
--R                  +---+                   +---+      3
--R           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                    +---+                +---+      2
--R           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                   +---+      2          +---+
--R           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                  +---+                   +---+      3
--R           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
--R      /
--R                +---+                    +---+      4
--R         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
--R    *
--R              6
--R       (x - a)
--R   + 
--R                            +---+                             +---+      4
--R           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
--R         + 
--R                                 +---+                             +---+
--R             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      3
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                             +---+      2
--R             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      2
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                               +---+                             +---+      3
--R             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                           +---+      4
--R           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
--R      /
--R                           +---+                            +---+      5
--R         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
--R    *
--R              8
--R       (x - a)
--R   + 
--R                                                              +---+
--R               - 12221152405486797005988545574943642796394656\|- 2
--R             + 
--R               37637519606679038130877931502289421788636480
--R          *
--R                       +---+      5
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               17253119387520025009474512785116571944492864\|- 2
--R             + 
--R               - 108013651440447643426633659223764934754997824
--R          *
--R                       +---+                +---+      4
--R             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               15685216146928883301596685922653051925359412\|- 2
--R             + 
--R               67214446812749454239537980137157117493694568
--R          *
--R                       +---+      2          +---+      3
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                              +---+
--R               - 26995359328188426534667967009323500335310964\|- 2
--R             + 
--R               55273964842367651019386962337683658570477492
--R          *
--R                       +---+      3          +---+      2
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               - 386525745609157558466191079238605101103613\|- 2
--R             + 
--R               - 65032045559085732400544188402961111578157364
--R          *
--R                       +---+      4          +---+
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                           +---+
--R               7027759893774203888781041210243035688470658\|- 2
--R             + 
--R               12868136868984040775294141040070021247885438
--R          *
--R                       +---+      5
--R             cosh(log(\|- 2  + 1))
--R      /
--R                                                          +---+
--R             18629821302375761537774756048822860358942720\|- 2
--R           + 
--R             94473907670457185816258586943170775874920448
--R        *
--R                     +---+      6
--R           cosh(log(\|- 2  + 1))
--R    *
--R              10
--R       (x - a)
--R   + 
--R              11
--R     O((x - a)  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 36

--S 37 of 38
acsch f3
 

   (37)
                       +-+                   +-+
          +-+         \|2  + 2        2    9\|2  + 12        4
     log(\|2  + 1) + --------- (x - a)  + ----------- (x - a)
                       +-+                   +-+
                     2\|2  + 2            16\|2  + 24
   + 
         +-+                        +-+
     221\|2  + 312        6   14425\|2  + 20400        8
     ------------- (x - a)  + ----------------- (x - a)
         +-+                        +-+
     576\|2  + 816            52224\|2  + 73856
   + 
               +-+
     124515259\|2  + 176091168        10            11
     ------------------------- (x - a)   + O((x - a)  )
               +-+
     602664960\|2  + 852296960
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (37)
--R                       +-+                   +-+
--R          +-+         \|2  + 2        2    9\|2  + 12        4
--R     log(\|2  + 1) + --------- (x - a)  + ----------- (x - a)
--R                       +-+                   +-+
--R                     2\|2  + 2            16\|2  + 24
--R   + 
--R         +-+                        +-+
--R     221\|2  + 312        6   14425\|2  + 20400        8
--R     ------------- (x - a)  + ----------------- (x - a)
--R         +-+                        +-+
--R     576\|2  + 816            52224\|2  + 73856
--R   + 
--R               +-+
--R     124515259\|2  + 176091168        10            11
--R     ------------------------- (x - a)   + O((x - a)  )
--R               +-+
--R     602664960\|2  + 852296960
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 37

--S 38 of 38
map(normalize,csch %)
 

                    2            11
   (38)  1 - (x - a)  + O((x - a)  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R                    2            11
--R   (38)  1 - (x - a)  + O((x - a)  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 38
)spool 
 
Starts dribbling to frac.output (2009/2/17, 17:46:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 12
a := 11/12
 

        11
   (1)  --
        12
                                                       Type: Fraction Integer
--R 
--R
--R        11
--R   (1)  --
--R        12
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 12
b := 23/24
 

        23
   (2)  --
        24
                                                       Type: Fraction Integer
--R 
--R
--R        23
--R   (2)  --
--R        24
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 12
3 - a*b**2 + a + b/a
 

        313271
   (3)  ------
         76032
                                                       Type: Fraction Integer
--R 
--R
--R        313271
--R   (3)  ------
--R         76032
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 12
numer(a)
 

   (4)  11
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  11
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 12
denom(b)
 

   (5)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  24
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 12
r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1)
 

         2
        x  + 2x + 1
   (6)  -----------
         2
        x  - 2x + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 2x + 1
--R   (6)  -----------
--R         2
--R        x  - 2x + 1
--R                                            Type: Fraction Polynomial Integer
--E 6

--S 7 of 12
factor(r)
 

         2
        x  + 2x + 1
   (7)  -----------
         2
        x  - 2x + 1
                                   Type: Factored Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 2x + 1
--R   (7)  -----------
--R         2
--R        x  - 2x + 1
--R                                   Type: Factored Fraction Polynomial Integer
--E 7

--S 8 of 12
map(factor,r)
 

               2
        (x + 1)
   (8)  --------
               2
        (x - 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R               2
--R        (x + 1)
--R   (8)  --------
--R               2
--R        (x - 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 8

--S 9 of 12
continuedFraction(7/12)
 

          1 |     1 |     1 |     1 |
   (9)  +---+ + +---+ + +---+ + +---+
        | 1     | 1     | 2     | 2
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1 |     1 |
--R   (9)  +---+ + +---+ + +---+ + +---+
--R        | 1     | 1     | 2     | 2
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 12
partialFraction(7,12)
 

              3   1
   (10)  1 - -- + -
              2   3
             2
                                                Type: PartialFraction Integer
--R 
--R
--R              3   1
--R   (10)  1 - -- + -
--R              2   3
--R             2
--R                                                Type: PartialFraction Integer
--E 10

--S 11 of 12
g := 2/3 + 4/5*%i
 

         2   4
   (11)  - + - %i
         3   5
                                               Type: Complex Fraction Integer
--R 
--R
--R         2   4
--R   (11)  - + - %i
--R         3   5
--R                                               Type: Complex Fraction Integer
--E 11

--S 12 of 12
g :: FRAC COMPLEX INT
 

         10 + 12%i
   (12)  ---------
             15
                                               Type: Fraction Complex Integer
--R 
--R
--R         10 + 12%i
--R   (12)  ---------
--R             15
--R                                               Type: Fraction Complex Integer
--E 12
)spool 
 
Starts dribbling to sersolve.output (2009/2/17, 18:0:19).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 10
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 10
eq := D(y x,x) - x*cos(y x) - exp(x)
 

         ,                      x
   (2)  y (x) - x cos(y(x)) - %e

                                                     Type: Expression Integer
--R 
--R
--R         ,                      x
--R   (2)  y (x) - x cos(y(x)) - %e
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 10
seriesSolve(eq,y,x=0,y(0) = 0)
 
   Compiling function %A with type UnivariateTaylorSeries(Expression 
      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 

   (3)
          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
              6      12      120      360      5040      4032      362880
   + 
      161   10      11
     ----- x   + O(x  )
     10368
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function %A with type UnivariateTaylorSeries(Expression 
--R      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 
--R
--R   (3)
--R          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
--R     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
--R              6      12      120      360      5040      4032      362880
--R   + 
--R      161   10      11
--R     ----- x   + O(x  )
--R     10368
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

)set streams calculate 10
 

--S 4  of 10
R := EXPR INT
 

   (4)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (4)  Expression Integer
--R                                                                 Type: Domain
--E 4

--S 5 of 10
uts := UTS(R,'x,0)
 

   (5)  UnivariateTaylorSeries(Expression Integer,x,0)
                                                                 Type: Domain
--R 
--R
--R   (5)  UnivariateTaylorSeries(Expression Integer,x,0)
--R                                                                 Type: Domain
--E 5

--S 6 of 10
foo: uts -> uts
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
foo y ==
  xx := monomial(1,1)$uts
  xx * cos(y) + exp(xx)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 10
y := ode1(foo,0)$UTSODE(R,uts)
 
   Compiling function foo with type UnivariateTaylorSeries(Expression 
      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 

   (8)
          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
              6      12      120      360      5040      4032      362880
   + 
      161   10      11
     ----- x   + O(x  )
     10368
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function foo with type UnivariateTaylorSeries(Expression 
--R      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 
--R
--R   (8)
--R          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
--R     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
--R              6      12      120      360      5040      4032      362880
--R   + 
--R      161   10      11
--R     ----- x   + O(x  )
--R     10368
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 8

--S 9 of 10
x : uts := x
 
   Compiled code for %A has been cleared.

   (9)  x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiled code for %A has been cleared.
--R
--R   (9)  x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 9

--S 10 of 10
x * cos(y) + exp(x)
 

   (10)
              1  2   1  3   23  4   37  5    61  6   271  7   21617  8    805  9
     1 + 2x + - x  - - x  - -- x  - -- x  + --- x  + --- x  + ----- x  + ---- x
              2      3      24      60      720      504      40320      5184
   + 
        841499  10      11
     - ------- x   + O(x  )
       3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (10)
--R              1  2   1  3   23  4   37  5    61  6   271  7   21617  8    805  9
--R     1 + 2x + - x  - - x  - -- x  - -- x  + --- x  + --- x  + ----- x  + ---- x
--R              2      3      24      60      720      504      40320      5184
--R   + 
--R        841499  10      11
--R     - ------- x   + O(x  )
--R       3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 10
)spool 
 
Starts dribbling to intbypart.output (2009/2/17, 17:46:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1
integrate(x*log(x),x)
 

          2          2
        2x log(x) - x
   (1)  --------------
               4
                                          Type: Union(Expression Integer,...)
--R
--R          2          2
--R        2x log(x) - x
--R   (1)  --------------
--R               4
--R                                          Type: Union(Expression Integer,...)
--E 1
--S 2
integrate(x*exp(x),x)
 

                 x
   (2)  (x - 1)%e
                                          Type: Union(Expression Integer,...)
--R
--R                 x
--R   (2)  (x - 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 2
--S 3
integrate(exp(x)*sin(x),x)
 

          x                 x
        %e sin(x) - cos(x)%e
   (3)  ---------------------
                  2
                                          Type: Union(Expression Integer,...)
--R
--R          x                 x
--R        %e sin(x) - cos(x)%e
--R   (3)  ---------------------
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E 3
--S 4
integrate(x^3*exp(x^2),x)
 

                   2
          2       x
        (x  - 1)%e
   (4)  ------------
              2
                                          Type: Union(Expression Integer,...)
--R
--R                   2
--R          2       x
--R        (x  - 1)%e
--R   (4)  ------------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5
integrate(log(x^2+2),x)
 

                                   +-+
               2          +-+     \|2
   (5)  x log(x  + 2) - 2\|2 atan(----) - 2x
                                    x
                                          Type: Union(Expression Integer,...)
--R
--R                                   +-+
--R               2          +-+     \|2
--R   (5)  x log(x  + 2) - 2\|2 atan(----) - 2x
--R                                    x
--R                                          Type: Union(Expression Integer,...)
--E 5
--S 6
integrate(x*sin(x),x)
 

   (6)  sin(x) - x cos(x)
                                          Type: Union(Expression Integer,...)
--R
--R   (6)  sin(x) - x cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 6
--S 7
integrate(x*cos(x),x)
 

   (7)  x sin(x) + cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (7)  x sin(x) + cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 7
--S 8
integrate(x^2*cos(x),x)
 

          2
   (8)  (x  - 2)sin(x) + 2x cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2
--R   (8)  (x  - 2)sin(x) + 2x cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 8
--S 9
integrate(sin(x)*cos(x),x)
 

                2
          cos(x)
   (9)  - -------
             2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R          cos(x)
--R   (9)  - -------
--R             2
--R                                          Type: Union(Expression Integer,...)
--E 9
--S 10
integrate(log(x),x)
 

   (10)  x log(x) - x
                                          Type: Union(Expression Integer,...)
--R
--R   (10)  x log(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 10
--S 11
integrate(x^2*log(x),x)
 

           3          3
         3x log(x) - x
   (11)  --------------
                9
                                          Type: Union(Expression Integer,...)
--R
--R           3          3
--R         3x log(x) - x
--R   (11)  --------------
--R                9
--R                                          Type: Union(Expression Integer,...)
--E 11
--S 12
integrate(x^2*exp(x),x)
 

           2            x
   (12)  (x  - 2x + 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2            x
--R   (12)  (x  - 2x + 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 12
--S 13
integrate(asin(x),x)
 

                     +--------+
                     |   2           +--------+
                  2x\|- x  + 1       |   2
         - x atan(-------------) + 2\|- x  + 1
                       2
                     2x  - 1
   (13)  --------------------------------------
                            2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +--------+
--R                     |   2           +--------+
--R                  2x\|- x  + 1       |   2
--R         - x atan(-------------) + 2\|- x  + 1
--R                       2
--R                     2x  - 1
--R   (13)  --------------------------------------
--R                            2
--R                                          Type: Union(Expression Integer,...)
--E 13
--S 14
integrate(atan(x),x)
 

                2                 2x
         - log(x  + 1) - x atan(------)
                                 2
                                x  - 1
   (14)  ------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2                 2x
--R         - log(x  + 1) - x atan(------)
--R                                 2
--R                                x  - 1
--R   (14)  ------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 14
--S 15
integrate(sec(x)^3,x)
 

   (15)
         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
                   cos(x) + 1                        cos(x) + 1
   --------------------------------------------------------------------------
                                           2
                                    2cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (15)
--R         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
--R   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
--R                   cos(x) + 1                        cos(x) + 1
--R   --------------------------------------------------------------------------
--R                                           2
--R                                    2cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 15
--S 16
integrate(x^3*exp(2*x),x)
 

            3     2            2x
         (4x  - 6x  + 6x - 3)%e
   (16)  ------------------------
                     8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            3     2            2x
--R         (4x  - 6x  + 6x - 3)%e
--R   (16)  ------------------------
--R                     8
--R                                          Type: Union(Expression Integer,...)
--E 16
)spool
 
Starts dribbling to exp.output (2009/2/17, 17:45:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
[[0.0,     1.000000000000000,  exp(0.0), exp(0.0)-     1.000000000000000],_
 [0.1,     1.105170918075648,  exp(0.1), exp(0.1)-     1.105170918075648],_
 [0.2,     1.221402758160170,  exp(0.2), exp(0.2)-     1.221402758160170],_
 [0.3,     1.349858807576003,  exp(0.3), exp(0.3)-     1.349858807576003],_
 [0.4,     1.491824697641270,  exp(0.4), exp(0.4)-     1.491824697641270],_
 [0.5,     1.648721270700128,  exp(0.5), exp(0.5)-     1.648721270700128],_
 [0.6,     1.822118800390509,  exp(0.6), exp(0.6)-     1.822118800390509],_
 [0.7,     2.013752707470477,  exp(0.7), exp(0.7)-     2.013752707470477],_
 [0.8,     2.225540928492468,  exp(0.8), exp(0.8)-     2.225540928492468],_
 [0.9,     2.459603111156950,  exp(0.9), exp(0.9)-     2.459603111156950],_
 [1.0,     2.718281828459045,  exp(1.0), exp(1.0)-     2.718281828459045],_
 [1.1,     3.004166023946433,  exp(1.1), exp(1.1)-     3.004166023946433],_
 [1.2,     3.320116922736547,  exp(1.2), exp(1.2)-     3.320116922736547],_
 [1.3,     3.669296667619244,  exp(1.3), exp(1.3)-     3.669296667619244],_
 [1.4,     4.055199966844675,  exp(1.4), exp(1.4)-     4.055199966844675],_
 [1.5,     4.481689070338065,  exp(1.5), exp(1.5)-     4.481689070338065],_
 [1.6,     4.953032424395115,  exp(1.6), exp(1.6)-     4.953032424395115],_
 [1.7,     5.473947391727200,  exp(1.7), exp(1.7)-     5.473947391727200],_
 [1.8,     6.049647464412946,  exp(1.8), exp(1.8)-     6.049647464412946],_
 [1.9,     6.685894442279269,  exp(1.9), exp(1.9)-     6.685894442279269],_
 [2.0,     7.389056098930650,  exp(2.0), exp(2.0)-     7.389056098930650],_
 [2.1,     8.166169912567650,  exp(2.1), exp(2.1)-     8.166169912567650],_
 [2.2,     9.025013499434121,  exp(2.2), exp(2.2)-     9.025013499434121],_
 [2.3,     9.974182454814721,  exp(2.3), exp(2.3)-     9.974182454814721],_
 [2.4,    11.023176380641602,  exp(2.4), exp(2.4)-    11.023176380641602],_
 [2.5,    12.182493960703473,  exp(2.5), exp(2.5)-    12.182493960703473],_
 [2.6,    13.463738035001690,  exp(2.6), exp(2.6)-    13.463738035001690],_
 [2.7,    14.879731724872834,  exp(2.7), exp(2.7)-    14.879731724872834],_
 [2.8,    16.444646771097050,  exp(2.8), exp(2.8)-    16.444646771097050],_
 [2.9,    18.174145369443061,  exp(2.9), exp(2.9)-    18.174145369443061],_
 [3.0,    20.085536923187668,  exp(3.0), exp(3.0)-    20.085536923187668],_
 [3.1,    22.197951281441633,  exp(3.1), exp(3.1)-    22.197951281441633],_
 [3.2,    24.532530197109349,  exp(3.2), exp(3.2)-    24.532530197109349],_
 [3.3,    27.112638920657887,  exp(3.3), exp(3.3)-    27.112638920657887],_
 [3.4,    29.964100047397013,  exp(3.4), exp(3.4)-    29.964100047397013],_
 [3.5,    33.115451958692314,  exp(3.5), exp(3.5)-    33.115451958692314],_
 [3.6,    36.598234443677988,  exp(3.6), exp(3.6)-    36.598234443677988],_
 [3.7,    40.447304360067391,  exp(3.7), exp(3.7)-    40.447304360067391],_
 [3.8,    44.701184493300823,  exp(3.8), exp(3.8)-    44.701184493300823],_
 [3.9,    49.402449105530174,  exp(3.9), exp(3.9)-    49.402449105530174],_
 [4.0,    54.598150033144239,  exp(4.0), exp(4.0)-    54.598150033144239],_
 [4.1,    60.340287597361969,  exp(4.1), exp(4.1)-    60.340287597361969],_
 [4.2,    66.686331040925142,  exp(4.2), exp(4.2)-    66.686331040925142],_
 [4.3,    73.699793699595797,  exp(4.3), exp(4.3)-    73.699793699595797],_
 [4.4,    81.450868664968117,  exp(4.4), exp(4.4)-    81.450868664968117],_
 [4.5,    90.017131300521814,  exp(4.5), exp(4.5)-    90.017131300521814],_
 [4.6,    99.484315641933809,  exp(4.6), exp(4.6)-    99.484315641933809],_
 [4.7,   109.947172452123499,  exp(4.7), exp(4.7)-   109.947172452123499],_
 [4.8,   121.510417518734881,  exp(4.8), exp(4.8)-   121.510417518734881],_
 [4.9,   134.289779684935485,  exp(4.9), exp(4.9)-   134.289779684935485],_
 [5.0,   148.413159102577,     exp(5.0), exp(5.0)-   148.413159102577],_
 [5.1,   164.021907299902,     exp(5.1), exp(5.1)-   164.021907299902],_
 [5.2,   181.272241875151,     exp(5.2), exp(5.2)-   181.272241875151],_
 [5.3,   200.336809974792,     exp(5.3), exp(5.3)-   200.336809974792],_
 [5.4,   221.406416204187,     exp(5.4), exp(5.4)-   221.406416204187],_
 [5.5,   244.691932264220,     exp(5.5), exp(5.5)-   244.691932264220],_
 [5.6,   270.426407426153,     exp(5.6), exp(5.6)-   270.426407426153],_
 [5.7,   298.867400967060,     exp(5.7), exp(5.7)-   298.867400967060],_
 [5.8,   330.299559909649,     exp(5.8), exp(5.8)-   330.299559909649],_
 [5.9,   365.037467865329,     exp(5.9), exp(5.9)-   365.037467865329],_
 [6.0,   403.428793492735,     exp(6.0), exp(6.0)-   403.428793492735],_
 [6.1,   445.857770082517,     exp(6.1), exp(6.1)-   445.857770082517],_
 [6.2,   492.749041093256,     exp(6.2), exp(6.2)-   492.749041093256],_
 [6.3,   544.571910125929,     exp(6.3), exp(6.3)-   544.571910125929],_
 [6.4,   601.845037872082,     exp(6.4), exp(6.4)-   601.845037872082],_
 [6.5,   665.141633044362,     exp(6.5), exp(6.5)-   665.141633044362],_
 [6.6,   735.095189241973,     exp(6.6), exp(6.6)-   735.095189241973],_
 [6.7,   812.405825167543,     exp(6.7), exp(6.7)-   812.405825167543],_
 [6.8,   897.847291650418,     exp(6.8), exp(6.8)-   897.847291650418],_
 [6.9,   992.274715605026,     exp(6.9), exp(6.9)-   992.274715605026],_
 [7.0,  1096.633158428459,     exp(7.0), exp(7.0)-  1096.633158428459],_
 [7.1,  1211.967074492577,     exp(7.1), exp(7.1)-  1211.967074492577],_
 [7.2,  1339.430764394418,     exp(7.2), exp(7.2)-  1339.430764394418],_
 [7.3,  1480.299927584545,     exp(7.3), exp(7.3)-  1480.299927584545],_
 [7.4,  1635.984429995927,     exp(7.4), exp(7.4)-  1635.984429995927],_
 [7.5,  1808.042414456063,     exp(7.5), exp(7.5)-  1808.042414456063],_
 [7.6,  1998.195895104118,     exp(7.6), exp(7.6)-  1998.195895104118],_
 [7.7,  2208.347991887209,     exp(7.7), exp(7.7)-  2208.347991887209],_
 [7.8,  2440.601977624499,     exp(7.8), exp(7.8)-  2440.601977624499],_
 [7.9,  2697.282328268509,     exp(7.9), exp(7.9)-  2697.282328268509],_
 [8.0,  2980.957987041728,     exp(8.0), exp(8.0)-  2980.957987041728],_
 [8.1,  3294.468075283841,     exp(8.1), exp(8.1)-  3294.468075283841],_
 [8.2,  3640.950307332355,     exp(8.2), exp(8.2)-  3640.950307332355],_
 [8.3,  4023.872393822310,     exp(8.3), exp(8.3)-  4023.872393822310],_
 [8.4,  4447.066747699856,     exp(8.4), exp(8.4)-  4447.066747699856],_
 [8.5,  4914.768840299134,     exp(8.5), exp(8.5)-  4914.768840299134],_
 [8.6,  5431.659591362980,     exp(8.6), exp(8.6)-  5431.659591362980],_
 [8.7,  6002.912217261022,     exp(8.7), exp(8.7)-  6002.912217261022],_
 [8.8,  6634.244006277885,     exp(8.8), exp(8.8)-  6634.244006277885],_
 [8.9,  7331.973539155993,     exp(8.9), exp(8.9)-  7331.973539155993],_
 [9.0,  8103.083927575384,     exp(9.0), exp(9.0)-  8103.083927575384],_
 [9.1,  8955.292703482512,     exp(9.1), exp(9.1)-  8955.292703482512],_
 [9.2,  9897.129058743916,     exp(9.2), exp(9.2)-  9897.129058743916],_
 [9.3, 10938.019208165184,     exp(9.3), exp(9.3)- 10938.019208165184],_
 [9.4, 12088.380730216984,     exp(9.4), exp(9.4)- 12088.380730216984],_
 [9.5, 13359.726829661872,     exp(9.5), exp(9.5)- 13359.726829661872],_
 [9.6, 14764.781565577273,     exp(9.6), exp(9.6)- 14764.781565577273],_
 [9.7, 16317.607198015432,     exp(9.7), exp(9.7)- 16317.607198015432],_
 [9.8, 18033.744927828511,     exp(9.8), exp(9.8)- 18033.744927828511],_
 [9.9, 19930.370438230289,     exp(9.9), exp(9.9)- 19930.370438230289],_
[10.0, 22026.465794806717,    exp(10.0), exp(10.0)-22026.465794806717]]
 

   (1)
   [[0.0,1.0,1.0,0.0],
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                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.0,1.0,1.0,0.0],
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--R    [1.0,2.7182818284 59045,2.7182818284 590452354,0.2354 E -15],
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--R    [1.6,4.9530324243 95115,4.9530324243 951148037,- 0.196 E -15],
--R    [1.7,5.4739473917 272,5.4739473917 271997608,- 0.239 E -15],
--R    [1.8,6.0496474644 12946,6.0496474644 129460837,0.837 E -16],
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--R    [3.7,40.4473043600 67391,40.4473043600 67390529,- 0.471 E -15],
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--R    [4.5,90.0171313005 21814,90.0171313005 2181355,- 0.45 E -15],
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--R    [4.7,109.9471724521 23499,109.9471724521 2349888,- 0.12 E -15],
--R    [4.8,121.5104175187 34881,121.5104175187 3488076,- 0.24 E -15],
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--R    [5.4,221.4064162041 87,221.4064162041 8708703,0.8703 E -13],
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--R    [7.6,1998.1958951041 18,1998.1958951041 179592,- 0.408 E -13],
--R    [7.7,2208.3479918872 09,2208.3479918872 08524,- 0.476 E -12],
--R    [7.8,2440.6019776244 99,2440.6019776244 990773,0.773 E -13],
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--R    [8.0,2980.9579870417 28,2980.9579870417 282747,0.2747 E -12],
--R    [8.1,3294.4680752838 41,3294.4680752838 413332,0.3332 E -12],
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--R    [8.4,4447.0667476998 56,4447.0667476998 560855,0.855 E -13],
--R    [8.5,4914.7688402991 34,4914.7688402991 343754,0.375 E -12],
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--R    [8.7,6002.9122172610 22,6002.9122172610 2198,- 0.2 E -13],
--R    [8.8,6634.2440062778 85,6634.2440062778 851586,0.159 E -12],
--R    [8.9,7331.9735391559 93,7331.9735391559 929051,- 0.949 E -13],
--R    [9.0,8103.0839275753 84,8103.0839275753 840077,0.77 E -14],
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--R    [9.6,14764.7815655772 73,14764.7815655772 72616,- 0.384 E -12],
--R    [9.7,16317.6071980154 32,16317.6071980154 32233,0.233 E -12],
--R    [9.8,18033.7449278285 11,18033.7449278285 11246,0.246 E -12],
--R    [9.9,19930.3704382302 89,19930.3704382302 8949,0.49 E -12],
--R    [10.0,22026.4657948067 17,22026.4657948067 16517,- 0.483 E -12]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
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 [5.4,0.00451658094261266798,exp(-5.4),exp(-5.4)-0.00451658094261266798],_
 [5.5,0.00408677143846406699,exp(-5.5),exp(-5.5)-0.00408677143846406699],_
 [5.6,0.00369786371648293082,exp(-5.6),exp(-5.6)-0.00369786371648293082],_
 [5.7,0.00334596545747127277,exp(-5.7),exp(-5.7)-0.00334596545747127277],_
 [5.8,0.00302755474537581475,exp(-5.8),exp(-5.8)-0.00302755474537581475],_
 [5.9,0.00273944481876836923,exp(-5.9),exp(-5.9)-0.00273944481876836923],_
 [6.0,0.00247875217666635842,exp(-6.0),exp(-6.0)-0.00247875217666635842],_
 [6.1,0.00224286771948580247,exp(-6.1),exp(-6.1)-0.00224286771948580247],_
 [6.2,0.00202943063629573436,exp(-6.2),exp(-6.2)-0.00202943063629573436],_
 [6.3,0.00183630477702890683,exp(-6.3),exp(-6.3)-0.00183630477702890683],_
 [6.4,0.00166155727317393450,exp(-6.4),exp(-6.4)-0.00166155727317393450],_
 [6.5,0.00150343919297757245,exp(-6.5),exp(-6.5)-0.00150343919297757245],_
 [6.6,0.00136036803754789342,exp(-6.6),exp(-6.6)-0.00136036803754789342],_
 [6.7,0.00123091190267348118,exp(-6.7),exp(-6.7)-0.00123091190267348118],_
 [6.8,0.00111377514784480308,exp(-6.8),exp(-6.8)-0.00111377514784480308],_
 [6.9,0.00100778542904851076,exp(-6.9),exp(-6.9)-0.00100778542904851076],_
 [7.0,0.00091188196555451621,exp(-7.0),exp(-7.0)-0.00091188196555451621],_
 [7.1,0.00082510492326590427,exp(-7.1),exp(-7.1)-0.00082510492326590427],_
 [7.2,0.00074658580837667937,exp(-7.2),exp(-7.2)-0.00074658580837667937],_
 [7.3,0.00067553877519384424,exp(-7.3),exp(-7.3)-0.00067553877519384424],_
 [7.4,0.00061125276112957256,exp(-7.4),exp(-7.4)-0.00061125276112957256],_
 [7.5,0.00055308437014783358,exp(-7.5),exp(-7.5)-0.00055308437014783358],_
 [7.6,0.00050045143344061070,exp(-7.6),exp(-7.6)-0.00050045143344061070],_
 [7.7,0.00045282718288679706,exp(-7.7),exp(-7.7)-0.00045282718288679706],_
 [7.8,0.00040973497897978671,exp(-7.8),exp(-7.8)-0.00040973497897978671],_
 [7.9,0.00037074354045908837,exp(-7.9),exp(-7.9)-0.00037074354045908837],_
 [8.0,0.00033546262790251184,exp(-8.0),exp(-8.0)-0.00033546262790251184],_
 [8.1,0.00030353913807886666,exp(-8.1),exp(-8.1)-0.00030353913807886666],_
 [8.2,0.00027465356997214233,exp(-8.2),exp(-8.2)-0.00027465356997214233],_
 [8.3,0.00024851682710795202,exp(-8.3),exp(-8.3)-0.00024851682710795202],_
 [8.4,0.00022486732417884827,exp(-8.4),exp(-8.4)-0.00022486732417884827],_
 [8.5,0.00020346836901064417,exp(-8.5),exp(-8.5)-0.00020346836901064417],_
 [8.6,0.00018410579366757912,exp(-8.6),exp(-8.6)-0.00018410579366757912],_
 [8.7,0.00016658581098763341,exp(-8.7),exp(-8.7)-0.00016658581098763341],_
 [8.8,0.00015073307509547660,exp(-8.8),exp(-8.8)-0.00015073307509547660],_
 [8.9,0.00013638892648201145,exp(-8.9),exp(-8.9)-0.00013638892648201145],_
 [9.0,0.00012340980408667955,exp(-9.0),exp(-9.0)-0.00012340980408667955],_
 [9.1,0.00011166580849011474,exp(-9.1),exp(-9.1)-0.00011166580849011474],_
 [9.2,0.00010103940183709335,exp(-9.2),exp(-9.2)-0.00010103940183709335],_
 [9.3,0.00009142423147817334,exp(-9.3),exp(-9.3)-0.00009142423147817334],_
 [9.4,0.00008272406555663226,exp(-9.4),exp(-9.4)-0.00008272406555663226],_
 [9.5,0.00007485182988770059,exp(-9.5),exp(-9.5)-0.00007485182988770059],_
 [9.6,0.00006772873649085387,exp(-9.6),exp(-9.6)-0.00006772873649085387],_
 [9.7,0.00006128349505322210,exp(-9.7),exp(-9.7)-0.00006128349505322210],_
 [9.8,0.00005545159943217698,exp(-9.8),exp(-9.8)-0.00005545159943217698],_
 [9.9,0.00005017468205617530,exp(-9.9),exp(-9.9)-0.00005017468205617530],_
[10.0,0.00004539992976248485,exp(-10.0),exp(-10.0)-0.00004539992976248485]]
 

   (2)
   [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20],
    [0.2,0.8187307530 7798185867,0.8187307530 7798185867,0.0],
    [0.3,0.7408182206 8171786607,0.7408182206 8171786606,- 0.7 E -20],
    [0.4,0.6703200460 3563930074,0.6703200460 3563930075,0.3 E -20],
    [0.5,0.6065306597 126334236,0.6065306597 126334236,0.3 E -20],
    [0.6,0.5488116360 9402643263,0.5488116360 9402643263,- 0.3 E -20],
    [0.7,0.4965853037 914095147,0.4965853037 9140951471,0.5 E -20],
    [0.8,0.4493289641 1722159143,0.4493289641 1722159143,0.0],
    [0.9,0.4065696597 4059911188,0.4065696597 4059911188,0.3 E -20],
    [1.0,0.3678794411 714423216,0.3678794411 7144232159,- 0.5 E -20],
    [1.1,0.3328710836 9807955329,0.3328710836 9807955329,- 0.2 E -20],
    [1.2,0.3011942119 1220209664,0.3011942119 1220209664,0.3 E -20],
    [1.3,0.2725317930 3401260312,0.2725317930 3401260312,0.3 E -20],
    [1.4,0.2465969639 4160647694,0.2465969639 4160647694,0.0],
    [1.5,0.2231301601 4842982893,0.2231301601 4842982893,0.3 E -20],
    [1.6,0.2018965179 9465540849,0.2018965179 9465540848,- 0.5 E -20],
    [1.7,0.1826835240 5273465022,0.1826835240 5273465022,0.3 E -20],
    [1.8,0.1652988882 215865383,0.1652988882 215865383,- 0.3 E -20],
    [1.9,0.1495686192 2263505264,0.1495686192 2263505264,0.8 E -21],
    [2.0,0.1353352832 3661269189,0.1353352832 3661269189,0.4 E -20],
    [2.1,0.1224564282 5298191022,0.1224564282 5298191022,- 0.8 E -21],
    [2.2,0.1108031583 6233388333,0.1108031583 6233388333,0.4 E -20],
    [2.3,0.1002588437 2280373373,0.1002588437 2280373373,0.0],
    [2.4,0.0907179532 8941250338,0.0907179532 8941250337 5,- 0.6 E -20],
    [2.5,0.0820849986 2389879517,0.0820849986 2389879516 9,- 0.4 E -21],
    [2.6,0.0742735782 1433388043,0.0742735782 1433388042 9,- 0.1 E -20],
    [2.7,0.0672055127 3974976513,0.0672055127 3974976512 6,- 0.4 E -20],
    [2.8,0.0608100626 25217965,0.0608100626 2521796499 6,- 0.4 E -20],
    [2.9,0.0550232200 5640722903,0.0550232200 5640722903,- 0.4 E -21],
    [3.0,0.0497870683 6786394298,0.0497870683 6786394297 9,- 0.6 E -21],
    [3.1,0.0450492023 9355780607,0.0450492023 9355780606 9,- 0.1 E -20],
    [3.2,0.0407622039 7836621517,0.0407622039 7836621516 6,- 0.4 E -20],
    [3.3,0.0368831674 0124000545,0.0368831674 0124000544 6,- 0.4 E -20],
    [3.4,0.0333732699 6032607948,0.0333732699 6032607948 2,0.2 E -20],
    [3.5,0.0301973834 2231850074,0.0301973834 2231850074,- 0.2 E -21],
    [3.6,0.0273237224 472925608,0.0273237224 4729256080 2,0.2 E -20],
    [3.7,0.0247235264 703393912,0.0247235264 7033939120 3,0.3 E -20],
    [3.8,0.0223707718 5616559578,0.0223707718 5616559577 9,- 0.1 E -20],
    [3.9,0.0202419114 4580438847,0.0202419114 4580438847 2,0.2 E -20],
    [4.0,0.0183156388 8873418029,0.0183156388 8873418029 4,0.4 E -20],
    [4.1,0.0165726754 0176124754,0.0165726754 0176124754 2,0.2 E -20],
    [4.2,0.0149955768 2047770621,0.0149955768 2047770621 2,0.2 E -20],
    [4.3,0.0135685590 1220093176,0.0135685590 1220093175 7,- 0.3 E -20],
    [4.4,0.0122773399 0306844118,0.0122773399 0306844117 9,- 0.1 E -20],
    [4.5,0.0111089965 382423065,0.0111089965 3824230649 6,- 0.4 E -20],
    [4.6,0.0100518357 4463358164,0.0100518357 4463358164 2,0.2 E -20],
    [4.7,0.0090952771 0169581709,0.0090952771 0169581709 21,0.2 E -20],
    [4.8,0.0082297470 4902002884,0.0082297470 4902002884 13,0.1 E -20],
    [4.9,0.0074465830 7092434052,0.0074465830 7092434051 82,- 0.2 E -20],
    [5.0,0.0067379469 990854671,0.0067379469 9908546709 66,- 0.3 E -20],
    [5.1,0.0060967465 6551563611,0.0060967465 6551563610 72,- 0.3 E -20],
    [5.2,0.0055165644 2076077242,0.0055165644 2076077241 81,- 0.2 E -20],
    [5.3,0.0049915939 0691021621,0.0049915939 0691021621 22,0.2 E -20],
    [5.4,0.0045165809 4261266798,0.0045165809 4261266798 16,0.2 E -20],
    [5.5,0.0040867714 3846406699,0.0040867714 3846406699 35,0.35 E -20],
    [5.6,0.0036978637 1648293082,0.0036978637 1648293082 07,0.7 E -21],
    [5.7,0.0033459654 5747127277,0.0033459654 5747127276 58,- 0.42 E -20],
    [5.8,0.0030275547 4537581475,0.0030275547 4537581474 82,- 0.18 E -20],
    [5.9,0.0027394448 1876836923,0.0027394448 1876836923 28,0.28 E -20],
    [6.0,0.0024787521 7666635842,0.0024787521 7666635842 3,0.3 E -20],
    [6.1,0.0022428677 1948580247,0.0022428677 1948580247 32,0.32 E -20],
    [6.2,0.0020294306 3629573436,0.0020294306 3629573436 34,0.34 E -20],
    [6.3,0.0018363047 7702890683,0.0018363047 7702890682 52,- 0.48 E -20],
    [6.4,0.0016615572 731739345,0.0016615572 7317393449 91,- 0.93 E -21],
    [6.5,0.0015034391 9297757245,0.0015034391 9297757244 74,- 0.26 E -20],
    [6.6,0.0013603680 3754789342,0.0013603680 3754789341 69,- 0.31 E -20],
    [6.7,0.0012309119 0267348118,0.0012309119 0267348118 46,0.46 E -20],
    [6.8,0.0011137751 4784480308,0.0011137751 4784480307 88,- 0.12 E -20],
    [6.9,0.0010077854 2904851076,0.0010077854 2904851076 14,0.14 E -20],
    [7.0,0.0009118819 6555451621,0.0009118819 6555451620 8,- 0.2 E -20],
    [7.1,0.0008251049 2326590427,0.0008251049 2326590427 015,0.1 E -21],
    [7.2,0.0007465858 0837667937,0.0007465858 0837667936 81,- 0.19 E -20],
    [7.3,0.0006755387 7519384424,0.0006755387 7519384423 783,- 0.22 E -20],
    [7.4,0.0006112527 6112957256,0.0006112527 6112957255 567,- 0.433 E -20],
    [7.5,0.0005530843 7014783358,0.0005530843 7014783358 31,0.31 E -20],
    [7.6,0.0005004514 334406107,0.0005004514 3344061069 551,- 0.449 E -20],
    [7.7,0.0004528271 8288679706,0.0004528271 8288679705 8,- 0.2 E -20],
    [7.8,0.0004097349 7897978671,0.0004097349 7897978670 846,- 0.15 E -20],
    [7.9,0.0003707435 4045908837,0.0003707435 4045908837 443,0.443 E -20],
    [8.0,0.0003354626 2790251184,0.0003354626 2790251183 882,- 0.12 E -20],
    [8.1,0.0003035391 3807886666,0.0003035391 3807886666 086,0.86 E -21],
    [8.2,0.0002746535 6997214233,0.0002746535 6997214232 763,- 0.237 E -20],
    [8.3,0.0002485168 2710795202,0.0002485168 2710795202 08,0.8 E -21],
    [8.4,0.0002248673 2417884827,0.0002248673 2417884827 28,0.28 E -20],
    [8.5,0.0002034683 6901064417,0.0002034683 6901064417 437,0.437 E -20],
    [8.6,0.0001841057 9366757912,0.0001841057 9366757912 495,0.495 E -20],
    [8.7,0.0001665858 1098763341,0.0001665858 1098763341 149,0.149 E -20],
    [8.8,0.0001507330 750954766,0.0001507330 7509547660 064,0.64 E -21],
    [8.9,0.0001363889 2648201145,0.0001363889 2648201144 785,- 0.215 E -20],
    [9.0,0.0001234098 0408667955,0.0001234098 0408667954 95,- 0.5 E -21],
    [9.1,0.0001116658 0849011474,0.0001116658 0849011473 564,- 0.436 E -20],
    [9.2,0.0001010394 0183709335,0.0001010394 0183709335 073,0.732 E -21],
    [9.3,0.0000914242 3147817334,0.0000914242 3147817333 7862,- 0.214 E -20],
    [9.4,0.0000827240 6555663226,0.0000827240 6555663226 2731,0.273 E -20],
    [9.5,0.0000748518 2988770059,0.0000748518 2988770059 1471,0.147 E -20],
    [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20],
    [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20],
    [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20],
    [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20],
    [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20],
--R    [0.2,0.8187307530 7798185867,0.8187307530 7798185867,0.0],
--R    [0.3,0.7408182206 8171786607,0.7408182206 8171786606,- 0.7 E -20],
--R    [0.4,0.6703200460 3563930074,0.6703200460 3563930075,0.3 E -20],
--R    [0.5,0.6065306597 126334236,0.6065306597 126334236,0.3 E -20],
--R    [0.6,0.5488116360 9402643263,0.5488116360 9402643263,- 0.3 E -20],
--R    [0.7,0.4965853037 914095147,0.4965853037 9140951471,0.5 E -20],
--R    [0.8,0.4493289641 1722159143,0.4493289641 1722159143,0.0],
--R    [0.9,0.4065696597 4059911188,0.4065696597 4059911188,0.3 E -20],
--R    [1.0,0.3678794411 714423216,0.3678794411 7144232159,- 0.5 E -20],
--R    [1.1,0.3328710836 9807955329,0.3328710836 9807955329,- 0.2 E -20],
--R    [1.2,0.3011942119 1220209664,0.3011942119 1220209664,0.3 E -20],
--R    [1.3,0.2725317930 3401260312,0.2725317930 3401260312,0.3 E -20],
--R    [1.4,0.2465969639 4160647694,0.2465969639 4160647694,0.0],
--R    [1.5,0.2231301601 4842982893,0.2231301601 4842982893,0.3 E -20],
--R    [1.6,0.2018965179 9465540849,0.2018965179 9465540848,- 0.5 E -20],
--R    [1.7,0.1826835240 5273465022,0.1826835240 5273465022,0.3 E -20],
--R    [1.8,0.1652988882 215865383,0.1652988882 215865383,- 0.3 E -20],
--R    [1.9,0.1495686192 2263505264,0.1495686192 2263505264,0.8 E -21],
--R    [2.0,0.1353352832 3661269189,0.1353352832 3661269189,0.4 E -20],
--R    [2.1,0.1224564282 5298191022,0.1224564282 5298191022,- 0.8 E -21],
--R    [2.2,0.1108031583 6233388333,0.1108031583 6233388333,0.4 E -20],
--R    [2.3,0.1002588437 2280373373,0.1002588437 2280373373,0.0],
--R    [2.4,0.0907179532 8941250338,0.0907179532 8941250337 5,- 0.6 E -20],
--R    [2.5,0.0820849986 2389879517,0.0820849986 2389879516 9,- 0.4 E -21],
--R    [2.6,0.0742735782 1433388043,0.0742735782 1433388042 9,- 0.1 E -20],
--R    [2.7,0.0672055127 3974976513,0.0672055127 3974976512 6,- 0.4 E -20],
--R    [2.8,0.0608100626 25217965,0.0608100626 2521796499 6,- 0.4 E -20],
--R    [2.9,0.0550232200 5640722903,0.0550232200 5640722903,- 0.4 E -21],
--R    [3.0,0.0497870683 6786394298,0.0497870683 6786394297 9,- 0.6 E -21],
--R    [3.1,0.0450492023 9355780607,0.0450492023 9355780606 9,- 0.1 E -20],
--R    [3.2,0.0407622039 7836621517,0.0407622039 7836621516 6,- 0.4 E -20],
--R    [3.3,0.0368831674 0124000545,0.0368831674 0124000544 6,- 0.4 E -20],
--R    [3.4,0.0333732699 6032607948,0.0333732699 6032607948 2,0.2 E -20],
--R    [3.5,0.0301973834 2231850074,0.0301973834 2231850074,- 0.2 E -21],
--R    [3.6,0.0273237224 472925608,0.0273237224 4729256080 2,0.2 E -20],
--R    [3.7,0.0247235264 703393912,0.0247235264 7033939120 3,0.3 E -20],
--R    [3.8,0.0223707718 5616559578,0.0223707718 5616559577 9,- 0.1 E -20],
--R    [3.9,0.0202419114 4580438847,0.0202419114 4580438847 2,0.2 E -20],
--R    [4.0,0.0183156388 8873418029,0.0183156388 8873418029 4,0.4 E -20],
--R    [4.1,0.0165726754 0176124754,0.0165726754 0176124754 2,0.2 E -20],
--R    [4.2,0.0149955768 2047770621,0.0149955768 2047770621 2,0.2 E -20],
--R    [4.3,0.0135685590 1220093176,0.0135685590 1220093175 7,- 0.3 E -20],
--R    [4.4,0.0122773399 0306844118,0.0122773399 0306844117 9,- 0.1 E -20],
--R    [4.5,0.0111089965 382423065,0.0111089965 3824230649 6,- 0.4 E -20],
--R    [4.6,0.0100518357 4463358164,0.0100518357 4463358164 2,0.2 E -20],
--R    [4.7,0.0090952771 0169581709,0.0090952771 0169581709 21,0.2 E -20],
--R    [4.8,0.0082297470 4902002884,0.0082297470 4902002884 13,0.1 E -20],
--R    [4.9,0.0074465830 7092434052,0.0074465830 7092434051 82,- 0.2 E -20],
--R    [5.0,0.0067379469 990854671,0.0067379469 9908546709 66,- 0.3 E -20],
--R    [5.1,0.0060967465 6551563611,0.0060967465 6551563610 72,- 0.3 E -20],
--R    [5.2,0.0055165644 2076077242,0.0055165644 2076077241 81,- 0.2 E -20],
--R    [5.3,0.0049915939 0691021621,0.0049915939 0691021621 22,0.2 E -20],
--R    [5.4,0.0045165809 4261266798,0.0045165809 4261266798 16,0.2 E -20],
--R    [5.5,0.0040867714 3846406699,0.0040867714 3846406699 35,0.35 E -20],
--R    [5.6,0.0036978637 1648293082,0.0036978637 1648293082 07,0.7 E -21],
--R    [5.7,0.0033459654 5747127277,0.0033459654 5747127276 58,- 0.42 E -20],
--R    [5.8,0.0030275547 4537581475,0.0030275547 4537581474 82,- 0.18 E -20],
--R    [5.9,0.0027394448 1876836923,0.0027394448 1876836923 28,0.28 E -20],
--R    [6.0,0.0024787521 7666635842,0.0024787521 7666635842 3,0.3 E -20],
--R    [6.1,0.0022428677 1948580247,0.0022428677 1948580247 32,0.32 E -20],
--R    [6.2,0.0020294306 3629573436,0.0020294306 3629573436 34,0.34 E -20],
--R    [6.3,0.0018363047 7702890683,0.0018363047 7702890682 52,- 0.48 E -20],
--R    [6.4,0.0016615572 731739345,0.0016615572 7317393449 91,- 0.93 E -21],
--R    [6.5,0.0015034391 9297757245,0.0015034391 9297757244 74,- 0.26 E -20],
--R    [6.6,0.0013603680 3754789342,0.0013603680 3754789341 69,- 0.31 E -20],
--R    [6.7,0.0012309119 0267348118,0.0012309119 0267348118 46,0.46 E -20],
--R    [6.8,0.0011137751 4784480308,0.0011137751 4784480307 88,- 0.12 E -20],
--R    [6.9,0.0010077854 2904851076,0.0010077854 2904851076 14,0.14 E -20],
--R    [7.0,0.0009118819 6555451621,0.0009118819 6555451620 8,- 0.2 E -20],
--R    [7.1,0.0008251049 2326590427,0.0008251049 2326590427 015,0.1 E -21],
--R    [7.2,0.0007465858 0837667937,0.0007465858 0837667936 81,- 0.19 E -20],
--R    [7.3,0.0006755387 7519384424,0.0006755387 7519384423 783,- 0.22 E -20],
--R    [7.4,0.0006112527 6112957256,0.0006112527 6112957255 567,- 0.433 E -20],
--R    [7.5,0.0005530843 7014783358,0.0005530843 7014783358 31,0.31 E -20],
--R    [7.6,0.0005004514 334406107,0.0005004514 3344061069 551,- 0.449 E -20],
--R    [7.7,0.0004528271 8288679706,0.0004528271 8288679705 8,- 0.2 E -20],
--R    [7.8,0.0004097349 7897978671,0.0004097349 7897978670 846,- 0.15 E -20],
--R    [7.9,0.0003707435 4045908837,0.0003707435 4045908837 443,0.443 E -20],
--R    [8.0,0.0003354626 2790251184,0.0003354626 2790251183 882,- 0.12 E -20],
--R    [8.1,0.0003035391 3807886666,0.0003035391 3807886666 086,0.86 E -21],
--R    [8.2,0.0002746535 6997214233,0.0002746535 6997214232 763,- 0.237 E -20],
--R    [8.3,0.0002485168 2710795202,0.0002485168 2710795202 08,0.8 E -21],
--R    [8.4,0.0002248673 2417884827,0.0002248673 2417884827 28,0.28 E -20],
--R    [8.5,0.0002034683 6901064417,0.0002034683 6901064417 437,0.437 E -20],
--R    [8.6,0.0001841057 9366757912,0.0001841057 9366757912 495,0.495 E -20],
--R    [8.7,0.0001665858 1098763341,0.0001665858 1098763341 149,0.149 E -20],
--R    [8.8,0.0001507330 750954766,0.0001507330 7509547660 064,0.64 E -21],
--R    [8.9,0.0001363889 2648201145,0.0001363889 2648201144 785,- 0.215 E -20],
--R    [9.0,0.0001234098 0408667955,0.0001234098 0408667954 95,- 0.5 E -21],
--R    [9.1,0.0001116658 0849011474,0.0001116658 0849011473 564,- 0.436 E -20],
--R    [9.2,0.0001010394 0183709335,0.0001010394 0183709335 073,0.732 E -21],
--R    [9.3,0.0000914242 3147817334,0.0000914242 3147817333 7862,- 0.214 E -20],
--R    [9.4,0.0000827240 6555663226,0.0000827240 6555663226 2731,0.273 E -20],
--R    [9.5,0.0000748518 2988770059,0.0000748518 2988770059 1471,0.147 E -20],
--R    [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20],
--R    [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20],
--R    [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20],
--R    [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20],
--R    [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to ipftest.output (2009/2/17, 17:46:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 8
gf2 := PF 2
 

   (1)  PrimeField 2
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 2
--R                                                                 Type: Domain
--E 1

--S 2 of 8
a : gf2 := primitiveElement()$gf2
 

   (2)  1
                                                           Type: PrimeField 2
--R 
--R
--R   (2)  1
--R                                                           Type: PrimeField 2
--E 2

--S 3 of 8
order a                          
 

   (3)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 8
primitive? a
 

   (4)  true
                                                                Type: Boolean
--R 
--R
--R   (4)  true
--R                                                                Type: Boolean
--E 4

--S 5 of 8
createPrimitivePoly(2)$FFPOLY(gf2)
 

         2
   (5)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         2
--R   (5)  ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 5

--S 6 of 8
createPrimitivePoly(4)$FFPOLY(gf2)
 

         4
   (6)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         4
--R   (6)  ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 6

--S 7 of 8
createPrimitivePoly(12)$FFPOLY(gf2)
 

         12    6    4
   (7)  ?   + ?  + ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         12    6    4
--R   (7)  ?   + ?  + ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 7

--S 8 of 8
createPrimitivePoly(5)$FFPOLY(PF 3)
 

         5    3
   (8)  ?  + ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         5    3
--R   (8)  ?  + ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 8
)spool 
 
Starts dribbling to free.output (2009/2/17, 17:46:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 8
Z2:=FreeAbelianGroup Symbol
 

   (1)  FreeAbelianGroup Symbol
                                                                 Type: Domain
--R
--R   (1)  FreeAbelianGroup Symbol
--R                                                                 Type: Domain
--E 1

--S 2 of 8
a:=a::FreeAbelianGroup Symbol
 

   (2)  a
                                                Type: FreeAbelianGroup Symbol
--R
--R   (2)  a
--R                                                Type: FreeAbelianGroup Symbol
--E 2

--S 3 of 8
b:=b::FreeAbelianGroup Symbol
 

   (3)  b
                                                Type: FreeAbelianGroup Symbol
--R
--R   (3)  b
--R                                                Type: FreeAbelianGroup Symbol
--E 3

--S 4 of 8
z:=0::FreeAbelianGroup Symbol
 

   (4)  0
                                                Type: FreeAbelianGroup Symbol
--R
--R   (4)  0
--R                                                Type: FreeAbelianGroup Symbol
--E 4

--S 5 of 8
a < -b
 

   (5)  false
                                                                Type: Boolean
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 8
-b < z
 

   (6)  true
                                                                Type: Boolean
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 8
z < a
 

   (7)  true
                                                                Type: Boolean
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 8
a < b
 

   (8)  true
                                                                Type: Boolean
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

)spool 
 
Starts dribbling to asinatan.output (2009/2/17, 17:43:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
[[0.01,0.010000166674,asin(0.01),asin(0.01)-0.010000166674],_
[0.02,0.020001333573,asin(0.02),asin(0.02)-0.020001333573],_
[0.03,0.030004501823,asin(0.03),asin(0.03)-0.030004501823],_
[0.04,0.040010674354,asin(0.04),asin(0.04)-0.040010674354],_
[0.05,0.050020856806,asin(0.05),asin(0.05)-0.050020856806],_
[0.06,0.060036058445,asin(0.06),asin(0.06)-0.060036058445],_
[0.07,0.070057293088,asin(0.07),asin(0.07)-0.070057293088],_
[0.08,0.080085580034,asin(0.08),asin(0.08)-0.080085580034],_
[0.09,0.090121945015,asin(0.09),asin(0.09)-0.090121945015],_
[0.10,0.100167421162,asin(0.10),asin(0.10)-0.100167421162],_
[0.11,0.110223049988,asin(0.11),asin(0.11)-0.110223049988],_
[0.12,0.120289882395,asin(0.12),asin(0.12)-0.120289882395],_
[0.13,0.130368979703,asin(0.13),asin(0.13)-0.130368979703],_
[0.14,0.140461414710,asin(0.14),asin(0.14)-0.140461414710],_
[0.15,0.150568272777,asin(0.15),asin(0.15)-0.150568272777],_
[0.16,0.160690652952,asin(0.16),asin(0.16)-0.160690652952],_
[0.17,0.170829669129,asin(0.17),asin(0.17)-0.170829669129],_
[0.18,0.180986451247,asin(0.18),asin(0.18)-0.180986451247],_
[0.19,0.191162146531,asin(0.19),asin(0.19)-0.191162146531],_
[0.20,0.201357920790,asin(0.20),asin(0.20)-0.201357920790],_
[0.21,0.211574959758,asin(0.21),asin(0.21)-0.211574959758],_
[0.22,0.221814470497,asin(0.22),asin(0.22)-0.221814470497],_
[0.23,0.232077682863,asin(0.23),asin(0.23)-0.232077682863],_
[0.24,0.242365851039,asin(0.24),asin(0.24)-0.242365851039],_
[0.25,0.252680255142,asin(0.25),asin(0.25)-0.252680255142],_
[0.26,0.263022202908,asin(0.26),asin(0.26)-0.263022202908],_
[0.27,0.273393031467,asin(0.27),asin(0.27)-0.273393031467],_
[0.28,0.283794109208,asin(0.28),asin(0.28)-0.283794109208],_
[0.29,0.294226837749,asin(0.29),asin(0.29)-0.294226837749],_
[0.30,0.304692654015,asin(0.30),asin(0.30)-0.304692654015],_
[0.31,0.315193032441,asin(0.31),asin(0.31)-0.315193032441],_
[0.32,0.325729487295,asin(0.32),asin(0.32)-0.325729487295],_
[0.33,0.336303575154,asin(0.33),asin(0.33)-0.336303575154],_
[0.34,0.346916897527,asin(0.34),asin(0.34)-0.346916897527],_
[0.35,0.357571103646,asin(0.35),asin(0.35)-0.357571103646],_
[0.36,0.368267893437,asin(0.36),asin(0.36)-0.368267893437],_
[0.37,0.379009020696,asin(0.37),asin(0.37)-0.379009020696],_
[0.38,0.389796296474,asin(0.38),asin(0.38)-0.389796296474],_
[0.39,0.400631592701,asin(0.39),asin(0.39)-0.400631592701],_
[0.40,0.411516846067,asin(0.40),asin(0.40)-0.411516846067],_
[0.41,0.422454062187,asin(0.41),asin(0.41)-0.422454062187],_
[0.42,0.433445320070,asin(0.42),asin(0.42)-0.433445320070],_
[0.43,0.444492776936,asin(0.43),asin(0.43)-0.444492776936],_
[0.44,0.455598673396,asin(0.44),asin(0.44)-0.455598673396],_
[0.45,0.466765339047,asin(0.45),asin(0.45)-0.466765339047],_
[0.46,0.477995198519,asin(0.46),asin(0.46)-0.477995198519],_
[0.47,0.489290778014,asin(0.47),asin(0.47)-0.489290778014],_
[0.48,0.500654712405,asin(0.48),asin(0.48)-0.500654712405],_
[0.49,0.512089752934,asin(0.49),asin(0.49)-0.512089752934],_
[0.50,0.523598775598,asin(0.50),asin(0.50)-0.523598775598],_
[0.51,0.535184790276,asin(0.51),asin(0.51)-0.535184790276],_
[0.52,0.546850950696,asin(0.52),asin(0.52)-0.546850950696],_
[0.53,0.558600565343,asin(0.53),asin(0.53)-0.558600565343],_
[0.54,0.570437109400,asin(0.54),asin(0.54)-0.570437109400],_
[0.55,0.582364237869,asin(0.55),asin(0.55)-0.582364237869],_
[0.56,0.594385800001,asin(0.56),asin(0.56)-0.594385800001],_
[0.57,0.606505855213,asin(0.57),asin(0.57)-0.606505855213],_
[0.58,0.618728690672,asin(0.58),asin(0.58)-0.618728690672],_
[0.59,0.631058840778,asin(0.59),asin(0.59)-0.631058840778],_
[0.60,0.643501108793,asin(0.60),asin(0.60)-0.643501108793],_
[0.61,0.656060590925,asin(0.61),asin(0.61)-0.656060590925],_
[0.62,0.668742703202,asin(0.62),asin(0.62)-0.668742703202],_
[0.63,0.681553211563,asin(0.63),asin(0.63)-0.681553211563],_
[0.64,0.694498265627,asin(0.64),asin(0.64)-0.694498265627],_
[0.65,0.707584436725,asin(0.65),asin(0.65)-0.707584436725],_
[0.66,0.720818760870,asin(0.66),asin(0.66)-0.720818760870],_
[0.67,0.734208787453,asin(0.67),asin(0.67)-0.734208787453],_
[0.68,0.747762634660,asin(0.68),asin(0.68)-0.747762634660],_
[0.69,0.761489052748,asin(0.69),asin(0.69)-0.761489052748],_
[0.70,0.775397496611,asin(0.70),asin(0.70)-0.775397496611],_
[0.71,0.789498209346,asin(0.71),asin(0.71)-0.789498209346],_
[0.72,0.803802318933,asin(0.72),asin(0.72)-0.803802318933],_
[0.73,0.818321950632,asin(0.73),asin(0.73)-0.818321950632],_
[0.74,0.833070358342,asin(0.74),asin(0.74)-0.833070358342],_
[0.75,0.848062078981,asin(0.75),asin(0.75)-0.848062078981],_
[0.76,0.863313115016,asin(0.76),asin(0.76)-0.863313115016],_
[0.77,0.878841151669,asin(0.77),asin(0.77)-0.878841151669],_
[0.78,0.894665817234,asin(0.78),asin(0.78)-0.894665817234],_
[0.79,0.910808997407,asin(0.79),asin(0.79)-0.910808997407],_
[0.80,0.927295218002,asin(0.80),asin(0.80)-0.927295218002],_
[0.81,0.944152115154,asin(0.81),asin(0.81)-0.944152115154],_
[0.82,0.961411018764,asin(0.82),asin(0.82)-0.961411018764],_
[0.83,0.979107684368,asin(0.83),asin(0.83)-0.979107684368],_
[0.84,0.997283222372,asin(0.84),asin(0.84)-0.997283222372],_
[0.85,1.015985293815,asin(0.85),asin(0.85)-1.015985293815],_
[0.86,1.035269672481,asin(0.86),asin(0.86)-1.035269672481],_
[0.87,1.055202320549,asin(0.87),asin(0.87)-1.055202320549],_
[0.88,1.075862200454,asin(0.88),asin(0.88)-1.075862200454],_
[0.89,1.097345169523,asin(0.89),asin(0.89)-1.097345169523],_
[0.90,1.119769514999,asin(0.90),asin(0.90)-1.119769514999],_
[0.91,1.143284061850,asin(0.91),asin(0.91)-1.143284061850],_
[0.92,1.168080485214,asin(0.92),asin(0.92)-1.168080485214],_
[0.93,1.194412844477,asin(0.93),asin(0.93)-1.194412844477],_
[0.94,1.222630305522,asin(0.94),asin(0.94)-1.222630305522],_
[0.95,1.253235897503,asin(0.95),asin(0.95)-1.253235897503],_
[0.96,1.287002217587,asin(0.96),asin(0.96)-1.287002217587],_
[0.97,1.325230809280,asin(0.97),asin(0.97)-1.325230809280],_
[0.98,1.370461484472,asin(0.98),asin(0.98)-1.370461484472],_
[0.99,1.429256853470,asin(0.99),asin(0.99)-1.429256853470],_
[1.00,1.570796326795,asin(1.00),asin(1.00)-1.570796326795]]
 

   (1)
   [[0.01,0.0100001666 74,0.0100001666 7416711312 6,0.167113126 E -12],
    [0.02,0.0200013335 73,0.0200013335 7339049175 1,0.390491751 E -12],
    [0.03,0.0300045018 23,0.0300045018 2347693769,0.47693769 E -12],
    [0.04,0.0400106743 54,0.0400106743 5398892622 1,- 0.1107378 E -13],
    [0.05,0.0500208568 06,0.0500208568 0577001466 3,- 0.229985337 E -12],
    [0.06,0.0600360584 45,0.0600360584 452784225,0.2784225 E -12],
    [0.07,0.0700572930 88,0.0700572930 8805025329 9,0.502533 E -13],
    [0.08,0.0800855800 34,0.0800855800 3365901374 8,- 0.34098625 E -12],
    [0.09,0.0901219450 15,0.0901219450 1459525581 5,- 0.40474419 E -12],
    [0.1,0.1001674211 62,0.1001674211 6155979635,- 0.44020365 E -12],
    [0.11,0.1102230499 88,0.1102230499 8774663318,- 0.25336682 E -12],
    [0.12,0.1202898823 95,0.1202898823 9478807132,- 0.21192868 E -12],
    [0.13,0.1303689797 03,0.1303689797 0314551294,0.14551294 E -12],
    [0.14,0.1404614147 1,0.1404614147 0985580027,- 0.14419973 E -12],
    [0.15,0.1505682727 77,0.1505682727 7668602642,- 0.31397358 E -12],
    [0.16,0.1606906529 52,0.1606906529 5191060036,- 0.8939964 E -13],
    [0.17,0.1708296691 29,0.1708296691 2910450072,0.1045007 E -12],
    [0.18,0.1809864512 47,0.1809864512 4654770725,- 0.45229275 E -12],
    [0.19,0.1911621465 31,0.1911621465 3105960346,0.5960346 E -13],
    [0.2,0.2013579207 9,0.2013579207 9033079146,0.33079146 E -12],
    [0.21,0.2115749597 58,0.2115749597 5809561381,0.9561381 E -13],
    [0.22,0.2218144704 97,0.2218144704 9679441094,- 0.20558906 E -12],
    [0.23,0.2320776828 63,0.2320776828 6271317742,- 0.28682258 E -12],
    [0.24,0.2423658510 39,0.2423658510 3896323277,- 0.3676723 E -13],
    [0.25,0.2526802551 42,0.2526802551 4207865349,0.7865349 E -13],
    [0.26,0.2630222029 08,0.2630222029 0846889582,0.46889582 E -12],
    [0.27,0.2733930314 67,0.2733930314 6747322258,0.47322258 E -12],
    [0.28,0.2837941092 08,0.2837941092 0832784562,0.32784563 E -12],
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    [1.0,1.5707963267 95,1.5707963267 948966192,- 0.103381 E -12]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.01,0.0100001666 74,0.0100001666 7416711312 6,0.167113126 E -12],
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--R    [0.15,0.1505682727 77,0.1505682727 7668602642,- 0.31397358 E -12],
--R    [0.16,0.1606906529 52,0.1606906529 5191060036,- 0.8939964 E -13],
--R    [0.17,0.1708296691 29,0.1708296691 2910450072,0.1045007 E -12],
--R    [0.18,0.1809864512 47,0.1809864512 4654770725,- 0.45229275 E -12],
--R    [0.19,0.1911621465 31,0.1911621465 3105960346,0.5960346 E -13],
--R    [0.2,0.2013579207 9,0.2013579207 9033079146,0.33079146 E -12],
--R    [0.21,0.2115749597 58,0.2115749597 5809561381,0.9561381 E -13],
--R    [0.22,0.2218144704 97,0.2218144704 9679441094,- 0.20558906 E -12],
--R    [0.23,0.2320776828 63,0.2320776828 6271317742,- 0.28682258 E -12],
--R    [0.24,0.2423658510 39,0.2423658510 3896323277,- 0.3676723 E -13],
--R    [0.25,0.2526802551 42,0.2526802551 4207865349,0.7865349 E -13],
--R    [0.26,0.2630222029 08,0.2630222029 0846889582,0.46889582 E -12],
--R    [0.27,0.2733930314 67,0.2733930314 6747322258,0.47322258 E -12],
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--R    [0.3,0.3046926540 15,0.3046926540 1539750797,0.39750797 E -12],
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--R    [0.36,0.3682678934 37,0.3682678934 3663998093,- 0.36001907 E -12],
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--R    [0.45,0.4667653390 47,0.4667653390 4729636185,0.29636185 E -12],
--R    [0.46,0.4779951985 19,0.4779951985 1895237921,- 0.4762079 E -13],
--R    [0.47,0.4892907780 14,0.4892907780 1411571422,0.1157142 E -12],
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--R    [0.49,0.5120897529 34,0.5120897529 3414777137,0.1477714 E -12],
--R    [0.5,0.5235987755 98,0.5235987755 9829887308,0.2988731 E -12],
--R    [0.51,0.5351847902 76,0.5351847902 7559984754,- 0.4001525 E -12],
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--R    [0.53,0.5586005653 43,0.5586005653 4280071945,- 0.1992805 E -12],
--R    [0.54,0.5704371094,0.5704371093 9992190735,- 0.7809265 E -13],
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--R    [0.74,0.8330703583 42,0.8330703583 4164781149,- 0.3521885 E -12],
--R    [0.75,0.8480620789 81,0.8480620789 8148100805,0.48100805 E -12],
--R    [0.76,0.8633131150 16,0.8633131150 1555364761,- 0.4463524 E -12],
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--R    [0.78,0.8946658172 34,0.8946658172 3423520948,0.2352095 E -12],
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--R    [0.92,1.1680804852 14,1.1680804852 142350363,0.2350363 E -12],
--R    [0.93,1.1944128444 77,1.1944128444 771683741,0.1683741 E -12],
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--R    [0.95,1.2532358975 03,1.2532358975 033752587,0.3752587 E -12],
--R    [0.96,1.2870022175 87,1.2870022175 865687736,- 0.4312264 E -12],
--R    [0.97,1.3252308092 8,1.3252308092 796046112,- 0.3953888 E -12],
--R    [0.98,1.3704614844 72,1.3704614844 717770265,- 0.2229735 E -12],
--R    [0.99,1.4292568534 7,1.4292568534 704694005,0.4694005 E -12],
--R    [1.0,1.5707963267 95,1.5707963267 948966192,- 0.103381 E -12]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
[[0.01,0.009999666687,atan(0.01),atan(0.01)-0.009999666687],_
[0.02,0.019997333973,atan(0.02),atan(0.02)-0.019997333973],_
[0.03,0.029991004857,atan(0.03),atan(0.03)-0.029991004857],_
[0.04,0.039978687123,atan(0.04),atan(0.04)-0.039978687123],_
[0.05,0.049958395722,atan(0.05),atan(0.05)-0.049958395722],_
[0.06,0.059928155121,atan(0.06),atan(0.06)-0.059928155121],_
[0.07,0.069886001635,atan(0.07),atan(0.07)-0.069886001635],_
[0.08,0.079829985712,atan(0.08),atan(0.08)-0.079829985712],_
[0.09,0.089758174190,atan(0.09),atan(0.09)-0.089758174190],_
[0.10,0.099668652491,atan(0.10),atan(0.10)-0.099668652491],_
[0.11,0.109559526774,atan(0.11),atan(0.11)-0.109559526774],_
[0.12,0.119428926018,atan(0.12),atan(0.12)-0.119428926018],_
[0.13,0.129275004048,atan(0.13),atan(0.13)-0.129275004048],_
[0.14,0.139095941482,atan(0.14),atan(0.14)-0.139095941482],_
[0.15,0.148889947609,atan(0.15),atan(0.15)-0.148889947609],_
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[0.17,0.168390157148,atan(0.17),atan(0.17)-0.168390157148],_
[0.18,0.178092938231,atan(0.18),atan(0.18)-0.178092938231],_
[0.19,0.187761946514,atan(0.19),atan(0.19)-0.187761946514],_
[0.20,0.197395559850,atan(0.20),atan(0.20)-0.197395559850],_
[0.21,0.206992194220,atan(0.21),atan(0.21)-0.206992194220],_
[0.22,0.216550304976,atan(0.22),atan(0.22)-0.216550304976],_
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[0.28,0.273008703087,atan(0.28),atan(0.28)-0.273008703087],_
[0.29,0.282257421981,atan(0.29),atan(0.29)-0.282257421981],_
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[0.31,0.300605670042,atan(0.31),atan(0.31)-0.300605670042],_
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[0.33,0.318747560421,atan(0.33),atan(0.33)-0.318747560421],_
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[0.35,0.336674819387,atan(0.35),atan(0.35)-0.336674819387],_
[0.36,0.345555580582,atan(0.36),atan(0.36)-0.345555580582],_
[0.37,0.354379919123,atan(0.37),atan(0.37)-0.354379919123],_
[0.38,0.363147009946,atan(0.38),atan(0.38)-0.363147009946],_
[0.39,0.371856073849,atan(0.39),atan(0.39)-0.371856073849],_
[0.40,0.380506377112,atan(0.40),atan(0.40)-0.380506377112],_
[0.41,0.389097231055,atan(0.41),atan(0.41)-0.389097231055],_
[0.42,0.397627991522,atan(0.42),atan(0.42)-0.397627991522],_
[0.43,0.406098058318,atan(0.43),atan(0.43)-0.406098058318],_
[0.44,0.414506874585,atan(0.44),atan(0.44)-0.414506874585],_
[0.45,0.422853926133,atan(0.45),atan(0.45)-0.422853926133],_
[0.46,0.431138740719,atan(0.46),atan(0.46)-0.431138740719],_
[0.47,0.439360887285,atan(0.47),atan(0.47)-0.439360887285],_
[0.48,0.447519975157,atan(0.48),atan(0.48)-0.447519975157],_
[0.49,0.455615653211,atan(0.49),atan(0.49)-0.455615653211],_
[0.50,0.463647609001,atan(0.50),atan(0.50)-0.463647609001],_
[0.51,0.471615567862,atan(0.51),atan(0.51)-0.471615567862],_
[0.52,0.479519291993,atan(0.52),atan(0.52)-0.479519291993],_
[0.53,0.487358579505,atan(0.53),atan(0.53)-0.487358579505],_
[0.54,0.495133263468,atan(0.54),atan(0.54)-0.495133263468],_
[0.55,0.502843210928,atan(0.55),atan(0.55)-0.502843210928],_
[0.56,0.510488321917,atan(0.56),atan(0.56)-0.510488321917],_
[0.57,0.518068528457,atan(0.57),atan(0.57)-0.518068528457],_
[0.58,0.525583793552,atan(0.58),atan(0.58)-0.525583793552],_
[0.59,0.533034110177,atan(0.59),atan(0.59)-0.533034110177],_
[0.60,0.540419500271,atan(0.60),atan(0.60)-0.540419500271],_
[0.61,0.547740013716,atan(0.61),atan(0.61)-0.547740013716],_
[0.62,0.554995727339,atan(0.62),atan(0.62)-0.554995727339],_
[0.63,0.562186743900,atan(0.63),atan(0.63)-0.562186743900],_
[0.64,0.569313191101,atan(0.64),atan(0.64)-0.569313191101],_
[0.65,0.576375220591,atan(0.65),atan(0.65)-0.576375220591],_
[0.66,0.583373006994,atan(0.66),atan(0.66)-0.583373006994],_
[0.67,0.590306746935,atan(0.67),atan(0.67)-0.590306746935],_
[0.68,0.597176658093,atan(0.68),atan(0.68)-0.597176658093],_
[0.69,0.603982978253,atan(0.69),atan(0.69)-0.603982978253],_
[0.70,0.610725964389,atan(0.70),atan(0.70)-0.610725964389],_
[0.71,0.617405891752,atan(0.71),atan(0.71)-0.617405891752],_
[0.72,0.624023052977,atan(0.72),atan(0.72)-0.624023052977],_
[0.73,0.630577757215,atan(0.73),atan(0.73)-0.630577757215],_
[0.74,0.637070329276,atan(0.74),atan(0.74)-0.637070329276],_
[0.75,0.643501108793,atan(0.75),atan(0.75)-0.643501108793],_
[0.76,0.649870449412,atan(0.76),atan(0.76)-0.649870449412],_
[0.77,0.656178717991,atan(0.77),atan(0.77)-0.656178717991],_
[0.78,0.662426293833,atan(0.78),atan(0.78)-0.662426293833],_
[0.79,0.668613567928,atan(0.79),atan(0.79)-0.668613567928],_
[0.80,0.674740942224,atan(0.80),atan(0.80)-0.674740942224],_
[0.81,0.680808828916,atan(0.81),atan(0.81)-0.680808828916],_
[0.82,0.686817649759,atan(0.82),atan(0.82)-0.686817649759],_
[0.83,0.692767835397,atan(0.83),atan(0.83)-0.692767835397],_
[0.84,0.698659824721,atan(0.84),atan(0.84)-0.698659824721],_
[0.85,0.704494064242,atan(0.85),atan(0.85)-0.704494064242],_
[0.86,0.710271007487,atan(0.86),atan(0.86)-0.710271007487],_
[0.87,0.715991114416,atan(0.87),atan(0.87)-0.715991114416],_
[0.88,0.721654850865,atan(0.88),atan(0.88)-0.721654850865],_
[0.89,0.727262687997,atan(0.89),atan(0.89)-0.727262687997],_
[0.90,0.732815101787,atan(0.90),atan(0.90)-0.732815101787],_
[0.91,0.738312572517,atan(0.91),atan(0.91)-0.738312572517],_
[0.92,0.743755584299,atan(0.92),atan(0.92)-0.743755584299],_
[0.93,0.749144624606,atan(0.93),atan(0.93)-0.749144624606],_
[0.94,0.754480183834,atan(0.94),atan(0.94)-0.754480183834],_
[0.95,0.759762754876,atan(0.95),atan(0.95)-0.759762754876],_
[0.96,0.764992832711,atan(0.96),atan(0.96)-0.764992832711],_
[0.97,0.770170914020,atan(0.97),atan(0.97)-0.770170914020],_
[0.98,0.775297496812,atan(0.98),atan(0.98)-0.775297496812],_
[0.99,0.780373080067,atan(0.99),atan(0.99)-0.780373080067],_
[1.00,0.785398163397,atan(1.00),atan(1.00)-0.785398163397]]
 

   (2)
   [[0.01,0.0099996666 87,0.0099996666 8666523820 63,- 0.334761794 E -12],
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    [0.18,0.1780929382 31,0.1780929382 3119754967,0.19754967 E -12],
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    [0.23,0.2260683879 94,0.2260683879 9388390584,- 0.11609416 E -12],
    [0.24,0.2355449807 21,0.2355449807 2086334143,- 0.13665857 E -12],
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    [0.35,0.3366748193 87,0.3366748193 867271814,- 0.2728186 E -12],
    [0.36,0.3455555805 82,0.3455555805 8171213686,- 0.28786314 E -12],
    [0.37,0.3543799191 23,0.3543799191 2343780983,0.43780983 E -12],
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    [0.43,0.4060980583 18,0.4060980583 1761564783,- 0.38435217 E -12],
    [0.44,0.4145068745 85,0.4145068745 8478593834,- 0.2140617 E -12],
    [0.45,0.4228539261 33,0.4228539261 3294071297,- 0.5928703 E -13],
    [0.46,0.4311387407 19,0.4311387407 1878218339,- 0.2178166 E -12],
    [0.47,0.4393608872 85,0.4393608872 8459143742,- 0.40856258 E -12],
    [0.48,0.4475199751 57,0.4475199751 5716987972,0.1698797 E -12],
    [0.49,0.4556156532 11,0.4556156532 1122449214,0.2244921 E -12],
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    [0.52,0.4795192919 93,0.4795192919 9259616542,- 0.40383458 E -12],
    [0.53,0.4873585795 05,0.4873585795 0519028312,0.1902831 E -12],
    [0.54,0.4951332634 68,0.4951332634 6840412185,0.40412185 E -12],
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    [0.75,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12],
    [0.76,0.6498704494 12,0.6498704494 1194757749,- 0.524225 E -13],
    [0.77,0.6561787179 91,0.6561787179 9139487538,0.3948754 E -12],
    [0.78,0.6624262938 33,0.6624262938 3315116177,0.1511618 E -12],
    [0.79,0.6686135679 28,0.6686135679 2782091069,- 0.1790893 E -12],
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    [0.82,0.6868176497 59,0.6868176497 5864527553,- 0.3547245 E -12],
    [0.83,0.6927678353 97,0.6927678353 9712221066,0.1222107 E -12],
    [0.84,0.6986598247 21,0.6986598247 214631978,0.4631978 E -12],
    [0.85,0.7044940642 42,0.7044940642 4221771666,0.2177167 E -12],
    [0.86,0.7102710074 87,0.7102710074 8668623033,- 0.3137697 E -12],
    [0.87,0.7159911144 16,0.7159911144 1630019894,0.3001989 E -12],
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    [0.97,0.7701709140 2,0.7701709140 2033100726,0.3310073 E -12],
    [0.98,0.7752974968 12,0.7752974968 1212640304,0.126403 E -12],
    [0.99,0.7803730800 67,0.7803730800 666358989,- 0.3641011 E -12],
    [1.0,0.7853981633 97,0.7853981633 9744830961,0.4483096 E -12]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,0.0099996666 87,0.0099996666 8666523820 63,- 0.334761794 E -12],
--R    [0.02,0.0199973339 73,0.0199973339 7315053306 1,0.150533061 E -12],
--R    [0.03,0.0299910048 57,0.0299910048 5687789967 7,- 0.122100323 E -12],
--R    [0.04,0.0399786871 23,0.0399786871 2329004141 4,0.290041414 E -12],
--R    [0.05,0.0499583957 22,0.0499583957 2194276141,- 0.5723859 E -13],
--R    [0.06,0.0599281551 21,0.0599281551 2120788443 2,0.20788443 E -12],
--R    [0.07,0.0698860016 35,0.0698860016 3464249929 5,- 0.35750071 E -12],
--R    [0.08,0.0798299857 12,0.0798299857 1223731589 3,0.23731589 E -12],
--R    [0.09,0.0897581741 9,0.0897581741 8995052315,- 0.4947685 E -13],
--R    [0.1,0.0996686524 91,0.0996686524 9116202737 9,0.16202738 E -12],
--R    [0.11,0.1095595267 74,0.1095595267 7394434487,- 0.5565513 E -13],
--R    [0.12,0.1194289260 18,0.1194289260 1833845181,0.33845181 E -12],
--R    [0.13,0.1292750040 48,0.1292750040 4814305472,0.14305472 E -12],
--R    [0.14,0.1390959414 82,0.1390959414 820713243,0.713243 E -13],
--R    [0.15,0.1488899476 09,0.1488899476 0949725059,0.49725059 E -12],
--R    [0.16,0.1586552621 86,0.1586552621 8640140386,0.40140386 E -12],
--R    [0.17,0.1683901571 48,0.1683901571 4752989727,- 0.47010272 E -12],
--R    [0.18,0.1780929382 31,0.1780929382 3119754967,0.19754967 E -12],
--R    [0.19,0.1877619465 14,0.1877619465 135934152,- 0.4065848 E -12],
--R    [0.2,0.1973955598 5,0.1973955598 4988075837,- 0.11924163 E -12],
--R    [0.21,0.2069921942 2,0.2069921942 198210249,- 0.1789751 E -12],
--R    [0.22,0.2165503049 76,0.2165503049 7608927648,0.8927648 E -13],
--R    [0.23,0.2260683879 94,0.2260683879 9388390584,- 0.11609416 E -12],
--R    [0.24,0.2355449807 21,0.2355449807 2086334143,- 0.13665857 E -12],
--R    [0.25,0.2449786631 27,0.2449786631 2686415417,- 0.13584583 E -12],
--R    [0.26,0.2543680585 53,0.2543680585 5326593143,0.26593143 E -12],
--R    [0.27,0.2637118344 62,0.2637118344 6226612016,0.26612016 E -12],
--R    [0.28,0.2730087030 87,0.2730087030 8671060295,- 0.28939705 E -12],
--R    [0.29,0.2822574219 81,0.2822574219 8149112127,0.49112127 E -12],
--R    [0.3,0.2914567944 78,0.2914567944 77867092,- 0.132908 E -12],
--R    [0.31,0.3006056700 42,0.3006056700 4239540423,0.39540423 E -12],
--R    [0.32,0.3097029445 42,0.3097029445 4245619992,0.45619992 E -12],
--R    [0.33,0.3187475604 21,0.3187475604 2064443712,- 0.35556288 E -12],
--R    [0.34,0.3277385067 81,0.3277385067 80555446,- 0.444554 E -12],
--R    [0.35,0.3366748193 87,0.3366748193 867271814,- 0.2728186 E -12],
--R    [0.36,0.3455555805 82,0.3455555805 8171213686,- 0.28786314 E -12],
--R    [0.37,0.3543799191 23,0.3543799191 2343780983,0.43780983 E -12],
--R    [0.38,0.3631470099 46,0.3631470099 4617628972,0.1762897 E -12],
--R    [0.39,0.3718560738 49,0.3718560738 485812575,- 0.4187425 E -12],
--R    [0.4,0.3805063771 12,0.3805063771 123648863,0.3648863 E -12],
--R    [0.41,0.3890972310 55,0.3890972310 5527841924,0.27841924 E -12],
--R    [0.42,0.3976279915 22,0.3976279915 22129314,0.129314 E -12],
--R    [0.43,0.4060980583 18,0.4060980583 1761564783,- 0.38435217 E -12],
--R    [0.44,0.4145068745 85,0.4145068745 8478593834,- 0.2140617 E -12],
--R    [0.45,0.4228539261 33,0.4228539261 3294071297,- 0.5928703 E -13],
--R    [0.46,0.4311387407 19,0.4311387407 1878218339,- 0.2178166 E -12],
--R    [0.47,0.4393608872 85,0.4393608872 8459143742,- 0.40856258 E -12],
--R    [0.48,0.4475199751 57,0.4475199751 5716987972,0.1698797 E -12],
--R    [0.49,0.4556156532 11,0.4556156532 1122449214,0.2244921 E -12],
--R    [0.5,0.4636476090 01,0.4636476090 0080611621,- 0.1938838 E -12],
--R    [0.51,0.4716155678 62,0.4716155678 6232766012,0.32766012 E -12],
--R    [0.52,0.4795192919 93,0.4795192919 9259616542,- 0.40383458 E -12],
--R    [0.53,0.4873585795 05,0.4873585795 0519028312,0.1902831 E -12],
--R    [0.54,0.4951332634 68,0.4951332634 6840412185,0.40412185 E -12],
--R    [0.55,0.5028432109 28,0.5028432109 2786082733,- 0.1391727 E -12],
--R    [0.56,0.5104883219 17,0.5104883219 1677576997,- 0.22423 E -12],
--R    [0.57,0.5180685284 57,0.5180685284 56720949,- 0.279051 E -12],
--R    [0.58,0.5255837935 52,0.5255837935 5161020277,- 0.3897972 E -12],
--R    [0.59,0.5330341101 77,0.5330341101 7749002604,0.49002604 E -12],
--R    [0.6,0.5404195002 71,0.5404195002 7058415544,- 0.4158446 E -12],
--R    [0.61,0.5477400137 16,0.5477400137 1590245052,- 0.9754948 E -13],
--R    [0.62,0.5549957273 39,0.5549957273 3858676242,- 0.4132376 E -12],
--R    [0.63,0.5621867439,0.5621867439 0002917485,0.291748 E -13],
--R    [0.64,0.5693131911 01,0.5693131911 0066188631,- 0.3381137 E -12],
--R    [0.65,0.5763752205 91,0.5763752205 9118368022,0.1836802 E -12],
--R    [0.66,0.5833730069 94,0.5833730069 9385593947,- 0.1440605 E -12],
--R    [0.67,0.5903067469 35,0.5903067469 3537198239,0.3719824 E -12],
--R    [0.68,0.5971766580 93,0.5971766580 9267754844,- 0.3224516 E -12],
--R    [0.69,0.6039829782 53,0.6039829782 5299790738,- 0.20926 E -14],
--R    [0.7,0.6107259643 89,0.6107259643 8920861654,0.2086165 E -12],
--R    [0.71,0.6174058917 52,0.6174058917 5157266652,- 0.4273335 E -12],
--R    [0.72,0.6240230529 77,0.6240230529 7675684759,- 0.2431524 E -12],
--R    [0.73,0.6305777572 15,0.6305777572 1493480666,- 0.6519333 E -13],
--R    [0.74,0.6370703292 76,0.6370703292 7568357172,- 0.3164283 E -12],
--R    [0.75,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12],
--R    [0.76,0.6498704494 12,0.6498704494 1194757749,- 0.524225 E -13],
--R    [0.77,0.6561787179 91,0.6561787179 9139487538,0.3948754 E -12],
--R    [0.78,0.6624262938 33,0.6624262938 3315116177,0.1511618 E -12],
--R    [0.79,0.6686135679 28,0.6686135679 2782091069,- 0.1790893 E -12],
--R    [0.8,0.6747409422 24,0.6747409422 2355266306,- 0.4473369 E -12],
--R    [0.81,0.6808088289 16,0.6808088289 1582756649,- 0.1724335 E -12],
--R    [0.82,0.6868176497 59,0.6868176497 5864527553,- 0.3547245 E -12],
--R    [0.83,0.6927678353 97,0.6927678353 9712221066,0.1222107 E -12],
--R    [0.84,0.6986598247 21,0.6986598247 214631978,0.4631978 E -12],
--R    [0.85,0.7044940642 42,0.7044940642 4221771666,0.2177167 E -12],
--R    [0.86,0.7102710074 87,0.7102710074 8668623033,- 0.3137697 E -12],
--R    [0.87,0.7159911144 16,0.7159911144 1630019894,0.3001989 E -12],
--R    [0.88,0.7216548508 65,0.7216548508 6476123707,- 0.2387629 E -12],
--R    [0.89,0.7272626879 97,0.7272626879 9669029805,- 0.309702 E -12],
--R    [0.9,0.7328151017 87,0.7328151017 8650659164,- 0.49340836 E -12],
--R    [0.91,0.7383125725 17,0.7383125725 1722800021,0.2280002 E -12],
--R    [0.92,0.7437555842 99,0.7437555842 9885988576,- 0.1401142 E -12],
--R    [0.93,0.7491446246 06,0.7491446246 0601721032,0.172103 E -13],
--R    [0.94,0.7544801838 34,0.7544801838 3440566231,0.4056623 E -12],
--R    [0.95,0.7597627548 76,0.7597627548 7577082892,- 0.2291711 E -12],
--R    [0.96,0.7649928327 11,0.7649928327 1091022317,- 0.8977683 E -13],
--R    [0.97,0.7701709140 2,0.7701709140 2033100726,0.3310073 E -12],
--R    [0.98,0.7752974968 12,0.7752974968 1212640304,0.126403 E -12],
--R    [0.99,0.7803730800 67,0.7803730800 666358989,- 0.3641011 E -12],
--R    [1.0,0.7853981633 97,0.7853981633 9744830961,0.4483096 E -12]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to kamke4.output (2009/2/17, 17:48:1).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 127
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 127
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 127
f0:=operator 'f0
 

   (3)  f0
                                                          Type: BasicOperator
--R 
--R
--R   (3)  f0
--R                                                          Type: BasicOperator
--E 3

--S 4 of 127
f1:=operator 'f1
 

   (4)  f1
                                                          Type: BasicOperator
--R 
--R
--R   (4)  f1
--R                                                          Type: BasicOperator
--E 4

--S 5 of 127
f2:=operator 'f2
 

   (5)  f2
                                                          Type: BasicOperator
--R 
--R
--R   (5)  f2
--R                                                          Type: BasicOperator
--E 5

--S 6 of 127
g:=operator 'g
 

   (6)  g
                                                          Type: BasicOperator
--R 
--R
--R   (6)  g
--R                                                          Type: BasicOperator
--E 6

--S 7 of 127
tg:=operator 'tg
 

   (7)  tg
                                                          Type: BasicOperator
--R 
--R
--R   (7)  tg
--R                                                          Type: BasicOperator
--E 7

--S 8 of 127
h:=operator 'h
 

   (8)  h
                                                          Type: BasicOperator
--R 
--R
--R   (8)  h
--R                                                          Type: BasicOperator
--E 8

--S 9 of 127
ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)**2-D(f(x),x)*y(x)-2*f(x)**2
 

              ,           ,               2        2
   (9)  2f(x)y (x) - y(x)f (x) + 2f(x)y(x)  - 2f(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,           ,               2        2
--R   (9)  2f(x)y (x) - y(x)f (x) + 2f(x)y(x)  - 2f(x)
--R
--R                                                     Type: Expression Integer
--E 9

--S 10 of 127
solve(ode201,y,x)
 

   (10)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (10)  "failed"
--R                                                    Type: Union("failed",...)
--E 10

--S 11 of 127
ode202 := f(x)*D(y(x),x)+g(x)*tg(y(x))+h(x)
 

              ,
   (11)  f(x)y (x) + g(x)tg(y(x)) + h(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,
--R   (11)  f(x)y (x) + g(x)tg(y(x)) + h(x)
--R
--R                                                     Type: Expression Integer
--E 11

--S 12 of 127
solve(ode202,y,x)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 127
ode203 := y(x)*D(y(x),x)+y(x)+x**3
 

              ,              3
   (13)  y(x)y (x) + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              ,              3
--R   (13)  y(x)y (x) + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 13

--S 14 of 127
solve(ode203,y,x)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 14

--S 15 of 127
ode204 := y(x)*D(y(x),x)+a*y(x)+x
 

              ,
   (15)  y(x)y (x) + a y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              ,
--R   (15)  y(x)y (x) + a y(x) + x
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 127
solve(ode204,y,x)
 

   (16)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (16)  "failed"
--R                                                    Type: Union("failed",...)
--E 16

--S 17 of 127
ode205 := y(x)*D(y(x),x)+a*y(x)+(a**2-1)/(4)*x+b*x**n
 

               ,          n               2
         4y(x)y (x) + 4b x  + 4a y(x) + (a  - 1)x

   (17)  ----------------------------------------
                             4
                                                     Type: Expression Integer
--R 
--R
--R               ,          n               2
--R         4y(x)y (x) + 4b x  + 4a y(x) + (a  - 1)x
--R
--R   (17)  ----------------------------------------
--R                             4
--R                                                     Type: Expression Integer
--E 17

--S 18 of 127
solve(ode205,y,x)
 

   (18)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (18)  "failed"
--R                                                    Type: Union("failed",...)
--E 18

--S 19 of 127
ode206 := y(x)*D(y(x),x)+a*y(x)+b*exp(x)-2*a
 

              ,          x
   (19)  y(x)y (x) + b %e  + a y(x) - 2a

                                                     Type: Expression Integer
--R 
--R
--R              ,          x
--R   (19)  y(x)y (x) + b %e  + a y(x) - 2a
--R
--R                                                     Type: Expression Integer
--E 19

--S 20 of 127
solve(ode206,y,x)
 

   (20)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (20)  "failed"
--R                                                    Type: Union("failed",...)
--E 20

--S 21 of 127
ode207 := y(x)*D(y(x),x)+y(x)**2+4*x*(x+1)
 

              ,          2     2
   (21)  y(x)y (x) + y(x)  + 4x  + 4x

                                                     Type: Expression Integer
--R 
--R
--R              ,          2     2
--R   (21)  y(x)y (x) + y(x)  + 4x  + 4x
--R
--R                                                     Type: Expression Integer
--E 21

--S 22 of 127
yx:=solve(ode207,y,x)
 

              2     2   2x
         (y(x)  + 4x )%e
   (22)  -----------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2     2   2x
--R         (y(x)  + 4x )%e
--R   (22)  -----------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 22

--S 23 of 127
ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1)
 

   (23)
             3     2        2x 2 ,
       (2y(x)  + 8x y(x))(%e  ) y (x)

     + 
             4       2          2      4      3    2x 2      2
       (3y(x)  + (24x  + 8x)y(x)  + 48x  + 32x )(%e  )  + 16x  + 16x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (23)
--R             3     2        2x 2 ,
--R       (2y(x)  + 8x y(x))(%e  ) y (x)
--R
--R     + 
--R             4       2          2      4      3    2x 2      2
--R       (3y(x)  + (24x  + 8x)y(x)  + 48x  + 32x )(%e  )  + 16x  + 16x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 23

--S 24 of 127
ode208 := y(x)*D(y(x),x)+a*y(x)**2-b*cos(x+c)
 

              ,                           2
   (24)  y(x)y (x) - b cos(x + c) + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,                           2
--R   (24)  y(x)y (x) - b cos(x + c) + a y(x)
--R
--R                                                     Type: Expression Integer
--E 24

--S 25 of 127
yx:=solve(ode208,y,x)
 

                2a x                                     2         2   2a x
         - 2b %e    sin(x + c) + (- 4a b cos(x + c) + (4a  + 1)y(x) )%e
   (25)  ------------------------------------------------------------------
                                         2
                                       8a  + 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2a x                                     2         2   2a x
--R         - 2b %e    sin(x + c) + (- 4a b cos(x + c) + (4a  + 1)y(x) )%e
--R   (25)  ------------------------------------------------------------------
--R                                         2
--R                                       8a  + 2
--R                                          Type: Union(Expression Integer,...)
--E 25

--S 26 of 127
ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c)
 

   (26)
                 2              2a x 2
           (- 16a  - 4)b y(x)(%e    ) sin(x + c)
         + 
                  3                             4      2         3    2a x 2
           ((- 32a  - 8a)b y(x)cos(x + c) + (32a  + 16a  + 2)y(x) )(%e    )
      *
          ,
         y (x)

     + 
           2   2a x 2          2
       4a b (%e    ) sin(x + c)
     + 
            2      2                   3            2    2a x 2
       ((32a  + 4)b cos(x + c) + (- 32a  - 8a)b y(x) )(%e    ) sin(x + c)
     + 
               3       2          2         4      2           2
           (48a  + 8a)b cos(x + c)  + (- 96a  - 32a  - 2)b y(x) cos(x + c)
         + 
               5      3          4
           (48a  + 24a  + 3a)y(x)
      *
            2a x 2
         (%e    )
     + 
             4      2
       (- 64a  - 32a  - 4)b cos(x + c)
  /
        4      2
     64a  + 32a  + 4
                                                     Type: Expression Integer
--R 
--R
--R   (26)
--R                 2              2a x 2
--R           (- 16a  - 4)b y(x)(%e    ) sin(x + c)
--R         + 
--R                  3                             4      2         3    2a x 2
--R           ((- 32a  - 8a)b y(x)cos(x + c) + (32a  + 16a  + 2)y(x) )(%e    )
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R           2   2a x 2          2
--R       4a b (%e    ) sin(x + c)
--R     + 
--R            2      2                   3            2    2a x 2
--R       ((32a  + 4)b cos(x + c) + (- 32a  - 8a)b y(x) )(%e    ) sin(x + c)
--R     + 
--R               3       2          2         4      2           2
--R           (48a  + 8a)b cos(x + c)  + (- 96a  - 32a  - 2)b y(x) cos(x + c)
--R         + 
--R               5      3          4
--R           (48a  + 24a  + 3a)y(x)
--R      *
--R            2a x 2
--R         (%e    )
--R     + 
--R             4      2
--R       (- 64a  - 32a  - 4)b cos(x + c)
--R  /
--R        4      2
--R     64a  + 32a  + 4
--R                                                     Type: Expression Integer
--E 26

--S 27 of 127
ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)**2+b)
 

                      +-----------+
              ,       |      2
   (27)  y(x)y (x) - \|a y(x)  + b

                                                     Type: Expression Integer
--R 
--R
--R                      +-----------+
--R              ,       |      2
--R   (27)  y(x)y (x) - \|a y(x)  + b
--R
--R                                                     Type: Expression Integer
--E 27

--S 28 of 127
yx:=solve(ode209,y,x)
 

                 +-----------+
             +-+ |      2            2 +-+
         - x\|b \|a y(x)  + b  + y(x) \|b  + b x
   (28)  ---------------------------------------
                       +-----------+
                   +-+ |      2
                  \|b \|a y(x)  + b  - b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-----------+
--R             +-+ |      2            2 +-+
--R         - x\|b \|a y(x)  + b  + y(x) \|b  + b x
--R   (28)  ---------------------------------------
--R                       +-----------+
--R                   +-+ |      2
--R                  \|b \|a y(x)  + b  - b
--R                                          Type: Union(Expression Integer,...)
--E 28

--S 29 of 127
ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b)
 

   (29)
                               +-----------+
                      2     2  |      2          2    4            2     2  +-+
         ((- 3a b y(x)  - 4b )\|a y(x)  + b  + (a y(x)  + 5a b y(x)  + 4b )\|b )
      *
         ROOT
                                                +-----------+
                      2       +-+            2  |      2                 2 +-+
                ((2a x  + 2b)\|b  + 2a x y(x) )\|a y(x)  + b  - 2a x y(x) \|b
              + 
                        4       2 2           2         2     2
                - a y(x)  + (- a x  - a b)y(x)  - 2a b x  - 2b
           /
                    +-----------+
                +-+ |      2              2
              2\|b \|a y(x)  + b  - a y(x)  - 2b
     + 
                                                    +-----------+
                     3              +-+          3  |      2
           ((a x y(x)  + 4b x y(x))\|b  + 2b y(x) )\|a y(x)  + b
         + 
                    5          3  +-+              3     2
           (- a y(x)  - 2b y(x) )\|b  - 3a b x y(x)  - 4b x y(x)
      *
          ,
         y (x)

     + 
                                                        +-----------+
               4          2  +-+              2     2   |      2
       ((a y(x)  + 2b y(x) )\|b  + 3a b x y(x)  + 4b x)\|a y(x)  + b
     + 
           2      4              2     2   +-+            4     2    2
       (- a x y(x)  - 5a b x y(x)  - 4b x)\|b  - 2a b y(x)  - 2b y(x)
  /
                        +-----------+
               2     2  |      2            2    4            2     2  +-+
     (3a b y(x)  + 4b )\|a y(x)  + b  + (- a y(x)  - 5a b y(x)  - 4b )\|b
                                                     Type: Expression Integer
--R 
--R
--R   (29)
--R                               +-----------+
--R                      2     2  |      2          2    4            2     2  +-+
--R         ((- 3a b y(x)  - 4b )\|a y(x)  + b  + (a y(x)  + 5a b y(x)  + 4b )\|b )
--R      *
--R         ROOT
--R                                                +-----------+
--R                      2       +-+            2  |      2                 2 +-+
--R                ((2a x  + 2b)\|b  + 2a x y(x) )\|a y(x)  + b  - 2a x y(x) \|b
--R              + 
--R                        4       2 2           2         2     2
--R                - a y(x)  + (- a x  - a b)y(x)  - 2a b x  - 2b
--R           /
--R                    +-----------+
--R                +-+ |      2              2
--R              2\|b \|a y(x)  + b  - a y(x)  - 2b
--R     + 
--R                                                    +-----------+
--R                     3              +-+          3  |      2
--R           ((a x y(x)  + 4b x y(x))\|b  + 2b y(x) )\|a y(x)  + b
--R         + 
--R                    5          3  +-+              3     2
--R           (- a y(x)  - 2b y(x) )\|b  - 3a b x y(x)  - 4b x y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                                                        +-----------+
--R               4          2  +-+              2     2   |      2
--R       ((a y(x)  + 2b y(x) )\|b  + 3a b x y(x)  + 4b x)\|a y(x)  + b
--R     + 
--R           2      4              2     2   +-+            4     2    2
--R       (- a x y(x)  - 5a b x y(x)  - 4b x)\|b  - 2a b y(x)  - 2b y(x)
--R  /
--R                        +-----------+
--R               2     2  |      2            2    4            2     2  +-+
--R     (3a b y(x)  + 4b )\|a y(x)  + b  + (- a y(x)  - 5a b y(x)  - 4b )\|b
--R                                                     Type: Expression Integer
--E 29

--S 30 of 127
ode210 := y(x)*D(y(x),x)+x*y(x)**2-4*x
 

              ,            2
   (30)  y(x)y (x) + x y(x)  - 4x

                                                     Type: Expression Integer
--R 
--R
--R              ,            2
--R   (30)  y(x)y (x) + x y(x)  - 4x
--R
--R                                                     Type: Expression Integer
--E 30

--S 31 of 127
yx:=solve(ode210,y,x)
 

                       2
              2       x
         (y(x)  - 4)%e
   (31)  ---------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       2
--R              2       x
--R         (y(x)  - 4)%e
--R   (31)  ---------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 31

--S 32 of 127
ode210expr := yx*D(yx,x)+x*yx**2-4*x
 

   (32)
                       2 2                                        2 2
         3            x    ,              4           2          x
   (2y(x)  - 8y(x))(%e  ) y (x) + (3x y(x)  - 24x y(x)  + 48x)(%e  )  - 16x

   ------------------------------------------------------------------------
                                       4
                                                     Type: Expression Integer
--R 
--R
--R   (32)
--R                       2 2                                        2 2
--R         3            x    ,              4           2          x
--R   (2y(x)  - 8y(x))(%e  ) y (x) + (3x y(x)  - 24x y(x)  + 48x)(%e  )  - 16x
--R
--R   ------------------------------------------------------------------------
--R                                       4
--R                                                     Type: Expression Integer
--E 32

--S 33 of 127
ode211 := y(x)*D(y(x),x)-x*exp(x/y(x))
 

                           x
                         ----
              ,          y(x)
   (33)  y(x)y (x) - x %e

                                                     Type: Expression Integer
--R 
--R
--R                           x
--R                         ----
--R              ,          y(x)
--R   (33)  y(x)y (x) - x %e
--R
--R                                                     Type: Expression Integer
--E 33

--S 34 of 127
solve(ode211,y,x)
 

   (34)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (34)  "failed"
--R                                                    Type: Union("failed",...)
--E 34

--S 35 of 127
ode212 := y(x)*D(y(x),x)+f(x**2+y(x)**2)*g(x)+x
 

              ,                2    2
   (35)  y(x)y (x) + g(x)f(y(x)  + x ) + x

                                                     Type: Expression Integer
--R 
--R
--R              ,                2    2
--R   (35)  y(x)y (x) + g(x)f(y(x)  + x ) + x
--R
--R                                                     Type: Expression Integer
--E 35

--S 36 of 127
solve(ode212,y,x)
 

   (36)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

--S 37 of 127
ode213 := (y(x)+1)*D(y(x),x)-y(x)-x
 

                    ,
   (37)  (y(x) + 1)y (x) - y(x) - x

                                                     Type: Expression Integer
--R 
--R
--R                    ,
--R   (37)  (y(x) + 1)y (x) - y(x) - x
--R
--R                                                     Type: Expression Integer
--E 37

--S 38 of 127
solve(ode213,y,x)
 

   (38)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (38)  "failed"
--R                                                    Type: Union("failed",...)
--E 38

--S 39 of 127
ode214 := (y(x)+x-1)*D(y(x),x)-y(x)+2*x+3
 

                        ,
   (39)  (y(x) + x - 1)y (x) - y(x) + 2x + 3

                                                     Type: Expression Integer
--R 
--R
--R                        ,
--R   (39)  (y(x) + x - 1)y (x) - y(x) + 2x + 3
--R
--R                                                     Type: Expression Integer
--E 39

--S 40 of 127
solve(ode214,y,x)
 

   (40)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (40)  "failed"
--R                                                    Type: Union("failed",...)
--E 40

--S 41 of 127
ode215 := (y(x)+2*x-2)*D(y(x),x)-y(x)+x+1
 

                         ,
   (41)  (y(x) + 2x - 2)y (x) - y(x) + x + 1

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (41)  (y(x) + 2x - 2)y (x) - y(x) + x + 1
--R
--R                                                     Type: Expression Integer
--E 41

--S 42 of 127
solve(ode215,y,x)
 

   (42)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (42)  "failed"
--R                                                    Type: Union("failed",...)
--E 42

--S 43 of 127
ode216 := (y(x)-2*x+1)*D(y(x),x)+y(x)+x
 

                         ,
   (43)  (y(x) - 2x + 1)y (x) + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (43)  (y(x) - 2x + 1)y (x) + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 43

--S 44 of 127
solve(ode216,y,x)
 

   (44)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (44)  "failed"
--R                                                    Type: Union("failed",...)
--E 44

--S 45 of 127
ode217 := (y(x)-x**2)*D(y(x),x)-x
 

                  2  ,
   (45)  (y(x) - x )y (x) - x

                                                     Type: Expression Integer
--R 
--R
--R                  2  ,
--R   (45)  (y(x) - x )y (x) - x
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 127
yx:=solve(ode217,y,x)
 

                    2       2y(x)
         (2y(x) - 2x  - 1)%e
   (46)  ------------------------
                     4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2       2y(x)
--R         (2y(x) - 2x  - 1)%e
--R   (46)  ------------------------
--R                     4
--R                                          Type: Union(Expression Integer,...)
--E 46

--S 47 of 127
ode217expr := (yx-x**2)*D(yx,x)-x
 

   (47)
                 2        2              4    2    2y(x) 2
           (2y(x)  + (- 4x  - 1)y(x) + 2x  + x )(%e     )
         + 
                2         4   2y(x)
           (- 4x y(x) + 4x )%e
      *
          ,
         y (x)

     + 
                      3        2y(x) 2     3  2y(x)
       (- 2x y(x) + 2x  + x)(%e     )  + 4x %e      - 4x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (47)
--R                 2        2              4    2    2y(x) 2
--R           (2y(x)  + (- 4x  - 1)y(x) + 2x  + x )(%e     )
--R         + 
--R                2         4   2y(x)
--R           (- 4x y(x) + 4x )%e
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                      3        2y(x) 2     3  2y(x)
--R       (- 2x y(x) + 2x  + x)(%e     )  + 4x %e      - 4x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 47

--S 48 of 127
ode218 := (y(x)-x**2)*D(y(x),x)+4*x*y(x)
 

                  2  ,
   (48)  (y(x) - x )y (x) + 4x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                  2  ,
--R   (48)  (y(x) - x )y (x) + 4x y(x)
--R
--R                                                     Type: Expression Integer
--E 48

--S 49 of 127
yx:=solve(ode218,y,x)
 

                   2
         2y(x) + 2x
   (49)  -----------
            +----+
           \|y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2
--R         2y(x) + 2x
--R   (49)  -----------
--R            +----+
--R           \|y(x)
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 127
ode218expr := (yx-x**2)*D(yx,x)+4*x*yx
 

   (50)
              2     4  +----+    2    2    4      ,
       ((2y(x)  - 2x )\|y(x)  - x y(x)  + x y(x))y (x)

     + 
               2     3      +----+          3     3    2
       (8x y(x)  + 8x y(x))\|y(x)  + 8x y(x)  + 4x y(x)
  /
         2 +----+
     y(x) \|y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (50)
--R              2     4  +----+    2    2    4      ,
--R       ((2y(x)  - 2x )\|y(x)  - x y(x)  + x y(x))y (x)
--R
--R     + 
--R               2     3      +----+          3     3    2
--R       (8x y(x)  + 8x y(x))\|y(x)  + 8x y(x)  + 4x y(x)
--R  /
--R         2 +----+
--R     y(x) \|y(x)
--R                                                     Type: Expression Integer
--E 50

--S 51 of 127
ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)**2-f1(x)*y(x)-f0(x)
 

                       ,               2
   (51)  (y(x) + g(x))y (x) - f2(x)y(x)  - f1(x)y(x) - f0(x)

                                                     Type: Expression Integer
--R 
--R
--R                       ,               2
--R   (51)  (y(x) + g(x))y (x) - f2(x)y(x)  - f1(x)y(x) - f0(x)
--R
--R                                                     Type: Expression Integer
--E 51

--S 52 of 127
solve(ode219,y,x)
 

   (52)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (52)  "failed"
--R                                                    Type: Union("failed",...)
--E 52

--S 53 of 127
ode220 := 2*y(x)*D(y(x),x)-x*y(x)**2-x**3
 

               ,            2    3
   (53)  2y(x)y (x) - x y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R               ,            2    3
--R   (53)  2y(x)y (x) - x y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 127
yx:=solve(ode220,y,x)
 

                              2
                             x
                           - --
              2    2          2
   (54)  (y(x)  + x  + 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              2
--R                             x
--R                           - --
--R              2    2          2
--R   (54)  (y(x)  + x  + 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 54

--S 55 of 127
ode220expr := 2*yx*D(yx,x)-x*yx**2-x**3
 

   (55)
                                   2 2
                                  x
                                - --
           3      2                2   ,
     (4y(x)  + (4x  + 8)y(x))(%e    ) y (x)

   + 
                                                            2 2
                                                           x
                                                         - --
               4        3          2     5     3            2      3
     (- 3x y(x)  + (- 6x  - 8x)y(x)  - 3x  - 8x  - 4x)(%e    )  - x
                                                     Type: Expression Integer
--R 
--R
--R   (55)
--R                                   2 2
--R                                  x
--R                                - --
--R           3      2                2   ,
--R     (4y(x)  + (4x  + 8)y(x))(%e    ) y (x)
--R
--R   + 
--R                                                            2 2
--R                                                           x
--R                                                         - --
--R               4        3          2     5     3            2      3
--R     (- 3x y(x)  + (- 6x  - 8x)y(x)  - 3x  - 8x  - 4x)(%e    )  - x
--R                                                     Type: Expression Integer
--E 55

--S 56 of 127
ode221 := (2*y(x)+x+1)*D(y(x),x)-(2*y(x)+x-1)
 

                         ,
   (56)  (2y(x) + x + 1)y (x) - 2y(x) - x + 1

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (56)  (2y(x) + x + 1)y (x) - 2y(x) - x + 1
--R
--R                                                     Type: Expression Integer
--E 56

--S 57 of 127
solve(ode221,y,x)
 

   (57)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (57)  "failed"
--R                                                    Type: Union("failed",...)
--E 57

--S 58 of 127
ode222 := (2*y(x)+x+7)*D(y(x),x)-y(x)+2*x+4
 

                         ,
   (58)  (2y(x) + x + 7)y (x) - y(x) + 2x + 4

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (58)  (2y(x) + x + 7)y (x) - y(x) + 2x + 4
--R
--R                                                     Type: Expression Integer
--E 58

--S 59 of 127
solve(ode222,y,x)
 

   (59)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (59)  "failed"
--R                                                    Type: Union("failed",...)
--E 59

--S 60 of 127
ode223 := (2*y(x)-x)*D(y(x),x)-y(x)-2*x
 

                     ,
   (60)  (2y(x) - x)y (x) - y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R                     ,
--R   (60)  (2y(x) - x)y (x) - y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 127
yx:=solve(ode223,y,x)
 

             2             2
   (61)  y(x)  - x y(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2             2
--R   (61)  y(x)  - x y(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 127
ode223expr := (2*yx-x)*D(yx,x)-yx-2*x
 

   (62)
           3          2        2               3    2  ,           3
     (4y(x)  - 6x y(x)  + (- 2x  - 2x)y(x) + 2x  + x )y (x) - 2y(x)

   + 
                   2      2               3     2
     (- 2x - 1)y(x)  + (6x  + 2x)y(x) + 4x  + 3x  - 2x
                                                     Type: Expression Integer
--R 
--R
--R   (62)
--R           3          2        2               3    2  ,           3
--R     (4y(x)  - 6x y(x)  + (- 2x  - 2x)y(x) + 2x  + x )y (x) - 2y(x)
--R
--R   + 
--R                   2      2               3     2
--R     (- 2x - 1)y(x)  + (6x  + 2x)y(x) + 4x  + 3x  - 2x
--R                                                     Type: Expression Integer
--E 62

--S 63 of 127
ode224 := (2*y(x)-6*x)*D(y(x),x)-y(x)+3*x+2
 

                      ,
   (63)  (2y(x) - 6x)y (x) - y(x) + 3x + 2

                                                     Type: Expression Integer
--R 
--R
--R                      ,
--R   (63)  (2y(x) - 6x)y (x) - y(x) + 3x + 2
--R
--R                                                     Type: Expression Integer
--E 63

--S 64 of 127
solve(ode224,y,x)
 

   (64)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (64)  "failed"
--R                                                    Type: Union("failed",...)
--E 64

--S 65 of 127
ode225 := (4*y(x)+2*x+3)*D(y(x),x)-2*y(x)-x-1
 

                          ,
   (65)  (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1

                                                     Type: Expression Integer
--R 
--R
--R                          ,
--R   (65)  (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1
--R
--R                                                     Type: Expression Integer
--E 65

--S 66 of 127
solve(ode225,y,x)
 

   (66)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (66)  "failed"
--R                                                    Type: Union("failed",...)
--E 66

--S 67 of 127
ode226 := (4*y(x)-2*x-3)*D(y(x),x)+2*y(x)-x-1
 

                          ,
   (67)  (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1

                                                     Type: Expression Integer
--R 
--R
--R                          ,
--R   (67)  (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1
--R
--R                                                     Type: Expression Integer
--E 67

--S 68 of 127
solve(ode226,y,x)
 

   (68)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (68)  "failed"
--R                                                    Type: Union("failed",...)
--E 68

--S 69 of 127
ode227 := (4*y(x)-3*x-5)*D(y(x),x)-3*y(x)+7*x+2
 

                          ,
   (69)  (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2

                                                     Type: Expression Integer
--R 
--R
--R                          ,
--R   (69)  (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2
--R
--R                                                     Type: Expression Integer
--E 69

--S 70 of 127
yx:=solve(ode227,y,x)
 

              2                       2
         4y(x)  + (- 6x - 10)y(x) + 7x  + 4x
   (70)  -----------------------------------
                          2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2                       2
--R         4y(x)  + (- 6x - 10)y(x) + 7x  + 4x
--R   (70)  -----------------------------------
--R                          2
--R                                          Type: Union(Expression Integer,...)
--E 70

--S 71 of 127
ode227expr := (4*yx-3*x-5)*D(yx,x)-3*yx+7*x+2
 

   (71)
                 3                     2        2                        3
           64y(x)  + (- 144x - 240)y(x)  + (184x  + 280x + 160)y(x) - 84x
         + 
                 2
           - 170x  - 20x + 50
      *
          ,
         y (x)

     + 
               3                   2          2                        3       2
       - 48y(x)  + (184x + 140)y(x)  + (- 252x  - 340x - 20)y(x) + 196x  + 105x
     + 
       - 48x - 16
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (71)
--R                 3                     2        2                        3
--R           64y(x)  + (- 144x - 240)y(x)  + (184x  + 280x + 160)y(x) - 84x
--R         + 
--R                 2
--R           - 170x  - 20x + 50
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R               3                   2          2                        3       2
--R       - 48y(x)  + (184x + 140)y(x)  + (- 252x  - 340x - 20)y(x) + 196x  + 105x
--R     + 
--R       - 48x - 16
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 71

--S 72 of 127
ode228 := (4*y(x)+11*x-11) *D(y(x),x)-25*y(x)-8*x+62
 

                            ,
   (72)  (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62

                                                     Type: Expression Integer
--R 
--R
--R                            ,
--R   (72)  (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 127
solve(ode228,y,x)
 

   (73)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (73)  "failed"
--R                                                    Type: Union("failed",...)
--E 73

--S 74 of 127
ode229 := (12*y(x)-5*x-8)*D(y(x),x)-5*y(x)+2*x+3
 

                           ,
   (74)  (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3

                                                     Type: Expression Integer
--R 
--R
--R                           ,
--R   (74)  (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 127
yx:=solve(ode229,y,x)
 

              2                     2
   (75)  6y(x)  + (- 5x - 8)y(x) + x  + 3x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2                     2
--R   (75)  6y(x)  + (- 5x - 8)y(x) + x  + 3x
--R                                          Type: Union(Expression Integer,...)
--E 75

--S 76 of 127
ode229expr := (12*yx-5*x-8)*D(yx,x)-5*yx+2*x+3
 

   (76)
                3                       2        2                         3
         864y(x)  + (- 1080x - 1728)y(x)  + (444x  + 1332x + 672)y(x) - 60x
       + 
               2
         - 251x  - 208x + 64
    *
        ,
       y (x)

   + 
              3                   2          2                        3      2
     - 360y(x)  + (444x + 666)y(x)  + (- 180x  - 502x - 208)y(x) + 24x  + 93x
   + 
     64x - 21
                                                     Type: Expression Integer
--R 
--R
--R   (76)
--R                3                       2        2                         3
--R         864y(x)  + (- 1080x - 1728)y(x)  + (444x  + 1332x + 672)y(x) - 60x
--R       + 
--R               2
--R         - 251x  - 208x + 64
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R              3                   2          2                        3      2
--R     - 360y(x)  + (444x + 666)y(x)  + (- 180x  - 502x - 208)y(x) + 24x  + 93x
--R   + 
--R     64x - 21
--R                                                     Type: Expression Integer
--E 76

--S 77 of 127
ode230 := a*y(x)*D(y(x),x)+b*y(x)**2+f(x)
 

                ,            2
   (77)  a y(x)y (x) + b y(x)  + f(x)

                                                     Type: Expression Integer
--R 
--R
--R                ,            2
--R   (77)  a y(x)y (x) + b y(x)  + f(x)
--R
--R                                                     Type: Expression Integer
--E 77

--S 78 of 127
solve(ode230,y,x)
 

                                 2%L b
            x                    -----
          ++         2             a
   (78)   |   (b y(x)  + f(%L))%e     d%L
         ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                                 2%I b
--R            x                    -----
--R          ++         2             a
--I   (78)   |   (b y(x)  + f(%I))%e     d%I
--R         ++
--R                                          Type: Union(Expression Integer,...)
--E 78

--S 79 of 127
ode231 := (a*y(x)+b*x+c)*D(y(x),x)+alpha*y(x)+beta*x+gamma
 

                            ,
   (79)  (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma

                                                     Type: Expression Integer
--R 
--R
--R                            ,
--R   (79)  (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma
--R
--R                                                     Type: Expression Integer
--E 79

--S 80 of 127
solve(ode231,y,x)
 

   (80)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (80)  "failed"
--R                                                    Type: Union("failed",...)
--E 80

--S 81 of 127
ode232 := x*y(x)*D(y(x),x)+y(x)**2+x**2
 

                ,          2    2
   (81)  x y(x)y (x) + y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R                ,          2    2
--R   (81)  x y(x)y (x) + y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 81

--S 82 of 127
yx:=solve(ode232,y,x)
 

           2    2    4
         2x y(x)  + x
   (82)  -------------
               4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2    2    4
--R         2x y(x)  + x
--R   (82)  -------------
--R               4
--R                                          Type: Union(Expression Integer,...)
--E 82

--S 83 of 127
ode232expr := x*yx*D(yx,x)+yx**2+x**2
 

            5    3     7      ,         4    4      6    2     8      2
         (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 16x y(x)  + 5x  + 16x

   (83)  --------------------------------------------------------------
                                       16
                                                     Type: Expression Integer
--R 
--R
--R            5    3     7      ,         4    4      6    2     8      2
--R         (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 16x y(x)  + 5x  + 16x
--R
--R   (83)  --------------------------------------------------------------
--R                                       16
--R                                                     Type: Expression Integer
--E 83

--S 84 of 127
ode233 := x*y(x)*D(y(x),x)-y(x)**2+a*x**3*cos(x)
 

                ,         3             2
   (84)  x y(x)y (x) + a x cos(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                ,         3             2
--R   (84)  x y(x)y (x) + a x cos(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 127
yx:=solve(ode233,y,x)
 

             2             2
         2a x sin(x) + y(x)
   (85)  -------------------
                   2
                 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2             2
--R         2a x sin(x) + y(x)
--R   (85)  -------------------
--R                   2
--R                 2x
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 127
ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x)
 

   (86)
            3                    3  ,        2 4      2
       (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x)

     + 
          2 5             2    2               3    2       7               4
       (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x)  + 4a x )cos(x) - 3y(x)
  /
       4
     4x
                                                     Type: Expression Integer
--R 
--R
--R   (86)
--R            3                    3  ,        2 4      2
--R       (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x)
--R
--R     + 
--R          2 5             2    2               3    2       7               4
--R       (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x)  + 4a x )cos(x) - 3y(x)
--R  /
--R       4
--R     4x
--R                                                     Type: Expression Integer
--E 86

--S 87 of 127
ode234 := x*y(x)*D(y(x),x)-y(x)**2+x*y(x)+x**3-2*x**2
 

                ,          2             3     2
   (87)  x y(x)y (x) - y(x)  + x y(x) + x  - 2x

                                                     Type: Expression Integer
--R 
--R
--R                ,          2             3     2
--R   (87)  x y(x)y (x) - y(x)  + x y(x) + x  - 2x
--R
--R                                                     Type: Expression Integer
--E 87

--S 88 of 127
solve(ode234,y,x)
 

   (88)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (88)  "failed"
--R                                                    Type: Union("failed",...)
--E 88

--S 89 of 127
ode235 := (x*y(x)+a)*D(y(x),x)+b*y(x)
 

                      ,
   (89)  (x y(x) + a)y (x) + b y(x)

                                                     Type: Expression Integer
--R 
--R
--R                      ,
--R   (89)  (x y(x) + a)y (x) + b y(x)
--R
--R                                                     Type: Expression Integer
--E 89

--S 90 of 127
yx:=solve(ode235,y,x)
 

               y(x)
               ----
                 b         y(x)
   (90)  b x %e     + a Ei(----)
                             b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               y(x)
--R               ----
--R                 b         y(x)
--R   (90)  b x %e     + a Ei(----)
--R                             b
--R                                          Type: Union(Expression Integer,...)
--E 90

--S 91 of 127
ode235expr := (x*yx+a)*D(yx,x)+b*yx
 

   (91)
                                 y(x) 2
                                 ----
               3            2      b
           (b x y(x) + a b x )(%e    )
         + 
                                                       y(x)
                                                       ----
                2        2     y(x)                2     b
           ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e
                                 b
      *
          ,
         y (x)

     + 
                  y(x) 2                                           y(x)
                  ----                                             ----
        2 2         b                    y(x)      2                 b
       b x y(x)(%e    )  + (a b x y(x)Ei(----) + (b x + a b)y(x))%e
                                           b
     + 
                  y(x)
       a b y(x)Ei(----)
                    b
  /
     y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (91)
--R                                 y(x) 2
--R                                 ----
--R               3            2      b
--R           (b x y(x) + a b x )(%e    )
--R         + 
--R                                                       y(x)
--R                                                       ----
--R                2        2     y(x)                2     b
--R           ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e
--R                                 b
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                  y(x) 2                                           y(x)
--R                  ----                                             ----
--R        2 2         b                    y(x)      2                 b
--R       b x y(x)(%e    )  + (a b x y(x)Ei(----) + (b x + a b)y(x))%e
--R                                           b
--R     + 
--R                  y(x)
--R       a b y(x)Ei(----)
--R                    b
--R  /
--R     y(x)
--R                                                     Type: Expression Integer
--E 91

--S 92 of 127
ode236 := x*(y(x)+4)*D(y(x),x)-y(x)**2-2*y(x)-2*x
 

                       ,          2
   (92)  (x y(x) + 4x)y (x) - y(x)  - 2y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R                       ,          2
--R   (92)  (x y(x) + 4x)y (x) - y(x)  - 2y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 92

--S 93 of 127
solve(ode236,y,x)
 

   (93)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (93)  "failed"
--R                                                    Type: Union("failed",...)
--E 93

--S 94 of 127
ode237 := x*(y(x)+a)*D(y(x),x)+b*y(x)+c*x
 

                        ,
   (94)  (x y(x) + a x)y (x) + b y(x) + c x

                                                     Type: Expression Integer
--R 
--R
--R                        ,
--R   (94)  (x y(x) + a x)y (x) + b y(x) + c x
--R
--R                                                     Type: Expression Integer
--E 94

--S 95 of 127
solve(ode237,y,x)
 

   (95)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (95)  "failed"
--R                                                    Type: Union("failed",...)
--E 95

--S 96 of 127
ode238 := (x*(y(x)+x)+a)*D(y(x),x)-y(x)*(y(x)+x)-b
 

                    2      ,          2
   (96)  (x y(x) + x  + a)y (x) - y(x)  - x y(x) - b

                                                     Type: Expression Integer
--R 
--R
--R                    2      ,          2
--R   (96)  (x y(x) + x  + a)y (x) - y(x)  - x y(x) - b
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 127
solve(ode238,y,x)
 

   (97)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (97)  "failed"
--R                                                    Type: Union("failed",...)
--E 97

--S 98 of 127
ode239 := (x*y(x)-x**2)*D(y(x),x)+y(x)**2-3*x*y(x)-2*x**2
 

                    2  ,          2               2
   (98)  (x y(x) - x )y (x) + y(x)  - 3x y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R                    2  ,          2               2
--R   (98)  (x y(x) - x )y (x) + y(x)  - 3x y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 98

--S 99 of 127
yx:=solve(ode239,y,x)
 

          2    2     3        4
         x y(x)  - 2x y(x) - x
   (99)  ----------------------
                    2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2     3        4
--R         x y(x)  - 2x y(x) - x
--R   (99)  ----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 99

--S 100 of 127
ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2
 

   (100)
          5    3     6    2      7     4          8     5  ,        4    4
       (2x y(x)  - 6x y(x)  + (2x  - 4x )y(x) + 2x  + 4x )y (x) + 3x y(x)

     + 
            5    3      6      3     2       7      4          8      5     2
       - 14x y(x)  + (8x  - 10x )y(x)  + (18x  + 24x )y(x) + 5x  + 14x  - 8x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (100)
--R          5    3     6    2      7     4          8     5  ,        4    4
--R       (2x y(x)  - 6x y(x)  + (2x  - 4x )y(x) + 2x  + 4x )y (x) + 3x y(x)
--R
--R     + 
--R            5    3      6      3     2       7      4          8      5     2
--R       - 14x y(x)  + (8x  - 10x )y(x)  + (18x  + 24x )y(x) + 5x  + 14x  - 8x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 100

--S 101 of 127
ode240 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x
 

                  ,          2
   (101)  2x y(x)y (x) - y(x)  + a x

                                                     Type: Expression Integer
--R 
--R
--R                  ,          2
--R   (101)  2x y(x)y (x) - y(x)  + a x
--R
--R                                                     Type: Expression Integer
--E 101

--S 102 of 127
yx:=solve(ode240,y,x)
 

                           2
          a x log(x) + y(x)
   (102)  ------------------
                   x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           2
--R          a x log(x) + y(x)
--R   (102)  ------------------
--R                   x
--R                                          Type: Union(Expression Integer,...)
--E 102

--S 103 of 127
ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x
 

   (103)
            2                    3  ,       2 2      2
       (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x)

     + 
                   2     2 2               4            2      3
       (- 4a x y(x)  + 2a x )log(x) - 3y(x)  + 2a x y(x)  + a x
  /
      2
     x
                                                     Type: Expression Integer
--R 
--R
--R   (103)
--R            2                    3  ,       2 2      2
--R       (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x)
--R
--R     + 
--R                   2     2 2               4            2      3
--R       (- 4a x y(x)  + 2a x )log(x) - 3y(x)  + 2a x y(x)  + a x
--R  /
--R      2
--R     x
--R                                                     Type: Expression Integer
--E 103

--S 104 of 127
ode241 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x**2
 

                  ,          2      2
   (104)  2x y(x)y (x) - y(x)  + a x

                                                     Type: Expression Integer
--R 
--R
--R                  ,          2      2
--R   (104)  2x y(x)y (x) - y(x)  + a x
--R
--R                                                     Type: Expression Integer
--E 104

--S 105 of 127
yx:=solve(ode241,y,x)
 

              2      2
          y(x)  + a x
   (105)  ------------
                x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2      2
--R          y(x)  + a x
--R   (105)  ------------
--R                x
--R                                          Type: Union(Expression Integer,...)
--E 105

--S 106 of 127
ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2
 

                  3       3      ,           4       2    2     2      4
          (4x y(x)  + 4a x y(x))y (x) - 3y(x)  - 2a x y(x)  + (a  + a)x

   (106)  --------------------------------------------------------------
                                         2
                                        x
                                                     Type: Expression Integer
--R 
--R
--R                  3       3      ,           4       2    2     2      4
--R          (4x y(x)  + 4a x y(x))y (x) - 3y(x)  - 2a x y(x)  + (a  + a)x
--R
--R   (106)  --------------------------------------------------------------
--R                                         2
--R                                        x
--R                                                     Type: Expression Integer
--E 106

--S 107 of 127
ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)**2+1
 

                  ,           2
   (107)  2x y(x)y (x) + 2y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R                  ,           2
--R   (107)  2x y(x)y (x) + 2y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 107

--S 108 of 127
yx:=solve(ode242,y,x)
 

            2    2    2
          2x y(x)  + x
   (108)  -------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2    2
--R          2x y(x)  + x
--R   (108)  -------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 108

--S 109 of 127
ode242expr := 2*x*yx*D(yx,x)+2*yx**2+1
 

             5    3     5      ,         4    4      4    2     4
          (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 12x y(x)  + 3x  + 2

   (109)  -----------------------------------------------------------
                                       2
                                                     Type: Expression Integer
--R 
--R
--R             5    3     5      ,         4    4      4    2     4
--R          (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 12x y(x)  + 3x  + 2
--R
--R   (109)  -----------------------------------------------------------
--R                                       2
--R                                                     Type: Expression Integer
--E 109

--S 110 of 127
ode243 := x*(2*y(x)+x-1)*D(y(x),x)-y(x)*(y(x)+2*x+1)
 

                      2      ,          2
   (110)  (2x y(x) + x  - x)y (x) - y(x)  + (- 2x - 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R                      2      ,          2
--R   (110)  (2x y(x) + x  - x)y (x) - y(x)  + (- 2x - 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 110

--S 111 of 127
solve(ode243,y,x)
 

   (111)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (111)  "failed"
--R                                                    Type: Union("failed",...)
--E 111

--S 112 of 127
ode244 := x*(2*y(x)-x-1)*D(y(x),x)+y(x)*(2*x-y(x)-1)
 

                      2      ,          2
   (112)  (2x y(x) - x  - x)y (x) - y(x)  + (2x - 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R                      2      ,          2
--R   (112)  (2x y(x) - x  - x)y (x) - y(x)  + (2x - 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 112

--S 113 of 127
solve(ode244,y,x)
 

   (113)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (113)  "failed"
--R                                                    Type: Union("failed",...)
--E 113

--S 114 of 127
ode245 := (2*x*y(x)+4*x**3)*D(y(x),x)+y(x)**2+112*x**2*y(x)
 

                       3  ,          2       2
   (114)  (2x y(x) + 4x )y (x) + y(x)  + 112x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                       3  ,          2       2
--R   (114)  (2x y(x) + 4x )y (x) + y(x)  + 112x y(x)
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 127
solve(ode245,y,x)
 

   (115)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (115)  "failed"
--R                                                    Type: Union("failed",...)
--E 115

--S 116 of 127
ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)**2
 

                       2  ,           2               2
   (116)  (3x y(x) + 2x )y (x) + 3y(x)  + 6x y(x) + 3x

                                                     Type: Expression Integer
--R 
--R
--R                       2  ,           2               2
--R   (116)  (3x y(x) + 2x )y (x) + 3y(x)  + 6x y(x) + 3x
--R
--R                                                     Type: Expression Integer
--E 116

--S 117 of 127
yx:=solve(ode246,y,x)
 

            2    2     3         4
          6x y(x)  + 8x y(x) + 3x
   (117)  ------------------------
                      4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2     3         4
--R          6x y(x)  + 8x y(x) + 3x
--R   (117)  ------------------------
--R                      4
--R                                          Type: Union(Expression Integer,...)
--E 117

--S 118 of 127
ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2
 

   (118)
            5    3       6    2        7      4           8      5  ,
       (216x y(x)  + 432x y(x)  + (300x  + 96x )y(x) + 72x  + 64x )y (x)

     + 
           4    4        5    3         6       3     2        7       4
       324x y(x)  + 1008x y(x)  + (1200x  + 240x )y(x)  + (648x  + 384x )y(x)
     + 
           8       5      2
       135x  + 168x  + 48x
  /
     16
                                                     Type: Expression Integer
--R 
--R
--R   (118)
--R            5    3       6    2        7      4           8      5  ,
--R       (216x y(x)  + 432x y(x)  + (300x  + 96x )y(x) + 72x  + 64x )y (x)
--R
--R     + 
--R           4    4        5    3         6       3     2        7       4
--R       324x y(x)  + 1008x y(x)  + (1200x  + 240x )y(x)  + (648x  + 384x )y(x)
--R     + 
--R           8       5      2
--R       135x  + 168x  + 48x
--R  /
--R     16
--R                                                     Type: Expression Integer
--E 118

--S 119 of 127
ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)**2+x*y(x)-7*x**2-9*x-3
 

                            2           ,          2              2
   (119)  ((3x + 2)y(x) - 6x  - 7x - 2)y (x) - y(x)  + x y(x) - 7x  - 9x - 3

                                                     Type: Expression Integer
--R 
--R
--R                            2           ,          2              2
--R   (119)  ((3x + 2)y(x) - 6x  - 7x - 2)y (x) - y(x)  + x y(x) - 7x  - 9x - 3
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 127
solve(ode247,y,x)
 

   (120)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (120)  "failed"
--R                                                    Type: Union("failed",...)
--E 120

--S 121 of 127
ode248 := (6*x*y(x)+x**2+3)*D(y(x),x)+3*y(x)**2+2*x*y(x)+2*x
 

                      2      ,           2
   (121)  (6x y(x) + x  + 3)y (x) + 3y(x)  + 2x y(x) + 2x

                                                     Type: Expression Integer
--R 
--R
--R                      2      ,           2
--R   (121)  (6x y(x) + x  + 3)y (x) + 3y(x)  + 2x y(x) + 2x
--R
--R                                                     Type: Expression Integer
--E 121

--S 122 of 127
yx:=solve(ode248,y,x)
 

                 2     2             2
   (122)  3x y(x)  + (x  + 3)y(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2     2             2
--R   (122)  3x y(x)  + (x  + 3)y(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 122

--S 123 of 127
ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x
 

   (123)
             3    3       4       2     2      5      4      3                5
         108x y(x)  + (54x  + 162x )y(x)  + (6x  + 36x  + 42x  + 72x)y(x) + 6x
       + 
          4      3     2
         x  + 18x  + 6x  + 9
    *
        ,
       y (x)

   + 
        2    4       3            3       4      3      2          2
     81x y(x)  + (72x  + 108x)y(x)  + (15x  + 72x  + 63x  + 36)y(x)
   + 
         4     3      2                 4     3
     (30x  + 4x  + 54x  + 12x)y(x) + 15x  + 4x  + 8x
                                                     Type: Expression Integer
--R 
--R
--R   (123)
--R             3    3       4       2     2      5      4      3                5
--R         108x y(x)  + (54x  + 162x )y(x)  + (6x  + 36x  + 42x  + 72x)y(x) + 6x
--R       + 
--R          4      3     2
--R         x  + 18x  + 6x  + 9
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R        2    4       3            3       4      3      2          2
--R     81x y(x)  + (72x  + 108x)y(x)  + (15x  + 72x  + 63x  + 36)y(x)
--R   + 
--R         4     3      2                 4     3
--R     (30x  + 4x  + 54x  + 12x)y(x) + 15x  + 4x  + 8x
--R                                                     Type: Expression Integer
--E 123

--S 124 of 127
ode249 := (a*x*y(x)+b*x**n)*D(y(x),x)+alpha*y(x)**3+beta*y(x)**2
 

              n             ,                3            2
   (124)  (b x  + a x y(x))y (x) + alpha y(x)  + beta y(x)

                                                     Type: Expression Integer
--R 
--R
--R              n             ,                3            2
--R   (124)  (b x  + a x y(x))y (x) + alpha y(x)  + beta y(x)
--R
--R                                                     Type: Expression Integer
--E 124

--S 125 of 127
solve(ode249,y,x)
 

   (125)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (125)  "failed"
--R                                                    Type: Union("failed",...)
--E 125

--S 126 of 127
ode250 := (B*x*y(x)+A*x**2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)**2+_
             A*x*y(x)+alpha*x+beta*y(x)+gamma
 

   (126)
                         2            ,                               2
     ((B x + b)y(x) + A x  + a x + c)y (x) + (A x + beta)y(x) - B g(x)

   + 
     alpha x + gamma
                                                     Type: Expression Integer
--R 
--R
--R   (126)
--R                         2            ,                               2
--R     ((B x + b)y(x) + A x  + a x + c)y (x) + (A x + beta)y(x) - B g(x)
--R
--R   + 
--R     alpha x + gamma
--R                                                     Type: Expression Integer
--E 126

--S 127 of 127
solve(ode250,y,x)
 

   (127)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (127)  "failed"
--R                                                    Type: Union("failed",...)
--E 127

)spool
 
Starts dribbling to eigen.output (2009/2/17, 17:45:29).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 36
m:=matrix([[1,2,1],[2,1,-2],[1,-2,4]])
 

        +1   2    1 +
        |           |
   (1)  |2   1   - 2|
        |           |
        +1  - 2   4 +
                                                         Type: Matrix Integer
--R 
--R
--R        +1   2    1 +
--R        |           |
--R   (1)  |2   1   - 2|
--R        |           |
--R        +1  - 2   4 +
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 36
characteristicPolynomial m
 

            3      2
   (2)  - %A  + 6%A  - 25
                                                     Type: Polynomial Integer
--R 
--R
--R            3      2
--R   (2)  - %A  + 6%A  - 25
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 36
characteristicPolynomial(m,x)
 

           3     2
   (3)  - x  + 6x  - 25
                                                     Type: Polynomial Integer
--R 
--R
--R           3     2
--R   (3)  - x  + 6x  - 25
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 36
p:=matrix([[x+1,2-x*y,x**2+1],[2-x,y+2*x,x**2-2],[y**2,x-2,4-x*y]])
 

        +                      2      +
        | x + 1   - x y + 2   x  + 1  |
        |                             |
   (4)  |                      2      |
        |- x + 2   y + 2x     x  - 2  |
        |                             |
        |   2                         |
        +  y        x - 2    - x y + 4+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +                      2      +
--R        | x + 1   - x y + 2   x  + 1  |
--R        |                             |
--R   (4)  |                      2      |
--R        |- x + 2   y + 2x     x  - 2  |
--R        |                             |
--R        |   2                         |
--R        +  y        x - 2    - x y + 4+
--R                                              Type: Matrix Polynomial Integer
--E 4

--S 5 of 36
characteristicPolynomial p
 

   (5)
         3    2           3       3            2                       2
     (- x  - x  + 2x - 1)y  + (- x  + (%B - 1)x  + (%B - 3)x + %B - 4)y
   + 
          3             2        2                  2                 4
     (- 2x  + (4%B - 8)x  + (- %B  - 2%B + 16)x + %B  - 5%B + 4)y - 2x
   + 
              3               2       2                   3      2
     (%B + 5)x  + (- 4%B + 7)x  + (3%B  - 18%B + 18)x - %B  + 5%B  + 4%B - 24
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)
--R         3    2           3       3            2                       2
--R     (- x  - x  + 2x - 1)y  + (- x  + (%B - 1)x  + (%B - 3)x + %B - 4)y
--R   + 
--R          3             2        2                  2                 4
--R     (- 2x  + (4%B - 8)x  + (- %B  - 2%B + 16)x + %B  - 5%B + 4)y - 2x
--R   + 
--R              3               2       2                   3      2
--R     (%B + 5)x  + (- 4%B + 7)x  + (3%B  - 18%B + 18)x - %B  + 5%B  + 4%B - 24
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 36
characteristicPolynomial(p,t)
 

   (6)
         3    2           3       3           2                     2
     (- x  - x  + 2x - 1)y  + (- x  + (t - 1)x  + (t - 3)x + t - 4)y
   + 
          3            2       2                2                4           3
     (- 2x  + (4t - 8)x  + (- t  - 2t + 16)x + t  - 5t + 4)y - 2x  + (t + 5)x
   + 
                2      2                 3     2
     (- 4t + 7)x  + (3t  - 18t + 18)x - t  + 5t  + 4t - 24
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)
--R         3    2           3       3           2                     2
--R     (- x  - x  + 2x - 1)y  + (- x  + (t - 1)x  + (t - 3)x + t - 4)y
--R   + 
--R          3            2       2                2                4           3
--R     (- 2x  + (4t - 8)x  + (- t  - 2t + 16)x + t  - 5t + 4)y - 2x  + (t + 5)x
--R   + 
--R                2      2                 3     2
--R     (- 4t + 7)x  + (3t  - 18t + 18)x - t  + 5t  + 4t - 24
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 36
n:=matrix([[a,b,c],[d,e,f],[g,h,k]])
 

        +a  b  c+
        |       |
   (7)  |d  e  f|
        |       |
        +g  h  k+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +a  b  c+
--R        |       |
--R   (7)  |d  e  f|
--R        |       |
--R        +g  h  k+
--R                                              Type: Matrix Polynomial Integer
--E 7

--S 8 of 36
characteristicPolynomial n
 

   (8)
                                 2
     ((a - %C)e - b d - %C a + %C )k + ((- a + %C)f + c d)h
   + 
                                       2                2      3
     (b f - c e + %C c)g + (- %C a + %C )e + %C b d + %C a - %C
                                                     Type: Polynomial Integer
--R 
--R
--R   (8)
--R                                 2
--R     ((a - %C)e - b d - %C a + %C )k + ((- a + %C)f + c d)h
--R   + 
--R                                       2                2      3
--R     (b f - c e + %C c)g + (- %C a + %C )e + %C b d + %C a - %C
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 36
leig := eigenvalues m
 

                  2
   (9)  [5,%D | %D  - %D - 5]
Type: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--R 
--R
--R                  2
--R   (9)  [5,%D | %D  - %D - 5]
--RType: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--E 9

--S 10 of 36
alpha:=leig.1
 

   (10)  5
                                 Type: Union(Fraction Polynomial Integer,...)
--R 
--R
--R   (10)  5
--R                                 Type: Union(Fraction Polynomial Integer,...)
--E 10

--S 11 of 36
eigenvector(alpha,m)
 

          + 0 +
          |   |
          |  1|
   (11)  [|- -|]
          |  2|
          |   |
          + 1 +
                       Type: List Matrix Fraction Polynomial Fraction Integer
--R 
--R
--R          + 0 +
--R          |   |
--R          |  1|
--R   (11)  [|- -|]
--R          |  2|
--R          |   |
--R          + 1 +
--R                       Type: List Matrix Fraction Polynomial Fraction Integer
--E 11

--S 12 of 36
beta:=leig.2
 

                2
   (12)  %D | %D  - %D - 5
                         Type: Union(SuchThat(Symbol,Polynomial Integer),...)
--R 
--R
--R                2
--R   (12)  %D | %D  - %D - 5
--R                         Type: Union(SuchThat(Symbol,Polynomial Integer),...)
--E 12

--S 13 of 36
eigenvector(beta,m)$EP(INT)
 

          +%D+
          |  |
   (13)  [|2 |]
          |  |
          +1 +
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +%D+
--R          |  |
--R   (13)  [|2 |]
--R          |  |
--R          +1 +
--R                                Type: List Matrix Fraction Polynomial Integer
--E 13

-- eigenvector(beta,m)  not accepted by the interpreter

--S 14 of 36
eigenvectors m
 

   (14)
                                   + 0 +
                                   |   |
                                   |  1|
   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
                                   |  2|
                                   |   |
                                   + 1 +
                                                     +%E+
                     2                               |  |
    [eigval= (%E | %E  - %E - 5),eigmult= 1,eigvec= [|2 |]]]
                                                     |  |
                                                     +1 +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (14)
--R                                   + 0 +
--R                                   |   |
--R                                   |  1|
--R   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
--R                                   |  2|
--R                                   |   |
--R                                   + 1 +
--R                                                     +%E+
--R                     2                               |  |
--R    [eigval= (%E | %E  - %E - 5),eigmult= 1,eigvec= [|2 |]]]
--R                                                     |  |
--R                                                     +1 +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 14

--S 15  of 36
q:=matrix [[x**2-y**2,(x-y)*(2*x+3*y)],[x+y,2*x+3*y]]
 

         +   2    2      2           2+
   (15)  |- y  + x   - 3y  + x y + 2x |
         |                            |
         +  y + x         3y + 2x     +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +   2    2      2           2+
--R   (15)  |- y  + x   - 3y  + x y + 2x |
--R         |                            |
--R         +  y + x         3y + 2x     +
--R                                              Type: Matrix Polynomial Integer
--E 15

--S 16 of 36
eigenvectors(q)
 

   (16)
                2         2                          +- y + x+
   [[eigval= - y  + 3y + x  + 2x,eigmult= 1,eigvec= [|       |]],
                                                     +   1   +
                                   +- 3y - 2x+
                                   |---------|
    [eigval= 0,eigmult= 1,eigvec= [|  y + x  |]]]
                                   |         |
                                   +    1    +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (16)
--R                2         2                          +- y + x+
--R   [[eigval= - y  + 3y + x  + 2x,eigmult= 1,eigvec= [|       |]],
--R                                                     +   1   +
--R                                   +- 3y - 2x+
--R                                   |---------|
--R    [eigval= 0,eigmult= 1,eigvec= [|  y + x  |]]]
--R                                   |         |
--R                                   +    1    +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 16

--S 17 of 36
p:=matrix([[76,-18,58,-10],[-4,78,2,-2],[-6,15,45,3],[22,-75,7,41]])
 

         +76   - 18  58  - 10+
         |                   |
         |- 4   78   2   - 2 |
   (17)  |                   |
         |- 6   15   45   3  |
         |                   |
         +22   - 75  7    41 +
                                                         Type: Matrix Integer
--R 
--R
--R         +76   - 18  58  - 10+
--R         |                   |
--R         |- 4   78   2   - 2 |
--R   (17)  |                   |
--R         |- 6   15   45   3  |
--R         |                   |
--R         +22   - 75  7    41 +
--R                                                         Type: Matrix Integer
--E 17

--S 18 of 36
ll := eigenvectors p
 

   (18)
                                    +10 +
                                    |-- |
                                    | 7 |
                                    |   |
                                    | 2 |
                                    | - |
   [[eigval= 48,eigmult= 2,eigvec= [| 7 |]],
                                    |   |
                                    |  3|
                                    |- -|
                                    |  7|
                                    |   |
                                    + 1 +
                                    +- 2+
                                    |   |
                                    |- 1|
    [eigval= 72,eigmult= 2,eigvec= [|   |]]]
                                    | 0 |
                                    |   |
                                    + 1 +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (18)
--R                                    +10 +
--R                                    |-- |
--R                                    | 7 |
--R                                    |   |
--R                                    | 2 |
--R                                    | - |
--R   [[eigval= 48,eigmult= 2,eigvec= [| 7 |]],
--R                                    |   |
--R                                    |  3|
--R                                    |- -|
--R                                    |  7|
--R                                    |   |
--R                                    + 1 +
--R                                    +- 2+
--R                                    |   |
--R                                    |- 1|
--R    [eigval= 72,eigmult= 2,eigvec= [|   |]]]
--R                                    | 0 |
--R                                    |   |
--R                                    + 1 +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 18


--S 19 of 36
generalizedEigenvectors p
 

   (19)
                            +  10+
                            |- --|
                            |   3| +0+                           +- 12+ +- 2+
                            |    | | |                           |    | |   |
                            |  2 | |0|                           |- 3 | |- 1|
   [[eigval= 48,geneigvec= [|- - |,| |]],[eigval= 72,geneigvec= [|    |,|   |]]]
                            |  3 | |0|                           | 1  | | 0 |
                            |    | | |                           |    | |   |
                            | 1  | +1+                           + 0  + + 1 +
                            |    |
                            + 0  +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),geneigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (19)
--R                            +  10+
--R                            |- --|
--R                            |   3| +0+                           +- 12+ +- 2+
--R                            |    | | |                           |    | |   |
--R                            |  2 | |0|                           |- 3 | |- 1|
--R   [[eigval= 48,geneigvec= [|- - |,| |]],[eigval= 72,geneigvec= [|    |,|   |]]]
--R                            |  3 | |0|                           | 1  | | 0 |
--R                            |    | | |                           |    | |   |
--R                            | 1  | +1+                           + 0  + + 1 +
--R                            |    |
--R                            + 0  +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),geneigvec: List Matrix Fraction Polynomial Integer)
--E 19

--S 20 of 36
generalizedEigenvector(ll.1,p)$EP(INT)
 

          +  10+
          |- --|
          |   3| +0+
          |    | | |
          |  2 | |0|
   (20)  [|- - |,| |]
          |  3 | |0|
          |    | | |
          | 1  | +1+
          |    |
          + 0  +
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +  10+
--R          |- --|
--R          |   3| +0+
--R          |    | | |
--R          |  2 | |0|
--R   (20)  [|- - |,| |]
--R          |  3 | |0|
--R          |    | | |
--R          | 1  | +1+
--R          |    |
--R          + 0  +
--R                                Type: List Matrix Fraction Polynomial Integer
--E 20

-- generalizedEigenvector(ll.1,p) the interpreter can not handle this

--S 21 of 36
m
 

         +1   2    1 +
         |           |
   (21)  |2   1   - 2|
         |           |
         +1  - 2   4 +
                                                         Type: Matrix Integer
--R 
--R
--R         +1   2    1 +
--R         |           |
--R   (21)  |2   1   - 2|
--R         |           |
--R         +1  - 2   4 +
--R                                                         Type: Matrix Integer
--E 21

--S 22 of 36
mm:=matrix([[30,4,24],[-17,8,-7],[-31,-54,-5]])
 

         + 30    4    24 +
         |               |
   (22)  |- 17   8    - 7|
         |               |
         +- 31  - 54  - 5+
                                                         Type: Matrix Integer
--R 
--R
--R         + 30    4    24 +
--R         |               |
--R   (22)  |- 17   8    - 7|
--R         |               |
--R         +- 31  - 54  - 5+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 36
le1:=radicalEigenvalues m
 

             +--+      +--+
          - \|21  + 1 \|21  + 1
   (23)  [-----------,---------,5]
               2          2
                                                Type: List Expression Integer
--R 
--R
--R             +--+      +--+
--R          - \|21  + 1 \|21  + 1
--R   (23)  [-----------,---------,5]
--R               2          2
--R                                                Type: List Expression Integer
--E 23

--S 24 of 36
le2:=radicalEigenvalues mm
 

             +---+      +---+
   (24)  [22\|- 1 ,- 22\|- 1 ,33]
                                                Type: List Expression Integer
--R 
--R
--R             +---+      +---+
--R   (24)  [22\|- 1 ,- 22\|- 1 ,33]
--R                                                Type: List Expression Integer
--E 24

--S 25 of 36
radicalEigenvector(le1.2, m)
 

          +    10   +
          |---------|
          | +--+    |
   (25)  [|\|21  - 1|]
          |         |
          |    2    |
          |         |
          +    1    +
                                         Type: List Matrix Expression Integer
--R 
--R
--R          +    10   +
--R          |---------|
--R          | +--+    |
--R   (25)  [|\|21  - 1|]
--R          |         |
--R          |    2    |
--R          |         |
--R          +    1    +
--R                                         Type: List Matrix Expression Integer
--E 25

--S 26 of 36
radicalEigenvector(le2.2,mm)
 

          +       +---+       +
          |- 1449\|- 1  + 1720|
          |-------------------|
          |      +---+        |
          |  328\|- 1  - 3343 |
          |                   |
   (26)  [|      +---+        |]
          |    7\|- 1  - 9    |
          |   ------------    |
          |      +---+        |
          |   38\|- 1  - 8    |
          |                   |
          +         1         +
                                         Type: List Matrix Expression Integer
--R 
--R
--R          +       +---+       +
--R          |- 1449\|- 1  + 1720|
--R          |-------------------|
--R          |      +---+        |
--R          |  328\|- 1  - 3343 |
--R          |                   |
--R   (26)  [|      +---+        |]
--R          |    7\|- 1  - 9    |
--R          |   ------------    |
--R          |      +---+        |
--R          |   38\|- 1  - 8    |
--R          |                   |
--R          +         1         +
--R                                         Type: List Matrix Expression Integer
--E 26

--S 27 of 36
radicalEigenvectors m
 

   (27)
                                            + +--+    +
              +--+                          |\|21  + 1|
             \|21  + 1                      |---------|
   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
                 2                          |         |
                                            |    2    |
                                            |         |
                                            +    1    +
                                              +   +--+    +
                +--+                          |- \|21  + 1|
             - \|21  + 1                      |-----------|
    [radval= -----------,radmult= 1,radvect= [|     2     |]],
                  2                           |           |
                                              |     2     |
                                              |           |
                                              +     1     +
                                    + 0 +
                                    |   |
                                    |  1|
    [radval= 5,radmult= 1,radvect= [|- -|]]]
                                    |  2|
                                    |   |
                                    + 1 +
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R 
--R
--R   (27)
--R                                            + +--+    +
--R              +--+                          |\|21  + 1|
--R             \|21  + 1                      |---------|
--R   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
--R                 2                          |         |
--R                                            |    2    |
--R                                            |         |
--R                                            +    1    +
--R                                              +   +--+    +
--R                +--+                          |- \|21  + 1|
--R             - \|21  + 1                      |-----------|
--R    [radval= -----------,radmult= 1,radvect= [|     2     |]],
--R                  2                           |           |
--R                                              |     2     |
--R                                              |           |
--R                                              +     1     +
--R                                    + 0 +
--R                                    |   |
--R                                    |  1|
--R    [radval= 5,radmult= 1,radvect= [|- -|]]]
--R                                    |  2|
--R                                    |   |
--R                                    + 1 +
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E 27

--S 28 of 36
radicalEigenvectors mm
 

   (28)
                                             +   +---+     +
                                             |11\|- 1  - 16|
                                             |-------------|
                                             |      29     |
                  +---+                      |             |
   [[radval= - 22\|- 1 ,radmult= 1,radvect= [|   +---+     |]],
                                             |11\|- 1  + 13|
                                             |-------------|
                                             |      58     |
                                             |             |
                                             +      1      +
                                           +     +---+     +
                                           |- 11\|- 1  - 16|
                                           |---------------|
                                           |       29      |
                +---+                      |               |
    [radval= 22\|- 1 ,radmult= 1,radvect= [|     +---+     |]],
                                           |- 11\|- 1  + 13|
                                           |---------------|
                                           |       58      |
                                           |               |
                                           +       1       +
                                     + 4 +
                                     |   |
    [radval= 33,radmult= 1,radvect= [|- 3|]]]
                                     |   |
                                     + 1 +
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R 
--R
--R   (28)
--R                                             +   +---+     +
--R                                             |11\|- 1  - 16|
--R                                             |-------------|
--R                                             |      29     |
--R                  +---+                      |             |
--R   [[radval= - 22\|- 1 ,radmult= 1,radvect= [|   +---+     |]],
--R                                             |11\|- 1  + 13|
--R                                             |-------------|
--R                                             |      58     |
--R                                             |             |
--R                                             +      1      +
--R                                           +     +---+     +
--R                                           |- 11\|- 1  - 16|
--R                                           |---------------|
--R                                           |       29      |
--R                +---+                      |               |
--R    [radval= 22\|- 1 ,radmult= 1,radvect= [|     +---+     |]],
--R                                           |- 11\|- 1  + 13|
--R                                           |---------------|
--R                                           |       58      |
--R                                           |               |
--R                                           +       1       +
--R                                     + 4 +
--R                                     |   |
--R    [radval= 33,radmult= 1,radvect= [|- 3|]]]
--R                                     |   |
--R                                     + 1 +
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E 28

--S 29 of 36
realEigenvalues(m,1/1000000)
 

            3756603   5853755
   (29)  [- -------,5,-------]
            2097152   2097152
                                                  Type: List Fraction Integer
--R 
--R
--R            3756603   5853755
--R   (29)  [- -------,5,-------]
--R            2097152   2097152
--R                                                  Type: List Fraction Integer
--E 29

--S 30 of 36
complexEigenvalues(mm,1/1000000)
 

   (30)  [- 22%i,22%i,33]
                                          Type: List Complex Fraction Integer
--R 
--R
--R   (30)  [- 22%i,22%i,33]
--R                                          Type: List Complex Fraction Integer
--E 30

--S 31 of 36
realEigenvectors(m,1/1000000)
 

   (31)
                                    + 0 +
                                    |   |
                                    |  1|
   [[outval= 5,outmult= 1,outvect= [|- -|]],
                                    |  2|
                                    |   |
                                    + 1 +
                                          +5853755+
                                          |-------|
             5853755                      |2097152|
    [outval= -------,outmult= 1,outvect= [|       |]],
             2097152                      |   2   |
                                          |       |
                                          +   1   +
                                            +  3756603+
                                            |- -------|
               3756603                      |  2097152|
    [outval= - -------,outmult= 1,outvect= [|         |]]]
               2097152                      |    2    |
                                            |         |
                                            +    1    +
Type: List Record(outval: Fraction Integer,outmult: Integer,outvect: List Matrix Fraction Integer)
--R 
--R
--R   (31)
--R                                    + 0 +
--R                                    |   |
--R                                    |  1|
--R   [[outval= 5,outmult= 1,outvect= [|- -|]],
--R                                    |  2|
--R                                    |   |
--R                                    + 1 +
--R                                          +5853755+
--R                                          |-------|
--R             5853755                      |2097152|
--R    [outval= -------,outmult= 1,outvect= [|       |]],
--R             2097152                      |   2   |
--R                                          |       |
--R                                          +   1   +
--R                                            +  3756603+
--R                                            |- -------|
--R               3756603                      |  2097152|
--R    [outval= - -------,outmult= 1,outvect= [|         |]]]
--R               2097152                      |    2    |
--R                                            |         |
--R                                            +    1    +
--RType: List Record(outval: Fraction Integer,outmult: Integer,outvect: List Matrix Fraction Integer)
--E 31

--S 32 of 36
complexEigenvectors(mm,1/1000000)
 

   (32)
                                     + 4 +
                                     |   |
   [[outval= 33,outmult= 1,outvect= [|- 3|]],
                                     |   |
                                     + 1 +
                                       +  16   11   +
                                       |- -- - -- %i|
                                       |  29   29   |
                                       |            |
    [outval= 22%i,outmult= 1,outvect= [| 13   11    |]],
                                       | -- - -- %i |
                                       | 58   58    |
                                       |            |
                                       +     1      +
                                         +  16   11   +
                                         |- -- + -- %i|
                                         |  29   29   |
                                         |            |
    [outval= - 22%i,outmult= 1,outvect= [| 13   11    |]]]
                                         | -- + -- %i |
                                         | 58   58    |
                                         |            |
                                         +     1      +
Type: List Record(outval: Complex Fraction Integer,outmult: Integer,outvect: List Matrix Complex Fraction Integer)
--R 
--R
--R   (32)
--R                                     + 4 +
--R                                     |   |
--R   [[outval= 33,outmult= 1,outvect= [|- 3|]],
--R                                     |   |
--R                                     + 1 +
--R                                       +  16   11   +
--R                                       |- -- - -- %i|
--R                                       |  29   29   |
--R                                       |            |
--R    [outval= 22%i,outmult= 1,outvect= [| 13   11    |]],
--R                                       | -- - -- %i |
--R                                       | 58   58    |
--R                                       |            |
--R                                       +     1      +
--R                                         +  16   11   +
--R                                         |- -- + -- %i|
--R                                         |  29   29   |
--R                                         |            |
--R    [outval= - 22%i,outmult= 1,outvect= [| 13   11    |]]]
--R                                         | -- + -- %i |
--R                                         | 58   58    |
--R                                         |            |
--R                                         +     1      +
--RType: List Record(outval: Complex Fraction Integer,outmult: Integer,outvect: List Matrix Complex Fraction Integer)
--E 32

--S 33 of 36
realEigenvalues(m,.000001)
 

   (33)  [- 1.7912878990 173339844,5.0,2.7912878990 173339844]
                                                             Type: List Float
--R 
--R
--R   (33)  [- 1.7912878990 173339844,5.0,2.7912878990 173339844]
--R                                                             Type: List Float
--E 33

--S 34 of 36
realEigenvectors(m,.000001)
 

   (34)
                                      + 0.0 +
                                      |     |
   [[outval= 5.0,outmult= 1,outvect= [|- 0.5|]],
                                      |     |
                                      + 1.0 +

     [outval= 2.7912878990 173339844, outmult= 1,
                +2.7912878990 173339844+
                |                      |
      outvect= [|         2.0          |]]
                |                      |
                +         1.0          +
     ,

     [outval= - 1.7912878990 173339844, outmult= 1,
                +- 1.7912878990 173339844+
                |                        |
      outvect= [|          2.0           |]]
                |                        |
                +          1.0           +
     ]
 Type: List Record(outval: Float,outmult: Integer,outvect: List Matrix Float)
--R 
--R
--R   (34)
--R                                      + 0.0 +
--R                                      |     |
--R   [[outval= 5.0,outmult= 1,outvect= [|- 0.5|]],
--R                                      |     |
--R                                      + 1.0 +
--R
--R     [outval= 2.7912878990 173339844, outmult= 1,
--R                +2.7912878990 173339844+
--R                |                      |
--R      outvect= [|         2.0          |]]
--R                |                      |
--R                +         1.0          +
--R     ,
--R
--R     [outval= - 1.7912878990 173339844, outmult= 1,
--R                +- 1.7912878990 173339844+
--R                |                        |
--R      outvect= [|          2.0           |]]
--R                |                        |
--R                +          1.0           +
--R     ]
--R Type: List Record(outval: Float,outmult: Integer,outvect: List Matrix Float)
--E 34

--S 35 of 36
complexEigenvalues(mm,.000001)
 

   (35)  [- 22.0 %i,22.0 %i,33.0]
                                                     Type: List Complex Float
--R 
--R
--R   (35)  [- 22.0 %i,22.0 %i,33.0]
--R                                                     Type: List Complex Float
--E 35

--S 36 of 36
complexEigenvectors(mm,.000001)
 

   (36)
                                       + 4.0 +
                                       |     |
   [[outval= 33.0,outmult= 1,outvect= [|- 3.0|]],
                                       |     |
                                       + 1.0 +

     [outval= 22.0 %i, outmult= 1,
                +- 0.5517241379 3103448276 - 0.3793103448 275862069 %i+
                |                                                     |
      outvect= [|0.2241379310 3448275862 - 0.1896551724 1379310345 %i |]]
                |                                                     |
                +                         1.0                         +
     ,

     [outval= - 22.0 %i, outmult= 1,
                +- 0.5517241379 3103448276 + 0.3793103448 275862069 %i+
                |                                                     |
      outvect= [|0.2241379310 3448275862 + 0.1896551724 1379310345 %i |]]
                |                                                     |
                +                         1.0                         +
     ]
Type: List Record(outval: Complex Float,outmult: Integer,outvect: List Matrix Complex Float)
--R 
--R
--R   (36)
--R                                       + 4.0 +
--R                                       |     |
--R   [[outval= 33.0,outmult= 1,outvect= [|- 3.0|]],
--R                                       |     |
--R                                       + 1.0 +
--R
--R     [outval= 22.0 %i, outmult= 1,
--R                +- 0.5517241379 3103448276 - 0.3793103448 275862069 %i+
--R                |                                                     |
--R      outvect= [|0.2241379310 3448275862 - 0.1896551724 1379310345 %i |]]
--R                |                                                     |
--R                +                         1.0                         +
--R     ,
--R
--R     [outval= - 22.0 %i, outmult= 1,
--R                +- 0.5517241379 3103448276 + 0.3793103448 275862069 %i+
--R                |                                                     |
--R      outvect= [|0.2241379310 3448275862 + 0.1896551724 1379310345 %i |]]
--R                |                                                     |
--R                +                         1.0                         +
--R     ]
--RType: List Record(outval: Complex Float,outmult: Integer,outvect: List Matrix Complex Float)
--E 36
)spool
 
Starts dribbling to genups.output (2009/2/17, 17:46:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 40
taylor(n +-> 1/factorial(n),x = 0)      -- expansion of exp(x) at x = 0
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 40
taylor(n +-> (-1)**(n-1)/n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (2)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10            11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
     7            8            9            10
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (2)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10            11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
--R     7            8            9            10
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 2

--S 3 of 40
taylor(n +-> (-1)**(n-1)/n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (3)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (3)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 3

--S 4 of 40
laurent(m +-> m**2,x = 7,-2..)          -- infinite Laurent expansion
 

   (4)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (4)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 4

--S 5 of 40
laurent(m +-> m**2,x = 7,-2..5)         --   finite Laurent expansion
 

   (5)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (5)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 5

--S 6 of 40
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)  -- sin(x) at x = 0
 

            1  3    1   5     1   7      1    9       1     11      12
   (6)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
            6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      1    9       1     11      12
--R   (6)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R            6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 6

--S 7 of 40
puiseux(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2)      -- cos(x) at x = 0
 

            1  2    1  4    1   6     1    8      1     10      11
   (7)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
            2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  2    1  4    1   6     1    8      1     10      11
--R   (7)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R            2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 7

-- puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 8 of 40
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
 

            1  3    1   5     1   7      1    9
   (8)  x - - x  + --- x  - ---- x  + ------ x
            6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      1    9
--R   (8)  x - - x  + --- x  - ---- x  + ------ x
--R            6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 8

--S 9 of 40
puiseux(j +-> j,x = 8,-4/3..,1/2)
 

   (9)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (9)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 9

--S 10 of 40
puiseux(j +-> j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (10)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (10)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 10

--S 11 of 40
taylor(1/factorial(n),n,x = 0)      -- expansion of exp(x) at x = 0
 

   (11)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (11)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 11

--S 12 of 40
taylor((-1)**(n-1)/n,n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (12)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10            11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
     7            8            9            10
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (12)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10            11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
--R     7            8            9            10
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 12

--S 13 of 40
taylor((-1)**(n-1)/n,n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (13)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (13)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 13

--S 14 of 40
laurent(m**2,m,x = 7,-2..)          -- infinite Laurent expansion
 

   (14)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (14)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 14

--S 15 of 40
laurent(m**2,m,x = 7,-2..5)         --   finite Laurent expansion
 

   (15)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (15)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 15

--S 16 of 40
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2)  -- sin(x) at x = 0
 

             1  3    1   5     1   7      1    9       1     11      12
   (16)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
             6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9       1     11      12
--R   (16)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R             6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 16

--S 17 of 40
puiseux((-1)**(i/2)/factorial(i),i,x = 0,0..,2)      -- cos(x) at x = 0
 

             1  2    1  4    1   6     1    8      1     10      11
   (17)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
             2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  2    1  4    1   6     1    8      1     10      11
--R   (17)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R             2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 17

-- puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 18 of 40
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
 

             1  3    1   5     1   7      1    9
   (18)  x - - x  + --- x  - ---- x  + ------ x
             6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9
--R   (18)  x - - x  + --- x  - ---- x  + ------ x
--R             6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 18

--S 19 of 40
puiseux(j,j,x = 8,-4/3..,1/2)
 

   (19)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (19)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 19

--S 20 of 40
puiseux(j,j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (20)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (20)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 20

--S 21 of 40
series(n +-> 1/factorial(n),x = 0)      -- expansion of exp(x) at x = 0
 

   (21)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (21)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 21

--S 22 of 40
series(n +-> (-1)**(n-1)/n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (22)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10    1        11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
     7            8            9            10             11
   + 
              12
     O((x - 1)  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (22)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10    1        11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
--R     7            8            9            10             11
--R   + 
--R              12
--R     O((x - 1)  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 22

--S 23 of 40
series(n +-> (-1)**(n-1)/n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (23)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (23)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 23

--S 24 of 40
series(m +-> m**2,x = 7,-2..)          -- infinite Laurent expansion
 

   (24)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (24)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 24

--S 25 of 40
series(m +-> m**2,x = 7,-2..5)         --   finite Laurent expansion
 

   (25)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (25)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 25

--S 26 of 40
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)  -- sin(x) at x = 0
 

             1  3    1   5     1   7      1    9       1     11      12
   (26)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
             6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9       1     11      12
--R   (26)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R             6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 26

--S 27 of 40
series(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2)      -- cos(x) at x = 0
 

             1  2    1  4    1   6     1    8      1     10      11
   (27)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
             2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  2    1  4    1   6     1    8      1     10      11
--R   (27)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R             2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 27

-- series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 28 of 40
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
 

             1  3    1   5     1   7      1    9
   (28)  x - - x  + --- x  - ---- x  + ------ x
             6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9
--R   (28)  x - - x  + --- x  - ---- x  + ------ x
--R             6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 28

--S 29 of 40
series(j +-> j,x = 8,-4/3..,1/2)
 

   (29)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (29)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 29

--S 30 of 40
series(j +-> j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (30)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (30)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 30

--S 31 of 40
series(1/factorial(n),n,x = 0)      -- expansion of exp(x) at x = 0
 

   (31)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (31)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 31

--S 32 of 40
series((-1)**(n-1)/n,n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (32)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10    1        11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
     7            8            9            10             11
   + 
              12
     O((x - 1)  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (32)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10    1        11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
--R     7            8            9            10             11
--R   + 
--R              12
--R     O((x - 1)  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 32

--S 33 of 40
series((-1)**(n-1)/n,n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (33)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (33)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 33

--S 34 of 40
series(m**2,m,x = 7,-2..)          -- infinite Laurent expansion
 

   (34)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (34)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 34

--S 35 of 40
series(m**2,m,x = 7,-2..5)         --   finite Laurent expansion
 

   (35)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (35)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 35

--S 36 of 40
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2)  -- sin(x) at x = 0
 

             1  3    1   5     1   7      1    9       1     11      12
   (36)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
             6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9       1     11      12
--R   (36)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R             6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 36

--S 37 of 40
series((-1)**(i/2)/factorial(i),i,x = 0,0..,2)      -- cos(x) at x = 0
 

             1  2    1  4    1   6     1    8      1     10      11
   (37)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
             2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  2    1  4    1   6     1    8      1     10      11
--R   (37)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R             2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 37

-- series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 38 of 40
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
 

             1  3    1   5     1   7      1    9
   (38)  x - - x  + --- x  - ---- x  + ------ x
             6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9
--R   (38)  x - - x  + --- x  - ---- x  + ------ x
--R             6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 38

--S 39 of 40
series(j,j,x = 8,-4/3..,1/2)
 

   (39)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (39)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 39

--S 40 of 40
series(j,j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (40)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (40)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 40
)spool 
 
Starts dribbling to coercels.output (2009/2/17, 17:44:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 8
alternatingGroup 4
 

   (1)  <(1 2)(3 4),(1 2 3)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (1)  <(1 2)(3 4),(1 2 3)>
--R                                               Type: PermutationGroup Integer
--E 1

--S 2 of 8
% :: List Permutation Integer
 

   (2)  [(1 2)(3 4),(1 2 3)]
                                               Type: List Permutation Integer
--R 
--R
--R   (2)  [(1 2)(3 4),(1 2 3)]
--R                                               Type: List Permutation Integer
--E 2

--S 3 of 8
li := %
 

   (3)  [(1 2)(3 4),(1 2 3)]
                                               Type: List Permutation Integer
--R 
--R
--R   (3)  [(1 2)(3 4),(1 2 3)]
--R                                               Type: List Permutation Integer
--E 3

--S 4 of 8
pgr := MonoidRing(Polynomial PrimeField 5, Permutation Integer)
 

   (4)  MonoidRing(Polynomial PrimeField 5,Permutation Integer)
                                                                 Type: Domain
--R 
--R
--R   (4)  MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R                                                                 Type: Domain
--E 4

--S 5 of 8
p : pgr := first  li
 

   (5)  (1 2)(3 4)
                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (5)  (1 2)(3 4)
--R                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 5

--S 6 of 8
q : pgr := first  li
 

   (6)  (1 2)(3 4)
                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (6)  (1 2)(3 4)
--R                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 6

--S 7 of 8
basis  := [p,q,p*p,p*q, q*p,q*q, p*q*q, p*q*p, q*p*q,q*q*p,q*p*q*q,q*q*p*q]
 

   (7)
   [(1 2)(3 4), (1 2)(3 4), 1, 1, 1, 1, (1 2)(3 4), (1 2)(3 4), (1 2)(3 4),
    (1 2)(3 4), 1, 1]
           Type: List MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (7)
--R   [(1 2)(3 4), (1 2)(3 4), 1, 1, 1, 1, (1 2)(3 4), (1 2)(3 4), (1 2)(3 4),
--R    (1 2)(3 4), 1, 1]
--R           Type: List MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 7

--S 8 of 8
% :: Set          MonoidRing(Polynomial PrimeField 5,Permutation Integer)
 

   (8)  {(1 2)(3 4),1}
            Type: Set MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (8)  {(1 2)(3 4),1}
--R            Type: Set MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 8
)spool
 
Starts dribbling to exit.output (2009/2/17, 17:45:46).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
n := 0
 

   (1)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (1)  0
--R                                                     Type: NonNegativeInteger
--E 1

--S 2 of 6
gasp(): Exit ==
    free n
    n := n + 1
    error "Oh no!"
 
   Function declaration gasp : () -> Exit has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration gasp : () -> Exit has been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 6
half(k) ==
  if odd? k then gasp()
  else k quo 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 6
half 4
 
   Compiling function gasp with type () -> Exit 
   Compiling function half with type PositiveInteger -> Integer 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling function gasp with type () -> Exit 
--R   Compiling function half with type PositiveInteger -> Integer 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 6
half 3
 
 
Daly Bug
   Error signalled from user code in function gasp: 
      Oh no!
--R 
--R 
--RDaly Bug
--R   Error signalled from user code in function gasp: 
--R      Oh no!
--E 5

--S 6 of 6
n
 

   (5)  1
                                                     Type: NonNegativeInteger
--R 
--R
--R   (5)  1
--R                                                     Type: NonNegativeInteger
--E 6
)spool 
 
Starts dribbling to liu.output (2009/2/17, 17:52:32).
)set message test on
 
)set message auto off
 
)set message type off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 9
Dx: LODO(EXPR INT, f+->D(f,x)) := D()
 

   (1)  D
--R
--R   (1)  D
--E 1

--S 2 of 9
u := operator 'u
 

   (2)  u
--R
--R   (2)  u
--E 2

--S 3 of 9
L := Dx + u(x)
 

   (3)  D + u(x)
--R
--R   (3)  D + u(x)
--E 3

--S 4 of 9
L**2 = L*L
 

         2                2   2             ,          2
   (4)  D  + 2u(x)D + u(x) = D  + 2u(x)D + u (x) + u(x)

--R
--R         2                2   2             ,          2
--R   (4)  D  + 2u(x)D + u(x) = D  + 2u(x)D + u (x) + u(x)
--R
--E 4

)clear all
 
   All user variables and function definitions have been cleared.

--S 5 of 9
f: INT->INT:=x+->x+1
 

   (1)  theMap(Closure)
--R
--R   (1)  theMap(Closure)
--E 5

--S 6 of 9
K := OREUP ( x, INT, 1, f);
 

--R
--E 6

--S 7 of 9
x:K
 
--E 7

--S 8 of 9
L:=x+1
 

   (4)  x + 1
--R
--R   (4)  x + 1
--E 8

--S 9 of 9
L^2=L*L
 

         2            2
   (5)  x  + 2x + 1= x  + 4x + 3
--R
--R         2            2
--R   (5)  x  + 2x + 1= x  + 4x + 3
--E 9

)spool 
 
Starts dribbling to schaum5.output (2009/2/17, 17:59:59).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
 

   (1)
   [
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
    /
        +---+
       \|a p
     ,
                   +---------------------------+
           +-----+ |     2                          +-----+ +---+
          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
    2atan(-------------------------------------------------------)
                                   a p x
    --------------------------------------------------------------]
                                +-----+
                               \|- a p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R    /
--R        +---+
--R       \|a p
--R     ,
--R                   +---------------------------+
--R           +-----+ |     2                          +-----+ +---+
--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R    2atan(-------------------------------------------------------)
--R                                   a p x
--R    --------------------------------------------------------------]
--R                                +-----+
--R                               \|- a p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 2
aa1:=aa.1
 

   (2)
     log
                                     +---------------------------+
               +---+ +---+           |     2
            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
          + 
                   +---+            2                          +---+
            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
       /
                  +---------------------------+
            +---+ |     2
          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (2)
--R     log
--R                                     +---------------------------+
--R               +---+ +---+           |     2
--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R          + 
--R                   +---+            2                          +---+
--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R       /
--R                  +---------------------------+
--R            +---+ |     2
--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 3
aa2:=aa.2
 

                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
        2atan(-------------------------------------------------------)
                                       a p x
   (3)  --------------------------------------------------------------
                                    +-----+
                                   \|- a p
                                                     Type: Expression Integer
--R
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R        2atan(-------------------------------------------------------)
--R                                       a p x
--R   (3)  --------------------------------------------------------------
--R                                    +-----+
--R                                   \|- a p
--R                                                     Type: Expression Integer
--E

--S 4
bb1:=2/sqrt(a*p)*log(sqrt(a*(p*x+q))+sqrt(p*(a*x+b)))
 

              +-----------+    +-----------+
        2log(\|a p x + a q  + \|a p x + b p )
   (4)  -------------------------------------
                         +---+
                        \|a p
                                                     Type: Expression Integer
--R
--R              +-----------+    +-----------+
--R        2log(\|a p x + a q  + \|a p x + b p )
--R   (4)  -------------------------------------
--R                         +---+
--R                        \|a p
--R                                                     Type: Expression Integer
--E

--S 5
bb2:=2/sqrt(-a*p)*atan(sqrt((-p*(a*x+b))/(a*(p*x+q))))
 

               +-------------+
               |- a p x - b p
        2atan( |------------- )
              \| a p x + a q
   (5)  -----------------------
                 +-----+
                \|- a p
                                                     Type: Expression Integer
--R
--R               +-------------+
--R               |- a p x - b p
--R        2atan( |------------- )
--R              \| a p x + a q
--R   (5)  -----------------------
--R                 +-----+
--R                \|- a p
--R                                                     Type: Expression Integer
--E

--S 6
cc1:=aa1-bb1
 

   (6)
               +-----------+    +-----------+
       - 2log(\|a p x + a q  + \|a p x + b p )
     + 
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (6)
--R               +-----------+    +-----------+
--R       - 2log(\|a p x + a q  + \|a p x + b p )
--R     + 
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 7
cc2:=aa1-bb2
 

   (7)
          +-----+
         \|- a p
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                      +-------------+
           +---+      |- a p x - b p
       - 2\|a p atan( |------------- )
                     \| a p x + a q
  /
      +-----+ +---+
     \|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (7)
--R          +-----+
--R         \|- a p
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                      +-------------+
--R           +---+      |- a p x - b p
--R       - 2\|a p atan( |------------- )
--R                     \| a p x + a q
--R  /
--R      +-----+ +---+
--R     \|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 8
cc3:=aa2-bb1
 

   (8)
           +-----+     +-----------+    +-----------+
       - 2\|- a p log(\|a p x + a q  + \|a p x + b p )
     + 
                            +---------------------------+
                    +-----+ |     2                          +-----+ +---+
         +---+     \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
       2\|a p atan(-------------------------------------------------------)
                                            a p x
  /
      +-----+ +---+
     \|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (8)
--R           +-----+     +-----------+    +-----------+
--R       - 2\|- a p log(\|a p x + a q  + \|a p x + b p )
--R     + 
--R                            +---------------------------+
--R                    +-----+ |     2                          +-----+ +---+
--R         +---+     \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R       2\|a p atan(-------------------------------------------------------)
--R                                            a p x
--R  /
--R      +-----+ +---+
--R     \|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 9      14:120 Axiom cannot simplify these answers
cc4:=aa2-bb2
 

   (9)
                      +---------------------------+
              +-----+ |     2                          +-----+ +---+
             \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
       2atan(-------------------------------------------------------)
                                      a p x
     + 
                +-------------+
                |- a p x - b p
       - 2atan( |------------- )
               \| a p x + a q
  /
      +-----+
     \|- a p
                                                     Type: Expression Integer
--R
--R   (9)
--R                      +---------------------------+
--R              +-----+ |     2                          +-----+ +---+
--R             \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R       2atan(-------------------------------------------------------)
--R                                      a p x
--R     + 
--R                +-------------+
--R                |- a p x - b p
--R       - 2atan( |------------- )
--R               \| a p x + a q
--R  /
--R      +-----+
--R     \|- a p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x)
 

   (1)
   [
                                 +---------------------------+
                           +---+ |     2
             (2a q + 2b p)\|b q \|a p x  + (a q + b p)x + b q
           + 
                 2 2               2 2           2     2
             (- a q  - 2a b p q - b p )x - 2a b q  - 2b p q
        *
           log
                                           +---------------------------+
                     +---+ +---+           |     2
                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
                + 
                           +---+            2                          +---+
                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
             /
                        +---------------------------+
                  +---+ |     2
                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
       + 
                                +---------------------------+
                          +---+ |     2
         (- 2a q - 2b p)x\|a p \|a p x  + (a q + b p)x + b q
       + 
                2                   +---+ +---+
         (4a p x  + (2a q + 2b p)x)\|a p \|b q
    /
                          +---------------------------+
              +---+ +---+ |     2
         4a p\|a p \|b q \|a p x  + (a q + b p)x + b q
       + 
               2            2               +---+
         ((- 2a p q - 2a b p )x - 4a b p q)\|a p
     ,

                                   +---------------------------+
                             +---+ |     2
             (- 2a q - 2b p)\|b q \|a p x  + (a q + b p)x + b q
           + 
               2 2               2 2           2     2
             (a q  + 2a b p q + b p )x + 2a b q  + 2b p q
        *
                         +---------------------------+
                 +-----+ |     2                          +-----+ +---+
                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
           atan(-------------------------------------------------------)
                                         a p x
       + 
                                +---------------------------+
                        +-----+ |     2
         (- a q - b p)x\|- a p \|a p x  + (a q + b p)x + b q
       + 
                2                 +-----+ +---+
         (2a p x  + (a q + b p)x)\|- a p \|b q
    /
                            +---------------------------+
              +-----+ +---+ |     2
         2a p\|- a p \|b q \|a p x  + (a q + b p)x + b q
       + 
              2           2               +-----+
         ((- a p q - a b p )x - 2a b p q)\|- a p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                                 +---------------------------+
--R                           +---+ |     2
--R             (2a q + 2b p)\|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R                 2 2               2 2           2     2
--R             (- a q  - 2a b p q - b p )x - 2a b q  - 2b p q
--R        *
--R           log
--R                                           +---------------------------+
--R                     +---+ +---+           |     2
--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R                + 
--R                           +---+            2                          +---+
--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R             /
--R                        +---------------------------+
--R                  +---+ |     2
--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R       + 
--R                                +---------------------------+
--R                          +---+ |     2
--R         (- 2a q - 2b p)x\|a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                2                   +---+ +---+
--R         (4a p x  + (2a q + 2b p)x)\|a p \|b q
--R    /
--R                          +---------------------------+
--R              +---+ +---+ |     2
--R         4a p\|a p \|b q \|a p x  + (a q + b p)x + b q
--R       + 
--R               2            2               +---+
--R         ((- 2a p q - 2a b p )x - 4a b p q)\|a p
--R     ,
--R
--R                                   +---------------------------+
--R                             +---+ |     2
--R             (- 2a q - 2b p)\|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R               2 2               2 2           2     2
--R             (a q  + 2a b p q + b p )x + 2a b q  + 2b p q
--R        *
--R                         +---------------------------+
--R                 +-----+ |     2                          +-----+ +---+
--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R           atan(-------------------------------------------------------)
--R                                         a p x
--R       + 
--R                                +---------------------------+
--R                        +-----+ |     2
--R         (- a q - b p)x\|- a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                2                 +-----+ +---+
--R         (2a p x  + (a q + b p)x)\|- a p \|b q
--R    /
--R                            +---------------------------+
--R              +-----+ +---+ |     2
--R         2a p\|- a p \|b q \|a p x  + (a q + b p)x + b q
--R       + 
--R              2           2               +-----+
--R         ((- a p q - a b p )x - 2a b p q)\|- a p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 11
bb1:=integrate(1/(sqrt(a*x+b)*(p*x+q)),x)
 

   (2)
                                                          +--------------+
                      2  +-------+                        |             2
        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
    log(------------------------------------------------------------------)
                                      p x + q
   [-----------------------------------------------------------------------,
                                +--------------+
                                |             2
                               \|- a p q + b p
           +------------+
           |           2  +-------+
          \|a p q - b p  \|a x + b
    2atan(-------------------------)
                  a q - b p
    --------------------------------]
              +------------+
              |           2
             \|a p q - b p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R                                                          +--------------+
--R                      2  +-------+                        |             2
--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R    log(------------------------------------------------------------------)
--R                                      p x + q
--R   [-----------------------------------------------------------------------,
--R                                +--------------+
--R                                |             2
--R                               \|- a p q + b p
--R           +------------+
--R           |           2  +-------+
--R          \|a p q - b p  \|a x + b
--R    2atan(-------------------------)
--R                  a q - b p
--R    --------------------------------]
--R              +------------+
--R              |           2
--R             \|a p q - b p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 12
bb2:=sqrt((a*x+b)*(p*x+q))/(a*p)-(b*p+a*q)/(2*a*p)
 

          +---------------------------+
          |     2
        2\|a p x  + (a q + b p)x + b q  - a q - b p
   (3)  -------------------------------------------
                            2a p
                                                     Type: Expression Integer
--R
--R          +---------------------------+
--R          |     2
--R        2\|a p x  + (a q + b p)x + b q  - a q - b p
--R   (3)  -------------------------------------------
--R                            2a p
--R                                                     Type: Expression Integer
--E

--S 13
bb:=bb2*bb1
 

   (4)
   [
            +---------------------------+
            |     2
         (2\|a p x  + (a q + b p)x + b q  - a q - b p)
      *
                                                             +--------------+
                         2  +-------+                        |             2
           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
       log(------------------------------------------------------------------)
                                         p x + q
    /
            +--------------+
            |             2
       2a p\|- a p q + b p
     ,
                                                       +------------+
       +---------------------------+                   |           2  +-------+
       |     2                                        \|a p q - b p  \|a x + b
    (2\|a p x  + (a q + b p)x + b q  - a q - b p)atan(-------------------------)
                                                              a q - b p
    ----------------------------------------------------------------------------
                                     +------------+
                                     |           2
                                 a p\|a p q - b p
     ]
                                              Type: Vector Expression Integer
--R
--R   (4)
--R   [
--R            +---------------------------+
--R            |     2
--R         (2\|a p x  + (a q + b p)x + b q  - a q - b p)
--R      *
--R                                                             +--------------+
--R                         2  +-------+                        |             2
--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R       log(------------------------------------------------------------------)
--R                                         p x + q
--R    /
--R            +--------------+
--R            |             2
--R       2a p\|- a p q + b p
--R     ,
--R                                                       +------------+
--R       +---------------------------+                   |           2  +-------+
--R       |     2                                        \|a p q - b p  \|a x + b
--R    (2\|a p x  + (a q + b p)x + b q  - a q - b p)atan(-------------------------)
--R                                                              a q - b p
--R    ----------------------------------------------------------------------------
--R                                     +------------+
--R                                     |           2
--R                                 a p\|a p q - b p
--R     ]
--R                                              Type: Vector Expression Integer
--E

--S 14     14:121 Axiom cannot simplify this answer
cc:=aa-bb
 

   (5)
   [
                              +---+ +---+                           +---+
               ((2a q + 2b p)\|a p \|b q  + ((2a q + 2b p)x + 4b q)\|a p )
            *
                +---------------------------+
                |     2
               \|a p x  + (a q + b p)x + b q
           + 
                      2                            +---+ +---+
             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|a p \|b q
           + 
                  2 2               2 2           2     2     +---+
             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|a p
        *
                                                               +--------------+
                           2  +-------+                        |             2
             (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
         log(------------------------------------------------------------------)
                                           p x + q
       + 
                           +--------------+       +---------------------------+
                           |             2  +---+ |     2
             (2a q + 2b p)\|- a p q + b p  \|b q \|a p x  + (a q + b p)x + b q
           + 
                                                              +--------------+
                  2 2               2 2           2     2     |             2
             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p q + b p
        *
           log
                                           +---------------------------+
                     +---+ +---+           |     2
                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
                + 
                           +---+            2                          +---+
                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
             /
                        +---------------------------+
                  +---+ |     2
                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
       + 
                          +--------------+       +---------------------------+
                          |             2  +---+ |     2
         (- 2a q - 2b p)x\|- a p q + b p  \|a p \|a p x  + (a q + b p)x + b q
       + 
                                    +--------------+
                2                   |             2  +---+ +---+
         (4a p x  + (2a q + 2b p)x)\|- a p q + b p  \|a p \|b q
    /
              +--------------+             +---------------------------+
              |             2  +---+ +---+ |     2
         4a p\|- a p q + b p  \|a p \|b q \|a p x  + (a q + b p)x + b q
       + 
                                            +--------------+
               2            2               |             2  +---+
         ((- 2a p q - 2a b p )x - 4a b p q)\|- a p q + b p  \|a p
     ,

                                   +------------+ +---------------------------+
                             +---+ |           2  |     2
             (- 2a q - 2b p)\|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
           + 
                                                            +------------+
                2 2               2 2           2     2     |           2
             ((a q  + 2a b p q + b p )x + 2a b q  + 2b p q)\|a p q - b p
        *
                         +---------------------------+
                 +-----+ |     2                          +-----+ +---+
                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
           atan(-------------------------------------------------------)
                                         a p x
       + 
                              +-----+ +---+                           +-----+
               ((2a q + 2b p)\|- a p \|b q  + ((2a q + 2b p)x + 4b q)\|- a p )
            *
                +---------------------------+
                |     2
               \|a p x  + (a q + b p)x + b q
           + 
                      2                            +-----+ +---+
             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|- a p \|b q
           + 
                  2 2               2 2           2     2     +-----+
             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p
        *
                 +------------+
                 |           2  +-------+
                \|a p q - b p  \|a x + b
           atan(-------------------------)
                        a q - b p
       + 
                                +------------+ +---------------------------+
                        +-----+ |           2  |     2
         (- a q - b p)x\|- a p \|a p q - b p  \|a p x  + (a q + b p)x + b q
       + 
                                                +------------+
                2                 +-----+ +---+ |           2
         (2a p x  + (a q + b p)x)\|- a p \|b q \|a p q - b p
    /
                            +------------+ +---------------------------+
              +-----+ +---+ |           2  |     2
         2a p\|- a p \|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
       + 
                                                  +------------+
              2           2               +-----+ |           2
         ((- a p q - a b p )x - 2a b p q)\|- a p \|a p q - b p
     ]
                                              Type: Vector Expression Integer
--R
--R   (5)
--R   [
--R                              +---+ +---+                           +---+
--R               ((2a q + 2b p)\|a p \|b q  + ((2a q + 2b p)x + 4b q)\|a p )
--R            *
--R                +---------------------------+
--R                |     2
--R               \|a p x  + (a q + b p)x + b q
--R           + 
--R                      2                            +---+ +---+
--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|a p \|b q
--R           + 
--R                  2 2               2 2           2     2     +---+
--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|a p
--R        *
--R                                                               +--------------+
--R                           2  +-------+                        |             2
--R             (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R         log(------------------------------------------------------------------)
--R                                           p x + q
--R       + 
--R                           +--------------+       +---------------------------+
--R                           |             2  +---+ |     2
--R             (2a q + 2b p)\|- a p q + b p  \|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R                                                              +--------------+
--R                  2 2               2 2           2     2     |             2
--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p q + b p
--R        *
--R           log
--R                                           +---------------------------+
--R                     +---+ +---+           |     2
--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R                + 
--R                           +---+            2                          +---+
--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R             /
--R                        +---------------------------+
--R                  +---+ |     2
--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R       + 
--R                          +--------------+       +---------------------------+
--R                          |             2  +---+ |     2
--R         (- 2a q - 2b p)x\|- a p q + b p  \|a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                                    +--------------+
--R                2                   |             2  +---+ +---+
--R         (4a p x  + (2a q + 2b p)x)\|- a p q + b p  \|a p \|b q
--R    /
--R              +--------------+             +---------------------------+
--R              |             2  +---+ +---+ |     2
--R         4a p\|- a p q + b p  \|a p \|b q \|a p x  + (a q + b p)x + b q
--R       + 
--R                                            +--------------+
--R               2            2               |             2  +---+
--R         ((- 2a p q - 2a b p )x - 4a b p q)\|- a p q + b p  \|a p
--R     ,
--R
--R                                   +------------+ +---------------------------+
--R                             +---+ |           2  |     2
--R             (- 2a q - 2b p)\|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
--R           + 
--R                                                            +------------+
--R                2 2               2 2           2     2     |           2
--R             ((a q  + 2a b p q + b p )x + 2a b q  + 2b p q)\|a p q - b p
--R        *
--R                         +---------------------------+
--R                 +-----+ |     2                          +-----+ +---+
--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R           atan(-------------------------------------------------------)
--R                                         a p x
--R       + 
--R                              +-----+ +---+                           +-----+
--R               ((2a q + 2b p)\|- a p \|b q  + ((2a q + 2b p)x + 4b q)\|- a p )
--R            *
--R                +---------------------------+
--R                |     2
--R               \|a p x  + (a q + b p)x + b q
--R           + 
--R                      2                            +-----+ +---+
--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|- a p \|b q
--R           + 
--R                  2 2               2 2           2     2     +-----+
--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p
--R        *
--R                 +------------+
--R                 |           2  +-------+
--R                \|a p q - b p  \|a x + b
--R           atan(-------------------------)
--R                        a q - b p
--R       + 
--R                                +------------+ +---------------------------+
--R                        +-----+ |           2  |     2
--R         (- a q - b p)x\|- a p \|a p q - b p  \|a p x  + (a q + b p)x + b q
--R       + 
--R                                                +------------+
--R                2                 +-----+ +---+ |           2
--R         (2a p x  + (a q + b p)x)\|- a p \|b q \|a p q - b p
--R    /
--R                            +------------+ +---------------------------+
--R              +-----+ +---+ |           2  |     2
--R         2a p\|- a p \|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
--R       + 
--R                                                  +------------+
--R              2           2               +-----+ |           2
--R         ((- a p q - a b p )x - 2a b p q)\|- a p \|a p q - b p
--R     ]
--R                                              Type: Vector Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(sqrt((a*x+b)*(p*x+q)),x)
 

   (1)
   [
                    3 3     2     2       2 2      3 3       2   3        2   2
                 (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
               + 
                   3 2
                 8b p q
            *
                      +---------------------------+
                +---+ |     2
               \|b q \|a p x  + (a q + b p)x + b q
           + 
                 4 4     3     3      2 2 2 2       3 3     4 4  2
             (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
           + 
                  3   4     2 2   3       3 2 2     4 3        2 2 4
             (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
           + 
                  3   3     4 2 2
             16a b p q  - 8b p q
        *
           log
                                           +---------------------------+
                     +---+ +---+           |     2
                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
                + 
                           +---+            2                          +---+
                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
             /
                        +---------------------------+
                  +---+ |     2
                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
       + 
                  3   2      2   2        2 3  3
             (- 4a p q  - 24a b p q - 4a b p )x
           + 
                  3 3      2     2        2 2      3 3  2
             (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
           + 
                  2   3        2   2     3 2
             (- 8a b q  - 48a b p q  - 8b p q)x
        *
                  +---------------------------+
            +---+ |     2
           \|a p \|a p x  + (a q + b p)x + b q
       + 
                 3 2       2   3  4       3   2      2   2         2 3  3
             (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
           + 
                3 3      2     2        2 2      3 3  2
             (6a q  + 74a b p q  + 74a b p q + 6b p )x
           + 
                2   3        2   2     3 2
             (8a b q  + 48a b p q  + 8b p q)x
        *
            +---+ +---+
           \|a p \|b q
    /
                2             2                +---+ +---+
           ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
        *
            +---------------------------+
            |     2
           \|a p x  + (a q + b p)x + b q
       + 
                  3   2      2   2        2 3  2         2     2        2 2
             (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
           + 
                    2   2
             - 64a b p q
        *
            +---+
           \|a p
     ,

                      3 3     2     2       2 2      3 3       2   3
                 (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q
               + 
                      2   2     3 2
                 16a b p q  - 8b p q
            *
                      +---------------------------+
                +---+ |     2
               \|b q \|a p x  + (a q + b p)x + b q
           + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
             (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
           + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
             (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
           + 
               4 2 2
             8b p q
        *
                         +---------------------------+
                 +-----+ |     2                          +-----+ +---+
                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
           atan(-------------------------------------------------------)
                                         a p x
       + 
                  3   2      2   2        2 3  3
             (- 2a p q  - 12a b p q - 2a b p )x
           + 
                 3 3      2     2        2 2     3 3  2
             (- a q  - 23a b p q  - 23a b p q - b p )x
           + 
                  2   3        2   2     3 2
             (- 4a b q  - 24a b p q  - 4b p q)x
        *
                    +---------------------------+
            +-----+ |     2
           \|- a p \|a p x  + (a q + b p)x + b q
       + 
                3 2      2   3  4       3   2      2   2         2 3  3
             (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
           + 
                3 3      2     2        2 2      3 3  2
             (3a q  + 37a b p q  + 37a b p q + 3b p )x
           + 
                2   3        2   2     3 2
             (4a b q  + 24a b p q  + 4b p q)x
        *
            +-----+ +---+
           \|- a p \|b q
    /
                2             2                +-----+ +---+
           ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
        *
            +---------------------------+
            |     2
           \|a p x  + (a q + b p)x + b q
       + 
                  3   2      2   2        2 3  2         2     2        2 2
             (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
           + 
                    2   2
             - 32a b p q
        *
            +-----+
           \|- a p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                    3 3     2     2       2 2      3 3       2   3        2   2
--R                 (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R               + 
--R                   3 2
--R                 8b p q
--R            *
--R                      +---------------------------+
--R                +---+ |     2
--R               \|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R                 4 4     3     3      2 2 2 2       3 3     4 4  2
--R             (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R           + 
--R                  3   4     2 2   3       3 2 2     4 3        2 2 4
--R             (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
--R           + 
--R                  3   3     4 2 2
--R             16a b p q  - 8b p q
--R        *
--R           log
--R                                           +---------------------------+
--R                     +---+ +---+           |     2
--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R                + 
--R                           +---+            2                          +---+
--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R             /
--R                        +---------------------------+
--R                  +---+ |     2
--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R       + 
--R                  3   2      2   2        2 3  3
--R             (- 4a p q  - 24a b p q - 4a b p )x
--R           + 
--R                  3 3      2     2        2 2      3 3  2
--R             (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
--R           + 
--R                  2   3        2   2     3 2
--R             (- 8a b q  - 48a b p q  - 8b p q)x
--R        *
--R                  +---------------------------+
--R            +---+ |     2
--R           \|a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                 3 2       2   3  4       3   2      2   2         2 3  3
--R             (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
--R           + 
--R                3 3      2     2        2 2      3 3  2
--R             (6a q  + 74a b p q  + 74a b p q + 6b p )x
--R           + 
--R                2   3        2   2     3 2
--R             (8a b q  + 48a b p q  + 8b p q)x
--R        *
--R            +---+ +---+
--R           \|a p \|b q
--R    /
--R                2             2                +---+ +---+
--R           ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R        *
--R            +---------------------------+
--R            |     2
--R           \|a p x  + (a q + b p)x + b q
--R       + 
--R                  3   2      2   2        2 3  2         2     2        2 2
--R             (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R           + 
--R                    2   2
--R             - 64a b p q
--R        *
--R            +---+
--R           \|a p
--R     ,
--R
--R                      3 3     2     2       2 2      3 3       2   3
--R                 (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q
--R               + 
--R                      2   2     3 2
--R                 16a b p q  - 8b p q
--R            *
--R                      +---------------------------+
--R                +---+ |     2
--R               \|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R             (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
--R           + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R             (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
--R           + 
--R               4 2 2
--R             8b p q
--R        *
--R                         +---------------------------+
--R                 +-----+ |     2                          +-----+ +---+
--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R           atan(-------------------------------------------------------)
--R                                         a p x
--R       + 
--R                  3   2      2   2        2 3  3
--R             (- 2a p q  - 12a b p q - 2a b p )x
--R           + 
--R                 3 3      2     2        2 2     3 3  2
--R             (- a q  - 23a b p q  - 23a b p q - b p )x
--R           + 
--R                  2   3        2   2     3 2
--R             (- 4a b q  - 24a b p q  - 4b p q)x
--R        *
--R                    +---------------------------+
--R            +-----+ |     2
--R           \|- a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                3 2      2   3  4       3   2      2   2         2 3  3
--R             (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
--R           + 
--R                3 3      2     2        2 2      3 3  2
--R             (3a q  + 37a b p q  + 37a b p q + 3b p )x
--R           + 
--R                2   3        2   2     3 2
--R             (4a b q  + 24a b p q  + 4b p q)x
--R        *
--R            +-----+ +---+
--R           \|- a p \|b q
--R    /
--R                2             2                +-----+ +---+
--R           ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
--R        *
--R            +---------------------------+
--R            |     2
--R           \|a p x  + (a q + b p)x + b q
--R       + 
--R                  3   2      2   2        2 3  2         2     2        2 2
--R             (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
--R           + 
--R                    2   2
--R             - 32a b p q
--R        *
--R            +-----+
--R           \|- a p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E
--S 16
aa1:=aa.1
 

   (2)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                3   2      2   2        2 3  3
           (- 4a p q  - 24a b p q - 4a b p )x
         + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
         + 
                2   3        2   2     3 2
           (- 8a b q  - 48a b p q  - 8b p q)x
      *
                +---------------------------+
          +---+ |     2
         \|a p \|a p x  + (a q + b p)x + b q
     + 
               3 2       2   3  4       3   2      2   2         2 3  3
           (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
         + 
              3 3      2     2        2 2      3 3  2
           (6a q  + 74a b p q  + 74a b p q + 6b p )x
         + 
              2   3        2   2     3 2
           (8a b q  + 48a b p q  + 8b p q)x
      *
          +---+ +---+
         \|a p \|b q
  /
              2             2                +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +---+
         \|a p
                                                     Type: Expression Integer
--R
--R   (2)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                3   2      2   2        2 3  3
--R           (- 4a p q  - 24a b p q - 4a b p )x
--R         + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
--R         + 
--R                2   3        2   2     3 2
--R           (- 8a b q  - 48a b p q  - 8b p q)x
--R      *
--R                +---------------------------+
--R          +---+ |     2
--R         \|a p \|a p x  + (a q + b p)x + b q
--R     + 
--R               3 2       2   3  4       3   2      2   2         2 3  3
--R           (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
--R         + 
--R              3 3      2     2        2 2      3 3  2
--R           (6a q  + 74a b p q  + 74a b p q + 6b p )x
--R         + 
--R              2   3        2   2     3 2
--R           (8a b q  + 48a b p q  + 8b p q)x
--R      *
--R          +---+ +---+
--R         \|a p \|b q
--R  /
--R              2             2                +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +---+
--R         \|a p
--R                                                     Type: Expression Integer
--E

--S 17
aa2:=aa.2
 

   (3)
                    3 3     2     2       2 2      3 3       2   3        2   2
               (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q  + 16a b p q
             + 
                   3 2
               - 8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
             4 4     3     3      2 2 2 2       3 3     4 4  2
           (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
         + 
              3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
         + 
             4 2 2
           8b p q
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                3   2      2   2        2 3  3
           (- 2a p q  - 12a b p q - 2a b p )x
         + 
               3 3      2     2        2 2     3 3  2
           (- a q  - 23a b p q  - 23a b p q - b p )x
         + 
                2   3        2   2     3 2
           (- 4a b q  - 24a b p q  - 4b p q)x
      *
                  +---------------------------+
          +-----+ |     2
         \|- a p \|a p x  + (a q + b p)x + b q
     + 
              3 2      2   3  4       3   2      2   2         2 3  3
           (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
         + 
              3 3      2     2        2 2      3 3  2
           (3a q  + 37a b p q  + 37a b p q + 3b p )x
         + 
              2   3        2   2     3 2
           (4a b q  + 24a b p q  + 4b p q)x
      *
          +-----+ +---+
         \|- a p \|b q
  /
              2             2                +-----+ +---+
         ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
         + 
                  2   2
           - 32a b p q
      *
          +-----+
         \|- a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                    3 3     2     2       2 2      3 3       2   3        2   2
--R               (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q  + 16a b p q
--R             + 
--R                   3 2
--R               - 8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R             4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
--R         + 
--R              3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
--R         + 
--R             4 2 2
--R           8b p q
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                3   2      2   2        2 3  3
--R           (- 2a p q  - 12a b p q - 2a b p )x
--R         + 
--R               3 3      2     2        2 2     3 3  2
--R           (- a q  - 23a b p q  - 23a b p q - b p )x
--R         + 
--R                2   3        2   2     3 2
--R           (- 4a b q  - 24a b p q  - 4b p q)x
--R      *
--R                  +---------------------------+
--R          +-----+ |     2
--R         \|- a p \|a p x  + (a q + b p)x + b q
--R     + 
--R              3 2      2   3  4       3   2      2   2         2 3  3
--R           (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
--R         + 
--R              3 3      2     2        2 2      3 3  2
--R           (3a q  + 37a b p q  + 37a b p q + 3b p )x
--R         + 
--R              2   3        2   2     3 2
--R           (4a b q  + 24a b p q  + 4b p q)x
--R      *
--R          +-----+ +---+
--R         \|- a p \|b q
--R  /
--R              2             2                +-----+ +---+
--R         ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
--R         + 
--R                  2   2
--R           - 32a b p q
--R      *
--R          +-----+
--R         \|- a p
--R                                                     Type: Expression Integer
--E
--S 18
bba:=((2*a*p*x+b*p+a*q)/(4*a*p))*sqrt((a*x+b)*(p*x+q))
 

                             +---------------------------+
                             |     2
        (2a p x + a q + b p)\|a p x  + (a q + b p)x + b q
   (4)  --------------------------------------------------
                               4a p
                                                     Type: Expression Integer
--R
--R                             +---------------------------+
--R                             |     2
--R        (2a p x + a q + b p)\|a p x  + (a q + b p)x + b q
--R   (4)  --------------------------------------------------
--R                               4a p
--R                                                     Type: Expression Integer
--E

--S 19
bbb:=-(b*p-a*q)^2/(8*a*p)
 

           2 2               2 2
        - a q  + 2a b p q - b p
   (5)  ------------------------
                  8a p
                                            Type: Fraction Polynomial Integer
--R
--R           2 2               2 2
--R        - a q  + 2a b p q - b p
--R   (5)  ------------------------
--R                  8a p
--R                                            Type: Fraction Polynomial Integer
--E

--S 20
bbc:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
 

   (6)
   [
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
    /
        +---+
       \|a p
     ,
                   +---------------------------+
           +-----+ |     2                          +-----+ +---+
          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
    2atan(-------------------------------------------------------)
                                   a p x
    --------------------------------------------------------------]
                                +-----+
                               \|- a p
                                     Type: Union(List Expression Integer,...)
--R
--R   (6)
--R   [
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R    /
--R        +---+
--R       \|a p
--R     ,
--R                   +---------------------------+
--R           +-----+ |     2                          +-----+ +---+
--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R    2atan(-------------------------------------------------------)
--R                                   a p x
--R    --------------------------------------------------------------]
--R                                +-----+
--R                               \|- a p
--R                                     Type: Union(List Expression Integer,...)
--E
--S 21
bbc1:=bbc.1
 

   (7)
     log
                                     +---------------------------+
               +---+ +---+           |     2
            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
          + 
                   +---+            2                          +---+
            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
       /
                  +---------------------------+
            +---+ |     2
          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (7)
--R     log
--R                                     +---------------------------+
--R               +---+ +---+           |     2
--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R          + 
--R                   +---+            2                          +---+
--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R       /
--R                  +---------------------------+
--R            +---+ |     2
--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 22
bbc2:=bbc.2
 

                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
        2atan(-------------------------------------------------------)
                                       a p x
   (8)  --------------------------------------------------------------
                                    +-----+
                                   \|- a p
                                                     Type: Expression Integer
--R
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R        2atan(-------------------------------------------------------)
--R                                       a p x
--R   (8)  --------------------------------------------------------------
--R                                    +-----+
--R                                   \|- a p
--R                                                     Type: Expression Integer
--E
--S 23
bb1:=bba+bbb*bbc1
 

   (9)
             2 2               2 2
         (- a q  + 2a b p q - b p )
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                                    +---------------------------+
                              +---+ |     2
       (4a p x + 2a q + 2b p)\|a p \|a p x  + (a q + b p)x + b q
  /
          +---+
     8a p\|a p
                                                     Type: Expression Integer
--R
--R   (9)
--R             2 2               2 2
--R         (- a q  + 2a b p q - b p )
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                                    +---------------------------+
--R                              +---+ |     2
--R       (4a p x + 2a q + 2b p)\|a p \|a p x  + (a q + b p)x + b q
--R  /
--R          +---+
--R     8a p\|a p
--R                                                     Type: Expression Integer
--E

--S 24
bb2:=bba+bbb*bbc2
 

   (10)
             2 2               2 2
         (- a q  + 2a b p q - b p )
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                                    +---------------------------+
                            +-----+ |     2
       (2a p x + a q + b p)\|- a p \|a p x  + (a q + b p)x + b q
  /
          +-----+
     4a p\|- a p
                                                     Type: Expression Integer
--R
--R   (10)
--R             2 2               2 2
--R         (- a q  + 2a b p q - b p )
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                                    +---------------------------+
--R                            +-----+ |     2
--R       (2a p x + a q + b p)\|- a p \|a p x  + (a q + b p)x + b q
--R  /
--R          +-----+
--R     4a p\|- a p
--R                                                     Type: Expression Integer
--E
--S 25
cc1:=aa1-bb1
 

   (11)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
             2   3        2   2     3 2           2 3      3   2  +---+
         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
         + 
                 2   3        2   2      3 2           2 3      3   2
           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
      *
          +---+ +---+
         \|a p \|b q
  /
              2             2                +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +---+
         \|a p
                                                     Type: Expression Integer
--R
--R   (11)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R             2   3        2   2     3 2           2 3      3   2  +---+
--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
--R         + 
--R                 2   3        2   2      3 2           2 3      3   2
--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
--R      *
--R          +---+ +---+
--R         \|a p \|b q
--R  /
--R              2             2                +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +---+
--R         \|a p
--R                                                     Type: Expression Integer
--E

--S 26
cc2:=aa1-bb2
 

   (12)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                            +---------------------------+
              +-----+ +---+ |     2
             \|- a p \|b q \|a p x  + (a q + b p)x + b q
         + 
                   4 4     3     3      2 2 2 2       3 3     4 4  2
               (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
             + 
                    3   4     2 2   3       3 2 2     4 3        2 2 4
               (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
             + 
                    3   3     4 2 2
               16a b p q  - 8b p q
          *
              +-----+
             \|- a p
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                  3 3     2     2       2 2      3 3        2   3        2   2
               (8a q  - 8a b p q  - 8a b p q + 8b p )x + 16a b q  - 32a b p q
             + 
                  3 2
               16b p q
          *
                          +---------------------------+
              +---+ +---+ |     2
             \|a p \|b q \|a p x  + (a q + b p)x + b q
         + 
                    4 4     3     3      2 2 2 2       3 3      4 4  2
               (- 2a q  - 8a b p q  + 20a b p q  - 8a b p q - 2b p )x
             + 
                     3   4      2 2   3        3 2 2      4 3         2 2 4
               (- 16a b q  + 16a b p q  + 16a b p q  - 16b p q)x - 16a b q
             + 
                    3   3      4 2 2
               32a b p q  - 16b p q
          *
              +---+
             \|a p
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
             2   3        2   2     3 2           2 3      3   2  +-----+ +---+
         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|- a p \|a p
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
         + 
                 2   3        2   2      3 2           2 3      3   2
           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
      *
          +-----+ +---+ +---+
         \|- a p \|a p \|b q
  /
              2             2                +-----+ +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|- a p \|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +-----+ +---+
         \|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (12)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                            +---------------------------+
--R              +-----+ +---+ |     2
--R             \|- a p \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R                   4 4     3     3      2 2 2 2       3 3     4 4  2
--R               (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R             + 
--R                    3   4     2 2   3       3 2 2     4 3        2 2 4
--R               (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
--R             + 
--R                    3   3     4 2 2
--R               16a b p q  - 8b p q
--R          *
--R              +-----+
--R             \|- a p
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                  3 3     2     2       2 2      3 3        2   3        2   2
--R               (8a q  - 8a b p q  - 8a b p q + 8b p )x + 16a b q  - 32a b p q
--R             + 
--R                  3 2
--R               16b p q
--R          *
--R                          +---------------------------+
--R              +---+ +---+ |     2
--R             \|a p \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R                    4 4     3     3      2 2 2 2       3 3      4 4  2
--R               (- 2a q  - 8a b p q  + 20a b p q  - 8a b p q - 2b p )x
--R             + 
--R                     3   4      2 2   3        3 2 2      4 3         2 2 4
--R               (- 16a b q  + 16a b p q  + 16a b p q  - 16b p q)x - 16a b q
--R             + 
--R                    3   3      4 2 2
--R               32a b p q  - 16b p q
--R          *
--R              +---+
--R             \|a p
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R             2   3        2   2     3 2           2 3      3   2  +-----+ +---+
--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|- a p \|a p
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
--R         + 
--R                 2   3        2   2      3 2           2 3      3   2
--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
--R      *
--R          +-----+ +---+ +---+
--R         \|- a p \|a p \|b q
--R  /
--R              2             2                +-----+ +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|- a p \|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +-----+ +---+
--R         \|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 27
cc3:=aa1-bb1
 

   (13)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
             2   3        2   2     3 2           2 3      3   2  +---+
         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
         + 
                 2   3        2   2      3 2           2 3      3   2
           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
      *
          +---+ +---+
         \|a p \|b q
  /
              2             2                +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +---+
         \|a p
                                                     Type: Expression Integer
--R
--R   (13)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R             2   3        2   2     3 2           2 3      3   2  +---+
--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
--R         + 
--R                 2   3        2   2      3 2           2 3      3   2
--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
--R      *
--R          +---+ +---+
--R         \|a p \|b q
--R  /
--R              2             2                +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +---+
--R         \|a p
--R                                                     Type: Expression Integer
--E

--S 28     14:122 Axiom cannot simplify this answer
cc4:=aa2-bb2
 

   (14)
             2   3       2   2     3 2          2 3     3   2
         ((4a b q  + 8a b p q  + 4b p q)x + 8a b q  + 8b p q )
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
               3 3     2     2       2 2     3 3  2
           (- a q  - 7a b p q  - 7a b p q - b p )x
         + 
                2   3        2   2     3 2          2 3     3   2
           (- 8a b q  - 16a b p q  - 8b p q)x - 8a b q  - 8b p q
      *
          +---+
         \|b q
  /
                                                 +---------------------------+
            2             2                +---+ |     2
       ((16a p q + 16a b p )x + 32a b p q)\|b q \|a p x  + (a q + b p)x + b q
     + 
            3   2      2   2        2 3  2         2     2        2 2
       (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
     + 
              2   2
       - 32a b p q
                                                     Type: Expression Integer
--R
--R   (14)
--R             2   3       2   2     3 2          2 3     3   2
--R         ((4a b q  + 8a b p q  + 4b p q)x + 8a b q  + 8b p q )
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R               3 3     2     2       2 2     3 3  2
--R           (- a q  - 7a b p q  - 7a b p q - b p )x
--R         + 
--R                2   3        2   2     3 2          2 3     3   2
--R           (- 8a b q  - 16a b p q  - 8b p q)x - 8a b q  - 8b p q
--R      *
--R          +---+
--R         \|b q
--R  /
--R                                                 +---------------------------+
--R            2             2                +---+ |     2
--R       ((16a p q + 16a b p )x + 32a b p q)\|b q \|a p x  + (a q + b p)x + b q
--R     + 
--R            3   2      2   2        2 3  2         2     2        2 2
--R       (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
--R     + 
--R              2   2
--R       - 32a b p q
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(sqrt((p*x+q)/(a*x+b)),x)
 

   (1)
   [
           (a q - b p)
        *
                                                              +-------+
                                    +---+      2              |p x + q
           log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                             \|a x + b
       + 
                     +-------+
                     |p x + q  +---+
         (2a x + 2b) |------- \|a p
                    \|a x + b
    /
          +---+
       2a\|a p
     ,
                             +-------+
                     +-----+ |p x + q
                    \|- a p  |-------                       +-------+
                            \|a x + b               +-----+ |p x + q
    (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
                             p                             \|a x + b
    -----------------------------------------------------------------]
                                  +-----+
                                a\|- a p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           (a q - b p)
--R        *
--R                                                              +-------+
--R                                    +---+      2              |p x + q
--R           log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                             \|a x + b
--R       + 
--R                     +-------+
--R                     |p x + q  +---+
--R         (2a x + 2b) |------- \|a p
--R                    \|a x + b
--R    /
--R          +---+
--R       2a\|a p
--R     ,
--R                             +-------+
--R                     +-----+ |p x + q
--R                    \|- a p  |-------                       +-------+
--R                            \|a x + b               +-----+ |p x + q
--R    (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
--R                             p                             \|a x + b
--R    -----------------------------------------------------------------]
--R                                  +-----+
--R                                a\|- a p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 30
aa1:=aa.1
 

   (2)
                                                                     +-------+
                                           +---+      2              |p x + q
       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                                    \|a x + b
     + 
                   +-------+
                   |p x + q  +---+
       (2a x + 2b) |------- \|a p
                  \|a x + b
  /
        +---+
     2a\|a p
                                                     Type: Expression Integer
--R
--R   (2)
--R                                                                     +-------+
--R                                           +---+      2              |p x + q
--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                                    \|a x + b
--R     + 
--R                   +-------+
--R                   |p x + q  +---+
--R       (2a x + 2b) |------- \|a p
--R                  \|a x + b
--R  /
--R        +---+
--R     2a\|a p
--R                                                     Type: Expression Integer
--E

--S 31
aa2:=aa.2
 

                                 +-------+
                         +-----+ |p x + q
                        \|- a p  |-------                       +-------+
                                \|a x + b               +-----+ |p x + q
        (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
                                 p                             \|a x + b
   (3)  -----------------------------------------------------------------
                                      +-----+
                                    a\|- a p
                                                     Type: Expression Integer
--R
--R                                 +-------+
--R                         +-----+ |p x + q
--R                        \|- a p  |-------                       +-------+
--R                                \|a x + b               +-----+ |p x + q
--R        (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
--R                                 p                             \|a x + b
--R   (3)  -----------------------------------------------------------------
--R                                      +-----+
--R                                    a\|- a p
--R                                                     Type: Expression Integer
--E

--S 32
bba:=sqrt((a*x+b)*(p*x+q))/a
 

         +---------------------------+
         |     2
        \|a p x  + (a q + b p)x + b q
   (4)  ------------------------------
                       a
                                                     Type: Expression Integer
--R
--R         +---------------------------+
--R         |     2
--R        \|a p x  + (a q + b p)x + b q
--R   (4)  ------------------------------
--R                       a
--R                                                     Type: Expression Integer
--E

--S 33
bbb:=(a*q-b*p)/(2*a)
 

        a q - b p
   (5)  ---------
            2a
                                            Type: Fraction Polynomial Integer
--R
--R        a q - b p
--R   (5)  ---------
--R            2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 34
bbc:=integrate(1/(sqrt((a*x+b)*(p*x+q))),x)
 

   (6)
   [
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
    /
        +---+
       \|a p
     ,
                   +---------------------------+
           +-----+ |     2                          +-----+ +---+
          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
    2atan(-------------------------------------------------------)
                                   a p x
    --------------------------------------------------------------]
                                +-----+
                               \|- a p
                                     Type: Union(List Expression Integer,...)
--R
--R   (6)
--R   [
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R    /
--R        +---+
--R       \|a p
--R     ,
--R                   +---------------------------+
--R           +-----+ |     2                          +-----+ +---+
--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R    2atan(-------------------------------------------------------)
--R                                   a p x
--R    --------------------------------------------------------------]
--R                                +-----+
--R                               \|- a p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 35
bbc1:=bbc.1
 

   (7)
     log
                                     +---------------------------+
               +---+ +---+           |     2
            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
          + 
                   +---+            2                          +---+
            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
       /
                  +---------------------------+
            +---+ |     2
          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (7)
--R     log
--R                                     +---------------------------+
--R               +---+ +---+           |     2
--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R          + 
--R                   +---+            2                          +---+
--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R       /
--R                  +---------------------------+
--R            +---+ |     2
--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 36
bbc2:=bbc.2
 

                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
        2atan(-------------------------------------------------------)
                                       a p x
   (8)  --------------------------------------------------------------
                                    +-----+
                                   \|- a p
                                                     Type: Expression Integer
--R
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R        2atan(-------------------------------------------------------)
--R                                       a p x
--R   (8)  --------------------------------------------------------------
--R                                    +-----+
--R                                   \|- a p
--R                                                     Type: Expression Integer
--E

--S 37
bb1:=bba+bbb*bbc1
 

   (9)
         (a q - b p)
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
               +---------------------------+
         +---+ |     2
       2\|a p \|a p x  + (a q + b p)x + b q
  /
        +---+
     2a\|a p
                                                     Type: Expression Integer
--R
--R   (9)
--R         (a q - b p)
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R               +---------------------------+
--R         +---+ |     2
--R       2\|a p \|a p x  + (a q + b p)x + b q
--R  /
--R        +---+
--R     2a\|a p
--R                                                     Type: Expression Integer
--E

--S 38
bb2:=bba+bbb*bbc2
 

   (10)
                                +---------------------------+
                        +-----+ |     2                          +-----+ +---+
                       \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
       (a q - b p)atan(-------------------------------------------------------)
                                                a p x
     + 
                +---------------------------+
        +-----+ |     2
       \|- a p \|a p x  + (a q + b p)x + b q
  /
       +-----+
     a\|- a p
                                                     Type: Expression Integer
--R
--R   (10)
--R                                +---------------------------+
--R                        +-----+ |     2                          +-----+ +---+
--R                       \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R       (a q - b p)atan(-------------------------------------------------------)
--R                                                a p x
--R     + 
--R                +---------------------------+
--R        +-----+ |     2
--R       \|- a p \|a p x  + (a q + b p)x + b q
--R  /
--R       +-----+
--R     a\|- a p
--R                                                     Type: Expression Integer
--E

--S 39
cc1:=aa1-bb1
 

   (11)
                                                                     +-------+
                                           +---+      2              |p x + q
       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                                    \|a x + b
     + 
         (- a q + b p)
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                 +---------------------------+               +-------+
           +---+ |     2                                     |p x + q  +---+
       - 2\|a p \|a p x  + (a q + b p)x + b q  + (2a x + 2b) |------- \|a p
                                                            \|a x + b
  /
        +---+
     2a\|a p
                                                     Type: Expression Integer
--R
--R   (11)
--R                                                                     +-------+
--R                                           +---+      2              |p x + q
--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                                    \|a x + b
--R     + 
--R         (- a q + b p)
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                 +---------------------------+               +-------+
--R           +---+ |     2                                     |p x + q  +---+
--R       - 2\|a p \|a p x  + (a q + b p)x + b q  + (2a x + 2b) |------- \|a p
--R                                                            \|a x + b
--R  /
--R        +---+
--R     2a\|a p
--R                                                     Type: Expression Integer
--E

--S 40
cc2:=aa1-bb2
 

   (12)
                     +-----+
         (a q - b p)\|- a p
      *
                                                            +-------+
                                  +---+      2              |p x + q
         log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                           \|a x + b
     + 
                         +---+
         (- 2a q + 2b p)\|a p
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                         +---------------------------+
           +-----+ +---+ |     2
       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
     + 
                           +-------+
                   +-----+ |p x + q  +---+
       (2a x + 2b)\|- a p  |------- \|a p
                          \|a x + b
  /
        +-----+ +---+
     2a\|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (12)
--R                     +-----+
--R         (a q - b p)\|- a p
--R      *
--R                                                            +-------+
--R                                  +---+      2              |p x + q
--R         log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                           \|a x + b
--R     + 
--R                         +---+
--R         (- 2a q + 2b p)\|a p
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                         +---------------------------+
--R           +-----+ +---+ |     2
--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
--R     + 
--R                           +-------+
--R                   +-----+ |p x + q  +---+
--R       (2a x + 2b)\|- a p  |------- \|a p
--R                          \|a x + b
--R  /
--R        +-----+ +---+
--R     2a\|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 41
cc3:=aa2-bb1
 

   (13)
                       +-----+
         (- a q + b p)\|- a p
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                                        +-------+
                                +-----+ |p x + q
                               \|- a p  |-------
                     +---+             \|a x + b
       (2a q - 2b p)\|a p atan(------------------)
                                        p
     + 
                         +---------------------------+
           +-----+ +---+ |     2
       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
     + 
                           +-------+
                   +-----+ |p x + q  +---+
       (2a x + 2b)\|- a p  |------- \|a p
                          \|a x + b
  /
        +-----+ +---+
     2a\|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (13)
--R                       +-----+
--R         (- a q + b p)\|- a p
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                                        +-------+
--R                                +-----+ |p x + q
--R                               \|- a p  |-------
--R                     +---+             \|a x + b
--R       (2a q - 2b p)\|a p atan(------------------)
--R                                        p
--R     + 
--R                         +---------------------------+
--R           +-----+ +---+ |     2
--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
--R     + 
--R                           +-------+
--R                   +-----+ |p x + q  +---+
--R       (2a x + 2b)\|- a p  |------- \|a p
--R                          \|a x + b
--R  /
--R        +-----+ +---+
--R     2a\|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 42     14:123 Axiom cannot simplify these results
cc4:=aa2-bb2
 

   (14)
         (- a q + b p)
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                                +-------+
                        +-----+ |p x + q
                       \|- a p  |-------
                               \|a x + b
       (a q - b p)atan(------------------)
                                p
     + 
                  +---------------------------+                     +-------+
          +-----+ |     2                                   +-----+ |p x + q
       - \|- a p \|a p x  + (a q + b p)x + b q  + (a x + b)\|- a p  |-------
                                                                   \|a x + b
  /
       +-----+
     a\|- a p
                                                     Type: Expression Integer
--R
--R   (14)
--R         (- a q + b p)
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                                +-------+
--R                        +-----+ |p x + q
--R                       \|- a p  |-------
--R                               \|a x + b
--R       (a q - b p)atan(------------------)
--R                                p
--R     + 
--R                  +---------------------------+                     +-------+
--R          +-----+ |     2                                   +-----+ |p x + q
--R       - \|- a p \|a p x  + (a q + b p)x + b q  + (a x + b)\|- a p  |-------
--R                                                                   \|a x + b
--R  /
--R       +-----+
--R     a\|- a p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 43
aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x)
 

                                 2x
   (1)  ---------------------------------------------------
          +---------------------------+
          |     2                                     +---+
        q\|a p x  + (a q + b p)x + b q  + (- p x - q)\|b q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 2x
--R   (1)  ---------------------------------------------------
--R          +---------------------------+
--R          |     2                                     +---+
--R        q\|a p x  + (a q + b p)x + b q  + (- p x - q)\|b q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 44
bb:=(2*sqrt(a*x+b))/((a*q-b*p)*sqrt(p*x+q))
 

               +-------+
             2\|a x + b
   (2)  ---------------------
                    +-------+
        (a q - b p)\|p x + q
                                                     Type: Expression Integer
--R
--R               +-------+
--R             2\|a x + b
--R   (2)  ---------------------
--R                    +-------+
--R        (a q - b p)\|p x + q
--R                                                     Type: Expression Integer
--E

--S 45     14:124 Axiom cannot simplify this result
cc:=aa-bb
 

   (3)
                      +---------------------------+
            +-------+ |     2                                        +-------+
       - 2q\|a x + b \|a p x  + (a q + b p)x + b q  + (2a q - 2b p)x\|p x + q
     + 
                   +---+ +-------+
       (2p x + 2q)\|b q \|a x + b
  /
                                +---------------------------+
           2          +-------+ |     2
       (a q  - b p q)\|p x + q \|a p x  + (a q + b p)x + b q
     + 
                      2        2          +---+ +-------+
       ((- a p q + b p )x - a q  + b p q)\|b q \|p x + q
                                                     Type: Expression Integer
--R
--R   (3)
--R                      +---------------------------+
--R            +-------+ |     2                                        +-------+
--R       - 2q\|a x + b \|a p x  + (a q + b p)x + b q  + (2a q - 2b p)x\|p x + q
--R     + 
--R                   +---+ +-------+
--R       (2p x + 2q)\|b q \|a x + b
--R  /
--R                                +---------------------------+
--R           2          +-------+ |     2
--R       (a q  - b p q)\|p x + q \|a p x  + (a q + b p)x + b q
--R     + 
--R                      2        2          +---+ +-------+
--R       ((- a p q + b p )x - a q  + b p q)\|b q \|p x + q
--R                                                     Type: Expression Integer
--E


)spool
 
Starts dribbling to intmix.output (2009/2/17, 17:46:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
(x + 1) / (x * (x + log x)**(3/2)) - 1/(x * log(x)**2)
 

                       +----------+                2
        (- log(x) - x)\|log(x) + x  + (x + 1)log(x)
   (1)  --------------------------------------------
                     3    2      2  +----------+
            (x log(x)  + x log(x) )\|log(x) + x
                                                     Type: Expression Integer
--R 
--R
--R                       +----------+                2
--R        (- log(x) - x)\|log(x) + x  + (x + 1)log(x)
--R   (1)  --------------------------------------------
--R                     3    2      2  +----------+
--R            (x log(x)  + x log(x) )\|log(x) + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 6
integrate(%, x)
 

                  +----------+
        - 2log(x)\|log(x) + x  + log(x) + x
   (2)  -----------------------------------
                       2
                 log(x)  + x log(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +----------+
--R        - 2log(x)\|log(x) + x  + log(x) + x
--R   (2)  -----------------------------------
--R                       2
--R                 log(x)  + x log(x)
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 6
((5*x**4+2*x-2)/x**2 * (1+1/sqrt(x**3+1))+x/sqrt(x**3+1)) * exp(x*sqrt(x**3+1))
 

                                                         +------+
                        +------+                         | 3
            4           | 3          4    3            x\|x  + 1
        ((5x  + 2x - 2)\|x  + 1  + 5x  + x  + 2x - 2)%e
   (3)  ---------------------------------------------------------
                                  +------+
                                2 | 3
                               x \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                                                         +------+
--R                        +------+                         | 3
--R            4           | 3          4    3            x\|x  + 1
--R        ((5x  + 2x - 2)\|x  + 1  + 5x  + x  + 2x - 2)%e
--R   (3)  ---------------------------------------------------------
--R                                  +------+
--R                                2 | 3
--R                               x \|x  + 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 6
integrate(%, x)
 

                            +------+
           +------+         | 3
           | 3            x\|x  + 1
        (2\|x  + 1  + 2)%e
   (4)  ----------------------------
                      x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            +------+
--R           +------+         | 3
--R           | 3            x\|x  + 1
--R        (2\|x  + 1  + 2)%e
--R   (4)  ----------------------------
--R                      x
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 6
log(1 + exp x)**(1/3) / (1 + log(1 + exp x))
 

          +------------+
         3|      x
         \|log(%e  + 1)
   (5)  ----------------
              x
        log(%e  + 1) + 1
                                                     Type: Expression Integer
--R 
--R
--R          +------------+
--R         3|      x
--R         \|log(%e  + 1)
--R   (5)  ----------------
--R              x
--R        log(%e  + 1) + 1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 6
integrate(%, x)
 

               +-------------+
           x  3|      %T
         ++   \|log(%e   + 1)
   (6)   |   ----------------- d%T
        ++         %T
             log(%e   + 1) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------------+
--R           x  3|      %T
--R         ++   \|log(%e   + 1)
--R   (6)   |   ----------------- d%T
--R        ++         %T
--R             log(%e   + 1) + 1
--R                                          Type: Union(Expression Integer,...)
--E 6
)spool 
 
Starts dribbling to schaum11.output (2009/2/17, 17:58:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(sqrt(a^2-x^2)),x)
 

                 +---------+
                 |   2    2
                \|- x  + a   - a
   (1)  - 2atan(----------------)
                        x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   - a
--R   (1)  - 2atan(----------------)
--R                        x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=asin(x/a)
 

             x
   (2)  asin(-)
             a
                                                     Type: Expression Integer
--R
--R             x
--R   (2)  asin(-)
--R             a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                 +---------+
                 |   2    2
                \|- x  + a   - a         x
   (3)  - 2atan(----------------) - asin(-)
                        x                a
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   - a         x
--R   (3)  - 2atan(----------------) - asin(-)
--R                        x                a
--R                                                     Type: Expression Integer
--E

--S 4
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 5
dd:=atanrule cc
 

                  +---------+
                  |   2    2
               - \|- x  + a   + %i x + a         x
   (5)  %i log(-------------------------) - asin(-)
                 +---------+                     a
                 |   2    2
                \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                  +---------+
--R                  |   2    2
--R               - \|- x  + a   + %i x + a         x
--R   (5)  %i log(-------------------------) - asin(-)
--R                 +---------+                     a
--R                 |   2    2
--R                \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 6
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 7
ee:=asinrule dd
 

                   +---------+
                   |   2    2
                   |- x  + a
                 a |---------  - %i x              +---------+
                   |     2                         |   2    2
                  \|    a                       - \|- x  + a   + %i x + a
   (7)  - %i log(--------------------) + %i log(-------------------------)
                           a                      +---------+
                                                  |   2    2
                                                 \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                   +---------+
--R                   |   2    2
--R                   |- x  + a
--R                 a |---------  - %i x              +---------+
--R                   |     2                         |   2    2
--R                  \|    a                       - \|- x  + a   + %i x + a
--R   (7)  - %i log(--------------------) + %i log(-------------------------)
--R                           a                      +---------+
--R                                                  |   2    2
--R                                                 \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 8
ff:=rootSimp ee
 

                    +-------+                     +-------+
                    | 2    2                      | 2    2
                 %i\|x  - a   - %i x           - \|x  - a   + x - %i a
   (8)  - %i log(-------------------) + %i log(-----------------------)
                          a                      +-------+
                                                 | 2    2
                                                \|x  - a   + x + %i a
                                             Type: Expression Complex Integer
--R
--R                    +-------+                     +-------+
--R                    | 2    2                      | 2    2
--R                 %i\|x  - a   - %i x           - \|x  - a   + x - %i a
--R   (8)  - %i log(-------------------) + %i log(-----------------------)
--R                          a                      +-------+
--R                                                 | 2    2
--R                                                \|x  - a   + x + %i a
--R                                             Type: Expression Complex Integer
--E

--S 9      14:238 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (9)  0
                                             Type: Expression Complex Integer
--R
--R   (9)  0
--R                                             Type: Expression Complex Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(x/(sqrt(a^2-x^2)),x)
 

                2
               x
   (1)  ----------------
         +---------+
         |   2    2
        \|- x  + a   - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R               x
--R   (1)  ----------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a   - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=-sqrt(a^2-x^2)
 

           +---------+
           |   2    2
   (2)  - \|- x  + a
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2
--R   (2)  - \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 12     14:238 Schaums and Axiom differ by a constant
cc:=aa-bb
 

   (3)  - a
                                                     Type: Expression Integer
--R
--R   (3)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(x^2/sqrt(a^2-x^2),x)
 

   (1)
                                              +---------+
              +---------+                     |   2    2
            3 |   2    2      2 2     4      \|- x  + a   - a
       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
                                                     x
     + 
                     +---------+
           3     2   |   2    2        3     3
       (- x  + 2a x)\|- x  + a   + 2a x  - 2a x
  /
        +---------+
        |   2    2      2     2
     4a\|- x  + a   + 2x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                              +---------+
--R              +---------+                     |   2    2
--R            3 |   2    2      2 2     4      \|- x  + a   - a
--R       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
--R                                                     x
--R     + 
--R                     +---------+
--R           3     2   |   2    2        3     3
--R       (- x  + 2a x)\|- x  + a   + 2a x  - 2a x
--R  /
--R        +---------+
--R        |   2    2      2     2
--R     4a\|- x  + a   + 2x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
 

            +---------+
            |   2    2     2     x
        - x\|- x  + a   + a asin(-)
                                 a
   (2)  ---------------------------
                     2
                                                     Type: Expression Integer
--R
--R            +---------+
--R            |   2    2     2     x
--R        - x\|- x  + a   + a asin(-)
--R                                 a
--R   (2)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 15
cc:=aa-bb
 

                   +---------+
                   |   2    2
            2     \|- x  + a   - a     2     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            2     \|- x  + a   - a     2     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 16
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 17
dd:=atanrule cc
 

                    +---------+
                    |   2    2
            2    - \|- x  + a   + %i x + a     2     x
        %i a log(-------------------------) - a asin(-)
                   +---------+                       a
                   |   2    2
                  \|- x  + a   + %i x - a
   (5)  -----------------------------------------------
                               2
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R            2    - \|- x  + a   + %i x + a     2     x
--R        %i a log(-------------------------) - a asin(-)
--R                   +---------+                       a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R   (5)  -----------------------------------------------
--R                               2
--R                                             Type: Expression Complex Integer
--E

--S 18
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 19
ee:=asinrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              2     \|    a                    2    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           2
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              2     \|    a                    2    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           2
--R                                             Type: Expression Complex Integer
--E

--S 20
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             2      |- x  + a                 2     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           2     |   2    2                    2             2
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             2      |- x  + a                 2     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           2     |   2    2                    2             2
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 21
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             2       | 2    2                    2       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           2       | 2    2                    2             2
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             2       | 2    2                    2       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           2       | 2    2                    2             2
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 22     14:239 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(x^3/sqrt(a^2-x^2),x)
 

                   +---------+
                 4 |   2    2     6     2 4
             3a x \|- x  + a   + x  - 3a x
   (1)  ---------------------------------------
                     +---------+
           2      2  |   2    2        2      3
        (3x  - 12a )\|- x  + a   - 9a x  + 12a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +---------+
--R                 4 |   2    2     6     2 4
--R             3a x \|- x  + a   + x  - 3a x
--R   (1)  ---------------------------------------
--R                     +---------+
--R           2      2  |   2    2        2      3
--R        (3x  - 12a )\|- x  + a   - 9a x  + 12a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2)
 

                     +---------+
            2     2  |   2    2
        (- x  - 2a )\|- x  + a
   (2)  ------------------------
                    3
                                                     Type: Expression Integer
--R
--R                     +---------+
--R            2     2  |   2    2
--R        (- x  - 2a )\|- x  + a
--R   (2)  ------------------------
--R                    3
--R                                                     Type: Expression Integer
--E

--S 25     14:240 Schaums and Axiom differ by a constant
cc:=aa-bb
 

            3
          2a
   (3)  - ---
           3
                                                     Type: Expression Integer
--R
--R            3
--R          2a
--R   (3)  - ---
--R           3
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 26
aa:=integrate(1/(x*sqrt(a^2-x^2)),x)
 

             +---------+
             |   2    2
            \|- x  + a   - a
        log(----------------)
                    x
   (1)  ---------------------
                  a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +---------+
--R             |   2    2
--R            \|- x  + a   - a
--R        log(----------------)
--R                    x
--R   (1)  ---------------------
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27
bb:=-1/a*log((a+sqrt(a^2-x^2))/x)
 

               +---------+
               |   2    2
              \|- x  + a   + a
          log(----------------)
                      x
   (2)  - ---------------------
                    a
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   + a
--R          log(----------------)
--R                      x
--R   (2)  - ---------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 28
cc:=aa-bb
 

             +---------+             +---------+
             |   2    2              |   2    2
            \|- x  + a   + a        \|- x  + a   - a
        log(----------------) + log(----------------)
                    x                       x
   (3)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R            \|- x  + a   + a        \|- x  + a   - a
--R        log(----------------) + log(----------------)
--R                    x                       x
--R   (3)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 29
dd:=expandLog cc
 

             +---------+             +---------+
             |   2    2              |   2    2
        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
   (4)  -------------------------------------------------------
                                   a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
--R   (4)  -------------------------------------------------------
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 30
ee:=complexNormalize dd
 

                  x
          2log(-------)
                +----+
                |   2
               \|- x
   (5)  - -------------
                a
                                                     Type: Expression Integer
--R
--R                  x
--R          2log(-------)
--R                +----+
--R                |   2
--R               \|- x
--R   (5)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 31     14:241 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

              +---+
        2log(\|- 1 )
   (6)  ------------
              a
                                                     Type: Expression Integer
--R
--R              +---+
--R        2log(\|- 1 )
--R   (6)  ------------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x)
 

          +---------+
          |   2    2     2    2
        a\|- x  + a   + x  - a
   (1)  -----------------------
             +---------+
          2  |   2    2     3
         a x\|- x  + a   - a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +---------+
--R          |   2    2     2    2
--R        a\|- x  + a   + x  - a
--R   (1)  -----------------------
--R             +---------+
--R          2  |   2    2     3
--R         a x\|- x  + a   - a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33
bb:=-sqrt(a^2-x^2)/(a^2*x)
 

           +---------+
           |   2    2
          \|- x  + a
   (2)  - ------------
                2
               a x
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2
--R          \|- x  + a
--R   (2)  - ------------
--R                2
--R               a x
--R                                                     Type: Expression Integer
--E

--S 34     14:242 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 35
aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x)
 

   (1)
                                            +---------+
              +---------+                   |   2    2
            2 |   2    2     4     2 2     \|- x  + a   - a
       (2a x \|- x  + a   + x  - 2a x )log(----------------)
                                                   x
     + 
                      +---------+
             2     3  |   2    2      2 2     4
       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
  /
           +---------+
       4 2 |   2    2      3 4     5 2
     4a x \|- x  + a   + 2a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                            +---------+
--R              +---------+                   |   2    2
--R            2 |   2    2     4     2 2     \|- x  + a   - a
--R       (2a x \|- x  + a   + x  - 2a x )log(----------------)
--R                                                   x
--R     + 
--R                      +---------+
--R             2     3  |   2    2      2 2     4
--R       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
--R  /
--R           +---------+
--R       4 2 |   2    2      3 4     5 2
--R     4a x \|- x  + a   + 2a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36
bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x)
 

                 +---------+
                 |   2    2           +---------+
           2    \|- x  + a   + a      |   2    2
        - x log(----------------) - a\|- x  + a
                        x
   (2)  -----------------------------------------
                            3 2
                          2a x
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2           +---------+
--R           2    \|- x  + a   + a      |   2    2
--R        - x log(----------------) - a\|- x  + a
--R                        x
--R   (2)  -----------------------------------------
--R                            3 2
--R                          2a x
--R                                                     Type: Expression Integer
--E

--S 37
cc:=aa-bb
 

             +---------+             +---------+
             |   2    2              |   2    2
            \|- x  + a   + a        \|- x  + a   - a
        log(----------------) + log(----------------)
                    x                       x
   (3)  ---------------------------------------------
                               3
                             2a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R            \|- x  + a   + a        \|- x  + a   - a
--R        log(----------------) + log(----------------)
--R                    x                       x
--R   (3)  ---------------------------------------------
--R                               3
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 38
dd:=expandLog cc
 

             +---------+             +---------+
             |   2    2              |   2    2
        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
   (4)  -------------------------------------------------------
                                    3
                                  2a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
--R   (4)  -------------------------------------------------------
--R                                    3
--R                                  2a
--R                                                     Type: Expression Integer
--E

--S 39
ee:=complexNormalize dd
 

                 x
          log(-------)
               +----+
               |   2
              \|- x
   (5)  - ------------
                3
               a
                                                     Type: Expression Integer
--R
--R                 x
--R          log(-------)
--R               +----+
--R               |   2
--R              \|- x
--R   (5)  - ------------
--R                3
--R               a
--R                                                     Type: Expression Integer
--E 

--S 40     14:243 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

             +---+
        log(\|- 1 )
   (6)  -----------
              3
             a
                                                     Type: Expression Integer
--R
--R             +---+
--R        log(\|- 1 )
--R   (6)  -----------
--R              3
--R             a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 41
aa:=integrate(sqrt(a^2-x^2),x)
 

   (1)
                                              +---------+
              +---------+                     |   2    2
            3 |   2    2      2 2     4      \|- x  + a   - a
       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
                                                     x
     + 
                   +---------+
         3     2   |   2    2        3     3
       (x  - 2a x)\|- x  + a   - 2a x  + 2a x
  /
        +---------+
        |   2    2      2     2
     4a\|- x  + a   + 2x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                              +---------+
--R              +---------+                     |   2    2
--R            3 |   2    2      2 2     4      \|- x  + a   - a
--R       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
--R                                                     x
--R     + 
--R                   +---------+
--R         3     2   |   2    2        3     3
--R       (x  - 2a x)\|- x  + a   - 2a x  + 2a x
--R  /
--R        +---------+
--R        |   2    2      2     2
--R     4a\|- x  + a   + 2x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42
bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
 

          +---------+
          |   2    2     2     x
        x\|- x  + a   + a asin(-)
                               a
   (2)  -------------------------
                    2
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2     2     x
--R        x\|- x  + a   + a asin(-)
--R                               a
--R   (2)  -------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 43
cc:=aa-bb
 

                   +---------+
                   |   2    2
            2     \|- x  + a   - a     2     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            2     \|- x  + a   - a     2     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 44
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 45
dd:=asinrule cc
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x             +---------+
                     |     2                        |   2    2
              2     \|    a                  2     \|- x  + a   - a
        - %i a log(--------------------) - 2a atan(----------------)
                             a                             x
   (5)  ------------------------------------------------------------
                                      2
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x             +---------+
--R                     |     2                        |   2    2
--R              2     \|    a                  2     \|- x  + a   - a
--R        - %i a log(--------------------) - 2a atan(----------------)
--R                             a                             x
--R   (5)  ------------------------------------------------------------
--R                                      2
--R                                             Type: Expression Complex Integer
--E

--S 46
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 47
ee:=atanrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              2     \|    a                    2    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           2
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              2     \|    a                    2    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           2
--R                                             Type: Expression Complex Integer
--E

--S 48
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             2      |- x  + a                 2     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           2     |   2    2                    2             2
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             2      |- x  + a                 2     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           2     |   2    2                    2             2
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 49
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             2       | 2    2                    2       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           2       | 2    2                    2             2
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             2       | 2    2                    2       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           2       | 2    2                    2             2
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 50     14:244 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 51
aa:=integrate(x*sqrt(a^2-x^2),x)
 

                          +---------+
               4     3 2  |   2    2     6     2 4     4 2
        (- 3a x  + 6a x )\|- x  + a   - x  + 6a x  - 6a x
   (1)  --------------------------------------------------
                           +---------+
                 2      2  |   2    2        2      3
              (3x  - 12a )\|- x  + a   - 9a x  + 12a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +---------+
--R               4     3 2  |   2    2     6     2 4     4 2
--R        (- 3a x  + 6a x )\|- x  + a   - x  + 6a x  - 6a x
--R   (1)  --------------------------------------------------
--R                           +---------+
--R                 2      2  |   2    2        2      3
--R              (3x  - 12a )\|- x  + a   - 9a x  + 12a
--R                                          Type: Union(Expression Integer,...)
--E

--S 52
bb:=-(a^2-x^2)^(3/2)/3
 

                  +---------+
          2    2  |   2    2
        (x  - a )\|- x  + a
   (2)  ---------------------
                  3
                                                     Type: Expression Integer
--R
--R                  +---------+
--R          2    2  |   2    2
--R        (x  - a )\|- x  + a
--R   (2)  ---------------------
--R                  3
--R                                                     Type: Expression Integer
--E

--S 53     14:245 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           3
          a
   (3)  - --
           3
                                                     Type: Expression Integer
--R
--R           3
--R          a
--R   (3)  - --
--R           3
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 54
aa:=integrate(x^2*sqrt(a^2-x^2),x)
 

   (1)
                           +---------+
               5 2      7  |   2    2      4 4      6 2      8
         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                    +---------+
        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
  /
                     +---------+
           2      3  |   2    2      4      2 2      4
     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +---------+
--R               5 2      7  |   2    2      4 4      6 2      8
--R         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                    +---------+
--R        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
--R     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
--R  /
--R                     +---------+
--R           2      3  |   2    2      4      2 2      4
--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 55
bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a)
 

                    +---------+
           3    2   |   2    2     4     x
        (2x  - a x)\|- x  + a   + a asin(-)
                                         a
   (2)  -----------------------------------
                         8
                                                     Type: Expression Integer
--R
--R                    +---------+
--R           3    2   |   2    2     4     x
--R        (2x  - a x)\|- x  + a   + a asin(-)
--R                                         a
--R   (2)  -----------------------------------
--R                         8
--R                                                     Type: Expression Integer
--E

--S 56
cc:=aa-bb
 

                   +---------+
                   |   2    2
            4     \|- x  + a   - a     4     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           8
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            4     \|- x  + a   - a     4     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           8
--R                                                     Type: Expression Integer
--E

--S 57
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 58
dd:=atanrule cc
 

                    +---------+
                    |   2    2
            4    - \|- x  + a   + %i x + a     4     x
        %i a log(-------------------------) - a asin(-)
                   +---------+                       a
                   |   2    2
                  \|- x  + a   + %i x - a
   (5)  -----------------------------------------------
                               8
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R            4    - \|- x  + a   + %i x + a     4     x
--R        %i a log(-------------------------) - a asin(-)
--R                   +---------+                       a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R   (5)  -----------------------------------------------
--R                               8
--R                                             Type: Expression Complex Integer
--E

--S 59
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 60
ee:=asinrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              4     \|    a                    4    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           8
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              4     \|    a                    4    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           8
--R                                             Type: Expression Complex Integer
--E

--S 61
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             4      |- x  + a                 4     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           4     |   2    2                    4             4
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             4      |- x  + a                 4     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           4     |   2    2                    4             4
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 62
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             4       | 2    2                    4       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           4       | 2    2                    4             4
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             4       | 2    2                    4       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           4       | 2    2                    4             4
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 63     14:246 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 64
aa:=integrate(x^3*sqrt(a^2-x^2),x)
 

   (1)
                                +---------+
           8      3 6      5 4  |   2    2      10      2 8      4 6      6 4
   (- 15a x  + 65a x  - 60a x )\|- x  + a   - 3x   + 40a x  - 95a x  + 60a x
   --------------------------------------------------------------------------
                                  +---------+
             4       2 2       4  |   2    2         4       3 2       5
         (15x  - 180a x  + 240a )\|- x  + a   - 75a x  + 300a x  - 240a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                +---------+
--R           8      3 6      5 4  |   2    2      10      2 8      4 6      6 4
--R   (- 15a x  + 65a x  - 60a x )\|- x  + a   - 3x   + 40a x  - 95a x  + 60a x
--R   --------------------------------------------------------------------------
--R                                  +---------+
--R             4       2 2       4  |   2    2         4       3 2       5
--R         (15x  - 180a x  + 240a )\|- x  + a   - 75a x  + 300a x  - 240a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 65
bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3
 

                           +---------+
           4    2 2     4  |   2    2
        (3x  - a x  - 2a )\|- x  + a
   (2)  ------------------------------
                      15
                                                     Type: Expression Integer
--R
--R                           +---------+
--R           4    2 2     4  |   2    2
--R        (3x  - a x  - 2a )\|- x  + a
--R   (2)  ------------------------------
--R                      15
--R                                                     Type: Expression Integer
--E 

--S 66     14:247 Schaums and Axiom differ by a constant
cc:=aa-bb
 

            5
          2a
   (3)  - ---
           15
                                                     Type: Expression Integer
--R
--R            5
--R          2a
--R   (3)  - ---
--R           15
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 67
aa:=integrate(sqrt(a^2-x^2)/x,x)
 

                                 +---------+
           +---------+           |   2    2
           |   2    2     2     \|- x  + a   - a     2
        (a\|- x  + a   - a )log(----------------) - x
                                        x
   (1)  ----------------------------------------------
                        +---------+
                        |   2    2
                       \|- x  + a   - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 +---------+
--R           +---------+           |   2    2
--R           |   2    2     2     \|- x  + a   - a     2
--R        (a\|- x  + a   - a )log(----------------) - x
--R                                        x
--R   (1)  ----------------------------------------------
--R                        +---------+
--R                        |   2    2
--R                       \|- x  + a   - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68
bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x)
 

                 +---------+
                 |   2    2          +---------+
                \|- x  + a   + a     |   2    2
   (2)  - a log(----------------) + \|- x  + a
                        x
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2          +---------+
--R                \|- x  + a   + a     |   2    2
--R   (2)  - a log(----------------) + \|- x  + a
--R                        x
--R                                                     Type: Expression Integer
--E

--S 69
cc:=aa-bb
 

               +---------+               +---------+
               |   2    2                |   2    2
              \|- x  + a   + a          \|- x  + a   - a
   (3)  a log(----------------) + a log(----------------) + a
                      x                         x
                                                     Type: Expression Integer
--R
--R               +---------+               +---------+
--R               |   2    2                |   2    2
--R              \|- x  + a   + a          \|- x  + a   - a
--R   (3)  a log(----------------) + a log(----------------) + a
--R                      x                         x
--R                                                     Type: Expression Integer
--E

--S 70
dd:=expandLog cc
 

               +---------+               +---------+
               |   2    2                |   2    2
   (4)  a log(\|- x  + a   + a) + a log(\|- x  + a   - a) - 2a log(x) + a
                                                     Type: Expression Integer
--R
--R               +---------+               +---------+
--R               |   2    2                |   2    2
--R   (4)  a log(\|- x  + a   + a) + a log(\|- x  + a   - a) - 2a log(x) + a
--R                                                     Type: Expression Integer
--E

--S 71
ee:=complexNormalize dd
 

                    x
   (5)  - 2a log(-------) + a
                  +----+
                  |   2
                 \|- x
                                                     Type: Expression Integer
--R
--R                    x
--R   (5)  - 2a log(-------) + a
--R                  +----+
--R                  |   2
--R                 \|- x
--R                                                     Type: Expression Integer
--E

--S 72     14:248 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

                +---+
   (6)  2a log(\|- 1 ) + a
                                                     Type: Expression Integer
--R
--R                +---+
--R   (6)  2a log(\|- 1 ) + a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 73
aa:=integrate(sqrt(a^2-x^2)/x^2,x)
 

   (1)
                                +---------+
       +---------+              |   2    2           +---------+
       |   2    2              \|- x  + a   - a      |   2    2     2    2
   (2x\|- x  + a   - 2a x)atan(----------------) + a\|- x  + a   + x  - a
                                       x
   -----------------------------------------------------------------------
                               +---------+
                               |   2    2
                             x\|- x  + a   - a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                +---------+
--R       +---------+              |   2    2           +---------+
--R       |   2    2              \|- x  + a   - a      |   2    2     2    2
--R   (2x\|- x  + a   - 2a x)atan(----------------) + a\|- x  + a   + x  - a
--R                                       x
--R   -----------------------------------------------------------------------
--R                               +---------+
--R                               |   2    2
--R                             x\|- x  + a   - a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 74
bb:=-sqrt(a^2-x^2)/x-asin(x/a)
 

           +---------+
           |   2    2           x
        - \|- x  + a   - x asin(-)
                                a
   (2)  --------------------------
                     x
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2           x
--R        - \|- x  + a   - x asin(-)
--R                                a
--R   (2)  --------------------------
--R                     x
--R                                                     Type: Expression Integer
--E

--S 75
cc:=aa-bb
 

               +---------+
               |   2    2
              \|- x  + a   - a         x
   (3)  2atan(----------------) + asin(-)
                      x                a
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a         x
--R   (3)  2atan(----------------) + asin(-)
--R                      x                a
--R                                                     Type: Expression Integer
--E

--S 76
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 77
dd:=asinrule cc
 

                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x           +---------+
                 |     2                      |   2    2
                \|    a                      \|- x  + a   - a
   (5)  %i log(--------------------) + 2atan(----------------)
                         a                           x
                                             Type: Expression Complex Integer
--R
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x           +---------+
--R                 |     2                      |   2    2
--R                \|    a                      \|- x  + a   - a
--R   (5)  %i log(--------------------) + 2atan(----------------)
--R                         a                           x
--R                                             Type: Expression Complex Integer
--E

--S 78
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 79
ee:=atanrule dd
 

                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x              +---------+
                 |     2                         |   2    2
                \|    a                       - \|- x  + a   + %i x + a
   (7)  %i log(--------------------) - %i log(-------------------------)
                         a                      +---------+
                                                |   2    2
                                               \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x              +---------+
--R                 |     2                         |   2    2
--R                \|    a                       - \|- x  + a   + %i x + a
--R   (7)  %i log(--------------------) - %i log(-------------------------)
--R                         a                      +---------+
--R                                                |   2    2
--R                                               \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 80
ff:=expandLog ee
 

   (8)
              +---------+
              |   2    2                    +---------+
              |- x  + a                     |   2    2
     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
              |     2
             \|    a
   + 
               +---------+
               |   2    2
     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (8)
--R              +---------+
--R              |   2    2                    +---------+
--R              |- x  + a                     |   2    2
--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
--R              |     2
--R             \|    a
--R   + 
--R               +---------+
--R               |   2    2
--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 81
gg:=rootSimp ff
 

   (9)
               +-------+                         +-------+
               | 2    2                          | 2    2
     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +-------+                         +-------+
--R               | 2    2                          | 2    2
--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 82     14:249 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 83
aa:=integrate(sqrt(a^2-x^2)/x^3,x)
 

   (1)
                                              +---------+
                +---------+                   |   2    2
              2 |   2    2     4     2 2     \|- x  + a   - a
       (- 2a x \|- x  + a   - x  + 2a x )log(----------------)
                                                     x
     + 
                      +---------+
             2     3  |   2    2      2 2     4
       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
  /
           +---------+
       2 2 |   2    2        4     3 2
     4a x \|- x  + a   + 2a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                              +---------+
--R                +---------+                   |   2    2
--R              2 |   2    2     4     2 2     \|- x  + a   - a
--R       (- 2a x \|- x  + a   - x  + 2a x )log(----------------)
--R                                                     x
--R     + 
--R                      +---------+
--R             2     3  |   2    2      2 2     4
--R       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
--R  /
--R           +---------+
--R       2 2 |   2    2        4     3 2
--R     4a x \|- x  + a   + 2a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84
bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x)
 

               +---------+
               |   2    2           +---------+
         2    \|- x  + a   + a      |   2    2
        x log(----------------) - a\|- x  + a
                      x
   (2)  ---------------------------------------
                             2
                         2a x
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2           +---------+
--R         2    \|- x  + a   + a      |   2    2
--R        x log(----------------) - a\|- x  + a
--R                      x
--R   (2)  ---------------------------------------
--R                             2
--R                         2a x
--R                                                     Type: Expression Integer
--E

--S 85
cc:=aa-bb
 

               +---------+             +---------+
               |   2    2              |   2    2
              \|- x  + a   + a        \|- x  + a   - a
        - log(----------------) - log(----------------)
                      x                       x
   (3)  -----------------------------------------------
                               2a
                                                     Type: Expression Integer
--R
--R               +---------+             +---------+
--R               |   2    2              |   2    2
--R              \|- x  + a   + a        \|- x  + a   - a
--R        - log(----------------) - log(----------------)
--R                      x                       x
--R   (3)  -----------------------------------------------
--R                               2a
--R                                                     Type: Expression Integer
--E

--S 86
dd:=expandLog cc
 

               +---------+             +---------+
               |   2    2              |   2    2
        - log(\|- x  + a   + a) - log(\|- x  + a   - a) + 2log(x)
   (4)  ---------------------------------------------------------
                                    2a
                                                     Type: Expression Integer
--R
--R               +---------+             +---------+
--R               |   2    2              |   2    2
--R        - log(\|- x  + a   + a) - log(\|- x  + a   - a) + 2log(x)
--R   (4)  ---------------------------------------------------------
--R                                    2a
--R                                                     Type: Expression Integer
--E

--S 87
ee:=complexNormalize dd
 

               x
        log(-------)
             +----+
             |   2
            \|- x
   (5)  ------------
              a
                                                     Type: Expression Integer
--R
--R               x
--R        log(-------)
--R             +----+
--R             |   2
--R            \|- x
--R   (5)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 88     14:250 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

               +---+
          log(\|- 1 )
   (6)  - -----------
               a
                                                     Type: Expression Integer
--R
--R               +---+
--R          log(\|- 1 )
--R   (6)  - -----------
--R               a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 89
aa:=integrate(1/(a^2-x^2)^(3/2),x)
 

               +---------+
               |   2    2
           - x\|- x  + a   + a x
   (1)  --------------------------
           +---------+
         3 |   2    2     2 2    4
        a \|- x  + a   + a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +---------+
--R               |   2    2
--R           - x\|- x  + a   + a x
--R   (1)  --------------------------
--R           +---------+
--R         3 |   2    2     2 2    4
--R        a \|- x  + a   + a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 90
bb:=x/(a^2*sqrt(a^2-x^2))
 

               x
   (2)  --------------
           +---------+
         2 |   2    2
        a \|- x  + a
                                                     Type: Expression Integer
--R
--R               x
--R   (2)  --------------
--R           +---------+
--R         2 |   2    2
--R        a \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 91     14:251 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 92
aa:=integrate(x/(a^2-x^2)^(3/2),x)
 

                     2
                    x
   (1)  --------------------------
           +---------+
         2 |   2    2       2    3
        a \|- x  + a   + a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R                    x
--R   (1)  --------------------------
--R           +---------+
--R         2 |   2    2       2    3
--R        a \|- x  + a   + a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 93
bb:=1/sqrt(a^2-x^2)
 

              1
   (2)  ------------
         +---------+
         |   2    2
        \|- x  + a
                                                     Type: Expression Integer
--R
--R              1
--R   (2)  ------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 94     14:252 Schaums and Axiom differ by a constant
cc:=aa-bb
 

        1
   (3)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (3)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 95
aa:=integrate(x^2/(a^2-x^2)^(3/2),x)
 

   (1)
                                     +---------+
       +---------+                   |   2    2           +---------+
       |   2    2      2     2      \|- x  + a   - a      |   2    2
   (2a\|- x  + a   + 2x  - 2a )atan(----------------) - x\|- x  + a   + a x
                                            x
   ------------------------------------------------------------------------
                              +---------+
                              |   2    2     2    2
                            a\|- x  + a   + x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                     +---------+
--R       +---------+                   |   2    2           +---------+
--R       |   2    2      2     2      \|- x  + a   - a      |   2    2
--R   (2a\|- x  + a   + 2x  - 2a )atan(----------------) - x\|- x  + a   + a x
--R                                            x
--R   ------------------------------------------------------------------------
--R                              +---------+
--R                              |   2    2     2    2
--R                            a\|- x  + a   + x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 96
bb:=x/sqrt(a^2-x^2)-asin(x/a)
 

                  +---------+
               x  |   2    2
        - asin(-)\|- x  + a   + x
               a
   (2)  -------------------------
                +---------+
                |   2    2
               \|- x  + a
                                                     Type: Expression Integer
--R
--R                  +---------+
--R               x  |   2    2
--R        - asin(-)\|- x  + a   + x
--R               a
--R   (2)  -------------------------
--R                +---------+
--R                |   2    2
--R               \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 97
cc:=aa-bb
 

               +---------+
               |   2    2
              \|- x  + a   - a         x
   (3)  2atan(----------------) + asin(-)
                      x                a
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a         x
--R   (3)  2atan(----------------) + asin(-)
--R                      x                a
--R                                                     Type: Expression Integer
--E

--S 98
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 99
dd:=atanrule cc
 

                    +---------+
                    |   2    2
                 - \|- x  + a   + %i x + a         x
   (5)  - %i log(-------------------------) + asin(-)
                   +---------+                     a
                   |   2    2
                  \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R                 - \|- x  + a   + %i x + a         x
--R   (5)  - %i log(-------------------------) + asin(-)
--R                   +---------+                     a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 100
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 101
ee:=asinrule dd
 

                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x              +---------+
                 |     2                         |   2    2
                \|    a                       - \|- x  + a   + %i x + a
   (7)  %i log(--------------------) - %i log(-------------------------)
                         a                      +---------+
                                                |   2    2
                                               \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x              +---------+
--R                 |     2                         |   2    2
--R                \|    a                       - \|- x  + a   + %i x + a
--R   (7)  %i log(--------------------) - %i log(-------------------------)
--R                         a                      +---------+
--R                                                |   2    2
--R                                               \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 102
ff:=expandLog ee
 

   (8)
              +---------+
              |   2    2                    +---------+
              |- x  + a                     |   2    2
     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
              |     2
             \|    a
   + 
               +---------+
               |   2    2
     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (8)
--R              +---------+
--R              |   2    2                    +---------+
--R              |- x  + a                     |   2    2
--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
--R              |     2
--R             \|    a
--R   + 
--R               +---------+
--R               |   2    2
--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 103
gg:=rootSimp ff
 

   (9)
               +-------+                         +-------+
               | 2    2                          | 2    2
     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +-------+                         +-------+
--R               | 2    2                          | 2    2
--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 104    14:253 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 105
aa:=integrate(x^3/(a^2-x^2)^(3/2),x)
 

                            4
                           x
   (1)  - ------------------------------------
                     +---------+
            2     2  |   2    2        2     3
          (x  - 2a )\|- x  + a   - 2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            4
--R                           x
--R   (1)  - ------------------------------------
--R                     +---------+
--R            2     2  |   2    2        2     3
--R          (x  - 2a )\|- x  + a   - 2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 106
bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2)
 

            2     2
         - x  + 2a
   (2)  ------------
         +---------+
         |   2    2
        \|- x  + a
                                                     Type: Expression Integer
--R
--R            2     2
--R         - x  + 2a
--R   (2)  ------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 107    14:254 Schaums and Axiom differ by a constant
cc:=aa-bb
 

   (3)  2a
                                                     Type: Expression Integer
--R
--R   (3)  2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 108
aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x)
 

                                      +---------+
           +---------+                |   2    2
           |   2    2     2    2     \|- x  + a   - a     2
        (a\|- x  + a   + x  - a )log(----------------) + x
                                             x
   (1)  ---------------------------------------------------
                        +---------+
                      4 |   2    2     3 2    5
                     a \|- x  + a   + a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                      +---------+
--R           +---------+                |   2    2
--R           |   2    2     2    2     \|- x  + a   - a     2
--R        (a\|- x  + a   + x  - a )log(----------------) + x
--R                                             x
--R   (1)  ---------------------------------------------------
--R                        +---------+
--R                      4 |   2    2     3 2    5
--R                     a \|- x  + a   + a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 109
bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x)
 

                           +---------+
           +---------+     |   2    2
           |   2    2     \|- x  + a   + a
        - \|- x  + a  log(----------------) + a
                                  x
   (2)  ---------------------------------------
                        +---------+
                      3 |   2    2
                     a \|- x  + a
                                                     Type: Expression Integer
--R
--R                           +---------+
--R           +---------+     |   2    2
--R           |   2    2     \|- x  + a   + a
--R        - \|- x  + a  log(----------------) + a
--R                                  x
--R   (2)  ---------------------------------------
--R                        +---------+
--R                      3 |   2    2
--R                     a \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 110
cc:=aa-bb
 

             +---------+             +---------+
             |   2    2              |   2    2
            \|- x  + a   + a        \|- x  + a   - a
        log(----------------) + log(----------------) + 1
                    x                       x
   (3)  -------------------------------------------------
                                 3
                                a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R            \|- x  + a   + a        \|- x  + a   - a
--R        log(----------------) + log(----------------) + 1
--R                    x                       x
--R   (3)  -------------------------------------------------
--R                                 3
--R                                a
--R                                                     Type: Expression Integer
--E

--S 111
dd:=expandLog cc
 

             +---------+             +---------+
             |   2    2              |   2    2
        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x) + 1
   (4)  -----------------------------------------------------------
                                      3
                                     a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x) + 1
--R   (4)  -----------------------------------------------------------
--R                                      3
--R                                     a
--R                                                     Type: Expression Integer
--E

--S 112
ee:=complexNormalize dd
 

                  x
        - 2log(-------) + 1
                +----+
                |   2
               \|- x
   (5)  -------------------
                  3
                 a
                                                     Type: Expression Integer
--R
--R                  x
--R        - 2log(-------) + 1
--R                +----+
--R                |   2
--R               \|- x
--R   (5)  -------------------
--R                  3
--R                 a
--R                                                     Type: Expression Integer
--E

--S 113    14:255 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

              +---+
        2log(\|- 1 ) + 1
   (6)  ----------------
                3
               a
                                                     Type: Expression Integer
--R
--R              +---+
--R        2log(\|- 1 ) + 1
--R   (6)  ----------------
--R                3
--R               a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 114
aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x)
 

                      +---------+
             2     3  |   2    2      4     2 2     4
        (4a x  - 2a )\|- x  + a   + 2x  - 5a x  + 2a
   (1)  ---------------------------------------------
                         +---------+
             4 3     6   |   2    2      5 3     7
           (a x  - 2a x)\|- x  + a   - 2a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      +---------+
--R             2     3  |   2    2      4     2 2     4
--R        (4a x  - 2a )\|- x  + a   + 2x  - 5a x  + 2a
--R   (1)  ---------------------------------------------
--R                         +---------+
--R             4 3     6   |   2    2      5 3     7
--R           (a x  - 2a x)\|- x  + a   - 2a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 115
bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2))
 

              2    2
            2x  - a
   (2)  ---------------
            +---------+
         4  |   2    2
        a x\|- x  + a
                                                     Type: Expression Integer
--R
--R              2    2
--R            2x  - a
--R   (2)  ---------------
--R            +---------+
--R         4  |   2    2
--R        a x\|- x  + a
--R                                                     Type: Expression Integer
--E

--S 116    14:256 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 117
aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x)
 

   (1)
                           +---------+
               4      3 2  |   2    2      6      2 4      4 2
         ((9a x  - 12a x )\|- x  + a   + 3x  - 15a x  + 12a x )
      *
              +---------+
              |   2    2
             \|- x  + a   - a
         log(----------------)
                     x
     + 
                             +---------+
            4     3 2     5  |   2    2      6    2 4     4 2     6
       (3a x  + 5a x  - 4a )\|- x  + a   + 2x  - a x  - 7a x  + 4a
  /
                     +---------+
        6 4     8 2  |   2    2      5 6      7 4     9 2
     (6a x  - 8a x )\|- x  + a   + 2a x  - 10a x  + 8a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +---------+
--R               4      3 2  |   2    2      6      2 4      4 2
--R         ((9a x  - 12a x )\|- x  + a   + 3x  - 15a x  + 12a x )
--R      *
--R              +---------+
--R              |   2    2
--R             \|- x  + a   - a
--R         log(----------------)
--R                     x
--R     + 
--R                             +---------+
--R            4     3 2     5  |   2    2      6    2 4     4 2     6
--R       (3a x  + 5a x  - 4a )\|- x  + a   + 2x  - a x  - 7a x  + 4a
--R  /
--R                     +---------+
--R        6 4     8 2  |   2    2      5 6      7 4     9 2
--R     (6a x  - 8a x )\|- x  + a   + 2a x  - 10a x  + 8a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 118
bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a^2-x^2))/x)
 

                              +---------+
              +---------+     |   2    2
            2 |   2    2     \|- x  + a   + a        2    3
        - 3x \|- x  + a  log(----------------) + 3a x  - a
                                     x
   (2)  ---------------------------------------------------
                               +---------+
                           5 2 |   2    2
                         2a x \|- x  + a
                                                     Type: Expression Integer
--R
--R                              +---------+
--R              +---------+     |   2    2
--R            2 |   2    2     \|- x  + a   + a        2    3
--R        - 3x \|- x  + a  log(----------------) + 3a x  - a
--R                                     x
--R   (2)  ---------------------------------------------------
--R                               +---------+
--R                           5 2 |   2    2
--R                         2a x \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 119
cc:=aa-bb
 

              +---------+              +---------+
              |   2    2               |   2    2
             \|- x  + a   + a         \|- x  + a   - a
        3log(----------------) + 3log(----------------) + 2
                     x                        x
   (3)  ---------------------------------------------------
                                  5
                                2a
                                                     Type: Expression Integer
--R
--R              +---------+              +---------+
--R              |   2    2               |   2    2
--R             \|- x  + a   + a         \|- x  + a   - a
--R        3log(----------------) + 3log(----------------) + 2
--R                     x                        x
--R   (3)  ---------------------------------------------------
--R                                  5
--R                                2a
--R                                                     Type: Expression Integer
--E

--S 120
dd:=expandLog cc
 

              +---------+              +---------+
              |   2    2               |   2    2
        3log(\|- x  + a   + a) + 3log(\|- x  + a   - a) - 6log(x) + 2
   (4)  -------------------------------------------------------------
                                       5
                                     2a
                                                     Type: Expression Integer
--R
--R              +---------+              +---------+
--R              |   2    2               |   2    2
--R        3log(\|- x  + a   + a) + 3log(\|- x  + a   - a) - 6log(x) + 2
--R   (4)  -------------------------------------------------------------
--R                                       5
--R                                     2a
--R                                                     Type: Expression Integer
--E

--S 121
ee:=complexNormalize dd
 

                  x
        - 3log(-------) + 1
                +----+
                |   2
               \|- x
   (5)  -------------------
                  5
                 a
                                                     Type: Expression Integer
--R
--R                  x
--R        - 3log(-------) + 1
--R                +----+
--R                |   2
--R               \|- x
--R   (5)  -------------------
--R                  5
--R                 a
--R                                                     Type: Expression Integer
--E

--S 122    14:257 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

              +---+
        3log(\|- 1 ) + 1
   (6)  ----------------
                5
               a
                                                     Type: Expression Integer
--R
--R              +---+
--R        3log(\|- 1 ) + 1
--R   (6)  ----------------
--R                5
--R               a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 123
aa:=integrate((a^2-x^2)^(3/2),x)
 

   (1)
                            +---------+
                5 2      7  |   2    2      4 4      6 2      8
         ((- 24a x  + 48a )\|- x  + a   - 6a x  + 48a x  - 48a )
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                         +---------+
            7      2 5      4 3      6   |   2    2        7      3 5      5 3
       (- 2x  + 21a x  - 56a x  + 40a x)\|- x  + a   + 8a x  - 44a x  + 76a x
     + 
            7
       - 40a x
  /
                     +---------+
           2      3  |   2    2      4      2 2      4
     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                            +---------+
--R                5 2      7  |   2    2      4 4      6 2      8
--R         ((- 24a x  + 48a )\|- x  + a   - 6a x  + 48a x  - 48a )
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                         +---------+
--R            7      2 5      4 3      6   |   2    2        7      3 5      5 3
--R       (- 2x  + 21a x  - 56a x  + 40a x)\|- x  + a   + 8a x  - 44a x  + 76a x
--R     + 
--R            7
--R       - 40a x
--R  /
--R                     +---------+
--R           2      3  |   2    2      4      2 2      4
--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 124
bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a)
 

                       +---------+
             3     2   |   2    2      4     x
        (- 2x  + 5a x)\|- x  + a   + 3a asin(-)
                                             a
   (2)  ---------------------------------------
                           8
                                                     Type: Expression Integer
--R
--R                       +---------+
--R             3     2   |   2    2      4     x
--R        (- 2x  + 5a x)\|- x  + a   + 3a asin(-)
--R                                             a
--R   (2)  ---------------------------------------
--R                           8
--R                                                     Type: Expression Integer
--E

--S 125
cc:=aa-bb
 

                   +---------+
                   |   2    2
            4     \|- x  + a   - a      4     x
        - 6a atan(----------------) - 3a asin(-)
                          x                   a
   (3)  ----------------------------------------
                            8
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            4     \|- x  + a   - a      4     x
--R        - 6a atan(----------------) - 3a asin(-)
--R                          x                   a
--R   (3)  ----------------------------------------
--R                            8
--R                                                     Type: Expression Integer
--E

--S 126
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 

--S 127
ee:=asinrule cc
 

                      +---------+
                      |   2    2
                      |- x  + a
                    a |---------  - %i x             +---------+
                      |     2                        |   2    2
               4     \|    a                  4     \|- x  + a   - a
        - 3%i a log(--------------------) - 6a atan(----------------)
                              a                             x
   (5)  -------------------------------------------------------------
                                      8
                                             Type: Expression Complex Integer
--R
--R                      +---------+
--R                      |   2    2
--R                      |- x  + a
--R                    a |---------  - %i x             +---------+
--R                      |     2                        |   2    2
--R               4     \|    a                  4     \|- x  + a   - a
--R        - 3%i a log(--------------------) - 6a atan(----------------)
--R                              a                             x
--R   (5)  -------------------------------------------------------------
--R                                      8
--R                                             Type: Expression Complex Integer
--E

--S 128
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 129
ff:=atanrule ee
 

   (7)
                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x                 +---------+
                 |     2                            |   2    2
          4     \|    a                     4    - \|- x  + a   + %i x + a
   - 3%i a log(--------------------) + 3%i a log(-------------------------)
                         a                         +---------+
                                                   |   2    2
                                                  \|- x  + a   + %i x - a
   ------------------------------------------------------------------------
                                       8
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x                 +---------+
--R                 |     2                            |   2    2
--R          4     \|    a                     4    - \|- x  + a   + %i x + a
--R   - 3%i a log(--------------------) + 3%i a log(-------------------------)
--R                         a                         +---------+
--R                                                   |   2    2
--R                                                  \|- x  + a   + %i x - a
--R   ------------------------------------------------------------------------
--R                                       8
--R                                             Type: Expression Complex Integer
--E

--S 130
gg:=expandLog ff
 

   (8)
                     +---------+
                     |   2    2                       +---------+
              4      |- x  + a                  4     |   2    2
       - 3%i a log(a |---------  - %i x) - 3%i a log(\|- x  + a   + %i x - a)
                     |     2
                    \|    a
     + 
                  +---------+
            4     |   2    2                     4              4
       3%i a log(\|- x  + a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                     +---------+
--R                     |   2    2                       +---------+
--R              4      |- x  + a                  4     |   2    2
--R       - 3%i a log(a |---------  - %i x) - 3%i a log(\|- x  + a   + %i x - a)
--R                     |     2
--R                    \|    a
--R     + 
--R                  +---------+
--R            4     |   2    2                     4              4
--R       3%i a log(\|- x  + a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 131
hh:=rootSimp gg
 

   (9)
                      +-------+                            +-------+
              4       | 2    2                     4       | 2    2
       - 3%i a log(%i\|x  - a   + %i x - a) - 3%i a log(%i\|x  - a   - %i x)
     + 
                    +-------+
            4       | 2    2                     4              4
       3%i a log(%i\|x  - a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                      +-------+                            +-------+
--R              4       | 2    2                     4       | 2    2
--R       - 3%i a log(%i\|x  - a   + %i x - a) - 3%i a log(%i\|x  - a   - %i x)
--R     + 
--R                    +-------+
--R            4       | 2    2                     4              4
--R       3%i a log(%i\|x  - a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 132    14:258 Schaums and Axiom agree
ii:=complexNormalize hh
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 133
aa:=integrate(x*(a^2-x^2)^(3/2),x)
 

   (1)
                                          +---------+
            8      3 6      5 4      7 2  |   2    2     10      2 8      4 6
       (5a x  - 30a x  + 60a x  - 40a x )\|- x  + a   + x   - 15a x  + 55a x
     + 
            6 4      8 2
       - 80a x  + 40a x
  /
                           +---------+
        4      2 2      4  |   2    2         4       3 2      5
     (5x  - 60a x  + 80a )\|- x  + a   - 25a x  + 100a x  - 80a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                          +---------+
--R            8      3 6      5 4      7 2  |   2    2     10      2 8      4 6
--R       (5a x  - 30a x  + 60a x  - 40a x )\|- x  + a   + x   - 15a x  + 55a x
--R     + 
--R            6 4      8 2
--R       - 80a x  + 40a x
--R  /
--R                           +---------+
--R        4      2 2      4  |   2    2         4       3 2      5
--R     (5x  - 60a x  + 80a )\|- x  + a   - 25a x  + 100a x  - 80a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 134
bb:=-(a^2-x^2)^(5/2)/5
 

                            +---------+
            4     2 2    4  |   2    2
        (- x  + 2a x  - a )\|- x  + a
   (2)  -------------------------------
                       5
                                                     Type: Expression Integer
--R
--R                            +---------+
--R            4     2 2    4  |   2    2
--R        (- x  + 2a x  - a )\|- x  + a
--R   (2)  -------------------------------
--R                       5
--R                                                     Type: Expression Integer
--E

--S 135    14:259 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           5
          a
   (3)  - --
           5
                                                     Type: Expression Integer
--R
--R           5
--R          a
--R   (3)  - --
--R           5
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 136
aa:=integrate(x^2*(a^2-x^2)^(3/2),x)
 

   (1)
                                         +---------+
                 7 4       9 2       11  |   2    2      6 6       8 4
           (- 36a x  + 192a x  - 192a  )\|- x  + a   - 6a x  + 108a x
         + 
                 10 2       12
           - 288a  x  + 192a
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                                                 +---------+
            11       2 9       4 7       6 5       8 3      10   |   2    2
       (- 8x   + 158a x  - 639a x  + 982a x  - 592a x  + 96a  x)\|- x  + a
     + 
            11       3 9        5 7        7 5       9 3      11
       48a x   - 388a x  + 1062a x  - 1266a x  + 640a x  - 96a  x
  /
                                     +---------+
              4        3 2        5  |   2    2       6       2 4        4 2
       (288a x  - 1536a x  + 1536a )\|- x  + a   + 48x  - 864a x  + 2304a x
     + 
              6
       - 1536a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         +---------+
--R                 7 4       9 2       11  |   2    2      6 6       8 4
--R           (- 36a x  + 192a x  - 192a  )\|- x  + a   - 6a x  + 108a x
--R         + 
--R                 10 2       12
--R           - 288a  x  + 192a
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                                                 +---------+
--R            11       2 9       4 7       6 5       8 3      10   |   2    2
--R       (- 8x   + 158a x  - 639a x  + 982a x  - 592a x  + 96a  x)\|- x  + a
--R     + 
--R            11       3 9        5 7        7 5       9 3      11
--R       48a x   - 388a x  + 1062a x  - 1266a x  + 640a x  - 96a  x
--R  /
--R                                     +---------+
--R              4        3 2        5  |   2    2       6       2 4        4 2
--R       (288a x  - 1536a x  + 1536a )\|- x  + a   + 48x  - 864a x  + 2304a x
--R     + 
--R              6
--R       - 1536a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 137
bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a^6/16*asin(x/a)
 

                                +---------+
             5      2 3     4   |   2    2      6     x
        (- 8x  + 14a x  - 3a x)\|- x  + a   + 3a asin(-)
                                                      a
   (2)  ------------------------------------------------
                               48
                                                     Type: Expression Integer
--R
--R                                +---------+
--R             5      2 3     4   |   2    2      6     x
--R        (- 8x  + 14a x  - 3a x)\|- x  + a   + 3a asin(-)
--R                                                      a
--R   (2)  ------------------------------------------------
--R                               48
--R                                                     Type: Expression Integer
--E

--S 138
cc:=aa-bb
 

                   +---------+
                   |   2    2
            6     \|- x  + a   - a     6     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           16
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            6     \|- x  + a   - a     6     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           16
--R                                                     Type: Expression Integer
--E 

--S 139
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 140
dd:=atanrule cc
 

                    +---------+
                    |   2    2
            6    - \|- x  + a   + %i x + a     6     x
        %i a log(-------------------------) - a asin(-)
                   +---------+                       a
                   |   2    2
                  \|- x  + a   + %i x - a
   (5)  -----------------------------------------------
                               16
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R            6    - \|- x  + a   + %i x + a     6     x
--R        %i a log(-------------------------) - a asin(-)
--R                   +---------+                       a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R   (5)  -----------------------------------------------
--R                               16
--R                                             Type: Expression Complex Integer
--E

--S 141
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 142
ee:=asinrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              6     \|    a                    6    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                          16
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              6     \|    a                    6    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                          16
--R                                             Type: Expression Complex Integer
--E

--S 143
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             6      |- x  + a                 6     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           6     |   2    2                    6             6
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     16
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             6      |- x  + a                 6     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           6     |   2    2                    6             6
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     16
--R                                             Type: Expression Complex Integer
--E

--S 144
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             6       | 2    2                    6       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           6       | 2    2                    6             6
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     16
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             6       | 2    2                    6       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           6       | 2    2                    6             6
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     16
--R                                             Type: Expression Complex Integer
--E

--S 145    14:260 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 146
aa:=integrate(x^3*(a^2-x^2)^(3/2),x)
 

   (1)
                                                            +---------+
             12       3 10        5 8        7 6       9 4  |   2    2      14
       (35a x   - 336a x   + 1015a x  - 1260a x  + 560a x )\|- x  + a   + 5x
     + 
             2 12       4 10        6 8        8 6       10 4
       - 133a x   + 721a x   - 1575a x  + 1540a x  - 560a  x
  /
                                            +---------+
           6       2 4        4 2        6  |   2    2          6        3 4
       (35x  - 840a x  + 2800a x  - 2240a )\|- x  + a   - 245a x  + 1960a x
     + 
              5 2        7
       - 3920a x  + 2240a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                            +---------+
--R             12       3 10        5 8        7 6       9 4  |   2    2      14
--R       (35a x   - 336a x   + 1015a x  - 1260a x  + 560a x )\|- x  + a   + 5x
--R     + 
--R             2 12       4 10        6 8        8 6       10 4
--R       - 133a x   + 721a x   - 1575a x  + 1540a x  - 560a  x
--R  /
--R                                            +---------+
--R           6       2 4        4 2        6  |   2    2          6        3 4
--R       (35x  - 840a x  + 2800a x  - 2240a )\|- x  + a   - 245a x  + 1960a x
--R     + 
--R              5 2        7
--R       - 3920a x  + 2240a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 147
bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5
 

                                     +---------+
             6     2 4    4 2     6  |   2    2
        (- 5x  + 8a x  - a x  - 2a )\|- x  + a
   (2)  ----------------------------------------
                           35
                                                     Type: Expression Integer
--R
--R                                     +---------+
--R             6     2 4    4 2     6  |   2    2
--R        (- 5x  + 8a x  - a x  - 2a )\|- x  + a
--R   (2)  ----------------------------------------
--R                           35
--R                                                     Type: Expression Integer
--E

--S 148    14:261 Schaums and Axiom differ by a constant
cc:=aa-bb
 

            7
          2a
   (3)  - ---
           35
                                                     Type: Expression Integer
--R
--R            7
--R          2a
--R   (3)  - ---
--R           35
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 149
aa:=integrate((a^2-x^2)^(3/2)/x,x)
 

   (1)
                                                       +---------+
                       +---------+                     |   2    2
           3 2      5  |   2    2      4 2      6     \|- x  + a   - a
       ((3a x  - 12a )\|- x  + a   - 9a x  + 12a )log(----------------)
                                                              x
     + 
                        +---------+
            4      3 2  |   2    2     6     2 4      4 2
       (3a x  - 12a x )\|- x  + a   + x  - 9a x  + 12a x
  /
                  +---------+
        2      2  |   2    2        2      3
     (3x  - 12a )\|- x  + a   - 9a x  + 12a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                       +---------+
--R                       +---------+                     |   2    2
--R           3 2      5  |   2    2      4 2      6     \|- x  + a   - a
--R       ((3a x  - 12a )\|- x  + a   - 9a x  + 12a )log(----------------)
--R                                                              x
--R     + 
--R                        +---------+
--R            4      3 2  |   2    2     6     2 4      4 2
--R       (3a x  - 12a x )\|- x  + a   + x  - 9a x  + 12a x
--R  /
--R                  +---------+
--R        2      2  |   2    2        2      3
--R     (3x  - 12a )\|- x  + a   - 9a x  + 12a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 150
bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x)
 

                  +---------+
                  |   2    2                      +---------+
            3    \|- x  + a   + a        2     2  |   2    2
        - 3a log(----------------) + (- x  + 4a )\|- x  + a
                         x
   (2)  -----------------------------------------------------
                                  3
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2                      +---------+
--R            3    \|- x  + a   + a        2     2  |   2    2
--R        - 3a log(----------------) + (- x  + 4a )\|- x  + a
--R                         x
--R   (2)  -----------------------------------------------------
--R                                  3
--R                                                     Type: Expression Integer
--E

--S 151
cc:=aa-bb
 

                +---------+                +---------+
                |   2    2                 |   2    2
          3    \|- x  + a   + a      3    \|- x  + a   - a      3
        3a log(----------------) + 3a log(----------------) + 4a
                       x                          x
   (3)  ---------------------------------------------------------
                                    3
                                                     Type: Expression Integer
--R
--R                +---------+                +---------+
--R                |   2    2                 |   2    2
--R          3    \|- x  + a   + a      3    \|- x  + a   - a      3
--R        3a log(----------------) + 3a log(----------------) + 4a
--R                       x                          x
--R   (3)  ---------------------------------------------------------
--R                                    3
--R                                                     Type: Expression Integer
--E

--S 152
dd:=expandLog cc
 

                +---------+                +---------+
          3     |   2    2           3     |   2    2           3           3
        3a log(\|- x  + a   + a) + 3a log(\|- x  + a   - a) - 6a log(x) + 4a
   (4)  ---------------------------------------------------------------------
                                          3
                                                     Type: Expression Integer
--R
--R                +---------+                +---------+
--R          3     |   2    2           3     |   2    2           3           3
--R        3a log(\|- x  + a   + a) + 3a log(\|- x  + a   - a) - 6a log(x) + 4a
--R   (4)  ---------------------------------------------------------------------
--R                                          3
--R                                                     Type: Expression Integer
--E

--S 153
ee:=complexNormalize dd
 

            3       x         3
        - 6a log(-------) + 4a
                  +----+
                  |   2
                 \|- x
   (5)  -----------------------
                   3
                                                     Type: Expression Integer
--R
--R            3       x         3
--R        - 6a log(-------) + 4a
--R                  +----+
--R                  |   2
--R                 \|- x
--R   (5)  -----------------------
--R                   3
--R                                                     Type: Expression Integer
--E

--S 154    14:262 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

          3     +---+      3
        6a log(\|- 1 ) + 4a
   (6)  --------------------
                  3
                                                     Type: Expression Integer
--R
--R          3     +---+      3
--R        6a log(\|- 1 ) + 4a
--R   (6)  --------------------
--R                  3
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 155
aa:=integrate((a^2-x^2)^{3/2}/x^2,x)
 

   (1)
                                                           +---------+
                        +---------+                        |   2    2
           2 3      4   |   2    2       3 3      5       \|- x  + a   - a
       ((6a x  - 24a x)\|- x  + a   - 18a x  + 24a x)atan(----------------)
                                                                  x
     + 
                             +---------+
            4     3 2     5  |   2    2     6     2 4     4 2     6
       (3a x  + 2a x  - 8a )\|- x  + a   + x  - 3a x  - 6a x  + 8a
  /
                  +---------+
        3     2   |   2    2        3     3
     (2x  - 8a x)\|- x  + a   - 6a x  + 8a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                           +---------+
--R                        +---------+                        |   2    2
--R           2 3      4   |   2    2       3 3      5       \|- x  + a   - a
--R       ((6a x  - 24a x)\|- x  + a   - 18a x  + 24a x)atan(----------------)
--R                                                                  x
--R     + 
--R                             +---------+
--R            4     3 2     5  |   2    2     6     2 4     4 2     6
--R       (3a x  + 2a x  - 8a )\|- x  + a   + x  - 3a x  - 6a x  + 8a
--R  /
--R                  +---------+
--R        3     2   |   2    2        3     3
--R     (2x  - 8a x)\|- x  + a   - 6a x  + 8a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 156
bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a)
 

                     +---------+
            2     2  |   2    2      2       x
        (- x  - 2a )\|- x  + a   - 3a x asin(-)
                                             a
   (2)  ---------------------------------------
                           2x
                                                     Type: Expression Integer
--R
--R                     +---------+
--R            2     2  |   2    2      2       x
--R        (- x  - 2a )\|- x  + a   - 3a x asin(-)
--R                                             a
--R   (2)  ---------------------------------------
--R                           2x
--R                                                     Type: Expression Integer
--E

--S 157
cc:=aa-bb
 

                 +---------+
                 |   2    2
          2     \|- x  + a   - a      2     x
        6a atan(----------------) + 3a asin(-)
                        x                   a
   (3)  --------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2
--R          2     \|- x  + a   - a      2     x
--R        6a atan(----------------) + 3a asin(-)
--R                        x                   a
--R   (3)  --------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 158
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 159
dd:=asinrule cc
 

                    +---------+
                    |   2    2
                    |- x  + a
                  a |---------  - %i x             +---------+
                    |     2                        |   2    2
             2     \|    a                  2     \|- x  + a   - a
        3%i a log(--------------------) + 6a atan(----------------)
                            a                             x
   (5)  -----------------------------------------------------------
                                     2
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R                    |- x  + a
--R                  a |---------  - %i x             +---------+
--R                    |     2                        |   2    2
--R             2     \|    a                  2     \|- x  + a   - a
--R        3%i a log(--------------------) + 6a atan(----------------)
--R                            a                             x
--R   (5)  -----------------------------------------------------------
--R                                     2
--R                                             Type: Expression Complex Integer
--E

--S 160
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 161
ee:=atanrule dd
 

                    +---------+
                    |   2    2
                    |- x  + a
                  a |---------  - %i x                 +---------+
                    |     2                            |   2    2
             2     \|    a                     2    - \|- x  + a   + %i x + a
        3%i a log(--------------------) - 3%i a log(-------------------------)
                            a                         +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           2
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R                    |- x  + a
--R                  a |---------  - %i x                 +---------+
--R                    |     2                            |   2    2
--R             2     \|    a                     2    - \|- x  + a   + %i x + a
--R        3%i a log(--------------------) - 3%i a log(-------------------------)
--R                            a                         +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           2
--R                                             Type: Expression Complex Integer
--E

--S 162
ff:=expandLog ee
 

   (8)
                   +---------+
                   |   2    2                       +---------+
            2      |- x  + a                  2     |   2    2
       3%i a log(a |---------  - %i x) + 3%i a log(\|- x  + a   + %i x - a)
                   |     2
                  \|    a
     + 
                    +---------+
              2     |   2    2                     2              2
       - 3%i a log(\|- x  + a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                   +---------+
--R                   |   2    2                       +---------+
--R            2      |- x  + a                  2     |   2    2
--R       3%i a log(a |---------  - %i x) + 3%i a log(\|- x  + a   + %i x - a)
--R                   |     2
--R                  \|    a
--R     + 
--R                    +---------+
--R              2     |   2    2                     2              2
--R       - 3%i a log(\|- x  + a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E 

--S 163
gg:=rootSimp ff
 

   (9)
                    +-------+                            +-------+
            2       | 2    2                     2       | 2    2
       3%i a log(%i\|x  - a   + %i x - a) + 3%i a log(%i\|x  - a   - %i x)
     + 
                      +-------+
              2       | 2    2                     2              2
       - 3%i a log(%i\|x  - a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                    +-------+                            +-------+
--R            2       | 2    2                     2       | 2    2
--R       3%i a log(%i\|x  - a   + %i x - a) + 3%i a log(%i\|x  - a   - %i x)
--R     + 
--R                      +-------+
--R              2       | 2    2                     2              2
--R       - 3%i a log(%i\|x  - a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 164    14:263 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 165
aa:=integrate((a^2-x^2)^(3/2)/x^3,x)
 

   (1)
                                                             +---------+
                           +---------+                       |   2    2
               4      3 2  |   2    2      2 4      4 2     \|- x  + a   - a
       ((- 3a x  + 12a x )\|- x  + a   + 9a x  - 12a x )log(----------------)
                                                                    x
     + 
                             +---------+
            4     3 2     5  |   2    2      6     2 4     4 2     6
       (4a x  + 3a x  - 4a )\|- x  + a   + 2x  - 3a x  - 5a x  + 4a
  /
                   +---------+
        4     2 2  |   2    2        4     3 2
     (2x  - 8a x )\|- x  + a   - 6a x  + 8a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                             +---------+
--R                           +---------+                       |   2    2
--R               4      3 2  |   2    2      2 4      4 2     \|- x  + a   - a
--R       ((- 3a x  + 12a x )\|- x  + a   + 9a x  - 12a x )log(----------------)
--R                                                                    x
--R     + 
--R                             +---------+
--R            4     3 2     5  |   2    2      6     2 4     4 2     6
--R       (4a x  + 3a x  - 4a )\|- x  + a   + 2x  - 3a x  - 5a x  + 4a
--R  /
--R                   +---------+
--R        4     2 2  |   2    2        4     3 2
--R     (2x  - 8a x )\|- x  + a   - 6a x  + 8a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 166
bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x)
 

                  +---------+
                  |   2    2                      +---------+
            2    \|- x  + a   + a         2    2  |   2    2
        3a x log(----------------) + (- 2x  - a )\|- x  + a
                         x
   (2)  -----------------------------------------------------
                                   2
                                 2x
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2                      +---------+
--R            2    \|- x  + a   + a         2    2  |   2    2
--R        3a x log(----------------) + (- 2x  - a )\|- x  + a
--R                         x
--R   (2)  -----------------------------------------------------
--R                                   2
--R                                 2x
--R                                                     Type: Expression Integer
--E

--S 167
cc:=aa-bb
 

                  +---------+                +---------+
                  |   2    2                 |   2    2
                 \|- x  + a   + a           \|- x  + a   - a
        - 3a log(----------------) - 3a log(----------------) - 2a
                         x                          x
   (3)  ----------------------------------------------------------
                                     2
                                                     Type: Expression Integer
--R
--R                  +---------+                +---------+
--R                  |   2    2                 |   2    2
--R                 \|- x  + a   + a           \|- x  + a   - a
--R        - 3a log(----------------) - 3a log(----------------) - 2a
--R                         x                          x
--R   (3)  ----------------------------------------------------------
--R                                     2
--R                                                     Type: Expression Integer
--E

--S 168
dd:=expandLog cc
 

                  +---------+                +---------+
                  |   2    2                 |   2    2
        - 3a log(\|- x  + a   + a) - 3a log(\|- x  + a   - a) + 6a log(x) - 2a
   (4)  ----------------------------------------------------------------------
                                           2
                                                     Type: Expression Integer
--R
--R                  +---------+                +---------+
--R                  |   2    2                 |   2    2
--R        - 3a log(\|- x  + a   + a) - 3a log(\|- x  + a   - a) + 6a log(x) - 2a
--R   (4)  ----------------------------------------------------------------------
--R                                           2
--R                                                     Type: Expression Integer
--E

--S 169
ee:=complexNormalize dd
 

                  x
   (5)  3a log(-------) - a
                +----+
                |   2
               \|- x
                                                     Type: Expression Integer
--R
--R                  x
--R   (5)  3a log(-------) - a
--R                +----+
--R                |   2
--R               \|- x
--R                                                     Type: Expression Integer
--E

--S 170    14:264 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

                  +---+
   (6)  - 3a log(\|- 1 ) - a
                                                     Type: Expression Integer
--R
--R                  +---+
--R   (6)  - 3a log(\|- 1 ) - a
--R                                                     Type: Expression Integer
--E

)spool
 
Starts dribbling to carten.output (2009/2/17, 17:44:7).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from CartesianTensorXmpPage

--S 1 of 48
CT := CARTEN(i0 := 1, 2, Integer)
 

   (1)  CartesianTensor(1,2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  CartesianTensor(1,2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 48
t0: CT := 8
 

   (2)  8
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (2)  8
--R                                           Type: CartesianTensor(1,2,Integer)
--E 2

--S 3 of 48
rank t0
 

   (3)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  0
--R                                                     Type: NonNegativeInteger
--E 3

--S 4 of 48
v: DirectProduct(2, Integer) := directProduct [3,4]
 

   (4)  [3,4]
                                               Type: DirectProduct(2,Integer)
--R 
--R
--R   (4)  [3,4]
--R                                               Type: DirectProduct(2,Integer)
--E 4

--S 5 of 48
Tv: CT := v
 

   (5)  [3,4]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (5)  [3,4]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 5

--S 6 of 48
m: SquareMatrix(2, Integer) := matrix [[1,2],[4,5]]
 

        +1  2+
   (6)  |    |
        +4  5+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (6)  |    |
--R        +4  5+
--R                                                Type: SquareMatrix(2,Integer)
--E 6

--S 7 of 48
Tm: CT := m
 

        +1  2+
   (7)  |    |
        +4  5+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +4  5+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 7

--S 8 of 48
n: SquareMatrix(2, Integer) := matrix [[2,3],[0,1]]
 

        +2  3+
   (8)  |    |
        +0  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +2  3+
--R   (8)  |    |
--R        +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 48
Tn: CT := n
 

        +2  3+
   (9)  |    |
        +0  1+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R        +2  3+
--R   (9)  |    |
--R        +0  1+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 9

--S 10 of 48
t1: CT := [2, 3]
 

   (10)  [2,3]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (10)  [2,3]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 10

--S 11 of 48
rank t1
 

   (11)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  1
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 48
t2: CT := [t1, t1]
 

         +2  3+
   (12)  |    |
         +2  3+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  3+
--R   (12)  |    |
--R         +2  3+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 12

--S 13 of 48
t3: CT := [t2, t2]
 

          +2  3+ +2  3+
   (13)  [|    |,|    |]
          +2  3+ +2  3+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R          +2  3+ +2  3+
--R   (13)  [|    |,|    |]
--R          +2  3+ +2  3+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 13

--S 14 of 48
tt: CT := [t3, t3]; tt := [tt, tt]
 

          ++2  3+  +2  3++ ++2  3+  +2  3++
          ||    |  |    || ||    |  |    ||
          |+2  3+  +2  3+| |+2  3+  +2  3+|
   (14)  [|              |,|              |]
          |+2  3+  +2  3+| |+2  3+  +2  3+|
          ||    |  |    || ||    |  |    ||
          ++2  3+  +2  3++ ++2  3+  +2  3++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R          ++2  3+  +2  3++ ++2  3+  +2  3++
--R          ||    |  |    || ||    |  |    ||
--R          |+2  3+  +2  3+| |+2  3+  +2  3+|
--R   (14)  [|              |,|              |]
--R          |+2  3+  +2  3+| |+2  3+  +2  3+|
--R          ||    |  |    || ||    |  |    ||
--R          ++2  3+  +2  3++ ++2  3+  +2  3++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 14

--S 15 of 48
rank tt
 

   (15)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  5
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 48
Tmn := product(Tm, Tn)
 

         ++2  3+    +4  6+ +
         ||    |    |    | |
         |+0  1+    +0  2+ |
   (16)  |                 |
         |+8  12+  +10  15+|
         ||     |  |      ||
         ++0  4 +  +0   5 ++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  3+    +4  6+ +
--R         ||    |    |    | |
--R         |+0  1+    +0  2+ |
--R   (16)  |                 |
--R         |+8  12+  +10  15+|
--R         ||     |  |      ||
--R         ++0  4 +  +0   5 ++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 16

--S 17 of 48
Tmv := contract(Tm,2,Tv,1)
 

   (17)  [11,32]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (17)  [11,32]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 17

--S 18 of 48
Tm*Tv
 

   (18)  [11,32]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (18)  [11,32]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 18

--S 19 of 48
Tmv = m * v
 

   (19)  [11,32]= [11,32]
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R   (19)  [11,32]= [11,32]
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 19

--S 20 of 48
t0()
 

   (20)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  8
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 48
t1(1+1)
 

   (21)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  3
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 48
t2(2,1)
 

   (22)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  2
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 48
t3(2,1,2)
 

   (23)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  3
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 48
Tmn(2,1,2,1)
 

   (24)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (24)  0
--R                                                     Type: NonNegativeInteger
--E 24

--S 25 of 48
t0[]
 

   (25)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  8
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 48
t1[2]
 

   (26)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  3
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 48
t2[2,1]
 

   (27)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  2
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 48
t3[2,1,2]
 

   (28)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  3
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 48
Tmn[2,1,2,1]
 

   (29)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (29)  0
--R                                                     Type: NonNegativeInteger
--E 29

--S 30 of 48
cTmn := contract(Tmn,1,2)
 

         +12  18+
   (30)  |      |
         +0   6 +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +12  18+
--R   (30)  |      |
--R         +0   6 +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 30

--S 31 of 48
trace(m) * n
 

         +12  18+
   (31)  |      |
         +0   6 +
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +12  18+
--R   (31)  |      |
--R         +0   6 +
--R                                                Type: SquareMatrix(2,Integer)
--E 31

--S 32 of 48
contract(Tmn,1,2) = trace(m) * n
 

         +12  18+  +12  18+
   (32)  |      |= |      |
         +0   6 +  +0   6 +
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +12  18+  +12  18+
--R   (32)  |      |= |      |
--R         +0   6 +  +0   6 +
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 32

--S 33 of 48
contract(Tmn,1,3) = transpose(m) * n
 

         +2  7 +  +2  7 +
   (33)  |     |= |     |
         +4  11+  +4  11+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  7 +  +2  7 +
--R   (33)  |     |= |     |
--R         +4  11+  +4  11+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 33

--S 34 of 48
contract(Tmn,1,4) = transpose(m) * transpose(n)
 

         +14  4+  +14  4+
   (34)  |     |= |     |
         +19  5+  +19  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +14  4+  +14  4+
--R   (34)  |     |= |     |
--R         +19  5+  +19  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 34

--S 35 of 48
contract(Tmn,2,3) = m * n
 

         +2  5 +  +2  5 +
   (35)  |     |= |     |
         +8  17+  +8  17+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  5 +  +2  5 +
--R   (35)  |     |= |     |
--R         +8  17+  +8  17+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 35

--S 36 of 48
contract(Tmn,2,4) = m * transpose(n)
 

         +8   2+  +8   2+
   (36)  |     |= |     |
         +23  5+  +23  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +8   2+  +8   2+
--R   (36)  |     |= |     |
--R         +23  5+  +23  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 36

--S 37 of 48
contract(Tmn,3,4) = trace(n) * m
 

         +3   6 +  +3   6 +
   (37)  |      |= |      |
         +12  15+  +12  15+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +3   6 +  +3   6 +
--R   (37)  |      |= |      |
--R         +12  15+  +12  15+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 37

--S 38 of 48
tTmn := transpose(Tmn,1,3)
 

         ++2  3 +  +4   6 ++
         ||     |  |      ||
         |+8  12+  +10  15+|
   (38)  |                 |
         |+0  1+    +0  2+ |
         ||    |    |    | |
         ++0  4+    +0  5+ +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  3 +  +4   6 ++
--R         ||     |  |      ||
--R         |+8  12+  +10  15+|
--R   (38)  |                 |
--R         |+0  1+    +0  2+ |
--R         ||    |    |    | |
--R         ++0  4+    +0  5+ +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 38

--S 39 of 48
transpose Tmn
 

         ++2  8+   +4  10++
         ||    |   |     ||
         |+0  0+   +0  0 +|
   (39)  |                |
         |+3  12+  +6  15+|
         ||     |  |     ||
         ++1  4 +  +2  5 ++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  8+   +4  10++
--R         ||    |   |     ||
--R         |+0  0+   +0  0 +|
--R   (39)  |                |
--R         |+3  12+  +6  15+|
--R         ||     |  |     ||
--R         ++1  4 +  +2  5 ++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 39

--S 40 of 48
transpose Tm = transpose m
 

         +1  4+  +1  4+
   (40)  |    |= |    |
         +2  5+  +2  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +1  4+  +1  4+
--R   (40)  |    |= |    |
--R         +2  5+  +2  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 40

--S 41 of 48
rTmn := reindex(Tmn, [1,4,2,3])
 

         ++2  0+   +3  1+ +
         ||    |   |    | |
         |+4  0+   +6  2+ |
   (41)  |                |
         |+8   0+  +12  4+|
         ||     |  |     ||
         ++10  0+  +15  5++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  0+   +3  1+ +
--R         ||    |   |    | |
--R         |+4  0+   +6  2+ |
--R   (41)  |                |
--R         |+8   0+  +12  4+|
--R         ||     |  |     ||
--R         ++10  0+  +15  5++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 41

--S 42 of 48
tt := transpose(Tm)*Tn - Tn*transpose(Tm)
 

         +- 6  - 16+
   (42)  |         |
         + 2    6  +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +- 6  - 16+
--R   (42)  |         |
--R         + 2    6  +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 42

--S 43 of 48
Tv*(tt+Tn)
 

   (43)  [- 4,- 11]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (43)  [- 4,- 11]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 43

--S 44 of 48
reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm)
 

         ++46   84 +  +57   114++
         ||        |  |        ||
         |+174  212+  +228  285+|
   (44)  |                      |
         | +18  24+    +17  30+ |
         | |      |    |      | |
         + +57  63+    +63  76+ +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++46   84 +  +57   114++
--R         ||        |  |        ||
--R         |+174  212+  +228  285+|
--R   (44)  |                      |
--R         | +18  24+    +17  30+ |
--R         | |      |    |      | |
--R         + +57  63+    +63  76+ +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 44

--S 45 of 48
delta:  CT := kroneckerDelta()
 

         +1  0+
   (45)  |    |
         +0  1+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +1  0+
--R   (45)  |    |
--R         +0  1+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 45

--S 46 of 48
contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2])
 

         + +2  4+   +0  0++  + +2  4+   +0  0++
         | |    |   |    ||  | |    |   |    ||
         | +3  6+   +1  2+|  | +3  6+   +1  2+|
   (46)  |                |= |                |
         |+8   10+  +0  0+|  |+8   10+  +0  0+|
         ||      |  |    ||  ||      |  |    ||
         ++12  15+  +4  5++  ++12  15+  +4  5++
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         + +2  4+   +0  0++  + +2  4+   +0  0++
--R         | |    |   |    ||  | |    |   |    ||
--R         | +3  6+   +1  2+|  | +3  6+   +1  2+|
--R   (46)  |                |= |                |
--R         |+8   10+  +0  0+|  |+8   10+  +0  0+|
--R         ||      |  |    ||  ||      |  |    ||
--R         ++12  15+  +4  5++  ++12  15+  +4  5++
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 46

--S 47 of 48
epsilon:CT := leviCivitaSymbol()
 

         + 0   1+
   (47)  |      |
         +- 1  0+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         + 0   1+
--R   (47)  |      |
--R         +- 1  0+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 47

--S 48 of 48
contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m
 

   (48)  - 6= - 6
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R   (48)  - 6= - 6
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 48
)spool
 
Starts dribbling to cyfactor.output (2009/2/17, 17:44:30).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 10
factor(x**84 - 1)
 

   (1)
                     2           2       2           4    2
     (x - 1)(x + 1)(x  - x + 1)(x  + 1)(x  + x + 1)(x  - x  + 1)
  *
       6    5    4    3    2           6    5    4    3    2
     (x  - x  + x  - x  + x  - x + 1)(x  + x  + x  + x  + x  + x + 1)
  *
       12    11    9    8    6    4    3
     (x   - x   + x  - x  + x  - x  + x  - x + 1)
  *
       12    10    8    6    4    2
     (x   - x   + x  - x  + x  - x  + 1)
  *
       12    11    9    8    6    4    3
     (x   + x   - x  - x  + x  - x  - x  + x + 1)
  *
       24    22    18    16    12    8    6    2
     (x   + x   - x   - x   + x   - x  - x  + x  + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (1)
--R                     2           2       2           4    2
--R     (x - 1)(x + 1)(x  - x + 1)(x  + 1)(x  + x + 1)(x  - x  + 1)
--R  *
--R       6    5    4    3    2           6    5    4    3    2
--R     (x  - x  + x  - x  + x  - x + 1)(x  + x  + x  + x  + x  + x + 1)
--R  *
--R       12    11    9    8    6    4    3
--R     (x   - x   + x  - x  + x  - x  + x  - x + 1)
--R  *
--R       12    10    8    6    4    2
--R     (x   - x   + x  - x  + x  - x  + 1)
--R  *
--R       12    11    9    8    6    4    3
--R     (x   + x   - x  - x  + x  - x  - x  + x + 1)
--R  *
--R       24    22    18    16    12    8    6    2
--R     (x   + x   - x   - x   + x   - x  - x  + x  + 1)
--R                                            Type: Factored Polynomial Integer
--E 1

--S 2 of 10
factor(-(x**68 -1))
 

   (2)
   -
                        2
        (x - 1)(x + 1)(x  + 1)
     *
           16    15    14    13    12    11    10    9    8    7    6    5    4
          x   - x   + x   - x   + x   - x   + x   - x  + x  - x  + x  - x  + x
        + 
             3    2
          - x  + x  - x + 1
     *
           16    15    14    13    12    11    10    9    8    7    6    5    4
          x   + x   + x   + x   + x   + x   + x   + x  + x  + x  + x  + x  + x
        + 
           3    2
          x  + x  + x + 1
     *
           32    30    28    26    24    22    20    18    16    14    12    10
          x   - x   + x   - x   + x   - x   + x   - x   + x   - x   + x   - x
        + 
           8    6    4    2
          x  - x  + x  - x  + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (2)
--R   -
--R                        2
--R        (x - 1)(x + 1)(x  + 1)
--R     *
--R           16    15    14    13    12    11    10    9    8    7    6    5    4
--R          x   - x   + x   - x   + x   - x   + x   - x  + x  - x  + x  - x  + x
--R        + 
--R             3    2
--R          - x  + x  - x + 1
--R     *
--R           16    15    14    13    12    11    10    9    8    7    6    5    4
--R          x   + x   + x   + x   + x   + x   + x   + x  + x  + x  + x  + x  + x
--R        + 
--R           3    2
--R          x  + x  + x + 1
--R     *
--R           32    30    28    26    24    22    20    18    16    14    12    10
--R          x   - x   + x   - x   + x   - x   + x   - x   + x   - x   + x   - x
--R        + 
--R           8    6    4    2
--R          x  - x  + x  - x  + 1
--R                                            Type: Factored Polynomial Integer
--E 2

--S 3 of 10
factor(x**99 + 1)
 

   (3)
              2           6    3
     (x + 1)(x  - x + 1)(x  - x  + 1)
  *
       10    9    8    7    6    5    4    3    2
     (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
  *
        20    19    17    16    14    13    11    10    9    7    6    4    3
       x   + x   - x   - x   + x   + x   - x   - x   - x  + x  + x  - x  - x
     + 
       x + 1
  *
        60    57    51    48    42    39    33    30    27    21    18    12
       x   + x   - x   - x   + x   + x   - x   - x   - x   + x   + x   - x
     + 
          9    3
       - x  + x  + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (3)
--R              2           6    3
--R     (x + 1)(x  - x + 1)(x  - x  + 1)
--R  *
--R       10    9    8    7    6    5    4    3    2
--R     (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
--R  *
--R        20    19    17    16    14    13    11    10    9    7    6    4    3
--R       x   + x   - x   - x   + x   + x   - x   - x   - x  + x  + x  - x  - x
--R     + 
--R       x + 1
--R  *
--R        60    57    51    48    42    39    33    30    27    21    18    12
--R       x   + x   - x   - x   + x   + x   - x   - x   - x   + x   + x   - x
--R     + 
--R          9    3
--R       - x  + x  + 1
--R                                            Type: Factored Polynomial Integer
--E 3

--S 4 of 10
factor(-(x**77 +1))
 

   (4)
   -
                 6    5    4    3    2
        (x + 1)(x  - x  + x  - x  + x  - x + 1)
     *
          10    9    8    7    6    5    4    3    2
        (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
     *
           60    59    53    52    49    48    46    45    42    41    39    37
          x   + x   - x   - x   - x   - x   + x   + x   + x   + x   - x   + x
        + 
             35    34    32    30    28    26    25    23    21    19    18
          - x   - x   + x   - x   + x   - x   - x   + x   - x   + x   + x
        + 
           15    14    12    11    8    7
          x   + x   - x   - x   - x  - x  + x + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (4)
--R   -
--R                 6    5    4    3    2
--R        (x + 1)(x  - x  + x  - x  + x  - x + 1)
--R     *
--R          10    9    8    7    6    5    4    3    2
--R        (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
--R     *
--R           60    59    53    52    49    48    46    45    42    41    39    37
--R          x   + x   - x   - x   - x   - x   + x   + x   + x   + x   - x   + x
--R        + 
--R             35    34    32    30    28    26    25    23    21    19    18
--R          - x   - x   + x   - x   + x   - x   - x   + x   - x   + x   + x
--R        + 
--R           15    14    12    11    8    7
--R          x   + x   - x   - x   - x  - x  + x + 1
--R                                            Type: Factored Polynomial Integer
--E 4

--S 5 of 10
ind := 2**6
 

   (5)  64
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  64
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
factor(x**ind + 1)
 

         64
   (6)  x   + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R         64
--R   (6)  x   + 1
--R                                            Type: Factored Polynomial Integer
--E 6

--S 7 of 10
ind := 2**7
 

   (7)  128
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  128
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 10
factor(-(x**ind + 1))
 

            128
   (8)  - (x    + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R            128
--R   (8)  - (x    + 1)
--R                                            Type: Factored Polynomial Integer
--E 8

--S 9 of 10
factor(x**84 + 1)
 

   (9)
       4       8    4       24    20    16    12    8    4
     (x  + 1)(x  - x  + 1)(x   - x   + x   - x   + x  - x  + 1)
  *
       48    44    36    32    24    16    12    4
     (x   + x   - x   - x   + x   - x   - x   + x  + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (9)
--R       4       8    4       24    20    16    12    8    4
--R     (x  + 1)(x  - x  + 1)(x   - x   + x   - x   + x  - x  + 1)
--R  *
--R       48    44    36    32    24    16    12    4
--R     (x   + x   - x   - x   + x   - x   - x   + x  + 1)
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10 of 10
D
 

   (10)  D
                                                             Type: Variable D
--R 
--R
--R   (10)  D
--R                                                             Type: Variable D
--E 10
)spool
 
Starts dribbling to schaum7.output (2009/2/17, 18:0:5).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(x^2-a^2),x)
 

        - log(x + a) + log(x - a)
   (1)  -------------------------
                    2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(x + a) + log(x - a)
--R   (1)  -------------------------
--R                    2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/(2*a)*log((x-a)/(x+a))
 

            x - a
        log(-----)
            x + a
   (2)  ----------
            2a
                                                     Type: Expression Integer
--R
--R            x - a
--R        log(-----)
--R            x + a
--R   (2)  ----------
--R            2a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 4
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5      14:144 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 6
aa:=integrate(x/(x^2-a^2),x)
 

             2    2
        log(x  - a )
   (1)  ------------
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R        log(x  - a )
--R   (1)  ------------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7
bb:=1/2*log(x^2-a^2)
 

             2    2
        log(x  - a )
   (2)  ------------
              2
                                                     Type: Expression Integer
--R
--R             2    2
--R        log(x  - a )
--R   (2)  ------------
--R              2
--R                                                     Type: Expression Integer
--E

--S 8      14:145 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 9
aa:=integrate(x^2/(x^2-a^2),x)
 

        - a log(x + a) + a log(x - a) + 2x
   (1)  ----------------------------------
                         2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - a log(x + a) + a log(x - a) + 2x
--R   (1)  ----------------------------------
--R                         2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 10
bb:=x+a/2*log((x-a)/(x+a))
 

              x - a
        a log(-----) + 2x
              x + a
   (2)  -----------------
                2
                                                     Type: Expression Integer
--R
--R              x - a
--R        a log(-----) + 2x
--R              x + a
--R   (2)  -----------------
--R                2
--R                                                     Type: Expression Integer
--E

--S 11
cc:=aa-bb
 

                                              x - a
        - a log(x + a) + a log(x - a) - a log(-----)
                                              x + a
   (3)  --------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R                                              x - a
--R        - a log(x + a) + a log(x - a) - a log(-----)
--R                                              x + a
--R   (3)  --------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 12
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 13     14:146 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 14
aa:=integrate(x^3/(x^2-a^2),x)
 

         2     2    2     2
        a log(x  - a ) + x
   (1)  -------------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         2     2    2     2
--R        a log(x  - a ) + x
--R   (1)  -------------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 15
bb:=x^2/2+a^2/2*log(x^2-a^2)
 

         2     2    2     2
        a log(x  - a ) + x
   (2)  -------------------
                 2
                                                     Type: Expression Integer
--R
--R         2     2    2     2
--R        a log(x  - a ) + x
--R   (2)  -------------------
--R                 2
--R                                                     Type: Expression Integer
--E

--S 16     14:147 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 17
aa:=integrate(1/(x*(x^2-a^2)),x)
 

             2    2
        log(x  - a ) - 2log(x)
   (1)  ----------------------
                    2
                  2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R        log(x  - a ) - 2log(x)
--R   (1)  ----------------------
--R                    2
--R                  2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 18
bb:=1/(2*a^2)*log((x^2-a^2)/x^2)
 

             2    2
            x  - a
        log(-------)
                2
               x
   (2)  ------------
               2
             2a
                                                     Type: Expression Integer
--R
--R             2    2
--R            x  - a
--R        log(-------)
--R                2
--R               x
--R   (2)  ------------
--R               2
--R             2a
--R                                                     Type: Expression Integer
--E

--S 19
cc:=aa-bb
 

                                      2    2
             2    2                  x  - a
        log(x  - a ) - 2log(x) - log(-------)
                                         2
                                        x
   (3)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                                      2    2
--R             2    2                  x  - a
--R        log(x  - a ) - 2log(x) - log(-------)
--R                                         2
--R                                        x
--R   (3)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 20
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 21
dd:=divlog cc
 

             2
        log(x ) - 2log(x)
   (5)  -----------------
                 2
               2a
                                                     Type: Expression Integer
--R
--R             2
--R        log(x ) - 2log(x)
--R   (5)  -----------------
--R                 2
--R               2a
--R                                                     Type: Expression Integer
--E

--S 22
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 23     14:148 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 24
aa:=integrate(1/(x^2*(x^2-a^2)),x)
 

        - x log(x + a) + x log(x - a) + 2a
   (1)  ----------------------------------
                         3
                       2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - x log(x + a) + x log(x - a) + 2a
--R   (1)  ----------------------------------
--R                         3
--R                       2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25
bb:=1/(a^2*x)+1/(2*a^3)*log((x-a)/(x+a))
 

              x - a
        x log(-----) + 2a
              x + a
   (2)  -----------------
                 3
               2a x
                                                     Type: Expression Integer
--R
--R              x - a
--R        x log(-----) + 2a
--R              x + a
--R   (2)  -----------------
--R                 3
--R               2a x
--R                                                     Type: Expression Integer
--E

--S 26
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                            3
                          2a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                            3
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 27
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 28     14:149 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(1/(x^3*(x^2-a^2)),x)
 

         2     2    2      2          2
        x log(x  - a ) - 2x log(x) + a
   (1)  -------------------------------
                       4 2
                     2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         2     2    2      2          2
--R        x log(x  - a ) - 2x log(x) + a
--R   (1)  -------------------------------
--R                       4 2
--R                     2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))
 

                    2
           2       x        2
        - x log(-------) + a
                 2    2
                x  - a
   (2)  ---------------------
                  4 2
                2a x
                                                     Type: Expression Integer
--R
--R                    2
--R           2       x        2
--R        - x log(-------) + a
--R                 2    2
--R                x  - a
--R   (2)  ---------------------
--R                  4 2
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 31
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 32
t1:=divlog bb
 

           2     2     2     2    2     2
        - x log(x ) + x log(x  - a ) + a
   (4)  ---------------------------------
                        4 2
                      2a x
                                                     Type: Expression Integer
--R
--R           2     2     2     2    2     2
--R        - x log(x ) + x log(x  - a ) + a
--R   (4)  ---------------------------------
--R                        4 2
--R                      2a x
--R                                                     Type: Expression Integer
--E

--S 33
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (5)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (5)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34
t2:=logpow t1
 

         2     2    2      2          2
        x log(x  - a ) - 2x log(x) + a
   (6)  -------------------------------
                       4 2
                     2a x
                                                     Type: Expression Integer
--R
--R         2     2    2      2          2
--R        x log(x  - a ) - 2x log(x) + a
--R   (6)  -------------------------------
--R                       4 2
--R                     2a x
--R                                                     Type: Expression Integer
--E

--S 35     14:150 Schaums and Axiom agree
cc:=aa-t2
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(1/((x^2-a^2)^2),x)
 

          2    2                  2    2
        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                              3 2     5
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2                  2    2
--R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                              3 2     5
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37
bb:=-x/(2*a^2*(x^2-a^2))-1/(4*a^3)*log((x-a)/(x+a))
 

            2    2     x - a
        (- x  + a )log(-----) - 2a x
                       x + a
   (2)  ----------------------------
                   3 2     5
                 4a x  - 4a
                                                     Type: Expression Integer
--R
--R            2    2     x - a
--R        (- x  + a )log(-----) - 2a x
--R                       x + a
--R   (2)  ----------------------------
--R                   3 2     5
--R                 4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 38
cc:=aa-bb
 

                                      x - a
        log(x + a) - log(x - a) + log(-----)
                                      x + a
   (3)  ------------------------------------
                           3
                         4a
                                                     Type: Expression Integer
--R
--R                                      x - a
--R        log(x + a) - log(x - a) + log(-----)
--R                                      x + a
--R   (3)  ------------------------------------
--R                           3
--R                         4a
--R                                                     Type: Expression Integer
--E

--S 39
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 40     14:151 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 41
aa:=integrate(x/((x^2-a^2)^2),x)
 

              1
   (1)  - ---------
            2     2
          2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            2     2
--R          2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42
bb:=-1/(2*(x^2-a^2))
 

              1
   (2)  - ---------
            2     2
          2x  - 2a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            2     2
--R          2x  - 2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 43     14:152 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 44
aa:=integrate(x^2/((x^2-a^2)^2),x)
 

            2    2                2    2
        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                                2     3
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2                2    2
--R        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                                2     3
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 45
bb:=-x/(2*(x^2-a^2))+1/(4*a)*log((x-a)/(x+a))
 

          2    2     x - a
        (x  - a )log(-----) - 2a x
                     x + a
   (2)  --------------------------
                    2     3
                4a x  - 4a
                                                     Type: Expression Integer
--R
--R          2    2     x - a
--R        (x  - a )log(-----) - 2a x
--R                     x + a
--R   (2)  --------------------------
--R                    2     3
--R                4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 46
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 47
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 48     14:153 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(x^3/((x^2-a^2)^2),x)
 

          2    2      2    2     2
        (x  - a )log(x  - a ) - a
   (1)  --------------------------
                   2     2
                 2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      2    2     2
--R        (x  - a )log(x  - a ) - a
--R   (1)  --------------------------
--R                   2     2
--R                 2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50
bb:=-a^2/(2*(x^2-a^2))+1/2*log(x^2-a^2)
 

          2    2      2    2     2
        (x  - a )log(x  - a ) - a
   (2)  --------------------------
                   2     2
                 2x  - 2a
                                                     Type: Expression Integer
--R
--R          2    2      2    2     2
--R        (x  - a )log(x  - a ) - a
--R   (2)  --------------------------
--R                   2     2
--R                 2x  - 2a
--R                                                     Type: Expression Integer
--E

--S 51     14:154 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 52
aa:=integrate(1/(x*(x^2-a^2)^2),x)
 

            2    2      2    2       2     2           2
        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
   (1)  ------------------------------------------------
                             4 2     6
                           2a x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2      2    2       2     2           2
--R        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
--R   (1)  ------------------------------------------------
--R                             4 2     6
--R                           2a x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53
bb:=-1/(2*a^2*(x^2-a^2))+1/(2*a^4)*log(x^2/(x^2-a^2))
 

                         2
          2    2        x        2
        (x  - a )log(-------) - a
                      2    2
                     x  - a
   (2)  --------------------------
                  4 2     6
                2a x  - 2a
                                                     Type: Expression Integer
--R
--R                         2
--R          2    2        x        2
--R        (x  - a )log(-------) - a
--R                      2    2
--R                     x  - a
--R   (2)  --------------------------
--R                  4 2     6
--R                2a x  - 2a
--R                                                     Type: Expression Integer
--E

--S 54
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  - a ) + 2log(x) - log(-------)
                                        2    2
                                       x  - a
   (3)  ---------------------------------------
                            4
                          2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  - a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  - a
--R   (3)  ---------------------------------------
--R                            4
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 55
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 56
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 57
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 58     14:155 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 59
aa:=integrate(1/(x^2*(x^2-a^2)^2),x)
 

           3     2                    3     2                   2     3
        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
   (1)  ---------------------------------------------------------------
                                    5 3     7
                                  4a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R
--R           3     2                    3     2                   2     3
--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
--R   (1)  ---------------------------------------------------------------
--R                                    5 3     7
--R                                  4a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 60
bb:=-1/(a^4*x)-x/(2*a^4*(x^2-a^2))-3/(4*a^5)*log((x-a)/(x+a))
 

             3     2      x - a        2     3
        (- 3x  + 3a x)log(-----) - 6a x  + 4a
                          x + a
   (2)  --------------------------------------
                       5 3     7
                     4a x  - 4a x
                                                     Type: Expression Integer
--R
--R             3     2      x - a        2     3
--R        (- 3x  + 3a x)log(-----) - 6a x  + 4a
--R                          x + a
--R   (2)  --------------------------------------
--R                       5 3     7
--R                     4a x  - 4a x
--R                                                     Type: Expression Integer
--E

--S 61
cc:=aa-bb
 

                                         x - a
        3log(x + a) - 3log(x - a) + 3log(-----)
                                         x + a
   (3)  ---------------------------------------
                            5
                          4a
                                                     Type: Expression Integer
--R
--R                                         x - a
--R        3log(x + a) - 3log(x - a) + 3log(-----)
--R                                         x + a
--R   (3)  ---------------------------------------
--R                            5
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 62
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 63     14:156 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 64
aa:=integrate(1/(x^3*(x^2-a^2)^2),x)
 

             4     2 2      2    2       4     2 2            2 2    4
        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
   (1)  --------------------------------------------------------------
                                   6 4     8 2
                                 2a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4     2 2      2    2       4     2 2            2 2    4
--R        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
--R   (1)  --------------------------------------------------------------
--R                                   6 4     8 2
--R                                 2a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 65
bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2-a^2))+1/a^6*log(x^2/(x^2-a^2))
 

                             2
           4     2 2        x         2 2    4
        (2x  - 2a x )log(-------) - 2a x  + a
                          2    2
                         x  - a
   (2)  --------------------------------------
                       6 4     8 2
                     2a x  - 2a x
                                                     Type: Expression Integer
--R
--R                             2
--R           4     2 2        x         2 2    4
--R        (2x  - 2a x )log(-------) - 2a x  + a
--R                          2    2
--R                         x  - a
--R   (2)  --------------------------------------
--R                       6 4     8 2
--R                     2a x  - 2a x
--R                                                     Type: Expression Integer
--E

--S 66
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  - a ) + 2log(x) - log(-------)
                                        2    2
                                       x  - a
   (3)  ---------------------------------------
                            6
                           a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  - a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  - a
--R   (3)  ---------------------------------------
--R                            6
--R                           a
--R                                                     Type: Expression Integer
--E

--S 67
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 68
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  6
                 a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  6
--R                 a
--R                                                     Type: Expression Integer
--E

--S 69
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 70     14:157 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 71     14:158 Axiom cannot do this integral
aa:=integrate(1/((x^2-a^2)^n),x)
 

           x
         ++        1
   (1)   |   ------------- d%L
        ++       2     2 n
             (- a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++        1
--I   (1)   |   ------------- d%L
--R        ++       2     2 n
--I             (- a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 72
aa:=integrate(x/((x^2-a^2)^n),x)
 

                   2    2
                - x  + a
   (1)  ------------------------
                         2    2
                  n log(x  - a )
        (2n - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2    2
--R                - x  + a
--R   (1)  ------------------------
--R                         2    2
--R                  n log(x  - a )
--R        (2n - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 73
bb:=-1/(2*(n-1)*(x^2-a^2)^(n-1))
 

                     1
   (2)  - ----------------------
                    2    2 n - 1
          (2n - 2)(x  - a )
                                                     Type: Expression Integer
--R
--R                     1
--R   (2)  - ----------------------
--R                    2    2 n - 1
--R          (2n - 2)(x  - a )
--R                                                     Type: Expression Integer
--E

--S 74
cc:=aa-bb
 

                 2    2
          n log(x  - a )       2    2   2    2 n - 1
        %e               + (- x  + a )(x  - a )
   (3)  --------------------------------------------
                                          2    2
                     2    2 n - 1  n log(x  - a )
           (2n - 2)(x  - a )     %e
                                                     Type: Expression Integer
--R
--R                 2    2
--R          n log(x  - a )       2    2   2    2 n - 1
--R        %e               + (- x  + a )(x  - a )
--R   (3)  --------------------------------------------
--R                                          2    2
--R                     2    2 n - 1  n log(x  - a )
--R           (2n - 2)(x  - a )     %e
--R                                                     Type: Expression Integer
--E

--S 75
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 76
dd:=explog cc
 

          2    2 n       2    2   2    2 n - 1
        (x  - a )  + (- x  + a )(x  - a )
   (5)  --------------------------------------
                     2    2 n - 1  2    2 n
           (2n - 2)(x  - a )     (x  - a )
                                                     Type: Expression Integer
--R
--R          2    2 n       2    2   2    2 n - 1
--R        (x  - a )  + (- x  + a )(x  - a )
--R   (5)  --------------------------------------
--R                     2    2 n - 1  2    2 n
--R           (2n - 2)(x  - a )     (x  - a )
--R                                                     Type: Expression Integer
--E

--S 77     14:159 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 78     14:160 Axiom cannot compute this integral
aa:=integrate(1/(x*(x^2-a^2)^n),x)
 

           x
         ++          1
   (1)   |   ---------------- d%L
        ++          2     2 n
             %L (- a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++          1
--I   (1)   |   ---------------- d%L
--R        ++          2     2 n
--I             %L (- a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 79     14:161 Axiom cannot compute this integral
aa:=integrate(x^m/((x^2-a^2)^n),x)
 

           x        m
         ++       %L
   (1)   |   ------------- d%L
        ++       2     2 n
             (- a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x        m
--I         ++       %L
--I   (1)   |   ------------- d%L
--R        ++       2     2 n
--I             (- a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 80     14:162 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(x^2-a^2)^n),x)
 

           x
         ++          1
   (1)   |   ---------------- d%L
        ++       2     2 n  m
             (- a  + %L ) %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++          1
--I   (1)   |   ---------------- d%L
--R        ++       2     2 n  m
--I             (- a  + %L ) %L
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to polycoer.output (2009/2/17, 17:56:15).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 41
u : UP(x,COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 41
u := (2+3*%i)*x**5 - 7*x**4 +x**2 + 89
 

                  5     4    2
   (2)  (2 + 3%i)x  - 7x  + x  + 89
                                Type: UnivariatePolynomial(x,Complex Integer)
--R 
--R
--R                  5     4    2
--R   (2)  (2 + 3%i)x  - 7x  + x  + 89
--R                                Type: UnivariatePolynomial(x,Complex Integer)
--E 2

--S 3 of 41
m : MPOLY([x,y,z],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 41
m := u
 

                  5     4    2
   (4)  (2 + 3%i)x  - 7x  + x  + 89
                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                  5     4    2
--R   (4)  (2 + 3%i)x  - 7x  + x  + 89
--R                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--E 4

--S 5 of 41
m := m*y - z**2
 

                    5       4      2          2
   (5)  (2 + 3%i)y x  - 7y x  + y x  + 89y - z
                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                    5       4      2          2
--R   (5)  (2 + 3%i)y x  - 7y x  + y x  + 89y - z
--R                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--E 5

--S 6 of 41
m1 : MPOLY([r,z,t,x,s,y],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 41
m1 := m
 

           2               5       4      2
   (7)  - z  + (2 + 3%i)y x  - 7y x  + y x  + 89y
                  Type: MultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--R 
--R
--R           2               5       4      2
--R   (7)  - z  + (2 + 3%i)y x  - 7y x  + y x  + 89y
--R                  Type: MultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--E 7

--S 8 of 41
v : DMP([x,y,z],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 41
v := u
 

                  5     4    2
   (9)  (2 + 3%i)x  - 7x  + x  + 89
             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                  5     4    2
--R   (9)  (2 + 3%i)x  - 7x  + x  + 89
--R             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--E 9

--S 10 of 41
u := v
 

                   5     4    2
   (10)  (2 + 3%i)x  - 7x  + x  + 89
                                Type: UnivariatePolynomial(x,Complex Integer)
--R 
--R
--R                   5     4    2
--R   (10)  (2 + 3%i)x  - 7x  + x  + 89
--R                                Type: UnivariatePolynomial(x,Complex Integer)
--E 11

--S 12 of 41
v1 : DMP([r,z,t,x,s,y],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 41
v1 := v
 

                   5     4    2
   (12)  (2 + 3%i)x  - 7x  + x  + 89
       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--R 
--R
--R                   5     4    2
--R   (12)  (2 + 3%i)x  - 7x  + x  + 89
--R       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--E 13

--S 14 of 41
v := m
 

                   5      4     2           2
   (13)  (2 + 3%i)x y - 7x y + x y + 89y - z
             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                   5      4     2           2
--R   (13)  (2 + 3%i)x y - 7x y + x y + 89y - z
--R             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--E 14

--S 15 of 41
v1 := m1
 

            2             5      4     2
   (14)  - z  + (2 + 3%i)x y - 7x y + x y + 89y
       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--R 
--R
--R            2             5      4     2
--R   (14)  - z  + (2 + 3%i)x y - 7x y + x y + 89y
--R       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--E 15

)clear all
 
   All user variables and function definitions have been cleared.

--S 16 of 41
u : DMP([x,y],INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 41
f : UP(x,UP(y,INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 41
u := x + y
 

   (3)  x + y
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R   (3)  x + y
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 18

--S 19 of 41
f := u
 

   (4)  x + y
                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--R 
--R
--R   (4)  x + y
--R                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--E 19

--S 20 of 41
u := x**2*y**9 - x**2*y**2
 

         2 9    2 2
   (5)  x y  - x y
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R         2 9    2 2
--R   (5)  x y  - x y
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 20

--S 21 of 41
f := u
 

          9    2  2
   (6)  (y  - y )x
                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--R 
--R
--R          9    2  2
--R   (6)  (y  - y )x
--R                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--E 21

)clear all
 
   All user variables and function definitions have been cleared.

--S 22 of 41
u : DMP([z,x,y],INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 41
f : UP(x,DMP([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 41
u := x + y + z
 

   (3)  z + x + y
                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--R 
--R
--R   (3)  z + x + y
--R                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--E 24

--S 25 of 41
f := u
 

   (4)  x + y + z
Type: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R   (4)  x + y + z
--RType: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--E 25

--S 26 of 41
u := x**2*y - z*x**2 + y*z - x**3*y*z + 3
 

             3       2          2
   (5)  - z x y - z x  + z y + x y + 3
                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--R 
--R
--R             3       2          2
--R   (5)  - z x y - z x  + z y + x y + 3
--R                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--E 26

--S 27 of 41
f := x**2*y - z*x**2 + y*z - x**3*y*z + 3
 

               3           2
   (6)  - y z x  + (y - z)x  + y z + 3
Type: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R               3           2
--R   (6)  - y z x  + (y - z)x  + y z + 3
--RType: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--E 27

--S 28 of 41
f := u
 

               3           2
   (7)  - y z x  + (y - z)x  + y z + 3
Type: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R               3           2
--R   (7)  - y z x  + (y - z)x  + y z + 3
--RType: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--E 28

)clear all
 
   All user variables and function definitions have been cleared.

--S 29 of 41
u : DMP([x,y,z,w],INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 41
f : UP(w,DMP([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 41
u := y**2 - w**5*y**2 - z*w + 3
 

           2 5    2
   (3)  - y w  + y  - z w + 3
                   Type: DistributedMultivariatePolynomial([x,y,z,w],Integer)
--R 
--R
--R           2 5    2
--R   (3)  - y w  + y  - z w + 3
--R                   Type: DistributedMultivariatePolynomial([x,y,z,w],Integer)
--E 31

--S 32 of 41
f := y**2 - w**5*y**2 - z*w + 3
 

           2 5          2
   (4)  - y w  - z w + y  + 3
Type: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R           2 5          2
--R   (4)  - y w  - z w + y  + 3
--RType: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--E 32

--S 33 of 41
f := u
 

           2 5          2
   (5)  - y w  - z w + y  + 3
Type: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R           2 5          2
--R   (5)  - y w  - z w + y  + 3
--RType: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--E 33

)clear all
 
   All user variables and function definitions have been cleared.

--S 34 of 41
(x1,x2,x3) : DMP([a,b,c,d,e,f],Fraction INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 41
x1 := 2*a + 3*b - c
 

   (2)  2a + 3b - c
      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (2)  2a + 3b - c
--R      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 35

--S 36 of 41
x2 := 3 - 3*e + f
 

   (3)  - 3e + f + 3
      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (3)  - 3e + f + 3
--R      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 36

--S 37 of 41
x3 := a + b + c + d + e + f
 

   (4)  a + b + c + d + e + f
      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (4)  a + b + c + d + e + f
--R      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 37

--S 38 of 41
l1 : List DMP([a,b,c,d,e,f],Fraction INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 38

--S 39 of 41
l2 : List UP(f,DMP([a,b,c,d,e],Fraction INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 39

--S 40 of 41
l1 := [x1,x2,x3]
 

   (7)  [2a + 3b - c,- 3e + f + 3,a + b + c + d + e + f]
 Type: List DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (7)  [2a + 3b - c,- 3e + f + 3,a + b + c + d + e + f]
--R Type: List DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 40

--S 41 of 41
l2 := l1
 

   (8)  [2a + 3b - c,f - 3e + 3,f + a + b + c + d + e]
Type: List UnivariatePolynomial(f,DistributedMultivariatePolynomial([a,b,c,d,e],Fraction Integer))
--R 
--R
--R   (8)  [2a + 3b - c,f - 3e + 3,f + a + b + c + d + e]
--RType: List UnivariatePolynomial(f,DistributedMultivariatePolynomial([a,b,c,d,e],Fraction Integer))
--E 41
)spool 
 
Starts dribbling to classtalk.output (2009/2/17, 17:44:9).
)set message test on
 
)set message auto off
 
)set break resume
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
1
 

   (1)  1
                                                        Type: PositiveInteger
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 1

--S 2
1/2
 

        1
   (2)  -
        2
                                                       Type: Fraction Integer
--R
--R        1
--R   (2)  -
--R        2
--R                                                       Type: Fraction Integer
--E 2

--S 3
3+4*%i
 

   (3)  3 + 4%i
                                                        Type: Complex Integer
--R
--R   (3)  3 + 4%i
--R                                                        Type: Complex Integer
--E 3

--S 4
3.4
 

   (4)  3.4
                                                                  Type: Float
--R
--R   (4)  3.4
--R                                                                  Type: Float
--E 4

--S 5
X::ROMAN
 

   (5)  X
                                                           Type: RomanNumeral
--R
--R   (5)  X
--R                                                           Type: RomanNumeral
--E 5

--S 6
binary(5)
 

   (6)  101
                                                        Type: BinaryExpansion
--R
--R   (6)  101
--R                                                        Type: BinaryExpansion
--E 6

--S 7
factor(60)
 

         2
   (7)  2 3 5
                                                       Type: Factored Integer
--R
--R         2
--R   (7)  2 3 5
--R                                                       Type: Factored Integer
--E 7

--S 8
q:=(y-1)*x*(z+5)
 

   (8)  (x y - x)z + 5x y - 5x
                                                     Type: Polynomial Integer
--R
--R   (8)  (x y - x)z + 5x y - 5x
--R                                                     Type: Polynomial Integer
--E 8

--S 9
factor q
 

   (9)  x(y - 1)(z + 5)
                                            Type: Factored Polynomial Integer
--R
--R   (9)  x(y - 1)(z + 5)
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10
eval(q,[x=5,y=6,z=7])
 

   (10)  300
                                                     Type: Polynomial Integer
--R
--R   (10)  300
--R                                                     Type: Polynomial Integer
--E 10

--S 11
eval(q,[x=5,y=6])
 

   (11)  25z + 125
                                                     Type: Polynomial Integer
--R
--R   (11)  25z + 125
--R                                                     Type: Polynomial Integer
--E 11

--S 12
b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a]
 

                   a
   (12)  [log(a),%e ,asin(a),acos(a),atan(a),acot(a),sinh(a)]
                                                Type: List Expression Integer
--R
--R                   a
--R   (12)  [log(a),%e ,asin(a),acos(a),atan(a),acot(a),sinh(a)]
--R                                                Type: List Expression Integer
--E 12

--S 13
[exp b.1, log b.2, sin b.3, cos b.4, tan b.5, cot b.6, asinh b.7]
 

   (13)  [a,a,a,a,a,a,a]
                                                Type: List Expression Integer
--R
--R   (13)  [a,a,a,a,a,a,a]
--R                                                Type: List Expression Integer
--E 13

--S 14
a:=.7
 

   (14)  0.7
                                                                  Type: Float
--R
--R   (14)  0.7
--R                                                                  Type: Float
--E 14

--S 15
b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a]
 

   (15)
   [- 0.3566749439 3873237891, 2.0137527074 704765216, 0.7753974966 1075306374,
    0.7953988301 8414355549, 0.6107259643 8920861654, 0.9600703624 0568800269,
    0.7585837018 3953350346]
                                                             Type: List Float
--R
--R   (15)
--R   [- 0.3566749439 3873237891, 2.0137527074 704765216, 0.7753974966 1075306374,
--R    0.7953988301 8414355549, 0.6107259643 8920861654, 0.9600703624 0568800269,
--R    0.7585837018 3953350346]
--R                                                             Type: List Float
--E 15

--S 16
[exp b.1, log b.2, sin b.3, cos b.4, tan b.5, cot b.6, asinh b.7]
 

   (16)  [0.7,0.7,0.7,0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R
--R   (16)  [0.7,0.7,0.7,0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 16

--S 17
simplify(sin(x)**2+cos(x)**2)
 

   (17)  1
                                                     Type: Expression Integer
--R
--R   (17)  1
--R                                                     Type: Expression Integer
--E 17

)clear all
 
   All user variables and function definitions have been cleared.
--S 18
eq1:=A*x^2 + B*x*y + C*y^2 + D*x + E*y + F
 

           2                   2
   (1)  C y  + (B x + E)y + A x  + D x + F
                                                     Type: Polynomial Integer
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 18

--S 19
rotatex:=x'*cos(t)-y'*sin(t)
 

   (2)  - y' sin(t) + x' cos(t)
                                                     Type: Expression Integer
--R
--R   (2)  - y' sin(t) + x' cos(t)
--R                                                     Type: Expression Integer
--E 19

--S 20
rotatey:=x'*sin(t)+y'*cos(t)
 

   (3)  x' sin(t) + y' cos(t)
                                                     Type: Expression Integer
--R
--R   (3)  x' sin(t) + y' cos(t)
--R                                                     Type: Expression Integer
--E 20

--S 21
eval(eq1,[x=rotatex, y=rotatey])
 

   (4)
          2                 2       2
     (A y'  - B x' y' + C x' )sin(t)
   + 
             2                        2
     ((- B y'  + (2C - 2A)x' y' + B x' )cos(t) - D y' + E x')sin(t)
   + 
          2                 2       2
     (C y'  + B x' y' + A x' )cos(t)  + (E y' + D x')cos(t) + F
                                                     Type: Expression Integer
--R
--R   (4)
--R          2                 2       2
--R     (A y'  - B x' y' + C x' )sin(t)
--R   + 
--R             2                        2
--R     ((- B y'  + (2C - 2A)x' y' + B x' )cos(t) - D y' + E x')sin(t)
--R   + 
--R          2                 2       2
--R     (C y'  + B x' y' + A x' )cos(t)  + (E y' + D x')cos(t) + F
--R                                                     Type: Expression Integer
--E 21

)clear all
 
   All user variables and function definitions have been cleared.
--S 22
a:=rootOf(a^2+a+1)
 

   (1)  a
                                                        Type: AlgebraicNumber
--R
--R   (1)  a
--R                                                        Type: AlgebraicNumber
--E 22

--S 23
factor(x^2+3)
 

         2
   (2)  x  + 3
                                            Type: Factored Polynomial Integer
--R
--R         2
--R   (2)  x  + 3
--R                                            Type: Factored Polynomial Integer
--E 23

--S 24
factor(x^2+3,[a])
 

   (3)  (x - 2a - 1)(x + 2a + 1)
                                    Type: Factored Polynomial AlgebraicNumber
--R
--R   (3)  (x - 2a - 1)(x + 2a + 1)
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 24

--S 25
definingPolynomial(a)
 

         2
   (4)  a  + a + 1
                                                        Type: AlgebraicNumber
--R
--R         2
--R   (4)  a  + a + 1
--R                                                        Type: AlgebraicNumber
--E 25

--S 26
zerosOf(b^2+b+1,b)
 

          +---+        +---+
         \|- 3  - 1 - \|- 3  - 1
   (5)  [----------,------------]
              2           2
                                                Type: List Expression Integer
--R
--R          +---+        +---+
--R         \|- 3  - 1 - \|- 3  - 1
--R   (5)  [----------,------------]
--R              2           2
--R                                                Type: List Expression Integer
--E 26

--S 27
differentiate(sin(x),x)
 

   (6)  cos(x)
                                                     Type: Expression Integer
--R
--R   (6)  cos(x)
--R                                                     Type: Expression Integer
--E 27

--S 28
differentiate(sin(x),x,2)
 

   (7)  - sin(x)
                                                     Type: Expression Integer
--R
--R   (7)  - sin(x)
--R                                                     Type: Expression Integer
--E 28

--S 29
differentiate(cos(z)/(x^2+y^3),[x,y,z],[1,2,3])
 

                    4      3
            (- 84x y  + 24x y)sin(z)
   (8)  --------------------------------
         12     2 9     4 6     6 3    8
        y   + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R
--R                    4      3
--R            (- 84x y  + 24x y)sin(z)
--R   (8)  --------------------------------
--R         12     2 9     4 6     6 3    8
--R        y   + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E 29

--S 30
y:=operator y
 

   (9)  y
                                                          Type: BasicOperator
--R
--R   (9)  y
--R                                                          Type: BasicOperator
--E 30

--S 31
deqx:=D(y(x),x,2)+D(y(x),x)+y(x)
 

          ,,       ,
   (10)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,,       ,
--R   (10)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 31

--S 32
solve(deqx,y,x)
 

                                              x     x
                                      +-+   - -   - -      +-+
                                    x\|3      2     2    x\|3
   (11)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                      2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                              x     x
--R                                      +-+   - -   - -      +-+
--R                                    x\|3      2     2    x\|3
--R   (11)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                      2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 32

)clear all
 
   All user variables and function definitions have been cleared.
--S 33
limit((x^2-3*x+2)/(x^2-1),x=1)
 

          1
   (1)  - -
          2
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R
--R          1
--R   (1)  - -
--R          2
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 33

--S 34
limit(x*log(x),x=0)
 

   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R
--R   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 34

--S 35
limit(sinh(a*x)/tan(b*x),x=0)
 

        a
   (3)  -
        b
                        Type: Union(OrderedCompletion Expression Integer,...)
--R
--R        a
--R   (3)  -
--R        b
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 35

--S 36
limit(sqrt(3*x^2+1)/(5*x),x=%plusInfinity)
 

         +-+
        \|3
   (4)  ----
          5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R
--R         +-+
--R        \|3
--R   (4)  ----
--R          5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 36

--S 37
complexLimit((2+z)/(1-z),z=%infinity)
 

   (5)  - 1
                         Type: OnePointCompletion Fraction Polynomial Integer
--R
--R   (5)  - 1
--R                         Type: OnePointCompletion Fraction Polynomial Integer
--E 37

)clear all
 
   All user variables and function definitions have been cleared.
--S 38
integrate(1+sqrt(x)/x,x)
 

          +-+
   (1)  2\|x  + x
                                          Type: Union(Expression Integer,...)
--R
--R          +-+
--R   (1)  2\|x  + x
--R                                          Type: Union(Expression Integer,...)
--E 38

--S 39
integrate(sin(x)/x,x)
 

   (2)  Si(x)
                                          Type: Union(Expression Integer,...)
--R
--R   (2)  Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 39

--S 40
integrate(exp(-a*x^2),x)
 

           x       2
         ++    - %Q a
   (3)   |   %e      d%Q
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x       2
--R         ++    - %Q a
--R   (3)   |   %e      d%Q
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 40

--S 41
integrate(sin(x)/x^2,x)
 

           x
         ++  sin(%Q)
   (4)   |   ------- d%Q
        ++       2
               %Q
                                          Type: Union(Expression Integer,...)
--R
--R           x
--R         ++  sin(%Q)
--R   (4)   |   ------- d%Q
--R        ++       2
--R               %Q
--R                                          Type: Union(Expression Integer,...)
--E 41

)clear all
 
   All user variables and function definitions have been cleared.
--S 42
integrate(exp(-x)/sqrt(x),x=0..%plusInfinity)
 

         _ 1
   (1)  | (-)
           2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R         _ 1
--R   (1)  | (-)
--R           2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 42

--S 43
integrate(1/x^2,x=-1..1)
 
 
Daly Bug
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 43

)clear all
 
   All user variables and function definitions have been cleared.

--S 44
integrate(sin(x)^3/(sin(x)^3+cos(x)^3),x=0..%pi/2,"noPole")
 

        2log(16) - 4log(4) + 3%pi
   (1)  -------------------------
                    12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R        2log(16) - 4log(4) + 3%pi
--R   (1)  -------------------------
--R                    12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 44

--S 45
integrate(exp(-x^2)*log(x)^2,x=0..%plusInfinity)
 

         _ 1             1     _ 1         1 2
        | (-)polygamma(1,-) + | (-)digamma(-)
           2             2       2         2
   (2)  --------------------------------------
                           8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R         _ 1             1     _ 1         1 2
--R        | (-)polygamma(1,-) + | (-)digamma(-)
--R           2             2       2         2
--R   (2)  --------------------------------------
--R                           8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 45

)clear all
 
   All user variables and function definitions have been cleared.

--S 46
laplace(sin(a*t)*cosh(a*t)-cos(a*t)*sinh(a*t),t,s)
 

             3
           4a
   (1)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R
--R             3
--R           4a
--R   (1)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 46

--S 47
laplace(2/t * (1-cos(a*t)),t,s)
 

             2    2
   (2)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R
--R             2    2
--R   (2)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 47

--S 48
laplace((exp(a*t)-exp(b*t))/t,t,s)
 

   (3)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R
--R   (3)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 48

--S 49
laplace(exp(a*t+b)*Ei(c*t),t,s)
 

          b    s + c - a
        %e log(---------)
                   c
   (4)  -----------------
              s - a
                                                     Type: Expression Integer
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (4)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 49

)clear all
 
   All user variables and function definitions have been cleared.
--S 50
K:=Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 50

--S 51
qf:QFORM(2,K):=quadraticForm matrix([[-1,0],[0,-1]])$(SQMATRIX(2,K))
 

        +- 1   0 +
   (2)  |        |
        + 0   - 1+
                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--R
--R        +- 1   0 +
--R   (2)  |        |
--R        + 0   - 1+
--R                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--E 51

--S 52
i:=e(1)$CLIF(2,K,qf)
 

   (3)  e
         1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (3)  e
--R         1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 52

--S 53
j:=e(2)$CLIF(2,K,qf)
 

   (4)  e
         2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (4)  e
--R         2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 53

--S 54
k:=i*j
 

   (5)  e e
         1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (5)  e e
--R         1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 54

--S 55
x:=a+b*i+c*j+d*k
 

   (6)  a + b e  + c e  + d e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (6)  a + b e  + c e  + d e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 55

--S 56
y:=m+f*i+g*j+h*k
 

   (7)  m + f e  + g e  + h e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (7)  m + f e  + g e  + h e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 56

--S 57
x+y
 

   (8)  m + a + (f + b)e  + (g + c)e  + (h + d)e e
                        1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (8)  m + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                        1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 57

--S 58
x*y
 

   (9)
     a m - d h - c g - b f + (b m + c h - d g + a f)e
                                                     1
   + 
     (c m - b h + a g + d f)e  + (d m + a h + b g - c f)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (9)
--R     a m - d h - c g - b f + (b m + c h - d g + a f)e
--R                                                     1
--R   + 
--R     (c m - b h + a g + d f)e  + (d m + a h + b g - c f)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 58

)clear all
 
   All user variables and function definitions have been cleared.
--S 59
taylor(sin(x),x=0)
 

            1  3    1   5     1   7      1    9      11
   (1)  x - - x  + --- x  - ---- x  + ------ x  + O(x  )
            6      120      5040      362880
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R
--R            1  3    1   5     1   7      1    9      11
--R   (1)  x - - x  + --- x  - ---- x  + ------ x  + O(x  )
--R            6      120      5040      362880
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 59

--S 60
laurent(x/log(x),x=1)
 

   (2)
            - 1   3    5            1        2    11        3    11         4
     (x - 1)    + - + -- (x - 1) - -- (x - 1)  + --- (x - 1)  - ---- (x - 1)
                  2   12           24            720            1440
   + 
      271         5    13         6     7297         7     425         8
     ----- (x - 1)  - ---- (x - 1)  + ------- (x - 1)  - ------ (x - 1)
     60480            4480            3628800            290304
   + 
       530113         9            10
     --------- (x - 1)  + O((x - 1)  )
     479001600
                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--R
--R   (2)
--R            - 1   3    5            1        2    11        3    11         4
--R     (x - 1)    + - + -- (x - 1) - -- (x - 1)  + --- (x - 1)  - ---- (x - 1)
--R                  2   12           24            720            1440
--R   + 
--R      271         5    13         6     7297         7     425         8
--R     ----- (x - 1)  - ---- (x - 1)  + ------- (x - 1)  - ------ (x - 1)
--R     60480            4480            3628800            290304
--R   + 
--R       530113         9            10
--R     --------- (x - 1)  + O((x - 1)  )
--R     479001600
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--E 60

--S 61
puiseux(sqrt(sec(x)),x=3*%pi/2)
 

                    1                3                 7
                  - -                -                 -
             3%pi   2    1      3%pi 2    1       3%pi 2          3%pi 5
   (3)  (x - ----)    + -- (x - ----)  + --- (x - ----)  + O((x - ----) )
               2        12        2      160        2               2
                 Type: UnivariatePuiseuxSeries(Expression Integer,x,(3*pi)/2)
--R 
--R
--R                    1                3                 7
--R                  - -                -                 -
--R             3%pi   2    1      3%pi 2    1       3%pi 2          3%pi 5
--R   (3)  (x - ----)    + -- (x - ----)  + --- (x - ----)  + O((x - ----) )
--R               2        12        2      160        2               2
--R                 Type: UnivariatePuiseuxSeries(Expression Integer,x,(3*pi)/2)
--E 61

--S 62
series(x^x,x=0)
 

   (4)
                         2            3            4            5
                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
                      2            6            24          120
   + 
           6            7            8            9            10
     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
       720          5040        40320        362880       3628800
                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--R
--R   (4)
--R                         2            3            4            5
--R                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
--R     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
--R                      2            6            24          120
--R   + 
--R           6            7            8            9            10
--R     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
--R     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
--R       720          5040        40320        362880       3628800
--R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--E 62

)clear all
 
   All user variables and function definitions have been cleared.
--S 63
m:=matrix [[1,2],[3,4]]
 

        +1  2+
   (1)  |    |
        +3  4+
                                                         Type: Matrix Integer
--R
--R        +1  2+
--R   (1)  |    |
--R        +3  4+
--R                                                         Type: Matrix Integer
--E 63

--S 64
4*m*(-5)
 

        +- 20  - 40+
   (2)  |          |
        +- 60  - 80+
                                                         Type: Matrix Integer
--R
--R        +- 20  - 40+
--R   (2)  |          |
--R        +- 60  - 80+
--R                                                         Type: Matrix Integer
--E 64

--S 65
n:=matrix [[1,0,-2],[-3,5,1]]
 

        + 1   0  - 2+
   (3)  |           |
        +- 3  5   1 +
                                                         Type: Matrix Integer
--R
--R        + 1   0  - 2+
--R   (3)  |           |
--R        +- 3  5   1 +
--R                                                         Type: Matrix Integer
--E 65

--S 66
m*n
 

        +- 5  10   0 +
   (4)  |            |
        +- 9  20  - 2+
                                                         Type: Matrix Integer
--R
--R        +- 5  10   0 +
--R   (4)  |            |
--R        +- 9  20  - 2+
--R                                                         Type: Matrix Integer
--E 66

--S 67
hilb:=matrix([[1/(i+j) for i in 1..3] for j in 1..3])
 

        +1  1  1+
        |-  -  -|
        |2  3  4|
        |       |
        |1  1  1|
   (5)  |-  -  -|
        |3  4  5|
        |       |
        |1  1  1|
        |-  -  -|
        +4  5  6+
                                                Type: Matrix Fraction Integer
--R
--R        +1  1  1+
--R        |-  -  -|
--R        |2  3  4|
--R        |       |
--R        |1  1  1|
--R   (5)  |-  -  -|
--R        |3  4  5|
--R        |       |
--R        |1  1  1|
--R        |-  -  -|
--R        +4  5  6+
--R                                                Type: Matrix Fraction Integer
--E 67

--S 68
inverse(hilb)
 

        + 72    - 240   180 +
        |                   |
   (6)  |- 240   900   - 720|
        |                   |
        + 180   - 720   600 +
                                     Type: Union(Matrix Fraction Integer,...)
--R
--R        + 72    - 240   180 +
--R        |                   |
--R   (6)  |- 240   900   - 720|
--R        |                   |
--R        + 180   - 720   600 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 68

)clear all
 
   All user variables and function definitions have been cleared.
--S 69
solve([x+y+z=8,3*x-2*y+z=0,x+2*y+2*z=17],[x,y,z])
 

   (1)  [[x= - 1,y= 2,z= 7]]
                         Type: List List Equation Fraction Polynomial Integer
--R
--R   (1)  [[x= - 1,y= 2,z= 7]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 69

--S 70
solve([x+2*y+3*z=2,2*x+3*y+4*z=2,3*x+4*y+5*z=2],[x,y,z])
 

   (2)  [[x= %BC - 2,y= - 2%BC + 2,z= %BC]]
                         Type: List List Equation Fraction Polynomial Integer
--R
--I   (2)  [[x= %W - 2,y= - 2%W + 2,z= %W]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 70

--S 71
solve([[1,1,1],[3,-2,1],[1,2,2]],[8,0,17])
 

   (3)  [particular= [- 1,2,7],basis= [[0,0,0]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R
--R   (3)  [particular= [- 1,2,7],basis= [[0,0,0]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 71

--S 72
solve([[1,2,3],[2,3,4],[3,4,5]],[2,2,2])
 

   (4)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R
--R   (4)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 72
)spool 
 
Starts dribbling to stream2.output (2009/2/17, 18:0:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set stream calculate 20
 
)set functions cache all
 
   In general, interpreter functions will cache all values.
)set functions compile on
 

--S 1  of 55
u==[i+j for i in (-4)..10 | i < 5 for j in 4.. | j < 10]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 55
u
 
   Compiling body of rule u to compute value of type Stream Integer 
   u will cache all previously computed values.

   (2)  [0,2,4,6,8,10]
                                                         Type: Stream Integer
--R 
--R   Compiling body of rule u to compute value of type Stream Integer 
--R   u will cache all previously computed values.
--R
--R   (2)  [0,2,4,6,8,10]
--R                                                         Type: Stream Integer
--E 2

--S 3 of 55
reduce(0::Integer,+,u)
 

   (3)  30
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  30
--R                                                        Type: PositiveInteger
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 55
u(m,n)==[i for i in m..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 55
u(3,6)
 
   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
      List PositiveInteger 
   u will cache all previously computed values.

   (2)  [3,4,5,6]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
--R      List PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (2)  [3,4,5,6]
--R                                                   Type: List PositiveInteger
--E 5

--S 6 of 55
reduce(+,u(3,6))
 

   (3)  18
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  18
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 55
reduce(+,u(3,8))
 

   (4)  33
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  33
--R                                                        Type: PositiveInteger
--E 7

)clear all
 
   All user variables and function definitions have been cleared.

--S 8 of 55
n==10
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 55
u:=[i for i in 0..n]
 
   Compiling body of rule n to compute value of type PositiveInteger 
   n will cache all previously computed values.

   (2)  [0,1,2,3,4,5,6,7,8,9,10]
                                                Type: List NonNegativeInteger
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   n will cache all previously computed values.
--R
--R   (2)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                Type: List NonNegativeInteger
--E 9

--S 10 of 55
v==[i for i in 0..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 55
v
 
   Compiling body of rule v to compute value of type List 
      NonNegativeInteger 
   v will cache all previously computed values.

   (4)  [0,1,2,3,4,5,6,7,8,9,10]
                                                Type: List NonNegativeInteger
--R 
--R   Compiling body of rule v to compute value of type List 
--R      NonNegativeInteger 
--R   v will cache all previously computed values.
--R
--R   (4)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                Type: List NonNegativeInteger
--E 11

--S 12 of 55
n==15
 
   Compiled code for n has been cleared.
   Compiled code for v has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for v has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 12

--S 13 of 55
u
 

   (6)  [0,1,2,3,4,5,6,7,8,9,10]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (6)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                Type: List NonNegativeInteger
--E 13

--S 14 of 55
v
 
   Compiling body of rule n to compute value of type PositiveInteger 
   n will cache all previously computed values.
   Compiling body of rule v to compute value of type List 
      NonNegativeInteger 
   v will cache all previously computed values.

   (7)  [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
                                                Type: List NonNegativeInteger
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   n will cache all previously computed values.
--R   Compiling body of rule v to compute value of type List 
--R      NonNegativeInteger 
--R   v will cache all previously computed values.
--R
--R   (7)  [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
--R                                                Type: List NonNegativeInteger
--E 14

)clear all
 
   All user variables and function definitions have been cleared.

--S 15 of 55
n:=2
 

   (1)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 55
m:=3
 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 55
u:=[[i*j for j in 1..n] for i in 1..m]
 

   (3)  [[1,2],[2,4],[3,6]]
                                              Type: List List PositiveInteger
--R 
--R
--R   (3)  [[1,2],[2,4],[3,6]]
--R                                              Type: List List PositiveInteger
--E 17

--S 18 of 55
n:=10
 

   (4)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  10
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 55
u
 

   (5)  [[1,2],[2,4],[3,6]]
                                              Type: List List PositiveInteger
--R 
--R
--R   (5)  [[1,2],[2,4],[3,6]]
--R                                              Type: List List PositiveInteger
--E 19

)clear all
 
   All user variables and function definitions have been cleared.

--S 20 of 55
u==[i for i in m..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

)set mes test off
 

--S 21  of 55
u
 
 
   The lower bound in a loop must be an integer.
--R 
--R 
--R   The lower bound in a loop must be an integer.
--E 21

)set mes test on
 

--S 22  of 55
n:=7
 

   (2)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  7
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 55
m:=3
 

   (3)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  3
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 55
u
 
   Compiling body of rule u to compute value of type List 
      PositiveInteger 
   u will cache all previously computed values.

   (4)  [3,4,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R   Compiling body of rule u to compute value of type List 
--R      PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (4)  [3,4,5,6,7]
--R                                                   Type: List PositiveInteger
--E 24

--S 25 of 55
reduce(+,u)
 

   (5)  25
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  25
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 55
n:=2
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 55
u
 

   (7)  [3,4,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (7)  [3,4,5,6,7]
--R                                                   Type: List PositiveInteger
--E 27

--S 28 of 55
reduce(+,u)
 

   (8)  25
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  25
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 55
m:=-3
 
   Compiled code for u has been cleared.

   (9)  - 3
                                                                Type: Integer
--R 
--R   Compiled code for u has been cleared.
--R
--R   (9)  - 3
--R                                                                Type: Integer
--E 29

--S 30 of 55
u
 
   Compiling body of rule u to compute value of type List Integer 
   u will cache all previously computed values.

   (10)  [- 3,- 2,- 1,0,1,2]
                                                           Type: List Integer
--R 
--R   Compiling body of rule u to compute value of type List Integer 
--R   u will cache all previously computed values.
--R
--R   (10)  [- 3,- 2,- 1,0,1,2]
--R                                                           Type: List Integer
--E 30

--S 31 of 55
reduce(+,u)
 

   (11)  - 3
                                                                Type: Integer
--R 
--R
--R   (11)  - 3
--R                                                                Type: Integer
--E 31

)clear all
 
   All user variables and function definitions have been cleared.

--S 32 of 55
u==[[i+j for i in 0..j] for j in 0..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

)set mes test off
 

--S 33  of 55
u
 
 
   The upper bound in a loop must be an integer.
--R 
--R 
--R   The upper bound in a loop must be an integer.
--E 33

)set mes test on
 

--S 34  of 55
n:=5
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 55
u
 
   Compiling body of rule u to compute value of type List List 
      NonNegativeInteger 
   u will cache all previously computed values.

   (3)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
                                           Type: List List NonNegativeInteger
--R 
--R   Compiling body of rule u to compute value of type List List 
--R      NonNegativeInteger 
--R   u will cache all previously computed values.
--R
--R   (3)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
--R                                           Type: List List NonNegativeInteger
--E 35

--S 36 of 55
n:=10
 

   (4)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  10
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 55
u
 

   (5)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
                                           Type: List List NonNegativeInteger
--R 
--R
--R   (5)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
--R                                           Type: List List NonNegativeInteger
--E 37

--S 38 of 55
n:=1
 

   (6)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  1
--R                                                        Type: PositiveInteger
--E 38

--S 39 of 55
u
 

   (7)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
                                           Type: List List NonNegativeInteger
--R 
--R
--R   (7)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
--R                                           Type: List List NonNegativeInteger
--E 39

--S 40 of 55
n:= 0
 
   Compiled code for u has been cleared.

   (8)  0
                                                     Type: NonNegativeInteger
--R 
--R   Compiled code for u has been cleared.
--R
--R   (8)  0
--R                                                     Type: NonNegativeInteger
--E 40

--S 41 of 55
u
 
   Compiling body of rule u to compute value of type List List 
      NonNegativeInteger 
   u will cache all previously computed values.

   (9)  [[0]]
                                           Type: List List NonNegativeInteger
--R 
--R   Compiling body of rule u to compute value of type List List 
--R      NonNegativeInteger 
--R   u will cache all previously computed values.
--R
--R   (9)  [[0]]
--R                                           Type: List List NonNegativeInteger
--E 41

--S 42 of 55
n:=-1
 
   Compiled code for u has been cleared.

   (10)  - 1
                                                                Type: Integer
--R 
--R   Compiled code for u has been cleared.
--R
--R   (10)  - 1
--R                                                                Type: Integer
--E 42

--S 43 of 55
u
 
   Compiling body of rule u to compute value of type List List Integer 
   u will cache all previously computed values.

   (11)  []
                                                      Type: List List Integer
--R 
--R   Compiling body of rule u to compute value of type List List Integer 
--R   u will cache all previously computed values.
--R
--R   (11)  []
--R                                                      Type: List List Integer
--E 43

)clear all
 
   All user variables and function definitions have been cleared.

)set streams calculate 10
 

--S 44  of 55
u==[[i+j for i in 0..] for j in 0..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 44

--S 45 of 55
u
 
   Compiling body of rule u to compute value of type Stream Stream 
      Integer 
   u will cache all previously computed values.

   (2)
   [[0,1,2,3,4,5,6,7,8,9,...], [1,2,3,4,5,6,7,8,9,10,...],
    [2,3,4,5,6,7,8,9,10,11,...], [3,4,5,6,7,8,9,10,11,12,...],
    [4,5,6,7,8,9,10,11,12,13,...], [5,6,7,8,9,10,11,12,13,14,...],
    [6,7,8,9,10,11,12,13,14,15,...], [7,8,9,10,11,12,13,14,15,16,...],
    [8,9,10,11,12,13,14,15,16,17,...], [9,10,11,12,13,14,15,16,17,18,...], ...]
                                                  Type: Stream Stream Integer
--R 
--R   Compiling body of rule u to compute value of type Stream Stream 
--R      Integer 
--R   u will cache all previously computed values.
--R
--R   (2)
--R   [[0,1,2,3,4,5,6,7,8,9,...], [1,2,3,4,5,6,7,8,9,10,...],
--R    [2,3,4,5,6,7,8,9,10,11,...], [3,4,5,6,7,8,9,10,11,12,...],
--R    [4,5,6,7,8,9,10,11,12,13,...], [5,6,7,8,9,10,11,12,13,14,...],
--R    [6,7,8,9,10,11,12,13,14,15,...], [7,8,9,10,11,12,13,14,15,16,...],
--R    [8,9,10,11,12,13,14,15,16,17,...], [9,10,11,12,13,14,15,16,17,18,...], ...]
--R                                                  Type: Stream Stream Integer
--E 45

)clear all
 
   All user variables and function definitions have been cleared.

--S 46 of 55
u(m,n)==[[i+j for j in 1..m] for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 46

--S 47 of 55
u(3,6)
 
   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
      List List PositiveInteger 
   u will cache all previously computed values.

   (2)  [[2,3,4],[3,4,5],[4,5,6],[5,6,7],[6,7,8],[7,8,9]]
                                              Type: List List PositiveInteger
--R 
--R   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
--R      List List PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (2)  [[2,3,4],[3,4,5],[4,5,6],[5,6,7],[6,7,8],[7,8,9]]
--R                                              Type: List List PositiveInteger
--E 47

--S 48 of 55
reduce(append,u(3,6))
 

   (3)  [2,3,4,3,4,5,4,5,6,5,6,7,6,7,8,7,8,9]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [2,3,4,3,4,5,4,5,6,5,6,7,6,7,8,7,8,9]
--R                                                   Type: List PositiveInteger
--E 48

)clear all
 
   All user variables and function definitions have been cleared.

--S 49 of 55
u(m,n)==[[i*j for j in m..] for i in n..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 49

--S 50 of 55
u(3,6)
 
   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
      Stream Stream Integer 
   u will cache all previously computed values.

   (2)
   [[18,24,30,36,42,48,54,60,66,72,...], [21,28,35,42,49,56,63,70,77,84,...],
    [24,32,40,48,56,64,72,80,88,96,...], [27,36,45,54,63,72,81,90,99,108,...],
    [30,40,50,60,70,80,90,100,110,120,...],
    [33,44,55,66,77,88,99,110,121,132,...],
    [36,48,60,72,84,96,108,120,132,144,...],
    [39,52,65,78,91,104,117,130,143,156,...],
    [42,56,70,84,98,112,126,140,154,168,...],
    [45,60,75,90,105,120,135,150,165,180,...], ...]
                                                  Type: Stream Stream Integer
--R 
--R   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
--R      Stream Stream Integer 
--R   u will cache all previously computed values.
--R
--R   (2)
--R   [[18,24,30,36,42,48,54,60,66,72,...], [21,28,35,42,49,56,63,70,77,84,...],
--R    [24,32,40,48,56,64,72,80,88,96,...], [27,36,45,54,63,72,81,90,99,108,...],
--R    [30,40,50,60,70,80,90,100,110,120,...],
--R    [33,44,55,66,77,88,99,110,121,132,...],
--R    [36,48,60,72,84,96,108,120,132,144,...],
--R    [39,52,65,78,91,104,117,130,143,156,...],
--R    [42,56,70,84,98,112,126,140,154,168,...],
--R    [45,60,75,90,105,120,135,150,165,180,...], ...]
--R                                                  Type: Stream Stream Integer
--E 50

)clear all
 
   All user variables and function definitions have been cleared.

)set streams calculate 3
 

--S 51  of 55
[[[i+j+k for i in 0..] for j in 0..] for k in 0..]
 

   (1)
   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...], ...]
                                           Type: Stream Stream Stream Integer
--R 
--R
--R   (1)
--R   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
--R    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
--R    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...], ...]
--R                                           Type: Stream Stream Stream Integer
--E 51

--S 52 of 55
n:=5
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 52

--S 53 of 55
[[[i+j+k for i in 0..] for j in 0..] for k in 0..n]
 

   (3)
   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...],
    [[3,4,5,...],[4,5,6,...],[5,6,7,...],...],
    [[4,5,6,...],[5,6,7,...],[6,7,8,...],...],
    [[5,6,7,...],[6,7,8,...],[7,8,9,...],...]]
                                             Type: List Stream Stream Integer
--R 
--R
--R   (3)
--R   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
--R    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
--R    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...],
--R    [[3,4,5,...],[4,5,6,...],[5,6,7,...],...],
--R    [[4,5,6,...],[5,6,7,...],[6,7,8,...],...],
--R    [[5,6,7,...],[6,7,8,...],[7,8,9,...],...]]
--R                                             Type: List Stream Stream Integer
--E 53

--S 54 of 55
[[[i+j+k for i in 0..j] for j in 0..k] for k in 0..]
 

   (4)  [[[0]],[[1],[2,3]],[[2],[3,4],[4,5,6]],...]
                                    Type: Stream List List NonNegativeInteger
--R 
--R
--R   (4)  [[[0]],[[1],[2,3]],[[2],[3,4],[4,5,6]],...]
--R                                    Type: Stream List List NonNegativeInteger
--E 54

--S 55 of 55
[[[i+j+k for i in 0..j] for j in 0..k] for k in 0..n]
 

   (5)
   [[[0]], [[1],[2,3]], [[2],[3,4],[4,5,6]], [[3],[4,5],[5,6,7],[6,7,8,9]],
    [[4],[5,6],[6,7,8],[7,8,9,10],[8,9,10,11,12]],
    [[5],[6,7],[7,8,9],[8,9,10,11],[9,10,11,12,13],[10,11,12,13,14,15]]]
                                      Type: List List List NonNegativeInteger
--R 
--R
--R   (5)
--R   [[[0]], [[1],[2,3]], [[2],[3,4],[4,5,6]], [[3],[4,5],[5,6,7],[6,7,8,9]],
--R    [[4],[5,6],[6,7,8],[7,8,9,10],[8,9,10,11,12]],
--R    [[5],[6,7],[7,8,9],[8,9,10,11],[9,10,11,12,13],[10,11,12,13,14,15]]]
--R                                      Type: List List List NonNegativeInteger
--E 55
)spool 
 
Starts dribbling to equation.output (2009/2/17, 17:45:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 12
eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x)
 

            3      2         4
   (1)  - 6x  + 13x  + 4= - x  + 12x
                                            Type: Equation Polynomial Integer
--R 
--R
--R            3      2         4
--R   (1)  - 6x  + 13x  + 4= - x  + 12x
--R                                            Type: Equation Polynomial Integer
--E 1

--S 2 of 12
eq2 := x**4+13*x**2-12*x = 6*x**3-4
 

         4      2          3
   (2)  x  + 13x  - 12x= 6x  - 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R         4      2          3
--R   (2)  x  + 13x  - 12x= 6x  - 4
--R                                            Type: Equation Polynomial Integer
--E 2

--S 3 of 12
eq := eq1*y**2+eq2
 

             3      2      2    4      2            4        2     3
   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R             3      2      2    4      2            4        2     3
--R   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
--R                                            Type: Equation Polynomial Integer
--E 3

--S 4 of 12
swap %
 

            4        2     3           3      2      2    4      2
   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
                                            Type: Equation Polynomial Integer
--R 
--R
--R            4        2     3           3      2      2    4      2
--R   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
--R                                            Type: Equation Polynomial Integer
--E 4

--S 5 of 12
% + 4
 

            4        2     3       3      2      2    4      2
   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R            4        2     3       3      2      2    4      2
--R   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E 5

--S 6 of 12
%-6*x**3
 

            4        2       3      2      2    4     3      2
   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R            4        2       3      2      2    4     3      2
--R   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E 6

--S 7 of 12
leftZero %
 

             4     3      2            2    4     3      2
   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R             4     3      2            2    4     3      2
--R   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E 7

--S 8 of 12
swap %
 

          4     3      2            2    4     3      2
   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R          4     3      2            2    4     3      2
--R   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
--R                                            Type: Equation Polynomial Integer
--E 8

--S 9 of 12
factor lhs %
 

               2       2  2
   (9)  (x - 2) (x - 1) (y  + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2       2  2
--R   (9)  (x - 2) (x - 1) (y  + 1)
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10 of 12
factorAndSplit eq
 

                             2
   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
                                       Type: List Equation Polynomial Integer
--R 
--R
--R                             2
--R   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
--R                                       Type: List Equation Polynomial Integer
--E 10

--S 11 of 12
inv (eq :: EQ FRAC POLY INT)
 

                             1                                1
   (11)  - ------------------------------------= - ----------------------
              3      2      2    4      2            4        2     3
           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
                                   Type: Equation Fraction Polynomial Integer
--R 
--R
--R                             1                                1
--R   (11)  - ------------------------------------= - ----------------------
--R              3      2      2    4      2            4        2     3
--R           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
--R                                   Type: Equation Fraction Polynomial Integer
--E 11

--S 12 of 12
- %
 

                           1                              1
   (12)  ------------------------------------= ----------------------
            3      2      2    4      2          4        2     3
         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
                                   Type: Equation Fraction Polynomial Integer
--R 
--R
--R                           1                              1
--R   (12)  ------------------------------------= ----------------------
--R            3      2      2    4      2          4        2     3
--R         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
--R                                   Type: Equation Fraction Polynomial Integer
--E 12
)spool
 
Starts dribbling to log.output (2009/2/17, 17:52:46).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 1
[[0.01, -4.6051701859880914, log(0.01), log(0.01)-(-4.6051701859880914)], _
[0.02, -3.9120230054281461, log(0.02), log(0.02)-(-3.9120230054281461)], _
[0.03, -3.5065578973199817, log(0.03), log(0.03)-(-3.5065578973199817)], _
[0.04, -3.2188758248682007, log(0.04), log(0.04)-(-3.2188758248682007)], _
[0.05, -2.9957322735539910, log(0.05), log(0.05)-(-2.9957322735539910)], _
[0.06, -2.8134107167600364, log(0.06), log(0.06)-(-2.8134107167600364)], _
[0.07, -2.6592600369327781, log(0.07), log(0.07)-(-2.6592600369327781)], _
[0.08, -2.5257286443082554, log(0.08), log(0.08)-(-2.5257286443082554)], _
[0.09, -2.4079456086518720, log(0.09), log(0.09)-(-2.4079456086518720)], _
[0.10, -2.3025850929940457, log(0.10), log(0.10)-(-2.3025850929940457)], _
[0.11, -2.2072749131897208, log(0.11), log(0.11)-(-2.2072749131897208)], _
[0.12, -2.1202635362000911, log(0.12), log(0.12)-(-2.1202635362000911)], _
[0.13, -2.0402208285265546, log(0.13), log(0.13)-(-2.0402208285265546)], _
[0.14, -1.9661128563728328, log(0.14), log(0.14)-(-1.9661128563728328)], _
[0.15, -1.8971199848858813, log(0.15), log(0.15)-(-1.8971199848858813)], _
[0.16, -1.8325814637483101, log(0.16), log(0.16)-(-1.8325814637483101)], _
[0.17, -1.7719568419318753, log(0.17), log(0.17)-(-1.7719568419318753)], _
[0.18, -1.7147984280919267, log(0.18), log(0.18)-(-1.7147984280919267)], _
[0.19, -1.6607312068216509, log(0.19), log(0.19)-(-1.6607312068216509)], _
[0.20, -1.6094379124341004, log(0.20), log(0.20)-(-1.6094379124341004)], _
[0.21, -1.5606477482646684, log(0.21), log(0.21)-(-1.5606477482646684)], _
[0.22, -1.5141277326297755, log(0.22), log(0.22)-(-1.5141277326297755)], _
[0.23, -1.4696759700589417, log(0.23), log(0.23)-(-1.4696759700589417)], _
[0.24, -1.4271163556401457, log(0.24), log(0.24)-(-1.4271163556401457)], _
[0.25, -1.3862943611198906, log(0.25), log(0.25)-(-1.3862943611198906)], _
[0.26, -1.3470736479666093, log(0.26), log(0.26)-(-1.3470736479666093)], _
[0.27, -1.3093333199837623, log(0.27), log(0.27)-(-1.3093333199837623)], _
[0.28, -1.2729656758128874, log(0.28), log(0.28)-(-1.2729656758128874)], _
[0.29, -1.2378743560016173, log(0.29), log(0.29)-(-1.2378743560016173)], _
[0.30, -1.2039728043259360, log(0.30), log(0.30)-(-1.2039728043259360)], _
[0.31, -1.1711829815029451, log(0.31), log(0.31)-(-1.1711829815029451)], _
[0.32, -1.1394342831883648, log(0.32), log(0.32)-(-1.1394342831883648)], _
[0.33, -1.1086626245216111, log(0.33), log(0.33)-(-1.1086626245216111)], _
[0.34, -1.0788096613719300, log(0.34), log(0.34)-(-1.0788096613719300)], _
[0.35, -1.0498221244986777, log(0.35), log(0.35)-(-1.0498221244986777)], _
[0.36, -1.0216512475319814, log(0.36), log(0.36)-(-1.0216512475319814)], _
[0.37, -0.9942522733438669, log(0.37), log(0.37)-(-0.9942522733438669)], _
[0.38, -0.9675840262617056, log(0.38), log(0.38)-(-0.9675840262617056)], _
[0.39, -0.9416085398584449, log(0.39), log(0.39)-(-0.9416085398584449)], _
[0.40, -0.9162907318741551, log(0.40), log(0.40)-(-0.9162907318741551)], _
[0.41, -0.8915981192837836, log(0.41), log(0.41)-(-0.8915981192837836)], _
[0.42, -0.8675005677047231, log(0.42), log(0.42)-(-0.8675005677047231)], _
[0.43, -0.8439700702945289, log(0.43), log(0.43)-(-0.8439700702945289)], _
[0.44, -0.8209805520698302, log(0.44), log(0.44)-(-0.8209805520698302)], _
[0.45, -0.7985076962177716, log(0.45), log(0.45)-(-0.7985076962177716)], _
[0.46, -0.7765287894989964, log(0.46), log(0.46)-(-0.7765287894989964)], _
[0.47, -0.7550225842780328, log(0.47), log(0.47)-(-0.7550225842780328)], _
[0.48, -0.7339691750802004, log(0.48), log(0.48)-(-0.7339691750802004)], _
[0.49, -0.7133498878774648, log(0.49), log(0.49)-(-0.7133498878774648)], _
[0.50, -0.6931471805599453, log(0.50), log(0.50)-(-0.6931471805599453)], _
[0.51, -0.6733445532637656, log(0.51), log(0.51)-(-0.6733445532637656)], _
[0.52, -0.6539264674066640, log(0.52), log(0.52)-(-0.6539264674066640)], _
[0.53, -0.6348782724359695, log(0.53), log(0.53)-(-0.6348782724359695)], _
[0.54, -0.6161861394238170, log(0.54), log(0.54)-(-0.6161861394238170)], _
[0.55, -0.5978370007556204, log(0.55), log(0.55)-(-0.5978370007556204)], _
[0.56, -0.5798184952529421, log(0.56), log(0.56)-(-0.5798184952529421)], _
[0.57, -0.5621189181535412, log(0.57), log(0.57)-(-0.5621189181535412)], _
[0.58, -0.5447271754416720, log(0.58), log(0.58)-(-0.5447271754416720)], _
[0.59, -0.5276327420823719, log(0.59), log(0.59)-(-0.5276327420823719)], _
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[2.00, 0.6931471805599453, log(2.00), log(2.00)-(0.6931471805599453)]]
 

   (1)
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--R 
--R
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--R    [0.81,- 0.2107210313 156526,- 0.2107210313 1565260246,- 0.246 E -17],
--R    [0.82,- 0.1984509387 238383,- 0.1984509387 2383825475,0.4525 E -16],
--R    [0.83,- 0.1863295781 914934,- 0.1863295781 9149344456,- 0.4456 E -16],
--R    [0.84,- 0.1743533871 447778,- 0.1743533871 447777527,0.473 E -16],
--R    [0.85,- 0.1625189294 977749,- 0.1625189294 9777491318,- 0.132 E -16],
--R    [0.86,- 0.1508228897 345836,- 0.1508228897 3458363515,- 0.3515 E -16],
--R    [0.87,- 0.1392620673 335076,- 0.1392620673 3350764946,- 0.4946 E -16],
--R    [0.88,- 0.1278333715 098849,- 0.1278333715 0988489572,0.428 E -17],
--R    [0.89,- 0.1165338162 559515,- 0.1165338162 5595152972,- 0.2972 E -16],
--R    [0.9,- 0.1053605156 578263,- 0.1053605156 5782630123,- 0.123 E -17],
--R    [0.91,- 0.0943106794 712413,- 0.0943106794 7124132687 7,- 0.2688 E -16],
--R    [0.92,- 0.0833816089 390511,- 0.0833816089 3905105839 3,0.4161 E -16],
--R    [0.93,- 0.0725706928 348354,- 0.0725706928 3483543071 2,- 0.3071 E -16],
--R    [0.94,- 0.0618754037 180875,- 0.0618754037 1808747179 7,0.28203 E -16],
--R    [0.95,- 0.0512932943 875505,- 0.0512932943 8755053342 7,- 0.33427 E -16],
--R    [0.96,- 0.0408219945 202551,- 0.0408219945 2025512955 4,- 0.29554 E -16],
--R    [0.97,- 0.0304592074 847085,- 0.0304592074 8470854592,- 0.4592 E -16],
--R    [0.98,- 0.0202027073 175194,- 0.0202027073 1751944840 8,- 0.48408 E -16],
--R    [0.99,- 0.0100503358 535014,- 0.0100503358 5350144118 5,- 0.41185 E -16],
--R    [1.0,0.0,0.0,0.0],
--R    [1.01,0.0099503308 531681,0.0099503308 5316808284 64,- 0.17154 E -16],
--R    [1.02,0.0198026272 961797,0.0198026272 9617971302 9,0.1303 E -16],
--R    [1.03,0.0295588022 415444,0.0295588022 4154440273 4,0.2734 E -17],
--R    [1.04,0.0392207131 532813,0.0392207131 5328129626 8,- 0.3732 E -17],
--R    [1.05,0.0487901641 69432,0.0487901641 6943200306 3,0.306 E -17],
--R    [1.06,0.0582689081 239758,0.0582689081 2397577552 8,- 0.2447 E -16],
--R    [1.07,0.0676586484 738148,0.0676586484 7381480526 9,0.527 E -17],
--R    [1.08,0.0769610411 361283,0.0769610411 3612832498 3,0.2498 E -16],
--R    [1.09,0.0861776962 410523,0.0861776962 4105233234 4,0.3234 E -16],
--R    [1.1,0.0953101798 043249,0.0953101798 0432486004 5,- 0.3995 E -16],
--R    [1.11,0.1043600153 242428,0.1043600153 2424276773,- 0.3227 E -16],
--R    [1.12,0.1133286853 070032,0.1133286853 0700317474,- 0.2526 E -16],
--R    [1.13,0.1222176327 242492,0.1222176327 2424920055,0.548 E -18],
--R    [1.14,0.1310282624 064041,0.1310282624 0640409279,- 0.721 E -17],
--R    [1.15,0.1397619423 751587,0.1397619423 7515869737,- 0.263 E -17],
--R    [1.16,0.1484200051 182733,0.1484200051 1827327798,- 0.2202 E -16],
--R    [1.17,0.1570037488 096648,0.1570037488 0966475081,- 0.4919 E -16],
--R    [1.18,0.1655144384 775734,0.1655144384 77573392,- 0.8 E -17],
--R    [1.19,0.1739533071 23438,0.1739533071 2343801732,0.1732 E -16],
--R    [1.2,0.1823215567 939546,0.1823215567 9395462621,0.2621 E -16],
--R    [1.21,0.1906203596 086497,0.1906203596 0864972009,0.2009 E -16],
--R    [1.22,0.1988508587 451652,0.1988508587 4516519013,- 0.987 E -17],
--R    [1.23,0.2070141693 843261,0.2070141693 8432612722,0.2722 E -16],
--R    [1.24,0.2151113796 169455,0.2151113796 1694549673,- 0.327 E -17],
--R    [1.25,0.2231435513 142098,0.2231435513 1420975577,- 0.4423 E -16],
--R    [1.26,0.2311117209 633866,0.2311117209 6338662928,0.2928 E -16],
--R    [1.27,0.2390169004 704999,0.2390169004 7049990501,0.501 E -17],
--R    [1.28,0.2468600779 315258,0.2468600779 3152579789,- 0.211 E -17],
--R    [1.29,0.2546422183 735807,0.2546422183 7358074683,0.4683 E -16],
--R    [1.3,0.2623642644 674911,0.2623642644 6749105203,- 0.4797 E -16],
--R    [1.31,0.2700271372 130602,0.2700271372 1306017612,- 0.239 E -16],
--R    [1.32,0.2776317365 982795,0.2776317365 9827948626,- 0.137 E -16],
--R    [1.33,0.2851789422 336624,0.2851789422 3366239708,- 0.292 E -17],
--R    [1.34,0.2926696139 6282,0.2926696139 6282000105,0.11 E -17],
--R    [1.35,0.3001045924 503381,0.3001045924 5033808075,- 0.192 E -16],
--R    [1.36,0.3074846997 479606,0.3074846997 4796064047,0.4046 E -16],
--R    [1.37,0.3148107398 400335,0.3148107398 4003354728,0.4728 E -16],
--R    [1.38,0.3220834991 691133,0.3220834991 6911332359,0.236 E -16],
--R    [1.39,0.3293037471 426004,0.3293037471 4260038915,- 0.108 E -16],
--R    [1.4,0.3364722366 212129,0.3364722366 212129305,0.305 E -16],
--R    [1.41,0.3435897043 900769,0.3435897043 9007691018,0.102 E -16],
--R    [1.42,0.3506568716 131694,0.3506568716 1316936271,- 0.3729 E -16],
--R    [1.43,0.3576744442 718159,0.3576744442 7181591208,0.121 E -16],
--R    [1.44,0.3646431135 879093,0.3646431135 8790925242,- 0.4758 E -16],
--R    [1.45,0.3715635564 32483,0.3715635564 3248303375,0.3375 E -16],
--R    [1.46,0.3784364357 202451,0.3784364357 2024507047,- 0.2953 E -16],
--R    [1.47,0.3852624007 906449,0.3852624007 9064493357,0.3357 E -16],
--R    [1.48,0.3920420877 760237,0.3920420877 7602369517,- 0.483 E -17],
--R    [1.49,0.3987761199 573678,0.3987761199 5736777296,- 0.27 E -16],
--R    [1.5,0.4054651081 081644,0.4054651081 0816438198,- 0.18 E -16],
--R    [1.51,0.4121096508 26833,0.4121096508 2683296076,- 0.3924 E -16],
--R    [1.52,0.4187103348 58185,0.4187103348 5818502023,0.202 E -16],
--R    [1.53,0.4252677354 043441,0.4252677354 0434409501,- 0.5 E -17],
--R    [1.54,0.4317824164 255378,0.4317824164 2553779055,- 0.945 E -17],
--R    [1.55,0.4382549309 311553,0.4382549309 3115525249,- 0.4751 E -16],
--R    [1.56,0.4446858212 614457,0.4446858212 6144567825,- 0.218 E -16],
--R    [1.57,0.4510756193 602167,0.4510756193 6021668939,- 0.106 E -16],
--R    [1.58,0.4574248470 388754,0.4574248470 3887543555,0.3555 E -16],
--R    [1.59,0.4637340162 321402,0.4637340162 3214015751,- 0.4249 E -16],
--R    [1.6,0.4700036292 457356,0.4700036292 4573555365,- 0.4635 E -16],
--R    [1.61,0.4762341789 963716,0.4762341789 9637162788,0.2788 E -16],
--R    [1.62,0.4824261492 442927,0.4824261492 4429270696,0.696 E -17],
--R    [1.63,0.4885800148 18671,0.4885800148 1867096603,- 0.3397 E -16],
--R    [1.64,0.4946962418 361071,0.4946962418 3610705467,- 0.4533 E -16],
--R    [1.65,0.5007752879 124892,0.5007752879 1248924202,0.42 E -16],
--R    [1.66,0.5068176023 684519,0.5068176023 6845186486,- 0.351 E -16],
--R    [1.67,0.5128236264 286637,0.5128236264 2866373922,0.392 E -16],
--R    [1.68,0.5187937934 151676,0.5187937934 1516755672,- 0.433 E -16],
--R    [1.69,0.5247285289 349821,0.5247285289 3498210407,0.407 E -17],
--R    [1.7,0.5306282510 621704,0.5306282510 6217039623,- 0.377 E -17],
--R    [1.71,0.5364933705 145685,0.5364933705 1456847476,- 0.252 E -16],
--R    [1.72,0.5423242908 253617,0.5423242908 2536167427,- 0.257 E -16],
--R    [1.73,0.5481214085 096876,0.5481214085 096875789,- 0.211 E -16],
--R    [1.74,0.5538851132 264377,0.5538851132 2643765996,- 0.4 E -16],
--R    [1.75,0.5596157879 354227,0.5596157879 3542268627,- 0.137 E -16],
--R    [1.76,0.5653138090 500604,0.5653138090 5006041369,0.137 E -16],
--R    [1.77,0.5709795465 857378,0.5709795465 8573777398,- 0.26 E -16],
--R    [1.78,0.5766133643 039938,0.5766133643 039937797,- 0.203 E -16],
--R    [1.79,0.5822156198 526636,0.5822156198 5266362814,0.281 E -16],
--R    [1.8,0.5877866649 02119,0.5877866649 0211900819,0.819 E -17],
--R    [1.81,0.5933268452 777344,0.5933268452 777343788,- 0.212 E -16],
--R    [1.82,0.5988365010 88704,0.5988365010 8870398254,- 0.175 E -16],
--R    [1.83,0.6043159668 533296,0.6043159668 5332957211,- 0.279 E -16],
--R    [1.84,0.6097655716 208943,0.6097655716 2089425102,- 0.49 E -16],
--R    [1.85,0.6151856390 902335,0.6151856390 9023345093,- 0.491 E -16],
--R    [1.86,0.6205764877 251099,0.6205764877 2510987871,- 0.213 E -16],
--R    [1.87,0.6259384308 664953,0.6259384308 6649525628,- 0.437 E -16],
--R    [1.88,0.6312717768 418578,0.6312717768 4185783762,0.376 E -16],
--R    [1.89,0.6365768290 71551,0.6365768290 7155101126,0.113 E -16],
--R    [1.9,0.6418538861 723948,0.6418538861 7239477599,- 0.24 E -16],
--R    [1.91,0.6471032420 585385,0.6471032420 5853850481,0.481 E -17],
--R    [1.92,0.6523251860 396902,0.6523251860 3969017986,- 0.201 E -16],
--R    [1.93,0.6575200029 167942,0.6575200029 1679418382,- 0.162 E -16],
--R    [1.94,0.6626879730 752368,0.6626879730 752367635,- 0.365 E -16],
--R    [1.95,0.6678293725 756554,0.6678293725 7565543401,0.34 E -16],
--R    [1.96,0.6729444732 424259,0.6729444732 4242586101,- 0.39 E -16],
--R    [1.97,0.6780335427 498971,0.6780335427 4989713874,0.387 E -16],
--R    [1.98,0.6830968447 064439,0.6830968447 0644386823,- 0.318 E -16],
--R    [1.99,0.6881346387 36401,0.6881346387 3640102737,0.274 E -16],
--R    [2.0,0.6931471805 599453,0.6931471805 5994530942,0.942 E -17]]
--R                                                        Type: List List Float
--E 1
)spool 
 
Starts dribbling to clifford.output (2009/2/17, 17:44:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 39
K := FRAC POLY INT
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--% The complex numbers as a Clifford Algebra
)clear p qf
 

--S 2  of 39
qf: QFORM(1, K) := quadraticForm(matrix([[-1]])$(SQMATRIX(1,K)))
 

   (2)  [- 1]
                           Type: QuadraticForm(1,Fraction Polynomial Integer)
--R 
--R
--R   (2)  [- 1]
--R                           Type: QuadraticForm(1,Fraction Polynomial Integer)
--E 2

--S 3 of 39
C := CLIF(1, K, qf)
 

   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 3

--S 4 of 39
i := e(1)$C
 

   (4)  e
         1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 4

--S 5 of 39
x := a + b * i
 

   (5)  a + b e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  a + b e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 5

--S 6 of 39
y := c + d * i
 

   (6)  c + d e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  c + d e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 6

--S 7 of 39
x * y
 

   (7)  - b d + a c + (a d + b c)e
                                  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  - b d + a c + (a d + b c)e
--R                                  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 7

--S 8 of 39
recip %
 

               - b d + a c                 - a d - b c
   (8)  ------------------------- + ------------------------- e
          2    2  2     2    2  2     2    2  2     2    2  2  1
        (b  + a )d  + (b  + a )c    (b  + a )d  + (b  + a )c
       Type: Union(CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX),...)
--R 
--R
--R               - b d + a c                 - a d - b c
--R   (8)  ------------------------- + ------------------------- e
--R          2    2  2     2    2  2     2    2  2     2    2  2  1
--R        (b  + a )d  + (b  + a )c    (b  + a )d  + (b  + a )c
--R       Type: Union(CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX),...)
--E 8

--S 9 of 39
x*%
 

           c         d
   (9)  ------- - ------- e
         2    2    2    2  1
        d  + c    d  + c
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R           c         d
--R   (9)  ------- - ------- e
--R         2    2    2    2  1
--R        d  + c    d  + c
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 9

--S 10 of 39
%*y
 

   (10)  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (10)  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 10
 
--% The quaternions as a Clifford Algebra
)clear p qf
 

--S 11  of 39
qf:QFORM(2, K) :=quadraticForm matrix([[-1, 0], [0, -1]])$(SQMATRIX(2,K))
 

         +- 1   0 +
   (11)  |        |
         + 0   - 1+
                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--R 
--R
--R         +- 1   0 +
--R   (11)  |        |
--R         + 0   - 1+
--R                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--E 11

--S 12 of 39
H  := CLIF(2, K, qf)
 

   (12)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (12)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 12

--S 13 of 39
i  := e(1)$H
 

   (13)  e
          1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (13)  e
--R          1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 13

--S 14 of 39
j  := e(2)$H
 

   (14)  e
          2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (14)  e
--R          2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 14

--S 15 of 39
k  := i * j
 

   (15)  e e
          1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (15)  e e
--R          1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 15

--S 16 of 39
x := a + b * i + c * j + d * k
 

   (16)  a + b e  + c e  + d e e
                1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (16)  a + b e  + c e  + d e e
--R                1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 16

--S 17 of 39
y := e + f * i + g * j + h * k
 

   (17)  e + f e  + g e  + h e e
                1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (17)  e + f e  + g e  + h e e
--R                1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 17

--S 18 of 39
x + y
 

   (18)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
                         1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (18)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                         1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 18

--S 19 of 39
x * y
 

   (19)
     - d h - c g - b f + a e + (c h - d g + a f + b e)e
                                                       1
   + 
     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
                               2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (19)
--R     - d h - c g - b f + a e + (c h - d g + a f + b e)e
--R                                                       1
--R   + 
--R     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
--R                               2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 19

--S 20 of 39
y * x
 

   (20)
     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
                                                         1
   + 
     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (20)
--R     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
--R                                                         1
--R   + 
--R     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 20
 
--% The exterior algebra on a 3 space.
)clear p qf
 
 
--S 21 of 39
qf: QFORM(3, K) := quadraticForm(0::SQMATRIX(3,K))
 

         +0  0  0+
         |       |
   (21)  |0  0  0|
         |       |
         +0  0  0+
                           Type: QuadraticForm(3,Fraction Polynomial Integer)
--R 
--R
--R         +0  0  0+
--R         |       |
--R   (21)  |0  0  0|
--R         |       |
--R         +0  0  0+
--R                           Type: QuadraticForm(3,Fraction Polynomial Integer)
--E 21

--S 22 of 39
Ext := CLIF(3,K,qf)
 

   (22)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (22)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 22

--S 23 of 39
i := e(1)$Ext
 

   (23)  e
          1
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (23)  e
--R          1
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 23

--S 24 of 39
j := e(2)$Ext
 

   (24)  e
          2
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (24)  e
--R          2
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 24

--S 25 of 39
k := e(3)$Ext
 

   (25)  e
          3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (25)  e
--R          3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 25

--S 26 of 39
x := x1*i + x2*j + x3*k
 

   (26)  x1 e  + x2 e  + x3 e
             1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (26)  x1 e  + x2 e  + x3 e
--R             1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 26

--S 27 of 39
y := y1*i + y2*j + y3*k
 

   (27)  y1 e  + y2 e  + y3 e
             1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (27)  y1 e  + y2 e  + y3 e
--R             1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 27

--S 28 of 39
x + y
 

   (28)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
                   1             2             3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (28)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
--R                   1             2             3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 28

--S 29 of 39
x * y + y * x
 

   (29)  0
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (29)  0
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 29

--S 30 of 39
dual2 a ==
    coefficient(a,[2,3])$Ext * i + _
    coefficient(a,[3,1])$Ext * j + _
    coefficient(a,[1,2])$Ext * k 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 39
dual2(x*y)
 
   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) 

   (31)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
                         1                     2                   3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) 
--R
--R   (31)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
--R                         1                     2                   3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 31

)clear p qf
 
 
--S 32 of 39
K := FRAC INT
 

   (32)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (32)  Fraction Integer
--R                                                                 Type: Domain
--E 32

--S 33 of 39
g: SQMATRIX(4, K) := [[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]]
 

         +1   0    0    0 +
         |                |
         |0  - 1   0    0 |
   (33)  |                |
         |0   0   - 1   0 |
         |                |
         +0   0    0   - 1+
                                       Type: SquareMatrix(4,Fraction Integer)
--R 
--R
--R         +1   0    0    0 +
--R         |                |
--R         |0  - 1   0    0 |
--R   (33)  |                |
--R         |0   0   - 1   0 |
--R         |                |
--R         +0   0    0   - 1+
--R                                       Type: SquareMatrix(4,Fraction Integer)
--E 33

--S 34 of 39
qf: QFORM(4, K) := quadraticForm g
 

         +1   0    0    0 +
         |                |
         |0  - 1   0    0 |
   (34)  |                |
         |0   0   - 1   0 |
         |                |
         +0   0    0   - 1+
                                      Type: QuadraticForm(4,Fraction Integer)
--R 
--R
--R         +1   0    0    0 +
--R         |                |
--R         |0  - 1   0    0 |
--R   (34)  |                |
--R         |0   0   - 1   0 |
--R         |                |
--R         +0   0    0   - 1+
--R                                      Type: QuadraticForm(4,Fraction Integer)
--E 34

--S 35 of 39
D := CLIF(4,K,qf)
 

   (35)  CliffordAlgebra(4,Fraction Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (35)  CliffordAlgebra(4,Fraction Integer,MATRIX)
--R                                                                 Type: Domain
--E 35

--S 36 of 39
gam := [e(i)$D for i in 1..4]
 

   (36)  [e ,e ,e ,e ]
           1  2  3  4
                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (36)  [e ,e ,e ,e ]
--R           1  2  3  4
--R                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 36
 

-- Verify this identity for m=1,n=2,r=3,s=4
--S 37 of 39
m := 1; n:= 2; r := 3; s := 4;
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 37

--S 38 of 39
lhs := reduce(+,[reduce(+,[g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t)
             for l in 1..4]) for t in 1..4])
 

   (38)  - 4e e e e
             1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (38)  - 4e e e e
--R             1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 38

--S 39 of 39
rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)
 

   (39)  - 4e e e e
             1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (39)  - 4e e e e
--R             1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 39
)spool
 
Starts dribbling to quat1.output (2009/2/17, 17:56:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 11
q := quatern(2/11,-8,3/4,1)
 

         2        3
   (1)  -- - 8i + - j + k
        11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         2        3
--R   (1)  -- - 8i + - j + k
--R        11        4
--R                                            Type: Quaternion Fraction Integer
--E 1

--S 2 of 11
[real q, imagI q, imagJ q, imagK q]
 

          2     3
   (2)  [--,- 8,-,1]
         11     4
                                                  Type: List Fraction Integer
--R 
--R
--R          2     3
--R   (2)  [--,- 8,-,1]
--R         11     4
--R                                                  Type: List Fraction Integer
--E 2

--S 3 of 11
inv q
 

          352     15488      484       1936
   (3)  ------ + ------ i - ----- j - ------ k
        126993   126993     42331     126993
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          352     15488      484       1936
--R   (3)  ------ + ------ i - ----- j - ------ k
--R        126993   126993     42331     126993
--R                                            Type: Quaternion Fraction Integer
--E 3

--S 4 of 11
q**6
 

          2029490709319345   48251690851     144755072553     48251690851
   (4)  - ---------------- - ----------- i + ------------ j + ----------- k
             7256313856        1288408         41229056         10307264
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2029490709319345   48251690851     144755072553     48251690851
--R   (4)  - ---------------- - ----------- i + ------------ j + ----------- k
--R             7256313856        1288408         41229056         10307264
--R                                            Type: Quaternion Fraction Integer
--E 4

--S 5 of 11
r := quatern(-2,3,23/9,-89); q + r
 

          20        119
   (5)  - -- - 5i + --- j - 88k
          11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          20        119
--R   (5)  - -- - 5i + --- j - 88k
--R          11         36
--R                                            Type: Quaternion Fraction Integer
--E 5

--S 6 of 11
q * r - r * q
 

          2495             817
   (6)  - ---- i - 1418j - --- k
           18               18
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2495             817
--R   (6)  - ---- i - 1418j - --- k
--R           18               18
--R                                            Type: Quaternion Fraction Integer
--E 6

--S 7 of 11
i:=quatern(0,1,0,0); j:=quatern(0,0,1,0); k:=quatern(0,0,0,1)
 

   (7)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (7)  k
--R                                                     Type: Quaternion Integer
--E 7

--S 8 of 11
[i*i, j*j, k*k, i*j, j*k, k*i, q*i]
 

                                2         3
   (8)  [- 1,- 1,- 1,k,i,j,8 + -- i + j - - k]
                               11         4
                                       Type: List Quaternion Fraction Integer
--R 
--R
--R                                2         3
--R   (8)  [- 1,- 1,- 1,k,i,j,8 + -- i + j - - k]
--R                               11         4
--R                                       Type: List Quaternion Fraction Integer
--E 8

--S 9 of 11
norm q
 

        126993
   (9)  ------
         1936
                                                       Type: Fraction Integer
--R 
--R
--R        126993
--R   (9)  ------
--R         1936
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 11
conjugate q
 

          2        3
   (10)  -- + 8i - - j - k
         11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2        3
--R   (10)  -- + 8i - - j - k
--R         11        4
--R                                            Type: Quaternion Fraction Integer
--E 10

--S 11 of 11
q * %
 

         126993
   (11)  ------
          1936
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         126993
--R   (11)  ------
--R          1936
--R                                            Type: Quaternion Fraction Integer
--E 11
)spool 
 
Starts dribbling to collect.output (2009/2/17, 17:44:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 55
a := [i**3 for i in 0..10]
 

   (1)  [0,1,8,27,64,125,216,343,512,729,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (1)  [0,1,8,27,64,125,216,343,512,729,1000]
--R                                                Type: List NonNegativeInteger
--E 1

--S 2 of 55
b := expand [0..10]
 

   (2)  [0,1,2,3,4,5,6,7,8,9,10]
                                                           Type: List Integer
--R 
--R
--R   (2)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                           Type: List Integer
--E 2

--S 3 of 55
c := [x**3 for x in b]
 

   (3)  [0,1,8,27,64,125,216,343,512,729,1000]
                                                           Type: List Integer
--R 
--R
--R   (3)  [0,1,8,27,64,125,216,343,512,729,1000]
--R                                                           Type: List Integer
--E 3

--S 4 of 55
d := [i**3 for i in 0..10 | even? i]
 

   (4)  [0,8,64,216,512,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (4)  [0,8,64,216,512,1000]
--R                                                Type: List NonNegativeInteger
--E 4

--S 5 of 55
d := [x**3 for x in b | even? x]
 

   (5)  [0,8,64,216,512,1000]
                                                           Type: List Integer
--R 
--R
--R   (5)  [0,8,64,216,512,1000]
--R                                                           Type: List Integer
--E 5

--S 6 of 55
d := [x for x in c | even? x]
 

   (6)  [0,8,64,216,512,1000]
                                                           Type: List Integer
--R 
--R
--R   (6)  [0,8,64,216,512,1000]
--R                                                           Type: List Integer
--E 6

--S 7 of 55
d := [i**3 for i in 0..10 by 2 | even? i]
 

   (7)  [0,8,64,216,512,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (7)  [0,8,64,216,512,1000]
--R                                                Type: List NonNegativeInteger
--E 7

--S 8 of 55
e := reverse [i**3 for i in 10..0 by -2 | even? i]
 

   (8)  [0,8,64,216,512,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (8)  [0,8,64,216,512,1000]
--R                                                Type: List NonNegativeInteger
--E 8

--S 9 of 55
[x - y for x in d for y in e]
 

   (9)  [0,0,0,0,0,0]
                                                           Type: List Integer
--R 
--R
--R   (9)  [0,0,0,0,0,0]
--R                                                           Type: List Integer
--E 9

--S 10 of 55
[x**3 - y for x in b | even? x for y in e]
 

   (10)  [0,- 56,- 448]
                                                           Type: List Integer
--R
--R   (10)  [0,- 56,- 448]
--R                                                           Type: List Integer
--E 10

--S 11 of 55
f := [i**3 for i in 0..]
 

   (11)  [0,1,8,27,64,125,216,343,512,729,...]
                                              Type: Stream NonNegativeInteger
--R
--R   (11)  [0,1,8,27,64,125,216,343,512,729,...]
--R                                              Type: Stream NonNegativeInteger
--E 11

--S 12 of 55
[i**3 for i in 0..10]
 

   (12)  [0,1,8,27,64,125,216,343,512,729,1000]
                                                Type: List NonNegativeInteger
--R
--R   (12)  [0,1,8,27,64,125,216,343,512,729,1000]
--R                                                Type: List NonNegativeInteger
--E 12

--S 13 of 55
[i**3 for i in 0.. while i < 11]
 

   (13)  [0,1,8,27,64,125,216,343,512,729,...]
                                              Type: Stream NonNegativeInteger
--R
--R   (13)  [0,1,8,27,64,125,216,343,512,729,...]
--R                                              Type: Stream NonNegativeInteger
--E 13

--S 14 of 55
[i**3 for i in 0.. for x in 0..10]
 

   (14)  [0,1,8,27,64,125,216,343,512,729,...]
                                              Type: Stream NonNegativeInteger
--R
--R   (14)  [0,1,8,27,64,125,216,343,512,729,...]
--R                                              Type: Stream NonNegativeInteger
--E 14

--S 15 of 55
[ [i**j for j in 0..3] for i in 0..]
 

   (15)
   [[1,0,0,0], [1,1,1,1], [1,2,4,8], [1,3,9,27], [1,4,16,64], [1,5,25,125],
    [1,6,36,216], [1,7,49,343], [1,8,64,512], [1,9,81,729], ...]
                                         Type: Stream List NonNegativeInteger
--R
--R   (15)
--R   [[1,0,0,0], [1,1,1,1], [1,2,4,8], [1,3,9,27], [1,4,16,64], [1,5,25,125],
--R    [1,6,36,216], [1,7,49,343], [1,8,64,512], [1,9,81,729], ...]
--R                                         Type: Stream List NonNegativeInteger
--E 15

--S 16 of 55
[ [i**j for j in 0..] for i in 0..3]
 

   (16)
   [[1,0,0,0,0,0,0,0,0,0,...], [1,1,1,1,1,1,1,1,1,1,...],
    [1,2,4,8,16,32,64,128,256,512,...],
    [1,3,9,27,81,243,729,2187,6561,19683,...]]
                                           Type: List Stream Fraction Integer
--R
--R   (16)
--R   [[1,0,0,0,0,0,0,0,0,0,...], [1,1,1,1,1,1,1,1,1,1,...],
--R    [1,2,4,8,16,32,64,128,256,512,...],
--R    [1,3,9,27,81,243,729,2187,6561,19683,...]]
--R                                           Type: List Stream Fraction Integer
--E 16

--S 17 of 55
brace [i**3 for i in 10..0 by -2]
 

   (17)  {0,8,64,216,512,1000}
                                                 Type: Set NonNegativeInteger
--R
--R   (17)  {0,8,64,216,512,1000}
--R                                                 Type: Set NonNegativeInteger
--E 17

-- Input generated from ContinuedFractionXmpPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 18 of 55
c := continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 18

--S 19 of 55
partialQuotients c
 

   (2)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (2)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 19

--S 20 of 55
convergents c
 

           22 333 355 9208 9563 76149 314159
   (3)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R           22 333 355 9208 9563 76149 314159
--R   (3)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 20

--S 21 of 55
approximants c
 

                                      ______
           22 333 355 9208 9563 76149 314159
   (4)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R                                      ______
--R           22 333 355 9208 9563 76149 314159
--R   (4)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 21

--S 22 of 55
pq := partialQuotients(1/c)
 

   (5)  [0,3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 22

--S 23 of 55
continuedFraction(first pq,repeating [1],rest pq)
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 23

--S 24 of 55
z:=continuedFraction(3,repeating [1],repeating [3,6])
 

   (7)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
   + 
       1 |
     +---+ + ...
     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
--R         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 6
--R                                              Type: ContinuedFraction Integer
--E 24

--S 25 of 55
dens:Stream Integer := cons(1,generate((x+->x+4),6))
 

   (8)  [1,6,10,14,18,22,26,30,34,38,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [1,6,10,14,18,22,26,30,34,38,...]
--R                                                         Type: Stream Integer
--E 25

--S 26 of 55
cf := continuedFraction(0,repeating [1],dens)
 

   (9)
       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
   + 
       1  |     1  |
     +----+ + +----+ + ...
     | 34     | 38
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (9)
--R       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
--R     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
--R     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
--R   + 
--R       1  |     1  |
--R     +----+ + +----+ + ...
--R     | 34     | 38
--R                                              Type: ContinuedFraction Integer
--E 26

--S 27 of 55
ccf := convergents cf
 

              6 61  860 15541 342762  8927353 268163352  9126481321
   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
              7 71 1001 18089 398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              6 61  860 15541 342762  8927353 268163352  9126481321
--R   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
--R              7 71 1001 18089 398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 27

--S 28 of 55
eConvergents := [2*e + 1 for e in ccf]
 

              19 193 2721 49171 1084483 28245729 848456353 28875761731
   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
               7  71 1001 18089  398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              19 193 2721 49171 1084483 28245729 848456353 28875761731
--R   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
--R               7  71 1001 18089  398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 28

--S 29 of 55
eConvergents :: Stream Float
 

   (12)
   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (12)
--R   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
--R    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
--R    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
--R    ...]
--R                                                           Type: Stream Float
--E 29

--S 30 of 55
exp 1.0
 

   (13)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (13)  2.7182818284 590452354
--R                                                                  Type: Float
--E 30

--S 31 of 55
cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])
 

   (14)
           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
   + 
       289 |     361 |
     +-----+ + +-----+ + ...
     |  2      |  2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (14)
--R           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
--R     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
--R         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
--R   + 
--R       289 |     361 |
--R     +-----+ + +-----+ + ...
--R     |  2      |  2
--R                                              Type: ContinuedFraction Integer
--E 31

--S 32 of 55
ccf := convergents cf
 

            3 15 105 315 3465 45045 45045 765765 14549535
   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
            2 13  76 263 2578 36979 33976 622637 11064338
                                                Type: Stream Fraction Integer
--R 
--R
--R            3 15 105 315 3465 45045 45045 765765 14549535
--R   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
--R            2 13  76 263 2578 36979 33976 622637 11064338
--R                                                Type: Stream Fraction Integer
--E 32

--S 33 of 55
piConvergents := [4/p for p in ccf]
 

            8 52 304 1052 10312 147916 135904 2490548 44257352
   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
            3 15 105  315  3465  45045  45045  765765 14549535
                                                Type: Stream Fraction Integer
--R 
--R
--R            8 52 304 1052 10312 147916 135904 2490548 44257352
--R   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
--R            3 15 105  315  3465  45045  45045  765765 14549535
--R                                                Type: Stream Fraction Integer
--E 33

--S 34 of 55
piConvergents :: Stream Float
 

   (17)
   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
    3.0418396189 294022111, ...]
                                                           Type: Stream Float
--R 
--R
--R   (17)
--R   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
--R    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
--R    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
--R    3.0418396189 294022111, ...]
--R                                                           Type: Stream Float
--E 34

--S 35 of 55
continuedFraction((- 122 + 597*%i)/(4 - 4*%i))
 

                            1    |         1     |
   (18)  - 90 + 59%i + +---------+ + +-----------+
                       | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1    |         1     |
--R   (18)  - 90 + 59%i + +---------+ + +-----------+
--R                       | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 35

--S 36 of 55
r : Fraction UnivariatePolynomial(x,Fraction Integer)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 55
r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))
 

           2
          x  - 3x + 2
   (20)  ------------
          2
         x  - 7x + 12
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2
--R          x  - 3x + 2
--R   (20)  ------------
--R          2
--R         x  - 7x + 12
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 37

--S 38 of 55
continuedFraction r
 

                  1    |         1     |
   (21)  1 + +---------+ + +-----------+
             | 1     9     | 16     40
             | - x - -     | -- x - --
             | 4     8     |  3      3
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                  1    |         1     |
--R   (21)  1 + +---------+ + +-----------+
--R             | 1     9     | 16     40
--R             | - x - -     | -- x - --
--R             | 4     8     |  3      3
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 38

--S 39 of 55
[i*i for i in convergents(z) :: Stream Float]
 

   (22)
   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (22)
--R   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
--R    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
--R    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
--R    ...]
--R                                                           Type: Stream Float
--E 39

-- Input for page ForCollectionDetailPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 40 of 55
u := [i**3 for i in 1..10]
 

   (1)  [1,8,27,64,125,216,343,512,729,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,8,27,64,125,216,343,512,729,1000]
--R                                                   Type: List PositiveInteger
--E 40

--S 41 of 55
u(4)
 

   (2)  64
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  64
--R                                                        Type: PositiveInteger
--E 41

--S 42 of 55
[8*i**3 for n in 1..5]
 

           3   3   3   3   3
   (3)  [8i ,8i ,8i ,8i ,8i ]
                                                Type: List Polynomial Integer
--R 
--R
--R           3   3   3   3   3
--R   (3)  [8i ,8i ,8i ,8i ,8i ]
--R                                                Type: List Polynomial Integer
--E 42

--S 43 of 55
[u(2*n) for n in 1..5]
 

   (4)  [8,64,216,512,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [8,64,216,512,1000]
--R                                                   Type: List PositiveInteger
--E 43

--S 44 of 55
[u(i) for i in 1..10 | even? i]
 

   (5)  [8,64,216,512,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [8,64,216,512,1000]
--R                                                   Type: List PositiveInteger
--E 44

--S 45 of 55
[x for x in u | even? x]
 

   (6)  [8,64,216,512,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (6)  [8,64,216,512,1000]
--R                                                   Type: List PositiveInteger
--E 45

-- Input for page ForStreamDetailPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 46 of 55
u := [i**3 for i in 1..]
 

   (1)  [1,8,27,64,125,216,343,512,729,1000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (1)  [1,8,27,64,125,216,343,512,729,1000,...]
--R                                                 Type: Stream PositiveInteger
--E 46

--S 47 of 55
u(4)
 

   (2)  64
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  64
--R                                                        Type: PositiveInteger
--E 47

--S 48 of 55
u
 

   (3)  [1,8,27,64,125,216,343,512,729,1000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (3)  [1,8,27,64,125,216,343,512,729,1000,...]
--R                                                 Type: Stream PositiveInteger
--E 48

--S 49 of 55
u(16)
 

   (4)  4096
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  4096
--R                                                        Type: PositiveInteger
--E 49

--S 50 of 55
[i**3 for i in 0.. | even? i]
 

   (5)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (5)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
--R                                              Type: Stream NonNegativeInteger
--E 50

--S 51 of 55
[8*i**3 for i in 0..]
 

   (6)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (6)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
--R                                              Type: Stream NonNegativeInteger
--E 51

--S 52 of 55
[i**3 for i in 0.. by 2]
 

   (7)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (7)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
--R                                              Type: Stream NonNegativeInteger
--E 52

--S 53 of 55
[u(i) for i in 1.. | even? i]
 

   (8)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (8)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
--R                                                 Type: Stream PositiveInteger
--E 53

--S 54 of 55
[u(2*i) for i in 1..]
 

   (9)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (9)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
--R                                                 Type: Stream PositiveInteger
--E 54

--S 55 of 55
[x for x in u | even? x]
 

   (10)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (10)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
--R                                                 Type: Stream PositiveInteger
--E 55
)spool
 
Starts dribbling to intmix2.output (2009/2/17, 17:46:52).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 4
(x + 1) / (x * (x + log x)**(3/2))
 

                    x + 1
   (1)  ----------------------------
                     2  +----------+
        (x log(x) + x )\|log(x) + x
                                                     Type: Expression Integer
--R 
--R
--R                    x + 1
--R   (1)  ----------------------------
--R                     2  +----------+
--R        (x log(x) + x )\|log(x) + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 4
integrate(%, x)
 

            +----------+
          2\|log(x) + x
   (2)  - --------------
            log(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +----------+
--R          2\|log(x) + x
--R   (2)  - --------------
--R            log(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 4
log(1 + exp x)**(1/3) / (1 + log(1 + exp x))
 

          +------------+
         3|      x
         \|log(%e  + 1)
   (3)  ----------------
              x
        log(%e  + 1) + 1
                                                     Type: Expression Integer
--R 
--R
--R          +------------+
--R         3|      x
--R         \|log(%e  + 1)
--R   (3)  ----------------
--R              x
--R        log(%e  + 1) + 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 4
integrate(%, x)
 

               +-------------+
           x  3|      %P
         ++   \|log(%e   + 1)
   (4)   |   ----------------- d%P
        ++         %P
             log(%e   + 1) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------------+
--R           x  3|      %P
--R         ++   \|log(%e   + 1)
--R   (4)   |   ----------------- d%P
--R        ++         %P
--R             log(%e   + 1) + 1
--R                                          Type: Union(Expression Integer,...)
--E 4
)spool 
 
Starts dribbling to kamke3.output (2009/2/17, 17:47:27).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 139
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 139
ode151 := (x**2+1)*D(y(x),x) + (y(x)**2+1)*(2*x*y(x) - 1)
 

          2      ,             3       2
   (2)  (x  + 1)y (x) + 2x y(x)  - y(x)  + 2x y(x) - 1

                                                     Type: Expression Integer
--R 
--R
--R          2      ,             3       2
--R   (2)  (x  + 1)y (x) + 2x y(x)  - y(x)  + 2x y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 139
ode151a:=solve(ode151,y,x)
 

   (3)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (3)  "failed"
--R                                                    Type: Union("failed",...)
--E 3

--S 4 of 139
ode152 := (x**2+1)*D(y(x),x) + x*sin(y(x))*cos(y(x)) - x*(x**2+1)*cos(y(x))**2
 

          2      ,                                 3              2
   (4)  (x  + 1)y (x) + x cos(y(x))sin(y(x)) + (- x  - x)cos(y(x))

                                                     Type: Expression Integer
--R 
--R
--R          2      ,                                 3              2
--R   (4)  (x  + 1)y (x) + x cos(y(x))sin(y(x)) + (- x  - x)cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 139
ode152a:=solve(ode152,y,x)
 

   (5)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (5)  "failed"
--R                                                    Type: Union("failed",...)
--E 5

--S 6 of 139
ode153 := (x**2-1)*D(y(x),x) - x*y(x) + a
 

          2      ,
   (6)  (x  - 1)y (x) - x y(x) + a

                                                     Type: Expression Integer
--R 
--R
--R          2      ,
--R   (6)  (x  - 1)y (x) - x y(x) + a
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 139
ode153a:=solve(ode153,y,x)
 

                                  +------+
                                  | 2
   (7)  [particular= a x,basis= [\|x  - 1 ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                  +------+
--R                                  | 2
--R   (7)  [particular= a x,basis= [\|x  - 1 ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 7

--S 8 of 139
yx:=ode153a.particular
 

   (8)  a x
                                                     Type: Expression Integer
--R 
--R
--R   (8)  a x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 139
ode153expr := (x**2-1)*D(yx,x) - x*yx + a
 

   (9)  0
                                                     Type: Expression Integer
--R 
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E 9

--S 10 of 139
ode154 := (x**2-1)*D(y(x),x) + 2*x*y(x) - cos(x)
 

           2      ,
   (10)  (x  - 1)y (x) - cos(x) + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,
--R   (10)  (x  - 1)y (x) - cos(x) + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 139
ode154a:=solve(ode154,y,x)
 

                      sin(x)            1
   (11)  [particular= ------,basis= [------]]
                       2              2
                      x  - 1         x  - 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                      sin(x)            1
--R   (11)  [particular= ------,basis= [------]]
--R                       2              2
--R                      x  - 1         x  - 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 11

--S 12 of 139
yx:=ode154a.particular
 

         sin(x)
   (12)  ------
          2
         x  - 1
                                                     Type: Expression Integer
--R 
--R
--R         sin(x)
--R   (12)  ------
--R          2
--R         x  - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 139
ode154expr := (x**2-1)*D(yx,x) + 2*x*yx - cos(x)
 

   (13)  0
                                                     Type: Expression Integer
--R 
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 139
ode155 := (x**2-1)*D(y(x),x) + y(x)**2 - 2*x*y(x) + 1
 

           2      ,          2
   (14)  (x  - 1)y (x) + y(x)  - 2x y(x) + 1

                                                     Type: Expression Integer
--R 
--R
--R           2      ,          2
--R   (14)  (x  - 1)y (x) + y(x)  - 2x y(x) + 1
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 139
yx:=solve(ode155,y,x)
 

         (y(x) - x)log(x + 1) + (- y(x) + x)log(x - 1) + 2
   (15)  -------------------------------------------------
                             2y(x) - 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         (y(x) - x)log(x + 1) + (- y(x) + x)log(x - 1) + 2
--R   (15)  -------------------------------------------------
--R                             2y(x) - 2x
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 139
ode155expr := (x**2-1)*D(yx,x) + yx**2 - 2*x*yx + 1
 

   (16)
            2      ,           2              2           2
       (- 4x  + 4)y (x) + (y(x)  - 2x y(x) + x )log(x + 1)

     + 
                   2               2                     2      2              3
           (- 2y(x)  + 4x y(x) - 2x )log(x - 1) - 4x y(x)  + (8x  + 4)y(x) - 4x
         + 
           - 4x
      *
         log(x + 1)
     + 
            2              2           2
       (y(x)  - 2x y(x) + x )log(x - 1)
     + 
               2        2              3                                2
       (4x y(x)  + (- 8x  - 4)y(x) + 4x  + 4x)log(x - 1) - 8x y(x) + 12x
  /
          2               2
     4y(x)  - 8x y(x) + 4x
                                                     Type: Expression Integer
--R 
--R
--R   (16)
--R            2      ,           2              2           2
--R       (- 4x  + 4)y (x) + (y(x)  - 2x y(x) + x )log(x + 1)
--R
--R     + 
--R                   2               2                     2      2              3
--R           (- 2y(x)  + 4x y(x) - 2x )log(x - 1) - 4x y(x)  + (8x  + 4)y(x) - 4x
--R         + 
--R           - 4x
--R      *
--R         log(x + 1)
--R     + 
--R            2              2           2
--R       (y(x)  - 2x y(x) + x )log(x - 1)
--R     + 
--R               2        2              3                                2
--R       (4x y(x)  + (- 8x  - 4)y(x) + 4x  + 4x)log(x - 1) - 8x y(x) + 12x
--R  /
--R          2               2
--R     4y(x)  - 8x y(x) + 4x
--R                                                     Type: Expression Integer
--E 16

--S 17 of 139
ode156 := (x**2-1)*D(y(x),x) - y(x)*(y(x)-x)
 

           2      ,          2
   (17)  (x  - 1)y (x) - y(x)  + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,          2
--R   (17)  (x  - 1)y (x) - y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 17

--S 18 of 139
yx:=solve(ode156,y,x)
 

          - x y(x) + 1
   (18)  -------------
              +------+
              | 2
         y(x)\|x  - 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          - x y(x) + 1
--R   (18)  -------------
--R              +------+
--R              | 2
--R         y(x)\|x  - 1
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 139
ode156expr := (x**2-1)*D(yx,x) - yx*(yx-x)
 

   (19)
                                                         +------+
           4     2      ,          2    2                | 2
       (- x  + 2x  - 1)y (x) + (- x y(x)  + 2x y(x) - 1)\|x  - 1

     + 
           4     2         2
       (- x  + 2x  - 1)y(x)
  /
                   +------+
       2         2 | 2
     (x  - 1)y(x) \|x  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (19)
--R                                                         +------+
--R           4     2      ,          2    2                | 2
--R       (- x  + 2x  - 1)y (x) + (- x y(x)  + 2x y(x) - 1)\|x  - 1
--R
--R     + 
--R           4     2         2
--R       (- x  + 2x  - 1)y(x)
--R  /
--R                   +------+
--R       2         2 | 2
--R     (x  - 1)y(x) \|x  - 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 139
ode157 := (x**2-1)*D(y(x),x) + a*(y(x)**2-2*x*y(x)+1)
 

           2      ,            2
   (20)  (x  - 1)y (x) + a y(x)  - 2a x y(x) + a

                                                     Type: Expression Integer
--R 
--R
--R           2      ,            2
--R   (20)  (x  - 1)y (x) + a y(x)  - 2a x y(x) + a
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 139
ode157a:=solve(ode157,y,x)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--S 22 of 139
ode158 := (x**2-1)*D(y(x),x) + a*x*y(x)**2 + x*y(x)
 

           2      ,              2
   (22)  (x  - 1)y (x) + a x y(x)  + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,              2
--R   (22)  (x  - 1)y (x) + a x y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 22

--S 23 of 139
yx:=solve(ode158,y,x)
 

           2 2    2
          a x y(x)  + 2a y(x) + 1
   (23)  ------------------------
           4    2     3         2
         2a y(x)  + 4a y(x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2    2
--R          a x y(x)  + 2a y(x) + 1
--R   (23)  ------------------------
--R           4    2     3         2
--R         2a y(x)  + 4a y(x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 23

--S 24 of 139
ode158expr := (x**2-1)*D(yx,x) + a*x*yx**2 + x*yx
 

   (24)
           4 4     4 2     4     2      3 4     3 2     3       ,
       ((4a x  - 8a x  + 4a )y(x)  + (4a x  - 8a x  + 4a )y(x))y (x)

     + 
         4 5     5 3     5      4        4     3  3     4      3
       (a x  + 6a x  - 4a x)y(x)  + ((12a  + 4a )x  - 4a x)y(x)
     + 
           3     2  3      3     2       2      2
       ((6a  + 2a )x  + (6a  + 4a )x)y(x)  + (8a  + 4a)x y(x) + (2a + 1)x
  /
       7    4      6    3      5    2      4         3
     4a y(x)  + 16a y(x)  + 24a y(x)  + 16a y(x) + 4a
                                                     Type: Expression Integer
--R 
--R
--R   (24)
--R           4 4     4 2     4     2      3 4     3 2     3       ,
--R       ((4a x  - 8a x  + 4a )y(x)  + (4a x  - 8a x  + 4a )y(x))y (x)
--R
--R     + 
--R         4 5     5 3     5      4        4     3  3     4      3
--R       (a x  + 6a x  - 4a x)y(x)  + ((12a  + 4a )x  - 4a x)y(x)
--R     + 
--R           3     2  3      3     2       2      2
--R       ((6a  + 2a )x  + (6a  + 4a )x)y(x)  + (8a  + 4a)x y(x) + (2a + 1)x
--R  /
--R       7    4      6    3      5    2      4         3
--R     4a y(x)  + 16a y(x)  + 24a y(x)  + 16a y(x) + 4a
--R                                                     Type: Expression Integer
--E 24

--S 25 of 139
ode159 := (x**2-1)*D(y(x),x) - 2*x*y(x)*log(y(x))
 

           2      ,
   (25)  (x  - 1)y (x) - 2x y(x)log(y(x))

                                                     Type: Expression Integer
--R 
--R
--R           2      ,
--R   (25)  (x  - 1)y (x) - 2x y(x)log(y(x))
--R
--R                                                     Type: Expression Integer
--E 25

--S 26 of 139
yx:=solve(ode159,y,x)
 

             2
          - x  + 1
   (26)  ---------
         log(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2
--R          - x  + 1
--R   (26)  ---------
--R         log(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 26

--S 27 of 139
ode159expr := (x**2-1)*D(yx,x) - 2*x*yx*log(yx)
 

   (27)
                                      2
          3                        - x  + 1      4     2      ,
       (2x  - 2x)y(x)log(y(x))log(---------) + (x  - 2x  + 1)y (x)
                                  log(y(x))
     + 
            3
       (- 2x  + 2x)y(x)log(y(x))
  /
                  2
     y(x)log(y(x))
                                                     Type: Expression Integer
--R 
--R
--R   (27)
--R                                      2
--R          3                        - x  + 1      4     2      ,
--R       (2x  - 2x)y(x)log(y(x))log(---------) + (x  - 2x  + 1)y (x)
--R                                  log(y(x))
--R     + 
--R            3
--R       (- 2x  + 2x)y(x)log(y(x))
--R  /
--R                  2
--R     y(x)log(y(x))
--R                                                     Type: Expression Integer
--E 27

--S 28 of 139
ode160 := (x**2-4)*D(y(x),x) + (x+2)*y(x)**2 - 4*y(x)
 

           2      ,                 2
   (28)  (x  - 4)y (x) + (x + 2)y(x)  - 4y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,                 2
--R   (28)  (x  - 4)y (x) + (x + 2)y(x)  - 4y(x)
--R
--R                                                     Type: Expression Integer
--E 28

--S 29 of 139
yx:=solve(ode160,y,x)
 

         (- x - 2)y(x)log(x + 2) + x - 2
   (29)  -------------------------------
                   (x + 2)y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         (- x - 2)y(x)log(x + 2) + x - 2
--R   (29)  -------------------------------
--R                   (x + 2)y(x)
--R                                          Type: Union(Expression Integer,...)
--E 29

--S 30 of 139
ode160expr := (x**2-4)*D(yx,x) + (x+2)*yx**2 - 4*yx
 

   (30)
           3     2           ,        2              2          2
       (- x  + 2x  + 4x - 8)y (x) + (x  + 4x + 4)y(x) log(x + 2)

     + 
                  2        2                           2         2    2
     ((4x + 8)y(x)  + (- 2x  + 8)y(x))log(x + 2) + (- x  + 4)y(x)  + x  - 4x + 4
  /
                2
     (x + 2)y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (30)
--R           3     2           ,        2              2          2
--R       (- x  + 2x  + 4x - 8)y (x) + (x  + 4x + 4)y(x) log(x + 2)
--R
--R     + 
--R                  2        2                           2         2    2
--R     ((4x + 8)y(x)  + (- 2x  + 8)y(x))log(x + 2) + (- x  + 4)y(x)  + x  - 4x + 4
--R  /
--R                2
--R     (x + 2)y(x)
--R                                                     Type: Expression Integer
--E 30

--S 31 of 139
ode161 := (x**2-5*x+6)*D(y(x),x) + 3*x*y(x) - 8*y(x) + x**2
 

           2           ,                      2
   (31)  (x  - 5x + 6)y (x) + (3x - 8)y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R           2           ,                      2
--R   (31)  (x  - 5x + 6)y (x) + (3x - 8)y(x) + x
--R
--R                                                     Type: Expression Integer
--E 31

--S 32 of 139
ode161a:=solve(ode161,y,x)
 

                              4     3
                          - 3x  + 8x  - 144                     1
   (32)  [particular= ------------------------,basis= [-------------------]]
                         3      2                       3     2
                      12x  - 84x  + 192x - 144         x  - 7x  + 16x - 12
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                              4     3
--R                          - 3x  + 8x  - 144                     1
--R   (32)  [particular= ------------------------,basis= [-------------------]]
--R                         3      2                       3     2
--R                      12x  - 84x  + 192x - 144         x  - 7x  + 16x - 12
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 32

--S 33 of 139
yx:=ode161a.particular
 

                 4     3
             - 3x  + 8x  - 144
   (33)  ------------------------
            3      2
         12x  - 84x  + 192x - 144
                                                     Type: Expression Integer
--R 
--R
--R                 4     3
--R             - 3x  + 8x  - 144
--R   (33)  ------------------------
--R            3      2
--R         12x  - 84x  + 192x - 144
--R                                                     Type: Expression Integer
--E 33

--S 34 of 139
ode161expr := (x**2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x**2
 

   (34)  0
                                                     Type: Expression Integer
--R 
--R
--R   (34)  0
--R                                                     Type: Expression Integer
--E 34

--S 35 of 139
ode162 := (x-a)*(x-b)*D(y(x),x) + y(x)**2 + k*(y(x)+x-a)*(y(x)+x-b)
 

   (35)
       2                     ,                 2
     (x  + (- b - a)x + a b)y (x) + (k + 1)y(x)  + (2k x + (- b - a)k)y(x)

   + 
        2
     k x  + (- b - a)k x + a b k
                                                     Type: Expression Integer
--R 
--R
--R   (35)
--R       2                     ,                 2
--R     (x  + (- b - a)x + a b)y (x) + (k + 1)y(x)  + (2k x + (- b - a)k)y(x)
--R
--R   + 
--R        2
--R     k x  + (- b - a)k x + a b k
--R                                                     Type: Expression Integer
--E 35
--S 36 of 139
ode163 := 2*x**2*D(y(x),x) - 2*y(x)**2 - x*y(x) + 2*a**2*x
 

           2 ,           2              2
   (36)  2x y (x) - 2y(x)  - x y(x) + 2a x

                                                     Type: Expression Integer
--R 
--R
--R           2 ,           2              2
--R   (36)  2x y (x) - 2y(x)  - x y(x) + 2a x
--R
--R                                                     Type: Expression Integer
--E 36

--S 37 of 139
yx:=solve(ode163,y,x)
 

                   +-+
                 a\|x  - y(x)
   (37)  ---------------------------
                                 4a
                              - ----
                                 +-+
            2 +-+               \|x
         (2a \|x  + 2a y(x))%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +-+
--R                 a\|x  - y(x)
--R   (37)  ---------------------------
--R                                 4a
--R                              - ----
--R                                 +-+
--R            2 +-+               \|x
--R         (2a \|x  + 2a y(x))%e
--R                                          Type: Union(Expression Integer,...)
--E 37

--S 38 of 139
ode163expr := 2*x**2*D(yx,x) - 2*yx**2 - x*yx + 2*a**2*x
 

   (38)
                                                                   4a
                                                                - ----
                                                                   +-+
              3 3    2     5 4  +-+     2 3    3      4 4         \|x  ,
       ((- 12a x y(x)  - 4a x )\|x  - 4a x y(x)  - 12a x y(x))%e      y (x)

     + 
              4      5      6 2    3      8 3      +-+      5 2    4
           (4a x y(x)  + 40a x y(x)  + 20a x y(x))\|x  + 20a x y(x)
         + 
              7 3    2     9 4
           40a x y(x)  + 4a x
      *
               4a  2
            - ----
               +-+
              \|x
         (%e      )
     + 
                       5      3      4     3 2    3     5 2    2    5 3
               a x y(x)  + 12a x y(x)  + 8a x y(x)  - 8a x y(x)  - a x y(x)
             + 
                   7 3
               - 4a x
          *
              +-+
             \|x
         + 
           2      5     2 2    4     4 2    3     4 3    2      6 3        6 4
         4a x y(x)  + 5a x y(x)  + 8a x y(x)  + 4a x y(x)  - 12a x y(x) - a x
      *
              4a
           - ----
              +-+
             \|x
         %e
     + 
              5     2      3    4 2      +-+           4     3 2    2    5 3
       (- y(x)  + 2a x y(x)  - a x y(x))\|x  - a x y(x)  + 2a x y(x)  - a x
  /
            2    5      4      3      6 2      +-+      3      4      5 2    2
         (2a y(x)  + 20a x y(x)  + 10a x y(x))\|x  + 10a x y(x)  + 20a x y(x)
       + 
           7 3
         2a x
    *
             4a  2
          - ----
             +-+
            \|x
       (%e      )
                                                     Type: Expression Integer
--R 
--R
--R   (38)
--R                                                                   4a
--R                                                                - ----
--R                                                                   +-+
--R              3 3    2     5 4  +-+     2 3    3      4 4         \|x  ,
--R       ((- 12a x y(x)  - 4a x )\|x  - 4a x y(x)  - 12a x y(x))%e      y (x)
--R
--R     + 
--R              4      5      6 2    3      8 3      +-+      5 2    4
--R           (4a x y(x)  + 40a x y(x)  + 20a x y(x))\|x  + 20a x y(x)
--R         + 
--R              7 3    2     9 4
--R           40a x y(x)  + 4a x
--R      *
--R               4a  2
--R            - ----
--R               +-+
--R              \|x
--R         (%e      )
--R     + 
--R                       5      3      4     3 2    3     5 2    2    5 3
--R               a x y(x)  + 12a x y(x)  + 8a x y(x)  - 8a x y(x)  - a x y(x)
--R             + 
--R                   7 3
--R               - 4a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R           2      5     2 2    4     4 2    3     4 3    2      6 3        6 4
--R         4a x y(x)  + 5a x y(x)  + 8a x y(x)  + 4a x y(x)  - 12a x y(x) - a x
--R      *
--R              4a
--R           - ----
--R              +-+
--R             \|x
--R         %e
--R     + 
--R              5     2      3    4 2      +-+           4     3 2    2    5 3
--R       (- y(x)  + 2a x y(x)  - a x y(x))\|x  - a x y(x)  + 2a x y(x)  - a x
--R  /
--R            2    5      4      3      6 2      +-+      3      4      5 2    2
--R         (2a y(x)  + 20a x y(x)  + 10a x y(x))\|x  + 10a x y(x)  + 20a x y(x)
--R       + 
--R           7 3
--R         2a x
--R    *
--R             4a  2
--R          - ----
--R             +-+
--R            \|x
--R       (%e      )
--R                                                     Type: Expression Integer
--E 38

--S 39 of 139
ode164 := 2*x**2*D(y(x),x) - 2*y(x)**2 - 3*x*y(x) + 2*a**2*x
 

           2 ,           2               2
   (39)  2x y (x) - 2y(x)  - 3x y(x) + 2a x

                                                     Type: Expression Integer
--R 
--R
--R           2 ,           2               2
--R   (39)  2x y (x) - 2y(x)  - 3x y(x) + 2a x
--R
--R                                                     Type: Expression Integer
--E 39

--S 40 of 139
yx:=solve(ode164,y,x)
 

                              +-+
                (- 2y(x) - x)\|x  + 2a x
   (40)  -------------------------------------
                                           4a
                                        - ----
                                           +-+
                           +-+     2      \|x
         ((4a y(x) + 2a x)\|x  + 4a x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              +-+
--R                (- 2y(x) - x)\|x  + 2a x
--R   (40)  -------------------------------------
--R                                           4a
--R                                        - ----
--R                                           +-+
--R                           +-+     2      \|x
--R         ((4a y(x) + 2a x)\|x  + 4a x)%e
--R                                          Type: Union(Expression Integer,...)
--E 40

--S 41 of 139
ode164expr := 2*x**2*D(yx,x) - 2*yx**2 - 3*x*yx + 2*a**2*x
 

   (41)
                     2 2    3       2 3    2         2 4       4 3           2 5
               - 128a x y(x)  - 192a x y(x)  + (- 96a x  - 384a x )y(x) - 16a x
             + 
                     4 4
               - 192a x
          *
              +-+
             \|x
         + 
                 3 3    2       3 4          3 5       5 4
           - 384a x y(x)  - 384a x y(x) - 96a x  - 128a x
      *
              4a
           - ----
              +-+
             \|x  ,
         %e      y (x)

     + 
                   5      4        5 2    3        5 3        7 2     2
               640a x y(x)  + 1280a x y(x)  + (960a x  + 1280a x )y(x)
             + 
                    5 4        7 3           5 5       7 4       9 3
               (320a x  + 1280a x )y(x) + 40a x  + 320a x  + 128a x
          *
              +-+
             \|x
         + 
               4      5       4 2    4        4 3        6 2     3
           128a x y(x)  + 320a x y(x)  + (320a x  + 1280a x )y(x)
         + 
                4 4        6 3     2       4 5       6 4       8 3          4 6
           (160a x  + 1920a x )y(x)  + (40a x  + 960a x  + 640a x )y(x) + 4a x
         + 
               6 5       8 4
           160a x  + 320a x
      *
               4a  2
            - ----
               +-+
              \|x
         (%e      )
     + 
                   2    5       2      4        2 2       4      3
               128a y(x)  + 672a x y(x)  + (960a x  + 256a x)y(x)
             + 
                    2 3       4 2     2        2 4       6 2           2 5
               (592a x  + 384a x )y(x)  + (168a x  - 384a x )y(x) + 18a x
             + 
                    4 4       6 3
               - 64a x  - 288a x
          *
              +-+
             \|x
         + 
                     5          2       3      4          3        3 2     3
           96a x y(x)  + (240a x  + 384a x)y(x)  + (240a x  + 1152a x )y(x)
         + 
                  4       3 3       5 2     2         5       3 4       5 3
           (120a x  + 960a x  - 256a x )y(x)  + (30a x  + 288a x  - 480a x )y(x)
         + 
               6      3 5       5 4       7 3
           3a x  + 24a x  - 240a x  - 128a x
      *
              4a
           - ----
              +-+
             \|x
         %e
     + 
                     4             3           2      3      2
           - 32a y(x)  - 64a x y(x)  + (- 48a x  + 64a x)y(x)
         + 
                   3      3 2            4      3 3      5 2
           (- 16a x  + 64a x )y(x) - 2a x  + 16a x  - 32a x
      *
          +-+
         \|x
     + 
               5           4         2      2      3         3      2 2     2
       - 32y(x)  - 80x y(x)  + (- 80x  + 64a x)y(x)  + (- 40x  + 96a x )y(x)
     + 
             4      2 3      4 2         5     2 4      4 3
       (- 10x  + 48a x  - 32a x )y(x) - x  + 8a x  - 16a x
  /
                 3    4       3      3        3 2       5      2
             320a y(x)  + 640a x y(x)  + (480a x  + 640a x)y(x)
           + 
                  3 3       5 2           3 4       5 3      7 2
             (160a x  + 640a x )y(x) + 20a x  + 160a x  + 64a x
        *
            +-+
           \|x
       + 
            2    5       2      4        2 2       4      3
         64a y(x)  + 160a x y(x)  + (160a x  + 640a x)y(x)
       + 
             2 3       4 2     2       2 4       4 3       6 2          2 5
         (80a x  + 960a x )y(x)  + (20a x  + 480a x  + 320a x )y(x) + 2a x
       + 
            4 4       6 3
         80a x  + 160a x
    *
             4a  2
          - ----
             +-+
            \|x
       (%e      )
                                                     Type: Expression Integer
--R 
--R
--R   (41)
--R                     2 2    3       2 3    2         2 4       4 3           2 5
--R               - 128a x y(x)  - 192a x y(x)  + (- 96a x  - 384a x )y(x) - 16a x
--R             + 
--R                     4 4
--R               - 192a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R                 3 3    2       3 4          3 5       5 4
--R           - 384a x y(x)  - 384a x y(x) - 96a x  - 128a x
--R      *
--R              4a
--R           - ----
--R              +-+
--R             \|x  ,
--R         %e      y (x)
--R
--R     + 
--R                   5      4        5 2    3        5 3        7 2     2
--R               640a x y(x)  + 1280a x y(x)  + (960a x  + 1280a x )y(x)
--R             + 
--R                    5 4        7 3           5 5       7 4       9 3
--R               (320a x  + 1280a x )y(x) + 40a x  + 320a x  + 128a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R               4      5       4 2    4        4 3        6 2     3
--R           128a x y(x)  + 320a x y(x)  + (320a x  + 1280a x )y(x)
--R         + 
--R                4 4        6 3     2       4 5       6 4       8 3          4 6
--R           (160a x  + 1920a x )y(x)  + (40a x  + 960a x  + 640a x )y(x) + 4a x
--R         + 
--R               6 5       8 4
--R           160a x  + 320a x
--R      *
--R               4a  2
--R            - ----
--R               +-+
--R              \|x
--R         (%e      )
--R     + 
--R                   2    5       2      4        2 2       4      3
--R               128a y(x)  + 672a x y(x)  + (960a x  + 256a x)y(x)
--R             + 
--R                    2 3       4 2     2        2 4       6 2           2 5
--R               (592a x  + 384a x )y(x)  + (168a x  - 384a x )y(x) + 18a x
--R             + 
--R                    4 4       6 3
--R               - 64a x  - 288a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R                     5          2       3      4          3        3 2     3
--R           96a x y(x)  + (240a x  + 384a x)y(x)  + (240a x  + 1152a x )y(x)
--R         + 
--R                  4       3 3       5 2     2         5       3 4       5 3
--R           (120a x  + 960a x  - 256a x )y(x)  + (30a x  + 288a x  - 480a x )y(x)
--R         + 
--R               6      3 5       5 4       7 3
--R           3a x  + 24a x  - 240a x  - 128a x
--R      *
--R              4a
--R           - ----
--R              +-+
--R             \|x
--R         %e
--R     + 
--R                     4             3           2      3      2
--R           - 32a y(x)  - 64a x y(x)  + (- 48a x  + 64a x)y(x)
--R         + 
--R                   3      3 2            4      3 3      5 2
--R           (- 16a x  + 64a x )y(x) - 2a x  + 16a x  - 32a x
--R      *
--R          +-+
--R         \|x
--R     + 
--R               5           4         2      2      3         3      2 2     2
--R       - 32y(x)  - 80x y(x)  + (- 80x  + 64a x)y(x)  + (- 40x  + 96a x )y(x)
--R     + 
--R             4      2 3      4 2         5     2 4      4 3
--R       (- 10x  + 48a x  - 32a x )y(x) - x  + 8a x  - 16a x
--R  /
--R                 3    4       3      3        3 2       5      2
--R             320a y(x)  + 640a x y(x)  + (480a x  + 640a x)y(x)
--R           + 
--R                  3 3       5 2           3 4       5 3      7 2
--R             (160a x  + 640a x )y(x) + 20a x  + 160a x  + 64a x
--R        *
--R            +-+
--R           \|x
--R       + 
--R            2    5       2      4        2 2       4      3
--R         64a y(x)  + 160a x y(x)  + (160a x  + 640a x)y(x)
--R       + 
--R             2 3       4 2     2       2 4       4 3       6 2          2 5
--R         (80a x  + 960a x )y(x)  + (20a x  + 480a x  + 320a x )y(x) + 2a x
--R       + 
--R            4 4       6 3
--R         80a x  + 160a x
--R    *
--R             4a  2
--R          - ----
--R             +-+
--R            \|x
--R       (%e      )
--R                                                     Type: Expression Integer
--E 41

--S 42 of 139
ode165 := x*(2*x-1)*D(y(x),x) + y(x)**2 - (4*x+1)*y(x) + 4*x
 

            2      ,          2
   (42)  (2x  - x)y (x) + y(x)  + (- 4x - 1)y(x) + 4x

                                                     Type: Expression Integer
--R 
--R
--R            2      ,          2
--R   (42)  (2x  - x)y (x) + y(x)  + (- 4x - 1)y(x) + 4x
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 139
yx:=solve(ode165,y,x)
 

                    2
         x y(x) - 2x
   (43)  ------------
           y(x) - 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2
--R         x y(x) - 2x
--R   (43)  ------------
--R           y(x) - 1
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 139
ode165expr := x*(2*x-1)*D(yx,x) + yx**2 - (4*x+1)*yx + 4*x
 

   (44)
          4     3    2  ,          2          2        3     2               4
       (4x  - 4x  + x )y (x) + (- x  + 2x)y(x)  + (- 4x  + 8x  - 6x)y(x) + 4x

     + 
           2
       - 6x  + 4x
  /
         2
     y(x)  - 2y(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R   (44)
--R          4     3    2  ,          2          2        3     2               4
--R       (4x  - 4x  + x )y (x) + (- x  + 2x)y(x)  + (- 4x  + 8x  - 6x)y(x) + 4x
--R
--R     + 
--R           2
--R       - 6x  + 4x
--R  /
--R         2
--R     y(x)  - 2y(x) + 1
--R                                                     Type: Expression Integer
--E 44

--S 45 of 139
ode166 := 2*x*(x-1)*D(y(x),x) + (x-1)*y(x)**2 - x
 

            2       ,                 2
   (45)  (2x  - 2x)y (x) + (x - 1)y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R            2       ,                 2
--R   (45)  (2x  - 2x)y (x) + (x - 1)y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 139
ode166a:=solve(ode166,y,x)
 

   (46)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (46)  "failed"
--R                                                    Type: Union("failed",...)
--E 46

--S 47 of 139
ode167 := 3*x**2*D(y(x),x) - 7*y(x)**2 - 3*x*y(x) - x**2
 

           2 ,           2              2
   (47)  3x y (x) - 7y(x)  - 3x y(x) - x

                                                     Type: Expression Integer
--R 
--R
--R           2 ,           2              2
--R   (47)  3x y (x) - 7y(x)  - 3x y(x) - x
--R
--R                                                     Type: Expression Integer
--E 47

--S 48 of 139
yx:=solve(ode167,y,x)
 

                        +---+                    +---+
                 (- 497\|- 7  + 1197)y(x) + 171x\|- 7  + 497x
   (48)  ------------------------------------------------------------
                                                          +---+
                                                        2\|- 7 log(x)
                                                      - -------------
               +---+                   +---+                  3
         ((342\|- 7  + 994)y(x) - 142x\|- 7  + 342x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        +---+                    +---+
--R                 (- 497\|- 7  + 1197)y(x) + 171x\|- 7  + 497x
--R   (48)  ------------------------------------------------------------
--R                                                          +---+
--R                                                        2\|- 7 log(x)
--R                                                      - -------------
--R               +---+                   +---+                  3
--R         ((342\|- 7  + 994)y(x) - 142x\|- 7  + 342x)%e
--R                                          Type: Union(Expression Integer,...)
--E 48

--S 49 of 139
ode167expr := 3*x**2*D(yx,x) - 7*yx**2 - 3*x*yx - x**2
 

   (49)
                        3 +---+             3                 4 +---+
           (- 275142420x \|- 7  + 547274532x )y(x) - 78182076x \|- 7
         + 
                       4
           - 275142420x
      *
               +---+
             2\|- 7 log(x)
           - -------------
                   3       ,
         %e               y (x)

     + 
                       2 +---+             2     3
           (- 91714140x \|- 7  + 182424844x )y(x)
         + 
                       3 +---+             3     2
           (- 78182076x \|- 7  - 275142420x )y(x)
         + 
                     4 +---+            4                5 +---+            5
           (39306060x \|- 7  - 78182076x )y(x) + 3722956x \|- 7  + 13102020x
      *
                +---+       2
              2\|- 7 log(x)
            - -------------
                    3
         (%e               )
     + 
                       +---+                   3
           (368361714x\|- 7  - 2239972378x)y(x)
         + 
                      2 +---+             2     2
           (595138474x \|- 7  - 178912818x )y(x)
         + 
                      3 +---+            3                 4 +---+            4
           (130805178x \|- 7  - 44853634x )y(x) + 45713722x \|- 7  + 52623102x
      *
               +---+
             2\|- 7 log(x)
           - -------------
                   3
         %e
     + 
                   +---+                  3
       (1123498215\|- 7  - 2234704339)y(x)
     + 
                     +---+                   2
       (- 319243477x\|- 7  - 1123498215x)y(x)
     + 
                  2 +---+             2                 3 +---+             3
       (160499745x \|- 7  - 319243477x )y(x) - 45606211x \|- 7  - 160499745x
  /
                   +---+                 3              +---+                  2
         (91714140\|- 7  - 182424844)y(x)  + (78182076x\|- 7  + 275142420x)y(x)
       + 
                     2 +---+            2                3 +---+            3
         (- 39306060x \|- 7  + 78182076x )y(x) - 3722956x \|- 7  - 13102020x
    *
              +---+       2
            2\|- 7 log(x)
          - -------------
                  3
       (%e               )
                                                     Type: Expression Integer
--R 
--R
--R   (49)
--R                        3 +---+             3                 4 +---+
--R           (- 275142420x \|- 7  + 547274532x )y(x) - 78182076x \|- 7
--R         + 
--R                       4
--R           - 275142420x
--R      *
--R               +---+
--R             2\|- 7 log(x)
--R           - -------------
--R                   3       ,
--R         %e               y (x)
--R
--R     + 
--R                       2 +---+             2     3
--R           (- 91714140x \|- 7  + 182424844x )y(x)
--R         + 
--R                       3 +---+             3     2
--R           (- 78182076x \|- 7  - 275142420x )y(x)
--R         + 
--R                     4 +---+            4                5 +---+            5
--R           (39306060x \|- 7  - 78182076x )y(x) + 3722956x \|- 7  + 13102020x
--R      *
--R                +---+       2
--R              2\|- 7 log(x)
--R            - -------------
--R                    3
--R         (%e               )
--R     + 
--R                       +---+                   3
--R           (368361714x\|- 7  - 2239972378x)y(x)
--R         + 
--R                      2 +---+             2     2
--R           (595138474x \|- 7  - 178912818x )y(x)
--R         + 
--R                      3 +---+            3                 4 +---+            4
--R           (130805178x \|- 7  - 44853634x )y(x) + 45713722x \|- 7  + 52623102x
--R      *
--R               +---+
--R             2\|- 7 log(x)
--R           - -------------
--R                   3
--R         %e
--R     + 
--R                   +---+                  3
--R       (1123498215\|- 7  - 2234704339)y(x)
--R     + 
--R                     +---+                   2
--R       (- 319243477x\|- 7  - 1123498215x)y(x)
--R     + 
--R                  2 +---+             2                 3 +---+             3
--R       (160499745x \|- 7  - 319243477x )y(x) - 45606211x \|- 7  - 160499745x
--R  /
--R                   +---+                 3              +---+                  2
--R         (91714140\|- 7  - 182424844)y(x)  + (78182076x\|- 7  + 275142420x)y(x)
--R       + 
--R                     2 +---+            2                3 +---+            3
--R         (- 39306060x \|- 7  + 78182076x )y(x) - 3722956x \|- 7  - 13102020x
--R    *
--R              +---+       2
--R            2\|- 7 log(x)
--R          - -------------
--R                  3
--R       (%e               )
--R                                                     Type: Expression Integer
--E 49

--S 50 of 139
ode168 := 3*(x**2-4)*D(y(x),x) + y(x)**2 - x*y(x) - 3
 

            2       ,          2
   (50)  (3x  - 12)y (x) + y(x)  - x y(x) - 3

                                                     Type: Expression Integer
--R 
--R
--R            2       ,          2
--R   (50)  (3x  - 12)y (x) + y(x)  - x y(x) - 3
--R
--R                                                     Type: Expression Integer
--E 50

--S 51 of 139
ode168a:=solve(ode168,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 51

--S 52 of 139
ode169 := (a*x+b)**2*D(y(x),x) + (a*x+b)*y(x)**3 + c*y(x)**2
 

           2 2             2  ,                   3         2
   (52)  (a x  + 2a b x + b )y (x) + (a x + b)y(x)  + c y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2 2             2  ,                   3         2
--R   (52)  (a x  + 2a b x + b )y (x) + (a x + b)y(x)  + c y(x)
--R
--R                                                     Type: Expression Integer
--E 52

--S 53 of 139
ode169a:=solve(ode169,y,x)
 

   (53)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (53)  "failed"
--R                                                    Type: Union("failed",...)
--E 53

--S 54 of 139
ode170 := x**3*D(y(x),x) - y(x)**2 - x**4
 

          3 ,          2    4
   (54)  x y (x) - y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R          3 ,          2    4
--R   (54)  x y (x) - y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 54

--S 55 of 139
yx:=solve(ode170,y,x)
 

                  2           2
         (y(x) - x )log(x) + x
   (55)  ----------------------
                        2
                y(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2           2
--R         (y(x) - x )log(x) + x
--R   (55)  ----------------------
--R                        2
--R                y(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 55

--S 56 of 139
ode170expr := x**3*D(yx,x) - yx**2 - x**4
 

   (56)
          5 ,             2     2        4       2        2         4
       - x y (x) + (- y(x)  + 2x y(x) - x )log(x)  + (- 2x y(x) + 2x )log(x)

     + 
           4    2     2     6        8    6    4
       (- x  + x )y(x)  + 2x y(x) - x  + x  - x
  /
         2     2        4
     y(x)  - 2x y(x) + x
                                                     Type: Expression Integer
--R 
--R
--R   (56)
--R          5 ,             2     2        4       2        2         4
--R       - x y (x) + (- y(x)  + 2x y(x) - x )log(x)  + (- 2x y(x) + 2x )log(x)
--R
--R     + 
--R           4    2     2     6        8    6    4
--R       (- x  + x )y(x)  + 2x y(x) - x  + x  - x
--R  /
--R         2     2        4
--R     y(x)  - 2x y(x) + x
--R                                                     Type: Expression Integer
--E 56

--S 57 of 139
ode171 := x**3*D(y(x),x) - y(x)**2 - x**2*y(x)
 

          3 ,          2    2
   (57)  x y (x) - y(x)  - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          3 ,          2    2
--R   (57)  x y (x) - y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 139
yx:=solve(ode171,y,x)
 

                   2
         - y(x) + x
   (58)  -----------
            x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2
--R         - y(x) + x
--R   (58)  -----------
--R            x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 139
ode171expr := x**3*D(yx,x) - yx**2 - x**2*yx
 

            6 ,         3         2     2        4
         - x y (x) + (2x  - 1)y(x)  + 2x y(x) - x

   (59)  -----------------------------------------
                           2    2
                          x y(x)
                                                     Type: Expression Integer
--R 
--R
--R            6 ,         3         2     2        4
--R         - x y (x) + (2x  - 1)y(x)  + 2x y(x) - x
--R
--R   (59)  -----------------------------------------
--R                           2    2
--R                          x y(x)
--R                                                     Type: Expression Integer
--E 59

--S 60 of 139
ode172 := x**3*D(y(x),x) - x**4*y(x)**2 + x**2*y(x) + 20
 

          3 ,       4    2    2
   (60)  x y (x) - x y(x)  + x y(x) + 20

                                                     Type: Expression Integer
--R 
--R
--R          3 ,       4    2    2
--R   (60)  x y (x) - x y(x)  + x y(x) + 20
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 139
yx:=solve(ode172,y,x)
 

              11      2           9
           (7x   - 11x )y(x) + 35x  + 44
   (61)  --------------------------------
             11      2            9
         (36x   - 36x )y(x) + 180x  + 144
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              11      2           9
--R           (7x   - 11x )y(x) + 35x  + 44
--R   (61)  --------------------------------
--R             11      2            9
--R         (36x   - 36x )y(x) + 180x  + 144
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 139
ode172expr := x**3*D(yx,x) - x**4*yx**2 + x**2*yx + 20
 

   (62)
              14 ,
       - 1296x  y (x)

     + 
                26       24         22       17       15         13       8
           - 49x   + 252x   + 25920x   + 154x   + 648x   - 51840x   - 121x
         + 
               6         4
           396x  + 25920x
      *
             2
         y(x)
     + 
                 24        22          20       15        13         11       6
           - 490x   + 2520x   + 259200x   + 154x   - 1944x   - 51840x   + 968x
         + 
                  4          2
           - 3168x  - 207360x
      *
         y(x)
     + 
              22        20          18        13         11           9        4
       - 1225x   + 6300x   + 648000x   - 3080x   - 12960x   + 1036800x  - 1936x
     + 
            2
       6336x  + 414720
  /
             22        13        4     2          20        11         2
       (1296x   - 2592x   + 1296x )y(x)  + (12960x   - 2592x   - 10368x )y(x)
     + 
             18         9
       32400x   + 51840x  + 20736
                                                     Type: Expression Integer
--R 
--R
--R   (62)
--R              14 ,
--R       - 1296x  y (x)
--R
--R     + 
--R                26       24         22       17       15         13       8
--R           - 49x   + 252x   + 25920x   + 154x   + 648x   - 51840x   - 121x
--R         + 
--R               6         4
--R           396x  + 25920x
--R      *
--R             2
--R         y(x)
--R     + 
--R                 24        22          20       15        13         11       6
--R           - 490x   + 2520x   + 259200x   + 154x   - 1944x   - 51840x   + 968x
--R         + 
--R                  4          2
--R           - 3168x  - 207360x
--R      *
--R         y(x)
--R     + 
--R              22        20          18        13         11           9        4
--R       - 1225x   + 6300x   + 648000x   - 3080x   - 12960x   + 1036800x  - 1936x
--R     + 
--R            2
--R       6336x  + 414720
--R  /
--R             22        13        4     2          20        11         2
--R       (1296x   - 2592x   + 1296x )y(x)  + (12960x   - 2592x   - 10368x )y(x)
--R     + 
--R             18         9
--R       32400x   + 51840x  + 20736
--R                                                     Type: Expression Integer
--E 62

--S 63 of 139
ode173 := x**3*D(y(x),x) - x**6*y(x)**2 - (2*x-3)*x**2*y(x) + 3
 

          3 ,       6    2        3     2
   (63)  x y (x) - x y(x)  + (- 2x  + 3x )y(x) + 3

                                                     Type: Expression Integer
--R 
--R
--R          3 ,       6    2        3     2
--R   (63)  x y (x) - x y(x)  + (- 2x  + 3x )y(x) + 3
--R
--R                                                     Type: Expression Integer
--E 63

--S 64 of 139
yx:=solve(ode173,y,x)
 

               3
            - x y(x) + 1
   (64)  ------------------
            3            4x
         (4x y(x) + 12)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3
--R            - x y(x) + 1
--R   (64)  ------------------
--R            3            4x
--R         (4x y(x) + 12)%e
--R                                          Type: Union(Expression Integer,...)
--E 64

--S 65 of 139
ode173expr := x**3*D(yx,x) - x**6*yx**2 - (2*x-3)*x**2*yx + 3
 

   (65)
            6  4x ,          6    2       3              4x 2
       - 16x %e  y (x) + (48x y(x)  + 288x y(x) + 432)(%e  )

     + 
            9      8     2       6      5           3      2   4x    12    2
       ((24x  - 12x )y(x)  + (48x  - 72x )y(x) - 72x  + 36x )%e   - x  y(x)
     + 
         9        6
       2x y(x) - x
  /
         6    2      3              4x 2
     (16x y(x)  + 96x y(x) + 144)(%e  )
                                                     Type: Expression Integer
--R 
--R
--R   (65)
--R            6  4x ,          6    2       3              4x 2
--R       - 16x %e  y (x) + (48x y(x)  + 288x y(x) + 432)(%e  )
--R
--R     + 
--R            9      8     2       6      5           3      2   4x    12    2
--R       ((24x  - 12x )y(x)  + (48x  - 72x )y(x) - 72x  + 36x )%e   - x  y(x)
--R     + 
--R         9        6
--R       2x y(x) - x
--R  /
--R         6    2      3              4x 2
--R     (16x y(x)  + 96x y(x) + 144)(%e  )
--R                                                     Type: Expression Integer
--E 65

--S 66 of 139
ode174 := x*(x**2+1)*D(y(x),x) + x**2*y(x)
 

           3      ,       2
   (66)  (x  + x)y (x) + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           3      ,       2
--R   (66)  (x  + x)y (x) + x y(x)
--R
--R                                                     Type: Expression Integer
--E 66

--S 67 of 139
ode174a:=solve(ode174,y,x)
 

                                    1
   (67)  [particular= 0,basis= [---------]]
                                 +------+
                                 | 2
                                \|x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                    1
--R   (67)  [particular= 0,basis= [---------]]
--R                                 +------+
--R                                 | 2
--R                                \|x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 67

--S 68 of 139
yx:=ode174a.particular
 

   (68)  0
                                                     Type: Expression Integer
--R 
--R
--R   (68)  0
--R                                                     Type: Expression Integer
--E 68

--S 69 of 139
ode174expr := x*(x**2+1)*D(yx,x) + x**2*yx
 

   (69)  0
                                                     Type: Expression Integer
--R 
--R
--R   (69)  0
--R                                                     Type: Expression Integer
--E 69

--S 70 of 139
ode175 := x*(x**2-1)*D(y(x),x) - (2*x**2-1)*y(x) + a*x**3
 

           3      ,           2               3
   (70)  (x  - x)y (x) + (- 2x  + 1)y(x) + a x

                                                     Type: Expression Integer
--R 
--R
--R           3      ,           2               3
--R   (70)  (x  - x)y (x) + (- 2x  + 1)y(x) + a x
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 139
ode175a:=solve(ode175,y,x)
 

                                    +------+
                                    | 2
   (71)  [particular= a x,basis= [x\|x  - 1 ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                    +------+
--R                                    | 2
--R   (71)  [particular= a x,basis= [x\|x  - 1 ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 71

--S 72 of 139
yx:=ode175a.particular
 

   (72)  a x
                                                     Type: Expression Integer
--R 
--R
--R   (72)  a x
--R                                                     Type: Expression Integer
--E 72

--S 73 of 139
ode175expr := x*(x**2-1)*D(yx,x) - (2*x**2-1)*yx + a*x**3
 

   (73)  0
                                                     Type: Expression Integer
--R 
--R
--R   (73)  0
--R                                                     Type: Expression Integer
--E 73

--S 74 of 139
ode176 := x*(x**2-1)*D(y(x),x) + (x**2-1)*y(x)**2 - x**2
 

           3      ,        2         2    2
   (74)  (x  - x)y (x) + (x  - 1)y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R           3      ,        2         2    2
--R   (74)  (x  - x)y (x) + (x  - 1)y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 139
ode176a:=solve(ode176,y,x)
 

   (75)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (75)  "failed"
--R                                                    Type: Union("failed",...)
--E 75

--S 76 of 139
ode177 := x**2*(x-1)*D(y(x),x) - y(x)**2 - x*(x-2)*y(x)
 

           3    2  ,          2       2
   (76)  (x  - x )y (x) - y(x)  + (- x  + 2x)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           3    2  ,          2       2
--R   (76)  (x  - x )y (x) - y(x)  + (- x  + 2x)y(x)
--R
--R                                                     Type: Expression Integer
--E 76

--S 77 of 139
yx:=solve(ode177,y,x)
 

                   2
         - y(x) + x
   (77)  -----------
         (x - 1)y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2
--R         - y(x) + x
--R   (77)  -----------
--R         (x - 1)y(x)
--R                                          Type: Union(Expression Integer,...)
--E 77

--S 78 of 139
ode177expr := x**2*(x-1)*D(yx,x) - yx**2 - x*(x-2)*yx
 

             6     5    4  ,         3     2              2     2        4
         (- x  + 2x  - x )y (x) + (2x  - 4x  + 2x - 1)y(x)  + 2x y(x) - x

   (78)  -----------------------------------------------------------------
                                   2              2
                                 (x  - 2x + 1)y(x)
                                                     Type: Expression Integer
--R 
--R
--R             6     5    4  ,         3     2              2     2        4
--R         (- x  + 2x  - x )y (x) + (2x  - 4x  + 2x - 1)y(x)  + 2x y(x) - x
--R
--R   (78)  -----------------------------------------------------------------
--R                                   2              2
--R                                 (x  - 2x + 1)y(x)
--R                                                     Type: Expression Integer
--E 78

--S 79 of 139
ode178 := 2*x*(x**2-1)*D(y(x),x) + 2*(x**2-1)*y(x)**2 _
           - (3*x**2-5)*y(x) + x**2 - 3
 

            3       ,         2         2        2             2
   (79)  (2x  - 2x)y (x) + (2x  - 2)y(x)  + (- 3x  + 5)y(x) + x  - 3

                                                     Type: Expression Integer
--R 
--R
--R            3       ,         2         2        2             2
--R   (79)  (2x  - 2x)y (x) + (2x  - 2)y(x)  + (- 3x  + 5)y(x) + x  - 3
--R
--R                                                     Type: Expression Integer
--E 79

--S 80 of 139
yx:=solve(ode178,y,x)
 

                      +------+   x      +---+
                      | 2      ++      \|%CL               +-+
         (- y(x) + 1)\|x  - 1  |   -------------- d%CL  + \|x
                              ++       +--------+
                                       |   2
                                   %CL\|%CL  - 1
   (80)  -----------------------------------------------------
                                     +------+
                                     | 2
                          (y(x) - 1)\|x  - 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      +------+   x      +---+
--I                      | 2      ++      \|%CL               +-+
--I         (- y(x) + 1)\|x  - 1  |   -------------- d%CL  + \|x
--R                              ++       +--------+
--R                                       |   2
--I                                   %CL\|%CL  - 1
--R   (80)  -----------------------------------------------------
--R                                     +------+
--R                                     | 2
--R                          (y(x) - 1)\|x  - 1
--R                                          Type: Union(Expression Integer,...)
--E 80

--S 81 of 139
ode178expr := 2*x*(x**2-1)*D(yx,x) + 2*(x**2-1)*yx**2 _
               - (3*x**2-5)*yx + x**2 - 3
 

   (81)
                                                          +------+
             2         2        2              2      +-+ | 2
         ((2x  - 2)y(x)  + (- 4x  + 4)y(x) + 2x  - 2)\|x \|x  - 1
      *
            x      +---+          2
          ++      \|%CL
          |   -------------- d%CL
         ++       +--------+
                  |   2
              %CL\|%CL  - 1
     + 
                                                             +------+
               2         2        2               2      +-+ | 2
           ((3x  - 5)y(x)  + (- 6x  + 10)y(x) + 3x  - 5)\|x \|x  - 1
         + 
                3               3
           (- 4x  + 4x)y(x) + 4x  - 4x
      *
            x      +---+
          ++      \|%CL
          |   -------------- d%CL
         ++       +--------+
                  |   2
              %CL\|%CL  - 1
     + 
            4     2  ,
       (- 2x  + 2x )y (x)

     + 
                                                           +------+
          2         2        2             2           +-+ | 2
       ((x  - 3)y(x)  + (- 2x  + 6)y(x) + x  + 2x - 3)\|x \|x  - 1
     + 
            3          2     3
       (- 2x  + 2x)y(x)  + 2x  - 2x
  /
                             +------+
          2              +-+ | 2
     (y(x)  - 2y(x) + 1)\|x \|x  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (81)
--R                                                          +------+
--R             2         2        2              2      +-+ | 2
--R         ((2x  - 2)y(x)  + (- 4x  + 4)y(x) + 2x  - 2)\|x \|x  - 1
--R      *
--R            x      +---+          2
--I          ++      \|%CL
--I          |   -------------- d%CL
--R         ++       +--------+
--R                  |   2
--I              %CL\|%CL  - 1
--R     + 
--R                                                             +------+
--R               2         2        2               2      +-+ | 2
--R           ((3x  - 5)y(x)  + (- 6x  + 10)y(x) + 3x  - 5)\|x \|x  - 1
--R         + 
--R                3               3
--R           (- 4x  + 4x)y(x) + 4x  - 4x
--R      *
--R            x      +---+
--I          ++      \|%CL
--I          |   -------------- d%CL
--R         ++       +--------+
--R                  |   2
--I              %CL\|%CL  - 1
--R     + 
--R            4     2  ,
--R       (- 2x  + 2x )y (x)
--R
--R     + 
--R                                                           +------+
--R          2         2        2             2           +-+ | 2
--R       ((x  - 3)y(x)  + (- 2x  + 6)y(x) + x  + 2x - 3)\|x \|x  - 1
--R     + 
--R            3          2     3
--R       (- 2x  + 2x)y(x)  + 2x  - 2x
--R  /
--R                             +------+
--R          2              +-+ | 2
--R     (y(x)  - 2y(x) + 1)\|x \|x  - 1
--R                                                     Type: Expression Integer
--E 81

--S 82 of 139
ode179 := 3*x*(x**2-1)*D(y(x),x) + x*y(x)**2 - (x**2+1)*y(x) - 3*x
 

            3       ,            2       2
   (82)  (3x  - 3x)y (x) + x y(x)  + (- x  - 1)y(x) - 3x

                                                     Type: Expression Integer
--R 
--R
--R            3       ,            2       2
--R   (82)  (3x  - 3x)y (x) + x y(x)  + (- x  - 1)y(x) - 3x
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 139
ode179a:=solve(ode179,y,x)
 

   (83)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (83)  "failed"
--R                                                    Type: Union("failed",...)
--E 83

--S 84 of 139
ode180 := (a*x**2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)**2 + x**2
 

             3      2        ,          2         2                   2
   (84)  (a x  + b x  + c x)y (x) - y(x)  + (- a x  - b x - c)y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R             3      2        ,          2         2                   2
--R   (84)  (a x  + b x  + c x)y (x) - y(x)  + (- a x  - b x - c)y(x) + x
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 139  random generation, FAILURE OK.
yx:=solve(ode180,y,x)
 
   WARNING (genufact): No known algorithm to factor
                     2            2
      4   - 4a c + 2b   2        b
     ?  + ------------ ?  - -----------, trying square-free.
             3     2 2        5     4 2
           4a c - a b       4a c - a b
   WARNING (genufact): No known algorithm to factor
                     2            2         2            2
      4   - 4a c + 2b  - 4a b + 4a   2   - b  + 4a b - 4a
     ?  + ------------------------- ?  + -----------------, trying square-free.
                   3     2 2                  5     4 2
                 4a c - a b                 4a c - a b
   WARNING (genufact): No known algorithm to factor
                           2              4      2
        9   9b  8   (144a b  - 24a)c - 36b  + 12b   7
       ?  - -- ?  + ------------------------------ ?
             a                  3     2 2
                              4a c - a b
     + 
                3                 5      3
       (- 336a b  + 168a b)c + 84b  - 84b   6
       ----------------------------------- ?
                     4     3 2
                   4a c - a b
     + 
                   2 4        2 2       2  2
             (2016a b  - 2016a b  + 144a )c
           + 
                       6          4         2         8       6      4
             (- 1008a b  + 1512a b  - 192a b )c + 126b  - 252b  + 48b
        /
              6 2     5 2     4 4
           16a c  - 8a b c + a b
      *
          5
         ?
     + 
                     2 5        2 3       2   2
             (- 2016a b  + 3360a b  - 720a b)c
           + 
                     7          5         3         9       7       5
             (1008a b  - 2520a b  + 960a b )c - 126b  + 420b  - 240b
        /
              7 2     6 2     5 4
           16a c  - 8a b c + a b
      *
          4
         ?
     + 
                   3 6         3 4        3 2       3  3
             (5376a b  - 13440a b  + 5760a b  - 256a )c
           + 
                     2 8         2 6        2 4       2 2  2
             (- 4032a b  + 13440a b  - 9120a b  + 640a b )c
           + 
                     10          8          6         4        12       10
             (1008a b   - 4200a b  + 3840a b  - 384a b )c - 84b   + 420b
           + 
                   8      6
             - 480b  + 64b
        /
              9 3      8 2 2      7 4     6 6
           64a c  - 48a b c  + 12a b c - a b
      *
          3
         ?
     + 
                     3 7        3 5        3 3       3   3
             (- 2304a b  + 8064a b  - 5760a b  + 768a b)c
           + 
                   2 9        2 7        2 5        2 3  2
             (1728a b  - 8064a b  + 9120a b  - 1920a b )c
           + 
                      11          9          7          5        13       11
             (- 432a b   + 2520a b  - 3840a b  + 1152a b )c + 36b   - 252b
           + 
                 9       7
             480b  - 192b
        /
              10 3      9 2 2      8 4     7 6
           64a  c  - 48a b c  + 12a b c - a b
      *
          2
         ?
     + 
                  3 8        3 6        3 4       3 2  3
             (576a b  - 2688a b  + 2880a b  - 768a b )c
           + 
                    2 10        2 8        2 6        2 4       2 2  2
             (- 432a b   + 2688a b  - 4560a b  + 1920a b  - 256a b )c
           + 
                    12         10          8          6       14      12
             (108a b   - 840a b   + 1920a b  - 1152a b )c - 9b   + 84b
           + 
                   10       8
             - 240b   + 192b
        /
              11 3      10 2 2      9 4     8 6
           64a  c  - 48a  b c  + 12a b c - a b
      *
         ?
     + 
                 3 9       3 7       3 5       3 3  3
           (- 64a b  + 384a b  - 576a b  + 256a b )c
         + 
               2 11       2 9       2 7       2 5       2 3  2
           (48a b   - 384a b  + 912a b  - 640a b  + 256a b )c
         + 
                   13         11         9         7      15      13      11
           (- 12a b   + 120a b   - 384a b  + 384a b )c + b   - 12b   + 48b
         + 
                9
           - 64b
      /
            12 3      11 2 2      10 4     9 6
         64a  c  - 48a  b c  + 12a  b c - a b
     , trying square-free.
   WARNING (genufact): No known algorithm to factor
        9   18b - 18a  8
       ?  + --------- ?
                a
     + 
                    2        2        3               4         3
             (576a b  - 1152a b + 576a  - 96a)c - 144b  + 288a b
           + 
                    2       2              2
             (- 144a  + 48)b  - 48a b + 24a
        /
             3     2 2
           4a c - a b
      *
          7
         ?
     + 
                     3        2 2         3                  4        2
             (2688a b  - 8064a b  + (8064a  - 1344a)b - 2688a  + 1344a )c
           + 
                   5          4           2        3        3          2
             - 672b  + 2016a b  + (- 2016a  + 672)b  + (672a  - 1344a)b
           + 
                  2        3
             1008a b - 336a
        /
             4     3 2
           4a c - a b
      *
          6
         ?
     + 
                       2 4          3 3           4         2  2
                 32256a b  - 129024a b  + (193536a  - 32256a )b
               + 
                           5         3           6         4        2
                 (- 129024a  + 64512a )b + 32256a  - 32256a  + 2304a
            *
                2
               c
           + 
                           6         2 5            3           4
                 - 16128a b  + 64512a b  + (- 96768a  + 24192a)b
               + 
                        4         2  3            5         3          2
                 (64512a  - 64512a )b  + (- 16128a  + 64512a  - 3072a)b
               + 
                          4        2          5        3
                 (- 32256a  + 3840a )b + 8064a  - 1920a
            *
               c
           + 
                  8          7          2         6           3           5
             2016b  - 8064a b  + (12096a  - 4032)b  + (- 8064a  + 12096a)b
           + 
                   4         2        4         3          3
             (2016a  - 14112a  + 768)b  + (8064a  - 1536a)b
           + 
                     4        2  2       3        4
             (- 2016a  + 1344a )b  - 576a b + 144a
        /
              6 2     5 2     4 4
           16a c  - 8a b c + a b
      *
          5
         ?
     + 
                       2 5          3 4           4          2  3
                 64512a b  - 322560a b  + (645120a  - 107520a )b
               + 
                           5          3  2           6          4         2
                 (- 645120a  + 322560a )b  + (322560a  - 322560a  + 23040a )b
               + 
                         7          5         3
                 - 64512a  + 107520a  - 23040a
            *
                2
               c
           + 
                           7          2 6             3           5
                 - 32256a b  + 161280a b  + (- 322560a  + 80640a)b
               + 
                         4          2  4             5          3           3
                 (322560a  - 295680a )b  + (- 161280a  + 430080a  - 30720a)b
               + 
                        6          4         2  2           5         3
                 (32256a  - 322560a  + 69120a )b  + (134400a  - 57600a )b
               + 
                         6         4
                 - 26880a  + 19200a
            *
               c
           + 
                  9           8          2          7            3           6
             4032b  - 20160a b  + (40320a  - 13440)b  + (- 40320a  + 53760a)b
           + 
                    4         2         5           5         3           4
             (20160a  - 87360a  + 7680)b  + (- 4032a  + 73920a  - 23040a)b
           + 
                      4         2  3         5         3  2        4         5
             (- 33600a  + 28800a )b  + (6720a  - 19200a )b  + 7200a b - 1440a
        /
              7 2     6 2     5 4
           16a c  - 8a b c + a b
      *
          4
         ?
     + 
                        3 6           4 5            5          3  4
                 344064a b  - 2064384a b  + (5160960a  - 860160a )b
               + 
                            6           4  3
                 (- 6881280a  + 3440640a )b
               + 
                          7           5          3  2
                 (5160960a  - 5160960a  + 368640a )b
               + 
                            8           6          4            9          7
                 (- 2064384a  + 3440640a  - 737280a )b + 344064a  - 860160a
               + 
                        5         3
                 368640a  - 16384a
            *
                3
               c
           + 
                          2 8           3 7              4          2  6
                 - 258048a b  + 1548288a b  + (- 3870720a  + 860160a )b
               + 
                          5           3  5
                 (5160960a  - 3870720a )b
               + 
                            6           4          2  4
                 (- 3870720a  + 7096320a  - 583680a )b
               + 
                          7           5           3  3
                 (1548288a  - 6881280a  + 1781760a )b
               + 
                           8           6           4         2  2
                 (- 258048a  + 3870720a  - 2119680a  + 40960a )b
               + 
                            7           5         3            8          6
                 (- 1290240a  + 1228800a  - 57344a )b + 215040a  - 307200a
               + 
                       4
                 28672a
            *
                2
               c
           + 
                         10          2 9           3            8
                 64512a b   - 387072a b  + (967680a  - 268800a)b
               + 
                            4           2  7
                 (- 1290240a  + 1290240a )b
               + 
                         5           3            6
                 (967680a  - 2580480a  + 245760a)b
               + 
                           6           4          2  5
                 (- 387072a  + 2795520a  - 890880a )b
               + 
                        7           5           3           4
                 (64512a  - 1774080a  + 1336320a  - 24576a)b
               + 
                         6           4         2  3
                 (645120a  - 1075200a  + 57344a )b
               + 
                           7          5         3  2             6         4
                 (- 107520a  + 499200a  - 57344a )b  + (- 138240a  + 28672a )b
               + 
                       7        5
                 23040a  - 7168a
            *
               c
           + 
                    12           11            2          10
             - 5376b   + 32256a b   + (- 80640a  + 26880)b
           + 
                     3            9            4          2          8
             (107520a  - 134400a)b  + (- 80640a  + 282240a  - 30720)b
           + 
                    5          3            7
             (32256a  - 322560a  + 122880a)b
           + 
                     6          4          2         6
             (- 5376a  + 215040a  - 207360a  + 4096)b
           + 
                      5          3           5
             (- 80640a  + 192000a  - 12288a)b
           + 
                    6          4         2  4          5         3  3
             (13440a  - 105600a  + 16384a )b  + (34560a  - 12288a )b
           + 
                     6        4  2        5        6
             (- 5760a  + 5632a )b  - 1536a b + 256a
        /
              9 3      8 2 2      7 4     6 6
           64a c  - 48a b c  + 12a b c - a b
      *
          3
         ?
     + 
                        3 7           4 6            5           3  5
                 294912a b  - 2064384a b  + (6193152a  - 1032192a )b
               + 
                             6           4  4
                 (- 10321920a  + 5160960a )b
               + 
                           7            5          3  3
                 (10321920a  - 10321920a  + 737280a )b
               + 
                            8            6           4  2
                 (- 6193152a  + 10321920a  - 2211840a )b
               + 
                          9           7           5         3            10
                 (2064384a  - 5160960a  + 2211840a  - 98304a )b - 294912a
               + 
                         8          6         4
                 1032192a  - 737280a  + 98304a
            *
                3
               c
           + 
                          2 9           3 8              4           2  7
                 - 221184a b  + 1548288a b  + (- 4644864a  + 1032192a )b
               + 
                          5           3  6
                 (7741440a  - 5677056a )b
               + 
                            6            4           2  5
                 (- 7741440a  + 13160448a  - 1167360a )b
               + 
                          7            5           3  4
                 (4644864a  - 16773120a  + 4730880a )b
               + 
                            8            6           4          2  3
                 (- 1548288a  + 12902400a  - 7802880a  + 245760a )b
               + 
                         9           7           5          3  2
                 (221184a  - 6193152a  + 6696960a  - 589824a )b
               + 
                          8           6          4            9          7
                 (1806336a  - 3072000a  + 516096a )b - 258048a  + 614400a
               + 
                          5
                 - 172032a
            *
                2
               c
           + 
                         11          2 10            3            9
                 55296a b   - 387072a b   + (1161216a  - 322560a)b
               + 
                            4           2  8
                 (- 1935360a  + 1870848a )b
               + 
                          5           3            7
                 (1935360a  - 4644864a  + 491520a)b
               + 
                            6           4           2  6
                 (- 1161216a  + 6451200a  - 2273280a )b
               + 
                         7           5           3            5
                 (387072a  - 5483520a  + 4454400a  - 147456a)b
               + 
                          8           6           4          2  4
                 (- 55296a  + 2903040a  - 4823040a  + 491520a )b
               + 
                           7           5          3  3
                 (- 903168a  + 3148800a  - 688128a )b
               + 
                         8           6          4  2           7          5
                 (129024a  - 1274880a  + 516096a )b  + (322560a  - 215040a )b
               + 
                         8         6
                 - 46080a  + 43008a
            *
               c
           + 
                    13           12            2          11
             - 4608b   + 32256a b   + (- 96768a  + 32256)b
           + 
                     3            10             4          2          9
             (161280a  - 193536a)b   + (- 161280a  + 499968a  - 61440)b
           + 
                    5          3            8
             (96768a  - 725760a  + 307200a)b
           + 
                      6          4          2          7
             (- 32256a  + 645120a  - 660480a  + 24576)b
           + 
                   7          5          3           6
             (4608a  - 354816a  + 798720a  - 98304a)b
           + 
                     6          4          2  5
             (112896a  - 595200a  + 172032a )b
           + 
                      7          5          3  4            6          4  3
             (- 16128a  + 280320a  - 172032a )b  + (- 80640a  + 107520a )b
           + 
                    7         5  2         6         7
             (11520a  - 43008a )b  + 10752a b - 1536a
        /
              10 3      9 2 2      8 4     7 6
           64a  c  - 48a b c  + 12a b c - a b
      *
          2
         ?
     + 
                        3 8           4 7            5          3  6
                 147456a b  - 1179648a b  + (4128768a  - 688128a )b
               + 
                            6           4  5
                 (- 8257536a  + 4128768a )b
               + 
                           7            5          3  4
                 (10321920a  - 10321920a  + 737280a )b
               + 
                            8            6           4  3
                 (- 8257536a  + 13762560a  - 2949120a )b
               + 
                          9            7           5          3  2
                 (4128768a  - 10321920a  + 4423680a  - 196608a )b
               + 
                            10           8           6          4            11
                 (- 1179648a   + 4128768a  - 2949120a  + 393216a )b + 147456a
               + 
                          9          7          5
                 - 688128a  + 737280a  - 196608a
            *
                3
               c
           + 
                          2 10          3 9              4          2  8
                 - 110592a b   + 884736a b  + (- 3096576a  + 688128a )b
               + 
                          5           3  7
                 (6193152a  - 4472832a )b
               + 
                            6            4           2  6
                 (- 7741440a  + 12558336a  - 1167360a )b
               + 
                          7            5           3  5
                 (6193152a  - 19955712a  + 5898240a )b
               + 
                            8            6            4          2  4
                 (- 3096576a  + 19783680a  - 12533760a  + 491520a )b
               + 
                         9            7            5           3  3
                 (884736a  - 12730368a  + 14499840a  - 1671168a )b
               + 
                           10           8           6           4         2  2
                 (- 110592a   + 5332992a  - 9768960a  + 2211840a  - 65536a )b
               + 
                            9           7           5          3            10
                 (- 1376256a  + 3686400a  - 1376256a  + 131072a )b + 172032a
               + 
                          8          6         4
                 - 614400a  + 344064a  - 65536a
            *
                2
               c
           + 
                         12          2 11           3            10
                 27648a b   - 221184a b   + (774144a  - 215040a)b
               + 
                            4           2  9
                 (- 1548288a  + 1462272a )b
               + 
                          5           3            8
                 (1935360a  - 4343808a  + 491520a)b
               + 
                            6           4           2  7
                 (- 1548288a  + 7397376a  - 2764800a )b
               + 
                         7           5           3            6
                 (774144a  - 7956480a  + 6727680a  - 294912a)b
               + 
                           8           6           4           2  5
                 (- 221184a  + 5591040a  - 9277440a  + 1277952a )b
               + 
                        9           7           5           3  4
                 (27648a  - 2537472a  + 7971840a  - 2359296a )b
               + 
                         8           6           4         2  3
                 (688128a  - 4423680a  + 2408448a  + 65536a )b
               + 
                          9           7           5          3  2
                 (- 86016a  + 1597440a  - 1462272a  - 163840a )b
               + 
                         8          6          4           9         7         5
               (- 368640a  + 516096a  + 131072a )b + 46080a  - 86016a  - 32768a
            *
               c
           + 
                    14           13            2          12
             - 2304b   + 18432a b   + (- 64512a  + 21504)b
           + 
                     3            11             4          2          10
             (129024a  - 150528a)b   + (- 161280a  + 462336a  - 61440)b
           + 
                     5          3            9
             (129024a  - 817152a  + 368640a)b
           + 
                      6          4          2          8
             (- 64512a  + 913920a  - 967680a  + 49152)b
           + 
                    7          5           3            7
             (18432a  - 666624a  + 1459200a  - 245760a)b
           + 
                     8          6           4          2  6
             (- 2304a  + 311808a  - 1393920a  + 540672a )b
           + 
                      7          5          3  5
             (- 86016a  + 875520a  - 688128a )b
           + 
                    8          6          4         2  4
             (10752a  - 360960a  + 559104a  - 16384a )b
           + 
                    7          5         3  3
             (92160a  - 301056a  + 49152a )b
           + 
                      8          6         4  2            7         5
             (- 11520a  + 107520a  - 53248a )b  + (- 24576a  + 24576a )b
           + 
                  8        6
             3072a  - 4096a
        /
              11 3      10 2 2      9 4     8 6
           64a  c  - 48a  b c  + 12a b c - a b
      *
         ?
     + 
                     3 9          4 8            5          3  7
               32768a b  - 294912a b  + (1179648a  - 196608a )b
             + 
                          6           4  6
               (- 2752512a  + 1376256a )b
             + 
                        7           5          3  5
               (4128768a  - 4128768a  + 294912a )b
             + 
                          8           6           4  4
               (- 4128768a  + 6881280a  - 1474560a )b
             + 
                        9           7           5          3  3
               (2752512a  - 6881280a  + 2949120a  - 131072a )b
             + 
                          10           8           6          4  2
               (- 1179648a   + 4128768a  - 2949120a  + 393216a )b
             + 
                       11           9           7          5           12
               (294912a   - 1376256a  + 1474560a  - 393216a )b - 32768a
             + 
                      10          8          6
               196608a   - 294912a  + 131072a
          *
              3
             c
         + 
                       2 11          3 10             4          2  9
               - 24576a b   + 221184a b   + (- 884736a  + 196608a )b
             + 
                        5           3  8
               (2064384a  - 1474560a )b
             + 
                          6           4          2  7
               (- 3096576a  + 4866048a  - 466944a )b
             + 
                        7           5           3  6
               (3096576a  - 9289728a  + 2826240a )b
             + 
                          8            6           4          2  5
               (- 2064384a  + 11354112a  - 7372800a  + 327680a )b
             + 
                       9           7            5           3  4
               (884736a  - 9289728a  + 10813440a  - 1441792a )b
             + 
                         10           8           6           4          2  3
               (- 221184a   + 5160960a  - 9707520a  + 2588672a  - 131072a )b
             + 
                      11           9           7           5          3  2
               (24576a   - 1916928a  + 5382144a  - 2392064a  + 393216a )b
             + 
                       10           8           6          4           11
               (442368a   - 1720320a  + 1146880a  - 393216a )b - 49152a
             + 
                      9          7          5
               245760a  - 229376a  + 131072a
          *
              2
             c
         + 
                      13         2 12           3           11
               6144a b   - 55296a b   + (221184a  - 61440a)b
             + 
                         4          2  10           5           3            9
               (- 516096a  + 479232a )b   + (774144a  - 1658880a  + 196608a)b
             + 
                         6           4           2  8
               (- 774144a  + 3354624a  - 1302528a )b
             + 
                       7           5           3            7
               (516096a  - 4386816a  + 3796992a  - 196608a)b
             + 
                         8           6           4           2  6
               (- 221184a  + 3870720a  - 6402048a  + 1048576a )b
             + 
                      9           7           5           3  5
               (55296a  - 2322432a  + 6899712a  - 2424832a )b
             + 
                       10          8           6           4          2  4
               (- 6144a   + 921600a  - 4958208a  + 3178496a  + 131072a )b
             + 
                         9           7           5          3  3
               (- 221184a  + 2408448a  - 2580480a  - 458752a )b
             + 
                      10          8           6          4  2
               (24576a   - 786432a  + 1318912a  + 589824a )b
             + 
                       9          7          5           10         8         6
               (165888a  - 401408a  - 327680a )b - 18432a   + 57344a  + 65536a
          *
             c
         + 
                 15          14            2         13          3           12
           - 512b   + 4608a b   + (- 18432a  + 6144)b   + (43008a  - 49152a)b
         + 
                    4          2          11          5          3            10
           (- 64512a  + 175104a  - 24576)b   + (64512a  - 365568a  + 172032a)b
         + 
                    6          4          2          9
           (- 43008a  + 494592a  - 534528a  + 32768)b
         + 
                  7          5          3            8
           (18432a  - 451584a  + 970752a  - 196608a)b
         + 
                   8          6           4          2  7
           (- 4608a  + 279552a  - 1141248a  + 524288a )b
         + 
                9          7          5          3  6
           (512a  - 113664a  + 907776a  - 819200a )b
         + 
                  8          6          4         2  5
           (27648a  - 494592a  + 831488a  - 32768a )b
         + 
                   9          7          5          3  4
           (- 3072a  + 181248a  - 573440a  + 131072a )b
         + 
                    8          6          4  3         9         7          5  2
           (- 41472a  + 272384a  - 204800a )b  + (4608a  - 88064a  + 155648a )b
         + 
                  8         6          9        7
           (18432a  - 57344a )b - 2048a  + 8192a
      /
            12 3      11 2 2      10 4     9 6
         64a  c  - 48a  b c  + 12a  b c - a b
     , trying square-free.

   (85)
     - y(x) + x
  /
       (2y(x) + 2x)
    *
         %e
      **
             2
          *
             log
                                                 +-----------+
                       2 2                    2  |          2       2        2
                    (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                  + 
                              3
                    4a b c - b
               /
                     2
                  a x  + b x + c
        /
            +-----------+
            |          2
           \|- 4a c + b
                                          Type: Union(Expression Integer,...)
--R 
--R   WARNING (genufact): No known algorithm to factor
--R                     2            2
--R      4   - 4a c + 2b   2        b
--R     ?  + ------------ ?  - -----------, trying square-free.
--R             3     2 2        5     4 2
--R           4a c - a b       4a c - a b
--R   WARNING (genufact): No known algorithm to factor
--R                     2            2         2            2
--R      4   - 4a c + 2b  - 4a b + 4a   2   - b  + 4a b - 4a
--R     ?  + ------------------------- ?  + -----------------, trying square-free.
--R                   3     2 2                  5     4 2
--R                 4a c - a b                 4a c - a b
--R   WARNING (genufact): No known algorithm to factor
--R                           2              4      2
--R        9   9b  8   (144a b  - 24a)c - 36b  + 12b   7
--R       ?  - -- ?  + ------------------------------ ?
--R             a                  3     2 2
--R                              4a c - a b
--R     + 
--R                3                 5      3
--R       (- 336a b  + 168a b)c + 84b  - 84b   6
--R       ----------------------------------- ?
--R                     4     3 2
--R                   4a c - a b
--R     + 
--R                   2 4        2 2       2  2
--R             (2016a b  - 2016a b  + 144a )c
--R           + 
--R                       6          4         2         8       6      4
--R             (- 1008a b  + 1512a b  - 192a b )c + 126b  - 252b  + 48b
--R        /
--R              6 2     5 2     4 4
--R           16a c  - 8a b c + a b
--R      *
--R          5
--R         ?
--R     + 
--R                     2 5        2 3       2   2
--R             (- 2016a b  + 3360a b  - 720a b)c
--R           + 
--R                     7          5         3         9       7       5
--R             (1008a b  - 2520a b  + 960a b )c - 126b  + 420b  - 240b
--R        /
--R              7 2     6 2     5 4
--R           16a c  - 8a b c + a b
--R      *
--R          4
--R         ?
--R     + 
--R                   3 6         3 4        3 2       3  3
--R             (5376a b  - 13440a b  + 5760a b  - 256a )c
--R           + 
--R                     2 8         2 6        2 4       2 2  2
--R             (- 4032a b  + 13440a b  - 9120a b  + 640a b )c
--R           + 
--R                     10          8          6         4        12       10
--R             (1008a b   - 4200a b  + 3840a b  - 384a b )c - 84b   + 420b
--R           + 
--R                   8      6
--R             - 480b  + 64b
--R        /
--R              9 3      8 2 2      7 4     6 6
--R           64a c  - 48a b c  + 12a b c - a b
--R      *
--R          3
--R         ?
--R     + 
--R                     3 7        3 5        3 3       3   3
--R             (- 2304a b  + 8064a b  - 5760a b  + 768a b)c
--R           + 
--R                   2 9        2 7        2 5        2 3  2
--R             (1728a b  - 8064a b  + 9120a b  - 1920a b )c
--R           + 
--R                      11          9          7          5        13       11
--R             (- 432a b   + 2520a b  - 3840a b  + 1152a b )c + 36b   - 252b
--R           + 
--R                 9       7
--R             480b  - 192b
--R        /
--R              10 3      9 2 2      8 4     7 6
--R           64a  c  - 48a b c  + 12a b c - a b
--R      *
--R          2
--R         ?
--R     + 
--R                  3 8        3 6        3 4       3 2  3
--R             (576a b  - 2688a b  + 2880a b  - 768a b )c
--R           + 
--R                    2 10        2 8        2 6        2 4       2 2  2
--R             (- 432a b   + 2688a b  - 4560a b  + 1920a b  - 256a b )c
--R           + 
--R                    12         10          8          6       14      12
--R             (108a b   - 840a b   + 1920a b  - 1152a b )c - 9b   + 84b
--R           + 
--R                   10       8
--R             - 240b   + 192b
--R        /
--R              11 3      10 2 2      9 4     8 6
--R           64a  c  - 48a  b c  + 12a b c - a b
--R      *
--R         ?
--R     + 
--R                 3 9       3 7       3 5       3 3  3
--R           (- 64a b  + 384a b  - 576a b  + 256a b )c
--R         + 
--R               2 11       2 9       2 7       2 5       2 3  2
--R           (48a b   - 384a b  + 912a b  - 640a b  + 256a b )c
--R         + 
--R                   13         11         9         7      15      13      11
--R           (- 12a b   + 120a b   - 384a b  + 384a b )c + b   - 12b   + 48b
--R         + 
--R                9
--R           - 64b
--R      /
--R            12 3      11 2 2      10 4     9 6
--R         64a  c  - 48a  b c  + 12a  b c - a b
--R     , trying square-free.
--R   WARNING (genufact): No known algorithm to factor
--R        9   9b - 18a  8
--R       ?  + -------- ?
--R                a
--R     + 
--R                    2       2        3              4         3
--R             (144a b  - 576a b + 576a  - 24a)c - 36b  + 144a b
--R           + 
--R                    2       2              2
--R             (- 144a  + 12)b  - 24a b + 24a
--R        /
--R             3     2 2
--R           4a c - a b
--R      *
--R          7
--R         ?
--R     + 
--R                    3        2 2         3                 4       2        5
--R             (336a b  - 2016a b  + (4032a  - 168a)b - 2688a  + 336a )c - 84b
--R           + 
--R                   4           2       3        3         2       2        3
--R             504a b  + (- 1008a  + 84)b  + (672a  - 336a)b  + 504a b - 336a
--R        /
--R             4     3 2
--R           4a c - a b
--R      *
--R          6
--R         ?
--R     + 
--R                      2 4         3 3          4        2  2
--R                 2016a b  - 16128a b  + (48384a  - 2016a )b
--R               + 
--R                          5        3           6        4       2
--R                 (- 64512a  + 8064a )b + 32256a  - 8064a  + 144a
--R            *
--R                2
--R               c
--R           + 
--R                          6        2 5            3          4
--R                 - 1008a b  + 8064a b  + (- 24192a  + 1512a)b
--R               + 
--R                        4        2  3            5         3         2
--R                 (32256a  - 8064a )b  + (- 16128a  + 16128a  - 192a)b
--R               + 
--R                          4       2          5       3
--R                 (- 16128a  + 480a )b + 8064a  - 480a
--R            *
--R               c
--R           + 
--R                 8          7         2        6           3          5
--R             126b  - 1008a b  + (3024a  - 252)b  + (- 4032a  + 1512a)b
--R           + 
--R                   4        2       4         3         3           4       2  2
--R             (2016a  - 3528a  + 48)b  + (4032a  - 192a)b  + (- 2016a  + 336a )b
--R           + 
--R                   3        4
--R             - 288a b + 144a
--R        /
--R              6 2     5 2     4 4
--R           16a c  - 8a b c + a b
--R      *
--R          5
--R         ?
--R     + 
--R                      2 5         3 4          4        2  3
--R                 2016a b  - 20160a b  + (80640a  - 3360a )b
--R               + 
--R                           5         3  2           6         4       2
--R                 (- 161280a  + 20160a )b  + (161280a  - 40320a  + 720a )b
--R               + 
--R                         7         5        3
--R                 - 64512a  + 26880a  - 1440a
--R            *
--R                2
--R               c
--R           + 
--R                          7         2 6            3          5
--R                 - 1008a b  + 10080a b  + (- 40320a  + 2520a)b
--R               + 
--R                        4         2  4            5         3         3
--R                 (80640a  - 18480a )b  + (- 80640a  + 53760a  - 960a)b
--R               + 
--R                        6         4        2  2          5        3           6
--R                 (32256a  - 80640a  + 4320a )b  + (67200a  - 7200a )b - 26880a
--R               + 
--R                      4
--R                 4800a
--R            *
--R               c
--R           + 
--R                 9          8         2        7            3          6
--R             126b  - 1260a b  + (5040a  - 420)b  + (- 10080a  + 3360a)b
--R           + 
--R                    4         2        5           5         3          4
--R             (10080a  - 10920a  + 240)b  + (- 4032a  + 18480a  - 1440a)b
--R           + 
--R                      4        2  3         5        3  2        4         5
--R             (- 16800a  + 3600a )b  + (6720a  - 4800a )b  + 3600a b - 1440a
--R        /
--R              7 2     6 2     5 4
--R           16a c  - 8a b c + a b
--R      *
--R          4
--R         ?
--R     + 
--R                      3 6         4 5           5         3  4
--R                 5376a b  - 64512a b  + (322560a  - 13440a )b
--R               + 
--R                           6          4  3            7          5        3  2
--R                 (- 860160a  + 107520a )b  + (1290240a  - 322560a  + 5760a )b
--R               + 
--R                            8          6         4            9          7
--R                 (- 1032192a  + 430080a  - 23040a )b + 344064a  - 215040a
--R               + 
--R                       5       3
--R                 23040a  - 256a
--R            *
--R                3
--R               c
--R           + 
--R                        2 8         3 7             4         2  6
--R                 - 4032a b  + 48384a b  + (- 241920a  + 13440a )b
--R               + 
--R                         5          3  5             6          4        2  4
--R                 (645120a  - 120960a )b  + (- 967680a  + 443520a  - 9120a )b
--R               + 
--R                         7          5         3  3
--R                 (774144a  - 860160a  + 55680a )b
--R               + 
--R                           8          6          4       2  2
--R                 (- 258048a  + 967680a  - 132480a  + 640a )b
--R               + 
--R                         7          5        3            8         6        4
--R               (- 645120a  + 153600a  - 1792a )b + 215040a  - 76800a  + 1792a
--R            *
--R                2
--R               c
--R           + 
--R                        10         2 9          3          8
--R                 1008a b   - 12096a b  + (60480a  - 4200a)b
--R               + 
--R                           4         2  7           5          3          6
--R                 (- 161280a  + 40320a )b  + (241920a  - 161280a  + 3840a)b
--R               + 
--R                           6          4         2  5
--R                 (- 193536a  + 349440a  - 27840a )b
--R               + 
--R                        7          5         3         4
--R                 (64512a  - 443520a  + 83520a  - 384a)b
--R               + 
--R                         6          4        2  3
--R                 (322560a  - 134400a  + 1792a )b
--R               + 
--R                           7          5        3  2            6        4
--R                 (- 107520a  + 124800a  - 3584a )b  + (- 69120a  + 3584a )b
--R               + 
--R                       7        5
--R                 23040a  - 1792a
--R            *
--R               c
--R           + 
--R                  12          11           2        10          3          9
--R             - 84b   + 1008a b   + (- 5040a  + 420)b   + (13440a  - 4200a)b
--R           + 
--R                      4         2        8          5         3          7
--R             (- 20160a  + 17640a  - 480)b  + (16128a  - 40320a  + 3840a)b
--R           + 
--R                     6         4         2       6
--R             (- 5376a  + 53760a  - 12960a  + 64)b
--R           + 
--R                      5         3         5          6         4        2  4
--R             (- 40320a  + 24000a  - 384a)b  + (13440a  - 26400a  + 1024a )b
--R           + 
--R                    5        3  3           6        4  2       5        6
--R             (17280a  - 1536a )b  + (- 5760a  + 1408a )b  - 768a b + 256a
--R        /
--R              9 3      8 2 2      7 4     6 6
--R           64a c  - 48a b c  + 12a b c - a b
--R      *
--R          3
--R         ?
--R     + 
--R                      3 7         4 6           5        3  5
--R                 2304a b  - 32256a b  + (193536a  - 8064a )b
--R               + 
--R                           6         4  4            7          5        3  3
--R                 (- 645120a  + 80640a )b  + (1290240a  - 322560a  + 5760a )b
--R               + 
--R                            8          6         4  2
--R                 (- 1548288a  + 645120a  - 34560a )b
--R               + 
--R                          9          7         5       3            10
--R                 (1032192a  - 645120a  + 69120a  - 768a )b - 294912a
--R               + 
--R                        8         6        4
--R                 258048a  - 46080a  + 1536a
--R            *
--R                3
--R               c
--R           + 
--R                        2 9         3 8             4        2  7
--R                 - 1728a b  + 24192a b  + (- 145152a  + 8064a )b
--R               + 
--R                         5         3  6             6          4        2  5
--R                 (483840a  - 88704a )b  + (- 967680a  + 411264a  - 9120a )b
--R               + 
--R                          7           5         3  4
--R                 (1161216a  - 1048320a  + 73920a )b
--R               + 
--R                           8           6          4        2  3
--R                 (- 774144a  + 1612800a  - 243840a  + 1920a )b
--R               + 
--R                         9           7          5        3  2
--R                 (221184a  - 1548288a  + 418560a  - 9216a )b
--R               + 
--R                       8          6         4            9          7         5
--R               (903168a  - 384000a  + 16128a )b - 258048a  + 153600a  - 10752a
--R            *
--R                2
--R               c
--R           + 
--R                       11        2 10          3          9
--R                 432a b   - 6048a b   + (36288a  - 2520a)b
--R               + 
--R                           4         2  8           5          3          7
--R                 (- 120960a  + 29232a )b  + (241920a  - 145152a  + 3840a)b
--R               + 
--R                           6          4         2  6
--R                 (- 290304a  + 403200a  - 35520a )b
--R               + 
--R                         7          5          3          5
--R                 (193536a  - 685440a  + 139200a  - 1152a)b
--R               + 
--R                          8          6          4        2  4
--R                 (- 55296a  + 725760a  - 301440a  + 7680a )b
--R               + 
--R                           7          5         3  3
--R                 (- 451584a  + 393600a  - 21504a )b
--R               + 
--R                         8          6         4  2           7         5
--R                 (129024a  - 318720a  + 32256a )b  + (161280a  - 26880a )b
--R               + 
--R                         8         6
--R                 - 46080a  + 10752a
--R            *
--R               c
--R           + 
--R                  13         12           2        11          3          10
--R             - 36b   + 504a b   + (- 3024a  + 252)b   + (10080a  - 3024a)b
--R           + 
--R                      4         2        9          5         3          8
--R             (- 20160a  + 15624a  - 480)b  + (24192a  - 45360a  + 4800a)b
--R           + 
--R                      6         4         2        7
--R             (- 16128a  + 80640a  - 20640a  + 192)b
--R           + 
--R                   7         5         3          6
--R             (4608a  - 88704a  + 49920a  - 1536a)b
--R           + 
--R                    6         4        2  5            7         5         3  4
--R             (56448a  - 74400a  + 5376a )b  + (- 16128a  + 70080a  - 10752a )b
--R           + 
--R                      6         4  3          7         5  2        6         7
--R             (- 40320a  + 13440a )b  + (11520a  - 10752a )b  + 5376a b - 1536a
--R        /
--R              10 3      9 2 2      8 4     7 6
--R           64a  c  - 48a b c  + 12a b c - a b
--R      *
--R          2
--R         ?
--R     + 
--R                     3 8        4 7          5        3  6
--R                 576a b  - 9216a b  + (64512a  - 2688a )b
--R               + 
--R                           6         4  5           7          5        3  4
--R                 (- 258048a  + 32256a )b  + (645120a  - 161280a  + 2880a )b
--R               + 
--R                            8          6         4  3
--R                 (- 1032192a  + 430080a  - 23040a )b
--R               + 
--R                          9          7         5       3  2
--R                 (1032192a  - 645120a  + 69120a  - 768a )b
--R               + 
--R                           10          8         6        4            11
--R                 (- 589824a   + 516096a  - 92160a  + 3072a )b + 147456a
--R               + 
--R                          9         7        5
--R                 - 172032a  + 46080a  - 3072a
--R            *
--R                3
--R               c
--R           + 
--R                       2 10        3 9            4        2  8
--R                 - 432a b   + 6912a b  + (- 48384a  + 2688a )b
--R               + 
--R                         5         3  7             6          4        2  6
--R                 (193536a  - 34944a )b  + (- 483840a  + 196224a  - 4560a )b
--R               + 
--R                         7          5         3  5
--R                 (774144a  - 623616a  + 46080a )b
--R               + 
--R                           8           6          4        2  4
--R                 (- 774144a  + 1236480a  - 195840a  + 1920a )b
--R               + 
--R                         9           7          5         3  3
--R                 (442368a  - 1591296a  + 453120a  - 13056a )b
--R               + 
--R                           10           8          6         4       2  2
--R                 (- 110592a   + 1333248a  - 610560a  + 34560a  - 256a )b
--R               + 
--R                           9          7         5        3            10
--R                 (- 688128a  + 460800a  - 43008a  + 1024a )b + 172032a
--R               + 
--R                          8         6        4
--R                 - 153600a  + 21504a  - 1024a
--R            *
--R                2
--R               c
--R           + 
--R                       12        2 11          3         10
--R                 108a b   - 1728a b   + (12096a  - 840a)b
--R               + 
--R                          4         2  9           5         3          8
--R                 (- 48384a  + 11424a )b  + (120960a  - 67872a  + 1920a)b
--R               + 
--R                           6          4         2  7
--R                 (- 193536a  + 231168a  - 21600a )b
--R               + 
--R                         7          5          3          6
--R                 (193536a  - 497280a  + 105120a  - 1152a)b
--R               + 
--R                           8          6          4        2  5
--R                 (- 110592a  + 698880a  - 289920a  + 9984a )b
--R               + 
--R                        9          7          5         3  4
--R                 (27648a  - 634368a  + 498240a  - 36864a )b
--R               + 
--R                         8          6         4       2  3
--R                 (344064a  - 552960a  + 75264a  + 512a )b
--R               + 
--R                          9          7         5        3  2
--R                 (- 86016a  + 399360a  - 91392a  - 2560a )b
--R               + 
--R                           8         6        4           9         7        5
--R                 (- 184320a  + 64512a  + 4096a )b + 46080a  - 21504a  - 2048a
--R            *
--R               c
--R           + 
--R                 14         13           2       12         3          11
--R             - 9b   + 144a b   + (- 1008a  + 84)b   + (4032a  - 1176a)b
--R           + 
--R                      4        2        10          5         3          9
--R             (- 10080a  + 7224a  - 240)b   + (16128a  - 25536a  + 2880a)b
--R           + 
--R                      6         4         2        8
--R             (- 16128a  + 57120a  - 15120a  + 192)b
--R           + 
--R                   7         5         3          7
--R             (9216a  - 83328a  + 45600a  - 1920a)b
--R           + 
--R                     8         6         4        2  6
--R             (- 2304a  + 77952a  - 87120a  + 8448a )b
--R           + 
--R                      7          5         3  5
--R             (- 43008a  + 109440a  - 21504a )b
--R           + 
--R                    8         6         4       2  4
--R             (10752a  - 90240a  + 34944a  - 256a )b
--R           + 
--R                    7         5        3  3            8         6        4  2
--R             (46080a  - 37632a  + 1536a )b  + (- 11520a  + 26880a  - 3328a )b
--R           + 
--R                      7        5          8        6
--R             (- 12288a  + 3072a )b + 3072a  - 1024a
--R        /
--R              11 3      10 2 2      9 4     8 6
--R           64a  c  - 48a  b c  + 12a b c - a b
--R      *
--R         ?
--R     + 
--R                  3 9        4 8         5       3  7            6        4  6
--R               64a b  - 1152a b  + (9216a  - 384a )b  + (- 43008a  + 5376a )b
--R             + 
--R                       7         5       3  5
--R               (129024a  - 32256a  + 576a )b
--R             + 
--R                         8          6        4  4
--R               (- 258048a  + 107520a  - 5760a )b
--R             + 
--R                       9          7         5       3  3
--R               (344064a  - 215040a  + 23040a  - 256a )b
--R             + 
--R                         10          8         6        4  2
--R               (- 294912a   + 258048a  - 46080a  + 1536a )b
--R             + 
--R                       11          9         7        5           12         10
--R               (147456a   - 172032a  + 46080a  - 3072a )b - 32768a   + 49152a
--R             + 
--R                       8        6
--R               - 18432a  + 2048a
--R          *
--R              3
--R             c
--R         + 
--R                    2 11       3 10           4       2  9
--R               - 48a b   + 864a b   + (- 6912a  + 384a )b
--R             + 
--R                      5        3  8            6         4       2  7
--R               (32256a  - 5760a )b  + (- 96768a  + 38016a  - 912a )b
--R             + 
--R                       7          5         3  6
--R               (193536a  - 145152a  + 11040a )b
--R             + 
--R                         8          6         4       2  5
--R               (- 258048a  + 354816a  - 57600a  + 640a )b
--R             + 
--R                       9          7          5        3  4
--R               (221184a  - 580608a  + 168960a  - 5632a )b
--R             + 
--R                         10          8          6         4       2  3
--R               (- 110592a   + 645120a  - 303360a  + 20224a  - 256a )b
--R             + 
--R                      11          9          7         5        3  2
--R               (24576a   - 479232a  + 336384a  - 37376a  + 1536a )b
--R             + 
--R                       10          8         6        4           11         9
--R               (221184a   - 215040a  + 35840a  - 3072a )b - 49152a   + 61440a
--R             + 
--R                       7        5
--R               - 14336a  + 2048a
--R          *
--R              2
--R             c
--R         + 
--R                    13       2 12         3         11           4        2  10
--R               12a b   - 216a b   + (1728a  - 120a)b   + (- 8064a  + 1872a )b
--R             + 
--R                      5         3         9            6         4        2  8
--R               (24192a  - 12960a  + 384a)b  + (- 48384a  + 52416a  - 5088a )b
--R             + 
--R                      7          5         3         7
--R               (64512a  - 137088a  + 29664a  - 384a)b
--R             + 
--R                        8          6          4        2  6
--R               (- 55296a  + 241920a  - 100032a  + 4096a )b
--R             + 
--R                      9          7          5         3  5
--R               (27648a  - 290304a  + 215616a  - 18944a )b
--R             + 
--R                       10          8          6         4       2  4
--R               (- 6144a   + 230400a  - 309888a  + 49664a  + 512a )b
--R             + 
--R                         9          7         5        3  3
--R               (- 110592a  + 301056a  - 80640a  - 3584a )b
--R             + 
--R                      10          8         6        4  2
--R               (24576a   - 196608a  + 82432a  + 9216a )b
--R             + 
--R                      9         7         5           10         8        6
--R               (82944a  - 50176a  - 10240a )b - 18432a   + 14336a  + 4096a
--R          *
--R             c
--R         + 
--R              15        14          2       13        3         12
--R           - b   + 18a b   + (- 144a  + 12)b   + (672a  - 192a)b
--R         + 
--R                   4        2       11         5        3         10
--R           (- 2016a  + 1368a  - 48)b   + (4032a  - 5712a  + 672a)b
--R         + 
--R                   6         4        2       9
--R           (- 5376a  + 15456a  - 4176a  + 64)b
--R         + 
--R                 7         5         3         8
--R           (4608a  - 28224a  + 15168a  - 768a)b
--R         + 
--R                   8         6         4        2  7
--R           (- 2304a  + 34944a  - 35664a  + 4096a )b
--R         + 
--R                9         7         5         3  6
--R           (512a  - 28416a  + 56736a  - 12800a )b
--R         + 
--R                  8         6         4       2  5
--R           (13824a  - 61824a  + 25984a  - 256a )b
--R         + 
--R                   9         7         5        3  4
--R           (- 3072a  + 45312a  - 35840a  + 2048a )b
--R         + 
--R                    8         6        4  3         9         7        5  2
--R           (- 20736a  + 34048a  - 6400a )b  + (4608a  - 22016a  + 9728a )b
--R         + 
--R                 8        6          9        7
--R           (9216a  - 7168a )b - 2048a  + 2048a
--R      /
--R            12 3      11 2 2      10 4     9 6
--R         64a  c  - 48a  b c  + 12a  b c - a b
--R     , trying square-free.
--R
--R   (85)
--R     - y(x) + x
--R  /
--R       (2y(x) + 2x)
--R    *
--R         %e
--R      **
--R             2
--R          *
--R             log
--R                                                 +-----------+
--R                       2 2                    2  |          2       2        2
--R                    (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                  + 
--R                              3
--R                    4a b c - b
--R               /
--R                     2
--R                  a x  + b x + c
--R        /
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 139
ode180expr := (a*x**2+b*x+c)*(x*D(yx,x)-yx) - yx**2 + x**2
 

   (86)
            2    2     3         4
         (4x y(x)  + 8x y(x) + 4x )
      *
             %e
          **
                 2
              *
                 log
                                                     +-----------+
                           2 2                    2  |          2
                        (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                      + 
                           2        2               3
                        (8a c - 2a b )x + 4a b c - b
                   /
                         2
                      a x  + b x + c
            /
                +-----------+
                |          2
               \|- 4a c + b
        **
           2
     + 
                  4       3       2  ,           2                      2
           (- 4a x  - 4b x  - 4c x )y (x) + (2a x  + (2b + 4)x + 2c)y(x)

         + 
                3       2                   4              3       2
           (4a x  + 4b x  + 4c x)y(x) - 2a x  + (- 2b - 4)x  - 2c x
      *
           %e
        **
               2
            *
               log
                                                   +-----------+
                         2 2                    2  |          2
                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                    + 
                         2        2               3
                      (8a c - 2a b )x + 4a b c - b
                 /
                       2
                    a x  + b x + c
          /
              +-----------+
              |          2
             \|- 4a c + b
     + 
             2              2
       - y(x)  + 2x y(x) - x
  /
             2               2
       (4y(x)  + 8x y(x) + 4x )
    *
           %e
        **
               2
            *
               log
                                                   +-----------+
                         2 2                    2  |          2
                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                    + 
                         2        2               3
                      (8a c - 2a b )x + 4a b c - b
                 /
                       2
                    a x  + b x + c
          /
              +-----------+
              |          2
             \|- 4a c + b
      **
         2
                                                     Type: Expression Integer
--R 
--R
--R   (86)
--R            2    2     3         4
--R         (4x y(x)  + 8x y(x) + 4x )
--R      *
--R             %e
--R          **
--R                 2
--R              *
--R                 log
--R                                                     +-----------+
--R                           2 2                    2  |          2
--R                        (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                      + 
--R                           2        2               3
--R                        (8a c - 2a b )x + 4a b c - b
--R                   /
--R                         2
--R                      a x  + b x + c
--R            /
--R                +-----------+
--R                |          2
--R               \|- 4a c + b
--R        **
--R           2
--R     + 
--R                  4       3       2  ,           2                      2
--R           (- 4a x  - 4b x  - 4c x )y (x) + (2a x  + (2b + 4)x + 2c)y(x)
--R
--R         + 
--R                3       2                   4              3       2
--R           (4a x  + 4b x  + 4c x)y(x) - 2a x  + (- 2b - 4)x  - 2c x
--R      *
--R           %e
--R        **
--R               2
--R            *
--R               log
--R                                                   +-----------+
--R                         2 2                    2  |          2
--R                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                    + 
--R                         2        2               3
--R                      (8a c - 2a b )x + 4a b c - b
--R                 /
--R                       2
--R                    a x  + b x + c
--R          /
--R              +-----------+
--R              |          2
--R             \|- 4a c + b
--R     + 
--R             2              2
--R       - y(x)  + 2x y(x) - x
--R  /
--R             2               2
--R       (4y(x)  + 8x y(x) + 4x )
--R    *
--R           %e
--R        **
--R               2
--R            *
--R               log
--R                                                   +-----------+
--R                         2 2                    2  |          2
--R                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                    + 
--R                         2        2               3
--R                      (8a c - 2a b )x + 4a b c - b
--R                 /
--R                       2
--R                    a x  + b x + c
--R          /
--R              +-----------+
--R              |          2
--R             \|- 4a c + b
--R      **
--R         2
--R                                                     Type: Expression Integer
--E 86

--S 87 of 139
ode181 := x**4*(D(y(x),x)+y(x)**2) + a
 

          4 ,       4    2
   (87)  x y (x) + x y(x)  + a

                                                     Type: Expression Integer
--R 
--R
--R          4 ,       4    2
--R   (87)  x y (x) + x y(x)  + a
--R
--R                                                     Type: Expression Integer
--E 87

--S 88 of 139
yx:=solve(ode181,y,x)
 
                                                     2
   WARNING (genufact): No known algorithm to factor ?  + a, trying square-free.

                   +---+    2
                  \|- a  - x y(x) + x
   (88)  ------------------------------------
                                        +---+
                                      2\|- a
                                      -------
             2           +---+           x
         ((2x y(x) - 2x)\|- a  - 2a)%e
                                          Type: Union(Expression Integer,...)
--R 
--R                                                     2
--R   WARNING (genufact): No known algorithm to factor ?  + a, trying square-free.
--R
--R                   +---+    2
--R                  \|- a  - x y(x) + x
--R   (88)  ------------------------------------
--R                                        +---+
--R                                      2\|- a
--R                                      -------
--R             2           +---+           x
--R         ((2x y(x) - 2x)\|- a  - 2a)%e
--R                                          Type: Union(Expression Integer,...)
--E 88

--S 89 of 139
ode181expr := x**4*(D(yx,x)+yx**2) + a
 

   (89)
                  +---+
                2\|- a
                -------
             6     x    ,
       - 4a x %e       y (x)

     + 
             2 2         2   +---+     2 4    2     2 3         2 2     3
         ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
      *
              +---+ 2
            2\|- a
            -------
               x
         (%e       )
     + 
                                 +---+
                               2\|- a
                               -------
              6    2     2 2      x         6         5  +---+    8    2
       (- 4a x y(x)  - 4a x )%e        + (2x y(x) - 2x )\|- a  - x y(x)
     + 
         7        6      4
       2x y(x) - x  + a x
  /
             2             +---+       4    2       3           2     2
       ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
    *
            +---+ 2
          2\|- a
          -------
             x
       (%e       )
                                                     Type: Expression Integer
--R 
--R
--R   (89)
--R                  +---+
--R                2\|- a
--R                -------
--R             6     x    ,
--R       - 4a x %e       y (x)
--R
--R     + 
--R             2 2         2   +---+     2 4    2     2 3         2 2     3
--R         ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
--R      *
--R              +---+ 2
--R            2\|- a
--R            -------
--R               x
--R         (%e       )
--R     + 
--R                                 +---+
--R                               2\|- a
--R                               -------
--R              6    2     2 2      x         6         5  +---+    8    2
--R       (- 4a x y(x)  - 4a x )%e        + (2x y(x) - 2x )\|- a  - x y(x)
--R     + 
--R         7        6      4
--R       2x y(x) - x  + a x
--R  /
--R             2             +---+       4    2       3           2     2
--R       ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
--R    *
--R            +---+ 2
--R          2\|- a
--R          -------
--R             x
--R       (%e       )
--R                                                     Type: Expression Integer
--E 89

--S 90 of 139
ode182 := x*(x**3-1)*D(y(x),x) - 2*x*y(x)**2 + y(x) + x**2
 

           4      ,             2           2
   (90)  (x  - x)y (x) - 2x y(x)  + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R           4      ,             2           2
--R   (90)  (x  - x)y (x) - 2x y(x)  + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 90

--S 91 of 139
ode183 := (2*x**4-x)*D(y(x),x) - 2*(x**3-1)*y(x)
 

            4      ,           3
   (91)  (2x  - x)y (x) + (- 2x  + 2)y(x)

                                                     Type: Expression Integer
--R 
--R
--R            4      ,           3
--R   (91)  (2x  - x)y (x) + (- 2x  + 2)y(x)
--R
--R                                                     Type: Expression Integer
--E 91

--S 92 of 139
ode183a:=solve(ode183,y,x)
 

                                     2
                                    x
   (92)  [particular= 0,basis= [----------]]
                                 +-------+
                                3|  3
                                \|2x  - 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                     2
--R                                    x
--R   (92)  [particular= 0,basis= [----------]]
--R                                 +-------+
--R                                3|  3
--R                                \|2x  - 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 92

--S 93 of 139
yx:=ode183a.particular
 

   (93)  0
                                                     Type: Expression Integer
--R 
--R
--R   (93)  0
--R                                                     Type: Expression Integer
--E 93

--S 94 of 139
ode183expr := (2*x**4-x)*D(yx,x) - 2*(x**3-1)*yx
 

   (94)  0
                                                     Type: Expression Integer
--R 
--R
--R   (94)  0
--R                                                     Type: Expression Integer
--E 94

--S 95 of 139
ode184 := (a*x**2+b*x+c)**2*(D(y(x),x)+y(x)**2) + A
 

   (95)
       2 4         3            2  2             2  ,
     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y (x)

   + 
       2 4         3            2  2             2     2
     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y(x)  + A
                                                     Type: Expression Integer
--R 
--R
--R   (95)
--R       2 4         3            2  2             2  ,
--R     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y (x)
--R
--R   + 
--R       2 4         3            2  2             2     2
--R     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y(x)  + A
--R                                                     Type: Expression Integer
--E 95


--S 96 of 139
ode185 := x**7*D(y(x),x) + 2*(x**2+1)*y(x)**3 + 5*x**3*y(x)**2
 

          7 ,         2         3     3    2
   (96)  x y (x) + (2x  + 2)y(x)  + 5x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          7 ,         2         3     3    2
--R   (96)  x y (x) + (2x  + 2)y(x)  + 5x y(x)
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 139
ode185a:=solve(ode185,y,x)
 

   (97)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (97)  "failed"
--R                                                    Type: Union("failed",...)
--E 97

--S 98 of 139
ode186 := x**n*D(y(x),x) + y(x)**2 -(n-1)*x**(n-1)*y(x) + x**(2*n-2)
 

          n ,       2n - 2                 n - 1       2
   (98)  x y (x) + x       + (- n + 1)y(x)x      + y(x)

                                                     Type: Expression Integer
--R 
--R
--R          n ,       2n - 2                 n - 1       2
--R   (98)  x y (x) + x       + (- n + 1)y(x)x      + y(x)
--R
--R                                                     Type: Expression Integer
--E 98

--S 99 of 139
ode186a:=solve(ode186,y,x)
 

   (99)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (99)  "failed"
--R                                                    Type: Union("failed",...)
--E 99

--S 100 of 139
ode187 := x**n*D(y(x),x) - a*y(x)**2 - b*x**(2*n-2)
 

           n ,         2n - 2         2
   (100)  x y (x) - b x       - a y(x)

                                                     Type: Expression Integer
--R 
--R
--R           n ,         2n - 2         2
--R   (100)  x y (x) - b x       - a y(x)
--R
--R                                                     Type: Expression Integer
--E 100

--S 101 of 139
ode187a:=solve(ode187,y,x)
 

   (101)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (101)  "failed"
--R                                                    Type: Union("failed",...)
--E 101

--S 102 of 139
ode188 := x**(2*n+1)*D(y(x),x) - a*y(x)**3 - b*x**3*n
 

           2n + 1 ,            3        3
   (102)  x      y (x) - a y(x)  - b n x

                                                     Type: Expression Integer
--R 
--R
--R           2n + 1 ,            3        3
--R   (102)  x      y (x) - a y(x)  - b n x
--R
--R                                                     Type: Expression Integer
--E 102

--S 103 of 139
ode188a:=solve(ode188,y,x)
 

   (103)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (103)  "failed"
--R                                                    Type: Union("failed",...)
--E 103

--S 104 of 139
ode189 := x**(m*(n-1)+n)*D(y(x),x) - a*y(x)**n - b*x**(n*(m+1))
 

           (m + 1)n - m ,            n      (m + 1)n
   (104)  x            y (x) - a y(x)  - b x

                                                     Type: Expression Integer
--R 
--R
--R           (m + 1)n - m ,            n      (m + 1)n
--R   (104)  x            y (x) - a y(x)  - b x
--R
--R                                                     Type: Expression Integer
--E 104

--S 105 of 139
ode189a:=solve(ode189,y,x)
 

   (105)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (105)  "failed"
--R                                                    Type: Union("failed",...)
--E 105

--S 106 of 139
ode190 := sqrt(x**2-1)*D(y(x),x) - sqrt(y(x)**2-1)
 

           +------+         +---------+
           | 2      ,       |    2
   (106)  \|x  - 1 y (x) - \|y(x)  - 1

                                                     Type: Expression Integer
--R 
--R
--R           +------+         +---------+
--R           | 2      ,       |    2
--R   (106)  \|x  - 1 y (x) - \|y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 106

--S 107 of 139
ode190a:=solve(ode190,y,x)
 

   (107)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (107)  "failed"
--R                                                    Type: Union("failed",...)
--E 107

--S 108 of 139
ode191 := sqrt(1-x**2)*D(y(x),x) - y(x)*sqrt(y(x)**2-1)
 

           +--------+             +---------+
           |   2      ,           |    2
   (108)  \|- x  + 1 y (x) - y(x)\|y(x)  - 1

                                                     Type: Expression Integer
--R 
--R
--R           +--------+             +---------+
--R           |   2      ,           |    2
--R   (108)  \|- x  + 1 y (x) - y(x)\|y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 108

--S 109 of 139
ode191a:=solve(ode191,y,x)
 

   (109)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (109)  "failed"
--R                                                    Type: Union("failed",...)
--E 109

--S 110 of 139
ode192 := sqrt(x**2+a**2)*D(y(x),x) + y(x) - sqrt(x**2+a**2) + x
 

           +-------+         +-------+
           | 2    2  ,       | 2    2
   (110)  \|x  + a  y (x) - \|x  + a   + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R           +-------+         +-------+
--R           | 2    2  ,       | 2    2
--R   (110)  \|x  + a  y (x) - \|x  + a   + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 110

--S 111 of 139
ode192a:=solve(ode192,y,x)
 

   (111)
                    +-------+          +-------+               +-------+
                    | 2    2           | 2    2                | 2    2
   [particular= (- \|x  + a   + x)log(\|x  + a   - x),basis= [\|x  + a   - x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (111)
--R                    +-------+          +-------+               +-------+
--R                    | 2    2           | 2    2                | 2    2
--R   [particular= (- \|x  + a   + x)log(\|x  + a   - x),basis= [\|x  + a   - x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 111

--S 112 of 139
yx:=ode192a.particular
 

              +-------+          +-------+
              | 2    2           | 2    2
   (112)  (- \|x  + a   + x)log(\|x  + a   - x)
                                                     Type: Expression Integer
--R 
--R
--R              +-------+          +-------+
--R              | 2    2           | 2    2
--R   (112)  (- \|x  + a   + x)log(\|x  + a   - x)
--R                                                     Type: Expression Integer
--E 112

--S 113 of 139
ode192expr := sqrt(x**2+a**2)*D(yx,x) + yx - sqrt(x**2+a**2) + x
 

   (113)  0
                                                     Type: Expression Integer
--R 
--R
--R   (113)  0
--R                                                     Type: Expression Integer
--E 113

--S 114 of 139
ode193 := x*D(y(x),x)*log(x) + y(x) - a*x*(log(x)+1)
 

                   ,
   (114)  x log(x)y (x) - a x log(x) + y(x) - a x

                                                     Type: Expression Integer
--R 
--R
--R                   ,
--R   (114)  x log(x)y (x) - a x log(x) + y(x) - a x
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 139
ode193a:=solve(ode193,y,x)
 

                                      1
   (115)  [particular= a x,basis= [------]]
                                   log(x)
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                      1
--R   (115)  [particular= a x,basis= [------]]
--R                                   log(x)
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 115

--S 116 of 139
yx:=ode193a.particular
 

   (116)  a x
                                                     Type: Expression Integer
--R
--R   (116)  a x
--R                                                     Type: Expression Integer
--E 116

--S 117 of 139
ode193expr := x*D(yx,x)*log(x) + yx - a*x*(log(x)+1)
 

   (117)  0
                                                     Type: Expression Integer
--R
--R   (117)  0
--R                                                     Type: Expression Integer
--E 117

--S 118 of 139
ode194 := x*D(y(x),x)*log(x) - y(x)**2*log(x) - _
            (2*log(x)**2+1)*y(x) - log(x)**3
 

                   ,            3              2       2
   (118)  x log(x)y (x) - log(x)  - 2y(x)log(x)  - y(x) log(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                   ,            3              2       2
--R   (118)  x log(x)y (x) - log(x)  - 2y(x)log(x)  - y(x) log(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 118

--S 119 of 139
ode194a:=solve(ode194,y,x)
 

   (119)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (119)  "failed"
--R                                                    Type: Union("failed",...)
--E 119

--S 120 of 139
ode195 := sin(x)*D(y(x),x) - y(x)**2*sin(x)**2 + (cos(x) - 3*sin(x))*y(x) + 4
 

                 ,          2      2
   (120)  sin(x)y (x) - y(x) sin(x)  - 3y(x)sin(x) + y(x)cos(x) + 4

                                                     Type: Expression Integer
--R 
--R
--R                 ,          2      2
--R   (120)  sin(x)y (x) - y(x) sin(x)  - 3y(x)sin(x) + y(x)cos(x) + 4
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 139
yx:=solve(ode195,y,x)
 

              - y(x)sin(x) + 1
   (121)  ------------------------
                 5x             5x
          5y(x)%e  sin(x) + 20%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - y(x)sin(x) + 1
--R   (121)  ------------------------
--R                 5x             5x
--R          5y(x)%e  sin(x) + 20%e
--R                                          Type: Union(Expression Integer,...)
--E 121

--S 122 of 139
ode195expr:=sin(x)*D(yx,x) - yx**2*sin(x)**2 + (cos(x) - 3*sin(x))*yx + 4
 

   (122)
             5x      2 ,          2      4          2  5x               3
       - 25%e  sin(x) y (x) - y(x) sin(x)  + (40y(x) %e   + 2y(x))sin(x)

     + 
               2   5x 2           2                   5x           2
       (100y(x) (%e  )  + (- 5y(x) cos(x) + 120y(x))%e   - 1)sin(x)
     + 
                  5x 2                           5x                 5x 2
       (800y(x)(%e  )  + (- 40y(x)cos(x) - 160)%e  )sin(x) + 1600(%e  )
     + 
                 5x
       20cos(x)%e
  /
           2   5x 2      2             5x 2               5x 2
     25y(x) (%e  ) sin(x)  + 200y(x)(%e  ) sin(x) + 400(%e  )
                                                     Type: Expression Integer
--R 
--R
--R   (122)
--R             5x      2 ,          2      4          2  5x               3
--R       - 25%e  sin(x) y (x) - y(x) sin(x)  + (40y(x) %e   + 2y(x))sin(x)
--R
--R     + 
--R               2   5x 2           2                   5x           2
--R       (100y(x) (%e  )  + (- 5y(x) cos(x) + 120y(x))%e   - 1)sin(x)
--R     + 
--R                  5x 2                           5x                 5x 2
--R       (800y(x)(%e  )  + (- 40y(x)cos(x) - 160)%e  )sin(x) + 1600(%e  )
--R     + 
--R                 5x
--R       20cos(x)%e
--R  /
--R           2   5x 2      2             5x 2               5x 2
--R     25y(x) (%e  ) sin(x)  + 200y(x)(%e  ) sin(x) + 400(%e  )
--R                                                     Type: Expression Integer
--E 122

--S 123 of 139
ode196 := cos(x)*D(y(x),x) + y(x) + (1 + sin(x))*cos(x)
 

                 ,
   (123)  cos(x)y (x) + cos(x)sin(x) + cos(x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 ,
--R   (123)  cos(x)y (x) + cos(x)sin(x) + cos(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 123

--S 124 of 139
ode196a:=solve(ode196,y,x)
 

   (124)
   [
     particular =
                                        sin(x) - cos(x) - 1
           (- 4sin(x) + 4cos(x) + 4)log(-------------------)
                                             cos(x) + 1
         + 
                                         2              2
         (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
                                    cos(x) + 1
      /
         sin(x) + cos(x) + 1
     ,
            sin(x) - cos(x) - 1
    basis= [-------------------]]
            sin(x) + cos(x) + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (124)
--R   [
--R     particular =
--R                                        sin(x) - cos(x) - 1
--R           (- 4sin(x) + 4cos(x) + 4)log(-------------------)
--R                                             cos(x) + 1
--R         + 
--R                                         2              2
--R         (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
--R                                    cos(x) + 1
--R      /
--R         sin(x) + cos(x) + 1
--R     ,
--R            sin(x) - cos(x) - 1
--R    basis= [-------------------]]
--R            sin(x) + cos(x) + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 124

--S 125 of 139
yx:=ode196a.particular
 

   (125)
                                    sin(x) - cos(x) - 1
       (- 4sin(x) + 4cos(x) + 4)log(-------------------)
                                         cos(x) + 1
     + 
                                       2              2
       (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
                                  cos(x) + 1
  /
     sin(x) + cos(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R   (125)
--R                                    sin(x) - cos(x) - 1
--R       (- 4sin(x) + 4cos(x) + 4)log(-------------------)
--R                                         cos(x) + 1
--R     + 
--R                                       2              2
--R       (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
--R                                  cos(x) + 1
--R  /
--R     sin(x) + cos(x) + 1
--R                                                     Type: Expression Integer
--E 125

--S 126 of 139
ode196expr := cos(x)*D(yx,x) + yx + (1 + sin(x))*cos(x)
 

   (126)
                     2                      2          4           3          2
           (- 8cos(x)  - 12cos(x) - 4)sin(x)  - 8cos(x)  - 12cos(x)  + 4cos(x)
         + 
           12cos(x) + 4
      *
             sin(x) - cos(x) - 1
         log(-------------------)
                  cos(x) + 1
     + 
                   2                     2          4          3          2
           (4cos(x)  + 6cos(x) + 2)sin(x)  + 4cos(x)  + 6cos(x)  - 2cos(x)
         + 
           - 6cos(x) - 2
      *
                  2
         log(----------)
             cos(x) + 1
     + 
                2                     3          3                2
       (- cos(x)  - 4cos(x) - 1)sin(x)  + (cos(x)  - cos(x))sin(x)
     + 
                4          3                              5          3
       (- cos(x)  - 4cos(x)  + 4cos(x) + 1)sin(x) + cos(x)  - 2cos(x)  + cos(x)
  /
                         2           2                              3          2
       (cos(x) + 1)sin(x)  + (2cos(x)  + 4cos(x) + 2)sin(x) + cos(x)  + 3cos(x)
     + 
       3cos(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R   (126)
--R                     2                      2          4           3          2
--R           (- 8cos(x)  - 12cos(x) - 4)sin(x)  - 8cos(x)  - 12cos(x)  + 4cos(x)
--R         + 
--R           12cos(x) + 4
--R      *
--R             sin(x) - cos(x) - 1
--R         log(-------------------)
--R                  cos(x) + 1
--R     + 
--R                   2                     2          4          3          2
--R           (4cos(x)  + 6cos(x) + 2)sin(x)  + 4cos(x)  + 6cos(x)  - 2cos(x)
--R         + 
--R           - 6cos(x) - 2
--R      *
--R                  2
--R         log(----------)
--R             cos(x) + 1
--R     + 
--R                2                     3          3                2
--R       (- cos(x)  - 4cos(x) - 1)sin(x)  + (cos(x)  - cos(x))sin(x)
--R     + 
--R                4          3                              5          3
--R       (- cos(x)  - 4cos(x)  + 4cos(x) + 1)sin(x) + cos(x)  - 2cos(x)  + cos(x)
--R  /
--R                         2           2                              3          2
--R       (cos(x) + 1)sin(x)  + (2cos(x)  + 4cos(x) + 2)sin(x) + cos(x)  + 3cos(x)
--R     + 
--R       3cos(x) + 1
--R                                                     Type: Expression Integer
--E 126

--S 127 of 139
ode197 := cos(x)*D(y(x),x) - y(x)**4 - y(x)*sin(x)
 

                 ,                       4
   (127)  cos(x)y (x) - y(x)sin(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 ,                       4
--R   (127)  cos(x)y (x) - y(x)sin(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 127

--S 128 of 139
yx:=solve(ode197,y,x)
 

                3      2       3
          (2y(x) cos(x)  + y(x) )sin(x) + 1
   (128)  ---------------------------------
                         3      3
                     y(x) cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3      2       3
--R          (2y(x) cos(x)  + y(x) )sin(x) + 1
--R   (128)  ---------------------------------
--R                         3      3
--R                     y(x) cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 128

--S 129 of 139
ode197expr := cos(x)*D(yx,x) - yx**4 - yx*sin(x)
 

   (129)
              8      10 ,
       - 3y(x) cos(x)  y (x)

     + 
                   12      8         12      6         12      4
           - 16y(x)  cos(x)  - 32y(x)  cos(x)  - 24y(x)  cos(x)
         + 
                  12      2       12
           - 8y(x)  cos(x)  - y(x)
      *
               4
         sin(x)
     + 
                9      6         9      4         9      2        9       3
       (- 32y(x) cos(x)  - 48y(x) cos(x)  - 24y(x) cos(x)  - 4y(x) )sin(x)
     + 
             12      9         6      4         6      2        6       2
       (2y(x)  cos(x)  - 24y(x) cos(x)  - 24y(x) cos(x)  - 6y(x) )sin(x)
     + 
             9      9        3      2        3               12      13
       (2y(x) cos(x)  - 8y(x) cos(x)  - 4y(x) )sin(x) + 2y(x)  cos(x)
     + 
           12      11
       y(x)  cos(x)   - 1
  /
         12      12
     y(x)  cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (129)
--R              8      10 ,
--R       - 3y(x) cos(x)  y (x)
--R
--R     + 
--R                   12      8         12      6         12      4
--R           - 16y(x)  cos(x)  - 32y(x)  cos(x)  - 24y(x)  cos(x)
--R         + 
--R                  12      2       12
--R           - 8y(x)  cos(x)  - y(x)
--R      *
--R               4
--R         sin(x)
--R     + 
--R                9      6         9      4         9      2        9       3
--R       (- 32y(x) cos(x)  - 48y(x) cos(x)  - 24y(x) cos(x)  - 4y(x) )sin(x)
--R     + 
--R             12      9         6      4         6      2        6       2
--R       (2y(x)  cos(x)  - 24y(x) cos(x)  - 24y(x) cos(x)  - 6y(x) )sin(x)
--R     + 
--R             9      9        3      2        3               12      13
--R       (2y(x) cos(x)  - 8y(x) cos(x)  - 4y(x) )sin(x) + 2y(x)  cos(x)
--R     + 
--R           12      11
--R       y(x)  cos(x)   - 1
--R  /
--R         12      12
--R     y(x)  cos(x)
--R                                                     Type: Expression Integer
--E 129

--S 130 of 139
ode198 := sin(x)*cos(x)*D(y(x),x) - y(x) - sin(x)**3
 

                       ,            3
   (130)  cos(x)sin(x)y (x) - sin(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                       ,            3
--R   (130)  cos(x)sin(x)y (x) - sin(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 130

--S 131 of 139
ode198a:=solve(ode198,y,x)
 

                                        sin(x)
   (131)  [particular= - sin(x),basis= [------]]
                                        cos(x)
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                        sin(x)
--R   (131)  [particular= - sin(x),basis= [------]]
--R                                        cos(x)
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 131

--S 132 of 139
yx:=ode198a.particular
 

   (132)  - sin(x)
                                                     Type: Expression Integer
--R 
--R
--R   (132)  - sin(x)
--R                                                     Type: Expression Integer
--E 132

--S 133 of 139
ode198expr := sin(x)*cos(x)*D(yx,x) - yx - sin(x)**3
 

                  3            2
   (133)  - sin(x)  + (- cos(x)  + 1)sin(x)
                                                     Type: Expression Integer
--R 
--R
--R                  3            2
--R   (133)  - sin(x)  + (- cos(x)  + 1)sin(x)
--R                                                     Type: Expression Integer
--E 133

--S 134 of 139
ode199 := sin(2*x)*D(y(x),x) + sin(2*y(x))
 

                  ,
   (134)  sin(2x)y (x) + sin(2y(x))

                                                     Type: Expression Integer
--R 
--R
--R                  ,
--R   (134)  sin(2x)y (x) + sin(2y(x))
--R
--R                                                     Type: Expression Integer
--E 134

--S 135 of 139
ode199a:=solve(ode199,y,x)
 

   (135)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (135)  "failed"
--R                                                    Type: Union("failed",...)
--E 135

--S 136 of 139
ode200 := (a*sin(x)**2+b)*D(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)**2+c)
 

                   2      ,                                  2
   (136)  (a sin(x)  + b)y (x) + a y(x)sin(2x) + A a x sin(x)  + A c x

                                                     Type: Expression Integer
--R 
--R
--R                   2      ,                                  2
--R   (136)  (a sin(x)  + b)y (x) + a y(x)sin(2x) + A a x sin(x)  + A c x
--R
--R                                                     Type: Expression Integer
--E 136

--S 137 of 139
ode200a:=solve(ode200,y,x)
 

   (137)
                                                  2                2
                - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
   [particular= ----------------------------------------------------,
                                         2
                                4a cos(x)  - 4b - 4a
                    1
    basis= [-----------------]]
                    2
            a cos(x)  - b - a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (137)
--R                                                  2                2
--R                - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
--R   [particular= ----------------------------------------------------,
--R                                         2
--R                                4a cos(x)  - 4b - 4a
--R                    1
--R    basis= [-----------------]]
--R                    2
--R            a cos(x)  - b - a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 137

--S 138 of 139
yx:=ode200a.particular
 

                                            2                2
          - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
   (138)  ----------------------------------------------------
                                   2
                          4a cos(x)  - 4b - 4a
                                                     Type: Expression Integer
--R 
--R
--R                                            2                2
--R          - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
--R   (138)  ----------------------------------------------------
--R                                   2
--R                          4a cos(x)  - 4b - 4a
--R                                                     Type: Expression Integer
--E 138

--S 139 of 139
ode200expr := (a*sin(x)**2+b)*D(yx,x) + a*yx*sin(2*x) + A*x*(a*sin(x)**2+c)
 

   (139)
                  3        3        2        3                      3      4
           (- 2A a x cos(x)  + (2A a b + 2A a )x cos(x))sin(x) - A a cos(x)
         + 
                 2       3  2      2       3       2
           ((2A a c + A a )x  + A a b + A a )cos(x)
         + 
                            2        2       3  2
           ((- 2A a b - 2A a )c - A a b - A a )x
      *
         sin(2x)
     + 
              3        2          2        3         4
       (- 2A a x cos(x)  + (- 2A a b - 2A a )x)sin(x)
     + 
              3      3        2        3  2             3
       (- 2A a cos(x)  + (4A a c + 2A a )x cos(x))sin(x)
     + 
               3        4        2        2        3         2
           2A a x cos(x)  + (4A a c - 8A a b - 4A a )x cos(x)
         + 
                            2           2       2        3
           ((- 4A a b - 4A a )c + 2A a b  + 4A a b + 2A a )x
      *
               2
         sin(x)
     + 
              2        3                   2   2
       (- 2A a b cos(x)  + (4A a b c + 2A a b)x cos(x))sin(x)
     + 
            2        2          4
       (4A a c - 2A a b)x cos(x)
     + 
                        2           2       2          2
       ((- 4A a b - 8A a )c + 2A a b  + 4A a b)x cos(x)
     + 
                      2           2       2
       ((4A a b + 4A a )c - 2A a b  - 2A a b)x
  /
       2      4               2       2     2            2
     4a cos(x)  + (- 8a b - 8a )cos(x)  + 4b  + 8a b + 4a
                                                     Type: Expression Integer
--R 
--R
--R   (139)
--R                  3        3        2        3                      3      4
--R           (- 2A a x cos(x)  + (2A a b + 2A a )x cos(x))sin(x) - A a cos(x)
--R         + 
--R                 2       3  2      2       3       2
--R           ((2A a c + A a )x  + A a b + A a )cos(x)
--R         + 
--R                            2        2       3  2
--R           ((- 2A a b - 2A a )c - A a b - A a )x
--R      *
--R         sin(2x)
--R     + 
--R              3        2          2        3         4
--R       (- 2A a x cos(x)  + (- 2A a b - 2A a )x)sin(x)
--R     + 
--R              3      3        2        3  2             3
--R       (- 2A a cos(x)  + (4A a c + 2A a )x cos(x))sin(x)
--R     + 
--R               3        4        2        2        3         2
--R           2A a x cos(x)  + (4A a c - 8A a b - 4A a )x cos(x)
--R         + 
--R                            2           2       2        3
--R           ((- 4A a b - 4A a )c + 2A a b  + 4A a b + 2A a )x
--R      *
--R               2
--R         sin(x)
--R     + 
--R              2        3                   2   2
--R       (- 2A a b cos(x)  + (4A a b c + 2A a b)x cos(x))sin(x)
--R     + 
--R            2        2          4
--R       (4A a c - 2A a b)x cos(x)
--R     + 
--R                        2           2       2          2
--R       ((- 4A a b - 8A a )c + 2A a b  + 4A a b)x cos(x)
--R     + 
--R                      2           2       2
--R       ((4A a b + 4A a )c - 2A a b  - 2A a b)x
--R  /
--R       2      4               2       2     2            2
--R     4a cos(x)  + (- 8a b - 8a )cos(x)  + 4b  + 8a b + 4a
--R                                                     Type: Expression Integer
--E 139

)spool
 
Starts dribbling to r20abugs.output (2009/2/17, 17:56:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 34
m : Matrix Expression Integer := matrix [[i*x^j for i in 1..3] for j in 1..3]
 

        +x   2x   3x +
        |            |
        | 2    2    2|
   (1)  |x   2x   3x |
        |            |
        | 3    3    3|
        +x   2x   3x +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +x   2x   3x +
--R        |            |
--R        | 2    2    2|
--R   (1)  |x   2x   3x |
--R        |            |
--R        | 3    3    3|
--R        +x   2x   3x +
--R                                              Type: Matrix Expression Integer
--E 1

--S 2 of 34
eval(m,x=0)
 

        +0  0  0+
        |       |
   (2)  |0  0  0|
        |       |
        +0  0  0+
                                              Type: Matrix Expression Integer
--R 
--R
--R        +0  0  0+
--R        |       |
--R   (2)  |0  0  0|
--R        |       |
--R        +0  0  0+
--R                                              Type: Matrix Expression Integer
--E 2


)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
--S 3 of 34
s:= seed();
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 34
r1 := randnum();
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 34
for i in 1..10 repeat randnum();
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 34
reseed s;
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 34
r2 := randnum();
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 34
r1 - r2
 

   (6)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (6)  0
--R                                                     Type: NonNegativeInteger
--E 8


)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 9 of 34
r3:=rule(3==%pi) -- biblical approximation
 

   (1)  3 == %pi
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)  3 == %pi
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 9

--S 10 of 34
numeric(%pi)
 

   (2)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 897932385
--R                                                                  Type: Float
--E 10

--S 11 of 34
numeric(r3(3))
 

   (3)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (3)  3.1415926535 897932385
--R                                                                  Type: Float
--E 11

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.


--S 12 of 34
sin(atan(sqrt 3)/2)
 

        1
   (1)  -
        2
                                                     Type: Expression Integer
--R 
--R
--R        1
--R   (1)  -
--R        2
--R                                                     Type: Expression Integer
--E 12

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 13 of 34
R := IntegerMod(4)
 

   (1)  IntegerMod 4
                                                                 Type: Domain
--R 
--R
--R   (1)  IntegerMod 4
--R                                                                 Type: Domain
--E 13

--S 14 of 34
PolR := UP('X, R)
 

   (2)  UnivariatePolynomial(X,IntegerMod 4)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(X,IntegerMod 4)
--R                                                                 Type: Domain
--E 14

--S 15 of 34
X : PolR := monomial(1, 1)
 

   (3)  X
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R   (3)  X
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 15

--S 16 of 34
a : PolR := 2 * X**2
 

          2
   (4)  2X
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R          2
--R   (4)  2X
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 16

--S 17 of 34
b : PolR := X**2 + 2*X + 1
 

         2
   (5)  X  + 2X + 1
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R         2
--R   (5)  X  + 2X + 1
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 17

--S 18 of 34
qr := monicDivide(a, b)
 

   (6)  [quotient= 2,remainder= 2]
Type: Record(quotient: UnivariatePolynomial(X,IntegerMod 4),remainder: UnivariatePolynomial(X,IntegerMod 4))
--R 
--R
--R   (6)  [quotient= 2,remainder= 2]
--RType: Record(quotient: UnivariatePolynomial(X,IntegerMod 4),remainder: UnivariatePolynomial(X,IntegerMod 4))
--E 18

--S 19 of 34
a - (qr.quotient * b + qr.remainder)
 

   (7)  0
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R   (7)  0
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 19

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 20 of 34
limit(%e^(1/x^2)/(%e^(1/x^2) + %e^(1/x^4)), x=0)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 20
)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 21 of 34
integrate((sin(t))*sin((%pi-t)/6),t)
 

   (1)
             t - %pi 6           t - %pi 4          t - %pi 2          t - %pi
   (- 960cos(-------)  + 1536cos(-------)  - 612cos(-------)  + 36)sin(-------)
                6                   6                  6                  6
   ----------------------------------------------------------------------------
                                        35
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R             t - %pi 6           t - %pi 4          t - %pi 2          t - %pi
--R   (- 960cos(-------)  + 1536cos(-------)  - 612cos(-------)  + 36)sin(-------)
--R                6                   6                  6                  6
--R   ----------------------------------------------------------------------------
--R                                        35
--R                                          Type: Union(Expression Integer,...)
--E 21

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 22 of 34
(x+1.0)/(x+1.0)
 

   (1)  1.0
                                              Type: Fraction Polynomial Float
--R 
--R
--R   (1)  1.0
--R                                              Type: Fraction Polynomial Float
--E 22

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 23 of 34
b := D(Ci(x),x)
 

        cos(x)
   (1)  ------
           x
                                                     Type: Expression Integer
--R 
--R
--R        cos(x)
--R   (1)  ------
--R           x
--R                                                     Type: Expression Integer
--E 23

--S 24 of 34
integrate(b,x)
 

   (2)  Ci(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)  Ci(x)
--R                                          Type: Union(Expression Integer,...)
--E 24

--S 25 of 34
integrate((1 - sin x)/x,x)
 

   (3)  log(x) - Si(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (3)  log(x) - Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 25

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 26 of 34
limit(erf(x),x=c)
 

   (1)  erf(c)
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  erf(c)
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 26

--S 27 of 34
(sqrt(2)*sqrt(3)=sqrt(6))@Boolean
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 34
integrate((a + b*x)*exp(-x^2),x)
 

                                2
                 +---+       - x
        a erf(x)\|%pi  - b %e
   (3)  -------------------------
                    2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                2
--R                 +---+       - x
--R        a erf(x)\|%pi  - b %e
--R   (3)  -------------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 28

--S 29 of 34
laplace(sin(t)^2/t^(3/2),t,s)
 

                       +---+ 4         +---+ 2
                     t\|- 1          t\|- 1
                - (%e       )  + 2(%e       )  - 1
   (4)  laplace(----------------------------------,t,s)
                                +---+ 2
                              t\|- 1    +-+
                        4t (%e       ) \|t
                                                     Type: Expression Integer
--R 
--R
--R                       +---+ 4         +---+ 2
--R                     t\|- 1          t\|- 1
--R                - (%e       )  + 2(%e       )  - 1
--R   (4)  laplace(----------------------------------,t,s)
--R                                +---+ 2
--R                              t\|- 1    +-+
--R                        4t (%e       ) \|t
--R                                                     Type: Expression Integer
--E 29

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 30 of 34
P:=x^4+x^3+x^2+x+1
 

         4    3    2
   (1)  x  + x  + x  + x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         4    3    2
--R   (1)  x  + x  + x  + x + 1
--R                                                     Type: Polynomial Integer
--E 30

--S 31 of 34
Q:=x^5+x^4+2*x^3+2*x^2+2*x-2+4*sqrt(-1+sqrt(3))
 

                                     +--------+
         5    4     3     2          | +-+
   (2)  x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R                                     +--------+
--R         5    4     3     2          | +-+
--R   (2)  x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
--R                                             Type: Polynomial AlgebraicNumber
--E 31

--S 32 of 34
int := P/Q
 

                     4    3    2
                    x  + x  + x  + x + 1
   (3)  -------------------------------------------
                                     +--------+
         5    4     3     2          | +-+
        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
                                    Type: Fraction Polynomial AlgebraicNumber
--R 
--R
--R                     4    3    2
--R                    x  + x  + x  + x + 1
--R   (3)  -------------------------------------------
--R                                     +--------+
--R         5    4     3     2          | +-+
--R        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
--R                                    Type: Fraction Polynomial AlgebraicNumber
--E 32

--S 33 of 34
int2 := int pretend FRAC POLY IAN
 

                     4    3    2
                    x  + x  + x  + x + 1
   (4)  -------------------------------------------
                                     +--------+
         5    4     3     2          | +-+
        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
                               Type: Fraction Polynomial InnerAlgebraicNumber
--R 
--R
--R                     4    3    2
--R                    x  + x  + x  + x + 1
--R   (4)  -------------------------------------------
--R                                     +--------+
--R         5    4     3     2          | +-+
--R        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
--R                               Type: Fraction Polynomial InnerAlgebraicNumber
--E 33

--S 34 of 34
ans:=integrate(int2,x)
 

   (5)
           ROOT
                                2
                - 7810694562%%F2
              + 
                (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
              + 
                                2
                - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
              + 
                                2
                - 7810694562%%F0  + 5207129708%%F0
              + 
                                             +--------+
                            +-+              | +-+                 +-+
                (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
              + 
                - 1685296141
         + 
              +----------+        +----------+        +----------+
           - \|2603564854 %%F2 - \|2603564854 %%F1 - \|2603564854 %%F0
         + 
            +----------+
           \|2603564854
      /
           +----------+
         2\|2603564854
    *
       log
            x
          + 
                                                +-+                 +----------+
                                  (791590596224\|3  + 598661610816)\|2603564854
                               *
                                   +--------+
                                   | +-+
                                  \|\|3  - 1
                              + 
                                               +-+                  +----------+
                              (- 2397286715776\|3  + 2403741928832)\|2603564854
                           *
                              %%F0
                          + 
                                              +-+                 +----------+
                              (- 148579737216\|3  - 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                          +-+                 +----------+
                            (507356852544\|3  - 475624619408)\|2603564854
                       *
                          %%F1
                      + 
                                              +-+                 +----------+
                              (- 148579737216\|3  - 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                          +-+                 +----------+
                            (507356852544\|3  - 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                                                     +--------+
                                     +-+                +----------+ | +-+
                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
                      + 
                                        +-+                +----------+
                        (- 105798682864\|3  + 94208190216)\|2603564854
                   *
                      %%F2
                  + 
                                              +-+                 +----------+
                              (- 148579737216\|3  - 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                          +-+                 +----------+
                            (507356852544\|3  - 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                                                     +--------+
                                     +-+                +----------+ | +-+
                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
                      + 
                                        +-+                +----------+
                        (- 105798682864\|3  + 94208190216)\|2603564854
                   *
                      %%F1
                  + 
                                                                     +--------+
                                     +-+                +----------+ | +-+
                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
                      + 
                                        +-+                +----------+
                        (- 105798682864\|3  + 94208190216)\|2603564854
                   *
                      %%F0
                  + 
                                                                  +--------+
                                  +-+                +----------+ | +-+
                    (- 5137573312\|3  - 12986675368)\|2603564854 \|\|3  - 1
                  + 
                                 +-+                +----------+
                    (21754940736\|3  - 18755586294)\|2603564854
               *
                  ROOT
                                       2
                       - 7810694562%%F2
                     + 
                       (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
                     + 
                                       2
                       - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
                     + 
                                       2
                       - 7810694562%%F0  + 5207129708%%F0
                     + 
                                                    +--------+
                                   +-+              | +-+                 +-+
                       (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
                     + 
                       - 1685296141
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F2
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F1
                  + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                              2
                          %%F0
                      + 
                                                         +-+
                                - 2447794436917844917760\|3
                              + 
                                - 2090231849158026910336
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                            7562427907875099825280\|3  - 7496617546780959556960
                       *
                          %%F0
                      + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F2
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F1
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F1
              + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F0
              + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F0
              + 
                                                                 +--------+
                                     +-+                         | +-+
                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
              + 
                                       +-+
                - 33670351123600429986\|3  + 29207247737687098805
           /
              99053573869819283
   + 
       %%F1
    *
       log
            x
          + 
                                                            +--------+
                                       +-+                  | +-+
                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
                      + 
                                        +-+
                        - 9589146863104\|3  + 9614967715328
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
                  + 
                                  +-+
                    2029427410176\|3  - 1902498477632
               *
                      3
                  %%F1
              + 
                                                            +--------+
                                       +-+                  | +-+
                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
                      + 
                                        +-+
                        - 9589146863104\|3  + 9614967715328
                   *
                          2
                      %%F0
                  + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                      %%F0
                  + 
                                                      +--------+
                                  +-+                 | +-+
                    (483359723712\|3  + 597247669440)\|\|3  - 1
                  + 
                                    +-+
                    - 1606232678720\|3  + 1525665716768
               *
                      2
                  %%F1
              + 
                                                            +--------+
                                       +-+                  | +-+
                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
                      + 
                                        +-+
                        - 9589146863104\|3  + 9614967715328
                   *
                          3
                      %%F0
                  + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                          2
                      %%F0
                  + 
                                                           +--------+
                                       +-+                 | +-+
                        (1266224220576\|3  + 930590163424)\|\|3  - 1
                      + 
                                        +-+
                        - 3826137578368\|3  + 3840459797248
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 147325640064\|3  - 153462964896)\|\|3  - 1
                  + 
                                 +-+
                    473720495592\|3  - 459140624672
               *
                  %%F1
              + 
                                                        +--------+
                                   +-+                  | +-+
                    (3166362384896\|3  + 2394646443264)\|\|3  - 1
                  + 
                                    +-+
                    - 9589146863104\|3  + 9614967715328
               *
                      4
                  %%F0
              + 
                                                          +--------+
                                     +-+                  | +-+
                    (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                  + 
                                  +-+
                    9589146863104\|3  - 9614967715328
               *
                      3
                  %%F0
              + 
                                                       +--------+
                                   +-+                 | +-+
                    (1266224220576\|3  + 930590163424)\|\|3  - 1
                  + 
                                    +-+
                    - 3826137578368\|3  + 3840459797248
               *
                      2
                  %%F0
              + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 253275272864\|3  - 176488982240)\|\|3  - 1
                  + 
                                 +-+
                    762298416608\|3  - 767050528864
               *
                  %%F0
              + 
                                                +--------+
                             +-+                | +-+                    +-+
                (19959069548\|3  + 16362854321)\|\|3  - 1  - 61872513890\|3
              + 
                61405017927
           /
              76090729
   + 
       %%F0
    *
       log
            x
          + 
                                                          +--------+
                                     +-+                  | +-+
                    (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                  + 
                                  +-+
                    9589146863104\|3  - 9614967715328
               *
                      4
                  %%F0
              + 
                                                        +--------+
                                   +-+                  | +-+
                    (2572043436032\|3  + 1577954638592)\|\|3  - 1
                  + 
                                    +-+
                    - 7559719452928\|3  + 7712469237696
               *
                      3
                  %%F0
              + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 782864496864\|3  - 333342493984)\|\|3  - 1
                  + 
                                  +-+
                    2219904899648\|3  - 2314794080480
               *
                      2
                  %%F0
              + 
                                                     +--------+
                                  +-+                | +-+
                    (105949632800\|3  + 23026017344)\|\|3  - 1
                  + 
                                   +-+
                    - 288577921016\|3  + 307909904192
               *
                  %%F0
              + 
                                               +--------+
                              +-+              | +-+                    +-+
                (- 5377952768\|3  - 147961292)\|\|3  - 1  + 14063435544\|3
              + 
                - 15251710219
           /
              76090729
   + 
       %%F2
    *
       log
            x
          + 
                                                                  +--------+
                                             +-+                  | +-+
                            (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                          + 
                                          +-+
                            9589146863104\|3  - 9614967715328
                       *
                          %%F0
                      + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                      %%F1
                  + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 110959225152\|3  - 219444135232)\|\|3  - 1
                  + 
                                 +-+
                    423194731456\|3  - 376832760864
               *
                      2
                  %%F2
              + 
                                                                  +--------+
                                             +-+                  | +-+
                            (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                          + 
                                          +-+
                            9589146863104\|3  - 9614967715328
                       *
                          %%F0
                      + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                          2
                      %%F1
                  + 
                                                                  +--------+
                                             +-+                  | +-+
                            (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                          + 
                                          +-+
                            9589146863104\|3  - 9614967715328
                       *
                              2
                          %%F0
                      + 
                                                                +--------+
                                           +-+                  | +-+
                            (3760681333760\|3  + 3211338247936)\|\|3  - 1
                          + 
                                             +-+
                            - 11618574273280\|3  + 11517466192960
                       *
                          %%F0
                      + 
                                                            +--------+
                                        +-+                 | +-+
                        (- 594318948864\|3  - 816691804672)\|\|3  - 1
                      + 
                                      +-+
                        2029427410176\|3  - 1902498477632
                   *
                      %%F1
                  + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                          2
                      %%F0
                  + 
                                                            +--------+
                                        +-+                 | +-+
                        (- 594318948864\|3  - 816691804672)\|\|3  - 1
                      + 
                                      +-+
                        2029427410176\|3  - 1902498477632
                   *
                      %%F0
                  + 
                                                     +--------+
                                 +-+                 | +-+
                    (90408931904\|3  + 167497433760)\|\|3  - 1
                  + 
                                   +-+
                    - 336174968512\|3  + 301810415688
               *
                  %%F2
              + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                      %%F0
                  + 
                                                      +--------+
                                  +-+                 | +-+
                    (594318948864\|3  + 816691804672)\|\|3  - 1
                  + 
                                    +-+
                    - 2029427410176\|3  + 1902498477632
               *
                      3
                  %%F1
              + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                          2
                      %%F0
                  + 
                                                            +--------+
                                       +-+                  | +-+
                        (3760681333760\|3  + 3211338247936)\|\|3  - 1
                      + 
                                         +-+
                        - 11618574273280\|3  + 11517466192960
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
                  + 
                                  +-+
                    2029427410176\|3  - 1902498477632
               *
                      2
                  %%F1
              + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                          3
                      %%F0
                  + 
                                                            +--------+
                                       +-+                  | +-+
                        (3760681333760\|3  + 3211338247936)\|\|3  - 1
                      + 
                                         +-+
                        - 11618574273280\|3  + 11517466192960
                   *
                          2
                      %%F0
                  + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 1860543169440\|3  - 1747281968096)\|\|3  - 1
                      + 
                                      +-+
                        5855564988544\|3  - 5742958274880
                   *
                      %%F0
                  + 
                                                      +--------+
                                  +-+                 | +-+
                    (237734571968\|3  + 320960398656)\|\|3  - 1
                  + 
                                   +-+
                    - 809895464104\|3  + 760951040360
               *
                  %%F1
              + 
                                                      +--------+
                                  +-+                 | +-+
                    (594318948864\|3  + 816691804672)\|\|3  - 1
                  + 
                                    +-+
                    - 2029427410176\|3  + 1902498477632
               *
                      3
                  %%F0
              + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
                  + 
                                  +-+
                    2029427410176\|3  - 1902498477632
               *
                      2
                  %%F0
              + 
                                                      +--------+
                                  +-+                 | +-+
                    (237734571968\|3  + 320960398656)\|\|3  - 1
                  + 
                                   +-+
                    - 809895464104\|3  + 760951040360
               *
                  %%F0
              + 
                                                  +--------+
                               +-+                | +-+                    +-+
                (- 27607601380\|3  - 45816414455)\|\|3  - 1  + 99538692182\|3
              + 
                - 90949919409
           /
              76090729
   + 
           -
              ROOT
                                   2
                   - 7810694562%%F2
                 + 
                   (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
                 + 
                                   2
                   - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
                 + 
                                   2
                   - 7810694562%%F0  + 5207129708%%F0
                 + 
                                                +--------+
                               +-+              | +-+                 +-+
                   (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
                 + 
                   - 1685296141
         + 
              +----------+        +----------+        +----------+
           - \|2603564854 %%F2 - \|2603564854 %%F1 - \|2603564854 %%F0
         + 
            +----------+
           \|2603564854
      /
           +----------+
         2\|2603564854
    *
       log
            x
          + 
                                                  +-+
                                  (- 791590596224\|3  - 598661610816)
                               *
                                                +--------+
                                   +----------+ | +-+
                                  \|2603564854 \|\|3  - 1
                              + 
                                             +-+                  +----------+
                              (2397286715776\|3  - 2403741928832)\|2603564854
                           *
                              %%F0
                          + 
                                            +-+                 +----------+
                              (148579737216\|3  + 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                            +-+                 +----------+
                            (- 507356852544\|3  + 475624619408)\|2603564854
                       *
                          %%F1
                      + 
                                            +-+                 +----------+
                              (148579737216\|3  + 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                            +-+                 +----------+
                            (- 507356852544\|3  + 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                         +-+                +----------+
                          (- 27739806288\|3  - 54861033808)\|2603564854
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                      +-+                +----------+
                        (105798682864\|3  - 94208190216)\|2603564854
                   *
                      %%F2
                  + 
                                            +-+                 +----------+
                              (148579737216\|3  + 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                            +-+                 +----------+
                            (- 507356852544\|3  + 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                         +-+                +----------+
                          (- 27739806288\|3  - 54861033808)\|2603564854
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                      +-+                +----------+
                        (105798682864\|3  - 94208190216)\|2603564854
                   *
                      %%F1
                  + 
                                         +-+                +----------+
                          (- 27739806288\|3  - 54861033808)\|2603564854
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                      +-+                +----------+
                        (105798682864\|3  - 94208190216)\|2603564854
                   *
                      %%F0
                  + 
                                                                +--------+
                                +-+                +----------+ | +-+
                    (5137573312\|3  + 12986675368)\|2603564854 \|\|3  - 1
                  + 
                                   +-+                +----------+
                    (- 21754940736\|3  + 18755586294)\|2603564854
               *
                  ROOT
                                       2
                       - 7810694562%%F2
                     + 
                       (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
                     + 
                                       2
                       - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
                     + 
                                       2
                       - 7810694562%%F0  + 5207129708%%F0
                     + 
                                                    +--------+
                                   +-+              | +-+                 +-+
                       (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
                     + 
                       - 1685296141
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F2
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F1
                  + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                              2
                          %%F0
                      + 
                                                         +-+
                                - 2447794436917844917760\|3
                              + 
                                - 2090231849158026910336
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                            7562427907875099825280\|3  - 7496617546780959556960
                       *
                          %%F0
                      + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F2
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F1
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F1
              + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F0
              + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F0
              + 
                                                                 +--------+
                                     +-+                         | +-+
                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
              + 
                                       +-+
                - 33670351123600429986\|3  + 29207247737687098805
           /
              99053573869819283
                             Type: Union(Expression InnerAlgebraicNumber,...)
--R 
--R
--R   (5)
--R           ROOT
--R                                2
--R                - 7810694562%%F2
--R              + 
--R                (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
--R              + 
--R                                2
--R                - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
--R              + 
--R                                2
--R                - 7810694562%%F0  + 5207129708%%F0
--R              + 
--R                                             +--------+
--R                            +-+              | +-+                 +-+
--R                (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
--R              + 
--R                - 1685296141
--R         + 
--R              +----------+        +----------+        +----------+
--R           - \|2603564854 %%F2 - \|2603564854 %%F1 - \|2603564854 %%F0
--R         + 
--R            +----------+
--R           \|2603564854
--R      /
--R           +----------+
--R         2\|2603564854
--R    *
--R       log
--R            x
--R          + 
--R                                                +-+                 +----------+
--R                                  (791590596224\|3  + 598661610816)\|2603564854
--R                               *
--R                                   +--------+
--R                                   | +-+
--R                                  \|\|3  - 1
--R                              + 
--R                                               +-+                  +----------+
--R                              (- 2397286715776\|3  + 2403741928832)\|2603564854
--R                           *
--R                              %%F0
--R                          + 
--R                                              +-+                 +----------+
--R                              (- 148579737216\|3  - 204172951168)\|2603564854
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                          +-+                 +----------+
--R                            (507356852544\|3  - 475624619408)\|2603564854
--R                       *
--R                          %%F1
--R                      + 
--R                                              +-+                 +----------+
--R                              (- 148579737216\|3  - 204172951168)\|2603564854
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                          +-+                 +----------+
--R                            (507356852544\|3  - 475624619408)\|2603564854
--R                       *
--R                          %%F0
--R                      + 
--R                                                                     +--------+
--R                                     +-+                +----------+ | +-+
--R                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
--R                      + 
--R                                        +-+                +----------+
--R                        (- 105798682864\|3  + 94208190216)\|2603564854
--R                   *
--R                      %%F2
--R                  + 
--R                                              +-+                 +----------+
--R                              (- 148579737216\|3  - 204172951168)\|2603564854
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                          +-+                 +----------+
--R                            (507356852544\|3  - 475624619408)\|2603564854
--R                       *
--R                          %%F0
--R                      + 
--R                                                                     +--------+
--R                                     +-+                +----------+ | +-+
--R                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
--R                      + 
--R                                        +-+                +----------+
--R                        (- 105798682864\|3  + 94208190216)\|2603564854
--R                   *
--R                      %%F1
--R                  + 
--R                                                                     +--------+
--R                                     +-+                +----------+ | +-+
--R                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
--R                      + 
--R                                        +-+                +----------+
--R                        (- 105798682864\|3  + 94208190216)\|2603564854
--R                   *
--R                      %%F0
--R                  + 
--R                                                                  +--------+
--R                                  +-+                +----------+ | +-+
--R                    (- 5137573312\|3  - 12986675368)\|2603564854 \|\|3  - 1
--R                  + 
--R                                 +-+                +----------+
--R                    (21754940736\|3  - 18755586294)\|2603564854
--R               *
--R                  ROOT
--R                                       2
--R                       - 7810694562%%F2
--R                     + 
--R                       (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
--R                     + 
--R                                       2
--R                       - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
--R                     + 
--R                                       2
--R                       - 7810694562%%F0  + 5207129708%%F0
--R                     + 
--R                                                    +--------+
--R                                   +-+              | +-+                 +-+
--R                       (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
--R                     + 
--R                       - 1685296141
--R              + 
--R                                                       +-+
--R                                2060957455085711511296\|3
--R                              + 
--R                                1558654329359563860864
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                                   +-+
--R                          - 6241491438155480936704\|3  + 6258298003993164470528
--R                       *
--R                          %%F0
--R                      + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                      %%F1
--R                  + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                      %%F0
--R                  + 
--R                                            +-+
--R                      (72222384708205001952\|3  + 142834259476614584032)
--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                            +-+
--R                    - 275453732304202461856\|3  + 245277133005324268464
--R               *
--R                      2
--R                  %%F2
--R              + 
--R                                                       +-+
--R                                2060957455085711511296\|3
--R                              + 
--R                                1558654329359563860864
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                                   +-+
--R                          - 6241491438155480936704\|3  + 6258298003993164470528
--R                       *
--R                          %%F0
--R                      + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                          2
--R                      %%F1
--R                  + 
--R                                                       +-+
--R                                2060957455085711511296\|3
--R                              + 
--R                                1558654329359563860864
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                                   +-+
--R                          - 6241491438155480936704\|3  + 6258298003993164470528
--R                       *
--R                              2
--R                          %%F0
--R                      + 
--R                                                         +-+
--R                                - 2447794436917844917760\|3
--R                              + 
--R                                - 2090231849158026910336
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                                   +-+
--R                            7562427907875099825280\|3  - 7496617546780959556960
--R                       *
--R                          %%F0
--R                      + 
--R                                                 +-+
--R                          (386836981832133406464\|3  + 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                                 +-+
--R                        - 1320936469719618888576\|3  + 1238319542787795086432
--R                   *
--R                      %%F1
--R                  + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                          2
--R                      %%F0
--R                  + 
--R                                                 +-+
--R                          (386836981832133406464\|3  + 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                                 +-+
--R                        - 1320936469719618888576\|3  + 1238319542787795086432
--R                   *
--R                      %%F0
--R                  + 
--R                                              +-+
--R                      (- 58846379398233425504\|3  - 109022607918182267760)
--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                          +-+
--R                    218813333203099969312\|3  - 196445747714101757388
--R               *
--R                  %%F2
--R              + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                      %%F0
--R                  + 
--R                                            +-+
--R                      (72222384708205001952\|3  + 142834259476614584032)
--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                            +-+
--R                    - 275453732304202461856\|3  + 245277133005324268464
--R               *
--R                      2
--R                  %%F1
--R              + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                          2
--R                      %%F0
--R                  + 
--R                                                 +-+
--R                          (386836981832133406464\|3  + 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
--R                      + 
--R                                                 +-+
--R                        - 1320936469719618888576\|3  + 1238319542787795086432
--R                   *
--R                      %%F0
--R                  + 
--R                                              +-+
--R                      (- 58846379398233425504\|3  - 109022607918182267760)
--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                          +-+
--R                    218813333203099969312\|3  - 196445747714101757388
--R               *
--R                  %%F1
--R              + 
--R                                            +-+
--R                      (72222384708205001952\|3  + 142834259476614584032)
--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                            +-+
--R                    - 275453732304202461856\|3  + 245277133005324268464
--R               *
--R                      2
--R                  %%F0
--R              + 
--R                                              +-+
--R                      (- 58846379398233425504\|3  - 109022607918182267760)
--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                          +-+
--R                    218813333203099969312\|3  - 196445747714101757388
--R               *
--R                  %%F0
--R              + 
--R                                                                 +--------+
--R                                     +-+                         | +-+
--R                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
--R              + 
--R                                       +-+
--R                - 33670351123600429986\|3  + 29207247737687098805
--R           /
--R              99053573869819283
--R   + 
--R       %%F1
--R    *
--R       log
--R            x
--R          + 
--R                                                            +--------+
--R                                       +-+                  | +-+
--R                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
--R                      + 
--R                                        +-+
--R                        - 9589146863104\|3  + 9614967715328
--R                   *
--R                      %%F0
--R                  + 
--R                                                        +--------+
--R                                    +-+                 | +-+
--R                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
--R                  + 
--R                                  +-+
--R                    2029427410176\|3  - 1902498477632
--R               *
--R                      3
--R                  %%F1
--R              + 
--R                                                            +--------+
--R                                       +-+                  | +-+
--R                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
--R                      + 
--R                                        +-+
--R                        - 9589146863104\|3  + 9614967715328
--R                   *
--R                          2
--R                      %%F0
--R                  + 
--R                                                              +--------+
--R                                         +-+                  | +-+
--R                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
--R                      + 
--R                                      +-+
--R                        9589146863104\|3  - 9614967715328
--R                   *
--R                      %%F0
--R                  + 
--R                                                      +--------+
--R                                  +-+                 | +-+
--R                    (483359723712\|3  + 597247669440)\|\|3  - 1
--R                  + 
--R                                    +-+
--R                    - 1606232678720\|3  + 1525665716768
--R               *
--R                      2
--R                  %%F1
--R              + 
--R                                                            +--------+
--R                                       +-+                  | +-+
--R                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
--R                      + 
--R                                        +-+
--R                        - 9589146863104\|3  + 9614967715328
--R                   *
--R                          3
--R                      %%F0
--R                  + 
--R                                                              +--------+
--R                                         +-+                  | +-+
--R                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
--R                      + 
--R                                      +-+
--R                        9589146863104\|3  - 9614967715328
--R                   *
--R                          2
--R                      %%F0
--R                  + 
--R                                                           +--------+
--R                                       +-+                 | +-+
--R                        (1266224220576\|3  + 930590163424)\|\|3  - 1
--R                      + 
--R                                        +-+
--R                        - 3826137578368\|3  + 3840459797248
--R                   *
--R                      %%F0
--R                  + 
--R                                                        +--------+
--R                                    +-+                 | +-+
--R                    (- 147325640064\|3  - 153462964896)\|\|3  - 1
--R                  + 
--R                                 +-+
--R                    473720495592\|3  - 459140624672
--R               *
--R                  %%F1
--R              + 
--R                                                        +--------+
--R                                   +-+                  | +-+
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--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                          +-+
--R                    218813333203099969312\|3  - 196445747714101757388
--R               *
--R                  %%F0
--R              + 
--R                                                                 +--------+
--R                                     +-+                         | +-+
--R                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
--R              + 
--R                                       +-+
--R                - 33670351123600429986\|3  + 29207247737687098805
--R           /
--R              99053573869819283
--R                             Type: Union(Expression InnerAlgebraicNumber,...)
--E 34
)spool 
 
Starts dribbling to schaum2.output (2009/2/17, 17:59:10).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/sqrt(a*x+b),x)
 

          +-------+
        2\|a x + b
   (1)  -----------
             a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +-------+
--R        2\|a x + b
--R   (1)  -----------
--R             a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=(2*sqrt(a*x+b))/a
 

          +-------+
        2\|a x + b
   (2)  -----------
             a
                                                     Type: Expression Integer
--R 
--R
--R          +-------+
--R        2\|a x + b
--R   (2)  -----------
--R             a
--R                                                     Type: Expression Integer
--E

--S 3      14:84 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x/sqrt(a*x+b),x)
 

                    +-------+
        (2a x - 4b)\|a x + b
   (1)  ---------------------
                   2
                 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-------+
--R        (2a x - 4b)\|a x + b
--R   (1)  ---------------------
--R                   2
--R                 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b)
 

                    +-------+
        (2a x - 4b)\|a x + b
   (2)  ---------------------
                   2
                 3a
                                                     Type: Expression Integer
--R 
--R
--R                    +-------+
--R        (2a x - 4b)\|a x + b
--R   (2)  ---------------------
--R                   2
--R                 3a
--R                                                     Type: Expression Integer
--E

--S 6      14:85 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2/sqrt(a*x+b),x)
 

           2 2               2  +-------+
        (6a x  - 8a b x + 16b )\|a x + b
   (1)  ---------------------------------
                          3
                       15a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2               2  +-------+
--R        (6a x  - 8a b x + 16b )\|a x + b
--R   (1)  ---------------------------------
--R                          3
--R                       15a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b)
 

           2 2               2  +-------+
        (6a x  - 8a b x + 16b )\|a x + b
   (2)  ---------------------------------
                          3
                       15a
                                                     Type: Expression Integer
--R 
--R
--R           2 2               2  +-------+
--R        (6a x  - 8a b x + 16b )\|a x + b
--R   (2)  ---------------------------------
--R                          3
--R                       15a
--R                                                     Type: Expression Integer
--E

--S 9      14:86 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (1)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (1)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E 
--S 11
bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b)))
 

             +-------+    +-+
            \|a x + b  - \|b
        log(-----------------)
             +-------+    +-+
            \|a x + b  + \|b
   (2)  ----------------------
                  +-+
                 \|b
                                                     Type: Expression Integer
--R 
--R
--R             +-------+    +-+
--R            \|a x + b  - \|b
--R        log(-----------------)
--R             +-------+    +-+
--R            \|a x + b  + \|b
--R   (2)  ----------------------
--R                  +-+
--R                 \|b
--R                                                     Type: Expression Integer
--E
--S 12
cc11:=aa.1-bb1
 

               +-------+    +-+             +-------+              +-+
              \|a x + b  - \|b         - 2b\|a x + b  + (a x + 2b)\|b
        - log(-----------------) + log(-------------------------------)
               +-------+    +-+                       x
              \|a x + b  + \|b
   (3)  ---------------------------------------------------------------
                                       +-+
                                      \|b
                                                     Type: Expression Integer
--R
--R               +-------+    +-+             +-------+              +-+
--R              \|a x + b  - \|b         - 2b\|a x + b  + (a x + 2b)\|b
--R        - log(-----------------) + log(-------------------------------)
--R               +-------+    +-+                       x
--R              \|a x + b  + \|b
--R   (3)  ---------------------------------------------------------------
--R                                       +-+
--R                                      \|b
--R                                                     Type: Expression Integer
--E
--S 13
ff:=exp(aa.1*sqrt(b))
 

             +-------+              +-+
        - 2b\|a x + b  + (a x + 2b)\|b
   (4)  -------------------------------
                       x
                                                     Type: Expression Integer
--R
--R             +-------+              +-+
--R        - 2b\|a x + b  + (a x + 2b)\|b
--R   (4)  -------------------------------
--R                       x
--R                                                     Type: Expression Integer
--E
--S 14
gg:=exp(bb1*sqrt(b))
 

         +-------+    +-+
        \|a x + b  - \|b
   (5)  -----------------
         +-------+    +-+
        \|a x + b  + \|b
                                                     Type: Expression Integer
--R
--R         +-------+    +-+
--R        \|a x + b  - \|b
--R   (5)  -----------------
--R         +-------+    +-+
--R        \|a x + b  + \|b
--R                                                     Type: Expression Integer
--E
--S 15
gg1:=gg*(sqrt(a*x+b) - sqrt(b))
 

            +-+ +-------+
        - 2\|b \|a x + b  + a x + 2b
   (6)  ----------------------------
               +-------+    +-+
              \|a x + b  + \|b
                                                     Type: Expression Integer
--R
--R            +-+ +-------+
--R        - 2\|b \|a x + b  + a x + 2b
--R   (6)  ----------------------------
--R               +-------+    +-+
--R              \|a x + b  + \|b
--R                                                     Type: Expression Integer
--E
--S 16
gg2:=gg1/(sqrt(a*x+b) - sqrt(b))
 

            +-+ +-------+
        - 2\|b \|a x + b  + a x + 2b
   (7)  ----------------------------
                     a x
                                                     Type: Expression Integer
--R
--R            +-+ +-------+
--R        - 2\|b \|a x + b  + a x + 2b
--R   (7)  ----------------------------
--R                     a x
--R                                                     Type: Expression Integer
--E
--S 17
gg3:=gg2*(a*sqrt(b))
 

             +-------+              +-+
        - 2b\|a x + b  + (a x + 2b)\|b
   (8)  -------------------------------
                       x
                                                     Type: Expression Integer
--R
--R             +-------+              +-+
--R        - 2b\|a x + b  + (a x + 2b)\|b
--R   (8)  -------------------------------
--R                       x
--R                                                     Type: Expression Integer
--E
--S 18     14:87a Schaums and Axiom differ by a constant
ff-gg3
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
--S 19
t1:=aa.2-bb1
 

                      +-------+    +-+               +---+ +-------+
            +---+    \|a x + b  - \|b       +-+     \|- b \|a x + b
         - \|- b log(-----------------) - 2\|b atan(----------------)
                      +-------+    +-+                      b
                     \|a x + b  + \|b
   (10)  ------------------------------------------------------------
                                   +---+ +-+
                                  \|- b \|b
                                                     Type: Expression Integer
--R
--R                      +-------+    +-+               +---+ +-------+
--R            +---+    \|a x + b  - \|b       +-+     \|- b \|a x + b
--R         - \|- b log(-----------------) - 2\|b atan(----------------)
--R                      +-------+    +-+                      b
--R                     \|a x + b  + \|b
--R   (10)  ------------------------------------------------------------
--R                                   +---+ +-+
--R                                  \|- b \|b
--R                                                     Type: Expression Integer
--E
--S 20
D(t1,x)
 

   (11)  0
                                                     Type: Expression Integer
--R
--R   (11)  0
--R                                                     Type: Expression Integer
--E
--S 21
target:=1/(x*sqrt(a*x+b))
 

              1
   (12)  -----------
           +-------+
         x\|a x + b
                                                     Type: Expression Integer
--R
--R              1
--R   (12)  -----------
--R           +-------+
--R         x\|a x + b
--R                                                     Type: Expression Integer
--E
--S 22
aa2:=aa.2
 

                  +---+ +-------+
                 \|- b \|a x + b
           2atan(----------------)
                         b
   (13)  - -----------------------
                     +---+
                    \|- b
                                                     Type: Expression Integer
--R
--R                  +---+ +-------+
--R                 \|- b \|a x + b
--R           2atan(----------------)
--R                         b
--R   (13)  - -----------------------
--R                     +---+
--R                    \|- b
--R                                                     Type: Expression Integer
--E
--S 23
ad2:=D(aa2,x)
 

              1
   (14)  -----------
           +-------+
         x\|a x + b
                                                     Type: Expression Integer
--R
--R              1
--R   (14)  -----------
--R           +-------+
--R         x\|a x + b
--R                                                     Type: Expression Integer
--E
--S 24
ad2-target
 

   (15)  0
                                                     Type: Expression Integer
--R
--R   (15)  0
--R                                                     Type: Expression Integer
--E
--S 25
ab1:=D(bb1,x)
 

                +-------+    +-+
               \|a x + b  + \|b
   (16)  ----------------------------
           +-+ +-------+      2
         x\|b \|a x + b  + a x  + b x
                                                     Type: Expression Integer
--R
--R                +-------+    +-+
--R               \|a x + b  + \|b
--R   (16)  ----------------------------
--R           +-+ +-------+      2
--R         x\|b \|a x + b  + a x  + b x
--R                                                     Type: Expression Integer
--E
--S 26     14:87b Schaums and Axiom differ by a constant
ab1-target
 

   (17)  0
                                                     Type: Expression Integer
--R
--R   (17)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(1/(x^2*sqrt(a*x+b)),x)
 

   (1)
               +-------+              +-+
            2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
    a x log(-----------------------------) - 2\|b \|a x + b
                          x
   [--------------------------------------------------------,
                                 +-+
                            2b x\|b
              +---+ +-------+
             \|- b \|a x + b      +---+ +-------+
    a x atan(----------------) - \|- b \|a x + b
                     b
    ---------------------------------------------]
                          +---+
                      b x\|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R               +-------+              +-+
--R            2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R    a x log(-----------------------------) - 2\|b \|a x + b
--R                          x
--R   [--------------------------------------------------------,
--R                                 +-+
--R                            2b x\|b
--R              +---+ +-------+
--R             \|- b \|a x + b      +---+ +-------+
--R    a x atan(----------------) - \|- b \|a x + b
--R                     b
--R    ---------------------------------------------]
--R                          +---+
--R                      b x\|- b
--R                                     Type: Union(List Expression Integer,...)
--E 
--S 28
dd:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (2)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (2)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E
--S 29
bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1
 

                       +-------+              +-+
                  - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
        - a x log(-------------------------------) - 2\|b \|a x + b
                                 x
   (3)  ------------------------------------------------------------
                                       +-+
                                  2b x\|b
                                                     Type: Expression Integer
--R 
--R
--R                       +-------+              +-+
--R                  - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R        - a x log(-------------------------------) - 2\|b \|a x + b
--R                                 x
--R   (3)  ------------------------------------------------------------
--R                                       +-+
--R                                  2b x\|b
--R                                                     Type: Expression Integer
--E
--S 30
bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2
 

                  +---+ +-------+
                 \|- b \|a x + b      +---+ +-------+
        a x atan(----------------) - \|- b \|a x + b
                         b
   (4)  ---------------------------------------------
                              +---+
                          b x\|- b
                                                     Type: Expression Integer
--R 
--R
--R                  +---+ +-------+
--R                 \|- b \|a x + b      +---+ +-------+
--R        a x atan(----------------) - \|- b \|a x + b
--R                         b
--R   (4)  ---------------------------------------------
--R                              +---+
--R                          b x\|- b
--R                                                     Type: Expression Integer
--E
--S 31
cc11:=bb1-aa.1
 

   (5)
                  +-------+              +-+
               2b\|a x + b  + (a x + 2b)\|b
       - a log(-----------------------------)
                             x
     + 
                    +-------+              +-+
               - 2b\|a x + b  + (a x + 2b)\|b
       - a log(-------------------------------)
                              x
  /
        +-+
     2b\|b
                                                     Type: Expression Integer
--R
--R   (5)
--R                  +-------+              +-+
--R               2b\|a x + b  + (a x + 2b)\|b
--R       - a log(-----------------------------)
--R                             x
--R     + 
--R                    +-------+              +-+
--R               - 2b\|a x + b  + (a x + 2b)\|b
--R       - a log(-------------------------------)
--R                              x
--R  /
--R        +-+
--R     2b\|b
--R                                                     Type: Expression Integer
--E
--S 32
D(cc11,x)
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
--S 33
target:=1/(x^2*sqrt(a*x+b))
 

              1
   (7)  ------------
         2 +-------+
        x \|a x + b
                                                     Type: Expression Integer
--R
--R              1
--R   (7)  ------------
--R         2 +-------+
--R        x \|a x + b
--R                                                     Type: Expression Integer
--E
--S 34
ad1:=D(aa.1,x)
 

                             +-+ +-------+              2
                  (a x + 2b)\|b \|a x + b  + 2a b x + 2b
   (8)  ----------------------------------------------------------
               3     2 2  +-------+     2 4         3     2 2  +-+
        (2a b x  + 2b x )\|a x + b  + (a x  + 3a b x  + 2b x )\|b
                                                     Type: Expression Integer
--R
--R                             +-+ +-------+              2
--R                  (a x + 2b)\|b \|a x + b  + 2a b x + 2b
--R   (8)  ----------------------------------------------------------
--R               3     2 2  +-------+     2 4         3     2 2  +-+
--R        (2a b x  + 2b x )\|a x + b  + (a x  + 3a b x  + 2b x )\|b
--R                                                     Type: Expression Integer
--E
--S 35
ad1-target
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
--S 36
bd1:=D(bb1,x)
 

                                +-+ +-------+              2
                   (- a x - 2b)\|b \|a x + b  + 2a b x + 2b
   (10)  ------------------------------------------------------------
                3     2 2  +-------+       2 4         3     2 2  +-+
         (2a b x  + 2b x )\|a x + b  + (- a x  - 3a b x  - 2b x )\|b
                                                     Type: Expression Integer
--R
--R                                +-+ +-------+              2
--R                   (- a x - 2b)\|b \|a x + b  + 2a b x + 2b
--R   (10)  ------------------------------------------------------------
--R                3     2 2  +-------+       2 4         3     2 2  +-+
--R         (2a b x  + 2b x )\|a x + b  + (- a x  - 3a b x  - 2b x )\|b
--R                                                     Type: Expression Integer
--E
--S 37     
bd1-target
 

   (11)  0
                                                     Type: Expression Integer
--R
--R   (11)  0
--R                                                     Type: Expression Integer
--E
--S 38     14:88 Schaums and Axiom differ by a constant
cc22:=bb2-aa.2
 

   (12)  0
                                                     Type: Expression Integer
--R 
--R
--R   (12)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(sqrt(a*x+b),x)
 

                    +-------+
        (2a x + 2b)\|a x + b
   (1)  ---------------------
                  3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-------+
--R        (2a x + 2b)\|a x + b
--R   (1)  ---------------------
--R                  3a
--R                                          Type: Union(Expression Integer,...)
--E 
--S 40
bb:=(2*sqrt((a*x+b)^3))/(3*a)
 

          +----------------------------+
          | 3 3     2   2       2     3
        2\|a x  + 3a b x  + 3a b x + b
   (2)  --------------------------------
                       3a
                                                     Type: Expression Integer
--R 
--R
--R          +----------------------------+
--R          | 3 3     2   2       2     3
--R        2\|a x  + 3a b x  + 3a b x + b
--R   (2)  --------------------------------
--R                       3a
--R                                                     Type: Expression Integer
--E
--S 41
cc:=aa-bb
 

            +----------------------------+
            | 3 3     2   2       2     3                +-------+
        - 2\|a x  + 3a b x  + 3a b x + b   + (2a x + 2b)\|a x + b
   (3)  ----------------------------------------------------------
                                    3a
                                                     Type: Expression Integer
--R
--R            +----------------------------+
--R            | 3 3     2   2       2     3                +-------+
--R        - 2\|a x  + 3a b x  + 3a b x + b   + (2a x + 2b)\|a x + b
--R   (3)  ----------------------------------------------------------
--R                                    3a
--R                                                     Type: Expression Integer
--E
--S 42
target:=sqrt(a*x+b)
 

         +-------+
   (4)  \|a x + b
                                                     Type: Expression Integer
--R
--R         +-------+
--R   (4)  \|a x + b
--R                                                     Type: Expression Integer
--E
--S 43
t1:=D(aa,x)
 

          a x + b
   (5)  ----------
         +-------+
        \|a x + b
                                                     Type: Expression Integer
--R
--R          a x + b
--R   (5)  ----------
--R         +-------+
--R        \|a x + b
--R                                                     Type: Expression Integer
--E
--S 44
t1-target
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
--S 45
t2:=D(bb,x)
 

                2 2             2
               a x  + 2a b x + b
   (7)  -------------------------------
         +----------------------------+
         | 3 3     2   2       2     3
        \|a x  + 3a b x  + 3a b x + b
                                                     Type: Expression Integer
--R
--R                2 2             2
--R               a x  + 2a b x + b
--R   (7)  -------------------------------
--R         +----------------------------+
--R         | 3 3     2   2       2     3
--R        \|a x  + 3a b x  + 3a b x + b
--R                                                     Type: Expression Integer
--E
--S 46
nn:=(a*x+b)^2
 

         2 2             2
   (8)  a x  + 2a b x + b
                                                     Type: Polynomial Integer
--R
--R         2 2             2
--R   (8)  a x  + 2a b x + b
--R                                                     Type: Polynomial Integer
--E
--S 47
mm:=(a*x+b)^3
 

         3 3     2   2       2     3
   (9)  a x  + 3a b x  + 3a b x + b
                                                     Type: Polynomial Integer
--R
--R         3 3     2   2       2     3
--R   (9)  a x  + 3a b x  + 3a b x + b
--R                                                     Type: Polynomial Integer
--E
--S 48     14:89 Schaums and Axiom differ by a constant
result=nn/sqrt(mm)
 

                         2 2             2
                        a x  + 2a b x + b
   (10)  result= -------------------------------
                  +----------------------------+
                  | 3 3     2   2       2     3
                 \|a x  + 3a b x  + 3a b x + b
                                            Type: Equation Expression Integer
--R
--R                         2 2             2
--R                        a x  + 2a b x + b
--R   (10)  result= -------------------------------
--R                  +----------------------------+
--R                  | 3 3     2   2       2     3
--R                 \|a x  + 3a b x  + 3a b x + b
--R                                            Type: Equation Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(x*sqrt(a*x+b),x)
 

           2 2              2  +-------+
        (6a x  + 2a b x - 4b )\|a x + b
   (1)  --------------------------------
                         2
                      15a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2              2  +-------+
--R        (6a x  + 2a b x - 4b )\|a x + b
--R   (1)  --------------------------------
--R                         2
--R                      15a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50
bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3)
 

                    +----------------------------+
                    | 3 3     2   2       2     3
        (6a x - 4b)\|a x  + 3a b x  + 3a b x + b
   (2)  ------------------------------------------
                              2
                           15a
                                                     Type: Expression Integer
--R 
--R
--R                    +----------------------------+
--R                    | 3 3     2   2       2     3
--R        (6a x - 4b)\|a x  + 3a b x  + 3a b x + b
--R   (2)  ------------------------------------------
--R                              2
--R                           15a
--R                                                     Type: Expression Integer
--E

--S 51
cc:=aa-bb
 

   (3)
                     +----------------------------+
                     | 3 3     2   2       2     3
       (- 6a x + 4b)\|a x  + 3a b x  + 3a b x + b
     + 
          2 2              2  +-------+
       (6a x  + 2a b x - 4b )\|a x + b
  /
        2
     15a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     +----------------------------+
--R                     | 3 3     2   2       2     3
--R       (- 6a x + 4b)\|a x  + 3a b x  + 3a b x + b
--R     + 
--R          2 2              2  +-------+
--R       (6a x  + 2a b x - 4b )\|a x + b
--R  /
--R        2
--R     15a
--R                                                     Type: Expression Integer
--E

--S 52     14:90 Schaums and Axiom agree
dd:=rootSimp cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 53
aa:=integrate(x^2*sqrt(a*x+b),x)
 

            3 3     2   2       2       3  +-------+
        (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
   (1)  --------------------------------------------
                                3
                            105a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            3 3     2   2       2       3  +-------+
--R        (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
--R   (1)  --------------------------------------------
--R                                3
--R                            105a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54
bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^3)*sqrt((a+b*x)^3)
 

                                  +----------------------------+
            2 2                2  | 3 3       2 2     2       3
        (30a x  - 24a b x + 16b )\|b x  + 3a b x  + 3a b x + a
   (2)  --------------------------------------------------------
                                      3
                                  105a
                                                     Type: Expression Integer
--R 
--R
--R                                  +----------------------------+
--R            2 2                2  | 3 3       2 2     2       3
--R        (30a x  - 24a b x + 16b )\|b x  + 3a b x  + 3a b x + a
--R   (2)  --------------------------------------------------------
--R                                      3
--R                                  105a
--R                                                     Type: Expression Integer
--E

--S 55     14:91 Axiom cannot simplify this expression. Schaums typo?
cc:=aa-bb
 

   (3)
                                   +----------------------------+
             2 2                2  | 3 3       2 2     2       3
       (- 30a x  + 24a b x - 16b )\|b x  + 3a b x  + 3a b x + a
     + 
           3 3     2   2       2       3  +-------+
       (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
  /
         3
     105a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                   +----------------------------+
--R             2 2                2  | 3 3       2 2     2       3
--R       (- 30a x  + 24a b x - 16b )\|b x  + 3a b x  + 3a b x + a
--R     + 
--R           3 3     2   2       2       3  +-------+
--R       (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
--R  /
--R         3
--R     105a
--R                                                     Type: Expression Integer
--E

--S 56
factor numer aa
 

                      2 2               2  +-------+
   (4)  2(a x + b)(15a x  - 12a b x + 8b )\|a x + b
Type: Factored SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R
--R                      2 2               2  +-------+
--R   (4)  2(a x + b)(15a x  - 12a b x + 8b )\|a x + b
--RType: Factored SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 57
aa:=integrate(sqrt(a*x+b)/x,x)
 

   (1)
                +-+ +-------+
     +-+    - 2\|b \|a x + b  + a x + 2b      +-------+
   [\|b log(----------------------------) + 2\|a x + b ,
                          x
                   +-------+
        +---+     \|a x + b       +-------+
    - 2\|- b atan(----------) + 2\|a x + b ]
                     +---+
                    \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                +-+ +-------+
--R     +-+    - 2\|b \|a x + b  + a x + 2b      +-------+
--R   [\|b log(----------------------------) + 2\|a x + b ,
--R                          x
--R                   +-------+
--R        +---+     \|a x + b       +-------+
--R    - 2\|- b atan(----------) + 2\|a x + b ]
--R                     +---+
--R                    \|- b
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 58
dd:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (2)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (2)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 59
bb1:=2*sqrt(a*x+b)+b*dd.1
 

                   +-------+              +-+
              - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
        b log(-------------------------------) + 2\|b \|a x + b
                             x
   (3)  --------------------------------------------------------
                                   +-+
                                  \|b
                                                     Type: Expression Integer
--R 
--R
--R                   +-------+              +-+
--R              - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R        b log(-------------------------------) + 2\|b \|a x + b
--R                             x
--R   (3)  --------------------------------------------------------
--R                                   +-+
--R                                  \|b
--R                                                     Type: Expression Integer
--E

--S 60
bb2:=2*sqrt(a*x+b)+b*dd.2
 

                   +---+ +-------+
                  \|- b \|a x + b       +---+ +-------+
        - 2b atan(----------------) + 2\|- b \|a x + b
                          b
   (4)  -----------------------------------------------
                              +---+
                             \|- b
                                                     Type: Expression Integer
--R 
--R
--R                   +---+ +-------+
--R                  \|- b \|a x + b       +---+ +-------+
--R        - 2b atan(----------------) + 2\|- b \|a x + b
--R                          b
--R   (4)  -----------------------------------------------
--R                              +---+
--R                             \|- b
--R                                                     Type: Expression Integer
--E

--S 61
cc11:=bb1-aa.1
 

   (5)
              +-------+              +-+              +-+ +-------+
         - 2b\|a x + b  + (a x + 2b)\|b           - 2\|b \|a x + b  + a x + 2b
   b log(-------------------------------) - b log(----------------------------)
                        x                                       x
   ----------------------------------------------------------------------------
                                        +-+
                                       \|b
                                                     Type: Expression Integer
--R 
--R
--R   (5)
--R              +-------+              +-+              +-+ +-------+
--R         - 2b\|a x + b  + (a x + 2b)\|b           - 2\|b \|a x + b  + a x + 2b
--R   b log(-------------------------------) - b log(----------------------------)
--R                        x                                       x
--R   ----------------------------------------------------------------------------
--R                                        +-+
--R                                       \|b
--R                                                     Type: Expression Integer
--E

--S 62
cc12:=bb1-aa.2
 

                   +-------+              +-+                     +-------+
              - 2b\|a x + b  + (a x + 2b)\|b       +---+ +-+     \|a x + b
        b log(-------------------------------) + 2\|- b \|b atan(----------)
                             x                                      +---+
                                                                   \|- b
   (6)  --------------------------------------------------------------------
                                         +-+
                                        \|b
                                                     Type: Expression Integer
--R 
--R
--R                   +-------+              +-+                     +-------+
--R              - 2b\|a x + b  + (a x + 2b)\|b       +---+ +-+     \|a x + b
--R        b log(-------------------------------) + 2\|- b \|b atan(----------)
--R                             x                                      +---+
--R                                                                   \|- b
--R   (6)  --------------------------------------------------------------------
--R                                         +-+
--R                                        \|b
--R                                                     Type: Expression Integer
--E

--S 63
cc21:=bb2-aa.1
 

   (7)
                       +-+ +-------+                        +---+ +-------+
      +---+ +-+    - 2\|b \|a x + b  + a x + 2b            \|- b \|a x + b
   - \|- b \|b log(----------------------------) - 2b atan(----------------)
                                 x                                 b
   -------------------------------------------------------------------------
                                      +---+
                                     \|- b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                       +-+ +-------+                        +---+ +-------+
--R      +---+ +-+    - 2\|b \|a x + b  + a x + 2b            \|- b \|a x + b
--R   - \|- b \|b log(----------------------------) - 2b atan(----------------)
--R                                 x                                 b
--R   -------------------------------------------------------------------------
--R                                      +---+
--R                                     \|- b
--R                                                     Type: Expression Integer
--E

--S 64
cc22:=bb2-aa.2
 

                   +---+ +-------+             +-------+
                  \|- b \|a x + b             \|a x + b
        - 2b atan(----------------) - 2b atan(----------)
                          b                      +---+
                                                \|- b
   (8)  -------------------------------------------------
                               +---+
                              \|- b
                                                     Type: Expression Integer
--R 
--R
--R                   +---+ +-------+             +-------+
--R                  \|- b \|a x + b             \|a x + b
--R        - 2b atan(----------------) - 2b atan(----------)
--R                          b                      +---+
--R                                                \|- b
--R   (8)  -------------------------------------------------
--R                               +---+
--R                              \|- b
--R                                                     Type: Expression Integer
--E

--S 65     14:92 Schaums and Axiom agree
dd22:=ratDenom cc22
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 65
aa:=integrate(sqrt(a*x+b)/x^2,x)
 

   (1)
                 +-------+              +-+
            - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
    a x log(-------------------------------) - 2\|b \|a x + b
                           x
   [----------------------------------------------------------,
                                 +-+
                              2x\|b
                +---+ +-------+
               \|- b \|a x + b      +---+ +-------+
    - a x atan(----------------) - \|- b \|a x + b
                       b
    -----------------------------------------------]
                          +---+
                        x\|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                 +-------+              +-+
--R            - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R    a x log(-------------------------------) - 2\|b \|a x + b
--R                           x
--R   [----------------------------------------------------------,
--R                                 +-+
--R                              2x\|b
--R                +---+ +-------+
--R               \|- b \|a x + b      +---+ +-------+
--R    - a x atan(----------------) - \|- b \|a x + b
--R                       b
--R    -----------------------------------------------]
--R                          +---+
--R                        x\|- b
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 66
dd:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (2)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (2)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 67
bb1:=-sqrt(a*x+b)/x+a/2*dd.1
 

                     +-------+              +-+
                - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
        a x log(-------------------------------) - 2\|b \|a x + b
                               x
   (3)  ----------------------------------------------------------
                                     +-+
                                  2x\|b
                                                     Type: Expression Integer
--R 
--R
--R                     +-------+              +-+
--R                - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R        a x log(-------------------------------) - 2\|b \|a x + b
--R                               x
--R   (3)  ----------------------------------------------------------
--R                                     +-+
--R                                  2x\|b
--R                                                     Type: Expression Integer
--E

--S 68
bb2:=-sqrt(a*x+b)/x+a/2*dd.2
 

                    +---+ +-------+
                   \|- b \|a x + b      +---+ +-------+
        - a x atan(----------------) - \|- b \|a x + b
                           b
   (4)  -----------------------------------------------
                              +---+
                            x\|- b
                                                     Type: Expression Integer
--R 
--R
--R                    +---+ +-------+
--R                   \|- b \|a x + b      +---+ +-------+
--R        - a x atan(----------------) - \|- b \|a x + b
--R                           b
--R   (4)  -----------------------------------------------
--R                              +---+
--R                            x\|- b
--R                                                     Type: Expression Integer
--E

--S 69
cc11:=bb1-aa.1
 

   (5)  0
                                                     Type: Expression Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

--S 70
cc21:=bb-aa.1
 

   (6)
                  +-------+              +-+
             - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+         +-+
   - a x log(-------------------------------) + 2\|b \|a x + b  + 2bb x\|b
                            x
   ------------------------------------------------------------------------
                                       +-+
                                    2x\|b
                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                  +-------+              +-+
--R             - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+         +-+
--R   - a x log(-------------------------------) + 2\|b \|a x + b  + 2bb x\|b
--R                            x
--R   ------------------------------------------------------------------------
--R                                       +-+
--R                                    2x\|b
--R                                                     Type: Expression Integer
--E

--S 71
cc12:=bb1-aa.2
 

   (7)
                   +-------+              +-+                +---+ +-------+
     +---+    - 2b\|a x + b  + (a x + 2b)\|b        +-+     \|- b \|a x + b
   a\|- b log(-------------------------------) + 2a\|b atan(----------------)
                             x                                      b
   --------------------------------------------------------------------------
                                     +---+ +-+
                                   2\|- b \|b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                   +-------+              +-+                +---+ +-------+
--R     +---+    - 2b\|a x + b  + (a x + 2b)\|b        +-+     \|- b \|a x + b
--R   a\|- b log(-------------------------------) + 2a\|b atan(----------------)
--R                             x                                      b
--R   --------------------------------------------------------------------------
--R                                     +---+ +-+
--R                                   2\|- b \|b
--R                                                     Type: Expression Integer
--E

--S 72     14:93 Schaums and Axiom agree
cc22:=bb2-aa.2
 

   (8)  0
                                                     Type: Expression Integer
--R 
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 73     14:94 Axiom cannot do this integral
aa:=integrate(x^m/sqrt(a*x+b),x)
 

           x       m
         ++      %L
   (1)   |   ----------- d%L
        ++    +--------+
             \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %L
--I   (1)   |   ----------- d%L
--R        ++    +--------+
--I             \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 74     14:95 Axiom cannot do this integral
aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++     m +--------+
             %L \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++     m +--------+
--I             %L \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 75     14:96 Axiom cannot do this integral
aa:=integrate(x^m*sqrt(a*x+b),x)
 

           x
         ++    m +--------+
   (1)   |   %L \|b + %L a d%L
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    m +--------+
--I   (1)   |   %L \|b + %L a d%L
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 76     14:97 Axiom cannot do this integral
aa:=integrate(sqrt(a*x+b)/x^m,x)
 

           x  +--------+
         ++  \|b + %L a
   (1)   |   ----------- d%L
        ++         m
                 %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +--------+
--I         ++  \|b + %L a
--I   (1)   |   ----------- d%L
--R        ++         m
--I                 %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 77     14:98 Axiom cannot do this integral
aa:=integrate(sqrt(a*x+b)/x^m,x)
 

           x  +--------+
         ++  \|b + %L a
   (1)   |   ----------- d%L
        ++         m
                 %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +--------+
--I         ++  \|b + %L a
--I   (1)   |   ----------- d%L
--R        ++         m
--I                 %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 78
aa:=integrate((a*x+b)^(m/2),x)
 

                     m log(a x + b)
                     --------------
                            2
        (2a x + 2b)%e
   (1)  ---------------------------
                  a m + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     m log(a x + b)
--R                     --------------
--R                            2
--R        (2a x + 2b)%e
--R   (1)  ---------------------------
--R                  a m + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 79
bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
 

                  m + 2
                  -----
                    2
        2(a x + b)
   (2)  ---------------
            a m + 2a
                                                     Type: Expression Integer
--R 
--R
--R                  m + 2
--R                  -----
--R                    2
--R        2(a x + b)
--R   (2)  ---------------
--R            a m + 2a
--R                                                     Type: Expression Integer
--E

--S 80
cc:=aa-bb
 

                     m log(a x + b)             m + 2
                     --------------             -----
                            2                     2
        (2a x + 2b)%e               - 2(a x + b)
   (3)  ---------------------------------------------
                           a m + 2a
                                                     Type: Expression Integer
--R 
--R
--R                     m log(a x + b)             m + 2
--R                     --------------             -----
--R                            2                     2
--R        (2a x + 2b)%e               - 2(a x + b)
--R   (3)  ---------------------------------------------
--R                           a m + 2a
--R                                                     Type: Expression Integer
--E

--S 81
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 82
dd:=explog cc
 

                    m + 2                       m
                    -----                       -
                      2                         2
        - 2(a x + b)      + (2a x + 2b)(a x + b)
   (5)  -----------------------------------------
                         a m + 2a
                                                     Type: Expression Integer
--R
--R                    m + 2                       m
--R                    -----                       -
--R                      2                         2
--R        - 2(a x + b)      + (2a x + 2b)(a x + b)
--R   (5)  -----------------------------------------
--R                         a m + 2a
--R                                                     Type: Expression Integer
--E

--S 83     14:99 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 84
aa:=integrate(x*(a*x+b)^(m/2),x)
 

                                           m log(a x + b)
                                           --------------
            2      2  2                2          2
        ((2a m + 4a )x  + 2a b m x - 4b )%e
   (1)  -------------------------------------------------
                         2 2     2      2
                        a m  + 6a m + 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                           m log(a x + b)
--R                                           --------------
--R            2      2  2                2          2
--R        ((2a m + 4a )x  + 2a b m x - 4b )%e
--R   (1)  -------------------------------------------------
--R                         2 2     2      2
--R                        a m  + 6a m + 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 85
bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2))
 

                         m + 4                         m + 2
                         -----                         -----
                           2                             2
        (2m + 4)(a x + b)      + (- 2b m - 8b)(a x + b)
   (2)  ----------------------------------------------------
                           2 2     2      2
                          a m  + 6a m + 8a
                                                     Type: Expression Integer
--R 
--R
--R                         m + 4                         m + 2
--R                         -----                         -----
--R                           2                             2
--R        (2m + 4)(a x + b)      + (- 2b m - 8b)(a x + b)
--R   (2)  ----------------------------------------------------
--R                           2 2     2      2
--R                          a m  + 6a m + 8a
--R                                                     Type: Expression Integer
--E

--S 86
cc:=aa-bb
 

   (3)
                                          m log(a x + b)
                                          --------------
           2      2  2                2          2
       ((2a m + 4a )x  + 2a b m x - 4b )%e
     + 
                          m + 4                       m + 2
                          -----                       -----
                            2                           2
       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
  /
      2 2     2      2
     a m  + 6a m + 8a
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                                          m log(a x + b)
--R                                          --------------
--R           2      2  2                2          2
--R       ((2a m + 4a )x  + 2a b m x - 4b )%e
--R     + 
--R                          m + 4                       m + 2
--R                          -----                       -----
--R                            2                           2
--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
--R  /
--R      2 2     2      2
--R     a m  + 6a m + 8a
--R                                                     Type: Expression Integer
--E

--S 87
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 88
dd:=explog cc
 

   (5)
                          m + 4                       m + 2
                          -----                       -----
                            2                           2
       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
     + 
                                                 m
                                                 -
           2      2  2                2          2
       ((2a m + 4a )x  + 2a b m x - 4b )(a x + b)
  /
      2 2     2      2
     a m  + 6a m + 8a
                                                     Type: Expression Integer
--R
--R   (5)
--R                          m + 4                       m + 2
--R                          -----                       -----
--R                            2                           2
--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
--R     + 
--R                                                 m
--R                                                 -
--R           2      2  2                2          2
--R       ((2a m + 4a )x  + 2a b m x - 4b )(a x + b)
--R  /
--R      2 2     2      2
--R     a m  + 6a m + 8a
--R                                                     Type: Expression Integer
--E

--S 89     14:100 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 90
aa:=integrate(x^2*(a*x+b)^(m/2),x)
 

   (1)
           3 2      3       3  3      2   2     2     2       2         3
       ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
    *
         m log(a x + b)
         --------------
                2
       %e
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R           3 2      3       3  3      2   2     2     2       2         3
--R       ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
--R    *
--R         m log(a x + b)
--R         --------------
--R                2
--R       %e
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91
bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
      (4*b*(a*x+b)^((m+4)/2))/(a^3*(m+4))+_
        (2*b^2*(a*x+b)^((m+2)/2))/(a^3*(m+2))
 

   (2)
                                m + 6                                   m + 4
                                -----                                   -----
          2                       2            2                          2
       (2m  + 12m + 16)(a x + b)      + (- 4b m  - 32b m - 48b)(a x + b)
     + 
                                      m + 2
                                      -----
          2 2      2       2            2
       (2b m  + 20b m + 48b )(a x + b)
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R                                m + 6                                   m + 4
--R                                -----                                   -----
--R          2                       2            2                          2
--R       (2m  + 12m + 16)(a x + b)      + (- 4b m  - 32b m - 48b)(a x + b)
--R     + 
--R                                      m + 2
--R                                      -----
--R          2 2      2       2            2
--R       (2b m  + 20b m + 48b )(a x + b)
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                                     Type: Expression Integer
--E

--S 92
cc:=aa-bb
 

   (3)
             3 2      3       3  3      2   2     2     2       2         3
         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
      *
           m log(a x + b)
           --------------
                  2
         %e
     + 
                                  m + 6                                 m + 4
                                  -----                                 -----
            2                       2          2                          2
       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
     + 
                                        m + 2
                                        -----
            2 2      2       2            2
       (- 2b m  - 20b m - 48b )(a x + b)
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R             3 2      3       3  3      2   2     2     2       2         3
--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
--R      *
--R           m log(a x + b)
--R           --------------
--R                  2
--R         %e
--R     + 
--R                                  m + 6                                 m + 4
--R                                  -----                                 -----
--R            2                       2          2                          2
--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
--R     + 
--R                                        m + 2
--R                                        -----
--R            2 2      2       2            2
--R       (- 2b m  - 20b m - 48b )(a x + b)
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                                     Type: Expression Integer
--E

--S 93
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 94
dd:=explog cc
 

   (5)
                                  m + 6                                 m + 4
                                  -----                                 -----
            2                       2          2                          2
       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
     + 
                                        m + 2
                                        -----
            2 2      2       2            2
       (- 2b m  - 20b m - 48b )(a x + b)
     + 
             3 2      3       3  3      2   2     2     2       2         3
         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
      *
                  m
                  -
                  2
         (a x + b)
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                  m + 6                                 m + 4
--R                                  -----                                 -----
--R            2                       2          2                          2
--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
--R     + 
--R                                        m + 2
--R                                        -----
--R            2 2      2       2            2
--R       (- 2b m  - 20b m - 48b )(a x + b)
--R     + 
--R             3 2      3       3  3      2   2     2     2       2         3
--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
--R      *
--R                  m
--R                  -
--R                  2
--R         (a x + b)
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                                     Type: Expression Integer
--E

--S 95     14:101 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 96     14:102 Axiom cannot do this integral
aa:=integrate((a*x+b)^(m/2)/x,x)
 

                       m
                       -
           x           2
         ++  (b + %L a)
   (1)   |   ----------- d%L
        ++        %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       m
--R                       -
--R           x           2
--I         ++  (b + %L a)
--I   (1)   |   ----------- d%L
--I        ++        %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 97     14:103 Axiom cannot do this integral
aa:=integrate((a*x+b)^(m/2)/x^2,x)
 

                       m
                       -
           x           2
         ++  (b + %L a)
   (1)   |   ----------- d%L
        ++         2
                 %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       m
--R                       -
--R           x           2
--I         ++  (b + %L a)
--I   (1)   |   ----------- d%L
--R        ++         2
--I                 %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 98     14:104 Axiom cannot do this integral
aa:=integrate(1/(x*(a*x+b)^(m/2)),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++                m
                          -
                          2
             %L (b + %L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++                m
--R                          -
--R                          2
--I             %L (b + %L a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to exprpoly.output (2009/2/17, 17:45:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 20
a := sin(i)*x**2 - y*x*sin(j)
 

                        2
   (1)  - x y sin(j) + x sin(i)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (1)  - x y sin(j) + x sin(i)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 20
a :: DMP([x,y], EXPR INT)
 

               2
   (2)  sin(i)x  - sin(j)x y
            Type: DistributedMultivariatePolynomial([x,y],Expression Integer)
--R 
--R
--R               2
--R   (2)  sin(i)x  - sin(j)x y
--R            Type: DistributedMultivariatePolynomial([x,y],Expression Integer)
--E 2

--S 3 of 20
leadingCoefficient %
 

   (3)  sin(i)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(i)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 20
a :: HDMP([x,y], EXPR INT)
 

               2
   (4)  sin(i)x  - sin(j)x y
 Type: HomogeneousDistributedMultivariatePolynomial([x,y],Expression Integer)
--R 
--R
--R               2
--R   (4)  sin(i)x  - sin(j)x y
--R Type: HomogeneousDistributedMultivariatePolynomial([x,y],Expression Integer)
--E 4

--S 5 of 20
a :: MPOLY([x,y], EXPR INT)
 

               2
   (5)  sin(i)x  - sin(j)y x
                       Type: MultivariatePolynomial([x,y],Expression Integer)
--R 
--R
--R               2
--R   (5)  sin(i)x  - sin(j)y x
--R                       Type: MultivariatePolynomial([x,y],Expression Integer)
--E 5

--S 6 of 20
a :: MPOLY([y,x], EXPR INT)
 

                             2
   (6)  - sin(j)x y + sin(i)x
                       Type: MultivariatePolynomial([y,x],Expression Integer)
--R 
--R
--R                             2
--R   (6)  - sin(j)x y + sin(i)x
--R                       Type: MultivariatePolynomial([y,x],Expression Integer)
--E 6

--S 7 of 20
% :: EXPR INT
 

                        2
   (7)  - x y sin(j) + x sin(i)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (7)  - x y sin(j) + x sin(i)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 20
a - %
 

   (8)  0
                                                     Type: Expression Integer
--R 
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E 8

--S 9 of 20
a :: UP(x, EXPR INT)
 

               2
   (9)  sin(i)x  - y sin(j)x
                             Type: UnivariatePolynomial(x,Expression Integer)
--R 
--R
--R               2
--R   (9)  sin(i)x  - y sin(j)x
--R                             Type: UnivariatePolynomial(x,Expression Integer)
--E 9

--S 10 of 20
a :: UP(y, EXPR INT)
 

                        2
   (10)  - x sin(j)y + x sin(i)
                             Type: UnivariatePolynomial(y,Expression Integer)
--R 
--R
--R                        2
--R   (10)  - x sin(j)y + x sin(i)
--R                             Type: UnivariatePolynomial(y,Expression Integer)
--E 10

--S 11 of 20
a :: UP(y, UP(x, EXPR INT))
 

                              2
   (11)  - sin(j)x y + sin(i)x
     Type: UnivariatePolynomial(y,UnivariatePolynomial(x,Expression Integer))
--R 
--R
--R                              2
--R   (11)  - sin(j)x y + sin(i)x
--R     Type: UnivariatePolynomial(y,UnivariatePolynomial(x,Expression Integer))
--E 11

--S 12 of 20
% :: EXPR INT
 

                         2
   (12)  - x y sin(j) + x sin(i)
                                                     Type: Expression Integer
--R 
--R
--R                         2
--R   (12)  - x y sin(j) + x sin(i)
--R                                                     Type: Expression Integer
--E 12

--S 13 of 20
a - %
 

   (13)  0
                                                     Type: Expression Integer
--R 
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 20
b : EXPR INT := (x - 2*y + 3*z)**3
 

   (14)
      3                 2       2             2       3        2     2     3
   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
                                                     Type: Expression Integer
--R 
--R
--R   (14)
--R      3                 2       2             2       3        2     2     3
--R   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
--R                                                     Type: Expression Integer
--E 14

--S 15 of 20
b :: DMP([x,y,z], Integer)
 

   (15)
    3     2      2         2                  2     3      2         2      3
   x  - 6x y + 9x z + 12x y  - 36x y z + 27x z  - 8y  + 36y z - 54y z  + 27z
                     Type: DistributedMultivariatePolynomial([x,y,z],Integer)
--R 
--R
--R   (15)
--R    3     2      2         2                  2     3      2         2      3
--R   x  - 6x y + 9x z + 12x y  - 36x y z + 27x z  - 8y  + 36y z - 54y z  + 27z
--R                     Type: DistributedMultivariatePolynomial([x,y,z],Integer)
--E 15

--S 16 of 20
b :: HDMP([y,x,z], Integer)
 

   (16)
       3      2        2    3      2                2         2        2      3
   - 8y  + 12y x - 6y x  + x  + 36y z - 36y x z + 9x z - 54y z  + 27x z  + 27z
          Type: HomogeneousDistributedMultivariatePolynomial([y,x,z],Integer)
--R 
--R
--R   (16)
--R       3      2        2    3      2                2         2        2      3
--R   - 8y  + 12y x - 6y x  + x  + 36y z - 36y x z + 9x z - 54y z  + 27x z  + 27z
--R          Type: HomogeneousDistributedMultivariatePolynomial([y,x,z],Integer)
--E 16

--S 17 of 20
b - (% :: EXPR INT)
 

   (17)  0
                                                     Type: Expression Integer
--R 
--R
--R   (17)  0
--R                                                     Type: Expression Integer
--E 17

--S 18 of 20
b :: MPOLY([z,y,x], Integer)
 

   (18)
      3                 2       2             2       3        2     2     3
   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
                                Type: MultivariatePolynomial([z,y,x],Integer)
--R 
--R
--R   (18)
--R      3                 2       2             2       3        2     2     3
--R   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
--R                                Type: MultivariatePolynomial([z,y,x],Integer)
--E 18

--S 19 of 20
b :: UP(y, HDMP([x,z], Integer))
 

   (19)
       3               2        2              2      3     2         2      3
   - 8y  + (12x + 36z)y  + (- 6x  - 36x z - 54z )y + x  + 9x z + 27x z  + 27z
Type: UnivariatePolynomial(y,HomogeneousDistributedMultivariatePolynomial([x,z],Integer))
--R 
--R
--R   (19)
--R       3               2        2              2      3     2         2      3
--R   - 8y  + (12x + 36z)y  + (- 6x  - 36x z - 54z )y + x  + 9x z + 27x z  + 27z
--RType: UnivariatePolynomial(y,HomogeneousDistributedMultivariatePolynomial([x,z],Integer))
--E 19

--S 20 of 20
b - (% :: EXPR INT)
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 20
)spool 
 
Starts dribbling to gstbl.output (2009/2/17, 17:46:26).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1
patrons: GeneralSparseTable(String, Integer, KeyedAccessFile(Integer), 0) := table() ;
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "kaf1404.sdata"

(1) -> Starts dribbling to sae.output (2009/2/17, 17:57:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
pol1:=x^2+1
 

         2
   (1)  x  + 1
                                                     Type: Polynomial Integer
--R
--R         2
--R   (1)  x  + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 6
pol2:=z^3-2
 

         3
   (2)  z  - 2
                                                     Type: Polynomial Integer
--R
--R         3
--R   (2)  z  - 2
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 6
primrec:=primitiveElement([pol1,pol2],[x,z])$PrimitiveElement(FRAC(INT))
 

   (3)
   [coef= [- 4,- 2],

     poly =
            3   5     9    4    20  3    39   2   1929     364
       [- ---- ?  - ----- ?  - --- ?  - ---- ?  - ---- ? + ---,
          7976      63808      997      1994      3988     997
          3   5     9    4    40  3    39  2   466     728
        ---- ?  + ----- ?  + --- ?  + --- ?  + --- ? - ---]
        3988      31904      997      997      997     997
     ,
           6      4      3       2
    prim= ?  + 48?  + 32?  + 768?  - 1536? + 4352]
Type: Record(coef: List Integer,poly: List SparseUnivariatePolynomial Fraction Integer,prim: SparseUnivariatePolynomial Fraction Integer)
--I
--I   (3)
--I   [coef= [- 3,- 1],
--I
--I     poly =
--I            2   5     1   4    20  3    13   2   2431      91
--I       [- ---- ?  - ---- ?  - --- ?  - ---- ?  - ---- ? + ---,
--I          1293      7758      431      1293      3879     862
--I         2   5     1   4    60  3    13  2   1138     273
--I        --- ?  + ---- ?  + --- ?  + --- ?  + ---- ? - ---]
--I        431      2586      431      431      1293     862
--I     ,
--I           6      4     3       2
--I    prim= ?  + 27?  + 4?  + 243?  - 108? + 733]
--IType: Record(coef: List Integer,poly: List SparseUnivariatePolynomial Fraction Integer,prim: SparseUnivariatePolynomial Fraction Integer)
--E 3

--S 4 of 6
Ae:=SAE(FRAC(INT),SparseUnivariatePolynomial(FRAC(INT)),primrec.prim)
 

   (4)
  SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction
   Integer,?**6+48*?**4+32*?**3+768*?*?+(-1536*?)+4352)
                                                                 Type: Domain
--I
--I   (4)
--I  SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction
--I   Integer,?**6+27*?**4+4*?**3+243*?*?+(-108*?)+733)
--I                                                                 Type: Domain
--E 4

--S 5 of 6
(primrec.poly.1::Ae)^2
 

   (5)  - 1
Type: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+48*?**4+32*?**3+768*?*?+(-1536*?)+4352)
--R
--R   (5)  - 1
--IType: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+27*?**4+4*?**3+243*?*?+(-108*?)+733)
--E 5

--S 6 of 6
(primrec.poly.2::Ae)^3
 

   (6)  2
Type: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+48*?**4+32*?**3+768*?*?+(-1536*?)+4352)
--R
--R   (6)  2
--IType: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+27*?**4+4*?**3+243*?*?+(-108*?)+733)
--E 6

)spool 
 
Starts dribbling to hexadec.output (2009/2/17, 17:46:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 7
r := hex(22/7)
 

          ___
   (1)  3.249
                                                   Type: HexadecimalExpansion
--R 
--R
--R          ___
--R   (1)  3.249
--R                                                   Type: HexadecimalExpansion
--E 1

--S 2 of 7
r + hex(6/7)
 

   (2)  4
                                                   Type: HexadecimalExpansion
--R 
--R
--R   (2)  4
--R                                                   Type: HexadecimalExpansion
--E 2

--S 3 of 7
[hex(1/i) for i in 350..354] 
 

   (3)
       _______________    _________      _____    ______________________
   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
       _____________________________
    0.00B92143FA36F5E02E4850FE8DBD78]
                                              Type: List HexadecimalExpansion
--R 
--R
--R   (3)
--R       _______________    _________      _____    ______________________
--R   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
--R       _____________________________
--R    0.00B92143FA36F5E02E4850FE8DBD78]
--R                                              Type: List HexadecimalExpansion
--E 3

--S 4 of 7
hex(1/1007) 
 

   (4)
   0.
     OVERBAR
        0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
          DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
                                                   Type: HexadecimalExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
--R          DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
--R                                                   Type: HexadecimalExpansion
--E 4

--S 5 of 7
p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)
 

            2     _      ___
   (5)  0.4x  + 0.Ax + 0.71C
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R            2     _      ___
--R   (5)  0.4x  + 0.Ax + 0.71C
--R                                        Type: Polynomial HexadecimalExpansion
--E 5

--S 6 of 7
q := D(p, x)
 

                 _
   (6)  0.8x + 0.A
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R                 _
--R   (6)  0.8x + 0.A
--R                                        Type: Polynomial HexadecimalExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              _
   (7)  x + 1.5
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R              _
--R   (7)  x + 1.5
--R                                        Type: Polynomial HexadecimalExpansion
--E 7
)spool 
 
Starts dribbling to nsfip.output (2009/2/17, 17:55:38).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.


--S 1 of 141
outputGeneral 4
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1


--S 2 of 141 used to work?
nagExpInt(2) :: Float
 
   There are no library operations named nagExpInt 
      Use HyperDoc Browse or issue
                             )what op nagExpInt
      to learn if there is any operation containing " nagExpInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagExpInt with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagExpInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagExpInt
--R      to learn if there is any operation containing " nagExpInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagExpInt with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 2
--       0.0489

--S 3 of 141
nagExpInt(-1) :: Float
 
   There are no library operations named nagExpInt 
      Use HyperDoc Browse or issue
                             )what op nagExpInt
      to learn if there is any operation containing " nagExpInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagExpInt with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagExpInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagExpInt
--R      to learn if there is any operation containing " nagExpInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagExpInt with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 3
--
-- ** ABNORMAL EXIT from NAG Library routine S13AAF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S13AAF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 4  of 141 used to work?
nagSinInt(0) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4
--       0.0

--S 5 of 141 used to work?
nagSinInt(0.2) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5
--       0.1996

--S 6 of 141 used to work?
nagSinInt(0.4) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6
--       0.3965

--S 7 of 141 used to work?
nagSinInt(0.6) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 7
--       0.5881

--S 8 of 141 used to work?
nagSinInt(0.8) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 8
--       0.7721

--S 9 of 141 used to work?
nagSinInt(1) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9
--       0.9461


--S 10 of 141 used to work?
nagCosInt(0.2) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 10
--       - 1.042

--S 11 of 141 used to work?
nagCosInt(0.4) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11
--       - 0.3788

--S 12 of 141
nagCosInt(0.6) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12
--       - 0.02227

--S 13 of 141
nagCosInt(0.8) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 13
--       0.1983

--S 14 of 141
nagCosInt(1) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 14
--       0.3374


--S 15 of 141
nagIncompleteGammaP(2,3) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15
--       0.8009

--S 16 of 141
nagIncompleteGammaP(7,1) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16
--       0.00008324

--S 17 of 141
nagIncompleteGammaP(0.5,99) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       1.0

--S 18 of 141
nagIncompleteGammaP(20,21) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18
--       0.6157

--S 19 of 141
nagIncompleteGammaP(21,20) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 19
--       0.4409


--S 20 of 141
nagIncompleteGammaP(7,1,0.1) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
--       0.00008313


--S 21 of 141
nagIncompleteGammaQ(2,3) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21
--       0.1991

--S 22 of 141
nagIncompleteGammaQ(7,1) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 22
--       0.9999

--S 23 of 141
nagIncompleteGammaQ(0.5,99) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23
--       0.5705 E -44

--S 24 of 141
nagIncompleteGammaQ(20,21) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24
--       0.3843

--S 25 of 141
nagIncompleteGammaQ(21,20) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25
--       0.5591

--S 26 of 141
nagIncompleteGammaQ(25,14) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 26
--       0.995


--S 27 of 141
nagIncompleteGammaQ(25,14,0.1) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 27
--       0.9953


--S 28 of 141
nagErf(-6) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 28
--       - 1.0

--S 29 of 141
nagErf(-4.5) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 29
--       - 1.0

--S 30 of 141
nagErf(-1) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 30
--       - 0.8427

--S 31 of 141
nagErf(1) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 31
--       0.8427

--S 32 of 141
nagErf(4.5) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 32
--       1.0

--S 33 of 141
nagErf(6) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 33
--       1.0


--S 34 of 141
nagErfC(-10) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 34
--       2.0

--S 35 of 141
nagErfC(-1) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 35
--       1.843

--S 36 of 141
nagErfC(0) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 36
--       1.0

--S 37 of 141
nagErfC(1) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 37
--       0.1573

--S 38 of 141
nagErfC(15) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 38
--       0.7213 E -99

--S 39 of 141
nagDAiryAi(-10) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 39
--       0.9963

--S 40 of 141
nagDAiryAi(-1) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 40
--       - 0.01016

--S 41 of 141
nagDAiryAi(0) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 41
--       - 0.2588

--S 42 of 141
nagDAiryAi(1) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 42
--       - 0.1591

--S 43 of 141
nagDAiryAi(5) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 43
--       - 0.0002474

--S 44 of 141
nagDAiryAi(10) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 44
--       - 0.3521 E -9

--S 45 of 141
nagDAiryAi(20) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 45
--       - 0.7586 E -26

--S 46 of 141
--RnagDAiryAi(0.3+0.4*%i) :: Complex Float
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 46
--       - 0.2612 + 0.03848 %i

--S 47 of 141
nagDAiryBi(-10) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 47
--       0.1194

--S 48 of 141
nagDAiryBi(-1) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 48
--       0.5924

--S 49 of 141
nagDAiryBi(0) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 49
--       0.4483

--S 50 of 141
nagDAiryBi(1) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 50
--       0.9324

--S 51 of 141
nagDAiryBi(5) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 51
--       1436.0

--S 52 of 141
nagDAiryBi(10) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 52
--       0.1429 E 10

--S 53 of 141
nagDAiryBi(20) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 53
--       0.9382 E 26


--S 54 of 141
nagDAiryBi(0.3+0.4*%i) :: Complex Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                                Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 54
--       0.4093 + 0.07966 %i

--S 55 of 141
nagScaledDAiryAi(0.3+0.4*%i) :: Complex Float
 
   There are no library operations named nagScaledDAiryAi 
      Use HyperDoc Browse or issue
                          )what op nagScaledDAiryAi
      to learn if there is any operation containing " nagScaledDAiryAi 
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledDAiryAi with argument type(s) 
                                Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledDAiryAi 
--R      Use HyperDoc Browse or issue
--R                          )what op nagScaledDAiryAi
--R      to learn if there is any operation containing " nagScaledDAiryAi 
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledDAiryAi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 55
--       - 0.2744 - 0.02356 %i

--S 56 of 141
nagScaledDAiryBi(0.3+0.4*%i) :: Complex Float
 
   There are no library operations named nagScaledDAiryBi 
      Use HyperDoc Browse or issue
                          )what op nagScaledDAiryBi
      to learn if there is any operation containing " nagScaledDAiryBi 
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledDAiryBi with argument type(s) 
                                Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledDAiryBi 
--R      Use HyperDoc Browse or issue
--R                          )what op nagScaledDAiryBi
--R      to learn if there is any operation containing " nagScaledDAiryBi 
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledDAiryBi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 56
--       0.3924 + 0.07638 %i

--S 57 of 141
nagHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH1 
      Use HyperDoc Browse or issue
                            )what op nagHankelH1
      to learn if there is any operation containing " nagHankelH1 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH1 with argument type(s) 
                             NonNegativeInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH1 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH1
--R      to learn if there is any operation containing " nagHankelH1 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH1 with argument type(s) 
--R                             NonNegativeInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 57
--       [0.3466 - 0.5588 %i  - 0.7912 - 0.8178 %i]

--S 58 of 141
nagHankelH1(2.3,2,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH1 
      Use HyperDoc Browse or issue
                            )what op nagHankelH1
      to learn if there is any operation containing " nagHankelH1 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH1 with argument type(s) 
                                    Float
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH1 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH1
--R      to learn if there is any operation containing " nagHankelH1 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH1 with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 58
--       [0.2721 - 0.7398 %i  0.08902 - 1.412 %i]

--S 59 of 141
nagHankelH1(2.12,-1,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH1 
      Use HyperDoc Browse or issue
                            )what op nagHankelH1
      to learn if there is any operation containing " nagHankelH1 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH1 with argument type(s) 
                                    Float
                                   Integer
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH1 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH1
--R      to learn if there is any operation containing " nagHankelH1 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH1 with argument type(s) 
--R                                    Float
--R                                   Integer
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 59
--       [- 0.7722 - 1.693 %i  2.601 + 6.527 %i]


--S 60 of 141
nagHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH2 
      Use HyperDoc Browse or issue
                            )what op nagHankelH2
      to learn if there is any operation containing " nagHankelH2 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH2 with argument type(s) 
                               PositiveInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH2 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH2
--R      to learn if there is any operation containing " nagHankelH2 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH2 with argument type(s) 
--R                               PositiveInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 60
--       [- 1.371 - 1.28 %i  - 1.491 - 5.993 %i]

--S 61 of 141
nagScaledHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagScaledHankelH1 
      Use HyperDoc Browse or issue
                         )what op nagScaledHankelH1
      to learn if there is any operation containing " nagScaledHankelH1
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledHankelH1 with argument type(s) 
                             NonNegativeInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledHankelH1 
--R      Use HyperDoc Browse or issue
--R                         )what op nagScaledHankelH1
--R      to learn if there is any operation containing " nagScaledHankelH1
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledHankelH1 with argument type(s) 
--R                             NonNegativeInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 61
--       [0.2477 - 0.9492 %i  - 1.488 - 0.8166 %i]


--S 62 of 141
nagScaledHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagScaledHankelH2 
      Use HyperDoc Browse or issue
                         )what op nagScaledHankelH2
      to learn if there is any operation containing " nagScaledHankelH2
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledHankelH2 with argument type(s) 
                               PositiveInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledHankelH2 
--R      Use HyperDoc Browse or issue
--R                         )what op nagScaledHankelH2
--R      to learn if there is any operation containing " nagScaledHankelH2
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledHankelH2 with argument type(s) 
--R                               PositiveInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 62
--       [7.05 + 6.052 %i  8.614 + 29.35 %i]


--S 63 of 141
nagKelvinBer(0.1) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 63
--       1.0

--S 64 of 141
nagKelvinBer(1) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 64
--       0.9844

--S 65 of 141
nagKelvinBer(2.5) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 65
--       0.4

--S 66 of 141
nagKelvinBer(5) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 66
--       - 6.23

--S 67 of 141
nagKelvinBer(10) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 67
--       138.8

--S 68 of 141
nagKelvinBer(15) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 68
--       - 2967.0

--S 69 of 141
nagKelvinBer(60) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 69
--
-- ** ABNORMAL EXIT from NAG Library routine S19AAF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19AAF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 70 of 141
nagKelvinBer(-1) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 70
--       0.9844

--S 71 of 141
nagKelvinBei(0.1) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 71
--       0.0025

--S 72 of 141
nagKelvinBei(1) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 72
--       0.2496

--S 73 of 141
nagKelvinBei(2.5) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 73
--       1.457

--S 74 of 141
nagKelvinBei(5) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 74
--       0.116

--S 75 of 141
nagKelvinBei(10) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 75
--       56.37

--S 76 of 141
nagKelvinBei(15) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 76
--       - 2953.0

--S 77 of 141
nagKelvinBei(60) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 77
--
-- ** ABNORMAL EXIT from NAG Library routine S19ABF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ABF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 77a of 141
nagKelvinBei(-1) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 77a
--       0.2496


--S 78 of 141
nagKelvinKer(0) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 78
--
-- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL =     2
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ACF. The error number (IFAIL value) is 2, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 79 of 141
nagKelvinKer(0.1) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 79
--       2.42

--S 80 of 141
nagKelvinKer(1) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 80
--       0.2867

--S 81 of 141
nagKelvinKer(2.5) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 81
--       - 0.06969

--S 82 of 141
nagKelvinKer(5) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 82
--       - 0.01151

--S 83 of 141
nagKelvinKer(10) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 83
--       0.0001295

--S 84 of 141
nagKelvinKer(15) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 84
--       - 0.1514 E -7

--S 85 of 141
nagKelvinKer(1100) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 85
--
-- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ACF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 86 of 141
nagKelvinKer(-1) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 86
--
-- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL =     2
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ACF. The error number (IFAIL value) is 2, please consult the 
--      NAG manual via the Browser for diagnostic information.


--S 87 of 141
nagKelvinKei(0) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 87
--       - 0.7854

--S 88 of 141
nagKelvinKei(0.1) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 88
--       - 0.7769

--S 89 of 141
nagKelvinKei(1) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 89
--       - 0.495

--S 90 of 141
nagKelvinKei(2.5) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 90
--       - 0.1107

--S 91 of 141
nagKelvinKei(5) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 91
--       0.01119

--S 92 of 141
nagKelvinKei(10) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 92
--       - 0.0003075

--S 93 of 141
nagKelvinKei(15) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 93
--       0.000007963

--S 94 of 141
nagKelvinKei(1100) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 94
--
-- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ADF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 95 of 141
nagKelvinKei(-1) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 95
--
-- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL =     2
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ADF. The error number (IFAIL value) is 2, please consult the 
--      NAG manual via the Browser for diagnostic information.


--S 96 of 141
nagFresnelS(0) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 96
--       0.0

--S 97 of 141
nagFresnelS(0.5) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 97
--       0.06473

--S 98 of 141
nagFresnelS(1) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 98
--       0.4383

--S 99 of 141
nagFresnelS(2) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 99
--       0.3434

--S 100 of 141
nagFresnelS(4) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 100
--       0.4205

--S 101 of 141
nagFresnelS(5) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 101
--       0.4992

--S 102 of 141
nagFresnelS(6) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 102
--       0.447

--S 103 of 141
nagFresnelS(8) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 103
--       0.4602

--S 104 of 141
nagFresnelS(10) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 104
--       0.4682

--S 105 of 141
nagFresnelS(-1) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 105
--       - 0.4383

--S 106 of 141
nagFresnelS(1000) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 106
--       0.4997


--S 107 of 141
nagFresnelC(0) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 107
--       0.0

--S 108 of 141
nagFresnelC(0.5) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 108
--       0.4923

--S 109 of 141
nagFresnelC(1) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 109
--       0.7799

--S 110 of 141
nagFresnelC(2) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 110
--       0.4883

--S 111 of 141
nagFresnelC(4) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 111
--       0.4984

--S 112 of 141
nagFresnelC(5) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 112
--       0.5636

--S 113 of 141
nagFresnelC(6) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 113
--       0.4995

--S 114 of 141
nagFresnelC(8) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 114
--       0.4998

--S 115 of 141
nagFresnelC(10) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 115
--       0.4999

--S 116 of 141
nagFresnelC(-1) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 116
--       - 0.7799

--S 117 of 141
nagFresnelC(1000) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 117
--       0.5


--S 118 of 141
nagEllipticIntegralRC(0.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRC 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRC
      to learn if there is any operation containing " 
      nagEllipticIntegralRC " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRC with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRC 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRC
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRC " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRC with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 118
--       1.111

--S 119 of 141
nagEllipticIntegralRC(1,1) :: Float
 
   There are no library operations named nagEllipticIntegralRC 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRC
      to learn if there is any operation containing " 
      nagEllipticIntegralRC " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRC with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRC 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRC
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRC " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRC with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 119
--       1.0

--S 120 of 141
nagEllipticIntegralRC(1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRC 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRC
      to learn if there is any operation containing " 
      nagEllipticIntegralRC " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRC with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRC 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRC
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRC " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRC with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 120
--       0.9312

--S 121 of 141
nagEllipticIntegralRD(0.5,0.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 121
--       1.479

--S 122 of 141
nagEllipticIntegralRD(0.5,1,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 122
--       1.211

--S 123 of 141
nagEllipticIntegralRD(0.5,1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 123
--       1.061

--S 124 of 141
nagEllipticIntegralRD(1,1,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 124
--       1.0

--S 125 of 141
nagEllipticIntegralRD(1,1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 125
--       0.8805

--S 126 of 141
nagEllipticIntegralRD(1.5,1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 126
--       0.7775

--S 127 of 141
nagEllipticIntegralRF(0.5,1,1.5) :: Float
 
   There are no library operations named nagEllipticIntegralRF 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRF
      to learn if there is any operation containing " 
      nagEllipticIntegralRF " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRF with argument type(s) 
                                    Float
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRF 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRF
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRF " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRF with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 127
--       1.028

--S 128 of 141
nagEllipticIntegralRF(1,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRF 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRF
      to learn if there is any operation containing " 
      nagEllipticIntegralRF " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRF with argument type(s) 
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRF 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRF
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRF " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRF with argument type(s) 
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 128
--       0.826

--S 129 of 141
nagEllipticIntegralRF(1.5,2,2.5) :: Float
 
   There are no library operations named nagEllipticIntegralRF 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRF
      to learn if there is any operation containing " 
      nagEllipticIntegralRF " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRF with argument type(s) 
                                    Float
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRF 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRF
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRF " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRF with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 129
--       0.7116

--S 130 of 141
nagEllipticIntegralRJ(0.5,0.5,0.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 130
--       1.118

--S 131 of 141
nagEllipticIntegralRJ(0.5,0.5,1,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 131
--       0.9221

--S 132 of 141
nagEllipticIntegralRJ(0.5,0.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 132
--       0.8115

--S 133 of 141
nagEllipticIntegralRJ(0.5,1,1,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 133
--       0.7671

--S 134 of 141
nagEllipticIntegralRJ(0.5,1,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 134
--       0.6784

--S 135 of 141
nagEllipticIntegralRJ(0.5,1.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 135
--       0.6017

--S 136 of 141
nagEllipticIntegralRJ(1,1,1,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 136
--       0.6438

--S 137 of 141
nagEllipticIntegralRJ(1,1,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 137
--       0.5722

--S 138 of 141
nagEllipticIntegralRJ(1,1.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                               PositiveInteger
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                               PositiveInteger
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 138
--       0.5101

--S 139 of 141
nagEllipticIntegralRJ(1.5,1.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 139
--       0.4561

--S 140 of 141
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 140

--S 141 of 141
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 141
)spool 
 
Starts dribbling to noonburg.output (2009/2/17, 17:55:33).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
RN := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 6
dmp0 := DMP([x,y,z,c],RN)
 

   (2)  DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3  of 6
px : dmp0 := 1-c*x +x*(y**2 + z**2)
 

           2      2
   (3)  x y  + x z  - x c + 1
          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R           2      2
--R   (3)  x y  + x z  - x c + 1
--R          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 3

--S 4 of 6
py : dmp0 := 1-c*y +y*(z**2 + x**2)
 

         2       2
   (4)  x y + y z  - y c + 1
          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R         2       2
--R   (4)  x y + y z  - y c + 1
--R          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 4

--S 5 of 6
pz : dmp0 := 1-c*z +z*(x**2 + y**2)
 

         2     2
   (5)  x z + y z - z c + 1
          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R         2     2
--R   (5)  x z + y z - z c + 1
--R          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 5

--S 6 of 6
gb0 := groebnerFactorize [px,py,pz]
 

   (6)
   [
           3 2     2    1    3       1  2       3 2     2    1    3       1  2
     [x - z c  + 2z c + - z c  - z + - c , y - z c  + 2z c + - z c  - z + - c ,
                        2            2                       2            2
       4     3   1  2 2         1
      z c - z  - - z c  - z c - -]
                 2              2
     ,

     [
              1    3   1      1  3 5   4  3 2    2  2 4   8  2    4    3
         x - -- y c  - - y + -- z c  - - z c  - -- z c  + - z c - - z c  + z
             15        5     15        5        15        5       3
       + 
            1  5   2  2
         - -- c  + - c
           30      5
       ,

          2    1    5    7    2    2  3 4   8  3     4  2 3   11  2    1    5
         y  + -- y c  - -- y c  - -- z c  + - z c + -- z c  - -- z  + -- z c
              90        15        15        5       15         5      18
       + 
           1    2    1  4   9
         - - z c  + -- c  - - c
           3        15      5
       ,

                1    5    7    2    2  3 4   2  3     4  2 3   1  2    1    5
         y z - -- y c  + -- y c  + -- z c  + - z c - -- z c  + - z  - -- z c
               90        15        15        5       15        5      18
       + 
           2    2    1  4   1
         - - z c  - -- c  - - c
           3        15      5
       ,
       4    1  3 5    3 2   1  2         1   5   1  2   6      3
      z  + -- z c  - z c  - - z c - z + --- c  - - c , c  - 54c  + 54]
           54               2           108      2
     ,
                  2             3             4   3  2    1     1  2
    [x - z,y z - z  + c,y c - 2z  + 2z c - 1,z  - - z c + - z + - c ],
                                                  2       2     2

           1    3   1      1   3 5    8  3 2    2    3   7      1   5    4  2
     [x - -- y c  - - y - --- z c  + -- z c  - -- z c  - - z - --- c  + -- c ,
          15        5     135        15        15        5     270      15

          2    1    5    7    2    2   3 4   16  3     2    1    5   31    2
         y  + -- y c  - -- y c  + --- z c  - -- z c + z  - -- z c  + -- z c
              90        15        135        15            30        15
       + 
          1   4   23
         --- c  - -- c
         135      15
       ,

                1    5    7    2    1  3 4   14  3     2    1    5   14    2
         y z - -- y c  + -- y c  + -- z c  - -- z c - z  - -- z c  + -- z c
               90        15        45        15            45        15
       + 
          1  4    8
         -- c  + -- c
         90      15
       ,
       4   3  2    1     1  2   6      3
      z  - - z c + - z + - c , c  - 54c  + 54]
           2       2     2
     ,
                2          2      3
    [x + y + z,y  + y z + z  - c,z  - z c - 1], [1],
            2             3                   4   3  2    1     1  2
    [x z - z  + c,x c - 2z  + 2z c - 1,y - z,z  - - z c + - z + - c ],
                                                  2       2     2
                  3   1       1
    [x - z,y - z,z  - - z c + -]]
                      2       2
Type: List List DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R   (6)
--R   [
--R           3 2     2    1    3       1  2       3 2     2    1    3       1  2
--R     [x - z c  + 2z c + - z c  - z + - c , y - z c  + 2z c + - z c  - z + - c ,
--R                        2            2                       2            2
--R       4     3   1  2 2         1
--R      z c - z  - - z c  - z c - -]
--R                 2              2
--R     ,
--R
--R     [
--R              1    3   1      1  3 5   4  3 2    2  2 4   8  2    4    3
--R         x - -- y c  - - y + -- z c  - - z c  - -- z c  + - z c - - z c  + z
--R             15        5     15        5        15        5       3
--R       + 
--R            1  5   2  2
--R         - -- c  + - c
--R           30      5
--R       ,
--R
--R          2    1    5    7    2    2  3 4   8  3     4  2 3   11  2    1    5
--R         y  + -- y c  - -- y c  - -- z c  + - z c + -- z c  - -- z  + -- z c
--R              90        15        15        5       15         5      18
--R       + 
--R           1    2    1  4   9
--R         - - z c  + -- c  - - c
--R           3        15      5
--R       ,
--R
--R                1    5    7    2    2  3 4   2  3     4  2 3   1  2    1    5
--R         y z - -- y c  + -- y c  + -- z c  + - z c - -- z c  + - z  - -- z c
--R               90        15        15        5       15        5      18
--R       + 
--R           2    2    1  4   1
--R         - - z c  - -- c  - - c
--R           3        15      5
--R       ,
--R       4    1  3 5    3 2   1  2         1   5   1  2   6      3
--R      z  + -- z c  - z c  - - z c - z + --- c  - - c , c  - 54c  + 54]
--R           54               2           108      2
--R     ,
--R                  2             3             4   3  2    1     1  2
--R    [x - z,y z - z  + c,y c - 2z  + 2z c - 1,z  - - z c + - z + - c ],
--R                                                  2       2     2
--R
--R           1    3   1      1   3 5    8  3 2    2    3   7      1   5    4  2
--R     [x - -- y c  - - y - --- z c  + -- z c  - -- z c  - - z - --- c  + -- c ,
--R          15        5     135        15        15        5     270      15
--R
--R          2    1    5    7    2    2   3 4   16  3     2    1    5   31    2
--R         y  + -- y c  - -- y c  + --- z c  - -- z c + z  - -- z c  + -- z c
--R              90        15        135        15            30        15
--R       + 
--R          1   4   23
--R         --- c  - -- c
--R         135      15
--R       ,
--R
--R                1    5    7    2    1  3 4   14  3     2    1    5   14    2
--R         y z - -- y c  + -- y c  + -- z c  - -- z c - z  - -- z c  + -- z c
--R               90        15        45        15            45        15
--R       + 
--R          1  4    8
--R         -- c  + -- c
--R         90      15
--R       ,
--R       4   3  2    1     1  2   6      3
--R      z  - - z c + - z + - c , c  - 54c  + 54]
--R           2       2     2
--R     ,
--R                2          2      3
--R    [x + y + z,y  + y z + z  - c,z  - z c - 1], [1],
--R            2             3                   4   3  2    1     1  2
--R    [x z - z  + c,x c - 2z  + 2z c - 1,y - z,z  - - z c + - z + - c ],
--R                                                  2       2     2
--R                  3   1       1
--R    [x - z,y - z,z  - - z c + -]]
--R                      2       2
--RType: List List DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 6
)spool 
 
Starts dribbling to oct.output (2009/2/17, 17:55:49).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 15
oci1 := octon(1,2,3,4,5,6,7,8)
 

   (1)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
                                                       Type: Octonion Integer
--R 
--R
--R   (1)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
--R                                                       Type: Octonion Integer
--E 1

--S 2 of 15
oci2 := octon(7,2,3,-4,5,6,-7,0)
 

   (2)  7 + 2i + 3j - 4k + 5E + 6I - 7J
                                                       Type: Octonion Integer
--R 
--R
--R   (2)  7 + 2i + 3j - 4k + 5E + 6I - 7J
--R                                                       Type: Octonion Integer
--E 2

--S 3 of 15
oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0))
 

   (3)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
                                                       Type: Octonion Integer
--R 
--R
--R   (3)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
--R                                                       Type: Octonion Integer
--E 3

--S 4 of 15
(oci1 * oci2) * oci3 - oci1 * (oci2 * oci3)
 

   (4)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
                                                       Type: Octonion Integer
--R 
--R
--R   (4)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
--R                                                       Type: Octonion Integer
--E 4

--S 5 of 15
[real oci1, imagi oci1, imagj oci1, imagk oci1, imagE oci1, imagI oci1, imagJ oci1, imagK oci1]
 

   (5)  [1,2,3,4,5,6,7,8]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [1,2,3,4,5,6,7,8]
--R                                                   Type: List PositiveInteger
--E 5

--S 6 of 15
q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk)
 

   (6)  q1 + qi i + qj j + qk k
                                          Type: Quaternion Polynomial Integer
--R 
--R
--R   (6)  q1 + qi i + qj j + qk k
--R                                          Type: Quaternion Polynomial Integer
--E 6

--S 7 of 15
E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0)
 

   (7)  E
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (7)  E
--R                                            Type: Octonion Polynomial Integer
--E 7

--S 8 of 15
q * E
 

   (8)  q1 E + qi I + qj J + qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (8)  q1 E + qi I + qj J + qk K
--R                                            Type: Octonion Polynomial Integer
--E 8

--S 9 of 15
E * q
 

   (9)  q1 E - qi I - qj J - qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (9)  q1 E - qi I - qj J - qk K
--R                                            Type: Octonion Polynomial Integer
--E 9

--S 10 of 15
q * 1$(Octonion Polynomial Integer)
 

   (10)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (10)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 10

--S 11 of 15
1$(Octonion Polynomial Integer) * q
 

   (11)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (11)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 11

--S 12 of 15
o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK)
 

   (12)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (12)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
--R                                            Type: Octonion Polynomial Integer
--E 12

--S 13 of 15
norm o
 

           2     2     2     2     2     2     2     2
   (13)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
                                                     Type: Polynomial Integer
--R 
--R
--R           2     2     2     2     2     2     2     2
--R   (13)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
--R                                                     Type: Polynomial Integer
--E 13

--S 14 of 15
p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK)
 

   (14)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (14)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
--R                                            Type: Octonion Polynomial Integer
--E 14

--S 15
norm(o*p)-norm(p)*norm(p)
 

   (15)
         4
     - pk
   + 
              2      2      2      2      2      2      2     2     2     2
         - 2pj  - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi
       + 
           2     2     2     2     2
         oK  + oJ  + oI  + oE  + o1
    *
         2
       pk
   + 
         4
     - pj
   + 
              2      2      2      2      2      2     2     2     2     2     2
         - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ
       + 
           2     2     2
         oI  + oE  + o1
    *
         2
       pj
   + 
         4
     - pi
   + 
              2      2      2      2      2     2     2     2     2     2     2
         - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI
       + 
           2     2
         oE  + o1
    *
         2
       pi
   + 
         4
     - pK
   + 
              2      2      2      2     2     2     2     2     2     2     2
         - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE
       + 
           2
         o1
    *
         2
       pK
   + 
         4
     - pJ
   + 
           2      2      2     2     2     2     2     2     2     2     2   2
     (- 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pJ
   + 
         4         2      2     2     2     2     2     2     2     2     2   2
     - pI  + (- 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pI
   + 
         4         2     2     2     2     2     2     2     2     2   2     4
     - pE  + (- 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pE  - p1
   + 
        2     2     2     2     2     2     2     2   2
     (ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )p1
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)
--R         4
--R     - pk
--R   + 
--R              2      2      2      2      2      2      2     2     2     2
--R         - 2pj  - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi
--R       + 
--R           2     2     2     2     2
--R         oK  + oJ  + oI  + oE  + o1
--R    *
--R         2
--R       pk
--R   + 
--R         4
--R     - pj
--R   + 
--R              2      2      2      2      2      2     2     2     2     2     2
--R         - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ
--R       + 
--R           2     2     2
--R         oI  + oE  + o1
--R    *
--R         2
--R       pj
--R   + 
--R         4
--R     - pi
--R   + 
--R              2      2      2      2      2     2     2     2     2     2     2
--R         - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI
--R       + 
--R           2     2
--R         oE  + o1
--R    *
--R         2
--R       pi
--R   + 
--R         4
--R     - pK
--R   + 
--R              2      2      2      2     2     2     2     2     2     2     2
--R         - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE
--R       + 
--R           2
--R         o1
--R    *
--R         2
--R       pK
--R   + 
--R         4
--R     - pJ
--R   + 
--R           2      2      2     2     2     2     2     2     2     2     2   2
--R     (- 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pJ
--R   + 
--R         4         2      2     2     2     2     2     2     2     2     2   2
--R     - pI  + (- 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pI
--R   + 
--R         4         2     2     2     2     2     2     2     2     2   2     4
--R     - pE  + (- 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pE  - p1
--R   + 
--R        2     2     2     2     2     2     2     2   2
--R     (ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )p1
--R                                                     Type: Polynomial Integer
--E 15
)spool 
 
Starts dribbling to cclass.output (2009/2/17, 17:44:7).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from CharacterClassXmpPage

--S 1 of 16
cl1 := charClass [char "a", char "e", char "i", char "o", char "u", char "y"]
 

   (1)  "aeiouy"
                                                         Type: CharacterClass
--R 
--R
--R   (1)  "aeiouy"
--R                                                         Type: CharacterClass
--E 1

--S 2 of 16
cl2 := charClass "bcdfghjklmnpqrstvwxyz"
 

   (2)  "bcdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (2)  "bcdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 2

--S 3 of 16
digit()
 

   (3)  "0123456789"
                                                         Type: CharacterClass
--R 
--R
--R   (3)  "0123456789"
--R                                                         Type: CharacterClass
--E 3

--S 4 of 16
hexDigit()
 

   (4)  "0123456789ABCDEFabcdef"
                                                         Type: CharacterClass
--R 
--R
--R   (4)  "0123456789ABCDEFabcdef"
--R                                                         Type: CharacterClass
--E 4

--S 5 of 16
upperCase()
 

   (5)  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
                                                         Type: CharacterClass
--R 
--R
--R   (5)  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
--R                                                         Type: CharacterClass
--E 5

--S 6 of 16
lowerCase()
 

   (6)  "abcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (6)  "abcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 6

--S 7 of 16
alphabetic()
 

   (7)  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (7)  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 7

--S 8 of 16
alphanumeric()
 

   (8)  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (8)  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 8

--S 9 of 16
member?(char "a", cl1)
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 16
member?(char "a", cl2)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 16
intersect(cl1, cl2)
 

   (11)  "y"
                                                         Type: CharacterClass
--R 
--R
--R   (11)  "y"
--R                                                         Type: CharacterClass
--E 11

--S 12 of 16
union(cl1,cl2)
 

   (12)  "abcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (12)  "abcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 12

--S 13 of 16
difference(cl1,cl2)
 

   (13)  "aeiou"
                                                         Type: CharacterClass
--R 
--R
--R   (13)  "aeiou"
--R                                                         Type: CharacterClass
--E 13

--S 14 of 16
intersect(complement(cl1),cl2)
 

   (14)  "bcdfghjklmnpqrstvwxz"
                                                         Type: CharacterClass
--R 
--R
--R   (14)  "bcdfghjklmnpqrstvwxz"
--R                                                         Type: CharacterClass
--E 14

--S 15 of 16
insert!(char "a", cl2)
 

   (15)  "abcdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (15)  "abcdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 15

--S 16 of 16
remove!(char "b", cl2)
 

   (16)  "acdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (16)  "acdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 16
)spool
 
Starts dribbling to fferr.output (2009/2/17, 17:46:2).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 7
pf := PF 3
 

   (1)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 3
--R                                                                 Type: Domain
--E 1

--S 2 of 7
createIrreduciblePoly(6)$FFPOLY(pf)
 

         6
   (2)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         6
--R   (2)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 2

--S 3 of 7
createNormalPoly(6)$FFPOLY(pf)
 

         6     5    3
   (3)  ?  + 2?  + ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         6     5    3
--R   (3)  ?  + 2?  + ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 3

--S 4 of 7
createPrimitivePoly(3)$FFPOLY(pf)
 

         3
   (4)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3
--R   (4)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 4

--S 5 of 7
createIrreduciblePoly(3)$FFPOLY(pf)
 

         3
   (5)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3
--R   (5)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 5

--S 6 of 7
createNormalPoly(3)$FFPOLY(pf)
 

         3     2
   (6)  ?  + 2?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3     2
--R   (6)  ?  + 2?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 6

--S 7 of 7
createPrimitivePoly(3)$FFPOLY(pf)
 

         3
   (7)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3
--R   (7)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 7
)spool 
 
Starts dribbling to sregset.output (2009/2/17, 18:0:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 23
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 23
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 23
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 23
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 23
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 23
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 23
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 23
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 23
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 23
ST := SREGSET(R,E,V,P)
 

   (10)
  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
  r,OrderedVariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
--R  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
--R  r,OrderedVariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 23
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 23
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 23
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 23
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 23
zeroSetSplit(lp)$ST
 

            5    4      2     3     8     5    3    2   4                2
   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R            5    4      2     3     8     5    3    2   4                2
--R   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 15

--S 16 of 23
zeroSetSplit(lp,false)$ST
 

   (16)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5            2    2
    {t  - 1,z  - t,t y + z ,z x  - t}, {t,z,y,x}]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5            2    2
--R    {t  - 1,z  - t,t y + z ,z x  - t}, {t,z,y,x}]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16

--S 17 of 23
T := REGSET(R,E,V,P)
 

   (17)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (17)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
--R  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
--R  ariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 17

--S 18 of 23
lts := zeroSetSplit(lp,false)$T
 

   (18)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5          2     3         2
    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (18)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5          2     3         2
--R    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 18

--S 19 of 23
ts := lts.2
 

           3      5          2     3         2
   (19)  {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}
Type: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R           3      5          2     3         2
--R   (19)  {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}
--RType: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 19

--S 20 of 23
pol := select(ts,'y)$T
 

              2     3
   (20)  t z y  + 2z y + 1
Type: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
--R 
--R
--R              2     3
--R   (20)  t z y  + 2z y + 1
--RType: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
--E 20

--S 21 of 23
tower := collectUnder(ts,'y)$T
 

           3      5
   (21)  {t  - 1,z  - t}
Type: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R           3      5
--R   (21)  {t  - 1,z  - t}
--RType: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 21

--S 22 of 23
pack := RegularTriangularSetGcdPackage(R,E,V,P,T)
 

   (22)
  RegularTriangularSetGcdPackage(Integer,IndexedExponents OrderedVariableList [
  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
  r,OrderedVariableList [x,y,z,t]),RegularTriangularSet(Integer,IndexedExponent
  s OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultiv
  ariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
                                                                 Type: Domain
--R 
--R
--R   (22)
--R  RegularTriangularSetGcdPackage(Integer,IndexedExponents OrderedVariableList [
--R  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
--R  r,OrderedVariableList [x,y,z,t]),RegularTriangularSet(Integer,IndexedExponent
--R  s OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultiv
--R  ariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--R                                                                 Type: Domain
--E 22

--S 23 of 23
toseSquareFreePart(pol,tower)$pack
 

                       2          3      5
   (23)  [[val= t y + z ,tower= {t  - 1,z  - t}]]
Type: List Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),tower: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--R 
--R
--R                       2          3      5
--R   (23)  [[val= t y + z ,tower= {t  - 1,z  - t}]]
--RType: List Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),tower: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--E 23
)spool 
 
Starts dribbling to schaum14.output (2009/2/17, 17:58:32).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(x^3+a^3),x)
 

                                                                    +-+
           +-+     2          2      +-+                   (2x - a)\|3
        - \|3 log(x  - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
                                                                3a
   (1)  ----------------------------------------------------------------
                                       2 +-+
                                     6a \|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                    +-+
--R           +-+     2          2      +-+                   (2x - a)\|3
--R        - \|3 log(x  - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
--R                                                                3a
--R   (1)  ----------------------------------------------------------------
--R                                       2 +-+
--R                                     6a \|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/(6*a^2)*log((x+a)^2/(x^2-a*x+a^2))+1/(a^2*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

             2           2                       +-+
            x  + 2a x + a       +-+     (2x - a)\|3
        log(--------------) + 2\|3 atan(------------)
              2          2                   3a
             x  - a x + a
   (2)  ---------------------------------------------
                               2
                             6a
                                                     Type: Expression Integer
--R
--R             2           2                       +-+
--R            x  + 2a x + a       +-+     (2x - a)\|3
--R        log(--------------) + 2\|3 atan(------------)
--R              2          2                   3a
--R             x  - a x + a
--R   (2)  ---------------------------------------------
--R                               2
--R                             6a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                                  2           2
               2          2                      x  + 2a x + a
        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
                                                   2          2
                                                  x  - a x + a
   (3)  --------------------------------------------------------
                                     2
                                   6a
                                                     Type: Expression Integer
--R
--R                                                  2           2
--R               2          2                      x  + 2a x + a
--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
--R                                                   2          2
--R                                                  x  - a x + a
--R   (3)  --------------------------------------------------------
--R                                     2
--R                                   6a
--R                                                     Type: Expression Integer
--E

--S 4      14:299 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 5
aa:=integrate(x/(x^3+a^3),x)
 

                                                                  +-+
         +-+     2          2      +-+                   (2x - a)\|3
        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
                                                              3a
   (1)  --------------------------------------------------------------
                                       +-+
                                    6a\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                  +-+
--R         +-+     2          2      +-+                   (2x - a)\|3
--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
--R                                                              3a
--R   (1)  --------------------------------------------------------------
--R                                       +-+
--R                                    6a\|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 6
bb:=1/(6*a)*log((x^2-a*x+a^2)/(x+a)^2)+1/(a*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

              2          2                       +-+
             x  - a x + a       +-+     (2x - a)\|3
        log(--------------) + 2\|3 atan(------------)
             2           2                   3a
            x  + 2a x + a
   (2)  ---------------------------------------------
                              6a
                                                     Type: Expression Integer
--R
--R              2          2                       +-+
--R             x  - a x + a       +-+     (2x - a)\|3
--R        log(--------------) + 2\|3 atan(------------)
--R             2           2                   3a
--R            x  + 2a x + a
--R   (2)  ---------------------------------------------
--R                              6a
--R                                                     Type: Expression Integer
--E

--S 7
cc:=aa-bb
 

                                                 2          2
             2          2                       x  - a x + a
        log(x  - a x + a ) - 2log(x + a) - log(--------------)
                                                2           2
                                               x  + 2a x + a
   (3)  ------------------------------------------------------
                                  6a
                                                     Type: Expression Integer
--R
--R                                                 2          2
--R             2          2                       x  - a x + a
--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
--R                                                2           2
--R                                               x  + 2a x + a
--R   (3)  ------------------------------------------------------
--R                                  6a
--R                                                     Type: Expression Integer
--E

--S 8      14:300 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 9
aa:=integrate(x^2/(x^3+a^3),x)
 

             3    3
        log(x  + a )
   (1)  ------------
              3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3    3
--R        log(x  + a )
--R   (1)  ------------
--R              3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 10
bb:=1/3*log(x^3+a^3)
 

             3    3
        log(x  + a )
   (2)  ------------
              3
                                                     Type: Expression Integer
--R
--R             3    3
--R        log(x  + a )
--R   (2)  ------------
--R              3
--R                                                     Type: Expression Integer
--E

--S 11     14:301 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 12
aa:=integrate(1/(x*(x^3+a^3)),x)
 

               3    3
        - log(x  + a ) + 3log(x)
   (1)  ------------------------
                     3
                   3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3    3
--R        - log(x  + a ) + 3log(x)
--R   (1)  ------------------------
--R                     3
--R                   3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13
bb:=1/(3*a^3)*log(x^3/(x^3+a^3))
 

                3
               x
        log(-------)
             3    3
            x  + a
   (2)  ------------
               3
             3a
                                                     Type: Expression Integer
--R
--R                3
--R               x
--R        log(-------)
--R             3    3
--R            x  + a
--R   (2)  ------------
--R               3
--R             3a
--R                                                     Type: Expression Integer
--E

--S 14
cc:=aa-bb
 

                                           3
               3    3                     x
        - log(x  + a ) + 3log(x) - log(-------)
                                        3    3
                                       x  + a
   (3)  ---------------------------------------
                            3
                          3a
                                                     Type: Expression Integer
--R
--R                                           3
--R               3    3                     x
--R        - log(x  + a ) + 3log(x) - log(-------)
--R                                        3    3
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            3
--R                          3a
--R                                                     Type: Expression Integer
--E

--S 15     14:302 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(1/(x^2*(x^3+a^3)),x)
 

   (1)
                                                                   +-+
       +-+     2          2       +-+                     (2x - a)\|3        +-+
   - x\|3 log(x  - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) - 6a\|3
                                                               3a
   -----------------------------------------------------------------------------
                                        4  +-+
                                      6a x\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                   +-+
--R       +-+     2          2       +-+                     (2x - a)\|3        +-+
--R   - x\|3 log(x  - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) - 6a\|3
--R                                                               3a
--R   -----------------------------------------------------------------------------
--R                                        4  +-+
--R                                      6a x\|3
--R                                          Type: Union(Expression Integer,...)
--E

--S 16
bb:=-1/(a^3*x)-1/(6*a^4)*log((x^2-a*x+a^2)/(x+a)^2)-1/(a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

                  2          2                        +-+
                 x  - a x + a        +-+     (2x - a)\|3
        - x log(--------------) - 2x\|3 atan(------------) - 6a
                 2           2                    3a
                x  + 2a x + a
   (2)  -------------------------------------------------------
                                    4
                                  6a x
                                                     Type: Expression Integer
--R
--R                  2          2                        +-+
--R                 x  - a x + a        +-+     (2x - a)\|3
--R        - x log(--------------) - 2x\|3 atan(------------) - 6a
--R                 2           2                    3a
--R                x  + 2a x + a
--R   (2)  -------------------------------------------------------
--R                                    4
--R                                  6a x
--R                                                     Type: Expression Integer
--E 

--S 17
cc:=aa-bb
 

                                                   2          2
               2          2                       x  - a x + a
        - log(x  - a x + a ) + 2log(x + a) + log(--------------)
                                                  2           2
                                                 x  + 2a x + a
   (3)  --------------------------------------------------------
                                     4
                                   6a
                                                     Type: Expression Integer
--R
--R                                                   2          2
--R               2          2                       x  - a x + a
--R        - log(x  - a x + a ) + 2log(x + a) + log(--------------)
--R                                                  2           2
--R                                                 x  + 2a x + a
--R   (3)  --------------------------------------------------------
--R                                     4
--R                                   6a
--R                                                     Type: Expression Integer
--E

--S 18     14:303 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19
aa:=integrate(1/(x^3+a^3)^2,x)
 

   (1)
           3    3  +-+     2          2       3     3  +-+
       (- x  - a )\|3 log(x  - a x + a ) + (2x  + 2a )\|3 log(x + a)
     + 
                                +-+
          3     3      (2x - a)\|3       2  +-+
       (6x  + 6a )atan(------------) + 3a x\|3
                            3a
  /
        5 3     8  +-+
     (9a x  + 9a )\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R           3    3  +-+     2          2       3     3  +-+
--R       (- x  - a )\|3 log(x  - a x + a ) + (2x  + 2a )\|3 log(x + a)
--R     + 
--R                                +-+
--R          3     3      (2x - a)\|3       2  +-+
--R       (6x  + 6a )atan(------------) + 3a x\|3
--R                            3a
--R  /
--R        5 3     8  +-+
--R     (9a x  + 9a )\|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 20
bb:=x/(3*a^3*(x^3+a^3))+1/(9*a^5)*log((x+a)^2/(x^2-a*x+a^2))+2/(3*a^5*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

   (2)
                 2           2                                 +-+
     3    3     x  + 2a x + a        3     3  +-+     (2x - a)\|3       2
   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 3a x
                  2          2                             3a
                 x  - a x + a
   -----------------------------------------------------------------------
                                   5 3     8
                                 9a x  + 9a
                                                     Type: Expression Integer
--R
--R   (2)
--R                 2           2                                 +-+
--R     3    3     x  + 2a x + a        3     3  +-+     (2x - a)\|3       2
--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 3a x
--R                  2          2                             3a
--R                 x  - a x + a
--R   -----------------------------------------------------------------------
--R                                   5 3     8
--R                                 9a x  + 9a
--R                                                     Type: Expression Integer
--E

--S 21
cc:=aa-bb
 

                                                  2           2
               2          2                      x  + 2a x + a
        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
                                                   2          2
                                                  x  - a x + a
   (3)  --------------------------------------------------------
                                     5
                                   9a
                                                     Type: Expression Integer
--R
--R                                                  2           2
--R               2          2                      x  + 2a x + a
--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
--R                                                   2          2
--R                                                  x  - a x + a
--R   (3)  --------------------------------------------------------
--R                                     5
--R                                   9a
--R                                                     Type: Expression Integer
--E

--S 22     14:304 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(x/(x^3+a^3)^2,x)
 

   (1)
         3    3  +-+     2          2         3     3  +-+
       (x  + a )\|3 log(x  - a x + a ) + (- 2x  - 2a )\|3 log(x + a)
     + 
                                +-+
          3     3      (2x - a)\|3         2 +-+
       (6x  + 6a )atan(------------) + 6a x \|3
                            3a
  /
         4 3      7  +-+
     (18a x  + 18a )\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R         3    3  +-+     2          2         3     3  +-+
--R       (x  + a )\|3 log(x  - a x + a ) + (- 2x  - 2a )\|3 log(x + a)
--R     + 
--R                                +-+
--R          3     3      (2x - a)\|3         2 +-+
--R       (6x  + 6a )atan(------------) + 6a x \|3
--R                            3a
--R  /
--R         4 3      7  +-+
--R     (18a x  + 18a )\|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=x^2/(3*a^3*(x^3+a^3))+1/(18*a^4)*log((x^2-a*x+a^2)/(x+a)^2)+1/(3*a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

   (2)
                  2          2                                 +-+
     3    3      x  - a x + a        3     3  +-+     (2x - a)\|3         2
   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 6a x
                 2           2                             3a
                x  + 2a x + a
   ------------------------------------------------------------------------
                                    4 3      7
                                 18a x  + 18a
                                                     Type: Expression Integer
--R
--R   (2)
--R                  2          2                                 +-+
--R     3    3      x  - a x + a        3     3  +-+     (2x - a)\|3         2
--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 6a x
--R                 2           2                             3a
--R                x  + 2a x + a
--R   ------------------------------------------------------------------------
--R                                    4 3      7
--R                                 18a x  + 18a
--R                                                     Type: Expression Integer
--E

--S 25
cc:=aa-bb
 

                                                 2          2
             2          2                       x  - a x + a
        log(x  - a x + a ) - 2log(x + a) - log(--------------)
                                                2           2
                                               x  + 2a x + a
   (3)  ------------------------------------------------------
                                    4
                                 18a
                                                     Type: Expression Integer
--R
--R                                                 2          2
--R             2          2                       x  - a x + a
--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
--R                                                2           2
--R                                               x  + 2a x + a
--R   (3)  ------------------------------------------------------
--R                                    4
--R                                 18a
--R                                                     Type: Expression Integer
--E

--S 26     14:305 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(x^2/(x^3+a^3)^2,x)
 

              1
   (1)  - ---------
            3     3
          3x  + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            3     3
--R          3x  + 3a
--R                                          Type: Union(Expression Integer,...)
--E

--S 28
bb:=-1/(3*(x^3+a^3))
 

              1
   (2)  - ---------
            3     3
          3x  + 3a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            3     3
--R          3x  + 3a
--R                                            Type: Fraction Polynomial Integer
--E 

--S 29     14:306 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 30
aa:=integrate(1/(x*(x^3+a^3)^2),x)
 

            3    3      3    3       3     3           3
        (- x  - a )log(x  + a ) + (3x  + 3a )log(x) + a
   (1)  ------------------------------------------------
                             6 3     9
                           3a x  + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            3    3      3    3       3     3           3
--R        (- x  - a )log(x  + a ) + (3x  + 3a )log(x) + a
--R   (1)  ------------------------------------------------
--R                             6 3     9
--R                           3a x  + 3a
--R                                          Type: Union(Expression Integer,...)
--E

--S 31
bb:=1/(3*a^3*(x^3+a^3))+1/(3*a^6)*log(x^3/(x^3+a^3))
 

                         3
          3    3        x        3
        (x  + a )log(-------) + a
                      3    3
                     x  + a
   (2)  --------------------------
                  6 3     9
                3a x  + 3a
                                                     Type: Expression Integer
--R
--R                         3
--R          3    3        x        3
--R        (x  + a )log(-------) + a
--R                      3    3
--R                     x  + a
--R   (2)  --------------------------
--R                  6 3     9
--R                3a x  + 3a
--R                                                     Type: Expression Integer
--E

--S 32
cc:=aa-bb
 

                                           3
               3    3                     x
        - log(x  + a ) + 3log(x) - log(-------)
                                        3    3
                                       x  + a
   (3)  ---------------------------------------
                            6
                          3a
                                                     Type: Expression Integer
--R
--R                                           3
--R               3    3                     x
--R        - log(x  + a ) + 3log(x) - log(-------)
--R                                        3    3
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            6
--R                          3a
--R                                                     Type: Expression Integer
--E

--S 33     14:307 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 34
aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
 

   (1)
            4     3   +-+     2          2       4     3   +-+
       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
     + 
                                     +-+
             4      3       (2x - a)\|3             3     4  +-+
       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
                                 3a
  /
        7 4     10   +-+
     (9a x  + 9a  x)\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            4     3   +-+     2          2       4     3   +-+
--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
--R     + 
--R                                     +-+
--R             4      3       (2x - a)\|3             3     4  +-+
--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
--R                                 3a
--R  /
--R        7 4     10   +-+
--R     (9a x  + 9a  x)\|3
--R                                          Type: Union(Expression Integer,...)
--E

--S 35
t1:=integrate(x/(x^3+a^3),x)
 

                                                                  +-+
         +-+     2          2      +-+                   (2x - a)\|3
        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
                                                              3a
   (2)  --------------------------------------------------------------
                                       +-+
                                    6a\|3
                                          Type: Union(Expression Integer,...)
--R
--R                                                                  +-+
--R         +-+     2          2      +-+                   (2x - a)\|3
--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
--R                                                              3a
--R   (2)  --------------------------------------------------------------
--R                                       +-+
--R                                    6a\|3
--R                                          Type: Union(Expression Integer,...)
--E

--S 36
bb:=-1/(a^6*x)-x^2/(3*a^6*(x^3+a^3))-4/(3*a^6)*t1
 

   (3)
            4     3   +-+     2          2       4     3   +-+
       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
     + 
                                     +-+
             4      3       (2x - a)\|3             3     4  +-+
       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
                                 3a
  /
        7 4     10   +-+
     (9a x  + 9a  x)\|3
                                                     Type: Expression Integer
--R
--R   (3)
--R            4     3   +-+     2          2       4     3   +-+
--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
--R     + 
--R                                     +-+
--R             4      3       (2x - a)\|3             3     4  +-+
--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
--R                                 3a
--R  /
--R        7 4     10   +-+
--R     (9a x  + 9a  x)\|3
--R                                                     Type: Expression Integer
--E 

--S 37     14:308 Schaums and Axiom agree
cc:=aa-bb
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 38     14:309 Axiom cannot compute this integral
aa:=integrate(x^m/(x^3+a^3),x)
 

           x      m
         ++     %Q
   (1)   |   -------- d%Q
        ++    3     3
             a  + %Q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x      m
--I         ++     %L
--I   (1)   |   -------- d%L
--R        ++    3     3
--I             a  + %L
--R                                          Type: Union(Expression Integer,...)
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39     14:310 Axiom cannot compute this integral
aa:=integrate(1/(x^n*(x^3+a^3)),x)
 

           x
         ++        1
   (1)   |   ------------- d%Q
        ++     3     3   n
             (a  + %Q )%Q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++        1
--I   (1)   |   ------------- d%L
--R        ++     3     3   n
--I             (a  + %L )%L
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to noptip.output (2009/2/17, 17:55:37).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
outputGeneral 5
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
f := %e^x*(4*x^2 + 2*y^2 + 4*x*y + 2*y + 1);
 

                                                     Type: Expression Integer
--R 
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
start := [x=-1.0, y=1.0];
 

                                         Type: List Equation Polynomial Float
--R 
--R
--R                                         Type: List Equation Polynomial Float
--E 3

--S 4 of 6 used to work?
nagMin(f,start) :: List Equation Polynomial Float
 
   There are no library operations named nagMin 
      Use HyperDoc Browse or issue
                               )what op nagMin
      to learn if there is any operation containing " nagMin " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagMin with argument type(s) 
                             Expression Integer
                       List Equation Polynomial Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagMin 
--R      Use HyperDoc Browse or issue
--R                               )what op nagMin
--R      to learn if there is any operation containing " nagMin " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagMin with argument type(s) 
--R                             Expression Integer
--R                       List Equation Polynomial Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4
--       [x= 0.5,y= - 1.0]

--S 5 of 6
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 6
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 6
)spool 
 
Starts dribbling to exseries.output (2009/2/17, 17:45:56).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 9
f := taylor(exp(x))
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 9
eval(f,1.0)
 

   (2)
   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
    2.7182787698 412698413, 2.7182815255 731922399, ...]
                                                Type: Stream Expression Float
--R 
--R
--R   (2)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                Type: Stream Expression Float
--E 2

)clear all
 
   All user variables and function definitions have been cleared.

--S 3 of 9
series(sin(a*x),x = 0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 3

--S 4 of 9
series(sin(a*x),a = %pi/4)
 

   (2)
                                           2    %pi x
                                          x sin(-----)
         %pi x          %pi x      %pi            4         %pi 2
     sin(-----) + x cos(-----)(a - ---) - ------------ (a - ---)
           4              4         4           2            4
   + 
        3    %pi x                4    %pi x
       x cos(-----)              x sin(-----)
               4         %pi 3           4         %pi 4
     - ------------ (a - ---)  + ------------ (a - ---)
             6            4           24            4
   + 
      5    %pi x                6    %pi x                7    %pi x
     x cos(-----)              x sin(-----)              x cos(-----)
             4         %pi 5           4         %pi 6           4         %pi 7
     ------------ (a - ---)  - ------------ (a - ---)  - ------------ (a - ---)
          120           4           720           4          5040           4
   + 
      8    %pi x                9    %pi x
     x sin(-----)              x cos(-----)
             4         %pi 8           4         %pi 9
     ------------ (a - ---)  + ------------ (a - ---)
         40320          4         362880          4
   + 
        10    %pi x
       x  sin(-----)
                4         %pi 10          %pi 11
     - ------------- (a - ---)   + O((a - ---)  )
          3628800          4               4
                     Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4)
--R 
--R
--R   (2)
--R                                           2    %pi x
--R                                          x sin(-----)
--R         %pi x          %pi x      %pi            4         %pi 2
--R     sin(-----) + x cos(-----)(a - ---) - ------------ (a - ---)
--R           4              4         4           2            4
--R   + 
--R        3    %pi x                4    %pi x
--R       x cos(-----)              x sin(-----)
--R               4         %pi 3           4         %pi 4
--R     - ------------ (a - ---)  + ------------ (a - ---)
--R             6            4           24            4
--R   + 
--R      5    %pi x                6    %pi x                7    %pi x
--R     x cos(-----)              x sin(-----)              x cos(-----)
--R             4         %pi 5           4         %pi 6           4         %pi 7
--R     ------------ (a - ---)  - ------------ (a - ---)  - ------------ (a - ---)
--R          120           4           720           4          5040           4
--R   + 
--R      8    %pi x                9    %pi x
--R     x sin(-----)              x cos(-----)
--R             4         %pi 8           4         %pi 9
--R     ------------ (a - ---)  + ------------ (a - ---)
--R         40320          4         362880          4
--R   + 
--R        10    %pi x
--R       x  sin(-----)
--R                4         %pi 10          %pi 11
--R     - ------------- (a - ---)   + O((a - ---)  )
--R          3628800          4               4
--R                     Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4)
--E 4

)clear all
 
   All user variables and function definitions have been cleared.

--S 5 of 9
f := series(1/(1-x),x = 0)
 

                 2    3    4    5    6    7    8    9    10      11
   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 5

--S 6 of 9
g := log(f)
 

   (2)
         1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9    1  10    1  11
     x + - x  + - x  + - x  + - x  + - x  + - x  + - x  + - x  + -- x   + -- x
         2      3      4      5      6      7      8      9      10       11
   + 
        12
     O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R         1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9    1  10    1  11
--R     x + - x  + - x  + - x  + - x  + - x  + - x  + - x  + - x  + -- x   + -- x
--R         2      3      4      5      6      7      8      9      10       11
--R   + 
--R        12
--R     O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 6

--S 7 of 9
exp(g)
 

                 2    3    4    5    6    7    8    9    10      11
   (3)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (3)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 7

)clear all
 
   All user variables and function definitions have been cleared.

--S 8 of 9
f := series(1/(1-x),x = 0)
 

                 2    3    4    5    6    7    8    9    10      11
   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 8

--S 9 of 9
f ** 2
 

   (2)
              2     3     4     5     6     7     8      9      10      11
   1 + 2x + 3x  + 4x  + 5x  + 6x  + 7x  + 8x  + 9x  + 10x  + 11x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R              2     3     4     5     6     7     8      9      10      11
--R   1 + 2x + 3x  + 4x  + 5x  + 6x  + 7x  + 8x  + 9x  + 10x  + 11x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 9
)spool 
 
Starts dribbling to schaum19.output (2009/2/17, 17:59:1).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(sin(a*x)*cos(a*x),x)
 

                  2
          cos(a x)
   (1)  - ---------
              2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R          cos(a x)
--R   (1)  - ---------
--R              2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=sin(a*x)^2/(2*a)
 

                2
        sin(a x)
   (2)  ---------
            2a
                                                     Type: Expression Integer
--R
--R                2
--R        sin(a x)
--R   (2)  ---------
--R            2a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                  2           2
        - sin(a x)  - cos(a x)
   (3)  -----------------------
                   2a
                                                     Type: Expression Integer
--R
--R                  2           2
--R        - sin(a x)  - cos(a x)
--R   (3)  -----------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 4
cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
 

              2            2
   (4)  cos(a)  == - sin(a)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2            2
--R   (4)  cos(a)  == - sin(a)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5      14:399 Schaums and Axiom differ by a constant
dd:=cossqrrule cc
 

           1
   (5)  - --
          2a
                                                     Type: Expression Integer
--R
--R           1
--R   (5)  - --
--R          2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 6
aa:=integrate(sin(p*x)*cos(q*x),x)
 

        q sin(p x)sin(q x) + p cos(p x)cos(q x)
   (1)  ---------------------------------------
                         2    2
                        q  - p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        q sin(p x)sin(q x) + p cos(p x)cos(q x)
--R   (1)  ---------------------------------------
--R                         2    2
--R                        q  - p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7
bb:=-cos((p-q)*x)/(2*(p-q))-cos((p+q)*x)/(2*(p+q))
 

        (- q + p)cos((q + p)x) + (q + p)cos((q - p)x)
   (2)  ---------------------------------------------
                            2     2
                          2q  - 2p
                                                     Type: Expression Integer
--R
--R        (- q + p)cos((q + p)x) + (q + p)cos((q - p)x)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 8
cc:=aa-bb
 

   (3)
       2q sin(p x)sin(q x) + (q - p)cos((q + p)x) + 2p cos(p x)cos(q x)
     + 
       (- q - p)cos((q - p)x)
  /
       2     2
     2q  - 2p
                                                     Type: Expression Integer
--R
--R   (3)
--R       2q sin(p x)sin(q x) + (q - p)cos((q + p)x) + 2p cos(p x)cos(q x)
--R     + 
--R       (- q - p)cos((q - p)x)
--R  /
--R       2     2
--R     2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 9      14:400 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(sin(a*x)^n*cos(a*x),x)
 

                  n log(sin(a x))
        sin(a x)%e
   (1)  -------------------------
                 a n + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  n log(sin(a x))
--R        sin(a x)%e
--R   (1)  -------------------------
--R                 a n + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=sin(a*x)^(n+1)/((n+1)*a)
 

                n + 1
        sin(a x)
   (2)  -------------
           a n + a
                                                     Type: Expression Integer
--R
--R                n + 1
--R        sin(a x)
--R   (2)  -------------
--R           a n + a
--R                                                     Type: Expression Integer
--E

--S 12
cc:=aa-bb
 

                  n log(sin(a x))           n + 1
        sin(a x)%e                - sin(a x)
   (3)  -----------------------------------------
                         a n + a
                                                     Type: Expression Integer
--R
--R                  n log(sin(a x))           n + 1
--R        sin(a x)%e                - sin(a x)
--R   (3)  -----------------------------------------
--R                         a n + a
--R                                                     Type: Expression Integer
--E

--S 13
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 14
dd:=explog cc
 

                  n + 1                   n
        - sin(a x)      + sin(a x)sin(a x)
   (5)  -----------------------------------
                      a n + a
                                                     Type: Expression Integer
--R
--R                  n + 1                   n
--R        - sin(a x)      + sin(a x)sin(a x)
--R   (5)  -----------------------------------
--R                      a n + a
--R                                                     Type: Expression Integer
--E

--S 15     14:401 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(cos(a*x)^n*sin(a*x),x)
 

                    n log(cos(a x))
          cos(a x)%e
   (1)  - -------------------------
                   a n + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    n log(cos(a x))
--R          cos(a x)%e
--R   (1)  - -------------------------
--R                   a n + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 17
bb:=-cos(a*x)^(n+1)/((n+1)*a)
 

                  n + 1
          cos(a x)
   (2)  - -------------
             a n + a
                                                     Type: Expression Integer
--R
--R                  n + 1
--R          cos(a x)
--R   (2)  - -------------
--R             a n + a
--R                                                     Type: Expression Integer
--E 

--S 18
cc:=aa-bb
 

                    n log(cos(a x))           n + 1
        - cos(a x)%e                + cos(a x)
   (3)  -------------------------------------------
                          a n + a
                                                     Type: Expression Integer
--R
--R                    n log(cos(a x))           n + 1
--R        - cos(a x)%e                + cos(a x)
--R   (3)  -------------------------------------------
--R                          a n + a
--R                                                     Type: Expression Integer
--E

--S 19
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20
dd:=explog cc
 

                n + 1                   n
        cos(a x)      - cos(a x)cos(a x)
   (5)  ---------------------------------
                     a n + a
                                                     Type: Expression Integer
--R
--R                n + 1                   n
--R        cos(a x)      - cos(a x)cos(a x)
--R   (5)  ---------------------------------
--R                     a n + a
--R                                                     Type: Expression Integer
--E

--S 21     14:402 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 22
aa:=integrate(sin(a*x)^2*cos(a*x)^2,x)
 

                    3
        (- 2cos(a x)  + cos(a x))sin(a x) + a x
   (1)  ---------------------------------------
                           8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    3
--R        (- 2cos(a x)  + cos(a x))sin(a x) + a x
--R   (1)  ---------------------------------------
--R                           8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 23
bb:=x/8-sin(4*a*x)/(32*a)
 

        - sin(4a x) + 4a x
   (2)  ------------------
                32a
                                                     Type: Expression Integer
--R
--R        - sin(4a x) + 4a x
--R   (2)  ------------------
--R                32a
--R                                                     Type: Expression Integer
--E

--S 24
cc:=aa-bb
 

                                3
        sin(4a x) + (- 8cos(a x)  + 4cos(a x))sin(a x)
   (3)  ----------------------------------------------
                              32a
                                                     Type: Expression Integer
--R
--R                                3
--R        sin(4a x) + (- 8cos(a x)  + 4cos(a x))sin(a x)
--R   (3)  ----------------------------------------------
--R                              32a
--R                                                     Type: Expression Integer
--E

--S 25     14:403 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 26
aa:=integrate(1/(sin(a*x)*cos(a*x)),x)
 

              sin(a x)              2cos(a x)
        log(------------) - log(- ------------)
            cos(a x) + 1          cos(a x) + 1
   (1)  ---------------------------------------
                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)              2cos(a x)
--R        log(------------) - log(- ------------)
--R            cos(a x) + 1          cos(a x) + 1
--R   (1)  ---------------------------------------
--R                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27
bb:=1/a*log(tan(a*x))
 

        log(tan(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(tan(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 28
cc:=aa-bb
 

                                sin(a x)              2cos(a x)
        - log(tan(a x)) + log(------------) - log(- ------------)
                              cos(a x) + 1          cos(a x) + 1
   (3)  ---------------------------------------------------------
                                    a
                                                     Type: Expression Integer
--R
--R                                sin(a x)              2cos(a x)
--R        - log(tan(a x)) + log(------------) - log(- ------------)
--R                              cos(a x) + 1          cos(a x) + 1
--R   (3)  ---------------------------------------------------------
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 29
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 30
dd:=tanrule cc
 

              sin(a x)          sin(a x)              2cos(a x)
        - log(--------) + log(------------) - log(- ------------)
              cos(a x)        cos(a x) + 1          cos(a x) + 1
   (5)  ---------------------------------------------------------
                                    a
                                                     Type: Expression Integer
--R
--R              sin(a x)          sin(a x)              2cos(a x)
--R        - log(--------) + log(------------) - log(- ------------)
--R              cos(a x)        cos(a x) + 1          cos(a x) + 1
--R   (5)  ---------------------------------------------------------
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 31     14:404 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

          log(- 2)
   (6)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 2)
--R   (6)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x)
 

   (1)
                   sin(a x) + cos(a x) + 1
       sin(a x)log(-----------------------)
                         cos(a x) + 1
     + 
                     sin(a x) - cos(a x) - 1
       - sin(a x)log(-----------------------) - 1
                           cos(a x) + 1
  /
     a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   sin(a x) + cos(a x) + 1
--R       sin(a x)log(-----------------------)
--R                         cos(a x) + 1
--R     + 
--R                     sin(a x) - cos(a x) - 1
--R       - sin(a x)log(-----------------------) - 1
--R                           cos(a x) + 1
--R  /
--R     a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33
bb:=1/a*log(tan(%pi/4+(a*x)/2))-1/(a*sin(a*x))
 

                        2a x + %pi
        sin(a x)log(tan(----------)) - 1
                             4
   (2)  --------------------------------
                   a sin(a x)
                                                     Type: Expression Integer
--R
--R                        2a x + %pi
--R        sin(a x)log(tan(----------)) - 1
--R                             4
--R   (2)  --------------------------------
--R                   a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 34
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 35
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------)
                 2a x + %pi
             cos(----------)
                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------)
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 37
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------))
                      4                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------))
--R                      4                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 38     14:405 Schaums and Axiom differ by a constant
ff:=complexNormalize %
 

        log(- 1)
   (7)  --------
            a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x)
 

                      sin(a x)
        cos(a x)log(------------) + cos(a x) + 1
                    cos(a x) + 1
   (1)  ----------------------------------------
                       a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      sin(a x)
--R        cos(a x)log(------------) + cos(a x) + 1
--R                    cos(a x) + 1
--R   (1)  ----------------------------------------
--R                       a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40
bb:=1/a*log(tan((a*x)/2))+1/(a*cos(a*x))
 

                        a x
        cos(a x)log(tan(---)) + 1
                         2
   (2)  -------------------------
                a cos(a x)
                                                     Type: Expression Integer
--R
--R                        a x
--R        cos(a x)log(tan(---)) + 1
--R                         2
--R   (2)  -------------------------
--R                a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 41
cc:=aa-bb
 

                  a x           sin(a x)
        - log(tan(---)) + log(------------) + 1
                   2          cos(a x) + 1
   (3)  ---------------------------------------
                           a
                                                     Type: Expression Integer
--R
--R                  a x           sin(a x)
--R        - log(tan(---)) + log(------------) + 1
--R                   2          cos(a x) + 1
--R   (3)  ---------------------------------------
--R                           a
--R                                                     Type: Expression Integer
--E

--S 42
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 43
dd:=tanrule cc
 

                                    a x
                                sin(---)
              sin(a x)               2
        log(------------) - log(--------) + 1
            cos(a x) + 1            a x
                                cos(---)
                                     2
   (5)  -------------------------------------
                          a
                                                     Type: Expression Integer
--R
--R                                    a x
--R                                sin(---)
--R              sin(a x)               2
--R        log(------------) - log(--------) + 1
--R            cos(a x) + 1            a x
--R                                cos(---)
--R                                     2
--R   (5)  -------------------------------------
--R                          a
--R                                                     Type: Expression Integer
--E

--S 44
ee:=expandLog dd
 

                                a x                                 a x
        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---)) + 1
                                 2                                   2
   (6)  ---------------------------------------------------------------------
                                          a
                                                     Type: Expression Integer
--R
--R                                a x                                 a x
--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---)) + 1
--R                                 2                                   2
--R   (6)  ---------------------------------------------------------------------
--R                                          a
--R                                                     Type: Expression Integer
--E

--S 45     14:406 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        1
   (7)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (7)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 46
aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x)
 

                    2
         - 2cos(a x)  + 1
   (1)  ------------------
        a cos(a x)sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2
--R         - 2cos(a x)  + 1
--R   (1)  ------------------
--R        a cos(a x)sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 47
bb:=-(2*cot(2*a*x))/a
 

          2cot(2a x)
   (2)  - ----------
               a
                                                     Type: Expression Integer
--R
--R          2cot(2a x)
--R   (2)  - ----------
--R               a
--R                                                     Type: Expression Integer
--E

--S 48
cc:=aa-bb
 

                                              2
        2cos(a x)cot(2a x)sin(a x) - 2cos(a x)  + 1
   (3)  -------------------------------------------
                     a cos(a x)sin(a x)
                                                     Type: Expression Integer
--R
--R                                              2
--R        2cos(a x)cot(2a x)sin(a x) - 2cos(a x)  + 1
--R   (3)  -------------------------------------------
--R                     a cos(a x)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 49
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 50
dd:=cotrule cc
 

                    2
        (- 2cos(a x)  + 1)sin(2a x) + 2cos(a x)cos(2a x)sin(a x)
   (5)  --------------------------------------------------------
                       a cos(a x)sin(a x)sin(2a x)
                                                     Type: Expression Integer
--R
--R                    2
--R        (- 2cos(a x)  + 1)sin(2a x) + 2cos(a x)cos(2a x)sin(a x)
--R   (5)  --------------------------------------------------------
--R                       a cos(a x)sin(a x)sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 51     14:407 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 52
aa:=integrate(sin(a*x)^2/cos(a*x),x)
 

            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
        log(-----------------------) - log(-----------------------) - sin(a x)
                  cos(a x) + 1                   cos(a x) + 1
   (1)  ----------------------------------------------------------------------
                                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R        log(-----------------------) - log(-----------------------) - sin(a x)
--R                  cos(a x) + 1                   cos(a x) + 1
--R   (1)  ----------------------------------------------------------------------
--R                                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53
bb:=-sin(a*x)/a+1/a*log(tan((a*x)/2+%pi/4))
 

                2a x + %pi
        log(tan(----------)) - sin(a x)
                     4
   (2)  -------------------------------
                       a
                                                     Type: Expression Integer
--R
--R                2a x + %pi
--R        log(tan(----------)) - sin(a x)
--R                     4
--R   (2)  -------------------------------
--R                       a
--R                                                     Type: Expression Integer
--E

--S 54
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 55
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 56
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------)
                 2a x + %pi
             cos(----------)
                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------)
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 57
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------))
                      4                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------))
--R                      4                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 58     14:408 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        log(- 1)
   (7)  --------
            a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 59
aa:=integrate(cos(a*x)^2/sin(a*x),x)
 

              sin(a x)
        log(------------) + cos(a x)
            cos(a x) + 1
   (1)  ----------------------------
                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)
--R        log(------------) + cos(a x)
--R            cos(a x) + 1
--R   (1)  ----------------------------
--R                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 60
bb:=cos(a*x)/a+1/a*log(tan((a*x)/2))
 

                a x
        log(tan(---)) + cos(a x)
                 2
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---)) + cos(a x)
--R                 2
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 61
cc:=aa-bb
 

                  a x           sin(a x)
        - log(tan(---)) + log(------------)
                   2          cos(a x) + 1
   (3)  -----------------------------------
                         a
                                                     Type: Expression Integer
--R
--R                  a x           sin(a x)
--R        - log(tan(---)) + log(------------)
--R                   2          cos(a x) + 1
--R   (3)  -----------------------------------
--R                         a
--R                                                     Type: Expression Integer
--E

--S 62
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 63
dd:=tanrule cc
 

                                    a x
                                sin(---)
              sin(a x)               2
        log(------------) - log(--------)
            cos(a x) + 1            a x
                                cos(---)
                                     2
   (5)  ---------------------------------
                        a
                                                     Type: Expression Integer
--R
--R                                    a x
--R                                sin(---)
--R              sin(a x)               2
--R        log(------------) - log(--------)
--R            cos(a x) + 1            a x
--R                                cos(---)
--R                                     2
--R   (5)  ---------------------------------
--R                        a
--R                                                     Type: Expression Integer
--E

--S 64
ee:=expandLog dd
 

                                a x                                 a x
        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
                                 2                                   2
   (6)  -----------------------------------------------------------------
                                        a
                                                     Type: Expression Integer
--R
--R                                a x                                 a x
--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
--R                                 2                                   2
--R   (6)  -----------------------------------------------------------------
--R                                        a
--R                                                     Type: Expression Integer
--E

--S 65     14:409 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 66
aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x)
 

   (1)
                         sin(a x) + cos(a x) + 1
       (sin(a x) + 1)log(-----------------------)
                               cos(a x) + 1
     + 
                           sin(a x) - cos(a x) - 1
       (- sin(a x) - 1)log(-----------------------) + sin(a x)
                                 cos(a x) + 1
  /
     2a sin(a x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                         sin(a x) + cos(a x) + 1
--R       (sin(a x) + 1)log(-----------------------)
--R                               cos(a x) + 1
--R     + 
--R                           sin(a x) - cos(a x) - 1
--R       (- sin(a x) - 1)log(-----------------------) + sin(a x)
--R                                 cos(a x) + 1
--R  /
--R     2a sin(a x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 67
bb:=-1/(2*a*(1+sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
 

                              2a x + %pi
        (sin(a x) + 1)log(tan(----------)) - 1
                                   4
   (2)  --------------------------------------
                   2a sin(a x) + 2a
                                                     Type: Expression Integer
--R
--R                              2a x + %pi
--R        (sin(a x) + 1)log(tan(----------)) - 1
--R                                   4
--R   (2)  --------------------------------------
--R                   2a sin(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 68
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------) + 1
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------) + 1
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 69
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 70
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------) + 1
                 2a x + %pi
             cos(----------)
                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------) + 1
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 71
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------)) + 1
                      4                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------)) + 1
--R                      4                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 72
ff:=complexNormalize ee
 

        log(- 1) + 1
   (7)  ------------
             2a
                                                     Type: Expression Integer
--R
--R        log(- 1) + 1
--R   (7)  ------------
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all 
 
   All user variables and function definitions have been cleared.

--S 73
aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x)
 

   (1)
                         sin(a x) + cos(a x) + 1
       (sin(a x) - 1)log(-----------------------)
                               cos(a x) + 1
     + 
                           sin(a x) - cos(a x) - 1
       (- sin(a x) + 1)log(-----------------------) - sin(a x)
                                 cos(a x) + 1
  /
     2a sin(a x) - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                         sin(a x) + cos(a x) + 1
--R       (sin(a x) - 1)log(-----------------------)
--R                               cos(a x) + 1
--R     + 
--R                           sin(a x) - cos(a x) - 1
--R       (- sin(a x) + 1)log(-----------------------) - sin(a x)
--R                                 cos(a x) + 1
--R  /
--R     2a sin(a x) - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 74
bb:=1/(2*a*(1-sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
 

                              2a x + %pi
        (sin(a x) - 1)log(tan(----------)) - 1
                                   4
   (2)  --------------------------------------
                   2a sin(a x) - 2a
                                                     Type: Expression Integer
--R
--R                              2a x + %pi
--R        (sin(a x) - 1)log(tan(----------)) - 1
--R                                   4
--R   (2)  --------------------------------------
--R                   2a sin(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 75
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------) - 1
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------) - 1
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 76
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 77
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------) - 1
                 2a x + %pi
             cos(----------)
                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------) - 1
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 78
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------)) - 1
                      4                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------)) - 1
--R                      4                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 79     14:410 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        log(- 1) - 1
   (7)  ------------
             2a
                                                     Type: Expression Integer
--R
--R        log(- 1) - 1
--R   (7)  ------------
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 80
aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x)
 

                             sin(a x)
        (2cos(a x) + 2)log(------------) - cos(a x) + 1
                           cos(a x) + 1
   (1)  -----------------------------------------------
                        4a cos(a x) + 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             sin(a x)
--R        (2cos(a x) + 2)log(------------) - cos(a x) + 1
--R                           cos(a x) + 1
--R   (1)  -----------------------------------------------
--R                        4a cos(a x) + 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 81
bb:=1/(2*a*(1+cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
 

                              a x
        (cos(a x) + 1)log(tan(---)) + 1
                               2
   (2)  -------------------------------
                2a cos(a x) + 2a
                                                     Type: Expression Integer
--R
--R                              a x
--R        (cos(a x) + 1)log(tan(---)) + 1
--R                               2
--R   (2)  -------------------------------
--R                2a cos(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 82
cc:=aa-bb
 

                   a x            sin(a x)
        - 2log(tan(---)) + 2log(------------) - 1
                    2           cos(a x) + 1
   (3)  -----------------------------------------
                            4a
                                                     Type: Expression Integer
--R
--R                   a x            sin(a x)
--R        - 2log(tan(---)) + 2log(------------) - 1
--R                    2           cos(a x) + 1
--R   (3)  -----------------------------------------
--R                            4a
--R                                                     Type: Expression Integer
--E

--S 83
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 84
dd:=tanrule cc
 

                                      a x
                                  sin(---)
               sin(a x)                2
        2log(------------) - 2log(--------) - 1
             cos(a x) + 1             a x
                                  cos(---)
                                       2
   (5)  ---------------------------------------
                           4a
                                                     Type: Expression Integer
--R
--R                                      a x
--R                                  sin(---)
--R               sin(a x)                2
--R        2log(------------) - 2log(--------) - 1
--R             cos(a x) + 1             a x
--R                                  cos(---)
--R                                       2
--R   (5)  ---------------------------------------
--R                           4a
--R                                                     Type: Expression Integer
--E

--S 85
ee:=expandLog dd
 

   (6)
                             a x                                   a x
   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) - 1
                              2                                     2
   -------------------------------------------------------------------------
                                       4a
                                                     Type: Expression Integer
--R
--R   (6)
--R                             a x                                   a x
--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) - 1
--R                              2                                     2
--R   -------------------------------------------------------------------------
--R                                       4a
--R                                                     Type: Expression Integer
--E

--S 86
ff:=complexNormalize ee
 

           1
   (7)  - --
          4a
                                                     Type: Expression Integer
--R
--R           1
--R   (7)  - --
--R          4a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 87
aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x)
 

                             sin(a x)
        (2cos(a x) - 2)log(------------) + cos(a x) + 1
                           cos(a x) + 1
   (1)  -----------------------------------------------
                        4a cos(a x) - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             sin(a x)
--R        (2cos(a x) - 2)log(------------) + cos(a x) + 1
--R                           cos(a x) + 1
--R   (1)  -----------------------------------------------
--R                        4a cos(a x) - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 88
bb:=-1/(2*a*(1-cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
 

                              a x
        (cos(a x) - 1)log(tan(---)) + 1
                               2
   (2)  -------------------------------
                2a cos(a x) - 2a
                                                     Type: Expression Integer
--R
--R                              a x
--R        (cos(a x) - 1)log(tan(---)) + 1
--R                               2
--R   (2)  -------------------------------
--R                2a cos(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 89
cc:=aa-bb
 

                   a x            sin(a x)
        - 2log(tan(---)) + 2log(------------) + 1
                    2           cos(a x) + 1
   (3)  -----------------------------------------
                            4a
                                                     Type: Expression Integer
--R
--R                   a x            sin(a x)
--R        - 2log(tan(---)) + 2log(------------) + 1
--R                    2           cos(a x) + 1
--R   (3)  -----------------------------------------
--R                            4a
--R                                                     Type: Expression Integer
--E

--S 90
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 91
dd:=tanrule cc
 

                                      a x
                                  sin(---)
               sin(a x)                2
        2log(------------) - 2log(--------) + 1
             cos(a x) + 1             a x
                                  cos(---)
                                       2
   (5)  ---------------------------------------
                           4a
                                                     Type: Expression Integer
--R
--R                                      a x
--R                                  sin(---)
--R               sin(a x)                2
--R        2log(------------) - 2log(--------) + 1
--R             cos(a x) + 1             a x
--R                                  cos(---)
--R                                       2
--R   (5)  ---------------------------------------
--R                           4a
--R                                                     Type: Expression Integer
--E

--S 92
ee:=expandLog dd
 

   (6)
                             a x                                   a x
   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) + 1
                              2                                     2
   -------------------------------------------------------------------------
                                       4a
                                                     Type: Expression Integer
--R
--R   (6)
--R                             a x                                   a x
--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) + 1
--R                              2                                     2
--R   -------------------------------------------------------------------------
--R                                       4a
--R                                                     Type: Expression Integer
--E

--S 93     14:411 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

         1
   (7)  --
        4a
                                                     Type: Expression Integer
--R
--R         1
--R   (7)  --
--R        4a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 94
aa:=integrate(1/(sin(a*x)+cos(a*x)),x)
 

                    +-+                  +-+                 +-+
         +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
        \|2 log(----------------------------------------------------)
                                 sin(a x) + cos(a x)
   (1)  -------------------------------------------------------------
                                      2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-+                  +-+                 +-+
--R         +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
--R        \|2 log(----------------------------------------------------)
--R                                 sin(a x) + cos(a x)
--R   (1)  -------------------------------------------------------------
--R                                      2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 95
bb:=1/(a*sqrt(2))*log(tan((a*x)/2+%pi/8))
 

         +-+        4a x + %pi
        \|2 log(tan(----------))
                         8
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R         +-+        4a x + %pi
--R        \|2 log(tan(----------))
--R                         8
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 96
cc:=aa-bb
 

   (3)
          +-+        4a x + %pi
       - \|2 log(tan(----------))
                          8
     + 
                   +-+                  +-+                 +-+
        +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
       \|2 log(----------------------------------------------------)
                                sin(a x) + cos(a x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R          +-+        4a x + %pi
--R       - \|2 log(tan(----------))
--R                          8
--R     + 
--R                   +-+                  +-+                 +-+
--R        +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
--R       \|2 log(----------------------------------------------------)
--R                                sin(a x) + cos(a x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 97
complexNormalize cc
 

                 +-+
         +-+    \|2  - 2
        \|2 log(--------)
                   +-+
                  \|2
   (4)  -----------------
                2a
                                                     Type: Expression Integer
--R
--R                 +-+
--R         +-+    \|2  - 2
--R        \|2 log(--------)
--R                   +-+
--R                  \|2
--R   (4)  -----------------
--R                2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 98
aa:=integrate(1/(sin(a*x)-cos(a*x)),x)
 

                    +-+                    +-+                 +-+
         +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
        \|2 log(------------------------------------------------------)
                                  sin(a x) - cos(a x)
   (1)  ---------------------------------------------------------------
                                       2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-+                    +-+                 +-+
--R         +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
--R        \|2 log(------------------------------------------------------)
--R                                  sin(a x) - cos(a x)
--R   (1)  ---------------------------------------------------------------
--R                                       2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 99
bb:=1/(a*sqrt(2))*log(tan((a*x)/2-%pi/8))
 

         +-+        4a x - %pi
        \|2 log(tan(----------))
                         8
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R         +-+        4a x - %pi
--R        \|2 log(tan(----------))
--R                         8
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 100
cc:=aa-bb
 

   (3)
          +-+        4a x - %pi
       - \|2 log(tan(----------))
                          8
     + 
                   +-+                    +-+                 +-+
        +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
       \|2 log(------------------------------------------------------)
                                 sin(a x) - cos(a x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R          +-+        4a x - %pi
--R       - \|2 log(tan(----------))
--R                          8
--R     + 
--R                   +-+                    +-+                 +-+
--R        +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
--R       \|2 log(------------------------------------------------------)
--R                                 sin(a x) - cos(a x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 101    14:412 Schaums and Axiom differ by a constant
complexNormalize cc
 

         +-+     +-+
        \|2 log(\|2  - 1)
   (4)  -----------------
                2a
                                                     Type: Expression Integer
--R
--R         +-+     +-+
--R        \|2 log(\|2  - 1)
--R   (4)  -----------------
--R                2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 102
aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x)
 

                  2             - 2sin(a x) - 2cos(a x)
        log(------------) - log(-----------------------) + a x
            cos(a x) + 1              cos(a x) + 1
   (1)  ------------------------------------------------------
                                  2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2             - 2sin(a x) - 2cos(a x)
--R        log(------------) - log(-----------------------) + a x
--R            cos(a x) + 1              cos(a x) + 1
--R   (1)  ------------------------------------------------------
--R                                  2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103
bb:=x/2-1/(2*a)*log(sin(a*x)+cos(a*x))
 

        - log(sin(a x) + cos(a x)) + a x
   (2)  --------------------------------
                       2a
                                                     Type: Expression Integer
--R
--R        - log(sin(a x) + cos(a x)) + a x
--R   (2)  --------------------------------
--R                       2a
--R                                                     Type: Expression Integer
--E

--S 104
cc:=aa-bb
 

   (3)
                                        2             - 2sin(a x) - 2cos(a x)
   log(sin(a x) + cos(a x)) + log(------------) - log(-----------------------)
                                  cos(a x) + 1              cos(a x) + 1
   ---------------------------------------------------------------------------
                                        2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                        2             - 2sin(a x) - 2cos(a x)
--R   log(sin(a x) + cos(a x)) + log(------------) - log(-----------------------)
--R                                  cos(a x) + 1              cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                        2a
--R                                                     Type: Expression Integer
--E

--S 105
dd:=expandLog cc
 

        log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x))
   (4)  -----------------------------------------------------
                                  2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x))
--R   (4)  -----------------------------------------------------
--R                                  2a
--R                                                     Type: Expression Integer
--E

--S 106
ee:=complexNormalize dd
 

        log(- 1)
   (5)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all 
 
   All user variables and function definitions have been cleared.

--S 107
aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x)
 

            2sin(a x) - 2cos(a x)              2
        log(---------------------) - log(------------) + a x
                 cos(a x) + 1            cos(a x) + 1
   (1)  ----------------------------------------------------
                                 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2sin(a x) - 2cos(a x)              2
--R        log(---------------------) - log(------------) + a x
--R                 cos(a x) + 1            cos(a x) + 1
--R   (1)  ----------------------------------------------------
--R                                 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 108
bb:=x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
 

        log(sin(a x) - cos(a x)) + a x
   (2)  ------------------------------
                      2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) - cos(a x)) + a x
--R   (2)  ------------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 109
cc:=aa-bb
 

   (3)
                                    2sin(a x) - 2cos(a x)              2
   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
                                         cos(a x) + 1            cos(a x) + 1
   ---------------------------------------------------------------------------
                                        2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2sin(a x) - 2cos(a x)              2
--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
--R                                         cos(a x) + 1            cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                        2a
--R                                                     Type: Expression Integer
--E

--S 110    14:413 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 111
aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x)
 

                    2             - 2sin(a x) - 2cos(a x)
        - log(------------) + log(-----------------------) + a x
              cos(a x) + 1              cos(a x) + 1
   (1)  --------------------------------------------------------
                                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2             - 2sin(a x) - 2cos(a x)
--R        - log(------------) + log(-----------------------) + a x
--R              cos(a x) + 1              cos(a x) + 1
--R   (1)  --------------------------------------------------------
--R                                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 112
bb:=x/2+1/(2*a)*log(sin(a*x)+cos(a*x))
 

        log(sin(a x) + cos(a x)) + a x
   (2)  ------------------------------
                      2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) + cos(a x)) + a x
--R   (2)  ------------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 113
cc:=aa-bb
 

   (3)
                                          2             - 2sin(a x) - 2cos(a x)
   - log(sin(a x) + cos(a x)) - log(------------) + log(-----------------------)
                                    cos(a x) + 1              cos(a x) + 1
   -----------------------------------------------------------------------------
                                         2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                          2             - 2sin(a x) - 2cos(a x)
--R   - log(sin(a x) + cos(a x)) - log(------------) + log(-----------------------)
--R                                    cos(a x) + 1              cos(a x) + 1
--R   -----------------------------------------------------------------------------
--R                                         2a
--R                                                     Type: Expression Integer
--E

--S 114
dd:=expandLog cc
 

        - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x))
   (4)  -------------------------------------------------------
                                   2a
                                                     Type: Expression Integer
--R
--R        - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x))
--R   (4)  -------------------------------------------------------
--R                                   2a
--R                                                     Type: Expression Integer
--E

--S 115
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 116
aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x)
 

            2sin(a x) - 2cos(a x)              2
        log(---------------------) - log(------------) - a x
                 cos(a x) + 1            cos(a x) + 1
   (1)  ----------------------------------------------------
                                 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2sin(a x) - 2cos(a x)              2
--R        log(---------------------) - log(------------) - a x
--R                 cos(a x) + 1            cos(a x) + 1
--R   (1)  ----------------------------------------------------
--R                                 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 117
bb:=-x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
 

        log(sin(a x) - cos(a x)) - a x
   (2)  ------------------------------
                      2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) - cos(a x)) - a x
--R   (2)  ------------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 118
cc:=aa-bb
 

   (3)
                                    2sin(a x) - 2cos(a x)              2
   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
                                         cos(a x) + 1            cos(a x) + 1
   ---------------------------------------------------------------------------
                                        2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2sin(a x) - 2cos(a x)              2
--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
--R                                         cos(a x) + 1            cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                        2a
--R                                                     Type: Expression Integer
--E

--S 119    14:414 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 120
aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x)
 

                  2             - 2q cos(a x) - 2p
        log(------------) - log(------------------)
            cos(a x) + 1           cos(a x) + 1
   (1)  -------------------------------------------
                            a q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2             - 2q cos(a x) - 2p
--R        log(------------) - log(------------------)
--R            cos(a x) + 1           cos(a x) + 1
--R   (1)  -------------------------------------------
--R                            a q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 121
bb:=-1/(a*q)*log(p+q*cos(a*x))
 

          log(q cos(a x) + p)
   (2)  - -------------------
                  a q
                                                     Type: Expression Integer
--R
--R          log(q cos(a x) + p)
--R   (2)  - -------------------
--R                  a q
--R                                                     Type: Expression Integer
--E

--S 122
cc:=aa-bb
 

                                        2             - 2q cos(a x) - 2p
        log(q cos(a x) + p) + log(------------) - log(------------------)
                                  cos(a x) + 1           cos(a x) + 1
   (3)  -----------------------------------------------------------------
                                       a q
                                                     Type: Expression Integer
--R
--R                                        2             - 2q cos(a x) - 2p
--R        log(q cos(a x) + p) + log(------------) - log(------------------)
--R                                  cos(a x) + 1           cos(a x) + 1
--R   (3)  -----------------------------------------------------------------
--R                                       a q
--R                                                     Type: Expression Integer
--E

--S 123
dd:=expandLog cc
 

        log(q cos(a x) + p) - log(- q cos(a x) - p)
   (4)  -------------------------------------------
                            a q
                                                     Type: Expression Integer
--R
--R        log(q cos(a x) + p) - log(- q cos(a x) - p)
--R   (4)  -------------------------------------------
--R                            a q
--R                                                     Type: Expression Integer
--E

--S 124    14:415 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        log(- 1)
   (5)  --------
           a q
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R           a q
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 125
aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x)
 

            2q sin(a x) + 2p              2
        log(----------------) - log(------------)
              cos(a x) + 1          cos(a x) + 1
   (1)  -----------------------------------------
                           a q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2q sin(a x) + 2p              2
--R        log(----------------) - log(------------)
--R              cos(a x) + 1          cos(a x) + 1
--R   (1)  -----------------------------------------
--R                           a q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 126
bb:=1/(a*q)*log(p+q*sin(a*x))
 

        log(q sin(a x) + p)
   (2)  -------------------
                a q
                                                     Type: Expression Integer
--R
--R        log(q sin(a x) + p)
--R   (2)  -------------------
--R                a q
--R                                                     Type: Expression Integer
--E

--S 127
cc:=aa-bb
 

                                    2q sin(a x) + 2p              2
        - log(q sin(a x) + p) + log(----------------) - log(------------)
                                      cos(a x) + 1          cos(a x) + 1
   (3)  -----------------------------------------------------------------
                                       a q
                                                     Type: Expression Integer
--R
--R                                    2q sin(a x) + 2p              2
--R        - log(q sin(a x) + p) + log(----------------) - log(------------)
--R                                      cos(a x) + 1          cos(a x) + 1
--R   (3)  -----------------------------------------------------------------
--R                                       a q
--R                                                     Type: Expression Integer
--E

--S 128    14:416 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 129
aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x)
 

                  q cos(a x) + p
   (1)  ----------------------------------
                     n log(q cos(a x) + p)
        (a n - a)q %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  q cos(a x) + p
--R   (1)  ----------------------------------
--R                     n log(q cos(a x) + p)
--R        (a n - a)q %e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 130
bb:=1/(a*q*(n-1)*(p+q*cos(a*x))^(n-1))
 

                        1
   (2)  --------------------------------
                                   n - 1
        (a n - a)q (q cos(a x) + p)
                                                     Type: Expression Integer
--R
--R                        1
--R   (2)  --------------------------------
--R                                   n - 1
--R        (a n - a)q (q cos(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 131
cc:=aa-bb
 

            n log(q cos(a x) + p)                                   n - 1
        - %e                      + (q cos(a x) + p)(q cos(a x) + p)
   (3)  -----------------------------------------------------------------
                                        n - 1  n log(q cos(a x) + p)
             (a n - a)q (q cos(a x) + p)     %e
                                                     Type: Expression Integer
--R
--R            n log(q cos(a x) + p)                                   n - 1
--R        - %e                      + (q cos(a x) + p)(q cos(a x) + p)
--R   (3)  -----------------------------------------------------------------
--R                                        n - 1  n log(q cos(a x) + p)
--R             (a n - a)q (q cos(a x) + p)     %e
--R                                                     Type: Expression Integer
--E

--S 132
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 133
dd:=explog cc
 

                          n                                   n - 1
        - (q cos(a x) + p)  + (q cos(a x) + p)(q cos(a x) + p)
   (5)  -----------------------------------------------------------
                                        n - 1                n
             (a n - a)q (q cos(a x) + p)     (q cos(a x) + p)
                                                     Type: Expression Integer
--R
--R                          n                                   n - 1
--R        - (q cos(a x) + p)  + (q cos(a x) + p)(q cos(a x) + p)
--R   (5)  -----------------------------------------------------------
--R                                        n - 1                n
--R             (a n - a)q (q cos(a x) + p)     (q cos(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 134    14:417 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 135
aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x)
 

                 - q sin(a x) - p
   (1)  ----------------------------------
                     n log(q sin(a x) + p)
        (a n - a)q %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 - q sin(a x) - p
--R   (1)  ----------------------------------
--R                     n log(q sin(a x) + p)
--R        (a n - a)q %e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 136
bb:=-1/(a*q*(n-1)*(p+q*sin(a*x))^(n-1))
 

                          1
   (2)  - --------------------------------
                                     n - 1
          (a n - a)q (q sin(a x) + p)
                                                     Type: Expression Integer
--R
--R                          1
--R   (2)  - --------------------------------
--R                                     n - 1
--R          (a n - a)q (q sin(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 137
cc:=aa-bb
 

          n log(q sin(a x) + p)                                     n - 1
        %e                      + (- q sin(a x) - p)(q sin(a x) + p)
   (3)  -----------------------------------------------------------------
                                        n - 1  n log(q sin(a x) + p)
             (a n - a)q (q sin(a x) + p)     %e
                                                     Type: Expression Integer
--R
--R          n log(q sin(a x) + p)                                     n - 1
--R        %e                      + (- q sin(a x) - p)(q sin(a x) + p)
--R   (3)  -----------------------------------------------------------------
--R                                        n - 1  n log(q sin(a x) + p)
--R             (a n - a)q (q sin(a x) + p)     %e
--R                                                     Type: Expression Integer
--E

--S 138
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 139
dd:=explog cc
 

                        n                                     n - 1
        (q sin(a x) + p)  + (- q sin(a x) - p)(q sin(a x) + p)
   (5)  -----------------------------------------------------------
                                        n - 1                n
             (a n - a)q (q sin(a x) + p)     (q sin(a x) + p)
                                                     Type: Expression Integer
--R
--R                        n                                     n - 1
--R        (q sin(a x) + p)  + (- q sin(a x) - p)(q sin(a x) + p)
--R   (5)  -----------------------------------------------------------
--R                                        n - 1                n
--R             (a n - a)q (q sin(a x) + p)     (q sin(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 140    14:418 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 141
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x)
 

   (1)
     log
                                                  +-------+
                             2            2    2  | 2    2
            (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
          + 
                3    2                 2    3               2    3
            (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
       /
          p sin(a x) + q cos(a x)
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     log
--R                                                  +-------+
--R                             2            2    2  | 2    2
--R            (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
--R          + 
--R                3    2                 2    3               2    3
--R            (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
--R       /
--R          p sin(a x) + q cos(a x)
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 142
bb:=1/(a*sqrt(p^2+q^2))*log(tan((a*x+atan(q/p))/2))
 

                     q
                atan(-) + a x
                     p
        log(tan(-------------))
                      2
   (2)  -----------------------
                +-------+
                | 2    2
              a\|q  + p
                                                     Type: Expression Integer
--R
--R                     q
--R                atan(-) + a x
--R                     p
--R        log(tan(-------------))
--R                      2
--R   (2)  -----------------------
--R                +-------+
--R                | 2    2
--R              a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 143
cc:=aa-bb
 

   (3)
                      q
                 atan(-) + a x
                      p
       - log(tan(-------------))
                       2
     + 
       log
                                                    +-------+
                               2            2    2  | 2    2
              (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
            + 
                  3    2                 2    3               2    3
              (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
         /
            p sin(a x) + q cos(a x)
  /
       +-------+
       | 2    2
     a\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                      q
--R                 atan(-) + a x
--R                      p
--R       - log(tan(-------------))
--R                       2
--R     + 
--R       log
--R                                                    +-------+
--R                               2            2    2  | 2    2
--R              (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
--R            + 
--R                  3    2                 2    3               2    3
--R              (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
--R         /
--R            p sin(a x) + q cos(a x)
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 144
dd:=normalize cc
 

                            +-------+
                            | 2    2     2     2
                       - 2p\|q  + p   + q  + 2p
          log(------------------------------------------)
                            +-------+
                   2     3  | 2    2     4     2 2     4
              (3p q  + 4p )\|q  + p   - q  - 5p q  - 4p
   (4)  - -----------------------------------------------
                              +-------+
                              | 2    2
                            a\|q  + p
                                                     Type: Expression Integer
--R
--R                            +-------+
--R                            | 2    2     2     2
--R                       - 2p\|q  + p   + q  + 2p
--R          log(------------------------------------------)
--R                            +-------+
--R                   2     3  | 2    2     4     2 2     4
--R              (3p q  + 4p )\|q  + p   - q  - 5p q  - 4p
--R   (4)  - -----------------------------------------------
--R                              +-------+
--R                              | 2    2
--R                            a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 145    14:419 Schaums and Axiom differ by a constant
ee:=ratDenom dd
 

                            +-------+
           +-------+        | 2    2     2    2
           | 2    2     - p\|q  + p   - q  - p
          \|q  + p  log(-----------------------)
                                4    2 2
                               q  + p q
   (5)  - --------------------------------------
                           2      2
                        a q  + a p
                                                     Type: Expression Integer
--R
--R                            +-------+
--R           +-------+        | 2    2     2    2
--R           | 2    2     - p\|q  + p   - q  - p
--R          \|q  + p  log(-----------------------)
--R                                4    2 2
--R                               q  + p q
--R   (5)  - --------------------------------------
--R                           2      2
--R                        a q  + a p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 146
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x)
 

   (1)
   [
       log
                                              2          2                   2
                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
                  + 
                     2
                    p
             *
                 +--------------+
                 |   2    2    2
                \|- r  + q  + p
            + 
                3      2       2    2      3    2
              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
            + 
                  2      2    3               2      2    3
              (p r  - p q  - p )cos(a x) + p r  - p q  - p
         /
            p sin(a x) + q cos(a x) + r
    /
         +--------------+
         |   2    2    2
       a\|- r  + q  + p
     ,
                                             +------------+
                                             | 2    2    2
          ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
    2atan(-------------------------------------------------)
                  2    2    2             2    2    2
                (r  - q  - p )cos(a x) + r  - q  - p
    --------------------------------------------------------]
                          +------------+
                          | 2    2    2
                        a\|r  - q  - p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                                              2          2                   2
--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
--R                  + 
--R                     2
--R                    p
--R             *
--R                 +--------------+
--R                 |   2    2    2
--R                \|- r  + q  + p
--R            + 
--R                3      2       2    2      3    2
--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
--R            + 
--R                  2      2    3               2      2    3
--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
--R         /
--R            p sin(a x) + q cos(a x) + r
--R    /
--R         +--------------+
--R         |   2    2    2
--R       a\|- r  + q  + p
--R     ,
--R                                             +------------+
--R                                             | 2    2    2
--R          ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
--R    2atan(-------------------------------------------------)
--R                  2    2    2             2    2    2
--R                (r  - q  - p )cos(a x) + r  - q  - p
--R    --------------------------------------------------------]
--R                          +------------+
--R                          | 2    2    2
--R                        a\|r  - q  - p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 147
bb1:=2/(a*sqrt(r^2-p^2-q^2))*atan((p+(r-q)*tan((a*x)/2))/sqrt(r^2-p^2-q^2))
 

                         a x
              (r - q)tan(---) + p
                          2
        2atan(-------------------)
                 +------------+
                 | 2    2    2
                \|r  - q  - p
   (2)  --------------------------
               +------------+
               | 2    2    2
             a\|r  - q  - p
                                                     Type: Expression Integer
--R
--R                         a x
--R              (r - q)tan(---) + p
--R                          2
--R        2atan(-------------------)
--R                 +------------+
--R                 | 2    2    2
--R                \|r  - q  - p
--R   (2)  --------------------------
--R               +------------+
--R               | 2    2    2
--R             a\|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 148
bb2:=1/(a*sqrt(p^2+q^2-r^2))*log((p-sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))/(p+sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2)))
 

               +--------------+
               |   2    2    2               a x
            - \|- r  + q  + p   + (r - q)tan(---) + p
                                              2
        log(-----------------------------------------)
              +--------------+
              |   2    2    2               a x
             \|- r  + q  + p   + (r - q)tan(---) + p
                                             2
   (3)  ----------------------------------------------
                        +--------------+
                        |   2    2    2
                      a\|- r  + q  + p
                                                     Type: Expression Integer
--R
--R               +--------------+
--R               |   2    2    2               a x
--R            - \|- r  + q  + p   + (r - q)tan(---) + p
--R                                              2
--R        log(-----------------------------------------)
--R              +--------------+
--R              |   2    2    2               a x
--R             \|- r  + q  + p   + (r - q)tan(---) + p
--R                                             2
--R   (3)  ----------------------------------------------
--R                        +--------------+
--R                        |   2    2    2
--R                      a\|- r  + q  + p
--R                                                     Type: Expression Integer
--E

--S 149
cc1:=aa.1-bb1
 

   (4)
          +------------+
          | 2    2    2
         \|r  - q  - p
      *
         log
                                              2          2                   2
                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
                  + 
                     2
                    p
               *
                   +--------------+
                   |   2    2    2
                  \|- r  + q  + p
              + 
                  3      2       2    2      3    2
                (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
              + 
                    2      2    3               2      2    3
                (p r  - p q  - p )cos(a x) + p r  - p q  - p
           /
              p sin(a x) + q cos(a x) + r
     + 
                                           a x
           +--------------+     (r - q)tan(---) + p
           |   2    2    2                  2
       - 2\|- r  + q  + p  atan(-------------------)
                                   +------------+
                                   | 2    2    2
                                  \|r  - q  - p
  /
       +--------------+ +------------+
       |   2    2    2  | 2    2    2
     a\|- r  + q  + p  \|r  - q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +------------+
--R          | 2    2    2
--R         \|r  - q  - p
--R      *
--R         log
--R                                              2          2                   2
--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
--R                  + 
--R                     2
--R                    p
--R               *
--R                   +--------------+
--R                   |   2    2    2
--R                  \|- r  + q  + p
--R              + 
--R                  3      2       2    2      3    2
--R                (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
--R              + 
--R                    2      2    3               2      2    3
--R                (p r  - p q  - p )cos(a x) + p r  - p q  - p
--R           /
--R              p sin(a x) + q cos(a x) + r
--R     + 
--R                                           a x
--R           +--------------+     (r - q)tan(---) + p
--R           |   2    2    2                  2
--R       - 2\|- r  + q  + p  atan(-------------------)
--R                                   +------------+
--R                                   | 2    2    2
--R                                  \|r  - q  - p
--R  /
--R       +--------------+ +------------+
--R       |   2    2    2  | 2    2    2
--R     a\|- r  + q  + p  \|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 150
cc2:=aa.2-bb1
 

   (5)
                                                +------------+
                                                | 2    2    2
             ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
       2atan(-------------------------------------------------)
                     2    2    2             2    2    2
                   (r  - q  - p )cos(a x) + r  - q  - p
     + 
                          a x
               (r - q)tan(---) + p
                           2
       - 2atan(-------------------)
                  +------------+
                  | 2    2    2
                 \|r  - q  - p
  /
       +------------+
       | 2    2    2
     a\|r  - q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                +------------+
--R                                                | 2    2    2
--R             ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
--R       2atan(-------------------------------------------------)
--R                     2    2    2             2    2    2
--R                   (r  - q  - p )cos(a x) + r  - q  - p
--R     + 
--R                          a x
--R               (r - q)tan(---) + p
--R                           2
--R       - 2atan(-------------------)
--R                  +------------+
--R                  | 2    2    2
--R                 \|r  - q  - p
--R  /
--R       +------------+
--R       | 2    2    2
--R     a\|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 151
cc3:=aa.1-bb2
 

   (6)
       log
                                              2          2                   2
                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
                  + 
                     2
                    p
             *
                 +--------------+
                 |   2    2    2
                \|- r  + q  + p
            + 
                3      2       2    2      3    2
              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
            + 
                  2      2    3               2      2    3
              (p r  - p q  - p )cos(a x) + p r  - p q  - p
         /
            p sin(a x) + q cos(a x) + r
     + 
                +--------------+
                |   2    2    2               a x
             - \|- r  + q  + p   + (r - q)tan(---) + p
                                               2
       - log(-----------------------------------------)
               +--------------+
               |   2    2    2               a x
              \|- r  + q  + p   + (r - q)tan(---) + p
                                              2
  /
       +--------------+
       |   2    2    2
     a\|- r  + q  + p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                                              2          2                   2
--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
--R                  + 
--R                     2
--R                    p
--R             *
--R                 +--------------+
--R                 |   2    2    2
--R                \|- r  + q  + p
--R            + 
--R                3      2       2    2      3    2
--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
--R            + 
--R                  2      2    3               2      2    3
--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
--R         /
--R            p sin(a x) + q cos(a x) + r
--R     + 
--R                +--------------+
--R                |   2    2    2               a x
--R             - \|- r  + q  + p   + (r - q)tan(---) + p
--R                                               2
--R       - log(-----------------------------------------)
--R               +--------------+
--R               |   2    2    2               a x
--R              \|- r  + q  + p   + (r - q)tan(---) + p
--R                                              2
--R  /
--R       +--------------+
--R       |   2    2    2
--R     a\|- r  + q  + p
--R                                                     Type: Expression Integer
--E

--S 152
cc4:=aa.2-bb2
 

   (7)
                               +--------------+
                               |   2    2    2               a x
          +------------+    - \|- r  + q  + p   + (r - q)tan(---) + p
          | 2    2    2                                       2
       - \|r  - q  - p  log(-----------------------------------------)
                              +--------------+
                              |   2    2    2               a x
                             \|- r  + q  + p   + (r - q)tan(---) + p
                                                             2
     + 
                                                               +------------+
       +--------------+                                        | 2    2    2
       |   2    2    2      ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
     2\|- r  + q  + p  atan(-------------------------------------------------)
                                    2    2    2             2    2    2
                                  (r  - q  - p )cos(a x) + r  - q  - p
  /
       +--------------+ +------------+
       |   2    2    2  | 2    2    2
     a\|- r  + q  + p  \|r  - q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                               +--------------+
--R                               |   2    2    2               a x
--R          +------------+    - \|- r  + q  + p   + (r - q)tan(---) + p
--R          | 2    2    2                                       2
--R       - \|r  - q  - p  log(-----------------------------------------)
--R                              +--------------+
--R                              |   2    2    2               a x
--R                             \|- r  + q  + p   + (r - q)tan(---) + p
--R                                                             2
--R     + 
--R                                                               +------------+
--R       +--------------+                                        | 2    2    2
--R       |   2    2    2      ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
--R     2\|- r  + q  + p  atan(-------------------------------------------------)
--R                                    2    2    2             2    2    2
--R                                  (r  - q  - p )cos(a x) + r  - q  - p
--R  /
--R       +--------------+ +------------+
--R       |   2    2    2  | 2    2    2
--R     a\|- r  + q  + p  \|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 153    14:420 Schaums and Axiom agree
dd2:=normalize cc2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 154
aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x)
 

            p sin(a x) + q cos(a x) + q
        log(---------------------------)
                    cos(a x) + 1
   (1)  --------------------------------
                       a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            p sin(a x) + q cos(a x) + q
--R        log(---------------------------)
--R                    cos(a x) + 1
--R   (1)  --------------------------------
--R                       a p
--R                                          Type: Union(Expression Integer,...)
--E

--S 155
bb:=1/(a*p)*log(q+p*tan((a*x)/2))
 

                  a x
        log(p tan(---) + q)
                   2
   (2)  -------------------
                a p
                                                     Type: Expression Integer
--R
--R                  a x
--R        log(p tan(---) + q)
--R                   2
--R   (2)  -------------------
--R                a p
--R                                                     Type: Expression Integer
--E 

--S 156
cc:=aa-bb
 

                    a x             p sin(a x) + q cos(a x) + q
        - log(p tan(---) + q) + log(---------------------------)
                     2                      cos(a x) + 1
   (3)  --------------------------------------------------------
                                   a p
                                                     Type: Expression Integer
--R
--R                    a x             p sin(a x) + q cos(a x) + q
--R        - log(p tan(---) + q) + log(---------------------------)
--R                     2                      cos(a x) + 1
--R   (3)  --------------------------------------------------------
--R                                   a p
--R                                                     Type: Expression Integer
--E

--S 157
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 158
dd:=tanrule cc
 

                                                     a x          a x
                                               p sin(---) + q cos(---)
            p sin(a x) + q cos(a x) + q               2            2
        log(---------------------------) - log(-----------------------)
                    cos(a x) + 1                           a x
                                                       cos(---)
                                                            2
   (5)  ---------------------------------------------------------------
                                      a p
                                                     Type: Expression Integer
--R
--R                                                     a x          a x
--R                                               p sin(---) + q cos(---)
--R            p sin(a x) + q cos(a x) + q               2            2
--R        log(---------------------------) - log(-----------------------)
--R                    cos(a x) + 1                           a x
--R                                                       cos(---)
--R                                                            2
--R   (5)  ---------------------------------------------------------------
--R                                      a p
--R                                                     Type: Expression Integer
--E

--S 159
ee:=expandLog dd
 

   (6)
                                                    a x          a x
       log(p sin(a x) + q cos(a x) + q) - log(p sin(---) + q cos(---))
                                                     2            2
     + 
                                     a x
       - log(cos(a x) + 1) + log(cos(---))
                                      2
  /
     a p
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                    a x          a x
--R       log(p sin(a x) + q cos(a x) + q) - log(p sin(---) + q cos(---))
--R                                                     2            2
--R     + 
--R                                     a x
--R       - log(cos(a x) + 1) + log(cos(---))
--R                                      2
--R  /
--R     a p
--R                                                     Type: Expression Integer
--E

--S 160    14:421 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 161
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x)
 

   (1)
                                                                 +-------+
            5      2 3      4                5      2 3      4   | 2    2
       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
     + 
             6      2 4      4 2     6               6      2 4      4 2     6
       (- 64q  - 96p q  - 36p q  - 2p )cos(a x) - 64q  - 96p q  - 36p q  - 2p
  /
                 6        2 4        4 2      6
           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
         + 
                   5        3 3       5                    5        3 3       5
         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
      *
          +-------+
          | 2    2
         \|q  + p
     + 
               7         2 5        4 3       6
       (- 64a q  - 112a p q  - 56a p q  - 7a p q)sin(a x)
     + 
               6        3 4        5 2      7                   6        3 4
       (32a p q  + 48a p q  + 18a p q  + a p )cos(a x) + 32a p q  + 48a p q
     + 
            5 2      7
       18a p q  + a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                 +-------+
--R            5      2 3      4                5      2 3      4   | 2    2
--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
--R     + 
--R             6      2 4      4 2     6               6      2 4      4 2     6
--R       (- 64q  - 96p q  - 36p q  - 2p )cos(a x) - 64q  - 96p q  - 36p q  - 2p
--R  /
--R                 6        2 4        4 2      6
--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
--R         + 
--R                   5        3 3       5                    5        3 3       5
--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R               7         2 5        4 3       6
--R       (- 64a q  - 112a p q  - 56a p q  - 7a p q)sin(a x)
--R     + 
--R               6        3 4        5 2      7                   6        3 4
--R       (32a p q  + 48a p q  + 18a p q  + a p )cos(a x) + 32a p q  + 48a p q
--R     + 
--R            5 2      7
--R       18a p q  + a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 162
bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4-(a*x+atan(q/p))/2)
 

                  q
            2atan(-) + 2a x - %pi
                  p
        tan(---------------------)
                      4
   (2)  --------------------------
                  +-------+
                  | 2    2
                a\|q  + p
                                                     Type: Expression Integer
--R
--R                  q
--R            2atan(-) + 2a x - %pi
--R                  p
--R        tan(---------------------)
--R                      4
--R   (2)  --------------------------
--R                  +-------+
--R                  | 2    2
--R                a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 163
cc:=aa-bb
 

   (3)
                   6      2 4      4 2    6
               (64q  + 80p q  + 24p q  + p )sin(a x)
             + 
                       5      3 3     5                  5      3 3     5
               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
          *
              +-------+
              | 2    2
             \|q  + p
         + 
                 7       2 5      4 3     6
           (- 64q  - 112p q  - 56p q  - 7p q)sin(a x)
         + 
               6      3 4      5 2    7                 6      3 4      5 2    7
         (32p q  + 48p q  + 18p q  + p )cos(a x) + 32p q  + 48p q  + 18p q  + p
      *
                   q
             2atan(-) + 2a x - %pi
                   p
         tan(---------------------)
                       4
     + 
              6      2 4      4 2     6               6      2 4      4 2     6
         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
      *
          +-------+
          | 2    2
         \|q  + p
     + 
             7       2 5      4 3      6                7       2 5      4 3
       (- 64q  - 128p q  - 76p q  - 12p q)cos(a x) - 64q  - 128p q  - 76p q
     + 
            6
       - 12p q
  /
                 7         2 5        4 3       6
           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
         + 
                     6        3 4        5 2      7                   6
           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
         + 
                  3 4        5 2      7
           - 48a p q  - 18a p q  - a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
               8         2 6         4 4        6 2      8
       (- 64a q  - 144a p q  - 104a p q  - 25a p q  - a p )sin(a x)
     + 
               7        3 5        5 3       7                    7        3 5
       (32a p q  + 64a p q  + 38a p q  + 6a p q)cos(a x) + 32a p q  + 64a p q
     + 
            5 3       7
       38a p q  + 6a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R                   6      2 4      4 2    6
--R               (64q  + 80p q  + 24p q  + p )sin(a x)
--R             + 
--R                       5      3 3     5                  5      3 3     5
--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
--R          *
--R              +-------+
--R              | 2    2
--R             \|q  + p
--R         + 
--R                 7       2 5      4 3     6
--R           (- 64q  - 112p q  - 56p q  - 7p q)sin(a x)
--R         + 
--R               6      3 4      5 2    7                 6      3 4      5 2    7
--R         (32p q  + 48p q  + 18p q  + p )cos(a x) + 32p q  + 48p q  + 18p q  + p
--R      *
--R                   q
--R             2atan(-) + 2a x - %pi
--R                   p
--R         tan(---------------------)
--R                       4
--R     + 
--R              6      2 4      4 2     6               6      2 4      4 2     6
--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R             7       2 5      4 3      6                7       2 5      4 3
--R       (- 64q  - 128p q  - 76p q  - 12p q)cos(a x) - 64q  - 128p q  - 76p q
--R     + 
--R            6
--R       - 12p q
--R  /
--R                 7         2 5        4 3       6
--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
--R         + 
--R                     6        3 4        5 2      7                   6
--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
--R         + 
--R                  3 4        5 2      7
--R           - 48a p q  - 18a p q  - a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R               8         2 6         4 4        6 2      8
--R       (- 64a q  - 144a p q  - 104a p q  - 25a p q  - a p )sin(a x)
--R     + 
--R               7        3 5        5 3       7                    7        3 5
--R       (32a p q  + 64a p q  + 38a p q  + 6a p q)cos(a x) + 32a p q  + 64a p q
--R     + 
--R            5 3       7
--R       38a p q  + 6a p q
--R                                                     Type: Expression Integer
--E

--S 164
dd:=normalize cc
 

   (4)
                                                                  +-------+
               6      2 5      3 4      4 3      5 2     6     7  | 2    2
       (- 32p q  - 16p q  - 48p q  - 20p q  - 18p q  - 5p q - p )\|q  + p
     + 
            7      2 6      3 5      4 4      5 3      6 2     7     8
       32p q  + 16p q  + 64p q  + 28p q  + 38p q  + 13p q  + 6p q + p
  /
                8          7         2 6        3 5         4 4        5 3
           64a q  + 32a p q  + 144a p q  + 64a p q  + 104a p q  + 38a p q
         + 
                6 2       7       8
           25a p q  + 6a p q + a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
              9          8         2 7        3 6         4 5        5 4
       - 64a q  - 32a p q  - 176a p q  - 80a p q  - 168a p q  - 66a p q
     + 
              6 3        7 2       8       9
       - 63a p q  - 19a p q  - 7a p q - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                  +-------+
--R               6      2 5      3 4      4 3      5 2     6     7  | 2    2
--R       (- 32p q  - 16p q  - 48p q  - 20p q  - 18p q  - 5p q - p )\|q  + p
--R     + 
--R            7      2 6      3 5      4 4      5 3      6 2     7     8
--R       32p q  + 16p q  + 64p q  + 28p q  + 38p q  + 13p q  + 6p q + p
--R  /
--R                8          7         2 6        3 5         4 4        5 3
--R           64a q  + 32a p q  + 144a p q  + 64a p q  + 104a p q  + 38a p q
--R         + 
--R                6 2       7       8
--R           25a p q  + 6a p q + a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R              9          8         2 7        3 6         4 5        5 4
--R       - 64a q  - 32a p q  - 176a p q  - 80a p q  - 168a p q  - 66a p q
--R     + 
--R              6 3        7 2       8       9
--R       - 63a p q  - 19a p q  - 7a p q - a p
--R                                                     Type: Expression Integer
--E

--S 165
ee:=ratDenom dd
 

            +-------+
            | 2    2     2    2
        - q\|q  + p   - q  - p
   (5)  -----------------------
                  2      3
             a p q  + a p
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2    2
--R        - q\|q  + p   - q  - p
--R   (5)  -----------------------
--R                  2      3
--R             a p q  + a p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 166
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x)
 

   (1)
                                                                 +-------+
            5      2 3      4                5      2 3      4   | 2    2
       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
     + 
           6      2 4      4 2     6               6      2 4      4 2     6
       (64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p
  /
                 6        2 4        4 2      6
           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
         + 
                   5        3 3       5                    5        3 3       5
         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
      *
          +-------+
          | 2    2
         \|q  + p
     + 
             7         2 5        4 3       6
       (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
     + 
                 6        3 4        5 2      7                   6        3 4
       (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q  - 48a p q
     + 
              5 2      7
       - 18a p q  - a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                 +-------+
--R            5      2 3      4                5      2 3      4   | 2    2
--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
--R     + 
--R           6      2 4      4 2     6               6      2 4      4 2     6
--R       (64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p
--R  /
--R                 6        2 4        4 2      6
--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
--R         + 
--R                   5        3 3       5                    5        3 3       5
--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R             7         2 5        4 3       6
--R       (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
--R     + 
--R                 6        3 4        5 2      7                   6        3 4
--R       (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q  - 48a p q
--R     + 
--R              5 2      7
--R       - 18a p q  - a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 167
bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4+(a*x+atan(q/p))/2)
 

                    q
              2atan(-) + 2a x + %pi
                    p
          tan(---------------------)
                        4
   (2)  - --------------------------
                    +-------+
                    | 2    2
                  a\|q  + p
                                                     Type: Expression Integer
--R
--R                    q
--R              2atan(-) + 2a x + %pi
--R                    p
--R          tan(---------------------)
--R                        4
--R   (2)  - --------------------------
--R                    +-------+
--R                    | 2    2
--R                  a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 168
cc:=aa-bb
 

   (3)
                   6      2 4      4 2    6
               (64q  + 80p q  + 24p q  + p )sin(a x)
             + 
                       5      3 3     5                  5      3 3     5
               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
          *
              +-------+
              | 2    2
             \|q  + p
         + 
               7       2 5      4 3     6
           (64q  + 112p q  + 56p q  + 7p q)sin(a x)
         + 
                   6      3 4      5 2    7                 6      3 4      5 2
           (- 32p q  - 48p q  - 18p q  - p )cos(a x) - 32p q  - 48p q  - 18p q
         + 
              7
           - p
      *
                   q
             2atan(-) + 2a x + %pi
                   p
         tan(---------------------)
                       4
     + 
              6      2 4      4 2     6               6      2 4      4 2     6
         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
      *
          +-------+
          | 2    2
         \|q  + p
     + 
         7       2 5      4 3      6                7       2 5      4 3      6
     (64q  + 128p q  + 76p q  + 12p q)cos(a x) + 64q  + 128p q  + 76p q  + 12p q
  /
                 7         2 5        4 3       6
           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
         + 
                     6        3 4        5 2      7                   6
           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
         + 
                  3 4        5 2      7
           - 48a p q  - 18a p q  - a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
             8         2 6         4 4        6 2      8
       (64a q  + 144a p q  + 104a p q  + 25a p q  + a p )sin(a x)
     + 
                 7        3 5        5 3       7                    7        3 5
       (- 32a p q  - 64a p q  - 38a p q  - 6a p q)cos(a x) - 32a p q  - 64a p q
     + 
              5 3       7
       - 38a p q  - 6a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R                   6      2 4      4 2    6
--R               (64q  + 80p q  + 24p q  + p )sin(a x)
--R             + 
--R                       5      3 3     5                  5      3 3     5
--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
--R          *
--R              +-------+
--R              | 2    2
--R             \|q  + p
--R         + 
--R               7       2 5      4 3     6
--R           (64q  + 112p q  + 56p q  + 7p q)sin(a x)
--R         + 
--R                   6      3 4      5 2    7                 6      3 4      5 2
--R           (- 32p q  - 48p q  - 18p q  - p )cos(a x) - 32p q  - 48p q  - 18p q
--R         + 
--R              7
--R           - p
--R      *
--R                   q
--R             2atan(-) + 2a x + %pi
--R                   p
--R         tan(---------------------)
--R                       4
--R     + 
--R              6      2 4      4 2     6               6      2 4      4 2     6
--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R         7       2 5      4 3      6                7       2 5      4 3      6
--R     (64q  + 128p q  + 76p q  + 12p q)cos(a x) + 64q  + 128p q  + 76p q  + 12p q
--R  /
--R                 7         2 5        4 3       6
--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
--R         + 
--R                     6        3 4        5 2      7                   6
--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
--R         + 
--R                  3 4        5 2      7
--R           - 48a p q  - 18a p q  - a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R             8         2 6         4 4        6 2      8
--R       (64a q  + 144a p q  + 104a p q  + 25a p q  + a p )sin(a x)
--R     + 
--R                 7        3 5        5 3       7                    7        3 5
--R       (- 32a p q  - 64a p q  - 38a p q  - 6a p q)cos(a x) - 32a p q  - 64a p q
--R     + 
--R              5 3       7
--R       - 38a p q  - 6a p q
--R                                                     Type: Expression Integer
--E

--S 169
dd:=normalize cc
 

   (4)
                                                                  +-------+
               6      2 5      3 4      4 3      5 2     6     7  | 2    2
       (- 32p q  + 16p q  - 48p q  + 20p q  - 18p q  + 5p q - p )\|q  + p
     + 
              7      2 6      3 5      4 4      5 3      6 2     7     8
       - 32p q  + 16p q  - 64p q  + 28p q  - 38p q  + 13p q  - 6p q + p
  /
                8          7         2 6        3 5         4 4        5 3
           64a q  - 32a p q  + 144a p q  - 64a p q  + 104a p q  - 38a p q
         + 
                6 2       7       8
           25a p q  - 6a p q + a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
            9          8         2 7        3 6         4 5        5 4
       64a q  - 32a p q  + 176a p q  - 80a p q  + 168a p q  - 66a p q
     + 
            6 3        7 2       8       9
       63a p q  - 19a p q  + 7a p q - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                  +-------+
--R               6      2 5      3 4      4 3      5 2     6     7  | 2    2
--R       (- 32p q  + 16p q  - 48p q  + 20p q  - 18p q  + 5p q - p )\|q  + p
--R     + 
--R              7      2 6      3 5      4 4      5 3      6 2     7     8
--R       - 32p q  + 16p q  - 64p q  + 28p q  - 38p q  + 13p q  - 6p q + p
--R  /
--R                8          7         2 6        3 5         4 4        5 3
--R           64a q  - 32a p q  + 144a p q  - 64a p q  + 104a p q  - 38a p q
--R         + 
--R                6 2       7       8
--R           25a p q  - 6a p q + a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R            9          8         2 7        3 6         4 5        5 4
--R       64a q  - 32a p q  + 176a p q  - 80a p q  + 168a p q  - 66a p q
--R     + 
--R            6 3        7 2       8       9
--R       63a p q  - 19a p q  + 7a p q - a p
--R                                                     Type: Expression Integer
--E

--S 170    14:422 Schaums and Axiom differ by a constant
ee:=ratDenom dd
 

          +-------+
          | 2    2     2    2
        q\|q  + p   - q  - p
   (5)  ---------------------
                 2      3
            a p q  + a p
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2    2
--R        q\|q  + p   - q  - p
--R   (5)  ---------------------
--R                 2      3
--R            a p q  + a p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 171
aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x)
 

                   2     2              2
                ((q  - 2p )cos(a x) - 2p )sin(a x)            q sin(a x)
        - atan(-----------------------------------) + atan(----------------)
                           2                               2p cos(a x) + 2p
               p q cos(a x)  + 2p q cos(a x) + p q
   (1)  --------------------------------------------------------------------
                                        a p q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2     2              2
--R                ((q  - 2p )cos(a x) - 2p )sin(a x)            q sin(a x)
--R        - atan(-----------------------------------) + atan(----------------)
--R                           2                               2p cos(a x) + 2p
--R               p q cos(a x)  + 2p q cos(a x) + p q
--R   (1)  --------------------------------------------------------------------
--R                                        a p q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 172
bb:=1/(a*p*q)*atan((p*tan(a*x))/q)
 

             p tan(a x)
        atan(----------)
                  q
   (2)  ----------------
              a p q
                                                     Type: Expression Integer
--R
--R             p tan(a x)
--R        atan(----------)
--R                  q
--R   (2)  ----------------
--R              a p q
--R                                                     Type: Expression Integer
--E

--S 173
cc:=aa-bb
 

   (3)
                                     2     2              2
              p tan(a x)          ((q  - 2p )cos(a x) - 2p )sin(a x)
       - atan(----------) - atan(-----------------------------------)
                   q                         2
                                 p q cos(a x)  + 2p q cos(a x) + p q
     + 
               q sin(a x)
       atan(----------------)
            2p cos(a x) + 2p
  /
     a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R                                     2     2              2
--R              p tan(a x)          ((q  - 2p )cos(a x) - 2p )sin(a x)
--R       - atan(----------) - atan(-----------------------------------)
--R                   q                         2
--R                                 p q cos(a x)  + 2p q cos(a x) + p q
--R     + 
--R               q sin(a x)
--R       atan(----------------)
--R            2p cos(a x) + 2p
--R  /
--R     a p q
--R                                                     Type: Expression Integer
--E

--S 174    14:423 Schaums and Axiom agree
dd:=normalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E


)clear all
 
   All user variables and function definitions have been cleared.

--S 175
aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x)
 

            2p sin(a x) - 2q cos(a x)        - 2p sin(a x) - 2q cos(a x)
        log(-------------------------) - log(---------------------------)
                   cos(a x) + 1                      cos(a x) + 1
   (1)  -----------------------------------------------------------------
                                      2a p q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2p sin(a x) - 2q cos(a x)        - 2p sin(a x) - 2q cos(a x)
--R        log(-------------------------) - log(---------------------------)
--R                   cos(a x) + 1                      cos(a x) + 1
--R   (1)  -----------------------------------------------------------------
--R                                      2a p q
--R                                          Type: Union(Expression Integer,...)
--E

--S 176
bb:=1/(2*a*p*q)*log((p*tan(a*x)-q)/(p*tan(a*x)+q))
 

            p tan(a x) - q
        log(--------------)
            p tan(a x) + q
   (2)  -------------------
               2a p q
                                                     Type: Expression Integer
--R
--R            p tan(a x) - q
--R        log(--------------)
--R            p tan(a x) + q
--R   (2)  -------------------
--R               2a p q
--R                                                     Type: Expression Integer
--E 

--S 177
cc:=aa-bb
 

   (3)
           2p sin(a x) - 2q cos(a x)        p tan(a x) - q
       log(-------------------------) - log(--------------)
                  cos(a x) + 1              p tan(a x) + q
     + 
             - 2p sin(a x) - 2q cos(a x)
       - log(---------------------------)
                     cos(a x) + 1
  /
     2a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R           2p sin(a x) - 2q cos(a x)        p tan(a x) - q
--R       log(-------------------------) - log(--------------)
--R                  cos(a x) + 1              p tan(a x) + q
--R     + 
--R             - 2p sin(a x) - 2q cos(a x)
--R       - log(---------------------------)
--R                     cos(a x) + 1
--R  /
--R     2a p q
--R                                                     Type: Expression Integer
--E

--S 178
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 179
dd:=tanrule cc
 

   (5)
           2p sin(a x) - 2q cos(a x)        p sin(a x) - q cos(a x)
       log(-------------------------) - log(-----------------------)
                  cos(a x) + 1              p sin(a x) + q cos(a x)
     + 
             - 2p sin(a x) - 2q cos(a x)
       - log(---------------------------)
                     cos(a x) + 1
  /
     2a p q
                                                     Type: Expression Integer
--R
--R   (5)
--R           2p sin(a x) - 2q cos(a x)        p sin(a x) - q cos(a x)
--R       log(-------------------------) - log(-----------------------)
--R                  cos(a x) + 1              p sin(a x) + q cos(a x)
--R     + 
--R             - 2p sin(a x) - 2q cos(a x)
--R       - log(---------------------------)
--R                     cos(a x) + 1
--R  /
--R     2a p q
--R                                                     Type: Expression Integer
--E

--S 180
ee:=expandLog dd
 

        log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x))
   (6)  -------------------------------------------------------------
                                    2a p q
                                                     Type: Expression Integer
--R
--R        log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x))
--R   (6)  -------------------------------------------------------------
--R                                    2a p q
--R                                                     Type: Expression Integer
--E

--S 181    14:424 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        log(- 1)
   (7)  --------
         2a p q
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R         2a p q
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 182    14:425 Axiom cannot compute this integral
aa:=integrate(sin(a*x)^m*cos(a*x)^n,x)
 

           x
         ++           n         m
   (1)   |   cos(%L a) sin(%L a) d%L
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n         m
--I   (1)   |   cos(%H a) sin(%H a) d%H
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 183    14:426 Axiom cannot compute this integral
aa:=integrate(sin(a*x)^m/cos(a*x)^n,x)
 

           x          m
         ++  sin(%L a)
   (1)   |   ---------- d%L
        ++            n
             cos(%L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x          m
--I         ++  sin(%H a)
--I   (1)   |   ---------- d%H
--R        ++            n
--I             cos(%H a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 184    14:427 Axiom cannot compute this integral
aa:=integrate(cos(a*x)^m/sin(a*x)^n,x)
 

           x          m
         ++  cos(%L a)
   (1)   |   ---------- d%L
        ++            n
             sin(%L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x          m
--I         ++  cos(%H a)
--I   (1)   |   ---------- d%H
--R        ++            n
--I             sin(%H a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 185    14:428 Axiom cannot compute this integral
aa:=integrate(1/(sin(a*x)^m*cos(a*x)^n),x)
 

           x
         ++            1
   (1)   |   -------------------- d%L
        ++            n         m
             cos(%L a) sin(%L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            1
--I   (1)   |   -------------------- d%H
--R        ++            n         m
--I             cos(%H a) sin(%H a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to nqip.output (2009/2/17, 17:55:37).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 14
outputGeneral 5
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 14
xvals := [0.00,0.04,0.08,0.12,0.22,0.26,0.30,0.38,0.39,0.42,0.45, 
               0.46,0.60,0.68,0.72,0.73,0.83,0.85,0.88,0.90,1.00];
 

                                                             Type: List Float
--R 
--R
--R                                                             Type: List Float
--E 2

--S 3 of 14
yvals := [4.0000,3.9936,3.9746,3.9432,3.8135,3.7467,3.6697,3.4943,
                 3.4719,3.4002,3.3264,3.3017,2.9412,2.7352,2.6344,
                        2.6094,2.3684,2.3222,2.2543,2.2099,2.0000];
 

                                                             Type: List Float
--R 
--R
--R                                                             Type: List Float
--E 3

--S 4 of 14
result := nagPolygonIntegrate(xvals,yvals);
 
   There are no library operations named nagPolygonIntegrate 
      Use HyperDoc Browse or issue
                        )what op nagPolygonIntegrate
      to learn if there is any operation containing " 
      nagPolygonIntegrate " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagPolygonIntegrate with argument type(s) 
                                 List Float
                                 List Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagPolygonIntegrate 
--R      Use HyperDoc Browse or issue
--R                        )what op nagPolygonIntegrate
--R      to learn if there is any operation containing " 
--R      nagPolygonIntegrate " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagPolygonIntegrate with argument type(s) 
--R                                 List Float
--R                                 List Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4

--S 5 of 14 used to work?
result.integral :: Float             
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                              Variable integral
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                              Variable integral
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5
--       3.1414

--S 6 of 14 used to work?
result.errorEstimate :: Float        
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                           Variable errorEstimate
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                           Variable errorEstimate
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6
--       - 0.000025627

--S 7 of 14
coords := transpose matrix [xvals, yvals];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 7

--S 8 of 14
result := nagPolygonIntegrate coords;
 
   There are no library operations named nagPolygonIntegrate 
      Use HyperDoc Browse or issue
                        )what op nagPolygonIntegrate
      to learn if there is any operation containing " 
      nagPolygonIntegrate " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagPolygonIntegrate with argument type(s) 
                                Matrix Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagPolygonIntegrate 
--R      Use HyperDoc Browse or issue
--R                        )what op nagPolygonIntegrate
--R      to learn if there is any operation containing " 
--R      nagPolygonIntegrate " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagPolygonIntegrate with argument type(s) 
--R                                Matrix Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 8

--S 9 of 14 used to work?
result.integral :: Float             
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                              Variable integral
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                              Variable integral
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9
--       3.1414

--S 10 of 14 used to work?
result.errorEstimate :: Float        
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                           Variable errorEstimate
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                           Variable errorEstimate
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 10
--       - 0.000025627

--S 11 of 14 broken
nagPolygonIntegrate([1,2,3],[1,2,3,4])
 
   There are no library operations named nagPolygonIntegrate 
      Use HyperDoc Browse or issue
                        )what op nagPolygonIntegrate
      to learn if there is any operation containing " 
      nagPolygonIntegrate " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagPolygonIntegrate with argument type(s) 
                            List PositiveInteger
                            List PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagPolygonIntegrate 
--R      Use HyperDoc Browse or issue
--R                        )what op nagPolygonIntegrate
--R      to learn if there is any operation containing " 
--R      nagPolygonIntegrate " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagPolygonIntegrate with argument type(s) 
--R                            List PositiveInteger
--R                            List PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11
-- 
--   Error signalled from user code:
--      The lists supplied to nagPolygonIntegrate are of different 
--      lengths: 3 and 4.

--S 12 of 14 broken
nagPolygonIntegrate([[1,2,3],[4,5,6]])
 

   (5)  nagPolygonIntegrate
                           [1,2,3],[4,5,6]
                                                                 Type: Symbol
--R 
--R
--R   (5)  nagPolygonIntegrate
--R                           [1,2,3],[4,5,6]
--R                                                                 Type: Symbol
--E 12
--
--   Error signalled from user code:
--      Please supply the coordinate matrix in nagPolygonIntegrate with
--      each row consisting of single a x-y pair.

--S 13 of 14
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 14
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 14
)spool 
 
Starts dribbling to patch51.output (2009/2/17, 17:56:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 bug #355 fix
D(besselK(a,x),x)
 

        - besselK(a + 1,x) - besselK(a - 1,x)
   (1)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R 
--R
--R        - besselK(a + 1,x) - besselK(a - 1,x)
--R   (1)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E 1
)spool 
 
Starts dribbling to int.output (2009/2/17, 17:46:38).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 47
2**(5678 - 4856 + 2 * 17)
 

   (1)
  4804810770435008147181540925125924391239526139871682263473855610088084200076_
   308293086342527091412083743074572278211496076276922026433435687527334980249_
   539302425425230458177649495442143929053063884787051467457680738771416988598_
   15495632935288783334250628775936
                                                        Type: PositiveInteger
--R 
--R
--R   (1)
--R  4804810770435008147181540925125924391239526139871682263473855610088084200076_
--R   308293086342527091412083743074572278211496076276922026433435687527334980249_
--R   539302425425230458177649495442143929053063884787051467457680738771416988598_
--R   15495632935288783334250628775936
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 47
x := -101
 

   (2)  - 101
                                                                Type: Integer
--R 
--R
--R   (2)  - 101
--R                                                                Type: Integer
--E 2

--S 3 of 47
abs(x)
 

   (3)  101
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  101
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 47
sign(x)
 

   (4)  - 1
                                                                Type: Integer
--R 
--R
--R   (4)  - 1
--R                                                                Type: Integer
--E 4

--S 5 of 47
x < 0
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5

--S 6 of 47
x <= -1
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 47
negative?(x)
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 47
x > 0
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 47
x >= 1
 

   (9)  false
                                                                Type: Boolean
--R 
--R
--R   (9)  false
--R                                                                Type: Boolean
--E 9

--S 10 of 47
positive?(x)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 47
zero?(x)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 47
one?(x)
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 47
(x = -101)@Boolean
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 47
odd?(x)
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 47
even?(x)
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 47
gcd(56788,43688)
 

   (16)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  4
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 47
lcm(56788,43688)
 

   (17)  620238536
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  620238536
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 47
max(678,567)
 

   (18)  678
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  678
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 47
min(678,567)
 

   (19)  567
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  567
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 47
reduce(max,[2,45,-89,78,100,-45])
 

   (20)  100
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  100
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 47
reduce(min,[2,45,-89,78,100,-45])
 

   (21)  - 89
                                                                Type: Integer
--R 
--R
--R   (21)  - 89
--R                                                                Type: Integer
--E 21

--S 22 of 47
reduce(gcd,[2,45,-89,78,100,-45])
 

   (22)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  1
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 47
reduce(lcm,[2,45,-89,78,100,-45])
 

   (23)  1041300
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1041300
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 47
13 / 4
 

         13
   (24)  --
          4
                                                       Type: Fraction Integer
--R 
--R
--R         13
--R   (24)  --
--R          4
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 47
13 quo 4
 

   (25)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  3
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 47
13 rem 4
 

   (26)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  1
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 47
zero?(167604736446952 rem 2003644)
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 47
d := divide(13,4)
 

   (28)  [quotient= 3,remainder= 1]
                           Type: Record(quotient: Integer,remainder: Integer)
--R 
--R
--R   (28)  [quotient= 3,remainder= 1]
--R                           Type: Record(quotient: Integer,remainder: Integer)
--E 28

--S 29 of 47
d.quotient
 

   (29)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (29)  3
--R                                                        Type: PositiveInteger
--E 29

--S 30 of 47
d.remainder
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

)clear all
 
   All user variables and function definitions have been cleared.

--S 31 of 47
factor 102400
 

         12 2
   (1)  2  5
                                                       Type: Factored Integer
--R 
--R
--R         12 2
--R   (1)  2  5
--R                                                       Type: Factored Integer
--E 31

--S 32 of 47
prime? 7
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 32

--S 33 of 47
prime? 8
 

   (3)  false
                                                                Type: Boolean
--R 
--R
--R   (3)  false
--R                                                                Type: Boolean
--E 33

--S 34 of 47
nextPrime 100
 

   (4)  101
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  101
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 47
prevPrime 100
 

   (5)  97
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  97
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 47
primes(100,175)
 

   (6)  [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101]
                                                           Type: List Integer
--R 
--R
--R   (6)  [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101]
--R                                                           Type: List Integer
--E 36

--S 37 of 47
factor(2 :: Complex Integer)
 

                     2
   (7)  - %i (1 + %i)
                                               Type: Factored Complex Integer
--R 
--R
--R                     2
--R   (7)  - %i (1 + %i)
--R                                               Type: Factored Complex Integer
--E 37

)clear all
 
   All user variables and function definitions have been cleared.

--S 38 of 47
[fibonacci(k) for k in 0..]
 

   (1)  [0,1,1,2,3,5,8,13,21,34,...]
                                                         Type: Stream Integer
--R 
--R
--R   (1)  [0,1,1,2,3,5,8,13,21,34,...]
--R                                                         Type: Stream Integer
--E 38

--S 39 of 47
[legendre(i,11) for i in 0..10]
 

   (2)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
                                                           Type: List Integer
--R 
--R
--R   (2)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
--R                                                           Type: List Integer
--E 39

--S 40 of 47
[jacobi(i,15) for i in 0..9]
 

   (3)  [0,1,1,0,1,0,0,- 1,1,0]
                                                           Type: List Integer
--R 
--R
--R   (3)  [0,1,1,0,1,0,0,- 1,1,0]
--R                                                           Type: List Integer
--E 40

--S 41 of 47
[eulerPhi i for i in 1..]
 

   (4)  [1,1,2,2,4,2,6,4,6,4,...]
                                                         Type: Stream Integer
--R 
--R
--R   (4)  [1,1,2,2,4,2,6,4,6,4,...]
--R                                                         Type: Stream Integer
--E 41

--S 42 of 47
[moebiusMu i for i in 1..]
 

   (5)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
--R                                                         Type: Stream Integer
--E 42

--S 43 of 47
a := roman(78)
 

   (6)  LXXVIII
                                                           Type: RomanNumeral
--R 
--R
--R   (6)  LXXVIII
--R                                                           Type: RomanNumeral
--E 43

--S 44 of 47
b := roman(87)
 

   (7)  LXXXVII
                                                           Type: RomanNumeral
--R 
--R
--R   (7)  LXXXVII
--R                                                           Type: RomanNumeral
--E 44

--S 45 of 47
a + b
 

   (8)  CLXV
                                                           Type: RomanNumeral
--R 
--R
--R   (8)  CLXV
--R                                                           Type: RomanNumeral
--E 45

--S 46 of 47
a * b
 

   (9)  MMMMMMDCCLXXXVI
                                                           Type: RomanNumeral
--R 
--R
--R   (9)  MMMMMMDCCLXXXVI
--R                                                           Type: RomanNumeral
--E 46

--S 47 of 47
b rem a
 

   (10)  IX
                                                           Type: RomanNumeral
--R 
--R
--R   (10)  IX
--R                                                           Type: RomanNumeral
--E 47
)spool 
 
Starts dribbling to e1.output (2009/2/17, 17:45:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 7
G:DFLOAT:=0.577215664901532860606512::DFLOAT
 

   (1)  0.57721566490153275
                                                            Type: DoubleFloat
--R
--R   (1)  0.57721566490153287
--R                                                            Type: DoubleFloat
--E 1
--S 2 of 7
f(x)==x^-1 * (E1(x)::DFLOAT + log(x) + G)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 2
--S 3 of 7
[[0.01,0.9975055452, f(0.01), f(0.01)-0.9975055452],_
[0.02,0.9950221392, f(0.02), f(0.02)-0.9950221392],_
[0.03,0.9925497201, f(0.03), f(0.03)-0.9925497201],_
[0.04,0.9900882265, f(0.04), f(0.04)-0.9900882265],_
[0.05,0.9876375971, f(0.05), f(0.05)-0.9876375971],_
[0.06,0.9851977714, f(0.06), f(0.06)-0.9851977714],_
[0.07,0.9827686889, f(0.07), f(0.07)-0.9827686889],_
[0.08,0.9803502898, f(0.08), f(0.08)-0.9803502898],_
[0.09,0.9779425142, f(0.09), f(0.09)-0.9779425142],_
[0.10,0.9755453033, f(0.10), f(0.10)-0.9755453033],_
[0.11,0.9731585980, f(0.11), f(0.11)-0.9731585980],_
[0.12,0.9707823399, f(0.12), f(0.12)-0.9707823399],_
[0.13,0.9684164710, f(0.13), f(0.13)-0.9684164710],_
[0.14,0.9660609336, f(0.14), f(0.14)-0.9660609336],_
[0.15,0.9637156702, f(0.15), f(0.15)-0.9637156702],_
[0.16,0.9613806240, f(0.16), f(0.16)-0.9613806240],_
[0.17,0.9590557383, f(0.17), f(0.17)-0.9590557383],_
[0.18,0.9567409569, f(0.18), f(0.18)-0.9567409569],_
[0.19,0.9544362237, f(0.19), f(0.19)-0.9544362237],_
[0.20,0.9521414833, f(0.20), f(0.20)-0.9521414833],_
[0.21,0.9498566804, f(0.21), f(0.21)-0.9498566804],_
[0.22,0.9475817603, f(0.22), f(0.22)-0.9475817603],_
[0.23,0.9453166684, f(0.23), f(0.23)-0.9453166684],_
[0.24,0.9430613506, f(0.24), f(0.24)-0.9430613506],_
[0.25,0.9408157528, f(0.25), f(0.25)-0.9408157528],_
[0.26,0.9385798221, f(0.26), f(0.26)-0.9385798221],_
[0.27,0.9363535046, f(0.27), f(0.27)-0.9363535046],_
[0.28,0.9341367481, f(0.28), f(0.28)-0.9341367481],_
[0.29,0.9319294997, f(0.29), f(0.29)-0.9319294997],_
[0.30,0.9297317075, f(0.30), f(0.30)-0.9297317075],_
[0.31,0.9275433196, f(0.31), f(0.31)-0.9275433196],_
[0.32,0.9253642845, f(0.32), f(0.32)-0.9253642845],_
[0.33,0.9231945510, f(0.33), f(0.33)-0.9231945510],_
[0.34,0.9210340684, f(0.34), f(0.34)-0.9210340684],_
[0.35,0.9188827858, f(0.35), f(0.35)-0.9188827858],_
[0.36,0.9167406533, f(0.36), f(0.36)-0.9167406533],_
[0.37,0.9146076209, f(0.37), f(0.37)-0.9146076209],_
[0.38,0.9124836388, f(0.38), f(0.38)-0.9124836388],_
[0.39,0.9103686582, f(0.39), f(0.39)-0.9103686582],_
[0.40,0.9082626297, f(0.40), f(0.40)-0.9082626297],_
[0.41,0.9061655048, f(0.41), f(0.41)-0.9061655048],_
[0.42,0.9040772350, f(0.42), f(0.42)-0.9040772350],_
[0.43,0.9019977725, f(0.43), f(0.43)-0.9019977725],_
[0.44,0.8999270693, f(0.44), f(0.44)-0.8999270693],_
[0.45,0.8978650778, f(0.45), f(0.45)-0.8978650778],_
[0.46,0.8958117511, f(0.46), f(0.46)-0.8958117511],_
[0.47,0.8937670423, f(0.47), f(0.47)-0.8937670423],_
[0.48,0.8917309048, f(0.48), f(0.48)-0.8917309048],_
[0.49,0.8897032920, f(0.49), f(0.49)-0.8897032920],_
[0.50,0.8876841584, f(0.50), f(0.50)-0.8876841584]]::LIST(LIST(DFLOAT))
 
   Compiling function f with type Float -> DoubleFloat 

   (3)
   [
     [0.0099999999999999985, 0.9975055451999999, 0.99750554515560808,
      - 4.4391823550427034E-11]
     ,

     [0.019999999999999997, 0.99502213919999993, 0.99502213915483306,
      - 4.5166870243917856E-11]
     ,

     [0.029999999999999999, 0.99254972009999998, 0.99254972009440801,
      - 5.5919713304319885E-12]
     ,

     [0.039999999999999994, 0.99008822649999995, 0.99008822646531325,
      - 3.4686697958363766E-11]
     ,

     [0.049999999999999996, 0.98763759709999999, 0.98763759715033039,
      5.0330406509146997E-11]
     ,

     [0.059999999999999998, 0.98519777139999998, 0.98519777142131992,
      2.1319945808784269E-11]
     ,

     [0.069999999999999993, 0.98276868889999991, 0.9827686889364845,
      3.6484593124441744E-11]
     ,

     [0.079999999999999988, 0.98035028979999994, 0.98035028973774141,
      - 6.2258531663417216E-11]
     ,

     [0.089999999999999997, 0.97794251419999989, 0.97794251424804612,
      4.8046233658283199E-11]
     ,

     [0.099999999999999992, 0.9755453033, 0.9755453032687833,
      - 3.1216695894897839E-11]
     ,

     [0.10999999999999999, 0.97315859799999993, 0.97315859797714266,
      - 2.2857271630982723E-11]
     ,
    [0.12,0.97078233989999996,0.9707823399235388,2.3538837545800106E-11],

     [0.12999999999999998, 0.96841647099999995, 0.96841647102903716,
      2.9037217075256194E-11]
     ,

     [0.13999999999999999, 0.96606093359999989, 0.96606093358279388,
      - 1.7206014391035751E-11]
     ,

     [0.14999999999999999, 0.96371567019999993, 0.96371567023951921,
      3.9519276739952147E-11]
     ,

     [0.15999999999999998, 0.96138062399999991, 0.9613806240169831,
      1.6983192629993482E-11]
     ,

     [0.16999999999999998, 0.9590557382999999, 0.95905573829349045,
      - 6.5094596379822178E-12]
     ,

     [0.17999999999999999, 0.95674095689999994, 0.95674095680541793,
      - 9.4582008891563873E-11]
     ,

     [0.18999999999999997, 0.95443622369999992, 0.95443622364475,
      - 5.5249915753563528E-11]
     ,

     [0.19999999999999998, 0.95214148329999992, 0.95214148325662884,
      - 4.3371084501586665E-11]
     ,

     [0.20999999999999999, 0.94985668039999993, 0.94985668043693716,
      3.6937231051581421E-11]
     ,

     [0.21999999999999997, 0.94758176029999996, 0.94758176032988617,
      2.9886204622187051E-11]
     ,

     [0.22999999999999998, 0.94531666839999995, 0.94531666842562345,
      2.5623503319138763E-11]
     ,

     [0.23999999999999999, 0.94306135059999996, 0.943061350557861,
      - 4.2138958988857667E-11]
     ,
    [0.25,0.94081575279999996,0.9408157529015222,1.0152223506310065E-10],

     [0.25999999999999995, 0.93857982209999991, 0.93857982197039946,
      - 1.2960044148968564E-10]
     ,

     [0.26999999999999996, 0.9363535046, 0.93635350461483258,
      1.4832579608992091E-11]
     ,

     [0.27999999999999997, 0.93413674809999991, 0.93413674801940594,
      - 8.0593975937404139E-11]
     ,

     [0.28999999999999998, 0.93192949969999994, 0.93192949970065853,
      6.5858429820764286E-13]
     ,

     [0.29999999999999999, 0.92973170749999989, 0.92973170750481271,
      4.8128168117500536E-12]
     ,
    [0.31,0.92754331959999992,0.92754331960551928,5.5193627446215032E-12],

     [0.31999999999999995, 0.92536428449999997, 0.92536428450162023,
      1.6202594821379535E-12]
     ,

     [0.32999999999999996, 0.92319455099999992, 0.92319455101492243,
      1.4922507673986729E-11]
     ,

     [0.33999999999999997, 0.92103406839999991, 0.9210340682879945,
      - 1.1200540495082123E-10]
     ,

     [0.34999999999999998, 0.91888278579999993, 0.9188827857819748,
      - 1.8025136938604192E-11]
     ,

     [0.35999999999999999, 0.91674065329999999, 0.91674065327439824,
      - 2.560174294785611E-11]
     ,
    [0.37,0.91460762089999992,0.9146076208570354,- 4.2964520829968933E-11],

     [0.37999999999999995, 0.91248363879999994, 0.91248363893375217,
      1.3375223151257387E-10]
     ,

     [0.38999999999999996, 0.9103686581999999, 0.91036865821837931,
      1.8379409105762079E-11]
     ,

     [0.39999999999999997, 0.90826262969999993, 0.90826262973260108,
      3.2601144006605409E-11]
     ,

     [0.40999999999999998, 0.90616550479999991, 0.90616550480385882,
      3.8589131889921191E-12]
     ,

     [0.41999999999999998, 0.90407723499999992, 0.90407723506326876,
      6.3268834615826108E-11]
     ,

     [0.42999999999999999, 0.90199777249999991, 0.90199777244355617,
      - 5.6443738571942959E-11]
     ,

     [0.43999999999999995, 0.89992706929999999, 0.89992706917700027,
      - 1.2299972151907923E-10]
     ,

     [0.44999999999999996, 0.89786507779999991, 0.89786507779340141,
      - 6.5984995245571554E-12]
     ,

     [0.45999999999999996, 0.8958117511, 0.89581175111805533,
      1.8055335004873996E-11]
     ,

     [0.46999999999999997, 0.89376704229999993, 0.89376704226974857,
      - 3.0251356974986265E-11]
     ,

     [0.47999999999999998, 0.89173090479999995, 0.89173090465876192,
      - 1.4123802127841145E-10]
     ,

     [0.48999999999999999, 0.88970329199999998, 0.88970329198489451,
      - 1.5105472428444955E-11]
     ,
    [0.5,0.88768415839999992,0.88768415823549662,- 1.6450329987094392E-10]]
                                                  Type: List List DoubleFloat
--R 
--R   Compiling function f with type Float -> DoubleFloat 
--R
--R   (3)
--R   [[1.0E-2,0.99750554520000001,0.99750554515544154,- 4.455846802642327E-11],
--R    [2.0E-2,0.99502213920000004,0.99502213915481641,- 4.5183634611589696E-11],
--R
--R     [2.9999999999999999E-2, 0.99254972009999998, 0.99254972009439713,
--R      - 5.602851516073315E-12]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.99008822649999995, 0.99008822646530492,
--R      - 3.4695024631048454E-11]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.98763759709999999, 0.98763759715033261,
--R      5.0332626955196247E-11]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.98519777139999998, 0.98519777142131459,
--R      2.1314616738266068E-11]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.98276868890000002, 0.98276868893648617,
--R      3.648614743667622E-11]
--R     ,
--R
--R     [8.0000000000000002E-2, 0.98035028980000005, 0.98035028973773719,
--R      - 6.2262861533213254E-11]
--R     ,
--R
--R     [8.9999999999999997E-2, 0.9779425142, 0.97794251424804735,
--R      4.8047343881307825E-11]
--R     ,
--R
--R     [0.10000000000000001, 0.9755453033, 0.97554530326877553,
--R      - 3.1224467456070215E-11]
--R     ,
--R    [0.11,0.97315859800000004,0.97315859797713988,- 2.2860158210846748E-11],
--R    [0.12,0.97078233989999996,0.97078233992354002,2.3540058791127194E-11],
--R    [0.13,0.96841647099999995,0.96841647102903816,2.9038216275978357E-11],
--R
--R     [0.14000000000000001, 0.9660609336, 0.96606093358279166,
--R      - 1.7208345859387464E-11]
--R     ,
--R
--R     [0.14999999999999999, 0.96371567020000004, 0.96371567023951998,
--R      3.9519942873766922E-11]
--R     ,
--R    [0.16,0.96138062400000002,0.96138062401698243,1.6982415473876245E-11],
--R
--R     [0.17000000000000001, 0.95905573830000002, 0.95905573829349,
--R      - 6.5100147494945304E-12]
--R     ,
--R
--R     [0.17999999999999999, 0.95674095690000005, 0.9567409568054186,
--R      - 9.4581453780051561E-11]
--R     ,
--R    [0.19,0.95443622370000003,0.95443622364474956,- 5.525047086507584E-11],
--R
--R     [0.20000000000000001, 0.95214148330000004, 0.9521414832566294,
--R      - 4.3370640412376815E-11]
--R     ,
--R
--R     [0.20999999999999999, 0.94985668040000004, 0.94985668043693772,
--R      3.6937675140791271E-11]
--R     ,
--R    [0.22,0.94758176029999996,0.94758176032988584,2.9885871555279664E-11],
--R
--R     [0.23000000000000001, 0.94531666839999995, 0.9453166684256229,
--R      2.562294820762645E-11]
--R     ,
--R
--R     [0.23999999999999999, 0.94306135059999996, 0.94306135055786067,
--R      - 4.2139292055765054E-11]
--R     ,
--R    [0.25,0.94081575279999996,0.94081575290152264,1.015226791523105E-10],
--R
--R     [0.26000000000000001, 0.93857982210000002, 0.93857982197039913,
--R      - 1.2960088557889549E-10]
--R     ,
--R
--R     [0.27000000000000002, 0.9363535046, 0.93635350461483224,
--R      1.4832246542084704E-11]
--R     ,
--R
--R     [0.28000000000000003, 0.93413674810000003, 0.93413674801940527,
--R      - 8.0594753093521376E-11]
--R     ,
--R
--R     [0.28999999999999998, 0.93192949970000005, 0.93192949970065808,
--R      6.5802918669533028E-13]
--R     ,
--R
--R     [0.29999999999999999, 0.9297317075, 0.92973170750481327,
--R      4.8132609009599037E-12]
--R     ,
--R    [0.31,0.92754331960000003,0.92754331960551961,5.5195847892264283E-12],
--R
--R     [0.32000000000000001, 0.92536428449999997, 0.92536428450162023,
--R      1.6202594821379535E-12]
--R     ,
--R
--R     [0.33000000000000002, 0.92319455100000003, 0.92319455101492243,
--R      1.4922396651684267E-11]
--R     ,
--R
--R     [0.34000000000000002, 0.92103406840000002, 0.92103406828799361,
--R      - 1.1200640415154339E-10]
--R     ,
--R
--R     [0.34999999999999998, 0.91888278580000005, 0.91888278578197524,
--R      - 1.8024803871696804E-11]
--R     ,
--R
--R     [0.35999999999999999, 0.91674065329999999, 0.91674065327439791,
--R      - 2.5602076014763497E-11]
--R     ,
--R    [0.37,0.91460762090000003,0.91460762085703573,- 4.2964298785364008E-11],
--R    [0.38,0.91248363880000005,0.91248363893375239,1.3375234253487633E-10],
--R
--R     [0.39000000000000001, 0.91036865820000001, 0.91036865821837942,
--R      1.8379409105762079E-11]
--R     ,
--R
--R     [0.40000000000000002, 0.90826262970000005, 0.90826262973260075,
--R      3.2600699917395559E-11]
--R     ,
--R
--R     [0.40999999999999998, 0.90616550480000002, 0.90616550480385905,
--R      3.8590242112945816E-12]
--R     ,
--R
--R     [0.41999999999999998, 0.90407723500000003, 0.90407723506326909,
--R      6.3269056660431033E-11]
--R     ,
--R
--R     [0.42999999999999999, 0.90199777250000002, 0.90199777244355628,
--R      - 5.6443738571942959E-11]
--R     ,
--R    [0.44,0.89992706929999999,0.89992706917700038,- 1.2299961049677677E-10],
--R
--R     [0.45000000000000001, 0.89786507780000002, 0.8978650777934013,
--R      - 6.5987215691620804E-12]
--R     ,
--R
--R     [0.46000000000000002, 0.8958117511, 0.89581175111805511,
--R      1.8055112960269071E-11]
--R     ,
--R
--R     [0.46999999999999997, 0.89376704230000004, 0.89376704226974857,
--R      - 3.0251467997288728E-11]
--R     ,
--R
--R     [0.47999999999999998, 0.89173090479999995, 0.89173090465876237,
--R      - 1.412375771892016E-10]
--R     ,
--R
--R     [0.48999999999999999, 0.88970329199999998, 0.88970329198489473,
--R      - 1.510525038384003E-11]
--R     ,
--R    [0.5,0.88768415840000003,0.88768415823549685,- 1.6450318884864146E-10]]
--R                                                  Type: List List DoubleFloat
--E 3
--S 4 of 7
[[0.50, 0.559773595, E1(0.50), E1(0.50)-0.559773595],_
[0.51, 0.547822352, E1(0.51), E1(0.51)-0.547822352],_
[0.52, 0.536219798, E1(0.52), E1(0.52)-0.536219798],_
[0.53, 0.524951510, E1(0.53), E1(0.53)-0.524951510],_
[0.54, 0.514003886, E1(0.54), E1(0.54)-0.514003886],_
[0.55, 0.503364081, E1(0.55), E1(0.55)-0.503364081],_
[0.56, 0.493019959, E1(0.56), E1(0.56)-0.493019959],_
[0.57, 0.482960034, E1(0.57), E1(0.57)-0.482960034],_
[0.58, 0.473173433, E1(0.58), E1(0.58)-0.473173433],_
[0.59, 0.463649849, E1(0.59), E1(0.59)-0.463649849],_
[0.60, 0.454379503, E1(0.60), E1(0.60)-0.454379503],_
[0.61, 0.445353112, E1(0.61), E1(0.61)-0.445353112],_
[0.62, 0.436561854, E1(0.62), E1(0.62)-0.436561854],_
[0.63, 0.427997338, E1(0.63), E1(0.63)-0.427997338],_
[0.64, 0.419651581, E1(0.64), E1(0.64)-0.419651581],_
[0.65, 0.411516976, E1(0.65), E1(0.65)-0.411516976],_
[0.66, 0.403586275, E1(0.66), E1(0.66)-0.403586275],_
[0.67, 0.395852563, E1(0.67), E1(0.67)-0.395852563],_
[0.68, 0.388309243, E1(0.68), E1(0.68)-0.388309243],_
[0.69, 0.380950010, E1(0.69), E1(0.69)-0.380950010],_
[0.70, 0.373768843, E1(0.70), E1(0.70)-0.373768843],_
[0.71, 0.366759981, E1(0.71), E1(0.71)-0.366759981],_
[0.72, 0.359917914, E1(0.72), E1(0.72)-0.359917914],_
[0.73, 0.353237364, E1(0.73), E1(0.73)-0.353237364],_
[0.74, 0.346713279, E1(0.74), E1(0.74)-0.346713279],_
[0.75, 0.340340813, E1(0.75), E1(0.75)-0.340340813],_
[0.76, 0.334115321, E1(0.76), E1(0.76)-0.334115321],_
[0.77, 0.328032346, E1(0.77), E1(0.77)-0.328032346],_
[0.78, 0.322087610, E1(0.78), E1(0.78)-0.322087610],_
[0.79, 0.316277004, E1(0.79), E1(0.79)-0.316277004],_
[0.80, 0.310596579, E1(0.80), E1(0.80)-0.310596579],_
[0.81, 0.305042539, E1(0.81), E1(0.81)-0.305042539],_
[0.82, 0.299611236, E1(0.82), E1(0.82)-0.299611236],_
[0.83, 0.294299155, E1(0.83), E1(0.83)-0.294299155],_
[0.84, 0.289102918, E1(0.84), E1(0.84)-0.289102918],_
[0.85, 0.284019269, E1(0.85), E1(0.85)-0.284019269],_
[0.86, 0.279045070, E1(0.86), E1(0.86)-0.279045070],_
[0.87, 0.274177301, E1(0.87), E1(0.87)-0.274177301],_
[0.88, 0.269413046, E1(0.88), E1(0.88)-0.269413046],_
[0.89, 0.264749496, E1(0.89), E1(0.89)-0.264749496],_
[0.90, 0.260183939, E1(0.90), E1(0.90)-0.260183939],_
[0.91, 0.255713758, E1(0.91), E1(0.91)-0.255713758],_
[0.92, 0.251336425, E1(0.92), E1(0.92)-0.251336425],_
[0.93, 0.247049501, E1(0.93), E1(0.93)-0.247049501],_
[0.94, 0.242850627, E1(0.94), E1(0.94)-0.242850627],_
[0.95, 0.238737524, E1(0.95), E1(0.95)-0.238737524],_
[0.96, 0.234707988, E1(0.96), E1(0.96)-0.234707988],_
[0.97, 0.230759890, E1(0.97), E1(0.97)-0.230759890],_
[0.98, 0.226891167, E1(0.98), E1(0.98)-0.226891167],_
[0.99, 0.223099826, E1(0.99), E1(0.99)-0.223099826],_
[1.00, 0.219383934, E1(1.00), E1(1.00)-0.219383934],_
[1.01, 0.215741624, E1(1.01), E1(1.01)-0.215741624],_
[1.02, 0.212171083, E1(1.02), E1(1.02)-0.212171083],_
[1.03, 0.208670559, E1(1.03), E1(1.03)-0.208670559],_
[1.04, 0.205238352, E1(1.04), E1(1.04)-0.205238352],_
[1.05, 0.201872813, E1(1.05), E1(1.05)-0.201872813],_
[1.06, 0.198572347, E1(1.06), E1(1.06)-0.198572347],_
[1.07, 0.195335403, E1(1.07), E1(1.07)-0.195335403],_
[1.08, 0.192160479, E1(1.08), E1(1.08)-0.192160479],_
[1.09, 0.189046118, E1(1.09), E1(1.09)-0.189046118],_
[1.10, 0.185990905, E1(1.10), E1(1.10)-0.185990905],_
[1.11, 0.182993465, E1(1.11), E1(1.11)-0.182993465],_
[1.12, 0.180052467, E1(1.12), E1(1.12)-0.180052467],_
[1.13, 0.177166615, E1(1.13), E1(1.13)-0.177166615],_
[1.14, 0.174334651, E1(1.14), E1(1.14)-0.174334651],_
[1.15, 0.171555354, E1(1.15), E1(1.15)-0.171555354],_
[1.16, 0.168827535, E1(1.16), E1(1.16)-0.168827535],_
[1.17, 0.166150040, E1(1.17), E1(1.17)-0.166150040],_
[1.18, 0.163521748, E1(1.18), E1(1.18)-0.163521748],_
[1.19, 0.160941567, E1(1.19), E1(1.19)-0.160941567],_
[1.20, 0.158408437, E1(1.20), E1(1.20)-0.158408437],_
[1.21, 0.155921324, E1(1.21), E1(1.21)-0.155921324],_
[1.22, 0.153479226, E1(1.22), E1(1.22)-0.153479226],_
[1.23, 0.151081164, E1(1.23), E1(1.23)-0.151081164],_
[1.24, 0.148726188, E1(1.24), E1(1.24)-0.148726188],_
[1.25, 0.146413373, E1(1.25), E1(1.25)-0.146413373],_
[1.26, 0.144141815, E1(1.26), E1(1.26)-0.144141815],_
[1.27, 0.141910639, E1(1.27), E1(1.27)-0.141910639],_
[1.28, 0.139718989, E1(1.28), E1(1.28)-0.139718989],_
[1.29, 0.137566032, E1(1.29), E1(1.29)-0.137566032],_
[1.30, 0.135450958, E1(1.30), E1(1.30)-0.135450958],_
[1.31, 0.133372975, E1(1.31), E1(1.31)-0.133372975],_
[1.32, 0.131331314, E1(1.32), E1(1.32)-0.131331314],_
[1.33, 0.129325224, E1(1.33), E1(1.33)-0.129325224],_
[1.34, 0.127353972, E1(1.34), E1(1.34)-0.127353972],_
[1.35, 0.125416844, E1(1.35), E1(1.35)-0.125416844],_
[1.36, 0.123513146, E1(1.36), E1(1.36)-0.123513146],_
[1.37, 0.121642198, E1(1.37), E1(1.37)-0.121642198],_
[1.38, 0.119803337, E1(1.38), E1(1.38)-0.119803337],_
[1.39, 0.117995919, E1(1.39), E1(1.39)-0.117995919],_
[1.40, 0.116219313, E1(1.40), E1(1.40)-0.116219313],_
[1.41, 0.114472903, E1(1.41), E1(1.41)-0.114472903],_
[1.42, 0.112756090, E1(1.42), E1(1.42)-0.112756090],_
[1.43, 0.111068287, E1(1.43), E1(1.43)-0.111068287],_
[1.44, 0.109408923, E1(1.44), E1(1.44)-0.109408923],_
[1.45, 0.107777440, E1(1.45), E1(1.45)-0.107777440],_
[1.46, 0.106173291, E1(1.46), E1(1.46)-0.106173291],_
[1.47, 0.104595946, E1(1.47), E1(1.47)-0.104595946],_
[1.48, 0.103044882, E1(1.48), E1(1.48)-0.103044882],_
[1.49, 0.101519593, E1(1.49), E1(1.49)-0.101519593],_
[1.50, 0.100019582, E1(1.50), E1(1.50)-0.100019582],_
[1.51, 0.098544365, E1(1.51), E1(1.51)-0.098544365],_
[1.52, 0.097093466, E1(1.52), E1(1.52)-0.097093466],_
[1.53, 0.095666424, E1(1.53), E1(1.53)-0.095666424],_
[1.54, 0.094262786, E1(1.54), E1(1.54)-0.094262786],_
[1.55, 0.092882108, E1(1.55), E1(1.55)-0.092882108],_
[1.56, 0.091523960, E1(1.56), E1(1.56)-0.091523960],_
[1.57, 0.090187917, E1(1.57), E1(1.57)-0.090187917],_
[1.58, 0.088873566, E1(1.58), E1(1.58)-0.088873566],_
[1.59, 0.087580504, E1(1.59), E1(1.59)-0.087580504],_
[1.60, 0.086308334, E1(1.60), E1(1.60)-0.086308334],_
[1.61, 0.085056670, E1(1.61), E1(1.61)-0.085056670],_
[1.62, 0.083825133, E1(1.62), E1(1.62)-0.083825133],_
[1.63, 0.082613354, E1(1.63), E1(1.63)-0.082613354],_
[1.64, 0.081420970, E1(1.64), E1(1.64)-0.081420970],_
[1.65, 0.080247627, E1(1.65), E1(1.65)-0.080247627],_
[1.66, 0.079092978, E1(1.66), E1(1.66)-0.079092978],_
[1.67, 0.077956684, E1(1.67), E1(1.67)-0.077956684],_
[1.68, 0.076838412, E1(1.68), E1(1.68)-0.076838412],_
[1.69, 0.075737839, E1(1.69), E1(1.69)-0.075737839],_
[1.70, 0.074654644, E1(1.70), E1(1.70)-0.074654644],_
[1.71, 0.073588518, E1(1.71), E1(1.71)-0.073588518],_
[1.72, 0.072539154, E1(1.72), E1(1.72)-0.072539154],_
[1.73, 0.071506255, E1(1.73), E1(1.73)-0.071506255],_
[1.74, 0.070489527, E1(1.74), E1(1.74)-0.070489527],_
[1.75, 0.069488685, E1(1.75), E1(1.75)-0.069488685],_
[1.76, 0.068503447, E1(1.76), E1(1.76)-0.068503447],_
[1.77, 0.067533539, E1(1.77), E1(1.77)-0.067533539],_
[1.78, 0.066578691, E1(1.78), E1(1.78)-0.066578691],_
[1.79, 0.065638641, E1(1.79), E1(1.79)-0.065638641],_
[1.80, 0.064713129, E1(1.80), E1(1.80)-0.064713129],_
[1.81, 0.063801903, E1(1.81), E1(1.81)-0.063801903],_
[1.82, 0.062904715, E1(1.82), E1(1.82)-0.062904715],_
[1.83, 0.062021320, E1(1.83), E1(1.83)-0.062021320],_
[1.84, 0.061151482, E1(1.84), E1(1.84)-0.061151482],_
[1.85, 0.060294967, E1(1.85), E1(1.85)-0.060294967],_
[1.86, 0.059451545, E1(1.86), E1(1.86)-0.059451545],_
[1.87, 0.058620994, E1(1.87), E1(1.87)-0.058620994],_
[1.88, 0.057803091, E1(1.88), E1(1.88)-0.057803091],_
[1.89, 0.056997623, E1(1.89), E1(1.89)-0.056997623],_
[1.90, 0.056204378, E1(1.90), E1(1.90)-0.056204378],_
[1.91, 0.055423149, E1(1.91), E1(1.91)-0.055423149],_
[1.92, 0.054653731, E1(1.92), E1(1.92)-0.054653731],_
[1.93, 0.053895927, E1(1.93), E1(1.93)-0.053895927],_
[1.94, 0.053149540, E1(1.94), E1(1.94)-0.053149540],_
[1.95, 0.052414380, E1(1.95), E1(1.95)-0.052414380],_
[1.96, 0.051690257, E1(1.96), E1(1.96)-0.051690257],_
[1.97, 0.050976988, E1(1.97), E1(1.97)-0.050976988],_
[1.98, 0.050274392, E1(1.98), E1(1.98)-0.050274392],_
[1.99, 0.049582291, E1(1.99), E1(1.99)-0.049582291],_
[2.00, 0.048900511, E1(2.00), E1(2.00)-0.048900511]]::LIST(LIST(DFLOAT))
 

   (4)
   [[0.5,0.5597735949999999,0.55977359477616084,- 2.2383905839973295E-10],

     [0.5099999999999999, 0.54782235199999996, 0.54782235178082872,
      - 2.1917123671499894E-10]
     ,

     [0.51999999999999991, 0.53621979799999997, 0.53621979784563623,
      - 1.5436374400934483E-10]
     ,

     [0.52999999999999992, 0.52495150999999995, 0.52495151011486563,
      1.1486567252916302E-10]
     ,

     [0.53999999999999992, 0.51400388599999991, 0.51400388570224931,
      - 2.9775060195191827E-10]
     ,

     [0.54999999999999993, 0.50336408099999996, 0.50336408139239386,
      3.9239389515444145E-10]
     ,

     [0.55999999999999994, 0.49301995899999995, 0.49301995877649302,
      - 2.2350693518191633E-10]
     ,

     [0.56999999999999995, 0.48296003399999998, 0.48296003424511297,
      2.451129854641465E-10]
     ,

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     [1.9399999999999999, 0.053149539999999995, 0.053149540219563529,
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    [1.98,0.050274391999999994,0.050274391553639219,- 4.4636077473070301E-10],
    [1.99,0.049582290999999994,0.04958229052673635,- 4.7326364355226858E-10],
    [2.0,0.048900510999999994,0.048900510708061007,- 2.91938986873852E-10]]
                                                  Type: List List DoubleFloat
--R 
--R
--R   (4)
--R   [[0.5,0.55977359500000001,0.55977359477616084,- 2.2383916942203541E-10],
--R
--R     [0.51000000000000001, 0.54782235199999996, 0.54782235178082872,
--R      - 2.1917123671499894E-10]
--R     ,
--R
--R     [0.52000000000000002, 0.53621979799999997, 0.53621979784563623,
--R      - 1.5436374400934483E-10]
--R     ,
--R
--R     [0.53000000000000003, 0.52495150999999995, 0.52495151011486541,
--R      1.148654504845581E-10]
--R     ,
--R
--R     [0.54000000000000004, 0.51400388600000002, 0.51400388570224909,
--R      - 2.9775093501882566E-10]
--R     ,
--R
--R     [0.55000000000000004, 0.50336408099999996, 0.50336408139239386,
--R      3.9239389515444145E-10]
--R     ,
--R
--R     [0.56000000000000005, 0.49301995900000001, 0.49301995877649291,
--R      - 2.2350710171537003E-10]
--R     ,
--R
--R     [0.56999999999999995, 0.48296003399999998, 0.48296003424511297,
--R      2.451129854641465E-10]
--R     ,
--R
--R     [0.57999999999999996, 0.47317343299999998, 0.47317343333112627,
--R      3.3112629305165342E-10]
--R     ,
--R
--R     [0.58999999999999997, 0.463649849, 0.46364984895652972,
--R      - 4.3470282928836923E-11]
--R     ,
--R
--R     [0.59999999999999998, 0.45437950300000002, 0.45437950318940223,
--R      1.8940221613306107E-10]
--R     ,
--R    [0.60999999999999999,0.445353112,0.44535311216282059,1.628205903436708E-10],
--R    [0.62,0.43656185400000003,0.43656185384719148,- 1.5280854359644991E-10],
--R    [0.63,0.427997338,0.42799733840201848,4.0201847406606817E-10],
--R
--R     [0.64000000000000001, 0.419651581, 0.41965158086333326,
--R      - 1.366667334856686E-10]
--R     ,
--R
--R     [0.65000000000000002, 0.41151697599999998, 0.41151697594947956,
--R      - 5.0520421179811592E-11]
--R     ,
--R
--R     [0.66000000000000003, 0.40358627499999999, 0.40358627479116588,
--R      - 2.088341166661678E-10]
--R     ,
--R
--R     [0.67000000000000004, 0.39585256299999999, 0.39585256341213687,
--R      4.1213688017904815E-10]
--R     ,
--R
--R     [0.68000000000000005, 0.38830924300000003, 0.38830924280482559,
--R      - 1.9517443217154096E-10]
--R     ,
--R
--R     [0.68999999999999995, 0.38095001000000001, 0.38095001046125104,
--R      4.6125103736471829E-10]
--R     ,
--R
--R     [0.69999999999999996, 0.37376884300000002, 0.37376884323350923,
--R      2.3350921196652052E-10]
--R     ,
--R
--R     [0.70999999999999996, 0.36675998100000001, 0.36675998141067723,
--R      4.1067721445742222E-10]
--R     ,
--R
--R     [0.71999999999999997, 0.35991791400000001, 0.35991791391003464,
--R      - 8.9965368488265085E-11]
--R     ,
--R    [0.72999999999999998,0.353237364,0.35323736449036641,4.9036641414090809E-10]
--R     ,
--R
--R     [0.73999999999999999, 0.34671327899999999, 0.34671327890389447,
--R      - 9.6105512437105745E-11]
--R     ,
--R    [0.75,0.34034081300000002,0.34034081291123008,- 8.8769935846499948E-11],
--R
--R     [0.76000000000000001, 0.33411532100000002, 0.33411532109074837,
--R      9.0748353276381977E-11]
--R     ,
--R
--R     [0.77000000000000002, 0.32803234599999997, 0.3280323463800649,
--R      3.8006492397713032E-10]
--R     ,
--R
--R     [0.78000000000000003, 0.32208761000000002, 0.32208761029292271,
--R      2.9292268610703331E-10]
--R     ,
--R
--R     [0.79000000000000004, 0.31627700399999997, 0.31627700375985612,
--R      - 2.4014384925052923E-10]
--R     ,
--R
--R     [0.80000000000000004, 0.31059657899999998, 0.31059657854554301,
--R      - 4.5445697205437341E-10]
--R     ,
--R    [0.81000000000000005,0.305042539,0.30504253919985258,1.9985257893040398E-10]
--R     ,
--R
--R     [0.81999999999999995, 0.299611236, 0.29961123550328894,
--R      - 4.967110611708847E-10]
--R     ,
--R
--R     [0.82999999999999996, 0.29429915499999998, 0.29429915537086676,
--R      3.7086678172926213E-10]
--R     ,
--R
--R     [0.83999999999999997, 0.28910291799999999, 0.28910291818146794,
--R      1.8146795177642616E-10]
--R     ,
--R
--R     [0.84999999999999998, 0.28401926900000002, 0.2840192685024614,
--R      - 4.975386214134403E-10]
--R     ,
--R
--R     [0.85999999999999999, 0.27904507000000001, 0.27904507018183955,
--R      1.818395434227682E-10]
--R     ,
--R    [0.87,0.27417730099999998,0.27417730078237224,- 2.1762774915501382E-10],
--R    [0.88,0.26941304599999999,0.26941304633432023,3.343202381600463E-10],
--R
--R     [0.89000000000000001, 0.26474949599999997, 0.26474949638510148,
--R      3.8510150623949357E-10]
--R     ,
--R
--R     [0.90000000000000002, 0.26018393899999998, 0.26018393932599954,
--R      3.259995606796906E-10]
--R     ,
--R
--R     [0.91000000000000003, 0.25571375800000001, 0.25571375797753926,
--R      - 2.2460755477737848E-11]
--R     ,
--R
--R     [0.92000000000000004, 0.25133642499999997, 0.25133642541656154,
--R      4.1656156302138925E-10]
--R     ,
--R    [0.93000000000000005,0.247049501,0.24704950102931605,2.9316049587890802E-11]
--R     ,
--R
--R     [0.93999999999999995, 0.24285062700000001, 0.24285062677606084,
--R      - 2.2393917276097852E-10]
--R     ,
--R
--R     [0.94999999999999996, 0.23873752400000001, 0.23873752365373468,
--R      - 3.4626532197101767E-10]
--R     ,
--R
--R     [0.95999999999999996, 0.23470798800000001, 0.23470798834425491,
--R      3.4425490236245082E-10]
--R     ,
--R    [0.96999999999999997,0.23075989,0.23075989003689171,3.6891711907571789E-11],
--R    [0.97999999999999998,0.226891167,0.22689116741400336,4.1400335937247235E-10]
--R     ,
--R
--R     [0.98999999999999999, 0.223099826, 0.22309982579017718,
--R      - 2.0982282578074773E-10]
--R     ,
--R    [1.,0.219383934,0.21938393439552029,3.9552028319178589E-10],
--R    [1.01,0.21574162399999999,0.21574162379448991,- 2.0551008117486447E-10],
--R    [1.02,0.21217108300000001,0.2121710834322488,4.3224879231473778E-10],
--R    [1.03,0.20867055900000001,0.20867055930107367,3.0107366599807506E-10],
--R    [1.04,0.20523835200000001,0.20523835171985597,- 2.8014404684917338E-10],
--R    [1.05,0.20187281300000001,0.20187281322019657,2.2019655543381589E-10],
--R
--R     [1.0600000000000001, 0.19857234700000001, 0.19857234653302808,
--R      - 4.6697193334388487E-10]
--R     ,
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--R     [1.0700000000000001, 0.19533540299999999, 0.19533540267009863,
--R      - 3.2990135623300887E-10]
--R     ,
--R    [1.0800000000000001,0.192160479,0.19216047909501838,9.5018382051392791E-11],
--R
--R     [1.0900000000000001, 0.18904611800000001, 0.18904611797891213,
--R      - 2.1087881441061995E-11]
--R     ,
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--R     [1.1000000000000001, 0.18599090500000001, 0.18599090453604011,
--R      - 4.6395989827807682E-10]
--R     ,
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--R     [1.1100000000000001, 0.18299346499999999, 0.1829934654350395,
--R      4.3503950442058681E-10]
--R     ,
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--R     [1.1200000000000001, 0.18005246699999999, 0.18005246728171573,
--R      2.8171573407398398E-10]
--R     ,
--R    [1.1299999999999999,0.177166615,0.17716661516956422,1.6956422377312208E-10],
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--R     [1.1399999999999999, 0.17433465100000001, 0.17433465129443812,
--R      2.9443811278007104E-10]
--R     ,
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--R     [1.1499999999999999, 0.17155535399999999, 0.1715553536299986,
--R      - 3.7000139063714244E-10]
--R     ,
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--R     [1.1599999999999999, 0.168827535, 0.16882753466078662,
--R      - 3.3921337960762799E-10]
--R     ,
--R    [1.1699999999999999,0.16615004,0.16615004016994619,1.6994619600474437E-10],
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--R     [1.1799999999999999, 0.16352174799999999, 0.16352174807880468,
--R      7.8804684999767005E-11]
--R     ,
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--R     [1.1899999999999999, 0.16094156700000001, 0.1609415673356836,
--R      3.3568359203428599E-10]
--R     ,
--R    [1.2,0.15840843700000001,0.15840843685146253,- 1.4853748786514132E-10],
--R    [1.21,0.155921324,0.15592132447956802,4.7956802418092082E-10],
--R    [1.22,0.153479226,0.15347922603818942,3.8189423845480519E-11],
--R    [1.23,0.15108116399999999,0.15108116437265298,3.7265299179800593E-10],
--R    [1.24,0.14872618800000001,0.14872618845599739,4.559973787454652E-10],
--R    [1.25,0.14641337300000001,0.14641337252591019,- 4.7408982295493729E-10],
--R    [1.26,0.14414181500000001,0.14414181525628297,2.5628296707047582E-10],
--R    [1.27,0.14191063900000001,0.14191063896174164,- 3.8258368695309741E-11],
--R    [1.28,0.13971898899999999,0.1397189888335964,- 1.6640358535546795E-10],
--R    [1.29,0.137566032,0.13756603220574354,2.0574353332136752E-10],
--R    [1.3,0.13545095800000001,0.13545095784912908,- 1.5087092686272285E-10],
--R    [1.3100000000000001,0.133372975,0.13337297529345732,2.9345731400454156E-10],
--R    [1.3200000000000001,0.131331314,0.13133131417489974,1.7489973358486566E-10],
--R
--R     [1.3300000000000001, 0.12932522399999999, 0.12932522360862764,
--R      - 3.9137235119390823E-10]
--R     ,
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--R     [1.3400000000000001, 0.12735397200000001, 0.12735397158504419,
--R      - 4.1495581970529827E-10]
--R     ,
--R    [1.3500000000000001,0.125416844,0.12541684438866441,3.8866440621454501E-10],
--R    [1.3600000000000001,0.123513146,0.12351314603863212,3.8632111398761992E-11],
--R
--R     [1.3700000000000001, 0.12164219800000001, 0.1216421977499248,
--R      - 2.5007521053943549E-10]
--R     ,
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--R    [1.3899999999999999,0.117995919,0.11799591910039325,1.0039324926935933E-10],
--R
--R     [1.3999999999999999, 0.116219313, 0.11621931257135804,
--R      - 4.2864196914127461E-10]
--R     ,
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--R     [1.4099999999999999, 0.114472903, 0.11447290282058709,
--R      - 1.7941291508005719E-10]
--R     ,
--R    [1.4199999999999999,0.11275609,0.11275608962347,- 3.7653000162229944E-10],
--R    [1.4299999999999999,0.111068287,0.11106828710526567,1.0526567117974395E-10],
--R
--R     [1.4399999999999999, 0.10940892300000001, 0.10940892332417007,
--R      3.2417006579077423E-10]
--R     ,
--R    [1.45,0.10777744,0.10777743986897642,- 1.3102358087380139E-10],
--R    [1.46,0.106173291,0.10617329147072579,4.7072579167917183E-10],
--R    [1.47,0.104595946,0.10459594562777519,- 3.7222480653298362E-10],
--R    [1.48,0.103044882,0.10304488224373387,2.4373386642295714E-10],
--R    [1.49,0.10151959300000001,0.10151959327774779,2.7774778310618586E-10],
--R    [1.5,0.100019582,0.10001958240663256,4.0663256095641032E-10],
--R    [1.51,9.8544364999999995E-2,9.85443646983854E-2,- 3.0161459441124805E-10],
--R    [1.52,9.7093466000000003E-2,9.7093466296618358E-2,2.9661835487804211E-10],
--R    [1.53,9.5666424E-2,9.5666424115486592E-2,1.1548659251126026E-10],
--R    [1.54,9.4262786000000001E-2,9.4262785544698136E-2,- 4.5530186565390096E-10],
--R    [1.55,9.2882108000000005E-2,9.2882108164209165E-2,1.6420916015835729E-10],
--R
--R     [1.5600000000000001, 9.1523960000000001E-2, 9.152395946823666E-2,
--R      - 5.3176334169346973E-10]
--R     ,
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--R     [1.5700000000000001, 9.0187917000000006E-2, 9.0187916598222728E-2,
--R      - 4.0177727811396835E-10]
--R     ,
--R
--R     [1.5800000000000001, 8.8873566000000001E-2, 8.8873566084412048E-2,
--R      8.441204679687786E-11]
--R     ,
--R
--R     [1.5900000000000001, 8.7580504000000003E-2, 8.7580503595714843E-2,
--R      - 4.0428516090429412E-10]
--R     ,
--R
--R     [1.6000000000000001, 8.6308334E-2, 8.6308333697539708E-2,
--R      - 3.0246029292246845E-10]
--R     ,
--R
--R     [1.6100000000000001, 8.5056670000000001E-2, 8.5056669617302794E-2,
--R      - 3.8269720725736533E-10]
--R     ,
--R
--R     [1.6200000000000001, 8.3825132999999996E-2, 8.3825133017319142E-2,
--R      1.7319146117245054E-11]
--R     ,
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--R     [1.6299999999999999, 8.2613354E-2, 8.2613353774808662E-2,
--R      - 2.25191337799302E-10]
--R     ,
--R
--R     [1.6399999999999999, 8.1420969999999995E-2, 8.1420969768751517E-2,
--R      - 2.3124847869926413E-10]
--R     ,
--R
--R     [1.6499999999999999, 8.0247627000000002E-2, 8.0247626673343175E-2,
--R      - 3.266568265880565E-10]
--R     ,
--R
--R     [1.6599999999999999, 7.9092977999999994E-2, 7.9092977757806437E-2,
--R      - 2.4219355687638E-10]
--R     ,
--R
--R     [1.6699999999999999, 7.7956683999999998E-2, 7.7956683692333661E-2,
--R      - 3.0766633685175293E-10]
--R     ,
--R
--R     [1.6799999999999999, 7.6838411999999995E-2, 7.6838412359934938E-2,
--R      3.5993494296171491E-10]
--R     ,
--R
--R     [1.6899999999999999, 7.5737839000000001E-2, 7.5737838673983093E-2,
--R      - 3.2601690791445037E-10]
--R     ,
--R    [1.7,7.4654644000000006E-2,7.4654644401252912E-2,4.0125290590165008E-10],
--R    [1.71,7.3588518000000006E-2,7.358851799025623E-2,- 9.7437752311080317E-12],
--R    [1.72,7.2539153999999995E-2,7.2539154404693273E-2,4.0469327888814632E-10],
--R    [1.73,7.1506255000000005E-2,7.150625496183538E-2,- 3.8164624238667955E-11],
--R    [1.74,7.0489526999999996E-2,7.0489527175668809E-2,1.7566881282959912E-10],
--R    [1.75,6.9488684999999994E-2,6.9488684604638751E-2,- 3.9536124374350834E-10],
--R    [1.76,6.8503446999999995E-2,6.8503446703828352E-2,- 2.9617164276629637E-10],
--R    [1.77,6.7533539000000004E-2,6.7533538681429195E-2,- 3.1857080862174314E-10],
--R    [1.78,6.6578690999999995E-2,6.657869135934702E-2,3.5934702435902466E-10],
--R    [1.79,6.5638640999999998E-2,6.5638641037815026E-2,3.7815028886001301E-11],
--R    [1.8,6.4713128999999994E-2,6.4713129363868749E-2,3.638687545715058E-10],
--R
--R     [1.8100000000000001, 6.3801902999999993E-2, 6.3801903203559385E-2,
--R      2.0355939156502245E-10]
--R     ,
--R
--R     [1.8200000000000001, 6.2904715E-2, 6.2904714517779237E-2,
--R      - 4.8222076332038455E-10]
--R     ,
--R
--R     [1.8300000000000001, 6.2021319999999998E-2, 6.2021320241580469E-2,
--R      2.4158047090550028E-10]
--R     ,
--R
--R     [1.8400000000000001, 6.1151482E-2, 6.1151482166870164E-2,
--R      1.6687016352046058E-10]
--R     ,
--R
--R     [1.8500000000000001, 6.0294966999999998E-2, 6.0294966828373431E-2,
--R      - 1.7162656712477187E-10]
--R     ,
--R
--R     [1.8600000000000001, 5.9451545000000001E-2, 5.9451545392755656E-2,
--R      3.9275565438812166E-10]
--R     ,
--R
--R     [1.8700000000000001, 5.8620994000000003E-2, 5.8620993550804079E-2,
--R      - 4.4919592351311266E-10]
--R     ,
--R
--R     [1.8799999999999999, 5.7803091000000001E-2, 5.7803091412567897E-2,
--R      4.1256789651278325E-10]
--R     ,
--R
--R     [1.8899999999999999, 5.6997622999999997E-2, 5.6997623405359299E-2,
--R      4.0535930168061896E-10]
--R     ,
--R
--R     [1.8999999999999999, 5.6204377999999999E-2, 5.6204378174534608E-2,
--R      1.7453460898764206E-10]
--R     ,
--R
--R     [1.9099999999999999, 5.5423148999999998E-2, 5.5423148486950402E-2,
--R      - 5.1304959586273569E-10]
--R     ,
--R
--R     [1.9199999999999999, 5.4653730999999997E-2, 5.4653731137026984E-2,
--R      1.3702698697937166E-10]
--R     ,
--R
--R     [1.9299999999999999, 5.3895927000000003E-2, 5.3895926855324849E-2,
--R      - 1.4467515380145457E-10]
--R     ,
--R
--R     [1.9399999999999999, 5.3149540000000002E-2, 5.3149540219563307E-2,
--R      2.1956330503725141E-10]
--R     ,
--R    [1.95,5.2414380000000003E-2,5.2414379567998548E-2,- 4.3200145544153301E-10],
--R    [1.96,5.1690257000000003E-2,5.1690256915094213E-2,- 8.4905790731504283E-11],
--R    [1.97,5.0976988000000001E-2,5.0976987869409074E-2,- 1.3059092696110497E-10],
--R    [1.98,5.0274392000000001E-2,5.0274391553638775E-2,- 4.4636122575880677E-10],
--R    [1.99,4.9582291000000001E-2,4.9582290526736128E-2,- 4.732638725357674E-10],
--R    [2.,4.8900511000000001E-2,4.8900510708061007E-2,- 2.9193899381274591E-10]]
--R                                                  Type: List List DoubleFloat
--E 4
--S 5 of 7
g(x)==x * %e^x * E1(x)::DFLOAT
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 5
--S 6 of 7
[[2.0,0.722657234,g(2.0),g(2.0)-0.722657234],_
[2.1,0.730791502,g(2.1),g(2.1)-0.730791502],_
[2.2,0.738431132,g(2.2),g(2.2)-0.738431132],_
[2.3,0.745622149,g(2.3),g(2.3)-0.745622149],_
[2.4,0.752404829,g(2.4),g(2.4)-0.752404829],_
[2.5,0.758814592,g(2.5),g(2.5)-0.758814592],_
[2.6,0.764882722,g(2.6),g(2.6)-0.764882722],_
[2.7,0.770636987,g(2.7),g(2.7)-0.770636987],_
[2.8,0.776102123,g(2.8),g(2.8)-0.776102123],_
[2.9,0.781300252,g(2.9),g(2.9)-0.781300252],_
[3.0,0.786251221,g(3.0),g(3.0)-0.786251221],_
[3.1,0.790972800,g(3.1),g(3.1)-0.790972800],_
[3.2,0.795481422,g(3.2),g(3.2)-0.795481422],_
[3.3,0.799791408,g(3.3),g(3.3)-0.799791408],_
[3.4,0.803916127,g(3.4),g(3.4)-0.803916127],_
[3.5,0.807867661,g(3.5),g(3.5)-0.807867661],_
[3.6,0.811657037,g(3.6),g(3.6)-0.811657037],_
[3.7,0.815294342,g(3.7),g(3.7)-0.815294342],_
[3.8,0.818788821,g(3.8),g(3.8)-0.818788821],_
[3.9,0.822148967,g(3.9),g(3.9)-0.822148967],_
[4.0,0.825382500,g(4.0),g(4.0)-0.825382500],_
[4.1,0.828496926,g(4.1),g(4.1)-0.828496926],_
[4.2,0.831498602,g(4.2),g(4.2)-0.831498602],_
[4.3,0.834393794,g(4.3),g(4.3)-0.834393794],_
[4.4,0.837188207,g(4.4),g(4.4)-0.837188207],_
[4.5,0.839887144,g(4.5),g(4.5)-0.839887144],_
[4.6,0.842495539,g(4.6),g(4.6)-0.842495539],_
[4.7,0.845017971,g(4.7),g(4.7)-0.845017971],_
[4.8,0.847458721,g(4.8),g(4.8)-0.847458721],_
[4.9,0.849821778,g(4.9),g(4.9)-0.849821778],_
[5.0,0.852110880,g(5.0),g(5.0)-0.852110880],_
[5.1,0.854329519,g(5.1),g(5.1)-0.854329519],_
[5.2,0.856480958,g(5.2),g(5.2)-0.856480958],_
[5.3,0.858568275,g(5.3),g(5.3)-0.858568275],_
[5.4,0.860594348,g(5.4),g(5.4)-0.860594348],_
[5.5,0.862561885,g(5.5),g(5.5)-0.862561885],_
[5.6,0.864473436,g(5.6),g(5.6)-0.864473436],_
[5.7,0.866331399,g(5.7),g(5.7)-0.866331399],_
[5.8,0.868138040,g(5.8),g(5.8)-0.868138040],_
[5.9,0.869895494,g(5.9),g(5.9)-0.869895494],_
[6.0,0.871605775,g(6.0),g(6.0)-0.871605775],_
[6.1,0.873270793,g(6.1),g(6.1)-0.873270793],_
[6.2,0.874892347,g(6.2),g(6.2)-0.874892347],_
[6.3,0.876472150,g(6.3),g(6.3)-0.876472150],_
[6.4,0.878011816,g(6.4),g(6.4)-0.878011816],_
[6.5,0.879512881,g(6.5),g(6.5)-0.879512881],_
[6.6,0.880976797,g(6.6),g(6.6)-0.880976797],_
[6.7,0.882404955,g(6.7),g(6.7)-0.882404955],_
[6.8,0.883798662,g(6.8),g(6.8)-0.883798662],_
[6.9,0.885159176,g(6.9),g(6.9)-0.885159176],_
[7.0,0.886487675,g(7.0),g(7.0)-0.886487675],_
[7.1,0.887785294,g(7.1),g(7.1)-0.887785294],_
[7.2,0.889053119,g(7.2),g(7.2)-0.889053119],_
[7.3,0.890292173,g(7.3),g(7.3)-0.890292173],_
[7.4,0.891503440,g(7.4),g(7.4)-0.891503440],_
[7.5,0.892687854,g(7.5),g(7.5)-0.892687854],_
[7.6,0.893846312,g(7.6),g(7.6)-0.893846312],_
[7.7,0.894979666,g(7.7),g(7.7)-0.894979666],_
[7.8,0.896088737,g(7.8),g(7.8)-0.896088737],_
[7.9,0.897174302,g(7.9),g(7.9)-0.897174302],_
[8.0,0.898237113,g(8.0),g(8.0)-0.898237113],_
[8.1,0.899277888,g(8.1),g(8.1)-0.899277888],_
[8.2,0.900297306,g(8.2),g(8.2)-0.900297306],_
[8.3,0.901296033,g(8.3),g(8.3)-0.901296033],_
[8.4,0.902274695,g(8.4),g(8.4)-0.902274695],_
[8.5,0.903233900,g(8.5),g(8.5)-0.903233900],_
[8.6,0.904174228,g(8.6),g(8.6)-0.904174228],_
[8.7,0.905096235,g(8.7),g(8.7)-0.905096235],_
[8.8,0.906000459,g(8.8),g(8.8)-0.906000459],_
[8.9,0.906887414,g(8.9),g(8.9)-0.906887414],_
[9.0,0.907757602,g(9.0),g(9.0)-0.907757602],_
[9.1,0.908611483,g(9.1),g(9.1)-0.908611483],_
[9.2,0.909449530,g(9.2),g(9.2)-0.909449530],_
[9.3,0.910272177,g(9.3),g(9.3)-0.910272177],_
[9.4,0.911079850,g(9.4),g(9.4)-0.911079850],_
[9.5,0.911872958,g(9.5),g(9.5)-0.911872958],_
[9.6,0.912651897,g(9.6),g(9.6)-0.912651897],_
[9.7,0.913417043,g(9.7),g(9.7)-0.913417043],_
[9.8,0.914168766,g(9.8),g(9.8)-0.914168766],_
[9.9,0.914907418,g(9.9),g(9.9)-0.914907418],_
[10.0,0.915633339,g(10.0),g(10.0)-0.915633339]]
 
   Compiling function g with type Float -> Expression DoubleFloat 

   (6)
   [[2.0,0.72265723399999993,0.72265723377644342,- 2.2355650663996585E-10],

     [2.0999999999999996, 0.73079150199999998, 0.73079150228850687,
      2.8850688504888922E-10]
     ,

     [2.1999999999999997, 0.73843113199999999, 0.73843113069658639,
      - 1.3034135992739948E-9]
     ,

     [2.2999999999999998, 0.7456221489999999, 0.74562214881923949,
      - 1.8076040664283255E-10]
     ,

     [2.3999999999999999, 0.75240482899999994, 0.75240483025619209,
      1.2561921503007056E-9]
     ,
    [2.5,0.7588145919999999,0.75881459121495143,- 7.8504847067506489E-10],

     [2.5999999999999996, 0.76488272199999996, 0.7648827221797786,
      1.7977863642215652E-10]
     ,

     [2.6999999999999997, 0.77063698699999994, 0.77063698825334992,
      1.2533499793576652E-9]
     ,

     [2.7999999999999998, 0.77610212299999992, 0.77610212535833478,
      2.3583348607303378E-9]
     ,

     [2.8999999999999999, 0.78130025199999997, 0.781300253147442,
      1.1474420302803878E-9]
     ,
    [3.0,0.78625122099999989,0.786251220765942,- 2.3405788418529028E-10],

     [3.0999999999999996, 0.79097279999999992, 0.79097289808240079,
      9.808240086783826E-8]
     ,

     [3.1999999999999997, 0.79548142199999994, 0.79548142232758956,
      3.2758962209555875E-10]
     ,

     [3.2999999999999998, 0.79979140799999993, 0.79979140803710758,
      3.7107650285861382E-11]
     ,

     [3.3999999999999999, 0.80391612699999992, 0.80391612661323786,
      - 3.8676206681742542E-10]
     ,
    [3.5,0.80786766099999996,0.80786766059300541,- 4.0699454917358935E-10],

     [3.5999999999999996, 0.81165703699999991, 0.81165703674708656,
      - 2.5291335692401162E-10]
     ,

     [3.6999999999999997, 0.81529434199999995, 0.81529434137295376,
      - 6.2704619274711604E-10]
     ,

     [3.7999999999999998, 0.81878882099999994, 0.81878882054065494,
      - 4.5934500647604182E-10]
     ,

     [3.8999999999999999, 0.82214896699999995, 0.8221489675671817,
      5.6718174601400051E-10]
     ,
    [4.0,0.82538249999999991,0.82538259960420768,9.9604207770553899E-8],

     [4.0999999999999996, 0.82849692599999991, 0.82849692490969951,
      - 1.0903004055151655E-9]
     ,

     [4.1999999999999993, 0.83149860199999992, 0.83149860211639337,
      1.163934504333497E-10]
     ,

     [4.2999999999999998, 0.83439379399999991, 0.83439379260257285,
      - 1.3974270629546481E-9]
     ,

     [4.3999999999999995, 0.83718820699999996, 0.83718820689462081,
      - 1.0537914985064845E-10]
     ,
    [4.5,0.83988714399999997,0.83988714589085844,1.8908584697996389E-9],

     [4.5999999999999996, 0.84249553899999996, 0.84249553757701456,
      - 1.4229853961822414E-9]
     ,

     [4.6999999999999993, 0.84501797099999998, 0.84501796980531507,
      - 1.1946849065580523E-9]
     ,

     [4.7999999999999998, 0.84745872099999997, 0.84745871962692254,
      - 1.3730774295339643E-9]
     ,

     [4.8999999999999995, 0.84982177799999992, 0.84982177959827798,
      1.5982780654510975E-9]
     ,
    [5.0,0.8521108799999999,0.85211088142366131,1.4236614109819357E-9],

     [5.0999999999999996, 0.85432951899999998, 0.85432951724709605,
      - 1.7529039331165563E-9]
     ,

     [5.1999999999999993, 0.8564809579999999, 0.85648095886487419,
      8.6487428330173088E-10]
     ,

     [5.2999999999999998, 0.85856827499999999, 0.8585682750944803,
      9.4480312462508209E-11]
     ,

     [5.3999999999999995, 0.8605943479999999, 0.8605943475053307,
      - 4.9466919449514535E-10]
     ,
    [5.5,0.86256188499999997,0.86256188469070161,- 3.0929836469795191E-10],

     [5.5999999999999996, 0.86447343599999993, 0.86447343523800835,
      - 7.6199158094425457E-10]
     ,

     [5.6999999999999993, 0.86633139899999989, 0.8663313995352464,
      5.3524651377756527E-10]
     ,

     [5.7999999999999998, 0.86813803999999994, 0.86813804053493848,
      5.3493853791053425E-10]
     ,

     [5.8999999999999995, 0.86989549399999999, 0.86989549358247453,
      - 4.1752545865136881E-10]
     ,
    [6.0,0.87160577499999992,0.87160577540332118,4.0332126527431456E-10],

     [6.0999999999999996, 0.87327079299999999, 0.8732707923327413,
      - 6.6725869274364413E-10]
     ,

     [6.1999999999999993, 0.87489234699999996, 0.87489234786216596,
      8.6216600525546028E-10]
     ,

     [6.2999999999999998, 0.87647214999999989, 0.87647214956817143,
      - 4.318284618776147E-10]
     ,

     [6.3999999999999995, 0.87801181599999989, 0.87801181548273333,
      - 5.1726656291606332E-10]
     ,
    [6.5,0.87951288099999991,0.87951287995710259,- 1.0428973240550476E-9],

     [6.5999999999999996, 0.88097679699999998, 0.88097679906610094,
      2.066100956987782E-9]
     ,

     [6.6999999999999993, 0.88240495499999994, 0.88240495559465981,
      5.946598768957756E-10]
     ,

     [6.7999999999999998, 0.8837986619999999, 0.88379866364416326,
      1.6441633610142503E-9]
     ,

     [6.8999999999999995, 0.88515917599999994, 0.88515917289225443,
      - 3.1077455053818426E-9]
     ,
    [7.0,0.88648767499999992,0.88648767253642924,- 2.4635706807885072E-9],

     [7.0999999999999996, 0.88778529399999995, 0.8877852949486843,
      9.4868435329686918E-10]
     ,

     [7.1999999999999993, 0.88905311899999995, 0.88905311906582596,
      6.5826011308445231E-11]
     ,

     [7.2999999999999998, 0.89029217299999996, 0.89029217353766832,
      5.3766835428348259E-10]
     ,

     [7.3999999999999995, 0.89150343999999992, 0.89150343965322776,
      - 3.4677216653733467E-10]
     ,
    [7.5,0.89268785399999995,0.89268785406308415,6.3084204526830945E-11],

     [7.5999999999999996, 0.89384631199999998, 0.89384631131444836,
      - 6.8555161547578791E-10]
     ,

     [7.6999999999999993, 0.8949796659999999, 0.89497966621388259,
      2.1388268933719701E-10]
     ,

     [7.7999999999999998, 0.89608873699999991, 0.89608873603132144,
      - 9.6867847076964608E-10]
     ,

     [7.8999999999999995, 0.89717430199999992, 0.89717430255777397,
      5.5777404917023432E-10]
     ,
    [8.0,0.89823711299999998,0.89823711402799544,1.0279954665293189E-9],

     [8.0999999999999996, 0.89927788799999997, 0.89927788691844668,
      - 1.0815532913710513E-9]
     ,

     [8.1999999999999993, 0.90029730599999991, 0.90029730762992666,
      1.629926749124877E-9]
     ,

     [8.2999999999999989, 0.90129603299999994, 0.9012960340634919,
      1.0634919611618443E-9]
     ,

     [8.3999999999999986, 0.9022746949999999, 0.90227469709753461,
      2.097534701483994E-9]
     ,
    [8.5,0.90323389999999992,0.90323390197320841,1.9732084854950926E-9],

     [8.5999999999999996, 0.90417422799999991, 0.90417422959485083,
      1.5948509179963821E-9]
     ,

     [8.6999999999999993, 0.90509623499999992, 0.90509623775141723,
      2.7514173162046518E-9]
     ,

     [8.7999999999999989, 0.90600045899999992, 0.90600046226454345,
      3.2645435243949805E-9]
     ,

     [8.8999999999999986, 0.90688741399999995, 0.90688741806836415,
      4.0683642010819199E-9]
     ,
    [9.0,0.907757602,0.9077576002257679,- 1.7742320945757228E-9],

     [9.0999999999999996, 0.90861148299999994, 0.9086114848854826,
      1.8854826588921014E-9]
     ,

     [9.1999999999999993, 0.90944952999999995, 0.90944953018395813,
      1.8395818202066039E-10]
     ,

     [9.2999999999999989, 0.91027217699999996, 0.91027217709579267,
      9.5792707099917607E-11]
     ,

     [9.3999999999999986, 0.91107984999999991, 0.91107985023607507,
      2.3607515942103419E-10]
     ,
    [9.5,0.9118729579999999,0.91187295861782758,6.1782767790674598E-10],

     [9.5999999999999996, 0.91265189699999993, 0.91265189636747834,
      - 6.3252159065996238E-10]
     ,

     [9.6999999999999993, 0.91341704299999993, 0.91341704340103569,
      4.0103576015582121E-10]
     ,

     [9.7999999999999989, 0.91416876599999997, 0.9141687660635136,
      6.3513638792755955E-11]
     ,

     [9.8999999999999986, 0.91490741799999997, 0.9149074177339076,
      - 2.6609237036012701E-10]
     ,
    [10.0,0.91563333899999999,0.91563333939788105,3.9788106143134883E-10]]
                                       Type: List List Expression DoubleFloat
--R 
--R   Compiling function g with type Float -> Expression DoubleFloat 
--R
--R   (6)
--R   [[2.,0.72265723400000004,0.72265723377644353,- 2.2355650663996585E-10],
--R
--R     [2.1000000000000001, 0.73079150199999998, 0.73079150228850298,
--R      2.8850299926830303E-10]
--R     ,
--R
--R     [2.2000000000000002, 0.73843113199999999, 0.73843113069659072,
--R      - 1.3034092694041988E-9]
--R     ,
--R
--R     [2.2999999999999998, 0.74562214900000001, 0.74562214881923961,
--R      - 1.8076040664283255E-10]
--R     ,
--R
--R     [2.3999999999999999, 0.75240482900000005, 0.75240483025618621,
--R      1.2561861550963727E-9]
--R     ,
--R    [2.5,0.75881459200000001,0.75881459121494477,- 7.850552430355151E-10],
--R
--R     [2.6000000000000001, 0.76488272199999996, 0.76488272217978248,
--R      1.7978252220274271E-10]
--R     ,
--R
--R     [2.7000000000000002, 0.77063698700000005, 0.77063698825333671,
--R      1.2533366566813697E-9]
--R     ,
--R
--R     [2.7999999999999998, 0.77610212300000003, 0.77610212535832457,
--R      2.3583245356562088E-9]
--R     ,
--R
--R     [2.8999999999999999, 0.78130025199999997, 0.78130025314743023,
--R      1.1474302619163268E-9]
--R     ,
--R    [3.,0.786251221,0.78625122076592868,- 2.3407131788388824E-10],
--R
--R     [3.1000000000000001, 0.79097280000000003, 0.79097289808240101,
--R      9.8082400978860562E-8]
--R     ,
--R
--R     [3.2000000000000002, 0.79548142200000005, 0.7954814223275547,
--R      3.2755465007028306E-10]
--R     ,
--R
--R     [3.2999999999999998, 0.79979140800000004, 0.79979140803702831,
--R      3.7028269339600683E-11]
--R     ,
--R
--R     [3.3999999999999999, 0.80391612700000004, 0.80391612661323797,
--R      - 3.8676206681742542E-10]
--R     ,
--R    [3.5,0.80786766099999996,0.80786766059300552,- 4.0699443815128689E-10],
--R
--R     [3.6000000000000001, 0.81165703700000003, 0.81165703674711587,
--R      - 2.5288415805846398E-10]
--R     ,
--R
--R     [3.7000000000000002, 0.81529434199999995, 0.81529434137285406,
--R      - 6.2714589077472738E-10]
--R     ,
--R
--R     [3.7999999999999998, 0.81878882100000006, 0.81878882054050406,
--R      - 4.5949599680739084E-10]
--R     ,
--R
--R     [3.8999999999999999, 0.82214896699999995, 0.8221489675670105,
--R      5.6701054962360331E-10]
--R     ,
--R    [4.,0.82538250000000002,0.82538259960411076,9.9604110737061546E-8],
--R
--R     [4.0999999999999996, 0.82849692600000002, 0.82849692490970006,
--R      - 1.0902999614259556E-9]
--R     ,
--R
--R     [4.2000000000000002, 0.83149860200000003, 0.83149860211639337,
--R      1.1639333941104724E-10]
--R     ,
--R
--R     [4.2999999999999998, 0.83439379400000002, 0.83439379260257418,
--R      - 1.397425841709321E-9]
--R     ,
--R
--R     [4.4000000000000004, 0.83718820699999996, 0.83718820689462137,
--R      - 1.0537859473913613E-10]
--R     ,
--R    [4.5,0.83988714399999997,0.83988714589085944,1.8908594690003611E-9],
--R
--R     [4.5999999999999996, 0.84249553899999996, 0.84249553757701434,
--R      - 1.4229856182268463E-9]
--R     ,
--R
--R     [4.7000000000000002, 0.84501797099999998, 0.84501796980531307,
--R      - 1.1946869049594966E-9]
--R     ,
--R
--R     [4.7999999999999998, 0.84745872099999997, 0.84745871962692243,
--R      - 1.3730775405562667E-9]
--R     ,
--R
--R     [4.9000000000000004, 0.84982177800000003, 0.84982177959827732,
--R      1.5982772882949803E-9]
--R     ,
--R    [5.,0.85211088000000001,0.85211088142366165,1.4236616330265406E-9],
--R
--R     [5.0999999999999996, 0.85432951899999998, 0.85432951724709605,
--R      - 1.7529039331165563E-9]
--R     ,
--R
--R     [5.2000000000000002, 0.85648095800000001, 0.85648095886487274,
--R      8.6487272898949641E-10]
--R     ,
--R
--R     [5.2999999999999998, 0.85856827499999999, 0.85856827509448064,
--R      9.4480645529415597E-11]
--R     ,
--R
--R     [5.4000000000000004, 0.86059434800000001, 0.86059434750532948,
--R      - 4.946705267627749E-10]
--R     ,
--R    [5.5,0.86256188499999997,0.86256188469070161,- 3.0929836469795191E-10],
--R
--R     [5.5999999999999996, 0.86447343600000004, 0.86447343523800879,
--R      - 7.6199124787734718E-10]
--R     ,
--R    [5.7000000000000002,0.866331399,0.8663313995352464,5.3524640275526281E-10],
--R
--R     [5.7999999999999998, 0.86813804000000006, 0.86813804053493893,
--R      5.3493887097744164E-10]
--R     ,
--R
--R     [5.9000000000000004, 0.86989549399999999, 0.86989549358247464,
--R      - 4.1752534762906635E-10]
--R     ,
--R    [6.,0.87160577500000003,0.87160577540332174,4.0332170936352441E-10],
--R
--R     [6.0999999999999996, 0.87327079299999999, 0.8732707923327413,
--R      - 6.6725869274364413E-10]
--R     ,
--R
--R     [6.2000000000000002, 0.87489234699999996, 0.8748923478621643,
--R      8.6216433992092334E-10]
--R     ,
--R
--R     [6.2999999999999998, 0.87647215000000001, 0.87647214956817143,
--R      - 4.3182857289991716E-10]
--R     ,
--R
--R     [6.4000000000000004, 0.878011816, 0.87801181548273155,
--R      - 5.1726845029520518E-10]
--R     ,
--R    [6.5,0.87951288100000002,0.87951287995710281,- 1.0428972130327452E-9],
--R
--R     [6.5999999999999996, 0.88097679699999998, 0.88097679906610149,
--R      2.0661015120992943E-9]
--R     ,
--R
--R     [6.7000000000000002, 0.88240495500000005, 0.8824049555946607,
--R      5.9466065405189283E-10]
--R     ,
--R
--R     [6.7999999999999998, 0.88379866200000001, 0.88379866364416337,
--R      1.6441633610142503E-9]
--R     ,
--R
--R     [6.9000000000000004, 0.88515917600000005, 0.88515917289225332,
--R      - 3.1077467266271697E-9]
--R     ,
--R    [7.,0.88648767500000003,0.88648767253642946,- 2.4635705697662047E-9],
--R
--R     [7.0999999999999996, 0.88778529399999995, 0.8877852949486843,
--R      9.4868435329686918E-10]
--R     ,
--R
--R     [7.2000000000000002, 0.88905311899999995, 0.88905311906582485,
--R      6.5824901085420606E-11]
--R     ,
--R
--R     [7.2999999999999998, 0.89029217299999996, 0.89029217353766843,
--R      5.3766846530578505E-10]
--R     ,
--R
--R     [7.4000000000000004, 0.89150344000000004, 0.89150343965322676,
--R      - 3.4677327676035929E-10]
--R     ,
--R    [7.5,0.89268785399999995,0.89268785406308437,6.308442657143587E-11],
--R
--R     [7.5999999999999996, 0.89384631199999998, 0.89384631131444836,
--R      - 6.8555161547578791E-10]
--R     ,
--R
--R     [7.7000000000000002, 0.89497966600000001, 0.89497966621388148,
--R      2.1388146809186992E-10]
--R     ,
--R
--R     [7.7999999999999998, 0.89608873700000002, 0.89608873603132189,
--R      - 9.686781377027387E-10]
--R     ,
--R
--R     [7.9000000000000004, 0.89717430200000003, 0.8971743025577732,
--R      5.5777316099181462E-10]
--R     ,
--R    [8.,0.89823711299999998,0.89823711402799578,1.0279957995962263E-9],
--R
--R     [8.0999999999999996, 0.89927788799999997, 0.89927788691844668,
--R      - 1.0815532913710513E-9]
--R     ,
--R
--R     [8.1999999999999993, 0.90029730600000002, 0.90029730762992677,
--R      1.629926749124877E-9]
--R     ,
--R
--R     [8.3000000000000007, 0.90129603300000005, 0.90129603406349046,
--R      1.0634904068496098E-9]
--R     ,
--R
--R     [8.4000000000000004, 0.90227469500000002, 0.90227469709753316,
--R      2.0975331471717595E-9]
--R     ,
--R    [8.5,0.90323390000000003,0.90323390197320852,1.9732084854950926E-9],
--R
--R     [8.5999999999999996, 0.90417422800000002, 0.9041742295948515,
--R      1.5948514731078944E-9]
--R     ,
--R
--R     [8.6999999999999993, 0.90509623500000003, 0.90509623775141723,
--R      2.7514172051823493E-9]
--R     ,
--R
--R     [8.8000000000000007, 0.90600045900000004, 0.90600046226454201,
--R      3.264541970082746E-9]
--R     ,
--R
--R     [8.9000000000000004, 0.90688741399999995, 0.90688741806836271,
--R      4.0683627577919879E-9]
--R     ,
--R    [9.,0.907757602,0.90775760022576812,- 1.7742318725311179E-9],
--R
--R     [9.0999999999999996, 0.90861148300000005, 0.90861148488548271,
--R      1.8854826588921014E-9]
--R     ,
--R
--R     [9.1999999999999993, 0.90944952999999995, 0.90944953018395813,
--R      1.8395818202066039E-10]
--R     ,
--R
--R     [9.3000000000000007, 0.91027217699999996, 0.91027217709579178,
--R      9.5791818921497907E-11]
--R     ,
--R
--R     [9.4000000000000004, 0.91107985000000002, 0.91107985023607185,
--R      2.3607182875196031E-10]
--R     ,
--R    [9.5,0.91187295800000001,0.91187295861782769,6.1782767790674598E-10],
--R
--R     [9.5999999999999996, 0.91265189700000005, 0.91265189636747834,
--R      - 6.3252170168226485E-10]
--R     ,
--R
--R     [9.6999999999999993, 0.91341704300000004, 0.91341704340103613,
--R      4.010360932227286E-10]
--R     ,
--R
--R     [9.8000000000000007, 0.91416876599999997, 0.91416876606351216,
--R      6.3512195502823943E-11]
--R     ,
--R
--R     [9.9000000000000004, 0.91490741799999997, 0.9149074177339066,
--R      - 2.6609336956084917E-10]
--R     ,
--R    [10.,0.91563333899999999,0.91563333939788116,3.9788117245365129E-10]]
--R                                       Type: List List Expression DoubleFloat
--E 6

--S 7 of 7
E1(0.0)
 

   (7)  infinity
                                         Type: OnePointCompletion DoubleFloat
--R
--R   (7)  infinity
--R                                         Type: OnePointCompletion DoubleFloat
--E 7
)spool 
 
Starts dribbling to mkfunc.output (2009/2/17, 17:55:6).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 9
expr := (x - exp x + 1)**2 * (sin(x**2) * x + 1)**3
 

   (1)
       3   x 2        4     3   x    5     4    3      2 3
     (x (%e )  + (- 2x  - 2x )%e  + x  + 2x  + x )sin(x )
   + 
        2   x 2        3     2   x     4     3     2      2 2
     (3x (%e )  + (- 6x  - 6x )%e  + 3x  + 6x  + 3x )sin(x )
   + 
            x 2        2        x     3     2           2       x 2
     (3x (%e )  + (- 6x  - 6x)%e  + 3x  + 6x  + 3x)sin(x ) + (%e )
   + 
                 x    2
     (- 2x - 2)%e  + x  + 2x + 1
                                                     Type: Expression Integer
--R 
--R
--R   (1)
--R       3   x 2        4     3   x    5     4    3      2 3
--R     (x (%e )  + (- 2x  - 2x )%e  + x  + 2x  + x )sin(x )
--R   + 
--R        2   x 2        3     2   x     4     3     2      2 2
--R     (3x (%e )  + (- 6x  - 6x )%e  + 3x  + 6x  + 3x )sin(x )
--R   + 
--R            x 2        2        x     3     2           2       x 2
--R     (3x (%e )  + (- 6x  - 6x)%e  + 3x  + 6x  + 3x)sin(x ) + (%e )
--R   + 
--R                 x    2
--R     (- 2x - 2)%e  + x  + 2x + 1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 9
function(expr, f, x)
 

   (2)  f
                                                                 Type: Symbol
--R 
--R
--R   (2)  f
--R                                                                 Type: Symbol
--E 2

--S 3 of 9
tbl := [f(0.1 * i - 1) for i in 0..20];
 
   Compiling function f with type Float -> Float 

                                                             Type: List Float
--R 
--R   Compiling function f with type Float -> Float 
--R
--R                                                             Type: List Float
--E 3

--S 4 of 9
e := (x - y + 1)**2 * (x**2 * y + 1)**2
 

   (4)
      4 4        5     4     2  3     6     5    4     3     2      2
     x y  + (- 2x  - 2x  + 2x )y  + (x  + 2x  + x  - 4x  - 4x  + 1)y
   + 
        4     3     2               2
     (2x  + 4x  + 2x  - 2x - 2)y + x  + 2x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)
--R      4 4        5     4     2  3     6     5    4     3     2      2
--R     x y  + (- 2x  - 2x  + 2x )y  + (x  + 2x  + x  - 4x  - 4x  + 1)y
--R   + 
--R        4     3     2               2
--R     (2x  + 4x  + 2x  - 2x - 2)y + x  + 2x + 1
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 9
function(e, g, [x, y])
 

   (5)  g
                                                                 Type: Symbol
--R 
--R
--R   (5)  g
--R                                                                 Type: Symbol
--E 5

--S 6 of 9
function(e, h, x, y)
 

   (6)  h
                                                                 Type: Symbol
--R 
--R
--R   (6)  h
--R                                                                 Type: Symbol
--E 6

--S 7 of 9
m1 := squareMatrix [[1, 2], [3, 4]]
 

        +1  2+
   (7)  |    |
        +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 7

--S 8 of 9
m2 := squareMatrix [[1, 0], [-1, 1]]
 

        + 1   0+
   (8)  |      |
        +- 1  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        + 1   0+
--R   (8)  |      |
--R        +- 1  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 9
h(m1, m2)
 
   Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix
      (2,Integer)) -> SquareMatrix(2,Integer) 

        +- 7836   8960 +
   (9)  |              |
        +- 17132  19588+
                                                Type: SquareMatrix(2,Integer)
--R 
--R   Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix
--R      (2,Integer)) -> SquareMatrix(2,Integer) 
--R
--R        +- 7836   8960 +
--R   (9)  |              |
--R        +- 17132  19588+
--R                                                Type: SquareMatrix(2,Integer)
--E 9
)spool 
 
Starts dribbling to schaum8.output (2009/2/17, 18:0:7).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(a^2-x^2),x)
 

        log(x + a) - log(x - a)
   (1)  -----------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        log(x + a) - log(x - a)
--R   (1)  -----------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/(2*a)*log((a+x)/(a-x))
 

            - x - a
        log(-------)
             x - a
   (2)  ------------
             2a
                                                     Type: Expression Integer
--R
--R            - x - a
--R        log(-------)
--R             x - a
--R   (2)  ------------
--R             2a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                      - x - a
        log(x + a) - log(x - a) - log(-------)
                                       x - a
   (3)  --------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                                      - x - a
--R        log(x + a) - log(x - a) - log(-------)
--R                                       x - a
--R   (3)  --------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 4
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5      
dd:=divlog cc
 

        log(x + a) - log(- x - a)
   (5)  -------------------------
                    2a
                                                     Type: Expression Integer
--R
--R        log(x + a) - log(- x - a)
--R   (5)  -------------------------
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 6
logminus:=rule(log(x + a) - log(- x - a) == log(-1))
 

   (6)  log(x + a) - log(- x - a) + %G == log(- 1) + %G
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(x + a) - log(- x - a) + %I == log(- 1) + %I
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 7      14:163 Schaums and Axiom differ by a constant
ee:=logminus dd
 

        log(- 1)
   (7)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(x/(a^2-x^2),x)
 

               2    2
          log(x  - a )
   (1)  - ------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R          log(x  - a )
--R   (1)  - ------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=-1/2*log(a^2-x^2)
 

                 2    2
          log(- x  + a )
   (2)  - --------------
                 2
                                                     Type: Expression Integer
--R
--R                 2    2
--R          log(- x  + a )
--R   (2)  - --------------
--R                 2
--R                                                     Type: Expression Integer
--E

--S 10
cc:=aa-bb
 

               2    2           2    2
        - log(x  - a ) + log(- x  + a )
   (3)  -------------------------------
                       2
                                                     Type: Expression Integer
--R
--R               2    2           2    2
--R        - log(x  - a ) + log(- x  + a )
--R   (3)  -------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E

--S 11
logminus1:=rule(-log(x^2-a^2)+log(-x^2+a^2) == log(-1))
 

               2    2           2    2
   (4)  - log(x  - a ) + log(- x  + a ) + %H == log(- 1) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    2           2    2
--I   (4)  - log(x  - a ) + log(- x  + a ) + %H == log(- 1) + %H
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12     14:164 Schaums and Axiom differ by a constant
dd:=logminus1 cc
 

        log(- 1)
   (5)  --------
            2
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R            2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(x^2/(a^2-x^2),x)
 

        a log(x + a) - a log(x - a) - 2x
   (1)  --------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a log(x + a) - a log(x - a) - 2x
--R   (1)  --------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=-x+a/2*log((a+x)/(a-x))
 

              - x - a
        a log(-------) - 2x
               x - a
   (2)  -------------------
                 2
                                                     Type: Expression Integer
--R
--R              - x - a
--R        a log(-------) - 2x
--R               x - a
--R   (2)  -------------------
--R                 2
--R                                                     Type: Expression Integer
--E

--S 15
cc:=aa-bb
 

                                            - x - a
        a log(x + a) - a log(x - a) - a log(-------)
                                             x - a
   (3)  --------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R                                            - x - a
--R        a log(x + a) - a log(x - a) - a log(-------)
--R                                             x - a
--R   (3)  --------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 16
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 17
dd:=divlog cc
 

        a log(x + a) - a log(- x - a)
   (5)  -----------------------------
                      2
                                                     Type: Expression Integer
--R
--R        a log(x + a) - a log(- x - a)
--R   (5)  -----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 18
logminusa:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
 

   (6)  b log(x + a) - b log(- x - a) + %I == b log(- 1) + %I
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  b log(x + a) - b log(- x - a) + %M == b log(- 1) + %M
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19     14:165 Schaums and Axiom differ by a constant
ee:=logminusa dd
 

        a log(- 1)
   (7)  ----------
             2
                                                     Type: Expression Integer
--R
--R        a log(- 1)
--R   (7)  ----------
--R             2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(x^3/(a^2-x^2),x)
 

           2     2    2     2
        - a log(x  - a ) - x
   (1)  ---------------------
                  2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2     2
--R        - a log(x  - a ) - x
--R   (1)  ---------------------
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21
bb:=-x^2/2-a^2/2*log(a^2-x^2)
 

           2       2    2     2
        - a log(- x  + a ) - x
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R           2       2    2     2
--R        - a log(- x  + a ) - x
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 22
cc:=aa-bb
 

           2     2    2     2       2    2
        - a log(x  - a ) + a log(- x  + a )
   (3)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R           2     2    2     2       2    2
--R        - a log(x  - a ) + a log(- x  + a )
--R   (3)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 23
logminus1b:=rule(-b*log(x^2-a^2)+b*log(-x^2+a^2) == b*log(-1))
 

                 2    2             2    2
   (4)  - b log(x  - a ) + b log(- x  + a ) + %J == b log(- 1) + %J
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                 2    2             2    2
--I   (4)  - b log(x  - a ) + b log(- x  + a ) + %N == b log(- 1) + %N
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 24     14:166 Schaums and Axiom differ by a constant
dd:=logminus1b cc
 

         2
        a log(- 1)
   (5)  ----------
             2
                                                     Type: Expression Integer
--R
--R         2
--R        a log(- 1)
--R   (5)  ----------
--R             2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 25
aa:=integrate(1/(x*(a^2-x^2)),x)
 

               2    2
        - log(x  - a ) + 2log(x)
   (1)  ------------------------
                     2
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R        - log(x  - a ) + 2log(x)
--R   (1)  ------------------------
--R                     2
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 26
bb:=1/(2*a^2)*log(x^2/(a^2-x^2))
 

                  2
                 x
        log(- -------)
               2    2
              x  - a
   (2)  --------------
                2
              2a
                                                     Type: Expression Integer
--R
--R                  2
--R                 x
--R        log(- -------)
--R               2    2
--R              x  - a
--R   (2)  --------------
--R                2
--R              2a
--R                                                     Type: Expression Integer
--E

--S 27
cc:=aa-bb
 

                                             2
               2    2                       x
        - log(x  - a ) + 2log(x) - log(- -------)
                                          2    2
                                         x  - a
   (3)  -----------------------------------------
                             2
                           2a
                                                     Type: Expression Integer
--R
--R                                             2
--R               2    2                       x
--R        - log(x  - a ) + 2log(x) - log(- -------)
--R                                          2    2
--R                                         x  - a
--R   (3)  -----------------------------------------
--R                             2
--R                           2a
--R                                                     Type: Expression Integer
--E

--S 28
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29
dd:=divlog cc
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  2
                2a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  2
--R                2a
--R                                                     Type: Expression Integer
--E

--S 30
logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
 

               n
   (6)  log(- a ) == n log(a) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- a ) == n log(a) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 31     14:167 Schaums and Axiom differ by a constant
ee:=logpowminus dd
 

          log(- 1)
   (7)  - --------
               2
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R               2
--R             2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 32
aa:=integrate(1/(x^2*(a^2-x^2)),x)
 

        x log(x + a) - x log(x - a) - 2a
   (1)  --------------------------------
                        3
                      2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        x log(x + a) - x log(x - a) - 2a
--R   (1)  --------------------------------
--R                        3
--R                      2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33
bb:=-1/(a^2*x)+1/(2*a^3)*log((a+x)/(a-x))
 

              - x - a
        x log(-------) - 2a
               x - a
   (2)  -------------------
                  3
                2a x
                                                     Type: Expression Integer
--R
--R              - x - a
--R        x log(-------) - 2a
--R               x - a
--R   (2)  -------------------
--R                  3
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 34
cc:=aa-bb
 

                                      - x - a
        log(x + a) - log(x - a) - log(-------)
                                       x - a
   (3)  --------------------------------------
                            3
                          2a
                                                     Type: Expression Integer
--R
--R                                      - x - a
--R        log(x + a) - log(x - a) - log(-------)
--R                                       x - a
--R   (3)  --------------------------------------
--R                            3
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 35
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36
dd:=divlog cc
 

        log(x + a) - log(- x - a)
   (5)  -------------------------
                     3
                   2a
                                                     Type: Expression Integer
--R
--R        log(x + a) - log(- x - a)
--R   (5)  -------------------------
--R                     3
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 37
logminus:=rule(log(x + a) - log(- x - a) == log(-1))
 

   (6)  log(x + a) - log(- x - a) + %K == log(- 1) + %K
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(x + a) - log(- x - a) + %O == log(- 1) + %O
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38     14:168 Schaums and Axiom differ by a constant
ee:=logminus dd
 

        log(- 1)
   (7)  --------
             3
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R             3
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(1/(x^3*(a^2-x^2)),x)
 

           2     2    2      2          2
        - x log(x  - a ) + 2x log(x) - a
   (1)  ---------------------------------
                        4 2
                      2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2      2          2
--R        - x log(x  - a ) + 2x log(x) - a
--R   (1)  ---------------------------------
--R                        4 2
--R                      2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40
bb:=-1/(2*a^2*x^2)+1/(2*a^4)*log(x^2/(a^2-x^2))
 

                    2
         2         x        2
        x log(- -------) - a
                 2    2
                x  - a
   (2)  ---------------------
                  4 2
                2a x
                                                     Type: Expression Integer
--R
--R                    2
--R         2         x        2
--R        x log(- -------) - a
--R                 2    2
--R                x  - a
--R   (2)  ---------------------
--R                  4 2
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 41
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 42
bb1:=divlog bb
 

           2     2    2     2       2     2
        - x log(x  - a ) + x log(- x ) - a
   (4)  -----------------------------------
                         4 2
                       2a x
                                                     Type: Expression Integer
--R
--R           2     2    2     2       2     2
--R        - x log(x  - a ) + x log(- x ) - a
--R   (4)  -----------------------------------
--R                         4 2
--R                       2a x
--R                                                     Type: Expression Integer
--E

--S 43
cc:=aa-bb1
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 44
logminuspow:=rule(log(-x^n) == n*log(x)+log(-1))
 

               n
   (6)  log(- x ) == n log(x) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- x ) == n log(x) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 45     14:169 Schaums and Axiom differ by a constant
dd:=logminuspow cc
 

          log(- 1)
   (7)  - --------
               4
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R               4
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 46
aa:=integrate(1/((a^2-x^2)^2),x)
 

          2    2                  2    2
        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                              3 2     5
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2                  2    2
--R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                              3 2     5
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 47
bb:=x/(2*a^2*(a^2-x^2))+1/(4*a^3)*log((a+x)/(a-x))
 

          2    2     - x - a
        (x  - a )log(-------) - 2a x
                      x - a
   (2)  ----------------------------
                   3 2     5
                 4a x  - 4a
                                                     Type: Expression Integer
--R
--R          2    2     - x - a
--R        (x  - a )log(-------) - 2a x
--R                      x - a
--R   (2)  ----------------------------
--R                   3 2     5
--R                 4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 48
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 49
bb1:=divlog bb
 

            2    2                2    2
        (- x  + a )log(x - a) + (x  - a )log(- x - a) - 2a x
   (4)  ----------------------------------------------------
                               3 2     5
                             4a x  - 4a
                                                     Type: Expression Integer
--R
--R            2    2                2    2
--R        (- x  + a )log(x - a) + (x  - a )log(- x - a) - 2a x
--R   (4)  ----------------------------------------------------
--R                               3 2     5
--R                             4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 50
cc:=aa-bb1
 

        log(x + a) - log(- x - a)
   (5)  -------------------------
                     3
                   4a
                                                     Type: Expression Integer
--R
--R        log(x + a) - log(- x - a)
--R   (5)  -------------------------
--R                     3
--R                   4a
--R                                                     Type: Expression Integer
--E

--S 51
logminus:=rule(log(x + a) - log(- x - a) == log(-1))
 

   (6)  log(x + a) - log(- x - a) + %L == log(- 1) + %L
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(x + a) - log(- x - a) + %P == log(- 1) + %P
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 52     14:170 Schaums and Axiom differ by a constant
dd:=logminus cc
 

        log(- 1)
   (7)  --------
             3
           4a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R             3
--R           4a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 53
aa:=integrate(x/((a^2-x^2)^2),x)
 

              1
   (1)  - ---------
            2     2
          2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            2     2
--R          2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54
bb:=1/(2*(a^2-x^2))
 

              1
   (2)  - ---------
            2     2
          2x  - 2a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            2     2
--R          2x  - 2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 55     14:171 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 56
aa:=integrate(x^2/((a^2-x^2)^2),x)
 

            2    2                2    2
        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                                2     3
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2                2    2
--R        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                                2     3
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 57
bb:=x/(2*(a^2-x^2))-1/(4*a)*log((a+x)/(a-x))
 

            2    2     - x - a
        (- x  + a )log(-------) - 2a x
                        x - a
   (2)  ------------------------------
                      2     3
                  4a x  - 4a
                                                     Type: Expression Integer
--R
--R            2    2     - x - a
--R        (- x  + a )log(-------) - 2a x
--R                        x - a
--R   (2)  ------------------------------
--R                      2     3
--R                  4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 58
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 59
bb1:=divlog bb
 

          2    2                  2    2
        (x  - a )log(x - a) + (- x  + a )log(- x - a) - 2a x
   (4)  ----------------------------------------------------
                                 2     3
                             4a x  - 4a
                                                     Type: Expression Integer
--R
--R          2    2                  2    2
--R        (x  - a )log(x - a) + (- x  + a )log(- x - a) - 2a x
--R   (4)  ----------------------------------------------------
--R                                 2     3
--R                             4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 60
cc:=aa-bb1
 

        - log(x + a) + log(- x - a)
   (5)  ---------------------------
                     4a
                                                     Type: Expression Integer
--R
--R        - log(x + a) + log(- x - a)
--R   (5)  ---------------------------
--R                     4a
--R                                                     Type: Expression Integer
--E

--S 61
logminus2:=rule(-log(x + a) + log(- x - a) == log(-1))
 

   (6)  - log(x + a) + log(- x - a) + %M == log(- 1) + %M
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  - log(x + a) + log(- x - a) + %S == log(- 1) + %S
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 62     14:172 Schaums and Axiom differ by a constant
dd:=logminus2 cc
 

        log(- 1)
   (7)  --------
           4a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R           4a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 63
aa:=integrate(x^3/((a^2-x^2)^2),x)
 

          2    2      2    2     2
        (x  - a )log(x  - a ) - a
   (1)  --------------------------
                   2     2
                 2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      2    2     2
--R        (x  - a )log(x  - a ) - a
--R   (1)  --------------------------
--R                   2     2
--R                 2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 64
bb:=a^2/(2*(a^2-x^2))+1/2*log(a^2-x^2)
 

          2    2        2    2     2
        (x  - a )log(- x  + a ) - a
   (2)  ----------------------------
                    2     2
                  2x  - 2a
                                                     Type: Expression Integer
--R
--R          2    2        2    2     2
--R        (x  - a )log(- x  + a ) - a
--R   (2)  ----------------------------
--R                    2     2
--R                  2x  - 2a
--R                                                     Type: Expression Integer
--E

--S 65
cc:=aa-bb
 

             2    2           2    2
        log(x  - a ) - log(- x  + a )
   (3)  -----------------------------
                      2
                                                     Type: Expression Integer
--R
--R             2    2           2    2
--R        log(x  - a ) - log(- x  + a )
--R   (3)  -----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 66
logminus3:=rule(log(x^2-a^2)-log(-x^2+a^2) == log(-1))
 

             2    2           2    2
   (4)  log(x  - a ) - log(- x  + a ) + %N == log(- 1) + %N
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             2    2           2    2
--I   (4)  log(x  - a ) - log(- x  + a ) + %T == log(- 1) + %T
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 67     14:173 Schaums and Axiom differ by a constant
dd:=logminus3 cc
 

        log(- 1)
   (5)  --------
            2
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R            2
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 68
aa:=integrate(1/(x*(a^2-x^2)^2),x)
 

            2    2      2    2       2     2           2
        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
   (1)  ------------------------------------------------
                             4 2     6
                           2a x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2      2    2       2     2           2
--R        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
--R   (1)  ------------------------------------------------
--R                             4 2     6
--R                           2a x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 69
bb:=1/(2*a^2*(a^2-x^2))+1/(2*a^4)*log(x^2/(a^2-x^2))
 

                           2
          2    2          x        2
        (x  - a )log(- -------) - a
                        2    2
                       x  - a
   (2)  ----------------------------
                   4 2     6
                 2a x  - 2a
                                                     Type: Expression Integer
--R
--R                           2
--R          2    2          x        2
--R        (x  - a )log(- -------) - a
--R                        2    2
--R                       x  - a
--R   (2)  ----------------------------
--R                   4 2     6
--R                 2a x  - 2a
--R                                                     Type: Expression Integer
--E

--S 70
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 71
bb1:=divlog bb
 

            2    2      2    2      2    2        2     2
        (- x  + a )log(x  - a ) + (x  - a )log(- x ) - a
   (4)  -------------------------------------------------
                             4 2     6
                           2a x  - 2a
                                                     Type: Expression Integer
--R
--R            2    2      2    2      2    2        2     2
--R        (- x  + a )log(x  - a ) + (x  - a )log(- x ) - a
--R   (4)  -------------------------------------------------
--R                             4 2     6
--R                           2a x  - 2a
--R                                                     Type: Expression Integer
--E

--S 72
cc:=aa-bb1
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 73
logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
 

               n
   (6)  log(- a ) == n log(a) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- a ) == n log(a) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 74     14:174 Schaums and Axiom differ by a constant
dd:=logpowminus cc
 

          log(- 1)
   (7)  - --------
               4
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R               4
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 75
aa:=integrate(1/(x^2*(a^2-x^2)^2),x)
 

           3     2                    3     2                   2     3
        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
   (1)  ---------------------------------------------------------------
                                    5 3     7
                                  4a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R
--R           3     2                    3     2                   2     3
--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
--R   (1)  ---------------------------------------------------------------
--R                                    5 3     7
--R                                  4a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 76
bb:=-1/(a^4*x)+x/(2*a^4*(a^2-x^2))+3/(4*a^5)*log((a+x)/(a-x))
 

           3     2      - x - a        2     3
        (3x  - 3a x)log(-------) - 6a x  + 4a
                         x - a
   (2)  --------------------------------------
                       5 3     7
                     4a x  - 4a x
                                                     Type: Expression Integer
--R
--R           3     2      - x - a        2     3
--R        (3x  - 3a x)log(-------) - 6a x  + 4a
--R                         x - a
--R   (2)  --------------------------------------
--R                       5 3     7
--R                     4a x  - 4a x
--R                                                     Type: Expression Integer
--E

--S 77
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 78
bb1:=divlog bb
 

             3     2                  3     2                     2     3
        (- 3x  + 3a x)log(x - a) + (3x  - 3a x)log(- x - a) - 6a x  + 4a
   (4)  -----------------------------------------------------------------
                                     5 3     7
                                   4a x  - 4a x
                                                     Type: Expression Integer
--R
--R             3     2                  3     2                     2     3
--R        (- 3x  + 3a x)log(x - a) + (3x  - 3a x)log(- x - a) - 6a x  + 4a
--R   (4)  -----------------------------------------------------------------
--R                                     5 3     7
--R                                   4a x  - 4a x
--R                                                     Type: Expression Integer
--E

--S 79
cc:=aa-bb
 

                                         - x - a
        3log(x + a) - 3log(x - a) - 3log(-------)
                                          x - a
   (5)  -----------------------------------------
                             5
                           4a
                                                     Type: Expression Integer
--R
--R                                         - x - a
--R        3log(x + a) - 3log(x - a) - 3log(-------)
--R                                          x - a
--R   (5)  -----------------------------------------
--R                             5
--R                           4a
--R                                                     Type: Expression Integer
--E

--S 80
dd:=divlog cc
 

        3log(x + a) - 3log(- x - a)
   (6)  ---------------------------
                      5
                    4a
                                                     Type: Expression Integer
--R
--R        3log(x + a) - 3log(- x - a)
--R   (6)  ---------------------------
--R                      5
--R                    4a
--R                                                     Type: Expression Integer
--E

--S 81
logminusb:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
 

   (7)  b log(x + a) - b log(- x - a) + %O == b log(- 1) + %O
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (7)  b log(x + a) - b log(- x - a) + %U == b log(- 1) + %U
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 82     14:175 Schaums and Axiom differ by a constant
ee:=logminusb dd
 

        3log(- 1)
   (8)  ---------
             5
           4a
                                                     Type: Expression Integer
--R
--R        3log(- 1)
--R   (8)  ---------
--R             5
--R           4a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 83
aa:=integrate(1/(x^3*(a^2-x^2)^2),x)
 

             4     2 2      2    2       4     2 2            2 2    4
        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
   (1)  --------------------------------------------------------------
                                   6 4     8 2
                                 2a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4     2 2      2    2       4     2 2            2 2    4
--R        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
--R   (1)  --------------------------------------------------------------
--R                                   6 4     8 2
--R                                 2a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84
bb:=-1/(2*a^4*x^2)+1/(2*a^4*(a^2-x^2))+1/a^6*log(x^2/(a^2-x^2))
 

                               2
           4     2 2          x         2 2    4
        (2x  - 2a x )log(- -------) - 2a x  + a
                            2    2
                           x  - a
   (2)  ----------------------------------------
                        6 4     8 2
                      2a x  - 2a x
                                                     Type: Expression Integer
--R
--R                               2
--R           4     2 2          x         2 2    4
--R        (2x  - 2a x )log(- -------) - 2a x  + a
--R                            2    2
--R                           x  - a
--R   (2)  ----------------------------------------
--R                        6 4     8 2
--R                      2a x  - 2a x
--R                                                     Type: Expression Integer
--E

--S 85
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 86
bb1:=divlog bb
 

             4     2 2      2    2       4     2 2        2      2 2    4
        (- 2x  + 2a x )log(x  - a ) + (2x  - 2a x )log(- x ) - 2a x  + a
   (4)  -----------------------------------------------------------------
                                    6 4     8 2
                                  2a x  - 2a x
                                                     Type: Expression Integer
--R
--R             4     2 2      2    2       4     2 2        2      2 2    4
--R        (- 2x  + 2a x )log(x  - a ) + (2x  - 2a x )log(- x ) - 2a x  + a
--R   (4)  -----------------------------------------------------------------
--R                                    6 4     8 2
--R                                  2a x  - 2a x
--R                                                     Type: Expression Integer
--E

--S 87
cc:=aa-bb1
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  6
                 a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  6
--R                 a
--R                                                     Type: Expression Integer
--E

--S 88
logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
 

               n
   (6)  log(- a ) == n log(a) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- a ) == n log(a) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 89     14:176 Schaums and Axiom differ by a constant
dd:=logpowminus cc
 

          log(- 1)
   (7)  - --------
              6
             a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R              6
--R             a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 90     14:177 Axiom cannot do this integration
aa:=integrate(1/((a^2-x^2)^n),x)
 

           x
         ++       1
   (1)   |   ----------- d%U
        ++     2     2 n
             (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 91
aa:=integrate(x/((a^2-x^2)^n),x)
 

                    2    2
                 - x  + a
   (1)  --------------------------
                           2    2
                  n log(- x  + a )
        (2n - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2    2
--R                 - x  + a
--R   (1)  --------------------------
--R                           2    2
--R                  n log(- x  + a )
--R        (2n - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 92
bb:=1/(2*(n-1)*(a^2-x^2)^(n-1))
 

                    1
   (2)  ------------------------
                    2    2 n - 1
        (2n - 2)(- x  + a )
                                                     Type: Expression Integer
--R
--R                    1
--R   (2)  ------------------------
--R                    2    2 n - 1
--R        (2n - 2)(- x  + a )
--R                                                     Type: Expression Integer
--E

--S 93
cc:=aa-bb
 

                     2    2
            n log(- x  + a )       2    2     2    2 n - 1
        - %e                 + (- x  + a )(- x  + a )
   (3)  --------------------------------------------------
                                               2    2
                        2    2 n - 1  n log(- x  + a )
            (2n - 2)(- x  + a )     %e
                                                     Type: Expression Integer
--R
--R                     2    2
--R            n log(- x  + a )       2    2     2    2 n - 1
--R        - %e                 + (- x  + a )(- x  + a )
--R   (3)  --------------------------------------------------
--R                                               2    2
--R                        2    2 n - 1  n log(- x  + a )
--R            (2n - 2)(- x  + a )     %e
--R                                                     Type: Expression Integer
--E

--S 94
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 95
dd:=explog cc
 

              2    2 n       2    2     2    2 n - 1
        - (- x  + a )  + (- x  + a )(- x  + a )
   (5)  --------------------------------------------
                        2    2 n - 1    2    2 n
            (2n - 2)(- x  + a )     (- x  + a )
                                                     Type: Expression Integer
--R
--R              2    2 n       2    2     2    2 n - 1
--R        - (- x  + a )  + (- x  + a )(- x  + a )
--R   (5)  --------------------------------------------
--R                        2    2 n - 1    2    2 n
--R            (2n - 2)(- x  + a )     (- x  + a )
--R                                                     Type: Expression Integer
--E

--S 96     14:178 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 97     14:179 Axiom cannot integrate this expression
aa:=integrate(1/(x*(a^2-x^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%U
        ++        2     2 n
             %U (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++        2     2 n
--I             %L (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 98     14:180 Axiom cannot integrate this expression
aa:=integrate(x^m/((a^2-x^2)^n),x)
 

           x       m
         ++      %U
   (1)   |   ----------- d%U
        ++     2     2 n
             (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %L
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 99     14:181 Axiom cannot integrate this expression
aa:=integrate(1/(x^m*(a^2-x^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%U
        ++     m  2     2 n
             %U (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++     m  2     2 n
--I             %L (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to bug101.output (2009/2/17, 17:44:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
laplace(log(z),z,w)
 

   (1)  laplace(log(z),z,w)
                                                     Type: Expression Integer
--R
--R   (1)  laplace(log(z),z,w)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 2
laplace(log(z),w,z)
 

        log(z)
   (2)  ------
           z
                                                     Type: Expression Integer
--R
--R        log(z)
--R   (2)  ------
--R           z
--R                                                     Type: Expression Integer
--E 2
)spool 
 
Starts dribbling to r20bugs.output (2009/2/17, 17:56:23).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 1 of 27
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
--R 
--R
--R   (1)  x
--R                                                          Type: BasicOperator
--E 1

--S 2 of 27
sum( (x i - mu)**2, i=1..N )
 

         N
        --+       2                2
   (2)  >     x(i)  - 2mu x(i) + mu
        --+
        i= 1
                                                     Type: Expression Integer
--R 
--R
--R         N
--R        --+       2                2
--R   (2)  >     x(i)  - 2mu x(i) + mu
--R        --+
--R        i= 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 27
D(%,mu)
 

         N
        --+
   (3)  >     - 2x(i) + 2mu
        --+
        i= 1
                                                     Type: Expression Integer
--R 
--R
--R         N
--R        --+
--R   (3)  >     - 2x(i) + 2mu
--R        --+
--R        i= 1
--R                                                     Type: Expression Integer
--E 3

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 4 of 27
z := log(x+.3*%i)
 

   (1)  log(x + 0.3 %i)
                                               Type: Expression Complex Float
--R 
--R
--R   (1)  log(x + 0.3 %i)
--R                                               Type: Expression Complex Float
--E 4

--S 5 of 27
z1 : EXPR Complex Float := z
 

   (2)  log(x + 0.3 %i)
                                               Type: Expression Complex Float
--R 
--R
--R   (2)  log(x + 0.3 %i)
--R                                               Type: Expression Complex Float
--E 5

--S 6 of 27
complexForm(z1)$CTRIGMNP(Float, EXPR Complex Float)
 

                 2                0.3
   (3)  0.5 log(x  + 0.09) + atan(---)%i
                                   x
                                               Type: Complex Expression Float
--R 
--R
--R                 2                0.3
--R   (3)  0.5 log(x  + 0.09) + atan(---)%i
--R                                   x
--R                                               Type: Complex Expression Float
--E 6

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 7 of 27
acot(-1)
 

        3%pi
   (1)  ----
          4
                                                     Type: Expression Integer
--R 
--R
--R        3%pi
--R   (1)  ----
--R          4
--R                                                     Type: Expression Integer
--E 7

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
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--S 8 of 27
sqrt(-1.0::COMPLEX FLOAT)
 

   (1)  %i
                                                          Type: Complex Float
--R 
--R
--R   (1)  %i
--R                                                          Type: Complex Float
--E 8

--S 9 of 27
log(x+%i)::EXPR COMPLEX FLOAT
 

   (2)  log(x + %i)
                                               Type: Expression Complex Float
--R 
--R
--R   (2)  log(x + %i)
--R                                               Type: Expression Complex Float
--E 9

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
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--S 10 of 27
positiveRemainder(-1,-5)
 

   (1)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  4
--R                                                        Type: PositiveInteger
--E 10

)clear completely
 
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--S 11 of 27
f:POLY FRAC COMPLEX INT := x^2+y^2
 

         2    2
   (1)  y  + x
                                    Type: Polynomial Fraction Complex Integer
--R 
--R
--R         2    2
--R   (1)  y  + x
--R                                    Type: Polynomial Fraction Complex Integer
--E 11

--S 12 of 27
factor f
 

   (2)  (y - %i x)(y + %i x)
                           Type: Factored Polynomial Fraction Complex Integer
--R 
--R
--R   (2)  (y - %i x)(y + %i x)
--R                           Type: Factored Polynomial Fraction Complex Integer
--E 12

)clear completely
 
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--S 13 of 27
acot(-y)
 

   (1)  acot(- y)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  acot(- y)
--R                                                     Type: Expression Integer
--E 13

)clear completely
 
   All user variables and function definitions have been cleared.
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--S 14 of 27
a:=matrix [[1,2],[2,-1]]
 

        +1   2 +
   (1)  |      |
        +2  - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +1   2 +
--R   (1)  |      |
--R        +2  - 1+
--R                                                         Type: Matrix Integer
--E 14

--S 15 of 27
eigenMatrix a
 

        +   +-+       +-+    +
        |- \|5  + 1  \|5  + 1|
   (2)  |----------  --------|
        |     2          2   |
        |                    |
        +    1          1    +
                                   Type: Union(Matrix Expression Integer,...)
--R 
--R
--R        +   +-+       +-+    +
--R        |- \|5  + 1  \|5  + 1|
--R   (2)  |----------  --------|
--R        |     2          2   |
--R        |                    |
--R        +    1          1    +
--R                                   Type: Union(Matrix Expression Integer,...)
--E 15

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 16 of 27
positiveRemainder(-1::SINT,-5::SINT)
 

   (1)  4
                                                          Type: SingleInteger
--R 
--R
--R   (1)  4
--R                                                          Type: SingleInteger
--E 16

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
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--S 17 of 27
complexRoots([u**2-v+1,v**2-4],[u,v],0.01)
 

   (1)
   [[1.732421875 %i,- 2.0],[- 1.732421875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]]
                                                Type: List List Complex Float
--R 
--R
--R   (1)  [[1.73046875 %i,- 2.0],[- 1.73046875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]]
--R                                                Type: List List Complex Float
--E 17

--S 18 of 27
complexRoots([u**2-v+1,v**2-4],[v,u],0.01)
 

   (2)  [[- 2.0,- 1.73046875 %i],[- 2.0,1.73046875 %i],[2.0,- 1.0],[2.0,1.0]]
                                                Type: List List Complex Float
--R 
--R
--R   (2)  [[- 2.0,- 1.73046875 %i],[- 2.0,1.73046875 %i],[2.0,- 1.0],[2.0,1.0]]
--R                                                Type: List List Complex Float
--E 18

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
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--S 19 of 27
R := Record(key:Symbol,entry:Integer)
 

   (1)  Record(key: Symbol,entry: Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Record(key: Symbol,entry: Integer)
--R                                                                 Type: Domain
--E 19

--S 20 of 27
tab := table([[a,1]$R,[b,2]$R,[c,3]$R])$Table(Symbol,Integer)
 

   (2)  table(c= 3,b= 2,a= 1)
                                                  Type: Table(Symbol,Integer)
--R 
--R
--R   (2)  table(c= 3,b= 2,a= 1)
--R                                                  Type: Table(Symbol,Integer)
--E 20

--S 21 of 27
remove!(b::Symbol,tab)
 

   (3)  2
                                                     Type: Union(Integer,...)
--R 
--R
--R   (3)  2
--R                                                     Type: Union(Integer,...)
--E 21

)clear completely
 
   All user variables and function definitions have been cleared.
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   )clear completely is finished.
 
--S 22 of 27
limit((x^a-a^x)/(x^x-a^a),x=a)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 22

)clear completely
 
   All user variables and function definitions have been cleared.
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   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 23 of 27
(4*x^6+16*x^4+16*x^2)*y^2+(-4*x^6+16*x^2)*y-8*x^6-16*x^4
 

           6      4      2  2        6      2       6      4
   (1)  (4x  + 16x  + 16x )y  + (- 4x  + 16x )y - 8x  - 16x
                                                     Type: Polynomial Integer
--R 
--R
--R           6      4      2  2        6      2       6      4
--R   (1)  (4x  + 16x  + 16x )y  + (- 4x  + 16x )y - 8x  - 16x
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 27
eval(%,x,z)
 

           2           6       2       4       2        2
   (2)  (4y  - 4y - 8)z  + (16y  - 16)z  + (16y  + 16y)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2           6       2       4       2        2
--R   (2)  (4y  - 4y - 8)z  + (16y  - 16)z  + (16y  + 16y)z
--R                                                     Type: Polynomial Integer
--E 24

--S 25 of 27
exquo(%,expand factor %)
 

   (3)  1
                                          Type: Union(Polynomial Integer,...)
--R 
--R
--R   (3)  1
--R                                          Type: Union(Polynomial Integer,...)
--E 25

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 26 of 27
log exp z
 

   (1)  z
                                                     Type: Expression Integer
--R 
--R
--R   (1)  z
--R                                                     Type: Expression Integer
--E 26

--S 27 of 27
normalize %
 

   (2)  z
                                                     Type: Expression Integer
--R 
--R
--R   (2)  z
--R                                                     Type: Expression Integer
--E 27
)spool 
 
Starts dribbling to lodesys.output (2009/2/17, 17:52:34).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 13
M := matrix [[ 1+4*t,  -5*t,   7*t,  -8*t,   8*t,  -6*t],_
             [ -10*t, 1+9*t, -14*t,  16*t, -16*t,  12*t],_
             [  -5*t,   5*t, 1-8*t,   8*t,  -8*t,   6*t],_
             [  10*t, -10*t,  14*t,1-17*t,  16*t, -12*t],_
             [   5*t,  -5*t,   7*t,  -8*t, 1+7*t,  -6*t],_
             [  -5*t,   5*t,  -7*t,   8*t,  -8*t, 1+5*t]]
 

        +4t + 1   - 5t      7t       - 8t       8t     - 6t +
        |                                                   |
        |- 10t   9t + 1   - 14t       16t     - 16t    12t  |
        |                                                   |
        | - 5t     5t    - 8t + 1     8t       - 8t     6t  |
   (1)  |                                                   |
        | 10t    - 10t     14t     - 17t + 1   16t    - 12t |
        |                                                   |
        |  5t     - 5t      7t       - 8t     7t + 1   - 6t |
        |                                                   |
        + - 5t     5t      - 7t       8t       - 8t   5t + 1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +4t + 1   - 5t      7t       - 8t       8t     - 6t +
--R        |                                                   |
--R        |- 10t   9t + 1   - 14t       16t     - 16t    12t  |
--R        |                                                   |
--R        | - 5t     5t    - 8t + 1     8t       - 8t     6t  |
--R   (1)  |                                                   |
--R        | 10t    - 10t     14t     - 17t + 1   16t    - 12t |
--R        |                                                   |
--R        |  5t     - 5t      7t       - 8t     7t + 1   - 6t |
--R        |                                                   |
--R        + - 5t     5t      - 7t       8t       - 8t   5t + 1+
--R                                              Type: Matrix Polynomial Integer
--E 1

--S 2 of 13
sol := solve(inv(t**2) * M, t)
 

   (2)
           1          1         1        1       1         1
         - -        - -       - -      - -     - -       - -
      5    t     5    t    5    t   5    t  5    t    5    t
   [[t %e   ,- 2t %e   ,- t %e   ,2t %e   ,t %e   ,- t %e   ],
         1        1       1      1     1       1           1     1
       - -      - -     - -    - -   - -     - -         - -   - -
         t        t       t      t     t       t           t     t
     %e      4%e      %e    2%e    %e      %e         7%e    %e
    [-----,- ------,- -----,------,-----,- -----], [0,------,-----,0,0,0],
       t       5t       t      t     t       t          5t     t
              1       1               1         1               1           1
            - -     - -             - -       - -             - -         - -
              t       t               t         t               t           t
         8%e      %e             8%e        %e             6%e          %e
    [0,- ------,0,-----,0,0], [0,------,0,0,-----,0], [0,- ------,0,0,0,-----]]
           5t       t              5t         t              5t           t
                              Type: Union(List Vector Expression Integer,...)
--R 
--R
--R   (2)
--R           1          1         1        1       1         1
--R         - -        - -       - -      - -     - -       - -
--R      5    t     5    t    5    t   5    t  5    t    5    t
--R   [[t %e   ,- 2t %e   ,- t %e   ,2t %e   ,t %e   ,- t %e   ],
--R         1        1       1      1     1       1           1     1
--R       - -      - -     - -    - -   - -     - -         - -   - -
--R         t        t       t      t     t       t           t     t
--R     %e      4%e      %e    2%e    %e      %e         7%e    %e
--R    [-----,- ------,- -----,------,-----,- -----], [0,------,-----,0,0,0],
--R       t       5t       t      t     t       t          5t     t
--R              1       1               1         1               1           1
--R            - -     - -             - -       - -             - -         - -
--R              t       t               t         t               t           t
--R         8%e      %e             8%e        %e             6%e          %e
--R    [0,- ------,0,-----,0,0], [0,------,0,0,-----,0], [0,- ------,0,0,0,-----]]
--R           5t       t              5t         t              5t           t
--R                              Type: Union(List Vector Expression Integer,...)
--E 2

--S 3 of 13
[t**2 * map(h +-> D(h, t), v) - M * v for v in sol]
 

   (3)
   [[0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0],
    [0,0,0,0,0,0]]
                                         Type: List Vector Expression Integer
--R 
--R
--R   (3)
--R   [[0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0],
--R    [0,0,0,0,0,0]]
--R                                         Type: List Vector Expression Integer
--E 3

--S 4 of 13
x := operator x
 

   (4)  x
                                                          Type: BasicOperator
--R 
--R
--R   (4)  x
--R                                                          Type: BasicOperator
--E 4

--S 5 of 13
y := operator y
 

   (5)  y
                                                          Type: BasicOperator
--R 
--R
--R   (5)  y
--R                                                          Type: BasicOperator
--E 5

--S 6 of 13
sys := [D(x t, t) = x t + sqrt 3 * y t, D(y t, t) = sqrt 3 * x t - y t]
 

          ,      +-+             ,               +-+
   (6)  [x (t)= \|3 y(t) + x(t),y (t)= - y(t) + \|3 x(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R          ,      +-+             ,               +-+
--R   (6)  [x (t)= \|3 y(t) + x(t),y (t)= - y(t) + \|3 x(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 6

--S 7 of 13
solve(sys, [x, y], t).basis
 

                 2t               - 2t
            2t %e       - 2t   3%e
   (7)  [[%e  ,----],[%e    ,- -------]]
                +-+               +-+
               \|3               \|3
                                         Type: List Vector Expression Integer
--R 
--R
--R                 2t               - 2t
--R            2t %e       - 2t   3%e
--R   (7)  [[%e  ,----],[%e    ,- -------]]
--R                +-+               +-+
--R               \|3               \|3
--R                                         Type: List Vector Expression Integer
--E 7

--S 8 of 13
v := vector [1, (-29*t + 19)/5, -1, t + 1, - 2*t + 3, -1]
 

             29     19
   (8)  [1,- -- t + --,- 1,t + 1,- 2t + 3,- 1]
              5      5
                                     Type: Vector Polynomial Fraction Integer
--R 
--R
--R             29     19
--R   (8)  [1,- -- t + --,- 1,t + 1,- 2t + 3,- 1]
--R              5      5
--R                                     Type: Vector Polynomial Fraction Integer
--E 8

--S 9 of 13
solp := solve(inv(t**2) * M, inv(t**2) * v, t).particular
 

               19
   (9)  [- 1,- --,1,- 1,- 3,1]
                5
                                              Type: Vector Expression Integer
--R 
--R
--R               19
--R   (9)  [- 1,- --,1,- 1,- 3,1]
--R                5
--R                                              Type: Vector Expression Integer
--E 9

--S 10 of 13
t**2 * map(h +-> D(h, t), solp) - M * solp - v
 

   (10)  [0,0,0,0,0,0]
                                              Type: Vector Expression Integer
--R 
--R
--R   (10)  [0,0,0,0,0,0]
--R                                              Type: Vector Expression Integer
--E 10

--S 11 of 13
z := operator z
 

   (11)  z
                                                          Type: BasicOperator
--R 
--R
--R   (11)  z
--R                                                          Type: BasicOperator
--E 11

--S 12 of 13
sys := [D(x t, t) = y t + z t + t, D(y t, t) = x t + z t, D(z t, t) = x t + y t]
 

           ,                      ,                  ,
   (12)  [x (t)= z(t) + y(t) + t,y (t)= z(t) + x(t),z (t)= y(t) + x(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R           ,                      ,                  ,
--R   (12)  [x (t)= z(t) + y(t) + t,y (t)= z(t) + x(t),z (t)= y(t) + x(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 12

--S 13 of 13
solve(sys, [x, y, z], t).particular
 

          2t - 3 - 2t + 1 - 2t + 1
   (13)  [------,--------,--------]
             4       4        4
                                              Type: Vector Expression Integer
--R 
--R
--R          2t - 3 - 2t + 1 - 2t + 1
--R   (13)  [------,--------,--------]
--R             4       4        4
--R                                              Type: Vector Expression Integer
--E 13
)spool 
 
Starts dribbling to rules.output (2009/2/17, 17:57:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 21
logrule := rule log(x) + log(y) == log(x * y)
 

   (1)  log(y) + log(x) + %B == log(x y) + %B
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)  log(y) + log(x) + %B == log(x y) + %B
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 1

--S 2 of 21
f := log sin x + log x
 

   (2)  log(sin(x)) + log(x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  log(sin(x)) + log(x)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 21
logrule f
 

   (3)  log(x sin(x))
                                                     Type: Expression Integer
--R 
--R
--R   (3)  log(x sin(x))
--R                                                     Type: Expression Integer
--E 3

--S 4 of 21
logrules := rule
  log(x) + log(y) == log(x * y)
  y * log x       == log(x ** y)
 

                                                                y
   (4)  {log(y) + log(x) + %C == log(x y) + %C,y log(x) == log(x )}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R                                                                y
--R   (4)  {log(y) + log(x) + %C == log(x y) + %C,y log(x) == log(x )}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 4

--S 5 of 21
f := a * log(sin x) - 2 * log x
 

   (5)  a log(sin(x)) - 2log(x)
                                                     Type: Expression Integer
--R 
--R
--R   (5)  a log(sin(x)) - 2log(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 21
logrules f
 

                  a
            sin(x)
   (6)  log(-------)
                2
               x
                                                     Type: Expression Integer
--R 
--R
--R                  a
--R            sin(x)
--R   (6)  log(-------)
--R                2
--R               x
--R                                                     Type: Expression Integer
--E 6

--S 7 of 21
logrules2 := rule
  log(x) + log(y)          == log(x * y)
  (y | integer? y) * log x == log(x ** y)
 

                                                                y
   (7)  {log(y) + log(x) + %D == log(x y) + %D,y log(x) == log(x )}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R                                                                y
--R   (7)  {log(y) + log(x) + %D == log(x y) + %D,y log(x) == log(x )}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 7

--S 8 of 21
logrules2 f
 

                             1
   (8)  a log(sin(x)) + log(--)
                             2
                            x
                                                     Type: Expression Integer
--R 
--R
--R                             1
--R   (8)  a log(sin(x)) + log(--)
--R                             2
--R                            x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 21
trigLinearize := rule
  sin(x) * sin(y)                      == cos(x-y)/2 - cos(x+y)/2
  cos(x) * cos(y)                      == cos(x+y)/2 + cos(x-y)/2
  sin(x) * cos(y)                      == sin(x+y)/2 + sin(x-y)/2
  sin(x) ** (n | integer? n and n > 1) == (1-cos(2*x))/2 * sin(x)**(n-2)
  cos(x) ** (n | integer? n and n > 1) == (1+cos(2*x))/2 * cos(x)**(n-2)
 

   (9)
                       - %F cos(y + x) + %F cos(y - x)
   {%F sin(x)sin(y) == -------------------------------,
                                      2
                       %G cos(y + x) + %G cos(y - x)
    %G cos(x)cos(y) == -----------------------------,
                                     2
                       %H sin(y + x) - %H sin(y - x)
    %H cos(y)sin(x) == -----------------------------,
                                     2
                                    n - 2                                n - 2
          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
    sin(x)  == --------------------------, cos(x)  == ------------------------}
                            2                                     2
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (9)
--R                       - %F cos(y + x) + %F cos(y - x)
--R   {%F sin(x)sin(y) == -------------------------------,
--R                                      2
--R                       %G cos(y + x) + %G cos(y - x)
--R    %G cos(x)cos(y) == -----------------------------,
--R                                     2
--R                       %H sin(y + x) - %H sin(y - x)
--R    %H cos(y)sin(x) == -----------------------------,
--R                                     2
--R                                    n - 2                                n - 2
--R          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
--R    sin(x)  == --------------------------, cos(x)  == ------------------------}
--R                            2                                     2
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 9

--S 10 of 21
g := sin(a)*cos(b) + sin(a)*cos(a) + cos(2*a)*cos(3*a)
 

   (10)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
                                                     Type: Expression Integer
--R 
--R
--R   (10)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
--R                                                     Type: Expression Integer
--E 10

--S 11 of 21
trigLinearize g
 

         sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
   (11)  ----------------------------------------------------
                                   2
                                                     Type: Expression Integer
--R 
--R
--R         sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
--R   (11)  ----------------------------------------------------
--R                                   2
--R                                                     Type: Expression Integer
--E 11

--S 12 of 21
eirule := rule integral((?y + exp x)/x,x) == integral(y/x,x) + Ei x
 

            x   %K
          ++  %e   + y                   y
   (12)   |   -------- d%K  == 'integral(-,x) + 'Ei(x)
         ++      %K                      x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R            x   %K
--R          ++  %e   + y                   y
--R   (12)   |   -------- d%K  == 'integral(-,x) + 'Ei(x)
--R         ++      %K                      x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 12

--S 13 of 21
eirule integral(exp u/u, u)
 

   (13)  Ei(u)
                                                     Type: Expression Integer
--R 
--R
--R   (13)  Ei(u)
--R                                                     Type: Expression Integer
--E 13

--S 14 of 21
eirule integral(sin u + exp u/u, u)
 

            u
          ++
   (14)   |   sin(%K)d%K  + Ei(u)
         ++
                                                     Type: Expression Integer
--R 
--R
--R            u
--R          ++
--R   (14)   |   sin(%K)d%K  + Ei(u)
--R         ++
--R                                                     Type: Expression Integer
--E 14

--S 15 of 21
u := operator u
 

   (15)  u
                                                          Type: BasicOperator
--R 
--R
--R   (15)  u
--R                                                          Type: BasicOperator
--E 15

--S 16 of 21
v := operator v
 

   (16)  v
                                                          Type: BasicOperator
--R 
--R
--R   (16)  v
--R                                                          Type: BasicOperator
--E 16

--S 17 of 21
myrule := rule u(x + y) == u x + v y
 

   (17)  u(y + x) == 'v(y) + 'u(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (17)  u(y + x) == 'v(y) + 'u(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 17

--S 18 of 21
h := u(a + b + c + d)
 

   (18)  u(d + c + b + a)
                                                     Type: Expression Integer
--R 
--R
--R   (18)  u(d + c + b + a)
--R                                                     Type: Expression Integer
--E 18

--S 19 of 21
myrule h
 

   (19)  v(d + c + b) + u(a)
                                                     Type: Expression Integer
--R 
--R
--R   (19)  v(d + c + b) + u(a)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 21
myrule2 := rule u(:x + y) == u x + v y
 

   (20)  u(y + x) == 'v(y) + 'u(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (20)  u(y + x) == 'v(y) + 'u(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 20

--S 21 of 21
myrule2 h
 

   (21)  v(c) + v(b) + v(a) + u(d)
                                                     Type: Expression Integer
--R 
--R
--R   (21)  v(c) + v(b) + v(a) + u(d)
--R                                                     Type: Expression Integer
--E 21
)spool 
 
Starts dribbling to schaum22.output (2009/2/17, 17:59:16).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(sec(a*x),x)
 

            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
        log(-----------------------) - log(-----------------------)
                  cos(a x) + 1                   cos(a x) + 1
   (1)  -----------------------------------------------------------
                                     a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R        log(-----------------------) - log(-----------------------)
--R                  cos(a x) + 1                   cos(a x) + 1
--R   (1)  -----------------------------------------------------------
--R                                     a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb1:=1/a*log(sec(a*x)+tan(a*x))
 

        log(tan(a x) + sec(a x))
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R        log(tan(a x) + sec(a x))
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 3
bb2:=1/a*log(tan((a*x)/2+%pi/4))
 

                2a x + %pi
        log(tan(----------))
                     4
   (3)  --------------------
                  a
                                                     Type: Expression Integer
--R
--R                2a x + %pi
--R        log(tan(----------))
--R                     4
--R   (3)  --------------------
--R                  a
--R                                                     Type: Expression Integer
--E

--S 4
cc1:=aa-bb1
 

   (4)
                                        sin(a x) + cos(a x) + 1
       - log(tan(a x) + sec(a x)) + log(-----------------------)
                                              cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                        sin(a x) + cos(a x) + 1
--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
--R                                              cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 5
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (5)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (5)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 6
dd1:=tanrule cc1
 

   (6)
             sin(a x) + cos(a x)sec(a x)        sin(a x) + cos(a x) + 1
       - log(---------------------------) + log(-----------------------)
                       cos(a x)                       cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (6)
--R             sin(a x) + cos(a x)sec(a x)        sin(a x) + cos(a x) + 1
--R       - log(---------------------------) + log(-----------------------)
--R                       cos(a x)                       cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 7
secrule:=rule(sec(a) == 1/cos(a))
 

                     1
   (7)  sec(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (7)  sec(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 8
ee1:=secrule dd1
 

   (8)
             sin(a x) + 1        sin(a x) + cos(a x) + 1
       - log(------------) + log(-----------------------)
               cos(a x)                cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (8)
--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
--R       - log(------------) + log(-----------------------)
--R               cos(a x)                cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 9
ff1:=expandLog ee1
 

   (9)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
     + 
       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
  /
     a
                                                     Type: Expression Integer
--R
--R   (9)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
--R     + 
--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 10
gg1:=complexNormalize ff1
 

         log(- 1)
   (10)  --------
             a
                                                     Type: Expression Integer
--R
--R         log(- 1)
--R   (10)  --------
--R             a
--R                                                     Type: Expression Integer
--E

--S 11
cc2:=aa-bb2
 

   (11)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (11)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 12
dd2:=tanrule cc2
 

   (12)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------)
                 2a x + %pi
             cos(----------)
                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (12)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------)
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 13
ee2:=expandLog dd2
 

   (13)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------))
                      4                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (13)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------))
--R                      4                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 14     14:451 Schaums and Axiom differ by a constant
ff2:=complexNormalize ee2
 

         log(- 1)
   (14)  --------
             a
                                                     Type: Expression Integer
--R
--R         log(- 1)
--R   (14)  --------
--R             a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(sec(a*x)^2,x)
 

         sin(a x)
   (1)  ----------
        a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         sin(a x)
--R   (1)  ----------
--R        a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16
bb:=tan(a*x)/a
 

        tan(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        tan(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E

--S 17
cc:=aa-bb
 

        - cos(a x)tan(a x) + sin(a x)
   (3)  -----------------------------
                  a cos(a x)
                                                     Type: Expression Integer
--R
--R        - cos(a x)tan(a x) + sin(a x)
--R   (3)  -----------------------------
--R                  a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 18
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19     14:452 Schaums and Axiom agree
dd:=tanrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(sec(a*x)^3,x)
 

   (1)
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
                 2    sin(a x) - cos(a x) - 1
       - cos(a x) log(-----------------------) + sin(a x)
                            cos(a x) + 1
  /
                2
     2a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R                 2    sin(a x) - cos(a x) - 1
--R       - cos(a x) log(-----------------------) + sin(a x)
--R                            cos(a x) + 1
--R  /
--R                2
--R     2a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21
bb:=(sec(a*x)*tan(a*x))/(2*a)+1/(2*a)*log(sec(a*x)+tan(a*x))
 

        log(tan(a x) + sec(a x)) + sec(a x)tan(a x)
   (2)  -------------------------------------------
                             2a
                                                     Type: Expression Integer
--R
--R        log(tan(a x) + sec(a x)) + sec(a x)tan(a x)
--R   (2)  -------------------------------------------
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 22
cc:=aa-bb
 

   (3)
                 2
       - cos(a x) log(tan(a x) + sec(a x))
     + 
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
                 2    sin(a x) - cos(a x) - 1            2
       - cos(a x) log(-----------------------) - cos(a x) sec(a x)tan(a x)
                            cos(a x) + 1
     + 
       sin(a x)
  /
                2
     2a cos(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2
--R       - cos(a x) log(tan(a x) + sec(a x))
--R     + 
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R                 2    sin(a x) - cos(a x) - 1            2
--R       - cos(a x) log(-----------------------) - cos(a x) sec(a x)tan(a x)
--R                            cos(a x) + 1
--R     + 
--R       sin(a x)
--R  /
--R                2
--R     2a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 23
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 24
dd:=tanrule cc
 

   (5)
                 2    sin(a x) + cos(a x)sec(a x)
       - cos(a x) log(---------------------------)
                                cos(a x)
     + 
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
               2    sin(a x) - cos(a x) - 1
     - cos(a x) log(-----------------------) + (- cos(a x)sec(a x) + 1)sin(a x)
                          cos(a x) + 1
  /
                2
     2a cos(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                 2    sin(a x) + cos(a x)sec(a x)
--R       - cos(a x) log(---------------------------)
--R                                cos(a x)
--R     + 
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R               2    sin(a x) - cos(a x) - 1
--R     - cos(a x) log(-----------------------) + (- cos(a x)sec(a x) + 1)sin(a x)
--R                          cos(a x) + 1
--R  /
--R                2
--R     2a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 25
secrule:=rule(sec(a) == 1/cos(a))
 

                     1
   (6)  sec(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (6)  sec(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26
ee:=secrule dd
 

   (7)
             sin(a x) + 1        sin(a x) + cos(a x) + 1
       - log(------------) + log(-----------------------)
               cos(a x)                cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (7)
--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
--R       - log(------------) + log(-----------------------)
--R               cos(a x)                cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 27
ff:=expandLog ee
 

   (8)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
     + 
       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
  /
     2a
                                                     Type: Expression Integer
--R
--R   (8)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
--R     + 
--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 28     14:453 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

        log(- 1)
   (9)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (9)  --------
--R           2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(sec(a*x)^n*tan(a*x),x)
 

                    1
          n log(---------)
                        2
                cos(a x)
          ----------------
                  2
        %e
   (1)  ------------------
                a n
                                          Type: Union(Expression Integer,...)
--R
--R                    1
--R          n log(---------)
--R                        2
--R                cos(a x)
--R          ----------------
--R                  2
--R        %e
--R   (1)  ------------------
--R                a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=sec(a*x)^n/(n*a)
 

                n
        sec(a x)
   (2)  ---------
           a n
                                                     Type: Expression Integer
--R
--R                n
--R        sec(a x)
--R   (2)  ---------
--R           a n
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

                    1
          n log(---------)
                        2
                cos(a x)
          ----------------
                  2                  n
        %e                 - sec(a x)
   (3)  ------------------------------
                      a n
                                                     Type: Expression Integer
--R
--R                    1
--R          n log(---------)
--R                        2
--R                cos(a x)
--R          ----------------
--R                  2                  n
--R        %e                 - sec(a x)
--R   (3)  ------------------------------
--R                      a n
--R                                                     Type: Expression Integer
--E

--S 32     14:454 Schaums and Axiom agree
normalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 33
aa:=integrate(1/sec(a*x),x)
 

        sin(a x)
   (1)  --------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sin(a x)
--R   (1)  --------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E

--S 34
bb:=sin(a*x)/a
 

        sin(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        sin(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E 

--S 35     14:455 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36     14:456 Axiom cannot compute this integral
aa:=integrate(x*sec(a*x),x)
 

           x
         ++
   (1)   |   %P sec(%P a)d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %N sec(%N a)d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 37     14:457 Axiom cannot compute this integral
aa:=integrate(sec(a*x)/x,x)
 

           x
         ++  sec(%P a)
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sec(%N a)
--I   (1)   |   --------- d%N
--I        ++       %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 38
aa:=integrate(x*sec(a*x)^2,x)
 

   (1)
                       2                         2cos(a x)
   - cos(a x)log(------------) + cos(a x)log(- ------------) + a x sin(a x)
                 cos(a x) + 1                  cos(a x) + 1
   ------------------------------------------------------------------------
                                   2
                                  a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       2                         2cos(a x)
--R   - cos(a x)log(------------) + cos(a x)log(- ------------) + a x sin(a x)
--R                 cos(a x) + 1                  cos(a x) + 1
--R   ------------------------------------------------------------------------
--R                                   2
--R                                  a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 39
bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x))
 

        log(cos(a x)) + a x tan(a x)
   (2)  ----------------------------
                      2
                     a
                                                     Type: Expression Integer
--R
--R        log(cos(a x)) + a x tan(a x)
--R   (2)  ----------------------------
--R                      2
--R                     a
--R                                                     Type: Expression Integer
--E

--S 40
cc:=aa-bb
 

   (3)
                                                   2
       - cos(a x)log(cos(a x)) - cos(a x)log(------------)
                                             cos(a x) + 1
     + 
                       2cos(a x)
       cos(a x)log(- ------------) - a x cos(a x)tan(a x) + a x sin(a x)
                     cos(a x) + 1
  /
      2
     a cos(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                   2
--R       - cos(a x)log(cos(a x)) - cos(a x)log(------------)
--R                                             cos(a x) + 1
--R     + 
--R                       2cos(a x)
--R       cos(a x)log(- ------------) - a x cos(a x)tan(a x) + a x sin(a x)
--R                     cos(a x) + 1
--R  /
--R      2
--R     a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 41
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 42
dd:=tanrule cc
 

                                    2                 2cos(a x)
        - log(cos(a x)) - log(------------) + log(- ------------)
                              cos(a x) + 1          cos(a x) + 1
   (5)  ---------------------------------------------------------
                                     2
                                    a
                                                     Type: Expression Integer
--R
--R                                    2                 2cos(a x)
--R        - log(cos(a x)) - log(------------) + log(- ------------)
--R                              cos(a x) + 1          cos(a x) + 1
--R   (5)  ---------------------------------------------------------
--R                                     2
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 43     14:458 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

        - log(2) + log(- 2)
   (6)  -------------------
                  2
                 a
                                                     Type: Expression Integer
--R
--R        - log(2) + log(- 2)
--R   (6)  -------------------
--R                  2
--R                 a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 44
aa:=integrate(1/(q+p*sec(a*x)),x)
 

   (1)
                             +-------+
                             | 2    2      2    2                 +-------+
          (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)        | 2    2
    p log(------------------------------------------------) + a x\|q  - p
                           q cos(a x) + p
   [-----------------------------------------------------------------------,
                                     +-------+
                                     | 2    2
                                 a q\|q  - p
                         +---------+
                         |   2    2          +---------+
                sin(a x)\|- q  + p           |   2    2
    - 2p atan(-----------------------) + a x\|- q  + p
              (q + p)cos(a x) + q + p
    ----------------------------------------------------]
                           +---------+
                           |   2    2
                       a q\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                             +-------+
--R                             | 2    2      2    2                 +-------+
--R          (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)        | 2    2
--R    p log(------------------------------------------------) + a x\|q  - p
--R                           q cos(a x) + p
--R   [-----------------------------------------------------------------------,
--R                                     +-------+
--R                                     | 2    2
--R                                 a q\|q  - p
--R                         +---------+
--R                         |   2    2          +---------+
--R                sin(a x)\|- q  + p           |   2    2
--R    - 2p atan(-----------------------) + a x\|- q  + p
--R              (q + p)cos(a x) + q + p
--R    ----------------------------------------------------]
--R                           +---------+
--R                           |   2    2
--R                       a q\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 45
t1:=integrate(1/(p+q*cos(a*x)),x)
 

   (2)
                           +-------+
                           | 2    2        2    2
        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
    log(--------------------------------------------------)
                          q cos(a x) + p
   [-------------------------------------------------------,
                            +-------+
                            | 2    2
                          a\|q  - p
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p
    2atan(-----------------------)
          (q + p)cos(a x) + q + p
    ------------------------------]
               +---------+
               |   2    2
             a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R                           +-------+
--R                           | 2    2        2    2
--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R    log(--------------------------------------------------)
--R                          q cos(a x) + p
--R   [-------------------------------------------------------,
--R                            +-------+
--R                            | 2    2
--R                          a\|q  - p
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p
--R    2atan(-----------------------)
--R          (q + p)cos(a x) + q + p
--R    ------------------------------]
--R               +---------+
--R               |   2    2
--R             a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 46
bb1:=x/q-p/q*t1.1
 

   (3)
                              +-------+
                              | 2    2        2    2                 +-------+
           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)        | 2    2
   - p log(--------------------------------------------------) + a x\|q  - p
                             q cos(a x) + p
   ---------------------------------------------------------------------------
                                      +-------+
                                      | 2    2
                                  a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R                              +-------+
--R                              | 2    2        2    2                 +-------+
--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)        | 2    2
--R   - p log(--------------------------------------------------) + a x\|q  - p
--R                             q cos(a x) + p
--R   ---------------------------------------------------------------------------
--R                                      +-------+
--R                                      | 2    2
--R                                  a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 47
bb2:=x/q-p/q*t1.2
 

                             +---------+
                             |   2    2          +---------+
                    sin(a x)\|- q  + p           |   2    2
        - 2p atan(-----------------------) + a x\|- q  + p
                  (q + p)cos(a x) + q + p
   (4)  ----------------------------------------------------
                               +---------+
                               |   2    2
                           a q\|- q  + p
                                                     Type: Expression Integer
--R
--R                             +---------+
--R                             |   2    2          +---------+
--R                    sin(a x)\|- q  + p           |   2    2
--R        - 2p atan(-----------------------) + a x\|- q  + p
--R                  (q + p)cos(a x) + q + p
--R   (4)  ----------------------------------------------------
--R                               +---------+
--R                               |   2    2
--R                           a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 48
cc1:=aa.1-bb1
 

   (5)
                                +-------+
                                | 2    2      2    2
             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p log(------------------------------------------------)
                              q cos(a x) + p
     + 
                                +-------+
                                | 2    2        2    2
             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p log(--------------------------------------------------)
                               q cos(a x) + p
  /
         +-------+
         | 2    2
     a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                +-------+
--R                                | 2    2      2    2
--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p log(------------------------------------------------)
--R                              q cos(a x) + p
--R     + 
--R                                +-------+
--R                                | 2    2        2    2
--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p log(--------------------------------------------------)
--R                               q cos(a x) + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 49
cc2:=aa.1-bb2
 

   (6)
                                           +-------+
         +---------+                       | 2    2      2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p\|- q  + p  log(------------------------------------------------)
                                         q cos(a x) + p
     + 
                                   +---------+
          +-------+                |   2    2
          | 2    2        sin(a x)\|- q  + p
       2p\|q  - p  atan(-----------------------)
                        (q + p)cos(a x) + q + p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                                           +-------+
--R         +---------+                       | 2    2      2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p\|- q  + p  log(------------------------------------------------)
--R                                         q cos(a x) + p
--R     + 
--R                                   +---------+
--R          +-------+                |   2    2
--R          | 2    2        sin(a x)\|- q  + p
--R       2p\|q  - p  atan(-----------------------)
--R                        (q + p)cos(a x) + q + p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 50
cc3:=aa.2-bb1
 

   (7)
                                           +-------+
         +---------+                       | 2    2        2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p\|- q  + p  log(--------------------------------------------------)
                                          q cos(a x) + p
     + 
                                     +---------+
            +-------+                |   2    2
            | 2    2        sin(a x)\|- q  + p
       - 2p\|q  - p  atan(-----------------------)
                          (q + p)cos(a x) + q + p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                           +-------+
--R         +---------+                       | 2    2        2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p\|- q  + p  log(--------------------------------------------------)
--R                                          q cos(a x) + p
--R     + 
--R                                     +---------+
--R            +-------+                |   2    2
--R            | 2    2        sin(a x)\|- q  + p
--R       - 2p\|q  - p  atan(-----------------------)
--R                          (q + p)cos(a x) + q + p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 51     14:459 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 52     14:460 Axiom cannot compute this integral
aa:=integrate(sec(a*x)^n,x)
 

           x
         ++           n
   (1)   |   sec(%P a) d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   sec(%N a) d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to t111293.output (2009/2/17, 18:0:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 13
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 13
deq := differentiate(y x, x, 2) + differentiate(y x, x) + y x
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 13
solve(deq, y, x).basis
 

                       x     x
               +-+   - -   - -      +-+
             x\|3      2     2    x\|3
   (3)  [cos(-----)%e   ,%e   sin(-----)]
               2                    2
                                                Type: List Expression Integer
--R 
--R
--R                       x     x
--R               +-+   - -   - -      +-+
--R             x\|3      2     2    x\|3
--R   (3)  [cos(-----)%e   ,%e   sin(-----)]
--R               2                    2
--R                                                Type: List Expression Integer
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 13
f := sin
 

   (1)  sin
                                                           Type: Variable sin
--R 
--R
--R   (1)  sin
--R                                                           Type: Variable sin
--E 4

--S 5 of 13
f 5
 

   (2)  sin(5)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  sin(5)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 13
f 5.6
 

   (3)  - 0.6312666378 7232131147
                                                                  Type: Float
--R 
--R
--R   (3)  - 0.6312666378 7232131147
--R                                                                  Type: Float
--E 6

--S 7 of 13
g(f,x) == f x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 13
g(cos, x)
 
   Compiling function g with type (Variable cos,Variable x) -> 
      Expression Integer 

   (5)  cos(x)
                                                     Type: Expression Integer
--R 
--R   Compiling function g with type (Variable cos,Variable x) -> 
--R      Expression Integer 
--R
--R   (5)  cos(x)
--R                                                     Type: Expression Integer
--E 8

--S 9 of 13
g(f, x)
 
   Compiling function g with type (Variable sin,Variable x) -> 
      Expression Integer 

   (6)  sin(x)
                                                     Type: Expression Integer
--R 
--R   Compiling function g with type (Variable sin,Variable x) -> 
--R      Expression Integer 
--R
--R   (6)  sin(x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 13
g(log, 8.38)
 
   Compiling function g with type (Variable log,Float) -> Float 

   (7)  2.1258479144 939916724
                                                                  Type: Float
--R 
--R   Compiling function g with type (Variable log,Float) -> Float 
--R
--R   (7)  2.1258479144 939916724
--R                                                                  Type: Float
--E 10

)clear all
 
   All user variables and function definitions have been cleared.

--S 11 of 13
sin := [1,2,3,4,5,6,7]
 

   (1)  [1,2,3,4,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6,7]
--R                                                   Type: List PositiveInteger
--E 11

--S 12 of 13
sin 4
 

   (2)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 13
sin(4)$Expression(Integer)
 

   (3)  sin(4)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(4)
--R                                                     Type: Expression Integer
--E 13
)spool 
 
Starts dribbling to exprode.output (2009/2/17, 17:45:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set streams calculate 7
 

--S 1  of 13
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2  of 13
eq := differentiate(y x, x, 3) - sin differentiate(y x, x, 2) * exp y x
           = cos x
 

         ,,,        y(x)     ,,
   (2)  y   (x) - %e    sin(y  (x))= cos(x)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,,        y(x)     ,,
--R   (2)  y   (x) - %e    sin(y  (x))= cos(x)
--R
--R                                            Type: Equation Expression Integer
--E 2

--S 3  of 13
seriesSolve(eq, y, x = 0, [1, 0, 0])
 
   Compiling function %B with type List UnivariateTaylorSeries(
      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
      Integer,x,0) 

   (3)
                          2            3              4      2
         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
         6      24        120           720                 5040
   + 
        8
     O(x )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function %B with type List UnivariateTaylorSeries(
--R      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,0) 
--R
--R   (3)
--R                          2            3              4      2
--R         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
--R     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
--R         6      24        120           720                 5040
--R   + 
--R        8
--R     O(x )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3
 
--S 4 of 13
airy := differentiate(y x, x, 2) - x * y x
 

         ,,
   (4)  y  (x) - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (4)  y  (x) - x y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5  of 13
seriesSolve(airy, y, x = 0, [a0, a1])
 
   Compiling function %D with type List UnivariateTaylorSeries(
      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
      Integer,x,0) 

                    a0  3   a1  4    a0  6    a1  7      8
   (5)  a0 + a1 x + -- x  + -- x  + --- x  + --- x  + O(x )
                     6      12      180      504
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function %D with type List UnivariateTaylorSeries(
--R      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,0) 
--R
--R                    a0  3   a1  4    a0  6    a1  7      8
--R   (5)  a0 + a1 x + -- x  + -- x  + --- x  + --- x  + O(x )
--R                     6      12      180      504
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 5

--S 6 of 13
seriesSolve(airy, y, x = 1, [a0, a1])
 
   Compiling function %F with type List UnivariateTaylorSeries(
      Expression Integer,x,1) -> UnivariateTaylorSeries(Expression 
      Integer,x,1) 

   (6)
                      a0        2   a1 + a0        3   2a1 + a0        4
     a0 + a1(x - 1) + -- (x - 1)  + ------- (x - 1)  + -------- (x - 1)
                       2               6                  24
   + 
     a1 + 4a0        5   6a1 + 5a0        6   11a1 + 9a0        7            8
     -------- (x - 1)  + --------- (x - 1)  + ---------- (x - 1)  + O((x - 1) )
        120                 720                  5040
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R   Compiling function %F with type List UnivariateTaylorSeries(
--R      Expression Integer,x,1) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,1) 
--R
--R   (6)
--R                      a0        2   a1 + a0        3   2a1 + a0        4
--R     a0 + a1(x - 1) + -- (x - 1)  + ------- (x - 1)  + -------- (x - 1)
--R                       2               6                  24
--R   + 
--R     a1 + 4a0        5   6a1 + 5a0        6   11a1 + 9a0        7            8
--R     -------- (x - 1)  + --------- (x - 1)  + ---------- (x - 1)  + O((x - 1) )
--R        120                 720                  5040
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 6

--S 7 of 13
x := operator 'x
 
   Compiled code for %F has been cleared.
   Compiled code for %D has been cleared.
   Compiled code for %B has been cleared.

   (7)  x
                                                          Type: BasicOperator
--R 
--R   Compiled code for %F has been cleared.
--R   Compiled code for %D has been cleared.
--R   Compiled code for %B has been cleared.
--R
--R   (7)  x
--R                                                          Type: BasicOperator
--E 7

--S 8 of 13
eq1 := differentiate(x t, t) = 1 + x(t)**2
 

         ,         2
   (8)  x (t)= x(t)  + 1

                                            Type: Equation Expression Integer
--R 
--R
--R         ,         2
--R   (8)  x (t)= x(t)  + 1
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 13
eq2 := differentiate(y t, t) = x(t) * y(t)
 

         ,
   (9)  y (t)= x(t)y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,
--R   (9)  y (t)= x(t)y(t)
--R
--R                                            Type: Equation Expression Integer
--E 9

--S 10 of 13
seriesSolve([eq2, eq1], [x, y], t = 0, [y 0 = 1, x 0 = 0])
 
   Compiling function %H with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 
   Compiling function %I with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 

              1  3    2  5    17  7      8      1  2    5  4    61  6      8
   (10)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
              3      15      315                2      24      720
                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function %H with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R   Compiling function %I with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R
--R              1  3    2  5    17  7      8      1  2    5  4    61  6      8
--R   (10)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
--R              3      15      315                2      24      720
--R                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--E 10

--S 11 of 13
eq1 := differentiate(x t, t) = y t
 

          ,
   (11)  x (t)= y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (11)  x (t)= y(t)
--R
--R                                            Type: Equation Expression Integer
--E 11

--S 12 of 13
eq2 := differentiate(y t, t) = - g * sin(x t) - c * y t
 

          ,
   (12)  y (t)= - g sin(x(t)) - c y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (12)  y (t)= - g sin(x(t)) - c y(t)
--R
--R                                            Type: Equation Expression Integer
--E 12

--S 13 of 13
seriesSolve([eq1, eq2], [x, y], t = 0, [y 0 = a, x 0 = b])
 
   Compiling function %K with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 
   Compiling function %L with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 

   (13)
   [
                                                                    2
                 - g sin(b) - a c  2   c g sin(b) - a g cos(b) + a c   3
       b + a t + ---------------- t  + ------------------------------ t
                         2                            6
     + 
         2             2    2                               3
       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   4
       ------------------------------------------------------ t
                                 24
     + 
                   2      2          2           3     2                2      2
             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
           + 
                    2    3               4
             (- 3a c  + a )g cos(b) + a c
        /
           120
      *
          5
         t
     + 
               3      3          2      2
             3g sin(b)  + 13a c g sin(b)
           + 
                 3      2      2      2  2             4      2 2    4
             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
           + 
                     2      2        3     3                5
             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
        /
           720
      *
          6
         t
     + 
                    3      3         3                 2      3  2       2
             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
           + 
                    3      2        3      2   2           5      2 3      4
               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
            *
               sin(b)
           + 
                  3      3        2      3  2      2
             - a g cos(b)  + (6a c  - 11a )g cos(b)
           + 
                    4      3 2    5               6
             (- 5a c  + 32a c  - a )g cos(b) + a c
        /
           5040
      *
          7
         t
     + 
          8
       O(t )
     ,

                                                              2
                                 c g sin(b) - a g cos(b) + a c   2
       a + (- g sin(b) - a c)t + ------------------------------ t
                                                2
     + 
         2             2    2                               3
       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   3
       ------------------------------------------------------ t
                                  6
     + 
                   2      2          2           3     2                2      2
             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
           + 
                    2    3               4
             (- 3a c  + a )g cos(b) + a c
        /
           24
      *
          4
         t
     + 
               3      3          2      2
             3g sin(b)  + 13a c g sin(b)
           + 
                 3      2      2      2  2             4      2 2    4
             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
           + 
                     2      2        3     3                5
             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
        /
           120
      *
          5
         t
     + 
                    3      3         3                 2      3  2       2
             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
           + 
                    3      2        3      2   2           5      2 3      4
               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
            *
               sin(b)
           + 
                  3      3        2      3  2      2
             - a g cos(b)  + (6a c  - 11a )g cos(b)
           + 
                    4      3 2    5               6
             (- 5a c  + 32a c  - a )g cos(b) + a c
        /
           720
      *
          6
         t
     + 
                   4             2      2  3       3
             (- 33g cos(b) + (38c  - 78a )g )sin(b)
           + 
                        3               3       3   2       2
             (- 228a c g cos(b) + (94a c  - 164a c)g )sin(b)
           + 
                  4      3        2       2  3      2
                 g cos(b)  + (- 6c  + 102a )g cos(b)
               + 
                  4       2 2      4  2             6      2 4      4 2    6
               (5c  - 334a c  + 57a )g cos(b) + (- c  + 57a c  - 76a c  + a )g
            *
               sin(b)
           + 
                   3      3           3       3   2      2
             4a c g cos(b)  + (- 10a c  + 108a c)g cos(b)
           + 
                  5       3 3      5                7
             (6a c  - 122a c  + 16a c)g cos(b) - a c
        /
           5040
      *
          7
         t
     + 
          8
       O(t )
     ]
                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function %K with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R   Compiling function %L with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R
--R   (13)
--R   [
--R                                                                    2
--R                 - g sin(b) - a c  2   c g sin(b) - a g cos(b) + a c   3
--R       b + a t + ---------------- t  + ------------------------------ t
--R                         2                            6
--R     + 
--R         2             2    2                               3
--R       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   4
--R       ------------------------------------------------------ t
--R                                 24
--R     + 
--R                   2      2          2           3     2                2      2
--R             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
--R           + 
--R                    2    3               4
--R             (- 3a c  + a )g cos(b) + a c
--R        /
--R           120
--R      *
--R          5
--R         t
--R     + 
--R               3      3          2      2
--R             3g sin(b)  + 13a c g sin(b)
--R           + 
--R                 3      2      2      2  2             4      2 2    4
--R             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
--R           + 
--R                     2      2        3     3                5
--R             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
--R        /
--R           720
--R      *
--R          6
--R         t
--R     + 
--R                    3      3         3                 2      3  2       2
--R             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
--R           + 
--R                    3      2        3      2   2           5      2 3      4
--R               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
--R            *
--R               sin(b)
--R           + 
--R                  3      3        2      3  2      2
--R             - a g cos(b)  + (6a c  - 11a )g cos(b)
--R           + 
--R                    4      3 2    5               6
--R             (- 5a c  + 32a c  - a )g cos(b) + a c
--R        /
--R           5040
--R      *
--R          7
--R         t
--R     + 
--R          8
--R       O(t )
--R     ,
--R
--R                                                              2
--R                                 c g sin(b) - a g cos(b) + a c   2
--R       a + (- g sin(b) - a c)t + ------------------------------ t
--R                                                2
--R     + 
--R         2             2    2                               3
--R       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   3
--R       ------------------------------------------------------ t
--R                                  6
--R     + 
--R                   2      2          2           3     2                2      2
--R             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
--R           + 
--R                    2    3               4
--R             (- 3a c  + a )g cos(b) + a c
--R        /
--R           24
--R      *
--R          4
--R         t
--R     + 
--R               3      3          2      2
--R             3g sin(b)  + 13a c g sin(b)
--R           + 
--R                 3      2      2      2  2             4      2 2    4
--R             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
--R           + 
--R                     2      2        3     3                5
--R             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
--R        /
--R           120
--R      *
--R          5
--R         t
--R     + 
--R                    3      3         3                 2      3  2       2
--R             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
--R           + 
--R                    3      2        3      2   2           5      2 3      4
--R               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
--R            *
--R               sin(b)
--R           + 
--R                  3      3        2      3  2      2
--R             - a g cos(b)  + (6a c  - 11a )g cos(b)
--R           + 
--R                    4      3 2    5               6
--R             (- 5a c  + 32a c  - a )g cos(b) + a c
--R        /
--R           720
--R      *
--R          6
--R         t
--R     + 
--R                   4             2      2  3       3
--R             (- 33g cos(b) + (38c  - 78a )g )sin(b)
--R           + 
--R                        3               3       3   2       2
--R             (- 228a c g cos(b) + (94a c  - 164a c)g )sin(b)
--R           + 
--R                  4      3        2       2  3      2
--R                 g cos(b)  + (- 6c  + 102a )g cos(b)
--R               + 
--R                  4       2 2      4  2             6      2 4      4 2    6
--R               (5c  - 334a c  + 57a )g cos(b) + (- c  + 57a c  - 76a c  + a )g
--R            *
--R               sin(b)
--R           + 
--R                   3      3           3       3   2      2
--R             4a c g cos(b)  + (- 10a c  + 108a c)g cos(b)
--R           + 
--R                  5       3 3      5                7
--R             (6a c  - 122a c  + 16a c)g cos(b) - a c
--R        /
--R           5040
--R      *
--R          7
--R         t
--R     + 
--R          8
--R       O(t )
--R     ]
--R                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--E 13
)spool 
 
Starts dribbling to heap.output (2009/2/17, 17:46:26).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1  of 8
h := heap [-4,9,11,2,7,-7]
 

   (1)  [11,7,9,- 4,2,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (1)  [11,7,9,- 4,2,- 7]
--R                                                           Type: Heap Integer
--E 1

--S 2 of 8
insert!(3,h)
 

   (2)  [11,7,9,- 4,2,- 7,3]
                                                           Type: Heap Integer
--R 
--R
--R   (2)  [11,7,9,- 4,2,- 7,3]
--R                                                           Type: Heap Integer
--E 2

--S 3 of 8
extract! h
 

   (3)  11
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  11
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 8
h
 

   (4)  [9,7,3,- 4,2,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (4)  [9,7,3,- 4,2,- 7]
--R                                                           Type: Heap Integer
--E 4

--S 5 of 8
[extract!(h) while not empty?(h)]
 

   (5)  [9,7,3,2,- 4,- 7]
                                                           Type: List Integer
--R 
--R
--R   (5)  [9,7,3,2,- 4,- 7]
--R                                                           Type: List Integer
--E 5

--S 6 of 8
heapsort(x) == (empty? x => []; cons(extract!(x),heapsort x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 8
h1 := heap [17,-4,9,-11,2,7,-7]
 

   (7)  [17,2,9,- 11,- 4,7,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (7)  [17,2,9,- 11,- 4,7,- 7]
--R                                                           Type: Heap Integer
--E 7

--S 8 of 8
heapsort h1
 
   Compiling function heapsort with type Heap Integer -> List Integer 

   (8)  [17,9,7,2,- 4,- 7,- 11]
                                                           Type: List Integer
--R 
--R   Compiling function heapsort with type Heap Integer -> List Integer 
--R
--R   (8)  [17,9,7,2,- 4,- 7,- 11]
--R                                                           Type: List Integer
--E 8
)spool 
 
Starts dribbling to psgenfcn.output (2009/2/17, 17:56:15).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 19
ORD := 20
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 19
approximateEquality(series1,series2) ==
  -- tests that 2 series are equal to order ORD
  uts1 := series1 :: UTS(EXPR INT,'t,0)
  uts2 := series2 :: UTS(EXPR INT,'t,0)
  flag := (order(uts1 - uts2,ORD) = ORD) :: Boolean
  flag => true
  error "series do not agree to specified order"
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 19
bernoulliPolynomial(n) ==
  -- returns the nth Bernoulli polynomial as an EXPR INT
  sup := bernoulli(n)$(PNTHEORY)
  p : POLY FRAC INT := multivariate(sup,'x)
  p :: (EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 19
eulerPolynomial(n) ==
  -- returns the nth Euler polynomial as an EXPR INT
  sup := euler(n)$(PNTHEORY)
  p : POLY FRAC INT := multivariate(sup,'x)
  p :: (EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 19
f1 := taylor(t/(1 - t - t**2))
 

             2     3     4     5     6      7      8      9      10      11
   (5)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             2     3     4     5     6      7      8      9      10      11
--R   (5)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 5

--S 6 of 19
f2 := taylor(n +-> fibonacci(n),t = 0)
 

             2     3     4     5     6      7      8      9      10      11
   (6)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             2     3     4     5     6      7      8      9      10      11
--R   (6)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 6

--S 7 of 19
approximateEquality(f1,f2)
 
   Compiling function approximateEquality with type (Any,Any) -> 
      Boolean 

   (7)  true
                                                                Type: Boolean
--R 
--R   Compiling function approximateEquality with type (Any,Any) -> 
--R      Boolean 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 19
g1 := taylor(t/(exp(t) - 1))
 

   (8)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (8)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 8

--S 9 of 19
g2 := taylor(n +-> bernoulli(n)/factorial(n),t = 0)
 

   (9)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (9)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 9

--S 10 of 19
approximateEquality(g1,g2)
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 19
gg1 := taylor(t*exp(t*x)/(exp(t) - 1),t = 0)
 

   (11)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
     ---------------------- t  + --------------------- t
               720                        720
   + 
        6       5       4      2            7      6      5     3
     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
     ------------------------------- t  + --------------------------- t
                  30240                              30240
   + 
        8       7       6      4      2
     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
     -------------------------------------- t
                     1209600
   + 
        9      8      7      5      3
     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
     ------------------------------------- t
                    3628800
   + 
        10       9       8       6       4      2
     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
     ------------------------------------------------ t   + O(t  )
                         239500800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (11)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
--R     ---------------------- t  + --------------------- t
--R               720                        720
--R   + 
--R        6       5       4      2            7      6      5     3
--R     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
--R     ------------------------------- t  + --------------------------- t
--R                  30240                              30240
--R   + 
--R        8       7       6      4      2
--R     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
--R     -------------------------------------- t
--R                     1209600
--R   + 
--R        9      8      7      5      3
--R     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
--R     ------------------------------------- t
--R                    3628800
--R   + 
--R        10       9       8       6       4      2
--R     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
--R     ------------------------------------------------ t   + O(t  )
--R                         239500800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 11

--S 12 of 19
gg2 := taylor(n +-> bernoulliPolynomial(n)/factorial(n),t = 0)
 
   Compiling function bernoulliPolynomial with type Integer -> 
      Expression Integer 

   (12)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
     ---------------------- t  + --------------------- t
               720                        720
   + 
        6       5       4      2            7      6      5     3
     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
     ------------------------------- t  + --------------------------- t
                  30240                              30240
   + 
        8       7       6      4      2
     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
     -------------------------------------- t
                     1209600
   + 
        9      8      7      5      3
     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
     ------------------------------------- t
                    3628800
   + 
        10       9       8       6       4      2
     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
     ------------------------------------------------ t   + O(t  )
                         239500800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function bernoulliPolynomial with type Integer -> 
--R      Expression Integer 
--R
--R   (12)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
--R     ---------------------- t  + --------------------- t
--R               720                        720
--R   + 
--R        6       5       4      2            7      6      5     3
--R     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
--R     ------------------------------- t  + --------------------------- t
--R                  30240                              30240
--R   + 
--R        8       7       6      4      2
--R     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
--R     -------------------------------------- t
--R                     1209600
--R   + 
--R        9      8      7      5      3
--R     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
--R     ------------------------------------- t
--R                    3628800
--R   + 
--R        10       9       8       6       4      2
--R     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
--R     ------------------------------------------------ t   + O(t  )
--R                         239500800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 12

--S 13 of 19
approximateEquality(gg1,gg2)
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 19
h1 := taylor(2*exp(t/2)/(exp(t) + 1))
 

             1  2    5   4     61   6     277    8      50521    10      11
   (14)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
             8      384      46080      2064384      3715891200
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             1  2    5   4     61   6     277    8      50521    10      11
--R   (14)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
--R             8      384      46080      2064384      3715891200
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 14

--S 15 of 19
h2 := taylor(n +-> euler(n)/(2**n * factorial(n)),t = 0)
 

             1  2    5   4     61   6     277    8      50521    10      11
   (15)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
             8      384      46080      2064384      3715891200
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             1  2    5   4     61   6     277    8      50521    10      11
--R   (15)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
--R             8      384      46080      2064384      3715891200
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 15

--S 16 of 19
approximateEquality(h1,h2)
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 19
hh1 := taylor(2*exp(t*x)/(exp(t) + 1),t = 0)
 

   (17)
                     2            3     2           4     3
         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
     1 + ------ t + ------ t  + ------------- t  + ------------ t
            2          2              24                24
   + 
       5     4     2           6     5     3
     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
     ------------------- t  + ------------------- t
             240                      720
   + 
       7      6      4      2            8     7      5      3
     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
     ----------------------------- t  + ---------------------------- t
                 40320                              40320
   + 
       9     8      6       4       2
     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
     ------------------------------------- t
                     725760
   + 
      10     9      7       5       3
     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
     --------------------------------------- t   + O(t  )
                     3628800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (17)
--R                     2            3     2           4     3
--R         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
--R     1 + ------ t + ------ t  + ------------- t  + ------------ t
--R            2          2              24                24
--R   + 
--R       5     4     2           6     5     3
--R     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
--R     ------------------- t  + ------------------- t
--R             240                      720
--R   + 
--R       7      6      4      2            8     7      5      3
--R     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
--R     ----------------------------- t  + ---------------------------- t
--R                 40320                              40320
--R   + 
--R       9     8      6       4       2
--R     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
--R     ------------------------------------- t
--R                     725760
--R   + 
--R      10     9      7       5       3
--R     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
--R     --------------------------------------- t   + O(t  )
--R                     3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 17

--S 18 of 19
hh2 := taylor(n +-> eulerPolynomial(n)/factorial(n),t = 0)
 
   Compiling function eulerPolynomial with type Integer -> Expression 
      Integer 

   (18)
                     2            3     2           4     3
         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
     1 + ------ t + ------ t  + ------------- t  + ------------ t
            2          2              24                24
   + 
       5     4     2           6     5     3
     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
     ------------------- t  + ------------------- t
             240                      720
   + 
       7      6      4      2            8     7      5      3
     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
     ----------------------------- t  + ---------------------------- t
                 40320                              40320
   + 
       9     8      6       4       2
     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
     ------------------------------------- t
                     725760
   + 
      10     9      7       5       3
     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
     --------------------------------------- t   + O(t  )
                     3628800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function eulerPolynomial with type Integer -> Expression 
--R      Integer 
--R
--R   (18)
--R                     2            3     2           4     3
--R         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
--R     1 + ------ t + ------ t  + ------------- t  + ------------ t
--R            2          2              24                24
--R   + 
--R       5     4     2           6     5     3
--R     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
--R     ------------------- t  + ------------------- t
--R             240                      720
--R   + 
--R       7      6      4      2            8     7      5      3
--R     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
--R     ----------------------------- t  + ---------------------------- t
--R                 40320                              40320
--R   + 
--R       9     8      6       4       2
--R     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
--R     ------------------------------------- t
--R                     725760
--R   + 
--R      10     9      7       5       3
--R     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
--R     --------------------------------------- t   + O(t  )
--R                     3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 18

--S 19 of 19
approximateEquality(hh1,hh2)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19
)spool 
 
Starts dribbling to laplace.output (2009/2/17, 17:48:13).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 27
f n == t**(n-1)*exp(-a*t)/factorial(n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 27
f 2
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

            - a t
   (2)  t %e
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R            - a t
--R   (2)  t %e
--R                                                     Type: Expression Integer
--E 2

--S 3 of 27
laplace(%, t, s)
 

               1
   (3)  --------------
         2           2
        s  + 2a s + a
                                                     Type: Expression Integer
--R 
--R
--R               1
--R   (3)  --------------
--R         2           2
--R        s  + 2a s + a
--R                                                     Type: Expression Integer
--E 3

--S 4 of 27
f 5
 

         4  - a t
        t %e
   (4)  ---------
            24
                                                     Type: Expression Integer
--R 
--R
--R         4  - a t
--R        t %e
--R   (4)  ---------
--R            24
--R                                                     Type: Expression Integer
--E 4

--S 5 of 27
laplace(%, t, s)
 

                            1
   (5)  ----------------------------------------
         5       4      2 3      3 2     4     5
        s  + 5a s  + 10a s  + 10a s  + 5a s + a
                                                     Type: Expression Integer
--R 
--R
--R                            1
--R   (5)  ----------------------------------------
--R         5       4      2 3      3 2     4     5
--R        s  + 5a s  + 10a s  + 10a s  + 5a s + a
--R                                                     Type: Expression Integer
--E 5

--S 6 of 27
sin(a*t) - a*t*cos(a*t)
 

   (6)  sin(a t) - a t cos(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (6)  sin(a t) - a t cos(a t)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 27
laplace(%, t, s)
 

                3
              2a
   (7)  ---------------
         4     2 2    4
        s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                3
--R              2a
--R   (7)  ---------------
--R         4     2 2    4
--R        s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 7

--S 8 of 27
(cosh(a*t) - cos(a*t))/(2*a**2)
 

        cosh(a t) - cos(a t)
   (8)  --------------------
                   2
                 2a
                                                     Type: Expression Integer
--R 
--R
--R        cosh(a t) - cos(a t)
--R   (8)  --------------------
--R                   2
--R                 2a
--R                                                     Type: Expression Integer
--E 8

--S 9 of 27
laplace(%, t, s)
 

           s
   (9)  -------
         4    4
        s  - a
                                                     Type: Expression Integer
--R 
--R
--R           s
--R   (9)  -------
--R         4    4
--R        s  - a
--R                                                     Type: Expression Integer
--E 9

--S 10 of 27
exp(-a*t) * sin(b*t) / b**2
 

           - a t
         %e     sin(b t)
   (10)  ---------------
                 2
                b
                                                     Type: Expression Integer
--R 
--R
--R           - a t
--R         %e     sin(b t)
--R   (10)  ---------------
--R                 2
--R                b
--R                                                     Type: Expression Integer
--E 10

--S 11 of 27
laplace(%, t, s)
 

                     1
   (11)  ------------------------
            2             3    2
         b s  + 2a b s + b  + a b
                                                     Type: Expression Integer
--R 
--R
--R                     1
--R   (11)  ------------------------
--R            2             3    2
--R         b s  + 2a b s + b  + a b
--R                                                     Type: Expression Integer
--E 11

--S 12 of 27
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
 

   (12)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (12)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
--R                                                     Type: Expression Integer
--E 12

--S 13 of 27
laplace(%, t, s)
 

              3
            4a
   (13)  --------
          4     4
         s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R              3
--R            4a
--R   (13)  --------
--R          4     4
--R         s  + 4a
--R                                                     Type: Expression Integer
--E 13

--S 14 of 27
(exp(a*t) - exp(b*t))/t
 

             b t     a t
         - %e    + %e
   (14)  ---------------
                t
                                                     Type: Expression Integer
--R 
--R
--R             b t     a t
--R         - %e    + %e
--R   (14)  ---------------
--R                t
--R                                                     Type: Expression Integer
--E 14

--S 15 of 27
laplace(%, t, s)
 

   (15)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (15)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 15

--S 16 of 27
2/t * (1 - cosh(a*t))
 

         - 2cosh(a t) + 2
   (16)  ----------------
                 t
                                                     Type: Expression Integer
--R 
--R
--R         - 2cosh(a t) + 2
--R   (16)  ----------------
--R                 t
--R                                                     Type: Expression Integer
--E 16

--S 17 of 27
laplace(%, t, s)
 

              2    2
   (17)  log(s  - a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R              2    2
--R   (17)  log(s  - a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 17

--S 18 of 27
2/t * (1 - cos(a*t))
 

         - 2cos(a t) + 2
   (18)  ---------------
                t
                                                     Type: Expression Integer
--R 
--R
--R         - 2cos(a t) + 2
--R   (18)  ---------------
--R                t
--R                                                     Type: Expression Integer
--E 18

--S 19 of 27
laplace(%, t, s)
 

              2    2
   (19)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R              2    2
--R   (19)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 27
(cos(a*t) - cos(b*t))/t
 

         - cos(b t) + cos(a t)
   (20)  ---------------------
                   t
                                                     Type: Expression Integer
--R 
--R
--R         - cos(b t) + cos(a t)
--R   (20)  ---------------------
--R                   t
--R                                                     Type: Expression Integer
--E 20

--S 21 of 27
laplace(%, t, s)
 

              2    2         2    2
         log(s  + b ) - log(s  + a )
   (21)  ---------------------------
                      2
                                                     Type: Expression Integer
--R 
--R
--R              2    2         2    2
--R         log(s  + b ) - log(s  + a )
--R   (21)  ---------------------------
--R                      2
--R                                                     Type: Expression Integer
--E 21

--S 22 of 27
a*Ci(b*t) + c*Si(d*t)
 

   (22)  c Si(d t) + a Ci(b t)
                                                     Type: Expression Integer
--R 
--R
--R   (22)  c Si(d t) + a Ci(b t)
--R                                                     Type: Expression Integer
--E 22

--S 23 of 27
laplace(%, t, s)
 

                2    2
               s  + b             d
         a log(-------) + 2c atan(-)
                   2              s
                  b
   (23)  ---------------------------
                      2s
                                                     Type: Expression Integer
--R 
--R
--R                2    2
--R               s  + b             d
--R         a log(-------) + 2c atan(-)
--R                   2              s
--R                  b
--R   (23)  ---------------------------
--R                      2s
--R                                                     Type: Expression Integer
--E 23

--S 24 of 27
exp(a*t+b)*Ei(c*t)
 

                  a t + b
   (24)  Ei(c t)%e
                                                     Type: Expression Integer
--R 
--R
--R                  a t + b
--R   (24)  Ei(c t)%e
--R                                                     Type: Expression Integer
--E 24

--S 25 of 27
laplace(%, t, s)
 

           b    s + c - a
         %e log(---------)
                    c
   (25)  -----------------
               s - a
                                                     Type: Expression Integer
--R 
--R
--R           b    s + c - a
--R         %e log(---------)
--R                    c
--R   (25)  -----------------
--R               s - a
--R                                                     Type: Expression Integer
--E 25

--S 26 of 27
sin(a*t) - a*t*cos(a*t) + exp(t**2)
 

                       2
                      t
   (26)  sin(a t) + %e   - a t cos(a t)
                                                     Type: Expression Integer
--R 
--R
--R                       2
--R                      t
--R   (26)  sin(a t) + %e   - a t cos(a t)
--R                                                     Type: Expression Integer
--E 26

--S 27 of 27
laplace(%, t, s)
 

                                     2
           4     2 2    4           t           3
         (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
   (27)  ----------------------------------------
                       4     2 2    4
                      s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                                     2
--R           4     2 2    4           t           3
--R         (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
--R   (27)  ----------------------------------------
--R                       4     2 2    4
--R                      s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 27
)spool 
 
Starts dribbling to fparfrac.output (2009/2/17, 17:46:5).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 

--S 1 of 18
Q := FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 18
Px := UP(x, Q)
 

   (2)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 18
Fx := FRAC Px
 

   (3)  Fraction UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (3)  Fraction UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 3

--S 4 of 18
f:Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2)
 

                     36
   (4)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (4)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 4

--S 5 of 18
g := fullPartialFraction f
 

          4       4        --+      - 3%A - 6
   (5)  ----- - ----- +    >        ---------
        x - 2   x + 1      --+              2
                          2         (x - %A)
                        %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          4       4        --+      - 3%A - 6
--R   (5)  ----- - ----- +    >        ---------
--R        x - 2   x + 1      --+              2
--R                          2         (x - %A)
--R                        %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 18
g::Fx
 

                     36
   (6)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (6)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 18
g5 := D(g, 5)
 

             480        480        --+      2160%A + 4320
   (7)  - -------- + -------- +    >        -------------
                 6          6      --+                7
          (x - 2)    (x + 1)      2           (x - %A)
                                %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R             480        480        --+      2160%A + 4320
--R   (7)  - -------- + -------- +    >        -------------
--R                 6          6      --+                7
--R          (x - 2)    (x + 1)      2           (x - %A)
--R                                %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 7

--S 8 of 18
f5 := D(f, 5)
 

   (8)
                10           9            8            7            6
       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
     + 
                5            4            3           2
       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
  /
        20      19      18      17       16       15       14        13
       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
     + 
            12        11        10        9        8        7        6        5
       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
     + 
           4        3       2
       276x  - 1184x  + 208x  + 192x - 64
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (8)
--R                10           9            8            7            6
--R       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
--R     + 
--R                5            4            3           2
--R       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
--R  /
--R        20      19      18      17       16       15       14        13
--R       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
--R     + 
--R            12        11        10        9        8        7        6        5
--R       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
--R     + 
--R           4        3       2
--R       276x  - 1184x  + 208x  + 192x - 64
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 18
g5::Fx - f5
 

   (9)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (9)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 18
f:Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)
 

                        6    5
                       x  - x
   (10)  -----------------------------------
          7     6     5     3     2
         x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                        6    5
--R                       x  - x
--R   (10)  -----------------------------------
--R          7     6     5     3     2
--R         x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 10

--S 11 of 18
g := fullPartialFraction f
 

   (11)
      1952       464        32                          179       135
      ----       ---        --                       - ---- %A + ----
      2401       343        49            --+          2401      2401
     ------ + -------- + -------- +       >          ----------------
      x - 2          2          3         --+             x - %A
              (x - 2)    (x - 2)      2
                                    %A  + %A + 1= 0
   + 
                       37        20
                      ---- %A + ----
           --+        1029      1029
           >          --------------
           --+                   2
       2                 (x - %A)
     %A  + %A + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (11)
--R      1952       464        32                          179       135
--R      ----       ---        --                       - ---- %A + ----
--R      2401       343        49            --+          2401      2401
--R     ------ + -------- + -------- +       >          ----------------
--R      x - 2          2          3         --+             x - %A
--R              (x - 2)    (x - 2)      2
--R                                    %A  + %A + 1= 0
--R   + 
--R                       37        20
--R                      ---- %A + ----
--R           --+        1029      1029
--R           >          --------------
--R           --+                   2
--R       2                 (x - %A)
--R     %A  + %A + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 11

--S 12 of 18
g::Fx - f
 

   (12)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (12)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 12

--S 13 of 18
f:Fx := (2*x**7-7*x**5+26*x**3+8*x)/(x**8-5*x**6+6*x**4+4*x**2-8)
 

             7     5      3
           2x  - 7x  + 26x  + 8x
   (13)  ------------------------
          8     6     4     2
         x  - 5x  + 6x  + 4x  - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             7     5      3
--R           2x  - 7x  + 26x  + 8x
--R   (13)  ------------------------
--R          8     6     4     2
--R         x  - 5x  + 6x  + 4x  - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 13

--S 14 of 18
g := fullPartialFraction f
 

                        1                                            1
                        -                                            -
            --+         2        --+          1          --+         2
   (14)     >        ------ +    >        --------- +    >        ------
            --+      x - %A      --+              3      --+      x - %A
           2                    2         (x - %A)      2
         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R                        1                                            1
--R                        -                                            -
--R            --+         2        --+          1          --+         2
--R   (14)     >        ------ +    >        --------- +    >        ------
--R            --+      x - %A      --+              3      --+      x - %A
--R           2                    2         (x - %A)      2
--R         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 14

--S 15 of 18
g::Fx - f
 

   (15)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (15)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 15

--S 16 of 18
f:Fx := x**3/(x**21+2*x**20+4*x**19+7*x**18+10*x**17+17*x**16+22*x**15+30*x**14
                +36*x**13+40*x**12+47*x**11+46*x**10+49*x**9+43*x**8+38*x**7
                  +32*x**6+23*x**5+19*x**4+10*x**3+7*x**2+2*x+1)
 

   (16)
      3
     x
  /
        21     20     19     18      17      16      15      14      13      12
       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
     + 
          11      10      9      8      7      6      5      4      3     2
       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
     + 
       1
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (16)
--R      3
--R     x
--R  /
--R        21     20     19     18      17      16      15      14      13      12
--R       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
--R     + 
--R          11      10      9      8      7      6      5      4      3     2
--R       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
--R     + 
--R       1
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 16

--S 17 of 18
g := fullPartialFraction f
 

   (17)
                  1                        1      19
                  - %A                     - %A - --
        --+       2             --+        9      27
        >        ------ +       >          ---------
        --+      x - %A         --+          x - %A
       2                    2
     %A  + 1= 0           %A  + %A + 1= 0
   + 
                       1       1
                      -- %A - --
           --+        27      27
           >          ----------
           --+                 2
       2               (x - %A)
     %A  + %A + 1= 0
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
               96556567040   4   420961732891   3    59101056149   2
            - ------------ %A  + ------------ %A  - ------------ %A
              912390759099       912390759099       912390759099
          + 
              373545875923      529673492498
            - ------------ %A + ------------
              912390759099      912390759099
       /
          x - %A
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
           5580868   4    2024443   3    4321919   2    84614        5070620
        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
          94070601       94070601       94070601       1542141      94070601
        --------------------------------------------------------------------
                                              2
                                      (x - %A)
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
         1610957   4    2763014   3    2016775   2    266953        4529359
        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
        94070601       94070601       94070601       94070601      94070601
        -------------------------------------------------------------------
                                             3
                                     (x - %A)
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (17)
--R                  1                        1      19
--R                  - %A                     - %A - --
--R        --+       2             --+        9      27
--R        >        ------ +       >          ---------
--R        --+      x - %A         --+          x - %A
--R       2                    2
--R     %A  + 1= 0           %A  + %A + 1= 0
--R   + 
--R                       1       1
--R                      -- %A - --
--R           --+        27      27
--R           >          ----------
--R           --+                 2
--R       2               (x - %A)
--R     %A  + %A + 1= 0
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R               96556567040   4   420961732891   3    59101056149   2
--R            - ------------ %A  + ------------ %A  - ------------ %A
--R              912390759099       912390759099       912390759099
--R          + 
--R              373545875923      529673492498
--R            - ------------ %A + ------------
--R              912390759099      912390759099
--R       /
--R          x - %A
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R           5580868   4    2024443   3    4321919   2    84614        5070620
--R        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
--R          94070601       94070601       94070601       1542141      94070601
--R        --------------------------------------------------------------------
--R                                              2
--R                                      (x - %A)
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R         1610957   4    2763014   3    2016775   2    266953        4529359
--R        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
--R        94070601       94070601       94070601       94070601      94070601
--R        -------------------------------------------------------------------
--R                                             3
--R                                     (x - %A)
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 17

--S 18 of 18
g::Fx - f
 

   (18)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (18)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 18
)spool 
 
Starts dribbling to expr.output (2009/2/17, 17:45:53).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 29
foo := operator 'foo
 

   (1)  foo
                                                          Type: BasicOperator
--R 
--R
--R   (1)  foo
--R                                                          Type: BasicOperator
--E 1

--S 2 of 29
bar := operator 'bar
 

   (2)  bar
                                                          Type: BasicOperator
--R 
--R
--R   (2)  bar
--R                                                          Type: BasicOperator
--E 2

--S 3 of 29
g := foo x
 

   (3)  foo(x)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  foo(x)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 29
eval(g, x = x**2 + 1)
 

             2
   (4)  foo(x  + 1)
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (4)  foo(x  + 1)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 29
differentiate(%, x)
 

             ,  2
   (5)  2xfoo (x  + 1)

                                                     Type: Expression Integer
--R 
--R
--R             ,  2
--R   (5)  2xfoo (x  + 1)
--R
--R                                                     Type: Expression Integer
--E 5

--S 6 of 29
f := bar(x, y)
 

   (6)  bar(x,y)
                                                     Type: Expression Integer
--R 
--R
--R   (6)  bar(x,y)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 29
eval(f, [x = y, y = x])
 

   (7)  bar(y,x)
                                                     Type: Expression Integer
--R 
--R
--R   (7)  bar(y,x)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 29
[differentiate(f, x), differentiate(f, y)]
 

   (8)  [bar  (x,y),bar  (x,y)]
            ,1         ,2
                                                Type: List Expression Integer
--R 
--R
--R   (8)  [bar  (x,y),bar  (x,y)]
--R            ,1         ,2
--R                                                Type: List Expression Integer
--E 8

--S 9 of 29
ff := eval(f, [x = x**2 * foo y, y = x + y])
 

             2
   (9)  bar(x foo(y),y + x)
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (9)  bar(x foo(y),y + x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 29
differentiate(ff, x)
 

                2                                2
   (10)  bar  (x foo(y),y + x) + 2x foo(y)bar  (x foo(y),y + x)
            ,2                               ,1
                                                     Type: Expression Integer
--R 
--R
--R                2                                2
--R   (10)  bar  (x foo(y),y + x) + 2x foo(y)bar  (x foo(y),y + x)
--R            ,2                               ,1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 29
differentiate(ff, y)
 

                2                 2       2                ,
   (11)  bar  (x foo(y),y + x) + x bar  (x foo(y),y + x)foo (y)
            ,2                        ,1
                                                     Type: Expression Integer
--R 
--R
--R                2                 2       2                ,
--R   (11)  bar  (x foo(y),y + x) + x bar  (x foo(y),y + x)foo (y)
--R            ,2                        ,1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 29
pbar(l:List OUTFORM):OUTFORM == infix(" @ "::SYMBOL::OUTFORM, l)
 
   Function declaration pbar : List OutputForm -> OutputForm has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration pbar : List OutputForm -> OutputForm has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 12

--S 13 of 29
display(bar, pbar)
 
   Compiling function pbar with type List OutputForm -> OutputForm 

   (13)  bar
                                                          Type: BasicOperator
--R 
--R   Compiling function pbar with type List OutputForm -> OutputForm 
--R
--R   (13)  bar
--R                                                          Type: BasicOperator
--E 13

--S 14 of 29
f
 

   (14)  x @ y
                                                     Type: Expression Integer
--R 
--R
--R   (14)  x @ y
--R                                                     Type: Expression Integer
--E 14

--S 15 of 29
ff
 

          2
   (15)  x foo(y) @ y + x
                                                     Type: Expression Integer
--R 
--R
--R          2
--R   (15)  x foo(y) @ y + x
--R                                                     Type: Expression Integer
--E 15

--S 16 of 29
deleteProperty(bar, "%display")
 
   There are no library operations named deleteProperty 
      Use HyperDoc Browse or issue
                           )what op deleteProperty
      to learn if there is any operation containing " deleteProperty " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      deleteProperty with argument type(s) 
                                BasicOperator
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named deleteProperty 
--R      Use HyperDoc Browse or issue
--R                           )what op deleteProperty
--R      to learn if there is any operation containing " deleteProperty " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      deleteProperty with argument type(s) 
--R                                BasicOperator
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16

--S 17 of 29
f
 

   (16)  x @ y
                                                     Type: Expression Integer
--R 
--R
--R   (16)  x @ y
--R                                                     Type: Expression Integer
--E 17

--S 18 of 29
bar1 l == last l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 29
bar2 l == first l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 29
derivative(bar, [bar1, bar2]$(LIST(LIST(EXPR INT) -> EXPR INT)))
 
   Compiling function bar1 with type List Expression Integer -> 
      Expression Integer 
   Compiling function bar2 with type List Expression Integer -> 
      Expression Integer 

   (19)  bar
                                                          Type: BasicOperator
--R 
--R   Compiling function bar1 with type List Expression Integer -> 
--R      Expression Integer 
--R   Compiling function bar2 with type List Expression Integer -> 
--R      Expression Integer 
--R
--R   (19)  bar
--R                                                          Type: BasicOperator
--E 20

--S 21 of 29
[differentiate(f, x), differentiate(f, y)]
 

   (20)  [y,x]
                                                Type: List Expression Integer
--R 
--R
--R   (20)  [y,x]
--R                                                Type: List Expression Integer
--E 21

--S 22 of 29
[differentiate(ff, x), differentiate(ff, y)]
 

                    2          2     3    ,       2
   (21)  [(2x y + 3x )foo(y),(x y + x )foo (y) + x foo(y)]

                                                Type: List Expression Integer
--R 
--R
--R                    2          2     3    ,       2
--R   (21)  [(2x y + 3x )foo(y),(x y + x )foo (y) + x foo(y)]
--R
--R                                                Type: List Expression Integer
--E 22

--S 23 of 29
h := inv(x + f + g**2)
 

                  1
   (22)  -------------------
               2
         foo(x)  + x @ y + x
                                                     Type: Expression Integer
--R 
--R
--R                  1
--R   (22)  -------------------
--R               2
--R         foo(x)  + x @ y + x
--R                                                     Type: Expression Integer
--E 23

--S 24 of 29
isPower h
 

                     2
   (23)  [val= foo(x)  + x @ y + x,exponent= - 1]
           Type: Union(Record(val: Expression Integer,exponent: Integer),...)
--R 
--R
--R                     2
--R   (23)  [val= foo(x)  + x @ y + x,exponent= - 1]
--R           Type: Union(Record(val: Expression Integer,exponent: Integer),...)
--E 24

--S 25 of 29
y * g**2 * h
 

                      2
              y foo(x)
   (24)  -------------------
               2
         foo(x)  + x @ y + x
                                                     Type: Expression Integer
--R 
--R
--R                      2
--R              y foo(x)
--R   (24)  -------------------
--R               2
--R         foo(x)  + x @ y + x
--R                                                     Type: Expression Integer
--E 25

--S 26 of 29
isTimes %
 

                2            1
   (25)  [foo(x) ,y,-------------------]
                          2
                    foo(x)  + x @ y + x
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                2            1
--R   (25)  [foo(x) ,y,-------------------]
--R                          2
--R                    foo(x)  + x @ y + x
--R                                     Type: Union(List Expression Integer,...)
--E 26

--S 27 of 29
isPlus(denom(h)::EXPR(INT))
 

                2
   (26)  [foo(x) ,x @ y,x]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                2
--R   (26)  [foo(x) ,x @ y,x]
--R                                     Type: Union(List Expression Integer,...)
--E 27

--S 28 of 29
isExpt(inv(g**2), "foo")
 

   (27)  [var= foo(x),exponent= - 2]
    Type: Union(Record(var: Kernel Expression Integer,exponent: Integer),...)
--R 
--R
--R   (27)  [var= foo(x),exponent= - 2]
--R    Type: Union(Record(var: Kernel Expression Integer,exponent: Integer),...)
--E 28

--S 29 of 29
isExpt(inv(g**2), "bar")
 

   (28)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (28)  "failed"
--R                                                    Type: Union("failed",...)
--E 29
)spool 
 
Starts dribbling to multiple.output (2009/2/17, 17:55:27).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 8
draw(sin(x),x=0..2*%pi)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (1)  TwoDimensionalViewport: "sin x"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (1)  TwoDimensionalViewport: "sin x"
--R                                                 Type: TwoDimensionalViewport
--E 1

--S 2 of 8
v1 := %
 

   (2)  TwoDimensionalViewport: "sin x"
                                                 Type: TwoDimensionalViewport
--R 
--R
--R   (2)  TwoDimensionalViewport: "sin x"
--R                                                 Type: TwoDimensionalViewport
--E 2

--S 3 of 8
draw(cos(x),x=0..2*%pi,curveColor==light red())
 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (3)  TwoDimensionalViewport: "cos x"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %D with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (3)  TwoDimensionalViewport: "cos x"
--R                                                 Type: TwoDimensionalViewport
--E 3

--S 4 of 8
v2 := %
 

   (4)  TwoDimensionalViewport: "cos x"
                                                 Type: TwoDimensionalViewport
--R 
--R
--R   (4)  TwoDimensionalViewport: "cos x"
--R                                                 Type: TwoDimensionalViewport
--E 4

--S 5 of 8
graphs v1
 

   (5)
   [Graph with 1 point list, undefined, undefined, undefined, undefined,
    undefined, undefined, undefined, undefined]
                                     Type: Vector Union(GraphImage,undefined)
--R 
--R
--R   (5)
--R   [Graph with 1 point list, undefined, undefined, undefined, undefined,
--R    undefined, undefined, undefined, undefined]
--R                                     Type: Vector Union(GraphImage,undefined)
--E 5

--g1 := elt(graphs v1,1)::GraphImage
--S 6 of 8
g1 := getGraph(v1,1)
 

   (6)  Graph with 1 point list
                                                             Type: GraphImage
--R 
--R
--R   (6)  Graph with 1 point list
--R                                                             Type: GraphImage
--E 6

--S 7 of 8
putGraph(v2,g1,2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 8
makeViewport2D(v2)
 
   AXIOM2D data being transmitted to the viewport manager...

   (8)  TwoDimensionalViewport: "cos x"
                                                 Type: TwoDimensionalViewport
--R 
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (8)  TwoDimensionalViewport: "cos x"
--R                                                 Type: TwoDimensionalViewport
--E 8
)spool 
 
Starts dribbling to bug100.output (2009/2/17, 17:43:59).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 1
integrate((z^a+1)^b,z)
 

           z
         ++     a     b
   (1)   |   (%I  + 1) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           z
--R         ++     a     b
--R   (1)   |   (%I  + 1) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 1
)spool 
 
Starts dribbling to bini.output (2009/2/17, 17:43:54).
)set message test on
 
)set message type off
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

)clear all
 
   All user variables and function definitions have been cleared.

--S 1
t1:=2*y^2*(y^2+x^2)+(b^2-3*a^2)*y^2-2*b*y^2*(x+y)+2*a^2*b*(y+x)_
    -a^2*x^2+a^2*(a^2-b^2)
 

   (1)
     4       3      2           2     2  2     2       2 2     2       2 2    4
   2y  - 2b y  + (2x  - 2b x + b  - 3a )y  + 2a b y - a x  + 2a b x - a b  + a
--R 
--R
--R   (1)
--R     4       3      2           2     2  2     2       2 2     2       2 2    4
--R   2y  - 2b y  + (2x  - 2b x + b  - 3a )y  + 2a b y - a x  + 2a b x - a b  + a
--E 1

--S 2
t2:=4*y^3+4*y*(y^2+x^2)-2*b*y^2-4*b*y*(y+x)+2*(b^2-3*a^2)*y+2*a^2*b
 

          3       2      2            2     2       2
   (2)  8y  - 6b y  + (4x  - 4b x + 2b  - 6a )y + 2a b
--R 
--R
--R          3       2      2            2     2       2
--R   (2)  8y  - 6b y  + (4x  - 4b x + 2b  - 6a )y + 2a b
--E 2

--S 3
t3:=4*x*y^2-2*b*y^2-2*a^2*x+2*a^2*b
 

                  2     2      2
   (3)  (4x - 2b)y  - 2a x + 2a b
--R 
--R
--R                  2     2      2
--R   (3)  (4x - 2b)y  - 2a x + 2a b
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4
t1:=8*x^2-2*x*y-6*x*z+3*x+3*y^2-7*y*z+10*y+10*z^2-8*z-4
 

           2                        2                    2
   (1)  10z  + (- 7y - 6x - 8)z + 3y  + (- 2x + 10)y + 8x  + 3x - 4
--R 
--R
--R           2                        2                    2
--R   (1)  10z  + (- 7y - 6x - 8)z + 3y  + (- 2x + 10)y + 8x  + 3x - 4
--E 4

--S 5
t2:=10*x^2-2*x*y+6*x*z-6*x+9*y^2-y*z-4*y-2*z^2+5*z-9
 

            2                       2                    2
   (2)  - 2z  + (- y + 6x + 5)z + 9y  + (- 2x - 4)y + 10x  - 6x - 9
--R 
--R
--R            2                       2                    2
--R   (2)  - 2z  + (- y + 6x + 5)z + 9y  + (- 2x - 4)y + 10x  - 6x - 9
--E 5

--S 6
t3:=5*x^2+8*x*y+4*x*z+8*x+9*y^2-6*y*z+2*y-z^2-7*x+5
 

           2                    2                 2
   (3)  - z  + (- 6y + 4x)z + 9y  + (8x + 2)y + 5x  + x + 5
--R 
--R
--R           2                    2                 2
--R   (3)  - z  + (- 6y + 4x)z + 9y  + (8x + 2)y + 5x  + x + 5
--E 6


)clear all
 
   All user variables and function definitions have been cleared.
--S 7
t1:=2*(b-1)^2 + 2*(q-p*q+p^2) + c^2*(q-1)^2 -2*b*q + 2*c*d*(1-q)*(q-p)_
    +2*b*p*q*d*(d-c) + b^2*d^2*(1-2*p) + 2*b*d^2*(p-q) + 2*b*d*c*(p-1)_
    +2*b*p*q*(c+1) + (b^2 - 2*b)*p^2*d^2 + 2*b^2*p^2 + 4*b*(1-b)*p_
    + d^2*(p-1)^2
 

   (1)
                2  2
     (- 2c d + c )q
   + 
           2                                         2            2
     ((2b d  + (- 2b + 2)c d + 2b c + 2b - 2)p - 2b d  + 2c d - 2c  - 2b + 2)q
   + 
        2           2     2      2
     ((b  - 2b + 1)d  + 2b  + 2)p
   + 
           2           2                   2            2      2             2
     ((- 2b  + 2b - 2)d  + (2b - 2)c d - 4b  + 4b)p + (b  + 1)d  - 2b c d + c
   + 
       2
     2b  - 4b + 2
--R 
--R
--R   (1)
--R                2  2
--R     (- 2c d + c )q
--R   + 
--R           2                                         2            2
--R     ((2b d  + (- 2b + 2)c d + 2b c + 2b - 2)p - 2b d  + 2c d - 2c  - 2b + 2)q
--R   + 
--R        2           2     2      2
--R     ((b  - 2b + 1)d  + 2b  + 2)p
--R   + 
--R           2           2                   2            2      2             2
--R     ((- 2b  + 2b - 2)d  + (2b - 2)c d - 4b  + 4b)p + (b  + 1)d  - 2b c d + c
--R   + 
--R       2
--R     2b  - 4b + 2
--E 7

--S 8
t2:=d*(2*p+1)*(q-p) + c*(p+2)*(1-q) + b*(b-2)*d + b*(1-2*b)*p*d_
    +b*c*(q+p-p*q-1) + b*(b+1)*p^2*d
 

   (2)
                                              2            2
     ((2d + (- b - 1)c)p + d + (b - 2)c)q + (b  + b - 2)d p
   + 
           2                            2
     ((- 2b  + b - 1)d + (b + 1)c)p + (b  - 2b)d + (- b + 2)c
--R 
--R
--R   (2)
--R                                              2            2
--R     ((2d + (- b - 1)c)p + d + (b - 2)c)q + (b  + b - 2)d p
--R   + 
--R           2                            2
--R     ((- 2b  + b - 1)d + (b + 1)c)p + (b  - 2b)d + (- b + 2)c
--E 8

--S 9
t3:=-b^2*(p-1)^2 + 2*p*(p-q) - 2*(q-1)
 

                          2      2     2     2
   (3)  (- 2p - 2)q + (- b  + 2)p  + 2b p - b  + 2
--R 
--R
--R                          2      2     2     2
--R   (3)  (- 2p - 2)q + (- b  + 2)p  + 2b p - b  + 2
--E 9

--S 10
t4:=b^2 + 4*(p-q^2) + 3*c^2*(q-1)^2 - 3*d^2*(p-q)^2 + 3*b^2*d^2*(p-1)^2_
    +b^2*p*(p-2) + 6*b*d*c*(p+q+q*p-1)
 

   (4)
          2     2      2       2                         2
     (- 3d  + 3c  - 4)q  + ((6d  + 6b c d)p + 6b c d - 6c )q
   + 
         2      2    2  2        2 2              2           2 2              2
     ((3b  - 3)d  + b )p  + (- 6b d  + 6b c d - 2b  + 4)p + 3b d  - 6b c d + 3c
   + 
      2
     b
--R 
--R
--R   (4)
--R          2     2      2       2                         2
--R     (- 3d  + 3c  - 4)q  + ((6d  + 6b c d)p + 6b c d - 6c )q
--R   + 
--R         2      2    2  2        2 2              2           2 2              2
--R     ((3b  - 3)d  + b )p  + (- 6b d  + 6b c d - 2b  + 4)p + 3b d  - 6b c d + 3c
--R   + 
--R      2
--R     b
--E 10


)clear all
 
   All user variables and function definitions have been cleared.

--S 11
t1:=a*x^2+b*x*y+c*x+d*y^2+e*y+f
 

           2                   2
   (1)  d y  + (b x + e)y + a x  + c x + f
--R 
--R
--R           2                   2
--R   (1)  d y  + (b x + e)y + a x  + c x + f
--E 11

--S 12
t2:=b*x^2+4*d*x*y+2*e*x+g*y^2+h*y+k
 

           2                    2
   (2)  g y  + (4d x + h)y + b x  + 2e x + k
--R 
--R
--R           2                    2
--R   (2)  g y  + (4d x + h)y + b x  + 2e x + k
--E 12

)clear all
 
   All user variables and function definitions have been cleared.

--S 13
t1:=x^2+a*y*z+d*x+g
 

                 2
   (1)  a y z + x  + d x + g
--R 
--R
--R                 2
--R   (1)  a y z + x  + d x + g
--E 13

--S 14
t2:=y^2+b*z*x+e*y+h
 

                 2
   (2)  b x z + y  + e y + h
--R 
--R
--R                 2
--R   (2)  b x z + y  + e y + h
--E 14

--S 15
t3:=z^2+c*x*y+f*z+k
 

         2
   (3)  z  + f z + c x y + k
--R 
--R
--R         2
--R   (3)  z  + f z + c x y + k
--E 15

)clear all
 
   All user variables and function definitions have been cleared.

--S 16
t1:=(x^2-A)^2 + (x^3+b*x-B)*(x^3+b*x-B-a)^2
 

   (1)
      9       7               6     2 5                      4
     x  + 3b x  + (- 2a - 3B)x  + 3b x  + ((- 4a - 6B)b + 1)x
   + 
       3    2            2  3                2       2     2            2
     (b  + a  + 4B a + 3B )x  + ((- 2a - 3B)b  - 2A)x  + (a  + 4B a + 3B )b x
   + 
          2     2     3    2
     - B a  - 2B a - B  + A
--R 
--R
--R   (1)
--R      9       7               6     2 5                      4
--R     x  + 3b x  + (- 2a - 3B)x  + 3b x  + ((- 4a - 6B)b + 1)x
--R   + 
--R       3    2            2  3                2       2     2            2
--R     (b  + a  + 4B a + 3B )x  + ((- 2a - 3B)b  - 2A)x  + (a  + 4B a + 3B )b x
--R   + 
--R          2     2     3    2
--R     - B a  - 2B a - B  + A
--E 16

--S 17
t2:=4*x*(x^2-A)+(3*x^2+b)*(x^3+b*x-B-a)*(3*(x^3+b*x-B)-a)
 

   (2)
       8        6                 5      2 4                        3
     9x  + 21b x  + (- 12a - 18B)x  + 15b x  + ((- 16a - 24B)b + 4)x
   + 
        3     2             2  2                2            2            2
     (3b  + 3a  + 12B a + 9B )x  + ((- 4a - 6B)b  - 4A)x + (a  + 4B a + 3B )b
--R 
--R
--R   (2)
--R       8        6                 5      2 4                        3
--R     9x  + 21b x  + (- 12a - 18B)x  + 15b x  + ((- 16a - 24B)b + 4)x
--R   + 
--R        3     2             2  2                2            2            2
--R     (3b  + 3a  + 12B a + 9B )x  + ((- 4a - 6B)b  - 4A)x + (a  + 4B a + 3B )b
--E 17

--S 18
t3:=12*x^2-4*A+6*x*(x^3+b*x-B-a)^2+4*(3*x^2+b)^2*(x^3+b*x-B-a)_
    +2*(x^3+b*x-B)*(3*x^2+b)^2+12*x*(x^3+b*x-B)*(x^3+b*x-B-a)
 

   (3)
        7         5                 4      2 3                         2
     72x  + 126b x  + (- 60a - 90B)x  + 60b x  + ((- 48a - 72B)b + 12)x
   + 
        3     2              2                 2
     (6b  + 6a  + 24B a + 18B )x + (- 4a - 6B)b  - 4A
--R 
--R
--R   (3)
--R        7         5                 4      2 3                         2
--R     72x  + 126b x  + (- 60a - 90B)x  + 60b x  + ((- 48a - 72B)b + 12)x
--R   + 
--R        3     2              2                 2
--R     (6b  + 6a  + 24B a + 18B )x + (- 4a - 6B)b  - 4A
--E 18

--S 19
t4:=24*x+6*(x^3+b*x-B-a)^2+72*x*(x^3+b*x-B-a)*(3*x^2+b)+6*(3*x^2+b)^3_
    +36*x*(x^3+b*x-B)*(3*x^2+b)+12*(x^3+b*x-B)*(x^3+b*x-B-a)
 

   (4)
         6         4                   3       2 2
     504x  + 630b x  + (- 240a - 360B)x  + 180b x  + ((- 96a - 144B)b + 24)x
   + 
       3     2              2
     6b  + 6a  + 24B a + 18B
--R 
--R
--R   (4)
--R         6         4                   3       2 2
--R     504x  + 630b x  + (- 240a - 360B)x  + 180b x  + ((- 96a - 144B)b + 24)x
--R   + 
--R       3     2              2
--R     6b  + 6a  + 24B a + 18B
--E 19

)clear all
 
   All user variables and function definitions have been cleared.

--S 20
t1:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1
 

                    4        2
   (1)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--R 
--R
--R                    4        2
--R   (1)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--E 20

--S 21
t2:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2
 

                    4        2
   (2)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--R 
--R
--R                    4        2
--R   (2)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--E 21

--S 22
t3:=2*z2+6*a*y2+20*y2^3+2*c
 

                  3
   (3)  2z2 + 20y2  + 6a y2 + 2c
--R 
--R
--R                  3
--R   (3)  2z2 + 20y2  + 6a y2 + 2c
--E 22

--S 23
t4:=3*z1^2+y1^2+b
 

           2     2
   (4)  3z1  + y1  + b
--R 
--R
--R           2     2
--R   (4)  3z1  + y1  + b
--E 23

--S 24
t5:=3*z2^2+y2^2+b
 

           2     2
   (5)  3z2  + y2  + b
--R 
--R
--R           2     2
--R   (5)  3z2  + y2  + b
--E 24

)clear all
 
   All user variables and function definitions have been cleared.

--S 25
t1:=3*z1^2+y1^2+b
 

           2     2
   (1)  3z1  + y1  + b
--R 
--R
--R           2     2
--R   (1)  3z1  + y1  + b
--E 25

--S 26
t2:=3*z1^2+y2^2+b
 

           2     2
   (2)  3z1  + y2  + b
--R 
--R
--R           2     2
--R   (2)  3z1  + y2  + b
--E 26

--S 27
t3:=3*z3^2+y3^2+b
 

           2     2
   (3)  3z3  + y3  + b
--R 
--R
--R           2     2
--R   (3)  3z3  + y3  + b
--E 27

--S 28
t4:=y1^2*z1+2*a*y1^3+4*y1^5+c*y1^2-z1^3-b*z1-y2^2*z2-2*a*y2^3_
    -4*y2^5-c*y2^2+z2^3+b*z2
 

   (4)
       3        2            3      2             5        3       2      5
     z2  + (- y2  + b)z2 - z1  + (y1  - b)z1 - 4y2  - 2a y2  - c y2  + 4y1
   + 
          3       2
     2a y1  + c y1
--R 
--R
--R   (4)
--R       3        2            3      2             5        3       2      5
--R     z2  + (- y2  + b)z2 - z1  + (y1  - b)z1 - 4y2  - 2a y2  - c y2  + 4y1
--R   + 
--R          3       2
--R     2a y1  + c y1
--E 28

--S 29
t5:=y2^2*z2+2*a*y2^3+4*y2^5+c*y2^2-z2^3-b*z2-y3^2*z3-2*a*y3^3_
    -4*y3^5-c*y3^2+z3^3+b*z3
 

   (5)
       3        2            3      2             5        3       2      5
     z3  + (- y3  + b)z3 - z2  + (y2  - b)z2 - 4y3  - 2a y3  - c y3  + 4y2
   + 
          3       2
     2a y2  + c y2
--R 
--R
--R   (5)
--R       3        2            3      2             5        3       2      5
--R     z3  + (- y3  + b)z3 - z2  + (y2  - b)z2 - 4y3  - 2a y3  - c y3  + 4y2
--R   + 
--R          3       2
--R     2a y2  + c y2
--E 29

--S 30
t6:=y3^2*z3+2*a*y3^3+4*y3^5+c*y3^2-z3^3-b*z3-y1^2*z1-2*a*y1^3_
    -4*y1^5-c*y1^2+z1^3+b*z1
 

   (6)
         3      2            3        2             5        3       2      5
     - z3  + (y3  - b)z3 + z1  + (- y1  + b)z1 + 4y3  + 2a y3  + c y3  - 4y1
   + 
            3       2
     - 2a y1  - c y1
--R 
--R
--R   (6)
--R         3      2            3        2             5        3       2      5
--R     - z3  + (y3  - b)z3 + z1  + (- y1  + b)z1 + 4y3  + 2a y3  + c y3  - 4y1
--R   + 
--R            3       2
--R     - 2a y1  - c y1
--E 30

)clear all
 
   All user variables and function definitions have been cleared.

--S 31
t1:=3*z1^2+y1^2+b
 

           2     2
   (1)  3z1  + y1  + b
--R 
--R
--R           2     2
--R   (1)  3z1  + y1  + b
--E 31

--S 32
t2:=3*z2^2+y2^2+b
 

           2     2
   (2)  3z2  + y2  + b
--R 
--R
--R           2     2
--R   (2)  3z2  + y2  + b
--E 32

--S 33
t3:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1
 

                    4        2
   (3)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--R 
--R
--R                    4        2
--R   (3)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--E 33

--S 34
t4:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2
 

                    4        2
   (4)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--R 
--R
--R                    4        2
--R   (4)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--E 34

--S 35
t5:=x*y1+z1^3+y1^2*z1+a*y1^3+y1^5+b*z1+c*y1^2-x*y2-z2^3-y2^2*z2_
    -a*y2^3-y2^5-b*z2-c*y2^2
 

   (5)
         3        2            3      2            5       3       2
     - z2  + (- y2  - b)z2 + z1  + (y1  + b)z1 - y2  - a y2  - c y2  - x y2
   + 
       5       3       2
     y1  + a y1  + c y1  + x y1
--R 
--R
--R   (5)
--R         3        2            3      2            5       3       2
--R     - z2  + (- y2  - b)z2 + z1  + (y1  + b)z1 - y2  - a y2  - c y2  - x y2
--R   + 
--R       5       3       2
--R     y1  + a y1  + c y1  + x y1
--E 35

--S 36
t6:=(6*z1^2+18*a*z1*y1+6*y1-y1^3*z1+6*c*y1^2*z1-2*y1^2)_
    *(3*z2^2*y2+9*a*y2^2*z2+45*y2^4*z2-y2^3-3*x*z2+b*y2)_
    -(6*z2^2+18*a*z2*y2+60*y2^3*z2+6*c*y2^2*z2-2*y2^2)_
    *(3*z1^2*y1+9*a*y1^2*z1+45*y1^4*z1-y1^3-3*x*z1+b*y1)
 

   (6)
                        2
         (18y2 - 18y1)z1
       + 
                3         2                    4         2
         ((- 3y1  + 18c y1  + 54a y1)y2 - 270y1  - 54a y1  + 18x)z1
       + 
               2                3
         (- 6y1  + 18y1)y2 + 6y1  - 6b y1
    *
         2
       z2
   + 
               4           3                     2                     2
         (270y2  - 180y1 y2  + (- 18c y1 + 54a)y2  - 54a y1 y2 - 18x)z1
       + 
                    3          2             4
             (- 45y1  + 270c y1  + 810a y1)y2
           + 
                      4          2          3
             (- 2700y1  - 540a y1  + 180x)y2
           + 
                       4        3       2             2
             (- 270c y1  - 9a y1  + 162a y1 + 18c x)y2
           + 
                       4       2  2                   3           2
             (- 810a y1  - 162a y1  + 54a x)y2 + 3x y1  - 18c x y1  - 54a x y1
        *
           z1
       + 
                2           4        3            3
         (- 90y1  + 270y1)y2  + (60y1  - 60b y1)y2
       + 
               3         2                      2          3
         (6c y1  - 18a y1  + (- 6b c + 54a)y1)y2  + (18a y1  - 18a b y1)y2
       + 
              2
         6x y1  - 18x y1
    *
       z2
   + 
           3         2           2
     (- 6y2  + 6y1 y2  + 6b y2)z1
   + 
            3        2            3        4         2        2
         (y1  - 6c y1  - 18a y1)y2  + (90y1  + 18a y1  - 6x)y2
       + 
                3          2
         (- b y1  + 6b c y1  + 18a b y1)y2
    *
       z1
   + 
         2         3         3           2           2
     (2y1  - 6y1)y2  + (- 2y1  + 2b y1)y2  + (- 2b y1  + 6b y1)y2
--R 
--R
--R   (6)
--R                        2
--R         (18y2 - 18y1)z1
--R       + 
--R                3         2                    4         2
--R         ((- 3y1  + 18c y1  + 54a y1)y2 - 270y1  - 54a y1  + 18x)z1
--R       + 
--R               2                3
--R         (- 6y1  + 18y1)y2 + 6y1  - 6b y1
--R    *
--R         2
--R       z2
--R   + 
--R               4           3                     2                     2
--R         (270y2  - 180y1 y2  + (- 18c y1 + 54a)y2  - 54a y1 y2 - 18x)z1
--R       + 
--R                    3          2             4
--R             (- 45y1  + 270c y1  + 810a y1)y2
--R           + 
--R                      4          2          3
--R             (- 2700y1  - 540a y1  + 180x)y2
--R           + 
--R                       4        3       2             2
--R             (- 270c y1  - 9a y1  + 162a y1 + 18c x)y2
--R           + 
--R                       4       2  2                   3           2
--R             (- 810a y1  - 162a y1  + 54a x)y2 + 3x y1  - 18c x y1  - 54a x y1
--R        *
--R           z1
--R       + 
--R                2           4        3            3
--R         (- 90y1  + 270y1)y2  + (60y1  - 60b y1)y2
--R       + 
--R               3         2                      2          3
--R         (6c y1  - 18a y1  + (- 6b c + 54a)y1)y2  + (18a y1  - 18a b y1)y2
--R       + 
--R              2
--R         6x y1  - 18x y1
--R    *
--R       z2
--R   + 
--R           3         2           2
--R     (- 6y2  + 6y1 y2  + 6b y2)z1
--R   + 
--R            3        2            3        4         2        2
--R         (y1  - 6c y1  - 18a y1)y2  + (90y1  + 18a y1  - 6x)y2
--R       + 
--R                3          2
--R         (- b y1  + 6b c y1  + 18a b y1)y2
--R    *
--R       z1
--R   + 
--R         2         3         3           2           2
--R     (2y1  - 6y1)y2  + (- 2y1  + 2b y1)y2  + (- 2b y1  + 6b y1)y2
--E 36

)clear all
 
   All user variables and function definitions have been cleared.

--S 37
t1:=x4*x13 + x5*x14 + x6*(1-x13-x14)
 

   (1)  (- x14 - x13 + 1)x6 + x14 x5 + x13 x4
--R 
--R
--R   (1)  (- x14 - x13 + 1)x6 + x14 x5 + x13 x4
--E 37

--S 38
t2:=x4*x15 + x5*x16 - x6*(x15+x16)
 

   (2)  (- x16 - x15)x6 + x16 x5 + x15 x4
--R 
--R
--R   (2)  (- x16 - x15)x6 + x16 x5 + x15 x4
--E 38

--S 39
t3:=x7*x13 + x8*x14 + x9*(1-x13-x14)
 

   (3)  (- x14 - x13 + 1)x9 + x14 x8 + x13 x7
--R 
--R
--R   (3)  (- x14 - x13 + 1)x9 + x14 x8 + x13 x7
--E 39

--S 40
t4:=x7*x15 + x8*x16 - x9*(x15+x16)-1
 

   (4)  (- x16 - x15)x9 + x16 x8 + x15 x7 - 1
--R 
--R
--R   (4)  (- x16 - x15)x9 + x16 x8 + x15 x7 - 1
--E 40

--S 41
t5:=x10*x13 + x11*x14 + x12*(1-x13-x14)
 

   (5)  (- x12 + x11)x14 + (- x12 + x10)x13 + x12
--R 
--R
--R   (5)  (- x12 + x11)x14 + (- x12 + x10)x13 + x12
--E 41

--S 42
t6:=x10*x15 + x11*x16 - x12*(x15+x16)
 

   (6)  (- x12 + x11)x16 + (- x12 + x10)x15
--R 
--R
--R   (6)  (- x12 + x11)x16 + (- x12 + x10)x15
--E 42

--S 43
t7:=x1*x13 + x2*x14 + x3*(1-x13-x14)
 

   (7)  (- x14 - x13 + 1)x3 + x14 x2 + x1 x13
--R 
--R
--R   (7)  (- x14 - x13 + 1)x3 + x14 x2 + x1 x13
--E 43

--S 44
t8:=x1*x15 + x2*x16 - x3*(x15+x16)
 

   (8)  (- x16 - x15)x3 + x16 x2 + x1 x15
--R 
--R
--R   (8)  (- x16 - x15)x3 + x16 x2 + x1 x15
--E 44

--S 45
t9:=x1*x4*x13 + x2*x5*x14 + x3*x6*(1-x13-x14)-1
 

   (9)  (- x14 - x13 + 1)x3 x6 + x14 x2 x5 + x1 x13 x4 - 1
--R 
--R
--R   (9)  (- x14 - x13 + 1)x3 x6 + x14 x2 x5 + x1 x13 x4 - 1
--E 45

--S 46
t10:=x1*x4*x15 + x2*x5*x16 - x3*x6*(x15+x16)
 

   (10)  (- x16 - x15)x3 x6 + x16 x2 x5 + x1 x15 x4
--R 
--R
--R   (10)  (- x16 - x15)x3 x6 + x16 x2 x5 + x1 x15 x4
--E 46

--S 47
t11:=x1*x7*x13 + x2*x8*x14 + x3*x9*(1-x13-x14)
 

   (11)  (- x14 - x13 + 1)x3 x9 + x14 x2 x8 + x1 x13 x7
--R 
--R
--R   (11)  (- x14 - x13 + 1)x3 x9 + x14 x2 x8 + x1 x13 x7
--E 47

--S 48
t12:=x1*x7*x15 + x2*x8*x16 - x3*x9*(x15+x16)
 

   (12)  (- x16 - x15)x3 x9 + x16 x2 x8 + x1 x15 x7
--R 
--R
--R   (12)  (- x16 - x15)x3 x9 + x16 x2 x8 + x1 x15 x7
--E 48

--S 49
t13:=x1*x10*x13 + x2*x11*x14 + x3*x12*(1-x13-x14)
 

   (13)  (- x12 x14 - x12 x13 + x12)x3 + x11 x14 x2 + x1 x10 x13
--R 
--R
--R   (13)  (- x12 x14 - x12 x13 + x12)x3 + x11 x14 x2 + x1 x10 x13
--E 49

--S 50
t14:=x1*x10*x15 + x2*x11*x16 - x3*x12*(x15+x16)-1
 

   (14)  (- x12 x16 - x12 x15)x3 + x11 x16 x2 + x1 x10 x15 - 1
--R 
--R
--R   (14)  (- x12 x16 - x12 x15)x3 + x11 x16 x2 + x1 x10 x15 - 1
--E 50

)clear all
 
   All user variables and function definitions have been cleared.

--S 51
t1:=2*x^2-2*y^2+2*z^2-2*t^2-1
 

          2     2     2     2
   (1)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          2     2     2     2
--R   (1)  2z  - 2y  + 2x  - 2t  - 1
--E 51

--S 52
t2:=2*x^3-2*y^3+2*z^3-2*t^3-1
 

          3     3     3     3
   (2)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          3     3     3     3
--R   (2)  2z  - 2y  + 2x  - 2t  - 1
--E 52

--S 53
t3:=2*x^4-2*y^4+2*z^4-2*t^4-1
 

          4     4     4     4
   (3)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          4     4     4     4
--R   (3)  2z  - 2y  + 2x  - 2t  - 1
--E 53

--S 54
t4:=2*x^5-2*y^5+2*z^5-2*t^5-1
 

          5     5     5     5
   (4)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          5     5     5     5
--R   (4)  2z  - 2y  + 2x  - 2t  - 1
--E 54

)clear all
 
   All user variables and function definitions have been cleared.

--S 55
t1:=2*x^2-2*y^2+2*z^2-2*t^2+2*u^2-1
 

          2     2     2     2     2
   (1)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          2     2     2     2     2
--R   (1)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 55

--S 56
t2:=2*x^3-2*y^3+2*z^3-2*t^3+2*u^3-1
 

          3     3     3     3     3
   (2)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          3     3     3     3     3
--R   (2)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 56

--S 57
t3:=2*x^4-2*y^4+2*z^4-2*t^4+2*u^4-1
 

          4     4     4     4     4
   (3)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          4     4     4     4     4
--R   (3)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 57

--S 58
t4:=2*x^5-2*y^5+2*z^5-2*t^5+2*u^5-1
 

          5     5     5     5     5
   (4)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          5     5     5     5     5
--R   (4)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 58

--S 59
t5:=2*x^6-2*y^6+2*z^6-2*t^6+2*u^6-1
 

          6     6     6     6     6
   (5)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          6     6     6     6     6
--R   (5)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 59

)clear all
 
   All user variables and function definitions have been cleared.

--S 60
t1:=y*w-1/2*z*w+t*w
 

          1
   (1)  - - w z + w y + t w
          2
--R 
--R
--R          1
--R   (1)  - - w z + w y + t w
--R          2
--E 60

--S 61
t2:=-2/7*u*w^2+10/7*v*w^2-20/7*w^3+t*u-5*t*v+10*t*w
 

          20  3    10     2    2
   (2)  - -- w  + (-- v - - u)w  + 10t w - 5t v + t u
           7        7     7
--R 
--R
--R          20  3    10     2    2
--R   (2)  - -- w  + (-- v - - u)w  + 10t w - 5t v + t u
--R           7        7     7
--E 61

--S 62
t3:=2/7*y*w^2-2/7*z*w^2+6/7*t*w^2-y*t+z*t-3*t^2
 

           2  2          2  2         6    2     2
   (3)  (- - w  + t)z + (- w  - t)y + - t w  - 3t
           7             7            7
--R 
--R
--R           2  2          2  2         6    2     2
--R   (3)  (- - w  + t)z + (- w  - t)y + - t w  - 3t
--R           7             7            7
--E 62

--S 63
t4:=-2*v^3+4*u*v*w+5*v^2*w-6*u*w^2-7*v*w^2+15*w^3+42*y*v_
    -14*z*v-63*y*w+21*z*w-42*t*w+147*x
 

   (4)
                                               3               2
     (21w - 14v)z + (- 63w + 42v)y + 147x + 15w  + (- 7v - 6u)w
   + 
        2                    3
     (5v  + 4u v - 42t)w - 2v
--R 
--R
--R   (4)
--R                                               3               2
--R     (21w - 14v)z + (- 63w + 42v)y + 147x + 15w  + (- 7v - 6u)w
--R   + 
--R        2                    3
--R     (5v  + 4u v - 42t)w - 2v
--E 63

--S 64
t5:=-9/7*u*w^3+45/7*v*w^3-135/7*w^4+2*z*v^2-2*t*v^2-4*z*u*w+10*t*u*w_
    -2*z*v*w-28*t*v*w+4*z*w^2+86*t*w^2-42*y*z+14*z^2+42*y*t_
    -14*z*t-21*x*u+105*x*v-315*x*w
 

   (5)
        2              2                    2
     14z  + (- 42y + 4w  + (- 2v - 4u)w + 2v  - 14t)z + 42t y
   + 
                              135  4    45     9    3        2
     (- 315w + 105v - 21u)x - --- w  + (-- v - - u)w  + 86t w
                               7         7     7
   + 
                              2
     (- 28t v + 10t u)w - 2t v
--R 
--R
--R   (5)
--R        2              2                    2
--R     14z  + (- 42y + 4w  + (- 2v - 4u)w + 2v  - 14t)z + 42t y
--R   + 
--R                              135  4    45     9    3        2
--R     (- 315w + 105v - 21u)x - --- w  + (-- v - - u)w  + 86t w
--R                               7         7     7
--R   + 
--R                              2
--R     (- 28t v + 10t u)w - 2t v
--E 64

--S 65
t6:=6/7*y*w^3-9/7*z*w^3+36/7*t*w^3-2*x*v^2-4*y*t*w+6*z*t*w_
    -24*t^2*w+4*x*u*w+2*x*v*w-4*x*w^2+56*x*y-35*x*z+84*x*t
 

   (6)
              9  3                   6  3
     (- 35x - - w  + 6t w)z + (56x + - w  - 4t w)y
              7                      7
   + 
          2                  2           36    3      2
     (- 4w  + (2v + 4u)w - 2v  + 84t)x + -- t w  - 24t w
                                          7
--R 
--R
--R   (6)
--R              9  3                   6  3
--R     (- 35x - - w  + 6t w)z + (56x + - w  - 4t w)y
--R              7                      7
--R   + 
--R          2                  2           36    3      2
--R     (- 4w  + (2v + 4u)w - 2v  + 84t)x + -- t w  - 24t w
--R                                          7
--E 65

--S 66
t7:=2*u*v*w-6*v^2*w-u*w^2+13*v*w^2-5*w^3+14*y*w-28*t*w
 

                  3             2        2
   (7)  14w y - 5w  + (13v - u)w  + (- 6v  + 2u v - 28t)w
--R 
--R
--R                  3             2        2
--R   (7)  14w y - 5w  + (13v - u)w  + (- 6v  + 2u v - 28t)w
--E 66

--S 67
t8:=u^2*w-3*u*v*w+5*u*w^2+14*y*w-28*t*w
 

                    2              2
   (8)  14w y + 5u w  + (- 3u v + u  - 28t)w
--R 
--R
--R                    2              2
--R   (8)  14w y + 5u w  + (- 3u v + u  - 28t)w
--E 67

--S 68
t9:=-2*z*u*w-2*t*u*w+4*y*v*w+6*z*v*w-2*t*v*w-16*y*w^2_
    -10*z*w^2+22*t*w^2+42*x*w
 

   (9)
         2                        2                         2
   (- 10w  + (6v - 2u)w)z + (- 16w  + 4v w)y + 42w x + 22t w  + (- 2t v - 2t u)w
--R 
--R
--R   (9)
--R         2                        2                         2
--R   (- 10w  + (6v - 2u)w)z + (- 16w  + 4v w)y + 42w x + 22t w  + (- 2t v - 2t u)w
--E 68

--S 69
t10:=28/3*y*u*w+8/3*z*u*w-20/3*t*u*w-88/3*y*v*w-8*z*v*w_
    +68/3*t*v*w+52*y*w^2+40/3*z*w^2-44*t*w^2-84*x*w
 

   (10)
      40  2           8             2      88     28                      2
     (-- w  + (- 8v + - u)w)z + (52w  + (- -- v + -- u)w)y - 84w x - 44t w
       3              3                     3      3
   + 
      68       20
     (-- t v - -- t u)w
       3        3
--R 
--R
--R   (10)
--R      40  2           8             2      88     28                      2
--R     (-- w  + (- 8v + - u)w)z + (52w  + (- -- v + -- u)w)y - 84w x - 44t w
--R       3              3                     3      3
--R   + 
--R      68       20
--R     (-- t v - -- t u)w
--R       3        3
--E 69

--S 70
t11:=-4*y*z*w+10*y*t*w+8*z*t*w-20*t^2*w+12*x*u*w-30*x*v*w+15*x*w^2
 

                                          2                         2
   (11)  (- 4w y + 8t w)z + 10t w y + (15w  + (- 30v + 12u)w)x - 20t w
--R 
--R
--R                                          2                         2
--R   (11)  (- 4w y + 8t w)z + 10t w y + (15w  + (- 30v + 12u)w)x - 20t w
--E 70

--S 71
t12:=-y^2*w+1/2*y*z*w+y*t*w-z*t*w+2*t^2*w-3*x*u*w+6*x*v*w-3*x*w^2
 

          1                  2                2                    2
   (12)  (- w y - t w)z - w y  + t w y + (- 3w  + (6v - 3u)w)x + 2t w
          2
--R 
--R
--R          1                  2                2                    2
--R   (12)  (- w y - t w)z - w y  + t w y + (- 3w  + (6v - 3u)w)x + 2t w
--R          2
--E 71

--S 72
t13:=8*x*y*w-4*x*z*w+8*x*t*w
 

   (13)  - 4w x z + 8w x y + 8t w x
--R 
--R
--R   (13)  - 4w x z + 8w x y + 8t w x
--E 72

)clear all
 
   All user variables and function definitions have been cleared.

--S 73
t1:=35*y^4-30*x*y^2-210*y^2*z+3*x^2+30*x*z-105*z^2+140*y*t-21*u
 

              2          2              4        2              2
   (1)  - 105z  + (- 210y  + 30x)z + 35y  - 30x y  + 140t y + 3x  - 21u
--R 
--R
--R              2          2              4        2              2
--R   (1)  - 105z  + (- 210y  + 30x)z + 35y  - 30x y  + 140t y + 3x  - 21u
--E 73

--S 74
t2:=5*x*y^3-140*y^3*z-3*x^2*y+45*x*y*z-420*y*z^2+210*y^2*t_
    -25*x*t+70*z*t+126*y*u
 

   (2)
             2          3                       3         2        2
     - 420y z  + (- 140y  + 45x y + 70t)z + 5x y  + 210t y  + (- 3x  + 126u)y
   + 
     - 25t x
--R 
--R
--R   (2)
--R             2          3                       3         2        2
--R     - 420y z  + (- 140y  + 45x y + 70t)z + 5x y  + 210t y  + (- 3x  + 126u)y
--R   + 
--R     - 25t x
--E 74

)clear all
 
   All user variables and function definitions have been cleared.

--S 75
t1:=6*x*y^2*t-x^2*z*t-6*x*y*z*t+3*x*z^2*t-2*z^3*t-6*x*y^2+6*x*y*z-2*x*z^2
 

              3              2                       2                2
   (1)  - 2t z  + (3t - 2)x z  + ((- 6t + 6)x y - t x )z + (6t - 6)x y
--R 
--R
--R              3              2                       2                2
--R   (1)  - 2t z  + (3t - 2)x z  + ((- 6t + 6)x y - t x )z + (6t - 6)x y
--E 75

--S 76
t2:=-63*x*y^2*t^2+9*x^2*z*t^2+63*x*y*z*t^2+18*y^2*z*t^2-27*x*z^2*t^2_
    -18*y*z^2*t^2+18*z^3*t^2+78*x*y^2*t-78*x*y*z*t-18*y^2*z*t_
    +24*x*z^2*t+18*y*z^2*t-9*z^3*t-15*x*y^2+15*x*y*z-5*x*z^2
 

   (2)
         2       3          2                 2              2
     (18t  - 9t)z  + ((- 18t  + 18t)y + (- 27t  + 24t - 5)x)z
   + 
          2        2       2                    2 2           2               2
     ((18t  - 18t)y  + (63t  - 78t + 15)x y + 9t x )z + (- 63t  + 78t - 15)x y
--R 
--R
--R   (2)
--R         2       3          2                 2              2
--R     (18t  - 9t)z  + ((- 18t  + 18t)y + (- 27t  + 24t - 5)x)z
--R   + 
--R          2        2       2                    2 2           2               2
--R     ((18t  - 18t)y  + (63t  - 78t + 15)x y + 9t x )z + (- 63t  + 78t - 15)x y
--E 76

--S 77
t3:=18*x^2*y^2*t-3*x^3*z*t-18*x^2*y*z*t+12*x*y^2*z*t+5*x^2*z^2*t_
    -12*x*y*z^2*t+6*x*z^3*t-8*z^4*t-18*x^2*y^2+18*x^2*y*z-12*x*y^2*z_
    -4*x^2*z^2+12*x*y*z^2-6*x*z^3
 

   (3)
           4              3                               2  2
     - 8t z  + (6t - 6)x z  + ((- 12t + 12)x y + (5t - 4)x )z
   + 
                   2                2        3                2 2
     ((12t - 12)x y  + (- 18t + 18)x y - 3t x )z + (18t - 18)x y
--R 
--R
--R   (3)
--R           4              3                               2  2
--R     - 8t z  + (6t - 6)x z  + ((- 12t + 12)x y + (5t - 4)x )z
--R   + 
--R                   2                2        3                2 2
--R     ((12t - 12)x y  + (- 18t + 18)x y - 3t x )z + (18t - 18)x y
--E 77

--S 78
t4:=-x^2*y*t+3*x*y^2*t+10*y^3*t-15*y^2*z*t+3*y*z^2*t-3*x*y^2-10*y^3+x*y*z_
    +15*y^2*z-5*y*z^2
 

   (4)
              2                 2                      3              2      2
   (3t - 5)y z  + ((- 15t + 15)y  + x y)z + (10t - 10)y  + (3t - 3)x y  - t x y
--R 
--R
--R   (4)
--R              2                 2                      3              2      2
--R   (3t - 5)y z  + ((- 15t + 15)y  + x y)z + (10t - 10)y  + (3t - 3)x y  - t x y
--E 78

)clear all
 
   All user variables and function definitions have been cleared.

--S 79
t1:=y*t-y*u-u*b+u*c
 

   (1)  (- u + t)y + (c - b)u
--R 
--R
--R   (1)  (- u + t)y + (c - b)u
--E 79

--S 80
t2:=2*x*y^2*t-x*y^2*u-2*y^2*t*v+y^2*u*v-x*y*z*a+12*x*t^2*a-4*x*t*u*a_
    -x*u^2*a+y*z*v*a-2*t*u*v*a+u^2*v*a-x*u*w*a+u*v*w*a-6*x*z*a*b
 

   (2)
                                                            2
     ((- a x + a v)y - 6a b x)z + ((- u + 2t)x + (u - 2t)v)y
   + 
                   2                 2                   2
     (- a u w - a u  - 4a t u + 12a t )x + a u v w + (a u  - 2a t u)v
--R 
--R
--R   (2)
--R                                                            2
--R     ((- a x + a v)y - 6a b x)z + ((- u + 2t)x + (u - 2t)v)y
--R   + 
--R                   2                 2                   2
--R     (- a u w - a u  - 4a t u + 12a t )x + a u v w + (a u  - 2a t u)v
--E 80

--S 81
t3:=x*y^2*z-y^2*z*v+6*x*z*t*a+x*z*u*a-z*u*v*a-2*x*y*z*b+2*y*z*v*b_
    -2*x*u*w*b+2*u*v*w*b-12*x*z*b^2+x*y*z*c-y*z*v*c+x*u*w*c_
    -u*v*w*c+6*x*z*b*c
 

   (3)
                 2                                                        2
         (x - v)y  + ((c - 2b)x + (- c + 2b)v)y + (a u + 6a t + 6b c - 12b )x
       + 
         - a u v
    *
       z
   + 
     (c - 2b)u w x + (- c + 2b)u v w
--R 
--R
--R   (3)
--R                 2                                                        2
--R         (x - v)y  + ((c - 2b)x + (- c + 2b)v)y + (a u + 6a t + 6b c - 12b )x
--R       + 
--R         - a u v
--R    *
--R       z
--R   + 
--R     (c - 2b)u w x + (- c + 2b)u v w
--E 81

--S 82
t4:=x*y*u-y*u*v+3*x*z*a+3*x*t*b+x*u*b-u*v*b
 

   (4)  3a x z + (u x - u v)y + (b u + 3b t)x - b u v
--R 
--R
--R   (4)  3a x z + (u x - u v)y + (b u + 3b t)x - b u v
--E 82

--S 83
t5:=5*x^2*y*t-5*x^2*y*u-10*x*y*t*v+10*x*y*u*v+5*y*t*v^2-5*y*u*v^2_
    -6*x^2*z*a-12*x*z*v*a+4*x^2*t*b-7*x^2*u*b+16*x*t*v*b+8*x*u*v*b_
    -2*t*v^2*b-u*v^2*b+8*x^2*t*c+x^2*u*c-10*x*t*v*c-2*x*u*v*c_
    +2*t*v^2*c+u*v^2*c
 

   (5)
            2                            2                                2
     (- 6a x  - 12a v x)z + ((- 5u + 5t)x  + (10u - 10t)v x + (- 5u + 5t)v )y
   + 
                              2
     ((c - 7b)u + (8c + 4b)t)x  + ((- 2c + 8b)u + (- 10c + 16b)t)v x
   + 
                             2
     ((c - b)u + (2c - 2b)t)v
--R 
--R
--R   (5)
--R            2                            2                                2
--R     (- 6a x  - 12a v x)z + ((- 5u + 5t)x  + (10u - 10t)v x + (- 5u + 5t)v )y
--R   + 
--R                              2
--R     ((c - 7b)u + (8c + 4b)t)x  + ((- 2c + 8b)u + (- 10c + 16b)t)v x
--R   + 
--R                             2
--R     ((c - b)u + (2c - 2b)t)v
--E 83

--S 84
t6:=-9*x^4*t*v*c+9*x^4*u*v*c-18*x^3*t*v^2*c-9*x^3*u*v^2*c+3*x^4*y*t_
    -4*x^4*y*u-9*x^3*y*t*v+10*x^3*y*u*v+9*x^2*y*t*v^2-6*x^2*y*u*v^2_
    -3*x*y*t*v^3-2*x*y*u*v^3+2*y*u*v^4-6*x^4*z*a-45*x^3*z*v*a_
    -27*x^2*z*v^2*a-3*x*z*v^3*a-6*x^4*t*b-2*x^4*u*b-45*x^3*t*v*b_
    +32*x^3*u*v*b-27*x^2*t*v^2*b-30*x^2*u*v^2*b-3*x*t*v^3*b-x*u*v^3*b+u*v^4*b
 

   (6)
            4          3        2 2       3
     (- 6a x  - 45a v x  - 27a v x  - 3a v x)z
   + 
                       4                3               2 2               3
           (- 4u + 3t)x  + (10u - 9t)v x  + (- 6u + 9t)v x  + (- 2u - 3t)v x
         + 
               4
           2u v
    *
       y
   + 
                                    4
     ((9c u - 9c t)v - 2b u - 6b t)x
   + 
                       2                     3                     2 2
     ((- 9c u - 18c t)v  + (32b u - 45b t)v)x  + (- 30b u - 27b t)v x
   + 
                    3         4
     (- b u - 3b t)v x + b u v
--R 
--R
--R   (6)
--R            4          3        2 2       3
--R     (- 6a x  - 45a v x  - 27a v x  - 3a v x)z
--R   + 
--R                       4                3               2 2               3
--R           (- 4u + 3t)x  + (10u - 9t)v x  + (- 6u + 9t)v x  + (- 2u - 3t)v x
--R         + 
--R               4
--R           2u v
--R    *
--R       y
--R   + 
--R                                    4
--R     ((9c u - 9c t)v - 2b u - 6b t)x
--R   + 
--R                       2                     3                     2 2
--R     ((- 9c u - 18c t)v  + (32b u - 45b t)v)x  + (- 30b u - 27b t)v x
--R   + 
--R                    3         4
--R     (- b u - 3b t)v x + b u v
--E 84

--S 85
t7:=w*b-t*c+u*c-w*c
 

   (7)  (- c + b)w + c u - c t
--R 
--R
--R   (7)  (- c + b)w + c u - c t
--E 85

--S 86
t8:=-6*z*t*v*a+x*z*w*a-z*v*w*a-2*x*w^2*b+2*v*w^2*b+12*z*v*b^2_
    +x*y*z*c-y*z*v*c+x*w^2*c-v*w^2*c-2*x*z*b*c-4*z*v*b*c+x*z*c^2-z*v*c^2
 

   (8)
                             2                               2             2
     ((c x - c v)y + (a w + c  - 2b c)x - a v w + (- 6a t - c  - 4b c + 12b )v)z
   + 
              2                 2
     (c - 2b)w x + (- c + 2b)v w
--R 
--R
--R   (8)
--R                             2                               2             2
--R     ((c x - c v)y + (a w + c  - 2b c)x - a v w + (- 6a t - c  - 4b c + 12b )v)z
--R   + 
--R              2                 2
--R     (c - 2b)w x + (- c + 2b)v w
--E 86

--S 87
t9:=-12*t^2*v*a+6*t*u*v*a+2*x*t*w*a-x*u*w*a-2*t*v*w*a+u*v*w*a_
    -x*w^2*a+v*w^2*a+6*z*v*a*b+2*x*y*t*c-x*y*u*c-2*y*t*v*c+y*u*v*c_
    -x*z*a*c+z*v*a*c
 

   (9)
     (- a c x + (a c + 6a b)v)z + ((- c u + 2c t)x + (c u - 2c t)v)y
   + 
         2                            2                                    2
   (- a w  + (- a u + 2a t)w)x + a v w  + (a u - 2a t)v w + (6a t u - 12a t )v
--R 
--R
--R   (9)
--R     (- a c x + (a c + 6a b)v)z + ((- c u + 2c t)x + (c u - 2c t)v)y
--R   + 
--R         2                            2                                    2
--R   (- a w  + (- a u + 2a t)w)x + a v w  + (a u - 2a t)v w + (6a t u - 12a t )v
--E 87

--S 88
t10:=3*z*v*a+3*t*v*b-x*t*c+t*v*c-x*w*c+v*w*c
 

   (10)  3a v z + (- c w - c t)x + c v w + (c + 3b)t v
--R 
--R
--R   (10)  3a v z + (- c w - c t)x + c v w + (c + 3b)t v
--E 88

--S 89
t11:=-12*x*z*v*a-6*z*v^2*a-2*x^2*t*b+2*x^2*u*b+16*x*t*v*b-10*x*u*v*b_
    +4*t*v^2*b+8*u*v^2*b+5*x^2*w*b-10*x*v*w*b+5*v^2*w*b-x^2*t*c_
    +x^2*u*c+8*x*t*v*c-2*x*u*v*c-7*t*v^2*c+u*v^2*c-5*x^2*w*c_
    +10*x*v*w*c-5*v^2*w*c
 

   (11)
                      2                                              2
     (- 12a v x - 6a v )z + ((- 5c + 5b)w + (c + 2b)u + (- c - 2b)t)x
   + 
                                                                      2
     ((10c - 10b)v w + ((- 2c - 10b)u + (8c + 16b)t)v)x + (- 5c + 5b)v w
   + 
                                2
     ((c + 8b)u + (- 7c + 4b)t)v
--R 
--R
--R   (11)
--R                      2                                              2
--R     (- 12a v x - 6a v )z + ((- 5c + 5b)w + (c + 2b)u + (- c - 2b)t)x
--R   + 
--R                                                                      2
--R     ((10c - 10b)v w + ((- 2c - 10b)u + (8c + 16b)t)v)x + (- 5c + 5b)v w
--R   + 
--R                                2
--R     ((c + 8b)u + (- 7c + 4b)t)v
--E 89

--S 90
t12:=-18*x^2*u*v^3*b-9*x*u*v^4*b-9*x^2*u*v^3*c+9*x*u*v^4*c-3*x^3*z*v*a_
    -27*x^2*z*v^2*a-45*x*z*v^3*a-6*z*v^4*a-3*x^3*t*v*b_
    -27*x^2*t*v^2*b-45*x*t*v^3*b-6*t*v^4*b-3*x^3*v*w*b_
    +9*x^2*v^2*w*b-9*x*v^3*w*b+3*v^4*w*b+x^4*t*c-x^3*t*v*c_
    -30*x^2*t*v^2*c+32*x*t*v^3*c-2*t*v^4*c+2*x^4*w*c-2*x^3*v*w*c_
    -6*x^2*v^2*w*c+10*x*v^3*w*c-4*v^4*w*c
 

   (12)
              3        2 2        3        4                  4
     (- 3a v x  - 27a v x  - 45a v x - 6a v )z + (2c w + c t)x
   + 
                                      3
     ((- 2c - 3b)v w + (- c - 3b)t v)x
   + 
                  2                   3                   2  2
     ((- 6c + 9b)v w + (- 9c - 18b)u v  + (- 30c - 27b)t v )x
   + 
                 3                4                 3                 4
     ((10c - 9b)v w + (9c - 9b)u v  + (32c - 45b)t v )x + (- 4c + 3b)v w
   + 
                   4
     (- 2c - 6b)t v
--R 
--R
--R   (12)
--R              3        2 2        3        4                  4
--R     (- 3a v x  - 27a v x  - 45a v x - 6a v )z + (2c w + c t)x
--R   + 
--R                                      3
--R     ((- 2c - 3b)v w + (- c - 3b)t v)x
--R   + 
--R                  2                   3                   2  2
--R     ((- 6c + 9b)v w + (- 9c - 18b)u v  + (- 30c - 27b)t v )x
--R   + 
--R                 3                4                 3                 4
--R     ((10c - 9b)v w + (9c - 9b)u v  + (32c - 45b)t v )x + (- 4c + 3b)v w
--R   + 
--R                   4
--R     (- 2c - 6b)t v
--E 90

)clear all
 
   All user variables and function definitions have been cleared.

--S 91
t1:=v*A
 

   (1)  A v
--R 
--R
--R   (1)  A v
--E 91

--S 92
t2:=u*A+14*B
 

   (2)  A u + 14B
--R 
--R
--R   (2)  A u + 14B
--E 92

--S 93
t3:=z*A
 

   (3)  A z
--R 
--R
--R   (3)  A z
--E 93

--S 94
t4:=u*a*A+3*z*A+2*t*A+168*B
 

   (4)  3A z + A a u + 2A t + 168B
--R 
--R
--R   (4)  3A z + A a u + 2A t + 168B
--E 94

--S 95
t5:=y*A+5*u*B
 

   (5)  A y + 5B u
--R 
--R
--R   (5)  A y + 5B u
--E 95

--S 96
t6:=5*v*C+21*D
 

   (6)  5C v + 21D
--R 
--R
--R   (6)  5C v + 21D
--E 96

--S 97
t7:=10*u*C+14*E
 

   (7)  10C u + 14E
--R 
--R
--R   (7)  10C u + 14E
--E 97

--S 98
t8:=-5*y*C-u*E+105*F
 

   (8)  - 5C y - E u + 105F
--R 
--R
--R   (8)  - 5C y - E u + 105F
--E 98

--S 99
t9:=5*z*C+2*u*D
 

   (9)  5C z + 2D u
--R 
--R
--R   (9)  5C z + 2D u
--E 99

--S 100
t10:=-2/7*v^2+t-4*u-A
 

           2  2
   (10)  - - v  - 4u + t - A
           7
--R 
--R
--R           2  2
--R   (10)  - - v  - 4u + t - A
--R           7
--E 100

--S 101
t11:=-2/7*u^2+y-B
 

             2  2
   (11)  y - - u  - B
             7
--R 
--R
--R             2  2
--R   (11)  y - - u  - B
--R             7
--E 101

--S 102
t12:=7*u-C
 

   (12)  7u - C
--R 
--R
--R   (12)  7u - C
--E 102

--S 103
t13:=3/7*v^3-2*t*v+6*u*v-7*z-D
 

                3  3
   (13)  - 7z + - v  + (6u - 2t)v - D
                7
--R 
--R
--R                3  3
--R   (13)  - 7z + - v  + (6u - 2t)v - D
--R                7
--E 103

--S 104
t14:=9/7*u*v^2-2*t*u+16*u^2-6*z*v-42*y-E
 

                        9    2      2
   (14)  - 6v z - 42y + - u v  + 16u  - 2t u - E
                        7
--R 
--R
--R                        9    2      2
--R   (14)  - 6v z - 42y + - u v  + 16u  - 2t u - E
--R                        7
--E 104

--S 105
t15:=3/7*u^3-2*y*u+7*x-F
 

                       3  3
   (15)  - 2u y + 7x + - u  - F
                       7
--R 
--R
--R                       3  3
--R   (15)  - 2u y + 7x + - u  - F
--R                       7
--E 105

)clear all
 
   All user variables and function definitions have been cleared.

--S 106
t1:=-2*y^3*z+6*x^2*z*t-6*x*y*z*t+3*y^2*z*t-y*z*t^2-6*x^2*t+6*x*y*t-2*y^2*t
 

             3       2              2         2         2                2
   (1)  (- 2y  + 3t y  + (- 6t x - t )y + 6t x )z - 2t y  + 6t x y - 6t x
--R 
--R
--R             3       2              2         2         2                2
--R   (1)  (- 2y  + 3t y  + (- 6t x - t )y + 6t x )z - 2t y  + 6t x y - 6t x
--E 106

--S 107
t1:=18*x^2*y*z^2-18*x*y^2*z^2+18*y^2*z^2-63*x^2*z^2*t+63*x*y*z^2*t_
    -27*y^2*z^2*t+9*y*z^2*t^2-18*x^2*y*z+18*x*y^2*z-9*y^3*z_
    +78*x^2*z*t-78*x*y*z*t+24*y^2*z*t-15*x^2*t+15*x*y*t-5*y^2*t
 

   (2)
                         2       2             2          2  2
     ((- 18x - 27t + 18)y  + (18x  + 63t x + 9t )y - 63t x )z
   + 
          3               2         2                  2         2
     (- 9y  + (18x + 24t)y  + (- 18x  - 78t x)y + 78t x )z - 5t y  + 15t x y
   + 
            2
     - 15t x
--R 
--R
--R   (2)
--R                         2       2             2          2  2
--R     ((- 18x - 27t + 18)y  + (18x  + 63t x + 9t )y - 63t x )z
--R   + 
--R          3               2         2                  2         2
--R     (- 9y  + (18x + 24t)y  + (- 18x  - 78t x)y + 78t x )z - 5t y  + 15t x y
--R   + 
--R            2
--R     - 15t x
--E 107

--S 108
t1:=-8*y^4*z+12*x^2*y*z*t-12*x*y^2*z*t+6*y^3*z*t+18*x^2*z*t^2_
    -18*x*y*z*t^2+5*y^2*z*t^2-3*y*z*t^3-12*x^2*y*t+12*x*y^2*t_
    -6*y^3*t-18*x^2*t^2+18*x*y*t^2-4*y^2*t^2
 

   (3)
          4       3                2  2         2      2      3        2 2
     (- 8y  + 6t y  + (- 12t x + 5t )y  + (12t x  - 18t x - 3t )y + 18t x )z
   + 
           3              2  2           2      2         2 2
     - 6t y  + (12t x - 4t )y  + (- 12t x  + 18t x)y - 18t x
--R 
--R
--R   (3)
--R          4       3                2  2         2      2      3        2 2
--R     (- 8y  + 6t y  + (- 12t x + 5t )y  + (12t x  - 18t x - 3t )y + 18t x )z
--R   + 
--R           3              2  2           2      2         2 2
--R     - 6t y  + (12t x - 4t )y  + (- 12t x  + 18t x)y - 18t x
--E 108

--S 109
t1:=10*x^3*z-15*x^2*y*z+3*x*y^3*z+3*x^2*z*t-x*z*t^2-10*x^3+15*x^2*y_
    -5*x*y^2-3*x^2*t+x*y*t
 

   (4)
        3      2       3       2    2          2       2              3       2
   (3x y  - 15x y + 10x  + 3t x  - t x)z - 5x y  + (15x  + t x)y - 10x  - 3t x
--R 
--R
--R   (4)
--R        3      2       3       2    2          2       2              3       2
--R   (3x y  - 15x y + 10x  + 3t x  - t x)z - 5x y  + (15x  + t x)y - 10x  - 3t x
--E 109

)clear all
 
   All user variables and function definitions have been cleared.

--S 110
t1:=a-f
 

   (1)  - f + a
--R 
--R
--R   (1)  - f + a
--E 110

--S 111
t2:=b-g-h
 

   (2)  - h - g + b
--R 
--R
--R   (2)  - h - g + b
--E 111

--S 112
t3:=c+d+e-1
 

   (3)  e + d + c - 1
--R 
--R
--R   (3)  e + d + c - 1
--E 112

--S 113
t4:=b*c+a*d-1/2
 

                    1
   (4)  a d + b c - -
                    2
--R 
--R
--R                    1
--R   (4)  a d + b c - -
--R                    2
--E 113

--S 114
t5:=b^2*c+a^2*d-1/3
 

         2     2    1
   (5)  a d + b c - -
                    3
--R 
--R
--R         2     2    1
--R   (5)  a d + b c - -
--R                    3
--E 114

--S 115
t6:=a*c*g-1/6
 

                1
   (6)  a c g - -
                6
--R 
--R
--R                1
--R   (6)  a c g - -
--R                6
--E 115

)clear all
 
   All user variables and function definitions have been cleared.

--S 116
t1:=d+e+f+g-1
 

   (1)  g + f + e + d - 1
--R 
--R
--R   (1)  g + f + e + d - 1
--E 116

--S 117
t2:=c*d+b*e+a*f-1/2
 

                          1
   (2)  a f + b e + c d - -
                          2
--R 
--R
--R                          1
--R   (2)  a f + b e + c d - -
--R                          2
--E 117

--S 118
t3:=c^2*d+b^2*e+a^2*f-1/3
 

         2     2     2    1
   (3)  a f + b e + c d - -
                          3
--R 
--R
--R         2     2     2    1
--R   (3)  a f + b e + c d - -
--R                          3
--E 118

--S 119
t4:=a*e*i+a*d*l+b*d*m-1/6
 

                                1
   (4)  b d m + a d l + a e i - -
                                6
--R 
--R
--R                                1
--R   (4)  b d m + a d l + a e i - -
--R                                6
--E 119

--S 120
t5:=c^3*d+b^3*e+a^3*f-1/4
 

         3     3     3    1
   (5)  a f + b e + c d - -
                          4
--R 
--R
--R         3     3     3    1
--R   (5)  a f + b e + c d - -
--R                          4
--E 120

--S 121
t6:=a*b*e*i+a*c*d*l+b*c*d*m-1/8
 

                                      1
   (6)  b c d m + a c d l + a b e i - -
                                      8
--R 
--R
--R                                      1
--R   (6)  b c d m + a c d l + a b e i - -
--R                                      8
--E 121

--S 122
t7:=a^2*e*i+a^2*d*l+b^2*d*m-1/2
 

         2       2       2      1
   (7)  b d m + a d l + a e i - -
                                2
--R 
--R
--R         2       2       2      1
--R   (7)  b d m + a d l + a e i - -
--R                                2
--E 122

--S 123
t8:=a*d*i*m-1/24
 

                   1
   (8)  a d i m - --
                  24
--R 
--R
--R                   1
--R   (8)  a d i m - --
--R                  24
--E 123

--S 124
t9:=a-h
 

   (9)  - h + a
--R 
--R
--R   (9)  - h + a
--E 124

--S 125
t10:=b-i-j
 

   (10)  - j - i + b
--R 
--R
--R   (10)  - j - i + b
--E 125

--S 126
t11:=c-k-l-m
 

   (11)  - m - l - k + c
--R 
--R
--R   (11)  - m - l - k + c
--E 126

)clear all
 
   All user variables and function definitions have been cleared.

--S 127
t1:=a*e+b*f+c*g+d*h-1/2
 

                                1
   (1)  d h + c g + b f + a e - -
                                2
--R 
--R
--R                                1
--R   (1)  d h + c g + b f + a e - -
--R                                2
--E 127

--S 128
t2:=a^2*e+b^2*f+c^2*g+d^2*h-1/3
 

         2     2     2     2    1
   (2)  d h + c g + b f + a e - -
                                3
--R 
--R
--R         2     2     2     2    1
--R   (2)  d h + c g + b f + a e - -
--R                                3
--E 128

--S 129
t3:=a*f*i+a*g*j+b*g*k+a*h*l+b*h*m+c*h*n-1/6
 

                                                        1
   (3)  c h n + b h m + a h l + b g k + a g j + a f i - -
                                                        6
--R 
--R
--R                                                        1
--R   (3)  c h n + b h m + a h l + b g k + a g j + a f i - -
--R                                                        6
--E 129

--S 130
t4:=a^3*e+b^3*f+c^3*g+d^3*h-1/4
 

         3     3     3     3    1
   (4)  d h + c g + b f + a e - -
                                4
--R 
--R
--R         3     3     3     3    1
--R   (4)  d h + c g + b f + a e - -
--R                                4
--E 130

--S 131
t5:=a*b*f*i+a*c*g*j+b*c*g*k+a*d*h*l+b*d*h*m+c*d*h*n-1/8
 

                                                                    1
   (5)  c d h n + b d h m + a d h l + b c g k + a c g j + a b f i - -
                                                                    8
--R 
--R
--R                                                                    1
--R   (5)  c d h n + b d h m + a d h l + b c g k + a c g j + a b f i - -
--R                                                                    8
--E 131

--S 132
t6:=a^2*f*i+a^2*g*j+b^2*g*k+a^2*h*l+b^2*h*m+c^2*h*n-1/12
 

         2       2       2       2       2       2       1
   (6)  c h n + b h m + a h l + b g k + a g j + a f i - --
                                                        12
--R 
--R
--R         2       2       2       2       2       2       1
--R   (6)  c h n + b h m + a h l + b g k + a g j + a f i - --
--R                                                        12
--E 132

--S 133
t7:=a*g*i*k+a*h*i*m+a*h*j*n+b*h*k*n-1/24
 

                                                1
   (7)  (b h k + a h j)n + a h i m + a g i k - --
                                               24
--R 
--R
--R                                                1
--R   (7)  (b h k + a h j)n + a h i m + a g i k - --
--R                                               24
--E 133

--S 134
t8:=a^4*e+b^4*f+c^4*g+d^4*h-1/5
 

         4     4     4     4    1
   (8)  d h + c g + b f + a e - -
                                5
--R 
--R
--R         4     4     4     4    1
--R   (8)  d h + c g + b f + a e - -
--R                                5
--E 134

--S 135
t9:=a*b^2*f*i+a*c^2*g*j+b*c^2*g*k+ad^2*h*l+b*d^2*h*m+c*d^2*h*n-1/10
 

           2         2        2         2         2         2       1
   (9)  c d h n + b d h m + ad h l + b c g k + a c g j + a b f i - --
                                                                   10
--R 
--R
--R           2         2        2         2         2         2       1
--R   (9)  c d h n + b d h m + ad h l + b c g k + a c g j + a b f i - --
--R                                                                   10
--E 135

--S 136
t10:=a^2*b*f*i+a^2*c*g*j+b^2*c*g*k+a^3*h*l+b^2*d*h*m+c^2*d*h*n-1/15
 

          2         2         3       2         2         2         1
   (10)  c d h n + b d h m + a h l + b c g k + a c g j + a b f i - --
                                                                   15
--R 
--R
--R          2         2         3       2         2         2         1
--R   (10)  c d h n + b d h m + a h l + b c g k + a c g j + a b f i - --
--R                                                                   15
--E 136

--S 137
t11:=a*c*g*i*k+a*d*h*i*m+a*d*h*j*n+b*d*h*k*n-1/30
 

                                                         1
   (11)  (b d h k + a d h j)n + a d h i m + a c g i k - --
                                                        30
--R 
--R
--R                                                         1
--R   (11)  (b d h k + a d h j)n + a d h i m + a c g i k - --
--R                                                        30
--E 137

--S 138
t12:=a^2*f*i^2+a^2*g*j^2+2*a*b*g*j*k+b^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m
    +b^2*h*m^2+2*a*c*h*l*n+2*b*c*h*m*n+c^2*h*n^2-1/20
 

   (12)
      2   2                             2   2                 2   2    2   2
     c h n  + (2b c h m + 2a c h l)n + b h m  + 2a b h l m + a h l  + b g k
   + 
                   2   2    2   2    1
     2a b g j k + a g j  + a f i  - --
                                    20
--R 
--R
--R   (12)
--R      2   2                             2   2                 2   2    2   2
--R     c h n  + (2b c h m + 2a c h l)n + b h m  + 2a b h l m + a h l  + b g k
--R   + 
--R                   2   2    2   2    1
--R     2a b g j k + a g j  + a f i  - --
--R                                    20
--E 138

--S 139
t13:=a^2*f*i+a^3*g*j+b^3*g*k+a^3*h*l+b^3*h*m+c^3*h*n-1/20
 

          3       3       3       3       3       2       1
   (13)  c h n + b h m + a h l + b g k + a g j + a f i - --
                                                         20
--R 
--R
--R          3       3       3       3       3       2       1
--R   (13)  c h n + b h m + a h l + b g k + a g j + a f i - --
--R                                                         20
--E 139

--S 140
t14:=a*b*g*i*k+a*b*h*i*m+a*c*h*j*n+b*c*h*k*n-1/40
 

                                                         1
   (14)  (b c h k + a c h j)n + a b h i m + a b g i k - --
                                                        40
--R 
--R
--R                                                         1
--R   (14)  (b c h k + a c h j)n + a b h i m + a b g i k - --
--R                                                        40
--E 140

--S 141
t15:=a^2*g*i*k+a^2*h*i*m+a^2*h*j*n+b^2*h*k*n-1/60
 

           2       2         2         2         1
   (15)  (b h k + a h j)n + a h i m + a g i k - --
                                                60
--R 
--R
--R           2       2         2         2         1
--R   (15)  (b h k + a h j)n + a h i m + a g i k - --
--R                                                60
--E 141

--S 142
t16:=a*h*i*k*n-1/120
 

                      1
   (16)  a h i k n - ---
                     120
--R 
--R
--R                      1
--R   (16)  a h i k n - ---
--R                     120
--E 142

)clear all
 
   All user variables and function definitions have been cleared.

--S 143
t1:=a*f+b*g+c*h+d*i+e*j-1/2
 

                                      1
   (1)  e j + d i + c h + b g + a f - -
                                      2
--R 
--R
--R                                      1
--R   (1)  e j + d i + c h + b g + a f - -
--R                                      2
--E 143

--S 144
t2:=a^2*f+b^2*g+c^2*h+d^2*i+e^2*j-1/3
 

         2     2     2     2     2    1
   (2)  e j + d i + c h + b g + a f - -
                                      3
--R 
--R
--R         2     2     2     2     2    1
--R   (2)  e j + d i + c h + b g + a f - -
--R                                      3
--E 144

--S 145
t3:=t*d*j+a*g*k+a*h*l+b*h*m+a*i*n+b*i*o+c*i*p+a*j*q+b*j*r+c*j*s-1/6
 

   (3)
     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
   + 
             1
     a g k - -
             6
--R 
--R
--R   (3)
--R     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
--R   + 
--R             1
--R     a g k - -
--R             6
--E 145

--S 146
t4:=a^3*f+b^3*g+c^3*h+d^3*i+e^3*j-1/4
 

         3     3     3     3     3    1
   (4)  e j + d i + c h + b g + a f - -
                                      4
--R 
--R
--R         3     3     3     3     3    1
--R   (4)  e j + d i + c h + b g + a f - -
--R                                      4
--E 146

--S 147
t5:=t*d*e*j+a*b*g*k+a*c*h*l+b*c*h*m+a*d*i*n+b*d*i*o+c*d*i*p+a*e*j*q_
    +b*e*j*r+c*e*j*s-1/8
 

   (5)
     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
   + 
                                   1
     b c h m + a c h l + a b g k - -
                                   8
--R 
--R
--R   (5)
--R     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
--R   + 
--R                                   1
--R     b c h m + a c h l + a b g k - -
--R                                   8
--E 147

--S 148
t6:=t*d^2*j+a^2*g*k+a^2*h*l+b^2*h*m+a^2*i*n+b^2*i*o+c^2*i*p+a^2*j*g_
    +b^2*j*r+c^2*j*s-1/12
 

   (6)
      2       2       2       2       2       2       2       2       2
     d j t + c j s + b j r + c i p + b i o + a i n + b h m + a h l + a g k
   + 
      2       1
     a g j - --
             12
--R 
--R
--R   (6)
--R      2       2       2       2       2       2       2       2       2
--R     d j t + c j s + b j r + c i p + b i o + a i n + b h m + a h l + a g k
--R   + 
--R      2       1
--R     a g j - --
--R             12
--E 148

--S 149
t7:=a*h*k*m+t*a*j*n+t*b*j*o+a*i*k*o+t*c*j*p+a*i*l*p+b*i*m*p+a*j*k*r_
    +a*j*l*s+b*j*m*s-1/24
 

   (7)
     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
   + 
                          1
     a i k o + a h k m - --
                         24
--R 
--R
--R   (7)
--R     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
--R   + 
--R                          1
--R     a i k o + a h k m - --
--R                         24
--E 149

--S 150
t8:=a^4*f+b^4*g+c^4*h+d^4*i+e^4*j-1/5
 

         4     4     4     4     4    1
   (8)  e j + d i + c h + b g + a f - -
                                      5
--R 
--R
--R         4     4     4     4     4    1
--R   (8)  e j + d i + c h + b g + a f - -
--R                                      5
--E 150

--S 151
t9:=t*d*e^2*j+a*b^2*g*k+a*c^2*h*l+b*c^2*h*m+a*d^2*i*n+b*d^2*i*o_
    +c*d^2*i*p+a*e^2*j*g+b*e^2*j*r+c*e^2*j*s-1/10
 

   (9)
        2         2         2         2         2         2         2
     d e j t + c e j s + b e j r + c d i p + b d i o + a d i n + b c h m
   + 
        2         2         2       1
     a c h l + a b g k + a e g j - --
                                   10
--R 
--R
--R   (9)
--R        2         2         2         2         2         2         2
--R     d e j t + c e j s + b e j r + c d i p + b d i o + a d i n + b c h m
--R   + 
--R        2         2         2       1
--R     a c h l + a b g k + a e g j - --
--R                                   10
--E 151

--S 152
t10:=t*d^2*e*j+a^2*b*g*k+a^2*c*h*l+b^2*c*h*m+a^2*d*i*n+b^2*d*i*o_
    +c^2*d*i*p+a^2*e*j*q+b^2*e*j*r+c^2*e*j*s-1/15
 

   (10)
      2         2         2         2         2         2         2
     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
   + 
      2         2         2         1
     b c h m + a c h l + a b g k - --
                                   15
--R 
--R
--R   (10)
--R      2         2         2         2         2         2         2
--R     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
--R   + 
--R      2         2         2         1
--R     b c h m + a c h l + a b g k - --
--R                                   15
--E 152

--S 153
t11:=a*c*h*k*m+t*a*e*j*n+t*b*e*j*o+a*d*i*k*o+t*c*e*j*p+a*d*i*l*p_
    +b*d*i*m*p+a*e*j*k*r+a*e*j*l*s+b*e*j*m*s-1/30
 

   (11)
     (c e j p + b e j o + a e j n)t + (b e j m + a e j l)s + a e j k r
   + 
                                                     1
     (b d i m + a d i l)p + a d i k o + a c h k m - --
                                                    30
--R 
--R
--R   (11)
--R     (c e j p + b e j o + a e j n)t + (b e j m + a e j l)s + a e j k r
--R   + 
--R                                                     1
--R     (b d i m + a d i l)p + a d i k o + a c h k m - --
--R                                                    30
--E 153

--S 154
t12:=t^2*d^2*j+a^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m+b^2*h*m^2+a^2*i*n^2_
    +2*a*b*i*n*o+b^2*i*o^2+2*a*c*i*n*p+2*b*c*i*o*p+c^2*i*p^2_
    +2*t*a*d*j*q+a^2*j*q^2+2*t*b*d*j*r+2*a*b*j*q*r+b^2*j*r^2_
    +2*t*c*d*j*s+2*a*c*j*q*s+2*b*c*j*r*s+c^2*j*s^2-1/20
 

   (12)
      2   2                                        2   2
     d j t  + (2c d j s + 2b d j r + 2a d j q)t + c j s
   + 
                               2   2                 2   2    2   2
     (2b c j r + 2a c j q)s + b j r  + 2a b j q r + a j q  + c i p
   + 
                               2   2                 2   2    2   2
     (2b c i o + 2a c i n)p + b i o  + 2a b i n o + a i n  + b h m  + 2a b h l m
   + 
      2   2    2   2    1
     a h l  + a g k  - --
                       20
--R 
--R
--R   (12)
--R      2   2                                        2   2
--R     d j t  + (2c d j s + 2b d j r + 2a d j q)t + c j s
--R   + 
--R                               2   2                 2   2    2   2
--R     (2b c j r + 2a c j q)s + b j r  + 2a b j q r + a j q  + c i p
--R   + 
--R                               2   2                 2   2    2   2
--R     (2b c i o + 2a c i n)p + b i o  + 2a b i n o + a i n  + b h m  + 2a b h l m
--R   + 
--R      2   2    2   2    1
--R     a h l  + a g k  - --
--R                       20
--E 154

--S 155
t13:=t*d^3*j+a^3*g*k+a^3*h*l+b^3*h*m+a^3*i*n+b^3*i*o+c^3*i*p_
    +a^3*j*q+b^3*j*r+c^3*j*s-1/20
 

   (13)
      3       3       3       3       3       3       3       3       3
     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
   + 
      3       1
     a g k - --
             20
--R 
--R
--R   (13)
--R      3       3       3       3       3       3       3       3       3
--R     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
--R   + 
--R      3       1
--R     a g k - --
--R             20
--E 155

--S 156
t14:=a*b*h*k*m+t*a*d*j*n+t*b*d*j*o+a*b*i*k*o+t*c*d*j*p+a*c*i*l*p_
    +b*c*i*m*p+a*b*j*k*r+a*c*j*l*s+b*c*j*m*s-1/40
 

   (14)
     (c d j p + b d j o + a d j n)t + (b c j m + a c j l)s + a b j k r
   + 
                                                     1
     (b c i m + a c i l)p + a b i k o + a b h k m - --
                                                    40
--R 
--R
--R   (14)
--R     (c d j p + b d j o + a d j n)t + (b c j m + a c j l)s + a b j k r
--R   + 
--R                                                     1
--R     (b c i m + a c i l)p + a b i k o + a b h k m - --
--R                                                    40
--E 156

--S 157
t15:=a^2*h*k*m+t*a^2*j*n+t*b^2*j*o+a^2*i*k*o+t*c^2*j*p+a^2*i*l*p_
    +b^2*i*m*p+a^2*j*k*r+a^2*j*l*s+b^2*j*m*s-1/60
 

   (15)
       2       2       2          2       2         2          2       2
     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
   + 
      2         2         1
     a i k o + a h k m - --
                         60
--R 
--R
--R   (15)
--R       2       2       2          2       2         2          2       2
--R     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
--R   + 
--R      2         2         1
--R     a i k o + a h k m - --
--R                         60
--E 157

--S 158
t16:=t*a*j*k*o+t*a*j*l*p+t*b*j*m*p+a*i*k*m*p+a*j*k*m*s-1/20
 

                                                                  1
   (16)  ((b j m + a j l)p + a j k o)t + a j k m s + a i k m p - --
                                                                 20
--R 
--R
--R                                                                  1
--R   (16)  ((b j m + a j l)p + a j k o)t + a j k m s + a i k m p - --
--R                                                                 20
--E 158

)clear all
 
   All user variables and function definitions have been cleared.

--S 159
t1:=c^2*p-a*c+c*l+a-p-h
 

          2
   (1)  (c  - 1)p + c l - h - a c + a
--R 
--R
--R          2
--R   (1)  (c  - 1)p + c l - h - a c + a
--E 159

--S 160
t2:=a*c*h+c^2+c*n+m*h
 

                             2
   (2)  c n + h m + a c h + c
--R 
--R
--R                             2
--R   (2)  c n + h m + a c h + c
--E 160

--S 161
t3:=-a^2*c+a*c*l+a*c*g-c*l*h+a^2+2*c^2-a*m-a*h+l*h-2
 

                                                      2    2     2
   (3)  - a m + ((- c + 1)h + a c)l - a h + a c g + 2c  - a c + a  - 2
--R 
--R
--R                                                      2    2     2
--R   (3)  - a m + ((- c + 1)h + a c)l - a h + a c g + 2c  - a c + a  - 2
--E 161

--S 162
t4:=-a*c^2+a*c*j-c^2*m+a*c*n+c^2*v-c*n*h-c*m+n*h
 

         2                              2                    2
   (4)  c v + ((- c + 1)h + a c)n + (- c  - c)m + a c j - a c
--R 
--R
--R         2                              2                    2
--R   (4)  c v + ((- c + 1)h + a c)n + (- c  - c)m + a c j - a c
--E 162

--S 163
t5:=-c*l*g-a*l-j-1
 

   (5)  (- c g - a)l - j - 1
--R 
--R
--R   (5)  (- c g - a)l - j - 1
--E 163

--S 164
t6:=-c*n*g-c*l-c*m+j*m+c*g+c*h
 

   (6)  - c g n + (j - c)m - c l + c h + c g
--R 
--R
--R   (6)  - c g n + (j - c)m - c l + c h + c g
--E 164

--S 165
t7:=-c*j*l-a*j+j*l-a*n+c*g+a-v+g
 

   (7)  - v - a n + (- c + 1)j l - a j + (c + 1)g + a
--R 
--R
--R   (7)  - v - a n + (- c + 1)j l - a j + (c + 1)g + a
--E 165

--S 166
t8:=-c*j*n+c*j-c*n+j*n
 

   (8)  ((- c + 1)j - c)n + c j
--R 
--R
--R   (8)  ((- c + 1)j - c)n + c j
--E 166

--S 167
t9:=c*m*p-l*n*p+a*l+l*m+a*p-l*p+c-n-2
 

   (9)  (- l n + c m - l + a)p - n + l m + a l + c - 2
--R 
--R
--R   (9)  (- l n + c m - l + a)p - n + l m + a l + c - 2
--E 167

--S 168
t10:=-n^2*p+c*l+c*m+2*m*n+c*p-c*h+m
 

             2
   (10)  (- n  + c)p + 2m n + (c + 1)m + c l - c h
--R 
--R
--R             2
--R   (10)  (- n  + c)p + 2m n + (c + 1)m + c l - c h
--E 168

--S 169
t11:=-l*m*h+a*c+2*c*m-l*n+m*n-c*g-a+p+h
 

   (11)  p + (m - l)n + (- h l + 2c)m + h - c g + a c - a
--R 
--R
--R   (11)  p + (m - l)n + (- h l + 2c)m + h - c g + a c - a
--E 169

--S 170
t12:=-c*l*m-c*m^2+a*m*n-m^2*n+c*m*v-m*n*h+c^2-c*j-n^2+n
 

                  2       2                         2                  2
   (12)  c m v - n  + (- m  + (- h + a)m + 1)n - c m  - c l m - c j + c
--R 
--R
--R                  2       2                         2                  2
--R   (12)  c m v - n  + (- m  + (- h + a)m + 1)n - c m  - c l m - c j + c
--E 170

--S 171
t13:=a^2*l-a*l^2+c*n*p-l*m*g-c*l-a*n+2*a-l+m-v+g
 

                                               2           2
   (13)  - v + c n p - a n + (- g l + 1)m - a l  + (- c + a  - 1)l + g + 2a
--R 
--R
--R                                               2           2
--R   (13)  - v + c n p - a n + (- g l + 1)m - a l  + (- c + a  - 1)l + g + 2a
--E 171

--S 172
t14:=a*c*l-c*l^2+a*m*n-l*m*n-m*n*g+c*l*h-m^2+c*n-n^2+m*v+2*c
 

                2                            2      2
   (14)  m v - n  + ((- l - g + a)m + c)n - m  - c l  + (c h + a c)l + 2c
--R 
--R
--R                2                            2      2
--R   (14)  m v - n  + ((- l - g + a)m + c)n - m  - c l  + (c h + a c)l + 2c
--E 172

--S 173
t15:=-j*l*m-l*n*v+c*l*g+a*l+c*n+n^2+j+1
 

                    2
   (15)  - l n v + n  + c n - j l m + (c g + a)l + j + 1
--R 
--R
--R                    2
--R   (15)  - l n v + n  + c n - j l m + (c g + a)l + j + 1
--E 173

--S 174
t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+c*n*v-n^2*v+n*v
 

             2                          2
   (16)  (- n  + (c + 1)n)v + (- m + a)n  + (- j m - c l)n + c j l
--R 
--R
--R             2                          2
--R   (16)  (- n  + (c + 1)n)v + (- m + a)n  + (- j m - c l)n + c j l
--E 174

--S 175
t17:=-j*l*p+c*m*p+n*p*h-a*l-a*m+a*g-p*g+a*h+c-j+n-1
 

   (17)  (h n + c m - j l - g)p + n - a m - a l - j + a h + a g + c - 1
--R 
--R
--R   (17)  (h n + c m - j l - g)p + n - a m - a l - j + a h + a g + c - 1
--E 175

--S 176
t18:=-j*n*p+l*m*h-c*l+j*m+c*g+n*h
 

   (18)  - j n p + h n + (h l + j)m - c l + c g
--R 
--R
--R   (18)  - j n p + h n + (h l + j)m - c l + c g
--E 176

--S 177
t19:=l^2*h-l*h^2+a*c-c*l-j*l+c*m+j*m-n*g+c*h+n*h-a-l-g+h
 

   (19)
                            2           2
   (h - g)n + (j + c)m + h l  + (- j - h  - c - 1)l + (c + 1)h - g + a c - a
--R 
--R
--R   (19)
--R                            2           2
--R   (h - g)n + (j + c)m + h l  + (- j - h  - c - 1)l + (c + 1)h - g + a c - a
--E 177

--S 178
t20:=a*j*m-j*m^2+c*m*v-c*m*g-c*m*h+l*n*h+n*v*h-n*h^2+c^2-c*n-2*j*n
 

                                     2            2                         2
   (20)  (h n + c m)v + (h l - 2j - h  - c)n - j m  + (a j - c h - c g)m + c
--R 
--R
--R                                     2            2                         2
--R   (20)  (h n + c m)v + (h l - 2j - h  - c)n - j m  + (a j - c h - c g)m + c
--E 178

--S 179
t21:=j*n*p-l*g*h-j*l-n*g-m+h
 

   (21)  j n p - g n - m + (- j - g h)l + h
--R 
--R
--R   (21)  j n p - g n - m + (- j - g h)l + h
--E 179

--S 180
t22:=j*l^2-j*l*v-a*n*g+n*g^2-j*l*h+2*j*n+l*g+m*g-v*g+j-1
 

                               2                    2
   (22)  (- j l - g)v + (2j + g  - a g)n + g m + j l  + (- h j + g)l + j - 1
--R 
--R
--R                               2                    2
--R   (22)  (- j l - g)v + (2j + g  - a g)n + g m + j l  + (- h j + g)l + j - 1
--E 180

--S 181
t23:=j*l*n-j*m*n-c*n*g+j*n*g-j*n*h+j*m
 

   (23)  (- j m + j l + (- h + g)j - c g)n + j m
--R 
--R
--R   (23)  (- j m + j l + (- h + g)j - c g)n + j m
--E 181

--S 182
t24:=-a^2*p+a*l*p+m^2*p-l*p*v+3*a+2*m-v
 

                          2          2
   (24)  (- l p - 1)v + (m  + a l - a )p + 2m + 3a
--R 
--R
--R                          2          2
--R   (24)  (- l p - 1)v + (m  + a l - a )p + 2m + 3a
--E 182

--S 183
t25:=-a*c*p+c*l*p-n*p*v+n*p*h-a*m+l*m+m*v-m*h+2*c+2*n
 

   (25)  (- n p + m)v + (h n + c l - a c)p + 2n + (l - h - a)m + 2c
--R 
--R
--R   (25)  (- n p + m)v + (h n + c l - a c)p + 2n + (l - h - a)m + 2c
--E 183

--S 184
t26:=-a*c*p+n*p*g+l^2-a*m-l*m+m^2+l*p-l*v+m*v-m*g-l*h-p*h+c+n
 

   (26)
                                          2                     2
   (m - l)v + (g n + l - h - a c)p + n + m  + (- l - g - a)m + l  - h l + c
--R 
--R
--R   (26)
--R                                          2                     2
--R   (m - l)v + (g n + l - h - a c)p + n + m  + (- l - g - a)m + l  - h l + c
--E 184

--S 185
t27:=-c^2*p+j*n*p-2*c*m-j*m+l*n-m*n-n*h
 

                 2
   (27)  (j n - c )p + (- m + l - h)n + (- j - 2c)m
--R 
--R
--R                 2
--R   (27)  (j n - c )p + (- m + l - h)n + (- j - 2c)m
--E 185

--S 186
t28:=m*n*p+n*p*v-a*l-l*m-a*p-l*v-l*g-p*g
 

   (28)  (n p - l)v + (m n - g - a)p - l m + (- g - a)l
--R 
--R
--R   (28)  (n p - l)v + (m n - g - a)p - l m + (- g - a)l
--E 186

--S 187
t29:=l*m*h-c*l-c*p-n*g+n*h-m
 

   (29)  - c p + (h - g)n + (h l - 1)m - c l
--R 
--R
--R   (29)  - c p + (h - g)n + (h l - 1)m - c l
--E 187

--S 188
t30:=l^2*v-l*v^2+l*m*g-j*l-a*n-l*n+m*n-j*p+2*n*v+n*g-v
 

              2          2
   (30)  - l v  + (2n + l  - 1)v - j p + (m - l + g - a)n + g l m - j l
--R 
--R
--R              2          2
--R   (30)  - l v  + (2n + l  - 1)v - j p + (m - l + g - a)n + g l m - j l
--E 188

--S 189
t31:=j*l*m+l*n*v-c*n-n^2
 

                  2
   (31)  l n v - n  - c n + j l m
--R 
--R
--R                  2
--R   (31)  l n v - n  - c n + j l m
--E 189

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 190
t1:=-a*b*k+a*c*k+b*k*l-c*k*l-b^2*p+c^2*p+b*k
 

          2    2
   (1)  (c  - b )p + (- c + b)k l + (a c + (- a + 1)b)k
--R 
--R
--R          2    2
--R   (1)  (c  - b )p + (- c + b)k l + (a c + (- a + 1)b)k
--E 190

--S 191
t2:=-c^2*k+a*c*l+b*l*m-c*k*n+a*c+c^2+b*m
 

                                        2     2
   (2)  - c k n + (b l + b)m + a c l - c k + c  + a c
--R 
--R
--R                                        2     2
--R   (2)  - c k n + (b l + b)m + a c l - c k + c  + a c
--E 191

--S 192
t3:=a^2*b-a^2*c+2*b^2*k-2*c^2*k-a*b*l+a*c*l+b*l^2-c*l^2-a*b*m+a*c*m_
-a*b-b^2+c^2+b*l-c*l
 

   (3)
                              2                                   2     2      2
     (a c - a b)m + (- c + b)l  + ((a - 1)c + (- a + 1)b)l + (- 2c  + 2b )k + c
   + 
        2     2     2
     - a c - b  + (a  - a)b
--R 
--R
--R   (3)
--R                              2                                   2     2      2
--R     (a c - a b)m + (- c + b)l  + ((a - 1)c + (- a + 1)b)l + (- 2c  + 2b )k + c
--R   + 
--R        2     2     2
--R     - a c - b  + (a  - a)b
--E 192

--S 193
t4:=-a*c^2+a*c*j-b*c*m-c^2*m+a*c*n+b*l*n-c*l*n+c^2*v+b*n-c*n
 

         2                                       2                      2
   (4)  c v + ((- c + b)l + (a - 1)c + b)n + (- c  - b c)m + a c j - a c
--R 
--R
--R         2                                       2                      2
--R   (4)  c v + ((- c + b)l + (a - 1)c + b)n + (- c  - b c)m + a c j - a c
--E 193

--S 194
t5:=b^2*k+b*j*k-a*b*l-c*l*m-b^2
 

                                  2      2
   (5)  - c l m - a b l + (b j + b )k - b
--R 
--R
--R                                  2      2
--R   (5)  - c l m - a b l + (b j + b )k - b
--E 194

--S 195
t6:=b*j*m-c*m*n+b*c
 

   (6)  - c m n + b j m + b c
--R 
--R
--R   (6)  - c m n + b j m + b c
--E 195

--S 196
t7:=a*b^2-a*b*j+b*j*l-c*j*l+b^2*m+b*c*m-a*b*n-b^2*v
 

           2                    2                               2
   (7)  - b v - a b n + (b c + b )m + (- c + b)j l - a b j + a b
--R 
--R
--R           2                    2                               2
--R   (7)  - b v - a b n + (b c + b )m + (- c + b)j l - a b j + a b
--E 196

--S 197
t8:=b*c*j-b*c*n+b*j*n-c*j*n
 

   (8)  ((- c + b)j - b c)n + b c j
--R 
--R
--R   (8)  ((- c + b)j - b c)n + b c j
--E 197

--S 198
t9:=-2*b*k^2+c*k^2-a*k*l-k*l*m-k^2*n+a*b*p-b*l*p+c*m*p-l*n*p+b*k
 

                                      2                             2
   (9)  (- l n + c m - b l + a b)p - k n - k l m - a k l + (c - 2b)k  + b k
--R 
--R
--R                                      2                             2
--R   (9)  (- l n + c m - b l + a b)p - k n - k l m - a k l + (c - 2b)k  + b k
--E 198

--S 199
t10:=-b*k*m-c*k*m-2*k*m*n+b*c*p-n^2*p+c*k+b*m+c*m
 

             2
   (10)  (- n  + b c)p - 2k m n + ((- c - b)k + c + b)m + c k
--R 
--R
--R             2
--R   (10)  (- n  + b c)p - 2k m n + ((- c - b)k + c + b)m + c k
--E 199

--S 200
t11:=a*b*k-a*c*k-b*k*l-c*k*m-l^2*m+k*l*n-k*m*n+b^2*p-b*k+c*m-l*m-l*n
 

   (11)
      2                              2
     b p + (- k m + (k - 1)l)n + (- l  - l - c k + c)m - b k l
   + 
     (- a c + (a - 1)b)k
--R 
--R
--R   (11)
--R      2                              2
--R     b p + (- k m + (k - 1)l)n + (- l  - l - c k + c)m - b k l
--R   + 
--R     (- a c + (a - 1)b)k
--E 200

--S 201
t12:=-c^2*k+c*j*k-c*l*m-c*m^2-b*k*n+a*m*n-l*m*n-m^2*n+k*n^2+c*m*v+b*n-m*n-n^2
 

   (12)
                     2       2                                   2
     c m v + (k - 1)n  + (- m  + (- l + a - 1)m - b k + b)n - c m  - c l m
   + 
             2
     (c j - c )k
--R 
--R
--R   (12)
--R                     2       2                                   2
--R     c m v + (k - 1)n  + (- m  + (- l + a - 1)m - b k + b)n - c m  - c l m
--R   + 
--R             2
--R     (c j - c )k
--E 201

--S 202
t13:=-2*a*b*k+a^2*l+b*k*l+c*k*l-a*l^2-2*b*k*m-l*m^2+a*k*n+c*n*p_
    +b*k*v+a*b-b*l-l*n
 

   (13)
                                       2               2                    2
     b k v + c n p + (- l + a k)n - l m  - 2b k m - a l  + ((c + b)k - b + a )l
   + 
     - 2a b k + a b
--R 
--R
--R   (13)
--R                                       2               2                    2
--R     b k v + c n p + (- l + a k)n - l m  - 2b k m - a l  + ((c + b)k - b + a )l
--R   + 
--R     - 2a b k + a b
--E 202

--S 203
t14:=-2*b*c*k+a*c*l-b*m^2-c*k*n+a*m*n-l*m*n-m^2*n+k*n^2+b*m*v_
    +b*c+c*l+c*n-n^2
 

   (14)
                     2       2                               2
     b m v + (k - 1)n  + (- m  + (- l + a)m - c k + c)n - b m  + (a + 1)c l
   + 
     - 2b c k + b c
--R 
--R
--R   (14)
--R                     2       2                               2
--R     b m v + (k - 1)n  + (- m  + (- l + a)m - c k + c)n - b m  + (a + 1)c l
--R   + 
--R     - 2b c k + b c
--E 203

--S 204
t15:=-b^2*k-b*j*k+a*b*l+c*l*m-j*l*m-c*k*n-k*n^2-l*n*v+b^2+c*n
 

   (15)
                2                                                   2      2
   - l n v - k n  + (- c k + c)n + (- j + c)l m + a b l + (- b j - b )k + b
--R 
--R
--R   (15)
--R                2                                                   2      2
--R   - l n v - k n  + (- c k + c)n + (- j + c)l m + a b l + (- b j - b )k + b
--E 204

--S 205
t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+b*n*v+c*n*v-n^2*v
 

             2                          2
   (16)  (- n  + (c + b)n)v + (- m + a)n  + (- j m - c l)n + c j l
--R 
--R
--R             2                          2
--R   (16)  (- n  + (c + b)n)v + (- m + a)n  + (- j m - c l)n + c j l
--E 205

--S 206
t17:=-b*k^2+c*k^2-j*k^2+k^2*n-j*l*p-b*m*p+c*m*p+l*n*p-a*k+n*p
 

                                         2                  2
   (17)  ((l + 1)n + (c - b)m - j l)p + k n + (- j + c - b)k  - a k
--R 
--R
--R                                         2                  2
--R   (17)  ((l + 1)n + (c - b)m - j l)p + k n + (- j + c - b)k  - a k
--E 206

--S 207
t18:=c*l*k-c*k*m-j*k*m+l^2*m-k*l*n-j*n*p+c*m+l*m-k*n+l*n+n
 

                                             2
   (18)  - j n p + ((- k + 1)l - k + 1)n + (l  + l + (- j - c)k + c)m + c k l
--R 
--R
--R                                             2
--R   (18)  - j n p + ((- k + 1)l - k + 1)n + (l  + l + (- j - c)k + c)m + c k l
--E 207

--S 208
t19:=a*b*k-a*c*k+j*k*l+b*k*m-c*k*m-j*k*m-k*l*n+k*m*n_
    -b*k-c*k-j*l-l^2-b*m+c*m-k*n+l*n-l+n
 

   (19)
                                                                2
     (k m + (- k + 1)l - k + 1)n + ((- j - c + b)k + c - b)m - l
   + 
     (j k - j - 1)l + ((- a - 1)c + (a - 1)b)k
--R 
--R
--R   (19)
--R                                                                2
--R     (k m + (- k + 1)l - k + 1)n + ((- j - c + b)k + c - b)m - l
--R   + 
--R     (j k - j - 1)l + ((- a - 1)c + (a - 1)b)k
--E 208

--S 209
t20:=-c^2*k+a*j*m-c*l*m-c*m^2-j*m^2+c*k*n+2*j*k*n+c*m*v+l*n*v_
    -c*m-j*n-l*n+n*v-n
 

   (20)
                                                                2
     ((l + 1)n + c m)v + (- l + (2j + c)k - j - 1)n + (- j - c)m
   + 
                           2
     (- c l + a j - c)m - c k
--R 
--R
--R   (20)
--R                                                                2
--R     ((l + 1)n + c m)v + (- l + (2j + c)k - j - 1)n + (- j - c)m
--R   + 
--R                           2
--R     (- c l + a j - c)m - c k
--E 209

--S 210
t21:=-b*k*l+j*k*l+b*k*m-l^2*m+k*m*n+j*n*p-b*k-j*l-b*m-l*m
 

                             2
   (21)  j n p + k m n + (- l  - l + b k - b)m + ((j - b)k - j)l - b k
--R 
--R
--R                             2
--R   (21)  j n p + k m n + (- l  - l + b k - b)m + ((j - b)k - j)l - b k
--E 210

--S 211
t22:=b^2*k-b*j*k+b*l*m+b*m^2-2*j*k*n-a*m*n+m^2*n-j*l*v-b*m*v-j*l+j*n
 

   (22)
                      2                         2                           2
   (- b m - j l)v + (m  - a m - 2j k + j)n + b m  + b l m - j l + (- b j + b )k
--R 
--R
--R   (22)
--R                      2                         2                           2
--R   (- b m - j l)v + (m  - a m - 2j k + j)n + b m  + b l m - j l + (- b j + b )k
--E 211

--S 212
t23:=b*j*m-c*m*n-j*n
 

   (23)  (- c m - j)n + b j m
--R 
--R
--R   (23)  (- c m - j)n + b j m
--E 212

--S 213
t24:=3*a*k^2+2*k^2*m-a^2*p+a*l*p+m^2*p-k^2*v-l*p*v-2*a*k-b*p+n*p
 

                   2           2              2       2        2
   (24)  (- l p - k )v + (n + m  + a l - b - a )p + 2k m + 3a k  - 2a k
--R 
--R
--R                   2           2              2       2        2
--R   (24)  (- l p - k )v + (n + m  + a l - b - a )p + 2k m + 3a k  - 2a k
--E 213

--S 214
t25:=2*c*k^2+a*k*m+2*k^2*n-a*c*p+c*l*p+l*n*p-k*m*v-n*p*v-c*k-a*m_
    +k*m+l*m+m^2-3*k*n+n*p+n
 

   (25)
                                                   2               2
     (- n p - k m)v + ((l + 1)n + c l - a c)p + (2k  - 3k + 1)n + m
   + 
                               2
     (l + (a + 1)k - a)m + 2c k  - c k
--R 
--R
--R   (25)
--R                                                   2               2
--R     (- n p - k m)v + ((l + 1)n + c l - a c)p + (2k  - 3k + 1)n + m
--R   + 
--R                               2
--R     (l + (a + 1)k - a)m + 2c k  - c k
--E 214

--S 215
t26:=c*k^2+a*k*m+k*l*m+k^2*n-a*c*p+m*n*p+k*l*v-k*m*v_
    +2*b*k-c*k+k*l-a*m+m^2-2*k*n-b*p-l*v-b-l+n
 

   (26)
                                                2               2
     (- k m + (k - 1)l)v + (m n - a c - b)p + (k  - 2k + 1)n + m
   + 
                                      2
     (k l + a k - a)m + (k - 1)l + c k  + (- c + 2b)k - b
--R 
--R
--R   (26)
--R                                                2               2
--R     (- k m + (k - 1)l)v + (m n - a c - b)p + (k  - 2k + 1)n + m
--R   + 
--R                                      2
--R     (k l + a k - a)m + (k - 1)l + c k  + (- c + 2b)k - b
--E 215

--S 216
t27:=2*c*k*m+j*k*m+k*m*n-c^2*p+j*n*p-2*c*m+k*n-n
 

                 2
   (27)  (j n - c )p + (k m + k - 1)n + ((j + 2c)k - 2c)m
--R 
--R
--R                 2
--R   (27)  (j n - c )p + (k m + k - 1)n + ((j + 2c)k - 2c)m
--E 216

--S 217
t28:=a*k*l+2*k*l*m-a*b*p-b*m*p+m*n*p+k*l*v+n*p*v+b*k-l*m+k*n-l*v-b
 

   (28)
   (n p + (k - 1)l)v + (m n - b m - a b)p + k n + (2k - 1)l m + a k l + b k - b
--R 
--R
--R   (28)
--R   (n p + (k - 1)l)v + (m n - b m - a b)p + k n + (2k - 1)l m + a k l + b k - b
--E 217

)clear all
 
   All user variables and function definitions have been cleared.

--S 218
t1:=-x^2+y^2
 

         2    2
   (1)  y  - x
--R 
--R
--R         2    2
--R   (1)  y  - x
--E 218

--S 219
t2:=x*u*v+y*u*a-x-w
 

   (2)  a u y + (u v - 1)x - w
--R 
--R
--R   (2)  a u y + (u v - 1)x - w
--E 219

--S 220
t3:=x*u^2-y*u^2+y*z*a-x*u*a+y*u*a-x*v*a+x*a^2-y*a^2
 

                    2          2               2          2
   (3)  a y z + (- u  + a u - a )y + (- a v + u  - a u + a )x
--R 
--R
--R                    2          2               2          2
--R   (3)  a y z + (- u  + a u - a )y + (- a v + u  - a u + a )x
--E 220

--S 221
t4:=-x*y*v-y^2*v+x*u*w-y*u*w+y*t*a+y*w*a-v^2+a^2
 

             2                                          2    2
   (4)  - v y  + (- v x + (- u + a)w + a t)y + u w x - v  + a
--R 
--R
--R             2                                          2    2
--R   (4)  - v y  + (- v x + (- u + a)w + a t)y + u w x - v  + a
--E 221

--S 222
t5:=-y*z*u-x*u*a+y+t
 

   (5)  - u y z + y - a u x + t
--R 
--R
--R   (5)  - u y z + y - a u x + t
--E 222

--S 223
t6:=x*y*z-x*y*v+x*t*v-y*z*w+z*u-u*v-z*a-v*a
 

   (6)  ((x - w)y + u - a)z - v x y + t v x + (- u - a)v
--R 
--R
--R   (6)  ((x - w)y + u - a)z - v x y + t v x + (- u - a)v
--E 223

--S 224
t7:=x^2*z+x*y*z+x*t*u-y*t*u-x*t*a-x*w*a+z^2-a^2
 

         2           2                                     2
   (7)  z  + (x y + x )z - t u y + (- a w + t u - a t)x - a
--R 
--R
--R         2           2                                     2
--R   (7)  z  + (x y + x )z - t u y + (- a w + t u - a t)x - a
--E 224

--S 225
t8:=x*y*t-x*y*w+x*t*w-y*t*w+x*z+z*t-y*v-v*w
 

   (8)  (x + t)z + ((- w + t)x - t w - v)y + t w x - v w
--R 
--R
--R   (8)  (x + t)z + ((- w + t)x - t w - v)y + t w x - v w
--E 225

--S 226
t9:=-x*u+y*v-u*w+x*a
 

   (9)  v y + (- u + a)x - u w
--R 
--R
--R   (9)  v y + (- u + a)x - u w
--E 226

--S 227
t10:=x*y-w^2
 

                2
   (10)  x y - w
--R 
--R
--R                2
--R   (10)  x y - w
--E 227

--S 228
t11:=-u^2*v+x^2+z
 

              2    2
   (11)  z + x  - u v
--R 
--R
--R              2    2
--R   (11)  z + x  - u v
--E 228

--S 229
t12:=-y*u*v-y*v^2-u*v*w-v^2*w+y*v*a+u*w*a+x+t
 

             2                          2
   (12)  (- v  + (- u + a)v)y + x + (- v  - u v + a u)w + t
--R 
--R
--R             2                          2
--R   (12)  (- v  + (- u + a)v)y + x + (- v  - u v + a u)w + t
--E 229

--S 230
t13:=-z*u*v-u^2*a+u*a^2+y*w+a
 

                            2    2
   (13)  - u v z + w y - a u  + a u + a
--R 
--R
--R                            2    2
--R   (13)  - u v z + w y - a u  + a u + a
--E 230

--S 231
t14:=-x*v^2-z*v*w-u*v*w+y*u*a+x*v*a+v*w*a
 

                               2
   (14)  - v w z + a u y + (- v  + a v)x + (- u + a)v w
--R 
--R
--R                               2
--R   (14)  - v w z + a u y + (- v  + a v)x + (- u + a)v w
--E 231

--S 232
t15:=y*z*u-t*u*v+x*u*a-u*w*a
 

   (15)  u y z + a u x - a u w - t u v
--R 
--R
--R   (15)  u y z + a u x - a u w - t u v
--E 232

--S 233
t16:=y*t*u-y*u*w-t*v*w-v*w^2+x*w*a+y*w*a-v^2+a^2
 

                                          2            2    2
   (16)  ((- u + a)w + t u)y + a w x - v w  - t v w - v  + a
--R 
--R
--R                                          2            2    2
--R   (16)  ((- u + a)w + t u)y + a w x - v w  - t v w - v  + a
--E 233

--S 234
t17:=-x*z-t*u+y*v+u*w
 

   (17)  - x z + v y + u w - t u
--R 
--R
--R   (17)  - x z + v y + u w - t u
--E 234

--S 235
t18:=u^2*v-t*w-z
 

                      2
   (18)  - z - t w + u v
--R 
--R
--R                      2
--R   (18)  - z - t w + u v
--E 235

--S 236
t19:=-y*z*v-y*u*v-t*v^2+y*v*a+t*v*a+u*w*a
 

                                             2
   (19)  - v y z + (- u + a)v y + a u w - t v  + a t v
--R 
--R
--R                                             2
--R   (19)  - v y z + (- u + a)v y + a u w - t v  + a t v
--E 236

--S 237
t20:=-z*u^2+t*w+v
 

            2
   (20)  - u z + t w + v
--R 
--R
--R            2
--R   (20)  - u z + t w + v
--E 237

--S 238
t21:=x*z*u+x*z*v+z^2*w-x*z*a-t*u*a-z*w*a
 

            2
   (21)  w z  + ((v + u - a)x - a w)z - a t u
--R 
--R
--R            2
--R   (21)  w z  + ((v + u - a)x - a w)z - a t u
--E 238

--S 239
t22:=x*t*v-y*z*w+z*t*w-t*v*w+z*u-u*v-z*a+v*a
 

   (22)  (- w y + t w + u - a)z + t v x - t v w + (- u + a)v
--R 
--R
--R   (22)  (- w y + t w + u - a)z + t v x - t v w + (- u + a)v
--E 239

--S 240
t23:=v^2-a^2
 

          2    2
   (23)  v  - a
--R 
--R
--R          2    2
--R   (23)  v  - a
--E 240

--S 241
t24:=y*u+u*w-y*a-w*a
 

   (24)  (u - a)y + (u - a)w
--R 
--R
--R   (24)  (u - a)y + (u - a)w
--E 241

--S 242
t25:=z*w-y*a
 

   (25)  w z - a y
--R 
--R
--R   (25)  w z - a y
--E 242

--S 243
t26:=-y^2+t*w
 

            2
   (26)  - y  + t w
--R 
--R
--R            2
--R   (26)  - y  + t w
--E 243

--S 244
t27:=-x*z+v*w-x*a+w*a
 

   (27)  - x z - a x + (v + a)w
--R 
--R
--R   (27)  - x z - a x + (v + a)w
--E 244

--S 245
t28:=u^2*v-x*y-z
 

                      2
   (28)  - z - x y + u v
--R 
--R
--R                      2
--R   (28)  - z - x y + u v
--E 245

--S 246
t29:=z*u*v+u^2*a-u*a^2-x*t-a
 

                          2    2
   (29)  u v z - t x + a u  - a u - a
--R 
--R
--R                          2    2
--R   (29)  u v z - t x + a u  - a u - a
--E 246

--S 247
t30:=t*u*v+u*w*a-y-t
 

   (30)  - y + a u w + t u v - t
--R 
--R
--R   (30)  - y + a u w + t u v - t
--E 247

--S 248
t31:=-x*z+y*u+t*u-y*a
 

   (31)  - x z + (u - a)y + t u
--R 
--R
--R   (31)  - x z + (u - a)y + t u
--E 248

)clear all
 
   All user variables and function definitions have been cleared.

--S 249
t1:=-x^5-y^5-z^5+5*x*y*z*t*u-u^5
 

           5                 5    5    5
   (1)  - z  + 5t u x y z - y  - x  - u
--R 
--R
--R           5                 5    5    5
--R   (1)  - z  + 5t u x y z - y  - x  - u
--E 249

--S 250
t2:=x*y^3*z+y*z^3*t+x^3*y*u+z*t^3*u+z*t*u^3
 

             3       3      3    3         3
   (2)  t y z  + (x y  + t u  + t u)z + u x y
--R 
--R
--R             3       3      3    3         3
--R   (2)  t y z  + (x y  + t u  + t u)z + u x y
--E 250

--S 251
t3:=x^2*y*z^2+y^2*z*t^2+x^2*t^2*u+x*y^2*u^2+z^2*t*u^2
 

          2       2  2    2 2     2   2    2   2
   (3)  (x y + t u )z  + t y z + u x y  + t u x
--R 
--R
--R          2       2  2    2 2     2   2    2   2
--R   (3)  (x y + t u )z  + t y z + u x y  + t u x
--E 251

--S 252
t4:=x*y*z^5-y^4*z^2*t-2*x^2*y^2*z*t*u+x*z^3*t^2*u-x^4*t*u^2_
    +y*z*t^2*u^3+x*y*u^5
 

             5    2     3      4 2            2 2    2 3       5         2 4
   (4)  x y z  + t u x z  - t y z  + (- 2t u x y  + t u y)z + u x y - t u x
--R 
--R
--R             5    2     3      4 2            2 2    2 3       5         2 4
--R   (4)  x y z  + t u x z  - t y z  + (- 2t u x y  + t u y)z + u x y - t u x
--E 252

--S 253
t5:=x*y^2*z^4-y^5*z*t-x^2*y^3*t*u+2*x*y*z^2*t^2*u+x*t^4*u^2_
    -x^2*y*z*u^3-z*t*u^5
 

           2 4     2       2         5    3 2       5          2 3    4 2
   (5)  x y z  + 2t u x y z  + (- t y  - u x y - t u )z - t u x y  + t u x
--R 
--R
--R           2 4     2       2         5    3 2       5          2 3    4 2
--R   (5)  x y z  + 2t u x y z  + (- t y  - u x y - t u )z - t u x y  + t u x
--E 253

--S 254
t6:=x^3*y^2*t-y*z^2*t^4+x*y^2*z^3*u-y^5*t*u-t^6*u+3*x*y*z*t^2*u^2_
    -x^2*y*u^4-t*u^6
 

             2 3    4   2     2 2             5      3 2    4 2       6    6
   (6)  u x y z  - t y z  + 3t u x y z - t u y  + t x y  - u x y - t u  - t u
--R 
--R
--R             2 3    4   2     2 2             5      3 2    4 2       6    6
--R   (6)  u x y z  - t y z  + 3t u x y z - t u y  + t x y  - u x y - t u  - t u
--E 254

--S 255
t7:=x^4*y^2*z-x*y*z^2*t^3-x*y^5*u-y^3*z^2*t*u-x*t^5*u_
    +2*x^2*y*z*t*u^2+z*t^2*u^4
 

                3    3     2     4 2       2 2     2 4          5    5
   (7)  (- t u y  - t x y)z  + (x y  + 2t u x y + t u )z - u x y  - t u x
--R 
--R
--R                3    3     2     4 2       2 2     2 4          5    5
--R   (7)  (- t u y  - t x y)z  + (x y  + 2t u x y + t u )z - u x y  - t u x
--E 255

--S 256
t8:=y^6*z+y*z^6+x^2*y^4*u-3*x*y^2*z^2*t*u+z^4*t^2*u-x^3*z*t*u^2_
-x*y*t^3*u^3+y*z*u^5
 

           6    2   4           2 2     6    5       2 3        2 4    3 3
   (8)  y z  + t u z  - 3t u x y z  + (y  + u y - t u x )z + u x y  - t u x y
--R 
--R
--R           6    2   4           2 2     6    5       2 3        2 4    3 3
--R   (8)  y z  + t u z  - 3t u x y z  + (y  + u y - t u x )z + u x y  - t u x y
--E 256

)clear all
 
   All user variables and function definitions have been cleared.

--S 257
t1:=a+b+c+d+e+f+g+h-1
 

   (1)  h + g + f + e + d + c + b + a - 1
--R 
--R
--R   (1)  h + g + f + e + d + c + b + a - 1
--E 257

--S 258
t2:=-a^2*k-2*a*b*k-b^2*k-a*c*k-b*c*k-a*d*k-b*d*k-a*e*k_
    -b*e*k-c*e*k-d*e*k-a*f*k-b*f*k-c*f*k-d*f*k+a+b
 

   (2)
                                                                              2
         (- d - c - b - a)f + (- d - c - b - a)e + (- b - a)d + (- b - a)c - b
       + 
                   2
         - 2a b - a
    *
       k
   + 
     b + a
--R 
--R
--R   (2)
--R                                                                              2
--R         (- d - c - b - a)f + (- d - c - b - a)e + (- b - a)d + (- b - a)c - b
--R       + 
--R                   2
--R         - 2a b - a
--R    *
--R       k
--R   + 
--R     b + a
--E 258

--S 259
t3:=-a^2*l-a*b*l-a*c*l-a*d*l-a*e*l-b*e*l-c*e*l-d*e*l_
    +a^2+2*a*b+b^2+a*e+b*e+a*f+b*f
 

   (3)
                                              2                            2
     ((- d - c - b - a)e - a d - a c - a b - a )l + (b + a)f + (b + a)e + b
   + 
             2
     2a b + a
--R 
--R
--R   (3)
--R                                              2                            2
--R     ((- d - c - b - a)e - a d - a c - a b - a )l + (b + a)f + (b + a)e + b
--R   + 
--R             2
--R     2a b + a
--E 259

--S 260
t4:=a+c+e+g-m
 

   (4)  - m + g + e + c + a
--R 
--R
--R   (4)  - m + g + e + c + a
--E 260

)clear all
 
   All user variables and function definitions have been cleared.

--S 261
t1:=-y*z+x*t
 

   (1)  - y z + t x
--R 
--R
--R   (1)  - y z + t x
--E 261

--S 262
t2:=-y*u+x*v+y-v
 

   (2)  (- u + 1)y + v x - v
--R 
--R
--R   (2)  (- u + 1)y + v x - v
--E 262

--S 263
t3:=z^2+t^2-w^2
 

         2    2    2
   (3)  z  - w  + t
--R 
--R
--R         2    2    2
--R   (3)  z  - w  + t
--E 263

--S 264
t4:=u^2+v^2-a^2-2*u+1
 

         2    2         2
   (4)  v  + u  - 2u - a  + 1
--R 
--R
--R         2    2         2
--R   (4)  v  + u  - 2u - a  + 1
--E 264

--S 265
t5:=z^2+t^2-2*z*u+u^2-2*t*v+v^2-b^2
 

         2           2           2    2    2
   (5)  z  - 2u z + v  - 2t v + u  + t  - b
--R 
--R
--R         2           2           2    2    2
--R   (5)  z  - 2u z + v  - 2t v + u  + t  - b
--E 265

)clear all
 
   All user variables and function definitions have been cleared.

--S 266
t1:=x*y+x*z+x*t-u^2
 

                           2
   (1)  x z + x y + t x - u
--R 
--R
--R                           2
--R   (1)  x z + x y + t x - u
--E 266

--S 267
t2:=x*y+y*z+y*t-v^2
 

                          2
   (2)  y z + (x + t)y - v
--R 
--R
--R                          2
--R   (2)  y z + (x + t)y - v
--E 267

--S 268
t3:=x*z+y*z+z*t-w^2
 

                        2
   (3)  (y + x + t)z - w
--R 
--R
--R                        2
--R   (3)  (y + x + t)z - w
--E 268

--S 269
t4:=x*t+y*t+z*t-a^2
 

                           2
   (4)  t z + t y + t x - a
--R 
--R
--R                           2
--R   (4)  t z + t y + t x - a
--E 269

)clear all
 
   All user variables and function definitions have been cleared.

--S 270
t1:=t+v-a
 

   (1)  v + t - a
--R 
--R
--R   (1)  v + t - a
--E 270

--S 271
t2:=x+y+z+t-u-w-a
 

   (2)  z + y + x - w - u + t - a
--R 
--R
--R   (2)  z + y + x - w - u + t - a
--E 271

--S 272
t3:=x*z+y*z+x*t+z*t-u*w-u*a-w*a
 

   (3)  (y + x + t)z + t x + (- u - a)w - a u
--R 
--R
--R   (3)  (y + x + t)z + t x + (- u - a)w - a u
--E 272

--S 273
t4:=x*z*t-u*w*a
 

   (4)  t x z - a u w
--R 
--R
--R   (4)  t x z - a u w
--E 273


--S 274
t1:=y^4-20/7*x^2
 

         4   20  2
   (5)  y  - -- x
              7
--R 
--R
--R         4   20  2
--R   (5)  y  - -- x
--R              7
--E 274

--S 275
t2:=x^2*z^4 + 7/10*x*z^4 + 7/48*z^4 - 50/27*x^2 - 35/27*x - 49/216
 

          2    7      7  4   50  2   35      49
   (6)  (x  + -- x + --)z  - -- x  - -- x - ---
              10     48      27      27     216
--R 
--R
--R          2    7      7  4   50  2   35      49
--R   (6)  (x  + -- x + --)z  - -- x  - -- x - ---
--R              10     48      27      27     216
--E 275

--S 276
t3:=3/5*x^6*y^2*z + x^5*y^3 + 3/7*x^5*y^2*z + 7/5*x^4*y^3_
   - 7/20*x^4*y*z^2 - 3/20*x^4*z^3 + 609/1000*x^3*y^3_
   + 63/200*x^3*y^2*z - 77/125*x^3*y*z^2 - 21/50*x^3*z^3_
   + 49/1250*x^2*y^3 + 147/2000*x^2*y^2*z - 23863/60000*x^2*y*z^2_
   - 91/400*x^2*z^3 - 27391/800000*x*y^3 + 4137/800000*x*y^2*z_
   - 1078/9375*x*y*z^2 - 5887/200000*x*z^3 - 1029/160000*y^3_
   - 24353/1920000*y*z^2 - 343/128000*z^3
 

   (7)
         3  4   21  3    91  2    5887        343   3
     (- -- x  - -- x  - --- x  - ------ x - ------)z
        20      50      400      200000     128000
   + 
         7  4    77  3   23863  2   1078      24353     2
     (- -- x  - --- x  - ----- x  - ---- x - -------)y z
        20      125      60000      9375     1920000
   + 
      3  6   3  5    63  3    147  2    4137     2
     (- x  + - x  + --- x  + ---- x  + ------ x)y z
      5      7      200      2000      800000
   + 
       5   7  4    609  3    49   2    27391      1029   3
     (x  + - x  + ---- x  + ---- x  - ------ x - ------)y
           5      1000      1250      800000     160000
--R 
--R
--R   (7)
--R         3  4   21  3    91  2    5887        343   3
--R     (- -- x  - -- x  - --- x  - ------ x - ------)z
--R        20      50      400      200000     128000
--R   + 
--R         7  4    77  3   23863  2   1078      24353     2
--R     (- -- x  - --- x  - ----- x  - ---- x - -------)y z
--R        20      125      60000      9375     1920000
--R   + 
--R      3  6   3  5    63  3    147  2    4137     2
--R     (- x  + - x  + --- x  + ---- x  + ------ x)y z
--R      5      7      200      2000      800000
--R   + 
--R       5   7  4    609  3    49   2    27391      1029   3
--R     (x  + - x  + ---- x  + ---- x  - ------ x - ------)y
--R           5      1000      1250      800000     160000
--E 276

)spool 
 
Starts dribbling to expr1.output (2009/2/17, 17:45:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 23
sin(x) + 3*cos(x)**2
 

                        2
   (1)  sin(x) + 3cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (1)  sin(x) + 3cos(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 23
tan(x) - 3.45*x
 

   (2)  tan(x) - 3.45 x
                                                       Type: Expression Float
--R 
--R
--R   (2)  tan(x) - 3.45 x
--R                                                       Type: Expression Float
--E 2

--S 3 of 23
(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))
 

               +-+ 2         +--+      +-+         +--+ 2
        - tan(\|7 )  + 2sin(\|11 )tan(\|7 ) - sin(\|11 )
   (3)  -------------------------------------------------
                          cos(y - x) - 4
                                                     Type: Expression Integer
--R 
--R
--R               +-+ 2         +--+      +-+         +--+ 2
--R        - tan(\|7 )  + 2sin(\|11 )tan(\|7 ) - sin(\|11 )
--R   (3)  -------------------------------------------------
--R                          cos(y - x) - 4
--R                                                     Type: Expression Integer
--E 3

--S 4 of 23
log(exp  x)@Expression(Integer)
 

   (4)  x
                                                     Type: Expression Integer
--R 
--R
--R   (4)  x
--R                                                     Type: Expression Integer
--E 4

--S 5 of 23
log(exp  x)@Expression(Complex Integer)
 

              x
   (5)  log(%e )
                                             Type: Expression Complex Integer
--R 
--R
--R              x
--R   (5)  log(%e )
--R                                             Type: Expression Complex Integer
--E 5

--S 6 of 23
sqrt 3 + sqrt(2 + sqrt(-5))
 

         +----------+
         | +---+         +-+
   (6)  \|\|- 5  + 2  + \|3
                                                        Type: AlgebraicNumber
--R 
--R
--R         +----------+
--R         | +---+         +-+
--R   (6)  \|\|- 5  + 2  + \|3
--R                                                        Type: AlgebraicNumber
--E 6

--S 7 of 23
% :: Expression Integer
 

         +----------+
         | +---+         +-+
   (7)  \|\|- 5  + 2  + \|3
                                                     Type: Expression Integer
--R 
--R
--R         +----------+
--R         | +---+         +-+
--R   (7)  \|\|- 5  + 2  + \|3
--R                                                     Type: Expression Integer
--E 7

--S 8 of 23
height mainKernel sin(x + 4)
 

   (8)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  2
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 23
e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) )
 

                2
        - sin(x)  + 8sin(x) - 16
   (9)  ------------------------
                 +---+
              2y\|- y  - 1
                                                     Type: Expression Integer
--R 
--R
--R                2
--R        - sin(x)  + 8sin(x) - 16
--R   (9)  ------------------------
--R                 +---+
--R              2y\|- y  - 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 23
numer e
 

                 2
   (10)  - sin(x)  + 8sin(x) - 16
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R
--R                 2
--R   (10)  - sin(x)  + 8sin(x) - 16
--R        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 10

--S 11 of 23
denom e
 

            +---+
   (11)  2y\|- y  - 1
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R
--R            +---+
--R   (11)  2y\|- y  - 1
--R        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 11

--S 12 of 23
D(e, x)
 

                                        +---+
         (4y cos(x)sin(x) - 16y cos(x))\|- y  - 2cos(x)sin(x) + 8cos(x)
   (12)  --------------------------------------------------------------
                                  +---+     3
                               4y\|- y  + 4y  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                        +---+
--R         (4y cos(x)sin(x) - 16y cos(x))\|- y  - 2cos(x)sin(x) + 8cos(x)
--R   (12)  --------------------------------------------------------------
--R                                  +---+     3
--R                               4y\|- y  + 4y  - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 23
D(e, [x, y], [1, 2])
 

   (13)
                7       4                      7        4         +---+
       ((- 2304y  + 960y )cos(x)sin(x) + (9216y  - 3840y )cos(x))\|- y
     + 
              9        6       3
       (- 960y  + 2160y  - 180y  - 3)cos(x)sin(x)
     + 
             9        6       3
       (3840y  - 8640y  + 720y  + 12)cos(x)
  /
            12        9        6       3      +---+        11        8       5
       (256y   - 1792y  + 1120y  - 112y  + 1)\|- y  - 1024y   + 1792y  - 448y
     + 
          2
       16y
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R                7       4                      7        4         +---+
--R       ((- 2304y  + 960y )cos(x)sin(x) + (9216y  - 3840y )cos(x))\|- y
--R     + 
--R              9        6       3
--R       (- 960y  + 2160y  - 180y  - 3)cos(x)sin(x)
--R     + 
--R             9        6       3
--R       (3840y  - 8640y  + 720y  + 12)cos(x)
--R  /
--R            12        9        6       3      +---+        11        8       5
--R       (256y   - 1792y  + 1120y  - 112y  + 1)\|- y  - 1024y   + 1792y  - 448y
--R     + 
--R          2
--R       16y
--R                                                     Type: Expression Integer
--E 13

--S 14 of 23
complexNumeric(cos(2 - 3*%i))
 

   (14)  - 4.1896256909 688072301 + 9.1092278937 55336598 %i
                                                          Type: Complex Float
--R 
--R
--R   (14)  - 4.1896256909 688072301 + 9.1092278937 55336598 %i
--R                                                          Type: Complex Float
--E 14

--S 15 of 23
numeric(tan 3.8)
 

   (15)  0.7735560905 0312607286
                                                                  Type: Float
--R 
--R
--R   (15)  0.7735560905 0312607286
--R                                                                  Type: Float
--E 15

--S 16 of 23
e2 := cos(x**2 - y + 3)
 

                  2
   (16)  cos(y - x  - 3)
                                                     Type: Expression Integer
--R 
--R
--R                  2
--R   (16)  cos(y - x  - 3)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 23
e3 := asin(e2) - %pi/2
 

                2
   (17)  - y + x  + 3
                                                     Type: Expression Integer
--R 
--R
--R                2
--R   (17)  - y + x  + 3
--R                                                     Type: Expression Integer
--E 17

--S 18 of 23
e3 :: Polynomial Integer
 

                2
   (18)  - y + x  + 3
                                                     Type: Polynomial Integer
--R 
--R
--R                2
--R   (18)  - y + x  + 3
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 23
e3 :: DMP([x, y], Integer)
 

          2
   (19)  x  - y + 3
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R          2
--R   (19)  x  - y + 3
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 19

--S 20 of 23
sin %pi
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 20

--S 21 of 23
cos(%pi / 4)
 

          +-+
         \|2
   (21)  ----
           2
                                                     Type: Expression Integer
--R 
--R
--R          +-+
--R         \|2
--R   (21)  ----
--R           2
--R                                                     Type: Expression Integer
--E 21

--S 22 of 23
tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1
 

               6          4          2
   (22)  tan(x)  + 3tan(x)  + 3tan(x)  + 1
                                                     Type: Expression Integer
--R 
--R
--R               6          4          2
--R   (22)  tan(x)  + 3tan(x)  + 3tan(x)  + 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 23
simplify %
 

            1
   (23)  -------
               6
         cos(x)
                                                     Type: Expression Integer
--R 
--R
--R            1
--R   (23)  -------
--R               6
--R         cos(x)
--R                                                     Type: Expression Integer
--E 23
)spool 
 
Starts dribbling to schaum27.output (2009/2/17, 17:59:30).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(sinh(a*x),x)
 

        cosh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R
--R        cosh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=cosh(a*x)/a
 

        cosh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        cosh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 3      14:540 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*sinh(a*x),x)
 

        - sinh(a x) + a x cosh(a x)
   (1)  ---------------------------
                      2
                     a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - sinh(a x) + a x cosh(a x)
--R   (1)  ---------------------------
--R                      2
--R                     a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=(x*cosh(a*x))/a-sinh(a*x)/a^2
 

        - sinh(a x) + a x cosh(a x)
   (2)  ---------------------------
                      2
                     a
                                                     Type: Expression Integer
--R
--R        - sinh(a x) + a x cosh(a x)
--R   (2)  ---------------------------
--R                      2
--R                     a
--R                                                     Type: Expression Integer
--E

--S 6      14:541 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2*sinh(a*x),x)
 

                             2 2
        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
   (1)  --------------------------------------
                           3
                          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             2 2
--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
--R   (1)  --------------------------------------
--R                           3
--R                          a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=(x^2/a+2/a^3)*cosh(a*x)-(2*x)/a^2*sinh(a*x)
 

                             2 2
        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
   (2)  --------------------------------------
                           3
                          a
                                                     Type: Expression Integer
--R
--R                             2 2
--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
--R   (2)  --------------------------------------
--R                           3
--R                          a
--R                                                     Type: Expression Integer
--E

--S 9      14:542 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10     14:543 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)/x,x)
 

           x
         ++  sinh(%N a)
   (1)   |   ---------- d%N
        ++       %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sinh(%N a)
--I   (1)   |   ---------- d%N
--I        ++       %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 11     14:544 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)/x^2,x)
 

           x
         ++  sinh(%N a)
   (1)   |   ---------- d%N
        ++         2
                 %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sinh(%N a)
--I   (1)   |   ---------- d%N
--R        ++         2
--I                 %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 12
aa:=integrate(1/sinh(a*x),x)
 

        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
   (1)  -----------------------------------------------------------------
                                        a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R   (1)  -----------------------------------------------------------------
--R                                        a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13
bb:=1/a*log(tanh(a*x)/2)
 

            tanh(a x)
        log(---------)
                2
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R            tanh(a x)
--R        log(---------)
--R                2
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 14     14:545 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
             tanh(a x)
       - log(---------) - log(sinh(a x) + cosh(a x) + 1)
                 2
     + 
       log(sinh(a x) + cosh(a x) - 1)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R             tanh(a x)
--R       - log(---------) - log(sinh(a x) + cosh(a x) + 1)
--R                 2
--R     + 
--R       log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 15     14:546 Axiom cannot compute this integral
aa:=integrate(x/sinh(a*x),x)
 

           x
         ++      %N
   (1)   |   ---------- d%N
        ++   sinh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %N
--I   (1)   |   ---------- d%N
--I        ++   sinh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 16
aa:=integrate(sinh(a*x)^2,x)
 

        cosh(a x)sinh(a x) - a x
   (1)  ------------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cosh(a x)sinh(a x) - a x
--R   (1)  ------------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 17
bb:=(sinh(a*x)*cosh(a*x))/(2*a)-x/2
 

        cosh(a x)sinh(a x) - a x
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R        cosh(a x)sinh(a x) - a x
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 18     14:547 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19
aa:=integrate(x*sinh(a*x)^2,x)
 

                   2                                      2     2 2
        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  - 2a x
   (1)  -----------------------------------------------------------
                                      2
                                    8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2                                      2     2 2
--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  - 2a x
--R   (1)  -----------------------------------------------------------
--R                                      2
--R                                    8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 20
bb:=(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)-x^2/4
 

                                         2 2
        2a x sinh(2a x) - cosh(2a x) - 2a x
   (2)  ------------------------------------
                           2
                         8a
                                                     Type: Expression Integer
--R
--R                                         2 2
--R        2a x sinh(2a x) - cosh(2a x) - 2a x
--R   (2)  ------------------------------------
--R                           2
--R                         8a
--R                                                     Type: Expression Integer
--E

--S 21
cc:=aa-bb
 

   (3)
                                    2
       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
     + 
                  2
       - cosh(a x)
  /
       2
     8a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2
--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
--R     + 
--R                  2
--R       - cosh(a x)
--R  /
--R       2
--R     8a
--R                                                     Type: Expression Integer
--E

--S 22
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 23
dd:=sinhsqrrule cc
 

   (5)
                                                                        2
   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
   --------------------------------------------------------------------------
                                         2
                                      16a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                                        2
--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
--R   --------------------------------------------------------------------------
--R                                         2
--R                                      16a
--R                                                     Type: Expression Integer
--E

--S 24
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25
ee:=coshsqrrule dd
 

        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
   (7)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
--R   (7)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 26
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (8)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %K sinh(y + x) - %K sinh(y - x)
--I   (8)  %K cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27     14:548 Schaums and Axiom agree
ff:=sinhcoshrule ee
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28
aa:=integrate(1/sinh(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29
bb:=-coth(a*x)/a
 

          coth(a x)
   (2)  - ---------
              a
                                                     Type: Expression Integer
--R
--R          coth(a x)
--R   (2)  - ---------
--R              a
--R                                                     Type: Expression Integer
--E

--S 30
cc:=aa-bb
 

   (3)
                         2
       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
     + 
                 2
       (cosh(a x)  - 1)coth(a x) - 2
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                         2
--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
--R     + 
--R                 2
--R       (cosh(a x)  - 1)coth(a x) - 2
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 31
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 32
dd:=sinhsqrrule cc
 

   (5)
                                                          2
   4cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) + 2cosh(a x)  - 3)coth(a x) - 4
   --------------------------------------------------------------------------
                                                               2
            4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                          2
--R   4cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) + 2cosh(a x)  - 3)coth(a x) - 4
--R   --------------------------------------------------------------------------
--R                                                               2
--R            4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
--R                                                     Type: Expression Integer
--E

--S 33
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34
ee:=coshsqrrule dd
 

        2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2
   (7)  ------------------------------------------------------------
                  2a cosh(a x)sinh(a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R        2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2
--R   (7)  ------------------------------------------------------------
--R                  2a cosh(a x)sinh(a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 35
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %Q sinh(y + x) - %Q sinh(y - x)
   (8)  %Q cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--I                             %B sinh(y + x) - %B sinh(y - x)
--I   (8)  %B cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36
ff:=sinhcoshrule ee
 

        coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2
   (9)  ---------------------------------------------------
                  a sinh(2a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R        coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2
--R   (9)  ---------------------------------------------------
--R                  a sinh(2a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 37
cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 

                    cosh(x)
   (10)  coth(x) == -------
                    sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    cosh(x)
--R   (10)  coth(x) == -------
--R                    sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38
gg:=cothrule ff
 

         cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x)
   (11)  ------------------------------------------------------------------
                 a sinh(a x)sinh(2a x) + (a cosh(2a x) - a)sinh(a x)
                                                     Type: Expression Integer
--R
--R         cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x)
--R   (11)  ------------------------------------------------------------------
--R                 a sinh(a x)sinh(2a x) + (a cosh(2a x) - a)sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 39
hh:=sinhcoshrule gg
 

         sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
   (12)  -----------------------------------------------------------
             a sinh(3a x) + 2a sinh(a x)sinh(2a x) - 3a sinh(a x)
                                                     Type: Expression Integer
--R
--R         sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
--R   (12)  -----------------------------------------------------------
--R             a sinh(3a x) + 2a sinh(a x)sinh(2a x) - 3a sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 40
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %R cosh(y + x) - %R cosh(y - x)
   (13)  %R sinh(x)sinh(y) == -------------------------------
                                             2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %M cosh(y + x) - %M cosh(y - x)
--I   (13)  %M sinh(x)sinh(y) == -------------------------------
--R                                             2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 41
ii:=sinhsinhrule gg
 

         2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
   (14)  ---------------------------------------------------------------------
               (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
                                                     Type: Expression Integer
--R
--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
--R   (14)  ---------------------------------------------------------------------
--R               (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 42
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                              %S cosh(y + x) + %S cosh(y - x)
   (15)  %S cosh(x)cosh(y) == -------------------------------
                                             2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %N cosh(y + x) + %N cosh(y - x)
--I   (15)  %N cosh(x)cosh(y) == -------------------------------
--R                                             2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 43
jj:=coshcoshrule ii
 

         2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x)
   (16)  ----------------------------------------------------------
         (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
                                                     Type: Expression Integer
--R
--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x)
--R   (16)  ----------------------------------------------------------
--R         (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 44     14:549 Schaums and Axiom differ by a constant
kk:=sinhcoshrule jj
 

         1
   (17)  -
         a
                                                     Type: Expression Integer
--R
--R         1
--R   (17)  -
--R         a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 45
aa:=integrate(sinh(a*x)*sinh(p*x),x)
 

        a cosh(a x)sinh(p x) - p cosh(p x)sinh(a x)
   (1)  -------------------------------------------
          2    2          2       2    2          2
        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a cosh(a x)sinh(p x) - p cosh(p x)sinh(a x)
--R   (1)  -------------------------------------------
--R          2    2          2       2    2          2
--R        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 46
bb:=(sinh(a+p)*x)/(2*(a+p))-(sinh(a-p)*x)/(2*(a-p))
 

        (p - a)x sinh(p + a) + (- p - a)x sinh(p - a)
   (2)  ---------------------------------------------
                            2     2
                          2p  - 2a
                                                     Type: Expression Integer
--R
--R        (p - a)x sinh(p + a) + (- p - a)x sinh(p - a)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 47     14:550 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       2a cosh(a x)sinh(p x)
     + 
                                                               2
       ((- p + a)x sinh(p + a) + (p + a)x sinh(p - a))sinh(a x)
     + 
                                                   2
       - 2p cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
     + 
                           2
       (- p - a)x cosh(a x) sinh(p - a)
  /
        2     2          2        2     2          2
     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       2a cosh(a x)sinh(p x)
--R     + 
--R                                                               2
--R       ((- p + a)x sinh(p + a) + (p + a)x sinh(p - a))sinh(a x)
--R     + 
--R                                                   2
--R       - 2p cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
--R     + 
--R                           2
--R       (- p - a)x cosh(a x) sinh(p - a)
--R  /
--R        2     2          2        2     2          2
--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 48
aa:=integrate(sinh(a*x)*sin(p*x),x)
 

   (1)
                                         2
       (a sin(p x) - p cos(p x))sinh(a x)
     + 
       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (a cosh(a x)  + a)sin(p x) - p cos(p x)cosh(a x)  + p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (a sin(p x) - p cos(p x))sinh(a x)
--R     + 
--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (a cosh(a x)  + a)sin(p x) - p cos(p x)cosh(a x)  + p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49
bb:=(a*cosh(a*x)*sin(p*x)-p*sinh(a*x)*cos(p*x))/(a^2+p^2)
 

        - p cos(p x)sinh(a x) + a cosh(a x)sin(p x)
   (2)  -------------------------------------------
                           2    2
                          p  + a
                                                     Type: Expression Integer
--R
--R        - p cos(p x)sinh(a x) + a cosh(a x)sin(p x)
--R   (2)  -------------------------------------------
--R                           2    2
--R                          p  + a
--R                                                     Type: Expression Integer
--E

--S 50
cc:=aa-bb
 

   (3)
                                         2                 2
       (a sin(p x) + p cos(p x))sinh(a x)  + (- a cosh(a x)  + a)sin(p x)
     + 
                            2
       - p cos(p x)cosh(a x)  + p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                         2                 2
--R       (a sin(p x) + p cos(p x))sinh(a x)  + (- a cosh(a x)  + a)sin(p x)
--R     + 
--R                            2
--R       - p cos(p x)cosh(a x)  + p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 51
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 52
dd:=sinhsqrrule cc
 

   (5)
                                   2
       (a cosh(2a x) - 2a cosh(a x)  + a)sin(p x) + p cos(p x)cosh(2a x)
     + 
                             2
       - 2p cos(p x)cosh(a x)  + p cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                   2
--R       (a cosh(2a x) - 2a cosh(a x)  + a)sin(p x) + p cos(p x)cosh(2a x)
--R     + 
--R                             2
--R       - 2p cos(p x)cosh(a x)  + p cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 53
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 54     14:551 Schaums and Axiom agree
ee:=coshsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 55
aa:=integrate(sinh(a*x)*cos(p*x),x)
 

   (1)
                                         2
       (p sin(p x) + a cos(p x))sinh(a x)
     + 
       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(a x)  + a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (p sin(p x) + a cos(p x))sinh(a x)
--R     + 
--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(a x)  + a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 56
bb:=(a*cosh(a*x)*cos(p*x)+p*sinh(a*x)*sin(p*x))/(a^2+p^2)
 

        p sin(p x)sinh(a x) + a cos(p x)cosh(a x)
   (2)  -----------------------------------------
                          2    2
                         p  + a
                                                     Type: Expression Integer
--R
--R        p sin(p x)sinh(a x) + a cos(p x)cosh(a x)
--R   (2)  -----------------------------------------
--R                          2    2
--R                         p  + a
--R                                                     Type: Expression Integer
--E

--S 57
cc:=aa-bb
 

   (3)
                                           2               2
       (- p sin(p x) + a cos(p x))sinh(a x)  + (p cosh(a x)  - p)sin(p x)
     + 
                            2
       - a cos(p x)cosh(a x)  + a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2               2
--R       (- p sin(p x) + a cos(p x))sinh(a x)  + (p cosh(a x)  - p)sin(p x)
--R     + 
--R                            2
--R       - a cos(p x)cosh(a x)  + a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 58
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 59
dd:=sinhsqrrule cc
 

   (5)
                                     2
       (- p cosh(2a x) + 2p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(2a x)
     + 
                             2
       - 2a cos(p x)cosh(a x)  + a cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                     2
--R       (- p cosh(2a x) + 2p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(2a x)
--R     + 
--R                             2
--R       - 2a cos(p x)cosh(a x)  + a cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 60
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 61     14:552 Schaums and Axiom agree
ee:=coshsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 62
aa:=integrate(1/(p+q*sinh(a*x)),x)
 

   (1)
     log
                 2         2      2                              2         2
                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
              + 
                                  2     2
                2p q cosh(a x) + q  + 2p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                 3     2                   3     2                  2     3
            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
       /
                       2                                             2
            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
          + 
            2p cosh(a x) - q
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     log
--R                 2         2      2                              2         2
--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R              + 
--R                                  2     2
--R                2p q cosh(a x) + q  + 2p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                 3     2                   3     2                  2     3
--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R       /
--R                       2                                             2
--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R          + 
--R            2p cosh(a x) - q
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63
bb:=1/(a*sqrt(p^2+q^2))*log((q*%e^(a*x)+p-sqrt(p^2+q^2))/(q*%e^(a*x)+p+sqrt(p^2+q^2)))
 

               +-------+
               | 2    2        a x
            - \|q  + p   + q %e    + p
        log(--------------------------)
              +-------+
              | 2    2        a x
             \|q  + p   + q %e    + p
   (2)  -------------------------------
                    +-------+
                    | 2    2
                  a\|q  + p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2        a x
--R            - \|q  + p   + q %e    + p
--R        log(--------------------------)
--R              +-------+
--R              | 2    2        a x
--R             \|q  + p   + q %e    + p
--R   (2)  -------------------------------
--R                    +-------+
--R                    | 2    2
--R                  a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 64     14:553 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) + q  + 2p
             *
                 +-------+
                 | 2    2
                \|q  + p
            + 
                   3     2                   3     2                  2     3
              (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) - q
     + 
                +-------+
                | 2    2        a x
             - \|q  + p   + q %e    + p
       - log(--------------------------)
               +-------+
               | 2    2        a x
              \|q  + p   + q %e    + p
  /
       +-------+
       | 2    2
     a\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) + q  + 2p
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R            + 
--R                   3     2                   3     2                  2     3
--R              (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) - q
--R     + 
--R                +-------+
--R                | 2    2        a x
--R             - \|q  + p   + q %e    + p
--R       - log(--------------------------)
--R               +-------+
--R               | 2    2        a x
--R              \|q  + p   + q %e    + p
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 65
aa:=integrate(1/(p*q*sinh(a*x))^2,x)
 

   (1)
                                         2
   - ------------------------------------------------------------------------
        2 2         2       2 2                        2 2         2      2 2
     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R   - ------------------------------------------------------------------------
--R        2 2         2       2 2                        2 2         2      2 2
--R     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 66
t1:=integrate(1/(p+q*sinh(a*x)),x)
 

   (2)
     log
                 2         2      2                              2         2
                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
              + 
                                  2     2
                2p q cosh(a x) + q  + 2p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                 3     2                   3     2                  2     3
            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
       /
                       2                                             2
            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
          + 
            2p cosh(a x) - q
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R
--R   (2)
--R     log
--R                 2         2      2                              2         2
--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R              + 
--R                                  2     2
--R                2p q cosh(a x) + q  + 2p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                 3     2                   3     2                  2     3
--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R       /
--R                       2                                             2
--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R          + 
--R            2p cosh(a x) - q
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E

--S 67
bb:=(-q*cosh(a*x))/(a*(p^2+q^2)*(p+q*sinh(a*x)))+p/(p^2+q^2)*t1
 

   (3)
                           2
         (p q sinh(a x) + p )
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
                     +-------+
                     | 2    2
       - q cosh(a x)\|q  + p
  /
                                               +-------+
          3      2                   2      3  | 2    2
     ((a q  + a p q)sinh(a x) + a p q  + a p )\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                           2
--R         (p q sinh(a x) + p )
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R                     +-------+
--R                     | 2    2
--R       - q cosh(a x)\|q  + p
--R  /
--R                                               +-------+
--R          3      2                   2      3  | 2    2
--R     ((a q  + a p q)sinh(a x) + a p q  + a p )\|q  + p
--R                                                     Type: Expression Integer
--E

--S 68     14:554 Axiom cannot simplify this expression
cc:=aa-bb
 

   (4)
              3 3         3        3 3             4 2          2
           - p q sinh(a x)  + (- 2p q cosh(a x) - p q )sinh(a x)
         + 
               3 3         2     4 2             3 3              4 2         2
           (- p q cosh(a x)  - 2p q cosh(a x) + p q )sinh(a x) - p q cosh(a x)
         + 
            4 2
           p q
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
            2 3                  2      2 3         2     3     2
           p q cosh(a x)sinh(a x)  + (2p q cosh(a x)  - 2q  - 2p q)sinh(a x)
         + 
            2 3         3    2 3                2     3
           p q cosh(a x)  - p q cosh(a x) - 2p q  - 2p
      *
          +-------+
          | 2    2
         \|q  + p
  /
             2 5      4 3          3
         (a p q  + a p q )sinh(a x)
       + 
               2 5       4 3                3 4      5 2          2
         ((2a p q  + 2a p q )cosh(a x) + a p q  + a p q )sinh(a x)
       + 
                 2 5      4 3          2        3 4       5 2                2 5
             (a p q  + a p q )cosh(a x)  + (2a p q  + 2a p q )cosh(a x) - a p q
           + 
                  4 3
             - a p q
        *
           sinh(a x)
       + 
             3 4      5 2          2      3 4      5 2
         (a p q  + a p q )cosh(a x)  - a p q  - a p q
    *
        +-------+
        | 2    2
       \|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R              3 3         3        3 3             4 2          2
--R           - p q sinh(a x)  + (- 2p q cosh(a x) - p q )sinh(a x)
--R         + 
--R               3 3         2     4 2             3 3              4 2         2
--R           (- p q cosh(a x)  - 2p q cosh(a x) + p q )sinh(a x) - p q cosh(a x)
--R         + 
--R            4 2
--R           p q
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R            2 3                  2      2 3         2     3     2
--R           p q cosh(a x)sinh(a x)  + (2p q cosh(a x)  - 2q  - 2p q)sinh(a x)
--R         + 
--R            2 3         3    2 3                2     3
--R           p q cosh(a x)  - p q cosh(a x) - 2p q  - 2p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R  /
--R             2 5      4 3          3
--R         (a p q  + a p q )sinh(a x)
--R       + 
--R               2 5       4 3                3 4      5 2          2
--R         ((2a p q  + 2a p q )cosh(a x) + a p q  + a p q )sinh(a x)
--R       + 
--R                 2 5      4 3          2        3 4       5 2                2 5
--R             (a p q  + a p q )cosh(a x)  + (2a p q  + 2a p q )cosh(a x) - a p q
--R           + 
--R                  4 3
--R             - a p q
--R        *
--R           sinh(a x)
--R       + 
--R             3 4      5 2          2      3 4      5 2
--R         (a p q  + a p q )cosh(a x)  - a p q  - a p q
--R    *
--R        +-------+
--R        | 2    2
--R       \|q  + p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 69
aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 

   (1)
   [
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                + 
                     4         3        4     2 2
                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4        4     2 2          2    4     2 2     4
                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                   4     3 2          2        4     3 2
              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                   4     3 2          2       4      3 2     5
              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
            + 
                 2         3        2     2                        2         4
              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                   2     2          2    2
              (- 2q  + 4p )cosh(a x)  + q
    /
            +---------+
            |   2    2
       2a p\|- q  + p
     ,

       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
    /
           +-------+
           | 2    2
       a p\|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3        4     2 2
--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4        4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                   4     3 2          2        4     3 2
--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                   4     3 2          2       4      3 2     5
--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3        2     2                        2         4
--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                   2     2          2    2
--R              (- 2q  + 4p )cosh(a x)  + q
--R    /
--R            +---------+
--R            |   2    2
--R       2a p\|- q  + p
--R     ,
--R
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R    /
--R           +-------+
--R           | 2    2
--R       a p\|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 70
bb1:=1/(a*p*sqrt(q^2-p^2))*atan((sqrt(q^2-p^2)*tanh(a*x))/p)
 

                       +-------+
                       | 2    2
             tanh(a x)\|q  - p
        atan(-------------------)
                      p
   (2)  -------------------------
                  +-------+
                  | 2    2
              a p\|q  - p
                                                     Type: Expression Integer
--R
--R                       +-------+
--R                       | 2    2
--R             tanh(a x)\|q  - p
--R        atan(-------------------)
--R                      p
--R   (2)  -------------------------
--R                  +-------+
--R                  | 2    2
--R              a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 71
bb2:=1/(2*a*p*sqrt(p^2-q^2))*log((p+sqrt(p^2-q^2)*tanh(a*x))/(p-sqrt(p^2-q^2)*tanh(a*x)))
 

                        +---------+
                        |   2    2
            - tanh(a x)\|- q  + p   - p
        log(---------------------------)
                       +---------+
                       |   2    2
             tanh(a x)\|- q  + p   - p
   (3)  --------------------------------
                     +---------+
                     |   2    2
                2a p\|- q  + p
                                                     Type: Expression Integer
--R
--R                        +---------+
--R                        |   2    2
--R            - tanh(a x)\|- q  + p   - p
--R        log(---------------------------)
--R                       +---------+
--R                       |   2    2
--R             tanh(a x)\|- q  + p   - p
--R   (3)  --------------------------------
--R                     +---------+
--R                     |   2    2
--R                2a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 72
cc1:=aa.1-bb1
 

   (4)
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     4         4     4                  3
                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
                  + 
                       4         2     4     2 2          2
                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                  + 
                       4         3        4     2 2
                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                  + 
                     4         4        4     2 2          2    4     2 2     4
                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     4     3 2          2        4     3 2
                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
              + 
                     4     3 2          2       4      3 2     5
                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
           /
                 2         4     2                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   2         2     2     2          2
                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
              + 
                   2         3        2     2                        2         4
                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                     2     2          2    2
                (- 2q  + 4p )cosh(a x)  + q
     + 
                                     +-------+
           +---------+               | 2    2
           |   2    2      tanh(a x)\|q  - p
       - 2\|- q  + p  atan(-------------------)
                                    p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     4         4     4                  3
--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                  + 
--R                       4         2     4     2 2          2
--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                  + 
--R                       4         3        4     2 2
--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                  + 
--R                     4         4        4     2 2          2    4     2 2     4
--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     4     3 2          2        4     3 2
--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R              + 
--R                     4     3 2          2       4      3 2     5
--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R           /
--R                 2         4     2                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   2         2     2     2          2
--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R              + 
--R                   2         3        2     2                        2         4
--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                     2     2          2    2
--R                (- 2q  + 4p )cosh(a x)  + q
--R     + 
--R                                     +-------+
--R           +---------+               | 2    2
--R           |   2    2      tanh(a x)\|q  - p
--R       - 2\|- q  + p  atan(-------------------)
--R                                    p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 73
cc2:=aa.2-bb1
 

   (5)
                        +-------+
                        | 2    2
              tanh(a x)\|q  - p
       - atan(-------------------)
                       p
     + 
       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
  /
         +-------+
         | 2    2
     a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                        +-------+
--R                        | 2    2
--R              tanh(a x)\|q  - p
--R       - atan(-------------------)
--R                       p
--R     + 
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 74
cc3:=aa.2-bb1
 

   (6)
                        +-------+
                        | 2    2
              tanh(a x)\|q  - p
       - atan(-------------------)
                       p
     + 
       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
  /
         +-------+
         | 2    2
     a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                        +-------+
--R                        | 2    2
--R              tanh(a x)\|q  - p
--R       - atan(-------------------)
--R                       p
--R     + 
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 75     14:555 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (7)
                                   +---------+
          +-------+                |   2    2
          | 2    2     - tanh(a x)\|- q  + p   - p
       - \|q  - p  log(---------------------------)
                                  +---------+
                                  |   2    2
                        tanh(a x)\|- q  + p   - p
     + 
           +---------+
           |   2    2
         2\|- q  + p
      *
         atan
                  2         2     2                      2         2    2     2
                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
             *
                 +-------+
                 | 2    2
                \|q  - p
           /
                  2     3
              2p q  - 2p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                   +---------+
--R          +-------+                |   2    2
--R          | 2    2     - tanh(a x)\|- q  + p   - p
--R       - \|q  - p  log(---------------------------)
--R                                  +---------+
--R                                  |   2    2
--R                        tanh(a x)\|- q  + p   - p
--R     + 
--R           +---------+
--R           |   2    2
--R         2\|- q  + p
--R      *
--R         atan
--R                  2         2     2                      2         2    2     2
--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  - p
--R           /
--R                  2     3
--R              2p q  - 2p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 76
aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 

   (1)
   [
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                + 
                     4         3        4     2 2
                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4        4     2 2          2    4     2 2     4
                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                   4     3 2          2        4     3 2
              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                   4     3 2          2       4      3 2     5
              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
            + 
                 2         3        2     2                        2         4
              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                   2     2          2    2
              (- 2q  + 4p )cosh(a x)  + q
    /
            +---------+
            |   2    2
       2a p\|- q  + p
     ,

       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
    /
           +-------+
           | 2    2
       a p\|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3        4     2 2
--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4        4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                   4     3 2          2        4     3 2
--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                   4     3 2          2       4      3 2     5
--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3        2     2                        2         4
--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                   2     2          2    2
--R              (- 2q  + 4p )cosh(a x)  + q
--R    /
--R            +---------+
--R            |   2    2
--R       2a p\|- q  + p
--R     ,
--R
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R    /
--R           +-------+
--R           | 2    2
--R       a p\|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 77
bb:=1/(2*a*p*sqrt(p^2+q^2))*log((p+sqrt(p^2+q^2)*tanh(a*x))/(p-sqrt(p^2+q^2)*tanh(a*x)))
 

                        +-------+
                        | 2    2
            - tanh(a x)\|q  + p   - p
        log(-------------------------)
                       +-------+
                       | 2    2
             tanh(a x)\|q  + p   - p
   (2)  ------------------------------
                     +-------+
                     | 2    2
                2a p\|q  + p
                                                     Type: Expression Integer
--R
--R                        +-------+
--R                        | 2    2
--R            - tanh(a x)\|q  + p   - p
--R        log(-------------------------)
--R                       +-------+
--R                       | 2    2
--R             tanh(a x)\|q  + p   - p
--R   (2)  ------------------------------
--R                     +-------+
--R                     | 2    2
--R                2a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 78
cc1:=aa.1-bb
 

   (3)
          +-------+
          | 2    2
         \|q  + p
      *
         log
                     4         4     4                  3
                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
                  + 
                       4         2     4     2 2          2
                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                  + 
                       4         3        4     2 2
                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                  + 
                     4         4        4     2 2          2    4     2 2     4
                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     4     3 2          2        4     3 2
                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
              + 
                     4     3 2          2       4      3 2     5
                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
           /
                 2         4     2                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   2         2     2     2          2
                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
              + 
                   2         3        2     2                        2         4
                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                     2     2          2    2
                (- 2q  + 4p )cosh(a x)  + q
     + 
                                     +-------+
          +---------+                | 2    2
          |   2    2     - tanh(a x)\|q  + p   - p
       - \|- q  + p  log(-------------------------)
                                    +-------+
                                    | 2    2
                          tanh(a x)\|q  + p   - p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R      *
--R         log
--R                     4         4     4                  3
--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                  + 
--R                       4         2     4     2 2          2
--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                  + 
--R                       4         3        4     2 2
--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                  + 
--R                     4         4        4     2 2          2    4     2 2     4
--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     4     3 2          2        4     3 2
--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R              + 
--R                     4     3 2          2       4      3 2     5
--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R           /
--R                 2         4     2                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   2         2     2     2          2
--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R              + 
--R                   2         3        2     2                        2         4
--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                     2     2          2    2
--R                (- 2q  + 4p )cosh(a x)  + q
--R     + 
--R                                     +-------+
--R          +---------+                | 2    2
--R          |   2    2     - tanh(a x)\|q  + p   - p
--R       - \|- q  + p  log(-------------------------)
--R                                    +-------+
--R                                    | 2    2
--R                          tanh(a x)\|q  + p   - p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  + p
--R                                                     Type: Expression Integer
--E

--S 79     14:556 Axiom cannot simplify this expression
cc2:=aa.2-bb
 

   (4)
                                   +-------+
          +-------+                | 2    2
          | 2    2     - tanh(a x)\|q  + p   - p
       - \|q  - p  log(-------------------------)
                                  +-------+
                                  | 2    2
                        tanh(a x)\|q  + p   - p
     + 
           +-------+
           | 2    2
         2\|q  + p
      *
         atan
                  2         2     2                      2         2    2     2
                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
             *
                 +-------+
                 | 2    2
                \|q  - p
           /
                  2     3
              2p q  - 2p
  /
          +-------+ +-------+
          | 2    2  | 2    2
     2a p\|q  - p  \|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                   +-------+
--R          +-------+                | 2    2
--R          | 2    2     - tanh(a x)\|q  + p   - p
--R       - \|q  - p  log(-------------------------)
--R                                  +-------+
--R                                  | 2    2
--R                        tanh(a x)\|q  + p   - p
--R     + 
--R           +-------+
--R           | 2    2
--R         2\|q  + p
--R      *
--R         atan
--R                  2         2     2                      2         2    2     2
--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  - p
--R           /
--R                  2     3
--R              2p q  - 2p
--R  /
--R          +-------+ +-------+
--R          | 2    2  | 2    2
--R     2a p\|q  - p  \|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 80     14:557 Axiom cannot compute this integral
aa:=integrate(x^m*sinh(a*x),x)
 

           x
         ++              m
   (1)   |   sinh(%N a)%N d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++              m
--I   (1)   |   sinh(%N a)%N d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 81     14:558 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)^n,x)
 

           x
         ++            n
   (1)   |   sinh(%N a) d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   sinh(%N a) d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 82     14:559 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)/x^n,x)
 

           x
         ++  sinh(%N a)
   (1)   |   ---------- d%N
        ++         n
                 %N
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++  sinh(%T a)
--I   (3)   |   ---------- d%T
--R        ++         n
--I                 %T
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 83     14:560 Axiom cannot compute this integral
aa:=integrate(1/sinh(a*x)^n,x)
 

           x
         ++       1
   (1)   |   ----------- d%N
        ++             n
             sinh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%N
--R        ++             n
--I             sinh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 84     14:561 Axiom cannot compute this integral
aa:=integrate(x/sinh(a*x)^n,x)
 

           x
         ++       %N
   (1)   |   ----------- d%N
        ++             n
             sinh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %N
--I   (1)   |   ----------- d%N
--R        ++             n
--I             sinh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to perman.output (2009/2/17, 17:56:8).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
kn n ==
  r : MATRIX INT := new(n,n,1)
  for i in 1..n repeat
    r.i.i := 0
  r
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 3
permanent(kn(5) :: SQMATRIX(5,INT))
 
   Compiling function kn with type PositiveInteger -> Matrix Integer 

   (2)  44
                                                        Type: PositiveInteger
--R 
--R   Compiling function kn with type PositiveInteger -> Matrix Integer 
--R
--R   (2)  44
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 3
[permanent(kn(n) :: SQMATRIX(n,INT)) for n in 1..13]
 
   Cannot compile conversion for types involving local variables. In 
      particular, could not compile the expression involving :: 
      SQMATRIX(n,INT) 
   AXIOM will attempt to step through and interpret the code.

   (3)
   [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932]
                                                Type: List NonNegativeInteger
--R 
--R   Cannot compile conversion for types involving local variables. In 
--R      particular, could not compile the expression involving :: 
--R      SQMATRIX(n,INT) 
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (3)
--R   [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932]
--R                                                Type: List NonNegativeInteger
--E 3
)spool 
 
Starts dribbling to r21bugsbig.output (2009/2/17, 17:56:31).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
)set expose add constructor CyclotomicPolynomialPackage
 
   CyclotomicPolynomialPackage is now explicitly exposed in frame 
      initial 
)set message type off
 
)set message time off
 

--S 1  of 22
n : PositiveInteger := 5
 

   (1)  5
--R 
--R
--R   (1)  5
--E 1

--S 2 of 22
UZn : List(PositiveInteger) := [i for i in 1 .. n-1 | gcd(i,n) = 1]
 

   (2)  [1,2,3,4]
--R 
--R
--R   (2)  [1,2,3,4]
--E 2

--S 3 of 22
vars : List(Symbol) := [concat("t", i::String)::Symbol for i in 0 ..#UZn-1] ;
 

--E 3

--S 4  of 22
Zt := DistributedMultivariatePolynomial(vars, Integer) ;   K :=Fraction(Zt) ;
 

--E 4 

--S 5 of 22
t : List(K) := [v::K for v in vars]
 

   (5)  [t0,t1,t2,t3]
--R 
--R
--R   (5)  [t0,t1,t2,t3]
--E 5

--S 6 of 22
t(#t) := 0 ; t
 

   (6)  [t0,t1,t2,0]
--R 
--R
--R   (6)  [t0,t1,t2,0]
--E 6

--S 7 of 22
Zn := IntegerMod(n) ;
 

--E 7 

--S 8 of 22
rapport(i : Integer, j : Integer) : Integer ==   -- returns <i/j> modulo n
   k : Zn := i * recip(j::Zn)::Zn
   return convert(k)
 
   Function declaration rapport : (Integer,Integer) -> Integer has been
      added to workspace.
--R 
--R   Function declaration rapport : (Integer,Integer) -> Integer has been
--R      added to workspace.
--E 8

--S 9 of 22
Phi : UP('xi, K) := map(coerce, cyclotomic(n))
 

          4     3     2
   (9)  xi  + xi  + xi  + xi + 1
--R 
--R
--R          4     3     2
--R   (9)  xi  + xi  + xi  + xi + 1
--E 9

--S 10 of 22
E := SimpleAlgebraicExtension(K, UP('xi, K), Phi) ;
 

--E 10 

--S 11 of 22
xi : E := generator()$E ;
 

--E 11 

--S 12 of 22
bList : List(E) := [reduce(+, [t(i+1) * xi**(i*j) for i in 0 .. #UZn-1]) for j in UZn]
 

   (12)
         2                      3              2
   [t2 xi  + t1 xi + t0, - t2 xi  + (t1 - t2)xi  - t2 xi + t0 - t2,
         3                            3        2
    t1 xi  + t2 xi + t0, (- t1 + t2)xi  - t1 xi  - t1 xi + t0 - t1]
--R 
--R
--R   (12)
--R         2                      3              2
--R   [t2 xi  + t1 xi + t0, - t2 xi  + (t1 - t2)xi  - t2 xi + t0 - t2,
--R         3                            3        2
--R    t1 xi  + t2 xi + t0, (- t1 + t2)xi  - t1 xi  - t1 xi + t0 - t1]
--E 12

--S 13 of 22
delta : List(E) :=
  [reduce(*, [b**((j*rapport(1,k)) quo n) for b in bList for k in UZn]) for j in UZn] ;
 
   Compiling function rapport with type (Integer,Integer) -> Integer 

--R 
--R   Compiling function rapport with type (Integer,Integer) -> Integer 
--R
--E 13

--S 14 of 22
B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) for j in UZn] ;
 

--E 14

--S 15  of 22
[B(1)**j - b * d**n for b in B for d in delta for j in UZn]
 

   (15)  [0,0,0,0]
--R
--R   (15)  [0,0,0,0]
--E 15 

--S 16 of 22
L := SimpleAlgebraicExtension(E, UP('C1, E), C1**n - B(1)) ;  C1 : L := generator()$L ;
 

--E 16 

--S 17 of 22
retraction(z : L) : Zt ==
   zE : E := retract(z)
   zK : K := retract(zE)
   zt : Zt := retract(zK)
   return zt
 
   Function declaration retraction : SimpleAlgebraicExtension(
      SimpleAlgebraicExtension(Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
      UnivariatePolynomial(xi,Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
      xi**3+xi*xi+xi+1),UnivariatePolynomial(C1,
      SimpleAlgebraicExtension(Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
      UnivariatePolynomial(xi,Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
      xi**3+xi*xi+xi+1)),C1**5+(2*t0**9*t1+(-t0**9*t2)+(-4*t0**8*t1*t1)
      +(-9*t0**8*t1*t2)+3*t0**8*t2*t2+7*t0**7*t1**3+24*t0**7*t1*t1*t2+9
      *t0**7*t1*t2*t2+(-7*t0**7*t2**3)+(-11*t0**6*t1**4)+(-32*t0**6*t1
      **3*t2)+(-35*t0**6*t1*t1*t2*t2)+(-t0**6*t1*t2**3)+8*t0**6*t2**4+
      11*t0**5*t1**5+36*t0**5*t1**4*t2+65*t0**5*t1**3*t2*t2+(-6*t0**5*
      t1*t2**4)+(-6*t0**5*t2**5)+(-8*t0**4*t1**6)+(-41*t0**4*t1**5*t2)+
      (-45*t0**4*t1**4*t2*t2)+(-20*t0**4*t1**3*t2**3)+20*t0**4*t1*t1*t2
      **4+(-3*t0**4*t1*t2**5)+4*t0**4*t2**6+6*t0**3*t1**7+26*t0**3*t1**
      6*t2+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**3+(-40*t0**3*t1**3*
      t2**4)+11*t0**3*t1*t1*t2**5+(-4*t0**3*t1*t2**6)+(-2*t0**3*t2**7)+
      (-3*t0*t0*t1**8)+(-t0*t0*t1**7*t2)+(-31*t0*t0*t1**6*t2*t2)+13*t0*
      t0*t1**5*t2**3+(-20*t0*t0*t1**4*t2**4)+47*t0*t0*t1**3*t2**5+(-41*
      t0*t0*t1*t1*t2**6)+19*t0*t0*t1*t2**7+(-2*t0*t0*t2**8)+(-t0*t1**9)
      +3*t0*t1**8*t2+10*t0*t1**7*t2*t2+(-6*t0*t1**6*t2**3)+(-7*t0*t1**5
      *t2**4)+14*t0*t1**4*t2**5+(-22*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+
      (-16*t0*t1*t2**8)+3*t0*t2**9+t1**10+(-4*t1**9*t2)+5*t1**8*t2*t2+(
      -5*t1**7*t2**3)+4*t1**6*t2**4+(-4*t1**4*t2**6)+5*t1**3*t2**7+(-5*
      t1*t1*t2**8)+4*t1*t2**9+(-t2**10))*xi**3+(t0**9*t1+2*t0**9*t2+(-3
      *t0**8*t1*t1)+(-11*t0**8*t1*t2)+(-5*t0**8*t2*t2)+7*t0**7*t1**3+16
      *t0**7*t1*t1*t2+26*t0**7*t1*t2*t2+4*t0**7*t2**3+(-8*t0**6*t1**4)+
      (-23*t0**6*t1**3*t2)+(-40*t0**6*t1*t1*t2*t2)+(-24*t0**6*t1*t2**3)
      +(-4*t0**6*t2**4)+6*t0**5*t1**5+28*t0**5*t1**4*t2+41*t0**5*t1**3*
      t2*t2+32*t0**5*t1*t1*t2**3+8*t0**5*t1*t2**4+5*t0**5*t2**5+(-4*t0
      **4*t1**6)+(-23*t0**4*t1**5*t2)+(-10*t0**4*t1**4*t2*t2)+(-45*t0**
      4*t1**3*t2**3)+5*t0**4*t1*t1*t2**4+(-14*t0**4*t1*t2**5)+(-3*t0**4
      *t2**6)+2*t0**3*t1**7+(-t0**3*t1**6*t2)+15*t0**3*t1**5*t2*t2+5*t0
      **3*t1**4*t2**3+30*t0**3*t1**3*t2**4+(-13*t0**3*t1*t1*t2**5)+9*t0
      **3*t1*t2**6+2*t0*t0*t1**8+6*t0*t0*t1**7*t2+(-14*t0*t0*t1**6*t2*
      t2)+4*t0*t0*t1**5*t2**3+(-25*t0*t0*t1**4*t2**4)+27*t0*t0*t1**3*t2
      **5+(-19*t0*t0*t1*t1*t2**6)+6*t0*t0*t1*t2**7+(-t0*t0*t2**8)+(-3*
      t0*t1**9)+2*t0*t1**8*t2+11*t0*t1**6*t2**3+(-24*t0*t1**5*t2**4)+37
      *t0*t1**4*t2**5+(-38*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+(-9*t0*t1*
      t2**8)+t0*t2**9+t1**10+(-2*t1**9*t2)+t1**8*t2*t2+2*t1**7*t2**3+(-
      7*t1**6*t2**4)+11*t1**5*t2**5+(-12*t1**4*t2**6)+11*t1**3*t2**7+(-
      8*t1*t1*t2**8)+3*t1*t2**9)*xi*xi+(3*t0**9*t1+t0**9*t2+(-8*t0**8*
      t1*t1)+(-9*t0**8*t1*t2)+(-t0**8*t2*t2)+11*t0**7*t1**3+25*t0**7*t1
      *t1*t2+6*t0**7*t1*t2*t2+(-12*t0**6*t1**4)+(-38*t0**6*t1**3*t2)+(-
      19*t0**6*t1*t1*t2*t2)+9*t0**6*t1*t2**3+(-3*t0**6*t2**4)+11*t0**5*
      t1**5+37*t0**5*t1**4*t2+27*t0**5*t1**3*t2*t2+(-13*t0**5*t1*t1*t2
      **3)+(-14*t0**5*t1*t2**4)+5*t0**5*t2**5+(-7*t0**4*t1**6)+(-24*t0
      **4*t1**5*t2)+(-25*t0**4*t1**4*t2*t2)+30*t0**4*t1**3*t2**3+5*t0**
      4*t1*t1*t2**4+8*t0**4*t1*t2**5+(-4*t0**4*t2**6)+2*t0**3*t1**7+11*
      t0**3*t1**6*t2+4*t0**3*t1**5*t2*t2+5*t0**3*t1**4*t2**3+(-45*t0**3
      *t1**3*t2**4)+32*t0**3*t1*t1*t2**5+(-24*t0**3*t1*t2**6)+4*t0**3*
      t2**7+t0*t0*t1**8+(-14*t0*t0*t1**6*t2*t2)+15*t0*t0*t1**5*t2**3+(-
      10*t0*t0*t1**4*t2**4)+41*t0*t0*t1**3*t2**5+(-40*t0*t0*t1*t1*t2**6
      )+26*t0*t0*t1*t2**7+(-5*t0*t0*t2**8)+(-2*t0*t1**9)+2*t0*t1**8*t2+
      6*t0*t1**7*t2*t2+(-t0*t1**6*t2**3)+(-23*t0*t1**5*t2**4)+28*t0*t1
      **4*t2**5+(-23*t0*t1**3*t2**6)+16*t0*t1*t1*t2**7+(-11*t0*t1*t2**8
      )+2*t0*t2**9+t1**10+(-3*t1**9*t2)+2*t1**8*t2*t2+2*t1**7*t2**3+(-4
      *t1**6*t2**4)+6*t1**5*t2**5+(-8*t1**4*t2**6)+7*t1**3*t2**7+(-3*t1
      *t1*t2**8)+t1*t2**9)*xi+(-t0**10)+4*t0**9*t1+3*t0**9*t2+(-5*t0**8
      *t1*t1)+(-16*t0**8*t1*t2)+(-2*t0**8*t2*t2)+5*t0**7*t1**3+25*t0**7
      *t1*t1*t2+19*t0**7*t1*t2*t2+(-2*t0**7*t2**3)+(-4*t0**6*t1**4)+(-
      22*t0**6*t1**3*t2)+(-41*t0**6*t1*t1*t2*t2)+(-4*t0**6*t1*t2**3)+4*
      t0**6*t2**4+14*t0**5*t1**4*t2+47*t0**5*t1**3*t2*t2+11*t0**5*t1*t1
      *t2**3+(-3*t0**5*t1*t2**4)+(-6*t0**5*t2**5)+4*t0**4*t1**6+(-7*t0
      **4*t1**5*t2)+(-20*t0**4*t1**4*t2*t2)+(-40*t0**4*t1**3*t2**3)+20*
      t0**4*t1*t1*t2**4+(-6*t0**4*t1*t2**5)+8*t0**4*t2**6+(-5*t0**3*t1
      **7)+(-6*t0**3*t1**6*t2)+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**
      3+(-20*t0**3*t1**3*t2**4)+(-t0**3*t1*t2**6)+(-7*t0**3*t2**7)+5*t0
      *t0*t1**8+10*t0*t0*t1**7*t2+(-31*t0*t0*t1**6*t2*t2)+13*t0*t0*t1**
      5*t2**3+(-45*t0*t0*t1**4*t2**4)+65*t0*t0*t1**3*t2**5+(-35*t0*t0*
      t1*t1*t2**6)+9*t0*t0*t1*t2**7+3*t0*t0*t2**8+(-4*t0*t1**9)+3*t0*t1
      **8*t2+(-t0*t1**7*t2*t2)+26*t0*t1**6*t2**3+(-41*t0*t1**5*t2**4)+
      36*t0*t1**4*t2**5+(-32*t0*t1**3*t2**6)+24*t0*t1*t1*t2**7+(-9*t0*
      t1*t2**8)+(-t0*t2**9)+t1**10+(-t1**9*t2)+(-3*t1**8*t2*t2)+6*t1**7
      *t2**3+(-8*t1**6*t2**4)+11*t1**5*t2**5+(-11*t1**4*t2**6)+7*t1**3*
      t2**7+(-4*t1*t1*t2**8)+2*t1*t2**9) -> 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) has been
      added to workspace.
--R 
--R   Function declaration retraction : SimpleAlgebraicExtension(
--R      SimpleAlgebraicExtension(Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
--R      UnivariatePolynomial(xi,Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
--R      xi**3+xi*xi+xi+1),UnivariatePolynomial(C1,
--R      SimpleAlgebraicExtension(Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
--R      UnivariatePolynomial(xi,Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
--R      xi**3+xi*xi+xi+1)),C1**5+(2*t0**9*t1+(-t0**9*t2)+(-4*t0**8*t1*t1)
--R      +(-9*t0**8*t1*t2)+3*t0**8*t2*t2+7*t0**7*t1**3+24*t0**7*t1*t1*t2+9
--R      *t0**7*t1*t2*t2+(-7*t0**7*t2**3)+(-11*t0**6*t1**4)+(-32*t0**6*t1
--R      **3*t2)+(-35*t0**6*t1*t1*t2*t2)+(-t0**6*t1*t2**3)+8*t0**6*t2**4+
--R      11*t0**5*t1**5+36*t0**5*t1**4*t2+65*t0**5*t1**3*t2*t2+(-6*t0**5*
--R      t1*t2**4)+(-6*t0**5*t2**5)+(-8*t0**4*t1**6)+(-41*t0**4*t1**5*t2)+
--R      (-45*t0**4*t1**4*t2*t2)+(-20*t0**4*t1**3*t2**3)+20*t0**4*t1*t1*t2
--R      **4+(-3*t0**4*t1*t2**5)+4*t0**4*t2**6+6*t0**3*t1**7+26*t0**3*t1**
--R      6*t2+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**3+(-40*t0**3*t1**3*
--R      t2**4)+11*t0**3*t1*t1*t2**5+(-4*t0**3*t1*t2**6)+(-2*t0**3*t2**7)+
--R      (-3*t0*t0*t1**8)+(-t0*t0*t1**7*t2)+(-31*t0*t0*t1**6*t2*t2)+13*t0*
--R      t0*t1**5*t2**3+(-20*t0*t0*t1**4*t2**4)+47*t0*t0*t1**3*t2**5+(-41*
--R      t0*t0*t1*t1*t2**6)+19*t0*t0*t1*t2**7+(-2*t0*t0*t2**8)+(-t0*t1**9)
--R      +3*t0*t1**8*t2+10*t0*t1**7*t2*t2+(-6*t0*t1**6*t2**3)+(-7*t0*t1**5
--R      *t2**4)+14*t0*t1**4*t2**5+(-22*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+
--R      (-16*t0*t1*t2**8)+3*t0*t2**9+t1**10+(-4*t1**9*t2)+5*t1**8*t2*t2+(
--R      -5*t1**7*t2**3)+4*t1**6*t2**4+(-4*t1**4*t2**6)+5*t1**3*t2**7+(-5*
--R      t1*t1*t2**8)+4*t1*t2**9+(-t2**10))*xi**3+(t0**9*t1+2*t0**9*t2+(-3
--R      *t0**8*t1*t1)+(-11*t0**8*t1*t2)+(-5*t0**8*t2*t2)+7*t0**7*t1**3+16
--R      *t0**7*t1*t1*t2+26*t0**7*t1*t2*t2+4*t0**7*t2**3+(-8*t0**6*t1**4)+
--R      (-23*t0**6*t1**3*t2)+(-40*t0**6*t1*t1*t2*t2)+(-24*t0**6*t1*t2**3)
--R      +(-4*t0**6*t2**4)+6*t0**5*t1**5+28*t0**5*t1**4*t2+41*t0**5*t1**3*
--R      t2*t2+32*t0**5*t1*t1*t2**3+8*t0**5*t1*t2**4+5*t0**5*t2**5+(-4*t0
--R      **4*t1**6)+(-23*t0**4*t1**5*t2)+(-10*t0**4*t1**4*t2*t2)+(-45*t0**
--R      4*t1**3*t2**3)+5*t0**4*t1*t1*t2**4+(-14*t0**4*t1*t2**5)+(-3*t0**4
--R      *t2**6)+2*t0**3*t1**7+(-t0**3*t1**6*t2)+15*t0**3*t1**5*t2*t2+5*t0
--R      **3*t1**4*t2**3+30*t0**3*t1**3*t2**4+(-13*t0**3*t1*t1*t2**5)+9*t0
--R      **3*t1*t2**6+2*t0*t0*t1**8+6*t0*t0*t1**7*t2+(-14*t0*t0*t1**6*t2*
--R      t2)+4*t0*t0*t1**5*t2**3+(-25*t0*t0*t1**4*t2**4)+27*t0*t0*t1**3*t2
--R      **5+(-19*t0*t0*t1*t1*t2**6)+6*t0*t0*t1*t2**7+(-t0*t0*t2**8)+(-3*
--R      t0*t1**9)+2*t0*t1**8*t2+11*t0*t1**6*t2**3+(-24*t0*t1**5*t2**4)+37
--R      *t0*t1**4*t2**5+(-38*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+(-9*t0*t1*
--R      t2**8)+t0*t2**9+t1**10+(-2*t1**9*t2)+t1**8*t2*t2+2*t1**7*t2**3+(-
--R      7*t1**6*t2**4)+11*t1**5*t2**5+(-12*t1**4*t2**6)+11*t1**3*t2**7+(-
--R      8*t1*t1*t2**8)+3*t1*t2**9)*xi*xi+(3*t0**9*t1+t0**9*t2+(-8*t0**8*
--R      t1*t1)+(-9*t0**8*t1*t2)+(-t0**8*t2*t2)+11*t0**7*t1**3+25*t0**7*t1
--R      *t1*t2+6*t0**7*t1*t2*t2+(-12*t0**6*t1**4)+(-38*t0**6*t1**3*t2)+(-
--R      19*t0**6*t1*t1*t2*t2)+9*t0**6*t1*t2**3+(-3*t0**6*t2**4)+11*t0**5*
--R      t1**5+37*t0**5*t1**4*t2+27*t0**5*t1**3*t2*t2+(-13*t0**5*t1*t1*t2
--R      **3)+(-14*t0**5*t1*t2**4)+5*t0**5*t2**5+(-7*t0**4*t1**6)+(-24*t0
--R      **4*t1**5*t2)+(-25*t0**4*t1**4*t2*t2)+30*t0**4*t1**3*t2**3+5*t0**
--R      4*t1*t1*t2**4+8*t0**4*t1*t2**5+(-4*t0**4*t2**6)+2*t0**3*t1**7+11*
--R      t0**3*t1**6*t2+4*t0**3*t1**5*t2*t2+5*t0**3*t1**4*t2**3+(-45*t0**3
--R      *t1**3*t2**4)+32*t0**3*t1*t1*t2**5+(-24*t0**3*t1*t2**6)+4*t0**3*
--R      t2**7+t0*t0*t1**8+(-14*t0*t0*t1**6*t2*t2)+15*t0*t0*t1**5*t2**3+(-
--R      10*t0*t0*t1**4*t2**4)+41*t0*t0*t1**3*t2**5+(-40*t0*t0*t1*t1*t2**6
--R      )+26*t0*t0*t1*t2**7+(-5*t0*t0*t2**8)+(-2*t0*t1**9)+2*t0*t1**8*t2+
--R      6*t0*t1**7*t2*t2+(-t0*t1**6*t2**3)+(-23*t0*t1**5*t2**4)+28*t0*t1
--R      **4*t2**5+(-23*t0*t1**3*t2**6)+16*t0*t1*t1*t2**7+(-11*t0*t1*t2**8
--R      )+2*t0*t2**9+t1**10+(-3*t1**9*t2)+2*t1**8*t2*t2+2*t1**7*t2**3+(-4
--R      *t1**6*t2**4)+6*t1**5*t2**5+(-8*t1**4*t2**6)+7*t1**3*t2**7+(-3*t1
--R      *t1*t2**8)+t1*t2**9)*xi+(-t0**10)+4*t0**9*t1+3*t0**9*t2+(-5*t0**8
--R      *t1*t1)+(-16*t0**8*t1*t2)+(-2*t0**8*t2*t2)+5*t0**7*t1**3+25*t0**7
--R      *t1*t1*t2+19*t0**7*t1*t2*t2+(-2*t0**7*t2**3)+(-4*t0**6*t1**4)+(-
--R      22*t0**6*t1**3*t2)+(-41*t0**6*t1*t1*t2*t2)+(-4*t0**6*t1*t2**3)+4*
--R      t0**6*t2**4+14*t0**5*t1**4*t2+47*t0**5*t1**3*t2*t2+11*t0**5*t1*t1
--R      *t2**3+(-3*t0**5*t1*t2**4)+(-6*t0**5*t2**5)+4*t0**4*t1**6+(-7*t0
--R      **4*t1**5*t2)+(-20*t0**4*t1**4*t2*t2)+(-40*t0**4*t1**3*t2**3)+20*
--R      t0**4*t1*t1*t2**4+(-6*t0**4*t1*t2**5)+8*t0**4*t2**6+(-5*t0**3*t1
--R      **7)+(-6*t0**3*t1**6*t2)+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**
--R      3+(-20*t0**3*t1**3*t2**4)+(-t0**3*t1*t2**6)+(-7*t0**3*t2**7)+5*t0
--R      *t0*t1**8+10*t0*t0*t1**7*t2+(-31*t0*t0*t1**6*t2*t2)+13*t0*t0*t1**
--R      5*t2**3+(-45*t0*t0*t1**4*t2**4)+65*t0*t0*t1**3*t2**5+(-35*t0*t0*
--R      t1*t1*t2**6)+9*t0*t0*t1*t2**7+3*t0*t0*t2**8+(-4*t0*t1**9)+3*t0*t1
--R      **8*t2+(-t0*t1**7*t2*t2)+26*t0*t1**6*t2**3+(-41*t0*t1**5*t2**4)+
--R      36*t0*t1**4*t2**5+(-32*t0*t1**3*t2**6)+24*t0*t1*t1*t2**7+(-9*t0*
--R      t1*t2**8)+(-t0*t2**9)+t1**10+(-t1**9*t2)+(-3*t1**8*t2*t2)+6*t1**7
--R      *t2**3+(-8*t1**6*t2**4)+11*t1**5*t2**5+(-11*t1**4*t2**6)+7*t1**3*
--R      t2**7+(-4*t1*t1*t2**8)+2*t1*t2**9) -> 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) has been
--R      added to workspace.
--E 17

--S 18  of 22
C : List(L) := [C1**j / d for j in UZn for d in delta] ;
 

--E 18 

--S 19 of 22
r : List(L) := [reduce(+, [c * xi**(k*j) for j in UZn for c in C]) for k in 0 .. n-1] ;
 
 
Daly Bug
   >> System error:
   Value stack overflow.

(19) -> Starts dribbling to roots.output (2009/2/17, 17:57:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 7
lr:=rootsOf(x**4+1,x)
 

   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
                                                Type: List Expression Integer
--R 
--R
--R   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
--R                                                Type: List Expression Integer
--E 1

--S 2 of 7
definingPolynomial %x0
 

           4
   (2)  %x0  + 1
                                                     Type: Expression Integer
--R 
--R
--R           4
--R   (2)  %x0  + 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 7
definingPolynomial %x1
 

           2
   (3)  %x1  + 1
                                                     Type: Expression Integer
--R 
--R
--R           2
--R   (3)  %x1  + 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 7
lr.1 * lr.2 * lr.3
 

             3
   (4)  - %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R             3
--R   (4)  - %x0 %x1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 7
%**4
 

   (5)  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (5)  - 1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 7
lr.1 + lr.2 + lr.3
 

   (6)  %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R   (6)  %x0 %x1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 7
%**4
 

   (7)  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (7)  - 1
--R                                                     Type: Expression Integer
--E 7
)spool 
 
Starts dribbling to schaum21.output (2009/2/17, 17:59:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(cot(a*x),x)
 

               sin(2a x)                2
        2log(-------------) - log(-------------)
             cos(2a x) + 1        cos(2a x) + 1
   (1)  ----------------------------------------
                           2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               sin(2a x)                2
--R        2log(-------------) - log(-------------)
--R             cos(2a x) + 1        cos(2a x) + 1
--R   (1)  ----------------------------------------
--R                           2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/a*log(sin(a*x))
 

        log(sin(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(sin(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

               sin(2a x)                                 2
        2log(-------------) - 2log(sin(a x)) - log(-------------)
             cos(2a x) + 1                         cos(2a x) + 1
   (3)  ---------------------------------------------------------
                                    2a
                                                     Type: Expression Integer
--R
--R               sin(2a x)                                 2
--R        2log(-------------) - 2log(sin(a x)) - log(-------------)
--R             cos(2a x) + 1                         cos(2a x) + 1
--R   (3)  ---------------------------------------------------------
--R                                    2a
--R                                                     Type: Expression Integer
--E

--S 4
dd:=expandLog cc
 

        2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2)
   (4)  --------------------------------------------------------------
                                      2a
                                                     Type: Expression Integer
--R
--R        2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2)
--R   (4)  --------------------------------------------------------------
--R                                      2a
--R                                                     Type: Expression Integer
--E

--S 5      14:440 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 6
aa:=integrate(cot(a*x)^2,x)
 

        - a x sin(2a x) - cos(2a x) - 1
   (1)  -------------------------------
                  a sin(2a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - a x sin(2a x) - cos(2a x) - 1
--R   (1)  -------------------------------
--R                  a sin(2a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7
bb:=-cot(a*x)/a-x
 

        - cot(a x) - a x
   (2)  ----------------
                a
                                                     Type: Expression Integer
--R
--R        - cot(a x) - a x
--R   (2)  ----------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 8
cc:=aa-bb
 

        cot(a x)sin(2a x) - cos(2a x) - 1
   (3)  ---------------------------------
                   a sin(2a x)
                                                     Type: Expression Integer
--R
--R        cot(a x)sin(2a x) - cos(2a x) - 1
--R   (3)  ---------------------------------
--R                   a sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 9
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 10
dd:=cotrule cc
 

        cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x)
   (5)  ---------------------------------------------
                     a sin(a x)sin(2a x)
                                                     Type: Expression Integer
--R
--R        cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x)
--R   (5)  ---------------------------------------------
--R                     a sin(a x)sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 11     14:441 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 12
aa:=integrate(cot(a*x)^3,x)
 

   (1)
                               sin(2a x)                               2
       (- 2cos(2a x) + 2)log(-------------) + (cos(2a x) - 1)log(-------------)
                             cos(2a x) + 1                       cos(2a x) + 1
     + 
       cos(2a x) + 1
  /
     2a cos(2a x) - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                               sin(2a x)                               2
--R       (- 2cos(2a x) + 2)log(-------------) + (cos(2a x) - 1)log(-------------)
--R                             cos(2a x) + 1                       cos(2a x) + 1
--R     + 
--R       cos(2a x) + 1
--R  /
--R     2a cos(2a x) - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13
bb:=-cot(a*x)^2/(2*a)-1/a*log(sin(a*x))
 

                                   2
        - 2log(sin(a x)) - cot(a x)
   (2)  ----------------------------
                     2a
                                                     Type: Expression Integer
--R
--R                                   2
--R        - 2log(sin(a x)) - cot(a x)
--R   (2)  ----------------------------
--R                     2a
--R                                                     Type: Expression Integer
--E

--S 14
cc:=aa-bb
 

   (3)
                               sin(2a x)
       (- 2cos(2a x) + 2)log(-------------) + (2cos(2a x) - 2)log(sin(a x))
                             cos(2a x) + 1
     + 
                                2                                 2
       (cos(2a x) - 1)log(-------------) + (cos(2a x) - 1)cot(a x)  + cos(2a x)
                          cos(2a x) + 1
     + 
       1
  /
     2a cos(2a x) - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                               sin(2a x)
--R       (- 2cos(2a x) + 2)log(-------------) + (2cos(2a x) - 2)log(sin(a x))
--R                             cos(2a x) + 1
--R     + 
--R                                2                                 2
--R       (cos(2a x) - 1)log(-------------) + (cos(2a x) - 1)cot(a x)  + cos(2a x)
--R                          cos(2a x) + 1
--R     + 
--R       1
--R  /
--R     2a cos(2a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 15
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 16
dd:=cotrule cc
 

   (5)
                                 2      sin(2a x)
       (- 2cos(2a x) + 2)sin(a x) log(-------------)
                                      cos(2a x) + 1
     + 
                               2
       (2cos(2a x) - 2)sin(a x) log(sin(a x))
     + 
                              2          2                                 2
       (cos(2a x) - 1)sin(a x) log(-------------) + (cos(2a x) + 1)sin(a x)
                                   cos(2a x) + 1
     + 
               2                    2
       cos(a x) cos(2a x) - cos(a x)
  /
                                2
     (2a cos(2a x) - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                 2      sin(2a x)
--R       (- 2cos(2a x) + 2)sin(a x) log(-------------)
--R                                      cos(2a x) + 1
--R     + 
--R                               2
--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
--R     + 
--R                              2          2                                 2
--R       (cos(2a x) - 1)sin(a x) log(-------------) + (cos(2a x) + 1)sin(a x)
--R                                   cos(2a x) + 1
--R     + 
--R               2                    2
--R       cos(a x) cos(2a x) - cos(a x)
--R  /
--R                                2
--R     (2a cos(2a x) - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 17
ee:=expandLog dd
 

   (6)
                                 2
       (- 2cos(2a x) + 2)sin(a x) log(sin(2a x))
     + 
                               2
       (2cos(2a x) - 2)sin(a x) log(sin(a x))
     + 
                              2
       (cos(2a x) - 1)sin(a x) log(cos(2a x) + 1)
     + 
                                                   2           2
       ((log(2) + 1)cos(2a x) - log(2) + 1)sin(a x)  + cos(a x) cos(2a x)
     + 
                 2
       - cos(a x)
  /
                                2
     (2a cos(2a x) - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (6)
--R                                 2
--R       (- 2cos(2a x) + 2)sin(a x) log(sin(2a x))
--R     + 
--R                               2
--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
--R     + 
--R                              2
--R       (cos(2a x) - 1)sin(a x) log(cos(2a x) + 1)
--R     + 
--R                                                   2           2
--R       ((log(2) + 1)cos(2a x) - log(2) + 1)sin(a x)  + cos(a x) cos(2a x)
--R     + 
--R                 2
--R       - cos(a x)
--R  /
--R                                2
--R     (2a cos(2a x) - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 18     14:442 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19
aa:=integrate(cot(a*x)^n*csc(a*x)^2,x)
 

                          cos(a x)
                    n log(--------)
                          sin(a x)
          cos(a x)%e
   (1)  - -------------------------
              (a n + a)sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          cos(a x)
--R                    n log(--------)
--R                          sin(a x)
--R          cos(a x)%e
--R   (1)  - -------------------------
--R              (a n + a)sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 20
bb:=-cot(a*x)^(n+1)/((n+1)*a)
 

                  n + 1
          cot(a x)
   (2)  - -------------
             a n + a
                                                     Type: Expression Integer
--R
--R                  n + 1
--R          cot(a x)
--R   (2)  - -------------
--R             a n + a
--R                                                     Type: Expression Integer
--E

--S 21
cc:=aa-bb
 

                          cos(a x)
                    n log(--------)
                          sin(a x)                    n + 1
        - cos(a x)%e                + sin(a x)cot(a x)
   (3)  ---------------------------------------------------
                         (a n + a)sin(a x)
                                                     Type: Expression Integer
--R
--R                          cos(a x)
--R                    n log(--------)
--R                          sin(a x)                    n + 1
--R        - cos(a x)%e                + sin(a x)cot(a x)
--R   (3)  ---------------------------------------------------
--R                         (a n + a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 22
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 23
dd:=explog cc
 

                        n + 1            cos(a x) n
        sin(a x)cot(a x)      - cos(a x)(--------)
                                         sin(a x)
   (5)  -------------------------------------------
                     (a n + a)sin(a x)
                                                     Type: Expression Integer
--R
--R                        n + 1            cos(a x) n
--R        sin(a x)cot(a x)      - cos(a x)(--------)
--R                                         sin(a x)
--R   (5)  -------------------------------------------
--R                     (a n + a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 24
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (6)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (6)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25
ee:=cotrule dd
 

                 cos(a x) n + 1            cos(a x) n
        sin(a x)(--------)      - cos(a x)(--------)
                 sin(a x)                  sin(a x)
   (7)  ---------------------------------------------
                      (a n + a)sin(a x)
                                                     Type: Expression Integer
--R
--R                 cos(a x) n + 1            cos(a x) n
--R        sin(a x)(--------)      - cos(a x)(--------)
--R                 sin(a x)                  sin(a x)
--R   (7)  ---------------------------------------------
--R                      (a n + a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 26     14:443 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(csc(a*x)^2/cot(a*x),x)
 

              sin(a x)              2cos(a x)
        log(------------) - log(- ------------)
            cos(a x) + 1          cos(a x) + 1
   (1)  ---------------------------------------
                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)              2cos(a x)
--R        log(------------) - log(- ------------)
--R            cos(a x) + 1          cos(a x) + 1
--R   (1)  ---------------------------------------
--R                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28
bb:=-1/a*log(cot(a*x))
 

          log(cot(a x))
   (2)  - -------------
                a
                                                     Type: Expression Integer
--R
--R          log(cot(a x))
--R   (2)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 29
cc:=aa-bb
 

              sin(a x)                              2cos(a x)
        log(------------) + log(cot(a x)) - log(- ------------)
            cos(a x) + 1                          cos(a x) + 1
   (3)  -------------------------------------------------------
                                   a
                                                     Type: Expression Integer
--R
--R              sin(a x)                              2cos(a x)
--R        log(------------) + log(cot(a x)) - log(- ------------)
--R            cos(a x) + 1                          cos(a x) + 1
--R   (3)  -------------------------------------------------------
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 30
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 31
dd:=cotrule cc
 

              sin(a x)          cos(a x)            2cos(a x)
        log(------------) + log(--------) - log(- ------------)
            cos(a x) + 1        sin(a x)          cos(a x) + 1
   (5)  -------------------------------------------------------
                                   a
                                                     Type: Expression Integer
--R
--R              sin(a x)          cos(a x)            2cos(a x)
--R        log(------------) + log(--------) - log(- ------------)
--R            cos(a x) + 1        sin(a x)          cos(a x) + 1
--R   (5)  -------------------------------------------------------
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 32     14:444 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

          log(- 2)
   (6)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 2)
--R   (6)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 33
aa:=integrate(1/cot(a*x),x)
 

                  2
        log(-------------)
            cos(2a x) + 1
   (1)  ------------------
                2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R        log(-------------)
--R            cos(2a x) + 1
--R   (1)  ------------------
--R                2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34
bb:=-1/a*log(cos(a*x))
 

          log(cos(a x))
   (2)  - -------------
                a
                                                     Type: Expression Integer
--R
--R          log(cos(a x))
--R   (2)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 35
cc:=aa-bb
 

                                   2
        2log(cos(a x)) + log(-------------)
                             cos(2a x) + 1
   (3)  -----------------------------------
                         2a
                                                     Type: Expression Integer
--R
--R                                   2
--R        2log(cos(a x)) + log(-------------)
--R                             cos(2a x) + 1
--R   (3)  -----------------------------------
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 36
dd:=expandLog cc
 

        - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2)
   (4)  ----------------------------------------------
                              2a
                                                     Type: Expression Integer
--R
--R        - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2)
--R   (4)  ----------------------------------------------
--R                              2a
--R                                                     Type: Expression Integer
--E

--S 37     14:445 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 38     14:446 Axiom cannot compute this integral
aa:=integrate(x*cot(a*x),x)
 

           x
         ++
   (1)   |   %R cot(%R a)d%R
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %I cot(%I a)d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 39     14:447 Axiom cannot compute this integral
aa:=integrate(cot(a*x)/x,x)
 

           x
         ++  cot(%R a)
   (1)   |   --------- d%R
        ++       %R
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cot(%I a)
--I   (1)   |   --------- d%I
--I        ++       %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 40
aa:=integrate(x*cot(a*x)^2,x)
 

   (1)
                       sin(2a x)                         2
       2sin(2a x)log(-------------) - sin(2a x)log(-------------)
                     cos(2a x) + 1                 cos(2a x) + 1
     + 
          2 2
       - a x sin(2a x) - 2a x cos(2a x) - 2a x
  /
       2
     2a sin(2a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       sin(2a x)                         2
--R       2sin(2a x)log(-------------) - sin(2a x)log(-------------)
--R                     cos(2a x) + 1                 cos(2a x) + 1
--R     + 
--R          2 2
--R       - a x sin(2a x) - 2a x cos(2a x) - 2a x
--R  /
--R       2
--R     2a sin(2a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 41
bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))-x^2/2
 

                                          2 2
        2log(sin(a x)) - 2a x cot(a x) - a x
   (2)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                                          2 2
--R        2log(sin(a x)) - 2a x cot(a x) - a x
--R   (2)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 42
cc:=aa-bb
 

   (3)
                       sin(2a x)
       2sin(2a x)log(-------------) - 2sin(2a x)log(sin(a x))
                     cos(2a x) + 1
     + 
                            2
       - sin(2a x)log(-------------) + 2a x cot(a x)sin(2a x) - 2a x cos(2a x)
                      cos(2a x) + 1
     + 
       - 2a x
  /
       2
     2a sin(2a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                       sin(2a x)
--R       2sin(2a x)log(-------------) - 2sin(2a x)log(sin(a x))
--R                     cos(2a x) + 1
--R     + 
--R                            2
--R       - sin(2a x)log(-------------) + 2a x cot(a x)sin(2a x) - 2a x cos(2a x)
--R                      cos(2a x) + 1
--R     + 
--R       - 2a x
--R  /
--R       2
--R     2a sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 43
dd:=expandLog cc
 

   (4)
       2sin(2a x)log(sin(2a x)) - 2sin(2a x)log(sin(a x))
     + 
       - sin(2a x)log(cos(2a x) + 1) + (2a x cot(a x) - log(2))sin(2a x)
     + 
       - 2a x cos(2a x) - 2a x
  /
       2
     2a sin(2a x)
                                                     Type: Expression Integer
--R
--R   (4)
--R       2sin(2a x)log(sin(2a x)) - 2sin(2a x)log(sin(a x))
--R     + 
--R       - sin(2a x)log(cos(2a x) + 1) + (2a x cot(a x) - log(2))sin(2a x)
--R     + 
--R       - 2a x cos(2a x) - 2a x
--R  /
--R       2
--R     2a sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 44     14:448 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 45
aa:=integrate(1/(p+q*cot(a*x)),x)
 

   (1)
            p sin(2a x) + q cos(2a x) + q                2
   - 2q log(-----------------------------) + q log(-------------) + 2a p x
                    cos(2a x) + 1                  cos(2a x) + 1
   -----------------------------------------------------------------------
                                    2       2
                                2a q  + 2a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            p sin(2a x) + q cos(2a x) + q                2
--R   - 2q log(-----------------------------) + q log(-------------) + 2a p x
--R                    cos(2a x) + 1                  cos(2a x) + 1
--R   -----------------------------------------------------------------------
--R                                    2       2
--R                                2a q  + 2a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 46
bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x))
 

        - q log(p sin(a x) + q cos(a x)) + a p x
   (2)  ----------------------------------------
                          2      2
                       a q  + a p
                                                     Type: Expression Integer
--R
--R        - q log(p sin(a x) + q cos(a x)) + a p x
--R   (2)  ----------------------------------------
--R                          2      2
--R                       a q  + a p
--R                                                     Type: Expression Integer
--E

--S 47
cc:=aa-bb
 

   (3)
                p sin(2a x) + q cos(2a x) + q
       - 2q log(-----------------------------) + 2q log(p sin(a x) + q cos(a x))
                        cos(2a x) + 1
     + 
                   2
       q log(-------------)
             cos(2a x) + 1
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                p sin(2a x) + q cos(2a x) + q
--R       - 2q log(-----------------------------) + 2q log(p sin(a x) + q cos(a x))
--R                        cos(2a x) + 1
--R     + 
--R                   2
--R       q log(-------------)
--R             cos(2a x) + 1
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 48
sindblrule:=rule(sin(2*a) == 2*sin(a)*cos(a))
 

   (4)  sin(2a) == 2cos(a)sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (4)  sin(2a) == 2cos(a)sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 49
dd:=sindblrule cc
 

   (5)
       2q log(p sin(a x) + q cos(a x))
     + 
                2p cos(a x)sin(a x) + q cos(2a x) + q                2
       - 2q log(-------------------------------------) + q log(-------------)
                            cos(2a x) + 1                      cos(2a x) + 1
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (5)
--R       2q log(p sin(a x) + q cos(a x))
--R     + 
--R                2p cos(a x)sin(a x) + q cos(2a x) + q                2
--R       - 2q log(-------------------------------------) + q log(-------------)
--R                            cos(2a x) + 1                      cos(2a x) + 1
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 50
cosdblrule:=rule(cos(2*a) == 2*cos(a)^2-1)
 

                          2
   (6)  cos(2a) == 2cos(a)  - 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          2
--R   (6)  cos(2a) == 2cos(a)  - 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 51
ee:=cosdblrule dd
 

   (7)
                                                p sin(a x) + q cos(a x)
       2q log(p sin(a x) + q cos(a x)) - 2q log(-----------------------)
                                                        cos(a x)
     + 
                 1
       q log(---------)
                     2
             cos(a x)
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                                p sin(a x) + q cos(a x)
--R       2q log(p sin(a x) + q cos(a x)) - 2q log(-----------------------)
--R                                                        cos(a x)
--R     + 
--R                 1
--R       q log(---------)
--R                     2
--R             cos(a x)
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 52     14:449 Schaums and Axiom agree
ff:=expandLog %
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 53     14:450 Axiom cannot compute this integral
aa:=integrate(cot(a*x)^n,x)
 

           x
         ++           n
   (1)   |   cot(%R a) d%R
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   cot(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to linalg.output (2009/2/17, 17:52:28).
)set message test on
 
)set message auto off
 
)set break resume
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input for page MatrixMoreFunctionsPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 82
m1 := matrix([[1,-2,1],[4,2,-4]])
 

        +1  - 2   1 +
   (1)  |           |
        +4   2   - 4+
                                                         Type: Matrix Integer
--R
--R        +1  - 2   1 +
--R   (1)  |           |
--R        +4   2   - 4+
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 82
m2 := matrix([[0,1,2],[2,3,4],[3,4,5]])
 

        +0  1  2+
        |       |
   (2)  |2  3  4|
        |       |
        +3  4  5+
                                                         Type: Matrix Integer
--R
--R        +0  1  2+
--R        |       |
--R   (2)  |2  3  4|
--R        |       |
--R        +3  4  5+
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 82
m3 := matrix([[1,2,3],[2,4,6]])
 

        +1  2  3+
   (3)  |       |
        +2  4  6+
                                                         Type: Matrix Integer
--R
--R        +1  2  3+
--R   (3)  |       |
--R        +2  4  6+
--R                                                         Type: Matrix Integer
--E 3

--S 4 of 82
m1 + m3
 

        +2  0  4+
   (4)  |       |
        +6  6  2+
                                                         Type: Matrix Integer
--R
--R        +2  0  4+
--R   (4)  |       |
--R        +6  6  2+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 82
100 * m1
 

        +100  - 200   100 +
   (5)  |                 |
        +400   200   - 400+
                                                         Type: Matrix Integer
--R
--R        +100  - 200   100 +
--R   (5)  |                 |
--R        +400   200   - 400+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 82
m1 * m2
 

        +- 1  - 1  - 1+
   (6)  |             |
        +- 8  - 6  - 4+
                                                         Type: Matrix Integer
--R
--R        +- 1  - 1  - 1+
--R   (6)  |             |
--R        +- 8  - 6  - 4+
--R                                                         Type: Matrix Integer
--E 6

--S 7 of 82
-m1 + m3 * m2
 

        +12  21  24+
   (7)  |          |
        +22  36  54+
                                                         Type: Matrix Integer
--R
--R        +12  21  24+
--R   (7)  |          |
--R        +22  36  54+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 82
m2 * m1
 
 
Daly Bug
   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   can't multiply matrices of incompatible dimensions
--R
--R   Continuing to read the file...
--R
--E 8

--S 9 of 82
v := vector([1,0,1])
 

   (8)  [1,0,1]
                                              Type: Vector NonNegativeInteger
--R
--R   (8)  [1,0,1]
--R                                              Type: Vector NonNegativeInteger
--E 9

--S 10 of 82
m3 * v
 

   (9)  [4,8]
                                                         Type: Vector Integer
--R
--R   (9)  [4,8]
--R                                                         Type: Vector Integer
--E 10

--S 11 of 82
m5 : MATRIX POLY INT := new(4,4,1)
 

         +1  1  1  1+
         |          |
         |1  1  1  1|
   (10)  |          |
         |1  1  1  1|
         |          |
         +1  1  1  1+
                                              Type: Matrix Polynomial Integer
--R
--R         +1  1  1  1+
--R         |          |
--R         |1  1  1  1|
--R   (10)  |          |
--R         |1  1  1  1|
--R         |          |
--R         +1  1  1  1+
--R                                              Type: Matrix Polynomial Integer
--E 11

--S 12 of 82
vars : LIST POLY INT := [x,y,z,u]
 

   (11)  [x,y,z,u]
                                                Type: List Polynomial Integer
--R
--R   (11)  [x,y,z,u]
--R                                                Type: List Polynomial Integer
--E 12

--S 13 of 82
for i in 1..4 repeat for j in 1..3 repeat m5(i,j + 1) := (vars.i)**j
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 13

--S 14 of 82
m5
 

         +       2   3+
         |1  x  x   x |
         |            |
         |       2   3|
         |1  y  y   y |
   (13)  |            |
         |       2   3|
         |1  z  z   z |
         |            |
         |       2   3|
         +1  u  u   u +
                                              Type: Matrix Polynomial Integer
--R
--R         +       2   3+
--R         |1  x  x   x |
--R         |            |
--R         |       2   3|
--R         |1  y  y   y |
--R   (13)  |            |
--R         |       2   3|
--R         |1  z  z   z |
--R         |            |
--R         |       2   3|
--R         +1  u  u   u +
--R                                              Type: Matrix Polynomial Integer
--E 14

--S 15 of 82
trace(m5)
 

          2        3
   (14)  z  + y + u  + 1
                                                     Type: Polynomial Integer
--R
--R          2        3
--R   (14)  z  + y + u  + 1
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 82
det := determinant(m5)
 

   (15)
                2     2    2        2    2   3
     ((- x + u)y  + (x  - u )y - u x  + u x)z
   + 
              3       3    3        3    3   2
     ((x - u)y  + (- x  + u )y + u x  - u x)z
   + 
          2    2  3     3    3  2    2 3    3 2         2    2   3
     ((- x  + u )y  + (x  - u )y  - u x  + u x )z + (u x  - u x)y
   + 
           3    3   2     2 3    3 2
     (- u x  + u x)y  + (u x  - u x )y
                                                     Type: Polynomial Integer
--R
--R   (15)
--R                2     2    2        2    2   3
--R     ((- x + u)y  + (x  - u )y - u x  + u x)z
--R   + 
--R              3       3    3        3    3   2
--R     ((x - u)y  + (- x  + u )y + u x  - u x)z
--R   + 
--R          2    2  3     3    3  2    2 3    3 2         2    2   3
--R     ((- x  + u )y  + (x  - u )y  - u x  + u x )z + (u x  - u x)y
--R   + 
--R           3    3   2     2 3    3 2
--R     (- u x  + u x)y  + (u x  - u x )y
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 82
factor(det)
 

   (16)  - (x - u)(y - x)(y - u)(z - y)(z - x)(z - u)
                                            Type: Factored Polynomial Integer
--R
--R   (16)  - (x - u)(y - x)(y - u)(z - y)(z - x)(z - u)
--R                                            Type: Factored Polynomial Integer
--E 17

--S 18 of 82
m6 := matrix([[1,2,1],[-2,3,4],[-1,5,6]])
 

         + 1   2  1+
         |         |
   (17)  |- 2  3  4|
         |         |
         +- 1  5  6+
                                                         Type: Matrix Integer
--R
--R         + 1   2  1+
--R         |         |
--R   (17)  |- 2  3  4|
--R         |         |
--R         +- 1  5  6+
--R                                                         Type: Matrix Integer
--E 18

--S 19 of 82
m6inv := inverse(m6)
 

         +  2        5 +
         |- -  - 1   - |
         |  7        7 |
         |             |
   (18)  | 8          6|
         | -    1   - -|
         | 7          7|
         |             |
         +- 1  - 1   1 +
                                     Type: Union(Matrix Fraction Integer,...)
--R
--R         +  2        5 +
--R         |- -  - 1   - |
--R         |  7        7 |
--R         |             |
--R   (18)  | 8          6|
--R         | -    1   - -|
--R         | 7          7|
--R         |             |
--R         +- 1  - 1   1 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 19

--S 20 of 82
m6 * m6inv
 

         +1  0  0+
         |       |
   (19)  |0  1  0|
         |       |
         +0  0  1+
                                                Type: Matrix Fraction Integer
--R
--R         +1  0  0+
--R         |       |
--R   (19)  |0  1  0|
--R         |       |
--R         +0  0  1+
--R                                                Type: Matrix Fraction Integer
--E 20

--S 21 of 82
m7 := matrix([[1,2,1],[-2,3,4],[-1,5,5]])
 

         + 1   2  1+
         |         |
   (20)  |- 2  3  4|
         |         |
         +- 1  5  5+
                                                         Type: Matrix Integer
--R
--R         + 1   2  1+
--R         |         |
--R   (20)  |- 2  3  4|
--R         |         |
--R         +- 1  5  5+
--R                                                         Type: Matrix Integer
--E 21

--S 22 of 82
inverse(m7)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 22

--S 23 of 82
determinant(m7)
 

   (22)  0
                                                     Type: NonNegativeInteger
--R
--R   (22)  0
--R                                                     Type: NonNegativeInteger
--E 23

--S 24 of 82
m8 : SQMATRIX(2,INT) := matrix([[1,2],[2,3]])
 

         +1  2+
   (23)  |    |
         +2  3+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +1  2+
--R   (23)  |    |
--R         +2  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 24

--S 25 of 82
m9 : SQMATRIX(2,INT) := matrix([[1,1],[0,1]])
 

         +1  1+
   (24)  |    |
         +0  1+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +1  1+
--R   (24)  |    |
--R         +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 25

--S 26 of 82
m8 ** 2
 

         +5  8 +
   (25)  |     |
         +8  13+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +5  8 +
--R   (25)  |     |
--R         +8  13+
--R                                                Type: SquareMatrix(2,Integer)
--E 26

--S 27 of 82
m9 ** 3
 

         +1  3+
   (26)  |    |
         +0  1+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +1  3+
--R   (26)  |    |
--R         +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 27

--S 28 of 82
mm : SQMATRIX(2,SQMATRIX(2,INT)) := matrix([[1,m8],[m9,0]])
 

         ++1  0+  +1  2++
         ||    |  |    ||
         |+0  1+  +2  3+|
   (27)  |              |
         |+1  1+  +0  0+|
         ||    |  |    ||
         ++0  1+  +0  0++
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++1  0+  +1  2++
--R         ||    |  |    ||
--R         |+0  1+  +2  3+|
--R   (27)  |              |
--R         |+1  1+  +0  0+|
--R         ||    |  |    ||
--R         ++0  1+  +0  0++
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 28

--S 29 of 82
100 * mm
 

         ++100   0 +  +100  200++
         ||        |  |        ||
         |+ 0   100+  +200  300+|
   (28)  |                      |
         |+100  100+    +0  0+  |
         ||        |    |    |  |
         ++ 0   100+    +0  0+  +
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++100   0 +  +100  200++
--R         ||        |  |        ||
--R         |+ 0   100+  +200  300+|
--R   (28)  |                      |
--R         |+100  100+    +0  0+  |
--R         ||        |    |    |  |
--R         ++ 0   100+    +0  0+  +
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 29

--S 30 of 82
m8 * mm
 

         ++1  2+  +5  8 ++
         ||    |  |     ||
         |+2  3+  +8  13+|
   (29)  |               |
         |+1  3+  +0  0+ |
         ||    |  |    | |
         ++2  5+  +0  0+ +
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++1  2+  +5  8 ++
--R         ||    |  |     ||
--R         |+2  3+  +8  13+|
--R   (29)  |               |
--R         |+1  3+  +0  0+ |
--R         ||    |  |    | |
--R         ++2  5+  +0  0+ +
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 30

--S 31 of 82
mm * mm
 

         ++2  3+  +1  2++
         ||    |  |    ||
         |+2  6+  +2  3+|
   (30)  |              |
         |+1  1+  +3  5+|
         ||    |  |    ||
         ++0  1+  +2  3++
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++2  3+  +1  2++
--R         ||    |  |    ||
--R         |+2  6+  +2  3+|
--R   (30)  |              |
--R         |+1  1+  +3  5+|
--R         ||    |  |    ||
--R         ++0  1+  +2  3++
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 31

--S 32 of 82
p : POLY SQMATRIX(2,INT) := m8 * x**2 + m9 * x + m8 * m9
 

         +1  2+ 2   +1  1+    +1  3+
   (31)  |    |x  + |    |x + |    |
         +2  3+     +0  1+    +2  5+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +1  2+ 2   +1  1+    +1  3+
--R   (31)  |    |x  + |    |x + |    |
--R         +2  3+     +0  1+    +2  5+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 32

--S 33 of 82
100 * p
 

         +100  200+ 2   +100  100+    +100  300+
   (32)  |        |x  + |        |x + |        |
         +200  300+     + 0   100+    +200  500+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +100  200+ 2   +100  100+    +100  300+
--R   (32)  |        |x  + |        |x + |        |
--R         +200  300+     + 0   100+    +200  500+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 33

--S 34 of 82
m8 * p
 

         +5  8 + 2   +1  3+    +5  13+
   (33)  |     |x  + |    |x + |     |
         +8  13+     +2  5+    +8  21+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +5  8 + 2   +1  3+    +5  13+
--R   (33)  |     |x  + |    |x + |     |
--R         +8  13+     +2  5+    +8  21+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 34

--S 35 of 82
p * p
 

         +5  8 + 4   +4  8+ 3   +13  26+ 2   +4  12+    +7   18+
   (34)  |     |x  + |    |x  + |      |x  + |     |x + |      |
         +8  13+     +4  8+     +20  41+     +4  12+    +12  31+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +5  8 + 4   +4  8+ 3   +13  26+ 2   +4  12+    +7   18+
--R   (34)  |     |x  + |    |x  + |      |x  + |     |x + |      |
--R         +8  13+     +4  8+     +20  41+     +4  12+    +12  31+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 35

-- Input for page MatrixCanonicalFormsPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 36 of 82
m1 := matrix([[0,4,1],[5,3,-7],[-5,5,9]])
 

        + 0   4   1 +
        |           |
   (1)  | 5   3  - 7|
        |           |
        +- 5  5   9 +
                                                         Type: Matrix Integer
--R
--R        + 0   4   1 +
--R        |           |
--R   (1)  | 5   3  - 7|
--R        |           |
--R        +- 5  5   9 +
--R                                                         Type: Matrix Integer
--E 36

--S 37 of 82
rank(m1)
 

   (2)  2
                                                        Type: PositiveInteger
--R
--R   (2)  2
--R                                                        Type: PositiveInteger
--E 37

--S 38 of 82
rowEchelon(m1)
 

        +5  3  - 7+
        |         |
   (3)  |0  4   1 |
        |         |
        +0  0   0 +
                                                         Type: Matrix Integer
--R
--R        +5  3  - 7+
--R        |         |
--R   (3)  |0  4   1 |
--R        |         |
--R        +0  0   0 +
--R                                                         Type: Matrix Integer
--E 38

--S 39 of 82
nullSpace(m1)
 

   (4)  [[31,- 5,20]]
                                                    Type: List Vector Integer
--R
--R   (4)  [[31,- 5,20]]
--R                                                    Type: List Vector Integer
--E 39

--S 40 of 82
t := eigenMatrix(m1)
 

        + +----+          +----+          +
        |\|- 11  + 2   - \|- 11  + 2   31 |
        |-----------   -------------   -- |
        |     5              5         20 |
        |                                 |
   (5)  |  +----+          +----+         |
        |2\|- 11  - 1  - 2\|- 11  - 1    1|
        |------------  --------------  - -|
        |      5              5          4|
        |                                 |
        +     1              1          1 +
                                   Type: Union(Matrix Expression Integer,...)
--R
--R        + +----+          +----+          +
--R        |\|- 11  + 2   - \|- 11  + 2   31 |
--R        |-----------   -------------   -- |
--R        |     5              5         20 |
--R        |                                 |
--R   (5)  |  +----+          +----+         |
--R        |2\|- 11  - 1  - 2\|- 11  - 1    1|
--R        |------------  --------------  - -|
--R        |      5              5          4|
--R        |                                 |
--R        +     1              1          1 +
--R                                   Type: Union(Matrix Expression Integer,...)
--E 40

--S 41 of 82
inverse(t) * m1 * t
 

        +           +----+                                +
        |5581634906\|- 11  - 55255461173                  |
        |-------------------------------        0        0|
        |            +----+                               |
        | 1888197247\|- 11  - 5747548576                  |
        |                                                 |
   (6)  |                                   +----+        |
        |                                 6\|- 11  + 11   |
        |               0                 -------------  0|
        |                                     +----+      |
        |                                    \|- 11       |
        |                                                 |
        +               0                       0        0+
                                              Type: Matrix Expression Integer
--R
--R        +           +----+                                +
--R        |5581634906\|- 11  - 55255461173                  |
--R        |-------------------------------        0        0|
--R        |            +----+                               |
--R        | 1888197247\|- 11  - 5747548576                  |
--R        |                                                 |
--R   (6)  |                                   +----+        |
--R        |                                 6\|- 11  + 11   |
--R        |               0                 -------------  0|
--R        |                                     +----+      |
--R        |                                    \|- 11       |
--R        |                                                 |
--R        +               0                       0        0+
--R                                              Type: Matrix Expression Integer
--E 41

-- Input for page MatrixBasicFunctionsPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 42 of 82
m1 := matrix([[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,7]])
 

        +1  2  3  4+
        |          |
        |2  3  4  5|
   (1)  |          |
        |3  4  5  6|
        |          |
        +4  5  6  7+
                                                         Type: Matrix Integer
--R
--R        +1  2  3  4+
--R        |          |
--R        |2  3  4  5|
--R   (1)  |          |
--R        |3  4  5  6|
--R        |          |
--R        +4  5  6  7+
--R                                                         Type: Matrix Integer
--E 42

--S 43 of 82
m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])
 

        +1    0    2 +
        |            |
   (2)  |20  30   10 |
        |            |
        +0   200  100+
                                                         Type: Matrix Integer
--R
--R        +1    0    2 +
--R        |            |
--R   (2)  |20  30   10 |
--R        |            |
--R        +0   200  100+
--R                                                         Type: Matrix Integer
--E 43

--S 44 of 82
(m3,m4) : MATRIX PF 7
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 44

--S 45 of 82
m3 := matrix([[1,0,1],[5,0,1]])
 

        +1  0  1+
   (4)  |       |
        +5  0  1+
                                                    Type: Matrix PrimeField 7
--R
--R        +1  0  1+
--R   (4)  |       |
--R        +5  0  1+
--R                                                    Type: Matrix PrimeField 7
--E 45

--S 46 of 82
m4 := matrix([[1],[2],[5],[6]])
 

        +1+
        | |
        |2|
   (5)  | |
        |5|
        | |
        +6+
                                                    Type: Matrix PrimeField 7
--R
--R        +1+
--R        | |
--R        |2|
--R   (5)  | |
--R        |5|
--R        | |
--R        +6+
--R                                                    Type: Matrix PrimeField 7
--E 46

--S 47 of 82
m2(1,1)
 

   (6)  1
                                                        Type: PositiveInteger
--R
--R   (6)  1
--R                                                        Type: PositiveInteger
--E 47

--S 48 of 82
m2(1,1) := 99
 

   (7)  99
                                                        Type: PositiveInteger
--R
--R   (7)  99
--R                                                        Type: PositiveInteger
--E 48

--S 49 of 82
m2
 

        +99   0    2 +
        |            |
   (8)  |20  30   10 |
        |            |
        +0   200  100+
                                                         Type: Matrix Integer
--R
--R        +99   0    2 +
--R        |            |
--R   (8)  |20  30   10 |
--R        |            |
--R        +0   200  100+
--R                                                         Type: Matrix Integer
--E 49

--S 50 of 82
row(m2,2)
 

   (9)  [20,30,10]
                                                         Type: Vector Integer
--R
--R   (9)  [20,30,10]
--R                                                         Type: Vector Integer
--E 50

--S 51 of 82
setRow!(m2,2,vector [66,77,88])
 

         +99   0    2 +
         |            |
   (10)  |66  77   88 |
         |            |
         +0   200  100+
                                                         Type: Matrix Integer
--R
--R         +99   0    2 +
--R         |            |
--R   (10)  |66  77   88 |
--R         |            |
--R         +0   200  100+
--R                                                         Type: Matrix Integer
--E 51

--S 52 of 82
r := column(m2,1)
 

   (11)  [99,66,0]
                                                         Type: Vector Integer
--R
--R   (11)  [99,66,0]
--R                                                         Type: Vector Integer
--E 52

--S 53 of 82
setColumn!(m2,2,r)
 

         +99  99   2 +
         |           |
   (12)  |66  66  88 |
         |           |
         +0   0   100+
                                                         Type: Matrix Integer
--R
--R         +99  99   2 +
--R         |           |
--R   (12)  |66  66  88 |
--R         |           |
--R         +0   0   100+
--R                                                         Type: Matrix Integer
--E 53

--S 54 of 82
nrows(m1)
 

   (13)  4
                                                        Type: PositiveInteger
--R
--R   (13)  4
--R                                                        Type: PositiveInteger
--E 54

--S 55 of 82
m5 : MATRIX INT := new(12,12,0)
 

         +0  0  0  0  0  0  0  0  0  0  0  0+
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
   (14)  |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         +0  0  0  0  0  0  0  0  0  0  0  0+
                                                         Type: Matrix Integer
--R
--R         +0  0  0  0  0  0  0  0  0  0  0  0+
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R   (14)  |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         +0  0  0  0  0  0  0  0  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 55

--S 56 of 82
for i in 2..nrows(m5) repeat m5(i-1,i):= 1
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 56

--S 57 of 82
m5
 

         +0  1  0  0  0  0  0  0  0  0  0  0+
         |                                  |
         |0  0  1  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  1  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  1  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  1  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  1  0  0  0  0  0|
   (16)  |                                  |
         |0  0  0  0  0  0  0  1  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  1  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  1  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  1  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  1|
         |                                  |
         +0  0  0  0  0  0  0  0  0  0  0  0+
                                                         Type: Matrix Integer
--R
--R         +0  1  0  0  0  0  0  0  0  0  0  0+
--R         |                                  |
--R         |0  0  1  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  1  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  1  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  1  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  1  0  0  0  0  0|
--R   (16)  |                                  |
--R         |0  0  0  0  0  0  0  1  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  1  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  1  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  1  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  1|
--R         |                                  |
--R         +0  0  0  0  0  0  0  0  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 57

--S 58 of 82
d : MATRIX INT := diagonalMatrix([1,2,3,2,1])
 

         +1  0  0  0  0+
         |             |
         |0  2  0  0  0|
         |             |
   (17)  |0  0  3  0  0|
         |             |
         |0  0  0  2  0|
         |             |
         +0  0  0  0  1+
                                                         Type: Matrix Integer
--R
--R         +1  0  0  0  0+
--R         |             |
--R         |0  2  0  0  0|
--R         |             |
--R   (17)  |0  0  3  0  0|
--R         |             |
--R         |0  0  0  2  0|
--R         |             |
--R         +0  0  0  0  1+
--R                                                         Type: Matrix Integer
--E 58

--S 59 of 82
m6 := matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])
 

         +0   1   2   3   4 +
         |                  |
   (18)  |5   6   7   8   9 |
         |                  |
         +10  11  12  13  14+
                                                         Type: Matrix Integer
--R
--R         +0   1   2   3   4 +
--R         |                  |
--R   (18)  |5   6   7   8   9 |
--R         |                  |
--R         +10  11  12  13  14+
--R                                                         Type: Matrix Integer
--E 59

--S 60 of 82
m7 := subMatrix(m6,1,3,2,4)
 

         +1   2   3 +
         |          |
   (19)  |6   7   8 |
         |          |
         +11  12  13+
                                                         Type: Matrix Integer
--R
--R         +1   2   3 +
--R         |          |
--R   (19)  |6   7   8 |
--R         |          |
--R         +11  12  13+
--R                                                         Type: Matrix Integer
--E 60

--S 61 of 82
horizConcat(m6,m7)
 

         +0   1   2   3   4   1   2   3 +
         |                              |
   (20)  |5   6   7   8   9   6   7   8 |
         |                              |
         +10  11  12  13  14  11  12  13+
                                                         Type: Matrix Integer
--R
--R         +0   1   2   3   4   1   2   3 +
--R         |                              |
--R   (20)  |5   6   7   8   9   6   7   8 |
--R         |                              |
--R         +10  11  12  13  14  11  12  13+
--R                                                         Type: Matrix Integer
--E 61

--S 62 of 82
vertConcat(m6,subMatrix(m6,1,1,1,5))
 

         +0   1   2   3   4 +
         |                  |
         |5   6   7   8   9 |
   (21)  |                  |
         |10  11  12  13  14|
         |                  |
         +0   1   2   3   4 +
                                                         Type: Matrix Integer
--R
--R         +0   1   2   3   4 +
--R         |                  |
--R         |5   6   7   8   9 |
--R   (21)  |                  |
--R         |10  11  12  13  14|
--R         |                  |
--R         +0   1   2   3   4 +
--R                                                         Type: Matrix Integer
--E 62

--S 63 of 82
transpose(m6)
 

         +0  5  10+
         |        |
         |1  6  11|
         |        |
   (22)  |2  7  12|
         |        |
         |3  8  13|
         |        |
         +4  9  14+
                                                         Type: Matrix Integer
--R
--R         +0  5  10+
--R         |        |
--R         |1  6  11|
--R         |        |
--R   (22)  |2  7  12|
--R         |        |
--R         |3  8  13|
--R         |        |
--R         +4  9  14+
--R                                                         Type: Matrix Integer
--E 63

--S 64 of 82
setsubMatrix!(m6,1,3,transpose(subMatrix(m6,1,3,1,3)))
 

         +0   1   0  5  10+
         |                |
   (23)  |5   6   1  6  11|
         |                |
         +10  11  2  7  12+
                                                         Type: Matrix Integer
--R
--R         +0   1   0  5  10+
--R         |                |
--R   (23)  |5   6   1  6  11|
--R         |                |
--R         +10  11  2  7  12+
--R                                                         Type: Matrix Integer
--E 64

--S 65 of 82
m6
 

         +0   1   0  5  10+
         |                |
   (24)  |5   6   1  6  11|
         |                |
         +10  11  2  7  12+
                                                         Type: Matrix Integer
--R
--R         +0   1   0  5  10+
--R         |                |
--R   (24)  |5   6   1  6  11|
--R         |                |
--R         +10  11  2  7  12+
--R                                                         Type: Matrix Integer
--E 65

--S 66 of 82
m8 := matrix([[1,2],[3,4]])
 

         +1  2+
   (25)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (25)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 66

--S 67 of 82
m9 := m8
 

         +1  2+
   (26)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (26)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 67

--S 68 of 82
m10 := copy(m8)
 

         +1  2+
   (27)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (27)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 68

--S 69 of 82
m8(1,1) := 1000000
 

   (28)  1000000
                                                        Type: PositiveInteger
--R
--R   (28)  1000000
--R                                                        Type: PositiveInteger
--E 69

--S 70 of 82
m8
 

         +1000000  2+
   (29)  |          |
         +   3     4+
                                                         Type: Matrix Integer
--R
--R         +1000000  2+
--R   (29)  |          |
--R         +   3     4+
--R                                                         Type: Matrix Integer
--E 70

--S 71 of 82
m9
 

         +1000000  2+
   (30)  |          |
         +   3     4+
                                                         Type: Matrix Integer
--R
--R         +1000000  2+
--R   (30)  |          |
--R         +   3     4+
--R                                                         Type: Matrix Integer
--E 71

--S 72 of 82
m10
 

         +1  2+
   (31)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (31)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 72

-- Input for page EigenPage
)clear all
 
   All user variables and function definitions have been cleared.

--S 73 of 82
m1 : MATRIX FRAC INT := [[1,2,1],[2,1,-2],[1,-2,4]]
 

        +1   2    1 +
        |           |
   (1)  |2   1   - 2|
        |           |
        +1  - 2   4 +
                                                Type: Matrix Fraction Integer
--R
--R        +1   2    1 +
--R        |           |
--R   (1)  |2   1   - 2|
--R        |           |
--R        +1  - 2   4 +
--R                                                Type: Matrix Fraction Integer
--E 73

--S 74 of 82
leig := eigenvalues(m1)
 

                  2
   (2)  [5,%B | %B  - %B - 5]
Type: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--R
--R                  2
--I   (2)  [5,%A | %A  - %A - 5]
--RType: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--E 74

--S 75 of 82
eigenvector(first(leig),m1)
 

         + 0 +
         |   |
         |  1|
   (3)  [|- -|]
         |  2|
         |   |
         + 1 +
                       Type: List Matrix Fraction Polynomial Fraction Integer
--R
--R         + 0 +
--R         |   |
--R         |  1|
--R   (3)  [|- -|]
--R         |  2|
--R         |   |
--R         + 1 +
--R                       Type: List Matrix Fraction Polynomial Fraction Integer
--E 75

--S 76 of 82
eigenvectors(m1)
 

   (4)
                                   + 0 +
                                   |   |
                                   |  1|
   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
                                   |  2|
                                   |   |
                                   + 1 +
                                                     +%C+
                     2                               |  |
    [eigval= (%C | %C  - %C - 5),eigmult= 1,eigvec= [|2 |]]]
                                                     |  |
                                                     +1 +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R
--R   (4)
--R                                   + 0 +
--R                                   |   |
--R                                   |  1|
--R   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
--R                                   |  2|
--R                                   |   |
--R                                   + 1 +
--R                                                     +%C+
--R                     2                               |  |
--R    [eigval= (%C | %C  - %C - 5),eigmult= 1,eigvec= [|2 |]]]
--R                                                     |  |
--R                                                     +1 +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 76

--S 77 of 82
radicalEigenvectors(m1)
 

   (5)
                                            + +--+    +
              +--+                          |\|21  + 1|
             \|21  + 1                      |---------|
   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
                 2                          |         |
                                            |    2    |
                                            |         |
                                            +    1    +
                                              +   +--+    +
                +--+                          |- \|21  + 1|
             - \|21  + 1                      |-----------|
    [radval= -----------,radmult= 1,radvect= [|     2     |]],
                  2                           |           |
                                              |     2     |
                                              |           |
                                              +     1     +
                                    + 0 +
                                    |   |
                                    |  1|
    [radval= 5,radmult= 1,radvect= [|- -|]]]
                                    |  2|
                                    |   |
                                    + 1 +
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R
--R   (5)
--R                                            + +--+    +
--R              +--+                          |\|21  + 1|
--R             \|21  + 1                      |---------|
--R   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
--R                 2                          |         |
--R                                            |    2    |
--R                                            |         |
--R                                            +    1    +
--R                                              +   +--+    +
--R                +--+                          |- \|21  + 1|
--R             - \|21  + 1                      |-----------|
--R    [radval= -----------,radmult= 1,radvect= [|     2     |]],
--R                  2                           |           |
--R                                              |     2     |
--R                                              |           |
--R                                              +     1     +
--R                                    + 0 +
--R                                    |   |
--R                                    |  1|
--R    [radval= 5,radmult= 1,radvect= [|- -|]]]
--R                                    |  2|
--R                                    |   |
--R                                    + 1 +
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E 77

--S 78 of 82
eigenMatrix(m1)
 

        + +--+         +--+         +
        |\|21  + 1  - \|21  + 1     |
        |---------  -----------   0 |
        |    2           2          |
   (6)  |                           |
        |                          1|
        |    2           2       - -|
        |                          2|
        |                           |
        +    1           1        1 +
                                   Type: Union(Matrix Expression Integer,...)
--R
--R        + +--+         +--+         +
--R        |\|21  + 1  - \|21  + 1     |
--R        |---------  -----------   0 |
--R        |    2           2          |
--R   (6)  |                           |
--R        |                          1|
--R        |    2           2       - -|
--R        |                          2|
--R        |                           |
--R        +    1           1        1 +
--R                                   Type: Union(Matrix Expression Integer,...)
--E 78

--S 79 of 82
m2 : MATRIX FRAC INT := [[-5,-2],[18,7]]
 

        +- 5  - 2+
   (7)  |        |
        +18    7 +
                                                Type: Matrix Fraction Integer
--R
--R        +- 5  - 2+
--R   (7)  |        |
--R        +18    7 +
--R                                                Type: Matrix Fraction Integer
--E 79

--S 80 of 82
eigenMatrix(m2)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 80

--S 81 of 82
m3 : MATRIX FRAC INT := [[1,2],[2,1]]
 

        +1  2+
   (9)  |    |
        +2  1+
                                                Type: Matrix Fraction Integer
--R
--R        +1  2+
--R   (9)  |    |
--R        +2  1+
--R                                                Type: Matrix Fraction Integer
--E 81

--S 82 of 82
orthonormalBasis(m3)
 

          +    1 + +  1 +
          |- ----| |----|
          |   +-+| | +-+|
          |  \|2 | |\|2 |
   (10)  [|      |,|    |]
          |   1  | |  1 |
          | ---- | |----|
          |  +-+ | | +-+|
          + \|2  + +\|2 +
                                         Type: List Matrix Expression Integer
--R
--R          +    1 + +  1 +
--R          |- ----| |----|
--R          |   +-+| | +-+|
--R          |  \|2 | |\|2 |
--R   (10)  [|      |,|    |]
--R          |   1  | |  1 |
--R          | ---- | |----|
--R          |  +-+ | | +-+|
--R          + \|2  + +\|2 +
--R                                         Type: List Matrix Expression Integer
--E 82

)spool 
 
Starts dribbling to ifthenelse.output (2009/2/17, 17:46:30).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

 
--S 1 of 20
i:=2
 

   (1)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2
--R                                                        Type: PositiveInteger
--E 1


--S 2 of 20
for i in 2..2 repeat
  if i>0 then output("positive") else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 2

--S 3 of 20
for i in 2..2 repeat
  if i>0 then output("positive") 
    else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 3

--S 4 of 20
for i in 2..2 repeat
  if i>0 then output("positive") 
  else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 4

--S 5 of 20
for i in 2..2 repeat
  if i>0 
  then output("positive") 
  else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 5

--S 6 of 20
for i in 2..2 repeat
  if i>0 
    then output("positive") 
    else output("nonpositive")
 
  Line  47: --R 
  Line  48: --R   positive
  Line  49: --R                                                                   Type: Void
  Line  50: --E 5
  Line  51: 
  Line  52: --S 6 of 20
  Line  53: for i in 2..2 repeat
  Line  54:   if i>0 
           ..A
  Error  A: (from #\A and on) Ignored from here
  Line  55:     then output("positive") 
           ....A
  Error  A: Improper syntax.
  Error  A: (from #\A up to ) Ignored.
  Line  56:     else output("nonpositive")
           ....A........................B
  Error  A: Improper syntax.
  Error  A: (from #\A up to #\B) Ignored.
  Error  B: Possibly missing a then 
  Error  B: (up to #\B) to here.
   7 error(s) parsing 
--R 
--R  Line  47: --R 
--R  Line  48: --R   positive
--R  Line  49: --R                                                                   Type: Void
--R  Line  50: --E 5
--R  Line  51: 
--R  Line  52: --S 6 of 20
--R  Line  53: for i in 2..2 repeat
--R  Line  54:   if i>0 
--R           ..A
--R  Error  A: (from #\A and on) Ignored from here
--R  Line  55:     then output("positive") 
--R           ....A
--R  Error  A: Improper syntax.
--R  Error  A: (from #\A up to ) Ignored.
--R  Line  56:     else output("nonpositive")
--R           ....A........................B
--R  Error  A: Improper syntax.
--R  Error  A: (from #\A up to #\B) Ignored.
--R  Error  B: Possibly missing a then 
--R  Error  B: (up to #\B) to here.
--R   7 error(s) parsing 
--E 6

--S 7 of 20
i:=2
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 20
for i in 2..2 repeat
  if i>0 then
    output(i)
    output("positive") 
  else
    output(i)
    else output("nonpositive")
 
  Line  83: --R 
  Line  84: --R
  Line  85: --R   (6)  2
  Line  86: --R                                                        Type: PositiveInteger
  Line  87: --E 7
  Line  88: 
  Line  89: --S 8 of 20
  Line  90: for i in 2..2 repeat
  Line  91:   if i>0 then
  Line  92:     output(i)
  Line  93:     output("positive") 
  Line  94:   else
  Line  95:     output(i)
  Line  96:     else output("nonpositive")
           ....A
  Error  A: (from #\A up to ) Ignored.
  Error  A: Improper syntax.
   2 error(s) parsing 
--R 
--R  Line  83: --R 
--R  Line  84: --R
--R  Line  85: --R   (6)  2
--R  Line  86: --R                                                        Type: PositiveInteger
--R  Line  87: --E 7
--R  Line  88: 
--R  Line  89: --S 8 of 20
--R  Line  90: for i in 2..2 repeat
--R  Line  91:   if i>0 then
--R  Line  92:     output(i)
--R  Line  93:     output("positive") 
--R  Line  94:   else
--R  Line  95:     output(i)
--R  Line  96:     else output("nonpositive")
--R           ....A
--R  Error  A: (from #\A up to ) Ignored.
--R  Error  A: Improper syntax.
--R   2 error(s) parsing 
--E 8

--S 9 of 20
i:=1.5
 

   (7)  1.5
                                                                  Type: Float
--R 
--R
--R   (7)  1.5
--R                                                                  Type: Float
--E 9

--S 10 of 20
a:=
  if i > 0 then
    j:=sin(i*pi())
    exp(j+1/j)
  else
    j:=cos(i*0.5*pi())
    log(abs(j)**5+1)
 

   (8)  0.1353352832 3661269189
                                                                  Type: Float
--R 
--R
--R   (8)  0.1353352832 3661269189
--R                                                                  Type: Float
--E 10


--S 11 of 20
test: (INT,INT) -> List(INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 20
test(a,b) ==
  x:=0; y:=0
  if (a rem b = 0) and b < 0 then
    x := 1
    y := 1
  [x,y]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 20
4 rem -2
 

   (11)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (11)  0
--R                                                     Type: NonNegativeInteger
--E 13

--S 14 of 20
test(4,-2)
 
   Compiling function test with type (Integer,Integer) -> List Integer 

   (12)  [1,1]
                                                           Type: List Integer
--R 
--R   Compiling function test with type (Integer,Integer) -> List Integer 
--R
--R   (12)  [1,1]
--R                                                           Type: List Integer
--E 14


--S 15 of 20
4 rem -3
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 20
test(4,-3)
 

   (14)  [0,0]
                                                           Type: List Integer
--R 
--R
--R   (14)  [0,0]
--R                                                           Type: List Integer
--E 16


--S 17 of 20
4 rem 2
 

   (15)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (15)  0
--R                                                     Type: NonNegativeInteger
--E 17

--S 18 of 20
test(4,2)
 

   (16)  [0,0]
                                                           Type: List Integer
--R 
--R
--R   (16)  [0,0]
--R                                                           Type: List Integer
--E 18


--S 19 of 20
test1: (INT,INT) -> List(INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 20
test1(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then x := 1 ; y := 1
  [x,y]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

)spool 
 
Starts dribbling to schaum16.output (2009/2/17, 17:58:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(x*(x^n+a^n)),x)
 

                n log(x)    n
        - log(%e         + a ) + n log(x)
   (1)  ---------------------------------
                          n
                       n a
                                          Type: Union(Expression Integer,...)
--R
--R                n log(x)    n
--R        - log(%e         + a ) + n log(x)
--R   (1)  ---------------------------------
--R                          n
--R                       n a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/(n*a^n)*log(x^n/(x^n+a^n))
 

                n
               x
        log(-------)
             n    n
            x  + a
   (2)  ------------
               n
            n a
                                                     Type: Expression Integer
--R
--R                n
--R               x
--R        log(-------)
--R             n    n
--R            x  + a
--R   (2)  ------------
--R               n
--R            n a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                         n
                n log(x)    n           x
        - log(%e         + a ) - log(-------) + n log(x)
                                      n    n
                                     x  + a
   (3)  ------------------------------------------------
                                 n
                              n a
                                                     Type: Expression Integer
--R
--R                                         n
--R                n log(x)    n           x
--R        - log(%e         + a ) - log(-------) + n log(x)
--R                                      n    n
--R                                     x  + a
--R   (3)  ------------------------------------------------
--R                                 n
--R                              n a
--R                                                     Type: Expression Integer
--E

--S 4
dd:=expandLog cc
 

                n log(x)    n         n    n         n
        - log(%e         + a ) + log(x  + a ) - log(x ) + n log(x)
   (4)  ----------------------------------------------------------
                                      n
                                   n a
                                                     Type: Expression Integer
--R
--R                n log(x)    n         n    n         n
--R        - log(%e         + a ) + log(x  + a ) - log(x ) + n log(x)
--R   (4)  ----------------------------------------------------------
--R                                      n
--R                                   n a
--R                                                     Type: Expression Integer
--E

--S 5      14:325 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(x^(n-1)/(x^n+a^n),x)
 

              n log(x)    n
        log(%e         + a )
   (1)  --------------------
                  n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              n log(x)    n
--R        log(%e         + a )
--R   (1)  --------------------
--R                  n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=1/n*log(x^n+a^n)
 

             n    n
        log(x  + a )
   (2)  ------------
              n
                                                     Type: Expression Integer
--R
--R             n    n
--R        log(x  + a )
--R   (2)  ------------
--R              n
--R                                                     Type: Expression Integer
--E

--S 10
cc:=aa-bb
 

              n log(x)    n         n    n
        log(%e         + a ) - log(x  + a )
   (3)  -----------------------------------
                         n
                                                     Type: Expression Integer
--R
--R              n log(x)    n         n    n
--R        log(%e         + a ) - log(x  + a )
--R   (3)  -----------------------------------
--R                         n
--R                                                     Type: Expression Integer
--E

--S 11
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12     14:326 Schaums and Axiom agree
dd:=explog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13     14:327 Axiom cannot compute this integral
aa:=integrate(x^m/(x^n+a^n)^r,x)
 

           x       m
         ++      %O
   (1)   |   ----------- d%O
        ++     n     n r
             (a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %J
--I   (1)   |   ----------- d%J
--R        ++     n     n r
--I             (a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 14     14:328 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(x^n+a^n)^r),x)
 

           x
         ++         1
   (1)   |   -------------- d%O
        ++     m  n     n r
             %O (a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%J
--R        ++     m  n     n r
--I             %J (a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(1/(x*sqrt(x^n+a^n)),x)
 

   (1)
              +---------------+                      +--+
            n |  n log(x)    n       n log(x)     n  | n
        - 2a \|%e         + a   + (%e         + 2a )\|a
    log(-------------------------------------------------)
                              n log(x)
                            %e
   [------------------------------------------------------,
                              +--+
                              | n
                            n\|a
             +----+ +---------------+
             |   n  |  n log(x)    n
            \|- a  \|%e         + a
      2atan(-------------------------)
                         n
                        a
    - --------------------------------]
                    +----+
                    |   n
                  n\|- a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R              +---------------+                      +--+
--R            n |  n log(x)    n       n log(x)     n  | n
--R        - 2a \|%e         + a   + (%e         + 2a )\|a
--R    log(-------------------------------------------------)
--R                              n log(x)
--R                            %e
--R   [------------------------------------------------------,
--R                              +--+
--R                              | n
--R                            n\|a
--R             +----+ +---------------+
--R             |   n  |  n log(x)    n
--R            \|- a  \|%e         + a
--R      2atan(-------------------------)
--R                         n
--R                        a
--R    - --------------------------------]
--R                    +----+
--R                    |   n
--R                  n\|- a
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 16
bb:=1/(n*sqrt(a^n))*log((sqrt(x^n+a^n)-sqrt(a^n))/(sqrt(x^n+a^n)+sqrt(a^n)))
 

             +-------+    +--+
             | n    n     | n
            \|x  + a   - \|a
        log(------------------)
             +-------+    +--+
             | n    n     | n
            \|x  + a   + \|a
   (2)  -----------------------
                   +--+
                   | n
                 n\|a
                                                     Type: Expression Integer
--R
--R             +-------+    +--+
--R             | n    n     | n
--R            \|x  + a   - \|a
--R        log(------------------)
--R             +-------+    +--+
--R             | n    n     | n
--R            \|x  + a   + \|a
--R   (2)  -----------------------
--R                   +--+
--R                   | n
--R                 n\|a
--R                                                     Type: Expression Integer
--E

--S 17
cc1:=aa.1-bb
 

   (3)
                 +---------------+                      +--+
               n |  n log(x)    n       n log(x)     n  | n
           - 2a \|%e         + a   + (%e         + 2a )\|a
       log(-------------------------------------------------)
                                 n log(x)
                               %e
     + 
              +-------+    +--+
              | n    n     | n
             \|x  + a   - \|a
       - log(------------------)
              +-------+    +--+
              | n    n     | n
             \|x  + a   + \|a
  /
       +--+
       | n
     n\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +---------------+                      +--+
--R               n |  n log(x)    n       n log(x)     n  | n
--R           - 2a \|%e         + a   + (%e         + 2a )\|a
--R       log(-------------------------------------------------)
--R                                 n log(x)
--R                               %e
--R     + 
--R              +-------+    +--+
--R              | n    n     | n
--R             \|x  + a   - \|a
--R       - log(------------------)
--R              +-------+    +--+
--R              | n    n     | n
--R             \|x  + a   + \|a
--R  /
--R       +--+
--R       | n
--R     n\|a
--R                                                     Type: Expression Integer
--E

--S 18
dd1:=expandLog cc1
 

   (4)
               +---------------+                        +--+
             n |  n log(x)    n         n log(x)     n  | n
       log(2a \|%e         + a   + (- %e         - 2a )\|a  )
     + 
            +-------+    +--+         +-------+    +--+
            | n    n     | n          | n    n     | n
       log(\|x  + a   + \|a  ) - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
  /
       +--+
       | n
     n\|a
                                                     Type: Expression Integer
--R
--R   (4)
--R               +---------------+                        +--+
--R             n |  n log(x)    n         n log(x)     n  | n
--R       log(2a \|%e         + a   + (- %e         - 2a )\|a  )
--R     + 
--R            +-------+    +--+         +-------+    +--+
--R            | n    n     | n          | n    n     | n
--R       log(\|x  + a   + \|a  ) - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
--R  /
--R       +--+
--R       | n
--R     n\|a
--R                                                     Type: Expression Integer
--E

--S 19
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (5)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (5)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20
ee1:=explog dd1
 

   (6)
               +-------+                +--+         +-------+    +--+
             n | n    n        n     n  | n          | n    n     | n
       log(2a \|x  + a   + (- x  - 2a )\|a  ) + log(\|x  + a   + \|a  )
     + 
              +-------+    +--+
              | n    n     | n
       - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
  /
       +--+
       | n
     n\|a
                                                     Type: Expression Integer
--R
--R   (6)
--R               +-------+                +--+         +-------+    +--+
--R             n | n    n        n     n  | n          | n    n     | n
--R       log(2a \|x  + a   + (- x  - 2a )\|a  ) + log(\|x  + a   + \|a  )
--R     + 
--R              +-------+    +--+
--R              | n    n     | n
--R       - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
--R  /
--R       +--+
--R       | n
--R     n\|a
--R                                                     Type: Expression Integer
--E

--S 21
ff1:=complexNormalize ee1
 

        n log(a) + 4log(- 1)
   (7)  --------------------
              +----------+
              |  n log(a)
           2n\|%e
                                                     Type: Expression Integer
--R
--R        n log(a) + 4log(- 1)
--R   (7)  --------------------
--R              +----------+
--R              |  n log(a)
--R           2n\|%e
--R                                                     Type: Expression Integer
--E

--S 22     14:329 Schaums and Axiom differ by a constant
gg1:=explog ff1
 

        n log(a) + 4log(- 1)
   (8)  --------------------
                  +--+
                  | n
               2n\|a
                                                     Type: Expression Integer
--R
--R        n log(a) + 4log(- 1)
--R   (8)  --------------------
--R                  +--+
--R                  | n
--R               2n\|a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(1/(x*(x^n-a^n)),x)
 

              n log(x)    n
        log(%e         - a ) - n log(x)
   (1)  -------------------------------
                         n
                      n a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              n log(x)    n
--R        log(%e         - a ) - n log(x)
--R   (1)  -------------------------------
--R                         n
--R                      n a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=1/(n*a^n)*log((x^n-a^n)/x^n)
 

             n    n
            x  - a
        log(-------)
                n
               x
   (2)  ------------
               n
            n a
                                                     Type: Expression Integer
--R
--R             n    n
--R            x  - a
--R        log(-------)
--R                n
--R               x
--R   (2)  ------------
--R               n
--R            n a
--R                                                     Type: Expression Integer
--E

--S 25
cc:=aa-bb
 

                                    n    n
              n log(x)    n        x  - a
        log(%e         - a ) - log(-------) - n log(x)
                                       n
                                      x
   (3)  ----------------------------------------------
                                n
                             n a
                                                     Type: Expression Integer
--R
--R                                    n    n
--R              n log(x)    n        x  - a
--R        log(%e         - a ) - log(-------) - n log(x)
--R                                       n
--R                                      x
--R   (3)  ----------------------------------------------
--R                                n
--R                             n a
--R                                                     Type: Expression Integer
--E

--S 26
dd:=expandLog cc
 

              n log(x)    n         n         n    n
        log(%e         - a ) + log(x ) - log(x  - a ) - n log(x)
   (4)  --------------------------------------------------------
                                     n
                                  n a
                                                     Type: Expression Integer
--R
--R              n log(x)    n         n         n    n
--R        log(%e         - a ) + log(x ) - log(x  - a ) - n log(x)
--R   (4)  --------------------------------------------------------
--R                                     n
--R                                  n a
--R                                                     Type: Expression Integer
--E

--S 27
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (5)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (5)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 28
ee:=explog dd
 

             n
        log(x ) - n log(x)
   (6)  ------------------
                  n
               n a
                                                     Type: Expression Integer
--R
--R             n
--R        log(x ) - n log(x)
--R   (6)  ------------------
--R                  n
--R               n a
--R                                                     Type: Expression Integer
--E

--S 29
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (7)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (7)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 30     14:330 Schaums and Axiom agree
ff:=logpow ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 31
aa:=integrate(x^(n-1)/(x^n-a^n),x)
 

              n log(x)    n
        log(%e         - a )
   (1)  --------------------
                  n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              n log(x)    n
--R        log(%e         - a )
--R   (1)  --------------------
--R                  n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 32
bb:=1/n*log(x^n-a^n)
 

             n    n
        log(x  - a )
   (2)  ------------
              n
                                                     Type: Expression Integer
--R
--R             n    n
--R        log(x  - a )
--R   (2)  ------------
--R              n
--R                                                     Type: Expression Integer
--E

--S 33
cc:=aa-bb
 

              n log(x)    n         n    n
        log(%e         - a ) - log(x  - a )
   (3)  -----------------------------------
                         n
                                                     Type: Expression Integer
--R
--R              n log(x)    n         n    n
--R        log(%e         - a ) - log(x  - a )
--R   (3)  -----------------------------------
--R                         n
--R                                                     Type: Expression Integer
--E

--S 34
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35     14:331 Schaums and Axiom agree
dd:=explog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 36     14:332 Axiom cannot compute this integral
aa:=integrate(x^m/(x^n-a^n)^r,x)
 

           x        m
         ++       %O
   (1)   |   ------------- d%O
        ++       n     n r
             (- a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x        m
--I         ++       %J
--I   (1)   |   ------------- d%J
--R        ++       n     n r
--I             (- a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 37     14:333 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(x^n-a^n)^r),x)
 

           x
         ++          1
   (1)   |   ---------------- d%O
        ++     m    n     n r
             %O (- a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++          1
--I   (1)   |   ---------------- d%J
--R        ++     m    n     n r
--I             %J (- a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 38
aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
 

   (1)
            +---------------+                      +----+
          n |  n log(x)    n       n log(x)     n  |   n
        2a \|%e         - a   + (%e         - 2a )\|- a
    log(-------------------------------------------------)
                              n log(x)
                            %e
   [------------------------------------------------------,
                             +----+
                             |   n
                           n\|- a
           +--+ +---------------+
           | n  |  n log(x)    n
          \|a  \|%e         - a
    2atan(-----------------------)
                      n
                     a
    ------------------------------]
                  +--+
                  | n
                n\|a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R            +---------------+                      +----+
--R          n |  n log(x)    n       n log(x)     n  |   n
--R        2a \|%e         - a   + (%e         - 2a )\|- a
--R    log(-------------------------------------------------)
--R                              n log(x)
--R                            %e
--R   [------------------------------------------------------,
--R                             +----+
--R                             |   n
--R                           n\|- a
--R           +--+ +---------------+
--R           | n  |  n log(x)    n
--R          \|a  \|%e         - a
--R    2atan(-----------------------)
--R                      n
--R                     a
--R    ------------------------------]
--R                  +--+
--R                  | n
--R                n\|a
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 39
bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n))
 

               +--+
               | n
               |a
        2acos( |-- )
               | n
              \|x
   (2)  ------------
             +--+
             | n
           n\|a
                                                     Type: Expression Integer
--R
--R               +--+
--R               | n
--R               |a
--R        2acos( |-- )
--R               | n
--R              \|x
--R   (2)  ------------
--R             +--+
--R             | n
--R           n\|a
--R                                                     Type: Expression Integer
--E

--S 40
cc1:=aa.1-bb
 

   (3)
                    +---------------+                      +----+
        +--+      n |  n log(x)    n       n log(x)     n  |   n
        | n     2a \|%e         - a   + (%e         - 2a )\|- a
       \|a  log(-------------------------------------------------)
                                      n log(x)
                                    %e
     + 
                       +--+
           +----+      | n
           |   n       |a
       - 2\|- a  acos( |-- )
                       | n
                      \|x
  /
       +----+ +--+
       |   n  | n
     n\|- a  \|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                    +---------------+                      +----+
--R        +--+      n |  n log(x)    n       n log(x)     n  |   n
--R        | n     2a \|%e         - a   + (%e         - 2a )\|- a
--R       \|a  log(-------------------------------------------------)
--R                                      n log(x)
--R                                    %e
--R     + 
--R                       +--+
--R           +----+      | n
--R           |   n       |a
--R       - 2\|- a  acos( |-- )
--R                       | n
--R                      \|x
--R  /
--R       +----+ +--+
--R       |   n  | n
--R     n\|- a  \|a
--R                                                     Type: Expression Integer
--E

--S 41     14:334 Axiom cannot simplify this expression
cc2:=aa.2-bb
 

               +--+ +---------------+           +--+
               | n  |  n log(x)    n            | n
              \|a  \|%e         - a             |a
        2atan(-----------------------) - 2acos( |-- )
                          n                     | n
                         a                     \|x
   (4)  ---------------------------------------------
                              +--+
                              | n
                            n\|a
                                                     Type: Expression Integer
--R
--R               +--+ +---------------+           +--+
--R               | n  |  n log(x)    n            | n
--R              \|a  \|%e         - a             |a
--R        2atan(-----------------------) - 2acos( |-- )
--R                          n                     | n
--R                         a                     \|x
--R   (4)  ---------------------------------------------
--R                              +--+
--R                              | n
--R                            n\|a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 42     14:335 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x)
 

           x     p - 1
         ++    %O
   (1)   |   ---------- d%O
        ++    2m     2m
             a   + %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x     p - 1
--I         ++    %J
--I   (1)   |   ---------- d%J
--R        ++    2m     2m
--I             a   + %J
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 43     14:336 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x)
 

           x       p - 1
         ++      %O
   (1)   |   - ---------- d%O
        ++      2m     2m
               a   - %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       p - 1
--I         ++      %J
--I   (1)   |   - ---------- d%J
--R        ++      2m     2m
--I               a   - %J
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 44     14:337 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x)
 

           x         p - 1
         ++        %O
   (1)   |   ------------------ d%O
        ++    2m + 1     2m + 1
             a       + %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x         p - 1
--I         ++        %J
--I   (1)   |   ------------------ d%J
--R        ++    2m + 1     2m + 1
--I             a       + %J
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 45     14:338 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x)
 

           x           p - 1
         ++          %O
   (1)   |   - ------------------ d%O
        ++      2m + 1     2m + 1
               a       - %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           p - 1
--I         ++          %J
--I   (1)   |   - ------------------ d%J
--R        ++      2m + 1     2m + 1
--I               a       - %J
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to exdiff.output (2009/2/17, 17:45:45).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 10
differentiate(sin(x) * exp(x**2),x)
 

              2                  2
             x                  x
   (1)  2x %e  sin(x) + cos(x)%e
                                                     Type: Expression Integer
--R 
--R
--R              2                  2
--R             x                  x
--R   (1)  2x %e  sin(x) + cos(x)%e
--R                                                     Type: Expression Integer
--E 1

-- Input for page ExDiffSeveralVariables
)clear all
 
   All user variables and function definitions have been cleared.

--S 2 of 10
differentiate(sin(x) * tan(y)/(x**2 + y**2),x)
 

                         2    2
        (- 2x sin(x) + (y  + x )cos(x))tan(y)
   (1)  -------------------------------------
                    4     2 2    4
                   y  + 2x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                         2    2
--R        (- 2x sin(x) + (y  + x )cos(x))tan(y)
--R   (1)  -------------------------------------
--R                    4     2 2    4
--R                   y  + 2x y  + x
--R                                                     Type: Expression Integer
--E 2

--S 3 of 10
differentiate(sin(x) * tan(y)/(x**2 + y**2),y)
 

          2    2             2                       2    2
        (y  + x )sin(x)tan(y)  - 2y sin(x)tan(y) + (y  + x )sin(x)
   (2)  ----------------------------------------------------------
                               4     2 2    4
                              y  + 2x y  + x
                                                     Type: Expression Integer
--R 
--R
--R          2    2             2                       2    2
--R        (y  + x )sin(x)tan(y)  - 2y sin(x)tan(y) + (y  + x )sin(x)
--R   (2)  ----------------------------------------------------------
--R                               4     2 2    4
--R                              y  + 2x y  + x
--R                                                     Type: Expression Integer
--E 3

-- Input for page ExDiffMultipleI
)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 10
differentiate(sin(x)/(x**2 + y**2),[x,y])
 

                           3     2
        8x y sin(x) + (- 2y  - 2x y)cos(x)
   (1)  ----------------------------------
               6     2 4     4 2    6
              y  + 3x y  + 3x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                           3     2
--R        8x y sin(x) + (- 2y  - 2x y)cos(x)
--R   (1)  ----------------------------------
--R               6     2 4     4 2    6
--R              y  + 3x y  + 3x y  + x
--R                                                     Type: Expression Integer
--E 4

--S 5 of 10
differentiate(sin(x)/(x**2 + y**2),[x,y,y])
 

                2     3             4     2 2     4
        (- 40x y  + 8x )sin(x) + (6y  + 4x y  - 2x )cos(x)
   (2)  --------------------------------------------------
                   8     2 6     4 4     6 2    8
                  y  + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                2     3             4     2 2     4
--R        (- 40x y  + 8x )sin(x) + (6y  + 4x y  - 2x )cos(x)
--R   (2)  --------------------------------------------------
--R                   8     2 6     4 4     6 2    8
--R                  y  + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E 5


-- Input for page ExDiffMultipleII
)clear all
 
   All user variables and function definitions have been cleared.

--S 6 of 10
differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])
 

                    4      3
            (- 84x y  + 24x y)sin(z)
   (1)  --------------------------------
         12     2 9     4 6     6 3    8
        y   + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                    4      3
--R            (- 84x y  + 24x y)sin(z)
--R   (1)  --------------------------------
--R         12     2 9     4 6     6 3    8
--R        y   + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E 6

-- Input for page ExDiffHigherOrder
)clear all
 
   All user variables and function definitions have been cleared.

--S 7 of 10
differentiate(exp(x**2),x,4)
 

                             2
            4      2        x
   (1)  (16x  + 48x  + 12)%e
                                                     Type: Expression Integer
--R 
--R
--R                             2
--R            4      2        x
--R   (1)  (16x  + 48x  + 12)%e
--R                                                     Type: Expression Integer
--E 7

-- Input for page ExDiffFormalIntegral
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 8 of 10
f := integrate(sqrt(1 + t**3),t)
 

           t  +-------+
         ++   |  3
   (1)   |   \|%M  + 1 d%M
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           t  +-------+
--R         ++   |  3
--R   (1)   |   \|%M  + 1 d%M
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 10
differentiate(f,t)
 

         +------+
         | 3
   (2)  \|t  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +------+
--R         | 3
--R   (2)  \|t  + 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 10
differentiate(f * t**2,t)
 

             t  +-------+          +------+
           ++   |  3             2 | 3
   (3)  2t |   \|%M  + 1 d%M  + t \|t  + 1
          ++
                                                     Type: Expression Integer
--R 
--R
--R             t  +-------+          +------+
--R           ++   |  3             2 | 3
--R   (3)  2t |   \|%M  + 1 d%M  + t \|t  + 1
--R          ++
--R                                                     Type: Expression Integer
--E 10
)spool
 
Starts dribbling to danzwill.output (2009/2/17, 17:44:35).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set break resume
 

--S 1 of 17
i1 := integrate( sin(x), x)
 

   (1)  - cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  - cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 1

--i2 := integrate( sqrt(tan(x)), x)

--S 2 of 17
i3 := integrate( x/(x**3-1),x)
 

                                                                 +-+
           +-+     2              +-+                   (2x + 1)\|3
        - \|3 log(x  + x + 1) + 2\|3 log(x - 1) + 6atan(------------)
                                                              3
   (2)  -------------------------------------------------------------
                                      +-+
                                    6\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                 +-+
--R           +-+     2              +-+                   (2x + 1)\|3
--R        - \|3 log(x  + x + 1) + 2\|3 log(x - 1) + 6atan(------------)
--R                                                              3
--R   (2)  -------------------------------------------------------------
--R                                      +-+
--R                                    6\|3
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 17
i4 := integrate( x/sin(x)**2, x)
 

                    sin(x)                     2
        sin(x)log(----------) - sin(x)log(----------) - x cos(x)
                  cos(x) + 1              cos(x) + 1
   (3)  --------------------------------------------------------
                                 sin(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    sin(x)                     2
--R        sin(x)log(----------) - sin(x)log(----------) - x cos(x)
--R                  cos(x) + 1              cos(x) + 1
--R   (3)  --------------------------------------------------------
--R                                 sin(x)
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 17
i5 := integrate( log(x)/sqrt(x+1), x)
 

              +-----+              +-----+                      +-----+
   (4)  2log(\|x + 1  + 1) - 2log(\|x + 1  - 1) + (2log(x) - 4)\|x + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              +-----+              +-----+                      +-----+
--R   (4)  2log(\|x + 1  + 1) - 2log(\|x + 1  - 1) + (2log(x) - 4)\|x + 1
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 17
i6 := integrate( exp(-a*x**2), x)
 

           x       2
         ++    - %N a
   (5)   |   %e      d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       2
--R         ++    - %N a
--R   (5)   |   %e      d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 17
i7 := integrate( x/(log(x))**3, x)
 

               2                2          2
        4log(x) Ei(2log(x)) - 2x log(x) - x
   (6)  ------------------------------------
                             2
                      2log(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2                2          2
--R        4log(x) Ei(2log(x)) - 2x log(x) - x
--R   (6)  ------------------------------------
--R                             2
--R                      2log(x)
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 17
i8 := integrate( x/(sqrt(1+x)+sqrt(1-x)),x)
 

                +-----+             +-------+
        (x + 1)\|x + 1  + (- x + 1)\|- x + 1
   (7)  -------------------------------------
                          3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +-----+             +-------+
--R        (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (7)  -------------------------------------
--R                          3
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 17
i9 := integrate( 1/(2+cos(x)),x)
 

                +-+
               \|3 sin(x)
        2atan(-----------)
              3cos(x) + 3
   (8)  ------------------
                +-+
               \|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +-+
--R               \|3 sin(x)
--R        2atan(-----------)
--R              3cos(x) + 3
--R   (8)  ------------------
--R                +-+
--R               \|3
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 17
i10:= integrate( sin(x)/x**2, x)
 

           x
         ++  sin(%N)
   (9)   |   ------- d%N
        ++       2
               %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++  sin(%N)
--R   (9)   |   ------- d%N
--R        ++       2
--R               %N
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 17
d1:= integrate( 1/(2+cos(x)),x=0..4*%pi)
 

   (10)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (10)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 10

)set mes test off
 
 
--S 11 of 17
d2:= integrate( sin(x)/x,x=%minusInfinity..%plusInfinity)
 
 
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 11

)set mes test on
 
 
--S 12 of 17
d3:= integrate( x**2/(1+x**3),x=0..%plusInfinity)
 

   (11)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (11)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 12

--S 13 of 17
d4:= integrate( exp(-x)/sqrt(x),x=0..%plusInfinity)
 

          _ 1
   (12)  | (-)
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          _ 1
--R   (12)  | (-)
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 13

--S 14 of 17
d5:= integrate( exp(-x**2)*log(x)**2,x=0..%plusInfinity)
 

          _ 1             1     _ 1         1 2
         | (-)polygamma(1,-) + | (-)digamma(-)
            2             2       2         2
   (13)  --------------------------------------
                            8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          _ 1             1     _ 1         1 2
--R         | (-)polygamma(1,-) + | (-)digamma(-)
--R            2             2       2         2
--R   (13)  --------------------------------------
--R                            8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 14

--S 15 of 17
d6:= integrate( exp(-x)*log(x)**2*x**3,x=1..%plusInfinity)
 

   (14)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (14)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 15

--S 16 of 17
d7:= integrate( exp(-x)*x**(1/3),x=1..%plusInfinity)
 

   (15)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (15)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 16

--S 17 of 17
d8:= integrate( exp(-x)*x**2/(1-exp(-2*x)),x=0..%plusInfinity)
 

   (16)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (16)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 17
)spool
 
Starts dribbling to mset2.output (2009/2/17, 17:55:15).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 12
s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10]
 

   (1)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (1)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 1

--S 2 of 12
insert!(3,s)
 

   (2)  {1,2: 2,4: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (2)  {1,2: 2,4: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 2

--S 3 of 12
remove!(3,s,1); s
 

   (3)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (3)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 3

--S 4 of 12
remove!(5,s); s
 

   (4)  {1,2: 2,3: 3,4: 4,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (4)  {1,2: 2,3: 3,4: 4,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 4

--S 5 of 12
count(5,s)
 

   (5)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (5)  0
--R                                                     Type: NonNegativeInteger
--E 5

--S 6 of 12
t := multiset [2,2,2,-9]
 

   (6)  {3: 2,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (6)  {3: 2,- 9}
--R                                                       Type: Multiset Integer
--E 6

--S 7 of 12
U := union(s,t)
 

   (7)  {1,5: 2,3: 3,4: 4,6,7,10,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (7)  {1,5: 2,3: 3,4: 4,6,7,10,- 9}
--R                                                       Type: Multiset Integer
--E 7

--S 8 of 12
I := intersect(s,t)
 

   (8)  {5: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (8)  {5: 2}
--R                                                       Type: Multiset Integer
--E 8

--S 9 of 12
difference(s,t)
 

   (9)  {1,3: 3,4: 4,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (9)  {1,3: 3,4: 4,6,7,10}
--R                                                       Type: Multiset Integer
--E 9

--S 10 of 12
S := symmetricDifference(s,t)
 

   (10)  {1,3: 3,4: 4,6,7,10,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {1,3: 3,4: 4,6,7,10,- 9}
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 12
(U = union(S,I))@Boolean
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 12
t1 := multiset [1,2,2,3]; [t1 < t, t1 < s, t < s, t1 <= s]
 

   (12)  [false,true,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (12)  [false,true,false,true]
--R                                                           Type: List Boolean
--E 12
)spool 
 
Starts dribbling to schaum13.output (2009/2/17, 17:58:19).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 2
bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)+2*a*x+b)
 

                  +--------------+
              +-+ |   2
        log(2\|a \|a x  + b x + c  + 2a x + b)
   (2)  --------------------------------------
                          +-+
                         \|a
                                                     Type: Expression Integer
--R
--R                  +--------------+
--R              +-+ |   2
--R        log(2\|a \|a x  + b x + c  + 2a x + b)
--R   (2)  --------------------------------------
--R                          +-+
--R                         \|a
--R                                                     Type: Expression Integer
--E

--S 3
bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c))
 

                  2a x + b
          asin(--------------)
                +-----------+
                |          2
               \|- 4a c + b
   (3)  - --------------------
                  +---+
                 \|- a
                                                     Type: Expression Integer
--R
--R                  2a x + b
--R          asin(--------------)
--R                +-----------+
--R                |          2
--R               \|- 4a c + b
--R   (3)  - --------------------
--R                  +---+
--R                 \|- a
--R                                                     Type: Expression Integer
--E

--S 4
bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2))
 

                2a x + b
        asinh(------------)
               +---------+
               |        2
              \|4a c - b
   (4)  -------------------
                 +-+
                \|a
                                                     Type: Expression Integer
--R
--R                2a x + b
--R        asinh(------------)
--R               +---------+
--R               |        2
--R              \|4a c - b
--R   (4)  -------------------
--R                 +-+
--R                \|a
--R                                                     Type: Expression Integer
--E

--S 5
cc1:=bb1-aa.1
 

   (5)
                 +--------------+
             +-+ |   2
       log(2\|a \|a x  + b x + c  + 2a x + b)
     + 
       -
          log
                                    +--------------+
                    +-+ +-+         |   2                   +-+
                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
               + 
                        2             +-+
                 (- 2a x  - b x - 2c)\|a
            /
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
  /
      +-+
     \|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                 +--------------+
--R             +-+ |   2
--R       log(2\|a \|a x  + b x + c  + 2a x + b)
--R     + 
--R       -
--R          log
--R                                    +--------------+
--R                    +-+ +-+         |   2                   +-+
--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R               + 
--R                        2             +-+
--R                 (- 2a x  - b x - 2c)\|a
--R            /
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R  /
--R      +-+
--R     \|a
--R                                                     Type: Expression Integer
--E

--S 6
cc2:=bb1-aa.2
 

   (6)
                       +--------------+
        +---+      +-+ |   2
       \|- a log(2\|a \|a x  + b x + c  + 2a x + b)
     + 
                          +--------------+
                    +---+ |   2               +---+ +-+
           +-+     \|- a \|a x  + b x + c  - \|- a \|c
       - 2\|a atan(------------------------------------)
                                    a x
  /
      +---+ +-+
     \|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R        +---+      +-+ |   2
--R       \|- a log(2\|a \|a x  + b x + c  + 2a x + b)
--R     + 
--R                          +--------------+
--R                    +---+ |   2               +---+ +-+
--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c
--R       - 2\|a atan(------------------------------------)
--R                                    a x
--R  /
--R      +---+ +-+
--R     \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 7
cc3:=bb2-aa.1
 

   (7)
       -
             +---+
            \|- a
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
          +-+        2a x + b
       - \|a asin(--------------)
                   +-----------+
                   |          2
                  \|- 4a c + b
  /
      +---+ +-+
     \|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R       -
--R             +---+
--R            \|- a
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R          +-+        2a x + b
--R       - \|a asin(--------------)
--R                   +-----------+
--R                   |          2
--R                  \|- 4a c + b
--R  /
--R      +---+ +-+
--R     \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 8
cc4:=bb2-aa.2
 

                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c             2a x + b
        - 2atan(------------------------------------) - asin(--------------)
                                 a x                          +-----------+
                                                              |          2
                                                             \|- 4a c + b
   (8)  --------------------------------------------------------------------
                                        +---+
                                       \|- a
                                                     Type: Expression Integer
--R
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c             2a x + b
--R        - 2atan(------------------------------------) - asin(--------------)
--R                                 a x                          +-----------+
--R                                                              |          2
--R                                                             \|- 4a c + b
--R   (8)  --------------------------------------------------------------------
--R                                        +---+
--R                                       \|- a
--R                                                     Type: Expression Integer
--E

--S 9
cc5:=bb3-aa.1
 

   (9)
       -
          log
                                    +--------------+
                    +-+ +-+         |   2                   +-+
                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
               + 
                        2             +-+
                 (- 2a x  - b x - 2c)\|a
            /
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
     + 
               2a x + b
       asinh(------------)
              +---------+
              |        2
             \|4a c - b
  /
      +-+
     \|a
                                                     Type: Expression Integer
--R
--R   (9)
--R       -
--R          log
--R                                    +--------------+
--R                    +-+ +-+         |   2                   +-+
--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R               + 
--R                        2             +-+
--R                 (- 2a x  - b x - 2c)\|a
--R            /
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R               2a x + b
--R       asinh(------------)
--R              +---------+
--R              |        2
--R             \|4a c - b
--R  /
--R      +-+
--R     \|a
--R                                                     Type: Expression Integer
--E

--S 10
cc6:=bb3-aa.2
 

   (10)
                      +--------------+
                +---+ |   2               +---+ +-+
       +-+     \|- a \|a x  + b x + c  - \|- a \|c      +---+        2a x + b
   - 2\|a atan(------------------------------------) + \|- a asinh(------------)
                                a x                                 +---------+
                                                                    |        2
                                                                   \|4a c - b
   -----------------------------------------------------------------------------
                                      +---+ +-+
                                     \|- a \|a
                                                     Type: Expression Integer
--R
--R   (10)
--R                      +--------------+
--R                +---+ |   2               +---+ +-+
--R       +-+     \|- a \|a x  + b x + c  - \|- a \|c      +---+        2a x + b
--R   - 2\|a atan(------------------------------------) + \|- a asinh(------------)
--R                                a x                                 +---------+
--R                                                                    |        2
--R                                                                   \|4a c - b
--R   -----------------------------------------------------------------------------
--R                                      +---+ +-+
--R                                     \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 11
dd1:=simplifyLog cc1
 

   (11)
     log
                                                  +--------------+
                         +-+                 +-+  |   2
            ((4a x + 2b)\|c  + (- 2b x - 4c)\|a )\|a x  + b x + c
          + 
                 2              +-+ +-+         2              2
            (4a x  + 4b x + 4c)\|a \|c  - 2a b x  + (- 4a c - b )x - 2b c
       /
                               +--------------+
               +-+ +-+         |   2                   +-+
            (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
          + 
                   2             +-+
            (- 2a x  - b x - 2c)\|a
  /
      +-+
     \|a
                                                     Type: Expression Integer
--R
--R   (11)
--R     log
--R                                                  +--------------+
--R                         +-+                 +-+  |   2
--R            ((4a x + 2b)\|c  + (- 2b x - 4c)\|a )\|a x  + b x + c
--R          + 
--R                 2              +-+ +-+         2              2
--R            (4a x  + 4b x + 4c)\|a \|c  - 2a b x  + (- 4a c - b )x - 2b c
--R       /
--R                               +--------------+
--R               +-+ +-+         |   2                   +-+
--R            (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R          + 
--R                   2             +-+
--R            (- 2a x  - b x - 2c)\|a
--R  /
--R      +-+
--R     \|a
--R                                                     Type: Expression Integer
--E

--S 12     14:280 Schaums and Axiom differ by a constant
ee1:=ratDenom dd1
 

                      +-+     +-+
          +-+    - 2a\|c  + b\|a
         \|a log(----------------)
                         a
   (12)  -------------------------
                     a
                                                     Type: Expression Integer
--R
--R                      +-+     +-+
--R          +-+    - 2a\|c  + b\|a
--R         \|a log(----------------)
--R                         a
--R   (12)  -------------------------
--R                     a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 11
aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                   +--------------+
               +-+ |   2               2
           (2b\|c \|a x  + b x + c  - b x - 2b c)
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                    +--------------+
                +-+ |   2                   2         +-+ +-+
         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
    /
                  +--------------+
          +-+ +-+ |   2                                +-+
       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
     ,

                     +--------------+
                 +-+ |   2               2
           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                     +--------------+
               +---+ |   2                   2        +---+ +-+
         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
    /
                    +--------------+
          +---+ +-+ |   2                               +---+
       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                   +--------------+
--R               +-+ |   2               2
--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                    +--------------+
--R                +-+ |   2                   2         +-+ +-+
--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
--R    /
--R                  +--------------+
--R          +-+ +-+ |   2                                +-+
--R       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
--R     ,
--R
--R                     +--------------+
--R                 +-+ |   2               2
--R           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                     +--------------+
--R               +---+ |   2                   2        +---+ +-+
--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
--R    /
--R                    +--------------+
--R          +---+ +-+ |   2                               +---+
--R       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 12
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 13
bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1
 

   (3)
       -
            b
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
             +--------------+
         +-+ |   2
       2\|a \|a x  + b x + c
  /
        +-+
     2a\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            b
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R             +--------------+
--R         +-+ |   2
--R       2\|a \|a x  + b x + c
--R  /
--R        +-+
--R     2a\|a
--R                                                     Type: Expression Integer
--E

--S 14
bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2
 

   (4)
                   +--------------+
             +---+ |   2               +---+ +-+           +--------------+
            \|- a \|a x  + b x + c  - \|- a \|c      +---+ |   2
   - b atan(------------------------------------) + \|- a \|a x  + b x + c
                             a x
   ------------------------------------------------------------------------
                                      +---+
                                    a\|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                   +--------------+
--R             +---+ |   2               +---+ +-+           +--------------+
--R            \|- a \|a x  + b x + c  - \|- a \|c      +---+ |   2
--R   - b atan(------------------------------------) + \|- a \|a x  + b x + c
--R                             a x
--R   ------------------------------------------------------------------------
--R                                      +---+
--R                                    a\|- a
--R                                                     Type: Expression Integer
--E

--S 15
cc1:=bb1-aa.1
 

   (5)
                   +--------------+
               +-+ |   2               2
         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   +--------------+
               +-+ |   2               2
         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                +--------------+
            +-+ |   2                          +-+ +-+
       - 4c\|a \|a x  + b x + c  + (2b x + 4c)\|a \|c
  /
                +--------------+
        +-+ +-+ |   2                                +-+
     4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                   +--------------+
--R               +-+ |   2               2
--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   +--------------+
--R               +-+ |   2               2
--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                +--------------+
--R            +-+ |   2                          +-+ +-+
--R       - 4c\|a \|a x  + b x + c  + (2b x + 4c)\|a \|c
--R  /
--R                +--------------+
--R        +-+ +-+ |   2                                +-+
--R     4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
--R                                                     Type: Expression Integer
--E

--S 16
cc2:=bb1-aa.2
 

   (6)
                         +--------------+
               +---+ +-+ |   2                2          +---+
         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                     +--------------+
             +-+ +-+ |   2                   2          +-+
         (4b\|a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|a )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                      +--------------+
            +---+ +-+ |   2                          +---+ +-+ +-+
       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
  /
                      +--------------+
        +---+ +-+ +-+ |   2                                +---+ +-+
     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                         +--------------+
--R               +---+ +-+ |   2                2          +---+
--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                     +--------------+
--R             +-+ +-+ |   2                   2          +-+
--R         (4b\|a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|a )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                      +--------------+
--R            +---+ +-+ |   2                          +---+ +-+ +-+
--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
--R  /
--R                      +--------------+
--R        +---+ +-+ +-+ |   2                                +---+ +-+
--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 17
cc3:=bb2-aa.1
 

   (7)
                         +--------------+
               +---+ +-+ |   2                2          +---+
         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                       +--------------+
               +-+ +-+ |   2                 2          +-+
         (- 4b\|a \|c \|a x  + b x + c  + (2b x + 4b c)\|a )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                      +--------------+
            +---+ +-+ |   2                          +---+ +-+ +-+
       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
  /
                      +--------------+
        +---+ +-+ +-+ |   2                                +---+ +-+
     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                         +--------------+
--R               +---+ +-+ |   2                2          +---+
--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                       +--------------+
--R               +-+ +-+ |   2                 2          +-+
--R         (- 4b\|a \|c \|a x  + b x + c  + (2b x + 4b c)\|a )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                      +--------------+
--R            +---+ +-+ |   2                          +---+ +-+ +-+
--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
--R  /
--R                      +--------------+
--R        +---+ +-+ +-+ |   2                                +---+ +-+
--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 18
cc4:=bb2-aa.2
 

             +--------------+
             |   2                         +-+
        - 2c\|a x  + b x + c  + (b x + 2c)\|c
   (8)  --------------------------------------
               +--------------+
           +-+ |   2
        2a\|c \|a x  + b x + c  - a b x - 2a c
                                                     Type: Expression Integer
--R
--R             +--------------+
--R             |   2                         +-+
--R        - 2c\|a x  + b x + c  + (b x + 2c)\|c
--R   (8)  --------------------------------------
--R               +--------------+
--R           +-+ |   2
--R        2a\|c \|a x  + b x + c  - a b x - 2a c
--R                                                     Type: Expression Integer
--E

--S 19     14:281 Schaums and Axiom differ by a constant
dd1:=ratDenom cc4
 

           +-+
          \|c
   (9)  - ----
            a
                                                     Type: Expression Integer
--R
--R           +-+
--R          \|c
--R   (9)  - ----
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19
aa:=integrate(x^2/sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                                                      +--------------+
                            3          2      2   +-+ |   2
             ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
           + 
                 2 2       2      4  2             2      3           3      2 2
           (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  2        2  3                 3  2           2      2     +-+
           ((- 16a c - 4a b )x  + (- 8a b c + 6b )x  + (- 32a c  + 24b c)x)\|a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                  2   4       2        2  3                 3  2
               16a b x  + (32a c - 8a b )x  + (24a b c - 18b )x
             + 
                     2      2
               (32a c  - 24b c)x
        *
            +-+ +-+
           \|a \|c
    /
                                   +--------------+
             2         2   +-+ +-+ |   2
         (32a b x + 64a c)\|a \|c \|a x  + b x + c
       + 
                3      2 2  2      2           2 2  +-+
         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
     ,

                                                        +--------------+
                              3          2      2   +-+ |   2
             ((- 16a b c + 12b )x - 32a c  + 24b c)\|c \|a x  + b x + c
           + 
                 2 2       2      4  2           2      3           3      2 2
             (16a c  - 8a b c - 3b )x  + (32a b c  - 24b c)x + 32a c  - 24b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                 2        2  3                 3  2           2      2     +---+
           ((- 8a c - 2a b )x  + (- 4a b c + 3b )x  + (- 16a c  + 12b c)x)\|- a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
              2   4       2        2  3                3  2         2      2
           (8a b x  + (16a c - 4a b )x  + (12a b c - 9b )x  + (16a c  - 12b c)x)
        *
            +---+ +-+
           \|- a \|c
    /
                                     +--------------+
             2         2   +---+ +-+ |   2
         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
       + 
                3      2 2  2      2           2 2  +---+
         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R                                                      +--------------+
--R                            3          2      2   +-+ |   2
--R             ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
--R           + 
--R                 2 2       2      4  2             2      3           3      2 2
--R           (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  2        2  3                 3  2           2      2     +-+
--R           ((- 16a c - 4a b )x  + (- 8a b c + 6b )x  + (- 32a c  + 24b c)x)\|a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                  2   4       2        2  3                 3  2
--R               16a b x  + (32a c - 8a b )x  + (24a b c - 18b )x
--R             + 
--R                     2      2
--R               (32a c  - 24b c)x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                                   +--------------+
--R             2         2   +-+ +-+ |   2
--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R       + 
--R                3      2 2  2      2           2 2  +-+
--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R     ,
--R
--R                                                        +--------------+
--R                              3          2      2   +-+ |   2
--R             ((- 16a b c + 12b )x - 32a c  + 24b c)\|c \|a x  + b x + c
--R           + 
--R                 2 2       2      4  2           2      3           3      2 2
--R             (16a c  - 8a b c - 3b )x  + (32a b c  - 24b c)x + 32a c  - 24b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                 2        2  3                 3  2           2      2     +---+
--R           ((- 8a c - 2a b )x  + (- 4a b c + 3b )x  + (- 16a c  + 12b c)x)\|- a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R              2   4       2        2  3                3  2         2      2
--R           (8a b x  + (16a c - 4a b )x  + (12a b c - 9b )x  + (16a c  - 12b c)x)
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                                     +--------------+
--R             2         2   +---+ +-+ |   2
--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
--R       + 
--R                3      2 2  2      2           2 2  +---+
--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 20
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 21
bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1
 

   (3)
                     2
         (- 4a c + 3b )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                       +--------------+
                   +-+ |   2
       (4a x - 6b)\|a \|a x  + b x + c
  /
       2 +-+
     8a \|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     2
--R         (- 4a c + 3b )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                       +--------------+
--R                   +-+ |   2
--R       (4a x - 6b)\|a \|a x  + b x + c
--R  /
--R       2 +-+
--R     8a \|a
--R                                                     Type: Expression Integer
--E

--S 22
bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2
 

   (4)
                                 +--------------+
                           +---+ |   2               +---+ +-+
                   2      \|- a \|a x  + b x + c  - \|- a \|c
       (- 4a c + 3b )atan(------------------------------------)
                                           a x
     + 
                         +--------------+
                   +---+ |   2
       (2a x - 3b)\|- a \|a x  + b x + c
  /
       2 +---+
     4a \|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                 +--------------+
--R                           +---+ |   2               +---+ +-+
--R                   2      \|- a \|a x  + b x + c  - \|- a \|c
--R       (- 4a c + 3b )atan(------------------------------------)
--R                                           a x
--R     + 
--R                         +--------------+
--R                   +---+ |   2
--R       (2a x - 3b)\|- a \|a x  + b x + c
--R  /
--R       2 +---+
--R     4a \|- a
--R                                                     Type: Expression Integer
--E

--S 23
cc1:=aa.1-bb1
 

   (5)
                                                    +--------------+
                          3          2      2   +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
         + 
               2 2       2      4  2             2      3           3      2 2
         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                    +--------------+
                          3          2      2   +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
         + 
               2 2       2      4  2             2      3           3      2 2
         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                +--------------+
             2           2  +-+ |   2
       (- 24b c x - 48b c )\|a \|a x  + b x + c
     + 
                     3  2      2           2  +-+ +-+
       ((24a b c + 6b )x  + 48b c x + 48b c )\|a \|c
  /
                                 +--------------+
           2         2   +-+ +-+ |   2
       (32a b x + 64a c)\|a \|c \|a x  + b x + c
     + 
              3      2 2  2      2           2 2  +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                    +--------------+
--R                          3          2      2   +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
--R         + 
--R               2 2       2      4  2             2      3           3      2 2
--R         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                    +--------------+
--R                          3          2      2   +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
--R         + 
--R               2 2       2      4  2             2      3           3      2 2
--R         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                +--------------+
--R             2           2  +-+ |   2
--R       (- 24b c x - 48b c )\|a \|a x  + b x + c
--R     + 
--R                     3  2      2           2  +-+ +-+
--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|a \|c
--R  /
--R                                 +--------------+
--R           2         2   +-+ +-+ |   2
--R       (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R     + 
--R              3      2 2  2      2           2 2  +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R                                                     Type: Expression Integer
--E

--S 24
cc2:=aa.2-bb1
 

   (6)
                                                          +--------------+
                          3          2      2   +---+ +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
         + 
                     2 2       2      4  2             2      3           3
               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
             + 
                  2 2
               24b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                          +--------------+
                            3          2      2   +-+ +-+ |   2
           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
         + 
                     2 2        2      4  2           2      3           3
                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
               + 
                      2 2
                 - 48b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                      +--------------+
             2           2  +---+ +-+ |   2
       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
     + 
                     3  2      2           2  +---+ +-+ +-+
       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
  /
                                       +--------------+
           2         2   +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              3      2 2  2      2           2 2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                          +--------------+
--R                          3          2      2   +---+ +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                     2 2       2      4  2             2      3           3
--R               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
--R             + 
--R                  2 2
--R               24b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                          +--------------+
--R                            3          2      2   +-+ +-+ |   2
--R           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
--R         + 
--R                     2 2        2      4  2           2      3           3
--R                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
--R               + 
--R                      2 2
--R                 - 48b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                      +--------------+
--R             2           2  +---+ +-+ |   2
--R       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                     3  2      2           2  +---+ +-+ +-+
--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R           2         2   +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              3      2 2  2      2           2 2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 25
cc3:=aa.2-bb1
 

   (7)
                                                          +--------------+
                          3          2      2   +---+ +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
         + 
                     2 2       2      4  2             2      3           3
               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
             + 
                  2 2
               24b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                          +--------------+
                            3          2      2   +-+ +-+ |   2
           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
         + 
                     2 2        2      4  2           2      3           3
                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
               + 
                      2 2
                 - 48b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                      +--------------+
             2           2  +---+ +-+ |   2
       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
     + 
                     3  2      2           2  +---+ +-+ +-+
       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
  /
                                       +--------------+
           2         2   +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              3      2 2  2      2           2 2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                                                          +--------------+
--R                          3          2      2   +---+ +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                     2 2       2      4  2             2      3           3
--R               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
--R             + 
--R                  2 2
--R               24b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                          +--------------+
--R                            3          2      2   +-+ +-+ |   2
--R           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
--R         + 
--R                     2 2        2      4  2           2      3           3
--R                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
--R               + 
--R                      2 2
--R                 - 48b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                      +--------------+
--R             2           2  +---+ +-+ |   2
--R       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                     3  2      2           2  +---+ +-+ +-+
--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R           2         2   +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              3      2 2  2      2           2 2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 26
cc4:=aa.2-bb2
 

   (8)
                            +--------------+
             2           2  |   2
       (- 12b c x - 24b c )\|a x  + b x + c
     + 
                     3  2      2           2  +-+
       ((12a b c + 3b )x  + 24b c x + 24b c )\|c
  /
                             +--------------+
           2         2   +-+ |   2                    3      2 2  2      2
       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
     + 
            2 2
       - 32a c
                                                     Type: Expression Integer
--R
--R   (8)
--R                            +--------------+
--R             2           2  |   2
--R       (- 12b c x - 24b c )\|a x  + b x + c
--R     + 
--R                     3  2      2           2  +-+
--R       ((12a b c + 3b )x  + 24b c x + 24b c )\|c
--R  /
--R                             +--------------+
--R           2         2   +-+ |   2                    3      2 2  2      2
--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
--R     + 
--R            2 2
--R       - 32a c
--R                                                     Type: Expression Integer
--E

--S 27     14:282 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

             +-+
          3b\|c
   (9)  - ------
              2
            4a
                                                     Type: Expression Integer
--R
--R             +-+
--R          3b\|c
--R   (9)  - ------
--R              2
--R            4a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (1)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (1)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28
bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x)
 

                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  + b x + 2c
          log(---------------------------------)
                              x
   (2)  - --------------------------------------
                            +-+
                           \|c
                                                     Type: Expression Integer
--R
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  + b x + 2c
--R          log(---------------------------------)
--R                              x
--R   (2)  - --------------------------------------
--R                            +-+
--R                           \|c
--R                                                     Type: Expression Integer
--E

--S 29
bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c)))
 

                 b x + 2c
        asin(---------------)
               +-----------+
               |          2
             x\|- 4a c + b
   (3)  ---------------------
                 +---+
                \|- c
                                                     Type: Expression Integer
--R
--R                 b x + 2c
--R        asin(---------------)
--R               +-----------+
--R               |          2
--R             x\|- 4a c + b
--R   (3)  ---------------------
--R                 +---+
--R                \|- c
--R                                                     Type: Expression Integer
--E

--S 30
bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(4*a*c-b^2)))
 

                   b x + 2c
          asinh(-------------)
                  +---------+
                  |        2
                x\|4a c - b
   (4)  - --------------------
                   +-+
                  \|c
                                                     Type: Expression Integer
--R
--R                   b x + 2c
--R          asinh(-------------)
--R                  +---------+
--R                  |        2
--R                x\|4a c - b
--R   (4)  - --------------------
--R                   +-+
--R                  \|c
--R                                                     Type: Expression Integer
--E

--S 31
cc1:=aa-bb1
 

   (5)
                 +--------------+
             +-+ |   2
           2\|c \|a x  + b x + c  + b x + 2c
       log(---------------------------------)
                           x
     + 
                 +--------------+
             +-+ |   2
           2\|c \|a x  + b x + c  - b x - 2c
       log(---------------------------------)
                           x
  /
      +-+
     \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                 +--------------+
--R             +-+ |   2
--R           2\|c \|a x  + b x + c  + b x + 2c
--R       log(---------------------------------)
--R                           x
--R     + 
--R                 +--------------+
--R             +-+ |   2
--R           2\|c \|a x  + b x + c  - b x - 2c
--R       log(---------------------------------)
--R                           x
--R  /
--R      +-+
--R     \|c
--R                                                     Type: Expression Integer
--E

--S 32
cc2:=aa-bb2
 

   (6)
                   +--------------+
               +-+ |   2
    +---+    2\|c \|a x  + b x + c  - b x - 2c     +-+         b x + 2c
   \|- c log(---------------------------------) - \|c asin(---------------)
                             x                               +-----------+
                                                             |          2
                                                           x\|- 4a c + b
   ------------------------------------------------------------------------
                                   +---+ +-+
                                  \|- c \|c
                                                     Type: Expression Integer
--R
--R   (6)
--R                   +--------------+
--R               +-+ |   2
--R    +---+    2\|c \|a x  + b x + c  - b x - 2c     +-+         b x + 2c
--R   \|- c log(---------------------------------) - \|c asin(---------------)
--R                             x                               +-----------+
--R                                                             |          2
--R                                                           x\|- 4a c + b
--R   ------------------------------------------------------------------------
--R                                   +---+ +-+
--R                                  \|- c \|c
--R                                                     Type: Expression Integer
--E

--S 33
cc3:=aa-bb3
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c             b x + 2c
        log(---------------------------------) + asinh(-------------)
                            x                            +---------+
                                                         |        2
                                                       x\|4a c - b
   (7)  -------------------------------------------------------------
                                      +-+
                                     \|c
                                                     Type: Expression Integer
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c             b x + 2c
--R        log(---------------------------------) + asinh(-------------)
--R                            x                            +---------+
--R                                                         |        2
--R                                                       x\|4a c - b
--R   (7)  -------------------------------------------------------------
--R                                      +-+
--R                                     \|c
--R                                                     Type: Expression Integer
--E

--S 34
dd1:=expandLog cc1
 

   (8)
                 +--------------+
             +-+ |   2
       log(2\|c \|a x  + b x + c  + b x + 2c)
     + 
                 +--------------+
             +-+ |   2
       log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)
  /
      +-+
     \|c
                                                     Type: Expression Integer
--R
--R   (8)
--R                 +--------------+
--R             +-+ |   2
--R       log(2\|c \|a x  + b x + c  + b x + 2c)
--R     + 
--R                 +--------------+
--R             +-+ |   2
--R       log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)
--R  /
--R      +-+
--R     \|c
--R                                                     Type: Expression Integer
--E

--S 35
ee1:=ratDenom dd1
 

   (9)
                     +--------------+
        +-+      +-+ |   2
       \|c log(2\|c \|a x  + b x + c  + b x + 2c)
     + 
                     +--------------+
        +-+      +-+ |   2                                  +-+
       \|c log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)\|c
  /
     c
                                                     Type: Expression Integer
--R
--R   (9)
--R                     +--------------+
--R        +-+      +-+ |   2
--R       \|c log(2\|c \|a x  + b x + c  + b x + 2c)
--R     + 
--R                     +--------------+
--R        +-+      +-+ |   2                                  +-+
--R       \|c log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)\|c
--R  /
--R     c
--R                                                     Type: Expression Integer
--E

--S 36     14:283 Schaums and Axiom differ by a constant
ff1:=complexNormalize ee1
 

                     2  +-+
         log(4a c - b )\|c
   (10)  ------------------
                  c
                                                     Type: Expression Integer
--R
--R                     2  +-+
--R         log(4a c - b )\|c
--R   (10)  ------------------
--R                  c
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 37
aa:=integrate(1/(x^2*sqrt(a*x^2+b*x+c)),x)
 

   (1)
                     +--------------+
                 +-+ |   2                2 2
         (- 4b x\|c \|a x  + b x + c  + 2b x  + 4b c x)
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                       +--------------+
                   +-+ |   2                         2  2              2
       (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
  /
          +--------------+
       2  |   2                       2     2   +-+
     8c x\|a x  + b x + c  + (- 4b c x  - 8c x)\|c
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                     +--------------+
--R                 +-+ |   2                2 2
--R         (- 4b x\|c \|a x  + b x + c  + 2b x  + 4b c x)
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                       +--------------+
--R                   +-+ |   2                         2  2              2
--R       (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
--R  /
--R          +--------------+
--R       2  |   2                       2     2   +-+
--R     8c x\|a x  + b x + c  + (- 4b c x  - 8c x)\|c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 38
t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (2)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (2)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 39
bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*c)*t1
 

                        +--------------+
                    +-+ |   2                                +--------------+
                  2\|c \|a x  + b x + c  - b x - 2c      +-+ |   2
        - b x log(---------------------------------) - 2\|c \|a x  + b x + c
                                  x
   (3)  ---------------------------------------------------------------------
                                            +-+
                                       2c x\|c
                                                     Type: Expression Integer
--R
--R                        +--------------+
--R                    +-+ |   2                                +--------------+
--R                  2\|c \|a x  + b x + c  - b x - 2c      +-+ |   2
--R        - b x log(---------------------------------) - 2\|c \|a x  + b x + c
--R                                  x
--R   (3)  ---------------------------------------------------------------------
--R                                            +-+
--R                                       2c x\|c
--R                                                     Type: Expression Integer
--E

--S 40
cc:=aa-bb
 

   (4)
               +--------------+
               |   2                   2          +-+
         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                 +--------------+
                 |   2                 2          +-+
         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
              +--------------+
              |   2                2          +-+
       - 2b c\|a x  + b x + c  + (b x + 2b c)\|c
  /
             +--------------+
       2 +-+ |   2                  2      3
     8c \|c \|a x  + b x + c  - 4b c x - 8c
                                                     Type: Expression Integer
--R
--R   (4)
--R               +--------------+
--R               |   2                   2          +-+
--R         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                 +--------------+
--R                 |   2                 2          +-+
--R         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R              +--------------+
--R              |   2                2          +-+
--R       - 2b c\|a x  + b x + c  + (b x + 2b c)\|c
--R  /
--R             +--------------+
--R       2 +-+ |   2                  2      3
--R     8c \|c \|a x  + b x + c  - 4b c x - 8c
--R                                                     Type: Expression Integer
--E

--S 41
dd:=expandLog cc
 

   (5)
               +--------------+
               |   2                   2          +-+
         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
      *
                   +--------------+
               +-+ |   2
         log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                 +--------------+
                 |   2                 2          +-+
         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
      *
                +--------------+
                |   2                           +-+
         log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                          +--------------+
                                          |   2
       (4b c log(c) + 4b c log(2) - 2b c)\|a x  + b x + c
     + 
             2                       2                   2          +-+
       ((- 2b x - 4b c)log(c) + (- 2b x - 4b c)log(2) + b x + 2b c)\|c
  /
             +--------------+
       2 +-+ |   2                  2      3
     8c \|c \|a x  + b x + c  - 4b c x - 8c
                                                     Type: Expression Integer
--R
--R   (5)
--R               +--------------+
--R               |   2                   2          +-+
--R         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R         log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                 +--------------+
--R                 |   2                 2          +-+
--R         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R         log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                          +--------------+
--R                                          |   2
--R       (4b c log(c) + 4b c log(2) - 2b c)\|a x  + b x + c
--R     + 
--R             2                       2                   2          +-+
--R       ((- 2b x - 4b c)log(c) + (- 2b x - 4b c)log(2) + b x + 2b c)\|c
--R  /
--R             +--------------+
--R       2 +-+ |   2                  2      3
--R     8c \|c \|a x  + b x + c  - 4b c x - 8c
--R                                                     Type: Expression Integer
--E

--S 42
ee:=ratDenom dd
 

   (6)
                       +--------------+
          +-+      +-+ |   2
       2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                      +--------------+
            +-+       |   2                           +-+
       - 2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                   +-+
       (2b log(c) + 2b log(2) - b)\|c
  /
       2
     4c
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R          +-+      +-+ |   2
--R       2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                      +--------------+
--R            +-+       |   2                           +-+
--R       - 2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                   +-+
--R       (2b log(c) + 2b log(2) - b)\|c
--R  /
--R       2
--R     4c
--R                                                     Type: Expression Integer
--E

--S 43     14:284 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

                                   +-+
        (b log(c) + 2b log(2) - b)\|c
   (7)  ------------------------------
                        2
                      4c
                                                     Type: Expression Integer
--R
--R                                   +-+
--R        (b log(c) + 2b log(2) - b)\|c
--R   (7)  ------------------------------
--R                        2
--R                      4c
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 44
aa:=integrate(sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  2        2  3                  3  2           2     2     +-+
           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                  2   4       2         2  3                3  2
               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
             + 
                     2     2
               (32a c  + 8b c)x
        *
            +-+ +-+
           \|a \|c
    /
                                   +--------------+
                           +-+ +-+ |   2
         (32a b x + 64a c)\|a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +-+
         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
     ,

                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                 2        2  3                 3  2           2     2     +---+
           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
              2   4       2         2  3                3  2         2     2
           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
        *
            +---+ +-+
           \|- a \|c
    /
                                     +--------------+
                           +---+ +-+ |   2
         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +---+
         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  2        2  3                  3  2           2     2     +-+
--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                  2   4       2         2  3                3  2
--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
--R             + 
--R                     2     2
--R               (32a c  + 8b c)x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                                   +--------------+
--R                           +-+ +-+ |   2
--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +-+
--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R     ,
--R
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                 2        2  3                 3  2           2     2     +---+
--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R              2   4       2         2  3                3  2         2     2
--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                                     +--------------+
--R                           +---+ +-+ |   2
--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +---+
--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 45
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 46
bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1
 

   (3)
                  2
         (4a c - b )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                       +--------------+
                   +-+ |   2
       (4a x + 2b)\|a \|a x  + b x + c
  /
        +-+
     8a\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2
--R         (4a c - b )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                       +--------------+
--R                   +-+ |   2
--R       (4a x + 2b)\|a \|a x  + b x + c
--R  /
--R        +-+
--R     8a\|a
--R                                                     Type: Expression Integer
--E

--S 47
bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2
 

   (4)
                              +--------------+
                        +---+ |   2               +---+ +-+
                2      \|- a \|a x  + b x + c  - \|- a \|c
       (4a c - b )atan(------------------------------------)
                                        a x
     + 
                        +--------------+
                  +---+ |   2
       (2a x + b)\|- a \|a x  + b x + c
  /
        +---+
     4a\|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                              +--------------+
--R                        +---+ |   2               +---+ +-+
--R                2      \|- a \|a x  + b x + c  - \|- a \|c
--R       (4a c - b )atan(------------------------------------)
--R                                        a x
--R     + 
--R                        +--------------+
--R                  +---+ |   2
--R       (2a x + b)\|- a \|a x  + b x + c
--R  /
--R        +---+
--R     4a\|- a
--R                                                     Type: Expression Integer
--E

--S 48
cc1:=aa.1-bb1
 

   (5)
                        +--------------+
          2          2  |   2
       (4b c x + 8b c )\|a x  + b x + c
     + 
                     3  2     2          2  +-+
       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
  /
                             +--------------+
                         +-+ |   2                    2        2  2
       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
     + 
              2
       - 32a c
                                                     Type: Expression Integer
--R
--R   (5)
--R                        +--------------+
--R          2          2  |   2
--R       (4b c x + 8b c )\|a x  + b x + c
--R     + 
--R                     3  2     2          2  +-+
--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
--R  /
--R                             +--------------+
--R                         +-+ |   2                    2        2  2
--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
--R     + 
--R              2
--R       - 32a c
--R                                                     Type: Expression Integer
--E

--S 49
cc2:=aa.2-bb1
 

   (6)
                                                          +--------------+
                           3          2     2   +---+ +-+ |   2
           ((- 16a b c + 4b )x - 32a c  + 8b c)\|- a \|c \|a x  + b x + c
         + 
                2 2    4  2           2     3           3     2 2  +---+
           ((16a c  - b )x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                       +--------------+
                         3          2      2   +-+ +-+ |   2
           ((32a b c - 8b )x + 64a c  - 16b c)\|a \|c \|a x  + b x + c
         + 
                  2 2     4  2             2      3           3      2 2  +-+
           ((- 32a c  + 2b )x  + (- 64a b c  + 16b c)x - 64a c  + 16b c )\|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                   +--------------+
          2           2  +---+ +-+ |   2
       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
     + 
                      3  2      2           2  +---+ +-+ +-+
       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
  /
                                       +--------------+
                         +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              2        2  2                    2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                          +--------------+
--R                           3          2     2   +---+ +-+ |   2
--R           ((- 16a b c + 4b )x - 32a c  + 8b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                2 2    4  2           2     3           3     2 2  +---+
--R           ((16a c  - b )x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                       +--------------+
--R                         3          2      2   +-+ +-+ |   2
--R           ((32a b c - 8b )x + 64a c  - 16b c)\|a \|c \|a x  + b x + c
--R         + 
--R                  2 2     4  2             2      3           3      2 2  +-+
--R           ((- 32a c  + 2b )x  + (- 64a b c  + 16b c)x - 64a c  + 16b c )\|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                   +--------------+
--R          2           2  +---+ +-+ |   2
--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                      3  2      2           2  +---+ +-+ +-+
--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R                         +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              2        2  2                    2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 50
cc3:=aa.1-bb2
 

   (7)
                                                        +--------------+
                         3          2     2   +---+ +-+ |   2
           ((16a b c - 4b )x + 32a c  - 8b c)\|- a \|c \|a x  + b x + c
         + 
                  2 2    4  2             2     3           3     2 2  +---+
           ((- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                         +--------------+
                           3          2      2   +-+ +-+ |   2
           ((- 32a b c + 8b )x - 64a c  + 16b c)\|a \|c \|a x  + b x + c
         + 
                2 2     4  2           2      3           3      2 2  +-+
           ((32a c  - 2b )x  + (64a b c  - 16b c)x + 64a c  - 16b c )\|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                   +--------------+
          2           2  +---+ +-+ |   2
       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
     + 
                      3  2      2           2  +---+ +-+ +-+
       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
  /
                                       +--------------+
                         +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              2        2  2                    2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                                                        +--------------+
--R                         3          2     2   +---+ +-+ |   2
--R           ((16a b c - 4b )x + 32a c  - 8b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                  2 2    4  2             2     3           3     2 2  +---+
--R           ((- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                         +--------------+
--R                           3          2      2   +-+ +-+ |   2
--R           ((- 32a b c + 8b )x - 64a c  + 16b c)\|a \|c \|a x  + b x + c
--R         + 
--R                2 2     4  2           2      3           3      2 2  +-+
--R           ((32a c  - 2b )x  + (64a b c  - 16b c)x + 64a c  - 16b c )\|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                   +--------------+
--R          2           2  +---+ +-+ |   2
--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                      3  2      2           2  +---+ +-+ +-+
--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R                         +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              2        2  2                    2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 51
cc4:=aa.2-bb2
 

   (8)
                        +--------------+
          2          2  |   2
       (4b c x + 8b c )\|a x  + b x + c
     + 
                     3  2     2          2  +-+
       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
  /
                             +--------------+
                         +-+ |   2                    2        2  2
       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
     + 
              2
       - 32a c
                                                     Type: Expression Integer
--R
--R   (8)
--R                        +--------------+
--R          2          2  |   2
--R       (4b c x + 8b c )\|a x  + b x + c
--R     + 
--R                     3  2     2          2  +-+
--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
--R  /
--R                             +--------------+
--R                         +-+ |   2                    2        2  2
--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
--R     + 
--R              2
--R       - 32a c
--R                                                     Type: Expression Integer
--E

--S 52     14:285 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

          +-+
        b\|c
   (9)  -----
          4a
                                                     Type: Expression Integer
--R
--R          +-+
--R        b\|c
--R   (9)  -----
--R          4a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 53
aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                     2   2        3       5  2          2 2      4
                 (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x
               + 
                         3      3 2
                 384a b c  - 96b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                    2 2 2        4      6  3
             (- 144a b c  + 24a b c + 3b )x
           + 
                    2   3         3 2      5   2            2 3       4 2
             (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
           + 
                       4      3 3
             - 384a b c  + 96b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                    3         2 3  5          3 2       2 2        4  4
             (- 192a b c - 16a b )x  + (- 384a c  - 336a b c - 4a b )x
           + 
                     2   2        3      5  3
             (- 1056a b c  - 16a b c + 6b )x
           + 
                    2 3         2 2      4   2              3      3 2
             (- 768a c  - 288a b c  + 72b c)x  + (- 384a b c  + 96b c )x
        *
                +--------------+
            +-+ |   2
           \|a \|a x  + b x + c
       + 
                  4       3 2  6        3          2 3  5
             (128a c + 96a b )x  + (672a b c + 120a b )x
           + 
                  3 2       2 2         4  4         2   2        3       5  3
             (768a c  + 816a b c - 12a b )x  + (1632a b c  + 64a b c - 30b )x
           + 
                  2 3         2 2       4   2            3      3 2
             (768a c  + 480a b c  - 120b c)x  + (384a b c  - 96b c )x
        *
            +-+ +-+
           \|a \|c
    /
                 3        2 2  2        2             2 2  +-+ +-+
           ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                    3         2 3  3           3 2       2 2   2        2   2
             (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
           + 
                    2 3
             - 1536a c
        *
            +-+
           \|a
     ,

                       2   2        3       5  2            2 2      4
                 (- 96a b c  - 48a b c + 18b )x  + (- 384a b c  + 96b c)x
               + 
                           3      3 2
                 - 384a b c  + 96b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                  2 2 2        4      6  3        2   3         3 2      5   2
             (144a b c  - 24a b c - 3b )x  + (288a b c  + 144a b c  - 54b c)x
           + 
                    2 3       4 2             4      3 3
             (576a b c  - 144b c )x + 384a b c  - 96b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                   3        2 3  5          3 2       2 2        4  4
             (- 96a b c - 8a b )x  + (- 192a c  - 168a b c - 2a b )x
           + 
                    2   2       3      5  3          2 3         2 2      4   2
             (- 528a b c  - 8a b c + 3b )x  + (- 384a c  - 144a b c  + 36b c)x
           + 
                        3      3 2
             (- 192a b c  + 48b c )x
        *
                  +--------------+
            +---+ |   2
           \|- a \|a x  + b x + c
       + 
                 4       3 2  6        3         2 3  5
             (64a c + 48a b )x  + (336a b c + 60a b )x
           + 
                  3 2       2 2        4  4        2   2        3       5  3
             (384a c  + 408a b c - 6a b )x  + (816a b c  + 32a b c - 15b )x
           + 
                  2 3         2 2      4   2            3      3 2
             (384a c  + 240a b c  - 60b c)x  + (192a b c  - 48b c )x
        *
            +---+ +-+
           \|- a \|c
    /
                 3        2 2  2       2            2 2  +---+ +-+
           ((192a c + 144a b )x  + 768a b c x + 768a c )\|- a \|c
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                    3         2 3  3          3 2       2 2   2        2   2
             (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x
           + 
                   2 3
             - 768a c
        *
            +---+
           \|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                     2   2        3       5  2          2 2      4
--R                 (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x
--R               + 
--R                         3      3 2
--R                 384a b c  - 96b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                    2 2 2        4      6  3
--R             (- 144a b c  + 24a b c + 3b )x
--R           + 
--R                    2   3         3 2      5   2            2 3       4 2
--R             (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
--R           + 
--R                       4      3 3
--R             - 384a b c  + 96b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                    3         2 3  5          3 2       2 2        4  4
--R             (- 192a b c - 16a b )x  + (- 384a c  - 336a b c - 4a b )x
--R           + 
--R                     2   2        3      5  3
--R             (- 1056a b c  - 16a b c + 6b )x
--R           + 
--R                    2 3         2 2      4   2              3      3 2
--R             (- 768a c  - 288a b c  + 72b c)x  + (- 384a b c  + 96b c )x
--R        *
--R                +--------------+
--R            +-+ |   2
--R           \|a \|a x  + b x + c
--R       + 
--R                  4       3 2  6        3          2 3  5
--R             (128a c + 96a b )x  + (672a b c + 120a b )x
--R           + 
--R                  3 2       2 2         4  4         2   2        3       5  3
--R             (768a c  + 816a b c - 12a b )x  + (1632a b c  + 64a b c - 30b )x
--R           + 
--R                  2 3         2 2       4   2            3      3 2
--R             (768a c  + 480a b c  - 120b c)x  + (384a b c  - 96b c )x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                 3        2 2  2        2             2 2  +-+ +-+
--R           ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                    3         2 3  3           3 2       2 2   2        2   2
--R             (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R           + 
--R                    2 3
--R             - 1536a c
--R        *
--R            +-+
--R           \|a
--R     ,
--R
--R                       2   2        3       5  2            2 2      4
--R                 (- 96a b c  - 48a b c + 18b )x  + (- 384a b c  + 96b c)x
--R               + 
--R                           3      3 2
--R                 - 384a b c  + 96b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                  2 2 2        4      6  3        2   3         3 2      5   2
--R             (144a b c  - 24a b c - 3b )x  + (288a b c  + 144a b c  - 54b c)x
--R           + 
--R                    2 3       4 2             4      3 3
--R             (576a b c  - 144b c )x + 384a b c  - 96b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                   3        2 3  5          3 2       2 2        4  4
--R             (- 96a b c - 8a b )x  + (- 192a c  - 168a b c - 2a b )x
--R           + 
--R                    2   2       3      5  3          2 3         2 2      4   2
--R             (- 528a b c  - 8a b c + 3b )x  + (- 384a c  - 144a b c  + 36b c)x
--R           + 
--R                        3      3 2
--R             (- 192a b c  + 48b c )x
--R        *
--R                  +--------------+
--R            +---+ |   2
--R           \|- a \|a x  + b x + c
--R       + 
--R                 4       3 2  6        3         2 3  5
--R             (64a c + 48a b )x  + (336a b c + 60a b )x
--R           + 
--R                  3 2       2 2        4  4        2   2        3       5  3
--R             (384a c  + 408a b c - 6a b )x  + (816a b c  + 32a b c - 15b )x
--R           + 
--R                  2 3         2 2      4   2            3      3 2
--R             (384a c  + 240a b c  - 60b c)x  + (192a b c  - 48b c )x
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                 3        2 2  2       2            2 2  +---+ +-+
--R           ((192a c + 144a b )x  + 768a b c x + 768a c )\|- a \|c
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                    3         2 3  3          3 2       2 2   2        2   2
--R             (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x
--R           + 
--R                   2 3
--R             - 768a c
--R        *
--R            +---+
--R           \|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 54
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 55
bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.1
 

   (3)
                        3
         (- 12a b c + 3b )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                           +--------------+
           2 2                      2  +-+ |   2
       (16a x  + 4a b x + 16a c - 6b )\|a \|a x  + b x + c
  /
        2 +-+
     48a \|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                        3
--R         (- 12a b c + 3b )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                           +--------------+
--R           2 2                      2  +-+ |   2
--R       (16a x  + 4a b x + 16a c - 6b )\|a \|a x  + b x + c
--R  /
--R        2 +-+
--R     48a \|a
--R                                                     Type: Expression Integer
--E

--S 56
bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.2
 

   (4)
                                    +--------------+
                              +---+ |   2               +---+ +-+
                      3      \|- a \|a x  + b x + c  - \|- a \|c
       (- 12a b c + 3b )atan(------------------------------------)
                                              a x
     + 
                                           +--------------+
          2 2                     2  +---+ |   2
       (8a x  + 2a b x + 8a c - 3b )\|- a \|a x  + b x + c
  /
        2 +---+
     24a \|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                    +--------------+
--R                              +---+ |   2               +---+ +-+
--R                      3      \|- a \|a x  + b x + c  - \|- a \|c
--R       (- 12a b c + 3b )atan(------------------------------------)
--R                                              a x
--R     + 
--R                                           +--------------+
--R          2 2                     2  +---+ |   2
--R       (8a x  + 2a b x + 8a c - 3b )\|- a \|a x  + b x + c
--R  /
--R        2 +---+
--R     24a \|- a
--R                                                     Type: Expression Integer
--E

--S 57
cc1:=aa.1-bb1
 

   (5)
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                  2 2 2        4      6  3          2   3         3 2      5   2
           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
         + 
                    2 3       4 2             4      3 3
           (- 576a b c  + 144b c )x - 384a b c  + 96b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                  2 2 2        4      6  3          2   3         3 2      5   2
           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
         + 
                    2 3       4 2             4      3 3
           (- 576a b c  + 144b c )x - 384a b c  + 96b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                2 3        2 2      4   2            3       3 2           4
           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
         + 
                 2 3
           - 192b c
      *
              +--------------+
          +-+ |   2
         \|a \|a x  + b x + c
     + 
                  2   2        3      5  3          2 3         2 2       4   2
           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
         + 
                      3       3 2           4       2 3
           (- 768a b c  + 288b c )x - 512a c  + 192b c
      *
          +-+ +-+
         \|a \|c
  /
                                                               +--------------+
             3        2 2  2        2             2 2  +-+ +-+ |   2
       ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c \|a x  + b x + c
     + 
                  3         2 3  3           3 2       2 2   2        2   2
           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
         + 
                  2 3
           - 1536a c
      *
          +-+
         \|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                  2 2 2        4      6  3          2   3         3 2      5   2
--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
--R         + 
--R                    2 3       4 2             4      3 3
--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                  2 2 2        4      6  3          2   3         3 2      5   2
--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
--R         + 
--R                    2 3       4 2             4      3 3
--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                2 3        2 2      4   2            3       3 2           4
--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
--R         + 
--R                 2 3
--R           - 192b c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|a \|a x  + b x + c
--R     + 
--R                  2   2        3      5  3          2 3         2 2       4   2
--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
--R         + 
--R                      3       3 2           4       2 3
--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
--R      *
--R          +-+ +-+
--R         \|a \|c
--R  /
--R                                                               +--------------+
--R             3        2 2  2        2             2 2  +-+ +-+ |   2
--R       ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c \|a x  + b x + c
--R     + 
--R                  3         2 3  3           3 2       2 2   2        2   2
--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R         + 
--R                  2 3
--R           - 1536a c
--R      *
--R          +-+
--R         \|a
--R                                                     Type: Expression Integer
--E

--S 58
cc2:=aa.2-bb1
 

   (6)
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                      2 2 2        4      6  3
               (- 144a b c  + 24a b c + 3b )x
             + 
                      2   3         3 2      5   2            2 3       4 2
               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
             + 
                         4      3 3
               - 384a b c  + 96b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                      2   2        3       5  2            2 2       4
               (- 192a b c  - 96a b c + 36b )x  + (- 768a b c  + 192b c)x
             + 
                         3       3 2
               - 768a b c  + 192b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                    2 2 2        4      6  3
               (288a b c  - 48a b c - 6b )x
             + 
                    2   3         3 2       5   2           2 3       4 2
               (576a b c  + 288a b c  - 108b c)x  + (1152a b c  - 288b c )x
             + 
                       4       3 3
               768a b c  - 192b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                2 3        2 2      4   2            3       3 2           4
           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
         + 
                 2 3
           - 192b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                  2   2        3      5  3          2 3         2 2       4   2
           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
         + 
                      3       3 2           4       2 3
           (- 768a b c  + 288b c )x - 512a c  + 192b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
               3        2 2  2        2             2 2  +---+ +-+ +-+
         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                  3         2 3  3           3 2       2 2   2        2   2
           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
         + 
                  2 3
           - 1536a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                      2 2 2        4      6  3
--R               (- 144a b c  + 24a b c + 3b )x
--R             + 
--R                      2   3         3 2      5   2            2 3       4 2
--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
--R             + 
--R                         4      3 3
--R               - 384a b c  + 96b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                      2   2        3       5  2            2 2       4
--R               (- 192a b c  - 96a b c + 36b )x  + (- 768a b c  + 192b c)x
--R             + 
--R                         3       3 2
--R               - 768a b c  + 192b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                    2 2 2        4      6  3
--R               (288a b c  - 48a b c - 6b )x
--R             + 
--R                    2   3         3 2       5   2           2 3       4 2
--R               (576a b c  + 288a b c  - 108b c)x  + (1152a b c  - 288b c )x
--R             + 
--R                       4       3 3
--R               768a b c  - 192b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                2 3        2 2      4   2            3       3 2           4
--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
--R         + 
--R                 2 3
--R           - 192b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                  2   2        3      5  3          2 3         2 2       4   2
--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
--R         + 
--R                      3       3 2           4       2 3
--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R               3        2 2  2        2             2 2  +---+ +-+ +-+
--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                  3         2 3  3           3 2       2 2   2        2   2
--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R         + 
--R                  2 3
--R           - 1536a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 59
cc3:=aa.1-bb2
 

   (7)
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                      2 2 2        4      6  3
               (- 144a b c  + 24a b c + 3b )x
             + 
                      2   3         3 2      5   2            2 3       4 2
               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
             + 
                         4      3 3
               - 384a b c  + 96b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                    2   2        3       5  2          2 2       4
               (192a b c  + 96a b c - 36b )x  + (768a b c  - 192b c)x
             + 
                       3       3 2
               768a b c  - 192b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                      2 2 2        4      6  3
               (- 288a b c  + 48a b c + 6b )x
             + 
                      2   3         3 2       5   2             2 3       4 2
               (- 576a b c  - 288a b c  + 108b c)x  + (- 1152a b c  + 288b c )x
             + 
                         4       3 3
               - 768a b c  + 192b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                2 3        2 2      4   2            3       3 2           4
           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
         + 
                 2 3
           - 192b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                  2   2        3      5  3          2 3         2 2       4   2
           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
         + 
                      3       3 2           4       2 3
           (- 768a b c  + 288b c )x - 512a c  + 192b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
               3        2 2  2        2             2 2  +---+ +-+ +-+
         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                  3         2 3  3           3 2       2 2   2        2   2
           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
         + 
                  2 3
           - 1536a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                      2 2 2        4      6  3
--R               (- 144a b c  + 24a b c + 3b )x
--R             + 
--R                      2   3         3 2      5   2            2 3       4 2
--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
--R             + 
--R                         4      3 3
--R               - 384a b c  + 96b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                    2   2        3       5  2          2 2       4
--R               (192a b c  + 96a b c - 36b )x  + (768a b c  - 192b c)x
--R             + 
--R                       3       3 2
--R               768a b c  - 192b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                      2 2 2        4      6  3
--R               (- 288a b c  + 48a b c + 6b )x
--R             + 
--R                      2   3         3 2       5   2             2 3       4 2
--R               (- 576a b c  - 288a b c  + 108b c)x  + (- 1152a b c  + 288b c )x
--R             + 
--R                         4       3 3
--R               - 768a b c  + 192b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                2 3        2 2      4   2            3       3 2           4
--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
--R         + 
--R                 2 3
--R           - 192b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                  2   2        3      5  3          2 3         2 2       4   2
--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
--R         + 
--R                      3       3 2           4       2 3
--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R               3        2 2  2        2             2 2  +---+ +-+ +-+
--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                  3         2 3  3           3 2       2 2   2        2   2
--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R         + 
--R                  2 3
--R           - 1536a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 60
cc4:=aa.2-bb2
 

   (8)
               2 3        2 2      4   2            3      3 2           4
           (64a c  + 24a b c  - 18b c)x  + (256a b c  - 96b c )x + 256a c
         + 
                2 3
           - 96b c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                 2   2        3      5  3          2 3        2 2      4   2
           (- 96a b c  + 28a b c + 3b )x  + (- 192a c  - 72a b c  + 54b c)x
         + 
                      3       3 2           4      2 3
           (- 384a b c  + 144b c )x - 256a c  + 96b c
      *
          +-+
         \|c
  /
                                                         +--------------+
             3        2 2  2       2            2 2  +-+ |   2
       ((192a c + 144a b )x  + 768a b c x + 768a c )\|c \|a x  + b x + c
     + 
            3         2 3  3          3 2       2 2   2        2   2        2 3
     (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x - 768a c
                                                     Type: Expression Integer
--R
--R   (8)
--R               2 3        2 2      4   2            3      3 2           4
--R           (64a c  + 24a b c  - 18b c)x  + (256a b c  - 96b c )x + 256a c
--R         + 
--R                2 3
--R           - 96b c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                 2   2        3      5  3          2 3        2 2      4   2
--R           (- 96a b c  + 28a b c + 3b )x  + (- 192a c  - 72a b c  + 54b c)x
--R         + 
--R                      3       3 2           4      2 3
--R           (- 384a b c  + 144b c )x - 256a c  + 96b c
--R      *
--R          +-+
--R         \|c
--R  /
--R                                                         +--------------+
--R             3        2 2  2       2            2 2  +-+ |   2
--R       ((192a c + 144a b )x  + 768a b c x + 768a c )\|c \|a x  + b x + c
--R     + 
--R            3         2 3  3          3 2       2 2   2        2   2        2 3
--R     (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x - 768a c
--R                                                     Type: Expression Integer
--E

--S 61     14:286 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

                  2  +-+
        (8a c - 3b )\|c
   (9)  ----------------
                 2
              24a
                                                     Type: Expression Integer
--R
--R                  2  +-+
--R        (8a c - 3b )\|c
--R   (9)  ----------------
--R                 2
--R              24a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 62
aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                       3   3        2 3 2        5        7  3
                 (1536a b c  - 1920a b c  - 96a b c + 120b )x
               + 
                       3 4       2 2 3          4 2        6   2
                 (3072a c  - 768a b c  - 4800a b c  + 1200b c)x
               + 
                       2   4           3 3        5 2          2 5          2 4
                 (9216a b c  - 13824a b c  + 2880b c )x + 6144a c  - 9216a b c
               + 
                      4 3
                 1920b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                    4 4        2 4 2         6       8  4
             (- 768a c  + 1440a b c  - 288a b c - 15b )x
           + 
                     3   4        2 3 3         5 2       7   3
             (- 6144a b c  + 7680a b c  + 384a b c  - 480b c)x
           + 
                     3 5        2 2 4          4 3        6 2  2
             (- 6144a c  + 1536a b c  + 9600a b c  - 2400b c )x
           + 
                      2   5           3 4        5 3          2 6          2 5
             (- 12288a b c  + 18432a b c  - 3840b c )x - 6144a c  + 9216a b c
           + 
                    4 4
             - 1920b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                     5 2        4 2       3 4  7
             (- 1536a c  - 2304a b c - 96a b )x
           + 
                      4   2        3 3       2 5  6
             (- 12544a b c  - 3456a b c - 16a b )x
           + 
                      4 3         3 2 2      2 4         6  5
             (- 13056a c  - 18240a b c  - 80a b c + 20a b )x
           + 
                      3   3       2 3 2        5       7  4
             (- 31104a b c  + 480a b c  + 24a b c - 30b )x
           + 
                      3 4       2 2 3          4 2       6   3
             (- 18432a c  + 768a b c  + 2816a b c  - 720b c)x
           + 
                     2   4           3 3        5 2  2
             (- 7680a b c  + 11520a b c  - 2400b c )x
           + 
                     2 5          2 4        4 3
             (- 6144a c  + 9216a b c  - 1920b c )x
        *
                +--------------+
            +-+ |   2
           \|a \|a x  + b x + c
       + 
                   5          4 3  8         5 2         4 2        3 4  7
             (3072a b c + 768a b )x  + (6144a c  + 11264a b c + 896a b )x
           + 
                    4   2        3 3       2 5  6
             (30208a b c  + 9984a b c - 32a b )x
           + 
                    4 3         3 2 2       2 4         6  5
             (21504a c  + 31488a b c  - 320a b c + 80a b )x
           + 
                    3   3        2 3 2         5        7  4
             (42624a b c  - 4896a b c  + 152a b c + 210b )x
           + 
                    3 4        2 2 3          4 2        6   3
             (21504a c  - 2304a b c  - 6464a b c  + 1680b c)x
           + 
                    2   4           3 3        5 2  2
             (10752a b c  - 16128a b c  + 3360b c )x
           + 
                   2 5          2 4        4 3
             (6144a c  - 9216a b c  + 1920b c )x
        *
            +-+ +-+
           \|a \|c
    /
                    4           3 3  3          4 2         3 2   2
             (12288a b c + 3072a b )x  + (24576a c  + 30720a b c)x
           + 
                   3   2          3 3
             73728a b c x + 49152a c
        *
                    +--------------+
            +-+ +-+ |   2
           \|a \|c \|a x  + b x + c
       + 
                     5 2        4 2        3 4  4
             (- 6144a c  - 9216a b c - 384a b )x
           + 
                      4   2         3 3   3            4 3         3 2 2  2
             (- 49152a b c  - 12288a b c)x  + (- 49152a c  - 61440a b c )x
           + 
                     3   3          3 4
             - 98304a b c x - 49152a c
        *
            +-+
           \|a
     ,

                         3   3        2 3 2        5        7  3
                 (- 1536a b c  + 1920a b c  + 96a b c - 120b )x
               + 
                         3 4       2 2 3          4 2        6   2
                 (- 3072a c  + 768a b c  + 4800a b c  - 1200b c)x
               + 
                         2   4           3 3        5 2          2 5
                 (- 9216a b c  + 13824a b c  - 2880b c )x - 6144a c
               + 
                        2 4        4 3
                 9216a b c  - 1920b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                  4 4        2 4 2         6       8  4
             (768a c  - 1440a b c  + 288a b c + 15b )x
           + 
                   3   4        2 3 3         5 2       7   3
             (6144a b c  - 7680a b c  - 384a b c  + 480b c)x
           + 
                   3 5        2 2 4          4 3        6 2  2
             (6144a c  - 1536a b c  - 9600a b c  + 2400b c )x
           + 
                    2   5           3 4        5 3          2 6          2 5
             (12288a b c  - 18432a b c  + 3840b c )x + 6144a c  - 9216a b c
           + 
                  4 4
             1920b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                    5 2        4 2       3 4  7
             (- 768a c  - 1152a b c - 48a b )x
           + 
                     4   2        3 3      2 5  6
             (- 6272a b c  - 1728a b c - 8a b )x
           + 
                     4 3        3 2 2      2 4         6  5
             (- 6528a c  - 9120a b c  - 40a b c + 10a b )x
           + 
                      3   3       2 3 2        5       7  4
             (- 15552a b c  + 240a b c  + 12a b c - 15b )x
           + 
                     3 4       2 2 3          4 2       6   3
             (- 9216a c  + 384a b c  + 1408a b c  - 360b c)x
           + 
                     2   4          3 3        5 2  2
             (- 3840a b c  + 5760a b c  - 1200b c )x
           + 
                     2 5          2 4       4 3
             (- 3072a c  + 4608a b c  - 960b c )x
        *
                  +--------------+
            +---+ |   2
           \|- a \|a x  + b x + c
       + 
                   5          4 3  8         5 2        4 2        3 4  7
             (1536a b c + 384a b )x  + (3072a c  + 5632a b c + 448a b )x
           + 
                    4   2        3 3       2 5  6
             (15104a b c  + 4992a b c - 16a b )x
           + 
                    4 3         3 2 2       2 4         6  5
             (10752a c  + 15744a b c  - 160a b c + 40a b )x
           + 
                    3   3        2 3 2        5        7  4
             (21312a b c  - 2448a b c  + 76a b c + 105b )x
           + 
                    3 4        2 2 3          4 2       6   3
             (10752a c  - 1152a b c  - 3232a b c  + 840b c)x
           + 
                   2   4          3 3        5 2  2
             (5376a b c  - 8064a b c  + 1680b c )x
           + 
                   2 5          2 4       4 3
             (3072a c  - 4608a b c  + 960b c )x
        *
            +---+ +-+
           \|- a \|c
    /
                   4           3 3  3          4 2         3 2   2
             (6144a b c + 1536a b )x  + (12288a c  + 15360a b c)x
           + 
                   3   2          3 3
             36864a b c x + 24576a c
        *
                      +--------------+
            +---+ +-+ |   2
           \|- a \|c \|a x  + b x + c
       + 
                     5 2        4 2        3 4  4
             (- 3072a c  - 4608a b c - 192a b )x
           + 
                      4   2        3 3   3            4 3         3 2 2  2
             (- 24576a b c  - 6144a b c)x  + (- 24576a c  - 30720a b c )x
           + 
                     3   3          3 4
             - 49152a b c x - 24576a c
        *
            +---+
           \|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                       3   3        2 3 2        5        7  3
--R                 (1536a b c  - 1920a b c  - 96a b c + 120b )x
--R               + 
--R                       3 4       2 2 3          4 2        6   2
--R                 (3072a c  - 768a b c  - 4800a b c  + 1200b c)x
--R               + 
--R                       2   4           3 3        5 2          2 5          2 4
--R                 (9216a b c  - 13824a b c  + 2880b c )x + 6144a c  - 9216a b c
--R               + 
--R                      4 3
--R                 1920b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                    4 4        2 4 2         6       8  4
--R             (- 768a c  + 1440a b c  - 288a b c - 15b )x
--R           + 
--R                     3   4        2 3 3         5 2       7   3
--R             (- 6144a b c  + 7680a b c  + 384a b c  - 480b c)x
--R           + 
--R                     3 5        2 2 4          4 3        6 2  2
--R             (- 6144a c  + 1536a b c  + 9600a b c  - 2400b c )x
--R           + 
--R                      2   5           3 4        5 3          2 6          2 5
--R             (- 12288a b c  + 18432a b c  - 3840b c )x - 6144a c  + 9216a b c
--R           + 
--R                    4 4
--R             - 1920b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                     5 2        4 2       3 4  7
--R             (- 1536a c  - 2304a b c - 96a b )x
--R           + 
--R                      4   2        3 3       2 5  6
--R             (- 12544a b c  - 3456a b c - 16a b )x
--R           + 
--R                      4 3         3 2 2      2 4         6  5
--R             (- 13056a c  - 18240a b c  - 80a b c + 20a b )x
--R           + 
--R                      3   3       2 3 2        5       7  4
--R             (- 31104a b c  + 480a b c  + 24a b c - 30b )x
--R           + 
--R                      3 4       2 2 3          4 2       6   3
--R             (- 18432a c  + 768a b c  + 2816a b c  - 720b c)x
--R           + 
--R                     2   4           3 3        5 2  2
--R             (- 7680a b c  + 11520a b c  - 2400b c )x
--R           + 
--R                     2 5          2 4        4 3
--R             (- 6144a c  + 9216a b c  - 1920b c )x
--R        *
--R                +--------------+
--R            +-+ |   2
--R           \|a \|a x  + b x + c
--R       + 
--R                   5          4 3  8         5 2         4 2        3 4  7
--R             (3072a b c + 768a b )x  + (6144a c  + 11264a b c + 896a b )x
--R           + 
--R                    4   2        3 3       2 5  6
--R             (30208a b c  + 9984a b c - 32a b )x
--R           + 
--R                    4 3         3 2 2       2 4         6  5
--R             (21504a c  + 31488a b c  - 320a b c + 80a b )x
--R           + 
--R                    3   3        2 3 2         5        7  4
--R             (42624a b c  - 4896a b c  + 152a b c + 210b )x
--R           + 
--R                    3 4        2 2 3          4 2        6   3
--R             (21504a c  - 2304a b c  - 6464a b c  + 1680b c)x
--R           + 
--R                    2   4           3 3        5 2  2
--R             (10752a b c  - 16128a b c  + 3360b c )x
--R           + 
--R                   2 5          2 4        4 3
--R             (6144a c  - 9216a b c  + 1920b c )x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                    4           3 3  3          4 2         3 2   2
--R             (12288a b c + 3072a b )x  + (24576a c  + 30720a b c)x
--R           + 
--R                   3   2          3 3
--R             73728a b c x + 49152a c
--R        *
--R                    +--------------+
--R            +-+ +-+ |   2
--R           \|a \|c \|a x  + b x + c
--R       + 
--R                     5 2        4 2        3 4  4
--R             (- 6144a c  - 9216a b c - 384a b )x
--R           + 
--R                      4   2         3 3   3            4 3         3 2 2  2
--R             (- 49152a b c  - 12288a b c)x  + (- 49152a c  - 61440a b c )x
--R           + 
--R                     3   3          3 4
--R             - 98304a b c x - 49152a c
--R        *
--R            +-+
--R           \|a
--R     ,
--R
--R                         3   3        2 3 2        5        7  3
--R                 (- 1536a b c  + 1920a b c  + 96a b c - 120b )x
--R               + 
--R                         3 4       2 2 3          4 2        6   2
--R                 (- 3072a c  + 768a b c  + 4800a b c  - 1200b c)x
--R               + 
--R                         2   4           3 3        5 2          2 5
--R                 (- 9216a b c  + 13824a b c  - 2880b c )x - 6144a c
--R               + 
--R                        2 4        4 3
--R                 9216a b c  - 1920b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                  4 4        2 4 2         6       8  4
--R             (768a c  - 1440a b c  + 288a b c + 15b )x
--R           + 
--R                   3   4        2 3 3         5 2       7   3
--R             (6144a b c  - 7680a b c  - 384a b c  + 480b c)x
--R           + 
--R                   3 5        2 2 4          4 3        6 2  2
--R             (6144a c  - 1536a b c  - 9600a b c  + 2400b c )x
--R           + 
--R                    2   5           3 4        5 3          2 6          2 5
--R             (12288a b c  - 18432a b c  + 3840b c )x + 6144a c  - 9216a b c
--R           + 
--R                  4 4
--R             1920b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                    5 2        4 2       3 4  7
--R             (- 768a c  - 1152a b c - 48a b )x
--R           + 
--R                     4   2        3 3      2 5  6
--R             (- 6272a b c  - 1728a b c - 8a b )x
--R           + 
--R                     4 3        3 2 2      2 4         6  5
--R             (- 6528a c  - 9120a b c  - 40a b c + 10a b )x
--R           + 
--R                      3   3       2 3 2        5       7  4
--R             (- 15552a b c  + 240a b c  + 12a b c - 15b )x
--R           + 
--R                     3 4       2 2 3          4 2       6   3
--R             (- 9216a c  + 384a b c  + 1408a b c  - 360b c)x
--R           + 
--R                     2   4          3 3        5 2  2
--R             (- 3840a b c  + 5760a b c  - 1200b c )x
--R           + 
--R                     2 5          2 4       4 3
--R             (- 3072a c  + 4608a b c  - 960b c )x
--R        *
--R                  +--------------+
--R            +---+ |   2
--R           \|- a \|a x  + b x + c
--R       + 
--R                   5          4 3  8         5 2        4 2        3 4  7
--R             (1536a b c + 384a b )x  + (3072a c  + 5632a b c + 448a b )x
--R           + 
--R                    4   2        3 3       2 5  6
--R             (15104a b c  + 4992a b c - 16a b )x
--R           + 
--R                    4 3         3 2 2       2 4         6  5
--R             (10752a c  + 15744a b c  - 160a b c + 40a b )x
--R           + 
--R                    3   3        2 3 2        5        7  4
--R             (21312a b c  - 2448a b c  + 76a b c + 105b )x
--R           + 
--R                    3 4        2 2 3          4 2       6   3
--R             (10752a c  - 1152a b c  - 3232a b c  + 840b c)x
--R           + 
--R                   2   4          3 3        5 2  2
--R             (5376a b c  - 8064a b c  + 1680b c )x
--R           + 
--R                   2 5          2 4       4 3
--R             (3072a c  - 4608a b c  + 960b c )x
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                   4           3 3  3          4 2         3 2   2
--R             (6144a b c + 1536a b )x  + (12288a c  + 15360a b c)x
--R           + 
--R                   3   2          3 3
--R             36864a b c x + 24576a c
--R        *
--R                      +--------------+
--R            +---+ +-+ |   2
--R           \|- a \|c \|a x  + b x + c
--R       + 
--R                     5 2        4 2        3 4  4
--R             (- 3072a c  - 4608a b c - 192a b )x
--R           + 
--R                      4   2        3 3   3            4 3         3 2 2  2
--R             (- 24576a b c  - 6144a b c)x  + (- 24576a c  - 30720a b c )x
--R           + 
--R                     3   3          3 4
--R             - 49152a b c x - 24576a c
--R        *
--R            +---+
--R           \|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 63
t1:=integrate(sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  2        2  3                  3  2           2     2     +-+
           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                  2   4       2         2  3                3  2
               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
             + 
                     2     2
               (32a c  + 8b c)x
        *
            +-+ +-+
           \|a \|c
    /
                                   +--------------+
                           +-+ +-+ |   2
         (32a b x + 64a c)\|a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +-+
         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
     ,

                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                 2        2  3                 3  2           2     2     +---+
           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
              2   4       2         2  3                3  2         2     2
           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
        *
            +---+ +-+
           \|- a \|c
    /
                                     +--------------+
                           +---+ +-+ |   2
         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +---+
         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  2        2  3                  3  2           2     2     +-+
--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                  2   4       2         2  3                3  2
--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
--R             + 
--R                     2     2
--R               (32a c  + 8b c)x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                                   +--------------+
--R                           +-+ +-+ |   2
--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +-+
--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R     ,
--R
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                 2        2  3                 3  2           2     2     +---+
--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R              2   4       2         2  3                3  2         2     2
--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                                     +--------------+
--R                           +---+ +-+ |   2
--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +---+
--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 64
bb1:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.1
 

   (3)
                     2   2         3       5         2 3         2 2       4
             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                3 3       2 2 2        4       6  2
           (192a c  - 240a b c  - 12a b c + 15b )x
         + 
                2   3         3 2       5          2 4         2 3       4 2
           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                  4       3 2  5          3         2 3  4
           (- 384a c - 96a b )x  + (- 832a b c - 16a b )x
         + 
                  3 2      2 2         4  3         2   2         3       5  2
           (- 960a c  - 96a b c + 20a b )x  + (- 96a b c  + 144a b c - 30b )x
         + 
                  2 3         2 2       4              3
           (- 384a c  + 896a b c  - 120b c)x + 640a b c
      *
              +--------------+
          +-+ |   2
         \|a \|a x  + b x + c
     + 
               4   6        4        3 2  5         3         2 3  4
           384a b x  + (768a c + 448a b )x  + (1472a b c - 16a b )x
         + 
                 3 2       2 2         4  3         2   2         3       5  2
           (1152a c  - 192a b c + 40a b )x  + (- 32a b c  - 512a b c + 90b )x
         + 
                2 3          2 2       4              3
           (384a c  - 1216a b c  + 120b c)x - 640a b c
      *
          +-+ +-+
         \|a \|c
  /
                                     +--------------+
             3           3   +-+ +-+ |   2
       (1536a b x + 3072a c)\|a \|c \|a x  + b x + c
     + 
                4        3 2  2        3             3 2  +-+
       ((- 1536a c - 384a b )x  - 3072a b c x - 3072a c )\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     2   2         3       5         2 3         2 2       4
--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                3 3       2 2 2        4       6  2
--R           (192a c  - 240a b c  - 12a b c + 15b )x
--R         + 
--R                2   3         3 2       5          2 4         2 3       4 2
--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                  4       3 2  5          3         2 3  4
--R           (- 384a c - 96a b )x  + (- 832a b c - 16a b )x
--R         + 
--R                  3 2      2 2         4  3         2   2         3       5  2
--R           (- 960a c  - 96a b c + 20a b )x  + (- 96a b c  + 144a b c - 30b )x
--R         + 
--R                  2 3         2 2       4              3
--R           (- 384a c  + 896a b c  - 120b c)x + 640a b c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|a \|a x  + b x + c
--R     + 
--R               4   6        4        3 2  5         3         2 3  4
--R           384a b x  + (768a c + 448a b )x  + (1472a b c - 16a b )x
--R         + 
--R                 3 2       2 2         4  3         2   2         3       5  2
--R           (1152a c  - 192a b c + 40a b )x  + (- 32a b c  - 512a b c + 90b )x
--R         + 
--R                2 3          2 2       4              3
--R           (384a c  - 1216a b c  + 120b c)x - 640a b c
--R      *
--R          +-+ +-+
--R         \|a \|c
--R  /
--R                                     +--------------+
--R             3           3   +-+ +-+ |   2
--R       (1536a b x + 3072a c)\|a \|c \|a x  + b x + c
--R     + 
--R                4        3 2  2        3             3 2  +-+
--R       ((- 1536a c - 384a b )x  - 3072a b c x - 3072a c )\|a
--R                                                     Type: Expression Integer
--E

--S 65
bb2:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.2
 

   (4)
                     2   2         3       5         2 3         2 2       4
             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                3 3       2 2 2        4       6  2
           (192a c  - 240a b c  - 12a b c + 15b )x
         + 
                2   3         3 2       5          2 4         2 3       4 2
           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                  4       3 2  5          3        2 3  4
           (- 192a c - 48a b )x  + (- 416a b c - 8a b )x
         + 
                  3 2      2 2         4  3         2   2        3       5  2
           (- 480a c  - 48a b c + 10a b )x  + (- 48a b c  + 72a b c - 15b )x
         + 
                  2 3         2 2      4              3
           (- 192a c  + 448a b c  - 60b c)x + 320a b c
      *
                +--------------+
          +---+ |   2
         \|- a \|a x  + b x + c
     + 
               4   6        4        3 2  5        3        2 3  4
           192a b x  + (384a c + 224a b )x  + (736a b c - 8a b )x
         + 
                3 2      2 2         4  3         2   2         3       5  2
           (576a c  - 96a b c + 20a b )x  + (- 16a b c  - 256a b c + 45b )x
         + 
                2 3         2 2      4              3
           (192a c  - 608a b c  + 60b c)x - 320a b c
      *
          +---+ +-+
         \|- a \|c
  /
                                      +--------------+
            3           3   +---+ +-+ |   2
       (768a b x + 1536a c)\|- a \|c \|a x  + b x + c
     + 
               4        3 2  2        3             3 2  +---+
       ((- 768a c - 192a b )x  - 1536a b c x - 1536a c )\|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                     2   2         3       5         2 3         2 2       4
--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                3 3       2 2 2        4       6  2
--R           (192a c  - 240a b c  - 12a b c + 15b )x
--R         + 
--R                2   3         3 2       5          2 4         2 3       4 2
--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                  4       3 2  5          3        2 3  4
--R           (- 192a c - 48a b )x  + (- 416a b c - 8a b )x
--R         + 
--R                  3 2      2 2         4  3         2   2        3       5  2
--R           (- 480a c  - 48a b c + 10a b )x  + (- 48a b c  + 72a b c - 15b )x
--R         + 
--R                  2 3         2 2      4              3
--R           (- 192a c  + 448a b c  - 60b c)x + 320a b c
--R      *
--R                +--------------+
--R          +---+ |   2
--R         \|- a \|a x  + b x + c
--R     + 
--R               4   6        4        3 2  5        3        2 3  4
--R           192a b x  + (384a c + 224a b )x  + (736a b c - 8a b )x
--R         + 
--R                3 2      2 2         4  3         2   2         3       5  2
--R           (576a c  - 96a b c + 20a b )x  + (- 16a b c  - 256a b c + 45b )x
--R         + 
--R                2 3         2 2      4              3
--R           (192a c  - 608a b c  + 60b c)x - 320a b c
--R      *
--R          +---+ +-+
--R         \|- a \|c
--R  /
--R                                      +--------------+
--R            3           3   +---+ +-+ |   2
--R       (768a b x + 1536a c)\|- a \|c \|a x  + b x + c
--R     + 
--R               4        3 2  2        3             3 2  +---+
--R       ((- 768a c - 192a b )x  - 1536a b c x - 1536a c )\|- a
--R                                                     Type: Expression Integer
--E

--S 66
cc1:=aa.1-bb1
 

   (5)
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                      5 5        4 2 4         3 4 3       2 6 2         8
               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
             + 
                    10
               - 15b
          *
              6
             x
         + 
                    4   5         3 3 4         2 5 3          7 2        9   5
           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
         + 
                    4 6          3 2 5          2 4 4         8 2  4
           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
         + 
                     3   6          2 3 5            5 4         7 3  3
           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
         + 
                     3 7          2 2 6            4 5          6 4  2
           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
         + 
                     2   7            3 6         5 5           2 8
           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
         + 
                    2 7         4 6
           147456a b c  - 30720b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                      5 5        4 2 4         3 4 3       2 6 2         8
               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
             + 
                    10
               - 15b
          *
              6
             x
         + 
                    4   5         3 3 4         2 5 3          7 2        9   5
           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
         + 
                    4 6          3 2 5          2 4 4         8 2  4
           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
         + 
                     3   6          2 3 5            5 4         7 3  3
           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
         + 
                     3 7          2 2 6            4 5          6 4  2
           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
         + 
                     2   7            3 6         5 5           2 8
           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
         + 
                    2 7         4 6
           147456a b c  - 30720b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                    3 2 4         2 4 3         6 2  5
           (- 15360a b c  - 12800a b c  - 960a b c )x
         + 
                    3   5          2 3 4           5 3  4
           (- 30720a b c  - 107520a b c  - 22400a b c )x
         + 
                     2 2 5            4 4  3             2   6            3 5  2
           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
         + 
                      2 6               7
           - 409600a b c x - 163840a b c
      *
              +--------------+
          +-+ |   2
         \|a \|a x  + b x + c
     + 
                 4   4         3 3 3        2 5 2        7   6
           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
         + 
                  3 2 4         2 4 3          6 2  5
           (92160a b c  + 76800a b c  + 5760a b c )x
         + 
                  3   5          2 3 4           5 3  4
           (92160a b c  + 322560a b c  + 67200a b c )x
         + 
                   2 2 5            4 4  3           2   6            3 5  2
           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
         + 
                    2 6               7
           491520a b c x + 163840a b c
      *
          +-+ +-+
         \|a \|c
  /
                  5   2         4 3         3 5  5
           (73728a b c  + 61440a b c + 4608a b )x
         + 
                   5 3          4 2 2          3 4   4
           (147456a c  + 516096a b c  + 107520a b c)x
         + 
                    4   3          3 3 2  3           4 4           3 2 3  2
           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
         + 
                   3   4           3 5
           1966080a b c x + 786432a c
      *
                  +--------------+
          +-+ +-+ |   2
         \|a \|c \|a x  + b x + c
     + 
                    6 3         5 2 2         4 4        3 6  6
           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
         + 
                     5   3          4 3 2         3 5   5
           (- 442368a b c  - 368640a b c  - 27648a b c)x
         + 
                     5 4           4 2 3          3 4 2  4
           (- 442368a c  - 1548288a b c  - 322560a b c )x
         + 
                      4   4           3 3 3  3
           (- 2359296a b c  - 1376256a b c )x
         + 
                      4 5           3 2 4  2           3   5           3 6
           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
      *
          +-+
         \|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                      5 5        4 2 4         3 4 3       2 6 2         8
--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R             + 
--R                    10
--R               - 15b
--R          *
--R              6
--R             x
--R         + 
--R                    4   5         3 3 4         2 5 3          7 2        9   5
--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
--R         + 
--R                    4 6          3 2 5          2 4 4         8 2  4
--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R         + 
--R                     3   6          2 3 5            5 4         7 3  3
--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R         + 
--R                     3 7          2 2 6            4 5          6 4  2
--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R         + 
--R                     2   7            3 6         5 5           2 8
--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R         + 
--R                    2 7         4 6
--R           147456a b c  - 30720b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                      5 5        4 2 4         3 4 3       2 6 2         8
--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R             + 
--R                    10
--R               - 15b
--R          *
--R              6
--R             x
--R         + 
--R                    4   5         3 3 4         2 5 3          7 2        9   5
--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
--R         + 
--R                    4 6          3 2 5          2 4 4         8 2  4
--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R         + 
--R                     3   6          2 3 5            5 4         7 3  3
--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R         + 
--R                     3 7          2 2 6            4 5          6 4  2
--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R         + 
--R                     2   7            3 6         5 5           2 8
--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R         + 
--R                    2 7         4 6
--R           147456a b c  - 30720b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                    3 2 4         2 4 3         6 2  5
--R           (- 15360a b c  - 12800a b c  - 960a b c )x
--R         + 
--R                    3   5          2 3 4           5 3  4
--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
--R         + 
--R                     2 2 5            4 4  3             2   6            3 5  2
--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
--R         + 
--R                      2 6               7
--R           - 409600a b c x - 163840a b c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|a \|a x  + b x + c
--R     + 
--R                 4   4         3 3 3        2 5 2        7   6
--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
--R         + 
--R                  3 2 4         2 4 3          6 2  5
--R           (92160a b c  + 76800a b c  + 5760a b c )x
--R         + 
--R                  3   5          2 3 4           5 3  4
--R           (92160a b c  + 322560a b c  + 67200a b c )x
--R         + 
--R                   2 2 5            4 4  3           2   6            3 5  2
--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
--R         + 
--R                    2 6               7
--R           491520a b c x + 163840a b c
--R      *
--R          +-+ +-+
--R         \|a \|c
--R  /
--R                  5   2         4 3         3 5  5
--R           (73728a b c  + 61440a b c + 4608a b )x
--R         + 
--R                   5 3          4 2 2          3 4   4
--R           (147456a c  + 516096a b c  + 107520a b c)x
--R         + 
--R                    4   3          3 3 2  3           4 4           3 2 3  2
--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
--R         + 
--R                   3   4           3 5
--R           1966080a b c x + 786432a c
--R      *
--R                  +--------------+
--R          +-+ +-+ |   2
--R         \|a \|c \|a x  + b x + c
--R     + 
--R                    6 3         5 2 2         4 4        3 6  6
--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
--R         + 
--R                     5   3          4 3 2         3 5   5
--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
--R         + 
--R                     5 4           4 2 3          3 4 2  4
--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
--R         + 
--R                      4   4           3 3 3  3
--R           (- 2359296a b c  - 1376256a b c )x
--R         + 
--R                      4 5           3 2 4  2           3   5           3 6
--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
--R      *
--R          +-+
--R         \|a
--R                                                     Type: Expression Integer
--E

--S 67
cc2:=aa.2-bb1
 

   (6)
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                          5 5        4 2 4         3 4 3       2 6 2         8
                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
                 + 
                        10
                   - 15b
              *
                  6
                 x
             + 
                           4   5         3 3 4         2 5 3          7 2
                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
                 + 
                          9
                   - 1080b c
              *
                  5
                 x
             + 
                        4 6          3 2 5          2 4 4         8 2  4
               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
             + 
                         3   6          2 3 5            5 4         7 3  3
               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
             + 
                         3 7          2 2 6            4 5          6 4  2
               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
             + 
                         2   7            3 6         5 5           2 8
               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
             + 
                        2 7         4 6
               147456a b c  - 30720b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                        4   4         3 3 3         2 5 2          7        9  5
               (- 18432a b c  + 12288a b c  + 16128a b c  - 3072a b c - 360b )x
             + 
                        4 5         3 2 4          2 4 3        8   4
               (- 36864a c  - 73728a b c  + 155136a b c  - 8400b c)x
             + 
                         3   5          2 3 4            5 3         7 2  3
               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
             + 
                         3 6          2 2 5            4 4          6 3  2
               (- 196608a c  - 147456a b c  + 602112a b c  - 138240b c )x
             + 
                         2   6            3 5          5 4            2 7
               (- 491520a b c  + 737280a b c  - 153600b c )x - 196608a c
             + 
                        2 6         4 5
               294912a b c  - 61440b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                        5 5         4 2 4         3 4 3        2 6 2          8
                   6144a c  + 13824a b c  - 26880a b c  - 1344a b c  + 1656a b c
                 + 
                      10
                   30b
              *
                  6
                 x
             + 
                          4   5         3 3 4         2 5 3           7 2
                   110592a b c  - 73728a b c  - 96768a b c  + 18432a b c
                 + 
                        9
                   2160b c
              *
                  5
                 x
             + 
                       4 6          3 2 5          2 4 4         8 2  4
               (110592a c  + 221184a b c  - 465408a b c  + 25200b c )x
             + 
                       3   6          2 3 5            5 4          7 3  3
               (589824a b c  - 540672a b c  - 331776a b c  + 107520b c )x
             + 
                       3 7          2 2 6            4 5          6 4  2
               (294912a c  + 221184a b c  - 903168a b c  + 207360b c )x
             + 
                       2   7            3 6          5 5            2 8
               (589824a b c  - 884736a b c  + 184320b c )x + 196608a c
             + 
                          2 7         4 6
               - 294912a b c  + 61440b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                    3 2 4         2 4 3         6 2  5
           (- 15360a b c  - 12800a b c  - 960a b c )x
         + 
                    3   5          2 3 4           5 3  4
           (- 30720a b c  - 107520a b c  - 22400a b c )x
         + 
                     2 2 5            4 4  3             2   6            3 5  2
           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
         + 
                      2 6               7
           - 409600a b c x - 163840a b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                 4   4         3 3 3        2 5 2        7   6
           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
         + 
                  3 2 4         2 4 3          6 2  5
           (92160a b c  + 76800a b c  + 5760a b c )x
         + 
                  3   5          2 3 4           5 3  4
           (92160a b c  + 322560a b c  + 67200a b c )x
         + 
                   2 2 5            4 4  3           2   6            3 5  2
           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
         + 
                    2 6               7
           491520a b c x + 163840a b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
                  5   2         4 3         3 5  5
           (73728a b c  + 61440a b c + 4608a b )x
         + 
                   5 3          4 2 2          3 4   4
           (147456a c  + 516096a b c  + 107520a b c)x
         + 
                    4   3          3 3 2  3           4 4           3 2 3  2
           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
         + 
                   3   4           3 5
           1966080a b c x + 786432a c
      *
                        +--------------+
          +---+ +-+ +-+ |   2
         \|- a \|a \|c \|a x  + b x + c
     + 
                    6 3         5 2 2         4 4        3 6  6
           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
         + 
                     5   3          4 3 2         3 5   5
           (- 442368a b c  - 368640a b c  - 27648a b c)x
         + 
                     5 4           4 2 3          3 4 2  4
           (- 442368a c  - 1548288a b c  - 322560a b c )x
         + 
                      4   4           3 3 3  3
           (- 2359296a b c  - 1376256a b c )x
         + 
                      4 5           3 2 4  2           3   5           3 6
           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                          5 5        4 2 4         3 4 3       2 6 2         8
--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R                 + 
--R                        10
--R                   - 15b
--R              *
--R                  6
--R                 x
--R             + 
--R                           4   5         3 3 4         2 5 3          7 2
--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
--R                 + 
--R                          9
--R                   - 1080b c
--R              *
--R                  5
--R                 x
--R             + 
--R                        4 6          3 2 5          2 4 4         8 2  4
--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R             + 
--R                         3   6          2 3 5            5 4         7 3  3
--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R             + 
--R                         3 7          2 2 6            4 5          6 4  2
--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R             + 
--R                         2   7            3 6         5 5           2 8
--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R             + 
--R                        2 7         4 6
--R               147456a b c  - 30720b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                        4   4         3 3 3         2 5 2          7        9  5
--R               (- 18432a b c  + 12288a b c  + 16128a b c  - 3072a b c - 360b )x
--R             + 
--R                        4 5         3 2 4          2 4 3        8   4
--R               (- 36864a c  - 73728a b c  + 155136a b c  - 8400b c)x
--R             + 
--R                         3   5          2 3 4            5 3         7 2  3
--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R             + 
--R                         3 6          2 2 5            4 4          6 3  2
--R               (- 196608a c  - 147456a b c  + 602112a b c  - 138240b c )x
--R             + 
--R                         2   6            3 5          5 4            2 7
--R               (- 491520a b c  + 737280a b c  - 153600b c )x - 196608a c
--R             + 
--R                        2 6         4 5
--R               294912a b c  - 61440b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                        5 5         4 2 4         3 4 3        2 6 2          8
--R                   6144a c  + 13824a b c  - 26880a b c  - 1344a b c  + 1656a b c
--R                 + 
--R                      10
--R                   30b
--R              *
--R                  6
--R                 x
--R             + 
--R                          4   5         3 3 4         2 5 3           7 2
--R                   110592a b c  - 73728a b c  - 96768a b c  + 18432a b c
--R                 + 
--R                        9
--R                   2160b c
--R              *
--R                  5
--R                 x
--R             + 
--R                       4 6          3 2 5          2 4 4         8 2  4
--R               (110592a c  + 221184a b c  - 465408a b c  + 25200b c )x
--R             + 
--R                       3   6          2 3 5            5 4          7 3  3
--R               (589824a b c  - 540672a b c  - 331776a b c  + 107520b c )x
--R             + 
--R                       3 7          2 2 6            4 5          6 4  2
--R               (294912a c  + 221184a b c  - 903168a b c  + 207360b c )x
--R             + 
--R                       2   7            3 6          5 5            2 8
--R               (589824a b c  - 884736a b c  + 184320b c )x + 196608a c
--R             + 
--R                          2 7         4 6
--R               - 294912a b c  + 61440b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                    3 2 4         2 4 3         6 2  5
--R           (- 15360a b c  - 12800a b c  - 960a b c )x
--R         + 
--R                    3   5          2 3 4           5 3  4
--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
--R         + 
--R                     2 2 5            4 4  3             2   6            3 5  2
--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
--R         + 
--R                      2 6               7
--R           - 409600a b c x - 163840a b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                 4   4         3 3 3        2 5 2        7   6
--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
--R         + 
--R                  3 2 4         2 4 3          6 2  5
--R           (92160a b c  + 76800a b c  + 5760a b c )x
--R         + 
--R                  3   5          2 3 4           5 3  4
--R           (92160a b c  + 322560a b c  + 67200a b c )x
--R         + 
--R                   2 2 5            4 4  3           2   6            3 5  2
--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
--R         + 
--R                    2 6               7
--R           491520a b c x + 163840a b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R                  5   2         4 3         3 5  5
--R           (73728a b c  + 61440a b c + 4608a b )x
--R         + 
--R                   5 3          4 2 2          3 4   4
--R           (147456a c  + 516096a b c  + 107520a b c)x
--R         + 
--R                    4   3          3 3 2  3           4 4           3 2 3  2
--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
--R         + 
--R                   3   4           3 5
--R           1966080a b c x + 786432a c
--R      *
--R                        +--------------+
--R          +---+ +-+ +-+ |   2
--R         \|- a \|a \|c \|a x  + b x + c
--R     + 
--R                    6 3         5 2 2         4 4        3 6  6
--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
--R         + 
--R                     5   3          4 3 2         3 5   5
--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
--R         + 
--R                     5 4           4 2 3          3 4 2  4
--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
--R         + 
--R                      4   4           3 3 3  3
--R           (- 2359296a b c  - 1376256a b c )x
--R         + 
--R                      4 5           3 2 4  2           3   5           3 6
--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 68
cc3:=aa.1-bb2
 

   (7)
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                          5 5        4 2 4         3 4 3       2 6 2         8
                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
                 + 
                        10
                   - 15b
              *
                  6
                 x
             + 
                           4   5         3 3 4         2 5 3          7 2
                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
                 + 
                          9
                   - 1080b c
              *
                  5
                 x
             + 
                        4 6          3 2 5          2 4 4         8 2  4
               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
             + 
                         3   6          2 3 5            5 4         7 3  3
               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
             + 
                         3 7          2 2 6            4 5          6 4  2
               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
             + 
                         2   7            3 6         5 5           2 8
               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
             + 
                        2 7         4 6
               147456a b c  - 30720b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                      4   4         3 3 3         2 5 2          7        9  5
               (18432a b c  - 12288a b c  - 16128a b c  + 3072a b c + 360b )x
             + 
                      4 5         3 2 4          2 4 3        8   4
               (36864a c  + 73728a b c  - 155136a b c  + 8400b c)x
             + 
                       3   5          2 3 4            5 3         7 2  3
               (294912a b c  - 270336a b c  - 165888a b c  + 53760b c )x
             + 
                       3 6          2 2 5            4 4          6 3  2
               (196608a c  + 147456a b c  - 602112a b c  + 138240b c )x
             + 
                       2   6            3 5          5 4            2 7
               (491520a b c  - 737280a b c  + 153600b c )x + 196608a c
             + 
                          2 6         4 5
               - 294912a b c  + 61440b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                          5 5         4 2 4         3 4 3        2 6 2
                   - 6144a c  - 13824a b c  + 26880a b c  + 1344a b c
                 + 
                            8       10
                   - 1656a b c - 30b
              *
                  6
                 x
             + 
                            4   5         3 3 4         2 5 3           7 2
                   - 110592a b c  + 73728a b c  + 96768a b c  - 18432a b c
                 + 
                          9
                   - 2160b c
              *
                  5
                 x
             + 
                         4 6          3 2 5          2 4 4         8 2  4
               (- 110592a c  - 221184a b c  + 465408a b c  - 25200b c )x
             + 
                         3   6          2 3 5            5 4          7 3  3
               (- 589824a b c  + 540672a b c  + 331776a b c  - 107520b c )x
             + 
                         3 7          2 2 6            4 5          6 4  2
               (- 294912a c  - 221184a b c  + 903168a b c  - 207360b c )x
             + 
                         2   7            3 6          5 5            2 8
               (- 589824a b c  + 884736a b c  - 184320b c )x - 196608a c
             + 
                        2 7         4 6
               294912a b c  - 61440b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                    3 2 4         2 4 3         6 2  5
           (- 15360a b c  - 12800a b c  - 960a b c )x
         + 
                    3   5          2 3 4           5 3  4
           (- 30720a b c  - 107520a b c  - 22400a b c )x
         + 
                     2 2 5            4 4  3             2   6            3 5  2
           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
         + 
                      2 6               7
           - 409600a b c x - 163840a b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                 4   4         3 3 3        2 5 2        7   6
           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
         + 
                  3 2 4         2 4 3          6 2  5
           (92160a b c  + 76800a b c  + 5760a b c )x
         + 
                  3   5          2 3 4           5 3  4
           (92160a b c  + 322560a b c  + 67200a b c )x
         + 
                   2 2 5            4 4  3           2   6            3 5  2
           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
         + 
                    2 6               7
           491520a b c x + 163840a b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
                  5   2         4 3         3 5  5
           (73728a b c  + 61440a b c + 4608a b )x
         + 
                   5 3          4 2 2          3 4   4
           (147456a c  + 516096a b c  + 107520a b c)x
         + 
                    4   3          3 3 2  3           4 4           3 2 3  2
           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
         + 
                   3   4           3 5
           1966080a b c x + 786432a c
      *
                        +--------------+
          +---+ +-+ +-+ |   2
         \|- a \|a \|c \|a x  + b x + c
     + 
                    6 3         5 2 2         4 4        3 6  6
           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
         + 
                     5   3          4 3 2         3 5   5
           (- 442368a b c  - 368640a b c  - 27648a b c)x
         + 
                     5 4           4 2 3          3 4 2  4
           (- 442368a c  - 1548288a b c  - 322560a b c )x
         + 
                      4   4           3 3 3  3
           (- 2359296a b c  - 1376256a b c )x
         + 
                      4 5           3 2 4  2           3   5           3 6
           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                          5 5        4 2 4         3 4 3       2 6 2         8
--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R                 + 
--R                        10
--R                   - 15b
--R              *
--R                  6
--R                 x
--R             + 
--R                           4   5         3 3 4         2 5 3          7 2
--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
--R                 + 
--R                          9
--R                   - 1080b c
--R              *
--R                  5
--R                 x
--R             + 
--R                        4 6          3 2 5          2 4 4         8 2  4
--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R             + 
--R                         3   6          2 3 5            5 4         7 3  3
--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R             + 
--R                         3 7          2 2 6            4 5          6 4  2
--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R             + 
--R                         2   7            3 6         5 5           2 8
--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R             + 
--R                        2 7         4 6
--R               147456a b c  - 30720b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                      4   4         3 3 3         2 5 2          7        9  5
--R               (18432a b c  - 12288a b c  - 16128a b c  + 3072a b c + 360b )x
--R             + 
--R                      4 5         3 2 4          2 4 3        8   4
--R               (36864a c  + 73728a b c  - 155136a b c  + 8400b c)x
--R             + 
--R                       3   5          2 3 4            5 3         7 2  3
--R               (294912a b c  - 270336a b c  - 165888a b c  + 53760b c )x
--R             + 
--R                       3 6          2 2 5            4 4          6 3  2
--R               (196608a c  + 147456a b c  - 602112a b c  + 138240b c )x
--R             + 
--R                       2   6            3 5          5 4            2 7
--R               (491520a b c  - 737280a b c  + 153600b c )x + 196608a c
--R             + 
--R                          2 6         4 5
--R               - 294912a b c  + 61440b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                          5 5         4 2 4         3 4 3        2 6 2
--R                   - 6144a c  - 13824a b c  + 26880a b c  + 1344a b c
--R                 + 
--R                            8       10
--R                   - 1656a b c - 30b
--R              *
--R                  6
--R                 x
--R             + 
--R                            4   5         3 3 4         2 5 3           7 2
--R                   - 110592a b c  + 73728a b c  + 96768a b c  - 18432a b c
--R                 + 
--R                          9
--R                   - 2160b c
--R              *
--R                  5
--R                 x
--R             + 
--R                         4 6          3 2 5          2 4 4         8 2  4
--R               (- 110592a c  - 221184a b c  + 465408a b c  - 25200b c )x
--R             + 
--R                         3   6          2 3 5            5 4          7 3  3
--R               (- 589824a b c  + 540672a b c  + 331776a b c  - 107520b c )x
--R             + 
--R                         3 7          2 2 6            4 5          6 4  2
--R               (- 294912a c  - 221184a b c  + 903168a b c  - 207360b c )x
--R             + 
--R                         2   7            3 6          5 5            2 8
--R               (- 589824a b c  + 884736a b c  - 184320b c )x - 196608a c
--R             + 
--R                        2 7         4 6
--R               294912a b c  - 61440b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                    3 2 4         2 4 3         6 2  5
--R           (- 15360a b c  - 12800a b c  - 960a b c )x
--R         + 
--R                    3   5          2 3 4           5 3  4
--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
--R         + 
--R                     2 2 5            4 4  3             2   6            3 5  2
--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
--R         + 
--R                      2 6               7
--R           - 409600a b c x - 163840a b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                 4   4         3 3 3        2 5 2        7   6
--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
--R         + 
--R                  3 2 4         2 4 3          6 2  5
--R           (92160a b c  + 76800a b c  + 5760a b c )x
--R         + 
--R                  3   5          2 3 4           5 3  4
--R           (92160a b c  + 322560a b c  + 67200a b c )x
--R         + 
--R                   2 2 5            4 4  3           2   6            3 5  2
--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
--R         + 
--R                    2 6               7
--R           491520a b c x + 163840a b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R                  5   2         4 3         3 5  5
--R           (73728a b c  + 61440a b c + 4608a b )x
--R         + 
--R                   5 3          4 2 2          3 4   4
--R           (147456a c  + 516096a b c  + 107520a b c)x
--R         + 
--R                    4   3          3 3 2  3           4 4           3 2 3  2
--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
--R         + 
--R                   3   4           3 5
--R           1966080a b c x + 786432a c
--R      *
--R                        +--------------+
--R          +---+ +-+ +-+ |   2
--R         \|- a \|a \|c \|a x  + b x + c
--R     + 
--R                    6 3         5 2 2         4 4        3 6  6
--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
--R         + 
--R                     5   3          4 3 2         3 5   5
--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
--R         + 
--R                     5 4           4 2 3          3 4 2  4
--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
--R         + 
--R                      4   4           3 3 3  3
--R           (- 2359296a b c  - 1376256a b c )x
--R         + 
--R                      4 5           3 2 4  2           3   5           3 6
--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 69
cc4:=aa.2-bb2
 

   (8)
                  2 2 4         4 3      6 2  5
           (- 960a b c  - 800a b c  - 60b c )x
         + 
                   2   5          3 4        5 3  4
           (- 1920a b c  - 6720a b c  - 1400b c )x
         + 
                      2 5        4 4  3                6         3 5  2
           (- 15360a b c  - 8960b c )x  + (- 10240a b c  - 23040b c )x
         + 
                   2 6            7
           - 25600b c x - 10240b c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                3   4        2 3 3         5 2     7   6
           (320a b c  + 1200a b c  + 300a b c  + 5b c)x
         + 
                 2 2 4          4 3       6 2  5
           (5760a b c  + 4800a b c  + 360b c )x
         + 
                 2   5           3 4        5 3  4            2 5         4 4  3
           (5760a b c  + 20160a b c  + 4200b c )x  + (30720a b c  + 17920b c )x
         + 
                      6         3 5  2         2 6            7
           (15360a b c  + 34560b c )x  + 30720b c x + 10240b c
      *
          +-+
         \|c
  /
                 4   2        3 3        2 5  5
           (4608a b c  + 3840a b c + 288a b )x
         + 
                 4 3         3 2 2        2 4   4
           (9216a c  + 32256a b c  + 6720a b c)x
         + 
                  3   3         2 3 2  3          3 4          2 2 3  2
           (73728a b c  + 43008a b c )x  + (49152a c  + 110592a b c )x
         + 
                  2   4          2 5
           122880a b c x + 49152a c
      *
              +--------------+
          +-+ |   2
         \|c \|a x  + b x + c
     + 
               5 3        4 2 2        3 4       2 6  6
       (- 1536a c  - 5760a b c  - 1440a b c - 24a b )x
     + 
                4   3         3 3 2        2 5   5
       (- 27648a b c  - 23040a b c  - 1728a b c)x
     + 
                4 4         3 2 3         2 4 2  4
       (- 27648a c  - 96768a b c  - 20160a b c )x
     + 
                 3   4         2 3 3  3            3 5          2 2 4  2
       (- 147456a b c  - 86016a b c )x  + (- 73728a c  - 165888a b c )x
     + 
                2   5          2 6
       - 147456a b c x - 49152a c
                                                     Type: Expression Integer
--R
--R   (8)
--R                  2 2 4         4 3      6 2  5
--R           (- 960a b c  - 800a b c  - 60b c )x
--R         + 
--R                   2   5          3 4        5 3  4
--R           (- 1920a b c  - 6720a b c  - 1400b c )x
--R         + 
--R                      2 5        4 4  3                6         3 5  2
--R           (- 15360a b c  - 8960b c )x  + (- 10240a b c  - 23040b c )x
--R         + 
--R                   2 6            7
--R           - 25600b c x - 10240b c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                3   4        2 3 3         5 2     7   6
--R           (320a b c  + 1200a b c  + 300a b c  + 5b c)x
--R         + 
--R                 2 2 4          4 3       6 2  5
--R           (5760a b c  + 4800a b c  + 360b c )x
--R         + 
--R                 2   5           3 4        5 3  4            2 5         4 4  3
--R           (5760a b c  + 20160a b c  + 4200b c )x  + (30720a b c  + 17920b c )x
--R         + 
--R                      6         3 5  2         2 6            7
--R           (15360a b c  + 34560b c )x  + 30720b c x + 10240b c
--R      *
--R          +-+
--R         \|c
--R  /
--R                 4   2        3 3        2 5  5
--R           (4608a b c  + 3840a b c + 288a b )x
--R         + 
--R                 4 3         3 2 2        2 4   4
--R           (9216a c  + 32256a b c  + 6720a b c)x
--R         + 
--R                  3   3         2 3 2  3          3 4          2 2 3  2
--R           (73728a b c  + 43008a b c )x  + (49152a c  + 110592a b c )x
--R         + 
--R                  2   4          2 5
--R           122880a b c x + 49152a c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|c \|a x  + b x + c
--R     + 
--R               5 3        4 2 2        3 4       2 6  6
--R       (- 1536a c  - 5760a b c  - 1440a b c - 24a b )x
--R     + 
--R                4   3         3 3 2        2 5   5
--R       (- 27648a b c  - 23040a b c  - 1728a b c)x
--R     + 
--R                4 4         3 2 3         2 4 2  4
--R       (- 27648a c  - 96768a b c  - 20160a b c )x
--R     + 
--R                 3   4         2 3 3  3            3 5          2 2 4  2
--R       (- 147456a b c  - 86016a b c )x  + (- 73728a c  - 165888a b c )x
--R     + 
--R                2   5          2 6
--R       - 147456a b c x - 49152a c
--R                                                     Type: Expression Integer
--E

--S 70     14:287 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

               +-+
          5b c\|c
   (9)  - --------
               2
            24a
                                                     Type: Expression Integer
--R
--R               +-+
--R          5b c\|c
--R   (9)  - --------
--R               2
--R            24a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 71
aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
 

   (1)
   [
                   +--------------+
               +-+ |   2                            +-+ +-+
           (4c\|a \|a x  + b x + c  + (- 2b x - 4c)\|a \|c )
        *
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
           log(---------------------------------)
                                +-+
                             2x\|c
       + 
                   +--------------+
               +-+ |   2               2
           (2b\|c \|a x  + b x + c  - b x - 2b c)
        *
           log
                              2           +-+          2              2  +-+
                    ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
                 *
                     +--------------+
                     |   2
                    \|a x  + b x + c
                + 
                           3              2  2              2  +-+ +-+     2   3
                  (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
                + 
                          2       2
                  6a b c x  + 8a c x
             /
                                 +--------------+
                              2  |   2
                  (4b c x + 8c )\|a x  + b x + c
                + 
                              2  2              2  +-+
                  ((- 4a c - b )x  - 8b c x - 8c )\|c
       + 
                    +--------------+
                +-+ |   2                   2         +-+ +-+
         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
    /
                 +--------------+
         +-+ +-+ |   2                            +-+
       4\|a \|c \|a x  + b x + c  + (- 2b x - 4c)\|a
     ,

                     +--------------+
               +---+ |   2                           +---+ +-+
           (2c\|- a \|a x  + b x + c  + (- b x - 2c)\|- a \|c )
        *
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
           log(---------------------------------)
                                +-+
                             2x\|c
       + 
                   +--------------+
               +-+ |   2               2
           (2b\|c \|a x  + b x + c  - b x - 2b c)
        *
                           +--------------+
                 +---+ +-+ |   2                +---+
                \|- a \|c \|a x  + b x + c  - c\|- a
           atan(-------------------------------------)
                                   +-+
                               a x\|c
       + 
                     +--------------+
               +---+ |   2                   2        +---+ +-+
         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
    /
                   +--------------+
         +---+ +-+ |   2                           +---+
       2\|- a \|c \|a x  + b x + c  + (- b x - 2c)\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                   +--------------+
--R               +-+ |   2                            +-+ +-+
--R           (4c\|a \|a x  + b x + c  + (- 2b x - 4c)\|a \|c )
--R        *
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R           log(---------------------------------)
--R                                +-+
--R                             2x\|c
--R       + 
--R                   +--------------+
--R               +-+ |   2               2
--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
--R        *
--R           log
--R                              2           +-+          2              2  +-+
--R                    ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
--R                 *
--R                     +--------------+
--R                     |   2
--R                    \|a x  + b x + c
--R                + 
--R                           3              2  2              2  +-+ +-+     2   3
--R                  (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
--R                + 
--R                          2       2
--R                  6a b c x  + 8a c x
--R             /
--R                                 +--------------+
--R                              2  |   2
--R                  (4b c x + 8c )\|a x  + b x + c
--R                + 
--R                              2  2              2  +-+
--R                  ((- 4a c - b )x  - 8b c x - 8c )\|c
--R       + 
--R                    +--------------+
--R                +-+ |   2                   2         +-+ +-+
--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
--R    /
--R                 +--------------+
--R         +-+ +-+ |   2                            +-+
--R       4\|a \|c \|a x  + b x + c  + (- 2b x - 4c)\|a
--R     ,
--R
--R                     +--------------+
--R               +---+ |   2                           +---+ +-+
--R           (2c\|- a \|a x  + b x + c  + (- b x - 2c)\|- a \|c )
--R        *
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R           log(---------------------------------)
--R                                +-+
--R                             2x\|c
--R       + 
--R                   +--------------+
--R               +-+ |   2               2
--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
--R        *
--R                           +--------------+
--R                 +---+ +-+ |   2                +---+
--R                \|- a \|c \|a x  + b x + c  - c\|- a
--R           atan(-------------------------------------)
--R                                   +-+
--R                               a x\|c
--R       + 
--R                     +--------------+
--R               +---+ |   2                   2        +---+ +-+
--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
--R    /
--R                   +--------------+
--R         +---+ +-+ |   2                           +---+
--R       2\|- a \|c \|a x  + b x + c  + (- b x - 2c)\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 72
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 73
t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (3)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (3)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 74
bb1:=sqrt(a*x^2+b*x+c)+b/2*t1.1+c*t2
 

   (4)
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|a log(---------------------------------)
                                 x
     + 
           +-+
         b\|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                 +--------------+
         +-+ +-+ |   2
       2\|a \|c \|a x  + b x + c
  /
       +-+ +-+
     2\|a \|c
                                                     Type: Expression Integer
--R
--R   (4)
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|a log(---------------------------------)
--R                                 x
--R     + 
--R           +-+
--R         b\|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                 +--------------+
--R         +-+ +-+ |   2
--R       2\|a \|c \|a x  + b x + c
--R  /
--R       +-+ +-+
--R     2\|a \|c
--R                                                     Type: Expression Integer
--E

--S 75
bb2:=sqrt(a*x^2+b*x+c)+b/2*t1.2+c*t2
 

   (5)
                        +--------------+
                    +-+ |   2
         +---+    2\|c \|a x  + b x + c  - b x - 2c
       c\|- a log(---------------------------------)
                                  x
     + 
                        +--------------+
                  +---+ |   2               +---+ +-+
         +-+     \|- a \|a x  + b x + c  - \|- a \|c
       b\|c atan(------------------------------------)
                                  a x
     + 
                  +--------------+
        +---+ +-+ |   2
       \|- a \|c \|a x  + b x + c
  /
      +---+ +-+
     \|- a \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                        +--------------+
--R                    +-+ |   2
--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       c\|- a log(---------------------------------)
--R                                  x
--R     + 
--R                        +--------------+
--R                  +---+ |   2               +---+ +-+
--R         +-+     \|- a \|a x  + b x + c  - \|- a \|c
--R       b\|c atan(------------------------------------)
--R                                  a x
--R     + 
--R                  +--------------+
--R        +---+ +-+ |   2
--R       \|- a \|c \|a x  + b x + c
--R  /
--R      +---+ +-+
--R     \|- a \|c
--R                                                     Type: Expression Integer
--E

--S 76
cc1:=aa.1-bb1
 

   (6)
                         +--------------+
                     +-+ |   2
            +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2c\|a log(---------------------------------)
                                   x
     + 
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|a log(---------------------------------)
                                  +-+
                               2x\|c
     + 
       -
              +-+
            b\|c
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
           +-+
         b\|c
      *
         log
                            2           +-+          2              2  +-+
                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
               *
                   +--------------+
                   |   2
                  \|a x  + b x + c
              + 
                         3              2  2              2  +-+ +-+     2   3
                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
              + 
                        2       2
                6a b c x  + 8a c x
           /
                               +--------------+
                            2  |   2
                (4b c x + 8c )\|a x  + b x + c
              + 
                            2  2              2  +-+
                ((- 4a c - b )x  - 8b c x - 8c )\|c
     + 
          +-+
       2c\|a
  /
       +-+ +-+
     2\|a \|c
                                                     Type: Expression Integer
--R
--R   (6)
--R                         +--------------+
--R                     +-+ |   2
--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2c\|a log(---------------------------------)
--R                                   x
--R     + 
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|a log(---------------------------------)
--R                                  +-+
--R                               2x\|c
--R     + 
--R       -
--R              +-+
--R            b\|c
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R           +-+
--R         b\|c
--R      *
--R         log
--R                            2           +-+          2              2  +-+
--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
--R               *
--R                   +--------------+
--R                   |   2
--R                  \|a x  + b x + c
--R              + 
--R                         3              2  2              2  +-+ +-+     2   3
--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
--R              + 
--R                        2       2
--R                6a b c x  + 8a c x
--R           /
--R                               +--------------+
--R                            2  |   2
--R                (4b c x + 8c )\|a x  + b x + c
--R              + 
--R                            2  2              2  +-+
--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
--R     + 
--R          +-+
--R       2c\|a
--R  /
--R       +-+ +-+
--R     2\|a \|c
--R                                                     Type: Expression Integer
--E

--S 77
cc2:=aa.2-bb1
 

   (7)
                               +--------------+
                           +-+ |   2
            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2c\|- a \|a log(---------------------------------)
                                         x
     + 
                             +--------------+
                         +-+ |   2
          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|- a \|a log(---------------------------------)
                                        +-+
                                     2x\|c
     + 
       -
              +---+ +-+
            b\|- a \|c
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
                                 +--------------+
                       +---+ +-+ |   2                +---+
          +-+ +-+     \|- a \|c \|a x  + b x + c  - c\|- a        +---+ +-+
       2b\|a \|c atan(-------------------------------------) + 2c\|- a \|a
                                         +-+
                                     a x\|c
  /
       +---+ +-+ +-+
     2\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (7)
--R                               +--------------+
--R                           +-+ |   2
--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2c\|- a \|a log(---------------------------------)
--R                                         x
--R     + 
--R                             +--------------+
--R                         +-+ |   2
--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|- a \|a log(---------------------------------)
--R                                        +-+
--R                                     2x\|c
--R     + 
--R       -
--R              +---+ +-+
--R            b\|- a \|c
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                 +--------------+
--R                       +---+ +-+ |   2                +---+
--R          +-+ +-+     \|- a \|c \|a x  + b x + c  - c\|- a        +---+ +-+
--R       2b\|a \|c atan(-------------------------------------) + 2c\|- a \|a
--R                                         +-+
--R                                     a x\|c
--R  /
--R       +---+ +-+ +-+
--R     2\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 78
cc3:=aa.1-bb2
 

   (8)
                               +--------------+
                           +-+ |   2
            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2c\|- a \|a log(---------------------------------)
                                         x
     + 
                             +--------------+
                         +-+ |   2
          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|- a \|a log(---------------------------------)
                                        +-+
                                     2x\|c
     + 
           +---+ +-+
         b\|- a \|c
      *
         log
                            2           +-+          2              2  +-+
                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
               *
                   +--------------+
                   |   2
                  \|a x  + b x + c
              + 
                         3              2  2              2  +-+ +-+     2   3
                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
              + 
                        2       2
                6a b c x  + 8a c x
           /
                               +--------------+
                            2  |   2
                (4b c x + 8c )\|a x  + b x + c
              + 
                            2  2              2  +-+
                ((- 4a c - b )x  - 8b c x - 8c )\|c
     + 
                               +--------------+
                         +---+ |   2               +---+ +-+
            +-+ +-+     \|- a \|a x  + b x + c  - \|- a \|c        +---+ +-+
       - 2b\|a \|c atan(------------------------------------) + 2c\|- a \|a
                                         a x
  /
       +---+ +-+ +-+
     2\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (8)
--R                               +--------------+
--R                           +-+ |   2
--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2c\|- a \|a log(---------------------------------)
--R                                         x
--R     + 
--R                             +--------------+
--R                         +-+ |   2
--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|- a \|a log(---------------------------------)
--R                                        +-+
--R                                     2x\|c
--R     + 
--R           +---+ +-+
--R         b\|- a \|c
--R      *
--R         log
--R                            2           +-+          2              2  +-+
--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
--R               *
--R                   +--------------+
--R                   |   2
--R                  \|a x  + b x + c
--R              + 
--R                         3              2  2              2  +-+ +-+     2   3
--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
--R              + 
--R                        2       2
--R                6a b c x  + 8a c x
--R           /
--R                               +--------------+
--R                            2  |   2
--R                (4b c x + 8c )\|a x  + b x + c
--R              + 
--R                            2  2              2  +-+
--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
--R     + 
--R                               +--------------+
--R                         +---+ |   2               +---+ +-+
--R            +-+ +-+     \|- a \|a x  + b x + c  - \|- a \|c        +---+ +-+
--R       - 2b\|a \|c atan(------------------------------------) + 2c\|- a \|a
--R                                         a x
--R  /
--R       +---+ +-+ +-+
--R     2\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 79
cc4:=aa.2-bb2
 

   (9)
                          +--------------+
                      +-+ |   2
           +---+    2\|c \|a x  + b x + c  - b x - 2c
       - c\|- a log(---------------------------------)
                                    x
     + 
                        +--------------+
                    +-+ |   2
         +---+    2\|c \|a x  + b x + c  - b x - 2c
       c\|- a log(---------------------------------)
                                   +-+
                                2x\|c
     + 
                            +--------------+
                  +---+ +-+ |   2                +---+
         +-+     \|- a \|c \|a x  + b x + c  - c\|- a
       b\|c atan(-------------------------------------)
                                    +-+
                                a x\|c
     + 
                          +--------------+
                    +---+ |   2               +---+ +-+
           +-+     \|- a \|a x  + b x + c  - \|- a \|c       +---+
       - b\|c atan(------------------------------------) + c\|- a
                                    a x
  /
      +---+ +-+
     \|- a \|c
                                                     Type: Expression Integer
--R
--R   (9)
--R                          +--------------+
--R                      +-+ |   2
--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       - c\|- a log(---------------------------------)
--R                                    x
--R     + 
--R                        +--------------+
--R                    +-+ |   2
--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       c\|- a log(---------------------------------)
--R                                   +-+
--R                                2x\|c
--R     + 
--R                            +--------------+
--R                  +---+ +-+ |   2                +---+
--R         +-+     \|- a \|c \|a x  + b x + c  - c\|- a
--R       b\|c atan(-------------------------------------)
--R                                    +-+
--R                                a x\|c
--R     + 
--R                          +--------------+
--R                    +---+ |   2               +---+ +-+
--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c       +---+
--R       - b\|c atan(------------------------------------) + c\|- a
--R                                    a x
--R  /
--R      +---+ +-+
--R     \|- a \|c
--R                                                     Type: Expression Integer
--E

--S 80
dd4:=ratDenom cc4
 

   (10)
                     +--------------+
                 +-+ |   2
        +-+    2\|c \|a x  + b x + c  - b x - 2c
     - \|c log(---------------------------------)
                               x
   + 
                +--------------+
                |   2                           +-+
      +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
     \|c log(--------------------------------------) + \|c
                              2c x
                                                     Type: Expression Integer
--R
--R   (10)
--R                     +--------------+
--R                 +-+ |   2
--R        +-+    2\|c \|a x  + b x + c  - b x - 2c
--R     - \|c log(---------------------------------)
--R                               x
--R   + 
--R                +--------------+
--R                |   2                           +-+
--R      +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
--R     \|c log(--------------------------------------) + \|c
--R                              2c x
--R                                                     Type: Expression Integer
--E

--S 81
ee4:=expandLog dd4
 

   (11)
                     +--------------+
        +-+      +-+ |   2
     - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
   + 
              +--------------+
    +-+       |   2                           +-+                            +-+
   \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c ) + (- log(c) - log(2) + 1)\|c
                                                     Type: Expression Integer
--R
--R   (11)
--R                     +--------------+
--R        +-+      +-+ |   2
--R     - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R   + 
--R              +--------------+
--R    +-+       |   2                           +-+                            +-+
--R   \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c ) + (- log(c) - log(2) + 1)\|c
--R                                                     Type: Expression Integer
--E

--S 82     14:288 Schaums and Axiom differ by a constant
ff4:=complexNormalize ee4
 

                                  +-+
         (- log(c) - 2log(2) + 2)\|c
   (12)  ----------------------------
                       2
                                                     Type: Expression Integer
--R
--R                                  +-+
--R         (- log(c) - 2log(2) + 2)\|c
--R   (12)  ----------------------------
--R                       2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 83
aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
 

   (1)
   [
                     +--------------+
                 +-+ |   2                2 2
           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
        *
                  +--------------+
                  |   2                           +-+
               2c\|a x  + b x + c  + (- b x - 2c)\|c
           log(--------------------------------------)
                                2c x
       + 
                     +--------------+
                 +-+ |   2                     2         +-+ +-+
           (8c x\|a \|a x  + b x + c  + (- 4b x  - 8c x)\|a \|c )
        *
                              +--------------+
                +-+      +-+  |   2                 +-+ +-+       2
             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
         log(-----------------------------------------------------------------)
                                   +--------------+
                               +-+ |   2
                             2\|c \|a x  + b x + c  - b x - 2c
       + 
                         +--------------+
                     +-+ |   2                         2  2              2
         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
    /
            +--------------+
            |   2                     2         +-+
       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
     ,

                     +--------------+
                 +-+ |   2                2 2
           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
        *
                  +--------------+
                  |   2                           +-+
               2c\|a x  + b x + c  + (- b x - 2c)\|c
           log(--------------------------------------)
                                2c x
       + 
                        +--------------+
                  +---+ |   2                     2          +---+ +-+
           (16c x\|- a \|a x  + b x + c  + (- 8b x  - 16c x)\|- a \|c )
        *
                 +--------------+
                 |   2               +-+
                \|a x  + b x + c  - \|c
           atan(------------------------)
                           +---+
                         x\|- a
       + 
                         +--------------+
                     +-+ |   2                         2  2              2
         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
    /
            +--------------+
            |   2                     2         +-+
       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                     +--------------+
--R                 +-+ |   2                2 2
--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
--R        *
--R                  +--------------+
--R                  |   2                           +-+
--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
--R           log(--------------------------------------)
--R                                2c x
--R       + 
--R                     +--------------+
--R                 +-+ |   2                     2         +-+ +-+
--R           (8c x\|a \|a x  + b x + c  + (- 4b x  - 8c x)\|a \|c )
--R        *
--R                              +--------------+
--R                +-+      +-+  |   2                 +-+ +-+       2
--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
--R         log(-----------------------------------------------------------------)
--R                                   +--------------+
--R                               +-+ |   2
--R                             2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                         +--------------+
--R                     +-+ |   2                         2  2              2
--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
--R    /
--R            +--------------+
--R            |   2                     2         +-+
--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
--R     ,
--R
--R                     +--------------+
--R                 +-+ |   2                2 2
--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
--R        *
--R                  +--------------+
--R                  |   2                           +-+
--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
--R           log(--------------------------------------)
--R                                2c x
--R       + 
--R                        +--------------+
--R                  +---+ |   2                     2          +---+ +-+
--R           (16c x\|- a \|a x  + b x + c  + (- 8b x  - 16c x)\|- a \|c )
--R        *
--R                 +--------------+
--R                 |   2               +-+
--R                \|a x  + b x + c  - \|c
--R           atan(------------------------)
--R                           +---+
--R                         x\|- a
--R       + 
--R                         +--------------+
--R                     +-+ |   2                         2  2              2
--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
--R    /
--R            +--------------+
--R            |   2                     2         +-+
--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 84
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 85
t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (3)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (3)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 86
bb1:=-sqrt(a*x^2+b*x+c)/x+a*t1.1+b/2*t2
 

   (4)
                        +--------------+
                    +-+ |   2
           +-+    2\|c \|a x  + b x + c  - b x - 2c
       b x\|a log(---------------------------------)
                                  x
     + 
              +-+
         2a x\|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   +--------------+
           +-+ +-+ |   2
       - 2\|a \|c \|a x  + b x + c
  /
        +-+ +-+
     2x\|a \|c
                                                     Type: Expression Integer
--R
--R   (4)
--R                        +--------------+
--R                    +-+ |   2
--R           +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       b x\|a log(---------------------------------)
--R                                  x
--R     + 
--R              +-+
--R         2a x\|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   +--------------+
--R           +-+ +-+ |   2
--R       - 2\|a \|c \|a x  + b x + c
--R  /
--R        +-+ +-+
--R     2x\|a \|c
--R                                                     Type: Expression Integer
--E

--S 87
bb2:=-sqrt(a*x^2+b*x+c)/x+a*t1.2+b/2*t2
 

   (5)
                          +--------------+
                      +-+ |   2
           +---+    2\|c \|a x  + b x + c  - b x - 2c
       b x\|- a log(---------------------------------)
                                    x
     + 
                           +--------------+
                     +---+ |   2               +---+ +-+
            +-+     \|- a \|a x  + b x + c  - \|- a \|c
       4a x\|c atan(------------------------------------)
                                     a x
     + 
                     +--------------+
           +---+ +-+ |   2
       - 2\|- a \|c \|a x  + b x + c
  /
        +---+ +-+
     2x\|- a \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                          +--------------+
--R                      +-+ |   2
--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       b x\|- a log(---------------------------------)
--R                                    x
--R     + 
--R                           +--------------+
--R                     +---+ |   2               +---+ +-+
--R            +-+     \|- a \|a x  + b x + c  - \|- a \|c
--R       4a x\|c atan(------------------------------------)
--R                                     a x
--R     + 
--R                     +--------------+
--R           +---+ +-+ |   2
--R       - 2\|- a \|c \|a x  + b x + c
--R  /
--R        +---+ +-+
--R     2x\|- a \|c
--R                                                     Type: Expression Integer
--E

--S 88
cc1:=aa.1-bb1
 

   (6)
                     +--------------+
                 +-+ |   2                 2          +-+ +-+
         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                   +--------------+
               +-+ |   2                   2          +-+ +-+
         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                     +--------------+
                 +-+ |   2                             2
         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   +--------------+
               +-+ |   2                             2
         (8a c\|c \|a x  + b x + c  - 4a b c x - 8a c )
      *
                              +--------------+
                +-+      +-+  |   2                 +-+ +-+       2
             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
         log(-----------------------------------------------------------------)
                                   +--------------+
                               +-+ |   2
                             2\|c \|a x  + b x + c  - b x - 2c
     + 
                  +--------------+
              +-+ |   2                2          +-+ +-+
       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
  /
                +--------------+
        +-+ +-+ |   2                            2  +-+
     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                     +--------------+
--R                 +-+ |   2                 2          +-+ +-+
--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                   +--------------+
--R               +-+ |   2                   2          +-+ +-+
--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                     +--------------+
--R                 +-+ |   2                             2
--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   +--------------+
--R               +-+ |   2                             2
--R         (8a c\|c \|a x  + b x + c  - 4a b c x - 8a c )
--R      *
--R                              +--------------+
--R                +-+      +-+  |   2                 +-+ +-+       2
--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
--R         log(-----------------------------------------------------------------)
--R                                   +--------------+
--R                               +-+ |   2
--R                             2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                  +--------------+
--R              +-+ |   2                2          +-+ +-+
--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
--R  /
--R                +--------------+
--R        +-+ +-+ |   2                            2  +-+
--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
--R                                                     Type: Expression Integer
--E

--S 89
cc2:=aa.2-bb1
 

   (7)
                     +--------------+
                 +-+ |   2                 2          +-+ +-+
         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                   +--------------+
               +-+ |   2                   2          +-+ +-+
         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                     +--------------+
                 +-+ |   2                             2
         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                            +--------------+
              +---+ +-+ +-+ |   2                             2  +---+ +-+
         (16c\|- a \|a \|c \|a x  + b x + c  + (- 8b c x - 16c )\|- a \|a )
      *
               +--------------+
               |   2               +-+
              \|a x  + b x + c  - \|c
         atan(------------------------)
                         +---+
                       x\|- a
     + 
                  +--------------+
              +-+ |   2                2          +-+ +-+
       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
  /
                +--------------+
        +-+ +-+ |   2                            2  +-+
     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                     +--------------+
--R                 +-+ |   2                 2          +-+ +-+
--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                   +--------------+
--R               +-+ |   2                   2          +-+ +-+
--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                     +--------------+
--R                 +-+ |   2                             2
--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                            +--------------+
--R              +---+ +-+ +-+ |   2                             2  +---+ +-+
--R         (16c\|- a \|a \|c \|a x  + b x + c  + (- 8b c x - 16c )\|- a \|a )
--R      *
--R               +--------------+
--R               |   2               +-+
--R              \|a x  + b x + c  - \|c
--R         atan(------------------------)
--R                         +---+
--R                       x\|- a
--R     + 
--R                  +--------------+
--R              +-+ |   2                2          +-+ +-+
--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
--R  /
--R                +--------------+
--R        +-+ +-+ |   2                            2  +-+
--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
--R                                                     Type: Expression Integer
--E

--S 90
cc3:=aa.1-bb2
 

   (8)
                       +--------------+
                 +---+ |   2                 2          +---+ +-+
         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                     +--------------+
               +---+ |   2                   2          +---+ +-+
         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                           +--------------+
             +---+ +-+ +-+ |   2                            2  +---+ +-+
         (8c\|- a \|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a \|a )
      *
                              +--------------+
                +-+      +-+  |   2                 +-+ +-+       2
             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
         log(-----------------------------------------------------------------)
                                   +--------------+
                               +-+ |   2
                             2\|c \|a x  + b x + c  - b x - 2c
     + 
                      +--------------+
                  +-+ |   2                              2
         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                    +--------------+
              +---+ |   2                2          +---+ +-+
       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
  /
                  +--------------+
        +---+ +-+ |   2                            2  +---+
     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
                                                     Type: Expression Integer
--R
--R   (8)
--R                       +--------------+
--R                 +---+ |   2                 2          +---+ +-+
--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                     +--------------+
--R               +---+ |   2                   2          +---+ +-+
--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                           +--------------+
--R             +---+ +-+ +-+ |   2                            2  +---+ +-+
--R         (8c\|- a \|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a \|a )
--R      *
--R                              +--------------+
--R                +-+      +-+  |   2                 +-+ +-+       2
--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
--R         log(-----------------------------------------------------------------)
--R                                   +--------------+
--R                               +-+ |   2
--R                             2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                      +--------------+
--R                  +-+ |   2                              2
--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                    +--------------+
--R              +---+ |   2                2          +---+ +-+
--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
--R  /
--R                  +--------------+
--R        +---+ +-+ |   2                            2  +---+
--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
--R                                                     Type: Expression Integer
--E

--S 91
cc4:=aa.2-bb2
 

   (9)
                       +--------------+
                 +---+ |   2                 2          +---+ +-+
         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                     +--------------+
               +---+ |   2                   2          +---+ +-+
         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                      +--------------+
                  +-+ |   2                              2
         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                      +--------------+
                  +-+ |   2                              2
         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
      *
               +--------------+
               |   2               +-+
              \|a x  + b x + c  - \|c
         atan(------------------------)
                         +---+
                       x\|- a
     + 
                    +--------------+
              +---+ |   2                2          +---+ +-+
       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
  /
                  +--------------+
        +---+ +-+ |   2                            2  +---+
     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
                                                     Type: Expression Integer
--R
--R   (9)
--R                       +--------------+
--R                 +---+ |   2                 2          +---+ +-+
--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                     +--------------+
--R               +---+ |   2                   2          +---+ +-+
--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                      +--------------+
--R                  +-+ |   2                              2
--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                      +--------------+
--R                  +-+ |   2                              2
--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
--R      *
--R               +--------------+
--R               |   2               +-+
--R              \|a x  + b x + c  - \|c
--R         atan(------------------------)
--R                         +---+
--R                       x\|- a
--R     + 
--R                    +--------------+
--R              +---+ |   2                2          +---+ +-+
--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
--R  /
--R                  +--------------+
--R        +---+ +-+ |   2                            2  +---+
--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
--R                                                     Type: Expression Integer
--E

--S 92
dd4:=ratDenom cc4
 

   (10)
                         +--------------+
                     +-+ |   2
            +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2b\|c log(---------------------------------)
                                   x
     + 
                    +--------------+
                    |   2                           +-+
          +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c       +-+
       2b\|c log(--------------------------------------) - b\|c
                                  2c x
  /
     4c
                                                     Type: Expression Integer
--R
--R   (10)
--R                         +--------------+
--R                     +-+ |   2
--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2b\|c log(---------------------------------)
--R                                   x
--R     + 
--R                    +--------------+
--R                    |   2                           +-+
--R          +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c       +-+
--R       2b\|c log(--------------------------------------) - b\|c
--R                                  2c x
--R  /
--R     4c
--R                                                     Type: Expression Integer
--E

--S 93
ee4:=expandLog dd4
 

   (11)
                         +--------------+
            +-+      +-+ |   2
       - 2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                    +--------------+
          +-+       |   2                           +-+
       2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                     +-+
       (- 2b log(c) - 2b log(2) - b)\|c
  /
     4c
                                                     Type: Expression Integer
--R
--R   (11)
--R                         +--------------+
--R            +-+      +-+ |   2
--R       - 2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                    +--------------+
--R          +-+       |   2                           +-+
--R       2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                     +-+
--R       (- 2b log(c) - 2b log(2) - b)\|c
--R  /
--R     4c
--R                                                     Type: Expression Integer
--E

--S 94     14:289 Schaums and Axiom differ by a constant
ff4:=complexNormalize ee4
 

                                      +-+
         (- b log(c) - 2b log(2) - b)\|c
   (12)  --------------------------------
                        4c
                                                     Type: Expression Integer
--R
--R                                      +-+
--R         (- b log(c) - 2b log(2) - b)\|c
--R   (12)  --------------------------------
--R                        4c
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 95
aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 

                          +--------------+
                          |   2                 +-+
                     - 2x\|a x  + b x + c  + 2x\|c
   (1)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +--------------+
--R                          |   2                 +-+
--R                     - 2x\|a x  + b x + c  + 2x\|c
--R   (1)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 96
bb:=(2*(2*a*x+b))/((4*a*c-b^2)*sqrt(a*x^2+b*x+c))
 

                  4a x + 2b
   (2)  ----------------------------
                    +--------------+
                 2  |   2
        (4a c - b )\|a x  + b x + c
                                                     Type: Expression Integer
--R
--R                  4a x + 2b
--R   (2)  ----------------------------
--R                    +--------------+
--R                 2  |   2
--R        (4a c - b )\|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 97
cc:=aa-bb
 

   (3)
                           +--------------+
                       +-+ |   2                2
                    4b\|c \|a x  + b x + c  - 2b x - 4b c
   -----------------------------------------------------------------------
                  +--------------+
        2     2   |   2                            3         2     2   +-+
   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
                                                     Type: Expression Integer
--R
--R   (3)
--R                           +--------------+
--R                       +-+ |   2                2
--R                    4b\|c \|a x  + b x + c  - 2b x - 4b c
--R   -----------------------------------------------------------------------
--R                  +--------------+
--R        2     2   |   2                            3         2     2   +-+
--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
--R                                                     Type: Expression Integer
--E

--S 98     14:290 Schaums and Axiom differ by a constant
dd:=ratDenom cc
 

              +-+
           2b\|c
   (4)  -----------
            2    2
        4a c  - b c
                                                     Type: Expression Integer
--R
--R              +-+
--R           2b\|c
--R   (4)  -----------
--R            2    2
--R        4a c  - b c
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 99
aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
 

                                   2 +-+
                                 2x \|c
   (1)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                   2 +-+
--R                                 2x \|c
--R   (1)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 100
bb:=(2*(b*x+2*c))/((b^2-4*a*c)*sqrt(a*x^2+b*x+c))
 

                 - 2b x - 4c
   (2)  ----------------------------
                    +--------------+
                 2  |   2
        (4a c - b )\|a x  + b x + c
                                                     Type: Expression Integer
--R
--R                 - 2b x - 4c
--R   (2)  ----------------------------
--R                    +--------------+
--R                 2  |   2
--R        (4a c - b )\|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 101
cc:=aa-bb
 

   (3)
                            +--------------+
                        +-+ |   2                         2
                   - 8c\|c \|a x  + b x + c  + 4b c x + 8c
   -----------------------------------------------------------------------
                  +--------------+
        2     2   |   2                            3         2     2   +-+
   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
                                                     Type: Expression Integer
--R
--R   (3)
--R                            +--------------+
--R                        +-+ |   2                         2
--R                   - 8c\|c \|a x  + b x + c  + 4b c x + 8c
--R   -----------------------------------------------------------------------
--R                  +--------------+
--R        2     2   |   2                            3         2     2   +-+
--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
--R                                                     Type: Expression Integer
--E

--S 102    14:291 Schaums and Axiom differ by a constant
dd:=ratDenom cc
 

              +-+
            4\|c
   (4)  - ---------
                  2
          4a c - b
                                                     Type: Expression Integer
--R
--R              +-+
--R            4\|c
--R   (4)  - ---------
--R                  2
--R          4a c - b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 103
aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
 

   (1)
   [
                           +--------------+
                       +-+ |   2                    2              2
           ((b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c )
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  +--------------+
              +-+ |   2                     2         +-+ +-+
         2c x\|a \|a x  + b x + c  + (- 2b x  - 2c x)\|a \|c
    /
                                +--------------+
                        +-+ +-+ |   2
         (a b x + 2a c)\|a \|c \|a x  + b x + c
       + 
              2   2                  2  +-+
         (- 2a c x  - 2a b c x - 2a c )\|a
     ,

                            +--------------+
                        +-+ |   2                    2              2
           ((2b x + 4c)\|c \|a x  + b x + c  - 4a c x  - 4b c x - 4c )
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                    +--------------+
              +---+ |   2                     2         +---+ +-+
         2c x\|- a \|a x  + b x + c  + (- 2b x  - 2c x)\|- a \|c
    /
                                  +--------------+
                        +---+ +-+ |   2
         (a b x + 2a c)\|- a \|c \|a x  + b x + c
       + 
              2   2                  2  +---+
         (- 2a c x  - 2a b c x - 2a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                           +--------------+
--R                       +-+ |   2                    2              2
--R           ((b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c )
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  +--------------+
--R              +-+ |   2                     2         +-+ +-+
--R         2c x\|a \|a x  + b x + c  + (- 2b x  - 2c x)\|a \|c
--R    /
--R                                +--------------+
--R                        +-+ +-+ |   2
--R         (a b x + 2a c)\|a \|c \|a x  + b x + c
--R       + 
--R              2   2                  2  +-+
--R         (- 2a c x  - 2a b c x - 2a c )\|a
--R     ,
--R
--R                            +--------------+
--R                        +-+ |   2                    2              2
--R           ((2b x + 4c)\|c \|a x  + b x + c  - 4a c x  - 4b c x - 4c )
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                    +--------------+
--R              +---+ |   2                     2         +---+ +-+
--R         2c x\|- a \|a x  + b x + c  + (- 2b x  - 2c x)\|- a \|c
--R    /
--R                                  +--------------+
--R                        +---+ +-+ |   2
--R         (a b x + 2a c)\|- a \|c \|a x  + b x + c
--R       + 
--R              2   2                  2  +---+
--R         (- 2a c x  - 2a b c x - 2a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 104
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 105
bb1:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.1
 

   (3)
                     +--------------+
                  2  |   2
         (4a c - b )\|a x  + b x + c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                    2           +-+
       ((- 4a c + 2b )x + 2b c)\|a
  /
                       +--------------+
        2       2  +-+ |   2
     (4a c - a b )\|a \|a x  + b x + c
                                                     Type: Expression Integer
--R
--R   (3)
--R                     +--------------+
--R                  2  |   2
--R         (4a c - b )\|a x  + b x + c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                    2           +-+
--R       ((- 4a c + 2b )x + 2b c)\|a
--R  /
--R                       +--------------+
--R        2       2  +-+ |   2
--R     (4a c - a b )\|a \|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 106
bb2:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.2
 

   (4)
                                                +--------------+
                    +--------------+      +---+ |   2               +---+ +-+
                 2  |   2                \|- a \|a x  + b x + c  - \|- a \|c
       (8a c - 2b )\|a x  + b x + c atan(------------------------------------)
                                                          a x
     + 
                    2           +---+
       ((- 4a c + 2b )x + 2b c)\|- a
  /
                         +--------------+
        2       2  +---+ |   2
     (4a c - a b )\|- a \|a x  + b x + c
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                +--------------+
--R                    +--------------+      +---+ |   2               +---+ +-+
--R                 2  |   2                \|- a \|a x  + b x + c  - \|- a \|c
--R       (8a c - 2b )\|a x  + b x + c atan(------------------------------------)
--R                                                          a x
--R     + 
--R                    2           +---+
--R       ((- 4a c + 2b )x + 2b c)\|- a
--R  /
--R                         +--------------+
--R        2       2  +---+ |   2
--R     (4a c - a b )\|- a \|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 107
cc1:=aa.1-bb1
 

   (5)
                              +--------------+
                          +-+ |   2                2          2
                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
   -----------------------------------------------------------------------------
                    +--------------+
      2 2       2   |   2                    2         3       2 2       2   +-+
   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                              +--------------+
--R                          +-+ |   2                2          2
--R                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
--R   -----------------------------------------------------------------------------
--R                    +--------------+
--R      2 2       2   |   2                    2         3       2 2       2   +-+
--R   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
--R                                                     Type: Expression Integer
--E

--S 108
cc2:=aa.2-bb1
 

   (6)
                                  +--------------+
                  2     2   +---+ |   2
           (- 8a c  + 2b c)\|- a \|a x  + b x + c
         + 
                       3         2     2   +---+ +-+
           ((4a b c - b )x + 8a c  - 2b c)\|- a \|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                               +--------------+
                 2     2   +-+ |   2
           (16a c  - 4b c)\|a \|a x  + b x + c
         + 
                          3          2     2   +-+ +-+
           ((- 8a b c + 2b )x - 16a c  + 4b c)\|a \|c
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                          +--------------+
            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
  /
                                  +--------------+
          2 2       2   +---+ +-+ |   2
       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
     + 
             2         3       2 2       2   +---+ +-+ +-+
       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (6)
--R                                  +--------------+
--R                  2     2   +---+ |   2
--R           (- 8a c  + 2b c)\|- a \|a x  + b x + c
--R         + 
--R                       3         2     2   +---+ +-+
--R           ((4a b c - b )x + 8a c  - 2b c)\|- a \|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                               +--------------+
--R                 2     2   +-+ |   2
--R           (16a c  - 4b c)\|a \|a x  + b x + c
--R         + 
--R                          3          2     2   +-+ +-+
--R           ((- 8a b c + 2b )x - 16a c  + 4b c)\|a \|c
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                          +--------------+
--R            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
--R       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
--R  /
--R                                  +--------------+
--R          2 2       2   +---+ +-+ |   2
--R       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
--R     + 
--R             2         3       2 2       2   +---+ +-+ +-+
--R       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 109
cc3:=aa.1-bb2
 

   (7)
                                +--------------+
                2     2   +---+ |   2
           (8a c  - 2b c)\|- a \|a x  + b x + c
         + 
                         3         2     2   +---+ +-+
           ((- 4a b c + b )x - 8a c  + 2b c)\|- a \|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                 +--------------+
                   2     2   +-+ |   2
           (- 16a c  + 4b c)\|a \|a x  + b x + c
         + 
                        3          2     2   +-+ +-+
           ((8a b c - 2b )x + 16a c  - 4b c)\|a \|c
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                          +--------------+
            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
  /
                                  +--------------+
          2 2       2   +---+ +-+ |   2
       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
     + 
             2         3       2 2       2   +---+ +-+ +-+
       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (7)
--R                                +--------------+
--R                2     2   +---+ |   2
--R           (8a c  - 2b c)\|- a \|a x  + b x + c
--R         + 
--R                         3         2     2   +---+ +-+
--R           ((- 4a b c + b )x - 8a c  + 2b c)\|- a \|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                 +--------------+
--R                   2     2   +-+ |   2
--R           (- 16a c  + 4b c)\|a \|a x  + b x + c
--R         + 
--R                        3          2     2   +-+ +-+
--R           ((8a b c - 2b )x + 16a c  - 4b c)\|a \|c
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                          +--------------+
--R            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
--R       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
--R  /
--R                                  +--------------+
--R          2 2       2   +---+ +-+ |   2
--R       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
--R     + 
--R             2         3       2 2       2   +---+ +-+ +-+
--R       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 110
cc4:=aa.2-bb2
 

   (8)
                              +--------------+
                          +-+ |   2                2          2
                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
   -----------------------------------------------------------------------------
                    +--------------+
      2 2       2   |   2                    2         3       2 2       2   +-+
   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
                                                     Type: Expression Integer
--R
--R   (8)
--R                              +--------------+
--R                          +-+ |   2                2          2
--R                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
--R   -----------------------------------------------------------------------------
--R                    +--------------+
--R      2 2       2   |   2                    2         3       2 2       2   +-+
--R   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
--R                                                     Type: Expression Integer
--E

--S 111    14:292 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

              +-+
           2b\|c
   (9)  -----------
          2       2
        4a c - a b
                                                     Type: Expression Integer
--R
--R              +-+
--R           2b\|c
--R   (9)  -----------
--R          2       2
--R        4a c - a b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 112
aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
 

   (1)
                     +--------------+
                     |   2                     2              +-+
         ((b x + 2c)\|a x  + b x + c  + (- 2a x  - 2b x - 2c)\|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
            +--------------+
            |   2                     2         +-+
       2b x\|a x  + b x + c  + (- 2a x  - 2b x)\|c
  /
                       +--------------+
                2  +-+ |   2                  2 2       2      3
     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     +--------------+
--R                     |   2                     2              +-+
--R         ((b x + 2c)\|a x  + b x + c  + (- 2a x  - 2b x - 2c)\|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R            +--------------+
--R            |   2                     2         +-+
--R       2b x\|a x  + b x + c  + (- 2a x  - 2b x)\|c
--R  /
--R                       +--------------+
--R                2  +-+ |   2                  2 2       2      3
--R     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 113
t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (2)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (2)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 114
t2:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 

                          +--------------+
                          |   2                 +-+
                     - 2x\|a x  + b x + c  + 2x\|c
   (3)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R
--R                          +--------------+
--R                          |   2                 +-+
--R                     - 2x\|a x  + b x + c  + 2x\|c
--R   (3)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E

--S 115
bb:=1/(c*sqrt(a*x^2+b*x+c))+1/c*t1-b/(2*c)*t2
 

   (4)
                                    +--------------+
                  2              2  |   2
           (2a c x  + 2b c x + 2c )\|a x  + b x + c
         + 
                   3              2  2              2  +-+
           (- a b x  + (- 2a c - b )x  - 3b c x - 2c )\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
             +--------------+
           2 |   2                      3            2  2             2  +-+
       - 2c \|a x  + b x + c  + (- a b x  + (2a c - b )x  + b c x + 2c )\|c
  /
                                    +--------------+
            2 2       2      3  +-+ |   2                   2 3
       (2a c x  + 2b c x + 2c )\|c \|a x  + b x + c  - a b c x
     + 
              3    2 2  2       3      4
       (- 2a c  - b c )x  - 3b c x - 2c
                                                     Type: Expression Integer
--R
--R   (4)
--R                                    +--------------+
--R                  2              2  |   2
--R           (2a c x  + 2b c x + 2c )\|a x  + b x + c
--R         + 
--R                   3              2  2              2  +-+
--R           (- a b x  + (- 2a c - b )x  - 3b c x - 2c )\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R             +--------------+
--R           2 |   2                      3            2  2             2  +-+
--R       - 2c \|a x  + b x + c  + (- a b x  + (2a c - b )x  + b c x + 2c )\|c
--R  /
--R                                    +--------------+
--R            2 2       2      3  +-+ |   2                   2 3
--R       (2a c x  + 2b c x + 2c )\|c \|a x  + b x + c  - a b c x
--R     + 
--R              3    2 2  2       3      4
--R       (- 2a c  - b c )x  - 3b c x - 2c
--R                                                     Type: Expression Integer
--E

--S 116
cc:=aa-bb
 

   (5)
                                            +--------------+
                       2  2              2  |   2
           ((- 4a c - b )x  - 8b c x - 8c )\|a x  + b x + c
         + 
                  3             2  2               2  +-+
           (4a b x  + (8a c + 4b )x  + 12b c x + 8c )\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                                          +--------------+
                     2  2              2  |   2
           ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
         + 
                    3               2  2               2  +-+
           (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
                                      +--------------+
                 2  2              2  |   2
       ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
     + 
                3               2  2               2  +-+
       (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
  /
                                            +--------------+
             2    2   2       2      3  +-+ |   2                    2 3
       ((4a c  + b c)x  + 8b c x + 8c )\|c \|a x  + b x + c  - 4a b c x
     + 
              3     2 2  2        3      4
       (- 8a c  - 4b c )x  - 12b c x - 8c
                                                     Type: Expression Integer
--R
--R   (5)
--R                                            +--------------+
--R                       2  2              2  |   2
--R           ((- 4a c - b )x  - 8b c x - 8c )\|a x  + b x + c
--R         + 
--R                  3             2  2               2  +-+
--R           (4a b x  + (8a c + 4b )x  + 12b c x + 8c )\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                                          +--------------+
--R                     2  2              2  |   2
--R           ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
--R         + 
--R                    3               2  2               2  +-+
--R           (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R                                      +--------------+
--R                 2  2              2  |   2
--R       ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
--R     + 
--R                3               2  2               2  +-+
--R       (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
--R  /
--R                                            +--------------+
--R             2    2   2       2      3  +-+ |   2                    2 3
--R       ((4a c  + b c)x  + 8b c x + 8c )\|c \|a x  + b x + c  - 4a b c x
--R     + 
--R              3     2 2  2        3      4
--R       (- 8a c  - 4b c )x  - 12b c x - 8c
--R                                                     Type: Expression Integer
--E

--S 117
dd:=ratDenom cc
 

   (6)
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       - \|c log(---------------------------------)
                                 x
     + 
                  +--------------+
                  |   2                           +-+
        +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
       \|c log(--------------------------------------) + \|c
                                2c x
  /
      2
     c
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - \|c log(---------------------------------)
--R                                 x
--R     + 
--R                  +--------------+
--R                  |   2                           +-+
--R        +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
--R       \|c log(--------------------------------------) + \|c
--R                                2c x
--R  /
--R      2
--R     c
--R                                                     Type: Expression Integer
--E

--S 118
ee:=expandLog dd
 

   (7)
                       +--------------+
          +-+      +-+ |   2
       - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                  +--------------+
        +-+       |   2                           +-+
       \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                               +-+
       (- log(c) - log(2) + 1)\|c
  /
      2
     c
                                                     Type: Expression Integer
--R
--R   (7)
--R                       +--------------+
--R          +-+      +-+ |   2
--R       - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                  +--------------+
--R        +-+       |   2                           +-+
--R       \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                               +-+
--R       (- log(c) - log(2) + 1)\|c
--R  /
--R      2
--R     c
--R                                                     Type: Expression Integer
--E

--S 119    14:293 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

                                 +-+
        (- log(c) - 2log(2) + 2)\|c
   (8)  ----------------------------
                       2
                     2c
                                                     Type: Expression Integer
--R
--R                                 +-+
--R        (- log(c) - 2log(2) + 2)\|c
--R   (8)  ----------------------------
--R                       2
--R                     2c
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 120
aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
 

   (1)
                                                          +--------------+
                           3  3      2   2        2   +-+ |   2
           ((- 24a b c - 6b )x  - 48b c x  - 48b c x)\|c \|a x  + b x + c
         + 
                2   4           2      3   3      2 2 2        3
           24a b c x  + (48a b c  + 24b c)x  + 72b c x  + 48b c x
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
                      3  3         2      2   2        2       3  +-+
         ((4a b c - 9b )x  + (64a c  - 24b c)x  + 40b c x + 32c )\|c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
             2 2        2   4             2      3   3           3     2 2  2
       (- 32a c  + 24a b c)x  + (- 48a b c  + 24b c)x  + (- 80a c  + 8b c )x
     + 
              3       4
       - 56b c x - 32c
  /
                                               +--------------+
              4     2 3  3        4 2      5   |   2
       ((16a c  + 4b c )x  + 32b c x  + 32c x)\|a x  + b x + c
     + 
                 3 4           4      2 3  3        4 2      5   +-+
       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                          +--------------+
--R                           3  3      2   2        2   +-+ |   2
--R           ((- 24a b c - 6b )x  - 48b c x  - 48b c x)\|c \|a x  + b x + c
--R         + 
--R                2   4           2      3   3      2 2 2        3
--R           24a b c x  + (48a b c  + 24b c)x  + 72b c x  + 48b c x
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R                      3  3         2      2   2        2       3  +-+
--R         ((4a b c - 9b )x  + (64a c  - 24b c)x  + 40b c x + 32c )\|c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R             2 2        2   4             2      3   3           3     2 2  2
--R       (- 32a c  + 24a b c)x  + (- 48a b c  + 24b c)x  + (- 80a c  + 8b c )x
--R     + 
--R              3       4
--R       - 56b c x - 32c
--R  /
--R                                               +--------------+
--R              4     2 3  3        4 2      5   |   2
--R       ((16a c  + 4b c )x  + 32b c x  + 32c x)\|a x  + b x + c
--R     + 
--R                 3 4           4      2 3  3        4 2      5   +-+
--R       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 121
t1:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 

                          +--------------+
                          |   2                 +-+
                     - 2x\|a x  + b x + c  + 2x\|c
   (2)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R
--R                          +--------------+
--R                          |   2                 +-+
--R                     - 2x\|a x  + b x + c  + 2x\|c
--R   (2)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E

--S 122
t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (3)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (3)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 123
bb:=-(a*x^2+2*b*x+c)/(c^2*x*sqrt(a*x^2+b*x+c))+(b^2-2*a*c)/(2*c^2)*t1-(3*b)/(2*c^2)*t2
 

   (4)
                                            +--------------+
                      3     2   2       2   |   2
           (- 6a b c x  - 6b c x  - 6b c x)\|a x  + b x + c
         + 
                2 4               3  3     2   2       2   +-+
           (3a b x  + (6a b c + 3b )x  + 9b c x  + 6b c x)\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                                                      +--------------+
                3        2     2   2        2      3  |   2
       (2a b c x  + (8a c  + 2b c)x  + 10b c x + 4c )\|a x  + b x + c
     + 
                2        2  4                  3  3           2     2   2
           (- 8a c + 2a b )x  + (- 16a b c + 2b )x  + (- 12a c  - 6b c)x
         + 
                  2      3
           - 12b c x - 4c
      *
          +-+
         \|c
  /
                                      +--------------+
            3 3       3 2     4   +-+ |   2                    3 4
       (4a c x  + 4b c x  + 4c x)\|c \|a x  + b x + c  - 2a b c x
     + 
              4     2 3  3       4 2     5
       (- 4a c  - 2b c )x  - 6b c x  - 4c x
                                                     Type: Expression Integer
--R
--R   (4)
--R                                            +--------------+
--R                      3     2   2       2   |   2
--R           (- 6a b c x  - 6b c x  - 6b c x)\|a x  + b x + c
--R         + 
--R                2 4               3  3     2   2       2   +-+
--R           (3a b x  + (6a b c + 3b )x  + 9b c x  + 6b c x)\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                                                      +--------------+
--R                3        2     2   2        2      3  |   2
--R       (2a b c x  + (8a c  + 2b c)x  + 10b c x + 4c )\|a x  + b x + c
--R     + 
--R                2        2  4                  3  3           2     2   2
--R           (- 8a c + 2a b )x  + (- 16a b c + 2b )x  + (- 12a c  - 6b c)x
--R         + 
--R                  2      3
--R           - 12b c x - 4c
--R      *
--R          +-+
--R         \|c
--R  /
--R                                      +--------------+
--R            3 3       3 2     4   +-+ |   2                    3 4
--R       (4a c x  + 4b c x  + 4c x)\|c \|a x  + b x + c  - 2a b c x
--R     + 
--R              4     2 3  3       4 2     5
--R       (- 4a c  - 2b c )x  - 6b c x  - 4c x
--R                                                     Type: Expression Integer
--E

--S 124
cc:=aa-bb
 

   (5)
                    2      4  3            2       3   2       2 2          3
             ((72a b c + 6b )x  + (144a b c  + 108b c)x  + 288b c x + 192b c )
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                 2   2        3   4            2 2      4   3
           (- 48a b c  - 36a b c)x  + (- 240a b c  - 36b c)x
         + 
                      3       3 2  2       2 3          4
           (- 240a b c  - 228b c )x  - 384b c x - 192b c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                         2      4  3              2       3   2       2 2
                 (- 72a b c - 6b )x  + (- 144a b c  - 108b c)x  - 288b c x
               + 
                         3
                 - 192b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
               2   2        3   4          2 2      4   3
           (48a b c  + 36a b c)x  + (240a b c  + 36b c)x
         + 
                    3       3 2  2       2 3          4
           (240a b c  + 228b c )x  + 384b c x + 192b c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
                  2      4  3              2      3   2       2 2          3
         ((- 60a b c - 5b )x  + (- 120a b c  - 90b c)x  - 240b c x - 160b c )
      *
              +--------------+
          +-+ |   2
         \|c \|a x  + b x + c
     + 
           2   2        3   4          2 2      4   3            3       3 2  2
       (40a b c  + 30a b c)x  + (200a b c  + 30b c)x  + (200a b c  + 190b c )x
     + 
           2 3          4
       320b c x + 160b c
  /
                  4     3 3  3         5      2 4  2         5        6
         ((48a b c  + 4b c )x  + (96a c  + 72b c )x  + 192b c x + 128c )
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                 2 4        2 3  4              4      3 3  3
           (- 32a c  - 24a b c )x  + (- 160a b c  - 24b c )x
         + 
                    5       2 4  2         5        6
           (- 160a c  - 152b c )x  - 256b c x - 128c
      *
          +-+
         \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                    2      4  3            2       3   2       2 2          3
--R             ((72a b c + 6b )x  + (144a b c  + 108b c)x  + 288b c x + 192b c )
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                 2   2        3   4            2 2      4   3
--R           (- 48a b c  - 36a b c)x  + (- 240a b c  - 36b c)x
--R         + 
--R                      3       3 2  2       2 3          4
--R           (- 240a b c  - 228b c )x  - 384b c x - 192b c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                         2      4  3              2       3   2       2 2
--R                 (- 72a b c - 6b )x  + (- 144a b c  - 108b c)x  - 288b c x
--R               + 
--R                         3
--R                 - 192b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R               2   2        3   4          2 2      4   3
--R           (48a b c  + 36a b c)x  + (240a b c  + 36b c)x
--R         + 
--R                    3       3 2  2       2 3          4
--R           (240a b c  + 228b c )x  + 384b c x + 192b c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R                  2      4  3              2      3   2       2 2          3
--R         ((- 60a b c - 5b )x  + (- 120a b c  - 90b c)x  - 240b c x - 160b c )
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|c \|a x  + b x + c
--R     + 
--R           2   2        3   4          2 2      4   3            3       3 2  2
--R       (40a b c  + 30a b c)x  + (200a b c  + 30b c)x  + (200a b c  + 190b c )x
--R     + 
--R           2 3          4
--R       320b c x + 160b c
--R  /
--R                  4     3 3  3         5      2 4  2         5        6
--R         ((48a b c  + 4b c )x  + (96a c  + 72b c )x  + 192b c x + 128c )
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                 2 4        2 3  4              4      3 3  3
--R           (- 32a c  - 24a b c )x  + (- 160a b c  - 24b c )x
--R         + 
--R                    5       2 4  2         5        6
--R           (- 160a c  - 152b c )x  - 256b c x - 128c
--R      *
--R          +-+
--R         \|c
--R                                                     Type: Expression Integer
--E

--S 125
dd:=ratDenom cc
 

   (6)
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       6b\|c log(---------------------------------)
                                 x
     + 
                      +--------------+
                      |   2                           +-+
            +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c        +-+
       - 6b\|c log(--------------------------------------) - 5b\|c
                                    2c x
  /
       3
     4c
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       6b\|c log(---------------------------------)
--R                                 x
--R     + 
--R                      +--------------+
--R                      |   2                           +-+
--R            +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c        +-+
--R       - 6b\|c log(--------------------------------------) - 5b\|c
--R                                    2c x
--R  /
--R       3
--R     4c
--R                                                     Type: Expression Integer
--E

--S 126
ee:=expandLog dd
 

   (7)
                       +--------------+
          +-+      +-+ |   2
       6b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                      +--------------+
            +-+       |   2                           +-+
       - 6b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                    +-+
       (6b log(c) + 6b log(2) - 5b)\|c
  /
       3
     4c
                                                     Type: Expression Integer
--R
--R   (7)
--R                       +--------------+
--R          +-+      +-+ |   2
--R       6b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                      +--------------+
--R            +-+       |   2                           +-+
--R       - 6b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                    +-+
--R       (6b log(c) + 6b log(2) - 5b)\|c
--R  /
--R       3
--R     4c
--R                                                     Type: Expression Integer
--E

--S 127    14:294 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

                                     +-+
        (3b log(c) + 6b log(2) - 5b)\|c
   (8)  --------------------------------
                         3
                       4c
                                                     Type: Expression Integer
--R
--R                                     +-+
--R        (3b log(c) + 6b log(2) - 5b)\|c
--R   (8)  --------------------------------
--R                         3
--R                       4c
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 128    14:295 Axiom cannot compute this integral
aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
 

                              2n + 1
           x                  ------
         ++                2     2
   (1)   |   (c + %Q b + %Q a)      d%Q
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              2n + 1
--R           x                  ------
--R         ++                2     2
--I   (1)   |   (c + %N b + %N a)      d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 129    14:296 Axiom cannot compute this integral
aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
 

                                 2n + 1
           x                     ------
         ++                   2     2
   (1)   |   %Q (c + %Q b + %Q a)      d%Q
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 2n + 1
--R           x                     ------
--R         ++                   2     2
--I   (1)   |   %N (c + %N b + %N a)      d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 130    14:297 Axiom cannot compute this integral
aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
 

           x
         ++             1
   (1)   |   ----------------------- d%Q
        ++                    2n + 1
                              ------
                           2     2
             (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             1
--I   (1)   |   ----------------------- d%N
--R        ++                    2n + 1
--R                              ------
--R                           2     2
--I             (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 131    14:298 Axiom cannot compute this integral
aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
 

           x
         ++               1
   (1)   |   -------------------------- d%Q
        ++                       2n + 1
                                 ------
                              2     2
             %Q (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++               1
--I   (1)   |   -------------------------- d%N
--R        ++                       2n + 1
--R                                 ------
--R                              2     2
--I             %N (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to solvetra.output (2009/2/17, 18:0:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 37
solve(sin(x)-8=0)
 

   (1)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (1)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 1

--S 2 of 37
solve(sin(x)-8=0,x)
 

   (2)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (2)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 2

--S 3 of 37
solve(sin(x)-8)    
 

   (3)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (3)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 3

--S 4 of 37
solve(sin(x)-8,x)
 

   (4)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (4)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 4

--S 5 of 37
solve(sin(x**2)-2,x)       
 

               +-------+     +-------+
   (5)  [x= - \|asin(2) ,x= \|asin(2) ]
                                       Type: List Equation Expression Integer
--R 
--R
--R               +-------+     +-------+
--R   (5)  [x= - \|asin(2) ,x= \|asin(2) ]
--R                                       Type: List Equation Expression Integer
--E 5

--S 6 of 37
solve(sin(x**2)-3,x)
 

               +-------+     +-------+
   (6)  [x= - \|asin(3) ,x= \|asin(3) ]
                                       Type: List Equation Expression Integer
--R 
--R
--R               +-------+     +-------+
--R   (6)  [x= - \|asin(3) ,x= \|asin(3) ]
--R                                       Type: List Equation Expression Integer
--E 6

--S 7 of 37
solve(sin(x**2)**2-3,x)
 

   (7)
          +----------+     +----------+       +------------+     +------------+
          |      +-+       |      +-+         |        +-+       |        +-+
   [x= - \|asin(\|3 ) ,x= \|asin(\|3 ) ,x= - \|- asin(\|3 ) ,x= \|- asin(\|3 ) ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (7)
--R          +----------+     +----------+       +------------+     +------------+
--R          |      +-+       |      +-+         |        +-+       |        +-+
--R   [x= - \|asin(\|3 ) ,x= \|asin(\|3 ) ,x= - \|- asin(\|3 ) ,x= \|- asin(\|3 ) ]
--R                                       Type: List Equation Expression Integer
--E 7

--S 8 of 37
solve(sin(x+2)-2,x)
 

   (8)  [x= asin(2) - 2]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (8)  [x= asin(2) - 2]
--R                                       Type: List Equation Expression Integer
--E 8

--S 9 of 37
solve(sin(x**2+2)-2,x)
 

               +-----------+     +-----------+
   (9)  [x= - \|asin(2) - 2 ,x= \|asin(2) - 2 ]
                                       Type: List Equation Expression Integer
--R 
--R
--R               +-----------+     +-----------+
--R   (9)  [x= - \|asin(2) - 2 ,x= \|asin(2) - 2 ]
--R                                       Type: List Equation Expression Integer
--E 9

--S 10 of 37
solve(sin(x)*cos(8)*tan(88)*567-y*3+3,x)
 

                        y - 1
   (10)  [x= asin(----------------)]
                  189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R                        y - 1
--R   (10)  [x= asin(----------------)]
--R                  189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 10

--S 11 of 37
solve(sin(x-77)*cos(8)*tan(88)*567-y*3+3,x)
 

                        y - 1
   (11)  [x= asin(----------------) + 77]
                  189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R                        y - 1
--R   (11)  [x= asin(----------------) + 77]
--R                  189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 11

--S 12 of 37
solve(sin(x**2-77)*cos(8)*tan(88)*567-y*3+3,x)
 

   (12)
          +---------------------------+     +---------------------------+
          |           y - 1                 |           y - 1
   [x= -  |asin(----------------) + 77 ,x=  |asin(----------------) + 77 ]
         \|     189cos(8)tan(88)           \|     189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R   (12)
--R          +---------------------------+     +---------------------------+
--R          |           y - 1                 |           y - 1
--R   [x= -  |asin(----------------) + 77 ,x=  |asin(----------------) + 77 ]
--R         \|     189cos(8)tan(88)           \|     189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 12

--S 13 of 37
solve(sin(x)*cos(x)-2,x)                      
 

                   +----+                 +----+
                  \|- 15  + 1            \|- 15  - 1
   (13)  [x= atan(-----------),x= - atan(-----------)]
                       4                      4
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +----+                 +----+
--R                  \|- 15  + 1            \|- 15  - 1
--R   (13)  [x= atan(-----------),x= - atan(-----------)]
--R                       4                      4
--R                                       Type: List Equation Expression Integer
--E 13

--S 14 of 37
solve(sin(x**3-77)*cos(8)*tan(88)*567-y*3+3,x)
 

   (14)
                       +---------------------------+
           +---+       |           y - 1
       (- \|- 3  - 1) 3|asin(----------------) + 77
                      \|     189cos(8)tan(88)
   [x= --------------------------------------------,
                             2
                     +---------------------------+
         +---+       |           y - 1
       (\|- 3  - 1) 3|asin(----------------) + 77
                    \|     189cos(8)tan(88)
    x= ------------------------------------------,
                            2
        +---------------------------+
        |           y - 1
    x= 3|asin(----------------) + 77 ]
       \|     189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R   (14)
--R                       +---------------------------+
--R           +---+       |           y - 1
--R       (- \|- 3  - 1) 3|asin(----------------) + 77
--R                      \|     189cos(8)tan(88)
--R   [x= --------------------------------------------,
--R                             2
--R                     +---------------------------+
--R         +---+       |           y - 1
--R       (\|- 3  - 1) 3|asin(----------------) + 77
--R                    \|     189cos(8)tan(88)
--R    x= ------------------------------------------,
--R                            2
--R        +---------------------------+
--R        |           y - 1
--R    x= 3|asin(----------------) + 77 ]
--R       \|     189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 14

--S 15 of 37
solve(cos(x)+cos(3*x)+cos(5*x) ,x)
 

             %pi      %pi    %pi      %pi
   (15)  [x= ---,x= - ---,x= ---,x= - ---]
              3        3      6        6
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi      %pi    %pi      %pi
--R   (15)  [x= ---,x= - ---,x= ---,x= - ---]
--R              3        3      6        6
--R                                       Type: List Equation Expression Integer
--E 15

--S 16 of 37
solve(3*tan(3*x)-tan(x)+2,x)
 

                   +-+                 +-+
                  \|7  + 2            \|7  - 2
   (16)  [x= atan(--------),x= - atan(--------)]
                      3                   3
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +-+                 +-+
--R                  \|7  + 2            \|7  - 2
--R   (16)  [x= atan(--------),x= - atan(--------)]
--R                      3                   3
--R                                       Type: List Equation Expression Integer
--E 16

--S 17 of 37
solve(3*sech(x)**2+4*tanh(x)+1,x)
 

                  +---+            +---+            +-+              +-+
   (17)  [x= log(\|- 3 ),x= log(- \|- 3 ),x= - log(\|5 ),x= - log(- \|5 )]
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +---+            +---+            +-+              +-+
--R   (17)  [x= log(\|- 3 ),x= log(- \|- 3 ),x= - log(\|5 ),x= - log(- \|5 )]
--R                                       Type: List Equation Expression Integer
--E 17

--S 18 of 37
solve(cosh(x)-3*sinh(x),x)
 

                  +-+            +-+
   (18)  [x= log(\|2 ),x= log(- \|2 )]
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +-+            +-+
--R   (18)  [x= log(\|2 ),x= log(- \|2 )]
--R                                       Type: List Equation Expression Integer
--E 18

--S 19 of 37
solve(2*sinh(x)+6*cosh(x)-5,x)
 

                  +---+                +---+
                 \|- 7  + 5         - \|- 7  + 5
   (19)  [x= log(----------),x= log(------------)]
                      8                   8
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +---+                +---+
--R                 \|- 7  + 5         - \|- 7  + 5
--R   (19)  [x= log(----------),x= log(------------)]
--R                      8                   8
--R                                       Type: List Equation Expression Integer
--E 19

--S 20 of 37
solve(exp(3*x)-4*exp(x)+3*exp(-x),x)
 

                                   +-+            +-+
   (20)  [x= 0,x= log(- 1),x= log(\|3 ),x= log(- \|3 )]
                                       Type: List Equation Expression Integer
--R 
--R
--R                                   +-+            +-+
--R   (20)  [x= 0,x= log(- 1),x= log(\|3 ),x= log(- \|3 )]
--R                                       Type: List Equation Expression Integer
--E 20

--S 21 of 37
solve(log(x+1)+log(x-1)-3,x)
 

                +-------+     +-------+
                |  3          |  3
   (21)  [x= - \|%e  + 1 ,x= \|%e  + 1 ]
                                       Type: List Equation Expression Integer
--R 
--R
--R                +-------+     +-------+
--R                |  3          |  3
--R   (21)  [x= - \|%e  + 1 ,x= \|%e  + 1 ]
--R                                       Type: List Equation Expression Integer
--E 21

--S 22 of 37
solve(sin(x)*cos(x)-2,x)
 

                   +----+                 +----+
                  \|- 15  + 1            \|- 15  - 1
   (22)  [x= atan(-----------),x= - atan(-----------)]
                       4                      4
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +----+                 +----+
--R                  \|- 15  + 1            \|- 15  - 1
--R   (22)  [x= atan(-----------),x= - atan(-----------)]
--R                       4                      4
--R                                       Type: List Equation Expression Integer
--E 22

--S 23 of 37
solve(- cos(- x + a)*sin(x) + 2*cos(x)*sin(- x + a),x)
 

   (23)
             +------------------------+
             |     a 4         a 2             a 2
             |9tan(-)  + 14tan(-)  + 9  + 3tan(-)  - 3
            \|     2           2               2
   [x= atan(------------------------------------------),
                                   a
                              4tan(-)
                                   2
               +------------------------+
               |     a 4         a 2             a 2
               |9tan(-)  + 14tan(-)  + 9  - 3tan(-)  + 3
              \|     2           2               2
    x= - atan(------------------------------------------)]
                                     a
                                4tan(-)
                                     2
                                       Type: List Equation Expression Integer
--R 
--R
--R   (23)
--R             +------------------------+
--R             |     a 4         a 2             a 2
--R             |9tan(-)  + 14tan(-)  + 9  + 3tan(-)  - 3
--R            \|     2           2               2
--R   [x= atan(------------------------------------------),
--R                                   a
--R                              4tan(-)
--R                                   2
--R               +------------------------+
--R               |     a 4         a 2             a 2
--R               |9tan(-)  + 14tan(-)  + 9  - 3tan(-)  + 3
--R              \|     2           2               2
--R    x= - atan(------------------------------------------)]
--R                                     a
--R                                4tan(-)
--R                                     2
--R                                       Type: List Equation Expression Integer
--E 23

--S 24 of 37
solve(sin(x)+cos(x)=2,x)
 

                    +---+                  +---+
                   \|- 2  + 1             \|- 2  - 1
   (24)  [x= 2atan(----------),x= - 2atan(----------)]
                        3                      3
                                       Type: List Equation Expression Integer
--R 
--R
--R                    +---+                  +---+
--R                   \|- 2  + 1             \|- 2  - 1
--R   (24)  [x= 2atan(----------),x= - 2atan(----------)]
--R                        3                      3
--R                                       Type: List Equation Expression Integer
--E 24

--S 25 of 37
solve(- cos(- x )*sin(x),x)
 

             %pi           %pi
   (25)  [x= ---,x= 0,x= - ---]
              2             2
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi           %pi
--R   (25)  [x= ---,x= 0,x= - ---]
--R              2             2
--R                                       Type: List Equation Expression Integer
--E 25

--S 26 of 37
solve(- cos(- x + a)*sin(x),x)
 

                              a                    a
                          tan(-) + 1           tan(-) - 1
                              2                    2
   (26)  [x= 0,x= - 2atan(----------),x= 2atan(----------)]
                              a                    a
                          tan(-) - 1           tan(-) + 1
                              2                    2
                                       Type: List Equation Expression Integer
--R 
--R
--R                              a                    a
--R                          tan(-) + 1           tan(-) - 1
--R                              2                    2
--R   (26)  [x= 0,x= - 2atan(----------),x= 2atan(----------)]
--R                              a                    a
--R                          tan(-) - 1           tan(-) + 1
--R                              2                    2
--R                                       Type: List Equation Expression Integer
--E 26

--S 27 of 37
solve(log(sqrt(sqrt(sqrt(x+1)+4)+7))+5,x)
 

                    5 8          5 6         5 4        5 2
             2024(%e )  - 1260(%e )  + 286(%e )  - 28(%e )  + 1
   (27)  [x= --------------------------------------------------]
                                      5 8
                                   (%e )
                                       Type: List Equation Expression Integer
--R 
--R
--R                    5 8          5 6         5 4        5 2
--R             2024(%e )  - 1260(%e )  + 286(%e )  - 28(%e )  + 1
--R   (27)  [x= --------------------------------------------------]
--R                                      5 8
--R                                   (%e )
--R                                       Type: List Equation Expression Integer
--E 27

--S 28 of 37
solve(2**x-6,x)
 

             log(6)
   (28)  [x= ------]
             log(2)
                                       Type: List Equation Expression Integer
--R 
--R
--R             log(6)
--R   (28)  [x= ------]
--R             log(2)
--R                                       Type: List Equation Expression Integer
--E 28

--S 29 of 37
solve(sqrt(x+1)+sqrt(x+7)+1,x)
 

   (29)  []
                                       Type: List Equation Expression Integer
--R 
--R
--R   (29)  []
--R                                       Type: List Equation Expression Integer
--E 29

--S 30 of 37
solve(sqrt(sin(x))+1,x)
 

             %pi
   (30)  [x= ---]
              2
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi
--R   (30)  [x= ---]
--R              2
--R                                       Type: List Equation Expression Integer
--E 30

--S 31 of 37
solve(sqrt(sin(x))+sqrt(cos(x))+1,x)
 

                           +---+                  +---+
             %pi          \|- 7  - 1             \|- 7  + 1
   (31)  [x= ---,x= 2atan(----------),x= - 2atan(----------)]
              2                2                      2
                                       Type: List Equation Expression Integer
--R 
--R
--R                           +---+                  +---+
--R             %pi          \|- 7  - 1             \|- 7  + 1
--R   (31)  [x= ---,x= 2atan(----------),x= - 2atan(----------)]
--R              2                2                      2
--R                                       Type: List Equation Expression Integer
--E 31

--S 32 of 37
solve(sqrt(sin(x)+1)+(sin(x)+1)**(1/3)+7,x)
 

   (32)
                             +----------------------------+
                             |        2
                            \|- 3%x111  + 374%x111 + 10409  - %x111 + 187
   [x= asin(%x111), x= asin(---------------------------------------------),
                                                  2
               +----------------------------+
               |        2
              \|- 3%x111  + 374%x111 + 10409  + %x111 - 187
    x= - asin(---------------------------------------------)]
                                    2
                                       Type: List Equation Expression Integer
--R 
--R
--R   (32)
--R                             +----------------------------+
--R                             |        2
--R                            \|- 3%x111  + 374%x111 + 10409  - %x111 + 187
--R   [x= asin(%x111), x= asin(---------------------------------------------),
--R                                                  2
--R               +----------------------------+
--R               |        2
--R              \|- 3%x111  + 374%x111 + 10409  + %x111 - 187
--R    x= - asin(---------------------------------------------)]
--R                                    2
--R                                       Type: List Equation Expression Integer
--E 32

--S 33 of 37
solve(sqrt(sqrt(sqrt(1+x)+7)+1)+8-2,x)
 

   (33)  []
                                       Type: List Equation Expression Integer
--R 
--R
--R   (33)  []
--R                                       Type: List Equation Expression Integer
--E 33

--S 34 of 37
solve(sqrt(sin(x)+1)+(sin(x)+5)**(1/3)+7,x)
 

   (34)
                             +----------------------------+
                             |        2
                            \|- 3%x119  + 374%x119 + 11113  - %x119 + 187
   [x= asin(%x119), x= asin(---------------------------------------------),
                                                  2
               +----------------------------+
               |        2
              \|- 3%x119  + 374%x119 + 11113  + %x119 - 187
    x= - asin(---------------------------------------------)]
                                    2
                                       Type: List Equation Expression Integer
--R 
--R
--R   (34)
--R                             +----------------------------+
--R                             |        2
--R                            \|- 3%x119  + 374%x119 + 11113  - %x119 + 187
--R   [x= asin(%x119), x= asin(---------------------------------------------),
--R                                                  2
--R               +----------------------------+
--R               |        2
--R              \|- 3%x119  + 374%x119 + 11113  + %x119 - 187
--R    x= - asin(---------------------------------------------)]
--R                                    2
--R                                       Type: List Equation Expression Integer
--E 34

--S 35 of 37
solve(sqrt(sin(x+1))+sqrt(sin(x+7))+1,x)
 

   (35)
   [x= 2atan(%x125) - 7, x= 2atan(%x126) - 7,

     x =
           2
        *
           atan
                  ROOT
                                    8           7           6            5
                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                         + 
                                      4            3           2
                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                      *
                              2
                         %x126
                     + 
                                        8           7           6            5
                               - 2tan(3)  + 16tan(3)  - 56tan(3)  + 112tan(3)
                             + 
                                          4            3           2
                               - 140tan(3)  + 112tan(3)  - 56tan(3)  + 16tan(3)
                             + 
                               - 2
                          *
                             %x125
                         + 
                                   7            6            5           4
                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                         + 
                                     3            2
                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                      *
                         %x126
                     + 
                                    8           7           6            5
                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                         + 
                                      4            3           2
                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                      *
                              2
                         %x125
                     + 
                                   7            6            5           4
                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                         + 
                                     3            2
                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                      *
                         %x125
                     + 
                                 8            7            6            5
                       - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
                     + 
                               4            3           2
                       80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
                + 
                           4          3          2
                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x126
                + 
                           4          3          2
                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x125
                + 
                          3          2
                  16tan(3)  + 8tan(3)  + 8
             /
                       4          3           2
                2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
       + 
         - 7
     ,

     x =
         -
              2
           *
              atan
                     ROOT
                                       8           7           6            5
                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                            + 
                                       4            3           2
                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                         *
                                 2
                            %x126
                        + 
                                           8           7           6
                                  - 2tan(3)  + 16tan(3)  - 56tan(3)
                                + 
                                           5            4            3
                                  112tan(3)  - 140tan(3)  + 112tan(3)
                                + 
                                            2
                                  - 56tan(3)  + 16tan(3) - 2
                             *
                                %x125
                            + 
                                      7            6            5           4
                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                            + 
                                        3            2
                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                         *
                            %x126
                        + 
                                       8           7           6            5
                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                            + 
                                       4            3           2
                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                         *
                                 2
                            %x125
                        + 
                                      7            6            5           4
                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                            + 
                                        3            2
                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                         *
                            %x125
                        + 
                                    8            7            6            5
                          - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
                        + 
                                  4            3           2
                          80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
                   + 
                            4          3          2
                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x126
                   + 
                            4          3          2
                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x125
                   + 
                               3          2
                     - 16tan(3)  - 8tan(3)  - 8
                /
                          4          3           2
                   2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
       + 
         - 7
     ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (35)
--R   [x= 2atan(%x125) - 7, x= 2atan(%x126) - 7,
--R
--R     x =
--R           2
--R        *
--R           atan
--R                  ROOT
--R                                    8           7           6            5
--R                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                         + 
--R                                      4            3           2
--R                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                      *
--R                              2
--R                         %x126
--R                     + 
--R                                        8           7           6            5
--R                               - 2tan(3)  + 16tan(3)  - 56tan(3)  + 112tan(3)
--R                             + 
--R                                          4            3           2
--R                               - 140tan(3)  + 112tan(3)  - 56tan(3)  + 16tan(3)
--R                             + 
--R                               - 2
--R                          *
--R                             %x125
--R                         + 
--R                                   7            6            5           4
--R                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                         + 
--R                                     3            2
--R                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                      *
--R                         %x126
--R                     + 
--R                                    8           7           6            5
--R                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                         + 
--R                                      4            3           2
--R                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                      *
--R                              2
--R                         %x125
--R                     + 
--R                                   7            6            5           4
--R                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                         + 
--R                                     3            2
--R                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                      *
--R                         %x125
--R                     + 
--R                                 8            7            6            5
--R                       - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
--R                     + 
--R                               4            3           2
--R                       80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
--R                + 
--R                           4          3          2
--R                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x126
--R                + 
--R                           4          3          2
--R                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x125
--R                + 
--R                          3          2
--R                  16tan(3)  + 8tan(3)  + 8
--R             /
--R                       4          3           2
--R                2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
--R       + 
--R         - 7
--R     ,
--R
--R     x =
--R         -
--R              2
--R           *
--R              atan
--R                     ROOT
--R                                       8           7           6            5
--R                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                            + 
--R                                       4            3           2
--R                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                         *
--R                                 2
--R                            %x126
--R                        + 
--R                                           8           7           6
--R                                  - 2tan(3)  + 16tan(3)  - 56tan(3)
--R                                + 
--R                                           5            4            3
--R                                  112tan(3)  - 140tan(3)  + 112tan(3)
--R                                + 
--R                                            2
--R                                  - 56tan(3)  + 16tan(3) - 2
--R                             *
--R                                %x125
--R                            + 
--R                                      7            6            5           4
--R                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                            + 
--R                                        3            2
--R                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                         *
--R                            %x126
--R                        + 
--R                                       8           7           6            5
--R                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                            + 
--R                                       4            3           2
--R                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                         *
--R                                 2
--R                            %x125
--R                        + 
--R                                      7            6            5           4
--R                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                            + 
--R                                        3            2
--R                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                         *
--R                            %x125
--R                        + 
--R                                    8            7            6            5
--R                          - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
--R                        + 
--R                                  4            3           2
--R                          80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
--R                   + 
--R                            4          3          2
--R                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x126
--R                   + 
--R                            4          3          2
--R                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x125
--R                   + 
--R                               3          2
--R                     - 16tan(3)  - 8tan(3)  - 8
--R                /
--R                          4          3           2
--R                   2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
--R       + 
--R         - 7
--R     ]
--R                                       Type: List Equation Expression Integer
--E 35

--S 36 of 37
solve(asin(x)+acot(x)-2,x)
 

   (36)
   [
     x =
           -
              ROOT
                             4                 4                      4
                          ------            ------                 ------
                           +---+             +---+                  +---+
                          \|- 1      2      \|- 1                  \|- 1      2
                     - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
                   + 
                             4   2         4
                          ------        ------
                           +---+         +---+
                          \|- 1         \|- 1
                     - (%e      )  - 2%e       - 1
                /
                        4
                     ------
                      +---+
                     \|- 1
                   %e
         + 
           - %x135 - %x134
      /
         2
     ,

     x =
           ROOT
                          4                 4                      4
                       ------            ------                 ------
                        +---+             +---+                  +---+
                       \|- 1      2      \|- 1                  \|- 1      2
                  - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
                + 
                          4   2         4
                       ------        ------
                        +---+         +---+
                       \|- 1         \|- 1
                  - (%e      )  - 2%e       - 1
             /
                     4
                  ------
                   +---+
                  \|- 1
                %e
         + 
           - %x135 - %x134
      /
         2
     ,
    x= %x135, x= %x134]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (36)
--R   [
--R     x =
--R           -
--R              ROOT
--R                             4                 4                      4
--R                          ------            ------                 ------
--R                           +---+             +---+                  +---+
--R                          \|- 1      2      \|- 1                  \|- 1      2
--R                     - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
--R                   + 
--R                             4   2         4
--R                          ------        ------
--R                           +---+         +---+
--R                          \|- 1         \|- 1
--R                     - (%e      )  - 2%e       - 1
--R                /
--R                        4
--R                     ------
--R                      +---+
--R                     \|- 1
--R                   %e
--R         + 
--R           - %x135 - %x134
--R      /
--R         2
--R     ,
--R
--R     x =
--R           ROOT
--R                          4                 4                      4
--R                       ------            ------                 ------
--R                        +---+             +---+                  +---+
--R                       \|- 1      2      \|- 1                  \|- 1      2
--R                  - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
--R                + 
--R                          4   2         4
--R                       ------        ------
--R                        +---+         +---+
--R                       \|- 1         \|- 1
--R                  - (%e      )  - 2%e       - 1
--R             /
--R                     4
--R                  ------
--R                   +---+
--R                  \|- 1
--R                %e
--R         + 
--R           - %x135 - %x134
--R      /
--R         2
--R     ,
--R    x= %x135, x= %x134]
--R                                       Type: List Equation Expression Integer
--E 26

--S 37 of 37
solve(asinh(x)+acoth(x)-2,x)
 

   (37)
   [
     x =
              +---------------------------------------------------------------+
              |     4     2      4                 4     2      4 2      4
              |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
           -  |---------------------------------------------------------------
              |                                4
             \|                              %e
         + 
           - %x140 - %x139
      /
         2
     ,

     x =
            +---------------------------------------------------------------+
            |     4     2      4                 4     2      4 2      4
            |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
            |---------------------------------------------------------------
            |                                4
           \|                              %e
         + 
           - %x140 - %x139
      /
         2
     ,
    x= %x140, x= %x139]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (37)
--R   [
--R     x =
--R              +---------------------------------------------------------------+
--R              |     4     2      4                 4     2      4 2      4
--R              |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
--R           -  |---------------------------------------------------------------
--R              |                                4
--R             \|                              %e
--R         + 
--R           - %x140 - %x139
--R      /
--R         2
--R     ,
--R
--R     x =
--R            +---------------------------------------------------------------+
--R            |     4     2      4                 4     2      4 2      4
--R            |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
--R            |---------------------------------------------------------------
--R            |                                4
--R           \|                              %e
--R         + 
--R           - %x140 - %x139
--R      /
--R         2
--R     ,
--R    x= %x140, x= %x139]
--R                                       Type: List Equation Expression Integer
--E 37
)spool 
 
Starts dribbling to textfile.output (2009/2/17, 18:1:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 10
f1: TextFile := open("/etc/group", "input")
 

   (1)  "/etc/group"
                                                               Type: TextFile
--R 
--R
--R   (1)  "/etc/group"
--R                                                               Type: TextFile
--E 1

--S 2 of 10
f2: TextFile := open("/tmp/MOTD", "output")
 

   (2)  "/tmp/MOTD"
                                                               Type: TextFile
--R 
--R
--R   (2)  "/tmp/MOTD"
--R                                                               Type: TextFile
--E 2

--S 3 of 10
l := readLine! f1
 

   (3)  "root:x:0:"
                                                                 Type: String
--R 
--R
--R   (3)  "root:x:0:root"
--R                                                                 Type: String
--E 3

--S 4 of 10
writeLine!(f2, upperCase l)
 

   (4)  "ROOT:X:0:"
                                                                 Type: String
--R 
--R
--R   (4)  "ROOT:X:0:ROOT"
--R                                                                 Type: String
--E 4

--S 5 of 10
while not endOfFile? f1 repeat
    s := readLine! f1
    writeLine!(f2, upperCase s)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
close! f1
 

   (6)  "/etc/group"
                                                               Type: TextFile
--R 
--R
--R   (6)  "/etc/group"
--R                                                               Type: TextFile
--E 6

--S 7 of 10
write!(f2, "-The-")
 

   (7)  "-The-"
                                                                 Type: String
--R 
--R
--R   (7)  "-The-"
--R                                                                 Type: String
--E 7

--S 8 of 10
write!(f2, "-End-")
 

   (8)  "-End-"
                                                                 Type: String
--R 
--R
--R   (8)  "-End-"
--R                                                                 Type: String
--E 8

--S 9 of 10
writeLine! f2
 

   (9)  ""
                                                                 Type: String
--R 
--R
--R   (9)  ""
--R                                                                 Type: String
--E 9

--S 10 of 10
close! f2
 

   (10)  "/tmp/MOTD"
                                                               Type: TextFile
--R 
--R
--R   (10)  "/tmp/MOTD"
--R                                                               Type: TextFile
--E 10

)system rm /tmp/MOTD
 
)spool 
 
Starts dribbling to stbl.output (2009/2/17, 18:0:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 7
t: SparseTable(Integer, String, "Try again!") := table()
 

   (1)  table()
                                 Type: SparseTable(Integer,String,Try again!)
--R 
--R
--R   (1)  table()
--R                                 Type: SparseTable(Integer,String,Try again!)
--E 1

--S 2 of 7
t.3 := "Number three"
 

   (2)  "Number three"
                                                                 Type: String
--R 
--R
--R   (2)  "Number three"
--R                                                                 Type: String
--E 2

--S 3 of 7
t.4 := "Number four"
 

   (3)  "Number four"
                                                                 Type: String
--R 
--R
--R   (3)  "Number four"
--R                                                                 Type: String
--E 3

--S 4 of 7
t.3
 

   (4)  "Number three"
                                                                 Type: String
--R 
--R
--R   (4)  "Number three"
--R                                                                 Type: String
--E 4

--S 5 of 7
t.2
 

   (5)  "Try again!"
                                                                 Type: String
--R 
--R
--R   (5)  "Try again!"
--R                                                                 Type: String
--E 5

--S 6 of 7
keys t
 

   (6)  [4,3]
                                                           Type: List Integer
--R 
--R
--R   (6)  [4,3]
--R                                                           Type: List Integer
--E 6

--S 7 of 7
entries t
 

   (7)  ["Number four","Number three"]
                                                            Type: List String
--R 
--R
--R   (7)  ["Number four","Number three"]
--R                                                            Type: List String
--E 7
)spool 
 
Starts dribbling to efi.output (2009/2/17, 17:45:22).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 15
EFI:=Expression Integer
 

   (1)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Expression Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 15
ber:=operator 'ber
 

   (2)  ber
                                                          Type: BasicOperator
--R 
--R
--R   (2)  ber
--R                                                          Type: BasicOperator
--E 2

--S 3 of 15
s:=operator 's
 

   (3)  s
                                                          Type: BasicOperator
--R 
--R
--R   (3)  s
--R                                                          Type: BasicOperator
--E 3

-- s:OP EFI:=operator 's

--S 4 of 15
br:LIST EFI->EFI
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4


--S 5 of 15
br(x) == 
 (x.1) = 0 => limit(br([y]),y=0) 
 (x.1)/(exp((x.1))-1) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 15
br([1])
 
   Compiling function br with type List Expression Integer -> 
      Expression Integer 

           1
   (6)  ------
        %e - 1
                                                     Type: Expression Integer
--R 
--R   Compiling function br with type List Expression Integer -> 
--R      Expression Integer 
--R
--R           1
--R   (6)  ------
--R        %e - 1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 15
br([0])
 

   (7)  1
                                                     Type: Expression Integer
--R 
--R
--R   (7)  1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 15
fJ:List FRAC INT -> EFI
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 15
J(i:PI,j:PI):EFI==ber(s(i)-s(j))
 
   Function declaration J : (PositiveInteger,PositiveInteger) -> 
      Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration J : (PositiveInteger,PositiveInteger) -> 
--R      Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 9

--S 10 of 15
function(J(1,2),'fJ,['s])
 
   Compiling function J with type (PositiveInteger,PositiveInteger) -> 
      Expression Integer 

   (10)  fJ
                                                                 Type: Symbol
--R 
--R   Compiling function J with type (PositiveInteger,PositiveInteger) -> 
--R      Expression Integer 
--R
--R   (10)  fJ
--R                                                                 Type: Symbol
--E 10

--S 11 of 15
evaluate(ber,br)$BOP1(EFI);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 11

--S 12 of 15
ss:=[1,2]
 

   (12)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (12)  [1,2]
--R                                                   Type: List PositiveInteger
--E 12

--S 13 of 15
fJ(ss)
 
   Compiling function fJ with type List Fraction Integer -> Expression 
      Integer 

           %e
   (13)  ------
         %e - 1
                                                     Type: Expression Integer
--R 
--R   Compiling function fJ with type List Fraction Integer -> Expression 
--R      Integer 
--R
--R           %e
--R   (13)  ------
--R         %e - 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 15
ss:=[1,1]
 

   (14)  [1,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (14)  [1,1]
--R                                                   Type: List PositiveInteger
--E 14

-- fJ doesn't know about the special definition at the origin
--S 15 of 15 of 15
fJ(ss)
 

   (15)  1
                                                     Type: Expression Integer
--R 
--R
--R   (15)  1
--R                                                     Type: Expression Integer
--E 15
)spool
 
Starts dribbling to fname.output (2009/2/17, 17:46:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
)system touch /tmp/reado
 
)system chmod +r,-w /tmp/reado
 
)system touch /tmp/writo
 
)system chmod +w,-r /tmp/writo
 
 
--S 1 of 9
nullo: FNAME := new("", "nullo", "x")
 

   (1)  "nullo1404.x"
                                                               Type: FileName
--R 
--R
--I   (1)  "nullo1406.x"
--R                                                               Type: FileName
--E 1

--S 2 of 9
reado: FNAME := filename("/tmp", "reado", "")
 

   (2)  "/tmp/reado"
                                                               Type: FileName
--R 
--R
--R   (2)  "/tmp/reado"
--R                                                               Type: FileName
--E 2

--S 3 of 9
writo: FNAME := "/tmp/writo"
 

   (3)  "/tmp/writo"
                                                               Type: FileName
--R 
--R
--R   (3)  "/tmp/writo"
--R                                                               Type: FileName
--E 3

--S 4 of 9
[directory reado, name reado, extension reado]
 

   (4)  ["/tmp","reado",""]
                                                            Type: List String
--R 
--R
--R   (4)  ["/tmp","reado",""]
--R                                                            Type: List String
--E 4

--S 5 of 9
[directory writo, name writo, extension writo]
 

   (5)  ["/tmp","writo",""]
                                                            Type: List String
--R 
--R
--R   (5)  ["/tmp","writo",""]
--R                                                            Type: List String
--E 5

--S 6 of 9
[directory nullo, name nullo, extension nullo]
 

   (6)  ["","nullo1404","x"]
                                                            Type: List String
--R 
--R
--I   (6)  ["","nullo1406","x"]
--R                                                            Type: List String
--E 6

--S 7 of 9
[exists? reado, readable? reado, writable? reado]
 

   (7)  [true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (7)  [true,true,false]
--R                                                           Type: List Boolean
--E 7

--S 8 of 9
[exists? writo, readable? writo, writable? writo]
 

   (8)  [true,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,true,true]
--R                                                           Type: List Boolean
--E 8

--S 9 of 9
[exists? nullo, readable? nullo, writable? nullo]
 

   (9)  [false,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [false,false,true]
--R                                                           Type: List Boolean
--E 9
)system rm -f /tmp/reado
 
)system rm -f /tmp/writo
 
)spool 
 
Starts dribbling to multfact.output (2009/2/17, 17:55:26).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 5
a := rootOf(a**2+a+1)
 

   (1)  a
                                                        Type: AlgebraicNumber
--R 
--R
--R   (1)  a
--R                                                        Type: AlgebraicNumber
--E 1

--S 2 of 5
p := y*z**2 + a*z*x**2 + a*a*x*y**2
 

           2      2                2
   (2)  y z  + a x z + (- a - 1)x y
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R           2      2                2
--R   (2)  y z  + a x z + (- a - 1)x y
--R                                             Type: Polynomial AlgebraicNumber
--E 2

--S 3 of 5
factor(p,[a])
 

           2      2                2
   (3)  y z  + a x z + (- a - 1)x y
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R           2      2                2
--R   (3)  y z  + a x z + (- a - 1)x y
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 3

--S 4 of 5
b:=rootOf(b**2+1)
 

   (4)  b
                                                        Type: AlgebraicNumber
--R 
--R
--R   (4)  b
--R                                                        Type: AlgebraicNumber
--E 4

--S 5 of 5
factor(x**2*y**2+u**2*v**2,[b])
 

   (5)  (x y - b u v)(x y + b u v)
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R   (5)  (x y - b u v)(x y + b u v)
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 5
)spool 
 
Starts dribbling to kamke7.output (2009/2/17, 17:48:7).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 97
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 97
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 97
g:=operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R 
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

--S 4 of 97
h:=operator 'h
 

   (4)  h
                                                          Type: BasicOperator
--R 
--R
--R   (4)  h
--R                                                          Type: BasicOperator
--E 4

--S 5 of 97
fa:=operator 'fa
 

   (5)  fa
                                                          Type: BasicOperator
--R 
--R
--R   (5)  fa
--R                                                          Type: BasicOperator
--E 5

--S 6 of 97
fb:=operator 'fb
 

   (6)  fb
                                                          Type: BasicOperator
--R 
--R
--R   (6)  fb
--R                                                          Type: BasicOperator
--E 6

--S 7 of 97
fc:=operator 'fc
 

   (7)  fc
                                                          Type: BasicOperator
--R 
--R
--R   (7)  fc
--R                                                          Type: BasicOperator
--E 7

--S 8 of 97
fd:=operator 'fd
 

   (8)  fd
                                                          Type: BasicOperator
--R 
--R
--R   (8)  fd
--R                                                          Type: BasicOperator
--E 8

--S 9 of 97
fe:=operator 'fe
 

   (9)  fe
                                                          Type: BasicOperator
--R 
--R
--R   (9)  fe
--R                                                          Type: BasicOperator
--E 9

--S 10 of 97
ff:=operator 'ff
 

   (10)  ff
                                                          Type: BasicOperator
--R 
--R
--R   (10)  ff
--R                                                          Type: BasicOperator
--E 10

--S 11 of 97
ode352 := D(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-_
            sin(alpha)*sin(y(x)))*cos(x)
 

   (11)
               2                              ,
     (cos(y(x))  - sin(alpha)sin(x)cos(y(x)))y (x) - cos(x)sin(alpha)sin(y(x))

   + 
           2
     cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (11)
--R               2                              ,
--R     (cos(y(x))  - sin(alpha)sin(x)cos(y(x)))y (x) - cos(x)sin(alpha)sin(y(x))
--R
--R   + 
--R           2
--R     cos(x)
--R                                                     Type: Expression Integer
--E 11

--S 12 of 97
yx:=solve(ode352,y,x)
 

         (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
   (12)  ------------------------------------------------------------------
                                          2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
--R   (12)  ------------------------------------------------------------------
--R                                          2
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 97
ode352expr := D(yx,x)*(cos(yx)-sin(alpha)*sin(x))*cos(yx)+(cos(x)-_
                sin(alpha)*sin(yx))*cos(x)
 

   (13)
       -
            2cos(x)sin(alpha)
         *
            sin
                   (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x)
                 + 
                   y(x) + x
              /
                 2
     + 
                       2            2                                   ,
           (- sin(y(x))  + cos(y(x))  - 2sin(alpha)sin(x)cos(y(x)) + 1)y (x)

         + 
                                                2         2
           - 2cos(x)sin(alpha)sin(y(x)) - sin(x)  + cos(x)  + 1
      *
           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x 2
       cos(------------------------------------------------------------------)
                                            2
     + 
                                        2                            2
               sin(alpha)sin(x)sin(y(x))  - sin(alpha)sin(x)cos(y(x))
             + 
                          2      2
               2sin(alpha) sin(x) cos(y(x)) - sin(alpha)sin(x)
          *
              ,
             y (x)

         + 
                            2                                  3
           2cos(x)sin(alpha) sin(x)sin(y(x)) + sin(alpha)sin(x)
         + 
                    2
           (- cos(x)  - 1)sin(alpha)sin(x)
      *
           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
       cos(------------------------------------------------------------------)
                                            2
     + 
              2
       2cos(x)
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R       -
--R            2cos(x)sin(alpha)
--R         *
--R            sin
--R                   (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x)
--R                 + 
--R                   y(x) + x
--R              /
--R                 2
--R     + 
--R                       2            2                                   ,
--R           (- sin(y(x))  + cos(y(x))  - 2sin(alpha)sin(x)cos(y(x)) + 1)y (x)
--R
--R         + 
--R                                                2         2
--R           - 2cos(x)sin(alpha)sin(y(x)) - sin(x)  + cos(x)  + 1
--R      *
--R           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x 2
--R       cos(------------------------------------------------------------------)
--R                                            2
--R     + 
--R                                        2                            2
--R               sin(alpha)sin(x)sin(y(x))  - sin(alpha)sin(x)cos(y(x))
--R             + 
--R                          2      2
--R               2sin(alpha) sin(x) cos(y(x)) - sin(alpha)sin(x)
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                            2                                  3
--R           2cos(x)sin(alpha) sin(x)sin(y(x)) + sin(alpha)sin(x)
--R         + 
--R                    2
--R           (- cos(x)  - 1)sin(alpha)sin(x)
--R      *
--R           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
--R       cos(------------------------------------------------------------------)
--R                                            2
--R     + 
--R              2
--R       2cos(x)
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 13

--S 14 of 97
ode353 := x*D(y(x),x)*cos(y(x))+sin(y(x))
 

                     ,
   (14)  x cos(y(x))y (x) + sin(y(x))

                                                     Type: Expression Integer
--R 
--R
--R                     ,
--R   (14)  x cos(y(x))y (x) + sin(y(x))
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 97
yx:=solve(ode353,y,x)
 

   (15)  x sin(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (15)  x sin(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 97
ode353expr := x*D(yx,x)*cos(yx)+sin(yx)
 

                              2          ,
   (16)  sin(x sin(y(x))) + (x cos(y(x))y (x) + x sin(y(x)))cos(x sin(y(x)))

                                                     Type: Expression Integer
--R 
--R
--R                              2          ,
--R   (16)  sin(x sin(y(x))) + (x cos(y(x))y (x) + x sin(y(x)))cos(x sin(y(x)))
--R
--R                                                     Type: Expression Integer
--E 16

--S 17 of 97
ode354 := (x*sin(y(x))-1)*D(y(x),x)+cos(y(x))
 

                           ,
   (17)  (x sin(y(x)) - 1)y (x) + cos(y(x))

                                                     Type: Expression Integer
--R 
--R
--R                           ,
--R   (17)  (x sin(y(x)) - 1)y (x) + cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 17

--S 18 of 97
yx:=solve(ode354,y,x)
 

         - sin(y(x)) + x
   (18)  ---------------
            cos(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - sin(y(x)) + x
--R   (18)  ---------------
--R            cos(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 97
ode354expr := (x*sin(yx)-1)*D(yx,x)+cos(yx)
 

   (19)
                      2    2                       2  ,
         ((x sin(y(x))  - x sin(y(x)) + x cos(y(x)) )y (x) - x cos(y(x)))

      *
             sin(y(x)) - x
         sin(-------------)
               cos(y(x))
     + 
                2    sin(y(x)) - x
       cos(y(x)) cos(-------------)
                       cos(y(x))
     + 
                 2                          2  ,
       (sin(y(x))  - x sin(y(x)) + cos(y(x)) )y (x) - cos(y(x))

  /
              2
     cos(y(x))
                                                     Type: Expression Integer
--R 
--R
--R   (19)
--R                      2    2                       2  ,
--R         ((x sin(y(x))  - x sin(y(x)) + x cos(y(x)) )y (x) - x cos(y(x)))
--R
--R      *
--R             sin(y(x)) - x
--R         sin(-------------)
--R               cos(y(x))
--R     + 
--R                2    sin(y(x)) - x
--R       cos(y(x)) cos(-------------)
--R                       cos(y(x))
--R     + 
--R                 2                          2  ,
--R       (sin(y(x))  - x sin(y(x)) + cos(y(x)) )y (x) - cos(y(x))
--R
--R  /
--R              2
--R     cos(y(x))
--R                                                     Type: Expression Integer
--E 19

--S 20 of 97
ode355 := (x*cos(y(x))+cos(x))*D(y(x),x)-y(x)*sin(x)+sin(y(x))
 

                                ,
   (20)  (x cos(y(x)) + cos(x))y (x) + sin(y(x)) - y(x)sin(x)

                                                     Type: Expression Integer
--R 
--R
--R                                ,
--R   (20)  (x cos(y(x)) + cos(x))y (x) + sin(y(x)) - y(x)sin(x)
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 97
yx:=solve(ode355,y,x)
 

   (21)  x sin(y(x)) + y(x)cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (21)  x sin(y(x)) + y(x)cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 21

--S 22 of 97
ode355expr := (x*cos(yx)+cos(x))*D(yx,x)-yx*sin(x)+sin(yx)
 

   (22)
     sin(x sin(y(x)) + y(x)cos(x))
   + 
          2                      ,
       ((x cos(y(x)) + x cos(x))y (x) + x sin(y(x)) - x y(x)sin(x))

    *
       cos(x sin(y(x)) + y(x)cos(x))
   + 
                                2  ,
     (x cos(x)cos(y(x)) + cos(x) )y (x) + (- x sin(x) + cos(x))sin(y(x))

   + 
     - 2y(x)cos(x)sin(x)
                                                     Type: Expression Integer
--R 
--R
--R   (22)
--R     sin(x sin(y(x)) + y(x)cos(x))
--R   + 
--R          2                      ,
--R       ((x cos(y(x)) + x cos(x))y (x) + x sin(y(x)) - x y(x)sin(x))
--R
--R    *
--R       cos(x sin(y(x)) + y(x)cos(x))
--R   + 
--R                                2  ,
--R     (x cos(x)cos(y(x)) + cos(x) )y (x) + (- x sin(x) + cos(x))sin(y(x))
--R
--R   + 
--R     - 2y(x)cos(x)sin(x)
--R                                                     Type: Expression Integer
--E 22

--S 23 of 97
ode356 := (x**2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)**2*cos(x)
 

           2                         ,                         2
   (23)  (x cos(y(x)) + 2y(x)sin(x))y (x) + 2x sin(y(x)) + y(x) cos(x)

                                                     Type: Expression Integer
--R 
--R
--R           2                         ,                         2
--R   (23)  (x cos(y(x)) + 2y(x)sin(x))y (x) + 2x sin(y(x)) + y(x) cos(x)
--R
--R                                                     Type: Expression Integer
--E 23

--S 24 of 97
yx:=solve(ode356,y,x)
 

          2                2
   (24)  x sin(y(x)) + y(x) sin(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2                2
--R   (24)  x sin(y(x)) + y(x) sin(x)
--R                                          Type: Union(Expression Integer,...)
--E 24

--S 25 of 97
ode356expr:=(x**2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx**2*cos(x)
 

   (25)
             2                2
     2x sin(x sin(y(x)) + y(x) sin(x))
   + 
          4              2            ,        3             2    2
       ((x cos(y(x)) + 2x y(x)sin(x))y (x) + 2x sin(y(x)) + x y(x) cos(x))

    *
            2                2
       cos(x sin(y(x)) + y(x) sin(x))
   + 
            4                    2          2
         (2x sin(x)cos(y(x)) + 4x y(x)sin(x) )sin(y(x))
       + 
           2    2      2                 3      3
         2x y(x) sin(x) cos(y(x)) + 4y(x) sin(x)
    *
        ,
       y (x)

   + 
        3          4                2
     (4x sin(x) + x cos(x))sin(y(x))
   + 
             2      2     2    2                              4            2
     (4x y(x) sin(x)  + 4x y(x) cos(x)sin(x))sin(y(x)) + 3y(x) cos(x)sin(x)
                                                     Type: Expression Integer
--R 
--R
--R   (25)
--R             2                2
--R     2x sin(x sin(y(x)) + y(x) sin(x))
--R   + 
--R          4              2            ,        3             2    2
--R       ((x cos(y(x)) + 2x y(x)sin(x))y (x) + 2x sin(y(x)) + x y(x) cos(x))
--R
--R    *
--R            2                2
--R       cos(x sin(y(x)) + y(x) sin(x))
--R   + 
--R            4                    2          2
--R         (2x sin(x)cos(y(x)) + 4x y(x)sin(x) )sin(y(x))
--R       + 
--R           2    2      2                 3      3
--R         2x y(x) sin(x) cos(y(x)) + 4y(x) sin(x)
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R        3          4                2
--R     (4x sin(x) + x cos(x))sin(y(x))
--R   + 
--R             2      2     2    2                              4            2
--R     (4x y(x) sin(x)  + 4x y(x) cos(x)sin(x))sin(y(x)) + 3y(x) cos(x)sin(x)
--R                                                     Type: Expression Integer
--E 25

--S 26 of 97
ode358 := D(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x)
 

                         ,
   (26)  cos(x)sin(y(x))y (x) + sin(x)cos(y(x))

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (26)  cos(x)sin(y(x))y (x) + sin(x)cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 26

--S 27 of 97
yx:=solve(ode358,y,x)
 

   (27)  - cos(x)cos(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (27)  - cos(x)cos(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 27

--S 28 of 97
ode358expr := D(yx,x)*sin(yx)*cos(x)+cos(yx)*sin(x)
 

   (28)
              2          ,
     (- cos(x) sin(y(x))y (x) - cos(x)sin(x)cos(y(x)))sin(cos(x)cos(y(x)))

   + 
     sin(x)cos(cos(x)cos(y(x)))
                                                     Type: Expression Integer
--R 
--R
--R   (28)
--R              2          ,
--R     (- cos(x) sin(y(x))y (x) - cos(x)sin(x)cos(y(x)))sin(cos(x)cos(y(x)))
--R
--R   + 
--R     sin(x)cos(cos(x)cos(y(x)))
--R                                                     Type: Expression Integer
--E 28

--S 29 of 97
ode361 := (x*sin(x*y(x))+cos(x+y(x))-sin(y(x)))*D(y(x),x)+_
              y(x)*sin(x*y(x))+cos(x+y(x))+cos(x)
 

   (29)
                                                 ,
     (x sin(x y(x)) - sin(y(x)) + cos(y(x) + x))y (x) + y(x)sin(x y(x))

   + 
     cos(y(x) + x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (29)
--R                                                 ,
--R     (x sin(x y(x)) - sin(y(x)) + cos(y(x) + x))y (x) + y(x)sin(x y(x))
--R
--R   + 
--R     cos(y(x) + x) + cos(x)
--R                                                     Type: Expression Integer
--E 29

--S 30 of 97
yx:=solve(ode361,y,x)
 

   (30)
          y(x) 2                     y(x)                  y(x)
     2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
            2                          2                     2
   + 
     cos(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (30)
--R          y(x) 2                     y(x)                  y(x)
--R     2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
--R            2                          2                     2
--R   + 
--R     cos(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 30

--S 31 of 97
ode361expr:=(x*sin(x*yx)+cos(x+yx)-sin(yx))*D(yx,x)+_
              yx*sin(x*yx)+cos(x+yx)+cos(x)
 

   (31)
              2                                               y(x) 2
             x sin(x y(x)) - x sin(y(x)) + x cos(y(x) + x)sin(----)
                                                                2
           + 
                   y(x) 2
             x cos(----) cos(y(x) + x)
                     2
        *
            ,
           y (x)

       + 
                                     y(x)     y(x)         y(x) 2
         x y(x)sin(x y(x)) + (2x cos(----)sin(----) + 2cos(----) )sin(y(x) + x)
                                       2        2            2
       + 
                y(x)                  y(x)
         - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
                  2                     2
       + 
                y(x) 2
         2x cos(----) cos(y(x) + x) + cos(y(x))
                  2
    *
       sin
                   y(x) 2                       y(x)                  y(x)
            2x cos(----) sin(y(x) + x) - 2x cos(----)cos(y(x) + x)sin(----)
                     2                            2                     2
          + 
            - x cos(x y(x)) + x cos(y(x))
   + 
                                                            y(x) 2
             - x sin(x y(x)) + sin(y(x)) - cos(y(x) + x)sin(----)
                                                              2
           + 
                   y(x) 2
             - cos(----) cos(y(x) + x)
                     2
        *
            ,
           y (x)

       + 
                                  y(x)     y(x)
         - y(x)sin(x y(x)) - 2cos(----)sin(----)sin(y(x) + x)
                                    2        2
       + 
                y(x) 2
         - 2cos(----) cos(y(x) + x)
                  2
    *
       sin
                 y(x) 2                     y(x)                  y(x)
            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
                   2                          2                     2
          + 
            - cos(x y(x)) + cos(y(x))
   + 
                                                          y(x) 2
             x sin(x y(x)) - sin(y(x)) + cos(y(x) + x)sin(----)
                                                            2
           + 
                 y(x) 2
             cos(----) cos(y(x) + x)
                   2
        *
            ,
           y (x)

       + 
                                y(x)     y(x)
         y(x)sin(x y(x)) + 2cos(----)sin(----)sin(y(x) + x)
                                  2        2
       + 
              y(x) 2
         2cos(----) cos(y(x) + x) + 1
                2
    *
       cos
                 y(x) 2                     y(x)                  y(x)
            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
                   2                          2                     2
          + 
            - cos(x y(x)) + cos(y(x)) + x
   + 
     cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (31)
--R              2                                               y(x) 2
--R             x sin(x y(x)) - x sin(y(x)) + x cos(y(x) + x)sin(----)
--R                                                                2
--R           + 
--R                   y(x) 2
--R             x cos(----) cos(y(x) + x)
--R                     2
--R        *
--R            ,
--R           y (x)
--R
--R       + 
--R                                     y(x)     y(x)         y(x) 2
--R         x y(x)sin(x y(x)) + (2x cos(----)sin(----) + 2cos(----) )sin(y(x) + x)
--R                                       2        2            2
--R       + 
--R                y(x)                  y(x)
--R         - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
--R                  2                     2
--R       + 
--R                y(x) 2
--R         2x cos(----) cos(y(x) + x) + cos(y(x))
--R                  2
--R    *
--R       sin
--R                   y(x) 2                       y(x)                  y(x)
--R            2x cos(----) sin(y(x) + x) - 2x cos(----)cos(y(x) + x)sin(----)
--R                     2                            2                     2
--R          + 
--R            - x cos(x y(x)) + x cos(y(x))
--R   + 
--R                                                            y(x) 2
--R             - x sin(x y(x)) + sin(y(x)) - cos(y(x) + x)sin(----)
--R                                                              2
--R           + 
--R                   y(x) 2
--R             - cos(----) cos(y(x) + x)
--R                     2
--R        *
--R            ,
--R           y (x)
--R
--R       + 
--R                                  y(x)     y(x)
--R         - y(x)sin(x y(x)) - 2cos(----)sin(----)sin(y(x) + x)
--R                                    2        2
--R       + 
--R                y(x) 2
--R         - 2cos(----) cos(y(x) + x)
--R                  2
--R    *
--R       sin
--R                 y(x) 2                     y(x)                  y(x)
--R            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
--R                   2                          2                     2
--R          + 
--R            - cos(x y(x)) + cos(y(x))
--R   + 
--R                                                          y(x) 2
--R             x sin(x y(x)) - sin(y(x)) + cos(y(x) + x)sin(----)
--R                                                            2
--R           + 
--R                 y(x) 2
--R             cos(----) cos(y(x) + x)
--R                   2
--R        *
--R            ,
--R           y (x)
--R
--R       + 
--R                                y(x)     y(x)
--R         y(x)sin(x y(x)) + 2cos(----)sin(----)sin(y(x) + x)
--R                                  2        2
--R       + 
--R              y(x) 2
--R         2cos(----) cos(y(x) + x) + 1
--R                2
--R    *
--R       cos
--R                 y(x) 2                     y(x)                  y(x)
--R            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
--R                   2                          2                     2
--R          + 
--R            - cos(x y(x)) + cos(y(x)) + x
--R   + 
--R     cos(x)
--R                                                     Type: Expression Integer
--E 31

--S 32 of 97
ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)**2+x
 

               y(x) 2 ,              y(x) 2
   (32)  x cos(----) y (x) - y(x)cos(----)  + x
                 x                     x
                                                     Type: Expression Integer
--R 
--R
--R               y(x) 2 ,              y(x) 2
--R   (32)  x cos(----) y (x) - y(x)cos(----)  + x
--R                 x                     x
--R                                                     Type: Expression Integer
--E 32

--S 33 of 97
yx:=solve(ode363,y,x)
 

               y(x)     y(x)
         x cos(----)sin(----) + 2x log(x) + y(x)
                 x        x
   (33)  ---------------------------------------
                            2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               y(x)     y(x)
--R         x cos(----)sin(----) + 2x log(x) + y(x)
--R                 x        x
--R   (33)  ---------------------------------------
--R                            2x
--R                                          Type: Union(Expression Integer,...)
--E 33

--S 34 of 97
ode363expr := (x*D(yx,x)-yx)*cos(yx/x)**2+x
 

   (34)
                    y(x) 2         y(x) 2      ,              y(x) 2
           (- x sin(----)  + x cos(----)  + x)y (x) + y(x)sin(----)
                      x              x                          x
         + 
                   y(x)     y(x)            y(x) 2
           - x cos(----)sin(----) - y(x)cos(----)  - 2x log(x) - 2y(x) + 2x
                     x        x               x
      *
                   y(x)     y(x)                     2
             x cos(----)sin(----) + 2x log(x) + y(x)
                     x        x
         cos(---------------------------------------)
                                 2
                               2x
     + 
         2
       2x
  /
     2x
                                                     Type: Expression Integer
--R 
--R
--R   (34)
--R                    y(x) 2         y(x) 2      ,              y(x) 2
--R           (- x sin(----)  + x cos(----)  + x)y (x) + y(x)sin(----)
--R                      x              x                          x
--R         + 
--R                   y(x)     y(x)            y(x) 2
--R           - x cos(----)sin(----) - y(x)cos(----)  - 2x log(x) - 2y(x) + 2x
--R                     x        x               x
--R      *
--R                   y(x)     y(x)                     2
--R             x cos(----)sin(----) + 2x log(x) + y(x)
--R                     x        x
--R         cos(---------------------------------------)
--R                                 2
--R                               2x
--R     + 
--R         2
--R       2x
--R  /
--R     2x
--R                                                     Type: Expression Integer
--E 34

--S 35 of 97
ode364 := (y(x)*sin(y(x)/x)-x*cos(y(x)/x))*x*D(y(x),x)-_
            (x*cos(y(x)/x)+y(x)*sin(y(x)/x))*y(x)
 

   (35)
              y(x)     2    y(x)   ,          2    y(x)              y(x)
   (x y(x)sin(----) - x cos(----))y (x) - y(x) sin(----) - x y(x)cos(----)
                x             x                      x                 x
                                                     Type: Expression Integer
--R 
--R
--R   (35)
--R              y(x)     2    y(x)   ,          2    y(x)              y(x)
--R   (x y(x)sin(----) - x cos(----))y (x) - y(x) sin(----) - x y(x)cos(----)
--R                x             x                      x                 x
--R                                                     Type: Expression Integer
--E 35

--S 36 of 97
yx:=solve(ode364,y,x)
 

                     y(x)
   (36)  - x y(x)cos(----)
                       x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     y(x)
--R   (36)  - x y(x)cos(----)
--R                       x
--R                                          Type: Union(Expression Integer,...)
--E 36

--S 37 of 97
ode364expr := (yx*sin(yx/x)-x*cos(yx/x))*x*D(yx,x)-_
                (x*cos(yx/x)+yx*sin(yx/x))*yx
 

   (37)
           2    2    y(x)     y(x)     3        y(x) 2  ,
         (x y(x) cos(----)sin(----) - x y(x)cos(----) )y (x)
                       x        x                 x
       + 
                 3    y(x)     y(x)
         - x y(x) cos(----)sin(----)
                        x        x
    *
                   y(x)
       sin(y(x)cos(----))
                     x
   + 
             2        y(x)     3    y(x)   ,            2    y(x)
         (- x y(x)sin(----) + x cos(----))y (x) + x y(x) sin(----)
                        x             x                        x
       + 
           2        y(x)
         2x y(x)cos(----)
                      x
    *
                   y(x)
       cos(y(x)cos(----))
                     x
                                                     Type: Expression Integer
--R 
--R
--R   (37)
--R           2    2    y(x)     y(x)     3        y(x) 2  ,
--R         (x y(x) cos(----)sin(----) - x y(x)cos(----) )y (x)
--R                       x        x                 x
--R       + 
--R                 3    y(x)     y(x)
--R         - x y(x) cos(----)sin(----)
--R                        x        x
--R    *
--R                   y(x)
--R       sin(y(x)cos(----))
--R                     x
--R   + 
--R             2        y(x)     3    y(x)   ,            2    y(x)
--R         (- x y(x)sin(----) + x cos(----))y (x) + x y(x) sin(----)
--R                        x             x                        x
--R       + 
--R           2        y(x)
--R         2x y(x)cos(----)
--R                      x
--R    *
--R                   y(x)
--R       cos(y(x)cos(----))
--R                     x
--R                                                     Type: Expression Integer
--E 37

--S 38 of 97
ode434 := D(y(x),x)-1
 

          ,
   (38)  y (x) - 1

                                                     Type: Expression Integer
--R 
--R
--R          ,
--R   (38)  y (x) - 1
--R
--R                                                     Type: Expression Integer
--E 38

--S 39 of 97
ode434a:=solve(ode434,y,x)
 

   (39)  [particular= x,basis= [1]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (39)  [particular= x,basis= [1]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 39

--S 40 of 97
yx:=ode434a.particular
 

   (40)  x
                                                     Type: Expression Integer
--R 
--R
--R   (40)  x
--R                                                     Type: Expression Integer
--E 40

--S 41 of 97
ode434expr := D(yx,x)-1
 

   (41)  0
                                                     Type: Expression Integer
--R 
--R
--R   (41)  0
--R                                                     Type: Expression Integer
--E 41

--S 42 of 97
ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x)
 

                  4    2    3          2
          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
   (42)  y (x)= ------------------------------------
                                  x
                                            Type: Equation Expression Integer
--R 
--R
--R                  4    2    3          2
--R          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
--R   (42)  y (x)= ------------------------------------
--R                                  x
--R                                            Type: Equation Expression Integer
--E 42

--S 43 of 97
solve(ode683,y,x)
 

                           - x y(x) + 1
   (43)  -----------------------------------------------
                           3     2          3     2
                         6x log(x  + x) - 4x  + 3x  - 6x
                         -------------------------------
               3+-----+                 18
         x y(x)\|x + 1 %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           - x y(x) + 1
--R   (43)  -----------------------------------------------
--R                           3     2          3     2
--R                         6x log(x  + x) - 4x  + 3x  - 6x
--R                         -------------------------------
--R               3+-----+                 18
--R         x y(x)\|x + 1 %e
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 97
ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_
            (x-1)/x)
 

                  2    2                    3    2       2
          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
   (44)  y (x)= -------------------------------------------------------
                                          2
                                         x  - x
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                    3    2       2
--R          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
--R   (44)  y (x)= -------------------------------------------------------
--R                                          2
--R                                         x  - x
--R                                            Type: Equation Expression Integer
--E 44

--S 45 of 97
solve(ode703,y,x)
 

                 - x y(x) + 1
   (45)  ----------------------------
           2           - dilog(x) + x
         (x  - x)y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 - x y(x) + 1
--R   (45)  ----------------------------
--R           2           - dilog(x) + x
--R         (x  - x)y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 45

--S 46 of 97
ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_
            y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x)
 

   (46)
            2    2                           1          x    3    2    2
          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
    ,                                        x
   y (x)= ------------------------------------------------------------------
                                         1        x
                                   x log(-) - x %e
                                         x
                                            Type: Equation Expression Integer
--R 
--R
--R   (46)
--R            2    2                           1          x    3    2    2
--R          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
--R    ,                                        x
--R   y (x)= ------------------------------------------------------------------
--R                                         1        x
--R                                   x log(-) - x %e
--R                                         x
--R                                            Type: Equation Expression Integer
--E 46

--S 47 of 97
solve(ode714,y,x)
 

   (47)
       -
                                         1      %L     2
                     x %L log(%L) + log(--) - %e   + %L
                   ++                   %L
                   |   --------------------------------- d%L
                  ++                  1         %L
                              %L log(--) - %L %e
                                     %L
            y(x)%e
         *
            INTSIGN
           ,
               x
           ,
                                                        2
                                       - %L log(%L) - %L
                 --------------------------------------------------------------
                                                           1      %L     2
                                      %L %L log(%L) + log(--) - %e   + %L
                                    ++                    %L
                                    |    --------------------------------- d%L
                                   ++                   1         %L
                                                %L log(--) - %L %e
                       1      %L                       %L
                 (log(--) - %e  )%e
                      %L
              *
                 d%L
     + 
       1
  /
                                  1      %L     2
              x %L log(%L) + log(--) - %e   + %L
            ++                   %L
            |   --------------------------------- d%L
           ++                  1         %L
                       %L log(--) - %L %e
                              %L
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (47)
--R       -
--I                                         1      %I     2
--I                     x %I log(%I) + log(--) - %e   + %I
--I                   ++                   %I
--I                   |   --------------------------------- d%I
--I                  ++                  1         %I
--I                              %I log(--) - %I %e
--I                                     %I
--R            y(x)%e
--R         *
--R            INTSIGN
--R           ,
--R               x
--R           ,
--R                                                        2
--I                                       - %I log(%I) - %I
--R                 --------------------------------------------------------------
--I                                                           1      %I     2
--I                                      %I %I log(%I) + log(--) - %e   + %I
--I                                    ++                    %I
--I                                    |    --------------------------------- d%I
--I                                   ++                   1         %I
--I                                                %I log(--) - %I %e
--I                       1      %I                       %I
--R                 (log(--) - %e  )%e
--I                      %I
--R              *
--I                 d%I
--R     + 
--R       1
--R  /
--I                                  1      %I     2
--I              x %I log(%I) + log(--) - %e   + %I
--I            ++                   %I
--I            |   --------------------------------- d%I
--I           ++                  1         %I
--I                       %I log(--) - %I %e
--I                              %I
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 47

--S 48 of 97
ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x))
 

                  2    2                          x
          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
   (48)  y (x)= -----------------------------------
                                   x
                               x %e
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                          x
--R          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
--R   (48)  y (x)= -----------------------------------
--R                                   x
--R                               x %e
--R                                            Type: Equation Expression Integer
--E 48

--S 49 of 97
solve(ode719,y,x)
 

                    - x y(x) + 1
   (49)  ----------------------------------
                  x                 %L
                ++  %L log(2%L) + %e
                |   ------------------ d%L
               ++              %L
                          %L %e
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    - x y(x) + 1
--R   (49)  ----------------------------------
--I                  x                 %I
--I                ++  %I log(2%I) + %e
--I                |   ------------------ d%I
--I               ++              %I
--I                          %I %e
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 97
ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1))
 

                    2     2        4     2
          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
   (50)  y (x)= -----------------------------------
                               x + 1
                                            Type: Equation Expression Integer
--R 
--R
--R                    2     2        4     2
--R          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
--R   (50)  y (x)= -----------------------------------
--R                               x + 1
--R                                            Type: Equation Expression Integer
--E 50

--S 51 of 97
solve(ode736,y,x)
 

           2                  4     3     2
         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
   (51)  -------------------------------------------
                                 2
                       2y(x) - 2x  - 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2                  4     3     2
--R         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
--R   (51)  -------------------------------------------
--R                                 2
--R                       2y(x) - 2x  - 2
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 97
ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_
            log((x-1)*(1+x)/x)*x*y(x))/x)
 

                                     2
                       2            x  - 1
                (x y(x)  - y(x))log(------) - y(x)
          ,                            x
   (52)  y (x)= ----------------------------------
                                 x
                                            Type: Equation Expression Integer
--R 
--R
--R                                     2
--R                       2            x  - 1
--R                (x y(x)  - y(x))log(------) - y(x)
--R          ,                            x
--R   (52)  y (x)= ----------------------------------
--R                                 x
--R                                            Type: Equation Expression Integer
--E 52

--S 53 of 97
solve(ode765,y,x)
 

                   - x y(x) + 1
   (53)  --------------------------------
                          2
                        %L  - 1
                  x log(-------) + 1
                ++         %L
                |   ---------------- d%L
               ++          %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   - x y(x) + 1
--R   (53)  --------------------------------
--R                          2
--I                        %I  - 1
--R                  x log(-------) + 1
--I                ++         %I
--I                |   ---------------- d%I
--I               ++          %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 53

--S 54 of 97
ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_
            log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x))
 

                                                      2
                                 2    2              x  - 1
                - y(x)log(x) + (x y(x)  - x y(x))log(------)
          ,                                             x
   (54)  y (x)= --------------------------------------------
                                  x log(x)
                                            Type: Equation Expression Integer
--R 
--R
--R                                                      2
--R                                 2    2              x  - 1
--R                - y(x)log(x) + (x y(x)  - x y(x))log(------)
--R          ,                                             x
--R   (54)  y (x)= --------------------------------------------
--R                                  x log(x)
--R                                            Type: Equation Expression Integer
--E 54

--S 55 of 97
solve(ode766,y,x)
 

   (55)
       -
                                          2
                                        %L  - 1
                     x log(%L) + %L log(-------)
                   ++                      %L
                   |   ------------------------- d%L
                  ++           %L log(%L)
            y(x)%e
         *
                                           2
                                         %L  - 1
               x                  %L log(-------)
             ++                             %L
             |   - --------------------------------------------- d%L
            ++                                       2
                                                   %L  - 1
                               %L log(%L) + %L log(-------)
                             ++                       %L
                             |    ------------------------- d%L
                            ++            %L log(%L)
                   log(%L)%e
     + 
       1
  /
                                   2
                                 %L  - 1
              x log(%L) + %L log(-------)
            ++                      %L
            |   ------------------------- d%L
           ++           %L log(%L)
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (55)
--R       -
--R                                          2
--I                                        %I  - 1
--I                     x log(%I) + %I log(-------)
--I                   ++                      %I
--I                   |   ------------------------- d%I
--I                  ++           %I log(%I)
--R            y(x)%e
--R         *
--R                                           2
--I                                         %I  - 1
--I               x                  %I log(-------)
--I             ++                             %I
--I             |   - --------------------------------------------- d%I
--R            ++                                       2
--I                                                   %I  - 1
--I                               %I log(%I) + %I log(-------)
--I                             ++                       %I
--I                             |    ------------------------- d%I
--I                            ++            %I log(%I)
--I                   log(%I)%e
--R     + 
--R       1
--R  /
--R                                   2
--I                                 %I  - 1
--I              x log(%I) + %I log(-------)
--I            ++                      %I
--I            |   ------------------------- d%I
--I           ++           %I log(%I)
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 55

--S 56 of 97
ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_
              log((x**2+1)/x)*x**2*y(x))/x/log(1/x))
 

                                       2
                  2    2              x  + 1            1
                (x y(x)  - x y(x))log(------) - y(x)log(-)
          ,                              x              x
   (56)  y (x)= ------------------------------------------
                                       1
                                 x log(-)
                                       x
                                            Type: Equation Expression Integer
--R 
--R
--R                                       2
--R                  2    2              x  + 1            1
--R                (x y(x)  - x y(x))log(------) - y(x)log(-)
--R          ,                              x              x
--R   (56)  y (x)= ------------------------------------------
--R                                       1
--R                                 x log(-)
--R                                       x
--R                                            Type: Equation Expression Integer
--E 56

--S 57 of 97
solve(ode776,y,x)
 

                        - x y(x) + 1
   (57)  -----------------------------------------
                             2
                           %L  + 1         1
                  x %L log(-------) + log(--)
                ++            %L          %L
                |   ------------------------- d%L
               ++                   1
                            %L log(--)
                                   %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        - x y(x) + 1
--R   (57)  -----------------------------------------
--R                             2
--I                           %I  + 1         1
--I                  x %I log(-------) + log(--)
--I                ++            %I          %I
--I                |   ------------------------- d%I
--R               ++                   1
--I                            %I log(--)
--I                                   %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 57

--S 58 of 97
ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_
            25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/_
            (-5*y(x)+2*x**3+10*x**(1/2)-5)/x)
 

                               3       +-+      3          6      3
          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
   (58)  y (x)= --------------------------------------------------------------
                                    +-+                 4
                                50x\|x  - 25x y(x) + 10x  - 25x
                                            Type: Equation Expression Integer
--R 
--R
--R                               3       +-+      3          6      3
--R          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
--R   (58)  y (x)= --------------------------------------------------------------
--R                                    +-+                 4
--R                                50x\|x  - 25x y(x) + 10x  - 25x
--R                                            Type: Equation Expression Integer
--E 58

--S 59 of 97
solve(ode872,y,x)
 

   (59)
               +-+                  3        +-+         2       3
       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
     + 
           6      3
       - 4x  + 20x  - 100x
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (59)
--R               +-+                  3        +-+         2       3
--R       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
--R     + 
--R           6      3
--R       - 4x  + 20x  - 100x
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 59

--S 60 of 97
ode555 := sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x)
 

          +----------+
          | ,   2          ,
   (60)   |y (x)  + 1  + xy (x) - y(x)
         \|
                                                     Type: Expression Integer
--R 
--R
--R          +----------+
--R          | ,   2          ,
--R   (60)   |y (x)  + 1  + xy (x) - y(x)
--R         \|
--R                                                     Type: Expression Integer
--E 60

--S 61 of 97
solve(ode555,y,x)
 

               +-----------+
               | ,    2
            x  |y (%L)  + 1  - y(x)
          ++  \|
   (61)   |   --------------------- d%L
         ++              2
                       %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-----------+
--R               | ,    2
--I            x  |y (%I)  + 1  - y(x)
--R          ++  \|
--I   (61)   |   --------------------- d%I
--R         ++              2
--I                       %I
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 97
ode557 := x*(sqrt(D(y(x),x)**2+1)+D(y(x),x))-y(x)
 

           +----------+
           | ,   2          ,
   (62)  x |y (x)  + 1  + xy (x) - y(x)
          \|
                                                     Type: Expression Integer
--R 
--R
--R           +----------+
--R           | ,   2          ,
--R   (62)  x |y (x)  + 1  + xy (x) - y(x)
--R          \|
--R                                                     Type: Expression Integer
--E 62

--S 63 of 97
solve(ode557,y,x)
 

                 +-----------+
                 | ,    2
            x %L |y (%L)  + 1  - y(x)
          ++    \|
   (63)   |   ----------------------- d%L
         ++               2
                        %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-----------+
--R                 | ,    2
--I            x %I |y (%I)  + 1  - y(x)
--R          ++    \|
--I   (63)   |   ----------------------- d%I
--R         ++               2
--I                        %I
--R                                          Type: Union(Expression Integer,...)
--E 63

--S 64 of 97
ode558 := a*x*sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x)
 

             +----------+
             | ,   2          ,
   (64)  a x |y (x)  + 1  + xy (x) - y(x)
            \|
                                                     Type: Expression Integer
--R 
--R
--R             +----------+
--R             | ,   2          ,
--R   (64)  a x |y (x)  + 1  + xy (x) - y(x)
--R            \|
--R                                                     Type: Expression Integer
--E 64

--S 65 of 97
solve(ode558,y,x)
 

                   +-----------+
                   | ,    2
            x %L a |y (%L)  + 1  - y(x)
          ++      \|
   (65)   |   ------------------------- d%L
         ++                2
                         %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +-----------+
--R                   | ,    2
--I            x %I a |y (%I)  + 1  - y(x)
--R          ++      \|
--I   (65)   |   ------------------------- d%I
--R         ++                2
--I                         %I
--R                                          Type: Union(Expression Integer,...)
--E 65

--S 66 of 97
ode562 := a*(D(y(x),x)**3+1)**(1/3)+b*x*D(y(x),x)-y(x)
 

            +----------+
            | ,   3           ,
   (66)  a 3|y (x)  + 1 + b xy (x) - y(x)
           \|
                                                     Type: Expression Integer
--R 
--R
--R            +----------+
--R            | ,   3           ,
--R   (66)  a 3|y (x)  + 1 + b xy (x) - y(x)
--R           \|
--R                                                     Type: Expression Integer
--E 66

--S 67 of 97
solve(ode562,y,x)
 

                    log(%L)                         log(%L)
                  - -------  +-----------+        - -------
                       b     | ,    3                  b
            x a %e          3|y (%L)  + 1 - y(x)%e
          ++                \|
   (67)   |   --------------------------------------------- d%L
         ++                         %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                    log(%I)                         log(%I)
--R                  - -------  +-----------+        - -------
--R                       b     | ,    3                  b
--I            x a %e          3|y (%I)  + 1 - y(x)%e
--R          ++                \|
--I   (67)   |   --------------------------------------------- d%I
--I         ++                         %I
--R                                          Type: Union(Expression Integer,...)
--E 67

--S 68 of 97
ode563 := log(D(y(x),x))+x*D(y(x),x)+a*y(x)+b
 

              ,         ,
   (68)  log(y (x)) + xy (x) + a y(x) + b

                                                     Type: Expression Integer
--R 
--R
--R              ,         ,
--R   (68)  log(y (x)) + xy (x) + a y(x) + b
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 97
solve(ode563,y,x)
 

                a log(%L)     ,                      a log(%L)
            x %e         log(y (%L)) + (a y(x) + b)%e
          ++
   (69)   |   ------------------------------------------------ d%L
         ++                          %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                a log(%I)     ,                      a log(%I)
--I            x %e         log(y (%I)) + (a y(x) + b)%e
--R          ++
--I   (69)   |   ------------------------------------------------ d%I
--I         ++                          %I
--R                                          Type: Union(Expression Integer,...)
--E 69

--S 70 of 97
ode564 := log(D(y(x),x))+a*(x*D(y(x),x)-y(x))
 

              ,           ,
   (70)  log(y (x)) + a xy (x) - a y(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,           ,
--R   (70)  log(y (x)) + a xy (x) - a y(x)
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 97
solve(ode564,y,x)
 

                   ,
            x log(y (%L)) - a y(x)
          ++
   (71)   |   -------------------- d%L
         ++              2
                       %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   ,
--I            x log(y (%I)) - a y(x)
--R          ++
--I   (71)   |   -------------------- d%I
--R         ++              2
--I                       %I
--R                                          Type: Union(Expression Integer,...)
--E 71

--S 72 of 97
ode571 := a*x**n*f(D(y(x),x))+x*D(y(x),x)-y(x)
 

            n   ,         ,
   (72)  a x f(y (x)) + xy (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R            n   ,         ,
--R   (72)  a x f(y (x)) + xy (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 97
solve(ode571,y,x)
 

                  n   ,
            x a %L f(y (%L)) - y(x)
          ++
   (73)   |   --------------------- d%L
         ++              2
                       %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  n   ,
--I            x a %I f(y (%I)) - y(x)
--R          ++
--I   (73)   |   --------------------- d%I
--R         ++              2
--I                       %I
--R                                          Type: Union(Expression Integer,...)
--E 73

--S 74 of 97
ode573 := f(x*D(y(x),x)**2)+2*x*D(y(x),x)-y(x)
 

              ,   2       ,
   (74)  f(x y (x) ) + 2xy (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,   2       ,
--R   (74)  f(x y (x) ) + 2xy (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 97
solve(ode573,y,x)
 

                    ,    2
            x f(%L y (%L) ) - y(x)
          ++
   (75)   |   -------------------- d%L
         ++             +--+
                     %L\|%L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    ,    2
--I            x f(%I y (%I) ) - y(x)
--R          ++
--I   (75)   |   -------------------- d%I
--R         ++             +--+
--I                     %I\|%I
--R                                          Type: Union(Expression Integer,...)
--E 75

--S 76 of 97
ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x)
 

                  4    2    3          2
          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
   (76)  y (x)= ------------------------------------
                                  x
                                            Type: Equation Expression Integer
--R 
--R
--R                  4    2    3          2
--R          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
--R   (76)  y (x)= ------------------------------------
--R                                  x
--R                                            Type: Equation Expression Integer
--E 76

--S 77 of 97
solve(ode683,y,x)
 

                           - x y(x) + 1
   (77)  -----------------------------------------------
                           3     2          3     2
                         6x log(x  + x) - 4x  + 3x  - 6x
                         -------------------------------
               3+-----+                 18
         x y(x)\|x + 1 %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           - x y(x) + 1
--R   (77)  -----------------------------------------------
--R                           3     2          3     2
--R                         6x log(x  + x) - 4x  + 3x  - 6x
--R                         -------------------------------
--R               3+-----+                 18
--R         x y(x)\|x + 1 %e
--R                                          Type: Union(Expression Integer,...)
--E 77

--S 78 of 97
ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_
            (x-1)/x)
 

                  2    2                    3    2       2
          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
   (78)  y (x)= -------------------------------------------------------
                                          2
                                         x  - x
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                    3    2       2
--R          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
--R   (78)  y (x)= -------------------------------------------------------
--R                                          2
--R                                         x  - x
--R                                            Type: Equation Expression Integer
--E 78

--S 79 of 97
solve(ode703,y,x)
 

                 - x y(x) + 1
   (79)  ----------------------------
           2           - dilog(x) + x
         (x  - x)y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 - x y(x) + 1
--R   (79)  ----------------------------
--R           2           - dilog(x) + x
--R         (x  - x)y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 79

--S 80 of 97
ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_
           y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x)
 

   (80)
            2    2                           1          x    3    2    2
          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
    ,                                        x
   y (x)= ------------------------------------------------------------------
                                         1        x
                                   x log(-) - x %e
                                         x
                                            Type: Equation Expression Integer
--R 
--R
--R   (80)
--R            2    2                           1          x    3    2    2
--R          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
--R    ,                                        x
--R   y (x)= ------------------------------------------------------------------
--R                                         1        x
--R                                   x log(-) - x %e
--R                                         x
--R                                            Type: Equation Expression Integer
--E 80

--S 81 of 97
solve(ode714,y,x)
 

   (81)
       -
                                         1      %L     2
                     x %L log(%L) + log(--) - %e   + %L
                   ++                   %L
                   |   --------------------------------- d%L
                  ++                  1         %L
                              %L log(--) - %L %e
                                     %L
            y(x)%e
         *
            INTSIGN
           ,
               x
           ,
                                                        2
                                       - %L log(%L) - %L
                 --------------------------------------------------------------
                                                           1      %L     2
                                      %L %L log(%L) + log(--) - %e   + %L
                                    ++                    %L
                                    |    --------------------------------- d%L
                                   ++                   1         %L
                                                %L log(--) - %L %e
                       1      %L                       %L
                 (log(--) - %e  )%e
                      %L
              *
                 d%L
     + 
       1
  /
                                  1      %L     2
              x %L log(%L) + log(--) - %e   + %L
            ++                   %L
            |   --------------------------------- d%L
           ++                  1         %L
                       %L log(--) - %L %e
                              %L
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (81)
--R       -
--I                                         1      %I     2
--I                     x %I log(%I) + log(--) - %e   + %I
--I                   ++                   %I
--I                   |   --------------------------------- d%I
--I                  ++                  1         %I
--I                              %I log(--) - %I %e
--I                                     %I
--R            y(x)%e
--R         *
--R            INTSIGN
--R           ,
--R               x
--R           ,
--R                                                        2
--I                                       - %I log(%I) - %I
--R                 --------------------------------------------------------------
--I                                                           1      %I     2
--I                                      %I %I log(%I) + log(--) - %e   + %I
--I                                    ++                    %I
--I                                    |    --------------------------------- d%I
--I                                   ++                   1         %I
--I                                                %I log(--) - %I %e
--I                       1      %I                       %I
--R                 (log(--) - %e  )%e
--I                      %I
--R              *
--I                 d%I
--R     + 
--R       1
--R  /
--I                                  1      %I     2
--I              x %I log(%I) + log(--) - %e   + %I
--I            ++                   %I
--I            |   --------------------------------- d%I
--I           ++                  1         %I
--I                       %I log(--) - %I %e
--I                              %I
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 81

--S 82 of 97
ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x))
 

                  2    2                          x
          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
   (82)  y (x)= -----------------------------------
                                   x
                               x %e
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                          x
--R          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
--R   (82)  y (x)= -----------------------------------
--R                                   x
--R                               x %e
--R                                            Type: Equation Expression Integer
--E 82

--S 83 of 97
solve(ode719,y,x)
 

                    - x y(x) + 1
   (83)  ----------------------------------
                  x                 %L
                ++  %L log(2%L) + %e
                |   ------------------ d%L
               ++              %L
                          %L %e
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    - x y(x) + 1
--R   (83)  ----------------------------------
--I                  x                 %I
--I                ++  %I log(2%I) + %e
--I                |   ------------------ d%I
--I               ++              %I
--I                          %I %e
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 83

--S 84 of 97
ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1))
 

                    2     2        4     2
          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
   (84)  y (x)= -----------------------------------
                               x + 1
                                            Type: Equation Expression Integer
--R 
--R
--R                    2     2        4     2
--R          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
--R   (84)  y (x)= -----------------------------------
--R                               x + 1
--R                                            Type: Equation Expression Integer
--E 84

--S 85 of 97
solve(ode736,y,x)
 

           2                  4     3     2
         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
   (85)  -------------------------------------------
                                 2
                       2y(x) - 2x  - 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2                  4     3     2
--R         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
--R   (85)  -------------------------------------------
--R                                 2
--R                       2y(x) - 2x  - 2
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 97
ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_
            log((x-1)*(1+x)/x)*x*y(x))/x)
 

                                     2
                       2            x  - 1
                (x y(x)  - y(x))log(------) - y(x)
          ,                            x
   (86)  y (x)= ----------------------------------
                                 x
                                            Type: Equation Expression Integer
--R 
--R
--R                                     2
--R                       2            x  - 1
--R                (x y(x)  - y(x))log(------) - y(x)
--R          ,                            x
--R   (86)  y (x)= ----------------------------------
--R                                 x
--R                                            Type: Equation Expression Integer
--E 86

--S 87 of 97
solve(ode765,y,x)
 

                   - x y(x) + 1
   (87)  --------------------------------
                          2
                        %L  - 1
                  x log(-------) + 1
                ++         %L
                |   ---------------- d%L
               ++          %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   - x y(x) + 1
--R   (87)  --------------------------------
--R                          2
--I                        %I  - 1
--R                  x log(-------) + 1
--I                ++         %I
--I                |   ---------------- d%I
--I               ++          %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 87

--S 88 of 97
ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_
           log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x))
 

                                                      2
                                 2    2              x  - 1
                - y(x)log(x) + (x y(x)  - x y(x))log(------)
          ,                                             x
   (88)  y (x)= --------------------------------------------
                                  x log(x)
                                            Type: Equation Expression Integer
--R 
--R
--R                                                      2
--R                                 2    2              x  - 1
--R                - y(x)log(x) + (x y(x)  - x y(x))log(------)
--R          ,                                             x
--R   (88)  y (x)= --------------------------------------------
--R                                  x log(x)
--R                                            Type: Equation Expression Integer
--E 88

--S 89 of 97
solve(ode766,y,x)
 

   (89)
       -
                                          2
                                        %L  - 1
                     x log(%L) + %L log(-------)
                   ++                      %L
                   |   ------------------------- d%L
                  ++           %L log(%L)
            y(x)%e
         *
                                           2
                                         %L  - 1
               x                  %L log(-------)
             ++                             %L
             |   - --------------------------------------------- d%L
            ++                                       2
                                                   %L  - 1
                               %L log(%L) + %L log(-------)
                             ++                       %L
                             |    ------------------------- d%L
                            ++            %L log(%L)
                   log(%L)%e
     + 
       1
  /
                                   2
                                 %L  - 1
              x log(%L) + %L log(-------)
            ++                      %L
            |   ------------------------- d%L
           ++           %L log(%L)
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (89)
--R       -
--R                                          2
--I                                        %I  - 1
--I                     x log(%I) + %I log(-------)
--I                   ++                      %I
--I                   |   ------------------------- d%I
--I                  ++           %I log(%I)
--R            y(x)%e
--R         *
--R                                           2
--I                                         %I  - 1
--I               x                  %I log(-------)
--I             ++                             %I
--I             |   - --------------------------------------------- d%I
--R            ++                                       2
--I                                                   %I  - 1
--I                               %I log(%I) + %I log(-------)
--I                             ++                       %I
--I                             |    ------------------------- d%I
--I                            ++            %I log(%I)
--I                   log(%I)%e
--R     + 
--R       1
--R  /
--R                                   2
--I                                 %I  - 1
--I              x log(%I) + %I log(-------)
--I            ++                      %I
--I            |   ------------------------- d%I
--I           ++           %I log(%I)
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 89

--S 90 of 97
ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_
            log((x**2+1)/x)*x**2*y(x))/x/log(1/x))
 

                                       2
                  2    2              x  + 1            1
                (x y(x)  - x y(x))log(------) - y(x)log(-)
          ,                              x              x
   (90)  y (x)= ------------------------------------------
                                       1
                                 x log(-)
                                       x
                                            Type: Equation Expression Integer
--R 
--R
--R                                       2
--R                  2    2              x  + 1            1
--R                (x y(x)  - x y(x))log(------) - y(x)log(-)
--R          ,                              x              x
--R   (90)  y (x)= ------------------------------------------
--R                                       1
--R                                 x log(-)
--R                                       x
--R                                            Type: Equation Expression Integer
--E 90

--S 91 of 97
solve(ode776,y,x)
 

                        - x y(x) + 1
   (91)  -----------------------------------------
                             2
                           %L  + 1         1
                  x %L log(-------) + log(--)
                ++            %L          %L
                |   ------------------------- d%L
               ++                   1
                            %L log(--)
                                   %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        - x y(x) + 1
--R   (91)  -----------------------------------------
--R                             2
--I                           %I  + 1         1
--I                  x %I log(-------) + log(--)
--I                ++            %I          %I
--I                |   ------------------------- d%I
--R               ++                   1
--I                            %I log(--)
--I                                   %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 91

--S 92 of 97
ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_
            25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/(-5*y(x)+2*x**3+_
            10*x**(1/2)-5)/x)
 

                               3       +-+      3          6      3
          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
   (92)  y (x)= --------------------------------------------------------------
                                    +-+                 4
                                50x\|x  - 25x y(x) + 10x  - 25x
                                            Type: Equation Expression Integer
--R 
--R
--R                               3       +-+      3          6      3
--R          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
--R   (92)  y (x)= --------------------------------------------------------------
--R                                    +-+                 4
--R                                50x\|x  - 25x y(x) + 10x  - 25x
--R                                            Type: Equation Expression Integer
--E 92

--S 93 of 97
solve(ode872,y,x)
 

   (93)
               +-+                  3        +-+         2       3
       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
     + 
           6      3
       - 4x  + 20x  - 100x
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (93)
--R               +-+                  3        +-+         2       3
--R       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
--R     + 
--R           6      3
--R       - 4x  + 20x  - 100x
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 93

--S 94 of 97
ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2-x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*log(x)+x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*y(x)+2*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)+x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)**2)/x)
 

   (94)
    ,
   y (x) =

             2    2      2      2    2    2               2    2    2
           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
        *
                     2
              2log(x)        2
             ---------- ----------
             log(x) + 1 log(x) + 1
           %e          x
       + 
         - y(x)
    /
       x log(x) + x
                                            Type: Equation Expression Integer
--R 
--R
--R   (94)
--R    ,
--R   y (x) =
--R
--R             2    2      2      2    2    2               2    2    2
--R           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
--R        *
--R                     2
--R              2log(x)        2
--R             ---------- ----------
--R             log(x) + 1 log(x) + 1
--R           %e          x
--R       + 
--R         - y(x)
--R    /
--R       x log(x) + x
--R                                            Type: Equation Expression Integer
--E 94

--S 95 of 97
solve(ode956,y,x)
 

          - y(x)log(x) - y(x) + 1
   (95)  -------------------------
                4                4
               x                x
               --               --
                4                4
         y(x)%e  log(x) + y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          - y(x)log(x) - y(x) + 1
--R   (95)  -------------------------
--R                4                4
--R               x                x
--R               --               --
--R                4                4
--R         y(x)%e  log(x) + y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 95

--S 96 of 97
ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)-x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*log(x)+x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*y(x)+2*x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)+x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)**2)/x)
 

   (96)
    ,
   y (x) =

             3    2      2      3    2    3               3    2    3
           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
        *
                     2
              2log(x)        2
             ---------- ----------
             log(x) + 1 log(x) + 1
           %e          x
       + 
         - y(x)
    /
       x log(x) + x
                                            Type: Equation Expression Integer
--R 
--R
--R   (96)
--R    ,
--R   y (x) =
--R
--R             3    2      2      3    2    3               3    2    3
--R           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
--R        *
--R                     2
--R              2log(x)        2
--R             ---------- ----------
--R             log(x) + 1 log(x) + 1
--R           %e          x
--R       + 
--R         - y(x)
--R    /
--R       x log(x) + x
--R                                            Type: Equation Expression Integer
--E 96

--S 97 of 97
solve(ode957,y,x)
 

          - y(x)log(x) - y(x) + 1
   (97)  -------------------------
                5                5
               x                x
               --               --
                5                5
         y(x)%e  log(x) + y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          - y(x)log(x) - y(x) + 1
--R   (97)  -------------------------
--R                5                5
--R               x                x
--R               --               --
--R                5                5
--R         y(x)%e  log(x) + y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 97
)spool
 
Starts dribbling to ruleset.output (2009/2/17, 17:57:55).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 9
TrigLinearRules := rule
   sin(x) * sin(y) == cos(x-y)/2 - cos(x+y)/2
   cos(x) * cos(y) == cos(x+y)/2 + cos(x-y)/2
   sin(x) * cos(y) == sin(x+y)/2 + sin(x-y)/2
   sin(x)**(n | integer? n and n > 0) == (1-cos(2*x))/2 * sin(x)**(n-2)
   cos(x)**(n | integer? n and n > 0) == (1+cos(2*x))/2 * cos(x)**(n-2)
 

   (1)
                       - %B cos(y + x) + %B cos(y - x)
   {%B sin(x)sin(y) == -------------------------------,
                                      2
                       %C cos(y + x) + %C cos(y - x)
    %C cos(x)cos(y) == -----------------------------,
                                     2
                       %D sin(y + x) - %D sin(y - x)
    %D cos(y)sin(x) == -----------------------------,
                                     2
                                    n - 2                                n - 2
          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
    sin(x)  == --------------------------, cos(x)  == ------------------------}
                            2                                     2
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)
--R                       - %B cos(y + x) + %B cos(y - x)
--R   {%B sin(x)sin(y) == -------------------------------,
--R                                      2
--R                       %C cos(y + x) + %C cos(y - x)
--R    %C cos(x)cos(y) == -----------------------------,
--R                                     2
--R                       %D sin(y + x) - %D sin(y - x)
--R    %D cos(y)sin(x) == -----------------------------,
--R                                     2
--R                                    n - 2                                n - 2
--R          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
--R    sin(x)  == --------------------------, cos(x)  == ------------------------}
--R                            2                                     2
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 1

--S 2 of 9
sin(a)*cos(b) + sin(a)*cos(a) + cos(2*a)*cos(3*a)
 

   (2)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 9
TrigLinearRules %
 

        sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
   (3)  ----------------------------------------------------
                                  2
                                                     Type: Expression Integer
--R 
--R
--R        sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
--R   (3)  ----------------------------------------------------
--R                                  2
--R                                                     Type: Expression Integer
--E 3

--S 4 of 9
sin(a) * sin(2*a) * sin(3*a) * sin(4*a)
 

   (4)  sin(a)sin(2a)sin(3a)sin(4a)
                                                     Type: Expression Integer
--R 
--R
--R   (4)  sin(a)sin(2a)sin(3a)sin(4a)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 9
TrigLinearRules %
 

        cos(10a) - cos(8a) - cos(6a) + 1
   (5)  --------------------------------
                        8
                                                     Type: Expression Integer
--R 
--R
--R        cos(10a) - cos(8a) - cos(6a) + 1
--R   (5)  --------------------------------
--R                        8
--R                                                     Type: Expression Integer
--E 5

--S 6 of 9
f := operator 'f
 

   (6)  f
                                                          Type: BasicOperator
--R 
--R
--R   (6)  f
--R                                                          Type: BasicOperator
--E 6

--S 7 of 9
FLinearRules := rule
  f(a + b, x) == f(a, x) + f(b, x)
  f(c * a, x | freeOf?(c, x)) == c * f(a, x)
 

   (7)  {f(b + a,x) == 'f(b,x) + 'f(a,x),f(a c,x) == c'f(a,x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (7)  {f(b + a,x) == 'f(b,x) + 'f(a,x),f(a c,x) == c'f(a,x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 7

--S 8 of 9
f(2*x + a * log(x) + x * log(x), x)
 

   (8)  f((x + a)log(x) + 2x,x)
                                                     Type: Expression Integer
--R 
--R
--R   (8)  f((x + a)log(x) + 2x,x)
--R                                                     Type: Expression Integer
--E 8

--S 9 of 9
FLinearRules %
 

   (9)  (f(x,x) + f(a,x))log(x) + 2f(x,x)
                                                     Type: Expression Integer
--R 
--R
--R   (9)  (f(x,x) + f(a,x))log(x) + 2f(x,x)
--R                                                     Type: Expression Integer
--E 9
)spool 
 
Starts dribbling to schaum17.output (2009/2/17, 17:58:44).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(sin(a*x),x)
 

          cos(a x)
   (1)  - --------
              a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          cos(a x)
--R   (1)  - --------
--R              a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=-cos(a*x)/a
 

          cos(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cos(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3      14:339 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*sin(a*x),x)
 

        sin(a x) - a x cos(a x)
   (1)  -----------------------
                    2
                   a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sin(a x) - a x cos(a x)
--R   (1)  -----------------------
--R                    2
--R                   a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=sin(a*x)/a^2-(x*cos(a*x))/a
 

        sin(a x) - a x cos(a x)
   (2)  -----------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R        sin(a x) - a x cos(a x)
--R   (2)  -----------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E

--S 6      14:340 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2*sin(a*x),x)
 

                            2 2
        2a x sin(a x) + (- a x  + 2)cos(a x)
   (1)  ------------------------------------
                          3
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            2 2
--R        2a x sin(a x) + (- a x  + 2)cos(a x)
--R   (1)  ------------------------------------
--R                          3
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=(2*x)/a^2*sin(a*x)+(2/a^3-x^2/a)*cos(a*x)
 

                            2 2
        2a x sin(a x) + (- a x  + 2)cos(a x)
   (2)  ------------------------------------
                          3
                         a
                                                     Type: Expression Integer
--R
--R                            2 2
--R        2a x sin(a x) + (- a x  + 2)cos(a x)
--R   (2)  ------------------------------------
--R                          3
--R                         a
--R                                                     Type: Expression Integer
--E

--S 9      14:341 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(x^3*sin(a*x),x)
 

           2 2                    3 3
        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
   (1)  ---------------------------------------------
                               4
                              a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2                    3 3
--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
--R   (1)  ---------------------------------------------
--R                               4
--R                              a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=((3*x^2)/a^2-6/a^4)*sin(a*x)+(6*x/a^3-x^3/a)*cos(a*x)
 

           2 2                    3 3
        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
   (2)  ---------------------------------------------
                               4
                              a
                                                     Type: Expression Integer
--R
--R           2 2                    3 3
--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
--R   (2)  ---------------------------------------------
--R                               4
--R                              a
--R                                                     Type: Expression Integer
--E

--S 12     14:342 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13     14:343 Schaums and Axiom agree by definition
aa:=integrate(sin(x)/x,x)
 

   (1)  Si(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 14     14:344 Axiom cannot compute this integral
aa:=integrate(sin(a*x)/x^2,x)
 

           x
         ++  sin(%I a)
   (1)   |   --------- d%I
        ++        2
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sin(%I a)
--I   (1)   |   --------- d%I
--R        ++        2
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(1/sin(a*x),x)
 

              sin(a x)
        log(------------)
            cos(a x) + 1
   (1)  -----------------
                a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)
--R        log(------------)
--R            cos(a x) + 1
--R   (1)  -----------------
--R                a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16
bb:=1/a*log(tan((a*x)/2))
 

                a x
        log(tan(---))
                 2
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---))
--R                 2
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 17
cc:=aa-bb
 

                  a x           sin(a x)
        - log(tan(---)) + log(------------)
                   2          cos(a x) + 1
   (3)  -----------------------------------
                         a
                                                     Type: Expression Integer
--R
--R                  a x           sin(a x)
--R        - log(tan(---)) + log(------------)
--R                   2          cos(a x) + 1
--R   (3)  -----------------------------------
--R                         a
--R                                                     Type: Expression Integer
--E

--S 18     14:345 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 19     14:346 Axiom cannot compute this integral
aa:=integrate(x/sin(a*x),x)
 

           x
         ++      %I
   (1)   |   --------- d%I
        ++   sin(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   --------- d%I
--I        ++   sin(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(sin(a*x)^2,x)
 

        - cos(a x)sin(a x) + a x
   (1)  ------------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - cos(a x)sin(a x) + a x
--R   (1)  ------------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 21
bb:=x/2-sin(2*a*x)/(4*a)
 

        - sin(2a x) + 2a x
   (2)  ------------------
                4a
                                                     Type: Expression Integer
--R
--R        - sin(2a x) + 2a x
--R   (2)  ------------------
--R                4a
--R                                                     Type: Expression Integer
--E

--S 22
cc:=aa-bb
 

        sin(2a x) - 2cos(a x)sin(a x)
   (3)  -----------------------------
                      4a
                                                     Type: Expression Integer
--R
--R        sin(2a x) - 2cos(a x)sin(a x)
--R   (3)  -----------------------------
--R                      4a
--R                                                     Type: Expression Integer
--E

--S 23     14:347 Schaums and Axiom agreee
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 24
aa:=integrate(x*sin(a*x)^2,x)
 

                                          2    2 2
        - 2a x cos(a x)sin(a x) - cos(a x)  + a x
   (1)  ------------------------------------------
                              2
                            4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          2    2 2
--R        - 2a x cos(a x)sin(a x) - cos(a x)  + a x
--R   (1)  ------------------------------------------
--R                              2
--R                            4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25
bb:=x^2/4-(x*sin(2*a*x))/(4*a)-cos(2*a*x)/(8*a^2)
 

                                         2 2
        - 2a x sin(2a x) - cos(2a x) + 2a x
   (2)  ------------------------------------
                           2
                         8a
                                                     Type: Expression Integer
--R
--R                                         2 2
--R        - 2a x sin(2a x) - cos(2a x) + 2a x
--R   (2)  ------------------------------------
--R                           2
--R                         8a
--R                                                     Type: Expression Integer
--E

--S 26
cc:=aa-bb
 

                                                                      2
        2a x sin(2a x) - 4a x cos(a x)sin(a x) + cos(2a x) - 2cos(a x)
   (3)  ---------------------------------------------------------------
                                        2
                                      8a
                                                     Type: Expression Integer
--R
--R                                                                      2
--R        2a x sin(2a x) - 4a x cos(a x)sin(a x) + cos(2a x) - 2cos(a x)
--R   (3)  ---------------------------------------------------------------
--R                                        2
--R                                      8a
--R                                                     Type: Expression Integer
--E

--S 27     14:348 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           1
   (4)  - ---
            2
          8a
                                                     Type: Expression Integer
--R
--R           1
--R   (4)  - ---
--R            2
--R          8a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28
aa:=integrate(sin(a*x)^3,x)
 

                3
        cos(a x)  - 3cos(a x)
   (1)  ---------------------
                  3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3
--R        cos(a x)  - 3cos(a x)
--R   (1)  ---------------------
--R                  3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29
bb:=-cos(a*x)/a+cos(a*x)^3/(3*a)
 

                3
        cos(a x)  - 3cos(a x)
   (2)  ---------------------
                  3a
                                                     Type: Expression Integer
--R
--R                3
--R        cos(a x)  - 3cos(a x)
--R   (2)  ---------------------
--R                  3a
--R                                                     Type: Expression Integer
--E

--S 30     14:349 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 31
aa:=integrate(sin(a*x)^4,x)
 

                  3
        (2cos(a x)  - 5cos(a x))sin(a x) + 3a x
   (1)  ---------------------------------------
                           8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  3
--R        (2cos(a x)  - 5cos(a x))sin(a x) + 3a x
--R   (1)  ---------------------------------------
--R                           8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 32
bb:=(3*x)/8-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
 

        sin(4a x) - 8sin(2a x) + 12a x
   (2)  ------------------------------
                      32a
                                                     Type: Expression Integer
--R
--R        sin(4a x) - 8sin(2a x) + 12a x
--R   (2)  ------------------------------
--R                      32a
--R                                                     Type: Expression Integer
--E

--S 33
cc:=aa-bb
 

                                             3
        - sin(4a x) + 8sin(2a x) + (8cos(a x)  - 20cos(a x))sin(a x)
   (3)  ------------------------------------------------------------
                                     32a
                                                     Type: Expression Integer
--R
--R                                             3
--R        - sin(4a x) + 8sin(2a x) + (8cos(a x)  - 20cos(a x))sin(a x)
--R   (3)  ------------------------------------------------------------
--R                                     32a
--R                                                     Type: Expression Integer
--E

--S 34     14:350 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 35
aa:=integrate(1/sin(a*x)^2,x)
 

           cos(a x)
   (1)  - ----------
          a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           cos(a x)
--R   (1)  - ----------
--R          a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36
bb:=-1/a*cot(a*x)
 

          cot(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cot(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 37
cc:=aa-bb
 

        cot(a x)sin(a x) - cos(a x)
   (3)  ---------------------------
                 a sin(a x)
                                                     Type: Expression Integer
--R
--R        cot(a x)sin(a x) - cos(a x)
--R   (3)  ---------------------------
--R                 a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 38     14:351 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39
aa:=integrate(1/sin(a*x)^3,x)
 

                 2           sin(a x)
        (cos(a x)  - 1)log(------------) + cos(a x)
                           cos(a x) + 1
   (1)  -------------------------------------------
                                2
                     2a cos(a x)  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2           sin(a x)
--R        (cos(a x)  - 1)log(------------) + cos(a x)
--R                           cos(a x) + 1
--R   (1)  -------------------------------------------
--R                                2
--R                     2a cos(a x)  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40
bb:=-cos(a*x)/(2*a*sin(a*x)^2)+1/(2*a)*log(tan((a*x)/2))
 

                2        a x
        sin(a x) log(tan(---)) - cos(a x)
                          2
   (2)  ---------------------------------
                              2
                   2a sin(a x)
                                                     Type: Expression Integer
--R
--R                2        a x
--R        sin(a x) log(tan(---)) - cos(a x)
--R                          2
--R   (2)  ---------------------------------
--R                              2
--R                   2a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 41
cc:=aa-bb
 

   (3)
                  2             2        a x
       (- cos(a x)  + 1)sin(a x) log(tan(---))
                                          2
     + 
                2             2      sin(a x)                      2           3
       (cos(a x)  - 1)sin(a x) log(------------) + cos(a x)sin(a x)  + cos(a x)
                                   cos(a x) + 1
     + 
       - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2             2        a x
--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
--R                                          2
--R     + 
--R                2             2      sin(a x)                      2           3
--R       (cos(a x)  - 1)sin(a x) log(------------) + cos(a x)sin(a x)  + cos(a x)
--R                                   cos(a x) + 1
--R     + 
--R       - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 42
dd:=expandLog cc
 

   (4)
                  2             2        a x
       (- cos(a x)  + 1)sin(a x) log(tan(---))
                                          2
     + 
                2             2
       (cos(a x)  - 1)sin(a x) log(sin(a x))
     + 
                  2             2                                    2
       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1) + cos(a x)sin(a x)
     + 
               3
       cos(a x)  - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (4)
--R                  2             2        a x
--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
--R                                          2
--R     + 
--R                2             2
--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
--R     + 
--R                  2             2                                    2
--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1) + cos(a x)sin(a x)
--R     + 
--R               3
--R       cos(a x)  - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 43     14:352 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 44
aa:=integrate(sin(p*x)*sin(q*x),x)
 

        p cos(p x)sin(q x) - q cos(q x)sin(p x)
   (1)  ---------------------------------------
                         2    2
                        q  - p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        p cos(p x)sin(q x) - q cos(q x)sin(p x)
--R   (1)  ---------------------------------------
--R                         2    2
--R                        q  - p
--R                                          Type: Union(Expression Integer,...)
--E

--S 45
bb:=sin((p-q)*x)/(2*(p-q))-sin((p+q)*x)/(2*(p+q))
 

        (- q + p)sin((q + p)x) + (q + p)sin((q - p)x)
   (2)  ---------------------------------------------
                            2     2
                          2q  - 2p
                                                     Type: Expression Integer
--R
--R        (- q + p)sin((q + p)x) + (q + p)sin((q - p)x)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2q  - 2p
--R                                                     Type: Expression Integer
--E 

--S 46
cc:=aa-bb
 

   (3)
       (q - p)sin((q + p)x) + 2p cos(p x)sin(q x) + (- q - p)sin((q - p)x)
     + 
       - 2q cos(q x)sin(p x)
  /
       2     2
     2q  - 2p
                                                     Type: Expression Integer
--R
--R   (3)
--R       (q - p)sin((q + p)x) + 2p cos(p x)sin(q x) + (- q - p)sin((q - p)x)
--R     + 
--R       - 2q cos(q x)sin(p x)
--R  /
--R       2     2
--R     2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 47     14:353 Schams and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 48
aa:=integrate(1/(1-sin(a*x)),x)
 

              - 2cos(a x) - 2
   (1)  ---------------------------
        a sin(a x) - a cos(a x) - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - 2cos(a x) - 2
--R   (1)  ---------------------------
--R        a sin(a x) - a cos(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E

--S 49
bb:=1/a*tan(%pi/4+(a*x)/2)
 

            2a x + %pi
        tan(----------)
                 4
   (2)  ---------------
               a
                                                     Type: Expression Integer
--R
--R            2a x + %pi
--R        tan(----------)
--R                 4
--R   (2)  ---------------
--R               a
--R                                                     Type: Expression Integer
--E 

--S 50
cc:=aa-bb
 

                                       2a x + %pi
        (- sin(a x) + cos(a x) + 1)tan(----------) - 2cos(a x) - 2
                                            4
   (3)  ----------------------------------------------------------
                        a sin(a x) - a cos(a x) - a
                                                     Type: Expression Integer
--R
--R                                       2a x + %pi
--R        (- sin(a x) + cos(a x) + 1)tan(----------) - 2cos(a x) - 2
--R                                            4
--R   (3)  ----------------------------------------------------------
--R                        a sin(a x) - a cos(a x) - a
--R                                                     Type: Expression Integer
--E

--S 51     14:354 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

        1
   (4)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (4)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 52
aa:=integrate(x/(1-sin(ax)),x)
 

                2
               x
   (1)  - ------------
          2sin(ax) - 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R               x
--R   (1)  - ------------
--R          2sin(ax) - 2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53
bb:=x/a*tan(%pi/4+(a*x)/2)+2/a^2*log(sin(%pi/4-(a*x)/2))
 

                   2a x - %pi             2a x + %pi
        2log(- sin(----------)) + a x tan(----------)
                        4                      4
   (2)  ---------------------------------------------
                               2
                              a
                                                     Type: Expression Integer
--R
--R                   2a x - %pi             2a x + %pi
--R        2log(- sin(----------)) + a x tan(----------)
--R                        4                      4
--R   (2)  ---------------------------------------------
--R                               2
--R                              a
--R                                                     Type: Expression Integer
--E

--S 54     14:355 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                                 2a x - %pi
       (- 4sin(ax) + 4)log(- sin(----------))
                                      4
     + 
                                  2a x + %pi     2 2
       (- 2a x sin(ax) + 2a x)tan(----------) - a x
                                       4
  /
       2            2
     2a sin(ax) - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                 2a x - %pi
--R       (- 4sin(ax) + 4)log(- sin(----------))
--R                                      4
--R     + 
--R                                  2a x + %pi     2 2
--R       (- 2a x sin(ax) + 2a x)tan(----------) - a x
--R                                       4
--R  /
--R       2            2
--R     2a sin(ax) - 2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 55
aa:=integrate(1/(1+sin(ax)),x)
 

             x
   (1)  -----------
        sin(ax) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R   (1)  -----------
--R        sin(ax) + 1
--R                                          Type: Union(Expression Integer,...)
--E 

--S 56
bb:=-1/a*tan(%pi/4-(a*x)/2)
 

            2a x - %pi
        tan(----------)
                 4
   (2)  ---------------
               a
                                                     Type: Expression Integer
--R
--R            2a x - %pi
--R        tan(----------)
--R                 4
--R   (2)  ---------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 57
cc:=aa-bb
 

                           2a x - %pi
        (- sin(ax) - 1)tan(----------) + a x
                                4
   (3)  ------------------------------------
                    a sin(ax) + a
                                                     Type: Expression Integer
--R
--R                           2a x - %pi
--R        (- sin(ax) - 1)tan(----------) + a x
--R                                4
--R   (3)  ------------------------------------
--R                    a sin(ax) + a
--R                                                     Type: Expression Integer
--E

--S 58
tanrule:=rule(tan(a/b) == sin(a)/cos(b))
 

            a     sin(a)
   (4)  tan(-) == ------
            b     cos(b)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a     sin(a)
--R   (4)  tan(-) == ------
--R            b     cos(b)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 59     14:356 Axiom cannot simplify this expression
dd:=tanrule cc
 

        (- sin(ax) - 1)sin(2a x - %pi) + a x cos(4)
   (5)  -------------------------------------------
                 a cos(4)sin(ax) + a cos(4)
                                                     Type: Expression Integer
--R
--R        (- sin(ax) - 1)sin(2a x - %pi) + a x cos(4)
--R   (5)  -------------------------------------------
--R                 a cos(4)sin(ax) + a cos(4)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 60
aa:=integrate(x/(1+sin(a*x)),x)
 

   (1)
                                      sin(a x) + cos(a x) + 1
       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
                                            cos(a x) + 1
     + 
                                            2
       (- sin(a x) - cos(a x) - 1)log(------------) + a x sin(a x)
                                      cos(a x) + 1
     + 
       - a x cos(a x) - a x
  /
      2            2            2
     a sin(a x) + a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                      sin(a x) + cos(a x) + 1
--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
--R                                            cos(a x) + 1
--R     + 
--R                                            2
--R       (- sin(a x) - cos(a x) - 1)log(------------) + a x sin(a x)
--R                                      cos(a x) + 1
--R     + 
--R       - a x cos(a x) - a x
--R  /
--R      2            2            2
--R     a sin(a x) + a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 61
bb:=-x/a*tan(%pi/4-(a*x)/2)+2/a^2*log(sin(%pi/4+(a*x)/2))
 

                 2a x + %pi             2a x - %pi
        2log(sin(----------)) + a x tan(----------)
                      4                      4
   (2)  -------------------------------------------
                              2
                             a
                                                     Type: Expression Integer
--R
--R                 2a x + %pi             2a x - %pi
--R        2log(sin(----------)) + a x tan(----------)
--R                      4                      4
--R   (2)  -------------------------------------------
--R                              2
--R                             a
--R                                                     Type: Expression Integer
--E

--S 62     14:257 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                                      sin(a x) + cos(a x) + 1
       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
                                            cos(a x) + 1
     + 
                                            2a x + %pi
       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
                                                 4
     + 
                                            2
       (- sin(a x) - cos(a x) - 1)log(------------)
                                      cos(a x) + 1
     + 
                                                2a x - %pi
       (- a x sin(a x) - a x cos(a x) - a x)tan(----------) + a x sin(a x)
                                                     4
     + 
       - a x cos(a x) - a x
  /
      2            2            2
     a sin(a x) + a cos(a x) + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      sin(a x) + cos(a x) + 1
--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
--R                                            cos(a x) + 1
--R     + 
--R                                            2a x + %pi
--R       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
--R                                                 4
--R     + 
--R                                            2
--R       (- sin(a x) - cos(a x) - 1)log(------------)
--R                                      cos(a x) + 1
--R     + 
--R                                                2a x - %pi
--R       (- a x sin(a x) - a x cos(a x) - a x)tan(----------) + a x sin(a x)
--R                                                     4
--R     + 
--R       - a x cos(a x) - a x
--R  /
--R      2            2            2
--R     a sin(a x) + a cos(a x) + a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 63
aa:=integrate(1/(1-sin(a*x))^2,x)
 

                                               2
             (3cos(a x) + 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
   (1)  ------------------------------------------------------------
                                                2
        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
                                          Type: Union(Expression Integer,...)
--R
--R                                               2
--R             (3cos(a x) + 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
--R   (1)  ------------------------------------------------------------
--R                                                2
--R        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
--R                                          Type: Union(Expression Integer,...)
--E

--S 64
bb:=1/(2*a)*tan(%pi/4+(a*x)/2)+1/(6*a)*tan(%pi/4+(a*x)/2)^3
 

            2a x + %pi 3        2a x + %pi
        tan(----------)  + 3tan(----------)
                 4                   4
   (2)  -----------------------------------
                         6a
                                                     Type: Expression Integer
--R
--R            2a x + %pi 3        2a x + %pi
--R        tan(----------)  + 3tan(----------)
--R                 4                   4
--R   (2)  -----------------------------------
--R                         6a
--R                                                     Type: Expression Integer
--E 

--S 65
cc:=aa-bb
 

   (3)
                                           2                    2a x + %pi 3
       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)tan(----------)
                                                                     4
     + 
                                             2                     2a x + %pi
       ((- 3cos(a x) - 6)sin(a x) - 3cos(a x)  + 3cos(a x) + 6)tan(----------)
                                                                        4
     + 
                                          2
       (6cos(a x) + 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
  /
                                              2
     (6a cos(a x) + 12a)sin(a x) + 6a cos(a x)  - 6a cos(a x) - 12a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2                    2a x + %pi 3
--R       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)tan(----------)
--R                                                                     4
--R     + 
--R                                             2                     2a x + %pi
--R       ((- 3cos(a x) - 6)sin(a x) - 3cos(a x)  + 3cos(a x) + 6)tan(----------)
--R                                                                        4
--R     + 
--R                                          2
--R       (6cos(a x) + 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
--R  /
--R                                              2
--R     (6a cos(a x) + 12a)sin(a x) + 6a cos(a x)  - 6a cos(a x) - 12a
--R                                                     Type: Expression Integer
--E

--S 66
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 67
dd:=tanrule cc
 

   (5)
                               2a x + %pi 3
           (- cos(a x) - 2)sin(----------)
                                    4
         + 
                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
                        4                           4                4
         + 
                2a x + %pi 3                2a x + %pi 3
           6cos(----------) cos(a x) + 6cos(----------)
                     4                           4
      *
         sin(a x)
     + 
                  2                    2a x + %pi 3
       (- cos(a x)  + cos(a x) + 2)sin(----------)
                                            4
     + 
                  2a x + %pi 2        2        2a x + %pi 2
           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
                       4                            4
         + 
                2a x + %pi 2
           6cos(----------)
                     4
      *
             2a x + %pi
         sin(----------)
                  4
     + 
          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
               4                            4                            4
  /
               2a x + %pi 3                   2a x + %pi 3
       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
                    4                              4
     + 
              2a x + %pi 3        2          2a x + %pi 3
       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
                   4                              4
     + 
                 2a x + %pi 3
       - 12a cos(----------)
                      4
                                                     Type: Expression Integer
--R
--R   (5)
--R                               2a x + %pi 3
--R           (- cos(a x) - 2)sin(----------)
--R                                    4
--R         + 
--R                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
--R                        4                           4                4
--R         + 
--R                2a x + %pi 3                2a x + %pi 3
--R           6cos(----------) cos(a x) + 6cos(----------)
--R                     4                           4
--R      *
--R         sin(a x)
--R     + 
--R                  2                    2a x + %pi 3
--R       (- cos(a x)  + cos(a x) + 2)sin(----------)
--R                                            4
--R     + 
--R                  2a x + %pi 2        2        2a x + %pi 2
--R           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
--R                       4                            4
--R         + 
--R                2a x + %pi 2
--R           6cos(----------)
--R                     4
--R      *
--R             2a x + %pi
--R         sin(----------)
--R                  4
--R     + 
--R          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
--R               4                            4                            4
--R  /
--R               2a x + %pi 3                   2a x + %pi 3
--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
--R                    4                              4
--R     + 
--R              2a x + %pi 3        2          2a x + %pi 3
--R       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
--R                   4                              4
--R     + 
--R                 2a x + %pi 3
--R       - 12a cos(----------)
--R                      4
--R                                                     Type: Expression Integer
--E

--S 68
sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4))
 

                 b - a              a     b           b     a
   (6)  - %Z sin(-----) == - %Z cos(-)sin(-) + %Z cos(-)sin(-)
                   4                4     4           4     4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                 b - a              a     b           b     a
--I   (6)  - %K sin(-----) == - %K cos(-)sin(-) + %K cos(-)sin(-)
--R                   4                4     4           4     4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 69
ee:=sindiffrule2 dd
 

   (7)
                               2a x + %pi 3
           (- cos(a x) - 2)sin(----------)
                                    4
         + 
                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
                        4                           4                4
         + 
                2a x + %pi 3                2a x + %pi 3
           6cos(----------) cos(a x) + 6cos(----------)
                     4                           4
      *
         sin(a x)
     + 
                  2                    2a x + %pi 3
       (- cos(a x)  + cos(a x) + 2)sin(----------)
                                            4
     + 
                  2a x + %pi 2        2        2a x + %pi 2
           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
                       4                            4
         + 
                2a x + %pi 2
           6cos(----------)
                     4
      *
             2a x + %pi
         sin(----------)
                  4
     + 
          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
               4                            4                            4
  /
               2a x + %pi 3                   2a x + %pi 3
       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
                    4                              4
     + 
              2a x + %pi 3        2          2a x + %pi 3
       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
                   4                              4
     + 
                 2a x + %pi 3
       - 12a cos(----------)
                      4
                                                     Type: Expression Integer
--R
--R   (7)
--R                               2a x + %pi 3
--R           (- cos(a x) - 2)sin(----------)
--R                                    4
--R         + 
--R                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
--R                        4                           4                4
--R         + 
--R                2a x + %pi 3                2a x + %pi 3
--R           6cos(----------) cos(a x) + 6cos(----------)
--R                     4                           4
--R      *
--R         sin(a x)
--R     + 
--R                  2                    2a x + %pi 3
--R       (- cos(a x)  + cos(a x) + 2)sin(----------)
--R                                            4
--R     + 
--R                  2a x + %pi 2        2        2a x + %pi 2
--R           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
--R                       4                            4
--R         + 
--R                2a x + %pi 2
--R           6cos(----------)
--R                     4
--R      *
--R             2a x + %pi
--R         sin(----------)
--R                  4
--R     + 
--R          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
--R               4                            4                            4
--R  /
--R               2a x + %pi 3                   2a x + %pi 3
--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
--R                    4                              4
--R     + 
--R              2a x + %pi 3        2          2a x + %pi 3
--R       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
--R                   4                              4
--R     + 
--R                 2a x + %pi 3
--R       - 12a cos(----------)
--R                      4
--R                                                     Type: Expression Integer
--E

--S 70
sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a))
 

              3    - sin(3a) + 3sin(a)
   (8)  sin(a)  == -------------------
                            4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              3    - sin(3a) + 3sin(a)
--R   (8)  sin(a)  == -------------------
--R                            4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 71
ff:=sincuberule ee
 

   (9)
                                         2                    6a x + 3%pi
       ((cos(a x) + 2)sin(a x) + cos(a x)  - cos(a x) - 2)sin(-----------)
                                                                   4
     + 
                       2a x + %pi 2                      2a x + %pi 2
             ((- 12cos(----------)  - 3)cos(a x) - 24cos(----------)  - 6)
                            4                                 4
          *
                 2a x + %pi
             sin(----------)
                      4
         + 
                 2a x + %pi 3                 2a x + %pi 3
           24cos(----------) cos(a x) + 24cos(----------)
                      4                            4
      *
         sin(a x)
     + 
                    2a x + %pi 2             2
           (- 12cos(----------)  - 3)cos(a x)
                         4
         + 
                  2a x + %pi 2                      2a x + %pi 2
           (12cos(----------)  + 3)cos(a x) + 24cos(----------)  + 6
                       4                                 4
      *
             2a x + %pi
         sin(----------)
                  4
     + 
            2a x + %pi 3        2         2a x + %pi 3
       8cos(----------) cos(a x)  - 32cos(----------) cos(a x)
                 4                             4
     + 
               2a x + %pi 3
       - 40cos(----------)
                    4
  /
                2a x + %pi 3                   2a x + %pi 3
       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
                     4                              4
     + 
               2a x + %pi 3        2           2a x + %pi 3
       24a cos(----------) cos(a x)  - 24a cos(----------) cos(a x)
                    4                               4
     + 
                 2a x + %pi 3
       - 48a cos(----------)
                      4
                                                     Type: Expression Integer
--R
--R   (9)
--R                                         2                    6a x + 3%pi
--R       ((cos(a x) + 2)sin(a x) + cos(a x)  - cos(a x) - 2)sin(-----------)
--R                                                                   4
--R     + 
--R                       2a x + %pi 2                      2a x + %pi 2
--R             ((- 12cos(----------)  - 3)cos(a x) - 24cos(----------)  - 6)
--R                            4                                 4
--R          *
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R         + 
--R                 2a x + %pi 3                 2a x + %pi 3
--R           24cos(----------) cos(a x) + 24cos(----------)
--R                      4                            4
--R      *
--R         sin(a x)
--R     + 
--R                    2a x + %pi 2             2
--R           (- 12cos(----------)  - 3)cos(a x)
--R                         4
--R         + 
--R                  2a x + %pi 2                      2a x + %pi 2
--R           (12cos(----------)  + 3)cos(a x) + 24cos(----------)  + 6
--R                       4                                 4
--R      *
--R             2a x + %pi
--R         sin(----------)
--R                  4
--R     + 
--R            2a x + %pi 3        2         2a x + %pi 3
--R       8cos(----------) cos(a x)  - 32cos(----------) cos(a x)
--R                 4                             4
--R     + 
--R               2a x + %pi 3
--R       - 40cos(----------)
--R                    4
--R  /
--R                2a x + %pi 3                   2a x + %pi 3
--R       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
--R                     4                              4
--R     + 
--R               2a x + %pi 3        2           2a x + %pi 3
--R       24a cos(----------) cos(a x)  - 24a cos(----------) cos(a x)
--R                    4                               4
--R     + 
--R                 2a x + %pi 3
--R       - 48a cos(----------)
--R                      4
--R                                                     Type: Expression Integer
--E

--S 72     14:358 Schaums and Axiom differ by a constant
complexNormalize %
 

          2
   (10)  --
         3a
                                                     Type: Expression Integer
--R
--R          2
--R   (10)  --
--R         3a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 73
aa:=integrate(1/(1+sin(a*x))^2,x)
 

                                                2
            (- 3cos(a x) - 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
   (1)  ------------------------------------------------------------
                                                2
        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
                                          Type: Union(Expression Integer,...)
--R
--R                                                2
--R            (- 3cos(a x) - 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
--R   (1)  ------------------------------------------------------------
--R                                                2
--R        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
--R                                          Type: Union(Expression Integer,...)
--E

--S 74
bb:=-1/(2*a)*tan(%pi/4-(a*x)/2)-1/(6*a)*tan(%pi/4-(a*x)/2)^3
 

            2a x - %pi 3        2a x - %pi
        tan(----------)  + 3tan(----------)
                 4                   4
   (2)  -----------------------------------
                         6a
                                                     Type: Expression Integer
--R
--R            2a x - %pi 3        2a x - %pi
--R        tan(----------)  + 3tan(----------)
--R                 4                   4
--R   (2)  -----------------------------------
--R                         6a
--R                                                     Type: Expression Integer
--E 

--S 75
cc:=aa-bb
 

   (3)
                                           2                    2a x - %pi 3
       ((- cos(a x) - 2)sin(a x) + cos(a x)  - cos(a x) - 2)tan(----------)
                                                                     4
     + 
                                             2                     2a x - %pi
       ((- 3cos(a x) - 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
                                                                        4
     + 
                                            2
       (- 6cos(a x) - 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
  /
                                              2
     (6a cos(a x) + 12a)sin(a x) - 6a cos(a x)  + 6a cos(a x) + 12a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2                    2a x - %pi 3
--R       ((- cos(a x) - 2)sin(a x) + cos(a x)  - cos(a x) - 2)tan(----------)
--R                                                                     4
--R     + 
--R                                             2                     2a x - %pi
--R       ((- 3cos(a x) - 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
--R                                                                        4
--R     + 
--R                                            2
--R       (- 6cos(a x) - 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
--R  /
--R                                              2
--R     (6a cos(a x) + 12a)sin(a x) - 6a cos(a x)  + 6a cos(a x) + 12a
--R                                                     Type: Expression Integer
--E

--S 76
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 77
dd:=tanrule cc
 

   (5)
                               2a x - %pi 3
           (- cos(a x) - 2)sin(----------)
                                    4
         + 
                   2a x - %pi 2                2a x - %pi 2     2a x - %pi
           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
                        4                           4                4
         + 
                  2a x - %pi 3                2a x - %pi 3
           - 6cos(----------) cos(a x) - 6cos(----------)
                       4                           4
      *
         sin(a x)
     + 
                2                    2a x - %pi 3
       (cos(a x)  - cos(a x) - 2)sin(----------)
                                          4
     + 
                2a x - %pi 2        2        2a x - %pi 2
           3cos(----------) cos(a x)  - 3cos(----------) cos(a x)
                     4                            4
         + 
                  2a x - %pi 2
           - 6cos(----------)
                       4
      *
             2a x - %pi
         sin(----------)
                  4
     + 
          2a x - %pi 3        2        2a x - %pi 3                 2a x - %pi 3
     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
               4                            4                            4
  /
               2a x - %pi 3                   2a x - %pi 3
       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
                    4                              4
     + 
                2a x - %pi 3        2          2a x - %pi 3
       - 6a cos(----------) cos(a x)  + 6a cos(----------) cos(a x)
                     4                              4
     + 
               2a x - %pi 3
       12a cos(----------)
                    4
                                                     Type: Expression Integer
--R
--R   (5)
--R                               2a x - %pi 3
--R           (- cos(a x) - 2)sin(----------)
--R                                    4
--R         + 
--R                   2a x - %pi 2                2a x - %pi 2     2a x - %pi
--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
--R                        4                           4                4
--R         + 
--R                  2a x - %pi 3                2a x - %pi 3
--R           - 6cos(----------) cos(a x) - 6cos(----------)
--R                       4                           4
--R      *
--R         sin(a x)
--R     + 
--R                2                    2a x - %pi 3
--R       (cos(a x)  - cos(a x) - 2)sin(----------)
--R                                          4
--R     + 
--R                2a x - %pi 2        2        2a x - %pi 2
--R           3cos(----------) cos(a x)  - 3cos(----------) cos(a x)
--R                     4                            4
--R         + 
--R                  2a x - %pi 2
--R           - 6cos(----------)
--R                       4
--R      *
--R             2a x - %pi
--R         sin(----------)
--R                  4
--R     + 
--R          2a x - %pi 3        2        2a x - %pi 3                 2a x - %pi 3
--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
--R               4                            4                            4
--R  /
--R               2a x - %pi 3                   2a x - %pi 3
--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
--R                    4                              4
--R     + 
--R                2a x - %pi 3        2          2a x - %pi 3
--R       - 6a cos(----------) cos(a x)  + 6a cos(----------) cos(a x)
--R                     4                              4
--R     + 
--R               2a x - %pi 3
--R       12a cos(----------)
--R                    4
--R                                                     Type: Expression Integer
--E

--S 78
sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4))
 

                  b - a               a     b            b     a
   (6)  - %BA sin(-----) == - %BA cos(-)sin(-) + %BA cos(-)sin(-)
                    4                 4     4            4     4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                 b - a              a     b           b     a
--I   (6)  - %U sin(-----) == - %U cos(-)sin(-) + %U cos(-)sin(-)
--I                   4                4     4           4     4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 79
ee:=sindiffrule2 dd
 

   (7)
                +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
           (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
                            4                               4            2
         + 
                                2a x - %pi 3
           (- 2cos(a x) - 4)sin(----------)
                                     4
         + 
              +-+    2a x - %pi 2    a x          2a x - %pi 3
           (3\|2 cos(----------) cos(---) - 12cos(----------) )cos(a x)
                          4           2                4
         + 
             +-+    2a x - %pi 2    a x          2a x - %pi 3
           6\|2 cos(----------) cos(---) - 12cos(----------)
                         4           2                4
      *
         sin(a x)
     + 
            +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
       (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
                        4                               4            2
     + 
                 2                     2a x - %pi 3
       (2cos(a x)  - 2cos(a x) - 4)sin(----------)
                                            4
     + 
            2a x - %pi 2        2    2a x - %pi         2a x - %pi 3        2
       6cos(----------) cos(a x) sin(----------) + 4cos(----------) cos(a x)
                 4                        4                  4
     + 
          +-+    2a x - %pi 2    a x          2a x - %pi 3
       (3\|2 cos(----------) cos(---) - 16cos(----------) )cos(a x)
                      4           2                4
     + 
         +-+    2a x - %pi 2    a x          2a x - %pi 3
       6\|2 cos(----------) cos(---) - 20cos(----------)
                     4           2                4
  /
                2a x - %pi 3                   2a x - %pi 3
       (12a cos(----------) cos(a x) + 24a cos(----------) )sin(a x)
                     4                              4
     + 
                 2a x - %pi 3        2           2a x - %pi 3
       - 12a cos(----------) cos(a x)  + 12a cos(----------) cos(a x)
                      4                               4
     + 
               2a x - %pi 3
       24a cos(----------)
                    4
                                                     Type: Expression Integer
--R
--R   (7)
--R                +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
--R           (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
--R                            4                               4            2
--R         + 
--R                                2a x - %pi 3
--R           (- 2cos(a x) - 4)sin(----------)
--R                                     4
--R         + 
--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           (3\|2 cos(----------) cos(---) - 12cos(----------) )cos(a x)
--R                          4           2                4
--R         + 
--R             +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           6\|2 cos(----------) cos(---) - 12cos(----------)
--R                         4           2                4
--R      *
--R         sin(a x)
--R     + 
--R            +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
--R       (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
--R                        4                               4            2
--R     + 
--R                 2                     2a x - %pi 3
--R       (2cos(a x)  - 2cos(a x) - 4)sin(----------)
--R                                            4
--R     + 
--R            2a x - %pi 2        2    2a x - %pi         2a x - %pi 3        2
--R       6cos(----------) cos(a x) sin(----------) + 4cos(----------) cos(a x)
--R                 4                        4                  4
--R     + 
--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       (3\|2 cos(----------) cos(---) - 16cos(----------) )cos(a x)
--R                      4           2                4
--R     + 
--R         +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       6\|2 cos(----------) cos(---) - 20cos(----------)
--R                     4           2                4
--R  /
--R                2a x - %pi 3                   2a x - %pi 3
--R       (12a cos(----------) cos(a x) + 24a cos(----------) )sin(a x)
--R                     4                              4
--R     + 
--R                 2a x - %pi 3        2           2a x - %pi 3
--R       - 12a cos(----------) cos(a x)  + 12a cos(----------) cos(a x)
--R                      4                               4
--R     + 
--R               2a x - %pi 3
--R       24a cos(----------)
--R                    4
--R                                                     Type: Expression Integer
--E

--S 80
sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a))
 

              3    - sin(3a) + 3sin(a)
   (8)  sin(a)  == -------------------
                            4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              3    - sin(3a) + 3sin(a)
--R   (8)  sin(a)  == -------------------
--R                            4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 81
ff:=sincuberule ee
 

   (9)
                                         2                    6a x - 3%pi
       ((cos(a x) + 2)sin(a x) - cos(a x)  + cos(a x) + 2)sin(-----------)
                                                                   4
     + 
                +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
           (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
                            4                                4            2
         + 
                                2a x - %pi
           (- 3cos(a x) - 6)sin(----------)
                                     4
         + 
              +-+    2a x - %pi 2    a x          2a x - %pi 3
           (6\|2 cos(----------) cos(---) - 24cos(----------) )cos(a x)
                          4           2                4
         + 
              +-+    2a x - %pi 2    a x          2a x - %pi 3
           12\|2 cos(----------) cos(---) - 24cos(----------)
                          4           2                4
      *
         sin(a x)
     + 
            +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
       (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
                        4                                4            2
     + 
               2a x - %pi 2             2                     2a x - %pi
       ((12cos(----------)  + 3)cos(a x)  - 3cos(a x) - 6)sin(----------)
                    4                                              4
     + 
            2a x - %pi 3        2
       8cos(----------) cos(a x)
                 4
     + 
          +-+    2a x - %pi 2    a x          2a x - %pi 3
       (6\|2 cos(----------) cos(---) - 32cos(----------) )cos(a x)
                      4           2                4
     + 
          +-+    2a x - %pi 2    a x          2a x - %pi 3
       12\|2 cos(----------) cos(---) - 40cos(----------)
                      4           2                4
  /
                2a x - %pi 3                   2a x - %pi 3
       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
                     4                              4
     + 
                 2a x - %pi 3        2           2a x - %pi 3
       - 24a cos(----------) cos(a x)  + 24a cos(----------) cos(a x)
                      4                               4
     + 
               2a x - %pi 3
       48a cos(----------)
                    4
                                                     Type: Expression Integer
--R
--R   (9)
--R                                         2                    6a x - 3%pi
--R       ((cos(a x) + 2)sin(a x) - cos(a x)  + cos(a x) + 2)sin(-----------)
--R                                                                   4
--R     + 
--R                +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
--R           (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
--R                            4                                4            2
--R         + 
--R                                2a x - %pi
--R           (- 3cos(a x) - 6)sin(----------)
--R                                     4
--R         + 
--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           (6\|2 cos(----------) cos(---) - 24cos(----------) )cos(a x)
--R                          4           2                4
--R         + 
--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           12\|2 cos(----------) cos(---) - 24cos(----------)
--R                          4           2                4
--R      *
--R         sin(a x)
--R     + 
--R            +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
--R       (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
--R                        4                                4            2
--R     + 
--R               2a x - %pi 2             2                     2a x - %pi
--R       ((12cos(----------)  + 3)cos(a x)  - 3cos(a x) - 6)sin(----------)
--R                    4                                              4
--R     + 
--R            2a x - %pi 3        2
--R       8cos(----------) cos(a x)
--R                 4
--R     + 
--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       (6\|2 cos(----------) cos(---) - 32cos(----------) )cos(a x)
--R                      4           2                4
--R     + 
--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       12\|2 cos(----------) cos(---) - 40cos(----------)
--R                      4           2                4
--R  /
--R                2a x - %pi 3                   2a x - %pi 3
--R       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
--R                     4                              4
--R     + 
--R                 2a x - %pi 3        2           2a x - %pi 3
--R       - 24a cos(----------) cos(a x)  + 24a cos(----------) cos(a x)
--R                      4                               4
--R     + 
--R               2a x - %pi 3
--R       48a cos(----------)
--R                    4
--R                                                     Type: Expression Integer
--E

--S 82     14:359 Schaums and Axiom differ by a constant
complexNormalize %
 

            2
   (10)  - --
           3a
                                                     Type: Expression Integer
--R
--R            2
--R   (10)  - --
--R           3a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 83
aa:=integrate(1/(p+q*sin(a*x)),x)
 

   (1)
   [
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
    /
         +-------+
         | 2    2
       a\|q  - p
     ,
                                          +---------+
                                          |   2    2
            (p sin(a x) + q cos(a x) + q)\|- q  + p
      2atan(-----------------------------------------)
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    - ------------------------------------------------]
                          +---------+
                          |   2    2
                        a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R    /
--R         +-------+
--R         | 2    2
--R       a\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
--R      2atan(-----------------------------------------)
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    - ------------------------------------------------]
--R                          +---------+
--R                          |   2    2
--R                        a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 84
bb1:=2/(a*sqrt(p^2-q^2))*atan((p*tan(a*x/2)+q)/sqrt(p^2-q^2))
 

                    a x
              p tan(---) + q
                     2
        2atan(--------------)
                +---------+
                |   2    2
               \|- q  + p
   (2)  ---------------------
              +---------+
              |   2    2
            a\|- q  + p
                                                     Type: Expression Integer
--R
--R                    a x
--R              p tan(---) + q
--R                     2
--R        2atan(--------------)
--R                +---------+
--R                |   2    2
--R               \|- q  + p
--R   (2)  ---------------------
--R              +---------+
--R              |   2    2
--R            a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 85
bb2:=1/(a*sqrt(q^2-p^2))*log((p*tan((a*x)/2)+q-sqrt(q^2-p^2))/(p*tan((a*x)/2)+q+sqrt(q^2-p^2)))
 

               +-------+
               | 2    2          a x
            - \|q  - p   + p tan(---) + q
                                  2
        log(-----------------------------)
              +-------+
              | 2    2          a x
             \|q  - p   + p tan(---) + q
                                 2
   (3)  ----------------------------------
                      +-------+
                      | 2    2
                    a\|q  - p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2          a x
--R            - \|q  - p   + p tan(---) + q
--R                                  2
--R        log(-----------------------------)
--R              +-------+
--R              | 2    2          a x
--R             \|q  - p   + p tan(---) + q
--R                                 2
--R   (3)  ----------------------------------
--R                      +-------+
--R                      | 2    2
--R                    a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 86
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |   2    2
         \|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                               a x
           +-------+     p tan(---) + q
           | 2    2             2
       - 2\|q  - p  atan(--------------)
                           +---------+
                           |   2    2
                          \|- q  + p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                               a x
--R           +-------+     p tan(---) + q
--R           | 2    2             2
--R       - 2\|q  - p  atan(--------------)
--R                           +---------+
--R                           |   2    2
--R                          \|- q  + p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 87
cc2:=aa.2-bb1
 

   (5)
                                         +---------+                a x
                                         |   2    2           p tan(---) + q
           (p sin(a x) + q cos(a x) + q)\|- q  + p                   2
   - 2atan(-----------------------------------------) - 2atan(--------------)
                    2    2             2    2                   +---------+
                  (q  - p )cos(a x) + q  - p                    |   2    2
                                                               \|- q  + p
   --------------------------------------------------------------------------
                                    +---------+
                                    |   2    2
                                  a\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                         +---------+                a x
--R                                         |   2    2           p tan(---) + q
--R           (p sin(a x) + q cos(a x) + q)\|- q  + p                   2
--R   - 2atan(-----------------------------------------) - 2atan(--------------)
--R                    2    2             2    2                   +---------+
--R                  (q  - p )cos(a x) + q  - p                    |   2    2
--R                                                               \|- q  + p
--R   --------------------------------------------------------------------------
--R                                    +---------+
--R                                    |   2    2
--R                                  a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 88
cc3:=aa.1-bb2
 

   (6)
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
     + 
                +-------+
                | 2    2          a x
             - \|q  - p   + p tan(---) + q
                                   2
       - log(-----------------------------)
               +-------+
               | 2    2          a x
              \|q  - p   + p tan(---) + q
                                  2
  /
       +-------+
       | 2    2
     a\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R     + 
--R                +-------+
--R                | 2    2          a x
--R             - \|q  - p   + p tan(---) + q
--R                                   2
--R       - log(-----------------------------)
--R               +-------+
--R               | 2    2          a x
--R              \|q  - p   + p tan(---) + q
--R                                  2
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 89
cc4:=aa.2-bb2
 

   (7)
                            +-------+
                            | 2    2          a x
          +---------+    - \|q  - p   + p tan(---) + q
          |   2    2                           2
       - \|- q  + p  log(-----------------------------)
                           +-------+
                           | 2    2          a x
                          \|q  - p   + p tan(---) + q
                                              2
     + 
                                                       +---------+
           +-------+                                   |   2    2
           | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       - 2\|q  - p  atan(-----------------------------------------)
                                  2    2             2    2
                                (q  - p )cos(a x) + q  - p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-------+
--R                            | 2    2          a x
--R          +---------+    - \|q  - p   + p tan(---) + q
--R          |   2    2                           2
--R       - \|- q  + p  log(-----------------------------)
--R                           +-------+
--R                           | 2    2          a x
--R                          \|q  - p   + p tan(---) + q
--R                                              2
--R     + 
--R                                                       +---------+
--R           +-------+                                   |   2    2
--R           | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       - 2\|q  - p  atan(-----------------------------------------)
--R                                  2    2             2    2
--R                                (q  - p )cos(a x) + q  - p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 90
dd2:=ratDenom cc2
 

   (8)
                                            +---------+
                                  a x       |   2    2
           +---------+     (p tan(---) + q)\|- q  + p
           |   2    2              2
       - 2\|- q  + p  atan(----------------------------)
                                       2    2
                                      q  - p
     + 
                                                       +---------+
         +---------+                                   |   2    2
         |   2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       2\|- q  + p  atan(-----------------------------------------)
                                  2    2             2    2
                                (q  - p )cos(a x) + q  - p
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (8)
--R                                            +---------+
--R                                  a x       |   2    2
--R           +---------+     (p tan(---) + q)\|- q  + p
--R           |   2    2              2
--R       - 2\|- q  + p  atan(----------------------------)
--R                                       2    2
--R                                      q  - p
--R     + 
--R                                                       +---------+
--R         +---------+                                   |   2    2
--R         |   2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       2\|- q  + p  atan(-----------------------------------------)
--R                                  2    2             2    2
--R                                (q  - p )cos(a x) + q  - p
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 91
atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
 

                     1                    1
   (9)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
                     2                    2
Type: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--R
--R                     1                    1
--R   (9)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
--R                     2                    2
--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--E

--S 92
ee2:=atanrule2 dd2
 

   (10)
                                                  +---------+
                                   1              |   2    2     2    2
          +---------+    (%i p tan(- a x) + %i q)\|- q  + p   + q  - p
          |   2    2               2
       %i\|- q  + p  log(----------------------------------------------)
                                              2    2
                                             q  - p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                                          +---------+
                                                          |   2    2
                   (%i p sin(a x) + %i q cos(a x) + %i q)\|- q  + p
                 + 
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
              /
                   2    2             2    2
                 (q  - p )cos(a x) + q  - p
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                                         +---------+
                                                         |   2    2
                (- %i p sin(a x) - %i q cos(a x) - %i q)\|- q  + p
              + 
                  2    2             2    2
                (q  - p )cos(a x) + q  - p
           /
                2    2             2    2
              (q  - p )cos(a x) + q  - p
     + 
                                                      +---------+
                                       1              |   2    2     2    2
            +---------+    (- %i p tan(- a x) - %i q)\|- q  + p   + q  - p
            |   2    2                 2
       - %i\|- q  + p  log(------------------------------------------------)
                                                 2    2
                                                q  - p
  /
        2      2
     a q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (10)
--R                                                  +---------+
--R                                   1              |   2    2     2    2
--R          +---------+    (%i p tan(- a x) + %i q)\|- q  + p   + q  - p
--R          |   2    2               2
--R       %i\|- q  + p  log(----------------------------------------------)
--R                                              2    2
--R                                             q  - p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                                          +---------+
--R                                                          |   2    2
--R                   (%i p sin(a x) + %i q cos(a x) + %i q)\|- q  + p
--R                 + 
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R              /
--R                   2    2             2    2
--R                 (q  - p )cos(a x) + q  - p
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                                         +---------+
--R                                                         |   2    2
--R                (- %i p sin(a x) - %i q cos(a x) - %i q)\|- q  + p
--R              + 
--R                  2    2             2    2
--R                (q  - p )cos(a x) + q  - p
--R           /
--R                2    2             2    2
--R              (q  - p )cos(a x) + q  - p
--R     + 
--R                                                      +---------+
--R                                       1              |   2    2     2    2
--R            +---------+    (- %i p tan(- a x) - %i q)\|- q  + p   + q  - p
--R            |   2    2                 2
--R       - %i\|- q  + p  log(------------------------------------------------)
--R                                                 2    2
--R                                                q  - p
--R  /
--R        2      2
--R     a q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 93
ff2:=expandLog ee2
 

   (11)
            +---------+                       +---------+
            |   2    2            1           |   2    2        2       2
       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
                                  2
     + 
          +---------+                       +---------+
          |   2    2            1           |   2    2        2       2
       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
                                2
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                            +---------+
                                            |   2    2
              (p sin(a x) + q cos(a x) + q)\|- q  + p
            + 
                   2       2                2       2
              (%i q  - %i p )cos(a x) + %i q  - %i p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                               +---------+
                                               |   2    2
                 (p sin(a x) + q cos(a x) + q)\|- q  + p
               + 
                        2       2                2       2
                 (- %i q  + %i p )cos(a x) - %i q  + %i p
  /
        2      2
     a q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (11)
--R            +---------+                       +---------+
--R            |   2    2            1           |   2    2        2       2
--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
--R                                  2
--R     + 
--R          +---------+                       +---------+
--R          |   2    2            1           |   2    2        2       2
--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
--R                                2
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                            +---------+
--R                                            |   2    2
--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
--R            + 
--R                   2       2                2       2
--R              (%i q  - %i p )cos(a x) + %i q  - %i p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                               +---------+
--R                                               |   2    2
--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
--R               + 
--R                        2       2                2       2
--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
--R  /
--R        2      2
--R     a q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 94
gg2:=numer(ff2)/denom(ff2)
 

   (12)
            +---------+                       +---------+
            |   2    2            1           |   2    2        2       2
       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
                                  2
     + 
          +---------+                       +---------+
          |   2    2            1           |   2    2        2       2
       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
                                2
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                            +---------+
                                            |   2    2
              (p sin(a x) + q cos(a x) + q)\|- q  + p
            + 
                   2       2                2       2
              (%i q  - %i p )cos(a x) + %i q  - %i p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                               +---------+
                                               |   2    2
                 (p sin(a x) + q cos(a x) + q)\|- q  + p
               + 
                        2       2                2       2
                 (- %i q  + %i p )cos(a x) - %i q  + %i p
  /
        2      2
     a q  - a p
Type: Fraction SparseMultivariatePolynomial(Complex Fraction Integer,Kernel Expression Complex Fraction Integer)
--R
--R   (12)
--R            +---------+                       +---------+
--R            |   2    2            1           |   2    2        2       2
--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
--R                                  2
--R     + 
--R          +---------+                       +---------+
--R          |   2    2            1           |   2    2        2       2
--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
--R                                2
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                            +---------+
--R                                            |   2    2
--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
--R            + 
--R                   2       2                2       2
--R              (%i q  - %i p )cos(a x) + %i q  - %i p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                               +---------+
--R                                               |   2    2
--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
--R               + 
--R                        2       2                2       2
--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
--R  /
--R        2      2
--R     a q  - a p
--RType: Fraction SparseMultivariatePolynomial(Complex Fraction Integer,Kernel Expression Complex Fraction Integer)
--E

--S 95
hh2:=gg2::Expression Complex Fraction Integer
 

   (13)
            +---------+                       +---------+
            |   2    2            1           |   2    2        2       2
       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
                                  2
     + 
          +---------+                       +---------+
          |   2    2            1           |   2    2        2       2
       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
                                2
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                            +---------+
                                            |   2    2
              (p sin(a x) + q cos(a x) + q)\|- q  + p
            + 
                   2       2                2       2
              (%i q  - %i p )cos(a x) + %i q  - %i p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                               +---------+
                                               |   2    2
                 (p sin(a x) + q cos(a x) + q)\|- q  + p
               + 
                        2       2                2       2
                 (- %i q  + %i p )cos(a x) - %i q  + %i p
  /
        2      2
     a q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (13)
--R            +---------+                       +---------+
--R            |   2    2            1           |   2    2        2       2
--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
--R                                  2
--R     + 
--R          +---------+                       +---------+
--R          |   2    2            1           |   2    2        2       2
--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
--R                                2
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                            +---------+
--R                                            |   2    2
--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
--R            + 
--R                   2       2                2       2
--R              (%i q  - %i p )cos(a x) + %i q  - %i p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                               +---------+
--R                                               |   2    2
--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
--R               + 
--R                        2       2                2       2
--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
--R  /
--R        2      2
--R     a q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 96     14:360 Schaums and Axiom agree
complexNormalize hh2
 

   (14)  0
                                    Type: Expression Complex Fraction Integer
--R
--R   (14)  0
--R                                    Type: Expression Complex Fraction Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 97
aa:=integrate(1/(p+q*sin(a*x))^2,x)
 

   (1)
   [
             2              3
           (p q sin(a x) + p )
        *
           log
                                                          +-------+
                                    2    2             2  | 2    2
                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
                + 
                      2    3              3    2              3    2
                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
             /
                q sin(a x) + p
       + 
                                             +-------+
             2                               | 2    2
         (- q sin(a x) - p q cos(a x) - p q)\|q  - p
    /
                                                  +-------+
              3      3                2 2      4  | 2    2
       ((a p q  - a p q)sin(a x) + a p q  - a p )\|q  - p
     ,

                                                                 +---------+
                                                                 |   2    2
            2               3      (p sin(a x) + q cos(a x) + q)\|- q  + p
         (2p q sin(a x) + 2p )atan(-----------------------------------------)
                                            2    2             2    2
                                          (q  - p )cos(a x) + q  - p
       + 
                                             +---------+
             2                               |   2    2
         (- q sin(a x) - p q cos(a x) - p q)\|- q  + p
    /
                                                  +---------+
              3      3                2 2      4  |   2    2
       ((a p q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R             2              3
--R           (p q sin(a x) + p )
--R        *
--R           log
--R                                                          +-------+
--R                                    2    2             2  | 2    2
--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R                + 
--R                      2    3              3    2              3    2
--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R             /
--R                q sin(a x) + p
--R       + 
--R                                             +-------+
--R             2                               | 2    2
--R         (- q sin(a x) - p q cos(a x) - p q)\|q  - p
--R    /
--R                                                  +-------+
--R              3      3                2 2      4  | 2    2
--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|q  - p
--R     ,
--R
--R                                                                 +---------+
--R                                                                 |   2    2
--R            2               3      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R         (2p q sin(a x) + 2p )atan(-----------------------------------------)
--R                                            2    2             2    2
--R                                          (q  - p )cos(a x) + q  - p
--R       + 
--R                                             +---------+
--R             2                               |   2    2
--R         (- q sin(a x) - p q cos(a x) - p q)\|- q  + p
--R    /
--R                                                  +---------+
--R              3      3                2 2      4  |   2    2
--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 98
t1:=integrate(1/(p+q*sin(a*x)),x)
 

   (2)
   [
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
    /
         +-------+
         | 2    2
       a\|q  - p
     ,
                                          +---------+
                                          |   2    2
            (p sin(a x) + q cos(a x) + q)\|- q  + p
      2atan(-----------------------------------------)
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    - ------------------------------------------------]
                          +---------+
                          |   2    2
                        a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R    /
--R         +-------+
--R         | 2    2
--R       a\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
--R      2atan(-----------------------------------------)
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    - ------------------------------------------------]
--R                          +---------+
--R                          |   2    2
--R                        a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 99
bb1:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.1
 

   (3)
                            2
         (- p q sin(a x) - p )
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                    +-------+
                    | 2    2
       - q cos(a x)\|q  - p
  /
                                              +-------+
          3      2                  2      3  | 2    2
     ((a q  - a p q)sin(a x) + a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R                            2
--R         (- p q sin(a x) - p )
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                    +-------+
--R                    | 2    2
--R       - q cos(a x)\|q  - p
--R  /
--R                                              +-------+
--R          3      2                  2      3  | 2    2
--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 100
bb2:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.2
 

   (4)
                                                               +---------+
                                                               |   2    2
                          2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       (2p q sin(a x) + 2p )atan(-----------------------------------------)
                                          2    2             2    2
                                        (q  - p )cos(a x) + q  - p
     + 
                    +---------+
                    |   2    2
       - q cos(a x)\|- q  + p
  /
                                              +---------+
          3      2                  2      3  |   2    2
     ((a q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                               +---------+
--R                                                               |   2    2
--R                          2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       (2p q sin(a x) + 2p )atan(-----------------------------------------)
--R                                          2    2             2    2
--R                                        (q  - p )cos(a x) + q  - p
--R     + 
--R                    +---------+
--R                    |   2    2
--R       - q cos(a x)\|- q  + p
--R  /
--R                                              +---------+
--R          3      2                  2      3  |   2    2
--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 101
cc1:=aa.1-bb1
 

   (5)
          2
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
          2
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
           +-------+
           | 2    2
       - q\|q  - p
  /
                     +-------+
           2      3  | 2    2
     (a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R          2
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R          2
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R           +-------+
--R           | 2    2
--R       - q\|q  - p
--R  /
--R                     +-------+
--R           2      3  | 2    2
--R     (a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 102
cc2:=aa.2-bb1
 

   (6)
            +---------+
          2 |   2    2
         p \|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                                                       +---------+
           +-------+                                   |   2    2
         2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       2p \|q  - p  atan(-----------------------------------------)
                                  2    2             2    2
                                (q  - p )cos(a x) + q  - p
     + 
           +---------+ +-------+
           |   2    2  | 2    2
       - q\|- q  + p  \|q  - p
  /
                     +---------+ +-------+
           2      3  |   2    2  | 2    2
     (a p q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R            +---------+
--R          2 |   2    2
--R         p \|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                       +---------+
--R           +-------+                                   |   2    2
--R         2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       2p \|q  - p  atan(-----------------------------------------)
--R                                  2    2             2    2
--R                                (q  - p )cos(a x) + q  - p
--R     + 
--R           +---------+ +-------+
--R           |   2    2  | 2    2
--R       - q\|- q  + p  \|q  - p
--R  /
--R                     +---------+ +-------+
--R           2      3  |   2    2  | 2    2
--R     (a p q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 103
cc3:=aa.1-bb2
 

   (7)
            +---------+
          2 |   2    2
         p \|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
                                                         +---------+
             +-------+                                   |   2    2
           2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       - 2p \|q  - p  atan(-----------------------------------------)
                                    2    2             2    2
                                  (q  - p )cos(a x) + q  - p
     + 
           +---------+ +-------+
           |   2    2  | 2    2
       - q\|- q  + p  \|q  - p
  /
                     +---------+ +-------+
           2      3  |   2    2  | 2    2
     (a p q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R            +---------+
--R          2 |   2    2
--R         p \|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                         +---------+
--R             +-------+                                   |   2    2
--R           2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       - 2p \|q  - p  atan(-----------------------------------------)
--R                                    2    2             2    2
--R                                  (q  - p )cos(a x) + q  - p
--R     + 
--R           +---------+ +-------+
--R           |   2    2  | 2    2
--R       - q\|- q  + p  \|q  - p
--R  /
--R                     +---------+ +-------+
--R           2      3  |   2    2  | 2    2
--R     (a p q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 104    14:361 Schaums and Axiom differ by a constant
cc4:=aa.2-bb2
 

                q
   (8)  - -------------
               2      3
          a p q  - a p
                                                     Type: Expression Integer
--R
--R                q
--R   (8)  - -------------
--R               2      3
--R          a p q  - a p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 105
aa:=integrate(1/(p^2+q^2*sin(a*x)^2),x)
 

   (1)
                             +-------+
                             | 2    2
                  p sin(a x)\|q  + p
       atan(-------------------------------)
               2     2              2     2
            (2q  + 2p )cos(a x) + 2q  + 2p
     + 
                 2    2              2     2
             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
       atan(-----------------------------------------)
                                            +-------+
                       2                    | 2    2
            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
  /
         +-------+
         | 2    2
     a p\|q  + p
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                             +-------+
--R                             | 2    2
--R                  p sin(a x)\|q  + p
--R       atan(-------------------------------)
--R               2     2              2     2
--R            (2q  + 2p )cos(a x) + 2q  + 2p
--R     + 
--R                 2    2              2     2
--R             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
--R       atan(-----------------------------------------)
--R                                            +-------+
--R                       2                    | 2    2
--R            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 106
bb:=1/(a*p*sqrt(p^2+q^2))*atan((sqrt(p^2+q^2)*tan(a*x))/p)
 

                      +-------+
                      | 2    2
             tan(a x)\|q  + p
        atan(------------------)
                      p
   (2)  ------------------------
                  +-------+
                  | 2    2
              a p\|q  + p
                                                     Type: Expression Integer
--R
--R                      +-------+
--R                      | 2    2
--R             tan(a x)\|q  + p
--R        atan(------------------)
--R                      p
--R   (2)  ------------------------
--R                  +-------+
--R                  | 2    2
--R              a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 107
cc:=aa-bb
 

   (3)
                       +-------+                          +-------+
                       | 2    2                           | 2    2
              tan(a x)\|q  + p                 p sin(a x)\|q  + p
       - atan(------------------) + atan(-------------------------------)
                       p                    2     2              2     2
                                         (2q  + 2p )cos(a x) + 2q  + 2p
     + 
                 2    2              2     2
             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
       atan(-----------------------------------------)
                                            +-------+
                       2                    | 2    2
            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
  /
         +-------+
         | 2    2
     a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                       +-------+                          +-------+
--R                       | 2    2                           | 2    2
--R              tan(a x)\|q  + p                 p sin(a x)\|q  + p
--R       - atan(------------------) + atan(-------------------------------)
--R                       p                    2     2              2     2
--R                                         (2q  + 2p )cos(a x) + 2q  + 2p
--R     + 
--R                 2    2              2     2
--R             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
--R       atan(-----------------------------------------)
--R                                            +-------+
--R                       2                    | 2    2
--R            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 108
dd:=ratDenom cc
 

   (4)
                                 +-------+
          +-------+              | 2    2
          | 2    2      tan(a x)\|q  + p
       - \|q  + p  atan(------------------)
                                 p
     + 
                                                                  +-------+
        +-------+            2    2              2     2          | 2    2
        | 2    2         ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
       \|q  + p  atan(--------------------------------------------------------)
                          2    3         2        2     3               2    3
                      (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                                       +-------+
        +-------+                      | 2    2
        | 2    2            p sin(a x)\|q  + p
       \|q  + p  atan(-------------------------------)
                         2     2              2     2
                      (2q  + 2p )cos(a x) + 2q  + 2p
  /
          2      3
     a p q  + a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                 +-------+
--R          +-------+              | 2    2
--R          | 2    2      tan(a x)\|q  + p
--R       - \|q  + p  atan(------------------)
--R                                 p
--R     + 
--R                                                                  +-------+
--R        +-------+            2    2              2     2          | 2    2
--R        | 2    2         ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R       \|q  + p  atan(--------------------------------------------------------)
--R                          2    3         2        2     3               2    3
--R                      (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                                       +-------+
--R        +-------+                      | 2    2
--R        | 2    2            p sin(a x)\|q  + p
--R       \|q  + p  atan(-------------------------------)
--R                         2     2              2     2
--R                      (2q  + 2p )cos(a x) + 2q  + 2p
--R  /
--R          2      3
--R     a p q  + a p
--R                                                     Type: Expression Integer
--E

--S 109
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (5)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (5)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 110
ee:=atanrule dd
 

   (6)
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                +-------+
                                | 2    2          2        2                 2
                   - p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
                 + 
                        2
                   2%i p
              /
                              +-------+
                              | 2    2          2        2                 2
                   p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
                 + 
                        2
                   2%i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                              +-------+
                         2    2              2     2          | 2    2
                   ((- 2q  - p )cos(a x) - 2q  - 2p )sin(a x)\|q  + p
                 + 
                          2       3         2           2        3
                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
                 + 
                         2       3
                   %i p q  + %i p
              /
                                                            +-------+
                       2    2              2     2          | 2    2
                   ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
                 + 
                          2       3         2           2        3
                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
                 + 
                         2       3
                   %i p q  + %i p
     + 
                                  +-------+
          +-------+               | 2    2
          | 2    2     - tan(a x)\|q  + p   + %i p
       %i\|q  + p  log(---------------------------)
                                 +-------+
                                 | 2    2
                        tan(a x)\|q  + p   + %i p
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (6)
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                +-------+
--R                                | 2    2          2        2                 2
--R                   - p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
--R                 + 
--R                        2
--R                   2%i p
--R              /
--R                              +-------+
--R                              | 2    2          2        2                 2
--R                   p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
--R                 + 
--R                        2
--R                   2%i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                              +-------+
--R                         2    2              2     2          | 2    2
--R                   ((- 2q  - p )cos(a x) - 2q  - 2p )sin(a x)\|q  + p
--R                 + 
--R                          2       3         2           2        3
--R                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
--R                 + 
--R                         2       3
--R                   %i p q  + %i p
--R              /
--R                                                            +-------+
--R                       2    2              2     2          | 2    2
--R                   ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R                 + 
--R                          2       3         2           2        3
--R                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
--R                 + 
--R                         2       3
--R                   %i p q  + %i p
--R     + 
--R                                  +-------+
--R          +-------+               | 2    2
--R          | 2    2     - tan(a x)\|q  + p   + %i p
--R       %i\|q  + p  log(---------------------------)
--R                                 +-------+
--R                                 | 2    2
--R                        tan(a x)\|q  + p   + %i p
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 111
ff:=expandLog ee
 

   (7)
            +-------+             +-------+
            | 2    2              | 2    2
       - %i\|q  + p  log(tan(a x)\|q  + p   + %i p)
     + 
          +-------+             +-------+
          | 2    2              | 2    2
       %i\|q  + p  log(tan(a x)\|q  + p   - %i p)
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
         log
                                                       +-------+
                  2    2              2     2          | 2    2
              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
            + 
                  3
              %i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                          +-------+
                     2    2              2     2          | 2    2
                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  - %i p
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
                      +-------+
                      | 2    2          2        2                 2        2
       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                            +-------+
                            | 2    2            2        2                 2
                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
               + 
                        2
                 - 2%i p
     + 
                     +-------+
                     | 2    2
       - %i log(- 1)\|q  + p
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (7)
--R            +-------+             +-------+
--R            | 2    2              | 2    2
--R       - %i\|q  + p  log(tan(a x)\|q  + p   + %i p)
--R     + 
--R          +-------+             +-------+
--R          | 2    2              | 2    2
--R       %i\|q  + p  log(tan(a x)\|q  + p   - %i p)
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R         log
--R                                                       +-------+
--R                  2    2              2     2          | 2    2
--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
--R            + 
--R                  3
--R              %i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                          +-------+
--R                     2    2              2     2          | 2    2
--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  - %i p
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R                      +-------+
--R                      | 2    2          2        2                 2        2
--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                            +-------+
--R                            | 2    2            2        2                 2
--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
--R               + 
--R                        2
--R                 - 2%i p
--R     + 
--R                     +-------+
--R                     | 2    2
--R       - %i log(- 1)\|q  + p
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 112
tanrule2:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (8)  tan(a) == ------
                  cos(a)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                  sin(a)
--R   (8)  tan(a) == ------
--R                  cos(a)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 113
gg:=tanrule2 ff
 

   (9)
            +-------+
            | 2    2
         %i\|q  + p
      *
         log
                                                       +-------+
                  2    2              2     2          | 2    2
              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
            + 
                  3
              %i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                          +-------+
                     2    2              2     2          | 2    2
                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  - %i p
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
                      +-------+
                      | 2    2          2        2                 2        2
       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                            +-------+
                            | 2    2            2        2                 2
                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
               + 
                        2
                 - 2%i p
     + 
                                  +-------+
            +-------+             | 2    2
            | 2    2     sin(a x)\|q  + p   + %i p cos(a x)
       - %i\|q  + p  log(----------------------------------)
                                      cos(a x)
     + 
                              +-------+
        +-------+             | 2    2                                 +-------+
        | 2    2     sin(a x)\|q  + p   - %i p cos(a x)                | 2    2
     %i\|q  + p  log(----------------------------------) - %i log(- 1)\|q  + p
                                  cos(a x)
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (9)
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R         log
--R                                                       +-------+
--R                  2    2              2     2          | 2    2
--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
--R            + 
--R                  3
--R              %i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                          +-------+
--R                     2    2              2     2          | 2    2
--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  - %i p
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R                      +-------+
--R                      | 2    2          2        2                 2        2
--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                            +-------+
--R                            | 2    2            2        2                 2
--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
--R               + 
--R                        2
--R                 - 2%i p
--R     + 
--R                                  +-------+
--R            +-------+             | 2    2
--R            | 2    2     sin(a x)\|q  + p   + %i p cos(a x)
--R       - %i\|q  + p  log(----------------------------------)
--R                                      cos(a x)
--R     + 
--R                              +-------+
--R        +-------+             | 2    2                                 +-------+
--R        | 2    2     sin(a x)\|q  + p   - %i p cos(a x)                | 2    2
--R     %i\|q  + p  log(----------------------------------) - %i log(- 1)\|q  + p
--R                                  cos(a x)
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 114
hh:=expandLog gg
 

   (10)
            +-------+
            | 2    2
         %i\|q  + p
      *
         log
                                                       +-------+
                  2    2              2     2          | 2    2
              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
            + 
                  3
              %i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                          +-------+
                     2    2              2     2          | 2    2
                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  - %i p
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
                      +-------+
                      | 2    2          2        2                 2        2
       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                            +-------+
                            | 2    2            2        2                 2
                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
               + 
                        2
                 - 2%i p
     + 
            +-------+             +-------+
            | 2    2              | 2    2
       - %i\|q  + p  log(sin(a x)\|q  + p   + %i p cos(a x))
     + 
        +-------+             +-------+                                +-------+
        | 2    2              | 2    2                                 | 2    2
     %i\|q  + p  log(sin(a x)\|q  + p   - %i p cos(a x)) - %i log(- 1)\|q  + p
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (10)
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R         log
--R                                                       +-------+
--R                  2    2              2     2          | 2    2
--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
--R            + 
--R                  3
--R              %i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                          +-------+
--R                     2    2              2     2          | 2    2
--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  - %i p
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R                      +-------+
--R                      | 2    2          2        2                 2        2
--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                            +-------+
--R                            | 2    2            2        2                 2
--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
--R               + 
--R                        2
--R                 - 2%i p
--R     + 
--R            +-------+             +-------+
--R            | 2    2              | 2    2
--R       - %i\|q  + p  log(sin(a x)\|q  + p   + %i p cos(a x))
--R     + 
--R        +-------+             +-------+                                +-------+
--R        | 2    2              | 2    2                                 | 2    2
--R     %i\|q  + p  log(sin(a x)\|q  + p   - %i p cos(a x)) - %i log(- 1)\|q  + p
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 115    14:362 Schaums and Axiom differ by a constant
ii:=complexNormalize hh
 

                                                   +-------+
                                                   | 2    2
         (%i log(%i) - %i log(- %i) - %i log(- 1))\|q  + p
   (11)  ---------------------------------------------------
                                 2       3
                           2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R                                                   +-------+
--R                                                   | 2    2
--R         (%i log(%i) - %i log(- %i) - %i log(- 1))\|q  + p
--R   (11)  ---------------------------------------------------
--R                                 2       3
--R                           2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 116
aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x)
 

   (1)
   [
       log
                                                +-------+
                   2     2         2    2    2  | 2    2
              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
            + 
                   2     3
              (2p q  - 2p )cos(a x)sin(a x)
         /
             2        2    2    2
            q cos(a x)  - q  + p
    /
            +-------+
            | 2    2
       2a p\|q  - p
     ,

                                +---------+
                                |   2    2
                     p sin(a x)\|- q  + p
         - atan(-------------------------------)
                   2     2              2     2
                (2q  - 2p )cos(a x) + 2q  - 2p
       + 
                      2    2              2     2
                  ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
         - atan(-------------------------------------------)
                                                +---------+
                           2                    |   2    2
                (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
    /
           +---------+
           |   2    2
       a p\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                                +-------+
--R                   2     2         2    2    2  | 2    2
--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
--R            + 
--R                   2     3
--R              (2p q  - 2p )cos(a x)sin(a x)
--R         /
--R             2        2    2    2
--R            q cos(a x)  - q  + p
--R    /
--R            +-------+
--R            | 2    2
--R       2a p\|q  - p
--R     ,
--R
--R                                +---------+
--R                                |   2    2
--R                     p sin(a x)\|- q  + p
--R         - atan(-------------------------------)
--R                   2     2              2     2
--R                (2q  - 2p )cos(a x) + 2q  - 2p
--R       + 
--R                      2    2              2     2
--R                  ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R         - atan(-------------------------------------------)
--R                                                +---------+
--R                           2                    |   2    2
--R                (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R    /
--R           +---------+
--R           |   2    2
--R       a p\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 117
bb1:=1/(a*p*sqrt(p^2-q^2))*atan((sqrt(p^2-q^2)*tan(a*x))/p)
 

                      +---------+
                      |   2    2
             tan(a x)\|- q  + p
        atan(--------------------)
                       p
   (2)  --------------------------
                  +---------+
                  |   2    2
              a p\|- q  + p
                                                     Type: Expression Integer
--R
--R                      +---------+
--R                      |   2    2
--R             tan(a x)\|- q  + p
--R        atan(--------------------)
--R                       p
--R   (2)  --------------------------
--R                  +---------+
--R                  |   2    2
--R              a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 118
bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((sqrt(q^2-p^2)*tan(a*x)+p)/(sqrt(q^2-p^2)*tan(a*x)-p))
 

                     +-------+
                     | 2    2
            tan(a x)\|q  - p   + p
        log(----------------------)
                     +-------+
                     | 2    2
            tan(a x)\|q  - p   - p
   (3)  ---------------------------
                    +-------+
                    | 2    2
               2a p\|q  - p
                                                     Type: Expression Integer
--R
--R                     +-------+
--R                     | 2    2
--R            tan(a x)\|q  - p   + p
--R        log(----------------------)
--R                     +-------+
--R                     | 2    2
--R            tan(a x)\|q  - p   - p
--R   (3)  ---------------------------
--R                    +-------+
--R                    | 2    2
--R               2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 119
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |   2    2
         \|- q  + p
      *
         log
                                                  +-------+
                     2     2         2    2    2  | 2    2
                ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
              + 
                     2     3
                (2p q  - 2p )cos(a x)sin(a x)
           /
               2        2    2    2
              q cos(a x)  - q  + p
     + 
                                  +---------+
           +-------+              |   2    2
           | 2    2      tan(a x)\|- q  + p
       - 2\|q  - p  atan(--------------------)
                                   p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R         log
--R                                                  +-------+
--R                     2     2         2    2    2  | 2    2
--R                ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
--R              + 
--R                     2     3
--R                (2p q  - 2p )cos(a x)sin(a x)
--R           /
--R               2        2    2    2
--R              q cos(a x)  - q  + p
--R     + 
--R                                  +---------+
--R           +-------+              |   2    2
--R           | 2    2      tan(a x)\|- q  + p
--R       - 2\|q  - p  atan(--------------------)
--R                                   p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 120
cc2:=aa.2-bb1
 

   (5)
                       +---------+                         +---------+
                       |   2    2                          |   2    2
              tan(a x)\|- q  + p                p sin(a x)\|- q  + p
       - atan(--------------------) - atan(-------------------------------)
                        p                     2     2              2     2
                                           (2q  - 2p )cos(a x) + 2q  - 2p
     + 
                    2    2              2     2
                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
       - atan(-------------------------------------------)
                                              +---------+
                         2                    |   2    2
              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
         +---------+
         |   2    2
     a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R                       +---------+                         +---------+
--R                       |   2    2                          |   2    2
--R              tan(a x)\|- q  + p                p sin(a x)\|- q  + p
--R       - atan(--------------------) - atan(-------------------------------)
--R                        p                     2     2              2     2
--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
--R     + 
--R                    2    2              2     2
--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R       - atan(-------------------------------------------)
--R                                              +---------+
--R                         2                    |   2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 121
cc3:=aa.1-bb2
 

   (6)
                      +-------+
                      | 2    2
             tan(a x)\|q  - p   + p
       - log(----------------------)
                      +-------+
                      | 2    2
             tan(a x)\|q  - p   - p
     + 
       log
                                                +-------+
                   2     2         2    2    2  | 2    2
              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
            + 
                   2     3
              (2p q  - 2p )cos(a x)sin(a x)
         /
             2        2    2    2
            q cos(a x)  - q  + p
  /
          +-------+
          | 2    2
     2a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                      +-------+
--R                      | 2    2
--R             tan(a x)\|q  - p   + p
--R       - log(----------------------)
--R                      +-------+
--R                      | 2    2
--R             tan(a x)\|q  - p   - p
--R     + 
--R       log
--R                                                +-------+
--R                   2     2         2    2    2  | 2    2
--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
--R            + 
--R                   2     3
--R              (2p q  - 2p )cos(a x)sin(a x)
--R         /
--R             2        2    2    2
--R            q cos(a x)  - q  + p
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 122
cc4:=aa.2-bb2
 

   (7)
                                  +-------+
          +---------+             | 2    2
          |   2    2     tan(a x)\|q  - p   + p
       - \|- q  + p  log(----------------------)
                                  +-------+
                                  | 2    2
                         tan(a x)\|q  - p   - p
     + 
                                         +---------+
           +-------+                     |   2    2
           | 2    2           p sin(a x)\|- q  + p
       - 2\|q  - p  atan(-------------------------------)
                            2     2              2     2
                         (2q  - 2p )cos(a x) + 2q  - 2p
     + 
           +-------+           2    2              2     2
           | 2    2        ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
       - 2\|q  - p  atan(-------------------------------------------)
                                                         +---------+
                                    2                    |   2    2
                         (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                  +-------+
--R          +---------+             | 2    2
--R          |   2    2     tan(a x)\|q  - p   + p
--R       - \|- q  + p  log(----------------------)
--R                                  +-------+
--R                                  | 2    2
--R                         tan(a x)\|q  - p   - p
--R     + 
--R                                         +---------+
--R           +-------+                     |   2    2
--R           | 2    2           p sin(a x)\|- q  + p
--R       - 2\|q  - p  atan(-------------------------------)
--R                            2     2              2     2
--R                         (2q  - 2p )cos(a x) + 2q  - 2p
--R     + 
--R           +-------+           2    2              2     2
--R           | 2    2        ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R       - 2\|q  - p  atan(-------------------------------------------)
--R                                                         +---------+
--R                                    2                    |   2    2
--R                         (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 123
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (8)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (8)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 124
dd2:=tanrule cc2
 

   (9)
                       +---------+                         +---------+
                       |   2    2                          |   2    2
              sin(a x)\|- q  + p                p sin(a x)\|- q  + p
       - atan(--------------------) - atan(-------------------------------)
                   p cos(a x)                 2     2              2     2
                                           (2q  - 2p )cos(a x) + 2q  - 2p
     + 
                    2    2              2     2
                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
       - atan(-------------------------------------------)
                                              +---------+
                         2                    |   2    2
              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
         +---------+
         |   2    2
     a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (9)
--R                       +---------+                         +---------+
--R                       |   2    2                          |   2    2
--R              sin(a x)\|- q  + p                p sin(a x)\|- q  + p
--R       - atan(--------------------) - atan(-------------------------------)
--R                   p cos(a x)                 2     2              2     2
--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
--R     + 
--R                    2    2              2     2
--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R       - atan(-------------------------------------------)
--R                                              +---------+
--R                         2                    |   2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 125
ee2:=ratDenom dd2
 

   (10)
       -
             +---------+
             |   2    2
            \|- q  + p
         *
                                                            +---------+
                       2    2              2     2          |   2    2
                   ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
            atan(--------------------------------------------------------)
                     2    3         2        2     3               2    3
                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                 +---------+
        +---------+              |   2    2
        |   2    2      sin(a x)\|- q  + p
       \|- q  + p  atan(--------------------)
                             p cos(a x)
     + 
                                        +---------+
        +---------+                     |   2    2
        |   2    2           p sin(a x)\|- q  + p
       \|- q  + p  atan(-------------------------------)
                           2     2              2     2
                        (2q  - 2p )cos(a x) + 2q  - 2p
  /
          2      3
     a p q  - a p
                                                     Type: Expression Integer
--R
--R   (10)
--R       -
--R             +---------+
--R             |   2    2
--R            \|- q  + p
--R         *
--R                                                            +---------+
--R                       2    2              2     2          |   2    2
--R                   ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R            atan(--------------------------------------------------------)
--R                     2    3         2        2     3               2    3
--R                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                 +---------+
--R        +---------+              |   2    2
--R        |   2    2      sin(a x)\|- q  + p
--R       \|- q  + p  atan(--------------------)
--R                             p cos(a x)
--R     + 
--R                                        +---------+
--R        +---------+                     |   2    2
--R        |   2    2           p sin(a x)\|- q  + p
--R       \|- q  + p  atan(-------------------------------)
--R                           2     2              2     2
--R                        (2q  - 2p )cos(a x) + 2q  - 2p
--R  /
--R          2      3
--R     a p q  - a p
--R                                                     Type: Expression Integer
--E

--S 126
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                             - x + %i
                      %i log(--------)
                              x + %i
   (11)  atan(x) == - ----------------
                              2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             - x + %i
--R                      %i log(--------)
--R                              x + %i
--R   (11)  atan(x) == - ----------------
--R                              2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 127
ff2:=atanrule ee2
 

   (12)
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                +---------+
                                |   2    2          2        2                 2
                   - p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
                 + 
                          2
                   - 2%i p
              /
                              +---------+
                              |   2    2          2        2                 2
                   p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
                 + 
                          2
                   - 2%i p
     + 
                                      +---------+
            +---------+               |   2    2
            |   2    2     - sin(a x)\|- q  + p   + %i p cos(a x)
       - %i\|- q  + p  log(--------------------------------------)
                                     +---------+
                                     |   2    2
                            sin(a x)\|- q  + p   + %i p cos(a x)
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                                           +---------+
                      2    2              2     2          |   2    2
                ((- 2q  + p )cos(a x) - 2q  + 2p )sin(a x)\|- q  + p
              + 
                       2       3         2           2        3
                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
              + 
                      2       3
                %i p q  - %i p
           /
                                                         +---------+
                    2    2              2     2          |   2    2
                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
              + 
                       2       3         2           2        3
                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
              + 
                      2       3
                %i p q  - %i p
  /
           2       3
     2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R   (12)
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                +---------+
--R                                |   2    2          2        2                 2
--R                   - p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
--R                 + 
--R                          2
--R                   - 2%i p
--R              /
--R                              +---------+
--R                              |   2    2          2        2                 2
--R                   p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
--R                 + 
--R                          2
--R                   - 2%i p
--R     + 
--R                                      +---------+
--R            +---------+               |   2    2
--R            |   2    2     - sin(a x)\|- q  + p   + %i p cos(a x)
--R       - %i\|- q  + p  log(--------------------------------------)
--R                                     +---------+
--R                                     |   2    2
--R                            sin(a x)\|- q  + p   + %i p cos(a x)
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                                           +---------+
--R                      2    2              2     2          |   2    2
--R                ((- 2q  + p )cos(a x) - 2q  + 2p )sin(a x)\|- q  + p
--R              + 
--R                       2       3         2           2        3
--R                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R              + 
--R                      2       3
--R                %i p q  - %i p
--R           /
--R                                                         +---------+
--R                    2    2              2     2          |   2    2
--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R              + 
--R                       2       3         2           2        3
--R                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R              + 
--R                      2       3
--R                %i p q  - %i p
--R  /
--R           2       3
--R     2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E

--S 128
gg2:=expandLog ff2
 

   (13)
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                                          +---------+
                     2    2              2     2          |   2    2
                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
               + 
                        2       3         2           2        3
                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
               + 
                       2       3
                 %i p q  - %i p
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                                       +---------+
                  2    2              2     2          |   2    2
              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
            + 
                       2       3         2             2        3
              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
            + 
                      2       3
              - %i p q  + %i p
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
                      +---------+
                      |   2    2          2        2                 2        2
       log(p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q  - 2%i p )
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                            +---------+
                            |   2    2            2        2                 2
                 p sin(a x)\|- q  + p   + (- 2%i q  + 2%i p )cos(a x) - 2%i q
               + 
                      2
                 2%i p
     + 
          +---------+             +---------+
          |   2    2              |   2    2
       %i\|- q  + p  log(sin(a x)\|- q  + p   + %i p cos(a x))
     + 
            +---------+             +---------+
            |   2    2              |   2    2
       - %i\|- q  + p  log(sin(a x)\|- q  + p   - %i p cos(a x))
     + 
                     +---------+
                     |   2    2
       - %i log(- 1)\|- q  + p
  /
           2       3
     2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R   (13)
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                                          +---------+
--R                     2    2              2     2          |   2    2
--R                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R               + 
--R                        2       3         2           2        3
--R                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R               + 
--R                       2       3
--R                 %i p q  - %i p
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                                       +---------+
--R                  2    2              2     2          |   2    2
--R              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R            + 
--R                       2       3         2             2        3
--R              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
--R            + 
--R                      2       3
--R              - %i p q  + %i p
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R                      +---------+
--R                      |   2    2          2        2                 2        2
--R       log(p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q  - 2%i p )
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                            +---------+
--R                            |   2    2            2        2                 2
--R                 p sin(a x)\|- q  + p   + (- 2%i q  + 2%i p )cos(a x) - 2%i q
--R               + 
--R                      2
--R                 2%i p
--R     + 
--R          +---------+             +---------+
--R          |   2    2              |   2    2
--R       %i\|- q  + p  log(sin(a x)\|- q  + p   + %i p cos(a x))
--R     + 
--R            +---------+             +---------+
--R            |   2    2              |   2    2
--R       - %i\|- q  + p  log(sin(a x)\|- q  + p   - %i p cos(a x))
--R     + 
--R                     +---------+
--R                     |   2    2
--R       - %i log(- 1)\|- q  + p
--R  /
--R           2       3
--R     2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E

--S 129
rootrule4a:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(sqrt(p^2-q^2)==sqrt(p-q)*sqrt(q+p))
 

          +---------+
          |   2    2      +-------+ +-----+
   (14)  \|- q  + p   == \|- q + p \|q + p
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R          +---------+
--R          |   2    2      +-------+ +-----+
--R   (14)  \|- q  + p   == \|- q + p \|q + p
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 130
hh2:=rootrule4a gg2
 

   (15)
       -
               +-------+ +-----+
            %i\|- q + p \|q + p
         *
            log
                     2    2              2     2          +-------+ +-----+
                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
               + 
                        2       3         2           2        3
                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
               + 
                       2       3
                 %i p q  - %i p
     + 
            +-------+ +-----+
         %i\|- q + p \|q + p
      *
         log
                  2    2              2     2          +-------+ +-----+
              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
            + 
                       2       3         2             2        3
              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
            + 
                      2       3
              - %i p q  + %i p
     + 
            +-------+ +-----+
         %i\|- q + p \|q + p
      *
         log
                         +-------+ +-----+         2        2                 2
              p sin(a x)\|- q + p \|q + p  + (2%i q  - 2%i p )cos(a x) + 2%i q
            + 
                     2
              - 2%i p
     + 
       -
               +-------+ +-----+
            %i\|- q + p \|q + p
         *
            log
                            +-------+ +-----+           2        2
                 p sin(a x)\|- q + p \|q + p  + (- 2%i q  + 2%i p )cos(a x)
               + 
                        2        2
                 - 2%i q  + 2%i p
     + 
          +-------+ +-----+             +-------+ +-----+
       %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  + %i p cos(a x))
     + 
            +-------+ +-----+             +-------+ +-----+
       - %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  - %i p cos(a x))
     + 
                     +-------+ +-----+
       - %i log(- 1)\|- q + p \|q + p
  /
           2       3
     2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R   (15)
--R       -
--R               +-------+ +-----+
--R            %i\|- q + p \|q + p
--R         *
--R            log
--R                     2    2              2     2          +-------+ +-----+
--R                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
--R               + 
--R                        2       3         2           2        3
--R                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R               + 
--R                       2       3
--R                 %i p q  - %i p
--R     + 
--R            +-------+ +-----+
--R         %i\|- q + p \|q + p
--R      *
--R         log
--R                  2    2              2     2          +-------+ +-----+
--R              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
--R            + 
--R                       2       3         2             2        3
--R              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
--R            + 
--R                      2       3
--R              - %i p q  + %i p
--R     + 
--R            +-------+ +-----+
--R         %i\|- q + p \|q + p
--R      *
--R         log
--R                         +-------+ +-----+         2        2                 2
--R              p sin(a x)\|- q + p \|q + p  + (2%i q  - 2%i p )cos(a x) + 2%i q
--R            + 
--R                     2
--R              - 2%i p
--R     + 
--R       -
--R               +-------+ +-----+
--R            %i\|- q + p \|q + p
--R         *
--R            log
--R                            +-------+ +-----+           2        2
--R                 p sin(a x)\|- q + p \|q + p  + (- 2%i q  + 2%i p )cos(a x)
--R               + 
--R                        2        2
--R                 - 2%i q  + 2%i p
--R     + 
--R          +-------+ +-----+             +-------+ +-----+
--R       %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  + %i p cos(a x))
--R     + 
--R            +-------+ +-----+             +-------+ +-----+
--R       - %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  - %i p cos(a x))
--R     + 
--R                     +-------+ +-----+
--R       - %i log(- 1)\|- q + p \|q + p
--R  /
--R           2       3
--R     2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E

--S 131    14:363 Schaums and Axiom differ by a constant
ii2:=complexNormalize hh2
 

                                                   +-------+ +-----+
         (%i log(%i) - %i log(- %i) - %i log(- 1))\|- q + p \|q + p
   (16)  -----------------------------------------------------------
                                     2       3
                               2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R                                                   +-------+ +-----+
--R         (%i log(%i) - %i log(- %i) - %i log(- 1))\|- q + p \|q + p
--R   (16)  -----------------------------------------------------------
--R                                     2       3
--R                               2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 132    14:364 Axiom cannot compute this integral
aa:=integrate(x^m*sin(a*x),x)
 

           x
         ++             m
   (1)   |   sin(%I a)%I d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             m
--I   (1)   |   sin(%I a)%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 133    14:365 Axiom cannot compute this integral
aa:=integrate(sin(a*x)/x^n,x)
 

           x
         ++  sin(%I a)
   (1)   |   --------- d%I
        ++        n
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sin(%I a)
--I   (1)   |   --------- d%I
--R        ++        n
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 134    14:366 Axiom cannot compute this integral
aa:=integrate(sin(a*x)^n,x)
 

           x
         ++           n
   (1)   |   sin(%I a) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   sin(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 135    14:367 Axiom cannot compute this integral
aa:=integrate(1/(sin(a*x))^n,x)
 

           x
         ++       1
   (1)   |   ---------- d%I
        ++            n
             sin(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ---------- d%I
--R        ++            n
--I             sin(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 136    14:368 Axiom cannot compute this integral
aa:=integrate(x/sin(a*x)^n,x)
 

           x
         ++      %I
   (1)   |   ---------- d%I
        ++            n
             sin(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   ---------- d%I
--R        ++            n
--I             sin(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to asinhatanh.output (2009/2/17, 17:43:49).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
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[0.01,0.009999833,asinh(0.01),asinh(0.01)-0.009999833],_
[0.02,0.019998667,asinh(0.02),asinh(0.02)-0.019998667],_
[0.03,0.029995502,asinh(0.03),asinh(0.03)-0.029995502],_
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[0.12,0.119713851,asinh(0.12),asinh(0.12)-0.119713851],_
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   (1)
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    [1.0,0.881373587,0.8813735870 1954302523,0.195430252 E -10]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.0,0.0,0.0,0.0],
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--R    [0.24,0.237753749,0.2377537491 5239999115,0.1523999911 5 E -9],
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--R    [0.76,0.701127988,0.7011279877 5258482712,- 0.2474151729 E -9],
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--R    [0.78,0.716974594,0.7169745940 9500523361,0.9500523361 E -10],
--R    [0.79,0.724840509,0.7248405091 2852755291,0.1285275529 E -9],
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--R    [0.81,0.740457912,0.7404579124 098567228,0.4098567228 E -9],
--R    [0.82,0.748209563,0.7482095630 9482316487,0.9482316487 E -10],
--R    [0.83,0.7559233,0.7559232999 9081426309,- 0.918573691 E -11],
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--R    [0.88,0.79392695,0.7939269495 9191660771,- 0.4080833923 E -9],
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--R    [0.91,0.816281421,0.8162814210 6387596132,0.6387596132 E -10],
--R    [0.92,0.823659091,0.8236590904 3241050549,- 0.5675894945 2 E -9],
--R    [0.93,0.831000091,0.8310000911 4624712798,0.146247128 E -9],
--R    [0.94,0.838304575,0.8383045748 1232348677,- 0.1876765132 E -9],
--R    [0.95,0.845572697,0.8455726970 3972738992,0.397273899 E -10],
--R    [0.96,0.852804617,0.8528046172 2893238837,0.2289323884 E -9],
--R    [0.97,0.860000498,0.8600004983 6713998068,0.3671399807 E -9],
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--R    [0.99,0.874284812,0.8742848121 8729492676,0.1872949268 E -9],
--R    [1.0,0.881373587,0.8813735870 1954302523,0.195430252 E -10]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
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[0.95,1.831780823,atanh(0.95),atanh(0.95)-1.831780823],_
[0.96,1.945910149,atanh(0.96),atanh(0.96)-1.945910149],_
[0.97,2.092295720,atanh(0.97),atanh(0.97)-2.092295720],_
[0.98,2.297559925,atanh(0.98),atanh(0.98)-2.297559925],_
[0.99,2.646652412,atanh(0.99),atanh(0.99)-2.646652412]]
 

   (2)
   [[0.0,0.0,0.0,0.0],
    [0.01,0.010000333,0.0100003333 5333476201 6,0.3533347620 16 E -9],
    [0.02,0.020002667,0.0200026673 0684958071 7,0.3068495807 17 E -9],
    [0.03,0.030009004,0.0300090048 6312647432 6,0.8631264743 26 E -9],
    [0.04,0.040021353,0.0400213538 3676821291 2,0.8367682129 12 E -9],
    [0.05,0.050041729,0.0500417292 7849126824 6,0.2784912682 46 E -9],
    [0.06,0.060072156,0.0600721559 2103162366 2,- 0.7896837633 8 E -10],
    [0.07,0.070114671,0.0701146706 5432511799,- 0.3456748820 1 E -9],
    [0.08,0.080171325,0.0801713250 3758969169,0.3758969169 E -10],
    [0.09,0.090244188,0.0902441878 5614682960 9,- 0.1438531703 9 E -9],
    [0.1,0.100335347,0.1003353477 3107558064,0.7310755806 36 E -9],
    [0.11,0.110446915,0.1104469157 9009714872,0.7900971487 22 E -9],
    [0.12,0.120581028,0.1205810284 0844403523,0.4084440352 3 E -9],
    [0.13,0.13073985,0.1307398500 28878425,0.28878425 E -10],
    [0.14,0.140925576,0.1409255760 7049386396,0.7049386396 E -10],
    [0.15,0.151140436,0.1511404359 3646680528,- 0.6353319472 E -10],
    [0.16,0.161386696,0.1613866961 3152551534,0.1315255153 4 E -9],
    [0.17,0.171666663,0.1716666635 0057909768,0.5005790976 8 E -9],
    [0.18,0.181982689,0.1819826886 0070582337,- 0.3992941766 3 E -9],
    [0.19,0.192337169,0.1923371692 1954530989,0.2195453098 9 E -9],
    [0.2,0.202732554,0.2027325540 5408219099,0.5408219099 E -10],
    [0.21,0.213171346,0.2131713465 6485979698,0.5648597969 8 E -9],
    [0.22,0.223656109,0.2236561090 2183241065,0.2183241065 E -10],
    [0.23,0.234189466,0.2341894667 5936682305,0.7593668230 5 E -9],
    [0.24,0.244774112,0.2447741126 5935289296,0.6593528929 6 E -9],
    [0.25,0.255412812,0.2554128118 829953416,- 0.1170046584 E -9],
    [0.26,0.266108407,0.2661084068 7365412176,- 0.1263458782 E -9],
    [0.27,0.276863823,0.2768638226 5510007198,- 0.3448999280 2 E -9],
    [0.28,0.287682072,0.2876820724 5178092744,0.4517809274 4 E -9],
    [0.29,0.298566264,0.2985662636 6017834677,- 0.3398216532 3 E -9],
    [0.3,0.309519604,0.3095196042 0311171547,0.2031117155 E -9],
    [0.31,0.320545409,0.3205454093 0194608097,0.3019460809 7 E -9],
    [0.32,0.331647108,0.3316471087 051320776,0.7051320776 E -9],
    [0.33,0.342828254,0.3428282544 1539385272,0.4153938527 2 E -9],
    [0.34,0.354092528,0.3540925289 6224291211,0.9622429121 E -9],
    [0.35,0.365443754,0.3654437542 7139616907,0.2713961690 7 E -9],
    [0.36,0.376885901,0.3768859011 88190076,0.188190076 E -9],
    [0.37,0.3884231,0.3884230997 1829611371,- 0.2817038862 9 E -9],
    [0.38,0.40005965,0.4000596500 5605656814,0.5605656814 E -10],
    [0.39,0.411800034,0.4118000344 7869025422,0.4786902542 2 E -9],
    [0.4,0.42364893,0.4236489301 9360180685,0.1936018069 E -9],
    [0.41,0.435611223,0.4356112232 362244138,0.2362244138 E -9],
    [0.42,0.447692023,0.4476920235 2742069707,0.5274206970 7 E -9],
    [0.43,0.459896681,0.4598966812 1267856435,0.2126785644 E -9],
    [0.44,0.472230804,0.4722308044 2042569355,0.4204256935 5 E -9],
    [0.45,0.484700279,0.4847002785 9405174156,- 0.4059482584 4 E -9],
    [0.46,0.497311288,0.4973112875 7203102745,- 0.4279689725 5 E -9],
    [0.47,0.510070337,0.5100703366 1330723373,- 0.3866927663 E -9],
    [0.48,0.522984278,0.5229842775 9134385416,- 0.4086561458 E -9],
    [0.49,0.536060337,0.5360603366 1056668467,- 0.3894333153 E -9],
    [0.5,0.549306144,0.5493061443 340548457,0.3340548457 E -9],
    [0.51,0.562729769,0.5627297693 521488593,0.3521488593 E -9],
    [0.52,0.576339754,0.5763397549 691927296,0.9691927296 E -9],
    [0.53,0.59014516,0.5901451598 4118843811,- 0.1588115619 E -9],
    [0.54,0.604155603,0.6041556029 6226707918,- 0.377329208 E -10],
    [0.55,0.618381313,0.6183813135 7446343157,0.5744634315 7 E -9],
    [0.56,0.632833186,0.6328331866 6563794169,0.6656379416 9 E -9],
    [0.57,0.647522844,0.6475228448 2737281698,0.8273728169 8 E -9],
    [0.58,0.662462707,0.6624627073 7179924883,0.3717992488 E -9],
    [0.59,0.677666068,0.6776660677 5796186084,- 0.2420381392 E -9],
    [0.6,0.69314718,0.6931471805 5994530942,0.5599453094 2 E -9],
    [0.61,0.708921359,0.7089213594 2740828423,0.4274082842 E -9],
    [0.62,0.725005087,0.7250050877 5299915279,0.7529991527 9 E -9],
    [0.63,0.741416144,0.7414161440 8126894485,0.8126894484 E -10],
    [0.64,0.758173745,0.7581737446 8404421054,- 0.3159557895 E -9],
    [0.65,0.775298706,0.7752987062 0558346517,0.2055834652 E -9],
    [0.66,0.792813631,0.7928136318 7019092161,0.8701909216 1 E -9],
    [0.67,0.810743125,0.8107431254 7513743591,0.4751374359 1 E -9],
    [0.68,0.829114038,0.8291140383 0176618883,0.3017661888 E -9],
    [0.69,0.847955755,0.8479557552 1896361309,0.2189636131 E -9],
    [0.7,0.867300527,0.8673005276 9405319443,0.6940531944 3 E -9],
    [0.71,0.887183863,0.8871838632 5809290781,0.2580929078 E -9],
    [0.72,0.907644983,0.9076449833 1912455918,0.3191245592 E -9],
    [0.73,0.928727364,0.9287273642 4672493638,0.2467249364 E -9],
    [0.74,0.950479381,0.9504793805 9652349126,- 0.4034765087 E -9],
    [0.75,0.972955074,0.9729550745 2765665255,0.5276566525 5 E -9],
    [0.76,0.996215082,0.9962150823 4510308105,0.345103081 E -9],
    [0.77,1.020327758,1.0203277583 223397256,0.3223397256 E -9],
    [0.78,1.045370548,1.0453705484 668846471,0.4668846471 E -9],
    [0.79,1.071431684,1.0714316840 586659998,0.586659998 E -10],
    [0.8,1.098612289,1.0986122886 681096914,- 0.3318903086 E -9],
    [0.81,1.127029026,1.1270290260 496926434,0.496926434 E -10],
    [0.82,1.156817465,1.1568174645 903153292,- 0.4096846708 E -9],
    [0.83,1.188136404,1.1881364043 926024299,0.3926024299 E -9],
    [0.84,1.221173518,1.2211735176 846021907,- 0.3153978093 E -9],
    [0.85,1.256152811,1.2561528119 880573765,0.9880573764 9 E -9],
    [0.86,1.293344672,1.2933446720 489713161,0.489713161 E -10],
    [0.87,1.333079629,1.3330796296 965249441,0.6965249441 E -9],
    [0.88,1.375767657,1.3757676565 209744477,- 0.4790255523 E -9],
    [0.89,1.421925871,1.4219258711 306359176,0.1306359176 E -9],
    [0.9,1.47221949,1.4722194895 8322023,- 0.41677977 E -9],
    [0.91,1.527524425,1.5275244253 55205245,0.355205245 E -9],
    [0.92,1.589026915,1.5890269151 739728098,0.1739728098 E -9],
    [0.93,1.65839002,1.6583900199 247861234,- 0.752138766 E -10],
    [0.94,1.738049345,1.7380493449 176365654,- 0.823634346 E -10],
    [0.95,1.831780823,1.8317808230 648232137,0.648232137 E -10],
    [0.96,1.945910149,1.9459101490 553133051,0.553133051 E -10],
    [0.97,2.09229572,2.0922957200 349394077,0.349394077 E -10],
    [0.98,2.297559925,2.2975599250 672949634,0.672949634 E -10],
    [0.99,2.646652412,2.6466524123 622461976,0.3622461976 E -9]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.0,0.0,0.0,0.0],
--R    [0.01,0.010000333,0.0100003333 5333476201 6,0.3533347620 16 E -9],
--R    [0.02,0.020002667,0.0200026673 0684958071 7,0.3068495807 17 E -9],
--R    [0.03,0.030009004,0.0300090048 6312647432 6,0.8631264743 26 E -9],
--R    [0.04,0.040021353,0.0400213538 3676821291 2,0.8367682129 12 E -9],
--R    [0.05,0.050041729,0.0500417292 7849126824 6,0.2784912682 46 E -9],
--R    [0.06,0.060072156,0.0600721559 2103162366 2,- 0.7896837633 8 E -10],
--R    [0.07,0.070114671,0.0701146706 5432511799,- 0.3456748820 1 E -9],
--R    [0.08,0.080171325,0.0801713250 3758969169,0.3758969169 E -10],
--R    [0.09,0.090244188,0.0902441878 5614682960 9,- 0.1438531703 9 E -9],
--R    [0.1,0.100335347,0.1003353477 3107558064,0.7310755806 36 E -9],
--R    [0.11,0.110446915,0.1104469157 9009714872,0.7900971487 22 E -9],
--R    [0.12,0.120581028,0.1205810284 0844403523,0.4084440352 3 E -9],
--R    [0.13,0.13073985,0.1307398500 28878425,0.28878425 E -10],
--R    [0.14,0.140925576,0.1409255760 7049386396,0.7049386396 E -10],
--R    [0.15,0.151140436,0.1511404359 3646680528,- 0.6353319472 E -10],
--R    [0.16,0.161386696,0.1613866961 3152551534,0.1315255153 4 E -9],
--R    [0.17,0.171666663,0.1716666635 0057909768,0.5005790976 8 E -9],
--R    [0.18,0.181982689,0.1819826886 0070582337,- 0.3992941766 3 E -9],
--R    [0.19,0.192337169,0.1923371692 1954530989,0.2195453098 9 E -9],
--R    [0.2,0.202732554,0.2027325540 5408219099,0.5408219099 E -10],
--R    [0.21,0.213171346,0.2131713465 6485979698,0.5648597969 8 E -9],
--R    [0.22,0.223656109,0.2236561090 2183241065,0.2183241065 E -10],
--R    [0.23,0.234189466,0.2341894667 5936682305,0.7593668230 5 E -9],
--R    [0.24,0.244774112,0.2447741126 5935289296,0.6593528929 6 E -9],
--R    [0.25,0.255412812,0.2554128118 829953416,- 0.1170046584 E -9],
--R    [0.26,0.266108407,0.2661084068 7365412176,- 0.1263458782 E -9],
--R    [0.27,0.276863823,0.2768638226 5510007198,- 0.3448999280 2 E -9],
--R    [0.28,0.287682072,0.2876820724 5178092744,0.4517809274 4 E -9],
--R    [0.29,0.298566264,0.2985662636 6017834677,- 0.3398216532 3 E -9],
--R    [0.3,0.309519604,0.3095196042 0311171547,0.2031117155 E -9],
--R    [0.31,0.320545409,0.3205454093 0194608097,0.3019460809 7 E -9],
--R    [0.32,0.331647108,0.3316471087 051320776,0.7051320776 E -9],
--R    [0.33,0.342828254,0.3428282544 1539385272,0.4153938527 2 E -9],
--R    [0.34,0.354092528,0.3540925289 6224291211,0.9622429121 E -9],
--R    [0.35,0.365443754,0.3654437542 7139616907,0.2713961690 7 E -9],
--R    [0.36,0.376885901,0.3768859011 88190076,0.188190076 E -9],
--R    [0.37,0.3884231,0.3884230997 1829611371,- 0.2817038862 9 E -9],
--R    [0.38,0.40005965,0.4000596500 5605656814,0.5605656814 E -10],
--R    [0.39,0.411800034,0.4118000344 7869025422,0.4786902542 2 E -9],
--R    [0.4,0.42364893,0.4236489301 9360180685,0.1936018069 E -9],
--R    [0.41,0.435611223,0.4356112232 362244138,0.2362244138 E -9],
--R    [0.42,0.447692023,0.4476920235 2742069707,0.5274206970 7 E -9],
--R    [0.43,0.459896681,0.4598966812 1267856435,0.2126785644 E -9],
--R    [0.44,0.472230804,0.4722308044 2042569355,0.4204256935 5 E -9],
--R    [0.45,0.484700279,0.4847002785 9405174156,- 0.4059482584 4 E -9],
--R    [0.46,0.497311288,0.4973112875 7203102745,- 0.4279689725 5 E -9],
--R    [0.47,0.510070337,0.5100703366 1330723373,- 0.3866927663 E -9],
--R    [0.48,0.522984278,0.5229842775 9134385416,- 0.4086561458 E -9],
--R    [0.49,0.536060337,0.5360603366 1056668467,- 0.3894333153 E -9],
--R    [0.5,0.549306144,0.5493061443 340548457,0.3340548457 E -9],
--R    [0.51,0.562729769,0.5627297693 521488593,0.3521488593 E -9],
--R    [0.52,0.576339754,0.5763397549 691927296,0.9691927296 E -9],
--R    [0.53,0.59014516,0.5901451598 4118843811,- 0.1588115619 E -9],
--R    [0.54,0.604155603,0.6041556029 6226707918,- 0.377329208 E -10],
--R    [0.55,0.618381313,0.6183813135 7446343157,0.5744634315 7 E -9],
--R    [0.56,0.632833186,0.6328331866 6563794169,0.6656379416 9 E -9],
--R    [0.57,0.647522844,0.6475228448 2737281698,0.8273728169 8 E -9],
--R    [0.58,0.662462707,0.6624627073 7179924883,0.3717992488 E -9],
--R    [0.59,0.677666068,0.6776660677 5796186084,- 0.2420381392 E -9],
--R    [0.6,0.69314718,0.6931471805 5994530942,0.5599453094 2 E -9],
--R    [0.61,0.708921359,0.7089213594 2740828423,0.4274082842 E -9],
--R    [0.62,0.725005087,0.7250050877 5299915279,0.7529991527 9 E -9],
--R    [0.63,0.741416144,0.7414161440 8126894485,0.8126894484 E -10],
--R    [0.64,0.758173745,0.7581737446 8404421054,- 0.3159557895 E -9],
--R    [0.65,0.775298706,0.7752987062 0558346517,0.2055834652 E -9],
--R    [0.66,0.792813631,0.7928136318 7019092161,0.8701909216 1 E -9],
--R    [0.67,0.810743125,0.8107431254 7513743591,0.4751374359 1 E -9],
--R    [0.68,0.829114038,0.8291140383 0176618883,0.3017661888 E -9],
--R    [0.69,0.847955755,0.8479557552 1896361309,0.2189636131 E -9],
--R    [0.7,0.867300527,0.8673005276 9405319443,0.6940531944 3 E -9],
--R    [0.71,0.887183863,0.8871838632 5809290781,0.2580929078 E -9],
--R    [0.72,0.907644983,0.9076449833 1912455918,0.3191245592 E -9],
--R    [0.73,0.928727364,0.9287273642 4672493638,0.2467249364 E -9],
--R    [0.74,0.950479381,0.9504793805 9652349126,- 0.4034765087 E -9],
--R    [0.75,0.972955074,0.9729550745 2765665255,0.5276566525 5 E -9],
--R    [0.76,0.996215082,0.9962150823 4510308105,0.345103081 E -9],
--R    [0.77,1.020327758,1.0203277583 223397256,0.3223397256 E -9],
--R    [0.78,1.045370548,1.0453705484 668846471,0.4668846471 E -9],
--R    [0.79,1.071431684,1.0714316840 586659998,0.586659998 E -10],
--R    [0.8,1.098612289,1.0986122886 681096914,- 0.3318903086 E -9],
--R    [0.81,1.127029026,1.1270290260 496926434,0.496926434 E -10],
--R    [0.82,1.156817465,1.1568174645 903153292,- 0.4096846708 E -9],
--R    [0.83,1.188136404,1.1881364043 926024299,0.3926024299 E -9],
--R    [0.84,1.221173518,1.2211735176 846021907,- 0.3153978093 E -9],
--R    [0.85,1.256152811,1.2561528119 880573765,0.9880573764 9 E -9],
--R    [0.86,1.293344672,1.2933446720 489713161,0.489713161 E -10],
--R    [0.87,1.333079629,1.3330796296 965249441,0.6965249441 E -9],
--R    [0.88,1.375767657,1.3757676565 209744477,- 0.4790255523 E -9],
--R    [0.89,1.421925871,1.4219258711 306359176,0.1306359176 E -9],
--R    [0.9,1.47221949,1.4722194895 8322023,- 0.41677977 E -9],
--R    [0.91,1.527524425,1.5275244253 55205245,0.355205245 E -9],
--R    [0.92,1.589026915,1.5890269151 739728098,0.1739728098 E -9],
--R    [0.93,1.65839002,1.6583900199 247861234,- 0.752138766 E -10],
--R    [0.94,1.738049345,1.7380493449 176365654,- 0.823634346 E -10],
--R    [0.95,1.831780823,1.8317808230 648232137,0.648232137 E -10],
--R    [0.96,1.945910149,1.9459101490 553133051,0.553133051 E -10],
--R    [0.97,2.09229572,2.0922957200 349394077,0.349394077 E -10],
--R    [0.98,2.297559925,2.2975599250 672949634,0.672949634 E -10],
--R    [0.99,2.646652412,2.6466524123 622461976,0.3622461976 E -9]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to exint.output (2009/2/17, 17:45:46).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 10
integrate(1/(x**2 + a),x)
 

               2      +---+
             (x  - a)\|- a  + 2a x         +-+
         log(---------------------)      x\|a
                      2             atan(-----)
                     x  + a                a
   (1)  [--------------------------,-----------]
                     +---+               +-+
                   2\|- a               \|a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R               2      +---+
--R             (x  - a)\|- a  + 2a x         +-+
--R         log(---------------------)      x\|a
--R                      2             atan(-----)
--R                     x  + a                a
--R   (1)  [--------------------------,-----------]
--R                     +---+               +-+
--R                   2\|- a               \|a
--R                                     Type: Union(List Expression Integer,...)
--E 1

)clear all
 
   All user variables and function definitions have been cleared.

--S 2 of 10
integrate((x**2+2*x+1)/((x+1)**6+1),x)
 

              3     2
        atan(x  + 3x  + 3x + 1)
   (1)  -----------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2
--R        atan(x  + 3x  + 3x + 1)
--R   (1)  -----------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 2

)clear all
 
   All user variables and function definitions have been cleared.

--S 3 of 10
integrate(tan(atan(x)/3),x)
 

                  atan(x) 2             atan(x) 2           atan(x)
        8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
                     3                     3                   3
   (1)  ------------------------------------------------------------
                                     18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  atan(x) 2             atan(x) 2           atan(x)
--R        8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
--R                     3                     3                   3
--R   (1)  ------------------------------------------------------------
--R                                     18
--R                                          Type: Union(Expression Integer,...)
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 10
complexIntegrate(1/(x**2 + a),x)
 

         +---+      +---+         +---+        +---+
         |  1       |  1          |  1         |  1
         |- - log(a |- -  + x) -  |- - log(- a |- -  + x)
        \|  a      \|  a         \|  a        \|  a
   (1)  -------------------------------------------------
                                2
                                                     Type: Expression Integer
--R 
--R
--R         +---+      +---+         +---+        +---+
--R         |  1       |  1          |  1         |  1
--R         |- - log(a |- -  + x) -  |- - log(- a |- -  + x)
--R        \|  a      \|  a         \|  a        \|  a
--R   (1)  -------------------------------------------------
--R                                2
--R                                                     Type: Expression Integer
--E 4

)clear all
 
   All user variables and function definitions have been cleared.

--S 5 of 10
integrate(log(1 + sqrt(a*x + b)) / x,x)
 

           x      +--------+
         ++  log(\|b + %P a  + 1)
   (1)   |   -------------------- d%P
        ++            %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x      +--------+
--R         ++  log(\|b + %P a  + 1)
--R   (1)   |   -------------------- d%P
--R        ++            %P
--R                                          Type: Union(Expression Integer,...)
--E 5

)clear all
 
   All user variables and function definitions have been cleared.

--S 6 of 10
integrate(x**3 / (a+b*x)**(1/3),x)
 

             3 3         2 2       2          3 3+-------+2
        (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
   (1)  ---------------------------------------------------
                                   4
                               440b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3 3         2 2       2          3 3+-------+2
--R        (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
--R   (1)  ---------------------------------------------------
--R                                   4
--R                               440b
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 10
integrate(1 / (x**3 * (a+b*x)**(1/3)),x)
 

   (2)
           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
     + 
         2 2 +-+    3+-+2 3+-------+
       4b x \|3 log(\|a   \|b x + a - a)
     + 
                  +-+3+-+2 3+-------+    +-+
        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
                             3a
  /
        2 2 +-+3+-+
     18a x \|3 \|a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)
--R           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
--R       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
--R     + 
--R         2 2 +-+    3+-+2 3+-------+
--R       4b x \|3 log(\|a   \|b x + a - a)
--R     + 
--R                  +-+3+-+2 3+-------+    +-+
--R        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
--R     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
--R                             3a
--R  /
--R        2 2 +-+3+-+
--R     18a x \|3 \|a
--R                                          Type: Union(Expression Integer,...)
--E 7

)clear all
 
   All user variables and function definitions have been cleared.

--S 8 of 10
integrate((x + 1) / (x * (x + log x)**(3/2)),x)
 

            +----------+
          2\|log(x) + x
   (1)  - --------------
            log(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +----------+
--R          2\|log(x) + x
--R   (1)  - --------------
--R            log(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 8

)clear all
 
   All user variables and function definitions have been cleared.

--S 9 of 10
integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)
 

                     +---+    erf(x) - 1      +---+
        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
                              erf(x) + 1
   (1)  -------------------------------------------
                        8erf(x) - 8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +---+    erf(x) - 1      +---+
--R        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
--R                              erf(x) + 1
--R   (1)  -------------------------------------------
--R                        8erf(x) - 8
--R                                          Type: Union(Expression Integer,...)
--E 9

)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 10
integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)
 

                             +-----+
                    - 2cosh(\|x + b  + 1) - 2x            +-----+
   (1)  2log(---------------------------------------) - 2\|x + b
                   +-----+              +-----+
             sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             +-----+
--R                    - 2cosh(\|x + b  + 1) - 2x            +-----+
--R   (1)  2log(---------------------------------------) - 2\|x + b
--R                   +-----+              +-----+
--R             sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
--R                                          Type: Union(Expression Integer,...)
--E 10
)spool 
 
Starts dribbling to schaum12.output (2009/2/17, 17:58:6).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(a*x^2+b*x+c),x)
 

   (1)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 2
bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2))
 

                2a x + b
        2atan(------------)
               +---------+
               |        2
              \|4a c - b
   (2)  -------------------
             +---------+
             |        2
            \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R                2a x + b
--R        2atan(------------)
--R               +---------+
--R               |        2
--R              \|4a c - b
--R   (2)  -------------------
--R             +---------+
--R             |        2
--R            \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 3
bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c)))
 

               +-----------+
               |          2
            - \|- 4a c + b   + 2a x + b
        log(---------------------------)
              +-----------+
              |          2
             \|- 4a c + b   + 2a x + b
   (3)  --------------------------------
                  +-----------+
                  |          2
                 \|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R               +-----------+
--R               |          2
--R            - \|- 4a c + b   + 2a x + b
--R        log(---------------------------)
--R              +-----------+
--R              |          2
--R             \|- 4a c + b   + 2a x + b
--R   (3)  --------------------------------
--R                  +-----------+
--R                  |          2
--R                 \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 4
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |        2
         \|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
           +-----------+
           |          2        2a x + b
       - 2\|- 4a c + b  atan(------------)
                              +---------+
                              |        2
                             \|4a c - b
  /
      +-----------+ +---------+
      |          2  |        2
     \|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |        2
--R         \|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R           +-----------+
--R           |          2        2a x + b
--R       - 2\|- 4a c + b  atan(------------)
--R                              +---------+
--R                              |        2
--R                             \|4a c - b
--R  /
--R      +-----------+ +---------+
--R      |          2  |        2
--R     \|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 5
cc2:=aa.1-bb2
 

   (5)
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
     + 
                +-----------+
                |          2
             - \|- 4a c + b   + 2a x + b
       - log(---------------------------)
               +-----------+
               |          2
              \|- 4a c + b   + 2a x + b
  /
      +-----------+
      |          2
     \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R     + 
--R                +-----------+
--R                |          2
--R             - \|- 4a c + b   + 2a x + b
--R       - log(---------------------------)
--R               +-----------+
--R               |          2
--R              \|- 4a c + b   + 2a x + b
--R  /
--R      +-----------+
--R      |          2
--R     \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 6
cc3:=aa.2-bb1
 

                         +---------+
                         |        2
              (2a x + b)\|4a c - b              2a x + b
        2atan(----------------------) - 2atan(------------)
                             2                 +---------+
                     4a c - b                  |        2
                                              \|4a c - b
   (6)  ---------------------------------------------------
                             +---------+
                             |        2
                            \|4a c - b
                                                     Type: Expression Integer
--R
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b              2a x + b
--R        2atan(----------------------) - 2atan(------------)
--R                             2                 +---------+
--R                     4a c - b                  |        2
--R                                              \|4a c - b
--R   (6)  ---------------------------------------------------
--R                             +---------+
--R                             |        2
--R                            \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 7
cc4:=aa.2-bb2
 

   (7)
                            +-----------+
          +---------+       |          2
          |        2     - \|- 4a c + b   + 2a x + b
       - \|4a c - b  log(---------------------------)
                           +-----------+
                           |          2
                          \|- 4a c + b   + 2a x + b
     + 
                                      +---------+
         +-----------+                |        2
         |          2      (2a x + b)\|4a c - b
       2\|- 4a c + b  atan(----------------------)
                                          2
                                  4a c - b
  /
      +-----------+ +---------+
      |          2  |        2
     \|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-----------+
--R          +---------+       |          2
--R          |        2     - \|- 4a c + b   + 2a x + b
--R       - \|4a c - b  log(---------------------------)
--R                           +-----------+
--R                           |          2
--R                          \|- 4a c + b   + 2a x + b
--R     + 
--R                                      +---------+
--R         +-----------+                |        2
--R         |          2      (2a x + b)\|4a c - b
--R       2\|- 4a c + b  atan(----------------------)
--R                                          2
--R                                  4a c - b
--R  /
--R      +-----------+ +---------+
--R      |          2  |        2
--R     \|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 8
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (8)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (8)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 9
dd3:=atanrule cc3
 

   (9)
               +---------+
               |        2
              \|4a c - b   + 2%i a x + %i b
       %i log(-----------------------------)
               +---------+
               |        2
              \|4a c - b   - 2%i a x - %i b
     + 
                             +---------+
                             |        2                  2
                (- 2a x - b)\|4a c - b   + 4%i a c - %i b
       - %i log(------------------------------------------)
                            +---------+
                            |        2                  2
                 (2a x + b)\|4a c - b   + 4%i a c - %i b
  /
      +---------+
      |        2
     \|4a c - b
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +---------+
--R               |        2
--R              \|4a c - b   + 2%i a x + %i b
--R       %i log(-----------------------------)
--R               +---------+
--R               |        2
--R              \|4a c - b   - 2%i a x - %i b
--R     + 
--R                             +---------+
--R                             |        2                  2
--R                (- 2a x - b)\|4a c - b   + 4%i a c - %i b
--R       - %i log(------------------------------------------)
--R                            +---------+
--R                            |        2                  2
--R                 (2a x + b)\|4a c - b   + 4%i a c - %i b
--R  /
--R      +---------+
--R      |        2
--R     \|4a c - b
--R                                             Type: Expression Complex Integer
--E

--S 10
ee3:=expandLog dd3
 

   (10)
                         +---------+
                         |        2                  2
       %i log((2a x + b)\|4a c - b   + 4%i a c - %i b )
     + 
                           +---------+
                           |        2                  2
       - %i log((2a x + b)\|4a c - b   - 4%i a c + %i b )
     + 
               +---------+
               |        2
       %i log(\|4a c - b   + 2%i a x + %i b)
     + 
                 +---------+
                 |        2
       - %i log(\|4a c - b   - 2%i a x - %i b) - %i log(- 1)
  /
      +---------+
      |        2
     \|4a c - b
                                             Type: Expression Complex Integer
--R
--R   (10)
--R                         +---------+
--R                         |        2                  2
--R       %i log((2a x + b)\|4a c - b   + 4%i a c - %i b )
--R     + 
--R                           +---------+
--R                           |        2                  2
--R       - %i log((2a x + b)\|4a c - b   - 4%i a c + %i b )
--R     + 
--R               +---------+
--R               |        2
--R       %i log(\|4a c - b   + 2%i a x + %i b)
--R     + 
--R                 +---------+
--R                 |        2
--R       - %i log(\|4a c - b   - 2%i a x - %i b) - %i log(- 1)
--R  /
--R      +---------+
--R      |        2
--R     \|4a c - b
--R                                             Type: Expression Complex Integer
--E

--S 11     14:265 Schaums and Axiom agree
ff3:=complexNormalize ee3
 

   (11)  0
                                             Type: Expression Complex Integer
--R
--R   (11)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 12
aa:=integrate(x/(a*x^2+b*x+c),x)
 

   (1)
   [
           b
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                             +-----------+
                2            |          2
         log(a x  + b x + c)\|- 4a c + b
    /
          +-----------+
          |          2
       2a\|- 4a c + b
     ,
                         +---------+
                         |        2                         +---------+
              (2a x + b)\|4a c - b             2            |        2
    - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
                             2
                     4a c - b
    -------------------------------------------------------------------]
                                  +---------+
                                  |        2
                               2a\|4a c - b
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R           b
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                             +-----------+
--R                2            |          2
--R         log(a x  + b x + c)\|- 4a c + b
--R    /
--R          +-----------+
--R          |          2
--R       2a\|- 4a c + b
--R     ,
--R                         +---------+
--R                         |        2                         +---------+
--R              (2a x + b)\|4a c - b             2            |        2
--R    - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
--R                             2
--R                     4a c - b
--R    -------------------------------------------------------------------]
--R                                  +---------+
--R                                  |        2
--R                               2a\|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 13
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 14
bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1
 

   (3)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
                           +-----------+
              2            |          2
       log(a x  + b x + c)\|- 4a c + b
  /
        +-----------+
        |          2
     2a\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                           +-----------+
--R              2            |          2
--R       log(a x  + b x + c)\|- 4a c + b
--R  /
--R        +-----------+
--R        |          2
--R     2a\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 15
bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2
 

                             +---------+
                             |        2                         +---------+
                  (2a x + b)\|4a c - b             2            |        2
        - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
                                 2
                         4a c - b
   (4)  -------------------------------------------------------------------
                                      +---------+
                                      |        2
                                   2a\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R                             +---------+
--R                             |        2                         +---------+
--R                  (2a x + b)\|4a c - b             2            |        2
--R        - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
--R                                 2
--R                         4a c - b
--R   (4)  -------------------------------------------------------------------
--R                                      +---------+
--R                                      |        2
--R                                   2a\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 16
cc1:=aa.1-bb1
 

   (5)
         b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
         b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
        +-----------+
        |          2
     2a\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R         b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R         b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R        +-----------+
--R        |          2
--R     2a\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 17
cc2:=aa.2-bb1
 

   (6)
           +---------+
           |        2
         b\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                         +---------+
            +-----------+                |        2
            |          2      (2a x + b)\|4a c - b
       - 2b\|- 4a c + b  atan(----------------------)
                                             2
                                     4a c - b
  /
        +-----------+ +---------+
        |          2  |        2
     2a\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (6)
--R           +---------+
--R           |        2
--R         b\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                         +---------+
--R            +-----------+                |        2
--R            |          2      (2a x + b)\|4a c - b
--R       - 2b\|- 4a c + b  atan(----------------------)
--R                                             2
--R                                     4a c - b
--R  /
--R        +-----------+ +---------+
--R        |          2  |        2
--R     2a\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 18
cc3:=aa.2-bb1
 

   (7)
           +---------+
           |        2
         b\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                         +---------+
            +-----------+                |        2
            |          2      (2a x + b)\|4a c - b
       - 2b\|- 4a c + b  atan(----------------------)
                                             2
                                     4a c - b
  /
        +-----------+ +---------+
        |          2  |        2
     2a\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (7)
--R           +---------+
--R           |        2
--R         b\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                         +---------+
--R            +-----------+                |        2
--R            |          2      (2a x + b)\|4a c - b
--R       - 2b\|- 4a c + b  atan(----------------------)
--R                                             2
--R                                     4a c - b
--R  /
--R        +-----------+ +---------+
--R        |          2  |        2
--R     2a\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 19     14:266 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(x^2/(a*x^2+b*x+c),x)
 

   (1)
   [
                    2
           (2a c - b )
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                          +-----------+
                     2                    |          2
         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
    /
           +-----------+
         2 |          2
       2a \|- 4a c + b
     ,

                                       +---------+
                                       |        2
                     2      (2a x + b)\|4a c - b
         (- 4a c + 2b )atan(----------------------)
                                           2
                                   4a c - b
       + 
                                          +---------+
                     2                    |        2
         (- b log(a x  + b x + c) + 2a x)\|4a c - b
    /
           +---------+
         2 |        2
       2a \|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                    2
--R           (2a c - b )
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                          +-----------+
--R                     2                    |          2
--R         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
--R    /
--R           +-----------+
--R         2 |          2
--R       2a \|- 4a c + b
--R     ,
--R
--R                                       +---------+
--R                                       |        2
--R                     2      (2a x + b)\|4a c - b
--R         (- 4a c + 2b )atan(----------------------)
--R                                           2
--R                                   4a c - b
--R       + 
--R                                          +---------+
--R                     2                    |        2
--R         (- b log(a x  + b x + c) + 2a x)\|4a c - b
--R    /
--R           +---------+
--R         2 |        2
--R       2a \|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 21
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 22
bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1
 

   (3)
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                        +-----------+
                   2                    |          2
       (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
  /
         +-----------+
       2 |          2
     2a \|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                        +-----------+
--R                   2                    |          2
--R       (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
--R  /
--R         +-----------+
--R       2 |          2
--R     2a \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 23
bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2
 

   (4)
                                     +---------+
                                     |        2
                   2      (2a x + b)\|4a c - b
       (- 4a c + 2b )atan(----------------------)
                                         2
                                 4a c - b
     + 
                                        +---------+
                   2                    |        2
       (- b log(a x  + b x + c) + 2a x)\|4a c - b
  /
         +---------+
       2 |        2
     2a \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                     +---------+
--R                                     |        2
--R                   2      (2a x + b)\|4a c - b
--R       (- 4a c + 2b )atan(----------------------)
--R                                         2
--R                                 4a c - b
--R     + 
--R                                        +---------+
--R                   2                    |        2
--R       (- b log(a x  + b x + c) + 2a x)\|4a c - b
--R  /
--R         +---------+
--R       2 |        2
--R     2a \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 24
cc1:=bb1-aa.1
 

   (5)
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
         +-----------+
       2 |          2
     2a \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R         +-----------+
--R       2 |          2
--R     2a \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 25     14:267 Schaums and Axiom differ by a constant
dd1:=complexNormalize cc1
 

                   2          3      2 2
        (- 2a c + b )log(- 16a c + 4a b )
   (6)  ---------------------------------
                    +-----------+
                  2 |          2
                2a \|- 4a c + b
                                                     Type: Expression Integer
--R
--R                   2          3      2 2
--R        (- 2a c + b )log(- 16a c + 4a b )
--R   (6)  ---------------------------------
--R                    +-----------+
--R                  2 |          2
--R                2a \|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 26     14:268 Axiom cannot compute this integral
aa:=integrate(x^m/(a*x^2+b*x+c),x)
 

           x         m
         ++        %Q
   (1)   |   --------------- d%Q
        ++                2
             c + %Q b + %Q a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x         m
--I         ++        %N
--I   (1)   |   --------------- d%N
--R        ++                2
--I             c + %N b + %N a
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(1/(x*(a*x^2+b*x+c)),x)
 

   (1)
   [
           b
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                           +-----------+
                   2                       |          2
         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
    /
          +-----------+
          |          2
       2c\|- 4a c + b
     ,

                              +---------+
                              |        2
                   (2a x + b)\|4a c - b
         - 2b atan(----------------------)
                                  2
                          4a c - b
       + 
                                           +---------+
                   2                       |        2
         (- log(a x  + b x + c) + 2log(x))\|4a c - b
    /
          +---------+
          |        2
       2c\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           b
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                           +-----------+
--R                   2                       |          2
--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
--R    /
--R          +-----------+
--R          |          2
--R       2c\|- 4a c + b
--R     ,
--R
--R                              +---------+
--R                              |        2
--R                   (2a x + b)\|4a c - b
--R         - 2b atan(----------------------)
--R                                  2
--R                          4a c - b
--R       + 
--R                                           +---------+
--R                   2                       |        2
--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
--R    /
--R          +---------+
--R          |        2
--R       2c\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 28
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 29
bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1
 

   (3)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
                  2        +-----------+
                 x         |          2
       log(--------------)\|- 4a c + b
              2
           a x  + b x + c
  /
        +-----------+
        |          2
     2c\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                  2        +-----------+
--R                 x         |          2
--R       log(--------------)\|- 4a c + b
--R              2
--R           a x  + b x + c
--R  /
--R        +-----------+
--R        |          2
--R     2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 30
bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2
 

                             +---------+
                             |        2                2        +---------+
                  (2a x + b)\|4a c - b                x         |        2
        - 2b atan(----------------------) + log(--------------)\|4a c - b
                                 2                 2
                         4a c - b               a x  + b x + c
   (4)  -------------------------------------------------------------------
                                      +---------+
                                      |        2
                                   2c\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R                             +---------+
--R                             |        2                2        +---------+
--R                  (2a x + b)\|4a c - b                x         |        2
--R        - 2b atan(----------------------) + log(--------------)\|4a c - b
--R                                 2                 2
--R                         4a c - b               a x  + b x + c
--R   (4)  -------------------------------------------------------------------
--R                                      +---------+
--R                                      |        2
--R                                   2c\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 31
cc1:=bb1-aa.1
 

   (5)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                 + 
                        2        2               3
                   (- 8a c + 2a b )x - 4a b c + b
              /
                    2
                 a x  + b x + c
     + 
                                                   2         +-----------+
               2                                  x          |          2
       (log(a x  + b x + c) - 2log(x) + log(--------------))\|- 4a c + b
                                               2
                                            a x  + b x + c
  /
        +-----------+
        |          2
     2c\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                 + 
--R                        2        2               3
--R                   (- 8a c + 2a b )x - 4a b c + b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                                                   2         +-----------+
--R               2                                  x          |          2
--R       (log(a x  + b x + c) - 2log(x) + log(--------------))\|- 4a c + b
--R                                               2
--R                                            a x  + b x + c
--R  /
--R        +-----------+
--R        |          2
--R     2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 32
dd1:=expandLog cc1
 

   (6)
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2       2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
               + 
                           3
                 4a b c - b
     + 
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2         2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
               + 
                             3
                 - 4a b c + b
     + 
                 2
       2b log(a x  + b x + c)
  /
        +-----------+
        |          2
     2c\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (6)
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2       2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R               + 
--R                           3
--R                 4a b c - b
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2         2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R               + 
--R                             3
--R                 - 4a b c + b
--R     + 
--R                 2
--R       2b log(a x  + b x + c)
--R  /
--R        +-----------+
--R        |          2
--R     2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 33     14:269 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                     3      2 2
          b log(- 16a c + 4a b )
   (7)  - ----------------------
                +-----------+
                |          2
             2c\|- 4a c + b
                                                     Type: Expression Integer
--R
--R                     3      2 2
--R          b log(- 16a c + 4a b )
--R   (7)  - ----------------------
--R                +-----------+
--R                |          2
--R             2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 34
aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
 

   (1)
   [
                    2
           (2a c - b )x
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                                      +-----------+
                     2                                |          2
         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
    /
            +-----------+
         2  |          2
       2c x\|- 4a c + b
     ,

                                         +---------+
                                         |        2
                     2        (2a x + b)\|4a c - b
         (- 4a c + 2b )x atan(----------------------)
                                             2
                                     4a c - b
       + 
                                                      +---------+
                     2                                |        2
         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
    /
            +---------+
         2  |        2
       2c x\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                    2
--R           (2a c - b )x
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                                      +-----------+
--R                     2                                |          2
--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
--R    /
--R            +-----------+
--R         2  |          2
--R       2c x\|- 4a c + b
--R     ,
--R
--R                                         +---------+
--R                                         |        2
--R                     2        (2a x + b)\|4a c - b
--R         (- 4a c + 2b )x atan(----------------------)
--R                                             2
--R                                     4a c - b
--R       + 
--R                                                      +---------+
--R                     2                                |        2
--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
--R    /
--R            +---------+
--R         2  |        2
--R       2c x\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 35
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 36
bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1
 

   (3)
                    2
         (- 2a c + b )x
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                   2                  +-----------+
                a x  + b x + c        |          2
       (b x log(--------------) - 2c)\|- 4a c + b
                       2
                      x
  /
          +-----------+
       2  |          2
     2c x\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                    2
--R         (- 2a c + b )x
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                   2                  +-----------+
--R                a x  + b x + c        |          2
--R       (b x log(--------------) - 2c)\|- 4a c + b
--R                       2
--R                      x
--R  /
--R          +-----------+
--R       2  |          2
--R     2c x\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 37
bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2
 

   (4)
                                       +---------+
                                       |        2
                   2        (2a x + b)\|4a c - b
       (- 4a c + 2b )x atan(----------------------)
                                           2
                                   4a c - b
     + 
                   2                  +---------+
                a x  + b x + c        |        2
       (b x log(--------------) - 2c)\|4a c - b
                       2
                      x
  /
          +---------+
       2  |        2
     2c x\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                       +---------+
--R                                       |        2
--R                   2        (2a x + b)\|4a c - b
--R       (- 4a c + 2b )x atan(----------------------)
--R                                           2
--R                                   4a c - b
--R     + 
--R                   2                  +---------+
--R                a x  + b x + c        |        2
--R       (b x log(--------------) - 2c)\|4a c - b
--R                       2
--R                      x
--R  /
--R          +---------+
--R       2  |        2
--R     2c x\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 38
cc1:=bb1-aa.1
 

   (5)
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                                                     2             +-----------+
                 2                                a x  + b x + c   |          2
     (- b log(a x  + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b
                                                         2
                                                        x
  /
         +-----------+
       2 |          2
     2c \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                                     2             +-----------+
--R                 2                                a x  + b x + c   |          2
--R     (- b log(a x  + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b
--R                                                         2
--R                                                        x
--R  /
--R         +-----------+
--R       2 |          2
--R     2c \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 39
dd1:=expandLog cc1
 

   (6)
                    2
         (- 2a c + b )
      *
         log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
     + 
                    2
         (- 2a c + b )
      *
         log
                                           +-----------+
                 2 2                    2  |          2         2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
            + 
                          3
              - 4a b c + b
     + 
                 2        2
       (4a c - 2b )log(a x  + b x + c)
  /
         +-----------+
       2 |          2
     2c \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (6)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R     + 
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2         2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R            + 
--R                          3
--R              - 4a b c + b
--R     + 
--R                 2        2
--R       (4a c - 2b )log(a x  + b x + c)
--R  /
--R         +-----------+
--R       2 |          2
--R     2c \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 40     14:270 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                   2          3      2 2
        (- 2a c + b )log(- 16a c + 4a b )
   (7)  ---------------------------------
                    +-----------+
                  2 |          2
                2c \|- 4a c + b
                                                     Type: Expression Integer
--R
--R                   2          3      2 2
--R        (- 2a c + b )log(- 16a c + 4a b )
--R   (7)  ---------------------------------
--R                    +-----------+
--R                  2 |          2
--R                2c \|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 41     14:271 Axiom cannot compute this integral
aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
 

           x
         ++            1
   (1)   |   -------------------- d%Q
        ++                 2    n
             (c + %Q b + %Q a)%Q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            1
--I   (1)   |   -------------------- d%N
--R        ++                 2    n
--I             (c + %N b + %N a)%N
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 42
aa:=integrate(1/(a*x^2+b*x+c)^2,x)
 

   (1)
   [
              2 2
           (2a x  + 2a b x + 2a c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                    +-----------+
                    |          2
         (2a x + b)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,
                                           +---------+
                                           |        2                +---------+
       2 2                      (2a x + b)\|4a c - b                 |        2
    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                               2
                                       4a c - b
    ----------------------------------------------------------------------------
                                                             +---------+
                2       2  2              3         2    2   |        2
            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R              2 2
--R           (2a x  + 2a b x + 2a c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                    +-----------+
--R                    |          2
--R         (2a x + b)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R                                           +---------+
--R                                           |        2                +---------+
--R       2 2                      (2a x + b)\|4a c - b                 |        2
--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                               2
--R                                       4a c - b
--R    ----------------------------------------------------------------------------
--R                                                             +---------+
--R                2       2  2              3         2    2   |        2
--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 43
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 44
bb1:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.1
 

   (3)
            2 2
         (2a x  + 2a b x + 2a c)
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                  +-----------+
                  |          2
       (2a x + b)\|- 4a c + b
  /
                                                      +-----------+
         2       2  2              3         2    2   |          2
     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (3)
--R            2 2
--R         (2a x  + 2a b x + 2a c)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                  +-----------+
--R                  |          2
--R       (2a x + b)\|- 4a c + b
--R  /
--R                                                      +-----------+
--R         2       2  2              3         2    2   |          2
--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 45
bb2:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.2
 

   (4)
                                          +---------+
                                          |        2                +---------+
      2 2                      (2a x + b)\|4a c - b                 |        2
   (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                              2
                                      4a c - b
   ----------------------------------------------------------------------------
                                                            +---------+
               2       2  2              3         2    2   |        2
           ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
                                                     Type: Expression Integer
--R
--R   (4)
--R                                          +---------+
--R                                          |        2                +---------+
--R      2 2                      (2a x + b)\|4a c - b                 |        2
--R   (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                              2
--R                                      4a c - b
--R   ----------------------------------------------------------------------------
--R                                                            +---------+
--R               2       2  2              3         2    2   |        2
--R           ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 46
cc1:=aa.1-bb1
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

--S 47
cc2:=aa.2-bb1
 

   (6)
       -
               +---------+
               |        2
            2a\|4a c - b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
                                       +---------+
          +-----------+                |        2
          |          2      (2a x + b)\|4a c - b
       4a\|- 4a c + b  atan(----------------------)
                                           2
                                   4a c - b
  /
                 +-----------+ +---------+
              2  |          2  |        2
     (4a c - b )\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (6)
--R       -
--R               +---------+
--R               |        2
--R            2a\|4a c - b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                                       +---------+
--R          +-----------+                |        2
--R          |          2      (2a x + b)\|4a c - b
--R       4a\|- 4a c + b  atan(----------------------)
--R                                           2
--R                                   4a c - b
--R  /
--R                 +-----------+ +---------+
--R              2  |          2  |        2
--R     (4a c - b )\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 48
cc3:=aa.1-bb2
 

   (7)
            +---------+
            |        2
         2a\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                         +---------+
            +-----------+                |        2
            |          2      (2a x + b)\|4a c - b
       - 4a\|- 4a c + b  atan(----------------------)
                                             2
                                     4a c - b
  /
                 +-----------+ +---------+
              2  |          2  |        2
     (4a c - b )\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (7)
--R            +---------+
--R            |        2
--R         2a\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                         +---------+
--R            +-----------+                |        2
--R            |          2      (2a x + b)\|4a c - b
--R       - 4a\|- 4a c + b  atan(----------------------)
--R                                             2
--R                                     4a c - b
--R  /
--R                 +-----------+ +---------+
--R              2  |          2  |        2
--R     (4a c - b )\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 49     14:272 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 50
aa:=integrate(x/(a*x^2+b*x+c)^2,x)
 

   (1)
   [
                 2    2
           (a b x  + b x + b c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                      +-----------+
                      |          2
         (- b x - 2c)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,

                                                  +---------+
                                                  |        2
                  2     2              (2a x + b)\|4a c - b
         (- 2a b x  - 2b x - 2b c)atan(----------------------)
                                                      2
                                              4a c - b
       + 
                      +---------+
                      |        2
         (- b x - 2c)\|4a c - b
    /
                                                        +---------+
           2       2  2              3         2    2   |        2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                 2    2
--R           (a b x  + b x + b c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                      +-----------+
--R                      |          2
--R         (- b x - 2c)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R
--R                                                  +---------+
--R                                                  |        2
--R                  2     2              (2a x + b)\|4a c - b
--R         (- 2a b x  - 2b x - 2b c)atan(----------------------)
--R                                                      2
--R                                              4a c - b
--R       + 
--R                      +---------+
--R                      |        2
--R         (- b x - 2c)\|4a c - b
--R    /
--R                                                        +---------+
--R           2       2  2              3         2    2   |        2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 51
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 52
bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1
 

   (3)
                 2    2
         (- a b x  - b x - b c)
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                    +-----------+
                    |          2
       (- b x - 2c)\|- 4a c + b
  /
                                                      +-----------+
         2       2  2              3         2    2   |          2
     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                 2    2
--R         (- a b x  - b x - b c)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                    +-----------+
--R                    |          2
--R       (- b x - 2c)\|- 4a c + b
--R  /
--R                                                      +-----------+
--R         2       2  2              3         2    2   |          2
--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 53
bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2
 

   (4)
                                                +---------+
                                                |        2
                2     2              (2a x + b)\|4a c - b
       (- 2a b x  - 2b x - 2b c)atan(----------------------)
                                                    2
                                            4a c - b
     + 
                    +---------+
                    |        2
       (- b x - 2c)\|4a c - b
  /
                                                      +---------+
         2       2  2              3         2    2   |        2
     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                                +---------+
--R                                                |        2
--R                2     2              (2a x + b)\|4a c - b
--R       (- 2a b x  - 2b x - 2b c)atan(----------------------)
--R                                                    2
--R                                            4a c - b
--R     + 
--R                    +---------+
--R                    |        2
--R       (- b x - 2c)\|4a c - b
--R  /
--R                                                      +---------+
--R         2       2  2              3         2    2   |        2
--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 54
cc1:=bb1-aa.1
 

   (5)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                 + 
                        2        2               3
                   (- 8a c + 2a b )x - 4a b c + b
              /
                    2
                 a x  + b x + c
  /
                 +-----------+
              2  |          2
     (4a c - b )\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                 + 
--R                        2        2               3
--R                   (- 8a c + 2a b )x - 4a b c + b
--R              /
--R                    2
--R                 a x  + b x + c
--R  /
--R                 +-----------+
--R              2  |          2
--R     (4a c - b )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 55
dd1:=expandLog cc1
 

   (6)
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2       2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
               + 
                           3
                 4a b c - b
     + 
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2         2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
               + 
                             3
                 - 4a b c + b
     + 
                 2
       2b log(a x  + b x + c)
  /
                 +-----------+
              2  |          2
     (4a c - b )\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (6)
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2       2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R               + 
--R                           3
--R                 4a b c - b
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2         2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R               + 
--R                             3
--R                 - 4a b c + b
--R     + 
--R                 2
--R       2b log(a x  + b x + c)
--R  /
--R                 +-----------+
--R              2  |          2
--R     (4a c - b )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 56     14:273 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                       3      2 2
            b log(- 16a c + 4a b )
   (7)  - -------------------------
                      +-----------+
                   2  |          2
          (4a c - b )\|- 4a c + b
                                                     Type: Expression Integer
--R
--R                       3      2 2
--R            b log(- 16a c + 4a b )
--R   (7)  - -------------------------
--R                      +-----------+
--R                   2  |          2
--R          (4a c - b )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 57
aa:=integrate(x^2/(a*x^2+b*x+c)^2,x)
 

   (1)
   [
              2   2                  2
           (2a c x  + 2a b c x + 2a c )
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                                +-----------+
                     2          |          2
         ((- 2a c + b )x + b c)\|- 4a c + b
    /
                                                            +-----------+
           3     2 2  2      2         3       2 2      2   |          2
       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
     ,

                                                     +---------+
                                                     |        2
            2   2                  2      (2a x + b)\|4a c - b
         (4a c x  + 4a b c x + 4a c )atan(----------------------)
                                                         2
                                                 4a c - b
       + 
                                +---------+
                     2          |        2
         ((- 2a c + b )x + b c)\|4a c - b
    /
                                                            +---------+
           3     2 2  2      2         3       2 2      2   |        2
       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R              2   2                  2
--R           (2a c x  + 2a b c x + 2a c )
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                +-----------+
--R                     2          |          2
--R         ((- 2a c + b )x + b c)\|- 4a c + b
--R    /
--R                                                            +-----------+
--R           3     2 2  2      2         3       2 2      2   |          2
--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
--R     ,
--R
--R                                                     +---------+
--R                                                     |        2
--R            2   2                  2      (2a x + b)\|4a c - b
--R         (4a c x  + 4a b c x + 4a c )atan(----------------------)
--R                                                         2
--R                                                 4a c - b
--R       + 
--R                                +---------+
--R                     2          |        2
--R         ((- 2a c + b )x + b c)\|4a c - b
--R    /
--R                                                            +---------+
--R           3     2 2  2      2         3       2 2      2   |        2
--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 58
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 59
bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1
 

   (3)
            2   2                  2
         (2a c x  + 2a b c x + 2a c )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                              +-----------+
                   2          |          2
       ((- 2a c + b )x + b c)\|- 4a c + b
  /
                                                          +-----------+
         3     2 2  2      2         3       2 2      2   |          2
     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (3)
--R            2   2                  2
--R         (2a c x  + 2a b c x + 2a c )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                              +-----------+
--R                   2          |          2
--R       ((- 2a c + b )x + b c)\|- 4a c + b
--R  /
--R                                                          +-----------+
--R         3     2 2  2      2         3       2 2      2   |          2
--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 60
bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2
 

   (4)
                                                   +---------+
                                                   |        2
          2   2                  2      (2a x + b)\|4a c - b
       (4a c x  + 4a b c x + 4a c )atan(----------------------)
                                                       2
                                               4a c - b
     + 
                              +---------+
                   2          |        2
       ((- 2a c + b )x + b c)\|4a c - b
  /
                                                          +---------+
         3     2 2  2      2         3       2 2      2   |        2
     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                   +---------+
--R                                                   |        2
--R          2   2                  2      (2a x + b)\|4a c - b
--R       (4a c x  + 4a b c x + 4a c )atan(----------------------)
--R                                                       2
--R                                               4a c - b
--R     + 
--R                              +---------+
--R                   2          |        2
--R       ((- 2a c + b )x + b c)\|4a c - b
--R  /
--R                                                          +---------+
--R         3     2 2  2      2         3       2 2      2   |        2
--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 61     14:274 Schaums and Axiom agree
cc1:=aa.1-bb1
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 62     14:275 Axiom cannot compute this integral
aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
 

           x           m
         ++          %Q
   (1)   |   ------------------ d%Q
        ++                 2  n
             (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           m
--I         ++          %N
--I   (1)   |   ------------------ d%N
--R        ++                 2  n
--I             (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 63     14:276 Axiom cannot compute this integral
aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
 

           x        2n - 1
         ++       %Q
   (1)   |   ------------------ d%Q
        ++                 2  n
             (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x        2n - 1
--I         ++       %N
--I   (1)   |   ------------------ d%N
--R        ++                 2  n
--I             (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 64
aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
 

   (1)
   [
               2         3  2        2     4           2    3
           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +-----------+
            |          2
           \|- 4a c + b
    /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
     ,

                  2          3  2           2      4            2     3
           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
        *
                           +---------+
                           |        2
                (2a x + b)\|4a c - b
           atan(----------------------)
                               2
                       4a c - b
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +---------+
            |        2
           \|4a c - b
    /
                                                                  +---------+
           2 3       2 2  2          3     3 2         4     2 3  |        2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R               2         3  2        2     4           2    3
--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R    /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R     ,
--R
--R                  2          3  2           2      4            2     3
--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
--R        *
--R                           +---------+
--R                           |        2
--R                (2a x + b)\|4a c - b
--R           atan(----------------------)
--R                               2
--R                       4a c - b
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +---------+
--R            |        2
--R           \|4a c - b
--R    /
--R                                                                  +---------+
--R           2 3       2 2  2          3     3 2         4     2 3  |        2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 65
t1:=integrate(1/(a*x^2+b*x+c)^2,x)
 

   (2)
   [
              2 2
           (2a x  + 2a b x + 2a c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                    +-----------+
                    |          2
         (2a x + b)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,
                                           +---------+
                                           |        2                +---------+
       2 2                      (2a x + b)\|4a c - b                 |        2
    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                               2
                                       4a c - b
    ----------------------------------------------------------------------------
                                                             +---------+
                2       2  2              3         2    2   |        2
            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R              2 2
--R           (2a x  + 2a b x + 2a c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                    +-----------+
--R                    |          2
--R         (2a x + b)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R                                           +---------+
--R                                           |        2                +---------+
--R       2 2                      (2a x + b)\|4a c - b                 |        2
--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                               2
--R                                       4a c - b
--R    ----------------------------------------------------------------------------
--R                                                             +---------+
--R                2       2  2              3         2    2   |        2
--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 66
t2:=integrate(1/(x*(a*x^2+b*x+c)),x)
 

   (3)
   [
           b
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                           +-----------+
                   2                       |          2
         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
    /
          +-----------+
          |          2
       2c\|- 4a c + b
     ,

                              +---------+
                              |        2
                   (2a x + b)\|4a c - b
         - 2b atan(----------------------)
                                  2
                          4a c - b
       + 
                                           +---------+
                   2                       |        2
         (- log(a x  + b x + c) + 2log(x))\|4a c - b
    /
          +---------+
          |        2
       2c\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (3)
--R   [
--R           b
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                           +-----------+
--R                   2                       |          2
--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
--R    /
--R          +-----------+
--R          |          2
--R       2c\|- 4a c + b
--R     ,
--R
--R                              +---------+
--R                              |        2
--R                   (2a x + b)\|4a c - b
--R         - 2b atan(----------------------)
--R                                  2
--R                          4a c - b
--R       + 
--R                                           +---------+
--R                   2                       |        2
--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
--R    /
--R          +---------+
--R          |        2
--R       2c\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 67
bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1
 

   (4)
              2     2       2            2
         (- 2a b c x  - 2a b c x - 2a b c )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
             2         3  2        2     4           2    3
         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +-----------+
          |          2
         \|- 4a c + b
  /
                                                                +-----------+
         2 3       2 2  2          3     3 2         4     2 3  |          2
     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R              2     2       2            2
--R         (- 2a b c x  - 2a b c x - 2a b c )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R             2         3  2        2     4           2    3
--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +-----------+
--R          |          2
--R         \|- 4a c + b
--R  /
--R                                                                +-----------+
--R         2 3       2 2  2          3     3 2         4     2 3  |          2
--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 68
bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1
 

   (5)
                                                              +---------+
             2         3  2        2     4           2    3   |        2
         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                                            +-----------+
              2     2       2            2  |          2
         (- 4a b c x  - 4a b c x - 4a b c )\|- 4a c + b
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (5)
--R                                                              +---------+
--R             2         3  2        2     4           2    3   |        2
--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                            +-----------+
--R              2     2       2            2  |          2
--R         (- 4a b c x  - 4a b c x - 4a b c )\|- 4a c + b
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 69
bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2
 

   (6)
                                            +---------+
              2     2       2            2  |        2
         (- 2a b c x  - 2a b c x - 2a b c )\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
               2          3  2          2      4           2     3
         ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x - 8a b c  + 2b c)
      *
                                       +---------+
          +-----------+                |        2
          |          2      (2a x + b)\|4a c - b
         \|- 4a c + b  atan(----------------------)
                                           2
                                   4a c - b
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                                            +---------+
--R              2     2       2            2  |        2
--R         (- 2a b c x  - 2a b c x - 2a b c )\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R               2          3  2          2      4           2     3
--R         ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x - 8a b c  + 2b c)
--R      *
--R                                       +---------+
--R          +-----------+                |        2
--R          |          2      (2a x + b)\|4a c - b
--R         \|- 4a c + b  atan(----------------------)
--R                                           2
--R                                   4a c - b
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 70
bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2
 

   (7)
                2          3  2           2      4            2     3
         ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +---------+
          |        2
         \|4a c - b
  /
                                                                +---------+
         2 3       2 2  2          3     3 2         4     2 3  |        2
     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                2          3  2           2      4            2     3
--R         ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +---------+
--R          |        2
--R         \|4a c - b
--R  /
--R                                                                +---------+
--R         2 3       2 2  2          3     3 2         4     2 3  |        2
--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 71
cc1:=aa.1-bb1
 

   (8)
         a b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
         a b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (8)
--R         a b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R         a b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 72
dd1:=expandLog cc1
 

   (9)
         a b
      *
         log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
     + 
         a b
      *
         log
                                           +-----------+
                 2 2                    2  |          2         2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
            + 
                          3
              - 4a b c + b
     + 
                     2
       - 2a b log(a x  + b x + c)
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (9)
--R         a b
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R     + 
--R         a b
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2         2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R            + 
--R                          3
--R              - 4a b c + b
--R     + 
--R                     2
--R       - 2a b log(a x  + b x + c)
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 73     14:277 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                        3      2 2
           a b log(- 16a c + 4a b )
   (10)  ---------------------------
                       +-----------+
              2    2   |          2
         (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R                        3      2 2
--R           a b log(- 16a c + 4a b )
--R   (10)  ---------------------------
--R                       +-----------+
--R              2    2   |          2
--R         (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 74
aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x)
 

   (1)
   [
                3 2     2 2       4  3      2   2       3     5  2
             (6a c  - 6a b c + a b )x  + (6a b c  - 6a b c + b )x
           + 
                2 3       2 2    4
             (6a c  - 6a b c  + b c)x
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                   2         3  3        2     4  2          2    3
               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
            *
                      2
               log(a x  + b x + c)
           + 
                     2          3  3          2      4  2            2     3
               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
            *
               log(x)
           + 
                  2 2       2   2            2     3          3    2 2
             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
        *
            +-----------+
            |          2
           \|- 4a c + b
    /
                                                                   +-----------+
           2 4      2 3  3          4    3 3  2        5    2 4    |          2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
     ,

                   3 2      2 2        4  3         2   2        3      5  2
             (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
           + 
                   2 3        2 2     4
             (- 12a c  + 12a b c  - 2b c)x
        *
                           +---------+
                           |        2
                (2a x + b)\|4a c - b
           atan(----------------------)
                               2
                       4a c - b
       + 
                   2         3  3        2     4  2          2    3
               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
            *
                      2
               log(a x  + b x + c)
           + 
                     2          3  3          2      4  2            2     3
               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
            *
               log(x)
           + 
                  2 2       2   2            2     3          3    2 2
             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
        *
            +---------+
            |        2
           \|4a c - b
    /
                                                                   +---------+
           2 4      2 3  3          4    3 3  2        5    2 4    |        2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                3 2     2 2       4  3      2   2       3     5  2
--R             (6a c  - 6a b c + a b )x  + (6a b c  - 6a b c + b )x
--R           + 
--R                2 3       2 2    4
--R             (6a c  - 6a b c  + b c)x
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                   2         3  3        2     4  2          2    3
--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                     2          3  3          2      4  2            2     3
--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R            *
--R               log(x)
--R           + 
--R                  2 2       2   2            2     3          3    2 2
--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R        *
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R    /
--R                                                                   +-----------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R     ,
--R
--R                   3 2      2 2        4  3         2   2        3      5  2
--R             (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
--R           + 
--R                   2 3        2 2     4
--R             (- 12a c  + 12a b c  - 2b c)x
--R        *
--R                           +---------+
--R                           |        2
--R                (2a x + b)\|4a c - b
--R           atan(----------------------)
--R                               2
--R                       4a c - b
--R       + 
--R                   2         3  3        2     4  2          2    3
--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                     2          3  3          2      4  2            2     3
--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R            *
--R               log(x)
--R           + 
--R                  2 2       2   2            2     3          3    2 2
--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R        *
--R            +---------+
--R            |        2
--R           \|4a c - b
--R    /
--R                                                                   +---------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |        2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 75
t1:=integrate(1/(a*x^2+b*x+c)^2,x)
 

   (2)
   [
              2 2
           (2a x  + 2a b x + 2a c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                    +-----------+
                    |          2
         (2a x + b)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,
                                           +---------+
                                           |        2                +---------+
       2 2                      (2a x + b)\|4a c - b                 |        2
    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                               2
                                       4a c - b
    ----------------------------------------------------------------------------
                                                             +---------+
                2       2  2              3         2    2   |        2
            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R              2 2
--R           (2a x  + 2a b x + 2a c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                    +-----------+
--R                    |          2
--R         (2a x + b)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R                                           +---------+
--R                                           |        2                +---------+
--R       2 2                      (2a x + b)\|4a c - b                 |        2
--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                               2
--R                                       4a c - b
--R    ----------------------------------------------------------------------------
--R                                                             +---------+
--R                2       2  2              3         2    2   |        2
--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 76
t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
 

   (3)
   [
               2         3  2        2     4           2    3
           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +-----------+
            |          2
           \|- 4a c + b
    /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
     ,

                  2          3  2           2      4            2     3
           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
        *
                           +---------+
                           |        2
                (2a x + b)\|4a c - b
           atan(----------------------)
                               2
                       4a c - b
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +---------+
            |        2
           \|4a c - b
    /
                                                                  +---------+
           2 3       2 2  2          3     3 2         4     2 3  |        2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (3)
--R   [
--R               2         3  2        2     4           2    3
--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R    /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R     ,
--R
--R                  2          3  2           2      4            2     3
--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
--R        *
--R                           +---------+
--R                           |        2
--R                (2a x + b)\|4a c - b
--R           atan(----------------------)
--R                               2
--R                       4a c - b
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +---------+
--R            |        2
--R           \|4a c - b
--R    /
--R                                                                  +---------+
--R           2 3       2 2  2          3     3 2         4     2 3  |        2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 77
bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1
 

   (4)
              3 2 3     2   2 2     2 3
         (- 6a c x  - 6a b c x  - 6a c x)
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
               2 2       4  3          3     5  2          2 2    4
         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +-----------+
          |          2
         \|- 4a c + b
  /
                                                                 +-----------+
         2 4      2 3  3          4    3 3  2        5    2 4    |          2
     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R              3 2 3     2   2 2     2 3
--R         (- 6a c x  - 6a b c x  - 6a c x)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R               2 2       4  3          3     5  2          2 2    4
--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +-----------+
--R          |          2
--R         \|- 4a c + b
--R  /
--R                                                                 +-----------+
--R         2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 78
bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1
 

   (5)
               2 2       4  3          3     5  2          2 2    4
         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
      *
          +---------+
          |        2
         \|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                                             +-----------+
               3 2 3      2   2 2      2 3   |          2
         (- 12a c x  - 12a b c x  - 12a c x)\|- 4a c + b
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                   +-----------+
           2 4      2 3  3          4    3 3  2        5    2 4    |          2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (5)
--R               2 2       4  3          3     5  2          2 2    4
--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
--R      *
--R          +---------+
--R          |        2
--R         \|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                             +-----------+
--R               3 2 3      2   2 2      2 3   |          2
--R         (- 12a c x  - 12a b c x  - 12a c x)\|- 4a c + b
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                   +-----------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 79
bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2
 

   (6)
                                          +---------+
              3 2 3     2   2 2     2 3   |        2
         (- 6a c x  - 6a b c x  - 6a c x)\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
              2 2        4  3         3      5  2         2 2     4
         ((12a b c - 2a b )x  + (12a b c - 2b )x  + (12a b c  - 2b c)x)
      *
                                       +---------+
          +-----------+                |        2
          |          2      (2a x + b)\|4a c - b
         \|- 4a c + b  atan(----------------------)
                                           2
                                   4a c - b
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                   +-----------+
           2 4      2 3  3          4    3 3  2        5    2 4    |          2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                                          +---------+
--R              3 2 3     2   2 2     2 3   |        2
--R         (- 6a c x  - 6a b c x  - 6a c x)\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R              2 2        4  3         3      5  2         2 2     4
--R         ((12a b c - 2a b )x  + (12a b c - 2b )x  + (12a b c  - 2b c)x)
--R      *
--R                                       +---------+
--R          +-----------+                |        2
--R          |          2      (2a x + b)\|4a c - b
--R         \|- 4a c + b  atan(----------------------)
--R                                           2
--R                                   4a c - b
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                   +-----------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 80
bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2
 

   (7)
                 3 2      2 2        4  3         2   2        3      5  2
           (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
         + 
                 2 3        2 2     4
           (- 12a c  + 12a b c  - 2b c)x
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +---------+
          |        2
         \|4a c - b
  /
                                                                 +---------+
         2 4      2 3  3          4    3 3  2        5    2 4    |        2
     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                 3 2      2 2        4  3         2   2        3      5  2
--R           (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
--R         + 
--R                 2 3        2 2     4
--R           (- 12a c  + 12a b c  - 2b c)x
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +---------+
--R          |        2
--R         \|4a c - b
--R  /
--R                                                                 +---------+
--R         2 4      2 3  3          4    3 3  2        5    2 4    |        2
--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 81
cc1:=aa.1-bb1
 

   (8)
           2
         6a
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
           2
         6a
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (8)
--R           2
--R         6a
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R           2
--R         6a
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 82
dd1:=expandLog cc1
 

   (9)
           2
         6a
      *
         log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
     + 
           2
         6a
      *
         log
                                           +-----------+
                 2 2                    2  |          2         2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
            + 
                          3
              - 4a b c + b
     + 
            2       2
       - 12a log(a x  + b x + c)
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (9)
--R           2
--R         6a
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R     + 
--R           2
--R         6a
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2         2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R            + 
--R                          3
--R              - 4a b c + b
--R     + 
--R            2       2
--R       - 12a log(a x  + b x + c)
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 83     14:278 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

             2         3      2 2
           6a log(- 16a c + 4a b )
   (10)  ---------------------------
                       +-----------+
              2    2   |          2
         (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R             2         3      2 2
--R           6a log(- 16a c + 4a b )
--R   (10)  ---------------------------
--R                       +-----------+
--R              2    2   |          2
--R         (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 84     14:279 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x)
 

           x
         ++            1
   (1)   |   --------------------- d%Q
        ++     m              2  n
             %Q (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            1
--I   (1)   |   --------------------- d%N
--R        ++     m              2  n
--I             %N (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to explim.output (2009/2/17, 17:45:49).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 12
limit(x/exp(x),x = %plusInfinity)              -- 0
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 1

--S 2 of 12
limit(x**10000/exp(x),x = %plusInfinity)       -- 0
 

   (2)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (2)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 2

--S 3 of 12
limit(x**(10**20)/exp(x),x = %plusInfinity)    -- 0
 

   (3)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (3)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 3

--S 4 of 12
limit(x**h/exp(x),x = %plusInfinity)           -- 0
 

   (4)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 12
limit(x/exp(x),x = %minusInfinity)             -- %minusInfinity
 

   (5)  - infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (5)  - infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 12
limit(x**10000/exp(x),x = %minusInfinity)      -- %plusInfinity
 

   (6)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (6)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 6

--S 7 of 12
limit(x**(10**20)/exp(x),x = %minusInfinity)   -- %plusInfinity
 

   (7)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (7)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 7

--S 8 of 12
limit(x**h/exp(x),x = %minusInfinity)          -- "failed"
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8

--S 9 of 12
limit(exp(-x) * sinh(x),x = %plusInfinity)     -- 1/2
 

        1
   (9)  -
        2
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        1
--R   (9)  -
--R        2
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 9

--S 10 of 12
limit(exp(-x) * cosh(x),x = %plusInfinity)     -- 1/2
 

         1
   (10)  -
         2
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         1
--R   (10)  -
--R         2
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 10

--S 11 of 12
limit(exp(-x) * exp(x),x = %plusInfinity)      -- 1
 

   (11)  1
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (11)  1
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 11

--S 12 of 12
limit((x + 1)**(x + 1)/x**x - x**x/(x - 1)**(x - 1),x = %plusInfinity)  -- %e
 

   (12)  %e
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (12)  %e
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 12
)spool 
 
Starts dribbling to lodo.output (2009/2/17, 17:52:35).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 55
RN:=FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 55
Dx: LODO2(RN, UP(x,RN))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 55
Dx := D()                  
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 55
a  := Dx  + 1
 

   (4)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 55
b  := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (5)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (5)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 55
p: UP(x,RN) := 4*x**2 + 2/3      
 

          2   2
   (6)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (6)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 6
 
--S 7 of 55
a p                        
 

          2        2
   (7)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (7)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 55
(a*b) p = a b p            
 

          2         37    2         37
   (8)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (8)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 8


--S 9 of 55
c := (1/9)*b*(a + b)**2    
 

         1  6    5  5   13  4   19  3   79  2    7     1
   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
        72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R         1  6    5  5   13  4   19  3   79  2    7     1
--R   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R        72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 55
(a**2 - 3/4*b + c) (p + 1) 
 

           2   44     541
   (10)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (10)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 10


)clear all
 
   All user variables and function definitions have been cleared.
--S 11 of 55
RFZ := FRAC UP(x,INT)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 11

--S 12 of 55
(Dx, a, b): LODO1 RFZ
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 55
Dx := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 55
b := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 14

--S 15 of 55
a := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 55
p: RFZ := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17  of 55
(a*b - b*a) p 
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18  of 55
leftDivide(a,b)      
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 55
a - (b * %.quotient + %.remainder)
 

   (9)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (9)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 55
rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 20

--S 21 of 55
a - (%.quotient * b + %.remainder)
 

   (11)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (11)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 21

--S 22 of 55
e := leftGcd(a,b)
 

           2 2        1
   (12)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (12)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 22

--S 23 of 55
leftRemainder(a, e)    
 

   (13)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 23

--S 24 of 55
rightRemainder(a, e)    
 

               5
   (14)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (14)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 24

--S 25 of 55
f := rightLcm(a,b)
 

            3 3       2        2         7
   (15)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (15)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 25

--S 26 of 55
leftRemainder(f, b)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 26

--S 27 of 55
rightRemainder(f, b)  
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 27

)clear all
 
   All user variables and function definitions have been cleared.
--S 28 of 55
Dx: LODO(EXPR INT, f +-> D(f, x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 55
Dx := D()
 

   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1498 envArg,SPADCALL(G1498,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R   (2)  D
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1500 envArg,SPADCALL(G1500,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 29

--S 30 of 55
Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1
 

                       3
         3    G     - x  + H
   (3)  D  + -- D + --------
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1498 envArg,SPADCALL(G1498,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R                       3
--R         3    G     - x  + H
--R   (3)  D  + -- D + --------
--R              2         3
--R             x         x
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1500 envArg,SPADCALL(G1500,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 30

--S 31 of 55
n == 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 55
phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 55
phi1 ==  Dop(phi) / exp x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 55
phi2 == phi1 *x**(n+3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 55
phi3 == retract(phi2)@(POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 35

--S 36 of 55
pans == phi3 ::UP(x,POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 55
pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 37

--S 38 of 55
leq == solve(pans1,[subscript(s,[i]) for i in 1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 38

--S 39 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling function G1624 with type Integer -> Boolean 

   (12)
                           2                                3        2
         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
          0        0     0       0         0       0      0        0        0
   [[s = ---,s = ------------------,s = --------------------------------------]]
      1   3   2          18          3                    162
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--I   Compiling function G3445 with type Integer -> Boolean 
--R
--R   (12)
--R                           2                                3        2
--R         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
--R          0        0     0       0         0       0      0        0        0
--R   [[s = ---,s = ------------------,s = --------------------------------------]]
--R      1   3   2          18          3                    162
--R                         Type: List List Equation Fraction Polynomial Integer
--E 39

--S 40 of 55
n==4
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 40

--S 41 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (14)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 41

--S 42 of 55
n==7
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 42

--S 43 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ,

       s  =
        5
                               2         3          2
             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
                  0         0          0          0           0          0
           + 
                5        4          3          2
             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
              0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                   4          3           2                                6
             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
                 0          0           0            0            0      0
           + 
                  5          4           3           2
             90s G  + 2628s G  + 27864s G  + 90720s G
                0          0           0           0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                    3           2                            2
             (945s G  + 81648s G  + 2082996s G + 14171760s )H
                  0           0             0             0
           + 
                   5          4            3             2
             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
                 0          0            0             0              0
           + 
                7         6          5           4             3              2
             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
              0         0          0           0             0              0
           + 
             - 97977600s G
                        0
        /
           11022480
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (16)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ,
--R
--R       s  =
--R        5
--R                               2         3          2
--R             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
--R                  0         0          0          0           0          0
--R           + 
--R                5        4          3          2
--R             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
--R              0        0          0          0           0
--R        /
--R           29160
--R       ,
--R
--R       s  =
--R        6
--R                   3          2                        2
--R             405s H  + (405s G  + 18468s G + 174960s )H
--R                 0          0           0           0
--R           + 
--R                   4          3           2                                6
--R             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
--R                 0          0           0            0            0      0
--R           + 
--R                  5          4           3           2
--R             90s G  + 2628s G  + 27864s G  + 90720s G
--R                0          0           0           0
--R        /
--R           524880
--R       ,
--R
--R       s  =
--R        7
--R                                 3
--R             (2835s G + 91854s )H
--R                   0          0
--R           + 
--R                    3           2                            2
--R             (945s G  + 81648s G  + 2082996s G + 14171760s )H
--R                  0           0             0             0
--R           + 
--R                   5          4            3             2
--R             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
--R                 0          0            0             0              0
--R           + 
--R                7         6          5           4             3              2
--R             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
--R              0         0          0           0             0              0
--R           + 
--R             - 97977600s G
--R                        0
--R        /
--R           11022480
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 43
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 44 of 55
PZ := UP(x,INT); Vect := DPMM(3, PZ, SQMATRIX(3,PZ), PZ);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 44

--S 45 of 55
Modo := LODO2(SQMATRIX(3,PZ), Vect);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 45

--S 46 of 55
p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect
 

           2          3
   (3)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (3)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 46

--S 47 of 55
m := [[x**2, 1, 0], [1, x**4, 0], [0, 0, 4*x**2]]::(SQMATRIX(3,PZ))
 

        + 2         +
        |x   1    0 |
        |           |
   (4)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (4)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 47

--S 48 of 55
q: Vect := m * p
 

           4    2        5     2        5     3
   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 48
 
--S 49 of 55
Dx:  Modo := D()
 

   (6)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (6)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 49

--S 50 of 55
a:   Modo := 1*Dx  + m
 

            + 2         +
            |x   1    0 |
            |           |
   (7)  D + |     4     |
            |1   x    0 |
            |           |
            |          2|
            +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R            + 2         +
--R            |x   1    0 |
--R            |           |
--R   (7)  D + |     4     |
--R            |1   x    0 |
--R            |           |
--R            |          2|
--R            +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 50

--S 51 of 55
b:   Modo := m*Dx  + 1
 

        + 2         +
        |x   1    0 |    +1  0  0+
        |           |    |       |
   (8)  |     4     |D + |0  1  0|
        |1   x    0 |    |       |
        |           |    +0  0  1+
        |          2|
        +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R        + 2         +
--R        |x   1    0 |    +1  0  0+
--R        |           |    |       |
--R   (8)  |     4     |D + |0  1  0|
--R        |1   x    0 |    |       |
--R        |           |    +0  0  1+
--R        |          2|
--R        +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 51

--S 52  of 55
a*b
 

   (9)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 52

--S 53 of 55
a p
 

            4    2        5     2        5     3      2
   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 53

--S 54 of 55
b p
 

            3     2       4         4     3     2
   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 54

--S 55 of 55
(a+b) (p + q)
 

   (12)
      6      5      4      3      2
   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
      9      8     6      5      4      3     2
    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
        7       6      5       4      3      2
    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (12)
--R      6      5      4      3      2
--R   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
--R      9      8     6      5      4      3     2
--R    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
--R        7       6      5       4      3      2
--R    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 55
)spool 
 
Starts dribbling to elemfun.output (2009/2/17, 17:45:30).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 28
cos 0
 

   (1)  1
                                                     Type: Expression Integer
--R 
--R
--R   (1)  1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 28
sin 0
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 2

--S 3 of 28
exp 0
 

   (3)  1
                                                     Type: Expression Integer
--R 
--R
--R   (3)  1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 28
log 1
 

   (4)  0
                                                     Type: Expression Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 4

--S 5 of 28
sin(%pi/2)
 

   (5)  1
                                                     Type: Expression Integer
--R 
--R
--R   (5)  1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 28
simplify %
 

   (6)  1
                                                     Type: Expression Integer
--R 
--R
--R   (6)  1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 28
sin(3)**2 + cos(3)**2
 

              2         2
   (7)  sin(3)  + cos(3)
                                                     Type: Expression Integer
--R 
--R
--R              2         2
--R   (7)  sin(3)  + cos(3)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 28
simplify %
 

   (8)  1
                                                     Type: Expression Integer
--R 
--R
--R   (8)  1
--R                                                     Type: Expression Integer
--E 8

--S 9  of 28
a := atan 1
 

        %pi
   (9)  ---
         4
                                                     Type: Expression Integer
--R 
--R
--R        %pi
--R   (9)  ---
--R         4
--R                                                     Type: Expression Integer
--E 9

--S 10 of 28
t := cos(a)*sin(a)*tan(a)*sec(a)*csc(a)*cot(a)
 

   (10)  1
                                                     Type: Expression Integer
--R 
--R
--R   (10)  1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 28
simplify t
 

   (11)  1
                                                     Type: Expression Integer
--R 
--R
--R   (11)  1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 28
cot2tan t
 

   (12)  1
                                                     Type: Expression Integer
--R 
--R
--R   (12)  1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 28
cot2trig t
 

   (13)  1
                                                     Type: Expression Integer
--R 
--R
--R   (13)  1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 28
tan2cot t
 

   (14)  1
                                                     Type: Expression Integer
--R 
--R
--R   (14)  1
--R                                                     Type: Expression Integer
--E 14

--S 15 of 28
tan2trig t
 

   (15)  1
                                                     Type: Expression Integer
--R 
--R
--R   (15)  1
--R                                                     Type: Expression Integer
--E 15

--S 16 of 28
cos2sec t
 

   (16)  1
                                                     Type: Expression Integer
--R 
--R
--R   (16)  1
--R                                                     Type: Expression Integer
--E 16
 
--S 17 of 28
t := sin(7)**2 - sec(7)/(1 - cot(7) + csc(7)**3)
 

                3                    2
         (csc(7)  - cot(7) + 1)sin(7)  - sec(7)
   (17)  --------------------------------------
                        3
                  csc(7)  - cot(7) + 1
                                                     Type: Expression Integer
--R 
--R
--R                3                    2
--R         (csc(7)  - cot(7) + 1)sin(7)  - sec(7)
--R   (17)  --------------------------------------
--R                        3
--R                  csc(7)  - cot(7) + 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 28
simplify t
 

   (18)
                5          3         2                             6          4
       (- cos(7)  + 2cos(7)  - cos(7)  - cos(7) + 1)sin(7) + cos(7)  - 2cos(7)
     + 
             3         2
       cos(7)  + cos(7)  - cos(7)
  /
            3                         4         2
     (cos(7)  - cos(7))sin(7) - cos(7)  + cos(7)  - cos(7)
                                                     Type: Expression Integer
--R 
--R
--R   (18)
--R                5          3         2                             6          4
--R       (- cos(7)  + 2cos(7)  - cos(7)  - cos(7) + 1)sin(7) + cos(7)  - 2cos(7)
--R     + 
--R             3         2
--R       cos(7)  + cos(7)  - cos(7)
--R  /
--R            3                         4         2
--R     (cos(7)  - cos(7))sin(7) - cos(7)  + cos(7)  - cos(7)
--R                                                     Type: Expression Integer
--E 18

--S 19 of 28
numeric %
 

   (19)  0.0390653254 8092347922 2
                                                                  Type: Float
--R 
--R
--R   (19)  0.0390653254 8092347922 2
--R                                                                  Type: Float
--E 19

--S 20 of 28
numeric t
 

   (20)  0.0390653254 8092347921 5
                                                                  Type: Float
--R 
--R
--R   (20)  0.0390653254 8092347921 5
--R                                                                  Type: Float
--E 20

--S 21 of 28
numeric(t, 100)
 

   (21)
  0.0390653254 8092347921 8900669391 6314051319 2684833219 8927261332 141491473
  3 4130898335 0601081135 3732125345 8
                                                                  Type: Float
--R 
--R
--R   (21)
--R  0.0390653254 8092347921 8900669391 6314051319 2684833219 8927261332 141491473
--R  3 4130898335 0601081135 3732125345 8
--R                                                                  Type: Float
--E 21
 
--S 22 of 28
u := exp(sin(x-1)**2 - cos(x-1)/sec(x-1))
 

                               2
           sec(x - 1)sin(x - 1)  - cos(x - 1)
           ----------------------------------
                       sec(x - 1)
   (22)  %e
                                                     Type: Expression Integer
--R 
--R
--R                               2
--R           sec(x - 1)sin(x - 1)  - cos(x - 1)
--R           ----------------------------------
--R                       sec(x - 1)
--R   (22)  %e
--R                                                     Type: Expression Integer
--E 22

--S 23 of 28
eval(u,x=1)
 

          1
   (23)  --
         %e
                                                     Type: Expression Integer
--R 
--R
--R          1
--R   (23)  --
--R         %e
--R                                                     Type: Expression Integer
--E 23
 
--S 24 of 28
v(x) == exp(sin(x-1)**2 - cos(x-1)/sec(x-1))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 28
v x
 
   Compiling function v with type Variable x -> Expression Integer 

                               2
           sec(x - 1)sin(x - 1)  - cos(x - 1)
           ----------------------------------
                       sec(x - 1)
   (25)  %e
                                                     Type: Expression Integer
--R 
--R   Compiling function v with type Variable x -> Expression Integer 
--R
--R                               2
--R           sec(x - 1)sin(x - 1)  - cos(x - 1)
--R           ----------------------------------
--R                       sec(x - 1)
--R   (25)  %e
--R                                                     Type: Expression Integer
--E 25

--S 26 of 28
v 1
 
   Compiling function v with type PositiveInteger -> Expression Integer
      

          1
   (26)  --
         %e
                                                     Type: Expression Integer
--R 
--R   Compiling function v with type PositiveInteger -> Expression Integer
--R      
--R
--R          1
--R   (26)  --
--R         %e
--R                                                     Type: Expression Integer
--E 26

--S 27 of 28
v(%pi/3)
 
   Compiling function v with type Pi -> Expression Integer 

               %pi - 3     %pi - 3 2       %pi - 3
           sec(-------)sin(-------)  - cos(-------)
                  3           3               3
           ----------------------------------------
                             %pi - 3
                         sec(-------)
                                3
   (27)  %e
                                                     Type: Expression Integer
--R 
--R   Compiling function v with type Pi -> Expression Integer 
--R
--R               %pi - 3     %pi - 3 2       %pi - 3
--R           sec(-------)sin(-------)  - cos(-------)
--R                  3           3               3
--R           ----------------------------------------
--R                             %pi - 3
--R                         sec(-------)
--R                                3
--R   (27)  %e
--R                                                     Type: Expression Integer
--E 27

--S 28 of 28
numeric %
 

   (28)  0.3695208585 287457761
                                                                  Type: Float
--R 
--R
--R   (28)  0.3695208585 287457761
--R                                                                  Type: Float
--E 28
)spool
 
Starts dribbling to eval.output (2009/2/17, 17:45:44).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--** This line will be optional interactively, since the a := f(x**2)
--** will prompt you if you don't declare f this way.
--S 1 of 23
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 1

--S 2 of 23
a := f(x**2)
 

           2
   (2)  f(x )
                                                     Type: Expression Integer
--R 
--R
--R           2
--R   (2)  f(x )
--R                                                     Type: Expression Integer
--E 2

--S 3 of 23
b := differentiate(a,x,2) + f 5
 

          2 ,,  2      ,  2
   (3)  4x f  (x ) + 2f (x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R          2 ,,  2      ,  2
--R   (3)  4x f  (x ) + 2f (x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 3

--S 4 of 23
eval(b, x = x + y)
 

           2            2  ,,  2           2      ,  2           2
   (4)  (4y  + 8x y + 4x )f  (y  + 2x y + x ) + 2f (y  + 2x y + x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R           2            2  ,,  2           2      ,  2           2
--R   (4)  (4y  + 8x y + 4x )f  (y  + 2x y + x ) + 2f (y  + 2x y + x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 23
eval(b, f 5 = 1)
 

          2 ,,  2      ,  2
   (5)  4x f  (x ) + 2f (x ) + 1

                                                     Type: Expression Integer
--R 
--R
--R          2 ,,  2      ,  2
--R   (5)  4x f  (x ) + 2f (x ) + 1
--R
--R                                                     Type: Expression Integer
--E 5

--** will eventually use the +-> notation in the eval statement
--S 6 of 23
foo(u:EXPR INT):EXPR INT == exp u
 
   Function declaration foo : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration foo : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 6

--S 7 of 23
c := eval(b, 'f, foo)
 
   Compiling function foo with type Expression Integer -> Expression 
      Integer 

                    2
           2       x      5
   (7)  (4x  + 2)%e   + %e
                                                     Type: Expression Integer
--R 
--R   Compiling function foo with type Expression Integer -> Expression 
--R      Integer 
--R
--R                    2
--R           2       x      5
--R   (7)  (4x  + 2)%e   + %e
--R                                                     Type: Expression Integer
--E 7


--S 8 of 23
oof(u:EXPR INT):EXPR INT == f u
 
   Function declaration oof : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration oof : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 8

--S 9 of 23
eval(c, 'exp, oof)
 
   Compiling function oof with type Expression Integer -> Expression 
      Integer 

           2        2
   (9)  (4x  + 2)f(x ) + f(5)
                                                     Type: Expression Integer
--R 
--R   Compiling function oof with type Expression Integer -> Expression 
--R      Integer 
--R
--R           2        2
--R   (9)  (4x  + 2)f(x ) + f(5)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 23
f'(u:EXPR INT):EXPR INT == f u
 
   Function declaration f' : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f' : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 10

--S 11 of 23
derivative(f,f')
 
   Compiling function f' with type Expression Integer -> Expression 
      Integer 

   (11)  f
                                                          Type: BasicOperator
--R 
--R   Compiling function f' with type Expression Integer -> Expression 
--R      Integer 
--R
--R   (11)  f
--R                                                          Type: BasicOperator
--E 11

--S 12 of 23
b
 

           2 ,,  2      ,  2
   (12)  4x f  (x ) + 2f (x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R           2 ,,  2      ,  2
--R   (12)  4x f  (x ) + 2f (x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 12

--** The coercion is needed to avoid an interpreter bug.
--** This will just be eval(b) eventually:
--S 13 of 23
eval(b, x = x::(EXPR INT))
 

           2 ,,  2      ,  2
   (13)  4x f  (x ) + 2f (x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R           2 ,,  2      ,  2
--R   (13)  4x f  (x ) + 2f (x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 13

--S 14 of 23
differentiate(%, x)
 

           3 ,,,  2        ,,  2
   (14)  8x f   (x ) + 12xf  (x )

                                                     Type: Expression Integer
--R 
--R
--R           3 ,,,  2        ,,  2
--R   (14)  8x f   (x ) + 12xf  (x )
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 23
a3 := a * a * a
 

            2 3
   (15)  f(x )
                                                     Type: Expression Integer
--R 
--R
--R            2 3
--R   (15)  f(x )
--R                                                     Type: Expression Integer
--E 15

--S 16 of 23
foo
 

   (16)  foo u == exp(u)
                                                     Type: FunctionCalled foo
--R 
--R
--R   (16)  foo u == exp(u)
--R                                                     Type: FunctionCalled foo
--E 16

--S 17 of 23
eval(a3,'f,2,foo)
 

                 2
            2   x
   (17)  f(x )%e
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R            2   x
--R   (17)  f(x )%e
--R                                                     Type: Expression Integer
--E 17

--S 18 of 23
g := operator 'g
 

   (18)  g
                                                          Type: BasicOperator
--R 
--R
--R   (18)  g
--R                                                          Type: BasicOperator
--E 18

--S 19 of 23
bar(u:EXPR INT):EXPR INT == sin(u) + cos(2*u)
 
   Function declaration bar : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration bar : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 19

--S 20 of 23
a + g a
 

              2        2
   (20)  g(f(x )) + f(x )
                                                     Type: Expression Integer
--R 
--R
--R              2        2
--R   (20)  g(f(x )) + f(x )
--R                                                     Type: Expression Integer
--E 20

--S 21 of 23
eval(%,['f,'g],[foo,bar])
 
   Compiling function bar with type Expression Integer -> Expression 
      Integer 

                2            2       2
               x            x       x
   (21)  sin(%e  ) + cos(2%e  ) + %e
                                                     Type: Expression Integer
--R 
--R   Compiling function bar with type Expression Integer -> Expression 
--R      Integer 
--R
--R                2            2       2
--R               x            x       x
--R   (21)  sin(%e  ) + cos(2%e  ) + %e
--R                                                     Type: Expression Integer
--E 21

--S 22 of 23
a3 + g a
 

              2        2 3
   (22)  g(f(x )) + f(x )
                                                     Type: Expression Integer
--R 
--R
--R              2        2 3
--R   (22)  g(f(x )) + f(x )
--R                                                     Type: Expression Integer
--E 22

--S 23 of 23
eval(%,['f,'g],[2,1],[foo,bar])
 

                                            2
                2             2        2   x
   (23)  sin(f(x )) + cos(2f(x )) + f(x )%e
                                                     Type: Expression Integer
--R 
--R
--R                                            2
--R                2             2        2   x
--R   (23)  sin(f(x )) + cos(2f(x )) + f(x )%e
--R                                                     Type: Expression Integer
--E 23
)spool
 
Starts dribbling to streams.output (2009/2/17, 18:0:52).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
)set streams calculate 5
 
 
)set streams showall on
 
 
--S 1 of 26
a := [i for i in 1..]
 

   (1)  [1,2,3,4,5,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,...]
--R                                                 Type: Stream PositiveInteger
--E 1

--S 2 of 26
b := [i+1 for i in a]
 

   (2)  [2,3,4,5,6,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (2)  [2,3,4,5,6,...]
--R                                                 Type: Stream PositiveInteger
--E 2

--S 3 of 26
b.20
 

   (3)  21
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  21
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 26
b
 

   (4)  [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (4)  [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,...]
--R                                                 Type: Stream PositiveInteger
--E 4

--S 5 of 26
a
 

   (5)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (5)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
--R                                                 Type: Stream PositiveInteger
--E 5

--S 6 of 26
first(a,10)
 

   (6)  [1,2,3,4,5,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (6)  [1,2,3,4,5,...]
--R                                                 Type: Stream PositiveInteger
--E 6

--S 7 of 26
rest(a,10)
 

   (7)  [11,12,13,14,15,16,17,18,19,20,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (7)  [11,12,13,14,15,16,17,18,19,20,...]
--R                                                 Type: Stream PositiveInteger
--E 7

--S 8 of 26
[i for i in a | odd? i]
 

   (8)  [1,3,5,7,9,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (8)  [1,3,5,7,9,...]
--R                                                 Type: Stream PositiveInteger
--E 8

--S 9 of 26
c := [[i,j] for i in a for j in b]
 

   (9)  [[1,2],[2,3],[3,4],[4,5],[5,6],...]
                                            Type: Stream List PositiveInteger
--R 
--R
--R   (9)  [[1,2],[2,3],[3,4],[4,5],[5,6],...]
--R                                            Type: Stream List PositiveInteger
--E 9

--S 10 of 26
[first i for i in c]
 

   (10)  [1,2,3,4,5,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (10)  [1,2,3,4,5,...]
--R                                                 Type: Stream PositiveInteger
--E 10

)set streams calculate 10
 

--S 11 of 26
concat([i for i in a while i<7],a)
 

   (11)  [1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (11)  [1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
--R                                                 Type: Stream PositiveInteger
--E 11

--S 12 of 26
concat(a,a)
 

   (12)  [1,2,3,4,5,6,7,8,9,10,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (12)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                 Type: Stream PositiveInteger
--E 12

--S 13 of 26
upto:NNI->STREAM INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 26
upto n == first(a,n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 26
d := [upto n for n in a]
 
   Compiling function upto with type NonNegativeInteger -> Stream 
      Integer 

   (15)
   [[1], [1,2], [1,2,3], [1,2,3,4], [1,2,3,4,5], [1,2,3,4,5,6],
    [1,2,3,4,5,6,7], [1,2,3,4,5,6,7,8], [1,2,3,4,5,6,7,8,9],
    [1,2,3,4,5,6,7,8,9,10,...], ...]
                                                  Type: Stream Stream Integer
--R 
--R   Compiling function upto with type NonNegativeInteger -> Stream 
--R      Integer 
--R
--R   (15)
--R   [[1], [1,2], [1,2,3], [1,2,3,4], [1,2,3,4,5], [1,2,3,4,5,6],
--R    [1,2,3,4,5,6,7], [1,2,3,4,5,6,7,8], [1,2,3,4,5,6,7,8,9],
--R    [1,2,3,4,5,6,7,8,9,10,...], ...]
--R                                                  Type: Stream Stream Integer
--E 15

--S 16 of 26
concat d
 

   (16)  [1,1,2,1,2,3,1,2,3,4,...]
                                                         Type: Stream Integer
--R 
--R
--R   (16)  [1,1,2,1,2,3,1,2,3,4,...]
--R                                                         Type: Stream Integer
--E 16

--S 17 of 26
reduce(0,_+$INT,first(a,10))
 

   (17)  55
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  55
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 26
scan(0,_+$INT,a)
 

   (18)  [1,3,6,10,15,21,28,36,45,55,...]
                                                         Type: Stream Integer
--R 
--R
--R   (18)  [1,3,6,10,15,21,28,36,45,55,...]
--R                                                         Type: Stream Integer
--E 18

--S 19 of 26
scan(0,_+$INT,[2*i-1 for i in a])
 

   (19)  [1,4,9,16,25,36,49,64,81,100,...]
                                                         Type: Stream Integer
--R 
--R
--R   (19)  [1,4,9,16,25,36,49,64,81,100,...]
--R                                                         Type: Stream Integer
--E 19

--S 20 of 26
ff:(LIST INT)->(LIST INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 26
ff(x)==[x.1+x.2,x.1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 26
fibs := generate(ff,[1,1])
 
   Compiling function ff with type List Integer -> List Integer 

   (22)
   [[1,1],[2,1],[3,2],[5,3],[8,5],[13,8],[21,13],[34,21],[55,34],[89,55],...]
                                             Type: InfiniteTuple List Integer
--R 
--R   Compiling function ff with type List Integer -> List Integer 
--R
--R   (22)
--R   [[1,1],[2,1],[3,2],[5,3],[8,5],[13,8],[21,13],[34,21],[55,34],[89,55],...]
--R                                             Type: InfiniteTuple List Integer
--E 22

--first([first i for i in fibs], 100)

--S 23 of 26
mt:SQMATRIX(2,INT) := matrix [[1,2],[3,4]]
 

         +1  2+
   (23)  |    |
         +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +1  2+
--R   (23)  |    |
--R         +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 23

--S 24 of 26
mplm:SQMATRIX(2,INT)->SQMATRIX(2,INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 26
mplm x == x*mt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 26
generate(mplm,mt)
 
   Compiling function mplm with type SquareMatrix(2,Integer) -> 
      SquareMatrix(2,Integer) 

   (26)
    +1  2+  +7   10+  +37  54 +  +199  290+  +1069  1558+  +5743   8370 +
   [|    |, |      |, |       |, |        |, |          |, |            |,
    +3  4+  +15  22+  +81  118+  +435  634+  +2337  3406+  +12555  18298+
    +30853  44966+  +165751  241570+  +890461   1297782+  +4783807   6972050 +
    |            |, |              |, |                |, |                  |,
    +67449  98302+  +362355  528106+  +1946673  2837134+  +10458075  15241882+
    ...]
                                  Type: InfiniteTuple SquareMatrix(2,Integer)
--R 
--R   Compiling function mplm with type SquareMatrix(2,Integer) -> 
--R      SquareMatrix(2,Integer) 
--R
--R   (26)
--R    +1  2+  +7   10+  +37  54 +  +199  290+  +1069  1558+  +5743   8370 +
--R   [|    |, |      |, |       |, |        |, |          |, |            |,
--R    +3  4+  +15  22+  +81  118+  +435  634+  +2337  3406+  +12555  18298+
--R    +30853  44966+  +165751  241570+  +890461   1297782+  +4783807   6972050 +
--R    |            |, |              |, |                |, |                  |,
--R    +67449  98302+  +362355  528106+  +1946673  2837134+  +10458075  15241882+
--R    ...]
--R                                  Type: InfiniteTuple SquareMatrix(2,Integer)
--E 26
)spool 
 
Starts dribbling to radix.output (2009/2/17, 17:57:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 17
111::RadixExpansion(5)
 

   (1)  421
                                                       Type: RadixExpansion 5
--R 
--R
--R   (1)  421
--R                                                       Type: RadixExpansion 5
--E 1

--S 2 of 17
(5/24)::RadixExpansion(2)
 

             __
   (2)  0.00110
                                                       Type: RadixExpansion 2
--R 
--R
--R             __
--R   (2)  0.00110
--R                                                       Type: RadixExpansion 2
--E 2

--S 3 of 17
(5/24)::RadixExpansion(3)
 

           __
   (3)  0.012
                                                       Type: RadixExpansion 3
--R 
--R
--R           __
--R   (3)  0.012
--R                                                       Type: RadixExpansion 3
--E 3

--S 4 of 17
(5/24)::RadixExpansion(8)
 

           __
   (4)  0.152
                                                       Type: RadixExpansion 8
--R 
--R
--R           __
--R   (4)  0.152
--R                                                       Type: RadixExpansion 8
--E 4

--S 5 of 17
(5/24)::RadixExpansion(10)
 

             _
   (5)  0.2083
                                                      Type: RadixExpansion 10
--R 
--R
--R             _
--R   (5)  0.2083
--R                                                      Type: RadixExpansion 10
--E 5

--S 6 of 17
(5/24)::RadixExpansion(12)
 

   (6)  0.26
                                                      Type: RadixExpansion 12
--R 
--R
--R   (6)  0.26
--R                                                      Type: RadixExpansion 12
--E 6

--S 7 of 17
(5/24)::RadixExpansion(16)
 

           _
   (7)  0.35
                                                      Type: RadixExpansion 16
--R 
--R
--R           _
--R   (7)  0.35
--R                                                      Type: RadixExpansion 16
--E 7

--S 8 of 17
(5/24)::RadixExpansion(36)
 

   (8)  0.7I
                                                      Type: RadixExpansion 36
--R 
--R
--R   (8)  0.7I
--R                                                      Type: RadixExpansion 36
--E 8

--S 9 of 17
(5/24)::RadixExpansion(38)
 

                    _____
   (9)  0 . 7 34 31 25 12
                                                      Type: RadixExpansion 38
--R 
--R
--R                    _____
--R   (9)  0 . 7 34 31 25 12
--R                                                      Type: RadixExpansion 38
--E 9

--S 10 of 17
a := (76543/210)::RadixExpansion(8)
 

              ____
   (10)  554.37307
                                                       Type: RadixExpansion 8
--R 
--R
--R              ____
--R   (10)  554.37307
--R                                                       Type: RadixExpansion 8
--E 10

--S 11 of 17
w := wholeRagits a
 

   (11)  [5,5,4]
                                                           Type: List Integer
--R 
--R
--R   (11)  [5,5,4]
--R                                                           Type: List Integer
--E 11

--S 12 of 17
f0 := prefixRagits a
 

   (12)  [3]
                                                           Type: List Integer
--R 
--R
--R   (12)  [3]
--R                                                           Type: List Integer
--E 12

--S 13 of 17
f1 := cycleRagits a
 

   (13)  [7,3,0,7]
                                                           Type: List Integer
--R 
--R
--R   (13)  [7,3,0,7]
--R                                                           Type: List Integer
--E 13

--S 14 of 17
u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1)
 

              ____
   (14)  554.37307
                                                       Type: RadixExpansion 8
--R 
--R
--R              ____
--R   (14)  554.37307
--R                                                       Type: RadixExpansion 8
--E 14

--S 15 of 17
v: RadixExpansion(12) := fractRadix([1,2,3,11], [0])
 

               _
   (15)  0.123B0
                                                      Type: RadixExpansion 12
--R 
--R
--R               _
--R   (15)  0.123B0
--R                                                      Type: RadixExpansion 12
--E 15

--S 16 of 17
fractRagits(u)
 

              _______
   (16)  [3,7,3,0,7,7]
                                                         Type: Stream Integer
--R 
--R
--R              _______
--R   (16)  [3,7,3,0,7,7]
--R                                                         Type: Stream Integer
--E 16

--S 17 of 17
a :: Fraction(Integer)
 

         76543
   (17)  -----
          210
                                                       Type: Fraction Integer
--R 
--R
--R         76543
--R   (17)  -----
--R          210
--R                                                       Type: Fraction Integer
--E 17
)spool 
 
Starts dribbling to directproduct.output (2009/2/17, 17:44:40).
)set message auto off
 
)set message test on
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
NNI has Monoid
 

   (1)  true
                                                                Type: Boolean
--R 
--R
--R   (1)  true
--R                                                                Type: Boolean
--E 1

--S 2
NNI2:=DirectProduct(2,NNI)
 

   (2)  DirectProduct(2,NonNegativeInteger)
                                                                 Type: Domain
--R 
--R
--R   (2)  DirectProduct(2,NonNegativeInteger)
--R                                                                 Type: Domain
--E 2

--S 3
NNI2 has Monoid
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4
a:NNI2:=directProduct([3,5])
 

   (4)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (4)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 4

--S 5
3*a
 

   (5)  [9,15]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (5)  [9,15]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 5

--S 6
b:NNI2:=1
 

   (6)  [1,1]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (6)  [1,1]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 6

--S 7
1*a
 

   (7)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (7)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 7

--S 8
b*a
 

   (8)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (8)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 8

--S 9
c:NNI2:=directProduct([1,1])
 

   (9)  [1,1]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (9)  [1,1]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 9

--S 10
c*a
 

   (10)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (10)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 10

--S 11
d:NNI2:=directProduct([1,2])
 

   (11)  [1,2]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (11)  [1,2]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 11

--S 12
d*a
 

   (12)  [3,10]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (12)  [3,10]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 12

)spool 
 
Starts dribbling to ndftip.output (2009/2/17, 17:55:29).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 45
outputGeneral 6
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 45
seqA := [0.34907,0.54890,0.74776,0.94459,1.1385,1.3285,1.5137];
 

                                                             Type: List Float
--R 
--R
--R                                                             Type: List Float
--E 2

--S 3 of 45
seqB := [0.34907 - 0.37168*%i,  _
         0.54890 - 0.35669*%i,  _
         0.74776 - 0.31175*%i,  _
         0.94459 - 0.23702*%i,  _
         1.13850 - 0.13274*%i,  _
         1.32850 + 0.00074*%i,  _
         1.51370 + 0.16298*%i];
 

                                                     Type: List Complex Float
--R 
--R
--R                                                     Type: List Complex Float
--E 3

--S 4 of 45
hseqC : PackedHermitianSequence DoubleFloat
 
 
Daly Bug
   Category, domain or package constructor PackedHermitianSequence is 
      not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is 
--R      not available.
--E 4 of 45

--S 5 of 45
hseqC := packHS [0.34907,        _
                 0.54890 + %i*1.51370,  _
                 0.74776 + %i*1.32850,  _
                 0.94459 + %i*1.13850,  _
                 0.94459 - %i*1.13850,  _
                 0.74776 - %i*1.32850,  _
                 0.54890 - %i*1.51370];
 

                                                                 Type: Symbol
--R 
--R
--R                                                                 Type: Symbol
--E 5

--S 6 of 45
seqsD : List Vector DoubleFloat;
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 45
seqsD := [vector [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _
          vector [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
          vector [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
 

                                                Type: List Vector DoubleFloat
--R 
--R
--R                                                Type: List Vector DoubleFloat
--E 7

--S 8 of 45
seqsE : List PackedHermitianSequence DoubleFloat;
 
 
Daly Bug
   Category, domain or package constructor PackedHermitianSequence is 
      not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is 
--R      not available.
--E 8

--S 9 of 45
seqsE := [pHS [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _
          pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
          pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
 

                                                            Type: List Symbol
--R 
--R
--R                                                            Type: List Symbol
--E 9

--S 10 of 45
seqsF : List Vector Complex DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 45
seqsF := [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i,   _
                  0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i,   _
                  0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i],  _
          vector [0.9172 + 0.9089*%i, 0.0644 + 0.3118*%i,   _
                  0.6037 + 0.3465*%i, 0.6430 + 0.6198*%i,   _
                  0.0428 + 0.2668*%i, 0.4815 + 0.1614*%i],  _
          vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i,   _
                  0.2060 + 0.7060*%i, 0.8630 + 0.8652*%i,   _
                  0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]];
 

                                        Type: List Vector Complex DoubleFloat
--R 
--R
--R                                        Type: List Vector Complex DoubleFloat
--E 11

--S 12 of 45
dftA := nagDFT seqA;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                                 List Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                                 List Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12

--S 13 of 45 used to work?
dftA :: Vector Complex Float :: Matrix Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftA to Vector Complex Float for 
      value
   dftA

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftA to Vector Complex Float for 
--R      value
--R   dftA
--R
--E 13
                             -- Matrix to force display as a column,
                             -- Float to allow outputGeneral to work.

--       +         2.48361         +
--       |                         |
--       |- 0.265985 + 0.530898 %i |
--       |                         |
--       |- 0.257682 + 0.202979 %i |
--       |                         |
--       |- 0.256363 + 0.0580623 %i|
--       |                         |
--       |- 0.256363 - 0.0580623 %i|
--       |                         |
--       |- 0.257682 - 0.202979 %i |
--       |                         |
--       +- 0.265985 - 0.530898 %i +

-- test  2

--S 14 of 45 used to work?
nagInverseDFT dftA :: Vector Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                                Variable dftA
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                                Variable dftA
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 14 
--       [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137]

-- test  3
--S 15 of 45
dftB := nagDFT seqB;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                             List Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                             List Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15

--S 16 of 45 used to work?
dftB :: Vector Complex Float :: Matrix Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftB to Vector Complex Float for 
      value
   dftB

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftB to Vector Complex Float for 
--R      value
--R   dftB
--R
--E 16

--       +  2.48361 - 0.471004 %i  +
--       |                         |
--       | - 0.5518 + 0.496841 %i  |
--       |                         |
--       |- 0.367113 + 0.0975621 %i|
--       |                         |
--       |- 0.287669 - 0.0586476 %i|
--       |                         |
--       |- 0.225057 - 0.174772 %i |
--       |                         |
--       |- 0.148251 - 0.308396 %i |
--       |                         |
--       + 0.0198297 - 0.564956 %i +
 
-- test  4

--S 17 of 45 used to work?
(nagInverseDFT dftB) :: Vector Complex Float :: Matrix Complex Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                                Variable dftB
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                                Variable dftB
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       +0.34907 - 0.37168 %i+
--       |                    |
--       |0.5489 - 0.35669 %i |
--       |                    |
--       |0.74776 - 0.31175 %i|
--       |                    |
--       |0.94459 - 0.23702 %i|
--       |                    |
--       |1.1385 - 0.13274 %i |
--       |                    |
--       |1.3285 + 0.00074 %i |
--       |                    |
--       +1.5137 + 0.16298 %i +

-- test  5

--S 18 of 45
hdftA := nagHermitianDFT seqA;
 
   There are no library operations named nagHermitianDFT 
      Use HyperDoc Browse or issue
                          )what op nagHermitianDFT
      to learn if there is any operation containing " nagHermitianDFT "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianDFT with argument type(s) 
                                 List Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianDFT 
--R      Use HyperDoc Browse or issue
--R                          )what op nagHermitianDFT
--R      to learn if there is any operation containing " nagHermitianDFT "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianDFT with argument type(s) 
--R                                 List Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18

--S 19 of 45 used to work?
(expand hdftA) :: Vector Complex Float :: Matrix Complex Float
 
 
Daly Bug
   Cannot convert from type Polynomial Integer to Vector Complex Float 
      for value
   hdftA

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Polynomial Integer to Vector Complex Float 
--R      for value
--R   hdftA
--R
--E 19
--       +         2.48361         +
--       |                         |
--       |- 0.265985 + 0.530898 %i |
--       |                         |
--       |- 0.257682 + 0.202979 %i |
--       |                         |
--       |- 0.256363 + 0.0580623 %i|
--       |                         |
--       |- 0.256363 - 0.0580623 %i|
--       |                         |
--       |- 0.257682 - 0.202979 %i |
--       |                         |
--       +- 0.265985 - 0.530898 %i +
 
-- test  6

--S 20 of 45 used to work? 
(nagInverseDFT hdftA) :: Vector Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable hdftA
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable hdftA
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
--       [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137]

-- test  7

--S 21 of 45
dftC := nagDFT hseqC;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21

--S 22 of 45 used to work?
dftC :: Vector Float
 
 
Daly Bug
   Cannot convert from type Variable dftC to Vector Float for value
   dftC

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftC to Vector Float for value
--R   dftC
--R
--E 22
-- [1.82616,1.86862,- 0.017503,0.502001,- 0.598725,- 0.0314404,- 2.62557]

-- test  8

--S 23 of 45 used to work?
(nagInverseDFT dftC) :: Vector Complex Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                                Variable dftC
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                                Variable dftC
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23 
-- [0.34907, 0.5489 + 1.5137 %i, 0.74776 + 1.3285 %i, 0.94459 + 1.1385 %i,
--  0.94459 - 1.1385 %i, 0.74776 - 1.3285 %i, 0.5489 - 1.5137 %i]

-- test  9

--S 24 of 45 used to work?
nagHermitianInverseDFT dftC
 
   There are no library operations named nagHermitianInverseDFT 
      Use HyperDoc Browse or issue
                       )what op nagHermitianInverseDFT
      to learn if there is any operation containing " 
      nagHermitianInverseDFT " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianInverseDFT with argument type(s) 
                                Variable dftC
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianInverseDFT 
--R      Use HyperDoc Browse or issue
--R                       )what op nagHermitianInverseDFT
--R      to learn if there is any operation containing " 
--R      nagHermitianInverseDFT " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianInverseDFT with argument type(s) 
--R                                Variable dftC
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24 
-- [0.34907000000000005, 0.54889999999999983, 0.74775999999999987,
--  0.94459000000000004, 1.1385000000000003, 1.3284999999999998,
--  1.5136999999999998]

-- test 10:

--S 25 of 45
dftsD := nagDFT seqsD;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                           List Vector DoubleFloat
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                           List Vector DoubleFloat
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25

--S 26 of 45 used to work?
dftsD :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftsD to List Vector Complex Float
      for value
   dftsD

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftsD to List Vector Complex Float
--R      for value
--R   dftsD
--R
--E 26
 
-- [
--   [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684,
--    0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i]
--   ,

--   [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072,
--    0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i]
--   ,

--   [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011,
--    0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i]
--   ]

-- test 11:

--S 27 of 45
invdftsD := nagInverseDFT dftsD ;
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable dftsD
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable dftsD
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 27

--S 28 of 45 used to work?
invdftsD :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable invdftsD to List Vector Complex 
      Float for value
   invdftsD

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable invdftsD to List Vector Complex 
--R      Float for value
--R   invdftsD
--R
--E 28 
-- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424],
--  [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723],
--  [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]]

-- test 12:
--S 29 of 45
dftsE := nagDFT seqsE;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                                 List Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                                 List Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 29

--S 30 of 45 used to work?
dftsE :: List Vector Float
 
 
Daly Bug
   Cannot convert from type Variable dftsE to List Vector Float for 
      value
   dftsE

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftsE to List Vector Float for 
--R      value
--R   dftsE
--R
--E 30
-- [[1.0788,0.662291,- 0.239146,- 0.578284,0.459192,- 0.438816],
--  [0.857321,1.22614,0.353348,- 0.222169,0.341327,- 1.22908],
--  [1.18245,0.262509,0.674406,0.552278,0.0539906,- 0.478963]]

-- test 13:
--S 31 of 45
invdftsE := nagInverseDFT dftsE;
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable dftsE
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable dftsE
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 31

--S 32 of 45 used to work?
invdftsE :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable invdftsE to List Vector Complex 
      Float for value
   invdftsE

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable invdftsE to List Vector Complex 
--R      Float for value
--R   invdftsE
--R
--E 32
-- [
--   [0.3854, 0.6772 + 0.1424 %i, 0.1138 + 0.6362 %i, 0.6751,
--    0.1138 - 0.6362 %i, 0.6772 - 0.1424 %i]
--   ,

--   [0.5417, 0.2983 + 0.8723 %i, 0.1181 + 0.8638 %i, 0.7255,
--    0.1181 - 0.8638 %i, 0.2983 - 0.8723 %i]
--   ,

--   [0.9172, 0.0644 + 0.4815 %i, 0.6037 + 0.0428 %i, 0.643,
--    0.6037 - 0.0428 %i, 0.0644 - 0.4815 %i]
--   ]

-- test 14:
--S 33 of 45
hdftsD := nagHermitianDFT seqsD;
 
   There are no library operations named nagHermitianDFT 
      Use HyperDoc Browse or issue
                          )what op nagHermitianDFT
      to learn if there is any operation containing " nagHermitianDFT "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianDFT with argument type(s) 
                           List Vector DoubleFloat
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianDFT 
--R      Use HyperDoc Browse or issue
--R                          )what op nagHermitianDFT
--R      to learn if there is any operation containing " nagHermitianDFT "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianDFT with argument type(s) 
--R                           List Vector DoubleFloat
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 33

--S 34 of 45 used to work?
map(expand,hdftsD) :: List Vector Complex Float
 
   There are 68 exposed and 8 unexposed library operations named map 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op map
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named map 
      with argument type(s) 
                               Variable expand
                               Variable hdftsD
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 68 exposed and 8 unexposed library operations named map 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op map
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named map 
--R      with argument type(s) 
--R                               Variable expand
--R                               Variable hdftsD
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 34 
-- [
--   [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684,
--    0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i]
--   ,

--   [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072,
--    0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i]
--   ,

--   [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011,
--    0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i]
--   ]

-- test 15:

--S 35 of 45 used to work?
(nagInverseDFT hdftsD) :: List Vector Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable hdftsD
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable hdftsD
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 35 
-- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424],
--  [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723],
--  [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]]

-- test 16:
--S 36 of 45
dftsF := nagDFT seqsF;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                       List Vector Complex DoubleFloat
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                       List Vector Complex DoubleFloat
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 36

--S 37 of 45 used to work?
dftsF :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftsF to List Vector Complex Float
      for value
   dftsF

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftsF to List Vector Complex Float
--R      for value
--R   dftsF
--R
--E 37
-- [
--   [1.07373 + 1.39609 %i, - 0.570647 - 0.0409019 %i, 0.173259 - 0.295822 %i,
--    - 0.146684 - 0.152072 %i, 0.0518489 + 0.451732 %i,
--    0.362522 - 0.0321337 %i]
--   ,

--   [1.12374 + 1.06765 %i, 0.172759 + 0.0385858 %i, 0.418548 + 0.748083 %i,
--    0.153011 + 0.17522 %i, 0.368555 + 0.0565331 %i, 0.0100542 + 0.140268 %i]
--   ,

--   [0.909985 + 1.76167 %i, - 0.305418 + 0.0624335 %i,
--    0.407884 - 0.0694786 %i, - 0.078547 + 0.0725049 %i,
--    - 0.119334 + 0.128511 %i, - 0.531409 - 0.433531 %i]
--   ]

-- test 17:
--S 38 of 45
invdftsF := nagInverseDFT dftsF ;
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable dftsF
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable dftsF
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 38

--S 39 of 45
invdftsF :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable invdftsF to List Vector Complex 
      Float for value
   invdftsF

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable invdftsF to List Vector Complex 
--R      Float for value
--R   invdftsF
--R
--E 39 
-- [
--   [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
--    0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
--   ,

--   [0.9172 + 0.9089 %i, 0.0644 + 0.3118 %i, 0.6037 + 0.3465 %i,
--    0.643 + 0.6198 %i, 0.0428 + 0.2668 %i, 0.4815 + 0.1614 %i]
--   ,

--   [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.206 + 0.706 %i,
--    0.863 + 0.8652 %i, 0.6967 + 0.919 %i, 0.2792 + 0.3355 %i]
--   ]

-- test 18:
--S 40 of 45 used to work?
nagHermitianInverseDFT dftsE
 
   There are no library operations named nagHermitianInverseDFT 
      Use HyperDoc Browse or issue
                       )what op nagHermitianInverseDFT
      to learn if there is any operation containing " 
      nagHermitianInverseDFT " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianInverseDFT with argument type(s) 
                               Variable dftsE
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianInverseDFT 
--R      Use HyperDoc Browse or issue
--R                       )what op nagHermitianInverseDFT
--R      to learn if there is any operation containing " 
--R      nagHermitianInverseDFT " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianInverseDFT with argument type(s) 
--R                               Variable dftsE
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 40 
-- [
--   [0.38540000000000013, 0.67720000000000025, 0.11380000000000001,
--    0.67510000000000014, 0.63620000000000021, 0.14240000000000003]
--   ,

--   [0.54170000000000018, 0.29830000000000012, 0.1181, 0.72550000000000014,
--    0.86380000000000023, 0.87230000000000019]
--   ,

--   [0.91720000000000035, 0.064399999999999999, 0.60370000000000024,
--    0.64300000000000013, 0.042799999999999991, 0.48150000000000015]
--   ]

-- error tests:

-- test 19:
--S 41 of 45
nagDFT [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i,   _
                0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i,   _
                0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i],  _
        vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i,   _
                0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]]
 

   (10)
   SUB
      nagDFT
  ,
      [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
       0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
  ,
      [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.6967 + 0.919 %i,
       0.2792 + 0.3355 %i]
                                                                 Type: Symbol
--R 
--R
--R   (10)
--R   SUB
--R      nagDFT
--R  ,
--R      [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
--R       0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
--R  ,
--R      [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.6967 + 0.919 %i,
--R       0.2792 + 0.3355 %i]
--R                                                                 Type: Symbol
--E 41

-- test 20:
--S 42 of 45
nagHermitianDFT [vector [0.3854, 0.6751, 0.6362, 0.1424], _
                 vector [0.5417, 0.7255, 0.8638, 0.8723], _
                 vector [0.9172, 0.0428, 0.4815]]
 

   (11)
   SUB
      nagHermitianDFT
  ,
      [0.3854,0.6751,0.6362,0.1424]
  ,
      [0.5417,0.7255,0.8638,0.8723]
  ,
      [0.9172,0.0428,0.4815]
                                                                 Type: Symbol
--R 
--R
--R   (11)
--R   SUB
--R      nagHermitianDFT
--R  ,
--R      [0.3854,0.6751,0.6362,0.1424]
--R  ,
--R      [0.5417,0.7255,0.8638,0.8723]
--R  ,
--R      [0.9172,0.0428,0.4815]
--R                                                                 Type: Symbol
--E 42

-- test 21:
--S 43 of 45 used to work?
badSeqs : List PackedHermitianSequence DoubleFloat
 
 
Daly Bug
   Category, domain or package constructor PackedHermitianSequence is 
      not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is 
--R      not available.
--E 43
--badSeqs := [pHS [0.3854, 0.1138, 0.6751, 0.6362, 0.1424],         _
--            pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
--            pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
-- 
--
--                                                            Type: List Symbol

--S 44  of 45
nagDFT badSeqs
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                              Variable badSeqs
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                              Variable badSeqs
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 44

--S 45 of 45
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 45
)spool 
 
Starts dribbling to negfloats.output (2009/2/17, 17:55:30).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
truncate(-9.6571)
 

   (1)  - 9.0
                                                                  Type: Float
--R 
--R
--R   (1)  - 9.0
--R                                                                  Type: Float
--E 1

--S 2 of 3
fractionPart(-3.432)
 

   (2)  - 0.432
                                                                  Type: Float
--R 
--R
--R   (2)  - 0.432
--R                                                                  Type: Float
--E 2

--S 3 of 3
round(-9.6571)
 

   (3)  - 10.0
                                                                  Type: Float
--R 
--R
--R   (3)  - 10.0
--R                                                                  Type: Float
--E 3
)spool 
 
Starts dribbling to fr2.output (2009/2/17, 17:46:10).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 6
double(x) == x + x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
f := factor(720)
 

         4 2
   (2)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         4 2
--R   (2)  2 3 5
--R                                                       Type: Factored Integer
--E 2

--S 3 of 6
map(double,f)
 
   Compiling function double with type Integer -> Integer 

           4 2
   (3)  2 4 6 10
                                                       Type: Factored Integer
--R 
--R   Compiling function double with type Integer -> Integer 
--R
--R           4 2
--R   (3)  2 4 6 10
--R                                                       Type: Factored Integer
--E 3

--S 4 of 6
makePoly(b) == x + b
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 6
g := map(makePoly,f)
 
   Compiling function makePoly with type Integer -> Polynomial Integer 

                      4       2
   (5)  (x + 1)(x + 2) (x + 3) (x + 5)
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function makePoly with type Integer -> Polynomial Integer 
--R
--R                      4       2
--R   (5)  (x + 1)(x + 2) (x + 3) (x + 5)
--R                                            Type: Factored Polynomial Integer
--E 5

--S 6 of 6
nthFlag(g,1)
 

   (6)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (6)  "nil"
--R                                                       Type: Union("nil",...)
--E 6
)spool 
 
Starts dribbling to fparfrc.output (2009/2/17, 17:46:5).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 16
Fx := FRAC UP(x, FRAC INT)
 

   (1)  Fraction UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 16
f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2)
 

                     36
   (2)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (2)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 2

--S 3 of 16
g := fullPartialFraction f
 

          4       4        --+      - 3%A - 6
   (3)  ----- - ----- +    >        ---------
        x - 2   x + 1      --+              2
                          2         (x - %A)
                        %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          4       4        --+      - 3%A - 6
--R   (3)  ----- - ----- +    >        ---------
--R        x - 2   x + 1      --+              2
--R                          2         (x - %A)
--R                        %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 16
g :: Fx
 

                     36
   (4)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (4)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 4

--S 5 of 16
g5 := D(g, 5)
 

             480        480        --+      2160%A + 4320
   (5)  - -------- + -------- +    >        -------------
                 6          6      --+                7
          (x - 2)    (x + 1)      2           (x - %A)
                                %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R             480        480        --+      2160%A + 4320
--R   (5)  - -------- + -------- +    >        -------------
--R                 6          6      --+                7
--R          (x - 2)    (x + 1)      2           (x - %A)
--R                                %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 16
f5 := D(f, 5)
 

   (6)
                10           9            8            7            6
       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
     + 
                5            4            3           2
       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
  /
        20      19      18      17       16       15       14        13
       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
     + 
            12        11        10        9        8        7        6        5
       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
     + 
           4        3       2
       276x  - 1184x  + 208x  + 192x - 64
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (6)
--R                10           9            8            7            6
--R       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
--R     + 
--R                5            4            3           2
--R       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
--R  /
--R        20      19      18      17       16       15       14        13
--R       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
--R     + 
--R            12        11        10        9        8        7        6        5
--R       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
--R     + 
--R           4        3       2
--R       276x  - 1184x  + 208x  + 192x - 64
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 16
g5::Fx - f5
 

   (7)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (7)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 16
f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)
 

                       6    5
                      x  - x
   (8)  -----------------------------------
         7     6     5     3     2
        x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                       6    5
--R                      x  - x
--R   (8)  -----------------------------------
--R         7     6     5     3     2
--R        x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 16
g := fullPartialFraction f
 

   (9)
      1952       464        32                          179       135
      ----       ---        --                       - ---- %A + ----
      2401       343        49            --+          2401      2401
     ------ + -------- + -------- +       >          ----------------
      x - 2          2          3         --+             x - %A
              (x - 2)    (x - 2)      2
                                    %A  + %A + 1= 0
   + 
                       37        20
                      ---- %A + ----
           --+        1029      1029
           >          --------------
           --+                   2
       2                 (x - %A)
     %A  + %A + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (9)
--R      1952       464        32                          179       135
--R      ----       ---        --                       - ---- %A + ----
--R      2401       343        49            --+          2401      2401
--R     ------ + -------- + -------- +       >          ----------------
--R      x - 2          2          3         --+             x - %A
--R              (x - 2)    (x - 2)      2
--R                                    %A  + %A + 1= 0
--R   + 
--R                       37        20
--R                      ---- %A + ----
--R           --+        1029      1029
--R           >          --------------
--R           --+                   2
--R       2                 (x - %A)
--R     %A  + %A + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 16
g :: Fx - f
 

   (10)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (10)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 10

--S 11 of 16
f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8)
 

             7     5      3
           2x  - 7x  + 26x  + 8x
   (11)  ------------------------
          8     6     4     2
         x  - 5x  + 6x  + 4x  - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             7     5      3
--R           2x  - 7x  + 26x  + 8x
--R   (11)  ------------------------
--R          8     6     4     2
--R         x  - 5x  + 6x  + 4x  - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 11

--S 12 of 16
g := fullPartialFraction f
 

                        1                                            1
                        -                                            -
            --+         2        --+          1          --+         2
   (12)     >        ------ +    >        --------- +    >        ------
            --+      x - %A      --+              3      --+      x - %A
           2                    2         (x - %A)      2
         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R                        1                                            1
--R                        -                                            -
--R            --+         2        --+          1          --+         2
--R   (12)     >        ------ +    >        --------- +    >        ------
--R            --+      x - %A      --+              3      --+      x - %A
--R           2                    2         (x - %A)      2
--R         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 12

--S 13 of 16
g :: Fx - f
 

   (13)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (13)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 13

--S 14 of 16
f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x**15 + 30*x**14 + 36*x**13 + 40*x**12 + 47*x**11 + 46*x**10 + 49*x**9 + 43*x**8 + 38*x**7 + 32*x**6 + 23*x**5 + 19*x**4 + 10*x**3 + 7*x**2 + 2*x + 1)
 

   (14)
      3
     x
  /
        21     20     19     18      17      16      15      14      13      12
       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
     + 
          11      10      9      8      7      6      5      4      3     2
       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
     + 
       1
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (14)
--R      3
--R     x
--R  /
--R        21     20     19     18      17      16      15      14      13      12
--R       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
--R     + 
--R          11      10      9      8      7      6      5      4      3     2
--R       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
--R     + 
--R       1
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 14

--S 15 of 16
g := fullPartialFraction f
 

   (15)
                  1                        1      19
                  - %A                     - %A - --
        --+       2             --+        9      27
        >        ------ +       >          ---------
        --+      x - %A         --+          x - %A
       2                    2
     %A  + 1= 0           %A  + %A + 1= 0
   + 
                       1       1
                      -- %A - --
           --+        27      27
           >          ----------
           --+                 2
       2               (x - %A)
     %A  + %A + 1= 0
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
               96556567040   4   420961732891   3    59101056149   2
            - ------------ %A  + ------------ %A  - ------------ %A
              912390759099       912390759099       912390759099
          + 
              373545875923      529673492498
            - ------------ %A + ------------
              912390759099      912390759099
       /
          x - %A
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
           5580868   4    2024443   3    4321919   2    84614        5070620
        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
          94070601       94070601       94070601       1542141      94070601
        --------------------------------------------------------------------
                                              2
                                      (x - %A)
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
         1610957   4    2763014   3    2016775   2    266953        4529359
        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
        94070601       94070601       94070601       94070601      94070601
        -------------------------------------------------------------------
                                             3
                                     (x - %A)
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (15)
--R                  1                        1      19
--R                  - %A                     - %A - --
--R        --+       2             --+        9      27
--R        >        ------ +       >          ---------
--R        --+      x - %A         --+          x - %A
--R       2                    2
--R     %A  + 1= 0           %A  + %A + 1= 0
--R   + 
--R                       1       1
--R                      -- %A - --
--R           --+        27      27
--R           >          ----------
--R           --+                 2
--R       2               (x - %A)
--R     %A  + %A + 1= 0
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R               96556567040   4   420961732891   3    59101056149   2
--R            - ------------ %A  + ------------ %A  - ------------ %A
--R              912390759099       912390759099       912390759099
--R          + 
--R              373545875923      529673492498
--R            - ------------ %A + ------------
--R              912390759099      912390759099
--R       /
--R          x - %A
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R           5580868   4    2024443   3    4321919   2    84614        5070620
--R        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
--R          94070601       94070601       94070601       1542141      94070601
--R        --------------------------------------------------------------------
--R                                              2
--R                                      (x - %A)
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R         1610957   4    2763014   3    2016775   2    266953        4529359
--R        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
--R        94070601       94070601       94070601       94070601      94070601
--R        -------------------------------------------------------------------
--R                                             3
--R                                     (x - %A)
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 15

--S 16 of 16
g :: Fx - f
 

   (16)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (16)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 16
)spool 
 
Starts dribbling to intaf.output (2009/2/17, 17:46:39).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 20
x**2 / sqrt(a + b*x**3)
 

              2
             x
   (1)  -----------
         +--------+
         |   3
        \|b x  + a
                                                     Type: Expression Integer
--R 
--R
--R              2
--R             x
--R   (1)  -----------
--R         +--------+
--R         |   3
--R        \|b x  + a
--R                                                     Type: Expression Integer
--E 1

--S 2 of 20
integrate(%,x)
 

          +--------+
          |   3
        2\|b x  + a
   (2)  ------------
             3b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +--------+
--R          |   3
--R        2\|b x  + a
--R   (2)  ------------
--R             3b
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 20
x**3 * sqrt(a + b*x**4)
 

           +--------+
         3 |   4
   (3)  x \|b x  + a
                                                     Type: Expression Integer
--R 
--R
--R           +--------+
--R         3 |   4
--R   (3)  x \|b x  + a
--R                                                     Type: Expression Integer
--E 3

--S 4 of 20
integrate(%,x)
 

                   +--------+
            4      |   4
        (b x  + a)\|b x  + a
   (4)  ---------------------
                  6b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +--------+
--R            4      |   4
--R        (b x  + a)\|b x  + a
--R   (4)  ---------------------
--R                  6b
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 20
1/sqrt(1+x**3)
 

            1
   (5)  ---------
         +------+
         | 3
        \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R            1
--R   (5)  ---------
--R         +------+
--R         | 3
--R        \|x  + 1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 20
integrate(%,x)
 

           x
         ++       1
   (6)   |   ---------- d%N
        ++    +-------+
              |  3
             \|%N  + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--R   (6)   |   ---------- d%N
--R        ++    +-------+
--R              |  3
--R             \|%N  + 1
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 20
sqrt(1+x**3)
 

         +------+
         | 3
   (7)  \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +------+
--R         | 3
--R   (7)  \|x  + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 20
integrate(%,x)
 

           x  +-------+
         ++   |  3
   (8)   |   \|%N  + 1 d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +-------+
--R         ++   |  3
--R   (8)   |   \|%N  + 1 d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 20
1/(x * sqrt(1 + x**3))
 

             1
   (9)  ----------
          +------+
          | 3
        x\|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R             1
--R   (9)  ----------
--R          +------+
--R          | 3
--R        x\|x  + 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 20
integrate(%,x)
 

                +------+             +------+
                | 3                  | 3
         - log(\|x  + 1  + 1) + log(\|x  + 1  - 1)
   (10)  -----------------------------------------
                             3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +------+             +------+
--R                | 3                  | 3
--R         - log(\|x  + 1  + 1) + log(\|x  + 1  - 1)
--R   (10)  -----------------------------------------
--R                             3
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 20
x**3/sqrt(1+x**8)
 

              3
             x
   (11)  ---------
          +------+
          | 8
         \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R              3
--R             x
--R   (11)  ---------
--R          +------+
--R          | 8
--R         \|x  + 1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 20
integrate(%,x)
 

                +------+
                | 8         4
           log(\|x  + 1  - x )
   (12)  - -------------------
                    4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +------+
--R                | 8         4
--R           log(\|x  + 1  - x )
--R   (12)  - -------------------
--R                    4
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 20
x/sqrt(1-x**4)
 

              x
   (13)  -----------
          +--------+
          |   4
         \|- x  + 1
                                                     Type: Expression Integer
--R 
--R
--R              x
--R   (13)  -----------
--R          +--------+
--R          |   4
--R         \|- x  + 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 20
integrate(%,x)
 

                 +--------+
                 |   4
                \|- x  + 1  - 1
   (14)  - atan(---------------)
                        2
                       x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +--------+
--R                 |   4
--R                \|- x  + 1  - 1
--R   (14)  - atan(---------------)
--R                        2
--R                       x
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 20
(x+1)/((x-2) * sqrt(1 + x**3))
 

               x + 1
   (15)  ----------------
                 +------+
                 | 3
         (x - 2)\|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R               x + 1
--R   (15)  ----------------
--R                 +------+
--R                 | 3
--R         (x - 2)\|x  + 1
--R                                                     Type: Expression Integer
--E 15

--S 16 of 20
integrate(%,x)
 

                        +------+
                        | 3         3      2
               (6x + 6)\|x  + 1  + x  + 12x  - 6x + 10
           log(---------------------------------------)
                           3     2
                          x  - 6x  + 12x - 8
   (16)  - --------------------------------------------
                                 3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        +------+
--R                        | 3         3      2
--R               (6x + 6)\|x  + 1  + x  + 12x  - 6x + 10
--R           log(---------------------------------------)
--R                           3     2
--R                          x  - 6x  + 12x - 8
--R   (16)  - --------------------------------------------
--R                                 3
--R                                          Type: Union(Expression Integer,...)
--E 16

--S 17 of 20
x**6/sqrt((x**7+1)*(x**7+2))
 

                 6
                x
   (17)  ----------------
          +-------------+
          | 14     7
         \|x   + 3x  + 2
                                                     Type: Expression Integer
--R 
--R
--R                 6
--R                x
--R   (17)  ----------------
--R          +-------------+
--R          | 14     7
--R         \|x   + 3x  + 2
--R                                                     Type: Expression Integer
--E 17

--S 18 of 20
integrate(%,x)
 

                 +-------------+
                 | 14     7          7
           log(2\|x   + 3x  + 2  - 2x  - 3)
   (18)  - --------------------------------
                           7
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-------------+
--R                 | 14     7          7
--R           log(2\|x   + 3x  + 2  - 2x  - 3)
--R   (18)  - --------------------------------
--R                           7
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 20
sqrt(1 + sqrt(1 + x))
 

          +------------+
          | +-----+
   (19)  \|\|x + 1  + 1
                                                     Type: Expression Integer
--R 
--R
--R          +------------+
--R          | +-----+
--R   (19)  \|\|x + 1  + 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 20
integrate(%,x)
 

                               +------------+
            +-----+            | +-----+
         (4\|x + 1  + 12x + 4)\|\|x + 1  + 1
   (20)  ------------------------------------
                          15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +------------+
--R            +-----+            | +-----+
--R         (4\|x + 1  + 12x + 4)\|\|x + 1  + 1
--R   (20)  ------------------------------------
--R                          15
--R                                          Type: Union(Expression Integer,...)
--E 20
)spool 
 
Starts dribbling to sincosex.output (2009/2/17, 18:0:23).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 1
sinCosExpand := rule
  sin(-x)    == - sin(x)
  cos(-x)    == cos(x)
  sin(x + y) == sin(x) * cos(y) + sin(y) * cos(x)
  cos(x + y) == cos(x) * cos(y) - sin(x) * sin(y)
  sin((n | integer? n and n > 1) * x) ==_
       sin(x) * cos((n-1)*x) + sin((n-1)*x) * cos(x)
  cos((n | integer? n and n > 1) * x) ==_
       cos(x) * cos((n-1)*x) - sin(x) * sin((n-1)*x)
 

   (1)
   {- %B sin(x) == - %B sin(x), cos(x) == cos(x),
    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)
--R   {- %B sin(x) == - %B sin(x), cos(x) == cos(x),
--R    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
--R    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
--R    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 1
)spool 
 
Starts dribbling to segbind.output (2009/2/17, 18:0:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 6
x = a..b
 

   (1)  x= a..b
                                                  Type: SegmentBinding Symbol
--R 
--R
--R   (1)  x= a..b
--R                                                  Type: SegmentBinding Symbol
--E 1

--S 2 of 6
sum(i**2, i = 0..n)
 

          3     2
        2n  + 3n  + n
   (2)  -------------
              6
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          3     2
--R        2n  + 3n  + n
--R   (2)  -------------
--R              6
--R                                            Type: Fraction Polynomial Integer
--E 2

--S 3 of 6
draw(x**2, x = -2..2)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (3)  TwoDimensionalViewport: "x*x"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (3)  TwoDimensionalViewport: "x*x"
--R                                                 Type: TwoDimensionalViewport
--E 3

--S 4 of 6
sb := y = 1/2..3/2
 

            1    3
   (4)  y= (-)..(-)
            2    2
                                        Type: SegmentBinding Fraction Integer
--R 
--R
--R            1    3
--R   (4)  y= (-)..(-)
--R            2    2
--R                                        Type: SegmentBinding Fraction Integer
--E 4

--S 5 of 6
variable(sb)
 

   (5)  y
                                                                 Type: Symbol
--R 
--R
--R   (5)  y
--R                                                                 Type: Symbol
--E 5

--S 6 of 6
segment(sb)
 

         1    3
   (6)  (-)..(-)
         2    2
                                               Type: Segment Fraction Integer
--R 
--R
--R         1    3
--R   (6)  (-)..(-)
--R         2    2
--R                                               Type: Segment Fraction Integer
--E 6
)spool 
 
Starts dribbling to alist.output (2009/2/17, 17:43:45).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 10
Data := Record(monthsOld : Integer, gender : String)
 

   (1)  Record(monthsOld: Integer,gender: String)
                                                                 Type: Domain
--R 
--R
--R   (1)  Record(monthsOld: Integer,gender: String)
--R                                                                 Type: Domain
--E 1

--S 2 of 10
al : AssociationList(String,Data)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 10
al := table()
 

   (3)  table()
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (3)  table()
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 3

--S 4 of 10
al."bob" := [407,"male"]$Data
 

   (4)  [monthsOld= 407,gender= "male"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (4)  [monthsOld= 407,gender= "male"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 4

--S 5 of 10
al."judith" := [366,"female"]$Data
 

   (5)  [monthsOld= 366,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (5)  [monthsOld= 366,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 5

--S 6 of 10
al."katie" := [24,"female"]$Data
 

   (6)  [monthsOld= 24,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (6)  [monthsOld= 24,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 6

--S 7 of 10
al."smokie" := [200,"female"]$Data
 

   (7)  [monthsOld= 200,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (7)  [monthsOld= 200,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 7

--S 8 of 10
al
 

   (8)
   table
      "smokie"= [monthsOld= 200,gender= "female"]
  ,
      "katie"= [monthsOld= 24,gender= "female"]
  ,
      "judith"= [monthsOld= 366,gender= "female"]
  ,
      "bob"= [monthsOld= 407,gender= "male"]
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (8)
--R   table
--R      "smokie"= [monthsOld= 200,gender= "female"]
--R  ,
--R      "katie"= [monthsOld= 24,gender= "female"]
--R  ,
--R      "judith"= [monthsOld= 366,gender= "female"]
--R  ,
--R      "bob"= [monthsOld= 407,gender= "male"]
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 8

--S 9 of 10
al."katie" := [23,"female"]$Data
 

   (9)  [monthsOld= 23,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (9)  [monthsOld= 23,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 9

--S 10 of 10 of 10
delete!(al,1)
 

   (10)
   table
      "katie"= [monthsOld= 23,gender= "female"]
  ,
      "judith"= [monthsOld= 366,gender= "female"]
  ,
      "bob"= [monthsOld= 407,gender= "male"]
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (10)
--R   table
--R      "katie"= [monthsOld= 23,gender= "female"]
--R  ,
--R      "judith"= [monthsOld= 366,gender= "female"]
--R  ,
--R      "bob"= [monthsOld= 407,gender= "male"]
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 10 
)spool
 
Starts dribbling to asec.output (2009/2/17, 17:43:48).
)set message test off
 
)set message auto off
 
)set break resume
 
digits(22)
 

   (1)  20
                                                        Type: PositiveInteger
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 10
asec(-2.0)
 

   (1)  2.0943951023 9319549230 8
                                                                  Type: Float
--R
--R   (1)  2.0943951023 9319549230 8
--R                                                                  Type: Float
--E 1

--S 2 of 10
asec(-1.5)
 

   (2)  2.3005239830 2186298268 6
                                                                  Type: Float
--R
--R   (2)  2.3005239830 2186298268 6
--R                                                                  Type: Float
--E 2

--S 3 of 10
asec(-1.0)
 

   (3)  3.1415926535 8979323846 3
                                                                  Type: Float
--R
--R   (3)  3.1415926535 8979323846 3
--R                                                                  Type: Float
--E 3

--S 4 of 10
asec(-0.5)
 
 
   >> Error detected within library code:
   acos: argument > 1 in magnitude

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   acos: argument > 1 in magnitude
--R
--R   Continuing to read the file...
--R
--E 4

--S 5 of 10
asec(-0.0)
 
 
   >> Error detected within library code:
   asec: no reciprocal

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   asec: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 5

--S 6 of 10
asec(0.0)
 
 
   >> Error detected within library code:
   asec: no reciprocal

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   asec: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 6

--S 7 of 10
asec(0.5)
 
 
   >> Error detected within library code:
   acos: argument > 1 in magnitude

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   acos: argument > 1 in magnitude
--R
--R   Continuing to read the file...
--R
--E 7

--S 8 of 10
asec(1.0)
 

   (4)  0.0
                                                                  Type: Float
--R
--R   (4)  0.0
--R                                                                  Type: Float
--E 8

--S 9 of 10
asec(1.5)
 

   (5)  0.8410686705 6793025577 652
                                                                  Type: Float
--R
--R   (5)  0.8410686705 6793025577 652
--R                                                                  Type: Float
--E 9

--S 10 of 10
asec(2.0)
 

   (6)  1.0471975511 9659774615 42
                                                                  Type: Float
--R
--R   (6)  1.0471975511 9659774615 42
--R                                                                  Type: Float
--E 10
)spool 
 
Starts dribbling to torus.output (2009/2/17, 18:1:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
f(x:SF):SF == x
 
   Function declaration f : DoubleFloat -> DoubleFloat has been added 
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : DoubleFloat -> DoubleFloat has been added 
--R      to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 3
torus : TUBE := tubePlot(sin t,cos t,0,f,0..2*%pi,0.5::SF,12,"closed")
 
 
Daly Bug
   Although TubePlot is the name of a constructor, a full type must be 
      specified in the context you have used it. Issue )show TubePlot 
      for more information.
--R 
--R 
--RDaly Bug
--R   Although TubePlot is the name of a constructor, a full type must be 
--R      specified in the context you have used it. Issue )show TubePlot 
--R      for more information.
--E 2

--S 3 of 3
makeViewport3D(torus,"torus")$VIEW3D
 
   There are 2 exposed and 0 unexposed library operations named 
      makeViewport3D having 2 argument(s) but none was determined to be
      applicable. Use HyperDoc Browse, or issue
                         )display op makeViewport3D
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      makeViewport3D with argument type(s) 
                                   Symbol
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 2 exposed and 0 unexposed library operations named 
--R      makeViewport3D having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                         )display op makeViewport3D
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      makeViewport3D with argument type(s) 
--R                                   Symbol
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 3
)spool 
 
Starts dribbling to pascal.output (2009/2/17, 17:56:2).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 10
)set fun cache all
 
   In general, interpreter functions will cache all values.
--R 
--R   In general, interpreter functions will cache all values.
--E 1

--S 2 of 10
p(m,n | m=1)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 10
p(m,n | m=n)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 10
p(i,n | 1 < i and i < n) == p(i-1,n-1) + p(i,n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 10
p(2,3)
 
   Compiling function p with type (Integer,Integer) -> PositiveInteger 
   p will cache all previously computed values.

   (4)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling function p with type (Integer,Integer) -> PositiveInteger 
--R   p will cache all previously computed values.
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
pn(n) == [p(i,n) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
pn(50)
 
   Compiling function pn with type PositiveInteger -> List 
      PositiveInteger 
   pn will cache all previously computed values.

   (6)
   [1, 49, 1176, 18424, 211876, 1906884, 13983816, 85900584, 450978066,
    2054455634, 8217822536, 29135916264, 92263734836, 262596783764,
    675248872536, 1575580702584, 3348108992991, 6499270398159, 11554258485616,
    18851684897584, 28277527346376, 39049918716424, 49699896548176,
    58343356817424, 63205303218876, 63205303218876, 58343356817424,
    49699896548176, 39049918716424, 28277527346376, 18851684897584,
    11554258485616, 6499270398159, 3348108992991, 1575580702584, 675248872536,
    262596783764, 92263734836, 29135916264, 8217822536, 2054455634, 450978066,
    85900584, 13983816, 1906884, 211876, 18424, 1176, 49, 1]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function pn with type PositiveInteger -> List 
--R      PositiveInteger 
--R   pn will cache all previously computed values.
--R
--R   (6)
--R   [1, 49, 1176, 18424, 211876, 1906884, 13983816, 85900584, 450978066,
--R    2054455634, 8217822536, 29135916264, 92263734836, 262596783764,
--R    675248872536, 1575580702584, 3348108992991, 6499270398159, 11554258485616,
--R    18851684897584, 28277527346376, 39049918716424, 49699896548176,
--R    58343356817424, 63205303218876, 63205303218876, 58343356817424,
--R    49699896548176, 39049918716424, 28277527346376, 18851684897584,
--R    11554258485616, 6499270398159, 3348108992991, 1575580702584, 675248872536,
--R    262596783764, 92263734836, 29135916264, 8217822536, 2054455634, 450978066,
--R    85900584, 13983816, 1906884, 211876, 18424, 1176, 49, 1]
--R                                                   Type: List PositiveInteger
--E 7

--S 8 of 10
pk n == [pn(i) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 10
pk 10
 
   Compiling function pk with type PositiveInteger -> List List 
      PositiveInteger 
   pk will cache all previously computed values.

   (8)
   [[1], [1,1], [1,2,1], [1,3,3,1], [1,4,6,4,1], [1,5,10,10,5,1],
    [1,6,15,20,15,6,1], [1,7,21,35,35,21,7,1], [1,8,28,56,70,56,28,8,1],
    [1,9,36,84,126,126,84,36,9,1]]
                                              Type: List List PositiveInteger
--R 
--R   Compiling function pk with type PositiveInteger -> List List 
--R      PositiveInteger 
--R   pk will cache all previously computed values.
--R
--R   (8)
--R   [[1], [1,1], [1,2,1], [1,3,3,1], [1,4,6,4,1], [1,5,10,10,5,1],
--R    [1,6,15,20,15,6,1], [1,7,21,35,35,21,7,1], [1,8,28,56,70,56,28,8,1],
--R    [1,9,36,84,126,126,84,36,9,1]]
--R                                              Type: List List PositiveInteger
--E 9

--S 10 of 10
)set fun cache 10
 
   In general, interpreter functions will cache the last 10 values.
--R 
--R   In general, interpreter functions will cache the last 10 values.
--E 10
)spool 
 
Starts dribbling to bug9057.output (2009/2/17, 17:44:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 9
g:=operator 'g
 

   (1)  g
                                                          Type: BasicOperator
--R 
--R
--R   (1)  g
--R                                                          Type: BasicOperator
--E 1

--S 2 of 9
f==n+->sum(g(j),j=1..n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 9
f(1)
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

   (3)  g(1)
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R   (3)  g(1)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 9
f==n+->product(sum(1/i,i=1..j),j=1..n)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
--R 
--R   Compiled code for f has been cleared.
--R   1 old definition(s) deleted for function or rule f 
--R                                                                   Type: Void
--E 4

--S 5 of 9
f(1)
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

   (5)  1
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R   (5)  1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 9
f==n+->product(product(1/i,i=1..j),j=1..n)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
--R 
--R   Compiled code for f has been cleared.
--R   1 old definition(s) deleted for function or rule f 
--R                                                                   Type: Void
--E 6

--S 7 of 9
f(1)
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

   (7)  1
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R   (7)  1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 9
f==n+->sum(sum(1/i,i=1..j),j=1..n)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
--R 
--R   Compiled code for f has been cleared.
--R   1 old definition(s) deleted for function or rule f 
--R                                                                   Type: Void
--E 8

--S 9 of 9
f(1)
 
   There are 6 exposed and 2 unexposed library operations named sum 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op sum
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named sum 
      with argument type(s) 
            Union(Fraction Polynomial Integer,Expression Integer)
                       SegmentBinding PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.

   (9)  1
                                                     Type: Expression Integer
--R 
--R   There are 6 exposed and 2 unexposed library operations named sum 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op sum
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named sum 
--R      with argument type(s) 
--R            Union(Fraction Polynomial Integer,Expression Integer)
--R                       SegmentBinding PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (9)  1
--R                                                     Type: Expression Integer
--E 9
)spool
 
Starts dribbling to pmint.output (2009/2/17, 17:56:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 29
f:=(x^7-24*x^4-4*x^2+8*x-8)/(x^8+6*x^6+12*x^4+8*x^2)
 

         7      4     2
        x  - 24x  - 4x  + 8x - 8
   (1)  ------------------------
           8     6      4     2
          x  + 6x  + 12x  + 8x
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         7      4     2
--R        x  - 24x  - 4x  + 8x - 8
--R   (1)  ------------------------
--R           8     6      4     2
--R          x  + 6x  + 12x  + 8x
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 29
g:=integrate(f,x)
 

          5     3                 3     2
        (x  + 4x  + 4x)log(x) + 3x  + 8x  + 6x + 4
   (2)  ------------------------------------------
                        5     3
                       x  + 4x  + 4x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          5     3                 3     2
--R        (x  + 4x  + 4x)log(x) + 3x  + 8x  + 6x + 4
--R   (2)  ------------------------------------------
--R                        5     3
--R                       x  + 4x  + 4x
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 29
differentiate(g,x)
 

         7      4     2
        x  - 24x  - 4x  + 8x - 8
   (3)  ------------------------
           8     6      4     2
          x  + 6x  + 12x  + 8x
                                                     Type: Expression Integer
--R 
--R
--R         7      4     2
--R        x  - 24x  - 4x  + 8x - 8
--R   (3)  ------------------------
--R           8     6      4     2
--R          x  + 6x  + 12x  + 8x
--R                                                     Type: Expression Integer
--E 3

)clear all
 
   All user variables and function definitions have been cleared.

--S 4 of 29
f:=(x-tan(x))/tan(x)^2 + tan(x)
 

              3
        tan(x)  - tan(x) + x
   (1)  --------------------
                     2
               tan(x)
                                                     Type: Expression Integer
--R 
--R
--R              3
--R        tan(x)  - tan(x) + x
--R   (1)  --------------------
--R                     2
--R               tan(x)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 29
g:=integrate(f,x)
 

                        2         2
        tan(x)log(tan(x)  + 1) - x tan(x) - 2x
   (2)  --------------------------------------
                        2tan(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2         2
--R        tan(x)log(tan(x)  + 1) - x tan(x) - 2x
--R   (2)  --------------------------------------
--R                        2tan(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 29
differentiate(g,x)
 

              3
        tan(x)  - tan(x) + x
   (3)  --------------------
                     2
               tan(x)
                                                     Type: Expression Integer
--R 
--R
--R              3
--R        tan(x)  - tan(x) + x
--R   (3)  --------------------
--R                     2
--R               tan(x)
--R                                                     Type: Expression Integer
--E 6

)clear all
 
   All user variables and function definitions have been cleared.

--S 7 of 29
f:=(1+x+x*exp(x))*(x+log(x)+exp(x)-1)/(x+log(x)+exp(x))^2/x
 

              x                       x 2     2       x    2
         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
   (1)  ---------------------------------------------------------
                2         x     2               x 2     2  x    3
        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R              x                       x 2     2       x    2
--R         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
--R   (1)  ---------------------------------------------------------
--R                2         x     2               x 2     2  x    3
--R        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 7

--S 8 of 29
g:=integrate(f,x)
 

                    x                    x
        (log(x) + %e  + x)log(log(x) + %e  + x) + 1
   (2)  -------------------------------------------
                                 x
                      log(x) + %e  + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    x                    x
--R        (log(x) + %e  + x)log(log(x) + %e  + x) + 1
--R   (2)  -------------------------------------------
--R                                 x
--R                      log(x) + %e  + x
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 29
differentiate(g,x)
 

              x                       x 2     2       x    2
         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
   (3)  ---------------------------------------------------------
                2         x     2               x 2     2  x    3
        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R              x                       x 2     2       x    2
--R         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
--R   (3)  ---------------------------------------------------------
--R                2         x     2               x 2     2  x    3
--R        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 9

)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 29
f:=exp(-x^2)+erf(x)/(erf(x)^3-erf(x)^2-erf(x)+1)
 

                                             2
               3         2                - x
        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
   (1)  -----------------------------------------------
                       3         2
                 erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R                                             2
--R               3         2                - x
--R        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
--R   (1)  -----------------------------------------------
--R                       3         2
--R                 erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 29 
g:=integrate(f,x)
 

                                                      2
           x         3          2                 - %G
         ++  (erf(%G)  - erf(%G)  - erf(%G) + 1)%e      + erf(%G)
   (2)   |   ---------------------------------------------------- d%G
        ++                    3          2
                       erf(%G)  - erf(%G)  - erf(%G) + 1
                                          Type: Union(Expression Integer,...)
--R
--R                                                      2
--I           x         3          2                 - %G
--I         ++  (erf(%G)  - erf(%G)  - erf(%G) + 1)%e      + erf(%G)
--I   (2)   |   ---------------------------------------------------- d%G
--R        ++                    3          2
--I                       erf(%G)  - erf(%G)  - erf(%G) + 1
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 29
differentiate(g,x)
 

                                             2
               3         2                - x
        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
   (3)  -----------------------------------------------
                       3         2
                 erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R
--R                                             2
--R               3         2                - x
--R        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
--R   (3)  -----------------------------------------------
--R                       3         2
--R                 erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 12

)clear all
 
   All user variables and function definitions have been cleared.

--S 13 of 29
f:=(exp(-x^2)+erf(x))/(erf(x)^3-erf(x)^2-erf(x)+1)
 

                     2
                  - x
                %e     + erf(x)
   (1)  ------------------------------
              3         2
        erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R                     2
--R                  - x
--R                %e     + erf(x)
--R   (1)  ------------------------------
--R              3         2
--R        erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 29 used to work!
g:=integrate(f,x)
 

                           2
           x           - %G
         ++          %e      + erf(%G)
   (2)   |   --------------------------------- d%G
        ++          3          2
             erf(%G)  - erf(%G)  - erf(%G) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           2
--I           x           - %G
--I         ++          %e      + erf(%G)
--I   (3)   |   --------------------------------- d%G
--R        ++          3          2
--I             erf(%G)  - erf(%G)  - erf(%G) + 1
--R                                          Type: Union(Expression Integer,...)
--E 14
-- should be:
--    1   sqrt(%pi)     1                           1
-- -  - ------------  - - sqrt(%pi) log(erf(x)+1) + - sqrt(%pi) log(erf(x)-1)
--    4  erf(x) - 1     8                           8

--S 15 of 29
differentiate(g,x)
 

                     2
                  - x
                %e     + erf(x)
   (3)  ------------------------------
              3         2
        erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R
--R                     2
--R                  - x
--R                %e     + erf(x)
--R   (3)  ------------------------------
--R              3         2
--R        erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 15

)clear all
 
   All user variables and function definitions have been cleared.
 
-- Axiom does not have a 2 argument form of the airyAi function
--  f:=(x-airyAi(x)*airyAi(1,x))/(x^2-airyAi(x)^2)
--it has the integral
--R
--R  1                    1
--R  - log(x+airyAi(x)) + - log(x-airyAi(x))
--R  2                    2


--S 16 of 29 will certainly fail
f:=(x-airyAi(x))/(x^2-airyAi(x)^2)
 

              1
   (1)  -------------
        airyAi(x) + x
                                                     Type: Expression Integer
--R
--R              1
--R   (1)  -------------
--R        airyAi(x) + x
--R                                                     Type: Expression Integer
--E 16

--S 17 of 29 will certainly fail
g:=integrate(f,x)
 

           x
         ++         1
   (2)   |   --------------- d%G
        ++   airyAi(%G) + %G
                                          Type: Union(Expression Integer,...)
--R
--R           x
--R         ++         1
--R   (2)   |   --------------- d%G
--R        ++   airyAi(%G) + %G
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 29
differentiate(g,x)
 

              1
   (3)  -------------
        airyAi(x) + x
                                                     Type: Expression Integer
--R
--R              1
--R   (3)  -------------
--R        airyAi(x) + x
--R                                                     Type: Expression Integer
--E 18

)clear all
 
   All user variables and function definitions have been cleared.

--S 19 of 29
f:=x^2*airyAi(x)
 

         2
   (1)  x airyAi(x)
                                                     Type: Expression Integer
--R 
--R
--R         2
--R   (1)  x airyAi(x)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 29 used to work
g:=integrate(f,x)
 

           x
         ++    2
   (2)   |   %G airyAi(%G)d%G
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    2
--I   (2)   |   %G airyAi(%G)d%G
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 20
-- should be:
--  -airyAi(x) + airyAi(1,x) x

--S 21 of 29
differentiate(g,x)
 

         2
   (3)  x airyAi(x)
                                                     Type: Expression Integer
--R
--R         2
--R   (3)  x airyAi(x)
--R                                                     Type: Expression Integer
--E 21

)clear all
 
   All user variables and function definitions have been cleared.

--S 22 of 29
f:=besselJ(y+1,x)/besselJ(y,x)
 

        besselJ(y + 1,x)
   (1)  ----------------
          besselJ(y,x)
                                                     Type: Expression Integer
--R 
--R
--R        besselJ(y + 1,x)
--R   (1)  ----------------
--R          besselJ(y,x)
--R                                                     Type: Expression Integer
--E 22

--S 23 of 29 used to work
g:=integrate(f,x)
 

           x
         ++  besselJ(y + 1,%G)
   (2)   |   ----------------- d%G
        ++     besselJ(y,%G)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  besselJ(y + 1,%G)
--I   (2)   |   ----------------- d%G
--I        ++     besselJ(y,%G)
--R                                          Type: Union(Expression Integer,...)
--E 23
-- should be:
--  y log(x) - log(besselJ(y,x))

--S 24 of 29
differentiate(g,x)
 

        besselJ(y + 1,x)
   (3)  ----------------
          besselJ(y,x)
                                                     Type: Expression Integer
--R
--R        besselJ(y + 1,x)
--R   (3)  ----------------
--R          besselJ(y,x)
--R                                                     Type: Expression Integer
--E 24

)clear all
 
   All user variables and function definitions have been cleared.


-- Axiom does not have Maple's normal function
--S 25 of 29 used to work
--f:=normal(y*besselJ(y,x)/x - besselJ(y+1,x))
f:=y*besselJ(y,x)/x - besselJ(y+1,x)
 

        - x besselJ(y + 1,x) + y besselJ(y,x)
   (1)  -------------------------------------
                          x
                                                     Type: Expression Integer
--R
--R        - x besselJ(y + 1,x) + y besselJ(y,x)
--R   (1)  -------------------------------------
--R                          x
--R                                                     Type: Expression Integer
--E 25

--S 26 of 29
g:=integrate(f,x)
 

           x
         ++  - %G besselJ(y + 1,%G) + y besselJ(y,%G)
   (2)   |   ---------------------------------------- d%G
        ++                      %G
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++  - %G besselJ(y + 1,%G) + y besselJ(y,%G)
--I   (2)   |   ---------------------------------------- d%G
--I        ++                      %G
--R                                          Type: Union(Expression Integer,...)
--E 26

--S 27 of 29
differentiate(g,x)
 

        - x besselJ(y + 1,x) + y besselJ(y,x)
   (3)  -------------------------------------
                          x
                                                     Type: Expression Integer
--R
--R        - x besselJ(y + 1,x) + y besselJ(y,x)
--R   (3)  -------------------------------------
--R                          x
--R                                                     Type: Expression Integer
--E 27
)clear all
 
   All user variables and function definitions have been cleared.

--S 28 of 29 used to work
f:=WhittakerW(u+1,n,x)/(WhittakerW(u,n,x)*x)
 
   There are no library operations named WhittakerW 
      Use HyperDoc Browse or issue
                             )what op WhittakerW
      to learn if there is any operation containing " WhittakerW " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      WhittakerW with argument type(s) 
                             Polynomial Integer
                                 Variable n
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named WhittakerW 
--R      Use HyperDoc Browse or issue
--R                             )what op WhittakerW
--R      to learn if there is any operation containing " WhittakerW " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      WhittakerW with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable n
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 28

-- Axiom does not implement WhittakerW
-- should be:
--  Whittaker(u+1,n,x)
--  ------------------
--  Whittaker(u,n,x) x

-- of 29 used to work
--integrate(f,x)
-- 22
-- should be:
--  x
--  -  - u log(x) - log(WhattakerW(u,n,x))
--  2

)clear all
 
   All user variables and function definitions have been cleared.

-- Axiom does not implement LambertW
--S 29 of 29 used to work
f:=LambertW(x)
 
   There are no library operations named LambertW 
      Use HyperDoc Browse or issue
                              )what op LambertW
      to learn if there is any operation containing " LambertW " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      LambertW with argument type(s) 
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named LambertW 
--R      Use HyperDoc Browse or issue
--R                              )what op LambertW
--R      to learn if there is any operation containing " LambertW " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      LambertW with argument type(s) 
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 29

-- of 29 used to work
-- g:=integrate(f,x)
-- 24
-- should be:
--    2             2  2                2
--   x + LambertW(x)  x  - LambertW(x) x
--   ------------------------------------
--          x LambertW(x)

-- of 29 used to work
-- integrate(sin(LambertW(x)),x)
-- 25
--should be:
-- +-                                                  -+
-- |                                     2              |
-- |                    +-             -+               |
-- |  1                 | 1             |  2            |
-- |  - LambertW(x) tan | - LambertW(x) | x   +         |
-- |  2                 | 2             |               |
-- |                    +-             -+               |
-- |                                                    |
-- |                  +-             -+                 |
-- |                  | 1             |  2              |
-- |  LambertW(x) tan | - LambertW(x) | x  +            |
-- |                  | 2             |                 |
-- |                  +-             -+                 |
-- |                                                    |
-- |      +-             -+                             |
-- |      | 1             |  2      1              2    |
-- |  tan | - LambertW(x) | x  -    - LambertW(x) x     |
-- |      | 2             |         2                   |
-- |      +-             -+                             |
-- +-                                                  -+
-- ------------------------------------------------------
--                  +-                         2 -+
--                  |         +-             -+   |
--                  |         | 1             |   |
--    x LambertW(x) | 1 + tan | - LambertW(x) |   |
--                  |         | 2             |   |
--                  |         +-             -+   |
--                  +-                           -+

-- of 29 used to work
--f:=((x^2+2)*LambertW(x^2)^2+x^2*(2*LambertW(x^2)+1))/(x*(1+LambertW(x^2)^3))
-- 26
--should be:
--                       2
--    2                2      2              2
--  (x  + 2) LambertW(x )  + x  (2 LambertW(x ) + 1)
--  ------------------------------------------------
--                               3
--                            2  
--           x (1 + LambertW(x ))

-- of 29 used to work
--integrate(f,x)
-- 27
--should be:
--                 2                    4
--1  4           2     4          2    x              2   2    2           2
--- x  LambertW(x ) + x LambertW(x ) + -- + LambertW(x ) x  + x  LambertW(x )
--2                                    2
-----------------------------------------------------------------------------
--                                              2
--              2          2                 2
--             x LambertW(x ) (1 + LambertW(x ))
--
--  +
--                     2
--   log(1 + LambertW(x ))

-- of 29 used to work
--f:=(2*LambertW(x^2)*cos(LambertW(x^2))*(a*x+LambertW(x^2))+a*x*(1+LambertW(x^2)) + 2*LambertW(x^2))/((1+LambertW(x^2))*(a*x+LambertW(x^2))*x)
--
-- 28
--+-                                                       -+
--|                                                         |
--|             2                2                    2     |
--| 2 LambertW(x ) cos(LambertW(x )) (a x + LambertW(x )) + |
--|                                                         |
--|                   2                 2                   |
--| a x (1 + LambertW(x )) + 2 LambertW(x )                 |
--|                                                         |
--+-                                                       -+
-------------------------------------------------------------
--                2                 2
-- (1 + LambertW(x ))(a x+LambertW(x )) x
--

-- 29 of 29 used to work
integrate(f,x)
 

   (1)  f x
                                            Type: Polynomial Fraction Integer
--
-- 29
--   
--        +-              -+
--        | 1           2  |
--  2 tan | - LambertW(x ) |
--        | 2              |
--        +-              -+                          2
--  --------------------------- + log(a x + LambertW(x ))
--                            2
--          +-              -+
--          | 1           2  |
--  1 + tan | - LambertW(x ) |
--          | 2              |
--          +-              -+
--
--
)spool 
 
Starts dribbling to perm.output (2009/2/17, 17:56:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 51
x : List List PrimeField 29 :=
 [[23,19,7,9,12,11,15],[22,4,14,18,2,5,8],[21,20,10,16,13,6,17]]
 

   (1)  [[23,19,7,9,12,11,15],[22,4,14,18,2,5,8],[21,20,10,16,13,6,17]]
                                                Type: List List PrimeField 29
--R 
--R
--R   (1)  [[23,19,7,9,12,11,15],[22,4,14,18,2,5,8],[21,20,10,16,13,6,17]]
--R                                                Type: List List PrimeField 29
--E 1

--S 2 of 51
px : PERM PrimeField 29 := x
 

   (2)  (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (2)  (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
--R                                              Type: Permutation PrimeField 29
--E 2

--S 3 of 51
w : List PrimeField 29 :=
 [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
 

   (3)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
                                                     Type: List PrimeField 29
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
--R                                                     Type: List PrimeField 29
--E 3

--S 4 of 51
pw : PERM PrimeField 29 := cycle w
 

   (4)  (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (4)  (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
--R                                              Type: Permutation PrimeField 29
--E 4

--S 5 of 51
k : List List PrimeField 29 :=
 [[23,24],[22,16],[21,9],[20,19],[18,12],[17,14],[15,7],[10,6]]
 

   (5)  [[23,24],[22,16],[21,9],[20,19],[18,12],[17,14],[15,7],[10,6]]
                                                Type: List List PrimeField 29
--R 
--R
--R   (5)  [[23,24],[22,16],[21,9],[20,19],[18,12],[17,14],[15,7],[10,6]]
--R                                                Type: List List PrimeField 29
--E 5

--S 6 of 51
pk : PERM PrimeField 29 := cycles k
 

   (6)  (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (6)  (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
--R                                              Type: Permutation PrimeField 29
--E 6

--S 7 of 51
pw*pk
 

   (7)  (13 14 18)(8 9 22 17 15)(1 2 3 4 5 6 11 12 19 21 10 7 16 23 24)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (7)  (13 14 18)(8 9 22 17 15)(1 2 3 4 5 6 11 12 19 21 10 7 16 23 24)
--R                                              Type: Permutation PrimeField 29
--E 7

--S 8 of 51
px**3
 

   (8)  (2 22 18 8 14 5 4)(6 20 13 21 16 17 10)(7 11 19 12 23 9 15)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (8)  (2 22 18 8 14 5 4)(6 20 13 21 16 17 10)(7 11 19 12 23 9 15)
--R                                              Type: Permutation PrimeField 29
--E 8

--S 9 of 51
inv px
 

   (9)  (2 18 14 4 22 8 5)(6 13 16 10 20 21 17)(7 19 23 15 11 12 9)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (9)  (2 18 14 4 22 8 5)(6 13 16 10 20 21 17)(7 19 23 15 11 12 9)
--R                                              Type: Permutation PrimeField 29
--E 9

--S 10 of 51
eval(px,17::PrimeField(29))
 

   (10)  21
                                                          Type: PrimeField 29
--R 
--R
--R   (10)  21
--R                                                          Type: PrimeField 29
--E 10

--S 11 of 51
commutator(pk,pw)
 

   (11)  (5 21 7 15 9)(6 17 11 14 10)(8 19 12 18 20)(13 22 23 24 16)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (11)  (5 21 7 15 9)(6 17 11 14 10)(8 19 12 18 20)(13 22 23 24 16)
--R                                              Type: Permutation PrimeField 29
--E 11

--S 12 of 51
orbit(px,11::PrimeField(29))
 

   (12)  {11,15,23,19,7,9,12}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (12)  {11,15,23,19,7,9,12}
--R                                                      Type: Set PrimeField 29
--E 12

--S 13 of 51
movedPoints(pk)
 

   (13)  {16,22,19,20,14,17,6,10,15,7,18,12,21,9,23,24}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (13)  {16,22,19,20,14,17,6,10,15,7,18,12,21,9,23,24}
--R                                                      Type: Set PrimeField 29
--E 13

--S 14 of 51
gp1 : PERMGRP PrimeField 29 := [ px , pk ]
 

   (14)
   <
       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
    ,
       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
     >
                                         Type: PermutationGroup PrimeField 29
--R 
--R
--R   (14)
--R   <
--R       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
--R    ,
--R       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
--R     >
--R                                         Type: PermutationGroup PrimeField 29
--E 14

--S 15 of 51
gp2 : PERMGRP PrimeField 29 := [ pw , px ]
 

   (15)
   <
       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
    ,
       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
     >
                                         Type: PermutationGroup PrimeField 29
--R 
--R
--R   (15)
--R   <
--R       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
--R    ,
--R       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
--R     >
--R                                         Type: PermutationGroup PrimeField 29
--E 15

--S 16 of 51
gp3 : PERMGRP PrimeField 29 := [ pw , pk ]
 

   (16)
   <
       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
    ,
       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
     >
                                         Type: PermutationGroup PrimeField 29
--R 
--R
--R   (16)
--R   <
--R       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
--R    ,
--R       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
--R     >
--R                                         Type: PermutationGroup PrimeField 29
--E 16

--S 17 of 51
order gp1
 

   (17)  443520
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  443520
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 51
order gp2
 

   (18)  10200960
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  10200960
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 51
order gp3
 

   (19)  244823040
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  244823040
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 51
(m1,m2,m3,m4): Matrix PrimeField 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 51
m1 := [[1,1,0],[0,1,0],[0,0,1]]
 

         +1  1  0+
         |       |
   (21)  |0  1  0|
         |       |
         +0  0  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  1  0+
--R         |       |
--R   (21)  |0  1  0|
--R         |       |
--R         +0  0  1+
--R                                                    Type: Matrix PrimeField 2
--E 21

--S 22 of 51
m2 := [[1,0,0],[0,1,1],[0,0,1]]
 

         +1  0  0+
         |       |
   (22)  |0  1  1|
         |       |
         +0  0  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  0  0+
--R         |       |
--R   (22)  |0  1  1|
--R         |       |
--R         +0  0  1+
--R                                                    Type: Matrix PrimeField 2
--E 22

--S 23 of 51
m3 := [[1,0,0],[1,1,0],[0,0,1]]
 

         +1  0  0+
         |       |
   (23)  |1  1  0|
         |       |
         +0  0  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  0  0+
--R         |       |
--R   (23)  |1  1  0|
--R         |       |
--R         +0  0  1+
--R                                                    Type: Matrix PrimeField 2
--E 23

--S 24 of 51
m4 := [[1,0,0],[0,1,0],[0,1,1]]
 

         +1  0  0+
         |       |
   (24)  |0  1  0|
         |       |
         +0  1  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  0  0+
--R         |       |
--R   (24)  |0  1  0|
--R         |       |
--R         +0  1  1+
--R                                                    Type: Matrix PrimeField 2
--E 24

--S 25 of 51
vl : List Vector PrimeField 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 51
vl := [[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
 

   (26)  [[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
                                               Type: List Vector PrimeField 2
--R 
--R
--R   (26)  [[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
--R                                               Type: List Vector PrimeField 2
--E 26

--S 28 of 51
ll1 : List List Vector PrimeField 2 :=
   [ [ vl.i , m1*(vl.i) ] for i in 1..7 ]
 

   (27)
   [[[0,0,1],[0,0,1]], [[0,1,0],[1,1,0]], [[0,1,1],[1,1,1]], [[1,0,0],[1,0,0]],
    [[1,0,1],[1,0,1]], [[1,1,0],[0,1,0]], [[1,1,1],[0,1,1]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (27)
--R   [[[0,0,1],[0,0,1]], [[0,1,0],[1,1,0]], [[0,1,1],[1,1,1]], [[1,0,0],[1,0,0]],
--R    [[1,0,1],[1,0,1]], [[1,1,0],[0,1,0]], [[1,1,1],[0,1,1]]]
--R                                          Type: List List Vector PrimeField 2
--E 28

--S 29 of 51
ll2 : List List Vector PrimeField 2 :=
   [ [ vl.i , m2*(vl.i) ] for i in 1..7 ]
 

   (28)
   [[[0,0,1],[0,1,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,0,1]], [[1,0,0],[1,0,0]],
    [[1,0,1],[1,1,1]], [[1,1,0],[1,1,0]], [[1,1,1],[1,0,1]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (28)
--R   [[[0,0,1],[0,1,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,0,1]], [[1,0,0],[1,0,0]],
--R    [[1,0,1],[1,1,1]], [[1,1,0],[1,1,0]], [[1,1,1],[1,0,1]]]
--R                                          Type: List List Vector PrimeField 2
--E 29

--S 30 of 51
ll3 : List List Vector PrimeField 2 :=
   [ [ vl.i , m3*(vl.i) ] for i in 1..7 ]
 

   (29)
   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,1,1]], [[1,0,0],[1,1,0]],
    [[1,0,1],[1,1,1]], [[1,1,0],[1,0,0]], [[1,1,1],[1,0,1]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (29)
--R   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,1,1]], [[1,0,0],[1,1,0]],
--R    [[1,0,1],[1,1,1]], [[1,1,0],[1,0,0]], [[1,1,1],[1,0,1]]]
--R                                          Type: List List Vector PrimeField 2
--E 30

--S 31 of 51
ll4 : List List Vector PrimeField 2 :=
   [ [ vl.i , m4*(vl.i) ] for i in 1..7 ]
 

   (30)
   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,1]], [[0,1,1],[0,1,0]], [[1,0,0],[1,0,0]],
    [[1,0,1],[1,0,1]], [[1,1,0],[1,1,1]], [[1,1,1],[1,1,0]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (30)
--R   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,1]], [[0,1,1],[0,1,0]], [[1,0,0],[1,0,0]],
--R    [[1,0,1],[1,0,1]], [[1,1,0],[1,1,1]], [[1,1,1],[1,1,0]]]
--R                                          Type: List List Vector PrimeField 2
--E 31

--S 32 of 51
el1 : PERM Vector PrimeField 2 := coerceListOfPairs ll1
 

   (31)  ([1,1,0] [0,1,0])([1,1,1] [0,1,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (31)  ([1,1,0] [0,1,0])([1,1,1] [0,1,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 32

--S 33 of 51
el2 : PERM Vector PrimeField 2 := coerceListOfPairs ll2
 

   (32)  ([0,1,1] [0,0,1])([1,1,1] [1,0,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (32)  ([0,1,1] [0,0,1])([1,1,1] [1,0,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 33

--S 34 of 51
el3 : PERM Vector PrimeField 2 := coerceListOfPairs ll3
 

   (33)  ([1,1,0] [1,0,0])([1,1,1] [1,0,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (33)  ([1,1,0] [1,0,0])([1,1,1] [1,0,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 34

--S 35 of 51
el4 : PERM Vector PrimeField 2 := coerceListOfPairs ll4
 

   (34)  ([0,1,1] [0,1,0])([1,1,1] [1,1,0])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (34)  ([0,1,1] [0,1,0])([1,1,1] [1,1,0])
--R                                        Type: Permutation Vector PrimeField 2
--E 35

--S 36 of 51
eval ( el3 , vl.5 )
 

   (35)  [1,1,1]
                                                    Type: Vector PrimeField 2
--R 
--R
--R   (35)  [1,1,1]
--R                                                    Type: Vector PrimeField 2
--E 36

--S 37 of 51
el2 * el1
 

   (36)  ([0,1,0] [1,1,0])([0,1,1] [1,0,1] [1,1,1] [0,0,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (36)  ([0,1,0] [1,1,0])([0,1,1] [1,0,1] [1,1,1] [0,0,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 37

--S 38 of 51
movedPoints el4
 

   (37)  {[1,1,1],[1,1,0],[0,1,1],[0,1,0]}
                                                Type: Set Vector PrimeField 2
--R 
--R
--R   (37)  {[1,1,1],[1,1,0],[0,1,1],[0,1,0]}
--R                                                Type: Set Vector PrimeField 2
--E 38

--S 39 of 51
gl : PERMGRP Vector PrimeField 2 := [ el1 , el2 , el3 , el4 ]
 

   (38)
   <
       ([1,1,0] [0,1,0])([1,1,1] [0,1,1]),([0,1,1] [0,0,1])([1,1,1] [1,0,1])
    ,
       ([1,1,0] [1,0,0])([1,1,1] [1,0,1]),([0,1,1] [0,1,0])([1,1,1] [1,1,0])
     >
                                   Type: PermutationGroup Vector PrimeField 2
--R 
--R
--R   (38)
--R   <
--R       ([1,1,0] [0,1,0])([1,1,1] [0,1,1]),([0,1,1] [0,0,1])([1,1,1] [1,0,1])
--R    ,
--R       ([1,1,0] [1,0,0])([1,1,1] [1,0,1]),([0,1,1] [0,1,0])([1,1,1] [1,1,0])
--R     >
--R                                   Type: PermutationGroup Vector PrimeField 2
--E 39

--S 40 of 51
order gl
 

   (39)  168
                                                        Type: PositiveInteger
--R 
--R
--R   (39)  168
--R                                                        Type: PositiveInteger
--E 40

--S 41 of 51
setOfVectors : Set Vector PrimeField 2 := brace [ vl.2 , vl.4 , vl.6 ]
 

   (40)  {[0,1,0],[1,0,0],[1,1,0]}
                                                Type: Set Vector PrimeField 2
--R 
--R
--R   (40)  {[0,1,0],[1,0,0],[1,1,0]}
--R                                                Type: Set Vector PrimeField 2
--E 41

--S 42 of 51
orbit ( gl, setOfVectors )
 

   (41)
   {{[0,1,0],[1,0,0],[1,1,0]}, {[0,1,1],[1,0,0],[1,1,1]},
    {[0,0,1],[1,0,0],[1,0,1]}, {[0,1,1],[1,1,0],[1,0,1]},
    {[0,0,1],[1,1,0],[1,1,1]}, {[1,1,1],[0,1,0],[1,0,1]},
    {[0,0,1],[0,1,0],[0,1,1]}}
                                            Type: Set Set Vector PrimeField 2
--R 
--R
--R   (41)
--R   {{[0,1,0],[1,0,0],[1,1,0]}, {[0,1,1],[1,0,0],[1,1,1]},
--R    {[0,0,1],[1,0,0],[1,0,1]}, {[0,1,1],[1,1,0],[1,0,1]},
--R    {[0,0,1],[1,1,0],[1,1,1]}, {[1,1,1],[0,1,0],[1,0,1]},
--R    {[0,0,1],[0,1,0],[0,1,1]}}
--R                                            Type: Set Set Vector PrimeField 2
--E 42

--S 43 of 51
listOfVectors : List Vector PrimeField 2 := parts setOfVectors
 

   (42)  [[0,1,0],[1,0,0],[1,1,0]]
                                               Type: List Vector PrimeField 2
--R 
--R
--R   (42)  [[0,1,0],[1,0,0],[1,1,0]]
--R                                               Type: List Vector PrimeField 2
--E 43

--S 44 of 51
orbit ( gl, listOfVectors )
 

   (43)
   {[[0,1,0],[1,0,0],[1,1,0]], [[1,1,0],[1,0,0],[0,1,0]],
    [[0,1,0],[1,1,0],[1,0,0]], [[0,1,1],[1,0,0],[1,1,1]],
    [[1,0,0],[1,1,0],[0,1,0]], [[1,1,1],[1,0,0],[0,1,1]],
    [[1,1,0],[0,1,0],[1,0,0]], [[0,1,1],[1,1,1],[1,0,0]],
    [[0,0,1],[1,0,0],[1,0,1]], [[0,1,1],[1,1,0],[1,0,1]],
    [[1,0,0],[0,1,0],[1,1,0]], [[1,0,0],[1,1,1],[0,1,1]],
    [[1,0,1],[1,0,0],[0,0,1]], [[1,0,1],[1,1,0],[0,1,1]],
    [[1,1,1],[0,1,1],[1,0,0]], [[0,0,1],[1,0,1],[1,0,0]],
    [[0,1,1],[1,0,1],[1,1,0]], [[0,0,1],[1,1,0],[1,1,1]],
    [[1,1,1],[0,1,0],[1,0,1]], [[0,1,0],[1,1,1],[1,0,1]],
    [[1,0,0],[0,1,1],[1,1,1]], [[1,0,0],[1,0,1],[0,0,1]],
    [[1,1,0],[1,0,1],[0,1,1]], [[1,1,1],[1,1,0],[0,0,1]],
    [[1,0,1],[0,1,0],[1,1,1]], [[1,0,1],[1,1,1],[0,1,0]],
    [[1,0,1],[0,0,1],[1,0,0]], [[1,0,1],[0,1,1],[1,1,0]],
    [[0,0,1],[1,1,1],[1,1,0]], [[1,1,1],[1,0,1],[0,1,0]],
    [[0,1,0],[1,0,1],[1,1,1]], [[0,0,1],[0,1,0],[0,1,1]],
    [[1,1,0],[0,1,1],[1,0,1]], [[1,0,0],[0,0,1],[1,0,1]],
    [[1,1,0],[1,1,1],[0,0,1]], [[0,1,1],[0,1,0],[0,0,1]],
    [[1,1,1],[0,0,1],[1,1,0]], [[0,0,1],[0,1,1],[0,1,0]],
    [[1,1,0],[0,0,1],[1,1,1]], [[0,1,0],[0,1,1],[0,0,1]],
    [[0,1,1],[0,0,1],[0,1,0]], [[0,1,0],[0,0,1],[0,1,1]]}
                                           Type: Set List Vector PrimeField 2
--R 
--R
--R   (43)
--R   {[[0,1,0],[1,0,0],[1,1,0]], [[1,1,0],[1,0,0],[0,1,0]],
--R    [[0,1,0],[1,1,0],[1,0,0]], [[0,1,1],[1,0,0],[1,1,1]],
--R    [[1,0,0],[1,1,0],[0,1,0]], [[1,1,1],[1,0,0],[0,1,1]],
--R    [[1,1,0],[0,1,0],[1,0,0]], [[0,1,1],[1,1,1],[1,0,0]],
--R    [[0,0,1],[1,0,0],[1,0,1]], [[0,1,1],[1,1,0],[1,0,1]],
--R    [[1,0,0],[0,1,0],[1,1,0]], [[1,0,0],[1,1,1],[0,1,1]],
--R    [[1,0,1],[1,0,0],[0,0,1]], [[1,0,1],[1,1,0],[0,1,1]],
--R    [[1,1,1],[0,1,1],[1,0,0]], [[0,0,1],[1,0,1],[1,0,0]],
--R    [[0,1,1],[1,0,1],[1,1,0]], [[0,0,1],[1,1,0],[1,1,1]],
--R    [[1,1,1],[0,1,0],[1,0,1]], [[0,1,0],[1,1,1],[1,0,1]],
--R    [[1,0,0],[0,1,1],[1,1,1]], [[1,0,0],[1,0,1],[0,0,1]],
--R    [[1,1,0],[1,0,1],[0,1,1]], [[1,1,1],[1,1,0],[0,0,1]],
--R    [[1,0,1],[0,1,0],[1,1,1]], [[1,0,1],[1,1,1],[0,1,0]],
--R    [[1,0,1],[0,0,1],[1,0,0]], [[1,0,1],[0,1,1],[1,1,0]],
--R    [[0,0,1],[1,1,1],[1,1,0]], [[1,1,1],[1,0,1],[0,1,0]],
--R    [[0,1,0],[1,0,1],[1,1,1]], [[0,0,1],[0,1,0],[0,1,1]],
--R    [[1,1,0],[0,1,1],[1,0,1]], [[1,0,0],[0,0,1],[1,0,1]],
--R    [[1,1,0],[1,1,1],[0,0,1]], [[0,1,1],[0,1,0],[0,0,1]],
--R    [[1,1,1],[0,0,1],[1,1,0]], [[0,0,1],[0,1,1],[0,1,0]],
--R    [[1,1,0],[0,0,1],[1,1,1]], [[0,1,0],[0,1,1],[0,0,1]],
--R    [[0,1,1],[0,0,1],[0,1,0]], [[0,1,0],[0,0,1],[0,1,1]]}
--R                                           Type: Set List Vector PrimeField 2
--E 44

--S 45 of 51
f : PERM INT := cycles [[11,13,15,17],[12,14,16,18],[51,31,21,41],[53,33,23,43],_
             [52,32,22,42]]
 

   (44)  (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
                                                    Type: Permutation Integer
--R 
--R
--R   (44)  (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
--R                                                    Type: Permutation Integer
--E 45

--S 46 of 51
r : PERM INT := cycles [[21,23,25,27],[22,24,26,28],[13,37,67,43],[15,31,61,45],_
             [14,38,68,44]]
 

   (45)  (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
                                                    Type: Permutation Integer
--R 
--R
--R   (45)  (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
--R                                                    Type: Permutation Integer
--E 46

--S 47 of 51
(f**2*r**2)**3
 

   (46)  (12 16)(24 28)(32 42)(38 44)
                                                    Type: Permutation Integer
--R 
--R
--R   (46)  (12 16)(24 28)(32 42)(38 44)
--R                                                    Type: Permutation Integer
--E 47

--S 48 of 51
rc := rubiksGroup()
 

   (47)
   <
       (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
    ,
       (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
    ,
       (11 57 61 23)(12 58 62 24)(13 51 63 25)(31 33 35 37)(32 34 36 38)
    ,
       (15 27 65 53)(16 28 66 54)(17 21 67 55)(41 43 45 47)(42 44 46 48)
    ,
       (11 41 65 35)(17 47 63 33)(18 48 64 34)(51 53 55 57)(52 54 56 58)
    ,
       (25 35 55 45)(26 36 56 46)(27 37 57 47)(61 63 65 67)(62 64 66 68)
     >
                                               Type: PermutationGroup Integer
--R 
--R
--R   (47)
--R   <
--R       (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
--R    ,
--R       (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
--R    ,
--R       (11 57 61 23)(12 58 62 24)(13 51 63 25)(31 33 35 37)(32 34 36 38)
--R    ,
--R       (15 27 65 53)(16 28 66 54)(17 21 67 55)(41 43 45 47)(42 44 46 48)
--R    ,
--R       (11 41 65 35)(17 47 63 33)(18 48 64 34)(51 53 55 57)(52 54 56 58)
--R    ,
--R       (25 35 55 45)(26 36 56 46)(27 37 57 47)(61 63 65 67)(62 64 66 68)
--R     >
--R                                               Type: PermutationGroup Integer
--E 48

--S 49 of 51
order rc
 

   (48)  43252003274489856000
                                                        Type: PositiveInteger
--R 
--R
--R   (48)  43252003274489856000
--R                                                        Type: PositiveInteger
--E 49

--S 50 of 51
orbits rc
 

   (49)
   {{11,13,15,17,21,23,25,27,31,33,35,37,41,43,45,47,51,53,55,57,61,63,65,67},
    {12,14,16,18,22,24,26,28,32,34,36,38,42,44,46,48,52,54,56,58,62,64,66,68}}
                                                        Type: Set Set Integer
--R 
--R
--R   (49)
--R   {{11,13,15,17,21,23,25,27,31,33,35,37,41,43,45,47,51,53,55,57,61,63,65,67},
--R    {12,14,16,18,22,24,26,28,32,34,36,38,42,44,46,48,52,54,56,58,62,64,66,68}}
--R                                                        Type: Set Set Integer
--E 50

--S 51 of 51
member? (cycles([[12,14],[32,22]])$(PERM INT),rc)
 

   (50)  false
                                                                Type: Boolean
--R 
--R
--R   (50)  false
--R                                                                Type: Boolean
--E 51
)spool 
 
Starts dribbling to tancot.output (2009/2/17, 18:0:56).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
[[0.01,0.010000333,tan(0.01),tan(0.01)-(0.010000333)],_
[0.02,0.020002667,tan(0.02),tan(0.02)-(0.020002667)],_
[0.03,0.030009003,tan(0.03),tan(0.03)-(0.030009003)],_
[0.04,0.040021347,tan(0.04),tan(0.04)-(0.040021347)],_
[0.05,0.050041708,tan(0.05),tan(0.05)-(0.050041708)],_
[0.06,0.060072104,tan(0.06),tan(0.06)-(0.060072104)],_
[0.07,0.070114558,tan(0.07),tan(0.07)-(0.070114558)],_
[0.08,0.080171105,tan(0.08),tan(0.08)-(0.080171105)],_
[0.09,0.090243790,tan(0.09),tan(0.09)-(0.090243790)],_
[0.10,0.10033467,tan(0.10),tan(0.10)-(0.10033467)],_
[0.11,0.11044582,tan(0.11),tan(0.11)-(0.11044582)],_
[0.12,0.12057934,tan(0.12),tan(0.12)-(0.12057934)],_
[0.13,0.13073732,tan(0.13),tan(0.13)-(0.13073732)],_
[0.14,0.14092189,tan(0.14),tan(0.14)-(0.14092189)],_
[0.15,0.15113522,tan(0.15),tan(0.15)-(0.15113522)],_
[0.16,0.16137946,tan(0.16),tan(0.16)-(0.16137946)],_
[0.17,0.17165682,tan(0.17),tan(0.17)-(0.17165682)],_
[0.18,0.18196953,tan(0.18),tan(0.18)-(0.18196953)],_
[0.19,0.19231984,tan(0.19),tan(0.19)-(0.19231984)],_
[0.20,0.20271004,tan(0.20),tan(0.20)-(0.20271004)],_
[0.21,0.21314244,tan(0.21),tan(0.21)-(0.21314244)],_
[0.22,0.22361942,tan(0.22),tan(0.22)-(0.22361942)],_
[0.23,0.23414336,tan(0.23),tan(0.23)-(0.23414336)],_
[0.24,0.24471670,tan(0.24),tan(0.24)-(0.24471670)],_
[0.25,0.25534192,tan(0.25),tan(0.25)-(0.25534192)],_
[0.26,0.26602154,tan(0.26),tan(0.26)-(0.26602154)],_
[0.27,0.27675814,tan(0.27),tan(0.27)-(0.27675814)],_
[0.28,0.28755433,tan(0.28),tan(0.28)-(0.28755433)],_
[0.29,0.29841279,tan(0.29),tan(0.29)-(0.29841279)],_
[0.30,0.30933625,tan(0.30),tan(0.30)-(0.30933625)],_
[0.31,0.32032751,tan(0.31),tan(0.31)-(0.32032751)],_
[0.32,0.33138941,tan(0.32),tan(0.32)-(0.33138941)],_
[0.33,0.34252487,tan(0.33),tan(0.33)-(0.34252487)],_
[0.34,0.35373688,tan(0.34),tan(0.34)-(0.35373688)],_
[0.35,0.36502849,tan(0.35),tan(0.35)-(0.36502849)],_
[0.36,0.37640285,tan(0.36),tan(0.36)-(0.37640285)],_
[0.37,0.38786316,tan(0.37),tan(0.37)-(0.38786316)],_
[0.38,0.39941272,tan(0.38),tan(0.38)-(0.39941272)],_
[0.39,0.41105492,tan(0.39),tan(0.39)-(0.41105492)],_
[0.40,0.42279322,tan(0.40),tan(0.40)-(0.42279322)],_
[0.41,0.43463120,tan(0.41),tan(0.41)-(0.43463120)],_
[0.42,0.44657255,tan(0.42),tan(0.42)-(0.44657255)],_
[0.43,0.45862102,tan(0.43),tan(0.43)-(0.45862102)],_
[0.44,0.47078053,tan(0.44),tan(0.44)-(0.47078053)],_
[0.45,0.48305507,tan(0.45),tan(0.45)-(0.48305507)],_
[0.46,0.49544877,tan(0.46),tan(0.46)-(0.49544877)],_
[0.47,0.50796590,tan(0.47),tan(0.47)-(0.50796590)],_
[0.48,0.52061084,tan(0.48),tan(0.48)-(0.52061084)],_
[0.49,0.53338815,tan(0.49),tan(0.49)-(0.53338815)],_
[0.50,0.54630249,tan(0.50),tan(0.50)-(0.54630249)],_
[0.51,0.55935872,tan(0.51),tan(0.51)-(0.55935872)],_
[0.52,0.57256183,tan(0.52),tan(0.52)-(0.57256183)],_
[0.53,0.58591701,tan(0.53),tan(0.53)-(0.58591701)],_
[0.54,0.59942962,tan(0.54),tan(0.54)-(0.59942962)],_
[0.55,0.61310521,tan(0.55),tan(0.55)-(0.61310521)],_
[0.56,0.62694954,tan(0.56),tan(0.56)-(0.62694954)],_
[0.57,0.64096855,tan(0.57),tan(0.57)-(0.64096855)],_
[0.58,0.65516845,tan(0.58),tan(0.58)-(0.65516845)],_
[0.59,0.66955565,tan(0.59),tan(0.59)-(0.66955565)],_
[0.60,0.68413681,tan(0.60),tan(0.60)-(0.68413681)],_
[0.61,0.69891886,tan(0.61),tan(0.61)-(0.69891886)],_
[0.62,0.71390901,tan(0.62),tan(0.62)-(0.71390901)],_
[0.63,0.72911473,tan(0.63),tan(0.63)-(0.72911473)],_
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[1.54,32.4611389,tan(1.54),tan(1.54)-(32.4611389)],_
[1.55,48.0784825,tan(1.55),tan(1.55)-(48.0784825)],_
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[1.58,-108.6492036,tan(1.58),tan(1.58)-(-108.6492036)],_
[1.59,-52.0669696,tan(1.59),tan(1.59)-(-52.0669696)],_
[1.60,-34.2325327,tan(1.60),tan(1.60)-(-34.2325327)]]
 

   (1)
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    [1.36,4.6734412,4.6734412029 885596449,0.2988559645 E -8],
    [1.37,4.9130581,4.9130580704 624720101,- 0.2953752799 E -7],
    [1.38,5.1774374,5.1774373886 304102949,- 0.1136958970 5 E -7],
    [1.39,5.4706886,5.4706886429 532054937,0.4295320549 37 E -7],
    [1.4,5.7978837,5.7978837154 828896437,0.1548288964 4 E -7],
    [1.41,6.1653561,6.1653561445 520255476,0.4455202554 75 E -7],
    [1.42,6.5811195,6.5811194561 942543239,- 0.4380574567 61 E -7],
    [1.43,7.0554638,7.0554637664 342109722,- 0.3356578902 78 E -7],
    [1.44,7.6018261,7.6018260620 257232407,- 0.3797427675 94 E -7],
    [1.45,8.2380928,8.2380927529 656070833,- 0.4703439291 7 E -7],
    [1.46,8.9886076,8.9886076017 241695008,0.1724169501 E -8],
    [1.47,9.8873749,9.8873748919 855531724,- 0.8014446827 5 E -8],
    [1.48,10.9833793,10.9833793143 26067301,0.1432606730 1 E -7],
    [1.49,12.3498564,12.3498564416 25802114,0.4162580211 4 E -7],
    [1.5,14.1014199,14.1014199471 71719388,0.4717171938 8 E -7],
    [1.51,16.4280917,16.4280917038 85335336,0.3885335336 E -8],
    [1.52,19.6695278,19.6695278205 58866232,0.2055886623 2 E -7],
    [1.53,24.4984104,24.4984104418 38034593,0.4183803459 3 E -7],
    [1.54,32.4611389,32.4611389128 56765176,0.1285676518 E -7],
    [1.55,48.0784825,48.0784824792 18968279,- 0.2078103172 E -7],
    [1.56,92.6204963,92.6204963167 04102469,0.1670410247 E -7],
    [1.57,1255.7655915,1255.7655915006 916051,0.6916051 E -9],
    [1.58,- 108.6492036,- 108.6492036048 4393447,- 0.484393447 E -8],
    [1.59,- 52.0669696,- 52.0669696509 12563554,- 0.5091256355 4 E -7],
    [1.6,- 34.2325327,- 34.2325327355 57417056,- 0.3555741705 7 E -7]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.01,0.010000333,0.0100003333 4666720637 1,0.3466672063 71 E -9],
--R    [0.02,0.020002667,0.0200026670 9340242389 7,0.9340242389 7 E -10],
--R    [0.03,0.030009003,0.0300090032 4118071632 9,0.2411807163 29 E -9],
--R    [0.04,0.040021347,0.0400213469 9551456207 2,- 0.4485437928 E -11],
--R    [0.05,0.050041708,0.0500417083 7553878891 2,0.3755387889 12 E -9],
--R    [0.06,0.060072104,0.0600721038 3129728751 1,- 0.1687027124 9 E -9],
--R    [0.07,0.070114558,0.0701145578 7200271322 9,- 0.1279972867 7 E -9],
--R    [0.08,0.080171105,0.0801711047 0807255711 8,- 0.2919274428 8 E -9],
--R    [0.09,0.09024379,0.0902437899 0978545046 6,- 0.9021454953 4 E -10],
--R    [0.1,0.10033467,0.1003346720 8545054506,0.2085450545 06 E -8],
--R    [0.11,0.11044582,0.1104458245 820405045,0.4582040504 5 E -8],
--R    [0.12,0.12057934,0.1205793372 1130531183,- 0.2788694688 17 E -8],
--R    [0.13,0.13073732,0.1307373180 0446004867,- 0.1995539951 33 E -8],
--R    [0.14,0.14092189,0.1409218949 9862537921,0.4998625379 21 E -8],
--R    [0.15,0.15113522,0.1511352180 5829507125,- 0.1941704928 75 E -8],
--R    [0.16,0.16137946,0.1613794607 3521095024,0.7352109502 4 E -9],
--R    [0.17,0.17165682,0.1716568221 7014270414,0.2170142704 14 E -8],
--R    [0.18,0.18196953,0.1819695290 4019848684,- 0.9598015131 64 E -9],
--R    [0.19,0.19231984,0.1923198375 554329145,- 0.2444567085 5 E -8],
--R    [0.2,0.20271004,0.2027100355 0867248332,- 0.4491327516 68 E -8],
--R    [0.21,0.21314244,0.2131424443 8264539723,0.4382645397 23 E -8],
--R    [0.22,0.22361942,0.2236194215 1868409245,0.1518684092 45 E -8],
--R    [0.23,0.23414336,0.2341433623 5146527061,0.2351465270 61 E -8],
--R    [0.24,0.2447167,0.2447167027 1446497862,0.2714464978 62 E -8],
--R    [0.25,0.25534192,0.2553419212 2103626651,0.1221036266 5 E -8],
--R    [0.26,0.26602154,0.2660215417 2626537908,0.1726265379 1 E -8],
--R    [0.27,0.27675814,0.2767581358 7503056579,- 0.4124969434 21 E -8],
--R    [0.28,0.28755433,0.2875543257 41976815,- 0.4258023185 E -8],
--R    [0.29,0.29841279,0.2984127865 694316513,- 0.3430568348 7 E -8],
--R    [0.3,0.30933625,0.3093362496 0962323304,- 0.3903767669 6 E -9],
--R    [0.31,0.32032751,0.3203275050 7792416023,- 0.4922075839 77 E -8],
--R    [0.32,0.33138941,0.3313894052 2423462352,- 0.4775765376 48 E -8],
--R    [0.33,0.34252487,0.3425248675 3003894803,- 0.2469961051 97 E -8],
--R    [0.34,0.35373688,0.3537368780 3912256577,- 0.1960877434 23 E -8],
--R    [0.35,0.36502849,0.3650284948 3042455832,0.4830424558 32 E -8],
--R    [0.36,0.37640285,0.3764028516 4202695764,0.1642026957 6 E -8],
--R    [0.37,0.38786316,0.3878631616 5584905222,0.1655849052 2 E -8],
--R    [0.38,0.39941272,0.3994127214 5322637827,0.1453226378 3 E -8],
--R    [0.39,0.41105492,0.4110549151 5221356343,- 0.4847786436 57 E -8],
--R    [0.4,0.42279322,0.4227932187 3816176198,- 0.1261838238 E -8],
--R    [0.41,0.4346312,0.4346312045 9988949299,0.4599889492 99 E -8],
--R    [0.42,0.44657255,0.4465725462 8459510803,- 0.3715404891 96 E -8],
--R    [0.43,0.45862102,0.4586210234 8555518632,0.3485555186 32 E -8],
--R    [0.44,0.47078053,0.4707805272 7762171492,- 0.2722378285 08 E -8],
--R    [0.45,0.48305507,0.4830550656 1657837051,- 0.4383421629 49 E -8],
--R    [0.46,0.49544877,0.4954487691 1954962242,- 0.8804503775 8 E -9],
--R    [0.47,0.5079659,0.5079658971 4488348004,- 0.285511652 E -8],
--R    [0.48,0.52061084,0.5206108441 9125804964,0.4191258049 65 E -8],
--R    [0.49,0.53338815,0.5333881466 3720305695,- 0.3362796943 1 E -8],
--R    [0.5,0.54630249,0.5463024898 4379051326,- 0.1562094867 E -9],
--R    [0.51,0.55935872,0.5593587156 4494521344,- 0.4355054786 56 E -8],
--R    [0.52,0.57256183,0.5725618302 5166841478,0.2516684148 E -9],
--R    [0.53,0.58591701,0.5859170125 9847085812,0.2598470858 1 E -8],
--R    [0.54,0.59942962,0.5994296231 6248975451,0.3162489754 5 E -8],
--R    [0.55,0.61310521,0.6131052132 8813564222,0.3288135642 2 E -8],
--R    [0.56,0.62694954,0.6269495350 5269815933,- 0.4947301840 67 E -8],
--R    [0.57,0.64096855,0.6409685517 1115591313,0.1711155913 1 E -8],
--R    [0.58,0.65516845,0.6551684487 6150824025,- 0.1238491759 7 E -8],
--R    [0.59,0.66955565,0.6695556456 753018611,- 0.4324698138 9 E -8],
--R    [0.6,0.68413681,0.6841368083 4169231707,- 0.1658307682 9 E -8],
--R    [0.61,0.69891886,0.6989188622 7739105048,0.2277391050 5 E -8],
--R    [0.62,0.71390901,0.7139090066 5924020594,- 0.3340759794 1 E -8],
--R    [0.63,0.72911473,0.7291147292 4096908976,- 0.7590309102 4 E -9],
--R    [0.64,0.74454382,0.7445438222 2096388599,0.2220963886 E -8],
--R    [0.65,0.7602044,0.7602043991 3367625635,- 0.8663237436 5 E -9],
--R    [0.66,0.77610491,0.7761049128 4366351779,0.2843663517 8 E -8],
--R    [0.67,0.79225417,0.7922541747 2825678628,0.4728256786 28 E -8],
--R    [0.68,0.80866138,0.8086613751 4256524544,- 0.4857434754 56 E -8],
--R    [0.69,0.82533611,0.8253361052 6902491172,- 0.4730975088 28 E -8],
--R    [0.7,0.84228838,0.8422883804 6307944813,0.4630794481 E -9],
--R    [0.71,0.85952867,0.8595286652 1694081593,- 0.4783059184 07 E -8],
--R    [0.72,0.8770679,0.8770678998 7483414069,- 0.1251658593 E -9],
--R    [0.73,0.89491753,0.8949175292 4581448181,- 0.7541855181 9 E -9],
--R    [0.74,0.91308953,0.9130895332 7430087206,0.3274300872 1 E -8],
--R    [0.75,0.93159646,0.9315964599 4407246117,- 0.559275388 E -10],
--R    [0.76,0.95045146,0.9504514606 0880299797,0.6088029979 7 E -9],
--R    [0.77,0.96966833,0.9696683279 6148947799,- 0.2038510522 E -8],
--R    [0.78,0.98926154,0.9892615368 7660491155,- 0.3123395088 4 E -8],
--R    [0.79,1.00924629,1.0092462883 827548811,- 0.1617245118 9 E -8],
--R    [0.8,1.02963857,1.0296385570 503640128,- 0.1294963598 73 E -7],
--R    [0.81,1.05045514,1.0504551421 088292806,0.2108829280 6 E -8],
--R    [0.82,1.07171372,1.0717137226 410736441,0.2641073644 1 E -8],
--R    [0.83,1.09343292,1.0934329172 409999188,- 0.2759000081 2 E -8],
--R    [0.84,1.11563235,1.1156323485 615378951,- 0.1438462104 9 E -8],
--R    [0.85,1.13833271,1.1383327132 284394134,0.3228439413 4 E -8],
--R    [0.86,1.16155586,1.1615558576 484476046,- 0.2351552395 4 E -8],
--R    [0.87,1.18532486,1.1853248603 008053505,0.3008053505 E -9],
--R    [0.88,1.20966412,1.2096641211 692683367,0.1169268336 7 E -8],
--R    [0.89,1.23459946,1.2345994590 490045825,- 0.9509954175 3 E -9],
--R    [0.9,1.26015822,1.2601582175 503391371,- 0.2449660862 9 E -8],
--R    [0.91,1.28636938,1.2863693807 208075758,0.7208075758 E -9],
--R    [0.92,1.3132637,1.3132636993 202478365,- 0.6797521635 E -9],
--R    [0.93,1.34087383,1.3408738289 128343042,- 0.1087165695 8 E -8],
--R    [0.94,1.36923448,1.3692344810 875628038,0.1087562803 8 E -8],
--R    [0.95,1.39838259,1.3983825892 876991461,- 0.7123008539 E -9],
--R    [0.96,1.42835749,1.4283574909 236105601,0.9236105601 E -9],
--R    [0.97,1.45920113,1.4592011276 663536858,- 0.2333646314 2 E -8],
--R    [0.98,1.49095827,1.4909582660 763114779,- 0.3923688522 1 E -8],
--R    [0.99,1.52367674,1.5236767410 179022725,0.1017902272 5 E -8],
--R    [1.0,1.55740772,1.5574077246 549022305,0.4654902230 5 E -8],
--R    [1.01,1.592206,1.5922060242 195703744,0.2421957037 44 E -7],
--R    [1.02,1.6281304,1.6281304122 125526001,0.1221255260 01 E -7],
--R    [1.03,1.665244,1.6652439932 315124346,- 0.6768487565 4 E -8],
--R    [1.04,1.7036146,1.7036146122 591331094,0.1225913310 94 E -7],
--R    [1.05,1.7433153,1.7433153099 831702625,0.9983170262 47 E -8],
--R    [1.06,1.7844248,1.7844248315 940126524,0.3159401265 24 E -7],
--R    [1.07,1.8270282,1.8270281965 348367381,- 0.3465163261 9 E -8],
--R    [1.08,1.8712173,1.8712173378 97878195,0.3789787819 5 E -7],
--R    [1.09,1.9170918,1.9170918216 068594024,0.2160685940 24 E -7],
--R    [1.1,1.9647597,1.9647596572 486519509,- 0.4275134804 91 E -7],
--R    [1.11,2.0143382,2.0143382144 768273135,0.1447682731 3 E -7],
--R    [1.12,2.0659553,2.0659552613 80510241,- 0.3861948975 9 E -7],
--R    [1.13,2.1197501,2.1197501441 871810139,0.4418718101 39 E -7],
--R    [1.14,2.1758751,2.1758751312 648761686,0.3126487616 86 E -7],
--R    [1.15,2.2344969,2.2344969487 553259802,0.4875532598 02 E -7],
--R    [1.16,2.2957985,2.2957985404 922076011,0.4049220760 11 E -7],
--R    [1.17,2.3599811,2.3599810913 765482032,- 0.8623451796 7 E -8],
--R    [1.18,2.4272664,2.4272663614 002235775,- 0.3859977642 25 E -7],
--R    [1.19,2.4978994,2.4978993874 226530062,- 0.1257734699 4 E -7],
--R    [1.2,2.5721516,2.5721516221 263189354,0.2212631893 54 E -7],
--R    [1.21,2.6503246,2.6503245949 706014665,- 0.5029398533 5 E -8],
--R    [1.22,2.7327542,2.7327541993 067149987,- 0.6932850013 E -9],
--R    [1.23,2.8198157,2.8198157342 681519748,0.3426815197 48 E -7],
--R    [1.24,2.9119299,2.9119298611 552260267,- 0.3884477397 34 E -7],
--R    [1.25,3.0095697,3.0095696738 628312882,- 0.2613716871 18 E -7],
--R    [1.26,3.1132691,3.1132691342 651312093,0.3426513120 93 E -7],
--R    [1.27,3.2236332,3.2236331902 040711359,- 0.9795928864 E -8],
--R    [1.28,3.34135,3.3413499811 153736983,- 0.1888462630 17 E -7],
--R    [1.29,3.4672057,3.4672056517 213857853,- 0.4827861421 47 E -7],
--R    [1.3,3.6021024,3.6021024479 679781512,0.4796797815 12 E -7],
--R    [1.31,3.747081,3.7470809761 884290733,- 0.2381157092 67 E -7],
--R    [1.32,3.9033478,3.9033477874 966235656,- 0.1250337643 4 E -7],
--R    [1.33,4.0723098,4.0723098354 650698554,0.3546506985 54 E -7],
--R    [1.34,4.2556179,4.2556178917 394653427,- 0.8260534657 3 E -8],
--R    [1.35,4.4552218,4.4552217595 627031753,- 0.4043729682 47 E -7],
--R    [1.36,4.6734412,4.6734412029 885596449,0.2988559645 E -8],
--R    [1.37,4.9130581,4.9130580704 624720101,- 0.2953752799 E -7],
--R    [1.38,5.1774374,5.1774373886 304102949,- 0.1136958970 5 E -7],
--R    [1.39,5.4706886,5.4706886429 532054937,0.4295320549 37 E -7],
--R    [1.4,5.7978837,5.7978837154 828896437,0.1548288964 4 E -7],
--R    [1.41,6.1653561,6.1653561445 520255476,0.4455202554 75 E -7],
--R    [1.42,6.5811195,6.5811194561 942543239,- 0.4380574567 61 E -7],
--R    [1.43,7.0554638,7.0554637664 342109722,- 0.3356578902 78 E -7],
--R    [1.44,7.6018261,7.6018260620 257232407,- 0.3797427675 94 E -7],
--R    [1.45,8.2380928,8.2380927529 656070833,- 0.4703439291 7 E -7],
--R    [1.46,8.9886076,8.9886076017 241695008,0.1724169501 E -8],
--R    [1.47,9.8873749,9.8873748919 855531724,- 0.8014446827 5 E -8],
--R    [1.48,10.9833793,10.9833793143 26067301,0.1432606730 1 E -7],
--R    [1.49,12.3498564,12.3498564416 25802114,0.4162580211 4 E -7],
--R    [1.5,14.1014199,14.1014199471 71719388,0.4717171938 8 E -7],
--R    [1.51,16.4280917,16.4280917038 85335336,0.3885335336 E -8],
--R    [1.52,19.6695278,19.6695278205 58866232,0.2055886623 2 E -7],
--R    [1.53,24.4984104,24.4984104418 38034593,0.4183803459 3 E -7],
--R    [1.54,32.4611389,32.4611389128 56765176,0.1285676518 E -7],
--R    [1.55,48.0784825,48.0784824792 18968279,- 0.2078103172 E -7],
--R    [1.56,92.6204963,92.6204963167 04102469,0.1670410247 E -7],
--R    [1.57,1255.7655915,1255.7655915006 916051,0.6916051 E -9],
--R    [1.58,- 108.6492036,- 108.6492036048 4393447,- 0.484393447 E -8],
--R    [1.59,- 52.0669696,- 52.0669696509 12563554,- 0.5091256355 4 E -7],
--R    [1.6,- 34.2325327,- 34.2325327355 57417056,- 0.3555741705 7 E -7]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
[[0.01,99.9966666,cot(0.01),cot(0.01)-(99.9966666)],_
[0.02,49.9933332,cot(0.02),cot(0.02)-(49.9933332)],_
[0.03,33.3233327,cot(0.03),cot(0.03)-(33.3233327)],_
[0.04,24.9866652,cot(0.04),cot(0.04)-(24.9866652)],_
[0.05,19.9833306,cot(0.05),cot(0.05)-(19.9833306)],_
[0.06,16.6466619,cot(0.06),cot(0.06)-(16.6466619)],_
[0.07,14.2623733,cot(0.07),cot(0.07)-(14.2623733)],_
[0.08,12.4733219,cot(0.08),cot(0.08)-(12.4733219)],_
[0.09,11.0810949,cot(0.09),cot(0.09)-(11.0810949)],_
[0.10,9.9666444,cot(0.10),cot(0.10)-(9.9666444)],_
[0.11,9.0542128,cot(0.11),cot(0.11)-(9.0542128)],_
[0.12,8.2932949,cot(0.12),cot(0.12)-(8.2932949)],_
[0.13,7.6489255,cot(0.13),cot(0.13)-(7.6489255)],_
[0.14,7.0961294,cot(0.14),cot(0.14)-(7.0961294)],_
[0.15,6.6165915,cot(0.15),cot(0.15)-(6.6165915)],_
[0.16,6.1965754,cot(0.16),cot(0.16)-(6.1965754)],_
[0.17,5.8255768,cot(0.17),cot(0.17)-(5.8255768)],_
[0.18,5.4954256,cot(0.18),cot(0.18)-(5.4954256)],_
[0.19,5.1996716,cot(0.19),cot(0.19)-(5.1996716)],_
[0.20,4.9331549,cot(0.20),cot(0.20)-(4.9331549)],_
[0.21,4.6916981,cot(0.21),cot(0.21)-(4.6916981)],_
[0.22,4.4718835,cot(0.22),cot(0.22)-(4.4718835)],_
[0.23,4.2708877,cot(0.23),cot(0.23)-(4.2708877)],_
[0.24,4.0863578,cot(0.24),cot(0.24)-(4.0863578)],_
[0.25,3.9163174,cot(0.25),cot(0.25)-(3.9163174)],_
[0.26,3.7590941,cot(0.26),cot(0.26)-(3.7590941)],_
[0.27,3.6132632,cot(0.27),cot(0.27)-(3.6132632)],_
[0.28,3.4776037,cot(0.28),cot(0.28)-(3.4776037)],_
[0.29,3.3510628,cot(0.29),cot(0.29)-(3.3510628)],_
[0.30,3.2327281,cot(0.30),cot(0.30)-(3.2327281)],_
[0.31,3.1218050,cot(0.31),cot(0.31)-(3.1218050)],_
[0.32,3.0175980,cot(0.32),cot(0.32)-(3.0175980)],_
[0.33,2.9194961,cot(0.33),cot(0.33)-(2.9194961)],_
[0.34,2.8269600,cot(0.34),cot(0.34)-(2.8269600)],_
[0.35,2.7395122,cot(0.35),cot(0.35)-(2.7395122)],_
[0.36,2.6567280,cot(0.36),cot(0.36)-(2.6567280)],_
[0.37,2.5782289,cot(0.37),cot(0.37)-(2.5782289)],_
[0.38,2.5036759,cot(0.38),cot(0.38)-(2.5036759)],_
[0.39,2.4327650,cot(0.39),cot(0.39)-(2.4327650)],_
[0.40,2.3652224,cot(0.40),cot(0.40)-(2.3652224)],_
[0.41,2.3008012,cot(0.41),cot(0.41)-(2.3008012)],_
[0.42,2.2392778,cot(0.42),cot(0.42)-(2.2392778)],_
[0.43,2.1804495,cot(0.43),cot(0.43)-(2.1804495)],_
[0.44,2.1241320,cot(0.44),cot(0.44)-(2.1241320)],_
[0.45,2.0701574,cot(0.45),cot(0.45)-(2.0701574)],_
[0.46,2.0183722,cot(0.46),cot(0.46)-(2.0183722)],_
[0.47,1.9686361,cot(0.47),cot(0.47)-(1.9686361)],_
[0.48,1.9208205,cot(0.48),cot(0.48)-(1.9208205)],_
[0.49,1.8748073,cot(0.49),cot(0.49)-(1.8748073)],_
[0.50,1.83048772,cot(0.50),cot(0.50)-(1.83048772)],_
[0.51,1.78776154,cot(0.51),cot(0.51)-(1.78776154)],_
[0.52,1.74653626,cot(0.52),cot(0.52)-(1.74653626)],_
[0.53,1.70672634,cot(0.53),cot(0.53)-(1.70672634)],_
[0.54,1.66825255,cot(0.54),cot(0.54)-(1.66825255)],_
[0.55,1.63104142,cot(0.55),cot(0.55)-(1.63104142)],_
[0.56,1.59502471,cot(0.56),cot(0.56)-(1.59502471)],_
[0.57,1.56013894,cot(0.57),cot(0.57)-(1.56013894)],_
[0.58,1.52632503,cot(0.58),cot(0.58)-(1.52632503)],_
[0.59,1.49352784,cot(0.59),cot(0.59)-(1.49352784)],_
[0.60,1.46169595,cot(0.60),cot(0.60)-(1.46169595)],_
[0.61,1.43078125,cot(0.61),cot(0.61)-(1.43078125)],_
[0.62,1.40073873,cot(0.62),cot(0.62)-(1.40073873)],_
[0.63,1.37152626,cot(0.63),cot(0.63)-(1.37152626)],_
[0.64,1.34310429,cot(0.64),cot(0.64)-(1.34310429)],_
[0.65,1.31543569,cot(0.65),cot(0.65)-(1.31543569)],_
[0.66,1.28848559,cot(0.66),cot(0.66)-(1.28848559)],_
[0.67,1.26222118,cot(0.67),cot(0.67)-(1.26222118)],_
[0.68,1.23661155,cot(0.68),cot(0.68)-(1.23661155)],_
[0.69,1.21162759,cot(0.69),cot(0.69)-(1.21162759)],_
[0.70,1.18724183,cot(0.70),cot(0.70)-(1.18724183)],_
[0.71,1.16342833,cot(0.71),cot(0.71)-(1.16342833)],_
[0.72,1.14016258,cot(0.72),cot(0.72)-(1.14016258)],_
[0.73,1.11742140,cot(0.73),cot(0.73)-(1.11742140)],_
[0.74,1.09518285,cot(0.74),cot(0.74)-(1.09518285)],_
[0.75,1.07342615,cot(0.75),cot(0.75)-(1.07342615)],_
[0.76,1.05213158,cot(0.76),cot(0.76)-(1.05213158)],_
[0.77,1.03128046,cot(0.77),cot(0.77)-(1.03128046)],_
[0.78,1.01085503,cot(0.78),cot(0.78)-(1.01085503)],_
[0.79,0.99083842,cot(0.79),cot(0.79)-(0.99083842)],_
[0.80,0.97121460,cot(0.80),cot(0.80)-(0.97121460)],_
[0.81,0.95196830,cot(0.81),cot(0.81)-(0.95196830)],_
[0.82,0.93308500,cot(0.82),cot(0.82)-(0.93308500)],_
[0.83,0.91455085,cot(0.83),cot(0.83)-(0.91455085)],_
[0.84,0.89635264,cot(0.84),cot(0.84)-(0.89635264)],_
[0.85,0.87847778,cot(0.85),cot(0.85)-(0.87847778)],_
[0.86,0.86091426,cot(0.86),cot(0.86)-(0.86091426)],_
[0.87,0.84365058,cot(0.87),cot(0.87)-(0.84365058)],_
[0.88,0.82667575,cot(0.88),cot(0.88)-(0.82667575)],_
[0.89,0.80997930,cot(0.89),cot(0.89)-(0.80997930)],_
[0.90,0.79355115,cot(0.90),cot(0.90)-(0.79355115)],_
[0.91,0.77738169,cot(0.91),cot(0.91)-(0.77738169)],_
[0.92,0.76146169,cot(0.92),cot(0.92)-(0.76146169)],_
[0.93,0.74578232,cot(0.93),cot(0.93)-(0.74578232)],_
[0.94,0.73033510,cot(0.94),cot(0.94)-(0.73033510)],_
[0.95,0.71511188,cot(0.95),cot(0.95)-(0.71511188)],_
[0.96,0.70010485,cot(0.96),cot(0.96)-(0.70010485)],_
[0.97,0.68530649,cot(0.97),cot(0.97)-(0.68530649)],_
[0.98,0.67070959,cot(0.98),cot(0.98)-(0.67070959)],_
[0.99,0.65630719,cot(0.99),cot(0.99)-(0.65630719)],_
[1.00,0.64209262,cot(1.00),cot(1.00)-(0.64209262)],_
[1.01,0.62805942,cot(1.01),cot(1.01)-(0.62805942)],_
[1.02,0.61420141,cot(1.02),cot(1.02)-(0.61420141)],_
[1.03,0.60051260,cot(1.03),cot(1.03)-(0.60051260)],_
[1.04,0.58698722,cot(1.04),cot(1.04)-(0.58698722)],_
[1.05,0.57361970,cot(1.05),cot(1.05)-(0.57361970)],_
[1.06,0.56040467,cot(1.06),cot(1.06)-(0.56040467)],_
[1.07,0.54733693,cot(1.07),cot(1.07)-(0.54733693)],_
[1.08,0.53441147,cot(1.08),cot(1.08)-(0.53441147)],_
[1.09,0.52162342,cot(1.09),cot(1.09)-(0.52162342)],_
[1.10,0.50896811,cot(1.10),cot(1.10)-(0.50896811)],_
[1.11,0.49644096,cot(1.11),cot(1.11)-(0.49644096)],_
[1.12,0.48403759,cot(1.12),cot(1.12)-(0.48403759)],_
[1.13,0.47175371,cot(1.13),cot(1.13)-(0.47175371)],_
[1.14,0.45958520,cot(1.14),cot(1.14)-(0.45958520)],_
[1.15,0.44752802,cot(1.15),cot(1.15)-(0.44752802)],_
[1.16,0.43557829,cot(1.16),cot(1.16)-(0.43557829)],_
[1.17,0.42373221,cot(1.17),cot(1.17)-(0.42373221)],_
[1.18,0.41198610,cot(1.18),cot(1.18)-(0.41198610)],_
[1.19,0.40033638,cot(1.19),cot(1.19)-(0.40033638)],_
[1.20,0.38877957,cot(1.20),cot(1.20)-(0.38877957)],_
[1.21,0.37731227,cot(1.21),cot(1.21)-(0.37731227)],_
[1.22,0.36593119,cot(1.22),cot(1.22)-(0.36593119)],_
[1.23,0.35463310,cot(1.23),cot(1.23)-(0.35463310)],_
[1.24,0.34341486,cot(1.24),cot(1.24)-(0.34341486)],_
[1.25,0.33227342,cot(1.25),cot(1.25)-(0.33227342)],_
[1.26,0.32120577,cot(1.26),cot(1.26)-(0.32120577)],_
[1.27,0.31020899,cot(1.27),cot(1.27)-(0.31020899)],_
[1.28,0.29928023,cot(1.28),cot(1.28)-(0.29928023)],_
[1.29,0.28841670,cot(1.29),cot(1.29)-(0.28841670)],_
[1.30,0.27761565,cot(1.30),cot(1.30)-(0.27761565)],_
[1.31,0.26687440,cot(1.31),cot(1.31)-(0.26687440)],_
[1.32,0.25619034,cot(1.32),cot(1.32)-(0.25619034)],_
[1.33,0.24556088,cot(1.33),cot(1.33)-(0.24556088)],_
[1.34,0.23498350,cot(1.34),cot(1.34)-(0.23498350)],_
[1.35,0.22445572,cot(1.35),cot(1.35)-(0.22445572)],_
[1.36,0.21397509,cot(1.36),cot(1.36)-(0.21397509)],_
[1.37,0.20353922,cot(1.37),cot(1.37)-(0.20353922)],_
[1.38,0.19314574,cot(1.38),cot(1.38)-(0.19314574)],_
[1.39,0.18279234,cot(1.39),cot(1.39)-(0.18279234)],_
[1.40,0.17247673,cot(1.40),cot(1.40)-(0.17247673)],_
[1.41,0.16219663,cot(1.41),cot(1.41)-(0.16219663)],_
[1.42,0.15194983,cot(1.42),cot(1.42)-(0.15194983)],_
[1.43,0.14173413,cot(1.43),cot(1.43)-(0.14173413)],_
[1.44,0.13154734,cot(1.44),cot(1.44)-(0.13154734)],_
[1.45,0.12138732,cot(1.45),cot(1.45)-(0.12138732)],_
[1.46,0.11125194,cot(1.46),cot(1.46)-(0.11125194)],_
[1.47,0.10113908,cot(1.47),cot(1.47)-(0.10113908)],_
[1.48,0.091046660,cot(1.48),cot(1.48)-(0.091046660)],_
[1.49,0.080972601,cot(1.49),cot(1.49)-(0.080972601)],_
[1.50,0.070914844,cot(1.50),cot(1.50)-(0.070914844)],_
[1.51,0.060871343,cot(1.51),cot(1.51)-(0.060871343)],_
[1.52,0.050840061,cot(1.52),cot(1.52)-(0.050840061)],_
[1.53,0.040818975,cot(1.53),cot(1.53)-(0.040818975)],_
[1.54,0.030806066,cot(1.54),cot(1.54)-(0.030806066)],_
[1.55,0.020799325,cot(1.55),cot(1.55)-(0.020799325)],_
[1.56,0.010796746,cot(1.56),cot(1.56)-(0.010796746)],_
[1.57,0.000796327,cot(1.57),cot(1.57)-(0.000796327)],_
[1.58,-0.009203933,cot(1.58),cot(1.58)-(-0.009203933)],_
[1.59,-0.019206034,cot(1.59),cot(1.59)-(-0.019206034)],_
[1.60,-0.029211978,cot(1.60),cot(1.60)-(-0.029211978)]]
 

   (2)
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                                                        Type: List List Float
--R 
--R
--R   (2)
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--R    [1.53,0.040818975,0.0408189748 6263901912 7,- 0.1373609808 7 E -9],
--R    [1.54,0.030806066,0.0308060663 7630738330 6,0.3763073833 07 E -9],
--R    [1.55,0.020799325,0.0207993253 6207296975 6,0.3620729697 56 E -9],
--R    [1.56,0.010796746,0.0107967462 901583485,0.2901583485 E -9],
--R    [1.57,0.000796327,0.0007963269 6322325475 679,- 0.3677674524 32 E -10],
--R    [1.58,- 0.009203933,- 0.0092039330 8759988693 76,- 0.8759988693 75 E -10],
--R    [1.59,- 0.019206034,- 0.0192060342 0373002777 9,- 0.2037300277 79 E -9],
--R    [1.6,- 0.029211978,- 0.0292119781 9994480011 4,- 0.1999448001 14 E -9]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to schaum33.output (2009/2/17, 17:59:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(csch(a*x),x)
 

        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
   (1)  -----------------------------------------------------------------
                                        a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R   (1)  -----------------------------------------------------------------
--R                                        a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/a*log(tanh((a*x)/2))
 

                 a x
        log(tanh(---))
                  2
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R                 a x
--R        log(tanh(---))
--R                  2
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

   (3)
                  a x
       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
                   2
     + 
       log(sinh(a x) + cosh(a x) - 1)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  a x
--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
--R                   2
--R     + 
--R       log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 4      14:636 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 5
aa:=integrate(csch(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 6
bb:=-coth(a*x)/a
 

          coth(a x)
   (2)  - ---------
              a
                                                     Type: Expression Integer
--R
--R          coth(a x)
--R   (2)  - ---------
--R              a
--R                                                     Type: Expression Integer
--E

--S 7      14:637 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                         2
       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
     + 
                 2
       (cosh(a x)  - 1)coth(a x) - 2
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                         2
--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
--R     + 
--R                 2
--R       (cosh(a x)  - 1)coth(a x) - 2
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(csch(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                   3                      2                2
       - 2sinh(a x)  - 6cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
     + 
                   3
       - 2cosh(a x)  - 2cosh(a x)
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
     + 
       2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                   3                      2                2
--R       - 2sinh(a x)  - 6cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
--R     + 
--R                   3
--R       - 2cosh(a x)  - 2cosh(a x)
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
--R     + 
--R       2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=-(csch(a*x)*coth(a*x))/(2*a)-1/(2*a)*log(tanh((a*x)/2))
 

                   a x
        - log(tanh(---)) - coth(a x)csch(a x)
                    2
   (2)  -------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                   a x
--R        - log(tanh(---)) - coth(a x)csch(a x)
--R                    2
--R   (2)  -------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 10     14:638 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
                  a x
         log(tanh(---))
                   2
     + 
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                  4
       coth(a x)csch(a x)sinh(a x)
     + 
                                                  3
       (4cosh(a x)coth(a x)csch(a x) - 2)sinh(a x)
     + 
                   2                                              2
       ((6cosh(a x)  - 2)coth(a x)csch(a x) - 6cosh(a x))sinh(a x)
     + 
                   3                                             2
       ((4cosh(a x)  - 4cosh(a x))coth(a x)csch(a x) - 6cosh(a x)  - 2)sinh(a x)
     + 
               4             2                                    3
     (cosh(a x)  - 2cosh(a x)  + 1)coth(a x)csch(a x) - 2cosh(a x)  - 2cosh(a x)
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
     + 
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                  4
--R       coth(a x)csch(a x)sinh(a x)
--R     + 
--R                                                  3
--R       (4cosh(a x)coth(a x)csch(a x) - 2)sinh(a x)
--R     + 
--R                   2                                              2
--R       ((6cosh(a x)  - 2)coth(a x)csch(a x) - 6cosh(a x))sinh(a x)
--R     + 
--R                   3                                             2
--R       ((4cosh(a x)  - 4cosh(a x))coth(a x)csch(a x) - 6cosh(a x)  - 2)sinh(a x)
--R     + 
--R               4             2                                    3
--R     (cosh(a x)  - 2cosh(a x)  + 1)coth(a x)csch(a x) - 2cosh(a x)  - 2cosh(a x)
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
--R     + 
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 11
aa:=integrate(csch(a*x)^n*coth(a*x),x)
 

   (1)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
  /
     a n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R  /
--R     a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12
bb:=-csch(a*x)^n/(n*a)
 

                   n
          csch(a x)
   (2)  - ----------
              a n
                                                     Type: Expression Integer
--R
--R                   n
--R          csch(a x)
--R   (2)  - ----------
--R              a n
--R                                                     Type: Expression Integer
--E

--S 13
cc:=aa-bb
 

   (3)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                n
       csch(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (3)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                n
--R       csch(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 14
cschrule:=rule(csch(x) == 1/sinh(x))
 

                      1
   (4)  csch(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (4)  csch(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 15
dd:=cschrule cc
 

   (5)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (5)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 16
ee:=expandLog dd
 

   (6)
       sinh
                           2                                  2
            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
                              2                                  2
               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (6)
--R       sinh
--R                           2                                  2
--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R                              2                                  2
--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 17
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (7)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (7)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 18
ff:=sinhsqrrule ee
 

   (8)
       sinh
                                                               2
                  4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
            n log(--------------------------------------------------)
                                           2
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
                                                                  2
                     4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
               n log(--------------------------------------------------)
                                              2
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (8)
--R       sinh
--R                                                               2
--R                  4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
--R            n log(--------------------------------------------------)
--R                                           2
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R                                                                  2
--R                     4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
--R               n log(--------------------------------------------------)
--R                                              2
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 19
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (9)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (9)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20
gg:=coshsqrrule ff
 

   (10)
       sinh
            n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
               n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (10)
--R       sinh
--R            n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R               n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 21
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %K sinh(y + x) - %K sinh(y - x)
   (11)  %K cosh(y)sinh(x) == -------------------------------
                                             2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %O sinh(y + x) - %O sinh(y - x)
--I   (11)  %O cosh(y)sinh(x) == -------------------------------
--R                                             2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 22
hh:=sinhcoshrule gg
 

   (12)
       sinh
            n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
          + 
            - n log(2)
     + 
       -
          cosh
               n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
             + 
               - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (12)
--R       sinh
--R            n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
--R          + 
--R            - n log(2)
--R     + 
--R       -
--R          cosh
--R               n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
--R             + 
--R               - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 23     14:639 Schaums and Axiom agree
ii:=complexNormalize hh
 

   (13)  0
                                                     Type: Expression Integer
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 24
aa:=integrate(1/csch(a*x),x)
 

        cosh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cosh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25
bb:=1/a*cosh(a*x)
 

        cosh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        cosh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 26     14:640 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27     14:641 Axiom cannot compute this integral
aa:=integrate(x*csch(a*x),x)
 

           x
         ++
   (1)   |   %P csch(%P a)d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O csch(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 28
aa:=integrate(x*csch(a*x)^2,x)
 

   (1)
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                       2                                           2
       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                       2                                           2
--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E

--S 29
bb:=-(x*coth(a*x))/a+1/a^2*log(sinh(a*x))
 

        log(sinh(a x)) - a x coth(a x)
   (2)  ------------------------------
                       2
                      a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x)) - a x coth(a x)
--R   (2)  ------------------------------
--R                       2
--R                      a
--R                                                     Type: Expression Integer
--E

--S 30
cc:=aa-bb
 

   (3)
                   2                                  2
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                                      2
       (a x coth(a x) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
     + 
                     2                                 2
       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                                      2
--R       (a x coth(a x) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
--R     + 
--R                     2                                 2
--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 31
dd:=expandLog cc
 

   (4)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                                                 2
       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
                     2                                             2
       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (4)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                                                 2
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R                     2                                             2
--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 32
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 33
ee:=sinhsqrrule dd
 

   (6)
                                                         2
         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
      *
         log(sinh(a x) - cosh(a x))
     + 
       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
     + 
                                       2
       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
     + 
                                                                2
       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
     + 
       2a x
  /
       2                      2               2         2     2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                         2
--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
--R     + 
--R                                       2
--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
--R     + 
--R                                                                2
--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
--R     + 
--R       2a x
--R  /
--R       2                      2               2         2     2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
--R                                                     Type: Expression Integer
--E

--S 34
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35
ff:=coshsqrrule ee
 

   (8)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 36
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %Q sinh(y + x) - %Q sinh(y - x)
   (9)  %Q cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %P sinh(y + x) - %P sinh(y - x)
--I   (9)  %P cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37
gg:=sinhcoshrule ff
 

   (10)
       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 38     14:642 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         - log(- 1) + log(- 2)
   (11)  ---------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R         - log(- 1) + log(- 2)
--R   (11)  ---------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 39     14:643 Axiom cannot compute this integral
aa:=integrate(csch(a*x)/x,x)
 

           x
         ++  csch(%P a)
   (1)   |   ---------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  csch(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 40
aa:=integrate(1/(q+p*csch(a*x)),x)
 

   (1)
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
           +-------+
           | 2    2
       a x\|q  + p
  /
         +-------+
         | 2    2
     a q\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R           +-------+
--R           | 2    2
--R       a x\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 41
t1:=integrate(1/(p+q*sinh(a*x)),x)
 

   (2)
     log
                 2         2      2                              2         2
                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
              + 
                                  2     2
                2p q cosh(a x) + q  + 2p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                 3     2                   3     2                  2     3
            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
       /
                       2                                             2
            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
          + 
            2p cosh(a x) - q
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R
--R   (2)
--R     log
--R                 2         2      2                              2         2
--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R              + 
--R                                  2     2
--R                2p q cosh(a x) + q  + 2p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                 3     2                   3     2                  2     3
--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R       /
--R                       2                                             2
--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R          + 
--R            2p cosh(a x) - q
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E

--S 42
bb:=x/q-p/q*t1
 

   (3)
       -
            p
         *
            log
                        2         2      2
                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                     + 
                        2         2                     2     2
                       q cosh(a x)  + 2p q cosh(a x) + q  + 2p
                  *
                      +-------+
                      | 2    2
                     \|q  + p
                 + 
                      3     2                   3     2                  2     3
                 (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
              /
                              2                                             2
                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                 + 
                   2p cosh(a x) - q
     + 
           +-------+
           | 2    2
       a x\|q  + p
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            p
--R         *
--R            log
--R                        2         2      2
--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                     + 
--R                        2         2                     2     2
--R                       q cosh(a x)  + 2p q cosh(a x) + q  + 2p
--R                  *
--R                      +-------+
--R                      | 2    2
--R                     \|q  + p
--R                 + 
--R                      3     2                   3     2                  2     3
--R                 (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R              /
--R                              2                                             2
--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                 + 
--R                   2p cosh(a x) - q
--R     + 
--R           +-------+
--R           | 2    2
--R       a x\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 43
cc:=aa-bb
 

   (4)
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 44
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 45
dd:=sinhsqrrule cc
 

   (6)
         p
      *
         log
                       2                              2
                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
                  + 
                      2         2                     2     2
                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (4q  + 4p q)sinh(a x) + (4q  + 4p q)cosh(a x) + 4p q  + 4p
           /
                                                                          2
                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
              + 
                4p cosh(a x) - 3q
     + 
         p
      *
         log
                       2                              2
                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
                  + 
                      2         2                     2     2
                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 4q  - 4p q)sinh(a x) + (- 4q  - 4p q)cosh(a x) - 4p q  - 4p
           /
                                                                          2
                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
              + 
                4p cosh(a x) - 3q
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (6)
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                      2         2                     2     2
--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (4q  + 4p q)sinh(a x) + (4q  + 4p q)cosh(a x) + 4p q  + 4p
--R           /
--R                                                                          2
--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
--R              + 
--R                4p cosh(a x) - 3q
--R     + 
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                      2         2                     2     2
--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 4q  - 4p q)sinh(a x) + (- 4q  - 4p q)cosh(a x) - 4p q  - 4p
--R           /
--R                                                                          2
--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
--R              + 
--R                4p cosh(a x) - 3q
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 46
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 47
ee:=coshsqrrule dd
 

   (8)
         p
      *
         log
                       2                              2
                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
           /
              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
     + 
         p
      *
         log
                       2                              2
                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (8)
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
--R           /
--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
--R     + 
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 48     14:644 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

               4    2 2
        p log(q  + p q )
   (9)  ----------------
              +-------+
              | 2    2
          a q\|q  + p
                                                     Type: Expression Integer
--R
--R               4    2 2
--R        p log(q  + p q )
--R   (9)  ----------------
--R              +-------+
--R              | 2    2
--R          a q\|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 49     14:645 Axiom cannot compute this integral
aa:=integrate(csch(a*x)^n,x)
 

           x
         ++            n
   (1)   |   csch(%P a) d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   csch(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to calcprob.output (2009/2/17, 17:44:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 
solve(3*x-(x-7)=4*x-5,x)
 

   (1)  [x= 6]
                              Type: List Equation Fraction Polynomial Integer
--R
--R   (1)  [x= 6]
--R                              Type: List Equation Fraction Polynomial Integer
--E 1

--S 2
solve(4*x-3*y=9,y)::List Equation Polynomial Fraction Integer
 

            4
   (2)  [y= - x - 3]
            3
                              Type: List Equation Polynomial Fraction Integer
--R
--R            4
--R   (2)  [y= - x - 3]
--R            3
--R                              Type: List Equation Polynomial Fraction Integer
--E 2

--S 3
solve(A*x+B*y=C,y)
 

            - A x + C
   (3)  [y= ---------]
                B
                              Type: List Equation Fraction Polynomial Integer
--R
--R            - A x + C
--R   (3)  [y= ---------]
--R                B
--R                              Type: List Equation Fraction Polynomial Integer
--E 3

--S 4
m:=3*x-4*(x-(2/3)*y)=(4/5)*x-(7*y+3)
 

        8               4
   (4)  - y - x= - 7y + - x - 3
        3               5
                                   Type: Equation Polynomial Fraction Integer
--R
--R        8               4
--R   (4)  - y - x= - 7y + - x - 3
--R        3               5
--R                                   Type: Equation Polynomial Fraction Integer
--E 4

--S 5
n:=solve(m*15,y)
 

            27x - 45
   (5)  [y= --------]
               145
                              Type: List Equation Fraction Polynomial Integer
--R
--R            27x - 45
--R   (5)  [y= --------]
--R               145
--R                              Type: List Equation Fraction Polynomial Integer
--E 5

--S 6
p:=n.1*145-27*x
 

   (6)  145y - 27x= - 45
                                   Type: Equation Fraction Polynomial Integer
--R
--R   (6)  145y - 27x= - 45
--R                                   Type: Equation Fraction Polynomial Integer
--E 6

--S 7
(x1,y1):=(-3,-8)
 

   (7)  - 8
                                                                Type: Integer
--R
--R   (7)  - 8
--R                                                                Type: Integer
--E 7

--S 8
(x2,y2):=(-6,2)
 

   (8)  2
                                                        Type: PositiveInteger
--R
--R   (8)  2
--R                                                        Type: PositiveInteger
--E 8

--S 9
m:=(y2-y1)/(x2-x1)
 

          10
   (9)  - --
           3
                                                       Type: Fraction Integer
--R
--R          10
--R   (9)  - --
--R           3
--R                                                       Type: Fraction Integer
--E 9

--S 10
solve(y1=m*x1+b,b)
 

   (10)  [b= - 18]
                              Type: List Equation Fraction Polynomial Integer
--R
--R   (10)  [b= - 18]
--R                              Type: List Equation Fraction Polynomial Integer
--E 10

--S 11
b:=-18
 

   (11)  - 18
                                                                Type: Integer
--R
--R   (11)  - 18
--R                                                                Type: Integer
--E 11

--S 12
y=m*x+b
 

              10
   (12)  y= - -- x - 18
               3
                                   Type: Equation Polynomial Fraction Integer
--R
--R              10
--R   (12)  y= - -- x - 18
--R               3
--R                                   Type: Equation Polynomial Fraction Integer
--E 12
)spool 
 
Starts dribbling to kamke6.output (2009/2/17, 17:48:5).
)set break resume
 
)set mes auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 120
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 120
--Rf:=operator 'f
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 120
--Rg:=operator 'g
--R 
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--R
--E 3

--S 4 of 120
--Rode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x)
--R 
--R
--R                2    2  ,           3
--R   (4)  (6x y(x)  + x )y (x) - 3y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 120
--Rsolve(ode301,y,x)
--R 
--R
--R   (5)  "failed"
--R                                                    Type: Union("failed",...)
--E 5

--S 6 of 120
--Rode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x)
--R 
--R
--R          2    2      ,
--R   (6)  (x y(x)  + x)y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 120
--Rsolve(ode302,y,x)
--R 
--R
--R   (7)  "failed"
--R                                                    Type: Union("failed",...)
--E 7

--S 8 of 120
--Rode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x)
--R 
--R
--R          3    2     2          ,       2    3
--R   (8)  (x y(x)  - 2x y(x) + x)y (x) + x y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 8

--S 9 of 120
--Rsolve(ode303,y,x)
--R 
--R
--R   (9)  "failed"
--R                                                    Type: Union("failed",...)
--E 9

--S 10 of 120
--Rode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2
--R 
--R
--R             3    2    2           ,        2    3         2
--R   (10)  (10x y(x)  + x y(x) + 2x)y (x) + 5x y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 120
--Rsolve(ode304,y,x)
--R 
--R
--R   (11)  "failed"
--R                                                    Type: Union("failed",...)
--E 11

--S 12 of 120
--Rode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2
--R 
--R
--R              3       ,               2
--R   (12)  (y(x)  - 3x)y (x) - 3y(x) + x
--R
--R                                                     Type: Expression Integer
--E 12

--S 13 of 120
--Ryx:=solve(ode305,y,x)
--R 
--R
--R              4                3
--R         3y(x)  - 36x y(x) + 4x
--R   (13)  -----------------------
--R                    12
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 120
--Rode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2
--R 
--R
--R   (14)
--R                 15             12       3    11         2    9        4    8
--R           27y(x)   - 1053x y(x)   + 108x y(x)   + 14580x y(x)  - 2916x y(x)
--R         + 
--R               6    7         3    6         5    5        7    4
--R           144x y(x)  - 81648x y(x)  + 23328x y(x)  - 2160x y(x)
--R         + 
--R               9          4             3         6    2        8           10
--R           (64x  + 139968x  - 5184x)y(x)  - 46656x y(x)  + 5184x y(x) - 192x
--R         + 
--R                 2
--R           15552x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R               13      2    12             10        3    9       5    8
--R       - 81y(x)   + 27x y(x)   + 2916x y(x)   - 1296x y(x)  + 108x y(x)
--R     + 
--R               2    7         4    6        6    5
--R       - 34992x y(x)  + 19440x y(x)  - 3024x y(x)
--R     + 
--R            8          3            4         5    3         7    2
--R       (144x  + 139968x  - 1296)y(x)  - 93312x y(x)  + 20736x y(x)
--R     + 
--R               9                    11        3        2
--R       (- 1920x  + 31104x)y(x) + 64x   - 6912x  + 1728x
--R  /
--R     1728
--R                                                     Type: Expression Integer
--E 14

--S 15 of 120
--Rode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x)
--R 
--R
--R              3    3  ,       2
--R   (15)  (y(x)  - x )y (x) - x y(x)
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 120
--Ryx:=solve(ode306,y,x)
--R 
--R
--R             6     3    3
--R         y(x)  - 2x y(x)
--R   (16)  ----------------
--R                 6
--R                                          Type: Union(Expression Integer,...)
--E 16

--S 17 of 120
--Rode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx
--R 
--R
--R   (17)
--R               23     3    20      6    17      9    14     12    11
--R           y(x)   - 7x y(x)   + 18x y(x)   - 20x y(x)   + 8x  y(x)
--R         + 
--R                 3    5       6    2
--R           - 216x y(x)  + 216x y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R        2    21     5    18      8    15     11    12      2    6       5    3
--R     - x y(x)   + 6x y(x)   - 12x y(x)   + 8x  y(x)   - 36x y(x)  + 288x y(x)
--R  /
--R     216
--R                                                     Type: Expression Integer
--E 17

--S 18 of 120
--Rode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x
--R 
--R
--R              3     2           ,            2    3
--R   (18)  (y(x)  + (x  + a)y(x))y (x) + x y(x)  + x  - a x
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 120
--Ryx:=solve(ode307,y,x)
--R 
--R
--R             4      2          2    4       2
--R         y(x)  + (2x  + 2a)y(x)  + x  - 2a x
--R   (19)  ------------------------------------
--R                           4
--R                                          Type: Union(Expression Integer,...)
--E 19

--S 20 of 120
--Rode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x
--R 
--R
--R   (20)
--R               15      2          13       4        2      2     11
--R           y(x)   + (7x  + 7a)y(x)   + (21x  + 30a x  + 18a )y(x)
--R         + 
--R               6        4      2 2      3     9
--R           (35x  + 45a x  + 30a x  + 20a )y(x)
--R         + 
--R               8        6      2 4         3       2     4           7
--R           (35x  + 20a x  - 12a x  + (- 16a  + 16)x  + 8a  + 16a)y(x)
--R         + 
--R                    10        8      2 6         3       4         4        2
--R                 21x   - 15a x  - 36a x  + (- 24a  + 48)x  + (- 24a  + 96a)x
--R               + 
--R                    2
--R                 48a
--R          *
--R                 5
--R             y(x)
--R         + 
--R                 12        10     2 8       3       6       4        4      2 2
--R               7x   - 18a x   - 6a x  + (16a  + 48)x  + (24a  + 80a)x  + 64a x
--R             + 
--R                  3
--R               32a
--R          *
--R                 3
--R             y(x)
--R         + 
--R             14       12     2 10      3       8     4 6      2 4      3 2
--R           (x   - 5a x   + 6a x   + (4a  + 16)x  - 8a x  - 48a x  - 32a x )y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             14      3            12       5        3     2      10
--R       x y(x)   + (7x  + 5a x)y(x)   + (21x  + 18a x  + 6a x)y(x)
--R     + 
--R           7        5     2 3        3           8
--R       (35x  + 15a x  - 6a x  + (- 4a  + 4)x)y(x)
--R     + 
--R           9        7      2 5         3       3        4             6
--R       (35x  - 20a x  - 36a x  + (- 16a  + 32)x  + (- 8a  + 32a)x)y(x)
--R     + 
--R           11        9      2 7       3       5       4        3      2      4
--R       (21x   - 45a x  - 12a x  + (24a  + 72)x  + (24a  + 80a)x  + 32a x)y(x)
--R     + 
--R          13        11      2 9       3       7      4 5      2 3      3      2
--R       (7x   - 30a x   + 30a x  + (16a  + 64)x  - 24a x  - 96a x  - 32a x)y(x)
--R     + 
--R        15       13      2 11         3       9      4        7       3       3
--R       x   - 7a x   + 18a x   + (- 20a  + 20)x  + (8a  - 48a)x  + (32a  + 64)x
--R     + 
--R       - 64a x
--R  /
--R     64
--R                                                     Type: Expression Integer
--E 20

--S 21 of 120
--Rode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2
--R 
--R
--R              3 ,            2
--R   (21)  2y(x) y (x) + x y(x)
--R
--R                                                     Type: Expression Integer
--E 21

--S 22 of 120
--Ryx:=solve(ode308,y,x)
--R 
--R
--R              2    2
--R         2y(x)  + x
--R   (22)  -----------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 22

--S 23 of 120
--Rode308expr := 2*yx**3*D(yx,x)+x*yx**2
--R 
--R
--R   (23)
--R              7      2    5      4    3     6      ,             6
--R       (16y(x)  + 24x y(x)  + 12x y(x)  + 2x y(x))y (x) + 8x y(x)
--R
--R     + 
--R           3          4      5     3     2    7    5
--R       (12x  + 4x)y(x)  + (6x  + 4x )y(x)  + x  + x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 23

--S 24 of 120
--Rode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x
--R 
--R
--R               3         ,        3
--R   (24)  (2y(x)  + y(x))y (x) - 2x  - x
--R
--R                                                     Type: Expression Integer
--E 24

--S 25 of 120
--Ryx:=solve(ode309,y,x)
--R 
--R
--R             4       2    4    2
--R         y(x)  + y(x)  - x  - x
--R   (25)  -----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 25

--S 26 of 120
--Rode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x
--R 
--R
--R   (26)
--R                15        13        4     2         11
--R           2y(x)   + 7y(x)   + (- 6x  - 6x  + 9)y(x)
--R         + 
--R                 4      2         9      8      6     4      2         7
--R           (- 15x  - 15x  + 5)y(x)  + (6x  + 12x  - 6x  - 12x  + 5)y(x)
--R         + 
--R              8      6     4     2         5
--R           (9x  + 18x  + 6x  - 3x  + 6)y(x)
--R         + 
--R                12     10     8     6    4     2         3
--R           (- 2x   - 6x   - 3x  + 4x  - x  - 4x  + 2)y(x)
--R         + 
--R               12     10     8    6     4     2
--R           (- x   - 3x   - 3x  - x  - 2x  - 2x )y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R            3         12        3          10      7     5     3          8
--R       (- 2x  - x)y(x)   + (- 6x  - 3x)y(x)   + (6x  + 9x  - 3x  - 3x)y(x)
--R     + 
--R           7      5     3         6        11      9     7     5    3          4
--R       (12x  + 18x  + 4x  - x)y(x)  + (- 6x   - 15x  - 6x  + 6x  - x  - 2x)y(x)
--R     + 
--R            11      9      7     5     3          2     15     13     11     9
--R       (- 6x   - 15x  - 12x  - 3x  - 4x  - 2x)y(x)  + 2x   + 7x   + 9x   + 5x
--R     + 
--R         7     5     3
--R       5x  + 6x  - 6x  - 4x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 26

--S 27 of 120
--Rode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3
--R 
--R
--R               3     2      ,             2    3
--R   (27)  (2y(x)  + 5x y(x))y (x) + 5x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 27

--S 28 of 120
--Ryx:=solve(ode310,y,x)
--R 
--R
--R              4      2    2    4
--R         2y(x)  + 10x y(x)  + x
--R   (28)  -----------------------
--R                    4
--R                                          Type: Union(Expression Integer,...)
--E 28

--S 29 of 120
--Rode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3
--R 
--R
--R   (29)
--R                 15       2    13        4    11        6    9
--R           16y(x)   + 280x y(x)   + 1824x y(x)   + 5300x y(x)
--R         + 
--R                 8       2     7         10        4     5
--R           (6212x  + 160x )y(x)  + (1590x   + 1200x )y(x)
--R         + 
--R                12        6     3      14       8
--R           (152x   + 2080x )y(x)  + (5x   + 200x )y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R               14       3    12        5    10         7           8
--R       40x y(x)   + 608x y(x)   + 3180x y(x)   + (6212x  + 40x)y(x)
--R     + 
--R             9       3     6        11        5     4       13       7     2
--R       (2650x  + 800x )y(x)  + (456x   + 3120x )y(x)  + (35x   + 800x )y(x)
--R     + 
--R        15      9      3
--R       x   + 50x  + 32x
--R  /
--R     32
--R                                                     Type: Expression Integer
--E 29

--S 30 of 120
--Rode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_
--R             y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3
--R 
--R
--R   (30)
--R          3          2     2         3  ,          3          2     2         3
--R   (20y(x)  - 3x y(x)  + 6x y(x) + 3x )y (x) - y(x)  + 6x y(x)  + 9x y(x) + 4x
--R
--R                                                     Type: Expression Integer
--E 30

--S 31 of 120
--Ryx:=solve(ode311,y,x)
--R 
--R
--R              4         3     2    2     3        4
--R   (31)  5y(x)  - x y(x)  + 3x y(x)  + 3x y(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 31

--S 32 of 120
--Rode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_
--R                yx**3+6*x*yx**2+9*x**2*yx+4*x**3
--R 
--R
--R   (32)
--R                  15              14          2    13         3    12
--R         50000y(x)   - 37500x y(x)   + 115500x y(x)   + 37700x y(x)
--R       + 
--R                4             11           5       2     10
--R         (67860x  - 1500x)y(x)   + (111540x  + 825x )y(x)
--R       + 
--R                6        3     9          7        4     8
--R         (90600x  - 2400x )y(x)  + (72720x  - 1206x )y(x)
--R       + 
--R                8        5       2     7          9        6       3     6
--R         (71880x  - 1032x  + 600x )y(x)  + (52080x  - 1554x  - 210x )y(x)
--R       + 
--R                10        7       4     5          11       8       5     4
--R         (29880x   - 1206x  + 558x )y(x)  + (17100x   - 630x  + 360x )y(x)
--R       + 
--R               12       9       6      3     3
--R         (8860x   - 420x  + 156x  + 60x )y(x)
--R       + 
--R               13       10       7     4     2
--R         (3180x   - 234x   + 144x  - 9x )y(x)
--R       + 
--R              14      11      8      5           15     12      9     6
--R         (660x   - 72x   + 90x  + 18x )y(x) + 60x   - 9x   + 18x  + 9x
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R               15              14        2    13          3           12
--R     - 2500y(x)   + 16500x y(x)   + 8700x y(x)   + (22620x  - 125)y(x)
--R   + 
--R            4            11          5       2     10          6       3     9
--R     (50700x  + 150x)y(x)   + (54360x  - 720x )y(x)   + (56560x  - 536x )y(x)
--R   + 
--R            7       4            8          8        5      2     7
--R     (71880x  - 645x  + 150x)y(x)  + (66960x  - 1332x  - 90x )y(x)
--R   + 
--R            9        6       3     6          10        7       4     5
--R     (49800x  - 1407x  + 372x )y(x)  + (37620x   - 1008x  + 360x )y(x)
--R   + 
--R            11       8       5      2     4
--R     (26580x   - 945x  + 234x  + 45x )y(x)
--R   + 
--R            12       9       6      3     3
--R     (13780x   - 780x  + 336x  - 12x )y(x)
--R   + 
--R           13       10       7      4     2
--R     (4620x   - 396x   + 360x  + 45x )y(x)
--R   + 
--R          14       11       8      5           15      12      9      6     3
--R     (900x   - 108x   + 162x  + 54x )y(x) + 80x   - 13x   + 30x  + 21x  + 4x
--R                                                     Type: Expression Integer
--E 32

--S 33 of 120
--Rode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_
--R             (y(x)*D(y(x),x)-x)
--R 
--R
--R   (33)
--R                2     3      2        2      2    2        ,
--R       ((a b + a )y(x)  + ((b  + a b)x  - a b  + a b)y(x))y (x)
--R
--R     + 
--R               2       2     2        3       2    2
--R       (a b + a )x y(x)  + (b  + a b)x  + (a b  - a b)x
--R  /
--R        2    2
--R     a b  + a b
--R                                                     Type: Expression Integer
--E 33

--S 34 of 120
--Rsolve(ode312,y,x)
--R 
--R
--R   (34)  "failed"
--R                                                    Type: Union("failed",...)
--E 34

--S 35 of 120
--Rode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_
--R             a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3
--R 
--R
--R   (35)
--R             3            2      3      2  ,            3         2       2
--R     (2a y(x)  + 3a x y(x)  - b x  + c x )y (x) - a y(x)  + c y(x)  + 3b x y(x)
--R
--R   + 
--R         3
--R     2b x
--R                                                     Type: Expression Integer
--E 35

--S 36 of 120
--Rsolve(ode313,y,x)
--R 
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

--S 37 of 120
--Rode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x)
--R 
--R
--R               3 ,                     4
--R   (37)  x y(x) y (x) - x sin(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 37

--S 38 of 120
--Ryx:=solve(ode314,y,x)
--R 
--R
--R               3                   4      2                4    4
--R         (- 16x  + 96x)sin(x) + (4x  - 48x  + 96)cos(x) + x y(x)
--R   (38)  --------------------------------------------------------
--R                                     4
--R                                          Type: Union(Expression Integer,...)
--E 38

--S 39 of 120
--Rode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x)
--R 
--R
--R   (39)
--R                    14          12           10           8     3      3
--R           (- 16384x   + 294912x   - 1769472x   + 3538944x )y(x) sin(x)
--R         + 
--R                        15          13           11           9            7
--R                 (12288x   - 294912x   + 2506752x   - 8847360x  + 10616832x )
--R              *
--R                     3
--R                 y(x) cos(x)
--R             + 
--R                     15         13          11     7
--R               (3072x   - 36864x   + 110592x  )y(x)
--R          *
--R                   2
--R             sin(x)
--R         + 
--R                          16         14           12           10            8
--R                   - 3072x   + 92160x   - 1032192x   + 5308416x   - 12386304x
--R                 + 
--R                            6
--R                   10616832x
--R              *
--R                     3      2
--R                 y(x) cos(x)
--R             + 
--R                       16         14          12          10     7
--R               (- 1536x   + 27648x   - 147456x   + 221184x  )y(x) cos(x)
--R             + 
--R                      16        14     11
--R               (- 192x   + 1152x  )y(x)
--R          *
--R             sin(x)
--R         + 
--R                   17        15          13          11           9           7
--R               256x   - 9216x   + 129024x   - 884736x   + 3096576x  - 5308416x
--R             + 
--R                       5
--R               3538944x
--R          *
--R                 3      3
--R             y(x) cos(x)
--R         + 
--R                17        15         13          11          9     7      2
--R           (192x   - 4608x   + 36864x   - 110592x   + 110592x )y(x) cos(x)
--R         + 
--R               17       15        13     11           17    15
--R           (48x   - 576x   + 1152x  )y(x)  cos(x) + 4x  y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                   14          12          10            8            6
--R             16384x   - 229376x   + 196608x   + 10616832x  - 56623104x
--R           + 
--R                      4
--R             84934656x
--R      *
--R               4
--R         sin(x)
--R     + 
--R                       15          13          11            9             7
--R               - 12288x   + 229376x   - 540672x   - 13959168x  + 116785152x
--R             + 
--R                           5             3
--R               - 339738624x  + 339738624x
--R          *
--R             cos(x)
--R         + 
--R                   15        13          11           9           7     4
--R           (- 3072x   + 4096x   + 479232x   - 3538944x  + 7077888x )y(x)
--R      *
--R               3
--R         sin(x)
--R     + 
--R                    16         14          12           10            8
--R               3072x   - 67584x   + 147456x   + 7372800x   - 79626240x
--R             + 
--R                         6             4             2
--R               343277568x  - 679477248x  + 509607936x
--R          *
--R                   2
--R             cos(x)
--R         + 
--R                    16        14          12           10            8
--R               1536x   - 3072x   - 442368x   + 4792320x   - 17694720x
--R             + 
--R                        6
--R               21233664x
--R          *
--R                 4
--R             y(x) cos(x)
--R         + 
--R                16        14         12          10     8
--R           (192x   + 3456x   - 55296x   + 165888x  )y(x)
--R      *
--R               2
--R         sin(x)
--R     + 
--R                     17        15         13           11            9
--R               - 256x   + 5120x   + 43008x   - 2064384x   + 23445504x
--R             + 
--R                           7             5             3
--R               - 129171456x  + 378667008x  - 566231040x  + 339738624x
--R          *
--R                   3
--R             cos(x)
--R         + 
--R                     17        15          13           11            9
--R               - 192x   - 1536x   + 147456x   - 1953792x   + 10506240x
--R             + 
--R                          7            5
--R               - 24772608x  + 21233664x
--R          *
--R                 4      2
--R             y(x) cos(x)
--R         + 
--R                 17        15         13          11          9     8
--R           (- 48x   - 1728x   + 40320x   - 221184x   + 331776x )y(x) cos(x)
--R         + 
--R                17       15        13     12
--R           (- 4x   - 256x   + 1536x  )y(x)   - 256x
--R      *
--R         sin(x)
--R     + 
--R               16         14          12           10            8            6
--R           256x   - 12288x   + 245760x   - 2654208x   + 16809984x  - 63700992x
--R         + 
--R                     4             2
--R           141557760x  - 169869312x  + 84934656
--R      *
--R               4
--R         cos(x)
--R     + 
--R               16         14          12           10           8            6
--R           512x   - 18432x   + 258048x   - 1769472x   + 6193152x  - 10616832x
--R         + 
--R                   4
--R           7077888x
--R      *
--R             4      3
--R         y(x) cos(x)
--R     + 
--R            16        14         12          10          8     8      2
--R       (288x   - 6912x   + 55296x   - 165888x   + 165888x )y(x) cos(x)
--R     + 
--R           16       14        12     12           16    16
--R       (64x   - 768x   + 1536x  )y(x)  cos(x) + 5x  y(x)
--R  /
--R     256
--R                                                     Type: Expression Integer
--E 39

--S 40 of 120
--Rode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x)
--R 
--R
--R                 3    4  ,          4     3
--R   (40)  (2x y(x)  - x )y (x) - y(x)  + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 40

--S 41 of 120
--Rsolve(ode315,y,x)
--R 
--R
--R   (41)  "failed"
--R                                                    Type: Union("failed",...)
--E 41

--S 42 of 120
--Rode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2
--R 
--R
--R                 3         ,           2
--R   (42)  (2x y(x)  + y(x))y (x) + 2y(x)
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 120
--Ryx:=solve(ode316,y,x)
--R 
--R
--R                  2
--R              y(x)
--R              -----          2
--R                2        y(x)
--R         4x %e      + Ei(-----)
--R                           2
--R   (43)  ----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 120
--Rode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2
--R 
--R
--R   (44)
--R                                     2 4                                     2 3
--R                                 y(x)                                    y(x)
--R                                 -----                              2    -----
--R                5    2      4      2           4    2      3    y(x)       2
--R           (128x y(x)  + 64x )(%e     )  + (96x y(x)  + 48x )Ei(-----)(%e     )
--R                                                                  2
--R         + 
--R                                                                 2 2
--R                                                             y(x)
--R                                     2 2                     -----
--R                3    2      2    y(x)         2    2           2
--R           ((24x y(x)  + 12x )Ei(-----)  + 16x y(x)  + 8x)(%e     )
--R                                   2
--R         + 
--R                                                                     2
--R                                                                 y(x)
--R                                 2 3                        2    -----
--R               2    2        y(x)              2        y(x)       2
--R           ((2x y(x)  + x)Ei(-----)  + (4x y(x)  + 2)Ei(-----))%e
--R                               2                          2
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                       2 4                           2 3
--R                   y(x)                          y(x)
--R                   -----                    2    -----
--R           4         2          3       y(x)       2
--R       128x y(x)(%e     )  + 96x y(x)Ei(-----)(%e     )
--R                                          2
--R     + 
--R                                                     2 2
--R                                                 y(x)
--R                       2 2                       -----
--R           2       y(x)          2                 2
--R       (24x y(x)Ei(-----)  + (32x  + 16x)y(x))(%e     )
--R                     2
--R     + 
--R                                                         2
--R                                                     y(x)
--R                      2 3                       2    -----               2 2
--R                  y(x)                      y(x)       2             y(x)
--R       (2x y(x)Ei(-----)  + (16x + 4)y(x)Ei(-----))%e      + 2y(x)Ei(-----)
--R                    2                         2                        2
--R  /
--R     4y(x)
--R                                                     Type: Expression Integer
--E 44

--S 45 of 120
--Rode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x)
--R 
--R
--R                 3             2  ,          2
--R   (45)  (2x y(x)  + x y(x) + x )y (x) + y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 120
--Rsolve(ode317,y,x)
--R 
--R
--R   (46)  "failed"
--R                                                    Type: Union("failed",...)
--E 46

--S 47 of 120
--Rode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2)
--R 
--R
--R                 3                   ,          4        2
--R   (47)  (3x y(x)  + (- 4x + 1)y(x))y (x) + y(x)  - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 47

--S 48 of 120
--Ryx:=solve(ode318,y,x)
--R 
--R
--R   (48)
--R                                       +---------+
--R                4               2      |    2              5                 3
--R       (- x y(x)  + (2x - 1)y(x)  + 2)\|y(x)  - 2  + x y(x)  + (- 2x + 1)y(x)
--R     + 
--R       - 2y(x)
--R  /
--R          +---------+
--R          |    2            2
--R     y(x)\|y(x)  - 2  - y(x)  + 2
--R                                          Type: Union(Expression Integer,...)
--E 48

--S 49 of 120
--Rode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2)
--R 
--R
--R   (49)
--R           5    11         5      4     9       5      4      3     7
--R         9x y(x)   + (- 30x  + 30x )y(x)  + (24x  - 96x  + 36x )y(x)
--R       + 
--R             4       3      2     5       3      2          3
--R         (72x  - 120x  + 21x )y(x)  + (88x  - 68x  + 7x)y(x)
--R       + 
--R             2
--R         (40x  - 14x + 1)y(x)
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R       4    12         4      3     10       4      3      2     8
--R     4x y(x)   + (- 16x  + 13x )y(x)   + (16x  - 52x  + 15x )y(x)
--R   + 
--R         3      2          6       2               4                2
--R     (52x  - 66x  + 8x)y(x)  + (72x  - 38x + 2)y(x)  + (44x - 8)y(x)  + 8
--R                                                     Type: Expression Integer
--E 49

--S 50 of 120
--Rode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x)
--R 
--R
--R                 3              ,          4
--R   (50)  (7x y(x)  + y(x) - 5x)y (x) + y(x)  - 5y(x)
--R
--R                                                     Type: Expression Integer
--E 50

--S 51 of 120
--Ryx:=solve(ode319,y,x)
--R 
--R
--R                 7        5            4         2
--R         10x y(x)  + 2y(x)  - 100x y(x)  - 25y(x)  + 250x y(x)
--R   (51)  -----------------------------------------------------
--R                                   10
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 120
--Rode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx
--R 
--R
--R   (52)
--R                  5    27          4    25            5    24          3    23
--R           490000x y(x)   + 364000x y(x)   - 17500000x y(x)   + 100800x y(x)
--R         + 
--R                      4    22              5         2     21           3    20
--R           - 13685000x y(x)   + (269500000x  + 12320x )y(x)   - 3969000x y(x)
--R         + 
--R                      4            19                 5          2     18
--R           (210000000x  + 560x)y(x)   + (- 2327500000x  - 505400x )y(x)
--R         + 
--R                    3    17                 4              16
--R           60952500x y(x)   + (- 1710625000x  - 23800x)y(x)
--R         + 
--R                        5           2     15             3    14
--R           (12250000000x  + 7784000x )y(x)   - 464625000x y(x)
--R         + 
--R                       4         2               13
--R           (7962500000x  + 70000x  + 367500x)y(x)
--R         + 
--R                          5            2     12               3              11
--R           (- 39812500000x  - 55168750x )y(x)   + (1842750000x  + 24000x)y(x)
--R         + 
--R                          4           2                10
--R           (- 20934375000x  - 1100000x  - 2406250x)y(x)
--R         + 
--R                        5             2            9
--R           (76562500000x  + 175000000x  + 2000)y(x)
--R         + 
--R                         3               8
--R           (- 3543750000x  - 405000x)y(x)
--R         + 
--R                        4           2                7
--R           (28000000000x  + 6000000x  + 5468750x)y(x)
--R         + 
--R                          5             2             6
--R           (- 76562500000x  - 191756250x  - 35000)y(x)
--R         + 
--R                       3                5
--R           (2460937500x  + 1800000x)y(x)
--R         + 
--R                          4            2              4
--R           (- 13671875000x  - 12500000x  - 50000x)y(x)
--R         + 
--R                        5           2              3                2
--R           (27343750000x  + 2000000x  + 125000)y(x)  - 1875000x y(x)
--R         + 
--R                    2                          2
--R           (6250000x  + 250000x)y(x) - 1250000x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             4    28         3    26           4    25         2    24
--R       80000x y(x)   + 50000x y(x)   - 3200000x y(x)   + 10800x y(x)
--R     + 
--R                 3    23             4            22          2    21
--R       - 2125000x y(x)   + (56000000x  + 880x)y(x)   - 486000x y(x)
--R     + 
--R                 3          20                4              19
--R       (37500000x  + 16)y(x)   + (- 560000000x  - 41800x)y(x)
--R     + 
--R               2    18                3           17
--R       8707500x y(x)   + (- 359375000x  - 800)y(x)
--R     + 
--R                   4               16            2    15
--R       (3500000000x  + 764500x)y(x)   - 79650000x y(x)
--R     + 
--R                   3                      14
--R       (2031250000x  + 10000x + 15000)y(x)
--R     + 
--R                      4                13              2            12
--R       (- 14000000000x  - 6668750x)y(x)   + (394875000x  + 2000)y(x)
--R     + 
--R                     3                        11
--R       (- 6796875000x  - 200000x - 125000)y(x)
--R     + 
--R                    4                 10                 2             9
--R       (35000000000x  + 27500000x)y(x)   + (- 1012500000x  - 45000)y(x)
--R     + 
--R                    3                         8
--R       (12500000000x  + 1500000x + 390625)y(x)
--R     + 
--R                      4                 7               2              6
--R       (- 50000000000x  - 43068750x)y(x)  + (1054687500x  + 300000)y(x)
--R     + 
--R                     3                        5
--R       (- 9765625000x  - 5000000x - 10000)y(x)
--R     + 
--R                    4                4             3                          2
--R       (31250000000x  + 1000000x)y(x)  - 625000y(x)  + (6250000x + 125000)y(x)
--R     + 
--R       - 2500000x y(x)
--R  /
--R     10000
--R                                                     Type: Expression Integer
--E 52

--S 53 of 120
--Rode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1
--R 
--R
--R           2    3           ,
--R   (53)  (x y(x)  + x y(x))y (x) - 1
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 120
--Rsolve(ode320,y,x)
--R 
--R
--R   (54)  "failed"
--R                                                    Type: Union("failed",...)
--E 54

--S 55 of 120
--Rode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1
--R 
--R
--R            2    3    2    2       ,
--R   (55)  (2x y(x)  + x y(x)  - 2x)y (x) - 2y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 55

--S 56 of 120
--Rsolve(ode321,y,x)
--R 
--R
--R   (56)  "failed"
--R                                                    Type: Union("failed",...)
--E 56

--S 57 of 120
--Rode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x
--R 
--R
--R             2    3        2      ,             4
--R   (57)  (10x y(x)  - 3y(x)  - 2)y (x) + 5x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 120
--Ryx:=solve(ode322,y,x)
--R 
--R
--R           2    4        3            2
--R         5x y(x)  - 2y(x)  - 4y(x) + x
--R   (58)  ------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 120
--Rode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x
--R 
--R
--R   (59)
--R                 10    15         8    14         6    13
--R           25000x  y(x)   - 37500x y(x)   + 21000x y(x)
--R         + 
--R                    8        4     12          10         6       2     11
--R           (- 65000x  - 5200x )y(x)   + (15000x   + 69000x  + 480x )y(x)
--R         + 
--R                    8         4     10          6        2     9
--R           (- 16500x  - 23100x )y(x)   + (66000x  + 2000x )y(x)
--R         + 
--R                    8         4           8         10         6        2     7
--R           (- 27000x  - 38520x  + 144)y(x)  + (3000x   + 18000x  + 3840x )y(x)
--R         + 
--R                   8         4           6          6        2     5
--R           (- 2100x  - 24920x  + 672)y(x)  + (14760x  + 4656x )y(x)
--R         + 
--R                   8        4           4        10       6        2     3
--R           (- 3000x  - 3600x  + 960)y(x)  + (200x   + 840x  + 1856x )y(x)
--R         + 
--R               8        4           2        6       2           8      4
--R         (- 60x  - 1884x  + 480)y(x)  + (480x  - 192x )y(x) - 40x  + 24x  + 64
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             9    16         7    15        5    14            7        3     13
--R       15625x y(x)   - 20000x y(x)   + 9000x y(x)   + (- 40000x  - 1600x )y(x)
--R     + 
--R              9         5           12            7        3     11
--R       (12500x  + 34500x  + 80x)y(x)   + (- 12000x  - 8400x )y(x)
--R     + 
--R              5            10            7         3     9
--R       (39600x  + 400x)y(x)   + (- 24000x  - 17120x )y(x)
--R     + 
--R             9         5            8           7         3     7
--R       (3750x  + 13500x  + 960x)y(x)  + (- 2400x  - 14240x )y(x)
--R     + 
--R              5             6           7        3     5
--R       (14760x  + 1552x)y(x)  + (- 4800x  - 2880x )y(x)
--R     + 
--R            9        5            4          7        3     3
--R       (500x  + 1260x  + 928x)y(x)  + (- 160x  - 2512x )y(x)
--R     + 
--R             5            2          7      3           9      5
--R       (1440x  - 192x)y(x)  + (- 320x  + 96x )y(x) + 25x  - 12x  - 16x
--R  /
--R     16
--R                                                     Type: Expression Integer
--E 59

--S 60 of 120
--Rode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x)
--R 
--R
--R             2    3        ,         3    2
--R   (60)  (a x y(x)  + c x)y (x) + b x y(x)  + c y(x)
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 120
--Rsolve(ode323,y,x)
--R 
--R
--R   (61)  "failed"
--R                                                    Type: Union("failed",...)
--E 61

--S 62 of 120
--Rode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x)
--R 
--R
--R            3    3      ,        3    3
--R   (62)  (2x y(x)  - x)y (x) + 2x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 62

--S 63 of 120
--Rsolve(ode324,y,x)
--R 
--R
--R   (63)  "failed"
--R                                                    Type: Union("failed",...)
--E 63

--S 64 of 120
--Rode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x
--R 
--R
--R              4     3      ,             3    4
--R   (64)  (y(x)  - 2x y(x))y (x) + 2x y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 64

--S 65 of 120
--Rsolve(ode325,y,x)
--R 
--R
--R   (65)  "failed"
--R                                                    Type: Union("failed",...)
--E 65

--S 66 of 120
--Rode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3)
--R 
--R
--R   (66)
--R       3    4     2        3       2 2    2     3      3      ,
--R     (a y(x)  + 3a b x y(x)  + 3a b x y(x)  + (b  + b)x y(x))y (x)
--R
--R   + 
--R       3           3     2   2    2       2 3        3 4
--R     (a  + a)x y(x)  + 3a b x y(x)  + 3a b x y(x) + b x
--R                                                     Type: Expression Integer
--E 66

--S 67 of 120
--Rsolve(ode326,y,x)
--R 
--R
--R   (67)  "failed"
--R                                                    Type: Union("failed",...)
--E 67

--S 68 of 120
--Rode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x)
--R 
--R
--R                4     2    3              ,          5
--R   (68)  (x y(x)  + 2x y(x)  + 2y(x) + x)y (x) + y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 120
--Rsolve(ode327,y,x)
--R 
--R
--R   (69)  "failed"
--R                                                    Type: Union("failed",...)
--E 69

--S 70 of 120
--Rode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x)
--R 
--R
--R             2    n       ,
--R   (70)  (a x y(x)  - 2x)y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 120
--Rsolve(ode328,y,x)
--R 
--R
--R   (71)  "failed"
--R                                                    Type: Union("failed",...)
--E 71

--S 72 of 120
--Rode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x)
--R 
--R
--R               n    m            ,             n    m
--R   (72)  (a x x y(x)  + alpha x)y (x) + b y(x)x y(x)  + beta y(x)
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 120
--Rsolve(ode329,y,x)
--R 
--R
--R   (73)  "failed"
--R                                                    Type: Union("failed",...)
--E 73

--S 74 of 120
--Rode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x))
--R 
--R
--R                           ,
--R   (74)  (f(y(x) + x) + 1)y (x) + f(y(x) + x)
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 120
--Rsolve(ode330,y,x)
--R 
--R 
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 75

--R
--S 76 of 120
--Rode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_
--R            x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x)
--R 
--R
--R   (75)
--R      2     +-+ +----+    2          ,            2 +-+ +----+         2
--R   (2x y(x)\|x \|y(x)  + x y(x) - x)y (x) - x y(x) \|x \|y(x)  + x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 76

--S 77 of 120
--Rsolve(ode333,y,x)
--R 
--R
--R   (76)  "failed"
--R                                                    Type: Union("failed",...)
--E 77

--S 78 of 120
--Rode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1
--R 
--R
--R           +--------+      ,
--R   (77)  (\|y(x) + x  + 1)y (x) + 1
--R
--R                                                     Type: Expression Integer
--E 78

--S 79 of 120
--Rsolve(ode334,y,x)
--R 
--R
--R   (78)  "failed"
--R                                                    Type: Union("failed",...)
--E 79

--S 80 of 120
--Rode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1)
--R 
--R
--R          +---------+         +------+
--R          |    2      ,       | 2
--R   (79)  \|y(x)  - 1 y (x) - \|x  - 1
--R
--R                                                     Type: Expression Integer
--E 80

--S 81 of 120
--Ryx:=solve(ode335,y,x)
--R 
--R
--R   (80)
--R                    +------+                    +---------+
--R                    | 2             2           |    2
--R           (4x y(x)\|x  - 1  + (- 4x  + 2)y(x))\|y(x)  - 1
--R         + 
--R                             +------+
--R                     2       | 2           2         2     2
--R           (- 4x y(x)  + 2x)\|x  - 1  + (4x  - 2)y(x)  - 2x  + 1
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  - 1  - y(x))
--R     + 
--R                      +------+                      +------+
--R                      | 2           2               | 2
--R           (- 4x y(x)\|x  - 1  + (4x  - 2)y(x))log(\|x  - 1  - x)
--R         + 
--R                                  +------+
--R                     3     3      | 2           2         3
--R           (- 4x y(x)  + 4x y(x))\|x  - 1  + (4x  - 2)y(x)
--R         + 
--R                4     2
--R           (- 4x  + 2x  + 1)y(x)
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                        +------+                                   +------+
--R                2       | 2             2         2     2          | 2
--R       ((4x y(x)  - 2x)\|x  - 1  + (- 4x  + 2)y(x)  + 2x  - 1)log(\|x  - 1  - x)
--R     + 
--R                                                +------+
--R               4        3          2     3      | 2             2         4
--R       (4x y(x)  + (- 4x  - 2x)y(x)  + 2x  - x)\|x  - 1  + (- 4x  + 2)y(x)
--R     + 
--R          4         2     4     2
--R       (4x  - 2)y(x)  - 2x  + 2x
--R  /
--R                +------+                    +---------+
--R                | 2             2           |    2
--R       (8x y(x)\|x  - 1  + (- 8x  + 4)y(x))\|y(x)  - 1
--R     + 
--R                         +------+
--R                 2       | 2           2         2     2
--R       (- 8x y(x)  + 4x)\|x  - 1  + (8x  - 4)y(x)  - 4x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 81

--S 82 of 120
--Rode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1)
--R 
--R
--R   (81)
--R                             4      2         5       4      2          3
--R                       (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R                     + 
--R                             4      2
--R                       (- 32x  + 32x  - 4)y(x)
--R                  *
--R                      +------+
--R                      | 2
--R                     \|x  - 1
--R                 + 
--R                       5      3           5         5       3           3
--R                   (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R                 + 
--R                       5      3
--R                   (32x  - 48x  + 16x)y(x)
--R              *
--R                  +---------+
--R                  |    2
--R                 \|y(x)  - 1
--R             + 
--R                       4      2         6          4       2          4
--R                   (64x  - 64x  + 8)y(x)  + (- 128x  + 128x  - 16)y(x)
--R                 + 
--R                       4      2         2     4     2
--R                   (72x  - 72x  + 9)y(x)  - 8x  + 8x  - 1
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     5      3           6        5       3           4
--R               (- 64x  + 96x  - 32x)y(x)  + (128x  - 192x  + 64x)y(x)
--R             + 
--R                     5       3           2     5      3
--R               (- 72x  + 108x  - 36x)y(x)  + 8x  - 12x  + 4x
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                       5      3           4         5      3           2     5
--R                   (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R                 + 
--R                        3
--R                   - 12x  + 4x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     6       4      2         4       6       4      2         2
--R               (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R             + 
--R                   6      4     2
--R               - 8x  + 16x  - 9x  + 1
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  - 1
--R         + 
--R                     5      3           5       5       3           3
--R               (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R             + 
--R                     5      3
--R               (- 32x  + 48x  - 16x)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R               6       4      2         5         6       4       2          3
--R           (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R         + 
--R               6      4      2
--R           (32x  - 64x  + 36x  - 4)y(x)
--R      *
--R         ROOT
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +---------+        2
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                      +------+
--R                                    3           3       3             | 2
--R                            ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
--R                          + 
--R                                 4       2          3         4      2
--R                            (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
--R                       *
--R                               +------+
--R                               | 2
--R                          log(\|x  - 1  - x)
--R                      + 
--R                                   3           5        5           3
--R                            (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
--R                          + 
--R                                  5      3
--R                            (- 64x  + 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                             4       2          5
--R                        (128x  - 128x  + 16)y(x)
--R                      + 
--R                               6      4      2          3
--R                        (- 128x  + 64x  + 64x  - 16)y(x)
--R                      + 
--R                            6      4      2
--R                        (64x  - 80x  + 16x  + 2)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                                   3           4          3           2      3
--R                              (128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x
--R                            + 
--R                              - 8x
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          4        4       2          2
--R                        (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
--R                      + 
--R                             4      2
--R                        - 16x  + 16x  - 2
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                             3           6          5      3           4
--R                        (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
--R                      + 
--R                             5      3           2      5      3
--R                        (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                           4       2          6        6       2          4
--R                    (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
--R                  + 
--R                           6       4         2      6      4     2
--R                    (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
--R               *
--R                       +---------+
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                           +------+     2
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                                 3           5          5           3
--R                            (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
--R                          + 
--R                                5      3
--R                            (64x  - 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  + 128x  - 16)y(x)
--R                      + 
--R                             6      4      2          3
--R                        (128x  - 64x  - 64x  + 16)y(x)
--R                      + 
--R                              6      4      2
--R                        (- 64x  + 80x  - 16x  - 2)y(x)
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                            3           7          5      3           5
--R                        (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
--R                      + 
--R                            7      5       3            3
--R                        (64x  + 32x  - 320x  + 128x)y(x)
--R                      + 
--R                              7      5       3
--R                        (- 32x  + 32x  + 128x  - 66x)y(x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                          4      2         7        6      4      2          5
--R                    (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
--R                  + 
--R                          8       4       2          3
--R                    (- 64x  + 344x  - 280x  + 28)y(x)
--R                  + 
--R                        8      6       4       2
--R                    (32x  - 48x  - 116x  + 132x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +------+     2
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                               3           6        5      3           4
--R                        (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
--R                      + 
--R                               5      3           2      5      3
--R                        (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                         4       2          6          6       2          4
--R                    (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
--R                  + 
--R                         6       4         2      6      4     2
--R                    (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
--R               *
--R                       +------+
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                          3           8        5           6
--R                    (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
--R                  + 
--R                          7      5       3            4
--R                    (- 64x  - 96x  + 344x  - 116x)y(x)
--R                  + 
--R                        7      5       3            2     7      5      3
--R                    (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                    4      2         8          6      4      2          6
--R                (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
--R              + 
--R                    8      6       4       2          4
--R                (64x  + 64x  - 400x  + 272x  - 23)y(x)
--R              + 
--R                      8      6       4       2          2     8      6      4
--R                (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
--R              + 
--R                   2
--R                31x  - 4
--R           /
--R                                                                +------+
--R                          3            3          3             | 2
--R                    ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
--R                  + 
--R                           4       2          3        4       2
--R                    (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                          3            4        3            2      3
--R                  ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                     4       2          4          4       2          2      4
--R                (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
--R              + 
--R                     2
--R                - 32x  + 4
--R     + 
--R                   5      3           4         5      3           2     5
--R               (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R             + 
--R                    3
--R               - 12x  + 4x
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R                 6       4      2         4       6       4      2         2
--R           (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R         + 
--R               6      4     2
--R           - 8x  + 16x  - 9x  + 1
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                 5      3           5       5       3           3
--R           (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R         + 
--R                 5      3
--R           (- 32x  + 48x  - 16x)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  - 1
--R     + 
--R           6       4      2         5         6       4       2          3
--R       (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R     + 
--R           6      4      2
--R       (32x  - 64x  + 36x  - 4)y(x)
--R  /
--R                  4      2         4         4      2         2     4     2
--R             ((64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x  + 1)
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R               5      3           4       5      3           2     5      3
--R         (- 64x  + 96x  - 32x)y(x)  + (64x  - 96x  + 32x)y(x)  - 8x  + 12x  - 4x
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                 4      2         5       4      2          3
--R           (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R         + 
--R                 4      2
--R           (- 32x  + 32x  - 4)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  - 1
--R     + 
--R           5      3           5         5       3           3
--R       (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R     + 
--R           5      3
--R       (32x  - 48x  + 16x)y(x)
--R                                                     Type: Expression Integer
--E 82

--S 83 of 120
--Rode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x)
--R 
--R
--R           +---------+                +------+
--R           |    2             ,       | 2
--R   (82)  (\|y(x)  + 1  + a x)y (x) + \|x  + 1  + a y(x)
--R
--R                                                     Type: Expression Integer
--E 83

--S 84 of 120
--Ryx:=solve(ode336,y,x)
--R 
--R
--R   (83)
--R                      +------+                  +---------+
--R                      | 2           2           |    2
--R           (- 4x y(x)\|x  + 1  + (4x  + 2)y(x))\|y(x)  + 1
--R         + 
--R                           +------+
--R                   2       | 2             2         2     2
--R           (4x y(x)  + 2x)\|x  + 1  + (- 4x  - 2)y(x)  - 2x  - 1
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  + 1  - y(x))
--R     + 
--R                      +------+                      +------+
--R                      | 2           2               | 2
--R           (- 4x y(x)\|x  + 1  + (4x  + 2)y(x))log(\|x  + 1  - x)
--R         + 
--R                                                        +------+
--R                     3       2    2        3            | 2
--R           (- 4x y(x)  + 8a x y(x)  + (- 4x  - 4x)y(x))\|x  + 1
--R         + 
--R              2         3          3            2      4     2
--R           (4x  + 2)y(x)  + (- 8a x  - 4a x)y(x)  + (4x  + 6x  + 1)y(x)
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  + 1
--R     + 
--R                        +------+                                   +------+
--R                2       | 2             2         2     2          | 2
--R       ((4x y(x)  + 2x)\|x  + 1  + (- 4x  - 2)y(x)  - 2x  - 1)log(\|x  + 1  - x)
--R     + 
--R                                                                       +------+
--R               4       2    3      3          2       2         3      | 2
--R       (4x y(x)  - 8a x y(x)  + (4x  + 6x)y(x)  - 4a x y(x) + 2x  + x)\|x  + 1
--R     + 
--R            2         4        3            3        4     2         2
--R       (- 4x  - 2)y(x)  + (8a x  + 4a x)y(x)  + (- 4x  - 8x  - 2)y(x)
--R     + 
--R            3                 4     2
--R       (4a x  + 2a x)y(x) - 2x  - 2x
--R  /
--R                +------+                    +---------+
--R                | 2             2           |    2
--R       (8x y(x)\|x  + 1  + (- 8x  - 4)y(x))\|y(x)  + 1
--R     + 
--R                         +------+
--R                 2       | 2           2         2     2
--R       (- 8x y(x)  - 4x)\|x  + 1  + (8x  + 4)y(x)  + 4x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 84

--S 85 of 120
--Rode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx
--R 
--R
--R   (84)
--R                               6        4        2          7
--R                       (- 2048x  - 3072x  - 1152x  - 64)y(x)
--R                     + 
--R                               7          5          3             6
--R                       (2048a x  + 3072a x  + 1152a x  + 64a x)y(x)
--R                     + 
--R                               6        4        2           5
--R                       (- 4096x  - 6144x  - 2304x  - 128)y(x)
--R                     + 
--R                               7          5          3             4
--R                       (3072a x  + 4608a x  + 1728a x  + 96a x)y(x)
--R                     + 
--R                               6        4        2          3
--R                       (- 2432x  - 3648x  - 1368x  - 76)y(x)
--R                     + 
--R                               7          5         3             2
--R                       (1152a x  + 1728a x  + 648a x  + 36a x)y(x)
--R                     + 
--R                              6       4       2                  7        5
--R                       (- 384x  - 576x  - 216x  - 12)y(x) + 64a x  + 96a x
--R                     + 
--R                            3
--R                       36a x  + 2a x
--R                  *
--R                      +------+
--R                      | 2
--R                     \|x  + 1
--R                 + 
--R                         7        5        3            7
--R                   (2048x  + 4096x  + 2432x  + 384x)y(x)
--R                 + 
--R                             8          6          4         2     6
--R                   (- 2048a x  - 4096a x  - 2432a x  - 384a x )y(x)
--R                 + 
--R                         7        5        3            5
--R                   (4096x  + 8192x  + 4864x  + 768x)y(x)
--R                 + 
--R                             8          6          4         2     4
--R                   (- 3072a x  - 6144a x  - 3648a x  - 576a x )y(x)
--R                 + 
--R                         7        5        3            3
--R                   (2432x  + 4864x  + 2888x  + 456x)y(x)
--R                 + 
--R                             8          6          4         2     2
--R                   (- 1152a x  - 2304a x  - 1368a x  - 216a x )y(x)
--R                 + 
--R                        7       5       3                   8         6        4
--R                   (384x  + 768x  + 456x  + 72x)y(x) - 64a x  - 128a x  - 76a x
--R                 + 
--R                          2
--R                   - 12a x
--R              *
--R                  +---------+
--R                  |    2
--R                 \|y(x)  + 1
--R             + 
--R                         6        4        2          8
--R                   (2048x  + 3072x  + 1152x  + 64)y(x)
--R                 + 
--R                             7          5          3             7
--R                   (- 2048a x  - 3072a x  - 1152a x  - 64a x)y(x)
--R                 + 
--R                         6        4        2           6
--R                   (5120x  + 7680x  + 2880x  + 160)y(x)
--R                 + 
--R                             7          5          3              5
--R                   (- 4096a x  - 6144a x  - 2304a x  - 128a x)y(x)
--R                 + 
--R                         6        4        2           4
--R                   (4224x  + 6336x  + 2376x  + 132)y(x)
--R                 + 
--R                             7          5          3             3
--R                   (- 2432a x  - 3648a x  - 1368a x  - 76a x)y(x)
--R                 + 
--R                         6        4       2          2
--R                   (1216x  + 1824x  + 684x  + 38)y(x)
--R                 + 
--R                            7         5         3                   6      4
--R                   (- 384a x  - 576a x  - 216a x  - 12a x)y(x) + 64x  + 96x
--R                 + 
--R                      2
--R                   36x  + 2
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       7        5        3            8
--R               (- 2048x  - 4096x  - 2432x  - 384x)y(x)
--R             + 
--R                       8          6          4         2     7
--R               (2048a x  + 4096a x  + 2432a x  + 384a x )y(x)
--R             + 
--R                       7         5        3            6
--R               (- 5120x  - 10240x  - 6080x  - 960x)y(x)
--R             + 
--R                       8          6          4         2     5
--R               (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R             + 
--R                       7        5        3            4
--R               (- 4224x  - 8448x  - 5016x  - 792x)y(x)
--R             + 
--R                       8          6          4         2     3
--R               (2432a x  + 4864a x  + 2888a x  + 456a x )y(x)
--R             + 
--R                       7        5        3            2
--R               (- 1216x  - 2432x  - 1444x  - 228x)y(x)
--R             + 
--R                      8         6         4        2           7       5      3
--R               (384a x  + 768a x  + 456a x  + 72a x )y(x) - 64x  - 128x  - 76x
--R             + 
--R               - 12x
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                           6          4          2           7
--R                   (2048a x  + 3072a x  + 1152a x  + 64a)y(x)
--R                 + 
--R                           7        5        3            6
--R                   (- 2048x  - 4096x  - 2432x  - 384x)y(x)
--R                 + 
--R                           6          4          2           5
--R                   (3072a x  + 4608a x  + 1728a x  + 96a)y(x)
--R                 + 
--R                           7        5        3            4
--R                   (- 3072x  - 6144x  - 3648x  - 576x)y(x)
--R                 + 
--R                           6          4         2           3
--R                   (1152a x  + 1728a x  + 648a x  + 36a)y(x)
--R                 + 
--R                           7        5        3            2
--R                   (- 1152x  - 2304x  - 1368x  - 216x)y(x)
--R                 + 
--R                       6        4        2                7       5      3
--R                 (64a x  + 96a x  + 36a x  + 2a)y(x) - 64x  - 128x  - 76x  - 12x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                         7          5          3              7
--R               (- 2048a x  - 4096a x  - 2432a x  - 384a x)y(x)
--R             + 
--R                     8        6        4        2          6
--R               (2048x  + 5120x  + 4224x  + 1216x  + 64)y(x)
--R             + 
--R                         7          5          3              5
--R               (- 3072a x  - 6144a x  - 3648a x  - 576a x)y(x)
--R             + 
--R                     8        6        4        2          4
--R               (3072x  + 7680x  + 6336x  + 1824x  + 96)y(x)
--R             + 
--R                         7          5          3              3
--R               (- 1152a x  - 2304a x  - 1368a x  - 216a x)y(x)
--R             + 
--R                     8        6        4       2          2
--R               (1152x  + 2880x  + 2376x  + 684x  + 36)y(x)
--R             + 
--R                       7         5        3                   8       6       4
--R               (- 64a x  - 128a x  - 76a x  - 12a x)y(x) + 64x  + 160x  + 132x
--R             + 
--R                  2
--R               38x  + 2
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  + 1
--R         + 
--R                         6          4          2           8
--R               (- 2048a x  - 3072a x  - 1152a x  - 64a)y(x)
--R             + 
--R                     7        5        3            7
--R               (2048x  + 4096x  + 2432x  + 384x)y(x)
--R             + 
--R                         6          4          2            6
--R               (- 4096a x  - 6144a x  - 2304a x  - 128a)y(x)
--R             + 
--R                     7        5        3            5
--R               (4096x  + 8192x  + 4864x  + 768x)y(x)
--R             + 
--R                         6          4          2           4
--R               (- 2432a x  - 3648a x  - 1368a x  - 76a)y(x)
--R             + 
--R                     7        5        3            3
--R               (2432x  + 4864x  + 2888x  + 456x)y(x)
--R             + 
--R                        6         4         2           2
--R               (- 384a x  - 576a x  - 216a x  - 12a)y(x)
--R             + 
--R                    7       5       3
--R               (384x  + 768x  + 456x  + 72x)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                   7          5          3              8
--R           (2048a x  + 4096a x  + 2432a x  + 384a x)y(x)
--R         + 
--R                   8        6        4        2          7
--R           (- 2048x  - 5120x  - 4224x  - 1216x  - 64)y(x)
--R         + 
--R                   7          5          3              6
--R           (4096a x  + 8192a x  + 4864a x  + 768a x)y(x)
--R         + 
--R                   8         6        4        2           5
--R           (- 4096x  - 10240x  - 8448x  - 2432x  - 128)y(x)
--R         + 
--R                   7          5          3              4
--R           (2432a x  + 4864a x  + 2888a x  + 456a x)y(x)
--R         + 
--R                   8        6        4        2          3
--R           (- 2432x  - 6080x  - 5016x  - 1444x  - 76)y(x)
--R         + 
--R                  7         5         3             2
--R           (384a x  + 768a x  + 456a x  + 72a x)y(x)
--R         + 
--R                  8       6       4       2
--R           (- 384x  - 960x  - 792x  - 228x  - 12)y(x)
--R      *
--R         ROOT
--R                                                               +------+
--R                             3           3       3             | 2
--R                        ((64x  + 32x)y(x)  + (32x  + 16x)y(x))\|x  + 1
--R                      + 
--R                              4      2         3         4      2
--R                        (- 64x  - 64x  - 8)y(x)  + (- 32x  - 32x  - 4)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  + 1
--R                  + 
--R                             3           4         3           2     3
--R                      ((- 64x  - 32x)y(x)  + (- 64x  - 32x)y(x)  - 8x  - 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                        4      2         4       4      2         2     4     2
--R                    (64x  + 64x  + 8)y(x)  + (64x  + 64x  + 8)y(x)  + 8x  + 8x
--R                  + 
--R                    1
--R               *
--R                       +---------+        2
--R                       |    2
--R                  log(\|y(x)  + 1  - y(x))
--R              + 
--R                                                                    +------+
--R                                  3           3       3             | 2
--R                            ((128x  + 64x)y(x)  + (64x  + 32x)y(x))\|x  + 1
--R                          + 
--R                                 4       2          3         4      2
--R                          (- 128x  - 128x  - 16)y(x)  + (- 64x  - 64x  - 8)y(x)
--R                       *
--R                               +------+
--R                               | 2
--R                          log(\|x  + 1  - x)
--R                      + 
--R                                 3           5            4         2     4
--R                            (128x  + 64x)y(x)  + (- 256a x  - 128a x )y(x)
--R                          + 
--R                                 5       3           3
--R                            (128x  + 256x  + 80x)y(x)
--R                          + 
--R                                     4        2     2       5      3
--R                            (- 128a x  - 64a x )y(x)  + (64x  + 80x  + 16x)y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  + 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  - 128x  - 16)y(x)
--R                      + 
--R                               5         3             4
--R                        (256a x  + 256a x  + 32a x)y(x)
--R                      + 
--R                               6       4       2          3
--R                        (- 128x  - 320x  - 192x  - 16)y(x)
--R                      + 
--R                               5         3             2
--R                        (128a x  + 128a x  + 16a x)y(x)
--R                      + 
--R                              6       4      2
--R                        (- 64x  - 112x  - 48x  - 2)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  + 1
--R                  + 
--R                                   3           4          3           2      3
--R                            (- 128x  - 64x)y(x)  + (- 128x  - 64x)y(x)  - 16x
--R                          + 
--R                            - 8x
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  + 1
--R                      + 
--R                             4       2          4        4       2          2
--R                        (128x  + 128x  + 16)y(x)  + (128x  + 128x  + 16)y(x)
--R                      + 
--R                           4      2
--R                        16x  + 16x  + 2
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  + 1  - x)
--R                  + 
--R                               3           6          4         2     5
--R                        (- 128x  - 64x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3            4          4         2     3
--R                        (- 128x  - 320x  - 112x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3           2         4        2
--R                        (- 128x  - 192x  - 48x)y(x)  + (32a x  + 16a x )y(x)
--R                      + 
--R                             5      3
--R                        - 16x  - 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                         4       2          6
--R                    (128x  + 128x  + 16)y(x)
--R                  + 
--R                             5         3             5
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2          4
--R                    (128x  + 384x  + 256x  + 24)y(x)
--R                  + 
--R                             5         3             3
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2         2
--R                    (128x  + 256x  + 128x  + 8)y(x)
--R                  + 
--R                            5        3                  6      4     2
--R                    (- 32a x  - 32a x  - 4a x)y(x) + 16x  + 24x  + 8x
--R               *
--R                       +---------+
--R                       |    2
--R                  log(\|y(x)  + 1  - y(x))
--R              + 
--R                                                               +------+
--R                             3           3       3             | 2
--R                        ((64x  + 32x)y(x)  + (32x  + 16x)y(x))\|x  + 1
--R                      + 
--R                              4      2         3         4      2
--R                        (- 64x  - 64x  - 8)y(x)  + (- 32x  - 32x  - 4)y(x)
--R                   *
--R                           +------+     2
--R                           | 2
--R                      log(\|x  + 1  - x)
--R                  + 
--R                                 3           5            4         2     4
--R                            (128x  + 64x)y(x)  + (- 256a x  - 128a x )y(x)
--R                          + 
--R                                 5       3           3
--R                            (128x  + 256x  + 80x)y(x)
--R                          + 
--R                                     4        2     2       5      3
--R                            (- 128a x  - 64a x )y(x)  + (64x  + 80x  + 16x)y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  + 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  - 128x  - 16)y(x)
--R                      + 
--R                               5         3             4
--R                        (256a x  + 256a x  + 32a x)y(x)
--R                      + 
--R                               6       4       2          3
--R                        (- 128x  - 320x  - 192x  - 16)y(x)
--R                      + 
--R                               5         3             2
--R                        (128a x  + 128a x  + 16a x)y(x)
--R                      + 
--R                              6       4      2
--R                        (- 64x  - 112x  - 48x  - 2)y(x)
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  + 1  - x)
--R                  + 
--R                            3           7            4         2     6
--R                        (64x  + 32x)y(x)  + (- 256a x  - 128a x )y(x)
--R                      + 
--R                              2        5        2        3           5
--R                        ((256a  + 128)x  + (128a  + 224)x  + 64x)y(x)
--R                      + 
--R                                 6         4         2     4
--R                        (- 256a x  - 512a x  - 160a x )y(x)
--R                      + 
--R                            7        2        5       2        3            3
--R                        (64x  + (128a  + 224)x  + (64a  + 448)x  + 160x)y(x)
--R                      + 
--R                                 6         4        2     2
--R                        (- 128a x  - 160a x  - 32a x )y(x)
--R                      + 
--R                            7      5       3
--R                        (32x  + 64x  + 160x  + 66x)y(x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                          4      2         7          5         3             6
--R                    (- 64x  - 64x  - 8)y(x)  + (256a x  + 256a x  + 32a x)y(x)
--R                  + 
--R                               2        6          2        4         2        2
--R                        (- 256a  - 128)x  + (- 256a  - 288)x  + (- 32a  - 160)x
--R                      + 
--R                        - 12
--R                   *
--R                          5
--R                      y(x)
--R                  + 
--R                           7         5         3             4
--R                    (256a x  + 640a x  + 384a x  + 32a x)y(x)
--R                  + 
--R                             8          2        6          2        4
--R                        - 64x  + (- 128a  - 256)x  + (- 128a  - 552)x
--R                      + 
--R                              2        2
--R                        (- 16a  - 360)x  - 36
--R                   *
--R                          3
--R                      y(x)
--R                  + 
--R                           7         5        3            2
--R                    (128a x  + 224a x  + 96a x  + 4a x)y(x)
--R                  + 
--R                          8      6       4       2
--R                    (- 32x  - 80x  - 188x  - 140x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  + 1
--R              + 
--R                             3           4         3           2     3
--R                      ((- 64x  - 32x)y(x)  + (- 64x  - 32x)y(x)  - 8x  - 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                        4      2         4       4      2         2     4     2
--R                    (64x  + 64x  + 8)y(x)  + (64x  + 64x  + 8)y(x)  + 8x  + 8x
--R                  + 
--R                    1
--R               *
--R                       +------+     2
--R                       | 2
--R                  log(\|x  + 1  - x)
--R              + 
--R                               3           6          4         2     5
--R                        (- 128x  - 64x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3            4          4         2     3
--R                        (- 128x  - 320x  - 112x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3           2         4        2
--R                        (- 128x  - 192x  - 48x)y(x)  + (32a x  + 16a x )y(x)
--R                      + 
--R                             5      3
--R                        - 16x  - 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                         4       2          6
--R                    (128x  + 128x  + 16)y(x)
--R                  + 
--R                             5         3             5
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2          4
--R                    (128x  + 384x  + 256x  + 24)y(x)
--R                  + 
--R                             5         3             3
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2         2
--R                    (128x  + 256x  + 128x  + 8)y(x)
--R                  + 
--R                            5        3                  6      4     2
--R                    (- 32a x  - 32a x  - 4a x)y(x) + 16x  + 24x  + 8x
--R               *
--R                       +------+
--R                       | 2
--R                  log(\|x  + 1  - x)
--R              + 
--R                          3           8          4         2     7
--R                    (- 64x  - 32x)y(x)  + (256a x  + 128a x )y(x)
--R                  + 
--R                            2        5          2        3           6
--R                    ((- 256a  - 128)x  + (- 128a  - 256)x  - 80x)y(x)
--R                  + 
--R                           6         4         2     5
--R                    (256a x  + 640a x  + 224a x )y(x)
--R                  + 
--R                          7          2        5          2        3            4
--R                    (- 64x  + (- 256a  - 288)x  + (- 128a  - 552)x  - 188x)y(x)
--R                  + 
--R                           6         4        2     3
--R                    (256a x  + 384a x  + 96a x )y(x)
--R                  + 
--R                          7         2        5         2        3            2
--R                    (- 64x  + (- 32a  - 160)x  + (- 16a  - 360)x  - 140x)y(x)
--R                  + 
--R                          6        4       2          7      5      3
--R                    (32a x  + 32a x  + 4a x )y(x) - 8x  - 12x  - 36x  - 16x
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  + 1
--R              + 
--R                    4      2         8            5         3             7
--R                (64x  + 64x  + 8)y(x)  + (- 256a x  - 256a x  - 32a x)y(x)
--R              + 
--R                      2        6        2        4       2        2          6
--R                ((256a  + 128)x  + (256a  + 320)x  + (32a  + 192)x  + 16)y(x)
--R              + 
--R                         7         5         3             5
--R                (- 256a x  - 768a x  - 512a x  - 48a x)y(x)
--R              + 
--R                         8        2        6        2        4       2        2
--R                      64x  + (256a  + 320)x  + (256a  + 688)x  + (32a  + 432)x
--R                    + 
--R                      41
--R               *
--R                      4
--R                  y(x)
--R              + 
--R                         7         5         3             3
--R                (- 256a x  - 512a x  - 256a x  - 16a x)y(x)
--R              + 
--R                      8       2        6       2        4      2        2
--R                  (64x  + (32a  + 192)x  + (32a  + 432)x  + (4a  + 304)x  + 33)
--R               *
--R                      2
--R                  y(x)
--R              + 
--R                        7        5        3          8      6      4      2
--R                (- 32a x  - 48a x  - 16a x )y(x) + 8x  + 16x  + 41x  + 33x  + 4
--R           /
--R                                                              +------+
--R                          3            3        3             | 2
--R                    ((256x  + 128x)y(x)  + (128x  + 64x)y(x))\|x  + 1
--R                  + 
--R                           4       2          3          4       2
--R                    (- 256x  - 256x  - 32)y(x)  + (- 128x  - 128x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  + 1
--R              + 
--R                          3            4          3            2      3
--R                  ((- 256x  - 128x)y(x)  + (- 256x  - 128x)y(x)  - 32x  - 16x)
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  + 1
--R              + 
--R                     4       2          4        4       2          2      4
--R                (256x  + 256x  + 32)y(x)  + (256x  + 256x  + 32)y(x)  + 32x
--R              + 
--R                   2
--R                32x  + 4
--R     + 
--R                             6          4         2           6
--R                   (- 1024a x  - 1536a x  - 576a x  - 32a)y(x)
--R                 + 
--R                             6          4         2           4
--R                   (- 1536a x  - 2304a x  - 864a x  - 48a)y(x)
--R                 + 
--R                            6         4         2           2        6        4
--R                   (- 576a x  - 864a x  - 324a x  - 18a)y(x)  - 32a x  - 48a x
--R                 + 
--R                          2
--R                   - 18a x  - a
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       7          5          3              6
--R               (1024a x  + 2048a x  + 1216a x  + 192a x)y(x)
--R             + 
--R                       7          5          3              4
--R               (1536a x  + 3072a x  + 1824a x  + 288a x)y(x)
--R             + 
--R                      7          5         3              2        7        5
--R               (576a x  + 1152a x  + 684a x  + 108a x)y(x)  + 32a x  + 64a x
--R             + 
--R                    3
--R               38a x  + 6a x
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  + 1
--R         + 
--R                       6          4         2           7
--R               (1024a x  + 1536a x  + 576a x  + 32a)y(x)
--R             + 
--R                       6          4          2           5
--R               (2048a x  + 3072a x  + 1152a x  + 64a)y(x)
--R             + 
--R                       6          4         2           3
--R               (1216a x  + 1824a x  + 684a x  + 38a)y(x)
--R             + 
--R                      6         4         2
--R               (192a x  + 288a x  + 108a x  + 6a)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                     7          5          3              7
--R           (- 1024a x  - 2048a x  - 1216a x  - 192a x)y(x)
--R         + 
--R                     7          5          3              5
--R           (- 2048a x  - 4096a x  - 2432a x  - 384a x)y(x)
--R         + 
--R                     7          5          3              3
--R           (- 1216a x  - 2432a x  - 1444a x  - 228a x)y(x)
--R         + 
--R                    7         5         3
--R           (- 192a x  - 384a x  - 228a x  - 36a x)y(x)
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  + 1  - y(x))
--R     + 
--R                             7          5          3             7
--R                   (- 2048a x  - 3072a x  - 1152a x  - 64a x)y(x)
--R                 + 
--R                         2 8        2 6        2 4      2 2     6
--R                   (2048a x  + 3072a x  + 1152a x  + 64a x )y(x)
--R                 + 
--R                             7          5          3              5
--R                   (- 4096a x  - 6144a x  - 2304a x  - 128a x)y(x)
--R                 + 
--R                         2 8        2 6        2 4      2 2     4
--R                   (3072a x  + 4608a x  + 1728a x  + 96a x )y(x)
--R                 + 
--R                             7          5          3             3
--R                   (- 2432a x  - 3648a x  - 1368a x  - 76a x)y(x)
--R                 + 
--R                         2 8        2 6       2 4      2 2     2
--R                   (1152a x  + 1728a x  + 648a x  + 36a x )y(x)
--R                 + 
--R                            7         5         3                   2 8      2 6
--R                   (- 384a x  - 576a x  - 216a x  - 12a x)y(x) + 64a x  + 96a x
--R                 + 
--R                      2 4     2 2
--R                   36a x  + 2a x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       8          6          4         2     7
--R               (2048a x  + 4096a x  + 2432a x  + 384a x )y(x)
--R             + 
--R                       2 9        2 7        2 5       2 3     6
--R               (- 2048a x  - 4096a x  - 2432a x  - 384a x )y(x)
--R             + 
--R                       8          6          4         2     5
--R               (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R             + 
--R                       2 9        2 7        2 5       2 3     4
--R               (- 3072a x  - 6144a x  - 3648a x  - 576a x )y(x)
--R             + 
--R                       8          6          4         2     3
--R               (2432a x  + 4864a x  + 2888a x  + 456a x )y(x)
--R             + 
--R                       2 9        2 7        2 5       2 3     2
--R               (- 1152a x  - 2304a x  - 1368a x  - 216a x )y(x)
--R             + 
--R                      8         6         4        2           2 9       2 7
--R               (384a x  + 768a x  + 456a x  + 72a x )y(x) - 64a x  - 128a x
--R             + 
--R                    2 5      2 3
--R               - 76a x  - 12a x
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  + 1
--R         + 
--R                       7          5          3             8
--R               (2048a x  + 3072a x  + 1152a x  + 64a x)y(x)
--R             + 
--R                       2 8        2 6        2 4      2 2     7
--R               (- 2048a x  - 3072a x  - 1152a x  - 64a x )y(x)
--R             + 
--R                       7          5          3              6
--R               (5120a x  + 7680a x  + 2880a x  + 160a x)y(x)
--R             + 
--R                       2 8        2 6        2 4       2 2     5
--R               (- 4096a x  - 6144a x  - 2304a x  - 128a x )y(x)
--R             + 
--R                       7          5          3              4
--R               (4224a x  + 6336a x  + 2376a x  + 132a x)y(x)
--R             + 
--R                       2 8        2 6        2 4      2 2     3
--R               (- 2432a x  - 3648a x  - 1368a x  - 76a x )y(x)
--R             + 
--R                       7          5         3             2
--R               (1216a x  + 1824a x  + 684a x  + 38a x)y(x)
--R             + 
--R                      2 8       2 6       2 4      2 2             7        5
--R               (- 384a x  - 576a x  - 216a x  - 12a x )y(x) + 64a x  + 96a x
--R             + 
--R                    3
--R               36a x  + 2a x
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                     8          6          4         2     8
--R           (- 2048a x  - 4096a x  - 2432a x  - 384a x )y(x)
--R         + 
--R                 2 9        2 7        2 5       2 3     7
--R           (2048a x  + 4096a x  + 2432a x  + 384a x )y(x)
--R         + 
--R                     8           6          4         2     6
--R           (- 5120a x  - 10240a x  - 6080a x  - 960a x )y(x)
--R         + 
--R                 2 9        2 7        2 5       2 3     5
--R           (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R         + 
--R                     8          6          4         2     4
--R           (- 4224a x  - 8448a x  - 5016a x  - 792a x )y(x)
--R         + 
--R                 2 9        2 7        2 5       2 3     3
--R           (2432a x  + 4864a x  + 2888a x  + 456a x )y(x)
--R         + 
--R                     8          6          4         2     2
--R           (- 1216a x  - 2432a x  - 1444a x  - 228a x )y(x)
--R         + 
--R                2 9       2 7       2 5      2 3             8         6
--R           (384a x  + 768a x  + 456a x  + 72a x )y(x) - 64a x  - 128a x
--R         + 
--R                  4        2
--R           - 76a x  - 12a x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                             6          4         2           6
--R                   (- 1024a x  - 1536a x  - 576a x  - 32a)y(x)
--R                 + 
--R                             6          4         2           4
--R                   (- 1536a x  - 2304a x  - 864a x  - 48a)y(x)
--R                 + 
--R                            6         4         2           2        6        4
--R                   (- 576a x  - 864a x  - 324a x  - 18a)y(x)  - 32a x  - 48a x
--R                 + 
--R                          2
--R                   - 18a x  - a
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       7          5          3              6
--R               (1024a x  + 2048a x  + 1216a x  + 192a x)y(x)
--R             + 
--R                       7          5          3              4
--R               (1536a x  + 3072a x  + 1824a x  + 288a x)y(x)
--R             + 
--R                      7          5         3              2        7        5
--R               (576a x  + 1152a x  + 684a x  + 108a x)y(x)  + 32a x  + 64a x
--R             + 
--R                    3
--R               38a x  + 6a x
--R          *
--R                  +------+
--R                  | 2
--R             log(\|x  + 1  - x)
--R         + 
--R                         6          4         2           8
--R               (- 1024a x  - 1536a x  - 576a x  - 32a)y(x)
--R             + 
--R                     2 7        2 5        2 3       2      7
--R               (4096a x  + 6144a x  + 2304a x  + 128a x)y(x)
--R             + 
--R                            8        7          6        5          4        3
--R                   - 3072a x  - 2048x  - 8192a x  - 4096x  - 6720a x  - 2432x
--R                 + 
--R                            2
--R                   - 1728a x  - 384x - 64a
--R              *
--R                     6
--R                 y(x)
--R             + 
--R                     2 7        2 5        2 3       2      5
--R               (6144a x  + 9216a x  + 3456a x  + 192a x)y(x)
--R             + 
--R                            8        7           6        5          4        3
--R                   - 4608a x  - 3072x  - 10432a x  - 6144x  - 7296a x  - 3648x
--R                 + 
--R                            2
--R                   - 1548a x  - 576x - 38a
--R              *
--R                     4
--R                 y(x)
--R             + 
--R                     2 7        2 5        2 3      2      3
--R               (2304a x  + 3456a x  + 1296a x  + 72a x)y(x)
--R             + 
--R                            8        7          6        5          4        3
--R                   - 1728a x  - 1152x  - 3648a x  - 2304x  - 2340a x  - 1368x
--R                 + 
--R                           2
--R                   - 432a x  - 216x - 6a
--R              *
--R                     2
--R                 y(x)
--R             + 
--R                    2 7       2 5      2 3     2              8      7         6
--R               (128a x  + 192a x  + 72a x  + 4a x)y(x) - 96a x  - 64x  - 192a x
--R             + 
--R                     5         4      3        2
--R               - 128x  - 114a x  - 76x  - 18a x  - 12x
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                   7          5          3              8
--R           (1024a x  + 2048a x  + 1216a x  + 192a x)y(x)
--R         + 
--R                   2 8        2 6        2 4       2 2     7
--R           (- 4096a x  - 8192a x  - 4864a x  - 768a x )y(x)
--R         + 
--R                      9        8          7        6           5        4
--R               3072a x  + 2048x  + 9728a x  + 5120x  + 10432a x  + 4224x
--R             + 
--R                      3        2
--R               4256a x  + 1216x  + 480a x + 64
--R          *
--R                 6
--R             y(x)
--R         + 
--R                   2 8         2 6        2 4        2 2     5
--R           (- 6144a x  - 12288a x  - 7296a x  - 1152a x )y(x)
--R         + 
--R                      9        8           7        6           5        4
--R               4608a x  + 3072x  + 12736a x  + 7680x  + 11936a x  + 6336x
--R             + 
--R                      3        2
--R               4180a x  + 1824x  + 372a x + 96
--R          *
--R                 4
--R             y(x)
--R         + 
--R                   2 8        2 6        2 4       2 2     3
--R           (- 2304a x  - 4608a x  - 2736a x  - 432a x )y(x)
--R         + 
--R                      9        8          7        6          5        4
--R               1728a x  + 1152x  + 4512a x  + 2880x  + 3948a x  + 2376x
--R             + 
--R                      3       2
--R               1254a x  + 684x  + 90a x + 36
--R          *
--R                 2
--R             y(x)
--R         + 
--R                  2 8       2 6       2 4      2 2             9      8
--R           (- 128a x  - 256a x  - 152a x  - 24a x )y(x) + 96a x  + 64x
--R         + 
--R                 7       6         5       4        3      2
--R           240a x  + 160x  + 198a x  + 132x  + 57a x  + 38x  + 3a x + 2
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  + 1
--R     + 
--R                       6          4         2           7
--R               (1024a x  + 1536a x  + 576a x  + 32a)y(x)
--R             + 
--R                       6          4          2           5
--R               (2048a x  + 3072a x  + 1152a x  + 64a)y(x)
--R             + 
--R                       6          4         2           3
--R               (1216a x  + 1824a x  + 684a x  + 38a)y(x)
--R             + 
--R                      6         4         2
--R               (192a x  + 288a x  + 108a x  + 6a)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                     7          5          3              7
--R           (- 1024a x  - 2048a x  - 1216a x  - 192a x)y(x)
--R         + 
--R                     7          5          3              5
--R           (- 2048a x  - 4096a x  - 2432a x  - 384a x)y(x)
--R         + 
--R                     7          5          3              3
--R           (- 1216a x  - 2432a x  - 1444a x  - 228a x)y(x)
--R         + 
--R                    7         5         3
--R           (- 192a x  - 384a x  - 228a x  - 36a x)y(x)
--R      *
--R              +------+
--R              | 2
--R         log(\|x  + 1  - x)
--R     + 
--R                   6          4         2           9
--R           (1024a x  + 1536a x  + 576a x  + 32a)y(x)
--R         + 
--R                   2 7        2 5        2 3       2      8
--R           (- 4096a x  - 6144a x  - 2304a x  - 128a x)y(x)
--R         + 
--R                      8        7          6        5          4        3
--R               3072a x  + 2048x  + 8704a x  + 4096x  + 7488a x  + 2432x
--R             + 
--R                      2
--R               2016a x  + 384x + 80a
--R          *
--R                 7
--R             y(x)
--R         + 
--R                   2 7         2 5        2 3       2      6
--R           (- 8192a x  - 12288a x  - 4608a x  - 256a x)y(x)
--R         + 
--R                      8        7           6        5           4        3
--R               6144a x  + 4096x  + 14400a x  + 8192x  + 10464a x  + 4864x
--R             + 
--R                      2
--R               2340a x  + 768x + 66a
--R          *
--R                 5
--R             y(x)
--R         + 
--R                   2 7        2 5        2 3       2      4
--R           (- 4864a x  - 7296a x  - 2736a x  - 152a x)y(x)
--R         + 
--R                      8        7          6        5          4        3
--R               3648a x  + 2432x  + 7904a x  + 4864x  + 5244a x  + 2888x
--R             + 
--R                      2
--R               1026a x  + 456x + 19a
--R          *
--R                 3
--R             y(x)
--R         + 
--R                  2 7        2 5       2 3      2      2
--R           (- 768a x  - 1152a x  - 432a x  - 24a x)y(x)
--R         + 
--R                     8       7          6       5         4       3         2
--R               576a x  + 384x  + 1184a x  + 768x  + 732a x  + 456x  + 126a x
--R             + 
--R               72x + a
--R          *
--R             y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  + 1
--R     + 
--R                 7          5          3              9
--R       (- 1024a x  - 2048a x  - 1216a x  - 192a x)y(x)
--R     + 
--R             2 8        2 6        2 4       2 2     8
--R       (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R     + 
--R                    9        8           7        6           5        4
--R           - 3072a x  - 2048x  - 10240a x  - 5120x  - 11456a x  - 4224x
--R         + 
--R                    3        2
--R           - 4864a x  - 1216x  - 576a x - 64
--R      *
--R             7
--R         y(x)
--R     + 
--R             2 8         2 6        2 4        2 2     6
--R       (8192a x  + 16384a x  + 9728a x  + 1536a x )y(x)
--R     + 
--R                    9        8           7         6           5        4
--R           - 6144a x  - 4096x  - 17472a x  - 10240x  - 16896a x  - 8448x
--R         + 
--R                    3        2
--R           - 6156a x  - 2432x  - 588a x - 128
--R      *
--R             5
--R         y(x)
--R     + 
--R             2 8        2 6        2 4       2 2     4
--R       (4864a x  + 9728a x  + 5776a x  + 912a x )y(x)
--R     + 
--R                    9        8          7        6          5        4
--R           - 3648a x  - 2432x  - 9728a x  - 6080x  - 8740a x  - 5016x
--R         + 
--R                    3        2
--R           - 2888a x  - 1444x  - 228a x - 76
--R      *
--R             3
--R         y(x)
--R     + 
--R            2 8        2 6       2 4       2 2     2
--R       (768a x  + 1536a x  + 912a x  + 144a x )y(x)
--R     + 
--R                   9       8          7       6          5       4         3
--R           - 576a x  - 384x  - 1472a x  - 960x  - 1252a x  - 792x  - 380a x
--R         + 
--R                 2
--R           - 228x  - 24a x - 12
--R      *
--R         y(x)
--R  /
--R                     6        4        2          6
--R               (2048x  + 3072x  + 1152x  + 64)y(x)
--R             + 
--R                     6        4        2          4
--R               (3072x  + 4608x  + 1728x  + 96)y(x)
--R             + 
--R                     6        4       2          2      6      4      2
--R               (1152x  + 1728x  + 648x  + 36)y(x)  + 64x  + 96x  + 36x  + 2
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                   7        5        3            6
--R           (- 2048x  - 4096x  - 2432x  - 384x)y(x)
--R         + 
--R                   7        5        3            4
--R           (- 3072x  - 6144x  - 3648x  - 576x)y(x)
--R         + 
--R                   7        5        3            2      7       5      3
--R           (- 1152x  - 2304x  - 1368x  - 216x)y(x)  - 64x  - 128x  - 76x  - 12x
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  + 1
--R     + 
--R                   6        4        2          7
--R           (- 2048x  - 3072x  - 1152x  - 64)y(x)
--R         + 
--R                   6        4        2           5
--R           (- 4096x  - 6144x  - 2304x  - 128)y(x)
--R         + 
--R                   6        4        2          3
--R           (- 2432x  - 3648x  - 1368x  - 76)y(x)
--R         + 
--R                  6       4       2
--R           (- 384x  - 576x  - 216x  - 12)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  + 1
--R     + 
--R             7        5        3            7
--R       (2048x  + 4096x  + 2432x  + 384x)y(x)
--R     + 
--R             7        5        3            5
--R       (4096x  + 8192x  + 4864x  + 768x)y(x)
--R     + 
--R           7        5        3            3        7       5       3
--R     (2432x  + 4864x  + 2888x  + 456x)y(x)  + (384x  + 768x  + 456x  + 72x)y(x)
--R                                                     Type: Expression Integer
--E 85

--S 86 of 120
--Rode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x)
--R 
--R
--R           +----------+
--R           |    2    2       ,
--R   (85)  (\|y(x)  + x   + x)y (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 86

--S 87 of 120
--Rsolve(ode337,y,x)
--R 
--R
--R   (86)  "failed"
--R                                                    Type: Union("failed",...)
--E 87

--S 88 of 120
--Rode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_
--R            2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_
--R            2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha)
--R 
--R
--R   (87)
--R           +----------+
--R           |    2    2         2    2                                 ,
--R     (y(x)\|y(x)  + x   + (y(x)  - x )sin(alpha) - 2x y(x)cos(alpha))y (x)
--R
--R   + 
--R       +----------+
--R       |    2    2                             2    2
--R     x\|y(x)  + x   + 2x y(x)sin(alpha) + (y(x)  - x )cos(alpha)
--R                                                     Type: Expression Integer
--E 88

--S 89 of 120
--Rsolve(ode338,y,x)
--R 
--R
--R   (88)  "failed"
--R                                                    Type: Union("failed",...)
--E 89

--S 90 of 120
--Rode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_
--R            y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2)
--R 
--R
--R   (89)
--R        +--------------+                               +--------------+
--R        |    2    2            3    2      ,           |    2    2
--R     (x\|y(x)  + x  + 1  - y(x)  - x y(x))y (x) - y(x)\|y(x)  + x  + 1
--R
--R   + 
--R             2    3
--R     - x y(x)  - x
--R                                                     Type: Expression Integer
--E 90

--S 91 of 120
--Rsolve(ode339,y,x)
--R 
--R
--R   (90)  "failed"
--R                                                    Type: Union("failed",...)
--E 91

--S 92 of 120
--Rode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_
--R           ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_
--R           (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2))
--R 
--R
--R   (91)
--R                               2       3         2    2        3
--R             ((e2 x - a e2)y(x)  + e2 x  + a e2 x  - a e2 x - a e2)
--R          *
--R              +----------------------+
--R              |    2    2           2
--R             \|y(x)  + x  + 2a x + a
--R         + 
--R                               2       3         2    2        3
--R             ((e1 x + a e1)y(x)  + e1 x  - a e1 x  - a e1 x + a e1)
--R          *
--R              +----------------------+
--R              |    2    2           2
--R             \|y(x)  + x  - 2a x + a
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                                                     +----------------------+
--R                 3          2              2         |    2    2           2
--R       (- e2 y(x)  + (- e2 x  - 2a e2 x - a e2)y(x))\|y(x)  + x  + 2a x + a
--R     + 
--R                                                     +----------------------+
--R                 3          2              2         |    2    2           2
--R       (- e1 y(x)  + (- e1 x  + 2a e1 x - a e1)y(x))\|y(x)  + x  - 2a x + a
--R  /
--R                                                    +----------------------+
--R            4      2     2     2    4     2 2    4  |    2    2           2
--R       (y(x)  + (2x  + 2a )y(x)  + x  - 2a x  + a )\|y(x)  + x  - 2a x + a
--R    *
--R        +----------------------+
--R        |    2    2           2
--R       \|y(x)  + x  + 2a x + a
--R                                                     Type: Expression Integer
--E 92

--S 93 of 120
--Rsolve(ode340,y,x)
--R 
--R
--R   (92)  "failed"
--R                                                    Type: Union("failed",...)
--E 93

--S 94 of 120
--Rode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x)
--R 
--R
--R              y(x)     x  ,        y(x)         x
--R   (93)  (x %e     + %e )y (x) + %e     + y(x)%e
--R
--R                                                     Type: Expression Integer
--E 94

--S 95 of 120
--Ryx:=solve(ode341,y,x)
--R 
--R
--R             y(x)         x
--R   (94)  x %e     + y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 95

--S 96 of 120
--Rode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x)
--R 
--R
--R   (95)
--R                                                               y(x)         x
--R        2  y(x)       x  ,          y(x)           x       x %e     + y(x)%e
--R     ((x %e     + x %e )y (x) + x %e     + x y(x)%e  + 1)%e
--R
--R   + 
--R          x  y(x)      x 2  ,               x  y(x)           x 2
--R     (x %e %e     + (%e ) )y (x) + (x + 1)%e %e     + 2y(x)(%e )
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 120
--Rode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1
--R 
--R
--R   (96)
--R      2  x y(x)     2  - x y(x)  ,               x y(x)            - x y(x)
--R   (3x %e       + 2x %e        )y (x) + 3x y(x)%e       + 2x y(x)%e         + 1
--R
--R                                                     Type: Expression Integer
--E 97

--S 98 of 120
--Ryx:=solve(ode342,y,x)
--R 
--R
--R             x y(x) 2           x y(x)
--R         3(%e      )  + log(x)%e       - 2
--R   (97)  ---------------------------------
--R                        x y(x)
--R                      %e
--R                                          Type: Union(Expression Integer,...)
--E 98

--S 99 of 120
--Rode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1
--R 
--R
--R   (98)
--R              3   x y(x) 2     3  ,         2             x y(x) 2
--R           (9x (%e      )  + 6x )y (x) + (9x y(x) + 9x)(%e      )
--R
--R         + 
--R                             x y(x)     2
--R           (3x log(x) + 3x)%e       + 6x y(x) - 6x
--R      *
--R                 x y(x) 2             x y(x)
--R           3x (%e      )  + x log(x)%e       - 2x
--R           --------------------------------------
--R                            x y(x)
--R                          %e
--R         %e
--R     + 
--R              3   x y(x) 2     3  ,         2             x y(x) 2
--R           (6x (%e      )  + 4x )y (x) + (6x y(x) + 6x)(%e      )
--R
--R         + 
--R                             x y(x)     2
--R           (2x log(x) + 2x)%e       + 4x y(x) - 4x
--R      *
--R                   x y(x) 2             x y(x)
--R           - 3x (%e      )  - x log(x)%e       + 2x
--R           ----------------------------------------
--R                             x y(x)
--R                           %e
--R         %e
--R     + 
--R         x y(x)
--R       %e
--R  /
--R       x y(x)
--R     %e
--R                                                     Type: Expression Integer
--E 99

--S 100 of 120
--Rode343 := (log(y(x))+x)*D(y(x),x)-1
--R 
--R
--R                         ,
--R   (99)  (log(y(x)) + x)y (x) - 1
--R
--R                                                     Type: Expression Integer
--E 100

--S 101 of 120
--Ryx:=solve(ode343,y,x)
--R 
--R
--R              - y(x)                - y(x)
--R   (100)  - %e      log(y(x)) - x %e       + Ei(- y(x))
--R                                          Type: Union(Expression Integer,...)
--E 101

--S 102 of 120
--Rode343expr := (log(yx)+x)*D(yx,x)-1
--R 
--R
--R   (101)
--R           - y(x)                - y(x)  ,        - y(x)
--R       ((%e      log(y(x)) + x %e      )y (x) - %e      )
--R
--R    *
--R               - y(x)                - y(x)
--R       log(- %e      log(y(x)) - x %e       + Ei(- y(x)))
--R   + 
--R          - y(x)             2  - y(x)  ,          - y(x)
--R     (x %e      log(y(x)) + x %e      )y (x) - x %e       - 1
--R
--R                                                     Type: Expression Integer
--E 102

--S 103 of 120
--Rode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x)
--R 
--R
--R                               ,
--R   (102)  (log(y(x)) + 2x - 1)y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 103

--S 104 of 120
--Ryx:=solve(ode344,y,x)
--R 
--R
--R          - log(y(x)) - 2x
--R   (103)  ----------------
--R                y(x)
--R                                          Type: Union(Expression Integer,...)
--E 104

--S 105 of 120
--Rode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx
--R 
--R
--R   (104)
--R                             ,                - log(y(x)) - 2x
--R       ((log(y(x)) + 2x - 1)y (x) - 2y(x))log(----------------)
--R                                                    y(x)
--R     + 
--R                              2           ,
--R       ((2x - 1)log(y(x)) + 4x  - 4x + 1)y (x) + 2y(x)log(y(x)) + 2y(x)
--R
--R  /
--R         2
--R     y(x)
--R                                                     Type: Expression Integer
--E 105

--S 106 of 120
--Rode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x)
--R 
--R
--R             3                   ,
--R   (105)  (2x y(x)log(y(x)) + x)y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 106

--S 107 of 120
--Ryx:=solve(ode345,y,x)
--R 
--R
--R            2    2             2    2
--R          2x y(x) log(y(x)) - x y(x)  + 2y(x)
--R   (106)  -----------------------------------
--R                            2
--R                          2x
--R                                          Type: Union(Expression Integer,...)
--E 107

--S 108 of 120
--Rode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx
--R 
--R
--R   (107)
--R                 5    3         2        5    3     3    2              3    2
--R               4x y(x) log(y(x))  + (- 2x y(x)  + 6x y(x) )log(y(x)) - x y(x)
--R             + 
--R               2x y(x)
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R               2    3              2    3        2
--R           - 4x y(x) log(y(x)) + 2x y(x)  - 4y(x)
--R      *
--R               2    2             2    2
--R             2x y(x) log(y(x)) - x y(x)  + 2y(x)
--R         log(-----------------------------------)
--R                               2
--R                             2x
--R     + 
--R          3                   ,        2    2             2    2
--R       (2x y(x)log(y(x)) + x)y (x) - 2x y(x) log(y(x)) + x y(x)  - 4y(x)
--R
--R  /
--R      2
--R     x
--R                                                     Type: Expression Integer
--E 108

--S 109 of 120
--Rode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_
--R              y(x)*(a*x*log(x*y(x))-y(x)+a*x)
--R 
--R
--R   (108)
--R                                      2  ,                                2
--R     (x y(x)log(x y(x)) + x y(x) - a x )y (x) - a x y(x)log(x y(x)) + y(x)
--R
--R   + 
--R     - a x y(x)
--R                                                     Type: Expression Integer
--E 109

--S 110 of 120
--Rsolve(ode346,y,x)
--R 
--R
--R   (109)  "failed"
--R                                                    Type: Union("failed",...)
--E 110

--S 111 of 120
--Rode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1)
--R 
--R
--R                                ,
--R   (110)  (sin(x) + 1)sin(y(x))y (x) + cos(x)cos(y(x)) - cos(x)
--R
--R                                                     Type: Expression Integer
--E 111

--S 112 of 120
--Ryx:=solve(ode347,y,x)
--R 
--R
--R   (111)
--R                     2                     2             2
--R           (- 4cos(x)  - 8cos(x) - 4)sin(x)  + (- 8cos(x)  - 16cos(x) - 8)sin(x)
--R         + 
--R                    2
--R           - 4cos(x)  - 8cos(x) - 4
--R      *
--R         cos(y(x))
--R     + 
--R               5                        4             2                      3
--R       - sin(x)  + (- 4cos(x) - 4)sin(x)  + (- 6cos(x)  - 12cos(x) - 6)sin(x)
--R     + 
--R                 3           2                      2
--R       (- 4cos(x)  - 12cos(x)  - 12cos(x) - 4)sin(x)
--R     + 
--R                4          3          2
--R       (- cos(x)  - 4cos(x)  - 6cos(x)  - 4cos(x) - 1)sin(x)
--R  /
--R             5                      4           2                       3
--R       sin(x)  + (4cos(x) + 5)sin(x)  + (6cos(x)  + 16cos(x) + 10)sin(x)
--R     + 
--R               3           2                       2
--R       (4cos(x)  + 18cos(x)  + 24cos(x) + 10)sin(x)
--R     + 
--R              4          3           2                               4
--R       (cos(x)  + 8cos(x)  + 18cos(x)  + 16cos(x) + 5)sin(x) + cos(x)
--R     + 
--R              3          2
--R       4cos(x)  + 6cos(x)  + 4cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 112

--S 113 of 120
--Rode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1)
--R 
--R
--R   (112)
--R                         2                     4
--R               (- 4cos(x)  - 8cos(x) - 4)sin(x)
--R             + 
--R                         3           2                       3
--R               (- 4cos(x)  - 24cos(x)  - 36cos(x) - 16)sin(x)
--R             + 
--R                          3           2                       2
--R               (- 12cos(x)  - 48cos(x)  - 60cos(x) - 24)sin(x)
--R             + 
--R                          3           2                                 3
--R               (- 12cos(x)  - 40cos(x)  - 44cos(x) - 16)sin(x) - 4cos(x)
--R             + 
--R                         2
--R               - 12cos(x)  - 12cos(x) - 4
--R          *
--R                       ,
--R             sin(y(x))y (x)
--R
--R         + 
--R                                    5           2                      4
--R               (- 8cos(x) - 8)sin(x)  + (8cos(x)  - 8cos(x) - 16)sin(x)
--R             + 
--R                          3                  3
--R               (- 12cos(x)  + 12cos(x))sin(x)
--R             + 
--R                       4           3           2                      2
--R               (4cos(x)  - 28cos(x)  - 44cos(x)  + 4cos(x) + 16)sin(x)
--R             + 
--R                       4           3           2
--R               (8cos(x)  - 20cos(x)  - 56cos(x)  - 20cos(x) + 8)sin(x)
--R             + 
--R                      4          3           2
--R               4cos(x)  - 4cos(x)  - 20cos(x)  - 12cos(x)
--R          *
--R             cos(y(x))
--R         + 
--R                       5           2                 4
--R           cos(x)sin(x)  + (5cos(x)  + 5cos(x))sin(x)
--R         + 
--R                    3           2                  3
--R           (10cos(x)  + 20cos(x)  + 10cos(x))sin(x)
--R         + 
--R                    4           3           2                  2
--R           (10cos(x)  + 30cos(x)  + 30cos(x)  + 10cos(x))sin(x)
--R         + 
--R                   5           4           3           2
--R           (5cos(x)  + 20cos(x)  + 30cos(x)  + 20cos(x)  + 5cos(x))sin(x)
--R         + 
--R                 6          5           4           3          2
--R           cos(x)  + 5cos(x)  + 10cos(x)  + 10cos(x)  + 5cos(x)  + cos(x)
--R      *
--R         sin
--R                            2                     2
--R                    (4cos(x)  + 8cos(x) + 4)sin(x)
--R                  + 
--R                            2                                2
--R                    (8cos(x)  + 16cos(x) + 8)sin(x) + 4cos(x)  + 8cos(x) + 4
--R               *
--R                  cos(y(x))
--R              + 
--R                      5                      4
--R                sin(x)  + (4cos(x) + 4)sin(x)
--R              + 
--R                        2                      3
--R                (6cos(x)  + 12cos(x) + 6)sin(x)
--R              + 
--R                        3           2                      2
--R                (4cos(x)  + 12cos(x)  + 12cos(x) + 4)sin(x)
--R              + 
--R                       4          3          2
--R                (cos(x)  + 4cos(x)  + 6cos(x)  + 4cos(x) + 1)sin(x)
--R           /
--R                      5                      4
--R                sin(x)  + (4cos(x) + 5)sin(x)
--R              + 
--R                        2                       3
--R                (6cos(x)  + 16cos(x) + 10)sin(x)
--R              + 
--R                        3           2                       2
--R                (4cos(x)  + 18cos(x)  + 24cos(x) + 10)sin(x)
--R              + 
--R                       4          3           2                               4
--R                (cos(x)  + 8cos(x)  + 18cos(x)  + 16cos(x) + 5)sin(x) + cos(x)
--R              + 
--R                       3          2
--R                4cos(x)  + 6cos(x)  + 4cos(x) + 1
--R     + 
--R                       6           2                 5
--R           cos(x)sin(x)  + (5cos(x)  + 6cos(x))sin(x)
--R         + 
--R                    3           2                  4
--R           (10cos(x)  + 25cos(x)  + 15cos(x))sin(x)
--R         + 
--R                    4           3           2                  3
--R           (10cos(x)  + 40cos(x)  + 50cos(x)  + 20cos(x))sin(x)
--R         + 
--R                   5           4           3           2                  2
--R           (5cos(x)  + 30cos(x)  + 60cos(x)  + 50cos(x)  + 15cos(x))sin(x)
--R         + 
--R                    6           5           4           3           2
--R             (cos(x)  + 10cos(x)  + 30cos(x)  + 40cos(x)  + 25cos(x)  + 6cos(x))
--R          *
--R             sin(x)
--R         + 
--R                 6          5           4           3          2
--R           cos(x)  + 5cos(x)  + 10cos(x)  + 10cos(x)  + 5cos(x)  + cos(x)
--R      *
--R         cos
--R                            2                     2
--R                    (4cos(x)  + 8cos(x) + 4)sin(x)
--R                  + 
--R                            2                                2
--R                    (8cos(x)  + 16cos(x) + 8)sin(x) + 4cos(x)  + 8cos(x) + 4
--R               *
--R                  cos(y(x))
--R              + 
--R                      5                      4
--R                sin(x)  + (4cos(x) + 4)sin(x)
--R              + 
--R                        2                      3
--R                (6cos(x)  + 12cos(x) + 6)sin(x)
--R              + 
--R                        3           2                      2
--R                (4cos(x)  + 12cos(x)  + 12cos(x) + 4)sin(x)
--R              + 
--R                       4          3          2
--R                (cos(x)  + 4cos(x)  + 6cos(x)  + 4cos(x) + 1)sin(x)
--R           /
--R                      5                      4
--R                sin(x)  + (4cos(x) + 5)sin(x)
--R              + 
--R                        2                       3
--R                (6cos(x)  + 16cos(x) + 10)sin(x)
--R              + 
--R                        3           2                       2
--R                (4cos(x)  + 18cos(x)  + 24cos(x) + 10)sin(x)
--R              + 
--R                       4          3           2                               4
--R                (cos(x)  + 8cos(x)  + 18cos(x)  + 16cos(x) + 5)sin(x) + cos(x)
--R              + 
--R                       3          2
--R                4cos(x)  + 6cos(x)  + 4cos(x) + 1
--R     + 
--R                     6             2                 5
--R       - cos(x)sin(x)  + (- 5cos(x)  - 6cos(x))sin(x)
--R     + 
--R                  3           2                  4
--R       (- 10cos(x)  - 25cos(x)  - 15cos(x))sin(x)
--R     + 
--R                  4           3           2                  3
--R       (- 10cos(x)  - 40cos(x)  - 50cos(x)  - 20cos(x))sin(x)
--R     + 
--R                 5           4           3           2                  2
--R       (- 5cos(x)  - 30cos(x)  - 60cos(x)  - 50cos(x)  - 15cos(x))sin(x)
--R     + 
--R                  6           5           4           3           2
--R         (- cos(x)  - 10cos(x)  - 30cos(x)  - 40cos(x)  - 25cos(x)  - 6cos(x))
--R      *
--R         sin(x)
--R     + 
--R               6          5           4           3          2
--R       - cos(x)  - 5cos(x)  - 10cos(x)  - 10cos(x)  - 5cos(x)  - cos(x)
--R  /
--R             6                      5            2                       4
--R       sin(x)  + (5cos(x) + 6)sin(x)  + (10cos(x)  + 25cos(x) + 15)sin(x)
--R     + 
--R                3           2                       3
--R       (10cos(x)  + 40cos(x)  + 50cos(x) + 20)sin(x)
--R     + 
--R               4           3           2                       2
--R       (5cos(x)  + 30cos(x)  + 60cos(x)  + 50cos(x) + 15)sin(x)
--R     + 
--R              5           4           3           2
--R       (cos(x)  + 10cos(x)  + 30cos(x)  + 40cos(x)  + 25cos(x) + 6)sin(x)
--R     + 
--R             5          4           3           2
--R       cos(x)  + 5cos(x)  + 10cos(x)  + 10cos(x)  + 5cos(x) + 1
--R                                                     Type: Expression Integer
--E 113 

--S 114 of 120
--Rode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x))
--R 
--R
--R                                 ,
--R   (113)  (x cos(y(x)) + sin(x))y (x) + sin(y(x)) + y(x)cos(x)
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 120
--Ryx:=solve(ode348,y,x)
--R 
--R
--R   (114)  x sin(y(x)) + y(x)sin(x)
--R                                          Type: Union(Expression Integer,...)
--E 115

--S 116 of 120
--Rode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx)
--R 
--R
--R   (115)
--R     sin(x sin(y(x)) + y(x)sin(x))
--R   + 
--R          2                      ,
--R       ((x cos(y(x)) + x sin(x))y (x) + x sin(y(x)) + x y(x)cos(x))
--R
--R    *
--R       cos(x sin(y(x)) + y(x)sin(x))
--R   + 
--R                                2  ,
--R     (x sin(x)cos(y(x)) + sin(x) )y (x) + (sin(x) + x cos(x))sin(y(x))
--R
--R   + 
--R     2y(x)cos(x)sin(x)
--R                                                     Type: Expression Integer
--E 116

--S 117 of 120
--Rode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x)
--R 
--R
--R                y(x)  ,             y(x)            y(x)
--R   (116)  x cot(----)y (x) + 2x sin(----) - y(x)cot(----)
--R                  x                   x               x
--R                                                     Type: Expression Integer
--E 117

--S 118 of 120
--Rsolve(ode349,y,x)
--R 
--R
--R   (117)  "failed"
--R                                                    Type: Union("failed",...)
--E 118

--S 119 of 120
--Rode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x))
--R 
--R
--R                    ,                     2
--R   (118)  cos(y(x))y (x) - cos(x)sin(y(x))  - sin(y(x))
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 120
--Rsolve(ode350,y,x)
--R 
--R
--R   (119)  "failed"
--R                                                    Type: Union("failed",...)
--E 120
 

)spool
 
Starts dribbling to tree.output (2009/2/17, 18:1:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 35
bt := BinaryTree INT
 

   (1)  BinaryTree Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  BinaryTree Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 35
ebtree:=empty()$(BTREE INT)
 

   (2)  []
                                                     Type: BinaryTree Integer
--R 
--R
--R   (2)  []
--R                                                     Type: BinaryTree Integer
--E 2

--S 3 of 35
insleaf:(INT,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 35
insleaf(x,t)==
     empty? t=> binaryTree(x)$(BTREE INT)
     x> value t => binaryTree(left t,value t,insleaf(x,right t))
     binaryTree(insleaf(x,left t),value t,right t)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 35
b:bt:=reduce(insleaf,[8,3,5,4,6,2,1,5,7],ebtree)
 
   Compiling function insleaf with type (Integer,BinaryTree Integer)
       -> BinaryTree Integer 

   (5)  [[[1,2,.],3,[[.,4,5],5,[.,6,7]]],8,.]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function insleaf with type (Integer,BinaryTree Integer)
--R       -> BinaryTree Integer 
--R
--R   (5)  [[[1,2,.],3,[[.,4,5],5,[.,6,7]]],8,.]
--R                                                     Type: BinaryTree Integer
--E 5

--S 6 of 35
bleaf x == reduce(insleaf,x,ebtree)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 35
fln:bt-> List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 35
fln t==
    empty? t => empty()$(List INT)
    concat(fln left t,concat(value t,fln right t))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 35
fln b
 
   Compiling function fln with type BinaryTree Integer -> List Integer 

   (9)  [1,2,3,4,5,5,6,7,8]
                                                           Type: List Integer
--R 
--R   Compiling function fln with type BinaryTree Integer -> List Integer 
--R
--R   (9)  [1,2,3,4,5,5,6,7,8]
--R                                                           Type: List Integer
--E 9

--S 10 of 35
split:(INT,bt)->List bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 35
split(x,t)==
     empty? t=> [ebtree,ebtree]
     x> value t =>
            a:=split(x,right t)
            [binaryTree(left t,value t,a.1),a.2]
     a:=split(x,left t)
     [a.1,binaryTree(a.2,value t,right t)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 35
split(3,b)
 
   Compiling function split with type (Integer,BinaryTree Integer) -> 
      List BinaryTree Integer 

   (12)  [[1,2,.],[[.,3,[[.,4,5],5,[.,6,7]]],8,.]]
                                                Type: List BinaryTree Integer
--R 
--R   Compiling function split with type (Integer,BinaryTree Integer) -> 
--R      List BinaryTree Integer 
--R
--R   (12)  [[1,2,.],[[.,3,[[.,4,5],5,[.,6,7]]],8,.]]
--R                                                Type: List BinaryTree Integer
--E 12

--S 13 of 35
insroot:(INT,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 35
insroot(x,t)==
      a:=split(x,t)
      binaryTree(a.1,x,a.2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 35
broot x == reduce(insroot,x,ebtree)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 35
a:List INT:=[8,3,9,4,6,2,1,5,7]
 

   (16)  [8,3,9,4,6,2,1,5,7]
                                                           Type: List Integer
--R 
--R
--R   (16)  [8,3,9,4,6,2,1,5,7]
--R                                                           Type: List Integer
--E 16

--S 17 of 35
l1:=bleaf a
 
   Compiling function bleaf with type List Integer -> BinaryTree 
      Integer 

   (17)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function bleaf with type List Integer -> BinaryTree 
--R      Integer 
--R
--R   (17)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
--R                                                     Type: BinaryTree Integer
--E 17

--S 18 of 35
r1:=broot reverse a
 
   Compiling function broot with type List Integer -> BinaryTree 
      Integer 
   Compiling function insroot with type (Integer,BinaryTree Integer)
       -> BinaryTree Integer 

   (18)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function broot with type List Integer -> BinaryTree 
--R      Integer 
--R   Compiling function insroot with type (Integer,BinaryTree Integer)
--R       -> BinaryTree Integer 
--R
--R   (18)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
--R                                                     Type: BinaryTree Integer
--E 18

--S 19 of 35
(l1=r1)::Boolean
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19

--S 20 of 35
broot a
 

   (20)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
                                                     Type: BinaryTree Integer
--R 
--R
--R   (20)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
--R                                                     Type: BinaryTree Integer
--E 20

--S 21 of 35
bleaf reverse a
 

   (21)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
                                                     Type: BinaryTree Integer
--R 
--R
--R   (21)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
--R                                                     Type: BinaryTree Integer
--E 21

--S 22 of 35
mg:(bt,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 35
mg(x,y)==
    empty? x => y
    empty? y => x
    value x > value y => binaryTree(mg(y,left x),value x,right x)
    binaryTree(left y,value y,mg(x,right y))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 35
mg1:(INT,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 35
mg1(x,t)==mg(binaryTree x,t)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 35
btourn:List INT-> bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

--S 27 of 35
btourn x == reduce(mg1,x,ebtree)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28 of 35
btourn a
 
   Compiling function btourn with type List Integer -> BinaryTree 
      Integer 
   Compiling function mg with type (BinaryTree Integer,BinaryTree 
      Integer) -> BinaryTree Integer 
   Compiling function mg1 with type (Integer,BinaryTree Integer) -> 
      BinaryTree Integer 

   (28)  [[.,8,3],9,[[4,6,[[.,2,1],5,.]],7,.]]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function btourn with type List Integer -> BinaryTree 
--R      Integer 
--R   Compiling function mg with type (BinaryTree Integer,BinaryTree 
--R      Integer) -> BinaryTree Integer 
--R   Compiling function mg1 with type (Integer,BinaryTree Integer) -> 
--R      BinaryTree Integer 
--R
--R   (28)  [[.,8,3],9,[[4,6,[[.,2,1],5,.]],7,.]]
--R                                                     Type: BinaryTree Integer
--E 28

--S 29 of 35
cmp:(List INT,List INT)-> Boolean
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 35
cmp(x,y)== x.2<y.2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 35
sort2 : List List INT -> List List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 35
sort2 x== sort(cmp,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 35
invert x==[i.1 for i in  sort2  [[k,l]
          for k in 1..#x for  l in x]]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 35
broot a
 

   (34)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
                                                     Type: BinaryTree Integer
--R 
--R
--R   (34)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
--R                                                     Type: BinaryTree Integer
--E 34

--S 35 of 35
btourn invert a
 
   Compiling function sort2 with type List List Integer -> List List 
      Integer 
   Compiling function invert with type List Integer -> List Integer 
   Compiling function cmp with type (List Integer,List Integer) -> 
      Boolean 

   (35)  [[[.,7,[.,6,[2,4,.]]],8,5],9,[1,3,.]]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function sort2 with type List List Integer -> List List 
--R      Integer 
--R   Compiling function invert with type List Integer -> List Integer 
--R   Compiling function cmp with type (List Integer,List Integer) -> 
--R      Boolean 
--R
--R   (35)  [[[.,7,[.,6,[2,4,.]]],8,5],9,[1,3,.]]
--R                                                     Type: BinaryTree Integer
--E 35
)spool 
 
Starts dribbling to reclos.output (2009/2/17, 17:57:29).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 70
Ran := RECLOS(FRAC INT)
 

   (1)  RealClosure Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  RealClosure Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 70
fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran == sqrt(a)+sqrt(b) - sqrt(c)-sqrt(d)
 
   Function declaration fourSquares : (RealClosure Fraction Integer,
      RealClosure Fraction Integer,RealClosure Fraction Integer,
      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration fourSquares : (RealClosure Fraction Integer,
--R      RealClosure Fraction Integer,RealClosure Fraction Integer,
--R      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 70
squareDiff1 := fourSquares(73,548,60,586)
 
   Compiling function fourSquares with type (RealClosure Fraction 
      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 

           +---+    +--+    +---+    +--+
   (3)  - \|586  - \|60  + \|548  + \|73
                                           Type: RealClosure Fraction Integer
--R 
--R   Compiling function fourSquares with type (RealClosure Fraction 
--R      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
--R      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 
--R
--R           +---+    +--+    +---+    +--+
--R   (3)  - \|586  - \|60  + \|548  + \|73
--R                                           Type: RealClosure Fraction Integer
--E 3

--S 4 of 70
recip(squareDiff1)
 

   (4)
             +---+          +--+  +--+         +--+ +---+            +---+
     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
   + 
             +--+ +---+             +--+            +---+            +--+
     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (4)
--R             +---+          +--+  +--+         +--+ +---+            +---+
--R     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
--R   + 
--R             +--+ +---+             +--+            +---+            +--+
--R     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 4

--S 5 of 70
sign(squareDiff1)
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 70
squareDiff2 := fourSquares(165,778,86,990)
 

           +---+    +--+    +---+    +---+
   (6)  - \|990  - \|86  + \|778  + \|165
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +--+    +---+    +---+
--R   (6)  - \|990  - \|86  + \|778  + \|165
--R                                           Type: RealClosure Fraction Integer
--E 6

--S 7 of 70
recip(squareDiff2)
 

   (7)
                +---+           +---+  +--+          +---+ +---+
       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
    *
        +---+
       \|990
   + 
              +---+ +---+              +--+             +---+             +---+
     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (7)
--R                +---+           +---+  +--+          +---+ +---+
--R       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
--R    *
--R        +---+
--R       \|990
--R   + 
--R              +---+ +---+              +--+             +---+             +---+
--R     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 7

--S 8 of 70
sign(squareDiff2)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 70
squareDiff3 := fourSquares(217,708,226,692)
 

           +---+    +---+    +---+    +---+
   (9)  - \|692  - \|226  + \|708  + \|217
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +---+    +---+    +---+
--R   (9)  - \|692  - \|226  + \|708  + \|217
--R                                           Type: RealClosure Fraction Integer
--E 9

--S 10 of 70
recip(squareDiff3)
 

   (10)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (10)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 10

--S 11 of 70
sign(squareDiff3)
 

   (11)  - 1
                                                                Type: Integer
--R 
--R
--R   (11)  - 1
--R                                                                Type: Integer
--E 11

--S 12 of 70
squareDiff4 := fourSquares(155,836,162,820)
 

            +---+    +---+    +---+    +---+
   (12)  - \|820  - \|162  + \|836  + \|155
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (12)  - \|820  - \|162  + \|836  + \|155
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 70
recip(squareDiff4)
 

   (13)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (13)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 13

--S 14 of 70
sign(squareDiff4)
 

   (14)  - 1
                                                                Type: Integer
--R 
--R
--R   (14)  - 1
--R                                                                Type: Integer
--E 14

--S 15 of 70
squareDiff5 := fourSquares(591,772,552,818)
 

            +---+    +---+    +---+    +---+
   (15)  - \|818  - \|552  + \|772  + \|591
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (15)  - \|818  - \|552  + \|772  + \|591
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 70
recip(squareDiff5)
 

   (16)
             +---+         +---+  +---+         +---+ +---+             +---+
     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
   + 
            +---+ +---+             +---+            +---+            +---+
     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (16)
--R             +---+         +---+  +---+         +---+ +---+             +---+
--R     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
--R   + 
--R            +---+ +---+             +---+            +---+            +---+
--R     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 16

--S 17 of 70
sign(squareDiff5)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 70
squareDiff6 := fourSquares(434,1053,412,1088)
 

            +----+    +---+    +----+    +---+
   (18)  - \|1088  - \|412  + \|1053  + \|434
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (18)  - \|1088  - \|412  + \|1053  + \|434
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 70
recip(squareDiff6)
 

   (19)
                +----+          +---+  +---+          +---+ +----+
       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
    *
        +----+
       \|1088
   + 
           +---+ +----+              +---+            +----+             +---+
   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (19)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
--R    *
--R        +----+
--R       \|1088
--R   + 
--R           +---+ +----+              +---+            +----+             +---+
--R   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 19

--S 20 of 70
sign(squareDiff6)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 70
squareDiff7 := fourSquares(514,1049,446,1152)
 

            +----+    +---+    +----+    +---+
   (21)  - \|1152  - \|446  + \|1049  + \|514
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (21)  - \|1152  - \|446  + \|1049  + \|514
--R                                           Type: RealClosure Fraction Integer
--E 21

--S 22 of 70
recip(squareDiff7)
 

   (22)
                +----+          +---+  +---+          +---+ +----+
       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
    *
        +----+
       \|1152
   + 
           +---+ +----+              +---+             +----+             +---+
   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (22)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
--R    *
--R        +----+
--R       \|1152
--R   + 
--R           +---+ +----+              +---+             +----+             +---+
--R   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 22

--S 23 of 70
sign(squareDiff7)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 70
squareDiff8 := fourSquares(190,1751,208,1698)
 

            +----+    +---+    +----+    +---+
   (24)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (24)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 24

--S 25 of 70
recip(squareDiff8)
 

   (25)
                     +----+          +---+  +---+          +---+ +----+
           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
         + 
           - 129571901
    *
        +----+
       \|1698
   + 
               +---+ +----+              +---+             +----+
     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
   + 
                 +---+
     - 387349387\|190
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (25)
--R                     +----+          +---+  +---+          +---+ +----+
--R           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
--R         + 
--R           - 129571901
--R    *
--R        +----+
--R       \|1698
--R   + 
--R               +---+ +----+              +---+             +----+
--R     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
--R   + 
--R                 +---+
--R     - 387349387\|190
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 25

--S 26 of 70
sign(squareDiff8)
 

   (26)  - 1
                                                                Type: Integer
--R 
--R
--R   (26)  - 1
--R                                                                Type: Integer
--E 26

--S 27 of 70
relativeApprox(squareDiff8,10**(-3))::Float
 

   (27)  - 0.2340527771 5937700123 E -10
                                                                  Type: Float
--R 
--R
--R   (27)  - 0.2340527771 5937700123 E -10
--R                                                                  Type: Float
--E 27

--S 28 of 70
allRootsOf((x-2)*(x-3)*(x-4))$RECLOS(FRAC INT)
 

   (28)  [2,3,4]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (28)  [2,3,4]
--R                                      Type: List RealClosure Fraction Integer
--E 28

--S 29 of 70
l := allRootsOf((x**2-2)**2-2)$Ran
 

   (29)  [%A33,%A34,%A35,%A36]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (29)  [%A33,%A34,%A35,%A36]
--R                                      Type: List RealClosure Fraction Integer
--E 29

--S 30 of 70
l.1+l.2+l.3+l.4
 

   (30)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (30)  0
--R                                           Type: RealClosure Fraction Integer
--E 30

--S 31 of 70
removeDuplicates map(mainDefiningPolynomial,l)
 

           4     2
   (31)  [?  - 4?  + 2]
Type: List Union(SparseUnivariatePolynomial RealClosure Fraction Integer,"failed")
--R 
--R
--R           4     2
--R   (31)  [?  - 4?  + 2]
--RType: List Union(SparseUnivariatePolynomial RealClosure Fraction Integer,"failed")
--E 31

--S 32 of 70
map(mainCharacterization,l)
 

   (32)  [[- 2,- 1[,[- 1,0[,[0,1[,[1,2[]
Type: List Union(RightOpenIntervalRootCharacterization(RealClosure Fraction Integer,SparseUnivariatePolynomial RealClosure Fraction Integer),"failed")
--R 
--R
--R   (32)  [[- 2,- 1[,[- 1,0[,[0,1[,[1,2[]
--RType: List Union(RightOpenIntervalRootCharacterization(RealClosure Fraction Integer,SparseUnivariatePolynomial RealClosure Fraction Integer),"failed")
--E 32

--S 33 of 70
[reduce(+,l),reduce(*,l)-2]
 

   (33)  [0,0]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (33)  [0,0]
--R                                      Type: List RealClosure Fraction Integer
--E 33

)cl prop s2 s5 10
 
 
--S 34 of 70
(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran)
 

          +--+
   (34)  \|10
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R   (34)  \|10
--R                                           Type: RealClosure Fraction Integer
--E 34

--S 35 of 70
eq1:=sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
 

            +---------+ +--------+    +---------+ +--------+   +-----------+
            | +--+      | +-+         | +--+      | +-+        |   +-+
   (35)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +---------+ +--------+    +---------+ +--------+   +-----------+
--R            | +--+      | +-+         | +--+      | +-+        |   +-+
--R   (35)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
--R                                  Type: Equation RealClosure Fraction Integer
--E 35

--S 36 of 70
eq1::Boolean
 

   (36)  true
                                                                Type: Boolean
--R 
--R
--R   (36)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 70
eq2:=sqrt(s5+2)*sqrt(s2+1) - sqrt(s5-2)*sqrt(s2-1) = sqrt(2*s10+2)
 

            +--------+ +--------+    +--------+ +--------+   +----------+
            | +-+      | +-+         | +-+      | +-+        |  +--+
   (37)  - \|\|5  - 2 \|\|2  - 1  + \|\|5  + 2 \|\|2  + 1 = \|2\|10  + 2
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +--------+ +--------+    +--------+ +--------+   +----------+
--R            | +-+      | +-+         | +-+      | +-+        |  +--+
--R   (37)  - \|\|5  - 2 \|\|2  - 1  + \|\|5  + 2 \|\|2  + 1 = \|2\|10  + 2
--R                                  Type: Equation RealClosure Fraction Integer
--E 37

--S 38 of 70
eq2::Boolean
 

   (38)  true
                                                                Type: Boolean
--R 
--R
--R   (38)  true
--R                                                                Type: Boolean
--E 38


)cl prop s4 s7 e1 e2
 

--S 39  of 70
s3 := sqrt(3)$Ran
 

          +-+
   (39)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (39)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 39

--S 40 of 70
s7:= sqrt(7)$Ran
 

          +-+
   (40)  \|7
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (40)  \|7
--R                                           Type: RealClosure Fraction Integer
--E 40

--S 41 of 70
e1 := sqrt(2*s7-3*s3,3)
 

          +-------------+
         3|  +-+     +-+
   (41)  \|2\|7  - 3\|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-------------+
--R         3|  +-+     +-+
--R   (41)  \|2\|7  - 3\|3
--R                                           Type: RealClosure Fraction Integer
--E 41

--S 42 of 70
e2 := sqrt(2*s7+3*s3,3)
 

          +-------------+
         3|  +-+     +-+
   (42)  \|2\|7  + 3\|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-------------+
--R         3|  +-+     +-+
--R   (42)  \|2\|7  + 3\|3
--R                                           Type: RealClosure Fraction Integer
--E 42

--S 43 of 70
ee1:=e2-e1=s3
 

          +-------------+    +-------------+
         3|  +-+     +-+    3|  +-+     +-+    +-+
   (43)  \|2\|7  + 3\|3   - \|2\|7  - 3\|3  = \|3
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +-------------+    +-------------+
--R         3|  +-+     +-+    3|  +-+     +-+    +-+
--R   (43)  \|2\|7  + 3\|3   - \|2\|7  - 3\|3  = \|3
--R                                  Type: Equation RealClosure Fraction Integer
--E 43

--S 44 of 70
ee1::Boolean
 

   (44)  true
                                                                Type: Boolean
--R 
--R
--R   (44)  true
--R                                                                Type: Boolean
--E 44

)cl prop pol r1 alpha beta
 

--S 45  of 70
pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3)
 

          4   7  2         100
   (45)  x  + - x  + 30x - ---
              3             3
                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--R 
--R
--R          4   7  2         100
--R   (45)  x  + - x  + 30x - ---
--R              3             3
--R                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--E 45

--S 46 of 70
r1 := sqrt(7633)$Ran
 

          +----+
   (46)  \|7633
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +----+
--R   (46)  \|7633
--R                                           Type: RealClosure Fraction Integer
--E 46

--S 47 of 70
alpha := sqrt(5*r1-436,3)/3
 

            +--------------+
         1 3|  +----+
   (47)  - \|5\|7633  - 436
         3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +--------------+
--R         1 3|  +----+
--R   (47)  - \|5\|7633  - 436
--R         3
--R                                           Type: RealClosure Fraction Integer
--E 47

--S 48 of 70
beta := -sqrt(5*r1+436,3)/3
 

              +--------------+
           1 3|  +----+
   (48)  - - \|5\|7633  + 436
           3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R              +--------------+
--R           1 3|  +----+
--R   (48)  - - \|5\|7633  + 436
--R           3
--R                                           Type: RealClosure Fraction Integer
--E 48


--S 49 of 70
pol.(alpha+beta-1/3)
 

   (49)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (49)  0
--R                                           Type: RealClosure Fraction Integer
--E 49

)cl prop qol r2 alpha beta
 

--S 50  of 70
r2 := sqrt(153)$Ran
 

          +---+
   (50)  \|153
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +---+
--R   (50)  \|153
--R                                           Type: RealClosure Fraction Integer
--E 50

--S 51 of 70
alpha2 := sqrt(r2-11,5)
 

          +-----------+
         5| +---+
   (51)  \|\|153  - 11
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-----------+
--R         5| +---+
--R   (51)  \|\|153  - 11
--R                                           Type: RealClosure Fraction Integer
--E 51

--S 52 of 70
beta2 := -sqrt(r2+11,5)
 

            +-----------+
           5| +---+
   (52)  - \|\|153  + 11
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +-----------+
--R           5| +---+
--R   (52)  - \|\|153  + 11
--R                                           Type: RealClosure Fraction Integer
--E 52

--S 53 of 70
qol : UP(x,Ran) := x**5+10*x**3+20*x+22
 

          5      3
   (53)  x  + 10x  + 20x + 22
                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--R 
--R
--R          5      3
--R   (53)  x  + 10x  + 20x + 22
--R                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--E 53

--S 54 of 70
qol(alpha2+beta2)
 

   (54)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (54)  0
--R                                           Type: RealClosure Fraction Integer
--E 54

--S 55 of 70
dst1:=sqrt(9+4*s2)=1+2*s2
 

          +---------+
          |  +-+         +-+
   (55)  \|4\|2  + 9 = 2\|2  + 1
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +---------+
--R          |  +-+         +-+
--R   (55)  \|4\|2  + 9 = 2\|2  + 1
--R                                  Type: Equation RealClosure Fraction Integer
--E 55

--S 56 of 70
dst1::Boolean
 

   (56)  true
                                                                Type: Boolean
--R 
--R
--R   (56)  true
--R                                                                Type: Boolean
--E 56

--S 57 of 70
s6:Ran:=sqrt 6
 

          +-+
   (57)  \|6
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (57)  \|6
--R                                           Type: RealClosure Fraction Integer
--E 57

--S 58 of 70
dst2:=sqrt(5+2*s6)+sqrt(5-2*s6) = 2*s3
 

          +-----------+    +---------+
          |    +-+         |  +-+         +-+
   (58)  \|- 2\|6  + 5  + \|2\|6  + 5 = 2\|3
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +-----------+    +---------+
--R          |    +-+         |  +-+         +-+
--R   (58)  \|- 2\|6  + 5  + \|2\|6  + 5 = 2\|3
--R                                  Type: Equation RealClosure Fraction Integer
--E 58

--S 59 of 70
dst2::Boolean
 

   (59)  true
                                                                Type: Boolean
--R 
--R
--R   (59)  true
--R                                                                Type: Boolean
--E 59

--S 60 of 70
s29:Ran:=sqrt 29
 

          +--+
   (60)  \|29
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R   (60)  \|29
--R                                           Type: RealClosure Fraction Integer
--E 60

--S 61 of 70
dst4:=sqrt(16-2*s29+2*sqrt(55-10*s29)) = sqrt(22+2*s5)-sqrt(11+2*s29)+s5
 

   (61)
    +--------------------------------+
    |  +--------------+                    +-----------+    +----------+
    |  |     +--+           +--+           |  +--+          |  +-+          +-+
   \|2\|- 10\|29  + 55  - 2\|29  + 16 = - \|2\|29  + 11  + \|2\|5  + 22  + \|5
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R   (61)
--R    +--------------------------------+
--R    |  +--------------+                    +-----------+    +----------+
--R    |  |     +--+           +--+           |  +--+          |  +-+          +-+
--R   \|2\|- 10\|29  + 55  - 2\|29  + 16 = - \|2\|29  + 11  + \|2\|5  + 22  + \|5
--R                                  Type: Equation RealClosure Fraction Integer
--E 61

--S 62 of 70
dst4::Boolean
 

   (62)  true
                                                                Type: Boolean
--R 
--R
--R   (62)  true
--R                                                                Type: Boolean
--E 62

--S 63 of 70
dst6:=sqrt((112+70*s2)+(46+34*s2)*s5) = (5+4*s2)+(3+s2)*s5
 

          +--------------------------------+
          |    +-+       +-+      +-+           +-+      +-+     +-+
   (63)  \|(34\|2  + 46)\|5  + 70\|2  + 112 = (\|2  + 3)\|5  + 4\|2  + 5
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +--------------------------------+
--R          |    +-+       +-+      +-+           +-+      +-+     +-+
--R   (63)  \|(34\|2  + 46)\|5  + 70\|2  + 112 = (\|2  + 3)\|5  + 4\|2  + 5
--R                                  Type: Equation RealClosure Fraction Integer
--E 63

--S 64 of 70
dst6::Boolean
 

   (64)  true
                                                                Type: Boolean
--R 
--R
--R   (64)  true
--R                                                                Type: Boolean
--E 64

--S 65 of 70
f3:Ran:=sqrt(3,5)
 

         5+-+
   (65)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         5+-+
--R   (65)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 65

--S 66 of 70
f25:Ran:=sqrt(1/25,5)
 

          +--+
          | 1
   (66)  5|--
         \|25
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          | 1
--R   (66)  5|--
--R         \|25
--R                                           Type: RealClosure Fraction Integer
--E 66

--S 67 of 70
f32:Ran:=sqrt(32/5,5)
 

          +--+
          |32
   (67)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |32
--R   (67)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 67

--S 68 of 70
f27:Ran:=sqrt(27/5,5)
 

          +--+
          |27
   (68)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |27
--R   (68)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 68

--S 69 of 70
dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3**2)
 

          +---------------+
          |   +--+    +--+                         +--+
          |   |27     |32       5+-+2   5+-+       | 1
   (69)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
         \|  \| 5    \| 5                         \|25
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +---------------+
--R          |   +--+    +--+                         +--+
--R          |   |27     |32       5+-+2   5+-+       | 1
--R   (69)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
--R         \|  \| 5    \| 5                         \|25
--R                                  Type: Equation RealClosure Fraction Integer
--E 69

--S 70 of 70
dst5::Boolean
 

   (70)  true
                                                                Type: Boolean
--R 
--R
--R   (70)  true
--R                                                                Type: Boolean
--E 70
)spool 
 
Starts dribbling to contfrc.output (2009/2/17, 17:44:16).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from ContinuedFractionXmpPage

--S 1 of 22
c := continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 1

--S 2 of 22
partialQuotients c
 

   (2)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (2)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 2

--S 3 of 22
convergents c
 

           22 333 355 9208 9563 76149 314159
   (3)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R           22 333 355 9208 9563 76149 314159
--R   (3)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 3

--S 4 of 22
approximants c
 

                                      ______
           22 333 355 9208 9563 76149 314159
   (4)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R                                      ______
--R           22 333 355 9208 9563 76149 314159
--R   (4)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 4

--S 5 of 22
pq := partialQuotients(1/c)
 

   (5)  [0,3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 5

--S 6 of 22
continuedFraction(first pq,repeating [1],rest pq)
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 6

--S 7 of 22
z:=continuedFraction(3,repeating [1],repeating [3,6])
 

   (7)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
   + 
       1 |
     +---+ + ...
     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
--R         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 6
--R                                              Type: ContinuedFraction Integer
--E 7

--S 8 of 22
dens:Stream Integer := cons(1,generate((x+->x+4),6))
 

   (8)  [1,6,10,14,18,22,26,30,34,38,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [1,6,10,14,18,22,26,30,34,38,...]
--R                                                         Type: Stream Integer
--E 8

--S 9 of 22
cf := continuedFraction(0,repeating [1],dens)
 

   (9)
       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
   + 
       1  |     1  |
     +----+ + +----+ + ...
     | 34     | 38
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (9)
--R       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
--R     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
--R     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
--R   + 
--R       1  |     1  |
--R     +----+ + +----+ + ...
--R     | 34     | 38
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 22
ccf := convergents cf
 

              6 61  860 15541 342762  8927353 268163352  9126481321
   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
              7 71 1001 18089 398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              6 61  860 15541 342762  8927353 268163352  9126481321
--R   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
--R              7 71 1001 18089 398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 10

--S 11 of 22
eConvergents := [2*e + 1 for e in ccf]
 

              19 193 2721 49171 1084483 28245729 848456353 28875761731
   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
               7  71 1001 18089  398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              19 193 2721 49171 1084483 28245729 848456353 28875761731
--R   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
--R               7  71 1001 18089  398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 11

--S 12 of 22
eConvergents :: Stream Float
 

   (12)
   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (12)
--R   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
--R    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
--R    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
--R    ...]
--R                                                           Type: Stream Float
--E 12

--S 13 of 22
exp 1.0
 

   (13)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (13)  2.7182818284 590452354
--R                                                                  Type: Float
--E 13

--S 14 of 22
cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])
 

   (14)
           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
   + 
       289 |     361 |
     +-----+ + +-----+ + ...
     |  2      |  2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (14)
--R           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
--R     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
--R         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
--R   + 
--R       289 |     361 |
--R     +-----+ + +-----+ + ...
--R     |  2      |  2
--R                                              Type: ContinuedFraction Integer
--E 14

--S 15 of 22
ccf := convergents cf
 

            3 15 105 315 3465 45045 45045 765765 14549535
   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
            2 13  76 263 2578 36979 33976 622637 11064338
                                                Type: Stream Fraction Integer
--R 
--R
--R            3 15 105 315 3465 45045 45045 765765 14549535
--R   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
--R            2 13  76 263 2578 36979 33976 622637 11064338
--R                                                Type: Stream Fraction Integer
--E 15

--S 16 of 22
piConvergents := [4/p for p in ccf]
 

            8 52 304 1052 10312 147916 135904 2490548 44257352
   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
            3 15 105  315  3465  45045  45045  765765 14549535
                                                Type: Stream Fraction Integer
--R 
--R
--R            8 52 304 1052 10312 147916 135904 2490548 44257352
--R   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
--R            3 15 105  315  3465  45045  45045  765765 14549535
--R                                                Type: Stream Fraction Integer
--E 16

--S 17 of 22
piConvergents :: Stream Float
 

   (17)
   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
    3.0418396189 294022111, ...]
                                                           Type: Stream Float
--R 
--R
--R   (17)
--R   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
--R    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
--R    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
--R    3.0418396189 294022111, ...]
--R                                                           Type: Stream Float
--E 17

--S 18 of 22
continuedFraction((- 122 + 597*%i)/(4 - 4*%i))
 

                            1    |         1     |
   (18)  - 90 + 59%i + +---------+ + +-----------+
                       | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1    |         1     |
--R   (18)  - 90 + 59%i + +---------+ + +-----------+
--R                       | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 18

--S 19 of 22
r : Fraction UnivariatePolynomial(x,Fraction Integer)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 22
r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))
 

           2
          x  - 3x + 2
   (20)  ------------
          2
         x  - 7x + 12
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2
--R          x  - 3x + 2
--R   (20)  ------------
--R          2
--R         x  - 7x + 12
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 20

--S 21 of 22
continuedFraction r
 

                  1    |         1     |
   (21)  1 + +---------+ + +-----------+
             | 1     9     | 16     40
             | - x - -     | -- x - --
             | 4     8     |  3      3
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                  1    |         1     |
--R   (21)  1 + +---------+ + +-----------+
--R             | 1     9     | 16     40
--R             | - x - -     | -- x - --
--R             | 4     8     |  3      3
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 21

--S 22 of 22
[i*i for i in convergents(z) :: Stream Float]
 

   (22)
   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (22)
--R   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
--R    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
--R    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
--R    ...]
--R                                                           Type: Stream Float
--E 22
)spool
 
Starts dribbling to dhtri.output (2009/2/17, 17:44:40).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 5
tri2tri(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  n1 := triangleNormal(t1)
  n2 := triangleNormal(t2)
  tet2tet(concat(t1, n1), concat(t2, n2))
 
   Function declaration tri2tri : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tri2tri : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 5
tet2tet(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  m1 := makeColumnMatrix t1
  m2 := makeColumnMatrix t2
  m2 * inverse(m1)
 
   Function declaration tet2tet : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tet2tet : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 5
makeColumnMatrix(t) ==
  m := new(4,4,0)$DHMATRIX(DoubleFloat)
  for x in t for i in 1..repeat
    for j in 1..3 repeat
      m(j,i) := x.j
    m(4,i) := 1
  m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
triangleNormal(t) ==
  a := triangleArea t
  p1 := t.2 - t.1
  p2 := t.3 - t.2
  c := cross(p1, p2)
  len := length(c)
  len = 0 => error "degenerate triangle!"
  c := (1/len)*c
  t.1 + sqrt(a) * c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
triangleArea t ==
  a := length(t.2 - t.1)
  b := length(t.3 - t.2)
  c := length(t.1 - t.3)
  s := (a+b+c)/2
  sqrt(s*(s-a)*(s-b)*(s-c))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
)spool
 
Starts dribbling to bug10069.output (2009/2/17, 17:44:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

)set break resume
 

--S 1  of 8
cot(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   csc: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   csc: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 1

--S 2 of 8
csc(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   csc: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   csc: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 2

--S 3 of 8
asec(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   asec: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   asec: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 3

--S 4 of 8
acsc(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   acsc: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   acsc: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 4

--S 5 of 8
asech(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   asech: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   asech: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 5

--S 6 of 8
acsch(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   acsch: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   acsch: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 6

--S 7 of 8
coth(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   csch: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   csch: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 7

--S 8 of 8
acoth(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   acoth: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   acoth: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 8
)spool
 
Starts dribbling to roman.output (2009/2/17, 17:57:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 10
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 1

--S 2 of 10
D(f x,x,7)
 

         (vii)
   (2)  f     (x)

                                                     Type: Expression Integer
--R 
--R
--R         (vii)
--R   (2)  f     (x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 10
a := roman(1978 - 1965)
 

   (3)  XIII
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XIII
--R                                                           Type: RomanNumeral
--E 3

--S 4 of 10
x : UTS(ROMAN,'x,0) := x
 

   (4)  x
                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--R 
--R
--R   (4)  x
--R                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--E 4

--S 5 of 10
recip(1 - x - x**2)
 

   (5)
                 2        3      4         5         6        7          8
     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
   + 
         9           10      11
     LV x  + LXXXIX x   + O(x  )
                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--R 
--R
--R   (5)
--R                 2        3      4         5         6        7          8
--R     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
--R   + 
--R         9           10      11
--R     LV x  + LXXXIX x   + O(x  )
--R                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--E 5

--S 6 of 10
m : MATRIX FRAC ROMAN
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
m := matrix [[1/(i + j) for i in 1..3] for j in 1..3]
 

        + I    I    I+
        |--   ---  --|
        |II   III  IV|
        |            |
        | I    I   I |
   (7)  |---  --   - |
        |III  IV   V |
        |            |
        | I    I    I|
        |--    -   --|
        +IV    V   VI+
                                           Type: Matrix Fraction RomanNumeral
--R 
--R
--R        + I    I    I+
--R        |--   ---  --|
--R        |II   III  IV|
--R        |            |
--R        | I    I   I |
--R   (7)  |---  --   - |
--R        |III  IV   V |
--R        |            |
--R        | I    I    I|
--R        |--    -   --|
--R        +IV    V   VI+
--R                                           Type: Matrix Fraction RomanNumeral
--E 7

--S 8 of 10
inverse m
 

        +LXXII   - CCXL    CLXXX +
        |                        |
   (8)  |- CCXL    CM     - DCCXX|
        |                        |
        +CLXXX   - DCCXX    DC   +
                                Type: Union(Matrix Fraction RomanNumeral,...)
--R 
--R
--R        +LXXII   - CCXL    CLXXX +
--R        |                        |
--R   (8)  |- CCXL    CM     - DCCXX|
--R        |                        |
--R        +CLXXX   - DCCXX    DC   +
--R                                Type: Union(Matrix Fraction RomanNumeral,...)
--E 8

--S 9 of 10
y := factorial 10
 

   (9)  3628800
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  3628800
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 10
roman y
 

   (10)
  ((((I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))(
  (I)) MMMMMMMMDCCC
                                                           Type: RomanNumeral
--R 
--R
--R   (10)
--R  ((((I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))(
--R  (I)) MMMMMMMMDCCC
--R                                                           Type: RomanNumeral
--E 10
)spool 
 
Starts dribbling to array2.output (2009/2/17, 17:43:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 20
arr : ARRAY2 INT := new(5,4,0)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
        |          |
   (1)  |0  0  0  0|
        |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R        |          |
--R   (1)  |0  0  0  0|
--R        |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 1

--S 2 of 20
setelt(arr,1,1,17)
 

   (2)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  17
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 20
arr
 

        +17  0  0  0+
        |           |
        |0   0  0  0|
        |           |
   (3)  |0   0  0  0|
        |           |
        |0   0  0  0|
        |           |
        +0   0  0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R        +17  0  0  0+
--R        |           |
--R        |0   0  0  0|
--R        |           |
--R   (3)  |0   0  0  0|
--R        |           |
--R        |0   0  0  0|
--R        |           |
--R        +0   0  0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 3

--S 4 of 20
elt(arr,1,1)
 

   (4)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  17
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 20
arr(3,2) := 15
 

   (5)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  15
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 20
arr(3,2)
 

   (6)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  15
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 20
row(arr,1)
 

   (7)  [17,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (7)  [17,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 7

--S 8 of 20
column(arr,1)
 

   (8)  [17,0,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (8)  [17,0,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 8

--S 9 of 20
nrows(arr)
 

   (9)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  5
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 20
ncols(arr)
 

   (10)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  4
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 20
map(-,arr)
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (11)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (11)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 11

--S 12 of 20
map((x +-> x + x),arr)
 

         +34  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (12)  |0   30  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +34  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (12)  |0   30  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 12

--S 13 of 20
arrc := copy(arr)
 

         +17  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (13)  |0   15  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +17  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (13)  |0   15  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 13

--S 14 of 20
map!(-,arrc)
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (14)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (14)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 14

--S 15 of 20
arrc
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (15)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (15)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 15

--S 16 of 20
arr
 

         +17  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (16)  |0   15  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +17  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (16)  |0   15  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 16

--S 17 of 20
member?(17,arr)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 20
member?(10317,arr)
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 20
count(17,arr)
 

   (19)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  1
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 20 of 20
count(0,arr)
 

   (20)  18
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  18
--R                                                        Type: PositiveInteger
--E 20
)spool
 
Starts dribbling to eq.output (2009/2/17, 17:45:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 12
eq1 := 3*x + 4*y = 5
 

   (1)  4y + 3x= 5
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (1)  4y + 3x= 5
--R                                            Type: Equation Polynomial Integer
--E 1

--S 2 of 12
eq2 := 2*x + 2*y = 3
 

   (2)  2y + 2x= 3
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (2)  2y + 2x= 3
--R                                            Type: Equation Polynomial Integer
--E 2

--S 3 of 12
lhs eq1
 

   (3)  4y + 3x
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)  4y + 3x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 12
rhs eq1
 

   (4)  5
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  5
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 12
eq1 + eq2
 

   (5)  6y + 5x= 8
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (5)  6y + 5x= 8
--R                                            Type: Equation Polynomial Integer
--E 5

--S 6 of 12
eq1 * eq2
 

          2             2
   (6)  8y  + 14x y + 6x = 15
                                            Type: Equation Polynomial Integer
--R 
--R
--R          2             2
--R   (6)  8y  + 14x y + 6x = 15
--R                                            Type: Equation Polynomial Integer
--E 6

--S 7 of 12
2*eq2 - eq1
 

   (7)  x= 1
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (7)  x= 1
--R                                            Type: Equation Polynomial Integer
--E 7

--S 8 of 12
eq1**2
 

           2             2
   (8)  16y  + 24x y + 9x = 25
                                            Type: Equation Polynomial Integer
--R 
--R
--R           2             2
--R   (8)  16y  + 24x y + 9x = 25
--R                                            Type: Equation Polynomial Integer
--E 8

--S 9 of 12
if x+1 = y then "equal" else "unequal"
 

   (9)  "unequal"
                                                                 Type: String
--R 
--R
--R   (9)  "unequal"
--R                                                                 Type: String
--E 9

--S 10 of 12
eqpol := x+1 = y
 

   (10)  x + 1= y
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (10)  x + 1= y
--R                                            Type: Equation Polynomial Integer
--E 10

--S 11 of 12
if eqpol then "equal" else "unequal"
 

   (11)  "unequal"
                                                                 Type: String
--R 
--R
--R   (11)  "unequal"
--R                                                                 Type: String
--E 11

--S 12 of 12
eqpol::Boolean
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12
)spool
 
Starts dribbling to antoine.output (2009/2/17, 17:43:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 11
)set expose add con DenavitHartenbergMatrix
 
   DenavitHartenbergMatrix is now explicitly exposed in frame initial 
--R 
--I   DenavitHartenbergMatrix is now explicitly exposed in frame frame0 
--E 1
--S 2 of 11
tri2tri(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  n1 := triangleNormal(t1)
  n2 := triangleNormal(t2)
  tet2tet(concat(t1, n1), concat(t2, n2))
 
   Function declaration tri2tri : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tri2tri : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 2
--S 3 of 11
tet2tet(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  m1 := makeColumnMatrix t1
  m2 := makeColumnMatrix t2
  m2 * inverse(m1)
 
   Function declaration tet2tet : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tet2tet : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 3
--S 4 of 11
makeColumnMatrix(t) ==
  m := new(4,4,0)$DHMATRIX(DoubleFloat)
  for x in t for i in 1..repeat
    for j in 1..3 repeat
      m(j,i) := x.j
    m(4,i) := 1
  m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
--S 5 of 11
triangleNormal(t) ==
  a := triangleArea t
  p1 := t.2 - t.1
  p2 := t.3 - t.2
  c := cross(p1, p2)
  len := length(c)
  len = 0 => error "degenerate triangle!"
  c := (1/len)*c
  t.1 + sqrt(a) * c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
--S 6 of 11
triangleArea t ==
  a := length(t.2 - t.1)
  b := length(t.3 - t.2)
  c := length(t.1 - t.3)
  s := (a+b+c)/2
  sqrt(s*(s-a)*(s-b)*(s-c))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6
--S 7 of 11
torusRot: DHMATRIX(DoubleFloat)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
--S 8 of 11
drawRings(n) ==
  s := create3Space()$ThreeSpace DoubleFloat
  -- create an identity transformation
  dh:DHMATRIX(DoubleFloat) := identity()
  drawRingsInner(s, n, dh)
  makeViewport3D(s, "Antoine's Necklace")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8
--S 9 of 11
drawRingsInner(s, n, dh) ==
  n = 0 =>
    drawRing(s, dh)
    void()
  t := 0.0@DoubleFloat             -- the current angle around the ring
  p := 0.0@DoubleFloat             -- the angle of the subring from the plane
  tr := 1.0@DoubleFloat            -- the amount to translate the subring
  inc := 0.1@DoubleFloat           -- translation increment
  -- subdivide the ring into 10 linked rings
  for i in 1..10 repeat
    tr := tr + inc
    inc := -inc
    dh' := dh * rotatez(t) * translate(tr, 0.0@DoubleFloat, 0.0@DoubleFloat) *
           rotatey(p) * scale(0.35@DoubleFloat, 0.48@DoubleFloat, 0.4@DoubleFloat)
    drawRingsInner(s, n-1, dh')
    t := t + 36.0@DoubleFloat
    p := p + 90.0@DoubleFloat
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9
--S 10 of 11
drawRing(s, dh) ==
  free torusRot
  torusRot := dh
  makeObject(torus, 0..2*%pi, 0..2*%pi, var1Steps == 6, space == s,
             var2Steps == 15)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10
--S 11 of 11
torus(u ,v) ==
  cu := cos(u)/6
  torusRot * point [(1+cu)*cos(v), (1+cu)*sin(v), (sin u)/6]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11
)spool
 
Starts dribbling to binary.output (2009/2/17, 17:43:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 7
r := binary(22/7)
 

           ___
   (1)  11.001
                                                        Type: BinaryExpansion
--R 
--R
--R           ___
--R   (1)  11.001
--R                                                        Type: BinaryExpansion
--E 1

--S 2 of 7
r + binary(6/7)
 

   (2)  100
                                                        Type: BinaryExpansion
--R 
--R
--R   (2)  100
--R                                                        Type: BinaryExpansion
--E 2

--S 3 of 7
[binary(1/i) for i in 102..106] 
 

   (3)
       ________    ___________________________________________________
   [0.000000101, 0.000000100111110001000101100101111001110010010101001,
         ____________    ____________
    0.000000100111011, 0.000000100111,
       ____________________________________________________
    0.00000010011010100100001110011111011001010110111100011]
                                                   Type: List BinaryExpansion
--R 
--R
--R   (3)
--R       ________    ___________________________________________________
--R   [0.000000101, 0.000000100111110001000101100101111001110010010101001,
--R         ____________    ____________
--R    0.000000100111011, 0.000000100111,
--R       ____________________________________________________
--R    0.00000010011010100100001110011111011001010110111100011]
--R                                                   Type: List BinaryExpansion
--E 3

--S 4 of 7
binary(1/1007) 
 

   (4)
   0.
     OVERBAR
        00000000010000010001010010010111100000111111000010111111001011000111110
          100010011100100110011000110010010101011110110100110000000011000011001
          111011100011010001011110100100011110110000101011101110011101010111001
          100101001011100000001110001111001000000100100100110111001010100111010
          001101110110101110001001000001100101101100000010110010111110001010000
          010101010110101100000110110111010010101111111010111010100110010000101
          0011011000100110001000100001000011000111010011110001
                                                        Type: BinaryExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        00000000010000010001010010010111100000111111000010111111001011000111110
--R          100010011100100110011000110010010101011110110100110000000011000011001
--R          111011100011010001011110100100011110110000101011101110011101010111001
--R          100101001011100000001110001111001000000100100100110111001010100111010
--R          001101110110101110001001000001100101101100000010110010111110001010000
--R          010101010110101100000110110111010010101111111010111010100110010000101
--R          0011011000100110001000100001000011000111010011110001
--R                                                        Type: BinaryExpansion
--E 4

--S 5 of 7
p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9)
 

             2     __      ______
   (5)  0.01x  + 0.10x + 0.011100
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R             2     __      ______
--R   (5)  0.01x  + 0.10x + 0.011100
--R                                             Type: Polynomial BinaryExpansion
--E 5

--S 6 of 7
q := D(p, x)
 

                 __
   (6)  0.1x + 0.10
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R                 __
--R   (6)  0.1x + 0.10
--R                                             Type: Polynomial BinaryExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              __
   (7)  x + 1.01
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R              __
--R   (7)  x + 1.01
--R                                             Type: Polynomial BinaryExpansion
--E 7
)spool
 
Starts dribbling to curl.output (2009/2/17, 17:44:22).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 1
draw(curve(sin(t)*sin(2*t)*sin(3*t),sin(4*t)*sin(5*t)*sin(6*t)),t = 0..2*%pi)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (1)  TwoDimensionalViewport: "DSIN(t)*DSIN(2*t)*DSIN(3*t)"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Compiling function %D with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (1)  TwoDimensionalViewport: "DSIN(t)*DSIN(2*t)*DSIN(3*t)"
--R                                                 Type: TwoDimensionalViewport
--E 1
)spool
 
Starts dribbling to lpoly.output (2009/2/17, 17:52:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 28
RN    := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 28
Lpoly := LiePolynomial(Symbol,RN)
 

   (2)  LiePolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  LiePolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 28
Dpoly := XDPOLY(Symbol,RN)
 

   (3)  XDistributedPolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (3)  XDistributedPolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 3

--S 4 of 28
Lword := LyndonWord Symbol
 

   (4)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 28
a:Symbol := 'a
 

   (5)  a
                                                                 Type: Symbol
--R 
--R
--R   (5)  a
--R                                                                 Type: Symbol
--E 5

--S 6 of 28
b:Symbol := 'b
 

   (6)  b
                                                                 Type: Symbol
--R 
--R
--R   (6)  b
--R                                                                 Type: Symbol
--E 6

--S 7 of 28
c:Symbol := 'c
 

   (7)  c
                                                                 Type: Symbol
--R 
--R
--R   (7)  c
--R                                                                 Type: Symbol
--E 7

--S 8 of 28
aa: Lpoly := a
 

   (8)  [a]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (8)  [a]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 8

--S 9 of 28
bb: Lpoly := b
 

   (9)  [b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (9)  [b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 9

--S 10 of 28
cc: Lpoly := c
 

   (10)  [c]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (10)  [c]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 10

--S 11 of 28
p : Lpoly := [aa,bb]
 

   (11)  [a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (11)  [a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 11

--S 12 of 28
q : Lpoly := [p,bb]
 

             2
   (12)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R             2
--R   (12)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 12

--S 13 of 28
liste : List Lword := LyndonWordsList([a,b], 4)
 

                          2       2    3     2 2      3
   (13)  [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R                          2       2    3     2 2      3
--R   (13)  [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 13

--S 14 of 28
r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly
 

                    2         2
   (14)  [a b] + 3[a b] + [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                    2         2
--R   (14)  [a b] + 3[a b] + [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 14

--S 15 of 28
s:Lpoly := [p,r]
 

              2                 2
   (15)  - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R              2                 2
--R   (15)  - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 15

--S 16 of 28
t:Lpoly  := s  + 2*LiePoly(liste.3) - 5*LiePoly(liste.5)
 

                       2       2                 2
   (16)  2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                       2       2                 2
--R   (16)  2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 16

--S 17 of 28
degree t
 

   (17)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  5
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 28
mirror t
 

                         2       2                 2
   (18)  - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                         2       2                 2
--R   (18)  - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 18

--S 19 of 28
Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == [[p,q]$Lpoly, r] + [[q,r]$Lpoly, p] + [[r,p]$Lpoly, q]
 
   Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer
      ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol,
      Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer
--R      ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol,
--R      Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 19

--S 20 of 28
test: Lpoly := Jacobi(a,b,b)
 
   Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction 
      Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(
      Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction 
      Integer) 

   (20)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R   Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction 
--R      Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(
--R      Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction 
--R      Integer) 
--R
--R   (20)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 20

--S 21 of 28
test: Lpoly := Jacobi(p,q,r)
 

   (21)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (21)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 21

--S 22 of 28
test: Lpoly := Jacobi(r,s,t)
 

   (22)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (22)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 22

--S 23 of 28
eval(p, a, p)$Lpoly
 

             2
   (23)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R             2
--R   (23)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 23

--S 24 of 28
eval(p, [a,b], [2*bb, 3*aa])$Lpoly
 

   (24)  - 6[a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (24)  - 6[a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 24

--S 25 of 28
r: Lpoly := [p,c]
 

   (25)  [a b c] + [a c b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (25)  [a b c] + [a c b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 25

--S 26 of 28
r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly
 

   (26)  - [a b c]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (26)  - [a b c]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 26

--S 27 of 28
r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly
 

   (27)  - [a c b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (27)  - [a c b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 27

--S 28 of 28
r + r1 + r2
 

   (28)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (28)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 28
)spool 
 
Starts dribbling to fns.output (2009/2/17, 17:46:4).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 20
odd(i) == 2*i - 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 20
[odd(i) for i in 1..10]
 
   Compiling function odd with type PositiveInteger -> Integer 

   (2)  [1,3,5,7,9,11,13,15,17,19]
                                                           Type: List Integer
--R 
--R   Compiling function odd with type PositiveInteger -> Integer 
--R
--R   (2)  [1,3,5,7,9,11,13,15,17,19]
--R                                                           Type: List Integer
--E 2

--S 3 of 20
odd == i +-> 2*i - 1
 
   Compiled code for odd has been cleared.
   1 old definition(s) deleted for function or rule odd 
                                                                   Type: Void
--R 
--R   Compiled code for odd has been cleared.
--R   1 old definition(s) deleted for function or rule odd 
--R                                                                   Type: Void
--E 3

--S 4 of 20
odd(1111)
 
   Compiling function odd with type PositiveInteger -> Integer 

   (4)  2221
                                                        Type: PositiveInteger
--R 
--R   Compiling function odd with type PositiveInteger -> Integer 
--R
--R   (4)  2221
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 20
[i for i in 2.. | prime? i]
 

   (5)  [2,3,5,7,11,13,17,19,23,29,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (5)  [2,3,5,7,11,13,17,19,23,29,...]
--R                                                 Type: Stream PositiveInteger
--E 5

--S 6 of 20
primes := /
 

   (6)  /
                                                             Type: Variable /
--R 
--R
--R   (6)  /
--R                                                             Type: Variable /
--E 6

--S 7 of 20
primes == [p := nextPrime(i = 0 => 2; p) for i in 1..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 20
primes
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 8

--S 9 of 20
primes(20)
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 9

--S 10 of 20
firstPrimes(n) == [primes(i) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 20
firstPrimes(25)
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 11

--S 12 of 20
primesLessThan(n) == [p for p in primes while p < n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 20
primesLessThan 1000
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 13

--S 14 of 20
isPrime? n == reduce(_or,[n = p for p in primes while n <= p])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 20
isPrime?(1111)
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 15

--S 16 of 20
twins := [p,p+2 for p in primes | prime?(p+2)]
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 16

--S 17 of 20
twins := [p, p+2 for i in 1.. | (p := primes(i)) + 2 = primes(i+1)]
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   Interpret-Code mode is not supported for stream bodies.
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   Interpret-Code mode is not supported for stream bodies.
--E 17

--S 18 of 20
firsts := [p for i in 1.. | (p := primes(i)) + 2 = primes(i+1)]
 
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   Interpret-Code mode is not supported for stream bodies.
--R 
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   Interpret-Code mode is not supported for stream bodies.
--E 18

--S 19 of 20
twins := [p, p + 2 for p in firsts]
 
 
Daly Bug
   AXIOM cannot iterate with p over your form now. Perhaps you should 
      try using a conversion to make sure your form is a list or 
      stream, for example.
--R 
--R 
--RDaly Bug
--R   AXIOM cannot iterate with p over your form now. Perhaps you should 
--R      try using a conversion to make sure your form is a list or 
--R      stream, for example.
--E 19

--S 20 of 20
twins(i) ==firsts(i),2 + firsts(i)
 
   There are no library operations named firsts 
      Use HyperDoc Browse or issue
                               )what op firsts
      to learn if there is any operation containing " firsts " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      firsts with argument type(s) 
                                 Variable i
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named firsts 
--R      Use HyperDoc Browse or issue
--R                               )what op firsts
--R      to learn if there is any operation containing " firsts " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      firsts with argument type(s) 
--R                                 Variable i
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
)spool 
 
Starts dribbling to heat.output (2009/2/17, 17:46:26).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 11
u:= operator('u);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 1

--S 2 of 11
heat:= D(u(x, t), t) - D(u(x, t), x, 2) = 0
 

   (2)  - u    (x,t) + u  (x,t)= 0
           ,1,1         ,2
                                            Type: Equation Expression Integer
--R 
--R
--R   (2)  - u    (x,t) + u  (x,t)= 0
--R           ,1,1         ,2
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 11
f:= operator('f);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 3

--S 4 of 11
s:= rule(u(x, t) == f(x/sqrt(t))/sqrt(t))
 

                       x
                  'f(----)
                      +-+
                     \|t
   (4)  u(x,t) == --------
                     +-+
                    \|t
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                       x
--R                  'f(----)
--R                      +-+
--R                     \|t
--R   (4)  u(x,t) == --------
--R                     +-+
--R                    \|t
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 4

--S 5 of 11
s(lhs(heat)) = 0
 

             ,,   x       +-+ ,   x           x
        - 2tf  (----) - x\|t f (----) - t f(----)
                 +-+             +-+         +-+
                \|t             \|t         \|t
   (5)  -----------------------------------------= 0
                           2 +-+
                         2t \|t
                                            Type: Equation Expression Integer
--R 
--R
--R             ,,   x       +-+ ,   x           x
--R        - 2tf  (----) - x\|t f (----) - t f(----)
--R                 +-+             +-+         +-+
--R                \|t             \|t         \|t
--R   (5)  -----------------------------------------= 0
--R                           2 +-+
--R                         2t \|t
--R                                            Type: Equation Expression Integer
--E 5

--S 6 of 11
subst(lhs(%), x = z*sqrt(t)) = 0
 

            ,,        ,
        - 2f  (z) - zf (z) - f(z)

   (6)  -------------------------= 0
                     +-+
                  2t\|t
                                            Type: Equation Expression Integer
--R 
--R
--R            ,,        ,
--R        - 2f  (z) - zf (z) - f(z)
--R
--R   (6)  -------------------------= 0
--R                     +-+
--R                  2t\|t
--R                                            Type: Equation Expression Integer
--E 6

--S 7 of 11
% * denom(lhs(%))
 

            ,,        ,
   (7)  - 2f  (z) - zf (z) - f(z)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            ,,        ,
--R   (7)  - 2f  (z) - zf (z) - f(z)= 0
--R
--R                                            Type: Equation Expression Integer
--E 7

--S 8 of 11
eq:=%
 

            ,,        ,
   (8)  - 2f  (z) - zf (z) - f(z)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            ,,        ,
--R   (8)  - 2f  (z) - zf (z) - f(z)= 0
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 11
solve(%, f, z=0,[k1,k2])
 

                2         2               2         2               2
               z        %P               z        %P               z
             - --   z   ---            - --   0   ---            - --
                4 ++     4                4 ++     4                4
   (9)  k2 %e     |   %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
                 ++                        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2         2               2         2               2
--R               z        %P               z        %P               z
--R             - --   z   ---            - --   0   ---            - --
--R                4 ++     4                4 ++     4                4
--R   (9)  k2 %e     |   %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
--R                 ++                        ++
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 11
subst(%, z = x/sqrt(t))/sqrt(t)
 

                       x
                 2   ----     2               2         2               2
                x     +-+   %P               x        %P               x
              - --   \|t    ---            - --   0   ---            - --
                4t ++        4               4t ++     4               4t
         k2 %e     |      %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
                  ++                           ++
   (10)  ----------------------------------------------------------------
                                        +-+
                                       \|t
                                                     Type: Expression Integer
--R 
--R
--R                       x
--R                 2   ----     2               2         2               2
--R                x     +-+   %P               x        %P               x
--R              - --   \|t    ---            - --   0   ---            - --
--R                4t ++        4               4t ++     4               4t
--R         k2 %e     |      %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
--R                  ++                           ++
--R   (10)  ----------------------------------------------------------------
--R                                        +-+
--R                                       \|t
--R                                                     Type: Expression Integer
--E 10

--S 11 of 11
subst(%, [k2 = 0, k1 = 1/(2*sqrt(%pi))])
 

                 2
                x
              - --
                4t
            %e
   (11)  -----------
           +---+ +-+
         2\|%pi \|t
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R                x
--R              - --
--R                4t
--R            %e
--R   (11)  -----------
--R           +---+ +-+
--R         2\|%pi \|t
--R                                                     Type: Expression Integer
--E 11
)spool 
 
Starts dribbling to lupfact.output (2009/2/17, 17:52:48).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1  of 18
field := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 18
permMat: (INT, INT, INT) -> Matrix field
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2
 
--S 3 of 18
permMat(dim, i, j) ==
  m : Matrix field :=
    diagonalMatrix [(if i = k or j = k then 0 else 1) for k in 1..dim]
  m(i,j) := 1
  m(j,i) := 1
  m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 18
nonZeroCol: Matrix field -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5  of 18
nonZeroCol(m) ==
  foundit := false
  col := 1
  for i in 1..ncols(m) while not foundit repeat
    for j in 1..nrows(m) while not foundit repeat
      if not(m(j,i) = 0) then
        col := i
        foundit := true
  col
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6  of 18
embedMatrix: (Matrix field,NNI,NNI) -> Matrix field
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6
 
--S 7 of 18
embedMatrix(m, oldDim, newDim) ==
  n := diagonalMatrix([1 for i in 1..newDim])$(Matrix(field))
  setsubMatrix!(n,1,1,m)
  n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
 
--S 8 of 18
lupFactorEngine: (Matrix field, INT, INT)  -> List Matrix field
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9  of 18
lupFactorEngine(a, m, p) ==
  m = 1 =>
    l : Matrix field := diagonalMatrix [1]
    pm : Matrix field := permMat(p,1,nonZeroCol a)
    [l,a*pm,pm]
  m2 : NNI := m quo 2
  b : Matrix field := subMatrix(a,1,m2,1,p)
  c : Matrix field := subMatrix(a,m2+1,m,1,p)
  lup := lupFactorEngine(b,m2,p)
  l1 := lup.1
  u1 := lup.2
  pm1 := lup.3
  d : Matrix field := c * (inverse(pm1) :: Matrix(field))
  e : Matrix field := subMatrix(u1,1,m2,1,m2)
  f : Matrix field := subMatrix(d,1,m2,1,m2)
  g : Matrix field := d - f * (inverse(e) :: Matrix(field)) * u1
  pmin2 : NNI := p - m2
  g' : Matrix field := subMatrix(g,1,nrows(g),p - pmin2 + 1,p)
  lup := lupFactorEngine(g',m2,pmin2)
  l2 := lup.1
  u2 := lup.2
  pm2 := lup.3
  pm3 := horizConcat(zero(pmin2,m2)$(Matrix field), pm2)
  pm3 := vertConcat(horizConcat(diagonalMatrix [1 for i in 1..m2],
    zero(m2,pmin2)$(Matrix field)),pm3)
  h : Matrix field := u1 * (inverse(pm3) :: Matrix(field))
  l : Matrix field := horizConcat(l1, zero(m2,m2)$(Matrix field))
  l := vertConcat(l,horizConcat(f * (inverse(e) :: Matrix(field)), l2))
  u : Matrix field := horizConcat(zero(m2,m2)$(Matrix field), u2)
  u := vertConcat(h,u)
  pm := pm3 * pm1
  [l,u,pm]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9
 
--S 10  of 18
intLog2: NNI -> NNI
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10
 
--S 11 of 18
intLog2 n == if n = 1 then 0 else 1 + intLog2(n quo 2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11
 
--S 12 of 18
lupFactor: Matrix field -> Union(List Matrix field,"failed")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12
 
--S 13 of 18
lupFactor m ==
  not((r := nrows m) = ncols m) =>
    messagePrint("Matrix must be square")$OUTFORM
    "failed"
  ilog := intLog2(2)
  not(r = 2 ** ilog) =>
    m := embedMatrix(m,r,(n := 2 ** (ilog + 1)))
    l := lupFactorEngine(m,n,n)
    [subMatrix(l.1,1,r,1,r),subMatrix(l.2,1,r,1,r),
      subMatrix(l.3,1,r,1,r)]
  lupFactorEngine(m,r,r)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13
 
--S 14 of 18
m : Matrix field := zero(4,4)
 

         +0  0  0  0+
         |          |
         |0  0  0  0|
   (14)  |          |
         |0  0  0  0|
         |          |
         +0  0  0  0+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +0  0  0  0+
--R         |          |
--R         |0  0  0  0|
--R   (14)  |          |
--R         |0  0  0  0|
--R         |          |
--R         +0  0  0  0+
--R                                                Type: Matrix Fraction Integer
--E 14

--S 15 of 18
for i in 4..1 by -1 repeat m(5-i,i) := i
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 18
m
 

         +0  0  0  4+
         |          |
         |0  0  3  0|
   (16)  |          |
         |0  2  0  0|
         |          |
         +1  0  0  0+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +0  0  0  4+
--R         |          |
--R         |0  0  3  0|
--R   (16)  |          |
--R         |0  2  0  0|
--R         |          |
--R         +1  0  0  0+
--R                                                Type: Matrix Fraction Integer
--E 16
 
--S 17 of 18
lupFactor m
 
   Compiling function intLog2 with type NonNegativeInteger -> 
      NonNegativeInteger 
   Compiling function embedMatrix with type (Matrix Fraction Integer,
      NonNegativeInteger,NonNegativeInteger) -> Matrix Fraction Integer
      
   Compiling function nonZeroCol with type Matrix Fraction Integer -> 
      Integer 
   Compiling function permMat with type (Integer,Integer,Integer) -> 
      Matrix Fraction Integer 
   Compiling function lupFactorEngine with type (Matrix Fraction 
      Integer,Integer,Integer) -> List Matrix Fraction Integer 
   Compiling function lupFactor with type Matrix Fraction Integer -> 
      Union(List Matrix Fraction Integer,"failed") 
   Compiling function G1599 with type Integer -> Boolean 

          +1  0  0  0+ +4  0  0  0+ +0  0  0  1+
          |          | |          | |          |
          |0  1  0  0| |0  3  0  0| |0  0  1  0|
   (17)  [|          |,|          |,|          |]
          |0  0  1  0| |0  0  2  0| |0  1  0  0|
          |          | |          | |          |
          +0  0  0  1+ +0  0  0  1+ +1  0  0  0+
                                Type: Union(List Matrix Fraction Integer,...)
--R 
--R   Compiling function intLog2 with type NonNegativeInteger -> 
--R      NonNegativeInteger 
--R   Compiling function embedMatrix with type (Matrix Fraction Integer,
--R      NonNegativeInteger,NonNegativeInteger) -> Matrix Fraction Integer
--R      
--R   Compiling function nonZeroCol with type Matrix Fraction Integer -> 
--R      Integer 
--R   Compiling function permMat with type (Integer,Integer,Integer) -> 
--R      Matrix Fraction Integer 
--R   Compiling function lupFactorEngine with type (Matrix Fraction 
--R      Integer,Integer,Integer) -> List Matrix Fraction Integer 
--R   Compiling function lupFactor with type Matrix Fraction Integer -> 
--R      Union(List Matrix Fraction Integer,"failed") 
--I   Compiling function G7005 with type Integer -> Boolean 
--R
--R          +1  0  0  0+ +4  0  0  0+ +0  0  0  1+
--R          |          | |          | |          |
--R          |0  1  0  0| |0  3  0  0| |0  0  1  0|
--R   (17)  [|          |,|          |,|          |]
--R          |0  0  1  0| |0  0  2  0| |0  1  0  0|
--R          |          | |          | |          |
--R          +0  0  0  1+ +0  0  0  1+ +1  0  0  0+
--R                                Type: Union(List Matrix Fraction Integer,...)
--E 17

--S 18 of 18
m := [[1,2,3],[2,3,1],[3,1,2]]
 

         +1  2  3+
         |       |
   (18)  |2  3  1|
         |       |
         +3  1  2+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (18)  |2  3  1|
--R         |       |
--R         +3  1  2+
--R                                                Type: Matrix Fraction Integer
--E 18
)spool 
 
Starts dribbling to slowint.output (2009/2/17, 18:0:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 5
k := 7/5
 

        7
   (1)  -
        5
                                                       Type: Fraction Integer
--R 
--R
--R        7
--R   (1)  -
--R        5
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 5
mu := sqrt ( ((k-1)*m**2 + 2)/(2*k*m**2 -(k-1)))
 

         +-------+
         |  2
         | m  + 5
   (2)   |-------
         |  2
        \|7m  - 1
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         |  2
--R         | m  + 5
--R   (2)   |-------
--R         |  2
--R        \|7m  - 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 5
km := 2/ ( (1+(2/(k+1)) * (1-mu**2)/mu)*(2*mu + 1 + 1/(m**2)))
 

                                +-------+
                                |  2
                       4     2  | m  + 5
                   (14m  - 2m ) |-------
                                |  2
                               \|7m  - 1
   (3)  -------------------------------------------
                         +-------+
                         |  2
            4     2      | m  + 5      4      2
        (17m  - 4m  - 1) |-------  + 7m  + 10m  - 5
                         |  2
                        \|7m  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                +-------+
--R                                |  2
--R                       4     2  | m  + 5
--R                   (14m  - 2m ) |-------
--R                                |  2
--R                               \|7m  - 1
--R   (3)  -------------------------------------------
--R                         +-------+
--R                         |  2
--R            4     2      | m  + 5      4      2
--R        (17m  - 4m  - 1) |-------  + 7m  + 10m  - 5
--R                         |  2
--R                        \|7m  - 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 5
f := - 2*m / ((m**2-1)*km)
 

                           +-------+
                           |  2
              4     2      | m  + 5      4      2
        (- 17m  + 4m  + 1) |-------  - 7m  - 10m  + 5
                           |  2
                          \|7m  - 1
   (4)  ---------------------------------------------
                                  +-------+
                                  |  2
                     5     3      | m  + 5
                  (7m  - 8m  + m) |-------
                                  |  2
                                 \|7m  - 1
                                                     Type: Expression Integer
--R 
--R
--R                           +-------+
--R                           |  2
--R              4     2      | m  + 5      4      2
--R        (- 17m  + 4m  + 1) |-------  - 7m  - 10m  + 5
--R                           |  2
--R                          \|7m  - 1
--R   (4)  ---------------------------------------------
--R                                  +-------+
--R                                  |  2
--R                     5     3      | m  + 5
--R                  (7m  - 8m  + m) |-------
--R                                  |  2
--R                                 \|7m  - 1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 5
integrate(f,m)
 

   (5)
                       +-------+
                       |  2
                2      | m  + 5      2
             (7m  - 1) |-------  + 4m  + 2
                       |  2
                      \|7m  - 1
       14log(-----------------------------)
                            2
                           m
     + 
                           +-------+
                           |  2
                    2      | m  + 5      2
               (- 7m  + 1) |-------  + 4m  + 2
                           |  2
                          \|7m  - 1
       - 14log(-------------------------------)
                               2
                              m
     + 
                                          +-------+
                                          |  2
         +-+          4       2       +-+ | m  + 5       4       2
       7\|7 log((- 49m  - 112m  + 17)\|7  |-------  + 49m  + 238m  + 127)
                                          |  2
                                         \|7m  - 1
     + 
                               2
            +-+             17m  - 5                   2               2
       - 14\|5 atan(-----------------------) - 20log(7m  - 1) - 28log(m  - 1)
                                  +-------+
                                  |  2
                       2      +-+ | m  + 5
                    (7m  - 1)\|5  |-------
                                  |  2
                                 \|7m  - 1
     + 
       28log(m)
  /
     28
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)
--R                       +-------+
--R                       |  2
--R                2      | m  + 5      2
--R             (7m  - 1) |-------  + 4m  + 2
--R                       |  2
--R                      \|7m  - 1
--R       14log(-----------------------------)
--R                            2
--R                           m
--R     + 
--R                           +-------+
--R                           |  2
--R                    2      | m  + 5      2
--R               (- 7m  + 1) |-------  + 4m  + 2
--R                           |  2
--R                          \|7m  - 1
--R       - 14log(-------------------------------)
--R                               2
--R                              m
--R     + 
--R                                          +-------+
--R                                          |  2
--R         +-+          4       2       +-+ | m  + 5       4       2
--R       7\|7 log((- 49m  - 112m  + 17)\|7  |-------  + 49m  + 238m  + 127)
--R                                          |  2
--R                                         \|7m  - 1
--R     + 
--R                               2
--R            +-+             17m  - 5                   2               2
--R       - 14\|5 atan(-----------------------) - 20log(7m  - 1) - 28log(m  - 1)
--R                                  +-------+
--R                                  |  2
--R                       2      +-+ | m  + 5
--R                    (7m  - 1)\|5  |-------
--R                                  |  2
--R                                 \|7m  - 1
--R     + 
--R       28log(m)
--R  /
--R     28
--R                                          Type: Union(Expression Integer,...)
--E 5
)spool 
 
Starts dribbling to cardinal.output (2009/2/17, 17:44:7).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 16
(c0, c1, c2, c3, A0, A1): CardinalNumber
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 16
c0 := 0::NNI
 

   (2)  0
                                                         Type: CardinalNumber
--R 
--R
--R   (2)  0
--R                                                         Type: CardinalNumber
--E 2

--S 3 of 16
c1 := 1::NNI
 

   (3)  1
                                                         Type: CardinalNumber
--R 
--R
--R   (3)  1
--R                                                         Type: CardinalNumber
--E 3

--S 4 of 16
c2 := 2::NNI
 

   (4)  2
                                                         Type: CardinalNumber
--R 
--R
--R   (4)  2
--R                                                         Type: CardinalNumber
--E 4

--S 5 of 16
c3 := 3::NNI
 

   (5)  3
                                                         Type: CardinalNumber
--R 
--R
--R   (5)  3
--R                                                         Type: CardinalNumber
--E 5

--S 6 of 16
A0 := Aleph 0
 

   (6)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (6)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 6

--S 7 of 16
A1 := Aleph 1
 

   (7)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (7)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 7

--S 8 of 16
[finite? c2,    finite? A0]
 

   (8)  [true,false]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,false]
--R                                                           Type: List Boolean
--E 8

--S 9 of 16
[finite?  c2,    finite?  A0]
 

   (9)  [true,false]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [true,false]
--R                                                           Type: List Boolean
--E 9

--S 10 of 16
[countable? c2, countable? A0, countable? A1]
 

   (10)  [true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (10)  [true,true,false]
--R                                                           Type: List Boolean
--E 10

--S 11 of 16
[c2 + c2, c2 + A1]
 

   (11)  [4,Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (11)  [4,Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 11

--S 12 of 16
[c2 - c1, c2 - c2, c2 - c3, A1 - c2, A1 - A0, A1 - A1]
 

   (12)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
                                    Type: List Union(CardinalNumber,"failed")
--R 
--R
--R   (12)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
--R                                    Type: List Union(CardinalNumber,"failed")
--E 12

--S 13 of 16
[c0 * c2, c1 * c2, c2 * c2, c0 * A1, c1 * A1, c2 * A1, A0 * A1]
 

   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 13

--S 14 of 16
[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]
 

   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 14

--S 15 of 16
generalizedContinuumHypothesisAssumed true
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 16
[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1]
 

   (16)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (16)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
--R                                                    Type: List CardinalNumber
--E 16
)spool
 
Starts dribbling to set.output (2009/2/17, 18:0:20).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 20
s := set [x**2-1, y**2-1, z**2-1]
 

          2      2      2
   (1)  {x  - 1,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      2      2
--R   (1)  {x  - 1,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 1

--S 2 of 20
t := set [x**i - i+1 for i in 2..10 | prime? i]
 

          2      3      5      7
   (2)  {x  - 1,x  - 2,x  - 4,x  - 6}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      3      5      7
--R   (2)  {x  - 1,x  - 2,x  - 4,x  - 6}
--R                                                 Type: Set Polynomial Integer
--E 2

--S 3 of 20
i := intersect(s,t)
 

          2
   (3)  {x  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2
--R   (3)  {x  - 1}
--R                                                 Type: Set Polynomial Integer
--E 3

--S 4 of 20
u := union(s,t)
 

          2      3      5      7      2      2
   (4)  {x  - 1,x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      3      5      7      2      2
--R   (4)  {x  - 1,x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 4

--S 5 of 20
difference(s,t)
 

          2      2
   (5)  {y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      2
--R   (5)  {y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 5

--S 6 of 20
symmetricDifference(s,t)
 

          3      5      7      2      2
   (6)  {x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          3      5      7      2      2
--R   (6)  {x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 6

--S 7 of 20
member?(y, s)
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 7

--S 8 of 20
member?((y+1)*(y-1), s)
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 20
subset?(i, s)
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 20
subset?(u, s)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 20
gs := set [g for i in 1..11 | primitive?(g := i::PF 11)]
 

   (11)  {2,6,7,8}
                                                      Type: Set PrimeField 11
--R 
--R
--R   (11)  {2,6,7,8}
--R                                                      Type: Set PrimeField 11
--E 11

--S 12 of 20
complement gs
 

   (12)  {1,3,4,5,9,10,0}
                                                      Type: Set PrimeField 11
--R 
--R
--R   (12)  {1,3,4,5,9,10,0}
--R                                                      Type: Set PrimeField 11
--E 12

--S 13 of 20
a := set [i**2 for i in 1..5]
 

   (13)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (13)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 13

--S 14 of 20
insert!(32, a)
 

   (14)  {1,4,9,16,25,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (14)  {1,4,9,16,25,32}
--R                                                    Type: Set PositiveInteger
--E 14

--S 15 of 20
remove!(25, a)
 

   (15)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (15)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 15

--S 16 of 20
a
 

   (16)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (16)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 16

--S 17 of 20
b := b0 := set [i**2 for i in 1..5]
 

   (17)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (17)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 17

--S 18 of 20
b := union(b, {32})
 

   (18)  {1,4,9,16,25,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (18)  {1,4,9,16,25,32}
--R                                                    Type: Set PositiveInteger
--E 18

--S 19 of 20
b := difference(b, {25})
 

   (19)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (19)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 19

--S 20 of 20
b0
 

   (20)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (20)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 20
)spool 
 
Starts dribbling to defintef.output (2009/2/17, 17:44:37).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 8
sin(x)**3/(sin(x)**3+cos(x)**3)
 

                   3
             sin(x)
   (1)  -----------------
              3         3
        sin(x)  + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                   3
--R             sin(x)
--R   (1)  -----------------
--R              3         3
--R        sin(x)  + cos(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 8
integrate(%, x = 0..%pi/2, "noPole")
 

        2log(16) - 4log(4) + 3%pi
   (2)  -------------------------
                    12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R        2log(16) - 4log(4) + 3%pi
--R   (2)  -------------------------
--R                    12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 2

--S 3 of 8
x**2/(1+x**3)
 

           2
          x
   (3)  ------
         3
        x  + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2
--R          x
--R   (3)  ------
--R         3
--R        x  + 1
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 8
integrate(%, x=0..%plusInfinity)
 

   (4)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 8
exp(-x**2)*log(x)**2
 

             2
          - x       2
   (5)  %e    log(x)
                                                     Type: Expression Integer
--R 
--R
--R             2
--R          - x       2
--R   (5)  %e    log(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 8
integrate(%, x=0..%plusInfinity)
 

         _ 1             1     _ 1         1 2
        | (-)polygamma(1,-) + | (-)digamma(-)
           2             2       2         2
   (6)  --------------------------------------
                           8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         _ 1             1     _ 1         1 2
--R        | (-)polygamma(1,-) + | (-)digamma(-)
--R           2             2       2         2
--R   (6)  --------------------------------------
--R                           8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 6

--S 7 of 8
x * asin(x/(x+1))
 

                 x
   (7)  x asin(-----)
               x + 1
                                                     Type: Expression Integer
--R 
--R
--R                 x
--R   (7)  x asin(-----)
--R               x + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 8
integrate(%, x=0..1)
 

          +-+
        3\|3  - 4
   (8)  ---------
            6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          +-+
--R        3\|3  - 4
--R   (8)  ---------
--R            6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 8
)spool
 
Starts dribbling to elfuts.output (2009/2/17, 17:45:33).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
)set streams calculate 10
 

 
)expose ELFUTS
 
   EllipticFunctionsUnivariateTaylorSeries is now explicitly exposed in
      frame initial 

--S 1 of 40
macro RN == FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 40
macro QF == FRAC
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 40
xx:UTS(RN,'x,0):=x
 

   (3)  x
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R   (3)  x
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 3

--S 4 of 40
sn(xx,1::RN)
 

            1  3    2  5    17  7    62   9      11
   (4)  x - - x  + -- x  - --- x  + ---- x  + O(x  )
            3      15      315      2835
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R            1  3    2  5    17  7    62   9      11
--R   (4)  x - - x  + -- x  - --- x  + ---- x  + O(x  )
--R            3      15      315      2835
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 4

--S 5 of 40
cn(xx,1::RN)
 

            1  2    5  4    61  6    277  8    50521   10      11
   (5)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
            2      24      720      8064      3628800
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R            1  2    5  4    61  6    277  8    50521   10      11
--R   (5)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
--R            2      24      720      8064      3628800
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 5

--S 6 of 40
dn(xx,1::RN)
 

            1  2    5  4    61  6    277  8    50521   10      11
   (6)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
            2      24      720      8064      3628800
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R            1  2    5  4    61  6    277  8    50521   10      11
--R   (6)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
--R            2      24      720      8064      3628800
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 6

--S 7 of 40
yy:UTS(FRAC UP(k,RN),'y,0):=y
 

   (7)  y
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (7)  y
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 7

--S 8 of 40
snn:=sn(yy,k::QF UP(k,RN))
 

   (8)
            1  2   1  3     1   4    7  2    1   5
     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
            6      6       120      60      120
   + 
          1   6    3   4    3   2     1   7
     (- ---- k  - --- k  - --- k  - ----)y
        5040      112      112      5040
   + 
         1    8    307   6    913   4    307   2      1    9      11
     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
      362880      90720      60480      90720      362880
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (8)
--R            1  2   1  3     1   4    7  2    1   5
--R     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
--R            6      6       120      60      120
--R   + 
--R          1   6    3   4    3   2     1   7
--R     (- ---- k  - --- k  - --- k  - ----)y
--R        5040      112      112      5040
--R   + 
--R         1    8    307   6    913   4    307   2      1    9      11
--R     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
--R      362880      90720      60480      90720      362880
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 8

--S 9 of 40
cnn:=cn(yy,k::QF UP(k,RN))
 

   (9)
         1  2    1  2    1  4       1  4    11  2    1   6
     1 - - y  + (- k  + --)y  + (- -- k  - --- k  - ---)y
         2       6      24         45      180      720
   + 
       1   6    19  4    17   2     1    8
     (--- k  + --- k  + ---- k  + -----)y
      630      840      1680      40320
   + 
          1    8    247   6    641   4     461   2      1     10      11
     (- ----- k  - ----- k  - ----- k  - ------ k  - -------)y   + O(y  )
        14175      56700      75600      453600      3628800
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (9)
--R         1  2    1  2    1  4       1  4    11  2    1   6
--R     1 - - y  + (- k  + --)y  + (- -- k  - --- k  - ---)y
--R         2       6      24         45      180      720
--R   + 
--R       1   6    19  4    17   2     1    8
--R     (--- k  + --- k  + ---- k  + -----)y
--R      630      840      1680      40320
--R   + 
--R          1    8    247   6    641   4     461   2      1     10      11
--R     (- ----- k  - ----- k  - ----- k  - ------ k  - -------)y   + O(y  )
--R        14175      56700      75600      453600      3628800
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 9

--S 10 of 40
dnn:=dn(yy,k::QF UP(k,RN))
 

   (10)
         1  2 2     1  4   1  2  4       1   6    11  4    1  2  6
     1 - - k y  + (-- k  + - k )y  + (- --- k  - --- k  - -- k )y
         2         24      6            720      180      45
   + 
        1    8    17   6    19  4    1   2  8
     (----- k  + ---- k  + --- k  + --- k )y
      40320      1680      840      630
   + 
           1     10     461   8    641   6    247   4     1    2  10      11
     (- ------- k   - ------ k  - ----- k  - ----- k  - ----- k )y   + O(y  )
        3628800       453600      75600      56700      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (10)
--R         1  2 2     1  4   1  2  4       1   6    11  4    1  2  6
--R     1 - - k y  + (-- k  + - k )y  + (- --- k  - --- k  - -- k )y
--R         2         24      6            720      180      45
--R   + 
--R        1    8    17   6    19  4    1   2  8
--R     (----- k  + ---- k  + --- k  + --- k )y
--R      40320      1680      840      630
--R   + 
--R           1     10     461   8    641   6    247   4     1    2  10      11
--R     (- ------- k   - ------ k  - ----- k  - ----- k  - ----- k )y   + O(y  )
--R        3628800       453600      75600      56700      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 10

--S 11 of 40
snn**2+cnn**2
 

                11
   (11)  1 + O(y  )
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R                11
--R   (11)  1 + O(y  )
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 11

--S 12 of 40
ksquared:=(k::UP(k,RN))**2
 

          2
   (12)  k
                               Type: UnivariatePolynomial(k,Fraction Integer)
--R 
--R
--R          2
--R   (12)  k
--R                               Type: UnivariatePolynomial(k,Fraction Integer)
--E 12

--S 13 of 40
dnn**2+ksquared*snn**2
 

                11
   (13)  1 + O(y  )
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R                11
--R   (13)  1 + O(y  )
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 13

--S 14 of 40
(differentiate snn)**2
 

   (14)
             2      2    1  4   5  2   1  4       2  6    4    2    2  6
     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
                         3      3      3         45                45
   + 
       1   8    94  6   104  4    94  2    1   8
     (--- k  + --- k  + --- k  + --- k  + ---)y
      315      315      105      315      315
   + 
        2    10    109  8    6977  6    6977  4    109  2     2    10      11
   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
      14175       2025      14175      14175      2025      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (14)
--R             2      2    1  4   5  2   1  4       2  6    4    2    2  6
--R     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
--R                         3      3      3         45                45
--R   + 
--R       1   8    94  6   104  4    94  2    1   8
--R     (--- k  + --- k  + --- k  + --- k  + ---)y
--R      315      315      105      315      315
--R   + 
--R        2    10    109  8    6977  6    6977  4    109  2     2    10      11
--R   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
--R      14175       2025      14175      14175      2025      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 14

--S 15 of 40
(1-snn**2)*(1-ksquared*snn**2)
 

   (15)
             2      2    1  4   5  2   1  4       2  6    4    2    2  6
     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
                         3      3      3         45                45
   + 
       1   8    94  6   104  4    94  2    1   8
     (--- k  + --- k  + --- k  + --- k  + ---)y
      315      315      105      315      315
   + 
        2    10    109  8    6977  6    6977  4    109  2     2    10      11
   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
      14175       2025      14175      14175      2025      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (15)
--R             2      2    1  4   5  2   1  4       2  6    4    2    2  6
--R     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
--R                         3      3      3         45                45
--R   + 
--R       1   8    94  6   104  4    94  2    1   8
--R     (--- k  + --- k  + --- k  + --- k  + ---)y
--R      315      315      105      315      315
--R   + 
--R        2    10    109  8    6977  6    6977  4    109  2     2    10      11
--R   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
--R      14175       2025      14175      14175      2025      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 15

--S 16 of 40
(differentiate cnn)**2
 

   (16)
      2      4  2   1  4    32  4   43  2    2  6
     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
             3      3       45      45      45
   + 
         64  6    94  4    31  2    1   8
     (- --- k  - --- k  - --- k  - ---)y
        315      105      105      315
   + 
       512   8    6101  6   2242  4    761   2     2    10      11
     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
      14175      14175      4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (16)
--R      2      4  2   1  4    32  4   43  2    2  6
--R     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
--R             3      3       45      45      45
--R   + 
--R         64  6    94  4    31  2    1   8
--R     (- --- k  - --- k  - --- k  - ---)y
--R        315      105      105      315
--R   + 
--R       512   8    6101  6   2242  4    761   2     2    10      11
--R     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
--R      14175      14175      4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 16

--S 17 of 40
(1-cnn**2)*(1-ksquared+ksquared*cnn**2)
 

   (17)
      2      4  2   1  4    32  4   43  2    2  6
     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
             3      3       45      45      45
   + 
         64  6    94  4    31  2    1   8
     (- --- k  - --- k  - --- k  - ---)y
        315      105      105      315
   + 
       512   8    6101  6   2242  4    761   2     2    10      11
     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
      14175      14175      4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (17)
--R      2      4  2   1  4    32  4   43  2    2  6
--R     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
--R             3      3       45      45      45
--R   + 
--R         64  6    94  4    31  2    1   8
--R     (- --- k  - --- k  - --- k  - ---)y
--R        315      105      105      315
--R   + 
--R       512   8    6101  6   2242  4    761   2     2    10      11
--R     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
--R      14175      14175      4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 17

--S 18 of 40
(differentiate dnn)**2
 

   (18)
      4 2      1  6   4  4  4     2  8   43  6   32  4  6
     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
               3      3          45      45      45
   + 
         1   10    31  8    94  6    64  4  8
     (- --- k   - --- k  - --- k  - --- k )y
        315       105      105      315
   + 
        2    12    761   10   2242  8    6101  6    512   4  10      11
     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
      14175       14175       4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (18)
--R      4 2      1  6   4  4  4     2  8   43  6   32  4  6
--R     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
--R               3      3          45      45      45
--R   + 
--R         1   10    31  8    94  6    64  4  8
--R     (- --- k   - --- k  - --- k  - --- k )y
--R        315       105      105      315
--R   + 
--R        2    12    761   10   2242  8    6101  6    512   4  10      11
--R     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
--R      14175       14175       4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 18

--S 19 of 40
(1-dnn**2)*(dnn**2-1+ksquared)
 

   (19)
      4 2      1  6   4  4  4     2  8   43  6   32  4  6
     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
               3      3          45      45      45
   + 
         1   10    31  8    94  6    64  4  8
     (- --- k   - --- k  - --- k  - --- k )y
        315       105      105      315
   + 
        2    12    761   10   2242  8    6101  6    512   4  10      11
     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
      14175       14175       4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (19)
--R      4 2      1  6   4  4  4     2  8   43  6   32  4  6
--R     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
--R               3      3          45      45      45
--R   + 
--R         1   10    31  8    94  6    64  4  8
--R     (- --- k   - --- k  - --- k  - --- k )y
--R        315       105      105      315
--R   + 
--R        2    12    761   10   2242  8    6101  6    512   4  10      11
--R     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
--R      14175       14175       4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 19

--S 20  of 40
kkk:=integrate(1/((1-yy**2)*(1-ksquared*yy**2))**(1/2))
 

   (20)
          1  2   1  3     3  4    1  2    3  5
     y + (- k  + -)y  + (-- k  + -- k  + --)y
          6      6       40      20      40
   + 
       5   6    3   4    3   2    5   7
     (--- k  + --- k  + --- k  + ---)y
      112      112      112      112
   + 
       35   8    5   6    1  4    5   2    35   9      11
     (---- k  + --- k  + -- k  + --- k  + ----)y  + O(y  )
      1152      288      64      288      1152
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (20)
--R          1  2   1  3     3  4    1  2    3  5
--R     y + (- k  + -)y  + (-- k  + -- k  + --)y
--R          6      6       40      20      40
--R   + 
--R       5   6    3   4    3   2    5   7
--R     (--- k  + --- k  + --- k  + ---)y
--R      112      112      112      112
--R   + 
--R       35   8    5   6    1  4    5   2    35   9      11
--R     (---- k  + --- k  + -- k  + --- k  + ----)y  + O(y  )
--R      1152      288      64      288      1152
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 20

--S 21 of 40
revert kkk
 

   (21)
            1  2   1  3     1   4    7  2    1   5
     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
            6      6       120      60      120
   + 
          1   6    3   4    3   2     1   7
     (- ---- k  - --- k  - --- k  - ----)y
        5040      112      112      5040
   + 
         1    8    307   6    913   4    307   2      1    9      11
     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
      362880      90720      60480      90720      362880
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (21)
--R            1  2   1  3     1   4    7  2    1   5
--R     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
--R            6      6       120      60      120
--R   + 
--R          1   6    3   4    3   2     1   7
--R     (- ---- k  - --- k  - --- k  - ----)y
--R        5040      112      112      5040
--R   + 
--R         1    8    307   6    913   4    307   2      1    9      11
--R     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
--R      362880      90720      60480      90720      362880
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 21

--S 22 of 40
snn
 

   (22)
            1  2   1  3     1   4    7  2    1   5
     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
            6      6       120      60      120
   + 
          1   6    3   4    3   2     1   7
     (- ---- k  - --- k  - --- k  - ----)y
        5040      112      112      5040
   + 
         1    8    307   6    913   4    307   2      1    9
     (------ k  + ----- k  + ----- k  + ----- k  + ------)y
      362880      90720      60480      90720      362880
   + 
               1     10     11069   8     82913   6     82913   4     11069   2
         - -------- k   - -------- k  - -------- k  - -------- k  - -------- k
           39916800       39916800      19958400      19958400      39916800
       + 
               1
         - --------
           39916800
    *
        11
       y
   + 
        12
     O(y  )
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (22)
--R            1  2   1  3     1   4    7  2    1   5
--R     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
--R            6      6       120      60      120
--R   + 
--R          1   6    3   4    3   2     1   7
--R     (- ---- k  - --- k  - --- k  - ----)y
--R        5040      112      112      5040
--R   + 
--R         1    8    307   6    913   4    307   2      1    9
--R     (------ k  + ----- k  + ----- k  + ----- k  + ------)y
--R      362880      90720      60480      90720      362880
--R   + 
--R               1     10     11069   8     82913   6     82913   4     11069   2
--R         - -------- k   - -------- k  - -------- k  - -------- k  - -------- k
--R           39916800       39916800      19958400      19958400      39916800
--R       + 
--R               1
--R         - --------
--R           39916800
--R    *
--R        11
--R       y
--R   + 
--R        12
--R     O(y  )
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 22
 
q0=*/[1-q**2*n for n in 1..]
 
   There are 13 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                          Stream Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
q1=*/[1+q**2*n for n in 1..]
 
   There are 13 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                          Stream Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
q2=*/[1+q**(2*n-1) for n in 1..]
 
   There are 13 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                     Stream Fraction Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
q3=*/[1-q**(2*n-1) for n in 1..]
 
   There are 13 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                     Stream Fraction Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--S 23 of 40
eprod x==exp evenlambert log x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 40
qq:UTS(RN,'q,0):=q
 

   (24)  q
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R   (24)  q
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 24

--S 25 of 40
q0:=eprod(1-qq)
 
   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 

              2    4    10      11
   (25)  1 - q  - q  + q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
--R      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 
--R
--R              2    4    10      11
--R   (25)  1 - q  - q  + q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 25

--S 26 of 40
q1:=eprod(1+qq)
 

              2    4     6     8     10      11
   (26)  1 + q  + q  + 2q  + 2q  + 3q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R              2    4     6     8     10      11
--R   (26)  1 + q  + q  + 2q  + 2q  + 3q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 26

--S 27 of 40
oprod x == exp oddlambert log x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28 of 40
q2:=oprod(1+qq)
 
   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 

                  3    4    5    6    7     8     9     10      11
   (28)  1 + q + q  + q  + q  + q  + q  + 2q  + 2q  + 2q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
--R      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 
--R
--R                  3    4    5    6    7     8     9     10      11
--R   (28)  1 + q + q  + q  + q  + q  + q  + 2q  + 2q  + 2q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 28

--S 29 of 40
q3:=oprod(1-qq)
 

                  3    4    5    6    7     8     9     10      11
   (29)  1 - q - q  + q  - q  + q  - q  + 2q  - 2q  + 2q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                  3    4    5    6    7     8     9     10      11
--R   (29)  1 - q - q  + q  - q  + q  - q  + 2q  - 2q  + 2q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 29

--S 30 of 40
q1*q2*q3
 

                11
   (30)  1 + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                11
--R   (30)  1 + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 30

--S 31 of 40
q2**8-q3**8
 

                   3       5        7        9      11
   (31)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                   3       5        7        9      11
--R   (31)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 31

--S 32 of 40
16*qq*q1**8
 

                   3       5        7        9      11
   (32)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                   3       5        7        9      11
--R   (32)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 32

--(q1**2/q2**2)**2
--(q3**2/q2**2)**2

--S 33 of 40
q0**3
 

               2     6      11
   (33)  1 - 3q  + 5q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R               2     6      11
--R   (33)  1 - 3q  + 5q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 33

--S 34 of 40
q1**2*q0
 

              2    6      11
   (34)  1 + q  + q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R              2    6      11
--R   (34)  1 + q  + q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 34

--S 35 of 40
q2**2*q0
 

                    4     9      11
   (35)  1 + 2q + 2q  + 2q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                    4     9      11
--R   (35)  1 + 2q + 2q  + 2q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 35

--S 36 of 40
q3**2*q0
 

                    4     9      11
   (36)  1 - 2q + 2q  - 2q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                    4     9      11
--R   (36)  1 - 2q + 2q  - 2q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 36

--S 37 of 40
qqq:UTS(FRAC UP(a,RN),'q,0):=q
 

   (37)  q
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--R 
--R
--R   (37)  q
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--E 37

--S 38 of 40
a:=a::FRAC UP(a,RN)
 

   (38)  a
                      Type: Fraction UnivariatePolynomial(a,Fraction Integer)
--R 
--R
--R   (38)  a
--R                      Type: Fraction UnivariatePolynomial(a,Fraction Integer)
--E 38

--S 39 of 40
eprod(1-qqq)*oprod(1-a*qqq)*oprod(1-qqq/a)
 
   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
      Integer),q,0) 
   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
      Integer),q,0) 

                2          4             6
             - a  - 1     a  + 1  4   - a  - 1  9      11
   (39)  1 + -------- q + ------ q  + -------- q  + O(q  )
                 a           2            3
                            a            a
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--R 
--R   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
--R      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
--R      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
--R      Integer),q,0) 
--R   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
--R      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
--R      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
--R      Integer),q,0) 
--R
--R                2          4             6
--R             - a  - 1     a  + 1  4   - a  - 1  9      11
--R   (39)  1 + -------- q + ------ q  + -------- q  + O(q  )
--R                 a           2            3
--R                            a            a
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--E 39

--S 40 of 40
sq:=ksquared*snn**2
 

   (40)
      2 2      1  4   1  2  4     2  6   13  4    2  2  6
     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
               3      3          45      45      45
   + 
         1   8    2  6    2  4    1   2  8
     (- --- k  - -- k  - -- k  - --- k )y
        315      21      21      315
   + 
        2    10    251   8    292  6    251   4     2    2  10      11
     (----- k   + ----- k  + ---- k  + ----- k  + ----- k )y   + O(y  )
      14175       14175      4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (40)
--R      2 2      1  4   1  2  4     2  6   13  4    2  2  6
--R     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
--R               3      3          45      45      45
--R   + 
--R         1   8    2  6    2  4    1   2  8
--R     (- --- k  - -- k  - -- k  - --- k )y
--R        315      21      21      315
--R   + 
--R        2    10    251   8    292  6    251   4     2    2  10      11
--R     (----- k   + ----- k  + ---- k  + ----- k  + ----- k )y   + O(y  )
--R      14175       14175      4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 40
)spool 
 
Starts dribbling to poly.output (2009/2/17, 17:56:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 54
a := rootOf(a**4+1,a)
 

   (1)  a
                                                     Type: Expression Integer
--R 
--R
--R   (1)  a
--R                                                     Type: Expression Integer
--E 1

--S 2 of 54
definingPolynomial a
 

         4
   (2)  a  + 1
                                                     Type: Expression Integer
--R 
--R
--R         4
--R   (2)  a  + 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 54
b := rootOf(b**2-a-1,b)
 

   (3)  b
                                                     Type: Expression Integer
--R 
--R
--R   (3)  b
--R                                                     Type: Expression Integer
--E 3

--S 4 of 54
a + b
 

   (4)  b + a
                                                     Type: Expression Integer
--R 
--R
--R   (4)  b + a
--R                                                     Type: Expression Integer
--E 4

--S 5 of 54
% ** 5
 

            3      2                 3      2
   (5)  (10a  + 11a  + 2a - 4)b + 15a  + 10a  + 4a - 10
                                                     Type: Expression Integer
--R 
--R
--R            3      2                 3      2
--R   (5)  (10a  + 11a  + 2a - 4)b + 15a  + 10a  + 4a - 10
--R                                                     Type: Expression Integer
--E 5

--S 6 of 54
rootOf(c**2+c+1,c)
 

   (6)  c
                                                     Type: Expression Integer
--R 
--R
--R   (6)  c
--R                                                     Type: Expression Integer
--E 6

--S 7 of 54
zeroOf(d**2+d+1,d)
 

         +---+
        \|- 3  - 1
   (7)  ----------
             2
                                                     Type: Expression Integer
--R 
--R
--R         +---+
--R        \|- 3  - 1
--R   (7)  ----------
--R             2
--R                                                     Type: Expression Integer
--E 7

--S 8 of 54
rootOf(e**5-2,e)
 

   (8)  e
                                                     Type: Expression Integer
--R 
--R
--R   (8)  e
--R                                                     Type: Expression Integer
--E 8

--S 9 of 54
zeroOf(f**5-2,f)
 

        5+-+
   (9)  \|2
                                                     Type: Expression Integer
--R 
--R
--R        5+-+
--R   (9)  \|2
--R                                                     Type: Expression Integer
--E 9

)clear all
 
   All user variables and function definitions have been cleared.

--S 10 of 54
p := 3*x**8 + 2*x**7 + 6*x**2 + 7*x + 2
 

          8     7     2
   (1)  3x  + 2x  + 6x  + 7x + 2
                                                     Type: Polynomial Integer
--R 
--R
--R          8     7     2
--R   (1)  3x  + 2x  + 6x  + 7x + 2
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 54
q := 2*x**13 + 9*x**7 + 2*x**6 + 10*x + 5
 

          13     7     6
   (2)  2x   + 9x  + 2x  + 10x + 5
                                                     Type: Polynomial Integer
--R 
--R
--R          13     7     6
--R   (2)  2x   + 9x  + 2x  + 10x + 5
--R                                                     Type: Polynomial Integer
--E 11

--S 12 of 54
gcd(p,q)
 

         7
   (3)  x  + 2x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         7
--R   (3)  x  + 2x + 1
--R                                                     Type: Polynomial Integer
--E 12

--S 13 of 54
resultant(p,q,x)
 

   (4)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Polynomial Integer
--E 13

)clear all
 
   All user variables and function definitions have been cleared.

--S 14 of 54
p := x**2 + y**2
 

         2    2
   (1)  y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2    2
--R   (1)  y  + x
--R                                                     Type: Polynomial Integer
--E 14

--S 15 of 54
eval(p,x=5)
 

         2
   (2)  y  + 25
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (2)  y  + 25
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 54
eval(p,[x = a + b,y = c + d])
 

         2           2    2           2
   (3)  d  + 2c d + c  + b  + 2a b + a
                                                     Type: Polynomial Integer
--R 
--R
--R         2           2    2           2
--R   (3)  d  + 2c d + c  + b  + 2a b + a
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 54
q := x**3 + 5*x - y**4
 

           4    3
   (4)  - y  + x  + 5x
                                                     Type: Polynomial Integer
--R 
--R
--R           4    3
--R   (4)  - y  + x  + 5x
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 54
eval(q,[x=y,y=x])
 

         3         4
   (5)  y  + 5y - x
                                                     Type: Polynomial Integer
--R 
--R
--R         3         4
--R   (5)  y  + 5y - x
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 54
px := eval(p, y = sin(2.0))
 

         2
   (6)  x  + 0.8268218104 3180595732
                                                       Type: Polynomial Float
--R 
--R
--R         2
--R   (6)  x  + 0.8268218104 3180595732
--R                                                       Type: Polynomial Float
--E 19

--S 20 of 54
eval(px, x = cos(2.0))
 

   (7)  1.0
                                                       Type: Polynomial Float
--R 
--R
--R   (7)  1.0
--R                                                       Type: Polynomial Float
--E 20

)clear all
 
   All user variables and function definitions have been cleared.

--S 21 of 54
factor(x**3 - 3*x + 2)
 

               2
   (1)  (x - 1) (x + 2)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2
--R   (1)  (x - 1) (x + 2)
--R                                            Type: Factored Polynomial Integer
--E 21

--S 22 of 54
factor(x**2/4 + x*y + y**2)
 

             1   2
   (2)  (y + - x)
             2
                                   Type: Factored Polynomial Fraction Integer
--R 
--R
--R             1   2
--R   (2)  (y + - x)
--R             2
--R                                   Type: Factored Polynomial Fraction Integer
--E 22

--S 23 of 54
p := x**3 + x*y + 2*x**2*y**2 + 2*y**3 + 3*x**2*z + 6*x*y**2*z
 

             2     2       3     2 2          3
   (3)  (6x y  + 3x )z + 2y  + 2x y  + x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R             2     2       3     2 2          3
--R   (3)  (6x y  + 3x )z + 2y  + 2x y  + x y + x
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 54
factors := factor p
 

           2                  2
   (4)  (2y  + x)(3x z + y + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R           2                  2
--R   (4)  (2y  + x)(3x z + y + x )
--R                                            Type: Factored Polynomial Integer
--E 24

--S 25 of 54
nthFactor(factors,1)
 

          2
   (5)  2y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (5)  2y  + x
--R                                                     Type: Polynomial Integer
--E 25

--S 26 of 54
nthFactor(factors,2)
 

                    2
   (6)  3x z + y + x
                                                     Type: Polynomial Integer
--R 
--R
--R                    2
--R   (6)  3x z + y + x
--R                                                     Type: Polynomial Integer
--E 26

)clear all
 
   All user variables and function definitions have been cleared.

--S 27 of 54
p := a*x**2 + b*x*y + c*y**2
 

           2              2
   (1)  c y  + b x y + a x
                                                     Type: Polynomial Integer
--R 
--R
--R           2              2
--R   (1)  c y  + b x y + a x
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 54
q := 13*x**2 + 3*z
 

                2
   (2)  3z + 13x
                                                     Type: Polynomial Integer
--R 
--R
--R                2
--R   (2)  3z + 13x
--R                                                     Type: Polynomial Integer
--E 28

--S 29 of 54
p + q
 

                2                    2
   (3)  3z + c y  + b x y + (a + 13)x
                                                     Type: Polynomial Integer
--R 
--R
--R                2                    2
--R   (3)  3z + c y  + b x y + (a + 13)x
--R                                                     Type: Polynomial Integer
--E 29

--S 30 of 54
p - 3*q
 

                  2                    2
   (4)  - 9z + c y  + b x y + (a - 39)x
                                                     Type: Polynomial Integer
--R 
--R
--R                  2                    2
--R   (4)  - 9z + c y  + b x y + (a - 39)x
--R                                                     Type: Polynomial Integer
--E 30

--S 31 of 54
p**2 + p*q
 

   (5)
          2                2      2 4           3                  2  2 2
     (3c y  + 3b x y + 3a x )z + c y  + 2b c x y  + ((2a + 13)c + b )x y
   + 
                 3      2        4
     (2a + 13)b x y + (a  + 13a)x
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)
--R          2                2      2 4           3                  2  2 2
--R     (3c y  + 3b x y + 3a x )z + c y  + 2b c x y  + ((2a + 13)c + b )x y
--R   + 
--R                 3      2        4
--R     (2a + 13)b x y + (a  + 13a)x
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 54
r := (p + q)**2
 

   (6)
       2        2                      2      2 4           3
     9z  + (6c y  + 6b x y + (6a + 78)x )z + c y  + 2b c x y
   + 
                    2  2 2               3      2              4
     ((2a + 26)c + b )x y  + (2a + 26)b x y + (a  + 26a + 169)x
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)
--R       2        2                      2      2 4           3
--R     9z  + (6c y  + 6b x y + (6a + 78)x )z + c y  + 2b c x y
--R   + 
--R                    2  2 2               3      2              4
--R     ((2a + 26)c + b )x y  + (2a + 26)b x y + (a  + 26a + 169)x
--R                                                     Type: Polynomial Integer
--E 32

--S 33 of 54
setVariableOrder [a,b,c,x,y,z]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 54
p
 

         2             2
   (8)  x a + y x b + y c
                                                     Type: Polynomial Integer
--R 
--R
--R         2             2
--R   (8)  x a + y x b + y c
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 54
q
 

           2
   (9)  13x  + 3z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (9)  13x  + 3z
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 54
r
 

   (10)
      4 2        3      2 2       4       2      2 2 2
     x a  + (2y x b + 2y x c + 26x  + 6z x )a + y x b
   + 
      3           3               4 2       2 2       2         4        2     2
   (2y x c + 26y x  + 6z y x)b + y c  + (26y x  + 6z y )c + 169x  + 78z x  + 9z
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)
--R      4 2        3      2 2       4       2      2 2 2
--R     x a  + (2y x b + 2y x c + 26x  + 6z x )a + y x b
--R   + 
--R      3           3               4 2       2 2       2         4        2     2
--R   (2y x c + 26y x  + 6z y x)b + y c  + (26y x  + 6z y )c + 169x  + 78z x  + 9z
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 54
resetVariableOrder()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 37

--S 38 of 54
p
 

            2              2
   (12)  c y  + b x y + a x
                                                     Type: Polynomial Integer
--R 
--R
--R            2              2
--R   (12)  c y  + b x y + a x
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 54
coefficient(q,x,2)
 

   (13)  13
                                                     Type: Polynomial Integer
--R 
--R
--R   (13)  13
--R                                                     Type: Polynomial Integer
--E 39

--S 40 of 54
coefficient(r,x,3)
 

   (14)  (2a + 26)b y
                                                     Type: Polynomial Integer
--R 
--R
--R   (14)  (2a + 26)b y
--R                                                     Type: Polynomial Integer
--E 40

--S 41 of 54
c := coefficient(r,z,1)
 

             2                      2
   (15)  6c y  + 6b x y + (6a + 78)x
                                                     Type: Polynomial Integer
--R 
--R
--R             2                      2
--R   (15)  6c y  + 6b x y + (6a + 78)x
--R                                                     Type: Polynomial Integer
--E 41

--S 42 of 54
coefficient(c,x,2)
 

   (16)  6a + 78
                                                     Type: Polynomial Integer
--R 
--R
--R   (16)  6a + 78
--R                                                     Type: Polynomial Integer
--E 42

--S 43 of 54
coefficient(q**2, [x,z], [2,1])
 

   (17)  78
                                                     Type: Polynomial Integer
--R 
--R
--R   (17)  78
--R                                                     Type: Polynomial Integer
--E 43

--S 44 of 54
coefficient(r, [x,y], [2,2])
 

                       2
   (18)  (2a + 26)c + b
                                                     Type: Polynomial Integer
--R 
--R
--R                       2
--R   (18)  (2a + 26)c + b
--R                                                     Type: Polynomial Integer
--E 44


)clear all
 
   All user variables and function definitions have been cleared.

--S 45 of 54
l := rootsOf(x**4+1,x)
 

   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
                                                Type: List Expression Integer
--R 
--R
--R   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
--R                                                Type: List Expression Integer
--E 45

--S 46 of 54
x0**5
 

          5
   (2)  x0
                                                     Type: Polynomial Integer
--R 
--R
--R          5
--R   (2)  x0
--R                                                     Type: Polynomial Integer
--E 46

--S 47 of 54
definingPolynomial x0
 

   (3)  - x0 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - x0 + %%var
--R                                                     Type: Expression Integer
--E 47

--S 48 of 54
definingPolynomial x1
 

   (4)  - x1 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (4)  - x1 + %%var
--R                                                     Type: Expression Integer
--E 48

--S 49 of 54
definingPolynomial x2
 

   (5)  - x2 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (5)  - x2 + %%var
--R                                                     Type: Expression Integer
--E 49

--S 50 of 54
x3 := last l
 

   (6)  - %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R   (6)  - %x0 %x1
--R                                                     Type: Expression Integer
--E 50

--S 51 of 54
x0 + x1 + x2 + x3
 

   (7)  - %x0 %x1 + x2 + x1 + x0
                                                     Type: Expression Integer
--R 
--R
--R   (7)  - %x0 %x1 + x2 + x1 + x0
--R                                                     Type: Expression Integer
--E 51

--S 52 of 54
x0 * x1 * x2 * x3
 

   (8)  - x0 x1 x2 %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R   (8)  - x0 x1 x2 %x0 %x1
--R                                                     Type: Expression Integer
--E 52

--S 53 of 54
zerosOf(y**4+1,y)
 

          +---+      +---+        +---+        +---+
         \|- 1  + 1 \|- 1  - 1 - \|- 1  - 1 - \|- 1  + 1
   (9)  [----------,----------,------------,------------]
             +-+        +-+         +-+          +-+
            \|2        \|2         \|2          \|2
                                                Type: List Expression Integer
--R 
--R
--R          +---+      +---+        +---+        +---+
--R         \|- 1  + 1 \|- 1  - 1 - \|- 1  - 1 - \|- 1  + 1
--R   (9)  [----------,----------,------------,------------]
--R             +-+        +-+         +-+          +-+
--R            \|2        \|2         \|2          \|2
--R                                                Type: List Expression Integer
--E 53

--S 54 of 54
definingPolynomial y1
 

   (10)  - y1 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (10)  - y1 + %%var
--R                                                     Type: Expression Integer
--E 54
)spool 
 
Starts dribbling to stream.output (2009/2/17, 18:0:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 12
ints := [i for i in 0..]
 

   (1)  [0,1,2,3,4,5,6,7,8,9,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (1)  [0,1,2,3,4,5,6,7,8,9,...]
--R                                              Type: Stream NonNegativeInteger
--E 1

--S 2 of 12
f : List INT -> List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 12
f x == [x.1 + x.2, x.1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 12
fibs := [i.2 for i in [generate(f,[1,1])]]
 
   Compiling function f with type List Integer -> List Integer 

   (4)  [1,1,2,3,5,8,13,21,34,55,...]
                                                         Type: Stream Integer
--R 
--R   Compiling function f with type List Integer -> List Integer 
--R
--R   (4)  [1,1,2,3,5,8,13,21,34,55,...]
--R                                                         Type: Stream Integer
--E 4

--S 5 of 12
[i for i in ints | odd? i]
 

   (5)  [1,3,5,7,9,11,13,15,17,19,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (5)  [1,3,5,7,9,11,13,15,17,19,...]
--R                                              Type: Stream NonNegativeInteger
--E 5

--S 6 of 12
odds := [2*i+1 for i in ints]
 

   (6)  [1,3,5,7,9,11,13,15,17,19,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (6)  [1,3,5,7,9,11,13,15,17,19,...]
--R                                              Type: Stream NonNegativeInteger
--E 6

--S 7 of 12
scan(0,+,odds)
 

   (7)  [1,4,9,16,25,36,49,64,81,100,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (7)  [1,4,9,16,25,36,49,64,81,100,...]
--R                                              Type: Stream NonNegativeInteger
--E 7

--S 8 of 12
[i*j for i in ints for j in odds]
 

   (8)  [0,3,10,21,36,55,78,105,136,171,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (8)  [0,3,10,21,36,55,78,105,136,171,...]
--R                                              Type: Stream NonNegativeInteger
--E 8

--S 9 of 12
map(*,ints,odds)
 

   (9)  [0,3,10,21,36,55,78,105,136,171,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (9)  [0,3,10,21,36,55,78,105,136,171,...]
--R                                              Type: Stream NonNegativeInteger
--E 9

--S 10 of 12
first ints
 

   (10)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (10)  0
--R                                                     Type: NonNegativeInteger
--E 10

--S 11 of 12
rest ints
 

   (11)  [1,2,3,4,5,6,7,8,9,10,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (11)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                              Type: Stream NonNegativeInteger
--E 11

--S 12 of 12
fibs 20
 

   (12)  6765
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  6765
--R                                                        Type: PositiveInteger
--E 12
)spool 
 
Starts dribbling to dmp.output (2009/2/17, 17:44:41).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input generated from DistributedMultivariatePolynomialXmpPage

--S 1 of 8
(d1,d2,d3) : DMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 8
d1 := -4*z + 4*y**2*x + 16*x**2 + 1
 

                 2       2
   (2)  - 4z + 4y x + 16x  + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R                 2       2
--R   (2)  - 4z + 4y x + 16x  + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 2

--S 3 of 8
d2 := 2*z*y**2 + 4*x + 1
 

            2
   (3)  2z y  + 4x + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (3)  2z y  + 4x + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 3

--S 4 of 8
d3 := 2*z*x**2 - 2*y**2 - x
 

            2     2
   (4)  2z x  - 2y  - x
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (4)  2z x  - 2y  - x
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 4

--S 5 of 8
groebner [d1,d2,d3]
 

   (5)
        1568  6   1264  5    6   4   182  3   2047  2    103      2857
   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
        2745       305      305      549       610      2745     10980
     2    112  6    84  5   1264  4    13  3    84  2   1772       2
    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
         2745      305       305      549      305      2745     2745
     7   29  6   17  4   11  3    1  2   15     1
    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
          4      16       8      32      16     4
       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (5)
--R        1568  6   1264  5    6   4   182  3   2047  2    103      2857
--R   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
--R        2745       305      305      549       610      2745     10980
--R     2    112  6    84  5   1264  4    13  3    84  2   1772       2
--R    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
--R         2745      305       305      549      305      2745     2745
--R     7   29  6   17  4   11  3    1  2   15     1
--R    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
--R          4      16       8      32      16     4
--R       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 5

--S 6 of 8
(n1,n2,n3) : HDMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 8
(n1,n2,n3) := (d1,d2,d3)
 

            2     2
   (7)  2z x  - 2y  - x
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (7)  2z x  - 2y  - x
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 7

--S 8 of 8
groebner [n1,n2,n3]
 

   (8)
     4     3   3  2   1     1   4   29  3   1  2   7        9     1
   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
               2      2     8        4      8      4       16     4
       2        1   2      2       1     2    2   1
    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
                2                  4              2
     2     2     2   1     3
    z  - 4y  + 2x  - - z - - x]
                     4     2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (8)
--R     4     3   3  2   1     1   4   29  3   1  2   7        9     1
--R   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
--R               2      2     8        4      8      4       16     4
--R       2        1   2      2       1     2    2   1
--R    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
--R                2                  4              2
--R     2     2     2   1     3
--R    z  - 4y  + 2x  - - z - - x]
--R                     4     2
--RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 8
)spool
 
Starts dribbling to r21bugs.output (2009/2/17, 17:56:26).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 95
)set expose add constructor PolynomialNumberTheoryFunctions
 
   PolynomialNumberTheoryFunctions is now explicitly exposed in frame 
      initial 
--R 
--R   PolynomialNumberTheoryFunctions is now explicitly exposed in frame 
--R      initial 
--E 1

--S 2 of 95
X : UP('x, Integer) := x
 

   (1)  x
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (1)  x
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 2

--S 3 of 95
[chebyshevU(n) - X*chebyshevU(n-1) - chebyshevT(n) for n in 1 .. ]
 

   (2)  [0,0,0,0,0,0,0,0,0,0,...]
                              Type: Stream SparseUnivariatePolynomial Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0,0,0,0,0,...]
--R                              Type: Stream SparseUnivariatePolynomial Integer
--E 3

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 4 of 95
Fp:=PF 2
 

   (1)  PrimeField 2
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 2
--R                                                                 Type: Domain
--E 4

--S 5 of 95
poly:=createIrreduciblePoly(4)$FFPOLY(Fp)
 

         4
   (2)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         4
--R   (2)  ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 5

--S 6 of 95
Fq:=FFP(Fp, poly)    -- Field with 16 elements
 

   (3)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
                                                                 Type: Domain
--R 
--R
--R   (3)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--R                                                                 Type: Domain
--E 6

--S 7 of 95
R:=DMP([X,Y,Z],Fq)
 

   (4)
  DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(Pr
  imeField 2,?**4+?+1))
                                                                 Type: Domain
--R 
--R
--R   (4)
--R  DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(Pr
--R  imeField 2,?**4+?+1))
--R                                                                 Type: Domain
--E 7

--S 8 of 95
Q:=FRAC R
 

   (5)
  Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPoly
  nomial(PrimeField 2,?**4+?+1))
                                                                 Type: Domain
--R 
--R
--R   (5)
--R  Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPoly
--R  nomial(PrimeField 2,?**4+?+1))
--R                                                                 Type: Domain
--E 8

--S 9 of 95
F:=X**4+X*Z**3
 

           3    4
   (6)  X Z  + X
                                                     Type: Polynomial Integer
--R 
--R
--R           3    4
--R   (6)  X Z  + X
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 95
G:=X**4+X**2*Y**2+Z**4
 

         4    2 2    4
   (7)  Z  + X Y  + X
                                                     Type: Polynomial Integer
--R 
--R
--R         4    2 2    4
--R   (7)  Z  + X Y  + X
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 95
h:Q:=F/G
 

            4      3
           X  + X Z
   (8)  --------------
         4    2 2    4
        X  + X Y  + Z
Type: Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R 
--R
--R            4      3
--R           X  + X Z
--R   (8)  --------------
--R         4    2 2    4
--R        X  + X Y  + Z
--RType: Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--E 11

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 12 of 95
squareFree ((c^15*e^8+c^23*d^4)::POLY PF 2) 
 

         15  2    2  4
   (1)  c  (e  + c d)
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R         15  2    2  4
--R   (1)  c  (e  + c d)
--R                                       Type: Factored Polynomial PrimeField 2
--E 12

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 13 of 95
FiniteFieldExtensionByPolynomial(FF(3,3),1+2*x**2+x**3)
 

   (1)  FiniteFieldExtensionByPolynomial(FiniteField(3,3),?**3+2*?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (1)  FiniteFieldExtensionByPolynomial(FiniteField(3,3),?**3+2*?*?+1)
--R                                                                 Type: Domain
--E 13

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 14 of 95
Field has Ring
 

   (1)  true
                                                                Type: Boolean
--R 
--R
--R   (1)  true
--R                                                                Type: Boolean
--E 14

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

-- from bmt
--S 15 of 95
y:=operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 15

--S 16 of 95
u:=operator u
 

   (2)  u
                                                          Type: BasicOperator
--R 
--R
--R   (2)  u
--R                                                          Type: BasicOperator
--E 16

--S 17 of 95
eval(y x, y, c[1]*x,x)
 
   Compiling function %B with type Expression Integer -> Expression 
      Integer 

   (3)  c x
         1
                                                     Type: Expression Integer
--R 
--R   Compiling function %B with type Expression Integer -> Expression 
--R      Integer 
--R
--R   (3)  c x
--R         1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 95
eval(y x, y, D(u t,t),t)
 
   Compiling function %C with type Expression Integer -> Expression 
      Integer 

         ,
   (4)  u (x)

                                                     Type: Expression Integer
--R 
--R   Compiling function %C with type Expression Integer -> Expression 
--R      Integer 
--R
--R         ,
--R   (4)  u (x)
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 95
eval(y x ,y, integral(u t,t),t)
 
   Compiling function %E with type Expression Integer -> Expression 
      Integer 

           x
         ++
   (5)   |   u(%D)d%D
        ++
                                                     Type: Expression Integer
--R 
--R   Compiling function %E with type Expression Integer -> Expression 
--R      Integer 
--R
--R           x
--R         ++
--R   (5)   |   u(%D)d%D
--R        ++
--R                                                     Type: Expression Integer
--E 19

--S 20 of 95
eval(y x ,y, integral(u z,z=z0..t),t)
 
   Compiling function %F with type Expression Integer -> Expression 
      Integer 

           x
         ++
   (6)   |   u(z)dz
        ++
        z0
                                                     Type: Expression Integer
--R 
--R   Compiling function %F with type Expression Integer -> Expression 
--R      Integer 
--R
--R           x
--R         ++
--R   (6)   |   u(z)dz
--R        ++
--R        z0
--R                                                     Type: Expression Integer
--E 20

--S 21 of 95
eval(y x+D(y x,x), y, u t+ D(u t,t),t)
 
   Compiling function %G with type Expression Integer -> Expression 
      Integer 

         ,,        ,
   (7)  u  (x) + 2u (x) + u(x)

                                                     Type: Expression Integer
--R 
--R   Compiling function %G with type Expression Integer -> Expression 
--R      Integer 
--R
--R         ,,        ,
--R   (7)  u  (x) + 2u (x) + u(x)
--R
--R                                                     Type: Expression Integer
--E 21

--S 22 of 95
eval(D(y x,x)+y(x),y,D(u x,x)+u(x),x)
 
   Compiling function %H with type Expression Integer -> Expression 
      Integer 

         ,,        ,
   (8)  u  (x) + 2u (x) + u(x)

                                                     Type: Expression Integer
--R 
--R   Compiling function %H with type Expression Integer -> Expression 
--R      Integer 
--R
--R         ,,        ,
--R   (8)  u  (x) + 2u (x) + u(x)
--R
--R                                                     Type: Expression Integer
--E 22

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 23 of 95
ps:=x::TS FRAC INT
 

   (1)  x
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (1)  x
--R                                          Type: TaylorSeries Fraction Integer
--E 23

--S 24 of 95
D(ps,x) -- fails to find function
 

   (2)  1
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (2)  1
--R                                          Type: TaylorSeries Fraction Integer
--E 24

--S 25 of 95
D(ps,[x]) -- works
 

   (3)  1
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (3)  1
--R                                          Type: TaylorSeries Fraction Integer
--E 25

--S 26 of 95
D(ps,[y]) -- causes ccl to disappear (at least under windows)
 

   (4)  0
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (4)  0
--R                                          Type: TaylorSeries Fraction Integer
--E 26

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 27 of 95
T1:=3
 

   (1)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  3
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 95
a | a^2+1
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
   a : SAEa := a

   (2)  a
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R   a : SAEa := a
--R
--R   (2)  a
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--E 28


)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 29 of 95
u1 := operator 'u1
 

   (1)  u1
                                                          Type: BasicOperator
--R 
--R
--R   (1)  u1
--R                                                          Type: BasicOperator
--E 29

--S 30 of 95
u2 := operator 'u2
 

   (2)  u2
                                                          Type: BasicOperator
--R 
--R
--R   (2)  u2
--R                                                          Type: BasicOperator
--E 30

--S 31 of 95
eq1 := D(u1(t),t,2) + 5*u1(t) = 2*u2(t)
 

          ,,
   (3)  u1  (t) + 5u1(t)= 2u2(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (3)  u1  (t) + 5u1(t)= 2u2(t)
--R
--R                                            Type: Equation Expression Integer
--E 31

--S 32 of 95
eq2 := D(u2(t),t,2) + 2*u2(t) = 2*u1(t)
 

          ,,
   (4)  u2  (t) + 2u2(t)= 2u1(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (4)  u2  (t) + 2u2(t)= 2u1(t)
--R
--R                                            Type: Equation Expression Integer
--E 32

--S 33 of 95
eq1/2
 

          ,,
        u1  (t) + 5u1(t)

   (5)  ----------------= u2(t)
                2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R        u1  (t) + 5u1(t)
--R
--R   (5)  ----------------= u2(t)
--R                2
--R                                            Type: Equation Expression Integer
--E 33

--S 34 of 95
_rule(rhs %, lhs %)
 

                   ,,
                 u1  (t) + 5u1(t)

   (6)  u2(t) == ----------------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                   ,,
--R                 u1  (t) + 5u1(t)
--R
--R   (6)  u2(t) == ----------------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 34

--S 35 of 95
%(lhs eq2)
 

          (iv)         ,,
        u1    (t) + 7u1  (t) + 10u1(t)

   (7)  ------------------------------
                       2
                                                     Type: Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (t) + 7u1  (t) + 10u1(t)
--R
--R   (7)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E 35

--S 36 of 95
eval(%,t=0)
 

          (iv)         ,,
        u1    (0) + 7u1  (0) + 10u1(0)

   (8)  ------------------------------
                       2
                                                     Type: Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (0) + 7u1  (0) + 10u1(0)
--R
--R   (8)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E 36

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 37 of 95
bug := [exp(sqrt(-5))]
 

            +---+
           \|- 5
   (1)  [%e      ]
                                                Type: List Expression Integer
--R 
--R
--R            +---+
--R           \|- 5
--R   (1)  [%e      ]
--R                                                Type: List Expression Integer
--E 37

--S 38 of 95
complexForm(bug.1) -- works
 

             +-+         +-+
   (2)  cos(\|5 ) + sin(\|5 )%i
                                             Type: Complex Expression Integer
--R 
--R
--R             +-+         +-+
--R   (2)  cos(\|5 ) + sin(\|5 )%i
--R                                             Type: Complex Expression Integer
--E 38

--S 39 of 95
map(complexForm,bug::List EXPR COMPLEX INT) -- works
 

              +-+         +-+
   (3)  [cos(\|5 ) + sin(\|5 )%i]
                                        Type: List Complex Expression Integer
--R 
--R
--R              +-+         +-+
--R   (3)  [cos(\|5 ) + sin(\|5 )%i]
--R                                        Type: List Complex Expression Integer
--E 39

--S 40 of 95
map(complexForm,bug) -- fails
 

              +-+         +-+
   (4)  [cos(\|5 ) + sin(\|5 )%i]
                                        Type: List Complex Expression Integer
--R 
--R
--R              +-+         +-+
--R   (4)  [cos(\|5 ) + sin(\|5 )%i]
--R                                        Type: List Complex Expression Integer
--E 40

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.


-- from bmt
--S 41 of 95
f x == c[1]*exp(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 41

--S 42 of 95
f x -- works
 
   Compiling function f with type Variable x -> Expression Integer 

            x
   (2)  c %e
         1
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type Variable x -> Expression Integer 
--R
--R            x
--R   (2)  c %e
--R         1
--R                                                     Type: Expression Integer
--E 42

--S 43 of 95
g(x:EXPR(INT)):EXPR(INT) == c[1]*exp(x) 
 
   Function declaration g : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration g : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 43

--S 44 of 95
g x -- fails
 
   There are no library operations named c 
      Use HyperDoc Browse or issue
                                 )what op c
      to learn if there is any operation containing " c " in its name.
   Cannot find a definition or applicable library operation named c 
      with argument type(s) 
                            List PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function g with type Expression Integer -> Expression 
      Integer 
   There are no library operations named c 
      Use HyperDoc Browse or issue
                                 )what op c
      to learn if there is any operation containing " c " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named c 
      with argument type(s) 
                            List PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named c 
--R      Use HyperDoc Browse or issue
--R                                 )what op c
--R      to learn if there is any operation containing " c " in its name.
--R   Cannot find a definition or applicable library operation named c 
--R      with argument type(s) 
--R                            List PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function g with type Expression Integer -> Expression 
--R      Integer 
--R   There are no library operations named c 
--R      Use HyperDoc Browse or issue
--R                                 )what op c
--R      to learn if there is any operation containing " c " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named c 
--R      with argument type(s) 
--R                            List PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 44

--S 45 of 95
g(x:EXPR(INT)):EXPR(INT) == (c[1]::EXPR INT)*exp(x) 
 
   Function declaration g : Expression Integer -> Expression Integer 
      has been added to workspace.
   Compiled code for g has been cleared.
   1 old definition(s) deleted for function or rule g 
                                                                   Type: Void
--R 
--R   Function declaration g : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R   Compiled code for g has been cleared.
--R   1 old definition(s) deleted for function or rule g 
--R                                                                   Type: Void
--E 45

--S 46 of 95
g x -- fails
 
   Compiling function g with type Expression Integer -> Expression 
      Integer 

            x
   (5)  c %e
         1
                                                     Type: Expression Integer
--R 
--R   Compiling function g with type Expression Integer -> Expression 
--R      Integer 
--R
--R            x
--R   (5)  c %e
--R         1
--R                                                     Type: Expression Integer
--E 46

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 47 of 95
a | a**8+a**4+a**3+a**2+(1::PF 2)
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEa := SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
   a : SAEa := a

   (1)  a
Type: SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEa := SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R   a : SAEa := a
--R
--R   (1)  a
--RType: SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 47

--S 48 of 95
tt:Matrix SAEa:=[_
[0,0,0,1,1,1,0,1],_
[1,0,0,0,0,0,0,0],_
[0,1,0,0,0,0,0,0],_
[0,0,1,0,0,0,0,0],_
[0,0,0,1,0,0,0,0],_
[0,0,0,0,1,0,0,0],_
[0,0,0,0,0,1,0,0],_
[0,0,0,0,0,0,1,0]];
 

Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 48

--S 49 of 95
T:=transpose tt
 

        +0  1  0  0  0  0  0  0+
        |                      |
        |0  0  1  0  0  0  0  0|
        |                      |
        |0  0  0  1  0  0  0  0|
        |                      |
        |1  0  0  0  1  0  0  0|
   (3)  |                      |
        |1  0  0  0  0  1  0  0|
        |                      |
        |1  0  0  0  0  0  1  0|
        |                      |
        |0  0  0  0  0  0  0  1|
        |                      |
        +1  0  0  0  0  0  0  0+
Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--R        +0  1  0  0  0  0  0  0+
--R        |                      |
--R        |0  0  1  0  0  0  0  0|
--R        |                      |
--R        |0  0  0  1  0  0  0  0|
--R        |                      |
--R        |1  0  0  0  1  0  0  0|
--R   (3)  |                      |
--R        |1  0  0  0  0  1  0  0|
--R        |                      |
--R        |1  0  0  0  0  0  1  0|
--R        |                      |
--R        |0  0  0  0  0  0  0  1|
--R        |                      |
--R        +1  0  0  0  0  0  0  0+
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 49

--S 50 of 95
T0:=T**91
 

        +0  1  1  1  0  1  0  1+
        |                      |
        |1  0  1  1  1  0  1  0|
        |                      |
        |0  1  0  1  1  1  0  1|
        |                      |
        |0  0  1  0  1  1  1  0|
   (4)  |                      |
        |0  1  1  0  0  0  1  0|
        |                      |
        |0  1  0  0  0  1  0  0|
        |                      |
        |1  1  0  1  0  1  1  1|
        |                      |
        +1  1  1  0  1  0  1  1+
Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--R        +0  1  1  1  0  1  0  1+
--R        |                      |
--R        |1  0  1  1  1  0  1  0|
--R        |                      |
--R        |0  1  0  1  1  1  0  1|
--R        |                      |
--R        |0  0  1  0  1  1  1  0|
--R   (4)  |                      |
--R        |0  1  1  0  0  0  1  0|
--R        |                      |
--R        |0  1  0  0  0  1  0  0|
--R        |                      |
--R        |1  1  0  1  0  1  1  1|
--R        |                      |
--R        +1  1  1  0  1  0  1  1+
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 50

--S 51 of 95
T1:=T**95
 

        +0  0  0  1  0  1  1  1+
        |                      |
        |1  0  0  0  1  0  1  1|
        |                      |
        |0  1  0  0  0  1  0  1|
        |                      |
        |0  0  1  0  0  0  1  0|
   (5)  |                      |
        |0  0  0  0  0  1  1  0|
        |                      |
        |1  0  0  1  0  1  0  0|
        |                      |
        |0  1  0  1  1  1  0  1|
        |                      |
        +0  0  1  0  1  1  1  0+
Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--R        +0  0  0  1  0  1  1  1+
--R        |                      |
--R        |1  0  0  0  1  0  1  1|
--R        |                      |
--R        |0  1  0  0  0  1  0  1|
--R        |                      |
--R        |0  0  1  0  0  0  1  0|
--R   (5)  |                      |
--R        |0  0  0  0  0  1  1  0|
--R        |                      |
--R        |1  0  0  1  0  1  0  0|
--R        |                      |
--R        |0  1  0  1  1  1  0  1|
--R        |                      |
--R        +0  0  1  0  1  1  1  0+
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 51

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 52 of 95
u1:=operator 'u1
 

   (1)  u1
                                                          Type: BasicOperator
--R 
--R
--R   (1)  u1
--R                                                          Type: BasicOperator
--E 52

--S 53 of 95
u2:=operator 'u2
 

   (2)  u2
                                                          Type: BasicOperator
--R 
--R
--R   (2)  u2
--R                                                          Type: BasicOperator
--E 53

--S 54 of 95
eq1 := D(u1(t),t,2) + 5*u1(t) = 2*u2(t)
 

          ,,
   (3)  u1  (t) + 5u1(t)= 2u2(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (3)  u1  (t) + 5u1(t)= 2u2(t)
--R
--R                                            Type: Equation Expression Integer
--E 54

--S 55 of 95
eq2 := D(u2(t),t,2) + 2*u2(t) = 2*u1(t)
 

          ,,
   (4)  u2  (t) + 2u2(t)= 2u1(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (4)  u2  (t) + 2u2(t)= 2u1(t)
--R
--R                                            Type: Equation Expression Integer
--E 55

--S 56 of 95
eq1/2
 

          ,,
        u1  (t) + 5u1(t)

   (5)  ----------------= u2(t)
                2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R        u1  (t) + 5u1(t)
--R
--R   (5)  ----------------= u2(t)
--R                2
--R                                            Type: Equation Expression Integer
--E 56

--S 57 of 95
_rule(rhs %, lhs %)
 

                   ,,
                 u1  (t) + 5u1(t)

   (6)  u2(t) == ----------------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                   ,,
--R                 u1  (t) + 5u1(t)
--R
--R   (6)  u2(t) == ----------------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 57

--S 58 of 95
%(lhs eq2)=%(rhs eq2)
 

          (iv)         ,,
        u1    (t) + 7u1  (t) + 10u1(t)

   (7)  ------------------------------= 2u1(t)
                       2
                                            Type: Equation Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (t) + 7u1  (t) + 10u1(t)
--R
--R   (7)  ------------------------------= 2u1(t)
--R                       2
--R                                            Type: Equation Expression Integer
--E 58

--S 59 of 95
rightZero %
 

          (iv)         ,,
        u1    (t) + 7u1  (t) + 6u1(t)

   (8)  -----------------------------= 0
                      2
                                            Type: Equation Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (t) + 7u1  (t) + 6u1(t)
--R
--R   (8)  -----------------------------= 0
--R                      2
--R                                            Type: Equation Expression Integer
--E 59

--S 60 of 95
-2*%
 

            (iv)         ,,
   (9)  - u1    (t) - 7u1  (t) - 6u1(t)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            (iv)         ,,
--R   (9)  - u1    (t) - 7u1  (t) - 6u1(t)= 0
--R
--R                                            Type: Equation Expression Integer
--E 60

--S 61 of 95
eval(lhs %,u1,exp(r*t),t)
 
   Compiling function %B with type Expression Integer -> Expression 
      Integer 

             4     2       r t
   (10)  (- r  - 7r  - 6)%e
                                                     Type: Expression Integer
--R 
--R   Compiling function %B with type Expression Integer -> Expression 
--R      Integer 
--R
--R             4     2       r t
--R   (10)  (- r  - 7r  - 6)%e
--R                                                     Type: Expression Integer
--E 61

--S 62 of 95
%/exp(r*t)
 

            4     2
   (11)  - r  - 7r  - 6
                                                     Type: Expression Integer
--R 
--R
--R            4     2
--R   (11)  - r  - 7r  - 6
--R                                                     Type: Expression Integer
--E 62

--S 63 of 95
solve(%,r)
 

              +---+       +---+     +---+       +---+
   (12)  [r= \|- 1 ,r= - \|- 1 ,r= \|- 6 ,r= - \|- 6 ]
                                       Type: List Equation Expression Integer
--R 
--R
--R              +---+       +---+     +---+       +---+
--R   (12)  [r= \|- 1 ,r= - \|- 1 ,r= \|- 6 ,r= - \|- 6 ]
--R                                       Type: List Equation Expression Integer
--E 63

--S 64 of 95
[eval(exp(r*t),eq) for eq in %]
 

              +---+       +---+     +---+       +---+
            t\|- 1    - t\|- 1    t\|- 6    - t\|- 6
   (13)  [%e       ,%e         ,%e       ,%e         ]
                                                Type: List Expression Integer
--R 
--R
--R              +---+       +---+     +---+       +---+
--R            t\|- 1    - t\|- 1    t\|- 6    - t\|- 6
--R   (13)  [%e       ,%e         ,%e       ,%e         ]
--R                                                Type: List Expression Integer
--E 64

--S 65 of 95
map(complexForm, %::List EXPR COMPLEX INT)
 

   (14)
                                                +-+          +-+
   [cos(t) + sin(t)%i, cos(t) - sin(t)%i, cos(t\|6 ) + sin(t\|6 )%i,
          +-+          +-+
    cos(t\|6 ) - sin(t\|6 )%i]
                                        Type: List Complex Expression Integer
--R 
--R
--R   (14)
--R                                                +-+          +-+
--R   [cos(t) + sin(t)%i, cos(t) - sin(t)%i, cos(t\|6 ) + sin(t\|6 )%i,
--R          +-+          +-+
--R    cos(t\|6 ) - sin(t\|6 )%i]
--R                                        Type: List Complex Expression Integer
--E 65

--S 66 of 95
[real %(1), imag %(1), real %(3), imag %(3)]
 

                              +-+        +-+
   (15)  [cos(t),sin(t),cos(t\|6 ),sin(t\|6 )]
                                                Type: List Expression Integer
--R 
--R
--R                              +-+        +-+
--R   (15)  [cos(t),sin(t),cos(t\|6 ),sin(t\|6 )]
--R                                                Type: List Expression Integer
--E 66

--S 67 of 95
gform:= u1(t)=reduce(+, [c[i]*%.i for i in 1..#%])
 

                        +-+                       +-+
   (16)  u1(t)= c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
                 4              2          3              1
                                            Type: Equation Expression Integer
--R 
--R
--R                        +-+                       +-+
--R   (16)  u1(t)= c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
--R                 4              2          3              1
--R                                            Type: Equation Expression Integer
--E 67

--S 68 of 95
_rule(lhs %, rhs %)
 

                          +-+                       +-+
   (17)  u1(t) == c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
                   4              2          3              1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                          +-+                       +-+
--R   (17)  u1(t) == c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
--R                   4              2          3              1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 68

--S 69 of 95
%(lhs eq1)=rhs eq1
 

                   +-+                        +-+
   (18)  - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)= 2u2(t)
            4               2          3               1
                                            Type: Equation Expression Integer
--R 
--R
--R                   +-+                        +-+
--R   (18)  - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)= 2u2(t)
--R            4               2          3               1
--R                                            Type: Equation Expression Integer
--E 69

--S 70 of 95
%/2
 

                   +-+                        +-+
         - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)
            4               2          3               1
   (19)  -----------------------------------------------------= u2(t)
                                   2
                                            Type: Equation Expression Integer
--R 
--R
--R                   +-+                        +-+
--R         - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)
--R            4               2          3               1
--R   (19)  -----------------------------------------------------= u2(t)
--R                                   2
--R                                            Type: Equation Expression Integer
--E 70

--part c
--S 71 of 95
inits := [u1(0)=1, eval(D(u1 t,t),t=0)=0, u2(0)=2, eval(D(u2 t,t),t=0)=0]
 

                     ,                  ,
   (20)  [u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]

                                       Type: List Equation Expression Integer
--R 
--R
--R                     ,                  ,
--R   (20)  [u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]
--R
--R                                       Type: List Equation Expression Integer
--E 71

--S 72 of 95
eqq := eq1-5*u1(t)
 

           ,,
   (21)  u1  (t)= 2u2(t) - 5u1(t)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (21)  u1  (t)= 2u2(t) - 5u1(t)
--R
--R                                            Type: Equation Expression Integer
--E 72

--S 73 of 95
eval(eqq,t=0)
 

           ,,
   (22)  u1  (0)= 2u2(0) - 5u1(0)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (22)  u1  (0)= 2u2(0) - 5u1(0)
--R
--R                                            Type: Equation Expression Integer
--E 73

--S 74 of 95
eval(%,inits)
 

           ,,
   (23)  u1  (0)= - 1

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (23)  u1  (0)= - 1
--R
--R                                            Type: Equation Expression Integer
--E 74

--S 75 of 95
inits:=cons(%,inits)
 

            ,,                    ,                  ,
   (24)  [u1  (0)= - 1,u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]

                                       Type: List Equation Expression Integer
--R 
--R
--R            ,,                    ,                  ,
--R   (24)  [u1  (0)= - 1,u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]
--R
--R                                       Type: List Equation Expression Integer
--E 75

--S 76 of 95
D(eqq,t)
 

           ,,,        ,         ,
   (25)  u1   (t)= 2u2 (t) - 5u1 (t)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,,        ,         ,
--R   (25)  u1   (t)= 2u2 (t) - 5u1 (t)
--R
--R                                            Type: Equation Expression Integer
--E 76

--S 77 of 95
eval(%,t=0)
 

           ,,,        ,         ,
   (26)  u1   (0)= 2u2 (0) - 5u1 (0)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,,        ,         ,
--R   (26)  u1   (0)= 2u2 (0) - 5u1 (0)
--R
--R                                            Type: Equation Expression Integer
--E 77

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 78 of 95
u:=operator 'u
 

   (1)  u
                                                          Type: BasicOperator
--R 
--R
--R   (1)  u
--R                                                          Type: BasicOperator
--E 78

--S 79 of 95
exp:=D(u t,t)
 

         ,
   (2)  u (t)

                                                     Type: Expression Integer
--R 
--R
--R         ,
--R   (2)  u (t)
--R
--R                                                     Type: Expression Integer
--E 79

--S 80 of 95
k:=kernels(exp).1
 

         ,
   (3)  u (t)

                                              Type: Kernel Expression Integer
--R 
--R
--R         ,
--R   (3)  u (t)
--R
--R                                              Type: Kernel Expression Integer
--E 80

--S 81 of 95
l:=argument %
 

   (4)  [u(%%01),%%01,t]
                                                Type: List Expression Integer
--R 
--R
--R   (4)  [u(%%01),%%01,t]
--R                                                Type: List Expression Integer
--E 81

--S 82 of 95
difop:=operator k
 

   (5)  %diff
                                                          Type: BasicOperator
--R 
--R
--R   (5)  %diff
--R                                                          Type: BasicOperator
--E 82

--S 83 of 95
l2:=[l.1+l.2,l.2,l.3]
 

   (6)  [u(%%01) + %%01,%%01,t]
                                                Type: List Expression Integer
--R 
--R
--R   (6)  [u(%%01) + %%01,%%01,t]
--R                                                Type: List Expression Integer
--E 83

--S 84 of 95
bug:=evaluate(difop,l2)
 

         ,
   (7)  u (t) + 1

                                          Type: Union(Expression Integer,...)
--R 
--R
--R         ,
--R   (7)  u (t) + 1
--R
--R                                          Type: Union(Expression Integer,...)
--E 84

--S 85 of 95
kernels(bug).1
 

         ,
   (8)  u (t)

                                              Type: Kernel Expression Integer
--R 
--R
--R         ,
--R   (8)  u (t)
--R
--R                                              Type: Kernel Expression Integer
--E 85

--S 86 of 95
argument %
 

   (9)  [u(%%01),%%01,t]
                                                Type: List Expression Integer
--R 
--R
--R   (9)  [u(%%01),%%01,t]
--R                                                Type: List Expression Integer
--E 86

--S 87 of 95
eval(bug,t=0)
 

          ,
   (10)  u (0) + 1

                                                     Type: Expression Integer
--R 
--R
--R          ,
--R   (10)  u (0) + 1
--R
--R                                                     Type: Expression Integer
--E 87

)clear completely
 
   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 88 of 95
R := Polynomial(PrimeField(3)) ; 
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 88

--S 89 of 95
A := UP('X, R) 
 

   (2)  UnivariatePolynomial(X,Polynomial PrimeField 3)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(X,Polynomial PrimeField 3)
--R                                                                 Type: Domain
--E 89

--S 90 of 95
X : A := monomial(1, 1) ;
 

                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--R 
--R
--R                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--E 90

--S 91 of 95
f : A := a*X^3 + b*X^2 + c*X + d
 

           3      2
   (4)  a X  + b X  + c X + d
                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--R 
--R
--R           3      2
--R   (4)  a X  + b X  + c X + d
--R                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--E 91

--S 92 of 95
discriminant(f)
 

          3        3    2 2
   (5)  2b d + 2a c  + b c
                                                Type: Polynomial PrimeField 3
--R 
--R
--R          3        3    2 2
--R   (5)  2b d + 2a c  + b c
--R                                                Type: Polynomial PrimeField 3
--E 92

--S 93 of 95
s := differentiate f
 

   (6)  2b X + c
                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--R 
--R
--R   (6)  2b X + c
--R                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--E 93

--S 94 of 95
resultant(f,s)
 

         3       3     2 2
   (7)  b d + a c  + 2b c
                                                Type: Polynomial PrimeField 3
--R 
--R
--R         3       3     2 2
--R   (7)  b d + a c  + 2b c
--R                                                Type: Polynomial PrimeField 3
--E 94

--S 95 of 95
exquo(%,leadingCoefficient(f))
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 95
)spool 
 
Starts dribbling to kovacic.output (2009/2/17, 17:48:12).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 3
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 3
eq := 2*x**3 * differentiate(y x,x,2) + 3*x**2 * differentiate(y x,x) - 2 * y x
 

          3 ,,        2 ,
   (2)  2x y  (x) + 3x y (x) - 2y(x)

                                                     Type: Expression Integer
--R 
--R
--R          3 ,,        2 ,
--R   (2)  2x y  (x) + 3x y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 3
solve(eq,y,x).basis
 

               2      2
           - ----   ----
              +-+    +-+
             \|x    \|x
   (3)  [%e      ,%e    ]
                                                Type: List Expression Integer
--R 
--R
--R               2      2
--R           - ----   ----
--R              +-+    +-+
--R             \|x    \|x
--R   (3)  [%e      ,%e    ]
--R                                                Type: List Expression Integer
--E 3
)spool 
 
Starts dribbling to function.output (2009/2/17, 17:46:11).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 33
f := (x - y) / (x + y)
 

        - y + x
   (1)  -------
         y + x
                                            Type: Fraction Polynomial Integer
--R
--R        - y + x
--R   (1)  -------
--R         y + x
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 33
numer f
 

   (2)  - y + x
                                                     Type: Polynomial Integer
--R
--R   (2)  - y + x
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 33
denom f
 

   (3)  y + x
                                                     Type: Polynomial Integer
--R
--R   (3)  y + x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 33
eval(f, x = 1/x)
 

        - x y + 1
   (4)  ---------
         x y + 1
                                            Type: Fraction Polynomial Integer
--R
--R        - x y + 1
--R   (4)  ---------
--R         x y + 1
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 33
eval(f, [x = y, y = x])
 

        y - x
   (5)  -----
        y + x
                                            Type: Fraction Polynomial Integer
--R
--R        y - x
--R   (5)  -----
--R        y + x
--R                                            Type: Fraction Polynomial Integer
--E 5

)clear all
 
   All user variables and function definitions have been cleared.

--S 6 of 33
f := sqrt(1 + x ** (1/3))
 

         +--------+
         |3+-+
   (1)  \|\|x  + 1
                                                     Type: Expression Integer
--R
--R         +--------+
--R         |3+-+
--R   (1)  \|\|x  + 1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 33
y := rootOf(y**3 + y**2 - x*y + x**3 - 1, y)
 

   (2)  y
                                                     Type: Expression Integer
--R
--R   (2)  y
--R                                                     Type: Expression Integer
--E 7

--S 8 of 33
differentiate(y, x)
 

                 2
           y - 3x
   (3)  ------------
          2
        3y  + 2y - x
                                                     Type: Expression Integer
--R
--R                 2
--R           y - 3x
--R   (3)  ------------
--R          2
--R        3y  + 2y - x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 33
(y + 1) ** 3
 

          2               3
   (4)  2y  + (x + 3)y - x  + 2
                                                     Type: Expression Integer
--R
--R          2               3
--R   (4)  2y  + (x + 3)y - x  + 2
--R                                                     Type: Expression Integer
--E 9

--S 10 of 33
g := inv f
 

             1
   (5)  -----------
         +--------+
         |3+-+
        \|\|x  + 1
                                                     Type: Expression Integer
--R
--R             1
--R   (5)  -----------
--R         +--------+
--R         |3+-+
--R        \|\|x  + 1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 33
ratPoly g
 

                6     4     2
   (6)  (x + 1)?  - 3?  + 3?  - 1
                          Type: SparseUnivariatePolynomial Expression Integer
--R
--R                6     4     2
--R   (6)  (x + 1)?  - 3?  + 3?  - 1
--R                          Type: SparseUnivariatePolynomial Expression Integer
--E 11

)clear all
 
   All user variables and function definitions have been cleared.

--S 12 of 33
f := x * log y * sin(1/(x+y))
 

                      1
   (1)  x log(y)sin(-----)
                    y + x
                                                     Type: Expression Integer
--R
--R                      1
--R   (1)  x log(y)sin(-----)
--R                    y + x
--R                                                     Type: Expression Integer
--E 12

--S 13 of 33
eval(f, [x = y, y = x])
 

                      1
   (2)  y log(x)sin(-----)
                    y + x
                                                     Type: Expression Integer
--R
--R                      1
--R   (2)  y log(x)sin(-----)
--R                    y + x
--R                                                     Type: Expression Integer
--E 13

--S 14 of 33
eval(f, log y = acosh(x + sqrt y))
 

                1          +-+
   (3)  x sin(-----)acosh(\|y  + x)
              y + x
                                                     Type: Expression Integer
--R
--R                1          +-+
--R   (3)  x sin(-----)acosh(\|y  + x)
--R              y + x
--R                                                     Type: Expression Integer
--E 14

)clear all
 
   All user variables and function definitions have been cleared.

--S 15 of 33
f := cos(x)/sec(x) * log(sin(x)**2/(cos(x)**2+sin(x)**2))
 

                             2
                       sin(x)
        cos(x)log(-----------------)
                        2         2
                  sin(x)  + cos(x)
   (1)  ----------------------------
                   sec(x)
                                                     Type: Expression Integer
--R
--R                             2
--R                       sin(x)
--R        cos(x)log(-----------------)
--R                        2         2
--R                  sin(x)  + cos(x)
--R   (1)  ----------------------------
--R                   sec(x)
--R                                                     Type: Expression Integer
--E 15

--S 16 of 33
g := simplify f
 

              2            2
   (2)  cos(x) log(- cos(x)  + 1)
                                                     Type: Expression Integer
--R
--R              2            2
--R   (2)  cos(x) log(- cos(x)  + 1)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 33
h := sin2csc cos2sec g
 

                  2
            sec(x)  - 1
        log(-----------)
                    2
              sec(x)
   (3)  ----------------
                   2
             sec(x)
                                                     Type: Expression Integer
--R
--R                  2
--R            sec(x)  - 1
--R        log(-----------)
--R                    2
--R              sec(x)
--R   (3)  ----------------
--R                   2
--R             sec(x)
--R                                                     Type: Expression Integer
--E 17

--S 18 of 33
expandLog h
 

                  2
        log(sec(x)  - 1) - 2log(sec(x))
   (4)  -------------------------------
                          2
                    sec(x)
                                                     Type: Expression Integer
--R
--R                  2
--R        log(sec(x)  - 1) - 2log(sec(x))
--R   (4)  -------------------------------
--R                          2
--R                    sec(x)
--R                                                     Type: Expression Integer
--E 18

--S 19 of 33
f1 := sqrt((x+1)**3)
 

         +-----------------+
         | 3     2
   (5)  \|x  + 3x  + 3x + 1
                                                     Type: Expression Integer
--R
--R         +-----------------+
--R         | 3     2
--R   (5)  \|x  + 3x  + 3x + 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 33
rootSimp f1
 

                +-----+
   (6)  (x + 1)\|x + 1
                                                     Type: Expression Integer
--R
--R                +-----+
--R   (6)  (x + 1)\|x + 1
--R                                                     Type: Expression Integer
--E 20

--S 21 of 33
g1 := sin(x + cos x)
 

   (7)  sin(cos(x) + x)
                                                     Type: Expression Integer
--R
--R   (7)  sin(cos(x) + x)
--R                                                     Type: Expression Integer
--E 21

--S 22 of 33
g2 := complexElementary g1
 

                              +---+ 2               +---+          2
                    +---+   x\|- 1         +---+  x\|- 1     +---+
                   \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
                   -----------------------------------------------
                                           +---+
                                         x\|- 1
           +---+                      2%e                               +---+
        - \|- 1 (%e                                               )  + \|- 1
   (8)  ---------------------------------------------------------------------
                                +---+ 2               +---+
                      +---+   x\|- 1         +---+  x\|- 1     +---+
                     \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
                     -----------------------------------------------
                                             +---+
                                           x\|- 1
                                        2%e
                  2%e
                                                     Type: Expression Integer
--R
--R                              +---+ 2               +---+          2
--R                    +---+   x\|- 1         +---+  x\|- 1     +---+
--R                   \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
--R                   -----------------------------------------------
--R                                           +---+
--R                                         x\|- 1
--R           +---+                      2%e                               +---+
--R        - \|- 1 (%e                                               )  + \|- 1
--R   (8)  ---------------------------------------------------------------------
--R                                +---+ 2               +---+
--R                      +---+   x\|- 1         +---+  x\|- 1     +---+
--R                     \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
--R                     -----------------------------------------------
--R                                             +---+
--R                                           x\|- 1
--R                                        2%e
--R                  2%e
--R                                                     Type: Expression Integer
--E 22

--S 23 of 33
trigs g2
 

   (9)  sin(cos(x) + x)
                                                     Type: Expression Integer
--R
--R   (9)  sin(cos(x) + x)
--R                                                     Type: Expression Integer
--E 23

--S 24 of 33
h1 := sinh(x + cosh x)
 

   (10)  sinh(cosh(x) + x)
                                                     Type: Expression Integer
--R
--R   (10)  sinh(cosh(x) + x)
--R                                                     Type: Expression Integer
--E 24

--S 25 of 33
h2 := realElementary h1
 

               x 2        x     2
            (%e )  + 2x %e  + 1
            -------------------
                       x
                    2%e
         (%e                   )  - 1
   (11)  ----------------------------
                  x 2        x
               (%e )  + 2x %e  + 1
               -------------------
                          x
                       2%e
            2%e
                                                     Type: Expression Integer
--R
--R               x 2        x     2
--R            (%e )  + 2x %e  + 1
--R            -------------------
--R                       x
--R                    2%e
--R         (%e                   )  - 1
--R   (11)  ----------------------------
--R                  x 2        x
--R               (%e )  + 2x %e  + 1
--R               -------------------
--R                          x
--R                       2%e
--R            2%e
--R                                                     Type: Expression Integer
--E 25

--S 26 of 33
htrigs h2
 

   (12)  sinh(cosh(x) + x)
                                                     Type: Expression Integer
--R
--R   (12)  sinh(cosh(x) + x)
--R                                                     Type: Expression Integer
--E 26

)clear all
 
   All user variables and function definitions have been cleared.

--S 27 of 33
groupSqrt := _rule(sqrt(a) * sqrt(b), sqrt(a*b))
 

           +-+ +-+       +---+
   (1)  %P\|a \|b  == %P\|a b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           +-+ +-+       +---+
--I   (1)  %B\|a \|b  == %B\|a b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 27

--S 28 of 33
a := sqrt(2) * sqrt(3)
 

         +-+ +-+
   (2)  \|2 \|3
                                                        Type: AlgebraicNumber
--R
--R         +-+ +-+
--R   (2)  \|2 \|3
--R                                                        Type: AlgebraicNumber
--E 28

--S 29 of 33
groupSqrt a
 

         +-+
   (3)  \|6
                                                     Type: Expression Integer
--R
--R         +-+
--R   (3)  \|6
--R                                                     Type: Expression Integer
--E 29

--S 30 of 33
a := (sqrt(x) + sqrt(y))**4
 

                  +-+ +-+    2           2
   (4)  (4y + 4x)\|x \|y  + y  + 6x y + x
                                                     Type: Expression Integer
--R
--R                  +-+ +-+    2           2
--R   (4)  (4y + 4x)\|x \|y  + y  + 6x y + x
--R                                                     Type: Expression Integer
--E 30

--S 31 of 33
groupSqrt a
 

                  +---+    2           2
   (5)  (4y + 4x)\|x y  + y  + 6x y + x
                                                     Type: Expression Integer
--R
--R                  +---+    2           2
--R   (5)  (4y + 4x)\|x y  + y  + 6x y + x
--R                                                     Type: Expression Integer
--E 31

--S 32 of 33
sinCosExpand := rule
  sin(-x)    == - sin(x)
  cos(-x)    == cos(x)
  sin(x + y) == sin(x) * cos(y) + sin(y) * cos(x)
  cos(x + y) == cos(x) * cos(y) - sin(x) * sin(y)
  sin((n | integer? n and n > 1) * x) ==_
       sin(x) * cos((n-1)*x) + sin((n-1)*x) * cos(x)
  cos((n | integer? n and n > 1) * x) ==_
       cos(x) * cos((n-1)*x) - sin(x) * sin((n-1)*x)
 

   (6)
   {- %Q sin(x) == - %Q sin(x), cos(x) == cos(x),
    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (6)
--I   {- %BC sin(x) == - %BC sin(x), cos(x) == cos(x),
--R    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
--R    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
--R    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 32

--S 33 of 33
sinCosExpand(sin(x+y-2*z) * cos y)
 

   (7)  - cos(y)sin(2z - y - x)
                                                     Type: Expression Integer
)lisp (by)
 
Starts dribbling to float.output (2009/2/17, 17:46:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- look at 28 digits of accuracy (default is 20)
--S 1 of 13
digits 28
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 13
p := numeric %pi
 

   (2)  3.1415926535 8979323846 2643383
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 8979323846 2643383
--R                                                                  Type: Float
--E 2

--S 3 of 13
a := 163.0
 

   (3)  163.0
                                                                  Type: Float
--R 
--R
--R   (3)  163.0
--R                                                                  Type: Float
--E 3

--S 4 of 13
b := sqrt a
 

   (4)  12.7671453348 0370466171 095201
                                                                  Type: Float
--R 
--R
--R   (4)  12.7671453348 0370466171 095201
--R                                                                  Type: Float
--E 4

-- following appears to be an integer
--S 5 of 13
exp(p * b)
 

   (5)  26253741 2640768744.0000000003
                                                                  Type: Float
--R 
--R
--R   (5)  26253741 2640768744.0000000003
--R                                                                  Type: Float
--E 5

-- increase the precision to 60 and recalculate
--S 6 of 13
digits 60
 

   (6)  28
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  28
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 13
p := numeric %pi
 

   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
                                                                  Type: Float
--R 
--R
--R   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
--R                                                                  Type: Float
--E 7

--S 8 of 13
a := 163.0
 

   (8)  163.0
                                                                  Type: Float
--R 
--R
--R   (8)  163.0
--R                                                                  Type: Float
--E 6

--S 9 of 13
b := sqrt a
 

   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
                                                                  Type: Float
--R 
--R
--R   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
--R                                                                  Type: Float
--E 9

--S 10 of 13
exp(p * b)
 

   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
                                                                  Type: Float
--R 
--R
--R   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
--R                                                                  Type: Float
--E 10

--S 11 of 13
c := cos(p/12)
 

   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
                                                                  Type: Float
--R 
--R
--R   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
--R                                                                  Type: Float
--E 11

-- we have enough precision to get 0 in following
--S 12 of 13
16*c**4 - 16*c**2 + 1
 

   (12)  0.0
                                                                  Type: Float
--R 
--R
--R   (12)  0.0
--R                                                                  Type: Float
--E 12

-- look at PI to 200 places
--S 13 of 13
numeric(%pi, 200)
 

   (13)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 54930382
                                                                  Type: Float
--R 
--R
--R   (13)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 54930382
--R                                                                  Type: Float
--E 13
)spool 
 
Starts dribbling to isprime.output (2009/2/17, 17:46:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 15
n := 6763*10627*29947 
 

   (1)  2152302898747
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2152302898747
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 15
prime?(n)  
 

   (2)  false
                                                                Type: Boolean
--R 
--R
--R   (2)  false
--R                                                                Type: Boolean
--E 2

--S 3 of 15
factor(n)
 

   (3)  6763 10627 29947
                                                       Type: Factored Integer
--R 
--R
--R   (3)  6763 10627 29947
--R                                                       Type: Factored Integer
--E 3

--S 4 of 15
n := 1303*16927*157543  
 

   (4)  3474749660383
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  3474749660383
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 15
prime?(n)
 

   (5)  false
                                                                Type: Boolean
--R 
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 15
factor(n)
 

   (6)  1303 16927 157543
                                                       Type: Factored Integer
--R 
--R
--R   (6)  1303 16927 157543
--R                                                       Type: Factored Integer
--E 6

--S 7 of 15
n := 3739*18691*153259  
 

   (7)  10710604680091
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  10710604680091
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 15
prime?(n)
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 15
factor(n)
 

   (9)  3739 18691 153259
                                                       Type: Factored Integer
--R 
--R
--R   (9)  3739 18691 153259
--R                                                       Type: Factored Integer
--E 9

--S 10 of 15
n := 46411*232051*417691  
 

   (10)  4498414682539051
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  4498414682539051
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 15
prime?(n)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 15
factor(n)
 

   (12)  46411 232051 417691
                                                       Type: Factored Integer
--R 
--R
--R   (12)  46411 232051 417691
--R                                                       Type: Factored Integer
--E 12

--S 13 of 15
n := 21319*106591*3005839  
 

   (13)  6830509209595831
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  6830509209595831
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 15
prime?(n)
 

   (14)  false
                                                                Type: Boolean
--R 
--R
--R   (14)  false
--R                                                                Type: Boolean
--E 14

--S 15 of 15
factor(n)
 

   (15)  21319 106591 3005839
                                                       Type: Factored Integer
--R 
--R
--R   (15)  21319 106591 3005839
--R                                                       Type: Factored Integer
--E 15
)spool 
 
Starts dribbling to help.output (2009/2/17, 17:46:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 2
a:= x**2 + 1
 

         2
   (1)  x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (1)  x  + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 2
(a - 2)**2
 

         4     2
   (2)  x  - 2x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         4     2
--R   (2)  x  - 2x  + 1
--R                                                     Type: Polynomial Integer
--E 2
)spool 
 
Starts dribbling to limit.output (2009/2/17, 17:52:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 15
limit((x^2-4)/(x-2),x=2)
 

   (1)  4
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (1)  4
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 1
--S 2 of 15
limit(sqrt(9-x^2),x=-4)
 

   (2)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (2)  "failed"
--R                                                    Type: Union("failed",...)
--E 2

--S 3 of 15
limit(sqrt(9-x^2),x=-3)
 

   (3)  [leftHandLimit= "failed",rightHandLimit= 0]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (3)  [leftHandLimit= "failed",rightHandLimit= 0]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 3

--S 4 of 15
limit(sqrt(9-x^2),x=-2)
 

         +-+
   (4)  \|5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         +-+
--R   (4)  \|5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 15
limit(sqrt(9-x^2),x=0)
 

   (5)  3
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (5)  3
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 15
limit(sqrt(9-x^2),x=2)
 

         +-+
   (6)  \|5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         +-+
--R   (6)  \|5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 6

--S 7 of 15
limit(sqrt(9-x^2),x=3)
 

   (7)  [leftHandLimit= 0,rightHandLimit= "failed"]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (7)  [leftHandLimit= 0,rightHandLimit= "failed"]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 7

--S 8 of 15
limit(sqrt(9-x^2),x=4)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8

--S 9 of 15
limit(1/x^2,x=0)
 

   (9)   + infinity
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (9)   + infinity
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 9

--S 10 of 15
limit(-1/(x-1)^2,x=1)
 

   (10)  - infinity
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (10)  - infinity
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 10

--S 11 of 15
limit(1/x,x=0)
 

   (11)  [leftHandLimit= - infinity,rightHandLimit=  + infinity]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed"),rightHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed")),...)
--R 
--R
--R   (11)  [leftHandLimit= - infinity,rightHandLimit=  + infinity]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed"),rightHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed")),...)
--E 11

--S 12 of 15
limit(1/x,x=%plusInfinity)
 

   (12)  0
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (12)  0
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 12

--S 13 of 15
limit(2+(1/x^2),x=%plusInfinity)
 

   (13)  2
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (13)  2
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 13

)clear all
 
   All user variables and function definitions have been cleared.

--S 14 of 15
f := exp(n) * (sin(1/n + exp(-n)) - sin(1/n))
 

                   - n
          n    n %e    + 1      n    1
   (1)  %e sin(-----------) - %e sin(-)
                    n                n
                                                     Type: Expression Integer
--R 
--R
--R                   - n
--R          n    n %e    + 1      n    1
--R   (1)  %e sin(-----------) - %e sin(-)
--R                    n                n
--R                                                     Type: Expression Integer
--E 14

--S 15 of 15
limit(f,n=%plusInfinity)
 

   (2)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (2)  "failed"
--R                                                    Type: Union("failed",...)
--E 15
)spool 
 
Starts dribbling to schaum1.output (2009/2/17, 17:57:56).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(1/(a*x+b),x)
 

        log(a x + b)
   (1)  ------------
              a
                                          Type: Union(Expression Integer,...)
--R
--R        log(a x + b)
--R   (1)  ------------
--R              a
--R                                          Type: Union(Expression Integer,...)
--E 1

--S 2
bb:=1/a*log(a*x+b)
 

        log(a x + b)
   (2)  ------------
              a
                                                     Type: Expression Integer
--R
--R        log(a x + b)
--R   (2)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3      14:59 Schaums and Axiom agree
cc:=bb-aa
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x/(a*x+b),x)
 

        - b log(a x + b) + a x
   (1)  ----------------------
                   2
                  a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - b log(a x + b) + a x
--R   (1)  ----------------------
--R                   2
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=x/a-b/a^2*log(a*x+b)
 

        - b log(a x + b) + a x
   (2)  ----------------------
                   2
                  a
                                                     Type: Expression Integer
--R
--R        - b log(a x + b) + a x
--R   (2)  ----------------------
--R                   2
--R                  a
--R                                                     Type: Expression Integer
--E

--S 6      14:60 Schaums and Axiom agree
cc:=bb-aa
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2/(a*x+b),x)
 

          2                2 2
        2b log(a x + b) + a x  - 2a b x
   (1)  -------------------------------
                        3
                      2a
                                          Type: Union(Expression Integer,...)
--R
--R          2                2 2
--R        2b log(a x + b) + a x  - 2a b x
--R   (1)  -------------------------------
--R                        3
--R                      2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b)
 

          2                2 2              2
        2b log(a x + b) + a x  - 2a b x - 3b
   (2)  -------------------------------------
                           3
                         2a
                                                     Type: Expression Integer
--R
--R          2                2 2              2
--R        2b log(a x + b) + a x  - 2a b x - 3b
--R   (2)  -------------------------------------
--R                           3
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 9
cc:=bb-aa
 

            2
          3b
   (3)  - ---
            3
          2a
                                                     Type: Expression Integer
--R
--R            2
--R          3b
--R   (3)  - ---
--R            3
--R          2a
--R                                                     Type: Expression Integer
--E
--S 10     14:61 Schaums and Axiom differ by a constant
differentiate(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 11
aa:=integrate(x^3/(a*x+b),x)
 

            3                 3 3     2   2       2
        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x
   (1)  --------------------------------------------
                               4
                             6a
                                          Type: Union(Expression Integer,...)
--R
--R            3                 3 3     2   2       2
--R        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x
--R   (1)  --------------------------------------------
--R                               4
--R                             6a
--R                                          Type: Union(Expression Integer,...)
--E
--S 12
bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(a*x+b)
 

            3                 3 3     2   2       2       3
        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x + 11b
   (2)  ---------------------------------------------------
                                  4
                                6a
                                                     Type: Expression Integer
--R
--R            3                 3 3     2   2       2       3
--R        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x + 11b
--R   (2)  ---------------------------------------------------
--R                                  4
--R                                6a
--R                                                     Type: Expression Integer
--E 
--S 13
cc:=aa-bb
 

             3
          11b
   (3)  - ----
             4
           6a
                                                     Type: Expression Integer
--R
--R             3
--R          11b
--R   (3)  - ----
--R             4
--R           6a
--R                                                     Type: Expression Integer
--E 
--S 14     14:62 Schaums and Axiom differ by a constant
dd:=D(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(1/(x*(a*x+b)),x)
 

        - log(a x + b) + log(x)
   (1)  -----------------------
                   b
                                          Type: Union(Expression Integer,...)
--R
--R        - log(a x + b) + log(x)
--R   (1)  -----------------------
--R                   b
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16
bb:=1/b*log(x/(a*x+b))
 

               x
        log(-------)
            a x + b
   (2)  ------------
              b
                                                     Type: Expression Integer
--R
--R               x
--R        log(-------)
--R            a x + b
--R   (2)  ------------
--R              b
--R                                                     Type: Expression Integer
--E

--S 17
cc:=aa-bb
 

                                         x
        - log(a x + b) + log(x) - log(-------)
                                      a x + b
   (3)  --------------------------------------
                           b
                                                     Type: Expression Integer
--R
--R                                         x
--R        - log(a x + b) + log(x) - log(-------)
--R                                      a x + b
--R   (3)  --------------------------------------
--R                           b
--R                                                     Type: Expression Integer
--E
--S 18
logdiv:=rule(log(a)-log(b) == log(a/b))
 

                                      a
   (4)  - log(b) + log(a) + %G == log(-) + %G
                                      b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                      a
--I   (4)  - log(b) + log(a) + %I == log(-) + %I
--R                                      b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 
--S 19     14:63 Schaums and Axiom agree
dd:=logdiv cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(1/(x^2*(a*x+b)),x)
 

        a x log(a x + b) - a x log(x) - b
   (1)  ---------------------------------
                        2
                       b x
                                          Type: Union(Expression Integer,...)
--R
--R        a x log(a x + b) - a x log(x) - b
--R   (1)  ---------------------------------
--R                        2
--R                       b x
--R                                          Type: Union(Expression Integer,...)
--E 
--S 21
bb:=-1/(b*x)+a/b^2*log((a*x+b)/x)
 

                a x + b
        a x log(-------) - b
                   x
   (2)  --------------------
                  2
                 b x
                                                     Type: Expression Integer
--R
--R                a x + b
--R        a x log(-------) - b
--R                   x
--R   (2)  --------------------
--R                  2
--R                 b x
--R                                                     Type: Expression Integer
--E 

--S 22
cc:=aa-bb
 

                                          a x + b
        a log(a x + b) - a log(x) - a log(-------)
                                             x
   (3)  ------------------------------------------
                             2
                            b
                                                     Type: Expression Integer
--R
--R                                          a x + b
--R        a log(a x + b) - a log(x) - a log(-------)
--R                                             x
--R   (3)  ------------------------------------------
--R                             2
--R                            b
--R                                                     Type: Expression Integer
--E
--S 23
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 
--S 24     14:64 Schaums and Axiom agree
divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.
--S 25
aa:=integrate(1/(x^3*(a*x+b)),x)
 

            2 2                 2 2                   2
        - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
   (1)  -----------------------------------------------
                               3 2
                             2b x
                                          Type: Union(Expression Integer,...)
--R
--R            2 2                 2 2                   2
--R        - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
--R   (1)  -----------------------------------------------
--R                               3 2
--R                             2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 26
bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b))
 

          2 2       x                 2
        2a x log(-------) + 2a b x - b
                 a x + b
   (2)  -------------------------------
                       3 2
                     2b x
                                                     Type: Expression Integer
--R
--R          2 2       x                 2
--R        2a x log(-------) + 2a b x - b
--R                 a x + b
--R   (2)  -------------------------------
--R                       3 2
--R                     2b x
--R                                                     Type: Expression Integer
--E

--S 27
cc:=aa-bb
 

           2                2          2       x
        - a log(a x + b) + a log(x) - a log(-------)
                                            a x + b
   (3)  --------------------------------------------
                              3
                             b
                                                     Type: Expression Integer
--R
--R           2                2          2       x
--R        - a log(a x + b) + a log(x) - a log(-------)
--R                                            a x + b
--R   (3)  --------------------------------------------
--R                              3
--R                             b
--R                                                     Type: Expression Integer
--E

--S 28
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29     14:65 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 30
aa:=integrate(1/(a*x+b)^2,x)
 

              1
   (1)  - ---------
           2
          a x + a b
                                          Type: Union(Expression Integer,...)
--R
--R              1
--R   (1)  - ---------
--R           2
--R          a x + a b
--R                                          Type: Union(Expression Integer,...)
--E 

--S 31
bb:=-1/(a*(a*x+b))
 

              1
   (2)  - ---------
           2
          a x + a b
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R           2
--R          a x + a b
--R                                            Type: Fraction Polynomial Integer
--E

--S 32     14:66 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 33
aa:=integrate(x/(a*x+b)^2,x)
 

        (a x + b)log(a x + b) + b
   (1)  -------------------------
                 3     2
                a x + a b
                                          Type: Union(Expression Integer,...)
--R
--R        (a x + b)log(a x + b) + b
--R   (1)  -------------------------
--R                 3     2
--R                a x + a b
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34
bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b)
 

        (a x + b)log(a x + b) + b
   (2)  -------------------------
                 3     2
                a x + a b
                                                     Type: Expression Integer
--R
--R        (a x + b)log(a x + b) + b
--R   (2)  -------------------------
--R                 3     2
--R                a x + a b
--R                                                     Type: Expression Integer
--E

--S 35     14:67 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(x^2/(a*x+b)^2,x)
 

                      2                 2 2            2
        (- 2a b x - 2b )log(a x + b) + a x  + a b x - b
   (1)  ------------------------------------------------
                             4     3
                            a x + a b
                                          Type: Union(Expression Integer,...)
--R
--R                      2                 2 2            2
--R        (- 2a b x - 2b )log(a x + b) + a x  + a b x - b
--R   (1)  ------------------------------------------------
--R                             4     3
--R                            a x + a b
--R                                          Type: Union(Expression Integer,...)
--E 
--S 37
bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b)
 

                      2                 2 2
        (- 2a b x - 2b )log(a x + b) + a x  + 2a b x
   (2)  --------------------------------------------
                           4     3
                          a x + a b
                                                     Type: Expression Integer
--R
--R                      2                 2 2
--R        (- 2a b x - 2b )log(a x + b) + a x  + 2a b x
--R   (2)  --------------------------------------------
--R                           4     3
--R                          a x + a b
--R                                                     Type: Expression Integer
--E 
--S 38
cc:=aa-bb
 

           b
   (3)  - --
           3
          a
                                                     Type: Expression Integer
--R
--R           b
--R   (3)  - --
--R           3
--R          a
--R                                                     Type: Expression Integer
--E 
--S 39     14:68 Schaums and Axiom differ by a constant
D(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 40
aa:=integrate(x^3/(a*x+b)^2,x)
 

             2      3                 3 3     2   2       2      3
        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 4a b x + 2b
   (1)  ----------------------------------------------------------
                                  5      4
                                2a x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R             2      3                 3 3     2   2       2      3
--R        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 4a b x + 2b
--R   (1)  ----------------------------------------------------------
--R                                  5      4
--R                                2a x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 41
bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b)
 

             2      3                 3 3     2   2       2      3
        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 9a b x - 3b
   (2)  ----------------------------------------------------------
                                  5      4
                                2a x + 2a b
                                                     Type: Expression Integer
--R
--R             2      3                 3 3     2   2       2      3
--R        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 9a b x - 3b
--R   (2)  ----------------------------------------------------------
--R                                  5      4
--R                                2a x + 2a b
--R                                                     Type: Expression Integer
--E

--S 42
cc:=aa-bb
 

          2
        5b
   (3)  ---
          4
        2a
                                                     Type: Expression Integer
--R
--R          2
--R        5b
--R   (3)  ---
--R          4
--R        2a
--R                                                     Type: Expression Integer
--E

--S 43     14:69 Schaums and Axiom differ by a constant
dd:=D(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 44
aa:=integrate(1/(x*(a*x+b)^2),x)
 

        (- a x - b)log(a x + b) + (a x + b)log(x) + b
   (1)  ---------------------------------------------
                             2     3
                          a b x + b
                                          Type: Union(Expression Integer,...)
--R
--R        (- a x - b)log(a x + b) + (a x + b)log(x) + b
--R   (1)  ---------------------------------------------
--R                             2     3
--R                          a b x + b
--R                                          Type: Union(Expression Integer,...)
--E
--S 45
bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b)))
 

                        x
        (a x + b)log(-------) + b
                     a x + b
   (2)  -------------------------
                   2     3
                a b x + b
                                                     Type: Expression Integer
--R
--R                        x
--R        (a x + b)log(-------) + b
--R                     a x + b
--R   (2)  -------------------------
--R                   2     3
--R                a b x + b
--R                                                     Type: Expression Integer
--E

--S 46
cc:=aa-bb
 

                                         x
        - log(a x + b) + log(x) - log(-------)
                                      a x + b
   (3)  --------------------------------------
                           2
                          b
                                                     Type: Expression Integer
--R
--R                                         x
--R        - log(a x + b) + log(x) - log(-------)
--R                                      a x + b
--R   (3)  --------------------------------------
--R                           2
--R                          b
--R                                                     Type: Expression Integer
--E
--S 47
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E
--S 48     14:70 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(1/(x^2*(a*x+b)^2),x)
 

           2 2                              2 2                             2
        (2a x  + 2a b x)log(a x + b) + (- 2a x  - 2a b x)log(x) - 2a b x - b
   (1)  ---------------------------------------------------------------------
                                        3 2    4
                                     a b x  + b x
                                          Type: Union(Expression Integer,...)
--R
--R           2 2                              2 2                             2
--R        (2a x  + 2a b x)log(a x + b) + (- 2a x  - 2a b x)log(x) - 2a b x - b
--R   (1)  ---------------------------------------------------------------------
--R                                        3 2    4
--R                                     a b x  + b x
--R                                          Type: Union(Expression Integer,...)
--E
--S 50
bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x)
 

           2 2              a x + b              2
        (2a x  + 2a b x)log(-------) - 2a b x - b
                               x
   (2)  ------------------------------------------
                          3 2    4
                       a b x  + b x
                                                     Type: Expression Integer
--R
--R           2 2              a x + b              2
--R        (2a x  + 2a b x)log(-------) - 2a b x - b
--R                               x
--R   (2)  ------------------------------------------
--R                          3 2    4
--R                       a b x  + b x
--R                                                     Type: Expression Integer
--E

--S 51
cc:=aa-bb
 

                                             a x + b
        2a log(a x + b) - 2a log(x) - 2a log(-------)
                                                x
   (3)  ---------------------------------------------
                               3
                              b
                                                     Type: Expression Integer
--R
--R                                             a x + b
--R        2a log(a x + b) - 2a log(x) - 2a log(-------)
--R                                                x
--R   (3)  ---------------------------------------------
--R                               3
--R                              b
--R                                                     Type: Expression Integer
--E
--S 52
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E
--S 53     14:71 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 54
aa:=integrate(1/(x^3*(a*x+b)^2),x)
 

   (1)
            3 3     2   2                   3 3     2   2            2   2
       (- 6a x  - 6a b x )log(a x + b) + (6a x  + 6a b x )log(x) + 6a b x
     + 
           2     3
       3a b x - b
  /
         4 3     5 2
     2a b x  + 2b x
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R            3 3     2   2                   3 3     2   2            2   2
--R       (- 6a x  - 6a b x )log(a x + b) + (6a x  + 6a b x )log(x) + 6a b x
--R     + 
--R           2     3
--R       3a b x - b
--R  /
--R         4 3     5 2
--R     2a b x  + 2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 55
bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/b^4)*log((a*x+b)/x)
 

             3 3     2   2     a x + b      3 3     2   2       2     3
        (- 6a x  - 6a b x )log(-------) + 3a x  + 9a b x  + 3a b x - b
                                  x
   (2)  ---------------------------------------------------------------
                                    4 3     5 2
                                2a b x  + 2b x
                                                     Type: Expression Integer
--R
--R             3 3     2   2     a x + b      3 3     2   2       2     3
--R        (- 6a x  - 6a b x )log(-------) + 3a x  + 9a b x  + 3a b x - b
--R                                  x
--R   (2)  ---------------------------------------------------------------
--R                                    4 3     5 2
--R                                2a b x  + 2b x
--R                                                     Type: Expression Integer
--E

--S 56
cc:=aa-bb
 

            2                 2           2    a x + b      2
        - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a
                                                  x
   (3)  -----------------------------------------------------
                                   4
                                 2b
                                                     Type: Expression Integer
--R
--R            2                 2           2    a x + b      2
--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a
--R                                                  x
--R   (3)  -----------------------------------------------------
--R                                   4
--R                                 2b
--R                                                     Type: Expression Integer
--E

--S 57
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 58
dd:=divlog cc
 

            2
          3a
   (5)  - ---
            4
          2b
                                                     Type: Expression Integer
--R
--R            2
--R          3a
--R   (5)  - ---
--R            4
--R          2b
--R                                                     Type: Expression Integer
--E

--S 59     14:72 Schaums and Axiom differ by a constant
ee:=D(dd,x)
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 60
aa:=integrate(1/(a*x+b)^3,x)
 

                     1
   (1)  - ----------------------
            3 2     2          2
          2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R                     1
--R   (1)  - ----------------------
--R            3 2     2          2
--R          2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 61
bb:=-1/(2*(a*x+b)^2)
 

                    1
   (2)  - --------------------
            2 2              2
          2a x  + 4a b x + 2b
                                            Type: Fraction Polynomial Integer
--R
--R                    1
--R   (2)  - --------------------
--R            2 2              2
--R          2a x  + 4a b x + 2b
--R                                            Type: Fraction Polynomial Integer
--E

--S 62
cc:=aa-bb
 

                 a - 1
   (3)  ----------------------
          3 2     2          2
        2a x  + 4a b x + 2a b
                                                     Type: Expression Integer
--R
--R                 a - 1
--R   (3)  ----------------------
--R          3 2     2          2
--R        2a x  + 4a b x + 2a b
--R                                                     Type: Expression Integer
--E

--S 63
dd:=aa/bb
 

        1
   (4)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (4)  -
--R        a
--R                                                     Type: Expression Integer
--E

--S 64     14:73 Schaums and Axiom differ by a constant
ee:=D(dd,x)
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 65
aa:=integrate(x/(a*x+b)^3,x)
 

              - 2a x - b
   (1)  ----------------------
          4 2     3        2 2
        2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R              - 2a x - b
--R   (1)  ----------------------
--R          4 2     3        2 2
--R        2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 66
bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2)
 

              - 2a x - b
   (2)  ----------------------
          4 2     3        2 2
        2a x  + 4a b x + 2a b
                                            Type: Fraction Polynomial Integer
--R
--R              - 2a x - b
--R   (2)  ----------------------
--R          4 2     3        2 2
--R        2a x  + 4a b x + 2a b
--R                                            Type: Fraction Polynomial Integer
--E

--S 67     14:74 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 68
aa:=integrate(x^2/(a*x+b)^3,x)
 

           2 2              2                           2
        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
   (1)  -------------------------------------------------
                        5 2     4        3 2
                      2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R           2 2              2                           2
--R        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
--R   (1)  -------------------------------------------------
--R                        5 2     4        3 2
--R                      2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 69
bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b)
 

           2 2              2                           2
        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
   (2)  -------------------------------------------------
                        5 2     4        3 2
                      2a x  + 4a b x + 2a b
                                                     Type: Expression Integer
--R
--R           2 2              2                           2
--R        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
--R   (2)  -------------------------------------------------
--R                        5 2     4        3 2
--R                      2a x  + 4a b x + 2a b
--R                                                     Type: Expression Integer
--E

--S 70     14:75 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.
--S 71
aa:=integrate(x^3/(a*x+b)^3,x)
 

   (1)
        2   2        2      3                  3 3     2   2       2      3
   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
   ------------------------------------------------------------------------
                              6 2     5        4 2
                            2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R        2   2        2      3                  3 3     2   2       2      3
--R   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
--R   ------------------------------------------------------------------------
--R                              6 2     5        4 2
--R                            2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 72
bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b)
 

   (2)
        2   2        2      3                  3 3     2   2       2      3
   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
   ------------------------------------------------------------------------
                              6 2     5        4 2
                            2a x  + 4a b x + 2a b
                                                     Type: Expression Integer
--R
--R   (2)
--R        2   2        2      3                  3 3     2   2       2      3
--R   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
--R   ------------------------------------------------------------------------
--R                              6 2     5        4 2
--R                            2a x  + 4a b x + 2a b
--R                                                     Type: Expression Integer
--E

--S 73     14:76 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 74
aa:=integrate(1/(x*(a*x+b)^3),x)
 

   (1)
            2 2              2                   2 2              2
       (- 2a x  - 4a b x - 2b )log(a x + b) + (2a x  + 4a b x + 2b )log(x)
     + 
                  2
       2a b x + 3b
  /
       2 3 2       4      5
     2a b x  + 4a b x + 2b
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R            2 2              2                   2 2              2
--R       (- 2a x  - 4a b x - 2b )log(a x + b) + (2a x  + 4a b x + 2b )log(x)
--R     + 
--R                  2
--R       2a b x + 3b
--R  /
--R       2 3 2       4      5
--R     2a b x  + 4a b x + 2b
--R                                          Type: Union(Expression Integer,...)
--E

--S 75
bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x)
 

             2 2              2     a x + b      2 2
        (- 2a x  - 4a b x - 2b )log(-------) - 3a x  - 4a b x
                                       x
   (2)  -----------------------------------------------------
                          2 3 2       4      5
                        2a b x  + 4a b x + 2b
                                                     Type: Expression Integer
--R
--R             2 2              2     a x + b      2 2
--R        (- 2a x  - 4a b x - 2b )log(-------) - 3a x  - 4a b x
--R                                       x
--R   (2)  -----------------------------------------------------
--R                          2 3 2       4      5
--R                        2a b x  + 4a b x + 2b
--R                                                     Type: Expression Integer
--E

--S 76
cc:=aa-bb
 

                                         a x + b
        - 2log(a x + b) + 2log(x) + 2log(-------) + 3
                                            x
   (3)  ---------------------------------------------
                               3
                             2b
                                                     Type: Expression Integer
--R
--R                                         a x + b
--R        - 2log(a x + b) + 2log(x) + 2log(-------) + 3
--R                                            x
--R   (3)  ---------------------------------------------
--R                               3
--R                             2b
--R                                                     Type: Expression Integer
--E

--S 77
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 78
dd:=divlog cc
 

         3
   (5)  ---
          3
        2b
                                                     Type: Expression Integer
--R
--R         3
--R   (5)  ---
--R          3
--R        2b
--R                                                     Type: Expression Integer
--E

--S 79     14:77 Schaums and Axiom differ by a constant
ee:=D(dd,x)
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 80
aa:=integrate(1/(x^2*(a*x+b)^3),x)
 

   (1)
          3 3      2   2       2
       (6a x  + 12a b x  + 6a b x)log(a x + b)
     + 
            3 3      2   2       2             2   2       2      3
       (- 6a x  - 12a b x  - 6a b x)log(x) - 6a b x  - 9a b x - 2b
  /
       2 4 3       5 2     6
     2a b x  + 4a b x  + 2b x
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R          3 3      2   2       2
--R       (6a x  + 12a b x  + 6a b x)log(a x + b)
--R     + 
--R            3 3      2   2       2             2   2       2      3
--R       (- 6a x  - 12a b x  - 6a b x)log(x) - 6a b x  - 9a b x - 2b
--R  /
--R       2 4 3       5 2     6
--R     2a b x  + 4a b x  + 2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 81
bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x)
 

           3 3      2   2       2      a x + b      2   2       2      3
        (6a x  + 12a b x  + 6a b x)log(-------) - 6a b x  - 9a b x - 2b
                                          x
   (2)  ----------------------------------------------------------------
                              2 4 3       5 2     6
                            2a b x  + 4a b x  + 2b x
                                                     Type: Expression Integer
--R
--R           3 3      2   2       2      a x + b      2   2       2      3
--R        (6a x  + 12a b x  + 6a b x)log(-------) - 6a b x  - 9a b x - 2b
--R                                          x
--R   (2)  ----------------------------------------------------------------
--R                              2 4 3       5 2     6
--R                            2a b x  + 4a b x  + 2b x
--R                                                     Type: Expression Integer
--E

--S 82
cc:=aa-bb
 

                                             a x + b
        3a log(a x + b) - 3a log(x) - 3a log(-------)
                                                x
   (3)  ---------------------------------------------
                               4
                              b
                                                     Type: Expression Integer
--R
--R                                             a x + b
--R        3a log(a x + b) - 3a log(x) - 3a log(-------)
--R                                                x
--R   (3)  ---------------------------------------------
--R                               4
--R                              b
--R                                                     Type: Expression Integer
--E

--S 83
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 84     14:78 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 85
aa:=integrate(1/(x^3*(a*x+b)^3),x)
 

   (1)
             4 4      3   3      2 2 2
       (- 12a x  - 24a b x  - 12a b x )log(a x + b)
     + 
           4 4      3   3      2 2 2             3   3      2 2 2       3     4
       (12a x  + 24a b x  + 12a b x )log(x) + 12a b x  + 18a b x  + 4a b x - b
  /
       2 5 4       6 3     7 2
     2a b x  + 4a b x  + 2b x
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R             4 4      3   3      2 2 2
--R       (- 12a x  - 24a b x  - 12a b x )log(a x + b)
--R     + 
--R           4 4      3   3      2 2 2             3   3      2 2 2       3     4
--R       (12a x  + 24a b x  + 12a b x )log(x) + 12a b x  + 18a b x  + 4a b x - b
--R  /
--R       2 5 4       6 3     7 2
--R     2a b x  + 4a b x  + 2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 86
bb:=-1/(2*b*x^2*(a*x+b)^2)_
    +(2*a)/(b^2*x*(a*x+b)^2)_
    +(9*a^2)/(b^3*(a*x+b)^2)_
    +(6*a^3*x)/(b^4*(a*x+b)^2)_
    +(-6*a^2)/b^5*log((a*x+b)/x)
 

   (2)
             4 4      3   3      2 2 2     a x + b       3   3      2 2 2
       (- 12a x  - 24a b x  - 12a b x )log(-------) + 12a b x  + 18a b x
                                              x
     + 
           3     4
       4a b x - b
  /
       2 5 4       6 3     7 2
     2a b x  + 4a b x  + 2b x
                                                     Type: Expression Integer
--R
--R   (2)
--R             4 4      3   3      2 2 2     a x + b       3   3      2 2 2
--R       (- 12a x  - 24a b x  - 12a b x )log(-------) + 12a b x  + 18a b x
--R                                              x
--R     + 
--R           3     4
--R       4a b x - b
--R  /
--R       2 5 4       6 3     7 2
--R     2a b x  + 4a b x  + 2b x
--R                                                     Type: Expression Integer
--E

--S 87
cc:=aa-bb
 

            2                 2           2    a x + b
        - 6a log(a x + b) + 6a log(x) + 6a log(-------)
                                                  x
   (3)  -----------------------------------------------
                                5
                               b
                                                     Type: Expression Integer
--R
--R            2                 2           2    a x + b
--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------)
--R                                                  x
--R   (3)  -----------------------------------------------
--R                                5
--R                               b
--R                                                     Type: Expression Integer
--E

--S 88
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 89     14:79 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.
--S 90
aa:=integrate((a*x+b)^n,x)
 

                   n log(a x + b)
        (a x + b)%e
   (1)  -------------------------
                 a n + a
                                          Type: Union(Expression Integer,...)
--R
--R                   n log(a x + b)
--R        (a x + b)%e
--R   (1)  -------------------------
--R                 a n + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 91
bb:=(a*x+b)^(n+1)/((n+1)*a)
 

                 n + 1
        (a x + b)
   (2)  --------------
            a n + a
                                                     Type: Expression Integer
--R
--R                 n + 1
--R        (a x + b)
--R   (2)  --------------
--R            a n + a
--R                                                     Type: Expression Integer
--E

--S 92
cc:=aa-bb
 

                   n log(a x + b)            n + 1
        (a x + b)%e               - (a x + b)
   (3)  ------------------------------------------
                          a n + a
                                                     Type: Expression Integer
--R
--R                   n log(a x + b)            n + 1
--R        (a x + b)%e               - (a x + b)
--R   (3)  ------------------------------------------
--R                          a n + a
--R                                                     Type: Expression Integer
--E
--S 93
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 94
dd:=explog cc
 

                   n + 1                     n
        - (a x + b)      + (a x + b)(a x + b)
   (5)  --------------------------------------
                        a n + a
                                                     Type: Expression Integer
--R
--R                   n + 1                     n
--R        - (a x + b)      + (a x + b)(a x + b)
--R   (5)  --------------------------------------
--R                        a n + a
--R                                                     Type: Expression Integer
--E

--S 95     14:80 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.
--S 96
aa:=integrate(x*(a*x+b)^n,x)
 

           2     2  2              2   n log(a x + b)
        ((a n + a )x  + a b n x - b )%e
   (1)  ---------------------------------------------
                       2 2     2      2
                      a n  + 3a n + 2a
                                          Type: Union(Expression Integer,...)
--R
--R           2     2  2              2   n log(a x + b)
--R        ((a n + a )x  + a b n x - b )%e
--R   (1)  ---------------------------------------------
--R                       2 2     2      2
--R                      a n  + 3a n + 2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 97
bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2)
 

                        n + 2                        n + 1
        (n + 1)(a x + b)      + (- b n - 2b)(a x + b)
   (2)  --------------------------------------------------
                          2 2     2      2
                         a n  + 3a n + 2a
                                                     Type: Expression Integer
--R
--R                        n + 2                        n + 1
--R        (n + 1)(a x + b)      + (- b n - 2b)(a x + b)
--R   (2)  --------------------------------------------------
--R                          2 2     2      2
--R                         a n  + 3a n + 2a
--R                                                     Type: Expression Integer
--E

--S 98
cc:=aa-bb
 

   (3)
          2     2  2              2   n log(a x + b)                     n + 2
       ((a n + a )x  + a b n x - b )%e               + (- n - 1)(a x + b)
     + 
                          n + 1
       (b n + 2b)(a x + b)
  /
      2 2     2      2
     a n  + 3a n + 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R          2     2  2              2   n log(a x + b)                     n + 2
--R       ((a n + a )x  + a b n x - b )%e               + (- n - 1)(a x + b)
--R     + 
--R                          n + 1
--R       (b n + 2b)(a x + b)
--R  /
--R      2 2     2      2
--R     a n  + 3a n + 2a
--R                                                     Type: Expression Integer
--E

--S 99
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 100
dd:=explog cc
 

   (5)
                         n + 2                      n + 1
       (- n - 1)(a x + b)      + (b n + 2b)(a x + b)
     + 
          2     2  2              2          n
       ((a n + a )x  + a b n x - b )(a x + b)
  /
      2 2     2      2
     a n  + 3a n + 2a
                                                     Type: Expression Integer
--R
--R   (5)
--R                         n + 2                      n + 1
--R       (- n - 1)(a x + b)      + (b n + 2b)(a x + b)
--R     + 
--R          2     2  2              2          n
--R       ((a n + a )x  + a b n x - b )(a x + b)
--R  /
--R      2 2     2      2
--R     a n  + 3a n + 2a
--R                                                     Type: Expression Integer
--E

--S 101
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.
--S 102
aa:=integrate(x^2*(a*x+b)^n,x)
 

   (1)
      3 2     3      3  3     2   2    2     2       2        3   n log(a x + b)
   ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )%e
   -----------------------------------------------------------------------------
                              3 3     3 2      3      3
                             a n  + 6a n  + 11a n + 6a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R      3 2     3      3  3     2   2    2     2       2        3   n log(a x + b)
--R   ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )%e
--R   -----------------------------------------------------------------------------
--R                              3 3     3 2      3      3
--R                             a n  + 6a n  + 11a n + 6a
--R                                          Type: Union(Expression Integer,...)
--E

--S 103
bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3)
 

   (2)
         2                   n + 3          2                      n + 2
       (n  + 3n + 2)(a x + b)      + (- 2b n  - 8b n - 6b)(a x + b)
     + 
         2 2     2      2          n + 1
       (b n  + 5b n + 6b )(a x + b)
  /
      3 3     3 2      3      3
     a n  + 6a n  + 11a n + 6a
                                                     Type: Expression Integer
--R
--R   (2)
--R         2                   n + 3          2                      n + 2
--R       (n  + 3n + 2)(a x + b)      + (- 2b n  - 8b n - 6b)(a x + b)
--R     + 
--R         2 2     2      2          n + 1
--R       (b n  + 5b n + 6b )(a x + b)
--R  /
--R      3 3     3 2      3      3
--R     a n  + 6a n  + 11a n + 6a
--R                                                     Type: Expression Integer
--E

--S 104
cc:=aa-bb
 

   (3)
            3 2     3      3  3     2   2    2     2       2        3
         ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )
      *
           n log(a x + b)
         %e
     + 
           2                   n + 3        2                      n + 2
       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
     + 
           2 2     2      2          n + 1
       (- b n  - 5b n - 6b )(a x + b)
  /
      3 3     3 2      3      3
     a n  + 6a n  + 11a n + 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R            3 2     3      3  3     2   2    2     2       2        3
--R         ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )
--R      *
--R           n log(a x + b)
--R         %e
--R     + 
--R           2                   n + 3        2                      n + 2
--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
--R     + 
--R           2 2     2      2          n + 1
--R       (- b n  - 5b n - 6b )(a x + b)
--R  /
--R      3 3     3 2      3      3
--R     a n  + 6a n  + 11a n + 6a
--R                                                     Type: Expression Integer
--E

--S 105
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 106
dd:=explog cc
 

   (5)
           2                   n + 3        2                      n + 2
       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
     + 
           2 2     2      2          n + 1
       (- b n  - 5b n - 6b )(a x + b)
     + 
          3 2     3      3  3     2   2    2     2       2        3          n
       ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )(a x + b)
  /
      3 3     3 2      3      3
     a n  + 6a n  + 11a n + 6a
                                                     Type: Expression Integer
--R
--R   (5)
--R           2                   n + 3        2                      n + 2
--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
--R     + 
--R           2 2     2      2          n + 1
--R       (- b n  - 5b n - 6b )(a x + b)
--R     + 
--R          3 2     3      3  3     2   2    2     2       2        3          n
--R       ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )(a x + b)
--R  /
--R      3 3     3 2      3      3
--R     a n  + 6a n  + 11a n + 6a
--R                                                     Type: Expression Integer
--E

--S 107    14:82 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
--S 108    14:83 Axiom cannot do this integration
aa:=integrate(x^m*(a*x+b)^n,x)
 

           x
         ++    m          n
   (7)   |   %M (b + %M a) d%M
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--R         ++    m          n
--I   (1)   |   %U (b + %U a) d%U
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)spool
 
Starts dribbling to contfrac.output (2009/2/17, 17:44:15).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 40
r1 := 3/4
 

        3
   (1)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (1)  -
--R        4
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 40
r2 := 314159/100000
 

        314159
   (2)  ------
        100000
                                                       Type: Fraction Integer
--R 
--R
--R        314159
--R   (2)  ------
--R        100000
--R                                                       Type: Fraction Integer
--E 2

--S 3  of 40
c1 := r1 :: ContinuedFraction Integer
 

          1 |     1 |
   (3)  +---+ + +---+
        | 1     | 3
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |
--R   (3)  +---+ + +---+
--R        | 1     | 3
--R                                              Type: ContinuedFraction Integer
--E 3

--S 4 of 40
c2 := r2 :: ContinuedFraction Integer
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (4)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (4)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 4

-- We can view these in the list notation
--S 5  of 40
partialQuotients c1
 

   (5)  [0,1,3]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,1,3]
--R                                                         Type: Stream Integer
--E 5

--S 6 of 40
partialQuotients c2
 

   (6)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (6)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 6
 
-- These are algebraic objects, so we can manipulate them accordingly
--S 7 of 40
c1 + c2
 

   (7)
         1 |     1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |
   3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+
       | 1     | 8     | 4     | 2     | 5     | 1     | 2     | 32     | 2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R         1 |     1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |
--R   3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+
--R       | 1     | 8     | 4     | 2     | 5     | 1     | 2     | 32     | 2
--R                                              Type: ContinuedFraction Integer
--E 7

--S 8 of 40
c1 * c2
 

   (8)
           1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |     1 |
     2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+ + +---+
         | 2     | 1     | 4     | 5     | 6     | 2     | 13     | 1     | 1
   + 
       1 |
     +---+ + ...
     | 1
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (8)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |     1 |
--R     2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+ + +---+
--R         | 2     | 1     | 4     | 5     | 6     | 2     | 13     | 1     | 1
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 1
--R                                              Type: ContinuedFraction Integer
--E 8

--S 9 of 40
1 / c2
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (9)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (9)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 40
c1 - c2
 

   (10)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
   - 3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
         | 1     | 1     | 1     | 1     | 4     | 6     | 2     | 2     | 131
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (10)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
--R   - 3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
--R         | 1     | 1     | 1     | 1     | 4     | 6     | 2     | 2     | 131
--R                                              Type: ContinuedFraction Integer
--E 10

--S 11 of 40
c2 - c1
 

               1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
   (11)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
             | 2     | 1     | 1     | 4     | 6     | 2     | 2     | 131
                                              Type: ContinuedFraction Integer
--R 
--R
--R               1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
--R   (11)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
--R             | 2     | 1     | 1     | 4     | 6     | 2     | 2     | 131
--R                                              Type: ContinuedFraction Integer
--E 11
 
-- and can convert them back to rational numbers.

--S 12 of 40
convergents %
 

            5 7 12 55 342 739 1820 239159
   (12)  [2,-,-,--,--,---,---,----,------]
            2 3  5 23 143 309  761 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R            5 7 12 55 342 739 1820 239159
--R   (12)  [2,-,-,--,--,---,---,----,------]
--R            2 3  5 23 143 309  761 100000
--R                                                Type: Stream Fraction Integer
--E 12 
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Continued fractions over other Euclidean domains
--S 13 of 40
a0 := ((-122 + 597* %i)/(4 - 4*%i))
 

          719   475
   (1)  - --- + --- %i
           8     8
                                               Type: Complex Fraction Integer
--R 
--R
--R          719   475
--R   (1)  - --- + --- %i
--R           8     8
--R                                               Type: Complex Fraction Integer
--E 13

--S 14 of 40
b0 := ((-595 - %i)/(3 - 4*%i))
 

          1781   2383
   (2)  - ---- - ---- %i
           25     25
                                               Type: Complex Fraction Integer
--R 
--R
--R          1781   2383
--R   (2)  - ---- - ---- %i
--R           25     25
--R                                               Type: Complex Fraction Integer
--E 14

--S 15 of 40
a  := continuedFraction(a0)
 

                           1    |         1     |
   (3)  - 90 + 59%i + +---------+ + +-----------+
                      | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                           1    |         1     |
--R   (3)  - 90 + 59%i + +---------+ + +-----------+
--R                      | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 15

--S 16 of 40
b  := continuedFraction(b0)
 

                            1     |      1  |
   (4)  - 71 - 95%i + +-----------+ + +-----+
                      | - 1 + 2%i     | - 2
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1     |      1  |
--R   (4)  - 71 - 95%i + +-----------+ + +-----+
--R                      | - 1 + 2%i     | - 2
--R                                      Type: ContinuedFraction Complex Integer
--E 16

--S 17 of 40
a + b
 

                             1     |      1  |        1     |
   (5)  - 161 - 36%i + +-----------+ + +-----+ + +----------+
                       | - 7 - 3%i     | 2%i     | - 1 - %i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                             1     |      1  |        1     |
--R   (5)  - 161 - 36%i + +-----------+ + +-----+ + +----------+
--R                       | - 7 - 3%i     | 2%i     | - 1 - %i
--R                                      Type: ContinuedFraction Complex Integer
--E 17

--S 18 of 40
convergents % 
 

                      - 1020 - 735%i - 2004 - 1631%i 362 - 4655%i
   (6)  [- 161 - 36%i,--------------,---------------,------------]
                          7 + 3%i        14 + 7%i      4 + 28%i
                                        Type: Stream Fraction Complex Integer
--R 
--R
--R                      - 1020 - 735%i - 2004 - 1631%i 362 - 4655%i
--R   (6)  [- 161 - 36%i,--------------,---------------,------------]
--R                          7 + 3%i        14 + 7%i      4 + 28%i
--R                                        Type: Stream Fraction Complex Integer
--E 18

--S 19 of 40
last % - (a0 + b0)
 

   (7)  0
                                               Type: Complex Fraction Integer
--R 
--R
--R   (7)  0
--R                                               Type: Complex Fraction Integer
--E 19

--S 20 of 40
a / b
 

   (8)
                 1    |     1 |        1     |        1     |      1  |
     - %i + +---------+ + +---+ + +----------+ + +----------+ + +-----+
            | 4 - 8%i     | 3     | - 4 - %i     | - 2 - %i     | 3%i
   + 
          1    |
     +---------+
     | 2 + 4%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (8)
--R                 1    |     1 |        1     |        1     |      1  |
--R     - %i + +---------+ + +---+ + +----------+ + +----------+ + +-----+
--R            | 4 - 8%i     | 3     | - 4 - %i     | - 2 - %i     | 3%i
--R   + 
--R          1    |
--R     +---------+
--R     | 2 + 4%i
--R                                      Type: ContinuedFraction Complex Integer
--E 20

--E 21
convergents %
 

   (9)
         4 - 7%i 13 - 21%i 69 - 64%i  215 - 80%i 709 - 171%i 2279 - 2022%i
   [- %i,-------,---------,---------,-----------,-----------,-------------]
         8 + 4%i 24 + 13%i 75 + 72%i 102 + 232%i 234 + 771%i 2376 + 2384%i
                                        Type: Stream Fraction Complex Integer
--R 
--R
--R   (9)
--R         4 - 7%i 13 - 21%i 69 - 64%i  215 - 80%i 709 - 171%i 2279 - 2022%i
--R   [- %i,-------,---------,---------,-----------,-----------,-------------]
--R         8 + 4%i 24 + 13%i 75 + 72%i 102 + 232%i 234 + 771%i 2376 + 2384%i
--R                                        Type: Stream Fraction Complex Integer
--E 21

--S 22 of 40
last % - (a0/b0)
 

   (10)  0
                                               Type: Complex Fraction Integer
--R 
--R
--R   (10)  0
--R                                               Type: Complex Fraction Integer
--E 22

--S 23 of 40
(a = b)::Boolean
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 32

--S 24 of 40
c := continuedFraction(3 + 4*%i, repeating [1 + %i], repeating [5 - %i])
 

   (12)
                 1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
     3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
               | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
   + 
       1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
     +--------+ + +--------+ + +--------+ + +--------+ + +--------+ + ...
     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (12)
--R                 1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
--R     3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
--R               | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
--R   + 
--R       1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
--R     +--------+ + +--------+ + +--------+ + +--------+ + +--------+ + ...
--R     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
--R                                      Type: ContinuedFraction Complex Integer
--E 24

--S 25 of 40
a/c
 

   (13)
                        1     |          1      |        1     |         1     |
     - 1 + 20%i + +-----------+ + +-------------+ + +----------+ + +-----------+
                  | - 1 - 2%i     | - 11 - 16%i     | - 1 + %i     | - 9 - 2%i
   + 
          1    |      1  |        1    |      1  |         1     |        1    |
     +---------+ + +-----+ + +---------+ + +-----+ + +-----------+ + +---------+
     | 1 + 2%i     | 2%i     | 8 - 2%i     | - 2     | - 1 + 8%i     | 3 - 3%i
   + 
     ...
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (13)
--R                        1     |          1      |        1     |         1     |
--R     - 1 + 20%i + +-----------+ + +-------------+ + +----------+ + +-----------+
--R                  | - 1 - 2%i     | - 11 - 16%i     | - 1 + %i     | - 9 - 2%i
--R   + 
--R          1    |      1  |        1    |      1  |         1     |        1    |
--R     +---------+ + +-----+ + +---------+ + +-----+ + +-----------+ + +---------+
--R     | 1 + 2%i     | 2%i     | 8 - 2%i     | - 2     | - 1 + 8%i     | 3 - 3%i
--R   + 
--R     ...
--R                                      Type: ContinuedFraction Complex Integer
--E 25

-- (a = c)::Boolean -- should give error

--S 26 of 40
d := complete continuedFraction(3+4*%i, repeating [1+%i],[i-%i for i in 1..5])
 

   (14)
               1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
   3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
             | 1 - %i     | 2 - %i     | 3 - %i     | 4 - %i     | 5 - %i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (14)
--R               1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
--R   3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
--R             | 1 - %i     | 2 - %i     | 3 - %i     | 4 - %i     | 5 - %i
--R                                      Type: ContinuedFraction Complex Integer
--E 26

--S 27 of 40
(a = d)::Boolean
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 27

--S 28 of 40
q : Fraction UnivariatePolynomial('x, Fraction Integer) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 40
q := (2*x**2 - x + 1) / (3*x**3 - x + 8)
 

         2  2   1     1
         - x  - - x + -
         3      3     3
   (17)  --------------
           3   1     8
          x  - - x + -
               3     3
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R         2  2   1     1
--R         - x  - - x + -
--R         3      3     3
--R   (17)  --------------
--R           3   1     8
--R          x  - - x + -
--R               3     3
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 29

--S 30  of 40
c := continuedFraction q
 

              1    |          1      |            1        |
   (18)  +---------+ + +-------------+ + +-----------------+
         | 3     3     |   8     204     |    343     1421
         | - x + -     | - - x - ---     | - ---- x + ----
         | 2     4     |   7      49     |   6112     6112
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R              1    |          1      |            1        |
--R   (18)  +---------+ + +-------------+ + +-----------------+
--R         | 3     3     |   8     204     |    343     1421
--R         | - x + -     | - - x - ---     | - ---- x + ----
--R         | 2     4     |   7      49     |   6112     6112
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 30

--S 31 of 40
d := continuedFraction differentiate q
 

   (19)
              1         |          1       |               1            |
     +------------------+ + +--------------+ + +------------------------+
     |   3  2   3     9     |    1      47     |   69696     6381055032
     | - - x  - - x + -     | - -- x + ---     | - ----- x - ----------
     |   2      2     4     |   11     264     |   32963     1086559369
   + 
                            1                      |
     +---------------------------------------------+
     |    35816256480347      79911907817759707445
     | - --------------- x + ---------------------
     |   218199728406528     307361810626373910528
   + 
                                   1                              |
     +------------------------------------------------------------+
     |   39359803441398779644674048     9259889268740766802477056
     | - -------------------------- x + -------------------------
     |    1979914602262093317951025     1979914602262093317951025
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (19)
--R              1         |          1       |               1            |
--R     +------------------+ + +--------------+ + +------------------------+
--R     |   3  2   3     9     |    1      47     |   69696     6381055032
--R     | - - x  - - x + -     | - -- x + ---     | - ----- x - ----------
--R     |   2      2     4     |   11     264     |   32963     1086559369
--R   + 
--R                            1                      |
--R     +---------------------------------------------+
--R     |    35816256480347      79911907817759707445
--R     | - --------------- x + ---------------------
--R     |   218199728406528     307361810626373910528
--R   + 
--R                                   1                              |
--R     +------------------------------------------------------------+
--R     |   39359803441398779644674048     9259889268740766802477056
--R     | - -------------------------- x + -------------------------
--R     |    1979914602262093317951025     1979914602262093317951025
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 31

--S 32 of 40
c/d
 

   (20)
           1         1     |              1          |
     - x - - + +-----------+ + +---------------------+
           2   | 6     219     |  686       83926465
               | - x + ---     | ----- x - ---------
               | 7      49     | 20131     405257161
   + 
                        1                  |
     +-------------------------------------+
     |   8158231908091     299222030081511
     | - ------------- x - ---------------
     |    268162004432     350018456284868
   + 
                              1                        |
     +-------------------------------------------------+
     |    7309785441053183312      1206863637270224864
     | - -------------------- x + --------------------
     |   30383172810229285385     30383172810229285385
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (20)
--R           1         1     |              1          |
--R     - x - - + +-----------+ + +---------------------+
--R           2   | 6     219     |  686       83926465
--R               | - x + ---     | ----- x - ---------
--R               | 7      49     | 20131     405257161
--R   + 
--R                        1                  |
--R     +-------------------------------------+
--R     |   8158231908091     299222030081511
--R     | - ------------- x - ---------------
--R     |    268162004432     350018456284868
--R   + 
--R                              1                        |
--R     +-------------------------------------------------+
--R     |    7309785441053183312      1206863637270224864
--R     | - -------------------- x + --------------------
--R     |   30383172810229285385     30383172810229285385
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 32

--S 33 of 40
convergents %
 

   (21)
                2   40     121     3   14615  2   114691     168376
             - x  - -- x - ---  - x  + ----- x  - ------ x - ------
          1          7      84         40262      120786      20131
   [- x - -, -----------------, -----------------------------------,
          2            73               2   17373     307727
                   x + --              x  - ----- x + ------
                       14                   20131     120786
       4    3497  3    791   2   15030     18082
    - x  + ----- x  + ----- x  - ----- x + -----
           10442      31326       5221     15663
    --------------------------------------------,
            3   4359  2   48833     25886
           x  - ---- x  + ----- x - -----
                5221      31326      5221
       5   1  4   1  3   17  2   3     4
    - x  + - x  - - x  - -- x  + - x - -
           2      6       6      2     3
    ------------------------------------]
          4    3   11  2   16     7
         x  - x  + -- x  - -- x + -
                    6       3     6
               Type: Stream Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (21)
--R                2   40     121     3   14615  2   114691     168376
--R             - x  - -- x - ---  - x  + ----- x  - ------ x - ------
--R          1          7      84         40262      120786      20131
--R   [- x - -, -----------------, -----------------------------------,
--R          2            73               2   17373     307727
--R                   x + --              x  - ----- x + ------
--R                       14                   20131     120786
--R       4    3497  3    791   2   15030     18082
--R    - x  + ----- x  + ----- x  - ----- x + -----
--R           10442      31326       5221     15663
--R    --------------------------------------------,
--R            3   4359  2   48833     25886
--R           x  - ---- x  + ----- x - -----
--R                5221      31326      5221
--R       5   1  4   1  3   17  2   3     4
--R    - x  + - x  - - x  - -- x  + - x - -
--R           2      6       6      2     3
--R    ------------------------------------]
--R          4    3   11  2   16     7
--R         x  - x  + -- x  - -- x + -
--R                    6       3     6
--R               Type: Stream Fraction UnivariatePolynomial(x,Fraction Integer)
--E 33

--S 34 of 40
q/differentiate q
 

            5   1  4   1  3   17  2   3     4
         - x  + - x  - - x  - -- x  + - x - -
                2      6       6      2     3
   (22)  ------------------------------------
               4    3   11  2   16     7
              x  - x  + -- x  - -- x + -
                         6       3     6
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R            5   1  4   1  3   17  2   3     4
--R         - x  + - x  - - x  - -- x  + - x - -
--R                2      6       6      2     3
--R   (22)  ------------------------------------
--R               4    3   11  2   16     7
--R              x  - x  + -- x  - -- x + -
--R                         6       3     6
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 34

)clear all
 
   All user variables and function definitions have been cleared.

)set streams calculate 7
 

--S 35 of 40
s := continuedFraction(0, expand [1..], expand [1..])
 

          1 |     2 |     3 |     4 |     5 |     6 |     7 |
   (1)  +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
        | 1     | 2     | 3     | 4     | 5     | 6     | 7
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     2 |     3 |     4 |     5 |     6 |     7 |
--R   (1)  +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
--R        | 1     | 2     | 3     | 4     | 5     | 6     | 7
--R                                              Type: ContinuedFraction Integer
--E 35

--S 36 of 40
t := reducedContinuedFraction(0, [4*i-2 for i in 1..])
 

          1 |     1 |     1  |     1  |     1  |     1  |     1  |
   (2)  +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + ...
        | 2     | 6     | 10     | 14     | 18     | 22     | 26
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1  |     1  |     1  |     1  |
--R   (2)  +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + ...
--R        | 2     | 6     | 10     | 14     | 18     | 22     | 26
--R                                              Type: ContinuedFraction Integer
--E 36

--S 37 of 40
e := 1/(s*t) - 1
 

              1 |     1 |     1 |     1 |     1 |     1 |     1 |
   (3)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
            | 1     | 2     | 1     | 1     | 4     | 1     | 1
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R   (3)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
--R            | 1     | 2     | 1     | 1     | 4     | 1     | 1
--R                                              Type: ContinuedFraction Integer
--E 37

--S 38 of 40
c := convergents e
 

             8 11 19 87 106
   (4)  [2,3,-,--,--,--,---,...]
             3  4  7 32  39
                                                Type: Stream Fraction Integer
--R 
--R
--R             8 11 19 87 106
--R   (4)  [2,3,-,--,--,--,---,...]
--R             3  4  7 32  39
--R                                                Type: Stream Fraction Integer
--E 38

--S 39 of 40
for i in 1..15 repeat
  output numeric c.i
 
   2.0
   3.0
   2.6666666666 666666667
   2.75
   2.7142857142 857142857
   2.71875
   2.7179487179 487179487
   2.7183098591 549295775
   2.7182795698 924731183
   2.7182835820 895522388
   2.7182817182 817182817
   2.7182818352 059925094
   2.7182818229 439497119
   2.7182818287 356957267
   2.7182818284 45401318
                                                                   Type: Void
--R 
--R   2.0
--R   3.0
--R   2.6666666666 666666667
--R   2.75
--R   2.7142857142 857142857
--R   2.71875
--R   2.7179487179 487179487
--R   2.7183098591 549295775
--R   2.7182795698 924731183
--R   2.7182835820 895522388
--R   2.7182817182 817182817
--R   2.7182818352 059925094
--R   2.7182818229 439497119
--R   2.7182818287 356957267
--R   2.7182818284 45401318
--R                                                                   Type: Void
--E 39

--S 40 of 40
(s = t)::Boolean
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 40
)spool
 
Starts dribbling to infprod.output (2009/2/17, 17:46:38).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 11
f : UTS(INT,x,0) := 1 - x
 

   (1)  1 - x
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (1)  1 - x
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 1

--S 2 of 11
g : UTS(INT,x,0) := recip f
 

                 2    3    4    5    6    7    8    9    10      11
   (2)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (2)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 2

--S 3 of 11
infiniteProduct g
 

   (3)
             2     3     4     5      6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 7x  + 11x  + 15x  + 22x  + 30x  + 42x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (3)
--R             2     3     4     5      6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 7x  + 11x  + 15x  + 22x  + 30x  + 42x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 3

--S 4 of 11
h := infiniteProduct(f ** 24)
 

   (4)
                   2        3        4        5         6         7          8
     1 - 24x + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
   + 
              9          10      11
     - 115920x  + 534612x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (4)
--R                   2        3        4        5         6         7          8
--R     1 - 24x + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
--R   + 
--R              9          10      11
--R     - 115920x  + 534612x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 4

--S 5 of 11
delta := x * h
 

   (5)
            2       3        4        5        6         7         8          9
     x - 24x  + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
   + 
              10      11
     - 115920x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (5)
--R            2       3        4        5        6         7         8          9
--R     x - 24x  + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
--R   + 
--R              10      11
--R     - 115920x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 5

--S 6 of 11
coefficient(delta,21)
 

   (6)  - 4219488
                                                                Type: Integer
--R 
--R
--R   (6)  - 4219488
--R                                                                Type: Integer
--E 6

--S 7 of 11
coefficient(delta,3) * coefficient(delta,7)
 

   (7)  - 4219488
                                                                Type: Integer
--R 
--R
--R   (7)  - 4219488
--R                                                                Type: Integer
--E 7

--S 8 of 11
coefficient(delta,20)
 

   (8)  - 7109760
                                                                Type: Integer
--R 
--R
--R   (8)  - 7109760
--R                                                                Type: Integer
--E 8

--S 9 of 11
coefficient(delta,4) * coefficient(delta,5)
 

   (9)  - 7109760
                                                                Type: Integer
--R 
--R
--R   (9)  - 7109760
--R                                                                Type: Integer
--E 9

--S 10 of 11
coefficient(delta,65)
 

   (10)  - 2790474540
                                                                Type: Integer
--R 
--R
--R   (10)  - 2790474540
--R                                                                Type: Integer
--E 10

--S 11 of 11
coefficient(delta,13) * coefficient(delta,5)
 

   (11)  - 2790474540
                                                                Type: Integer
--R 
--R
--R   (11)  - 2790474540
--R                                                                Type: Integer
--E 11
)spool 
 
Starts dribbling to card.output (2009/2/17, 17:44:7).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 20
c0 := 0 :: CardinalNumber
 

   (1)  0
                                                         Type: CardinalNumber
--R 
--R
--R   (1)  0
--R                                                         Type: CardinalNumber
--E 1

--S 2 of 20
c1 := 1 :: CardinalNumber
 

   (2)  1
                                                         Type: CardinalNumber
--R 
--R
--R   (2)  1
--R                                                         Type: CardinalNumber
--E 2

--S 3 of 20
c2 := 2 :: CardinalNumber
 

   (3)  2
                                                         Type: CardinalNumber
--R 
--R
--R   (3)  2
--R                                                         Type: CardinalNumber
--E 3

--S 4 of 20
c3 := 3 :: CardinalNumber
 

   (4)  3
                                                         Type: CardinalNumber
--R 
--R
--R   (4)  3
--R                                                         Type: CardinalNumber
--E 4

--S 5 of 20
A0 := Aleph 0
 

   (5)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (5)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 5

--S 6 of 20
A1 := Aleph 1
 

   (6)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (6)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 6

--S 7 of 20
finite? c2
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 20
finite? A0
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 20
countable? c2
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 20
countable? A0
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 20
countable? A1
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 20
[c2 + c2, c2 + A1]
 

   (12)  [4,Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (12)  [4,Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 12

--S 13 of 20
[c0*c2, c1*c2, c2*c2, c0*A1, c1*A1, c2*A1, A0*A1]
 

   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 13

--S 14 of 20
[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]
 

   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 14

--S 15 of 20
[c2-c1, c2-c2, c2-c3, A1-c2, A1-A0, A1-A1]
 

   (15)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
                                    Type: List Union(CardinalNumber,"failed")
--R 
--R
--R   (15)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
--R                                    Type: List Union(CardinalNumber,"failed")
--E 15

--S 16 of 20
generalizedContinuumHypothesisAssumed true
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 20
[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1]
 

   (17)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (17)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
--R                                                    Type: List CardinalNumber
--E 17

--S 18 of 20
a := Aleph 0
 

   (18)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (18)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 18

--S 19 of 20
c := 2**a
 

   (19)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (19)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 19

--S 20 of 20
f := 2**c
 

   (20)  Aleph(2)
                                                         Type: CardinalNumber
--R 
--R
--R   (20)  Aleph(2)
--R                                                         Type: CardinalNumber
--E 20
)spool
 
Starts dribbling to ffx72.output (2009/2/17, 17:46:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 

--S 1  of 13
gf72 := FF(7, 2)
 

   (1)  FiniteField(7,2)
                                                                 Type: Domain
--R 
--R
--R   (1)  FiniteField(7,2)
--R                                                                 Type: Domain
--E 1

--S 2 of 13
u: UP(x,PF 7) := x**2 + 1
 

         2
   (2)  x  + 1
                                   Type: UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R         2
--R   (2)  x  + 1
--R                                   Type: UnivariatePolynomial(x,PrimeField 7)
--E 2

--S 3 of 13
factor u
 

         2
   (3)  x  + 1
                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R         2
--R   (3)  x  + 1
--R                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--E 3 

--S 4 of 13
u2 : UP(x,gf72) := u
 

         2
   (4)  x  + 1
                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R         2
--R   (4)  x  + 1
--R                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--E 4

--S 5 of 13
factor u2
 

   (5)  (x + %A)(x + 6%A)
                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R   (5)  (x + %A)(x + 6%A)
--R                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--E 5

--S 6 of 13
definingPolynomial()$gf72
 

         2
   (6)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R         2
--R   (6)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 6

--S 7 of 13
e := index(size()$gf72 quo 3)$gf72
 

   (7)  2%A + 2
                                                       Type: FiniteField(7,2)
--R 
--R
--R   (7)  2%A + 2
--R                                                       Type: FiniteField(7,2)
--E 7

--S 8 of 13
norm e
 

   (8)  1
                                                           Type: PrimeField 7
--R 
--R
--R   (8)  1
--R                                                           Type: PrimeField 7
--E 8

--S 9 of 13
trace e
 

   (9)  4
                                                           Type: PrimeField 7
--R 
--R
--R   (9)  4
--R                                                           Type: PrimeField 7
--E 9

--S 10  of 13
order e
 

   (10)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  8
--R                                                        Type: PositiveInteger
--E 10

--S 11  of 13
allElts := [index(i :: PI)$gf72 for i in 1..48]
 

   (11)
   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
    6%A + 5, 6%A + 6]
                                                  Type: List FiniteField(7,2)
--R 
--R
--R   (11)
--R   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
--R    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
--R    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
--R    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
--R    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
--R    6%A + 5, 6%A + 6]
--R                                                  Type: List FiniteField(7,2)
--E 11

--S 12  of 13
reduce(+,allElts)
 

   (12)  0
                                                       Type: FiniteField(7,2)
--R 
--R
--R   (12)  0
--R                                                       Type: FiniteField(7,2)
--E 12 
--S 13 of 13
[order e for e in allElts]
 

   (13)
   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
    48, 4, 24, 48, 48, 48, 48, 24]
                                                   Type: List PositiveInteger
--R 
--R
--R   (13)
--R   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
--R    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
--R    48, 4, 24, 48, 48, 48, 48, 24]
--R                                                   Type: List PositiveInteger
--E 13
)spool 
 
Starts dribbling to ico.output (2009/2/17, 17:46:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 65
)se exp add con InnerTrigonometricManipulations
 
   InnerTrigonometricManipulations is now explicitly exposed in frame 
      initial 
--R 
--R   InnerTrigonometricManipulations is now explicitly exposed in frame 
--R      initial 
--E 1

--S 2 of 65
exp(%i*2*%pi/5)
 

          2%i %pi
          -------
             5
   (1)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R          2%i %pi
--R          -------
--R             5
--R   (1)  %e
--R                                             Type: Expression Complex Integer
--E 2

--S 3 of 65
FG2F %
 

               +---+
          2%pi\|- 1
          ----------
               5
   (2)  %e
                                                     Type: Expression Integer
--R 
--R
--R               +---+
--R          2%pi\|- 1
--R          ----------
--R               5
--R   (2)  %e
--R                                                     Type: Expression Integer
--E 3

--S 4 of 65
% -1
 

               +---+
          2%pi\|- 1
          ----------
               5
   (3)  %e           - 1
                                                     Type: Expression Integer
--R 
--R
--R               +---+
--R          2%pi\|- 1
--R          ----------
--R               5
--R   (3)  %e           - 1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 65
complexForm %
 

            2%pi            2%pi
   (4)  cos(----) - 1 + sin(----)%i
              5               5
                                             Type: Complex Expression Integer
--R 
--R
--R            2%pi            2%pi
--R   (4)  cos(----) - 1 + sin(----)%i
--R              5               5
--R                                             Type: Complex Expression Integer
--E 5

--S 6 of 65
norm %
 

            2%pi 2       2%pi 2        2%pi
   (5)  sin(----)  + cos(----)  - 2cos(----) + 1
              5            5             5
                                                     Type: Expression Integer
--R 
--R
--R            2%pi 2       2%pi 2        2%pi
--R   (5)  sin(----)  + cos(----)  - 2cos(----) + 1
--R              5            5             5
--R                                                     Type: Expression Integer
--E 6

--S 7 of 65
simplify %
 

               2%pi
   (6)  - 2cos(----) + 2
                 5
                                                     Type: Expression Integer
--R 
--R
--R               2%pi
--R   (6)  - 2cos(----) + 2
--R                 5
--R                                                     Type: Expression Integer
--E 7

--S 8 of 65
s:=sqrt %
 

         +----------------+
         |       2%pi
   (7)   |- 2cos(----) + 2
        \|         5
                                                     Type: Expression Integer
--R 
--R
--R         +----------------+
--R         |       2%pi
--R   (7)   |- 2cos(----) + 2
--R        \|         5
--R                                                     Type: Expression Integer
--E 8

--S 9 of 65
ph:=exp(%i*2*%pi/5)
 

          2%i %pi
          -------
             5
   (8)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R          2%i %pi
--R          -------
--R             5
--R   (8)  %e
--R                                             Type: Expression Complex Integer
--E 9

--S 10 of 65
A1:=complex(1,0)
 

   (9)  1
                                                        Type: Complex Integer
--R 
--R
--R   (9)  1
--R                                                        Type: Complex Integer
--E 10

--S 11 of 65
A2:=A1*ph
 

           2%i %pi
           -------
              5
   (10)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R           2%i %pi
--R           -------
--R              5
--R   (10)  %e
--R                                             Type: Expression Complex Integer
--E 11

--S 12 of 65
A3:=A2*ph
 

            2%i %pi 2
            -------
               5
   (11)  (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R            2%i %pi 2
--R            -------
--R               5
--R   (11)  (%e       )
--R                                             Type: Expression Complex Integer
--E 12

--S 13 of 65
A4:=A3*ph
 

            2%i %pi 3
            -------
               5
   (12)  (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R            2%i %pi 3
--R            -------
--R               5
--R   (12)  (%e       )
--R                                             Type: Expression Complex Integer
--E 13

--S 14 of 65
A5:=A4*ph
 

            2%i %pi 4
            -------
               5
   (13)  (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R            2%i %pi 4
--R            -------
--R               5
--R   (13)  (%e       )
--R                                             Type: Expression Complex Integer
--E 14

--S 15 of 65
ca1:=map(numeric , complexForm FG2F simplify A1)
 

   (14)  1.0
                                                          Type: Complex Float
--R 
--R
--R   (14)  1.0
--R                                                          Type: Complex Float
--E 15

--S 16 of 65
ca2:=map(numeric , complexForm FG2F simplify A2)
 

   (15)  0.3090169943 749474241 + 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (15)  0.3090169943 749474241 + 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 16

--S 17 of 65
ca3:=map(numeric ,complexForm FG2F simplify A3)
 

   (16)  - 0.8090169943 749474241 + 0.5877852522 9247312917 %i
                                                          Type: Complex Float
--R 
--R
--R   (16)  - 0.8090169943 749474241 + 0.5877852522 9247312917 %i
--R                                                          Type: Complex Float
--E 17

--S 18 of 65
ca4:=map(numeric ,complexForm FG2F simplify A4)
 

   (17)  - 0.8090169943 7494742411 - 0.5877852522 9247312917 %i
                                                          Type: Complex Float
--R 
--R
--R   (17)  - 0.8090169943 7494742411 - 0.5877852522 9247312917 %i
--R                                                          Type: Complex Float
--E 18

--S 19 of 65
ca5:=map(numeric ,complexForm FG2F simplify A5)
 

   (18)  0.3090169943 749474241 - 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (18)  0.3090169943 749474241 - 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 19

--S 20 of 65
B1:=A1*exp(2*%i*%pi/10)
 

           %i %pi
           ------
              5
   (19)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi
--R           ------
--R              5
--R   (19)  %e
--R                                             Type: Expression Complex Integer
--E 20

--S 21 of 65
B2:=B1*ph
 

           %i %pi  2%i %pi
           ------  -------
              5       5
   (20)  %e      %e
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi  2%i %pi
--R           ------  -------
--R              5       5
--R   (20)  %e      %e
--R                                             Type: Expression Complex Integer
--E 21

--S 22 of 65
B3:=B2*ph
 

           %i %pi   2%i %pi 2
           ------   -------
              5        5
   (21)  %e      (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi   2%i %pi 2
--R           ------   -------
--R              5        5
--R   (21)  %e      (%e       )
--R                                             Type: Expression Complex Integer
--E 22

--S 23 of 65
B4:=B3*ph
 

           %i %pi   2%i %pi 3
           ------   -------
              5        5
   (22)  %e      (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi   2%i %pi 3
--R           ------   -------
--R              5        5
--R   (22)  %e      (%e       )
--R                                             Type: Expression Complex Integer
--E 23

--S 24 of 65
B5:=B4*ph
 

           %i %pi   2%i %pi 4
           ------   -------
              5        5
   (23)  %e      (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi   2%i %pi 4
--R           ------   -------
--R              5        5
--R   (23)  %e      (%e       )
--R                                             Type: Expression Complex Integer
--E 24

--S 25 of 65
cb1:=map (numeric ,complexForm FG2F simplify B1)
 

   (24)  0.8090169943 749474241 + 0.5877852522 9247312917 %i
                                                          Type: Complex Float
--R 
--R
--R   (24)  0.8090169943 749474241 + 0.5877852522 9247312917 %i
--R                                                          Type: Complex Float
--E 25

--S 26 of 65
cb2:=map (numeric ,complexForm FG2F simplify B2)
 

   (25)  - 0.3090169943 749474241 + 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (25)  - 0.3090169943 749474241 + 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 26

--S 27 of 65
cb3:=map (numeric ,complexForm FG2F simplify B3)
 

   (26)  - 1.0
                                                          Type: Complex Float
--R 
--R
--R   (26)  - 1.0
--R                                                          Type: Complex Float
--E 27

--S 28 of 65
cb4:=map (numeric ,complexForm FG2F simplify B4)
 

   (27)  - 0.3090169943 7494742409 - 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (27)  - 0.3090169943 7494742409 - 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 28

--S 29 of 65
cb5:=map (numeric ,complexForm FG2F simplify B5)
 

   (28)  0.8090169943 7494742411 - 0.5877852522 9247312916 %i
                                                          Type: Complex Float
--R 
--R
--R   (28)  0.8090169943 7494742411 - 0.5877852522 9247312916 %i
--R                                                          Type: Complex Float
--E 29

--S 30 of 65
u:=numeric sqrt(s*s-1)
 

   (29)  0.6180339887 4989484821
                                                                  Type: Float
--R 
--R
--R   (29)  0.6180339887 4989484821
--R                                                                  Type: Float
--E 30

--S 31 of 65
p0:=point([0,0,u+1/2])@Point(SF)
 

   (30)  [0.0,0.0,1.1180339887498947]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (30)  [0.,0.,1.1180339887498949]
--R                                                      Type: Point DoubleFloat
--E 31

--S 32 of 65
p1:=point([real ca1,imag ca1,0.5])@Point(SF)
 

   (31)  [1.0,0.0,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (31)  [1.,0.,0.5]
--R                                                      Type: Point DoubleFloat
--E 32

--S 33 of 65
p2:=point([real ca2,imag ca2,0.5])@Point(SF)
 

   (32)  [0.3090169943749474,0.95105651629515353,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (32)  [0.30901699437494745,0.95105651629515353,0.5]
--R                                                      Type: Point DoubleFloat
--E 33

--S 34 of 65
p2:=point([real ca2,imag ca2,0.5])@Point(SF)
 

   (33)  [0.3090169943749474,0.95105651629515353,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (33)  [0.30901699437494745,0.95105651629515353,0.5]
--R                                                      Type: Point DoubleFloat
--E 34

--S 35 of 65
p3:=point([real ca3,imag ca3,0.5])@Point(SF)
 

   (34)  [- 0.80901699437494734,0.58778525229247303,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (34)  [- 0.80901699437494745,0.58778525229247314,0.5]
--R                                                      Type: Point DoubleFloat
--E 35

--S 36 of 65
p4:=point([real ca4,imag ca4,0.5])@Point(SF)
 

   (35)  [- 0.80901699437494734,- 0.58778525229247303,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (35)  [- 0.80901699437494745,- 0.58778525229247314,0.5]
--R                                                      Type: Point DoubleFloat
--E 36

--S 37 of 65
p5:=point([real ca5,imag ca5,0.5])@Point(SF)
 

   (36)  [0.3090169943749474,- 0.95105651629515353,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (36)  [0.30901699437494745,- 0.95105651629515353,0.5]
--R                                                      Type: Point DoubleFloat
--E 37

--S 38 of 65
p6:=point([real cb1,imag cb1,-0.5])@Point(SF)
 

   (37)  [0.80901699437494734,0.58778525229247303,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (37)  [0.80901699437494745,0.58778525229247314,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 38

--S 39 of 65
p7:=point([real cb2,imag cb2,-0.5])@Point(SF)
 

   (38)  [- 0.3090169943749474,0.95105651629515353,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (38)  [- 0.30901699437494745,0.95105651629515353,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 39

--S 40 of 65
p8:=point([real cb3,imag cb3,-0.5])@Point(SF)
 

   (39)  [- 1.0,0.0,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (39)  [- 1.,0.,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 40

--S 41 of 65
p9:=point([real cb4,imag cb4,-0.5])@Point(SF)
 

   (40)  [- 0.3090169943749474,- 0.95105651629515353,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (40)  [- 0.30901699437494745,- 0.95105651629515353,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 41

--S 42 of 65
p10:=point([real cb5,imag cb5,-0.5])@Point(SF)
 

   (41)  [0.80901699437494734,- 0.58778525229247303,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (41)  [0.80901699437494745,- 0.58778525229247314,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 42

--S 43 of 65
p11:=point([0,0,-u-1/2])@Point(SF)
 

   (42)  [0.0,0.0,- 1.1180339887498947]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (42)  [0.,0.,- 1.1180339887498949]
--R                                                      Type: Point DoubleFloat
--E 43

--S 44 of 65
space:=create3Space()$ThreeSpace DFLOAT
 

   (43)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (43)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 44

--S 45 of 65
polygon(space,[p0,p1,p2])
 

   (44)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (44)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 45

--S 46 of 65
polygon(space,[p0,p2,p3])
 

   (45)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (45)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 46

--S 47 of 65
polygon(space,[p0,p3,p4])
 

   (46)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (46)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 47

--S 48 of 65
polygon(space,[p0,p4,p5])
 

   (47)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (47)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 48

--S 49 of 65
polygon(space,[p0,p5,p1])
 

   (48)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (48)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 49

--S 50 of 65
polygon(space,[p1,p6,p2])
 

   (49)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (49)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 50

--S 51 of 65
polygon(space,[p2,p7,p3])
 

   (50)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (50)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 51

--S 52 of 65
polygon(space,[p3,p8,p4])
 

   (51)  3-Space with 8 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (51)  3-Space with 8 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 52

--S 53 of 65
polygon(space,[p4,p9,p5])
 

   (52)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (52)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 53

--S 54 of 65
polygon(space,[p5,p10,p1])
 

   (53)  3-Space with 10 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (53)  3-Space with 10 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 54

--S 55 of 65
polygon(space,[p2,p6,p7])
 

   (54)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (54)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 55

--S 56 of 65
polygon(space,[p3,p7,p8])
 

   (55)  3-Space with 12 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (55)  3-Space with 12 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 56

--S 57 of 65
polygon(space,[p4,p8,p9])
 

   (56)  3-Space with 13 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (56)  3-Space with 13 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 57

--S 58 of 65
polygon(space,[p5,p9,p10])
 

   (57)  3-Space with 14 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (57)  3-Space with 14 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 58

--S 59 of 65
polygon(space,[p1,p10,p6])
 

   (58)  3-Space with 15 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (58)  3-Space with 15 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 59

--S 60 of 65
polygon(space,[p6,p11,p7])
 

   (59)  3-Space with 16 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (59)  3-Space with 16 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 60

--S 61 of 65
polygon(space,[p7,p11,p8])
 

   (60)  3-Space with 17 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (60)  3-Space with 17 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 61

--S 62 of 65
polygon(space,[p8,p11,p9])
 

   (61)  3-Space with 18 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (61)  3-Space with 18 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 62

--S 63 of 65
polygon(space,[p9,p11,p10])
 

   (62)  3-Space with 19 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (62)  3-Space with 19 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 63

--S 64 of 65
polygon(space,[p10,p11,p6])
 

   (63)  3-Space with 20 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (63)  3-Space with 20 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 64

--S 65 of 65
makeViewport3D(space,title=="Icosahedron")
 
   Transmitting data...

   (64)  ThreeDimensionalViewport: "Icosahedron"
                                               Type: ThreeDimensionalViewport
--R 
--R   Transmitting data...
--R
--R   (64)  ThreeDimensionalViewport: "Icosahedron"
--R                                               Type: ThreeDimensionalViewport
--E 65
)spool 
 
Starts dribbling to bags.output (2009/2/17, 17:43:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 44
a:Stack INT:= stack [1,2,3,4,5]
 

   (1)  [1,2,3,4,5]
                                                          Type: Stack Integer
--R 
--R
--R   (1)  [1,2,3,4,5]
--R                                                          Type: Stack Integer
--E 1

--S 2 of 44
pop! a
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 44
a
 

   (3)  [2,3,4,5]
                                                          Type: Stack Integer
--R 
--R
--R   (3)  [2,3,4,5]
--R                                                          Type: Stack Integer
--E 3

--S 4 of 44
push!(9,a)
 

   (4)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  9
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 44
a
 

   (5)  [9,2,3,4,5]
                                                          Type: Stack Integer
--R 
--R
--R   (5)  [9,2,3,4,5]
--R                                                          Type: Stack Integer
--E 5

--S 6 of 44
empty? a
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 44
b:=empty()$(Stack INT)
 

   (7)  []
                                                          Type: Stack Integer
--R 
--R
--R   (7)  []
--R                                                          Type: Stack Integer
--E 7

--S 8 of 44
empty? b
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 44
c:ArrayStack INT:= arrayStack [1,2,3,4,5]
 

   (9)  [1,2,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (9)  [1,2,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 9

--S 10 of 44
pop! c
 

   (10)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  5
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 44
c
 

   (11)  [1,2,3,4]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (11)  [1,2,3,4]
--R                                                     Type: ArrayStack Integer
--E 11

--S 12 of 44
push!(9,c)
 

   (12)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  9
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 44
c
 

   (13)  [9,1,2,3,4]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (13)  [9,1,2,3,4]
--R                                                     Type: ArrayStack Integer
--E 13

--S 14 of 44
empty? c
 

   (14)  false
                                                                Type: Boolean
--R 
--R
--R   (14)  false
--R                                                                Type: Boolean
--E 14

--S 15 of 44
d:=empty()$(ArrayStack INT)
 

   (15)  []
                                                     Type: ArrayStack Integer
--R 
--R
--R   (15)  []
--R                                                     Type: ArrayStack Integer
--E 15

--S 16 of 44
empty? d
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 44
e:Queue INT:= queue [1,2,3,4,5]
 

   (17)  [1,2,3,4,5]
                                                          Type: Queue Integer
--R 
--R
--R   (17)  [1,2,3,4,5]
--R                                                          Type: Queue Integer
--E 17

--S 18 of 44
dequeue! e
 

   (18)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  1
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 44
e
 

   (19)  [2,3,4,5]
                                                          Type: Queue Integer
--R 
--R
--R   (19)  [2,3,4,5]
--R                                                          Type: Queue Integer
--E 19

--S 20 of 44
enqueue!(9,e)
 

   (20)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  9
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 44
e
 

   (21)  [2,3,4,5,9]
                                                          Type: Queue Integer
--R 
--R
--R   (21)  [2,3,4,5,9]
--R                                                          Type: Queue Integer
--E 21

--S 22 of 44
empty? e
 

   (22)  false
                                                                Type: Boolean
--R 
--R
--R   (22)  false
--R                                                                Type: Boolean
--E 22

--S 23 of 44
f:=empty()$(Queue INT)
 

   (23)  []
                                                          Type: Queue Integer
--R 
--R
--R   (23)  []
--R                                                          Type: Queue Integer
--E 23

--S 24 of 44
empty? f
 

   (24)  true
                                                                Type: Boolean
--R 
--R
--R   (24)  true
--R                                                                Type: Boolean
--E 24

--S 25 of 44
g:Dequeue INT:= dequeue [1,2,3,4,5]
 

   (25)  [1,2,3,4,5]
                                                        Type: Dequeue Integer
--R 
--R
--R   (25)  [1,2,3,4,5]
--R                                                        Type: Dequeue Integer
--E 25

--S 26 of 44
extractBottom! g
 

   (26)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  5
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 44
g
 

   (27)  [1,2,3,4]
                                                        Type: Dequeue Integer
--R 
--R
--R   (27)  [1,2,3,4]
--R                                                        Type: Dequeue Integer
--E 27

--S 28 of 44
insertBottom!(9,g)
 

   (28)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  9
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 44
g
 

   (29)  [1,2,3,4,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (29)  [1,2,3,4,9]
--R                                                        Type: Dequeue Integer
--E 29

--S 30 of 44
extractTop! g
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 44
g
 

   (31)  [2,3,4,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (31)  [2,3,4,9]
--R                                                        Type: Dequeue Integer
--E 31

--S 32 of 44
insertTop!(9,g)
 

   (32)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (32)  9
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 44
g
 

   (33)  [9,2,3,4,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (33)  [9,2,3,4,9]
--R                                                        Type: Dequeue Integer
--E 33

--S 34 of 44
empty? g
 

   (34)  false
                                                                Type: Boolean
--R 
--R
--R   (34)  false
--R                                                                Type: Boolean
--E 34

--S 35 of 44
h:=empty()$(Dequeue INT)
 

   (35)  []
                                                        Type: Dequeue Integer
--R 
--R
--R   (35)  []
--R                                                        Type: Dequeue Integer
--E 35

--S 36 of 44
empty? h
 

   (36)  true
                                                                Type: Boolean
--R 
--R
--R   (36)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 44
i:Heap INT := bag [1,6,3,7,5,2,4]
 

   (37)  [7,6,4,1,5,2,3]
                                                           Type: Heap Integer
--R 
--R
--R   (37)  [7,6,4,1,5,2,3]
--R                                                           Type: Heap Integer
--E 37

--S 38 of 44
insert!(10,i)
 

   (38)  [10,7,4,6,5,2,3,1]
                                                           Type: Heap Integer
--R 
--R
--R   (38)  [10,7,4,6,5,2,3,1]
--R                                                           Type: Heap Integer
--E 38

--S 39 of 44
i
 

   (39)  [10,7,4,6,5,2,3,1]
                                                           Type: Heap Integer
--R 
--R
--R   (39)  [10,7,4,6,5,2,3,1]
--R                                                           Type: Heap Integer
--E 39

--S 40 of 44
max i
 

   (40)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (40)  10
--R                                                        Type: PositiveInteger
--E 40

--S 41 of 44
extract! i
 

   (41)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (41)  10
--R                                                        Type: PositiveInteger
--E 41

--S 42 of 44
i
 

   (42)  [7,6,4,1,5,2,3]
                                                           Type: Heap Integer
--R 
--R
--R   (42)  [7,6,4,1,5,2,3]
--R                                                           Type: Heap Integer
--E 42

--S 43 of 44
heapsort x ==
       empty? x => []
       cons(extract! x,heapsort x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 43

--S 44 of 44
heapsort i
 
   Compiling function heapsort with type Heap Integer -> List Integer 

   (44)  [7,6,5,4,3,2,1]
                                                           Type: List Integer
--R 
--R   Compiling function heapsort with type Heap Integer -> List Integer 
--R
--R   (44)  [7,6,5,4,3,2,1]
--R                                                           Type: List Integer
--E 44
)spool
 
Starts dribbling to bop.output (2009/2/17, 17:43:59).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 17
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 17
deq := D(y x, x, 2) + D(y x, x) + y x = 0
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 17
nary? y
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 17
unary? y
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 17
opOne := operator('opOne, 1)
 

   (5)  opOne
                                                          Type: BasicOperator
--R 
--R
--R   (5)  opOne
--R                                                          Type: BasicOperator
--E 5

--S 6 of 17
nary? opOne
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 17
unary? opOne
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 17
arity opOne
 

   (8)  1
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (8)  1
--R                                          Type: Union(NonNegativeInteger,...)
--E 8

--S 9 of 17
name opOne
 

   (9)  opOne
                                                                 Type: Symbol
--R 
--R
--R   (9)  opOne
--R                                                                 Type: Symbol
--E 9

--S 10 of 17
is?(opOne, 'z2)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 17
is?(opOne, "opOne")
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 17
properties y
 

   (12)  table()
                                           Type: AssociationList(String,None)
--R 
--R
--R   (12)  table()
--R                                           Type: AssociationList(String,None)
--E 12

--S 13 of 17
setProperty(y, "use", "unknown function" :: None )
 

   (13)  y
                                                          Type: BasicOperator
--R 
--R
--R   (13)  y
--R                                                          Type: BasicOperator
--E 13

--S 14 of 17
properties y
 

   (14)  table("use"= NONE)
                                           Type: AssociationList(String,None)
--R 
--R
--R   (14)  table("use"= NONE)
--R                                           Type: AssociationList(String,None)
--E 14

--S 15 of 17
property(y, "use") :: None pretend String
 

   (15)  "unknown function"
                                                                 Type: String
--R 
--R
--R   (15)  "unknown function"
--R                                                                 Type: String
--E 15

--S 16 of 17
deleteProperty!(y, "use")
 

   (16)  y
                                                          Type: BasicOperator
--R 
--R
--R   (16)  y
--R                                                          Type: BasicOperator
--E 16

--S 17 of 17
properties y
 

   (17)  table()
                                           Type: AssociationList(String,None)
--R 
--R
--R   (17)  table()
--R                                           Type: AssociationList(String,None)
--E 17
)spool
 
Starts dribbling to octonion.output (2009/2/17, 17:55:49).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 39
e0:Octonion(Fraction(Integer)):=octon(1,0,0,0,0,0,0,0)
 

   (1)  1
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (1)  1
--R                                              Type: Octonion Fraction Integer
--E 1

--S 2 of 39
e1:Octonion(Fraction(Integer)):=octon(0,1,0,0,0,0,0,0)
 

   (2)  i
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (2)  i
--R                                              Type: Octonion Fraction Integer
--E 2

--S 3 of 39
e2:Octonion(Fraction(Integer)):=octon(0,0,1,0,0,0,0,0)
 

   (3)  j
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (3)  j
--R                                              Type: Octonion Fraction Integer
--E 3

--S 4 of 39
e3:Octonion(Fraction(Integer)):=octon(0,0,0,1,0,0,0,0)
 

   (4)  k
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (4)  k
--R                                              Type: Octonion Fraction Integer
--E 4

--S 5 of 39
e4:Octonion(Fraction(Integer)):=octon(0,0,0,0,1,0,0,0)
 

   (5)  E
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (5)  E
--R                                              Type: Octonion Fraction Integer
--E 5

--S 6 of 39
e5:Octonion(Fraction(Integer)):=octon(0,0,0,0,0,1,0,0)
 

   (6)  I
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (6)  I
--R                                              Type: Octonion Fraction Integer
--E 6

--S 7 of 39
e6:Octonion(Fraction(Integer)):=octon(0,0,0,0,0,0,1,0)
 

   (7)  J
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (7)  J
--R                                              Type: Octonion Fraction Integer
--E 7

--S 8 of 39
e7:Octonion(Fraction(Integer)):=octon(0,0,0,0,0,0,0,1)
 

   (8)  K
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (8)  K
--R                                              Type: Octonion Fraction Integer
--E 8

--S 9 of 39
[e0,e1,e2,e3,e4,e5,e6,e7]
 

   (9)  [1,i,j,k,E,I,J,K]
                                         Type: List Octonion Fraction Integer
--R 
--R
--R   (9)  [1,i,j,k,E,I,J,K]
--R                                         Type: List Octonion Fraction Integer
--E 9
--S 10 of 39
for i in [e0,e1,e2,e3,e4,e5,e6,e7] repeat _
  print [ (i*e0),(i*e1),(i*e2),(i*e3),(i*e4),(i*e5),(i*e6),(i*e7) ]
 
   [1,i,j,k,E,I,J,K]
   [i,- 1,k,- j,I,- E,- K,J]
   [j,- k,- 1,i,J,K,- E,- I]
   [k,j,- i,- 1,K,- J,I,- E]
   [E,- I,- J,- K,- 1,i,j,k]
   [I,E,- K,J,- i,- 1,- k,j]
   [J,K,E,- I,- j,k,- 1,- i]
   [K,- J,I,E,- k,- j,i,- 1]
                                                                   Type: Void
--R 
--R   [1,i,j,k,E,I,J,K]
--R   [i,- 1,k,- j,I,- E,- K,J]
--R   [j,- k,- 1,i,J,K,- E,- I]
--R   [k,j,- i,- 1,K,- J,I,- E]
--R   [E,- I,- J,- K,- 1,i,j,k]
--R   [I,E,- K,J,- i,- 1,- k,j]
--R   [J,K,E,- I,- j,k,- 1,- i]
--R   [K,- J,I,E,- k,- j,i,- 1]
--R                                                                   Type: Void
--E 10
--S 11 of 39
oci1 := octon(1,2,3,4,5,6,7,8)
 

   (11)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
                                                       Type: Octonion Integer
--R 
--R
--R   (11)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
--R                                                       Type: Octonion Integer
--E 11

--S 12 of 39
oci2 := octon(7,2,3,-4,5,6,-7,0)
 

   (12)  7 + 2i + 3j - 4k + 5E + 6I - 7J
                                                       Type: Octonion Integer
--R 
--R
--R   (12)  7 + 2i + 3j - 4k + 5E + 6I - 7J
--R                                                       Type: Octonion Integer
--E 12

--S 13 of 39
oci3 := octon(-7,-12,3,-10,5,6,9,0)
 

   (13)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
                                                       Type: Octonion Integer
--R 
--R
--R   (13)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
--R                                                       Type: Octonion Integer
--E 13

--S 14 of 39
oci := oci1 * oci2 * oci3
 

   (14)  - 324 + 2104i - 1100j - 2984k - 1444E + 528I - 44J + 128K
                                                       Type: Octonion Integer
--R 
--R
--R   (14)  - 324 + 2104i - 1100j - 2984k - 1444E + 528I - 44J + 128K
--R                                                       Type: Octonion Integer
--E 14

--S 15 of 39
(oci1 * oci2) * oci3 - oci1 * (oci2 * oci3)
 

   (15)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
                                                       Type: Octonion Integer
--R 
--R
--R   (15)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
--R                                                       Type: Octonion Integer
--E 15

--S 16 of 39
octon(1,0,0,0,0,0,0,0)
 

   (16)  1
                                                       Type: Octonion Integer
--R 
--R
--R   (16)  1
--R                                                       Type: Octonion Integer
--E 16

--S 17 of 39
i := octon(0,1,0,0,0,0,0,0)
 

   (17)  i
                                                       Type: Octonion Integer
--R 
--R
--R   (17)  i
--R                                                       Type: Octonion Integer
--E 17

--S 18 of 39
j := octon(0,0,1,0,0,0,0,0)
 

   (18)  j
                                                       Type: Octonion Integer
--R 
--R
--R   (18)  j
--R                                                       Type: Octonion Integer
--E 18

--S 19 of 39
octon(0,0,0,1,0,0,0,0)
 

   (19)  k
                                                       Type: Octonion Integer
--R 
--R
--R   (19)  k
--R                                                       Type: Octonion Integer
--E 19

--S 20 of 39
octon(0,0,0,0,1,0,0,0)
 

   (20)  E
                                                       Type: Octonion Integer
--R 
--R
--R   (20)  E
--R                                                       Type: Octonion Integer
--E 20

--S 21 of 39
octon(0,0,0,0,0,1,0,0)
 

   (21)  I
                                                       Type: Octonion Integer
--R 
--R
--R   (21)  I
--R                                                       Type: Octonion Integer
--E 21

--S 22 of 39
J := octon(0,0,0,0,0,0,1,0)
 

   (22)  J
                                                       Type: Octonion Integer
--R 
--R
--R   (22)  J
--R                                                       Type: Octonion Integer
--E 22

--S 23 of 39
octon(0,0,0,0,0,0,0,1)
 

   (23)  K
                                                       Type: Octonion Integer
--R 
--R
--R   (23)  K
--R                                                       Type: Octonion Integer
--E 23

--S 24 of 39
i*(j*J)
 

   (24)  - I
                                                       Type: Octonion Integer
--R 
--R
--R   (24)  - I
--R                                                       Type: Octonion Integer
--E 24

--S 25 of 39
(i*j)*J
 

   (25)  I
                                                       Type: Octonion Integer
--R 
--R
--R   (25)  I
--R                                                       Type: Octonion Integer
--E 25

--S 26 of 39
imagi oci
 

   (26)  2104
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  2104
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 39
imagE oci
 

   (27)  - 1444
                                                                Type: Integer
--R 
--R
--R   (27)  - 1444
--R                                                                Type: Integer
--E 27

--S 28 of 39
qs := Quaternion Polynomial Integer
 

   (28)  Quaternion Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (28)  Quaternion Polynomial Integer
--R                                                                 Type: Domain
--E 28

--S 29 of 39
os := Octonion Polynomial Integer
 

   (29)  Octonion Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (29)  Octonion Polynomial Integer
--R                                                                 Type: Domain
--E 29

--S 30 of 39
q : qs := quatern(q1,qi,qj,qk)
 

   (30)  q1 + qi i + qj j + qk k
                                          Type: Quaternion Polynomial Integer
--R 
--R
--R   (30)  q1 + qi i + qj j + qk k
--R                                          Type: Quaternion Polynomial Integer
--E 30

--S 31 of 39
E := octon(0,0,0,0,1,0,0,0)$os
 

   (31)  E
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (31)  E
--R                                            Type: Octonion Polynomial Integer
--E 31

--S 32 of 39
q * E
 

   (32)  q1 E + qi I + qj J + qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (32)  q1 E + qi I + qj J + qk K
--R                                            Type: Octonion Polynomial Integer
--E 32

--S 33 of 39
E * q
 

   (33)  q1 E - qi I - qj J - qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (33)  q1 E - qi I - qj J - qk K
--R                                            Type: Octonion Polynomial Integer
--E 33

--S 34 of 39
q * 1$os
 

   (34)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (34)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 34

--S 35 of 39
1$os * q
 

   (35)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (35)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 35

--S 36 of 39
o : os := octon(o1,oi,oj,ok,oE,oI,oJ,oK)
 

   (36)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (36)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
--R                                            Type: Octonion Polynomial Integer
--E 36

--S 37 of 39
p : os := octon(p1,pi,pj,pk,pE,pI,pJ,pK)
 

   (37)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (37)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
--R                                            Type: Octonion Polynomial Integer
--E 37


--S 38 of 39
norm o
 

           2     2     2     2     2     2     2     2
   (38)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
                                                     Type: Polynomial Integer
--R 
--R
--R           2     2     2     2     2     2     2     2
--R   (38)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 39
norm(o*p)-norm(p*o)
 

   (39)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (39)  0
--R                                                     Type: Polynomial Integer
--E 39
)spool 
 
Starts dribbling to matrix22.output (2009/2/17, 17:55:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 8
m:SQMATRIX(2,INT) := squareMatrix matrix [[0,1],[-1,0]]
 

        + 0   1+
   (1)  |      |
        +- 1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        + 0   1+
--R   (1)  |      |
--R        +- 1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 1

--S 2 of 8
determinant m
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 8
n:SQMATRIX(2,SQMATRIX(2,INT)) :=
  squareMatrix matrix [[m,m**2],[m**3,m**4]]
 

        ++ 0   1+  +- 1   0 ++
        ||      |  |        ||
        |+- 1  0+  + 0   - 1+|
   (3)  |                    |
        |+0  - 1+    +1  0+  |
        ||      |    |    |  |
        ++1   0 +    +0  1+  +
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R 
--R
--R        ++ 0   1+  +- 1   0 ++
--R        ||      |  |        ||
--R        |+- 1  0+  + 0   - 1+|
--R   (3)  |                    |
--R        |+0  - 1+    +1  0+  |
--R        ||      |    |    |  |
--R        ++1   0 +    +0  1+  +
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 3

)set mes test off
 
--S 4  of 8
determinant n
 
   There are 3 exposed and 1 unexposed library operations named 
      determinant having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op determinant
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named 
      determinant with argument type(s) 
                   SquareMatrix(2,SquareMatrix(2,Integer))
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 3 exposed and 1 unexposed library operations named 
--R      determinant having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                           )display op determinant
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named 
--R      determinant with argument type(s) 
--R                   SquareMatrix(2,SquareMatrix(2,Integer))
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4
)set mes test on
 

--S 5 of 8
o:SQMATRIX(2,SQMATRIX(2,SQMATRIX(2,INT))) :=
   squareMatrix matrix [[n,n**2],[n**3,n**4]]
 

        +++ 0   1+  +- 1   0 ++  ++- 1   1 +  +- 1  - 1+++
        |||      |  |        ||  ||        |  |        |||
        ||+- 1  0+  + 0   - 1+|  |+- 1  - 1+  + 1   - 1+||
        ||                    |  |                      ||
        ||+0  - 1+    +1  0+  |  | +1  - 1+    + 1   1+ ||
        |||      |    |    |  |  | |      |    |      | ||
        |++1   0 +    +0  1+  +  + +1   1 +    +- 1  1+ +|
   (4)  |                                                |
        |++- 2   0 +  +0  - 2++  ++- 2  - 2+   +2  - 2+ +|
        |||        |  |      ||  ||        |   |      | ||
        ||+ 0   - 2+  +2   0 +|  |+ 2   - 2+   +2   2 + ||
        ||                    |  |                      ||
        ||  +2  0+    + 0   2+|  | + 2   2+   +- 2   2 +||
        ||  |    |    |      ||  | |      |   |        |||
        ++  +0  2+    +- 2  0++  + +- 2  2+   +- 2  - 2+++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        +++ 0   1+  +- 1   0 ++  ++- 1   1 +  +- 1  - 1+++
--R        |||      |  |        ||  ||        |  |        |||
--R        ||+- 1  0+  + 0   - 1+|  |+- 1  - 1+  + 1   - 1+||
--R        ||                    |  |                      ||
--R        ||+0  - 1+    +1  0+  |  | +1  - 1+    + 1   1+ ||
--R        |||      |    |    |  |  | |      |    |      | ||
--R        |++1   0 +    +0  1+  +  + +1   1 +    +- 1  1+ +|
--R   (4)  |                                                |
--R        |++- 2   0 +  +0  - 2++  ++- 2  - 2+   +2  - 2+ +|
--R        |||        |  |      ||  ||        |   |      | ||
--R        ||+ 0   - 2+  +2   0 +|  |+ 2   - 2+   +2   2 + ||
--R        ||                    |  |                      ||
--R        ||  +2  0+    + 0   2+|  | + 2   2+   +- 2   2 +||
--R        ||  |    |    |      ||  | |      |   |        |||
--R        ++  +0  2+    +- 2  0++  + +- 2  2+   +- 2  - 2+++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 5

--S 6 of 8
o ** 2
 

        +++- 1  - 3+   +3  - 1+ +  + +2  - 4+    + 4   2+ ++
        |||        |   |      | |  | |      |    |      | ||
        ||+ 3   - 1+   +1   3 + |  | +4   2 +    +- 2  4+ ||
        ||                      |  |                      ||
        || + 1   3+   +- 3   1 +|  |+- 2   4 +  +- 4  - 2+||
        || |      |   |        ||  ||        |  |        |||
        |+ +- 3  1+   +- 1  - 3++  ++- 4  - 2+  + 2   - 4++|
   (5)  |                                                  |
        |+ +6  - 2+    + 2   6+ +  + + 8   4+   +- 4   8 ++|
        || |      |    |      | |  | |      |   |        |||
        || +2   6 +    +- 6  2+ |  | +- 4  8+   +- 8  - 4+||
        ||                      |  |                      ||
        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +4  - 8+ ||
        |||        |  |        ||  ||        |   |      | ||
        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   4 + ++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        +++- 1  - 3+   +3  - 1+ +  + +2  - 4+    + 4   2+ ++
--R        |||        |   |      | |  | |      |    |      | ||
--R        ||+ 3   - 1+   +1   3 + |  | +4   2 +    +- 2  4+ ||
--R        ||                      |  |                      ||
--R        || + 1   3+   +- 3   1 +|  |+- 2   4 +  +- 4  - 2+||
--R        || |      |   |        ||  ||        |  |        |||
--R        |+ +- 3  1+   +- 1  - 3++  ++- 4  - 2+  + 2   - 4++|
--R   (5)  |                                                  |
--R        |+ +6  - 2+    + 2   6+ +  + + 8   4+   +- 4   8 ++|
--R        || |      |    |      | |  | |      |   |        |||
--R        || +2   6 +    +- 6  2+ |  | +- 4  8+   +- 8  - 4+||
--R        ||                      |  |                      ||
--R        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +4  - 8+ ||
--R        |||        |  |        ||  ||        |   |      | ||
--R        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   4 + ++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 6

--S 7 of 8
% + 2
 

        + ++1  - 3+   +3  - 1+ +   + +2  - 4+    + 4   2+ ++
        | ||      |   |      | |   | |      |    |      | ||
        | |+3   1 +   +1   3 + |   | +4   2 +    +- 2  4+ ||
        | |                    |   |                      ||
        | |+ 1   3+  +- 1   1 +|   |+- 2   4 +  +- 4  - 2+||
        | ||      |  |        ||   ||        |  |        |||
        | ++- 3  1+  +- 1  - 1++   ++- 4  - 2+  + 2   - 4++|
   (6)  |                                                  |
        |+ +6  - 2+    + 2   6+ +  ++10   4 +   +- 4   8 ++|
        || |      |    |      | |  ||       |   |        |||
        || +2   6 +    +- 6  2+ |  |+- 4  10+   +- 8  - 4+||
        ||                      |  |                      ||
        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +6  - 8+ ||
        |||        |  |        ||  ||        |   |      | ||
        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   6 + ++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        + ++1  - 3+   +3  - 1+ +   + +2  - 4+    + 4   2+ ++
--R        | ||      |   |      | |   | |      |    |      | ||
--R        | |+3   1 +   +1   3 + |   | +4   2 +    +- 2  4+ ||
--R        | |                    |   |                      ||
--R        | |+ 1   3+  +- 1   1 +|   |+- 2   4 +  +- 4  - 2+||
--R        | ||      |  |        ||   ||        |  |        |||
--R        | ++- 3  1+  +- 1  - 1++   ++- 4  - 2+  + 2   - 4++|
--R   (6)  |                                                  |
--R        |+ +6  - 2+    + 2   6+ +  ++10   4 +   +- 4   8 ++|
--R        || |      |    |      | |  ||       |   |        |||
--R        || +2   6 +    +- 6  2+ |  |+- 4  10+   +- 8  - 4+||
--R        ||                      |  |                      ||
--R        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +6  - 8+ ||
--R        |||        |  |        ||  ||        |   |      | ||
--R        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   6 + ++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 7

--S 8 of 8
o := 2
 

        +++2  0+  +0  0++  ++0  0+  +0  0+++
        |||    |  |    ||  ||    |  |    |||
        ||+0  2+  +0  0+|  |+0  0+  +0  0+||
        ||              |  |              ||
        ||+0  0+  +2  0+|  |+0  0+  +0  0+||
        |||    |  |    ||  ||    |  |    |||
        |++0  0+  +0  2++  ++0  0+  +0  0++|
   (7)  |                                  |
        |++0  0+  +0  0++  ++2  0+  +0  0++|
        |||    |  |    ||  ||    |  |    |||
        ||+0  0+  +0  0+|  |+0  2+  +0  0+||
        ||              |  |              ||
        ||+0  0+  +0  0+|  |+0  0+  +2  0+||
        |||    |  |    ||  ||    |  |    |||
        +++0  0+  +0  0++  ++0  0+  +0  2+++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        +++2  0+  +0  0++  ++0  0+  +0  0+++
--R        |||    |  |    ||  ||    |  |    |||
--R        ||+0  2+  +0  0+|  |+0  0+  +0  0+||
--R        ||              |  |              ||
--R        ||+0  0+  +2  0+|  |+0  0+  +0  0+||
--R        |||    |  |    ||  ||    |  |    |||
--R        |++0  0+  +0  2++  ++0  0+  +0  0++|
--R   (7)  |                                  |
--R        |++0  0+  +0  0++  ++2  0+  +0  0++|
--R        |||    |  |    ||  ||    |  |    |||
--R        ||+0  0+  +0  0+|  |+0  2+  +0  0+||
--R        ||              |  |              ||
--R        ||+0  0+  +0  0+|  |+0  0+  +2  0+||
--R        |||    |  |    ||  ||    |  |    |||
--R        +++0  0+  +0  0++  ++0  0+  +0  2+++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 8
)spool 
 
Starts dribbling to sint.output (2009/2/17, 18:0:27).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 11
min()$SingleInteger
 

   (1)  - 2147483648
                                                          Type: SingleInteger
--R 
--R
--R   (1)  - 2147483648
--R                                                          Type: SingleInteger
--E 1

--S 2 of 11
max()$SingleInteger
 

   (2)  2147483647
                                                          Type: SingleInteger
--R 
--R
--R   (2)  2147483647
--R                                                          Type: SingleInteger
--E 2

--S 3 of 11
a := 1234 :: SingleInteger
 

   (3)  1234
                                                          Type: SingleInteger
--R 
--R
--R   (3)  1234
--R                                                          Type: SingleInteger
--E 3

--S 4 of 11
b := 124$SingleInteger
 

   (4)  124
                                                          Type: SingleInteger
--R 
--R
--R   (4)  124
--R                                                          Type: SingleInteger
--E 4

--S 5 of 11
gcd(a,b)
 

   (5)  2
                                                          Type: SingleInteger
--R 
--R
--R   (5)  2
--R                                                          Type: SingleInteger
--E 5

--S 6 of 11
lcm(a,b)
 

   (6)  76508
                                                          Type: SingleInteger
--R 
--R
--R   (6)  76508
--R                                                          Type: SingleInteger
--E 6

--S 7 of 11
mulmod(5,6,13)$SingleInteger
 

   (7)  4
                                                          Type: SingleInteger
--R 
--R
--R   (7)  4
--R                                                          Type: SingleInteger
--E 7

--S 8 of 11
positiveRemainder(37,13)$SingleInteger
 

   (8)  11
                                                          Type: SingleInteger
--R 
--R
--R   (8)  11
--R                                                          Type: SingleInteger
--E 8

--S 9 of 11
And(3,4)$SingleInteger
 

   (9)  0
                                                          Type: SingleInteger
--R 
--R
--R   (9)  0
--R                                                          Type: SingleInteger
--E 9

--S 10 of 11
shift(1,4)$SingleInteger
 

   (10)  16
                                                          Type: SingleInteger
--R 
--R
--R   (10)  16
--R                                                          Type: SingleInteger
--E 10

--S 11 of 11
shift(31,-1)$SingleInteger
 

   (11)  15
                                                          Type: SingleInteger
--R 
--R
--R   (11)  15
--R                                                          Type: SingleInteger
--E 11
)spool 
 
Starts dribbling to elt.output (2009/2/17, 17:45:34).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 4
u : Bits := new(10,true)
 

   (1)  "1111111111"
                                                                   Type: Bits
--R 
--R
--R   (1)  "1111111111"
--R                                                                   Type: Bits
--E 1

--S 2 of 4
u(3..5) := false; u
 

   (2)  "1100011111"
                                                                   Type: Bits
--R 
--R
--R   (2)  "1100011111"
--R                                                                   Type: Bits
--E 2

)clear all
 
   All user variables and function definitions have been cleared.

--S 3 of 4
u:Any := [1, 7.2, 3/2, x**2, "wally"]
 

               3  2
   (1)  [1,7.2,-,x ,"wally"]
               2
                                                               Type: List Any
--R 
--R
--R               3  2
--R   (1)  [1,7.2,-,x ,"wally"]
--R               2
--R                                                               Type: List Any
--E 3

--S 4 of 4
u.1
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 4
)spool
 
Starts dribbling to patmatch.output (2009/2/17, 17:56:3).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 22
p := 3 * n ** 2 + 1
 

          2
   (1)  3n  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (1)  3n  + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 22
q := 3 * n% ** 2 + 1
 

           2
   (2)  3n%  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (2)  3n%  + 1
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 22
a := roman 49
 

   (3)  XLIX
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XLIX
--R                                                           Type: RomanNumeral
--E 3

--S 4 of 22
b := roman IV
 

   (4)  IV
                                                           Type: RomanNumeral
--R 
--R
--R   (4)  IV
--R                                                           Type: RomanNumeral
--E 4

--S 5 of 22
c := a - 1
 

   (5)  XLVIII
                                                           Type: RomanNumeral
--R 
--R
--R   (5)  XLVIII
--R                                                           Type: RomanNumeral
--E 5

--S 6 of 22
Is(a, p)
 

   (6)  [n= IV]
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (6)  [n= IV]
--R                                  Type: List Equation Polynomial RomanNumeral
--E 6

--S 7 of 22
Is(a, q)
 

   (7)  [n%= IV]
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (7)  [n%= IV]
--R                                  Type: List Equation Polynomial RomanNumeral
--E 7

--S 8 of 22
Is(b, p)
 

   (8)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (8)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 8

--S 9 of 22
Is(b, q)
 

   (9)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (9)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 9

--S 10 of 22
Is(c, p)
 

   (10)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (10)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 10

--S 11 of 22
Is(c, q)
 

   (11)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (11)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 11

--S 12 of 22
ab := a / b
 

         XLIX
   (12)  ----
          IV
                                                  Type: Fraction RomanNumeral
--R 
--R
--R         XLIX
--R   (12)  ----
--R          IV
--R                                                  Type: Fraction RomanNumeral
--E 12

--S 13 of 22
pq := p / q
 

            2
          3n  + 1
   (13)  --------
            2
         3n%  + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            2
--R          3n  + 1
--R   (13)  --------
--R            2
--R         3n%  + 1
--R                                            Type: Fraction Polynomial Integer
--E 13

--S 14 of 22
Is(ab, pq)
 

   (14)  []
                         Type: List Equation Polynomial Fraction RomanNumeral
--R 
--R
--R   (14)  []
--R                         Type: List Equation Polynomial Fraction RomanNumeral
--E 14

--S 15 of 22
ab := rational ab
 

         49
   (15)  --
          4
                                                       Type: Fraction Integer
--R 
--R
--R         49
--R   (15)  --
--R          4
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 22
a  := rational a
 

   (16)  49
                                                       Type: Fraction Integer
--R 
--R
--R   (16)  49
--R                                                       Type: Fraction Integer
--E 16

--Is([ab, a], [pq, _:l, p])
--Is([ab, a], [pq, _:l%, p])
--Is([ab, 1, 2, a], [pq, _:l, p])
-- foo?(x:LIST FRAC INT):BOOLEAN == odd? _# x
-- qq := suchThat(_:l%, foo?)
-- Is([ab, 1, 2, a], [pq, qq, p])
-- Is([ab, 1, 2, 3, a], [pq, qq, p])
-- creating streams using pattern matching
-- want the streams of all primes of the form m**2+1

--S 17 of 22
bar?(n:INT):BOOLEAN == prime? n and is?(n, m**2 + 1)
 
   Function declaration bar? : Integer -> Boolean has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration bar? : Integer -> Boolean has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 17

--S 18 of 22
myprimes := [i for i in 1.. | bar? i]
 
   Compiling function bar? with type Integer -> Boolean 

   (18)  [5,17,37,101,197,257,401,577,677,1297,...]
                                                 Type: Stream PositiveInteger
--R 
--R   Compiling function bar? with type Integer -> Boolean 
--R
--R   (18)  [5,17,37,101,197,257,401,577,677,1297,...]
--R                                                 Type: Stream PositiveInteger
--E 18

--S 19 of 22
p := x**2 + 3*x + 1
 

          2
   (19)  x  + 3x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (19)  x  + 3x + 1
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 22
Is(p, n * y**2 + (2*n+1)*y + 1)
 

   (20)  []
                                       Type: List Equation Polynomial Integer
--R 
--R
--R   (20)  []
--R                                       Type: List Equation Polynomial Integer
--E 20

--S 21 of 22
Is(p, n% * y**2 + (2*n%+1)*y + 1)
 

   (21)  []
                                       Type: List Equation Polynomial Integer
--R 
--R
--R   (21)  []
--R                                       Type: List Equation Polynomial Integer
--E 21

--S 22 of 22
Is(3*x**2 + 9*x + 1, n * y**2 + n**2 * y + 1)
 

   (22)  [n= x,y= 3]
                                       Type: List Equation Polynomial Integer
--R 
--R
--R   (22)  [n= x,y= 3]
--R                                       Type: List Equation Polynomial Integer
--E 22
)spool 
 
Starts dribbling to schaum28.output (2009/2/17, 17:59:33).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(cosh(a*x),x)
 

        sinh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sinh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=sinh(a*x)/a
 

        sinh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        sinh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 3      14:562 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*cosh(a*x),x)
 

        a x sinh(a x) - cosh(a x)
   (1)  -------------------------
                     2
                    a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a x sinh(a x) - cosh(a x)
--R   (1)  -------------------------
--R                     2
--R                    a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=(x*sinh(a*x))/a-cosh(a*x)/a^2
 

        a x sinh(a x) - cosh(a x)
   (2)  -------------------------
                     2
                    a
                                                     Type: Expression Integer
--R
--R        a x sinh(a x) - cosh(a x)
--R   (2)  -------------------------
--R                     2
--R                    a
--R                                                     Type: Expression Integer
--E

--S 6      14:563 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2*cosh(a*x),x)
 

          2 2
        (a x  + 2)sinh(a x) - 2a x cosh(a x)
   (1)  ------------------------------------
                          3
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2 2
--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
--R   (1)  ------------------------------------
--R                          3
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=-(2*x*cosh(a*x))/a^2+(x^2/a+2/a^3)*sinh(a*x)
 

          2 2
        (a x  + 2)sinh(a x) - 2a x cosh(a x)
   (2)  ------------------------------------
                          3
                         a
                                                     Type: Expression Integer
--R
--R          2 2
--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
--R   (2)  ------------------------------------
--R                          3
--R                         a
--R                                                     Type: Expression Integer
--E

--S 9      14:564 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10     14:565 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)/x,x)
 

           x
         ++  cosh(%N a)
   (1)   |   ---------- d%N
        ++       %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cosh(%N a)
--I   (1)   |   ---------- d%N
--I        ++       %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 11     14:566 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)/x^2,x)
 

           x
         ++  cosh(%N a)
   (1)   |   ---------- d%N
        ++         2
                 %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cosh(%N a)
--I   (1)   |   ---------- d%N
--R        ++         2
--I                 %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 12
aa:=integrate(1/cosh(a*x),x)
 

        2atan(sinh(a x) + cosh(a x))
   (1)  ----------------------------
                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        2atan(sinh(a x) + cosh(a x))
--R   (1)  ----------------------------
--R                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13
bb:=2/a*atan(%e^(a*x))
 

                a x
        2atan(%e   )
   (2)  ------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        2atan(%e   )
--R   (2)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 14
cc:=aa-bb
 

                                               a x
        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
   (3)  -------------------------------------------
                             a
                                                     Type: Expression Integer
--R
--R                                               a x
--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
--R   (3)  -------------------------------------------
--R                             a
--R                                                     Type: Expression Integer
--E

--S 15     14:567 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 16     14:568 Axiom cannot compute this integral
aa:=integrate(x/cosh(a*x),x)
 

           x
         ++      %N
   (1)   |   ---------- d%N
        ++   cosh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %N
--I   (1)   |   ---------- d%N
--I        ++   cosh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 17
aa:=integrate(cosh(a*x)^2,x)
 

        cosh(a x)sinh(a x) + a x
   (1)  ------------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cosh(a x)sinh(a x) + a x
--R   (1)  ------------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 18
bb:=x/2+(sinh(a*x)*cosh(a*x))/(2*a)
 

        cosh(a x)sinh(a x) + a x
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R        cosh(a x)sinh(a x) + a x
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 19     14:569 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 20
aa:=integrate(x*cosh(a*x)^2,x)
 

                   2                                      2     2 2
        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  + 2a x
   (1)  -----------------------------------------------------------
                                      2
                                    8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2                                      2     2 2
--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  + 2a x
--R   (1)  -----------------------------------------------------------
--R                                      2
--R                                    8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21
bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)
 

                                         2 2
        2a x sinh(2a x) - cosh(2a x) + 2a x
   (2)  ------------------------------------
                           2
                         8a
                                                     Type: Expression Integer
--R
--R                                         2 2
--R        2a x sinh(2a x) - cosh(2a x) + 2a x
--R   (2)  ------------------------------------
--R                           2
--R                         8a
--R                                                     Type: Expression Integer
--E

--S 22
cc:=aa-bb
 

   (3)
                                    2
       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
     + 
                  2
       - cosh(a x)
  /
       2
     8a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2
--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
--R     + 
--R                  2
--R       - cosh(a x)
--R  /
--R       2
--R     8a
--R                                                     Type: Expression Integer
--E

--S 23
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 24
dd:=sinhsqrrule cc
 

   (5)
                                                                        2
   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
   --------------------------------------------------------------------------
                                         2
                                      16a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                                        2
--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
--R   --------------------------------------------------------------------------
--R                                         2
--R                                      16a
--R                                                     Type: Expression Integer
--E

--S 25
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26
ee:=coshsqrrule dd
 

        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
   (7)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
--R   (7)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 27
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (8)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %S sinh(y + x) - %S sinh(y - x)
--I   (8)  %S cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 28     14:570 Schaums and Axiom agree
ff:=sinhcoshrule ee
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(1/cosh(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30
bb:=tanh(a*x)/a
 

        tanh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        tanh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

                    2                                  2
        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
   (3)  ------------------------------------------------------------------
                         2                                      2
              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R                    2                                  2
--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
--R   (3)  ------------------------------------------------------------------
--R                         2                                      2
--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 32     14:571 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

          1
   (4)  - -
          a
                                                     Type: Expression Integer
--R
--R          1
--R   (4)  - -
--R          a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 33 
aa:=integrate(cosh(a*x)*cosh(p*x),x)
 

        - p cosh(a x)sinh(p x) + a cosh(p x)sinh(a x)
   (1)  ---------------------------------------------
           2    2          2       2    2          2
         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - p cosh(a x)sinh(p x) + a cosh(p x)sinh(a x)
--R   (1)  ---------------------------------------------
--R           2    2          2       2    2          2
--R         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34
bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p))
 

        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
   (2)  -------------------------------------------
                           2     2
                         2p  - 2a
                                                     Type: Expression Integer
--R
--R        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
--R   (2)  -------------------------------------------
--R                           2     2
--R                         2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 35
cc:=aa-bb
 

   (3)
       - 2p cosh(a x)sinh(p x)
     + 
                                                                 2
       ((- p + a)x sinh(p + a) + (- p - a)x sinh(p - a))sinh(a x)
     + 
                                                 2
       2a cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
     + 
                         2
       (p + a)x cosh(a x) sinh(p - a)
  /
        2     2          2        2     2          2
     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - 2p cosh(a x)sinh(p x)
--R     + 
--R                                                                 2
--R       ((- p + a)x sinh(p + a) + (- p - a)x sinh(p - a))sinh(a x)
--R     + 
--R                                                 2
--R       2a cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
--R     + 
--R                         2
--R       (p + a)x cosh(a x) sinh(p - a)
--R  /
--R        2     2          2        2     2          2
--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 36
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37
dd:=sinhsqrrule cc
 

   (5)
       - 4p cosh(a x)sinh(p x) + 4a cosh(p x)sinh(a x)
     + 
                                                    2
       ((- p + a)x cosh(2a x) + (2p - 2a)x cosh(a x)  + (p - a)x)sinh(p + a)
     + 
                                                    2
       ((- p - a)x cosh(2a x) + (2p + 2a)x cosh(a x)  + (p + a)x)sinh(p - a)
  /
        2     2                   2     2          2     2     2
     (2p  - 2a )cosh(2a x) + (- 4p  + 4a )cosh(a x)  - 2p  + 2a
                                                     Type: Expression Integer
--R
--R   (5)
--R       - 4p cosh(a x)sinh(p x) + 4a cosh(p x)sinh(a x)
--R     + 
--R                                                    2
--R       ((- p + a)x cosh(2a x) + (2p - 2a)x cosh(a x)  + (p - a)x)sinh(p + a)
--R     + 
--R                                                    2
--R       ((- p - a)x cosh(2a x) + (2p + 2a)x cosh(a x)  + (p + a)x)sinh(p - a)
--R  /
--R        2     2                   2     2          2     2     2
--R     (2p  - 2a )cosh(2a x) + (- 4p  + 4a )cosh(a x)  - 2p  + 2a
--R                                                     Type: Expression Integer
--E

--S 38
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 39
ee:=coshsqrrule dd
 

   (7)
       2p cosh(a x)sinh(p x) - 2a cosh(p x)sinh(a x) + (- p + a)x sinh(p + a)
     + 
       (- p - a)x sinh(p - a)
  /
       2     2
     2p  - 2a
                                                     Type: Expression Integer
--R
--R   (7)
--R       2p cosh(a x)sinh(p x) - 2a cosh(p x)sinh(a x) + (- p + a)x sinh(p + a)
--R     + 
--R       (- p - a)x sinh(p - a)
--R  /
--R       2     2
--R     2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 40
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %Q sinh(y + x) - %Q sinh(y - x)
   (8)  %Q cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %V sinh(y + x) - %V sinh(y - x)
--I   (8)  %V cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 41     14:572 Axiom cannot simplify this expression
ff:=sinhcoshrule ee
 

   (9)
       (p - a)sinh((p + a)x) + (p + a)sinh((p - a)x) + (- p + a)x sinh(p + a)
     + 
       (- p - a)x sinh(p - a)
  /
       2     2
     2p  - 2a
                                                     Type: Expression Integer
--R
--R   (9)
--R       (p - a)sinh((p + a)x) + (p + a)sinh((p - a)x) + (- p + a)x sinh(p + a)
--R     + 
--R       (- p - a)x sinh(p - a)
--R  /
--R       2     2
--R     2p  - 2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 42
aa:=integrate(cosh(a*x)*sin(p*x),x)
 

   (1)
                                         2
       (a sin(p x) - p cos(p x))sinh(a x)
     + 
       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (a cosh(a x)  - a)sin(p x) - p cos(p x)cosh(a x)  - p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (a sin(p x) - p cos(p x))sinh(a x)
--R     + 
--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (a cosh(a x)  - a)sin(p x) - p cos(p x)cosh(a x)  - p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 43
bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2)
 

        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
   (2)  -----------------------------------------
                          2    2
                         p  + a
                                                     Type: Expression Integer
--R
--R        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
--R   (2)  -----------------------------------------
--R                          2    2
--R                         p  + a
--R                                                     Type: Expression Integer
--E

--S 44
cc:=aa-bb
 

   (3)
                                           2               2
       (- a sin(p x) - p cos(p x))sinh(a x)  + (a cosh(a x)  - a)sin(p x)
     + 
                          2
       p cos(p x)cosh(a x)  - p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2               2
--R       (- a sin(p x) - p cos(p x))sinh(a x)  + (a cosh(a x)  - a)sin(p x)
--R     + 
--R                          2
--R       p cos(p x)cosh(a x)  - p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 45
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (4)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (4)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 46
dd:=coshsqrrule cc
 

   (5)
                                             2
       (- 2a sin(p x) - 2p cos(p x))sinh(a x)  + (a cosh(2a x) - a)sin(p x)
     + 
       p cos(p x)cosh(2a x) - p cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                             2
--R       (- 2a sin(p x) - 2p cos(p x))sinh(a x)  + (a cosh(2a x) - a)sin(p x)
--R     + 
--R       p cos(p x)cosh(2a x) - p cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 47
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 48     14:573 Schaums and Axiom agree
ee:=sinhsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(cosh(a*x)*cos(p*x),x)
 

   (1)
                                         2
       (p sin(p x) + a cos(p x))sinh(a x)
     + 
       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (p cosh(a x)  + p)sin(p x) + a cos(p x)cosh(a x)  - a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (p sin(p x) + a cos(p x))sinh(a x)
--R     + 
--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (p cosh(a x)  + p)sin(p x) + a cos(p x)cosh(a x)  - a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50
bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2)
 

        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
   (2)  -----------------------------------------
                          2    2
                         p  + a
                                                     Type: Expression Integer
--R
--R        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
--R   (2)  -----------------------------------------
--R                          2    2
--R                         p  + a
--R                                                     Type: Expression Integer
--E

--S 51
cc:=aa-bb
 

   (3)
                                         2                 2
       (p sin(p x) - a cos(p x))sinh(a x)  + (- p cosh(a x)  + p)sin(p x)
     + 
                          2
       a cos(p x)cosh(a x)  - a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                         2                 2
--R       (p sin(p x) - a cos(p x))sinh(a x)  + (- p cosh(a x)  + p)sin(p x)
--R     + 
--R                          2
--R       a cos(p x)cosh(a x)  - a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 52
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (4)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (4)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 53
dd:=coshsqrrule cc
 

   (5)
                                           2
       (2p sin(p x) - 2a cos(p x))sinh(a x)  + (- p cosh(2a x) + p)sin(p x)
     + 
       a cos(p x)cosh(2a x) - a cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                           2
--R       (2p sin(p x) - 2a cos(p x))sinh(a x)  + (- p cosh(2a x) + p)sin(p x)
--R     + 
--R       a cos(p x)cosh(2a x) - a cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 54
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 55     14:574 Schaums and Axiom agree
ee:=sinhsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 56
aa:=integrate(1/(cosh(a*x)+1),x)
 

                        2
   (1)  - -----------------------------
          a sinh(a x) + a cosh(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2
--R   (1)  - -----------------------------
--R          a sinh(a x) + a cosh(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 57
bb:=1/a*tanh((a*x)/2)
 

             a x
        tanh(---)
              2
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R             a x
--R        tanh(---)
--R              2
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 58
cc:=aa-bb
 

                                          a x
        (- sinh(a x) - cosh(a x) - 1)tanh(---) - 2
                                           2
   (3)  ------------------------------------------
               a sinh(a x) + a cosh(a x) + a
                                                     Type: Expression Integer
--R
--R                                          a x
--R        (- sinh(a x) - cosh(a x) - 1)tanh(---) - 2
--R                                           2
--R   (3)  ------------------------------------------
--R               a sinh(a x) + a cosh(a x) + a
--R                                                     Type: Expression Integer
--E

--S 59
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 60
dd:=tanhrule cc
 

               a x                                   a x          a x
        - sinh(---)sinh(a x) + (- cosh(a x) - 1)sinh(---) - 2cosh(---)
                2                                     2            2
   (5)  --------------------------------------------------------------
                  a x                    a x                    a x
           a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
                   2                      2                      2
                                                     Type: Expression Integer
--R
--R               a x                                   a x          a x
--R        - sinh(---)sinh(a x) + (- cosh(a x) - 1)sinh(---) - 2cosh(---)
--R                2                                     2            2
--R   (5)  --------------------------------------------------------------
--R                  a x                    a x                    a x
--R           a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
--R                   2                      2                      2
--R                                                     Type: Expression Integer
--E

--S 61
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BB sinh(y + x) - %BB sinh(y - x)
   (6)  %BB cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BC sinh(y + x) - %BC sinh(y - x)
--I   (6)  %BC cosh(y)sinh(x) == -------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 62
ee:=sinhcoshrule dd
 

                  3a x          a x                  a x          a x
           - sinh(----) - 2sinh(---)sinh(a x) - sinh(---) - 4cosh(---)
                    2            2                    2            2
   (7)  -----------------------------------------------------------------
               3a x           a x            a x                     a x
        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
                 2             2              2                       2
                                                     Type: Expression Integer
--R
--R                  3a x          a x                  a x          a x
--R           - sinh(----) - 2sinh(---)sinh(a x) - sinh(---) - 4cosh(---)
--R                    2            2                    2            2
--R   (7)  -----------------------------------------------------------------
--R               3a x           a x            a x                     a x
--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
--R                 2             2              2                       2
--R                                                     Type: Expression Integer
--E

--S 63
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %BC cosh(y + x) - %BC cosh(y - x)
   (8)  %BC sinh(x)sinh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BD sinh(y + x) - %BD sinh(y - x)
--I   (8)  %BD cosh(y)sinh(x) == -------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 64
ff:=sinhsinhrule ee
 

                       3a x         a x         3a x          a x
                - sinh(----) - sinh(---) - cosh(----) - 3cosh(---)
                         2           2            2            2
   (9)  -----------------------------------------------------------------
               3a x           a x            a x                     a x
        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
                 2             2              2                       2
                                                     Type: Expression Integer
--R
--R                       3a x         a x         3a x          a x
--R                - sinh(----) - sinh(---) - cosh(----) - 3cosh(---)
--R                         2           2            2            2
--R   (9)  -----------------------------------------------------------------
--R               3a x           a x            a x                     a x
--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
--R                 2             2              2                       2
--R                                                     Type: Expression Integer
--E

--S 65
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                               %BD cosh(y + x) + %BD cosh(y - x)
   (10)  %BD cosh(x)cosh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BC cosh(y + x) + %BC cosh(y - x)
--I   (10)  %BC cosh(x)cosh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 66     14:575 Schaums and Axiom differ by a constant
gg:=coshcoshrule ff
 

           1
   (11)  - -
           a
                                                     Type: Expression Integer
--R
--R           1
--R   (11)  - -
--R           a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 67
aa:=integrate(1/(cosh(a*x)-1),x)
 

                        2
   (1)  - -----------------------------
          a sinh(a x) + a cosh(a x) - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2
--R   (1)  - -----------------------------
--R          a sinh(a x) + a cosh(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68
bb:=-1/a*coth((a*x)/2)
 

               a x
          coth(---)
                2
   (2)  - ---------
              a
                                                     Type: Expression Integer
--R
--R               a x
--R          coth(---)
--R                2
--R   (2)  - ---------
--R              a
--R                                                     Type: Expression Integer
--E

--S 69
cc:=aa-bb
 

             a x                                 a x
        coth(---)sinh(a x) + (cosh(a x) - 1)coth(---) - 2
              2                                   2
   (3)  -------------------------------------------------
                  a sinh(a x) + a cosh(a x) - a
                                                     Type: Expression Integer
--R
--R             a x                                 a x
--R        coth(---)sinh(a x) + (cosh(a x) - 1)coth(---) - 2
--R              2                                   2
--R   (3)  -------------------------------------------------
--R                  a sinh(a x) + a cosh(a x) - a
--R                                                     Type: Expression Integer
--E

--S 70
cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 

                   cosh(x)
   (4)  coth(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   cosh(x)
--R   (4)  coth(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 71
dd:=cothrule cc
 

             a x                   a x         a x                  a x
        cosh(---)sinh(a x) - 2sinh(---) + cosh(---)cosh(a x) - cosh(---)
              2                     2           2                    2
   (5)  ----------------------------------------------------------------
                       a x                                   a x
                a sinh(---)sinh(a x) + (a cosh(a x) - a)sinh(---)
                        2                                     2
                                                     Type: Expression Integer
--R
--R             a x                   a x         a x                  a x
--R        cosh(---)sinh(a x) - 2sinh(---) + cosh(---)cosh(a x) - cosh(---)
--R              2                     2           2                    2
--R   (5)  ----------------------------------------------------------------
--R                       a x                                   a x
--R                a sinh(---)sinh(a x) + (a cosh(a x) - a)sinh(---)
--R                        2                                     2
--R                                                     Type: Expression Integer
--E

--S 72
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BE sinh(y + x) - %BE sinh(y - x)
   (6)  %BE cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BD sinh(y + x) - %BD sinh(y - x)
--I   (6)  %BD cosh(y)sinh(x) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 73
ee:=sinhcoshrule dd
 

             3a x          a x          a x                   a x
        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
               2            2            2                     2
   (7)  ----------------------------------------------------------
                   3a x            a x                     a x
            a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
                     2              2                       2
                                                     Type: Expression Integer
--R
--R             3a x          a x          a x                   a x
--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
--R               2            2            2                     2
--R   (7)  ----------------------------------------------------------
--R                   3a x            a x                     a x
--R            a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
--R                     2              2                       2
--R                                                     Type: Expression Integer
--E

--S 74
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %BF cosh(y + x) - %BF cosh(y - x)
   (8)  %BF sinh(x)sinh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BE cosh(y + x) - %BE cosh(y - x)
--I   (8)  %BE sinh(x)sinh(y) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 75
ff:=sinhsinhrule ee
 

             3a x          a x          a x                   a x
        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
               2            2            2                     2
   (9)  ----------------------------------------------------------
                3a x            a x           3a x           a x
         a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
                  2              2              2             2
                                                     Type: Expression Integer
--R
--R             3a x          a x          a x                   a x
--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
--R               2            2            2                     2
--R   (9)  ----------------------------------------------------------
--R                3a x            a x           3a x           a x
--R         a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
--R                  2              2              2             2
--R                                                     Type: Expression Integer
--E

--S 76
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                               %BG cosh(y + x) + %BG cosh(y - x)
   (10)  %BG cosh(x)cosh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BF cosh(y + x) + %BF cosh(y - x)
--I   (10)  %BF cosh(x)cosh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 77     14:576 Schaums and Axiom differ by a constant
gg:=coshcoshrule ff
 

         1
   (11)  -
         a
                                                     Type: Expression Integer
--R
--R         1
--R   (11)  -
--R         a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 78
aa:=integrate(x/(cosh(a*x)+1),x)
 

   (1)
       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
     + 
       2a x sinh(a x) + 2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R       2a x sinh(a x) + 2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 79
bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2))
 

                    a x              a x
        - 2log(cosh(---)) + a x tanh(---)
                     2                2
   (2)  ---------------------------------
                         2
                        a
                                                     Type: Expression Integer
--R
--R                    a x              a x
--R        - 2log(cosh(---)) + a x tanh(---)
--R                     2                2
--R   (2)  ---------------------------------
--R                         2
--R                        a
--R                                                     Type: Expression Integer
--E

--S 80
cc:=aa-bb
 

   (3)
       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
     + 
                                             a x
       (2sinh(a x) + 2cosh(a x) + 2)log(cosh(---))
                                              2
     + 
                                                   a x
       (- a x sinh(a x) - a x cosh(a x) - a x)tanh(---) + 2a x sinh(a x)
                                                    2
     + 
       2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) + a
                                                     Type: Expression Integer
--R
--R   (3)
--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                             a x
--R       (2sinh(a x) + 2cosh(a x) + 2)log(cosh(---))
--R                                              2
--R     + 
--R                                                   a x
--R       (- a x sinh(a x) - a x cosh(a x) - a x)tanh(---) + 2a x sinh(a x)
--R                                                    2
--R     + 
--R       2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) + a
--R                                                     Type: Expression Integer
--E

--S 81
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 82
dd:=tanhrule cc
 

   (5)
                  a x                   a x                   a x
         (- 2cosh(---)sinh(a x) - 2cosh(---)cosh(a x) - 2cosh(---))
                   2                     2                     2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
              a x                   a x                   a x           a x
       (2cosh(---)sinh(a x) + 2cosh(---)cosh(a x) + 2cosh(---))log(cosh(---))
               2                     2                     2             2
     + 
                   a x              a x
       (- a x sinh(---) + 2a x cosh(---))sinh(a x)
                    2                2
     + 
                                   a x              a x
       (- a x cosh(a x) - a x)sinh(---) + 2a x cosh(---)cosh(a x)
                                    2                2
  /
      2     a x              2     a x              2     a x
     a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
             2                      2                      2
                                                     Type: Expression Integer
--R
--R   (5)
--R                  a x                   a x                   a x
--R         (- 2cosh(---)sinh(a x) - 2cosh(---)cosh(a x) - 2cosh(---))
--R                   2                     2                     2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R              a x                   a x                   a x           a x
--R       (2cosh(---)sinh(a x) + 2cosh(---)cosh(a x) + 2cosh(---))log(cosh(---))
--R               2                     2                     2             2
--R     + 
--R                   a x              a x
--R       (- a x sinh(---) + 2a x cosh(---))sinh(a x)
--R                    2                2
--R     + 
--R                                   a x              a x
--R       (- a x cosh(a x) - a x)sinh(---) + 2a x cosh(---)cosh(a x)
--R                                    2                2
--R  /
--R      2     a x              2     a x              2     a x
--R     a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
--R             2                      2                      2
--R                                                     Type: Expression Integer
--E

--S 83
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                              %BH cosh(y + x) + %BH cosh(y - x)
   (6)  %BH cosh(x)cosh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BG cosh(y + x) + %BG cosh(y - x)
--I   (6)  %BG cosh(x)cosh(y) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 84
ee:=coshcoshrule dd
 

   (7)
                  a x                   3a x          a x
         (- 4cosh(---)sinh(a x) - 2cosh(----) - 6cosh(---))
                   2                      2            2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
              a x                   3a x          a x           a x
       (4cosh(---)sinh(a x) + 2cosh(----) + 6cosh(---))log(cosh(---))
               2                      2            2             2
     + 
                    a x              a x
       (- 2a x sinh(---) + 4a x cosh(---))sinh(a x)
                     2                2
     + 
                                     a x              3a x              a x
       (- 2a x cosh(a x) - 2a x)sinh(---) + 2a x cosh(----) + 2a x cosh(---)
                                      2                 2                2
  /
       2     a x              2     3a x      2     a x
     2a cosh(---)sinh(a x) + a cosh(----) + 3a cosh(---)
              2                       2              2
                                                     Type: Expression Integer
--R
--R   (7)
--R                  a x                   3a x          a x
--R         (- 4cosh(---)sinh(a x) - 2cosh(----) - 6cosh(---))
--R                   2                      2            2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R              a x                   3a x          a x           a x
--R       (4cosh(---)sinh(a x) + 2cosh(----) + 6cosh(---))log(cosh(---))
--R               2                      2            2             2
--R     + 
--R                    a x              a x
--R       (- 2a x sinh(---) + 4a x cosh(---))sinh(a x)
--R                     2                2
--R     + 
--R                                     a x              3a x              a x
--R       (- 2a x cosh(a x) - 2a x)sinh(---) + 2a x cosh(----) + 2a x cosh(---)
--R                                      2                 2                2
--R  /
--R       2     a x              2     3a x      2     a x
--R     2a cosh(---)sinh(a x) + a cosh(----) + 3a cosh(---)
--R              2                       2              2
--R                                                     Type: Expression Integer
--E

--S 85
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BI sinh(y + x) - %BI sinh(y - x)
   (8)  %BI cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BH sinh(y + x) - %BH sinh(y - x)
--I   (8)  %BH cosh(y)sinh(x) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 86
ff:=sinhcoshrule ee
 

   (9)
                  3a x          a x          3a x          a x
         (- 2sinh(----) - 2sinh(---) - 2cosh(----) - 6cosh(---))
                    2            2             2            2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
              3a x          a x          3a x          a x           a x
       (2sinh(----) + 2sinh(---) + 2cosh(----) + 6cosh(---))log(cosh(---))
                2            2             2            2             2
     + 
                3a x              a x                      a x
       a x sinh(----) - 2a x sinh(---)sinh(a x) + a x sinh(---)
                  2                2                        2
     + 
                 3a x              a x
       2a x cosh(----) + 2a x cosh(---)
                   2                2
  /
      2     3a x     2     a x     2     3a x      2     a x
     a sinh(----) + a sinh(---) + a cosh(----) + 3a cosh(---)
              2             2              2              2
                                                     Type: Expression Integer
--R
--R   (9)
--R                  3a x          a x          3a x          a x
--R         (- 2sinh(----) - 2sinh(---) - 2cosh(----) - 6cosh(---))
--R                    2            2             2            2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R              3a x          a x          3a x          a x           a x
--R       (2sinh(----) + 2sinh(---) + 2cosh(----) + 6cosh(---))log(cosh(---))
--R                2            2             2            2             2
--R     + 
--R                3a x              a x                      a x
--R       a x sinh(----) - 2a x sinh(---)sinh(a x) + a x sinh(---)
--R                  2                2                        2
--R     + 
--R                 3a x              a x
--R       2a x cosh(----) + 2a x cosh(---)
--R                   2                2
--R  /
--R      2     3a x     2     a x     2     3a x      2     a x
--R     a sinh(----) + a sinh(---) + a cosh(----) + 3a cosh(---)
--R              2             2              2              2
--R                                                     Type: Expression Integer
--E

--S 87
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                               %BJ cosh(y + x) - %BJ cosh(y - x)
   (10)  %BJ sinh(x)sinh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BI cosh(y + x) - %BI cosh(y - x)
--I   (10)  %BI sinh(x)sinh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 88
gg:=sinhsinhrule ff
 

                                                       a x
         - 2log(sinh(a x) + cosh(a x) + 1) + 2log(cosh(---)) + a x
                                                        2
   (11)  ---------------------------------------------------------
                                      2
                                     a
                                                     Type: Expression Integer
--R
--R                                                       a x
--R         - 2log(sinh(a x) + cosh(a x) + 1) + 2log(cosh(---)) + a x
--R                                                        2
--R   (11)  ---------------------------------------------------------
--R                                      2
--R                                     a
--R                                                     Type: Expression Integer
--E

--S 89     14:577 Schaums and Axiom differ by a constant
complexNormalize gg
 

           2log(2)
   (12)  - -------
               2
              a
                                                     Type: Expression Integer
--R
--R           2log(2)
--R   (12)  - -------
--R               2
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 90
aa:=integrate(x/(cosh(a*x)-1),x)
 

   (1)
       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
     + 
       - 2a x sinh(a x) - 2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       - 2a x sinh(a x) - 2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91
bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2))
 

                  a x              a x
        2log(sinh(---)) - a x coth(---)
                   2                2
   (2)  -------------------------------
                        2
                       a
                                                     Type: Expression Integer
--R
--R                  a x              a x
--R        2log(sinh(---)) - a x coth(---)
--R                   2                2
--R   (2)  -------------------------------
--R                        2
--R                       a
--R                                                     Type: Expression Integer
--E

--S 92
cc:=aa-bb
 

   (3)
       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
     + 
                                               a x
       (- 2sinh(a x) - 2cosh(a x) + 2)log(sinh(---))
                                                2
     + 
                 a x                                               a x
       (a x coth(---) - 2a x)sinh(a x) + (a x cosh(a x) - a x)coth(---)
                  2                                                 2
     + 
       - 2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) - a
                                                     Type: Expression Integer
--R
--R   (3)
--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                               a x
--R       (- 2sinh(a x) - 2cosh(a x) + 2)log(sinh(---))
--R                                                2
--R     + 
--R                 a x                                               a x
--R       (a x coth(---) - 2a x)sinh(a x) + (a x cosh(a x) - a x)coth(---)
--R                  2                                                 2
--R     + 
--R       - 2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) - a
--R                                                     Type: Expression Integer
--E

--S 93
cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 

                   cosh(x)
   (4)  coth(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   cosh(x)
--R   (4)  coth(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 94
dd:=cothrule cc
 

   (5)
                a x                                  a x
         (2sinh(---)sinh(a x) + (2cosh(a x) - 2)sinh(---))
                 2                                    2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                a x                                    a x           a x
       (- 2sinh(---)sinh(a x) + (- 2cosh(a x) + 2)sinh(---))log(sinh(---))
                 2                                      2             2
     + 
                    a x             a x                                 a x
       (- 2a x sinh(---) + a x cosh(---))sinh(a x) - 2a x cosh(a x)sinh(---)
                     2               2                                   2
     + 
                a x                      a x
       a x cosh(---)cosh(a x) - a x cosh(---)
                 2                        2
  /
      2     a x               2             2      a x
     a sinh(---)sinh(a x) + (a cosh(a x) - a )sinh(---)
             2                                      2
                                                     Type: Expression Integer
--R
--R   (5)
--R                a x                                  a x
--R         (2sinh(---)sinh(a x) + (2cosh(a x) - 2)sinh(---))
--R                 2                                    2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                a x                                    a x           a x
--R       (- 2sinh(---)sinh(a x) + (- 2cosh(a x) + 2)sinh(---))log(sinh(---))
--R                 2                                      2             2
--R     + 
--R                    a x             a x                                 a x
--R       (- 2a x sinh(---) + a x cosh(---))sinh(a x) - 2a x cosh(a x)sinh(---)
--R                     2               2                                   2
--R     + 
--R                a x                      a x
--R       a x cosh(---)cosh(a x) - a x cosh(---)
--R                 2                        2
--R  /
--R      2     a x               2             2      a x
--R     a sinh(---)sinh(a x) + (a cosh(a x) - a )sinh(---)
--R             2                                      2
--R                                                     Type: Expression Integer
--E

--S 95
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BK sinh(y + x) - %BK sinh(y - x)
   (6)  %BK cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BJ sinh(y + x) - %BJ sinh(y - x)
--I   (6)  %BJ cosh(y)sinh(x) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 96
ee:=sinhcoshrule dd
 

   (7)
                3a x          a x                   a x
         (2sinh(----) + 4sinh(---)sinh(a x) - 6sinh(---))
                  2            2                     2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                3a x          a x                   a x           a x
       (- 2sinh(----) - 4sinh(---)sinh(a x) + 6sinh(---))log(sinh(---))
                  2            2                     2             2
     + 
                  3a x              a x                       a x
       - a x sinh(----) - 4a x sinh(---)sinh(a x) + 3a x sinh(---)
                    2                2                         2
     + 
                 a x                       a x
       2a x cosh(---)cosh(a x) - 2a x cosh(---)
                  2                         2
  /
      2     3a x      2     a x               2     a x
     a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
              2              2                       2
                                                     Type: Expression Integer
--R
--R   (7)
--R                3a x          a x                   a x
--R         (2sinh(----) + 4sinh(---)sinh(a x) - 6sinh(---))
--R                  2            2                     2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                3a x          a x                   a x           a x
--R       (- 2sinh(----) - 4sinh(---)sinh(a x) + 6sinh(---))log(sinh(---))
--R                  2            2                     2             2
--R     + 
--R                  3a x              a x                       a x
--R       - a x sinh(----) - 4a x sinh(---)sinh(a x) + 3a x sinh(---)
--R                    2                2                         2
--R     + 
--R                 a x                       a x
--R       2a x cosh(---)cosh(a x) - 2a x cosh(---)
--R                  2                         2
--R  /
--R      2     3a x      2     a x               2     a x
--R     a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
--R              2              2                       2
--R                                                     Type: Expression Integer
--E

--S 97
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %BL cosh(y + x) - %BL cosh(y - x)
   (8)  %BL sinh(x)sinh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BK cosh(y + x) - %BK cosh(y - x)
--I   (8)  %BK sinh(x)sinh(y) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 98
ff:=sinhsinhrule ee
 

   (9)
                3a x          a x          3a x          a x
         (2sinh(----) - 6sinh(---) + 2cosh(----) - 2cosh(---))
                  2            2             2            2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                3a x          a x          3a x          a x           a x
       (- 2sinh(----) + 6sinh(---) - 2cosh(----) + 2cosh(---))log(sinh(---))
                  2            2             2            2             2
     + 
                  3a x              a x              3a x
       - a x sinh(----) + 3a x sinh(---) - 2a x cosh(----)
                    2                2                 2
     + 
                 a x
       2a x cosh(---)cosh(a x)
                  2
  /
      2     3a x      2     a x     2     3a x     2     a x
     a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
              2              2              2             2
                                                     Type: Expression Integer
--R
--R   (9)
--R                3a x          a x          3a x          a x
--R         (2sinh(----) - 6sinh(---) + 2cosh(----) - 2cosh(---))
--R                  2            2             2            2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                3a x          a x          3a x          a x           a x
--R       (- 2sinh(----) + 6sinh(---) - 2cosh(----) + 2cosh(---))log(sinh(---))
--R                  2            2             2            2             2
--R     + 
--R                  3a x              a x              3a x
--R       - a x sinh(----) + 3a x sinh(---) - 2a x cosh(----)
--R                    2                2                 2
--R     + 
--R                 a x
--R       2a x cosh(---)cosh(a x)
--R                  2
--R  /
--R      2     3a x      2     a x     2     3a x     2     a x
--R     a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
--R              2              2              2             2
--R                                                     Type: Expression Integer
--E

--S 99
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                               %BM cosh(y + x) + %BM cosh(y - x)
   (10)  %BM cosh(x)cosh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BL cosh(y + x) + %BL cosh(y - x)
--I   (10)  %BL cosh(x)cosh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 100
gg:=coshcoshrule ff
 

                                                     a x
         2log(sinh(a x) + cosh(a x) - 1) - 2log(sinh(---)) - a x
                                                      2
   (11)  -------------------------------------------------------
                                     2
                                    a
                                                     Type: Expression Integer
--R
--R                                                     a x
--R         2log(sinh(a x) + cosh(a x) - 1) - 2log(sinh(---)) - a x
--R                                                      2
--R   (11)  -------------------------------------------------------
--R                                     2
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 101    14:578 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         2log(2)
   (12)  -------
             2
            a
                                                     Type: Expression Integer
--R
--R         2log(2)
--R   (12)  -------
--R             2
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 102
aa:=integrate(1/(cosh(a*x)+1)^2,x)
 

   (1)
     - 6sinh(a x) - 6cosh(a x) - 2
  /
                   3                               2
       3a sinh(a x)  + (9a cosh(a x) + 9a)sinh(a x)
     + 
                    2                                              3
       (9a cosh(a x)  + 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
     + 
                   2
       9a cosh(a x)  + 9a cosh(a x) + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     - 6sinh(a x) - 6cosh(a x) - 2
--R  /
--R                   3                               2
--R       3a sinh(a x)  + (9a cosh(a x) + 9a)sinh(a x)
--R     + 
--R                    2                                              3
--R       (9a cosh(a x)  + 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
--R     + 
--R                   2
--R       9a cosh(a x)  + 9a cosh(a x) + 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103
bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3
 

               a x 3         a x
        - tanh(---)  + 3tanh(---)
                2             2
   (2)  -------------------------
                    6a
                                                     Type: Expression Integer
--R
--R               a x 3         a x
--R        - tanh(---)  + 3tanh(---)
--R                2             2
--R   (2)  -------------------------
--R                    6a
--R                                                     Type: Expression Integer
--E

--S 104    14:579 Axiom cannot compute this integral
cc:=aa-bb
 

   (3)
                    3                            2
           sinh(a x)  + (3cosh(a x) + 3)sinh(a x)
         + 
                      2                                       3             2
           (3cosh(a x)  + 6cosh(a x) + 3)sinh(a x) + cosh(a x)  + 3cosh(a x)
         + 
           3cosh(a x) + 1
      *
              a x 3
         tanh(---)
               2
     + 
                       3                              2
           - 3sinh(a x)  + (- 9cosh(a x) - 9)sinh(a x)
         + 
                        2                                         3
           (- 9cosh(a x)  - 18cosh(a x) - 9)sinh(a x) - 3cosh(a x)
         + 
                       2
           - 9cosh(a x)  - 9cosh(a x) - 3
      *
              a x
         tanh(---)
               2
     + 
       - 12sinh(a x) - 12cosh(a x) - 4
  /
                   3                                 2
       6a sinh(a x)  + (18a cosh(a x) + 18a)sinh(a x)
     + 
                     2                                               3
       (18a cosh(a x)  + 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
     + 
                    2
       18a cosh(a x)  + 18a cosh(a x) + 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R                    3                            2
--R           sinh(a x)  + (3cosh(a x) + 3)sinh(a x)
--R         + 
--R                      2                                       3             2
--R           (3cosh(a x)  + 6cosh(a x) + 3)sinh(a x) + cosh(a x)  + 3cosh(a x)
--R         + 
--R           3cosh(a x) + 1
--R      *
--R              a x 3
--R         tanh(---)
--R               2
--R     + 
--R                       3                              2
--R           - 3sinh(a x)  + (- 9cosh(a x) - 9)sinh(a x)
--R         + 
--R                        2                                         3
--R           (- 9cosh(a x)  - 18cosh(a x) - 9)sinh(a x) - 3cosh(a x)
--R         + 
--R                       2
--R           - 9cosh(a x)  - 9cosh(a x) - 3
--R      *
--R              a x
--R         tanh(---)
--R               2
--R     + 
--R       - 12sinh(a x) - 12cosh(a x) - 4
--R  /
--R                   3                                 2
--R       6a sinh(a x)  + (18a cosh(a x) + 18a)sinh(a x)
--R     + 
--R                     2                                               3
--R       (18a cosh(a x)  + 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
--R     + 
--R                    2
--R       18a cosh(a x)  + 18a cosh(a x) + 6a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 105
aa:=integrate(1/(cosh(a*x)-1)^2,x)
 

   (1)
     - 6sinh(a x) - 6cosh(a x) + 2
  /
                   3                               2
       3a sinh(a x)  + (9a cosh(a x) - 9a)sinh(a x)
     + 
                    2                                              3
       (9a cosh(a x)  - 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
     + 
                     2
       - 9a cosh(a x)  + 9a cosh(a x) - 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     - 6sinh(a x) - 6cosh(a x) + 2
--R  /
--R                   3                               2
--R       3a sinh(a x)  + (9a cosh(a x) - 9a)sinh(a x)
--R     + 
--R                    2                                              3
--R       (9a cosh(a x)  - 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
--R     + 
--R                     2
--R       - 9a cosh(a x)  + 9a cosh(a x) - 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 106
bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
 

               a x 3         a x
        - coth(---)  + 3coth(---)
                2             2
   (2)  -------------------------
                    6a
                                                     Type: Expression Integer
--R
--R               a x 3         a x
--R        - coth(---)  + 3coth(---)
--R                2             2
--R   (2)  -------------------------
--R                    6a
--R                                                     Type: Expression Integer
--E

--S 107    14:580 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
             a x 3         a x           3
       (coth(---)  - 3coth(---))sinh(a x)
              2             2
     + 
                             a x 3                          a x           2
       ((3cosh(a x) - 3)coth(---)  + (- 9cosh(a x) + 9)coth(---))sinh(a x)
                              2                              2
     + 
                      2                       a x 3
           (3cosh(a x)  - 6cosh(a x) + 3)coth(---)
                                               2
         + 
                        2                        a x
           (- 9cosh(a x)  + 18cosh(a x) - 9)coth(---) - 12
                                                  2
      *
         sinh(a x)
     + 
                 3             2                       a x 3
       (cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1)coth(---)
                                                        2
     + 
                  3             2                       a x
     (- 3cosh(a x)  + 9cosh(a x)  - 9cosh(a x) + 3)coth(---) - 12cosh(a x) + 4
                                                         2
  /
                   3                                 2
       6a sinh(a x)  + (18a cosh(a x) - 18a)sinh(a x)
     + 
                     2                                               3
       (18a cosh(a x)  - 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
     + 
                      2
       - 18a cosh(a x)  + 18a cosh(a x) - 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R             a x 3         a x           3
--R       (coth(---)  - 3coth(---))sinh(a x)
--R              2             2
--R     + 
--R                             a x 3                          a x           2
--R       ((3cosh(a x) - 3)coth(---)  + (- 9cosh(a x) + 9)coth(---))sinh(a x)
--R                              2                              2
--R     + 
--R                      2                       a x 3
--R           (3cosh(a x)  - 6cosh(a x) + 3)coth(---)
--R                                               2
--R         + 
--R                        2                        a x
--R           (- 9cosh(a x)  + 18cosh(a x) - 9)coth(---) - 12
--R                                                  2
--R      *
--R         sinh(a x)
--R     + 
--R                 3             2                       a x 3
--R       (cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1)coth(---)
--R                                                        2
--R     + 
--R                  3             2                       a x
--R     (- 3cosh(a x)  + 9cosh(a x)  - 9cosh(a x) + 3)coth(---) - 12cosh(a x) + 4
--R                                                         2
--R  /
--R                   3                                 2
--R       6a sinh(a x)  + (18a cosh(a x) - 18a)sinh(a x)
--R     + 
--R                     2                                               3
--R       (18a cosh(a x)  - 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
--R     + 
--R                      2
--R       - 18a cosh(a x)  + 18a cosh(a x) - 6a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 108
aa:=integrate(1/(p+q*cosh(a*x)),x)
 

   (1)
   [
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
    /
         +---------+
         |   2    2
       a\|- q  + p
     ,
                                          +-------+
                                          | 2    2
          (q sinh(a x) + q cosh(a x) + p)\|q  - p
    2atan(-----------------------------------------)
                            2    2
                           q  - p
    ------------------------------------------------]
                         +-------+
                         | 2    2
                       a\|q  - p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R    /
--R         +---------+
--R         |   2    2
--R       a\|- q  + p
--R     ,
--R                                          +-------+
--R                                          | 2    2
--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R    2atan(-----------------------------------------)
--R                            2    2
--R                           q  - p
--R    ------------------------------------------------]
--R                         +-------+
--R                         | 2    2
--R                       a\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 109
bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2))
 

                  a x
              q %e    + p
        2atan(-----------)
                +-------+
                | 2    2
               \|q  - p
   (2)  ------------------
              +-------+
              | 2    2
            a\|q  - p
                                                     Type: Expression Integer
--R
--R                  a x
--R              q %e    + p
--R        2atan(-----------)
--R                +-------+
--R                | 2    2
--R               \|q  - p
--R   (2)  ------------------
--R              +-------+
--R              | 2    2
--R            a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 110
bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2-q^2)))
 

               +---------+
               |   2    2        a x
            - \|- q  + p   + q %e    + p
        log(----------------------------)
              +---------+
              |   2    2        a x
             \|- q  + p   + q %e    + p
   (3)  ---------------------------------
                    +---------+
                    |   2    2
                  a\|- q  + p
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2        a x
--R            - \|- q  + p   + q %e    + p
--R        log(----------------------------)
--R              +---------+
--R              |   2    2        a x
--R             \|- q  + p   + q %e    + p
--R   (3)  ---------------------------------
--R                    +---------+
--R                    |   2    2
--R                  a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 111
cc1:=aa.1-bb1
 

   (4)
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
           +---------+         a x
           |   2    2      q %e    + p
       - 2\|- q  + p  atan(-----------)
                             +-------+
                             | 2    2
                            \|q  - p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R           +---------+         a x
--R           |   2    2      q %e    + p
--R       - 2\|- q  + p  atan(-----------)
--R                             +-------+
--R                             | 2    2
--R                            \|q  - p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 112
cc2:=aa.2-bb1
 

                                              +-------+
                                              | 2    2               a x
              (q sinh(a x) + q cosh(a x) + p)\|q  - p            q %e    + p
        2atan(-----------------------------------------) - 2atan(-----------)
                                2    2                             +-------+
                               q  - p                              | 2    2
                                                                  \|q  - p
   (5)  ---------------------------------------------------------------------
                                       +-------+
                                       | 2    2
                                     a\|q  - p
                                                     Type: Expression Integer
--R
--R                                              +-------+
--R                                              | 2    2               a x
--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p            q %e    + p
--R        2atan(-----------------------------------------) - 2atan(-----------)
--R                                2    2                             +-------+
--R                               q  - p                              | 2    2
--R                                                                  \|q  - p
--R   (5)  ---------------------------------------------------------------------
--R                                       +-------+
--R                                       | 2    2
--R                                     a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 113
cc3:=aa.1-bb2
 

   (6)
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
     + 
                +---------+
                |   2    2        a x
             - \|- q  + p   + q %e    + p
       - log(----------------------------)
               +---------+
               |   2    2        a x
              \|- q  + p   + q %e    + p
  /
       +---------+
       |   2    2
     a\|- q  + p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R     + 
--R                +---------+
--R                |   2    2        a x
--R             - \|- q  + p   + q %e    + p
--R       - log(----------------------------)
--R               +---------+
--R               |   2    2        a x
--R              \|- q  + p   + q %e    + p
--R  /
--R       +---------+
--R       |   2    2
--R     a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 114    14:581 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (7)
                          +---------+
          +-------+       |   2    2        a x
          | 2    2     - \|- q  + p   + q %e    + p
       - \|q  - p  log(----------------------------)
                         +---------+
                         |   2    2        a x
                        \|- q  + p   + q %e    + p
     + 
                                                         +-------+
         +---------+                                     | 2    2
         |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       2\|- q  + p  atan(-----------------------------------------)
                                           2    2
                                          q  - p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                          +---------+
--R          +-------+       |   2    2        a x
--R          | 2    2     - \|- q  + p   + q %e    + p
--R       - \|q  - p  log(----------------------------)
--R                         +---------+
--R                         |   2    2        a x
--R                        \|- q  + p   + q %e    + p
--R     + 
--R                                                         +-------+
--R         +---------+                                     | 2    2
--R         |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       2\|- q  + p  atan(-----------------------------------------)
--R                                           2    2
--R                                          q  - p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 115
aa:=integrate(1/(p+q*cosh(a*x))^2,x)
 

   (1)
   [
                          2                       2                          2
             p q sinh(a x)  + (2p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
           + 
               2
             2p cosh(a x) + p q
        *
           log
                       2         2      2
                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                    + 
                       2         2                     2     2
                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
                 *
                     +---------+
                     |   2    2
                    \|- q  + p
                + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
             /
                             2                                             2
                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                + 
                  2p cosh(a x) + q
       + 
                                              +---------+
                                              |   2    2
         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|- q  + p
    /
               3      2           2
           (a q  - a p q)sinh(a x)
         + 
                 3       2                    2       3
           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
         + 
               3      2           2          2       3                3      2
           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
      *
          +---------+
          |   2    2
         \|- q  + p
     ,

                             2                         2
             - 2p q sinh(a x)  + (- 4p q cosh(a x) - 4p )sinh(a x)
           + 
                             2     2
             - 2p q cosh(a x)  - 4p cosh(a x) - 2p q
        *
                                                +-------+
                                                | 2    2
                (q sinh(a x) + q cosh(a x) + p)\|q  - p
           atan(-----------------------------------------)
                                  2    2
                                 q  - p
       + 
                                              +-------+
                                              | 2    2
         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|q  - p
    /
               3      2           2
           (a q  - a p q)sinh(a x)
         + 
                 3       2                    2       3
           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
         + 
               3      2           2          2       3                3      2
           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
      *
          +-------+
          | 2    2
         \|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                          2                       2                          2
--R             p q sinh(a x)  + (2p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R           + 
--R               2
--R             2p cosh(a x) + p q
--R        *
--R           log
--R                       2         2      2
--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                    + 
--R                       2         2                     2     2
--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
--R                 *
--R                     +---------+
--R                     |   2    2
--R                    \|- q  + p
--R                + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R             /
--R                             2                                             2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                + 
--R                  2p cosh(a x) + q
--R       + 
--R                                              +---------+
--R                                              |   2    2
--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|- q  + p
--R    /
--R               3      2           2
--R           (a q  - a p q)sinh(a x)
--R         + 
--R                 3       2                    2       3
--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
--R         + 
--R               3      2           2          2       3                3      2
--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
--R      *
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R     ,
--R
--R                             2                         2
--R             - 2p q sinh(a x)  + (- 4p q cosh(a x) - 4p )sinh(a x)
--R           + 
--R                             2     2
--R             - 2p q cosh(a x)  - 4p cosh(a x) - 2p q
--R        *
--R                                                +-------+
--R                                                | 2    2
--R                (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R           atan(-----------------------------------------)
--R                                  2    2
--R                                 q  - p
--R       + 
--R                                              +-------+
--R                                              | 2    2
--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|q  - p
--R    /
--R               3      2           2
--R           (a q  - a p q)sinh(a x)
--R         + 
--R                 3       2                    2       3
--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
--R         + 
--R               3      2           2          2       3                3      2
--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 116
t1:=integrate(1/(p+q*cosh(a*x)),x)
 

   (2)
   [
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
    /
         +---------+
         |   2    2
       a\|- q  + p
     ,
                                          +-------+
                                          | 2    2
          (q sinh(a x) + q cosh(a x) + p)\|q  - p
    2atan(-----------------------------------------)
                            2    2
                           q  - p
    ------------------------------------------------]
                         +-------+
                         | 2    2
                       a\|q  - p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R    /
--R         +---------+
--R         |   2    2
--R       a\|- q  + p
--R     ,
--R                                          +-------+
--R                                          | 2    2
--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R    2atan(-----------------------------------------)
--R                            2    2
--R                           q  - p
--R    ------------------------------------------------]
--R                         +-------+
--R                         | 2    2
--R                       a\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 117
bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1
 

   (3)
                             2
         (- p q cosh(a x) - p )
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                   +---------+
                   |   2    2
       q sinh(a x)\|- q  + p
  /
                                               +---------+
          3      2                   2      3  |   2    2
     ((a q  - a p q)cosh(a x) + a p q  - a p )\|- q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                             2
--R         (- p q cosh(a x) - p )
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                   +---------+
--R                   |   2    2
--R       q sinh(a x)\|- q  + p
--R  /
--R                                               +---------+
--R          3      2                   2      3  |   2    2
--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 118
bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2
 

   (4)
                                                                    +-------+
                                                                    | 2    2
                             2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       (- 2p q cosh(a x) - 2p )atan(-----------------------------------------)
                                                      2    2
                                                     q  - p
     + 
                   +-------+
                   | 2    2
       q sinh(a x)\|q  - p
  /
                                               +-------+
          3      2                   2      3  | 2    2
     ((a q  - a p q)cosh(a x) + a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                    +-------+
--R                                                                    | 2    2
--R                             2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       (- 2p q cosh(a x) - 2p )atan(-----------------------------------------)
--R                                                      2    2
--R                                                     q  - p
--R     + 
--R                   +-------+
--R                   | 2    2
--R       q sinh(a x)\|q  - p
--R  /
--R                                               +-------+
--R          3      2                   2      3  | 2    2
--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 119
cc1:=aa.1-bb1
 

   (5)
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
              2         3        2                          2
           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
         + 
               2         2                     2     2
           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
         + 
                           2        2     2
           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
      *
          +---------+
          |   2    2
         \|- q  + p
  /
              4      2 2                  3      3           2
         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
       + 
                  4       2 2          2          3       3                  2 2
             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
           + 
                   4
             - 2a p
        *
           sinh(a x)
       + 
             4      2 2          3          3       3           2
         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
       + 
             4      2 2       4                  3      3
         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
    *
        +---------+
        |   2    2
       \|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R              2         3        2                          2
--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R               2         2                     2     2
--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
--R         + 
--R                           2        2     2
--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
--R      *
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R  /
--R              4      2 2                  3      3           2
--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R       + 
--R                  4       2 2          2          3       3                  2 2
--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R           + 
--R                   4
--R             - 2a p
--R        *
--R           sinh(a x)
--R       + 
--R             4      2 2          3          3       3           2
--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R       + 
--R             4      2 2       4                  3      3
--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R    *
--R        +---------+
--R        |   2    2
--R       \|- q  + p
--R                                                     Type: Expression Integer
--E

--S 120
cc2:=aa.2-bb1
 

   (6)
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                  2              2           2
           (- 2p q cosh(a x) - 2p q)sinh(a x)
         + 
                  2         2     2                3                 2         3
           (- 4p q cosh(a x)  - 8p q cosh(a x) - 4p )sinh(a x) - 2p q cosh(a x)
         + 
               2           2          2     3               2
           - 6p q cosh(a x)  + (- 2p q  - 4p )cosh(a x) - 2p q
      *
                                                          +-------+
          +---------+                                     | 2    2
          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
         \|- q  + p  atan(-----------------------------------------)
                                            2    2
                                           q  - p
     + 
              2         3        2                          2
           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
         + 
               2         2                     2     2
           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
         + 
                           2        2     2
           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
      *
          +---------+ +-------+
          |   2    2  | 2    2
         \|- q  + p  \|q  - p
  /
              4      2 2                  3      3           2
         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
       + 
                  4       2 2          2          3       3                  2 2
             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
           + 
                   4
             - 2a p
        *
           sinh(a x)
       + 
             4      2 2          3          3       3           2
         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
       + 
             4      2 2       4                  3      3
         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
    *
        +---------+ +-------+
        |   2    2  | 2    2
       \|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                  2              2           2
--R           (- 2p q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R                  2         2     2                3                 2         3
--R           (- 4p q cosh(a x)  - 8p q cosh(a x) - 4p )sinh(a x) - 2p q cosh(a x)
--R         + 
--R               2           2          2     3               2
--R           - 6p q cosh(a x)  + (- 2p q  - 4p )cosh(a x) - 2p q
--R      *
--R                                                          +-------+
--R          +---------+                                     | 2    2
--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R         \|- q  + p  atan(-----------------------------------------)
--R                                            2    2
--R                                           q  - p
--R     + 
--R              2         3        2                          2
--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R               2         2                     2     2
--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
--R         + 
--R                           2        2     2
--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
--R      *
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R         \|- q  + p  \|q  - p
--R  /
--R              4      2 2                  3      3           2
--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R       + 
--R                  4       2 2          2          3       3                  2 2
--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R           + 
--R                   4
--R             - 2a p
--R        *
--R           sinh(a x)
--R       + 
--R             4      2 2          3          3       3           2
--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R       + 
--R             4      2 2       4                  3      3
--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R    *
--R        +---------+ +-------+
--R        |   2    2  | 2    2
--R       \|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 121
cc3:=aa.1-bb2
 

   (7)
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                2              2           2
           (2p q cosh(a x) + 2p q)sinh(a x)
         + 
                2         2     2                3                 2         3
           (4p q cosh(a x)  + 8p q cosh(a x) + 4p )sinh(a x) + 2p q cosh(a x)
         + 
             2           2        2     3               2
           6p q cosh(a x)  + (2p q  + 4p )cosh(a x) + 2p q
      *
                                                          +-------+
          +---------+                                     | 2    2
          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
         \|- q  + p  atan(-----------------------------------------)
                                            2    2
                                           q  - p
     + 
              2         3        2                          2
           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
         + 
               2         2                     2     2
           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
         + 
                           2        2     2
           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
      *
          +---------+ +-------+
          |   2    2  | 2    2
         \|- q  + p  \|q  - p
  /
              4      2 2                  3      3           2
         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
       + 
                  4       2 2          2          3       3                  2 2
             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
           + 
                   4
             - 2a p
        *
           sinh(a x)
       + 
             4      2 2          3          3       3           2
         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
       + 
             4      2 2       4                  3      3
         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
    *
        +---------+ +-------+
        |   2    2  | 2    2
       \|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                2              2           2
--R           (2p q cosh(a x) + 2p q)sinh(a x)
--R         + 
--R                2         2     2                3                 2         3
--R           (4p q cosh(a x)  + 8p q cosh(a x) + 4p )sinh(a x) + 2p q cosh(a x)
--R         + 
--R             2           2        2     3               2
--R           6p q cosh(a x)  + (2p q  + 4p )cosh(a x) + 2p q
--R      *
--R                                                          +-------+
--R          +---------+                                     | 2    2
--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R         \|- q  + p  atan(-----------------------------------------)
--R                                            2    2
--R                                           q  - p
--R     + 
--R              2         3        2                          2
--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R               2         2                     2     2
--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
--R         + 
--R                           2        2     2
--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
--R      *
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R         \|- q  + p  \|q  - p
--R  /
--R              4      2 2                  3      3           2
--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R       + 
--R                  4       2 2          2          3       3                  2 2
--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R           + 
--R                   4
--R             - 2a p
--R        *
--R           sinh(a x)
--R       + 
--R             4      2 2          3          3       3           2
--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R       + 
--R             4      2 2       4                  3      3
--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R    *
--R        +---------+ +-------+
--R        |   2    2  | 2    2
--R       \|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 122    14:582 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (8)
          2         3        2                          2
       - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
     + 
           2         2                     2     2                           2
       (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x) - 2p q cosh(a x)
     + 
            2     2
       (- 2q  - 2p )cosh(a x) - 2p q
  /
            4      2 2                  3      3           2
       ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
     + 
                4       2 2          2          3       3                  2 2
           (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
         + 
                 4
           - 2a p
      *
         sinh(a x)
     + 
           4      2 2          3          3       3           2
       (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
     + 
           4      2 2       4                  3      3
       (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
                                                     Type: Expression Integer
--R
--R   (8)
--R          2         3        2                          2
--R       - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R     + 
--R           2         2                     2     2                           2
--R       (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x) - 2p q cosh(a x)
--R     + 
--R            2     2
--R       (- 2q  - 2p )cosh(a x) - 2p q
--R  /
--R            4      2 2                  3      3           2
--R       ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R     + 
--R                4       2 2          2          3       3                  2 2
--R           (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R         + 
--R                 4
--R           - 2a p
--R      *
--R         sinh(a x)
--R     + 
--R           4      2 2          3          3       3           2
--R       (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R     + 
--R           4      2 2       4                  3      3
--R       (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 123
aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
 

   (1)
   [
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  - 4p )cosh(a x)  + q
    /
            +---------+
            |   2    2
       2a p\|- q  + p
     ,

     -
          atan
                      2         2     2                      2         2    2
                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
                   + 
                         2
                     - 2p
              *
                  +-------+
                  | 2    2
                 \|q  - p
            /
                   2     3
               2p q  - 2p
       /
              +-------+
              | 2    2
          a p\|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  - 4p )cosh(a x)  + q
--R    /
--R            +---------+
--R            |   2    2
--R       2a p\|- q  + p
--R     ,
--R
--R     -
--R          atan
--R                      2         2     2                      2         2    2
--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
--R                   + 
--R                         2
--R                     - 2p
--R              *
--R                  +-------+
--R                  | 2    2
--R                 \|q  - p
--R            /
--R                   2     3
--R               2p q  - 2p
--R       /
--R              +-------+
--R              | 2    2
--R          a p\|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 124
bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p^2-q^2)))
 

               +---------+
               |   2    2
            - \|- q  + p   - p tanh(a x)
        log(----------------------------)
              +---------+
              |   2    2
             \|- q  + p   - p tanh(a x)
   (2)  ---------------------------------
                      +---------+
                      |   2    2
                 2a p\|- q  + p
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R            - \|- q  + p   - p tanh(a x)
--R        log(----------------------------)
--R              +---------+
--R              |   2    2
--R             \|- q  + p   - p tanh(a x)
--R   (2)  ---------------------------------
--R                      +---------+
--R                      |   2    2
--R                 2a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 125
bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2))
 

               p tanh(a x)
          atan(-----------)
                 +-------+
                 | 2    2
                \|q  - p
   (3)  - -----------------
                +-------+
                | 2    2
            a p\|q  - p
                                                     Type: Expression Integer
--R
--R               p tanh(a x)
--R          atan(-----------)
--R                 +-------+
--R                 | 2    2
--R                \|q  - p
--R   (3)  - -----------------
--R                +-------+
--R                | 2    2
--R            a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 126
cc1:=aa.1-bb1
 

   (4)
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  - 4p )cosh(a x)  + q
     + 
                +---------+
                |   2    2
             - \|- q  + p   - p tanh(a x)
       - log(----------------------------)
               +---------+
               |   2    2
              \|- q  + p   - p tanh(a x)
  /
          +---------+
          |   2    2
     2a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  - 4p )cosh(a x)  + q
--R     + 
--R                +---------+
--R                |   2    2
--R             - \|- q  + p   - p tanh(a x)
--R       - log(----------------------------)
--R               +---------+
--R               |   2    2
--R              \|- q  + p   - p tanh(a x)
--R  /
--R          +---------+
--R          |   2    2
--R     2a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 127
cc2:=aa.2-bb1
 

   (5)
                          +---------+
          +-------+       |   2    2
          | 2    2     - \|- q  + p   - p tanh(a x)
       - \|q  - p  log(----------------------------)
                         +---------+
                         |   2    2
                        \|- q  + p   - p tanh(a x)
     + 
       -
              +---------+
              |   2    2
            2\|- q  + p
         *
            atan
                      2         2     2                      2         2    2
                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
                   + 
                         2
                     - 2p
                *
                    +-------+
                    | 2    2
                   \|q  - p
              /
                     2     3
                 2p q  - 2p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                          +---------+
--R          +-------+       |   2    2
--R          | 2    2     - \|- q  + p   - p tanh(a x)
--R       - \|q  - p  log(----------------------------)
--R                         +---------+
--R                         |   2    2
--R                        \|- q  + p   - p tanh(a x)
--R     + 
--R       -
--R              +---------+
--R              |   2    2
--R            2\|- q  + p
--R         *
--R            atan
--R                      2         2     2                      2         2    2
--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
--R                   + 
--R                         2
--R                     - 2p
--R                *
--R                    +-------+
--R                    | 2    2
--R                   \|q  - p
--R              /
--R                     2     3
--R                 2p q  - 2p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 128
cc3:=aa.1-bb2
 

   (6)
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     4         4     4                  3
                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
                  + 
                       4         2     4     2 2          2
                    (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
                  + 
                       4         3      4     2 2
                    (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
                  + 
                     4         4      4     2 2          2    4     2 2     4
                    q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                       4     3 2          2
                (- 4p q  + 4p q )sinh(a x)
              + 
                       4     3 2
                (- 8p q  + 8p q )cosh(a x)sinh(a x)
              + 
                       4     3 2          2       4      3 2     5
                (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
           /
                 2         4     2                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   2         2     2     2          2
                (6q cosh(a x)  + 2q  - 4p )sinh(a x)
              + 
                   2         3      2     2                        2         4
                (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                   2     2          2    2
                (2q  - 4p )cosh(a x)  + q
     + 
         +---------+
         |   2    2      p tanh(a x)
       2\|- q  + p  atan(-----------)
                           +-------+
                           | 2    2
                          \|q  - p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     4         4     4                  3
--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                  + 
--R                       4         2     4     2 2          2
--R                    (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
--R                  + 
--R                       4         3      4     2 2
--R                    (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
--R                  + 
--R                     4         4      4     2 2          2    4     2 2     4
--R                    q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                       4     3 2          2
--R                (- 4p q  + 4p q )sinh(a x)
--R              + 
--R                       4     3 2
--R                (- 8p q  + 8p q )cosh(a x)sinh(a x)
--R              + 
--R                       4     3 2          2       4      3 2     5
--R                (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R           /
--R                 2         4     2                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   2         2     2     2          2
--R                (6q cosh(a x)  + 2q  - 4p )sinh(a x)
--R              + 
--R                   2         3      2     2                        2         4
--R                (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                   2     2          2    2
--R                (2q  - 4p )cosh(a x)  + q
--R     + 
--R         +---------+
--R         |   2    2      p tanh(a x)
--R       2\|- q  + p  atan(-----------)
--R                           +-------+
--R                           | 2    2
--R                          \|q  - p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 129    14:583 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (7)
       -
          atan
                      2         2     2                      2         2    2
                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
                   + 
                         2
                     - 2p
              *
                  +-------+
                  | 2    2
                 \|q  - p
            /
                   2     3
               2p q  - 2p
     + 
            p tanh(a x)
       atan(-----------)
              +-------+
              | 2    2
             \|q  - p
  /
         +-------+
         | 2    2
     a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R       -
--R          atan
--R                      2         2     2                      2         2    2
--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
--R                   + 
--R                         2
--R                     - 2p
--R              *
--R                  +-------+
--R                  | 2    2
--R                 \|q  - p
--R            /
--R                   2     3
--R               2p q  - 2p
--R     + 
--R            p tanh(a x)
--R       atan(-----------)
--R              +-------+
--R              | 2    2
--R             \|q  - p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  - p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 130
aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
 

   (1)
     log
                 4         4     4                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   4         2     4     2 2          2
                (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
              + 
                   4         3      4     2 2                        4         4
                (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                   4     2 2          2    4     2 2     4
                (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                   4     3 2          2          4     3 2
            (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
          + 
                   4     3 2          2       4      3 2     5
            (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
       /
             2         4     2                  3
            q sinh(a x)  + 4q cosh(a x)sinh(a x)
          + 
               2         2     2     2          2
            (6q cosh(a x)  + 2q  + 4p )sinh(a x)
          + 
               2         3      2     2                        2         4
            (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
          + 
               2     2          2    2
            (2q  + 4p )cosh(a x)  + q
  /
          +-------+
          | 2    2
     2a p\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     log
--R                 4         4     4                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   4         2     4     2 2          2
--R                (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
--R              + 
--R                   4         3      4     2 2                        4         4
--R                (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                   4     2 2          2    4     2 2     4
--R                (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                   4     3 2          2          4     3 2
--R            (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
--R          + 
--R                   4     3 2          2       4      3 2     5
--R            (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
--R       /
--R             2         4     2                  3
--R            q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R          + 
--R               2         2     2     2          2
--R            (6q cosh(a x)  + 2q  + 4p )sinh(a x)
--R          + 
--R               2         3      2     2                        2         4
--R            (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R          + 
--R               2     2          2    2
--R            (2q  + 4p )cosh(a x)  + q
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 131
bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p^2+q^2)))
 

               +-------+
               | 2    2
            - \|q  + p   - p tanh(a x)
        log(--------------------------)
              +-------+
              | 2    2
             \|q  + p   - p tanh(a x)
   (2)  -------------------------------
                      +-------+
                      | 2    2
                 2a p\|q  + p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R            - \|q  + p   - p tanh(a x)
--R        log(--------------------------)
--R              +-------+
--R              | 2    2
--R             \|q  + p   - p tanh(a x)
--R   (2)  -------------------------------
--R                      +-------+
--R                      | 2    2
--R                 2a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 132
bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2))
 

             p tanh(a x)
        atan(-----------)
               +-------+
               | 2    2
              \|q  + p
   (3)  -----------------
              +-------+
              | 2    2
          a p\|q  + p
                                                     Type: Expression Integer
--R
--R             p tanh(a x)
--R        atan(-----------)
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R   (3)  -----------------
--R              +-------+
--R              | 2    2
--R          a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 133
cc1:=aa-bb1
 

   (4)
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
             *
                 +-------+
                 | 2    2
                \|q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  + 4p )cosh(a x)  + q
     + 
                +-------+
                | 2    2
             - \|q  + p   - p tanh(a x)
       - log(--------------------------)
               +-------+
               | 2    2
              \|q  + p   - p tanh(a x)
  /
          +-------+
          | 2    2
     2a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  + 4p )cosh(a x)  + q
--R     + 
--R                +-------+
--R                | 2    2
--R             - \|q  + p   - p tanh(a x)
--R       - log(--------------------------)
--R               +-------+
--R               | 2    2
--R              \|q  + p   - p tanh(a x)
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 134    14:584 Axiom cannot simplify this expression
cc2:=aa-bb2
 

   (5)
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
             *
                 +-------+
                 | 2    2
                \|q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  + 4p )cosh(a x)  + q
     + 
               p tanh(a x)
       - 2atan(-----------)
                 +-------+
                 | 2    2
                \|q  + p
  /
          +-------+
          | 2    2
     2a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  + 4p )cosh(a x)  + q
--R     + 
--R               p tanh(a x)
--R       - 2atan(-----------)
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 135    14:585 Axiom cannot compute this integral
aa:=integrate(x^m*cosh(a*x),x)
 

           x
         ++              m
   (1)   |   cosh(%N a)%N d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++              m
--I   (1)   |   cosh(%N a)%N d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 136    14:586 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)^n,x)
 

           x
         ++            n
   (1)   |   cosh(%N a) d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   cosh(%N a) d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 137    14:587 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)/x^n,x)
 

           x
         ++  cosh(%N a)
   (1)   |   ---------- d%N
        ++         n
                 %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cosh(%N a)
--I   (1)   |   ---------- d%N
--R        ++         n
--I                 %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 138    14:588 Axiom cannot compute this integral
aa:=integrate(1/cosh(a*x)^n,x)
 

           x
         ++       1
   (1)   |   ----------- d%N
        ++             n
             cosh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%N
--R        ++             n
--I             cosh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 139    14:589 Axiom cannot compute this integral
aa:=integrate(1/cosh(a*x)^n,x)
 

           x
         ++       1
   (1)   |   ----------- d%N
        ++             n
             cosh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%N
--R        ++             n
--I             cosh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to schaum18.output (2009/2/17, 17:58:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(cos(a*x),x)
 

        sin(a x)
   (1)  --------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sin(a x)
--R   (1)  --------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=sin(a*x)/a
 

        sin(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        sin(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E

--S 3      14:369 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 4
aa:=integrate(x*cos(a*x),x)
 

        a x sin(a x) + cos(a x)
   (1)  -----------------------
                    2
                   a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a x sin(a x) + cos(a x)
--R   (1)  -----------------------
--R                    2
--R                   a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5
bb:=cos(a*x)/a^2+(x*sin(a*x))/a
 

        a x sin(a x) + cos(a x)
   (2)  -----------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R        a x sin(a x) + cos(a x)
--R   (2)  -----------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E

--S 6      14:370 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 7
aa:=integrate(x^2*cos(a*x),x)
 

          2 2
        (a x  - 2)sin(a x) + 2a x cos(a x)
   (1)  ----------------------------------
                         3
                        a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2 2
--R        (a x  - 2)sin(a x) + 2a x cos(a x)
--R   (1)  ----------------------------------
--R                         3
--R                        a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8
bb:=(2*x)/a^2*cos(a*x)+(x^2/a-2/a^3)*sin(a*x)
 

          2 2
        (a x  - 2)sin(a x) + 2a x cos(a x)
   (2)  ----------------------------------
                         3
                        a
                                                     Type: Expression Integer
--R
--R          2 2
--R        (a x  - 2)sin(a x) + 2a x cos(a x)
--R   (2)  ----------------------------------
--R                         3
--R                        a
--R                                                     Type: Expression Integer
--E

--S 9      14:371 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(x^3*cos(a*x),x)
 

          3 3                      2 2
        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
   (1)  -------------------------------------------
                              4
                             a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          3 3                      2 2
--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
--R   (1)  -------------------------------------------
--R                              4
--R                             a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=((3*x^2)/a^2-6/a^4)*cos(a*x)+(x^3/a-(6*x)/a^3)*sin(a*x)
 

          3 3                      2 2
        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
   (2)  -------------------------------------------
                              4
                             a
                                                     Type: Expression Integer
--R
--R          3 3                      2 2
--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
--R   (2)  -------------------------------------------
--R                              4
--R                             a
--R                                                     Type: Expression Integer
--E

--S 12     14:372 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13     14:373 Schaums and Axiom agree by definition
aa:=integrate(cos(x)/x,x)
 

   (1)  Ci(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  Ci(x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 14     14:374 Axiom cannot compute this integral
aa:=integrate(cos(a*x)/x^2,x)
 

           x
         ++  cos(%I a)
   (1)   |   --------- d%I
        ++        2
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cos(%I a)
--I   (1)   |   --------- d%I
--R        ++        2
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(1/cos(a*x),x)
 

            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
        log(-----------------------) - log(-----------------------)
                  cos(a x) + 1                   cos(a x) + 1
   (1)  -----------------------------------------------------------
                                     a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R        log(-----------------------) - log(-----------------------)
--R                  cos(a x) + 1                   cos(a x) + 1
--R   (1)  -----------------------------------------------------------
--R                                     a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16
bb1:=1/a*log(sec(a*x)+tan(a*x))
 

        log(tan(a x) + sec(a x))
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R        log(tan(a x) + sec(a x))
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 17
bb2:=1/a*log(tan(%pi/4+(a*x)/2))
 

                2a x + %pi
        log(tan(----------))
                     4
   (3)  --------------------
                  a
                                                     Type: Expression Integer
--R
--R                2a x + %pi
--R        log(tan(----------))
--R                     4
--R   (3)  --------------------
--R                  a
--R                                                     Type: Expression Integer
--E

--S 18
cc1:=aa-bb1
 

   (4)
                                        sin(a x) + cos(a x) + 1
       - log(tan(a x) + sec(a x)) + log(-----------------------)
                                              cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                        sin(a x) + cos(a x) + 1
--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
--R                                              cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 19
cc2:=aa-bb2
 

   (5)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 20     14:375 Schaums and Axiom differ by a constant
complexNormalize cc1
 

        log(- 1)
   (6)  --------
            a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (6)  --------
--R            a
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 21     14:376 Axiom cannot compute this integral
aa:=integrate(x/cos(a*x),x)
 

           x
         ++      %I
   (1)   |   --------- d%I
        ++   cos(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   --------- d%I
--I        ++   cos(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 22
aa:=integrate(cos(a*x)^2,x)
 

        cos(a x)sin(a x) + a x
   (1)  ----------------------
                  2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cos(a x)sin(a x) + a x
--R   (1)  ----------------------
--R                  2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 23
bb:=x/2+sin(2*a*x)/(4*a)
 

        sin(2a x) + 2a x
   (2)  ----------------
               4a
                                                     Type: Expression Integer
--R
--R        sin(2a x) + 2a x
--R   (2)  ----------------
--R               4a
--R                                                     Type: Expression Integer
--E

--S 24
cc:=aa-bb
 

        - sin(2a x) + 2cos(a x)sin(a x)
   (3)  -------------------------------
                       4a
                                                     Type: Expression Integer
--R
--R        - sin(2a x) + 2cos(a x)sin(a x)
--R   (3)  -------------------------------
--R                       4a
--R                                                     Type: Expression Integer
--E

--S 25
cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
 

                           %S sin(b + a) - %S sin(b - a)
   (4)  %S cos(b)sin(a) == -----------------------------
                                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                           %M sin(b + a) - %M sin(b - a)
--I   (4)  %M cos(b)sin(a) == -----------------------------
--R                                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26     14:377 Schaums and Axiom agree
dd:=cossinrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 27
aa:=integrate(x*cos(a*x)^2,x)
 

                                        2    2 2
        2a x cos(a x)sin(a x) + cos(a x)  + a x
   (1)  ----------------------------------------
                             2
                           4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                        2    2 2
--R        2a x cos(a x)sin(a x) + cos(a x)  + a x
--R   (1)  ----------------------------------------
--R                             2
--R                           4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28
bb:=x^2/4+(x*sin(2*a*x))/(4*a)+cos(2*a*x)/(8*a^2)
 

                                       2 2
        2a x sin(2a x) + cos(2a x) + 2a x
   (2)  ----------------------------------
                          2
                        8a
                                                     Type: Expression Integer
--R
--R                                       2 2
--R        2a x sin(2a x) + cos(2a x) + 2a x
--R   (2)  ----------------------------------
--R                          2
--R                        8a
--R                                                     Type: Expression Integer
--E

--S 29
cc:=aa-bb
 

                                                                        2
        - 2a x sin(2a x) + 4a x cos(a x)sin(a x) - cos(2a x) + 2cos(a x)
   (3)  -----------------------------------------------------------------
                                         2
                                       8a
                                                     Type: Expression Integer
--R
--R                                                                        2
--R        - 2a x sin(2a x) + 4a x cos(a x)sin(a x) - cos(2a x) + 2cos(a x)
--R   (3)  -----------------------------------------------------------------
--R                                         2
--R                                       8a
--R                                                     Type: Expression Integer
--E

--S 30
cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
 

                           %T sin(b + a) - %T sin(b - a)
   (4)  %T cos(b)sin(a) == -----------------------------
                                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                           %N sin(b + a) - %N sin(b - a)
--I   (4)  %N cos(b)sin(a) == -----------------------------
--R                                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 31
dd:=cossinrule cc
 

                               2
        - cos(2a x) + 2cos(a x)
   (5)  ------------------------
                     2
                   8a
                                                     Type: Expression Integer
--R
--R                               2
--R        - cos(2a x) + 2cos(a x)
--R   (5)  ------------------------
--R                     2
--R                   8a
--R                                                     Type: Expression Integer
--E

--S 32
coscosrule:=rule(cos(a)*cos(b) == 1/2*(cos(a-b)+cos(a+b)))
 

                           %U cos(b + a) + %U cos(b - a)
   (6)  %U cos(a)cos(b) == -----------------------------
                                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                           %O cos(b + a) + %O cos(b - a)
--I   (6)  %O cos(a)cos(b) == -----------------------------
--I                                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 33
ee:=coscosrule dd
 

                               2
        - cos(2a x) + 2cos(a x)
   (7)  ------------------------
                     2
                   8a
                                                     Type: Expression Integer
--R
--R                               2
--R        - cos(2a x) + 2cos(a x)
--R   (7)  ------------------------
--R                     2
--R                   8a
--R                                                     Type: Expression Integer
--E

--S 34
cossqrrule1:=rule(cos(a)^2 == 1/2+1/2*cos(2*a))
 

              2    cos(2a) + 1
   (8)  cos(a)  == -----------
                        2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2    cos(2a) + 1
--R   (8)  cos(a)  == -----------
--R                        2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35     14:378 Schaums and Axiom differ by a constant
ff:=cossqrrule1 ee
 

         1
   (9)  ---
          2
        8a
                                                     Type: Expression Integer
--R
--R         1
--R   (9)  ---
--R          2
--R        8a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 36
aa:=integrate(cos(a*x)^3,x)
 

                 2
        (cos(a x)  + 2)sin(a x)
   (1)  -----------------------
                   3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2
--R        (cos(a x)  + 2)sin(a x)
--R   (1)  -----------------------
--R                   3a
--R                                          Type: Union(Expression Integer,...)
--E

--S 37
bb:=sin(a*x)/a-sin(a*x)^3/(3*a)
 

                  3
        - sin(a x)  + 3sin(a x)
   (2)  -----------------------
                   3a
                                                     Type: Expression Integer
--R
--R                  3
--R        - sin(a x)  + 3sin(a x)
--R   (2)  -----------------------
--R                   3a
--R                                                     Type: Expression Integer
--E 

--S 38
cc:=aa-bb
 

                3            2
        sin(a x)  + (cos(a x)  - 1)sin(a x)
   (3)  -----------------------------------
                         3a
                                                     Type: Expression Integer
--R
--R                3            2
--R        sin(a x)  + (cos(a x)  - 1)sin(a x)
--R   (3)  -----------------------------------
--R                         3a
--R                                                     Type: Expression Integer
--E

--S 39
cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
 

              2            2
   (4)  cos(a)  == - sin(a)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2            2
--R   (4)  cos(a)  == - sin(a)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 40     14:379 Schaums and Axiom agree
dd:=cossqrrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 41
aa:=integrate(cos(a*x)^4,x)
 

                  3
        (2cos(a x)  + 3cos(a x))sin(a x) + 3a x
   (1)  ---------------------------------------
                           8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  3
--R        (2cos(a x)  + 3cos(a x))sin(a x) + 3a x
--R   (1)  ---------------------------------------
--R                           8a
--R                                          Type: Union(Expression Integer,...)
--E

--S 42
bb:=(3*x)/8+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
 

        sin(4a x) + 8sin(2a x) + 12a x
   (2)  ------------------------------
                      32a
                                                     Type: Expression Integer
--R
--R        sin(4a x) + 8sin(2a x) + 12a x
--R   (2)  ------------------------------
--R                      32a
--R                                                     Type: Expression Integer
--E 

--S 43
cc:=aa-bb
 

                                             3
        - sin(4a x) - 8sin(2a x) + (8cos(a x)  + 12cos(a x))sin(a x)
   (3)  ------------------------------------------------------------
                                     32a
                                                     Type: Expression Integer
--R
--R                                             3
--R        - sin(4a x) - 8sin(2a x) + (8cos(a x)  + 12cos(a x))sin(a x)
--R   (3)  ------------------------------------------------------------
--R                                     32a
--R                                                     Type: Expression Integer
--E

--S 44     14:380 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 45
aa:=integrate(1/cos(a*x)^2,x)
 

         sin(a x)
   (1)  ----------
        a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         sin(a x)
--R   (1)  ----------
--R        a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 46
bb:=tan(a*x)/a
 

        tan(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        tan(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E 

--S 47
cc:=aa-bb
 

        - cos(a x)tan(a x) + sin(a x)
   (3)  -----------------------------
                  a cos(a x)
                                                     Type: Expression Integer
--R
--R        - cos(a x)tan(a x) + sin(a x)
--R   (3)  -----------------------------
--R                  a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 48
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 49     14:381 Schaums and Axiom agree
dd:=tanrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 50
aa:=integrate(1/cos(a*x)^3,x)
 

   (1)
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
                 2    sin(a x) - cos(a x) - 1
       - cos(a x) log(-----------------------) + sin(a x)
                            cos(a x) + 1
  /
                2
     2a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R                 2    sin(a x) - cos(a x) - 1
--R       - cos(a x) log(-----------------------) + sin(a x)
--R                            cos(a x) + 1
--R  /
--R                2
--R     2a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 51
bb:=sin(a*x)/(2*a*cos(a*x)^2)+1/(2*a)*log(tan(%pi/4+(a*x)/2))
 

                2        2a x + %pi
        cos(a x) log(tan(----------)) + sin(a x)
                              4
   (2)  ----------------------------------------
                                 2
                      2a cos(a x)
                                                     Type: Expression Integer
--R
--R                2        2a x + %pi
--R        cos(a x) log(tan(----------)) + sin(a x)
--R                              4
--R   (2)  ----------------------------------------
--R                                 2
--R                      2a cos(a x)
--R                                                     Type: Expression Integer
--E 

--S 52
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 53     14:382 Schaums and Axiom differ by a constant
complexNormalize cc
 

        log(- 1)
   (4)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (4)  --------
--R           2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 54
aa:=integrate(cos(a*x)*cos(p*x),x)
 

        p cos(a x)sin(p x) - a cos(p x)sin(a x)
   (1)  ---------------------------------------
                         2    2
                        p  - a
                                          Type: Union(Expression Integer,...)
--R
--R        p cos(a x)sin(p x) - a cos(p x)sin(a x)
--R   (1)  ---------------------------------------
--R                         2    2
--R                        p  - a
--R                                          Type: Union(Expression Integer,...)
--E

--S 55
bb:=(sin((a-p)*x))/(2*(a-p))+(sin((a+p)*x))/(2*(a+p))
 

        (p - a)sin((p + a)x) + (p + a)sin((p - a)x)
   (2)  -------------------------------------------
                           2     2
                         2p  - 2a
                                                     Type: Expression Integer
--R
--R        (p - a)sin((p + a)x) + (p + a)sin((p - a)x)
--R   (2)  -------------------------------------------
--R                           2     2
--R                         2p  - 2a
--R                                                     Type: Expression Integer
--E 

--S 56
cc:=aa-bb
 

   (3)
       (- p + a)sin((p + a)x) + 2p cos(a x)sin(p x) + (- p - a)sin((p - a)x)
     + 
       - 2a cos(p x)sin(a x)
  /
       2     2
     2p  - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R       (- p + a)sin((p + a)x) + 2p cos(a x)sin(p x) + (- p - a)sin((p - a)x)
--R     + 
--R       - 2a cos(p x)sin(a x)
--R  /
--R       2     2
--R     2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 57     14:383 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 58
aa:=integrate(1/(1-cos(a*x)),x)
 

        - cos(a x) - 1
   (1)  --------------
          a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - cos(a x) - 1
--R   (1)  --------------
--R          a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 59
bb:=-1/a*cot((a*x)/2)
 

              a x
          cot(---)
               2
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R              a x
--R          cot(---)
--R               2
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 60
cc:=aa-bb
 

            a x
        cot(---)sin(a x) - cos(a x) - 1
             2
   (3)  -------------------------------
                   a sin(a x)
                                                     Type: Expression Integer
--R
--R            a x
--R        cot(---)sin(a x) - cos(a x) - 1
--R             2
--R   (3)  -------------------------------
--R                   a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 61     14:384 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 62
aa:=integrate(x/(1-cos(a*x)),x)
 

   (1)
                  sin(a x)                        2
   2sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x) - a x
                cos(a x) + 1                cos(a x) + 1
   ---------------------------------------------------------------------------
                                     2
                                    a sin(a x)
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                  sin(a x)                        2
--R   2sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x) - a x
--R                cos(a x) + 1                cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                     2
--R                                    a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63
bb:=-x/a*cot((a*x)/2)+2/a^2*log(sin((a*x)/2))
 

                 a x             a x
        2log(sin(---)) - a x cot(---)
                  2               2
   (2)  -----------------------------
                       2
                      a
                                                     Type: Expression Integer
--R
--R                 a x             a x
--R        2log(sin(---)) - a x cot(---)
--R                  2               2
--R   (2)  -----------------------------
--R                       2
--R                      a
--R                                                     Type: Expression Integer
--E

--S 64
cc:=aa-bb
 

   (3)
                      sin(a x)                       a x
       2sin(a x)log(------------) - 2sin(a x)log(sin(---))
                    cos(a x) + 1                      2
     + 
                           2                 a x
       - sin(a x)log(------------) + a x cot(---)sin(a x) - a x cos(a x) - a x
                     cos(a x) + 1             2
  /
      2
     a sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                      sin(a x)                       a x
--R       2sin(a x)log(------------) - 2sin(a x)log(sin(---))
--R                    cos(a x) + 1                      2
--R     + 
--R                           2                 a x
--R       - sin(a x)log(------------) + a x cot(---)sin(a x) - a x cos(a x) - a x
--R                     cos(a x) + 1             2
--R  /
--R      2
--R     a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 65
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 66
dd:=cotrule cc
 

   (5)
            a x               sin(a x)           a x                 a x
       2sin(---)sin(a x)log(------------) - 2sin(---)sin(a x)log(sin(---))
             2              cos(a x) + 1          2                   2
     + 
             a x                   2                 a x
       - sin(---)sin(a x)log(------------) + a x cos(---)sin(a x)
              2              cos(a x) + 1             2
     + 
                                 a x
       (- a x cos(a x) - a x)sin(---)
                                  2
  /
      2    a x
     a sin(---)sin(a x)
            2
                                                     Type: Expression Integer
--R
--R   (5)
--R            a x               sin(a x)           a x                 a x
--R       2sin(---)sin(a x)log(------------) - 2sin(---)sin(a x)log(sin(---))
--R             2              cos(a x) + 1          2                   2
--R     + 
--R             a x                   2                 a x
--R       - sin(---)sin(a x)log(------------) + a x cos(---)sin(a x)
--R              2              cos(a x) + 1             2
--R     + 
--R                                 a x
--R       (- a x cos(a x) - a x)sin(---)
--R                                  2
--R  /
--R      2    a x
--R     a sin(---)sin(a x)
--R            2
--R                                                     Type: Expression Integer
--E

--S 67
ee:=expandLog dd
 

   (6)
            a x                              a x                 a x
       2sin(---)sin(a x)log(sin(a x)) - 2sin(---)sin(a x)log(sin(---))
             2                                2                   2
     + 
             a x
       - sin(---)sin(a x)log(cos(a x) + 1)
              2
     + 
                  a x            a x                                       a x
     (- log(2)sin(---) + a x cos(---))sin(a x) + (- a x cos(a x) - a x)sin(---)
                   2              2                                         2
  /
      2    a x
     a sin(---)sin(a x)
            2
                                                     Type: Expression Integer
--R
--R   (6)
--R            a x                              a x                 a x
--R       2sin(---)sin(a x)log(sin(a x)) - 2sin(---)sin(a x)log(sin(---))
--R             2                                2                   2
--R     + 
--R             a x
--R       - sin(---)sin(a x)log(cos(a x) + 1)
--R              2
--R     + 
--R                  a x            a x                                       a x
--R     (- log(2)sin(---) + a x cos(---))sin(a x) + (- a x cos(a x) - a x)sin(---)
--R                   2              2                                         2
--R  /
--R      2    a x
--R     a sin(---)sin(a x)
--R            2
--R                                                     Type: Expression Integer
--E

--S 68     14:385 Schaums and Axiom agree
complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 69
aa:=integrate(1/(1+cos(a*x)),x)
 

           sin(a x)
   (1)  --------------
        a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R
--R           sin(a x)
--R   (1)  --------------
--R        a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 70
bb:=1/a*tan((a*x)/2)
 

            a x
        tan(---)
             2
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R            a x
--R        tan(---)
--R             2
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E

--S 71
cc:=aa-bb
 

                            a x
        (- cos(a x) - 1)tan(---) + sin(a x)
                             2
   (3)  -----------------------------------
                   a cos(a x) + a
                                                     Type: Expression Integer
--R
--R                            a x
--R        (- cos(a x) - 1)tan(---) + sin(a x)
--R                             2
--R   (3)  -----------------------------------
--R                   a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 72     14:386 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 73
aa:=integrate(x/(1+cos(a*x)),x)
 

                                  2
        (- cos(a x) - 1)log(------------) + a x sin(a x)
                            cos(a x) + 1
   (1)  ------------------------------------------------
                          2            2
                         a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                  2
--R        (- cos(a x) - 1)log(------------) + a x sin(a x)
--R                            cos(a x) + 1
--R   (1)  ------------------------------------------------
--R                          2            2
--R                         a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 74
bb:=x/a*tan((a*x)/2)+2/a^2*log(cos((a*x)/2))
 

                 a x             a x
        2log(cos(---)) + a x tan(---)
                  2               2
   (2)  -----------------------------
                       2
                      a
                                                     Type: Expression Integer
--R
--R                 a x             a x
--R        2log(cos(---)) + a x tan(---)
--R                  2               2
--R   (2)  -----------------------------
--R                       2
--R                      a
--R                                                     Type: Expression Integer
--E

--S 75
cc:=aa-bb
 

   (3)
                                a x                               2
       (- 2cos(a x) - 2)log(cos(---)) + (- cos(a x) - 1)log(------------)
                                 2                          cos(a x) + 1
     + 
                                 a x
       (- a x cos(a x) - a x)tan(---) + a x sin(a x)
                                  2
  /
      2            2
     a cos(a x) + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                a x                               2
--R       (- 2cos(a x) - 2)log(cos(---)) + (- cos(a x) - 1)log(------------)
--R                                 2                          cos(a x) + 1
--R     + 
--R                                 a x
--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x)
--R                                  2
--R  /
--R      2            2
--R     a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 76
dd:=expandLog cc
 

   (4)
                                                                  a x
       (cos(a x) + 1)log(cos(a x) + 1) + (- 2cos(a x) - 2)log(cos(---))
                                                                   2
     + 
                                 a x
       (- a x cos(a x) - a x)tan(---) + a x sin(a x) - log(2)cos(a x) - log(2)
                                  2
  /
      2            2
     a cos(a x) + a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                  a x
--R       (cos(a x) + 1)log(cos(a x) + 1) + (- 2cos(a x) - 2)log(cos(---))
--R                                                                   2
--R     + 
--R                                 a x
--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x) - log(2)cos(a x) - log(2)
--R                                  2
--R  /
--R      2            2
--R     a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 77     14:387 Schaums and Axiom agree
complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 78
aa:=integrate(1/(1-cos(a*x))^2,x)
 

                  2
        - cos(a x)  + cos(a x) + 2
   (1)  --------------------------
        (3a cos(a x) - 3a)sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R        - cos(a x)  + cos(a x) + 2
--R   (1)  --------------------------
--R        (3a cos(a x) - 3a)sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 79
bb:=-1/(2*a)*cot((a*x)/2)-1/(6*a)*cot((a*x)/2)^3
 

              a x 3        a x
        - cot(---)  - 3cot(---)
               2            2
   (2)  -----------------------
                   6a
                                                     Type: Expression Integer
--R
--R              a x 3        a x
--R        - cot(---)  - 3cot(---)
--R               2            2
--R   (2)  -----------------------
--R                   6a
--R                                                     Type: Expression Integer
--E 

--S 80
cc:=aa-bb
 

   (3)
                          a x 3                      a x                      2
       ((cos(a x) - 1)cot(---)  + (3cos(a x) - 3)cot(---))sin(a x) - 2cos(a x)
                           2                          2
     + 
       2cos(a x) + 4
  /
     (6a cos(a x) - 6a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                          a x 3                      a x                      2
--R       ((cos(a x) - 1)cot(---)  + (3cos(a x) - 3)cot(---))sin(a x) - 2cos(a x)
--R                           2                          2
--R     + 
--R       2cos(a x) + 4
--R  /
--R     (6a cos(a x) - 6a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 81     14:388 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 82
aa:=integrate(1/(1+cos(a*x))^2,x)
 

             (cos(a x) + 2)sin(a x)
   (1)  -------------------------------
                   2
        3a cos(a x)  + 6a cos(a x) + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             (cos(a x) + 2)sin(a x)
--R   (1)  -------------------------------
--R                   2
--R        3a cos(a x)  + 6a cos(a x) + 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 83
bb:=1/(2*a)*tan((a*x)/2)+1/(6*a)*tan((a*x)/2)^3
 

            a x 3        a x
        tan(---)  + 3tan(---)
             2            2
   (2)  ---------------------
                  6a
                                                     Type: Expression Integer
--R
--R            a x 3        a x
--R        tan(---)  + 3tan(---)
--R             2            2
--R   (2)  ---------------------
--R                  6a
--R                                                     Type: Expression Integer
--E

--S 84
cc:=aa-bb
 

   (3)
                  2                     a x 3
       (- cos(a x)  - 2cos(a x) - 1)tan(---)
                                         2
     + 
                   2                     a x
       (- 3cos(a x)  - 6cos(a x) - 3)tan(---) + (2cos(a x) + 4)sin(a x)
                                          2
  /
                2
     6a cos(a x)  + 12a cos(a x) + 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2                     a x 3
--R       (- cos(a x)  - 2cos(a x) - 1)tan(---)
--R                                         2
--R     + 
--R                   2                     a x
--R       (- 3cos(a x)  - 6cos(a x) - 3)tan(---) + (2cos(a x) + 4)sin(a x)
--R                                          2
--R  /
--R                2
--R     6a cos(a x)  + 12a cos(a x) + 6a
--R                                                     Type: Expression Integer
--E

--S 85     14:389 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 86
aa:=integrate(1/(p+q*cos(a*x)),x)
 

   (1)
                           +-------+
                           | 2    2        2    2
        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
    log(--------------------------------------------------)
                          q cos(a x) + p
   [-------------------------------------------------------,
                            +-------+
                            | 2    2
                          a\|q  - p
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p
    2atan(-----------------------)
          (q + p)cos(a x) + q + p
    ------------------------------]
               +---------+
               |   2    2
             a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R                           +-------+
--R                           | 2    2        2    2
--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R    log(--------------------------------------------------)
--R                          q cos(a x) + p
--R   [-------------------------------------------------------,
--R                            +-------+
--R                            | 2    2
--R                          a\|q  - p
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p
--R    2atan(-----------------------)
--R          (q + p)cos(a x) + q + p
--R    ------------------------------]
--R               +---------+
--R               |   2    2
--R             a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 87
bb1:=2/(a*sqrt(p^2-q^2))*atan(sqrt((p-q)/(p+q))*tan(1/2*a*x))
 

                       +-------+
                  a x  |- q + p
        2atan(tan(---) |------- )
                   2  \| q + p
   (2)  -------------------------
                +---------+
                |   2    2
              a\|- q  + p
                                                     Type: Expression Integer
--R 
--R
--R                       +-------+
--R                  a x  |- q + p
--R        2atan(tan(---) |------- )
--R                   2  \| q + p
--R   (2)  -------------------------
--R                +---------+
--R                |   2    2
--R              a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 88
bb2:=1/(a*sqrt(q^2-p^2))*log((tan(1/2*a*x)+sqrt((q+p)/(q-p)))/(tan(1/2*a*x)-sqrt((q+p)/(q-p))))
 

               +-----+
               |q + p        a x
            -  |-----  - tan(---)
              \|q - p         2
        log(---------------------)
              +-----+
              |q + p        a x
              |-----  - tan(---)
             \|q - p         2
   (3)  --------------------------
                  +-------+
                  | 2    2
                a\|q  - p
                                                     Type: Expression Integer
--R
--R               +-----+
--R               |q + p        a x
--R            -  |-----  - tan(---)
--R              \|q - p         2
--R        log(---------------------)
--R              +-----+
--R              |q + p        a x
--R              |-----  - tan(---)
--R             \|q - p         2
--R   (3)  --------------------------
--R                  +-------+
--R                  | 2    2
--R                a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 89
cc1:=aa.1-bb1
 

   (4)
                                          +-------+
        +---------+                       | 2    2        2    2
        |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       \|- q  + p  log(--------------------------------------------------)
                                         q cos(a x) + p
     + 
           +-------+              +-------+
           | 2    2          a x  |- q + p
       - 2\|q  - p  atan(tan(---) |------- )
                              2  \| q + p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                          +-------+
--R        +---------+                       | 2    2        2    2
--R        |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       \|- q  + p  log(--------------------------------------------------)
--R                                         q cos(a x) + p
--R     + 
--R           +-------+              +-------+
--R           | 2    2          a x  |- q + p
--R       - 2\|q  - p  atan(tan(---) |------- )
--R                              2  \| q + p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 90
cc2:=aa.2-bb1
 

                                                       +---------+
                         +-------+                     |   2    2
                    a x  |- q + p             sin(a x)\|- q  + p
        - 2atan(tan(---) |------- ) + 2atan(-----------------------)
                     2  \| q + p            (q + p)cos(a x) + q + p
   (5)  ------------------------------------------------------------
                                  +---------+
                                  |   2    2
                                a\|- q  + p
                                                     Type: Expression Integer
--R 
--R
--R                                                       +---------+
--R                         +-------+                     |   2    2
--R                    a x  |- q + p             sin(a x)\|- q  + p
--R        - 2atan(tan(---) |------- ) + 2atan(-----------------------)
--R                     2  \| q + p            (q + p)cos(a x) + q + p
--R   (5)  ------------------------------------------------------------
--R                                  +---------+
--R                                  |   2    2
--R                                a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 91
cc3:=aa.1-bb2
 

   (6)
                +-----+
                |q + p        a x
             -  |-----  - tan(---)
               \|q - p         2
       - log(---------------------)
               +-----+
               |q + p        a x
               |-----  - tan(---)
              \|q - p         2
     + 
                              +-------+
                              | 2    2        2    2
           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       log(--------------------------------------------------)
                             q cos(a x) + p
  /
       +-------+
       | 2    2
     a\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                +-----+
--R                |q + p        a x
--R             -  |-----  - tan(---)
--R               \|q - p         2
--R       - log(---------------------)
--R               +-----+
--R               |q + p        a x
--R               |-----  - tan(---)
--R              \|q - p         2
--R     + 
--R                              +-------+
--R                              | 2    2        2    2
--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       log(--------------------------------------------------)
--R                             q cos(a x) + p
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 92     14:390 Axiom cannot simplify these expressions
cc4:=aa.2-bb2
 

   (7)
                            +-----+
                            |q + p        a x
          +---------+    -  |-----  - tan(---)
          |   2    2       \|q - p         2
       - \|- q  + p  log(---------------------)
                           +-----+
                           |q + p        a x
                           |-----  - tan(---)
                          \|q - p         2
     + 
                                  +---------+
         +-------+                |   2    2
         | 2    2        sin(a x)\|- q  + p
       2\|q  - p  atan(-----------------------)
                       (q + p)cos(a x) + q + p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-----+
--R                            |q + p        a x
--R          +---------+    -  |-----  - tan(---)
--R          |   2    2       \|q - p         2
--R       - \|- q  + p  log(---------------------)
--R                           +-----+
--R                           |q + p        a x
--R                           |-----  - tan(---)
--R                          \|q - p         2
--R     + 
--R                                  +---------+
--R         +-------+                |   2    2
--R         | 2    2        sin(a x)\|- q  + p
--R       2\|q  - p  atan(-----------------------)
--R                       (q + p)cos(a x) + q + p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 93
aa:=integrate(1/(p+q*cos(a*x))^2,x)
 

   (1)
   [
                            2
           (p q cos(a x) + p )
        *
                                  +-------+
                                  | 2    2      2    2
               (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
           log(------------------------------------------------)
                                q cos(a x) + p
       + 
                    +-------+
                    | 2    2
         q sin(a x)\|q  - p
    /
                                                +-------+
            3      2                  2      3  | 2    2
       ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
     ,

                                                +---------+
                                                |   2    2
                              2        sin(a x)\|- q  + p
         (- 2p q cos(a x) - 2p )atan(-----------------------)
                                     (q + p)cos(a x) + q + p
       + 
                    +---------+
                    |   2    2
         q sin(a x)\|- q  + p
    /
                                                +---------+
            3      2                  2      3  |   2    2
       ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                            2
--R           (p q cos(a x) + p )
--R        *
--R                                  +-------+
--R                                  | 2    2      2    2
--R               (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R           log(------------------------------------------------)
--R                                q cos(a x) + p
--R       + 
--R                    +-------+
--R                    | 2    2
--R         q sin(a x)\|q  - p
--R    /
--R                                                +-------+
--R            3      2                  2      3  | 2    2
--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
--R     ,
--R
--R                                                +---------+
--R                                                |   2    2
--R                              2        sin(a x)\|- q  + p
--R         (- 2p q cos(a x) - 2p )atan(-----------------------)
--R                                     (q + p)cos(a x) + q + p
--R       + 
--R                    +---------+
--R                    |   2    2
--R         q sin(a x)\|- q  + p
--R    /
--R                                                +---------+
--R            3      2                  2      3  |   2    2
--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 94
t1:=integrate(1/(p+q*cos(a*x)),x)
 

   (2)
                           +-------+
                           | 2    2        2    2
        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
    log(--------------------------------------------------)
                          q cos(a x) + p
   [-------------------------------------------------------,
                            +-------+
                            | 2    2
                          a\|q  - p
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p
    2atan(-----------------------)
          (q + p)cos(a x) + q + p
    ------------------------------]
               +---------+
               |   2    2
             a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R                           +-------+
--R                           | 2    2        2    2
--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R    log(--------------------------------------------------)
--R                          q cos(a x) + p
--R   [-------------------------------------------------------,
--R                            +-------+
--R                            | 2    2
--R                          a\|q  - p
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p
--R    2atan(-----------------------)
--R          (q + p)cos(a x) + q + p
--R    ------------------------------]
--R               +---------+
--R               |   2    2
--R             a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 95
bb1:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.1
 

   (3)
                            2
         (- p q cos(a x) - p )
      *
                                +-------+
                                | 2    2        2    2
             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
         log(--------------------------------------------------)
                               q cos(a x) + p
     + 
                  +-------+
                  | 2    2
       q sin(a x)\|q  - p
  /
                                              +-------+
          3      2                  2      3  | 2    2
     ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R                            2
--R         (- p q cos(a x) - p )
--R      *
--R                                +-------+
--R                                | 2    2        2    2
--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R         log(--------------------------------------------------)
--R                               q cos(a x) + p
--R     + 
--R                  +-------+
--R                  | 2    2
--R       q sin(a x)\|q  - p
--R  /
--R                                              +-------+
--R          3      2                  2      3  | 2    2
--R     ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 96
bb2:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.2
 

   (4)
                                          +---------+
                                          |   2    2                 +---------+
                        2        sin(a x)\|- q  + p                  |   2    2
   (- 2p q cos(a x) - 2p )atan(-----------------------) + q sin(a x)\|- q  + p
                               (q + p)cos(a x) + q + p
   -----------------------------------------------------------------------------
                                                         +---------+
                     3      2                  2      3  |   2    2
                ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                          +---------+
--R                                          |   2    2                 +---------+
--R                        2        sin(a x)\|- q  + p                  |   2    2
--R   (- 2p q cos(a x) - 2p )atan(-----------------------) + q sin(a x)\|- q  + p
--R                               (q + p)cos(a x) + q + p
--R   -----------------------------------------------------------------------------
--R                                                         +---------+
--R                     3      2                  2      3  |   2    2
--R                ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 97
cc1:=aa.1-bb1
 

   (5)
                                +-------+
                                | 2    2      2    2
             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p log(------------------------------------------------)
                              q cos(a x) + p
     + 
                                +-------+
                                | 2    2        2    2
             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p log(--------------------------------------------------)
                               q cos(a x) + p
  /
                   +-------+
         2      2  | 2    2
     (a q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                +-------+
--R                                | 2    2      2    2
--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p log(------------------------------------------------)
--R                              q cos(a x) + p
--R     + 
--R                                +-------+
--R                                | 2    2        2    2
--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p log(--------------------------------------------------)
--R                               q cos(a x) + p
--R  /
--R                   +-------+
--R         2      2  | 2    2
--R     (a q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 98
cc2:=aa.2-bb1
 

   (6)
                                           +-------+
         +---------+                       | 2    2        2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p\|- q  + p  log(--------------------------------------------------)
                                          q cos(a x) + p
     + 
                                     +---------+
            +-------+                |   2    2
            | 2    2        sin(a x)\|- q  + p
       - 2p\|q  - p  atan(-----------------------)
                          (q + p)cos(a x) + q + p
  /
                   +---------+ +-------+
         2      2  |   2    2  | 2    2
     (a q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                                           +-------+
--R         +---------+                       | 2    2        2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p\|- q  + p  log(--------------------------------------------------)
--R                                          q cos(a x) + p
--R     + 
--R                                     +---------+
--R            +-------+                |   2    2
--R            | 2    2        sin(a x)\|- q  + p
--R       - 2p\|q  - p  atan(-----------------------)
--R                          (q + p)cos(a x) + q + p
--R  /
--R                   +---------+ +-------+
--R         2      2  |   2    2  | 2    2
--R     (a q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 99
cc3:=aa.1-bb2
 

   (7)
                                           +-------+
         +---------+                       | 2    2      2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p\|- q  + p  log(------------------------------------------------)
                                         q cos(a x) + p
     + 
                                   +---------+
          +-------+                |   2    2
          | 2    2        sin(a x)\|- q  + p
       2p\|q  - p  atan(-----------------------)
                        (q + p)cos(a x) + q + p
  /
                   +---------+ +-------+
         2      2  |   2    2  | 2    2
     (a q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                           +-------+
--R         +---------+                       | 2    2      2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p\|- q  + p  log(------------------------------------------------)
--R                                         q cos(a x) + p
--R     + 
--R                                   +---------+
--R          +-------+                |   2    2
--R          | 2    2        sin(a x)\|- q  + p
--R       2p\|q  - p  atan(-----------------------)
--R                        (q + p)cos(a x) + q + p
--R  /
--R                   +---------+ +-------+
--R         2      2  |   2    2  | 2    2
--R     (a q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 100    14:391 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 101
aa:=integrate(1/(p^2+q^2*cos(a*x)^2),x)
 

   (1)
                 +-------+
                 | 2    2                 2    2              2
        sin(a x)\|q  + p               ((q  - p )cos(a x) - 2p )sin(a x)
   atan(------------------) - atan(-----------------------------------------)
         2p cos(a x) + 2p                                          +-------+
                                              2                    | 2    2
                                   (p cos(a x)  + 2p cos(a x) + p)\|q  + p
   --------------------------------------------------------------------------
                                      +-------+
                                      | 2    2
                                  a p\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                 +-------+
--R                 | 2    2                 2    2              2
--R        sin(a x)\|q  + p               ((q  - p )cos(a x) - 2p )sin(a x)
--R   atan(------------------) - atan(-----------------------------------------)
--R         2p cos(a x) + 2p                                          +-------+
--R                                              2                    | 2    2
--R                                   (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R   --------------------------------------------------------------------------
--R                                      +-------+
--R                                      | 2    2
--R                                  a p\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 102
bb:=1/(a*p*sqrt(p^2+q^2))*atan((p*tan(a*x))/sqrt(p^2+q^2))
 

             p tan(a x)
        atan(----------)
              +-------+
              | 2    2
             \|q  + p
   (2)  ----------------
              +-------+
              | 2    2
          a p\|q  + p
                                                     Type: Expression Integer
--R
--R             p tan(a x)
--R        atan(----------)
--R              +-------+
--R              | 2    2
--R             \|q  + p
--R   (2)  ----------------
--R              +-------+
--R              | 2    2
--R          a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 103
cc:=aa-bb
 

   (3)
                     +-------+
                     | 2    2
            sin(a x)\|q  + p           p tan(a x)
       atan(------------------) - atan(----------)
             2p cos(a x) + 2p           +-------+
                                        | 2    2
                                       \|q  + p
     + 
                     2    2              2
                  ((q  - p )cos(a x) - 2p )sin(a x)
       - atan(-----------------------------------------)
                                              +-------+
                         2                    | 2    2
              (p cos(a x)  + 2p cos(a x) + p)\|q  + p
  /
         +-------+
         | 2    2
     a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                     +-------+
--R                     | 2    2
--R            sin(a x)\|q  + p           p tan(a x)
--R       atan(------------------) - atan(----------)
--R             2p cos(a x) + 2p           +-------+
--R                                        | 2    2
--R                                       \|q  + p
--R     + 
--R                     2    2              2
--R                  ((q  - p )cos(a x) - 2p )sin(a x)
--R       - atan(-----------------------------------------)
--R                                              +-------+
--R                         2                    | 2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 104
dd:=ratDenom cc
 

   (4)
                                   +-------+
          +-------+                | 2    2
          | 2    2      p tan(a x)\|q  + p
       - \|q  + p  atan(--------------------)
                                2    2
                               q  + p
     + 
       -
             +-------+
             | 2    2
            \|q  + p
         *
                                                          +-------+
                           2    2              2          | 2    2
                        ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
            atan(--------------------------------------------------------)
                     2    3         2        2     3               2    3
                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                               +-------+
        +-------+              | 2    2
        | 2    2      sin(a x)\|q  + p
       \|q  + p  atan(------------------)
                       2p cos(a x) + 2p
  /
          2      3
     a p q  + a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                   +-------+
--R          +-------+                | 2    2
--R          | 2    2      p tan(a x)\|q  + p
--R       - \|q  + p  atan(--------------------)
--R                                2    2
--R                               q  + p
--R     + 
--R       -
--R             +-------+
--R             | 2    2
--R            \|q  + p
--R         *
--R                                                          +-------+
--R                           2    2              2          | 2    2
--R                        ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
--R            atan(--------------------------------------------------------)
--R                     2    3         2        2     3               2    3
--R                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                               +-------+
--R        +-------+              | 2    2
--R        | 2    2      sin(a x)\|q  + p
--R       \|q  + p  atan(------------------)
--R                       2p cos(a x) + 2p
--R  /
--R          2      3
--R     a p q  + a p
--R                                                     Type: Expression Integer
--E

--S 105
atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
 

                     1                    1
   (5)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
                     2                    2
Type: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--R
--R                     1                    1
--R   (5)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
--R                     2                    2
--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--E

--S 106
ee:=atanrule2 dd
 

   (6)
                                       +-------+
            +-------+                  | 2    2     2    2
       1    | 2    2     %i p tan(a x)\|q  + p   + q  + p
       - %i\|q  + p  log(---------------------------------)
       2                               2    2
                                      q  + p
     + 
              +-------+
         1    | 2    2
         - %i\|q  + p
         2
      *
         log
                                                           +-------+
                      2       2                 2          | 2    2
                ((%i q  - %i p )cos(a x) - 2%i p )sin(a x)\|q  + p
              + 
                    2    3         2        2     3               2    3
                (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
           /
                  2    3         2        2     3               2    3
              (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                                         +-------+
                           1             | 2    2
              +-------+    - %i sin(a x)\|q  + p   + p cos(a x) + p
         1    | 2    2     2
       - - %i\|q  + p  log(----------------------------------------)
         2                              p cos(a x) + p
     + 
                                         +-------+
                           1             | 2    2
            +-------+    - - %i sin(a x)\|q  + p   + p cos(a x) + p
       1    | 2    2       2
       - %i\|q  + p  log(------------------------------------------)
       2                               p cos(a x) + p
     + 
       -
                 +-------+
            1    | 2    2
            - %i\|q  + p
            2
         *
            log
                                                                +-------+
                           2       2                 2          | 2    2
                   ((- %i q  + %i p )cos(a x) + 2%i p )sin(a x)\|q  + p
                 + 
                       2    3         2        2     3               2    3
                   (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
              /
                     2    3         2        2     3               2    3
                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                                           +-------+
              +-------+                    | 2    2     2    2
         1    | 2    2     - %i p tan(a x)\|q  + p   + q  + p
       - - %i\|q  + p  log(-----------------------------------)
         2                                2    2
                                         q  + p
  /
          2      3
     a p q  + a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (6)
--R                                       +-------+
--R            +-------+                  | 2    2     2    2
--R       1    | 2    2     %i p tan(a x)\|q  + p   + q  + p
--R       - %i\|q  + p  log(---------------------------------)
--R       2                               2    2
--R                                      q  + p
--R     + 
--R              +-------+
--R         1    | 2    2
--R         - %i\|q  + p
--R         2
--R      *
--R         log
--R                                                           +-------+
--R                      2       2                 2          | 2    2
--R                ((%i q  - %i p )cos(a x) - 2%i p )sin(a x)\|q  + p
--R              + 
--R                    2    3         2        2     3               2    3
--R                (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R           /
--R                  2    3         2        2     3               2    3
--R              (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                                         +-------+
--R                           1             | 2    2
--R              +-------+    - %i sin(a x)\|q  + p   + p cos(a x) + p
--R         1    | 2    2     2
--R       - - %i\|q  + p  log(----------------------------------------)
--R         2                              p cos(a x) + p
--R     + 
--R                                         +-------+
--R                           1             | 2    2
--R            +-------+    - - %i sin(a x)\|q  + p   + p cos(a x) + p
--R       1    | 2    2       2
--R       - %i\|q  + p  log(------------------------------------------)
--R       2                               p cos(a x) + p
--R     + 
--R       -
--R                 +-------+
--R            1    | 2    2
--R            - %i\|q  + p
--R            2
--R         *
--R            log
--R                                                                +-------+
--R                           2       2                 2          | 2    2
--R                   ((- %i q  + %i p )cos(a x) + 2%i p )sin(a x)\|q  + p
--R                 + 
--R                       2    3         2        2     3               2    3
--R                   (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R              /
--R                     2    3         2        2     3               2    3
--R                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                                           +-------+
--R              +-------+                    | 2    2     2    2
--R         1    | 2    2     - %i p tan(a x)\|q  + p   + q  + p
--R       - - %i\|q  + p  log(-----------------------------------)
--R         2                                2    2
--R                                         q  + p
--R  /
--R          2      3
--R     a p q  + a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 107
ff:=expandLog ee
 

   (7)
              +-------+               +-------+
         1    | 2    2                | 2    2        2       2
       - - %i\|q  + p  log(p tan(a x)\|q  + p   + %i q  + %i p )
         2
     + 
            +-------+               +-------+
       1    | 2    2                | 2    2        2       2
       - %i\|q  + p  log(p tan(a x)\|q  + p   - %i q  - %i p )
       2
     + 
       -
                 +-------+
            1    | 2    2
            - %i\|q  + p
            2
         *
            log
                                                   +-------+
                    2    2              2          | 2    2
                 ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
               + 
                        2       3         2           2        3
                 (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
               + 
                       2       3
                 %i p q  + %i p
     + 
              +-------+
         1    | 2    2
         - %i\|q  + p
         2
      *
         log
                                                +-------+
                 2    2              2          | 2    2
              ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
            + 
                       2       3         2             2        3
              (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
            + 
                      2       3
              - %i p q  - %i p
     + 
            +-------+             +-------+
       1    | 2    2              | 2    2
       - %i\|q  + p  log(sin(a x)\|q  + p   + 2%i p cos(a x) + 2%i p)
       2
     + 
              +-------+             +-------+
         1    | 2    2              | 2    2
       - - %i\|q  + p  log(sin(a x)\|q  + p   - 2%i p cos(a x) - 2%i p)
         2
     + 
                                                                     +-------+
                   1        1       1          1                     | 2    2
     (%i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i))\|q  + p
                   2        2       2          2
  /
          2      3
     a p q  + a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (7)
--R              +-------+               +-------+
--R         1    | 2    2                | 2    2        2       2
--R       - - %i\|q  + p  log(p tan(a x)\|q  + p   + %i q  + %i p )
--R         2
--R     + 
--R            +-------+               +-------+
--R       1    | 2    2                | 2    2        2       2
--R       - %i\|q  + p  log(p tan(a x)\|q  + p   - %i q  - %i p )
--R       2
--R     + 
--R       -
--R                 +-------+
--R            1    | 2    2
--R            - %i\|q  + p
--R            2
--R         *
--R            log
--R                                                   +-------+
--R                    2    2              2          | 2    2
--R                 ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
--R               + 
--R                        2       3         2           2        3
--R                 (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
--R               + 
--R                       2       3
--R                 %i p q  + %i p
--R     + 
--R              +-------+
--R         1    | 2    2
--R         - %i\|q  + p
--R         2
--R      *
--R         log
--R                                                +-------+
--R                 2    2              2          | 2    2
--R              ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
--R            + 
--R                       2       3         2             2        3
--R              (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R            + 
--R                      2       3
--R              - %i p q  - %i p
--R     + 
--R            +-------+             +-------+
--R       1    | 2    2              | 2    2
--R       - %i\|q  + p  log(sin(a x)\|q  + p   + 2%i p cos(a x) + 2%i p)
--R       2
--R     + 
--R              +-------+             +-------+
--R         1    | 2    2              | 2    2
--R       - - %i\|q  + p  log(sin(a x)\|q  + p   - 2%i p cos(a x) - 2%i p)
--R         2
--R     + 
--R                                                                     +-------+
--R                   1        1       1          1                     | 2    2
--R     (%i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i))\|q  + p
--R                   2        2       2          2
--R  /
--R          2      3
--R     a p q  + a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 108    14:392 Schaums and Axiom differ by a constant
complexNormalize ff
 

   (8)
                      1        1       1          1
         %i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i)
                      2        2       2          2
       + 
           1
         - - %i log(- 1)
           2
    *
        +-------+
        | 2    2
       \|q  + p
  /
          2      3
     a p q  + a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (8)
--R                      1        1       1          1
--R         %i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i)
--R                      2        2       2          2
--R       + 
--R           1
--R         - - %i log(- 1)
--R           2
--R    *
--R        +-------+
--R        | 2    2
--R       \|q  + p
--R  /
--R          2      3
--R     a p q  + a p
--R                                    Type: Expression Complex Fraction Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 109
aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x)
 

   (1)
                                   +-------+
           2     2         2    2  | 2    2           2     3
        ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
    log(----------------------------------------------------------------------)
                                    2        2    2
                                   q cos(a x)  - p
   [---------------------------------------------------------------------------,
                                        +-------+
                                        | 2    2
                                   2a p\|q  - p

                       +---------+
                       |   2    2
              sin(a x)\|- q  + p
         atan(--------------------)
                2p cos(a x) + 2p
       + 
                      2    2              2
                   ((q  + p )cos(a x) + 2p )sin(a x)
         atan(-------------------------------------------)
                                              +---------+
                         2                    |   2    2
              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
    /
           +---------+
           |   2    2
       a p\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                                   +-------+
--R           2     2         2    2  | 2    2           2     3
--R        ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
--R    log(----------------------------------------------------------------------)
--R                                    2        2    2
--R                                   q cos(a x)  - p
--R   [---------------------------------------------------------------------------,
--R                                        +-------+
--R                                        | 2    2
--R                                   2a p\|q  - p
--R
--R                       +---------+
--R                       |   2    2
--R              sin(a x)\|- q  + p
--R         atan(--------------------)
--R                2p cos(a x) + 2p
--R       + 
--R                      2    2              2
--R                   ((q  + p )cos(a x) + 2p )sin(a x)
--R         atan(-------------------------------------------)
--R                                              +---------+
--R                         2                    |   2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R    /
--R           +---------+
--R           |   2    2
--R       a p\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 110
bb1:=1/(a*p*sqrt(p^2-q^2))*atan((p*tan(a*x))/sqrt(p^2-q^2))
 

              p tan(a x)
        atan(------------)
              +---------+
              |   2    2
             \|- q  + p
   (2)  ------------------
              +---------+
              |   2    2
          a p\|- q  + p
                                                     Type: Expression Integer
--R
--R              p tan(a x)
--R        atan(------------)
--R              +---------+
--R              |   2    2
--R             \|- q  + p
--R   (2)  ------------------
--R              +---------+
--R              |   2    2
--R          a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 111
bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((p*tan(a*x)-sqrt(q^2-p^2))/(p*tan(a*x)+sqrt(q^2-p^2)))
 

               +-------+
               | 2    2
            - \|q  - p   + p tan(a x)
        log(-------------------------)
              +-------+
              | 2    2
             \|q  - p   + p tan(a x)
   (3)  ------------------------------
                     +-------+
                     | 2    2
                2a p\|q  - p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R            - \|q  - p   + p tan(a x)
--R        log(-------------------------)
--R              +-------+
--R              | 2    2
--R             \|q  - p   + p tan(a x)
--R   (3)  ------------------------------
--R                     +-------+
--R                     | 2    2
--R                2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 112
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |   2    2
         \|- q  + p
      *
         log
                                           +-------+
                   2     2         2    2  | 2    2
                ((q  - 2p )cos(a x)  + p )\|q  - p
              + 
                       2     3
                (- 2p q  + 2p )cos(a x)sin(a x)
           /
               2        2    2
              q cos(a x)  - p
     + 
           +-------+
           | 2    2       p tan(a x)
       - 2\|q  - p  atan(------------)
                          +---------+
                          |   2    2
                         \|- q  + p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R         log
--R                                           +-------+
--R                   2     2         2    2  | 2    2
--R                ((q  - 2p )cos(a x)  + p )\|q  - p
--R              + 
--R                       2     3
--R                (- 2p q  + 2p )cos(a x)sin(a x)
--R           /
--R               2        2    2
--R              q cos(a x)  - p
--R     + 
--R           +-------+
--R           | 2    2       p tan(a x)
--R       - 2\|q  - p  atan(------------)
--R                          +---------+
--R                          |   2    2
--R                         \|- q  + p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 113
cc2:=aa.2-bb1
 

   (5)
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p            p tan(a x)
       atan(--------------------) - atan(------------)
              2p cos(a x) + 2p            +---------+
                                          |   2    2
                                         \|- q  + p
     + 
                    2    2              2
                 ((q  + p )cos(a x) + 2p )sin(a x)
       atan(-------------------------------------------)
                                            +---------+
                       2                    |   2    2
            (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
         +---------+
         |   2    2
     a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p            p tan(a x)
--R       atan(--------------------) - atan(------------)
--R              2p cos(a x) + 2p            +---------+
--R                                          |   2    2
--R                                         \|- q  + p
--R     + 
--R                    2    2              2
--R                 ((q  + p )cos(a x) + 2p )sin(a x)
--R       atan(-------------------------------------------)
--R                                            +---------+
--R                       2                    |   2    2
--R            (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 114
cc3:=aa.1-bb2
 

   (6)
       log
                                     +-------+
             2     2         2    2  | 2    2           2     3
          ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
          ----------------------------------------------------------------------
                                      2        2    2
                                     q cos(a x)  - p
     + 
                +-------+
                | 2    2
             - \|q  - p   + p tan(a x)
       - log(-------------------------)
               +-------+
               | 2    2
              \|q  - p   + p tan(a x)
  /
          +-------+
          | 2    2
     2a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                                     +-------+
--R             2     2         2    2  | 2    2           2     3
--R          ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
--R          ----------------------------------------------------------------------
--R                                      2        2    2
--R                                     q cos(a x)  - p
--R     + 
--R                +-------+
--R                | 2    2
--R             - \|q  - p   + p tan(a x)
--R       - log(-------------------------)
--R               +-------+
--R               | 2    2
--R              \|q  - p   + p tan(a x)
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 115
cc4:=aa.2-bb2
 

   (7)
                            +-------+
          +---------+       | 2    2
          |   2    2     - \|q  - p   + p tan(a x)
       - \|- q  + p  log(-------------------------)
                           +-------+
                           | 2    2
                          \|q  - p   + p tan(a x)
     + 
                                +---------+
         +-------+              |   2    2
         | 2    2      sin(a x)\|- q  + p
       2\|q  - p  atan(--------------------)
                         2p cos(a x) + 2p
     + 
         +-------+             2    2              2
         | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
       2\|q  - p  atan(-------------------------------------------)
                                                       +---------+
                                  2                    |   2    2
                       (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-------+
--R          +---------+       | 2    2
--R          |   2    2     - \|q  - p   + p tan(a x)
--R       - \|- q  + p  log(-------------------------)
--R                           +-------+
--R                           | 2    2
--R                          \|q  - p   + p tan(a x)
--R     + 
--R                                +---------+
--R         +-------+              |   2    2
--R         | 2    2      sin(a x)\|- q  + p
--R       2\|q  - p  atan(--------------------)
--R                         2p cos(a x) + 2p
--R     + 
--R         +-------+             2    2              2
--R         | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
--R       2\|q  - p  atan(-------------------------------------------)
--R                                                       +---------+
--R                                  2                    |   2    2
--R                       (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 116
dd2:=ratDenom cc2
 

   (8)
                                     +---------+
          +---------+                |   2    2
          |   2    2      p tan(a x)\|- q  + p
       - \|- q  + p  atan(----------------------)
                                   2    2
                                  q  - p
     + 
          +---------+
          |   2    2
         \|- q  + p
      *
                                                      +---------+
                       2    2              2          |   2    2
                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
         atan(--------------------------------------------------------)
                  2    3         2        2     3               2    3
              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                   +---------+
          +---------+              |   2    2
          |   2    2      sin(a x)\|- q  + p
       - \|- q  + p  atan(--------------------)
                            2p cos(a x) + 2p
  /
          2      3
     a p q  - a p
                                                     Type: Expression Integer
--R
--R   (8)
--R                                     +---------+
--R          +---------+                |   2    2
--R          |   2    2      p tan(a x)\|- q  + p
--R       - \|- q  + p  atan(----------------------)
--R                                   2    2
--R                                  q  - p
--R     + 
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R                                                      +---------+
--R                       2    2              2          |   2    2
--R                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R         atan(--------------------------------------------------------)
--R                  2    3         2        2     3               2    3
--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                   +---------+
--R          +---------+              |   2    2
--R          |   2    2      sin(a x)\|- q  + p
--R       - \|- q  + p  atan(--------------------)
--R                            2p cos(a x) + 2p
--R  /
--R          2      3
--R     a p q  - a p
--R                                                     Type: Expression Integer
--E

--S 117
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (9)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (9)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 118
ee2:=tanrule dd2
 

   (10)
          +---------+
          |   2    2
         \|- q  + p
      *
                                                      +---------+
                       2    2              2          |   2    2
                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
         atan(--------------------------------------------------------)
                  2    3         2        2     3               2    3
              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                   +---------+
          +---------+              |   2    2
          |   2    2      sin(a x)\|- q  + p
       - \|- q  + p  atan(--------------------)
                            2p cos(a x) + 2p
     + 
                                     +---------+
          +---------+                |   2    2
          |   2    2      p sin(a x)\|- q  + p
       - \|- q  + p  atan(----------------------)
                               2    2
                             (q  - p )cos(a x)
  /
          2      3
     a p q  - a p
                                                     Type: Expression Integer
--R
--R   (10)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R                                                      +---------+
--R                       2    2              2          |   2    2
--R                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R         atan(--------------------------------------------------------)
--R                  2    3         2        2     3               2    3
--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                   +---------+
--R          +---------+              |   2    2
--R          |   2    2      sin(a x)\|- q  + p
--R       - \|- q  + p  atan(--------------------)
--R                            2p cos(a x) + 2p
--R     + 
--R                                     +---------+
--R          +---------+                |   2    2
--R          |   2    2      p sin(a x)\|- q  + p
--R       - \|- q  + p  atan(----------------------)
--R                               2    2
--R                             (q  - p )cos(a x)
--R  /
--R          2      3
--R     a p q  - a p
--R                                                     Type: Expression Integer
--E

--S 119
atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
 

                      1                    1
   (11)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
                      2                    2
Type: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--R
--R                      1                    1
--R   (11)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
--R                      2                    2
--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--E

--S 120
ff2:=atanrule2 ee2
 

   (12)
       -
                 +---------+
            1    |   2    2
            - %i\|- q  + p
            2
         *
            log
                                                              +---------+
                         2       2                 2          |   2    2
                   ((%i q  + %i p )cos(a x) + 2%i p )sin(a x)\|- q  + p
                 + 
                       2    3         2        2     3               2    3
                   (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
              /
                     2    3         2        2     3               2    3
                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                         +---------+
                           1             |   2    2
            +---------+    - %i sin(a x)\|- q  + p   + p cos(a x) + p
       1    |   2    2     2
       - %i\|- q  + p  log(------------------------------------------)
       2                                 p cos(a x) + p
     + 
                                         +---------+
            +---------+                  |   2    2      2    2
       1    |   2    2     %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
       - %i\|- q  + p  log(---------------------------------------------)
       2                                   2    2
                                         (q  - p )cos(a x)
     + 
                                             +---------+
              +---------+                    |   2    2      2    2
         1    |   2    2     - %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
       - - %i\|- q  + p  log(-----------------------------------------------)
         2                                    2    2
                                            (q  - p )cos(a x)
     + 
                                             +---------+
                               1             |   2    2
              +---------+    - - %i sin(a x)\|- q  + p   + p cos(a x) + p
         1    |   2    2       2
       - - %i\|- q  + p  log(--------------------------------------------)
         2                                  p cos(a x) + p
     + 
              +---------+
         1    |   2    2
         - %i\|- q  + p
         2
      *
         log
                                                             +---------+
                        2       2                 2          |   2    2
                ((- %i q  - %i p )cos(a x) - 2%i p )sin(a x)\|- q  + p
              + 
                    2    3         2        2     3               2    3
                (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
           /
                  2    3         2        2     3               2    3
              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
  /
          2      3
     a p q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (12)
--R       -
--R                 +---------+
--R            1    |   2    2
--R            - %i\|- q  + p
--R            2
--R         *
--R            log
--R                                                              +---------+
--R                         2       2                 2          |   2    2
--R                   ((%i q  + %i p )cos(a x) + 2%i p )sin(a x)\|- q  + p
--R                 + 
--R                       2    3         2        2     3               2    3
--R                   (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R              /
--R                     2    3         2        2     3               2    3
--R                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                         +---------+
--R                           1             |   2    2
--R            +---------+    - %i sin(a x)\|- q  + p   + p cos(a x) + p
--R       1    |   2    2     2
--R       - %i\|- q  + p  log(------------------------------------------)
--R       2                                 p cos(a x) + p
--R     + 
--R                                         +---------+
--R            +---------+                  |   2    2      2    2
--R       1    |   2    2     %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
--R       - %i\|- q  + p  log(---------------------------------------------)
--R       2                                   2    2
--R                                         (q  - p )cos(a x)
--R     + 
--R                                             +---------+
--R              +---------+                    |   2    2      2    2
--R         1    |   2    2     - %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
--R       - - %i\|- q  + p  log(-----------------------------------------------)
--R         2                                    2    2
--R                                            (q  - p )cos(a x)
--R     + 
--R                                             +---------+
--R                               1             |   2    2
--R              +---------+    - - %i sin(a x)\|- q  + p   + p cos(a x) + p
--R         1    |   2    2       2
--R       - - %i\|- q  + p  log(--------------------------------------------)
--R         2                                  p cos(a x) + p
--R     + 
--R              +---------+
--R         1    |   2    2
--R         - %i\|- q  + p
--R         2
--R      *
--R         log
--R                                                             +---------+
--R                        2       2                 2          |   2    2
--R                ((- %i q  - %i p )cos(a x) - 2%i p )sin(a x)\|- q  + p
--R              + 
--R                    2    3         2        2     3               2    3
--R                (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R           /
--R                  2    3         2        2     3               2    3
--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R  /
--R          2      3
--R     a p q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 121
gg2:=expandLog ff2
 

   (13)
              +---------+
         1    |   2    2
         - %i\|- q  + p
         2
      *
         log
                                                +---------+
                 2    2              2          |   2    2
              ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x) + %i p q
            + 
                    3
              - %i p
     + 
       -
                 +---------+
            1    |   2    2
            - %i\|- q  + p
            2
         *
            log
                                                   +---------+
                    2    2              2          |   2    2
                 ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  + %i p
     + 
              +---------+               +---------+
         1    |   2    2                |   2    2         2       2
       - - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (%i q  - %i p )cos(a x))
         2
     + 
            +---------+               +---------+
       1    |   2    2                |   2    2           2       2
       - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (- %i q  + %i p )cos(a x))
       2
     + 
              +---------+             +---------+
         1    |   2    2              |   2    2
       - - %i\|- q  + p  log(sin(a x)\|- q  + p   + 2%i p cos(a x) + 2%i p)
         2
     + 
            +---------+             +---------+
       1    |   2    2              |   2    2
       - %i\|- q  + p  log(sin(a x)\|- q  + p   - 2%i p cos(a x) - 2%i p)
       2
     + 
                                           +---------+
        1        1       1          1      |   2    2
       (- %i log(- %i) - - %i log(- - %i))\|- q  + p
        2        2       2          2
  /
          2      3
     a p q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (13)
--R              +---------+
--R         1    |   2    2
--R         - %i\|- q  + p
--R         2
--R      *
--R         log
--R                                                +---------+
--R                 2    2              2          |   2    2
--R              ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x) + %i p q
--R            + 
--R                    3
--R              - %i p
--R     + 
--R       -
--R                 +---------+
--R            1    |   2    2
--R            - %i\|- q  + p
--R            2
--R         *
--R            log
--R                                                   +---------+
--R                    2    2              2          |   2    2
--R                 ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  + %i p
--R     + 
--R              +---------+               +---------+
--R         1    |   2    2                |   2    2         2       2
--R       - - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (%i q  - %i p )cos(a x))
--R         2
--R     + 
--R            +---------+               +---------+
--R       1    |   2    2                |   2    2           2       2
--R       - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (- %i q  + %i p )cos(a x))
--R       2
--R     + 
--R              +---------+             +---------+
--R         1    |   2    2              |   2    2
--R       - - %i\|- q  + p  log(sin(a x)\|- q  + p   + 2%i p cos(a x) + 2%i p)
--R         2
--R     + 
--R            +---------+             +---------+
--R       1    |   2    2              |   2    2
--R       - %i\|- q  + p  log(sin(a x)\|- q  + p   - 2%i p cos(a x) - 2%i p)
--R       2
--R     + 
--R                                           +---------+
--R        1        1       1          1      |   2    2
--R       (- %i log(- %i) - - %i log(- - %i))\|- q  + p
--R        2        2       2          2
--R  /
--R          2      3
--R     a p q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 122    14:393 Schaums and Axiom differ by a constant
hh2:=complexNormalize gg2
 

   (14)
          1              1        1       1          1       1
       (- - %i log(%i) + - %i log(- %i) - - %i log(- - %i) + - %i log(- %i))
          2              2        2       2          2       2
    *
        +---------+
        |   2    2
       \|- q  + p
  /
          2      3
     a p q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (14)
--R          1              1        1       1          1       1
--R       (- - %i log(%i) + - %i log(- %i) - - %i log(- - %i) + - %i log(- %i))
--R          2              2        2       2          2       2
--R    *
--R        +---------+
--R        |   2    2
--R       \|- q  + p
--R  /
--R          2      3
--R     a p q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 123    14:394 Axiom cannot compute this integral
aa:=integrate(x^m*cos(a*x),x)
 

           x
         ++             m
   (1)   |   cos(%I a)%I d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             m
--I   (1)   |   cos(%I a)%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 124    14:395 Axiom cannot compute this integral
aa:=integrate(cos(a*x)/x^n,x)
 

           x
         ++  cos(%I a)
   (1)   |   --------- d%I
        ++        n
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cos(%I a)
--I   (1)   |   --------- d%I
--R        ++        n
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 125    14:396 Axiom cannot compute this integral
aa:=integrate(cos(a*x)^n,x)
 

           x
         ++           n
   (1)   |   cos(%I a) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   cos(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 126    14:397 Axiom cannot compute this integral
aa:=integrate(1/(cos(a*x))^n,x)
 

           x
         ++       1
   (1)   |   ---------- d%I
        ++            n
             cos(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ---------- d%I
--R        ++            n
--I             cos(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 127    14:398 Axiom cannot compute this integral
aa:=integrate(x/cos(a*x)^n,x)
 

           x
         ++      %I
   (1)   |   ---------- d%I
        ++            n
             cos(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   ---------- d%I
--R        ++            n
--I             cos(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to heugcd.output (2009/2/17, 17:46:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 5
gcd([0,0,x^2-1,x^2+2*x+1])
 

   (1)  x + 1
                                                     Type: Polynomial Integer
--R
--R   (1)  x + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 5
gcd([0,0,x^2-1,x^2+2*x+1])$HeuGcd(SparseUnivariatePolynomial Integer)
 

   (2)  ? + 1
                                     Type: SparseUnivariatePolynomial Integer
--R
--R   (2)  ? + 1
--R                                     Type: SparseUnivariatePolynomial Integer
--E 2

--S 3 of 5
gcd(6*x^2-1,36*x^2+12*x+1)
 

   (3)  1
                                                     Type: Polynomial Integer
--R
--R   (3)  1
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 5
gcd([36*x^2-1,36*x^2+12*x+1])
 

   (4)  6x + 1
                                                     Type: Polynomial Integer
--R
--R   (4)  6x + 1
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 5
gcd([36*x^2-1,36*x^2+12*x+1])$HeuGcd(SparseUnivariatePolynomial Integer)
 

   (5)  6? + 1
                                     Type: SparseUnivariatePolynomial Integer
--R
--R   (5)  6? + 1
--R                                     Type: SparseUnivariatePolynomial Integer
--E 5
)spool 
 
Starts dribbling to en.output (2009/2/17, 17:45:34).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 7
f(x)==En(2,x)-x*log(x)
 
                                                                   Type: Void
--E 1

--S 2 of 7
[[0.01,0.9957222,f(0.01),f(0.01)-0.9957222],_
[0.02,0.9913450,f(0.02),f(0.02)-0.9913450],_
[0.03,0.9868687,f(0.03),f(0.03)-0.9868687],_
[0.04,0.9822939,f(0.04),f(0.04)-0.9822939],_
[0.05,0.9776211,f(0.05),f(0.05)-0.9776211],_
[0.06,0.9728508,f(0.06),f(0.06)-0.9728508],_
[0.07,0.9679834,f(0.07),f(0.07)-0.9679834],_
[0.08,0.9630194,f(0.08),f(0.08)-0.9630194],_
[0.09,0.9579593,f(0.09),f(0.09)-0.9579593],_
[0.10,0.9528035,f(0.10),f(0.10)-0.9528035],_
[0.11,0.9475526,f(0.11),f(0.11)-0.9475526],_
[0.12,0.9422071,f(0.12),f(0.12)-0.9422071],_
[0.13,0.9367672,f(0.13),f(0.13)-0.9367672],_
[0.14,0.9312336,f(0.14),f(0.14)-0.9312336],_
[0.15,0.9256067,f(0.15),f(0.15)-0.9256067],_
[0.16,0.9198870,f(0.16),f(0.16)-0.9198870],_
[0.17,0.9140748,f(0.17),f(0.17)-0.9140748],_
[0.18,0.9081706,f(0.18),f(0.18)-0.9081706],_
[0.19,0.9021750,f(0.19),f(0.19)-0.9021750],_
[0.20,0.8960882,f(0.20),f(0.20)-0.8960882],_
[0.21,0.8899109,f(0.21),f(0.21)-0.8899109],_
[0.22,0.8836433,f(0.22),f(0.22)-0.8836433],_
[0.23,0.8772860,f(0.23),f(0.23)-0.8772860],_
[0.24,0.8708393,f(0.24),f(0.24)-0.8708393],_
[0.25,0.8643037,f(0.25),f(0.25)-0.8643037],_
[0.26,0.8576797,f(0.26),f(0.26)-0.8576797],_
[0.27,0.8509676,f(0.27),f(0.27)-0.8509676],_
[0.28,0.8441678,f(0.28),f(0.28)-0.8441678],_
[0.29,0.8372808,f(0.29),f(0.29)-0.8372808],_
[0.30,0.8303071,f(0.30),f(0.30)-0.8303071],_
[0.31,0.8232469,f(0.31),f(0.31)-0.8232469],_
[0.32,0.8161007,f(0.32),f(0.32)-0.8161007],_
[0.33,0.8088690,f(0.33),f(0.33)-0.8088690],_
[0.34,0.8015521,f(0.34),f(0.34)-0.8015521],_
[0.35,0.7941504,f(0.35),f(0.35)-0.7941504],_
[0.36,0.7866644,f(0.36),f(0.36)-0.7866644],_
[0.37,0.7790943,f(0.37),f(0.37)-0.7790943],_
[0.38,0.7714407,f(0.38),f(0.38)-0.7714407],_
[0.39,0.7637039,f(0.39),f(0.39)-0.7637039],_
[0.40,0.7558843,f(0.40),f(0.40)-0.7558843],_
[0.41,0.7479823,f(0.41),f(0.41)-0.7479823],_
[0.42,0.7399982,f(0.42),f(0.42)-0.7399982],_
[0.43,0.7319324,f(0.43),f(0.43)-0.7319324],_
[0.44,0.7237854,f(0.44),f(0.44)-0.7237854],_
[0.45,0.7155575,f(0.45),f(0.45)-0.7155575],_
[0.46,0.7072491,f(0.46),f(0.46)-0.7072491],_
[0.47,0.6988605,f(0.47),f(0.47)-0.6988605],_
[0.48,0.6903921,f(0.48),f(0.48)-0.6903921],_
[0.49,0.6818443,f(0.49),f(0.49)-0.6818443],_
[0.50,0.6732175,f(0.50),f(0.50)-0.6732175]]
 
   Compiling function f with type Float -> OnePointCompletion 
      DoubleFloat 

   (2)
   [
     [0.0099999999999999985, 0.99572219999999989, 0.99572223984366792,
      3.9843668031558366E-8]
     ,

     [0.019999999999999997, 0.99134499999999992, 0.991344977749124,
      - 2.2250875919560542E-8]
     ,

     [0.029999999999999999, 0.98686869999999993, 0.98686870874746913,
      8.747469193437496E-9]
     ,

     [0.039999999999999994, 0.98229389999999994, 0.98229392458604003,
      2.4586040092700046E-8]
     ,

     [0.049999999999999996, 0.97762109999999991, 0.97762111375291483,
      1.375291491800823E-8]
     ,

     [0.059999999999999998, 0.9728507999999999, 0.97285076150122396,
      - 3.8498775944972863E-8]
     ,

     [0.069999999999999993, 0.96798339999999994, 0.96798334987326684,
      - 5.0126733097677345E-8]
     ,

     [0.079999999999999988, 0.96301939999999997, 0.96301935772443681,
      - 4.2275563161275898E-8]
     ,

     [0.089999999999999997, 0.95795929999999996, 0.95795926074695692,
      - 3.9253043038200985E-8]
     ,

     [0.099999999999999992, 0.95280349999999991, 0.95280353149342512,
      3.1493425201034597E-8]
     ,

     [0.10999999999999999, 0.94755259999999997, 0.94755263940017342,
      3.9400173457160292E-8]
     ,
    [0.12,0.94220709999999996,0.94220705081044243,- 4.9189557538298345E-8],

     [0.12999999999999998, 0.93676719999999991, 0.93676722899736986,
      2.899736994965707E-8]
     ,

     [0.13999999999999999, 0.93123359999999999, 0.93123363418679772,
      3.4186797726043494E-8]
     ,

     [0.14999999999999999, 0.92560669999999989, 0.92560672357989859,
      2.3579898700276658E-8]
     ,

     [0.15999999999999998, 0.9198869999999999, 0.91988695137562182,
      - 4.8624378079509256E-8]
     ,

     [0.16999999999999998, 0.91407479999999997, 0.91407476879296246,
      - 3.1207037509695112E-8]
     ,

     [0.17999999999999999, 0.90817059999999994, 0.90817062409305227,
      2.4093052330975695E-8]
     ,

     [0.18999999999999997, 0.90217499999999995, 0.90217496260107799,
      - 3.7398921959308495E-8]
     ,

     [0.19999999999999998, 0.89608819999999989, 0.89608822672802324,
      2.6728023350131025E-8]
     ,

     [0.20999999999999999, 0.88991089999999995, 0.88991085599223996,
      - 4.4007759991693263E-8]
     ,

     [0.21999999999999997, 0.88364329999999991, 0.88364328704084927,
      - 1.2959150641478345E-8]
     ,

     [0.22999999999999998, 0.8772859999999999, 0.87728595367097117,
      - 4.632902872447886E-8]
     ,

     [0.23999999999999999, 0.87083929999999998, 0.8708392868507886,
      - 1.3149211386398463E-8]
     ,
    [0.25,0.8643036999999999,0.86430371474044287,1.4740442977334567E-8],

     [0.25999999999999995, 0.85767969999999993, 0.85767966271276586,
      - 3.7287234078142717E-8]
     ,

     [0.26999999999999996, 0.85096759999999994, 0.85096755337384578,
      - 4.6626154159845612E-8]
     ,

     [0.27999999999999997, 0.84416779999999991, 0.84416780658343327,
      6.5834333540237822E-9]
     ,

     [0.28999999999999998, 0.83728079999999994, 0.83728083947518439,
      3.9475184454573764E-8]
     ,

     [0.29999999999999999, 0.83030709999999996, 0.83030706647674457,
      - 3.352325539385248E-8]
     ,
    [0.31,0.82324689999999989,0.82324689932967399,- 6.7032590589377605E-10],

     [0.31999999999999995, 0.8161006999999999, 0.81610074710921554,
      4.7109215639551394E-8]
     ,

     [0.32999999999999996, 0.80886899999999995, 0.80886901624390695,
      1.6243906997281954E-8]
     ,

     [0.33999999999999997, 0.80155209999999999, 0.80155211053503883,
      1.0535038841297251E-8]
     ,

     [0.34999999999999998, 0.79415039999999992, 0.79415043117595796,
      3.1175958037366058E-8]
     ,

     [0.35999999999999999, 0.78666439999999993, 0.78666437677122092,
      - 2.3228779011397194E-8]
     ,
    [0.37,0.77909429999999991,0.77909434335559369,4.3355593781768675E-8],

     [0.37999999999999995, 0.77144069999999998, 0.77144072441290457,
      2.4412904586768036E-8]
     ,

     [0.38999999999999996, 0.76370389999999999, 0.7637039108947471,
      1.0894747104472913E-8]
     ,

     [0.39999999999999997, 0.75588429999999995, 0.75588429123903633,
      - 8.7609636212349074E-9]
     ,

     [0.40999999999999998, 0.74798229999999999, 0.74798225138841912,
      - 4.8611580871771309E-8]
     ,

     [0.41999999999999998, 0.73999819999999994, 0.7399981748085398,
      - 2.5191460140128186E-8]
     ,

     [0.42999999999999999, 0.73193239999999993, 0.73193244250616207,
      4.2506162145627968E-8]
     ,

     [0.43999999999999995, 0.72378539999999991, 0.7237854330471486,
      3.3047148684239858E-8]
     ,

     [0.44999999999999996, 0.71555749999999996, 0.71555752257429928,
      2.2574299318733893E-8]
     ,

     [0.45999999999999996, 0.70724909999999996, 0.70724908482505056,
      - 1.517494940816988E-8]
     ,
    [0.46999999999999997,0.6988605,0.6988604911490337,- 8.8509662932167998E-9],

     [0.47999999999999998, 0.69039209999999995, 0.69039211052549776,
      1.0525497806668227E-8]
     ,

     [0.48999999999999999, 0.68184429999999996, 0.68184430958059394,
      9.5805939848148114E-9]
     ,
    [0.5,0.67321749999999991,0.67321745260452559,- 4.7395474322975417E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R   Compiling function f with type Float -> OnePointCompletion 
--R      DoubleFloat 
--R
--R   (2)
--R   [[1.0E-2,0.9957222,0.99572223984366792,3.9843667920536063E-8],
--R    [2.0E-2,0.99134500000000003,0.991344977749124,- 2.2250876030582845E-8],
--R
--R     [2.9999999999999999E-2, 0.98686870000000004, 0.98686870874746913,
--R      8.7474690824151935E-9]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.98229390000000005, 0.98229392458604003,
--R      2.4586039981677743E-8]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.97762110000000002, 0.97762111375291483,
--R      1.3752914806985927E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.97285080000000002, 0.97285076150122396,
--R      - 3.8498776055995165E-8]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.96798340000000005, 0.96798334987326684,
--R      - 5.0126733208699648E-8]
--R     ,
--R
--R     [8.0000000000000002E-2, 0.96301939999999997, 0.96301935772443681,
--R      - 4.2275563161275898E-8]
--R     ,
--R
--R     [8.9999999999999997E-2, 0.95795929999999996, 0.95795926074695703,
--R      - 3.9253042927178683E-8]
--R     ,
--R
--R     [0.10000000000000001, 0.95280350000000003, 0.95280353149342489,
--R      3.149342486796769E-8]
--R     ,
--R    [0.11,0.94755259999999997,0.94755263940017342,3.9400173457160292E-8],
--R    [0.12,0.94220709999999996,0.94220705081044254,- 4.9189557427276043E-8],
--R    [0.13,0.93676720000000002,0.93676722899736986,2.8997369838634768E-8],
--R
--R     [0.14000000000000001, 0.93123359999999999, 0.93123363418679772,
--R      3.4186797726043494E-8]
--R     ,
--R    [0.14999999999999999,0.9256067,0.92560672357989859,2.3579898589254356E-8],
--R    [0.16,0.91988700000000001,0.91988695137562182,- 4.8624378190531559E-8],
--R
--R     [0.17000000000000001, 0.91407479999999997, 0.91407476879296246,
--R      - 3.1207037509695112E-8]
--R     ,
--R
--R     [0.17999999999999999, 0.90817060000000005, 0.90817062409305238,
--R      2.4093052330975695E-8]
--R     ,
--R    [0.19,0.90217499999999995,0.90217496260107799,- 3.7398921959308495E-8],
--R    [0.20000000000000001,0.8960882,0.89608822672802324,2.6728023239108722E-8],
--R
--R     [0.20999999999999999, 0.88991089999999995, 0.88991085599224007,
--R      - 4.400775988067096E-8]
--R     ,
--R    [0.22,0.88364330000000002,0.88364328704084927,- 1.2959150752500648E-8],
--R
--R     [0.23000000000000001, 0.87728600000000001, 0.87728595367097117,
--R      - 4.6329028835501163E-8]
--R     ,
--R
--R     [0.23999999999999999, 0.87083929999999998, 0.8708392868507886,
--R      - 1.3149211386398463E-8]
--R     ,
--R    [0.25,0.86430370000000001,0.86430371474044287,1.4740442866312264E-8],
--R
--R     [0.26000000000000001, 0.85767970000000004, 0.85767966271276586,
--R      - 3.7287234189165019E-8]
--R     ,
--R
--R     [0.27000000000000002, 0.85096760000000005, 0.85096755337384578,
--R      - 4.6626154270867914E-8]
--R     ,
--R
--R     [0.28000000000000003, 0.84416780000000002, 0.84416780658343327,
--R      6.5834332430014797E-9]
--R     ,
--R
--R     [0.28999999999999998, 0.83728080000000005, 0.8372808394751845,
--R      3.9475184454573764E-8]
--R     ,
--R
--R     [0.29999999999999999, 0.83030709999999996, 0.83030706647674468,
--R      - 3.3523255282830178E-8]
--R     ,
--R    [0.31,0.8232469,0.82324689932967399,- 6.7032601691607852E-10],
--R
--R     [0.32000000000000001, 0.81610070000000001, 0.81610074710921554,
--R      4.7109215528529091E-8]
--R     ,
--R
--R     [0.33000000000000002, 0.80886899999999995, 0.80886901624390695,
--R      1.6243906997281954E-8]
--R     ,
--R
--R     [0.34000000000000002, 0.80155209999999999, 0.80155211053503872,
--R      1.0535038730274948E-8]
--R     ,
--R
--R     [0.34999999999999998, 0.79415040000000003, 0.79415043117595796,
--R      3.1175957926343756E-8]
--R     ,
--R
--R     [0.35999999999999999, 0.78666440000000004, 0.78666437677122092,
--R      - 2.3228779122419496E-8]
--R     ,
--R    [0.37,0.77909430000000002,0.77909434335559369,4.3355593670746373E-8],
--R    [0.38,0.77144069999999998,0.77144072441290445,2.4412904475745734E-8],
--R
--R     [0.39000000000000001, 0.76370389999999999, 0.76370391089474698,
--R      1.089474699345061E-8]
--R     ,
--R
--R     [0.40000000000000002, 0.75588429999999995, 0.75588429123903633,
--R      - 8.7609636212349074E-9]
--R     ,
--R
--R     [0.40999999999999998, 0.74798229999999999, 0.74798225138841923,
--R      - 4.8611580760749007E-8]
--R     ,
--R
--R     [0.41999999999999998, 0.73999820000000005, 0.73999817480853991,
--R      - 2.5191460140128186E-8]
--R     ,
--R
--R     [0.42999999999999999, 0.73193240000000004, 0.73193244250616207,
--R      4.2506162034605666E-8]
--R     ,
--R    [0.44,0.72378540000000002,0.7237854330471486,3.3047148573217555E-8],
--R
--R     [0.45000000000000001, 0.71555749999999996, 0.71555752257429939,
--R      2.2574299429756195E-8]
--R     ,
--R
--R     [0.46000000000000002, 0.70724909999999996, 0.70724908482505056,
--R      - 1.517494940816988E-8]
--R     ,
--R    [0.46999999999999997,0.6988605,0.6988604911490337,- 8.8509662932167998E-9],
--R
--R     [0.47999999999999998, 0.69039209999999995, 0.69039211052549776,
--R      1.0525497806668227E-8]
--R     ,
--R
--R     [0.48999999999999999, 0.68184429999999996, 0.68184430958059394,
--R      9.5805939848148114E-9]
--R     ,
--R    [0.5,0.67321750000000002,0.67321745260452559,- 4.739547443399772E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 2

--S 3 of 7
[[0.50,0.3266439,En(2,0.50),En(2,0.50)-0.3266439],_
[0.51,0.3211062,En(2,0.51),En(2,0.51)-0.3211062],_
[0.52,0.3156863,En(2,0.52),En(2,0.52)-0.3156863],_
[0.53,0.3103807,En(2,0.53),En(2,0.53)-0.3103807],_
[0.54,0.3051862,En(2,0.54),En(2,0.54)-0.3051862],_
[0.55,0.3000996,En(2,0.55),En(2,0.55)-0.3000996],_
[0.56,0.2951179,En(2,0.56),En(2,0.56)-0.2951179],_
[0.57,0.2902382,En(2,0.57),En(2,0.57)-0.2902382],_
[0.58,0.2854578,En(2,0.58),En(2,0.58)-0.2854578],_
[0.59,0.2807739,En(2,0.59),En(2,0.59)-0.2807739],_
[0.60,0.2761839,En(2,0.60),En(2,0.60)-0.2761839],_
[0.61,0.2716855,En(2,0.61),En(2,0.61)-0.2716855],_
[0.62,0.2672761,En(2,0.62),En(2,0.62)-0.2672761],_
[0.63,0.2629535,En(2,0.63),En(2,0.63)-0.2629535],_
[0.64,0.2587154,En(2,0.64),En(2,0.64)-0.2587154],_
[0.65,0.2545597,En(2,0.65),En(2,0.65)-0.2545597],_
[0.66,0.2504844,En(2,0.66),En(2,0.66)-0.2504844],_
[0.67,0.2464874,En(2,0.67),En(2,0.67)-0.2464874],_
[0.68,0.2425667,En(2,0.68),En(2,0.68)-0.2425667],_
[0.69,0.2387206,En(2,0.69),En(2,0.69)-0.2387206],_
[0.70,0.2349471,En(2,0.70),En(2,0.70)-0.2349471],_
[0.71,0.2312446,En(2,0.71),En(2,0.71)-0.2312446],_
[0.72,0.2276114,En(2,0.72),En(2,0.72)-0.2276114],_
[0.73,0.2240457,En(2,0.73),En(2,0.73)-0.2240457],_
[0.74,0.2205461,En(2,0.74),En(2,0.74)-0.2205461],_
[0.75,0.2171109,En(2,0.75),En(2,0.75)-0.2171109],_
[0.76,0.2137388,En(2,0.76),En(2,0.76)-0.2137388],_
[0.77,0.2104282,En(2,0.77),En(2,0.77)-0.2104282],_
[0.78,0.2071777,En(2,0.78),En(2,0.78)-0.2071777],_
[0.79,0.2039860,En(2,0.79),En(2,0.79)-0.2039860],_
[0.80,0.2008517,En(2,0.80),En(2,0.80)-0.2008517],_
[0.81,0.1977736,En(2,0.81),En(2,0.81)-0.1977736],_
[0.82,0.1947504,En(2,0.82),En(2,0.82)-0.1947504],_
[0.83,0.1917810,En(2,0.83),En(2,0.83)-0.1917810],_
[0.84,0.1888641,En(2,0.84),En(2,0.84)-0.1888641],_
[0.85,0.1859986,En(2,0.85),En(2,0.85)-0.1859986],_
[0.86,0.1831833,En(2,0.86),En(2,0.86)-0.1831833],_
[0.87,0.1804173,En(2,0.87),En(2,0.87)-0.1804173],_
[0.88,0.1776994,En(2,0.88),En(2,0.88)-0.1776994],_
[0.89,0.1750287,En(2,0.89),En(2,0.89)-0.1750287],_
[0.90,0.1724041,En(2,0.90),En(2,0.90)-0.1724041],_
[0.91,0.1698247,En(2,0.91),En(2,0.91)-0.1698247],_
[0.92,0.1672895,En(2,0.92),En(2,0.92)-0.1672895],_
[0.93,0.1647977,En(2,0.93),En(2,0.93)-0.1647977],_
[0.94,0.1623482,En(2,0.94),En(2,0.94)-0.1623482],_
[0.95,0.1599404,En(2,0.95),En(2,0.95)-0.1599404],_
[0.96,0.1575732,En(2,0.96),En(2,0.96)-0.1575732],_
[0.97,0.1552459,En(2,0.97),En(2,0.97)-0.1552459],_
[0.98,0.1529578,En(2,0.98),En(2,0.98)-0.1529578],_
[0.99,0.1507079,En(2,0.99),En(2,0.99)-0.1507079],_
[1.00,0.1484955,En(2,1.00),En(2,1.00)-0.1484955],_
[1.01,0.1463199,En(2,1.01),En(2,1.01)-0.1463199],_
[1.02,0.1441804,En(2,1.02),En(2,1.02)-0.1441804],_
[1.03,0.1420763,En(2,1.03),En(2,1.03)-0.1420763],_
[1.04,0.1400068,En(2,1.04),En(2,1.04)-0.1400068],_
[1.05,0.1379713,En(2,1.05),En(2,1.05)-0.1379713],_
[1.06,0.1359691,En(2,1.06),En(2,1.06)-0.1359691],_
[1.07,0.1339996,En(2,1.07),En(2,1.07)-0.1339996],_
[1.08,0.1320622,En(2,1.08),En(2,1.08)-0.1320622],_
[1.09,0.1301562,En(2,1.09),En(2,1.09)-0.1301562],_
[1.10,0.1282811,En(2,1.10),En(2,1.10)-0.1282811],_
[1.11,0.1264362,En(2,1.11),En(2,1.11)-0.1264362],_
[1.12,0.1246210,En(2,1.12),En(2,1.12)-0.1246210],_
[1.13,0.1228350,En(2,1.13),En(2,1.13)-0.1228350],_
[1.14,0.1210775,En(2,1.14),En(2,1.14)-0.1210775],_
[1.15,0.1193481,En(2,1.15),En(2,1.15)-0.1193481],_
[1.16,0.1176462,En(2,1.16),En(2,1.16)-0.1176462],_
[1.17,0.1159714,En(2,1.17),En(2,1.17)-0.1159714],_
[1.18,0.1143231,En(2,1.18),En(2,1.18)-0.1143231],_
[1.19,0.1127008,En(2,1.19),En(2,1.19)-0.1127008],_
[1.20,0.1111041,En(2,1.20),En(2,1.20)-0.1111041],_
[1.21,0.1095325,En(2,1.21),En(2,1.21)-0.1095325],_
[1.22,0.1079855,En(2,1.22),En(2,1.22)-0.1079855],_
[1.23,0.1064627,En(2,1.23),En(2,1.23)-0.1064627],_
[1.24,0.1049637,En(2,1.24),En(2,1.24)-0.1049637],_
[1.25,0.1034881,En(2,1.25),En(2,1.25)-0.1034881],_
[1.26,0.1020353,En(2,1.26),En(2,1.26)-0.1020353],_
[1.27,0.1006051,En(2,1.27),En(2,1.27)-0.1006051],_
[1.28,0.0991970,En(2,1.28),En(2,1.28)-0.0991970],_
[1.29,0.0978106,En(2,1.29),En(2,1.29)-0.0978106],_
[1.30,0.0964455,En(2,1.30),En(2,1.30)-0.0964455],_
[1.31,0.0951015,En(2,1.31),En(2,1.31)-0.0951015],_
[1.32,0.0937780,En(2,1.32),En(2,1.32)-0.0937780],_
[1.33,0.0924747,En(2,1.33),En(2,1.33)-0.0924747],_
[1.34,0.0911913,En(2,1.34),En(2,1.34)-0.0911913],_
[1.35,0.0899275,En(2,1.35),En(2,1.35)-0.0899275],_
[1.36,0.0886829,En(2,1.36),En(2,1.36)-0.0886829],_
[1.37,0.0874571,En(2,1.37),En(2,1.37)-0.0874571],_
[1.38,0.0862499,En(2,1.38),En(2,1.38)-0.0862499],_
[1.39,0.0850610,En(2,1.39),En(2,1.39)-0.0850610],_
[1.40,0.0838899,En(2,1.40),En(2,1.40)-0.0838899],_
[1.41,0.0827365,En(2,1.41),En(2,1.41)-0.0827365],_
[1.42,0.0816004,En(2,1.42),En(2,1.42)-0.0816004],_
[1.43,0.0804813,En(2,1.43),En(2,1.43)-0.0804813],_
[1.44,0.0793789,En(2,1.44),En(2,1.44)-0.0793789],_
[1.45,0.0782930,En(2,1.45),En(2,1.45)-0.0782930],_
[1.46,0.0772233,En(2,1.46),En(2,1.46)-0.0772233],_
[1.47,0.0761694,En(2,1.47),En(2,1.47)-0.0761694],_
[1.48,0.0751313,En(2,1.48),En(2,1.48)-0.0751313],_
[1.49,0.0741085,En(2,1.49),En(2,1.49)-0.0741085],_
[1.50,0.0731008,En(2,1.50),En(2,1.50)-0.0731008],_
[1.51,0.0721080,En(2,1.51),En(2,1.51)-0.0721080],_
[1.52,0.0711298,En(2,1.52),En(2,1.52)-0.0711298],_
[1.53,0.0701660,En(2,1.53),En(2,1.53)-0.0701660],_
[1.54,0.0692164,En(2,1.54),En(2,1.54)-0.0692164],_
[1.55,0.0682807,En(2,1.55),En(2,1.55)-0.0682807],_
[1.56,0.0673587,En(2,1.56),En(2,1.56)-0.0673587],_
[1.57,0.0664502,En(2,1.57),En(2,1.57)-0.0664502],_
[1.58,0.0655549,En(2,1.58),En(2,1.58)-0.0655549],_
[1.59,0.0646726,En(2,1.59),En(2,1.59)-0.0646726],_
[1.60,0.0638032,En(2,1.60),En(2,1.60)-0.0638032],_
[1.61,0.0629464,En(2,1.61),En(2,1.61)-0.0629464],_
[1.62,0.0621020,En(2,1.62),En(2,1.62)-0.0621020],_
[1.63,0.0612698,En(2,1.63),En(2,1.63)-0.0612698],_
[1.64,0.0604497,En(2,1.64),En(2,1.64)-0.0604497],_
[1.65,0.0596413,En(2,1.65),En(2,1.65)-0.0596413],_
[1.66,0.0588446,En(2,1.66),En(2,1.66)-0.0588446],_
[1.67,0.0580594,En(2,1.67),En(2,1.67)-0.0580594],_
[1.68,0.0572854,En(2,1.68),En(2,1.68)-0.0572854],_
[1.69,0.0565226,En(2,1.69),En(2,1.69)-0.0565226],_
[1.70,0.0557706,En(2,1.70),En(2,1.70)-0.0557706],_
[1.71,0.0550294,En(2,1.71),En(2,1.71)-0.0550294],_
[1.72,0.0542988,En(2,1.72),En(2,1.72)-0.0542988],_
[1.73,0.0535786,En(2,1.73),En(2,1.73)-0.0535786],_
[1.74,0.0528686,En(2,1.74),En(2,1.74)-0.0528686],_
[1.75,0.0521687,En(2,1.75),En(2,1.75)-0.0521687],_
[1.76,0.0514788,En(2,1.76),En(2,1.76)-0.0514788],_
[1.77,0.0507986,En(2,1.77),En(2,1.77)-0.0507986],_
[1.78,0.0501281,En(2,1.78),En(2,1.78)-0.0501281],_
[1.79,0.0494670,En(2,1.79),En(2,1.79)-0.0494670],_
[1.80,0.0488153,En(2,1.80),En(2,1.80)-0.0488153],_
[1.81,0.0481727,En(2,1.81),En(2,1.81)-0.0481727],_
[1.82,0.0475392,En(2,1.82),En(2,1.82)-0.0475392],_
[1.83,0.0469146,En(2,1.83),En(2,1.83)-0.0469146],_
[1.84,0.0462987,En(2,1.84),En(2,1.84)-0.0462987],_
[1.85,0.0456915,En(2,1.85),En(2,1.85)-0.0456915],_
[1.86,0.0450928,En(2,1.86),En(2,1.86)-0.0450928],_
[1.87,0.0445024,En(2,1.87),En(2,1.87)-0.0445024],_
[1.88,0.0439203,En(2,1.88),En(2,1.88)-0.0439203],_
[1.89,0.0433463,En(2,1.89),En(2,1.89)-0.0433463],_
[1.90,0.0427803,En(2,1.90),En(2,1.90)-0.0427803],_
[1.91,0.0422222,En(2,1.91),En(2,1.91)-0.0422222],_
[1.92,0.0416718,En(2,1.92),En(2,1.92)-0.0416718],_
[1.93,0.0411291,En(2,1.93),En(2,1.93)-0.0411291],_
[1.94,0.0405938,En(2,1.94),En(2,1.94)-0.0405938],_
[1.95,0.0400660,En(2,1.95),En(2,1.95)-0.0400660],_
[1.96,0.0395455,En(2,1.96),En(2,1.96)-0.0395455],_
[1.97,0.0390322,En(2,1.97),En(2,1.97)-0.0390322],_
[1.98,0.0385259,En(2,1.98),En(2,1.98)-0.0385259],_
[1.99,0.0380267,En(2,1.99),En(2,1.99)-0.0380267],_
[2.00,0.0375343,En(2,2.00),En(2,2.00)-0.0375343]]
 

   (3)
   [[0.5,0.32664389999999999,0.326643862324553,- 3.7675446984408723E-8],

     [0.5099999999999999, 0.32110619999999995, 0.3211061794040434,
      - 2.059595655135027E-8]
     ,

     [0.51999999999999991, 0.31568629999999998, 0.31568625309046361,
      - 4.6909536366435134E-8]
     ,

     [0.52999999999999992, 0.31038069999999995, 0.31038066931747654,
      - 3.0682523410874296E-8]
     ,

     [0.53999999999999992, 0.30518619999999996, 0.30518615409477517,
      - 4.5905224788089782E-8]
     ,

     [0.54999999999999993, 0.30009959999999997, 0.30009956561467016,
      - 3.4385329805708409E-8]
     ,

     [0.55999999999999994, 0.29511789999999999, 0.29511788693397883,
      - 1.3066021153917973E-8]
     ,

     [0.56999999999999995, 0.29023819999999995, 0.29023821917982273,
      1.91798227855422E-8]
     ,

     [0.57999999999999996, 0.28545779999999998, 0.28545777523334881,
      - 2.4766651174346066E-8]
     ,

     [0.58999999999999997, 0.28077389999999997, 0.28077387385015457,
      - 2.6149845400169625E-8]
     ,

     [0.59999999999999998, 0.27618389999999998, 0.27618393418038506,
      3.4180385077853259E-8]
     ,

     [0.60999999999999999, 0.27168549999999997, 0.27168547065517928,
      - 2.9344820684507056E-8]
     ,
    [0.62,0.26727609999999996,0.26727608820941567,- 1.1790584286686112E-8],

     [0.62999999999999989, 0.26295349999999995, 0.2629534778136256,
      - 2.2186374348809323E-8]
     ,

     [0.6399999999999999, 0.25871539999999998, 0.25871541229051531,
      1.2290515327695317E-8]
     ,
    [0.64999999999999991,0.2545597,0.25455974239385426,4.2393854260414088E-8],
    [0.65999999999999992,0.2504844,0.2504843931295298,- 6.8704701927657652E-9],
    [0.66999999999999993,0.2464874,0.24648736030041074,- 3.969958925487127E-8],
    [0.67999999999999994,0.2425667,0.24256670725830815,7.2583081489607792E-9],

     [0.68999999999999995, 0.23872059999999998, 0.23872056184779239,
      - 3.8152207587627274E-8]
     ,

     [0.69999999999999996, 0.23494709999999999, 0.23494711352795306,
      1.3527953063308118E-8]
     ,

     [0.70999999999999996, 0.23124459999999999, 0.23124461065938429,
      1.0659384291900054E-8]
     ,

     [0.71999999999999997, 0.22761139999999999, 0.22761135794474674,
      - 4.2055253252071267E-8]
     ,

     [0.72999999999999998, 0.22404569999999999, 0.22404571401223494,
      1.4012234955673719E-8]
     ,

     [0.73999999999999999, 0.22054609999999999, 0.22054608913215246,
      - 1.0867847538564845E-8]
     ,
    [0.75,0.2171109,0.21711094305759215,4.3057592158390889E-8],

     [0.7599999999999999, 0.21373879999999998, 0.21373878298094046,
      - 1.7019059522782598E-8]
     ,

     [0.76999999999999991, 0.21042819999999998, 0.21042816159857819,
      - 3.8401421792455537E-8]
     ,

     [0.77999999999999992, 0.20717769999999999, 0.20717767527674386,
      - 2.4723256136782723E-8]
     ,

     [0.78999999999999992, 0.20398599999999997, 0.20398596231206956,
      - 3.7687930415364335E-8]
     ,

     [0.79999999999999993, 0.20085169999999999, 0.20085170128078722,
      1.2807872262765585E-9]
     ,

     [0.80999999999999994, 0.19777359999999999, 0.1977736094710606,
      9.4710606024506205E-9]
     ,

     [0.81999999999999995, 0.19475039999999999, 0.1947504413933023,
      4.1393302313563751E-8]
     ,

     [0.82999999999999996, 0.19178099999999998, 0.19178098736371621,
      - 1.2636283769351664E-8]
     ,

     [0.83999999999999997, 0.18886409999999998, 0.18886407215664666,
      - 2.784335331740273E-8]
     ,

     [0.84999999999999998, 0.18599859999999999, 0.18599855372163443,
      - 4.6278365556373657E-8]
     ,

     [0.85999999999999999, 0.18318329999999999, 0.1831833219613668,
      2.1961366808431748E-8]
     ,
    [0.87,0.18041729999999997,0.18041729756697505,- 2.4330249204229659E-9],

     [0.87999999999999989, 0.17769939999999998, 0.17769943090737961,
      3.0907379627853615E-8]
     ,

     [0.8899999999999999, 0.17502869999999998, 0.17502870096960521,
      9.6960522943945193E-10]
     ,

     [0.89999999999999991, 0.17240409999999998, 0.17240411434719941,
      1.434719942849938E-8]
     ,
    [0.90999999999999992,0.1698247,0.16982470427407523,4.2740752326242415E-9],

     [0.91999999999999993, 0.16728949999999998, 0.16728952970127758,
      2.9701277604043952E-8]
     ,

     [0.92999999999999994, 0.16479769999999999, 0.1647976744143371,
      - 2.5585662893901073E-8]
     ,
    [0.93999999999999995,0.1623482,0.16234824618902396,4.6189023966691778E-8],

     [0.94999999999999996, 0.15994039999999998, 0.15994037598345329,
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     [0.96999999999999997, 0.15524589999999999, 0.15524594476761389,
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     [0.98999999999999999, 0.15070789999999998, 0.15070786348977019,
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     [1.0099999999999998, 0.14631989999999997, 0.1463199395390884,
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     [1.0199999999999998, 0.14418039999999999, 0.1441804350721845,
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     ,

     [1.0299999999999998, 0.14207629999999999, 0.1420762844890415,
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     [1.0399999999999998, 0.14000679999999999, 0.14000679617012995,
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     ,

     [1.0499999999999998, 0.13797129999999999, 0.13797129522994897,
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     [1.0599999999999998, 0.13596909999999998, 0.13596912300504765,
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    [1.0699999999999998,0.1339996,0.13399963656170114,3.6561701138859704E-8],

     [1.0799999999999998, 0.13206219999999999, 0.13206220822231929,
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     ,
    [1.0899999999999999,0.1301562,0.13015622510971897,2.5109718970739436E-8],

     [1.0999999999999999, 0.12828109999999998, 0.12828108870843541,
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    [1.1099999999999999,0.1264362,0.12643621444229519,1.4442295193095589E-8],
    [1.1199999999999999,0.124621,0.12462103126751795,3.1267517949795653E-8],
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     [1.1399999999999999, 0.12107749999999999, 0.12107751934064426,
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    [1.1499999999999999,0.1193481,0.11934811270455489,1.270455489421618E-8],

     [1.1599999999999999, 0.11764619999999999, 0.11764624067609286,
      4.0676092868952018E-8]
     ,

     [1.1699999999999999, 0.11597139999999999, 0.11597139426664799,
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     [1.1899999999999999, 0.11270079999999999, 0.11270079893724061,
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     [1.2699999999999998, 0.10060509999999999, 0.10060511029696792,
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     [1.2799999999999998, 0.099196999999999994, 0.099196994746190897,
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     [1.2899999999999998, 0.097810599999999998, 0.097810601544343179,
      1.5443431811146269E-9]
     ,

     [1.2999999999999998, 0.09644549999999999, 0.09644554783014464,
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     ,

     [1.3099999999999998, 0.095101499999999992, 0.095101458750257939,
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     ,

     [1.3199999999999998, 0.093777999999999986, 0.093777967254982525,
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     [1.3299999999999998, 0.092474699999999993, 0.092474713900349365,
      1.3900349371542831E-8]
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     [1.3399999999999999, 0.091191299999999989, 0.091191346656366634,
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     [1.3499999999999999, 0.089927499999999994, 0.089927520721194698,
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     [1.3599999999999999, 0.088682899999999995, 0.088682898341016059,
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     [1.3699999999999999, 0.087457099999999996, 0.087457148635403437,
      4.863540344068884E-8]
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     [1.3799999999999999, 0.08624989999999999, 0.086249947427970763,
      4.74279707729508E-8]
     ,

     [1.3899999999999999, 0.085060999999999998, 0.085060977082121292,
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     ,

     [1.3999999999999999, 0.083889899999999989, 0.083889926341705251,
      2.6341705261501147E-8]
     ,

     [1.4099999999999999, 0.082736499999999991, 0.082736490176409022,
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     ,

     [1.4199999999999999, 0.08160039999999999, 0.081600369631709052,
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     [1.4299999999999999, 0.080481299999999992, 0.080481271683224637,
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     ,

     [1.4399999999999999, 0.079378899999999988, 0.079378909095316558,
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     [1.5099999999999998, 0.072107999999999992, 0.07210798726481607,
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     ,

     [1.5199999999999998, 0.071129799999999993, 0.071129818181354998,
      1.8181355004864841E-8]
     ,

     [1.5299999999999998, 0.070165999999999992, 0.070166038419312127,
      3.8419312134441164E-8]
     ,

     [1.5399999999999998, 0.069216399999999997, 0.069216411688142632,
      1.1688142634302956E-8]
     ,
    [1.5499999999999998,0.0682807,0.068280706172218653,6.1722186528445633E-9],

     [1.5599999999999998, 0.067358699999999994, 0.067358694430315336,
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     ,

     [1.5699999999999998, 0.066450199999999987, 0.066450153297810566,
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     ,

     [1.5799999999999998, 0.065554899999999999, 0.065554863791512208,
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     ,

     [1.5899999999999999, 0.064672599999999997, 0.064672611017026621,
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     ,

     [1.5999999999999999, 0.06380319999999999, 0.063803184078591646,
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    [1.6099999999999999,0.0629464,0.062946375991286774,- 2.4008713225831535E-8],

     [1.6199999999999999, 0.062101999999999997, 0.062101983595557797,
      - 1.6404442200468328E-8]
     ,

     [1.6299999999999999, 0.061269799999999999, 0.061269807473971261,
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     [1.6399999999999999, 0.060449699999999995, 0.060449651870139065,
      - 4.8129860930057333E-8]
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     [1.6499999999999999, 0.059641299999999994, 0.059641324609737895,
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     [1.6599999999999999, 0.058844599999999997, 0.05884463702356188,
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     [1.6699999999999999, 0.058059399999999997, 0.058059403872549598,
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     [1.6799999999999999, 0.057285399999999993, 0.057285443274719294,
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     [1.6899999999999999, 0.056522599999999999, 0.056522576633957461,
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     [1.7599999999999998, 0.051478799999999998, 0.051478797624312095,
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     [1.7699999999999998, 0.050798599999999999, 0.05079862535927962,
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     [1.7799999999999998, 0.050128099999999995, 0.050128076648957673,
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     [1.7899999999999998, 0.049466999999999997, 0.049467002209351629,
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     [1.7999999999999998, 0.048815299999999999, 0.048815255366623025,
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     [1.8099999999999998, 0.048172699999999999, 0.04817269200426183,
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     [1.8199999999999998, 0.047539199999999997, 0.047539170511522399,
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     [1.8299999999999998, 0.046914599999999994, 0.046914551733080345,
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     [1.8399999999999999, 0.046298699999999998, 0.046298698919879006,
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     [1.8499999999999999, 0.045691499999999996, 0.045691477681137002,
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     [1.8599999999999999, 0.045092799999999995, 0.045092755937471404,
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     [1.8699999999999999, 0.044502399999999998, 0.044502403875126564,
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     ,

     [1.8799999999999999, 0.043920299999999995, 0.043920293901256249,
      - 6.0987437461301752E-9]
     ,

     [1.8899999999999999, 0.043346299999999997, 0.043346300600240958,
      6.0024096110167235E-10]
     ,

     [1.8999999999999999, 0.042780299999999993, 0.042780300691018888,
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     ,

     [1.9099999999999999, 0.042222199999999994, 0.042222172985386774,
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     [1.9199999999999999, 0.041671799999999995, 0.041671798347258343,
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     ,

     [1.9299999999999999, 0.041129099999999995, 0.041129059652846342,
      - 4.0347153652808831E-8]
     ,

     [1.9399999999999999, 0.040593799999999999, 0.040593841751749682,
      4.1751749682572559E-8]
     ,
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    [1.96,0.039545499999999997,0.039545517367460342,1.7367460344863694E-8],
    [1.97,0.039032199999999996,0.039032190112314194,- 9.8876858020680025E-9],
    [1.98,0.038525899999999995,0.038525942034687163,4.2034687168512885E-8],
    [1.99,0.038026699999999997,0.038026667297318517,- 3.2702681479479523E-8],
    [2.0,0.0375343,0.037534261820490689,- 3.817950931100933E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (3)
--R   [[0.5,0.32664389999999999,0.326643862324553,- 3.7675446984408723E-8],
--R
--R     [0.51000000000000001, 0.32110620000000001, 0.32110617940404323,
--R      - 2.0595956773394875E-8]
--R     ,
--R
--R     [0.52000000000000002, 0.31568629999999998, 0.31568625309046355,
--R      - 4.6909536421946285E-8]
--R     ,
--R
--R     [0.53000000000000003, 0.31038070000000001, 0.31038066931747649,
--R      - 3.0682523521896599E-8]
--R     ,
--R
--R     [0.54000000000000004, 0.30518620000000002, 0.30518615409477512,
--R      - 4.5905224899112085E-8]
--R     ,
--R
--R     [0.55000000000000004, 0.30009960000000002, 0.30009956561466999,
--R      - 3.4385330027753014E-8]
--R     ,
--R
--R     [0.56000000000000005, 0.29511789999999999, 0.29511788693397883,
--R      - 1.3066021153917973E-8]
--R     ,
--R    [0.56999999999999995,0.2902382,0.29023821917982273,1.9179822730031049E-8],
--R
--R     [0.57999999999999996, 0.28545779999999998, 0.28545777523334881,
--R      - 2.4766651174346066E-8]
--R     ,
--R
--R     [0.58999999999999997, 0.28077390000000002, 0.28077387385015457,
--R      - 2.6149845455680776E-8]
--R     ,
--R
--R     [0.59999999999999998, 0.27618389999999998, 0.27618393418038506,
--R      3.4180385077853259E-8]
--R     ,
--R
--R     [0.60999999999999999, 0.27168550000000002, 0.27168547065517928,
--R      - 2.9344820740018207E-8]
--R     ,
--R    [0.62,0.26727610000000002,0.26727608820941573,- 1.1790584286686112E-8],
--R    [0.63,0.26295350000000001,0.26295347781362555,- 2.2186374459831626E-8],
--R
--R     [0.64000000000000001, 0.25871539999999998, 0.25871541229051526,
--R      1.2290515272184166E-8]
--R     ,
--R    [0.65000000000000002,0.2545597,0.25455974239385432,4.2393854315925239E-8],
--R    [0.66000000000000003,0.2504844,0.25048439312952969,- 6.8704703037880677E-9],
--R    [0.67000000000000004,0.2464874,0.24648736030041074,- 3.969958925487127E-8],
--R    [0.68000000000000005,0.2425667,0.24256670725830815,7.2583081489607792E-9],
--R
--R     [0.68999999999999995, 0.23872060000000001, 0.23872056184779239,
--R      - 3.8152207615382849E-8]
--R     ,
--R
--R     [0.69999999999999996, 0.23494709999999999, 0.23494711352795306,
--R      1.3527953063308118E-8]
--R     ,
--R
--R     [0.70999999999999996, 0.23124459999999999, 0.23124461065938429,
--R      1.0659384291900054E-8]
--R     ,
--R
--R     [0.71999999999999997, 0.22761139999999999, 0.22761135794474674,
--R      - 4.2055253252071267E-8]
--R     ,
--R
--R     [0.72999999999999998, 0.22404569999999999, 0.22404571401223494,
--R      1.4012234955673719E-8]
--R     ,
--R
--R     [0.73999999999999999, 0.22054609999999999, 0.22054608913215246,
--R      - 1.0867847538564845E-8]
--R     ,
--R    [0.75,0.2171109,0.21711094305759215,4.3057592158390889E-8],
--R
--R     [0.76000000000000001, 0.21373880000000001, 0.21373878298094046,
--R      - 1.7019059550538174E-8]
--R     ,
--R
--R     [0.77000000000000002, 0.21042820000000001, 0.21042816159857808,
--R      - 3.8401421931233415E-8]
--R     ,
--R
--R     [0.78000000000000003, 0.20717769999999999, 0.2071776752767438,
--R      - 2.4723256192293874E-8]
--R     ,
--R    [0.79000000000000004,0.203986,0.20398596231206947,- 3.7687930526386637E-8],
--R
--R     [0.80000000000000004, 0.20085169999999999, 0.20085170128078714,
--R      1.2807871430098317E-9]
--R     ,
--R
--R     [0.81000000000000005, 0.19777359999999999, 0.19777360947106051,
--R      9.4710605191838937E-9]
--R     ,
--R
--R     [0.81999999999999995, 0.19475039999999999, 0.19475044139330239,
--R      4.1393302396830478E-8]
--R     ,
--R
--R     [0.82999999999999996, 0.19178100000000001, 0.19178098736371621,
--R      - 1.2636283797107239E-8]
--R     ,
--R
--R     [0.83999999999999997, 0.18886410000000001, 0.18886407215664666,
--R      - 2.7843353345158306E-8]
--R     ,
--R
--R     [0.84999999999999998, 0.18599859999999999, 0.18599855372163451,
--R      - 4.627836547310693E-8]
--R     ,
--R
--R     [0.85999999999999999, 0.18318329999999999, 0.1831833219613668,
--R      2.1961366808431748E-8]
--R     ,
--R    [0.87,0.1804173,0.18041729756697517,- 2.4330248371562391E-9],
--R    [0.88,0.17769940000000001,0.17769943090737958,3.0907379572342464E-8],
--R
--R     [0.89000000000000001, 0.17502870000000001, 0.17502870096960518,
--R      9.696051739283007E-10]
--R     ,
--R    [0.90000000000000002,0.1724041,0.17240411434719952,1.4347199511766107E-8],
--R    [0.91000000000000003,0.1698247,0.16982470427407523,4.2740752326242415E-9],
--R
--R     [0.92000000000000004, 0.16728950000000001, 0.1672895297012775,
--R      2.9701277493021649E-8]
--R     ,
--R
--R     [0.93000000000000005, 0.16479769999999999, 0.16479767441433715,
--R      - 2.5585662838389922E-8]
--R     ,
--R    [0.93999999999999995,0.1623482,0.16234824618902396,4.6189023966691778E-8],
--R
--R     [0.94999999999999996, 0.15994040000000001, 0.15994037598345329,
--R      - 2.4016546723570897E-8]
--R     ,
--R    [0.95999999999999996,0.1575732,0.15757321716462735,1.7164627358345896E-8],
--R
--R     [0.96999999999999997, 0.15524589999999999, 0.15524594476761389,
--R      4.4767613893714753E-8]
--R     ,
--R    [0.97999999999999998,0.1529578,0.15295775478567628,- 4.5214323729503292E-8],
--R
--R     [0.98999999999999999, 0.15070790000000001, 0.15070786348977031,
--R      - 3.6510229700636998E-8]
--R     ,
--R    [1.,0.1484955,0.14849550677592205,6.7759220456764524E-9],
--R    [1.01,0.1463199,0.14631993953908851,3.9539088503293129E-8],
--R    [1.02,0.14418039999999999,0.14418043507218453,3.5072184545459351E-8],
--R    [1.03,0.14207629999999999,0.1420762844890415,- 1.551095848983941E-8],
--R    [1.04,0.14000679999999999,0.14000679617012995,- 3.8298700322236812E-9],
--R    [1.05,0.13797129999999999,0.13797129522994891,- 4.7700510763526438E-9],
--R
--R     [1.0600000000000001, 0.13596910000000001, 0.13596912300504763,
--R      2.3005047616875274E-8]
--R     ,
--R    [1.0700000000000001,0.1339996,0.13399963656170108,3.6561701083348552E-8],
--R
--R     [1.0800000000000001, 0.13206219999999999, 0.13206220822231926,
--R      8.2223192698904768E-9]
--R     ,
--R    [1.0900000000000001,0.1301562,0.13015622510971911,2.5109719109517314E-8],
--R
--R     [1.1000000000000001, 0.12828110000000001, 0.12828108870843541,
--R      - 1.1291564600002246E-8]
--R     ,
--R    [1.1100000000000001,0.1264362,0.12643621444229519,1.4442295193095589E-8],
--R    [1.1200000000000001,0.124621,0.12462103126751783,3.1267517838773351E-8],
--R    [1.1299999999999999,0.122835,0.12283498128064541,- 1.871935459418772E-8],
--R    [1.1399999999999999,0.1210775,0.12107751934064451,1.934064450259676E-8],
--R    [1.1499999999999999,0.1193481,0.11934811270455489,1.270455489421618E-8],
--R
--R     [1.1599999999999999, 0.11764620000000001, 0.11764624067609286,
--R      4.0676092855074231E-8]
--R     ,
--R    [1.1699999999999999,0.1159714,0.11597139426664799,- 5.7333520153690642E-9],
--R    [1.1799999999999999,0.1143231,0.11432307586814175,- 2.4131858247788962E-8],
--R    [1.1899999999999999,0.1127008,0.11270079893724061,- 1.0627593943768332E-9],
--R    [1.2,0.1111041,0.11110408769044711,- 1.2309552890887865E-8],
--R    [1.21,0.1095325,0.10953247680961009,- 2.3190389913940734E-8],
--R    [1.22,0.1079855,0.10798551115742314,1.1157423138175027E-8],
--R    [1.23,0.10646269999999999,0.10646274550249626,4.5502496270888315E-8],
--R    [1.24,0.10496369999999999,0.10496374425361385,4.4253613856737317E-8],
--R    [1.25,0.1034881,0.10348808120280234,- 1.8797197659514708E-8],
--R    [1.26,0.1020353,0.10203533927685385,3.9276853852632243E-8],
--R    [1.27,0.1006051,0.10060511029696789,1.0296967889455999E-8],
--R    [1.28,9.9196999999999994E-2,9.9196994746190731E-2,- 5.2538092626397415E-9],
--R    [1.29,9.7810599999999998E-2,9.7810601544343179E-2,1.5443431811146269E-9],
--R    [1.3,9.6445500000000003E-2,9.6445547830144779E-2,4.7830144775384831E-8],
--R
--R     [1.3100000000000001, 9.5101500000000005E-2, 9.5101458750257717E-2,
--R      - 4.1249742288584912E-8]
--R     ,
--R    [1.3200000000000001,9.3778E-2,9.3777967254982664E-2,- 3.2745017336521798E-8]
--R     ,
--R
--R     [1.3300000000000001, 9.2474700000000007E-2, 9.2474713900349198E-2,
--R      1.3900349191131589E-8]
--R     ,
--R
--R     [1.3400000000000001, 9.1191300000000003E-2, 9.1191346656366773E-2,
--R      4.6656366770037039E-8]
--R     ,
--R
--R     [1.3500000000000001, 8.9927499999999994E-2, 8.9927520721194559E-2,
--R      2.072119456575372E-8]
--R     ,
--R
--R     [1.3600000000000001, 8.8682899999999995E-2, 8.8682898341016198E-2,
--R      - 1.6589837975589106E-9]
--R     ,
--R
--R     [1.3700000000000001, 8.7457099999999996E-2, 8.7457148635403298E-2,
--R      4.8635403301910962E-8]
--R     ,
--R
--R     [1.3799999999999999, 8.6249900000000004E-2, 8.6249947427970763E-2,
--R      4.7427970759073013E-8]
--R     ,
--R
--R     [1.3899999999999999, 8.5060999999999998E-2, 8.5060977082121597E-2,
--R      - 2.2917878400585678E-8]
--R     ,
--R
--R     [1.3999999999999999, 8.3889900000000003E-2, 8.3889926341705251E-2,
--R      2.6341705247623359E-8]
--R     ,
--R
--R     [1.4099999999999999, 8.2736500000000004E-2, 8.2736490176409327E-2,
--R      - 9.8235906770272052E-9]
--R     ,
--R
--R     [1.4199999999999999, 8.1600400000000003E-2, 8.1600369631709052E-2,
--R      - 3.0368290951376942E-8]
--R     ,
--R
--R     [1.4299999999999999, 8.0481300000000006E-2, 8.0481271683224637E-2,
--R      - 2.8316775368963931E-8]
--R     ,
--R
--R     [1.4399999999999999, 7.9378900000000002E-2, 7.9378909095316863E-2,
--R      9.0953168607743606E-9]
--R     ,
--R    [1.45,7.8293000000000001E-2,7.8293000283781833E-2,2.8378183136723578E-10],
--R    [1.46,7.7223299999999995E-2,7.7223269182499166E-2,- 3.0817500829005695E-8],
--R    [1.47,7.6169399999999998E-2,7.6169445113894313E-2,4.5113894314718905E-8],
--R    [1.48,7.5131299999999998E-2,7.5131262663086618E-2,- 3.7336913380481285E-8],
--R    [1.49,7.4108499999999994E-2,7.4108461555594529E-2,- 3.844440546463268E-8],
--R    [1.5,7.3100799999999994E-2,7.3100786538480983E-2,- 1.3461519010604661E-8],
--R    [1.51,7.2108000000000005E-2,7.2107987264816237E-2,- 1.2735183768652902E-8],
--R    [1.52,7.1129800000000007E-2,7.1129818181354831E-2,1.8181354824453599E-8],
--R    [1.53,7.0166000000000006E-2,7.0166038419312571E-2,3.8419312564652586E-8],
--R    [1.54,6.9216399999999997E-2,6.9216411688142798E-2,1.168814280083641E-8],
--R    [1.55,6.82807E-2,6.8280706172218819E-2,6.172218819378017E-9],
--R
--R     [1.5600000000000001, 6.7358699999999994E-2, 6.735869443031553E-2,
--R      - 5.5696844636354825E-9]
--R     ,
--R
--R     [1.5700000000000001, 6.6450200000000001E-2, 6.6450153297810788E-2,
--R      - 4.670218921309921E-8]
--R     ,
--R
--R     [1.5800000000000001, 6.5554899999999999E-2, 6.5554863791512402E-2,
--R      - 3.6208487597111372E-8]
--R     ,
--R
--R     [1.5900000000000001, 6.4672599999999997E-2, 6.4672611017026815E-2,
--R      1.1017026818604947E-8]
--R     ,
--R
--R     [1.6000000000000001, 6.3803200000000004E-2, 6.380318407859184E-2,
--R      - 1.5921408164087936E-8]
--R     ,
--R    [1.6100000000000001,6.29464E-2,6.2946375991286996E-2,- 2.400871300378693E-8]
--R     ,
--R
--R     [1.6200000000000001, 6.2101999999999997E-2, 6.210198359555763E-2,
--R      - 1.6404442367001781E-8]
--R     ,
--R
--R     [1.6299999999999999, 6.1269799999999999E-2, 6.1269807473971261E-2,
--R      7.4739712613292042E-9]
--R     ,
--R
--R     [1.6399999999999999, 6.0449700000000002E-2, 6.0449651870139426E-2,
--R      - 4.8129860576173744E-8]
--R     ,
--R
--R     [1.6499999999999999, 5.9641300000000001E-2, 5.9641324609737895E-2,
--R      2.460973789336629E-8]
--R     ,
--R
--R     [1.6599999999999999, 5.8844599999999997E-2, 5.884463702356188E-2,
--R      3.702356188295397E-8]
--R     ,
--R
--R     [1.6699999999999999, 5.8059399999999997E-2, 5.8059403872549598E-2,
--R      3.8725496004365922E-9]
--R     ,
--R    [1.6799999999999999,5.72854E-2,5.7285443274719294E-2,4.3274719294106312E-8],
--R
--R     [1.6899999999999999, 5.6522599999999999E-2, 5.6522576633957849E-2,
--R      - 2.3366042149752797E-8]
--R     ,
--R    [1.7,5.5770599999999997E-2,5.5770628570604719E-2,2.8570604722333304E-8],
--R    [1.71,5.5029399999999999E-2,5.5029426853783953E-2,2.685378395345106E-8],
--R    [1.72,5.4298800000000001E-2,5.4298802335420795E-2,2.3354207942527516E-9],
--R    [1.73,5.3578599999999997E-2,5.3578588885902612E-2,- 1.1114097385467314E-8],
--R    [1.74,5.2868600000000002E-2,5.2868623331333131E-2,2.3331333129372744E-8],
--R    [1.75,5.2168699999999998E-2,5.2168745392327326E-2,4.539232732747589E-8],
--R    [1.76,5.1478799999999998E-2,5.1478797624312636E-2,- 2.375687362110579E-9],
--R    [1.77,5.0798599999999999E-2,5.0798625359279745E-2,2.5359279745562624E-8],
--R    [1.78,5.0128100000000002E-2,5.0128076648957798E-2,- 2.3351042204022843E-8],
--R    [1.79,4.9466999999999997E-2,4.9467002209351796E-2,2.209351798732051E-9],
--R    [1.8,4.8815299999999999E-2,4.8815255366622776E-2,- 4.4633377223324278E-8],
--R
--R     [1.8100000000000001, 4.8172699999999999E-2, 4.8172692004261553E-2,
--R      - 7.995738446342493E-9]
--R     ,
--R
--R     [1.8200000000000001, 4.7539199999999997E-2, 4.7539170511522538E-2,
--R      - 2.9488477458483597E-8]
--R     ,
--R
--R     [1.8300000000000001, 4.6914600000000001E-2, 4.691455173308047E-2,
--R      - 4.8266919530637331E-8]
--R     ,
--R
--R     [1.8400000000000001, 4.6298699999999998E-2, 4.6298698919879575E-2,
--R      - 1.0801204236576822E-9]
--R     ,
--R
--R     [1.8500000000000001, 4.5691500000000003E-2, 4.5691477681136752E-2,
--R      - 2.2318863250603282E-8]
--R     ,
--R
--R     [1.8600000000000001, 4.5092800000000002E-2, 4.5092755937471779E-2,
--R      - 4.4062528223309805E-8]
--R     ,
--R
--R     [1.8700000000000001, 4.4502399999999998E-2, 4.4502403875127772E-2,
--R      3.8751277742221646E-9]
--R     ,
--R
--R     [1.8799999999999999, 4.3920300000000002E-2, 4.3920293901256249E-2,
--R      - 6.0987437530690691E-9]
--R     ,
--R
--R     [1.8899999999999999, 4.3346299999999997E-2, 4.3346300600241791E-2,
--R      6.0024179376894082E-10]
--R     ,
--R    [1.8999999999999999,4.27803E-2,4.2780300691019318E-2,6.9101931815529483E-10]
--R     ,
--R
--R     [1.9099999999999999, 4.2222200000000001E-2, 4.2222172985387205E-2,
--R      - 2.701461279674966E-8]
--R     ,
--R
--R     [1.9199999999999999, 4.1671800000000002E-2, 4.1671798347258343E-2,
--R      - 1.6527416588085764E-9]
--R     ,
--R
--R     [1.9299999999999999, 4.1129100000000002E-2, 4.1129059652846772E-2,
--R      - 4.0347153229536303E-8]
--R     ,
--R
--R     [1.9399999999999999, 4.0593799999999999E-2, 4.0593841751750112E-2,
--R      4.1751750112783981E-8]
--R     ,
--R    [1.95,4.0065999999999997E-2,4.0066031428916418E-2,3.1428916420772612E-8],
--R    [1.96,3.9545499999999997E-2,3.9545517367460342E-2,1.7367460344863694E-8],
--R    [1.97,3.9032200000000003E-2,3.9032190112315068E-2,- 9.8876849347062645E-9],
--R    [1.98,3.8525900000000002E-2,3.8525942034688052E-2,4.2034688049752411E-8],
--R    [1.99,3.8026699999999997E-2,3.8026667297318961E-2,- 3.2702681035390313E-8],
--R    [2.,3.75343E-2,3.7534261820490689E-2,- 3.817950931100933E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 3

--S 4 of 7
[[0.01,0.4902766,En(3,0.01),En(3,0.01)-0.4902766],_
[0.02,0.4809683,En(3,0.02),En(3,0.02)-0.4809683],_
[0.03,0.4719977,En(3,0.03),En(3,0.03)-0.4719977],_
[0.04,0.4633239,En(3,0.04),En(3,0.04)-0.4633239],_
[0.05,0.4549188,En(3,0.05),En(3,0.05)-0.4549188],_
[0.06,0.4467609,En(3,0.06),En(3,0.06)-0.4467609],_
[0.07,0.4388327,En(3,0.07),En(3,0.07)-0.4388327],_
[0.08,0.4311197,En(3,0.08),En(3,0.08)-0.4311197],_
[0.09,0.4236096,En(3,0.09),En(3,0.09)-0.4236096],_
[0.10,0.4162915,En(3,0.10),En(3,0.10)-0.4162915],_
[0.11,0.4091557,En(3,0.11),En(3,0.11)-0.4091557],_
[0.12,0.4021937,En(3,0.12),En(3,0.12)-0.4021937],_
[0.13,0.3953977,En(3,0.13),En(3,0.13)-0.3953977],_
[0.14,0.3887607,En(3,0.14),En(3,0.14)-0.3887607],_
[0.15,0.3822761,En(3,0.15),En(3,0.15)-0.3822761],_
[0.16,0.3759380,En(3,0.16),En(3,0.16)-0.3759380],_
[0.17,0.3697408,En(3,0.17),En(3,0.17)-0.3697408],_
[0.18,0.3636795,En(3,0.18),En(3,0.18)-0.3636795],_
[0.19,0.3577491,En(3,0.19),En(3,0.19)-0.3577491],_
[0.20,0.3519453,En(3,0.20),En(3,0.20)-0.3519453],_
[0.21,0.3462638,En(3,0.21),En(3,0.21)-0.3462638],_
[0.22,0.3407005,En(3,0.22),En(3,0.22)-0.3407005],_
[0.23,0.3352518,En(3,0.23),En(3,0.23)-0.3352518],_
[0.24,0.3299142,En(3,0.24),En(3,0.24)-0.3299142],_
[0.25,0.3246841,En(3,0.25),En(3,0.25)-0.3246841],_
[0.26,0.3195585,En(3,0.26),En(3,0.26)-0.3195585],_
[0.27,0.3145343,En(3,0.27),En(3,0.27)-0.3145343],_
[0.28,0.3096086,En(3,0.28),En(3,0.28)-0.3096086],_
[0.29,0.3047787,En(3,0.29),En(3,0.29)-0.3047787],_
[0.30,0.3000418,En(3,0.30),En(3,0.30)-0.3000418],_
[0.31,0.2953956,En(3,0.31),En(3,0.31)-0.2953956],_
[0.32,0.2908374,En(3,0.32),En(3,0.32)-0.2908374],_
[0.33,0.2863652,En(3,0.33),En(3,0.33)-0.2863652],_
[0.34,0.2819765,En(3,0.34),En(3,0.34)-0.2819765],_
[0.35,0.2776693,En(3,0.35),En(3,0.35)-0.2776693],_
[0.36,0.2734416,En(3,0.36),En(3,0.36)-0.2734416],_
[0.37,0.2692913,En(3,0.37),En(3,0.37)-0.2692913],_
[0.38,0.2652165,En(3,0.38),En(3,0.38)-0.2652165],_
[0.39,0.2612155,En(3,0.39),En(3,0.39)-0.2612155],_
[0.40,0.2572864,En(3,0.40),En(3,0.40)-0.2572864],_
[0.41,0.2534276,En(3,0.41),En(3,0.41)-0.2534276],_
[0.42,0.2496373,En(3,0.42),En(3,0.42)-0.2496373],_
[0.43,0.2459141,En(3,0.43),En(3,0.43)-0.2459141],_
[0.44,0.2422563,En(3,0.44),En(3,0.44)-0.2422563],_
[0.45,0.2386625,En(3,0.45),En(3,0.45)-0.2386625],_
[0.46,0.2351313,En(3,0.46),En(3,0.46)-0.2351313],_
[0.47,0.2316612,En(3,0.47),En(3,0.47)-0.2316612],_
[0.48,0.2282508,En(3,0.48),En(3,0.48)-0.2282508],_
[0.49,0.2248990,En(3,0.49),En(3,0.49)-0.2248990],_
[0.50,0.2216044,En(3,0.50),En(3,0.50)-0.2216044],_
[0.51,0.2183657,En(3,0.51),En(3,0.51)-0.2183657],_
[0.52,0.2151818,En(3,0.52),En(3,0.52)-0.2151818],_
[0.53,0.2120516,En(3,0.53),En(3,0.53)-0.2120516],_
[0.54,0.2089739,En(3,0.54),En(3,0.54)-0.2089739],_
[0.55,0.2059475,En(3,0.55),En(3,0.55)-0.2059475],_
[0.56,0.2029715,En(3,0.56),En(3,0.56)-0.2029715],_
[0.57,0.2000448,En(3,0.57),En(3,0.57)-0.2000448],_
[0.58,0.1971664,En(3,0.58),En(3,0.58)-0.1971664],_
[0.59,0.1943353,En(3,0.59),En(3,0.59)-0.1943353],_
[0.60,0.1915506,En(3,0.60),En(3,0.60)-0.1915506],_
[0.61,0.1888114,En(3,0.61),En(3,0.61)-0.1888114],_
[0.62,0.1861166,En(3,0.62),En(3,0.62)-0.1861166],_
[0.63,0.1834656,En(3,0.63),En(3,0.63)-0.1834656],_
[0.64,0.1808573,En(3,0.64),En(3,0.64)-0.1808573],_
[0.65,0.1782910,En(3,0.65),En(3,0.65)-0.1782910],_
[0.66,0.1757658,En(3,0.66),En(3,0.66)-0.1757658],_
[0.67,0.1732810,En(3,0.67),En(3,0.67)-0.1732810],_
[0.68,0.1708358,En(3,0.68),En(3,0.68)-0.1708358],_
[0.69,0.1684294,En(3,0.69),En(3,0.69)-0.1684294],_
[0.70,0.1660612,En(3,0.70),En(3,0.70)-0.1660612],_
[0.71,0.1637303,En(3,0.71),En(3,0.71)-0.1637303],_
[0.72,0.1614360,En(3,0.72),En(3,0.72)-0.1614360],_
[0.73,0.1591778,En(3,0.73),En(3,0.73)-0.1591778],_
[0.74,0.1569549,En(3,0.74),En(3,0.74)-0.1569549],_
[0.75,0.1547667,En(3,0.75),En(3,0.75)-0.1547667],_
[0.76,0.1526125,En(3,0.76),En(3,0.76)-0.1526125],_
[0.77,0.1504917,En(3,0.77),En(3,0.77)-0.1504917],_
[0.78,0.1484037,En(3,0.78),En(3,0.78)-0.1484037],_
[0.79,0.1463479,En(3,0.79),En(3,0.79)-0.1463479],_
[0.80,0.1443238,En(3,0.80),En(3,0.80)-0.1443238],_
[0.81,0.1423307,En(3,0.81),En(3,0.81)-0.1423307],_
[0.82,0.1403681,En(3,0.82),En(3,0.82)-0.1403681],_
[0.83,0.1384355,En(3,0.83),En(3,0.83)-0.1384355],_
[0.84,0.1365324,En(3,0.84),En(3,0.84)-0.1365324],_
[0.85,0.1346581,En(3,0.85),En(3,0.85)-0.1346581],_
[0.86,0.1328122,En(3,0.86),En(3,0.86)-0.1328122],_
[0.87,0.1309943,En(3,0.87),En(3,0.87)-0.1309943],_
[0.88,0.1292037,En(3,0.88),En(3,0.88)-0.1292037],_
[0.89,0.1274401,En(3,0.89),En(3,0.89)-0.1274401],_
[0.90,0.1257030,En(3,0.90),En(3,0.90)-0.1257030],_
[0.91,0.1239919,En(3,0.91),En(3,0.91)-0.1239919],_
[0.92,0.1223063,En(3,0.92),En(3,0.92)-0.1223063],_
[0.93,0.1206459,En(3,0.93),En(3,0.93)-0.1206459],_
[0.94,0.1190102,En(3,0.94),En(3,0.94)-0.1190102],_
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[0.98,0.1127063,En(3,0.98),En(3,0.98)-0.1127063],_
[0.99,0.1111880,En(3,0.99),En(3,0.99)-0.1111880],_
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[1.01,0.1082179,En(3,1.01),En(3,1.01)-0.1082179],_
[1.02,0.1067654,En(3,1.02),En(3,1.02)-0.1067654],_
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[1.04,0.1039238,En(3,1.04),En(3,1.04)-0.1039238],_
[1.05,0.1025339,En(3,1.05),En(3,1.05)-0.1025339],_
[1.06,0.1011643,En(3,1.06),En(3,1.06)-0.1011643],_
[1.07,0.0998145,En(3,1.07),En(3,1.07)-0.0998145],_
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[1.09,0.0971731,En(3,1.09),En(3,1.09)-0.0971731],_
[1.10,0.0958809,En(3,1.10),En(3,1.10)-0.0958809],_
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[1.12,0.0933521,En(3,1.12),En(3,1.12)-0.0933521],_
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[1.14,0.0908953,En(3,1.14),En(3,1.14)-0.0908953],_
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[1.42,0.0629207,En(3,1.42),En(3,1.42)-0.0629207],_
[1.43,0.0621104,En(3,1.43),En(3,1.43)-0.0621104],_
[1.44,0.0613111,En(3,1.44),En(3,1.44)-0.0613111],_
[1.45,0.0605227,En(3,1.45),En(3,1.45)-0.0605227],_
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[1.47,0.0589782,En(3,1.47),En(3,1.47)-0.0589782],_
[1.48,0.0582217,En(3,1.48),En(3,1.48)-0.0582217],_
[1.49,0.0574755,En(3,1.49),En(3,1.49)-0.0574755],_
[1.50,0.0567395,En(3,1.50),En(3,1.50)-0.0567395],_
[1.51,0.0560135,En(3,1.51),En(3,1.51)-0.0560135],_
[1.52,0.0552973,En(3,1.52),En(3,1.52)-0.0552973],_
[1.53,0.0545908,En(3,1.53),En(3,1.53)-0.0545908],_
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[1.55,0.0532064,En(3,1.55),En(3,1.55)-0.0532064],_
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[1.99,0.0305112,En(3,1.99),En(3,1.99)-0.0305112],_
[2.00,0.0301334,En(3,2.00),En(3,2.00)-0.0301334]]
 

   (4)
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     [1.1399999999999999, 0.090895299999999998, 0.09089532488398476,
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     [1.3099999999999998, 0.072618599999999991, 0.07261857271092452,
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     [1.3699999999999999, 0.067145299999999991, 0.067145332961148815,
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     [1.3799999999999999, 0.066276799999999997, 0.066276812804578436,
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     [1.3899999999999999, 0.065420299999999987, 0.065420273243759819,
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     [1.3999999999999999, 0.064575499999999994, 0.06457553353160958,
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     [1.4099999999999999, 0.063742399999999991, 0.0637424160023502,
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     [1.4299999999999999, 0.062110399999999996, 0.06211035186837166,
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     [1.4399999999999999, 0.061311099999999993, 0.061311064792432965,
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     [1.5099999999999998, 0.056013499999999994, 0.056013458594752999,
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     [1.5199999999999998, 0.055297299999999994, 0.05529728165827761,
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     [1.5299999999999998, 0.054590799999999995, 0.054590814267229781,
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     [1.5399999999999998, 0.053893899999999995, 0.053893913713619179,
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     [1.5499999999999998, 0.053206399999999994, 0.053206439629902097,
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     [1.5699999999999998, 0.051859199999999994, 0.051859220839728958,
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     [1.5799999999999998, 0.051199199999999993, 0.051199206707147109,
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     [1.5899999999999999, 0.050548099999999999, 0.050548080108570578,
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     [1.5999999999999999, 0.049905699999999997, 0.049905711734454405,
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     [1.6099999999999999, 0.049271999999999996, 0.049271974364586413,
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     [1.6199999999999999, 0.048646699999999994, 0.048646742829405544,
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     [1.6299999999999999, 0.048029899999999993, 0.048029893972168107,
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     [1.6499999999999999, 0.046820899999999999, 0.046820861507343305,
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     [1.6599999999999999, 0.046228399999999996, 0.04622844132120392,
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     [1.6699999999999999, 0.045643899999999994, 0.045643930585794489,
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     [1.6799999999999999, 0.045067199999999995, 0.045067215668940779,
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     [1.6899999999999999, 0.044498199999999995, 0.044498184740800577,
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     [1.7599999999999998, 0.040721099999999996, 0.040721090002130644,
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     [1.7699999999999998, 0.040209699999999994, 0.040209710969742282,
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     [1.7799999999999998, 0.039705099999999993, 0.039705085416725454,
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     [1.7899999999999998, 0.039207099999999995, 0.039207117856150657,
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     [1.7999999999999998, 0.038715699999999999, 0.038715714280832564,
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     [1.8099999999999998, 0.038230799999999995, 0.038230782137495097,
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     [1.8299999999999998, 0.037279999999999994, 0.037279969051817886,
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     [1.8399999999999999, 0.036813899999999997, 0.036813910047171675,
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     [1.8499999999999999, 0.036353999999999997, 0.036353966301762096,
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     [1.8599999999999999, 0.035900099999999997, 0.03590005216215026,
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     [1.8699999999999999, 0.035452099999999993, 0.03545208328432238,
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     [1.8799999999999999, 0.035009999999999999, 0.035009976611261075,
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     ,

     [1.8899999999999999, 0.034573699999999999, 0.034573650350957726,
      - 4.964904227328093E-8]
     ,
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     [1.9099999999999999, 0.033717999999999998, 0.033718018096686862,
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     ,

     [1.9199999999999999, 0.033298599999999998, 0.033298554651807068,
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     [1.9399999999999999, 0.032475899999999995, 0.032475948389654272,
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     ,
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    [1.96,0.031674599999999997,0.03167460344041137,3.4404113724573193E-9],
    [1.97,0.031281699999999996,0.03128172084689599,2.0846895994186543E-8],
    [1.98,0.030893899999999998,0.030893936041106122,3.6041106123846367E-8],
    [1.99,0.030511199999999999,0.030511178761929998,- 2.1238070000567655E-8],
    [2.0,0.030133399999999998,0.030133379797815663,- 2.0202184335127438E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (4)
--R   [[1.0E-2,0.49027660000000001,0.49027656418466514,- 3.5815334864519599E-8],
--R    [2.0E-2,0.48096830000000002,0.48096829147697201,- 8.5230280055803576E-9],
--R
--R     [2.9999999999999999E-2, 0.47199770000000002, 0.47199768719683605,
--R      - 1.2803163973451603E-8]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.46332390000000001, 0.46332394174433533,
--R      4.1744335321780568E-8]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.45491880000000001, 0.45491884974847663,
--R      4.9748476615985027E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.44676090000000002, 0.44676088323725571,
--R      - 1.6762744303733257E-8]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.43883270000000002, 0.43883267979789509,
--R      - 2.0202104933364495E-8]
--R     ,
--R
--R     [8.0000000000000002E-2, 0.43111969999999999, 0.43111973054612684,
--R      3.054612685016167E-8]
--R     ,
--R
--R     [8.9999999999999997E-2, 0.42360959999999998, 0.42360960561704109,
--R      5.6170411100175954E-9]
--R     ,
--R
--R     [0.10000000000000001, 0.41629149999999998, 0.41629145790827876,
--R      - 4.2091721219605915E-8]
--R     ,
--R    [0.11,0.40915570000000001,0.40915568570605237,- 1.4293947636634385E-8],
--R    [0.12,0.40219369999999999,0.40219369277059286,- 7.2294071284950689E-9],
--R    [0.13,0.39539770000000002,0.395397711576501,1.1576500980048365E-8],
--R
--R     [0.14000000000000001, 0.38876070000000001, 0.38876066929878084,
--R      - 3.0701219178030925E-8]
--R     ,
--R
--R     [0.14999999999999999, 0.38227610000000001, 0.38227608377400268,
--R      - 1.6225997323537911E-8]
--R     ,
--R    [0.16,0.37593799999999999,0.37593798110903431,- 1.8890965680640193E-8],
--R
--R     [0.17000000000000001, 0.36974079999999998, 0.36974082931670565,
--R      2.9316705674187205E-8]
--R     ,
--R
--R     [0.17999999999999999, 0.36367949999999999, 0.36367948407235051,
--R      - 1.5927649477109895E-8]
--R     ,
--R    [0.19,0.35774909999999999,0.3577491438077095,4.3807709515508719E-8],
--R
--R     [0.20000000000000001, 0.35194530000000002, 0.35194531211487057,
--R      1.2114870551194201E-8]
--R     ,
--R
--R     [0.20999999999999999, 0.34626380000000001, 0.3462637659551443,
--R      - 3.4044855712345168E-8]
--R     ,
--R    [0.22,0.34070050000000002,0.34070052853638638,2.8536386365018984E-8],
--R
--R     [0.23000000000000001, 0.33525179999999999, 0.33525184598756436,
--R      4.5987564367688805E-8]
--R     ,
--R
--R     [0.23999999999999999, 0.32991419999999999, 0.32991416715361832,
--R      - 3.2846381670115221E-8]
--R     ,
--R    [0.25,0.32468409999999998,0.32468412597814367,2.5978143691762767E-8],
--R
--R     [0.26000000000000001, 0.31955850000000002, 0.31955852605039498,
--R      2.6050394952292777E-8]
--R     ,
--R
--R     [0.27000000000000002, 0.31453429999999999, 0.31453432697636552,
--R      2.6976365530284596E-8]
--R     ,
--R
--R     [0.28000000000000003, 0.30960860000000001, 0.30960863229804725,
--R      3.2298047236700711E-8]
--R     ,
--R
--R     [0.28999999999999998, 0.30477870000000001, 0.30477867873524889,
--R      - 2.126475112662618E-8]
--R     ,
--R
--R     [0.29999999999999999, 0.30004180000000003, 0.30004182656401435,
--R      2.6564014321550644E-8]
--R     ,
--R    [0.31,0.29539559999999998,0.29539555097726167,- 4.9022738313198033E-8],
--R
--R     [0.32000000000000001, 0.29083740000000002, 0.29083743429861525,
--R      3.4298615225747398E-8]
--R     ,
--R
--R     [0.33000000000000002, 0.28636519999999999, 0.28636515894092018,
--R      - 4.1059079802785448E-8]
--R     ,
--R
--R     [0.34000000000000002, 0.28197650000000002, 0.28197650101764582,
--R      1.0176458009603095E-9]
--R     ,
--R
--R     [0.34999999999999998, 0.27766930000000001, 0.27766932452910809,
--R      2.4529108078041872E-8]
--R     ,
--R
--R     [0.35999999999999999, 0.27344160000000001, 0.27344157605676817,
--R      - 2.3943231841627721E-8]
--R     ,
--R    [0.37,0.26929130000000001,0.26929127990828022,- 2.0091719787895812E-8],
--R    [0.38,0.26521650000000002,0.2652165336638212,3.3663821175089481E-8],
--R
--R     [0.39000000000000001, 0.26121549999999999, 0.26121550408084138,
--R      4.0808413870330185E-9]
--R     ,
--R
--R     [0.40000000000000002, 0.25728640000000003, 0.25728642331994478,
--R      2.3319944753019684E-8]
--R     ,
--R
--R     [0.40999999999999998, 0.25342759999999998, 0.25342758545933575,
--R      - 1.45406642282353E-8]
--R     ,
--R
--R     [0.41999999999999998, 0.24963730000000001, 0.24963734326929157,
--R      4.3269291566394585E-8]
--R     ,
--R    [0.42999999999999999,0.2459141,0.24591410522156262,5.2215626267226867E-9],
--R    [0.44,0.24225630000000001,0.24225633271155758,3.2711557573783523E-8],
--R    [0.45000000000000001,0.2386625,0.23866253747371868,3.7473718683678214E-8],
--R
--R     [0.46000000000000002, 0.23513129999999999, 0.23513127917269516,
--R      - 2.082730482522166E-8]
--R     ,
--R
--R     [0.46999999999999997, 0.23166120000000001, 0.2316611631548362,
--R      - 3.6845163808862935E-8]
--R     ,
--R    [0.47999999999999998,0.2282508,0.22825083834619003,3.8346190028848426E-8],
--R
--R     [0.48999999999999999, 0.22489899999999999, 0.22489899528465218,
--R      - 4.7153478066608301E-9]
--R     ,
--R    [0.5,0.22160440000000001,0.22160436427517846,- 3.572482154545753E-8],
--R    [0.51000000000000001,0.2183657,0.21836571365810192,1.3658101927216393E-8],
--R
--R     [0.52000000000000002, 0.21518180000000001, 0.21518184818157665,
--R      4.8181576645101032E-8]
--R     ,
--R
--R     [0.53000000000000003, 0.21205160000000001, 0.21205160747004631,
--R      7.4700463037480347E-9]
--R     ,
--R
--R     [0.54000000000000004, 0.20897389999999999, 0.20897386458140554,
--R      - 3.541859444622375E-8]
--R     ,
--R
--R     [0.55000000000000004, 0.20594750000000001, 0.20594752464620908,
--R      2.4646209073608816E-8]
--R     ,
--R    [0.56000000000000005,0.2029715,0.20297152358289336,2.3582893360352131E-8],
--R
--R     [0.56999999999999995, 0.20004479999999999, 0.20004482688351907,
--R      2.6883519077536278E-8]
--R     ,
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--R     [0.59999999999999998, 0.19155059999999999, 0.19155063779289766,
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--R     [0.65000000000000002, 0.17829100000000001, 0.17829097210250539,
--R      - 2.7897494619955054E-8]
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--R     [0.67000000000000004, 0.17328099999999999, 0.17328102319263361,
--R      2.3192633619162351E-8]
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--R     [0.68000000000000005, 0.17083580000000001, 0.17083581571497,
--R      1.5714969991975636E-8]
--R     ,
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--R     [0.68999999999999995, 0.16842940000000001, 0.16842944069553942,
--R      4.0695539410551262E-8]
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--R     [0.69999999999999996, 0.16606119999999999, 0.16606116216092121,
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--R    [0.71999999999999997,0.161436,0.16143603911987703,3.9119877032200989E-8],
--R
--R     [0.72999999999999998, 0.15917780000000001, 0.15917780943063548,
--R      9.4306354669893011E-9]
--R     ,
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--R     [0.73999999999999999, 0.15695490000000001, 0.15695490478162077,
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--R     [0.76000000000000001, 0.15261250000000001, 0.15261247597219724,
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--R     [0.82999999999999996, 0.13843549999999999, 0.13843553340482559,
--R      3.3404825600102939E-8]
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--R     [0.85999999999999999, 0.13281219999999999, 0.13281221271548668,
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--R     [0.90000000000000002, 0.12570300000000001, 0.12570297841405975,
--R      - 2.1585940257473624E-8]
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--R     [0.92000000000000004, 0.12230630000000001, 0.12230633687966941,
--R      3.6879669401690407E-8]
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--R    [0.94999999999999996,0.1173988,0.11739883313511031,3.3135110308335491E-8],
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--R     [0.95999999999999996, 0.11581130000000001, 0.11581129874853491,
--R      - 1.2514650982176079E-9]
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--R     [0.96999999999999997, 0.11424719999999999, 0.11424723583940669,
--R      3.5839406692383946E-8]
--R     ,
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--R    [0.98999999999999999,0.111188,0.11118795308358656,- 4.6916413434794357E-8],
--R    [1.,0.109692,0.10969196719776014,- 3.2802239854912152E-8],
--R    [1.01,0.10821790000000001,0.10821792031852197,2.031852196215933E-8],
--R    [1.02,0.1067654,0.10676544819972504,4.8199725044550945E-8],
--R    [1.03,0.1053342,0.10533419377271731,- 6.2272826895082289E-9],
--R    [1.04,0.1039238,0.1039238069709225,6.9709225059000346E-9],
--R    [1.05,0.1025339,0.10253394455985448,4.455985448681421E-8],
--R    [1.0600000000000001,0.1011643,0.10116426997235345,- 3.0027646549801723E-8],
--R
--R     [1.0700000000000001, 9.98145E-2, 9.9814453148843241E-2,
--R      - 4.6851156759730728E-8]
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--R     [1.0800000000000001, 9.8484199999999994E-2, 9.8484170382417149E-2,
--R      - 2.9617582844587709E-8]
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--R     [1.0900000000000001, 9.7173099999999998E-2, 9.7173104168569752E-2,
--R      4.1685697532711785E-9]
--R     ,
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--R     [1.1000000000000001, 9.5880900000000005E-2, 9.58809430594003E-2,
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--R     ,
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--R     [1.1100000000000001, 9.4607399999999994E-2, 9.4607381522120698E-2,
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--R     [1.1200000000000001, 9.3352099999999993E-2, 9.3352119801709738E-2,
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--R     [1.1299999999999999, 9.21149E-2, 9.2114863787561826E-2,
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--R     [1.1399999999999999, 9.0895299999999998E-2, 9.0895324883984607E-2,
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--R     [1.1499999999999999, 8.9693200000000001E-2, 8.969321988440758E-2,
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--R     [1.1599999999999999, 8.8508299999999998E-2, 8.8508270849168805E-2,
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--R     [1.1699999999999999, 8.7340200000000007E-2, 8.7340204986753447E-2,
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--R     [1.1799999999999999, 8.6188799999999996E-2, 8.6188754538362E-2,
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--R     [1.3100000000000001, 7.2618600000000005E-2, 7.2618572710924589E-2,
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--R     [1.3200000000000001, 7.1674199999999993E-2, 7.1674192594636615E-2,
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--R     [1.3300000000000001, 7.0742899999999997E-2, 7.0742945906179772E-2,
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--R     [1.3400000000000001, 6.9824600000000001E-2, 6.9824632030397252E-2,
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--R     [1.3600000000000001, 6.8026000000000003E-2, 6.8026017604886913E-2,
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--R     [1.3700000000000001, 6.7145300000000005E-2, 6.7145332961148871E-2,
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--R     [1.5600000000000001, 5.25283E-2, 5.2528253944736245E-2,
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--R     [1.5700000000000001, 5.1859200000000001E-2, 5.1859220839728763E-2,
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--R     [1.5900000000000001, 5.0548099999999999E-2, 5.0548080108570391E-2,
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--R     [1.6000000000000001, 4.9905699999999997E-2, 4.9905711734454218E-2,
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--R     [1.6200000000000001, 4.8646700000000001E-2, 4.8646742829405641E-2,
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--R     [1.6299999999999999, 4.80299E-2, 4.8029893972168107E-2,
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--R     [1.6499999999999999, 4.6820899999999999E-2, 4.6820861507343305E-2,
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--R     [1.6599999999999999, 4.6228400000000003E-2, 4.622844132120392E-2,
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--R     [1.6699999999999999, 4.5643900000000001E-2, 4.5643930585794489E-2,
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--R     [1.6799999999999999, 4.5067200000000002E-2, 4.5067215668940779E-2,
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--R     [1.6899999999999999, 4.4498200000000002E-2, 4.4498184740800251E-2,
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--R     [1.8100000000000001, 3.8230800000000002E-2, 3.8230782137495319E-2,
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--R     [1.8300000000000001, 3.7280000000000001E-2, 3.7279969051817741E-2,
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--R     [1.8400000000000001, 3.6813899999999997E-2, 3.6813910047171126E-2,
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--R     [1.8500000000000001, 3.6353999999999997E-2, 3.6353966301762304E-2,
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--R     [1.8600000000000001, 3.5900099999999997E-2, 3.5900052162149899E-2,
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--R     [1.8700000000000001, 3.54521E-2, 3.5452083284321229E-2,
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--R     [1.9099999999999999, 3.3717999999999998E-2, 3.3718018096686453E-2,
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--R     [1.9199999999999999, 3.3298599999999998E-2, 3.3298554651807068E-2,
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--R     [1.9299999999999999, 3.28846E-2, 3.2884556676814732E-2,
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--R     [1.9399999999999999, 3.2475900000000002E-2, 3.2475948389653855E-2,
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--R    [1.97,3.1281700000000003E-2,3.1281720846895129E-2,2.0846895126824805E-8],
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--R    [1.99,3.0511199999999999E-2,3.0511178761929561E-2,- 2.1238070437717971E-8],
--R    [2.,3.0133400000000001E-2,3.0133379797815663E-2,- 2.0202184338596885E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 4

--S 5 of 7
[[0.01,0.3283824,En(4,0.01),En(4,0.01)-0.3283824],_
[0.02,0.3235264,En(4,0.02),En(4,0.02)-0.3235264],_
[0.03,0.3187619,En(4,0.03),En(4,0.03)-0.3187619],_
[0.04,0.3140855,En(4,0.04),En(4,0.04)-0.3140855],_
[0.05,0.3094945,En(4,0.05),En(4,0.05)-0.3094945],_
[0.06,0.3049863,En(4,0.06),En(4,0.06)-0.3049863],_
[0.07,0.3005585,En(4,0.07),En(4,0.07)-0.3005585],_
[0.08,0.2962089,En(4,0.08),En(4,0.08)-0.2962089],_
[0.09,0.2919354,En(4,0.09),En(4,0.09)-0.2919354],_
[0.10,0.2877361,En(4,0.10),En(4,0.10)-0.2877361],_
[0.11,0.2836090,En(4,0.11),En(4,0.11)-0.2836090],_
[0.12,0.2795524,En(4,0.12),En(4,0.12)-0.2795524],_
[0.13,0.2755646,En(4,0.13),En(4,0.13)-0.2755646],_
[0.14,0.2716439,En(4,0.14),En(4,0.14)-0.2716439],_
[0.15,0.2677889,En(4,0.15),En(4,0.15)-0.2677889],_
[0.16,0.2639979,En(4,0.16),En(4,0.16)-0.2639979],_
[0.17,0.2602696,En(4,0.17),En(4,0.17)-0.2602696],_
[0.18,0.2566026,En(4,0.18),En(4,0.18)-0.2566026],_
[0.19,0.2529956,En(4,0.19),En(4,0.19)-0.2529956],_
[0.20,0.2494472,En(4,0.20),En(4,0.20)-0.2494472],_
[0.21,0.2459563,En(4,0.21),En(4,0.21)-0.2459563],_
[0.22,0.2425216,En(4,0.22),En(4,0.22)-0.2425216],_
[0.23,0.2391419,En(4,0.23),En(4,0.23)-0.2391419],_
[0.24,0.2358162,En(4,0.24),En(4,0.24)-0.2358162],_
[0.25,0.2325432,En(4,0.25),En(4,0.25)-0.2325432],_
[0.26,0.2293221,En(4,0.26),En(4,0.26)-0.2293221],_
[0.27,0.2261517,En(4,0.27),En(4,0.27)-0.2261517],_
[0.28,0.2230311,En(4,0.28),En(4,0.28)-0.2230311],_
[0.29,0.2199593,En(4,0.29),En(4,0.29)-0.2199593],_
[0.30,0.2169352,En(4,0.30),En(4,0.30)-0.2169352],_
[0.31,0.2139581,En(4,0.31),En(4,0.31)-0.2139581],_
[0.32,0.2110270,En(4,0.32),En(4,0.32)-0.2110270],_
[0.33,0.2081411,En(4,0.33),En(4,0.33)-0.2081411],_
[0.34,0.2052994,En(4,0.34),En(4,0.34)-0.2052994],_
[0.35,0.2025013,En(4,0.35),En(4,0.35)-0.2025013],_
[0.36,0.1997458,En(4,0.36),En(4,0.36)-0.1997458],_
[0.37,0.1970322,En(4,0.37),En(4,0.37)-0.1970322],_
[0.38,0.1943597,En(4,0.38),En(4,0.38)-0.1943597],_
[0.39,0.1917276,En(4,0.39),En(4,0.39)-0.1917276],_
[0.40,0.1891352,En(4,0.40),En(4,0.40)-0.1891352],_
[0.41,0.1865816,En(4,0.41),En(4,0.41)-0.1865816],_
[0.42,0.1840664,En(4,0.42),En(4,0.42)-0.1840664],_
[0.43,0.1815887,En(4,0.43),En(4,0.43)-0.1815887],_
[0.44,0.1791479,En(4,0.44),En(4,0.44)-0.1791479],_
[0.45,0.1767433,En(4,0.45),En(4,0.45)-0.1767433],_
[0.46,0.1743744,En(4,0.46),En(4,0.46)-0.1743744],_
[0.47,0.1720405,En(4,0.47),En(4,0.47)-0.1720405],_
[0.48,0.1697410,En(4,0.48),En(4,0.48)-0.1697410],_
[0.49,0.1674753,En(4,0.49),En(4,0.49)-0.1674753],_
[0.50,0.1652428,En(4,0.50),En(4,0.50)-0.1652428],_
[0.51,0.1630430,En(4,0.51),En(4,0.51)-0.1630430],_
[0.52,0.1608753,En(4,0.52),En(4,0.52)-0.1608753],_
[0.53,0.1587392,En(4,0.53),En(4,0.53)-0.1587392],_
[0.54,0.1566341,En(4,0.54),En(4,0.54)-0.1566341],_
[0.55,0.1545596,En(4,0.55),En(4,0.55)-0.1545596],_
[0.56,0.1525150,En(4,0.56),En(4,0.56)-0.1525150],_
[0.57,0.1505000,En(4,0.57),En(4,0.57)-0.1505000],_
[0.58,0.1485139,En(4,0.58),En(4,0.58)-0.1485139],_
[0.59,0.1465565,En(4,0.59),En(4,0.59)-0.1465565],_
[0.60,0.1446271,En(4,0.60),En(4,0.60)-0.1446271],_
[0.61,0.1427253,En(4,0.61),En(4,0.61)-0.1427253],_
[0.62,0.1408507,En(4,0.62),En(4,0.62)-0.1408507],_
[0.63,0.1390028,En(4,0.63),En(4,0.63)-0.1390028],_
[0.64,0.1371813,En(4,0.64),En(4,0.64)-0.1371813],_
[0.65,0.1353855,En(4,0.65),En(4,0.65)-0.1353855],_
[0.66,0.1336153,En(4,0.66),En(4,0.66)-0.1336153],_
[0.67,0.1318701,En(4,0.67),En(4,0.67)-0.1318701],_
[0.68,0.1301495,En(4,0.68),En(4,0.68)-0.1301495],_
[0.69,0.1284533,En(4,0.69),En(4,0.69)-0.1284533],_
[0.70,0.1267808,En(4,0.70),En(4,0.70)-0.1267808],_
[0.71,0.1251319,En(4,0.71),En(4,0.71)-0.1251319],_
[0.72,0.1235061,En(4,0.72),En(4,0.72)-0.1235061],_
[0.73,0.1219031,En(4,0.73),En(4,0.73)-0.1219031],_
[0.74,0.1203224,En(4,0.74),En(4,0.74)-0.1203224],_
[0.75,0.1187638,En(4,0.75),En(4,0.75)-0.1187638],_
[0.76,0.1172270,En(4,0.76),En(4,0.76)-0.1172270],_
[0.77,0.1157115,En(4,0.77),En(4,0.77)-0.1157115],_
[0.78,0.1142170,En(4,0.78),En(4,0.78)-0.1142170],_
[0.79,0.1127433,En(4,0.79),En(4,0.79)-0.1127433],_
[0.80,0.1112900,En(4,0.80),En(4,0.80)-0.1112900],_
[0.81,0.1098567,En(4,0.81),En(4,0.81)-0.1098567],_
[0.82,0.1084433,En(4,0.82),En(4,0.82)-0.1084433],_
[0.83,0.1070493,En(4,0.83),En(4,0.83)-0.1070493],_
[0.84,0.1056744,En(4,0.84),En(4,0.84)-0.1056744],_
[0.85,0.1043185,En(4,0.85),En(4,0.85)-0.1043185],_
[0.86,0.1029812,En(4,0.86),En(4,0.86)-0.1029812],_
[0.87,0.1016622,En(4,0.87),En(4,0.87)-0.1016622],_
[0.88,0.1003612,En(4,0.88),En(4,0.88)-0.1003612],_
[0.89,0.0990780,En(4,0.89),En(4,0.89)-0.0990780],_
[0.90,0.0978123,En(4,0.90),En(4,0.90)-0.0978123],_
[0.91,0.0965639,En(4,0.91),En(4,0.91)-0.0965639],_
[0.92,0.0953324,En(4,0.92),En(4,0.92)-0.0953324],_
[0.93,0.0941177,En(4,0.93),En(4,0.93)-0.0941177],_
[0.94,0.0929194,En(4,0.94),En(4,0.94)-0.0929194],_
[0.95,0.0917374,En(4,0.95),En(4,0.95)-0.0917374],_
[0.96,0.0905713,En(4,0.96),En(4,0.96)-0.0905713],_
[0.97,0.0894211,En(4,0.97),En(4,0.97)-0.0894211],_
[0.98,0.0882863,En(4,0.98),En(4,0.98)-0.0882863],_
[0.99,0.0871669,En(4,0.99),En(4,0.99)-0.0871669],_
[1.00,0.0860625,En(4,1.00),En(4,1.00)-0.0860625],_
[1.01,0.0849730,En(4,1.01),En(4,1.01)-0.0849730],_
[1.02,0.0838981,En(4,1.02),En(4,1.02)-0.0838981],_
[1.03,0.0828376,En(4,1.03),En(4,1.03)-0.0828376],_
[1.04,0.0817913,En(4,1.04),En(4,1.04)-0.0817913],_
[1.05,0.0807590,En(4,1.05),En(4,1.05)-0.0807590],_
[1.06,0.0797406,En(4,1.06),En(4,1.06)-0.0797406],_
[1.07,0.0787357,En(4,1.07),En(4,1.07)-0.0787357],_
[1.08,0.0777442,En(4,1.08),En(4,1.08)-0.0777442],_
[1.09,0.0767659,En(4,1.09),En(4,1.09)-0.0767659],_
[1.10,0.0758007,En(4,1.10),En(4,1.10)-0.0758007],_
[1.11,0.0748483,En(4,1.11),En(4,1.11)-0.0748483],_
[1.12,0.0739085,En(4,1.12),En(4,1.12)-0.0739085],_
[1.13,0.0729812,En(4,1.13),En(4,1.13)-0.0729812],_
[1.14,0.0720661,En(4,1.14),En(4,1.14)-0.0720661],_
[1.15,0.0711632,En(4,1.15),En(4,1.15)-0.0711632],_
[1.16,0.0702722,En(4,1.16),En(4,1.16)-0.0702722],_
[1.17,0.0693930,En(4,1.17),En(4,1.17)-0.0693930],_
[1.18,0.0685253,En(4,1.18),En(4,1.18)-0.0685253],_
[1.19,0.0676691,En(4,1.19),En(4,1.19)-0.0676691],_
[1.20,0.0668242,En(4,1.20),En(4,1.20)-0.0668242],_
[1.21,0.0659904,En(4,1.21),En(4,1.21)-0.0659904],_
[1.22,0.0651675,En(4,1.22),En(4,1.22)-0.0651675],_
[1.23,0.0643555,En(4,1.23),En(4,1.23)-0.0643555],_
[1.24,0.0635540,En(4,1.24),En(4,1.24)-0.0635540],_
[1.25,0.0627631,En(4,1.25),En(4,1.25)-0.0627631],_
[1.26,0.0619825,En(4,1.26),En(4,1.26)-0.0619825],_
[1.27,0.0612122,En(4,1.27),En(4,1.27)-0.0612122],_
[1.28,0.0604519,En(4,1.28),En(4,1.28)-0.0604519],_
[1.29,0.0597015,En(4,1.29),En(4,1.29)-0.0597015],_
[1.30,0.0589609,En(4,1.30),En(4,1.30)-0.0589609],_
[1.31,0.0582299,En(4,1.31),En(4,1.31)-0.0582299],_
[1.32,0.0575085,En(4,1.32),En(4,1.32)-0.0575085],_
[1.33,0.0567964,En(4,1.33),En(4,1.33)-0.0567964],_
[1.34,0.0560936,En(4,1.34),En(4,1.34)-0.0560936],_
[1.35,0.0553998,En(4,1.35),En(4,1.35)-0.0553998],_
[1.36,0.0547151,En(4,1.36),En(4,1.36)-0.0547151],_
[1.37,0.0540393,En(4,1.37),En(4,1.37)-0.0540393],_
[1.38,0.0533722,En(4,1.38),En(4,1.38)-0.0533722],_
[1.39,0.0527137,En(4,1.39),En(4,1.39)-0.0527137],_
[1.40,0.0520637,En(4,1.40),En(4,1.40)-0.0520637],_
[1.41,0.0514222,En(4,1.41),En(4,1.41)-0.0514222],_
[1.42,0.0507889,En(4,1.42),En(4,1.42)-0.0507889],_
[1.43,0.0501637,En(4,1.43),En(4,1.43)-0.0501637],_
[1.44,0.0495466,En(4,1.44),En(4,1.44)-0.0495466],_
[1.45,0.0489374,En(4,1.45),En(4,1.45)-0.0489374],_
[1.46,0.0483361,En(4,1.46),En(4,1.46)-0.0483361],_
[1.47,0.0477425,En(4,1.47),En(4,1.47)-0.0477425],_
[1.48,0.0471565,En(4,1.48),En(4,1.48)-0.0471565],_
[1.49,0.0465780,En(4,1.49),En(4,1.49)-0.0465780],_
[1.50,0.0460070,En(4,1.50),En(4,1.50)-0.0460070],_
[1.51,0.0454432,En(4,1.51),En(4,1.51)-0.0454432],_
[1.52,0.0448867,En(4,1.52),En(4,1.52)-0.0448867],_
[1.53,0.0443372,En(4,1.53),En(4,1.53)-0.0443372],_
[1.54,0.0437948,En(4,1.54),En(4,1.54)-0.0437948],_
[1.55,0.0432593,En(4,1.55),En(4,1.55)-0.0432593],_
[1.56,0.0427307,En(4,1.56),En(4,1.56)-0.0427307],_
[1.57,0.0422087,En(4,1.57),En(4,1.57)-0.0422087],_
[1.58,0.0416935,En(4,1.58),En(4,1.58)-0.0416935],_
[1.59,0.0411847,En(4,1.59),En(4,1.59)-0.0411847],_
[1.60,0.0406825,En(4,1.60),En(4,1.60)-0.0406825],_
[1.61,0.0401866,En(4,1.61),En(4,1.61)-0.0401866],_
[1.62,0.0396970,En(4,1.62),En(4,1.62)-0.0396970],_
[1.63,0.0392136,En(4,1.63),En(4,1.63)-0.0392136],_
[1.64,0.0387364,En(4,1.64),En(4,1.64)-0.0387364],_
[1.65,0.0382652,En(4,1.65),En(4,1.65)-0.0382652],_
[1.66,0.0377999,En(4,1.66),En(4,1.66)-0.0377999],_
[1.67,0.0373406,En(4,1.67),En(4,1.67)-0.0373406],_
[1.68,0.0368870,En(4,1.68),En(4,1.68)-0.0368870],_
[1.69,0.0364392,En(4,1.69),En(4,1.69)-0.0364392],_
[1.70,0.0359970,En(4,1.70),En(4,1.70)-0.0359970],_
[1.71,0.0355604,En(4,1.71),En(4,1.71)-0.0355604],_
[1.72,0.0351293,En(4,1.72),En(4,1.72)-0.0351293],_
[1.73,0.0347037,En(4,1.73),En(4,1.73)-0.0347037],_
[1.74,0.0342834,En(4,1.74),En(4,1.74)-0.0342834],_
[1.75,0.0338684,En(4,1.75),En(4,1.75)-0.0338684],_
[1.76,0.0334586,En(4,1.76),En(4,1.76)-0.0334586],_
[1.77,0.0330539,En(4,1.77),En(4,1.77)-0.0330539],_
[1.78,0.0326544,En(4,1.78),En(4,1.78)-0.0326544],_
[1.79,0.0322598,En(4,1.79),En(4,1.79)-0.0322598],_
[1.80,0.0318702,En(4,1.80),En(4,1.80)-0.0318702],_
[1.81,0.0314855,En(4,1.81),En(4,1.81)-0.0314855],_
[1.82,0.0311056,En(4,1.82),En(4,1.82)-0.0311056],_
[1.83,0.0307304,En(4,1.83),En(4,1.83)-0.0307304],_
[1.84,0.0303599,En(4,1.84),En(4,1.84)-0.0303599],_
[1.85,0.0299941,En(4,1.85),En(4,1.85)-0.0299941],_
[1.86,0.0296328,En(4,1.86),En(4,1.86)-0.0296328],_
[1.87,0.0292761,En(4,1.87),En(4,1.87)-0.0292761],_
[1.88,0.0289238,En(4,1.88),En(4,1.88)-0.0289238],_
[1.89,0.0285759,En(4,1.89),En(4,1.89)-0.0285759],_
[1.90,0.0282323,En(4,1.90),En(4,1.90)-0.0282323],_
[1.91,0.0278930,En(4,1.91),En(4,1.91)-0.0278930],_
[1.92,0.0275579,En(4,1.92),En(4,1.92)-0.0275579],_
[1.93,0.0272270,En(4,1.93),En(4,1.93)-0.0272270],_
[1.94,0.0269002,En(4,1.94),En(4,1.94)-0.0269002],_
[1.95,0.0265775,En(4,1.95),En(4,1.95)-0.0265775],_
[1.96,0.0262587,En(4,1.96),En(4,1.96)-0.0262587],_
[1.97,0.0259440,En(4,1.97),En(4,1.97)-0.0259440],_
[1.98,0.0256331,En(4,1.98),En(4,1.98)-0.0256331],_
[1.99,0.0253261,En(4,1.99),En(4,1.99)-0.0253261],_
[2.00,0.0250228,En(4,2.00),En(4,2.00)-0.0250228]]
 

   (5)
   [
     [0.0099999999999999985, 0.32838239999999996, 0.32838235603577381,
      - 4.3964226148496266E-8]
     ,

     [0.019999999999999997, 0.32352639999999999, 0.32352643582573859,
      3.5825738597949908E-8]
     ,

     [0.029999999999999999, 0.31876189999999999, 0.318761867644201,
      - 3.2355798984529116E-8]
     ,

     [0.039999999999999994, 0.31408549999999996, 0.3140854938275166,
      - 6.1724833577692095E-9]
     ,

     [0.049999999999999996, 0.30949449999999995, 0.30949449400443008,
      - 5.9955698739067032E-9]
     ,

     [0.059999999999999998, 0.30498629999999999, 0.30498629353000445,
      - 6.4699955393265896E-9]
     ,

     [0.069999999999999993, 0.30055849999999995, 0.30055851077336521,
      1.0773365255456469E-8]
     ,
    [0.079999999999999988,0.2962089,0.29620892264764853,2.2647648534324105E-8],

     [0.089999999999999997, 0.29193539999999996, 0.29193544025523149,
      4.0255231537056346E-8]
     ,

     [0.099999999999999992, 0.28773609999999999, 0.28773609074837725,
      - 9.2516227456762579E-9]
     ,
    [0.10999999999999999,0.283609,0.2836090032896208,3.2896207979860037E-9],
    [0.12,0.27955239999999998,0.27955239786156211,- 2.1384378712241414E-9],

     [0.12999999999999998, 0.27556459999999999, 0.27556457613853869,
      - 2.3861461306839971E-8]
     ,

     [0.13999999999999999, 0.27164389999999999, 0.27164391389899217,
      1.3898992179406378E-8]
     ,
    [0.14999999999999999,0.2677889,0.26778885461965246,- 4.5380347535317611E-8],

     [0.15999999999999998, 0.26399789999999995, 0.26399790399625528,
      3.9962553266548184E-9]
     ,

     [0.16999999999999998, 0.26026959999999999, 0.26026962520418123,
      2.5204181242077794E-8]
     ,

     [0.17999999999999999, 0.25660259999999996, 0.25660263475941625,
      3.4759416289720235E-8]
     ,

     [0.18999999999999997, 0.25299559999999999, 0.25299559887329914,
      - 1.1267008437343407E-9]
     ,

     [0.19999999999999998, 0.24944719999999998, 0.24944723021833592,
      3.0218335944631747E-8]
     ,

     [0.20999999999999999, 0.24595629999999999, 0.24595628503986891,
      - 1.496013107837868E-8]
     ,

     [0.21999999999999997, 0.24252159999999998, 0.24252156056149116,
      - 3.943850881982236E-8]
     ,

     [0.22999999999999998, 0.23914189999999999, 0.23914189264206476,
      - 7.3579352333208448E-9]
     ,

     [0.23999999999999999, 0.23581619999999998, 0.235816153649895,
      - 4.6350104976333739E-8]
     ,
    [0.25,0.23254319999999998,0.232543250525623,5.0525623018771171E-8],

     [0.25999999999999995, 0.22932209999999997, 0.22932212301015456,
      2.3010154587277398E-8]
     ,

     [0.26999999999999996, 0.22615169999999998, 0.22615174201774485,
      4.2017744866784668E-8]
     ,

     [0.27999999999999997, 0.22303109999999998, 0.22303110813742405,
      8.1374240679110699E-9]
     ,
    [0.28999999999999998,0.2199593,0.21995925024844767,- 4.9751552322341297E-8],

     [0.29999999999999999, 0.21693519999999999, 0.2169352242375045,
      2.4237504503421547E-8]
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                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (5)
--R   [[1.0E-2,0.32838240000000002,0.32838235603577381,- 4.3964226204007417E-8],
--R    [2.0E-2,0.32352639999999999,0.32352643582573859,3.5825738597949908E-8],
--R
--R     [2.9999999999999999E-2, 0.31876189999999999, 0.318761867644201,
--R      - 3.2355798984529116E-8]
--R     ,
--R
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--R     ,
--R
--R     [1.5800000000000001, 4.1693500000000001E-2, 4.1693450535863763E-2,
--R      - 4.9464136238352996E-8]
--R     ,
--R
--R     [1.5900000000000001, 4.1184699999999998E-2, 4.1184721453862164E-2,
--R      2.1453862165954352E-8]
--R     ,
--R
--R     [1.6000000000000001, 4.0682500000000003E-2, 4.0682459739842872E-2,
--R      - 4.0260157131710717E-8]
--R     ,
--R
--R     [1.6100000000000001, 4.0186600000000003E-2, 4.0186578449386889E-2,
--R      - 2.1550613113485717E-8]
--R     ,
--R
--R     [1.6200000000000001, 3.9697000000000003E-2, 3.9696991899992498E-2,
--R      - 8.1000075050075004E-9]
--R     ,
--R
--R     [1.6299999999999999, 3.9213600000000001E-2, 3.9213615650758454E-2,
--R      1.5650758453111813E-8]
--R     ,
--R
--R     [1.6399999999999999, 3.8736399999999997E-2, 3.8736366482441345E-2,
--R      - 3.3517558652162993E-8]
--R     ,
--R
--R     [1.6499999999999999, 3.8265199999999999E-2, 3.8265162377879226E-2,
--R      - 3.7622120772906609E-8]
--R     ,
--R
--R     [1.6599999999999999, 3.7799899999999997E-2, 3.7799922502774017E-2,
--R      2.2502774019161897E-8]
--R     ,
--R
--R     [1.6699999999999999, 3.7340600000000002E-2, 3.7340567186823333E-2,
--R      - 3.2813176668866628E-8]
--R     ,
--R
--R     [1.6799999999999999, 3.6887000000000003E-2, 3.6887017905196488E-2,
--R      1.7905196485201724E-8]
--R     ,
--R
--R     [1.6899999999999999, 3.6439199999999998E-2, 3.6439197260345613E-2,
--R      - 2.7396543852975519E-9]
--R     ,
--R    [1.7,3.5997000000000001E-2,3.5997028964144667E-2,2.8964144666021596E-8],
--R    [1.71,3.5560399999999999E-2,3.5560437820352508E-2,3.7820352509487787E-8],
--R    [1.72,3.5129300000000002E-2,3.5129349707387826E-2,4.9707387823894056E-8],
--R    [1.73,3.4703699999999997E-2,3.4703691561414153E-2,- 8.4385858439839367E-9],
--R    [1.74,3.4283399999999999E-2,3.4283391359727231E-2,- 8.6402727680900959E-9],
--R    [1.75,3.38684E-2,3.3868378104435617E-2,- 2.1895564382423682E-8],
--R    [1.76,3.3458599999999998E-2,3.3458581806433824E-2,- 1.8193566174440345E-8],
--R    [1.77,3.3053899999999997E-2,3.3053933469655281E-2,3.3469655283391297E-8],
--R    [1.78,3.26544E-2,3.2654365075608149E-2,- 3.4924391850710279E-8],
--R    [1.79,3.2259799999999998E-2,3.2259809568177103E-2,9.5681771047906317E-9],
--R    [1.8,3.1870200000000001E-2,3.187020083869585E-2,8.3869584888152104E-10],
--R    [1.8100000000000001,3.14855E-2,3.1485473711279174E-2,- 2.628872082521827E-8]
--R     ,
--R
--R     [1.8200000000000001, 3.1105600000000001E-2, 3.1105563928410965E-2,
--R      - 3.6071589035180374E-8]
--R     ,
--R
--R     [1.8300000000000001, 3.0730400000000001E-2, 3.073040813678209E-2,
--R      8.1367820883859743E-9]
--R     ,
--R
--R     [1.8400000000000001, 3.0359899999999999E-2, 3.0359943873375265E-2,
--R      4.387337526612356E-8]
--R     ,
--R
--R     [1.8500000000000001, 2.9994099999999999E-2, 2.9994109551789112E-2,
--R      9.5517891131324806E-9]
--R     ,
--R
--R     [1.8600000000000001, 2.9632800000000001E-2, 2.9632844448799496E-2,
--R      4.4448799495222513E-8]
--R     ,
--R
--R     [1.8700000000000001, 2.9276099999999999E-2, 2.9276088691150233E-2,
--R      - 1.1308849766356044E-8]
--R     ,
--R
--R     [1.8799999999999999, 2.89238E-2, 2.8923783242571027E-2,
--R      - 1.6757428972224986E-8]
--R     ,
--R
--R     [1.8899999999999999, 2.8575900000000001E-2, 2.8575869891020747E-2,
--R      - 3.0108979254261925E-8]
--R     ,
--R
--R     [1.8999999999999999, 2.8232299999999998E-2, 2.8232291236140537E-2,
--R      - 8.7638594610528475E-9]
--R     ,
--R
--R     [1.9099999999999999, 2.7893000000000001E-2, 2.7892990676930449E-2,
--R      - 9.3230695524804119E-9]
--R     ,
--R    [1.9199999999999999,2.75579E-2,2.7557912399626863E-2,1.2399626863474067E-8],
--R
--R     [1.9299999999999999, 2.7227000000000001E-2, 2.7227001365790433E-2,
--R      1.3657904321395797E-9]
--R     ,
--R
--R     [1.9399999999999999, 2.6900199999999999E-2, 2.6900203300591483E-2,
--R      3.300591484151072E-9]
--R     ,
--R    [1.95,2.65775E-2,2.6577464681296726E-2,- 3.5318703274500596E-8],
--R    [1.96,2.6258699999999999E-2,2.6258732725946241E-2,3.2725946241124459E-8],
--R    [1.97,2.5943999999999998E-2,2.5943955382222512E-2,- 4.4617777486544163E-8],
--R    [1.98,2.5633099999999999E-2,2.5633081316501483E-2,- 1.8683498515664754E-8],
--R    [1.99,2.5326100000000001E-2,2.5326059903094673E-2,- 4.0096905327274834E-8],
--R    [2.,2.5022800000000001E-2,2.5022841213660458E-2,4.1213660456618229E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 5

--S 6 of 7
[[0.01,0.1098682,En(10,0.01),En(10,0.01)-0.1098682],_
[0.02,0.1086395,En(10,0.02),En(10,0.02)-0.1086395],_
[0.03,0.1074246,En(10,0.03),En(10,0.03)-0.1074246],_
[0.04,0.1062236,En(10,0.04),En(10,0.04)-0.1062236],_
[0.05,0.1050363,En(10,0.05),En(10,0.05)-0.1050363],_
[0.06,0.1038624,En(10,0.06),En(10,0.06)-0.1038624],_
[0.07,0.1027018,En(10,0.07),En(10,0.07)-0.1027018],_
[0.08,0.1015544,En(10,0.08),En(10,0.08)-0.1015544],_
[0.09,0.1004200,En(10,0.09),En(10,0.09)-0.1004200],_
[0.10,0.0992984,En(10,0.10),En(10,0.10)-0.0992984],_
[0.11,0.0981896,En(10,0.11),En(10,0.11)-0.0981896],_
[0.12,0.0970934,En(10,0.12),En(10,0.12)-0.0970934],_
[0.13,0.0960095,En(10,0.13),En(10,0.13)-0.0960095],_
[0.14,0.0949380,En(10,0.14),En(10,0.14)-0.0949380],_
[0.15,0.0938786,En(10,0.15),En(10,0.15)-0.0938786],_
[0.16,0.0928312,En(10,0.16),En(10,0.16)-0.0928312],_
[0.17,0.0917956,En(10,0.17),En(10,0.17)-0.0917956],_
[0.18,0.0907718,En(10,0.18),En(10,0.18)-0.0907718],_
[0.19,0.0897595,En(10,0.19),En(10,0.19)-0.0897595],_
[0.20,0.0887587,En(10,0.20),En(10,0.20)-0.0887587],_
[0.21,0.0877693,En(10,0.21),En(10,0.21)-0.0877693],_
[0.22,0.0867910,En(10,0.22),En(10,0.22)-0.0867910],_
[0.23,0.0858238,En(10,0.23),En(10,0.23)-0.0858238],_
[0.24,0.0848675,En(10,0.24),En(10,0.24)-0.0848675],_
[0.25,0.0839220,En(10,0.25),En(10,0.25)-0.0839220],_
[0.26,0.0829872,En(10,0.26),En(10,0.26)-0.0829872],_
[0.27,0.0820630,En(10,0.27),En(10,0.27)-0.0820630],_
[0.28,0.0811492,En(10,0.28),En(10,0.28)-0.0811492],_
[0.29,0.0802457,En(10,0.29),En(10,0.29)-0.0802457],_
[0.30,0.0793524,En(10,0.30),En(10,0.30)-0.0793524],_
[0.31,0.0784693,En(10,0.31),En(10,0.31)-0.0784693],_
[0.32,0.0775960,En(10,0.32),En(10,0.32)-0.0775960],_
[0.33,0.0767327,En(10,0.33),En(10,0.33)-0.0767327],_
[0.34,0.0758790,En(10,0.34),En(10,0.34)-0.0758790],_
[0.35,0.0750350,En(10,0.35),En(10,0.35)-0.0750350],_
[0.36,0.0742006,En(10,0.36),En(10,0.36)-0.0742006],_
[0.37,0.0733755,En(10,0.37),En(10,0.37)-0.0733755],_
[0.38,0.0725597,En(10,0.38),En(10,0.38)-0.0725597],_
[0.39,0.0717531,En(10,0.39),En(10,0.39)-0.0717531],_
[0.40,0.0709557,En(10,0.40),En(10,0.40)-0.0709557],_
[0.41,0.0701671,En(10,0.41),En(10,0.41)-0.0701671],_
[0.42,0.0693875,En(10,0.42),En(10,0.42)-0.0693875],_
[0.43,0.0686167,En(10,0.43),En(10,0.43)-0.0686167],_
[0.44,0.0678545,En(10,0.44),En(10,0.44)-0.0678545],_
[0.45,0.0671009,En(10,0.45),En(10,0.45)-0.0671009],_
[0.46,0.0663558,En(10,0.46),En(10,0.46)-0.0663558],_
[0.47,0.0656191,En(10,0.47),En(10,0.47)-0.0656191],_
[0.48,0.0648907,En(10,0.48),En(10,0.48)-0.0648907],_
[0.49,0.0641704,En(10,0.49),En(10,0.49)-0.0641704],_
[0.50,0.0634583,En(10,0.50),En(10,0.50)-0.0634583],_
[0.51,0.0627542,En(10,0.51),En(10,0.51)-0.0627542],_
[0.52,0.0620580,En(10,0.52),En(10,0.52)-0.0620580],_
[0.53,0.0613696,En(10,0.53),En(10,0.53)-0.0613696],_
[0.54,0.0606889,En(10,0.54),En(10,0.54)-0.0606889],_
[0.55,0.0600159,En(10,0.55),En(10,0.55)-0.0600159],_
[0.56,0.0593505,En(10,0.56),En(10,0.56)-0.0593505],_
[0.57,0.0586925,En(10,0.57),En(10,0.57)-0.0586925],_
[0.58,0.0580419,En(10,0.58),En(10,0.58)-0.0580419],_
[0.59,0.0573986,En(10,0.59),En(10,0.59)-0.0573986],_
[0.60,0.0567626,En(10,0.60),En(10,0.60)-0.0567626],_
[0.61,0.0561336,En(10,0.61),En(10,0.61)-0.0561336],_
[0.62,0.0555118,En(10,0.62),En(10,0.62)-0.0555118],_
[0.63,0.0548969,En(10,0.63),En(10,0.63)-0.0548969],_
[0.64,0.0542889,En(10,0.64),En(10,0.64)-0.0542889],_
[0.65,0.0536877,En(10,0.65),En(10,0.65)-0.0536877],_
[0.66,0.0530933,En(10,0.66),En(10,0.66)-0.0530933],_
[0.67,0.0525055,En(10,0.67),En(10,0.67)-0.0525055],_
[0.68,0.0519243,En(10,0.68),En(10,0.68)-0.0519243],_
[0.69,0.0513497,En(10,0.69),En(10,0.69)-0.0513497],_
[0.70,0.0507815,En(10,0.70),En(10,0.70)-0.0507815],_
[0.71,0.0502196,En(10,0.71),En(10,0.71)-0.0502196],_
[0.72,0.0496640,En(10,0.72),En(10,0.72)-0.0496640],_
[0.73,0.0491147,En(10,0.73),En(10,0.73)-0.0491147],_
[0.74,0.0485715,En(10,0.74),En(10,0.74)-0.0485715],_
[0.75,0.0480344,En(10,0.75),En(10,0.75)-0.0480344],_
[0.76,0.0475033,En(10,0.76),En(10,0.76)-0.0475033],_
[0.77,0.0469781,En(10,0.77),En(10,0.77)-0.0469781],_
[0.78,0.0464588,En(10,0.78),En(10,0.78)-0.0464588],_
[0.79,0.0459453,En(10,0.79),En(10,0.79)-0.0459453],_
[0.80,0.0454376,En(10,0.80),En(10,0.80)-0.0454376],_
[0.81,0.0449356,En(10,0.81),En(10,0.81)-0.0449356],_
[0.82,0.0444391,En(10,0.82),En(10,0.82)-0.0444391],_
[0.83,0.0439482,En(10,0.83),En(10,0.83)-0.0439482],_
[0.84,0.0434628,En(10,0.84),En(10,0.84)-0.0434628],_
[0.85,0.0429829,En(10,0.85),En(10,0.85)-0.0429829],_
[0.86,0.0425082,En(10,0.86),En(10,0.86)-0.0425082],_
[0.87,0.0420389,En(10,0.87),En(10,0.87)-0.0420389],_
[0.88,0.0415749,En(10,0.88),En(10,0.88)-0.0415749],_
[0.89,0.0411160,En(10,0.89),En(10,0.89)-0.0411160],_
[0.90,0.0406622,En(10,0.90),En(10,0.90)-0.0406622],_
[0.91,0.0402135,En(10,0.91),En(10,0.91)-0.0402135],_
[0.92,0.0397698,En(10,0.92),En(10,0.92)-0.0397698],_
[0.93,0.0393311,En(10,0.93),En(10,0.93)-0.0393311],_
[0.94,0.0388973,En(10,0.94),En(10,0.94)-0.0388973],_
[0.95,0.0384683,En(10,0.95),En(10,0.95)-0.0384683],_
[0.96,0.0380441,En(10,0.96),En(10,0.96)-0.0380441],_
[0.97,0.0376246,En(10,0.97),En(10,0.97)-0.0376246],_
[0.98,0.0372098,En(10,0.98),En(10,0.98)-0.0372098],_
[0.99,0.0367996,En(10,0.99),En(10,0.99)-0.0367996],_
[1.00,0.0363940,En(10,1.00),En(10,1.00)-0.0363940],_
[1.01,0.0359929,En(10,1.01),En(10,1.01)-0.0359929],_
[1.02,0.0355963,En(10,1.02),En(10,1.02)-0.0355963],_
[1.03,0.0352041,En(10,1.03),En(10,1.03)-0.0352041],_
[1.04,0.0348163,En(10,1.04),En(10,1.04)-0.0348163],_
[1.05,0.0344328,En(10,1.05),En(10,1.05)-0.0344328],_
[1.06,0.0340535,En(10,1.06),En(10,1.06)-0.0340535],_
[1.07,0.0336785,En(10,1.07),En(10,1.07)-0.0336785],_
[1.08,0.0333077,En(10,1.08),En(10,1.08)-0.0333077],_
[1.09,0.0329410,En(10,1.09),En(10,1.09)-0.0329410],_
[1.10,0.0325784,En(10,1.10),En(10,1.10)-0.0325784],_
[1.11,0.0322198,En(10,1.11),En(10,1.11)-0.0322198],_
[1.12,0.0318652,En(10,1.12),En(10,1.12)-0.0318652],_
[1.13,0.0315145,En(10,1.13),En(10,1.13)-0.0315145],_
[1.14,0.0311678,En(10,1.14),En(10,1.14)-0.0311678],_
[1.15,0.0308249,En(10,1.15),En(10,1.15)-0.0308249],_
[1.16,0.0304858,En(10,1.16),En(10,1.16)-0.0304858],_
[1.17,0.0301505,En(10,1.17),En(10,1.17)-0.0301505],_
[1.18,0.0298189,En(10,1.18),En(10,1.18)-0.0298189],_
[1.19,0.0294910,En(10,1.19),En(10,1.19)-0.0294910],_
[1.20,0.0291668,En(10,1.20),En(10,1.20)-0.0291668],_
[1.21,0.0288461,En(10,1.21),En(10,1.21)-0.0288461],_
[1.22,0.0285290,En(10,1.22),En(10,1.22)-0.0285290],_
[1.23,0.0282155,En(10,1.23),En(10,1.23)-0.0282155],_
[1.24,0.0279054,En(10,1.24),En(10,1.24)-0.0279054],_
[1.25,0.0275988,En(10,1.25),En(10,1.25)-0.0275988],_
[1.26,0.0272955,En(10,1.26),En(10,1.26)-0.0272955],_
[1.27,0.0269957,En(10,1.27),En(10,1.27)-0.0269957],_
[1.28,0.0266991,En(10,1.28),En(10,1.28)-0.0266991],_
[1.29,0.0264059,En(10,1.29),En(10,1.29)-0.0264059],_
[1.30,0.0261159,En(10,1.30),En(10,1.30)-0.0261159],_
[1.31,0.0258291,En(10,1.31),En(10,1.31)-0.0258291],_
[1.32,0.0255455,En(10,1.32),En(10,1.32)-0.0255455],_
[1.33,0.0252651,En(10,1.33),En(10,1.33)-0.0252651],_
[1.34,0.0249878,En(10,1.34),En(10,1.34)-0.0249878],_
[1.35,0.0247135,En(10,1.35),En(10,1.35)-0.0247135],_
[1.36,0.0244423,En(10,1.36),En(10,1.36)-0.0244423],_
[1.37,0.0241741,En(10,1.37),En(10,1.37)-0.0241741],_
[1.38,0.0239088,En(10,1.38),En(10,1.38)-0.0239088],_
[1.39,0.0236465,En(10,1.39),En(10,1.39)-0.0236465],_
[1.40,0.0233872,En(10,1.40),En(10,1.40)-0.0233872],_
[1.41,0.0231306,En(10,1.41),En(10,1.41)-0.0231306],_
[1.42,0.0228770,En(10,1.42),En(10,1.42)-0.0228770],_
[1.43,0.0226261,En(10,1.43),En(10,1.43)-0.0226261],_
[1.44,0.0223780,En(10,1.44),En(10,1.44)-0.0223780],_
[1.45,0.0221327,En(10,1.45),En(10,1.45)-0.0221327],_
[1.46,0.0218901,En(10,1.46),En(10,1.46)-0.0218901],_
[1.47,0.0216501,En(10,1.47),En(10,1.47)-0.0216501],_
[1.48,0.0214128,En(10,1.48),En(10,1.48)-0.0214128],_
[1.49,0.0211782,En(10,1.49),En(10,1.49)-0.0211782],_
[1.50,0.0209461,En(10,1.50),En(10,1.50)-0.0209461],_
[1.51,0.0207167,En(10,1.51),En(10,1.51)-0.0207167],_
[1.52,0.0204897,En(10,1.52),En(10,1.52)-0.0204897],_
[1.53,0.0202653,En(10,1.53),En(10,1.53)-0.0202653],_
[1.54,0.0200433,En(10,1.54),En(10,1.54)-0.0200433],_
[1.55,0.0198238,En(10,1.55),En(10,1.55)-0.0198238],_
[1.56,0.0196067,En(10,1.56),En(10,1.56)-0.0196067],_
[1.57,0.0193921,En(10,1.57),En(10,1.57)-0.0193921],_
[1.58,0.0191798,En(10,1.58),En(10,1.58)-0.0191798],_
[1.59,0.0189698,En(10,1.59),En(10,1.59)-0.0189698],_
[1.60,0.0187622,En(10,1.60),En(10,1.60)-0.0187622],_
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[1.64,0.0179543,En(10,1.64),En(10,1.64)-0.0179543],_
[1.65,0.0177579,En(10,1.65),En(10,1.65)-0.0177579],_
[1.66,0.0175637,En(10,1.66),En(10,1.66)-0.0175637],_
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[1.68,0.0171816,En(10,1.68),En(10,1.68)-0.0171816],_
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[1.76,0.0157354,En(10,1.76),En(10,1.76)-0.0157354],_
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[1.96,0.0126341,En(10,1.96),En(10,1.96)-0.0126341],_
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[1.98,0.0123601,En(10,1.98),En(10,1.98)-0.0123601],_
[1.99,0.0122254,En(10,1.99),En(10,1.99)-0.0122254],_
[2.00,0.0120921,En(10,2.00),En(10,2.00)-0.0120921]]
 

   (6)
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     [1.3999999999999999, 0.023387199999999997, 0.023387152750639354,
      - 4.7249360642792615E-8]
     ,

     [1.4099999999999999, 0.023130599999999998, 0.023130637413929071,
      3.7413929072915852E-8]
     ,

     [1.4199999999999999, 0.022876999999999998, 0.022876964100573671,
      - 3.5899426327479222E-8]
     ,
    [1.4299999999999999,0.0226261,0.022626100933719476,9.3371947673670519E-10],

     [1.4399999999999999, 0.022377999999999999, 0.02237801639953766,
      1.6399537661887509E-8]
     ,
    [1.45,0.022132699999999998,0.022132679343009602,- 2.0656990395995223E-8],
    [1.46,0.021890099999999999,0.0218900589637624,- 4.1036237598962577E-8],
    [1.47,0.021650099999999999,0.021650124811953917,2.4811953918540963E-8],
    [1.48,0.021412799999999999,0.021412846784206772,4.678420677250994E-8],
    [1.49,0.021178199999999998,0.021178195119590685,- 4.8804093127907677E-9],
    [1.5,0.020946099999999999,0.02094614039565253,4.0395652531333148E-8],

     [1.5099999999999998, 0.020716699999999998, 0.020716653524493596,
      - 4.6475506401688627E-8]
     ,
    [1.5199999999999998,0.0204897,0.020489705748893368,5.7488933682958709E-9],
    [1.5299999999999998,0.0202653,0.020265268638479383,- 3.1361520616557392E-8],

     [1.5399999999999998, 0.020043299999999997, 0.020043314085942485,
      1.4085942488806236E-8]
     ,

     [1.5499999999999998, 0.019823799999999999, 0.01982381430329697,
      1.4303296970441526E-8]
     ,

     [1.5599999999999998, 0.019606699999999998, 0.0196067418181851,
      4.1818185102238115E-8]
     ,

     [1.5699999999999998, 0.019392099999999999, 0.019392069470225381,
      - 3.0529774618093253E-8]
     ,

     [1.5799999999999998, 0.019179799999999997, 0.019179770407404123,
      - 2.9592595873761951E-8]
     ,

     [1.5899999999999999, 0.018969799999999998, 0.018969818082509721,
      1.8082509722211482E-8]
     ,
    [1.5999999999999999,0.0187622,0.018762186249609156,- 1.3750390843308979E-8],

     [1.6099999999999999, 0.018556799999999998, 0.018556848960566176,
      4.8960566177702614E-8]
     ,
    [1.6199999999999999,0.0183538,0.018353780561600697,- 1.9438399303378651E-8],

     [1.6299999999999999, 0.018152999999999999, 0.018152955689888815,
      - 4.431011118438688E-8]
     ,

     [1.6399999999999999, 0.017954299999999999, 0.017954349270203122,
      4.927020312225916E-8]
     ,

     [1.6499999999999999, 0.017757899999999997, 0.0177579365115926,
      3.6511592603483134E-8]
     ,

     [1.6599999999999999, 0.017563699999999998, 0.017563692904101796,
      - 7.0958982023583417E-9]
     ,

     [1.6699999999999999, 0.017371599999999997, 0.017371594215528752,
      - 5.7844712457455483E-9]
     ,

     [1.6799999999999999, 0.017181599999999998, 0.01718161648822112,
      1.6488221121768731E-8]
     ,

     [1.6899999999999999, 0.016993699999999997, 0.016993736035910194,
      3.6035910196824394E-8]
     ,
    [1.7,0.016807899999999997,0.016807929440582167,2.9440582170053853E-8],
    [1.71,0.016624199999999999,0.016624173549386351,- 2.6450613647283072E-8],
    [1.72,0.016442399999999999,0.016442445471579824,4.5471579824402086E-8],
    [1.73,0.016262699999999998,0.016262722575508065,2.2575508067113059E-8],
    [1.74,0.016084999999999999,0.016084982485621131,- 1.7514378867350411E-8],
    [1.75,0.015909199999999998,0.01590920307952504,3.0795250412218866E-9],

     [1.7599999999999998, 0.015735399999999997, 0.015735362485067746,
      - 3.7514932250959365E-8]
     ,
    [1.7699999999999998,0.0155634,0.015563439077459492,3.9077459492234401E-8],
    [1.7799999999999998,0.0153934,0.01539341147642701,1.1476427010104207E-8],

     [1.7899999999999998, 0.015225299999999999, 0.015225258543401145,
      - 4.1456598853448212E-8]
     ,

     [1.7999999999999998, 0.015058999999999999, 0.015058959378737588,
      - 4.062126241106967E-8]
     ,
    [1.8099999999999998,0.0148945,0.014894493318970206,- 6.6810297936342744E-9],
    [1.8199999999999998,0.0147318,0.014731839934096687,3.993409668744119E-8],

     [1.8299999999999998, 0.014570999999999999, 0.014570979024896026,
      - 2.0975103973142062E-8]
     ,

     [1.8399999999999999, 0.014411899999999998, 0.014411890620277507,
      - 9.3797224917646638E-9]
     ,

     [1.8499999999999999, 0.014254599999999999, 0.014254554974660785,
      - 4.5025339213966564E-8]
     ,

     [1.8599999999999999, 0.014098999999999999, 0.014098952565386716,
      - 4.7434613282409943E-8]
     ,

     [1.8699999999999999, 0.013945099999999998, 0.01394506409015852,
      - 3.590984147885945E-8]
     ,

     [1.8799999999999999, 0.013792899999999999, 0.013792870464512974,
      - 2.9535487024862084E-8]
     ,

     [1.8899999999999999, 0.013642399999999999, 0.013642352819321198,
      - 4.7180678801328479E-8]
     ,

     [1.8999999999999999, 0.013493499999999999, 0.013493492498318767,
      - 7.5016812310646497E-9]
     ,

     [1.9099999999999999, 0.013346299999999998, 0.013346271055664704,
      - 2.8944335294864287E-8]
     ,

     [1.9199999999999999, 0.013200699999999999, 0.013200670253529076,
      - 2.9746470923616708E-8]
     ,

     [1.9299999999999999, 0.013056699999999999, 0.013056672059708807,
      - 2.7940291191796973E-8]
     ,

     [1.9399999999999999, 0.012914299999999998, 0.012914258645271409,
      - 4.1354728589487744E-8]
     ,
    [1.95,0.012773399999999999,0.012773412382226235,1.2382226235660432E-8],
    [1.96,0.012634099999999999,0.012634115841222995,1.5841222996554327E-8],
    [1.97,0.0124964,0.012496351789277165,- 4.8210722834035602E-8],
    [1.98,0.012360099999999999,0.01236010318752195,3.1875219512478292E-9],
    [1.99,0.012225399999999999,0.01222535318898654,- 4.681101345958838E-8],
    [2.0,0.0120921,0.012092085136400298,- 1.4863599701736563E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (6)
--R   [[1.0E-2,0.1098682,0.10986822627360165,2.6273601655413259E-8],
--R    [2.0E-2,0.1086395,0.10863946164415648,- 3.8355843515192056E-8],
--R    [2.9999999999999999E-2,0.1074246,0.10742465352510716,5.3525107165941499E-8],
--R    [4.0000000000000001E-2,0.1062236,0.10622364016949924,4.016949924079416E-8],
--R
--R     [5.0000000000000003E-2, 0.1050363, 0.10503626175690921,
--R      - 3.8243090791367784E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.10386239999999999, 0.10386236036958028,
--R      - 3.9630419709779652E-8]
--R     ,
--R    [7.0000000000000007E-2,0.1027018,0.1027017799688722,- 2.0031127798136872E-8]
--R     ,
--R    [8.0000000000000002E-2,0.1015544,0.1015543663720207,- 3.3627979303951783E-8]
--R     ,
--R    [8.9999999999999997E-2,0.10042,0.1004199672292018,- 3.2770798200076889E-8],
--R
--R     [0.10000000000000001, 9.9298399999999995E-2, 9.9298432000896802E-2,
--R      3.2000896807438117E-8]
--R     ,
--R    [0.11,9.8189600000000002E-2,9.8189611935553478E-2,1.1935553476116745E-8],
--R    [0.12,9.7093399999999996E-2,9.7093360047539198E-2,- 3.9952460798020617E-8],
--R    [0.13,9.6009499999999998E-2,9.6009531095381809E-2,3.109538181111926E-8],
--R
--R     [0.14000000000000001, 9.4937999999999995E-2, 9.4937981560294218E-2,
--R      - 1.8439705776196469E-8]
--R     ,
--R
--R     [0.14999999999999999, 9.3878600000000006E-2, 9.3878569624978384E-2,
--R      - 3.037502162295258E-8]
--R     ,
--R    [0.16,9.2831200000000003E-2,9.2831155152705111E-2,- 4.4847294891625644E-8],
--R
--R     [0.17000000000000001, 9.1795600000000005E-2, 9.1795599666665256E-2,
--R      - 3.3333474869223778E-10]
--R     ,
--R
--R     [0.17999999999999999, 9.07718E-2, 9.0771766329588957E-2,
--R      - 3.3670411042630022E-8]
--R     ,
--R    [0.19,8.9759500000000006E-2,8.9759519923628739E-2,1.9923628732931853E-8],
--R
--R     [0.20000000000000001, 8.8758699999999996E-2, 8.8758726830502982E-2,
--R      2.6830502986019411E-8]
--R     ,
--R
--R     [0.20999999999999999, 8.7769299999999995E-2, 8.7769255011895919E-2,
--R      - 4.4988104075383006E-8]
--R     ,
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--R
--R     [0.23000000000000001, 8.5823800000000006E-2, 8.5823754828972157E-2,
--R      - 4.5171027848733836E-8]
--R     ,
--R
--R     [0.23999999999999999, 8.4867499999999998E-2, 8.4867470114974794E-2,
--R      - 2.9885025204512417E-8]
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--R
--R     [0.26000000000000001, 8.2987199999999997E-2, 8.2987201876317501E-2,
--R      1.8763175041458524E-9]
--R     ,
--R
--R     [0.27000000000000002, 8.2062999999999997E-2, 8.2062970971708463E-2,
--R      - 2.9028291534394235E-8]
--R     ,
--R
--R     [0.28000000000000003, 8.1149200000000005E-2, 8.1149179718306999E-2,
--R      - 2.0281693005608226E-8]
--R     ,
--R
--R     [0.28999999999999998, 8.0245700000000003E-2, 8.0245708041556577E-2,
--R      8.041556573412656E-9]
--R     ,
--R
--R     [0.29999999999999999, 7.9352400000000003E-2, 7.9352437281438454E-2,
--R      3.7281438450276205E-8]
--R     ,
--R    [0.31,7.8469300000000006E-2,7.8469250175248736E-2,- 4.9824751269245127E-8],
--R
--R     [0.32000000000000001, 7.7595999999999998E-2, 7.7596030840595492E-2,
--R      3.0840595494074918E-8]
--R     ,
--R
--R     [0.33000000000000002, 7.6732700000000001E-2, 7.6732664758612748E-2,
--R      - 3.5241387252860079E-8]
--R     ,
--R
--R     [0.34000000000000002, 7.5879000000000002E-2, 7.5879038757388551E-2,
--R      3.8757388548527061E-8]
--R     ,
--R
--R     [0.34999999999999998, 7.5035000000000004E-2, 7.5035040995603944E-2,
--R      4.0995603939331104E-8]
--R     ,
--R
--R     [0.35999999999999999, 7.4200600000000005E-2, 7.4200560946380167E-2,
--R      - 3.9053619838025355E-8]
--R     ,
--R    [0.37,7.3375499999999996E-2,7.3375489381331219E-2,- 1.0618668777606644E-8],
--R    [0.38,7.2559700000000005E-2,7.2559718354818795E-2,1.8354818789867444E-8],
--R    [0.39000000000000001,7.17531E-2,7.1753141188407144E-2,4.1188407143288863E-8]
--R     ,
--R
--R     [0.40000000000000002, 7.0955699999999997E-2, 7.0955652455514773E-2,
--R      - 4.7544485223816046E-8]
--R     ,
--R
--R     [0.40999999999999998, 7.0167099999999996E-2, 7.0167147966260709E-2,
--R      4.7966260713350195E-8]
--R     ,
--R
--R     [0.41999999999999998, 6.9387500000000005E-2, 6.93875247525024E-2,
--R      2.4752502394975728E-8]
--R     ,
--R
--R     [0.42999999999999999, 6.8616700000000003E-2, 6.8616681053062775E-2,
--R      - 1.8946937227481975E-8]
--R     ,
--R    [0.44,6.7854499999999998E-2,6.7854516299143935E-2,1.6299143937303917E-8],
--R
--R     [0.45000000000000001, 6.7100900000000005E-2, 6.7100931099924779E-2,
--R      3.1099924774347087E-8]
--R     ,
--R
--R     [0.46000000000000002, 6.6355800000000006E-2, 6.6355827228340464E-2,
--R      2.7228340457319256E-8]
--R     ,
--R    [0.46999999999999997,6.56191E-2,6.5619107607040858E-2,7.6070408583372995E-9]
--R     ,
--R
--R     [0.47999999999999998, 6.4890699999999996E-2, 6.4890676294525704E-2,
--R      - 2.3705474291868533E-8]
--R     ,
--R
--R     [0.48999999999999999, 6.4170400000000002E-2, 6.4170438471454316E-2,
--R      3.8471454313904196E-8]
--R     ,
--R    [0.5,6.3458299999999995E-2,6.3458300427127218E-2,4.2712722247983947E-10],
--R
--R     [0.51000000000000001, 6.2754199999999996E-2, 6.2754169546137606E-2,
--R      - 3.0453862390200648E-8]
--R     ,
--R
--R     [0.52000000000000002, 6.2058000000000002E-2, 6.2057954295190239E-2,
--R      - 4.5704809763236209E-8]
--R     ,
--R
--R     [0.53000000000000003, 6.1369600000000003E-2, 6.136956421008552E-2,
--R      - 3.5789914483441709E-8]
--R     ,
--R
--R     [0.54000000000000004, 6.0688899999999997E-2, 6.06889098828668E-2,
--R      9.8828668027017841E-9]
--R     ,
--R
--R     [0.55000000000000004, 6.0015899999999997E-2, 6.0015902949128445E-2,
--R      2.9491284483929014E-9]
--R     ,
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--R     [0.56000000000000005, 5.93505E-2, 5.9350456075482616E-2,
--R      - 4.3924517384441586E-8]
--R     ,
--R
--R     [0.56999999999999995, 5.8692500000000002E-2, 5.8692482947182836E-2,
--R      - 1.7052817165297274E-8]
--R     ,
--R
--R     [0.57999999999999996, 5.80419E-2, 5.8041898255901947E-2,
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--R     ,
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--R     [0.58999999999999997, 5.7398600000000001E-2, 5.7398617687662766E-2,
--R      1.7687662764998002E-8]
--R     ,
--R
--R     [0.59999999999999998, 5.6762600000000003E-2, 5.6762557910919068E-2,
--R      - 4.2089080935781009E-8]
--R     ,
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--R     [0.60999999999999999, 5.6133599999999999E-2, 5.6133636564785275E-2,
--R      3.6564785275972067E-8]
--R     ,
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--R    [0.63,5.4896899999999998E-2,5.4896884504509566E-2,- 1.5495490432448911E-8],
--R
--R     [0.64000000000000001, 5.4288900000000001E-2, 5.4288893818006168E-2,
--R      - 6.1819938335094804E-9]
--R     ,
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--R     [0.65000000000000002, 5.3687699999999998E-2, 5.3687721594857608E-2,
--R      2.1594857610440776E-8]
--R     ,
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--R     [0.66000000000000003, 5.3093300000000003E-2, 5.3093290155987988E-2,
--R      - 9.8440120152587518E-9]
--R     ,
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--R     [0.67000000000000004, 5.2505499999999997E-2, 5.2505522725370901E-2,
--R      2.2725370904530529E-8]
--R     ,
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--R
--R     [0.68999999999999995, 5.1349699999999998E-2, 5.1349677235465116E-2,
--R      - 2.2764534882147025E-8]
--R     ,
--R
--R     [0.69999999999999996, 5.07815E-2, 5.0781450042980847E-2,
--R      - 4.9957019153390458E-8]
--R     ,
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--R     [0.70999999999999996, 5.0219600000000003E-2, 5.0219588571451021E-2,
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--R     ,
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--R     [0.72999999999999998, 4.9114699999999997E-2, 4.9114673951996674E-2,
--R      - 2.6048003323730917E-8]
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--R     [0.73999999999999999, 4.8571499999999997E-2, 4.85714784752228E-2,
--R      - 2.1524777196746392E-8]
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--R     [0.76000000000000001, 4.7503299999999998E-2, 4.7503261533576278E-2,
--R      - 3.8466423719907272E-8]
--R     ,
--R
--R     [0.77000000000000002, 4.6978100000000002E-2, 4.6978102633344329E-2,
--R      2.6333443273185431E-9]
--R     ,
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--R     [0.78000000000000003, 4.6458800000000001E-2, 4.6458819815439867E-2,
--R      1.9815439865344953E-8]
--R     ,
--R
--R     [0.79000000000000004, 4.5945300000000001E-2, 4.5945346336274485E-2,
--R      4.6336274484026774E-8]
--R     ,
--R
--R     [0.80000000000000004, 4.5437600000000002E-2, 4.5437616225057327E-2,
--R      1.6225057325458536E-8]
--R     ,
--R
--R     [0.81000000000000005, 4.4935599999999999E-2, 4.4935564274618756E-2,
--R      - 3.5725381243578713E-8]
--R     ,
--R
--R     [0.81999999999999995, 4.4439100000000002E-2, 4.4439126032346843E-2,
--R      2.6032346840676457E-8]
--R     ,
--R    [0.82999999999999996,4.39482E-2,4.3948237791235037E-2,3.7791235037165638E-8]
--R     ,
--R
--R     [0.83999999999999997, 4.3462800000000003E-2, 4.3462836581039874E-2,
--R      3.6581039870864362E-8]
--R     ,
--R
--R     [0.84999999999999998, 4.2982899999999997E-2, 4.2982860159546922E-2,
--R      - 3.9840453075479232E-8]
--R     ,
--R
--R     [0.85999999999999999, 4.2508200000000003E-2, 4.2508247003943962E-2,
--R      4.7003943959289529E-8]
--R     ,
--R    [0.87,4.2038899999999997E-2,4.2038936302299747E-2,3.6302299749602085E-8],
--R    [0.88,4.1574899999999998E-2,4.1574867945147087E-2,- 3.2054852910912146E-8],
--R    [0.89000000000000001,4.1116E-2,4.111598251716897E-2,- 1.7482831030091184E-8]
--R     ,
--R
--R     [0.90000000000000002, 4.0662200000000003E-2, 4.0662221288986326E-2,
--R      2.1288986323808601E-8]
--R     ,
--R
--R     [0.91000000000000003, 4.0213499999999999E-2, 4.0213526209046141E-2,
--R      2.6209046141700831E-8]
--R     ,
--R
--R     [0.92000000000000004, 3.9769800000000001E-2, 3.9769839895608665E-2,
--R      3.9895608663909066E-8]
--R     ,
--R
--R     [0.93000000000000005, 3.9331100000000001E-2, 3.9331105628832443E-2,
--R      5.628832441817444E-9]
--R     ,
--R
--R     [0.93999999999999995, 3.8897300000000003E-2, 3.8897267342955913E-2,
--R      - 3.2657044089778875E-8]
--R     ,
--R
--R     [0.94999999999999996, 3.8468299999999997E-2, 3.8468269618574302E-2,
--R      - 3.038142569466995E-8]
--R     ,
--R
--R     [0.95999999999999996, 3.8044099999999997E-2, 3.8044057675010727E-2,
--R      - 4.2324989270314806E-8]
--R     ,
--R
--R     [0.96999999999999997, 3.7624600000000001E-2, 3.7624577362780139E-2,
--R      - 2.2637219862509106E-8]
--R     ,
--R
--R     [0.97999999999999998, 3.7209800000000001E-2, 3.7209775156145049E-2,
--R      - 2.4843854952438793E-8]
--R     ,
--R
--R     [0.98999999999999999, 3.6799600000000002E-2, 3.6799598145761836E-2,
--R      - 1.8542381657882245E-9]
--R     ,
--R    [1.,3.6394000000000003E-2,3.6393994031416403E-2,- 5.9685835995804126E-9],
--R    [1.01,3.5992900000000001E-2,3.5992911114848265E-2,1.1114848263993338E-8],
--R    [1.02,3.5596299999999997E-2,3.5596298292661678E-2,- 1.7073383193344505E-9],
--R    [1.03,3.5204100000000002E-2,3.5204105049322892E-2,5.0493228903603082E-9],
--R    [1.04,3.4816300000000001E-2,3.4816281450242362E-2,- 1.8549757639652054E-8],
--R    [1.05,3.44328E-2,3.4432778134940903E-2,- 2.1865059096626283E-8],
--R    [1.0600000000000001,3.40535E-2,3.405354631029861E-2,4.6310298609797407E-8],
--R    [1.0700000000000001,3.36785E-2,3.3678537743885642E-2,3.7743885641927655E-8],
--R
--R     [1.0800000000000001, 3.3307700000000003E-2, 3.3307704757373741E-2,
--R      4.757373738006887E-9]
--R     ,
--R
--R     [1.0900000000000001, 3.2940999999999998E-2, 3.2941000220027501E-2,
--R      2.20027503161635E-10]
--R     ,
--R
--R     [1.1000000000000001, 3.25784E-2, 3.2578377542274328E-2,
--R      - 2.2457725672164752E-8]
--R     ,
--R
--R     [1.1100000000000001, 3.22198E-2, 3.2219790669352259E-2,
--R      - 9.3306477405574739E-9]
--R     ,
--R
--R     [1.1200000000000001, 3.1865200000000003E-2, 3.186519407503445E-2,
--R      - 5.924965552905892E-9]
--R     ,
--R
--R     [1.1299999999999999, 3.1514500000000001E-2, 3.1514542755429475E-2,
--R      4.275542947462796E-8]
--R     ,
--R
--R     [1.1399999999999999, 3.1167799999999999E-2, 3.1167792222856549E-2,
--R      - 7.777143450071744E-9]
--R     ,
--R
--R     [1.1499999999999999, 3.0824899999999999E-2, 3.0824898499794556E-2,
--R      - 1.5002054425117262E-9]
--R     ,
--R    [1.1599999999999999,3.04858E-2,3.0485818112904201E-2,1.811290420081213E-8],
--R    [1.1699999999999999,3.01505E-2,3.0150508087122076E-2,8.0871220761724594E-9],
--R
--R     [1.1799999999999999, 2.9818899999999999E-2, 2.9818925939826001E-2,
--R      2.5939826002463473E-8]
--R     ,
--R    [1.1899999999999999,2.9491E-2,2.9491029675070599E-2,2.9675070598728093E-8],
--R    [1.2,2.91668E-2,2.9166777777892276E-2,- 2.222210772340194E-8],
--R    [1.21,2.88461E-2,2.8846129208682729E-2,2.9208682729431334E-8],
--R    [1.22,2.8528999999999999E-2,2.8529043397630106E-2,4.33976301075778E-8],
--R    [1.23,2.8215500000000001E-2,2.8215480239227052E-2,- 1.9760772948518301E-8],
--R    [1.24,2.79054E-2,2.7905400086844646E-2,8.6844646057793184E-11],
--R    [1.25,2.75988E-2,2.7598763747371625E-2,- 3.6252628374949802E-8],
--R    [1.26,2.72955E-2,2.7295532475917882E-2,3.2475917881996663E-8],
--R    [1.27,2.6995700000000001E-2,2.699566797058155E-2,- 3.2029418450818525E-8],
--R    [1.28,2.66991E-2,2.6699132367278861E-2,3.2367278860606641E-8],
--R    [1.29,2.64059E-2,2.6405888234635966E-2,- 1.1765364033716752E-8],
--R    [1.3,2.6115900000000001E-2,2.6115898568942E-2,- 1.4310580012666385E-9],
--R
--R     [1.3100000000000001, 2.5829100000000001E-2, 2.5829126789162573E-2,
--R      2.678916257228825E-8]
--R     ,
--R
--R     [1.3200000000000001, 2.5545499999999999E-2, 2.5545536732012972E-2,
--R      3.673201297293982E-8]
--R     ,
--R
--R     [1.3300000000000001, 2.5265099999999999E-2, 2.5265092647090353E-2,
--R      - 7.3529096457358722E-9]
--R     ,
--R
--R     [1.3400000000000001, 2.4987800000000001E-2, 2.4987759192064113E-2,
--R      - 4.0807935888093061E-8]
--R     ,
--R
--R     [1.3500000000000001, 2.4713499999999999E-2, 2.471350142792382E-2,
--R      1.42792382085144E-9]
--R     ,
--R
--R     [1.3600000000000001, 2.44423E-2, 2.4442284814283937E-2,
--R      - 1.5185716063098598E-8]
--R     ,
--R
--R     [1.3700000000000001, 2.41741E-2, 2.4174075204744596E-2,
--R      - 2.4795255404441718E-8]
--R     ,
--R
--R     [1.3799999999999999, 2.3908800000000001E-2, 2.3908838842307847E-2,
--R      3.8842307845815549E-8]
--R     ,
--R
--R     [1.3899999999999999, 2.3646500000000001E-2, 2.3646542354848549E-2,
--R      4.2354848548559199E-8]
--R     ,
--R
--R     [1.3999999999999999, 2.33872E-2, 2.3387152750639354E-2,
--R      - 4.7249360646262062E-8]
--R     ,
--R
--R     [1.4099999999999999, 2.3130600000000001E-2, 2.3130637413929071E-2,
--R      3.7413929069446406E-8]
--R     ,
--R
--R     [1.4199999999999999, 2.2877000000000002E-2, 2.2876964100573671E-2,
--R      - 3.5899426330948669E-8]
--R     ,
--R    [1.4299999999999999,2.26261E-2,2.2626100933719476E-2,9.3371947673670519E-10]
--R     ,
--R
--R     [1.4399999999999999, 2.2377999999999999E-2, 2.237801639953766E-2,
--R      1.6399537661887509E-8]
--R     ,
--R    [1.45,2.2132700000000002E-2,2.2132679343009602E-2,- 2.065699039946467E-8],
--R    [1.46,2.1890099999999999E-2,2.18900589637624E-2,- 4.1036237598962577E-8],
--R    [1.47,2.1650099999999999E-2,2.1650124811953917E-2,2.4811953918540963E-8],
--R    [1.48,2.1412799999999999E-2,2.1412846784206772E-2,4.678420677250994E-8],
--R    [1.49,2.1178200000000001E-2,2.1178195119590685E-2,- 4.8804093162602147E-9],
--R    [1.5,2.0946099999999999E-2,2.094614039565253E-2,4.0395652531333148E-8],
--R    [1.51,2.0716700000000001E-2,2.0716653524493592E-2,- 4.647550640862752E-8],
--R    [1.52,2.04897E-2,2.0489705748893364E-2,5.748893364826424E-9],
--R    [1.53,2.02653E-2,2.0265268638479383E-2,- 3.1361520616557392E-8],
--R    [1.54,2.00433E-2,2.0043314085942482E-2,1.4085942481867342E-8],
--R    [1.55,1.9823799999999999E-2,1.9823814303296966E-2,1.4303296966972079E-8],
--R
--R     [1.5600000000000001, 1.9606700000000001E-2, 1.9606741818185093E-2,
--R      4.1818185091829774E-8]
--R     ,
--R
--R     [1.5700000000000001, 1.9392099999999999E-2, 1.9392069470225374E-2,
--R      - 3.0529774625032147E-8]
--R     ,
--R
--R     [1.5800000000000001, 1.91798E-2, 1.9179770407404116E-2,
--R      - 2.9592595884170292E-8]
--R     ,
--R
--R     [1.5900000000000001, 1.8969799999999998E-2, 1.8969818082509717E-2,
--R      1.8082509718742035E-8]
--R     ,
--R
--R     [1.6000000000000001, 1.87622E-2, 1.8762186249609149E-2,
--R      - 1.3750390850247873E-8]
--R     ,
--R
--R     [1.6100000000000001, 1.8556799999999998E-2, 1.8556848960566173E-2,
--R      4.8960566174233167E-8]
--R     ,
--R    [1.6200000000000001,1.83538E-2,1.835378056160069E-2,- 1.9438399310317545E-8]
--R     ,
--R
--R     [1.6299999999999999, 1.8152999999999999E-2, 1.8152955689888815E-2,
--R      - 4.431011118438688E-8]
--R     ,
--R
--R     [1.6399999999999999, 1.7954299999999999E-2, 1.7954349270203122E-2,
--R      4.927020312225916E-8]
--R     ,
--R    [1.6499999999999999,1.77579E-2,1.77579365115926E-2,3.6511592600013687E-8],
--R
--R     [1.6599999999999999, 1.7563700000000002E-2, 1.7563692904101796E-2,
--R      - 7.0958982058277886E-9]
--R     ,
--R
--R     [1.6699999999999999, 1.7371600000000001E-2, 1.7371594215528752E-2,
--R      - 5.7844712492149952E-9]
--R     ,
--R
--R     [1.6799999999999999, 1.7181600000000002E-2, 1.718161648822112E-2,
--R      1.6488221118299284E-8]
--R     ,
--R    [1.6899999999999999,1.69937E-2,1.6993736035910194E-2,3.6035910193354947E-8],
--R    [1.7,1.6807900000000001E-2,1.6807929440582167E-2,2.9440582166584406E-8],
--R    [1.71,1.6624199999999999E-2,1.6624173549386351E-2,- 2.6450613647283072E-8],
--R    [1.72,1.6442399999999999E-2,1.6442445471579824E-2,4.5471579824402086E-8],
--R    [1.73,1.6262700000000001E-2,1.6262722575508065E-2,2.2575508063643612E-8],
--R    [1.74,1.6084999999999999E-2,1.6084982485621131E-2,- 1.7514378867350411E-8],
--R    [1.75,1.5909199999999998E-2,1.590920307952504E-2,3.0795250412218866E-9],
--R    [1.76,1.57354E-2,1.5735362485067742E-2,- 3.7514932257898259E-8],
--R    [1.77,1.55634E-2,1.5563439077459485E-2,3.9077459485295507E-8],
--R    [1.78,1.53934E-2,1.5393411476427005E-2,1.1476427004900036E-8],
--R    [1.79,1.5225300000000001E-2,1.5225258543401145E-2,- 4.1456598855182936E-8],
--R    [1.8,1.5058999999999999E-2,1.5058959378737585E-2,- 4.0621262414539117E-8],
--R
--R     [1.8100000000000001, 1.48945E-2, 1.4894493318970201E-2,
--R      - 6.6810297988384448E-9]
--R     ,
--R    [1.8200000000000001,1.47318E-2,1.4731839934096682E-2,3.9934096682237019E-8],
--R
--R     [1.8300000000000001, 1.4571000000000001E-2, 1.4570979024896022E-2,
--R      - 2.0975103978346232E-8]
--R     ,
--R
--R     [1.8400000000000001, 1.44119E-2, 1.4411890620277503E-2,
--R      - 9.3797224969688342E-9]
--R     ,
--R
--R     [1.8500000000000001, 1.4254599999999999E-2, 1.4254554974660784E-2,
--R      - 4.5025339215701288E-8]
--R     ,
--R    [1.8600000000000001,1.4099E-2,1.4098952565386716E-2,- 4.7434613284144667E-8]
--R     ,
--R    [1.8700000000000001,1.39451E-2,1.3945064090158516E-2,- 3.590984148406362E-8]
--R     ,
--R
--R     [1.8799999999999999, 1.37929E-2, 1.3792870464512974E-2,
--R      - 2.9535487026596807E-8]
--R     ,
--R
--R     [1.8899999999999999, 1.3642400000000001E-2, 1.3642352819321199E-2,
--R      - 4.7180678801328479E-8]
--R     ,
--R
--R     [1.8999999999999999, 1.34935E-2, 1.3493492498318767E-2,
--R      - 7.5016812327993732E-9]
--R     ,
--R
--R     [1.9099999999999999, 1.33463E-2, 1.3346271055664704E-2,
--R      - 2.8944335296599011E-8]
--R     ,
--R
--R     [1.9199999999999999, 1.3200699999999999E-2, 1.3200670253529076E-2,
--R      - 2.9746470923616708E-8]
--R     ,
--R
--R     [1.9299999999999999, 1.3056699999999999E-2, 1.3056672059708809E-2,
--R      - 2.794029119006225E-8]
--R     ,
--R
--R     [1.9399999999999999, 1.29143E-2, 1.2914258645271409E-2,
--R      - 4.1354728591222467E-8]
--R     ,
--R    [1.95,1.2773400000000001E-2,1.2773412382226235E-2,1.2382226233925708E-8],
--R    [1.96,1.2634100000000001E-2,1.2634115841222995E-2,1.5841222994819604E-8],
--R    [1.97,1.24964E-2,1.2496351789277165E-2,- 4.8210722834035602E-8],
--R    [1.98,1.2360100000000001E-2,1.236010318752195E-2,3.1875219495131057E-9],
--R    [1.99,1.2225400000000001E-2,1.222535318898654E-2,- 4.6811013461323103E-8],
--R    [2.,1.20921E-2,1.2092085136400298E-2,- 1.4863599701736563E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 6

--S 7 of 7
[[0.01,0.0520790,En(20,0.01),En(20,0.01)-0.0520790],_
[0.02,0.0515321,En(20,0.02),En(20,0.02)-0.0515321],_
[0.03,0.0509911,En(20,0.03),En(20,0.03)-0.0509911],_
[0.04,0.0504558,En(20,0.04),En(20,0.04)-0.0504558],_
[0.05,0.0499260,En(20,0.05),En(20,0.05)-0.0499260],_
[0.06,0.0494019,En(20,0.06),En(20,0.06)-0.0494019],_
[0.07,0.0488833,En(20,0.07),En(20,0.07)-0.0488833],_
[0.08,0.0483702,En(20,0.08),En(20,0.08)-0.0483702],_
[0.09,0.0478624,En(20,0.09),En(20,0.09)-0.0478624],_
[0.10,0.0473600,En(20,0.10),En(20,0.10)-0.0473600],_
[0.11,0.0468629,En(20,0.11),En(20,0.11)-0.0468629],_
[0.12,0.0463710,En(20,0.12),En(20,0.12)-0.0463710],_
[0.13,0.0458843,En(20,0.13),En(20,0.13)-0.0458843],_
[0.14,0.0454027,En(20,0.14),En(20,0.14)-0.0454027],_
[0.15,0.0449262,En(20,0.15),En(20,0.15)-0.0449262],_
[0.16,0.0444547,En(20,0.16),En(20,0.16)-0.0444547],_
[0.17,0.0439882,En(20,0.17),En(20,0.17)-0.0439882],_
[0.18,0.0435266,En(20,0.18),En(20,0.18)-0.0435266],_
[0.19,0.0430698,En(20,0.19),En(20,0.19)-0.0430698],_
[0.20,0.0426179,En(20,0.20),En(20,0.20)-0.0426179],_
[0.21,0.0421707,En(20,0.21),En(20,0.21)-0.0421707],_
[0.22,0.0417282,En(20,0.22),En(20,0.22)-0.0417282],_
[0.23,0.0412903,En(20,0.23),En(20,0.23)-0.0412903],_
[0.24,0.0408571,En(20,0.24),En(20,0.24)-0.0408571],_
[0.25,0.0404285,En(20,0.25),En(20,0.25)-0.0404285],_
[0.26,0.0400043,En(20,0.26),En(20,0.26)-0.0400043],_
[0.27,0.0395846,En(20,0.27),En(20,0.27)-0.0395846],_
[0.28,0.0391693,En(20,0.28),En(20,0.28)-0.0391693],_
[0.29,0.0387584,En(20,0.29),En(20,0.29)-0.0387584],_
[0.30,0.0383518,En(20,0.30),En(20,0.30)-0.0383518],_
[0.31,0.0379495,En(20,0.31),En(20,0.31)-0.0379495],_
[0.32,0.0375515,En(20,0.32),En(20,0.32)-0.0375515],_
[0.33,0.0371576,En(20,0.33),En(20,0.33)-0.0371576],_
[0.34,0.0367678,En(20,0.34),En(20,0.34)-0.0367678],_
[0.35,0.0363822,En(20,0.35),En(20,0.35)-0.0363822],_
[0.36,0.0360006,En(20,0.36),En(20,0.36)-0.0360006],_
[0.37,0.0356231,En(20,0.37),En(20,0.37)-0.0356231],_
[0.38,0.0352495,En(20,0.38),En(20,0.38)-0.0352495],_
[0.39,0.0348798,En(20,0.39),En(20,0.39)-0.0348798],_
[0.40,0.0345140,En(20,0.40),En(20,0.40)-0.0345140],_
[0.41,0.0341521,En(20,0.41),En(20,0.41)-0.0341521],_
[0.42,0.0337939,En(20,0.42),En(20,0.42)-0.0337939],_
[0.43,0.0334396,En(20,0.43),En(20,0.43)-0.0334396],_
[0.44,0.0330889,En(20,0.44),En(20,0.44)-0.0330889],_
[0.45,0.0327420,En(20,0.45),En(20,0.45)-0.0327420],_
[0.46,0.0323987,En(20,0.46),En(20,0.46)-0.0323987],_
[0.47,0.0320590,En(20,0.47),En(20,0.47)-0.0320590],_
[0.48,0.0317229,En(20,0.48),En(20,0.48)-0.0317229],_
[0.49,0.0313903,En(20,0.49),En(20,0.49)-0.0313903],_
[0.50,0.0310612,En(20,0.50),En(20,0.50)-0.0310612],_
[0.51,0.0307356,En(20,0.51),En(20,0.51)-0.0307356],_
[0.52,0.0304134,En(20,0.52),En(20,0.52)-0.0304134],_
[0.53,0.0300946,En(20,0.53),En(20,0.53)-0.0300946],_
[0.54,0.0297791,En(20,0.54),En(20,0.54)-0.0297791],_
[0.55,0.0294670,En(20,0.55),En(20,0.55)-0.0294670],_
[0.56,0.0291581,En(20,0.56),En(20,0.56)-0.0291581],_
[0.57,0.0288525,En(20,0.57),En(20,0.57)-0.0288525],_
[0.58,0.0285501,En(20,0.58),En(20,0.58)-0.0285501],_
[0.59,0.0282508,En(20,0.59),En(20,0.59)-0.0282508],_
[0.60,0.0279548,En(20,0.60),En(20,0.60)-0.0279548],_
[0.61,0.0276618,En(20,0.61),En(20,0.61)-0.0276618],_
[0.62,0.0273719,En(20,0.62),En(20,0.62)-0.0273719],_
[0.63,0.0270850,En(20,0.63),En(20,0.63)-0.0270850],_
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[0.75,0.0238692,En(20,0.75),En(20,0.75)-0.0238692],_
[0.76,0.0236191,En(20,0.76),En(20,0.76)-0.0236191],_
[0.77,0.0233717,En(20,0.77),En(20,0.77)-0.0233717],_
[0.78,0.0231269,En(20,0.78),En(20,0.78)-0.0231269],_
[0.79,0.0228846,En(20,0.79),En(20,0.79)-0.0228846],_
[0.80,0.0226449,En(20,0.80),En(20,0.80)-0.0226449],_
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[0.82,0.0221731,En(20,0.82),En(20,0.82)-0.0221731],_
[0.83,0.0219408,En(20,0.83),En(20,0.83)-0.0219408],_
[0.84,0.0217111,En(20,0.84),En(20,0.84)-0.0217111],_
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[0.90,0.0203821,En(20,0.90),En(20,0.90)-0.0203821],_
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[2.00,0.0064143,En(20,2.00),En(20,2.00)-0.0064143]]
 

   (7)
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     [1.8999999999999999, 0.0071241999999999998, 0.0071241682687884587,
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     [1.9099999999999999, 0.0070497999999999993, 0.007049773957284575,
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     [1.9299999999999999, 0.0069032999999999994, 0.0069033134072140311,
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     ,

     [1.9399999999999999, 0.0068311999999999999, 0.0068312309073605745,
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     ,
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    [2.0,0.0064142999999999995,0.0064143058553248998,5.8553249002862851E-9]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (7)
--R   [[1.0E-2,5.2079E-2,5.2078954179335148E-2,- 4.5820664852647131E-8],
--R    [2.0E-2,5.1532099999999997E-2,5.1532149651352818E-2,4.9651352820867523E-8],
--R
--R     [2.9999999999999999E-2, 5.0991099999999998E-2, 5.0991103854550281E-2,
--R      3.8545502831222045E-9]
--R     ,
--R
--R     [4.0000000000000001E-2, 5.0455800000000002E-2, 5.0455755932602576E-2,
--R      - 4.4067397425573418E-8]
--R     ,
--R
--R     [5.0000000000000003E-2, 4.9925999999999998E-2, 4.9926045674777729E-2,
--R      4.5674777730819738E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 4.9401899999999999E-2, 4.9401913509057829E-2,
--R      1.3509057830707327E-8]
--R     ,
--R
--R     [7.0000000000000007E-2, 4.8883299999999998E-2, 4.8883300495333924E-2,
--R      4.9533392665335185E-10]
--R     ,
--R
--R     [8.0000000000000002E-2, 4.8370200000000002E-2, 4.83701483186737E-2,
--R      - 5.1681326301844521E-8]
--R     ,
--R
--R     [8.9999999999999997E-2, 4.7862399999999999E-2, 4.786239928266129E-2,
--R      - 7.1733870926626864E-10]
--R     ,
--R
--R     [0.10000000000000001, 4.7359999999999999E-2, 4.7359996302808287E-2,
--R      - 3.6971917125039333E-9]
--R     ,
--R    [0.11,4.6862899999999999E-2,4.6862882900035485E-2,- 1.7099964513822563E-8],
--R    [0.12,4.6371000000000002E-2,4.6371003194224242E-2,3.1942242392779541E-9],
--R    [0.13,4.5884300000000003E-2,4.5884301897836918E-2,1.8978369153987984E-9],
--R
--R     [0.14000000000000001, 4.5402699999999997E-2, 4.5402724309605645E-2,
--R      2.430960564792084E-8]
--R     ,
--R
--R     [0.14999999999999999, 4.4926199999999999E-2, 4.4926216308288566E-2,
--R      1.6308288566801998E-8]
--R     ,
--R    [0.16,4.44547E-2,4.4454724346493016E-2,2.4346493016080828E-8],
--R
--R     [0.17000000000000001, 4.3988199999999998E-2, 4.398819544456465E-2,
--R      - 4.5554353483856502E-9]
--R     ,
--R
--R     [0.17999999999999999, 4.3526599999999999E-2, 4.3526577184542115E-2,
--R      - 2.2815457884073354E-8]
--R     ,
--R    [0.19,4.3069799999999998E-2,4.3069817704176359E-2,1.7704176361044155E-8],
--R
--R     [0.20000000000000001, 4.26179E-2, 4.2617865691013848E-2,
--R      - 3.4308986152087328E-8]
--R     ,
--R
--R     [0.20999999999999999, 4.2170699999999998E-2, 4.2170670376543248E-2,
--R      - 2.962345675011635E-8]
--R     ,
--R    [0.22,4.17282E-2,4.1728181530404598E-2,- 1.8469595401693351E-8],
--R
--R     [0.23000000000000001, 4.1290300000000002E-2, 4.1290349454660515E-2,
--R      4.9454660512593396E-8]
--R     ,
--R    [0.23999999999999999,4.08571E-2,4.0857124978128601E-2,2.4978128600194882E-8]
--R     ,
--R    [0.25,4.0428499999999999E-2,4.0428459450774591E-2,- 4.0549225407970901E-8],
--R    [0.26000000000000001,4.00043E-2,4.0004304738165339E-2,4.7381653392464251E-9]
--R     ,
--R
--R     [0.27000000000000002, 3.9584599999999998E-2, 3.9584613215981258E-2,
--R      1.3215981260750187E-8]
--R     ,
--R
--R     [0.28000000000000003, 3.9169299999999997E-2, 3.916933776458735E-2,
--R      3.7764587353106283E-8]
--R     ,
--R
--R     [0.28999999999999998, 3.8758399999999998E-2, 3.8758431763662324E-2,
--R      3.1763662325379194E-8]
--R     ,
--R
--R     [0.29999999999999999, 3.8351799999999998E-2, 3.8351849086885194E-2,
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--R    [1.71,8.6972000000000004E-3,8.6971547951488551E-3,- 4.5204851145327907E-8],
--R    [1.72,8.6063000000000008E-3,8.6062898323516594E-3,- 1.0167648341330437E-8],
--R    [1.73,8.5164000000000004E-3,8.5163765494153266E-3,- 2.345058467377592E-8],
--R    [1.74,8.4273999999999998E-3,8.4274049515430643E-3,4.9515430644575531E-9],
--R    [1.75,8.3394000000000003E-3,8.3393651492258501E-3,- 3.4850774150232966E-8],
--R    [1.76,8.2521999999999995E-3,8.2522473571295107E-3,4.7357129511274576E-8],
--R    [1.77,8.1659999999999996E-3,8.1660418929936432E-3,4.1892993643544152E-8],
--R    [1.78,8.0806999999999997E-3,8.0807391765421923E-3,3.9176542192612129E-8],
--R    [1.79,7.9962999999999996E-3,7.9963297284055979E-3,2.9728405598339336E-8],
--R    [1.8,7.9127999999999993E-3,7.9128041690543771E-3,4.1690543777644917E-9],
--R
--R     [1.8100000000000001, 7.8302000000000007E-3, 7.8301532177440097E-3,
--R      - 4.6782255990959754E-8]
--R     ,
--R
--R     [1.8200000000000001, 7.7483999999999999E-3, 7.7483676914710427E-3,
--R      - 3.2308528957226967E-8]
--R     ,
--R
--R     [1.8300000000000001, 7.6674000000000004E-3, 7.6674385039402267E-3,
--R      3.8503940226301825E-8]
--R     ,
--R
--R     [1.8400000000000001, 7.5874000000000002E-3, 7.5873566645426526E-3,
--R      - 4.3335457347581929E-8]
--R     ,
--R
--R     [1.8500000000000001, 7.5081000000000002E-3, 7.50811327734469E-3,
--R      1.327734468984515E-8]
--R     ,
--R    [1.8600000000000001,7.4297E-3,7.429699540087673E-3,- 4.5991232697217832E-10]
--R     ,
--R
--R     [1.8700000000000001, 7.3521000000000003E-3, 7.3521067431981824E-3,
--R      6.743198182126986E-9]
--R     ,
--R
--R     [1.8799999999999999, 7.2753000000000002E-3, 7.2753262688088375E-3,
--R      2.6268808837361102E-8]
--R     ,
--R
--R     [1.8899999999999999, 7.1992999999999996E-3, 7.1993495897894446E-3,
--R      4.9589789444942634E-8]
--R     ,
--R
--R     [1.8999999999999999, 7.1241999999999998E-3, 7.1241682687884587E-3,
--R      - 3.1731211541131954E-8]
--R     ,
--R
--R     [1.9099999999999999, 7.0498000000000002E-3, 7.049773957284575E-3,
--R      - 2.6042715425139695E-8]
--R     ,
--R
--R     [1.9199999999999999, 6.9762000000000001E-3, 6.9761583946483935E-3,
--R      - 4.1605351606618934E-8]
--R     ,
--R
--R     [1.9299999999999999, 6.9033000000000002E-3, 6.9033134072140311E-3,
--R      1.3407214030820847E-8]
--R     ,
--R
--R     [1.9399999999999999, 6.8311999999999999E-3, 6.8312309073605745E-3,
--R      3.0907360574518317E-8]
--R     ,
--R    [1.95,6.7599000000000001E-3,6.759902892603269E-3,2.8926032688905701E-9],
--R    [1.96,6.6892999999999996E-3,6.6893214446943419E-3,2.1444694342336035E-8],
--R    [1.97,6.6195000000000004E-3,6.6194787287333721E-3,- 2.1271266628306029E-8],
--R    [1.98,6.5503999999999996E-3,6.5503669922870687E-3,- 3.3007712930965827E-8],
--R    [1.99,6.4819999999999999E-3,6.4819785645183897E-3,- 2.1435481610196372E-8],
--R    [2.,6.4143000000000004E-3,6.4143058553248998E-3,5.8553248994189233E-9]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 7
)spool 
 
Starts dribbling to sqmatrix.output (2009/2/17, 18:0:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 6
)set expose add constructor SquareMatrix
 
   SquareMatrix is now explicitly exposed in frame initial 
--R 
--R   SquareMatrix is now explicitly exposed in frame initial 
--E 1

--S 2 of 6
m := squareMatrix [[1,-%i],[%i,4]]
 

        +1   - %i+
   (1)  |        |
        +%i   4  +
                                        Type: SquareMatrix(2,Complex Integer)
--R 
--R
--R        +1   - %i+
--R   (1)  |        |
--R        +%i   4  +
--R                                        Type: SquareMatrix(2,Complex Integer)
--E 2

--S 3 of 6
m*m - m
 

        + 1   - 4%i+
   (2)  |          |
        +4%i   13  +
                                        Type: SquareMatrix(2,Complex Integer)
--R 
--R
--R        + 1   - 4%i+
--R   (2)  |          |
--R        +4%i   13  +
--R                                        Type: SquareMatrix(2,Complex Integer)
--E 3

--S 4 of 6
mm := squareMatrix [[m, 1], [1-m, m**2]]
 

        ++1   - %i+      +1  0+   +
        ||        |      |    |   |
        |+%i   4  +      +0  1+   |
   (3)  |                         |
        |+ 0    %i +  + 2   - 5%i+|
        ||         |  |          ||
        ++- %i  - 3+  +5%i   17  ++
                        Type: SquareMatrix(2,SquareMatrix(2,Complex Integer))
--R 
--R
--R        ++1   - %i+      +1  0+   +
--R        ||        |      |    |   |
--R        |+%i   4  +      +0  1+   |
--R   (3)  |                         |
--R        |+ 0    %i +  + 2   - 5%i+|
--R        ||         |  |          ||
--R        ++- %i  - 3+  +5%i   17  ++
--R                        Type: SquareMatrix(2,SquareMatrix(2,Complex Integer))
--E 4

--S 5 of 6
p := (x + m)**2
 

         2   + 2   - 2%i+    + 2   - 5%i+
   (4)  x  + |          |x + |          |
             +2%i    8  +    +5%i   17  +
                             Type: Polynomial SquareMatrix(2,Complex Integer)
--R 
--R
--R         2   + 2   - 2%i+    + 2   - 5%i+
--R   (4)  x  + |          |x + |          |
--R             +2%i    8  +    +5%i   17  +
--R                             Type: Polynomial SquareMatrix(2,Complex Integer)
--E 5

--S 6 of 6
p::SquareMatrix(2, ?)
 

        + 2                        +
        |x  + 2x + 2  - 2%i x - 5%i|
   (5)  |                          |
        |              2           |
        +2%i x + 5%i  x  + 8x + 17 +
                             Type: SquareMatrix(2,Polynomial Complex Integer)
--R 
--R
--R        + 2                        +
--R        |x  + 2x + 2  - 2%i x - 5%i|
--R   (5)  |                          |
--R        |              2           |
--R        +2%i x + 5%i  x  + 8x + 17 +
--R                             Type: SquareMatrix(2,Polynomial Complex Integer)
--E 6
)spool 
 
Starts dribbling to defintrf.output (2009/2/17, 17:44:38).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 3
f := (x**4 - 3*x**2 + 6)/(x**6-5*x**4+5*x**2+4)
 

            4     2
           x  - 3x  + 6
   (1)  ------------------
         6     4     2
        x  - 5x  + 5x  + 4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            4     2
--R           x  - 3x  + 6
--R   (1)  ------------------
--R         6     4     2
--R        x  - 5x  + 5x  + 4
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 3
integrate(f, x = 1..2)
 

                                               1
        2atan(8) + 2atan(5) + 2atan(2) + 2atan(-) - %pi
                                               2
   (2)  -----------------------------------------------
                               2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                                               1
--R        2atan(8) + 2atan(5) + 2atan(2) + 2atan(-) - %pi
--R                                               2
--R   (2)  -----------------------------------------------
--R                               2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 2

--S 3 of 3
numeric %
 

   (3)  2.8198420991 931510451
                                                                  Type: Float
--R 
--R
--R   (3)  2.8198420991 931510451
--R                                                                  Type: Float
--E 3
)spool
 
Starts dribbling to pfr.output (2009/2/17, 17:56:10).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
)set out len 57
 
)time off
 
--S 1 of 16
partialFraction(1,factor factorial 10)
 

        159   23   12   1
   (1)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                            Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (1)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                            Type: PartialFraction Integer
--E 1

--S 2 of 16
f := padicFraction %
 

   (2)
   1    1    1    1    1    1    2    1    2   2    2   1
   - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
   2    4    5    6    7    8    2    3    4   5    2   7
       2    2    2    2    2    3    3    3        5
                            Type: PartialFraction Integer
--R 
--R
--R   (2)
--R   1    1    1    1    1    1    2    1    2   2    2   1
--R   - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
--R   2    4    5    6    7    8    2    3    4   5    2   7
--R       2    2    2    2    2    3    3    3        5
--R                            Type: PartialFraction Integer
--E 2

--S 3 of 16
compactFraction %
 

        159   23   12   1
   (3)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                            Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (3)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                            Type: PartialFraction Integer
--E 3

--S 4 of 16
numberOfFractionalTerms f
 

   (4)  12
                                    Type: PositiveInteger
--R 
--R
--R   (4)  12
--R                                    Type: PositiveInteger
--E 4

--S 5 of 16
wholePart f
 

   (5)  0
                                 Type: NonNegativeInteger
--R 
--R
--R   (5)  0
--R                                 Type: NonNegativeInteger
--E 5

--S 6 of 16
t3 := nthFractionalTerm(f,3)
 

         1
   (6)  --
         5
        2
                            Type: PartialFraction Integer
--R 
--R
--R         1
--R   (6)  --
--R         5
--R        2
--R                            Type: PartialFraction Integer
--E 6

--S 7 of 16
firstNumer t3
 

   (7)  1
                                    Type: PositiveInteger
--R 
--R
--R   (7)  1
--R                                    Type: PositiveInteger
--E 7

--S 8 of 16
firstDenom t3
 

         5
   (8)  2
                                   Type: Factored Integer
--R 
--R
--R         5
--R   (8)  2
--R                                   Type: Factored Integer
--E 8

--S 9 of 16
g := - 13 + 14 * %i
 

   (9)  - 13 + 14%i
                                    Type: Complex Integer
--R 
--R
--R   (9)  - 13 + 14%i
--R                                    Type: Complex Integer
--E 9

--S 10 of 16
1/g
 

               %i
   (10)  - ---------
           14 + 13%i
                           Type: Fraction Complex Integer
--R 
--R
--R               %i
--R   (10)  - ---------
--R           14 + 13%i
--R                           Type: Fraction Complex Integer
--E 10

--S 11 of 16
partialFraction(1,factor g)
 

              1         4
   (11)  - ------- + -------
           1 + 2%i   3 + 8%i
                    Type: PartialFraction Complex Integer
--R 
--R
--R              1         4
--R   (11)  - ------- + -------
--R           1 + 2%i   3 + 8%i
--R                    Type: PartialFraction Complex Integer
--E 11

--S 12 of 16
% :: FRAC COMPLEX INT
 

               %i
   (12)  - ---------
           14 + 13%i
                           Type: Fraction Complex Integer
--R 
--R
--R               %i
--R   (12)  - ---------
--R           14 + 13%i
--R                           Type: Fraction Complex Integer
--E 12

--S 13 of 16
% :: COMPLEX FRAC INT
 

            13    14
   (13)  - --- - --- %i
           365   365
                           Type: Complex Fraction Integer
--R 
--R
--R            13    14
--R   (13)  - --- - --- %i
--R           365   365
--R                           Type: Complex Fraction Integer
--E 13

)clear all
 
   All user variables and function definitions have
      been cleared.

--S 14 of 16
u : FR UP(x,FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 0..4])
 

                      2       3       4
   (1)  (x + 1)(x + 2) (x + 3) (x + 4)
  Type: Factored UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                      2       3       4
--R   (1)  (x + 1)(x + 2) (x + 3) (x + 4)
--R  Type: Factored UnivariatePolynomial(x,Fraction Integer)
--E 14

--S 15 of 16
partialFraction(1,u)
 

   (2)
       1     1      7     17  2         139
      ---    - x + --   - -- x  - 12x - ---
      648    4     16      8             8
     ----- + -------- + -------------------
     x + 1          2                3
             (x + 2)          (x + 3)
   + 
     607  3   10115  2   391     44179
     --- x  + ----- x  + --- x + -----
     324       432        4       324
     ---------------------------------
                         4
                  (x + 4)
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (2)
--R       1     1      7     17  2         139
--R      ---    - x + --   - -- x  - 12x - ---
--R      648    4     16      8             8
--R     ----- + -------- + -------------------
--R     x + 1          2                3
--R             (x + 2)          (x + 3)
--R   + 
--R     607  3   10115  2   391     44179
--R     --- x  + ----- x  + --- x + -----
--R     324       432        4       324
--R     ---------------------------------
--R                         4
--R                  (x + 4)
--RType: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 15

--S 16 of 16
padicFraction %
 

   (3)
       1       1         1        17        3          1
      ---      -        --        --        -          -
      648      4        16         8        4          2
     ----- + ----- - -------- - ----- + -------- - --------
     x + 1   x + 2          2   x + 3          2          3
                     (x + 2)            (x + 3)    (x + 3)
   + 
      607       403        13          1
      ---       ---        --         --
      324       432        36         12
     ----- + -------- + -------- + --------
     x + 4          2          3          4
             (x + 4)    (x + 4)    (x + 4)
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (3)
--R       1       1         1        17        3          1
--R      ---      -        --        --        -          -
--R      648      4        16         8        4          2
--R     ----- + ----- - -------- - ----- + -------- - --------
--R     x + 1   x + 2          2   x + 3          2          3
--R                     (x + 2)            (x + 3)    (x + 3)
--R   + 
--R      607       403        13          1
--R      ---       ---        --         --
--R      324       432        36         12
--R     ----- + -------- + -------- + --------
--R     x + 4          2          3          4
--R             (x + 4)    (x + 4)    (x + 4)
--RType: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 16
)spool 
 
Starts dribbling to schaum31.output (2009/2/17, 17:59:47).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(coth(a*x),x)
 

                    2sinh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2sinh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/a*log(sinh(a*x))
 

        log(sinh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                       2sinh(a x)
        - log(sinh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2sinh(a x)
--R        - log(sinh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 4
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 5      14:615 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 6
aa:=integrate(coth(a*x)^2,x)
 

        (a x + 1)sinh(a x) - cosh(a x)
   (1)  ------------------------------
                  a sinh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        (a x + 1)sinh(a x) - cosh(a x)
--R   (1)  ------------------------------
--R                  a sinh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7
bb:=x-coth(a*x)/a
 

        - coth(a x) + a x
   (2)  -----------------
                a
                                                     Type: Expression Integer
--R
--R        - coth(a x) + a x
--R   (2)  -----------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 8
cc:=aa-bb
 

        (coth(a x) + 1)sinh(a x) - cosh(a x)
   (3)  ------------------------------------
                     a sinh(a x)
                                                     Type: Expression Integer
--R
--R        (coth(a x) + 1)sinh(a x) - cosh(a x)
--R   (3)  ------------------------------------
--R                     a sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 9      14:616 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

        1
   (4)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (4)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 10
aa:=integrate(coth(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                      4                          3
       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
     + 
                        2                     2
       (- 6a x cosh(a x)  + 2a x - 2)sinh(a x)
     + 
                        3                                                4
       (- 4a x cosh(a x)  + (4a x - 4)cosh(a x))sinh(a x) - a x cosh(a x)
     + 
                          2
       (2a x - 2)cosh(a x)  - a x
  /
                  4                        3                2               2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  - 2a)sinh(a x)
     + 
                  3                                       4               2
     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                      4                          3
--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
--R     + 
--R                        2                     2
--R       (- 6a x cosh(a x)  + 2a x - 2)sinh(a x)
--R     + 
--R                        3                                                4
--R       (- 4a x cosh(a x)  + (4a x - 4)cosh(a x))sinh(a x) - a x cosh(a x)
--R     + 
--R                          2
--R       (2a x - 2)cosh(a x)  - a x
--R  /
--R                  4                        3                2               2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  - 2a)sinh(a x)
--R     + 
--R                  3                                       4               2
--R     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11
bb:=1/a*log(sinh(a*x)-coth(a*x)^2)/(2*a)
 

                                 2
        log(sinh(a x) - coth(a x) )
   (2)  ---------------------------
                      2
                    2a
                                                     Type: Expression Integer
--R
--R                                 2
--R        log(sinh(a x) - coth(a x) )
--R   (2)  ---------------------------
--R                      2
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 12     14:617 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
      *
                                  2
         log(sinh(a x) - coth(a x) )
     + 
                       4                        3
           2a sinh(a x)  + 8a cosh(a x)sinh(a x)
         + 
                         2               2
           (12a cosh(a x)  - 4a)sinh(a x)
         + 
                        3                                        4
           (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)
         + 
                         2
           - 4a cosh(a x)  + 2a
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
           2           4     2                    3
       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
     + 
             2           2     2                2
       (- 12a x cosh(a x)  + 4a x - 4a)sinh(a x)
     + 
            2           3      2                               2           4
       (- 8a x cosh(a x)  + (8a x - 8a)cosh(a x))sinh(a x) - 2a x cosh(a x)
     + 
          2                2     2
       (4a x - 4a)cosh(a x)  - 2a x
  /
         2         4     2                  3       2         2     2          2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a )sinh(a x)
     + 
          2         3     2                        2         4     2         2
       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
     + 
         2
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
--R      *
--R                                  2
--R         log(sinh(a x) - coth(a x) )
--R     + 
--R                       4                        3
--R           2a sinh(a x)  + 8a cosh(a x)sinh(a x)
--R         + 
--R                         2               2
--R           (12a cosh(a x)  - 4a)sinh(a x)
--R         + 
--R                        3                                        4
--R           (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)
--R         + 
--R                         2
--R           - 4a cosh(a x)  + 2a
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R           2           4     2                    3
--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
--R     + 
--R             2           2     2                2
--R       (- 12a x cosh(a x)  + 4a x - 4a)sinh(a x)
--R     + 
--R            2           3      2                               2           4
--R       (- 8a x cosh(a x)  + (8a x - 8a)cosh(a x))sinh(a x) - 2a x cosh(a x)
--R     + 
--R          2                2     2
--R       (4a x - 4a)cosh(a x)  - 2a x
--R  /
--R         2         4     2                  3       2         2     2          2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a )sinh(a x)
--R     + 
--R          2         3     2                        2         4     2         2
--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
--R     + 
--R         2
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 13
aa:=integrate(coth(a*x)^n*csch(a*x)^2,x)
 

                              cosh(a x)                         cosh(a x)
        - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
                              sinh(a x)                         sinh(a x)
   (1)  -------------------------------------------------------------------
                                 (a n + a)sinh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              cosh(a x)                         cosh(a x)
--R        - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
--R                              sinh(a x)                         sinh(a x)
--R   (1)  -------------------------------------------------------------------
--R                                 (a n + a)sinh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14
bb:=-coth(a*x)^(n+1)/((n+1)*a)
 

                   n + 1
          coth(a x)
   (2)  - --------------
              a n + a
                                                     Type: Expression Integer
--R
--R                   n + 1
--R          coth(a x)
--R   (2)  - --------------
--R              a n + a
--R                                                     Type: Expression Integer
--E

--S 15
cc:=aa-bb
 

   (3)
                             cosh(a x)                         cosh(a x)
       - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
                             sinh(a x)                         sinh(a x)
     + 
                         n + 1
       sinh(a x)coth(a x)
  /
     (a n + a)sinh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                             cosh(a x)                         cosh(a x)
--R       - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
--R                             sinh(a x)                         sinh(a x)
--R     + 
--R                         n + 1
--R       sinh(a x)coth(a x)
--R  /
--R     (a n + a)sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 16
dd:=expandLog cc
 

   (4)
       cosh(a x)sinh(n log(sinh(a x)) - n log(cosh(a x)))
     + 
       - cosh(a x)cosh(n log(sinh(a x)) - n log(cosh(a x)))
     + 
                         n + 1
       sinh(a x)coth(a x)
  /
     (a n + a)sinh(a x)
                                                     Type: Expression Integer
--R
--R   (4)
--R       cosh(a x)sinh(n log(sinh(a x)) - n log(cosh(a x)))
--R     + 
--R       - cosh(a x)cosh(n log(sinh(a x)) - n log(cosh(a x)))
--R     + 
--R                         n + 1
--R       sinh(a x)coth(a x)
--R  /
--R     (a n + a)sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 17     14:618 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 18
aa:=integrate(csch(a*x)^2/coth(a*x),x)
 

                      2cosh(a x)                     2sinh(a x)
        - log(- ---------------------) + log(- ---------------------)
                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   (1)  -------------------------------------------------------------
                                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2cosh(a x)                     2sinh(a x)
--R        - log(- ---------------------) + log(- ---------------------)
--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   (1)  -------------------------------------------------------------
--R                                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 19
bb:=-1/a*log(coth(a*x))
 

          log(coth(a x))
   (2)  - --------------
                 a
                                                     Type: Expression Integer
--R
--R          log(coth(a x))
--R   (2)  - --------------
--R                 a
--R                                                     Type: Expression Integer
--E

--S 20
cc:=aa-bb
 

   (3)
                                2cosh(a x)                     2sinh(a x)
   log(coth(a x)) - log(- ---------------------) + log(- ---------------------)
                          sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   ----------------------------------------------------------------------------
                                         a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                2cosh(a x)                     2sinh(a x)
--R   log(coth(a x)) - log(- ---------------------) + log(- ---------------------)
--R                          sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   ----------------------------------------------------------------------------
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 21
dd:=expandLog cc
 

        log(sinh(a x)) + log(coth(a x)) - log(cosh(a x))
   (4)  ------------------------------------------------
                                a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x)) + log(coth(a x)) - log(cosh(a x))
--R   (4)  ------------------------------------------------
--R                                a
--R                                                     Type: Expression Integer
--E

--S 22     14:619 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(1/coth(a*x),x)
 

                    2cosh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2cosh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=1/a*log(cosh(a*x))
 

        log(cosh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(cosh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 25
cc:=aa-bb
 

                                       2cosh(a x)
        - log(cosh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2cosh(a x)
--R        - log(cosh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 26
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 27     14:620 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28     14:621 Axiom cannot compute this integral
aa:=integrate(x*coth(a*x),x)
 

           x
         ++
   (1)   |   %O coth(%O a)d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O coth(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(x*coth(a*x)^2,x)
 

   (1)
                    2                                   2
         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  - 2)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
         2 2                 2      2 2
       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
     + 
         2 2                 2    2 2
       (a x  - 4a x)cosh(a x)  - a x
  /
       2         2     2                       2         2     2
     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    2                                   2
--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  - 2)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R         2 2                 2      2 2
--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
--R     + 
--R         2 2                 2    2 2
--R       (a x  - 4a x)cosh(a x)  - a x
--R  /
--R       2         2     2                       2         2     2
--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 30
bb:=x^2/2-(x*coth(a*x)/a)+1/a^2*log(sinh(a*x))
 

                                            2 2
        2log(sinh(a x)) - 2a x coth(a x) + a x
   (2)  ---------------------------------------
                            2
                          2a
                                                     Type: Expression Integer
--R
--R                                            2 2
--R        2log(sinh(a x)) - 2a x coth(a x) + a x
--R   (2)  ---------------------------------------
--R                            2
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

   (3)
                   2                                  2
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                                      2
       (a x coth(a x) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
     + 
                     2                                 2
       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                                      2
--R       (a x coth(a x) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
--R     + 
--R                     2                                 2
--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 32
dd:=expandLog cc
 

   (4)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                                                 2
       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
                     2                                             2
       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (4)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                                                 2
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R                     2                                             2
--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 33
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34
ee:=sinhsqrrule dd
 

   (6)
                                                         2
         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
      *
         log(sinh(a x) - cosh(a x))
     + 
       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
     + 
                                       2
       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
     + 
                                                                2
       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
     + 
       2a x
  /
       2                      2               2         2     2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                         2
--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
--R     + 
--R                                       2
--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
--R     + 
--R                                                                2
--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
--R     + 
--R       2a x
--R  /
--R       2                      2               2         2     2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
--R                                                     Type: Expression Integer
--E

--S 35
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36
ff:=coshsqrrule ee
 

   (8)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 37
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (9)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %L sinh(y + x) - %L sinh(y - x)
--I   (9)  %L cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38
gg:=sinhcoshrule ff
 

   (10)
       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 39     14:622 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         - log(- 1) + log(- 2)
   (11)  ---------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R         - log(- 1) + log(- 2)
--R   (11)  ---------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 40     14:623 Axiom cannot compute this integral
aa:=integrate(coth(a*x)/x,x)
 

           x
         ++  coth(%O a)
   (1)   |   ---------- d%O
        ++       %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  coth(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 41
aa:=integrate(1/(p+q*coth(a*x)),x)
 

              - 2p sinh(a x) - 2q cosh(a x)
        q log(-----------------------------) + (- a q - a p)x
                  sinh(a x) - cosh(a x)
   (1)  -----------------------------------------------------
                                2      2
                             a q  - a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - 2p sinh(a x) - 2q cosh(a x)
--R        q log(-----------------------------) + (- a q - a p)x
--R                  sinh(a x) - cosh(a x)
--R   (1)  -----------------------------------------------------
--R                                2      2
--R                             a q  - a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42
bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(p*sinh(a*x)+q*cosh(a*x))
 

        q log(p sinh(a x) + q cosh(a x)) - a p x
   (2)  ----------------------------------------
                          2      2
                       a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(p sinh(a x) + q cosh(a x)) - a p x
--R   (2)  ----------------------------------------
--R                          2      2
--R                       a q  - a p
--R                                                     Type: Expression Integer
--E

--S 43
cc:=aa-bb
 

   (3)
                                                  - 2p sinh(a x) - 2q cosh(a x)
       - q log(p sinh(a x) + q cosh(a x)) + q log(-----------------------------)
                                                      sinh(a x) - cosh(a x)
     + 
       - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                  - 2p sinh(a x) - 2q cosh(a x)
--R       - q log(p sinh(a x) + q cosh(a x)) + q log(-----------------------------)
--R                                                      sinh(a x) - cosh(a x)
--R     + 
--R       - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 44
dd:=expandLog cc
 

   (4)
       - q log(p sinh(a x) + q cosh(a x)) - q log(sinh(a x) - cosh(a x))
     + 
       q log(- p sinh(a x) - q cosh(a x)) + q log(2) - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R       - q log(p sinh(a x) + q cosh(a x)) - q log(sinh(a x) - cosh(a x))
--R     + 
--R       q log(- p sinh(a x) - q cosh(a x)) + q log(2) - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 45     14:624 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        q log(2) - 2q log(- 1)
   (5)  ----------------------
                 2      2
              a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(2) - 2q log(- 1)
--R   (5)  ----------------------
--R                 2      2
--R              a q  - a p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 46     14:625 Axiom cannot compute this integral
aa:=integrate(coth(a*x)^n,x)
 

           x
         ++            n
   (1)   |   coth(%O a) d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   coth(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to magma.output (2009/2/17, 17:52:51).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 22
x:Symbol :='x
 

   (1)  x
                                                                 Type: Symbol
--R 
--R
--R   (1)  x
--R                                                                 Type: Symbol
--E 1

--S 2 of 22
y:Symbol :='y
 

   (2)  y
                                                                 Type: Symbol
--R 
--R
--R   (2)  y
--R                                                                 Type: Symbol
--E 2

--S 3 of 22
z:Symbol :='z
 

   (3)  z
                                                                 Type: Symbol
--R 
--R
--R   (3)  z
--R                                                                 Type: Symbol
--E 3

--S 4 of 22
word := OrderedFreeMonoid(Symbol)
 

   (4)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 22
tree := Magma(Symbol)
 

   (5)  Magma Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  Magma Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 22
a:tree := x*x
 

   (6)  [x,x]
                                                           Type: Magma Symbol
--R 
--R
--R   (6)  [x,x]
--R                                                           Type: Magma Symbol
--E 6

--S 7 of 22
b:tree := y*y
 

   (7)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (7)  [y,y]
--R                                                           Type: Magma Symbol
--E 7

--S 8 of 22
c:tree := a*b
 

   (8)  [[x,x],[y,y]]
                                                           Type: Magma Symbol
--R 
--R
--R   (8)  [[x,x],[y,y]]
--R                                                           Type: Magma Symbol
--E 8

--S 9 of 22
left c
 

   (9)  [x,x]
                                                           Type: Magma Symbol
--R 
--R
--R   (9)  [x,x]
--R                                                           Type: Magma Symbol
--E 9

--S 10 of 22
right c
 

   (10)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (10)  [y,y]
--R                                                           Type: Magma Symbol
--E 10

--S 11 of 22
length c
 

   (11)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 22
c::word
 

          2 2
   (12)  x y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R          2 2
--R   (12)  x y
--R                                               Type: OrderedFreeMonoid Symbol
--E 12

--S 13 of 22
a < b
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 22
a < c
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 22
b < c
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 22
first c
 

   (16)  x
                                                                 Type: Symbol
--R 
--R
--R   (16)  x
--R                                                                 Type: Symbol
--E 16

--S 17 of 22
rest c
 

   (17)  [x,[y,y]]
                                                           Type: Magma Symbol
--R 
--R
--R   (17)  [x,[y,y]]
--R                                                           Type: Magma Symbol
--E 17

--S 18 of 22
rest rest c
 

   (18)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (18)  [y,y]
--R                                                           Type: Magma Symbol
--E 18

--S 19 of 22
ax:tree := a*x
 

   (19)  [[x,x],x]
                                                           Type: Magma Symbol
--R 
--R
--R   (19)  [[x,x],x]
--R                                                           Type: Magma Symbol
--E 19

--S 20 of 22
xa:tree := x*a
 

   (20)  [x,[x,x]]
                                                           Type: Magma Symbol
--R 
--R
--R   (20)  [x,[x,x]]
--R                                                           Type: Magma Symbol
--E 20

--S 21 of 22
xa < ax
 

   (21)  true
                                                                Type: Boolean
--R 
--R
--R   (21)  true
--R                                                                Type: Boolean
--E 21

--S 22 of 22
lexico(xa,ax)
 

   (22)  false
                                                                Type: Boolean
--R 
--R
--R   (22)  false
--R                                                                Type: Boolean
--E 22
)spool 
 
Starts dribbling to repa6.output (2009/2/17, 17:57:46).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 33
genA6 : List PERM INT := [cycle [1,2,3], cycle [2,3,4,5,6]]
 

   (1)  [(1 2 3),(2 3 4 5 6)]
                                               Type: List Permutation Integer
--R 
--R
--R   (1)  [(1 2 3),(2 3 4 5 6)]
--R                                               Type: List Permutation Integer
--E 1

--S 2 of 33
pRA6 := permutationRepresentation (genA6, 6)
 

         +0  0  1  0  0  0+ +1  0  0  0  0  0+
         |                | |                |
         |1  0  0  0  0  0| |0  0  0  0  0  1|
         |                | |                |
         |0  1  0  0  0  0| |0  1  0  0  0  0|
   (2)  [|                |,|                |]
         |0  0  0  1  0  0| |0  0  1  0  0  0|
         |                | |                |
         |0  0  0  0  1  0| |0  0  0  1  0  0|
         |                | |                |
         +0  0  0  0  0  1+ +0  0  0  0  1  0+
                                                    Type: List Matrix Integer
--R 
--R
--R         +0  0  1  0  0  0+ +1  0  0  0  0  0+
--R         |                | |                |
--R         |1  0  0  0  0  0| |0  0  0  0  0  1|
--R         |                | |                |
--R         |0  1  0  0  0  0| |0  1  0  0  0  0|
--R   (2)  [|                |,|                |]
--R         |0  0  0  1  0  0| |0  0  1  0  0  0|
--R         |                | |                |
--R         |0  0  0  0  1  0| |0  0  0  1  0  0|
--R         |                | |                |
--R         +0  0  0  0  0  1+ +0  0  0  0  1  0+
--R                                                    Type: List Matrix Integer
--E 2

--S 3 of 33
pRA6m2 : List Matrix PrimeField 2 := pRA6
 

         +0  0  1  0  0  0+ +1  0  0  0  0  0+
         |                | |                |
         |1  0  0  0  0  0| |0  0  0  0  0  1|
         |                | |                |
         |0  1  0  0  0  0| |0  1  0  0  0  0|
   (3)  [|                |,|                |]
         |0  0  0  1  0  0| |0  0  1  0  0  0|
         |                | |                |
         |0  0  0  0  1  0| |0  0  0  1  0  0|
         |                | |                |
         +0  0  0  0  0  1+ +0  0  0  0  1  0+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R         +0  0  1  0  0  0+ +1  0  0  0  0  0+
--R         |                | |                |
--R         |1  0  0  0  0  0| |0  0  0  0  0  1|
--R         |                | |                |
--R         |0  1  0  0  0  0| |0  1  0  0  0  0|
--R   (3)  [|                |,|                |]
--R         |0  0  0  1  0  0| |0  0  1  0  0  0|
--R         |                | |                |
--R         |0  0  0  0  1  0| |0  0  0  1  0  0|
--R         |                | |                |
--R         +0  0  0  0  0  1+ +0  0  0  0  1  0+
--R                                               Type: List Matrix PrimeField 2
--E 3
 
--S 4 of 33
sp0 := meatAxe pRA6m2
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

          +0  0  1  0  0+ +1  0  0  0  0+
          |             | |             |
          |1  0  0  0  0| |1  1  1  1  1|
          |             | |             |
   (4)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
          |             | |             |
          |0  0  0  1  0| |0  0  1  0  0|
          |             | |             |
          +0  0  0  0  1+ +0  0  0  1  0+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R          +0  0  1  0  0+ +1  0  0  0  0+
--R          |             | |             |
--R          |1  0  0  0  0| |1  1  1  1  1|
--R          |             | |             |
--R   (4)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
--R          |             | |             |
--R          |0  0  0  1  0| |0  0  1  0  0|
--R          |             | |             |
--R          +0  0  0  0  1+ +0  0  0  1  0+
--R                                          Type: List List Matrix PrimeField 2
--E 4
 
--S 5 of 33
dA6d1 := sp0.2
 

   (5)  [[1],[1]]
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (5)  [[1],[1]]
--R                                               Type: List Matrix PrimeField 2
--E 5

--S 6 of 33
sp1 := meatAxe sp0.1
 
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices
     Representation is not irreducible and it will be split:

                    +0  1  0  0+ +0  1  1  1+
                    |          | |          |
                    |0  0  1  0| |1  1  0  1|
   (6)  [[[1],[1]],[|          |,|          |]]
                    |1  0  0  0| |1  1  1  0|
                    |          | |          |
                    +0  0  0  1+ +1  1  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R     Representation is not irreducible and it will be split:
--R
--R                    +0  1  0  0+ +0  1  1  1+
--R                    |          | |          |
--R                    |0  0  1  0| |1  1  0  1|
--R   (6)  [[[1],[1]],[|          |,|          |]]
--R                    |1  0  0  0| |1  1  1  0|
--R                    |          | |          |
--R                    +0  0  0  1+ +1  1  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 6
 
--S 7 of 33
dA6d4a := sp1.2
 

         +0  1  0  0+ +0  1  1  1+
         |          | |          |
         |0  0  1  0| |1  1  0  1|
   (7)  [|          |,|          |]
         |1  0  0  0| |1  1  1  0|
         |          | |          |
         +0  0  0  1+ +1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R         +0  1  0  0+ +0  1  1  1+
--R         |          | |          |
--R         |0  0  1  0| |1  1  0  1|
--R   (7)  [|          |,|          |]
--R         |1  0  0  0| |1  1  1  0|
--R         |          | |          |
--R         +0  0  0  1+ +1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 7
 
--S 8 of 33 random input, FAILURE OK
isAbsolutelyIrreducible? dA6d4a
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (8)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

-- lambda : PRTITION := partition [2,2,1,1]
--S 9 of 33
lambda := [2,2,1,1]
 

   (9)  [2,2,1,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (9)  [2,2,1,1]
--R                                                   Type: List PositiveInteger
--E 9

--S 10 of 33
dimensionOfIrreducibleRepresentation lambda
 

   (10)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  9
--R                                                        Type: PositiveInteger
--E 10


--S 11 of 33
d2211  := irreducibleRepresentation(lambda, genA6)
 

   (11)
    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
    |                                     | |                                 |
    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
    |                                     | |                                 |
    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
    |                                     | |                                 |
   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
    |                                     | |                                 |
    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
    |                                     | |                                 |
    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
    |                                     | |                                 |
    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
                                                    Type: List Matrix Integer
--R 
--R
--R   (11)
--R    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
--R    |                                     | |                                 |
--R    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
--R    |                                     | |                                 |
--R   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
--R    |                                     | |                                 |
--R    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
--R                                                    Type: List Matrix Integer
--E 11

--S 12 of 33
d2211m2 : List Matrix PrimeField 2 := d2211
 

          +1  0  0  1  1  0  0  0  0+ +0  0  1  0  0  0  1  0  0+
          |                         | |                         |
          |0  1  0  1  0  1  0  0  0| |0  0  0  0  1  0  1  0  0|
          |                         | |                         |
          |0  0  1  0  1  1  0  0  0| |0  0  0  0  0  1  1  0  0|
          |                         | |                         |
          |0  0  0  1  0  0  1  0  0| |0  0  0  0  0  0  1  1  0|
          |                         | |                         |
   (12)  [|0  0  0  0  1  0  0  1  0|,|0  0  0  0  0  0  1  0  1|]
          |                         | |                         |
          |0  0  0  0  0  1  0  0  1| |0  0  0  0  0  0  1  0  0|
          |                         | |                         |
          |0  0  0  1  0  0  0  0  0| |1  0  0  0  0  0  1  0  0|
          |                         | |                         |
          |0  0  0  0  1  0  0  0  0| |0  1  0  0  0  0  1  0  0|
          |                         | |                         |
          +0  0  0  0  0  1  0  0  0+ +0  0  0  1  0  0  1  0  0+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  0  1  1  0  0  0  0+ +0  0  1  0  0  0  1  0  0+
--R          |                         | |                         |
--R          |0  1  0  1  0  1  0  0  0| |0  0  0  0  1  0  1  0  0|
--R          |                         | |                         |
--R          |0  0  1  0  1  1  0  0  0| |0  0  0  0  0  1  1  0  0|
--R          |                         | |                         |
--R          |0  0  0  1  0  0  1  0  0| |0  0  0  0  0  0  1  1  0|
--R          |                         | |                         |
--R   (12)  [|0  0  0  0  1  0  0  1  0|,|0  0  0  0  0  0  1  0  1|]
--R          |                         | |                         |
--R          |0  0  0  0  0  1  0  0  1| |0  0  0  0  0  0  1  0  0|
--R          |                         | |                         |
--R          |0  0  0  1  0  0  0  0  0| |1  0  0  0  0  0  1  0  0|
--R          |                         | |                         |
--R          |0  0  0  0  1  0  0  0  0| |0  1  0  0  0  0  1  0  0|
--R          |                         | |                         |
--R          +0  0  0  0  0  1  0  0  0+ +0  0  0  1  0  0  1  0  0+
--R                                               Type: List Matrix PrimeField 2
--E 12

--S 13 of 33
sp2 := meatAxe d2211m2
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

                                       +1  0  0  0  0+ +1  1  1  0  0+
           +1  0  1  1+ +0  0  1  0+   |             | |             |
           |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
           |0  1  0  1| |1  1  1  1|   |             | |             |
   (13)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
           |1  1  0  0| |1  0  1  1|   |             | |             |
           |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
           +0  1  0  0+ +0  1  0  1+   |             | |             |
                                       +0  1  1  1  0+ +1  0  0  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R                                       +1  0  0  0  0+ +1  1  1  0  0+
--R           +1  0  1  1+ +0  0  1  0+   |             | |             |
--R           |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
--R           |0  1  0  1| |1  1  1  1|   |             | |             |
--R   (13)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
--R           |1  1  0  0| |1  0  1  1|   |             | |             |
--R           |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
--R           +0  1  0  0+ +0  1  0  1+   |             | |             |
--R                                       +0  1  1  1  0+ +1  0  0  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 13

--S 14 of 33
dA6d4b := sp2.1
 

          +1  0  1  1+ +0  0  1  0+
          |          | |          |
          |0  1  0  1| |1  1  1  1|
   (14)  [|          |,|          |]
          |1  1  0  0| |1  0  1  1|
          |          | |          |
          +0  1  0  0+ +0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  1  1+ +0  0  1  0+
--R          |          | |          |
--R          |0  1  0  1| |1  1  1  1|
--R   (14)  [|          |,|          |]
--R          |1  1  0  0| |1  0  1  1|
--R          |          | |          |
--R          +0  1  0  0+ +0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 14

--S 15 of 33 random generation, FAILURE OK.
isAbsolutelyIrreducible? dA6d4b
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (15)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 33 random generation, FAILURE OK.
areEquivalent? ( dA6d4a , dA6d4b )
 
   Dimensions of kernels differ

   Representations are not equivalent.

   (16)  [0]
                                                    Type: Matrix PrimeField 2
--R 
--R   Dimensions of kernels differ
--R
--R   Representations are not equivalent.
--R
--R   (16)  [0]
--R                                                    Type: Matrix PrimeField 2
--E 16

--S 17 of 33
dA6d16 := tensorProduct ( dA6d4a , dA6d4b )
 

   (17)
    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
    |                                              |
    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
   [|                                              |,
    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
    |                                              |
    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
    |                                              |
    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
    |                                              |
    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
    |                                              |]
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
    |                                              |
    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (17)
--R    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R   [|                                              |,
--R    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
--R    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
--R    |                                              |
--R    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R    |                                              |]
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 17

--S 18 of 33
sp3 := meatAxe dA6d16
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is irreducible, but we don't know
       whether it is absolutely irreducible

   (18)
   [
      +0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0+
      |                                              |
      |0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
      |                                              |
      |1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
     [|                                              |,
      |0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0|
      |                                              |
      |0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1|
      |                                              |
      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0|
      |                                              |
      +0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0+
      +0  0  0  0  0  1  1  0  0  1  1  0  0  1  1  0+
      |                                              |
      |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
      |                                              |
      |0  0  0  0  1  1  1  0  1  1  1  0  1  1  1  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
      |                                              |
      |0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0|
      |                                              |
      |0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1|
      |                                              |
      |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
      |                                              |
      |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
      |                                              |]
      |0  1  1  0  0  0  0  0  0  1  1  0  0  1  1  0|
      |                                              |
      |0  1  0  1  0  0  0  0  0  1  0  1  0  1  0  1|
      |                                              |
      |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
      |                                              |
      |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
      |                                              |
      |0  1  1  0  0  1  1  0  0  0  0  0  0  1  1  0|
      |                                              |
      |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
      |                                              |
      |1  1  1  0  1  1  1  0  0  0  0  0  1  1  1  0|
      |                                              |
      +0  1  1  1  0  1  1  1  0  0  0  0  0  1  1  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is irreducible, but we don't know
--R       whether it is absolutely irreducible
--R
--R   (18)
--R   [
--R      +0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0+
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R     [|                                              |,
--R      |0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0|
--R      |                                              |
--R      +0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0+
--R      +0  0  0  0  0  1  1  0  0  1  1  0  0  1  1  0+
--R      |                                              |
--R      |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R      |                                              |
--R      |0  0  0  0  1  1  1  0  1  1  1  0  1  1  1  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
--R      |                                              |
--R      |0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0|
--R      |                                              |
--R      |0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1|
--R      |                                              |
--R      |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
--R      |                                              |
--R      |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
--R      |                                              |]
--R      |0  1  1  0  0  0  0  0  0  1  1  0  0  1  1  0|
--R      |                                              |
--R      |0  1  0  1  0  0  0  0  0  1  0  1  0  1  0  1|
--R      |                                              |
--R      |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
--R      |                                              |
--R      |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
--R      |                                              |
--R      |0  1  1  0  0  1  1  0  0  0  0  0  0  1  1  0|
--R      |                                              |
--R      |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R      |                                              |
--R      |1  1  1  0  1  1  1  0  0  0  0  0  1  1  1  0|
--R      |                                              |
--R      +0  1  1  1  0  1  1  1  0  0  0  0  0  1  1  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 18

--S 19 of 33
isAbsolutelyIrreducible? dA6d16
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   We have not found a one-dimensional kernel so far,
     as we do a random search you could try again

   (19)  false
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   We have not found a one-dimensional kernel so far,
--R     as we do a random search you could try again
--R
--R   (19)  false
--R                                                                Type: Boolean
--E 19

--S 20 of 33
gf4 := FiniteField(2,2)
 

   (20)  FiniteField(2,2)
                                                                 Type: Domain
--R 
--R
--R   (20)  FiniteField(2,2)
--R                                                                 Type: Domain
--E 20

--S 21 of 33
dA6d16gf4 : List Matrix gf4 := dA6d16
 

   (21)
    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
    |                                              |
    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
   [|                                              |,
    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
    |                                              |
    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
    |                                              |
    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
    |                                              |
    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
    |                                              |]
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
    |                                              |
    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (21)
--R    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R   [|                                              |,
--R    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
--R    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
--R    |                                              |
--R    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R    |                                              |]
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
--R                                           Type: List Matrix FiniteField(2,2)
--E 21

--S 22 of 33
sp4 := meatAxe dA6d16gf4
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (22)
   [
      +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
      |                                                          |
      |  0       0       %A    %A + 1    %A      %A      0     0 |
      |                                                          |
      |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
      |                                                          |
      |  %A    %A + 1    %A      1       %A      0       0     0 |
     [|                                                          |,
      |%A + 1    1       1       1       0       0     %A + 1  %A|
      |                                                          |
      |  0       0     %A + 1    1       0       0       %A    0 |
      |                                                          |
      |  1       0       1       1       0       0       0     0 |
      |                                                          |
      +  1       1       0       0       0       0       0     0 +
      +  1       0       %A      0       1       1       %A    %A + 1+
      |                                                              |
      |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
      |                                                              |
      |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
      |                                                              |
      |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
      |                                                              |]
      |  1       0     %A + 1    0       1       1       %A      %A  |
      |                                                              |
      |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
      |                                                              |
      |  0       0       1       0       0       1       0       1   |
      |                                                              |
      +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
     ,

      +0     1       1     %A + 1  0  0  0  0+
      |                                      |
      |1     1     %A + 1    0     0  0  0  0|
      |                                      |
      |%A    0       0       0     0  0  0  0|
      |                                      |
      |1     %A      0       0     0  0  0  0|
     [|                                      |,
      |%A  %A + 1    1       1     1  0  1  1|
      |                                      |
      |0     0       %A      1     0  1  0  1|
      |                                      |
      |%A    1       0       1     1  1  0  0|
      |                                      |
      +1     %A    %A + 1    %A    0  1  0  0+
      +%A + 1    1       %A      0       0     %A + 1    0       1   +
      |                                                              |
      |  0       %A      1       1       1       0     %A + 1    %A  |
      |                                                              |
      |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
      |                                                              |
      |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
      |                                                              |]
      |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
      |                                                              |
      |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
      |                                                              |
      |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
      |                                                              |
      +  %A      %A      %A      1       %A      %A      1     %A + 1+
     ]
                                      Type: List List Matrix FiniteField(2,2)
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (22)
--R   [
--R      +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
--R      |                                                          |
--R      |  0       0       %A    %A + 1    %A      %A      0     0 |
--R      |                                                          |
--R      |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
--R      |                                                          |
--R      |  %A    %A + 1    %A      1       %A      0       0     0 |
--R     [|                                                          |,
--R      |%A + 1    1       1       1       0       0     %A + 1  %A|
--R      |                                                          |
--R      |  0       0     %A + 1    1       0       0       %A    0 |
--R      |                                                          |
--R      |  1       0       1       1       0       0       0     0 |
--R      |                                                          |
--R      +  1       1       0       0       0       0       0     0 +
--R      +  1       0       %A      0       1       1       %A    %A + 1+
--R      |                                                              |
--R      |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
--R      |                                                              |
--R      |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
--R      |                                                              |
--R      |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
--R      |                                                              |]
--R      |  1       0     %A + 1    0       1       1       %A      %A  |
--R      |                                                              |
--R      |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
--R      |                                                              |
--R      |  0       0       1       0       0       1       0       1   |
--R      |                                                              |
--R      +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
--R     ,
--R
--R      +0     1       1     %A + 1  0  0  0  0+
--R      |                                      |
--R      |1     1     %A + 1    0     0  0  0  0|
--R      |                                      |
--R      |%A    0       0       0     0  0  0  0|
--R      |                                      |
--R      |1     %A      0       0     0  0  0  0|
--R     [|                                      |,
--R      |%A  %A + 1    1       1     1  0  1  1|
--R      |                                      |
--R      |0     0       %A      1     0  1  0  1|
--R      |                                      |
--R      |%A    1       0       1     1  1  0  0|
--R      |                                      |
--R      +1     %A    %A + 1    %A    0  1  0  0+
--R      +%A + 1    1       %A      0       0     %A + 1    0       1   +
--R      |                                                              |
--R      |  0       %A      1       1       1       0     %A + 1    %A  |
--R      |                                                              |
--R      |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
--R      |                                                              |
--R      |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
--R      |                                                              |]
--R      |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
--R      |                                                              |
--R      |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
--R      |                                                              |
--R      |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
--R      |                                                              |
--R      +  %A      %A      %A      1       %A      %A      1     %A + 1+
--R     ]
--R                                      Type: List List Matrix FiniteField(2,2)
--E 22

--S 23 of 33
dA6d8a : List Matrix gf4  := sp4.1
 

   (23)
    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
    |                                                          |
    |  0       0       %A    %A + 1    %A      %A      0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1       %A      0       0     0 |
   [|                                                          |,
    |%A + 1    1       1       1       0       0     %A + 1  %A|
    |                                                          |
    |  0       0     %A + 1    1       0       0       %A    0 |
    |                                                          |
    |  1       0       1       1       0       0       0     0 |
    |                                                          |
    +  1       1       0       0       0       0       0     0 +
    +  1       0       %A      0       1       1       %A    %A + 1+
    |                                                              |
    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
    |                                                              |
    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
    |                                                              |
    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
    |                                                              |]
    |  1       0     %A + 1    0       1       1       %A      %A  |
    |                                                              |
    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
    |                                                              |
    |  0       0       1       0       0       1       0       1   |
    |                                                              |
    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (23)
--R    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
--R    |                                                          |
--R    |  0       0       %A    %A + 1    %A      %A      0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1       %A      0       0     0 |
--R   [|                                                          |,
--R    |%A + 1    1       1       1       0       0     %A + 1  %A|
--R    |                                                          |
--R    |  0       0     %A + 1    1       0       0       %A    0 |
--R    |                                                          |
--R    |  1       0       1       1       0       0       0     0 |
--R    |                                                          |
--R    +  1       1       0       0       0       0       0     0 +
--R    +  1       0       %A      0       1       1       %A    %A + 1+
--R    |                                                              |
--R    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
--R    |                                                              |
--R    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
--R    |                                                              |
--R    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
--R    |                                                              |]
--R    |  1       0     %A + 1    0       1       1       %A      %A  |
--R    |                                                              |
--R    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
--R    |                                                              |
--R    |  0       0       1       0       0       1       0       1   |
--R    |                                                              |
--R    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
--R                                           Type: List Matrix FiniteField(2,2)
--E 23

--S 24 of 33
dA6d8b : List Matrix gf4  := sp4.2
 

   (24)
    +0     1       1     %A + 1  0  0  0  0+
    |                                      |
    |1     1     %A + 1    0     0  0  0  0|
    |                                      |
    |%A    0       0       0     0  0  0  0|
    |                                      |
    |1     %A      0       0     0  0  0  0|
   [|                                      |,
    |%A  %A + 1    1       1     1  0  1  1|
    |                                      |
    |0     0       %A      1     0  1  0  1|
    |                                      |
    |%A    1       0       1     1  1  0  0|
    |                                      |
    +1     %A    %A + 1    %A    0  1  0  0+
    +%A + 1    1       %A      0       0     %A + 1    0       1   +
    |                                                              |
    |  0       %A      1       1       1       0     %A + 1    %A  |
    |                                                              |
    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
    |                                                              |
    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
    |                                                              |]
    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
    |                                                              |
    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
    |                                                              |
    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
    |                                                              |
    +  %A      %A      %A      1       %A      %A      1     %A + 1+
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (24)
--R    +0     1       1     %A + 1  0  0  0  0+
--R    |                                      |
--R    |1     1     %A + 1    0     0  0  0  0|
--R    |                                      |
--R    |%A    0       0       0     0  0  0  0|
--R    |                                      |
--R    |1     %A      0       0     0  0  0  0|
--R   [|                                      |,
--R    |%A  %A + 1    1       1     1  0  1  1|
--R    |                                      |
--R    |0     0       %A      1     0  1  0  1|
--R    |                                      |
--R    |%A    1       0       1     1  1  0  0|
--R    |                                      |
--R    +1     %A    %A + 1    %A    0  1  0  0+
--R    +%A + 1    1       %A      0       0     %A + 1    0       1   +
--R    |                                                              |
--R    |  0       %A      1       1       1       0     %A + 1    %A  |
--R    |                                                              |
--R    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
--R    |                                                              |
--R    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
--R    |                                                              |]
--R    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
--R    |                                                              |
--R    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
--R    |                                                              |
--R    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
--R    |                                                              |
--R    +  %A      %A      %A      1       %A      %A      1     %A + 1+
--R                                           Type: List Matrix FiniteField(2,2)
--E 24

--S 25 of 33 random generation, FAILURE OK.
isAbsolutelyIrreducible? dA6d8a
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (25)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (25)  true
--R                                                                Type: Boolean
--E 25

--S 26 of 33 random generation, FAILURE OK.
isAbsolutelyIrreducible? dA6d8b
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (26)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26

--S 27 of 33 random generation, FAILURE OK.
areEquivalent? ( dA6d8a, dA6d8b )
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     There is no isomorphism, as the only possible one
       fails to do the necessary base change

   Representations are not equivalent.

   (27)  [0]
                                                Type: Matrix FiniteField(2,2)
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     There is no isomorphism, as the only possible one
--R       fails to do the necessary base change
--R
--R   Representations are not equivalent.
--R
--R   (27)  [0]
--R                                                Type: Matrix FiniteField(2,2)
--E 27

--S 28 of 33
dA6d1
 

   (28)  [[1],[1]]
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (28)  [[1],[1]]
--R                                               Type: List Matrix PrimeField 2
--E 28

--S 29 of 33
dA6d4a
 

          +0  1  0  0+ +0  1  1  1+
          |          | |          |
          |0  0  1  0| |1  1  0  1|
   (29)  [|          |,|          |]
          |1  0  0  0| |1  1  1  0|
          |          | |          |
          +0  0  0  1+ +1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +0  1  0  0+ +0  1  1  1+
--R          |          | |          |
--R          |0  0  1  0| |1  1  0  1|
--R   (29)  [|          |,|          |]
--R          |1  0  0  0| |1  1  1  0|
--R          |          | |          |
--R          +0  0  0  1+ +1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 29

--S 30 of 33
dA6d4b
 

          +1  0  1  1+ +0  0  1  0+
          |          | |          |
          |0  1  0  1| |1  1  1  1|
   (30)  [|          |,|          |]
          |1  1  0  0| |1  0  1  1|
          |          | |          |
          +0  1  0  0+ +0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  1  1+ +0  0  1  0+
--R          |          | |          |
--R          |0  1  0  1| |1  1  1  1|
--R   (30)  [|          |,|          |]
--R          |1  1  0  0| |1  0  1  1|
--R          |          | |          |
--R          +0  1  0  0+ +0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 30

--S 31 of 33
dA6d8a
 

   (31)
    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
    |                                                          |
    |  0       0       %A    %A + 1    %A      %A      0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1       %A      0       0     0 |
   [|                                                          |,
    |%A + 1    1       1       1       0       0     %A + 1  %A|
    |                                                          |
    |  0       0     %A + 1    1       0       0       %A    0 |
    |                                                          |
    |  1       0       1       1       0       0       0     0 |
    |                                                          |
    +  1       1       0       0       0       0       0     0 +
    +  1       0       %A      0       1       1       %A    %A + 1+
    |                                                              |
    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
    |                                                              |
    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
    |                                                              |
    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
    |                                                              |]
    |  1       0     %A + 1    0       1       1       %A      %A  |
    |                                                              |
    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
    |                                                              |
    |  0       0       1       0       0       1       0       1   |
    |                                                              |
    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (31)
--R    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
--R    |                                                          |
--R    |  0       0       %A    %A + 1    %A      %A      0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1       %A      0       0     0 |
--R   [|                                                          |,
--R    |%A + 1    1       1       1       0       0     %A + 1  %A|
--R    |                                                          |
--R    |  0       0     %A + 1    1       0       0       %A    0 |
--R    |                                                          |
--R    |  1       0       1       1       0       0       0     0 |
--R    |                                                          |
--R    +  1       1       0       0       0       0       0     0 +
--R    +  1       0       %A      0       1       1       %A    %A + 1+
--R    |                                                              |
--R    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
--R    |                                                              |
--R    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
--R    |                                                              |
--R    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
--R    |                                                              |]
--R    |  1       0     %A + 1    0       1       1       %A      %A  |
--R    |                                                              |
--R    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
--R    |                                                              |
--R    |  0       0       1       0       0       1       0       1   |
--R    |                                                              |
--R    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
--R                                           Type: List Matrix FiniteField(2,2)
--E 31

--S 32 of 33
dA6d8b
 

   (32)
    +0     1       1     %A + 1  0  0  0  0+
    |                                      |
    |1     1     %A + 1    0     0  0  0  0|
    |                                      |
    |%A    0       0       0     0  0  0  0|
    |                                      |
    |1     %A      0       0     0  0  0  0|
   [|                                      |,
    |%A  %A + 1    1       1     1  0  1  1|
    |                                      |
    |0     0       %A      1     0  1  0  1|
    |                                      |
    |%A    1       0       1     1  1  0  0|
    |                                      |
    +1     %A    %A + 1    %A    0  1  0  0+
    +%A + 1    1       %A      0       0     %A + 1    0       1   +
    |                                                              |
    |  0       %A      1       1       1       0     %A + 1    %A  |
    |                                                              |
    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
    |                                                              |
    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
    |                                                              |]
    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
    |                                                              |
    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
    |                                                              |
    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
    |                                                              |
    +  %A      %A      %A      1       %A      %A      1     %A + 1+
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (32)
--R    +0     1       1     %A + 1  0  0  0  0+
--R    |                                      |
--R    |1     1     %A + 1    0     0  0  0  0|
--R    |                                      |
--R    |%A    0       0       0     0  0  0  0|
--R    |                                      |
--R    |1     %A      0       0     0  0  0  0|
--R   [|                                      |,
--R    |%A  %A + 1    1       1     1  0  1  1|
--R    |                                      |
--R    |0     0       %A      1     0  1  0  1|
--R    |                                      |
--R    |%A    1       0       1     1  1  0  0|
--R    |                                      |
--R    +1     %A    %A + 1    %A    0  1  0  0+
--R    +%A + 1    1       %A      0       0     %A + 1    0       1   +
--R    |                                                              |
--R    |  0       %A      1       1       1       0     %A + 1    %A  |
--R    |                                                              |
--R    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
--R    |                                                              |
--R    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
--R    |                                                              |]
--R    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
--R    |                                                              |
--R    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
--R    |                                                              |
--R    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
--R    |                                                              |
--R    +  %A      %A      %A      1       %A      %A      1     %A + 1+
--R                                           Type: List Matrix FiniteField(2,2)
--E 32

--S 33 of 33
dA6d16
 

   (33)
    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
    |                                              |
    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
   [|                                              |,
    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
    |                                              |
    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
    |                                              |
    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
    |                                              |
    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
    |                                              |]
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
    |                                              |
    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (33)
--R    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R   [|                                              |,
--R    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
--R    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
--R    |                                              |
--R    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R    |                                              |]
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 33
)spool 
 
Starts dribbling to series.output (2009/2/17, 18:0:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1
\section{Expression To Power Series}
 
   There are no library operations named Power 
      Use HyperDoc Browse or issue
                               )what op Power
      to learn if there is any operation containing " Power " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named Power
      with argument type(s) 
                               Variable Series
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
We compute series expansions of various functions using EXPR2UPS.
 
  Line   7: We compute series expansions of various functions using EXPR2UPS.
           ................................................................A
  Error  A: syntax error at top level
  Error  A: Improper syntax.
   2 error(s) parsing 

Test functions in EXPR2UPS:
 
  Line   8: 
  Line   9: Test functions in EXPR2UPS:
           ...............A
  Error  A: Improper syntax.
   1 error(s) parsing 
--S 1 of 17
xT := taylor(x)
 

   (1)  x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 17
sin(tan(xT))
 

            1  3    1  5    55   7    143  9      11
   (2)  x + - x  - -- x  - ---- x  - ---- x  + O(x  )
            6      40      1008      3456
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1  5    55   7    143  9      11
--R   (2)  x + - x  - -- x  - ---- x  - ---- x  + O(x  )
--R            6      40      1008      3456
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 2

--S 3 of 17
taylor(asec(2+x))
 

   (3)
                 1          7    2     13    3      205    4      1069    5
     asec(2) + ----- x - ------ x  + ------ x  - -------- x  + --------- x
                 +-+        +-+         +-+           +-+            +-+
               2\|3      24\|3       72\|3       1728\|3       12960\|3
   + 
          1877    6      10043    7      54593     8      33437     9
     - --------- x  + ---------- x  - ----------- x  + ----------- x
             +-+             +-+              +-+              +-+
       31104\|3       217728\|3       1492992\|3       1119744\|3
   + 
          5034373     10      11
     - ------------- x   + O(x  )
                 +-+
       201553920\|3
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (3)
--R                 1          7    2     13    3      205    4      1069    5
--R     asec(2) + ----- x - ------ x  + ------ x  - -------- x  + --------- x
--R                 +-+        +-+         +-+           +-+            +-+
--R               2\|3      24\|3       72\|3       1728\|3       12960\|3
--R   + 
--R          1877    6      10043    7      54593     8      33437     9
--R     - --------- x  + ---------- x  - ----------- x  + ----------- x
--R             +-+             +-+              +-+              +-+
--R       31104\|3       217728\|3       1492992\|3       1119744\|3
--R   + 
--R          5034373     10      11
--R     - ------------- x   + O(x  )
--R                 +-+
--R       201553920\|3
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 17
sec %
 

                   11
   (4)  2 + x + O(x  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R                   11
--R   (4)  2 + x + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 17
taylor(sin(x),x = %pi/4)
 

   (5)
      +-+    +-+              +-+               +-+               +-+
     \|2    \|2       %pi    \|2       %pi 2   \|2       %pi 3   \|2       %pi 4
     ---- + ---- (x - ---) - ---- (x - ---)  - ---- (x - ---)  + ---- (x - ---)
       2      2        4       4        4       12        4       48        4
   + 
      +-+               +-+                +-+                +-+
     \|2       %pi 5   \|2       %pi 6    \|2       %pi 7    \|2       %pi 8
     ---- (x - ---)  - ---- (x - ---)  - ----- (x - ---)  + ----- (x - ---)
      240       4      1440       4      10080       4      80640       4
   + 
       +-+                  +-+
      \|2        %pi 9     \|2        %pi 10          %pi 11
     ------ (x - ---)  - ------- (x - ---)   + O((x - ---)  )
     725760       4      7257600       4               4
                      Type: UnivariateTaylorSeries(Expression Integer,x,pi/4)
--R 
--R
--R   (5)
--R      +-+    +-+              +-+               +-+               +-+
--R     \|2    \|2       %pi    \|2       %pi 2   \|2       %pi 3   \|2       %pi 4
--R     ---- + ---- (x - ---) - ---- (x - ---)  - ---- (x - ---)  + ---- (x - ---)
--R       2      2        4       4        4       12        4       48        4
--R   + 
--R      +-+               +-+                +-+                +-+
--R     \|2       %pi 5   \|2       %pi 6    \|2       %pi 7    \|2       %pi 8
--R     ---- (x - ---)  - ---- (x - ---)  - ----- (x - ---)  + ----- (x - ---)
--R      240       4      1440       4      10080       4      80640       4
--R   + 
--R       +-+                  +-+
--R      \|2        %pi 9     \|2        %pi 10          %pi 11
--R     ------ (x - ---)  - ------- (x - ---)   + O((x - ---)  )
--R     725760       4      7257600       4               4
--R                      Type: UnivariateTaylorSeries(Expression Integer,x,pi/4)
--E 5

--S 6 of 17
xL := laurent(x)
 

   (6)  x
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R   (6)  x
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 6

--S 7 of 17
1/xL - cot(xL)
 

        1      1  3    2   5     1   7     2    9      1382    11      12
   (7)  - x + -- x  + --- x  + ---- x  + ----- x  + --------- x   + O(x  )
        3     45      945      4725      93555      638512875
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R        1      1  3    2   5     1   7     2    9      1382    11      12
--R   (7)  - x + -- x  + --- x  + ---- x  + ----- x  + --------- x   + O(x  )
--R        3     45      945      4725      93555      638512875
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 7

--S 8 of 17
laurent(csc(x))
 

         - 1   1      7   3     31   5     127   7      73    9      10
   (8)  x    + - x + --- x  + ----- x  + ------ x  + ------- x  + O(x  )
               6     360      15120      604800      3421440
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R         - 1   1      7   3     31   5     127   7      73    9      10
--R   (8)  x    + - x + --- x  + ----- x  + ------ x  + ------- x  + O(x  )
--R               6     360      15120      604800      3421440
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 8

--S 9 of 17
laurent(1/log(x),x = 1)
 

   (9)
            - 1   1    1            1        2    19        3    3         4
     (x - 1)    + - - -- (x - 1) + -- (x - 1)  - --- (x - 1)  + --- (x - 1)
                  2   12           24            720            160
   + 
        863         5    275         6    33953         7     8183         8
     - ----- (x - 1)  + ----- (x - 1)  - ------- (x - 1)  + ------- (x - 1)
       60480            24192            3628800            1036800
   + 
        3250433         9            10
     - --------- (x - 1)  + O((x - 1)  )
       479001600
                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--R 
--R
--R   (9)
--R            - 1   1    1            1        2    19        3    3         4
--R     (x - 1)    + - - -- (x - 1) + -- (x - 1)  - --- (x - 1)  + --- (x - 1)
--R                  2   12           24            720            160
--R   + 
--R        863         5    275         6    33953         7     8183         8
--R     - ----- (x - 1)  + ----- (x - 1)  - ------- (x - 1)  + ------- (x - 1)
--R       60480            24192            3628800            1036800
--R   + 
--R        3250433         9            10
--R     - --------- (x - 1)  + O((x - 1)  )
--R       479001600
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--E 9

--S 10 of 17
xP := puiseux(x)
 

   (10)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (10)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 10

--S 11 of 17
sqrt(xP) - sqrt(sin(xP))
 

             5         9          13
             -         -          --
          1  2     1   2     1     2      8
   (11)  -- x  - ---- x  + ----- x   + O(x )
         12      1440      24192
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             5         9          13
--R             -         -          --
--R          1  2     1   2     1     2      8
--R   (11)  -- x  - ---- x  + ----- x   + O(x )
--R         12      1440      24192
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11

--S 12 of 17
puiseux(sqrt(1 - cos(x))/x)
 

   (12)
       1       1    2       1     4        1      6         1       8
     ---- - ------ x  + -------- x  - ---------- x  + ------------ x
      +-+      +-+           +-+             +-+               +-+
     \|2    24\|2       1920\|2       322560\|2       92897280\|2
   + 
              1         10      11
     - --------------- x   + O(x  )
                   +-+
       40874803200\|2
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (12)
--R       1       1    2       1     4        1      6         1       8
--R     ---- - ------ x  + -------- x  - ---------- x  + ------------ x
--R      +-+      +-+           +-+             +-+               +-+
--R     \|2    24\|2       1920\|2       322560\|2       92897280\|2
--R   + 
--R              1         10      11
--R     - --------------- x   + O(x  )
--R                   +-+
--R       40874803200\|2
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 12

--S 13 of 17
puiseux(sqrt(1 - tan(x)),x = %pi/2)
 

   (13)
                1              1               3               5
              - -              -               -               -
          %pi   2   1      %pi 2    7      %pi 2    7      %pi 2
     (x - ---)    + - (x - ---)  - -- (x - ---)  + -- (x - ---)
           2        2       2      24       2      48       2
   + 
                    7                  9
                    -                  -
        81      %pi 2    1219      %pi 2          %pi 5
     - --- (x - ---)  + ----- (x - ---)  + O((x - ---) )
       640       2      11520       2              2
                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--R 
--R
--R   (13)
--R                1              1               3               5
--R              - -              -               -               -
--R          %pi   2   1      %pi 2    7      %pi 2    7      %pi 2
--R     (x - ---)    + - (x - ---)  - -- (x - ---)  + -- (x - ---)
--R           2        2       2      24       2      48       2
--R   + 
--R                    7                  9
--R                    -                  -
--R        81      %pi 2    1219      %pi 2          %pi 5
--R     - --- (x - ---)  + ----- (x - ---)  + O((x - ---) )
--R       640       2      11520       2              2
--R                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--E 13

--S 14 of 17
xS := series(x)
 

   (14)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (14)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 14

--S 15 of 17
sin(xS)**(1/3) - sin(xS**(1/3))
 

   (15)
              5        7                         11               13      14
              -        -                         --               --      --
   1      1   3    31  3      1    3       1      3     1921921    3       3
   - x - --- x  - --- x  - ------ x  + -------- x   - ---------- x   + O(x  )
   6     120      560      362880      39916800       6227020800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (15)
--R              5        7                         11               13      14
--R              -        -                         --               --      --
--R   1      1   3    31  3      1    3       1      3     1921921    3       3
--R   - x - --- x  - --- x  - ------ x  + -------- x   - ---------- x   + O(x  )
--R   6     120      560      362880      39916800       6227020800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 15

--S 16 of 17
series(log(tan(x)))
 

                  1  2    7  4    62   6    127   8    146   10      11
   (16)  log(x) + - x  + -- x  + ---- x  + ----- x  + ----- x   + O(x  )
                  3      90      2835      18900      66825
                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--R 
--R
--R                  1  2    7  4    62   6    127   8    146   10      11
--R   (16)  log(x) + - x  + -- x  + ---- x  + ----- x  + ----- x   + O(x  )
--R                  3      90      2835      18900      66825
--R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--E 16

--S 17 of 17
series(log(cot(x)),x = %pi/2)
 

   (17)
         - 2x + %pi    1      %pi 2    7      %pi 4    62       %pi 6
     log(----------) + - (x - ---)  + -- (x - ---)  + ---- (x - ---)
              2        3       2      90       2      2835       2
   + 
      127       %pi 8    146       %pi 10          %pi 11
     ----- (x - ---)  + ----- (x - ---)   + O((x - ---)  )
     18900       2      66825       2               2
                Type: GeneralUnivariatePowerSeries(Expression Integer,x,pi/2)
--R 
--R
--R   (17)
--R         - 2x + %pi    1      %pi 2    7      %pi 4    62       %pi 6
--R     log(----------) + - (x - ---)  + -- (x - ---)  + ---- (x - ---)
--R              2        3       2      90       2      2835       2
--R   + 
--R      127       %pi 8    146       %pi 10          %pi 11
--R     ----- (x - ---)  + ----- (x - ---)   + O((x - ---)  )
--R     18900       2      66825       2               2
--R                Type: GeneralUnivariatePowerSeries(Expression Integer,x,pi/2)
--E 17
)spool 
 
Starts dribbling to intef2.output (2009/2/17, 17:46:42).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1  of 10
(a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x)
 

                        a x + b
   (1)  --------------------------------------
         2        2         2          2 3
        b x log(x)  + 2a b x log(x) + a x  + x
                                                     Type: Expression Integer
--R 
--R
--R                        a x + b
--R   (1)  --------------------------------------
--R         2        2         2          2 3
--R        b x log(x)  + 2a b x log(x) + a x  + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 10
integrate(%,x)
 

   (2)  atan(b log(x) + a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)  atan(b log(x) + a x)
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 10
((exp(x)-x**2+2*x)/(x**2*(exp(x)+x)**2))*exp((x**2-1)/x+1/(exp(x)+x))
 

                           2       x    3
                         (x  - 1)%e  + x
                         ----------------
                                x    2
           x    2           x %e  + x
        (%e  - x  + 2x)%e
   (3)  ---------------------------------
               2   x 2     3  x    4
              x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R                           2       x    3
--R                         (x  - 1)%e  + x
--R                         ----------------
--R                                x    2
--R           x    2           x %e  + x
--R        (%e  - x  + 2x)%e
--R   (3)  ---------------------------------
--R               2   x 2     3  x    4
--R              x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 3

--S 4 of 10
integrate(%,x)
 

            2       x    3
          (x  - 1)%e  + x
          ----------------
                 x    2
             x %e  + x
        %e
   (4)  ------------------
                  x
                %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2       x    3
--R          (x  - 1)%e  + x
--R          ----------------
--R                 x    2
--R             x %e  + x
--R        %e
--R   (4)  ------------------
--R                  x
--R                %e
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 10
x * cot x
 

   (5)  x cot(x)
                                                     Type: Expression Integer
--R 
--R
--R   (5)  x cot(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 10
integrate(%,x)
 

           x
         ++
   (6)   |   %J cot(%J)d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--R   (6)   |   %J cot(%J)d%J
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 10
tan x + cos x
 

   (7)  tan(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (7)  tan(x) + cos(x)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 10
integrate(%,x)
 

                 2                2cos(x)
   (8)  log(----------) - log(- ----------) + sin(x)
            cos(x) + 1          cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2                2cos(x)
--R   (8)  log(----------) - log(- ----------) + sin(x)
--R            cos(x) + 1          cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 10
cosh(a*x)*sinh(a*x)
 

   (9)  cosh(a x)sinh(a x)
                                                     Type: Expression Integer
--R 
--R
--R   (9)  cosh(a x)sinh(a x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 10
integrate(%,x)
 

                  2            2
         sinh(a x)  + cosh(a x)
   (10)  -----------------------
                    4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2            2
--R         sinh(a x)  + cosh(a x)
--R   (10)  -----------------------
--R                    4a
--R                                          Type: Union(Expression Integer,...)
--E 10
)spool 
 
Starts dribbling to nlode.output (2009/2/17, 17:55:32).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 16
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 16
deq := (sin y x - x / y(x)) * differentiate(y x, x) = 1
 

                            ,
        (y(x)sin(y(x)) - x)y (x)

   (2)  ------------------------= 1
                  y(x)
                                            Type: Equation Expression Integer
--R 
--R
--R                            ,
--R        (y(x)sin(y(x)) - x)y (x)
--R
--R   (2)  ------------------------= 1
--R                  y(x)
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 16
solve(deq, y, x)
 

   (3)  sin(y(x)) - y(x)cos(y(x)) - x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (3)  sin(y(x)) - y(x)cos(y(x)) - x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 16
deq := differentiate(y x, x) = y(x) / (x + y(x) * log y x)
 

         ,            y(x)
   (4)  y (x)= -----------------
               y(x)log(y(x)) + x
                                            Type: Equation Expression Integer
--R 
--R
--R         ,            y(x)
--R   (4)  y (x)= -----------------
--R               y(x)log(y(x)) + x
--R                                            Type: Equation Expression Integer
--E 4

--S 5 of 16
solve(deq, y, x)
 

                     2
        y(x)log(y(x))  - 2x
   (5)  -------------------
               2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R        y(x)log(y(x))  - 2x
--R   (5)  -------------------
--R               2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 16
solve(deq, y, x = 1, [1])
 

                     2
        y(x)log(y(x))  + 2y(x) - 2x
   (6)  ---------------------------
                   2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R        y(x)log(y(x))  + 2y(x) - 2x
--R   (6)  ---------------------------
--R                   2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 16
deq := (exp(- 2 * y x) - 2 * x * y x) * differentiate(y x, x) = y x
 

           - 2y(x)            ,
   (7)  (%e        - 2x y(x))y (x)= y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R           - 2y(x)            ,
--R   (7)  (%e        - 2x y(x))y (x)= y(x)
--R
--R                                            Type: Equation Expression Integer
--E 7

--S 8 of 16
solve(deq, y, x)
 

                        2y(x)
   (8)  log(y(x)) - x %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2y(x)
--R   (8)  log(y(x)) - x %e
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 16
deq := differentiate(y x, x) = w + y(x) / (1 - y x)
 

         ,     (w - 1)y(x) - w
   (9)  y (x)= ---------------
                   y(x) - 1
                                            Type: Equation Expression Integer
--R 
--R
--R         ,     (w - 1)y(x) - w
--R   (9)  y (x)= ---------------
--R                   y(x) - 1
--R                                            Type: Equation Expression Integer
--E 9

--S 10 of 16
solve(deq, y, x = 0, [0])
 

                                                             2
         log((w - 1)y(x) - w) - log(- w) + (w - 1)y(x) + (- w  + 2w - 1)x
   (10)  ----------------------------------------------------------------
                                     2
                                    w  - 2w + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                             2
--R         log((w - 1)y(x) - w) - log(- w) + (w - 1)y(x) + (- w  + 2w - 1)x
--R   (10)  ----------------------------------------------------------------
--R                                     2
--R                                    w  - 2w + 1
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 16
deq := x**2 * differentiate(y x, x) + 2 * x * y x - y(x)**3
 

          2 ,          3
   (11)  x y (x) - y(x)  + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          2 ,          3
--R   (11)  x y (x) - y(x)  + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 11

--S 12 of 16
solve(deq, y, x)
 

              5         2
         (- 3x  - 2)y(x)  + 5x
   (12)  ---------------------
                  5    2
                5x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              5         2
--R         (- 3x  - 2)y(x)  + 5x
--R   (12)  ---------------------
--R                  5    2
--R                5x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 16
deq := differentiate(y x,x) = 1 + x**2 - 2 * x * y x + y(x)**2
 

          ,         2              2
   (13)  y (x)= y(x)  - 2x y(x) + x  + 1

                                            Type: Equation Expression Integer
--R 
--R
--R          ,         2              2
--R   (13)  y (x)= y(x)  - 2x y(x) + x  + 1
--R
--R                                            Type: Equation Expression Integer
--E 13

--S 14 of 16
solve(deq, y, x)
 

            - y(x) + x
   (14)  ---------------
                   2
         x y(x) - x  + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            - y(x) + x
--R   (14)  ---------------
--R                   2
--R         x y(x) - x  + 1
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 16
deq := x**2 * differentiate(y x,x) = -1 - x * y x + x**2 * y(x)**2
 

          2 ,      2    2
   (15)  x y (x)= x y(x)  - x y(x) - 1

                                            Type: Equation Expression Integer
--R 
--R
--R          2 ,      2    2
--R   (15)  x y (x)= x y(x)  - x y(x) - 1
--R
--R                                            Type: Equation Expression Integer
--E 15

--S 16 of 16
solve(deq, y, x)
 

               3              2
           (- x  - 8x)y(x) - x  + 8
   (16)  ----------------------------
             3                 2
         (18x  - 18x)y(x) + 18x  + 18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3              2
--R           (- x  - 8x)y(x) - x  + 8
--R   (16)  ----------------------------
--R             3                 2
--R         (18x  - 18x)y(x) + 18x  + 18
--R                                          Type: Union(Expression Integer,...)
--E 16
)spool 
 
Starts dribbling to ch.output (2009/2/17, 17:44:7).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--Cyclohexan

--S 1  of 7
mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) :=_
  [[0,1,1,1,1,1],[1,0,1,8/3,x,8/3],[1,1,0,1,8/3,y],_
   [1,8/3,1,0,1,8/3],[1,x,8/3,1,0,1],[1,8/3,y,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  x  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  y|
        |            3   |
        |                |
   (1)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  x  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  y  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  x  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  y|
--R        |            3   |
--R        |                |
--R   (1)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  x  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  y  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 1

--S 2 of 7
fzn := determinant mfzn
 

   (2)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (2)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 2

--S 3 of 7
mfxn : SQMATRIX(6,DMP([x,y,z],Fraction Integer)) :=_
  [[0,1,1,1,1,1],[1,0,1,8/3,y,8/3],[1,1,0,1,8/3,z],_
   [1,8/3,1,0,1,8/3],[1,y,8/3,1,0,1],[1,8/3,z,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  y  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  z|
        |            3   |
        |                |
   (3)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  y  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  z  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  y  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  z|
--R        |            3   |
--R        |                |
--R   (3)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  y  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  z  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 3

--S 4 of 7
fxn := determinant mfxn
 

   (4)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - y z  + -- y z - -- y  + -- y z  - --- y z - --- y - -- z  - --- z + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (4)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - y z  + -- y z - -- y  + -- y z  - --- y z - --- y - -- z  - --- z + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 4

--S 5 of 7
mfyn : SQMATRIX(6,DMP([x,y,z],Fraction Integer)) :=_
  [[0,1,1,1,1,1],[1,0,1,8/3,z,8/3],[1,1,0,1,8/3,x],_
   [1,8/3,1,0,1,8/3],[1,z,8/3,1,0,1],[1,8/3,x,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  z  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  x|
        |            3   |
        |                |
   (5)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  z  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  x  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  z  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  x|
--R        |            3   |
--R        |                |
--R   (5)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  z  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  x  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 5

--S 6 of 7
fyn := determinant mfyn
 

   (6)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x z  + -- x z - -- x  + -- x z  - --- x z - --- x - -- z  - --- z + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (6)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x z  + -- x z - -- x  + -- x z  - --- x z - --- x - -- z  - --- z + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 6

--S 7 of 7
gb := groebnerFactorize [fxn,fyn,fzn] 
 

   (7)
   [
                  22           22     22     121
     [x y + x z - -- x + y z - -- y - -- z + ---,
                   3            3      3      3
         2   22       25        2   22       25     22  2   388     250
      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
              3        9             3        9      3       9       27
       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
              3        9       3         9         27      9       27       81
     ,
             21994  2   21994     4427     463
    [x + y - -----,y  - ----- y + ----,z - ---],
              5625       5625      675      87
      2   1       11     5     265        2   38     265
    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
          2        2     6      18             3      9
         25     11     11        11     11     11        5     5     5
    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
          9      3      3         3      3      3        3     3     3
         19     5     5
    [x - --,y + -,z + -]]
          3     3     3
  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (7)
--R   [
--R                  22           22     22     121
--R     [x y + x z - -- x + y z - -- y - -- z + ---,
--R                   3            3      3      3
--R         2   22       25        2   22       25     22  2   388     250
--R      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
--R              3        9             3        9      3       9       27
--R       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
--R              3        9       3         9         27      9       27       81
--R     ,
--R             21994  2   21994     4427     463
--R    [x + y - -----,y  - ----- y + ----,z - ---],
--R              5625       5625      675      87
--R      2   1       11     5     265        2   38     265
--R    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
--R          2        2     6      18             3      9
--R         25     11     11        11     11     11        5     5     5
--R    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
--R          9      3      3         3      3      3        3     3     3
--R         19     5     5
--R    [x - --,y + -,z + -]]
--R          3     3     3
--R  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 7
)spool
 
Starts dribbling to easter.output (2009/2/17, 17:45:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

)set break resume
 
)set messages time off
 
)set quit unprotected
 
)set streams calculate 7
 
 
--S 1 of 200
factorial(50)
 

   (1)  30414093201713378043612608166064768844377641568960512000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  30414093201713378043612608166064768844377641568960512000000000000
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 200
factor(%)
 

         47 22 12 8  4  3  2  2  2
   (2)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
                                                       Type: Factored Integer
--R 
--R
--R         47 22 12 8  4  3  2  2  2
--R   (2)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
--R                                                       Type: Factored Integer
--E 2

--S 3 of 200
1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10
 

        4861
   (3)  ----
        2520
                                                       Type: Fraction Integer
--R 
--R
--R        4861
--R   (3)  ----
--R        2520
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 200
digits(50);
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 200
exp(sqrt(163.)*%pi)
 

   (5)  26253741 2640768743.9999999999 9925007259 7198185688 9
                                                                  Type: Float
--R 
--R
--R   (5)  26253741 2640768743.9999999999 9925007259 7198185688 9
--R                                                                  Type: Float
--E 5

--S 6 of 200
digits(20);
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 200
besselJ(2, 1 + %i)
 

   (7)  0.041579886943962127 + 0.24739764151330626%i
                                                    Type: Complex DoubleFloat
--R 
--R
--R   (7)  4.1579886943962155E-2 + 0.24739764151330637 %i
--R                                                    Type: Complex DoubleFloat
--E 7

--S 8 of 200
decimal(1/7)
 

          ______
   (8)  0.142857
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (8)  0.142857
--R                                                       Type: DecimalExpansion
--E 8

--S 9 of 200
continuedFraction(3.1415926535)
 

              1 |     1  |     1 |      1  |     1 |     1 |     1 |
   (9)  3 + +---+ + +----+ + +---+ + +-----+ + +---+ + +---+ + +---+ + ...
            | 7     | 15     | 1     | 292     | 1     | 1     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |      1  |     1 |     1 |     1 |
--R   (9)  3 + +---+ + +----+ + +---+ + +-----+ + +---+ + +---+ + +---+ + ...
--R            | 7     | 15     | 1     | 292     | 1     | 1     | 6
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 200
sqrt(2*sqrt(3) + 4)
 

          +---------+
          |  +-+
   (10)  \|2\|3  + 4
                                                        Type: AlgebraicNumber
--R 
--R
--R          +---------+
--R          |  +-+
--R   (10)  \|2\|3  + 4
--R                                                        Type: AlgebraicNumber
--E 10

--S 11 of 200
simplify(%)
 

          +---------+
          |  +-+
   (11)  \|2\|3  + 4
                                                     Type: Expression Integer
--R 
--R
--R          +---------+
--R          |  +-+
--R   (11)  \|2\|3  + 4
--R                                                     Type: Expression Integer
--E 11

--S 12 of 200
sqrt(14 + 3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2)))))
 

          +---------------------------------------+
          |  +------------------------------+
          |  |  +----------------------+
          |  |  |     +-----------+
          |  |  |     |    +-+
   (12)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
                                                        Type: AlgebraicNumber
--R 
--R
--R          +---------------------------------------+
--R          |  +------------------------------+
--R          |  |  +----------------------+
--R          |  |  |     +-----------+
--R          |  |  |     |    +-+
--R   (12)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
--R                                                        Type: AlgebraicNumber
--E 12

--S 13 of 200
simplify(%)
 

          +---------------------------------------+
          |  +------------------------------+
          |  |  +----------------------+
          |  |  |     +-----------+
          |  |  |     |    +-+
   (13)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
                                                     Type: Expression Integer
--R 
--R
--R          +---------------------------------------+
--R          |  +------------------------------+
--R          |  |  +----------------------+
--R          |  |  |     +-----------+
--R          |  |  |     |    +-+
--R   (13)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
--R                                                     Type: Expression Integer
--E 13

--S 14 of 200
2*Aleph(0) - 3
 

   (14)  Aleph(0)
                                              Type: Union(CardinalNumber,...)
--R 
--R
--R   (14)  Aleph(0)
--R                                              Type: Union(CardinalNumber,...)
--E 14

--S 15 of 200
(x**2 - 4)/(x**2 + 4*x + 4)
 

         x - 2
   (15)  -----
         x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         x - 2
--R   (15)  -----
--R         x + 2
--R                                            Type: Fraction Polynomial Integer
--E 15

--S 16 of 200
(%e**x - 1)/(%e**(x/2) + 1)
 

           x
         %e  - 1
   (16)  -------
           x
           -
           2
         %e  + 1
                                                     Type: Expression Integer
--R 
--R
--R           x
--R         %e  - 1
--R   (16)  -------
--R           x
--R           -
--R           2
--R         %e  + 1
--R                                                     Type: Expression Integer
--E 16

--S 17 of 200
normalize(%)
 

           x
           -
           2
   (17)  %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R           x
--R           -
--R           2
--R   (17)  %e  - 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 200
(x + 1)**20
 

   (18)
      20      19       18        17        16         15         14         13
     x   + 20x   + 190x   + 1140x   + 4845x   + 15504x   + 38760x   + 77520x
   + 
            12          11          10          9          8         7         6
     125970x   + 167960x   + 184756x   + 167960x  + 125970x  + 77520x  + 38760x
   + 
           5        4        3       2
     15504x  + 4845x  + 1140x  + 190x  + 20x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (18)
--R      20      19       18        17        16         15         14         13
--R     x   + 20x   + 190x   + 1140x   + 4845x   + 15504x   + 38760x   + 77520x
--R   + 
--R            12          11          10          9          8         7         6
--R     125970x   + 167960x   + 184756x   + 167960x  + 125970x  + 77520x  + 38760x
--R   + 
--R           5        4        3       2
--R     15504x  + 4845x  + 1140x  + 190x  + 20x + 1
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 200
D(%, x)
 

   (19)
        19       18        17         16         15          14          13
     20x   + 380x   + 3420x   + 19380x   + 77520x   + 232560x   + 542640x
   + 
             12           11           10           9           8           7
     1007760x   + 1511640x   + 1847560x   + 1847560x  + 1511640x  + 1007760x
   + 
            6          5         4         3        2
     542640x  + 232560x  + 77520x  + 19380x  + 3420x  + 380x + 20
                                                     Type: Polynomial Integer
--R 
--R
--R   (19)
--R        19       18        17         16         15          14          13
--R     20x   + 380x   + 3420x   + 19380x   + 77520x   + 232560x   + 542640x
--R   + 
--R             12           11           10           9           8           7
--R     1007760x   + 1511640x   + 1847560x   + 1847560x  + 1511640x  + 1007760x
--R   + 
--R            6          5         4         3        2
--R     542640x  + 232560x  + 77520x  + 19380x  + 3420x  + 380x + 20
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 200
factor(%)
 

                  19
   (20)  20(x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  19
--R   (20)  20(x + 1)
--R                                            Type: Factored Polynomial Integer
--E 20

--S 21 of 200
x**100 - 1
 

          100
   (21)  x    - 1
                                                     Type: Polynomial Integer
--R 
--R
--R          100
--R   (21)  x    - 1
--R                                                     Type: Polynomial Integer
--E 21

--S 22 of 200
factor(%)
 

   (22)
                     2       4    3    2           4    3    2
     (x - 1)(x + 1)(x  + 1)(x  - x  + x  - x + 1)(x  + x  + x  + x + 1)
  *
       8    6    4    2       20    15    10    5       20    15    10    5
     (x  - x  + x  - x  + 1)(x   - x   + x   - x  + 1)(x   + x   + x   + x  + 1)
  *
       40    30    20    10
     (x   - x   + x   - x   + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (22)
--R                     2       4    3    2           4    3    2
--R     (x - 1)(x + 1)(x  + 1)(x  - x  + x  - x + 1)(x  + x  + x  + x + 1)
--R  *
--R       8    6    4    2       20    15    10    5       20    15    10    5
--R     (x  - x  + x  - x  + 1)(x   - x   + x   - x  + 1)(x   + x   + x   + x  + 1)
--R  *
--R       40    30    20    10
--R     (x   - x   + x   - x   + 1)
--R                                            Type: Factored Polynomial Integer
--E 22

--S 23 of 200
p:= x**4 - 3*x**2 + 1
 

          4     2
   (23)  x  - 3x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          4     2
--R   (23)  x  - 3x  + 1
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 200
factor(p)
 

           2           2
   (24)  (x  - x - 1)(x  + x - 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R           2           2
--R   (24)  (x  - x - 1)(x  + x - 1)
--R                                            Type: Factored Polynomial Integer
--E 24

--S 25 of 200
phi:= rootOf(phi**2 - phi - 1);
 

                                                        Type: AlgebraicNumber
--R 
--R
--R                                                        Type: AlgebraicNumber
--E 25

--S 26 of 200
factor(p, [phi])
 

   (26)  (x - phi)(x - phi + 1)(x + phi - 1)(x + phi)
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R   (26)  (x - phi)(x - phi + 1)(x + phi - 1)(x + phi)
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 26

--S 27 of 200
factor(p :: Polynomial(PrimeField(5)))
 

                2       2
   (27)  (x + 2) (x + 3)
                                       Type: Factored Polynomial PrimeField 5
--R 
--R
--R                2       2
--R   (27)  (x + 2) (x + 3)
--R                                       Type: Factored Polynomial PrimeField 5
--E 27

--S 28 of 200
expand(%)
 

          4     2
   (28)  x  + 2x  + 1
                                                Type: Polynomial PrimeField 5
--R 
--R
--R          4     2
--R   (28)  x  + 2x  + 1
--R                                                Type: Polynomial PrimeField 5
--E 28

--S 29 of 200
(x**2 + 2*x + 3)/(x**3 + 4*x**2 + 5*x + 2)
 

             2
            x  + 2x + 3
   (29)  -----------------
          3     2
         x  + 4x  + 5x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             2
--R            x  + 2x + 3
--R   (29)  -----------------
--R          3     2
--R         x  + 4x  + 5x + 2
--R                                            Type: Fraction Polynomial Integer
--E 29

--S 30 of 200
padicFraction(
   partialFraction(numerator(%) :: UnivariatePolynomial(x, Fraction Integer),
                   factor(denominator(%) :: Polynomial Integer) ::
                      Factored UnivariatePolynomial(x, Fraction Integer)))
 

             2         2        3
   (30)  - ----- + -------- + -----
           x + 1          2   x + 2
                   (x + 1)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             2         2        3
--R   (30)  - ----- + -------- + -----
--R           x + 1          2   x + 2
--R                   (x + 1)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 30

--S 31 of 200
r:= cos(3*x)/cos(x)
 

         cos(3x)
   (31)  -------
          cos(x)
                                                     Type: Expression Integer
--R 
--R
--R         cos(3x)
--R   (31)  -------
--R          cos(x)
--R                                                     Type: Expression Integer
--E 31

--S 32 of 200
real(complexNormalize(%))
 

                  2          2
   (32)  - 2sin(x)  + 2cos(x)  - 1
                                                     Type: Expression Integer
--R 
--R
--R                  2          2
--R   (32)  - 2sin(x)  + 2cos(x)  - 1
--R                                                     Type: Expression Integer
--E 32

--S 33 of 200
real(normalize(simplify(complexNormalize(r))))
 

   (33)  2cos(2x) - 1
                                                     Type: Expression Integer
--R 
--R
--R   (33)  2cos(2x) - 1
--R                                                     Type: Expression Integer
--E 33

--S 34 of 200
sincosAngles:= rule _
  (cos((n | integer?(n)) * x) == _
      cos((n - 1)*x) * cos(x) - sin((n - 1)*x) * sin(x); _
   sin((n | integer?(n)) * x) == _
      sin((n - 1)*x) * cos(x) + cos((n - 1)*x) * sin(x) )
 

   (34)
   {cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x),
    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (34)
--R   {cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 34

--S 35 of 200
sincosAngles r
 

                  2         2
   (35)  - 3sin(x)  + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                  2         2
--R   (35)  - 3sin(x)  + cos(x)
--R                                                     Type: Expression Integer
--E 35

--S 36 of 200
r:= 'r;
 

                                                             Type: Variable r
--R 
--R
--R                                                             Type: Variable r
--E 36

--S 37 of 200
sqrt(997) - (997**3)**(1/6)
 

   (37)  0
                                                        Type: AlgebraicNumber
--R 
--R
--R   (37)  0
--R                                                        Type: AlgebraicNumber
--E 37

--S 38 of 200
sqrt(999983) - (999983**3)**(1/6)
 

   (38)  0
                                                        Type: AlgebraicNumber
--R 
--R
--R   (38)  0
--R                                                        Type: AlgebraicNumber
--E 38

--S 39 of 200
(2**(1/3) + 4**(1/3))**3 - 6*(2**(1/3) + 4**(1/3)) - 6
 

          3+-+3+-+2     3+-+2     3+-+    3+-+
   (39)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
                                                        Type: AlgebraicNumber
--R 
--R
--R          3+-+3+-+2     3+-+2     3+-+    3+-+
--R   (39)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
--R                                                        Type: AlgebraicNumber
--E 39

--S 40 of 200
simplify(%)
 

          3+-+3+-+2     3+-+2     3+-+    3+-+
   (40)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
                                                     Type: Expression Integer
--R 
--R
--R          3+-+3+-+2     3+-+2     3+-+    3+-+
--R   (40)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
--R                                                     Type: Expression Integer
--E 40

--S 41 of 200
x**(1/n)*y**(1/n) - (x*y)**(1/n)
 

                1    1 1
                -    - -
                n    n n
   (41)  - (x y)  + x y
                                                     Type: Expression Integer
--R 
--R
--R                1    1 1
--R                -    - -
--R                n    n n
--R   (41)  - (x y)  + x y
--R                                                     Type: Expression Integer
--E 41

--S 42 of 200
normalize(%)
 

   (42)  0
                                                     Type: Expression Integer
--R 
--R
--R   (42)  0
--R                                                     Type: Expression Integer
--E 42

--S 43 of 200
expr:= log(tan(1/2*x + %pi/4)) - asinh(tan(x))
 

                 2x + %pi
   (43)  log(tan(--------)) - asinh(tan(x))
                     4
                                                     Type: Expression Integer
--R 
--R
--R                 2x + %pi
--R   (43)  log(tan(--------)) - asinh(tan(x))
--R                     4
--R                                                     Type: Expression Integer
--E 43

--S 44 of 200
complexNormalize(%)
 

   (44)
     -
        log
                                +---+ 4
                     (2x + %pi)\|- 1
                     ----------------
                             4
                 ((%e                )  - 1)
              *
                  +----------------------------------------------------+
                  |                               +---+ 4
                  |                    (2x + %pi)\|- 1
                  |                    ----------------
                  |                            4
                  |                4(%e                )
                  |- --------------------------------------------------
                  |                +---+ 8                  +---+ 4
                  |     (2x + %pi)\|- 1          (2x + %pi)\|- 1
                  |     ----------------         ----------------
                  |             4                        4
                 \|  (%e                )  - 2(%e                )  + 1
             + 
                                     +---+ 4
                          (2x + %pi)\|- 1
                          ----------------
                  +---+           4             +---+
               - \|- 1 (%e                )  - \|- 1
          /
                           +---+ 4
                (2x + %pi)\|- 1
                ----------------
                        4
             (%e                )  - 1
   + 
                               +---+ 2
                    (2x + %pi)\|- 1
                    ----------------
            +---+           4             +---+
         - \|- 1 (%e                )  + \|- 1
     log(--------------------------------------)
                              +---+ 2
                   (2x + %pi)\|- 1
                   ----------------
                           4
                (%e                )  + 1
                                                     Type: Expression Integer
--R 
--R
--R   (44)
--R     -
--R        log
--R                                +---+ 4
--R                     (2x + %pi)\|- 1
--R                     ----------------
--R                             4
--R                 ((%e                )  - 1)
--R              *
--R                  +----------------------------------------------------+
--R                  |                               +---+ 4
--R                  |                    (2x + %pi)\|- 1
--R                  |                    ----------------
--R                  |                            4
--R                  |                4(%e                )
--R                  |- --------------------------------------------------
--R                  |                +---+ 8                  +---+ 4
--R                  |     (2x + %pi)\|- 1          (2x + %pi)\|- 1
--R                  |     ----------------         ----------------
--R                  |             4                        4
--R                 \|  (%e                )  - 2(%e                )  + 1
--R             + 
--R                                     +---+ 4
--R                          (2x + %pi)\|- 1
--R                          ----------------
--R                  +---+           4             +---+
--R               - \|- 1 (%e                )  - \|- 1
--R          /
--R                           +---+ 4
--R                (2x + %pi)\|- 1
--R                ----------------
--R                        4
--R             (%e                )  - 1
--R   + 
--R                               +---+ 2
--R                    (2x + %pi)\|- 1
--R                    ----------------
--R            +---+           4             +---+
--R         - \|- 1 (%e                )  + \|- 1
--R     log(--------------------------------------)
--R                              +---+ 2
--R                   (2x + %pi)\|- 1
--R                   ----------------
--R                           4
--R                (%e                )  + 1
--R                                                     Type: Expression Integer
--E 44

--S 45 of 200
D(expr, x)
 

   (45)
                        +-----------+
        2x + %pi 2      |      2             2x + %pi       2        2x + %pi
   (tan(--------)  + 1)\|tan(x)  + 1  - 2tan(--------)tan(x)  - 2tan(--------)
            4                                    4                       4
   ---------------------------------------------------------------------------
                                          +-----------+
                                2x + %pi  |      2
                           2tan(--------)\|tan(x)  + 1
                                    4
                                                     Type: Expression Integer
--R 
--R
--R   (45)
--R                        +-----------+
--R        2x + %pi 2      |      2             2x + %pi       2        2x + %pi
--R   (tan(--------)  + 1)\|tan(x)  + 1  - 2tan(--------)tan(x)  - 2tan(--------)
--R            4                                    4                       4
--R   ---------------------------------------------------------------------------
--R                                          +-----------+
--R                                2x + %pi  |      2
--R                           2tan(--------)\|tan(x)  + 1
--R                                    4
--R                                                     Type: Expression Integer
--E 45

--S 46 of 200
simplify(real(complexNormalize(expand(simplify(%)))))
 

   (46)
                       +------------------------------------------------+
             x 2       |                        1
       (2cos(-)  - 1)  |------------------------------------------------ - 1
             2         |      x 8         x 6         x 4        x 2
                      4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
                      \|      2           2           2          2
   ----------------------------------------------------------------------------
                              +------------------------------------------------+
         x 4        x 2       |                        1
   (4cos(-)  - 4cos(-)  + 1)  |------------------------------------------------
         2          2         |      x 8         x 6         x 4        x 2
                             4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
                             \|      2           2           2          2
                                                     Type: Expression Integer
--R 
--R
--R   (46)
--R                       +------------------------------------------------+
--R             x 2       |                        1
--R       (2cos(-)  - 1)  |------------------------------------------------ - 1
--R             2         |      x 8         x 6         x 4        x 2
--R                      4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
--R                      \|      2           2           2          2
--R   ----------------------------------------------------------------------------
--R                              +------------------------------------------------+
--R         x 4        x 2       |                        1
--R   (4cos(-)  - 4cos(-)  + 1)  |------------------------------------------------
--R         2          2         |      x 8         x 6         x 4        x 2
--R                             4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
--R                             \|      2           2           2          2
--R                                                     Type: Expression Integer
--E 46

--S 47 of 200
normalize(eval(expr, x = 0))
 

   (47)  0
                                                     Type: Expression Integer
--R 
--R
--R   (47)  0
--R                                                     Type: Expression Integer
--E 47

--S 48 of 200
log((2*sqrt(r) + 1)/sqrt(4*r + 4*sqrt(r) + 1))
 

                   +-+
                 2\|r  + 1
   (48)  log(-----------------)
              +--------------+
              |  +-+
             \|4\|r  + 4r + 1
                                                     Type: Expression Integer
--R 
--R
--R                   +-+
--R                 2\|r  + 1
--R   (48)  log(-----------------)
--R              +--------------+
--R              |  +-+
--R             \|4\|r  + 4r + 1
--R                                                     Type: Expression Integer
--E 48

--S 49 of 200
simplify(%)
 

                   +-+
                 2\|r  + 1
   (49)  log(-----------------)
              +--------------+
              |  +-+
             \|4\|r  + 4r + 1
                                                     Type: Expression Integer
--R 
--R
--R                   +-+
--R                 2\|r  + 1
--R   (49)  log(-----------------)
--R              +--------------+
--R              |  +-+
--R             \|4\|r  + 4r + 1
--R                                                     Type: Expression Integer
--E 49

--S 50 of 200
(4*r + 4*sqrt(r) + 1)**(sqrt(r)/(2*sqrt(r) + 1)) _
   * (2*sqrt(r) + 1)**(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1
 

                                                 +-+
                        1                       \|r
                    ---------                ---------
                      +-+                      +-+
            +-+     2\|r  + 1   +-+          2\|r  + 1     +-+
   (50)  (2\|r  + 1)         (4\|r  + 4r + 1)          - 2\|r  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                                 +-+
--R                        1                       \|r
--R                    ---------                ---------
--R                      +-+                      +-+
--R            +-+     2\|r  + 1   +-+          2\|r  + 1     +-+
--R   (50)  (2\|r  + 1)         (4\|r  + 4r + 1)          - 2\|r  - 1
--R                                                     Type: Expression Integer
--E 50

--S 51 of 200
normalize(%)
 

   (51)  0
                                                     Type: Expression Integer
--R 
--R
--R   (51)  0
--R                                                     Type: Expression Integer
--E 51

--S 52 of 200
rectform(z) == real(z) + %i*imag(z)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 52

--S 53 of 200
rectform(log(3 + 4*%i))
 
   Compiling function rectform with type Expression Complex Integer -> 
      Expression Complex Integer 

                            4
         log(25) + 2%i atan(-)
                            3
   (53)  ---------------------
                   2
                                             Type: Expression Complex Integer
--R 
--R   Compiling function rectform with type Expression Complex Integer -> 
--R      Expression Complex Integer 
--R
--R                            4
--R         log(25) + 2%i atan(-)
--R                            3
--R   (53)  ---------------------
--R                   2
--R                                             Type: Expression Complex Integer
--E 53

--S 54 of 200
simplify(rectform(tan(x + %i*y)))
 

                       - 2y                   2       - 2y
         - 2%i cos(x)%e    sin(x) + (- 2cos(x)  + 1)%e     + 1
   (54)  -----------------------------------------------------
                  - 2y                      2        - 2y
         2cos(x)%e    sin(x) + (- 2%i cos(x)  + %i)%e     - %i
                                             Type: Expression Complex Integer
--R 
--R
--R                       - 2y                   2       - 2y
--R         - 2%i cos(x)%e    sin(x) + (- 2cos(x)  + 1)%e     + 1
--R   (54)  -----------------------------------------------------
--R                  - 2y                      2        - 2y
--R         2cos(x)%e    sin(x) + (- 2%i cos(x)  + %i)%e     - %i
--R                                             Type: Expression Complex Integer
--E 54

--S 55 of 200
sqrt(x*y*abs(z)**2) / (sqrt(x)*abs(z))
 

          +-----------+
          |          2
         \|x y abs(z)
   (55)  --------------
                  +-+
           abs(z)\|x
                                                     Type: Expression Integer
--R 
--R
--R          +-----------+
--R          |          2
--R         \|x y abs(z)
--R   (55)  --------------
--R                  +-+
--R           abs(z)\|x
--R                                                     Type: Expression Integer
--E 55

--S 56 of 200
sqrt(1/z) - 1/sqrt(z)
 

          +-+
          |1  +-+
          |- \|z  - 1
         \|z
   (56)  ------------
              +-+
             \|z
                                                     Type: Expression Integer
--R 
--R
--R          +-+
--R          |1  +-+
--R          |- \|z  - 1
--R         \|z
--R   (56)  ------------
--R              +-+
--R             \|z
--R                                                     Type: Expression Integer
--E 56

--S 57 of 200
log(%e**z)
 

   (57)  z
                                                     Type: Expression Integer
--R 
--R
--R   (57)  z
--R                                                     Type: Expression Integer
--E 57

--S 58 of 200
normalize(%)
 

   (58)  z
                                                     Type: Expression Integer
--R 
--R
--R   (58)  z
--R                                                     Type: Expression Integer
--E 58

--S 59 of 200
log(%e**(10*%i))
 

               10%i
   (59)  log(%e    )
                                             Type: Expression Complex Integer
--R 
--R
--R               10%i
--R   (59)  log(%e    )
--R                                             Type: Expression Complex Integer
--E 59

--S 60 of 200
normalize(%)
 

               10%i
   (60)  log(%e    )
                                             Type: Expression Complex Integer
--R 
--R
--R               10%i
--R   (60)  log(%e    )
--R                                             Type: Expression Complex Integer
--E 60

--S 61 of 200
atan(tan(z))
 

   (61)  z
                                                     Type: Expression Integer
--R 
--R
--R   (61)  z
--R                                                     Type: Expression Integer
--E 61

--S 62 of 200
sqrt(%e**z) - %e**(z/2)
 

                    z
          +---+     -
          |  z      2
   (62)  \|%e   - %e
                                                     Type: Expression Integer
--R 
--R
--R                    z
--R          +---+     -
--R          |  z      2
--R   (62)  \|%e   - %e
--R                                                     Type: Expression Integer
--E 62

--S 63 of 200
(x = 0)/2 + 1
 

         x + 2
   (63)  -----= 1
           2
                                   Type: Equation Fraction Polynomial Integer
--R 
--R
--R         x + 2
--R   (63)  -----= 1
--R           2
--R                                   Type: Equation Fraction Polynomial Integer
--E 63

--S 64 of 200
radicalSolve(3*x**3 - 18*x**2 + 33*x - 19 = 0, x)
 

   (64)
                        +-------------+2                 +-------------+
                        | +-+    +---+                   | +-+    +---+
            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
       (- 3\|- 3  + 3)  |-------------  + (6\|- 3  + 6)  |------------- - 2
                       3|      +-+                      3|      +-+
                       \|    6\|3                       \|    6\|3
   [x= --------------------------------------------------------------------,
                                          +-------------+
                                          | +-+    +---+
                              +---+       |\|3  + \|- 1
                           (3\|- 3  + 3)  |-------------
                                         3|      +-+
                                         \|    6\|3
                        +-------------+2                 +-------------+
                        | +-+    +---+                   | +-+    +---+
            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
       (- 3\|- 3  - 3)  |-------------  + (6\|- 3  - 6)  |------------- + 2
                       3|      +-+                      3|      +-+
                       \|    6\|3                       \|    6\|3
    x= --------------------------------------------------------------------,
                                          +-------------+
                                          | +-+    +---+
                              +---+       |\|3  + \|- 1
                           (3\|- 3  - 3)  |-------------
                                         3|      +-+
                                         \|    6\|3
          +-------------+2     +-------------+
          | +-+    +---+       | +-+    +---+
          |\|3  + \|- 1        |\|3  + \|- 1
       3  |-------------  + 6  |------------- + 1
         3|      +-+          3|      +-+
         \|    6\|3           \|    6\|3
    x= ------------------------------------------]
                       +-------------+
                       | +-+    +---+
                       |\|3  + \|- 1
                    3  |-------------
                      3|      +-+
                      \|    6\|3
                                       Type: List Equation Expression Integer
--R 
--R
--R   (64)
--R                        +-------------+2                 +-------------+
--R                        | +-+    +---+                   | +-+    +---+
--R            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
--R       (- 3\|- 3  + 3)  |-------------  + (6\|- 3  + 6)  |------------- - 2
--R                       3|      +-+                      3|      +-+
--R                       \|    6\|3                       \|    6\|3
--R   [x= --------------------------------------------------------------------,
--R                                          +-------------+
--R                                          | +-+    +---+
--R                              +---+       |\|3  + \|- 1
--R                           (3\|- 3  + 3)  |-------------
--R                                         3|      +-+
--R                                         \|    6\|3
--R                        +-------------+2                 +-------------+
--R                        | +-+    +---+                   | +-+    +---+
--R            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
--R       (- 3\|- 3  - 3)  |-------------  + (6\|- 3  - 6)  |------------- + 2
--R                       3|      +-+                      3|      +-+
--R                       \|    6\|3                       \|    6\|3
--R    x= --------------------------------------------------------------------,
--R                                          +-------------+
--R                                          | +-+    +---+
--R                              +---+       |\|3  + \|- 1
--R                           (3\|- 3  - 3)  |-------------
--R                                         3|      +-+
--R                                         \|    6\|3
--R          +-------------+2     +-------------+
--R          | +-+    +---+       | +-+    +---+
--R          |\|3  + \|- 1        |\|3  + \|- 1
--R       3  |-------------  + 6  |------------- + 1
--R         3|      +-+          3|      +-+
--R         \|    6\|3           \|    6\|3
--R    x= ------------------------------------------]
--R                       +-------------+
--R                       | +-+    +---+
--R                       |\|3  + \|- 1
--R                    3  |-------------
--R                      3|      +-+
--R                      \|    6\|3
--R                                       Type: List Equation Expression Integer
--E 64

--S 65 of 200
map(e +-> lhs(e) = rectform(rhs(e)), %)
 
   Compiling function rectform with type Expression Integer -> 
      Expression Complex Integer 

   (65)
   [
     x =
             +-+          %pi 2           +-+         %pi      +-+     %pi
           (\|3  - %i)sin(---)  + ((- 2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
                           18                          18               18
         + 
               +-+          %pi 2       +-+    %pi     +-+
           (- \|3  + %i)cos(---)  - 4%i\|3 cos(---) + \|3  + %i
                             18                 18
      /
           +-+    %pi        +-+    %pi
         2\|3 sin(---) - 2%i\|3 cos(---)
                   18                18
     ,

     x =
               +-+          %pi 2         +-+         %pi      +-+     %pi
           (- \|3  - %i)sin(---)  + ((2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
                             18                        18               18
         + 
             +-+          %pi 2       +-+    %pi     +-+
           (\|3  + %i)cos(---)  - 4%i\|3 cos(---) - \|3  + %i
                           18                 18
      /
           +-+    %pi        +-+    %pi
         2\|3 sin(---) - 2%i\|3 cos(---)
                   18                18
     ,

     x =
                  %pi 2         %pi      +-+     %pi           %pi 2
           %i sin(---)  + (2cos(---) + 2\|3 )sin(---) - %i cos(---)
                   18            18               18            18
         + 
                 +-+    %pi
           - 2%i\|3 cos(---) - %i
                         18
      /
          +-+    %pi       +-+    %pi
         \|3 sin(---) - %i\|3 cos(---)
                  18               18
     ]
                               Type: List Equation Expression Complex Integer
--R 
--R   Compiling function rectform with type Expression Integer -> 
--R      Expression Complex Integer 
--R
--R   (65)
--R   [
--R     x =
--R             +-+          %pi 2           +-+         %pi      +-+     %pi
--R           (\|3  - %i)sin(---)  + ((- 2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
--R                           18                          18               18
--R         + 
--R               +-+          %pi 2       +-+    %pi     +-+
--R           (- \|3  + %i)cos(---)  - 4%i\|3 cos(---) + \|3  + %i
--R                             18                 18
--R      /
--R           +-+    %pi        +-+    %pi
--R         2\|3 sin(---) - 2%i\|3 cos(---)
--R                   18                18
--R     ,
--R
--R     x =
--R               +-+          %pi 2         +-+         %pi      +-+     %pi
--R           (- \|3  - %i)sin(---)  + ((2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
--R                             18                        18               18
--R         + 
--R             +-+          %pi 2       +-+    %pi     +-+
--R           (\|3  + %i)cos(---)  - 4%i\|3 cos(---) - \|3  + %i
--R                           18                 18
--R      /
--R           +-+    %pi        +-+    %pi
--R         2\|3 sin(---) - 2%i\|3 cos(---)
--R                   18                18
--R     ,
--R
--R     x =
--R                  %pi 2         %pi      +-+     %pi           %pi 2
--R           %i sin(---)  + (2cos(---) + 2\|3 )sin(---) - %i cos(---)
--R                   18            18               18            18
--R         + 
--R                 +-+    %pi
--R           - 2%i\|3 cos(---) - %i
--R                         18
--R      /
--R          +-+    %pi       +-+    %pi
--R         \|3 sin(---) - %i\|3 cos(---)
--R                  18               18
--R     ]
--R                               Type: List Equation Expression Complex Integer
--E 65

--S 66 of 200
eqn:= x**4 + x**3 + x**2 + x + 1 = 0
 

          4    3    2
   (66)  x  + x  + x  + x + 1= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R          4    3    2
--R   (66)  x  + x  + x  + x + 1= 0
--R                                            Type: Equation Polynomial Integer
--E 66

--S 67 of 200
radicalSolve(eqn, x)
 

   (67)
   [
     x =
           -
                2
             *
                ROOT
                                 +-------------------+2
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 36  |-------------------
                                3|          +-+
                                \|       54\|3
                         + 
                                 +-------------------+
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 30  |------------------- - 40
                                3|          +-+
                                \|       54\|3
                      *
                         ROOT
                                    +-------------------+2
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                                36  |-------------------
                                   3|          +-+
                                   \|       54\|3
                              + 
                                      +-------------------+
                                      |     +-+      +---+
                                      |- 25\|3  + 45\|- 5
                                - 15  |------------------- + 40
                                     3|          +-+
                                     \|       54\|3
                           /
                                  +-------------------+
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                     + 
                             +-------------------+
                             |     +-+      +---+
                             |- 25\|3  + 45\|- 5
                       - 45  |-------------------
                            3|          +-+
                            \|       54\|3
                  /
                           +-------------------+
                           |     +-+      +---+
                           |- 25\|3  + 45\|- 5
                       36  |-------------------
                          3|          +-+
                          \|       54\|3
                    *
                       ROOT
                                  +-------------------+2
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                            + 
                                    +-------------------+
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                              - 15  |------------------- + 40
                                   3|          +-+
                                   \|       54\|3
                         /
                                +-------------------+
                                |     +-+      +---+
                                |- 25\|3  + 45\|- 5
                            36  |-------------------
                               3|          +-+
                               \|       54\|3
         + 
             +---------------------------------------------------------+
             |    +-------------------+2      +-------------------+
             |    |     +-+      +---+        |     +-+      +---+
             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
             |36  |-------------------  - 15  |------------------- + 40
             |   3|          +-+             3|          +-+
             |   \|       54\|3              \|       54\|3
           2 |---------------------------------------------------------  - 1
             |                     +-------------------+
             |                     |     +-+      +---+
             |                     |- 25\|3  + 45\|- 5
             |                 36  |-------------------
             |                    3|          +-+
            \|                    \|       54\|3
      /
         4
     ,

     x =
             2
          *
             ROOT
                              +-------------------+2      +-------------------+
                              |     +-+      +---+        |     +-+      +---+
                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                        - 36  |-------------------  - 30  |-------------------
                             3|          +-+             3|          +-+
                             \|       54\|3              \|       54\|3
                      + 
                        - 40
                   *
                     +---------------------------------------------------------+
                     |    +-------------------+2      +-------------------+
                     |    |     +-+      +---+        |     +-+      +---+
                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                     |36  |-------------------  - 15  |------------------- + 40
                     |   3|          +-+             3|          +-+
                     |   \|       54\|3              \|       54\|3
                     |---------------------------------------------------------
                     |                     +-------------------+
                     |                     |     +-+      +---+
                     |                     |- 25\|3  + 45\|- 5
                     |                 36  |-------------------
                     |                    3|          +-+
                    \|                    \|       54\|3
                  + 
                          +-------------------+
                          |     +-+      +---+
                          |- 25\|3  + 45\|- 5
                    - 45  |-------------------
                         3|          +-+
                         \|       54\|3
               /
                        +-------------------+
                        |     +-+      +---+
                        |- 25\|3  + 45\|- 5
                    36  |-------------------
                       3|          +-+
                       \|       54\|3
                 *
                   +---------------------------------------------------------+
                   |    +-------------------+2      +-------------------+
                   |    |     +-+      +---+        |     +-+      +---+
                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                   |36  |-------------------  - 15  |------------------- + 40
                   |   3|          +-+             3|          +-+
                   |   \|       54\|3              \|       54\|3
                   |---------------------------------------------------------
                   |                     +-------------------+
                   |                     |     +-+      +---+
                   |                     |- 25\|3  + 45\|- 5
                   |                 36  |-------------------
                   |                    3|          +-+
                  \|                    \|       54\|3
         + 
             +---------------------------------------------------------+
             |    +-------------------+2      +-------------------+
             |    |     +-+      +---+        |     +-+      +---+
             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
             |36  |-------------------  - 15  |------------------- + 40
             |   3|          +-+             3|          +-+
             |   \|       54\|3              \|       54\|3
           2 |---------------------------------------------------------  - 1
             |                     +-------------------+
             |                     |     +-+      +---+
             |                     |- 25\|3  + 45\|- 5
             |                 36  |-------------------
             |                    3|          +-+
            \|                    \|       54\|3
      /
         4
     ,

     x =
           -
                2
             *
                ROOT
                                 +-------------------+2
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 36  |-------------------
                                3|          +-+
                                \|       54\|3
                         + 
                                 +-------------------+
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 30  |------------------- - 40
                                3|          +-+
                                \|       54\|3
                      *
                         ROOT
                                    +-------------------+2
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                                36  |-------------------
                                   3|          +-+
                                   \|       54\|3
                              + 
                                      +-------------------+
                                      |     +-+      +---+
                                      |- 25\|3  + 45\|- 5
                                - 15  |------------------- + 40
                                     3|          +-+
                                     \|       54\|3
                           /
                                  +-------------------+
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                     + 
                           +-------------------+
                           |     +-+      +---+
                           |- 25\|3  + 45\|- 5
                       45  |-------------------
                          3|          +-+
                          \|       54\|3
                  /
                           +-------------------+
                           |     +-+      +---+
                           |- 25\|3  + 45\|- 5
                       36  |-------------------
                          3|          +-+
                          \|       54\|3
                    *
                       ROOT
                                  +-------------------+2
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                            + 
                                    +-------------------+
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                              - 15  |------------------- + 40
                                   3|          +-+
                                   \|       54\|3
                         /
                                +-------------------+
                                |     +-+      +---+
                                |- 25\|3  + 45\|- 5
                            36  |-------------------
                               3|          +-+
                               \|       54\|3
         + 
               +---------------------------------------------------------+
               |    +-------------------+2      +-------------------+
               |    |     +-+      +---+        |     +-+      +---+
               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
               |36  |-------------------  - 15  |------------------- + 40
               |   3|          +-+             3|          +-+
               |   \|       54\|3              \|       54\|3
           - 2 |---------------------------------------------------------  - 1
               |                     +-------------------+
               |                     |     +-+      +---+
               |                     |- 25\|3  + 45\|- 5
               |                 36  |-------------------
               |                    3|          +-+
              \|                    \|       54\|3
      /
         4
     ,

     x =
             2
          *
             ROOT
                              +-------------------+2      +-------------------+
                              |     +-+      +---+        |     +-+      +---+
                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                        - 36  |-------------------  - 30  |-------------------
                             3|          +-+             3|          +-+
                             \|       54\|3              \|       54\|3
                      + 
                        - 40
                   *
                     +---------------------------------------------------------+
                     |    +-------------------+2      +-------------------+
                     |    |     +-+      +---+        |     +-+      +---+
                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                     |36  |-------------------  - 15  |------------------- + 40
                     |   3|          +-+             3|          +-+
                     |   \|       54\|3              \|       54\|3
                     |---------------------------------------------------------
                     |                     +-------------------+
                     |                     |     +-+      +---+
                     |                     |- 25\|3  + 45\|- 5
                     |                 36  |-------------------
                     |                    3|          +-+
                    \|                    \|       54\|3
                  + 
                        +-------------------+
                        |     +-+      +---+
                        |- 25\|3  + 45\|- 5
                    45  |-------------------
                       3|          +-+
                       \|       54\|3
               /
                        +-------------------+
                        |     +-+      +---+
                        |- 25\|3  + 45\|- 5
                    36  |-------------------
                       3|          +-+
                       \|       54\|3
                 *
                   +---------------------------------------------------------+
                   |    +-------------------+2      +-------------------+
                   |    |     +-+      +---+        |     +-+      +---+
                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                   |36  |-------------------  - 15  |------------------- + 40
                   |   3|          +-+             3|          +-+
                   |   \|       54\|3              \|       54\|3
                   |---------------------------------------------------------
                   |                     +-------------------+
                   |                     |     +-+      +---+
                   |                     |- 25\|3  + 45\|- 5
                   |                 36  |-------------------
                   |                    3|          +-+
                  \|                    \|       54\|3
         + 
               +---------------------------------------------------------+
               |    +-------------------+2      +-------------------+
               |    |     +-+      +---+        |     +-+      +---+
               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
               |36  |-------------------  - 15  |------------------- + 40
               |   3|          +-+             3|          +-+
               |   \|       54\|3              \|       54\|3
           - 2 |---------------------------------------------------------  - 1
               |                     +-------------------+
               |                     |     +-+      +---+
               |                     |- 25\|3  + 45\|- 5
               |                 36  |-------------------
               |                    3|          +-+
              \|                    \|       54\|3
      /
         4
     ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (67)
--R   [
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                                 +-------------------+2
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 36  |-------------------
--R                                3|          +-+
--R                                \|       54\|3
--R                         + 
--R                                 +-------------------+
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 30  |------------------- - 40
--R                                3|          +-+
--R                                \|       54\|3
--R                      *
--R                         ROOT
--R                                    +-------------------+2
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                                36  |-------------------
--R                                   3|          +-+
--R                                   \|       54\|3
--R                              + 
--R                                      +-------------------+
--R                                      |     +-+      +---+
--R                                      |- 25\|3  + 45\|- 5
--R                                - 15  |------------------- + 40
--R                                     3|          +-+
--R                                     \|       54\|3
--R                           /
--R                                  +-------------------+
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                     + 
--R                             +-------------------+
--R                             |     +-+      +---+
--R                             |- 25\|3  + 45\|- 5
--R                       - 45  |-------------------
--R                            3|          +-+
--R                            \|       54\|3
--R                  /
--R                           +-------------------+
--R                           |     +-+      +---+
--R                           |- 25\|3  + 45\|- 5
--R                       36  |-------------------
--R                          3|          +-+
--R                          \|       54\|3
--R                    *
--R                       ROOT
--R                                  +-------------------+2
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                            + 
--R                                    +-------------------+
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                              - 15  |------------------- + 40
--R                                   3|          +-+
--R                                   \|       54\|3
--R                         /
--R                                +-------------------+
--R                                |     +-+      +---+
--R                                |- 25\|3  + 45\|- 5
--R                            36  |-------------------
--R                               3|          +-+
--R                               \|       54\|3
--R         + 
--R             +---------------------------------------------------------+
--R             |    +-------------------+2      +-------------------+
--R             |    |     +-+      +---+        |     +-+      +---+
--R             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R             |36  |-------------------  - 15  |------------------- + 40
--R             |   3|          +-+             3|          +-+
--R             |   \|       54\|3              \|       54\|3
--R           2 |---------------------------------------------------------  - 1
--R             |                     +-------------------+
--R             |                     |     +-+      +---+
--R             |                     |- 25\|3  + 45\|- 5
--R             |                 36  |-------------------
--R             |                    3|          +-+
--R            \|                    \|       54\|3
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                              +-------------------+2      +-------------------+
--R                              |     +-+      +---+        |     +-+      +---+
--R                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                        - 36  |-------------------  - 30  |-------------------
--R                             3|          +-+             3|          +-+
--R                             \|       54\|3              \|       54\|3
--R                      + 
--R                        - 40
--R                   *
--R                     +---------------------------------------------------------+
--R                     |    +-------------------+2      +-------------------+
--R                     |    |     +-+      +---+        |     +-+      +---+
--R                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                     |36  |-------------------  - 15  |------------------- + 40
--R                     |   3|          +-+             3|          +-+
--R                     |   \|       54\|3              \|       54\|3
--R                     |---------------------------------------------------------
--R                     |                     +-------------------+
--R                     |                     |     +-+      +---+
--R                     |                     |- 25\|3  + 45\|- 5
--R                     |                 36  |-------------------
--R                     |                    3|          +-+
--R                    \|                    \|       54\|3
--R                  + 
--R                          +-------------------+
--R                          |     +-+      +---+
--R                          |- 25\|3  + 45\|- 5
--R                    - 45  |-------------------
--R                         3|          +-+
--R                         \|       54\|3
--R               /
--R                        +-------------------+
--R                        |     +-+      +---+
--R                        |- 25\|3  + 45\|- 5
--R                    36  |-------------------
--R                       3|          +-+
--R                       \|       54\|3
--R                 *
--R                   +---------------------------------------------------------+
--R                   |    +-------------------+2      +-------------------+
--R                   |    |     +-+      +---+        |     +-+      +---+
--R                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                   |36  |-------------------  - 15  |------------------- + 40
--R                   |   3|          +-+             3|          +-+
--R                   |   \|       54\|3              \|       54\|3
--R                   |---------------------------------------------------------
--R                   |                     +-------------------+
--R                   |                     |     +-+      +---+
--R                   |                     |- 25\|3  + 45\|- 5
--R                   |                 36  |-------------------
--R                   |                    3|          +-+
--R                  \|                    \|       54\|3
--R         + 
--R             +---------------------------------------------------------+
--R             |    +-------------------+2      +-------------------+
--R             |    |     +-+      +---+        |     +-+      +---+
--R             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R             |36  |-------------------  - 15  |------------------- + 40
--R             |   3|          +-+             3|          +-+
--R             |   \|       54\|3              \|       54\|3
--R           2 |---------------------------------------------------------  - 1
--R             |                     +-------------------+
--R             |                     |     +-+      +---+
--R             |                     |- 25\|3  + 45\|- 5
--R             |                 36  |-------------------
--R             |                    3|          +-+
--R            \|                    \|       54\|3
--R      /
--R         4
--R     ,
--R
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                                 +-------------------+2
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 36  |-------------------
--R                                3|          +-+
--R                                \|       54\|3
--R                         + 
--R                                 +-------------------+
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 30  |------------------- - 40
--R                                3|          +-+
--R                                \|       54\|3
--R                      *
--R                         ROOT
--R                                    +-------------------+2
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                                36  |-------------------
--R                                   3|          +-+
--R                                   \|       54\|3
--R                              + 
--R                                      +-------------------+
--R                                      |     +-+      +---+
--R                                      |- 25\|3  + 45\|- 5
--R                                - 15  |------------------- + 40
--R                                     3|          +-+
--R                                     \|       54\|3
--R                           /
--R                                  +-------------------+
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                     + 
--R                           +-------------------+
--R                           |     +-+      +---+
--R                           |- 25\|3  + 45\|- 5
--R                       45  |-------------------
--R                          3|          +-+
--R                          \|       54\|3
--R                  /
--R                           +-------------------+
--R                           |     +-+      +---+
--R                           |- 25\|3  + 45\|- 5
--R                       36  |-------------------
--R                          3|          +-+
--R                          \|       54\|3
--R                    *
--R                       ROOT
--R                                  +-------------------+2
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                            + 
--R                                    +-------------------+
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                              - 15  |------------------- + 40
--R                                   3|          +-+
--R                                   \|       54\|3
--R                         /
--R                                +-------------------+
--R                                |     +-+      +---+
--R                                |- 25\|3  + 45\|- 5
--R                            36  |-------------------
--R                               3|          +-+
--R                               \|       54\|3
--R         + 
--R               +---------------------------------------------------------+
--R               |    +-------------------+2      +-------------------+
--R               |    |     +-+      +---+        |     +-+      +---+
--R               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R               |36  |-------------------  - 15  |------------------- + 40
--R               |   3|          +-+             3|          +-+
--R               |   \|       54\|3              \|       54\|3
--R           - 2 |---------------------------------------------------------  - 1
--R               |                     +-------------------+
--R               |                     |     +-+      +---+
--R               |                     |- 25\|3  + 45\|- 5
--R               |                 36  |-------------------
--R               |                    3|          +-+
--R              \|                    \|       54\|3
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                              +-------------------+2      +-------------------+
--R                              |     +-+      +---+        |     +-+      +---+
--R                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                        - 36  |-------------------  - 30  |-------------------
--R                             3|          +-+             3|          +-+
--R                             \|       54\|3              \|       54\|3
--R                      + 
--R                        - 40
--R                   *
--R                     +---------------------------------------------------------+
--R                     |    +-------------------+2      +-------------------+
--R                     |    |     +-+      +---+        |     +-+      +---+
--R                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                     |36  |-------------------  - 15  |------------------- + 40
--R                     |   3|          +-+             3|          +-+
--R                     |   \|       54\|3              \|       54\|3
--R                     |---------------------------------------------------------
--R                     |                     +-------------------+
--R                     |                     |     +-+      +---+
--R                     |                     |- 25\|3  + 45\|- 5
--R                     |                 36  |-------------------
--R                     |                    3|          +-+
--R                    \|                    \|       54\|3
--R                  + 
--R                        +-------------------+
--R                        |     +-+      +---+
--R                        |- 25\|3  + 45\|- 5
--R                    45  |-------------------
--R                       3|          +-+
--R                       \|       54\|3
--R               /
--R                        +-------------------+
--R                        |     +-+      +---+
--R                        |- 25\|3  + 45\|- 5
--R                    36  |-------------------
--R                       3|          +-+
--R                       \|       54\|3
--R                 *
--R                   +---------------------------------------------------------+
--R                   |    +-------------------+2      +-------------------+
--R                   |    |     +-+      +---+        |     +-+      +---+
--R                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                   |36  |-------------------  - 15  |------------------- + 40
--R                   |   3|          +-+             3|          +-+
--R                   |   \|       54\|3              \|       54\|3
--R                   |---------------------------------------------------------
--R                   |                     +-------------------+
--R                   |                     |     +-+      +---+
--R                   |                     |- 25\|3  + 45\|- 5
--R                   |                 36  |-------------------
--R                   |                    3|          +-+
--R                  \|                    \|       54\|3
--R         + 
--R               +---------------------------------------------------------+
--R               |    +-------------------+2      +-------------------+
--R               |    |     +-+      +---+        |     +-+      +---+
--R               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R               |36  |-------------------  - 15  |------------------- + 40
--R               |   3|          +-+             3|          +-+
--R               |   \|       54\|3              \|       54\|3
--R           - 2 |---------------------------------------------------------  - 1
--R               |                     +-------------------+
--R               |                     |     +-+      +---+
--R               |                     |- 25\|3  + 45\|- 5
--R               |                 36  |-------------------
--R               |                    3|          +-+
--R              \|                    \|       54\|3
--R      /
--R         4
--R     ]
--R                                       Type: List Equation Expression Integer
--E 67

--S 68 of 200
eval(eqn, %.1)
 

   (68)
                                      +-------------------+
                                      |     +-+      +---+
             +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
         (90\|- 5 \|3   - 270\|- 5 )  |-------------------
                                     3|          +-+
                                     \|       54\|3
      *
         ROOT
                         +-------------------+2      +-------------------+
                         |     +-+      +---+        |     +-+      +---+
                         |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                  (- 36  |-------------------  - 30  |------------------- - 40)
                        3|          +-+             3|          +-+
                        \|       54\|3              \|       54\|3
               *
                   +---------------------------------------------------------+
                   |    +-------------------+2      +-------------------+
                   |    |     +-+      +---+        |     +-+      +---+
                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                   |36  |-------------------  - 15  |------------------- + 40
                   |   3|          +-+             3|          +-+
                   |   \|       54\|3              \|       54\|3
                   |---------------------------------------------------------
                   |                     +-------------------+
                   |                     |     +-+      +---+
                   |                     |- 25\|3  + 45\|- 5
                   |                 36  |-------------------
                   |                    3|          +-+
                  \|                    \|       54\|3
              + 
                      +-------------------+
                      |     +-+      +---+
                      |- 25\|3  + 45\|- 5
                - 45  |-------------------
                     3|          +-+
                     \|       54\|3
           /
                    +-------------------+
                    |     +-+      +---+
                    |- 25\|3  + 45\|- 5
                36  |-------------------
                   3|          +-+
                   \|       54\|3
             *
                 +---------------------------------------------------------+
                 |    +-------------------+2      +-------------------+
                 |    |     +-+      +---+        |     +-+      +---+
                 |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                 |36  |-------------------  - 15  |------------------- + 40
                 |   3|          +-+             3|          +-+
                 |   \|       54\|3              \|       54\|3
                 |---------------------------------------------------------
                 |                     +-------------------+
                 |                     |     +-+      +---+
                 |                     |- 25\|3  + 45\|- 5
                 |                 36  |-------------------
                 |                    3|          +-+
                \|                    \|       54\|3
     + 
                                       +-------------------+
                                       |     +-+      +---+
              +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
       (- 135\|- 5 \|3   + 405\|- 5 )  |-------------------
                                      3|          +-+
                                      \|       54\|3
  /
                                    +-------------------+2
                                    |     +-+      +---+
            +---+ +-+2        +-+   |- 25\|3  + 45\|- 5
       (432\|- 5 \|3   + 1584\|3 )  |-------------------
                                   3|          +-+
                                   \|       54\|3
     + 
                                   +-------------------+
                                   |     +-+      +---+
            +---+ +-+2       +-+   |- 25\|3  + 45\|- 5         +-+        +---+
     (- 180\|- 5 \|3   - 660\|3 )  |------------------- + 1760\|3  + 1440\|- 5
                                  3|          +-+
                                  \|       54\|3
     =
     0
                                            Type: Equation Expression Integer
--R 
--R
--R   (68)
--R                                      +-------------------+
--R                                      |     +-+      +---+
--R             +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
--R         (90\|- 5 \|3   - 270\|- 5 )  |-------------------
--R                                     3|          +-+
--R                                     \|       54\|3
--R      *
--R         ROOT
--R                         +-------------------+2      +-------------------+
--R                         |     +-+      +---+        |     +-+      +---+
--R                         |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                  (- 36  |-------------------  - 30  |------------------- - 40)
--R                        3|          +-+             3|          +-+
--R                        \|       54\|3              \|       54\|3
--R               *
--R                   +---------------------------------------------------------+
--R                   |    +-------------------+2      +-------------------+
--R                   |    |     +-+      +---+        |     +-+      +---+
--R                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                   |36  |-------------------  - 15  |------------------- + 40
--R                   |   3|          +-+             3|          +-+
--R                   |   \|       54\|3              \|       54\|3
--R                   |---------------------------------------------------------
--R                   |                     +-------------------+
--R                   |                     |     +-+      +---+
--R                   |                     |- 25\|3  + 45\|- 5
--R                   |                 36  |-------------------
--R                   |                    3|          +-+
--R                  \|                    \|       54\|3
--R              + 
--R                      +-------------------+
--R                      |     +-+      +---+
--R                      |- 25\|3  + 45\|- 5
--R                - 45  |-------------------
--R                     3|          +-+
--R                     \|       54\|3
--R           /
--R                    +-------------------+
--R                    |     +-+      +---+
--R                    |- 25\|3  + 45\|- 5
--R                36  |-------------------
--R                   3|          +-+
--R                   \|       54\|3
--R             *
--R                 +---------------------------------------------------------+
--R                 |    +-------------------+2      +-------------------+
--R                 |    |     +-+      +---+        |     +-+      +---+
--R                 |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                 |36  |-------------------  - 15  |------------------- + 40
--R                 |   3|          +-+             3|          +-+
--R                 |   \|       54\|3              \|       54\|3
--R                 |---------------------------------------------------------
--R                 |                     +-------------------+
--R                 |                     |     +-+      +---+
--R                 |                     |- 25\|3  + 45\|- 5
--R                 |                 36  |-------------------
--R                 |                    3|          +-+
--R                \|                    \|       54\|3
--R     + 
--R                                       +-------------------+
--R                                       |     +-+      +---+
--R              +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
--R       (- 135\|- 5 \|3   + 405\|- 5 )  |-------------------
--R                                      3|          +-+
--R                                      \|       54\|3
--R  /
--R                                    +-------------------+2
--R                                    |     +-+      +---+
--R            +---+ +-+2        +-+   |- 25\|3  + 45\|- 5
--R       (432\|- 5 \|3   + 1584\|3 )  |-------------------
--R                                   3|          +-+
--R                                   \|       54\|3
--R     + 
--R                                   +-------------------+
--R                                   |     +-+      +---+
--R            +---+ +-+2       +-+   |- 25\|3  + 45\|- 5         +-+        +---+
--R     (- 180\|- 5 \|3   - 660\|3 )  |------------------- + 1760\|3  + 1440\|- 5
--R                                  3|          +-+
--R                                  \|       54\|3
--R     =
--R     0
--R                                            Type: Equation Expression Integer
--E 68

--S 69 of 200
%e**(2*x) + 2*%e**x + 1 = z
 

           2x      x
   (69)  %e   + 2%e  + 1= z
                                            Type: Equation Expression Integer
--R 
--R
--R           2x      x
--R   (69)  %e   + 2%e  + 1= z
--R                                            Type: Equation Expression Integer
--E 69

--S 70 of 200
solve(%, x)
 

                  +-+                +-+
   (70)  [x= log(\|z  - 1),x= log(- \|z  - 1)]
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +-+                +-+
--R   (70)  [x= log(\|z  - 1),x= log(- \|z  - 1)]
--R                                       Type: List Equation Expression Integer
--E 70

--S 71 of 200
(x + 1) * (sin(x)**2 + 1)**2 * cos(3*x)**3 = 0
 

                       3      4                  3      2                 3
   (71)  (x + 1)cos(3x) sin(x)  + (2x + 2)cos(3x) sin(x)  + (x + 1)cos(3x) = 0
                                            Type: Equation Expression Integer
--R 
--R
--R                       3      4                  3      2                 3
--R   (71)  (x + 1)cos(3x) sin(x)  + (2x + 2)cos(3x) sin(x)  + (x + 1)cos(3x) = 0
--R                                            Type: Equation Expression Integer
--E 71

--S 72 of 200
solve(%, x)
 

                   +---+             +---+     %pi
   (72)  [x= asin(\|- 1 ),x= - asin(\|- 1 ),x= ---,x= - 1]
                                                6
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +---+             +---+     %pi
--R   (72)  [x= asin(\|- 1 ),x= - asin(\|- 1 ),x= ---,x= - 1]
--R                                                6
--R                                       Type: List Equation Expression Integer
--E 72

--S 73 of 200
solve(%e**z = 1, z)
 

   (73)  [z= 0]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (73)  [z= 0]
--R                                       Type: List Equation Expression Integer
--E 73

--S 74 of 200
solve(sin(x) = cos(x), x)
 

             %pi
   (74)  [x= ---]
              4
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi
--R   (74)  [x= ---]
--R              4
--R                                       Type: List Equation Expression Integer
--E 74

--S 75 of 200
solve(tan(x) = 1, x)
 

             %pi
   (75)  [x= ---]
              4
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi
--R   (75)  [x= ---]
--R              4
--R                                       Type: List Equation Expression Integer
--E 75

--S 76 of 200
solve(sin(x) = tan(x), x)
 

   (76)  [x= 0]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (76)  [x= 0]
--R                                       Type: List Equation Expression Integer
--E 76

--S 77 of 200
solve(sqrt(x**2 + 1) = x - 2, x)
 

   (77)  []
                                       Type: List Equation Expression Integer
--R 
--R
--R   (77)  []
--R                                       Type: List Equation Expression Integer
--E 77

--S 78 of 200
eq1:=   x +   y +   z =  6
 

   (78)  z + y + x= 6
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (78)  z + y + x= 6
--R                                            Type: Equation Polynomial Integer
--E 78

--S 79 of 200
eq2:= 2*x +   y + 2*z = 10
 

   (79)  2z + y + 2x= 10
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (79)  2z + y + 2x= 10
--R                                            Type: Equation Polynomial Integer
--E 79

--S 80 of 200
eq3:=   x + 3*y +   z = 10
 

   (80)  z + 3y + x= 10
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (80)  z + 3y + x= 10
--R                                            Type: Equation Polynomial Integer
--E 80

--S 81 of 200
solve([eq1, eq2, eq3], [x, y, z])
 

   (81)  [[x= - %CA + 4,y= 2,z= %CA]]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--I   (81)  [[x= - %BU + 4,y= 2,z= %BU]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 81
--S 82 of 200
eq1:= x**2*y + 3*y*z - 4 = 0
 

                 2
   (82)  3y z + x y - 4= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R                 2
--R   (82)  3y z + x y - 4= 0
--R                                            Type: Equation Polynomial Integer
--E 82

--S 83 of 200
eq2:= -3*x**2*z + 2*y**2 + 1 = 0
 

             2      2
   (83)  - 3x z + 2y  + 1= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R             2      2
--R   (83)  - 3x z + 2y  + 1= 0
--R                                            Type: Equation Polynomial Integer
--E 83

--S 84 of 200
eq3:= 2*y*z**2 - z**2 - 1 = 0
 

                  2
   (84)  (2y - 1)z  - 1= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R                  2
--R   (84)  (2y - 1)z  - 1= 0
--R                                            Type: Equation Polynomial Integer
--E 84

--S 85 of 200
solve([eq1, eq2, eq3], [x, y, z])
 

   (85)
   [[x= 1,y= 1,z= 1], [x= - 1,y= 1,z= 1],
             2                      2
    [- 3z + x  + 2= 0,y= - 3z + 1,3z  - 2z + 1= 0],

                                                4      3      2
         4      3      2          2        - 18z  + 24z  + 21z  + 12z + 3
     [12z  - 12z  - 30z  + 7z + 3x = 0, y= ------------------------------,
                                                          2
        5     4     3     2
      6z  - 6z  - 9z  - 7z  - 3z - 1= 0]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R   (85)
--R   [[x= 1,y= 1,z= 1], [x= - 1,y= 1,z= 1],
--R             2                      2
--R    [- 3z + x  + 2= 0,y= - 3z + 1,3z  - 2z + 1= 0],
--R
--R                                                4      3      2
--R         4      3      2          2        - 18z  + 24z  + 21z  + 12z + 3
--R     [12z  - 12z  - 30z  + 7z + 3x = 0, y= ------------------------------,
--R                                                          2
--R        5     4     3     2
--R      6z  - 6z  - 9z  - 7z  - 3z - 1= 0]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 85

--S 86 of 200
m:= matrix([[a, b], [1, a*b]])
 

         +a   b +
   (86)  |      |
         +1  a b+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +a   b +
--R   (86)  |      |
--R         +1  a b+
--R                                              Type: Matrix Polynomial Integer
--E 86

--S 87 of 200
minv:= inverse(m)
 

         +     a            1   +
         |  ------     - ------ |
         |   2            2     |
         |  a  - 1       a  - 1 |
   (87)  |                      |
         |      1          a    |
         |- ---------  ---------|
         |    2          2      |
         +  (a  - 1)b  (a  - 1)b+
                          Type: Union(Matrix Fraction Polynomial Integer,...)
--R 
--R
--R         +     a            1   +
--R         |  ------     - ------ |
--R         |   2            2     |
--R         |  a  - 1       a  - 1 |
--R   (87)  |                      |
--R         |      1          a    |
--R         |- ---------  ---------|
--R         |    2          2      |
--R         +  (a  - 1)b  (a  - 1)b+
--R                          Type: Union(Matrix Fraction Polynomial Integer,...)
--E 87

--S 88 of 200
m * minv
 

         +1  0+
   (88)  |    |
         +0  1+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +1  0+
--R   (88)  |    |
--R         +0  1+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 88

--S 89 of 200
matrix([[1,    1,    1,    1   ], _
        [w,    x,    y,    z   ], _
        [w**2, x**2, y**2, z**2], _
        [w**3, x**3, y**3, z**3]])
 

         +1   1   1   1 +
         |              |
         |w   x   y   z |
         |              |
   (89)  | 2   2   2   2|
         |w   x   y   z |
         |              |
         | 3   3   3   3|
         +w   x   y   z +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +1   1   1   1 +
--R         |              |
--R         |w   x   y   z |
--R         |              |
--R   (89)  | 2   2   2   2|
--R         |w   x   y   z |
--R         |              |
--R         | 3   3   3   3|
--R         +w   x   y   z +
--R                                              Type: Matrix Polynomial Integer
--E 89

--S 90 of 200
determinant(%)
 

   (90)
              2       2    2        2    2   3
     ((x - w)y  + (- x  + w )y + w x  - w x)z
   + 
                3     3    3        3    3   2
     ((- x + w)y  + (x  - w )y - w x  + w x)z
   + 
        2    2  3       3    3  2    2 3    3 2           2    2   3
     ((x  - w )y  + (- x  + w )y  + w x  - w x )z + (- w x  + w x)y
   + 
         3    3   2       2 3    3 2
     (w x  - w x)y  + (- w x  + w x )y
                                                     Type: Polynomial Integer
--R 
--R
--R   (90)
--R              2       2    2        2    2   3
--R     ((x - w)y  + (- x  + w )y + w x  - w x)z
--R   + 
--R                3     3    3        3    3   2
--R     ((- x + w)y  + (x  - w )y - w x  + w x)z
--R   + 
--R        2    2  3       3    3  2    2 3    3 2           2    2   3
--R     ((x  - w )y  + (- x  + w )y  + w x  - w x )z + (- w x  + w x)y
--R   + 
--R         3    3   2       2 3    3 2
--R     (w x  - w x)y  + (- w x  + w x )y
--R                                                     Type: Polynomial Integer
--E 90

--S 91 of 200
factor(%)
 

   (91)  (x - w)(y - x)(y - w)(z - y)(z - x)(z - w)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (91)  (x - w)(y - x)(y - w)(z - y)(z - x)(z - w)
--R                                            Type: Factored Polynomial Integer
--E 91

--S 92 of 200
m:= matrix([[ 5, -3, -7], _
            [-2,  1,  2], _
            [ 2, -3, -4]])
 

         + 5   - 3  - 7+
         |             |
   (92)  |- 2   1    2 |
         |             |
         + 2   - 3  - 4+
                                                         Type: Matrix Integer
--R 
--R
--R         + 5   - 3  - 7+
--R         |             |
--R   (92)  |- 2   1    2 |
--R         |             |
--R         + 2   - 3  - 4+
--R                                                         Type: Matrix Integer
--E 92

--S 93 of 200
characteristicPolynomial(m, lambda)
 

                 3          2
   (93)  - lambda  + 2lambda  + 5lambda - 6
                                                     Type: Polynomial Integer
--R 
--R
--R                 3          2
--R   (93)  - lambda  + 2lambda  + 5lambda - 6
--R                                                     Type: Polynomial Integer
--E 93

--S 94 of 200
solve(% = 0, lambda)
 

   (94)  [lambda= 3,lambda= 1,lambda= - 2]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R   (94)  [lambda= 3,lambda= 1,lambda= - 2]
--R                              Type: List Equation Fraction Polynomial Integer
--E 94

--S 95 of 200
m:= 'm;
 

                                                             Type: Variable m
--R 
--R
--R                                                             Type: Variable m
--E 95

--S 96 of 200
summation(k**3, k = 1..n)
 

          n
         --+    3
   (96)  >     k
         --+
         k= 1
                                                     Type: Expression Integer
--R 
--R
--R          n
--R         --+    3
--R   (96)  >     k
--R         --+
--R         k= 1
--R                                                     Type: Expression Integer
--E 96

--S 97 of 200
sum(k**3, k = 1..n)
 

          4     3    2
         n  + 2n  + n
   (97)  -------------
               4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          4     3    2
--R         n  + 2n  + n
--R   (97)  -------------
--R               4
--R                                            Type: Fraction Polynomial Integer
--E 97

--S 98 of 200
limit(sum(1/k**2 + 1/k**3, k = 1..n), n = %plusInfinity)
 

   (98)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (98)  "failed"
--R                                                    Type: Union("failed",...)
--E 98
--S 99 of 200
product(k, k = 1..n)
 

           n
         ++-++
   (99)   | |   k
          | |
         k= 1
                                                     Type: Expression Integer
--R 
--R
--R           n
--R         ++-++
--R   (99)   | |   k
--R          | |
--R         k= 1
--R                                                     Type: Expression Integer
--E 99

--S 100 of 200
limit((1 + 1/n)**n, n = %plusInfinity)
 

   (100)  %e
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (100)  %e
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 100

--S 101 of 200
limit((1 - cos(x))/x**2, x = 0)
 

          1
   (101)  -
          2
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (101)  -
--R          2
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 101

--S 102 of 200
y:= operator('y);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 102

--S 103 of 200
x:= operator('x);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 103

--S 104 of 200
D(y(x(t)), t, 2)
 

           ,   2 ,,          ,       ,,
   (104)  x (t) y  (x(t)) + y (x(t))x  (t)

                                                     Type: Expression Integer
--R 
--R
--R           ,   2 ,,          ,       ,,
--R   (104)  x (t) y  (x(t)) + y (x(t))x  (t)
--R
--R                                                     Type: Expression Integer
--E 104

)clear properties x y
 

--S 105 of 200
1/(x**3 + 2)
 

             1
   (105)  ------
           3
          x  + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             1
--R   (105)  ------
--R           3
--R          x  + 2
--R                                            Type: Fraction Polynomial Integer
--E 105

--S 106 of 200
integrate(%, x)
 

   (106)
          +-+     2 3+-+2    3+-+          +-+     3+-+
       - \|3 log(x  \|4  - 2x\|4  + 4) + 2\|3 log(x\|4  + 2)
     + 
               +-+3+-+    +-+
             x\|3 \|4  - \|3
       6atan(----------------)
                     3
  /
       +-+3+-+
     6\|3 \|4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (106)
--R          +-+     2 3+-+2    3+-+          +-+     3+-+
--R       - \|3 log(x  \|4  - 2x\|4  + 4) + 2\|3 log(x\|4  + 2)
--R     + 
--R               +-+3+-+    +-+
--R             x\|3 \|4  - \|3
--R       6atan(----------------)
--R                     3
--R  /
--R       +-+3+-+
--R     6\|3 \|4
--R                                          Type: Union(Expression Integer,...)
--E 106

--S 107 of 200
D(%, x)
 

             1
   (107)  ------
           3
          x  + 2
                                                     Type: Expression Integer
--R 
--R
--R             1
--R   (107)  ------
--R           3
--R          x  + 2
--R                                                     Type: Expression Integer
--E 107

--S 108 of 200
integrate(1/(a + b*cos(x)), x)
 

   (108)
                         +-------+
                         | 2    2        2    2
        (- a cos(x) - b)\|b  - a   + (- b  + a )sin(x)
    log(----------------------------------------------)
                         b cos(x) + a
   [---------------------------------------------------,
                          +-------+
                          | 2    2
                         \|b  - a
                   +---------+
                   |   2    2
            sin(x)\|- b  + a
    2atan(---------------------)
          (b + a)cos(x) + b + a
    ----------------------------]
             +---------+
             |   2    2
            \|- b  + a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (108)
--R                         +-------+
--R                         | 2    2        2    2
--R        (- a cos(x) - b)\|b  - a   + (- b  + a )sin(x)
--R    log(----------------------------------------------)
--R                         b cos(x) + a
--R   [---------------------------------------------------,
--R                          +-------+
--R                          | 2    2
--R                         \|b  - a
--R                   +---------+
--R                   |   2    2
--R            sin(x)\|- b  + a
--R    2atan(---------------------)
--R          (b + a)cos(x) + b + a
--R    ----------------------------]
--R             +---------+
--R             |   2    2
--R            \|- b  + a
--R                                     Type: Union(List Expression Integer,...)
--E 108

--S 109 of 200
map(simplify, map(f +-> D(f, x), %))
 

                 1            1
   (109)  [------------,------------]
           b cos(x) + a b cos(x) + a
                                                Type: List Expression Integer
--R 
--R
--R                 1            1
--R   (109)  [------------,------------]
--R           b cos(x) + a b cos(x) + a
--R                                                Type: List Expression Integer
--E 109

--S 110 of 200
D(abs(x), x)
 

          abs(x)
   (110)  ------
             x
                                                     Type: Expression Integer
--R 
--R
--R          abs(x)
--R   (110)  ------
--R             x
--R                                                     Type: Expression Integer
--E 110

--S 111 of 200
integrate(abs(x), x)
 

             x
           ++
   (111)   |   abs(%M)d%M
          ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R           ++
--I   (111)   |   abs(%J)d%J
--R          ++
--R                                          Type: Union(Expression Integer,...)
--E 111

--S 112 of 200
a(x) == if x < 0 then -x else x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 112

--S 113 of 200
D(a(x), x)
 
   Compiling function a with type Variable x -> Polynomial Integer 

   (113)  1
                                                     Type: Polynomial Integer
--R 
--R   Compiling function a with type Variable x -> Polynomial Integer 
--R
--R   (113)  1
--R                                                     Type: Polynomial Integer
--E 113

--S 114 of 200
integrate(a(x), x)
 

          1  2
   (114)  - x
          2
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1  2
--R   (114)  - x
--R          2
--R                                            Type: Polynomial Fraction Integer
--E 114

)clear properties a
 
   Compiled code for a has been cleared.
 
--S 115 of 200
integrate(x/(sqrt(1 + x) + sqrt(1 - x)), x)
 

                  +-----+             +-------+
          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
   (115)  -------------------------------------
                            3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +-----+             +-------+
--R          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (115)  -------------------------------------
--R                            3
--R                                          Type: Union(Expression Integer,...)
--E 115

--S 116 of 200
integrate((sqrt(1 + x) - sqrt(1 - x))/2, x)
 

                  +-----+             +-------+
          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
   (116)  -------------------------------------
                            3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +-----+             +-------+
--R          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (116)  -------------------------------------
--R                            3
--R                                          Type: Union(Expression Integer,...)
--E 116

--S 117 of 200
integrate(1/x, x = -1..1)
 
 
Daly Bug
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 117

--S 118 of 200
integrate(1/x**2, x = -1..1)
 
 
Daly Bug
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 118

--S 119 of 200
integrate(sqrt(x + 1/x - 2), x = 0..1)
 

   (117)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (117)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 119

--S 120 of 200
integrate(sqrt(x + 1/x - 2), x = 0..1, "noPole")
 

            4
   (118)  - -
            3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            4
--R   (118)  - -
--R            3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 120

--S 121 of 200
integrate(sqrt(x + 1/x - 2), x = 1..2)
 

   (119)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (119)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 121

--S 122 of 200
integrate(sqrt(x + 1/x - 2), x = 1..2, "noPole")
 

              +-+
          - 2\|2  + 4
   (120)  -----------
               3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R              +-+
--R          - 2\|2  + 4
--R   (120)  -----------
--R               3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 122

--S 123 of 200
integrate(sqrt(x + 1/x - 2), x = 0..2)
 

   (121)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (121)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 123

--S 124 of 200
integrate(sqrt(x + 1/x - 2), x = 0..2, "noPole")
 

              +-+
            2\|2
   (122)  - -----
              3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R              +-+
--R            2\|2
--R   (122)  - -----
--R              3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 124

--S 125 of 200
integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity)
 

   (123)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (123)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 125

--S 126 of 200
integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity, "noPole")
 

   (124)  "failed"
                                                Type: Union(fail: failed,...)
--R 
--R
--R   (124)  "failed"
--R                                                Type: Union(fail: failed,...)
--E 126

--S 127 of 200
integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity)
 

   (125)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (125)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 127

--S 128 of 200
integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity, "noPole")
 

   (126)  "failed"
                                                Type: Union(fail: failed,...)
--R 
--R
--R   (126)  "failed"
--R                                                Type: Union(fail: failed,...)
--E 128

--S 129 of 200
integrate(integrate(integrate(1, z = 0..c*(1 - x/a - y/b)), _
                    y = 0..b*(1 - x/a)), _
          x = 0..a)
 

          a b c
   (127)  -----
            6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          a b c
--R   (127)  -----
--R            6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 129

--S 130 of 200
1/sqrt(1 - (v/c)**2)
 

                1
   (128)  ------------
           +---------+
           |   2    2
           |- v  + c
           |---------
           |     2
          \|    c
                                                     Type: Expression Integer
--R 
--R
--R                1
--R   (128)  ------------
--R           +---------+
--R           |   2    2
--R           |- v  + c
--R           |---------
--R           |     2
--R          \|    c
--R                                                     Type: Expression Integer
--E 130

--S 131 of 200
series(%, v = 0)
 

               1   2    3   4     5   6      8
   (129)  1 + --- v  + --- v  + ---- v  + O(v )
                2        4         6
              2c       8c       16c
                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--R 
--R
--R               1   2    3   4     5   6      8
--R   (129)  1 + --- v  + --- v  + ---- v  + O(v )
--R                2        4         6
--R              2c       8c       16c
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--E 131

--S 132 of 200
1/%**2
 

               1  2      8
   (130)  1 - -- v  + O(v )
               2
              c
                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--R 
--R
--R               1  2      8
--R   (130)  1 - -- v  + O(v )
--R               2
--R              c
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--E 132

--S 133 of 200
tsin:= series(sin(x), x = 0)
 

              1  3    1   5     1   7      9
   (131)  x - - x  + --- x  - ---- x  + O(x )
              6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  3    1   5     1   7      9
--R   (131)  x - - x  + --- x  - ---- x  + O(x )
--R              6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 133 

--S 134 of 200
tcos:= series(cos(x), x = 0)
 

              1  2    1  4    1   6      8
   (132)  1 - - x  + -- x  - --- x  + O(x )
              2      24      720
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  2    1  4    1   6      8
--R   (132)  1 - - x  + -- x  - --- x  + O(x )
--R              2      24      720
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 134

--S 135 of 200
tsin/tcos
 

              1  3    2  5    17  7      9
   (133)  x + - x  + -- x  + --- x  + O(x )
              3      15      315
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  3    2  5    17  7      9
--R   (133)  x + - x  + -- x  + --- x  + O(x )
--R              3      15      315
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 135

--S 136 of 200
series(tan(x), x = 0)
 

              1  3    2  5    17  7      9
   (134)  x + - x  + -- x  + --- x  + O(x )
              3      15      315
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  3    2  5    17  7      9
--R   (134)  x + - x  + -- x  + --- x  + O(x )
--R              3      15      315
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 136


)set streams calculate 1
 

--S 137 of 200
log(x)**a*exp(-b*x)
 

            - b x      a
   (135)  %e     log(x)
                                                     Type: Expression Integer
--R 
--R
--R            - b x      a
--R   (135)  %e     log(x)
--R                                                     Type: Expression Integer
--E 137

--S 138 of 200
series(%, x = 1)
 
 
Daly Bug
   >> Error detected within library code:
   No series expansion

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   No series expansion
--R
--R   Continuing to read the file...
--R
--E 138

)set streams calculate 7
 

--S 139 of 200
taylor(log(sinh(z)) + log(cosh(z + w)), z = 0)
 
 
Daly Bug
   >> Error detected within library code:
   No Taylor expansion: logarithmic singularity

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   No Taylor expansion: logarithmic singularity
--R
--R   Continuing to read the file...
--R
--E 139

--S 140 of 200
% - taylor(log(sinh(z) * cosh(z + w)), z = 0)
 
 
Daly Bug
   >> Error detected within library code:
   No Taylor expansion: logarithmic singularity

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   No Taylor expansion: logarithmic singularity
--R
--R   Continuing to read the file...
--R
--E 140

--S 141 of 200
log(sin(x)/x)
 

              sin(x)
   (136)  log(------)
                 x
                                                     Type: Expression Integer
--R 
--R
--R              sin(x)
--R   (136)  log(------)
--R                 x
--R                                                     Type: Expression Integer
--E 141

--S 142 of 200
series(%, x = 0)
 

            1  2    1   4     1   6     1    8      10
   (137)  - - x  - --- x  - ---- x  - ----- x  + O(x  )
            6      180      2835      37800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  2    1   4     1   6     1    8      10
--R   (137)  - - x  - --- x  - ---- x  - ----- x  + O(x  )
--R            6      180      2835      37800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 142

--S 143 of 200
exp(-x)*sin(x)
 

            - x
   (138)  %e   sin(x)
                                                     Type: Expression Integer
--R 
--R
--R            - x
--R   (138)  %e   sin(x)
--R                                                     Type: Expression Integer
--E 143

--S 144 of 200
series(%, x = 0)
 

               2   1  3    1  5    1  6    1   7      9
   (139)  x - x  + - x  - -- x  + -- x  - --- x  + O(x )
                   3      30      90      630
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               2   1  3    1  5    1  6    1   7      9
--R   (139)  x - x  + - x  - -- x  + -- x  - --- x  + O(x )
--R                   3      30      90      630
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 144

--S 145 of 200
y:= operator('y);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 145

--S 146 of 200
x = sin(y(x)) + cos(y(x))
 

   (141)  x= sin(y(x)) + cos(y(x))
                                            Type: Equation Expression Integer
--R 
--R
--R   (141)  x= sin(y(x)) + cos(y(x))
--R                                            Type: Equation Expression Integer
--E 146

--S 147 of 200
seriesSolve(%, y, x = 1, 0)
 
 
Daly Bug
   >> Error detected within library code:
   Improper initial value

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   Improper initial value
--R
--R   Continuing to read the file...
--R
--E 147

)clear properties y
 

--S 148 of 200
pade(1, 1, taylor(exp(-x), x = 0))
 

          - x + 2
   (142)  -------
           x + 2
         Type: Union(Fraction UnivariatePolynomial(x,Expression Integer),...)
--R 
--R
--R          - x + 2
--R   (142)  -------
--R           x + 2
--R         Type: Union(Fraction UnivariatePolynomial(x,Expression Integer),...)
--E 148

--S 149 of 200
laplace(cos((w - 1)*t), t, s)
 

                  s
   (143)  ----------------
           2         2
          w  - 2w + s  + 1
                                                     Type: Expression Integer
--R 
--R
--R                  s
--R   (143)  ----------------
--R           2         2
--R          w  - 2w + s  + 1
--R                                                     Type: Expression Integer
--E 149

--S 150 of 200
inverseLaplace(%, s, t)
 

                +-----------+
                | 2
   (144)  cos(t\|w  - 2w + 1 )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +-----------+
--R                | 2
--R   (144)  cos(t\|w  - 2w + 1 )
--R                                          Type: Union(Expression Integer,...)
--E 150

--S 151 of 200
r:= operator('r);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 151

--S 152 of 200
r(n + 2) - 2 * r(n + 1) + r(n) = 2
 

   (146)  r(n + 2) - 2r(n + 1) + r(n)= 2
                                            Type: Equation Expression Integer
--R 
--R
--R   (146)  r(n + 2) - 2r(n + 1) + r(n)= 2
--R                                            Type: Equation Expression Integer
--E 152

--S 153 of 200
[%, r(0) = 1, r(1) = m]
 

   (147)  [r(n + 2) - 2r(n + 1) + r(n)= 2,r(0)= 1,r(1)= m]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (147)  [r(n + 2) - 2r(n + 1) + r(n)= 2,r(0)= 1,r(1)= m]
--R                                       Type: List Equation Expression Integer
--E 153

)clear properties r
 
 
--S 154 of 200
f:= operator('f);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 154

--S 155 of 200
ode:= D(f(t), t, 2) + 4*f(t) = sin(2*t)
 

           ,,
   (149)  f  (t) + 4f(t)= sin(2t)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (149)  f  (t) + 4f(t)= sin(2t)
--R
--R                                            Type: Equation Expression Integer
--E 155

--S 156 of 200
map(e +-> laplace(e, t, s), %)
 

            2                          ,                2
   (150)  (s  + 4)laplace(f(t),t,s) - f (0) - f(0)s= ------
                                                      2
                                                     s  + 4
                                            Type: Equation Expression Integer
--R 
--R
--R            2                          ,                2
--R   (150)  (s  + 4)laplace(f(t),t,s) - f (0) - f(0)s= ------
--R                                                      2
--R                                                     s  + 4
--R                                            Type: Equation Expression Integer
--E 156

--S 157 of 200
solve(ode, f, t = 0, [0, 0])
 

          sin(2t) - 2t cos(2t)
   (151)  --------------------
                    8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          sin(2t) - 2t cos(2t)
--R   (151)  --------------------
--R                    8
--R                                          Type: Union(Expression Integer,...)
--E 157

--S 158 of 200
y:= operator('y);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 158

--S 159 of 200
x**2 * D(y(x), x) + 3*x*y(x) = sin(x)/x
 

           2 ,               sin(x)
   (153)  x y (x) + 3x y(x)= ------
                                x
                                            Type: Equation Expression Integer
--R 
--R
--R           2 ,               sin(x)
--R   (153)  x y (x) + 3x y(x)= ------
--R                                x
--R                                            Type: Equation Expression Integer
--E 159

--S 160 of 200
solve(%, y, x)
 

                         cos(x)          1
   (154)  [particular= - ------,basis= [--]]
                            3            3
                           x            x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                         cos(x)          1
--R   (154)  [particular= - ------,basis= [--]]
--R                            3            3
--R                           x            x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 160

--S 161 of 200
D(y(x), x, 2) + y(x)*D(y(x), x)**3 = 0
 

           ,,           ,   3
   (155)  y  (x) + y(x)y (x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,           ,   3
--R   (155)  y  (x) + y(x)y (x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 161

--S 162 of 200
solve(%, y, x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 162

--S 163 of 200
D(y(x, a), x) = a*y(x, a)
 

   (156)  y  (x,a)= a y(x,a)
           ,1
                                            Type: Equation Expression Integer
--R 
--R
--R   (156)  y  (x,a)= a y(x,a)
--R           ,1
--R                                            Type: Equation Expression Integer
--E 163

--S 164 of 200
solve(%, y, x);
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseODE: equation has order 0
--R
--R   Continuing to read the file...
--R
--E 164

--S 165 of 200
solve(D(y(x), x, 2) + k**2*y(x) = 0, y, x)
 

   (157)  [particular= 0,basis= [cos(k x),sin(k x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (157)  [particular= 0,basis= [cos(k x),sin(k x)]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 165

-- bc(%, x = 0, y = 0, x = 1, D(y(x), x) = 0)

--S 166 of 200
x:= operator('x);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 166

--S 167 of 200
system:= [D(x(t), t) = x(t) - y(t), D(y(t), t) = x(t) + y(t)]
 

            ,                    ,
   (159)  [x (t)= - y(t) + x(t),y (t)= y(t) + x(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R            ,                    ,
--R   (159)  [x (t)= - y(t) + x(t),y (t)= y(t) + x(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 167

--S 168 of 200
system:= [D(x(t), t) = x(t) * (1 + cos(t)/(2 + sin(t))), _
          D(y(t), t) = x(t) - y(t)]
 

            ,     x(t)sin(t) + x(t)cos(t) + 2x(t)  ,
   (160)  [x (t)= -------------------------------,y (t)= - y(t) + x(t)]
                             sin(t) + 2
                                       Type: List Equation Expression Integer
--R 
--R
--R            ,     x(t)sin(t) + x(t)cos(t) + 2x(t)  ,
--R   (160)  [x (t)= -------------------------------,y (t)= - y(t) + x(t)]
--R                             sin(t) + 2
--R                                       Type: List Equation Expression Integer
--E 168

--S 169 of 200
s:=solve(system.1, x, t)
 

                                   t            t
   (161)  [particular= 0,basis= [%e sin(t) + 2%e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                   t            t
--R   (161)  [particular= 0,basis= [%e sin(t) + 2%e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 169

--S 170 of 200
eq1 := x(t) = C1 * s.basis.1
 

                     t               t
   (162)  x(t)= C1 %e sin(t) + 2C1 %e
                                            Type: Equation Expression Integer
--R 
--R
--R                     t               t
--R   (162)  x(t)= C1 %e sin(t) + 2C1 %e
--R                                            Type: Equation Expression Integer
--E 170

--S 171 of 200
s1:=solve(map(e +-> subst(e, eq1), system.2), y, t)
 

   (163)
                      - t   t 2                              - t   t 2
                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
   [particular= ------------------------------------------------------,
                                           5
              - t
    basis= [%e   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (163)
--R                      - t   t 2                              - t   t 2
--R                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
--R   [particular= ------------------------------------------------------,
--R                                           5
--R              - t
--R    basis= [%e   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 171

--S 172 of 200
eq2 := y(t) = simplify(s1.particular) + C2 * s1.basis.1
 

                      t                              t         - t
                2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
   (164)  y(t)= --------------------------------------------------
                                         5
                                            Type: Equation Expression Integer
--R 
--R
--R                      t                              t         - t
--R                2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
--R   (164)  y(t)= --------------------------------------------------
--R                                         5
--R                                            Type: Equation Expression Integer
--E 172

--S 173 of 200
map(e +-> rightZero eval(e, [eq1, D(eq1,t), eq2 , D(eq2,t)]), system)
 

   (165)  [0= 0,0= 0]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (165)  [0= 0,0= 0]
--R                                       Type: List Equation Expression Integer
--E 173
)clear properties x y
 
 
--S 174 of 200
DD:= operator("D") :: Operator(Expression Integer)
 

   (166)  D
                                            Type: Operator Expression Integer
--R 
--R
--R   (166)  D
--R                                            Type: Operator Expression Integer
--E 174

--S 175 of 200
evaluate(DD, e +-> D(e, x))$Operator(Expression Integer)
 

   (167)  D
                                            Type: Operator Expression Integer
--R 
--R
--R   (167)  D
--R                                            Type: Operator Expression Integer
--E 175

--S 176 of 200
L:= (DD - 1) * (DD + 2)
 

                 2
   (168)  D 2 + D  - D - 2
                                            Type: Operator Expression Integer
--R 
--R
--R                 2
--R   (168)  D 2 + D  - D - 2
--R                                            Type: Operator Expression Integer
--E 176

--S 177 of 200
g:= operator('g)
 

   (169)  g
                                                          Type: BasicOperator
--R 
--R
--R   (169)  g
--R                                                          Type: BasicOperator
--E 177

--S 178 of 200
L(f(x))
 

           ,,       ,
   (170)  f  (x) + f (x) - 2f(x)

                                                     Type: Expression Integer
--R 
--R
--R           ,,       ,
--R   (170)  f  (x) + f (x) - 2f(x)
--R
--R                                                     Type: Expression Integer
--E 178

--S 179 of 200
subst(L(subst(g(y), y = x)), x = y)
 

           ,,       ,
   (171)  g  (y) + g (y) - 2g(y)

                                                     Type: Expression Integer
--R 
--R
--R           ,,       ,
--R   (171)  g  (y) + g (y) - 2g(y)
--R
--R                                                     Type: Expression Integer
--E 179

--S 180 of 200
subst(L(subst(A * sin(z**2), z = x)), x = z)
 

                 2           2                    2
   (172)  (- 4A z  - 2A)sin(z ) + (2A z + 2A)cos(z )
                                                     Type: Expression Integer
--R 
--R
--R                 2           2                    2
--R   (172)  (- 4A z  - 2A)sin(z ) + (2A z + 2A)cos(z )
--R                                                     Type: Expression Integer
--E 180

--S 181 of 200
T:= (f, xx, a) +-> subst((DD**0)(f(x)), x = a)/factorial(0) * (xx - a)**0 + _
                   subst((DD**1)(f(x)), x = a)/factorial(1) * (xx - a)**1 + _
                   subst((DD**2)(f(x)), x = a)/factorial(2) * (xx - a)**2
 

   (173)
     (f,xx,a)
   +-> 
               0                                 1
       subst(DD (f(x)),x= a)         0   subst(DD (f(x)),x= a)         1
       --------------------- (xx - a)  + --------------------- (xx - a)
            factorial(0)                      factorial(1)
     + 
               2
       subst(DD (f(x)),x= a)         2
       --------------------- (xx - a)
            factorial(2)
                                                      Type: AnonymousFunction
--R 
--R
--R   (173)
--R     (f,xx,a)
--R   +-> 
--R               0                                 1
--R       subst(DD (f(x)),x= a)         0   subst(DD (f(x)),x= a)         1
--R       --------------------- (xx - a)  + --------------------- (xx - a)
--R            factorial(0)                      factorial(1)
--R     + 
--R               2
--R       subst(DD (f(x)),x= a)         2
--R       --------------------- (xx - a)
--R            factorial(2)
--R                                                      Type: AnonymousFunction
--E 181

--S 182 of 200
T(f, x, a)
 

            2           2  ,,                ,
          (x  - 2a x + a )f  (a) + (2x - 2a)f (a) + 2f(a)

   (174)  -----------------------------------------------
                                 2
                                                     Type: Expression Integer
--R 
--R
--R            2           2  ,,                ,
--R          (x  - 2a x + a )f  (a) + (2x - 2a)f (a) + 2f(a)
--R
--R   (174)  -----------------------------------------------
--R                                 2
--R                                                     Type: Expression Integer
--E 182

--S 183 of 200
T(g, y, b)
 

            2           2  ,,                ,
          (y  - 2b y + b )g  (b) + (2y - 2b)g (b) + 2g(b)

   (175)  -----------------------------------------------
                                 2
                                                     Type: Expression Integer
--R 
--R
--R            2           2  ,,                ,
--R          (y  - 2b y + b )g  (b) + (2y - 2b)g (b) + 2g(b)
--R
--R   (175)  -----------------------------------------------
--R                                 2
--R                                                     Type: Expression Integer
--E 183

--S 184 of 200
Sin:= operator("sin") :: Operator(Expression Integer)
 

   (176)  sin
                                            Type: Operator Expression Integer
--R 
--R
--R   (176)  sin
--R                                            Type: Operator Expression Integer
--E 184

--S 185 of 200
evaluate(Sin, x +-> sin(x))$Operator(Expression Integer)
 

   (177)  sin
                                            Type: Operator Expression Integer
--R 
--R
--R   (177)  sin
--R                                            Type: Operator Expression Integer
--E 185

--S 186 of 200
T(Sin, z, c)
 

              2           2
          (- z  + 2c z - c  + 2)sin(c) + (2z - 2c)cos(c)
   (178)  ----------------------------------------------
                                 2
                                                     Type: Expression Integer
--R 
--R
--R              2           2
--R          (- z  + 2c z - c  + 2)sin(c) + (2z - 2c)cos(c)
--R   (178)  ----------------------------------------------
--R                                 2
--R                                                     Type: Expression Integer
--E 186

--S 187 of 200
p(n, x) == 1/(2**n*factorial(n)) * D((x**2 - 1)**n, x, n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 187

--S 188 of 200
for i in 0..4 repeat {  output("");    output(concat(["p(", string(i), ", x) = "]));    output(p(i, x))}
 
   Compiling function p with type (NonNegativeInteger,Variable x) -> 
      Polynomial Fraction Integer 

   p(0, x) =
   1

   p(1, x) =
   x

   p(2, x) =
   3  2   1
   - x  - -
   2      2

   p(3, x) =
   5  3   3
   - x  - - x
   2      2

   p(4, x) =
   35  4   15  2   3
   -- x  - -- x  + -
    8       4      8
                                                                   Type: Void
--R 
--R   Compiling function p with type (NonNegativeInteger,Variable x) -> 
--R      Polynomial Fraction Integer 
--R
--R   p(0, x) =
--R   1
--R
--R   p(1, x) =
--R   x
--R
--R   p(2, x) =
--R   3  2   1
--R   - x  - -
--R   2      2
--R
--R   p(3, x) =
--R   5  3   3
--R   - x  - - x
--R   2      2
--R
--R   p(4, x) =
--R   35  4   15  2   3
--R   -- x  - -- x  + -
--R    8       4      8
--R                                                                   Type: Void
--E 188

--S 189 of 200
eval(p(4, x), x = 1)
 
   Compiling function p with type (PositiveInteger,Variable x) -> 
      Polynomial Fraction Integer 

   (181)  1
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function p with type (PositiveInteger,Variable x) -> 
--R      Polynomial Fraction Integer 
--R
--R   (181)  1
--R                                            Type: Polynomial Fraction Integer
--E 189

--S 190 of 200
pp(0, x) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 190

--S 191 of 200
pp(1, x) == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 191

--S 192 of 200
pp(n, x) == ((2*n - 1)*x*pp(n - 1, x) - (n - 1)*pp(n - 2, x))/n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 192

--S 193 of 200
for i in 0..4 repeat {   output("");   output(concat(["pp(", string(i), ", x) = "]));   output(pp(i, x))}
 
   Compiling function pp with type (Integer,Variable x) -> Polynomial 
      Fraction Integer 

   pp(0, x) =
   1

   pp(1, x) =
   x

   pp(2, x) =
   3  2   1
   - x  - -
   2      2

   pp(3, x) =
   5  3   3
   - x  - - x
   2      2

   pp(4, x) =
   35  4   15  2   3
   -- x  - -- x  + -
    8       4      8
                                                                   Type: Void
--R 
--R   Compiling function pp with type (Integer,Variable x) -> Polynomial 
--R      Fraction Integer 
--R
--R   pp(0, x) =
--R   1
--R
--R   pp(1, x) =
--R   x
--R
--R   pp(2, x) =
--R   3  2   1
--R   - x  - -
--R   2      2
--R
--R   pp(3, x) =
--R   5  3   3
--R   - x  - - x
--R   2      2
--R
--R   pp(4, x) =
--R   35  4   15  2   3
--R   -- x  - -- x  + -
--R    8       4      8
--R                                                                   Type: Void
--E 193

)clear properties p pp
 
   Compiled code for p has been cleared.
   Compiled code for pp has been cleared.

--S 194 of 200
a:= operator('a)
 

   (186)  a
                                                          Type: BasicOperator
--R 
--R
--R   (186)  a
--R                                                          Type: BasicOperator
--E 194

--S 195 of 200
sum(a(i)*x**i, i = 1..5)
 

               5        4        3        2
   (187)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
                                                     Type: Expression Integer
--R 
--R
--R               5        4        3        2
--R   (187)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
--R                                                     Type: Expression Integer
--E 195

--S 196 of 200
p:= factor(%)
 

               5        4        3        2
   (188)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
                                            Type: Factored Expression Integer
--R 
--R
--R               5        4        3        2
--R   (188)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
--R                                            Type: Factored Expression Integer
--E 196


)set fortran ints2floats off
 

--S 197 of 200
outputAsFortran('p = p)
 
      p=a(5)*x**5+a(4)*x**4+a(3)*x**3+a(2)*x*x+a(1)*x
                                                                   Type: Void
--R 
--R      p=a(5)*x**5+a(4)*x**4+a(3)*x**3+a(2)*x*x+a(1)*x
--R                                                                   Type: Void
--E 197

--S 198 of 200
true and false
 

   (190)  false
                                                                Type: Boolean
--R 
--R
--R   (190)  false
--R                                                                Type: Boolean
--E 198

--S 199 of 200
x or (not x)
 
 
Daly Bug
   Argument number 1 to "or" must be a Boolean.
--R 
--R 
--RDaly Bug
--R   Argument number 1 to "or" must be a Boolean.
--E 199

--S 200 of 200
x or y or (x and y)
 
 
Daly Bug
   Argument number 1 to "or" must be a Boolean.
--R 
--R 
--RDaly Bug
--R   Argument number 1 to "or" must be a Boolean.
--E 200
)spool
 
Starts dribbling to bug10312.output (2009/2/17, 17:44:0).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 2
p:=(1/2+n)::UTS(FRAC INT, 'n, 0)
 

        1
   (1)  - + n
        2
                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--R 
--R
--R        1
--R   (1)  - + n
--R        2
--R                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--E 1

--S 2 of 2
(p**(-1))$UTS(FRAC INT, 'n, 0)
 
   Compiling function G1471 with type Integer -> Boolean 

   (2)
                2      3      4      5       6       7       8        9
     2 - 4n + 8n  - 16n  + 32n  - 64n  + 128n  - 256n  + 512n  - 1024n
   + 
          10      11
     2048n   + O(n  )
                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--R 
--I   Compiling function G1473 with type Integer -> Boolean 
--R
--R   (2)
--R                2      3      4      5       6       7       8        9
--R     2 - 4n + 8n  - 16n  + 32n  - 64n  + 128n  - 256n  + 512n  - 1024n
--R   + 
--R          10      11
--R     2048n   + O(n  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--E 2
)spool
 
Starts dribbling to evalex.output (2009/2/17, 17:45:45).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- Input for page PrefixEval
--S 1 of 3
cos(2)
 

   (1)  cos(2)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  cos(2)
--R                                                     Type: Expression Integer
--E 1

-- Input for page PrefixEval
)clear all
 
   All user variables and function definitions have been cleared.

--S 2 of 3
cos(2)
 

   (1)  cos(2)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  cos(2)
--R                                                     Type: Expression Integer
--E 2

-- Input for page InfixEval
)clear all
 
   All user variables and function definitions have been cleared.

--S 3 of 3
2 + 3.4
 

   (1)  5.4
                                                                  Type: Float
--R 
--R
--R   (1)  5.4
--R                                                                  Type: Float
--E 3
)spool
 
Starts dribbling to seg.output (2009/2/17, 18:0:17).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 10
s := 3..10
 

   (1)  3..10
                                                Type: Segment PositiveInteger
--R 
--R
--R   (1)  3..10
--R                                                Type: Segment PositiveInteger
--E 1

--S 2 of 10
lo s
 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 10
hi s
 

   (3)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  10
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 10
t := 10..3 by -2
 

   (4)  10..3 by - 2
                                                Type: Segment PositiveInteger
--R 
--R
--R   (4)  10..3 by - 2
--R                                                Type: Segment PositiveInteger
--E 4

--S 5 of 10
incr s
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
incr t
 

   (6)  - 2
                                                                Type: Integer
--R 
--R
--R   (6)  - 2
--R                                                                Type: Integer
--E 6

--S 7 of 10
l := [1..3, 5, 9, 15..11 by -1]
 

   (7)  [1..3,5..5,9..9,15..11 by - 1]
                                           Type: List Segment PositiveInteger
--R 
--R
--R   (7)  [1..3,5..5,9..9,15..11 by - 1]
--R                                           Type: List Segment PositiveInteger
--E 7

--S 8 of 10
expand s
 

   (8)  [3,4,5,6,7,8,9,10]
                                                           Type: List Integer
--R 
--R
--R   (8)  [3,4,5,6,7,8,9,10]
--R                                                           Type: List Integer
--E 8

--S 9 of 10
expand t
 

   (9)  [10,8,6,4]
                                                           Type: List Integer
--R 
--R
--R   (9)  [10,8,6,4]
--R                                                           Type: List Integer
--E 9

--S 10 of 10
expand l
 

   (10)  [1,2,3,5,9,15,14,13,12,11]
                                                           Type: List Integer
--R 
--R
--R   (10)  [1,2,3,5,9,15,14,13,12,11]
--R                                                           Type: List Integer
--E 10
)spool 
 
Starts dribbling to constant.output (2009/2/17, 17:44:14).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

-- knuth volume 2 p596 tables of numerical quantities
--S 1 of 37
digits(42)
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 37
outputSpacing(5)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 37
numeric(sqrt(2))
 

   (3)  1.41421 35623 73095 04880 16887 24209 69807 85696 7
                                                                  Type: Float
--R 
--R
--R   (3)  1.41421 35623 73095 04880 16887 24209 69807 85696 7
--R                                                                  Type: Float
--E 3

--S 4 of 37
numeric(sqrt(3))
 

   (4)  1.73205 08075 68877 29352 74463 41505 87236 69428 1
                                                                  Type: Float
--R 
--R
--R   (4)  1.73205 08075 68877 29352 74463 41505 87236 69428 1
--R                                                                  Type: Float
--E 4

--S 5 of 37
numeric(sqrt(5))
 

   (5)  2.23606 79774 99789 69640 91736 68731 27623 54406 2
                                                                  Type: Float
--R 
--R
--R   (5)  2.23606 79774 99789 69640 91736 68731 27623 54406 2
--R                                                                  Type: Float
--E 5

--S 6 of 37
numeric(sqrt(10))
 

   (6)  3.16227 76601 68379 33199 88935 44432 71853 37195 6
                                                                  Type: Float
--R 
--R
--R   (6)  3.16227 76601 68379 33199 88935 44432 71853 37195 6
--R                                                                  Type: Float
--E 6

--S 7 of 37
numeric(2**(1/3))
 

   (7)  1.25992 10498 94873 16476 72106 07278 22835 05702 5
                                                                  Type: Float
--R 
--R
--R   (7)  1.25992 10498 94873 16476 72106 07278 22835 05702 5
--R                                                                  Type: Float
--E 7

--S 8 of 37
numeric(3**(1/3))
 

   (8)  1.44224 95703 07408 38232 16383 10780 10958 83918 7
                                                                  Type: Float
--R 
--R
--R   (8)  1.44224 95703 07408 38232 16383 10780 10958 83918 7
--R                                                                  Type: Float
--E 8

--S 9 of 37
numeric(2**(1/4))
 

   (9)  1.18920 71150 02721 06671 74999 70560 47591 52929 7
                                                                  Type: Float
--R 
--R
--R   (9)  1.18920 71150 02721 06671 74999 70560 47591 52929 7
--R                                                                  Type: Float
--E 9

--S 10 of 37
numeric(log(2))
 

   (10)  0.69314 71805 59945 30941 72321 21458 17656 80755
                                                                  Type: Float
--R 
--R
--R   (10)  0.69314 71805 59945 30941 72321 21458 17656 80755
--R                                                                  Type: Float
--E 10

--S 11 of 37
numeric(log(3))
 

   (11)  1.09861 22886 68109 69139 52452 36922 52570 46474 9
                                                                  Type: Float
--R 
--R
--R   (11)  1.09861 22886 68109 69139 52452 36922 52570 46474 9
--R                                                                  Type: Float
--E 11

--S 12 of 37
numeric(log(10))
 

   (12)  2.30258 50929 94045 68401 79914 54684 36420 76011
                                                                  Type: Float
--R 
--R
--R   (12)  2.30258 50929 94045 68401 79914 54684 36420 76011
--R                                                                  Type: Float
--E 12

--S 13 of 37
numeric(1/log(2))
 

   (13)  1.44269 50408 88963 40735 99246 81001 89213 74266 5
                                                                  Type: Float
--R 
--R
--R   (13)  1.44269 50408 88963 40735 99246 81001 89213 74266 5
--R                                                                  Type: Float
--E 13

--S 14 of 37
numeric(1/log(10))
 

   (14)  0.43429 44819 03251 82765 11289 18916 60508 22943 97
                                                                  Type: Float
--R 
--R
--R   (14)  0.43429 44819 03251 82765 11289 18916 60508 22943 97
--R                                                                  Type: Float
--E 14

--S 15 of 37
numeric(%pi)
 

   (15)  3.14159 26535 89793 23846 26433 83279 50288 41971 7
                                                                  Type: Float
--R 
--R
--R   (15)  3.14159 26535 89793 23846 26433 83279 50288 41971 7
--R                                                                  Type: Float
--E 15

--S 16 of 37
numeric(%pi/180)
 

   (16)  0.01745 32925 19943 29576 92369 07684 88612 71344 287
                                                                  Type: Float
--R 
--R
--R   (16)  0.01745 32925 19943 29576 92369 07684 88612 71344 287
--R                                                                  Type: Float
--E 16

--S 17 of 37
numeric(1/%pi)
 

   (17)  0.31830 98861 83790 67153 77675 26745 02872 40689 19
                                                                  Type: Float
--R 
--R
--R   (17)  0.31830 98861 83790 67153 77675 26745 02872 40689 19
--R                                                                  Type: Float
--E 17

--S 18 of 37
numeric(%pi**2)
 

   (18)  9.86960 44010 89358 61883 44909 99876 15113 53136 9
                                                                  Type: Float
--R 
--R
--R   (18)  9.86960 44010 89358 61883 44909 99876 15113 53136 9
--R                                                                  Type: Float
--E 18

--S 19 of 37
numeric(sqrt(%pi))
 

   (19)  1.77245 38509 05516 02729 81674 83341 14518 27975 5
                                                                  Type: Float
--R 
--R
--R   (19)  1.77245 38509 05516 02729 81674 83341 14518 27975 5
--R                                                                  Type: Float
--E 19

--S 20 of 37
numeric(Gamma(1/2))
 

   (20)  1.77245 38509 05516 32600 86374 06630 44154 64401 2
                                                                  Type: Float
--R 
--R
--R   (20)  1.77245 38509 05516 32600 86374 06630 44154 64401 2
--R                                                                  Type: Float
--E 20

--S 21 of 37
numeric(Gamma(1/3))
 

   (21)  2.67893 85347 07747 45417 77064 58722 24122 28584 3
                                                                  Type: Float
--R 
--R
--R   (21)  2.67893 85347 07747 45417 77064 58722 24122 28584 3
--R                                                                  Type: Float
--E 21

--S 22 of 37
numeric(Gamma(2/3))
 

   (22)  1.35411 79394 26400 68522 10968 64552 23709 34486 4
                                                                  Type: Float
--R 
--R
--R   (22)  1.35411 79394 26400 46317 64919 39520 92900 87223 1
--R                                                                  Type: Float
--E 22

--S 23 of 37
numeric(%e)
 

   (23)  2.71828 18284 59045 23536 02874 71352 66249 77572 5
                                                                  Type: Float
--R 
--R
--R   (23)  2.71828 18284 59045 23536 02874 71352 66249 77572 5
--R                                                                  Type: Float
--E 23

--S 24 of 37
numeric(1/%e)
 

   (24)  0.36787 94411 71442 32159 55237 70161 46086 74458 11
                                                                  Type: Float
--R 
--R
--R   (24)  0.36787 94411 71442 32159 55237 70161 46086 74458 11
--R                                                                  Type: Float
--E 24

--S 25 of 37
numeric(%e**2)
 

   (25)  7.38905 60989 30650 22723 04274 60575 00781 31803 1
                                                                  Type: Float
--R 
--R
--R   (25)  7.38905 60989 30650 22723 04274 60575 00781 31803 1
--R                                                                  Type: Float
--E 25

--S 26 of 37
gamma:=numeric(sum(1/x,x=1..10000)-log(10000))
 

   (26)  0.57726 56640 68199 52810 65120 86114 14850 44548 58
                                                                  Type: Float
--R 
--R
--R   (26)  0.57726 56640 68199 52810 65120 86114 14850 44548 58
--R                                                                  Type: Float
--E 26

--S 27 of 37
numeric(log(%pi))
 

   (27)  1.14472 98858 49400 17414 34273 51353 05871 16472 9
                                                                  Type: Float
--R 
--R
--R   (27)  1.14472 98858 49400 17414 34273 51353 05871 16472 9
--R                                                                  Type: Float
--E 27

--S 28 of 37
phi:=(1+sqrt(5))/2
 

          +-+
         \|5  + 1
   (28)  --------
             2
                                                        Type: AlgebraicNumber
--R 
--R
--R          +-+
--R         \|5  + 1
--R   (28)  --------
--R             2
--R                                                        Type: AlgebraicNumber
--E 28

--S 29 of 37
numeric(phi)
 

   (29)  1.61803 39887 49894 84820 45868 34365 63811 77203 1
                                                                  Type: Float
--R 
--R
--R   (29)  1.61803 39887 49894 84820 45868 34365 63811 77203 1
--R                                                                  Type: Float
--E 29

--S 30 of 37
gamma:=0.5772156649015328606065120900824024310422
 

   (30)  0.57721 56649 01532 86060 65120 90082 40243 10422
                                                                  Type: Float
--R 
--R
--R   (30)  0.57721 56649 01532 86060 65120 90082 40243 10422
--R                                                                  Type: Float
--E 30

--S 31 of 37
numeric(%e**gamma)
 

   (31)  1.78107 24179 90197 98523 65041 03107 17954 91697 2
                                                                  Type: Float
--R 
--R
--R   (31)  1.78107 24179 90197 98523 65041 03107 17954 91697 2
--R                                                                  Type: Float
--E 31

--S 32 of 37
numeric(%e**(%pi/4))
 

   (32)  2.19328 00507 38015 45655 97696 59278 73822 34616 4
                                                                  Type: Float
--R 
--R
--R   (32)  2.19328 00507 38015 45655 97696 59278 73822 34616 4
--R                                                                  Type: Float
--E 32

--S 33 of 37
numeric(sin(1))
 

   (33)  0.84147 09848 07896 50665 25023 21630 29899 96225 63
                                                                  Type: Float
--R 
--R
--R   (33)  0.84147 09848 07896 50665 25023 21630 29899 96225 63
--R                                                                  Type: Float
--E 33

--S 34 of 37
numeric(cos(1))
 

   (34)  0.54030 23058 68139 71740 09366 07442 97660 37323 1
                                                                  Type: Float
--R 
--R
--R   (34)  0.54030 23058 68139 71740 09366 07442 97660 37323 1
--R                                                                  Type: Float
--E 34

--S 35 of 37
numeric(log(phi))
 

   (35)  0.48121 18250 59603 44749 77589 13424 36842 31351 85
                                                                  Type: Float
--R 
--R
--R   (35)  0.48121 18250 59603 44749 77589 13424 36842 31351 85
--R                                                                  Type: Float
--E 35

--S 36 of 37
numeric(1/log(phi))
 

   (36)  2.07808 69212 35027 53760 13226 06117 79576 77421 9
                                                                  Type: Float
--R 
--R
--R   (36)  2.07808 69212 35027 53760 13226 06117 79576 77421 9
--R                                                                  Type: Float
--E 36

--S 37 of 37
numeric(-log(log(2)))
 

   (37)  0.36651 29205 81664 32701 24391 58232 66946 94542 64
                                                                  Type: Float
--R 
--R
--R   (37)  0.36651 29205 81664 32701 24391 58232 66946 94542 64
--R                                                                  Type: Float
--E 37
)spool
 
Starts dribbling to bstree.output (2009/2/17, 17:43:59).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 12
lv := [8,3,5,4,6,2,1,5,7]
 

   (1)  [8,3,5,4,6,2,1,5,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [8,3,5,4,6,2,1,5,7]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 12
t := binarySearchTree lv
 

   (2)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
                                       Type: BinarySearchTree PositiveInteger
--R 
--R
--R   (2)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
--R                                       Type: BinarySearchTree PositiveInteger
--E 2

--S 3 of 12
emptybst := empty()$BSTREE(INT)
 

   (3)  []
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (3)  []
--R                                               Type: BinarySearchTree Integer
--E 3

--S 4 of 12
t1 := insert!(8,emptybst)
 

   (4)  8
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (4)  8
--R                                               Type: BinarySearchTree Integer
--E 4

--S 5 of 12
insert!(3,t1)
 

   (5)  [3,8,.]
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (5)  [3,8,.]
--R                                               Type: BinarySearchTree Integer
--E 5

--S 6 of 12
leaves t
 

   (6)  [1,4,5,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (6)  [1,4,5,7]
--R                                                   Type: List PositiveInteger
--E 6

--S 7 of 12
split(3,t)
 

   (7)  [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]]
Type: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger)
--R 
--R
--R   (7)  [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]]
--RType: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger)
--E 7

--S 8 of 12
insertRoot: (INT,BSTREE INT) -> BSTREE INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 12
insertRoot(x, t) ==
    a := split(x, t)
    node(a.less, x, a.greater)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 12
buildFromRoot ls == reduce(insertRoot,ls,emptybst)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 12
rt := buildFromRoot reverse lv
 
   Compiling function buildFromRoot with type List PositiveInteger -> 
      BinarySearchTree Integer 
   Compiling function insertRoot with type (Integer,BinarySearchTree 
      Integer) -> BinarySearchTree Integer 

   (11)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
                                               Type: BinarySearchTree Integer
--R 
--R   Compiling function buildFromRoot with type List PositiveInteger -> 
--R      BinarySearchTree Integer 
--R   Compiling function insertRoot with type (Integer,BinarySearchTree 
--R      Integer) -> BinarySearchTree Integer 
--R
--R   (11)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
--R                                               Type: BinarySearchTree Integer
--E 11

--S 12 of 12
(t = rt)@Boolean
 

   (12)  true
                                                                Type: Boolean
--R 
--R
--R   (12)  true
--R                                                                Type: Boolean
--E 12 
)spool
 
Starts dribbling to algfacob.output (2009/2/17, 17:43:43).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1 of 37
(w,x,y,z): FR INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 37
x := 2**8 * 78**7 * 111**3 * 74534
 

         16 10  7  3
   (2)  2  3  13 37 83 449
                                                       Type: Factored Integer
--R 
--R
--R         16 10  7  3
--R   (2)  2  3  13 37 83 449
--R                                                       Type: Factored Integer
--E 2

--S 3 of 37
y := nilFactor(2,10) * nilFactor(3,20) * nilFactor(5,30)
 

         10 20 30
   (3)  2  3  5
                                                       Type: Factored Integer
--R 
--R
--R         10 20 30
--R   (3)  2  3  5
--R                                                       Type: Factored Integer
--E 3

--S 4 of 37
x*y
 

         26 30 30  7  3
   (4)  2  3  5  13 37 83 449
                                                       Type: Factored Integer
--R 
--R
--R         26 30 30  7  3
--R   (4)  2  3  5  13 37 83 449
--R                                                       Type: Factored Integer
--E 4

--S 5 of 37
w := x+y
 

         10 10
   (5)  2  3  13535311 4062978256593778783
                                                       Type: Factored Integer
--R 
--R
--R         10 10
--R   (5)  2  3  13535311 4062978256593778783
--R                                                       Type: Factored Integer
--E 5

--S 6 of 37
expand w
 

   (6)  3325257188459534016841161201804288
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  3325257188459534016841161201804288
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 37
f := x/y
 

         6  7  3
        2 13 37 83 449
   (7)  --------------
             10 30
            3  5
                                              Type: Fraction Factored Integer
--R 
--R
--R         6  7  3
--R        2 13 37 83 449
--R   (7)  --------------
--R             10 30
--R            3  5
--R                                              Type: Fraction Factored Integer
--E 7

--S 8 of 37
g := (x**9)/y
 

         134 70  63  27  9   9
        2   3  13  37  83 449
   (8)  ----------------------
                   30
                  5
                                              Type: Fraction Factored Integer
--R 
--R
--R         134 70  63  27  9   9
--R        2   3  13  37  83 449
--R   (8)  ----------------------
--R                   30
--R                  5
--R                                              Type: Fraction Factored Integer
--E 8

--S 9 of 37
f*g
 

         140 60  70  30  10   10
        2   3  13  37  83  449
   (9)  ------------------------
                    60
                   5
                                              Type: Fraction Factored Integer
--R 
--R
--R         140 60  70  30  10   10
--R        2   3  13  37  83  449
--R   (9)  ------------------------
--R                    60
--R                   5
--R                                              Type: Fraction Factored Integer
--E 9

--S 10 of 37
h := (f*g)/(g*nilFactor(2,200))
 

           7  3
         13 37 83 449
   (10)  ------------
           194 10 30
          2   3  5
                                              Type: Fraction Factored Integer
--R 
--R
--R           7  3
--R         13 37 83 449
--R   (10)  ------------
--R           194 10 30
--R          2   3  5
--R                                              Type: Fraction Factored Integer
--E 10

)clear all
 
   All user variables and function definitions have been cleared.

--S 11  of 37
(u,v,w) : FR POLY INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 37
u := factor (x**4 - y**4)
 

                          2    2
   (2)  - (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                          2    2
--R   (2)  - (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 12

--S 13 of 37
v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1)
 

               2       2  2    2
   (3)  (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2       2  2    2
--R   (3)  (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 13

--S 14 of 37
w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * nilFactor(x-y,2)
 

               2           2
   (4)  (y - x) (y + x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2           2
--R   (4)  (y - x) (y + x + 1)
--R                                            Type: Factored Polynomial Integer
--E 14

--S 15 of 37
nthFactor(u,1)
 

   (5)  y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)  y - x
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 37
nthFactor(u,2)
 

   (6)  y + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  y + x
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 37
nthFactor(u,3)
 

         2    2
   (7)  y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2    2
--R   (7)  y  + x
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 37
nthFactor(u,4)
 

   (8)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (8)  1
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 37
gcd(u,v)
 

                        2    2
   (9)  (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                        2    2
--R   (9)  (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 19

--S 20 of 37
u + v
 

                         2    2       2    2
   (10)  (y - x)(y + x)(y  - x  - 1)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2       2    2
--R   (10)  (y - x)(y + x)(y  - x  - 1)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 20

--S 21 of 37
lcm(u,v)
 

                  2       2  2    2
   (11)  - (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  2       2  2    2
--R   (11)  - (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 21

--S 22 of 37
u * v * w
 

                  5       3           2  2    2 2
   (12)  - (y - x) (y + x) (y + x + 1) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  5       3           2  2    2 2
--R   (12)  - (y - x) (y + x) (y + x + 1) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 22

--S 23 of 37
expand %
 

   (13)
        14     13      2           12      2       11       4     3  10
     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
   + 
        4     3  9        6     5     4  8        6     5  7      8     7  6
     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
   + 
        8     7  5     10     9     8  4      10     9  3        12     11  2
     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
   + 
          12     11      14     13    12
     (- 2x   - 2x  )y + x   + 2x   + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (13)
--R        14     13      2           12      2       11       4     3  10
--R     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
--R   + 
--R        4     3  9        6     5     4  8        6     5  7      8     7  6
--R     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
--R   + 
--R        8     7  5     10     9     8  4      10     9  3        12     11  2
--R     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
--R   + 
--R          12     11      14     13    12
--R     (- 2x   - 2x  )y + x   + 2x   + x
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 37
u/w
 

                      2    2
             (y + x)(y  + x )
   (14)  - -------------------
                             2
           (y - x)(y + x + 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                      2    2
--R             (y + x)(y  + x )
--R   (14)  - -------------------
--R                             2
--R           (y - x)(y + x + 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 24

--S 25 of 37
w/(u*v)
 

                             2
                  (y + x + 1)
   (15)  - -------------------------
                         3  2    2 2
           (y - x)(y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                             2
--R                  (y + x + 1)
--R   (15)  - -------------------------
--R                         3  2    2 2
--R           (y - x)(y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 25

--S 26 of 37
%%(-1) * %%(-2)
 

                     1
   (16)  -------------------------
                2       2  2    2
         (y - x) (y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                     1
--R   (16)  -------------------------
--R                2       2  2    2
--R         (y - x) (y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 26

--S 27 of 37
%%(-1) + %%(-2)
 

             2        2           3     2
           2y  + (- 2x  + 1)y - 2x  - 2x  - x
   (17)  - ----------------------------------
                      2       3  2    2 2
               (y - x) (y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R             2        2           3     2
--R           2y  + (- 2x  + 1)y - 2x  - 2x  - x
--R   (17)  - ----------------------------------
--R                      2       3  2    2 2
--R               (y - x) (y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 27

)clear all
 
   All user variables and function definitions have been cleared.
 
--S 28 of 37
f : FR INT := 144000
 

         7 2 3
   (1)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         7 2 3
--R   (1)  2 3 5
--R                                                       Type: Factored Integer
--E 28

--S 29 of 37
nthFactor(f,1)
 

   (2)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  2
--R                                                        Type: PositiveInteger
--E 29

--S 30 of 37
nthExponent(f,1)
 

   (3)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  7
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 37
nthFlag(f,1)
 

   (4)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (4)  "prime"
--R                                                     Type: Union("prime",...)
--E 31

--S 32 of 37
nthFlag(nilFactor(20,4),1)
 

   (5)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (5)  "nil"
--R                                                       Type: Union("nil",...)
--E 32

--S 33 of 37
nthFlag(primeFactor(7,9),1)
 

   (6)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (6)  "prime"
--R                                                     Type: Union("prime",...)
--E 33

--S 34 of 37
factors f
 

   (7)
   [[factor= 2,exponent= 7],[factor= 3,exponent= 2],[factor= 5,exponent= 3]]
                         Type: List Record(factor: Integer,exponent: Integer)
--R 
--R
--R   (7)
--R   [[factor= 2,exponent= 7],[factor= 3,exponent= 2],[factor= 5,exponent= 3]]
--R                         Type: List Record(factor: Integer,exponent: Integer)
--E 34

--S 35 of 37
numberOfFactors f
 

   (8)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  3
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 37
f
 

         7 2 3
   (9)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         7 2 3
--R   (9)  2 3 5
--R                                                       Type: Factored Integer
--E 36

--S 37 of 37
reduce(*,[nthFactor(f,i) :: (FR INT) for i in 1..numberOfFactors(f)])
 

   (10)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R   (10)  2 3 5
--R                                                       Type: Factored Integer
--E 37
)spool
 
Starts dribbling to schaum30.output (2009/2/17, 17:59:45).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(tanh(a*x),x)
 

                    2cosh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2cosh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=1/a*log(cosh(a*x))
 

        log(cosh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(cosh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

                                       2cosh(a x)
        - log(cosh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2cosh(a x)
--R        - log(cosh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 4
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 5      14:604 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 6
aa:=integrate(tanh(a*x)^2,x)
 

        - sinh(a x) + (a x + 1)cosh(a x)
   (1)  --------------------------------
                   a cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - sinh(a x) + (a x + 1)cosh(a x)
--R   (1)  --------------------------------
--R                   a cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7
bb:=x-tanh(a*x)/a
 

        - tanh(a x) + a x
   (2)  -----------------
                a
                                                     Type: Expression Integer
--R
--R        - tanh(a x) + a x
--R   (2)  -----------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 8
cc:=aa-bb
 

        cosh(a x)tanh(a x) - sinh(a x) + cosh(a x)
   (3)  ------------------------------------------
                        a cosh(a x)
                                                     Type: Expression Integer
--R
--R        cosh(a x)tanh(a x) - sinh(a x) + cosh(a x)
--R   (3)  ------------------------------------------
--R                        a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 9
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 10     14:605 Schaums and Axiom differ by a constant
dd:=tanhrule cc
 

        1
   (5)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (5)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 11
aa:=integrate(tanh(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                      4                          3
       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
     + 
                        2                     2
       (- 6a x cosh(a x)  - 2a x + 2)sinh(a x)
     + 
                        3                                                  4
       (- 4a x cosh(a x)  + (- 4a x + 4)cosh(a x))sinh(a x) - a x cosh(a x)
     + 
                            2
       (- 2a x + 2)cosh(a x)  - a x
  /
                  4                        3                2               2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
     + 
                  3                                       4               2
     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                      4                          3
--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
--R     + 
--R                        2                     2
--R       (- 6a x cosh(a x)  - 2a x + 2)sinh(a x)
--R     + 
--R                        3                                                  4
--R       (- 4a x cosh(a x)  + (- 4a x + 4)cosh(a x))sinh(a x) - a x cosh(a x)
--R     + 
--R                            2
--R       (- 2a x + 2)cosh(a x)  - a x
--R  /
--R                  4                        3                2               2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
--R     + 
--R                  3                                       4               2
--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12
bb:=1/a*log(cosh(a*x))-tanh(a*x)^2/(2*a)
 

                                   2
        2log(cosh(a x)) - tanh(a x)
   (2)  ----------------------------
                     2a
                                                     Type: Expression Integer
--R
--R                                   2
--R        2log(cosh(a x)) - tanh(a x)
--R   (2)  ----------------------------
--R                     2a
--R                                                     Type: Expression Integer
--E

--S 13     14:606 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                       4                      3                 2              2
           - 2sinh(a x)  - 8cosh(a x)sinh(a x)  + (- 12cosh(a x)  - 4)sinh(a x)
         + 
                      3                                    4             2
         (- 8cosh(a x)  - 8cosh(a x))sinh(a x) - 2cosh(a x)  - 4cosh(a x)  - 2
      *
         log(cosh(a x))
     + 
                     4                      3               2              2
           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
         + 
                      3                                    4             2
           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
      *
                  2
         tanh(a x)
     + 
                       4                          3
       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
     + 
                         2                     2
       (- 12a x cosh(a x)  - 4a x + 4)sinh(a x)
     + 
                        3                                                   4
       (- 8a x cosh(a x)  + (- 8a x + 8)cosh(a x))sinh(a x) - 2a x cosh(a x)
     + 
                            2
       (- 4a x + 4)cosh(a x)  - 2a x
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
     + 
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                       4                      3                 2              2
--R           - 2sinh(a x)  - 8cosh(a x)sinh(a x)  + (- 12cosh(a x)  - 4)sinh(a x)
--R         + 
--R                      3                                    4             2
--R         (- 8cosh(a x)  - 8cosh(a x))sinh(a x) - 2cosh(a x)  - 4cosh(a x)  - 2
--R      *
--R         log(cosh(a x))
--R     + 
--R                     4                      3               2              2
--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
--R         + 
--R                      3                                    4             2
--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
--R      *
--R                  2
--R         tanh(a x)
--R     + 
--R                       4                          3
--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
--R     + 
--R                         2                     2
--R       (- 12a x cosh(a x)  - 4a x + 4)sinh(a x)
--R     + 
--R                        3                                                   4
--R       (- 8a x cosh(a x)  + (- 8a x + 8)cosh(a x))sinh(a x) - 2a x cosh(a x)
--R     + 
--R                            2
--R       (- 4a x + 4)cosh(a x)  - 2a x
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
--R     + 
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 14
aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x)
 

                            sinh(a x)                         sinh(a x)
        sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
                            cosh(a x)                         cosh(a x)
   (1)  -----------------------------------------------------------------
                                (a n + a)cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            sinh(a x)                         sinh(a x)
--R        sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
--R                            cosh(a x)                         cosh(a x)
--R   (1)  -----------------------------------------------------------------
--R                                (a n + a)cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 15
bb:=tanh(a*x)^(n+1)/((n+1)*a)
 

                 n + 1
        tanh(a x)
   (2)  --------------
            a n + a
                                                     Type: Expression Integer
--R
--R                 n + 1
--R        tanh(a x)
--R   (2)  --------------
--R            a n + a
--R                                                     Type: Expression Integer
--E

--S 16     14:607 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                           sinh(a x)                         sinh(a x)
       sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
                           cosh(a x)                         cosh(a x)
     + 
                           n + 1
       - cosh(a x)tanh(a x)
  /
     (a n + a)cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                           sinh(a x)                         sinh(a x)
--R       sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
--R                           cosh(a x)                         cosh(a x)
--R     + 
--R                           n + 1
--R       - cosh(a x)tanh(a x)
--R  /
--R     (a n + a)cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 17
aa:=integrate(sech(a*x)^2/tanh(a*x),x)
 

                      2cosh(a x)                     2sinh(a x)
        - log(- ---------------------) + log(- ---------------------)
                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   (1)  -------------------------------------------------------------
                                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2cosh(a x)                     2sinh(a x)
--R        - log(- ---------------------) + log(- ---------------------)
--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   (1)  -------------------------------------------------------------
--R                                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 18
bb:=1/a*log(tanh(a*x))
 

        log(tanh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(tanh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 19
cc:=aa-bb
 

   (3)
                                      2cosh(a x)
       - log(tanh(a x)) - log(- ---------------------)
                                sinh(a x) - cosh(a x)
     + 
                   2sinh(a x)
       log(- ---------------------)
             sinh(a x) - cosh(a x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      2cosh(a x)
--R       - log(tanh(a x)) - log(- ---------------------)
--R                                sinh(a x) - cosh(a x)
--R     + 
--R                   2sinh(a x)
--R       log(- ---------------------)
--R             sinh(a x) - cosh(a x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 20
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 21
dd:=tanhrule cc
 

   (5)
             sinh(a x)                2cosh(a x)
       - log(---------) - log(- ---------------------)
             cosh(a x)          sinh(a x) - cosh(a x)
     + 
                   2sinh(a x)
       log(- ---------------------)
             sinh(a x) - cosh(a x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R             sinh(a x)                2cosh(a x)
--R       - log(---------) - log(- ---------------------)
--R             cosh(a x)          sinh(a x) - cosh(a x)
--R     + 
--R                   2sinh(a x)
--R       log(- ---------------------)
--R             sinh(a x) - cosh(a x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 22     14:608 Schaums and Axiom agree
ee:=expandLog dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(1/tanh(a*x),x)
 

                    2sinh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2sinh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=1/a*log(sinh(a*x))
 

        log(sinh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 25
cc:=aa-bb
 

                                       2sinh(a x)
        - log(sinh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2sinh(a x)
--R        - log(sinh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 26
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 27     14:609 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 28     14:610 Axiom cannot compute this integral
aa:=integrate(x*tanh(a*x),x)
 

           x
         ++
   (1)   |   %O tanh(%O a)d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O tanh(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 29
aa:=integrate(x*tanh(a*x)^2,x)
 

   (1)
                    2                                   2
         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  + 2)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
         2 2                 2      2 2
       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
     + 
         2 2                 2    2 2
       (a x  - 4a x)cosh(a x)  + a x
  /
       2         2     2                       2         2     2
     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    2                                   2
--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  + 2)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R         2 2                 2      2 2
--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
--R     + 
--R         2 2                 2    2 2
--R       (a x  - 4a x)cosh(a x)  + a x
--R  /
--R       2         2     2                       2         2     2
--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 30
bb:=x^2/2-(x*tanh(a*x))/a+1/a^2*log(cosh(a*x))
 

                                            2 2
        2log(cosh(a x)) - 2a x tanh(a x) + a x
   (2)  ---------------------------------------
                            2
                          2a
                                                     Type: Expression Integer
--R
--R                                            2 2
--R        2log(cosh(a x)) - 2a x tanh(a x) + a x
--R   (2)  ---------------------------------------
--R                            2
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 31
cc:=aa-bb
 

   (3)
                   2                                  2
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(cosh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                       2                                          2
         (a x sinh(a x)  + 2a x cosh(a x)sinh(a x) + a x cosh(a x)  + a x)
      *
         tanh(a x)
     + 
                       2                                           2
       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(cosh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                       2                                          2
--R         (a x sinh(a x)  + 2a x cosh(a x)sinh(a x) + a x cosh(a x)  + a x)
--R      *
--R         tanh(a x)
--R     + 
--R                       2                                           2
--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 32
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 33
dd:=sinhsqrrule cc
 

   (5)
                                                       2
       (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)log(cosh(a x))
     + 
                                                       2
         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                                                                   2
         (4a x cosh(a x)sinh(a x) + a x cosh(2a x) + 2a x cosh(a x)  + a x)
      *
         tanh(a x)
     + 
                                                                   2
       - 8a x cosh(a x)sinh(a x) - 2a x cosh(2a x) - 4a x cosh(a x)  + 2a x
  /
       2                      2               2         2    2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                       2
--R       (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)log(cosh(a x))
--R     + 
--R                                                       2
--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                                                                   2
--R         (4a x cosh(a x)sinh(a x) + a x cosh(2a x) + 2a x cosh(a x)  + a x)
--R      *
--R         tanh(a x)
--R     + 
--R                                                                   2
--R       - 8a x cosh(a x)sinh(a x) - 2a x cosh(2a x) - 4a x cosh(a x)  + 2a x
--R  /
--R       2                      2               2         2    2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 34
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35
ee:=coshsqrrule dd
 

   (7)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(cosh(a x))
     + 
                                                         2cosh(a x)
       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(- ---------------------)
                                                   sinh(a x) - cosh(a x)
     + 
       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
     + 
       - 4a x cosh(a x)sinh(a x) - 2a x cosh(2a x)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (7)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(cosh(a x))
--R     + 
--R                                                         2cosh(a x)
--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(- ---------------------)
--R                                                   sinh(a x) - cosh(a x)
--R     + 
--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
--R     + 
--R       - 4a x cosh(a x)sinh(a x) - 2a x cosh(2a x)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 36
ff:=expandLog ee
 

   (8)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
     + 
       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
     + 
       (2log(- 2) - 4a x)cosh(a x)sinh(a x) + (log(- 2) - 2a x)cosh(2a x)
     + 
       log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
--R     + 
--R       (2log(- 2) - 4a x)cosh(a x)sinh(a x) + (log(- 2) - 2a x)cosh(2a x)
--R     + 
--R       log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 37
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (9)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %N sinh(y + x) - %N sinh(y - x)
--I   (9)  %N cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38
gg:=sinhcoshrule ff
 

   (10)
       (- sinh(2a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
     + 
       (a x sinh(2a x) + a x cosh(2a x) + a x)tanh(a x)
     + 
       (log(- 2) - 2a x)sinh(2a x) + (log(- 2) - 2a x)cosh(2a x) + log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (- sinh(2a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (a x sinh(2a x) + a x cosh(2a x) + a x)tanh(a x)
--R     + 
--R       (log(- 2) - 2a x)sinh(2a x) + (log(- 2) - 2a x)cosh(2a x) + log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 39     14:611 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         - log(- 1) + log(- 2)
   (11)  ---------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R         - log(- 1) + log(- 2)
--R   (11)  ---------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 40     14:612 Axiom cannot compute this integral
aa:=integrate(tanh(a*x)/x,x)
 

           x
         ++  tanh(%O a)
   (1)   |   ---------- d%O
        ++       %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  tanh(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 41
aa:=integrate(1/(p+q*tanh(a*x)),x)
 

              - 2q sinh(a x) - 2p cosh(a x)
        q log(-----------------------------) + (- a q - a p)x
                  sinh(a x) - cosh(a x)
   (1)  -----------------------------------------------------
                                2      2
                             a q  - a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - 2q sinh(a x) - 2p cosh(a x)
--R        q log(-----------------------------) + (- a q - a p)x
--R                  sinh(a x) - cosh(a x)
--R   (1)  -----------------------------------------------------
--R                                2      2
--R                             a q  - a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42
bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(q*sinh(a*x)+p*cosh(a*x))
 

        q log(q sinh(a x) + p cosh(a x)) - a p x
   (2)  ----------------------------------------
                          2      2
                       a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(q sinh(a x) + p cosh(a x)) - a p x
--R   (2)  ----------------------------------------
--R                          2      2
--R                       a q  - a p
--R                                                     Type: Expression Integer
--E

--S 43
cc:=aa-bb
 

   (3)
                                                  - 2q sinh(a x) - 2p cosh(a x)
       - q log(q sinh(a x) + p cosh(a x)) + q log(-----------------------------)
                                                      sinh(a x) - cosh(a x)
     + 
       - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                  - 2q sinh(a x) - 2p cosh(a x)
--R       - q log(q sinh(a x) + p cosh(a x)) + q log(-----------------------------)
--R                                                      sinh(a x) - cosh(a x)
--R     + 
--R       - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 44
dd:=expandLog cc
 

   (4)
       - q log(q sinh(a x) + p cosh(a x)) - q log(sinh(a x) - cosh(a x))
     + 
       q log(- q sinh(a x) - p cosh(a x)) + q log(2) - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R       - q log(q sinh(a x) + p cosh(a x)) - q log(sinh(a x) - cosh(a x))
--R     + 
--R       q log(- q sinh(a x) - p cosh(a x)) + q log(2) - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 45     14:613 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        q log(2) - 2q log(- 1)
   (5)  ----------------------
                 2      2
              a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(2) - 2q log(- 1)
--R   (5)  ----------------------
--R                 2      2
--R              a q  - a p
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 46     14:614 Axiom cannot compute this integral
aa:=integrate(tanh(a*x)^n,x)
 

           x
         ++            n
   (1)   |   tanh(%O a) d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   tanh(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to macros.output (2009/2/17, 17:52:50).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
--S 1 of 4
macro I == Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 4
macro M(R) == Matrix(R)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
macro p(n) == x < n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
macro q(i,j) == if x < i then i else j
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
)spool 
 
Starts dribbling to schaum34.output (2009/2/17, 17:59:54).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.

--S 1
aa:=integrate(asinh(x/a),x)
 

                               +-------+
           +-------+           | 2    2           +-------+
           | 2    2     2     \|x  + a   + x      | 2    2     2    2
        (x\|x  + a   - x )log(--------------) + x\|x  + a   - x  - a
                                     a
   (1)  -------------------------------------------------------------
                                 +-------+
                                 | 2    2
                                \|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R           +-------+           | 2    2           +-------+
--R           | 2    2     2     \|x  + a   + x      | 2    2     2    2
--R        (x\|x  + a   - x )log(--------------) + x\|x  + a   - x  - a
--R                                     a
--R   (1)  -------------------------------------------------------------
--R                                 +-------+
--R                                 | 2    2
--R                                \|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2
bb:=x*asinh(x/a)-sqrt(x^2+a^2)
 

           +-------+
           | 2    2            x
   (2)  - \|x  + a   + x asinh(-)
                               a
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2            x
--R   (2)  - \|x  + a   + x asinh(-)
--R                               a
--R                                                     Type: Expression Integer
--E

--S 3
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  + a   + x            x
   (3)  x log(--------------) - x asinh(-)
                     a                  a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  + a   + x            x
--R   (3)  x log(--------------) - x asinh(-)
--R                     a                  a
--R                                                     Type: Expression Integer
--E

--S 4
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5
dd:=asinhlogrule cc
 

                                        +-------+
                                        | 2    2
                                        |x  + a
               +-------+              a |-------  + x
               | 2    2                 |    2
              \|x  + a   + x           \|   a
   (5)  x log(--------------) - x log(---------------)
                     a                       a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  + a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R              \|x  + a   + x           \|   a
--R   (5)  x log(--------------) - x log(---------------)
--R                     a                       a
--R                                                     Type: Expression Integer
--E

--S 6
ee:=expandLog dd
 

                                        +-------+
               +-------+                | 2    2
               | 2    2                 |x  + a
   (6)  x log(\|x  + a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R               | 2    2                 |x  + a
--R   (6)  x log(\|x  + a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R                                                     Type: Expression Integer
--E

--S 7      14:646 Schaums and Axiom agree
ff:=rootSimp ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 8
aa:=integrate(x*asinh(x/a),x)
 

   (1)
                                                       +-------+
                     +-------+                         | 2    2
           3     2   | 2    2      4     2 2    4     \|x  + a   + x
       ((4x  + 2a x)\|x  + a   - 4x  - 4a x  - a )log(--------------)
                                                             a
     + 
                   +-------+
          3    2   | 2    2      4     2 2
       (2x  + a x)\|x  + a   - 2x  - 2a x
  /
        +-------+
        | 2    2      2     2
     8x\|x  + a   - 8x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                       +-------+
--R                     +-------+                         | 2    2
--R           3     2   | 2    2      4     2 2    4     \|x  + a   + x
--R       ((4x  + 2a x)\|x  + a   - 4x  - 4a x  - a )log(--------------)
--R                                                             a
--R     + 
--R                   +-------+
--R          3    2   | 2    2      4     2 2
--R       (2x  + a x)\|x  + a   - 2x  - 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     8x\|x  + a   - 8x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9
bb:=(x^2/2+a^2/4)*asinh(x/a)-(x*sqrt(x^2+a^2))/4
 

            +-------+
            | 2    2       2    2       x
        - x\|x  + a   + (2x  + a )asinh(-)
                                        a
   (2)  ----------------------------------
                         4
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2       2    2       x
--R        - x\|x  + a   + (2x  + a )asinh(-)
--R                                        a
--R   (2)  ----------------------------------
--R                         4
--R                                                     Type: Expression Integer
--E

--S 10
cc:=aa-bb
 

                       +-------+
                       | 2    2
           2    2     \|x  + a   + x         2    2       x
        (2x  + a )log(--------------) + (- 2x  - a )asinh(-)
                             a                            a
   (3)  ----------------------------------------------------
                                  4
                                                     Type: Expression Integer
--R
--R                       +-------+
--R                       | 2    2
--R           2    2     \|x  + a   + x         2    2       x
--R        (2x  + a )log(--------------) + (- 2x  - a )asinh(-)
--R                             a                            a
--R   (3)  ----------------------------------------------------
--R                                  4
--R                                                     Type: Expression Integer
--E

--S 11
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12
dd:=asinhlogrule cc
 

                                                          +-------+
                                                          | 2    2
                                                          |x  + a
                       +-------+                        a |-------  + x
                       | 2    2                           |    2
           2    2     \|x  + a   + x         2    2      \|   a
        (2x  + a )log(--------------) + (- 2x  - a )log(---------------)
                             a                                 a
   (5)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                                                          | 2    2
--R                                                          |x  + a
--R                       +-------+                        a |-------  + x
--R                       | 2    2                           |    2
--R           2    2     \|x  + a   + x         2    2      \|   a
--R        (2x  + a )log(--------------) + (- 2x  - a )log(---------------)
--R                             a                                 a
--R   (5)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 13
ee:=expandLog dd
 

                                                          +-------+
                       +-------+                          | 2    2
           2    2      | 2    2              2    2       |x  + a
        (2x  + a )log(\|x  + a   + x) + (- 2x  - a )log(a |-------  + x)
                                                          |    2
                                                         \|   a
   (6)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                       +-------+                          | 2    2
--R           2    2      | 2    2              2    2       |x  + a
--R        (2x  + a )log(\|x  + a   + x) + (- 2x  - a )log(a |-------  + x)
--R                                                          |    2
--R                                                         \|   a
--R   (6)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 14     14:647 Schaums and Axiom agree
ff:=rootSimp ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 15
aa:=integrate(x^2*asinh(x/a),x)
 

   (1)
                                                     +-------+
                       +-------+                     | 2    2
            5     2 3  | 2    2       6     2 4     \|x  + a   + x
       ((12x  + 3a x )\|x  + a   - 12x  - 9a x )log(--------------)
                                                           a
     + 
                            +-------+
          5     2 3     4   | 2    2      6     2 4     4 2     6
       (4x  - 5a x  - 6a x)\|x  + a   - 4x  + 3a x  + 9a x  + 2a
  /
                  +-------+
         2     2  | 2    2       3      2
     (36x  + 9a )\|x  + a   - 36x  - 27a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                     +-------+
--R                       +-------+                     | 2    2
--R            5     2 3  | 2    2       6     2 4     \|x  + a   + x
--R       ((12x  + 3a x )\|x  + a   - 12x  - 9a x )log(--------------)
--R                                                           a
--R     + 
--R                            +-------+
--R          5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (4x  - 5a x  - 6a x)\|x  + a   - 4x  + 3a x  + 9a x  + 2a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3      2
--R     (36x  + 9a )\|x  + a   - 36x  - 27a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16
bb:=x^3/3*asinh(x/a)+((2*a^2-x^2)*sqrt(x^2+a^2))/9
 

                     +-------+
            2     2  | 2    2      3      x
        (- x  + 2a )\|x  + a   + 3x asinh(-)
                                          a
   (2)  ------------------------------------
                          9
                                                     Type: Expression Integer
--R
--R                     +-------+
--R            2     2  | 2    2      3      x
--R        (- x  + 2a )\|x  + a   + 3x asinh(-)
--R                                          a
--R   (2)  ------------------------------------
--R                          9
--R                                                     Type: Expression Integer
--E

--S 17
cc:=aa-bb
 

               +-------+
               | 2    2
         3    \|x  + a   + x     3      x
        x log(--------------) - x asinh(-)
                     a                  a
   (3)  ----------------------------------
                         3
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R         3    \|x  + a   + x     3      x
--R        x log(--------------) - x asinh(-)
--R                     a                  a
--R   (3)  ----------------------------------
--R                         3
--R                                                     Type: Expression Integer
--E

--S 18
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19
dd:=asinhlogrule cc
 

                                        +-------+
                                        | 2    2
                                        |x  + a
               +-------+              a |-------  + x
               | 2    2                 |    2
         3    \|x  + a   + x     3     \|   a
        x log(--------------) - x log(---------------)
                     a                       a
   (5)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  + a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R         3    \|x  + a   + x     3     \|   a
--R        x log(--------------) - x log(---------------)
--R                     a                       a
--R   (5)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 20
ee:=expandLog dd
 

                                        +-------+
               +-------+                | 2    2
         3     | 2    2          3      |x  + a
        x log(\|x  + a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
   (6)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R         3     | 2    2          3      |x  + a
--R        x log(\|x  + a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R   (6)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 21     14:648 Schaums and Axiom agree
ff:=rootSimp ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 22     14:649 Axiom cannot compute this integral
aa:=integrate(asinh(x/a)/x,x)
 

                   %P
           x asinh(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x asinh(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 23
aa:=integrate(asinh(x/a)/x^2,x)
 

   (1)
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
                +-------+
                | 2    2
               \|x  + a   + x
       - a log(--------------)
                      a
  /
     a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R                +-------+
--R                | 2    2
--R               \|x  + a   + x
--R       - a log(--------------)
--R                      a
--R  /
--R     a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24
bb:=-asinh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2
                \|x  + a   + a            x
        - x log(--------------) - a asinh(-)
                       x                  a
   (2)  ------------------------------------
                         a x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  + a   + a            x
--R        - x log(--------------) - a asinh(-)
--R                       x                  a
--R   (2)  ------------------------------------
--R                         a x
--R                                                     Type: Expression Integer
--E

--S 25
cc:=aa-bb
 

   (3)
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
                +-------+               +-------+
                | 2    2                | 2    2
               \|x  + a   + x          \|x  + a   + a            x
       - a log(--------------) + x log(--------------) + a asinh(-)
                      a                       x                  a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R                +-------+               +-------+
--R                | 2    2                | 2    2
--R               \|x  + a   + x          \|x  + a   + a            x
--R       - a log(--------------) + x log(--------------) + a asinh(-)
--R                      a                       x                  a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 26
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27
dd:=asinhlogrule cc
 

   (5)
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
                                                                 +-------+
                                                                 | 2    2
                                                                 |x  + a
                +-------+               +-------+              a |-------  + x
                | 2    2                | 2    2                 |    2
               \|x  + a   + x          \|x  + a   + a           \|   a
       - a log(--------------) + x log(--------------) + a log(---------------)
                      a                       x                       a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (5)
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R                                                                 +-------+
--R                                                                 | 2    2
--R                                                                 |x  + a
--R                +-------+               +-------+              a |-------  + x
--R                | 2    2                | 2    2                 |    2
--R               \|x  + a   + x          \|x  + a   + a           \|   a
--R       - a log(--------------) + x log(--------------) + a log(---------------)
--R                      a                       x                       a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 28
ee:=expandLog dd
 

   (6)
                +-------+               +-------+
                | 2    2                | 2    2
       - a log(\|x  + a   + x) + x log(\|x  + a   + a)
     + 
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
               +-------+
               | 2    2
               |x  + a
       a log(a |-------  + x) - x log(x)
               |    2
              \|   a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (6)
--R                +-------+               +-------+
--R                | 2    2                | 2    2
--R       - a log(\|x  + a   + x) + x log(\|x  + a   + a)
--R     + 
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R               +-------+
--R               | 2    2
--R               |x  + a
--R       a log(a |-------  + x) - x log(x)
--R               |    2
--R              \|   a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 29
ff:=rootSimp ee
 

   (7)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (7)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 30     14:650 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

          log(- 1)
   (8)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (8)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 31
aa:=integrate(acosh(x/a),x)
 

                               +-------+
           +-------+           | 2    2           +-------+
           | 2    2     2     \|x  - a   + x      | 2    2     2    2
        (x\|x  - a   - x )log(--------------) + x\|x  - a   - x  + a
                                     a
   (1)  -------------------------------------------------------------
                                 +-------+
                                 | 2    2
                                \|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R           +-------+           | 2    2           +-------+
--R           | 2    2     2     \|x  - a   + x      | 2    2     2    2
--R        (x\|x  - a   - x )log(--------------) + x\|x  - a   - x  + a
--R                                     a
--R   (1)  -------------------------------------------------------------
--R                                 +-------+
--R                                 | 2    2
--R                                \|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 32
bb1:=x*acosh(x/a)-sqrt(x^2-a^2)
 

           +-------+
           | 2    2            x
   (2)  - \|x  - a   + x acosh(-)
                               a
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2            x
--R   (2)  - \|x  - a   + x acosh(-)
--R                               a
--R                                                     Type: Expression Integer
--E

--S 33
bb2:=x*acosh(x/a)+sqrt(x^2-a^2)
 

         +-------+
         | 2    2            x
   (3)  \|x  - a   + x acosh(-)
                             a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2            x
--R   (3)  \|x  - a   + x acosh(-)
--R                             a
--R                                                     Type: Expression Integer
--E

--S 34
cc1:=aa-bb1
 

               +-------+
               | 2    2
              \|x  - a   + x            x
   (4)  x log(--------------) - x acosh(-)
                     a                  a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   + x            x
--R   (4)  x log(--------------) - x acosh(-)
--R                     a                  a
--R                                                     Type: Expression Integer
--E

--S 35
cc2:=aa-bb2
 

   (5)
                              +-------+
          +-------+           | 2    2                             +-------+
          | 2    2     2     \|x  - a   + x               x        | 2    2
       (x\|x  - a   - x )log(--------------) + (- x acosh(-) + 2x)\|x  - a
                                    a                     a
     + 
        2      x      2     2
       x acosh(-) - 2x  + 2a
               a
  /
      +-------+
      | 2    2
     \|x  - a   - x
                                                     Type: Expression Integer
--R
--R   (5)
--R                              +-------+
--R          +-------+           | 2    2                             +-------+
--R          | 2    2     2     \|x  - a   + x               x        | 2    2
--R       (x\|x  - a   - x )log(--------------) + (- x acosh(-) + 2x)\|x  - a
--R                                    a                     a
--R     + 
--R        2      x      2     2
--R       x acosh(-) - 2x  + 2a
--R               a
--R  /
--R      +-------+
--R      | 2    2
--R     \|x  - a   - x
--R                                                     Type: Expression Integer
--E

--S 36
acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (6)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (6)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37
dd1:=acoshlogrule cc1
 

                                        +-------+
                                        | 2    2
                                        |x  - a
               +-------+              a |-------  + x
               | 2    2                 |    2
              \|x  - a   + x           \|   a
   (7)  x log(--------------) - x log(---------------)
                     a                       a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  - a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R              \|x  - a   + x           \|   a
--R   (7)  x log(--------------) - x log(---------------)
--R                     a                       a
--R                                                     Type: Expression Integer
--E

--S 38
ee1:=expandLog dd1
 

                                        +-------+
               +-------+                | 2    2
               | 2    2                 |x  - a
   (8)  x log(\|x  - a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R               | 2    2                 |x  - a
--R   (8)  x log(\|x  - a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R                                                     Type: Expression Integer
--E

--S 39     14:651 Schaums and Axiom agree
ff1:=rootSimp ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 40
aa:=integrate(x*acosh(x/a),x)
 

   (1)
                                                       +-------+
                     +-------+                         | 2    2
           3     2   | 2    2      4     2 2    4     \|x  - a   + x
       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
                                                             a
     + 
                   +-------+
          3    2   | 2    2      4     2 2
       (2x  - a x)\|x  - a   - 2x  + 2a x
  /
        +-------+
        | 2    2      2     2
     8x\|x  - a   - 8x  + 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                       +-------+
--R                     +-------+                         | 2    2
--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
--R                                                             a
--R     + 
--R                   +-------+
--R          3    2   | 2    2      4     2 2
--R       (2x  - a x)\|x  - a   - 2x  + 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     8x\|x  - a   - 8x  + 4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 41
bb1:=1/4*(2*x^2-a^2)*acosh(x/a)-1/4*x*sqrt(x^2-a^2)
 

            +-------+
            | 2    2       2    2       x
        - x\|x  - a   + (2x  - a )acosh(-)
                                        a
   (2)  ----------------------------------
                         4
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2       2    2       x
--R        - x\|x  - a   + (2x  - a )acosh(-)
--R                                        a
--R   (2)  ----------------------------------
--R                         4
--R                                                     Type: Expression Integer
--E

--S 42
bb2:=1/4*(2*x^2-a^2)*acosh(x/a)+1/4*x*sqrt(x^2-a^2)
 

          +-------+
          | 2    2       2    2       x
        x\|x  - a   + (2x  - a )acosh(-)
                                      a
   (3)  --------------------------------
                        4
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2       2    2       x
--R        x\|x  - a   + (2x  - a )acosh(-)
--R                                      a
--R   (3)  --------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E

--S 43
cc1:=aa-bb1
 

                       +-------+
                       | 2    2
           2    2     \|x  - a   + x         2    2       x
        (2x  - a )log(--------------) + (- 2x  + a )acosh(-)
                             a                            a
   (4)  ----------------------------------------------------
                                  4
                                                     Type: Expression Integer
--R
--R                       +-------+
--R                       | 2    2
--R           2    2     \|x  - a   + x         2    2       x
--R        (2x  - a )log(--------------) + (- 2x  + a )acosh(-)
--R                             a                            a
--R   (4)  ----------------------------------------------------
--R                                  4
--R                                                     Type: Expression Integer
--E

--S 44
cc2:=aa-bb2
 

   (5)
                                                       +-------+
                     +-------+                         | 2    2
           3     2   | 2    2      4     2 2    4     \|x  - a   + x
       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
                                                             a
     + 
                                             +-------+
             3     2        x      3     2   | 2    2
       ((- 4x  + 2a x)acosh(-) + 4x  - 2a x)\|x  - a
                            a
     + 
          4     2 2    4       x      4     2 2
       (4x  - 4a x  + a )acosh(-) - 4x  + 4a x
                               a
  /
        +-------+
        | 2    2      2     2
     8x\|x  - a   - 8x  + 4a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                       +-------+
--R                     +-------+                         | 2    2
--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
--R                                                             a
--R     + 
--R                                             +-------+
--R             3     2        x      3     2   | 2    2
--R       ((- 4x  + 2a x)acosh(-) + 4x  - 2a x)\|x  - a
--R                            a
--R     + 
--R          4     2 2    4       x      4     2 2
--R       (4x  - 4a x  + a )acosh(-) - 4x  + 4a x
--R                               a
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     8x\|x  - a   - 8x  + 4a
--R                                                     Type: Expression Integer
--E

--S 45
acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (6)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (6)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 46
dd1:=acoshlogrule cc1
 

                                                          +-------+
                                                          | 2    2
                                                          |x  - a
                       +-------+                        a |-------  + x
                       | 2    2                           |    2
           2    2     \|x  - a   + x         2    2      \|   a
        (2x  - a )log(--------------) + (- 2x  + a )log(---------------)
                             a                                 a
   (7)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                                                          | 2    2
--R                                                          |x  - a
--R                       +-------+                        a |-------  + x
--R                       | 2    2                           |    2
--R           2    2     \|x  - a   + x         2    2      \|   a
--R        (2x  - a )log(--------------) + (- 2x  + a )log(---------------)
--R                             a                                 a
--R   (7)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 47
ee1:=expandLog dd1
 

                                                          +-------+
                       +-------+                          | 2    2
           2    2      | 2    2              2    2       |x  - a
        (2x  - a )log(\|x  - a   + x) + (- 2x  + a )log(a |-------  + x)
                                                          |    2
                                                         \|   a
   (8)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                       +-------+                          | 2    2
--R           2    2      | 2    2              2    2       |x  - a
--R        (2x  - a )log(\|x  - a   + x) + (- 2x  + a )log(a |-------  + x)
--R                                                          |    2
--R                                                         \|   a
--R   (8)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 48     14:652 Schaums and Axiom agree
ff1:=rootSimp ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 49
aa:=integrate(x^2*acosh(x/a),x)
 

   (1)
                                                     +-------+
                       +-------+                     | 2    2
            5     2 3  | 2    2       6     2 4     \|x  - a   + x
       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
                                                           a
     + 
                            +-------+
          5     2 3     4   | 2    2      6     2 4     4 2     6
       (4x  + 5a x  - 6a x)\|x  - a   - 4x  - 3a x  + 9a x  - 2a
  /
                  +-------+
         2     2  | 2    2       3      2
     (36x  - 9a )\|x  - a   - 36x  + 27a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                     +-------+
--R                       +-------+                     | 2    2
--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
--R                                                           a
--R     + 
--R                            +-------+
--R          5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (4x  + 5a x  - 6a x)\|x  - a   - 4x  - 3a x  + 9a x  - 2a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3      2
--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50
bb1:=1/3*x^3*acosh(x/a)-1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
 

                     +-------+
            2     2  | 2    2      3      x
        (- x  - 2a )\|x  - a   + 3x acosh(-)
                                          a
   (2)  ------------------------------------
                          9
                                                     Type: Expression Integer
--R
--R                     +-------+
--R            2     2  | 2    2      3      x
--R        (- x  - 2a )\|x  - a   + 3x acosh(-)
--R                                          a
--R   (2)  ------------------------------------
--R                          9
--R                                                     Type: Expression Integer
--E

--S 51
bb2:=1/3*x^3*acosh(x/a)+1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
 

                   +-------+
          2     2  | 2    2      3      x
        (x  + 2a )\|x  - a   + 3x acosh(-)
                                        a
   (3)  ----------------------------------
                         9
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2      3      x
--R        (x  + 2a )\|x  - a   + 3x acosh(-)
--R                                        a
--R   (3)  ----------------------------------
--R                         9
--R                                                     Type: Expression Integer
--E

--S 52
cc1:=aa-bb1
 

               +-------+
               | 2    2
         3    \|x  - a   + x     3      x
        x log(--------------) - x acosh(-)
                     a                  a
   (4)  ----------------------------------
                         3
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R         3    \|x  - a   + x     3      x
--R        x log(--------------) - x acosh(-)
--R                     a                  a
--R   (4)  ----------------------------------
--R                         3
--R                                                     Type: Expression Integer
--E

--S 53
cc2:=aa-bb2
 

   (5)
                                                     +-------+
                       +-------+                     | 2    2
            5     2 3  | 2    2       6     2 4     \|x  - a   + x
       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
                                                           a
     + 
                                                         +-------+
              5     2 3       x      5      2 3      4   | 2    2
       ((- 12x  + 3a x )acosh(-) + 8x  + 10a x  - 12a x)\|x  - a
                              a
     + 
           6     2 4       x      6     2 4      4 2     6
       (12x  - 9a x )acosh(-) - 8x  - 6a x  + 18a x  - 4a
                           a
  /
                  +-------+
         2     2  | 2    2       3      2
     (36x  - 9a )\|x  - a   - 36x  + 27a x
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                     +-------+
--R                       +-------+                     | 2    2
--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
--R                                                           a
--R     + 
--R                                                         +-------+
--R              5     2 3       x      5      2 3      4   | 2    2
--R       ((- 12x  + 3a x )acosh(-) + 8x  + 10a x  - 12a x)\|x  - a
--R                              a
--R     + 
--R           6     2 4       x      6     2 4      4 2     6
--R       (12x  - 9a x )acosh(-) - 8x  - 6a x  + 18a x  - 4a
--R                           a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3      2
--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
--R                                                     Type: Expression Integer
--E

--S 54
acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (6)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (6)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 55
dd1:=acoshlogrule cc1
 

                                        +-------+
                                        | 2    2
                                        |x  - a
               +-------+              a |-------  + x
               | 2    2                 |    2
         3    \|x  - a   + x     3     \|   a
        x log(--------------) - x log(---------------)
                     a                       a
   (7)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  - a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R         3    \|x  - a   + x     3     \|   a
--R        x log(--------------) - x log(---------------)
--R                     a                       a
--R   (7)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 56
ee1:=expandLog dd1
 

                                        +-------+
               +-------+                | 2    2
         3     | 2    2          3      |x  - a
        x log(\|x  - a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
   (8)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R         3     | 2    2          3      |x  - a
--R        x log(\|x  - a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R   (8)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 57     14:653 Schaums and Axiom agree
ff1:=rootSimp ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 58     14:654 Axiom cannot compute this integral
aa:=integrate(acosh(x/a)/x,x)
 

                   %P
           x acosh(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x acosh(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 59
aa:=integrate(acosh(x/a)/x^2,x)
 

                 +-------+                 +-------+
                 | 2    2                  | 2    2
                \|x  - a   + x            \|x  - a   - x
        - a log(--------------) + 2x atan(--------------)
                       a                         a
   (1)  -------------------------------------------------
                               a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-------+                 +-------+
--R                 | 2    2                  | 2    2
--R                \|x  - a   + x            \|x  - a   - x
--R        - a log(--------------) + 2x atan(--------------)
--R                       a                         a
--R   (1)  -------------------------------------------------
--R                               a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 60
bb1:=-acosh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2
                \|x  + a   + a            x
        - x log(--------------) - a acosh(-)
                       x                  a
   (2)  ------------------------------------
                         a x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  + a   + a            x
--R        - x log(--------------) - a acosh(-)
--R                       x                  a
--R   (2)  ------------------------------------
--R                         a x
--R                                                     Type: Expression Integer
--E

--S 61
bb2:=-acosh(x/a)/x+1/a*log((a+sqrt(x^2+a^2))/x)
 

               +-------+
               | 2    2
              \|x  + a   + a            x
        x log(--------------) - a acosh(-)
                     x                  a
   (3)  ----------------------------------
                        a x
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  + a   + a            x
--R        x log(--------------) - a acosh(-)
--R                     x                  a
--R   (3)  ----------------------------------
--R                        a x
--R                                                     Type: Expression Integer
--E

--S 62
cc1:=aa-bb1
 

   (4)
              +-------+               +-------+                 +-------+
              | 2    2                | 2    2                  | 2    2
             \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
       x log(--------------) - a log(--------------) + 2x atan(--------------)
                    x                       a                         a
     + 
               x
       a acosh(-)
               a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (4)
--R              +-------+               +-------+                 +-------+
--R              | 2    2                | 2    2                  | 2    2
--R             \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
--R       x log(--------------) - a log(--------------) + 2x atan(--------------)
--R                    x                       a                         a
--R     + 
--R               x
--R       a acosh(-)
--R               a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 63     14:655 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                +-------+               +-------+                 +-------+
                | 2    2                | 2    2                  | 2    2
               \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
       - x log(--------------) - a log(--------------) + 2x atan(--------------)
                      x                       a                         a
     + 
               x
       a acosh(-)
               a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (5)
--R                +-------+               +-------+                 +-------+
--R                | 2    2                | 2    2                  | 2    2
--R               \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
--R       - x log(--------------) - a log(--------------) + 2x atan(--------------)
--R                      x                       a                         a
--R     + 
--R               x
--R       a acosh(-)
--R               a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 64
aa:=integrate(atanh(x/a),x)
 

               2    2          - x - a
        a log(x  - a ) + x log(-------)
                                x - a
   (1)  -------------------------------
                       2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2          - x - a
--R        a log(x  - a ) + x log(-------)
--R                                x - a
--R   (1)  -------------------------------
--R                       2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 65
bb:=x*atanh(x/a)+a/2*log(a^2-x^2)
 

                 2    2             x
        a log(- x  + a ) + 2x atanh(-)
                                    a
   (2)  ------------------------------
                       2
                                                     Type: Expression Integer
--R
--R                 2    2             x
--R        a log(- x  + a ) + 2x atanh(-)
--R                                    a
--R   (2)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E

--S 66
cc:=aa-bb
 

               2    2          - x - a             2    2             x
        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
                                x - a                                 a
   (3)  ----------------------------------------------------------------
                                        2
                                                     Type: Expression Integer
--R
--R               2    2          - x - a             2    2             x
--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
--R                                x - a                                 a
--R   (3)  ----------------------------------------------------------------
--R                                        2
--R                                                     Type: Expression Integer
--E

--S 67
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 68
dd:=atanhrule cc
 

               2    2             2    2
        a log(x  - a ) - a log(- x  + a )
   (5)  ---------------------------------
                        2
                                                     Type: Expression Integer
--R
--R               2    2             2    2
--R        a log(x  - a ) - a log(- x  + a )
--R   (5)  ---------------------------------
--R                        2
--R                                                     Type: Expression Integer
--E

--S 69     14:656 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        a log(- 1)
   (6)  ----------
             2
                                                     Type: Expression Integer
--R
--R        a log(- 1)
--R   (6)  ----------
--R             2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 70
aa:=integrate(x*atanh(x/a),x)
 

          2    2     - x - a
        (x  - a )log(-------) + 2a x
                      x - a
   (1)  ----------------------------
                      4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2     - x - a
--R        (x  - a )log(-------) + 2a x
--R                      x - a
--R   (1)  ----------------------------
--R                      4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 71
bb:=(a*x)/2+1/2*(x^2-a^2)*atanh(x/a)
 

          2    2       x
        (x  - a )atanh(-) + a x
                       a
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          2    2       x
--R        (x  - a )atanh(-) + a x
--R                       a
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 72
cc:=aa-bb
 

          2    2     - x - a         2     2       x
        (x  - a )log(-------) + (- 2x  + 2a )atanh(-)
                      x - a                        a
   (3)  ---------------------------------------------
                              4
                                                     Type: Expression Integer
--R
--R          2    2     - x - a         2     2       x
--R        (x  - a )log(-------) + (- 2x  + 2a )atanh(-)
--R                      x - a                        a
--R   (3)  ---------------------------------------------
--R                              4
--R                                                     Type: Expression Integer
--E

--S 73
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 74     14:657 Schaums and Axiom agree
dd:=atanhrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 75
aa:=integrate(x^2*atanh(x/a),x)
 

         3     2    2     3    - x - a       2
        a log(x  - a ) + x log(-------) + a x
                                x - a
   (1)  --------------------------------------
                           6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         3     2    2     3    - x - a       2
--R        a log(x  - a ) + x log(-------) + a x
--R                                x - a
--R   (1)  --------------------------------------
--R                           6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 76
bb:=(a*x^2)/6+x^3/3*atanh(x/a)+a^3/6*log(a^2-x^2)
 

         3       2    2      3      x       2
        a log(- x  + a ) + 2x atanh(-) + a x
                                    a
   (2)  -------------------------------------
                          6
                                                     Type: Expression Integer
--R
--R         3       2    2      3      x       2
--R        a log(- x  + a ) + 2x atanh(-) + a x
--R                                    a
--R   (2)  -------------------------------------
--R                          6
--R                                                     Type: Expression Integer
--E

--S 77
cc:=aa-bb
 

         3     2    2     3    - x - a     3       2    2      3      x
        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
                                x - a                                 a
   (3)  ----------------------------------------------------------------
                                        6
                                                     Type: Expression Integer
--R
--R         3     2    2     3    - x - a     3       2    2      3      x
--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
--R                                x - a                                 a
--R   (3)  ----------------------------------------------------------------
--R                                        6
--R                                                     Type: Expression Integer
--E

--S 78
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 79
dd:=atanhrule cc
 

         3     2    2     3       2    2
        a log(x  - a ) - a log(- x  + a )
   (5)  ---------------------------------
                        6
                                                     Type: Expression Integer
--R
--R         3     2    2     3       2    2
--R        a log(x  - a ) - a log(- x  + a )
--R   (5)  ---------------------------------
--R                        6
--R                                                     Type: Expression Integer
--E

--S 80     14:658 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

         3
        a log(- 1)
   (6)  ----------
             6
                                                     Type: Expression Integer
--R
--R         3
--R        a log(- 1)
--R   (6)  ----------
--R             6
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 81     14:659 Axiom cannot compute this integral
aa:=integrate(atanh(x/a)/x,x)
 

                   %P
           x atanh(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x atanh(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 82
aa:=integrate(atanh(x/a)/x^2,x)
 

                 2    2                      - x - a
        - x log(x  - a ) + 2x log(x) - a log(-------)
                                              x - a
   (1)  ---------------------------------------------
                             2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2                      - x - a
--R        - x log(x  - a ) + 2x log(x) - a log(-------)
--R                                              x - a
--R   (1)  ---------------------------------------------
--R                             2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 83
bb:=-atanh(x/a)/x+1/(2*a)*log(x^2/(a^2-x^2))
 

                    2
                   x                x
        x log(- -------) - 2a atanh(-)
                 2    2             a
                x  - a
   (2)  ------------------------------
                     2a x
                                                     Type: Expression Integer
--R
--R                    2
--R                   x                x
--R        x log(- -------) - 2a atanh(-)
--R                 2    2             a
--R                x  - a
--R   (2)  ------------------------------
--R                     2a x
--R                                                     Type: Expression Integer
--E

--S 84
cc:=aa-bb
 

   (3)
                                                  2
                2    2                           x             - x - a
       - x log(x  - a ) + 2x log(x) - x log(- -------) - a log(-------)
                                               2    2           x - a
                                              x  - a
     + 
                x
       2a atanh(-)
                a
  /
     2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                  2
--R                2    2                           x             - x - a
--R       - x log(x  - a ) + 2x log(x) - x log(- -------) - a log(-------)
--R                                               2    2           x - a
--R                                              x  - a
--R     + 
--R                x
--R       2a atanh(-)
--R                a
--R  /
--R     2a x
--R                                                     Type: Expression Integer
--E

--S 85
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 86
dd:=atanhrule cc
 

                                             2
               2    2                       x
        - log(x  - a ) + 2log(x) - log(- -------)
                                          2    2
                                         x  - a
   (5)  -----------------------------------------
                            2a
                                                     Type: Expression Integer
--R
--R                                             2
--R               2    2                       x
--R        - log(x  - a ) + 2log(x) - log(- -------)
--R                                          2    2
--R                                         x  - a
--R   (5)  -----------------------------------------
--R                            2a
--R                                                     Type: Expression Integer
--E

--S 87     14:660 Schaums and Axiom agree
ee:=expandLog dd
 

          log(- 1)
   (6)  - --------
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (6)  - --------
--R             2a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 88
aa:=integrate(acoth(x/a),x)
 

               2    2          x + a
        a log(x  - a ) + x log(-----)
                               x - a
   (1)  -----------------------------
                      2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2          x + a
--R        a log(x  - a ) + x log(-----)
--R                               x - a
--R   (1)  -----------------------------
--R                      2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 89
bb:=x*acoth(x/a)+a/2*log(x^2-a^2)
 

               2    2             x
        a log(x  - a ) + 2x acoth(-)
                                  a
   (2)  ----------------------------
                      2
                                                     Type: Expression Integer
--R
--R               2    2             x
--R        a log(x  - a ) + 2x acoth(-)
--R                                  a
--R   (2)  ----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 90
cc:=aa-bb
 

              x + a             x
        x log(-----) - 2x acoth(-)
              x - a             a
   (3)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R              x + a             x
--R        x log(-----) - 2x acoth(-)
--R              x - a             a
--R   (3)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 91
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 92     14:661 Schaums and Axiom agree
dd:=acothrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 93
aa:=integrate(x*acoth(x/a),x)
 

          2    2     x + a
        (x  - a )log(-----) + 2a x
                     x - a
   (1)  --------------------------
                     4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2     x + a
--R        (x  - a )log(-----) + 2a x
--R                     x - a
--R   (1)  --------------------------
--R                     4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 94
bb:=(a*x)/2+1/2*(x^2-a^2)*acoth(x/a)
 

          2    2       x
        (x  - a )acoth(-) + a x
                       a
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          2    2       x
--R        (x  - a )acoth(-) + a x
--R                       a
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 95
cc:=aa-bb
 

          2    2     x + a         2     2       x
        (x  - a )log(-----) + (- 2x  + 2a )acoth(-)
                     x - a                       a
   (3)  -------------------------------------------
                             4
                                                     Type: Expression Integer
--R
--R          2    2     x + a         2     2       x
--R        (x  - a )log(-----) + (- 2x  + 2a )acoth(-)
--R                     x - a                       a
--R   (3)  -------------------------------------------
--R                             4
--R                                                     Type: Expression Integer
--E

--S 96
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 97     14:662 Schaums and Axiom agree
dd:=acothrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 98
aa:=integrate(x^2*acoth(x/a),x)
 

         3     2    2     3    x + a       2
        a log(x  - a ) + x log(-----) + a x
                               x - a
   (1)  ------------------------------------
                          6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         3     2    2     3    x + a       2
--R        a log(x  - a ) + x log(-----) + a x
--R                               x - a
--R   (1)  ------------------------------------
--R                          6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 99
bb:=(a*x^2)/6+x^3/3*acoth(x/a)+a^3/6*log(x^2-a^2)
 

         3     2    2      3      x       2
        a log(x  - a ) + 2x acoth(-) + a x
                                  a
   (2)  -----------------------------------
                         6
                                                     Type: Expression Integer
--R
--R         3     2    2      3      x       2
--R        a log(x  - a ) + 2x acoth(-) + a x
--R                                  a
--R   (2)  -----------------------------------
--R                         6
--R                                                     Type: Expression Integer
--E

--S 100
cc:=aa-bb
 

         3    x + a      3      x
        x log(-----) - 2x acoth(-)
              x - a             a
   (3)  --------------------------
                     6
                                                     Type: Expression Integer
--R
--R         3    x + a      3      x
--R        x log(-----) - 2x acoth(-)
--R              x - a             a
--R   (3)  --------------------------
--R                     6
--R                                                     Type: Expression Integer
--E

--S 101
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 102    14:663 Schaums and Axiom agree
dd:=acothrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 103    14:664 Axiom cannot compute this integral
aa:=integrate(acoth(x/a)/x,x)
 

                   %P
           x acoth(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x acoth(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 104
aa:=integrate(acoth(x/a)/x^2,x)
 

                 2    2                      x + a
        - x log(x  - a ) + 2x log(x) - a log(-----)
                                             x - a
   (1)  -------------------------------------------
                            2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2                      x + a
--R        - x log(x  - a ) + 2x log(x) - a log(-----)
--R                                             x - a
--R   (1)  -------------------------------------------
--R                            2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 105
bb:=-acoth(x/a)/x+1/(2*a)*log(x^2/(x^2-a^2))
 

                  2
                 x                x
        x log(-------) - 2a acoth(-)
               2    2             a
              x  - a
   (2)  ----------------------------
                    2a x
                                                     Type: Expression Integer
--R
--R                  2
--R                 x                x
--R        x log(-------) - 2a acoth(-)
--R               2    2             a
--R              x  - a
--R   (2)  ----------------------------
--R                    2a x
--R                                                     Type: Expression Integer
--E

--S 106
cc:=aa-bb
 

   (3)
                                                           2
            2    2                      x + a             x                x
   - x log(x  - a ) + 2x log(x) - a log(-----) - x log(-------) + 2a acoth(-)
                                        x - a           2    2             a
                                                       x  - a
   --------------------------------------------------------------------------
                                      2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                           2
--R            2    2                      x + a             x                x
--R   - x log(x  - a ) + 2x log(x) - a log(-----) - x log(-------) + 2a acoth(-)
--R                                        x - a           2    2             a
--R                                                       x  - a
--R   --------------------------------------------------------------------------
--R                                      2a x
--R                                                     Type: Expression Integer
--E

--S 107
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 108
dd:=acothrule cc
 

                                           2
               2    2                     x
        - log(x  - a ) + 2log(x) - log(-------)
                                        2    2
                                       x  - a
   (5)  ---------------------------------------
                           2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  - a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  - a
--R   (5)  ---------------------------------------
--R                           2a
--R                                                     Type: Expression Integer
--E

--S 109    14:665 Schaums and Axiom agree
ee:=expandLog dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 110
aa:=integrate(asech(x/a),x)
 

               +---------+                 +---------+
               |   2    2                  |   2    2
              \|- x  + a   + a            \|- x  + a   - a
   (1)  x log(----------------) - 2a atan(----------------)
                      x                           x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +---------+                 +---------+
--R               |   2    2                  |   2    2
--R              \|- x  + a   + a            \|- x  + a   - a
--R   (1)  x log(----------------) - 2a atan(----------------)
--R                      x                           x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 111
bb1:=x*asech(x/a)+a*asin(x/a)
 

               x            x
   (2)  a asin(-) + x asech(-)
               a            a
                                                     Type: Expression Integer
--R
--R               x            x
--R   (2)  a asin(-) + x asech(-)
--R               a            a
--R                                                     Type: Expression Integer
--E

--S 112
bb2:=x*asech(x/a)-a*asin(x/a)
 

                 x            x
   (3)  - a asin(-) + x asech(-)
                 a            a
                                                     Type: Expression Integer
--R
--R                 x            x
--R   (3)  - a asin(-) + x asech(-)
--R                 a            a
--R                                                     Type: Expression Integer
--E

--S 113
cc1:=aa-bb1
 

   (4)
          +---------+                 +---------+
          |   2    2                  |   2    2
         \|- x  + a   + a            \|- x  + a   - a           x            x
   x log(----------------) - 2a atan(----------------) - a asin(-) - x asech(-)
                 x                           x                  a            a
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+                 +---------+
--R          |   2    2                  |   2    2
--R         \|- x  + a   + a            \|- x  + a   - a           x            x
--R   x log(----------------) - 2a atan(----------------) - a asin(-) - x asech(-)
--R                 x                           x                  a            a
--R                                                     Type: Expression Integer
--E

--S 114
cc2:=aa-bb2
 

   (5)
          +---------+                 +---------+
          |   2    2                  |   2    2
         \|- x  + a   + a            \|- x  + a   - a           x            x
   x log(----------------) - 2a atan(----------------) + a asin(-) - x asech(-)
                 x                           x                  a            a
                                                     Type: Expression Integer
--R
--R   (5)
--R          +---------+                 +---------+
--R          |   2    2                  |   2    2
--R         \|- x  + a   + a            \|- x  + a   - a           x            x
--R   x log(----------------) - 2a atan(----------------) + a asin(-) - x asech(-)
--R                 x                           x                  a            a
--R                                                     Type: Expression Integer
--E

--S 115
asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
 

                          +--------+
                          |   2
                          |- x  + 1
                        x |--------  + 1
                          |    2
                         \|   x
   (6)  asech(x) == log(----------------)
                                x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          +--------+
--R                          |   2
--R                          |- x  + 1
--R                        x |--------  + 1
--R                          |    2
--R                         \|   x
--R   (6)  asech(x) == log(----------------)
--R                                x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 116
dd1:=asechrule cc1
 

   (7)
               +---------+
               |   2    2
               |- x  + a
             x |---------  + a           +---------+
               |     2                   |   2    2
              \|    x                   \|- x  + a   + a
     - x log(-----------------) + x log(----------------)
                     x                          x
   + 
                +---------+
                |   2    2
               \|- x  + a   - a           x
     - 2a atan(----------------) - a asin(-)
                       x                  a
                                                     Type: Expression Integer
--R
--R   (7)
--R               +---------+
--R               |   2    2
--R               |- x  + a
--R             x |---------  + a           +---------+
--R               |     2                   |   2    2
--R              \|    x                   \|- x  + a   + a
--R     - x log(-----------------) + x log(----------------)
--R                     x                          x
--R   + 
--R                +---------+
--R                |   2    2
--R               \|- x  + a   - a           x
--R     - 2a atan(----------------) - a asin(-)
--R                       x                  a
--R                                                     Type: Expression Integer
--E

--S 117
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (8)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (8)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 118
ee1:=asinrule dd1
 

   (9)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) - %i a log(--------------------)
                     x                               a
   + 
            +---------+                 +---------+
            |   2    2                  |   2    2
           \|- x  + a   + a            \|- x  + a   - a
     x log(----------------) - 2a atan(----------------)
                   x                           x
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) - %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                 +---------+
--R            |   2    2                  |   2    2
--R           \|- x  + a   + a            \|- x  + a   - a
--R     x log(----------------) - 2a atan(----------------)
--R                   x                           x
--R                                             Type: Expression Complex Integer
--E

--S 119
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                             - x + %i
                      %i log(--------)
                              x + %i
   (10)  atan(x) == - ----------------
                              2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             - x + %i
--R                      %i log(--------)
--R                              x + %i
--R   (10)  atan(x) == - ----------------
--R                              2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 120
ff1:=atanrule ee1
 

   (11)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) - %i a log(--------------------)
                     x                               a
   + 
            +---------+                    +---------+
            |   2    2                     |   2    2
           \|- x  + a   + a             - \|- x  + a   + %i x + a
     x log(----------------) + %i a log(-------------------------)
                   x                      +---------+
                                          |   2    2
                                         \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R   (11)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) - %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                    +---------+
--R            |   2    2                     |   2    2
--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
--R     x log(----------------) + %i a log(-------------------------)
--R                   x                      +---------+
--R                                          |   2    2
--R                                         \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 121
gg1:=expandLog ff1
 

   (12)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
     - x log(x |---------  + a) - %i a log(a |---------  - %i x)
               |     2                       |     2
              \|    x                       \|    a
   + 
                 +---------+                      +---------+
                 |   2    2                       |   2    2
     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
   + 
               +---------+
               |   2    2
     %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (12)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R     - x log(x |---------  + a) - %i a log(a |---------  - %i x)
--R               |     2                       |     2
--R              \|    x                       \|    a
--R   + 
--R                 +---------+                      +---------+
--R                 |   2    2                       |   2    2
--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
--R   + 
--R               +---------+
--R               |   2    2
--R     %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 122
hh1:=rootSimp gg1
 

   (13)
                   +-------+                           +-------+
                   | 2    2                            | 2    2
     - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (13)
--R                   +-------+                           +-------+
--R                   | 2    2                            | 2    2
--R     - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 123    14:666 Schaums and Axiom agree
ii1:=complexNormalize hh1
 

   (14)  0
                                             Type: Expression Complex Integer
--R
--R   (14)  0
--R                                             Type: Expression Complex Integer
--E

--S 124
dd2:=asechrule cc2
 

   (15)
               +---------+
               |   2    2
               |- x  + a
             x |---------  + a           +---------+
               |     2                   |   2    2
              \|    x                   \|- x  + a   + a
     - x log(-----------------) + x log(----------------)
                     x                          x
   + 
                +---------+
                |   2    2
               \|- x  + a   - a           x
     - 2a atan(----------------) + a asin(-)
                       x                  a
                                                     Type: Expression Integer
--R
--R   (15)
--R               +---------+
--R               |   2    2
--R               |- x  + a
--R             x |---------  + a           +---------+
--R               |     2                   |   2    2
--R              \|    x                   \|- x  + a   + a
--R     - x log(-----------------) + x log(----------------)
--R                     x                          x
--R   + 
--R                +---------+
--R                |   2    2
--R               \|- x  + a   - a           x
--R     - 2a atan(----------------) + a asin(-)
--R                       x                  a
--R                                                     Type: Expression Integer
--E

--S 125
ee2:=asinrule dd2
 

   (16)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) + %i a log(--------------------)
                     x                               a
   + 
            +---------+                 +---------+
            |   2    2                  |   2    2
           \|- x  + a   + a            \|- x  + a   - a
     x log(----------------) - 2a atan(----------------)
                   x                           x
                                             Type: Expression Complex Integer
--R
--R   (16)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) + %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                 +---------+
--R            |   2    2                  |   2    2
--R           \|- x  + a   + a            \|- x  + a   - a
--R     x log(----------------) - 2a atan(----------------)
--R                   x                           x
--R                                             Type: Expression Complex Integer
--E

--S 126
ff2:=atanrule ee2
 

   (17)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) + %i a log(--------------------)
                     x                               a
   + 
            +---------+                    +---------+
            |   2    2                     |   2    2
           \|- x  + a   + a             - \|- x  + a   + %i x + a
     x log(----------------) + %i a log(-------------------------)
                   x                      +---------+
                                          |   2    2
                                         \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R   (17)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) + %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                    +---------+
--R            |   2    2                     |   2    2
--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
--R     x log(----------------) + %i a log(-------------------------)
--R                   x                      +---------+
--R                                          |   2    2
--R                                         \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 127
gg2:=expandLog ff2
 

   (18)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
     - x log(x |---------  + a) + %i a log(a |---------  - %i x)
               |     2                       |     2
              \|    x                       \|    a
   + 
                 +---------+                      +---------+
                 |   2    2                       |   2    2
     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
   + 
               +---------+
               |   2    2
     %i a log(\|- x  + a   - %i x - a) - %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (18)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R     - x log(x |---------  + a) + %i a log(a |---------  - %i x)
--R               |     2                       |     2
--R              \|    x                       \|    a
--R   + 
--R                 +---------+                      +---------+
--R                 |   2    2                       |   2    2
--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
--R   + 
--R               +---------+
--R               |   2    2
--R     %i a log(\|- x  + a   - %i x - a) - %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 128
hh2:=rootSimp gg2
 

   (19)
                   +-------+                           +-------+
                   | 2    2                            | 2    2
     - %i a log(%i\|x  - a   + %i x - a) + %i a log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     %i a log(%i\|x  - a   - %i x - a) - %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (19)
--R                   +-------+                           +-------+
--R                   | 2    2                            | 2    2
--R     - %i a log(%i\|x  - a   + %i x - a) + %i a log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     %i a log(%i\|x  - a   - %i x - a) - %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 129
ii2:=complexNormalize hh2
 

                      +-------+
                      | 2    2
   (20)  2%i a log(%i\|x  - a   - %i x) - 2%i a log(a)
                                             Type: Expression Complex Integer
--R
--R                      +-------+
--R                      | 2    2
--R   (20)  2%i a log(%i\|x  - a   - %i x) - 2%i a log(a)
--R                                             Type: Expression Complex Integer
--E

)clear all
 
   All user variables and function definitions have been cleared.

--S 130
aa:=integrate(x*asech(x/a),x)
 

                                    +---------+
            +---------+             |   2    2
          2 |   2    2       2     \|- x  + a   + a       2
        (x \|- x  + a   - a x )log(----------------) + a x
                                           x
   (1)  ---------------------------------------------------
                           +---------+
                           |   2    2
                         2\|- x  + a   - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                    +---------+
--R            +---------+             |   2    2
--R          2 |   2    2       2     \|- x  + a   + a       2
--R        (x \|- x  + a   - a x )log(----------------) + a x
--R                                           x
--R   (1)  ---------------------------------------------------
--R                           +---------+
--R                           |   2    2
--R                         2\|- x  + a   - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 131
bb1:=1/2*x^2*asech(x/a)-1/2*a*sqrt(a^2-x^2)
 

            +---------+
            |   2    2     2      x
        - a\|- x  + a   + x asech(-)
                                  a
   (2)  ----------------------------
                      2
                                                     Type: Expression Integer
--R
--R            +---------+
--R            |   2    2     2      x
--R        - a\|- x  + a   + x asech(-)
--R                                  a
--R   (2)  ----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 132
bb2:=1/2*x^2*asech(x/a)+1/2*a*sqrt(a^2-x^2)
 

          +---------+
          |   2    2     2      x
        a\|- x  + a   + x asech(-)
                                a
   (3)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2     2      x
--R        a\|- x  + a   + x asech(-)
--R                                a
--R   (3)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 133
cc1:=aa-bb1
 

               +---------+
               |   2    2
         2    \|- x  + a   + a     2      x     2
        x log(----------------) - x asech(-) - a
                      x                   a
   (4)  -----------------------------------------
                            2
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R         2    \|- x  + a   + a     2      x     2
--R        x log(----------------) - x asech(-) - a
--R                      x                   a
--R   (4)  -----------------------------------------
--R                            2
--R                                                     Type: Expression Integer
--E

--S 134
cc2:=aa-bb2
 

   (5)
                                   +---------+
           +---------+             |   2    2
         2 |   2    2       2     \|- x  + a   + a
       (x \|- x  + a   - a x )log(----------------)
                                          x
     + 
                           +---------+
           2      x     2  |   2    2       2      x        2    3
       (- x asech(-) + a )\|- x  + a   + a x asech(-) + 2a x  - a
                  a                                a
  /
       +---------+
       |   2    2
     2\|- x  + a   - 2a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                   +---------+
--R           +---------+             |   2    2
--R         2 |   2    2       2     \|- x  + a   + a
--R       (x \|- x  + a   - a x )log(----------------)
--R                                          x
--R     + 
--R                           +---------+
--R           2      x     2  |   2    2       2      x        2    3
--R       (- x asech(-) + a )\|- x  + a   + a x asech(-) + 2a x  - a
--R                  a                                a
--R  /
--R       +---------+
--R       |   2    2
--R     2\|- x  + a   - 2a
--R                                                     Type: Expression Integer
--E

--S 135
asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
 

                          +--------+
                          |   2
                          |- x  + 1
                        x |--------  + 1
                          |    2
                         \|   x
   (6)  asech(x) == log(----------------)
                                x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          +--------+
--R                          |   2
--R                          |- x  + 1
--R                        x |--------  + 1
--R                          |    2
--R                         \|   x
--R   (6)  asech(x) == log(----------------)
--R                                x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 136
dd1:=asechrule cc1
 

                  +---------+
                  |   2    2
                  |- x  + a
                x |---------  + a           +---------+
                  |     2                   |   2    2
           2     \|    x              2    \|- x  + a   + a     2
        - x log(-----------------) + x log(----------------) - a
                        x                          x
   (7)  ---------------------------------------------------------
                                    2
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2
--R                  |- x  + a
--R                x |---------  + a           +---------+
--R                  |     2                   |   2    2
--R           2     \|    x              2    \|- x  + a   + a     2
--R        - x log(-----------------) + x log(----------------) - a
--R                        x                          x
--R   (7)  ---------------------------------------------------------
--R                                    2
--R                                                     Type: Expression Integer
--E

--S 137
ee1:=expandLog dd1
 

                  +---------+
                  |   2    2                +---------+
           2      |- x  + a           2     |   2    2          2
        - x log(x |---------  + a) + x log(\|- x  + a   + a) - a
                  |     2
                 \|    x
   (8)  ---------------------------------------------------------
                                    2
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2                +---------+
--R           2      |- x  + a           2     |   2    2          2
--R        - x log(x |---------  + a) + x log(\|- x  + a   + a) - a
--R                  |     2
--R                 \|    x
--R   (8)  ---------------------------------------------------------
--R                                    2
--R                                                     Type: Expression Integer
--E

--S 138    14:667 Schaums and Axiom differ by a constant
ff1:=rootSimp ee1
 

           2
          a
   (9)  - --
           2
                                                     Type: Expression Integer
--R
--R           2
--R          a
--R   (9)  - --
--R           2
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 139    14:668 Axiom cannot compute this integral
aa:=integrate(asech(x/a)/x,x)
 

                   %P
           x asech(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x asech(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 140
aa:=integrate(acsch(x/a),x)
 

                                         +-------+
                 +-------+               | 2    2
                 | 2    2               \|x  + a   + a
   (1)  - a log(\|x  + a   - x) + x log(--------------)
                                               x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                         +-------+
--R                 +-------+               | 2    2
--R                 | 2    2               \|x  + a   + a
--R   (1)  - a log(\|x  + a   - x) + x log(--------------)
--R                                               x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 141
bb1:=x*acsch(x/a)+a*asinh(x/a)
 

                x            x
   (2)  a asinh(-) + x acsch(-)
                a            a
                                                     Type: Expression Integer
--R
--R                x            x
--R   (2)  a asinh(-) + x acsch(-)
--R                a            a
--R                                                     Type: Expression Integer
--E

--S 142
bb2:=x*acsch(x/a)-a*asinh(x/a)
 

                  x            x
   (3)  - a asinh(-) + x acsch(-)
                  a            a
                                                     Type: Expression Integer
--R
--R                  x            x
--R   (3)  - a asinh(-) + x acsch(-)
--R                  a            a
--R                                                     Type: Expression Integer
--E

--S 143
cc1:=aa-bb1
 

   (4)
                                    +-------+
            +-------+               | 2    2
            | 2    2               \|x  + a   + a            x            x
   - a log(\|x  + a   - x) + x log(--------------) - a asinh(-) - x acsch(-)
                                          x                  a            a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                    +-------+
--R            +-------+               | 2    2
--R            | 2    2               \|x  + a   + a            x            x
--R   - a log(\|x  + a   - x) + x log(--------------) - a asinh(-) - x acsch(-)
--R                                          x                  a            a
--R                                                     Type: Expression Integer
--E

--S 144    14:669 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                    +-------+
            +-------+               | 2    2
            | 2    2               \|x  + a   + a            x            x
   - a log(\|x  + a   - x) + x log(--------------) + a asinh(-) - x acsch(-)
                                          x                  a            a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                    +-------+
--R            +-------+               | 2    2
--R            | 2    2               \|x  + a   + a            x            x
--R   - a log(\|x  + a   - x) + x log(--------------) + a asinh(-) - x acsch(-)
--R                                          x                  a            a
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 145
aa:=integrate(x*acsch(x/a),x)
 

                                +-------+
            +-------+           | 2    2             +-------+
          2 | 2    2     3     \|x  + a   + a        | 2    2       2    3
        (x \|x  + a   - x )log(--------------) - a x\|x  + a   + a x  + a
                                      x
   (1)  ------------------------------------------------------------------
                                   +-------+
                                   | 2    2
                                 2\|x  + a   - 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                +-------+
--R            +-------+           | 2    2             +-------+
--R          2 | 2    2     3     \|x  + a   + a        | 2    2       2    3
--R        (x \|x  + a   - x )log(--------------) - a x\|x  + a   + a x  + a
--R                                      x
--R   (1)  ------------------------------------------------------------------
--R                                   +-------+
--R                                   | 2    2
--R                                 2\|x  + a   - 2x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 146
bb1:=x^2/2*acsch(x/a)+(a*sqrt(x^2+a^2))/2
 

          +-------+
          | 2    2     2      x
        a\|x  + a   + x acsch(-)
                              a
   (2)  ------------------------
                    2
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2      x
--R        a\|x  + a   + x acsch(-)
--R                              a
--R   (2)  ------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 147
bb2:=x^2/2*acsch(x/a)-(a*sqrt(x^2+a^2))/2
 

            +-------+
            | 2    2     2      x
        - a\|x  + a   + x acsch(-)
                                a
   (3)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2      x
--R        - a\|x  + a   + x acsch(-)
--R                                a
--R   (3)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 148
cc1:=aa-bb1
 

               +-------+
               | 2    2
         2    \|x  + a   + a     2      x
        x log(--------------) - x acsch(-)
                     x                  a
   (4)  ----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R         2    \|x  + a   + a     2      x
--R        x log(--------------) - x acsch(-)
--R                     x                  a
--R   (4)  ----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 149    14:670 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                               +-------+
           +-------+           | 2    2                               +-------+
         2 | 2    2     3     \|x  + a   + a        2      x          | 2    2
       (x \|x  + a   - x )log(--------------) + (- x acsch(-) - 2a x)\|x  + a
                                     x                     a
     + 
        3      x        2     3
       x acsch(-) + 2a x  + 2a
               a
  /
       +-------+
       | 2    2
     2\|x  + a   - 2x
                                                     Type: Expression Integer
--R
--R   (5)
--R                               +-------+
--R           +-------+           | 2    2                               +-------+
--R         2 | 2    2     3     \|x  + a   + a        2      x          | 2    2
--R       (x \|x  + a   - x )log(--------------) + (- x acsch(-) - 2a x)\|x  + a
--R                                     x                     a
--R     + 
--R        3      x        2     3
--R       x acsch(-) + 2a x  + 2a
--R               a
--R  /
--R       +-------+
--R       | 2    2
--R     2\|x  + a   - 2x
--R                                                     Type: Expression Integer
--E
)clear all
 
   All user variables and function definitions have been cleared.

--S 150    14:671 Axiom cannot compute this integral
aa:=integrate(acsch(x/a)/x,x)
 

                   %P
           x acsch(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x acsch(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 
   All user variables and function definitions have been cleared.

--S 151    14:672 Axiom cannot compute this integral
aa:=integrate(x^m*asinh(x/a),x)
 

           x
         ++        %P   m
   (1)   |   asinh(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   asinh(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 152    14:673 Axiom cannot compute this integral
aa:=integrate(x^m*acosh(x/a),x)
 

           x
         ++        %P   m
   (1)   |   acosh(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   acosh(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 153    14:674 Axiom cannot compute this integral
aa:=integrate(x^m*atanh(x/a),x)
 

           x
         ++        %P   m
   (1)   |   atanh(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   atanh(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 154    14:675 Axiom cannot compute this integral
aa:=integrate(x^m*acoth(x/a),x)
 

           x
         ++        %P   m
   (1)   |   acoth(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   acoth(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 155    14:676 Axiom cannot compute this integral
aa:=integrate(x^m*asech(x/a),x)
 

           x
         ++        %P   m
   (1)   |   asech(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   asech(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 
   All user variables and function definitions have been cleared.

--S 156    14:677 Axiom cannot compute this integral
aa:=integrate(x^m*acsch(x/a),x)
 

           x
         ++        %P   m
   (1)   |   acsch(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   acsch(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to allfact.output (2009/2/17, 17:43:45).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
-- factorization of integer numbers
--S 1 of 21
n:=45234258258293
 

   (1)  45234258258293
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  45234258258293
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 21
factor n
 

   (2)  13 19 269 8387 81173
                                                       Type: Factored Integer
--R 
--R
--R   (2)  13 19 269 8387 81173
--R                                                       Type: Factored Integer
--E 2

-- factorization of gaussian integers
--S 3 of 21
m:(Complex Integer) := 1324567+%i*53523582
 

   (3)  1324567 + 53523582%i
                                                        Type: Complex Integer
--R 
--R
--R   (3)  1324567 + 53523582%i
--R                                                        Type: Complex Integer
--E 3

--S 4 of 21
factor m
 

   (4)  (2 + 7%i)(7119136 + 1844815%i)
                                               Type: Factored Complex Integer
--R 
--R
--R   (4)  (2 + 7%i)(7119136 + 1844815%i)
--R                                               Type: Factored Complex Integer
--E 4

-- factorization of polynomials over finite fields
--S 5 of 21
u:UP(x,PF(19)) :=3*x**4+2*x**2+15*x+18
 

          4     2
   (5)  3x  + 2x  + 15x + 18
                                  Type: UnivariatePolynomial(x,PrimeField 19)
--R 
--R
--R          4     2
--R   (5)  3x  + 2x  + 15x + 18
--R                                  Type: UnivariatePolynomial(x,PrimeField 19)
--E 5

--S 6 of 21
factor u
 

                   3    2
   (6)  3(x + 18)(x  + x  + 8x + 13)
                         Type: Factored UnivariatePolynomial(x,PrimeField 19)
--R 
--R
--R                   3    2
--R   (6)  3(x + 18)(x  + x  + 8x + 13)
--R                         Type: Factored UnivariatePolynomial(x,PrimeField 19)
--E 6

-- factorization of polynomials over the integers
--S 7 of 21
v:UP(x,INT):= (4*x**3+2*x**2+1)*(12*x**5-x**3+12)
 

           8      7     6      5      3      2
   (7)  48x  + 24x  - 4x  + 10x  + 47x  + 24x  + 12
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R           8      7     6      5      3      2
--R   (7)  48x  + 24x  - 4x  + 10x  + 47x  + 24x  + 12
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 21
factor v
 

           3     2         5    3
   (8)  (4x  + 2x  + 1)(12x  - x  + 12)
                               Type: Factored UnivariatePolynomial(x,Integer)
--R 
--R
--R           3     2         5    3
--R   (8)  (4x  + 2x  + 1)(12x  - x  + 12)
--R                               Type: Factored UnivariatePolynomial(x,Integer)
--E 8

-- factorization of multivariate polynomial over the integers
--S 9 of 21
w:MPOLY([x,y,z],INT) :=(x**2-y**2-z**2)*(x**2+y**2+z**2)*(z*y+3*z)
 

                   4      5       4     3 3     3 2    5      5
   (9)  (z y + 3z)x  - z y  - 3z y  - 2z y  - 6z y  - z y - 3z
                                Type: MultivariatePolynomial([x,y,z],Integer)
--R 
--R
--R                   4      5       4     3 3     3 2    5      5
--R   (9)  (z y + 3z)x  - z y  - 3z y  - 2z y  - 6z y  - z y - 3z
--R                                Type: MultivariatePolynomial([x,y,z],Integer)
--E 9

--S 10 of 21
factor w
 

                   2    2    2   2    2    2
   (10)  z(y + 3)(x  - y  - z )(x  + y  + z )
                       Type: Factored MultivariatePolynomial([x,y,z],Integer)
--R 
--R
--R                   2    2    2   2    2    2
--R   (10)  z(y + 3)(x  - y  - z )(x  + y  + z )
--R                       Type: Factored MultivariatePolynomial([x,y,z],Integer)
--E 10

-- factorization of univariate and multivariate over the rational numbers
--S 11 of 21
f:MPOLY([x,y,z],FRAC INT) :=(4/9*x**2-1/16)*(x**3/27+125)
 

          4   5    1   3   500  2   125
   (11)  --- x  - --- x  + --- x  - ---
         243      432       9        16
                       Type: MultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R          4   5    1   3   500  2   125
--R   (11)  --- x  - --- x  + --- x  - ---
--R         243      432       9        16
--R                       Type: MultivariatePolynomial([x,y,z],Fraction Integer)
--E 11

--S 12 of 21
factor f
 

          4       3      3           2
   (12)  --- (x - -)(x + -)(x + 15)(x  - 15x + 225)
         243      8      8
              Type: Factored MultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R          4       3      3           2
--R   (12)  --- (x - -)(x + -)(x + 15)(x  - 15x + 225)
--R         243      8      8
--R              Type: Factored MultivariatePolynomial([x,y,z],Fraction Integer)
--E 12

-- factorization over rational functions
--S 13 of 21
g:DMP([x,y],FRAC POLY INT):=a**2*x**2/b**2 -c**2*y**2/d**2
 

          2       2
         a   2   c   2
   (13)  -- x  - -- y
          2       2
         b       d
   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R          2       2
--R         a   2   c   2
--R   (13)  -- x  - -- y
--R          2       2
--R         b       d
--R   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 13

--S 14 of 21
factor g
 

          2
         a       b c        b c
   (14)  -- (x - --- y)(x + --- y)
          2      a d        a d
         b
Type: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R          2
--R         a       b c        b c
--R   (14)  -- (x - --- y)(x + --- y)
--R          2      a d        a d
--R         b
--RType: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 14

-- decomposition of a rational function
--S 15 of 21
r:FRAC POLY INT:= (a**3/b**3-c**3/(b+1)**3)*(a*d+a/c)
 

   (15)
         3 4     4 3     4 2     4     4          3 3    4 3     4 2     4     4
   (- a b c  + (a b  + 3a b  + 3a b + a )c)d - a b c  + a b  + 3a b  + 3a b + a
   -----------------------------------------------------------------------------
                                 6     5     4    3
                               (b  + 3b  + 3b  + b )c
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (15)
--R         3 4     4 3     4 2     4     4          3 3    4 3     4 2     4     4
--R   (- a b c  + (a b  + 3a b  + 3a b + a )c)d - a b c  + a b  + 3a b  + 3a b + a
--R   -----------------------------------------------------------------------------
--R                                 6     5     4    3
--R                               (b  + 3b  + 3b  + b )c
--R                                            Type: Fraction Polynomial Integer
--E 15

--S 16 of 21
factorFraction r
 

                             2 2       2            2 2     2     2
           a(b c - a b - a)(b c  + (a b  + a b)c + a b  + 2a b + a )(c d + 1)
   (16)  - ------------------------------------------------------------------
                                        3       3
                                       b (b + 1) c
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                             2 2       2            2 2     2     2
--R           a(b c - a b - a)(b c  + (a b  + a b)c + a b  + 2a b + a )(c d + 1)
--R   (16)  - ------------------------------------------------------------------
--R                                        3       3
--R                                       b (b + 1) c
--R                                   Type: Fraction Factored Polynomial Integer
--E 16

-- factorization over simple algebraic extensions
--S 17 of 21
aa|aa**2+aa+1
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEaa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
   aa : SAEaa := aa

   (17)  aa
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEaa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
--R   aa : SAEaa := aa
--R
--R   (17)  aa
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
--E 17

--S 18 of 21
p:UP(x,SAEaa) :=(x**3+aa**2*x+1)*(aa*x**2+aa*x+aa)**2
 

   (18)
                7               6               5              4     3
     (- aa - 1)x  + (- 2aa - 2)x  + (- 2aa - 3)x  + (- aa - 3)x  - 3x
   + 
                2
     (- aa - 3)x  + (- aa - 2)x - aa - 1
Type: UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--R 
--R
--R   (18)
--R                7               6               5              4     3
--R     (- aa - 1)x  + (- 2aa - 2)x  + (- 2aa - 3)x  + (- aa - 3)x  - 3x
--R   + 
--R                2
--R     (- aa - 3)x  + (- aa - 2)x - aa - 1
--RType: UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--E 18

--S 19 of 21
factor(p)$SAEFACT(UP('aa,FRAC INT),SAEaa,UP(x,SAEaa))
 

                           2            2  3
   (19)  (- aa - 1)(x - aa) (x + aa + 1) (x  + (- aa - 1)x + 1)
Type: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--R 
--R
--R                           2            2  3
--R   (19)  (- aa - 1)(x - aa) (x + aa + 1) (x  + (- aa - 1)x + 1)
--RType: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--E 19

-- factorization over algebraic numbers
--S 20 of 21
a:=rootOf(a**2+3)$AN
 

   (20)  a
                                                        Type: AlgebraicNumber
--R 
--R
--R   (20)  a
--R                                                        Type: AlgebraicNumber
--E 20

--S 21 of 21
factor(x**2+x+1,[a])
 

              - a + 1      a + 1
   (21)  (x + -------)(x + -----)
                 2           2
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R              - a + 1      a + 1
--R   (21)  (x + -------)(x + -----)
--R                 2           2
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 21
)spool
 
Starts dribbling to realclos.output (2009/2/17, 17:57:28).
)set message test on
 
)set message auto off
 
)clear all
 
   All user variables and function definitions have been cleared.
 
--S 1 of 31
Ran := RECLOS(FRAC INT)
 

   (1)  RealClosure Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  RealClosure Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 31
fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran ==
           sqrt(a)+sqrt(b) - sqrt(c)-sqrt(d)
 
   Function declaration fourSquares : (RealClosure Fraction Integer,
      RealClosure Fraction Integer,RealClosure Fraction Integer,
      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration fourSquares : (RealClosure Fraction Integer,
--R      RealClosure Fraction Integer,RealClosure Fraction Integer,
--R      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 31
squareDiff := fourSquares(73,548,60,586)
 
   Compiling function fourSquares with type (RealClosure Fraction 
      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 

           +---+    +--+    +---+    +--+
   (3)  - \|586  - \|60  + \|548  + \|73
                                           Type: RealClosure Fraction Integer
--R 
--R   Compiling function fourSquares with type (RealClosure Fraction 
--R      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
--R      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 
--R
--R           +---+    +--+    +---+    +--+
--R   (3)  - \|586  - \|60  + \|548  + \|73
--R                                           Type: RealClosure Fraction Integer
--E 3

--S 4 of 31
recip(squareDiff)
 

   (4)
             +---+          +--+  +--+         +--+ +---+            +---+
     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
   + 
             +--+ +---+             +--+            +---+            +--+
     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (4)
--R             +---+          +--+  +--+         +--+ +---+            +---+
--R     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
--R   + 
--R             +--+ +---+             +--+            +---+            +--+
--R     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 4

--S 5 of 31
sign(squareDiff)
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 31
squareDiff := fourSquares(165,778,86,990)
 

           +---+    +--+    +---+    +---+
   (6)  - \|990  - \|86  + \|778  + \|165
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +--+    +---+    +---+
--R   (6)  - \|990  - \|86  + \|778  + \|165
--R                                           Type: RealClosure Fraction Integer
--E 6

--S 7 of 31
recip(squareDiff)
 

   (7)
                +---+           +---+  +--+          +---+ +---+
       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
    *
        +---+
       \|990
   + 
              +---+ +---+              +--+             +---+             +---+
     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (7)
--R                +---+           +---+  +--+          +---+ +---+
--R       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
--R    *
--R        +---+
--R       \|990
--R   + 
--R              +---+ +---+              +--+             +---+             +---+
--R     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 7

--S 8 of 31
sign(squareDiff)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 31
squareDiff := fourSquares(217,708,226,692)
 

           +---+    +---+    +---+    +---+
   (9)  - \|692  - \|226  + \|708  + \|217
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +---+    +---+    +---+
--R   (9)  - \|692  - \|226  + \|708  + \|217
--R                                           Type: RealClosure Fraction Integer
--E 9

--S 10 of 31
recip(squareDiff)
 

   (10)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (10)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 10

--S 11 of 31
sign(squareDiff)
 

   (11)  - 1
                                                                Type: Integer
--R 
--R
--R   (11)  - 1
--R                                                                Type: Integer
--E 11

--S 12 of 31
squareDiff := fourSquares(155,836,162,820) 
 

            +---+    +---+    +---+    +---+
   (12)  - \|820  - \|162  + \|836  + \|155
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (12)  - \|820  - \|162  + \|836  + \|155
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 31
recip(squareDiff)
 

   (13)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (13)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 13

--S 14 of 31
sign(squareDiff)
 

   (14)  - 1
                                                                Type: Integer
--R 
--R
--R   (14)  - 1
--R                                                                Type: Integer
--E 14

--S 15 of 31
squareDiff := fourSquares(591,772,552,818)
 

            +---+    +---+    +---+    +---+
   (15)  - \|818  - \|552  + \|772  + \|591
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (15)  - \|818  - \|552  + \|772  + \|591
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 31
recip(squareDiff)
 

   (16)
             +---+         +---+  +---+         +---+ +---+             +---+
     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
   + 
            +---+ +---+             +---+            +---+            +---+
     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (16)
--R             +---+         +---+  +---+         +---+ +---+             +---+
--R     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
--R   + 
--R            +---+ +---+             +---+            +---+            +---+
--R     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 16

--S 17 of 31
sign(squareDiff)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 31
squareDiff := fourSquares(434,1053,412,1088)
 

            +----+    +---+    +----+    +---+
   (18)  - \|1088  - \|412  + \|1053  + \|434
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (18)  - \|1088  - \|412  + \|1053  + \|434
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 31
recip(squareDiff)
 

   (19)
                +----+          +---+  +---+          +---+ +----+
       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
    *
        +----+
       \|1088
   + 
           +---+ +----+              +---+            +----+             +---+
   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (19)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
--R    *
--R        +----+
--R       \|1088
--R   + 
--R           +---+ +----+              +---+            +----+             +---+
--R   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 19

--S 20 of 31
sign(squareDiff)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 31
squareDiff := fourSquares(514,1049,446,1152)
 

            +----+    +---+    +----+    +---+
   (21)  - \|1152  - \|446  + \|1049  + \|514
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (21)  - \|1152  - \|446  + \|1049  + \|514
--R                                           Type: RealClosure Fraction Integer
--E 21

--S 22 of 31
recip(squareDiff)
 

   (22)
                +----+          +---+  +---+          +---+ +----+
       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
    *
        +----+
       \|1152
   + 
           +---+ +----+              +---+             +----+             +---+
   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (22)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
--R    *
--R        +----+
--R       \|1152
--R   + 
--R           +---+ +----+              +---+             +----+             +---+
--R   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 22

--S 23 of 31
sign(squareDiff)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 31
squareDiff := fourSquares(190,1751,208,1698)
 

            +----+    +---+    +----+    +---+
   (24)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (24)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 24

--S 25 of 31
recip(squareDiff)
 

   (25)
                     +----+          +---+  +---+          +---+ +----+
           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
         + 
           - 129571901
    *
        +----+
       \|1698
   + 
               +---+ +----+              +---+             +----+
     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
   + 
                 +---+
     - 387349387\|190
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (25)
--R                     +----+          +---+  +---+          +---+ +----+
--R           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
--R         + 
--R           - 129571901
--R    *
--R        +----+
--R       \|1698
--R   + 
--R               +---+ +----+              +---+             +----+
--R     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
--R   + 
--R                 +---+
--R     - 387349387\|190
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 25

--S 26 of 31
sign(squareDiff)
 

   (26)  - 1
                                                                Type: Integer
--R 
--R
--R   (26)  - 1
--R                                                                Type: Integer
--E 26

)cl prop s2 s5 s10 l
 

--S 27 of 31
(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran);
 

                                           Type: RealClosure Fraction Integer
--R 
--R
--R                                           Type: RealClosure Fraction Integer
--E 27

--S 28 of 31
sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
 

            +---------+ +--------+    +---------+ +--------+   +-----------+
            | +--+      | +-+         | +--+      | +-+        |   +-+
   (28)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +---------+ +--------+    +---------+ +--------+   +-----------+
--R            | +--+      | +-+         | +--+      | +-+        |   +-+
--R   (28)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
--R                                  Type: Equation RealClosure Fraction Integer
--E 28

--S 29 of 31
%::Boolean
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 31
l := allRootsOf((x^2-2)^2-2)$Ran
 

   (30)  [%A41,%A42,%A43,%A44]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (30)  [%A41,%A42,%A43,%A44]
--R                                      Type: List RealClosure Fraction Integer
--E 30

--S 31 of 31
l.1+l.2+l.3+l.4
 

   (31)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (31)  0
--R                                           Type: RealClosure Fraction Integer
--E 31
)spool 
 
Starts dribbling to schaum4.output (2010/3/27, 18:37:14).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 25
aa:=integrate((p*x+q)/sqrt(a*x+b),x)
 

                               +-------+
        (2a p x + 6a q - 4b p)\|a x + b
   (1)  --------------------------------
                         2
                       3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R        (2a p x + 6a q - 4b p)\|a x + b
--R   (1)  --------------------------------
--R                         2
--R                       3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 25
bb:=(2*(a*p*x+3*a*q-2*b*p))/(3*a^2)*sqrt(a*x+b)
 

                               +-------+
        (2a p x + 6a q - 4b p)\|a x + b
   (2)  --------------------------------
                         2
                       3a
                                                     Type: Expression Integer
--R
--R                               +-------+
--R        (2a p x + 6a q - 4b p)\|a x + b
--R   (2)  --------------------------------
--R                         2
--R                       3a
--R                                                     Type: Expression Integer
--E

--S 3 of 25      14:113 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 25
aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x)
 

   (1)
                                                          +--------------+
                      2  +-------+                        |             2
        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
    log(------------------------------------------------------------------)
                                      p x + q
   [-----------------------------------------------------------------------,
                                +--------------+
                                |             2
                               \|- a p q + b p
           +------------+
           |           2  +-------+
          \|a p q - b p  \|a x + b
    2atan(-------------------------)
                  a q - b p
    --------------------------------]
              +------------+
              |           2
             \|a p q - b p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                                                          +--------------+
--R                      2  +-------+                        |             2
--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R    log(------------------------------------------------------------------)
--R                                      p x + q
--R   [-----------------------------------------------------------------------,
--R                                +--------------+
--R                                |             2
--R                               \|- a p q + b p
--R           +------------+
--R           |           2  +-------+
--R          \|a p q - b p  \|a x + b
--R    2atan(-------------------------)
--R                  a q - b p
--R    --------------------------------]
--R              +------------+
--R              |           2
--R             \|a p q - b p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 5 of 25
aa1:=aa.1
 

   (2)
                                                         +--------------+
                     2  +-------+                        |             2
       (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
   log(------------------------------------------------------------------)
                                     p x + q
   -----------------------------------------------------------------------
                               +--------------+
                               |             2
                              \|- a p q + b p
                                                     Type: Expression Integer
--R
--R   (2)
--R                                                         +--------------+
--R                     2  +-------+                        |             2
--R       (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R   log(------------------------------------------------------------------)
--R                                     p x + q
--R   -----------------------------------------------------------------------
--R                               +--------------+
--R                               |             2
--R                              \|- a p q + b p
--R                                                     Type: Expression Integer
--E

--S 6 of 25
aa2:=aa.2
 

               +------------+
               |           2  +-------+
              \|a p q - b p  \|a x + b
        2atan(-------------------------)
                      a q - b p
   (3)  --------------------------------
                  +------------+
                  |           2
                 \|a p q - b p
                                                     Type: Expression Integer
--R
--R               +------------+
--R               |           2  +-------+
--R              \|a p q - b p  \|a x + b
--R        2atan(-------------------------)
--R                      a q - b p
--R   (3)  --------------------------------
--R                  +------------+
--R                  |           2
--R                 \|a p q - b p
--R                                                     Type: Expression Integer
--E

--S 7 of 25
bb1:=1/sqrt(b*p-a*q)*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
 

             +-----------+    +-----------+
            \|a p x + b p  - \|- a q + b p
        log(-------------------------------)
             +-----------+    +-----------+
            \|a p x + b p  + \|- a q + b p
   (4)  ------------------------------------
                    +-----------+
                   \|- a q + b p
                                                     Type: Expression Integer
--R
--R             +-----------+    +-----------+
--R            \|a p x + b p  - \|- a q + b p
--R        log(-------------------------------)
--R             +-----------+    +-----------+
--R            \|a p x + b p  + \|- a q + b p
--R   (4)  ------------------------------------
--R                    +-----------+
--R                   \|- a q + b p
--R                                                     Type: Expression Integer
--E

--S 8 of 25
bb2:=2/(sqrt(a*q-b*p)*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
 

               +-----------+
               |a p x + b p
        2atan( |----------- )
              \| a q - b p
   (5)  ---------------------
            +-+ +---------+
           \|p \|a q - b p
                                                     Type: Expression Integer
--R
--R               +-----------+
--R               |a p x + b p
--R        2atan( |----------- )
--R              \| a q - b p
--R   (5)  ---------------------
--R            +-+ +---------+
--R           \|p \|a q - b p
--R                                                     Type: Expression Integer
--E

--S 9 of 25
cc1:=aa1-bb1
 

   (6)
          +-----------+
         \|- a q + b p
      *
                                                             +--------------+
                         2  +-------+                        |             2
           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
       log(------------------------------------------------------------------)
                                         p x + q
     + 
          +--------------+     +-----------+    +-----------+
          |             2     \|a p x + b p  - \|- a q + b p
       - \|- a p q + b p  log(-------------------------------)
                               +-----------+    +-----------+
                              \|a p x + b p  + \|- a q + b p
  /
      +--------------+
      |             2  +-----------+
     \|- a p q + b p  \|- a q + b p
                                                     Type: Expression Integer
--R
--R   (6)
--R          +-----------+
--R         \|- a q + b p
--R      *
--R                                                             +--------------+
--R                         2  +-------+                        |             2
--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R       log(------------------------------------------------------------------)
--R                                         p x + q
--R     + 
--R          +--------------+     +-----------+    +-----------+
--R          |             2     \|a p x + b p  - \|- a q + b p
--R       - \|- a p q + b p  log(-------------------------------)
--R                               +-----------+    +-----------+
--R                              \|a p x + b p  + \|- a q + b p
--R  /
--R      +--------------+
--R      |             2  +-----------+
--R     \|- a p q + b p  \|- a q + b p
--R                                                     Type: Expression Integer
--E

--S 10 of 25
cc2:=aa1-bb2
 

   (7)
          +-+ +---------+
         \|p \|a q - b p
      *
                                                             +--------------+
                         2  +-------+                        |             2
           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
       log(------------------------------------------------------------------)
                                         p x + q
     + 
           +--------------+      +-----------+
           |             2       |a p x + b p
       - 2\|- a p q + b p  atan( |----------- )
                                \| a q - b p
  /
      +--------------+
      |             2  +-+ +---------+
     \|- a p q + b p  \|p \|a q - b p
                                                     Type: Expression Integer
--R
--R   (7)
--R          +-+ +---------+
--R         \|p \|a q - b p
--R      *
--R                                                             +--------------+
--R                         2  +-------+                        |             2
--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R       log(------------------------------------------------------------------)
--R                                         p x + q
--R     + 
--R           +--------------+      +-----------+
--R           |             2       |a p x + b p
--R       - 2\|- a p q + b p  atan( |----------- )
--R                                \| a q - b p
--R  /
--R      +--------------+
--R      |             2  +-+ +---------+
--R     \|- a p q + b p  \|p \|a q - b p
--R                                                     Type: Expression Integer
--E

--S 11 of 25
cc3:=aa2-bb1
 

   (8)
          +------------+     +-----------+    +-----------+
          |           2     \|a p x + b p  - \|- a q + b p
       - \|a p q - b p  log(-------------------------------)
                             +-----------+    +-----------+
                            \|a p x + b p  + \|- a q + b p
     + 
                            +------------+
                            |           2  +-------+
         +-----------+     \|a p q - b p  \|a x + b
       2\|- a q + b p atan(-------------------------)
                                   a q - b p
  /
                    +------------+
      +-----------+ |           2
     \|- a q + b p \|a p q - b p
                                                     Type: Expression Integer
--R
--R   (8)
--R          +------------+     +-----------+    +-----------+
--R          |           2     \|a p x + b p  - \|- a q + b p
--R       - \|a p q - b p  log(-------------------------------)
--R                             +-----------+    +-----------+
--R                            \|a p x + b p  + \|- a q + b p
--R     + 
--R                            +------------+
--R                            |           2  +-------+
--R         +-----------+     \|a p q - b p  \|a x + b
--R       2\|- a q + b p atan(-------------------------)
--R                                   a q - b p
--R  /
--R                    +------------+
--R      +-----------+ |           2
--R     \|- a q + b p \|a p q - b p
--R                                                     Type: Expression Integer
--E

--S 12 of 25     14:114 Axiom cannot simplify these answers
cc4:=aa2-bb2
 

   (9)
                              +------------+
                              |           2  +-------+
         +-+ +---------+     \|a p q - b p  \|a x + b
       2\|p \|a q - b p atan(-------------------------)
                                     a q - b p
     + 
           +------------+      +-----------+
           |           2       |a p x + b p
       - 2\|a p q - b p  atan( |----------- )
                              \| a q - b p
  /
                      +------------+
      +-+ +---------+ |           2
     \|p \|a q - b p \|a p q - b p
                                                     Type: Expression Integer
--R
--R   (9)
--R                              +------------+
--R                              |           2  +-------+
--R         +-+ +---------+     \|a p q - b p  \|a x + b
--R       2\|p \|a q - b p atan(-------------------------)
--R                                     a q - b p
--R     + 
--R           +------------+      +-----------+
--R           |           2       |a p x + b p
--R       - 2\|a p q - b p  atan( |----------- )
--R                              \| a q - b p
--R  /
--R                      +------------+
--R      +-+ +---------+ |           2
--R     \|p \|a q - b p \|a p q - b p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 13 of 25
aa:=integrate(sqrt(a*x+b)/(p*x+q),x)
 

   (1)
   [
                                +-----------+
                                |- a q + b p  +-------+
          +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
          |- a q + b p         \|     p
          |----------- log(-------------------------------------------------)
         \|     p                               p x + q
       + 
           +-------+
         2\|a x + b
    /
       p
     ,
         +---------+       +-------+
         |a q - b p       \|a x + b       +-------+
    - 2  |--------- atan(------------ + 2\|a x + b
        \|    p           +---------+
                          |a q - b p
                          |---------
                         \|    p
    -----------------------------------------------]
                           p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                                +-----------+
--R                                |- a q + b p  +-------+
--R          +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R          |- a q + b p         \|     p
--R          |----------- log(-------------------------------------------------)
--R         \|     p                               p x + q
--R       + 
--R           +-------+
--R         2\|a x + b
--R    /
--R       p
--R     ,
--R         +---------+       +-------+
--R         |a q - b p       \|a x + b       +-------+
--R    - 2  |--------- atan(------------ + 2\|a x + b
--R        \|    p           +---------+
--R                          |a q - b p
--R                          |---------
--R                         \|    p
--R    -----------------------------------------------]
--R                           p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 14 of 25
aa1:=aa.1
 

   (2)
                              +-----------+
                              |- a q + b p  +-------+
        +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
        |- a q + b p         \|     p
        |----------- log(-------------------------------------------------)
       \|     p                               p x + q
     + 
         +-------+
       2\|a x + b
  /
     p
                                                     Type: Expression Integer
--R
--R   (2)
--R                              +-----------+
--R                              |- a q + b p  +-------+
--R        +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R        |- a q + b p         \|     p
--R        |----------- log(-------------------------------------------------)
--R       \|     p                               p x + q
--R     + 
--R         +-------+
--R       2\|a x + b
--R  /
--R     p
--R                                                     Type: Expression Integer
--E

--S 15 of 25
aa2:=aa.2
 

             +---------+       +-------+
             |a q - b p       \|a x + b       +-------+
        - 2  |--------- atan(------------ + 2\|a x + b
            \|    p           +---------+
                              |a q - b p
                              |---------
                             \|    p
   (3)  -----------------------------------------------
                               p
                                                     Type: Expression Integer
--R
--R             +---------+       +-------+
--R             |a q - b p       \|a x + b       +-------+
--R        - 2  |--------- atan(------------ + 2\|a x + b
--R            \|    p           +---------+
--R                              |a q - b p
--R                              |---------
--R                             \|    p
--R   (3)  -----------------------------------------------
--R                               p
--R                                                     Type: Expression Integer
--E

--S 16 of 25
bb1:=(2*sqrt(a*x+b))/p+sqrt(b*p-a*q)/(p*sqrt(p))*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
 

                           +-----------+    +-----------+
         +-----------+    \|a p x + b p  - \|- a q + b p       +-+ +-------+
        \|- a q + b p log(-------------------------------) + 2\|p \|a x + b
                           +-----------+    +-----------+
                          \|a p x + b p  + \|- a q + b p
   (4)  --------------------------------------------------------------------
                                          +-+
                                        p\|p
                                                     Type: Expression Integer
--R
--R                           +-----------+    +-----------+
--R         +-----------+    \|a p x + b p  - \|- a q + b p       +-+ +-------+
--R        \|- a q + b p log(-------------------------------) + 2\|p \|a x + b
--R                           +-----------+    +-----------+
--R                          \|a p x + b p  + \|- a q + b p
--R   (4)  --------------------------------------------------------------------
--R                                          +-+
--R                                        p\|p
--R                                                     Type: Expression Integer
--E

--S 17 of 25
bb2:=(2*sqrt(a*x+b))/p-(2*sqrt(a*q-b*p))/(p*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
 

                             +-----------+
            +---------+      |a p x + b p       +-+ +-------+
        - 2\|a q - b p atan( |----------- ) + 2\|p \|a x + b
                            \| a q - b p
   (5)  -----------------------------------------------------
                                  +-+
                                p\|p
                                                     Type: Expression Integer
--R
--R                             +-----------+
--R            +---------+      |a p x + b p       +-+ +-------+
--R        - 2\|a q - b p atan( |----------- ) + 2\|p \|a x + b
--R                            \| a q - b p
--R   (5)  -----------------------------------------------------
--R                                  +-+
--R                                p\|p
--R                                                     Type: Expression Integer
--E

--S 18 of 25
cc1:=aa1-bb1
 

   (6)
                            +-----------+    +-----------+
          +-----------+    \|a p x + b p  - \|- a q + b p
       - \|- a q + b p log(-------------------------------)
                            +-----------+    +-----------+
                           \|a p x + b p  + \|- a q + b p
     + 
                                  +-----------+
                                  |- a q + b p  +-------+
        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
        |- a q + b p  +-+        \|     p
        |----------- \|p log(-------------------------------------------------)
       \|     p                                   p x + q
  /
       +-+
     p\|p
                                                     Type: Expression Integer
--R
--R   (6)
--R                            +-----------+    +-----------+
--R          +-----------+    \|a p x + b p  - \|- a q + b p
--R       - \|- a q + b p log(-------------------------------)
--R                            +-----------+    +-----------+
--R                           \|a p x + b p  + \|- a q + b p
--R     + 
--R                                  +-----------+
--R                                  |- a q + b p  +-------+
--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R        |- a q + b p  +-+        \|     p
--R        |----------- \|p log(-------------------------------------------------)
--R       \|     p                                   p x + q
--R  /
--R       +-+
--R     p\|p
--R                                                     Type: Expression Integer
--E

--S 19 of 25
cc2:=aa1-bb2
 

   (7)
                                  +-----------+
                                  |- a q + b p  +-------+
        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
        |- a q + b p  +-+        \|     p
        |----------- \|p log(-------------------------------------------------)
       \|     p                                   p x + q
     + 
                          +-----------+
         +---------+      |a p x + b p
       2\|a q - b p atan( |----------- )
                         \| a q - b p
  /
       +-+
     p\|p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                  +-----------+
--R                                  |- a q + b p  +-------+
--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
--R        |- a q + b p  +-+        \|     p
--R        |----------- \|p log(-------------------------------------------------)
--R       \|     p                                   p x + q
--R     + 
--R                          +-----------+
--R         +---------+      |a p x + b p
--R       2\|a q - b p atan( |----------- )
--R                         \| a q - b p
--R  /
--R       +-+
--R     p\|p
--R                                                     Type: Expression Integer
--E

--S 20 of 25
cc3:=aa2-bb1
 

   (8)
                            +-----------+    +-----------+
          +-----------+    \|a p x + b p  - \|- a q + b p
       - \|- a q + b p log(-------------------------------)
                            +-----------+    +-----------+
                           \|a p x + b p  + \|- a q + b p
     + 
               +---------+       +-------+
           +-+ |a q - b p       \|a x + b
       - 2\|p  |--------- atan(------------)
              \|    p           +---------+
                                |a q - b p
                                |---------
                               \|    p
  /
       +-+
     p\|p
                                                     Type: Expression Integer
--R
--R   (8)
--R                            +-----------+    +-----------+
--R          +-----------+    \|a p x + b p  - \|- a q + b p
--R       - \|- a q + b p log(-------------------------------)
--R                            +-----------+    +-----------+
--R                           \|a p x + b p  + \|- a q + b p
--R     + 
--R               +---------+       +-------+
--R           +-+ |a q - b p       \|a x + b
--R       - 2\|p  |--------- atan(------------)
--R              \|    p           +---------+
--R                                |a q - b p
--R                                |---------
--R                               \|    p
--R  /
--R       +-+
--R     p\|p
--R                                                     Type: Expression Integer
--E

--S 21 of 25     14:115 Axiom cannot simplify these answers
cc4:=aa2-bb2
 

   (9)
           +---------+       +-------+                        +-----------+
       +-+ |a q - b p       \|a x + b        +---------+      |a p x + b p
   - 2\|p  |--------- atan(------------) + 2\|a q - b p atan( |----------- )
          \|    p           +---------+                      \| a q - b p
                            |a q - b p
                            |---------
                           \|    p
   -------------------------------------------------------------------------
                                       +-+
                                     p\|p
                                                     Type: Expression Integer
--R
--R   (9)
--R           +---------+       +-------+                        +-----------+
--R       +-+ |a q - b p       \|a x + b        +---------+      |a p x + b p
--R   - 2\|p  |--------- atan(------------) + 2\|a q - b p atan( |----------- )
--R          \|    p           +---------+                      \| a q - b p
--R                            |a q - b p
--R                            |---------
--R                           \|    p
--R   -------------------------------------------------------------------------
--R                                       +-+
--R                                     p\|p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 22 of 25     14:116 Axiom cannot compute this integral
aa:=integrate((p*x+q)^n*sqrt(a*x+b),x)
 

           x
         ++            n +--------+
   (1)   |   (q + %L p) \|b + %L a d%L
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n +--------+
--I   (1)   |   (q + %L p) \|b + %L a d%L
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 23 of 25     14:117 Axiom cannot compute this integral
aa:=integrate(1/((p*x+q)^n*sqrt(a*x+b)),x)
 

           x
         ++             1
   (1)   |   ---------------------- d%L
        ++             n +--------+
             (q + %L p) \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             1
--I   (1)   |   ---------------------- d%L
--R        ++             n +--------+
--I             (q + %L p) \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 24 of 25     14:118 Axiom cannot compute this integral
aa:=integrate((p*x+q)^n/sqrt(a*x+b),x)
 

           x           n
         ++  (q + %L p)
   (1)   |   ----------- d%L
        ++    +--------+
             \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           n
--I         ++  (q + %L p)
--I   (1)   |   ----------- d%L
--R        ++    +--------+
--I             \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E
)clear all
 

--S 25 of 25     14:119 Axiom cannot compute this integral
aa:=integrate(sqrt(a*x+b)/(p*x+q)^n,x)
 

           x  +--------+
         ++  \|b + %L a
   (1)   |   ----------- d%L
        ++             n
             (q + %L p)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +--------+
--I         ++  \|b + %L a
--I   (1)   |   ----------- d%L
--R        ++             n
--I             (q + %L p)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to danzwill2.output (2010/3/27, 18:24:51).
)set message test on
 
)set message auto off
 
)clear all
 
)set break resume
 

--S 1 of 50
i1:= integrate(e^(1991*x),x)
 

          1991x log(e)
        %e
   (1)  --------------
          1991log(e)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          1991x log(e)
--R        %e
--R   (1)  --------------
--R          1991log(e)
--R                                          Type: Union(Expression Integer,...)
--E 1

--S 2 of 50
i2:= integrate((sin(x)-cos(x))^2,x)
 

              2
   (2)  cos(x)  + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R   (2)  cos(x)  + x
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 50
i3:= integrate(log(x),x)
 

   (3)  x log(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (3)  x log(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 50
i4:= integrate(1/(%pi*x),x)
 

        log(x)
   (4)  ------
          %pi
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        log(x)
--R   (4)  ------
--R          %pi
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 50
i5:= integrate(%e^(sin(x)^2)*%e^(cos(x)^2),x)
 

   (5)  x %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)  x %e
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 50
i6:= integrate(1/(x*log(x)),x)
 

   (6)  log(log(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (6)  log(log(x))
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 50
i7:= integrate(x/(x^4+1),x)
 

              2
        atan(x )
   (7)  --------
            2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R        atan(x )
--R   (7)  --------
--R            2
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 50
i8:= integrate((x+1)/(x^2+2*x+2)^(1/3),x)
 

          +-----------+2
         3| 2
        3\|x  + 2x + 2
   (8)  ----------------
                4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +-----------+2
--R         3| 2
--R        3\|x  + 2x + 2
--R   (8)  ----------------
--R                4
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 50
i9:= integrate(x*%e^x*sin(x),x)
 

            x                          x
        x %e sin(x) + (- x + 1)cos(x)%e
   (9)  --------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x                          x
--R        x %e sin(x) + (- x + 1)cos(x)%e
--R   (9)  --------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 50
i10:= integrate(%e^(%e^x+x),x)
 

             x
           %e  + x
         %e
   (10)  ---------
              x
            %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R           %e  + x
--R         %e
--R   (10)  ---------
--R              x
--R            %e
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 50
i11:= integrate(1/(sec(x)+tan(x)*sin(x)),x)
 

               (2cos(x) + 3)sin(x)             sin(x)
   (11)  atan(---------------------) - atan(-----------)
                    2                       2cos(x) + 2
              cos(x)  + 2cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               (2cos(x) + 3)sin(x)             sin(x)
--R   (11)  atan(---------------------) - atan(-----------)
--R                    2                       2cos(x) + 2
--R              cos(x)  + 2cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 50
i12:= integrate((%e^(5*x)+%e^(7*x))/(%e^x+%e^(-x)),x)
 

            x 6
         (%e )
   (12)  ------
            6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x 6
--R         (%e )
--R   (12)  ------
--R            6
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 50
i13:= integrate(sqrt(-1+2/(1+3*x)),x)
 

                  +--------+             +--------+
                  |- 3x + 1              |- 3x + 1
         - 2atan( |-------- ) + (3x + 1) |--------
                 \| 3x + 1              \| 3x + 1
   (13)  ------------------------------------------
                              3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +--------+             +--------+
--R                  |- 3x + 1              |- 3x + 1
--R         - 2atan( |-------- ) + (3x + 1) |--------
--R                 \| 3x + 1              \| 3x + 1
--R   (13)  ------------------------------------------
--R                              3
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 50
i14:= integrate(sinh(x)-cosh(x),x)
 

                 1
   (14)  -----------------
         sinh(x) + cosh(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 1
--R   (14)  -----------------
--R         sinh(x) + cosh(x)
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 50
i15:= integrate((sin(x)*%e^sec(x))/cos(x)^2,x)
 

              1
           ------
           cos(x)
   (15)  %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R           ------
--R           cos(x)
--R   (15)  %e
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 50
i16:= integrate((x^2+1)/(x^4-x^2+1),x)
 

               3
   (16)  atan(x ) + atan(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3
--R   (16)  atan(x ) + atan(x)
--R                                          Type: Union(Expression Integer,...)
--E 16

--S 17 of 50
i17:= integrate(1/(%pi*x^2+atan(x)+x^2*atan(x)+%pi),x)
 

                    2x   2               2x          2
         log(atan(------)  - 4%pi atan(------) + 4%pi )
                   2                    2
                  x  - 1               x  - 1
   (17)  ----------------------------------------------
                                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2x   2               2x          2
--R         log(atan(------)  - 4%pi atan(------) + 4%pi )
--R                   2                    2
--R                  x  - 1               x  - 1
--R   (17)  ----------------------------------------------
--R                                2
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 50
i18:= integrate(sec(x)^3,x)
 

   (18)
         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
                   cos(x) + 1                        cos(x) + 1
   --------------------------------------------------------------------------
                                           2
                                    2cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (18)
--R         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
--R   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
--R                   cos(x) + 1                        cos(x) + 1
--R   --------------------------------------------------------------------------
--R                                           2
--R                                    2cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 18
 
--S 19 of 50
i19:= integrate(1/(x^2-10*x+26),x)
 

   (19)  atan(x - 5)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (19)  atan(x - 5)
--R                                          Type: Union(Expression Integer,...)
--E 19 

--S 20 of 50
i20:= integrate(1/(x^2-11*x-26),x)
 

         - log(x + 2) + log(x - 13)
   (20)  --------------------------
                     15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - log(x + 2) + log(x - 13)
--R   (20)  --------------------------
--R                     15
--R                                          Type: Union(Expression Integer,...)
--E 20 

--S 21 of 50
i21:= integrate(1/(12+13*cos(x)),x)
 

             sin(x) + 5cos(x) + 5        sin(x) - 5cos(x) - 5
         log(--------------------) - log(--------------------)
                  cos(x) + 1                  cos(x) + 1
   (21)  -----------------------------------------------------
                                   5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             sin(x) + 5cos(x) + 5        sin(x) - 5cos(x) - 5
--R         log(--------------------) - log(--------------------)
--R                  cos(x) + 1                  cos(x) + 1
--R   (21)  -----------------------------------------------------
--R                                   5
--R                                          Type: Union(Expression Integer,...)
--E 21 

--S 22 of 50
i22:= integrate((x^3+1)/(x+1),x)
 

           3     2
         2x  - 3x  + 6x
   (22)  --------------
                6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           3     2
--R         2x  - 3x  + 6x
--R   (22)  --------------
--R                6
--R                                          Type: Union(Expression Integer,...)
--E 22 

--S 23 of 50
i23:= integrate((1-4*x^4)^(-1/2)/(4*x)^(-1),x)
 

                  +---------+
                  |    4
                 \|- 4x  + 1  - 1
   (23)  - 2atan(----------------)
                          2
                        2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+
--R                  |    4
--R                 \|- 4x  + 1  - 1
--R   (23)  - 2atan(----------------)
--R                          2
--R                        2x
--R                                          Type: Union(Expression Integer,...)
--E 23 

--S 24 of 50
i24:= integrate(%e^(1991),x)
 

             1991
   (24)  x %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             1991
--R   (24)  x %e
--R                                          Type: Union(Expression Integer,...)
--E 24 

--S 25 of 50
i25:= integrate((log(x)+1)*x^x,x)
 

           x log(x)
   (25)  %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x log(x)
--R   (25)  %e
--R                                          Type: Union(Expression Integer,...)
--E 25 

--S 26 of 50
i26:= integrate(cos(2*x)*sin(6*x),x)
 

                   4          2
         - 2cos(2x)  + cos(2x)
   (26)  ----------------------
                    4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   4          2
--R         - 2cos(2x)  + cos(2x)
--R   (26)  ----------------------
--R                    4
--R                                          Type: Union(Expression Integer,...)
--E 26 

--S 27 of 50
i27:= integrate(1/(sqrt(x)*(1+sqrt(x))),x)
 

               +-+
   (27)  2log(\|x  + 1)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-+
--R   (27)  2log(\|x  + 1)
--R                                          Type: Union(Expression Integer,...)
--E 27 

--S 28 of 50
i28:= integrate(e^(1/x)*x^(-3),x)
 

                         log(e)
                         ------
                            x
         (- log(e) + x)%e
   (28)  ----------------------
                        2
                x log(e)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         log(e)
--R                         ------
--R                            x
--R         (- log(e) + x)%e
--R   (28)  ----------------------
--R                        2
--R                x log(e)
--R                                          Type: Union(Expression Integer,...)
--E 28 

--S 29 of 50
i29:= integrate(sqrt(csc(x)-sin(x)),x)
 

                         +--------------------------------+
                         |         - 16cos(x) + 16
   (29)  (- cos(x) - 1)  |--------------------------------
                        4|      3          2
                        \|cos(x)  + 3cos(x)  + 3cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         +--------------------------------+
--R                         |         - 16cos(x) + 16
--R   (29)  (- cos(x) - 1)  |--------------------------------
--R                        4|      3          2
--R                        \|cos(x)  + 3cos(x)  + 3cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 29 

--S 30 of 50
i30:= integrate((x^2+1)/(x^3-x),x)
 

              2
   (30)  log(x  - 1) - log(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R   (30)  log(x  - 1) - log(x)
--R                                          Type: Union(Expression Integer,...)
--E 30 

--S 31 of 50
i31:= integrate(42^x,x)
 

           x log(42)
         %e
   (31)  -----------
           log(42)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x log(42)
--R         %e
--R   (31)  -----------
--R           log(42)
--R                                          Type: Union(Expression Integer,...)
--E 31 

--S 32 of 50
i32:= integrate(x^5*%e^x,x)
 

           5     4      3      2                x
   (32)  (x  - 5x  + 20x  - 60x  + 120x - 120)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           5     4      3      2                x
--R   (32)  (x  - 5x  + 20x  - 60x  + 120x - 120)%e
--R                                          Type: Union(Expression Integer,...)
--E 32 

--S 33 of 50
i33:= integrate(x*%e^(x^2),x)
 

            2
           x
         %e
   (33)  ----
           2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2
--R           x
--R         %e
--R   (33)  ----
--R           2
--R                                          Type: Union(Expression Integer,...)
--E 33 

--S 34 of 50
i34:= integrate(1/(x^2+1)^2,x)
 

           2
         (x  + 1)atan(x) + x
   (34)  -------------------
                 2
               2x  + 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2
--R         (x  + 1)atan(x) + x
--R   (34)  -------------------
--R                 2
--R               2x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 34 

--S 35 of 50
i35:= integrate(1/(%e^x+%e^(-x)),x)
 

                x
   (35)  atan(%e )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                x
--R   (35)  atan(%e )
--R                                          Type: Union(Expression Integer,...)
--E 35 

--S 36 of 50
i36:= integrate(tan(x)*log(abs(sec(x))),x)
 

              +-------+ 2
              |   1
         log( |------- )
              |      2
             \|cos(x)
   (36)  ----------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              +-------+ 2
--R              |   1
--R         log( |------- )
--R              |      2
--R             \|cos(x)
--R   (36)  ----------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 36 

--S 37 of 50
i37:= integrate(cos(sin(x))*cos(x),x)
 

   (37)  sin(sin(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (37)  sin(sin(x))
--R                                          Type: Union(Expression Integer,...)
--E 37 

--S 38 of 50
i38:= integrate(1/(x^2-9),x)
 

         - log(x + 3) + log(x - 3)
   (38)  -------------------------
                     6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - log(x + 3) + log(x - 3)
--R   (38)  -------------------------
--R                     6
--R                                          Type: Union(Expression Integer,...)
--E 38 

--S 39 of 50
i39:= integrate(%pi/sqrt(16-%e^2),x)
 

             %pi x
   (39)  -------------
          +----------+
          |    2
         \|- %e  + 16
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             %pi x
--R   (39)  -------------
--R          +----------+
--R          |    2
--R         \|- %e  + 16
--R                                          Type: Union(Expression Integer,...)
--E 39 

--S 40 of 50
i40:= integrate(sqrt(tan(x)),x)
 

   (40)
          +-+
         \|2
      *
                                                  +------+
                  +-+                 +-+      2  |sin(x)
         log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------  + 4cos(x)sin(x) + 1)
                                                 \|cos(x)
     + 
                              +------+
                              |sin(x)     +-+                +-+      2    +-+
                2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)  - \|2
        +-+                  \|cos(x)
       \|2 atan(--------------------------------------------------------------)
                               +------+
                             2 |sin(x)     +-+                +-+      2
                      2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)
                              \|cos(x)
     + 
       -
             +-+
            \|2
         *
                             +------+
                             |sin(x)      +-+                 +-+      2    +-+
               4cos(x)sin(x) |------  - 2\|2 cos(x)sin(x) + 2\|2 cos(x)  - \|2
                            \|cos(x)
          atan(----------------------------------------------------------------)
                           +------+
                         2 |sin(x)      +-+                 +-+      2    +-+
                  4cos(x)  |------  - 2\|2 cos(x)sin(x) - 2\|2 cos(x)  + \|2
                          \|cos(x)
     + 
                                 +------+
                                 |sin(x)     +-+                +-+      2
                   2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)
          +-+                   \|cos(x)
       - \|2 atan(---------------------------------------------------------)
                           +------+
                         2 |sin(x)     +-+                +-+      2    +-+
                  2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)  + \|2
                          \|cos(x)
  /
     4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (40)
--R          +-+
--R         \|2
--R      *
--R                                                  +------+
--R                  +-+                 +-+      2  |sin(x)
--R         log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------  + 4cos(x)sin(x) + 1)
--R                                                 \|cos(x)
--R     + 
--R                              +------+
--R                              |sin(x)     +-+                +-+      2    +-+
--R                2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)  - \|2
--R        +-+                  \|cos(x)
--R       \|2 atan(--------------------------------------------------------------)
--R                               +------+
--R                             2 |sin(x)     +-+                +-+      2
--R                      2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)
--R                              \|cos(x)
--R     + 
--R       -
--R             +-+
--R            \|2
--R         *
--R                             +------+
--R                             |sin(x)      +-+                 +-+      2    +-+
--R               4cos(x)sin(x) |------  - 2\|2 cos(x)sin(x) + 2\|2 cos(x)  - \|2
--R                            \|cos(x)
--R          atan(----------------------------------------------------------------)
--R                           +------+
--R                         2 |sin(x)      +-+                 +-+      2    +-+
--R                  4cos(x)  |------  - 2\|2 cos(x)sin(x) - 2\|2 cos(x)  + \|2
--R                          \|cos(x)
--R     + 
--R                                 +------+
--R                                 |sin(x)     +-+                +-+      2
--R                   2cos(x)sin(x) |------  - \|2 cos(x)sin(x) + \|2 cos(x)
--R          +-+                   \|cos(x)
--R       - \|2 atan(---------------------------------------------------------)
--R                           +------+
--R                         2 |sin(x)     +-+                +-+      2    +-+
--R                  2cos(x)  |------  - \|2 cos(x)sin(x) - \|2 cos(x)  + \|2
--R                          \|cos(x)
--R  /
--R     4
--R                                          Type: Union(Expression Integer,...)
--E 40 

--S 41 of 50
i41:= integrate(sin(x)^(-1),x)
 

               sin(x)
   (41)  log(----------)
             cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               sin(x)
--R   (41)  log(----------)
--R             cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 41 

--S 42 of 50
i42:= integrate((x^2-2*x+2)/(x^2+1),x)
 

                2
   (42)  - log(x  + 1) + atan(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R   (42)  - log(x  + 1) + atan(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 42 

--S 43 of 50
i43:= integrate((sin(x)^2*cos(x)^2)/(1+cos(2*x)),x)
 

         - cos(x)sin(x) + x
   (43)  ------------------
                  4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - cos(x)sin(x) + x
--R   (43)  ------------------
--R                  4
--R                                          Type: Union(Expression Integer,...)
--E 43 

--S 44 of 50
i44:= integrate(sqrt(x+x^2*sqrt(x)),x)
 

                       +----------+
            +-+     2  | 2 +-+
         (4\|x  + 4x )\|x \|x  + x
   (44)  --------------------------
                     9x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       +----------+
--R            +-+     2  | 2 +-+
--R         (4\|x  + 4x )\|x \|x  + x
--R   (44)  --------------------------
--R                     9x
--R                                          Type: Union(Expression Integer,...)
--E 44 

--S 45 of 50
i45:= integrate(cos(4*x)*cos(2*x),x)
 

                  2
         (2cos(2x)  + 1)sin(2x)
   (45)  ----------------------
                    6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R         (2cos(2x)  + 1)sin(2x)
--R   (45)  ----------------------
--R                    6
--R                                          Type: Union(Expression Integer,...)
--E 45 

--S 46 of 50
i46:= integrate(sqrt(x^3-1)/x,x)
 

                  +------+      +------+
                  | 3           | 3
         - 2atan(\|x  - 1 ) + 2\|x  - 1
   (46)  -------------------------------
                        3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +------+      +------+
--R                  | 3           | 3
--R         - 2atan(\|x  - 1 ) + 2\|x  - 1
--R   (46)  -------------------------------
--R                        3
--R                                          Type: Union(Expression Integer,...)
--E 46 

--S 47 of 50
i47:= integrate((%e^x*(x-2))/x^3,x)
 

           x
         %e
   (47)  ---
           2
          x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         %e
--R   (47)  ---
--R           2
--R          x
--R                                          Type: Union(Expression Integer,...)
--E 47 

--S 48 of 50
i48:= integrate(cot(x)/log(sin(x)),x)
 

   (48)  log(log(sin(x)))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (48)  log(log(sin(x)))
--R                                          Type: Union(Expression Integer,...)
--E 48 

--S 49 of 50
i49:= integrate(x*sec(x)^2,x)
 

                          2                      2cos(x)
         - cos(x)log(----------) + cos(x)log(- ----------) + x sin(x)
                     cos(x) + 1                cos(x) + 1
   (49)  ------------------------------------------------------------
                                    cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2                      2cos(x)
--R         - cos(x)log(----------) + cos(x)log(- ----------) + x sin(x)
--R                     cos(x) + 1                cos(x) + 1
--R   (49)  ------------------------------------------------------------
--R                                    cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 49 

--S 50 of 50
i50:= integrate(x*sec(x)*(x*tan(x)+2),x)
 

            2
           x
   (50)  ------
         cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2
--R           x
--R   (50)  ------
--R         cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 50 
)spool
 
Starts dribbling to unittest2.output (2010/3/27, 18:41:34).
)lisp (setq *print-circle* t)
 
Value = T
)set mes auto off
 
)clear all
 

--S 1 of 237
)lisp (identity |$abbreviateTypes|)
 
Value = NIL
--R 
--RValue = NIL
--E 1

--S 2 of 237
)lisp (identity |$algebraFormat|)
 
Value = T
--R 
--RValue = T
--E 2

--S 3 of 237
)lisp (identity |$algebraOutputFile|)
 
Value = "CONSOLE"
--R 
--RValue = "CONSOLE"
--E 3

--S 4 of 237
)lisp (identity |$algebraOutputStream|)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 4

--S 5 of 237
)lisp (identity |$asharpCmdlineFlags|)
 
Value = "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra"
--R 
--RValue = "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra"
--E 5

--S 6 of 237
)lisp (identity |$BreakMode|)
 
Value = |resume|
--R 
--RValue = |resume|
--E 6

--S 7 of 237
)lisp (identity |$clearExcept|)
 
 
   >> System error:
   The variable |$clearExcept| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$clearExcept| is unbound.
--R
--R   Continuing to read the file...
--R
--E 7

--S 8 of 237
)lisp (identity |$clearOptions|)
 
Value = (|modes| |operations| |properties| |types| |values|)
--R 
--RValue = (|modes| |operations| |properties| |types| |values|)
--E 8

--S 9 of 237
)lisp (identity |$CommandSynonymAlist|)
 
Value = ((? . "what commands") (|ap| . "what things") (|apr| . "what things") (|apropos| . "what things") (|cache| . "set functions cache") (|cl| . "clear") (|cls| . "zsystemdevelopment )cls") (|cms| . "system") (|co| . "compiler") (|d| . "display") (|dep| . "display dependents") (|dependents| . "display dependents") (|e| . "edit") (|expose| . "set expose add constructor") (|fc| . "zsystemdevelopment )c") (|fd| . "zsystemdevelopment )d") (|fdt| . "zsystemdevelopment )dt") (|fct| . "zsystemdevelopment )ct") (|fctl| . "zsystemdevelopment )ctl") (|fe| . "zsystemdevelopment )e") (|fec| . "zsystemdevelopment )ec") (|fect| . "zsystemdevelopment )ect") (|fns| . "exec spadfn") (|fortran| . "set output fortran") (|h| . "help") (|hd| . "system hypertex &") (|kclam| . "boot clearClams ( )") (|killcaches| . "boot clearConstructorAndLisplibCaches ( )") (|patch| . "zsystemdevelopment )patch") (|pause| . "zsystemdevelopment )pause") (|prompt| . "set message prompt") (|recurrence| . "set functions recurrence") (|restore| . "history )restore") (|save| . "history )save") (|startGraphics| . "system $AXIOM/lib/viewman &") (|startNAGLink| . "system $AXIOM/lib/nagman &") (|stopGraphics| . "lisp (|sockSendSignal| 2 15)") (|stopNAGLink| . "lisp (|sockSendSignal| 8 15)") (|time| . "set message time") (|type| . "set message type") (|unexpose| . "set expose drop constructor") (|up| . "zsystemdevelopment )update") (|version| . "lisp *yearweek*") (|w| . "what") (|wc| . "what categories") (|wd| . "what domains") (|who| . "lisp (pprint credits)") (|wp| . "what packages") (|ws| . "what synonyms"))
--R 
--RValue = ((? . "what commands") (|ap| . "what things") (|apr| . "what things") (|apropos| . "what things") (|cache| . "set functions cache") (|cl| . "clear") (|cls| . "zsystemdevelopment )cls") (|cms| . "system") (|co| . "compiler") (|d| . "display") (|dep| . "display dependents") (|dependents| . "display dependents") (|e| . "edit") (|expose| . "set expose add constructor") (|fc| . "zsystemdevelopment )c") (|fd| . "zsystemdevelopment )d") (|fdt| . "zsystemdevelopment )dt") (|fct| . "zsystemdevelopment )ct") (|fctl| . "zsystemdevelopment )ctl") (|fe| . "zsystemdevelopment )e") (|fec| . "zsystemdevelopment )ec") (|fect| . "zsystemdevelopment )ect") (|fns| . "exec spadfn") (|fortran| . "set output fortran") (|h| . "help") (|hd| . "system hypertex &") (|kclam| . "boot clearClams ( )") (|killcaches| . "boot clearConstructorAndLisplibCaches ( )") (|patch| . "zsystemdevelopment )patch") (|pause| . "zsystemdevelopment )pause") (|prompt| . "set message prompt") (|recurrence| . "set functions recurrence") (|restore| . "history )restore") (|save| . "history )save") (|startGraphics| . "system $AXIOM/lib/viewman &") (|startNAGLink| . "system $AXIOM/lib/nagman &") (|stopGraphics| . "lisp (|sockSendSignal| 2 15)") (|stopNAGLink| . "lisp (|sockSendSignal| 8 15)") (|time| . "set message time") (|type| . "set message type") (|unexpose| . "set expose drop constructor") (|up| . "zsystemdevelopment )update") (|version| . "lisp *yearweek*") (|w| . "what") (|wc| . "what categories") (|wd| . "what domains") (|who| . "lisp (pprint credits)") (|wp| . "what packages") (|ws| . "what synonyms"))
--E 9

--S 10 of 237
)lisp (identity |$compileDontDefineFunctions|)
 
Value = T
--R 
--RValue = T
--E 10

--S 11 of 237
)lisp (identity |$compileRecurrence|)
 
Value = T
--R 
--RValue = T
--E 11

--S 12 of 237
)lisp (identity compiler::*compile-verbose*)
 
Value = NIL
--R 
--RValue = NIL
--E 12

--S 13 of 237
)lisp (identity credits)
 
Value = ("An alphabetical listing of contributors to AXIOM:" "Cyril Alberga          Roy Adler              Christian Aistleitner" "Richard Anderson       George Andrews         S.J. Atkins" "Henry Baker            Stephen Balzac         Yurij Baransky" "David R. Barton        Gerald Baumgartner     Gilbert Baumslag" "Michael Becker         Jay Belanger           David Bindel" "Fred Blair             Vladimir Bondarenko    Mark Botch" "Alexandre Bouyer       Peter A. Broadbery     Martin Brock" "Manuel Bronstein       Stephen Buchwald       Florian Bundschuh" "Luanne Burns           William Burge" "Quentin Carpent        Robert Caviness        Bruce Char" "Ondrej Certik          Cheekai Chin           David V. Chudnovsky" "Gregory V. Chudnovsky  Josh Cohen             Christophe Conil" "Don Coppersmith        George Corliss         Robert Corless" "Gary Cornell           Meino Cramer           Claire Di Crescenzo" "David Cyganski" "Timothy Daly Sr.       Timothy Daly Jr.       James H. Davenport" "Didier Deshommes       Michael Dewar" "Jean Della Dora        Gabriel Dos Reis       Claire DiCrescendo" "Sam Dooley             Lionel Ducos           Martin Dunstan" "Brian Dupee            Dominique Duval" "Robert Edwards         Heow Eide-Goodman      Lars Erickson" "Richard Fateman        Bertfried Fauser       Stuart Feldman" "Brian Ford             Albrecht Fortenbacher  George Frances" "Constantine Frangos    Timothy Freeman        Korrinn Fu" "Marc Gaetano           Rudiger Gebauer        Kathy Gerber" "Patricia Gianni        Samantha Goldrich      Holger Gollan" "Teresa Gomez-Diaz      Laureano Gonzalez-Vega Stephen Gortler" "Johannes Grabmeier     Matt Grayson           Klaus Ebbe Grue" "James Griesmer         Vladimir Grinberg      Oswald Gschnitzer" "Jocelyn Guidry" "Steve Hague            Satoshi Hamaguchi      Mike Hansen" "Richard Harke          Vilya Harvey           Martin Hassner" "Arthur S. Hathaway     Dan Hatton             Waldek Hebisch" "Karl Hegbloom          Ralf Hemmecke          Henderson" "Antoine Hersen         Gernot Hueber" "Pietro Iglio" "Alejandro Jakubi       Richard Jenks" "Kai Kaminski           Grant Keady            Tony Kennedy" "Paul Kosinski          Klaus Kusche           Bernhard Kutzler" "Tim Lahey              Larry Lambe            Franz Lehner" "Frederic Lehobey       Michel Levaud          Howard Levy" "Liu Xiaojun            Rudiger Loos           Michael Lucks" "Richard Luczak" "Camm Maguire           Francois Maltey        Alasdair McAndrew" "Bob McElrath           Michael McGettrick     Ian Meikle" "David Mentre           Victor S. Miller       Gerard Milmeister" "Mohammed Mobarak       H. Michael Moeller     Michael Monagan" "Marc Moreno-Maza       Scott Morrison         Joel Moses" "Mark Murray" "William Naylor         C. Andrew Neff         John Nelder" "Godfrey Nolan          Arthur Norman          Jinzhong Niu" "Michael O'Connor       Summat Oemrawsingh     Kostas Oikonomou" "Humberto Ortiz-Zuazaga" "Julian A. Padget       Bill Page              Susan Pelzel" "Michel Petitot         Didier Pinchon         Ayal Pinkus" "Jose Alfredo Portes" "Claude Quitte" "Arthur C. Ralfs        Norman Ramsey          Anatoly Raportirenko" "Michael Richardson     Renaud Rioboo          Jean Rivlin" "Nicolas Robidoux       Simon Robinson         Raymond Rogers" "Michael Rothstein      Martin Rubey" "Philip Santas          Alfred Scheerhorn      William Schelter" "Gerhard Schneider      Martin Schoenert       Marshall Schor" "Frithjof Schulze       Fritz Schwarz          Steven Segletes" "Nick Simicich          William Sit            Elena Smirnova" "Jonathan Steinbach     Fabio Stumbo           Christine Sundaresan" "Robert Sutor           Moss E. Sweedler       Eugene Surowitz" "Max Tegmark            James Thatcher         Balbir Thomas" "Mike Thomas            Dylan Thurston         Barry Trager" "Themos T. Tsikas" "Gregory Vanuxem" "Bernhard Wall          Stephen Watt           Jaap Weel" "Juergen Weiss          M. Weller              Mark Wegman" "James Wen              Thorsten Werther       Michael Wester" "John M. Wiley          Berhard Will           Clifton J. Williamson" "Stephen Wilson         Shmuel Winograd        Robert Wisbauer" "Sandra Wityak          Waldemar Wiwianka      Knut Wolf" "Clifford Yapp          David Yun" "Vadim Zhytnikov        Richard Zippel         Evelyn Zoernack" "Bruno Zuercher         Dan Zwillinger")
--R 
--RValue = ("An alphabetical listing of contributors to AXIOM:" "Cyril Alberga          Roy Adler              Christian Aistleitner" "Richard Anderson       George Andrews         S.J. Atkins" "Henry Baker            Stephen Balzac         Yurij Baransky" "David R. Barton        Gerald Baumgartner     Gilbert Baumslag" "Michael Becker         Jay Belanger           David Bindel" "Fred Blair             Vladimir Bondarenko    Mark Botch" "Alexandre Bouyer       Peter A. Broadbery     Martin Brock" "Manuel Bronstein       Stephen Buchwald       Florian Bundschuh" "Luanne Burns           William Burge" "Quentin Carpent        Robert Caviness        Bruce Char" "Ondrej Certik          Cheekai Chin           David V. Chudnovsky" "Gregory V. Chudnovsky  Josh Cohen             Christophe Conil" "Don Coppersmith        George Corliss         Robert Corless" "Gary Cornell           Meino Cramer           Claire Di Crescenzo" "David Cyganski" "Timothy Daly Sr.       Timothy Daly Jr.       James H. Davenport" "Didier Deshommes       Michael Dewar" "Jean Della Dora        Gabriel Dos Reis       Claire DiCrescendo" "Sam Dooley             Lionel Ducos           Martin Dunstan" "Brian Dupee            Dominique Duval" "Robert Edwards         Heow Eide-Goodman      Lars Erickson" "Richard Fateman        Bertfried Fauser       Stuart Feldman" "Brian Ford             Albrecht Fortenbacher  George Frances" "Constantine Frangos    Timothy Freeman        Korrinn Fu" "Marc Gaetano           Rudiger Gebauer        Kathy Gerber" "Patricia Gianni        Samantha Goldrich      Holger Gollan" "Teresa Gomez-Diaz      Laureano Gonzalez-Vega Stephen Gortler" "Johannes Grabmeier     Matt Grayson           Klaus Ebbe Grue" "James Griesmer         Vladimir Grinberg      Oswald Gschnitzer" "Jocelyn Guidry" "Steve Hague            Satoshi Hamaguchi      Mike Hansen" "Richard Harke          Vilya Harvey           Martin Hassner" "Arthur S. Hathaway     Dan Hatton             Waldek Hebisch" "Karl Hegbloom          Ralf Hemmecke          Henderson" "Antoine Hersen         Gernot Hueber" "Pietro Iglio" "Alejandro Jakubi       Richard Jenks" "Kai Kaminski           Grant Keady            Tony Kennedy" "Paul Kosinski          Klaus Kusche           Bernhard Kutzler" "Tim Lahey              Larry Lambe            Franz Lehner" "Frederic Lehobey       Michel Levaud          Howard Levy" "Liu Xiaojun            Rudiger Loos           Michael Lucks" "Richard Luczak" "Camm Maguire           Francois Maltey        Alasdair McAndrew" "Bob McElrath           Michael McGettrick     Ian Meikle" "David Mentre           Victor S. Miller       Gerard Milmeister" "Mohammed Mobarak       H. Michael Moeller     Michael Monagan" "Marc Moreno-Maza       Scott Morrison         Joel Moses" "Mark Murray" "William Naylor         C. Andrew Neff         John Nelder" "Godfrey Nolan          Arthur Norman          Jinzhong Niu" "Michael O'Connor       Summat Oemrawsingh     Kostas Oikonomou" "Humberto Ortiz-Zuazaga" "Julian A. Padget       Bill Page              Susan Pelzel" "Michel Petitot         Didier Pinchon         Ayal Pinkus" "Jose Alfredo Portes" "Claude Quitte" "Arthur C. Ralfs        Norman Ramsey          Anatoly Raportirenko" "Michael Richardson     Renaud Rioboo          Jean Rivlin" "Nicolas Robidoux       Simon Robinson         Raymond Rogers" "Michael Rothstein      Martin Rubey" "Philip Santas          Alfred Scheerhorn      William Schelter" "Gerhard Schneider      Martin Schoenert       Marshall Schor" "Frithjof Schulze       Fritz Schwarz          Steven Segletes" "Nick Simicich          William Sit            Elena Smirnova" "Jonathan Steinbach     Fabio Stumbo           Christine Sundaresan" "Robert Sutor           Moss E. Sweedler       Eugene Surowitz" "Max Tegmark            James Thatcher         Balbir Thomas" "Mike Thomas            Dylan Thurston         Barry Trager" "Themos T. Tsikas" "Gregory Vanuxem" "Bernhard Wall          Stephen Watt           Jaap Weel" "Juergen Weiss          M. Weller              Mark Wegman" "James Wen              Thorsten Werther       Michael Wester" "John M. Wiley          Berhard Will           Clifton J. Williamson" "Stephen Wilson         Shmuel Winograd        Robert Wisbauer" "Sandra Wityak          Waldemar Wiwianka      Knut Wolf" "Clifford Yapp          David Yun" "Vadim Zhytnikov        Richard Zippel         Evelyn Zoernack" "Bruno Zuercher         Dan Zwillinger")
--E 13

--S 14 of 237
)lisp (identity |$defaultFortranType|)
 
Value = REAL
--R 
--RValue = REAL
--E 14

--S 15 of 237
)lisp (identity *default-pathname-defaults*)
 
Value = #p"/home/camm/debian/axiom/axiom-20091101/int/input/"
--R 
--IValue = #p"/tmp/"
--E 15

--S 16 of 237
)lisp (identity |$defaultSpecialCharacters|)
 
Value = (#\^\ #\^[ #\^^ #\^_ #\O #\- #\\220 #\\255 #\\275 #\\300 #\\320 #\; #\> #\? #\= #\, #\\340)
--R 
--RValue = (#\^\ #\^[ #\^^ #\^_ #\O #\- #\\220 #\\255 #\\275 #\\300 #\\320 #\; #\> #\? #\= #\, #\\340)
--E 16

--S 17 of 237
)lisp (identity |$displayDroppedMap|)
 
Value = NIL
--R 
--RValue = NIL
--E 17

--S 18 of 237
)lisp (identity |$displayMsgNumber|)
 
Value = NIL
--R 
--RValue = NIL
--E 18

--S 19 of 237
)lisp (identity |$displayOptions| )
 
Value = (|abbreviations| |all| |macros| |modes| |names| |operations| |properties| |types| |values|)
--R 
--RValue = (|abbreviations| |all| |macros| |modes| |names| |operations| |properties| |types| |values|)
--E 19

--S 20 of 237
)lisp (identity |$displaySetValue|)
 
Value = NIL
--R 
--RValue = NIL
--E 20

--S 21 of 237
)lisp (identity |$displayStartMsgs|)
 
Value = T
--R 
--RValue = T
--E 21

--S 22 of 237
)lisp (identity |$formulaFormat|)
 
Value = NIL
--R 
--RValue = NIL
--E 22

--S 23 of 237
)lisp (identity |$formulaOutputFile|)
 
Value = "CONSOLE"
--R 
--RValue = "CONSOLE"
--E 23

--S 24 of 237
)lisp (identity |$fortIndent|)
 
Value = 6
--R 
--RValue = 6
--E 24

--S 25 of 237
)lisp (identity |$fortInts2Floats|)
 
Value = T
--R 
--RValue = T
--E 25

--S 26 of 237
)lisp (identity |$fortLength|)
 
Value = 72
--R 
--RValue = 72
--E 26

--S 27 of 237
)lisp (identity |$fortranArrayStartingIndex|)
 
Value = 1
--R 
--RValue = 1
--E 27

--S 28 of 237
)lisp (identity |$fortranDirectory|)
 
Value = "./"
--R 
--RValue = "./"
--E 28

--S 29 of 237
)lisp (identity |$fortranFormat|)
 
Value = NIL
--R 
--RValue = NIL
--E 29

--S 30 of 237
)lisp (identity |$fortranLibraries|)
 
Value = "-lxlf"
--R 
--RValue = "-lxlf"
--E 30

--S 31 of 237
)lisp (identity |$fortranOptimizationLevel|)
 
Value = 0
--R 
--RValue = 0
--E 31

--S 32 of 237
)lisp (identity |$fortranOutputFile|)
 
Value = "CONSOLE"
--R 
--RValue = "CONSOLE"
--E 32

--S 33 of 237
)lisp (identity |$fortranPrecision|)
 
Value = |double|
--R 
--RValue = |double|
--E 33

--S 34 of 237
)lisp (identity |$fortranSegment|)
 
Value = T
--R 
--RValue = T
--E 34

--S 35 of 237
)lisp (identity |$fortranTmpDir|)
 
Value = "/tmp/"
--R 
--RValue = "/tmp/"
--E 35

--S 36 of 237
)lisp (identity |$fortPersistence|)
 
Value = 1
--R 
--RValue = 1
--E 36

--S 37 of 237
)lisp (identity |$fractionDisplayType|)
 
Value = |vertical|
--R 
--RValue = |vertical|
--E 37

--S 38 of 237
)lisp (identity |$frameMessages|)
 
Value = NIL
--R 
--RValue = NIL
--E 38

--S 39 of 237
)lisp (identity |$fullScreenSysVars|)
 
Value = NIL
--R 
--RValue = NIL
--E 39

--S 40 of 237
)lisp (identity |$giveExposureWarning|)
 
Value = NIL
--R 
--RValue = NIL
--E 40

--S 41 of 237
)lisp (identity |$HiFiAccess|)
 
Value = T
--R 
--RValue = T
--E 41

--S 42 of 237
)lisp (identity |$highlightAllowed|)
 
Value = NIL
--R 
--RValue = NIL
--E 42

--S 43 of 237
)lisp (identity |$historyDirectory|)
 
Value = A
--R 
--RValue = A
--E 43

--S 44 of 237
)lisp (identity |$historyDisplayWidth|)
 
Value = 120
--R 
--RValue = 120
--E 44

--S 45 of 237
)lisp (identity |$historyFileType|)
 
Value = |axh|
--R 
--RValue = |axh|
--E 45

--S 46 of 237
)lisp (identity |$InitialCommandSynonymAlist|)
 
Value = ((? . "what commands") (|ap| . "what things") (|apr| . "what things") (|apropos| . "what things") (|cache| . "set functions cache") (|cl| . "clear") (|cls| . "zsystemdevelopment )cls") (|cms| . "system") (|co| . "compiler") (|d| . "display") (|dep| . "display dependents") (|dependents| . "display dependents") (|e| . "edit") (|expose| . "set expose add constructor") (|fc| . "zsystemdevelopment )c") (|fd| . "zsystemdevelopment )d") (|fdt| . "zsystemdevelopment )dt") (|fct| . "zsystemdevelopment )ct") (|fctl| . "zsystemdevelopment )ctl") (|fe| . "zsystemdevelopment )e") (|fec| . "zsystemdevelopment )ec") (|fect| . "zsystemdevelopment )ect") (|fns| . "exec spadfn") (|fortran| . "set output fortran") (|h| . "help") (|hd| . "system hypertex &") (|kclam| . "boot clearClams ( )") (|killcaches| . "boot clearConstructorAndLisplibCaches ( )") (|patch| . "zsystemdevelopment )patch") (|pause| . "zsystemdevelopment )pause") (|prompt| . "set message prompt") (|recurrence| . "set functions recurrence") (|restore| . "history )restore") (|save| . "history )save") (|startGraphics| . "system $AXIOM/lib/viewman &") (|startNAGLink| . "system $AXIOM/lib/nagman &") (|stopGraphics| . "lisp (|sockSendSignal| 2 15)") (|stopNAGLink| . "lisp (|sockSendSignal| 8 15)") (|time| . "set message time") (|type| . "set message type") (|unexpose| . "set expose drop constructor") (|up| . "zsystemdevelopment )update") (|version| . "lisp *yearweek*") (|w| . "what") (|wc| . "what categories") (|wd| . "what domains") (|who| . "lisp (pprint credits)") (|wp| . "what packages") (|ws| . "what synonyms"))
--R 
--RValue = ((? . "what commands") (|ap| . "what things") (|apr| . "what things") (|apropos| . "what things") (|cache| . "set functions cache") (|cl| . "clear") (|cls| . "zsystemdevelopment )cls") (|cms| . "system") (|co| . "compiler") (|d| . "display") (|dep| . "display dependents") (|dependents| . "display dependents") (|e| . "edit") (|expose| . "set expose add constructor") (|fc| . "zsystemdevelopment )c") (|fd| . "zsystemdevelopment )d") (|fdt| . "zsystemdevelopment )dt") (|fct| . "zsystemdevelopment )ct") (|fctl| . "zsystemdevelopment )ctl") (|fe| . "zsystemdevelopment )e") (|fec| . "zsystemdevelopment )ec") (|fect| . "zsystemdevelopment )ect") (|fns| . "exec spadfn") (|fortran| . "set output fortran") (|h| . "help") (|hd| . "system hypertex &") (|kclam| . "boot clearClams ( )") (|killcaches| . "boot clearConstructorAndLisplibCaches ( )") (|patch| . "zsystemdevelopment )patch") (|pause| . "zsystemdevelopment )pause") (|prompt| . "set message prompt") (|recurrence| . "set functions recurrence") (|restore| . "history )restore") (|save| . "history )save") (|startGraphics| . "system $AXIOM/lib/viewman &") (|startNAGLink| . "system $AXIOM/lib/nagman &") (|stopGraphics| . "lisp (|sockSendSignal| 2 15)") (|stopNAGLink| . "lisp (|sockSendSignal| 8 15)") (|time| . "set message time") (|type| . "set message type") (|unexpose| . "set expose drop constructor") (|up| . "zsystemdevelopment )update") (|version| . "lisp *yearweek*") (|w| . "what") (|wc| . "what categories") (|wd| . "what domains") (|who| . "lisp (pprint credits)") (|wp| . "what packages") (|ws| . "what synonyms"))
--E 46

--S 47 of 237
)lisp (identity |$inputPromptType|)
 
Value = |step|
--R 
--RValue = |step|
--E 47

--S 48 of 237
)lisp (identity |$linearFormatScripts|)
 
Value = NIL
--R 
--RValue = NIL
--E 48

--S 49 of 237
)lisp (identity $linelength)
 
Value = 77
--R 
--RValue = 77
--E 49

--S 50 of 237
)lisp (identity |$mapSubNameAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 50

--S 51 of 237
)lisp (identity |$mathmlFormat|)
 
Value = NIL
--R 
--RValue = NIL
--E 51

--S 52 of 237
)lisp (identity |$mathmlOutputFile|)
 
Value = "CONSOLE"
--R 
--RValue = "CONSOLE"
--E 52

--S 53 of 237
)lisp (identity |$maximumFortranExpressionLength|)
 
Value = 1320
--R 
--RValue = 1320
--E 53

--S 54 of 237
)lisp (identity |$nagEnforceDouble|)
 
Value = T
--R 
--RValue = T
--E 54

--S 55 of 237
)lisp (identity |$nagHost|)
 
Value = "localhost"
--R 
--RValue = "localhost"
--E 55

--S 56 of 237
)lisp (identity |$nagMessages|)
 
Value = T
--R 
--RValue = T
--E 56

--S 57 of 237
)lisp (identity |$noParseCommands| )
 
Value = (|boot| |copyright| |credits| |fin| |lisp| |pquit| |quit| |synonym| |system| |trademark|)
--R 
--RValue = (|boot| |copyright| |credits| |fin| |lisp| |pquit| |quit| |synonym| |system| |trademark|)
--E 57

--S 58 of 237
)lisp (identity |$oldHistoryFileName|)
 
Value = |last|
--R 
--RValue = |last|
--E 58

--S 59 of 237
)lisp (identity |$openMathFormat|)
 
Value = NIL
--R 
--RValue = NIL
--E 59

--S 60 of 237
)lisp (identity |$openMathOutputFile|)
 
Value = "CONSOLE"
--R 
--RValue = "CONSOLE"
--E 60

--S 61 of 237
)lisp (identity $openServerIfTrue)
 
Value = T
--R 
--RValue = T
--E 61

--S 62 of 237
)lisp (identity |$optionAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 62

--S 63 of 237
)lisp (identity |$options|)
 
Value = NIL
--R 
--RValue = NIL
--E 63

--S 64 of 237
)lisp (identity |$plainRTspecialCharacters|)
 
Value = (+ + + + |\|| - ? [ ] { } + + + + + |\\|)
--R 
--RValue = (+ + + + |\|| - ? [ ] { } + + + + + |\\|)
--E 64

--S 65 of 237
)lisp (identity |$plainSpecialCharacters0|)
 
Value = (#\N #\N #\N #\N #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--R 
--RValue = (#\N #\N #\N #\N #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--E 65

--S 66 of 237
)lisp (identity |$plainSpecialCharacters1|)
 
Value = (#\k #\k #\} #\} #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--R 
--RValue = (#\k #\k #\} #\} #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--E 66

--S 67 of 237
)lisp (identity |$plainSpecialCharacters2|)
 
Value = (#\O #\O #\O #\O #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--R 
--RValue = (#\O #\O #\O #\O #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--E 67

--S 68 of 237
)lisp (identity |$plainSpecialCharacters3|)
 
Value = (#\` #\` #\` #\` #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--R 
--RValue = (#\` #\` #\` #\` #\O #\` #\o #\\255 #\\275 #\\300 #\\320 #\N #\N #\N #\N #\N #\\340)
--E 68

--S 69 of 237
)lisp (identity $prettyprint)
 
Value = T
--R 
--RValue = T
--E 69

--S 70 of 237
)lisp (identity |$printAnyIfTrue|)
 
Value = T
--R 
--RValue = T
--E 70

--S 71 of 237
)lisp (identity |$printFortranDecs|)
 
Value = T
--R 
--RValue = T
--E 71

--S 72 of 237
)lisp (identity |$printLoadMsgs|)
 
Value = NIL
--R 
--RValue = NIL
--E 72

--S 73 of 237
)lisp (identity |$printMsgsToFile|)
 
Value = NIL
--R 
--RValue = NIL
--E 73

--S 74 of 237
)lisp (identity |$printStatisticsSummaryIfTrue|)
 
Value = NIL
--R 
--RValue = NIL
--E 74

--S 75 of 237
)lisp (identity |$printTimeIfTrue|)
 
Value = NIL
--R 
--RValue = NIL
--E 75

--S 76 of 237
)lisp (identity |$printTypeIfTrue|)
 
Value = T
--R 
--RValue = T
--E 76

--S 77 of 237
)lisp (identity |$printVoidIfTrue|)
 
Value = NIL
--R 
--RValue = NIL
--E 77

--S 78 of 237
)lisp (identity |$quitCommandType|)
 
Value = |protected|
--R 
--RValue = |protected|
--E 78

--S 79 of 237
)lisp (identity |$reportBottomUpFlag|)
 
Value = NIL
--R 
--RValue = NIL
--E 79

--S 80 of 237
)lisp (identity |$reportCoerceIfTrue|)
 
Value = NIL
--R 
--RValue = NIL
--E 80

--S 81 of 237
)lisp (identity |$reportCompilation|)
 
Value = NIL
--R 
--RValue = NIL
--E 81

--S 82 of 237
)lisp (identity |$reportEachInstantiation|)
 
Value = NIL
--R 
--RValue = NIL
--E 82

--S 83 of 237
)lisp (identity |$reportInstantiations|)
 
Value = NIL
--R 
--RValue = NIL
--E 83

--S 84 of 237
)lisp (identity |$reportInterpOnly|)
 
Value = T
--R 
--RValue = T
--E 84

--S 85 of 237
)lisp (identity |$reportOptimization|)
 
Value = NIL
--R 
--RValue = NIL
--E 85

--S 86 of 237
)lisp (identity |$reportSpadTrace|)
 
Value = NIL
--R 
--RValue = NIL
--E 86


--S 88 of 237
)lisp (identity *standard-input*)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 88

--S 89 of 237
)lisp (identity *standard-output*)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 89

--S 90 of 237
)lisp (identity |$SpadServer|)
 
Value = NIL
--R 
--RValue = NIL
--E 90

--S 91 of 237
)lisp (identity $SpadServerName)
 
Value = "/tmp/.d"
--R 
--RValue = "/tmp/.d"
--E 91

--S 92 of 237
)lisp (identity |$specialCharacterAlist| )
 
Value = ((|ulc| . 0) (|urc| . 1) (|llc| . 2) (|lrc| . 3) (|vbar| . 4) (|hbar| . 5) (|quad| . 6) (|lbrk| . 7) (|rbrk| . 8) (|lbrc| . 9) (|rbrc| . 10) (|ttee| . 11) (|btee| . 12) (|rtee| . 13) (|ltee| . 14) (|ctee| . 15) (|bslash| . 16))
--R 
--RValue = ((|ulc| . 0) (|urc| . 1) (|llc| . 2) (|lrc| . 3) (|vbar| . 4) (|hbar| . 5) (|quad| . 6) (|lbrk| . 7) (|rbrk| . 8) (|lbrc| . 9) (|rbrc| . 10) (|ttee| . 11) (|btee| . 12) (|rtee| . 13) (|ltee| . 14) (|ctee| . 15) (|bslash| . 16))
--E 92

--S 93 of 237
)lisp (identity |$specialCharacters|)
 
Value = (+ + + + |\|| - ? [ ] { } + + + + + |\\|)
--R 
--RValue = (+ + + + |\|| - ? [ ] { } + + + + + |\\|)
--E 93

--S 94 of 237
)lisp (identity |$streamCount|)
 
Value = 10
--R 
--RValue = 10
--E 94

--S 95 of 237
)lisp (identity |$streamsShowAll|)
 
Value = NIL
--R 
--RValue = NIL
--E 95

--S 96 of 237
)lisp (identity compiler::*suppress-compiler-notes*)
 
Value = T
--R 
--RValue = T
--E 96

--S 97 of 237
)lisp (identity compiler::*suppress-compiler-warnings*)
 
Value = T
--R 
--RValue = T
--E 97

--S 98 of 237
)lisp (identity |$systemCommandFunction|)
 
Value = #<compiled-function |InterpExecuteSpadSystemCommand|>
--R 
--RValue = #<compiled-function |InterpExecuteSpadSystemCommand|>
--E 98

--S 99 of 237
)lisp (identity $syscommands)
 
Value = (|abbreviations| |boot| |browse| |cd| |clear| |close| |compiler| |copyright| |credits| |describe| |display| |edit| |fin| |frame| |help| |history| |lisp| |library| |load| |ltrace| |pquit| |quit| |read| |savesystem| |set| |show| |spool| |summary| |synonym| |system| |trace| |trademark| |undo| |what| |with| |workfiles| |zsystemdevelopment|)
--R 
--RValue = (|abbreviations| |boot| |browse| |cd| |clear| |close| |compiler| |copyright| |credits| |describe| |display| |edit| |fin| |frame| |help| |history| |lisp| |library| |load| |ltrace| |pquit| |quit| |read| |savesystem| |set| |show| |spool| |summary| |synonym| |system| |trace| |trademark| |undo| |what| |with| |workfiles| |zsystemdevelopment|)
--E 99

--S 100 of 237
)lisp (identity |$systemCommands|)
 
Value = ((|abbreviations| . |compiler|) (|boot| . |development|) (|browse| . |development|) (|cd| . |interpreter|) (|clear| . |interpreter|) (|close| . |interpreter|) (|compiler| . |compiler|) (|copyright| . |interpreter|) (|credits| . |interpreter|) (|describe| . |interpreter|) (|display| . |interpreter|) (|edit| . |interpreter|) (|fin| . |development|) (|frame| . |interpreter|) (|help| . |interpreter|) (|history| . |interpreter|) (|lisp| . |development|) (|library| . |interpreter|) (|load| . |interpreter|) (|ltrace| . |interpreter|) (|pquit| . |interpreter|) (|quit| . |interpreter|) (|read| . |interpreter|) (|savesystem| . |interpreter|) (|set| . |interpreter|) (|show| . |interpreter|) (|spool| . |interpreter|) (|summary| . |interpreter|) (|synonym| . |interpreter|) (|system| . |interpreter|) (|trace| . |interpreter|) (|trademark| . |interpreter|) (|undo| . |interpreter|) (|what| . |interpreter|) (|with| . |interpreter|) (|workfiles| . |development|) (|zsystemdevelopment| . |interpreter|))
--R 
--RValue = ((|abbreviations| . |compiler|) (|boot| . |development|) (|browse| . |development|) (|cd| . |interpreter|) (|clear| . |interpreter|) (|close| . |interpreter|) (|compiler| . |compiler|) (|copyright| . |interpreter|) (|credits| . |interpreter|) (|describe| . |interpreter|) (|display| . |interpreter|) (|edit| . |interpreter|) (|fin| . |development|) (|frame| . |interpreter|) (|help| . |interpreter|) (|history| . |interpreter|) (|lisp| . |development|) (|library| . |interpreter|) (|load| . |interpreter|) (|ltrace| . |interpreter|) (|pquit| . |interpreter|) (|quit| . |interpreter|) (|read| . |interpreter|) (|savesystem| . |interpreter|) (|set| . |interpreter|) (|show| . |interpreter|) (|spool| . |interpreter|) (|summary| . |interpreter|) (|synonym| . |interpreter|) (|system| . |interpreter|) (|trace| . |interpreter|) (|trademark| . |interpreter|) (|undo| . |interpreter|) (|what| . |interpreter|) (|with| . |interpreter|) (|workfiles| . |development|) (|zsystemdevelopment| . |interpreter|))
--E 100

--S 101 of 237
)lisp (identity *terminal-io*)
 
Value = #<two-way stream 092e572c>
--R 
--IValue = #<two-way stream 090631d4>
--E 101

--S 102 of 237
)lisp (identity |$testingSystem|)
 
Value = NIL
--R 
--RValue = NIL
--E 102

--S 103 of 237
)lisp (identity |$texFormat|)
 
Value = NIL
--R 
--RValue = NIL
--E 103

--S 104 of 237
)lisp (identity |$texOutputFile|)
 
Value = "CONSOLE"
--R 
--RValue = "CONSOLE"
--E 104

--S 105 of 237
)lisp (identity |$tokenCommands|)
 
Value = (|abbreviations| |cd| |clear| |close| |compiler| |depends| |display| |describe| |edit| |frame| |frame| |help| |history| |input| |library| |load| |ltrace| |read| |savesystem| |set| |spool| |undo| |what| |with| |workfiles| |zsystemdevelopment|)
--R 
--RValue = (|abbreviations| |cd| |clear| |close| |compiler| |depends| |display| |describe| |edit| |frame| |frame| |help| |history| |input| |library| |load| |ltrace| |read| |savesystem| |set| |spool| |undo| |what| |with| |workfiles| |zsystemdevelopment|)
--E 105

--S 106 of 237
)lisp (identity system::*top-level-hook*)
 
Value = RESTART
--R 
--RValue = RESTART
--E 106

--S 107 of 237
)lisp (identity |$tracedMapSignatures|)
 
Value = NIL
--R 
--RValue = NIL
--E 107

--S 108 of 237
)lisp (identity |$traceNoisely|)
 
Value = NIL
--R 
--RValue = NIL
--E 108

--S 109 of 237
)lisp (identity |$traceOptionList|)
 
Value = (|after| |before| |break| |cond| |count| |depth| |local| |mathprint| |nonquietly| |nt| |of| |only| |ops| |restore| |timer| |varbreak| |vars| |within|)
--R 
--RValue = (|after| |before| |break| |cond| |count| |depth| |local| |mathprint| |nonquietly| |nt| |of| |only| |ops| |restore| |timer| |varbreak| |vars| |within|)
--E 109

--S 110 of 237
)lisp (identity underbar)
 
Value = "_"
--R 
--RValue = "_"
--E 110

--S 111 of 237
)lisp (identity |$useEditorForShowOutput|)
 
Value = NIL
--R 
--RValue = NIL
--E 111

--S 112 of 237
)lisp (identity |$useFullScreenHelp|)
 
Value = NIL
--R 
--RValue = NIL
--E 112

--S 113 of 237
)lisp (identity |$useInternalHistoryTable|)
 
Value = T
--R 
--RValue = T
--E 113

--S 114 of 237
)lisp (identity |$useIntrinsicFunctions|)
 
Value = NIL
--R 
--RValue = NIL
--E 114

--S 115 of 237
)lisp (identity |$UserLevel|)
 
Value = |development|
--R 
--RValue = |development|
--E 115

--S 116 of 237
)lisp (identity |$whatOptions|)
 
Value = (|operations| |categories| |domains| |packages| |commands| |synonyms| |things|)
--R 
--RValue = (|operations| |categories| |domains| |packages| |commands| |synonyms| |things|)
--E 116





--S 117 of 237
)lisp (identity |$attributeDb|)
 
Value = NIL
--R 
--RValue = NIL
--E 117

--S 118 of 237
)lisp (identity $boot)
 
Value = NIL
--R 
--RValue = NIL
--E 118

--S 119 of 237
)lisp (identity |$cacheAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 119

--S 120 of 237
)lisp (identity |$cacheCount| )
 
Value = 0
--R 
--RValue = 0
--E 120

--S 121 of 237
)lisp (identity |$CatOfCatDatabase|)
 
Value = NIL
--R 
--RValue = NIL
--E 121

--S 122 of 237
)lisp (identity |$CloseClient|)
 
Value = 10
--R 
--RValue = 10
--E 122

--S 123 of 237
)lisp (identity |$coerceIntByMapCounter|)
 
Value = 0
--R 
--RValue = 0
--E 123

--S 124 of 237
)lisp (identity |$compileMapFlag|)
 
Value = NIL
--R 
--RValue = NIL
--E 124

--S 125 of 237
)lisp (identity |$ConstructorCache|)
 
Value = #<hash-table 08bf4ab8>
--R 
--IValue = #<hash-table 08a68f18>
--E 125

--S 126 of 237
)lisp (identity |$constructors|)
 
 
   >> System error:
   The variable |$constructors| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$constructors| is unbound.
--R
--R   Continuing to read the file...
--R
--E 126

--S 127 of 237
)lisp (identity /countlist)
 
Value = NIL
--R 
--RValue = NIL
--E 127

--S 128 of 237
)lisp (identity $current-directory)
 
Value = "/home/camm/debian/axiom/axiom-20091101/int/input/"
--R 
--IValue = "/tmp/"
--E 128

--S 129 of 237
)lisp (identity |$currentFrameNum|)
 
Value = 0
--R 
--RValue = 0
--E 129

--S 130 of 237
)lisp (identity |$currentLine|)
 
Value = ")lisp (identity |$currentLine|)"
--R 
--RValue = ")lisp (identity |$currentLine|)"
--E 130

--S 131 of 237
)lisp (identity $dalymode)
 
Value = NIL
--R 
--RValue = NIL
--E 131

--S 132 of 237
)lisp (identity |$defaultMsgDatabaseName|)
 
Value = #p"/home/camm/debian/axiom/axiom-20091101/mnt/linux/doc/msgs/s2-us.msgs"
--R 
--IValue = #p"/research/reference/mnt/ubuntu/doc/msgs/s2-us.msgs"
--E 132

--S 133 of 237
)lisp (identity |$dependeeClosureAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 133

--S 134 of 237
)lisp (identity $directory-list)
 
Value = ("/home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/input/" "/home/camm/debian/axiom/axiom-20091101/mnt/linux/doc/msgs/" "/home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/algebra/" "/home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/" "/home/camm/debian/axiom/axiom-20091101/mnt/linux/doc/spadhelp/")
--R 
--IValue = ("/research/reference/mnt/ubuntu/../../src/input/" "/research/reference/mnt/ubuntu/doc/msgs/" "/research/reference/mnt/ubuntu/../../src/algebra/" "/research/reference/mnt/ubuntu/../../src/interp/" "/research/reference/mnt/ubuntu/doc/spadhelp/")
--E 134

--S 135 of 237
)lisp (identity |$displayStartMsgs| )
 
Value = T
--R 
--RValue = T
--E 135

--S 136 of 237
)lisp (identity |$domains|)
 
 
   >> System error:
   The variable |$domains| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$domains| is unbound.
--R
--R   Continuing to read the file...
--R
--E 136

--S 137 of 237
)lisp (identity |$DomOfCatDatabase|)
 
Value = NIL
--R 
--RValue = NIL
--E 137

--S 138 of 237
)lisp (identity |$domainTraceNameAssoc|)
 
Value = NIL
--R 
--RValue = NIL
--E 138

--S 139 of 237
)lisp (identity |$doNotAddEmptyModeIfTrue|)
 
 
   >> System error:
   The variable |$doNotAddEmptyModeIfTrue| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$doNotAddEmptyModeIfTrue| is unbound.
--R
--R   Continuing to read the file...
--R
--E 139

--S 140 of 237
)lisp (identity |$e|)
 
Value = ((((|Category| (|modemap| (((|Category|) (|Category|)) (T *)))) (|Join| (|modemap| (((|Category|) (|Category|) (|Category|) (|Category|)) (T *)) (((|Category|) (|Category|) (|List| (|Category|)) (|Category|)) (T *)))))))
--R 
--RValue = ((((|Category| (|modemap| (((|Category|) (|Category|)) (T *)))) (|Join| (|modemap| (((|Category|) (|Category|) (|Category|) (|Category|)) (T *)) (((|Category|) (|Category|) (|List| (|Category|)) (|Category|)) (T *)))))))
--E 140

--S 141 of 237
)lisp (identity |$echoLineStack|)
 
Value = NIL
--R 
--RValue = NIL
--E 141

--S 142 of 237
)lisp (identity /editfile)
 
Value = #p"/home/camm/debian/axiom/axiom-20091101/int/input/unittest2.input"
--R 
--IValue = #p"/tmp/u.input"
--E 142

--S 143 of 237
)lisp (identity |$EmptyEnvironment|)
 
Value = ((NIL))
--R 
--RValue = ((NIL))
--E 143

--S 144 of 237
)lisp (identity |$env|)
 
Value = ((NIL))
--R 
--RValue = ((NIL))
--E 144

--S 145 of 237
)lisp (identity *eof*)
 
Value = NIL
--R 
--RValue = NIL
--E 145

--S 146 of 237
)lisp (identity |$erMsgToss|)
 
Value = NIL
--R 
--RValue = NIL
--E 146

--S 147 of 237
)lisp (identity |$existingFiles|)
 
Value = #<hash-table 08bf45e8>
--R 
--IValue = #<hash-table 08c5b230>
--E 147

--S 148 of 237
)lisp (identity |$fn|)
 
Value = "/home/camm/debian/axiom/axiom-20091101/int/input/unittest2.input"
--R 
--IValue = "/tmp/u.input"
--E 148

--S 149 of 237
)lisp (identity |$formulaOutputStream|)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 149

--S 150 of 237
)lisp (identity |$fortranOutputStream|)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 150

--S 151 of 237
)lisp (identity |$frameMessages|)
 
Value = NIL
--R 
--RValue = NIL
--E 151

--S 152 of 237
)lisp (identity |$frameRecord|)
 
Value = NIL
--R 
--RValue = NIL
--E 152

--S 153 of 237
)lisp (identity |$fromSpadTrace|)
 
Value = NIL
--R 
--RValue = NIL
--E 153

--S 154 of 237
)lisp (identity |$functionTable|)
 
Value = NIL
--R 
--RValue = NIL
--E 154

--S 155 of 237
)lisp (identity |$globalExposureGroupAlist|)
 
Value = ((|basic| (|AlgebraicManipulations| . ALGMANIP) (|AlgebraicNumber| . AN) (|AlgFactor| . ALGFACT) (|AlgebraicMultFact| . ALGMFACT) (|AlgebraPackage| . ALGPKG) (|AlgebraGivenByStructuralConstants| . ALGSC) (|Any| . ANY) (|AnyFunctions1| . ANY1) (|ApplicationProgramInterface| . API) (|ArrayStack| . ASTACK) (|AssociatedJordanAlgebra| . JORDAN) (|AssociatedLieAlgebra| . LIE) (|AttachPredicates| . PMPRED) (|AxiomServer| . AXSERV) (|BalancedBinaryTree| . BBTREE) (|BasicOperator| . BOP) (|BasicOperatorFunctions1| . BOP1) (|Bezier| . BEZIER) (|BinaryExpansion| . BINARY) (|BinaryFile| . BINFILE) (|BinarySearchTree| . BSTREE) (|BinaryTournament| . BTOURN) (|BinaryTree| . BTREE) (|Bits| . BITS) (|Boolean| . BOOLEAN) (|CardinalNumber| . CARD) (|CartesianTensor| . CARTEN) (|CartesianTensorFunctions2| . CARTEN2) (|Character| . CHAR) (|CharacterClass| . CCLASS) (|CharacteristicPolynomialPackage| . CHARPOL) (|CliffordAlgebra| . CLIF) (|Color| . COLOR) (|CommonDenominator| . CDEN) (|Commutator| . COMM) (|Complex| . COMPLEX) (|ComplexFactorization| . COMPFACT) (|ComplexFunctions2| . COMPLEX2) (|ComplexRootPackage| . CMPLXRT) (|ComplexTrigonometricManipulations| . CTRIGMNP) (|ContinuedFraction| . CONTFRAC) (|CoordinateSystems| . COORDSYS) (|CRApackage| . CRAPACK) (|CycleIndicators| . CYCLES) (|Database| . DBASE) (|DataList| . DLIST) (|DecimalExpansion| . DECIMAL) (|DenavitHartenbergMatrix| . DHMATRIX) (|Dequeue| . DEQUEUE) (|DiophantineSolutionPackage| . DIOSP) (|DirectProductFunctions2| . DIRPROD2) (|DisplayPackage| . DISPLAY) (|DistinctDegreeFactorize| . DDFACT) (|DoubleFloat| . DFLOAT) (|DoubleFloatSpecialFunctions| . DFSFUN) (|DrawComplex| . DRAWCX) (|DrawNumericHack| . DRAWHACK) (|DrawOption| . DROPT) (|EigenPackage| . EP) (|ElementaryFunctionDefiniteIntegration| . DEFINTEF) (|ElementaryFunctionLODESolver| . LODEEF) (|ElementaryFunctionODESolver| . ODEEF) (|ElementaryFunctionSign| . SIGNEF) (|ElementaryFunctionStructurePackage| . EFSTRUC) (|Equation| . EQ) (|EquationFunctions2| . EQ2) (|ErrorFunctions| . ERROR) (|EuclideanGroebnerBasisPackage| . GBEUCLID) (|Exit| . EXIT) (|Expression| . EXPR) (|ExpressionFunctions2| . EXPR2) (|ExpressionSolve| . EXPRSOL) (|ExpressionSpaceFunctions2| . ES2) (|ExpressionSpaceODESolver| . EXPRODE) (|ExpressionToOpenMath| . OMEXPR) (|ExpressionToUnivariatePowerSeries| . EXPR2UPS) (|Factored| . FR) (|FactoredFunctions2| . FR2) (|File| . FILE) (|FileName| . FNAME) (|FiniteAbelianMonoidRingFunctions2| . FAMR2) (|FiniteDivisorFunctions2| . FDIV2) (|FiniteField| . FF) (|FiniteFieldCyclicGroup| . FFCG) (|FiniteFieldPolynomialPackage2| . FFPOLY2) (|FiniteFieldNormalBasis| . FFNB) (|FiniteFieldHomomorphisms| . FFHOM) (|FiniteLinearAggregateFunctions2| . FLAGG2) (|FiniteLinearAggregateSort| . FLASORT) (|FiniteSetAggregateFunctions2| . FSAGG2) (|FlexibleArray| . FARRAY) (|Float| . FLOAT) (|FloatingRealPackage| . FLOATRP) (|FloatingComplexPackage| . FLOATCP) (|FourierSeries| . FSERIES) (|Fraction| . FRAC) (|FractionalIdealFunctions2| . FRIDEAL2) (|FractionFreeFastGaussian| . FFFG) (|FractionFreeFastGaussianFractions| . FFFGF) (|FractionFunctions2| . FRAC2) (|FreeNilpotentLie| . FNLA) (|FullPartialFractionExpansion| . FPARFRAC) (|FunctionFieldCategoryFunctions2| . FFCAT2) (|FunctionSpaceAssertions| . PMASSFS) (|FunctionSpaceAttachPredicates| . PMPREDFS) (|FunctionSpaceComplexIntegration| . FSCINT) (|FunctionSpaceFunctions2| . FS2) (|FunctionSpaceIntegration| . FSINT) (|FunctionSpacePrimitiveElement| . FSPRMELT) (|FunctionSpaceSum| . SUMFS) (|GaussianFactorizationPackage| . GAUSSFAC) (|GeneralUnivariatePowerSeries| . GSERIES) (|GenerateUnivariatePowerSeries| . GENUPS) (|GraphicsDefaults| . GRDEF) (|GroebnerPackage| . GB) (|GroebnerFactorizationPackage| . GBF) (|Guess| . GUESS) (|GuessAlgebraicNumber| . GUESSAN) (|GuessFinite| . GUESSF) (|GuessFiniteFunctions| . GUESSF1) (|GuessInteger| . GUESSINT) (|GuessOption| . GOPT) (|GuessOptionFunctions0| . GOPT0) (|GuessPolynomial| . GUESSP) (|GuessUnivariatePolynomial| . GUESSUP) (|HallBasis| . HB) (|Heap| . HEAP) (|HexadecimalExpansion| . HEXADEC) (|IndexCard| . ICARD) (|IdealDecompositionPackage| . IDECOMP) (|InfiniteProductCharacteristicZero| . INFPROD0) (|InfiniteProductFiniteField| . INPRODFF) (|InfiniteProductPrimeField| . INPRODPF) (|InfiniteTuple| . ITUPLE) (|InfiniteTupleFunctions2| . ITFUN2) (|InfiniteTupleFunctions3| . ITFUN3) (|Infinity| . INFINITY) (|Integer| . INT) (|IntegerCombinatoricFunctions| . COMBINAT) (|IntegerLinearDependence| . ZLINDEP) (|IntegerNumberTheoryFunctions| . INTHEORY) (|IntegerPrimesPackage| . PRIMES) (|IntegerRetractions| . INTRET) (|IntegerRoots| . IROOT) (|IntegrationResultFunctions2| . IR2) (|IntegrationResultRFToFunction| . IRRF2F) (|IntegrationResultToFunction| . IR2F) (|Interval| . INTRVL) (|InventorDataSink| . IVDATA) (|InventorViewPort| . IVVIEW) (|InventorRenderPackage| . IVREND) (|InverseLaplaceTransform| . INVLAPLA) (|IrrRepSymNatPackage| . IRSN) (|KernelFunctions2| . KERNEL2) (|KeyedAccessFile| . KAFILE) (|LaplaceTransform| . LAPLACE) (|LazardMorenoSolvingPackage| . LAZM3PK) (|Library| . LIB) (|LieSquareMatrix| . LSQM) (|LinearOrdinaryDifferentialOperator| . LODO) (|LinearSystemMatrixPackage| . LSMP) (|LinearSystemMatrixPackage1| . LSMP1) (|LinearSystemPolynomialPackage| . LSPP) (|List| . LIST) (|ListFunctions2| . LIST2) (|ListFunctions3| . LIST3) (|ListToMap| . LIST2MAP) (|MakeFloatCompiledFunction| . MKFLCFN) (|MakeFunction| . MKFUNC) (|MakeRecord| . MKRECORD) (|MappingPackage1| . MAPPKG1) (|MappingPackage2| . MAPPKG2) (|MappingPackage3| . MAPPKG3) (|MappingPackage4| . MAPPKG4) (|MathMLFormat| . MMLFORM) (|Matrix| . MATRIX) (|MatrixCategoryFunctions2| . MATCAT2) (|MatrixCommonDenominator| . MCDEN) (|MatrixLinearAlgebraFunctions| . MATLIN) (|MergeThing| . MTHING) (|ModularDistinctDegreeFactorizer| . MDDFACT) (|ModuleOperator| . MODOP) (|MonoidRingFunctions2| . MRF2) (|MoreSystemCommands| . MSYSCMD) (|MPolyCatFunctions2| . MPC2) (|MPolyCatRationalFunctionFactorizer| . MPRFF) (|Multiset| . MSET) (|MultivariateFactorize| . MULTFACT) (|MultivariatePolynomial| . MPOLY) (|MultFiniteFactorize| . MFINFACT) (|MyUnivariatePolynomial| . MYUP) (|MyExpression| . MYEXPR) (|NoneFunctions1| . NONE1) (|NonNegativeInteger| . NNI) (|NottinghamGroup| . NOTTING) (|NormalizationPackage| . NORMPK) (|NormInMonogenicAlgebra| . NORMMA) (|NumberTheoreticPolynomialFunctions| . NTPOLFN) (|Numeric| . NUMERIC) (|NumericalOrdinaryDifferentialEquations| . NUMODE) (|NumericalQuadrature| . NUMQUAD) (|NumericComplexEigenPackage| . NCEP) (|NumericRealEigenPackage| . NREP) (|NumericContinuedFraction| . NCNTFRAC) (|Octonion| . OCT) (|OctonionCategoryFunctions2| . OCTCT2) (|OneDimensionalArray| . ARRAY1) (|OneDimensionalArrayFunctions2| . ARRAY12) (|OnePointCompletion| . ONECOMP) (|OnePointCompletionFunctions2| . ONECOMP2) (|OpenMathConnection| . OMCONN) (|OpenMathDevice| . OMDEV) (|OpenMathEncoding| . OMENC) (|OpenMathError| . OMERR) (|OpenMathErrorKind| . OMERRK) (|OpenMathPackage| . OMPKG) (|OpenMathServerPackage| . OMSERVER) (|OperationsQuery| . OPQUERY) (|OrderedCompletion| . ORDCOMP) (|OrderedCompletionFunctions2| . ORDCOMP2) (|OrdinaryDifferentialRing| . ODR) (|OrdSetInts| . OSI) (|OrthogonalPolynomialFunctions| . ORTHPOL) (|OutputPackage| . OUT) (|PadeApproximantPackage| . PADEPAC) (|Palette| . PALETTE) (|PartialFraction| . PFR) (|PatternFunctions2| . PATTERN2) (|ParametricPlaneCurve| . PARPCURV) (|ParametricSpaceCurve| . PARSCURV) (|ParametricSurface| . PARSURF) (|ParametricPlaneCurveFunctions2| . PARPC2) (|ParametricSpaceCurveFunctions2| . PARSC2) (|ParametricSurfaceFunctions2| . PARSU2) (|PartitionsAndPermutations| . PARTPERM) (|PatternMatch| . PATMATCH) (|PatternMatchAssertions| . PMASS) (|PatternMatchResultFunctions2| . PATRES2) (|PendantTree| . PENDTREE) (|Permanent| . PERMAN) (|PermutationGroupExamples| . PGE) (|PermutationGroup| . PERMGRP) (|Permutation| . PERM) (|Pi| . HACKPI) (|PiCoercions| . PICOERCE) (|PointFunctions2| . PTFUNC2) (|PolyGroebner| . PGROEB) (|Polynomial| . POLY) (|PolynomialAN2Expression| . PAN2EXPR) (|PolynomialComposition| . PCOMP) (|PolynomialDecomposition| . PDECOMP) (|PolynomialFunctions2| . POLY2) (|PolynomialIdeals| . IDEAL) (|PolynomialToUnivariatePolynomial| . POLY2UP) (|PositiveInteger| . PI) (|PowerSeriesLimitPackage| . LIMITPS) (|PrimeField| . PF) (|PrimitiveArrayFunctions2| . PRIMARR2) (|PrintPackage| . PRINT) (|QuadraticForm| . QFORM) (|QuasiComponentPackage| . QCMPACK) (|Quaternion| . QUAT) (|QuaternionCategoryFunctions2| . QUATCT2) (|QueryEquation| . QEQUAT) (|Queue| . QUEUE) (|QuotientFieldCategoryFunctions2| . QFCAT2) (|RadicalEigenPackage| . REP) (|RadicalSolvePackage| . SOLVERAD) (|RadixExpansion| . RADIX) (|RadixUtilities| . RADUTIL) (|RandomNumberSource| . RANDSRC) (|RationalFunction| . RF) (|RationalFunctionDefiniteIntegration| . DEFINTRF) (|RationalFunctionFactor| . RFFACT) (|RationalFunctionFactorizer| . RFFACTOR) (|RationalFunctionIntegration| . INTRF) (|RationalFunctionLimitPackage| . LIMITRF) (|RationalFunctionSign| . SIGNRF) (|RationalFunctionSum| . SUMRF) (|RationalRetractions| . RATRET) (|RealClosure| . RECLOS) (|RealPolynomialUtilitiesPackage| . POLUTIL) (|RealZeroPackage| . REAL0) (|RealZeroPackageQ| . REAL0Q) (|RecurrenceOperator| . RECOP) (|RectangularMatrixCategoryFunctions2| . RMCAT2) (|RegularSetDecompositionPackage| . RSDCMPK) (|RegularTriangularSet| . REGSET) (|RegularTriangularSetGcdPackage| . RSETGCD) (|RepresentationPackage1| . REP1) (|RepresentationPackage2| . REP2) (|ResolveLatticeCompletion| . RESLATC) (|RewriteRule| . RULE) (|RightOpenIntervalRootCharacterization| . ROIRC) (|RomanNumeral| . ROMAN) (|Ruleset| . RULESET) (|ScriptFormulaFormat| . FORMULA) (|ScriptFormulaFormat1| . FORMULA1) (|Segment| . SEG) (|SegmentBinding| . SEGBIND) (|SegmentBindingFunctions2| . SEGBIND2) (|SegmentFunctions2| . SEG2) (|Set| . SET) (|SimpleAlgebraicExtensionAlgFactor| . SAEFACT) (|SimplifyAlgebraicNumberConvertPackage| . SIMPAN) (|SingleInteger| . SINT) (|SmithNormalForm| . SMITH) (|SparseUnivariatePolynomialExpressions| . SUPEXPR) (|SparseUnivariatePolynomialFunctions2| . SUP2) (|SpecialOutputPackage| . SPECOUT) (|SquareFreeRegularSetDecompositionPackage| . SRDCMPK) (|SquareFreeRegularTriangularSet| . SREGSET) (|SquareFreeRegularTriangularSetGcdPackage| . SFRGCD) (|SquareFreeQuasiComponentPackage| . SFQCMPK) (|Stack| . STACK) (|Stream| . STREAM) (|StreamFunctions1| . STREAM1) (|StreamFunctions2| . STREAM2) (|StreamFunctions3| . STREAM3) (|String| . STRING) (|SturmHabichtPackage| . SHP) (|Symbol| . SYMBOL) (|SymmetricGroupCombinatoricFunctions| . SGCF) (|SystemSolvePackage| . SYSSOLP) (|SAERationalFunctionAlgFactor| . SAERFFC) (|Tableau| . TABLEAU) (|TaylorSeries| . TS) (|TaylorSolve| . UTSSOL) (|TexFormat| . TEX) (|TexFormat1| . TEX1) (|TextFile| . TEXTFILE) (|ThreeDimensionalViewport| . VIEW3D) (|ThreeSpace| . SPACE3) (|Timer| . TIMER) (|TopLevelDrawFunctions| . DRAW) (|TopLevelDrawFunctionsForAlgebraicCurves| . DRAWCURV) (|TopLevelDrawFunctionsForCompiledFunctions| . DRAWCFUN) (|TopLevelDrawFunctionsForPoints| . DRAWPT) (|TopLevelThreeSpace| . TOPSP) (|TranscendentalManipulations| . TRMANIP) (|TransSolvePackage| . SOLVETRA) (|Tree| . TREE) (|TrigonometricManipulations| . TRIGMNIP) (|UnivariateLaurentSeriesFunctions2| . ULS2) (|UnivariateFormalPowerSeries| . UFPS) (|UnivariateFormalPowerSeriesFunctions| . UFPS1) (|UnivariatePolynomial| . UP) (|UnivariatePolynomialCategoryFunctions2| . UPOLYC2) (|UnivariatePolynomialCommonDenominator| . UPCDEN) (|UnivariatePolynomialFunctions2| . UP2) (|UnivariatePolynomialMultiplicationPackage| . UPMP) (|UnivariatePuiseuxSeriesFunctions2| . UPXS2) (|UnivariateTaylorSeriesFunctions2| . UTS2) (|UniversalSegment| . UNISEG) (|UniversalSegmentFunctions2| . UNISEG2) (|UserDefinedVariableOrdering| . UDVO) (|Vector| . VECTOR) (|VectorFunctions2| . VECTOR2) (|ViewDefaultsPackage| . VIEWDEF) (|Void| . VOID) (|WuWenTsunTriangularSet| . WUTSET)) (|naglink| (|Asp1| . ASP1) (|Asp4| . ASP4) (|Asp6| . ASP6) (|Asp7| . ASP7) (|Asp8| . ASP8) (|Asp9| . ASP9) (|Asp10| . ASP10) (|Asp12| . ASP12) (|Asp19| . ASP19) (|Asp20| . ASP20) (|Asp24| . ASP24) (|Asp27| . ASP27) (|Asp28| . ASP28) (|Asp29| . ASP29) (|Asp30| . ASP30) (|Asp31| . ASP31) (|Asp33| . ASP33) (|Asp34| . ASP34) (|Asp35| . ASP35) (|Asp41| . ASP41) (|Asp42| . ASP42) (|Asp49| . ASP49) (|Asp50| . ASP50) (|Asp55| . ASP55) (|Asp73| . ASP73) (|Asp74| . ASP74) (|Asp77| . ASP77) (|Asp78| . ASP78) (|Asp80| . ASP80) (|FortranCode| . FC) (|FortranCodePackage1| . FCPAK1) (|FortranExpression| . FEXPR) (|FortranMachineTypeCategory| . FMTC) (|FortranMatrixCategory| . FMC) (|FortranMatrixFunctionCategory| . FMFUN) (|FortranOutputStackPackage| . FOP) (|FortranPackage| . FORT) (|FortranProgramCategory| . FORTCAT) (|FortranProgram| . FORTRAN) (|FortranFunctionCategory| . FORTFN) (|FortranScalarType| . FST) (|FortranType| . FT) (|FortranTemplate| . FTEM) (|FortranVectorFunctionCategory| . FVFUN) (|FortranVectorCategory| . FVC) (|MachineComplex| . MCMPLX) (|MachineFloat| . MFLOAT) (|MachineInteger| . MINT) (|MultiVariableCalculusFunctions| . MCALCFN) (|NagDiscreteFourierTransformInterfacePackage| . NAGDIS) (|NagEigenInterfacePackage| . NAGEIG) (|NAGLinkSupportPackage| . NAGSP) (|NagOptimisationInterfacePackage| . NAGOPT) (|NagQuadratureInterfacePackage| . NAGQUA) (|NagResultChecks| . NAGRES) (|NagSpecialFunctionsInterfacePackage| . NAGSPE) (|NagPolynomialRootsPackage| . NAGC02) (|NagRootFindingPackage| . NAGC05) (|NagSeriesSummationPackage| . NAGC06) (|NagIntegrationPackage| . NAGD01) (|NagOrdinaryDifferentialEquationsPackage| . NAGD02) (|NagPartialDifferentialEquationsPackage| . NAGD03) (|NagInterpolationPackage| . NAGE01) (|NagFittingPackage| . NAGE02) (|NagOptimisationPackage| . NAGE04) (|NagMatrixOperationsPackage| . NAGF01) (|NagEigenPackage| . NAGF02) (|NagLinearEquationSolvingPackage| . NAGF04) (|NagLapack| . NAGF07) (|NagSpecialFunctionsPackage| . NAGS) (|PackedHermitianSequence| . PACKED) (|Result| . RESULT) (|SimpleFortranProgram| . SFORT) (|Switch| . SWITCH) (|SymbolTable| . SYMTAB) (|TemplateUtilities| . TEMUTL) (|TheSymbolTable| . SYMS) (|ThreeDimensionalMatrix| . M3D)) (|anna| (|AnnaNumericalIntegrationPackage| . INTPACK) (|AnnaNumericalOptimizationPackage| . OPTPACK) (|AnnaOrdinaryDifferentialEquationPackage| . ODEPACK) (|AnnaPartialDifferentialEquationPackage| . PDEPACK) (|AttributeButtons| . ATTRBUT) (|BasicFunctions| . BFUNCT) (|d01ajfAnnaType| . D01AJFA) (|d01akfAnnaType| . D01AKFA) (|d01alfAnnaType| . D01ALFA) (|d01amfAnnaType| . D01AMFA) (|d01anfAnnaType| . D01ANFA) (|d01apfAnnaType| . D01APFA) (|d01aqfAnnaType| . D01AQFA) (|d01asfAnnaType| . D01ASFA) (|d01fcfAnnaType| . D01FCFA) (|d01gbfAnnaType| . D01GBFA) (|d01AgentsPackage| . D01AGNT) (|d01TransformFunctionType| . D01TRNS) (|d01WeightsPackage| . D01WGTS) (|d02AgentsPackage| . D02AGNT) (|d02bbfAnnaType| . D02BBFA) (|d02bhfAnnaType| . D02BHFA) (|d02cjfAnnaType| . D02CJFA) (|d02ejfAnnaType| . D02EJFA) (|d03AgentsPackage| . D03AGNT) (|d03eefAnnaType| . D03EEFA) (|d03fafAnnaType| . D03FAFA) (|e04AgentsPackage| . E04AGNT) (|e04dgfAnnaType| . E04DGFA) (|e04fdfAnnaType| . E04FDFA) (|e04gcfAnnaType| . E04GCFA) (|e04jafAnnaType| . E04JAFA) (|e04mbfAnnaType| . E04MBFA) (|e04nafAnnaType| . E04NAFA) (|e04ucfAnnaType| . E04UCFA) (|ExpertSystemContinuityPackage| . ESCONT) (|ExpertSystemContinuityPackage1| . ESCONT1) (|ExpertSystemToolsPackage| . ESTOOLS) (|ExpertSystemToolsPackage1| . ESTOOLS1) (|ExpertSystemToolsPackage2| . ESTOOLS2) (|NumericalIntegrationCategory| . NUMINT) (|NumericalIntegrationProblem| . NIPROB) (|NumericalODEProblem| . ODEPROB) (|NumericalOptimizationCategory| . OPTCAT) (|NumericalOptimizationProblem| . OPTPROB) (|NumericalPDEProblem| . PDEPROB) (|ODEIntensityFunctionsTable| . ODEIFTBL) (|IntegrationFunctionsTable| . INTFTBL) (|OrdinaryDifferentialEquationsSolverCategory| . ODECAT) (|PartialDifferentialEquationsSolverCategory| . PDECAT) (|RoutinesTable| . ROUTINE)) (|categories| (|AbelianGroup| . ABELGRP) (|AbelianMonoid| . ABELMON) (|AbelianMonoidRing| . AMR) (|AbelianSemiGroup| . ABELSG) (|Aggregate| . AGG) (|Algebra| . ALGEBRA) (|AlgebraicallyClosedField| . ACF) (|AlgebraicallyClosedFunctionSpace| . ACFS) (|ArcHyperbolicFunctionCategory| . AHYP) (|ArcTrigonometricFunctionCategory| . ATRIG) (|AssociationListAggregate| . ALAGG) (|AttributeRegistry| . ATTREG) (|BagAggregate| . BGAGG) (|BasicType| . BASTYPE) (|BiModule| . BMODULE) (|BinaryRecursiveAggregate| . BRAGG) (|BinaryTreeCategory| . BTCAT) (|BitAggregate| . BTAGG) (|CachableSet| . CACHSET) (|CancellationAbelianMonoid| . CABMON) (|CharacteristicNonZero| . CHARNZ) (|CharacteristicZero| . CHARZ) (|CoercibleTo| . KOERCE) (|Collection| . CLAGG) (|CombinatorialFunctionCategory| . CFCAT) (|CombinatorialOpsCategory| . COMBOPC) (|CommutativeRing| . COMRING) (|ComplexCategory| . COMPCAT) (|ConvertibleTo| . KONVERT) (|DequeueAggregate| . DQAGG) (|Dictionary| . DIAGG) (|DictionaryOperations| . DIOPS) (|DifferentialExtension| . DIFEXT) (|DifferentialPolynomialCategory| . DPOLCAT) (|DifferentialRing| . DIFRING) (|DifferentialVariableCategory| . DVARCAT) (|DirectProductCategory| . DIRPCAT) (|DivisionRing| . DIVRING) (|DoublyLinkedAggregate| . DLAGG) (|ElementaryFunctionCategory| . ELEMFUN) (|Eltable| . ELTAB) (|EltableAggregate| . ELTAGG) (|EntireRing| . ENTIRER) (|EuclideanDomain| . EUCDOM) (|Evalable| . EVALAB) (|ExpressionSpace| . ES) (|ExtensibleLinearAggregate| . ELAGG) (|ExtensionField| . XF) (|Field| . FIELD) (|FieldOfPrimeCharacteristic| . FPC) (|Finite| . FINITE) (|FileCategory| . FILECAT) (|FileNameCategory| . FNCAT) (|FiniteAbelianMonoidRing| . FAMR) (|FiniteAlgebraicExtensionField| . FAXF) (|FiniteDivisorCategory| . FDIVCAT) (|FiniteFieldCategory| . FFIELDC) (|FiniteLinearAggregate| . FLAGG) (|FiniteRankNonAssociativeAlgebra| . FINAALG) (|FiniteRankAlgebra| . FINRALG) (|FiniteSetAggregate| . FSAGG) (|FloatingPointSystem| . FPS) (|FramedAlgebra| . FRAMALG) (|FramedNonAssociativeAlgebra| . FRNAALG) (|FramedNonAssociativeAlgebraFunctions2| . FRNAAF2) (|FreeAbelianMonoidCategory| . FAMONC) (|FreeLieAlgebra| . FLALG) (|FreeModuleCat| . FMCAT) (|FullyEvalableOver| . FEVALAB) (|FullyLinearlyExplicitRingOver| . FLINEXP) (|FullyPatternMatchable| . FPATMAB) (|FullyRetractableTo| . FRETRCT) (|FunctionFieldCategory| . FFCAT) (|FunctionSpace| . FS) (|GcdDomain| . GCDDOM) (|GradedAlgebra| . GRALG) (|GradedModule| . GRMOD) (|Group| . GROUP) (|HomogeneousAggregate| . HOAGG) (|HyperbolicFunctionCategory| . HYPCAT) (|IndexedAggregate| . IXAGG) (|IndexedDirectProductCategory| . IDPC) (|InnerEvalable| . IEVALAB) (|IntegerNumberSystem| . INS) (|IntegralDomain| . INTDOM) (|IntervalCategory| . INTCAT) (|KeyedDictionary| . KDAGG) (|LazyStreamAggregate| . LZSTAGG) (|LeftAlgebra| . LALG) (|LeftModule| . LMODULE) (|LieAlgebra| . LIECAT) (|LinearAggregate| . LNAGG) (|LinearlyExplicitRingOver| . LINEXP) (|LinearOrdinaryDifferentialOperatorCategory| . LODOCAT) (|LiouvillianFunctionCategory| . LFCAT) (|ListAggregate| . LSAGG) (|Logic| . LOGIC) (|MatrixCategory| . MATCAT) (|Module| . MODULE) (|Monad| . MONAD) (|MonadWithUnit| . MONADWU) (|Monoid| . MONOID) (|MonogenicAlgebra| . MONOGEN) (|MonogenicLinearOperator| . MLO) (|MultiDictionary| . MDAGG) (|MultisetAggregate| . MSETAGG) (|MultivariateTaylorSeriesCategory| . MTSCAT) (|NonAssociativeAlgebra| . NAALG) (|NonAssociativeRing| . NASRING) (|NonAssociativeRng| . NARNG) (|NormalizedTriangularSetCategory| . NTSCAT) (|Object| . OBJECT) (|OctonionCategory| . OC) (|OneDimensionalArrayAggregate| . A1AGG) (|OpenMath| . OM) (|OrderedAbelianGroup| . OAGROUP) (|OrderedAbelianMonoid| . OAMON) (|OrderedAbelianMonoidSup| . OAMONS) (|OrderedAbelianSemiGroup| . OASGP) (|OrderedCancellationAbelianMonoid| . OCAMON) (|OrderedFinite| . ORDFIN) (|OrderedIntegralDomain| . OINTDOM) (|OrderedMonoid| . ORDMON) (|OrderedMultisetAggregate| . OMSAGG) (|OrderedRing| . ORDRING) (|OrderedSet| . ORDSET) (|PAdicIntegerCategory| . PADICCT) (|PartialDifferentialRing| . PDRING) (|PartialTranscendentalFunctions| . PTRANFN) (|Patternable| . PATAB) (|PatternMatchable| . PATMAB) (|PermutationCategory| . PERMCAT) (|PlottablePlaneCurveCategory| . PPCURVE) (|PlottableSpaceCurveCategory| . PSCURVE) (|PointCategory| . PTCAT) (|PolynomialCategory| . POLYCAT) (|PolynomialFactorizationExplicit| . PFECAT) (|PolynomialSetCategory| . PSETCAT) (|PowerSeriesCategory| . PSCAT) (|PrimitiveFunctionCategory| . PRIMCAT) (|PrincipalIdealDomain| . PID) (|PriorityQueueAggregate| . PRQAGG) (|QuaternionCategory| . QUATCAT) (|QueueAggregate| . QUAGG) (|QuotientFieldCategory| . QFCAT) (|RadicalCategory| . RADCAT) (|RealClosedField| . RCFIELD) (|RealConstant| . REAL) (|RealNumberSystem| . RNS) (|RealRootCharacterizationCategory| . RRCC) (|RectangularMatrixCategory| . RMATCAT) (|RecursiveAggregate| . RCAGG) (|RecursivePolynomialCategory| . RPOLCAT) (|RegularChain| . RGCHAIN) (|RegularTriangularSetCategory| . RSETCAT) (|RetractableTo| . RETRACT) (|RightModule| . RMODULE) (|Ring| . RING) (|Rng| . RNG) (|SegmentCategory| . SEGCAT) (|SegmentExpansionCategory| . SEGXCAT) (|SemiGroup| . SGROUP) (|SetAggregate| . SETAGG) (|SetCategory| . SETCAT) (|SExpressionCategory| . SEXCAT) (|SpecialFunctionCategory| . SPFCAT) (|SquareFreeNormalizedTriangularSetCategory| . SNTSCAT) (|SquareFreeRegularTriangularSetCategory| . SFRTCAT) (|SquareMatrixCategory| . SMATCAT) (|StackAggregate| . SKAGG) (|StepThrough| . STEP) (|StreamAggregate| . STAGG) (|StringAggregate| . SRAGG) (|StringCategory| . STRICAT) (|StructuralConstantsPackage| . SCPKG) (|TableAggregate| . TBAGG) (|ThreeSpaceCategory| . SPACEC) (|TranscendentalFunctionCategory| . TRANFUN) (|TriangularSetCategory| . TSETCAT) (|TrigonometricFunctionCategory| . TRIGCAT) (|TwoDimensionalArrayCategory| . ARR2CAT) (|Type| . TYPE) (|UnaryRecursiveAggregate| . URAGG) (|UniqueFactorizationDomain| . UFD) (|UnivariateLaurentSeriesCategory| . ULSCAT) (|UnivariateLaurentSeriesConstructorCategory| . ULSCCAT) (|UnivariatePolynomialCategory| . UPOLYC) (|UnivariatePowerSeriesCategory| . UPSCAT) (|UnivariatePuiseuxSeriesCategory| . UPXSCAT) (|UnivariatePuiseuxSeriesConstructorCategory| . UPXSCCA) (|UnivariateSkewPolynomialCategory| . OREPCAT) (|UnivariateTaylorSeriesCategory| . UTSCAT) (|VectorCategory| . VECTCAT) (|VectorSpace| . VSPACE) (|XAlgebra| . XALG) (|XFreeAlgebra| . XFALG) (|XPolynomialsCat| . XPOLYC) (|ZeroDimensionalSolvePackage| . ZDSOLVE)) (|Hidden| (|AlgebraicFunction| . AF) (|AlgebraicFunctionField| . ALGFF) (|AlgebraicHermiteIntegration| . INTHERAL) (|AlgebraicIntegrate| . INTALG) (|AlgebraicIntegration| . INTAF) (|AnonymousFunction| . ANON) (|AntiSymm| . ANTISYM) (|ApplyRules| . APPRULE) (|ApplyUnivariateSkewPolynomial| . APPLYORE) (|ArrayStack| . ASTACK) (|AssociatedEquations| . ASSOCEQ) (|AssociationList| . ALIST) (|Automorphism| . AUTOMOR) (|BalancedFactorisation| . BALFACT) (|BalancedPAdicInteger| . BPADIC) (|BalancedPAdicRational| . BPADICRT) (|BezoutMatrix| . BEZOUT) (|BoundIntegerRoots| . BOUNDZRO) (|BrillhartTests| . BRILL) (|ChangeOfVariable| . CHVAR) (|CharacteristicPolynomialInMonogenicalAlgebra| . CPIMA) (|ChineseRemainderToolsForIntegralBases| . IBACHIN) (|CoerceVectorMatrixPackage| . CVMP) (|CombinatorialFunction| . COMBF) (|CommonOperators| . COMMONOP) (|CommuteUnivariatePolynomialCategory| . COMMUPC) (|ComplexIntegerSolveLinearPolynomialEquation| . CINTSLPE) (|ComplexPattern| . COMPLPAT) (|ComplexPatternMatch| . CPMATCH) (|ComplexRootFindingPackage| . CRFP) (|ConstantLODE| . ODECONST) (|CyclicStreamTools| . CSTTOOLS) (|CyclotomicPolynomialPackage| . CYCLOTOM) (|DefiniteIntegrationTools| . DFINTTLS) (|DegreeReductionPackage| . DEGRED) (|DeRhamComplex| . DERHAM) (|DifferentialSparseMultivariatePolynomial| . DSMP) (|DirectProduct| . DIRPROD) (|DirectProductMatrixModule| . DPMM) (|DirectProductModule| . DPMO) (|DiscreteLogarithmPackage| . DLP) (|DistributedMultivariatePolynomial| . DMP) (|DoubleResultantPackage| . DBLRESP) (|DrawOptionFunctions0| . DROPT0) (|DrawOptionFunctions1| . DROPT1) (|ElementaryFunction| . EF) (|ElementaryFunctionsUnivariateLaurentSeries| . EFULS) (|ElementaryFunctionsUnivariatePuiseuxSeries| . EFUPXS) (|ElementaryIntegration| . INTEF) (|ElementaryRischDE| . RDEEF) (|ElementaryRischDESystem| . RDEEFS) (|EllipticFunctionsUnivariateTaylorSeries| . ELFUTS) (|EqTable| . EQTBL) (|EuclideanModularRing| . EMR) (|EvaluateCycleIndicators| . EVALCYC) (|ExponentialExpansion| . EXPEXPAN) (|ExponentialOfUnivariatePuiseuxSeries| . EXPUPXS) (|ExpressionSpaceFunctions1| . ES1) (|ExpressionTubePlot| . EXPRTUBE) (|ExtAlgBasis| . EAB) (|FactoredFunctions| . FACTFUNC) (|FactoredFunctionUtilities| . FRUTIL) (|FactoringUtilities| . FACUTIL) (|FGLMIfCanPackage| . FGLMICPK) (|FindOrderFinite| . FORDER) (|FiniteDivisor| . FDIV) (|FiniteFieldCyclicGroupExtension| . FFCGX) (|FiniteFieldCyclicGroupExtensionByPolynomial| . FFCGP) (|FiniteFieldExtension| . FFX) (|FiniteFieldExtensionByPolynomial| . FFP) (|FiniteFieldFunctions| . FFF) (|FiniteFieldNormalBasisExtension| . FFNBX) (|FiniteFieldNormalBasisExtensionByPolynomial| . FFNBP) (|FiniteFieldPolynomialPackage| . FFPOLY) (|FiniteFieldSolveLinearPolynomialEquation| . FFSLPE) (|FormalFraction| . FORMAL) (|FourierComponent| . FCOMP) (|FractionalIdeal| . FRIDEAL) (|FramedModule| . FRMOD) (|FreeAbelianGroup| . FAGROUP) (|FreeAbelianMonoid| . FAMONOID) (|FreeGroup| . FGROUP) (|FreeModule| . FM) (|FreeModule1| . FM1) (|FreeMonoid| . FMONOID) (|FunctionalSpecialFunction| . FSPECF) (|FunctionCalled| . FUNCTION) (|FunctionFieldIntegralBasis| . FFINTBAS) (|FunctionSpaceReduce| . FSRED) (|FunctionSpaceToUnivariatePowerSeries| . FS2UPS) (|FunctionSpaceToExponentialExpansion| . FS2EXPXP) (|FunctionSpaceUnivariatePolynomialFactor| . FSUPFACT) (|GaloisGroupFactorizationUtilities| . GALFACTU) (|GaloisGroupFactorizer| . GALFACT) (|GaloisGroupPolynomialUtilities| . GALPOLYU) (|GaloisGroupUtilities| . GALUTIL) (|GeneralHenselPackage| . GHENSEL) (|GeneralDistributedMultivariatePolynomial| . GDMP) (|GeneralPolynomialGcdPackage| . GENPGCD) (|GeneralSparseTable| . GSTBL) (|GenericNonAssociativeAlgebra| . GCNAALG) (|GenExEuclid| . GENEEZ) (|GeneralizedMultivariateFactorize| . GENMFACT) (|GeneralModulePolynomial| . GMODPOL) (|GeneralPolynomialSet| . GPOLSET) (|GeneralTriangularSet| . GTSET) (|GenUFactorize| . GENUFACT) (|GenusZeroIntegration| . INTG0) (|GosperSummationMethod| . GOSPER) (|GraphImage| . GRIMAGE) (|GrayCode| . GRAY) (|GroebnerInternalPackage| . GBINTERN) (|GroebnerSolve| . GROEBSOL) (|HashTable| . HASHTBL) (|Heap| . HEAP) (|HeuGcd| . HEUGCD) (|HomogeneousDistributedMultivariatePolynomial| . HDMP) (|HyperellipticFiniteDivisor| . HELLFDIV) (|IncrementingMaps| . INCRMAPS) (|IndexedBits| . IBITS) (|IndexedDirectProductAbelianGroup| . IDPAG) (|IndexedDirectProductAbelianMonoid| . IDPAM) (|IndexedDirectProductObject| . IDPO) (|IndexedDirectProductOrderedAbelianMonoid| . IDPOAM) (|IndexedDirectProductOrderedAbelianMonoidSup| . IDPOAMS) (|IndexedExponents| . INDE) (|IndexedFlexibleArray| . IFARRAY) (|IndexedList| . ILIST) (|IndexedMatrix| . IMATRIX) (|IndexedOneDimensionalArray| . IARRAY1) (|IndexedString| . ISTRING) (|IndexedTwoDimensionalArray| . IARRAY2) (|IndexedVector| . IVECTOR) (|InnerAlgFactor| . IALGFACT) (|InnerAlgebraicNumber| . IAN) (|InnerCommonDenominator| . ICDEN) (|InnerFiniteField| . IFF) (|InnerFreeAbelianMonoid| . IFAMON) (|InnerIndexedTwoDimensionalArray| . IIARRAY2) (|InnerMatrixLinearAlgebraFunctions| . IMATLIN) (|InnerMatrixQuotientFieldFunctions| . IMATQF) (|InnerModularGcd| . INMODGCD) (|InnerMultFact| . INNMFACT) (|InnerNormalBasisFieldFunctions| . INBFF) (|InnerNumericEigenPackage| . INEP) (|InnerNumericFloatSolvePackage| . INFSP) (|InnerPAdicInteger| . IPADIC) (|InnerPolySign| . INPSIGN) (|InnerPolySum| . ISUMP) (|InnerPrimeField| . IPF) (|InnerSparseUnivariatePowerSeries| . ISUPS) (|InnerTable| . INTABL) (|InnerTaylorSeries| . ITAYLOR) (|InnerTrigonometricManipulations| . ITRIGMNP) (|InputForm| . INFORM) (|InputFormFunctions1| . INFORM1) (|IntegerBits| . INTBIT) (|IntegerFactorizationPackage| . INTFACT) (|IntegerMod| . ZMOD) (|IntegerSolveLinearPolynomialEquation| . INTSLPE) (|IntegralBasisPolynomialTools| . IBPTOOLS) (|IntegralBasisTools| . IBATOOL) (|IntegrationResult| . IR) (|IntegrationTools| . INTTOOLS) (|InternalPrintPackage| . IPRNTPK) (|InternalRationalUnivariateRepresentationPackage| . IRURPK) (|IrredPolyOverFiniteField| . IRREDFFX) (|Kernel| . KERNEL) (|Kovacic| . KOVACIC) (|LaurentPolynomial| . LAUPOL) (|LeadingCoefDetermination| . LEADCDET) (|LexTriangularPackage| . LEXTRIPK) (|LieExponentials| . LEXP) (|LiePolynomial| . LPOLY) (|LinearDependence| . LINDEP) (|LinearOrdinaryDifferentialOperatorFactorizer| . LODOF) (|LinearOrdinaryDifferentialOperator1| . LODO1) (|LinearOrdinaryDifferentialOperator2| . LODO2) (|LinearOrdinaryDifferentialOperatorsOps| . LODOOPS) (|LinearPolynomialEquationByFractions| . LPEFRAC) (|LinGroebnerPackage| . LGROBP) (|LiouvillianFunction| . LF) (|ListMonoidOps| . LMOPS) (|ListMultiDictionary| . LMDICT) (|LocalAlgebra| . LA) (|Localize| . LO) (|LyndonWord| . LWORD) (|Magma| . MAGMA) (|MakeBinaryCompiledFunction| . MKBCFUNC) (|MakeCachableSet| . MKCHSET) (|MakeUnaryCompiledFunction| . MKUCFUNC) (|MappingPackageInternalHacks1| . MAPHACK1) (|MappingPackageInternalHacks2| . MAPHACK2) (|MappingPackageInternalHacks3| . MAPHACK3) (|MeshCreationRoutinesForThreeDimensions| . MESH) (|ModMonic| . MODMON) (|ModularField| . MODFIELD) (|ModularHermitianRowReduction| . MHROWRED) (|ModularRing| . MODRING) (|ModuleMonomial| . MODMONOM) (|MoebiusTransform| . MOEBIUS) (|MonoidRing| . MRING) (|MonomialExtensionTools| . MONOTOOL) (|MPolyCatPolyFactorizer| . MPCPF) (|MPolyCatFunctions3| . MPC3) (|MRationalFactorize| . MRATFAC) (|MultipleMap| . MMAP) (|MultivariateLifting| . MLIFT) (|MultivariateSquareFree| . MULTSQFR) (|HomogeneousDirectProduct| . HDP) (|NewSparseMultivariatePolynomial| . NSMP) (|NewSparseUnivariatePolynomial| . NSUP) (|NewSparseUnivariatePolynomialFunctions2| . NSUP2) (|NonCommutativeOperatorDivision| . NCODIV) (|NewtonInterpolation| . NEWTON) (|None| . NONE) (|NonLinearFirstOrderODESolver| . NODE1) (|NonLinearSolvePackage| . NLINSOL) (|NormRetractPackage| . NORMRETR) (|NPCoef| . NPCOEF) (|NumberFormats| . NUMFMT) (|NumberFieldIntegralBasis| . NFINTBAS) (|NumericTubePlot| . NUMTUBE) (|ODEIntegration| . ODEINT) (|ODETools| . ODETOOLS) (|Operator| . OP) (|OppositeMonogenicLinearOperator| . OMLO) (|OrderedDirectProduct| . ODP) (|OrderedFreeMonoid| . OFMONOID) (|OrderedVariableList| . OVAR) (|OrderingFunctions| . ORDFUNS) (|OrderlyDifferentialPolynomial| . ODPOL) (|OrderlyDifferentialVariable| . ODVAR) (|OrdinaryWeightedPolynomials| . OWP) (|OutputForm| . OUTFORM) (|PadeApproximants| . PADE) (|PAdicInteger| . PADIC) (|PAdicRational| . PADICRAT) (|PAdicRationalConstructor| . PADICRC) (|PAdicWildFunctionFieldIntegralBasis| . PWFFINTB) (|ParadoxicalCombinatorsForStreams| . YSTREAM) (|ParametricLinearEquations| . PLEQN) (|PartialFractionPackage| . PFRPAC) (|Partition| . PRTITION) (|Pattern| . PATTERN) (|PatternFunctions1| . PATTERN1) (|PatternMatchFunctionSpace| . PMFS) (|PatternMatchIntegerNumberSystem| . PMINS) (|PatternMatchIntegration| . INTPM) (|PatternMatchKernel| . PMKERNEL) (|PatternMatchListAggregate| . PMLSAGG) (|PatternMatchListResult| . PATLRES) (|PatternMatchPolynomialCategory| . PMPLCAT) (|PatternMatchPushDown| . PMDOWN) (|PatternMatchQuotientFieldCategory| . PMQFCAT) (|PatternMatchResult| . PATRES) (|PatternMatchSymbol| . PMSYM) (|PatternMatchTools| . PMTOOLS) (|PlaneAlgebraicCurvePlot| . ACPLOT) (|Plot| . PLOT) (|PlotFunctions1| . PLOT1) (|PlotTools| . PLOTTOOL) (|Plot3D| . PLOT3D) (|PoincareBirkhoffWittLyndonBasis| . PBWLB) (|Point| . POINT) (|PointsOfFiniteOrder| . PFO) (|PointsOfFiniteOrderRational| . PFOQ) (|PointsOfFiniteOrderTools| . PFOTOOLS) (|PointPackage| . PTPACK) (|PolToPol| . POLTOPOL) (|PolynomialCategoryLifting| . POLYLIFT) (|PolynomialCategoryQuotientFunctions| . POLYCATQ) (|PolynomialFactorizationByRecursion| . PFBR) (|PolynomialFactorizationByRecursionUnivariate| . PFBRU) (|PolynomialGcdPackage| . PGCD) (|PolynomialInterpolation| . PINTERP) (|PolynomialInterpolationAlgorithms| . PINTERPA) (|PolynomialNumberTheoryFunctions| . PNTHEORY) (|PolynomialRing| . PR) (|PolynomialRoots| . POLYROOT) (|PolynomialSetUtilitiesPackage| . PSETPK) (|PolynomialSolveByFormulas| . SOLVEFOR) (|PolynomialSquareFree| . PSQFR) (|PrecomputedAssociatedEquations| . PREASSOC) (|PrimitiveArray| . PRIMARR) (|PrimitiveElement| . PRIMELT) (|PrimitiveRatDE| . ODEPRIM) (|PrimitiveRatRicDE| . ODEPRRIC) (|Product| . PRODUCT) (|PseudoRemainderSequence| . PRS) (|PseudoLinearNormalForm| . PSEUDLIN) (|PureAlgebraicIntegration| . INTPAF) (|PureAlgebraicLODE| . ODEPAL) (|PushVariables| . PUSHVAR) (|QuasiAlgebraicSet| . QALGSET) (|QuasiAlgebraicSet2| . QALGSET2) (|RadicalFunctionField| . RADFF) (|RandomDistributions| . RDIST) (|RandomFloatDistributions| . RFDIST) (|RandomIntegerDistributions| . RIDIST) (|RationalFactorize| . RATFACT) (|RationalIntegration| . INTRAT) (|RationalInterpolation| . RINTERP) (|RationalLODE| . ODERAT) (|RationalRicDE| . ODERTRIC) (|RationalUnivariateRepresentationPackage| . RURPK) (|RealSolvePackage| . REALSOLV) (|RectangularMatrix| . RMATRIX) (|ReducedDivisor| . RDIV) (|ReduceLODE| . ODERED) (|ReductionOfOrder| . REDORDER) (|Reference| . REF) (|RepeatedDoubling| . REPDB) (|RepeatedSquaring| . REPSQ) (|ResidueRing| . RESRING) (|RetractSolvePackage| . RETSOL) (|RuleCalled| . RULECOLD) (|SetOfMIntegersInOneToN| . SETMN) (|SExpression| . SEX) (|SExpressionOf| . SEXOF) (|SequentialDifferentialPolynomial| . SDPOL) (|SequentialDifferentialVariable| . SDVAR) (|SimpleAlgebraicExtension| . SAE) (|SingletonAsOrderedSet| . SAOS) (|SortedCache| . SCACHE) (|SortPackage| . SORTPAK) (|SparseMultivariatePolynomial| . SMP) (|SparseMultivariateTaylorSeries| . SMTS) (|SparseTable| . STBL) (|SparseUnivariatePolynomial| . SUP) (|SparseUnivariateSkewPolynomial| . ORESUP) (|SparseUnivariateLaurentSeries| . SULS) (|SparseUnivariatePuiseuxSeries| . SUPXS) (|SparseUnivariateTaylorSeries| . SUTS) (|SplitHomogeneousDirectProduct| . SHDP) (|SplittingNode| . SPLNODE) (|SplittingTree| . SPLTREE) (|SquareMatrix| . SQMATRIX) (|Stack| . STACK) (|StorageEfficientMatrixOperations| . MATSTOR) (|StreamInfiniteProduct| . STINPROD) (|StreamTaylorSeriesOperations| . STTAYLOR) (|StreamTranscendentalFunctions| . STTF) (|StreamTranscendentalFunctionsNonCommutative| . STTFNC) (|StringTable| . STRTBL) (|SubResultantPackage| . SUBRESP) (|SubSpace| . SUBSPACE) (|SubSpaceComponentProperty| . COMPPROP) (|SuchThat| . SUCH) (|SupFractionFactorizer| . SUPFRACF) (|SymmetricFunctions| . SYMFUNC) (|SymmetricPolynomial| . SYMPOLY) (|SystemODESolver| . ODESYS) (|Table| . TABLE) (|TableauxBumpers| . TABLBUMP) (|TabulatedComputationPackage| . TBCMPPK) (|TangentExpansions| . TANEXP) (|ToolsForSign| . TOOLSIGN) (|TranscendentalHermiteIntegration| . INTHERTR) (|TranscendentalIntegration| . INTTR) (|TranscendentalRischDE| . RDETR) (|TranscendentalRischDESystem| . RDETRS) (|TransSolvePackageService| . SOLVESER) (|TriangularMatrixOperations| . TRIMAT) (|TubePlot| . TUBE) (|TubePlotTools| . TUBETOOL) (|Tuple| . TUPLE) (|TwoDimensionalArray| . ARRAY2) (|TwoDimensionalPlotClipping| . CLIP) (|TwoDimensionalViewport| . VIEW2D) (|TwoFactorize| . TWOFACT) (|UnivariateFactorize| . UNIFACT) (|UnivariateLaurentSeries| . ULS) (|UnivariateLaurentSeriesConstructor| . ULSCONS) (|UnivariatePolynomialDecompositionPackage| . UPDECOMP) (|UnivariatePolynomialDivisionPackage| . UPDIVP) (|UnivariatePolynomialSquareFree| . UPSQFREE) (|UnivariatePuiseuxSeries| . UPXS) (|UnivariatePuiseuxSeriesConstructor| . UPXSCONS) (|UnivariatePuiseuxSeriesWithExponentialSingularity| . UPXSSING) (|UnivariateSkewPolynomial| . OREUP) (|UnivariateSkewPolynomialCategoryOps| . OREPCTO) (|UnivariateTaylorSeries| . UTS) (|UnivariateTaylorSeriesODESolver| . UTSODE) (|UserDefinedPartialOrdering| . UDPO) (|UTSodetools| . UTSODETL) (|Variable| . VARIABLE) (|ViewportPackage| . VIEW) (|WeierstrassPreparation| . WEIER) (|WeightedPolynomials| . WP) (|WildFunctionFieldIntegralBasis| . WFFINTBS) (|XDistributedPolynomial| . XDPOLY) (|XExponentialPackage| . XEXPPKG) (|XPBWPolynomial| . XPBWPOLY) (|XPolynomial| . XPOLY) (|XPolynomialRing| . XPR) (|XRecursivePolynomial| . XRPOLY)) (|defaults| (|AbelianGroup&| . ABELGRP-) (|AbelianMonoid&| . ABELMON-) (|AbelianMonoidRing&| . AMR-) (|AbelianSemiGroup&| . ABELSG-) (|Aggregate&| . AGG-) (|Algebra&| . ALGEBRA-) (|AlgebraicallyClosedField&| . ACF-) (|AlgebraicallyClosedFunctionSpace&| . ACFS-) (|ArcTrigonometricFunctionCategory&| . ATRIG-) (|BagAggregate&| . BGAGG-) (|BasicType&| . BASTYPE-) (|BinaryRecursiveAggregate&| . BRAGG-) (|BinaryTreeCategory&| . BTCAT-) (|BitAggregate&| . BTAGG-) (|Collection&| . CLAGG-) (|ComplexCategory&| . COMPCAT-) (|Dictionary&| . DIAGG-) (|DictionaryOperations&| . DIOPS-) (|DifferentialExtension&| . DIFEXT-) (|DifferentialPolynomialCategory&| . DPOLCAT-) (|DifferentialRing&| . DIFRING-) (|DifferentialVariableCategory&| . DVARCAT-) (|DirectProductCategory&| . DIRPCAT-) (|DivisionRing&| . DIVRING-) (|ElementaryFunctionCategory&| . ELEMFUN-) (|EltableAggregate&| . ELTAGG-) (|EuclideanDomain&| . EUCDOM-) (|Evalable&| . EVALAB-) (|ExpressionSpace&| . ES-) (|ExtensibleLinearAggregate&| . ELAGG-) (|ExtensionField&| . XF-) (|Field&| . FIELD-) (|FieldOfPrimeCharacteristic&| . FPC-) (|FiniteAbelianMonoidRing&| . FAMR-) (|FiniteAlgebraicExtensionField&| . FAXF-) (|FiniteDivisorCategory&| . FDIVCAT-) (|FiniteFieldCategory&| . FFIELDC-) (|FiniteLinearAggregate&| . FLAGG-) (|FiniteSetAggregate&| . FSAGG-) (|FiniteRankAlgebra&| . FINRALG-) (|FiniteRankNonAssociativeAlgebra&| . FINAALG-) (|FloatingPointSystem&| . FPS-) (|FramedAlgebra&| . FRAMALG-) (|FramedNonAssociativeAlgebra&| . FRNAALG-) (|FullyEvalableOver&| . FEVALAB-) (|FullyLinearlyExplicitRingOver&| . FLINEXP-) (|FullyRetractableTo&| . FRETRCT-) (|FunctionFieldCategory&| . FFCAT-) (|FunctionSpace&| . FS-) (|GcdDomain&| . GCDDOM-) (|GradedAlgebra&| . GRALG-) (|GradedModule&| . GRMOD-) (|Group&| . GROUP-) (|HomogeneousAggregate&| . HOAGG-) (|HyperbolicFunctionCategory&| . HYPCAT-) (|IndexedAggregate&| . IXAGG-) (|InnerEvalable&| . IEVALAB-) (|IntegerNumberSystem&| . INS-) (|IntegralDomain&| . INTDOM-) (|KeyedDictionary&| . KDAGG-) (|LazyStreamAggregate&| . LZSTAGG-) (|LeftAlgebra&| . LALG-) (|LieAlgebra&| . LIECAT-) (|LinearAggregate&| . LNAGG-) (|ListAggregate&| . LSAGG-) (|Logic&| . LOGIC-) (|LinearOrdinaryDifferentialOperatorCategory&| . LODOCAT-) (|MatrixCategory&| . MATCAT-) (|Module&| . MODULE-) (|Monad&| . MONAD-) (|MonadWithUnit&| . MONADWU-) (|Monoid&| . MONOID-) (|MonogenicAlgebra&| . MONOGEN-) (|NonAssociativeAlgebra&| . NAALG-) (|NonAssociativeRing&| . NASRING-) (|NonAssociativeRng&| . NARNG-) (|OctonionCategory&| . OC-) (|OneDimensionalArrayAggregate&| . A1AGG-) (|OrderedRing&| . ORDRING-) (|OrderedSet&| . ORDSET-) (|PartialDifferentialRing&| . PDRING-) (|PolynomialCategory&| . POLYCAT-) (|PolynomialFactorizationExplicit&| . PFECAT-) (|PolynomialSetCategory&| . PSETCAT-) (|PowerSeriesCategory&| . PSCAT-) (|QuaternionCategory&| . QUATCAT-) (|QuotientFieldCategory&| . QFCAT-) (|RadicalCategory&| . RADCAT-) (|RealClosedField&| . RCFIELD-) (|RealNumberSystem&| . RNS-) (|RealRootCharacterizationCategory&| . RRCC-) (|RectangularMatrixCategory&| . RMATCAT-) (|RecursiveAggregate&| . RCAGG-) (|RecursivePolynomialCategory&| . RPOLCAT-) (|RegularTriangularSetCategory&| . RSETCAT-) (|RetractableTo&| . RETRACT-) (|Ring&| . RING-) (|SemiGroup&| . SGROUP-) (|SetAggregate&| . SETAGG-) (|SetCategory&| . SETCAT-) (|SquareMatrixCategory&| . SMATCAT-) (|StreamAggregate&| . STAGG-) (|StringAggregate&| . SRAGG-) (|TableAggregate&| . TBAGG-) (|TranscendentalFunctionCategory&| . TRANFUN-) (|TriangularSetCategory&| . TSETCAT-) (|TrigonometricFunctionCategory&| . TRIGCAT-) (|TwoDimensionalArrayCategory&| . ARR2CAT-) (|UnaryRecursiveAggregate&| . URAGG-) (|UniqueFactorizationDomain&| . UFD-) (|UnivariateLaurentSeriesConstructorCategory&| . ULSCCAT-) (|UnivariatePolynomialCategory&| . UPOLYC-) (|UnivariatePowerSeriesCategory&| . UPSCAT-) (|UnivariatePuiseuxSeriesConstructorCategory&| . UPXSCCA-) (|UnivariateSkewPolynomialCategory&| . OREPCAT-) (|UnivariateTaylorSeriesCategory&| . UTSCAT-) (|VectorCategory&| . VECTCAT-) (|VectorSpace&| . VSPACE-)))
--R 
--RValue = ((|basic| (|AlgebraicManipulations| . ALGMANIP) (|AlgebraicNumber| . AN) (|AlgFactor| . ALGFACT) (|AlgebraicMultFact| . ALGMFACT) (|AlgebraPackage| . ALGPKG) (|AlgebraGivenByStructuralConstants| . ALGSC) (|Any| . ANY) (|AnyFunctions1| . ANY1) (|ApplicationProgramInterface| . API) (|ArrayStack| . ASTACK) (|AssociatedJordanAlgebra| . JORDAN) (|AssociatedLieAlgebra| . LIE) (|AttachPredicates| . PMPRED) (|AxiomServer| . AXSERV) (|BalancedBinaryTree| . BBTREE) (|BasicOperator| . BOP) (|BasicOperatorFunctions1| . BOP1) (|Bezier| . BEZIER) (|BinaryExpansion| . BINARY) (|BinaryFile| . BINFILE) (|BinarySearchTree| . BSTREE) (|BinaryTournament| . BTOURN) (|BinaryTree| . BTREE) (|Bits| . BITS) (|Boolean| . BOOLEAN) (|CardinalNumber| . CARD) (|CartesianTensor| . CARTEN) (|CartesianTensorFunctions2| . CARTEN2) (|Character| . CHAR) (|CharacterClass| . CCLASS) (|CharacteristicPolynomialPackage| . CHARPOL) (|CliffordAlgebra| . CLIF) (|Color| . COLOR) (|CommonDenominator| . CDEN) (|Commutator| . COMM) (|Complex| . COMPLEX) (|ComplexFactorization| . COMPFACT) (|ComplexFunctions2| . COMPLEX2) (|ComplexRootPackage| . CMPLXRT) (|ComplexTrigonometricManipulations| . CTRIGMNP) (|ContinuedFraction| . CONTFRAC) (|CoordinateSystems| . COORDSYS) (|CRApackage| . CRAPACK) (|CycleIndicators| . CYCLES) (|Database| . DBASE) (|DataList| . DLIST) (|DecimalExpansion| . DECIMAL) (|DenavitHartenbergMatrix| . DHMATRIX) (|Dequeue| . DEQUEUE) (|DiophantineSolutionPackage| . DIOSP) (|DirectProductFunctions2| . DIRPROD2) (|DisplayPackage| . DISPLAY) (|DistinctDegreeFactorize| . DDFACT) (|DoubleFloat| . DFLOAT) (|DoubleFloatSpecialFunctions| . DFSFUN) (|DrawComplex| . DRAWCX) (|DrawNumericHack| . DRAWHACK) (|DrawOption| . DROPT) (|EigenPackage| . EP) (|ElementaryFunctionDefiniteIntegration| . DEFINTEF) (|ElementaryFunctionLODESolver| . LODEEF) (|ElementaryFunctionODESolver| . ODEEF) (|ElementaryFunctionSign| . SIGNEF) (|ElementaryFunctionStructurePackage| . EFSTRUC) (|Equation| . EQ) (|EquationFunctions2| . EQ2) (|ErrorFunctions| . ERROR) (|EuclideanGroebnerBasisPackage| . GBEUCLID) (|Exit| . EXIT) (|Expression| . EXPR) (|ExpressionFunctions2| . EXPR2) (|ExpressionSolve| . EXPRSOL) (|ExpressionSpaceFunctions2| . ES2) (|ExpressionSpaceODESolver| . EXPRODE) (|ExpressionToOpenMath| . OMEXPR) (|ExpressionToUnivariatePowerSeries| . EXPR2UPS) (|Factored| . FR) (|FactoredFunctions2| . FR2) (|File| . FILE) (|FileName| . FNAME) (|FiniteAbelianMonoidRingFunctions2| . FAMR2) (|FiniteDivisorFunctions2| . FDIV2) (|FiniteField| . FF) (|FiniteFieldCyclicGroup| . FFCG) (|FiniteFieldPolynomialPackage2| . FFPOLY2) (|FiniteFieldNormalBasis| . FFNB) (|FiniteFieldHomomorphisms| . FFHOM) (|FiniteLinearAggregateFunctions2| . FLAGG2) (|FiniteLinearAggregateSort| . FLASORT) (|FiniteSetAggregateFunctions2| . FSAGG2) (|FlexibleArray| . FARRAY) (|Float| . FLOAT) (|FloatingRealPackage| . FLOATRP) (|FloatingComplexPackage| . FLOATCP) (|FourierSeries| . FSERIES) (|Fraction| . FRAC) (|FractionalIdealFunctions2| . FRIDEAL2) (|FractionFreeFastGaussian| . FFFG) (|FractionFreeFastGaussianFractions| . FFFGF) (|FractionFunctions2| . FRAC2) (|FreeNilpotentLie| . FNLA) (|FullPartialFractionExpansion| . FPARFRAC) (|FunctionFieldCategoryFunctions2| . FFCAT2) (|FunctionSpaceAssertions| . PMASSFS) (|FunctionSpaceAttachPredicates| . PMPREDFS) (|FunctionSpaceComplexIntegration| . FSCINT) (|FunctionSpaceFunctions2| . FS2) (|FunctionSpaceIntegration| . FSINT) (|FunctionSpacePrimitiveElement| . FSPRMELT) (|FunctionSpaceSum| . SUMFS) (|GaussianFactorizationPackage| . GAUSSFAC) (|GeneralUnivariatePowerSeries| . GSERIES) (|GenerateUnivariatePowerSeries| . GENUPS) (|GraphicsDefaults| . GRDEF) (|GroebnerPackage| . GB) (|GroebnerFactorizationPackage| . GBF) (|Guess| . GUESS) (|GuessAlgebraicNumber| . GUESSAN) (|GuessFinite| . GUESSF) (|GuessFiniteFunctions| . GUESSF1) (|GuessInteger| . GUESSINT) (|GuessOption| . GOPT) (|GuessOptionFunctions0| . GOPT0) (|GuessPolynomial| . GUESSP) (|GuessUnivariatePolynomial| . GUESSUP) (|HallBasis| . HB) (|Heap| . HEAP) (|HexadecimalExpansion| . HEXADEC) (|IndexCard| . ICARD) (|IdealDecompositionPackage| . IDECOMP) (|InfiniteProductCharacteristicZero| . INFPROD0) (|InfiniteProductFiniteField| . INPRODFF) (|InfiniteProductPrimeField| . INPRODPF) (|InfiniteTuple| . ITUPLE) (|InfiniteTupleFunctions2| . ITFUN2) (|InfiniteTupleFunctions3| . ITFUN3) (|Infinity| . INFINITY) (|Integer| . INT) (|IntegerCombinatoricFunctions| . COMBINAT) (|IntegerLinearDependence| . ZLINDEP) (|IntegerNumberTheoryFunctions| . INTHEORY) (|IntegerPrimesPackage| . PRIMES) (|IntegerRetractions| . INTRET) (|IntegerRoots| . IROOT) (|IntegrationResultFunctions2| . IR2) (|IntegrationResultRFToFunction| . IRRF2F) (|IntegrationResultToFunction| . IR2F) (|Interval| . INTRVL) (|InventorDataSink| . IVDATA) (|InventorViewPort| . IVVIEW) (|InventorRenderPackage| . IVREND) (|InverseLaplaceTransform| . INVLAPLA) (|IrrRepSymNatPackage| . IRSN) (|KernelFunctions2| . KERNEL2) (|KeyedAccessFile| . KAFILE) (|LaplaceTransform| . LAPLACE) (|LazardMorenoSolvingPackage| . LAZM3PK) (|Library| . LIB) (|LieSquareMatrix| . LSQM) (|LinearOrdinaryDifferentialOperator| . LODO) (|LinearSystemMatrixPackage| . LSMP) (|LinearSystemMatrixPackage1| . LSMP1) (|LinearSystemPolynomialPackage| . LSPP) (|List| . LIST) (|ListFunctions2| . LIST2) (|ListFunctions3| . LIST3) (|ListToMap| . LIST2MAP) (|MakeFloatCompiledFunction| . MKFLCFN) (|MakeFunction| . MKFUNC) (|MakeRecord| . MKRECORD) (|MappingPackage1| . MAPPKG1) (|MappingPackage2| . MAPPKG2) (|MappingPackage3| . MAPPKG3) (|MappingPackage4| . MAPPKG4) (|MathMLFormat| . MMLFORM) (|Matrix| . MATRIX) (|MatrixCategoryFunctions2| . MATCAT2) (|MatrixCommonDenominator| . MCDEN) (|MatrixLinearAlgebraFunctions| . MATLIN) (|MergeThing| . MTHING) (|ModularDistinctDegreeFactorizer| . MDDFACT) (|ModuleOperator| . MODOP) (|MonoidRingFunctions2| . MRF2) (|MoreSystemCommands| . MSYSCMD) (|MPolyCatFunctions2| . MPC2) (|MPolyCatRationalFunctionFactorizer| . MPRFF) (|Multiset| . MSET) (|MultivariateFactorize| . MULTFACT) (|MultivariatePolynomial| . MPOLY) (|MultFiniteFactorize| . MFINFACT) (|MyUnivariatePolynomial| . MYUP) (|MyExpression| . MYEXPR) (|NoneFunctions1| . NONE1) (|NonNegativeInteger| . NNI) (|NottinghamGroup| . NOTTING) (|NormalizationPackage| . NORMPK) (|NormInMonogenicAlgebra| . NORMMA) (|NumberTheoreticPolynomialFunctions| . NTPOLFN) (|Numeric| . NUMERIC) (|NumericalOrdinaryDifferentialEquations| . NUMODE) (|NumericalQuadrature| . NUMQUAD) (|NumericComplexEigenPackage| . NCEP) (|NumericRealEigenPackage| . NREP) (|NumericContinuedFraction| . NCNTFRAC) (|Octonion| . OCT) (|OctonionCategoryFunctions2| . OCTCT2) (|OneDimensionalArray| . ARRAY1) (|OneDimensionalArrayFunctions2| . ARRAY12) (|OnePointCompletion| . ONECOMP) (|OnePointCompletionFunctions2| . ONECOMP2) (|OpenMathConnection| . OMCONN) (|OpenMathDevice| . OMDEV) (|OpenMathEncoding| . OMENC) (|OpenMathError| . OMERR) (|OpenMathErrorKind| . OMERRK) (|OpenMathPackage| . OMPKG) (|OpenMathServerPackage| . OMSERVER) (|OperationsQuery| . OPQUERY) (|OrderedCompletion| . ORDCOMP) (|OrderedCompletionFunctions2| . ORDCOMP2) (|OrdinaryDifferentialRing| . ODR) (|OrdSetInts| . OSI) (|OrthogonalPolynomialFunctions| . ORTHPOL) (|OutputPackage| . OUT) (|PadeApproximantPackage| . PADEPAC) (|Palette| . PALETTE) (|PartialFraction| . PFR) (|PatternFunctions2| . PATTERN2) (|ParametricPlaneCurve| . PARPCURV) (|ParametricSpaceCurve| . PARSCURV) (|ParametricSurface| . PARSURF) (|ParametricPlaneCurveFunctions2| . PARPC2) (|ParametricSpaceCurveFunctions2| . PARSC2) (|ParametricSurfaceFunctions2| . PARSU2) (|PartitionsAndPermutations| . PARTPERM) (|PatternMatch| . PATMATCH) (|PatternMatchAssertions| . PMASS) (|PatternMatchResultFunctions2| . PATRES2) (|PendantTree| . PENDTREE) (|Permanent| . PERMAN) (|PermutationGroupExamples| . PGE) (|PermutationGroup| . PERMGRP) (|Permutation| . PERM) (|Pi| . HACKPI) (|PiCoercions| . PICOERCE) (|PointFunctions2| . PTFUNC2) (|PolyGroebner| . PGROEB) (|Polynomial| . POLY) (|PolynomialAN2Expression| . PAN2EXPR) (|PolynomialComposition| . PCOMP) (|PolynomialDecomposition| . PDECOMP) (|PolynomialFunctions2| . POLY2) (|PolynomialIdeals| . IDEAL) (|PolynomialToUnivariatePolynomial| . POLY2UP) (|PositiveInteger| . PI) (|PowerSeriesLimitPackage| . LIMITPS) (|PrimeField| . PF) (|PrimitiveArrayFunctions2| . PRIMARR2) (|PrintPackage| . PRINT) (|QuadraticForm| . QFORM) (|QuasiComponentPackage| . QCMPACK) (|Quaternion| . QUAT) (|QuaternionCategoryFunctions2| . QUATCT2) (|QueryEquation| . QEQUAT) (|Queue| . QUEUE) (|QuotientFieldCategoryFunctions2| . QFCAT2) (|RadicalEigenPackage| . REP) (|RadicalSolvePackage| . SOLVERAD) (|RadixExpansion| . RADIX) (|RadixUtilities| . RADUTIL) (|RandomNumberSource| . RANDSRC) (|RationalFunction| . RF) (|RationalFunctionDefiniteIntegration| . DEFINTRF) (|RationalFunctionFactor| . RFFACT) (|RationalFunctionFactorizer| . RFFACTOR) (|RationalFunctionIntegration| . INTRF) (|RationalFunctionLimitPackage| . LIMITRF) (|RationalFunctionSign| . SIGNRF) (|RationalFunctionSum| . SUMRF) (|RationalRetractions| . RATRET) (|RealClosure| . RECLOS) (|RealPolynomialUtilitiesPackage| . POLUTIL) (|RealZeroPackage| . REAL0) (|RealZeroPackageQ| . REAL0Q) (|RecurrenceOperator| . RECOP) (|RectangularMatrixCategoryFunctions2| . RMCAT2) (|RegularSetDecompositionPackage| . RSDCMPK) (|RegularTriangularSet| . REGSET) (|RegularTriangularSetGcdPackage| . RSETGCD) (|RepresentationPackage1| . REP1) (|RepresentationPackage2| . REP2) (|ResolveLatticeCompletion| . RESLATC) (|RewriteRule| . RULE) (|RightOpenIntervalRootCharacterization| . ROIRC) (|RomanNumeral| . ROMAN) (|Ruleset| . RULESET) (|ScriptFormulaFormat| . FORMULA) (|ScriptFormulaFormat1| . FORMULA1) (|Segment| . SEG) (|SegmentBinding| . SEGBIND) (|SegmentBindingFunctions2| . SEGBIND2) (|SegmentFunctions2| . SEG2) (|Set| . SET) (|SimpleAlgebraicExtensionAlgFactor| . SAEFACT) (|SimplifyAlgebraicNumberConvertPackage| . SIMPAN) (|SingleInteger| . SINT) (|SmithNormalForm| . SMITH) (|SparseUnivariatePolynomialExpressions| . SUPEXPR) (|SparseUnivariatePolynomialFunctions2| . SUP2) (|SpecialOutputPackage| . SPECOUT) (|SquareFreeRegularSetDecompositionPackage| . SRDCMPK) (|SquareFreeRegularTriangularSet| . SREGSET) (|SquareFreeRegularTriangularSetGcdPackage| . SFRGCD) (|SquareFreeQuasiComponentPackage| . SFQCMPK) (|Stack| . STACK) (|Stream| . STREAM) (|StreamFunctions1| . STREAM1) (|StreamFunctions2| . STREAM2) (|StreamFunctions3| . STREAM3) (|String| . STRING) (|SturmHabichtPackage| . SHP) (|Symbol| . SYMBOL) (|SymmetricGroupCombinatoricFunctions| . SGCF) (|SystemSolvePackage| . SYSSOLP) (|SAERationalFunctionAlgFactor| . SAERFFC) (|Tableau| . TABLEAU) (|TaylorSeries| . TS) (|TaylorSolve| . UTSSOL) (|TexFormat| . TEX) (|TexFormat1| . TEX1) (|TextFile| . TEXTFILE) (|ThreeDimensionalViewport| . VIEW3D) (|ThreeSpace| . SPACE3) (|Timer| . TIMER) (|TopLevelDrawFunctions| . DRAW) (|TopLevelDrawFunctionsForAlgebraicCurves| . DRAWCURV) (|TopLevelDrawFunctionsForCompiledFunctions| . DRAWCFUN) (|TopLevelDrawFunctionsForPoints| . DRAWPT) (|TopLevelThreeSpace| . TOPSP) (|TranscendentalManipulations| . TRMANIP) (|TransSolvePackage| . SOLVETRA) (|Tree| . TREE) (|TrigonometricManipulations| . TRIGMNIP) (|UnivariateLaurentSeriesFunctions2| . ULS2) (|UnivariateFormalPowerSeries| . UFPS) (|UnivariateFormalPowerSeriesFunctions| . UFPS1) (|UnivariatePolynomial| . UP) (|UnivariatePolynomialCategoryFunctions2| . UPOLYC2) (|UnivariatePolynomialCommonDenominator| . UPCDEN) (|UnivariatePolynomialFunctions2| . UP2) (|UnivariatePolynomialMultiplicationPackage| . UPMP) (|UnivariatePuiseuxSeriesFunctions2| . UPXS2) (|UnivariateTaylorSeriesFunctions2| . UTS2) (|UniversalSegment| . UNISEG) (|UniversalSegmentFunctions2| . UNISEG2) (|UserDefinedVariableOrdering| . UDVO) (|Vector| . VECTOR) (|VectorFunctions2| . VECTOR2) (|ViewDefaultsPackage| . VIEWDEF) (|Void| . VOID) (|WuWenTsunTriangularSet| . WUTSET)) (|naglink| (|Asp1| . ASP1) (|Asp4| . ASP4) (|Asp6| . ASP6) (|Asp7| . ASP7) (|Asp8| . ASP8) (|Asp9| . ASP9) (|Asp10| . ASP10) (|Asp12| . ASP12) (|Asp19| . ASP19) (|Asp20| . ASP20) (|Asp24| . ASP24) (|Asp27| . ASP27) (|Asp28| . ASP28) (|Asp29| . ASP29) (|Asp30| . ASP30) (|Asp31| . ASP31) (|Asp33| . ASP33) (|Asp34| . ASP34) (|Asp35| . ASP35) (|Asp41| . ASP41) (|Asp42| . ASP42) (|Asp49| . ASP49) (|Asp50| . ASP50) (|Asp55| . ASP55) (|Asp73| . ASP73) (|Asp74| . ASP74) (|Asp77| . ASP77) (|Asp78| . ASP78) (|Asp80| . ASP80) (|FortranCode| . FC) (|FortranCodePackage1| . FCPAK1) (|FortranExpression| . FEXPR) (|FortranMachineTypeCategory| . FMTC) (|FortranMatrixCategory| . FMC) (|FortranMatrixFunctionCategory| . FMFUN) (|FortranOutputStackPackage| . FOP) (|FortranPackage| . FORT) (|FortranProgramCategory| . FORTCAT) (|FortranProgram| . FORTRAN) (|FortranFunctionCategory| . FORTFN) (|FortranScalarType| . FST) (|FortranType| . FT) (|FortranTemplate| . FTEM) (|FortranVectorFunctionCategory| . FVFUN) (|FortranVectorCategory| . FVC) (|MachineComplex| . MCMPLX) (|MachineFloat| . MFLOAT) (|MachineInteger| . MINT) (|MultiVariableCalculusFunctions| . MCALCFN) (|NagDiscreteFourierTransformInterfacePackage| . NAGDIS) (|NagEigenInterfacePackage| . NAGEIG) (|NAGLinkSupportPackage| . NAGSP) (|NagOptimisationInterfacePackage| . NAGOPT) (|NagQuadratureInterfacePackage| . NAGQUA) (|NagResultChecks| . NAGRES) (|NagSpecialFunctionsInterfacePackage| . NAGSPE) (|NagPolynomialRootsPackage| . NAGC02) (|NagRootFindingPackage| . NAGC05) (|NagSeriesSummationPackage| . NAGC06) (|NagIntegrationPackage| . NAGD01) (|NagOrdinaryDifferentialEquationsPackage| . NAGD02) (|NagPartialDifferentialEquationsPackage| . NAGD03) (|NagInterpolationPackage| . NAGE01) (|NagFittingPackage| . NAGE02) (|NagOptimisationPackage| . NAGE04) (|NagMatrixOperationsPackage| . NAGF01) (|NagEigenPackage| . NAGF02) (|NagLinearEquationSolvingPackage| . NAGF04) (|NagLapack| . NAGF07) (|NagSpecialFunctionsPackage| . NAGS) (|PackedHermitianSequence| . PACKED) (|Result| . RESULT) (|SimpleFortranProgram| . SFORT) (|Switch| . SWITCH) (|SymbolTable| . SYMTAB) (|TemplateUtilities| . TEMUTL) (|TheSymbolTable| . SYMS) (|ThreeDimensionalMatrix| . M3D)) (|anna| (|AnnaNumericalIntegrationPackage| . INTPACK) (|AnnaNumericalOptimizationPackage| . OPTPACK) (|AnnaOrdinaryDifferentialEquationPackage| . ODEPACK) (|AnnaPartialDifferentialEquationPackage| . PDEPACK) (|AttributeButtons| . ATTRBUT) (|BasicFunctions| . BFUNCT) (|d01ajfAnnaType| . D01AJFA) (|d01akfAnnaType| . D01AKFA) (|d01alfAnnaType| . D01ALFA) (|d01amfAnnaType| . D01AMFA) (|d01anfAnnaType| . D01ANFA) (|d01apfAnnaType| . D01APFA) (|d01aqfAnnaType| . D01AQFA) (|d01asfAnnaType| . D01ASFA) (|d01fcfAnnaType| . D01FCFA) (|d01gbfAnnaType| . D01GBFA) (|d01AgentsPackage| . D01AGNT) (|d01TransformFunctionType| . D01TRNS) (|d01WeightsPackage| . D01WGTS) (|d02AgentsPackage| . D02AGNT) (|d02bbfAnnaType| . D02BBFA) (|d02bhfAnnaType| . D02BHFA) (|d02cjfAnnaType| . D02CJFA) (|d02ejfAnnaType| . D02EJFA) (|d03AgentsPackage| . D03AGNT) (|d03eefAnnaType| . D03EEFA) (|d03fafAnnaType| . D03FAFA) (|e04AgentsPackage| . E04AGNT) (|e04dgfAnnaType| . E04DGFA) (|e04fdfAnnaType| . E04FDFA) (|e04gcfAnnaType| . E04GCFA) (|e04jafAnnaType| . E04JAFA) (|e04mbfAnnaType| . E04MBFA) (|e04nafAnnaType| . E04NAFA) (|e04ucfAnnaType| . E04UCFA) (|ExpertSystemContinuityPackage| . ESCONT) (|ExpertSystemContinuityPackage1| . ESCONT1) (|ExpertSystemToolsPackage| . ESTOOLS) (|ExpertSystemToolsPackage1| . ESTOOLS1) (|ExpertSystemToolsPackage2| . ESTOOLS2) (|NumericalIntegrationCategory| . NUMINT) (|NumericalIntegrationProblem| . NIPROB) (|NumericalODEProblem| . ODEPROB) (|NumericalOptimizationCategory| . OPTCAT) (|NumericalOptimizationProblem| . OPTPROB) (|NumericalPDEProblem| . PDEPROB) (|ODEIntensityFunctionsTable| . ODEIFTBL) (|IntegrationFunctionsTable| . INTFTBL) (|OrdinaryDifferentialEquationsSolverCategory| . ODECAT) (|PartialDifferentialEquationsSolverCategory| . PDECAT) (|RoutinesTable| . ROUTINE)) (|categories| (|AbelianGroup| . ABELGRP) (|AbelianMonoid| . ABELMON) (|AbelianMonoidRing| . AMR) (|AbelianSemiGroup| . ABELSG) (|Aggregate| . AGG) (|Algebra| . ALGEBRA) (|AlgebraicallyClosedField| . ACF) (|AlgebraicallyClosedFunctionSpace| . ACFS) (|ArcHyperbolicFunctionCategory| . AHYP) (|ArcTrigonometricFunctionCategory| . ATRIG) (|AssociationListAggregate| . ALAGG) (|AttributeRegistry| . ATTREG) (|BagAggregate| . BGAGG) (|BasicType| . BASTYPE) (|BiModule| . BMODULE) (|BinaryRecursiveAggregate| . BRAGG) (|BinaryTreeCategory| . BTCAT) (|BitAggregate| . BTAGG) (|CachableSet| . CACHSET) (|CancellationAbelianMonoid| . CABMON) (|CharacteristicNonZero| . CHARNZ) (|CharacteristicZero| . CHARZ) (|CoercibleTo| . KOERCE) (|Collection| . CLAGG) (|CombinatorialFunctionCategory| . CFCAT) (|CombinatorialOpsCategory| . COMBOPC) (|CommutativeRing| . COMRING) (|ComplexCategory| . COMPCAT) (|ConvertibleTo| . KONVERT) (|DequeueAggregate| . DQAGG) (|Dictionary| . DIAGG) (|DictionaryOperations| . DIOPS) (|DifferentialExtension| . DIFEXT) (|DifferentialPolynomialCategory| . DPOLCAT) (|DifferentialRing| . DIFRING) (|DifferentialVariableCategory| . DVARCAT) (|DirectProductCategory| . DIRPCAT) (|DivisionRing| . DIVRING) (|DoublyLinkedAggregate| . DLAGG) (|ElementaryFunctionCategory| . ELEMFUN) (|Eltable| . ELTAB) (|EltableAggregate| . ELTAGG) (|EntireRing| . ENTIRER) (|EuclideanDomain| . EUCDOM) (|Evalable| . EVALAB) (|ExpressionSpace| . ES) (|ExtensibleLinearAggregate| . ELAGG) (|ExtensionField| . XF) (|Field| . FIELD) (|FieldOfPrimeCharacteristic| . FPC) (|Finite| . FINITE) (|FileCategory| . FILECAT) (|FileNameCategory| . FNCAT) (|FiniteAbelianMonoidRing| . FAMR) (|FiniteAlgebraicExtensionField| . FAXF) (|FiniteDivisorCategory| . FDIVCAT) (|FiniteFieldCategory| . FFIELDC) (|FiniteLinearAggregate| . FLAGG) (|FiniteRankNonAssociativeAlgebra| . FINAALG) (|FiniteRankAlgebra| . FINRALG) (|FiniteSetAggregate| . FSAGG) (|FloatingPointSystem| . FPS) (|FramedAlgebra| . FRAMALG) (|FramedNonAssociativeAlgebra| . FRNAALG) (|FramedNonAssociativeAlgebraFunctions2| . FRNAAF2) (|FreeAbelianMonoidCategory| . FAMONC) (|FreeLieAlgebra| . FLALG) (|FreeModuleCat| . FMCAT) (|FullyEvalableOver| . FEVALAB) (|FullyLinearlyExplicitRingOver| . FLINEXP) (|FullyPatternMatchable| . FPATMAB) (|FullyRetractableTo| . FRETRCT) (|FunctionFieldCategory| . FFCAT) (|FunctionSpace| . FS) (|GcdDomain| . GCDDOM) (|GradedAlgebra| . GRALG) (|GradedModule| . GRMOD) (|Group| . GROUP) (|HomogeneousAggregate| . HOAGG) (|HyperbolicFunctionCategory| . HYPCAT) (|IndexedAggregate| . IXAGG) (|IndexedDirectProductCategory| . IDPC) (|InnerEvalable| . IEVALAB) (|IntegerNumberSystem| . INS) (|IntegralDomain| . INTDOM) (|IntervalCategory| . INTCAT) (|KeyedDictionary| . KDAGG) (|LazyStreamAggregate| . LZSTAGG) (|LeftAlgebra| . LALG) (|LeftModule| . LMODULE) (|LieAlgebra| . LIECAT) (|LinearAggregate| . LNAGG) (|LinearlyExplicitRingOver| . LINEXP) (|LinearOrdinaryDifferentialOperatorCategory| . LODOCAT) (|LiouvillianFunctionCategory| . LFCAT) (|ListAggregate| . LSAGG) (|Logic| . LOGIC) (|MatrixCategory| . MATCAT) (|Module| . MODULE) (|Monad| . MONAD) (|MonadWithUnit| . MONADWU) (|Monoid| . MONOID) (|MonogenicAlgebra| . MONOGEN) (|MonogenicLinearOperator| . MLO) (|MultiDictionary| . MDAGG) (|MultisetAggregate| . MSETAGG) (|MultivariateTaylorSeriesCategory| . MTSCAT) (|NonAssociativeAlgebra| . NAALG) (|NonAssociativeRing| . NASRING) (|NonAssociativeRng| . NARNG) (|NormalizedTriangularSetCategory| . NTSCAT) (|Object| . OBJECT) (|OctonionCategory| . OC) (|OneDimensionalArrayAggregate| . A1AGG) (|OpenMath| . OM) (|OrderedAbelianGroup| . OAGROUP) (|OrderedAbelianMonoid| . OAMON) (|OrderedAbelianMonoidSup| . OAMONS) (|OrderedAbelianSemiGroup| . OASGP) (|OrderedCancellationAbelianMonoid| . OCAMON) (|OrderedFinite| . ORDFIN) (|OrderedIntegralDomain| . OINTDOM) (|OrderedMonoid| . ORDMON) (|OrderedMultisetAggregate| . OMSAGG) (|OrderedRing| . ORDRING) (|OrderedSet| . ORDSET) (|PAdicIntegerCategory| . PADICCT) (|PartialDifferentialRing| . PDRING) (|PartialTranscendentalFunctions| . PTRANFN) (|Patternable| . PATAB) (|PatternMatchable| . PATMAB) (|PermutationCategory| . PERMCAT) (|PlottablePlaneCurveCategory| . PPCURVE) (|PlottableSpaceCurveCategory| . PSCURVE) (|PointCategory| . PTCAT) (|PolynomialCategory| . POLYCAT) (|PolynomialFactorizationExplicit| . PFECAT) (|PolynomialSetCategory| . PSETCAT) (|PowerSeriesCategory| . PSCAT) (|PrimitiveFunctionCategory| . PRIMCAT) (|PrincipalIdealDomain| . PID) (|PriorityQueueAggregate| . PRQAGG) (|QuaternionCategory| . QUATCAT) (|QueueAggregate| . QUAGG) (|QuotientFieldCategory| . QFCAT) (|RadicalCategory| . RADCAT) (|RealClosedField| . RCFIELD) (|RealConstant| . REAL) (|RealNumberSystem| . RNS) (|RealRootCharacterizationCategory| . RRCC) (|RectangularMatrixCategory| . RMATCAT) (|RecursiveAggregate| . RCAGG) (|RecursivePolynomialCategory| . RPOLCAT) (|RegularChain| . RGCHAIN) (|RegularTriangularSetCategory| . RSETCAT) (|RetractableTo| . RETRACT) (|RightModule| . RMODULE) (|Ring| . RING) (|Rng| . RNG) (|SegmentCategory| . SEGCAT) (|SegmentExpansionCategory| . SEGXCAT) (|SemiGroup| . SGROUP) (|SetAggregate| . SETAGG) (|SetCategory| . SETCAT) (|SExpressionCategory| . SEXCAT) (|SpecialFunctionCategory| . SPFCAT) (|SquareFreeNormalizedTriangularSetCategory| . SNTSCAT) (|SquareFreeRegularTriangularSetCategory| . SFRTCAT) (|SquareMatrixCategory| . SMATCAT) (|StackAggregate| . SKAGG) (|StepThrough| . STEP) (|StreamAggregate| . STAGG) (|StringAggregate| . SRAGG) (|StringCategory| . STRICAT) (|StructuralConstantsPackage| . SCPKG) (|TableAggregate| . TBAGG) (|ThreeSpaceCategory| . SPACEC) (|TranscendentalFunctionCategory| . TRANFUN) (|TriangularSetCategory| . TSETCAT) (|TrigonometricFunctionCategory| . TRIGCAT) (|TwoDimensionalArrayCategory| . ARR2CAT) (|Type| . TYPE) (|UnaryRecursiveAggregate| . URAGG) (|UniqueFactorizationDomain| . UFD) (|UnivariateLaurentSeriesCategory| . ULSCAT) (|UnivariateLaurentSeriesConstructorCategory| . ULSCCAT) (|UnivariatePolynomialCategory| . UPOLYC) (|UnivariatePowerSeriesCategory| . UPSCAT) (|UnivariatePuiseuxSeriesCategory| . UPXSCAT) (|UnivariatePuiseuxSeriesConstructorCategory| . UPXSCCA) (|UnivariateSkewPolynomialCategory| . OREPCAT) (|UnivariateTaylorSeriesCategory| . UTSCAT) (|VectorCategory| . VECTCAT) (|VectorSpace| . VSPACE) (|XAlgebra| . XALG) (|XFreeAlgebra| . XFALG) (|XPolynomialsCat| . XPOLYC) (|ZeroDimensionalSolvePackage| . ZDSOLVE)) (|Hidden| (|AlgebraicFunction| . AF) (|AlgebraicFunctionField| . ALGFF) (|AlgebraicHermiteIntegration| . INTHERAL) (|AlgebraicIntegrate| . INTALG) (|AlgebraicIntegration| . INTAF) (|AnonymousFunction| . ANON) (|AntiSymm| . ANTISYM) (|ApplyRules| . APPRULE) (|ApplyUnivariateSkewPolynomial| . APPLYORE) (|ArrayStack| . ASTACK) (|AssociatedEquations| . ASSOCEQ) (|AssociationList| . ALIST) (|Automorphism| . AUTOMOR) (|BalancedFactorisation| . BALFACT) (|BalancedPAdicInteger| . BPADIC) (|BalancedPAdicRational| . BPADICRT) (|BezoutMatrix| . BEZOUT) (|BoundIntegerRoots| . BOUNDZRO) (|BrillhartTests| . BRILL) (|ChangeOfVariable| . CHVAR) (|CharacteristicPolynomialInMonogenicalAlgebra| . CPIMA) (|ChineseRemainderToolsForIntegralBases| . IBACHIN) (|CoerceVectorMatrixPackage| . CVMP) (|CombinatorialFunction| . COMBF) (|CommonOperators| . COMMONOP) (|CommuteUnivariatePolynomialCategory| . COMMUPC) (|ComplexIntegerSolveLinearPolynomialEquation| . CINTSLPE) (|ComplexPattern| . COMPLPAT) (|ComplexPatternMatch| . CPMATCH) (|ComplexRootFindingPackage| . CRFP) (|ConstantLODE| . ODECONST) (|CyclicStreamTools| . CSTTOOLS) (|CyclotomicPolynomialPackage| . CYCLOTOM) (|DefiniteIntegrationTools| . DFINTTLS) (|DegreeReductionPackage| . DEGRED) (|DeRhamComplex| . DERHAM) (|DifferentialSparseMultivariatePolynomial| . DSMP) (|DirectProduct| . DIRPROD) (|DirectProductMatrixModule| . DPMM) (|DirectProductModule| . DPMO) (|DiscreteLogarithmPackage| . DLP) (|DistributedMultivariatePolynomial| . DMP) (|DoubleResultantPackage| . DBLRESP) (|DrawOptionFunctions0| . DROPT0) (|DrawOptionFunctions1| . DROPT1) (|ElementaryFunction| . EF) (|ElementaryFunctionsUnivariateLaurentSeries| . EFULS) (|ElementaryFunctionsUnivariatePuiseuxSeries| . EFUPXS) (|ElementaryIntegration| . INTEF) (|ElementaryRischDE| . RDEEF) (|ElementaryRischDESystem| . RDEEFS) (|EllipticFunctionsUnivariateTaylorSeries| . ELFUTS) (|EqTable| . EQTBL) (|EuclideanModularRing| . EMR) (|EvaluateCycleIndicators| . EVALCYC) (|ExponentialExpansion| . EXPEXPAN) (|ExponentialOfUnivariatePuiseuxSeries| . EXPUPXS) (|ExpressionSpaceFunctions1| . ES1) (|ExpressionTubePlot| . EXPRTUBE) (|ExtAlgBasis| . EAB) (|FactoredFunctions| . FACTFUNC) (|FactoredFunctionUtilities| . FRUTIL) (|FactoringUtilities| . FACUTIL) (|FGLMIfCanPackage| . FGLMICPK) (|FindOrderFinite| . FORDER) (|FiniteDivisor| . FDIV) (|FiniteFieldCyclicGroupExtension| . FFCGX) (|FiniteFieldCyclicGroupExtensionByPolynomial| . FFCGP) (|FiniteFieldExtension| . FFX) (|FiniteFieldExtensionByPolynomial| . FFP) (|FiniteFieldFunctions| . FFF) (|FiniteFieldNormalBasisExtension| . FFNBX) (|FiniteFieldNormalBasisExtensionByPolynomial| . FFNBP) (|FiniteFieldPolynomialPackage| . FFPOLY) (|FiniteFieldSolveLinearPolynomialEquation| . FFSLPE) (|FormalFraction| . FORMAL) (|FourierComponent| . FCOMP) (|FractionalIdeal| . FRIDEAL) (|FramedModule| . FRMOD) (|FreeAbelianGroup| . FAGROUP) (|FreeAbelianMonoid| . FAMONOID) (|FreeGroup| . FGROUP) (|FreeModule| . FM) (|FreeModule1| . FM1) (|FreeMonoid| . FMONOID) (|FunctionalSpecialFunction| . FSPECF) (|FunctionCalled| . FUNCTION) (|FunctionFieldIntegralBasis| . FFINTBAS) (|FunctionSpaceReduce| . FSRED) (|FunctionSpaceToUnivariatePowerSeries| . FS2UPS) (|FunctionSpaceToExponentialExpansion| . FS2EXPXP) (|FunctionSpaceUnivariatePolynomialFactor| . FSUPFACT) (|GaloisGroupFactorizationUtilities| . GALFACTU) (|GaloisGroupFactorizer| . GALFACT) (|GaloisGroupPolynomialUtilities| . GALPOLYU) (|GaloisGroupUtilities| . GALUTIL) (|GeneralHenselPackage| . GHENSEL) (|GeneralDistributedMultivariatePolynomial| . GDMP) (|GeneralPolynomialGcdPackage| . GENPGCD) (|GeneralSparseTable| . GSTBL) (|GenericNonAssociativeAlgebra| . GCNAALG) (|GenExEuclid| . GENEEZ) (|GeneralizedMultivariateFactorize| . GENMFACT) (|GeneralModulePolynomial| . GMODPOL) (|GeneralPolynomialSet| . GPOLSET) (|GeneralTriangularSet| . GTSET) (|GenUFactorize| . GENUFACT) (|GenusZeroIntegration| . INTG0) (|GosperSummationMethod| . GOSPER) (|GraphImage| . GRIMAGE) (|GrayCode| . GRAY) (|GroebnerInternalPackage| . GBINTERN) (|GroebnerSolve| . GROEBSOL) (|HashTable| . HASHTBL) (|Heap| . HEAP) (|HeuGcd| . HEUGCD) (|HomogeneousDistributedMultivariatePolynomial| . HDMP) (|HyperellipticFiniteDivisor| . HELLFDIV) (|IncrementingMaps| . INCRMAPS) (|IndexedBits| . IBITS) (|IndexedDirectProductAbelianGroup| . IDPAG) (|IndexedDirectProductAbelianMonoid| . IDPAM) (|IndexedDirectProductObject| . IDPO) (|IndexedDirectProductOrderedAbelianMonoid| . IDPOAM) (|IndexedDirectProductOrderedAbelianMonoidSup| . IDPOAMS) (|IndexedExponents| . INDE) (|IndexedFlexibleArray| . IFARRAY) (|IndexedList| . ILIST) (|IndexedMatrix| . IMATRIX) (|IndexedOneDimensionalArray| . IARRAY1) (|IndexedString| . ISTRING) (|IndexedTwoDimensionalArray| . IARRAY2) (|IndexedVector| . IVECTOR) (|InnerAlgFactor| . IALGFACT) (|InnerAlgebraicNumber| . IAN) (|InnerCommonDenominator| . ICDEN) (|InnerFiniteField| . IFF) (|InnerFreeAbelianMonoid| . IFAMON) (|InnerIndexedTwoDimensionalArray| . IIARRAY2) (|InnerMatrixLinearAlgebraFunctions| . IMATLIN) (|InnerMatrixQuotientFieldFunctions| . IMATQF) (|InnerModularGcd| . INMODGCD) (|InnerMultFact| . INNMFACT) (|InnerNormalBasisFieldFunctions| . INBFF) (|InnerNumericEigenPackage| . INEP) (|InnerNumericFloatSolvePackage| . INFSP) (|InnerPAdicInteger| . IPADIC) (|InnerPolySign| . INPSIGN) (|InnerPolySum| . ISUMP) (|InnerPrimeField| . IPF) (|InnerSparseUnivariatePowerSeries| . ISUPS) (|InnerTable| . INTABL) (|InnerTaylorSeries| . ITAYLOR) (|InnerTrigonometricManipulations| . ITRIGMNP) (|InputForm| . INFORM) (|InputFormFunctions1| . INFORM1) (|IntegerBits| . INTBIT) (|IntegerFactorizationPackage| . INTFACT) (|IntegerMod| . ZMOD) (|IntegerSolveLinearPolynomialEquation| . INTSLPE) (|IntegralBasisPolynomialTools| . IBPTOOLS) (|IntegralBasisTools| . IBATOOL) (|IntegrationResult| . IR) (|IntegrationTools| . INTTOOLS) (|InternalPrintPackage| . IPRNTPK) (|InternalRationalUnivariateRepresentationPackage| . IRURPK) (|IrredPolyOverFiniteField| . IRREDFFX) (|Kernel| . KERNEL) (|Kovacic| . KOVACIC) (|LaurentPolynomial| . LAUPOL) (|LeadingCoefDetermination| . LEADCDET) (|LexTriangularPackage| . LEXTRIPK) (|LieExponentials| . LEXP) (|LiePolynomial| . LPOLY) (|LinearDependence| . LINDEP) (|LinearOrdinaryDifferentialOperatorFactorizer| . LODOF) (|LinearOrdinaryDifferentialOperator1| . LODO1) (|LinearOrdinaryDifferentialOperator2| . LODO2) (|LinearOrdinaryDifferentialOperatorsOps| . LODOOPS) (|LinearPolynomialEquationByFractions| . LPEFRAC) (|LinGroebnerPackage| . LGROBP) (|LiouvillianFunction| . LF) (|ListMonoidOps| . LMOPS) (|ListMultiDictionary| . LMDICT) (|LocalAlgebra| . LA) (|Localize| . LO) (|LyndonWord| . LWORD) (|Magma| . MAGMA) (|MakeBinaryCompiledFunction| . MKBCFUNC) (|MakeCachableSet| . MKCHSET) (|MakeUnaryCompiledFunction| . MKUCFUNC) (|MappingPackageInternalHacks1| . MAPHACK1) (|MappingPackageInternalHacks2| . MAPHACK2) (|MappingPackageInternalHacks3| . MAPHACK3) (|MeshCreationRoutinesForThreeDimensions| . MESH) (|ModMonic| . MODMON) (|ModularField| . MODFIELD) (|ModularHermitianRowReduction| . MHROWRED) (|ModularRing| . MODRING) (|ModuleMonomial| . MODMONOM) (|MoebiusTransform| . MOEBIUS) (|MonoidRing| . MRING) (|MonomialExtensionTools| . MONOTOOL) (|MPolyCatPolyFactorizer| . MPCPF) (|MPolyCatFunctions3| . MPC3) (|MRationalFactorize| . MRATFAC) (|MultipleMap| . MMAP) (|MultivariateLifting| . MLIFT) (|MultivariateSquareFree| . MULTSQFR) (|HomogeneousDirectProduct| . HDP) (|NewSparseMultivariatePolynomial| . NSMP) (|NewSparseUnivariatePolynomial| . NSUP) (|NewSparseUnivariatePolynomialFunctions2| . NSUP2) (|NonCommutativeOperatorDivision| . NCODIV) (|NewtonInterpolation| . NEWTON) (|None| . NONE) (|NonLinearFirstOrderODESolver| . NODE1) (|NonLinearSolvePackage| . NLINSOL) (|NormRetractPackage| . NORMRETR) (|NPCoef| . NPCOEF) (|NumberFormats| . NUMFMT) (|NumberFieldIntegralBasis| . NFINTBAS) (|NumericTubePlot| . NUMTUBE) (|ODEIntegration| . ODEINT) (|ODETools| . ODETOOLS) (|Operator| . OP) (|OppositeMonogenicLinearOperator| . OMLO) (|OrderedDirectProduct| . ODP) (|OrderedFreeMonoid| . OFMONOID) (|OrderedVariableList| . OVAR) (|OrderingFunctions| . ORDFUNS) (|OrderlyDifferentialPolynomial| . ODPOL) (|OrderlyDifferentialVariable| . ODVAR) (|OrdinaryWeightedPolynomials| . OWP) (|OutputForm| . OUTFORM) (|PadeApproximants| . PADE) (|PAdicInteger| . PADIC) (|PAdicRational| . PADICRAT) (|PAdicRationalConstructor| . PADICRC) (|PAdicWildFunctionFieldIntegralBasis| . PWFFINTB) (|ParadoxicalCombinatorsForStreams| . YSTREAM) (|ParametricLinearEquations| . PLEQN) (|PartialFractionPackage| . PFRPAC) (|Partition| . PRTITION) (|Pattern| . PATTERN) (|PatternFunctions1| . PATTERN1) (|PatternMatchFunctionSpace| . PMFS) (|PatternMatchIntegerNumberSystem| . PMINS) (|PatternMatchIntegration| . INTPM) (|PatternMatchKernel| . PMKERNEL) (|PatternMatchListAggregate| . PMLSAGG) (|PatternMatchListResult| . PATLRES) (|PatternMatchPolynomialCategory| . PMPLCAT) (|PatternMatchPushDown| . PMDOWN) (|PatternMatchQuotientFieldCategory| . PMQFCAT) (|PatternMatchResult| . PATRES) (|PatternMatchSymbol| . PMSYM) (|PatternMatchTools| . PMTOOLS) (|PlaneAlgebraicCurvePlot| . ACPLOT) (|Plot| . PLOT) (|PlotFunctions1| . PLOT1) (|PlotTools| . PLOTTOOL) (|Plot3D| . PLOT3D) (|PoincareBirkhoffWittLyndonBasis| . PBWLB) (|Point| . POINT) (|PointsOfFiniteOrder| . PFO) (|PointsOfFiniteOrderRational| . PFOQ) (|PointsOfFiniteOrderTools| . PFOTOOLS) (|PointPackage| . PTPACK) (|PolToPol| . POLTOPOL) (|PolynomialCategoryLifting| . POLYLIFT) (|PolynomialCategoryQuotientFunctions| . POLYCATQ) (|PolynomialFactorizationByRecursion| . PFBR) (|PolynomialFactorizationByRecursionUnivariate| . PFBRU) (|PolynomialGcdPackage| . PGCD) (|PolynomialInterpolation| . PINTERP) (|PolynomialInterpolationAlgorithms| . PINTERPA) (|PolynomialNumberTheoryFunctions| . PNTHEORY) (|PolynomialRing| . PR) (|PolynomialRoots| . POLYROOT) (|PolynomialSetUtilitiesPackage| . PSETPK) (|PolynomialSolveByFormulas| . SOLVEFOR) (|PolynomialSquareFree| . PSQFR) (|PrecomputedAssociatedEquations| . PREASSOC) (|PrimitiveArray| . PRIMARR) (|PrimitiveElement| . PRIMELT) (|PrimitiveRatDE| . ODEPRIM) (|PrimitiveRatRicDE| . ODEPRRIC) (|Product| . PRODUCT) (|PseudoRemainderSequence| . PRS) (|PseudoLinearNormalForm| . PSEUDLIN) (|PureAlgebraicIntegration| . INTPAF) (|PureAlgebraicLODE| . ODEPAL) (|PushVariables| . PUSHVAR) (|QuasiAlgebraicSet| . QALGSET) (|QuasiAlgebraicSet2| . QALGSET2) (|RadicalFunctionField| . RADFF) (|RandomDistributions| . RDIST) (|RandomFloatDistributions| . RFDIST) (|RandomIntegerDistributions| . RIDIST) (|RationalFactorize| . RATFACT) (|RationalIntegration| . INTRAT) (|RationalInterpolation| . RINTERP) (|RationalLODE| . ODERAT) (|RationalRicDE| . ODERTRIC) (|RationalUnivariateRepresentationPackage| . RURPK) (|RealSolvePackage| . REALSOLV) (|RectangularMatrix| . RMATRIX) (|ReducedDivisor| . RDIV) (|ReduceLODE| . ODERED) (|ReductionOfOrder| . REDORDER) (|Reference| . REF) (|RepeatedDoubling| . REPDB) (|RepeatedSquaring| . REPSQ) (|ResidueRing| . RESRING) (|RetractSolvePackage| . RETSOL) (|RuleCalled| . RULECOLD) (|SetOfMIntegersInOneToN| . SETMN) (|SExpression| . SEX) (|SExpressionOf| . SEXOF) (|SequentialDifferentialPolynomial| . SDPOL) (|SequentialDifferentialVariable| . SDVAR) (|SimpleAlgebraicExtension| . SAE) (|SingletonAsOrderedSet| . SAOS) (|SortedCache| . SCACHE) (|SortPackage| . SORTPAK) (|SparseMultivariatePolynomial| . SMP) (|SparseMultivariateTaylorSeries| . SMTS) (|SparseTable| . STBL) (|SparseUnivariatePolynomial| . SUP) (|SparseUnivariateSkewPolynomial| . ORESUP) (|SparseUnivariateLaurentSeries| . SULS) (|SparseUnivariatePuiseuxSeries| . SUPXS) (|SparseUnivariateTaylorSeries| . SUTS) (|SplitHomogeneousDirectProduct| . SHDP) (|SplittingNode| . SPLNODE) (|SplittingTree| . SPLTREE) (|SquareMatrix| . SQMATRIX) (|Stack| . STACK) (|StorageEfficientMatrixOperations| . MATSTOR) (|StreamInfiniteProduct| . STINPROD) (|StreamTaylorSeriesOperations| . STTAYLOR) (|StreamTranscendentalFunctions| . STTF) (|StreamTranscendentalFunctionsNonCommutative| . STTFNC) (|StringTable| . STRTBL) (|SubResultantPackage| . SUBRESP) (|SubSpace| . SUBSPACE) (|SubSpaceComponentProperty| . COMPPROP) (|SuchThat| . SUCH) (|SupFractionFactorizer| . SUPFRACF) (|SymmetricFunctions| . SYMFUNC) (|SymmetricPolynomial| . SYMPOLY) (|SystemODESolver| . ODESYS) (|Table| . TABLE) (|TableauxBumpers| . TABLBUMP) (|TabulatedComputationPackage| . TBCMPPK) (|TangentExpansions| . TANEXP) (|ToolsForSign| . TOOLSIGN) (|TranscendentalHermiteIntegration| . INTHERTR) (|TranscendentalIntegration| . INTTR) (|TranscendentalRischDE| . RDETR) (|TranscendentalRischDESystem| . RDETRS) (|TransSolvePackageService| . SOLVESER) (|TriangularMatrixOperations| . TRIMAT) (|TubePlot| . TUBE) (|TubePlotTools| . TUBETOOL) (|Tuple| . TUPLE) (|TwoDimensionalArray| . ARRAY2) (|TwoDimensionalPlotClipping| . CLIP) (|TwoDimensionalViewport| . VIEW2D) (|TwoFactorize| . TWOFACT) (|UnivariateFactorize| . UNIFACT) (|UnivariateLaurentSeries| . ULS) (|UnivariateLaurentSeriesConstructor| . ULSCONS) (|UnivariatePolynomialDecompositionPackage| . UPDECOMP) (|UnivariatePolynomialDivisionPackage| . UPDIVP) (|UnivariatePolynomialSquareFree| . UPSQFREE) (|UnivariatePuiseuxSeries| . UPXS) (|UnivariatePuiseuxSeriesConstructor| . UPXSCONS) (|UnivariatePuiseuxSeriesWithExponentialSingularity| . UPXSSING) (|UnivariateSkewPolynomial| . OREUP) (|UnivariateSkewPolynomialCategoryOps| . OREPCTO) (|UnivariateTaylorSeries| . UTS) (|UnivariateTaylorSeriesODESolver| . UTSODE) (|UserDefinedPartialOrdering| . UDPO) (|UTSodetools| . UTSODETL) (|Variable| . VARIABLE) (|ViewportPackage| . VIEW) (|WeierstrassPreparation| . WEIER) (|WeightedPolynomials| . WP) (|WildFunctionFieldIntegralBasis| . WFFINTBS) (|XDistributedPolynomial| . XDPOLY) (|XExponentialPackage| . XEXPPKG) (|XPBWPolynomial| . XPBWPOLY) (|XPolynomial| . XPOLY) (|XPolynomialRing| . XPR) (|XRecursivePolynomial| . XRPOLY)) (|defaults| (|AbelianGroup&| . ABELGRP-) (|AbelianMonoid&| . ABELMON-) (|AbelianMonoidRing&| . AMR-) (|AbelianSemiGroup&| . ABELSG-) (|Aggregate&| . AGG-) (|Algebra&| . ALGEBRA-) (|AlgebraicallyClosedField&| . ACF-) (|AlgebraicallyClosedFunctionSpace&| . ACFS-) (|ArcTrigonometricFunctionCategory&| . ATRIG-) (|BagAggregate&| . BGAGG-) (|BasicType&| . BASTYPE-) (|BinaryRecursiveAggregate&| . BRAGG-) (|BinaryTreeCategory&| . BTCAT-) (|BitAggregate&| . BTAGG-) (|Collection&| . CLAGG-) (|ComplexCategory&| . COMPCAT-) (|Dictionary&| . DIAGG-) (|DictionaryOperations&| . DIOPS-) (|DifferentialExtension&| . DIFEXT-) (|DifferentialPolynomialCategory&| . DPOLCAT-) (|DifferentialRing&| . DIFRING-) (|DifferentialVariableCategory&| . DVARCAT-) (|DirectProductCategory&| . DIRPCAT-) (|DivisionRing&| . DIVRING-) (|ElementaryFunctionCategory&| . ELEMFUN-) (|EltableAggregate&| . ELTAGG-) (|EuclideanDomain&| . EUCDOM-) (|Evalable&| . EVALAB-) (|ExpressionSpace&| . ES-) (|ExtensibleLinearAggregate&| . ELAGG-) (|ExtensionField&| . XF-) (|Field&| . FIELD-) (|FieldOfPrimeCharacteristic&| . FPC-) (|FiniteAbelianMonoidRing&| . FAMR-) (|FiniteAlgebraicExtensionField&| . FAXF-) (|FiniteDivisorCategory&| . FDIVCAT-) (|FiniteFieldCategory&| . FFIELDC-) (|FiniteLinearAggregate&| . FLAGG-) (|FiniteSetAggregate&| . FSAGG-) (|FiniteRankAlgebra&| . FINRALG-) (|FiniteRankNonAssociativeAlgebra&| . FINAALG-) (|FloatingPointSystem&| . FPS-) (|FramedAlgebra&| . FRAMALG-) (|FramedNonAssociativeAlgebra&| . FRNAALG-) (|FullyEvalableOver&| . FEVALAB-) (|FullyLinearlyExplicitRingOver&| . FLINEXP-) (|FullyRetractableTo&| . FRETRCT-) (|FunctionFieldCategory&| . FFCAT-) (|FunctionSpace&| . FS-) (|GcdDomain&| . GCDDOM-) (|GradedAlgebra&| . GRALG-) (|GradedModule&| . GRMOD-) (|Group&| . GROUP-) (|HomogeneousAggregate&| . HOAGG-) (|HyperbolicFunctionCategory&| . HYPCAT-) (|IndexedAggregate&| . IXAGG-) (|InnerEvalable&| . IEVALAB-) (|IntegerNumberSystem&| . INS-) (|IntegralDomain&| . INTDOM-) (|KeyedDictionary&| . KDAGG-) (|LazyStreamAggregate&| . LZSTAGG-) (|LeftAlgebra&| . LALG-) (|LieAlgebra&| . LIECAT-) (|LinearAggregate&| . LNAGG-) (|ListAggregate&| . LSAGG-) (|Logic&| . LOGIC-) (|LinearOrdinaryDifferentialOperatorCategory&| . LODOCAT-) (|MatrixCategory&| . MATCAT-) (|Module&| . MODULE-) (|Monad&| . MONAD-) (|MonadWithUnit&| . MONADWU-) (|Monoid&| . MONOID-) (|MonogenicAlgebra&| . MONOGEN-) (|NonAssociativeAlgebra&| . NAALG-) (|NonAssociativeRing&| . NASRING-) (|NonAssociativeRng&| . NARNG-) (|OctonionCategory&| . OC-) (|OneDimensionalArrayAggregate&| . A1AGG-) (|OrderedRing&| . ORDRING-) (|OrderedSet&| . ORDSET-) (|PartialDifferentialRing&| . PDRING-) (|PolynomialCategory&| . POLYCAT-) (|PolynomialFactorizationExplicit&| . PFECAT-) (|PolynomialSetCategory&| . PSETCAT-) (|PowerSeriesCategory&| . PSCAT-) (|QuaternionCategory&| . QUATCAT-) (|QuotientFieldCategory&| . QFCAT-) (|RadicalCategory&| . RADCAT-) (|RealClosedField&| . RCFIELD-) (|RealNumberSystem&| . RNS-) (|RealRootCharacterizationCategory&| . RRCC-) (|RectangularMatrixCategory&| . RMATCAT-) (|RecursiveAggregate&| . RCAGG-) (|RecursivePolynomialCategory&| . RPOLCAT-) (|RegularTriangularSetCategory&| . RSETCAT-) (|RetractableTo&| . RETRACT-) (|Ring&| . RING-) (|SemiGroup&| . SGROUP-) (|SetAggregate&| . SETAGG-) (|SetCategory&| . SETCAT-) (|SquareMatrixCategory&| . SMATCAT-) (|StreamAggregate&| . STAGG-) (|StringAggregate&| . SRAGG-) (|TableAggregate&| . TBAGG-) (|TranscendentalFunctionCategory&| . TRANFUN-) (|TriangularSetCategory&| . TSETCAT-) (|TrigonometricFunctionCategory&| . TRIGCAT-) (|TwoDimensionalArrayCategory&| . ARR2CAT-) (|UnaryRecursiveAggregate&| . URAGG-) (|UniqueFactorizationDomain&| . UFD-) (|UnivariateLaurentSeriesConstructorCategory&| . ULSCCAT-) (|UnivariatePolynomialCategory&| . UPOLYC-) (|UnivariatePowerSeriesCategory&| . UPSCAT-) (|UnivariatePuiseuxSeriesConstructorCategory&| . UPXSCCA-) (|UnivariateSkewPolynomialCategory&| . OREPCAT-) (|UnivariateTaylorSeriesCategory&| . UTSCAT-) (|VectorCategory&| . VECTCAT-) (|VectorSpace&| . VSPACE-)))
--E 155

--S 156 of 237
)lisp (identity |$HistList|)
 
Value = #0=(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL . #0#)
--R 
--RValue = #0=(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL . #0#)
--E 156

--S 157 of 237
)lisp (identity |$HistListAct|)
 
Value = 0
--R 
--RValue = 0
--E 157

--S 158 of 237
)lisp (identity |$HistListLen|)
 
Value = 20
--R 
--RValue = 20
--E 158

--S 159 of 237
)lisp (identity |$HistRecord|)
 
Value = NIL
--R 
--RValue = NIL
--E 159

--S 160 of 237
)lisp (identity |$inLispVM|)
 
Value = NIL
--R 
--RValue = NIL
--E 160

--S 161 of 237
)lisp (identity |$inclAssertions|)
 
Value = (AIX |CommonLisp|)
--R 
--RValue = (AIX |CommonLisp|)
--E 161

--S 162 of 237
)lisp (identity |$InitialModemapFrame|)) )
 
Value = ((NIL))
--R 
--RValue = ((NIL))
--E 162

--S 163 of 237
)lisp (identity in-stream)
 
Value = #<synonym stream to *STANDARD-INPUT*>
--R 
--RValue = #<synonym stream to *STANDARD-INPUT*>
--E 163

--S 164 of 237
)lisp (identity |$InteractiveMode|)
 
Value = T
--R 
--RValue = T
--E 164

--S 165 of 237
)lisp (identity |$InteractiveFrame| )
 
Value = ((NIL))
--R 
--RValue = ((NIL))
--E 165

--S 166 of 237
)lisp (identity |$internalHistoryTable|)
 
Value = NIL
--R 
--RValue = NIL
--E 166

--S 167 of 237
)lisp (identity |$interpreterFrameName|)
 
Value = |initial|
--R 
--IValue = |frame0|
--E 167

--S 168 of 237
)lisp (identity |$interpreterFrameRing|)
 
Value = ((|initial| ((NIL)) 1 T #0=(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL . #0#) 20 0 NIL NIL #<vector 08bf4850>))
--R 
--IValue = ((|frame0| ((NIL)) 1 T #0=(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL . #0#) 20 0 NIL NIL #<vector 08cc0e8c>) (|initial| ((NIL)) 1 T #1=(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL . #1#) 20 0 NIL NIL #<vector 086b1a48>))
--E 168

--S 169 of 237
)lisp (identity |$intRestart|)
 
Value = |restart|
--R 
--RValue = |restart|
--E 169

--S 170 of 237
)lisp (identity |$intTopLevel|)
 
Value = |top_level|
--R 
--RValue = |top_level|
--E 170

--S 171 of 237
)lisp (identity |$IOindex| )
 
Value = 1
--R 
--RValue = 1
--E 171

--S 172 of 237
)lisp (identity |$JoinOfCatDatabase|)
 
Value = NIL
--R 
--RValue = NIL
--E 172

--S 173 of 237
)lisp (identity |$JoinOfDomDatabase|)
 
Value = NIL
--R 
--RValue = NIL
--E 173

--S 174 of 237
)lisp (identity |$lastPos|)
 
Value = (|noposition|)
--R 
--RValue = (|noposition|)
--E 174

--S 175 of 237
)lisp (identity |$lastUntraced|)
 
Value = NIL
--R 
--RValue = NIL
--E 175

--S 176 of 237
)lisp (identity |$letAssoc| )
 
Value = NIL
--R 
--RValue = NIL
--E 176

--S 177 of 237
)lisp (identity |$libQuiet|)
 
Value = T
--R 
--RValue = T
--E 177

--S 178 of 237
)lisp (identity $library-directory-list)
 
Value = ("/home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/")
--R 
--IValue = ("/research/reference/mnt/ubuntu/algebra/")
--E 178

--S 179 of 237
)lisp (identity |$localExposureData|)
 
Value = #<vector 08bf4850>
--R 
--IValue = #<vector 08cc0e8c>
--E 179

--S 180 of 237
)lisp (identity |$localExposureDataDefault|)
 
Value = #<vector 08eafe1c>
--R 
--IValue = #<vector 08a687fc>
--E 180

--S 181 of 237
)lisp (identity |$lookupDefaults|)
 
 
   >> System error:
   The variable |$lookupDefaults| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$lookupDefaults| is unbound.
--R
--R   Continuing to read the file...
--R
--E 181

--S 182 of 237
)lisp (identity |$mathmlOutputStream|)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 182

--S 183 of 237
)lisp (identity |$mathTraceList|)
 
Value = NIL
--R 
--RValue = NIL
--E 183

--S 184 of 237
)lisp (identity |$mkTestInputStack|)
 
Value = NIL
--R 
--RValue = NIL
--E 184

--S 185 of 237
)lisp (identity |$msgAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 185

--S 186 of 237
)lisp (identity |$msgDatabase|)
 
Value = NIL
--R 
--RValue = NIL
--E 186

--S 187 of 237
)lisp (identity |$msgDatabaseName|)
 
Value = NIL
--R 
--RValue = NIL
--E 187

--S 188 of 237
)lisp (identity |$ncMsgList|)
 
Value = NIL
--R 
--RValue = NIL
--E 188

--S 189 of 237
)lisp (identity |$newConlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 189

--S 190 of 237
)lisp (identity |$NonNullStream| )
 
Value = "NonNullStream"
--R 
--RValue = "NonNullStream"
--E 190

--S 191 of 237
)lisp (identity |$nopos|)
 
Value = (|noposition|)
--R 
--RValue = (|noposition|)
--E 191

--S 192 of 237
)lisp (identity |$newcompErrorCount|)
 
Value = 0
--R 
--RValue = 0
--E 192

--S 193 of 237
)lisp (identity |$newcompMode|)
 
Value = NIL
--R 
--RValue = NIL
--E 193

--S 194 of 237
)lisp (identity $newspad)
 
Value = T
--R 
--RValue = T
--E 194

--S 195 of 237
)lisp (identity |$NullStream|)
 
Value = "NullStream"
--R 
--RValue = "NullStream"
--E 195

--S 196 of 237
)lisp (identity |$okToExecuteMachineCode|)
 
Value = T
--R 
--RValue = T
--E 196

--S 197 of 237
)lisp (identity |$openMathOutputStream|)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 197

--S 198 of 237
)lisp (identity |$operationNameList|)
 
Value = NIL
--R 
--RValue = NIL
--E 198

--S 199 of 237
)lisp (identity |$outputLibraryName|)
 
Value = NIL
--R 
--RValue = NIL
--E 199

--S 200 of 237
)lisp (identity |$OutputForm|)
 
Value = (|OutputForm|)
--R 
--RValue = (|OutputForm|)
--E 200

--S 201 of 237
)lisp (identity |$packages|)
 
 
   >> System error:
   The variable |$packages| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$packages| is unbound.
--R
--R   Continuing to read the file...
--R
--E 201

--S 202 of 237
)lisp (identity /pretty)
 
Value = NIL
--R 
--RValue = NIL
--E 202

--S 203 of 237
)lisp (identity |$previousBindings|)
 
Value = NIL
--R 
--RValue = NIL
--E 203

--S 204 of 237
)lisp (identity |$PrintCompilerMessageIfTrue|)
 
Value = NIL
--R 
--RValue = NIL
--E 204

--S 205 of 237
)lisp (identity |$printLoadMsgs| )
 
Value = NIL
--R 
--RValue = NIL
--E 205

--S 206 of 237
)lisp (identity |$promptMsg|)
 
Value = S2CTP023
--R 
--RValue = S2CTP023
--E 206

--S 207 of 237
)lisp (identity |$QuickLet)
 
 
   >> System error:
   Unexpected end of #<string-input stream from " (identity |$Qui...">.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   Unexpected end of #<string-input stream from " (identity |$Qui...">.
--R
--R   Continuing to read the file...
--R
--E 207

--S 208 of 237
)lisp (identity |$quitTag|)
 
Value = (NIL)
--R 
--RValue = (NIL)
--E 208

--S 209 of 237
)lisp (identity $relative-directory-list)
 
Value = ("/../../src/input/" "/doc/msgs/" "/../../src/algebra/" "/../../src/interp/" "/doc/spadhelp/")
--R 
--RValue = ("/../../src/input/" "/doc/msgs/" "/../../src/algebra/" "/../../src/interp/" "/doc/spadhelp/")
--E 209

--S 210 of 237
)lisp (identity $relative-library-directory-list)
 
Value = ("/algebra/")
--R 
--RValue = ("/algebra/")
--E 210

--S 211 of 237
)lisp (identity |$seen|)
 
 
   >> System error:
   The variable |$seen| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$seen| is unbound.
--R
--R   Continuing to read the file...
--R
--E 211

--S 212 of 237
)lisp (identity |$SessionManager|)
 
Value = 1
--R 
--RValue = 1
--E 212

--S 213 of 237
)lisp (identity |$setOptions|)
 
Value = ((|breakmode| "execute break processing on error" |interpreter| LITERALS |$BreakMode| (|nobreak| |break| |query| |resume| |fastlinks|) |nobreak|) (|compiler| "Library compiler options" |interpreter| TREE |novar| ((|output| "library in which to place compiled code" |interpreter| FUNCTION |setOutputLibrary| NIL |htSetOutputLibrary|) (|input| "controls libraries from which to load compiled code" |interpreter| FUNCTION |setInputLibrary| NIL |htSetInputLibrary|) (|args| "arguments for compiling AXIOM code" |interpreter| FUNCTION |setAsharpArgs| (("enter compiler options " STRING |$asharpCmdlineFlags| |chkDirectory| "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL__W__WillObsolete -DAxiom -Y $AXIOM/algebra")) NIL))) (|debug| "debug options" |interpreter| TREE |novar| ((|lambdatype| "show type information for #1 syntax" |interpreter| LITERALS $LAMBDATYPE (|on| |off|) |off|) (|dalymode| "Interpret leading open paren as lisp" |interpreter| LITERALS $DALYMODE (|on| |off|) |off|))) (|expose| "control interpreter constructor exposure" |interpreter| FUNCTION |setExpose| NIL |htSetExpose|) (|functions| "some interpreter function options" |interpreter| TREE |novar| ((|cache| "number of function results to cache" |interpreter| FUNCTION |setFunctionsCache| NIL |htSetCache|) (|compile| "compile, don't just define function bodies" |interpreter| LITERALS |$compileDontDefineFunctions| (|on| |off|) |on|) (|recurrence| "specially compile recurrence relations" |interpreter| LITERALS |$compileRecurrence| (|on| |off|) |on|))) (|fortran| "view and set options for FORTRAN output" |interpreter| TREE |novar| ((|ints2floats| "where sensible, coerce integers to reals" |interpreter| LITERALS |$fortInts2Floats| (|on| |off|) |on|) (|fortindent| "the number of characters indented" |interpreter| INTEGER |$fortIndent| (0 NIL) 6) (|fortlength| "the number of characters on a line" |interpreter| INTEGER |$fortLength| (1 NIL) 72) (|typedecs| "print type and dimension lines" |interpreter| LITERALS |$printFortranDecs| (|on| |off|) |on|) (|defaulttype| "default generic type for FORTRAN object" |interpreter| LITERALS |$defaultFortranType| (REAL INTEGER COMPLEX LOGICAL CHARACTER) REAL) (|precision| "precision of generated FORTRAN objects" |interpreter| LITERALS |$fortranPrecision| (|single| |double|) |double|) (|intrinsic| "whether to use INTRINSIC FORTRAN functions" |interpreter| LITERALS |$useIntrinsicFunctions| (|on| |off|) |off|) (|explength| "character limit for FORTRAN expressions" |interpreter| INTEGER |$maximumFortranExpressionLength| (0 NIL) 1320) (|segment| "split long FORTRAN expressions" |interpreter| LITERALS |$fortranSegment| (|on| |off|) |on|) (|optlevel| "FORTRAN optimisation level" |interpreter| INTEGER |$fortranOptimizationLevel| (0 2) 0) (|startindex| "starting index for FORTRAN arrays" |interpreter| INTEGER |$fortranArrayStartingIndex| (0 1) 1) (|calling| "options for external FORTRAN calls" |interpreter| TREE |novar| ((|tempfile| "set location of temporary data files" |interpreter| FUNCTION |setFortTmpDir| (("enter directory name for which you have write-permission" DIRECTORY |$fortranTmpDir| |chkDirectory| "/tmp/")) NIL) (|directory| "set location of generated FORTRAN files" |interpreter| FUNCTION |setFortDir| (("enter directory name for which you have write-permission" DIRECTORY |$fortranDirectory| |chkDirectory| "./")) NIL) (|linker| "linker arguments (e.g. libraries to search)" |interpreter| FUNCTION |setLinkerArgs| (("enter linker arguments " STRING |$fortranLibraries| |chkDirectory| "-lxlf")) NIL))))) (|kernel| "library functions built into the kernel for efficiency" |interpreter| TREE |novar| ((|warn| "warn when re-definition is attempted" |interpreter| FUNCTION |protectedSymbolsWarning| NIL |htSetKernelWarn|) (|protect| "prevent re-definition of kernel functions" |interpreter| FUNCTION |protectSymbols| NIL |htSetKernelProtect|))) (|hyperdoc| "options in using HyperDoc" |interpreter| TREE |novar| ((|fullscreen| "use full screen for this facility" |interpreter| LITERALS |$fullScreenSysVars| (|on| |off|) |off|) (|mathwidth| "screen width for history output" |interpreter| INTEGER |$historyDisplayWidth| (0 NIL) 120))) (|help| "view and set some help options" |interpreter| TREE |novar| ((|fullscreen| "use fullscreen facility, if possible" |interpreter| LITERALS |$useFullScreenHelp| (|on| |off|) |off|))) (|history| "save workspace values in a history file" |interpreter| LITERALS |$HiFiAccess| (|on| |off|) |on|) (|messages| "show messages for various system features" |interpreter| TREE |novar| ((|any| "print the internal type of objects of domain Any" |interpreter| LITERALS |$printAnyIfTrue| (|on| |off|) |on|) (|autoload| "print file auto-load messages" |interpreter| LITERALS |$printLoadMsgs| (|on| |off|) |on|) (|bottomup| "display bottom up modemap selection" |development| LITERALS |$reportBottomUpFlag| (|on| |off|) |off|) (|coercion| "display datatype coercion messages" |development| LITERALS |$reportCoerceIfTrue| (|on| |off|) |off|) (|dropmap| "display old map defn when replaced" |interpreter| LITERALS |$displayDroppedMap| (|on| |off|) |off|) (|expose| "warning for unexposed functions" |interpreter| LITERALS |$giveExposureWarning| (|on| |off|) |off|) (|file| "print msgs also to SPADMSG LISTING" |development| LITERALS |$printMsgsToFile| (|on| |off|) |off|) (|frame| "display messages about frames" |interpreter| LITERALS |$frameMessages| (|on| |off|) |off|) (|highlighting| "use highlighting in system messages" |interpreter| LITERALS |$highlightAllowed| (|on| |off|) |off|) (|instant| "present instantiation summary" |development| LITERALS |$reportInstantiations| (|on| |off|) |off|) (|insteach| "present instantiation info" |development| LITERALS |$reportEachInstantiation| (|on| |off|) |off|) (|interponly| "say when function code is interpreted" |interpreter| LITERALS |$reportInterpOnly| (|on| |off|) |on|) (|naglink| "show NAGLink messages" |interpreter| LITERALS |$nagMessages| (|on| |off|) |on|) (|number| "display message number with message" |interpreter| LITERALS |$displayMsgNumber| (|on| |off|) |off|) (|prompt| "set type of input prompt to display" |interpreter| LITERALS |$inputPromptType| (|none| |frame| |plain| |step| |verbose|) |step|) (|selection| "display function selection msgs" |interpreter| LITERALS |$reportBottomUpFlag| (|on| |off|) |off|) (|set| "show )set setting after assignment" |interpreter| LITERALS |$displaySetValue| (|on| |off|) |off|) (|startup| "display messages on start-up" |interpreter| LITERALS |$displayStartMsgs| (|on| |off|) |on|) (|summary| "print statistics after computation" |interpreter| LITERALS |$printStatisticsSummaryIfTrue| (|on| |off|) |off|) (|testing| "print system testing header" |development| LITERALS |$testingSystem| (|on| |off|) |off|) (|time| "print timings after computation" |interpreter| LITERALS |$printTimeIfTrue| (|on| |off| |long|) |off|) (|type| "print type after computation" |interpreter| LITERALS |$printTypeIfTrue| (|on| |off|) |on|) (|void| "print Void value when it occurs" |interpreter| LITERALS |$printVoidIfTrue| (|on| |off|) |off|))) (|naglink| "options for NAGLink" |interpreter| TREE |novar| ((|host| "internet address of host for NAGLink" |interpreter| FUNCTION |setNagHost| (("enter host name" DIRECTORY |$nagHost| |chkDirectory| "localhost")) NIL) (|persistence| "number of (fortran) functions to remember" |interpreter| FUNCTION |setFortPers| (("Requested remote storage (for asps):" INTEGER |$fortPersistence| (0 NIL) 10)) NIL) (|messages| "show NAGLink messages" |interpreter| LITERALS |$nagMessages| (|on| |off|) |on|) (|double| "enforce DOUBLE PRECISION ASPs" |interpreter| LITERALS |$nagEnforceDouble| (|on| |off|) |on|))) (|output| "view and set some output options" |interpreter| TREE |novar| ((|abbreviate| "abbreviate type names" |interpreter| LITERALS |$abbreviateTypes| (|on| |off|) |off|) (|algebra| "display output in algebraic form" |interpreter| FUNCTION |setOutputAlgebra| (("display output in algebraic form" LITERALS |$algebraFormat| (|off| |on|) |on|) (BREAK $ALGEBRAFORMAT) ("where algebra printing goes (enter {em console} or a pathname)?" FILENAME |$algebraOutputFile| |chkOutputFileName| "console")) NIL) (|characters| "choose special output character set" |interpreter| FUNCTION |setOutputCharacters| NIL |htSetOutputCharacters|) (|fortran| "create output in FORTRAN format" |interpreter| FUNCTION |setOutputFortran| (("create output in FORTRAN format" LITERALS |$fortranFormat| (|off| |on|) |off|) (|break| |$fortranFormat|) ("where FORTRAN output goes (enter {em console} or a a pathname)" FILENAME |$fortranOutputFile| |chkOutputFileName| "console")) NIL) (|fraction| "how fractions are formatted" |interpreter| LITERALS |$fractionDisplayType| (|vertical| |horizontal|) |vertical|) (|length| "line length of output displays" |interpreter| INTEGER $LINELENGTH (10 245) 77) (|mathml| "create output in MathML style" |interpreter| FUNCTION |setOutputMathml| (("create output in MathML format" LITERALS |$mathmlFormat| (|off| |on|) |off|) (|break| |$mathmlFormat|) ("where MathML output goes (enter {em console} or a pathname)" FILENAME |$mathmlOutputFile| |chkOutputFileName| "console")) NIL) (|openmath| "create output in OpenMath style" |interpreter| FUNCTION |setOutputOpenMath| (("create output in OpenMath format" LITERALS |$openMathFormat| (|off| |on|) |off|) (|break| |$openMathFormat|) ("where TeX output goes (enter {em console} or a pathname)" FILENAME |$openMathOutputFile| |chkOutputFileName| "console")) NIL) (|script| "display output in SCRIPT formula format" |interpreter| FUNCTION |setOutputFormula| (("display output in SCRIPT format" LITERALS |$formulaFormat| (|off| |on|) |off|) (|break| |$formulaFormat|) ("where script output goes (enter {em console} or a a pathname)" FILENAME |$formulaOutputFile| |chkOutputFileName| "console")) NIL) (|scripts| "show subscripts,... linearly" |interpreter| LITERALS |$linearFormatScripts| (|on| |off|) |off|) (|showeditor| "view output of )show in editor" |interpreter| LITERALS |$useEditorForShowOutput| (|on| |off|) |off|) (|tex| "create output in TeX style" |interpreter| FUNCTION |setOutputTex| (("create output in TeX format" LITERALS |$texFormat| (|off| |on|) |off|) (|break| |$texFormat|) ("where TeX output goes (enter {em console} or a pathname)" FILENAME |$texOutputFile| |chkOutputFileName| "console")) NIL))) (|quit| "protected or unprotected quit" |interpreter| LITERALS |$quitCommandType| (|protected| |unprotected|) |protected|) (|streams| "set some options for working with streams" |interpreter| TREE |novar| ((|calculate| "specify number of elements to calculate" |interpreter| FUNCTION |setStreamsCalculate| (("number of initial stream elements you want calculated" INTEGER |$streamCount| (0 NIL) 10)) NIL) (|showall| "display all stream elements computed" |interpreter| LITERALS |$streamsShowAll| (|on| |off|) |off|))) (|system| "set some system development variables" |development| TREE |novar| ((|functioncode| "show gen. LISP for functions when compiled" |development| LITERALS |$reportCompilation| (|on| |off|) |off|) (|optimization| "show optimized LISP code" |development| LITERALS |$reportOptimization| (|on| |off|) |off|) (|prettyprint| "prettyprint BOOT func's as they compile" |development| LITERALS $PRETTYPRINT (|on| |off|) |on|))) (|userlevel| "operation access level of system user" |interpreter| LITERALS |$UserLevel| (|interpreter| |compiler| |development|) |development|))
--R 
--RValue = ((|breakmode| "execute break processing on error" |interpreter| LITERALS |$BreakMode| (|nobreak| |break| |query| |resume| |fastlinks|) |nobreak|) (|compiler| "Library compiler options" |interpreter| TREE |novar| ((|output| "library in which to place compiled code" |interpreter| FUNCTION |setOutputLibrary| NIL |htSetOutputLibrary|) (|input| "controls libraries from which to load compiled code" |interpreter| FUNCTION |setInputLibrary| NIL |htSetInputLibrary|) (|args| "arguments for compiling AXIOM code" |interpreter| FUNCTION |setAsharpArgs| (("enter compiler options " STRING |$asharpCmdlineFlags| |chkDirectory| "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL__W__WillObsolete -DAxiom -Y $AXIOM/algebra")) NIL))) (|debug| "debug options" |interpreter| TREE |novar| ((|lambdatype| "show type information for #1 syntax" |interpreter| LITERALS $LAMBDATYPE (|on| |off|) |off|) (|dalymode| "Interpret leading open paren as lisp" |interpreter| LITERALS $DALYMODE (|on| |off|) |off|))) (|expose| "control interpreter constructor exposure" |interpreter| FUNCTION |setExpose| NIL |htSetExpose|) (|functions| "some interpreter function options" |interpreter| TREE |novar| ((|cache| "number of function results to cache" |interpreter| FUNCTION |setFunctionsCache| NIL |htSetCache|) (|compile| "compile, don't just define function bodies" |interpreter| LITERALS |$compileDontDefineFunctions| (|on| |off|) |on|) (|recurrence| "specially compile recurrence relations" |interpreter| LITERALS |$compileRecurrence| (|on| |off|) |on|))) (|fortran| "view and set options for FORTRAN output" |interpreter| TREE |novar| ((|ints2floats| "where sensible, coerce integers to reals" |interpreter| LITERALS |$fortInts2Floats| (|on| |off|) |on|) (|fortindent| "the number of characters indented" |interpreter| INTEGER |$fortIndent| (0 NIL) 6) (|fortlength| "the number of characters on a line" |interpreter| INTEGER |$fortLength| (1 NIL) 72) (|typedecs| "print type and dimension lines" |interpreter| LITERALS |$printFortranDecs| (|on| |off|) |on|) (|defaulttype| "default generic type for FORTRAN object" |interpreter| LITERALS |$defaultFortranType| (REAL INTEGER COMPLEX LOGICAL CHARACTER) REAL) (|precision| "precision of generated FORTRAN objects" |interpreter| LITERALS |$fortranPrecision| (|single| |double|) |double|) (|intrinsic| "whether to use INTRINSIC FORTRAN functions" |interpreter| LITERALS |$useIntrinsicFunctions| (|on| |off|) |off|) (|explength| "character limit for FORTRAN expressions" |interpreter| INTEGER |$maximumFortranExpressionLength| (0 NIL) 1320) (|segment| "split long FORTRAN expressions" |interpreter| LITERALS |$fortranSegment| (|on| |off|) |on|) (|optlevel| "FORTRAN optimisation level" |interpreter| INTEGER |$fortranOptimizationLevel| (0 2) 0) (|startindex| "starting index for FORTRAN arrays" |interpreter| INTEGER |$fortranArrayStartingIndex| (0 1) 1) (|calling| "options for external FORTRAN calls" |interpreter| TREE |novar| ((|tempfile| "set location of temporary data files" |interpreter| FUNCTION |setFortTmpDir| (("enter directory name for which you have write-permission" DIRECTORY |$fortranTmpDir| |chkDirectory| "/tmp/")) NIL) (|directory| "set location of generated FORTRAN files" |interpreter| FUNCTION |setFortDir| (("enter directory name for which you have write-permission" DIRECTORY |$fortranDirectory| |chkDirectory| "./")) NIL) (|linker| "linker arguments (e.g. libraries to search)" |interpreter| FUNCTION |setLinkerArgs| (("enter linker arguments " STRING |$fortranLibraries| |chkDirectory| "-lxlf")) NIL))))) (|kernel| "library functions built into the kernel for efficiency" |interpreter| TREE |novar| ((|warn| "warn when re-definition is attempted" |interpreter| FUNCTION |protectedSymbolsWarning| NIL |htSetKernelWarn|) (|protect| "prevent re-definition of kernel functions" |interpreter| FUNCTION |protectSymbols| NIL |htSetKernelProtect|))) (|hyperdoc| "options in using HyperDoc" |interpreter| TREE |novar| ((|fullscreen| "use full screen for this facility" |interpreter| LITERALS |$fullScreenSysVars| (|on| |off|) |off|) (|mathwidth| "screen width for history output" |interpreter| INTEGER |$historyDisplayWidth| (0 NIL) 120))) (|help| "view and set some help options" |interpreter| TREE |novar| ((|fullscreen| "use fullscreen facility, if possible" |interpreter| LITERALS |$useFullScreenHelp| (|on| |off|) |off|))) (|history| "save workspace values in a history file" |interpreter| LITERALS |$HiFiAccess| (|on| |off|) |on|) (|messages| "show messages for various system features" |interpreter| TREE |novar| ((|any| "print the internal type of objects of domain Any" |interpreter| LITERALS |$printAnyIfTrue| (|on| |off|) |on|) (|autoload| "print file auto-load messages" |interpreter| LITERALS |$printLoadMsgs| (|on| |off|) |on|) (|bottomup| "display bottom up modemap selection" |development| LITERALS |$reportBottomUpFlag| (|on| |off|) |off|) (|coercion| "display datatype coercion messages" |development| LITERALS |$reportCoerceIfTrue| (|on| |off|) |off|) (|dropmap| "display old map defn when replaced" |interpreter| LITERALS |$displayDroppedMap| (|on| |off|) |off|) (|expose| "warning for unexposed functions" |interpreter| LITERALS |$giveExposureWarning| (|on| |off|) |off|) (|file| "print msgs also to SPADMSG LISTING" |development| LITERALS |$printMsgsToFile| (|on| |off|) |off|) (|frame| "display messages about frames" |interpreter| LITERALS |$frameMessages| (|on| |off|) |off|) (|highlighting| "use highlighting in system messages" |interpreter| LITERALS |$highlightAllowed| (|on| |off|) |off|) (|instant| "present instantiation summary" |development| LITERALS |$reportInstantiations| (|on| |off|) |off|) (|insteach| "present instantiation info" |development| LITERALS |$reportEachInstantiation| (|on| |off|) |off|) (|interponly| "say when function code is interpreted" |interpreter| LITERALS |$reportInterpOnly| (|on| |off|) |on|) (|naglink| "show NAGLink messages" |interpreter| LITERALS |$nagMessages| (|on| |off|) |on|) (|number| "display message number with message" |interpreter| LITERALS |$displayMsgNumber| (|on| |off|) |off|) (|prompt| "set type of input prompt to display" |interpreter| LITERALS |$inputPromptType| (|none| |frame| |plain| |step| |verbose|) |step|) (|selection| "display function selection msgs" |interpreter| LITERALS |$reportBottomUpFlag| (|on| |off|) |off|) (|set| "show )set setting after assignment" |interpreter| LITERALS |$displaySetValue| (|on| |off|) |off|) (|startup| "display messages on start-up" |interpreter| LITERALS |$displayStartMsgs| (|on| |off|) |on|) (|summary| "print statistics after computation" |interpreter| LITERALS |$printStatisticsSummaryIfTrue| (|on| |off|) |off|) (|testing| "print system testing header" |development| LITERALS |$testingSystem| (|on| |off|) |off|) (|time| "print timings after computation" |interpreter| LITERALS |$printTimeIfTrue| (|on| |off| |long|) |off|) (|type| "print type after computation" |interpreter| LITERALS |$printTypeIfTrue| (|on| |off|) |on|) (|void| "print Void value when it occurs" |interpreter| LITERALS |$printVoidIfTrue| (|on| |off|) |off|))) (|naglink| "options for NAGLink" |interpreter| TREE |novar| ((|host| "internet address of host for NAGLink" |interpreter| FUNCTION |setNagHost| (("enter host name" DIRECTORY |$nagHost| |chkDirectory| "localhost")) NIL) (|persistence| "number of (fortran) functions to remember" |interpreter| FUNCTION |setFortPers| (("Requested remote storage (for asps):" INTEGER |$fortPersistence| (0 NIL) 10)) NIL) (|messages| "show NAGLink messages" |interpreter| LITERALS |$nagMessages| (|on| |off|) |on|) (|double| "enforce DOUBLE PRECISION ASPs" |interpreter| LITERALS |$nagEnforceDouble| (|on| |off|) |on|))) (|output| "view and set some output options" |interpreter| TREE |novar| ((|abbreviate| "abbreviate type names" |interpreter| LITERALS |$abbreviateTypes| (|on| |off|) |off|) (|algebra| "display output in algebraic form" |interpreter| FUNCTION |setOutputAlgebra| (("display output in algebraic form" LITERALS |$algebraFormat| (|off| |on|) |on|) (BREAK $ALGEBRAFORMAT) ("where algebra printing goes (enter {em console} or a pathname)?" FILENAME |$algebraOutputFile| |chkOutputFileName| "console")) NIL) (|characters| "choose special output character set" |interpreter| FUNCTION |setOutputCharacters| NIL |htSetOutputCharacters|) (|fortran| "create output in FORTRAN format" |interpreter| FUNCTION |setOutputFortran| (("create output in FORTRAN format" LITERALS |$fortranFormat| (|off| |on|) |off|) (|break| |$fortranFormat|) ("where FORTRAN output goes (enter {em console} or a a pathname)" FILENAME |$fortranOutputFile| |chkOutputFileName| "console")) NIL) (|fraction| "how fractions are formatted" |interpreter| LITERALS |$fractionDisplayType| (|vertical| |horizontal|) |vertical|) (|length| "line length of output displays" |interpreter| INTEGER $LINELENGTH (10 245) 77) (|mathml| "create output in MathML style" |interpreter| FUNCTION |setOutputMathml| (("create output in MathML format" LITERALS |$mathmlFormat| (|off| |on|) |off|) (|break| |$mathmlFormat|) ("where MathML output goes (enter {em console} or a pathname)" FILENAME |$mathmlOutputFile| |chkOutputFileName| "console")) NIL) (|openmath| "create output in OpenMath style" |interpreter| FUNCTION |setOutputOpenMath| (("create output in OpenMath format" LITERALS |$openMathFormat| (|off| |on|) |off|) (|break| |$openMathFormat|) ("where TeX output goes (enter {em console} or a pathname)" FILENAME |$openMathOutputFile| |chkOutputFileName| "console")) NIL) (|script| "display output in SCRIPT formula format" |interpreter| FUNCTION |setOutputFormula| (("display output in SCRIPT format" LITERALS |$formulaFormat| (|off| |on|) |off|) (|break| |$formulaFormat|) ("where script output goes (enter {em console} or a a pathname)" FILENAME |$formulaOutputFile| |chkOutputFileName| "console")) NIL) (|scripts| "show subscripts,... linearly" |interpreter| LITERALS |$linearFormatScripts| (|on| |off|) |off|) (|showeditor| "view output of )show in editor" |interpreter| LITERALS |$useEditorForShowOutput| (|on| |off|) |off|) (|tex| "create output in TeX style" |interpreter| FUNCTION |setOutputTex| (("create output in TeX format" LITERALS |$texFormat| (|off| |on|) |off|) (|break| |$texFormat|) ("where TeX output goes (enter {em console} or a pathname)" FILENAME |$texOutputFile| |chkOutputFileName| "console")) NIL))) (|quit| "protected or unprotected quit" |interpreter| LITERALS |$quitCommandType| (|protected| |unprotected|) |protected|) (|streams| "set some options for working with streams" |interpreter| TREE |novar| ((|calculate| "specify number of elements to calculate" |interpreter| FUNCTION |setStreamsCalculate| (("number of initial stream elements you want calculated" INTEGER |$streamCount| (0 NIL) 10)) NIL) (|showall| "display all stream elements computed" |interpreter| LITERALS |$streamsShowAll| (|on| |off|) |off|))) (|system| "set some system development variables" |development| TREE |novar| ((|functioncode| "show gen. LISP for functions when compiled" |development| LITERALS |$reportCompilation| (|on| |off|) |off|) (|optimization| "show optimized LISP code" |development| LITERALS |$reportOptimization| (|on| |off|) |off|) (|prettyprint| "prettyprint BOOT func's as they compile" |development| LITERALS $PRETTYPRINT (|on| |off|) |on|))) (|userlevel| "operation access level of system user" |interpreter| LITERALS |$UserLevel| (|interpreter| |compiler| |development|) |development|))
--E 213

--S 214 of 237 obsolete |$shoeReadLineFunction|
)lisp nil
 
Value = NIL
--R 
--RValue = NIL
--E 214

--S 215 of 237
)lisp (identity |$slamFlag|)
 
Value = NIL
--R 
--RValue = NIL
--E 215

--S 216 of 237
)lisp (identity /sourcefiles)
 
Value = NIL
--R 
--RValue = NIL
--E 216

--S 217 of 237
)lisp (identity |$sourceFiles|)
 
Value = NIL
--R 
--RValue = NIL
--E 217

--S 218 of 237
)lisp (identity /spacelist)
 
Value = NIL
--R 
--RValue = NIL
--E 218

--S 219 of 237
)lisp (identity $spad)
 
Value = T
--R 
--RValue = T
--E 219

--S 220 of 237
)lisp (identity $spadroot)
 
Value = "/home/camm/debian/axiom/axiom-20091101/mnt/linux"
--R 
--IValue = "/research/reference/mnt/ubuntu"
--E 220

--S 221 of 237
)lisp (identity |$texOutputStream|)
 
Value = #<synonym stream to *TERMINAL-IO*>
--R 
--RValue = #<synonym stream to *TERMINAL-IO*>
--E 221

--S 222 of 237
)lisp (identity /timerlist)
 
Value = NIL
--R 
--RValue = NIL
--E 222

--S 223 of 237
)lisp (identity |$timerTicksPerSecond|)
 
Value = 100
--R 
--RValue = 100
--E 223

--S 224 of 237
)lisp (identity |$tracedMapSignatures|)
 
Value = NIL
--R 
--RValue = NIL
--E 224

--S 225 of 237
)lisp (identity |$tracedModemap|)
 
Value = NIL
--R 
--RValue = NIL
--E 225

--S 226 of 237
)lisp (identity |$tracedSpadModemap|)
 
Value = NIL
--R 
--RValue = NIL
--E 226

--S 227 of 237
)lisp (identity |$traceErrorStack|)
 
 
   >> System error:
   The variable |$traceErrorStack| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$traceErrorStack| is unbound.
--R
--R   Continuing to read the file...
--R
--E 227

--S 228 of 237
)lisp (identity $traceletflag)
 
Value = NIL
--R 
--RValue = NIL
--E 228

--S 229 of 237
)lisp (identity |$traceletFunctions|)
 
Value = NIL
--R 
--RValue = NIL
--E 229

--S 230 of 237
)lisp (identity |$undoFlag|)
 
Value = T
--R 
--RValue = T
--E 230

--S 231 of 237
)lisp (identity |$useFullScreenHelp|)
 
Value = NIL
--R 
--RValue = NIL
--E 231

--S 232 of 237
)lisp (identity |$UserAbbreviationsAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 232

--S 233 of 237
)lisp (identity |$variableNumberAlist|)
 
Value = NIL
--R 
--RValue = NIL
--E 233

--S 234 of 237
)lisp (identity |$Void|)
 
Value = (|Void|)
--R 
--RValue = (|Void|)
--E 234

--S 235 of 237
)lisp (identity |$writifyComplained|)
 
 
   >> System error:
   The variable |$writifyComplained| is unbound.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The variable |$writifyComplained| is unbound.
--R
--R   Continuing to read the file...
--R
--E 235

--S 236 of 237
)lisp (identity /wsname)
 
Value = NOBOOT
--R 
--RValue = NOBOOT
--E 236

--S 237 of 237
)lisp (identity |$xdatabase|)
 
Value = NIL
--R 
--RValue = NIL
--E 237


)spool
 
Starts dribbling to testprob.output (2010/3/27, 18:41:22).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 9
ex:=(3/7)^(4*x-5)*(7/3)^(2*x-7)=1
 

         3 4x - 5 7 2x - 7
   (1)  (-)      (-)      = 1
         7        3
                                            Type: Equation Expression Integer
--R
--R         3 4x - 5 7 2x - 7
--R   (1)  (-)      (-)      = 1
--R         7        3
--R                                            Type: Equation Expression Integer
--E 1

--S 2 of 9
rule1:=(rule log(7/3)==-log(3/7))
 

            7           3
   (2)  log(-) == - log(-)
            3           7
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            7           3
--R   (2)  log(-) == - log(-)
--R            3           7
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 2

--S 3 of 9
rule1 rhs solve(map(expandLog,map(log,ex)),x).1
 

   (3)  - 1
                                                     Type: Expression Integer
--R
--R   (3)  - 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 9
rule1 rhs solve(expandLog log lhs ex,x).1
 

   (4)  - 1
                                                     Type: Expression Integer
--R
--R   (4)  - 1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 9
rule2:=rule((a/b)^c*(b/a)^d == (a/b)^(c-d))
 

            a c b d        a - d + c
   (5)  %P (-) (-)  == %P (-)
            b   a          b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a c b d        a - d + c
--I   (5)  %P (-) (-)  == %P (-)
--R            b   a          b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 5

--S 6 of 9
solve((rule2 lhs ex)=(rhs ex),x)
 

   (6)  [x= - 1]
                                       Type: List Equation Expression Integer
--R
--R   (6)  [x= - 1]
--R                                       Type: List Equation Expression Integer
--E 6

--S 7 of 9
res:=solve(ex,x)
 

   (7)  []
                                       Type: List Equation Expression Integer
--R
--R   (7)  []
--R                                       Type: List Equation Expression Integer
--E 7

--S 8 of 9
res1:=normalize rhs(res.1)
 
 
Daly Bug
   >> Error detected within library code:
   index out of range

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   index out of range
--R
--R   Continuing to read the file...
--R
--E 8

--S 9 of 9
eval(ex,x=res1)
 

         3 4res1 - 5 7 2res1 - 7
   (8)  (-)         (-)         = 1
         7           3
                                            Type: Equation Expression Integer
--R
--R         3 4res1 - 5 7 2res1 - 7
--R   (8)  (-)         (-)         = 1
--R         7           3
--R                                            Type: Equation Expression Integer
--E 9
)spool 
 
Starts dribbling to kamke2.output (2010/3/27, 18:27:48).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 126
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 126
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 126
g:=operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

-------------------------------------------------------------------
--S 4 of 126
ode101 := x*D(y(x),x) + x*y(x)**2 - y(x)
 

          ,            2
   (4)  xy (x) + x y(x)  - y(x)

                                                     Type: Expression Integer
--R
--R          ,            2
--R   (4)  xy (x) + x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 126
yx:=solve(ode101,y,x)
 

         2
        x y(x) - 2x
   (5)  -----------
           2y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         2
--R        x y(x) - 2x
--R   (5)  -----------
--R           2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 126
ode101expr := x*D(yx,x) + x*yx**2 - yx
 

          2 ,        5     2     2     4         3
        4x y (x) + (x  + 2x )y(x)  - 4x y(x) + 4x

   (6)  ------------------------------------------
                               2
                          4y(x)
                                                     Type: Expression Integer
--R
--R          2 ,        5     2     2     4         3
--R        4x y (x) + (x  + 2x )y(x)  - 4x y(x) + 4x
--R
--R   (6)  ------------------------------------------
--R                               2
--R                          4y(x)
--R                                                     Type: Expression Integer
--E 6

-------------------------------------------------------------------
--S 7 of 126
ode102 := x*D(y(x),x) + x*y(x)**2 - y(x) - a*x**3
 

          ,            2             3
   (7)  xy (x) + x y(x)  - y(x) - a x

                                                     Type: Expression Integer
--R
--R          ,            2             3
--R   (7)  xy (x) + x y(x)  - y(x) - a x
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 126
yx:=solve(ode102,y,x)
 

                            +-+
               (2y(x) + 3x)\|a  + 3y(x) + 2a x
   (8)  ---------------------------------------------
                                                2 +-+
                        +-+                    x \|a
        ((6y(x) - 4a x)\|a  + 4a y(x) - 6a x)%e
                                          Type: Union(Expression Integer,...)
--R
--R                            +-+
--R               (2y(x) + 3x)\|a  + 3y(x) + 2a x
--R   (8)  ---------------------------------------------
--R                                                2 +-+
--R                        +-+                    x \|a
--R        ((6y(x) - 4a x)\|a  + 4a y(x) - 6a x)%e
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 126
ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3
 

   (9)
                   2         2           3       2  3  +-+
           ((- 144a  - 108a)x y(x) + (32a  + 216a )x )\|a
         + 
                 3       2  2            3       2  3
           (- 32a  - 216a )x y(x) + (144a  + 108a )x
      *
            2 +-+
           x \|a  ,
         %e      y (x)

     + 
                      3       2  3    3       4       3  4    2
               (- 144a  - 108a )x y(x)  + (96a  + 648a )x y(x)
             + 
                      4       3  5           5       4  6
               (- 432a  - 324a )x y(x) + (32a  + 216a )x
          *
              +-+
             \|a
         + 
                 4       3  3    3        4       3  4    2
           (- 32a  - 216a )x y(x)  + (432a  + 324a )x y(x)
         + 
                 5       4  5            5       4  6
           (- 96a  - 648a )x y(x) + (144a  + 108a )x
      *
             2 +-+ 2
            x \|a
         (%e      )
     + 
                       2         2      2            3
               ((- 144a  - 108a)x  - 16a  - 108a)y(x)
             + 
                    3       2  3        2              2
               ((32a  + 216a )x  + (216a  + 162a)x)y(x)
             + 
                     3       2  4         3       2  2              4       3  5
               ((144a  + 108a )x  + (- 16a  - 108a )x )y(x) + (- 32a  - 216a )x
             + 
                     3      2  3
               (- 72a  - 54a )x
          *
              +-+
             \|a
         + 
                  3       2  2      2           3
           ((- 32a  - 216a )x  - 72a  - 54a)y(x)
         + 
                 3       2  3       3       2       2
           ((144a  + 108a )x  + (48a  + 324a )x)y(x)
         + 
                4       3  4         3      2  2               4       3  5
           ((32a  + 216a )x  + (- 72a  - 54a )x )y(x) + (- 144a  - 108a )x
         + 
                 4       3  3
           (- 16a  - 108a )x
      *
            2 +-+
           x \|a
         %e
     + 
                           3      2        2    2         2        3
           (36a + 27)x y(x)  + (8a  + 54a)x y(x)  + (- 36a  - 27a)x y(x)
         + 
                3      2  4
           (- 8a  - 54a )x
      *
          +-+
         \|a
     + 
          2             3       2        2    2        3      2  3
       (8a  + 54a)x y(x)  + (36a  + 27a)x y(x)  + (- 8a  - 54a )x y(x)
     + 
             3      2  4
       (- 36a  - 27a )x
  /
                  2            3         3       2       2
             (144a  + 108a)y(x)  + (- 96a  - 648a )x y(x)
           + 
                  3       2  2             4       3  3
             (432a  + 324a )x y(x) + (- 32a  - 216a )x
        *
            +-+
           \|a
       + 
             3       2     3          3       2       2       4       3  2
         (32a  + 216a )y(x)  + (- 432a  - 324a )x y(x)  + (96a  + 648a )x y(x)
       + 
                4       3  3
         (- 144a  - 108a )x
    *
           2 +-+ 2
          x \|a
       (%e      )
                                                     Type: Expression Integer
--R
--R   (9)
--R                   2         2           3       2  3  +-+
--R           ((- 144a  - 108a)x y(x) + (32a  + 216a )x )\|a
--R         + 
--R                 3       2  2            3       2  3
--R           (- 32a  - 216a )x y(x) + (144a  + 108a )x
--R      *
--R            2 +-+
--R           x \|a  ,
--R         %e      y (x)
--R
--R     + 
--R                      3       2  3    3       4       3  4    2
--R               (- 144a  - 108a )x y(x)  + (96a  + 648a )x y(x)
--R             + 
--R                      4       3  5           5       4  6
--R               (- 432a  - 324a )x y(x) + (32a  + 216a )x
--R          *
--R              +-+
--R             \|a
--R         + 
--R                 4       3  3    3        4       3  4    2
--R           (- 32a  - 216a )x y(x)  + (432a  + 324a )x y(x)
--R         + 
--R                 5       4  5            5       4  6
--R           (- 96a  - 648a )x y(x) + (144a  + 108a )x
--R      *
--R             2 +-+ 2
--R            x \|a
--R         (%e      )
--R     + 
--R                       2         2      2            3
--R               ((- 144a  - 108a)x  - 16a  - 108a)y(x)
--R             + 
--R                    3       2  3        2              2
--R               ((32a  + 216a )x  + (216a  + 162a)x)y(x)
--R             + 
--R                     3       2  4         3       2  2              4       3  5
--R               ((144a  + 108a )x  + (- 16a  - 108a )x )y(x) + (- 32a  - 216a )x
--R             + 
--R                     3      2  3
--R               (- 72a  - 54a )x
--R          *
--R              +-+
--R             \|a
--R         + 
--R                  3       2  2      2           3
--R           ((- 32a  - 216a )x  - 72a  - 54a)y(x)
--R         + 
--R                 3       2  3       3       2       2
--R           ((144a  + 108a )x  + (48a  + 324a )x)y(x)
--R         + 
--R                4       3  4         3      2  2               4       3  5
--R           ((32a  + 216a )x  + (- 72a  - 54a )x )y(x) + (- 144a  - 108a )x
--R         + 
--R                 4       3  3
--R           (- 16a  - 108a )x
--R      *
--R            2 +-+
--R           x \|a
--R         %e
--R     + 
--R                           3      2        2    2         2        3
--R           (36a + 27)x y(x)  + (8a  + 54a)x y(x)  + (- 36a  - 27a)x y(x)
--R         + 
--R                3      2  4
--R           (- 8a  - 54a )x
--R      *
--R          +-+
--R         \|a
--R     + 
--R          2             3       2        2    2        3      2  3
--R       (8a  + 54a)x y(x)  + (36a  + 27a)x y(x)  + (- 8a  - 54a )x y(x)
--R     + 
--R             3      2  4
--R       (- 36a  - 27a )x
--R  /
--R                  2            3         3       2       2
--R             (144a  + 108a)y(x)  + (- 96a  - 648a )x y(x)
--R           + 
--R                  3       2  2             4       3  3
--R             (432a  + 324a )x y(x) + (- 32a  - 216a )x
--R        *
--R            +-+
--R           \|a
--R       + 
--R             3       2     3          3       2       2       4       3  2
--R         (32a  + 216a )y(x)  + (- 432a  - 324a )x y(x)  + (96a  + 648a )x y(x)
--R       + 
--R                4       3  3
--R         (- 144a  - 108a )x
--R    *
--R           2 +-+ 2
--R          x \|a
--R       (%e      )
--R                                                     Type: Expression Integer
--E 9

-------------------------------------------------------------------
--S 10 of 126
ode103 := x*D(y(x),x) + x*y(x)**2 - (2*x**2+1)*y(x) - x**3
 

           ,            2        2             3
   (10)  xy (x) + x y(x)  + (- 2x  - 1)y(x) - x

                                                     Type: Expression Integer
--R
--R           ,            2        2             3
--R   (10)  xy (x) + x y(x)  + (- 2x  - 1)y(x) - x
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 126
yx:=solve(ode103,y,x)
 

                   +-+              +-+
                (2\|2  + 3)y(x) + x\|2  + x
   (11)  -----------------------------------------
                                             2 +-+
             +-+                +-+         x \|2
         ((6\|2  + 8)y(x) - 14x\|2  - 20x)%e
                                          Type: Union(Expression Integer,...)
--R
--R                   +-+              +-+
--R                (2\|2  + 3)y(x) + x\|2  + x
--R   (11)  -----------------------------------------
--R                                             2 +-+
--R             +-+                +-+         x \|2
--R         ((6\|2  + 8)y(x) - 14x\|2  - 20x)%e
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 126
ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3
 

   (12)
                                                            2 +-+
               2 +-+        2             3 +-+        3   x \|2  ,
       ((- 792x \|2  - 1120x )y(x) + 1912x \|2  + 2704x )%e      y (x)

     + 
                  3 +-+        3     3         4 +-+        4     2
           (- 792x \|2  - 1120x )y(x)  + (5736x \|2  + 8112x )y(x)
         + 
                    5 +-+         5              6 +-+         6
           (- 13848x \|2  - 19584x )y(x) + 11144x \|2  + 15760x
      *
             2 +-+ 2
            x \|2
         (%e      )
     + 
                    2        +-+        2           3
           ((- 1352x  - 280)\|2  - 1912x  - 396)y(x)
         + 
                  3          +-+        3             2
           ((5968x  + 2028x)\|2  + 8440x  + 2868x)y(x)
         + 
                    4        2  +-+        4        2
           ((- 5176x  - 2984x )\|2  - 7320x  - 4220x )y(x)
         + 
                   5       3  +-+        5       3
           (- 3264x  - 676x )\|2  - 4616x  - 956x
      *
            2 +-+
           x \|2
         %e
     + 
            +-+            3          2 +-+       2     2
       (99x\|2  + 140x)y(x)  + (- 157x \|2  - 222x )y(x)
     + 
              3 +-+       3           4 +-+      4
       (- 181x \|2  - 256x )y(x) - 41x \|2  - 58x
  /
              +-+            3            +-+             2
         (792\|2  + 1120)y(x)  + (- 5736x\|2  - 8112x)y(x)
       + 
                2 +-+         2              3 +-+         3
         (13848x \|2  + 19584x )y(x) - 11144x \|2  - 15760x
    *
           2 +-+ 2
          x \|2
       (%e      )
                                                     Type: Expression Integer
--R
--R   (12)
--R                                                            2 +-+
--R               2 +-+        2             3 +-+        3   x \|2  ,
--R       ((- 792x \|2  - 1120x )y(x) + 1912x \|2  + 2704x )%e      y (x)
--R
--R     + 
--R                  3 +-+        3     3         4 +-+        4     2
--R           (- 792x \|2  - 1120x )y(x)  + (5736x \|2  + 8112x )y(x)
--R         + 
--R                    5 +-+         5              6 +-+         6
--R           (- 13848x \|2  - 19584x )y(x) + 11144x \|2  + 15760x
--R      *
--R             2 +-+ 2
--R            x \|2
--R         (%e      )
--R     + 
--R                    2        +-+        2           3
--R           ((- 1352x  - 280)\|2  - 1912x  - 396)y(x)
--R         + 
--R                  3          +-+        3             2
--R           ((5968x  + 2028x)\|2  + 8440x  + 2868x)y(x)
--R         + 
--R                    4        2  +-+        4        2
--R           ((- 5176x  - 2984x )\|2  - 7320x  - 4220x )y(x)
--R         + 
--R                   5       3  +-+        5       3
--R           (- 3264x  - 676x )\|2  - 4616x  - 956x
--R      *
--R            2 +-+
--R           x \|2
--R         %e
--R     + 
--R            +-+            3          2 +-+       2     2
--R       (99x\|2  + 140x)y(x)  + (- 157x \|2  - 222x )y(x)
--R     + 
--R              3 +-+       3           4 +-+      4
--R       (- 181x \|2  - 256x )y(x) - 41x \|2  - 58x
--R  /
--R              +-+            3            +-+             2
--R         (792\|2  + 1120)y(x)  + (- 5736x\|2  - 8112x)y(x)
--R       + 
--R                2 +-+         2              3 +-+         3
--R         (13848x \|2  + 19584x )y(x) - 11144x \|2  - 15760x
--R    *
--R           2 +-+ 2
--R          x \|2
--R       (%e      )
--R                                                     Type: Expression Integer
--E 12

-------------------------------------------------------------------
--S 13 of 126
ode106 := x*D(y(x),x) + x**a*y(x)**2 + (a-b)*y(x)/2 + x**b
 

            ,        b        2 a
         2xy (x) + 2x  + 2y(x) x  + (- b + a)y(x)

   (13)  ----------------------------------------
                             2
                                                     Type: Expression Integer
--R
--R            ,        b        2 a
--R         2xy (x) + 2x  + 2y(x) x  + (- b + a)y(x)
--R
--R   (13)  ----------------------------------------
--R                             2
--R                                                     Type: Expression Integer
--E 13

--S 14 of 126
yx:=solve(ode106,y,x)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 14

-------------------------------------------------------------------
--S 15 of 126
ode107 := x*D(y(x),x) + a*x**alpha*y(x)**2 + b*y(x) - c*x**beta
 

           ,         beta         2 alpha
   (15)  xy (x) - c x     + a y(x) x      + b y(x)

                                                     Type: Expression Integer
--R
--R           ,         beta         2 alpha
--R   (15)  xy (x) - c x     + a y(x) x      + b y(x)
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 126
yx:=solve(ode107,y,x)
 

   (16)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (16)  "failed"
--R                                                    Type: Union("failed",...)
--E 16

-------------------------------------------------------------------
--S 17 of 126
ode108 := x*D(y(x),x) - y(x)**2*log(x) + y(x)
 

           ,          2
   (17)  xy (x) - y(x) log(x) + y(x)

                                                     Type: Expression Integer
--R
--R           ,          2
--R   (17)  xy (x) - y(x) log(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 17
--S 18 of 126
yx:=solve(ode108,y,x)
 

         - y(x)log(x) - y(x) + 1
   (18)  -----------------------
                  x y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         - y(x)log(x) - y(x) + 1
--R   (18)  -----------------------
--R                  x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 126
ode108expr := x*D(yx,x) - yx**2*log(x) + yx
 

   (19)
          2 ,          2      3           2               2
       - x y (x) - y(x) log(x)  + (- 2y(x)  + 2y(x))log(x)

     + 
              2                            2
       (- y(x)  + 2y(x) - 1)log(x) - x y(x)
  /
      2    2
     x y(x)
                                                     Type: Expression Integer
--R
--R   (19)
--R          2 ,          2      3           2               2
--R       - x y (x) - y(x) log(x)  + (- 2y(x)  + 2y(x))log(x)
--R
--R     + 
--R              2                            2
--R       (- y(x)  + 2y(x) - 1)log(x) - x y(x)
--R  /
--R      2    2
--R     x y(x)
--R                                                     Type: Expression Integer
--E 19

-------------------------------------------------------------------
--S 20 of 126
ode109 := x*D(y(x),x) - y(x)*(2*y(x)*log(x)-1)
 

           ,           2
   (20)  xy (x) - 2y(x) log(x) + y(x)

                                                     Type: Expression Integer
--R
--R           ,           2
--R   (20)  xy (x) - 2y(x) log(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 126
yx:=solve(ode109,y,x)
 

         - 2y(x)log(x) - 2y(x) + 1
   (21)  -------------------------
                   x y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         - 2y(x)log(x) - 2y(x) + 1
--R   (21)  -------------------------
--R                   x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 21

--S 22 of 126
ode109expr := x*D(yx,x) - yx*(2*yx*log(x)-1)
 

   (22)
          2 ,           2      3            2               2
       - x y (x) - 8y(x) log(x)  + (- 16y(x)  + 8y(x))log(x)

     + 
               2                             2
       (- 8y(x)  + 8y(x) - 2)log(x) - 2x y(x)
  /
      2    2
     x y(x)
                                                     Type: Expression Integer
--R
--R   (22)
--R          2 ,           2      3            2               2
--R       - x y (x) - 8y(x) log(x)  + (- 16y(x)  + 8y(x))log(x)
--R
--R     + 
--R               2                             2
--R       (- 8y(x)  + 8y(x) - 2)log(x) - 2x y(x)
--R  /
--R      2    2
--R     x y(x)
--R                                                     Type: Expression Integer
--E 22

-------------------------------------------------------------------
--S 23 of 126
ode110 := x*D(y(x),x) + f(x)*(y(x)**2-x**2)
 

           ,              2    2
   (23)  xy (x) + f(x)y(x)  - x f(x)

                                                     Type: Expression Integer
--R
--R           ,              2    2
--R   (23)  xy (x) + f(x)y(x)  - x f(x)
--R
--R                                                     Type: Expression Integer
--E 23

--S 24 of 126
yx:=solve(ode110,y,x)
 

   (24)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (24)  "failed"
--R                                                    Type: Union("failed",...)
--E 24

-------------------------------------------------------------------
--S 25 of 126
ode111 := x*D(y(x),x) + y(x)**3 + 3*x*y(x)**2
 

           ,          3          2
   (25)  xy (x) + y(x)  + 3x y(x)

                                                     Type: Expression Integer
--R
--R           ,          3          2
--R   (25)  xy (x) + y(x)  + 3x y(x)
--R
--R                                                     Type: Expression Integer
--E 25


--S 26 of 126
yx:=solve(ode111,y,x)
 

   (26)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (26)  "failed"
--R                                                    Type: Union("failed",...)
--E 26

-------------------------------------------------------------------
--S 27 of 126
ode112 := x*D(y(x),x) - sqrt(y(x)**2 + x**2) - y(x)
 

                   +----------+
           ,       |    2    2
   (27)  xy (x) - \|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                   +----------+
--R           ,       |    2    2
--R   (27)  xy (x) - \|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 27


--S 28 of 126
yx:=solve(ode112,y,x)
 

   (28)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (28)  "failed"
--R                                                    Type: Union("failed",...)
--E 28

-------------------------------------------------------------------
--S 29 of 126
ode113 := x*D(y(x),x) + a*sqrt(y(x)**2 + x**2) - y(x)
 

                    +----------+
           ,        |    2    2
   (29)  xy (x) + a\|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                    +----------+
--R           ,        |    2    2
--R   (29)  xy (x) + a\|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 29

--S 30 of 126
yx:=solve(ode113,y,x)
 

   (30)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (30)  "failed"
--R                                                    Type: Union("failed",...)
--E 30

-------------------------------------------------------------------
--S 31 of 126
ode114 := x*D(y(x),x) - x*sqrt(y(x)**2 + x**2) - y(x)
 

                    +----------+
           ,        |    2    2
   (31)  xy (x) - x\|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                    +----------+
--R           ,        |    2    2
--R   (31)  xy (x) - x\|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 31

--S 32 of 126
yx:=solve(ode114,y,x)
 

   (32)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (32)  "failed"
--R                                                    Type: Union("failed",...)
--E 32

-------------------------------------------------------------------
--S 33 of 126
ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)**2 + x**2) - y(x)
 

                                  +----------+
           ,                   2  |    2    2
   (33)  xy (x) + (- x y(x) + x )\|y(x)  + x   - y(x)

                                                     Type: Expression Integer
--R
--R                                  +----------+
--R           ,                   2  |    2    2
--R   (33)  xy (x) + (- x y(x) + x )\|y(x)  + x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 33

--S 34 of 126
yx:=solve(ode115,y,x)
 

   (34)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (34)  "failed"
--R                                                    Type: Union("failed",...)
--E 34

-------------------------------------------------------------------
--S 35 of 126
ode116 := x*D(y(x),x) - x*sqrt((y(x)**2 - x**2)*(y(x)**2-4*x**2)) - y(x)
 

                    +----------------------+
           ,        |    4     2    2     4
   (35)  xy (x) - x\|y(x)  - 5x y(x)  + 4x   - y(x)

                                                     Type: Expression Integer
--R
--R                    +----------------------+
--R           ,        |    4     2    2     4
--R   (35)  xy (x) - x\|y(x)  - 5x y(x)  + 4x   - y(x)
--R
--R                                                     Type: Expression Integer
--E 35

--S 36 of 126
yx:=solve(ode116,y,x)
 

   (36)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

-------------------------------------------------------------------
--S 37 of 126
ode117 := x*D(y(x),x) - x*exp(y(x)/x) - y(x) - x
 

                      y(x)
                      ----
           ,            x
   (37)  xy (x) - x %e     - y(x) - x

                                                     Type: Expression Integer
--R
--R                      y(x)
--R                      ----
--R           ,            x
--R   (37)  xy (x) - x %e     - y(x) - x
--R
--R                                                     Type: Expression Integer
--E 37

--S 38 of 126
yx:=solve(ode117,y,x)
 

   (38)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (38)  "failed"
--R                                                    Type: Union("failed",...)
--E 38

-------------------------------------------------------------------
--S 39 of 126
ode118 := x*D(y(x),x) - y(x)*log(y(x))
 

           ,
   (39)  xy (x) - y(x)log(y(x))

                                                     Type: Expression Integer
--R
--R           ,
--R   (39)  xy (x) - y(x)log(y(x))
--R
--R                                                     Type: Expression Integer
--E 39

--S 40 of 126
yx:=solve(ode118,y,x)
 

               x
   (40)  - ---------
           log(y(x))
                                          Type: Union(Expression Integer,...)
--R
--R               x
--R   (40)  - ---------
--R           log(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 40

--S 41 of 126
ode118expr := x*D(yx,x) - yx*log(yx)
 

                                  x         2 ,
         x y(x)log(y(x))log(- ---------) + x y (x) - x y(x)log(y(x))
                              log(y(x))
   (41)  -----------------------------------------------------------
                                             2
                                y(x)log(y(x))
                                                     Type: Expression Integer
--R
--R                                  x         2 ,
--R         x y(x)log(y(x))log(- ---------) + x y (x) - x y(x)log(y(x))
--R                              log(y(x))
--R   (41)  -----------------------------------------------------------
--R                                             2
--R                                y(x)log(y(x))
--R                                                     Type: Expression Integer
--E 41

-------------------------------------------------------------------
--S 42 of 126
ode119 := x*D(y(x),x) - y(x)*(log(x*y(x))-1)
 

           ,
   (42)  xy (x) - y(x)log(x y(x)) + y(x)

                                                     Type: Expression Integer
--R
--R           ,
--R   (42)  xy (x) - y(x)log(x y(x)) + y(x)
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 126
yx:=solve(ode119,y,x)
 

   (43)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (43)  "failed"
--R                                                    Type: Union("failed",...)
--E 43

-------------------------------------------------------------------
--S 44 of 126
ode120 := x*D(y(x),x) - y(x)*(x*log(x**2/y(x))+2)
 

                              2
           ,                 x
   (44)  xy (x) - x y(x)log(----) - 2y(x)
                            y(x)
                                                     Type: Expression Integer
--R
--R                              2
--R           ,                 x
--R   (44)  xy (x) - x y(x)log(----) - 2y(x)
--R                            y(x)
--R                                                     Type: Expression Integer
--E 44

--S 45 of 126
yx:=solve(ode120,y,x)
 

   (45)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (45)  "failed"
--R                                                    Type: Union("failed",...)
--E 45

-------------------------------------------------------------------
--S 46 of 126
ode121 := x*D(y(x),x) + sin(y(x)-x)
 

           ,
   (46)  xy (x) + sin(y(x) - x)

                                                     Type: Expression Integer
--R
--R           ,
--R   (46)  xy (x) + sin(y(x) - x)
--R
--R                                                     Type: Expression Integer
--E 46

--S 47 of 126
yx:=solve(ode121,y,x)
 

   (47)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (47)  "failed"
--R                                                    Type: Union("failed",...)
--E 47

-------------------------------------------------------------------
--S 48 of 126
ode122 := x*D(y(x),x) + (sin(y(x))-3*x**2*cos(y(x)))*cos(y(x))
 

           ,                             2         2
   (48)  xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x))

                                                     Type: Expression Integer
--R
--R           ,                             2         2
--R   (48)  xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 48

--S 49 of 126
yx:=solve(ode122,y,x)
 

   (49)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (49)  "failed"
--R                                                    Type: Union("failed",...)
--E 49

-------------------------------------------------------------------
--S 50 of 126
ode123 := x*D(y(x),x) - x*sin(y(x)/x) - y(x)
 

           ,            y(x)
   (50)  xy (x) - x sin(----) - y(x)
                          x
                                                     Type: Expression Integer
--R
--R           ,            y(x)
--R   (50)  xy (x) - x sin(----) - y(x)
--R                          x
--R                                                     Type: Expression Integer
--E 50

--S 51 of 126
yx:=solve(ode123,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 51

-------------------------------------------------------------------
--S 52 of 126
ode124 := x*D(y(x),x) + x*cos(y(x)/x) - y(x) + x
 

           ,            y(x)
   (52)  xy (x) + x cos(----) - y(x) + x
                          x
                                                     Type: Expression Integer
--R
--R           ,            y(x)
--R   (52)  xy (x) + x cos(----) - y(x) + x
--R                          x
--R                                                     Type: Expression Integer
--E 52

--S 53 of 126
yx:=solve(ode124,y,x)
 

   (53)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (53)  "failed"
--R                                                    Type: Union("failed",...)
--E 53

-------------------------------------------------------------------
--S 54 of 126
ode125 := x*D(y(x),x) + x*tan(y(x)/x) - y(x)
 

           ,            y(x)
   (54)  xy (x) + x tan(----) - y(x)
                          x
                                                     Type: Expression Integer
--R
--R           ,            y(x)
--R   (54)  xy (x) + x tan(----) - y(x)
--R                          x
--R                                                     Type: Expression Integer
--E 54

--S 55 of 126
yx:=solve(ode125,y,x)
 

   (55)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (55)  "failed"
--R                                                    Type: Union("failed",...)
--E 55

-------------------------------------------------------------------
--S 56 of 126
ode126 := x*D(y(x),x) - y(x)*f(x*y(x))
 

           ,
   (56)  xy (x) - y(x)f(x y(x))

                                                     Type: Expression Integer
--R
--R           ,
--R   (56)  xy (x) - y(x)f(x y(x))
--R
--R                                                     Type: Expression Integer
--E 56

--S 57 of 126
yx:=solve(ode126,y,x)
 

   (57)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (57)  "failed"
--R                                                    Type: Union("failed",...)
--E 57

-------------------------------------------------------------------
--S 58 of 126
ode127 := x*D(y(x),x) - y(x)*f(x**a*y(x)**b)
 

                  a    b      ,
   (58)  - y(x)f(x y(x) ) + xy (x)

                                                     Type: Expression Integer
--R
--R                  a    b      ,
--R   (58)  - y(x)f(x y(x) ) + xy (x)
--R
--R                                                     Type: Expression Integer
--E 58
--S 59 of 126
yx:=solve(ode127,y,x)
 

   (59)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (59)  "failed"
--R                                                    Type: Union("failed",...)
--E 59

-------------------------------------------------------------------
--S 60 of 126
ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x**a*y(x))
 

           ,                 a
   (60)  xy (x) - f(x)g(y(x)x ) + a y(x)

                                                     Type: Expression Integer
--R
--R           ,                 a
--R   (60)  xy (x) - f(x)g(y(x)x ) + a y(x)
--R
--R                                                     Type: Expression Integer
--E 60
--S 61 of 126
yx:=solve(ode128,y,x)
 

   (61)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (61)  "failed"
--R                                                    Type: Union("failed",...)
--E 61

-------------------------------------------------------------------
--S 62 of 126
ode129 := (x+1)*D(y(x),x) + y(x)*(y(x)-x)
 

                 ,          2
   (62)  (x + 1)y (x) + y(x)  - x y(x)

                                                     Type: Expression Integer
--R
--R                 ,          2
--R   (62)  (x + 1)y (x) + y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 62
--S 63 of 126
yx:=solve(ode129,y,x)
 

                              x
                        - x ++            1
         (- x - 1)y(x)%e    |   --------------------- d%U  + 1
                           ++      2             - %U
                                (%U  + 2%U + 1)%e
   (63)  -----------------------------------------------------
                                         - x
                            (x + 1)y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              x
--R                        - x ++            1
--I         (- x - 1)y(x)%e    |   --------------------- d%U  + 1
--I                           ++      2             - %U
--I                                (%U  + 2%U + 1)%e
--R   (63)  -----------------------------------------------------
--R                                         - x
--R                            (x + 1)y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 63

-------------------------------------------------------------------
--S 64 of 126
ode130 := 2*x*D(y(x),x) - y(x) -2*x**3
 

            ,               3
   (64)  2xy (x) - y(x) - 2x

                                                     Type: Expression Integer
--R
--R            ,               3
--R   (64)  2xy (x) - y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 64
--S 65 of 126
ode130a:=solve(ode130,y,x)
 

                        3
                      2x           +-+
   (65)  [particular= ---,basis= [\|x ]]
                       5
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                        3
--R                      2x           +-+
--R   (65)  [particular= ---,basis= [\|x ]]
--R                       5
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 65

--S 66 of 126
yx:=ode130a.particular
 

           3
         2x
   (66)  ---
          5
                                                     Type: Expression Integer
--R
--R           3
--R         2x
--R   (66)  ---
--R          5
--R                                                     Type: Expression Integer
--E 66

--S 67 of 126
ode130expr := 2*x*D(yx,x) - yx -2*x**3
 

   (67)  0
                                                     Type: Expression Integer
--R
--R   (67)  0
--R                                                     Type: Expression Integer
--E 67

-------------------------------------------------------------------
--S 68 of 126
ode131 := (2*x+1)*D(y(x),x) - 4*exp(-y(x)) + 2
 

                  ,         - y(x)
   (68)  (2x + 1)y (x) - 4%e       + 2

                                                     Type: Expression Integer
--R
--R                  ,         - y(x)
--R   (68)  (2x + 1)y (x) - 4%e       + 2
--R
--R                                                     Type: Expression Integer
--E 68
--S 69 of 126
yx:=solve(ode131,y,x)
 

                 - y(x)            y(x)
   (69)  (- 4x %e       + 2x + 1)%e
                                          Type: Union(Expression Integer,...)
--R
--R                 - y(x)            y(x)
--R   (69)  (- 4x %e       + 2x + 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 69

--S 70 of 126
ode131expr := (2*x+1)*D(yx,x) - 4*exp(-yx) + 2
 

   (70)
                - y(x)            y(x)
          (4x %e       - 2x - 1)%e          2            y(x) ,
     - 4%e                             + (4x  + 4x + 1)%e    y (x)

   + 
                  - y(x)            y(x)
     ((- 8x - 4)%e       + 4x + 2)%e     + 2
                                                     Type: Expression Integer
--R
--R   (70)
--R                - y(x)            y(x)
--R          (4x %e       - 2x - 1)%e          2            y(x) ,
--R     - 4%e                             + (4x  + 4x + 1)%e    y (x)
--R
--R   + 
--R                  - y(x)            y(x)
--R     ((- 8x - 4)%e       + 4x + 2)%e     + 2
--R                                                     Type: Expression Integer
--E 70

-------------------------------------------------------------------
--S 71 of 126
ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)**4 - y(x)
 

            ,             4
   (71)  3xy (x) - 3x y(x) log(x) - y(x)

                                                     Type: Expression Integer
--R
--R            ,             4
--R   (71)  3xy (x) - 3x y(x) log(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 71
--S 72 of 126
yx:=solve(ode132,y,x)
 

             2    3           2    3
         - 6x y(x) log(x) + 3x y(x)  - 4x
   (72)  --------------------------------
                           3
                      4y(x)
                                          Type: Union(Expression Integer,...)
--R
--R             2    3           2    3
--R         - 6x y(x) log(x) + 3x y(x)  - 4x
--R   (72)  --------------------------------
--R                           3
--R                      4y(x)
--R                                          Type: Union(Expression Integer,...)
--E 72

--S 73 of 126
ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx
 

   (73)
            2    8 ,           9    12      5
       2304x y(x) y (x) - 3888x y(x)  log(x)

     + 
             9    12         8    9       4
       (7776x y(x)   - 10368x y(x) )log(x)
     + 
               9    12         8    9         7    6       3
       (- 5832x y(x)   + 15552x y(x)  - 10368x y(x) )log(x)
     + 
             9    12        8    9         7    6        6    3       2
       (1944x y(x)   - 7776x y(x)  + 10368x y(x)  - 4608x y(x) )log(x)
     + 
                  9        2     12        8    9        7    6        6    3
           (- 243x  - 1920x )y(x)   + 1296x y(x)  - 2592x y(x)  + 2304x y(x)
         + 
                 5
           - 768x
      *
         log(x)
     + 
             2    12            9
       - 192x y(x)   - 512x y(x)
  /
            12
     256y(x)
                                                     Type: Expression Integer
--R
--R   (73)
--R            2    8 ,           9    12      5
--R       2304x y(x) y (x) - 3888x y(x)  log(x)
--R
--R     + 
--R             9    12         8    9       4
--R       (7776x y(x)   - 10368x y(x) )log(x)
--R     + 
--R               9    12         8    9         7    6       3
--R       (- 5832x y(x)   + 15552x y(x)  - 10368x y(x) )log(x)
--R     + 
--R             9    12        8    9         7    6        6    3       2
--R       (1944x y(x)   - 7776x y(x)  + 10368x y(x)  - 4608x y(x) )log(x)
--R     + 
--R                  9        2     12        8    9        7    6        6    3
--R           (- 243x  - 1920x )y(x)   + 1296x y(x)  - 2592x y(x)  + 2304x y(x)
--R         + 
--R                 5
--R           - 768x
--R      *
--R         log(x)
--R     + 
--R             2    12            9
--R       - 192x y(x)   - 512x y(x)
--R  /
--R            12
--R     256y(x)
--R                                                     Type: Expression Integer
--E 73

-------------------------------------------------------------------
--S 74 of 126
ode133 := x**2*D(y(x),x) + y(x) - x
 

          2 ,
   (74)  x y (x) + y(x) - x

                                                     Type: Expression Integer
--R
--R          2 ,
--R   (74)  x y (x) + y(x) - x
--R
--R                                                     Type: Expression Integer
--E 74
--S 75 of 126
yx:=solve(ode133,y,x)
 

                        1                            1
                        -   x                        -
                        x ++     1                   x
   (75)  [particular= %e  |   ------- d%U ,basis= [%e ]]
                         ++         1
                                   --
                                   %U
                              %U %e
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                        1                            1
--R                        -   x                        -
--R                        x ++     1                   x
--I   (75)  [particular= %e  |   ------- d%U ,basis= [%e ]]
--R                         ++         1
--R                                   --
--I                                   %U
--I                              %U %e
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 75

-------------------------------------------------------------------
--S 76 of 126
ode134 := x**2*D(y(x),x) - y(x) + x**2*exp(x-1/x)
 

                        2
                       x  - 1
                       ------
          2 ,       2     x
   (76)  x y (x) + x %e       - y(x)

                                                     Type: Expression Integer
--R
--R                        2
--R                       x  - 1
--R                       ------
--R          2 ,       2     x
--R   (76)  x y (x) + x %e       - y(x)
--R
--R                                                     Type: Expression Integer
--E 76
--S 77 of 126
ode134a:=solve(ode134,y,x)
 

                           2
                          x  - 1             1
                          ------           - -
                             x               x
   (77)  [particular= - %e      ,basis= [%e   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                           2
--R                          x  - 1             1
--R                          ------           - -
--R                             x               x
--R   (77)  [particular= - %e      ,basis= [%e   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 77

--S 78 of 126
yx:=ode134a.particular
 

              2
             x  - 1
             ------
                x
   (78)  - %e
                                                     Type: Expression Integer
--R
--R              2
--R             x  - 1
--R             ------
--R                x
--R   (78)  - %e
--R                                                     Type: Expression Integer
--E 78

--S 79 of 126
ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x)
 

   (79)  0
                                                     Type: Expression Integer
--R
--R   (79)  0
--R                                                     Type: Expression Integer
--E 79

-------------------------------------------------------------------
--S 80 of 126
ode135 := x**2*D(y(x),x) - (x-1)*y(x)
 

          2 ,
   (80)  x y (x) + (- x + 1)y(x)

                                                     Type: Expression Integer
--R
--R          2 ,
--R   (80)  x y (x) + (- x + 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 80
--S 81 of 126
ode135a:=solve(ode135,y,x)
 

                                    1
                                    -
                                    x
   (81)  [particular= 0,basis= [x %e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                    1
--R                                    -
--R                                    x
--R   (81)  [particular= 0,basis= [x %e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 81

--S 82 of 126
yx:=ode135a.particular
 

   (82)  0
                                                     Type: Expression Integer
--R
--R   (82)  0
--R                                                     Type: Expression Integer
--E 82

--S 83 of 126
ode135expr := x**2*D(yx,x) - (x-1)*yx
 

   (83)  0
                                                     Type: Expression Integer
--R
--R   (83)  0
--R                                                     Type: Expression Integer
--E 83

-------------------------------------------------------------------
--S 84 of 126
ode136 := x**2*D(y(x),x) + y(x)**2 + x*y(x) + x**2
 

          2 ,          2             2
   (84)  x y (x) + y(x)  + x y(x) + x

                                                     Type: Expression Integer
--R
--R          2 ,          2             2
--R   (84)  x y (x) + y(x)  + x y(x) + x
--R
--R                                                     Type: Expression Integer
--E 84
--S 85 of 126
yx:=solve(ode136,y,x)
 

         (- y(x) - x)log(x) + x
   (85)  ----------------------
                y(x) + x
                                          Type: Union(Expression Integer,...)
--R
--R         (- y(x) - x)log(x) + x
--R   (85)  ----------------------
--R                y(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 126
ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2
 

   (86)
          3 ,           2              2       2
       - x y (x) + (y(x)  + 2x y(x) + x )log(x)

     + 
                2        2              3     2            2         2     3
       (- x y(x)  + (- 2x  - 2x)y(x) - x  - 2x )log(x) + (x  - x)y(x)  + 2x y(x)
     + 
        4    2
       x  + x
  /
         2              2
     y(x)  + 2x y(x) + x
                                                     Type: Expression Integer
--R
--R   (86)
--R          3 ,           2              2       2
--R       - x y (x) + (y(x)  + 2x y(x) + x )log(x)
--R
--R     + 
--R                2        2              3     2            2         2     3
--R       (- x y(x)  + (- 2x  - 2x)y(x) - x  - 2x )log(x) + (x  - x)y(x)  + 2x y(x)
--R     + 
--R        4    2
--R       x  + x
--R  /
--R         2              2
--R     y(x)  + 2x y(x) + x
--R                                                     Type: Expression Integer
--E 86

-------------------------------------------------------------------
--S 87 of 126
ode137 := x**2*D(y(x),x) - y(x)**2 - x*y(x)
 

          2 ,          2
   (87)  x y (x) - y(x)  - x y(x)

                                                     Type: Expression Integer
--R
--R          2 ,          2
--R   (87)  x y (x) - y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 87
--S 88 of 126
yx:=solve(ode137,y,x)
 

         y(x)log(x) + x
   (88)  --------------
              y(x)
                                          Type: Union(Expression Integer,...)
--R
--R         y(x)log(x) + x
--R   (88)  --------------
--R              y(x)
--R                                          Type: Union(Expression Integer,...)
--E 88

--S 89 of 126
ode137expr := x**2*D(yx,x) - yx**2 - x*yx
 

            3 ,          2      2            2                          2    2
         - x y (x) - y(x) log(x)  + (- x y(x)  - 2x y(x))log(x) + x y(x)  - x

   (89)  ---------------------------------------------------------------------
                                             2
                                         y(x)
                                                     Type: Expression Integer
--R
--R            3 ,          2      2            2                          2    2
--R         - x y (x) - y(x) log(x)  + (- x y(x)  - 2x y(x))log(x) + x y(x)  - x
--R
--R   (89)  ---------------------------------------------------------------------
--R                                             2
--R                                         y(x)
--R                                                     Type: Expression Integer
--E 89

-------------------------------------------------------------------
--S 90 of 126
ode138 := x**2*D(y(x),x) - y(x)**2 - x*y(x) - x**2
 

          2 ,          2             2
   (90)  x y (x) - y(x)  - x y(x) - x

                                                     Type: Expression Integer
--R
--R          2 ,          2             2
--R   (90)  x y (x) - y(x)  - x y(x) - x
--R
--R                                                     Type: Expression Integer
--E 90

--S 91 of 126
yx:=solve(ode138,y,x)
 

                         +---+               +---+
                    (- 7\|- 1  + 9)y(x) + 9x\|- 1  + 7x
   (91)  --------------------------------------------------------
                                                      +---+
              +---+                 +---+         - 2\|- 1 log(x)
         ((18\|- 1  + 14)y(x) - 14x\|- 1  + 18x)%e
                                          Type: Union(Expression Integer,...)
--R
--R                         +---+               +---+
--R                    (- 7\|- 1  + 9)y(x) + 9x\|- 1  + 7x
--R   (91)  --------------------------------------------------------
--R                                                      +---+
--R              +---+                 +---+         - 2\|- 1 log(x)
--R         ((18\|- 1  + 14)y(x) - 14x\|- 1  + 18x)%e
--R                                          Type: Union(Expression Integer,...)
--E 91

--S 92 of 126
ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2
 

   (92)
                  3 +---+        3             4 +---+        4
         ((- 1188x \|- 1  + 2716x )y(x) - 2716x \|- 1  - 1188x )
      *
               +---+
           - 2\|- 1 log(x) ,
         %e               y (x)

     + 
                   2 +---+        2     3           3 +---+        3     2
           (- 1188x \|- 1  + 2716x )y(x)  + (- 8148x \|- 1  - 3564x )y(x)
         + 
                 4 +---+        4             5 +---+        5
           (3564x \|- 1  - 8148x )y(x) + 2716x \|- 1  + 1188x
      *
                +---+       2
            - 2\|- 1 log(x)
         (%e               )
     + 
                   +---+             3         2 +---+        2     2
           (- 170x\|- 1  - 3310x)y(x)  + (4498x \|- 1  - 2886x )y(x)
         + 
                 3 +---+        3             4 +---+       4
           (2546x \|- 1  - 2122x )y(x) + 3310x \|- 1  - 170x
      *
               +---+
           - 2\|- 1 log(x)
         %e
     + 
            +---+           3           +---+            2
       (297\|- 1  - 679)y(x)  + (- 679x\|- 1  - 297x)y(x)
     + 
            2 +---+       2            3 +---+       3
       (297x \|- 1  - 679x )y(x) - 679x \|- 1  - 297x
  /
               +---+            3          +---+             2
         (1188\|- 1  - 2716)y(x)  + (8148x\|- 1  + 3564x)y(x)
       + 
                 2 +---+        2             3 +---+        3
         (- 3564x \|- 1  + 8148x )y(x) - 2716x \|- 1  - 1188x
    *
              +---+       2
          - 2\|- 1 log(x)
       (%e               )
                                                     Type: Expression Integer
--R
--R   (92)
--R                  3 +---+        3             4 +---+        4
--R         ((- 1188x \|- 1  + 2716x )y(x) - 2716x \|- 1  - 1188x )
--R      *
--R               +---+
--R           - 2\|- 1 log(x) ,
--R         %e               y (x)
--R
--R     + 
--R                   2 +---+        2     3           3 +---+        3     2
--R           (- 1188x \|- 1  + 2716x )y(x)  + (- 8148x \|- 1  - 3564x )y(x)
--R         + 
--R                 4 +---+        4             5 +---+        5
--R           (3564x \|- 1  - 8148x )y(x) + 2716x \|- 1  + 1188x
--R      *
--R                +---+       2
--R            - 2\|- 1 log(x)
--R         (%e               )
--R     + 
--R                   +---+             3         2 +---+        2     2
--R           (- 170x\|- 1  - 3310x)y(x)  + (4498x \|- 1  - 2886x )y(x)
--R         + 
--R                 3 +---+        3             4 +---+       4
--R           (2546x \|- 1  - 2122x )y(x) + 3310x \|- 1  - 170x
--R      *
--R               +---+
--R           - 2\|- 1 log(x)
--R         %e
--R     + 
--R            +---+           3           +---+            2
--R       (297\|- 1  - 679)y(x)  + (- 679x\|- 1  - 297x)y(x)
--R     + 
--R            2 +---+       2            3 +---+       3
--R       (297x \|- 1  - 679x )y(x) - 679x \|- 1  - 297x
--R  /
--R               +---+            3          +---+             2
--R         (1188\|- 1  - 2716)y(x)  + (8148x\|- 1  + 3564x)y(x)
--R       + 
--R                 2 +---+        2             3 +---+        3
--R         (- 3564x \|- 1  + 8148x )y(x) - 2716x \|- 1  - 1188x
--R    *
--R              +---+       2
--R          - 2\|- 1 log(x)
--R       (%e               )
--R                                                     Type: Expression Integer
--E 92

-------------------------------------------------------------------
--S 93 of 126
ode139 := x**2*(D(y(x),x)+y(x)**2) + a*x**k - b*(b-1)
 

          2 ,         k    2    2    2
   (93)  x y (x) + a x  + x y(x)  - b  + b

                                                     Type: Expression Integer
--R
--R          2 ,         k    2    2    2
--R   (93)  x y (x) + a x  + x y(x)  - b  + b
--R
--R                                                     Type: Expression Integer
--E 93


--S 94 of 126
yx:=solve(ode139,y,x)
 

   (94)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (94)  "failed"
--R                                                    Type: Union("failed",...)
--E 94

-------------------------------------------------------------------
--S 95 of 126
ode140 := x**2*(D(y(x),x)+y(x)**2) + 4*x*y(x) + 2
 

          2 ,       2    2
   (95)  x y (x) + x y(x)  + 4x y(x) + 2

                                                     Type: Expression Integer
--R
--R          2 ,       2    2
--R   (95)  x y (x) + x y(x)  + 4x y(x) + 2
--R
--R                                                     Type: Expression Integer
--E 95
--S 96 of 126
yx:=solve(ode140,y,x)
 

              x y(x) + 2
   (96)  --------------------
           2
         (x  - x)y(x) + x - 2
                                          Type: Union(Expression Integer,...)
--R
--R              x y(x) + 2
--R   (96)  --------------------
--R           2
--R         (x  - x)y(x) + x - 2
--R                                          Type: Union(Expression Integer,...)
--E 96

--S 97 of 126
ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2
 

   (97)
      4 ,         4     3     2     2       3      2                2
   - x y (x) + (6x  - 8x  + 2x )y(x)  + (16x  - 28x  + 8x)y(x) + 12x  - 24x + 8

   ----------------------------------------------------------------------------
               4     3    2     2      3     2              2
             (x  - 2x  + x )y(x)  + (2x  - 6x  + 4x)y(x) + x  - 4x + 4
                                                     Type: Expression Integer
--R
--R   (97)
--R      4 ,         4     3     2     2       3      2                2
--R   - x y (x) + (6x  - 8x  + 2x )y(x)  + (16x  - 28x  + 8x)y(x) + 12x  - 24x + 8
--R
--R   ----------------------------------------------------------------------------
--R               4     3    2     2      3     2              2
--R             (x  - 2x  + x )y(x)  + (2x  - 6x  + 4x)y(x) + x  - 4x + 4
--R                                                     Type: Expression Integer
--E 97

-------------------------------------------------------------------
--S 98 of 126
ode141 := x**2*(D(y(x),x)+y(x)**2) + a*x*y(x) + b
 

          2 ,       2    2
   (98)  x y (x) + x y(x)  + a x y(x) + b

                                                     Type: Expression Integer
--R
--R          2 ,       2    2
--R   (98)  x y (x) + x y(x)  + a x y(x) + b
--R
--R                                                     Type: Expression Integer
--E 98


--S 99 of 126
yx:=solve(ode141,y,x)
 
                                                     2
   WARNING (genufact): No known algorithm to factor ?  + (a - 1)? + b
     , trying square-free.

   (99)
      +------------------+
      |        2
     \|- 4b + a  - 2a + 1  - 2x y(x) - a + 1
  /
                          +------------------+
                          |        2                   2
       ((2x y(x) + a - 1)\|- 4b + a  - 2a + 1  - 4b + a  - 2a + 1)
    *
                  +------------------+
                  |        2
         - log(x)\|- 4b + a  - 2a + 1
       %e
                                          Type: Union(Expression Integer,...)
--R                                                     2
--R   WARNING (genufact): No known algorithm to factor ?  + (a - 1)? + b
--R     , trying square-free.
--R
--R   (99)
--R      +------------------+
--R      |        2
--R     \|- 4b + a  - 2a + 1  - 2x y(x) - a + 1
--R  /
--R                          +------------------+
--R                          |        2                   2
--R       ((2x y(x) + a - 1)\|- 4b + a  - 2a + 1  - 4b + a  - 2a + 1)
--R    *
--R                  +------------------+
--R                  |        2
--R         - log(x)\|- 4b + a  - 2a + 1
--R       %e
--R                                          Type: Union(Expression Integer,...)
--E 99

--S 100 of 126
ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b
 

   (100)
                        2           4                       3     2           3
             ((- 8b + 2a  - 4a + 2)x y(x) + ((- 4a + 4)b + a  - 3a  + 3a - 1)x )
          *
              +------------------+
              |        2
             \|- 4b + a  - 2a + 1
         + 
               2        2                4     3     2           3
           (16b  + (- 8a  + 16a - 8)b + a  - 4a  + 6a  - 4a + 1)x
      *
                    +------------------+
                    |        2
           - log(x)\|- 4b + a  - 2a + 1  ,
         %e                             y (x)

     + 
                  2        2             3    3
               (8b  + (- 2a  + 4a - 2)b)x y(x)
             + 
                           2        3     2             2    2
               ((12a - 12)b  + (- 3a  + 9a  - 9a + 3)b)x y(x)
             + 
                          3       2             2
                     - 24b  + (18a  - 36a + 18)b
                   + 
                          4      3      2
                     (- 3a  + 12a  - 18a  + 12a - 3)b
              *
                 x y(x)
             + 
                            3      3      2            2
               (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b
             + 
                   5     4      3      2
               (- a  + 5a  - 10a  + 10a  - 5a + 1)b
          *
              +------------------+
              |        2
             \|- 4b + a  - 2a + 1
         + 
                   3       2             2        4      3      2              2
             (- 48b  + (24a  - 48a + 24)b  + (- 3a  + 12a  - 18a  + 12a - 3)b)x
          *
                 2
             y(x)
         + 
                            3       3      2             2
               (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b
             + 
                    5      4      3      2
               (- 3a  + 15a  - 30a  + 30a  - 15a + 3)b
          *
             x y(x)
         + 
              4         2             3      4      3      2            2
           16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b
         + 
               6     5      4      3      2
           (- a  + 6a  - 15a  + 20a  - 15a  + 6a - 1)b
      *
                     +------------------+ 2
                     |        2
            - log(x)\|- 4b + a  - 2a + 1
         (%e                             )
     + 
                         2           4    3
               (- 8b + 2a  - 4a + 2)x y(x)
             + 
                                 3     2           3    2
               ((- 16a + 4)b + 4a  - 9a  + 6a - 1)x y(x)
             + 
                    2        2                4     3     2       2
               (- 8b  + (- 6a  + 4a + 2)b + 2a  - 6a  + 6a  - 2a)x y(x)
             + 
                           2      3     2
               ((- 8a + 4)b  + (2a  - 5a  + 4a - 1)b)x
          *
              +------------------+
              |        2
             \|- 4b + a  - 2a + 1
         + 
                       3     2       4    3
           (- 8a b + 2a  - 4a  + 2a)x y(x)
         + 
               2         2                 4      3      2           3    2
           (16b  + (- 20a  + 28a - 8)b + 4a  - 13a  + 15a  - 7a + 1)x y(x)
         + 
                2         3      2             5     4      3     2       2
           (8a b  + (- 10a  + 20a  - 10a)b + 2a  - 8a  + 12a  - 8a  + 2a)x y(x)
         + 
               3         2            2      4     3     2
           (16b  + (- 12a  + 20a - 8)b  + (2a  - 7a  + 9a  - 5a + 1)b)x
      *
                    +------------------+
                    |        2
           - log(x)\|- 4b + a  - 2a + 1
         %e
     + 
               5    3              4    2            2           3
           - 2x y(x)  + (- 3a + 3)x y(x)  + (- 2b - a  + 2a - 1)x y(x)
         + 
                       2
           (- a + 1)b x
      *
          +------------------+
          |        2
         \|- 4b + a  - 2a + 1
     + 
                2           4    2                   3     2           3
       (- 4b + a  - 2a + 1)x y(x)  + ((- 4a + 4)b + a  - 3a  + 3a - 1)x y(x)
     + 
            2     2             2
       (- 4b  + (a  - 2a + 1)b)x
  /
                     2           3    3
             (8b - 2a  + 4a - 2)x y(x)
           + 
                              3     2           2    2
             ((12a - 12)b - 3a  + 9a  - 9a + 3)x y(x)
           + 
                   2       2                  4      3      2
             (- 24b  + (18a  - 36a + 18)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
           + 
                          2      3      2                5     4      3      2
             (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b - a  + 5a  - 10a  + 10a
           + 
             - 5a + 1
        *
            +------------------+
            |        2
           \|- 4b + a  - 2a + 1
       + 
               2       2                  4      3      2            2    2
         (- 48b  + (24a  - 48a + 24)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
       + 
                          2       3      2                  5      4      3
             (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b - 3a  + 15a  - 30a
           + 
                2
             30a  - 15a + 3
        *
           x y(x)
       + 
            3         2             2      4      3      2                6
         16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b - a
       + 
           5      4      3      2
         6a  - 15a  + 20a  - 15a  + 6a - 1
    *
                   +------------------+ 2
                   |        2
          - log(x)\|- 4b + a  - 2a + 1
       (%e                             )
                                                     Type: Expression Integer
--R
--R   (100)
--R                        2           4                       3     2           3
--R             ((- 8b + 2a  - 4a + 2)x y(x) + ((- 4a + 4)b + a  - 3a  + 3a - 1)x )
--R          *
--R              +------------------+
--R              |        2
--R             \|- 4b + a  - 2a + 1
--R         + 
--R               2        2                4     3     2           3
--R           (16b  + (- 8a  + 16a - 8)b + a  - 4a  + 6a  - 4a + 1)x
--R      *
--R                    +------------------+
--R                    |        2
--R           - log(x)\|- 4b + a  - 2a + 1  ,
--R         %e                             y (x)
--R
--R     + 
--R                  2        2             3    3
--R               (8b  + (- 2a  + 4a - 2)b)x y(x)
--R             + 
--R                           2        3     2             2    2
--R               ((12a - 12)b  + (- 3a  + 9a  - 9a + 3)b)x y(x)
--R             + 
--R                          3       2             2
--R                     - 24b  + (18a  - 36a + 18)b
--R                   + 
--R                          4      3      2
--R                     (- 3a  + 12a  - 18a  + 12a - 3)b
--R              *
--R                 x y(x)
--R             + 
--R                            3      3      2            2
--R               (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b
--R             + 
--R                   5     4      3      2
--R               (- a  + 5a  - 10a  + 10a  - 5a + 1)b
--R          *
--R              +------------------+
--R              |        2
--R             \|- 4b + a  - 2a + 1
--R         + 
--R                   3       2             2        4      3      2              2
--R             (- 48b  + (24a  - 48a + 24)b  + (- 3a  + 12a  - 18a  + 12a - 3)b)x
--R          *
--R                 2
--R             y(x)
--R         + 
--R                            3       3      2             2
--R               (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b
--R             + 
--R                    5      4      3      2
--R               (- 3a  + 15a  - 30a  + 30a  - 15a + 3)b
--R          *
--R             x y(x)
--R         + 
--R              4         2             3      4      3      2            2
--R           16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b
--R         + 
--R               6     5      4      3      2
--R           (- a  + 6a  - 15a  + 20a  - 15a  + 6a - 1)b
--R      *
--R                     +------------------+ 2
--R                     |        2
--R            - log(x)\|- 4b + a  - 2a + 1
--R         (%e                             )
--R     + 
--R                         2           4    3
--R               (- 8b + 2a  - 4a + 2)x y(x)
--R             + 
--R                                 3     2           3    2
--R               ((- 16a + 4)b + 4a  - 9a  + 6a - 1)x y(x)
--R             + 
--R                    2        2                4     3     2       2
--R               (- 8b  + (- 6a  + 4a + 2)b + 2a  - 6a  + 6a  - 2a)x y(x)
--R             + 
--R                           2      3     2
--R               ((- 8a + 4)b  + (2a  - 5a  + 4a - 1)b)x
--R          *
--R              +------------------+
--R              |        2
--R             \|- 4b + a  - 2a + 1
--R         + 
--R                       3     2       4    3
--R           (- 8a b + 2a  - 4a  + 2a)x y(x)
--R         + 
--R               2         2                 4      3      2           3    2
--R           (16b  + (- 20a  + 28a - 8)b + 4a  - 13a  + 15a  - 7a + 1)x y(x)
--R         + 
--R                2         3      2             5     4      3     2       2
--R           (8a b  + (- 10a  + 20a  - 10a)b + 2a  - 8a  + 12a  - 8a  + 2a)x y(x)
--R         + 
--R               3         2            2      4     3     2
--R           (16b  + (- 12a  + 20a - 8)b  + (2a  - 7a  + 9a  - 5a + 1)b)x
--R      *
--R                    +------------------+
--R                    |        2
--R           - log(x)\|- 4b + a  - 2a + 1
--R         %e
--R     + 
--R               5    3              4    2            2           3
--R           - 2x y(x)  + (- 3a + 3)x y(x)  + (- 2b - a  + 2a - 1)x y(x)
--R         + 
--R                       2
--R           (- a + 1)b x
--R      *
--R          +------------------+
--R          |        2
--R         \|- 4b + a  - 2a + 1
--R     + 
--R                2           4    2                   3     2           3
--R       (- 4b + a  - 2a + 1)x y(x)  + ((- 4a + 4)b + a  - 3a  + 3a - 1)x y(x)
--R     + 
--R            2     2             2
--R       (- 4b  + (a  - 2a + 1)b)x
--R  /
--R                     2           3    3
--R             (8b - 2a  + 4a - 2)x y(x)
--R           + 
--R                              3     2           2    2
--R             ((12a - 12)b - 3a  + 9a  - 9a + 3)x y(x)
--R           + 
--R                   2       2                  4      3      2
--R             (- 24b  + (18a  - 36a + 18)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
--R           + 
--R                          2      3      2                5     4      3      2
--R             (- 12a + 12)b  + (7a  - 21a  + 21a - 7)b - a  + 5a  - 10a  + 10a
--R           + 
--R             - 5a + 1
--R        *
--R            +------------------+
--R            |        2
--R           \|- 4b + a  - 2a + 1
--R       + 
--R               2       2                  4      3      2            2    2
--R         (- 48b  + (24a  - 48a + 24)b - 3a  + 12a  - 18a  + 12a - 3)x y(x)
--R       + 
--R                          2       3      2                  5      4      3
--R             (- 48a + 48)b  + (24a  - 72a  + 72a - 24)b - 3a  + 15a  - 30a
--R           + 
--R                2
--R             30a  - 15a + 3
--R        *
--R           x y(x)
--R       + 
--R            3         2             2      4      3      2                6
--R         16b  + (- 24a  + 48a - 24)b  + (9a  - 36a  + 54a  - 36a + 9)b - a
--R       + 
--R           5      4      3      2
--R         6a  - 15a  + 20a  - 15a  + 6a - 1
--R    *
--R                   +------------------+ 2
--R                   |        2
--R          - log(x)\|- 4b + a  - 2a + 1
--R       (%e                             )
--R                                                     Type: Expression Integer
--E 100

-------------------------------------------------------------------
--S 101 of 126
ode142 := x**2*(D(y(x),x)-y(x)**2) - a*x**2*y(x) + a*x + 2
 

           2 ,       2    2      2
   (101)  x y (x) - x y(x)  - a x y(x) + a x + 2

                                                     Type: Expression Integer
--R
--R           2 ,       2    2      2
--R   (101)  x y (x) - x y(x)  - a x y(x) + a x + 2
--R
--R                                                     Type: Expression Integer
--E 101


--S 102 of 126
yx:=solve(ode142,y,x)
 

            2 3       2              3 3    2 2
          (a x  - 2a x  + 2x)y(x) + a x  - a x  + 2a x - 2
   (102)  ------------------------------------------------
                         3          3   - a x
                       (a x y(x) - a )%e
                                          Type: Union(Expression Integer,...)
--R
--R            2 3       2              3 3    2 2
--R          (a x  - 2a x  + 2x)y(x) + a x  - a x  + 2a x - 2
--R   (102)  ------------------------------------------------
--R                         3          3   - a x
--R                       (a x y(x) - a )%e
--R                                          Type: Union(Expression Integer,...)
--E 102

--S 103 of 126
ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2
 

   (103)
          6 6  - a x ,
       - a x %e     y (x)

     + 
          7 3     6 2     2        7 2     6          7      6    - a x 2
       ((a x  + 2a x )y(x)  + (- 2a x  - 4a x)y(x) + a x + 2a )(%e     )
     + 
              5 5     4 4     2      6 5     5 4     4 3          6 4     5 3
           (2a x  - 2a x )y(x)  + (2a x  - 4a x  + 4a x )y(x) - 3a x  + 2a x
         + 
               4 2
           - 2a x
      *
           - a x
         %e
     + 
           4 8     3 7     2 6       5     4     2
       (- a x  + 4a x  - 8a x  + 8a x  - 4x )y(x)
     + 
            5 8     4 7      3 6      2 5        4     3         6 8     5 7
       (- 2a x  + 6a x  - 12a x  + 16a x  - 16a x  + 8x )y(x) - a x  + 2a x
     + 
           4 6     3 5     2 4       3     2
       - 5a x  + 8a x  - 8a x  + 8a x  - 4x
  /
       6 2    2     6          6    - a x 2
     (a x y(x)  - 2a x y(x) + a )(%e     )
                                                     Type: Expression Integer
--R
--R   (103)
--R          6 6  - a x ,
--R       - a x %e     y (x)
--R
--R     + 
--R          7 3     6 2     2        7 2     6          7      6    - a x 2
--R       ((a x  + 2a x )y(x)  + (- 2a x  - 4a x)y(x) + a x + 2a )(%e     )
--R     + 
--R              5 5     4 4     2      6 5     5 4     4 3          6 4     5 3
--R           (2a x  - 2a x )y(x)  + (2a x  - 4a x  + 4a x )y(x) - 3a x  + 2a x
--R         + 
--R               4 2
--R           - 2a x
--R      *
--R           - a x
--R         %e
--R     + 
--R           4 8     3 7     2 6       5     4     2
--R       (- a x  + 4a x  - 8a x  + 8a x  - 4x )y(x)
--R     + 
--R            5 8     4 7      3 6      2 5        4     3         6 8     5 7
--R       (- 2a x  + 6a x  - 12a x  + 16a x  - 16a x  + 8x )y(x) - a x  + 2a x
--R     + 
--R           4 6     3 5     2 4       3     2
--R       - 5a x  + 8a x  - 8a x  + 8a x  - 4x
--R  /
--R       6 2    2     6          6    - a x 2
--R     (a x y(x)  - 2a x y(x) + a )(%e     )
--R                                                     Type: Expression Integer
--E 103

-------------------------------------------------------------------
--S 104 of 126
ode143 := x**2*(D(y(x),x)+a*y(x)**2) - b
 

           2 ,         2    2
   (104)  x y (x) + a x y(x)  - b

                                                     Type: Expression Integer
--R
--R           2 ,         2    2
--R   (104)  x y (x) + a x y(x)  - b
--R
--R                                                     Type: Expression Integer
--E 104


--S 105 of 126
yx:=solve(ode143,y,x)
 
                                                     2
   WARNING (genufact): No known algorithm to factor ?  - ? - a b
     , trying square-free.

                            +--------+     2
                          a\|4a b + 1  - 2a x y(x) + a
   (105)  ------------------------------------------------------------
                                                            +--------+
                           +--------+              - log(x)\|4a b + 1
          ((2a x y(x) - 1)\|4a b + 1  + 4a b + 1)%e
                                          Type: Union(Expression Integer,...)
--R                                                     2
--R   WARNING (genufact): No known algorithm to factor ?  - ? - a b
--R     , trying square-free.
--R
--R                            +--------+     2
--R                          a\|4a b + 1  - 2a x y(x) + a
--R   (105)  ------------------------------------------------------------
--R                                                            +--------+
--R                           +--------+              - log(x)\|4a b + 1
--R          ((2a x y(x) - 1)\|4a b + 1  + 4a b + 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 105

--S 106 of 126
ode143expr := x**2*(D(yx,x)+a*yx**2) - b
 

   (106)
                                  +--------+
            3      2  3  - log(x)\|4a b + 1  ,
       (- 8a b - 2a )x %e                   y (x)

     + 
                 2 2                     2      +--------+
           ((- 8a b  - 2a b)x y(x) + 4a b  + b)\|4a b + 1
         + 
                3 2     2   2    2      2 2                   2 3       2
           (- 8a b  - 2a b)x y(x)  + (8a b  + 2a b)x y(x) - 8a b  - 6a b  - b
      *
                     +--------+ 2
            - log(x)\|4a b + 1
         (%e                   )
     + 
                                                           +--------+
             4      3  3    2      3 2     2      - log(x)\|4a b + 1
       ((- 8a b - 2a )x y(x)  + (8a b  + 2a b)x)%e
     + 
            4 3        3 2  +--------+     5 4    2     4 3          4     3  2
       (- 2a x y(x) + a x )\|4a b + 1  + 2a x y(x)  - 2a x y(x) + (2a b + a )x
  /
             2                          +--------+      3      2  2    2
         ((8a b + 2a)x y(x) - 4a b - 1)\|4a b + 1  + (8a b + 2a )x y(x)
       + 
              2                  2 2
         (- 8a b - 2a)x y(x) + 8a b  + 6a b + 1
    *
                   +--------+ 2
          - log(x)\|4a b + 1
       (%e                   )
                                                     Type: Expression Integer
--R
--R   (106)
--R                                  +--------+
--R            3      2  3  - log(x)\|4a b + 1  ,
--R       (- 8a b - 2a )x %e                   y (x)
--R
--R     + 
--R                 2 2                     2      +--------+
--R           ((- 8a b  - 2a b)x y(x) + 4a b  + b)\|4a b + 1
--R         + 
--R                3 2     2   2    2      2 2                   2 3       2
--R           (- 8a b  - 2a b)x y(x)  + (8a b  + 2a b)x y(x) - 8a b  - 6a b  - b
--R      *
--R                     +--------+ 2
--R            - log(x)\|4a b + 1
--R         (%e                   )
--R     + 
--R                                                           +--------+
--R             4      3  3    2      3 2     2      - log(x)\|4a b + 1
--R       ((- 8a b - 2a )x y(x)  + (8a b  + 2a b)x)%e
--R     + 
--R            4 3        3 2  +--------+     5 4    2     4 3          4     3  2
--R       (- 2a x y(x) + a x )\|4a b + 1  + 2a x y(x)  - 2a x y(x) + (2a b + a )x
--R  /
--R             2                          +--------+      3      2  2    2
--R         ((8a b + 2a)x y(x) - 4a b - 1)\|4a b + 1  + (8a b + 2a )x y(x)
--R       + 
--R              2                  2 2
--R         (- 8a b - 2a)x y(x) + 8a b  + 6a b + 1
--R    *
--R                   +--------+ 2
--R          - log(x)\|4a b + 1
--R       (%e                   )
--R                                                     Type: Expression Integer
--E 106

-------------------------------------------------------------------
--S 107 of 126
ode144 := x**2*(D(y(x),x)+a*y(x)**2) + b*x**alpha + c
 

           2 ,         alpha      2    2
   (107)  x y (x) + b x      + a x y(x)  + c

                                                     Type: Expression Integer
--R
--R           2 ,         alpha      2    2
--R   (107)  x y (x) + b x      + a x y(x)  + c
--R
--R                                                     Type: Expression Integer
--E 107

--S 108 of 126
yx:=solve(ode144,y,x)
 

   (108)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (108)  "failed"
--R                                                    Type: Union("failed",...)
--E 108

-------------------------------------------------------------------
--S 109 of 126
ode145 := x**2*D(y(x),x) + a*y(x)**3 - a*x**2*y(x)**2
 

           2 ,            3      2    2
   (109)  x y (x) + a y(x)  - a x y(x)

                                                     Type: Expression Integer
--R
--R           2 ,            3      2    2
--R   (109)  x y (x) + a y(x)  - a x y(x)
--R
--R                                                     Type: Expression Integer
--E 109

--S 110 of 126
yx:=solve(ode145,y,x)
 

   (110)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (110)  "failed"
--R                                                    Type: Union("failed",...)
--E 110

-------------------------------------------------------------------
--S 111 of 126
ode146 := x**2*D(y(x),x) + x*y(x)**3 + a*y(x)**2
 

           2 ,            3         2
   (111)  x y (x) + x y(x)  + a y(x)

                                                     Type: Expression Integer
--R
--R           2 ,            3         2
--R   (111)  x y (x) + x y(x)  + a y(x)
--R
--R                                                     Type: Expression Integer
--E 111

--S 112 of 126
yx:=solve(ode146,y,x)
 

   (112)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (112)  "failed"
--R                                                    Type: Union("failed",...)
--E 112

-------------------------------------------------------------------
--S 113 of 126
ode147 := x**2*D(y(x),x) + a*x**2*y(x)**3 + b*y(x)**2
 

           2 ,         2    3         2
   (113)  x y (x) + a x y(x)  + b y(x)

                                                     Type: Expression Integer
--R
--R           2 ,         2    3         2
--R   (113)  x y (x) + a x y(x)  + b y(x)
--R
--R                                                     Type: Expression Integer
--E 113
--S 114 of 126
yx:=solve(ode147,y,x)
 

   (114)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (114)  "failed"
--R                                                    Type: Union("failed",...)
--E 114

-------------------------------------------------------------------
--S 115 of 126
ode148 := (x**2+1)*D(y(x),x) + x*y(x) - 1
 

            2      ,
   (115)  (x  + 1)y (x) + x y(x) - 1

                                                     Type: Expression Integer
--R
--R            2      ,
--R   (115)  (x  + 1)y (x) + x y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 115
--S 116 of 126
ode148a:=solve(ode148,y,x)
 

                              +------+
                              | 2
                         log(\|x  + 1  - x)             1
   (116)  [particular= - ------------------,basis= [---------]]
                               +------+              +------+
                               | 2                   | 2
                              \|x  + 1              \|x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                              +------+
--R                              | 2
--R                         log(\|x  + 1  - x)             1
--R   (116)  [particular= - ------------------,basis= [---------]]
--R                               +------+              +------+
--R                               | 2                   | 2
--R                              \|x  + 1              \|x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 116

--S 117 of 126
yx:=ode148a.particular
 

                 +------+
                 | 2
            log(\|x  + 1  - x)
   (117)  - ------------------
                  +------+
                  | 2
                 \|x  + 1
                                                     Type: Expression Integer
--R
--R                 +------+
--R                 | 2
--R            log(\|x  + 1  - x)
--R   (117)  - ------------------
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R                                                     Type: Expression Integer
--E 117

--S 118 of 126
ode148expr := (x**2+1)*D(yx,x) + x*yx - 1
 

   (118)  0
                                                     Type: Expression Integer
--R
--R   (118)  0
--R                                                     Type: Expression Integer
--E 118

-------------------------------------------------------------------
--S 119 of 126
ode149 := (x**2+1)*D(y(x),x) + x*y(x) - x*(x**2+1)
 

            2      ,                3
   (119)  (x  + 1)y (x) + x y(x) - x  - x

                                                     Type: Expression Integer
--R
--R            2      ,                3
--R   (119)  (x  + 1)y (x) + x y(x) - x  - x
--R
--R                                                     Type: Expression Integer
--E 119
--S 120 of 126
ode149a:=solve(ode149,y,x)
 

                        2
                       x  + 1             1
   (120)  [particular= ------,basis= [---------]]
                          3            +------+
                                       | 2
                                      \|x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                        2
--R                       x  + 1             1
--R   (120)  [particular= ------,basis= [---------]]
--R                          3            +------+
--R                                       | 2
--R                                      \|x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 120

--S 121 of 126
yx:=ode149a.particular
 

           2
          x  + 1
   (121)  ------
             3
                                                     Type: Expression Integer
--R
--R           2
--R          x  + 1
--R   (121)  ------
--R             3
--R                                                     Type: Expression Integer
--E 121

--S 122 of 126
ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1)
 

   (122)  0
                                                     Type: Expression Integer
--R
--R   (122)  0
--R                                                     Type: Expression Integer
--E 122

-------------------------------------------------------------------
--S 123 of 126
ode150 := (x**2+1)*D(y(x),x) + 2*x*y(x) - 2*x**2
 

            2      ,                  2
   (123)  (x  + 1)y (x) + 2x y(x) - 2x

                                                     Type: Expression Integer
--R
--R            2      ,                  2
--R   (123)  (x  + 1)y (x) + 2x y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 123

--S 124 of 126
ode150a:=solve(ode150,y,x)
 

                         3
                       2x  + 3            1
   (124)  [particular= -------,basis= [------]]
                         2              2
                       3x  + 3         x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                         3
--R                       2x  + 3            1
--R   (124)  [particular= -------,basis= [------]]
--R                         2              2
--R                       3x  + 3         x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 124

--S 125 of 126
yx:=ode150a.particular
 

            3
          2x  + 3
   (125)  -------
            2
          3x  + 3
                                                     Type: Expression Integer
--R
--R            3
--R          2x  + 3
--R   (125)  -------
--R            2
--R          3x  + 3
--R                                                     Type: Expression Integer
--E 125

--S 126 of 126
ode150expr := (x**2+1)*D(yx,x) + 2*x*yx - 2*x**2
 

   (126)  0
                                                     Type: Expression Integer
--R
--R   (126)  0
--R                                                     Type: Expression Integer
--E 126
)spool
 
Starts dribbling to is.output (2010/3/27, 18:27:18).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
f: INT -> INT
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 1

--S 2 of 5
f n ==
   not empty?(u := Is(n, 2*m%)) => integer eval(m%, u)
   3 * n + 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

)set stream showall on
 
 
--S 3 of 5
g(n:INT):STREAM(INT) == generate(f, n)
 
   Function declaration g : Integer -> Stream Integer has been added to
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration g : Integer -> Stream Integer has been added to
--R      workspace.
--R                                                                   Type: Void
--E 3

--S 4 of 5
s := g 27
 
   Compiling function g with type Integer -> Stream Integer 
   Compiling function f with type Integer -> Integer 

   (4)  [27,82,41,124,62,31,94,47,142,71,...]
                                                         Type: Stream Integer
--R 
--R   Compiling function g with type Integer -> Stream Integer 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (4)  [27,82,41,124,62,31,94,47,142,71,...]
--R                                                         Type: Stream Integer
--E 4

--S 5 of 5
extend(s, 150)
 

   (5)
   [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242,
    121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350,
    175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167,
    502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479,
    1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734,
    1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433,
    1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53,
    160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20,
    10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4,
    2, 7, 22, 11, 34, 17, 52, 26, ...]
                                                         Type: Stream Integer
--R 
--R
--R   (5)
--R   [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242,
--R    121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350,
--R    175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167,
--R    502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479,
--R    1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734,
--R    1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433,
--R    1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53,
--R    160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20,
--R    10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4,
--R    2, 7, 22, 11, 34, 17, 52, 26, ...]
--R                                                         Type: Stream Integer
--E 5
)spool 
 
Starts dribbling to void.output (2010/3/27, 18:41:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 4
a : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

)set message void on
 

--S 2 of 4
b : Fraction Integer
 

   (2)  "()"
                                                                   Type: Void
--R 
--R
--R   (2)  "()"
--R                                                                   Type: Void
--E 2

)set message void off
 

--S 3 of 4
3::Void
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
% :: PositiveInteger
 
 
Daly Bug
   Cannot convert from type Void to PositiveInteger for value
   "()"

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Void to PositiveInteger for value
--R   "()"
--R
--E 4
)spool 
 
Starts dribbling to seccsc.output (2010/3/27, 18:38:52).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.01,1.0000500,sec(0.01),sec(0.01)-1.0000500],_
[0.02,1.0002000,sec(0.02),sec(0.02)-1.0002000],_
[0.03,1.0004502,sec(0.03),sec(0.03)-1.0004502],_
[0.04,1.0008005,sec(0.04),sec(0.04)-1.0008005],_
[0.05,1.0012513,sec(0.05),sec(0.05)-1.0012513],_
[0.06,1.0018027,sec(0.06),sec(0.06)-1.0018027],_
[0.07,1.0024550,sec(0.07),sec(0.07)-1.0024550],_
[0.08,1.0032086,sec(0.08),sec(0.08)-1.0032086],_
[0.09,1.0040637,sec(0.09),sec(0.09)-1.0040637],_
[0.10,1.0050209,sec(0.10),sec(0.10)-1.0050209],_
[0.11,1.0060807,sec(0.11),sec(0.11)-1.0060807],_
[0.12,1.0072435,sec(0.12),sec(0.12)-1.0072435],_
[0.13,1.0085099,sec(0.13),sec(0.13)-1.0085099],_
[0.14,1.0098807,sec(0.14),sec(0.14)-1.0098807],_
[0.15,1.0113564,sec(0.15),sec(0.15)-1.0113564],_
[0.16,1.0129380,sec(0.16),sec(0.16)-1.0129380],_
[0.17,1.0146261,sec(0.17),sec(0.17)-1.0146261],_
[0.18,1.0164216,sec(0.18),sec(0.18)-1.0164216],_
[0.19,1.0183255,sec(0.19),sec(0.19)-1.0183255],_
[0.20,1.0203388,sec(0.20),sec(0.20)-1.0203388],_
[0.21,1.0224626,sec(0.21),sec(0.21)-1.0224626],_
[0.22,1.0246978,sec(0.22),sec(0.22)-1.0246978],_
[0.23,1.0270458,sec(0.23),sec(0.23)-1.0270458],_
[0.24,1.0295078,sec(0.24),sec(0.24)-1.0295078],_
[0.25,1.0320850,sec(0.25),sec(0.25)-1.0320850],_
[0.26,1.0347789,sec(0.26),sec(0.26)-1.0347789],_
[0.27,1.0375910,sec(0.27),sec(0.27)-1.0375910],_
[0.28,1.0405227,sec(0.28),sec(0.28)-1.0405227],_
[0.29,1.0435757,sec(0.29),sec(0.29)-1.0435757],_
[0.30,1.0467516,sec(0.30),sec(0.30)-1.0467516],_
[0.31,1.0500522,sec(0.31),sec(0.31)-1.0500522],_
[0.32,1.0534794,sec(0.32),sec(0.32)-1.0534794],_
[0.33,1.0570351,sec(0.33),sec(0.33)-1.0570351],_
[0.34,1.0607213,sec(0.34),sec(0.34)-1.0607213],_
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R                                                        Type: List List Float
--E 1

--S 2 of 2
[[0.01,100.0016667,csc(0.01),csc(0.01)-100.0016667],_
[0.02,50.0033335,csc(0.02),csc(0.02)-50.0033335],_
[0.03,33.3383339,csc(0.03),csc(0.03)-33.3383339],_
[0.04,25.0066679,csc(0.04),csc(0.04)-25.0066679],_
[0.05,20.0083358,csc(0.05),csc(0.05)-20.0083358],_
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   (2)
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                                                        Type: List List Float
--R 
--R
--R   (2)
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--R    [1.34,1.0272377,1.0272376778 151033218,- 0.2218489667 82 E -7],
--R    [1.35,1.0248807,1.0248806610 794017372,- 0.3892059826 28 E -7],
--R    [1.36,1.0226365,1.0226364647 10509886,- 0.3528949011 4 E -7],
--R    [1.37,1.0205039,1.0205039017 361575009,0.1736157500 9 E -8],
--R    [1.38,1.0184818,1.0184818499 565392157,0.4995653921 57 E -7],
--R    [1.39,1.0165693,1.0165692504 705818114,- 0.4952941818 86 E -7],
--R    [1.4,1.0147651,1.0147651062 948794009,0.6294879400 9 E -8],
--R    [1.41,1.0130685,1.0130684810 718793105,- 0.1892812068 95 E -7],
--R    [1.42,1.0114785,1.0114784978 641485933,- 0.2135851406 7 E -8],
--R    [1.43,1.0099943,1.0099943380 317855887,0.3803178558 87 E -7],
--R    [1.44,1.0086152,1.0086152401 902637594,0.4019026375 94 E -7],
--R    [1.45,1.0073405,1.0073404992 46207189,- 0.753792811 E -9],
--R    [1.46,1.0061695,1.0061694655 087995079,- 0.3449120049 21 E -7],
--R    [1.47,1.0051015,1.0051015438 747215132,0.4387472151 32 E -7],
--R    [1.48,1.0041362,1.0041361930 846981533,- 0.6915301846 7 E -8],
--R    [1.49,1.0032729,1.0032729250 49913637,0.2504991363 7 E -7],
--R    [1.5,1.0025113,1.0025113042 4672491,0.424672491 E -8],
--R    [1.51,1.0018509,1.0018509471 78269319,0.4717826931 9 E -7],
--R    [1.52,1.0012915,1.0012915219 017225962,0.2190172259 62 E -7],
--R    [1.53,1.0008327,1.0008327476 201189712,0.4762011897 12 E -7],
--R    [1.54,1.0004744,1.0004743943 377968613,- 0.5662203138 7 E -8],
--R    [1.55,1.0002163,1.0002162825 786817653,- 0.1742131823 47 E -7],
--R    [1.56,1.0000583,1.0000582831 667632601,- 0.1683323673 99 E -7],
--R    [1.57,1.0000003,1.0000003170 68265912,0.1706826591 2 E -7],
--R    [1.58,1.0000424,1.0000423552 951549942,- 0.4470484500 58 E -7],
--R    [1.59,1.0001844,1.0001844188 697576625,0.1886975766 25 E -7],
--R    [1.6,1.0004266,1.0004265788 504192126,- 0.2114958078 74 E -7]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to mathml.output (2010/3/27, 18:29:52).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 21
(x+y)**2
 

         2           2
   (1)  y  + 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2           2
--R   (1)  y  + 2x y + x
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 21
coerce(%)$MMLFORM
 

   (2)
  "<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mro
  w><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0
  .3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><m
  n>2</mn></mrow></msup></mrow></mrow>"
                                                                 Type: String
--R 
--R
--R   (2)
--R  "<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mro
--R  w><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0
--R  .3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><m
--R  n>2</mn></mrow></msup></mrow></mrow>"
--R                                                                 Type: String
--E 2

--S 3 of 21
(x+y)**2
 

         2           2
   (3)  y  + 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2           2
--R   (3)  y  + 2x y + x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 21
display(coerce(%)$MMLFORM)$MMLFORM
 
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
</math>
                                                                   Type: Void
--R 
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
--R</math>
--R                                                                   Type: Void
--E 4

)set output mathml on
 

--S 5 of 21
(x+y)**2
 

         2           2
   (5)  y  + 2x y + x
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
</math>

                                                     Type: Polynomial Integer
--R 
--R
--R         2           2
--R   (5)  y  + 2x y + x
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mrow><mn>2</mn><mspace width='0.3em'/><mi>x</mi><mspace width='0.3em'/><mi>y</mi></mrow><mo>+</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow>
--R</math>
--R
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 21
integrate(x**x,x)
 

           x
         ++    %I
   (6)   |   %I  d%I
        ++
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
</math>

                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    %I
--R   (6)   |   %I  d%I
--R        ++
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
--R</math>
--R
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 21
integral(x**x,x)
 

           x
         ++    %I
   (7)   |   %I  d%I
        ++
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
</math>

                                                     Type: Expression Integer
--R 
--R
--R           x
--R         ++    %I
--R   (7)   |   %I  d%I
--R        ++
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>&#x0222B;</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mo>&#x02146;</mo><mi>x</mi></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 21
(5+sqrt 63 + sqrt 847)**(1/3)
 

         +----------+
        3|   +-+
   (8)  \|14\|7  + 5
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mroot><mrow><mrow><mrow><mrow><mrow><mn>14</mn></mrow><mspace width='0.3em'/><msqrt><mrow><mn>7</mn></mrow></msqrt></mrow><mo>+</mo><mn>5</mn></mrow></mrow></mrow><mn>3</mn></mroot></mrow>
</math>

                                                        Type: AlgebraicNumber
--R 
--R
--R         +----------+
--R        3|   +-+
--R   (8)  \|14\|7  + 5
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mroot><mrow><mrow><mrow><mrow><mrow><mn>14</mn></mrow><mspace width='0.3em'/><msqrt><mrow><mn>7</mn></mrow></msqrt></mrow><mo>+</mo><mn>5</mn></mrow></mrow></mrow><mn>3</mn></mroot></mrow>
--R</math>
--R
--R                                                        Type: AlgebraicNumber
--E 8

--S 9 of 21
set [1,2,3]
 

   (9)  {1,2,3}
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow>
</math>

                                                    Type: Set PositiveInteger
--R 
--R
--R   (9)  {1,2,3}
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow>
--R</math>
--R
--R                                                    Type: Set PositiveInteger
--E 9

--S 10 of 21
multiset [x rem 5 for x in primes(2,1000)]
 

   (10)  {0,40: 1,47: 2,42: 3,38: 4}
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>{</mo><mn>0</mn><mo>,</mo><mrow><mrow><mn>40</mn></mrow><mtext>: </mtext><mn>1</mn></mrow><mo>,</mo><mrow><mrow><mn>47</mn></mrow><mtext>: </mtext><mn>2</mn></mrow><mo>,</mo><mrow><mrow><mn>42</mn></mrow><mtext>: </mtext><mn>3</mn></mrow><mo>,</mo><mrow><mrow><mn>38</mn></mrow><mtext>: </mtext><mn>4</mn></mrow><mo>}</mo></mrow>
</math>

                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {0,40: 1,47: 2,42: 3,38: 4}
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>{</mo><mn>0</mn><mo>,</mo><mrow><mrow><mn>40</mn></mrow><mtext>: </mtext><mn>1</mn></mrow><mo>,</mo><mrow><mrow><mn>47</mn></mrow><mtext>: </mtext><mn>2</mn></mrow><mo>,</mo><mrow><mrow><mn>42</mn></mrow><mtext>: </mtext><mn>3</mn></mrow><mo>,</mo><mrow><mrow><mn>38</mn></mrow><mtext>: </mtext><mn>4</mn></mrow><mo>}</mo></mrow>
--R</math>
--R
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 21
series(sin(a*x),x=0)
 

                3        5        7          9            11
               a   3    a   5    a    7     a     9      a      11      12
   (11)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
                6      120      5040      362880      39916800
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><mi>a</mi><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>39916800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>12</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                3        5        7          9            11
--R               a   3    a   5    a    7     a     9      a      11      12
--R   (11)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R                6      120      5040      362880      39916800
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><mi>a</mi><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>39916800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>12</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11

--S 12 of 21
matrix [[xi+yj for i in 1..10] for j in 1..10]
 

   (12)
   [
     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ,

     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
      yj + xi, yj + xi]
     ]
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>[</mo><mtable><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr></mtable><mo>]</mo></mrow>
</math>

                                              Type: Matrix Polynomial Integer
--R 
--R
--R   (12)
--R   [
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ,
--R
--R     [yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi, yj + xi,
--R      yj + xi, yj + xi]
--R     ]
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>[</mo><mtable><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd><mtd><mrow><mi>yj</mi><mo>+</mo><mi>xi</mi></mrow></mtd></mtr></mtable><mo>]</mo></mrow>
--R</math>
--R
--R                                              Type: Matrix Polynomial Integer
--E 12

--S 13 of 21
y:=operator 'y
 

   (13)  y
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mi>y</mi>
</math>

                                                          Type: BasicOperator
--R 
--R
--R   (13)  y
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mi>y</mi>
--R</math>
--R
--R                                                          Type: BasicOperator
--E 13

--S 14 of 21
D(y(x,z),[x,x,z,x])
 

   (14)  y        (x,z)
          ,1,1,2,1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<msub><mi>y</mi><mrow><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>(</mo><mi><mi>x</mi></mi><mo>,</mo><mi><mi>z</mi></mi><mo>)</mo>
</math>

                                                     Type: Expression Integer
--R 
--R
--R   (14)  y        (x,z)
--R          ,1,1,2,1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<msub><mi>y</mi><mrow><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>(</mo><mi><mi>x</mi></mi><mo>,</mo><mi><mi>z</mi></mi><mo>)</mo>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 14

)clear all
 

--S 15 of 21
y:=operator 'y
 

   (1)  y
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mi>y</mi>
</math>

                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mi>y</mi>
--R</math>
--R
--R                                                          Type: BasicOperator
--E 15

--S 16 of 21
D(y x,x,2)
 

         ,,
   (2)  y  (x)

<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<msup><mi>y</mi><mrow><mo>&#x02032;</mo><mo>&#x02032;</mo></mrow></msup><mo>&#x02061;</mo><mo>(</mo><mi>x</mi><mo>)</mo>
</math>

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (2)  y  (x)
--R
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<msup><mi>y</mi><mrow><mo>&#x02032;</mo><mo>&#x02032;</mo></mrow></msup><mo>&#x02061;</mo><mo>(</mo><mi>x</mi><mo>)</mo>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 16

--S 17 of 21
x:=series 'x
 

   (3)  x
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mi>x</mi>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)  x
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mi>x</mi>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 17

--S 18 of 21
sin(1+x)
 

   (4)
                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
                           2           6          24          120
   + 
       sin(1)  6   cos(1)  7   sin(1)  8   cos(1)  9    sin(1)  10      11
     - ------ x  - ------ x  + ------ x  + ------ x  - ------- x   + O(x  )
         720        5040        40320      362880      3628800
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>40320</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (4)
--R                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
--R     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
--R                           2           6          24          120
--R   + 
--R       sin(1)  6   cos(1)  7   sin(1)  8   cos(1)  9    sin(1)  10      11
--R     - ------ x  - ------ x  + ------ x  + ------ x  - ------- x   + O(x  )
--R         720        5040        40320      362880      3628800
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mspace width='0.3em'/><mi>x</mi></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>120</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>5040</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>40320</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>cos</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>362880</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mo><mo>sin</mo></mo><mo>(</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 18

)clear all
 

--S 19 of 21
series(1/log(y),y=1)
 

   (1)
            - 1   1    1            1        2    19        3    3         4
     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
                  2   12           24            720            160
   + 
        863         5    275         6    33953         7     8183         8
     - ----- (y - 1)  + ----- (y - 1)  - ------- (y - 1)  + ------- (y - 1)
       60480            24192            3628800            1036800
   + 
        3250433         9            10
     - --------- (y - 1)  + O((y - 1)  )
       479001600
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup></mrow><mo>+</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>12</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>19</mn></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mrow><mn>160</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>863</mn></mrow></mrow><mrow><mrow><mn>60480</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>275</mn></mrow></mrow><mrow><mrow><mn>24192</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>33953</mn></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>8183</mn></mrow></mrow><mrow><mrow><mn>1036800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>3250433</mn></mrow></mrow><mrow><mrow><mn>479001600</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--R 
--R
--R   (1)
--R            - 1   1    1            1        2    19        3    3         4
--R     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
--R                  2   12           24            720            160
--R   + 
--R        863         5    275         6    33953         7     8183         8
--R     - ----- (y - 1)  + ----- (y - 1)  - ------- (y - 1)  + ------- (y - 1)
--R       60480            24192            3628800            1036800
--R   + 
--R        3250433         9            10
--R     - --------- (y - 1)  + O((y - 1)  )
--R       479001600
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup></mrow><mo>+</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>12</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mn>24</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>19</mn></mrow></mrow><mrow><mrow><mn>720</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mrow><mn>160</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>863</mn></mrow></mrow><mrow><mrow><mn>60480</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>275</mn></mrow></mrow><mrow><mrow><mn>24192</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>33953</mn></mrow></mrow><mrow><mrow><mn>3628800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mrow><mfrac><mrow><mrow><mn>8183</mn></mrow></mrow><mrow><mrow><mn>1036800</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>-</mo><mrow><mrow><mfrac><mrow><mrow><mn>3250433</mn></mrow></mrow><mrow><mrow><mn>479001600</mn></mrow></mrow></mfrac></mrow><mspace width='0.3em'/><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--E 19

)clear all
 

--S 20 of 21
y:UTS(FLOAT,'z,0):=exp(z)
 

   (1)
                    2                            3
     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
   + 
                                4                               5
     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
   + 
                                 6                               7
     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 z  + 0.0000027557 3192239858 90653 z
   + 
                                   10      11
     0.2755731922 3985890653 E -6 z   + O(z  )
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mn>1.0</mn><mo>+</mo><mi>z</mi><mo>+</mo><mrow><mn>0.5</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.1666666666 6666666667</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0416666666 6666666666 7</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0083333333 3333333333 34</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0013888888 8888888888 89</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0001984126 9841269841 27</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000248015 8730158730 1587</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000027557 3192239858 90653</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.2755731922 3985890653 E -6</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
</math>

                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--R 
--R
--R   (1)
--R                    2                            3
--R     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 z  + 0.0000027557 3192239858 90653 z
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 z   + O(z  )
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mn>1.0</mn><mo>+</mo><mi>z</mi><mo>+</mo><mrow><mn>0.5</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.1666666666 6666666667</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0416666666 6666666666 7</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0083333333 3333333333 34</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0013888888 8888888888 89</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>6</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0001984126 9841269841 27</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>7</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000248015 8730158730 1587</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>8</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.0000027557 3192239858 90653</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn>9</mn></mrow></msup></mrow></mrow><mo>+</mo><mrow><mn>0.2755731922 3985890653 E -6</mn><mspace width='0.3em'/><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>10</mn></mrow></mrow></msup></mrow></mrow><mo>+</mo><mrow><mo><mi>O</mi></mo><mo>(</mo><mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mrow><mn>11</mn></mrow></mrow></msup></mrow></mrow><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--E 20

--S 21 of 21
c:=continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (2)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mn>3</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>15</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>25</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow>
</math>

                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (2)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mn>3</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>15</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mrow><mn>25</mn></mrow></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>1</mn></mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn><mn>7</mn></mn><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow></mfrac></mrow>
--R</math>
--R
--R                                              Type: ContinuedFraction Integer
--E 21
)spool
 
Starts dribbling to complex.output (2010/3/27, 18:24:34).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from ComplexXmpPage

--S 1 of 16
a := complex(4/3,5/2)
 

        4   5
   (1)  - + - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (1)  - + - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 1

--S 2 of 16
b := complex(4/3,-5/2)
 

        4   5
   (2)  - - - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (2)  - - - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 2

--S 3 of 16
a + b
 

        8
   (3)  -
        3
                                               Type: Complex Fraction Integer
--R 
--R
--R        8
--R   (3)  -
--R        3
--R                                               Type: Complex Fraction Integer
--E 3

--S 4 of 16
a - b
 

   (4)  5%i
                                               Type: Complex Fraction Integer
--R 
--R
--R   (4)  5%i
--R                                               Type: Complex Fraction Integer
--E 4

--S 5 of 16
a * b
 

        289
   (5)  ---
         36
                                               Type: Complex Fraction Integer
--R 
--R
--R        289
--R   (5)  ---
--R         36
--R                                               Type: Complex Fraction Integer
--E 5

--S 6 of 16
a / b
 

          161   240
   (6)  - --- + --- %i
          289   289
                                               Type: Complex Fraction Integer
--R 
--R
--R          161   240
--R   (6)  - --- + --- %i
--R          289   289
--R                                               Type: Complex Fraction Integer
--E 6

--S 7 of 16
% :: Fraction Complex Integer
 

        - 15 + 8%i
   (7)  ----------
         15 + 8%i
                                               Type: Fraction Complex Integer
--R 
--R
--R        - 15 + 8%i
--R   (7)  ----------
--R         15 + 8%i
--R                                               Type: Fraction Complex Integer
--E 7

--S 8 of 16
3.4 + 6.7 * %i
 

   (8)  3.4 + 6.7 %i
                                                          Type: Complex Float
--R 
--R
--R   (8)  3.4 + 6.7 %i
--R                                                          Type: Complex Float
--E 8

--S 9 of 16
conjugate a
 

        4   5
   (9)  - - - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (9)  - - - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 9

--S 10 of 16
norm a
 

         289
   (10)  ---
          36
                                                       Type: Fraction Integer
--R 
--R
--R         289
--R   (10)  ---
--R          36
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 16
real a
 

         4
   (11)  -
         3
                                                       Type: Fraction Integer
--R 
--R
--R         4
--R   (11)  -
--R         3
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 16
imag a
 

         5
   (12)  -
         2
                                                       Type: Fraction Integer
--R 
--R
--R         5
--R   (12)  -
--R         2
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 16
gcd(13 - 13*%i,31 + 27*%i)
 

   (13)  5 + %i
                                                        Type: Complex Integer
--R 
--R
--R   (13)  5 + %i
--R                                                        Type: Complex Integer
--E 13

--S 14 of 16
lcm(13 - 13*%i,31 + 27*%i)
 

   (14)  143 - 39%i
                                                        Type: Complex Integer
--R 
--R
--R   (14)  143 - 39%i
--R                                                        Type: Complex Integer
--E 14

--S 15 of 16
factor(13 - 13*%i)
 

   (15)  - (1 + %i)(2 + 3%i)(3 + 2%i)
                                               Type: Factored Complex Integer
--R 
--R
--R   (15)  - (1 + %i)(2 + 3%i)(3 + 2%i)
--R                                               Type: Factored Complex Integer
--E 15

--S 16 of 16
factor complex(2,0)
 

                      2
   (16)  - %i (1 + %i)
                                               Type: Factored Complex Integer
--R 
--R
--R                      2
--R   (16)  - %i (1 + %i)
--R                                               Type: Factored Complex Integer
--E 16
)spool
 
Starts dribbling to macbug.output (2010/3/27, 18:28:58).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
macro ff(x) == x**2 + 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 5
ff z
 

         2
   (2)  z  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (2)  z  + 1
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 5
macro gg(x) == ff(2*x - 2/3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
gg(1/w)
 

           2
        13w  - 24w + 36
   (4)  ---------------
                2
              9w
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2
--R        13w  - 24w + 36
--R   (4)  ---------------
--R                2
--R              9w
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 5
macro ff(x) == gg(-x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
)spool 
 
Starts dribbling to lindep.output (2010/3/27, 18:28:40).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
v(i:INT):DIRPROD(5, FRAC INT) ==
   directProduct vector [i / (i + j) for j in 0..4]
 
   Function declaration v : Integer -> DirectProduct(5,Fraction Integer
      ) has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration v : Integer -> DirectProduct(5,Fraction Integer
--R      ) has been added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 10
V := vector [v i for i in 1..6]
 
   Compiling function v with type Integer -> DirectProduct(5,Fraction 
      Integer) 

   (2)
       1 1 1 1     2 1 2 1     3 3 1 3     4 2 4 1     5 5 5 5     6 3 2 3
   [[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-]]
       2 3 4 5     3 2 5 3     4 5 2 7     5 3 7 2     6 7 8 9     7 4 3 5
                               Type: Vector DirectProduct(5,Fraction Integer)
--R 
--R   Compiling function v with type Integer -> DirectProduct(5,Fraction 
--R      Integer) 
--R
--R   (2)
--R       1 1 1 1     2 1 2 1     3 3 1 3     4 2 4 1     5 5 5 5     6 3 2 3
--R   [[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-],[1,-,-,-,-]]
--R       2 3 4 5     3 2 5 3     4 5 2 7     5 3 7 2     6 7 8 9     7 4 3 5
--R                               Type: Vector DirectProduct(5,Fraction Integer)
--E 2

--S 3 of 10
linearlyDependentOverZ? V
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 10
linearDependenceOverZ V
 

   (4)  [- 1,15,- 70,140,- 126,42]
                                              Type: Union(Vector Integer,...)
--R 
--R
--R   (4)  [- 1,15,- 70,140,- 126,42]
--R                                              Type: Union(Vector Integer,...)
--E 4

--S 5 of 10
solveLinearlyOverQ(delete(V, 2), V.2)
 

          1 14   28 42   14
   (5)  [--,--,- --,--,- --]
         15  3    3  5    5
                                     Type: Union(Vector Fraction Integer,...)
--R 
--R
--R          1 14   28 42   14
--R   (5)  [--,--,- --,--,- --]
--R         15  3    3  5    5
--R                                     Type: Union(Vector Fraction Integer,...)
--E 5

--S 6 of 10
w(i:INT):SQMATRIX(2, INT) ==
   squareMatrix matrix [[i, i + 1], [i - 1, -i]]
 
   Function declaration w : Integer -> SquareMatrix(2,Integer) has been
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration w : Integer -> SquareMatrix(2,Integer) has been
--R      added to workspace.
--R                                                                   Type: Void
--E 6

--S 7 of 10
W := vector [w i for i in 1..3]
 
   Compiling function w with type Integer -> SquareMatrix(2,Integer) 

         +1   2 + +2   3 + +3   4 +
   (7)  [|      |,|      |,|      |]
         +0  - 1+ +1  - 2+ +2  - 3+
                                         Type: Vector SquareMatrix(2,Integer)
--R 
--R   Compiling function w with type Integer -> SquareMatrix(2,Integer) 
--R
--R         +1   2 + +2   3 + +3   4 +
--R   (7)  [|      |,|      |,|      |]
--R         +0  - 1+ +1  - 2+ +2  - 3+
--R                                         Type: Vector SquareMatrix(2,Integer)
--E 7

--S 8 of 10
linearlyDependentOverZ? W
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 10
linearDependenceOverZ W
 

   (9)  [1,- 2,1]
                                              Type: Union(Vector Integer,...)
--R 
--R
--R   (9)  [1,- 2,1]
--R                                              Type: Union(Vector Integer,...)
--E 9

--S 10 of 10
solveLinearlyOverQ(delete(W, 2), W.2)
 

          1 1
   (10)  [-,-]
          2 2
                                     Type: Union(Vector Fraction Integer,...)
--R 
--R
--R          1 1
--R   (10)  [-,-]
--R          2 2
--R                                     Type: Union(Vector Fraction Integer,...)
--E 10
)spool 
 
Starts dribbling to atansqrt.output (2010/3/27, 18:23:10).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
z:=atan sqrt ((1-cos x)/(1+cos x))
 

              +------------+
              |- cos(x) + 1
   (1)  atan( |------------ )
             \| cos(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R              +------------+
--R              |- cos(x) + 1
--R   (1)  atan( |------------ )
--R             \| cos(x) + 1
--R                                                     Type: Expression Integer
--E 1
--S 2 of 3
integrate(differentiate(z,x),x)
 

        x
   (2)  -
        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        x
--R   (2)  -
--R        2
--R                                          Type: Union(Expression Integer,...)
--E 2
--S 3 of 3
rootSimp(normalize(z))
 

        x
   (3)  -
        2
                                                     Type: Expression Integer
--R 
--R
--R        x
--R   (3)  -
--R        2
--R                                                     Type: Expression Integer
--E 3
)spool
 
Starts dribbling to regset.output (2010/3/27, 18:36:50).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 34
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 34
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 34
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 34
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 34
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 34
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 34
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 34
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 34
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 34
T := REGSET(R,E,V,P)
 

   (10)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
--R  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
--R  ariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 34
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 34
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 34
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 34
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 34
zeroSetSplit(lp)$T
 

            5    4      2     3     8     5    3    2   4                2
   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R            5    4      2     3     8     5    3    2   4                2
--R   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 15

--S 16 of 34
lts := zeroSetSplit(lp,false)$T
 

   (16)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5          2     3         2
    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5          2     3         2
--R    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16

--S 17 of 34
[coHeight(ts) for ts in lts]
 

   (17)  [1,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (17)  [1,0,0]
--R                                                Type: List NonNegativeInteger
--E 17

--S 18 of 34
f1 := y**2*z+2*x*y*t-2*x-z
 

                          2
   (18)  (2t y - 2)x + z y  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                          2
--R   (18)  (2t y - 2)x + z y  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 18

--S 19 of 34
f2 :=   -x**3*z+ 4*x*y**2*z+ 4*x**2*y*t+ 2*y**3*t+ 4*x**2- 10*y**2+ 4*x*z- 10*y*t+ 2
 

              3              2        2              3      2
   (19)  - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R              3              2        2              3      2
--R   (19)  - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 19

--S 20 of 34
f3 :=  2*y*z*t+x*t**2-x-2*z
 

           2
   (20)  (t  - 1)x + 2t z y - 2z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           2
--R   (20)  (t  - 1)x + 2t z y - 2z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 20

--S 21 of 34
f4 :=   -x*z**3+ 4*y*z**2*t+ 4*x*z*t**2+ 2*y*t**3+ 4*x*z+ 4*z**2-10*y*t- 10*t**2+2
 

             3      2                2     3             2      2
   (21)  (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R             3      2                2     3             2      2
--R   (21)  (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 21

--S 22 of 34
lf := [f1, f2, f3, f4]
 

   (22)
                     2
   [(2t y - 2)x + z y  - z,
         3              2        2              3      2
    - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2,
      2
    (t  - 1)x + 2t z y - 2z,
        3      2                2     3             2      2
    (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (22)
--R                     2
--R   [(2t y - 2)x + z y  - z,
--R         3              2        2              3      2
--R    - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2,
--R      2
--R    (t  - 1)x + 2t z y - 2z,
--R        3      2                2     3             2      2
--R    (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 22

--S 23 of 34
zeroSetSplit(lf)$T
 

   (23)
      2      8      6       2                 3            2
   [{t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
       2      2     2
    {3t  + 1,z  - 7t  - 1,y + t,x + z},
      8      6      2         3            2
    {t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
      2      2
    {t  + 3,z  - 4,y + t,x - z}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (23)
--R      2      8      6       2                 3            2
--R   [{t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
--R       2      2     2
--R    {3t  + 1,z  - 7t  - 1,y + t,x + z},
--R      8      6      2         3            2
--R    {t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
--R      2      2
--R    {t  + 3,z  - 4,y + t,x - z}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 23

--S 24 of 34
lts2 := zeroSetSplit(lf,false)$T
 

   (24)
      8      6      2         3            2
   [{t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
      2      8      6       2                 3            2
    {t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
       2      2     2                     2      2
    {3t  + 1,z  - 7t  - 1,y + t,x + z}, {t  + 3,z  - 4,y + t,x - z}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (24)
--R      8      6      2         3            2
--R   [{t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
--R      2      8      6       2                 3            2
--R    {t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
--R       2      2     2                     2      2
--R    {3t  + 1,z  - 7t  - 1,y + t,x + z}, {t  + 3,z  - 4,y + t,x - z}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 24

--S 25 of 34
[coHeight(ts) for ts in lts2]
 

   (25)  [0,0,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (25)  [0,0,0,0]
--R                                                Type: List NonNegativeInteger
--E 25

--S 26 of 34
degrees := [degree(ts) for ts in lts2]
 

   (26)  [8,16,4,4]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (26)  [8,16,4,4]
--R                                                Type: List NonNegativeInteger
--E 26

--S 27 of 34
reduce(+,degrees)
 

   (27)  32
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  32
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 34
u : R := 2
 

   (28)  2
                                                                Type: Integer
--R 
--R
--R   (28)  2
--R                                                                Type: Integer
--E 28

--S 29 of 34
q1 := 2*(u-1)**2+ 2*(x-z*x+z**2)+ y**2*(x-1)**2- 2*u*x+ 2*y*t*(1-x)*(x-z)+ 2*u*z*t*(t-y)+ u**2*t**2*(1-2*z)+ 2*u*t**2*(z-x)+ 2*u*t*y*(z-1)+ 2*u*z*x*(y+1)+ (u**2-2*u)*z**2*t**2+ 2*u**2*z**2+ 4*u*(1-u)*z+ t**2*(z-x)**2
 

   (29)
       2           2  2        2                            2           2
     (y  - 2t y + t )x  + (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x
   + 
      2                      2       2          2
     y  + (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (29)
--R       2           2  2        2                            2           2
--R     (y  - 2t y + t )x  + (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x
--R   + 
--R      2                      2       2          2
--R     y  + (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 29

--S 30 of 34
q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+ u*y*(x+u-z*x-1)+ u*(u+1)*z**2*t
 

                                               2
   (30)  (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                                               2
--R   (30)  (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 30

--S 31 of 34
q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1)
 

                         2
   (31)  (- 2z - 2)x - 2z  + 8z - 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                         2
--R   (31)  (- 2z - 2)x - 2z  + 8z - 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 31

--S 32 of 34
q4 :=   u**2+4*(z-x**2)+3*y**2*(x-1)**2- 3*t**2*(z-x)**2 +3*u**2*t**2*(z-1)**2+u**2*z*(z-2)+6*u*t*y*(z+x+z*x-1)
 

   (32)
        2     2      2        2                      2        2
     (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y  + (12t z - 12t)y
   + 
        2      2         2            2
     (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (32)
--R        2     2      2        2                      2        2
--R     (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y  + (12t z - 12t)y
--R   + 
--R        2      2         2            2
--R     (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 32

--S 33 of 34
lq := [q1, q2, q3, q4]
 

   (33)
   [
         2           2  2
       (y  - 2t y + t )x
     + 
            2                            2           2          2
       (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x + y
     + 
                          2       2          2
       (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
     ,
                                          2                         2
    (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z, (- 2z - 2)x - 2z  + 8z - 2,

          2     2      2        2                      2        2
       (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y
     + 
                           2      2         2            2
       (12t z - 12t)y + (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
     ]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (33)
--R   [
--R         2           2  2
--R       (y  - 2t y + t )x
--R     + 
--R            2                            2           2          2
--R       (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x + y
--R     + 
--R                          2       2          2
--R       (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
--R     ,
--R                                          2                         2
--R    (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z, (- 2z - 2)x - 2z  + 8z - 2,
--R
--R          2     2      2        2                      2        2
--R       (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y
--R     + 
--R                           2      2         2            2
--R       (12t z - 12t)y + (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
--R     ]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 33

--S 34 of 34
zeroSetSplit(lq,true,true)$T
 
[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; {0}][2 <4,1>,<3,1> -> |7|; {0}][1 <3,1> -> |3|; {0}]G[2 <4,1>,<4,1> -> |8|; {0}]W[3 <5,1>,<4,1>,<3,2> -> |12|; {0}]GI[3 <4,2>,<4,1>,<3,2> -> |11|; {0}]GWw[3 <4,1>,<3,2>,<5,2> -> |12|; {0}][3 <3,2>,<3,2>,<5,2> -> |11|; {0}]GIwWWWw[4 <3,2>,<4,2>,<5,2>,<2,3> -> |14|; {0}][4 <2,2>,<4,2>,<5,2>,<2,3> -> |13|; {0}]Gwww[5 <3,2>,<3,2>,<4,2>,<5,2>,<2,3> -> |17|; {0}]Gwwwwww[8 <3,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}]Gwwwwww[8 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |31|; {0}][8 <3,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}][8 <2,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |29|; {0}][8 <1,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |28|; {0}][7 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |27|; {0}][6 <4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |23|; {0}][5 <4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |19|; {0}]GIGIWwww[6 <5,2>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |23|; {0}][6 <4,3>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |22|; {0}]GIGI[6 <3,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |21|; {0}][6 <2,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |20|; {0}]GGG[5 <4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |18|; {0}]GIGIWwwwW[6 <5,2>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |22|; {0}][6 <4,3>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |21|; {0}]GIwwWwWWWWWWWwWWWWwwwww[8 <4,2>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][8 <3,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}][8 <2,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |25|; {0}]Gwwwwwwwwwwwwwwwwwwww[9 <5,2>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |29|; {0}]GI[9 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |28|; {0}][9 <3,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][9 <2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}]GGwwwwwwwwwwwwWWwwwwwwww[11 <3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {0}][11 <2,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {0}][11 <1,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |31|; {0}]GGGwwwwwwwwwwwww[12 <2,3>,<2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {0}]GGwwwwwwwwwwwww[13 <3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}]Gwwwwwwwwwwwww[13 <2,3>,<3,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]GGGwwwwwwwwwwwww[15 <3,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {0}][14 <4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {0}]GIGGGGIGGI[14 <3,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GGG[14 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}][14 <1,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}]GGG[13 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]Gwwwwwwwwwwwww[15 <3,3>,<3,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]Gwwwwwwwwwwwww[15 <4,3>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |49|; {0}]GIGI[15 <3,4>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]G[14 <4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {0}][13 <3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]Gwwwwwwwwwwwww[13 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GIGGGGIGGI[13 <3,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]GGGGGGGG[13 <2,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}][13 <1,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}][13 <0,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}][12 <4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][11 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {1}][10 <3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |30|; {1}][10 <2,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |29|; {1}]GGGwwwwwwwwwwwww[11 <3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {1}]GGGwwwwwwwwwwwww[12 <4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}]Gwwwwwwwwwwwww[12 <3,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]GGwwwwwwwwwwwww[13 <5,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}]GIGGGGIGGIW[13 <4,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GGW[13 <3,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {1}]GGG[12 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]Gwwwwwwwwwwwww[12 <4,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]Gwwwwwwwwwwwww[13 <5,3>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {1}]GIGIW[13 <4,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {1}][13 <3,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}][13 <2,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GG[12 <5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {1}]GIGGGGIGGIW[12 <4,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]GGGGGGW[12 <3,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}][12 <2,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][12 <1,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |37|; {1}]GGG[11 <4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |36|; {1}][10 <5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {1}][9 <3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |27|; {1}]W[9 <2,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |26|; {1}][9 <1,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |25|; {1}][8 <3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |24|; {1}]W[8 <2,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}][8 <1,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][7 <4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]w[7 <3,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}][7 <2,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}][7 <1,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}][6 <2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}]GGwwwwww[7 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]GIW[7 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}]GG[6 <3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]Gwwwwww[7 <4,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}]GIW[7 <3,4>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][6 <4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}]GIW[6 <3,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]GGW[6 <2,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}][6 <1,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |16|; {1}]GGG[5 <3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |15|; {1}]GIW[5 <2,4>,<3,3>,<3,3>,<3,4>,<3,4> -> |14|; {1}]GG[4 <3,3>,<3,3>,<3,4>,<3,4> -> |12|; {1}][3 <3,3>,<3,4>,<3,4> -> |9|; {1}]W[3 <2,4>,<3,4>,<3,4> -> |8|; {1}][3 <1,4>,<3,4>,<3,4> -> |7|; {1}]G[2 <3,4>,<3,4> -> |6|; {1}]G[1 <3,4> -> |3|; {1}][1 <2,4> -> |2|; {1}][1 <1,4> -> |1|; {1}]
   *** QCMPACK Statistics ***
      Table     size:  36
      Entries reused:  255

   *** REGSETGCD: Gcd Statistics ***
      Table     size:  125
      Entries reused:  0

   *** REGSETGCD: Inv Set Statistics ***
      Table     size:  30
      Entries reused:  0

   (34)
   [
     {
                         24                   23                    22
         960725655771966t   + 386820897948702t   + 8906817198608181t
       + 
                          21                     20                    19
         2704966893949428t   + 37304033340228264t   + 7924782817170207t
       + 
                           18                     17                      16
         93126799040354990t   + 13101273653130910t   + 156146250424711858t
       + 
                           15                      14                     13
         16626490957259119t   + 190699288479805763t   + 24339173367625275t
       + 
                            12                     11                      10
         180532313014960135t   + 35288089030975378t   + 135054975747656285t
       + 
                           9                     8                     7
         34733736952488540t  + 75947600354493972t  + 19772555692457088t
       + 
                           6                    5                    4
         28871558573755428t  + 5576152439081664t  + 6321711820352976t
       + 
                       3                   2
       438314209312320t  + 581105748367008t  - 60254467992576t + 1449115951104
       ,

                                                                         23
             26604210869491302385515265737052082361668474181372891857784t
           + 
                                                                          22
             443104378424686086067294899528296664238693556855017735265295t
           + 
                                                                          21
             279078393286701234679141342358988327155321305829547090310242t
           + 
                                                                           20
             3390276361413232465107617176615543054620626391823613392185226t
           + 
                                                                          19
             941478179503540575554198645220352803719793196473813837434129t
           + 
                                                                            18
             11547855194679475242211696749673949352585747674184320988144390t
           + 
                                                                           17
             1343609566765597789881701656699413216467215660333356417241432t
           + 
                                                                            16
             23233813868147873503933551617175640859899102987800663566699334t
           + 
                                                                          15
             869574020537672336950845440508790740850931336484983573386433t
           + 
                                                                            14
             31561554305876934875419461486969926554241750065103460820476969t
           + 
                                                                           13
             1271400990287717487442065952547731879554823889855386072264931t
           + 
                                                                            12
             31945089913863736044802526964079540198337049550503295825160523t
           + 
                                                                           11
             3738735704288144509871371560232845884439102270778010470931960t
           + 
                                                                            10
             25293997512391412026144601435771131587561905532992045692885927t
           + 
                                                                           9
             5210239009846067123469262799870052773410471135950175008046524t
           + 
                                                                            8
             15083887986930297166259870568608270427403187606238713491129188t
           + 
                                                                           7
             3522087234692930126383686270775779553481769125670839075109000t
           + 
                                                                           6
             6079945200395681013086533792568886491101244247440034969288588t
           + 
                                                                           5
             1090634852433900888199913756247986023196987723469934933603680t
           + 
                                                                           4
             1405819430871907102294432537538335402102838994019667487458352t
           + 
                                                                         3
             88071527950320450072536671265507748878347828884933605202432t
           + 
                                                                          2
             135882489433640933229781177155977768016065765482378657129440t
           + 
             - 13957283442882262230559894607400314082516690749975646520320t
           + 
             334637692973189299277258325709308472592117112855749713920
        *
           z
       + 
                                                                    23
         8567175484043952879756725964506833932149637101090521164936t
       + 
                                                                      22
         149792392864201791845708374032728942498797519251667250945721t
       + 
                                                                     21
         77258371783645822157410861582159764138123003074190374021550t
       + 
                                                                       20
         1108862254126854214498918940708612211184560556764334742191654t
       + 
                                                                      19
         213250494460678865219774480106826053783815789621501732672327t
       + 
                                                                       18
         3668929075160666195729177894178343514501987898410131431699882t
       + 
                                                                      17
         171388906471001872879490124368748236314765459039567820048872t
       + 
                                                                       16
         7192430746914602166660233477331022483144921771645523139658986t
       + 
                                                                        15
         - 128798674689690072812879965633090291959663143108437362453385t
       + 
                                                                       14
         9553010858341425909306423132921134040856028790803526430270671t
       + 
                                                                       13
         - 13296096245675492874538687646300437824658458709144441096603t
       + 
                                                                       12
         9475806805814145326383085518325333106881690568644274964864413t
       + 
                                                                      11
         803234687925133458861659855664084927606298794799856265539336t
       + 
                                                                       10
         7338202759292865165994622349207516400662174302614595173333825t
       + 
                                                                       9
         1308004628480367351164369613111971668880538855640917200187108t
       + 
                                                                       8
         4268059455741255498880229598973705747098216067697754352634748t
       + 
                                                                      7
         892893526858514095791318775904093300103045601514470613580600t
       + 
                                                                       6
         1679152575460683956631925852181341501981598137465328797013652t
       + 
                                                                      5
         269757415767922980378967154143357835544113158280591408043936t
       + 
                                                                      4
         380951527864657529033580829801282724081345372680202920198224t
       + 
                                                                     3
         19785545294228495032998826937601341132725035339452913286656t
       + 
                                                                     2
         36477412057384782942366635303396637763303928174935079178528t
       + 
         - 3722212879279038648713080422224976273210890229485838670848t
       + 
         89079724853114348361230634484013862024728599906874105856
       ,
         3      2                  3       2
      (3z  - 11z  + 8z + 4)y + 2t z  + 4t z  - 5t z - t,
                  2
      (z + 1)x + z  - 4z + 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; {0}][2 <4,1>,<3,1> -> |7|; {0}][1 <3,1> -> |3|; {0}]G[2 <4,1>,<4,1> -> |8|; {0}]W[3 <5,1>,<4,1>,<3,2> -> |12|; {0}]GI[3 <4,2>,<4,1>,<3,2> -> |11|; {0}]GWw[3 <4,1>,<3,2>,<5,2> -> |12|; {0}][3 <3,2>,<3,2>,<5,2> -> |11|; {0}]GIwWWWw[4 <3,2>,<4,2>,<5,2>,<2,3> -> |14|; {0}][4 <2,2>,<4,2>,<5,2>,<2,3> -> |13|; {0}]Gwww[5 <3,2>,<3,2>,<4,2>,<5,2>,<2,3> -> |17|; {0}]Gwwwwww[8 <3,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}]Gwwwwww[8 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |31|; {0}][8 <3,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}][8 <2,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |29|; {0}][8 <1,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |28|; {0}][7 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |27|; {0}][6 <4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |23|; {0}][5 <4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |19|; {0}]GIGIWwww[6 <5,2>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |23|; {0}][6 <4,3>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |22|; {0}]GIGI[6 <3,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |21|; {0}][6 <2,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |20|; {0}]GGG[5 <4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |18|; {0}]GIGIWwwwW[6 <5,2>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |22|; {0}][6 <4,3>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |21|; {0}]GIwwWwWWWWWWWwWWWWwwwww[8 <4,2>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][8 <3,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}][8 <2,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |25|; {0}]Gwwwwwwwwwwwwwwwwwwww[9 <5,2>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |29|; {0}]GI[9 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |28|; {0}][9 <3,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][9 <2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}]GGwwwwwwwwwwwwWWwwwwwwww[11 <3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {0}][11 <2,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {0}][11 <1,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |31|; {0}]GGGwwwwwwwwwwwww[12 <2,3>,<2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {0}]GGwwwwwwwwwwwww[13 <3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}]Gwwwwwwwwwwwww[13 <2,3>,<3,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]GGGwwwwwwwwwwwww[15 <3,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {0}][14 <4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {0}]GIGGGGIGGI[14 <3,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GGG[14 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}][14 <1,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}]GGG[13 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]Gwwwwwwwwwwwww[15 <3,3>,<3,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]Gwwwwwwwwwwwww[15 <4,3>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |49|; {0}]GIGI[15 <3,4>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]G[14 <4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {0}][13 <3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]Gwwwwwwwwwwwww[13 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GIGGGGIGGI[13 <3,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]GGGGGGGG[13 <2,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}][13 <1,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}][13 <0,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}][12 <4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][11 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {1}][10 <3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |30|; {1}][10 <2,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |29|; {1}]GGGwwwwwwwwwwwww[11 <3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {1}]GGGwwwwwwwwwwwww[12 <4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}]Gwwwwwwwwwwwww[12 <3,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]GGwwwwwwwwwwwww[13 <5,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}]GIGGGGIGGIW[13 <4,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GGW[13 <3,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {1}]GGG[12 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]Gwwwwwwwwwwwww[12 <4,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]Gwwwwwwwwwwwww[13 <5,3>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {1}]GIGIW[13 <4,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {1}][13 <3,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}][13 <2,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GG[12 <5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {1}]GIGGGGIGGIW[12 <4,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]GGGGGGW[12 <3,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}][12 <2,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][12 <1,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |37|; {1}]GGG[11 <4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |36|; {1}][10 <5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {1}][9 <3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |27|; {1}]W[9 <2,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |26|; {1}][9 <1,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |25|; {1}][8 <3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |24|; {1}]W[8 <2,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}][8 <1,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][7 <4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]w[7 <3,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}][7 <2,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}][7 <1,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}][6 <2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}]GGwwwwww[7 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]GIW[7 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}]GG[6 <3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]Gwwwwww[7 <4,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}]GIW[7 <3,4>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][6 <4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}]GIW[6 <3,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]GGW[6 <2,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}][6 <1,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |16|; {1}]GGG[5 <3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |15|; {1}]GIW[5 <2,4>,<3,3>,<3,3>,<3,4>,<3,4> -> |14|; {1}]GG[4 <3,3>,<3,3>,<3,4>,<3,4> -> |12|; {1}][3 <3,3>,<3,4>,<3,4> -> |9|; {1}]W[3 <2,4>,<3,4>,<3,4> -> |8|; {1}][3 <1,4>,<3,4>,<3,4> -> |7|; {1}]G[2 <3,4>,<3,4> -> |6|; {1}]G[1 <3,4> -> |3|; {1}][1 <2,4> -> |2|; {1}][1 <1,4> -> |1|; {1}]
--R   *** QCMPACK Statistics ***
--R      Table     size:  36
--R      Entries reused:  255
--R
--R   *** REGSETGCD: Gcd Statistics ***
--R      Table     size:  125
--R      Entries reused:  0
--R
--R   *** REGSETGCD: Inv Set Statistics ***
--R      Table     size:  30
--R      Entries reused:  0
--R
--R   (34)
--R   [
--R     {
--R                         24                   23                    22
--R         960725655771966t   + 386820897948702t   + 8906817198608181t
--R       + 
--R                          21                     20                    19
--R         2704966893949428t   + 37304033340228264t   + 7924782817170207t
--R       + 
--R                           18                     17                      16
--R         93126799040354990t   + 13101273653130910t   + 156146250424711858t
--R       + 
--R                           15                      14                     13
--R         16626490957259119t   + 190699288479805763t   + 24339173367625275t
--R       + 
--R                            12                     11                      10
--R         180532313014960135t   + 35288089030975378t   + 135054975747656285t
--R       + 
--R                           9                     8                     7
--R         34733736952488540t  + 75947600354493972t  + 19772555692457088t
--R       + 
--R                           6                    5                    4
--R         28871558573755428t  + 5576152439081664t  + 6321711820352976t
--R       + 
--R                       3                   2
--R       438314209312320t  + 581105748367008t  - 60254467992576t + 1449115951104
--R       ,
--R
--R                                                                         23
--R             26604210869491302385515265737052082361668474181372891857784t
--R           + 
--R                                                                          22
--R             443104378424686086067294899528296664238693556855017735265295t
--R           + 
--R                                                                          21
--R             279078393286701234679141342358988327155321305829547090310242t
--R           + 
--R                                                                           20
--R             3390276361413232465107617176615543054620626391823613392185226t
--R           + 
--R                                                                          19
--R             941478179503540575554198645220352803719793196473813837434129t
--R           + 
--R                                                                            18
--R             11547855194679475242211696749673949352585747674184320988144390t
--R           + 
--R                                                                           17
--R             1343609566765597789881701656699413216467215660333356417241432t
--R           + 
--R                                                                            16
--R             23233813868147873503933551617175640859899102987800663566699334t
--R           + 
--R                                                                          15
--R             869574020537672336950845440508790740850931336484983573386433t
--R           + 
--R                                                                            14
--R             31561554305876934875419461486969926554241750065103460820476969t
--R           + 
--R                                                                           13
--R             1271400990287717487442065952547731879554823889855386072264931t
--R           + 
--R                                                                            12
--R             31945089913863736044802526964079540198337049550503295825160523t
--R           + 
--R                                                                           11
--R             3738735704288144509871371560232845884439102270778010470931960t
--R           + 
--R                                                                            10
--R             25293997512391412026144601435771131587561905532992045692885927t
--R           + 
--R                                                                           9
--R             5210239009846067123469262799870052773410471135950175008046524t
--R           + 
--R                                                                            8
--R             15083887986930297166259870568608270427403187606238713491129188t
--R           + 
--R                                                                           7
--R             3522087234692930126383686270775779553481769125670839075109000t
--R           + 
--R                                                                           6
--R             6079945200395681013086533792568886491101244247440034969288588t
--R           + 
--R                                                                           5
--R             1090634852433900888199913756247986023196987723469934933603680t
--R           + 
--R                                                                           4
--R             1405819430871907102294432537538335402102838994019667487458352t
--R           + 
--R                                                                         3
--R             88071527950320450072536671265507748878347828884933605202432t
--R           + 
--R                                                                          2
--R             135882489433640933229781177155977768016065765482378657129440t
--R           + 
--R             - 13957283442882262230559894607400314082516690749975646520320t
--R           + 
--R             334637692973189299277258325709308472592117112855749713920
--R        *
--R           z
--R       + 
--R                                                                    23
--R         8567175484043952879756725964506833932149637101090521164936t
--R       + 
--R                                                                      22
--R         149792392864201791845708374032728942498797519251667250945721t
--R       + 
--R                                                                     21
--R         77258371783645822157410861582159764138123003074190374021550t
--R       + 
--R                                                                       20
--R         1108862254126854214498918940708612211184560556764334742191654t
--R       + 
--R                                                                      19
--R         213250494460678865219774480106826053783815789621501732672327t
--R       + 
--R                                                                       18
--R         3668929075160666195729177894178343514501987898410131431699882t
--R       + 
--R                                                                      17
--R         171388906471001872879490124368748236314765459039567820048872t
--R       + 
--R                                                                       16
--R         7192430746914602166660233477331022483144921771645523139658986t
--R       + 
--R                                                                        15
--R         - 128798674689690072812879965633090291959663143108437362453385t
--R       + 
--R                                                                       14
--R         9553010858341425909306423132921134040856028790803526430270671t
--R       + 
--R                                                                       13
--R         - 13296096245675492874538687646300437824658458709144441096603t
--R       + 
--R                                                                       12
--R         9475806805814145326383085518325333106881690568644274964864413t
--R       + 
--R                                                                      11
--R         803234687925133458861659855664084927606298794799856265539336t
--R       + 
--R                                                                       10
--R         7338202759292865165994622349207516400662174302614595173333825t
--R       + 
--R                                                                       9
--R         1308004628480367351164369613111971668880538855640917200187108t
--R       + 
--R                                                                       8
--R         4268059455741255498880229598973705747098216067697754352634748t
--R       + 
--R                                                                      7
--R         892893526858514095791318775904093300103045601514470613580600t
--R       + 
--R                                                                       6
--R         1679152575460683956631925852181341501981598137465328797013652t
--R       + 
--R                                                                      5
--R         269757415767922980378967154143357835544113158280591408043936t
--R       + 
--R                                                                      4
--R         380951527864657529033580829801282724081345372680202920198224t
--R       + 
--R                                                                     3
--R         19785545294228495032998826937601341132725035339452913286656t
--R       + 
--R                                                                     2
--R         36477412057384782942366635303396637763303928174935079178528t
--R       + 
--R         - 3722212879279038648713080422224976273210890229485838670848t
--R       + 
--R         89079724853114348361230634484013862024728599906874105856
--R       ,
--R         3      2                  3       2
--R      (3z  - 11z  + 8z + 4)y + 2t z  + 4t z  - 5t z - t,
--R                  2
--R      (z + 1)x + z  - 4z + 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 34
)spool 
 
Starts dribbling to newlodo.output (2010/3/27, 18:30:4).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 55
RN:=FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 55
Dx: LODO2(RN, UP(x,RN))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 55
Dx := D()                  -- definition of an operator
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 55
a  := Dx  + 1
 

   (4)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 55
b  := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (5)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (5)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 55
p: UP(x,RN) := 4*x**2 + 2/3      -- something to work on
 

          2   2
   (6)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (6)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 55
a p                        -- application of an operator to a polynomial
 

          2        2
   (7)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (7)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 55
(a*b) p = a b p            -- multiplication is defined by this identity
 

          2         37    2         37
   (8)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (8)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 55
c := (1/9)*b*(a + b)**2    -- exponentiation follows from multiplication
 

         1  6    5  5   13  4   19  3   79  2    7     1
   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
        72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R         1  6    5  5   13  4   19  3   79  2    7     1
--R   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R        72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 55
(a**2 - 3/4*b + c) (p + 1) -- general application of operator expressions
 

           2   44     541
   (10)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (10)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 10

)clear all
 

--S 11 of 55
RFZ := FRAC UP(x,INT)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 11

--S 12 of 55
(Dx, a, b): LODO1 RFZ
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 55
Dx := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 55
b := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 14

--S 15 of 55
a := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 55
p: RFZ := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 55
(a*b - b*a) p  -- operator multiplication is not commutative
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18 of 55
leftDivide(a,b)      -- result is the quotient/remainder pair
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 55
a - (b * %.quotient + %.remainder)
 

   (9)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (9)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 55
rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 20

--S 21 of 55
a - (%.quotient * b + %.remainder)
 

   (11)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (11)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 21

--S 22 of 55
e := leftGcd(a,b)
 

           2 2        1
   (12)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (12)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 22

--S 23 of 55
leftRemainder(a, e)    -- remainder from left division
 

   (13)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 23

--S 24 of 55
rightRemainder(a, e)    -- remainder from right division
 

               5
   (14)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (14)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 24

--S 25 of 55
f := rightLcm(a,b)
 

            3 3       2        2         7
   (15)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (15)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 25

--S 26 of 55
leftRemainder(f, b)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 26

--S 27 of 55
rightRemainder(f, b)  -- the remainder is non-zero
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 27

)clear all
 
--S 28 of 55
Dx: LODO(EXPR INT, f +-> D(f, x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 55
Dx := D()
 

   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1774 envArg,SPADCALL(G1774,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R   (2)  D
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1500 envArg,SPADCALL(G1500,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 29

--S 30 of 55
Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1
 

                       3
         3    G     - x  + H
   (3)  D  + -- D + --------
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1774 envArg,SPADCALL(G1774,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R                       3
--R         3    G     - x  + H
--R   (3)  D  + -- D + --------
--R              2         3
--R             x         x
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1500 envArg,SPADCALL(G1500,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 30

--S 31 of 55
n == 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 55
phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 55
phi1 ==  Dop(phi) / exp x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 55
phi2 == phi1 *x**(n+3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 55
phi3 == retract(phi2)@(POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 35

--S 36 of 55
pans == phi3 ::UP(x,POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 55
pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 37

--S 38 of 55
leq == solve(pans1,[subscript(s,[i]) for i in 1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 38

--S 39 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling function G1900 with type Integer -> Boolean 

   (12)
                           2                                3        2
         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
          0        0     0       0         0       0      0        0        0
   [[s = ---,s = ------------------,s = --------------------------------------]]
      1   3   2          18          3                    162
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--I   Compiling function G3445 with type Integer -> Boolean 
--R
--R   (12)
--R                           2                                3        2
--R         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
--R          0        0     0       0         0       0      0        0        0
--R   [[s = ---,s = ------------------,s = --------------------------------------]]
--R      1   3   2          18          3                    162
--R                         Type: List List Equation Fraction Polynomial Integer
--E 39

--S 40 of 55
n==4
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 40

--S 41 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (14)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 41

--S 42 of 55
n==7
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 42

--S 43 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ,

       s  =
        5
                               2         3          2
             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
                  0         0          0          0           0          0
           + 
                5        4          3          2
             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
              0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                   4          3           2                                6
             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
                 0          0           0            0            0      0
           + 
                  5          4           3           2
             90s G  + 2628s G  + 27864s G  + 90720s G
                0          0           0           0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                    3           2                            2
             (945s G  + 81648s G  + 2082996s G + 14171760s )H
                  0           0             0             0
           + 
                   5          4            3             2
             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
                 0          0            0             0              0
           + 
                7         6          5           4             3              2
             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
              0         0          0           0             0              0
           + 
             - 97977600s G
                        0
        /
           11022480
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (16)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ,
--R
--R       s  =
--R        5
--R                               2         3          2
--R             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
--R                  0         0          0          0           0          0
--R           + 
--R                5        4          3          2
--R             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
--R              0        0          0          0           0
--R        /
--R           29160
--R       ,
--R
--R       s  =
--R        6
--R                   3          2                        2
--R             405s H  + (405s G  + 18468s G + 174960s )H
--R                 0          0           0           0
--R           + 
--R                   4          3           2                                6
--R             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
--R                 0          0           0            0            0      0
--R           + 
--R                  5          4           3           2
--R             90s G  + 2628s G  + 27864s G  + 90720s G
--R                0          0           0           0
--R        /
--R           524880
--R       ,
--R
--R       s  =
--R        7
--R                                 3
--R             (2835s G + 91854s )H
--R                   0          0
--R           + 
--R                    3           2                            2
--R             (945s G  + 81648s G  + 2082996s G + 14171760s )H
--R                  0           0             0             0
--R           + 
--R                   5          4            3             2
--R             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
--R                 0          0            0             0              0
--R           + 
--R                7         6          5           4             3              2
--R             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
--R              0         0          0           0             0              0
--R           + 
--R             - 97977600s G
--R                        0
--R        /
--R           11022480
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 43

)clear all
 

--S 44 of 55
PZ := UP(x,INT); Vect := DPMM(3, PZ, SQMATRIX(3,PZ), PZ);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 44

--S 45 of 55
Modo := LODO2(SQMATRIX(3,PZ), Vect);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 45

--S 46 of 55
p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect
 

           2          3
   (3)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (3)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 46

--S 47 of 55
m := [[x**2, 1, 0], [1, x**4, 0], [0, 0, 4*x**2]]::(SQMATRIX(3,PZ))
 

        + 2         +
        |x   1    0 |
        |           |
   (4)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (4)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 47

--S 48 of 55
q: Vect := m * p
 

           4    2        5     2        5     3
   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 48

--S 49 of 55
Dx:  Modo := D()
 

   (6)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (6)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 49

--S 50 of 55
a:   Modo := 1*Dx  + m
 

            + 2         +
            |x   1    0 |
            |           |
   (7)  D + |     4     |
            |1   x    0 |
            |           |
            |          2|
            +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R            + 2         +
--R            |x   1    0 |
--R            |           |
--R   (7)  D + |     4     |
--R            |1   x    0 |
--R            |           |
--R            |          2|
--R            +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 50

--S 51 of 55
b:   Modo := m*Dx  + 1
 

        + 2         +
        |x   1    0 |    +1  0  0+
        |           |    |       |
   (8)  |     4     |D + |0  1  0|
        |1   x    0 |    |       |
        |           |    +0  0  1+
        |          2|
        +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R        + 2         +
--R        |x   1    0 |    +1  0  0+
--R        |           |    |       |
--R   (8)  |     4     |D + |0  1  0|
--R        |1   x    0 |    |       |
--R        |           |    +0  0  1+
--R        |          2|
--R        +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 51

--S 52 of 55
a*b
 

   (9)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 52

--S 53 of 55
a p
 

            4    2        5     2        5     3      2
   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 53

--S 54 of 55
b p
 

            3     2       4         4     3     2
   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 54

--S 55 of 55
(a+b) (p + q)
 

   (12)
      6      5      4      3      2
   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
      9      8     6      5      4      3     2
    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
        7       6      5       4      3      2
    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (12)
--R      6      5      4      3      2
--R   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
--R      9      8     6      5      4      3     2
--R    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
--R        7       6      5       4      3      2
--R    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 55
)spool 
 
Starts dribbling to schaum32.output (2010/3/27, 18:38:45).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 52
aa:=integrate(sech(a*x),x)
 

        2atan(sinh(a x) + cosh(a x))
   (1)  ----------------------------
                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        2atan(sinh(a x) + cosh(a x))
--R   (1)  ----------------------------
--R                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 52
bb:=2/a*atan(%e^(a*x))
 

                a x
        2atan(%e   )
   (2)  ------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        2atan(%e   )
--R   (2)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3 of 52
cc:=aa-bb
 

                                               a x
        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
   (3)  -------------------------------------------
                             a
                                                     Type: Expression Integer
--R
--R                                               a x
--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
--R   (3)  -------------------------------------------
--R                             a
--R                                                     Type: Expression Integer
--E

--S 4 of 52
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 5 of 52
dd:=atanrule cc
 

                   a x
               - %e    + %i           - sinh(a x) - cosh(a x) + %i
        %i log(------------) - %i log(----------------------------)
                  a x                  sinh(a x) + cosh(a x) + %i
                %e    + %i
   (5)  -----------------------------------------------------------
                                     a
                                             Type: Expression Complex Integer
--R
--R                   a x
--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
--R        %i log(------------) - %i log(----------------------------)
--R                  a x                  sinh(a x) + cosh(a x) + %i
--R                %e    + %i
--R   (5)  -----------------------------------------------------------
--R                                     a
--R                                             Type: Expression Complex Integer
--E

--S 6 of 52
ee:=expandLog dd
 

   (6)
       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
     + 
                  a x                  a x
       - %i log(%e    + %i) + %i log(%e    - %i)
  /
     a
                                             Type: Expression Complex Integer
--R
--R   (6)
--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
--R     + 
--R                  a x                  a x
--R       - %i log(%e    + %i) + %i log(%e    - %i)
--R  /
--R     a
--R                                             Type: Expression Complex Integer
--E

--S 7 of 52      14:626 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                             Type: Expression Complex Integer
--R
--R   (7)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 8 of 52
aa:=integrate(sech(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 52
bb:=tanh(a*x)/a
 

        tanh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        tanh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 10 of 52
cc:=aa-bb
 

                    2                                  2
        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
   (3)  ------------------------------------------------------------------
                         2                                      2
              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R                    2                                  2
--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
--R   (3)  ------------------------------------------------------------------
--R                         2                                      2
--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 11 of 52
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12 of 52
dd:=sinhsqrrule cc
 

                                                        2
        (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)tanh(a x) - 4
   (5)  -------------------------------------------------------------------
                                                                 2
              4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R                                                        2
--R        (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)tanh(a x) - 4
--R   (5)  -------------------------------------------------------------------
--R                                                                 2
--R              4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 13 of 52
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 14 of 52
ee:=coshsqrrule dd
 

        (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2
   (7)  -----------------------------------------------------
               2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R        (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2
--R   (7)  -----------------------------------------------------
--R               2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 15 of 52
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %O sinh(y + x) - %O sinh(y - x)
   (8)  %O cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %L sinh(y + x) - %L sinh(y - x)
--I   (8)  %L cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 16 of 52
ff:=sinhcoshrule ee
 

        (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2
   (9)  --------------------------------------------
               a sinh(2a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R        (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2
--R   (9)  --------------------------------------------
--R               a sinh(2a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 17 of 52     14:627 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

           1
   (10)  - -
           a
                                                     Type: Expression Integer
--R
--R           1
--R   (10)  - -
--R           a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 18 of 52
aa:=integrate(sech(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
      *
         atan(sinh(a x) + cosh(a x))
     + 
                3                      2              2
       sinh(a x)  + 3cosh(a x)sinh(a x)  + (3cosh(a x)  - 1)sinh(a x)
     + 
                3
       cosh(a x)  - cosh(a x)
  /
                  4                        3                2               2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
     + 
                  3                                       4               2
     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R                3                      2              2
--R       sinh(a x)  + 3cosh(a x)sinh(a x)  + (3cosh(a x)  - 1)sinh(a x)
--R     + 
--R                3
--R       cosh(a x)  - cosh(a x)
--R  /
--R                  4                        3                2               2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
--R     + 
--R                  3                                       4               2
--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 19 of 52
bb:=(sech(a*x)*tanh(a*x))/(2*a)+1/(2*a)*atan(sinh(a*x))
 

        atan(sinh(a x)) + sech(a x)tanh(a x)
   (2)  ------------------------------------
                         2a
                                                     Type: Expression Integer
--R
--R        atan(sinh(a x)) + sech(a x)tanh(a x)
--R   (2)  ------------------------------------
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 20 of 52     14:628 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                     4                      3               2              2
           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
         + 
                      3                                    4             2
           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
      *
         atan(sinh(a x) + cosh(a x))
     + 
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  - 4cosh(a x))sinh(a x) - cosh(a x)  - 2cosh(a x)  - 1
      *
         atan(sinh(a x))
     + 
                               4                               3
           - sech(a x)sinh(a x)  - 4cosh(a x)sech(a x)sinh(a x)
         + 
                        2                       2
           (- 6cosh(a x)  - 2)sech(a x)sinh(a x)
         + 
                        3
           (- 4cosh(a x)  - 4cosh(a x))sech(a x)sinh(a x)
         + 
                       4             2
           (- cosh(a x)  - 2cosh(a x)  - 1)sech(a x)
      *
         tanh(a x)
     + 
                 3                      2              2
       2sinh(a x)  + 6cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
     + 
                 3
       2cosh(a x)  - 2cosh(a x)
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
     + 
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     4                      3               2              2
--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
--R         + 
--R                      3                                    4             2
--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  - 4cosh(a x))sinh(a x) - cosh(a x)  - 2cosh(a x)  - 1
--R      *
--R         atan(sinh(a x))
--R     + 
--R                               4                               3
--R           - sech(a x)sinh(a x)  - 4cosh(a x)sech(a x)sinh(a x)
--R         + 
--R                        2                       2
--R           (- 6cosh(a x)  - 2)sech(a x)sinh(a x)
--R         + 
--R                        3
--R           (- 4cosh(a x)  - 4cosh(a x))sech(a x)sinh(a x)
--R         + 
--R                       4             2
--R           (- cosh(a x)  - 2cosh(a x)  - 1)sech(a x)
--R      *
--R         tanh(a x)
--R     + 
--R                 3                      2              2
--R       2sinh(a x)  + 6cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R     + 
--R                 3
--R       2cosh(a x)  - 2cosh(a x)
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
--R     + 
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 21 of 52
aa:=integrate(sech(a*x)^n*tanh(a*x),x)
 

   (1)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
  /
     a n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R  /
--R     a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22 of 52
bb:=-sech(a*x)^n/(n*a)
 

                   n
          sech(a x)
   (2)  - ----------
              a n
                                                     Type: Expression Integer
--R
--R                   n
--R          sech(a x)
--R   (2)  - ----------
--R              a n
--R                                                     Type: Expression Integer
--E

--S 23 of 52
cc:=aa-bb
 

   (3)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                n
       sech(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (3)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                n
--R       sech(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 24 of 52
sechrule:=rule(sech(x) == 1/cosh(x))
 

                      1
   (4)  sech(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (4)  sech(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25 of 52
dd:=sechrule cc
 

   (5)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
     + 
            1     n
       (---------)
        cosh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (5)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R     + 
--R            1     n
--R       (---------)
--R        cosh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 26 of 52
ee:=expandLog dd
 

   (6)
       sinh
                           2                                  2
            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
                              2                                  2
               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        cosh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (6)
--R       sinh
--R                           2                                  2
--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R                              2                                  2
--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        cosh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 27 of 52     14:629 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 52
aa:=integrate(1/sech(a*x),x)
 

        sinh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sinh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29 of 52
bb:=sinh(a*x)/a
 

        sinh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        sinh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 30 of 52     14:630 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 31 of 52     14:631 Axiom cannot compute this integral
aa:=integrate(x*sech(a*x),x)
 

           x
         ++
   (1)   |   %T sech(%T a)d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O sech(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 32 of 52
aa:=integrate(x*sech(a*x)^2,x)
 

   (1)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                     2                                           2
       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                     2                                           2
--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 33 of 52
bb:=(x*tanh(a*x))/a-1/a^2*log(cosh(a*x))
 

        - log(cosh(a x)) + a x tanh(a x)
   (2)  --------------------------------
                        2
                       a
                                                     Type: Expression Integer
--R
--R        - log(cosh(a x)) + a x tanh(a x)
--R   (2)  --------------------------------
--R                        2
--R                       a
--R                                                     Type: Expression Integer
--E

--S 34 of 52
cc:=aa-bb
 

   (3)
                 2                                  2
       (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)log(cosh(a x))
     + 
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                         2                                          2
         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
      *
         tanh(a x)
     + 
                     2                                           2
       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2                                  2
--R       (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)log(cosh(a x))
--R     + 
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                         2                                          2
--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
--R      *
--R         tanh(a x)
--R     + 
--R                     2                                           2
--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 35 of 52
dd:=expandLog cc
 

   (4)
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                         2                                          2
         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
      *
         tanh(a x)
     + 
                                   2
       (- log(- 2) + 2a x)sinh(a x)  + (- 2log(- 2) + 4a x)cosh(a x)sinh(a x)
     + 
                                   2
       (- log(- 2) + 2a x)cosh(a x)  - log(- 2)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (4)
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                         2                                          2
--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
--R      *
--R         tanh(a x)
--R     + 
--R                                   2
--R       (- log(- 2) + 2a x)sinh(a x)  + (- 2log(- 2) + 4a x)cosh(a x)sinh(a x)
--R     + 
--R                                   2
--R       (- log(- 2) + 2a x)cosh(a x)  - log(- 2)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 36 of 52
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37 of 52
ee:=sinhsqrrule dd
 

   (6)
                                                       2
         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                                                                     2
         (- 4a x cosh(a x)sinh(a x) - a x cosh(2a x) - 2a x cosh(a x)  - a x)
      *
         tanh(a x)
     + 
       (- 4log(- 2) + 8a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
     + 
                                    2
       (- 2log(- 2) + 4a x)cosh(a x)  - log(- 2) - 2a x
  /
       2                      2               2         2    2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                       2
--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                                                                     2
--R         (- 4a x cosh(a x)sinh(a x) - a x cosh(2a x) - 2a x cosh(a x)  - a x)
--R      *
--R         tanh(a x)
--R     + 
--R       (- 4log(- 2) + 8a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
--R     + 
--R                                    2
--R       (- 2log(- 2) + 4a x)cosh(a x)  - log(- 2) - 2a x
--R  /
--R       2                      2               2         2    2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 38 of 52
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 39 of 52
ff:=coshsqrrule ee
 

   (8)
       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (- 2a x cosh(a x)sinh(a x) - a x cosh(2a x) - a x)tanh(a x)
     + 
       (- 2log(- 2) + 4a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
     + 
       - log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (- 2a x cosh(a x)sinh(a x) - a x cosh(2a x) - a x)tanh(a x)
--R     + 
--R       (- 2log(- 2) + 4a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
--R     + 
--R       - log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 40 of 52
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %U sinh(y + x) - %U sinh(y - x)
   (9)  %U cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %P sinh(y + x) - %P sinh(y - x)
--I   (9)  %P cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 41 of 52
gg:=sinhcoshrule ff
 

   (10)
       (sinh(2a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (- a x sinh(2a x) - a x cosh(2a x) - a x)tanh(a x)
     + 
       (- log(- 2) + 2a x)sinh(2a x) + (- log(- 2) + 2a x)cosh(2a x) - log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (sinh(2a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (- a x sinh(2a x) - a x cosh(2a x) - a x)tanh(a x)
--R     + 
--R       (- log(- 2) + 2a x)sinh(2a x) + (- log(- 2) + 2a x)cosh(2a x) - log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 42 of 52     14:632 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         log(- 1) - log(- 2)
   (11)  -------------------
                   2
                  a
                                                     Type: Expression Integer
--R
--R         log(- 1) - log(- 2)
--R   (11)  -------------------
--R                   2
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 43 of 52     14:633 Axiom cannot compute this integral
aa:=integrate(sech(a*x)/x,x)
 

           x
         ++  sech(%T a)
   (1)   |   ---------- d%T
        ++       %T
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sech(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 44 of 52
aa:=integrate(1/(q+p*sech(a*x)),x)
 

   (1)
   [
           p
        *
           log
                       2         2      2
                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                    + 
                       2         2                     2     2
                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
                 *
                     +---------+
                     |   2    2
                    \|- q  + p
                + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
             /
                             2                                             2
                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                + 
                  2p cosh(a x) + q
       + 
             +---------+
             |   2    2
         a x\|- q  + p
    /
           +---------+
           |   2    2
       a q\|- q  + p
     ,
                                              +-------+
                                              | 2    2         +-------+
              (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
    - 2p atan(-----------------------------------------) + a x\|q  - p
                                2    2
                               q  - p
    --------------------------------------------------------------------]
                                    +-------+
                                    | 2    2
                                a q\|q  - p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           p
--R        *
--R           log
--R                       2         2      2
--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                    + 
--R                       2         2                     2     2
--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
--R                 *
--R                     +---------+
--R                     |   2    2
--R                    \|- q  + p
--R                + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R             /
--R                             2                                             2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                + 
--R                  2p cosh(a x) + q
--R       + 
--R             +---------+
--R             |   2    2
--R         a x\|- q  + p
--R    /
--R           +---------+
--R           |   2    2
--R       a q\|- q  + p
--R     ,
--R                                              +-------+
--R                                              | 2    2         +-------+
--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
--R    - 2p atan(-----------------------------------------) + a x\|q  - p
--R                                2    2
--R                               q  - p
--R    --------------------------------------------------------------------]
--R                                    +-------+
--R                                    | 2    2
--R                                a q\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 45 of 52
t1:=integrate(1/(p+q*cosh(a*x)),x)
 

   (2)
   [
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
    /
         +---------+
         |   2    2
       a\|- q  + p
     ,
                                          +-------+
                                          | 2    2
          (q sinh(a x) + q cosh(a x) + p)\|q  - p
    2atan(-----------------------------------------)
                            2    2
                           q  - p
    ------------------------------------------------]
                         +-------+
                         | 2    2
                       a\|q  - p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R    /
--R         +---------+
--R         |   2    2
--R       a\|- q  + p
--R     ,
--R                                          +-------+
--R                                          | 2    2
--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R    2atan(-----------------------------------------)
--R                            2    2
--R                           q  - p
--R    ------------------------------------------------]
--R                         +-------+
--R                         | 2    2
--R                       a\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 46 of 52
bb1:=x/q-p/q*t1.1
 

   (3)
       -
            p
         *
            log
                        2         2      2
                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                     + 
                        2         2                     2     2
                       q cosh(a x)  + 2p q cosh(a x) - q  + 2p
                  *
                      +---------+
                      |   2    2
                     \|- q  + p
                 + 
                      3     2                 3     2                  2     3
                   (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
              /
                              2                                             2
                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                 + 
                   2p cosh(a x) + q
     + 
           +---------+
           |   2    2
       a x\|- q  + p
  /
         +---------+
         |   2    2
     a q\|- q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            p
--R         *
--R            log
--R                        2         2      2
--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                     + 
--R                        2         2                     2     2
--R                       q cosh(a x)  + 2p q cosh(a x) - q  + 2p
--R                  *
--R                      +---------+
--R                      |   2    2
--R                     \|- q  + p
--R                 + 
--R                      3     2                 3     2                  2     3
--R                   (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R              /
--R                              2                                             2
--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                 + 
--R                   2p cosh(a x) + q
--R     + 
--R           +---------+
--R           |   2    2
--R       a x\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 47 of 52
bb2:=x/q-p/q*t1.2
 

                                                  +-------+
                                                  | 2    2         +-------+
                  (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
        - 2p atan(-----------------------------------------) + a x\|q  - p
                                    2    2
                                   q  - p
   (4)  --------------------------------------------------------------------
                                        +-------+
                                        | 2    2
                                    a q\|q  - p
                                                     Type: Expression Integer
--R
--R                                                  +-------+
--R                                                  | 2    2         +-------+
--R                  (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
--R        - 2p atan(-----------------------------------------) + a x\|q  - p
--R                                    2    2
--R                                   q  - p
--R   (4)  --------------------------------------------------------------------
--R                                        +-------+
--R                                        | 2    2
--R                                    a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 48 of 52
cc1:=aa.1-bb1
 

   (5)
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
  /
         +---------+
         |   2    2
     a q\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R  /
--R         +---------+
--R         |   2    2
--R     a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 49 of 52
cc2:=aa.2-bb1
 

   (6)
           +-------+
           | 2    2
         p\|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                                                            +-------+
            +---------+                                     | 2    2
            |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       - 2p\|- q  + p  atan(-----------------------------------------)
                                              2    2
                                             q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R           +-------+
--R           | 2    2
--R         p\|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                                                            +-------+
--R            +---------+                                     | 2    2
--R            |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       - 2p\|- q  + p  atan(-----------------------------------------)
--R                                              2    2
--R                                             q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 50 of 52
cc3:=aa.1-bb2
 

   (7)
           +-------+
           | 2    2
         p\|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                                                          +-------+
          +---------+                                     | 2    2
          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       2p\|- q  + p  atan(-----------------------------------------)
                                            2    2
                                           q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R           +-------+
--R           | 2    2
--R         p\|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                                                          +-------+
--R          +---------+                                     | 2    2
--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       2p\|- q  + p  atan(-----------------------------------------)
--R                                            2    2
--R                                           q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 51 of 52     14:634 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 52 of 52     14:635 Axiom cannot compute this integral
aa:=integrate(sech(a*x)^n,x)
 

           x
         ++            n
   (1)   |   sech(%T a) d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   sech(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to TextFile.output (2010/3/27, 18:46:38).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
f1: TextFile := open("/etc/group", "input")
 

   (1)  "/etc/group"
                                                               Type: TextFile
--R 
--R
--R   (1)  "/etc/group"
--R                                                               Type: TextFile
--E 1

--S 2 of 10
f2: TextFile := open("MOTD", "output")
 

   (2)  "MOTD"
                                                               Type: TextFile
--R 
--R
--R   (2)  "MOTD"
--R                                                               Type: TextFile
--E 2

--S 3 of 10
l := readLine! f1
 

   (3)  "root:x:0:"
                                                                 Type: String
--R 
--R
--I   (3)  "ROOT:x:0:"
--R                                                                 Type: String
--E 3

--S 4 of 10
writeLine!(f2, upperCase l)
 

   (4)  "ROOT:X:0:"
                                                                 Type: String
--R 
--R
--I   (4)  "ROOT:X:0:"
--R                                                                 Type: String
--E 4

--S 5 of 10
while not endOfFile? f1 repeat
  s := readLine! f1
  writeLine!(f2, upperCase s)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
close! f1
 

   (6)  "/etc/group"
                                                               Type: TextFile
--R 
--R
--R   (6)  "/etc/group"
--R                                                               Type: TextFile
--E 6

--S 7 of 10
write!(f2, "-The-")
 

   (7)  "-The-"
                                                                 Type: String
--R 
--R
--R   (7)  "-The-"
--R                                                                 Type: String
--E 7

--S 8 of 10
write!(f2, "-End-")
 

   (8)  "-End-"
                                                                 Type: String
--R 
--R
--R   (8)  "-End-"
--R                                                                 Type: String
--E 8

--S 9 of 10
writeLine! f2
 

   (9)  ""
                                                                 Type: String
--R 
--R
--R   (9)  ""
--R                                                                 Type: String
--E 9

--S 10 of 10
close! f2
 

   (10)  "MOTD"
                                                               Type: TextFile
--R 
--R
--R   (10)  "MOTD"
--R                                                               Type: TextFile
--E 10
)system rm -f MOTD
 
)spool
 
Starts dribbling to IntegerLinearDependence.output (2010/3/27, 18:42:13).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 8
M := SQMATRIX(2,INT)
 

   (1)  SquareMatrix(2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  SquareMatrix(2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 8
m1: M := squareMatrix matrix [ [1, 2], [0, -1] ]
 

        +1   2 +
   (2)  |      |
        +0  - 1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1   2 +
--R   (2)  |      |
--R        +0  - 1+
--R                                                Type: SquareMatrix(2,Integer)
--E 2

--S 3 of 8
m2: M := squareMatrix matrix [ [2, 3], [1, -2] ]
 

        +2   3 +
   (3)  |      |
        +1  - 2+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +2   3 +
--R   (3)  |      |
--R        +1  - 2+
--R                                                Type: SquareMatrix(2,Integer)
--E 3

--S 4 of 8
m3: M := squareMatrix matrix [ [3, 4], [2, -3] ]
 

        +3   4 +
   (4)  |      |
        +2  - 3+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +3   4 +
--R   (4)  |      |
--R        +2  - 3+
--R                                                Type: SquareMatrix(2,Integer)
--E 4

--S 5 of 8
linearlyDependentOverZ? vector [m1, m2, m3]
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5

--S 6 of 8
c := linearDependenceOverZ vector [m1, m2, m3]
 

   (6)  [1,- 2,1]
                                              Type: Union(Vector Integer,...)
--R 
--R
--R   (6)  [1,- 2,1]
--R                                              Type: Union(Vector Integer,...)
--E 6

--S 7 of 8
c.1 * m1 + c.2 * m2 + c.3 * m3
 

        +0  0+
   (7)  |    |
        +0  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  0+
--R   (7)  |    |
--R        +0  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 7

--S 8 of 8
solveLinearlyOverQ(vector [m1, m3], m2)
 

         1 1
   (8)  [-,-]
         2 2
                                     Type: Union(Vector Fraction Integer,...)
--R 
--R
--R         1 1
--R   (8)  [-,-]
--R         2 2
--R                                     Type: Union(Vector Fraction Integer,...)
--E 8
)spool
 
Starts dribbling to ContinuedFraction.output (2010/3/27, 18:41:50).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
c := continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 1

--S 2 of 22
partialQuotients c
 

   (2)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (2)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 2

--S 3 of 22
convergents c
 

           22 333 355 9208 9563 76149 314159
   (3)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R           22 333 355 9208 9563 76149 314159
--R   (3)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 3

--S 4 of 22
approximants c
 

                                      ______
           22 333 355 9208 9563 76149 314159
   (4)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R                                      ______
--R           22 333 355 9208 9563 76149 314159
--R   (4)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 4

--S 5 of 22
pq := partialQuotients(1/c)
 

   (5)  [0,3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 5

--S 6 of 22
continuedFraction(first pq,repeating [1],rest pq)
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 6

--S 7 of 22
z:=continuedFraction(3,repeating [1],repeating [3,6])
 

   (7)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
   + 
       1 |
     +---+ + ...
     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
--R         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 6
--R                                              Type: ContinuedFraction Integer
--E 7

--S 8 of 22
dens:Stream Integer := cons(1,generate((x+->x+4),6))
 

   (8)  [1,6,10,14,18,22,26,30,34,38,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [1,6,10,14,18,22,26,30,34,38,...]
--R                                                         Type: Stream Integer
--E 8

--S 9 of 22
cf := continuedFraction(0,repeating [1],dens)
 

   (9)
       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
   + 
       1  |     1  |
     +----+ + +----+ + ...
     | 34     | 38
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (9)
--R       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
--R     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
--R     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
--R   + 
--R       1  |     1  |
--R     +----+ + +----+ + ...
--R     | 34     | 38
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 22
ccf := convergents cf
 

              6 61  860 15541 342762  8927353 268163352  9126481321
   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
              7 71 1001 18089 398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              6 61  860 15541 342762  8927353 268163352  9126481321
--R   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
--R              7 71 1001 18089 398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 10

--S 11 of 22
eConvergents := [2*e + 1 for e in ccf]
 

              19 193 2721 49171 1084483 28245729 848456353 28875761731
   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
               7  71 1001 18089  398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              19 193 2721 49171 1084483 28245729 848456353 28875761731
--R   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
--R               7  71 1001 18089  398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 11

--S 12 of 22
eConvergents :: Stream Float
 

   (12)
   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (12)
--R   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
--R    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
--R    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
--R    ...]
--R                                                           Type: Stream Float
--E 12

--S 13 of 22
exp 1.0
 

   (13)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (13)  2.7182818284 590452354
--R                                                                  Type: Float
--E 13

--S 14 of 22
cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])
 

   (14)
           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
   + 
       289 |     361 |
     +-----+ + +-----+ + ...
     |  2      |  2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (14)
--R           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
--R     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
--R         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
--R   + 
--R       289 |     361 |
--R     +-----+ + +-----+ + ...
--R     |  2      |  2
--R                                              Type: ContinuedFraction Integer
--E 14

--S 15 of 22
ccf := convergents cf
 

            3 15 105 315 3465 45045 45045 765765 14549535
   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
            2 13  76 263 2578 36979 33976 622637 11064338
                                                Type: Stream Fraction Integer
--R 
--R
--R            3 15 105 315 3465 45045 45045 765765 14549535
--R   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
--R            2 13  76 263 2578 36979 33976 622637 11064338
--R                                                Type: Stream Fraction Integer
--E 15

--S 16 of 22
piConvergents := [4/p for p in ccf] 
 

            8 52 304 1052 10312 147916 135904 2490548 44257352
   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
            3 15 105  315  3465  45045  45045  765765 14549535
                                                Type: Stream Fraction Integer
--R 
--R
--R            8 52 304 1052 10312 147916 135904 2490548 44257352
--R   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
--R            3 15 105  315  3465  45045  45045  765765 14549535
--R                                                Type: Stream Fraction Integer
--E 16

--S 17 of 22
piConvergents :: Stream Float
 

   (17)
   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
    3.0418396189 294022111, ...]
                                                           Type: Stream Float
--R 
--R
--R   (17)
--R   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
--R    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
--R    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
--R    3.0418396189 294022111, ...]
--R                                                           Type: Stream Float
--E 17

--S 18 of 22
continuedFraction((- 122 + 597*%i)/(4 - 4*%i))
 

                            1    |         1     |
   (18)  - 90 + 59%i + +---------+ + +-----------+
                       | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1    |         1     |
--R   (18)  - 90 + 59%i + +---------+ + +-----------+
--R                       | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 18

--S 19 of 22
r : Fraction UnivariatePolynomial(x,Fraction Integer) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 22
r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))
 

           2
          x  - 3x + 2
   (20)  ------------
          2
         x  - 7x + 12
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2
--R          x  - 3x + 2
--R   (20)  ------------
--R          2
--R         x  - 7x + 12
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 20

--S 21 of 22
continuedFraction r 
 

                  1    |         1     |
   (21)  1 + +---------+ + +-----------+
             | 1     9     | 16     40
             | - x - -     | -- x - --
             | 4     8     |  3      3
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                  1    |         1     |
--R   (21)  1 + +---------+ + +-----------+
--R             | 1     9     | 16     40
--R             | - x - -     | -- x - --
--R             | 4     8     |  3      3
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 21

--S 22 of 22
[i*i for i in convergents(z) :: Stream Float] 
 

   (22)
   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (22)
--R   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
--R    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
--R    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
--R    ...]
--R                                                           Type: Stream Float
--E 22
)spool
 
Starts dribbling to dpol.output (2010/3/27, 18:25:3).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 18
odvar:=ODVAR Symbol
 

   (1)  OrderlyDifferentialVariable Symbol
                                                                 Type: Domain
--R 
--R
--R   (1)  OrderlyDifferentialVariable Symbol
--R                                                                 Type: Domain
--E 1

--S 2 of 18
[makeVariable('w,i)$odvar for i in 5..0 by -1]
 

   (2)  [w ,w ,w ,w ,w ,w]
          5  4  3  2  1
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (2)  [w ,w ,w ,w ,w ,w]
--R          5  4  3  2  1
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 2

--S 3 of 18
sort %
 

   (3)  [w,w ,w ,w ,w ,w ]
            1  2  3  4  5
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (3)  [w,w ,w ,w ,w ,w ]
--R            1  2  3  4  5
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 3

--S 4 of 18
dpol:=DSMP (FRAC INT, Symbol, odvar)
 

   (4)
  DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDiffe
  rentialVariable Symbol)
                                                                 Type: Domain
--R 
--R
--R   (4)
--R  DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDiffe
--R  rentialVariable Symbol)
--R                                                                 Type: Domain
--E 4

--S 5 of 18
w := makeVariable('w)$dpol
 

   (5)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
Type: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--R 
--R
--R   (5)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--RType: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--E 5

--S 6 of 18
z := makeVariable('z)$dpol
 

   (6)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
Type: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--R 
--R
--R   (6)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--RType: (NonNegativeInteger -> DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol))
--E 6

--S 7 of 18
(f,b):dpol
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 18
f:=w.4::dpol - w.1 * w.1 * z.3
 

               2
   (8)  w  - w  z
         4    1  3
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R               2
--R   (8)  w  - w  z
--R         4    1  3
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 8

--S 9 of 18
b:=(z.1::dpol)**3 * (z.2)**2 - w.2
 

          3  2
   (9)  z  z   - w
         1  2     2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R          3  2
--R   (9)  z  z   - w
--R         1  2     2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 9

--S 10 of 18
lb:=leader b
 

   (10)  z
          2
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (10)  z
--R          2
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 10

--S 11 of 18
sb:=separant b
 

            3
   (11)  2z  z
           1  2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            3
--R   (11)  2z  z
--R           1  2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 11

--S 12 of 18
bprime:= differentiate b
 

            3               2  3
   (12)  2z  z z  - w  + 3z  z
           1  2 3    3     1  2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            3               2  3
--R   (12)  2z  z z  - w  + 3z  z
--R           1  2 3    3     1  2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 12

--S 13 of 18
lbprime:= leader bprime
 

   (13)  z
          3
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (13)  z
--R          3
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 13

--S 14 of 18
pbf:=differentiate (f, lbprime)
 

             2
   (14)  - w
            1
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R             2
--R   (14)  - w
--R            1
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 14

--S 15 of 18
ftilde:=sb * f- pbf * bprime
 

            3         2        2  2  3
   (15)  2z  z w  - w  w  + 3w  z  z
           1  2 4    1  3     1  1  2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            3         2        2  2  3
--R   (15)  2z  z w  - w  w  + 3w  z  z
--R           1  2 4    1  3     1  1  2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 15

--S 16 of 18
ib:=initial b
 

           3
   (16)  z
          1
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R           3
--R   (16)  z
--R          1
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 16

--S 17 of 18
lcef:=leadingCoefficient univariate(ftilde, lb)
 

            2  2
   (17)  3w  z
           1  1
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            2  2
--R   (17)  3w  z
--R           1  1
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 17

--S 18 of 18
f0:=ib * ftilde - lcef * b * lb
 

            6         2  3        2  2
   (18)  2z  z w  - w  z  w  + 3w  z  w z
           1  2 4    1  1  3     1  1  2 2
Type: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--R 
--R
--R            6         2  3        2  2
--R   (18)  2z  z w  - w  z  w  + 3w  z  w z
--R           1  2 4    1  1  3     1  1  2 2
--RType: DifferentialSparseMultivariatePolynomial(Fraction Integer,Symbol,OrderlyDifferentialVariable Symbol)
--E 18
)spool
 
Starts dribbling to FileName.output (2010/3/27, 18:42:2).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 18
fn: FileName
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
fn := "fname.input"
 

   (2)  "fname.input"
                                                               Type: FileName
--R 
--R
--R   (2)  "fname.input"
--R                                                               Type: FileName
--E 2

--S 3 of 18
directory fn
 

   (3)  ""
                                                                 Type: String
--R 
--R
--R   (3)  ""
--R                                                                 Type: String
--E 3

--S 4 of 18
name fn
 

   (4)  "fname"
                                                                 Type: String
--R 
--R
--R   (4)  "fname"
--R                                                                 Type: String
--E 4

--S 5 of 18
extension fn
 

   (5)  "input"
                                                                 Type: String
--R 
--R
--R   (5)  "input"
--R                                                                 Type: String
--E 5

--S 6 of 18
fn := filename("/tmp", "fname", "input") 
 

   (6)  "/tmp/fname.input"
                                                               Type: FileName
--R 
--R
--R   (6)  "/tmp/fname.input"
--R                                                               Type: FileName
--E 6

--S 7 of 18
objdir := "/tmp"
 

   (7)  "/tmp"
                                                                 Type: String
--R 
--R
--R   (7)  "/tmp"
--R                                                                 Type: String
--E 7

--S 8 of 18
fn := filename(objdir, "table", "spad")
 

   (8)  "/tmp/table.spad"
                                                               Type: FileName
--R 
--R
--R   (8)  "/tmp/table.spad"
--R                                                               Type: FileName
--E 8

--S 9 of 18
fn := filename("", "letter", "") 
 

   (9)  "letter"
                                                               Type: FileName
--R 
--R
--R   (9)  "letter"
--R                                                               Type: FileName
--E 9

--S 10 of 18
exists? "/etc/passwd"
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 18
readable? "/etc/passwd"
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 18
readable? "/etc/security/passwd"
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 18
readable? "/ect/passwd"
 

   (13)  false
                                                                Type: Boolean
--R 
--R
--R   (13)  false
--R                                                                Type: Boolean
--E 13

--S 14 of 18
writable? "/etc/passwd"
 

   (14)  false
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 18
writable? "/dev/null"
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 18
writable? "/etc/DoesNotExist"
 

   (16)  false
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 18
writable? "/tmp/DoesNotExist"
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 18
fn := new(objdir, "xxx", "yy") 
 

   (18)  "NIL"
                                                               Type: FileName
--R 
--R
--I   (18)  "/tmp/xxx1419.yy"
--R                                                               Type: FileName
--E 18
)spool
 
Starts dribbling to overload.output (2010/3/27, 18:30:35).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 51
cos(1.237)
 

   (1)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R
--R   (1)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 1


--S 2 of 51
cos(1.237/2)
 

   (2)  0.8147490934 6341557739
                                                                  Type: Float
--R 
--R
--R   (2)  0.8147490934 6341557739
--R                                                                  Type: Float
--E 2


--S 3 of 51
cos(2/3)
 

            2
   (3)  cos(-)
            3
                                                     Type: Expression Integer
--R 
--R
--R            2
--R   (3)  cos(-)
--R            3
--R                                                     Type: Expression Integer
--E 3


--S 4 of 51
cos(2/3::Float)
 

   (4)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (4)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 4

--S 5 of 51
cos((2/3)::Float)
 

   (5)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (5)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 5

--S 6 of 51
cos(2/3$Float)
 

   (6)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (6)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 6

--S 7 of 51
cos((2/3)$Float)
 

   (7)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (7)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 7

--S 8 of 51
cos(2/3@Float)
 

   (8)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (8)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 8

--S 9 of 51
cos((2/3)@Float)
 

   (9)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (9)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 9


--S 10 of 51
cos(2/3)::Float
 
 
Daly Bug
   Cannot convert from type Expression Integer to Float for value
       2
   cos(-)
       3

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Expression Integer to Float for value
--R       2
--R   cos(-)
--R       3
--R
--E 10


--S 11 of 51
cosf(x:Expression Integer):Expression Integer == 1+cos(x/2)
 
   Function declaration cosf : Expression Integer -> Expression Integer
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration cosf : Expression Integer -> Expression Integer
--R      has been added to workspace.
--R                                                                   Type: Void
--E 11


--S 12 of 51
cosf(2/3)
 
   Compiling function cosf with type Expression Integer -> Expression 
      Integer 

             1
   (11)  cos(-) + 1
             3
                                                     Type: Expression Integer
--R 
--R   Compiling function cosf with type Expression Integer -> Expression 
--R      Integer 
--R
--R             1
--R   (11)  cos(-) + 1
--R             3
--R                                                     Type: Expression Integer
--E 12

--S 13 of 51
cosf((2/3)::Float)
 
   Conversion failed in the compiled user function cosf .
 
Daly Bug
   Cannot convert from type Float to Expression Integer for value
   0.6666666666 6666666667

--R 
--R   Conversion failed in the compiled user function cosf .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Expression Integer for value
--R   0.6666666666 6666666667
--R
--E 13


--S 14 of 51
--draw(cosf(x),x=0..15)
--E 14


--S 15 of 51
cos(2/3)+1.2323
 

   (12)  2.0181872607 769480007
                                                       Type: Expression Float
--R 
--R
--R   (12)  2.0181872607 769480007
--R                                                       Type: Expression Float
--E 15


--S 16 of 51
3/4+%pi
 

         4%pi + 3
   (13)  --------
             4
                                                                     Type: Pi
--R 
--R
--R         4%pi + 3
--R   (13)  --------
--R             4
--R                                                                     Type: Pi
--E 16


--S 17 of 51
C:=Complex Expression Integer
 

   (14)  Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (14)  Complex Expression Integer
--R                                                                 Type: Domain
--E 17

--S 18 of 51
Q:=Quaternion C
 

   (15)  Quaternion Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (15)  Quaternion Complex Expression Integer
--R                                                                 Type: Domain
--E 18


--S 19 of 51
((x:Q)/(y:Q)):Q == x*inv(y)
 
   Function declaration ?/? : (Quaternion Complex Expression Integer,
      Quaternion Complex Expression Integer) -> Quaternion Complex 
      Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration ?/? : (Quaternion Complex Expression Integer,
--R      Quaternion Complex Expression Integer) -> Quaternion Complex 
--R      Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 19


--S 20 of 51
x:=15/6
 
   Compiling function / with type (Quaternion Complex Expression 
      Integer,Quaternion Complex Expression Integer) -> Quaternion 
      Complex Expression Integer 

         5
   (17)  -
         2
                                  Type: Quaternion Complex Expression Integer
--R 
--R   Compiling function / with type (Quaternion Complex Expression 
--R      Integer,Quaternion Complex Expression Integer) -> Quaternion 
--R      Complex Expression Integer 
--R
--R         5
--R   (17)  -
--R         2
--R                                  Type: Quaternion Complex Expression Integer
--E 20


--S 21 of 51
cos(x)
 

             5
   (18)  cos(-)
             2
                                                     Type: Expression Integer
--R 
--R
--R             5
--R   (18)  cos(-)
--R             2
--R                                                     Type: Expression Integer
--E 21


--S 22 of 51
cos(1.237)
 

   (19)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R
--R   (19)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 22


--S 23 of 51
cos(15.457/6)
 
   Conversion failed in the compiled user function / .
 
Daly Bug
   Cannot convert from type Float to Quaternion Complex Expression 
      Integer for value
   15.457

--R 
--R   Conversion failed in the compiled user function / .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Quaternion Complex Expression 
--R      Integer for value
--R   15.457
--R
--E 23


--S 24 of 51
c(y:Float):Float == cos(y)
 
   Function declaration c : Float -> Float has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration c : Float -> Float has been added to workspace.
--R                                                                   Type: Void
--E 24


--S 25 of 51
c(1.237)
 
   Compiling function c with type Float -> Float 

   (21)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R   Compiling function c with type Float -> Float 
--R
--R   (21)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 25


--S 26 of 51
c(x)
 

   (22)  - 0.8011436155 4693371483
                                                                  Type: Float
--R 
--R
--R   (22)  - 0.8011436155 4693371483
--R                                                                  Type: Float
--E 26


--S 27 of 51
c(1.237/2)
 
   Conversion failed in the compiled user function / .
 
Daly Bug
   Cannot convert from type Float to Quaternion Complex Expression 
      Integer for value
   1.237

--R 
--R   Conversion failed in the compiled user function / .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Quaternion Complex Expression 
--R      Integer for value
--R   1.237
--R
--E 27


--S 28 of 51
cos(2/3::Float)
 

             2
   (23)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (23)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 28

--S 29 of 51
cos((2/3)::Float)
 

   (24)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (24)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 29

--S 30 of 51
cos(2/3$Float)
 

             2
   (25)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (25)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 30

--S 31 of 51
cos((2/3)$Float)
 

   (26)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (26)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 31

--S 32 of 51
cos(2/3@Float)
 

             2
   (27)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (27)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 32

--S 33 of 51
cos((2/3)@Float)
 
 
Daly Bug
   An expression involving @ Float actually evaluated to one of type 
      Quaternion Complex Expression Integer . Perhaps you should use ::
      Float .
--R 
--R 
--RDaly Bug
--R   An expression involving @ Float actually evaluated to one of type 
--R      Quaternion Complex Expression Integer . Perhaps you should use ::
--R      Float .
--E 33


--S 34 of 51
c(2/3::Float)
 

   (28)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (28)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 34

--S 35 of 51
c((2/3)::Float)
 

   (29)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (29)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 35

--S 36 of 51
c(2/3$Float)
 

   (30)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (30)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 36

--S 37 of 51
c((2/3)$Float)
 

   (31)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (31)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 37

--S 38 of 51
c(2/3@Float)
 

   (32)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (32)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 38

--S 39 of 51
c((2/3)@Float)
 
 
Daly Bug
   An expression involving @ Float actually evaluated to one of type 
      Quaternion Complex Expression Integer . Perhaps you should use ::
      Float .
--R 
--R 
--RDaly Bug
--R   An expression involving @ Float actually evaluated to one of type 
--R      Quaternion Complex Expression Integer . Perhaps you should use ::
--R      Float .
--E 39


--S 40 of 51
c2(y) == cos(y)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 40

--S 41 of 51
c2(1.237)
 
   Compiling function c2 with type Float -> Float 

   (34)  0.3276321705 9891498386
                                                                  Type: Float
--R 
--R   Compiling function c2 with type Float -> Float 
--R
--R   (34)  0.3276321705 9891498386
--R                                                                  Type: Float
--E 41

--S 42 of 51
c2(x)
 
   There are 2 exposed and 6 unexposed library operations named cos 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op cos
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named cos 
      with argument type(s) 
                    Quaternion Complex Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.

             5
   (35)  cos(-)
             2
                                                     Type: Expression Integer
--R 
--R   There are 2 exposed and 6 unexposed library operations named cos 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op cos
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named cos 
--R      with argument type(s) 
--R                    Quaternion Complex Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R
--R             5
--R   (35)  cos(-)
--R             2
--R                                                     Type: Expression Integer
--E 42


--S 43 of 51
c2(1.237/2)
 
   Conversion failed in the compiled user function / .
 
Daly Bug
   Cannot convert from type Float to Quaternion Complex Expression 
      Integer for value
   1.237

--R 
--R   Conversion failed in the compiled user function / .
--R 
--RDaly Bug
--R   Cannot convert from type Float to Quaternion Complex Expression 
--R      Integer for value
--R   1.237
--R
--E 43


--S 44 of 51
c2(2/3::Float)
 

             2
   (36)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (36)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 44

--S 45 of 51
c2((2/3)::Float)
 

   (37)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (37)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 45

--S 46 of 51
c2(2/3$Float)
 

             2
   (38)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (38)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 46

--S 47 of 51
c2((2/3)$Float)
 

   (39)  0.7858872607 7694800072
                                                                  Type: Float
--R 
--R
--R   (39)  0.7858872607 7694800072
--R                                                                  Type: Float
--E 47

--S 48 of 51
c2(2/3@Float)
 

             2
   (40)  cos(-)
             3
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (40)  cos(-)
--R             3
--R                                                     Type: Expression Integer
--E 48

--S 49 of 51
c2((2/3)@Float)
 
 
Daly Bug
   An expression involving @ Float actually evaluated to one of type 
      Quaternion Complex Expression Integer . Perhaps you should use ::
      Float .
--R 
--R 
--RDaly Bug
--R   An expression involving @ Float actually evaluated to one of type 
--R      Quaternion Complex Expression Integer . Perhaps you should use ::
--R      Float .
--E 49


--S 50 of 51
--draw(c(x),x=0..15)
--E 50


--S 51 of 51
--draw(cos(x),x=0..15)
--E 51

)spool 
 
Starts dribbling to shannonmatrix.output (2010/3/27, 18:38:58).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 27
vprod(v1:Vector PF 2,v2:Vector PF 2):Vector PF 2 ==
   [v1.i * v2.i for i in 1..#v1]
 
   Function declaration vprod : (Vector PrimeField 2,Vector PrimeField 
      2) -> Vector PrimeField 2 has been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration vprod : (Vector PrimeField 2,Vector PrimeField 
--      2) -> Vector PrimeField 2 has been added to workspace.
--                                                                   Type: Void
--E 1

--S 2 of 27
varmat(nvar) ==
   N := 2^nvar
   vmat := zero(nvar, N)$Matrix PF 2
   for i in 0..N-1 repeat
    for j in 0..nvar-1 repeat
        if bit?(i,j) then vmat(nvar-j,i+1):=1
   vmat
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 2

--S 3 of 27
prodvec(bvec:Vector PF 2, vmat:Matrix PF 2):Vector PF 2 ==
   vec := new(ncols vmat,1)$Vector PF 2
   for i in 1..#bvec repeat
       if bvec(i)=1 then
           vec := vprod(vec, row(vmat,i))
   vec
 
   Function declaration prodvec : (Vector PrimeField 2,Matrix 
      PrimeField 2) -> Vector PrimeField 2 has been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration prodvec : (Vector PrimeField 2,Matrix 
--      PrimeField 2) -> Vector PrimeField 2 has been added to workspace.
--                                                                   Type: Void
--E 3

--S 4 of 27
B(r,m) ==
   vmat := varmat m
   r = 0 => matrix [prodvec(column(vmat,1), vmat)]
   r = 1 => vmat
   rows : List Vector PF 2 := []
   for j in 1..ncols vmat repeat
       colj := column(vmat,j)
       if reduce(+, colj::Vector INT) = r then
           rows := concat(prodvec(colj, vmat),rows)
   matrix rows
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 4

--S 5 of 27
G(r,m) ==
   gmat := B(0, m)
   for i in 1..r repeat
       gmat := vertConcat(gmat, B(i,m))
   gmat
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 5

--S 6 of 27
Galt(r,m) ==
   vmat := varmat m
   rows : List Vector PF 2 := []
   for j in 1..ncols vmat repeat
       colj := column(vmat,j)
       if reduce(+, colj::Vector INT) <= r then
           rows := concat(prodvec(colj, vmat),rows)
   matrix rows
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 6

--S 7 of 27
orvec(vec:Vector PF 2):INT ==
   for i in 1..#vec repeat
       if vec(i) = 1 then return 1
   return 0
 
   Function declaration orvec : Vector PrimeField 2 -> Integer has been
      added to workspace.
                                                                   Type: Void
-- 
--   Function declaration orvec : Vector PrimeField 2 -> Integer has been
--      added to workspace.
--                                                                   Type: Void
--E 7

--S 8 of 27
countNonzRows(mat) ==
   reduce(+,[orvec(row(mat,i)) for i in 1..nrows mat])
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 8

--S 9 of 27
testTOGM(mat) == -- 0 if test succeeds otherise failing col
   for i in 1..ncols(mat) repeat
       mi := subMatrix(mat,1,nrows(mat),1,i)
       if rank(mi) ~= countNonzRows mi then return( i)
       rmi := subMatrix(mat,1,nrows(mat),ncols(mat)-i+1,ncols mat)
       if rank(rmi) ~= countNonzRows rmi then return(-i)
   return 0
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 9

--S 10 of 27
leftind(v:Vector PF 2):INT ==
   n := #v
   for i in 1..n repeat
       if v.i = 1 then return i
   return( -1)
 
   Function declaration leftind : Vector PrimeField 2 -> Integer has 
      been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration leftind : Vector PrimeField 2 -> Integer has 
--      been added to workspace.
--                                                                   Type: Void
--E 10

--S 11 of 27
rightind(v:Vector PF 2):INT ==
   n := #v
   for i in n..1 by -1 repeat
       if v.i = 1 then return i
   return( -1)
 
   Function declaration rightind : Vector PrimeField 2 -> Integer has 
      been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration rightind : Vector PrimeField 2 -> Integer has 
--      been added to workspace.
--                                                                   Type: Void
--E 11

--S 12 of 27
makeActive m ==
   mm := copy m
   for i in 1..nrows mm repeat
       v := row(mm,i)
       for j in leftind(v)..rightind(v) repeat
           mm(i,j) := 1
   mm
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 12

--S 13 of 27
makeTOGM(mat) ==
   m := rowEchelon mat
   nr := nrows m
   for i in nr..1 by -1 repeat
       r := rightind(row(m,i))
       for ii in 1.. i-1 repeat
           if m(ii,r) = 1 then
              setRow!(m,ii,row(m,ii)+row(m,i))
   m
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 13

--S 14 of 27
countActives m ==
   mm := makeActive m
   nc1 : NNI := (ncols(mm)-1)::NNI
   v:=new(nc1,0)$Vector INT
   for j in 1..nc1 repeat
       for i in 1..nrows(mm) repeat
           if mm(i,j)=1 and mm(i,j+1) = 1 then v.j := v.j + 1
   v::List INT
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 14

--S 15 of 27
nstates m ==
   reduce(+,[2^i for i in countActives m])
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 15

--S 16 of 27
rowmats(vec:Vector PF 2):Vector Matrix POLY INT ==
   left := leftind(vec)
   right := rightind(vec)
   lmat:Matrix POLY INT := matrix [[1]]
   lmats : Vector Matrix POLY INT := new(#vec, lmat)
   lmats.left := matrix [[1, I*D]]
   for i in left+1..right-1 repeat
       if vec.i = 0 then lmats.i := matrix [[1,0],[0,1]]
       else lmats.i := matrix [[1, 0],[0,D]]
   lmats.right := matrix [[1], [D]]
   lmats
 
   Function declaration rowmats : Vector PrimeField 2 -> Vector Matrix 
      Polynomial Integer has been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration rowmats : Vector PrimeField 2 -> Vector Matrix 
--      Polynomial Integer has been added to workspace.
--                                                                   Type: Void
--E 16

--S 17 of 27
rowmats1(vec:Vector PF 2):Vector Matrix POLY INT == -- no input weights I=1
   left := leftind(vec)
   right := rightind(vec)
   lmat:Matrix POLY INT := matrix [[1]]
   lmats : Vector Matrix POLY INT := new(#vec, lmat)
   lmats.left := matrix [[1, D]]
   for i in left+1..right-1 repeat
       if vec.i = 0 then lmats.i := matrix [[1,0],[0,1]]
       else lmats.i := matrix [[1, 0],[0,D]]
   lmats.right := matrix [[1], [D]]
   lmats
 
   Function declaration rowmats1 : Vector PrimeField 2 -> Vector Matrix
      Polynomial Integer has been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration rowmats1 : Vector PrimeField 2 -> Vector Matrix
--      Polynomial Integer has been added to workspace.
--                                                                   Type: Void
--E 17

--S 18 of 27
shannonMatProd(mat1, mat2) ==
   mat:Matrix POLY INT:=zero(nrows(mat1)*nrows(mat2), ncols(mat1)*ncols(mat2))
   for i1 in 1..nrows(mat1) repeat
       for i2 in 1..nrows(mat2) repeat
           for j1 in 1..ncols(mat1) repeat
               for j2 in 1..ncols(mat2) repeat
                   p1 := mat1(i1,j1)
                   p2 := mat2(i2,j2)
                   if p1 ~= 0 and p2~=0 then
                       mat((i1-1)*nrows(mat2)+i2, (j1-1)*ncols(mat2)+j2) := _
                          I^(degree(p1,I) + degree(p2,I))_
                            * D ^ ((degree(p1,D) + degree(p2,D)) rem 2)
   mat
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 18

--S 19 of 27
shannonProd(lpmats1, lpmats2) ==
   olmats := copy lpmats1
   for i in 1..#olmats repeat
       olmats.i := shannonMatProd(olmats.i, lpmats2.i)
   olmats
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 19

--S 20 of 27
makeMatList(m) ==
   lpmats := rowmats(row(m,1))
   for i in 2..nrows m repeat
       print ["processing row",i]
       lpmats := shannonProd(lpmats, rowmats(row(m,i)))
   lpmats
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 20

--S 21 of 27
part(l,i,k) == -- extracts section i out of k from list l
   n := (#l/k)::INT
   [l.j for j in (i-1)*n+1..i*n]
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 21

--S 22 of 27
saveMatList(m, fn) ==
   lpmats := makeMatList m
   fn.'lpmats1:=part(lpmats,1,8)
   fn.'lpmats2:=part(lpmats,2,8)
   fn.'lpmats3:=part(lpmats,3,8)
   fn.'lpmats4:=part(lpmats,4,8)
   fn.'lpmats5:=part(lpmats,5,8)
   fn.'lpmats6:=part(lpmats,6,8)
   fn.'lpmats7:=part(lpmats,7,8)
   fn.'lpmats8:=part(lpmats,8,8)
   keys fn
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 22

--S 23 of 27
wtpoly(m:Matrix PF 2):POLY INT ==
   lpmats := rowmats1(row(m,1))
   for i in 2..nrows m repeat
       print ["processing row",i]
       lpmats := shannonProd(lpmats, rowmats1(row(m,i)))
   pmat := lpmats.1
   print "multiplying matrices"
   for i in 2..#lpmats repeat
       pmat := pmat * lpmats.i
   pmat(1,1)
 
   Function declaration wtpoly : Matrix PrimeField 2 -> Polynomial 
      Integer has been added to workspace.
                                                                   Type: Void
-- 
--   Function declaration wtpoly : Matrix PrimeField 2 -> Polynomial 
--      Integer has been added to workspace.
--                                                                   Type: Void
--E 23

--S 24 of 27
saveWtPoly(m, fn) ==
   pol := wtpoly m
   fn.'T := pol
 
                                                                   Type: Void
-- 
--                                                                   Type: Void
--E 24

--S 25 of 27
g57 := makeTOGM G(5,7)
 
   Compiling function varmat with type PositiveInteger -> Matrix 
      PrimeField 2 
   Compiling function vprod with type (Vector PrimeField 2,Vector 
      PrimeField 2) -> Vector PrimeField 2 
   Compiling function prodvec with type (Vector PrimeField 2,Matrix 
      PrimeField 2) -> Vector PrimeField 2 
   Compiling function B with type (NonNegativeInteger,PositiveInteger)
       -> Matrix PrimeField 2 
   Compiling function G with type (PositiveInteger,PositiveInteger) -> 
      Matrix PrimeField 2 
   Compiling function rightind with type Vector PrimeField 2 -> Integer
      
   Compiling function makeTOGM with type Matrix PrimeField 2 -> Matrix 
      PrimeField 2 

   (25)
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      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0,
      1, 0, 0, 0, 1, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,
      0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
      1, 0, 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
      1, 1, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      1, 1, 1, 1, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 1, 0, 1, 1, 0, 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 1, 1, 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 1, 1, 1, 1]
     ]
                                                    Type: Matrix PrimeField 2
-- 
--   Compiling function varmat with type PositiveInteger -> Matrix 
--      PrimeField 2 
--   Compiling function vprod with type (Vector PrimeField 2,Vector 
--      PrimeField 2) -> Vector PrimeField 2 
--   Compiling function prodvec with type (Vector PrimeField 2,Matrix 
--      PrimeField 2) -> Vector PrimeField 2 
--   Compiling function B with type (NonNegativeInteger,PositiveInteger)
--       -> Matrix PrimeField 2 
--   Compiling function G with type (PositiveInteger,PositiveInteger) -> 
--      Matrix PrimeField 2 
--   Compiling function rightind with type Vector PrimeField 2 -> Integer
--      
--   Compiling function makeTOGM with type Matrix PrimeField 2 -> Matrix 
--      PrimeField 2 
--
--   (25)
--   [
--     [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
--      1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0,
--      1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0,
--      1, 0, 0, 0, 1, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,
--      0, 0, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
--      1, 0, 1, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
--      1, 1, 0, 0, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      1, 1, 1, 1, 0, 0, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 1, 0, 1, 1, 0, 1, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 1, 1, 1, 1, 0, 0]
--     ,
--
--     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--      0, 0, 0, 0, 1, 1, 1, 1]
--     ]
--                                                    Type: Matrix PrimeField 2
--E 25

--S 26 of 27
p:=wtpoly g57
 
   Compiling function leftind with type Vector PrimeField 2 -> Integer 
   Compiling function rowmats1 with type Vector PrimeField 2 -> Vector 
      Matrix Polynomial Integer 
   Compiling function shannonMatProd with type (Matrix Polynomial 
      Integer,Matrix Polynomial Integer) -> Matrix Polynomial Integer 
   Compiling function shannonProd with type (Vector Matrix Polynomial 
      Integer,Vector Matrix Polynomial Integer) -> Vector Matrix 
      Polynomial Integer 
   Compiling function wtpoly with type Matrix PrimeField 2 -> 
      Polynomial Integer 
   ["processing row",2]
   ["processing row",3]
   ["processing row",4]
   ["processing row",5]
   ["processing row",6]
   ["processing row",7]
   ["processing row",8]
   ["processing row",9]
   ["processing row",10]
   ["processing row",11]
   ["processing row",12]
   ["processing row",13]
   ["processing row",14]
   ["processing row",15]
   ["processing row",16]
   ["processing row",17]
   ["processing row",18]
   ["processing row",19]
   ["processing row",20]
   ["processing row",21]
   ["processing row",22]
   ["processing row",23]
   ["processing row",24]
   ["processing row",25]
   ["processing row",26]
   ["processing row",27]
   ["processing row",28]
   ["processing row",29]
   ["processing row",30]
   ["processing row",31]
   ["processing row",32]
   ["processing row",33]
   ["processing row",34]
   ["processing row",35]
   ["processing row",36]
   ["processing row",37]
   ["processing row",38]
   ["processing row",39]
   ["processing row",40]
   ["processing row",41]
   ["processing row",42]
   ["processing row",43]
   ["processing row",44]
   ["processing row",45]
   ["processing row",46]
   ["processing row",47]
   ["processing row",48]
   ["processing row",49]
   ["processing row",50]
   ["processing row",51]
   ["processing row",52]
   ["processing row",53]
   ["processing row",54]
   ["processing row",55]
   ["processing row",56]
   ["processing row",57]
   ["processing row",58]
   ["processing row",59]
   ["processing row",60]
   ["processing row",61]
   ["processing row",62]
   ["processing row",63]
   ["processing row",64]
   ["processing row",65]
   ["processing row",66]
   ["processing row",67]
   ["processing row",68]
   ["processing row",69]
   ["processing row",70]
   ["processing row",71]
   ["processing row",72]
   ["processing row",73]
   ["processing row",74]
   ["processing row",75]
   ["processing row",76]
   ["processing row",77]
   ["processing row",78]
   ["processing row",79]
   ["processing row",80]
   ["processing row",81]
   ["processing row",82]
   ["processing row",83]
   ["processing row",84]
   ["processing row",85]
   ["processing row",86]
   ["processing row",87]
   ["processing row",88]
   ["processing row",89]
   ["processing row",90]
   ["processing row",91]
   ["processing row",92]
   ["processing row",93]
   ["processing row",94]
   ["processing row",95]
   ["processing row",96]
   ["processing row",97]
   ["processing row",98]
   ["processing row",99]
   ["processing row",100]
   ["processing row",101]
   ["processing row",102]
   ["processing row",103]
   ["processing row",104]
   ["processing row",105]
   ["processing row",106]
   ["processing row",107]
   ["processing row",108]
   ["processing row",109]
   ["processing row",110]
   ["processing row",111]
   ["processing row",112]
   ["processing row",113]
   ["processing row",114]
   ["processing row",115]
   ["processing row",116]
   ["processing row",117]
   ["processing row",118]
   ["processing row",119]
   ["processing row",120]
   "multiplying matrices"

   (26)
      128         124            122               120                 118
     D    + 85344D    + 42330624D    + 11170182384D    + 1772228014592D
   + 
                     116                     114                      112
     185359804775712D    + 13586256544975872D    + 729242357526446712D
   + 
                          110                         108
     29627257927486958592D    + 934817955092922629344D
   + 
                             106                            104
     23382589365749366429184D    + 471464166034059302122704D
   + 
                               102                               100
     7769729456174562056216064D    + 105877979970476869275385504D
   + 
                                  98                                 96
     1204818392766796825789470720D   + 11545366574237052418777217820D
   + 
                                   94                                  92
     93844690870798540052434360320D   + 651103402851220082586931517920D
   + 
                                     90                                    88
     3876982708869397190103809681920D   + 19906815062848699462140058602480D
   + 
                                      86                                     84
     88505561045975275152200314606080D   + 341953304041268345847846829061280D
   + 
                                        82
     1151738374770880217441839661716480D
   + 
                                        80
     3390889310828097487679807613566280D
   + 
                                        78
     8747110385483091255323050018747392D
   + 
                                         76
     19809632343594061105640384790579552D
   + 
                                         74
     39453146176969302060067713110615552D
   + 
                                         72
     69196719366229927819863672056678992D
   + 
                                          70
     106997468058126854441956301420662272D
   + 
                                          68
     145988070825071389633119654266397216D
   + 
                                          66
     175865058349821585715411392357912576D
   + 
                                          64
     187118328452563149209991044344449606D
   + 
                                          62
     175865058349821585715411392357912576D
   + 
                                          60
     145988070825071389633119654266397216D
   + 
                                          58
     106997468058126854441956301420662272D
   + 
                                         56
     69196719366229927819863672056678992D
   + 
                                         54
     39453146176969302060067713110615552D
   + 
                                         52
     19809632343594061105640384790579552D
   + 
                                        50
     8747110385483091255323050018747392D
   + 
                                        48
     3390889310828097487679807613566280D
   + 
                                        46
     1151738374770880217441839661716480D
   + 
                                       44                                    42
     341953304041268345847846829061280D   + 88505561045975275152200314606080D
   + 
                                      40                                   38
     19906815062848699462140058602480D   + 3876982708869397190103809681920D
   + 
                                    36                                 34
     651103402851220082586931517920D   + 93844690870798540052434360320D
   + 
                                   32                                30
     11545366574237052418777217820D   + 1204818392766796825789470720D
   + 
                                 28                             26
     105877979970476869275385504D   + 7769729456174562056216064D
   + 
                              24                           22
     471464166034059302122704D   + 23382589365749366429184D
   + 
                           20                        18                      16
     934817955092922629344D   + 29627257927486958592D   + 729242357526446712D
   + 
                       14                   12                 10
     13586256544975872D   + 185359804775712D   + 1772228014592D
   + 
                 8            6         4
     11170182384D  + 42330624D  + 85344D  + 1
                                                     Type: Polynomial Integer
-- 
--   Compiling function leftind with type Vector PrimeField 2 -> Integer 
--   Compiling function rowmats1 with type Vector PrimeField 2 -> Vector 
--      Matrix Polynomial Integer 
--   Compiling function shannonMatProd with type (Matrix Polynomial 
--      Integer,Matrix Polynomial Integer) -> Matrix Polynomial Integer 
--   Compiling function shannonProd with type (Vector Matrix Polynomial 
--      Integer,Vector Matrix Polynomial Integer) -> Vector Matrix 
--      Polynomial Integer 
--   Compiling function wtpoly with type Matrix PrimeField 2 -> 
--      Polynomial Integer 
--   ["processing row",2]
--   ["processing row",3]
--   ["processing row",4]
--   ["processing row",5]
--   ["processing row",6]
--   ["processing row",7]
--   ["processing row",8]
--   ["processing row",9]
--   ["processing row",10]
--   ["processing row",11]
--   ["processing row",12]
--   ["processing row",13]
--   ["processing row",14]
--   ["processing row",15]
--   ["processing row",16]
--   ["processing row",17]
--   ["processing row",18]
--   ["processing row",19]
--   ["processing row",20]
--   ["processing row",21]
--   ["processing row",22]
--   ["processing row",23]
--   ["processing row",24]
--   ["processing row",25]
--   ["processing row",26]
--   ["processing row",27]
--   ["processing row",28]
--   ["processing row",29]
--   ["processing row",30]
--   ["processing row",31]
--   ["processing row",32]
--   ["processing row",33]
--   ["processing row",34]
--   ["processing row",35]
--   ["processing row",36]
--   ["processing row",37]
--   ["processing row",38]
--   ["processing row",39]
--   ["processing row",40]
--   ["processing row",41]
--   ["processing row",42]
--   ["processing row",43]
--   ["processing row",44]
--   ["processing row",45]
--   ["processing row",46]
--   ["processing row",47]
--   ["processing row",48]
--   ["processing row",49]
--   ["processing row",50]
--   ["processing row",51]
--   ["processing row",52]
--   ["processing row",53]
--   ["processing row",54]
--   ["processing row",55]
--   ["processing row",56]
--   ["processing row",57]
--   ["processing row",58]
--   ["processing row",59]
--   ["processing row",60]
--   ["processing row",61]
--   ["processing row",62]
--   ["processing row",63]
--   ["processing row",64]
--   ["processing row",65]
--   ["processing row",66]
--   ["processing row",67]
--   ["processing row",68]
--   ["processing row",69]
--   ["processing row",70]
--   ["processing row",71]
--   ["processing row",72]
--   ["processing row",73]
--   ["processing row",74]
--   ["processing row",75]
--   ["processing row",76]
--   ["processing row",77]
--   ["processing row",78]
--   ["processing row",79]
--   ["processing row",80]
--   ["processing row",81]
--   ["processing row",82]
--   ["processing row",83]
--   ["processing row",84]
--   ["processing row",85]
--   ["processing row",86]
--   ["processing row",87]
--   ["processing row",88]
--   ["processing row",89]
--   ["processing row",90]
--   ["processing row",91]
--   ["processing row",92]
--   ["processing row",93]
--   ["processing row",94]
--   ["processing row",95]
--   ["processing row",96]
--   ["processing row",97]
--   ["processing row",98]
--   ["processing row",99]
--   ["processing row",100]
--   ["processing row",101]
--   ["processing row",102]
--   ["processing row",103]
--   ["processing row",104]
--   ["processing row",105]
--   ["processing row",106]
--   ["processing row",107]
--   ["processing row",108]
--   ["processing row",109]
--   ["processing row",110]
--   ["processing row",111]
--   ["processing row",112]
--   ["processing row",113]
--   ["processing row",114]
--   ["processing row",115]
--   ["processing row",116]
--   ["processing row",117]
--   ["processing row",118]
--   ["processing row",119]
--   ["processing row",120]
--   "multiplying matrices"
--
--   (26)
--      128         124            122               120                 118
--     D    + 85344D    + 42330624D    + 11170182384D    + 1772228014592D
--   + 
--                     116                     114                      112
--     185359804775712D    + 13586256544975872D    + 729242357526446712D
--   + 
--                          110                         108
--     29627257927486958592D    + 934817955092922629344D
--   + 
--                             106                            104
--     23382589365749366429184D    + 471464166034059302122704D
--   + 
--                               102                               100
--     7769729456174562056216064D    + 105877979970476869275385504D
--   + 
--                                  98                                 96
--     1204818392766796825789470720D   + 11545366574237052418777217820D
--   + 
--                                   94                                  92
--     93844690870798540052434360320D   + 651103402851220082586931517920D
--   + 
--                                     90                                    88
--     3876982708869397190103809681920D   + 19906815062848699462140058602480D
--   + 
--                                      86                                     84
--     88505561045975275152200314606080D   + 341953304041268345847846829061280D
--   + 
--                                        82
--     1151738374770880217441839661716480D
--   + 
--                                        80
--     3390889310828097487679807613566280D
--   + 
--                                        78
--     8747110385483091255323050018747392D
--   + 
--                                         76
--     19809632343594061105640384790579552D
--   + 
--                                         74
--     39453146176969302060067713110615552D
--   + 
--                                         72
--     69196719366229927819863672056678992D
--   + 
--                                          70
--     106997468058126854441956301420662272D
--   + 
--                                          68
--     145988070825071389633119654266397216D
--   + 
--                                          66
--     175865058349821585715411392357912576D
--   + 
--                                          64
--     187118328452563149209991044344449606D
--   + 
--                                          62
--     175865058349821585715411392357912576D
--   + 
--                                          60
--     145988070825071389633119654266397216D
--   + 
--                                          58
--     106997468058126854441956301420662272D
--   + 
--                                         56
--     69196719366229927819863672056678992D
--   + 
--                                         54
--     39453146176969302060067713110615552D
--   + 
--                                         52
--     19809632343594061105640384790579552D
--   + 
--                                        50
--     8747110385483091255323050018747392D
--   + 
--                                        48
--     3390889310828097487679807613566280D
--   + 
--                                        46
--     1151738374770880217441839661716480D
--   + 
--                                       44                                    42
--     341953304041268345847846829061280D   + 88505561045975275152200314606080D
--   + 
--                                      40                                   38
--     19906815062848699462140058602480D   + 3876982708869397190103809681920D
--   + 
--                                    36                                 34
--     651103402851220082586931517920D   + 93844690870798540052434360320D
--   + 
--                                   32                                30
--     11545366574237052418777217820D   + 1204818392766796825789470720D
--   + 
--                                 28                             26
--     105877979970476869275385504D   + 7769729456174562056216064D
--   + 
--                              24                           22
--     471464166034059302122704D   + 23382589365749366429184D
--   + 
--                           20                        18                      16
--     934817955092922629344D   + 29627257927486958592D   + 729242357526446712D
--   + 
--                       14                   12                 10
--     13586256544975872D   + 185359804775712D   + 1772228014592D
--   + 
--                 8            6         4
--     11170182384D  + 42330624D  + 85344D  + 1
--                                                     Type: Polynomial Integer
--E 26

--S 27 of 27
reduce(+,coefficients p)-2^120
 

   (27)  0
                                                     Type: NonNegativeInteger
-- 
--
--   (27)  0
--                                                     Type: NonNegativeInteger
--E 27

)spool 
 
Starts dribbling to reclos2.output (2010/3/27, 18:36:49).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 31
LR:=radicalSolve(p^3-p+1/10=0,p)
 

   (1)
                        +------------------+2
                        |    +-+    +-----+
            +---+       |- 3\|3  + \|- 373
       (- 3\|- 3  + 3)  |------------------  - 2
                       3|         +-+
                       \|      60\|3
   [p= -----------------------------------------,
                          +------------------+
                          |    +-+    +-----+
              +---+       |- 3\|3  + \|- 373
           (3\|- 3  + 3)  |------------------
                         3|         +-+
                         \|      60\|3
                        +------------------+2
                        |    +-+    +-----+
            +---+       |- 3\|3  + \|- 373
       (- 3\|- 3  - 3)  |------------------  + 2
                       3|         +-+
                       \|      60\|3
    p= -----------------------------------------,
                          +------------------+
                          |    +-+    +-----+
              +---+       |- 3\|3  + \|- 373
           (3\|- 3  - 3)  |------------------
                         3|         +-+
                         \|      60\|3
          +------------------+2
          |    +-+    +-----+
          |- 3\|3  + \|- 373
       3  |------------------  + 1
         3|         +-+
         \|      60\|3
    p= ---------------------------]
             +------------------+
             |    +-+    +-----+
             |- 3\|3  + \|- 373
          3  |------------------
            3|         +-+
            \|      60\|3
                                       Type: List Equation Expression Integer
--R
--R   (1)
--R                        +------------------+2
--R                        |    +-+    +-----+
--R            +---+       |- 3\|3  + \|- 373
--R       (- 3\|- 3  + 3)  |------------------  - 2
--R                       3|         +-+
--R                       \|      60\|3
--R   [p= -----------------------------------------,
--R                          +------------------+
--R                          |    +-+    +-----+
--R              +---+       |- 3\|3  + \|- 373
--R           (3\|- 3  + 3)  |------------------
--R                         3|         +-+
--R                         \|      60\|3
--R                        +------------------+2
--R                        |    +-+    +-----+
--R            +---+       |- 3\|3  + \|- 373
--R       (- 3\|- 3  - 3)  |------------------  + 2
--R                       3|         +-+
--R                       \|      60\|3
--R    p= -----------------------------------------,
--R                          +------------------+
--R                          |    +-+    +-----+
--R              +---+       |- 3\|3  + \|- 373
--R           (3\|- 3  - 3)  |------------------
--R                         3|         +-+
--R                         \|      60\|3
--R          +------------------+2
--R          |    +-+    +-----+
--R          |- 3\|3  + \|- 373
--R       3  |------------------  + 1
--R         3|         +-+
--R         \|      60\|3
--R    p= ---------------------------]
--R             +------------------+
--R             |    +-+    +-----+
--R             |- 3\|3  + \|- 373
--R          3  |------------------
--R            3|         +-+
--R            \|      60\|3
--R                                       Type: List Equation Expression Integer
--E 1

--S 2 of 31
t2:=map(eq +-> (rhs eq)::Complex Float,LR)
 

   (2)
   [0.1010312578 8101081769 - 0.6 E -20 %i, - 1.0466805318 046022612,
    0.9456492739 2359144347 + 0.3 E -20 %i]
                                                     Type: List Complex Float
--R
--R   (2)
--R   [0.1010312578 8101081769 - 0.6 E -20 %i, - 1.0466805318 046022612,
--R    0.9456492739 2359144347 + 0.3 E -20 %i]
--R                                                     Type: List Complex Float
--E 2

--S 3 of 31
t3:=reduce('+, map (eq +-> (rhs eq)::Complex Float, LR))
 

   (3)  0.3 E -20 - 0.2 E -20 %i
                                                          Type: Complex Float
--R
--R   (3)  0.3 E -20 - 0.2 E -20 %i
--R                                                          Type: Complex Float
--E 3

--S 4 of 31
t4:=reduce('*, map (eq +-> (rhs eq)::Complex Float, LR))
 

   (4)  - 0.0999999999 9999999999 8 + 0.5405624429 3105340769 E -20 %i
                                                          Type: Complex Float
--R
--R   (4)  - 0.0999999999 9999999999 8 + 0.5405624429 3105340769 E -20 %i
--R                                                          Type: Complex Float
--E 4

--S 5 of 31
t5:=map(eq +-> numeric real rhs eq, LR)
 

   (5)
   [- 0.9456492739 2359144347,- 0.1010312578 8101081769,1.0466805318 046022612]
                                                             Type: List Float
--R
--R   (5)
--R   [- 0.9456492739 2359144347,- 0.1010312578 8101081769,1.0466805318 046022612]
--R                                                             Type: List Float
--E 5

--S 6 of 31
t6:=map(eq +-> numeric imag rhs eq, LR)
 

   (6)  [0.4890347001 0975238235 E -21,- 0.4890347001 0975238235 E -21,0.0]
                                                             Type: List Float
--R
--R   (6)  [0.4890347001 0975238235 E -21,- 0.4890347001 0975238235 E -21,0.0]
--R                                                             Type: List Float
--E 6

--S 7 of 31
t7:=numeric(sqrt(3)::Complex EXPR INT)
 

   (7)  1.7320508075 688772935
                                                                  Type: Float
--R
--R   (7)  1.7320508075 688772935
--R                                                                  Type: Float
--E 7

--S 8 of 31
t8:=discriminant(p^3-p+1/10)
 

        373
   (8)  ---
        100
                                                       Type: Fraction Integer
--R
--R        373
--R   (8)  ---
--R        100
--R                                                       Type: Fraction Integer
--E 8

--S 9 of 31
t9:=select(p+->rhs(p)::AlgebraicNumber > 0, radicalSolve(p^3-p+1/10=0,p))
 

                             +------------------+2
                             |    +-+    +-----+
                 +---+       |- 3\|3  + \|- 373
            (- 3\|- 3  - 3)  |------------------  + 2
                            3|         +-+
                            \|      60\|3
   (9)  [p= -----------------------------------------]
                               +------------------+
                               |    +-+    +-----+
                   +---+       |- 3\|3  + \|- 373
                (3\|- 3  - 3)  |------------------
                              3|         +-+
                              \|      60\|3
                                       Type: List Equation Expression Integer
--R
--R                             +------------------+2
--R                             |    +-+    +-----+
--R                 +---+       |- 3\|3  + \|- 373
--R            (- 3\|- 3  - 3)  |------------------  + 2
--R                            3|         +-+
--R                            \|      60\|3
--R   (9)  [p= -----------------------------------------]
--R                               +------------------+
--R                               |    +-+    +-----+
--R                   +---+       |- 3\|3  + \|- 373
--R                (3\|- 3  - 3)  |------------------
--R                              3|         +-+
--R                              \|      60\|3
--R                                       Type: List Equation Expression Integer
--E 9

--S 10 of 31
t10:=complexNumeric rhs t9.1
 

   (10)  - 1.0466805318 046022612
                                                          Type: Complex Float
--R
--R   (10)  - 1.0466805318 046022612
--R                                                          Type: Complex Float
--E 10

--S 11 of 31
t11:=select(p+->rhs(p)::AN < 0, radicalSolve(p^2-p+1/10=0,p))
 

                +--+
             - \|15  + 5
   (11)  [p= -----------]
                  10
                                       Type: List Equation Expression Integer
--R
--R                +--+
--R             - \|15  + 5
--R   (11)  [p= -----------]
--R                  10
--R                                       Type: List Equation Expression Integer
--E 11

--S 12 of 31
t12:=p^3-p+1/10
 

          3        1
   (12)  p  - p + --
                  10
                                            Type: Polynomial Fraction Integer
--R
--R          3        1
--R   (12)  p  - p + --
--R                  10
--R                                            Type: Polynomial Fraction Integer
--E 12

--S 13 of 31
t13:=select(positive?,allRootsOf(t12)$RealClosure(Fraction Integer))
 

   (13)  [%B2,%B3]
                                      Type: List RealClosure Fraction Integer
--R
--I   (13)  [%B2,%B3]
--R                                      Type: List RealClosure Fraction Integer
--E 13

--S 14 of 31
t14:=approximate(t13.1,1/10^20)::Float
 

   (14)  0.1010312578 8101081769
                                                                  Type: Float
--R
--R   (14)  0.1010312578 8101081769
--R                                                                  Type: Float
--E 14

--S 15 of 31
t15:=eval(t12,p=t14)
 

   (15)  0.3 E -20
                                                       Type: Polynomial Float
--R
--R   (15)  0.3 E -20
--R                                                       Type: Polynomial Float
--E 15

--S 16 of 31
t16:=approximate(t13.2,1/10^20)::Float
 

   (16)  0.9456492739 2359144347
                                                                  Type: Float
--R
--R   (16)  0.9456492739 2359144347
--R                                                                  Type: Float
--E 16

--S 17 of 31
t17:=eval(t12,p=t16)
 

   (17)  0.1 E -20
                                                       Type: Polynomial Float
--R
--R   (17)  0.1 E -20
--R                                                       Type: Polynomial Float
--E 17

)clear all
 
--S 18 of 31
t1:=(x^3+x^2-4*x-4)/(2*x^2+7*x-4)
 

         3    2
        x  + x  - 4x - 4
   (1)  ----------------
            2
          2x  + 7x - 4
                                            Type: Fraction Polynomial Integer
--R
--R         3    2
--R        x  + x  - 4x - 4
--R   (1)  ----------------
--R            2
--R          2x  + 7x - 4
--R                                            Type: Fraction Polynomial Integer
--E 18

--S 19 of 31
t2:=differentiate(t1,x)
 

           4      3     2
         2x  + 14x  + 3x  + 8x + 44
   (2)  ----------------------------
          4      3      2
        4x  + 28x  + 33x  - 56x + 16
                                            Type: Fraction Polynomial Integer
--R
--R           4      3     2
--R         2x  + 14x  + 3x  + 8x + 44
--R   (2)  ----------------------------
--R          4      3      2
--R        4x  + 28x  + 33x  - 56x + 16
--R                                            Type: Fraction Polynomial Integer
--E 19

--S 20 of 31
t3:=allRootsOf(numer t2)$RealClosure(Fraction Integer)
 

   (3)  [%B4,%B5]
                                      Type: List RealClosure Fraction Integer
--R
--I   (3)  [%B4,%B5]
--R                                      Type: List RealClosure Fraction Integer
--E 20

--S 21 of 31
t4:=approximate(t3.1,1/10^20)::Float
 

   (4)  - 6.7957899636 620037966
                                                                  Type: Float
--R
--R   (4)  - 6.7957899636 620037966
--R                                                                  Type: Float
--E 21

--S 22 of 31
t5:=eval(t2,x=t4)
 

   (5)  0.3908839188 6520300529 E -20
                                              Type: Fraction Polynomial Float
--R
--R   (5)  0.3908839188 6520300529 E -20
--R                                              Type: Fraction Polynomial Float
--E 22

--S 23 of 31
t6:=approximate(t3.2,1/10^20)::Float
 

   (6)  - 1.5241463459 294127043
                                                                  Type: Float
--R
--R   (6)  - 1.5241463459 294127043
--R                                                                  Type: Float
--E 23

--S 24 of 31
t7:=eval(t2,x=t6)
 

   (7)  - 0.2158472497 0513415786 E -20
                                              Type: Fraction Polynomial Float
--R
--R   (7)  - 0.2158472497 0513415786 E -20
--R                                              Type: Fraction Polynomial Float
--E 24

)clear all
 

--S 25 of 31
t1:=(x^3+x^2-4*x-4)/(2*x^2+7*x-4)
 

         3    2
        x  + x  - 4x - 4
   (1)  ----------------
            2
          2x  + 7x - 4
                                            Type: Fraction Polynomial Integer
--R
--R         3    2
--R        x  + x  - 4x - 4
--R   (1)  ----------------
--R            2
--R          2x  + 7x - 4
--R                                            Type: Fraction Polynomial Integer
--E 25

--S 26 of 31
t2:=differentiate(t1,x)
 

           4      3     2
         2x  + 14x  + 3x  + 8x + 44
   (2)  ----------------------------
          4      3      2
        4x  + 28x  + 33x  - 56x + 16
                                            Type: Fraction Polynomial Integer
--R
--R           4      3     2
--R         2x  + 14x  + 3x  + 8x + 44
--R   (2)  ----------------------------
--R          4      3      2
--R        4x  + 28x  + 33x  - 56x + 16
--R                                            Type: Fraction Polynomial Integer
--E 26

--S 27 of 31
t3:=allRootsOf(numer t2)$RealClosure(Fraction Integer)
 

   (3)  [%B6,%B7]
                                      Type: List RealClosure Fraction Integer
--R
--I   (3)  [%B6,%B7]
--R                                      Type: List RealClosure Fraction Integer
--E 27

--S 28 of 31
t4:=radicalSolve(t2)
 

   (4)
   [
     x =
           -
                2
             *
                ROOT
                              +----------------+2      +----------------+
                             3|    +---+              3|    +---+
                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                      *
                          +---------------------------------------------------+
                          |  +----------------+2      +----------------+
                          | 3|    +---+              3|    +---+
                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                          |---------------------------------------------------
                          |                  +----------------+
                          |                 3|    +---+
                         \|                4\|324\|145  + 3969
                     + 
                             +----------------+
                            3|    +---+
                       - 333\|324\|145  + 3969
                  /
                         +----------------+
                        3|    +---+
                       4\|324\|145  + 3969
                    *
                        +---------------------------------------------------+
                        |  +----------------+2      +----------------+
                        | 3|    +---+              3|    +---+
                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                        |---------------------------------------------------
                        |                  +----------------+
                        |                 3|    +---+
                       \|                4\|324\|145  + 3969
         + 
             +---------------------------------------------------+
             |  +----------------+2      +----------------+
             | 3|    +---+              3|    +---+
             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           2 |---------------------------------------------------  - 7
             |                  +----------------+
             |                 3|    +---+
            \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
             2
          *
             ROOT
                           +----------------+2      +----------------+
                          3|    +---+              3|    +---+
                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                   *
                       +---------------------------------------------------+
                       |  +----------------+2      +----------------+
                       | 3|    +---+              3|    +---+
                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                       |---------------------------------------------------
                       |                  +----------------+
                       |                 3|    +---+
                      \|                4\|324\|145  + 3969
                  + 
                          +----------------+
                         3|    +---+
                    - 333\|324\|145  + 3969
               /
                      +----------------+
                     3|    +---+
                    4\|324\|145  + 3969
                 *
                     +---------------------------------------------------+
                     |  +----------------+2      +----------------+
                     | 3|    +---+              3|    +---+
                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                     |---------------------------------------------------
                     |                  +----------------+
                     |                 3|    +---+
                    \|                4\|324\|145  + 3969
         + 
             +---------------------------------------------------+
             |  +----------------+2      +----------------+
             | 3|    +---+              3|    +---+
             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           2 |---------------------------------------------------  - 7
             |                  +----------------+
             |                 3|    +---+
            \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
           -
                2
             *
                ROOT
                              +----------------+2      +----------------+
                             3|    +---+              3|    +---+
                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                      *
                          +---------------------------------------------------+
                          |  +----------------+2      +----------------+
                          | 3|    +---+              3|    +---+
                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                          |---------------------------------------------------
                          |                  +----------------+
                          |                 3|    +---+
                         \|                4\|324\|145  + 3969
                     + 
                           +----------------+
                          3|    +---+
                       333\|324\|145  + 3969
                  /
                         +----------------+
                        3|    +---+
                       4\|324\|145  + 3969
                    *
                        +---------------------------------------------------+
                        |  +----------------+2      +----------------+
                        | 3|    +---+              3|    +---+
                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                        |---------------------------------------------------
                        |                  +----------------+
                        |                 3|    +---+
                       \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
             2
          *
             ROOT
                           +----------------+2      +----------------+
                          3|    +---+              3|    +---+
                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                   *
                       +---------------------------------------------------+
                       |  +----------------+2      +----------------+
                       | 3|    +---+              3|    +---+
                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                       |---------------------------------------------------
                       |                  +----------------+
                       |                 3|    +---+
                      \|                4\|324\|145  + 3969
                  + 
                        +----------------+
                       3|    +---+
                    333\|324\|145  + 3969
               /
                      +----------------+
                     3|    +---+
                    4\|324\|145  + 3969
                 *
                     +---------------------------------------------------+
                     |  +----------------+2      +----------------+
                     | 3|    +---+              3|    +---+
                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                     |---------------------------------------------------
                     |                  +----------------+
                     |                 3|    +---+
                    \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ]
                                       Type: List Equation Expression Integer
--R
--R   (4)
--R   [
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                              +----------------+2      +----------------+
--R                             3|    +---+              3|    +---+
--R                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                      *
--R                          +---------------------------------------------------+
--R                          |  +----------------+2      +----------------+
--R                          | 3|    +---+              3|    +---+
--R                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                          |---------------------------------------------------
--R                          |                  +----------------+
--R                          |                 3|    +---+
--R                         \|                4\|324\|145  + 3969
--R                     + 
--R                             +----------------+
--R                            3|    +---+
--R                       - 333\|324\|145  + 3969
--R                  /
--R                         +----------------+
--R                        3|    +---+
--R                       4\|324\|145  + 3969
--R                    *
--R                        +---------------------------------------------------+
--R                        |  +----------------+2      +----------------+
--R                        | 3|    +---+              3|    +---+
--R                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                        |---------------------------------------------------
--R                        |                  +----------------+
--R                        |                 3|    +---+
--R                       \|                4\|324\|145  + 3969
--R         + 
--R             +---------------------------------------------------+
--R             |  +----------------+2      +----------------+
--R             | 3|    +---+              3|    +---+
--R             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           2 |---------------------------------------------------  - 7
--R             |                  +----------------+
--R             |                 3|    +---+
--R            \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                           +----------------+2      +----------------+
--R                          3|    +---+              3|    +---+
--R                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                   *
--R                       +---------------------------------------------------+
--R                       |  +----------------+2      +----------------+
--R                       | 3|    +---+              3|    +---+
--R                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                       |---------------------------------------------------
--R                       |                  +----------------+
--R                       |                 3|    +---+
--R                      \|                4\|324\|145  + 3969
--R                  + 
--R                          +----------------+
--R                         3|    +---+
--R                    - 333\|324\|145  + 3969
--R               /
--R                      +----------------+
--R                     3|    +---+
--R                    4\|324\|145  + 3969
--R                 *
--R                     +---------------------------------------------------+
--R                     |  +----------------+2      +----------------+
--R                     | 3|    +---+              3|    +---+
--R                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                     |---------------------------------------------------
--R                     |                  +----------------+
--R                     |                 3|    +---+
--R                    \|                4\|324\|145  + 3969
--R         + 
--R             +---------------------------------------------------+
--R             |  +----------------+2      +----------------+
--R             | 3|    +---+              3|    +---+
--R             |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           2 |---------------------------------------------------  - 7
--R             |                  +----------------+
--R             |                 3|    +---+
--R            \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                              +----------------+2      +----------------+
--R                             3|    +---+              3|    +---+
--R                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                      *
--R                          +---------------------------------------------------+
--R                          |  +----------------+2      +----------------+
--R                          | 3|    +---+              3|    +---+
--R                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                          |---------------------------------------------------
--R                          |                  +----------------+
--R                          |                 3|    +---+
--R                         \|                4\|324\|145  + 3969
--R                     + 
--R                           +----------------+
--R                          3|    +---+
--R                       333\|324\|145  + 3969
--R                  /
--R                         +----------------+
--R                        3|    +---+
--R                       4\|324\|145  + 3969
--R                    *
--R                        +---------------------------------------------------+
--R                        |  +----------------+2      +----------------+
--R                        | 3|    +---+              3|    +---+
--R                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                        |---------------------------------------------------
--R                        |                  +----------------+
--R                        |                 3|    +---+
--R                       \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                           +----------------+2      +----------------+
--R                          3|    +---+              3|    +---+
--R                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                   *
--R                       +---------------------------------------------------+
--R                       |  +----------------+2      +----------------+
--R                       | 3|    +---+              3|    +---+
--R                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                       |---------------------------------------------------
--R                       |                  +----------------+
--R                       |                 3|    +---+
--R                      \|                4\|324\|145  + 3969
--R                  + 
--R                        +----------------+
--R                       3|    +---+
--R                    333\|324\|145  + 3969
--R               /
--R                      +----------------+
--R                     3|    +---+
--R                    4\|324\|145  + 3969
--R                 *
--R                     +---------------------------------------------------+
--R                     |  +----------------+2      +----------------+
--R                     | 3|    +---+              3|    +---+
--R                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                     |---------------------------------------------------
--R                     |                  +----------------+
--R                     |                 3|    +---+
--R                    \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ]
--R                                       Type: List Equation Expression Integer
--E 28

--S 29 of 31
bound?(x,s) == (a:=complexNumeric rhs x; imag a < 10^-digits() and real a >= left(mainCharacterization s)::Float and real a < right(mainCharacterization s)::Float)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 29

--S 30 of 31
t6:=[ (B:=select(x+->bound?(x,s),t4); #B=1 => B.1; error "failed") for s in t3 ]
 
   Compiling function bound? with type (Equation Expression Integer,
      RealClosure Fraction Integer) -> Boolean 

   (6)
   [
     x =
           -
                2
             *
                ROOT
                              +----------------+2      +----------------+
                             3|    +---+              3|    +---+
                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                      *
                          +---------------------------------------------------+
                          |  +----------------+2      +----------------+
                          | 3|    +---+              3|    +---+
                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                          |---------------------------------------------------
                          |                  +----------------+
                          |                 3|    +---+
                         \|                4\|324\|145  + 3969
                     + 
                           +----------------+
                          3|    +---+
                       333\|324\|145  + 3969
                  /
                         +----------------+
                        3|    +---+
                       4\|324\|145  + 3969
                    *
                        +---------------------------------------------------+
                        |  +----------------+2      +----------------+
                        | 3|    +---+              3|    +---+
                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                        |---------------------------------------------------
                        |                  +----------------+
                        |                 3|    +---+
                       \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ,

     x =
             2
          *
             ROOT
                           +----------------+2      +----------------+
                          3|    +---+              3|    +---+
                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
                   *
                       +---------------------------------------------------+
                       |  +----------------+2      +----------------+
                       | 3|    +---+              3|    +---+
                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                       |---------------------------------------------------
                       |                  +----------------+
                       |                 3|    +---+
                      \|                4\|324\|145  + 3969
                  + 
                        +----------------+
                       3|    +---+
                    333\|324\|145  + 3969
               /
                      +----------------+
                     3|    +---+
                    4\|324\|145  + 3969
                 *
                     +---------------------------------------------------+
                     |  +----------------+2      +----------------+
                     | 3|    +---+              3|    +---+
                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
                     |---------------------------------------------------
                     |                  +----------------+
                     |                 3|    +---+
                    \|                4\|324\|145  + 3969
         + 
               +---------------------------------------------------+
               |  +----------------+2      +----------------+
               | 3|    +---+              3|    +---+
               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
           - 2 |---------------------------------------------------  - 7
               |                  +----------------+
               |                 3|    +---+
              \|                4\|324\|145  + 3969
      /
         4
     ]
                                       Type: List Equation Expression Integer
--R   Compiling function bound? with type (Equation Expression Integer,
--R      RealClosure Fraction Integer) -> Boolean 
--R
--R   (6)
--R   [
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                              +----------------+2      +----------------+
--R                             3|    +---+              3|    +---+
--R                         (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                      *
--R                          +---------------------------------------------------+
--R                          |  +----------------+2      +----------------+
--R                          | 3|    +---+              3|    +---+
--R                          |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                          |---------------------------------------------------
--R                          |                  +----------------+
--R                          |                 3|    +---+
--R                         \|                4\|324\|145  + 3969
--R                     + 
--R                           +----------------+
--R                          3|    +---+
--R                       333\|324\|145  + 3969
--R                  /
--R                         +----------------+
--R                        3|    +---+
--R                       4\|324\|145  + 3969
--R                    *
--R                        +---------------------------------------------------+
--R                        |  +----------------+2      +----------------+
--R                        | 3|    +---+              3|    +---+
--R                        |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                        |---------------------------------------------------
--R                        |                  +----------------+
--R                        |                 3|    +---+
--R                       \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                           +----------------+2      +----------------+
--R                          3|    +---+              3|    +---+
--R                      (- 2\|324\|145  + 3969   + 90\|324\|145  + 3969  - 162)
--R                   *
--R                       +---------------------------------------------------+
--R                       |  +----------------+2      +----------------+
--R                       | 3|    +---+              3|    +---+
--R                       |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                       |---------------------------------------------------
--R                       |                  +----------------+
--R                       |                 3|    +---+
--R                      \|                4\|324\|145  + 3969
--R                  + 
--R                        +----------------+
--R                       3|    +---+
--R                    333\|324\|145  + 3969
--R               /
--R                      +----------------+
--R                     3|    +---+
--R                    4\|324\|145  + 3969
--R                 *
--R                     +---------------------------------------------------+
--R                     |  +----------------+2      +----------------+
--R                     | 3|    +---+              3|    +---+
--R                     |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R                     |---------------------------------------------------
--R                     |                  +----------------+
--R                     |                 3|    +---+
--R                    \|                4\|324\|145  + 3969
--R         + 
--R               +---------------------------------------------------+
--R               |  +----------------+2      +----------------+
--R               | 3|    +---+              3|    +---+
--R               |2\|324\|145  + 3969   + 45\|324\|145  + 3969  + 162
--R           - 2 |---------------------------------------------------  - 7
--R               |                  +----------------+
--R               |                 3|    +---+
--R              \|                4\|324\|145  + 3969
--R      /
--R         4
--R     ]
--R                                       Type: List Equation Expression Integer
--E 30

--S 31 of 31
t7:=map(x+->real complexNumeric rhs x,t6)
 

   (7)  [- 6.7957899636 620037966,- 1.5241463459 294127044]
                                                             Type: List Float
--R
--R   (7)  [- 6.7957899636 620037966,- 1.5241463459 294127044]
--R                                                             Type: List Float
--E 31

)spool 
 
Starts dribbling to Matrix.output (2010/3/27, 18:46:6).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 38
m : Matrix(Integer) := new(3,3,0)
 

        +0  0  0+
        |       |
   (1)  |0  0  0|
        |       |
        +0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  0  0+
--R        |       |
--R   (1)  |0  0  0|
--R        |       |
--R        +0  0  0+
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 38
setelt(m,2,3,5)
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 38
m(1,2) := 10
 

   (3)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  10
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 38
m
 

        +0  10  0+
        |        |
   (4)  |0  0   5|
        |        |
        +0  0   0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  10  0+
--R        |        |
--R   (4)  |0  0   5|
--R        |        |
--R        +0  0   0+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 38
matrix [ [1,2,3,4],[0,9,8,7] ]
 

        +1  2  3  4+
   (5)  |          |
        +0  9  8  7+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2  3  4+
--R   (5)  |          |
--R        +0  9  8  7+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 38
dm := diagonalMatrix [1,x**2,x**3,x**4,x**5]
 

        +1  0   0   0   0 +
        |                 |
        |    2            |
        |0  x   0   0   0 |
        |                 |
        |        3        |
   (6)  |0  0   x   0   0 |
        |                 |
        |            4    |
        |0  0   0   x   0 |
        |                 |
        |                5|
        +0  0   0   0   x +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  0   0   0   0 +
--R        |                 |
--R        |    2            |
--R        |0  x   0   0   0 |
--R        |                 |
--R        |        3        |
--R   (6)  |0  0   x   0   0 |
--R        |                 |
--R        |            4    |
--R        |0  0   0   x   0 |
--R        |                 |
--R        |                5|
--R        +0  0   0   0   x +
--R                                              Type: Matrix Polynomial Integer
--E 6

--S 7 of 38
setRow!(dm,5,vector [1,1,1,1,1])
 

        +1  0   0   0   0+
        |                |
        |    2           |
        |0  x   0   0   0|
        |                |
   (7)  |        3       |
        |0  0   x   0   0|
        |                |
        |            4   |
        |0  0   0   x   0|
        |                |
        +1  1   1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  0   0   0   0+
--R        |                |
--R        |    2           |
--R        |0  x   0   0   0|
--R        |                |
--R   (7)  |        3       |
--R        |0  0   x   0   0|
--R        |                |
--R        |            4   |
--R        |0  0   0   x   0|
--R        |                |
--R        +1  1   1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 7

--S 8 of 38
setColumn!(dm,2,vector [y,y,y,y,y])
 

        +1  y  0   0   0+
        |               |
        |0  y  0   0   0|
        |               |
        |       3       |
   (8)  |0  y  x   0   0|
        |               |
        |           4   |
        |0  y  0   x   0|
        |               |
        +1  y  1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  y  0   0   0+
--R        |               |
--R        |0  y  0   0   0|
--R        |               |
--R        |       3       |
--R   (8)  |0  y  x   0   0|
--R        |               |
--R        |           4   |
--R        |0  y  0   x   0|
--R        |               |
--R        +1  y  1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 8

--S 9 of 38
cdm := copy(dm)
 

        +1  y  0   0   0+
        |               |
        |0  y  0   0   0|
        |               |
        |       3       |
   (9)  |0  y  x   0   0|
        |               |
        |           4   |
        |0  y  0   x   0|
        |               |
        +1  y  1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  y  0   0   0+
--R        |               |
--R        |0  y  0   0   0|
--R        |               |
--R        |       3       |
--R   (9)  |0  y  x   0   0|
--R        |               |
--R        |           4   |
--R        |0  y  0   x   0|
--R        |               |
--R        +1  y  1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 9

--S 10 of 38
setelt(dm,4,1,1-x**7)
 

            7
   (10)  - x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R            7
--R   (10)  - x  + 1
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 38
[dm,cdm]
 

          +   1      y  0   0   0+ +1  y  0   0   0+
          |                      | |               |
          |   0      y  0   0   0| |0  y  0   0   0|
          |                      | |               |
          |              3       | |       3       |
   (11)  [|   0      y  x   0   0|,|0  y  x   0   0|]
          |                      | |               |
          |   7              4   | |           4   |
          |- x  + 1  y  0   x   0| |0  y  0   x   0|
          |                      | |               |
          +   1      y  1   1   1+ +1  y  1   1   1+
                                         Type: List Matrix Polynomial Integer
--R 
--R
--R          +   1      y  0   0   0+ +1  y  0   0   0+
--R          |                      | |               |
--R          |   0      y  0   0   0| |0  y  0   0   0|
--R          |                      | |               |
--R          |              3       | |       3       |
--R   (11)  [|   0      y  x   0   0|,|0  y  x   0   0|]
--R          |                      | |               |
--R          |   7              4   | |           4   |
--R          |- x  + 1  y  0   x   0| |0  y  0   x   0|
--R          |                      | |               |
--R          +   1      y  1   1   1+ +1  y  1   1   1+
--R                                         Type: List Matrix Polynomial Integer
--E 11

--S 12 of 38
subMatrix(dm,2,3,2,4)
 

         +y  0   0+
   (12)  |        |
         |    3   |
         +y  x   0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +y  0   0+
--R   (12)  |        |
--R         |    3   |
--R         +y  x   0+
--R                                              Type: Matrix Polynomial Integer
--E 12

--S 13 of 38
d := diagonalMatrix [1.2,-1.3,1.4,-1.5]
 

         +1.2   0.0   0.0   0.0 +
         |                      |
         |0.0  - 1.3  0.0   0.0 |
   (13)  |                      |
         |0.0   0.0   1.4   0.0 |
         |                      |
         +0.0   0.0   0.0  - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2   0.0   0.0   0.0 +
--R         |                      |
--R         |0.0  - 1.3  0.0   0.0 |
--R   (13)  |                      |
--R         |0.0   0.0   1.4   0.0 |
--R         |                      |
--R         +0.0   0.0   0.0  - 1.5+
--R                                                           Type: Matrix Float
--E 13

--S 14 of 38
e := matrix [ [6.7,9.11],[-31.33,67.19] ]
 

         +  6.7    9.11 +
   (14)  |              |
         +- 31.33  67.19+
                                                           Type: Matrix Float
--R 
--R
--R         +  6.7    9.11 +
--R   (14)  |              |
--R         +- 31.33  67.19+
--R                                                           Type: Matrix Float
--E 14

--S 15 of 38
setsubMatrix!(d,1,2,e)
 

         +1.2    6.7    9.11    0.0 +
         |                          |
         |0.0  - 31.33  67.19   0.0 |
   (15)  |                          |
         |0.0    0.0     1.4    0.0 |
         |                          |
         +0.0    0.0     0.0   - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2    6.7    9.11    0.0 +
--R         |                          |
--R         |0.0  - 31.33  67.19   0.0 |
--R   (15)  |                          |
--R         |0.0    0.0     1.4    0.0 |
--R         |                          |
--R         +0.0    0.0     0.0   - 1.5+
--R                                                           Type: Matrix Float
--E 15

--S 16 of 38
d
 

         +1.2    6.7    9.11    0.0 +
         |                          |
         |0.0  - 31.33  67.19   0.0 |
   (16)  |                          |
         |0.0    0.0     1.4    0.0 |
         |                          |
         +0.0    0.0     0.0   - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2    6.7    9.11    0.0 +
--R         |                          |
--R         |0.0  - 31.33  67.19   0.0 |
--R   (16)  |                          |
--R         |0.0    0.0     1.4    0.0 |
--R         |                          |
--R         +0.0    0.0     0.0   - 1.5+
--R                                                           Type: Matrix Float
--E 16

--S 17 of 38
a := matrix [ [1/2,1/3,1/4],[1/5,1/6,1/7] ]
 

         +1  1  1+
         |-  -  -|
         |2  3  4|
   (17)  |       |
         |1  1  1|
         |-  -  -|
         +5  6  7+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1+
--R         |-  -  -|
--R         |2  3  4|
--R   (17)  |       |
--R         |1  1  1|
--R         |-  -  -|
--R         +5  6  7+
--R                                                Type: Matrix Fraction Integer
--E 17

--S 18 of 38
b := matrix [ [3/5,3/7,3/11],[3/13,3/17,3/19] ] 
 

         +3   3    3+
         |-   -   --|
         |5   7   11|
   (18)  |          |
         | 3   3   3|
         |--  --  --|
         +13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +3   3    3+
--R         |-   -   --|
--R         |5   7   11|
--R   (18)  |          |
--R         | 3   3   3|
--R         |--  --  --|
--R         +13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 18

--S 19 of 38
horizConcat(a,b)
 

         +1  1  1  3   3    3+
         |-  -  -  -   -   --|
         |2  3  4  5   7   11|
   (19)  |                   |
         |1  1  1   3   3   3|
         |-  -  -  --  --  --|
         +5  6  7  13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1  3   3    3+
--R         |-  -  -  -   -   --|
--R         |2  3  4  5   7   11|
--R   (19)  |                   |
--R         |1  1  1   3   3   3|
--R         |-  -  -  --  --  --|
--R         +5  6  7  13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 19

--S 20 of 38
vab := vertConcat(a,b)
 

         +1   1   1 +
         |-   -   - |
         |2   3   4 |
         |          |
         |1   1   1 |
         |-   -   - |
         |5   6   7 |
   (20)  |          |
         |3   3    3|
         |-   -   --|
         |5   7   11|
         |          |
         | 3   3   3|
         |--  --  --|
         +13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1   1   1 +
--R         |-   -   - |
--R         |2   3   4 |
--R         |          |
--R         |1   1   1 |
--R         |-   -   - |
--R         |5   6   7 |
--R   (20)  |          |
--R         |3   3    3|
--R         |-   -   --|
--R         |5   7   11|
--R         |          |
--R         | 3   3   3|
--R         |--  --  --|
--R         +13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 20

--S 21 of 38
transpose vab
 

         +1  1  3    3+
         |-  -  -   --|
         |2  5  5   13|
         |            |
         |1  1  3    3|
   (21)  |-  -  -   --|
         |3  6  7   17|
         |            |
         |1  1   3   3|
         |-  -  --  --|
         +4  7  11  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  3    3+
--R         |-  -  -   --|
--R         |2  5  5   13|
--R         |            |
--R         |1  1  3    3|
--R   (21)  |-  -  -   --|
--R         |3  6  7   17|
--R         |            |
--R         |1  1   3   3|
--R         |-  -  --  --|
--R         +4  7  11  19+
--R                                                Type: Matrix Fraction Integer
--E 21

--S 22 of 38
m := matrix [ [1,2],[3,4] ]
 

         +1  2+
   (22)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2+
--R   (22)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 38
4 * m * (-5)
 

         +- 20  - 40+
   (23)  |          |
         +- 60  - 80+
                                                         Type: Matrix Integer
--R 
--R
--R         +- 20  - 40+
--R   (23)  |          |
--R         +- 60  - 80+
--R                                                         Type: Matrix Integer
--E 23

--S 24 of 38
n := matrix([ [1,0,-2],[-3,5,1] ])
 

         + 1   0  - 2+
   (24)  |           |
         +- 3  5   1 +
                                                         Type: Matrix Integer
--R 
--R
--R         + 1   0  - 2+
--R   (24)  |           |
--R         +- 3  5   1 +
--R                                                         Type: Matrix Integer
--E 24

--S 25 of 38
m * n
 

         +- 5  10   0 +
   (25)  |            |
         +- 9  20  - 2+
                                                         Type: Matrix Integer
--R 
--R
--R         +- 5  10   0 +
--R   (25)  |            |
--R         +- 9  20  - 2+
--R                                                         Type: Matrix Integer
--E 25

--S 26 of 38
vec := column(n,3)
 

   (26)  [- 2,1]
                                                         Type: Vector Integer
--R 
--R
--R   (26)  [- 2,1]
--R                                                         Type: Vector Integer
--E 26

--S 27 of 38
vec * m
 

   (27)  [1,0]
                                                         Type: Vector Integer
--R 
--R
--R   (27)  [1,0]
--R                                                         Type: Vector Integer
--E 27

--S 28 of 38
m * vec
 

   (28)  [0,- 2]
                                                         Type: Vector Integer
--R 
--R
--R   (28)  [0,- 2]
--R                                                         Type: Vector Integer
--E 28

--S 29 of 38
hilb := matrix([ [1/(i + j) for i in 1..3] for j in 1..3])
 

         +1  1  1+
         |-  -  -|
         |2  3  4|
         |       |
         |1  1  1|
   (29)  |-  -  -|
         |3  4  5|
         |       |
         |1  1  1|
         |-  -  -|
         +4  5  6+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1+
--R         |-  -  -|
--R         |2  3  4|
--R         |       |
--R         |1  1  1|
--R   (29)  |-  -  -|
--R         |3  4  5|
--R         |       |
--R         |1  1  1|
--R         |-  -  -|
--R         +4  5  6+
--R                                                Type: Matrix Fraction Integer
--E 29

--S 30 of 38
inverse(hilb)
 

         + 72    - 240   180 +
         |                   |
   (30)  |- 240   900   - 720|
         |                   |
         + 180   - 720   600 +
                                     Type: Union(Matrix Fraction Integer,...)
--R 
--R
--R         + 72    - 240   180 +
--R         |                   |
--R   (30)  |- 240   900   - 720|
--R         |                   |
--R         + 180   - 720   600 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 30

--S 31 of 38
mm := matrix([ [1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16] ])
 

         +1   2   3   4 +
         |              |
         |5   6   7   8 |
   (31)  |              |
         |9   10  11  12|
         |              |
         +13  14  15  16+
                                                         Type: Matrix Integer
--R 
--R
--R         +1   2   3   4 +
--R         |              |
--R         |5   6   7   8 |
--R   (31)  |              |
--R         |9   10  11  12|
--R         |              |
--R         +13  14  15  16+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 38
inverse(mm)
 

   (32)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (32)  "failed"
--R                                                    Type: Union("failed",...)
--E 32

--S 33 of 38
determinant(mm)
 

   (33)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (33)  0
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 38
trace(mm)
 

   (34)  34
                                                        Type: PositiveInteger
--R 
--R
--R   (34)  34
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 38
rank(mm)
 

   (35)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  2
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 38
nullity(mm)
 

   (36)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (36)  2
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 38
nullSpace(mm)
 

   (37)  [[1,- 2,1,0],[2,- 3,0,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (37)  [[1,- 2,1,0],[2,- 3,0,1]]
--R                                                    Type: List Vector Integer
--E 37

--S 38 of 38
rowEchelon(mm)
 

         +1  2  3  4 +
         |           |
         |0  4  8  12|
   (38)  |           |
         |0  0  0  0 |
         |           |
         +0  0  0  0 +
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3  4 +
--R         |           |
--R         |0  4  8  12|
--R   (38)  |           |
--R         |0  0  0  0 |
--R         |           |
--R         +0  0  0  0 +
--R                                                         Type: Matrix Integer
--E 38
)spool
 
Starts dribbling to CycleIndicators.output (2010/3/27, 18:41:51).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 47
complete 1
 

   (1)  (1)
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (1)  (1)
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 1

--S 2 of 47
complete 2
 

        1       1   2
   (2)  - (2) + - (1 )
        2       2
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1   2
--R   (2)  - (2) + - (1 )
--R        2       2
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 2

--S 3 of 47
complete 3
 

        1       1         1   3
   (3)  - (3) + - (2 1) + - (1 )
        3       2         6
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1         1   3
--R   (3)  - (3) + - (2 1) + - (1 )
--R        3       2         6
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 3

--S 4 of 47
complete 7
 

   (4)
     1       1          1          1     2     1         1            1     3
     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
      1      5      1    7
     --- (2 1 ) + ---- (1 )
     240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (4)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R      1      5      1    7
--R     --- (2 1 ) + ---- (1 )
--R     240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 4

--S 5 of 47
elementary 7
 

   (5)
     1       1          1          1     2     1         1            1     3
     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
        1      5      1    7
     - --- (2 1 ) + ---- (1 )
       240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (5)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R        1      5      1    7
--R     - --- (2 1 ) + ---- (1 )
--R       240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 5

--S 6 of 47
alternating 7
 

   (6)
     2       1     2    1           1   2      1     2     1     4     1   2 3
     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
     7       5          4           9         12          36          24
   + 
       1    7
     ---- (1 )
     2520
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (6)
--R     2       1     2    1           1   2      1     2     1     4     1   2 3
--R     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
--R     7       5          4           9         12          36          24
--R   + 
--R       1    7
--R     ---- (1 )
--R     2520
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 6

--S 7 of 47
cyclic 7
 

        6       1   7
   (7)  - (7) + - (1 )
        7       7
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        6       1   7
--R   (7)  - (7) + - (1 )
--R        7       7
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 7

--S 8 of 47
dihedral 7
 

        3       1   3      1   7
   (8)  - (7) + - (2 1) + -- (1 )
        7       2         14
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        3       1   3      1   7
--R   (8)  - (7) + - (2 1) + -- (1 )
--R        7       2         14
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 8

--S 9 of 47
graphs 5
 

   (9)
   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
   6           5        4         6         8          12          120
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (9)
--R   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
--R   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
--R   6           5        4         6         8          12          120
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 9

--S 10 of 47
cap(complete 2**2, complete 2*complete 1**2)
 

   (10)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (10)  4
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 47
cap(elementary 2**2, complete 2*complete 1**2)
 

   (11)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  2
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 47
cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)
 

   (12)  24
                                                       Type: Fraction Integer
--R 
--R
--R   (12)  24
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 47
cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)
 

   (13)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  8
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 47
cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)
 

   (14)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (14)  8
--R                                                       Type: Fraction Integer
--E 14

--S 15 of 47
eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))
 

   (15)  1500
                                                       Type: Fraction Integer
--R 
--R
--R   (15)  1500
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 47
square:=dihedral 4
 

         1       3   2    1     2    1   4
   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
         4       8        4          8
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1       3   2    1     2    1   4
--R   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
--R         4       8        4          8
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 16

--S 17 of 47
cap(complete 2**2,square)
 

   (17)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  2
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 47
cap(complete 3*complete 2**2,dihedral 7)
 

   (18)  18
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  18
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 47
cap(graphs 5,complete 7*complete 3)
 

   (19)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (19)  4
--R                                                       Type: Fraction Integer
--E 19

--S 20 of 47
s(x) == powerSum(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 47
cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)
 
   Compiling function s with type PositiveInteger -> 
      SymmetricPolynomial Fraction Integer 

         1   2    1   2 2    3   4     1   8
   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
         4        3          8        24
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R   Compiling function s with type PositiveInteger -> 
--R      SymmetricPolynomial Fraction Integer 
--R
--R         1   2    1   2 2    3   4     1   8
--R   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
--R         4        3          8        24
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 21

--S 22 of 47
cap(complete 4**2,cube)
 

   (22)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  7
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 47
cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))
 

   (23)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (23)  7
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 47
cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))
 

   (24)  17
                                                       Type: Fraction Integer
--R 
--R
--R   (24)  17
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 47
cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))
 

   (25)  10
                                                       Type: Fraction Integer
--R 
--R
--R   (25)  10
--R                                                       Type: Fraction Integer
--E 25

--S 26 of 47
cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))
 

   (26)  23
                                                       Type: Fraction Integer
--R 
--R
--R   (26)  23
--R                                                       Type: Fraction Integer
--E 26

--S 27 of 47
x: ULS(FRAC INT,'x,0) := 'x 
 

   (27)  x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (27)  x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 27

--S 28 of 47
ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 47
Integers: INT -> ULS(FRAC INT, 'x, 0) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 47
ZeroOrOne n == 1+x**n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 47
ZeroOrOne 5 
 
   Compiling function ZeroOrOne with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5
   (31)  1 + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function ZeroOrOne with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5
--R   (31)  1 + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 31

--S 32 of 47
Integers n == 1/(1-x**n) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 47
Integers 5 
 
   Compiling function Integers with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5    10      11
   (33)  1 + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function Integers with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5    10      11
--R   (33)  1 + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 33

--S 34 of 47
)expose EVALCYC
 
   EvaluateCycleIndicators is now explicitly exposed in frame initial 
--R 
--I   EvaluateCycleIndicators is now explicitly exposed in frame frame0 
--E 34

--S 35 of 47
eval(ZeroOrOne, graphs 5) 
 

                   2     3     4     5     6     7     8    9    10      11
   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6     7     8    9    10      11
--R   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 35

--S 36 of 47
eval(ZeroOrOne,dihedral 8) 
 

                   2     3     4     5     6    7    8
   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 36

--S 37 of 47
eval(Integers,complete 4) 
 

   (36)
             2     3     4     5     6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (36)
--R             2     3     4     5     6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 37

--S 38 of 47
eval(Integers,elementary 4)
 

   (37)
      6    7     8     9     10     11     12      13      14      15      16
     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
   + 
        17
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (37)
--R      6    7     8     9     10     11     12      13      14      15      16
--R     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
--R   + 
--R        17
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 38

--S 39 of 47
eval(ZeroOrOne,cube) 
 

                   2     3     4     5     6    7    8
   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 39

--S 40 of 47
eval(Integers,cube) 
 

   (39)
               2     3      4      5      6       7       8       9       10
     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (39)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 40

--S 41 of 47
eval(Integers,graphs 5) 
 

   (40)
               2     3      4      5      6       7       8       9       10
     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (40)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 41

--S 42 of 47
eval(ZeroOrOne ,graphs 15) 
 

   (41)
               2     3      4      5      6       7       8        9        10
     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (41)
--R               2     3      4      5      6       7       8        9        10
--R     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 42

--S 43 of 47
cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)
 

   (42)  49958972383320
                                                       Type: Fraction Integer
--R 
--R
--R   (42)  49958972383320
--R                                                       Type: Fraction Integer
--E 43

--S 44 of 47
sf3221:= SFunction [3,2,2,1] 
 

   (43)
      1          1     2     1   2     1            1     4     1   2
     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
     12         12          16        12           24          36
   + 
      1   2 2     1     2      1       3     1     5     1    4     1   3 2
     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
     36          24           36            72          192        48
   + 
      1   2 4     1      6     1    8
     -- (2 1 ) - --- (2 1 ) + --- (1 )
     96          144          576
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (43)
--R      1          1     2     1   2     1            1     4     1   2
--R     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
--R     12         12          16        12           24          36
--R   + 
--R      1   2 2     1     2      1       3     1     5     1    4     1   3 2
--R     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
--R     36          24           36            72          192        48
--R   + 
--R      1   2 4     1      6     1    8
--R     -- (2 1 ) - --- (2 1 ) + --- (1 )
--R     96          144          576
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 44

--S 45 of 47
cap(sf3221,complete 2**4) 
 

   (44)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (44)  3
--R                                                       Type: Fraction Integer
--E 45

--S 46 of 47
cap(sf3221, powerSum 1**8)
 

   (45)  70
                                                       Type: Fraction Integer
--R 
--R
--R   (45)  70
--R                                                       Type: Fraction Integer
--E 46

--S 47 of 47
eval(Integers, sf3221)
 

   (46)
      9     10     11      12      13      14      15       16       17       18
     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
   + 
         19      20
     432x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (46)
--R      9     10     11      12      13      14      15       16       17       18
--R     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
--R   + 
--R         19      20
--R     432x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 47
)spool
 
Starts dribbling to opalg.output (2010/3/27, 18:30:32).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 9
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 9
L 5
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

        63  5   35  3   15
   (2)  -- x  - -- x  + -- x
         8       4       8
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R        63  5   35  3   15
--R   (2)  -- x  - -- x  + -- x
--R         8       4       8
--R                                            Type: Polynomial Fraction Integer
--E 2

--S 3 of 9
dx := operator("D")::OP(POLY FRAC INT)
 

   (3)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (3)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 3

--S 4 of 9
evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT)
 

   (4)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (4)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 4

--S 5 of 9
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 9
E 5
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                      2      2
   (6)  30 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                      2      2
--R   (6)  30 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 6

--S 7 of 9
[L i for i in 1..10]
 

   (7)
       3  2   1  5  3   3    35  4   15  2   3  63  5   35  3   15
   [x, - x  - -, - x  - - x, -- x  - -- x  + -, -- x  - -- x  + -- x,
       2      2  2      2     8       4      8   8       4       8
    231  6   315  4   105  2    5  429  7   693  5   315  3   35
    --- x  - --- x  + --- x  - --, --- x  - --- x  + --- x  - -- x,
     16       16       16      16   16       16       16      16
    6435  8   3003  6   3465  4   315  2    35
    ---- x  - ---- x  + ---- x  - --- x  + ---,
     128       32        64        32      128
    12155  9   6435  7   9009  5   1155  3   315
    ----- x  - ---- x  + ---- x  - ---- x  + --- x,
     128        32        64        32       128
    46189  10   109395  8   45045  6   15015  4   3465  2    63
    ----- x   - ------ x  + ----- x  - ----- x  + ---- x  - ---]
     256          256        128        128        256      256
                                       Type: List Polynomial Fraction Integer
--R 
--R
--R   (7)
--R       3  2   1  5  3   3    35  4   15  2   3  63  5   35  3   15
--R   [x, - x  - -, - x  - - x, -- x  - -- x  + -, -- x  - -- x  + -- x,
--R       2      2  2      2     8       4      8   8       4       8
--R    231  6   315  4   105  2    5  429  7   693  5   315  3   35
--R    --- x  - --- x  + --- x  - --, --- x  - --- x  + --- x  - -- x,
--R     16       16       16      16   16       16       16      16
--R    6435  8   3003  6   3465  4   315  2    35
--R    ---- x  - ---- x  + ---- x  - --- x  + ---,
--R     128       32        64        32      128
--R    12155  9   6435  7   9009  5   1155  3   315
--R    ----- x  - ---- x  + ---- x  - ---- x  + --- x,
--R     128        32        64        32       128
--R    46189  10   109395  8   45045  6   15015  4   3465  2    63
--R    ----- x   - ------ x  + ----- x  - ----- x  + ---- x  - ---]
--R     256          256        128        128        256      256
--R                                       Type: List Polynomial Fraction Integer
--E 7

--S 8 of 9
[E i for i in 1..10]
 

   (8)
                 2      2               2      2                2      2
   [2 - 2x D - (x  - 1)D , 6 - 2x D - (x  - 1)D , 12 - 2x D - (x  - 1)D ,
                  2      2                2      2                2      2
    20 - 2x D - (x  - 1)D , 30 - 2x D - (x  - 1)D , 42 - 2x D - (x  - 1)D ,
                  2      2                2      2                2      2
    56 - 2x D - (x  - 1)D , 72 - 2x D - (x  - 1)D , 90 - 2x D - (x  - 1)D ,
                   2      2
    110 - 2x D - (x  - 1)D ]
                              Type: List Operator Polynomial Fraction Integer
--R 
--R
--R   (8)
--R                 2      2               2      2                2      2
--R   [2 - 2x D - (x  - 1)D , 6 - 2x D - (x  - 1)D , 12 - 2x D - (x  - 1)D ,
--R                  2      2                2      2                2      2
--R    20 - 2x D - (x  - 1)D , 30 - 2x D - (x  - 1)D , 42 - 2x D - (x  - 1)D ,
--R                  2      2                2      2                2      2
--R    56 - 2x D - (x  - 1)D , 72 - 2x D - (x  - 1)D , 90 - 2x D - (x  - 1)D ,
--R                   2      2
--R    110 - 2x D - (x  - 1)D ]
--R                              Type: List Operator Polynomial Fraction Integer
--E 8

--S 9 of 9
[(E i)(L i) for i in 1..10]
 

   (9)  [0,0,0,0,0,0,0,0,0,0]
                                       Type: List Polynomial Fraction Integer
--R 
--R
--R   (9)  [0,0,0,0,0,0,0,0,0,0]
--R                                       Type: List Polynomial Fraction Integer
--E 9
)spool 
 
Starts dribbling to DecimalExpansion.output (2010/3/27, 18:41:55).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
r := decimal(22/7)
 

          ______
   (1)  3.142857
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (1)  3.142857
--R                                                       Type: DecimalExpansion
--E 1

--S 2 of 7
r + decimal(6/7)
 

   (2)  4
                                                       Type: DecimalExpansion
--R 
--R
--R   (2)  4
--R                                                       Type: DecimalExpansion
--E 2

--S 3 of 7
[decimal(1/i) for i in 350..354]
 

   (3)
        ______    ______         __    ________________________________
   [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983,
       __________________________________________________________
    0.00282485875706214689265536723163841807909604519774011299435]
                                                  Type: List DecimalExpansion
--R 
--R
--R   (3)
--R        ______    ______         __    ________________________________
--R   [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983,
--R       __________________________________________________________
--R    0.00282485875706214689265536723163841807909604519774011299435]
--R                                                  Type: List DecimalExpansion
--E 3

--S 4 of 7
decimal(1/2049)
 

   (4)
   0.
     OVERBAR
        00048804294777940458760370912640312347486578818936066373840897999023914
          104441190824792581747193753050268423621278672523182040019521717911176
          183504148365056124938994631527574426549536359199609565641776476329917
          032698877501220107369448511469009272816007808687164470473401659346022
          449975597852611029770619814543679843826256710590531966813079551
                                                       Type: DecimalExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        00048804294777940458760370912640312347486578818936066373840897999023914
--R          104441190824792581747193753050268423621278672523182040019521717911176
--R          183504148365056124938994631527574426549536359199609565641776476329917
--R          032698877501220107369448511469009272816007808687164470473401659346022
--R          449975597852611029770619814543679843826256710590531966813079551
--R                                                       Type: DecimalExpansion
--E 4

--S 5 of 7
p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9) 
 

             2     _      _
   (5)  0.25x  + 0.6x + 0.4
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R             2     _      _
--R   (5)  0.25x  + 0.6x + 0.4
--R                                            Type: Polynomial DecimalExpansion
--E 5

--S 6 of 7
q := differentiate(p, x)
 

                 _
   (6)  0.5x + 0.6
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R                 _
--R   (6)  0.5x + 0.6
--R                                            Type: Polynomial DecimalExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              _
   (7)  x + 1.3
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R              _
--R   (7)  x + 1.3
--R                                            Type: Polynomial DecimalExpansion
--E 7
)spool
 
Starts dribbling to parabola.output (2010/3/27, 18:30:37).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 1
draw(curve(t**2 + 2*t - 1,t**2 + t - 2),t = -4..3)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (1)  TwoDimensionalViewport: "t*t+2*t-1"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Compiling function %D with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (1)  TwoDimensionalViewport: "t*t+2*t-1"
--R                                                 Type: TwoDimensionalViewport
--E 1
)spool 
 
Starts dribbling to EqTable.output (2010/3/27, 18:41:58).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
e: EqTable(List Integer, Integer) := table()
 

   (1)  table()
                                          Type: EqTable(List Integer,Integer)
--R 
--R
--R   (1)  table()
--R                                          Type: EqTable(List Integer,Integer)
--E 1

--S 2 of 6
l1 := [1,2,3]
 

   (2)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 6
l2 := [1,2,3]
 

   (3)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 3

--S 4 of 6
e.l1 := 111
 

   (4)  111
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  111
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 6
e.l2 := 222
 

   (5)  222
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  222
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 6
e.l1
 

   (6)  111
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  111
--R                                                        Type: PositiveInteger
--E 6
)spool
 
Starts dribbling to eqtbl.output (2010/3/27, 18:25:32).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 6
e: EqTable(List Integer, Integer) := table()
 

   (1)  table()
                                          Type: EqTable(List Integer,Integer)
--R 
--R
--R   (1)  table()
--R                                          Type: EqTable(List Integer,Integer)
--E 1

--S 2 of 6
l1 := [1,2,3]
 

   (2)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 6
l2 := [1,2,3]
 

   (3)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 3

--S 4 of 6
e.l1 := 111
 

   (4)  111
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  111
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 6
e.l2 := 222
 

   (5)  222
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  222
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 6
e.l1
 

   (6)  111
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  111
--R                                                        Type: PositiveInteger
--E 6
)spool
 
Starts dribbling to ifact.output (2010/3/27, 18:26:55).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
factor(3**17-1)
 

   (1)  2 1871 34511
                                                       Type: Factored Integer
--R 
--R
--R   (1)  2 1871 34511
--R                                                       Type: Factored Integer
--E 1

--S 2 of 7
factor(3**23-1)
 

   (2)  2 47 1001523179
                                                       Type: Factored Integer
--R 
--R
--R   (2)  2 47 1001523179
--R                                                       Type: Factored Integer
--E 2

--S 3 of 7
factor(3**31-1)
 

   (3)  2 683 102673 4404047
                                                       Type: Factored Integer
--R 
--R
--R   (3)  2 683 102673 4404047
--R                                                       Type: Factored Integer
--E 3

--S 4 of 7
factor(3**41-1)
 

   (4)  2 83 2526913 86950696619
                                                       Type: Factored Integer
--R 
--R
--R   (4)  2 83 2526913 86950696619
--R                                                       Type: Factored Integer
--E 4

--S 5 of 7
factor(3**53-1)
 

   (5)  2 107 24169 3747607031112307667
                                                       Type: Factored Integer
--R 
--R
--R   (5)  2 107 24169 3747607031112307667
--R                                                       Type: Factored Integer
--E 5

--S 6 of 7
factor(111111111111111111111111)
 

   (6)  3 7 11 13 37 73 101 137 9901 99990001
                                                       Type: Factored Integer
--R 
--R
--R   (6)  3 7 11 13 37 73 101 137 9901 99990001
--R                                                       Type: Factored Integer
--E 6

--S 7 of 7
factor(11111111111111111111111111111111111111111111111)
 

   (7)  35121409 316362908763458525001406154038726382279
                                                       Type: Factored Integer
--R 
--R
--R   (7)  35121409 316362908763458525001406154038726382279
--R                                                       Type: Factored Integer
--E 7
)spool 
 
Starts dribbling to derham.output (2010/3/27, 18:24:55).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 33
coefRing := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 33
lv : List Symbol := [x,y,z]
 

   (2)  [x,y,z]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z]
--R                                                            Type: List Symbol
--E 2

--S 3 of 33
der := DERHAM(coefRing,lv)
 

   (3)  DeRhamComplex(Integer,[x,y,z])
                                                                 Type: Domain
--R 
--R
--R   (3)  DeRhamComplex(Integer,[x,y,z])
--R                                                                 Type: Domain
--E 3

--S 4 of 33
R := Expression coefRing
 

   (4)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (4)  Expression Integer
--R                                                                 Type: Domain
--E 4

--S 5 of 33
f : R := x**2*y*z-5*x**3*y**2*z**5
 

            3 2 5    2
   (5)  - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3 2 5    2
--R   (5)  - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 5

--S 6 of 33
g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2
 

            2     3 2       2
   (6)  - 7z sin(x y ) + y z cos(z)
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2
--R   (6)  - 7z sin(x y ) + y z cos(z)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 33
h : R :=x*y*z-2*x**3*y*z**2
 

            3   2
   (7)  - 2x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3   2
--R   (7)  - 2x y z  + x y z
--R                                                     Type: Expression Integer
--E 7

--S 8 of 33
dx : der := generator(1)
 

   (8)  dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (8)  dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 8

--S 9 of 33
dy : der := generator(2)
 

   (9)  dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (9)  dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 9

--S 10 of 33
dz : der := generator(3)
 

   (10)  dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (10)  dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 10

--S 11 of 33
[dx,dy,dz] := [generator(i)$der for i in 1..3]
 

   (11)  [dx,dy,dz]
                                    Type: List DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (11)  [dx,dy,dz]
--R                                    Type: List DeRhamComplex(Integer,[x,y,z])
--E 11

--S 12 of 33
alpha : der := f*dx + g*dy + h*dz
 

   (12)
          3   2                   2     3 2       2
     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
   + 
          3 2 5    2
     (- 5x y z  + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (12)
--R          3   2                   2     3 2       2
--R     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
--R   + 
--R          3 2 5    2
--R     (- 5x y z  + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 12

--S 13 of 33
beta  : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy
 

   (13)  x dy + cos(tan(x y z) + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (13)  x dy + cos(tan(x y z) + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 13

--S 14 of 33
exteriorDifferential alpha;
 

                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 14

--S 15 of 33
exteriorDifferential %
 

   (15)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (15)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 15

--S 16 of 33
gamma := alpha * beta
 

   (16)
        4   2    2               3   2
     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
   + 
       2     3 2       2                                   4 2 5    3
   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (16)
--R        4   2    2               3   2
--R     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
--R   + 
--R       2     3 2       2                                   4 2 5    3
--R   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 16

--S 17 of 33
exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))
 

   (17)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (17)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 17

--S 18 of 33
a : BOP := operator('a)
 

   (18)  a
                                                          Type: BasicOperator
--R 
--R
--R   (18)  a
--R                                                          Type: BasicOperator
--E 18

--S 19 of 33
b : BOP := operator('b)
 

   (19)  b
                                                          Type: BasicOperator
--R 
--R
--R   (19)  b
--R                                                          Type: BasicOperator
--E 19

--S 20 of 33
c : BOP := operator('c)
 

   (20)  c
                                                          Type: BasicOperator
--R 
--R
--R   (20)  c
--R                                                          Type: BasicOperator
--E 20

--S 21 of 33
sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz
 

   (21)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (21)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 21

--S 22 of 33
theta  := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz
 

   (22)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (22)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 22

--S 23 of 33
totalDifferential(a(x,y,z))$der
 

   (23)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
          ,3             ,2             ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (23)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
--R          ,3             ,2             ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 23

--S 24 of 33
exteriorDifferential sigma
 

   (24)
     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
       ,2           ,3                  ,1           ,3
   + 
     (b  (x,y,z) - a  (x,y,z))dx dy
       ,1           ,2
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (24)
--R     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
--R       ,2           ,3                  ,1           ,3
--R   + 
--R     (b  (x,y,z) - a  (x,y,z))dx dy
--R       ,1           ,2
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 24

--S 25 of 33
exteriorDifferential theta
 

   (25)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
           ,1           ,2           ,3
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (25)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
--R           ,1           ,2           ,3
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 25

--S 26 of 33
one : der := 1
 

   (26)  1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (26)  1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 26

--S 27 of 33
g1 : der := a([x,t,y,u,v,z,e]) * one
 

   (27)  a(x,t,y,u,v,z,e)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (27)  a(x,t,y,u,v,z,e)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 27

--S 28 of 33
h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one
 

   (28)  a(x,y,x,t,x,z,y,r,u,x)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (28)  a(x,y,x,t,x,z,y,r,u,x)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 28

--S 29 of 33
exteriorDifferential g1
 

   (29)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
          ,6                     ,3                     ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (29)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
--R          ,6                     ,3                     ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 29

--S 30 of 33
exteriorDifferential h1
 

   (30)
     a  (x,y,x,t,x,z,y,r,u,x)dz
      ,6
   + 
     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
       ,7                         ,2
   + 
         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,10                         ,5
       + 
         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,3                         ,1
    *
       dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (30)
--R     a  (x,y,x,t,x,z,y,r,u,x)dz
--R      ,6
--R   + 
--R     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
--R       ,7                         ,2
--R   + 
--R         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,10                         ,5
--R       + 
--R         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,3                         ,1
--R    *
--R       dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 30

--S 31 of 33
coefficient(gamma, dx*dy)
 

            2     3 2       2                                   4 2 5    3
   (31)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2                                   4 2 5    3
--R   (31)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 31

--S 32 of 33
coefficient(gamma, one)
 

   (32)  0
                                                     Type: Expression Integer
--R 
--R
--R   (32)  0
--R                                                     Type: Expression Integer
--E 32

--S 33 of 33
coefficient(g1,one)
 

   (33)  a(x,t,y,u,v,z,e)
                                                     Type: Expression Integer
--R 
--R
--R   (33)  a(x,t,y,u,v,z,e)
--R                                                     Type: Expression Integer
--E 33
)spool
 
Starts dribbling to radff.output (2010/3/27, 18:36:40).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 27
P0 := UP(x, INT)
 

   (1)  UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 27
P1 := UP(y, FRAC P0)
 

   (2)  UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 2

--S 3 of 27
R := RADFF(INT, P0, P1, 1 - x**20, 20)
 

   (3)
  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
  mial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
                                                                 Type: Domain
--R 
--R
--R   (3)
--R  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
--R  mial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--R                                                                 Type: Domain
--E 3

--S 4 of 27
definingPolynomial()$R
 

         20    20
   (4)  y   + x   - 1
       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R         20    20
--R   (4)  y   + x   - 1
--R       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--E 4

--S 5 of 27
genus()$R
 

   (5)  171
                                                     Type: NonNegativeInteger
--R 
--R
--R   (5)  171
--R                                                     Type: NonNegativeInteger
--E 5

--S 6 of 27
rank()$R
 

   (6)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  20
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 27
numberOfComponents()$R
 

   (7)  1
                                                     Type: NonNegativeInteger
--R 
--R
--R   (7)  1
--R                                                     Type: NonNegativeInteger
--E 7

--S 8 of 27
integralBasisAtInfinity()$R
 

   (8)
       1     1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9   1   10
   [1, - y, -- y , -- y , -- y , -- y , -- y , -- y , -- y , -- y , --- y  ,
       x     2      3      4      5      6      7      8      9      10
            x      x      x      x      x      x      x      x      x
     1   11   1   12   1   13   1   14   1   15   1   16   1   17   1   18
    --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  ,
     11       12       13       14       15       16       17       18
    x        x        x        x        x        x        x        x
     1   19
    --- y  ]
     19
    x
Type: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--R 
--R
--R   (8)
--R       1     1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9   1   10
--R   [1, - y, -- y , -- y , -- y , -- y , -- y , -- y , -- y , -- y , --- y  ,
--R       x     2      3      4      5      6      7      8      9      10
--R            x      x      x      x      x      x      x      x      x
--R     1   11   1   12   1   13   1   14   1   15   1   16   1   17   1   18
--R    --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  , --- y  ,
--R     11       12       13       14       15       16       17       18
--R    x        x        x        x        x        x        x        x
--R     1   19
--R    --- y  ]
--R     19
--R    x
--RType: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--E 8

--S 9 of 27
branchPoint?(0)$R
 

   (9)  false
                                                                Type: Boolean
--R 
--R
--R   (9)  false
--R                                                                Type: Boolean
--E 9

--S 10 of 27
branchPoint?(1)$R
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 27
y := generator()$R
 

   (11)  y
Type: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--R 
--R
--R   (11)  y
--RType: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),(-x**20)+1,20)
--E 11

--S 12 of 27
norm y
 

          20
   (12)  x   - 1
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          20
--R   (12)  x   - 1
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 12

--S 13 of 27
trace y
 

   (13)  0
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)  0
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 27
R2 := RADFF(INT, P0, P1, 2 * x**2, 4)
 

   (14)
  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
  mial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
                                                                 Type: Domain
--R 
--R
--R   (14)
--R  RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolyno
--R  mial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R                                                                 Type: Domain
--E 14

--S 15 of 27
definingPolynomial()$R2
 

          4     2
   (15)  y  - 2x
       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R          4     2
--R   (15)  y  - 2x
--R       Type: UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer))
--E 15

--S 16 of 27
rank()$R2
 

   (16)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  4
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 27
absolutelyIrreducible?()$R2
 

   (17)  false
                                                                Type: Boolean
--R 
--R
--R   (17)  false
--R                                                                Type: Boolean
--E 17

--S 18 of 27
numberOfComponents()$R2
 

   (18)  2
                                                     Type: NonNegativeInteger
--R 
--R
--R   (18)  2
--R                                                     Type: NonNegativeInteger
--E 18

--S 19 of 27
genus()$R2
 

   (19)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (19)  0
--R                                                     Type: NonNegativeInteger
--E 19

--S 20 of 27
integralBasis()$R2
 

              1  2 1  3
   (20)  [1,y,- y ,- y ]
              x    x
Type: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R 
--R
--R              1  2 1  3
--R   (20)  [1,y,- y ,- y ]
--R              x    x
--RType: Vector RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--E 20

--S 21 of 27
y := generator()$R2
 

   (21)  y
Type: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R 
--R
--R   (21)  y
--RType: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--E 21

--S 22 of 27
integralCoordinates(y**3)
 

   (22)  [num= [0,0,0,x],den= 1]
Type: Record(num: Vector UnivariatePolynomial(x,Integer),den: UnivariatePolynomial(x,Integer))
--R 
--R
--R   (22)  [num= [0,0,0,x],den= 1]
--RType: Record(num: Vector UnivariatePolynomial(x,Integer),den: UnivariatePolynomial(x,Integer))
--E 23

--S 24 of 27
integralRepresents(%.num, %.den)$R2
 

          3
   (23)  y
Type: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--R 
--R
--R          3
--R   (23)  y
--RType: RadicalFunctionField(Integer,UnivariatePolynomial(x,Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Integer)),2*x*x,4)
--E 24

--S 25 of 27
norm y
 

             2
   (24)  - 2x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             2
--R   (24)  - 2x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 25

--S 26 of 27
trace y
 

   (25)  0
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (25)  0
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 26

--S 27 of 27
regularRepresentation y
 

         + 0   1  0  0+
         |            |
         | 0   0  1  0|
   (26)  |            |
         | 0   0  0  1|
         |            |
         |  2         |
         +2x   0  0  0+
                        Type: Matrix Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         + 0   1  0  0+
--R         |            |
--R         | 0   0  1  0|
--R   (26)  |            |
--R         | 0   0  0  1|
--R         |            |
--R         |  2         |
--R         +2x   0  0  0+
--R                        Type: Matrix Fraction UnivariatePolynomial(x,Integer)
--E 27
)spool 
 
Starts dribbling to list.output (2010/3/27, 18:28:41).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 33
[2, 4, 5, 6]
 

   (1)  [2,4,5,6]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [2,4,5,6]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 33
[1]
 

   (2)  [1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 33
list(1)
 

   (3)  [1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [1]
--R                                                   Type: List PositiveInteger
--E 3

--S 4 of 33
append([1,2,3],[5,6,7])
 

   (4)  [1,2,3,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [1,2,3,5,6,7]
--R                                                   Type: List PositiveInteger
--E 4

--S 5 of 33
cons(10,[9,8,7])
 

   (5)  [10,9,8,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [10,9,8,7]
--R                                                   Type: List PositiveInteger
--E 5

)clear all
 

--S 6 of 33
empty? [x+1]
 

   (1)  false
                                                                Type: Boolean
--R 
--R
--R   (1)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 33
([] = nil)@Boolean
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 33
k := [4,3,7,3,8,5,9,2]
 

   (3)  [4,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [4,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 8

--S 9 of 33
first k
 

   (4)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 33
k.first
 

   (5)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  4
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 33
k.1
 

   (6)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 33
k(1)
 

   (7)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 33
n := #k
 

   (8)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  8
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 33
last k
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 33
k.last
 

   (10)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  2
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 33
k.(#k)
 

   (11)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  2
--R                                                        Type: PositiveInteger
--E 16

)clear all
 

--S 17 of 33
k := [4,3,7,3,8,5,9,2]
 

   (1)  [4,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [4,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 17

--S 18 of 33
k.1 := 999
 

   (2)  999
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  999
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 33
k
 

   (3)  [999,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [999,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 19

--S 20 of 33
k := [1,2]
 

   (4)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [1,2]
--R                                                   Type: List PositiveInteger
--E 20

--S 21 of 33
m := cons(0,k)
 

   (5)  [0,1,2]
                                                           Type: List Integer
--R 
--R
--R   (5)  [0,1,2]
--R                                                           Type: List Integer
--E 21

--S 22 of 33
m.2 := 99
 

   (6)  99
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  99
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 33
m
 

   (7)  [0,99,2]
                                                           Type: List Integer
--R 
--R
--R   (7)  [0,99,2]
--R                                                           Type: List Integer
--E 23

--S 24 of 33
k
 

   (8)  [99,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (8)  [99,2]
--R                                                   Type: List PositiveInteger
--E 24

)clear all
 

--S 25 of 33
k := [1,2,3]
 

   (1)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 25

--S 26 of 33
rest k
 

   (2)  [2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [2,3]
--R                                                   Type: List PositiveInteger
--E 26

--S 27 of 33
removeDuplicates [4,3,4,3,5,3,4]
 

   (3)  [4,3,5]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [4,3,5]
--R                                                   Type: List PositiveInteger
--E 27

--S 28 of 33
reverse [1,2,3,4,5,6]
 

   (4)  [6,5,4,3,2,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [6,5,4,3,2,1]
--R                                                   Type: List PositiveInteger
--E 28

--S 29 of 33
member?(1/2,[3/4,5/6,1/2])
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 33
member?(1/12,[3/4,5/6,1/2])
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 30

)clear all
 

--S 31 of 33
[1..3,10,20..23]
 

   (1)  [1..3,10..10,20..23]
                                           Type: List Segment PositiveInteger
--R 
--R
--R   (1)  [1..3,10..10,20..23]
--R                                           Type: List Segment PositiveInteger
--E 31

--S 32 of 33
expand [1..3,10,20..23]
 

   (2)  [1,2,3,10,20,21,22,23]
                                                           Type: List Integer
--R 
--R
--R   (2)  [1,2,3,10,20,21,22,23]
--R                                                           Type: List Integer
--E 32

--S 33 of 33
expand [1..]
 

   (3)  [1,2,3,4,5,6,7,8,9,10,...]
                                                         Type: Stream Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                         Type: Stream Integer
--E 33
)spool 
 
Starts dribbling to pfr1.output (2010/3/27, 18:30:46).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
partialFraction(1,factorial 10)
 

        159   23   12   1
   (1)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                                                Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (1)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                                                Type: PartialFraction Integer
--E 1

--S 2 of 10
f := padicFraction(%)
 

        1    1    1    1    1    1    2    1    2   2    2   1
   (2)  - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
        2    4    5    6    7    8    2    3    4   5    2   7
            2    2    2    2    2    3    3    3        5
                                                Type: PartialFraction Integer
--R 
--R
--R        1    1    1    1    1    1    2    1    2   2    2   1
--R   (2)  - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
--R        2    4    5    6    7    8    2    3    4   5    2   7
--R            2    2    2    2    2    3    3    3        5
--R                                                Type: PartialFraction Integer
--E 2

--S 3 of 10
compactFraction(f)
 

        159   23   12   1
   (3)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                                                Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (3)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                                                Type: PartialFraction Integer
--E 3

--S 4 of 10
numberOfFractionalTerms(f)
 

   (4)  12
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  12
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 10
nthFractionalTerm(f,3)
 

         1
   (5)  --
         5
        2
                                                Type: PartialFraction Integer
--R 
--R
--R         1
--R   (5)  --
--R         5
--R        2
--R                                                Type: PartialFraction Integer
--E 5

--S 6 of 10
partialFraction(1,- 13 + 14 * %i)
 

             1         4
   (6)  - ------- + -------
          1 + 2%i   3 + 8%i
                                        Type: PartialFraction Complex Integer
--R 
--R
--R             1         4
--R   (6)  - ------- + -------
--R          1 + 2%i   3 + 8%i
--R                                        Type: PartialFraction Complex Integer
--E 6

--S 7 of 10
% :: Fraction Complex Integer
 

              %i
   (7)  - ---------
          14 + 13%i
                                               Type: Fraction Complex Integer
--R 
--R
--R              %i
--R   (7)  - ---------
--R          14 + 13%i
--R                                               Type: Fraction Complex Integer
--E 7

--S 8 of 10
u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])
 

                      2       3       4
   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
                      Type: Factored UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                      2       3       4
--R   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
--R                      Type: Factored UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 10
partialFraction(1,u)
 

   (9)
     1     1      7     17  2         139   607  3   10115  2   391     44179
    ---    - x + --   - -- x  - 12x - ---   --- x  + ----- x  + --- x + -----
    648    4     16      8             8    324       432        4       324
   ----- + -------- + ------------------- + ---------------------------------
   x + 1          2                3                            4
           (x + 2)          (x + 3)                      (x + 4)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (9)
--R     1     1      7     17  2         139   607  3   10115  2   391     44179
--R    ---    - x + --   - -- x  - 12x - ---   --- x  + ----- x  + --- x + -----
--R    648    4     16      8             8    324       432        4       324
--R   ----- + -------- + ------------------- + ---------------------------------
--R   x + 1          2                3                            4
--R           (x + 2)          (x + 3)                      (x + 4)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 10
padicFraction %
 

   (10)
       1       1         1        17        3          1       607       403
      ---      -        --        --        -          -       ---       ---
      648      4        16         8        4          2       324       432
     ----- + ----- - -------- - ----- + -------- - -------- + ----- + --------
     x + 1   x + 2          2   x + 3          2          3   x + 4          2
                     (x + 2)            (x + 3)    (x + 3)            (x + 4)
   + 
        13          1
        --         --
        36         12
     -------- + --------
            3          4
     (x + 4)    (x + 4)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (10)
--R       1       1         1        17        3          1       607       403
--R      ---      -        --        --        -          -       ---       ---
--R      648      4        16         8        4          2       324       432
--R     ----- + ----- - -------- - ----- + -------- - -------- + ----- + --------
--R     x + 1   x + 2          2   x + 3          2          3   x + 4          2
--R                     (x + 2)            (x + 3)    (x + 3)            (x + 4)
--R   + 
--R        13          1
--R        --         --
--R        36         12
--R     -------- + --------
--R            3          4
--R     (x + 4)    (x + 4)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 10
)spool 
 
Starts dribbling to sinhcosh.output (2010/3/27, 18:40:43).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.00,0.000000000,sinh(0.00),sinh(0.00)-0.000000000],_
[0.01,0.010000167,sinh(0.01),sinh(0.01)-0.010000167],_
[0.02,0.020001333,sinh(0.02),sinh(0.02)-0.020001333],_
[0.03,0.030004500,sinh(0.03),sinh(0.03)-0.030004500],_
[0.04,0.040010668,sinh(0.04),sinh(0.04)-0.040010668],_
[0.05,0.050020836,sinh(0.05),sinh(0.05)-0.050020836],_
[0.06,0.060036006,sinh(0.06),sinh(0.06)-0.060036006],_
[0.07,0.070057181,sinh(0.07),sinh(0.07)-0.070057181],_
[0.08,0.080085361,sinh(0.08),sinh(0.08)-0.080085361],_
[0.09,0.090121549,sinh(0.09),sinh(0.09)-0.090121549],_
[0.10,0.100166750,sinh(0.10),sinh(0.10)-0.100166750],_
[0.11,0.110221968,sinh(0.11),sinh(0.11)-0.110221968],_
[0.12,0.120288207,sinh(0.12),sinh(0.12)-0.120288207],_
[0.13,0.130366476,sinh(0.13),sinh(0.13)-0.130366476],_
[0.14,0.140457782,sinh(0.14),sinh(0.14)-0.140457782],_
[0.15,0.150563133,sinh(0.15),sinh(0.15)-0.150563133],_
[0.16,0.160683541,sinh(0.16),sinh(0.16)-0.160683541],_
[0.17,0.170820017,sinh(0.17),sinh(0.17)-0.170820017],_
[0.18,0.180973576,sinh(0.18),sinh(0.18)-0.180973576],_
[0.19,0.191145232,sinh(0.19),sinh(0.19)-0.191145232],_
[0.20,0.201336003,sinh(0.20),sinh(0.20)-0.201336003],_
[0.21,0.211546907,sinh(0.21),sinh(0.21)-0.211546907],_
[0.22,0.221778966,sinh(0.22),sinh(0.22)-0.221778966],_
[0.23,0.232033204,sinh(0.23),sinh(0.23)-0.232033204],_
[0.24,0.242310645,sinh(0.24),sinh(0.24)-0.242310645],_
[0.25,0.252612317,sinh(0.25),sinh(0.25)-0.252612317],_
[0.26,0.262939250,sinh(0.26),sinh(0.26)-0.262939250],_
[0.27,0.273292478,sinh(0.27),sinh(0.27)-0.273292478],_
[0.28,0.283673035,sinh(0.28),sinh(0.28)-0.283673035],_
[0.29,0.294081960,sinh(0.29),sinh(0.29)-0.294081960],_
[0.30,0.304520293,sinh(0.30),sinh(0.30)-0.304520293],_
[0.31,0.314989079,sinh(0.31),sinh(0.31)-0.314989079],_
[0.32,0.325489364,sinh(0.32),sinh(0.32)-0.325489364],_
[0.33,0.336022198,sinh(0.33),sinh(0.33)-0.336022198],_
[0.34,0.346588634,sinh(0.34),sinh(0.34)-0.346588634],_
[0.35,0.357189729,sinh(0.35),sinh(0.35)-0.357189729],_
[0.36,0.367826544,sinh(0.36),sinh(0.36)-0.367826544],_
[0.37,0.378500142,sinh(0.37),sinh(0.37)-0.378500142],_
[0.38,0.389211590,sinh(0.38),sinh(0.38)-0.389211590],_
[0.39,0.399961960,sinh(0.39),sinh(0.39)-0.399961960],_
[0.40,0.410752326,sinh(0.40),sinh(0.40)-0.410752326],_
[0.41,0.421583767,sinh(0.41),sinh(0.41)-0.421583767],_
[0.42,0.432457368,sinh(0.42),sinh(0.42)-0.432457368],_
[0.43,0.443374214,sinh(0.43),sinh(0.43)-0.443374214],_
[0.44,0.454335399,sinh(0.44),sinh(0.44)-0.454335399],_
[0.45,0.465342017,sinh(0.45),sinh(0.45)-0.465342017],_
[0.46,0.476395170,sinh(0.46),sinh(0.46)-0.476395170],_
[0.47,0.487495962,sinh(0.47),sinh(0.47)-0.487495962],_
[0.48,0.498645505,sinh(0.48),sinh(0.48)-0.498645505],_
[0.49,0.509844913,sinh(0.49),sinh(0.49)-0.509844913],_
[0.50,0.521095305,sinh(0.50),sinh(0.50)-0.521095305],_
[0.51,0.532397808,sinh(0.51),sinh(0.51)-0.532397808],_
[0.52,0.543753551,sinh(0.52),sinh(0.52)-0.543753551],_
[0.53,0.555163669,sinh(0.53),sinh(0.53)-0.555163669],_
[0.54,0.566629305,sinh(0.54),sinh(0.54)-0.566629305],_
[0.55,0.578151604,sinh(0.55),sinh(0.55)-0.578151604],_
[0.56,0.589731718,sinh(0.56),sinh(0.56)-0.589731718],_
[0.57,0.601370806,sinh(0.57),sinh(0.57)-0.601370806],_
[0.58,0.613070032,sinh(0.58),sinh(0.58)-0.613070032],_
[0.59,0.624830565,sinh(0.59),sinh(0.59)-0.624830565],_
[0.60,0.636653582,sinh(0.60),sinh(0.60)-0.636653582],_
[0.61,0.648540265,sinh(0.61),sinh(0.61)-0.648540265],_
[0.62,0.660491802,sinh(0.62),sinh(0.62)-0.660491802],_
[0.63,0.672509389,sinh(0.63),sinh(0.63)-0.672509389],_
[0.64,0.684594228,sinh(0.64),sinh(0.64)-0.684594228],_
[0.65,0.696747526,sinh(0.65),sinh(0.65)-0.696747526],_
[0.66,0.708970500,sinh(0.66),sinh(0.66)-0.708970500],_
[0.67,0.721264371,sinh(0.67),sinh(0.67)-0.721264371],_
[0.68,0.733630370,sinh(0.68),sinh(0.68)-0.733630370],_
[0.69,0.746069732,sinh(0.69),sinh(0.69)-0.746069732],_
[0.70,0.758583702,sinh(0.70),sinh(0.70)-0.758583702],_
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R    [1.13,1.386311622,1.3863116218 51229278,- 0.148770722 E -9],
--R    [1.14,1.403474672,1.4034746716 849259325,- 0.3150740675 E -9],
--R    [1.15,1.42077807,1.4207780701 553572045,0.1553572045 E -9],
--R    [1.16,1.438223548,1.4382235476 16789684,- 0.383210316 E -9],
--R    [1.17,1.455812849,1.4558128486 315074606,- 0.3684925394 E -9],
--R    [1.18,1.473547732,1.4735477321 442698057,0.1442698057 E -9],
--R    [1.19,1.491429972,1.4914299716 582071144,- 0.3417928856 E -9],
--R    [1.2,1.509461355,1.5094613554 121726964,0.4121726964 E -9],
--R    [1.21,1.527643687,1.5276436865 595681515,- 0.4404318485 E -9],
--R    [1.22,1.545978783,1.5459787833 486602124,0.3486602124 E -9],
--R    [1.23,1.564468479,1.5644684793 044070864,0.3044070864 E -9],
--R    [1.24,1.583114623,1.5831146234 118124797,0.4118124797 E -9],
--R    [1.25,1.60191908,1.6019190803 008256379,0.3008256379 E -9],
--R    [1.26,1.62088373,1.6208837304 328058954,0.4328058954 E -9],
--R    [1.27,1.64001047,1.6400104702 88570378,0.288570378 E -9],
--R    [1.28,1.659301213,1.6593012125 580436651,- 0.4419563349 E -9],
--R    [1.29,1.678757886,1.6787578863 315283762,0.3315283762 E -9],
--R    [1.3,1.698382437,1.6983824372 926158087,0.2926158087 E -9],
--R    [1.31,1.718176828,1.7181768279 127559182,- 0.872440818 E -10],
--R    [1.32,1.738143038,1.7381430376 475060993,- 0.3524939007 E -9],
--R    [1.33,1.758283063,1.7582830631 344783905,0.1344783905 E -9],
--R    [1.34,1.778598918,1.7785989183 930048997,0.3930048997 E -9],
--R    [1.35,1.799092635,1.7990926350 255414153,0.255414153 E -10],
--R    [1.36,1.819766262,1.8197662624 20829345,0.420829345 E -9],
--R    [1.37,1.840621868,1.8406218679 588362979,- 0.411637021 E -10],
--R    [1.38,1.861661537,1.8616615372 174958039,0.2174958039 E -9],
--R    [1.39,1.882887374,1.8828873741 812668452,0.1812668451 E -9],
--R    [1.4,1.904301501,1.9043015014 515340551,0.4515340551 E -9],
--R    [1.41,1.92590606,1.9259060604 588696261,0.4588696261 E -9],
--R    [1.42,1.947703212,1.9477032116 771781509,- 0.3228218491 E -9],
--R    [1.43,1.969695135,1.9696951348 397458135,- 0.1602541865 E -9],
--R    [1.44,1.991884029,1.9918840291 572155345,0.1572155345 E -9],
--R    [1.45,2.014272114,2.0142721135 375098676,- 0.4624901324 E -9],
--R    [1.46,2.036861627,2.0368616268 077236416,- 0.192276358 E -9],
--R    [1.47,2.059654828,2.0596548279 380085349,- 0.619914651 E -10],
--R    [1.48,2.082653996,2.0826539962 674719736,0.2674719736 E -9],
--R    [1.49,2.105861432,2.1058614317 321129415,- 0.2678870585 E -9],
--R    [1.5,2.129279455,2.1292794550 948174968,0.948174968 E -10],
--R    [1.51,2.152910408,2.1529104081 774369945,0.177436994 E -9],
--R    [1.52,2.176756654,2.1767566540 94972223,0.94972223 E -10],
--R    [1.53,2.200820577,2.2008205774 918868736,0.4918868736 E -9],
--R    [1.54,2.225104585,2.2251045847 805739743,- 0.219426026 E -9],
--R    [1.55,2.249611104,2.2496111043 819991339,0.3819991339 E -9],
--R    [1.56,2.274342587,2.2743425869 685446626,- 0.314553374 E -10],
--R    [1.57,2.299301506,2.2993015057 090788526,- 0.2909211474 E -9],
--R    [1.58,2.324490357,2.3244903565 162749255,- 0.4837250745 E -9],
--R    [1.59,2.349911658,2.3499116582 962043799,0.2962043799 E -9],
--R    [1.6,2.375567953,2.3755679532 002296976,0.200229698 E -9],
--R    [1.61,2.401461807,2.4014618068 79221598,- 0.120778402 E -9],
--R    [1.62,2.427595809,2.4275958087 401262638,- 0.2598737362 E -9],
--R    [1.63,2.453972572,2.4539725722 049081927,0.204908193 E -9],
--R    [1.64,2.480594735,2.4805947349 718945727,- 0.281054273 E -10],
--R    [1.65,2.507464959,2.5074649592 795473117,0.2795473117 E -9],
--R    [1.66,2.534585932,2.5345859321 726891034,0.172689103 E -9],
--R    [1.67,2.561960366,2.5619603657 712101481,- 0.228789852 E -9],
--R    [1.68,2.589590998,2.5895909975 412824018,- 0.4587175982 E -9],
--R    [1.69,2.617480591,2.6174805905 69108475,- 0.430891525 E -9],
--R    [1.7,2.645631934,2.6456319338 372325553,- 0.162767445 E -9],
--R    [1.71,2.674047843,2.6740478425 034409861,- 0.4965590139 E -9],
--R    [1.72,2.702731158,2.7027311581 822803909,0.182280391 E -9],
--R    [1.73,2.731684749,2.7316847492 292214966,0.229221497 E -9],
--R    [1.74,2.760911511,2.7609115110 274970701,0.274970701 E -10],
--R    [1.75,2.790414366,2.7904143662 776426551,0.2776426551 E -9],
--R    [1.76,2.820196265,2.8201962652 897690607,0.2897690607 E -9],
--R    [1.77,2.850260186,2.8502601862 785958316,0.2785958316 E -9],
--R    [1.78,2.880609136,2.8806091356 612752013,- 0.3387247987 E -9],
--R    [1.79,2.911246148,2.9112461483 580363133,0.3580363133 E -9],
--R    [1.8,2.942174288,2.9421742880 956797727,0.956797727 E -10],
--R    [1.81,2.973396648,2.9733966477 139528796,- 0.2860471204 E -9],
--R    [1.82,3.004916349,3.0049163494 748361809,0.4748361809 E -9],
--R    [1.83,3.036736545,3.0367365453 747722708,0.3747722708 E -9],
--R    [1.84,3.068860417,3.0688604174 598680611,0.4598680611 E -9],
--R    [1.85,3.101291178,3.1012911781 441020441,0.144102044 E -9],
--R    [1.86,3.134032071,3.1340320705 305683671,- 0.4694316329 E -9],
--R    [1.87,3.167086369,3.1670863687 357898447,- 0.2642101554 E -9],
--R    [1.88,3.200457378,3.2004573782 171323393,0.217132339 E -9],
--R    [1.89,3.234148436,3.2341484361 033532526,0.103353253 E -9],
--R    [1.9,3.268162912,3.2681629115 283171817,- 0.4716828183 E -9],
--R    [1.91,3.302504206,3.3025042059 679121137,- 0.320878863 E -10],
--R    [1.92,3.337175754,3.3371757535 801998489,- 0.4198001511 E -9],
--R    [1.93,3.372181022,3.3721810215 488346686,- 0.4511653313 E -9],
--R    [1.94,3.40752351,3.4075235104 297845903,0.4297845903 E -9],
--R    [1.95,3.443206754,3.4432067545 013898812,0.5013898812 E -9],
--R    [1.96,3.479234322,3.4792343221 177938377,0.117793838 E -9],
--R    [1.97,3.515609816,3.5156098160 657811731,0.657811731 E -10],
--R    [1.98,3.552336874,3.5523368739 25059699,- 0.74940301 E -10],
--R    [1.99,3.589419168,3.5894191684 320213268,0.4320213268 E -9],
--R    [2.0,3.626860408,3.6268604078 470187677,- 0.152981232 E -9]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
[[0.00,1.000000000,cosh(0.00),cosh(0.00)-1.000000000],_
[0.01,1.000050000,cosh(0.01),cosh(0.01)-1.000050000],_
[0.02,1.000200007,cosh(0.02),cosh(0.02)-1.000200007],_
[0.03,1.000450034,cosh(0.03),cosh(0.03)-1.000450034],_
[0.04,1.000800107,cosh(0.04),cosh(0.04)-1.000800107],_
[0.05,1.001250260,cosh(0.05),cosh(0.05)-1.001250260],_
[0.06,1.001800540,cosh(0.06),cosh(0.06)-1.001800540],_
[0.07,1.002451001,cosh(0.07),cosh(0.07)-1.002451001],_
[0.08,1.003201707,cosh(0.08),cosh(0.08)-1.003201707],_
[0.09,1.004052734,cosh(0.09),cosh(0.09)-1.004052734],_
[0.10,1.005004168,cosh(0.10),cosh(0.10)-1.005004168],_
[0.11,1.006056103,cosh(0.11),cosh(0.11)-1.006056103],_
[0.12,1.007208644,cosh(0.12),cosh(0.12)-1.007208644],_
[0.13,1.008461907,cosh(0.13),cosh(0.13)-1.008461907],_
[0.14,1.009816017,cosh(0.14),cosh(0.14)-1.009816017],_
[0.15,1.011271110,cosh(0.15),cosh(0.15)-1.011271110],_
[0.16,1.012827330,cosh(0.16),cosh(0.16)-1.012827330],_
[0.17,1.014484834,cosh(0.17),cosh(0.17)-1.014484834],_
[0.18,1.016243787,cosh(0.18),cosh(0.18)-1.016243787],_
[0.19,1.018104366,cosh(0.19),cosh(0.19)-1.018104366],_
[0.20,1.020066756,cosh(0.20),cosh(0.20)-1.020066756],_
[0.21,1.022131153,cosh(0.21),cosh(0.21)-1.022131153],_
[0.22,1.024297764,cosh(0.22),cosh(0.22)-1.024297764],_
[0.23,1.026566806,cosh(0.23),cosh(0.23)-1.026566806],_
[0.24,1.028938506,cosh(0.24),cosh(0.24)-1.028938506],_
[0.25,1.031413100,cosh(0.25),cosh(0.25)-1.031413100],_
[0.26,1.033990836,cosh(0.26),cosh(0.26)-1.033990836],_
[0.27,1.036671973,cosh(0.27),cosh(0.27)-1.036671973],_
[0.28,1.039456777,cosh(0.28),cosh(0.28)-1.039456777],_
[0.29,1.042345528,cosh(0.29),cosh(0.29)-1.042345528],_
[0.30,1.045338514,cosh(0.30),cosh(0.30)-1.045338514],_
[0.31,1.048436035,cosh(0.31),cosh(0.31)-1.048436035],_
[0.32,1.051638401,cosh(0.32),cosh(0.32)-1.051638401],_
[0.33,1.054945931,cosh(0.33),cosh(0.33)-1.054945931],_
[0.34,1.058358957,cosh(0.34),cosh(0.34)-1.058358957],_
[0.35,1.061877819,cosh(0.35),cosh(0.35)-1.061877819],_
[0.36,1.065502870,cosh(0.36),cosh(0.36)-1.065502870],_
[0.37,1.069234473,cosh(0.37),cosh(0.37)-1.069234473],_
[0.38,1.073072999,cosh(0.38),cosh(0.38)-1.073072999],_
[0.39,1.077018834,cosh(0.39),cosh(0.39)-1.077018834],_
[0.40,1.081072372,cosh(0.40),cosh(0.40)-1.081072372],_
[0.41,1.085234018,cosh(0.41),cosh(0.41)-1.085234018],_
[0.42,1.089504188,cosh(0.42),cosh(0.42)-1.089504188],_
[0.43,1.093883309,cosh(0.43),cosh(0.43)-1.093883309],_
[0.44,1.098371820,cosh(0.44),cosh(0.44)-1.098371820],_
[0.45,1.102970169,cosh(0.45),cosh(0.45)-1.102970169],_
[0.46,1.107678815,cosh(0.46),cosh(0.46)-1.107678815],_
[0.47,1.112498231,cosh(0.47),cosh(0.47)-1.112498231],_
[0.48,1.117428897,cosh(0.48),cosh(0.48)-1.117428897],_
[0.49,1.122471307,cosh(0.49),cosh(0.49)-1.122471307],_
[0.50,1.127625965,cosh(0.50),cosh(0.50)-1.127625965],_
[0.51,1.132893387,cosh(0.51),cosh(0.51)-1.132893387],_
[0.52,1.138274099,cosh(0.52),cosh(0.52)-1.138274099],_
[0.53,1.143768639,cosh(0.53),cosh(0.53)-1.143768639],_
[0.54,1.149377557,cosh(0.54),cosh(0.54)-1.149377557],_
[0.55,1.155101414,cosh(0.55),cosh(0.55)-1.155101414],_
[0.56,1.160940782,cosh(0.56),cosh(0.56)-1.160940782],_
[0.57,1.166896245,cosh(0.57),cosh(0.57)-1.166896245],_
[0.58,1.172968399,cosh(0.58),cosh(0.58)-1.172968399],_
[0.59,1.179157850,cosh(0.59),cosh(0.59)-1.179157850],_
[0.60,1.185465218,cosh(0.60),cosh(0.60)-1.185465218],_
[0.61,1.191891134,cosh(0.61),cosh(0.61)-1.191891134],_
[0.62,1.198436240,cosh(0.62),cosh(0.62)-1.198436240],_
[0.63,1.205101190,cosh(0.63),cosh(0.63)-1.205101190],_
[0.64,1.211886652,cosh(0.64),cosh(0.64)-1.211886652],_
[0.65,1.218793303,cosh(0.65),cosh(0.65)-1.218793303],_
[0.66,1.225821834,cosh(0.66),cosh(0.66)-1.225821834],_
[0.67,1.232972949,cosh(0.67),cosh(0.67)-1.232972949],_
[0.68,1.240247362,cosh(0.68),cosh(0.68)-1.240247362],_
[0.69,1.247645801,cosh(0.69),cosh(0.69)-1.247645801],_
[0.70,1.255169006,cosh(0.70),cosh(0.70)-1.255169006],_
[0.71,1.262817728,cosh(0.71),cosh(0.71)-1.262817728],_
[0.72,1.270592733,cosh(0.72),cosh(0.72)-1.270592733],_
[0.73,1.278494799,cosh(0.73),cosh(0.73)-1.278494799],_
[0.74,1.286524715,cosh(0.74),cosh(0.74)-1.286524715],_
[0.75,1.294683285,cosh(0.75),cosh(0.75)-1.294683285],_
[0.76,1.302971324,cosh(0.76),cosh(0.76)-1.302971324],_
[0.77,1.311389661,cosh(0.77),cosh(0.77)-1.311389661],_
[0.78,1.319939138,cosh(0.78),cosh(0.78)-1.319939138],_
[0.79,1.328620611,cosh(0.79),cosh(0.79)-1.328620611],_
[0.80,1.337434946,cosh(0.80),cosh(0.80)-1.337434946],_
[0.81,1.346383026,cosh(0.81),cosh(0.81)-1.346383026],_
[0.82,1.355465746,cosh(0.82),cosh(0.82)-1.355465746],_
[0.83,1.364684013,cosh(0.83),cosh(0.83)-1.364684013],_
[0.84,1.374038750,cosh(0.84),cosh(0.84)-1.374038750],_
[0.85,1.383530892,cosh(0.85),cosh(0.85)-1.383530892],_
[0.86,1.393161388,cosh(0.86),cosh(0.86)-1.393161388],_
[0.87,1.402931201,cosh(0.87),cosh(0.87)-1.402931201],_
[0.88,1.412841309,cosh(0.88),cosh(0.88)-1.412841309],_
[0.89,1.422892702,cosh(0.89),cosh(0.89)-1.422892702],_
[0.90,1.433086385,cosh(0.90),cosh(0.90)-1.433086385],_
[0.91,1.443423379,cosh(0.91),cosh(0.91)-1.443423379],_
[0.92,1.453904716,cosh(0.92),cosh(0.92)-1.453904716],_
[0.93,1.464531444,cosh(0.93),cosh(0.93)-1.464531444],_
[0.94,1.475304627,cosh(0.94),cosh(0.94)-1.475304627],_
[0.95,1.486225341,cosh(0.95),cosh(0.95)-1.486225341],_
[0.96,1.497294680,cosh(0.96),cosh(0.96)-1.497294680],_
[0.97,1.508513749,cosh(0.97),cosh(0.97)-1.508513749],_
[0.98,1.519883670,cosh(0.98),cosh(0.98)-1.519883670],_
[0.99,1.531405582,cosh(0.99),cosh(0.99)-1.531405582],_
[1.00,1.543080635,cosh(1.00),cosh(1.00)-1.543080635],_
[1.01,1.554909997,cosh(1.01),cosh(1.01)-1.554909997],_
[1.02,1.566894852,cosh(1.02),cosh(1.02)-1.566894852],_
[1.03,1.579036398,cosh(1.03),cosh(1.03)-1.579036398],_
[1.04,1.591335848,cosh(1.04),cosh(1.04)-1.591335848],_
[1.05,1.603794434,cosh(1.05),cosh(1.05)-1.603794434],_
[1.06,1.616413400,cosh(1.06),cosh(1.06)-1.616413400],_
[1.07,1.629194009,cosh(1.07),cosh(1.07)-1.629194009],_
[1.08,1.642137538,cosh(1.08),cosh(1.08)-1.642137538],_
[1.09,1.655245283,cosh(1.09),cosh(1.09)-1.655245283],_
[1.10,1.668518554,cosh(1.10),cosh(1.10)-1.668518554],_
[1.11,1.681958678,cosh(1.11),cosh(1.11)-1.681958678],_
[1.12,1.695566999,cosh(1.12),cosh(1.12)-1.695566999],_
[1.13,1.709344878,cosh(1.13),cosh(1.13)-1.709344878],_
[1.14,1.723293694,cosh(1.14),cosh(1.14)-1.723293694],_
[1.15,1.737414840,cosh(1.15),cosh(1.15)-1.737414840],_
[1.16,1.751709728,cosh(1.16),cosh(1.16)-1.751709728],_
[1.17,1.766179790,cosh(1.17),cosh(1.17)-1.766179790],_
[1.18,1.780826471,cosh(1.18),cosh(1.18)-1.780826471],_
[1.19,1.795651236,cosh(1.19),cosh(1.19)-1.795651236],_
[1.20,1.810655567,cosh(1.20),cosh(1.20)-1.810655567],_
[1.21,1.825840966,cosh(1.21),cosh(1.21)-1.825840966],_
[1.22,1.841208950,cosh(1.22),cosh(1.22)-1.841208950],_
[1.23,1.856761057,cosh(1.23),cosh(1.23)-1.856761057],_
[1.24,1.872498841,cosh(1.24),cosh(1.24)-1.872498841],_
[1.25,1.888423877,cosh(1.25),cosh(1.25)-1.888423877],_
[1.26,1.904537757,cosh(1.26),cosh(1.26)-1.904537757],_
[1.27,1.920842092,cosh(1.27),cosh(1.27)-1.920842092],_
[1.28,1.937338513,cosh(1.28),cosh(1.28)-1.937338513],_
[1.29,1.954028669,cosh(1.29),cosh(1.29)-1.954028669],_
[1.30,1.970914230,cosh(1.30),cosh(1.30)-1.970914230],_
[1.31,1.987996884,cosh(1.31),cosh(1.31)-1.987996884],_
[1.32,2.005278340,cosh(1.32),cosh(1.32)-2.005278340],_
[1.33,2.022760324,cosh(1.33),cosh(1.33)-2.022760324],_
[1.34,2.040444587,cosh(1.34),cosh(1.34)-2.040444587],_
[1.35,2.058332896,cosh(1.35),cosh(1.35)-2.058332896],_
[1.36,2.076427039,cosh(1.36),cosh(1.36)-2.076427039],_
[1.37,2.094728828,cosh(1.37),cosh(1.37)-2.094728828],_
[1.38,2.113240090,cosh(1.38),cosh(1.38)-2.113240090],_
[1.39,2.131962679,cosh(1.39),cosh(1.39)-2.131962679],_
[1.40,2.150898465,cosh(1.40),cosh(1.40)-2.150898465],_
[1.41,2.170049344,cosh(1.41),cosh(1.41)-2.170049344],_
[1.42,2.189417229,cosh(1.42),cosh(1.42)-2.189417229],_
[1.43,2.209004057,cosh(1.43),cosh(1.43)-2.209004057],_
[1.44,2.228811788,cosh(1.44),cosh(1.44)-2.228811788],_
[1.45,2.248842402,cosh(1.45),cosh(1.45)-2.248842402],_
[1.46,2.269097902,cosh(1.46),cosh(1.46)-2.269097902],_
[1.47,2.289580313,cosh(1.47),cosh(1.47)-2.289580313],_
[1.48,2.310291685,cosh(1.48),cosh(1.48)-2.310291685],_
[1.49,2.331234087,cosh(1.49),cosh(1.49)-2.331234087],_
[1.50,2.352409615,cosh(1.50),cosh(1.50)-2.352409615],_
[1.51,2.373820386,cosh(1.51),cosh(1.51)-2.373820386],_
[1.52,2.395468541,cosh(1.52),cosh(1.52)-2.395468541],_
[1.53,2.417356245,cosh(1.53),cosh(1.53)-2.417356245],_
[1.54,2.439485686,cosh(1.54),cosh(1.54)-2.439485686],_
[1.55,2.461859078,cosh(1.55),cosh(1.55)-2.461859078],_
[1.56,2.484478658,cosh(1.56),cosh(1.56)-2.484478658],_
[1.57,2.507346688,cosh(1.57),cosh(1.57)-2.507346688],_
[1.58,2.530465455,cosh(1.58),cosh(1.58)-2.530465455],_
[1.59,2.553837270,cosh(1.59),cosh(1.59)-2.553837270],_
[1.60,2.577464471,cosh(1.60),cosh(1.60)-2.577464471],_
[1.61,2.601349421,cosh(1.61),cosh(1.61)-2.601349421],_
[1.62,2.625494508,cosh(1.62),cosh(1.62)-2.625494508],_
[1.63,2.649902146,cosh(1.63),cosh(1.63)-2.649902146],_
[1.64,2.674574777,cosh(1.64),cosh(1.64)-2.674574777],_
[1.65,2.699514868,cosh(1.65),cosh(1.65)-2.699514868],_
[1.66,2.724724912,cosh(1.66),cosh(1.66)-2.724724912],_
[1.67,2.750207431,cosh(1.67),cosh(1.67)-2.750207431],_
[1.68,2.775964974,cosh(1.68),cosh(1.68)-2.775964974],_
[1.69,2.802000115,cosh(1.69),cosh(1.69)-2.802000115],_
[1.70,2.828315458,cosh(1.70),cosh(1.70)-2.828315458],_
[1.71,2.854913635,cosh(1.71),cosh(1.71)-2.854913635],_
[1.72,2.881797306,cosh(1.72),cosh(1.72)-2.881797306],_
[1.73,2.908969159,cosh(1.73),cosh(1.73)-2.908969159],_
[1.74,2.936431912,cosh(1.74),cosh(1.74)-2.936431912],_
[1.75,2.964188310,cosh(1.75),cosh(1.75)-2.964188310],_
[1.76,2.992241129,cosh(1.76),cosh(1.76)-2.992241129],_
[1.77,3.020593175,cosh(1.77),cosh(1.77)-3.020593175],_
[1.78,3.049247283,cosh(1.78),cosh(1.78)-3.049247283],_
[1.79,3.078206318,cosh(1.79),cosh(1.79)-3.078206318],_
[1.80,3.107473176,cosh(1.80),cosh(1.80)-3.107473176],_
[1.81,3.137050785,cosh(1.81),cosh(1.81)-3.137050785],_
[1.82,3.166942100,cosh(1.82),cosh(1.82)-3.166942100],_
[1.83,3.197150113,cosh(1.83),cosh(1.83)-3.197150113],_
[1.84,3.227677844,cosh(1.84),cosh(1.84)-3.227677844],_
[1.85,3.258528344,cosh(1.85),cosh(1.85)-3.258528344],_
[1.86,3.289704701,cosh(1.86),cosh(1.86)-3.289704701],_
[1.87,3.321210031,cosh(1.87),cosh(1.87)-3.321210031],_
[1.88,3.353047484,cosh(1.88),cosh(1.88)-3.353047484],_
[1.89,3.385220245,cosh(1.89),cosh(1.89)-3.385220245],_
[1.90,3.417731531,cosh(1.90),cosh(1.90)-3.417731531],_
[1.91,3.450584593,cosh(1.91),cosh(1.91)-3.450584593],_
[1.92,3.483782716,cosh(1.92),cosh(1.92)-3.483782716],_
[1.93,3.517329220,cosh(1.93),cosh(1.93)-3.517329220],_
[1.94,3.551227460,cosh(1.94),cosh(1.94)-3.551227460],_
[1.95,3.585480826,cosh(1.95),cosh(1.95)-3.585480826],_
[1.96,3.620092743,cosh(1.96),cosh(1.96)-3.620092743],_
[1.97,3.655066672,cosh(1.97),cosh(1.97)-3.655066672],_
[1.98,3.690406111,cosh(1.98),cosh(1.98)-3.690406111],_
[1.99,3.726114594,cosh(1.99),cosh(1.99)-3.726114594],_
[2.00,3.762195691,cosh(2.00),cosh(2.00)-3.762195691]]
 

   (2)
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    [1.71,2.854913635,2.8549136351 205630698,0.12056307 E -9],
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    [1.73,2.908969159,2.9089691591 990993011,0.199099301 E -9],
    [1.74,2.936431912,2.9364319116 444939418,- 0.3555060582 E -9],
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    [2.0,3.762195691,3.7621956910 836314596,0.836314596 E -10]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.0,1.0,1.0,0.0], [0.01,1.00005,1.0000500004 166680556,0.4166680556 E -9],
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--R    [1.82,3.1669421,3.1669421004 087169461,0.4087169461 E -9],
--R    [1.83,3.197150113,3.1971501131 499450329,0.149945033 E -9],
--R    [1.84,3.227677844,3.2276778435 667887561,- 0.4332112439 E -9],
--R    [1.85,3.258528344,3.2585283444 577296603,0.4577296603 E -9],
--R    [1.86,3.289704701,3.2897047008 98565676,- 0.101434324 E -9],
--R    [1.87,3.321210031,3.3212100305 509212704,- 0.4490787296 E -9],
--R    [1.88,3.353047484,3.3530474839 74016208,- 0.25983792 E -10],
--R    [1.89,3.385220245,3.3852202449 397240979,- 0.602759021 E -10],
--R    [1.9,3.417731531,3.4177315307 509522343,- 0.2490477656 E -9],
--R    [1.91,3.450584593,3.4505845925 633745687,- 0.4366254312 E -9],
--R    [1.92,3.483782716,3.4837827157 105499861,- 0.289450014 E -9],
--R    [1.93,3.51732922,3.5173292200 324583986,0.324583986 E -10],
--R    [1.94,3.55122746,3.5512274602 074875108,0.207487511 E -9],
--R    [1.95,3.585480826,3.5854808260 879034531,0.879034531 E -10],
--R    [1.96,3.620092743,3.6200927430 388388338,0.388388338 E -10],
--R    [1.97,3.655066672,3.6550666722 808321068,0.2808321068 E -9],
--R    [1.98,3.690406111,3.6904061112 359525095,0.2359525095 E -9],
--R    [1.99,3.726114594,3.7261145938 775451847,- 0.122454815 E -9],
--R    [2.0,3.762195691,3.7621956910 836314596,0.836314596 E -10]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to TexFormat.output (2010/3/27, 18:46:38).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 11
(1/2)::TEX
 

   (1)  ["$$","\frac{1}{2} ","$$"]
                                                              Type: TexFormat
--R 
--R
--R   (1)  ["$$","\frac{1}{2} ","$$"]
--R                                                              Type: TexFormat
--E 1

--S 2 of 11
(1/(x+5))::TEX
 

   (2)  ["$$","\frac{1}{{x+5}} ","$$"]
                                                              Type: TexFormat
--R 
--R
--R   (2)  ["$$","\frac{1}{{x+5}} ","$$"]
--R                                                              Type: TexFormat
--E 2

--S 3 of 11
((x+3)/(y-5))::TEX
 

   (3)  ["$$","\frac{{x+3}}{{y -5}} ","$$"]
                                                              Type: TexFormat
--R 
--R
--R   (3)  ["$$","\frac{{x+3}}{{y -5}} ","$$"]
--R                                                              Type: TexFormat
--E 3

--S 4 of 11
)set output fraction horizontal
 
--R 
--E 4

--S 5 of 11
(1/2)::TEX
 

   (4)  ["$$","SLASH ","\left(","{1, \: 2} ","\right)","$$"]
                                                              Type: TexFormat
--R 
--R
--R   (4)  ["$$","SLASH ","\left(","{1, \: 2} ","\right)","$$"]
--R                                                              Type: TexFormat
--E 5

--S 6 of 11
(1/(x+5))::TEX
 

   (5)
   ["$$","SLASH ","\left(","{1, \: {\left( x+5 ","\right)}}","\right)","$$"]
                                                              Type: TexFormat
--R 
--R
--R   (5)
--R   ["$$","SLASH ","\left(","{1, \: {\left( x+5 ","\right)}}","\right)","$$"]
--R                                                              Type: TexFormat
--E 6

--S 7 of 11
)set output mathml on
 
--R 
--E 7

--S 8 of 11
1/2
 

   (6)  1/2
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow>
</math>

                                                       Type: Fraction Integer
--R 
--R
--R   (6)  1/2
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow>
--R</math>
--R
--R                                                       Type: Fraction Integer
--E 8

--S 9 of 11
1/(x+5)
 

   (7)  1/(x + 5)
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>)</mo></mrow></mrow>
</math>

                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (7)  1/(x + 5)
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                                            Type: Fraction Polynomial Integer
--E 9

--S 10 of 11
(x+3)/(y-5)
 

   (8)  (x + 3)/(y - 5)
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>)</mo></mrow></mrow>
</math>

                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (8)  (x + 3)/(y - 5)
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>)</mo></mrow></mrow>
--R</math>
--R
--R                                            Type: Fraction Polynomial Integer
--E 10

--S 11 of 11
)show TexFormat
 
 TexFormat  is a domain constructor
 Abbreviation for TexFormat is TEX 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for TEX 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                coerce : OutputForm -> %
 coerce : % -> OutputForm              display : % -> Void
 display : (%,Integer) -> Void         epilogue : % -> List String
 hash : % -> SingleInteger             latex : % -> String
 new : () -> %                         prologue : % -> List String
 tex : % -> List String                ?~=? : (%,%) -> Boolean
 convert : (OutputForm,Integer,OutputForm) -> %
 convert : (OutputForm,Integer) -> %
 setEpilogue! : (%,List String) -> List String
 setPrologue! : (%,List String) -> List String
 setTex! : (%,List String) -> List String

--R 
--R TexFormat  is a domain constructor
--R Abbreviation for TexFormat is TEX 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for TEX 
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean                coerce : OutputForm -> %
--R coerce : % -> OutputForm              display : % -> Void
--R display : (%,Integer) -> Void         epilogue : % -> List String
--R hash : % -> SingleInteger             latex : % -> String
--R new : () -> %                         prologue : % -> List String
--R tex : % -> List String                ?~=? : (%,%) -> Boolean
--R convert : (OutputForm,Integer,OutputForm) -> %
--R convert : (OutputForm,Integer) -> %
--R setEpilogue! : (%,List String) -> List String
--R setPrologue! : (%,List String) -> List String
--R setTex! : (%,List String) -> List String
--R
--E 11

)spool
 
Starts dribbling to GeneralDistributedMultivariatePolynomial.output (2010/3/27, 18:42:5).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
(d1,d2,d3) : DMP([z,y,x],FRAC INT) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 10
d1 := -4*z + 4*y**2*x + 16*x**2 + 1 
 

                 2       2
   (2)  - 4z + 4y x + 16x  + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R                 2       2
--R   (2)  - 4z + 4y x + 16x  + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 2

--S 3 of 10
d2 := 2*z*y**2 + 4*x + 1 
 

            2
   (3)  2z y  + 4x + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (3)  2z y  + 4x + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 3

--S 4 of 10
d3 := 2*z*x**2 - 2*y**2 - x 
 

            2     2
   (4)  2z x  - 2y  - x
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (4)  2z x  - 2y  - x
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 4

--S 5 of 10
groebner [d1,d2,d3]
 

   (5)
        1568  6   1264  5    6   4   182  3   2047  2    103      2857
   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
        2745       305      305      549       610      2745     10980
     2    112  6    84  5   1264  4    13  3    84  2   1772       2
    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
         2745      305       305      549      305      2745     2745
     7   29  6   17  4   11  3    1  2   15     1
    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
          4      16       8      32      16     4
       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (5)
--R        1568  6   1264  5    6   4   182  3   2047  2    103      2857
--R   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
--R        2745       305      305      549       610      2745     10980
--R     2    112  6    84  5   1264  4    13  3    84  2   1772       2
--R    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
--R         2745      305       305      549      305      2745     2745
--R     7   29  6   17  4   11  3    1  2   15     1
--R    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
--R          4      16       8      32      16     4
--R       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 5

--S 6 of 10
(n1,n2,n3) : HDMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
n1 := d1
 

          2       2
   (7)  4y x + 16x  - 4z + 1
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R          2       2
--R   (7)  4y x + 16x  - 4z + 1
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 7

--S 8 of 10
n2 := d2
 

            2
   (8)  2z y  + 4x + 1
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (8)  2z y  + 4x + 1
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 8

--S 9 of 10
n3 := d3
 

            2     2
   (9)  2z x  - 2y  - x
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (9)  2z x  - 2y  - x
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 9

--S 10 of 10
groebner [n1,n2,n3]
 

   (10)
     4     3   3  2   1     1   4   29  3   1  2   7        9     1
   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
               2      2     8        4      8      4       16     4
       2        1   2      2       1     2    2   1
    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
                2                  4              2
     2     2     2   1     3
    z  - 4y  + 2x  - - z - - x]
                     4     2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (10)
--R     4     3   3  2   1     1   4   29  3   1  2   7        9     1
--R   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
--R               2      2     8        4      8      4       16     4
--R       2        1   2      2       1     2    2   1
--R    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
--R                2                  4              2
--R     2     2     2   1     3
--R    z  - 4y  + 2x  - - z - - x]
--R                     4     2
--RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 10
)spool
 
Starts dribbling to lodo2.output (2010/3/27, 18:28:45).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 26
Q  := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 26
PQ := UnivariatePolynomial('x, Q)
 

   (2)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 26
x: PQ := 'x
 

   (3)  x
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (3)  x
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 3

--S 4 of 26
Dx: LODO2(Q, PQ) := D()
 

   (4)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 26
a := Dx  + 1
 

   (5)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (5)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 26
b := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (6)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (6)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 6

--S 7 of 26
p := 4*x**2 + 2/3
 

          2   2
   (7)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (7)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 26
a p
 

          2        2
   (8)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (8)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 26
(a * b) p = a b p
 

          2         37    2         37
   (9)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (9)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 26
c := (1/9)*b*(a + b)**2
 

          1  6    5  5   13  4   19  3   79  2    7     1
   (10)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
         72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          1  6    5  5   13  4   19  3   79  2    7     1
--R   (10)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R         72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 10

--S 11 of 26
(a**2 - 3/4*b + c) (p + 1)
 

           2   44     541
   (11)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (11)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 11

)clear all
 

--S 12 of 26
PZ   := UnivariatePolynomial(x,Integer)
 

   (1)  UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 12

--S 13 of 26
x:PZ := 'x
 

   (2)  x
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (2)  x
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 26
Mat  := SquareMatrix(3,PZ)
 

   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
                                                                 Type: Domain
--R 
--R
--R   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 14

--S 15 of 26
Vect := DPMM(3, PZ, Mat, PZ);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 15

--S 16 of 26
Modo := LODO2(Mat, Vect);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 16

--S 17 of 26
m:Mat := matrix [[x**2,1,0],[1,x**4,0],[0,0,4*x**2]]
 

        + 2         +
        |x   1    0 |
        |           |
   (6)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (6)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 17

--S 18 of 26
p:Vect := directProduct [3*x**2+1,2*x,7*x**3+2*x]
 

           2          3
   (7)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (7)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 26
q: Vect := m * p
 

           4    2        5     2        5     3
   (8)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (8)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 19

--S 20 of 26
Dx : Modo := D()
 

   (9)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 20

--S 21 of 26
a : Modo := Dx  + m
 

             + 2         +
             |x   1    0 |
             |           |
   (10)  D + |     4     |
             |1   x    0 |
             |           |
             |          2|
             +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R             + 2         +
--R             |x   1    0 |
--R             |           |
--R   (10)  D + |     4     |
--R             |1   x    0 |
--R             |           |
--R             |          2|
--R             +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 21

--S 22 of 26
b : Modo := m*Dx  + 1
 

         + 2         +
         |x   1    0 |    +1  0  0+
         |           |    |       |
   (11)  |     4     |D + |0  1  0|
         |1   x    0 |    |       |
         |           |    +0  0  1+
         |          2|
         +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R         + 2         +
--R         |x   1    0 |    +1  0  0+
--R         |           |    |       |
--R   (11)  |     4     |D + |0  1  0|
--R         |1   x    0 |    |       |
--R         |           |    +0  0  1+
--R         |          2|
--R         +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 22

--S 23 of 26
c := a*b
 

   (12)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (12)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 23

--S 24 of 26
a p
 

            4    2        5     2        5     3      2
   (13)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (13)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 24

--S 25 of 26
b p
 

            3     2       4         4     3     2
   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 25

--S 26 of 26
(a + b + c) (p + q)
 

   (15)
       8      7      6      5      4      3      2
   [10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x  + 40x + 17,
       12      9      8      7     6      5      4      3      2
    10x   + 10x  + 12x  + 92x  + 6x  + 32x  + 72x  + 28x  + 49x  + 32x + 19,
         8       7        6        5       4       3      2
    2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x  + 98x  + 18x + 4]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (15)
--R       8      7      6      5      4      3      2
--R   [10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x  + 40x + 17,
--R       12      9      8      7     6      5      4      3      2
--R    10x   + 10x  + 12x  + 92x  + 6x  + 32x  + 72x  + 28x  + 49x  + 32x + 19,
--R         8       7        6        5       4       3      2
--R    2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x  + 98x  + 18x + 4]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 26
)spool 
 
Starts dribbling to ei.output (2010/3/27, 18:25:6).
)set message test on
 
)set message auto off
 
)clear all
 
digits 35
 

   (1)  20
                                                        Type: PositiveInteger

--S 1 of 20
gamma:=0.577215664901532860606512090082
 

   (2)  0.5772156649 0153286060 6512090082
                                                                  Type: Float
--R 
--R
--R   (2)  0.5772156649 0153286060 6512090082
--R                                                                  Type: Float
--E 1


--S 2 of 20
aChebyshev:=_
[0.191217322586055345391519326510E1,_
-0.420835505286848437550974986680E-01,_
 0.172281962728432678337118157835E-02,_
-0.991578217344456364559842322973E-04,_
 0.717609316802277505265590665592E-05,_
-0.615273314509512696827956791331E-06,_
 0.602485710656275831293999701610E-07,_
-0.657384884528830482295894189637E-08,_
 0.785316754183239981994810079871E-09,_
-0.101373028800387898554202774257E-09,_
 0.139977041322676860277823488623E-10,_
-0.205100837678381899618962318711E-11,_
 0.316838872600247781814907985818E-12,_
-0.513276008283918065415984751899E-13,_
 0.868093304076654934187433687383E-14,_
-0.152701504090308497198572355351E-14,_
 0.278468625164935739650105251453E-15,_
-0.524989043742176696808472933696E-16,_
 0.102071799124856129247455787226E-16,_
-0.204226467989971841308462421876E-17,_
 0.419706417272648474408827228562E-18,_
-0.884450817617281050816483737536E-19,_
 0.190827262959471741995060168262E-19,_
-0.420974622293519950336450865676E-20,_
 0.948390405819837327641500214512E-21,_
-0.217946786013667431994032574014E-21,_
 0.510393686907145094993452562741E-22,_
-0.121688311333441509089746779693E-22,_
 0.295128916644787519294773757144E-23,_
-0.727535376377284689714438950920E-24,_
 0.182163904862307396121667115976E-24,_
-0.462962996316331716612753482064E-25,_
 0.119353979097157791523052371292E-25,_
-0.311949328522014244931062147473E-26,_
 0.826141973453346642284170028518E-27,_
-0.221580337366098298302591177697E-27,_
 0.601603167165426389045303124429E-28,_
-0.165272509838212659649744302314E-28,_
 0.459223035877302702795636377166E-29,_
-0.129006276721326384737453212670E-29,_
 0.366271848103200259081177078922E-30]
 

   (3)
   [1.9121732258 6055345391 51932651, - 0.0420835505 2868484375 5097498668,
    0.0017228196 2728432678 3371181578 35,
    - 0.0000991578 2173444563 6455984232 2973,
    0.0000071760 9316802277 5052655906 65592,
    - 0.6152733145 0951269682 7956791331 E -6,
    0.6024857106 5627583129 399970161 E -7,
    - 0.6573848845 2883048229 5894189637 E -8,
    0.7853167541 8323998199 4810079871 E -9,
    - 0.1013730288 0038789855 4202774257 E -9,
    0.1399770413 2267686027 7823488623 E -10,
    - 0.2051008376 7838189961 8962318711 E -11,
    0.3168388726 0024778181 4907985818 E -12,
    - 0.5132760082 8391806541 5984751899 E -13,
    0.8680933040 7665493418 7433687383 E -14,
    - 0.1527015040 9030849719 8572355351 E -14,
    0.2784686251 6493573965 0105251453 E -15,
    - 0.5249890437 4217669680 8472933696 E -16,
    0.1020717991 2485612924 7455787226 E -16,
    - 0.2042264679 8997184130 8462421876 E -17,
    0.4197064172 7264847440 8827228562 E -18,
    - 0.8844508176 1728105081 6483737536 E -19,
    0.1908272629 5947174199 5060168262 E -19,
    - 0.4209746222 9351995033 6450865676 E -20,
    0.9483904058 1983732764 1500214512 E -21,
    - 0.2179467860 1366743199 4032574014 E -21,
    0.5103936869 0714509499 3452562741 E -22,
    - 0.1216883113 3344150908 9746779693 E -22,
    0.2951289166 4478751929 4773757144 E -23,
    - 0.7275353763 7728468971 443895092 E -24,
    0.1821639048 6230739612 1667115976 E -24,
    - 0.4629629963 1633171661 2753482064 E -25,
    0.1193539790 9715779152 3052371292 E -25,
    - 0.3119493285 2201424493 1062147473 E -26,
    0.8261419734 5334664228 4170028518 E -27,
    - 0.2215803373 6609829830 2591177697 E -27,
    0.6016031671 6542638904 5303124429 E -28,
    - 0.1652725098 3821265964 9744302314 E -28,
    0.4592230358 7730270279 5636377166 E -29,
    - 0.1290062767 2132638473 745321267 E -29,
    0.3662718481 0320025908 1177078922 E -30]
                                                             Type: List Float
--R 
--R
--R   (3)
--R   [1.9121732258 6055345391 51932651, - 0.0420835505 2868484375 5097498668,
--R    0.0017228196 2728432678 3371181578 35,
--R    - 0.0000991578 2173444563 6455984232 2973,
--R    0.0000071760 9316802277 5052655906 65592,
--R    - 0.6152733145 0951269682 7956791331 E -6,
--R    0.6024857106 5627583129 399970161 E -7,
--R    - 0.6573848845 2883048229 5894189637 E -8,
--R    0.7853167541 8323998199 4810079871 E -9,
--R    - 0.1013730288 0038789855 4202774257 E -9,
--R    0.1399770413 2267686027 7823488623 E -10,
--R    - 0.2051008376 7838189961 8962318711 E -11,
--R    0.3168388726 0024778181 4907985818 E -12,
--R    - 0.5132760082 8391806541 5984751899 E -13,
--R    0.8680933040 7665493418 7433687383 E -14,
--R    - 0.1527015040 9030849719 8572355351 E -14,
--R    0.2784686251 6493573965 0105251453 E -15,
--R    - 0.5249890437 4217669680 8472933696 E -16,
--R    0.1020717991 2485612924 7455787226 E -16,
--R    - 0.2042264679 8997184130 8462421876 E -17,
--R    0.4197064172 7264847440 8827228562 E -18,
--R    - 0.8844508176 1728105081 6483737536 E -19,
--R    0.1908272629 5947174199 5060168262 E -19,
--R    - 0.4209746222 9351995033 6450865676 E -20,
--R    0.9483904058 1983732764 1500214512 E -21,
--R    - 0.2179467860 1366743199 4032574014 E -21,
--R    0.5103936869 0714509499 3452562741 E -22,
--R    - 0.1216883113 3344150908 9746779693 E -22,
--R    0.2951289166 4478751929 4773757144 E -23,
--R    - 0.7275353763 7728468971 443895092 E -24,
--R    0.1821639048 6230739612 1667115976 E -24,
--R    - 0.4629629963 1633171661 2753482064 E -25,
--R    0.1193539790 9715779152 3052371292 E -25,
--R    - 0.3119493285 2201424493 1062147473 E -26,
--R    0.8261419734 5334664228 4170028518 E -27,
--R    - 0.2215803373 6609829830 2591177697 E -27,
--R    0.6016031671 6542638904 5303124429 E -28,
--R    - 0.1652725098 3821265964 9744302314 E -28,
--R    0.4592230358 7730270279 5636377166 E -29,
--R    - 0.1290062767 2132638473 745321267 E -29,
--R    0.3662718481 0320025908 1177078922 E -30]
--R                                                             Type: List Float
--E 2

--S 3 of 20
[[-160.,0.993826695674061273878797850088,_
 Ei1(-160.0),Ei1(-160.0)-0.993826695674061273878797850088],_
[-80.0,0.987801333094288773564522608410,_
 Ei1(-80.0),Ei1(-80.0)-0.987801333094288773564522608410],_
[-53.0-1.0/3.0,0.981916290143194439617735426105,_
 Ei1(-53.0-1.0/3.0),Ei1(-53.0-1.0/3.0)-0.981916290143194439617735426105],_
[-40.0,0.976164603185143050808000604060,_
 Ei1(-40.0),Ei1(-40.0)-0.976164603185143050808000604060],_
[-32.0,0.970539884074663920462584664361,_
 Ei1(-32.0),Ei1(-32.0)-0.970539884074663920462584664361],_
[-26.0-2.0/3.0,0.965036251123377035763536593528,_
 Ei1(-26.0-2.0/3.0),Ei1(-26.0-2.0/3.0)-0.965036251123377035763536593528],_
[-22.0-6.0/7.0,0.959648271079367276165478970820,_
 Ei1(-22.0-6.0/7.0),Ei1(-22.0-6.0/7.0)-0.959648271079367276165478970820],_
[-20.0,0.954370909919216833975195829433,_
 Ei1(-20.0),Ei1(-20.0)-0.954370909919216833975195829433],_
[-17.0-7.0/9.0,0.949199490779745744606445346803,_
 Ei1(-17.0-7.0/9.0),Ei1(-17.0-7.0/9.0)-0.949199490779745744606445346803],_
[-16.0,0.944129657736902978984149471583,_
 Ei1(-16.0),Ei1(-16.0)-0.944129657736902978984149471583],_
[-14.0-6.0/11.0,0.939157344419284241240422409988,_
 Ei1(-14.0-6.0/11.0),Ei1(-14.0-6.0/11.0)-0.939157344419284241240422409988],_
[-13.0-1.0/3.0,0.934278746653410464809375801650,_
 Ei1(-13.0-1.0/3.0),Ei1(-13.0-1.0/3.0)-0.934278746653410464809375801650],_
[-12.0-4.0/13.0,0.929490298497214037725319679042,_
 Ei1(-12.0-4.0/13.0),Ei1(-12.0-4.0/13.0)-0.929490298497214037725319679042],_
[-11.0-3.0/7.0,0.924788651140841696055993585492,_
 Ei1(-11.0-3.0/7.0),Ei1(-11.0-3.0/7.0)-0.924788651140841696055993585492],_
[-10.0-2.0/3.0,0.920170654249445676202148012149,_
 Ei1(-10.0-2.0/3.0),Ei1(-10.0-2.0/3.0)-0.920170654249445676202148012149],_
[-10.0,0.915633339397880818760698157666,_
 Ei1(-10.0),Ei1(-10.0)-0.915633339397880818760698157666]]
 

   (4)
   [[- 160.,0.99382669567406123,0.99382669567406123,0.],
    [- 80.,0.98780133309428875,0.98780133309428886,1.1102230246251565E-16],

     [- 53.333333333333329, 0.98191629014319437, 0.98191629014319448,
      1.1102230246251565E-16]
     ,
    [- 40.,0.97616460318514298,0.97616460318514309,1.1102230246251565E-16],
    [- 32.,0.97053988407466396,0.97053988407466363,- 3.3306690738754696E-16],
    [- 26.666666666666664,0.96503625112337699,0.96503625112337699,0.],

     [- 22.857142857142854, 0.95964827107936723, 0.95964827107936734,
      1.1102230246251565E-16]
     ,
    [- 20.,0.9543709099192168,0.95437090991921691,1.1102230246251565E-16],

     [- 17.777777777777775, 0.94919949077974564, 0.94919949077974575,
      1.1102230246251565E-16]
     ,
    [- 16.,0.94412965773690294,0.94412965773690294,0.],

     [- 14.545454545454547, 0.93915734441928422, 0.93915734441928411,
      - 1.1102230246251565E-16]
     ,

     [- 13.333333333333332, 0.93427874665341037, 0.9342787466534106,
      2.2204460492503131E-16]
     ,

     [- 12.307692307692307, 0.92949029849721398, 0.92949029849721387,
      - 1.1102230246251565E-16]
     ,

     [- 11.428571428571427, 0.92478865114084163, 0.92478865114084174,
      1.1102230246251565E-16]
     ,

     [- 10.666666666666668, 0.92017065424944566, 0.92017065424944577,
      1.1102230246251565E-16]
     ,
    [- 10.,0.91563333939788083,0.91563333939788094,1.1102230246251565E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (4)
--R   [[- 160.,0.99382669567406123,0.99382669567406123,0.],
--R    [- 80.,0.98780133309428875,0.98780133309428886,1.1102230246251565E-16],
--R    [- 53.333333333333336,0.98191629014319448,0.98191629014319448,0.],
--R    [- 40.,0.97616460318514309,0.97616460318514309,0.],
--R    [- 32.,0.97053988407466396,0.97053988407466363,- 3.3306690738754696E-16],
--R    [- 26.666666666666668,0.96503625112337699,0.96503625112337699,0.],
--R
--R     [- 22.857142857142858, 0.95964827107936723, 0.95964827107936734,
--R      1.1102230246251565E-16]
--R     ,
--R    [- 20.,0.9543709099192168,0.95437090991921691,1.1102230246251565E-16],
--R    [- 17.777777777777779,0.94919949077974575,0.94919949077974575,0.],
--R    [- 16.,0.94412965773690294,0.94412965773690294,0.],
--R
--R     [- 14.545454545454545, 0.93915734441928422, 0.93915734441928411,
--R      - 1.1102230246251565E-16]
--R     ,
--R
--R     [- 13.333333333333334, 0.93427874665341049, 0.9342787466534106,
--R      1.1102230246251565E-16]
--R     ,
--R
--R     [- 12.307692307692308, 0.92949029849721398, 0.92949029849721387,
--R      - 1.1102230246251565E-16]
--R     ,
--R    [- 11.428571428571429,0.92478865114084174,0.92478865114084174,0.],
--R
--R     [- 10.666666666666666, 0.92017065424944566, 0.92017065424944577,
--R      1.1102230246251565E-16]
--R     ,
--R    [- 10.,0.91563333939788083,0.91563333939788094,1.1102230246251565E-16]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 3

--S 4 of 20
bChebyshev:=[_
 0.175755649606129373848762834691E1,_
-0.435854151773616611705001867964E-01,_
-0.797950713955842540133217027492E-02,_
-0.148437232730371213850970210001E-02,_
-0.280030198437751457486203954948E-03,_
-0.534864851286579323039177361553E-04,_
-0.103286724357355486610233266460E-04,_
-0.201408331300553687732226198639E-05,_
-0.396175843427386645822338443500E-06,_
-0.785387276709663163067607656069E-07,_
-0.156792598100746982624616270279E-07,_
-0.315005593937639988250007372851E-08,_
-0.636509682252420373040380263972E-09,_
-0.129288811328056318356593121259E-09,_
-0.263869099965925576132149942808E-10,_
-0.540895828704506873491922207896E-11,_
-0.111322278460108989997676692708E-11,_
-0.229962472607446246184338864145E-12,_
-0.476668238949519026223913482091E-13,_
-0.991175674733527094506246643371E-14,_
-0.206710358049570724000900805021E-14,_
-0.432277678338338505645764394579E-15,_
-0.906301479966501725514905603356E-16,_
-0.190466997958166139744015963342E-16,_
-0.401179232635027866346744227520E-17,_
-0.846777213001683223134166334685E-18,_
-0.179084273365869665555826492204E-18,_
-0.379449063817147824401106175166E-19,_
-0.805399923679827985260999654058E-20,_
-0.171233901123620129743228671244E-20,_
-0.364627405877496862086576562816E-21,_
-0.777596963889394794353098157647E-22,_
-0.166062849844840205662531950966E-22,_
-0.355117862578825093005927145352E-23,_
-0.760372268594135809295734653294E-24,_
-0.163007413725849002889638374755E-24,_
-0.349857520272863223507538497255E-25,_
-0.751717962789009882460645145143E-26,_
-0.161687744005272276298777317918E-26,_
-0.348127008572475691748202271565E-27,_
-0.750270777550246547010642233720E-28,_
-0.161845436449591026807612330206E-28,_
-0.349436677170516166749482836452E-29,_
-0.755103690612616785856037026797E-30]
 

   (5)
   [1.7575564960 6129373848 762834691, - 0.0435854151 7736166117 0500186796 4,
    - 0.0079795071 3955842540 1332170274 92,
    - 0.0014843723 2730371213 8509702100 01,
    - 0.0002800301 9843775145 7486203954 948,
    - 0.0000534864 8512865793 2303917736 1553,
    - 0.0000103286 7243573554 8661023326 646,
    - 0.0000020140 8331300553 6877322261 98639,
    - 0.3961758434 2738664582 23384435 E -6,
    - 0.7853872767 0966316306 7607656069 E -7,
    - 0.1567925981 0074698262 4616270279 E -7,
    - 0.3150055939 3763998825 0007372851 E -8,
    - 0.6365096822 5242037304 0380263972 E -9,
    - 0.1292888113 2805631835 6593121259 E -9,
    - 0.2638690999 6592557613 2149942808 E -10,
    - 0.5408958287 0450687349 1922207896 E -11,
    - 0.1113222784 6010898999 7676692708 E -11,
    - 0.2299624726 0744624618 4338864145 E -12,
    - 0.4766682389 4951902622 3913482091 E -13,
    - 0.9911756747 3352709450 6246643371 E -14,
    - 0.2067103580 4957072400 0900805021 E -14,
    - 0.4322776783 3833850564 5764394579 E -15,
    - 0.9063014799 6650172551 4905603356 E -16,
    - 0.1904669979 5816613974 4015963342 E -16,
    - 0.4011792326 3502786634 674422752 E -17,
    - 0.8467772130 0168322313 4166334685 E -18,
    - 0.1790842733 6586966555 5826492204 E -18,
    - 0.3794490638 1714782440 1106175166 E -19,
    - 0.8053999236 7982798526 0999654058 E -20,
    - 0.1712339011 2362012974 3228671244 E -20,
    - 0.3646274058 7749686208 6576562816 E -21,
    - 0.7775969638 8939479435 3098157647 E -22,
    - 0.1660628498 4484020566 2531950966 E -22,
    - 0.3551178625 7882509300 5927145352 E -23,
    - 0.7603722685 9413580929 5734653294 E -24,
    - 0.1630074137 2584900288 9638374755 E -24,
    - 0.3498575202 7286322350 7538497255 E -25,
    - 0.7517179627 8900988246 0645145143 E -26,
    - 0.1616877440 0527227629 8777317918 E -26,
    - 0.3481270085 7247569174 8202271565 E -27,
    - 0.7502707775 5024654701 064223372 E -28,
    - 0.1618454364 4959102680 7612330206 E -28,
    - 0.3494366771 7051616674 9482836452 E -29,
    - 0.7551036906 1261678585 6037026797 E -30]
                                                             Type: List Float
--R 
--R
--R   (5)
--R   [1.7575564960 6129373848 762834691, - 0.0435854151 7736166117 0500186796 4,
--R    - 0.0079795071 3955842540 1332170274 92,
--R    - 0.0014843723 2730371213 8509702100 01,
--R    - 0.0002800301 9843775145 7486203954 948,
--R    - 0.0000534864 8512865793 2303917736 1553,
--R    - 0.0000103286 7243573554 8661023326 646,
--R    - 0.0000020140 8331300553 6877322261 98639,
--R    - 0.3961758434 2738664582 23384435 E -6,
--R    - 0.7853872767 0966316306 7607656069 E -7,
--R    - 0.1567925981 0074698262 4616270279 E -7,
--R    - 0.3150055939 3763998825 0007372851 E -8,
--R    - 0.6365096822 5242037304 0380263972 E -9,
--R    - 0.1292888113 2805631835 6593121259 E -9,
--R    - 0.2638690999 6592557613 2149942808 E -10,
--R    - 0.5408958287 0450687349 1922207896 E -11,
--R    - 0.1113222784 6010898999 7676692708 E -11,
--R    - 0.2299624726 0744624618 4338864145 E -12,
--R    - 0.4766682389 4951902622 3913482091 E -13,
--R    - 0.9911756747 3352709450 6246643371 E -14,
--R    - 0.2067103580 4957072400 0900805021 E -14,
--R    - 0.4322776783 3833850564 5764394579 E -15,
--R    - 0.9063014799 6650172551 4905603356 E -16,
--R    - 0.1904669979 5816613974 4015963342 E -16,
--R    - 0.4011792326 3502786634 674422752 E -17,
--R    - 0.8467772130 0168322313 4166334685 E -18,
--R    - 0.1790842733 6586966555 5826492204 E -18,
--R    - 0.3794490638 1714782440 1106175166 E -19,
--R    - 0.8053999236 7982798526 0999654058 E -20,
--R    - 0.1712339011 2362012974 3228671244 E -20,
--R    - 0.3646274058 7749686208 6576562816 E -21,
--R    - 0.7775969638 8939479435 3098157647 E -22,
--R    - 0.1660628498 4484020566 2531950966 E -22,
--R    - 0.3551178625 7882509300 5927145352 E -23,
--R    - 0.7603722685 9413580929 5734653294 E -24,
--R    - 0.1630074137 2584900288 9638374755 E -24,
--R    - 0.3498575202 7286322350 7538497255 E -25,
--R    - 0.7517179627 8900988246 0645145143 E -26,
--R    - 0.1616877440 0527227629 8777317918 E -26,
--R    - 0.3481270085 7247569174 8202271565 E -27,
--R    - 0.7502707775 5024654701 064223372 E -28,
--R    - 0.1618454364 4959102680 7612330206 E -28,
--R    - 0.3494366771 7051616674 9482836452 E -29,
--R    - 0.7551036906 1261678585 6037026797 E -30]
--R                                                             Type: List Float
--E 4

--S 5 of 20
[[-10.000,0.915633339397880818760698157661,_
  Ei2(-10.000),Ei2(-10.000)-0.915633339397880818760698157661],_
[ -9.625,0.912844461467993418856575662217,_
  Ei2( -9.625),Ei2( -9.625)-0.912844461467993418856575662217],_
[ -9.250,0.909862751525424139378954274597,_
  Ei2( -9.250),Ei2( -9.250)-0.909862751525424139378954274597],_
[ -8.875,0.906667270654753880334995756418,_
  Ei2( -8.875),Ei2( -8.875)-0.906667270654753880334995756418],_
[ -8.500,0.903233901973207844144682926135,_
  Ei2( -8.500),Ei2( -8.500)-0.903233901973207844144682926135],_
[ -8.125,0.899534717688473836301415777697,_
  Ei2( -8.125),Ei2( -8.125)-0.899534717688473836301415777697],_
[ -7.750,0.895537187087539157179475513219,_
  Ei2( -7.750),Ei2( -7.750)-0.895537187087539157179475513219],_
[ -7.375,0.891203176321254316267087476258,_
  Ei2( -7.375),Ei2( -7.375)-0.891203176321254316267087476258],_
[ -7.000,0.886487672536429352893993846569,_
  Ei2( -7.000),Ei2( -7.000)-0.886487672536429352893993846569],_
[ -6.625,0.881337138468210200394305706270,_
  Ei2( -6.625),Ei2( -6.625)-0.881337138468210200394305706270],_
[ -6.250,0.875687364788465932276462155532,_
  Ei2( -6.250),Ei2( -6.250)-0.875687364788465932276462155532],_
[ -5.875,0.869460629454113410302047153364,_
  Ei2( -5.875),Ei2( -5.875)-0.869460629454113410302047153364],_
[ -5.500,0.862561884690701422090918986586,_
  Ei2( -5.500),Ei2( -5.500)-0.862561884690701422090918986586],_
[ -5.125,0.854873553890199542392425567234,_
  Ei2( -5.125),Ei2( -5.125)-0.854873553890199542392425567234],_
[ -4.750,0.846248299103587361171665798810,_
  Ei2( -4.750),Ei2( -4.750)-0.846248299103587361171665798810],_
[ -4.375,0.836498754556298741742152267582,_
  Ei2( -4.375),Ei2( -4.375)-0.836498754556298741742152267582],_
[ -4.000,0.825382599604223332408183035504,_
  Ei2( -4.000),Ei2( -4.000)-0.825382599604223332408183035504]]
 

   (6)
   [[- 10.,0.91563333939788083,0.91563333939788083,0.],
    [- 9.625,0.91284446146799336,0.91284446146799336,0.],
    [- 9.25,0.90986275152542406,0.90986275152542395,- 1.1102230246251565E-16],
    [- 8.875,0.90666727065475383,0.90666727065475394,1.1102230246251565E-16],
    [- 8.5,0.90323390197320785,0.90323390197320796,1.1102230246251565E-16],
    [- 8.125,0.89953471768847382,0.89953471768847415,3.3306690738754696E-16],
    [- 7.75,0.89553718708753915,0.89553718708753927,1.1102230246251565E-16],
    [- 7.375,0.89120317632125423,0.89120317632125412,- 1.1102230246251565E-16],
    [- 7.,0.88648767253642935,0.88648767253642924,- 1.1102230246251565E-16],
    [- 6.625,0.88133713846821016,0.88133713846821005,- 1.1102230246251565E-16],
    [- 6.25,0.87568736478846598,0.87568736478846598,0.],
    [- 5.875,0.8694606294541134,0.86946062945411307,- 3.3306690738754696E-16],
    [- 5.5,0.86256188469070139,0.86256188469070139,0.],
    [- 5.125,0.85487355389019948,0.85487355389019937,- 1.1102230246251565E-16],
    [- 4.75,0.84624829910358734,0.84624829910358745,1.1102230246251565E-16],
    [- 4.375,0.83649875455629874,0.83649875455629874,0.],
    [- 4.,0.82538259960422322,0.82538259960422322,0.]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (6)
--R   [[- 10.,0.91563333939788083,0.91563333939788083,0.],
--R    [- 9.625,0.91284446146799347,0.91284446146799336,- 1.1102230246251565E-16],
--R    [- 9.25,0.90986275152542417,0.90986275152542395,- 2.2204460492503131E-16],
--R    [- 8.875,0.90666727065475383,0.90666727065475394,1.1102230246251565E-16],
--R    [- 8.5,0.90323390197320785,0.90323390197320796,1.1102230246251565E-16],
--R    [- 8.125,0.89953471768847382,0.89953471768847415,3.3306690738754696E-16],
--R    [- 7.75,0.89553718708753915,0.89553718708753927,1.1102230246251565E-16],
--R    [- 7.375,0.89120317632125434,0.89120317632125423,- 1.1102230246251565E-16],
--R    [- 7.,0.88648767253642935,0.88648767253642924,- 1.1102230246251565E-16],
--R    [- 6.625,0.88133713846821016,0.88133713846821005,- 1.1102230246251565E-16],
--R    [- 6.25,0.87568736478846598,0.87568736478846598,0.],
--R    [- 5.875,0.8694606294541134,0.86946062945411307,- 3.3306690738754696E-16],
--R    [- 5.5,0.86256188469070139,0.86256188469070139,0.],
--R    [- 5.125,0.85487355389019959,0.85487355389019937,- 2.2204460492503131E-16],
--R    [- 4.75,0.84624829910358734,0.84624829910358745,1.1102230246251565E-16],
--R    [- 4.375,0.83649875455629874,0.83649875455629874,0.],
--R    [- 4.,0.82538259960422333,0.82538259960422322,- 1.1102230246251565E-16]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 5

--S 6 of 20
cChebyshev:=[_
0.329370010376739129393905231421E1,_
0.167983505237130291565505796064E1,_
0.722043610567875435240299679644E0,_
0.260031236054809561713740181192E0,_
0.801049430817375022394742889237E-01,_
0.215140366397633375480552483005E-01,_
0.511620778993033120621968910894E-02,_
0.109093286100739135605066199014E-02,_
0.210741532023938916318348675226E-03,_
0.371990451665188857095940815956E-04,_
0.604349163712387875704767032866E-05,_
0.909295427396260952649596541772E-06,_
0.127380516065926478865567184969E-06,_
0.166918574841098907390896143814E-07,_
0.205441702640104792547612484551E-08,_
0.238358444446681765914052321417E-09,_
0.261538637888544296669068664148E-10,_
0.272185862285416706446550268995E-11,_
0.269375003198357929925326427442E-12,_
0.254122094670726355467884089307E-13,_
0.229013040686503709418510620516E-14,_
0.197546573907462299401057650412E-15,_
0.163402455192893174068635419984E-16,_
0.129823543707963760991961293204E-17,_
0.992258792507371059644632581302E-19,_
0.730625280672210329447230880087E-20,_
0.518967683460434512720780080019E-21,_
0.356040945409970681128043162227E-22,_
0.236197943257938642370187203948E-23,_
0.151683776772145297549624516819E-24,_
0.943908972224487442925310405245E-26,_
0.569722755950369211989581737831E-27,_
0.333833362779543303156597939562E-28,_
0.190062601281619148526680482237E-29]
 

   (7)
   [3.2937001037 6739129393 905231421, 1.6798350523 7130291565 505796064,
    0.7220436105 6787543524 0299679644, 0.2600312360 5480956171 3740181192,
    0.0801049430 8173750223 9474288923 7, 0.0215140366 3976333754 8055248300 5,
    0.0051162077 8993033120 6219689108 94,
    0.0010909328 6100739135 6050661990 14,
    0.0002107415 3202393891 6318348675 226,
    0.0000371990 4516651888 5709594081 5956,
    0.0000060434 9163712387 8757047670 32866,
    0.9092954273 9626095264 9596541772 E -6,
    0.1273805160 6592647886 5567184969 E -6,
    0.1669185748 4109890739 0896143814 E -7,
    0.2054417026 4010479254 7612484551 E -8,
    0.2383584444 4668176591 4052321417 E -9,
    0.2615386378 8854429666 9068664148 E -10,
    0.2721858622 8541670644 6550268995 E -11,
    0.2693750031 9835792992 5326427442 E -12,
    0.2541220946 7072635546 7884089307 E -13,
    0.2290130406 8650370941 8510620516 E -14,
    0.1975465739 0746229940 1057650412 E -15,
    0.1634024551 9289317406 8635419984 E -16,
    0.1298235437 0796376099 1961293204 E -17,
    0.9922587925 0737105964 4632581302 E -19,
    0.7306252806 7221032944 7230880087 E -20,
    0.5189676834 6043451272 0780080019 E -21,
    0.3560409454 0997068112 8043162227 E -22,
    0.2361979432 5793864237 0187203948 E -23,
    0.1516837767 7214529754 9624516819 E -24,
    0.9439089722 2448744292 5310405245 E -26,
    0.5697227559 5036921198 9581737831 E -27,
    0.3338333627 7954330315 6597939562 E -28,
    0.1900626012 8161914852 6680482237 E -29]
                                                             Type: List Float
--R 
--R
--R   (7)
--R   [3.2937001037 6739129393 905231421, 1.6798350523 7130291565 505796064,
--R    0.7220436105 6787543524 0299679644, 0.2600312360 5480956171 3740181192,
--R    0.0801049430 8173750223 9474288923 7, 0.0215140366 3976333754 8055248300 5,
--R    0.0051162077 8993033120 6219689108 94,
--R    0.0010909328 6100739135 6050661990 14,
--R    0.0002107415 3202393891 6318348675 226,
--R    0.0000371990 4516651888 5709594081 5956,
--R    0.0000060434 9163712387 8757047670 32866,
--R    0.9092954273 9626095264 9596541772 E -6,
--R    0.1273805160 6592647886 5567184969 E -6,
--R    0.1669185748 4109890739 0896143814 E -7,
--R    0.2054417026 4010479254 7612484551 E -8,
--R    0.2383584444 4668176591 4052321417 E -9,
--R    0.2615386378 8854429666 9068664148 E -10,
--R    0.2721858622 8541670644 6550268995 E -11,
--R    0.2693750031 9835792992 5326427442 E -12,
--R    0.2541220946 7072635546 7884089307 E -13,
--R    0.2290130406 8650370941 8510620516 E -14,
--R    0.1975465739 0746229940 1057650412 E -15,
--R    0.1634024551 9289317406 8635419984 E -16,
--R    0.1298235437 0796376099 1961293204 E -17,
--R    0.9922587925 0737105964 4632581302 E -19,
--R    0.7306252806 7221032944 7230880087 E -20,
--R    0.5189676834 6043451272 0780080019 E -21,
--R    0.3560409454 0997068112 8043162227 E -22,
--R    0.2361979432 5793864237 0187203948 E -23,
--R    0.1516837767 7214529754 9624516819 E -24,
--R    0.9439089722 2448744292 5310405245 E -26,
--R    0.5697227559 5036921198 9581737831 E -27,
--R    0.3338333627 7954330315 6597939562 E -28,
--R    0.1900626012 8161914852 6680482237 E -29]
--R                                                             Type: List Float
--E 6

--S 7 of 20
[[-4.0,0.491822344607818096479962798267,_
  Ei3(-4.0),Ei3(-4.0)-0.491822344607818096479962798267],_
[-3.5,0.524842506644128356918258753311,_
  Ei3(-3.5),Ei3(-3.5)-0.524842506644128356918258753311],_
[-3.0,0.562958778221279863138086024270,_
  Ei3(-3.0),Ei3(-3.0)-0.562958778221279863138086024270],_
[-2.5,0.607368525858383064514266925640,_
  Ei3(-2.5),Ei3(-2.5)-0.607368525858383064514266925640],_
[-2.0,0.659631678084769644795492023380,_
  Ei3(-2.0),Ei3(-2.0)-0.659631678084769644795492023380],_
[-1.5,0.721800236944219929657623030310,_
  Ei3(-1.5),Ei3(-1.5)-0.721800236944219929657623030310],_
[-1.0,0.796599599297053134283675865540,_
  Ei3(-1.0),Ei3(-1.0)-0.796599599297053134283675865540],_
[-0.5,0.887684158235496725872151815870,_
  Ei3(-0.5),Ei3(-0.5)-0.887684158235496725872151815870],_
[0.0,1.00000000000000000000000000000,_
  Ei3(0.0),Ei3(0.0)-1.00000000000000000000000000000],_
[0.5,1.14030284104317205746248768807,_
  Ei3(0.5),Ei3(0.5)-1.14030284104317205746248768807],_
[1.0,1.31790215145440389486000884424,_
  Ei3(1.0),Ei3(1.0)-1.31790215145440389486000884424],_
[1.5,1.54573645074673373024859074039,_
  Ei3(1.5),Ei3(1.5)-1.54573645074673373024859074039],_
[2.0,1.84193575527020599667788045934,_
  Ei3(2.0),Ei3(2.0)-1.84193575527020599667788045934],_
[2.5,2.23210379912116511445340506423,_
  Ei3(2.5),Ei3(2.5)-2.23210379912116511445340506423],_
[3.0,2.75266820568525800200219289740,_
  Ei3(3.0),Ei3(3.0)-2.75266820568525800200219289740],_
[3.5,3.45582153193012412437300898811,_
  Ei3(3.5),Ei3(3.5)-3.45582153193012412437300898811],_
[4.0,4.41684111100869913580118598668,_
  Ei3(4.0),Ei3(4.0)-4.41684111100869913580118598668]]
 

   (8)
   [[- 4.,0.4918223446078181,0.49182234460781815,5.5511151231257827E-17],
    [- 3.5,0.52484250664412835,0.52484250664412835,0.],
    [- 3.,0.56295877822127982,0.56295877822128015,3.3306690738754696E-16],
    [- 2.5,0.60736852585838297,0.60736852585838341,4.4408920985006262E-16],
    [- 2.,0.65963167808476963,0.65963167808476986,2.2204460492503131E-16],
    [- 1.5,0.72180023694421991,0.72180023694422035,4.4408920985006262E-16],
    [- 1.,0.79659959929705315,0.79659959929705304,- 1.1102230246251565E-16],
    [- 0.5,0.88768415823549662,0.88768415823549707,4.4408920985006262E-16],
    [0.,1.,1.,0.],
    [0.5,1.1403028410431721,1.1403028410431715,- 6.6613381477509392E-16],
    [1.,1.3179021514544038,1.3179021514544034,- 4.4408920985006262E-16],
    [1.5,1.5457364507467337,1.5457364507467335,- 2.2204460492503131E-16],
    [2.,1.8419357552702058,1.8419357552702071,1.3322676295501878E-15],
    [2.5,2.2321037991211652,2.2321037991211647,- 4.4408920985006262E-16],
    [3.,2.7526682056852581,2.7526682056852585,4.4408920985006262E-16],
    [3.5,3.4558215319301242,3.4558215319301238,- 4.4408920985006262E-16],
    [4.,4.4168411110086989,4.4168411110087007,1.7763568394002505E-15]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (8)
--R   [[- 4.,0.4918223446078181,0.49182234460781826,1.6653345369377348E-16],
--R    [- 3.5,0.52484250664412835,0.52484250664412835,0.],
--R    [- 3.,0.56295877822127982,0.56295877822128015,3.3306690738754696E-16],
--R    [- 2.5,0.60736852585838308,0.60736852585838341,3.3306690738754696E-16],
--R    [- 2.,0.65963167808476963,0.65963167808476975,1.1102230246251565E-16],
--R    [- 1.5,0.72180023694421991,0.72180023694422013,2.2204460492503131E-16],
--R    [- 1.,0.79659959929705315,0.79659959929705293,- 2.2204460492503131E-16],
--R    [- 0.5,0.88768415823549673,0.88768415823549696,2.2204460492503131E-16],
--R    [0.,1.,1.,0.],
--R    [0.5,1.1403028410431721,1.1403028410431715,- 6.6613381477509392E-16],
--R    [1.,1.3179021514544038,1.3179021514544034,- 4.4408920985006262E-16],
--R    [1.5,1.5457364507467337,1.5457364507467335,- 2.2204460492503131E-16],
--R    [2.,1.841935755270206,1.8419357552702071,1.1102230246251565E-15],
--R    [2.5,2.2321037991211652,2.2321037991211647,- 4.4408920985006262E-16],
--R    [3.,2.7526682056852581,2.7526682056852589,8.8817841970012523E-16],
--R    [3.5,3.4558215319301242,3.4558215319301238,- 4.4408920985006262E-16],
--R    [4.,4.4168411110086989,4.4168411110087007,1.7763568394002505E-15]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 7

--S 8 of 20
dChebyshev:=[_
 0.245513353878129528673420457043E1,_
-0.162438379130376524396002276856E0,_
 0.449575308093572641480785417193E-01,_
-0.674157867998922998848718835050E-02,_
-0.130669714280329428051599341387E-02,_
 0.138108314600072576020202089820E-02,_
-0.585022879015965798687368242394E-03,_
 0.174929934107891970038740976432E-03,_
-0.404728149905293035522869333800E-04,_
 0.721710241217099750035752600049E-05,_
-0.861277697019867752414815450193E-06,_
-0.251447529653225597779084739054E-09,_ -- E-06? or wrong place?
 0.379474713820149510814074505574E-07,_
-0.144211796952119806160265640172E-07,_
 0.393504929597610131087190848042E-08,_
-0.928468940106331753047289210353E-09,_
 0.203178956800654613366090995698E-09,_
-0.429249850499236831427918026902E-10,_
 0.899264717778123935268001544182E-11,_
-0.190086911841210975242396635722E-11,_
 0.409219891222373834526121178338E-12,_
-0.899925343729319019825435824585E-13,_
 0.201965467082426383354948543451E-13,_
-0.461293026138308207194950531726E-14,_
 0.106902307293863695668857256409E-14,_
-0.250703007057007295692572254042E-15,_
 0.593732250379155160706073763509E-16,_
-0.141773458243766252344732005648E-16,_
 0.340920375436080893426806402093E-17,_
-0.824829026950549379288702529656E-18,_
 0.200636971262144231398824095937E-18,_
-0.490385166796742224403498152027E-19,_
 0.120373448234833217166664609324E-19,_
-0.296628244714136825381453572575E-20,_
 0.733551238428807599242142328436E-21,_
-0.181992414290851127344263485604E-21,_
 0.452862937429576060217359526404E-22,_
-0.112998004375060961338906717853E-22,_
 0.282668125129011656923764408445E-23,_
-0.708771797716904961666732640699E-24,_
 0.178110452401870951534401530034E-24,_
-0.448500407661896357312006142358E-25,_
 0.113154029257547662245053090840E-25,_
-0.285995789977932163790414326136E-26,_
 0.724077580692267361758172726753E-27,_
-0.183613223412577898050666710105E-27,_
 0.466312873522730486582600122073E-28,_
-0.118595958891902887946724005478E-28,_
 0.302029059055671310731137614875E-29,_
-0.770165054816636606098827057102E-30]
 

   (9)
   [2.4551335387 8129528673 420457043, - 0.1624383791 3037652439 6002276856,
    0.0449575308 0935726414 8078541719 3,
    - 0.0067415786 7998922998 8487188350 5,
    - 0.0013066971 4280329428 0515993413 87,
    0.0013810831 4600072576 0202020898 2,
    - 0.0005850228 7901596579 8687368242 394,
    0.0001749299 3410789197 0038740976 432,
    - 0.0000404728 1499052930 3552286933 38,
    0.0000072171 0241217099 7500357526 00049,
    - 0.8612776970 1986775241 4815450193 E -6,
    - 0.2514475296 5322559777 9084739054 E -9,
    0.3794747138 2014951081 4074505574 E -7,
    - 0.1442117969 5211980616 0265640172 E -7,
    0.3935049295 9761013108 7190848042 E -8,
    - 0.9284689401 0633175304 7289210353 E -9,
    0.2031789568 0065461336 6090995698 E -9,
    - 0.4292498504 9923683142 7918026902 E -10,
    0.8992647177 7812393526 8001544182 E -11,
    - 0.1900869118 4121097524 2396635722 E -11,
    0.4092198912 2237383452 6121178338 E -12,
    - 0.8999253437 2931901982 5435824585 E -13,
    0.2019654670 8242638335 4948543451 E -13,
    - 0.4612930261 3830820719 4950531726 E -14,
    0.1069023072 9386369566 8857256409 E -14,
    - 0.2507030070 5700729569 2572254042 E -15,
    0.5937322503 7915516070 6073763509 E -16,
    - 0.1417734582 4376625234 4732005648 E -16,
    0.3409203754 3608089342 6806402093 E -17,
    - 0.8248290269 5054937928 8702529656 E -18,
    0.2006369712 6214423139 8824095937 E -18,
    - 0.4903851667 9674222440 3498152027 E -19,
    0.1203734482 3483321716 6664609324 E -19,
    - 0.2966282447 1413682538 1453572575 E -20,
    0.7335512384 2880759924 2142328436 E -21,
    - 0.1819924142 9085112734 4263485604 E -21,
    0.4528629374 2957606021 7359526404 E -22,
    - 0.1129980043 7506096133 8906717853 E -22,
    0.2826681251 2901165692 3764408445 E -23,
    - 0.7087717977 1690496166 6732640699 E -24,
    0.1781104524 0187095153 4401530034 E -24,
    - 0.4485004076 6189635731 2006142358 E -25,
    0.1131540292 5754766224 505309084 E -25,
    - 0.2859957899 7793216379 0414326136 E -26,
    0.7240775806 9226736175 8172726753 E -27,
    - 0.1836132234 1257789805 0666710105 E -27,
    0.4663128735 2273048658 2600122073 E -28,
    - 0.1185959588 9190288794 6724005478 E -28,
    0.3020290590 5567131073 1137614875 E -29,
    - 0.7701650548 1663660609 8827057102 E -30]
                                                             Type: List Float
--R 
--R
--R   (9)
--R   [2.4551335387 8129528673 420457043, - 0.1624383791 3037652439 6002276856,
--R    0.0449575308 0935726414 8078541719 3,
--R    - 0.0067415786 7998922998 8487188350 5,
--R    - 0.0013066971 4280329428 0515993413 87,
--R    0.0013810831 4600072576 0202020898 2,
--R    - 0.0005850228 7901596579 8687368242 394,
--R    0.0001749299 3410789197 0038740976 432,
--R    - 0.0000404728 1499052930 3552286933 38,
--R    0.0000072171 0241217099 7500357526 00049,
--R    - 0.8612776970 1986775241 4815450193 E -6,
--R    - 0.2514475296 5322559777 9084739054 E -9,
--R    0.3794747138 2014951081 4074505574 E -7,
--R    - 0.1442117969 5211980616 0265640172 E -7,
--R    0.3935049295 9761013108 7190848042 E -8,
--R    - 0.9284689401 0633175304 7289210353 E -9,
--R    0.2031789568 0065461336 6090995698 E -9,
--R    - 0.4292498504 9923683142 7918026902 E -10,
--R    0.8992647177 7812393526 8001544182 E -11,
--R    - 0.1900869118 4121097524 2396635722 E -11,
--R    0.4092198912 2237383452 6121178338 E -12,
--R    - 0.8999253437 2931901982 5435824585 E -13,
--R    0.2019654670 8242638335 4948543451 E -13,
--R    - 0.4612930261 3830820719 4950531726 E -14,
--R    0.1069023072 9386369566 8857256409 E -14,
--R    - 0.2507030070 5700729569 2572254042 E -15,
--R    0.5937322503 7915516070 6073763509 E -16,
--R    - 0.1417734582 4376625234 4732005648 E -16,
--R    0.3409203754 3608089342 6806402093 E -17,
--R    - 0.8248290269 5054937928 8702529656 E -18,
--R    0.2006369712 6214423139 8824095937 E -18,
--R    - 0.4903851667 9674222440 3498152027 E -19,
--R    0.1203734482 3483321716 6664609324 E -19,
--R    - 0.2966282447 1413682538 1453572575 E -20,
--R    0.7335512384 2880759924 2142328436 E -21,
--R    - 0.1819924142 9085112734 4263485604 E -21,
--R    0.4528629374 2957606021 7359526404 E -22,
--R    - 0.1129980043 7506096133 8906717853 E -22,
--R    0.2826681251 2901165692 3764408445 E -23,
--R    - 0.7087717977 1690496166 6732640699 E -24,
--R    0.1781104524 0187095153 4401530034 E -24,
--R    - 0.4485004076 6189635731 2006142358 E -25,
--R    0.1131540292 5754766224 505309084 E -25,
--R    - 0.2859957899 7793216379 0414326136 E -26,
--R    0.7240775806 9226736175 8172726753 E -27,
--R    - 0.1836132234 1257789805 0666710105 E -27,
--R    0.4663128735 2273048658 2600122073 E -28,
--R    - 0.1185959588 9190288794 6724005478 E -28,
--R    0.3020290590 5567131073 1137614875 E -29,
--R    - 0.7701650548 1663660609 8827057102 E -30]
--R                                                             Type: List Float
--E 8

--S 9 of 20
[[4.0,1.43820803145448278470968670330,_
  Ei4(4.0),Ei4(4.0)-1.43820803145448278470968670330],_
[4.5,1.39641902962974607100674523183,_
  Ei4(4.5), Ei4(4.5)-1.39641902962974607100674523183],_
[5.0,1.35383127745528597790189174047,_
  Ei4(5.0),Ei4(5.0)-1.35383127745528597790189174047],_
[5.5,1.31414356574211924541219816991,_
  Ei4(5.5),Ei4(5.5)-1.31414356574211924541219816991],_
[6.0,1.27888386048956161892314099578,_
  Ei4(6.0),Ei4(6.0)-1.27888386048956161892314099578],_
[6.5,1.24839115500170148640741941387,_
  Ei4(6.5),Ei4(6.5)-1.24839115500170148640741941387],_
[7.0,1.22240805236053105903656846622,_
  Ei4(7.0),Ei4(7.0)-1.22240805236053105903656846622],_
[7.5,1.20042149959963078643879158950,_
  Ei4(7.5),Ei4(7.5)-1.20042149959963078643879158950],_
[8.0,1.18184798698720797317739362644,_
  Ei4(8.0),Ei4(8.0)-1.18184798698720797317739362644],_
[8.5,1.16612652581174849439918142965,_
  Ei4(8.5),Ei4(8.5)-1.16612652581174849439918142965],_
[9.0,1.15275920870892481322396814952,_
  Ei4(9.0),Ei4(9.0)-1.15275920870892481322396814952],_
[9.5,1.14132347595262420155338560641,_
  Ei4(9.5),Ei4(9.5)-1.14132347595262420155338560641],_
[10.0,1.13147020473410778034051681355,_
  Ei4(10.0),Ei4(10.0)-1.13147020473410778034051681355],_
[10.5,1.12291557001776060642888630755,_
  Ei4(10.5),Ei4(10.5)-1.12291557001776060642888630755],_
[11.0,1.11543093899803844164779434229,_
  Ei4(11.0),Ei4(11.0)-1.11543093899803844164779434229],_
[11.5,1.10883292630507730586855234934,_
  Ei4(11.5),Ei4(11.5)-1.10883292630507730586855234934],_
[12.0,1.10297454490675907267241234953,_
  Ei4(12.0),Ei4(12.0)-1.10297454490675907267241234953]]
 

   (10)
   [[4.,1.4382080314544827,1.4382080314544827,0.],
    [4.5,1.3964190296297461,1.3964190296297465,4.4408920985006262E-16],
    [5.,1.3538312774552859,1.3538312774552856,- 2.2204460492503131E-16],
    [5.5,1.3141435657421192,1.3141435657421192,0.],
    [6.,1.2788838604895616,1.2788838604895618,2.2204460492503131E-16],
    [6.5,1.2483911550017015,1.2483911550017011,- 4.4408920985006262E-16],
    [7.,1.222408052360531,1.222408052360531,0.],
    [7.5,1.2004214995996307,1.2004214995996305,- 2.2204460492503131E-16],
    [8.,1.1818479869872078,1.1818479869872081,2.2204460492503131E-16],
    [8.5,1.1661265258117486,1.1661265258117477,- 8.8817841970012523E-16],
    [9.,1.1527592087089249,1.1527592087089251,2.2204460492503131E-16],
    [9.5,1.1413234759526243,1.1413234759526236,- 6.6613381477509392E-16],
    [10.,1.1314702047341076,1.1314702047341079,2.2204460492503131E-16],
    [10.5,1.1229155700177604,1.1229155700177604,0.],
    [11.,1.1154309389980384,1.115430938998039,6.6613381477509392E-16],
    [11.5,1.1088329263050771,1.1088329263050771,0.],
    [12.,1.1029745449067589,1.1029745449067592,2.2204460492503131E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (10)
--R   [[4.,1.4382080314544827,1.4382080314544827,0.],
--R    [4.5,1.3964190296297461,1.3964190296297465,4.4408920985006262E-16],
--R    [5.,1.3538312774552861,1.3538312774552856,- 4.4408920985006262E-16],
--R    [5.5,1.3141435657421192,1.314143565742119,- 2.2204460492503131E-16],
--R    [6.,1.2788838604895616,1.2788838604895618,2.2204460492503131E-16],
--R    [6.5,1.2483911550017015,1.2483911550017011,- 4.4408920985006262E-16],
--R    [7.,1.222408052360531,1.222408052360531,0.],
--R    [7.5,1.2004214995996307,1.2004214995996305,- 2.2204460492503131E-16],
--R    [8.,1.1818479869872081,1.1818479869872081,0.],
--R    [8.5,1.1661265258117486,1.1661265258117477,- 8.8817841970012523E-16],
--R    [9.,1.1527592087089249,1.1527592087089251,2.2204460492503131E-16],
--R    [9.5,1.1413234759526243,1.1413234759526236,- 6.6613381477509392E-16],
--R    [10.,1.1314702047341079,1.1314702047341079,0.],
--R    [10.5,1.1229155700177607,1.1229155700177604,- 2.2204460492503131E-16],
--R    [11.,1.1154309389980384,1.115430938998039,6.6613381477509392E-16],
--R    [11.5,1.1088329263050773,1.1088329263050771,- 2.2204460492503131E-16],
--R    [12.,1.1029745449067592,1.1029745449067592,0.]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 9

--S 10 of 20
eChebyshev:=[_
 0.211702864043698668329789991614E1,_
-0.320423727375485794990618303177E-01,_
 0.889173207735316835890182400335E-02,_
-0.250795280518929937088352442063E-02,_
 0.720278946595987548875760902487E-03,_
-0.210349005850113053423531441256E-03,_
 0.620573231827693216588857730842E-04,_
-0.182656674981670265449155689733E-04,_
 0.527065157528936375807788296811E-05,_ --? 7560 or 7580?
-0.145966654761994575323066719367E-05,_
 0.378171997358963671980484193981E-06,_
-0.884258128284071920077971589012E-07,_
 0.174174919853839361377350309156E-07,_
-0.231351774704369063506474480152E-08,_
-0.122860981918086238832104835230E-09,_
 0.234996623632286370478311381926E-09,_
-0.110071940102726287690738963049E-09,_
 0.384827515786120711149705563369E-10,_
-0.114844096749001589658439301603E-10,_
 0.305687629308852082630893626200E-11,_
-0.738827872928473566454163131431E-12,_
 0.163093309416594110564148013749E-12,_
-0.327698937331271249657111774748E-13,_
 0.589811434707131961711164283918E-14,_
-0.909970763595649204643554720718E-15,_
 0.104075238266955386585405697541E-15,_
-0.180981542605922793227163355935E-17,_
-0.377709884256394773369593494417E-17,_
 0.158033290102847957136759888420E-17,_
-0.468429175880882730648433752957E-18,_
 0.119951685259198093707533478542E-18,_
-0.282359474984186517679349931117E-19,_
 0.629373806564463522627520190349E-20,_
-0.135241024950479756305343973177E-20,_
 0.283710605385529141590980426210E-21,_
-0.586700742024638323531936371015E-22,_
 0.120524763609547311112449686917E-22,_
-0.247444661699884869728416011246E-23,_
 0.509996258583785008142986465688E-24,_
-0.105838257877542240887093294733E-24,_
 0.221527624507048278566429387155E-25,_
-0.467927875475696258671852546231E-26,_
 0.997287299060207704824269828079E-27,_
-0.214326794521678804591907805844E-27,_
 0.464065690883818114338414829515E-28,_
-0.101144734921151390948461800780E-28,_
 0.221721152271007711093046878345E-29,_
-0.488489046924378553224914645512E-30]
 

   (11)
   [2.1170286404 3698668329 789991614, - 0.0320423727 3754857949 9061830317 7,
    0.0088917320 7735316835 8901824003 35,
    - 0.0025079528 0518929937 0883524420 63,
    0.0007202789 4659598754 8875760902 487,
    - 0.0002103490 0585011305 3423531441 256,
    0.0000620573 2318276932 1658885773 0842,
    - 0.0000182656 6749816702 6544915568 9733,
    0.0000052706 5157528936 3758077882 96811,
    - 0.0000014596 6654761994 5753230667 19367,
    0.3781719973 5896367198 0484193981 E -6,
    - 0.8842581282 8407192007 7971589012 E -7,
    0.1741749198 5383936137 7350309156 E -7,
    - 0.2313517747 0436906350 6474480152 E -8,
    - 0.1228609819 1808623883 210483523 E -9,
    0.2349966236 3228637047 8311381926 E -9,
    - 0.1100719401 0272628769 0738963049 E -9,
    0.3848275157 8612071114 9705563369 E -10,
    - 0.1148440967 4900158965 8439301603 E -10,
    0.3056876293 0885208263 08936262 E -11,
    - 0.7388278729 2847356645 4163131431 E -12,
    0.1630933094 1659411056 4148013749 E -12,
    - 0.3276989373 3127124965 7111774748 E -13,
    0.5898114347 0713196171 1164283918 E -14,
    - 0.9099707635 9564920464 3554720718 E -15,
    0.1040752382 6695538658 5405697541 E -15,
    - 0.1809815426 0592279322 7163355935 E -17,
    - 0.3777098842 5639477336 9593494417 E -17,
    0.1580332901 0284795713 675988842 E -17,
    - 0.4684291758 8088273064 8433752957 E -18,
    0.1199516852 5919809370 7533478542 E -18,
    - 0.2823594749 8418651767 9349931117 E -19,
    0.6293738065 6446352262 7520190349 E -20,
    - 0.1352410249 5047975630 5343973177 E -20,
    0.2837106053 8552914159 098042621 E -21,
    - 0.5867007420 2463832353 1936371015 E -22,
    0.1205247636 0954731111 2449686917 E -22,
    - 0.2474446616 9988486972 8416011246 E -23,
    0.5099962585 8378500814 2986465688 E -24,
    - 0.1058382578 7754224088 7093294733 E -24,
    0.2215276245 0704827856 6429387155 E -25,
    - 0.4679278754 7569625867 1852546231 E -26,
    0.9972872990 6020770482 4269828079 E -27,
    - 0.2143267945 2167880459 1907805844 E -27,
    0.4640656908 8381811433 8414829515 E -28,
    - 0.1011447349 2115139094 846180078 E -28,
    0.2217211522 7100771109 3046878345 E -29,
    - 0.4884890469 2437855322 4914645512 E -30]
                                                             Type: List Float
--R 
--R
--R   (11)
--R   [2.1170286404 3698668329 789991614, - 0.0320423727 3754857949 9061830317 7,
--R    0.0088917320 7735316835 8901824003 35,
--R    - 0.0025079528 0518929937 0883524420 63,
--R    0.0007202789 4659598754 8875760902 487,
--R    - 0.0002103490 0585011305 3423531441 256,
--R    0.0000620573 2318276932 1658885773 0842,
--R    - 0.0000182656 6749816702 6544915568 9733,
--R    0.0000052706 5157528936 3758077882 96811,
--R    - 0.0000014596 6654761994 5753230667 19367,
--R    0.3781719973 5896367198 0484193981 E -6,
--R    - 0.8842581282 8407192007 7971589012 E -7,
--R    0.1741749198 5383936137 7350309156 E -7,
--R    - 0.2313517747 0436906350 6474480152 E -8,
--R    - 0.1228609819 1808623883 210483523 E -9,
--R    0.2349966236 3228637047 8311381926 E -9,
--R    - 0.1100719401 0272628769 0738963049 E -9,
--R    0.3848275157 8612071114 9705563369 E -10,
--R    - 0.1148440967 4900158965 8439301603 E -10,
--R    0.3056876293 0885208263 08936262 E -11,
--R    - 0.7388278729 2847356645 4163131431 E -12,
--R    0.1630933094 1659411056 4148013749 E -12,
--R    - 0.3276989373 3127124965 7111774748 E -13,
--R    0.5898114347 0713196171 1164283918 E -14,
--R    - 0.9099707635 9564920464 3554720718 E -15,
--R    0.1040752382 6695538658 5405697541 E -15,
--R    - 0.1809815426 0592279322 7163355935 E -17,
--R    - 0.3777098842 5639477336 9593494417 E -17,
--R    0.1580332901 0284795713 675988842 E -17,
--R    - 0.4684291758 8088273064 8433752957 E -18,
--R    0.1199516852 5919809370 7533478542 E -18,
--R    - 0.2823594749 8418651767 9349931117 E -19,
--R    0.6293738065 6446352262 7520190349 E -20,
--R    - 0.1352410249 5047975630 5343973177 E -20,
--R    0.2837106053 8552914159 098042621 E -21,
--R    - 0.5867007420 2463832353 1936371015 E -22,
--R    0.1205247636 0954731111 2449686917 E -22,
--R    - 0.2474446616 9988486972 8416011246 E -23,
--R    0.5099962585 8378500814 2986465688 E -24,
--R    - 0.1058382578 7754224088 7093294733 E -24,
--R    0.2215276245 0704827856 6429387155 E -25,
--R    - 0.4679278754 7569625867 1852546231 E -26,
--R    0.9972872990 6020770482 4269828079 E -27,
--R    - 0.2143267945 2167880459 1907805844 E -27,
--R    0.4640656908 8381811433 8414829515 E -28,
--R    - 0.1011447349 2115139094 846180078 E -28,
--R    0.2217211522 7100771109 3046878345 E -29,
--R    - 0.4884890469 2437855322 4914645512 E -30]
--R                                                             Type: List Float
--E 10

--S 11 of 20
[[12.00,1.10297454490675907267241234952,_
  Ei5(12.00),Ei5(12.00)-1.10297454490675907267241234952],_
[13.25,1.09084489821547569266468614954,_
  Ei5(13.25),Ei5(13.25)-1.09084489821547569266468614954],_
[14.50,1.08135139573519128506346643795,_
  Ei5(14.50),Ei5(14.50)-1.08135139573519128506346643795],_
[15.75,1.07370138419975723712157900374,_
  Ei5(15.75),Ei5(15.75)-1.07370138419975723712157900374],_
[17.00,1.06739369195853783129572196197,_
  Ei5(17.00),Ei5(17.00)-1.06739369195853783129572196197],_
[18.25,1.06209660862215024268372647556,_
  Ei5(18.25),Ei5(18.25)-1.06209660862215024268372647556],_
[19.50,1.05758134215872503195393949410,_
  Ei5(19.50),Ei5(19.50)-1.05758134215872503195393949410],_
[20.75,1.05368445128940944082102194964,_
  Ei5(20.75),Ei5(20.75)-1.05368445128940944082102194964],_
[22.00,1.05028571968518979411780664532,_
  Ei5(22.00),Ei5(22.00)-1.05028571968518979411780664532],_
[23.25,1.04729455170532485811492365591,_
  Ei5(23.25),Ei5(23.25)-1.04729455170532485811492365591],_
[24.50,1.04464126790464363689761075289,_
  Ei5(24.50),Ei5(24.50)-1.04464126790464363689761075289],_
[25.75,1.04227133720232023885710928048,_
  Ei5(25.75),Ei5(25.75)-1.04227133720232023885710928048],_
[27.00,1.04014143832301043813713899754,_
  Ei5(27.00),Ei5(27.00)-1.04014143832301043813713899754],_
[28.25,1.03821670036014587680056548394,_
  Ei5(28.25),Ei5(28.25)-1.03821670036014587680056548394],_
[29.50,1.03646872629241184575154685419,_
  Ei5(29.50),Ei5(29.50)-1.03646872629241184575154685419],_
[30.75,1.03487414989647969472990938990,_
  Ei5(30.75),Ei5(30.75)-1.03487414989647969472990938990],_
[32.00,1.03341356421624104943493552567,_
  Ei5(32.00),Ei5(32.00)-1.03341356421624104943493552567]]
 

   (12)
   [[12.,1.1029745449067589,1.1029745449067585,- 4.4408920985006262E-16],
    [13.25,1.0908448982154755,1.090844898215475,- 4.4408920985006262E-16],
    [14.5,1.0813513957351912,1.0813513957351915,2.2204460492503131E-16],
    [15.75,1.0737013841997571,1.0737013841997574,2.2204460492503131E-16],
    [17.,1.0673936919585376,1.0673936919585385,8.8817841970012523E-16],
    [18.25,1.0620966086221502,1.0620966086221502,0.],
    [19.5,1.057581342158725,1.0575813421587252,2.2204460492503131E-16],
    [20.75,1.0536844512894095,1.0536844512894095,0.],
    [22.,1.0502857196851898,1.0502857196851898,0.],
    [23.25,1.0472945517053249,1.0472945517053245,- 4.4408920985006262E-16],
    [24.5,1.0446412679046437,1.0446412679046437,0.],
    [25.75,1.0422713372023202,1.04227133720232,- 2.2204460492503131E-16],
    [27.,1.0401414383230105,1.0401414383230101,- 4.4408920985006262E-16],
    [28.25,1.0382167003601457,1.0382167003601459,2.2204460492503131E-16],
    [29.5,1.0364687262924117,1.0364687262924113,- 4.4408920985006262E-16],
    [30.75,1.0348741498964795,1.0348741498964795,0.],
    [32.,1.033413564216241,1.0334135642162412,2.2204460492503131E-16]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (12)
--R   [[12.,1.1029745449067592,1.1029745449067585,- 6.6613381477509392E-16],
--R    [13.25,1.0908448982154757,1.090844898215475,- 6.6613381477509392E-16],
--R    [14.5,1.0813513957351912,1.0813513957351915,2.2204460492503131E-16],
--R    [15.75,1.0737013841997571,1.0737013841997574,2.2204460492503131E-16],
--R    [17.,1.0673936919585378,1.0673936919585385,6.6613381477509392E-16],
--R    [18.25,1.0620966086221502,1.0620966086221502,0.],
--R    [19.5,1.057581342158725,1.0575813421587252,2.2204460492503131E-16],
--R    [20.75,1.0536844512894095,1.0536844512894095,0.],
--R    [22.,1.0502857196851898,1.0502857196851898,0.],
--R    [23.25,1.0472945517053249,1.0472945517053245,- 4.4408920985006262E-16],
--R    [24.5,1.0446412679046437,1.0446412679046437,0.],
--R    [25.75,1.0422713372023202,1.04227133720232,- 2.2204460492503131E-16],
--R    [27.,1.0401414383230105,1.0401414383230101,- 4.4408920985006262E-16],
--R    [28.25,1.0382167003601459,1.0382167003601459,0.],
--R    [29.5,1.0364687262924119,1.0364687262924113,- 6.6613381477509392E-16],
--R    [30.75,1.0348741498964797,1.0348741498964795,- 2.2204460492503131E-16],
--R    [32.,1.033413564216241,1.0334135642162412,2.2204460492503131E-16]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 11


--S 12 of 20
fChebyshev:=[_
 0.203284394579616699087873844202E1,_
 0.166992045203136285147618434339E-01,_
 0.284528472436134680742489985325E-03,_
 0.756394435851620648948786693854E-05,_
 0.279897128945085915750484318090E-06,_
 0.135790182853453106952556392593E-07,_
 0.834359620204046925585610289412E-09,_
 0.637097172764024843827524337306E-10,_
 0.600724760881186123576083084850E-11,_
 0.702287617467977359075059216588E-12,_
 0.101830267370368769309667322152E-12,_
 0.176181290343088004040656741554E-13,_
 0.325082861423536069424072007647E-14,_
 0.507177002550581867881479300685E-15,_
 0.166517738704329429853520036957E-16,_
-0.316675389079751440072410018963E-16,_
-0.158840376366414151548423134074E-16,_
-0.417551325613801883089626455063E-17,_
-0.289234774970714188202868862358E-18,_
 0.280062590339660807289978777339E-18,_
 0.132293863953927089140532005364E-18,_
 0.180444744417730199585334811191E-19,_
-0.790538408652261656202021080364E-20,_
-0.443571136636957344718167314045E-20,_
-0.426410399497810261760579779746E-21,_
 0.392010176693714390725625388636E-21,_
 0.152737805134396364472804486402E-21,_
-0.102484952704949060786953149788E-22,_
-0.213490787477108937948904287231E-22,_
-0.323913947516023687614279789345E-23,_
 0.214218376229645970296249355934E-23,_
 0.823460941961899553169207838151E-24,_
-0.152465282962067210811495038147E-24,_
-0.137820828248824401290438126477E-24,_
 0.213131120142873706791513005998E-26,_
 0.201264965187132665859213006507E-25,_
 0.199553566205637402320607178286E-26,_
-0.279899581220179711426020884464E-26,_
-0.553451183050700250949784942560E-27,_
 0.388499542268455253129749000696E-27,_
 0.112130440723307012540043264712E-27,_
-0.556656828674459488057823816866E-28,_
-0.204548261246513576288865878722E-28,_
 0.845381406448938089437361193598E-29,_
 0.356575515120151526590791715785E-29,_
-0.138365242347797751810195772006E-29,_
-0.606214265320934505767865286306E-30]
 

   (13)
   [2.0328439457 9616699087 873844202, 0.0166992045 2031362851 4761843433 9,
    0.0002845284 7243613468 0742489985 325,
    0.0000075639 4435851620 6489487866 93854,
    0.2798971289 4508591575 048431809 E -6,
    0.1357901828 5345310695 2556392593 E -7,
    0.8343596202 0404692558 5610289412 E -9,
    0.6370971727 6402484382 7524337306 E -10,
    0.6007247608 8118612357 608308485 E -11,
    0.7022876174 6797735907 5059216588 E -12,
    0.1018302673 7036876930 9667322152 E -12,
    0.1761812903 4308800404 0656741554 E -13,
    0.3250828614 2353606942 4072007647 E -14,
    0.5071770025 5058186788 1479300685 E -15,
    0.1665177387 0432942985 3520036957 E -16,
    - 0.3166753890 7975144007 2410018963 E -16,
    - 0.1588403763 6641415154 8423134074 E -16,
    - 0.4175513256 1380188308 9626455063 E -17,
    - 0.2892347749 7071418820 2868862358 E -18,
    0.2800625903 3966080728 9978777339 E -18,
    0.1322938639 5392708914 0532005364 E -18,
    0.1804447444 1773019958 5334811191 E -19,
    - 0.7905384086 5226165620 2021080364 E -20,
    - 0.4435711366 3695734471 8167314045 E -20,
    - 0.4264103994 9781026176 0579779746 E -21,
    0.3920101766 9371439072 5625388636 E -21,
    0.1527378051 3439636447 2804486402 E -21,
    - 0.1024849527 0494906078 6953149788 E -22,
    - 0.2134907874 7710893794 8904287231 E -22,
    - 0.3239139475 1602368761 4279789345 E -23,
    0.2142183762 2964597029 6249355934 E -23,
    0.8234609419 6189955316 9207838151 E -24,
    - 0.1524652829 6206721081 1495038147 E -24,
    - 0.1378208282 4882440129 0438126477 E -24,
    0.2131311201 4287370679 1513005998 E -26,
    0.2012649651 8713266585 9213006507 E -25,
    0.1995535662 0563740232 0607178286 E -26,
    - 0.2798995812 2017971142 6020884464 E -26,
    - 0.5534511830 5070025094 978494256 E -27,
    0.3884995422 6845525312 9749000696 E -27,
    0.1121304407 2330701254 0043264712 E -27,
    - 0.5566568286 7445948805 7823816866 E -28,
    - 0.2045482612 4651357628 8865878722 E -28,
    0.8453814064 4893808943 7361193598 E -29,
    0.3565755151 2015152659 0791715785 E -29,
    - 0.1383652423 4779775181 0195772006 E -29,
    - 0.6062142653 2093450576 7865286306 E -30]
                                                             Type: List Float
--R 
--R
--R   (13)
--R   [2.0328439457 9616699087 873844202, 0.0166992045 2031362851 4761843433 9,
--R    0.0002845284 7243613468 0742489985 325,
--R    0.0000075639 4435851620 6489487866 93854,
--R    0.2798971289 4508591575 048431809 E -6,
--R    0.1357901828 5345310695 2556392593 E -7,
--R    0.8343596202 0404692558 5610289412 E -9,
--R    0.6370971727 6402484382 7524337306 E -10,
--R    0.6007247608 8118612357 608308485 E -11,
--R    0.7022876174 6797735907 5059216588 E -12,
--R    0.1018302673 7036876930 9667322152 E -12,
--R    0.1761812903 4308800404 0656741554 E -13,
--R    0.3250828614 2353606942 4072007647 E -14,
--R    0.5071770025 5058186788 1479300685 E -15,
--R    0.1665177387 0432942985 3520036957 E -16,
--R    - 0.3166753890 7975144007 2410018963 E -16,
--R    - 0.1588403763 6641415154 8423134074 E -16,
--R    - 0.4175513256 1380188308 9626455063 E -17,
--R    - 0.2892347749 7071418820 2868862358 E -18,
--R    0.2800625903 3966080728 9978777339 E -18,
--R    0.1322938639 5392708914 0532005364 E -18,
--R    0.1804447444 1773019958 5334811191 E -19,
--R    - 0.7905384086 5226165620 2021080364 E -20,
--R    - 0.4435711366 3695734471 8167314045 E -20,
--R    - 0.4264103994 9781026176 0579779746 E -21,
--R    0.3920101766 9371439072 5625388636 E -21,
--R    0.1527378051 3439636447 2804486402 E -21,
--R    - 0.1024849527 0494906078 6953149788 E -22,
--R    - 0.2134907874 7710893794 8904287231 E -22,
--R    - 0.3239139475 1602368761 4279789345 E -23,
--R    0.2142183762 2964597029 6249355934 E -23,
--R    0.8234609419 6189955316 9207838151 E -24,
--R    - 0.1524652829 6206721081 1495038147 E -24,
--R    - 0.1378208282 4882440129 0438126477 E -24,
--R    0.2131311201 4287370679 1513005998 E -26,
--R    0.2012649651 8713266585 9213006507 E -25,
--R    0.1995535662 0563740232 0607178286 E -26,
--R    - 0.2798995812 2017971142 6020884464 E -26,
--R    - 0.5534511830 5070025094 978494256 E -27,
--R    0.3884995422 6845525312 9749000696 E -27,
--R    0.1121304407 2330701254 0043264712 E -27,
--R    - 0.5566568286 7445948805 7823816866 E -28,
--R    - 0.2045482612 4651357628 8865878722 E -28,
--R    0.8453814064 4893808943 7361193598 E -29,
--R    0.3565755151 2015152659 0791715785 E -29,
--R    - 0.1383652423 4779775181 0195772006 E -29,
--R    - 0.6062142653 2093450576 7865286306 E -30]
--R                                                             Type: List Float
--E 12

--S 13 of 20
[[32,1.03341356421624104943493552567,_
  Ei6(32.0),Ei6(32.0)-1.03341356421624104943493552567],_
[34+2/15,1.03118521236465926355875784663,_
  Ei6(34.0+2/15),Ei6(34.0+2/15)-1.03118521236465926355875784663],_
[36+4/7,1.02897740410580800863378435059,_
  Ei6(36.0+4/7),Ei6(36.0+4/7)-1.02897740410580800863378435059],_
[39+5/13,1.02678968370902852450984510823,_
  Ei6(39.0+5/13),Ei6(39.0+5/13)-1.02678968370902852450984510823],_
[42+2/3,1.02462161468107839101187804247,_
  Ei6(42.0+2/3),Ei6(42.0+2/3)-1.02462161468107839101187804247],_
[46+6/11,1.02247277840542059591275364791,_
  Ei6(46.0+6/11),Ei6(46.0+6/11)-1.02247277840542059591275364791],_
[51+1/5,1.02034277293078377487217829808,_
  Ei6(51.0+1/5),Ei6(51.0+1/5)-1.02034277293078377487217829808],_
[56+8/9,1.01823121188483269682337017143,_
  Ei6(56.0+8/9),Ei6(56.0+8/9)-1.01823121188483269682337017143],_
[64,1.01613772349432532170357100831,_
  Ei6(64.0),Ei6(64.0)-1.01613772349432532170357100831],_
[73+1/7,1.01406194969697133145942329335,_
  Ei6(73.0+1/7),Ei6(73.0+1/7)-1.01406194969697133145942329335],_
[85+1/3,1.01200354533298848201864466702,_
  Ei6(85.0+1/3),Ei6(85.0+1/3)-1.01200354533298848201864466702],_
[102+2/5,1.00996217740644975574367545570,_
  Ei6(102.0+2/5),Ei6(102.0+2/5)-1.00996217740644975574367545570],_
[128,1.00793752440814018281776821694,_
  Ei6(128.0),Ei6(128.0)-1.00793752440814018281776821694],_
[170+2/3,1.00592927569292911294663030932,_
  Ei6(170.0+2/3),Ei6(170.0+2/3)-1.00592927569292911294663030932],_
[256,1.00393713090569862788009078297,_
  Ei6(256.0),Ei6(256.0)-1.00393713090569862788009078297],_
[512,1.00196079945071192531337468473,_
  Ei6(512.0),Ei6(512.0)-1.00196079945071192531337468473],_
[infinity(),1.00000000000000000000000000001,_
  Ei6(infinity()),Ei6(infinity())-1.00000000000000000000000000001]]
 

   (14)
   [[32.,1.033413564216241,1.0334135642162412,2.2204460492503131E-16],

      512
     [---, 1.0311852123 6465926355 875784663, 1.0311852123646588,
       15
      - 4.4408920985006262E-16]
     ,
     256
    [---,1.0289774041 0580800863 378435059,1.028977404105808,0.],
      7
     512
    [---,1.0267896837 0902852450 984510823,1.0267896837090285,0.],
      13

      128
     [---, 1.0246216146 8107839101 187804247, 1.0246216146810787,
       3
      4.4408920985006262E-16]
     ,
     512
    [---,1.0224727784 0542059591 275364791,1.0224727784054206,0.],
      11
     256
    [---,1.0203427729 3078377487 217829808,1.0203427729307837,0.],
      5

      512
     [---, 1.0182312118 8483269682 337017143, 1.0182312118848329,
       9
      2.2204460492503131E-16]
     ,
    [64.,1.0161377234943254,1.0161377234943252,- 2.2204460492503131E-16],
     512
    [---,1.0140619496 9697133145 942329335,1.0140619496969712,0.],
      7
     256
    [---,1.0120035453 3298848201 864466702,1.0120035453329885,0.],
      3

      512
     [---, 1.0099621774 0644975574 36754557, 1.0099621774064493,
       5
      - 4.4408920985006262E-16]
     ,
    [128.,1.0079375244081401,1.0079375244081401,0.],

      512
     [---, 1.0059292756 9292911294 663030932, 1.0059292756929286,
       3
      - 4.4408920985006262E-16]
     ,
    [256.,1.0039371309056986,1.0039371309056981,- 4.4408920985006262E-16],
    [512.,1.0019607994507118,1.0019607994507116,- 2.2204460492503131E-16],
    [infinity,1.,1.,0.]]
                                                          Type: List List Any
--R 
--R
--R   (14)
--R   [[32.,1.033413564216241,1.0334135642162412,2.2204460492503131E-16],
--R
--R      512
--R     [---, 1.0311852123 6465926355 875784663, 1.0311852123646588,
--R       15
--R      - 4.4408920985006262E-16]
--R     ,
--R     256
--R    [---,1.0289774041 0580800863 378435059,1.028977404105808,0.],
--R      7
--R     512
--R    [---,1.0267896837 0902852450 984510823,1.0267896837090285,0.],
--R      13
--R
--R      128
--R     [---, 1.0246216146 8107839101 187804247, 1.0246216146810787,
--R       3
--R      2.2204460492503131E-16]
--R     ,
--R     512
--R    [---,1.0224727784 0542059591 275364791,1.0224727784054206,0.],
--R      11
--R     256
--R    [---,1.0203427729 3078377487 217829808,1.0203427729307837,0.],
--R      5
--R
--R      512
--R     [---, 1.0182312118 8483269682 337017143, 1.0182312118848329,
--R       9
--R      2.2204460492503131E-16]
--R     ,
--R    [64.,1.0161377234943254,1.0161377234943252,- 2.2204460492503131E-16],
--R
--R      512
--R     [---, 1.0140619496 9697133145 942329335, 1.0140619496969712,
--R       7
--R      - 2.2204460492503131E-16]
--R     ,
--R     256
--R    [---,1.0120035453 3298848201 864466702,1.0120035453329885,0.],
--R      3
--R
--R      512
--R     [---, 1.0099621774 0644975574 36754557, 1.0099621774064493,
--R       5
--R      - 4.4408920985006262E-16]
--R     ,
--R    [128.,1.0079375244081401,1.0079375244081401,0.],
--R
--R      512
--R     [---, 1.0059292756 9292911294 663030932, 1.0059292756929286,
--R       3
--R      - 4.4408920985006262E-16]
--R     ,
--R    [256.,1.0039371309056986,1.0039371309056981,- 4.4408920985006262E-16],
--R    [512.,1.001960799450712,1.0019607994507116,- 4.4408920985006262E-16],
--R    [infinity,1.,1.,0.]]
--R                                                          Type: List List Any
--E 13

--S 14 of 20
h(x:DFLOAT):DFLOAT==
  x=0.0::DFLOAT => 1.0 
  y:DFLOAT:=retract(Ei(x))
  (y-log(x)-gamma)/x
 
   Function declaration h : DoubleFloat -> DoubleFloat has been added 
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration h : DoubleFloat -> DoubleFloat has been added 
--R      to workspace.
--R                                                                   Type: Void
--E 14

--S 15 of 20
[[0.00,1.000000000,h(0.00),h(0.00)-1.000000000],_
 [0.01,1.002505566,h(0.01),h(0.01)-1.002505566],_
 [0.02,1.005022306,h(0.02),h(0.02)-1.005022306],_
 [0.03,1.007550283,h(0.03),h(0.03)-1.007550283],_
 [0.04,1.010089560,h(0.04),h(0.04)-1.010089560],_
 [0.05,1.012640202,h(0.05),h(0.05)-1.012640202],_
 [0.06,1.015202272,h(0.06),h(0.06)-1.015202272],_
 [0.07,1.017775836,h(0.07),h(0.07)-1.017775836],_
 [0.08,1.020360958,h(0.08),h(0.08)-1.020360958],_
 [0.09,1.022957705,h(0.09),h(0.09)-1.022957705],_
 [0.10,1.025566141,h(0.10),h(0.10)-1.025566141],_
 [0.11,1.028186335,h(0.11),h(0.11)-1.028186335],_
 [0.12,1.030818352,h(0.12),h(0.12)-1.030818352],_
 [0.13,1.033462259,h(0.13),h(0.13)-1.033462259],_
 [0.14,1.036118125,h(0.14),h(0.14)-1.036118125],_
 [0.15,1.038786018,h(0.15),h(0.15)-1.038786018],_
 [0.16,1.041466006,h(0.16),h(0.16)-1.041466006],_
 [0.17,1.044158158,h(0.17),h(0.17)-1.044158158],_
 [0.18,1.046862544,h(0.18),h(0.18)-1.046862544],_
 [0.19,1.049579234,h(0.19),h(0.19)-1.049579234],_
 [0.20,1.052308298,h(0.20),h(0.20)-1.052308298],_
 [0.21,1.055049807,h(0.21),h(0.21)-1.055049807],_
 [0.22,1.057803833,h(0.22),h(0.22)-1.057803833],_
 [0.23,1.060570446,h(0.23),h(0.23)-1.060570446],_
 [0.24,1.063349719,h(0.24),h(0.24)-1.063349719],_
 [0.25,1.066141726,h(0.25),h(0.25)-1.066141726],_
 [0.26,1.068946539,h(0.26),h(0.26)-1.068946539],_
 [0.27,1.071764232,h(0.27),h(0.27)-1.071764232],_
 [0.28,1.074594879,h(0.28),h(0.28)-1.074594879],_
 [0.29,1.077438555,h(0.29),h(0.29)-1.077438555],_
 [0.30,1.080295334,h(0.30),h(0.30)-1.080295334],_
 [0.31,1.083165293,h(0.31),h(0.31)-1.083165293],_
 [0.32,1.086048507,h(0.32),h(0.32)-1.086048507],_
 [0.33,1.088945053,h(0.33),h(0.33)-1.088945053],_
 [0.34,1.091855008,h(0.34),h(0.34)-1.091855008],_
 [0.35,1.094778451,h(0.35),h(0.35)-1.094778451],_
 [0.36,1.097715458,h(0.36),h(0.36)-1.097715458],_
 [0.37,1.100666108,h(0.37),h(0.37)-1.100666108],_
 [0.38,1.103630481,h(0.38),h(0.38)-1.103630481],_
 [0.39,1.106608656,h(0.39),h(0.39)-1.106608656],_
 [0.40,1.109600714,h(0.40),h(0.40)-1.109600714],_
 [0.41,1.112606735,h(0.41),h(0.41)-1.112606735],_
 [0.42,1.115626800,h(0.42),h(0.42)-1.115626800],_
 [0.43,1.118660991,h(0.43),h(0.43)-1.118660991],_
 [0.44,1.121709391,h(0.44),h(0.44)-1.121709391],_
 [0.45,1.124772082,h(0.45),h(0.45)-1.124772082],_
 [0.46,1.127849147,h(0.46),h(0.46)-1.127849147],_
 [0.47,1.130940671,h(0.47),h(0.47)-1.130940671],_
 [0.48,1.134046738,h(0.48),h(0.48)-1.134046738],_
 [0.49,1.137167432,h(0.49),h(0.49)-1.137167432],_
 [0.50,1.140302841,h(0.50),h(0.50)-1.140302841]]
 
   Compiling function h with type DoubleFloat -> DoubleFloat 

   (16)
   [[0.,1.,1.,0.],

     [9.9999999999999985E-3, 1.002505566, 1.0025055659888873,
      - 1.1112666342683042E-11]
     ,

     [1.9999999999999997E-2, 1.0050223059999999, 1.0050223058229559,
      - 1.7704393506789984E-10]
     ,

     [2.9999999999999999E-2, 1.007550283, 1.0075502826056404,
      - 3.9435965604184275E-10]
     ,

     [3.9999999999999994E-2, 1.0100895599999999, 1.0100895598460393,
      - 1.5396062202910343E-10]
     ,

     [5.0000000000000003E-2, 1.012640202, 1.0126402014616698,
      - 5.383302692507641E-10]
     ,

     [5.9999999999999998E-2, 1.0152022719999998, 1.0152022717813347,
      - 2.1866508603807233E-10]
     ,

     [7.0000000000000007E-2, 1.017775836, 1.0177758355479658,
      - 4.5203418785888516E-10]
     ,

     [7.9999999999999988E-2, 1.0203609579999999, 1.020360957921568,
      - 7.8431927619249109E-11]
     ,

     [8.9999999999999997E-2, 1.0229577050000001, 1.0229577044820883,
      - 5.17911713515673E-10]
     ,

     [0.10000000000000001, 1.0255661410000001, 1.0255661412323613,
      2.3236124135905811E-10]
     ,

     [0.10999999999999999, 1.028186335, 1.0281863346010789,
      - 3.9892111836081767E-10]
     ,
    [0.12,1.0308183519999998,1.0308183514457614,- 5.5423843292601305E-10],
    [0.13,1.033462259,1.0334622590557532,5.5753179850626111E-11],

     [0.14000000000000001, 1.0361181249999998, 1.0361181251552545,
      1.5525469798660652E-10]
     ,

     [0.14999999999999999, 1.0387860179999999, 1.038786017906365,
      - 9.3634877629256152E-11]
     ,

     [0.15999999999999998, 1.0414660059999998, 1.0414660059121479,
      - 8.7851947938588637E-11]
     ,

     [0.16999999999999998, 1.0441581579999999, 1.0441581582197252,
      2.1972534902658936E-10]
     ,

     [0.17999999999999999, 1.0468625439999999, 1.0468625443233892,
      3.233893153264944E-10]
     ,
    [0.19,1.0495792339999999,1.0495792341677359,1.6773604727404745E-10],

     [0.20000000000000001, 1.0523082979999998, 1.0523082981508358,
      1.5083601034859839E-10]
     ,

     [0.20999999999999999, 1.0550498070000001, 1.055049807127405,
      1.2740497545848939E-10]
     ,

     [0.21999999999999997, 1.0578038329999999, 1.0578038324120198,
      - 5.8798010904581588E-10]
     ,

     [0.22999999999999998, 1.0605704459999998, 1.0605704457823433,
      - 2.1765655944250284E-10]
     ,

     [0.23999999999999999, 1.0633497190000001, 1.0633497194823853,
      4.8238524286148277E-10]
     ,
    [0.25,1.0661417259999999,1.0661417262257764,2.2577650860000631E-10],

     [0.26000000000000001, 1.0689465389999999, 1.0689465391990731,
      1.9907320236711712E-10]
     ,
    [0.27000000000000002,1.071764232,1.0717642320650862,6.5086158684835027E-11],

     [0.28000000000000003, 1.0745948789999999, 1.0745948789662336,
      - 3.3766323070949511E-11]
     ,

     [0.28999999999999998, 1.0774385550000001, 1.0774385545279166,
      - 4.7208348341598594E-10]
     ,

     [0.29999999999999999, 1.0802953340000001, 1.0802953338619241,
      - 1.3807599508197654E-10]
     ,
    [0.31,1.083165293,1.0831652925698596,- 4.3014036776867215E-10],

     [0.31999999999999995, 1.0860485070000001, 1.0860485067465937,
      - 2.5340640696924766E-10]
     ,

     [0.32999999999999996, 1.088945053, 1.0889450529837439,
      - 1.6256107571166467E-11]
     ,
    [0.33999999999999997,1.091855008,1.0918550083731846,3.7318459433777207E-10],

     [0.34999999999999998, 1.0947784509999998, 1.0947784505105673,
      - 4.8943249453259341E-10]
     ,

     [0.35999999999999999, 1.0977154579999999, 1.0977154574988892,
      - 5.0111070848402051E-10]
     ,
    [0.37,1.100666108,1.1006661079520708,- 4.7929216151487708E-11],
    [0.38,1.1036304809999999,1.103630480998568,- 1.4319656571615269E-12],

     [0.39000000000000001, 1.1066086559999999, 1.106608656285011,
      2.8501112581125199E-10]
     ,

     [0.40000000000000002, 1.1096007139999999, 1.109600713979868,
      - 2.0131896150132889E-11]
     ,

     [0.40999999999999998, 1.112606735, 1.1126067347771351,
      - 2.2286483769562437E-10]
     ,

     [0.41999999999999998, 1.1156267999999998, 1.1156267999000617,
      - 9.9938057829263016E-11]
     ,
    [0.42999999999999999,1.118660991,1.1186609911048897,1.0488965251909121E-10],

     [0.43999999999999995, 1.121709391, 1.1217093906846378,
      - 3.1536218081384959E-10]
     ,

     [0.44999999999999996, 1.1247720819999998, 1.1247720814728979,
      - 5.2710191766891512E-10]
     ,

     [0.45999999999999996, 1.1278491470000001, 1.1278491468476703,
      - 1.5232970440592908E-10]
     ,

     [0.46999999999999997, 1.1309406709999998, 1.1309406707352236,
      - 2.6477620096443388E-10]
     ,

     [0.47999999999999998, 1.1340467379999999, 1.1340467376139862,
      - 3.860136654765256E-10]
     ,
    [0.48999999999999999,1.137167432,1.1371674325184591,5.184590534668132E-10],
    [0.5,1.140302841,1.1403028410431713,4.3171244357154137E-11]]
                                                  Type: List List DoubleFloat
--R 
--R   Compiling function h with type DoubleFloat -> DoubleFloat 
--R
--R   (16)
--R   [[0.,1.,1.,0.],
--R    [1.0E-2,1.002505566,1.002505565988876,- 1.1123990617534218E-11],
--R    [2.0E-2,1.0050223060000001,1.0050223058229502,- 1.7704993027223281E-10],
--R
--R     [2.9999999999999999E-2, 1.007550283, 1.0075502826056368,
--R      - 3.9436320875552155E-10]
--R     ,
--R
--R     [4.0000000000000001E-2, 1.0100895599999999, 1.0100895598460362,
--R      - 1.5396373065357238E-10]
--R     ,
--R
--R     [5.0000000000000003E-2, 1.012640202, 1.0126402014616676,
--R      - 5.3833248969681335E-10]
--R     ,
--R
--R     [5.9999999999999998E-2, 1.015202272, 1.0152022717813329,
--R      - 2.1866708443951666E-10]
--R     ,
--R
--R     [7.0000000000000007E-2, 1.017775836, 1.0177758355479642,
--R      - 4.5203574217111964E-10]
--R     ,
--R
--R     [8.0000000000000002E-2, 1.0203609579999999, 1.0203609579215664,
--R      - 7.8433481931483584E-11]
--R     ,
--R
--R     [8.9999999999999997E-2, 1.0229577050000001, 1.0229577044820872,
--R      - 5.1791282373869763E-10]
--R     ,
--R
--R     [0.10000000000000001, 1.0255661410000001, 1.0255661412323602,
--R      2.3236013113603349E-10]
--R     ,
--R    [0.11,1.028186335,1.0281863346010778,- 3.989222285838423E-10],
--R    [0.12,1.030818352,1.0308183514457605,- 5.5423954314903767E-10],
--R    [0.13,1.033462259,1.0334622590557541,5.5754068029045811E-11],
--R    [0.14000000000000001,1.036118125,1.0361181251552536,1.5525358776358189E-10],
--R
--R     [0.14999999999999999, 1.0387860179999999, 1.0387860179063644,
--R      - 9.3635543763070928E-11]
--R     ,
--R    [0.16,1.0414660060000001,1.0414660059121499,- 8.7850171581749237E-11],
--R
--R     [0.17000000000000001, 1.0441581579999999, 1.0441581582197257,
--R      2.1972579311579921E-10]
--R     ,
--R
--R     [0.17999999999999999, 1.0468625439999999, 1.0468625443233892,
--R      3.233893153264944E-10]
--R     ,
--R    [0.19,1.0495792340000001,1.0495792341677359,1.6773582522944253E-10],
--R    [0.20000000000000001,1.052308298,1.0523082981508358,1.5083578830399347E-10],
--R
--R     [0.20999999999999999, 1.0550498070000001, 1.055049807127405,
--R      1.2740497545848939E-10]
--R     ,
--R    [0.22,1.0578038329999999,1.0578038324120198,- 5.8798010904581588E-10],
--R
--R     [0.23000000000000001, 1.0605704460000001, 1.0605704457823433,
--R      - 2.1765678148710776E-10]
--R     ,
--R
--R     [0.23999999999999999, 1.0633497190000001, 1.0633497194823853,
--R      4.8238524286148277E-10]
--R     ,
--R    [0.25,1.0661417259999999,1.0661417262257755,2.2577562042158661E-10],
--R
--R     [0.26000000000000001, 1.0689465389999999, 1.0689465391990731,
--R      1.9907320236711712E-10]
--R     ,
--R    [0.27000000000000002,1.071764232,1.0717642320650853,6.5085270506415327E-11],
--R
--R     [0.28000000000000003, 1.0745948789999999, 1.0745948789662336,
--R      - 3.3766323070949511E-11]
--R     ,
--R
--R     [0.28999999999999998, 1.0774385550000001, 1.0774385545279166,
--R      - 4.7208348341598594E-10]
--R     ,
--R
--R     [0.29999999999999999, 1.0802953340000001, 1.0802953338619241,
--R      - 1.3807599508197654E-10]
--R     ,
--R    [0.31,1.083165293,1.0831652925698594,- 4.3014058981327707E-10],
--R
--R     [0.32000000000000001, 1.0860485070000001, 1.0860485067465939,
--R      - 2.5340618492464273E-10]
--R     ,
--R
--R     [0.33000000000000002, 1.088945053, 1.0889450529837443,
--R      - 1.6255663481956617E-11]
--R     ,
--R    [0.34000000000000002,1.091855008,1.0918550083731842,3.7318415024856222E-10],
--R
--R     [0.34999999999999998, 1.094778451, 1.0947784505105673,
--R      - 4.8943271657719833E-10]
--R     ,
--R
--R     [0.35999999999999999, 1.0977154579999999, 1.0977154574988892,
--R      - 5.0111070848402051E-10]
--R     ,
--R    [0.37,1.100666108,1.1006661079520708,- 4.7929216151487708E-11],
--R    [0.38,1.1036304809999999,1.1036304809985678,- 1.4321877017664519E-12],
--R
--R     [0.39000000000000001, 1.1066086559999999, 1.1066086562850108,
--R      2.8501090376664706E-10]
--R     ,
--R
--R     [0.40000000000000002, 1.1096007139999999, 1.1096007139798676,
--R      - 2.0132340239342739E-11]
--R     ,
--R    [0.40999999999999998,1.112606735,1.1126067347771349,- 2.228650597402293E-10]
--R     ,
--R    [0.41999999999999998,1.1156268,1.1156267999000615,- 9.9938501918472866E-11],
--R    [0.42999999999999999,1.118660991,1.1186609911048895,1.0488943047448629E-10],
--R    [0.44,1.121709391,1.1217093906846374,- 3.1536262490305944E-10],
--R
--R     [0.45000000000000001, 1.124772082, 1.1247720814728976,
--R      - 5.2710236175812497E-10]
--R     ,
--R
--R     [0.46000000000000002, 1.1278491470000001, 1.1278491468476701,
--R      - 1.52329926450534E-10]
--R     ,
--R
--R     [0.46999999999999997, 1.1309406710000001, 1.1309406707352239,
--R      - 2.6477620096443388E-10]
--R     ,
--R
--R     [0.47999999999999998, 1.1340467380000001, 1.134046737613986,
--R      - 3.8601410956573545E-10]
--R     ,
--R    [0.48999999999999999,1.137167432,1.1371674325184589,5.1845883142220828E-10],
--R    [0.5,1.140302841,1.1403028410431715,4.3171466401759062E-11]]
--R                                                  Type: List List DoubleFloat
--E 15

--S 16 of 20
[[0.50,0.454219905,Ei(0.50),Ei(0.50)-0.454219905],_
 [0.51,0.487032167,Ei(0.51),Ei(0.51)-0.487032167],_
 [0.52,0.519530633,Ei(0.52),Ei(0.52)-0.519530633],_
 [0.53,0.551730445,Ei(0.53),Ei(0.53)-0.551730445],_
 [0.54,0.583645931,Ei(0.54),Ei(0.54)-0.583645931],_
 [0.55,0.615290657,Ei(0.55),Ei(0.55)-0.615290657],_
 [0.56,0.646677490,Ei(0.56),Ei(0.56)-0.646677490],_
 [0.57,0.677818642,Ei(0.57),Ei(0.57)-0.677818642],_
 [0.58,0.708725720,Ei(0.58),Ei(0.58)-0.708725720],_
 [0.59,0.739409764,Ei(0.59),Ei(0.59)-0.739409764],_
 [0.60,0.769881290,Ei(0.60),Ei(0.60)-0.769881290],_
 [0.61,0.800150320,Ei(0.61),Ei(0.61)-0.800150320],_
 [0.62,0.830226417,Ei(0.62),Ei(0.62)-0.830226417],_
 [0.63,0.860118716,Ei(0.63),Ei(0.63)-0.860118716],_
 [0.64,0.889835949,Ei(0.64),Ei(0.64)-0.889835949],_
 [0.65,0.919386468,Ei(0.65),Ei(0.65)-0.919386468],_
 [0.66,0.948778277,Ei(0.66),Ei(0.66)-0.948778277],_
 [0.67,0.978019042,Ei(0.67),Ei(0.67)-0.978019042],_
 [0.68,1.007116121,Ei(0.68),Ei(0.68)-1.007116121],_
 [0.69,1.036076576,Ei(0.69),Ei(0.69)-1.036076576],_
 [0.70,1.064907195,Ei(0.70),Ei(0.70)-1.064907195],_
 [0.71,1.093614501,Ei(0.71),Ei(0.71)-1.093614501],_
 [0.72,1.122204777,Ei(0.72),Ei(0.72)-1.122204777],_
 [0.73,1.150684069,Ei(0.73),Ei(0.73)-1.150684069],_
 [0.74,1.179058208,Ei(0.74),Ei(0.74)-1.179058208],_
 [0.75,1.207332816,Ei(0.75),Ei(0.75)-1.207332816],_
 [0.76,1.235513319,Ei(0.76),Ei(0.76)-1.235513319],_
 [0.77,1.263604960,Ei(0.77),Ei(0.77)-1.263604960],_
 [0.78,1.291612805,Ei(0.78),Ei(0.78)-1.291612805],_
 [0.79,1.319541753,Ei(0.79),Ei(0.79)-1.319541753],_
 [0.80,1.347396548,Ei(0.80),Ei(0.80)-1.347396548],_
 [0.81,1.375181783,Ei(0.81),Ei(0.81)-1.375181783],_
 [0.82,1.402901910,Ei(0.82),Ei(0.82)-1.402901910],_
 [0.83,1.430561245,Ei(0.83),Ei(0.83)-1.430561245],_
 [0.84,1.458163978,Ei(0.84),Ei(0.84)-1.458163978],_
 [0.85,1.485714176,Ei(0.85),Ei(0.85)-1.485714176],_
 [0.86,1.513215791,Ei(0.86),Ei(0.86)-1.513215791],_
 [0.87,1.540672664,Ei(0.87),Ei(0.87)-1.540672664],_
 [0.88,1.568088534,Ei(0.88),Ei(0.88)-1.568088534],_
 [0.89,1.595467036,Ei(0.89),Ei(0.89)-1.595467036],_
 [0.90,1.622811714,Ei(0.90),Ei(0.90)-1.622811714],_
 [0.91,1.650126019,Ei(0.91),Ei(0.91)-1.650126019],_
 [0.92,1.677413317,Ei(0.92),Ei(0.92)-1.677413317],_
 [0.93,1.704676891,Ei(0.93),Ei(0.93)-1.704676891],_
 [0.94,1.731919946,Ei(0.94),Ei(0.94)-1.731919946],_
 [0.95,1.759145612,Ei(0.95),Ei(0.95)-1.759145612],_
 [0.96,1.786356947,Ei(0.96),Ei(0.96)-1.786356947],_
 [0.97,1.813556941,Ei(0.97),Ei(0.97)-1.813556941],_
 [0.98,1.840748519,Ei(0.98),Ei(0.98)-1.840748519],_
 [0.99,1.867934543,Ei(0.99),Ei(0.99)-1.867934543],_
 [1.00,1.895117816,Ei(1.00),Ei(1.00)-1.895117816],_
 [1.01,1.922301085,Ei(1.01),Ei(1.01)-1.922301085],_
 [1.02,1.949487042,Ei(1.02),Ei(1.02)-1.949487042],_
 [1.03,1.976678325,Ei(1.03),Ei(1.03)-1.976678325],_
 [1.04,2.003877525,Ei(1.04),Ei(1.04)-2.003877525],_
 [1.05,2.031087184,Ei(1.05),Ei(1.05)-2.031087184],_
 [1.06,2.058309800,Ei(1.06),Ei(1.06)-2.058309800],_
 [1.07,2.085547825,Ei(1.07),Ei(1.07)-2.085547825],_
 [1.08,2.112803672,Ei(1.08),Ei(1.08)-2.112803672],_
 [1.09,2.140079712,Ei(1.09),Ei(1.09)-2.140079712],_
 [1.10,2.167378280,Ei(1.10),Ei(1.10)-2.167378280],_
 [1.11,2.194701672,Ei(1.11),Ei(1.11)-2.194701672],_
 [1.12,2.222052152,Ei(1.12),Ei(1.12)-2.222052152],_
 [1.13,2.249431949,Ei(1.13),Ei(1.13)-2.249431949],_
 [1.14,2.276843260,Ei(1.14),Ei(1.14)-2.276843260],_
 [1.15,2.304288252,Ei(1.15),Ei(1.15)-2.304288252],_
 [1.16,2.331769062,Ei(1.16),Ei(1.16)-2.331769062],_
 [1.17,2.359287800,Ei(1.17),Ei(1.17)-2.359287800],_
 [1.18,2.386846549,Ei(1.18),Ei(1.18)-2.386846549],_
 [1.19,2.414447367,Ei(1.19),Ei(1.19)-2.414447367],_
 [1.20,2.442092285,Ei(1.20),Ei(1.20)-2.442092285],_
 [1.21,2.469783315,Ei(1.21),Ei(1.21)-2.469783315],_
 [1.22,2.497522442,Ei(1.22),Ei(1.22)-2.497522442],_
 [1.23,2.525311634,Ei(1.23),Ei(1.23)-2.525311634],_
 [1.24,2.553152836,Ei(1.24),Ei(1.24)-2.553152836],_
 [1.25,2.581047974,Ei(1.25),Ei(1.25)-2.581047974],_
 [1.26,2.608998956,Ei(1.26),Ei(1.26)-2.608998956],_
 [1.27,2.637007673,Ei(1.27),Ei(1.27)-2.637007673],_
 [1.28,2.665075997,Ei(1.28),Ei(1.28)-2.665075997],_
 [1.29,2.693205785,Ei(1.29),Ei(1.29)-2.693205785],_
 [1.30,2.721398880,Ei(1.30),Ei(1.30)-2.721398880],_
 [1.31,2.749657110,Ei(1.31),Ei(1.31)-2.749657110],_
 [1.32,2.777982287,Ei(1.32),Ei(1.32)-2.777982287],_
 [1.33,2.806376214,Ei(1.33),Ei(1.33)-2.806376214],_
 [1.34,2.834840677,Ei(1.34),Ei(1.34)-2.834840677],_
 [1.35,2.863377453,Ei(1.35),Ei(1.35)-2.863377453],_
 [1.36,2.891988308,Ei(1.36),Ei(1.36)-2.891988308],_
 [1.37,2.920674997,Ei(1.37),Ei(1.37)-2.920674997],_
 [1.38,2.949439263,Ei(1.38),Ei(1.38)-2.949439263],_
 [1.39,2.978282844,Ei(1.39),Ei(1.39)-2.978282844],_
 [1.40,3.007207464,Ei(1.40),Ei(1.40)-3.007207464],_
 [1.41,3.036214843,Ei(1.41),Ei(1.41)-3.036214843],_
 [1.42,3.065306691,Ei(1.42),Ei(1.42)-3.065306691],_
 [1.43,3.094484712,Ei(1.43),Ei(1.43)-3.094484712],_
 [1.44,3.123750601,Ei(1.44),Ei(1.44)-3.123750601],_
 [1.45,3.153106049,Ei(1.45),Ei(1.45)-3.153106049],_
 [1.46,3.182552741,Ei(1.46),Ei(1.46)-3.182552741],_
 [1.47,3.212092355,Ei(1.47),Ei(1.47)-3.212092355],_
 [1.48,3.241726566,Ei(1.48),Ei(1.48)-3.241726566],_
 [1.49,3.271457042,Ei(1.49),Ei(1.49)-3.271457042],_
 [1.50,3.301285449,Ei(1.50),Ei(1.50)-3.301285449],_
 [1.51,3.331213449,Ei(1.51),Ei(1.51)-3.331213449],_
 [1.52,3.361242701,Ei(1.52),Ei(1.52)-3.361242701],_
 [1.53,3.391374858,Ei(1.53),Ei(1.53)-3.391374858],_
 [1.54,3.421611576,Ei(1.54),Ei(1.54)-3.421611576],_
 [1.55,3.451954503,Ei(1.55),Ei(1.55)-3.451954503],_
 [1.56,3.482405289,Ei(1.56),Ei(1.56)-3.482405289],_
 [1.57,3.512965580,Ei(1.57),Ei(1.57)-3.512965580],_
 [1.58,3.543637024,Ei(1.58),Ei(1.58)-3.543637024],_
 [1.59,3.574421266,Ei(1.59),Ei(1.59)-3.574421266],_
 [1.60,3.605319949,Ei(1.60),Ei(1.60)-3.605319949],_
 [1.61,3.636334719,Ei(1.61),Ei(1.61)-3.636334719],_
 [1.62,3.667467221,Ei(1.62),Ei(1.62)-3.667467221],_
 [1.63,3.698719099,Ei(1.63),Ei(1.63)-3.698719099],_
 [1.64,3.730091999,Ei(1.64),Ei(1.64)-3.730091999],_
 [1.65,3.761587569,Ei(1.65),Ei(1.65)-3.761587569],_
 [1.66,3.793207456,Ei(1.66),Ei(1.66)-3.793207456],_
 [1.67,3.824953310,Ei(1.67),Ei(1.67)-3.824953310],_
 [1.68,3.856826783,Ei(1.68),Ei(1.68)-3.856826783],_
 [1.69,3.888829528,Ei(1.69),Ei(1.69)-3.888829528],_
 [1.70,3.920963201,Ei(1.70),Ei(1.70)-3.920963201],_
 [1.71,3.953229462,Ei(1.71),Ei(1.71)-3.953229462],_
 [1.72,3.985629972,Ei(1.72),Ei(1.72)-3.985629972],_
 [1.73,4.018166395,Ei(1.73),Ei(1.73)-4.018166395],_
 [1.74,4.050840400,Ei(1.74),Ei(1.74)-4.050840400],_
 [1.75,4.083653659,Ei(1.75),Ei(1.75)-4.083653659],_
 [1.76,4.116607847,Ei(1.76),Ei(1.76)-4.116607847],_
 [1.77,4.149704645,Ei(1.77),Ei(1.77)-4.149704645],_
 [1.78,4.182945736,Ei(1.78),Ei(1.78)-4.182945736],_
 [1.79,4.216332809,Ei(1.79),Ei(1.79)-4.216332809],_
 [1.80,4.249867557,Ei(1.80),Ei(1.80)-4.249867557],_
 [1.81,4.283551681,Ei(1.81),Ei(1.81)-4.283551681],_
 [1.82,4.317386883,Ei(1.82),Ei(1.82)-4.317386883],_
 [1.83,4.351374872,Ei(1.83),Ei(1.83)-4.351374872],_
 [1.84,4.385517364,Ei(1.84),Ei(1.84)-4.385517364],_
 [1.85,4.419816080,Ei(1.85),Ei(1.85)-4.419816080],_
 [1.86,4.454272746,Ei(1.86),Ei(1.86)-4.454272746],_
 [1.87,4.488889097,Ei(1.87),Ei(1.87)-4.488889097],_
 [1.88,4.523666872,Ei(1.88),Ei(1.88)-4.523666872],_
 [1.89,4.558607817,Ei(1.89),Ei(1.89)-4.558607817],_
 [1.90,4.593713687,Ei(1.90),Ei(1.90)-4.593713687],_
 [1.91,4.628986242,Ei(1.91),Ei(1.91)-4.628986242],_
 [1.92,4.664427249,Ei(1.92),Ei(1.92)-4.664427249],_
 [1.93,4.700038485,Ei(1.93),Ei(1.93)-4.700038485],_
 [1.94,4.735821734,Ei(1.94),Ei(1.94)-4.735821734],_
 [1.95,4.771778785,Ei(1.95),Ei(1.95)-4.771778785],_
 [1.96,4.807911438,Ei(1.96),Ei(1.96)-4.807911438],_
 [1.97,4.844221501,Ei(1.97),Ei(1.97)-4.844221501],_
 [1.98,4.880710791,Ei(1.98),Ei(1.98)-4.880710791],_
 [1.99,4.917381131,Ei(1.99),Ei(1.99)-4.917381131],_
 [2.00,4.954234356,Ei(2.00),Ei(2.00)-4.954234356]]
 

   (17)
   [[0.5,0.45421990499999998,0.45421990486317321,- 1.3682677213466832E-10],

     [0.51000000000000001, 0.48703216699999996, 0.48703216680456007,
      - 1.9543988649672883E-10]
     ,

     [0.52000000000000002, 0.51953063300000002, 0.51953063245569719,
      - 5.443028250340376E-10]
     ,

     [0.53000000000000003, 0.55173044500000001, 0.5517304452326639,
      2.3266388815557093E-10]
     ,

     [0.54000000000000004, 0.58364593099999995, 0.58364593072977944,
      - 2.7022051263259073E-10]
     ,

     [0.55000000000000004, 0.61529065699999996, 0.61529065706218633,
      6.2186367166816581E-11]
     ,

     [0.56000000000000005, 0.64667748999999997, 0.64667748977430584,
      - 2.2569413005157912E-10]
     ,

     [0.56999999999999995, 0.67781864199999997, 0.67781864189137597,
      - 1.0862399868472039E-10]
     ,

     [0.57999999999999996, 0.70872571999999989, 0.70872571962101094,
      - 3.7898895133281485E-10]
     ,

     [0.58999999999999997, 0.73940976399999991, 0.73940976415103654,
      1.5103662764914816E-10]
     ,

     [0.59999999999999998, 0.76988129000000005, 0.76988128993735927,
      - 6.2640781450795657E-11]
     ,

     [0.60999999999999999, 0.80015031999999997, 0.80015031983004981,
      - 1.699501650520574E-10]
     ,
    [0.62,0.83022641699999999,0.83022641734618519,3.4618519162421535E-10],

     [0.62999999999999989, 0.86011871599999989, 0.86011871636343873,
      3.6343883458300752E-10]
     ,

     [0.6399999999999999, 0.88983594899999996, 0.88983594847818603,
      - 5.218139254026255E-10]
     ,

     [0.64999999999999991, 0.9193864679999999, 0.9193864682454429,
      2.4544299925821633E-10]
     ,

     [0.65999999999999992, 0.94877827699999995, 0.94877827649472768,
      - 5.0527226846952544E-10]
     ,

     [0.66999999999999993, 0.97801904199999989, 0.97801904189549638,
      - 1.0450351695112658E-10]
     ,

     [0.67999999999999994, 1.0071161209999999, 1.007116120927791,
      - 7.2208905521620181E-11]
     ,

     [0.68999999999999995, 1.0360765759999999, 1.0360765763978432,
      3.9784331384851157E-10]
     ,

     [0.69999999999999996, 1.064907195, 1.0649071946242903,
      - 3.7570968558497952E-10]
     ,

     [0.70999999999999996, 1.0936145009999998, 1.0936145014081782,
      4.0817837998474715E-10]
     ,

     [0.71999999999999997, 1.1222047769999999, 1.1222047768888614,
      - 1.1113843179089145E-10]
     ,
    [0.72999999999999998,1.150684069,1.1506840693780342,3.7803427055393968E-10],

     [0.73999999999999999, 1.1790582079999998, 1.1790582082553465,
      2.5534663272708258E-10]
     ,
    [0.75,1.2073328160000001,1.2073328160012218,1.2216894162975223E-12],

     [0.76000000000000001, 1.2355133189999998, 1.2355133194354742,
      4.3547432326818125E-10]
     ,

     [0.77000000000000002, 1.2636049599999999, 1.2636049602240513,
      2.2405144406434374E-10]
     ,

     [0.78000000000000003, 1.291612805, 1.2916128047105977,
      - 2.8940227991824941E-10]
     ,
    [0.79000000000000004,1.319541753,1.3195417531244751,1.244750968965036E-10],

     [0.80000000000000004, 1.3473965479999999, 1.3473965482123256,
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     ,

     [0.81000000000000005, 1.3751817829999999, 1.3751817833361946,
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     [0.82999999999999996, 1.4305612449999998, 1.4305612453827297,
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     ,
    [0.83999999999999997,1.458163978,1.4581639782841676,2.8416757835714179E-10],

     [0.84999999999999998, 1.4857141760000001, 1.4857141762252539,
      2.2525381560001279E-10]
     ,

     [0.85999999999999999, 1.5132157909999999, 1.5132157910189581,
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     ,
    [0.87,1.5406726639999999,1.5406726644642921,4.6429216027377151E-10],

     [0.87999999999999989, 1.5680885339999999, 1.5680885336445418,
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     ,

     [0.8899999999999999, 1.5954670360000001, 1.5954670359288243,
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     ,

     [0.89999999999999991, 1.622811714, 1.6228117136968674,
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     ,

     [0.90999999999999992, 1.650126019, 1.6501260188054059,
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     ,

     [0.91999999999999993, 1.6774133170000001, 1.677413316813162,
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     ,

     [0.92999999999999994, 1.7046768910000001, 1.7046768909800787,
      - 1.9921397864663959E-11]
     ,

     [0.93999999999999995, 1.7319199460000001, 1.7319199460553549,
      5.5354831829390605E-11]
     ,

     [0.94999999999999996, 1.759145612, 1.7591456118676903,
      - 1.3230971873667841E-10]
     ,

     [0.95999999999999996, 1.7863569469999998, 1.7863569467301945,
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     ,

     [0.96999999999999997, 1.8135569409999999, 1.8135569406715357,
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     ,

     [0.97999999999999998, 1.8407485189999999, 1.8407485185040213,
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     ,

     [0.98999999999999999, 1.8679345430000001, 1.8679345427385858,
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     ,
    [1.,1.895117816,1.8951178163559361,3.5593616942719564E-10],
    [1.0099999999999998,1.922301085,1.9223010854424849,4.4248493757947926E-10],
    [1.02,1.9494870419999999,1.9494870416990668,- 3.0093305625200628E-10],
    [1.0299999999999998,1.976678325,1.9766783248299273,- 1.7007262265167356E-10]
     ,
    [1.04,2.003877525,2.0038775248189595,- 1.8104051591194548E-10],
    [1.0499999999999998,2.031087184,2.0310871840996638,9.9663832742180603E-11],
    [1.0600000000000001,2.0583098,2.0583097996249284,- 3.7507152939042498E-10],

     [1.0699999999999998, 2.0855478249999999, 2.0855478248422825,
      - 1.5771739469983004E-10]
     ,

     [1.0800000000000001, 2.1128036720000001, 2.1128036715799325,
      - 4.2006753631085303E-10]
     ,

     [1.0899999999999999, 2.1400797119999999, 2.1400797118485415,
      - 1.5145840137620326E-10]
     ,

     [1.1000000000000001, 2.1673782799999999, 2.1673782795634038,
      - 4.3659609261226251E-10]
     ,

     [1.1099999999999999, 2.1947016719999999, 2.1947016721913268,
      1.9132695427970248E-10]
     ,

     [1.1200000000000001, 2.2220521519999998, 2.2220521523263717,
      3.2637181845984742E-10]
     ,

     [1.1299999999999999, 2.2494319489999999, 2.2494319491981756,
      1.9817569807401014E-10]
     ,

     [1.1399999999999999, 2.2768432599999997, 2.2768432601165491,
      1.1654943676830953E-10]
     ,

     [1.1499999999999999, 2.3042882520000001, 2.3042882518556285,
      - 1.4437162576541596E-10]
     ,

     [1.1599999999999999, 2.3317690619999998, 2.3317690619808027,
      - 1.9197088363398507E-11]
     ,

     [1.1699999999999999, 2.3592877999999997, 2.3592878001213737,
      1.2137402194412061E-10]
     ,

     [1.1799999999999999, 2.3868465489999999, 2.3868465491917359,
      1.9173596044197438E-10]
     ,

     [1.1899999999999999, 2.4144473670000002, 2.4144473665637345,
      - 4.3626569024013406E-10]
     ,
    [1.2,2.4420922850000002,2.4420922851926514,1.9265122830347536E-10],
    [1.21,2.4697833149999999,2.4697833146991774,- 3.0082247803875362E-10],
    [1.22,2.4975224420000002,2.4975224424095606,4.0956038560580055E-10],
    [1.23,2.5253116339999999,2.5253116343560089,3.5600900005761105E-10],
    [1.24,2.5531528359999998,2.5531528362393034,2.3930368797664414E-10],
    [1.25,2.5810479739999996,2.5810479743554762,3.5547653709500082E-10],

     [1.2599999999999998, 2.6089989559999998, 2.6089989564882821,
      4.8828230347908175E-10]
     ,
    [1.27,2.6370076729999998,2.6370076727691489,- 2.3085089395635805E-10],

     [1.2799999999999998, 2.6650759969999998, 2.6650759965061082,
      - 4.9389159428869789E-10]
     ,
    [1.29,2.693205785,2.6932057849832498,- 1.6750156817124662E-11],

     [1.2999999999999998, 2.7213988799999997, 2.7213988802320226,
      2.3202284538115237E-10]
     ,

     [1.3100000000000001, 2.7496571099999998, 2.7496571097757787,
      - 2.2422108614250646E-10]
     ,

     [1.3199999999999998, 2.7779822869999999, 2.7779822873487241,
      3.4872416065923062E-10]
     ,

     [1.3300000000000001, 2.8063762140000001, 2.8063762135905539,
      - 4.0944625467886908E-10]
     ,

     [1.3399999999999999, 2.8348406769999999, 2.8348406767178056,
      - 2.8219426795317304E-10]
     ,
    [1.3500000000000001,2.863377453,2.8633774531730753,1.7307533184407475E-10],

     [1.3599999999999999, 2.8919883080000002, 2.8919883082530298,
      2.5302959727468988E-10]
     ,

     [1.3700000000000001, 2.9206749969999999, 2.9206749967162478,
      - 2.8375213290132706E-10]
     ,

     [1.3799999999999999, 2.9494392629999999, 2.9494392633717355,
      3.7173553124603131E-10]
     ,

     [1.3899999999999999, 2.9782828439999998, 2.9782828436490232,
      - 3.5097658113159014E-10]
     ,

     [1.3999999999999999, 3.0072074639999999, 3.0072074641506457,
      1.5064571812217764E-10]
     ,

     [1.4099999999999999, 3.0362148429999998, 3.0362148431877856,
      1.8778578692035808E-10]
     ,
    [1.4199999999999999,3.065306691,3.065306691299837,2.9983704408209633E-10],

     [1.4299999999999999, 3.0944847119999999, 3.0944847117585681,
      - 2.4143176347024564E-10]
     ,

     [1.4399999999999999, 3.1237506009999998, 3.1237506010575933,
      5.7593485536244771E-11]
     ,
    [1.45,3.1531060489999998,3.1531060493877443,3.8774450317191622E-10],
    [1.46,3.1825527409999999,3.1825527410990038,9.9003916176343409E-11],
    [1.47,3.2120923549999998,3.2120923551495331,1.4953327465150323E-10],
    [1.48,3.2417265659999996,3.2417265655423861,- 4.5761350264683642E-10],
    [1.49,3.2714570419999998,3.2714570417503985,- 2.4960122857464739E-10],
    [1.5,3.3012854489999999,3.3012854491297974,1.297975060765566E-10],

     [1.5099999999999998, 3.3312134489999998, 3.3312134493229735,
      3.2297364782607474E-10]
     ,
    [1.52,3.3612427010000001,3.3612427006508958,- 3.4910430102286227E-10],

     [1.5299999999999998, 3.3913748579999998, 3.3913748584955847,
      4.9558490644585618E-10]
     ,
    [1.54,3.4216115760000001,3.4216115756731122,- 3.2688785012169319E-10],

     [1.5499999999999998, 3.4519545029999996, 3.4519545027974372,
      - 2.0256241128890906E-10]
     ,

     [1.5600000000000001, 3.4824052889999999, 3.4824052886355648,
      - 3.6443514872530614E-10]
     ,

     [1.5699999999999998, 3.5129655799999999, 3.5129655804542939,
      4.5429393580320721E-10]
     ,

     [1.5800000000000001, 3.5436370239999997, 3.5436370243589819,
      3.5898217731755722E-10]
     ,

     [1.5899999999999999, 3.5744212659999999, 3.5744212656246064,
      - 3.7539349406756628E-10]
     ,

     [1.6000000000000001, 3.6053199490000001, 3.6053199490194707,
      1.9470647316666145E-11]
     ,

     [1.6099999999999999, 3.6363347189999997, 3.6363347191218365,
      1.2183676290078438E-10]
     ,

     [1.6200000000000001, 3.6674672209999999, 3.6674672206298222,
      - 3.7017766629787729E-10]
     ,

     [1.6299999999999999, 3.6987190989999998, 3.6987190986647671,
      - 3.3523273046398572E-10]
     ,

     [1.6399999999999999, 3.7300919989999999, 3.7300919990684158,
      6.8415939580290797E-11]
     ,

     [1.6499999999999999, 3.7615875689999996, 3.7615875686941349,
      - 3.0586466692739123E-10]
     ,

     [1.6599999999999999, 3.7932074560000002, 3.7932074556923925,
      - 3.0760771707605272E-10]
     ,

     [1.6699999999999999, 3.8249533099999997, 3.824953309790788,
      - 2.0921175902799405E-10]
     ,

     [1.6799999999999999, 3.8568267829999998, 3.8568267825688243,
      - 4.3117553971683265E-10]
     ,

     [1.6899999999999999, 3.8888295279999996, 3.8888295277276343,
      - 2.723652414715616E-10]
     ,
    [1.7,3.9209632010000002,3.9209632013549043,3.5490410610350409E-10],
    [1.71,3.9532294619999999,3.9532294621851576,1.8515766697646541E-10],
    [1.72,3.9856299719999999,3.985629971855627,- 1.4437295803304551E-10],
    [1.73,4.0181663949999997,4.0181663951578663,1.5786660867433966E-10],
    [1.74,4.0508404000000002,4.0508404002853169,2.8531665918762883E-10],
    [1.75,4.0836536589999994,4.0836536590769557,7.6956219174917351E-11],

     [1.7599999999999998, 4.1166078469999992, 4.1166078472572485,
      2.5724933294668517E-10]
     ,
    [1.77,4.1497046449999999,4.1497046446724992,- 3.2750069323128628E-10],

     [1.7799999999999998, 4.1829457359999997, 4.1829457355238064,
      - 4.7619330700854334E-10]
     ,
    [1.79,4.2163328089999998,4.2163328085967509,- 4.0324898975541146E-10],
    [1.7999999999999998,4.249867557,4.2498675574879332,4.879332493601396E-10],

     [1.8100000000000001, 4.2835516809999996, 4.2835516808285554,
      - 1.7144419217629547E-10]
     ,

     [1.8199999999999998, 4.3173868829999993, 4.3173868825051116,
      - 4.9488768638639158E-10]
     ,

     [1.8300000000000001, 4.3513748719999992, 4.3513748718773684,
      - 1.2263079440799629E-10]
     ,
    [1.8399999999999999,4.385517364,4.3855173639937206,- 6.2794214272798854E-12]
     ,

     [1.8500000000000001, 4.4198160800000004, 4.4198160798040753,
      - 1.9592505395849003E-10]
     ,

     [1.8599999999999999, 4.4542727459999991, 4.4542727463703331,
      3.7033398569974452E-10]
     ,

     [1.8700000000000001, 4.4888890969999995, 4.4888890970746314,
      7.4631856250562123E-11]
     ,

     [1.8799999999999999, 4.5236668719999997, 4.523666871825391,
      - 1.7460877188568702E-10]
     ,

     [1.8899999999999999, 4.5586078170000004, 4.5586078172613478,
      2.6134738817518155E-10]
     ,

     [1.8999999999999999, 4.5937136869999993, 4.5937136869535857,
      - 4.6413539678269444E-11]
     ,

     [1.9099999999999999, 4.6289862419999999, 4.6289862416057304,
      - 3.9426950593224319E-10]
     ,

     [1.9199999999999999, 4.6644272489999992, 4.6644272492523706,
      2.5237145706569208E-10]
     ,

     [1.9299999999999999, 4.7000384850000003, 4.7000384854557851,
      4.5578474328067387E-10]
     ,

     [1.9399999999999999, 4.7358217339999999, 4.7358217335010906,
      - 4.9890935827079375E-10]
     ,
    [1.95,4.7717787850000004,4.7717787845898796,- 4.1012082618863133E-10],
    [1.96,4.8079114379999996,4.8079114380324146,3.241495960537577E-11],
    [1.97,4.8442215009999998,4.8442215014384953,4.3849546216279123E-10],
    [1.98,4.8807107910000003,4.8807107909070337,- 9.2966523368431808E-11],
    [1.99,4.917381131,4.9173811312144435,2.1444357400923764E-10],
    [2.,4.9542343559999997,4.9542343560018924,1.8927082123809669E-12]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (17)
--R   [[0.5,0.45421990499999998,0.45421990486317332,- 1.3682666111236585E-10],
--R
--R     [0.51000000000000001, 0.48703216700000002, 0.48703216680456007,
--R      - 1.9543994200788006E-10]
--R     ,
--R
--R     [0.52000000000000002, 0.51953063300000002, 0.51953063245569719,
--R      - 5.443028250340376E-10]
--R     ,
--R
--R     [0.53000000000000003, 0.55173044500000001, 0.55173044523266401,
--R      2.3266399917787339E-10]
--R     ,
--R
--R     [0.54000000000000004, 0.58364593099999995, 0.58364593072977955,
--R      - 2.7022040161028826E-10]
--R     ,
--R
--R     [0.55000000000000004, 0.61529065699999996, 0.61529065706218644,
--R      6.2186478189119043E-11]
--R     ,
--R
--R     [0.56000000000000005, 0.64667748999999997, 0.64667748977430584,
--R      - 2.2569413005157912E-10]
--R     ,
--R
--R     [0.56999999999999995, 0.67781864199999997, 0.67781864189137597,
--R      - 1.0862399868472039E-10]
--R     ,
--R
--R     [0.57999999999999996, 0.70872572, 0.70872571962101083,
--R      - 3.7898917337741977E-10]
--R     ,
--R
--R     [0.58999999999999997, 0.73940976400000002, 0.73940976415103654,
--R      1.510365166268457E-10]
--R     ,
--R
--R     [0.59999999999999998, 0.76988129000000005, 0.76988128993735938,
--R      - 6.2640670428493195E-11]
--R     ,
--R
--R     [0.60999999999999999, 0.80015031999999997, 0.80015031983004981,
--R      - 1.699501650520574E-10]
--R     ,
--R    [0.62,0.83022641699999999,0.83022641734618519,3.4618519162421535E-10],
--R    [0.63,0.86011871600000001,0.86011871636343917,3.6343916764991491E-10],
--R
--R     [0.64000000000000001, 0.88983594899999996, 0.88983594847818637,
--R      - 5.2181359233571811E-10]
--R     ,
--R
--R     [0.65000000000000002, 0.91938646800000001, 0.91938646824544334,
--R      2.4544333232512372E-10]
--R     ,
--R
--R     [0.66000000000000003, 0.94877827699999995, 0.94877827649472835,
--R      - 5.0527160233571067E-10]
--R     ,
--R
--R     [0.67000000000000004, 0.97801904200000001, 0.97801904189549682,
--R      - 1.045031838842192E-10]
--R     ,
--R
--R     [0.68000000000000005, 1.0071161209999999, 1.0071161209277915,
--R      - 7.2208461432410331E-11]
--R     ,
--R
--R     [0.68999999999999995, 1.0360765759999999, 1.0360765763978435,
--R      3.978435358931165E-10]
--R     ,
--R    [0.69999999999999996,1.064907195,1.0649071946242905,- 3.757094635403746E-10]
--R     ,
--R    [0.70999999999999996,1.093614501,1.0936145014081782,4.0817815794014223E-10],
--R
--R     [0.71999999999999997, 1.1222047770000001, 1.1222047768888612,
--R      - 1.111388758801013E-10]
--R     ,
--R    [0.72999999999999998,1.150684069,1.1506840693780345,3.780344925985446E-10],
--R
--R     [0.73999999999999999, 1.1790582080000001, 1.1790582082553465,
--R      2.5534641068247765E-10]
--R     ,
--R    [0.75,1.2073328160000001,1.2073328160012218,1.2216894162975223E-12],
--R
--R     [0.76000000000000001, 1.2355133190000001, 1.2355133194354742,
--R      4.3547410122357633E-10]
--R     ,
--R
--R     [0.77000000000000002, 1.2636049600000001, 1.2636049602240513,
--R      2.2405122201973882E-10]
--R     ,
--R
--R     [0.78000000000000003, 1.291612805, 1.2916128047105979,
--R      - 2.8940205787364448E-10]
--R     ,
--R    [0.79000000000000004,1.319541753,1.3195417531244753,1.2447531894110853E-10],
--R
--R     [0.80000000000000004, 1.3473965480000001, 1.3473965482123258,
--R      2.1232571256746269E-10]
--R     ,
--R
--R     [0.81000000000000005, 1.3751817829999999, 1.3751817833361941,
--R      3.361941836033111E-10]
--R     ,
--R    [0.81999999999999995,1.40290191,1.4029019100774811,7.7481132620960125E-11],
--R    [0.82999999999999996,1.430561245,1.4305612453827297,3.8272962576968439E-10],
--R    [0.83999999999999997,1.458163978,1.4581639782841678,2.8416780040174672E-10],
--R
--R     [0.84999999999999998, 1.4857141760000001, 1.4857141762252541,
--R      2.2525403764461771E-10]
--R     ,
--R
--R     [0.85999999999999999, 1.5132157909999999, 1.5132157910189581,
--R      1.8958168368499173E-11]
--R     ,
--R    [0.87,1.5406726639999999,1.5406726644642923,4.6429238231837644E-10],
--R    [0.88,1.5680885339999999,1.5680885336445423,- 3.5545766330358219E-10],
--R
--R     [0.89000000000000001, 1.5954670360000001, 1.5954670359288246,
--R      - 7.1175509930299086E-11]
--R     ,
--R
--R     [0.90000000000000002, 1.622811714, 1.6228117136968674,
--R      - 3.0313263010839364E-10]
--R     ,
--R
--R     [0.91000000000000003, 1.650126019, 1.6501260188054063,
--R      - 1.9459367450735954E-10]
--R     ,
--R
--R     [0.92000000000000004, 1.6774133170000001, 1.677413316813162,
--R      - 1.8683810054653804E-10]
--R     ,
--R
--R     [0.93000000000000005, 1.7046768910000001, 1.7046768909800791,
--R      - 1.9920953775454109E-11]
--R     ,
--R
--R     [0.93999999999999995, 1.7319199460000001, 1.7319199460553549,
--R      5.5354831829390605E-11]
--R     ,
--R
--R     [0.94999999999999996, 1.759145612, 1.7591456118676905,
--R      - 1.3230949669207348E-10]
--R     ,
--R
--R     [0.95999999999999996, 1.786356947, 1.7863569467301943,
--R      - 2.6980573331059077E-10]
--R     ,
--R
--R     [0.96999999999999997, 1.8135569410000001, 1.8135569406715355,
--R      - 3.2846458886126584E-10]
--R     ,
--R
--R     [0.97999999999999998, 1.8407485189999999, 1.8407485185040211,
--R      - 4.9597881357499318E-10]
--R     ,
--R
--R     [0.98999999999999999, 1.8679345430000001, 1.8679345427385856,
--R      - 2.6141444564586891E-10]
--R     ,
--R    [1.,1.895117816,1.8951178163559361,3.5593616942719564E-10],
--R    [1.01,1.922301085,1.9223010854424856,4.4248560371329404E-10],
--R    [1.02,1.9494870419999999,1.9494870416990668,- 3.0093305625200628E-10],
--R    [1.03,1.976678325,1.976678324829928,- 1.7007195651785878E-10],
--R    [1.04,2.003877525,2.0038775248189595,- 1.8104051591194548E-10],
--R    [1.05,2.031087184,2.0310871840996643,9.9664276831390453E-11],
--R    [1.0600000000000001,2.0583098,2.0583097996249284,- 3.7507152939042498E-10],
--R
--R     [1.0700000000000001, 2.0855478249999999, 2.085547824842283,
--R      - 1.5771695061062019E-10]
--R     ,
--R
--R     [1.0800000000000001, 2.1128036720000001, 2.1128036715799325,
--R      - 4.2006753631085303E-10]
--R     ,
--R
--R     [1.0900000000000001, 2.1400797119999999, 2.1400797118485424,
--R      - 1.5145751319778356E-10]
--R     ,
--R
--R     [1.1000000000000001, 2.1673782799999999, 2.1673782795634038,
--R      - 4.3659609261226251E-10]
--R     ,
--R
--R     [1.1100000000000001, 2.1947016719999999, 2.1947016721913277,
--R      1.9132784245812218E-10]
--R     ,
--R
--R     [1.1200000000000001, 2.2220521519999998, 2.2220521523263717,
--R      3.2637181845984742E-10]
--R     ,
--R
--R     [1.1299999999999999, 2.2494319489999999, 2.2494319491981756,
--R      1.9817569807401014E-10]
--R     ,
--R
--R     [1.1399999999999999, 2.2768432600000001, 2.2768432601165496,
--R      1.1654943676830953E-10]
--R     ,
--R
--R     [1.1499999999999999, 2.3042882520000001, 2.304288251855628,
--R      - 1.4437206985462581E-10]
--R     ,
--R
--R     [1.1599999999999999, 2.3317690619999998, 2.3317690619808027,
--R      - 1.9197088363398507E-11]
--R     ,
--R
--R     [1.1699999999999999, 2.3592878000000002, 2.3592878001213737,
--R      1.2137357785491076E-10]
--R     ,
--R
--R     [1.1799999999999999, 2.3868465489999999, 2.3868465491917359,
--R      1.9173596044197438E-10]
--R     ,
--R
--R     [1.1899999999999999, 2.4144473670000002, 2.4144473665637345,
--R      - 4.3626569024013406E-10]
--R     ,
--R    [1.2,2.4420922850000002,2.4420922851926514,1.9265122830347536E-10],
--R    [1.21,2.4697833149999999,2.4697833146991774,- 3.0082247803875362E-10],
--R    [1.22,2.4975224420000002,2.497522442409561,4.095608296950104E-10],
--R    [1.23,2.5253116339999999,2.5253116343560089,3.5600900005761105E-10],
--R    [1.24,2.5531528360000002,2.5531528362393039,2.3930368797664414E-10],
--R    [1.25,2.5810479740000001,2.5810479743554762,3.5547609300579097E-10],
--R    [1.26,2.6089989560000002,2.6089989564882825,4.8828230347908175E-10],
--R    [1.27,2.6370076729999998,2.6370076727691485,- 2.308513380455679E-10],
--R    [1.28,2.6650759970000002,2.6650759965061086,- 4.9389159428869789E-10],
--R    [1.29,2.693205785,2.6932057849832494,- 1.6750600906334512E-11],
--R    [1.3,2.7213988800000002,2.7213988802320226,2.3202240129194251E-10],
--R
--R     [1.3100000000000001, 2.7496571099999998, 2.7496571097757787,
--R      - 2.2422108614250646E-10]
--R     ,
--R
--R     [1.3200000000000001, 2.7779822869999999, 2.777982287348725,
--R      3.4872504883765032E-10]
--R     ,
--R
--R     [1.3300000000000001, 2.8063762140000001, 2.8063762135905539,
--R      - 4.0944625467886908E-10]
--R     ,
--R
--R     [1.3400000000000001, 2.8348406769999999, 2.8348406767178056,
--R      - 2.8219426795317304E-10]
--R     ,
--R    [1.3500000000000001,2.863377453,2.8633774531730753,1.7307533184407475E-10],
--R
--R     [1.3600000000000001, 2.8919883080000002, 2.8919883082530298,
--R      2.5302959727468988E-10]
--R     ,
--R
--R     [1.3700000000000001, 2.9206749969999999, 2.9206749967162473,
--R      - 2.8375257699053691E-10]
--R     ,
--R
--R     [1.3799999999999999, 2.9494392629999999, 2.9494392633717355,
--R      3.7173553124603131E-10]
--R     ,
--R
--R     [1.3899999999999999, 2.9782828440000002, 2.9782828436490232,
--R      - 3.5097702522079999E-10]
--R     ,
--R
--R     [1.3999999999999999, 3.0072074639999999, 3.0072074641506457,
--R      1.5064571812217764E-10]
--R     ,
--R
--R     [1.4099999999999999, 3.0362148430000002, 3.0362148431877847,
--R      1.8778445465272853E-10]
--R     ,
--R    [1.4199999999999999,3.065306691,3.065306691299837,2.9983704408209633E-10],
--R
--R     [1.4299999999999999, 3.0944847119999999, 3.0944847117585681,
--R      - 2.4143176347024564E-10]
--R     ,
--R
--R     [1.4399999999999999, 3.1237506009999998, 3.1237506010575933,
--R      5.7593485536244771E-11]
--R     ,
--R    [1.45,3.1531060489999998,3.1531060493877443,3.8774450317191622E-10],
--R    [1.46,3.1825527409999999,3.1825527410990038,9.9003916176343409E-11],
--R    [1.47,3.2120923549999998,3.2120923551495331,1.4953327465150323E-10],
--R    [1.48,3.2417265660000001,3.2417265655423857,- 4.5761439082525612E-10],
--R    [1.49,3.2714570420000002,3.2714570417503985,- 2.4960167266385724E-10],
--R    [1.5,3.3012854489999999,3.3012854491297974,1.297975060765566E-10],
--R    [1.51,3.3312134489999998,3.3312134493229739,3.2297409191528459E-10],
--R    [1.52,3.3612427010000001,3.3612427006508958,- 3.4910430102286227E-10],
--R    [1.53,3.3913748579999998,3.3913748584955847,4.9558490644585618E-10],
--R    [1.54,3.4216115760000001,3.4216115756731122,- 3.2688785012169319E-10],
--R    [1.55,3.4519545030000001,3.4519545027974381,- 2.0256196719969921E-10],
--R
--R     [1.5600000000000001, 3.4824052889999999, 3.4824052886355643,
--R      - 3.6443559281451599E-10]
--R     ,
--R
--R     [1.5700000000000001, 3.5129655799999999, 3.5129655804542947,
--R      4.5429482398162691E-10]
--R     ,
--R
--R     [1.5800000000000001, 3.5436370240000001, 3.5436370243589819,
--R      3.5898173322834737E-10]
--R     ,
--R
--R     [1.5900000000000001, 3.5744212659999999, 3.5744212656246064,
--R      - 3.7539349406756628E-10]
--R     ,
--R
--R     [1.6000000000000001, 3.6053199490000001, 3.6053199490194707,
--R      1.9470647316666145E-11]
--R     ,
--R
--R     [1.6100000000000001, 3.6363347190000002, 3.6363347191218383,
--R      1.2183809516841393E-10]
--R     ,
--R
--R     [1.6200000000000001, 3.6674672209999999, 3.6674672206298222,
--R      - 3.7017766629787729E-10]
--R     ,
--R
--R     [1.6299999999999999, 3.6987190989999998, 3.6987190986647667,
--R      - 3.3523317455319557E-10]
--R     ,
--R
--R     [1.6399999999999999, 3.7300919989999999, 3.7300919990684158,
--R      6.8415939580290797E-11]
--R     ,
--R    [1.6499999999999999,3.761587569,3.7615875686941349,- 3.0586511101660108E-10]
--R     ,
--R
--R     [1.6599999999999999, 3.7932074560000002, 3.7932074556923925,
--R      - 3.0760771707605272E-10]
--R     ,
--R
--R     [1.6699999999999999, 3.8249533100000002, 3.824953309790788,
--R      - 2.092122031172039E-10]
--R     ,
--R
--R     [1.6799999999999999, 3.8568267829999998, 3.8568267825688243,
--R      - 4.3117553971683265E-10]
--R     ,
--R    [1.6899999999999999,3.888829528,3.8888295277276339,- 2.723661296499813E-10],
--R    [1.7,3.9209632010000002,3.9209632013549038,3.5490366201429424E-10],
--R    [1.71,3.9532294619999999,3.953229462185158,1.8515811106567526E-10],
--R    [1.72,3.9856299719999999,3.985629971855627,- 1.4437295803304551E-10],
--R    [1.73,4.0181663949999997,4.0181663951578672,1.5786749685275936E-10],
--R    [1.74,4.0508404000000002,4.0508404002853169,2.8531665918762883E-10],
--R    [1.75,4.0836536590000003,4.0836536590769557,7.6955330996497651E-11],
--R    [1.76,4.116607847,4.1166078472572494,2.5724933294668517E-10],
--R    [1.77,4.1497046449999999,4.1497046446724992,- 3.2750069323128628E-10],
--R    [1.78,4.1829457359999997,4.1829457355238073,- 4.7619241883012364E-10],
--R    [1.79,4.2163328089999998,4.2163328085967509,- 4.0324898975541146E-10],
--R    [1.8,4.249867557,4.2498675574879341,4.879341375385593E-10],
--R
--R     [1.8100000000000001, 4.2835516809999996, 4.2835516808285554,
--R      - 1.7144419217629547E-10]
--R     ,
--R
--R     [1.8200000000000001, 4.3173868830000002, 4.3173868825051116,
--R      - 4.9488857456481128E-10]
--R     ,
--R
--R     [1.8300000000000001, 4.3513748720000001, 4.3513748718773684,
--R      - 1.2263168258641599E-10]
--R     ,
--R    [1.8400000000000001,4.385517364,4.3855173639937215,- 6.2785332488601853E-12]
--R     ,
--R
--R     [1.8500000000000001, 4.4198160800000004, 4.4198160798040753,
--R      - 1.9592505395849003E-10]
--R     ,
--R    [1.8600000000000001,4.454272746,4.4542727463703349,3.7033487387816422E-10],
--R
--R     [1.8700000000000001, 4.4888890970000004, 4.4888890970746314,
--R      7.4630968072142423E-11]
--R     ,
--R
--R     [1.8799999999999999, 4.5236668719999997, 4.523666871825391,
--R      - 1.7460877188568702E-10]
--R     ,
--R
--R     [1.8899999999999999, 4.5586078170000004, 4.5586078172613478,
--R      2.6134738817518155E-10]
--R     ,
--R
--R     [1.8999999999999999, 4.5937136870000002, 4.5937136869535857,
--R      - 4.6414427856689144E-11]
--R     ,
--R
--R     [1.9099999999999999, 4.6289862419999999, 4.6289862416057304,
--R      - 3.9426950593224319E-10]
--R     ,
--R
--R     [1.9199999999999999, 4.6644272490000001, 4.6644272492523706,
--R      2.5237056888727238E-10]
--R     ,
--R
--R     [1.9299999999999999, 4.7000384850000003, 4.7000384854557851,
--R      4.5578474328067387E-10]
--R     ,
--R
--R     [1.9399999999999999, 4.7358217339999999, 4.7358217335010897,
--R      - 4.9891024644921345E-10]
--R     ,
--R    [1.95,4.7717787850000004,4.7717787845898787,- 4.1012171436705103E-10],
--R    [1.96,4.8079114379999996,4.8079114380324146,3.241495960537577E-11],
--R    [1.97,4.8442215009999998,4.8442215014384944,4.3849457398437153E-10],
--R    [1.98,4.8807107910000003,4.8807107909070337,- 9.2966523368431808E-11],
--R    [1.99,4.917381131,4.9173811312144435,2.1444357400923764E-10],
--R    [2.,4.9542343559999997,4.9542343560018924,1.8927082123809669E-12]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 16

--S 17 of 20
f(x)==x/10.0*exp(-x/10.0)*Ei(x/10.0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 20
[[2.0,1.340965420,f(2.0),f(2.0)-1.340965420],_
 [2.1,1.371486802,f(2.1),f(2.1)-1.371486802],_
 [2.2,1.397421992,f(2.2),f(2.2)-1.397421992],_
 [2.3,1.419171534,f(2.3),f(2.3)-1.419171534],_
 [2.4,1.437118315,f(2.4),f(2.4)-1.437118315],_
 [2.5,1.451625159,f(2.5),f(2.5)-1.451625159],_
 [2.6,1.463033397,f(2.6),f(2.6)-1.463033397],_
 [2.7,1.471662153,f(2.7),f(2.7)-1.471662153],_
 [2.8,1.477808187,f(2.8),f(2.8)-1.477808187],_
 [2.9,1.481746162,f(2.9),f(2.9)-1.481746162],_
 [3.0,1.483729204,f(3.0),f(3.0)-1.483729204],_
 [3.1,1.483989691,f(3.1),f(3.1)-1.483989691],_
 [3.2,1.482740191,f(3.2),f(3.2)-1.482740191],_
 [3.3,1.480174491,f(3.3),f(3.3)-1.480174491],_
 [3.4,1.476468706,f(3.4),f(3.4)-1.476468706],_
 [3.5,1.471782389,f(3.5),f(3.5)-1.471782389],_
 [3.6,1.466259659,f(3.6),f(3.6)-1.466259659],_
 [3.7,1.460030313,f(3.7),f(3.7)-1.460030313],_
 [3.8,1.453210902,f(3.8),f(3.8)-1.453210902],_
 [3.9,1.445905765,f(3.9),f(3.9)-1.445905765],_
 [4.0,1.438208032,f(4.0),f(4.0)-1.438208032],_
 [4.1,1.430200557,f(4.1),f(4.1)-1.430200557],_
 [4.2,1.421956813,f(4.2),f(4.2)-1.421956813],_
 [4.3,1.413541719,f(4.3),f(4.3)-1.413541719],_
 [4.4,1.405012424,f(4.4),f(4.4)-1.405012424],_
 [4.5,1.396419030,f(4.5),f(4.5)-1.396419030],_
 [4.6,1.387805263,f(4.6),f(4.6)-1.387805263],_
 [4.7,1.379209093,f(4.7),f(4.7)-1.379209093],_
 [4.8,1.370663313,f(4.8),f(4.8)-1.370663313],_
 [4.9,1.362196054,f(4.9),f(4.9)-1.362196054],_
 [5.0,1.353831278,f(5.0),f(5.0)-1.353831278],_
 [5.1,1.345589212,f(5.1),f(5.1)-1.345589212],_
 [5.2,1.337486755,f(5.2),f(5.2)-1.337486755],_
 [5.3,1.329537845,f(5.3),f(5.3)-1.329537845],_
 [5.4,1.321753788,f(5.4),f(5.4)-1.321753788],_
 [5.5,1.314143566,f(5.5),f(5.5)-1.314143566],_
 [5.6,1.306714107,f(5.6),f(5.6)-1.306714107],_
 [5.7,1.299470536,f(5.7),f(5.7)-1.299470536],_
 [5.8,1.292416395,f(5.8),f(5.8)-1.292416395],_
 [5.9,1.285553849,f(5.9),f(5.9)-1.285553849],_
 [6.0,1.278883860,f(6.0),f(6.0)-1.278883860],_
 [6.1,1.272406357,f(6.1),f(6.1)-1.272406357],_
 [6.2,1.266120373,f(6.2),f(6.2)-1.266120373],_
 [6.3,1.260024184,f(6.3),f(6.3)-1.260024184],_
 [6.4,1.254115417,f(6.4),f(6.4)-1.254115417],_
 [6.5,1.248391155,f(6.5),f(6.5)-1.248391155],_
 [6.6,1.242848032,f(6.6),f(6.6)-1.242848032],_
 [6.7,1.237482309,f(6.7),f(6.7)-1.237482309],_
 [6.8,1.232289952,f(6.8),f(6.8)-1.232289952],_
 [6.9,1.227266684,f(6.9),f(6.9)-1.227266684],_
 [7.0,1.222408053,f(7.0),f(7.0)-1.222408053],_
 [7.1,1.217709472,f(7.1),f(7.1)-1.217709472],_
 [7.2,1.213166264,f(7.2),f(7.2)-1.213166264],_
 [7.3,1.208773699,f(7.3),f(7.3)-1.208773699],_
 [7.4,1.204527026,f(7.4),f(7.4)-1.204527026],_
 [7.5,1.200421500,f(7.5),f(7.5)-1.200421500],_
 [7.6,1.196452401,f(7.6),f(7.6)-1.196452401],_
 [7.7,1.192615063,f(7.7),f(7.7)-1.192615063],_
 [7.8,1.188904881,f(7.8),f(7.8)-1.188904881],_
 [7.9,1.185317334,f(7.9),f(7.9)-1.185317334],_
 [8.0,1.181847987,f(8.0),f(8.0)-1.181847987],_
 [8.1,1.178492509,f(8.1),f(8.1)-1.178492509],_
 [8.2,1.175246676,f(8.2),f(8.2)-1.175246676],_
 [8.3,1.172106376,f(8.3),f(8.3)-1.172106376],_
 [8.4,1.169067617,f(8.4),f(8.4)-1.169067617],_
 [8.5,1.166126526,f(8.5),f(8.5)-1.166126526],_
 [8.6,1.163279354,f(8.6),f(8.6)-1.163279354],_
 [8.7,1.160522476,f(8.7),f(8.7)-1.160522476],_
 [8.8,1.157852390,f(8.8),f(8.8)-1.157852390],_
 [8.9,1.155265719,f(8.9),f(8.9)-1.155265719],_
 [9.0,1.152759209,f(9.0),f(9.0)-1.152759209],_
 [9.1,1.150329724,f(9.1),f(9.1)-1.150329724],_
 [9.2,1.147974251,f(9.2),f(9.2)-1.147974251],_
 [9.3,1.145689889,f(9.3),f(9.3)-1.145689889],_
 [9.4,1.143473855,f(9.4),f(9.4)-1.143473855],_
 [9.5,1.141323476,f(9.5),f(9.5)-1.141323476],_
 [9.6,1.139236185,f(9.6),f(9.6)-1.139236185],_
 [9.7,1.137209523,f(9.7),f(9.7)-1.137209523],_
 [9.8,1.135241130,f(9.8),f(9.8)-1.135241130],_
 [9.9,1.133328746,f(9.9),f(9.9)-1.133328746],_
 [10.0,1.131470205,f(10.0),f(10.0)-1.131470205]]
 
   Compiling function f with type Float -> OnePointCompletion 
      DoubleFloat 

   (19)
   [[2.,1.3409654199999999,- 0.13456013299662747,- 1.4755255529966274],

     [2.0999999999999996, 1.3714868019999999, - 0.12968783850914051,
      - 1.5011746405091404]
     ,

     [2.2000000000000002, 1.3974219919999999, - 0.12432857913849613,
      - 1.521750571138496]
     ,
    [2.2999999999999998,1.419171534,- 0.11851397777493737,- 1.5376855117749373],
    [2.3999999999999999,1.437118315,- 0.11227320930676461,- 1.5493915243067646],
    [2.5,1.451625159,- 0.10563327984220371,- 1.5572584388422037],

     [2.5999999999999996, 1.4630333969999998, - 9.8619263183169478E-2,
      - 1.5616526601831693]
     ,

     [2.7000000000000002, 1.471662153, - 9.1254502584207572E-2,
      - 1.5629166555842076]
     ,

     [2.7999999999999998, 1.4778081869999999, - 8.356078406918252E-2,
      - 1.5613689710691825]
     ,

     [2.8999999999999999, 1.4817461619999999, - 7.5558486253840151E-2,
      - 1.55730464825384]
     ,
    [3.,1.4837292039999999,- 6.7266710614573191E-2,- 1.5509959146145731],

     [3.0999999999999996, 1.4839896910000001, - 5.8703395368669309E-2,
      - 1.5426930863686694]
     ,

     [3.2000000000000002, 1.482740191, - 4.9885415529372618E-2,
      - 1.5326256065293726]
     ,

     [3.2999999999999998, 1.4801744910000001, - 4.0828671227296956E-2,
      - 1.521003162227297]
     ,

     [3.3999999999999999, 1.4764687059999999, - 3.1548166016793965E-2,
      - 1.5080168720167939]
     ,
    [3.5,1.4717823889999999,- 2.205807658873344E-2,- 1.4938404655887334],

     [3.5999999999999996, 1.4662596589999999, - 1.2371815072632754E-2,
      - 1.4786314740726327]
     ,

     [3.7000000000000002, 1.4600303129999999, - 2.5020849182828615E-3,
      - 1.4625323979182827]
     ,

     [3.7999999999999998, 1.4532109019999999, 7.539068809849777E-3,
      - 1.4456718331901501]
     ,
    [3.8999999999999999,1.445905765,1.7740214020573353E-2,- 1.4281655509794267],
    [4.,1.4382080319999999,2.8090490467135878E-2,- 1.4101175415328639],
    [4.0999999999999996,1.430200557,3.8579572390008435E-2,- 1.3916209846099916],
    [4.1999999999999993,1.421956813,4.9197634492545113E-2,- 1.3727591785074549],

     [4.2999999999999998, 1.4135417189999999, 5.9935320871702939E-2,
      - 1.3536063981282971]
     ,

     [4.4000000000000004, 1.4050124239999999, 7.0783716577210276E-2,
      - 1.3342287074227897]
     ,
    [4.5,1.3964190299999999,8.1734321515770564E-2,- 1.3146847084842292],
    [4.5999999999999996,1.387805263,9.277902645351864E-2,- 1.2950262365464813],

     [4.6999999999999993, 1.3792090930000001, 0.10391009090110487,
      - 1.2752990020988952]
     ,

     [4.7999999999999998, 1.3706633130000001, 0.11512012269240561,
      - 1.2555431903075944]
     ,
    [4.9000000000000004,1.362196054,0.12640205909068,- 1.23579399490932],
    [5.,1.3538312779999999,0.13774914927563503,- 1.2160821287243648],

     [5.0999999999999996, 1.3455892119999999, 0.14915493808180313,
      - 1.1964342739181968]
     ,
    [5.1999999999999993,1.337486755,0.16061325087332862,- 1.1768735041266714],

     [5.2999999999999998, 1.3295378449999999, 0.17211817945300267,
      - 1.1574196655469973]
     ,

     [5.4000000000000004, 1.3217537880000001, 0.18366406891450357,
      - 1.1380897190854966]
     ,
    [5.5,1.3141435659999998,0.1952455053565024,- 1.1188980606434975],

     [5.5999999999999996, 1.3067141069999999, 0.20685730438580635,
      - 1.0998568026141935]
     ,

     [5.6999999999999993, 1.2994705359999998, 0.21849450034417656,
      - 1.0809760356558233]
     ,

     [5.7999999999999998, 1.2924163950000001, 0.23015233620004202,
      - 1.0622640587999581]
     ,

     [5.9000000000000004, 1.2855538489999998, 0.24182625405213551,
      - 1.0437275949478644]
     ,
    [6.,1.2788838600000001,0.25351188619722098,- 1.0253719738027791],

     [6.0999999999999996, 1.2724063569999999, 0.26520504671863687,
      - 1.0072013102813631]
     ,

     [6.1999999999999993, 1.2661203729999999, 0.27690172355643178,
      - 0.98921864944356819]
     ,

     [6.2999999999999998, 1.2600241839999999, 0.28859807102347901,
      - 0.97142611297652093]
     ,
    [6.4000000000000004,1.254115417,0.3002904027351731,- 0.9538250142648268],
    [6.5,1.248391155,0.31197518492319365,- 0.93641597007680633],

     [6.5999999999999996, 1.2428480319999999, 0.32364903010640272,
      - 0.91919900189359716]
     ,

     [6.6999999999999993, 1.2374823089999998, 0.33530869109425587,
      - 0.90217361790574391]
     ,

     [6.7999999999999998, 1.2322899519999999, 0.3469510553001891,
      - 0.88533889669981081]
     ,

     [6.9000000000000004, 1.2272666839999999, 0.35857313934432239,
      - 0.86869354465567761]
     ,
    [7.,1.2224080530000001,0.37017208392651257,- 0.85223596907348753],

     [7.0999999999999996, 1.2177094719999999, 0.38174514895231304,
      - 0.83596432304768686]
     ,

     [7.1999999999999993, 1.2131662639999998, 0.39328970889579112,
      - 0.81987655510420865]
     ,
    [7.2999999999999998,1.208773699,0.40480324838440257,- 0.80397045061559735],

     [7.4000000000000004, 1.2045270260000001, 0.4162833579922634,
      - 0.78824366800773671]
     ,
    [7.5,1.2004215,0.42772773022919913,- 0.77269376977080095],

     [7.5999999999999996, 1.1964524009999999, 0.43913415571389103,
      - 0.75731824528610892]
     ,

     [7.6999999999999993, 1.1926150629999999, 0.45050051952030151,
      - 0.7421145434796983]
     ,
    [7.7999999999999998,1.188904881,0.46182479768734741,- 0.72708008331265261],

     [7.9000000000000004, 1.1853173340000001, 0.47310505388250562,
      - 0.71221228011749438]
     ,
    [8.,1.1818479869999998,0.48433943621069137,- 0.6975085507893084],

     [8.0999999999999996, 1.1784925089999998, 0.4955261741603636,
      - 0.6829663348396362]
     ,
    [8.1999999999999993,1.175246676,0.50666357567934228,- 0.66858310032065771],

     [8.3000000000000007, 1.1721063759999999, 0.51775002437336082,
      - 0.65435635162663908]
     ,

     [8.3999999999999986, 1.1690676170000001, 0.52878397682080924,
      - 0.64028364017919082]
     ,
    [8.5,1.166126526,0.53976395999758908,- 0.62636256600241091],

     [8.5999999999999996, 1.1632793539999999, 0.5506885688063663,
      - 0.61259078519363364]
     ,

     [8.6999999999999993, 1.1605224759999999, 0.56155646370489865,
      - 0.59896601229510127]
     ,
    [8.8000000000000007,1.15785239,0.57236636842843436,- 0.5854860215715656],
    [8.8999999999999986,1.155265719,0.58311706780150518,- 0.57214865119849478],
    [9.,1.1527592090000001,0.59380740563471446,- 0.5589518033652856],

     [9.0999999999999996, 1.1503297240000001, 0.60443628270239658,
      - 0.54589344129760353]
     ,

     [9.1999999999999993, 1.1479742509999999, 0.61500265479727356,
      - 0.53297159620272638]
     ,

     [9.3000000000000007, 1.1456898889999998, 0.62550553085845129,
      - 0.52018435814154851]
     ,

     [9.3999999999999986, 1.1434738549999999, 0.63594397116933887,
      - 0.507529883830661]
     ,
    [9.5,1.1413234759999999,0.64631708562224499,- 0.49500639037775496],

     [9.5999999999999996, 1.1392361849999999, 0.65662403204660502,
      - 0.48261215295339488]
     ,

     [9.6999999999999993, 1.1372095230000001, 0.66686401459797295,
      - 0.47034550840202716]
     ,

     [9.8000000000000007, 1.1352411299999998, 0.67703628220505341,
      - 0.45820484779494641]
     ,

     [9.8999999999999986, 1.1333287460000001, 0.68714012707221594,
      - 0.44618861892778416]
     ,
    [10.,1.1314702049999998,0.69717488323506582,- 0.43429532176493402]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R   Compiling function f with type Float -> OnePointCompletion 
--R      DoubleFloat 
--R
--R   (19)
--R   [[2.,1.3409654200000001,- 0.13456013299662745,- 1.4755255529966276],
--R
--R     [2.1000000000000001, 1.3714868019999999, - 0.12968783850914051,
--R      - 1.5011746405091404]
--R     ,
--R
--R     [2.2000000000000002, 1.3974219919999999, - 0.12432857913849607,
--R      - 1.521750571138496]
--R     ,
--R    [2.2999999999999998,1.419171534,- 0.11851397777493734,- 1.5376855117749373],
--R    [2.3999999999999999,1.437118315,- 0.1122732093067646,- 1.5493915243067646],
--R    [2.5,1.451625159,- 0.10563327984220373,- 1.5572584388422037],
--R
--R     [2.6000000000000001, 1.463033397, - 9.8619263183169451E-2,
--R      - 1.5616526601831695]
--R     ,
--R
--R     [2.7000000000000002, 1.471662153, - 9.1254502584207586E-2,
--R      - 1.5629166555842076]
--R     ,
--R
--R     [2.7999999999999998, 1.4778081869999999, - 8.3560784069182492E-2,
--R      - 1.5613689710691825]
--R     ,
--R
--R     [2.8999999999999999, 1.4817461620000001, - 7.5558486253840138E-2,
--R      - 1.5573046482538402]
--R     ,
--R    [3.,1.4837292040000001,- 6.7266710614573164E-2,- 1.5509959146145733],
--R
--R     [3.1000000000000001, 1.4839896910000001, - 5.8703395368669309E-2,
--R      - 1.5426930863686694]
--R     ,
--R
--R     [3.2000000000000002, 1.482740191, - 4.9885415529372513E-2,
--R      - 1.5326256065293724]
--R     ,
--R
--R     [3.2999999999999998, 1.4801744910000001, - 4.0828671227296824E-2,
--R      - 1.5210031622272968]
--R     ,
--R
--R     [3.3999999999999999, 1.4764687059999999, - 3.1548166016793916E-2,
--R      - 1.5080168720167939]
--R     ,
--R    [3.5,1.4717823889999999,- 2.2058076588733416E-2,- 1.4938404655887334],
--R
--R     [3.6000000000000001, 1.4662596590000001, - 1.2371815072632724E-2,
--R      - 1.4786314740726327]
--R     ,
--R
--R     [3.7000000000000002, 1.4600303130000001, - 2.5020849182828334E-3,
--R      - 1.4625323979182829]
--R     ,
--R
--R     [3.7999999999999998, 1.4532109019999999, 7.5390688098497787E-3,
--R      - 1.4456718331901501]
--R     ,
--R    [3.8999999999999999,1.445905765,1.774021402057336E-2,- 1.4281655509794267],
--R    [4.,1.4382080319999999,2.8090490467135878E-2,- 1.4101175415328639],
--R    [4.0999999999999996,1.430200557,3.8579572390008463E-2,- 1.3916209846099916],
--R    [4.2000000000000002,1.421956813,4.9197634492545148E-2,- 1.3727591785074549],
--R
--R     [4.2999999999999998, 1.4135417189999999, 5.9935320871702981E-2,
--R      - 1.3536063981282969]
--R     ,
--R
--R     [4.4000000000000004, 1.4050124239999999, 7.0783716577210318E-2,
--R      - 1.3342287074227897]
--R     ,
--R    [4.5,1.3964190299999999,8.1734321515770605E-2,- 1.3146847084842292],
--R    [4.5999999999999996,1.387805263,9.2779026453518668E-2,- 1.2950262365464813],
--R
--R     [4.7000000000000002, 1.3792090930000001, 0.10391009090110491,
--R      - 1.2752990020988952]
--R     ,
--R
--R     [4.7999999999999998, 1.3706633130000001, 0.11512012269240564,
--R      - 1.2555431903075944]
--R     ,
--R    [4.9000000000000004,1.362196054,0.12640205909068003,- 1.23579399490932],
--R    [5.,1.3538312779999999,0.13774914927563506,- 1.2160821287243648],
--R
--R     [5.0999999999999996, 1.3455892119999999, 0.14915493808180313,
--R      - 1.1964342739181968]
--R     ,
--R    [5.2000000000000002,1.337486755,0.16061325087332862,- 1.1768735041266714],
--R
--R     [5.2999999999999998, 1.3295378449999999, 0.17211817945300276,
--R      - 1.1574196655469973]
--R     ,
--R
--R     [5.4000000000000004, 1.3217537880000001, 0.1836640689145036,
--R      - 1.1380897190854964]
--R     ,
--R    [5.5,1.314143566,0.19524550535650245,- 1.1188980606434975],
--R
--R     [5.5999999999999996, 1.3067141069999999, 0.20685730438580638,
--R      - 1.0998568026141935]
--R     ,
--R
--R     [5.7000000000000002, 1.2994705360000001, 0.21849450034417656,
--R      - 1.0809760356558236]
--R     ,
--R
--R     [5.7999999999999998, 1.2924163950000001, 0.23015233620004197,
--R      - 1.0622640587999581]
--R     ,
--R    [5.9000000000000004,1.285553849,0.24182625405213551,- 1.0437275949478646],
--R    [6.,1.2788838600000001,0.25351188619722104,- 1.0253719738027791],
--R
--R     [6.0999999999999996, 1.2724063569999999, 0.26520504671863687,
--R      - 1.0072013102813631]
--R     ,
--R
--R     [6.2000000000000002, 1.2661203729999999, 0.27690172355643178,
--R      - 0.98921864944356819]
--R     ,
--R
--R     [6.2999999999999998, 1.2600241839999999, 0.28859807102347912,
--R      - 0.97142611297652082]
--R     ,
--R    [6.4000000000000004,1.254115417,0.30029040273517321,- 0.9538250142648268],
--R    [6.5,1.248391155,0.31197518492319382,- 0.93641597007680621],
--R
--R     [6.5999999999999996, 1.2428480319999999, 0.32364903010640295,
--R      - 0.91919900189359693]
--R     ,
--R    [6.7000000000000002,1.237482309,0.33530869109425609,- 0.90217361790574391],
--R
--R     [6.7999999999999998, 1.2322899519999999, 0.34695105530018927,
--R      - 0.88533889669981058]
--R     ,
--R
--R     [6.9000000000000004, 1.2272666839999999, 0.3585731393443225,
--R      - 0.86869354465567739]
--R     ,
--R    [7.,1.2224080530000001,0.37017208392651269,- 0.85223596907348742],
--R
--R     [7.0999999999999996, 1.2177094719999999, 0.38174514895231304,
--R      - 0.83596432304768686]
--R     ,
--R    [7.2000000000000002,1.213166264,0.39328970889579112,- 0.81987655510420887],
--R    [7.2999999999999998,1.208773699,0.40480324838440268,- 0.80397045061559735],
--R
--R     [7.4000000000000004, 1.2045270260000001, 0.4162833579922634,
--R      - 0.78824366800773671]
--R     ,
--R    [7.5,1.2004215,0.42772773022919919,- 0.77269376977080084],
--R
--R     [7.5999999999999996, 1.1964524009999999, 0.43913415571389103,
--R      - 0.75731824528610892]
--R     ,
--R
--R     [7.7000000000000002, 1.1926150630000001, 0.45050051952030151,
--R      - 0.74211454347969852]
--R     ,
--R    [7.7999999999999998,1.188904881,0.46182479768734747,- 0.7270800833126525],
--R
--R     [7.9000000000000004, 1.1853173340000001, 0.47310505388250573,
--R      - 0.71221228011749438]
--R     ,
--R    [8.,1.181847987,0.48433943621069148,- 0.69750855078930862],
--R    [8.0999999999999996,1.178492509,0.49552617416036354,- 0.68296633483963642],
--R    [8.1999999999999993,1.175246676,0.50666357567934228,- 0.66858310032065771],
--R
--R     [8.3000000000000007, 1.1721063759999999, 0.51775002437336082,
--R      - 0.65435635162663908]
--R     ,
--R
--R     [8.4000000000000004, 1.1690676170000001, 0.52878397682080924,
--R      - 0.64028364017919082]
--R     ,
--R    [8.5,1.166126526,0.53976395999758919,- 0.6263625660024108],
--R
--R     [8.5999999999999996, 1.1632793539999999, 0.5506885688063663,
--R      - 0.61259078519363364]
--R     ,
--R
--R     [8.6999999999999993, 1.1605224759999999, 0.56155646370489876,
--R      - 0.59896601229510116]
--R     ,
--R    [8.8000000000000007,1.15785239,0.57236636842843447,- 0.58548602157156548],
--R    [8.9000000000000004,1.155265719,0.58311706780150541,- 0.57214865119849456],
--R    [9.,1.1527592090000001,0.59380740563471446,- 0.5589518033652856],
--R
--R     [9.0999999999999996, 1.1503297240000001, 0.60443628270239691,
--R      - 0.5458934412976032]
--R     ,
--R
--R     [9.1999999999999993, 1.1479742509999999, 0.61500265479727367,
--R      - 0.53297159620272627]
--R     ,
--R    [9.3000000000000007,1.145689889,0.62550553085845151,- 0.52018435814154851],
--R
--R     [9.4000000000000004, 1.1434738550000001, 0.63594397116933887,
--R      - 0.50752988383066122]
--R     ,
--R    [9.5,1.1413234759999999,0.6463170856222451,- 0.49500639037775485],
--R
--R     [9.5999999999999996, 1.1392361849999999, 0.65662403204660502,
--R      - 0.48261215295339488]
--R     ,
--R
--R     [9.6999999999999993, 1.1372095230000001, 0.66686401459797295,
--R      - 0.47034550840202716]
--R     ,
--R    [9.8000000000000007,1.13524113,0.6770362822050533,- 0.45820484779494675],
--R
--R     [9.9000000000000004, 1.1333287460000001, 0.68714012707221583,
--R      - 0.44618861892778428]
--R     ,
--R    [10.,1.1314702050000001,0.69717488323506582,- 0.43429532176493424]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 18

--S 19 of 20
g(y)==(y=0 => 1 ; (x:DFLOAT:=y^-1) ; x*exp(-x)*Ei(x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 20
[[0.100,1.13147021,g(0.100),g(0.100)-1.13147021],_
 [0.095,1.12249671,g(0.095),g(0.095)-1.12249671],_
 [0.090,1.11389377,g(0.090),g(0.090)-1.11389377],_
 [0.085,1.10564739,g(0.085),g(0.085)-1.10564739],_
 [0.080,1.09773775,g(0.080),g(0.080)-1.09773775],_
 [0.075,1.09014087,g(0.075),g(0.075)-1.09014087],_
 [0.070,1.08283054,g(0.070),g(0.070)-1.08283054],_
 [0.065,1.07578038,g(0.065),g(0.065)-1.07578038],_
 [0.060,1.06896548,g(0.060),g(0.060)-1.06896548],_
 [0.055,1.06236365,g(0.055),g(0.055)-1.06236365],_
 [0.050,1.05595591,g(0.050),g(0.050)-1.05595591],_
 [0.045,1.04972640,g(0.045),g(0.045)-1.04972640],_
 [0.040,1.04366194,g(0.040),g(0.040)-1.04366194],_
 [0.035,1.03775135,g(0.035),g(0.035)-1.03775135],_
 [0.030,1.03198503,g(0.030),g(0.030)-1.03198503],_
 [0.025,1.02635451,g(0.025),g(0.025)-1.02635451],_
 [0.020,1.02085228,g(0.020),g(0.020)-1.02085228],_
 [0.015,1.01547157,g(0.015),g(0.015)-1.01547157],_
 [0.010,1.01020625,g(0.010),g(0.010)-1.01020625],_
 [0.005,1.00505077,g(0.005),g(0.005)-1.00505077],_
 [0.000,1.00000000,g(0.000),g(0.000)-1.00000000]]
 
   Compiling function g with type Float -> OnePointCompletion 
      DoubleFloat 

   (21)
   [
     [0.10000000000000001, 1.1314702099999998, 1.1314702047341079,
      - 5.2658919447168273E-9]
     ,

     [9.5000000000000001E-2, 1.1224967100000001, 1.1224967463528539,
      3.6352853838295118E-8]
     ,

     [8.9999999999999997E-2, 1.1138937699999998, 1.1138937808537757,
      1.0853775878061356E-8]
     ,

     [8.4999999999999992E-2, 1.1056473899999999, 1.1056473901733923,
      1.733924115399077E-10]
     ,

     [7.9999999999999988E-2, 1.0977377499999998, 1.0977377526473173,
      2.6473174763452789E-9]
     ,

     [7.4999999999999997E-2, 1.0901408699999999, 1.0901408684282585,
      - 1.5717414036942046E-9]
     ,

     [7.0000000000000007E-2, 1.0828305399999998, 1.0828305423224371,
      2.3224373535413179E-9]
     ,

     [6.5000000000000002E-2, 1.0757803799999999, 1.0757803749062493,
      - 5.0937505324810672E-9]
     ,

     [5.9999999999999998E-2, 1.0689654799999999, 1.0689654755715123,
      - 4.4284875766464893E-9]
     ,

     [5.4999999999999993E-2, 1.06236365, 1.0623636462639567,
      - 3.7360432525446186E-9]
     ,

     [5.0000000000000003E-2, 1.05595591, 1.0559559055929626,
      - 4.4070374016769165E-9]
     ,

     [4.4999999999999998E-2, 1.0497263999999999, 1.0497264028491122,
      2.8491122794349621E-9]
     ,

     [3.9999999999999994E-2, 1.0436619399999998, 1.0436619362666135,
      - 3.7333862668020856E-9]
     ,
    [3.5000000000000003E-2,1.03775135,1.0377513519241477,1.924147730036907E-9],

     [2.9999999999999999E-2, 1.03198503, 1.0319850279857541,
      - 2.0142458811989172E-9]
     ,
    [2.5000000000000001E-2,1.02635451,1.026354511439006,1.4390060254498849E-9],

     [1.9999999999999997E-2, 1.0208522799999999, 1.0208522777971993,
      - 2.2028006085861307E-9]
     ,

     [1.4999999999999999E-2, 1.0154715699999999, 1.0154715653071829,
      - 4.692817023865814E-9]
     ,
    [9.9999999999999985E-3,1.01020625,1.0102062527748354,2.7748354725076751E-9],

     [4.9999999999999992E-3, 1.00505077, 1.0050507653866605,
      - 4.6133394882019729E-9]
     ,
    [0.,1.,1.,0.]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R   Compiling function g with type Float -> OnePointCompletion 
--R      DoubleFloat 
--R
--R   (21)
--R   [[0.10000000000000001,1.13147021,1.1314702047341079,- 5.2658921667614322E-9],
--R
--R     [9.5000000000000001E-2, 1.1224967100000001, 1.1224967463528539,
--R      3.6352853838295118E-8]
--R     ,
--R    [8.9999999999999997E-2,1.11389377,1.1138937808537757,1.0853775656016751E-8],
--R
--R     [8.5000000000000006E-2, 1.1056473899999999, 1.1056473901733923,
--R      1.733924115399077E-10]
--R     ,
--R
--R     [8.0000000000000002E-2, 1.0977377500000001, 1.0977377526473173,
--R      2.647317254300674E-9]
--R     ,
--R
--R     [7.4999999999999997E-2, 1.0901408699999999, 1.0901408684282585,
--R      - 1.5717414036942046E-9]
--R     ,
--R    [7.0000000000000007E-2,1.08283054,1.0828305423224371,2.3224371314967129E-9],
--R
--R     [6.5000000000000002E-2, 1.0757803800000001, 1.0757803749062493,
--R      - 5.0937507545256722E-9]
--R     ,
--R
--R     [5.9999999999999998E-2, 1.0689654799999999, 1.0689654755715123,
--R      - 4.4284875766464893E-9]
--R     ,
--R    [5.5E-2,1.06236365,1.0623636462639567,- 3.7360432525446186E-9],
--R
--R     [5.0000000000000003E-2, 1.05595591, 1.0559559055929626,
--R      - 4.4070374016769165E-9]
--R     ,
--R
--R     [4.4999999999999998E-2, 1.0497263999999999, 1.0497264028491122,
--R      2.8491122794349621E-9]
--R     ,
--R
--R     [4.0000000000000001E-2, 1.04366194, 1.0436619362666135,
--R      - 3.7333864888466906E-9]
--R     ,
--R    [3.5000000000000003E-2,1.03775135,1.0377513519241477,1.924147730036907E-9],
--R
--R     [2.9999999999999999E-2, 1.03198503, 1.0319850279857541,
--R      - 2.0142458811989172E-9]
--R     ,
--R    [2.5000000000000001E-2,1.02635451,1.026354511439006,1.4390060254498849E-9],
--R    [2.0E-2,1.0208522799999999,1.0208522777971993,- 2.2028006085861307E-9],
--R
--R     [1.4999999999999999E-2, 1.0154715700000001, 1.0154715653071829,
--R      - 4.6928172459104189E-9]
--R     ,
--R    [1.0E-2,1.01020625,1.0102062527748354,2.7748354725076751E-9],
--R
--R     [5.0000000000000001E-3, 1.00505077, 1.0050507653866605,
--R      - 4.6133394882019729E-9]
--R     ,
--R    [0.,1.,1.,0.]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 20

)spool 
 
Starts dribbling to schaum23.output (2010/3/27, 18:38:25).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 55
aa:=integrate(csc(a*x),x)
 

              sin(a x)
        log(------------)
            cos(a x) + 1
   (1)  -----------------
                a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)
--R        log(------------)
--R            cos(a x) + 1
--R   (1)  -----------------
--R                a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 55
bb1:=1/a*log(csc(a*x)-cot(a*x))
 

        log(csc(a x) - cot(a x))
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R        log(csc(a x) - cot(a x))
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 3 of 55
bb2:=1/a*log(tan((a*x)/2))
 

                a x
        log(tan(---))
                 2
   (3)  -------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---))
--R                 2
--R   (3)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 4 of 55
cc1:=aa-bb1
 

              sin(a x)
        log(------------) - log(csc(a x) - cot(a x))
            cos(a x) + 1
   (4)  --------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R              sin(a x)
--R        log(------------) - log(csc(a x) - cot(a x))
--R            cos(a x) + 1
--R   (4)  --------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 5 of 55
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (5)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (5)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 6 of 55
dd1:=cotrule cc1
 

              sin(a x)          csc(a x)sin(a x) - cos(a x)
        log(------------) - log(---------------------------)
            cos(a x) + 1                  sin(a x)
   (6)  ----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R              sin(a x)          csc(a x)sin(a x) - cos(a x)
--R        log(------------) - log(---------------------------)
--R            cos(a x) + 1                  sin(a x)
--R   (6)  ----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 7 of 55
cscrule:=rule(csc(a) == 1/sin(a))
 

                     1
   (7)  csc(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (7)  csc(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 8 of 55
ee1:=cscrule dd1
 

              sin(a x)          - cos(a x) + 1
        log(------------) - log(--------------)
            cos(a x) + 1           sin(a x)
   (8)  ---------------------------------------
                           a
                                                     Type: Expression Integer
--R
--R              sin(a x)          - cos(a x) + 1
--R        log(------------) - log(--------------)
--R            cos(a x) + 1           sin(a x)
--R   (8)  ---------------------------------------
--R                           a
--R                                                     Type: Expression Integer
--E

--S 9 of 55
ff1:=expandLog ee1
 

        2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1)
   (9)  -----------------------------------------------------------------
                                        a
                                                     Type: Expression Integer
--R
--R        2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1)
--R   (9)  -----------------------------------------------------------------
--R                                        a
--R                                                     Type: Expression Integer
--E

--S 10 of 55
gg1:=complexNormalize ff1
 

           2log(- 1)
   (10)  - ---------
               a
                                                     Type: Expression Integer
--R
--R           2log(- 1)
--R   (10)  - ---------
--R               a
--R                                                     Type: Expression Integer
--E

--S 11 of 55
cc2:=aa-bb2
 

                   a x           sin(a x)
         - log(tan(---)) + log(------------)
                    2          cos(a x) + 1
   (11)  -----------------------------------
                          a
                                                     Type: Expression Integer
--R
--R                   a x           sin(a x)
--R         - log(tan(---)) + log(------------)
--R                    2          cos(a x) + 1
--R   (11)  -----------------------------------
--R                          a
--R                                                     Type: Expression Integer
--E

--S 12 of 55
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                   sin(a)
   (12)  tan(a) == ------
                   cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sin(a)
--R   (12)  tan(a) == ------
--R                   cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 13 of 55
dd2:=tanrule cc2
 

                                     a x
                                 sin(---)
               sin(a x)               2
         log(------------) - log(--------)
             cos(a x) + 1            a x
                                 cos(---)
                                      2
   (13)  ---------------------------------
                         a
                                                     Type: Expression Integer
--R
--R                                     a x
--R                                 sin(---)
--R               sin(a x)               2
--R         log(------------) - log(--------)
--R             cos(a x) + 1            a x
--R                                 cos(---)
--R                                      2
--R   (13)  ---------------------------------
--R                         a
--R                                                     Type: Expression Integer
--E

--S 14 of 55
ee2:=expandLog dd2
 

                                 a x                                 a x
         log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
                                  2                                   2
   (14)  -----------------------------------------------------------------
                                         a
                                                     Type: Expression Integer
--R
--R                                 a x                                 a x
--R         log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
--R                                  2                                   2
--R   (14)  -----------------------------------------------------------------
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 15 of 55     14:461 Schaums and Axiom agree
ff2:=complexNormalize ee2
 

   (15)  0
                                                     Type: Expression Integer
--R
--R   (15)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 55
aa:=integrate(csc(a*x)^2,x)
 

           cos(a x)
   (1)  - ----------
          a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           cos(a x)
--R   (1)  - ----------
--R          a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17 of 55
bb:=-cot(a*x)/a
 

          cot(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cot(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 18 of 55
cc:=aa-bb
 

        cot(a x)sin(a x) - cos(a x)
   (3)  ---------------------------
                 a sin(a x)
                                                     Type: Expression Integer
--R
--R        cot(a x)sin(a x) - cos(a x)
--R   (3)  ---------------------------
--R                 a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 19 of 55
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20 of 55     14:462 Schaums and Axiom agree
dd:=cotrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 21 of 55
aa:=integrate(csc(a*x)^3,x)
 

                 2           sin(a x)
        (cos(a x)  - 1)log(------------) + cos(a x)
                           cos(a x) + 1
   (1)  -------------------------------------------
                                2
                     2a cos(a x)  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2           sin(a x)
--R        (cos(a x)  - 1)log(------------) + cos(a x)
--R                           cos(a x) + 1
--R   (1)  -------------------------------------------
--R                                2
--R                     2a cos(a x)  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22 of 55
bb:=-(csc(a*x)*cot(a*x))/(2*a)+1/(2*a)*log(tan((a*x)/2))
 

                a x
        log(tan(---)) - cot(a x)csc(a x)
                 2
   (2)  --------------------------------
                       2a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---)) - cot(a x)csc(a x)
--R                 2
--R   (2)  --------------------------------
--R                       2a
--R                                                     Type: Expression Integer
--E

--S 23 of 55
cc:=aa-bb
 

   (3)
                  2             a x              2           sin(a x)
       (- cos(a x)  + 1)log(tan(---)) + (cos(a x)  - 1)log(------------)
                                 2                         cos(a x) + 1
     + 
                2
       (cos(a x)  - 1)cot(a x)csc(a x) + cos(a x)
  /
                2
     2a cos(a x)  - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2             a x              2           sin(a x)
--R       (- cos(a x)  + 1)log(tan(---)) + (cos(a x)  - 1)log(------------)
--R                                 2                         cos(a x) + 1
--R     + 
--R                2
--R       (cos(a x)  - 1)cot(a x)csc(a x) + cos(a x)
--R  /
--R                2
--R     2a cos(a x)  - 2a
--R                                                     Type: Expression Integer
--E

--S 24 of 55
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25 of 55
dd:=cotrule cc
 

   (5)
                  2                     a x
       (- cos(a x)  + 1)sin(a x)log(tan(---))
                                         2
     + 
                2                   sin(a x)
       (cos(a x)  - 1)sin(a x)log(------------) + cos(a x)sin(a x)
                                  cos(a x) + 1
     + 
                3
       (cos(a x)  - cos(a x))csc(a x)
  /
                 2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                  2                     a x
--R       (- cos(a x)  + 1)sin(a x)log(tan(---))
--R                                         2
--R     + 
--R                2                   sin(a x)
--R       (cos(a x)  - 1)sin(a x)log(------------) + cos(a x)sin(a x)
--R                                  cos(a x) + 1
--R     + 
--R                3
--R       (cos(a x)  - cos(a x))csc(a x)
--R  /
--R                 2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 26 of 55
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (6)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (6)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27 of 55
ee:=tanrule dd
 

   (7)
                2                   sin(a x)
       (cos(a x)  - 1)sin(a x)log(------------)
                                  cos(a x) + 1
     + 
                                        a x
                                    sin(---)
                  2                      2
       (- cos(a x)  + 1)sin(a x)log(--------) + cos(a x)sin(a x)
                                        a x
                                    cos(---)
                                         2
     + 
                3
       (cos(a x)  - cos(a x))csc(a x)
  /
                 2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (7)
--R                2                   sin(a x)
--R       (cos(a x)  - 1)sin(a x)log(------------)
--R                                  cos(a x) + 1
--R     + 
--R                                        a x
--R                                    sin(---)
--R                  2                      2
--R       (- cos(a x)  + 1)sin(a x)log(--------) + cos(a x)sin(a x)
--R                                        a x
--R                                    cos(---)
--R                                         2
--R     + 
--R                3
--R       (cos(a x)  - cos(a x))csc(a x)
--R  /
--R                 2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 28 of 55
cscrule:=rule(csc(a) == 1/sin(a))
 

                     1
   (8)  csc(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (8)  csc(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29 of 55
ff:=cscrule ee
 

   (9)
                2             2      sin(a x)
       (cos(a x)  - 1)sin(a x) log(------------)
                                   cos(a x) + 1
     + 
                                         a x
                                     sin(---)
                  2             2         2                      2           3
       (- cos(a x)  + 1)sin(a x) log(--------) + cos(a x)sin(a x)  + cos(a x)
                                         a x
                                     cos(---)
                                          2
     + 
       - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (9)
--R                2             2      sin(a x)
--R       (cos(a x)  - 1)sin(a x) log(------------)
--R                                   cos(a x) + 1
--R     + 
--R                                         a x
--R                                     sin(---)
--R                  2             2         2                      2           3
--R       (- cos(a x)  + 1)sin(a x) log(--------) + cos(a x)sin(a x)  + cos(a x)
--R                                         a x
--R                                     cos(---)
--R                                          2
--R     + 
--R       - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 30 of 55
gg:=expandLog ff
 

   (10)
                2             2
       (cos(a x)  - 1)sin(a x) log(sin(a x))
     + 
                  2             2        a x
       (- cos(a x)  + 1)sin(a x) log(sin(---))
                                          2
     + 
                  2             2
       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1)
     + 
                2             2        a x                     2           3
       (cos(a x)  - 1)sin(a x) log(cos(---)) + cos(a x)sin(a x)  + cos(a x)
                                        2
     + 
       - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (10)
--R                2             2
--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
--R     + 
--R                  2             2        a x
--R       (- cos(a x)  + 1)sin(a x) log(sin(---))
--R                                          2
--R     + 
--R                  2             2
--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1)
--R     + 
--R                2             2        a x                     2           3
--R       (cos(a x)  - 1)sin(a x) log(cos(---)) + cos(a x)sin(a x)  + cos(a x)
--R                                        2
--R     + 
--R       - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 31 of 55     14:463 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (11)  0
                                                     Type: Expression Integer
--R
--R   (11)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 32 of 55
aa:=integrate(csc(a*x)^n*cot(a*x),x)
 

                          1
            n log(- -------------)
                            2
                    cos(a x)  - 1
            ----------------------
                       2
          %e
   (1)  - ------------------------
                     a n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          1
--R            n log(- -------------)
--R                            2
--R                    cos(a x)  - 1
--R            ----------------------
--R                       2
--R          %e
--R   (1)  - ------------------------
--R                     a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33 of 55
bb:=-csc(a*x)^n/(n*a)
 

                  n
          csc(a x)
   (2)  - ---------
             a n
                                                     Type: Expression Integer
--R
--R                  n
--R          csc(a x)
--R   (2)  - ---------
--R             a n
--R                                                     Type: Expression Integer
--E

--S 34 of 55
cc:=aa-bb
 

                          1
            n log(- -------------)
                            2
                    cos(a x)  - 1
            ----------------------
                       2                     n
        - %e                       + csc(a x)
   (3)  --------------------------------------
                          a n
                                                     Type: Expression Integer
--R
--R                          1
--R            n log(- -------------)
--R                            2
--R                    cos(a x)  - 1
--R            ----------------------
--R                       2                     n
--R        - %e                       + csc(a x)
--R   (3)  --------------------------------------
--R                          a n
--R                                                     Type: Expression Integer
--E

--S 35 of 55     14:464 Schaums and Axiom agree
normalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 36 of 55
aa:=integrate(1/csc(a*x),x)
 

          cos(a x)
   (1)  - --------
              a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          cos(a x)
--R   (1)  - --------
--R              a
--R                                          Type: Union(Expression Integer,...)
--E

--S 37 of 55
bb:=-cos(a*x)/a
 

          cos(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cos(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E 

--S 38 of 55     14:465 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 55     14:466 Axiom cannot compute this integral
aa:=integrate(x*csc(a*x),x)
 

           x
         ++
   (1)   |   %P csc(%P a)d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %H csc(%H a)d%H
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 40 of 55     14:467 Axiom cannot compute this integral
aa:=integrate(csc(a*x)/x,x)
 

           x
         ++  csc(%P a)
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  csc(%H a)
--I   (1)   |   --------- d%H
--I        ++       %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 41 of 55
aa:=integrate(x*csc(a*x)^2,x)
 

                      sin(a x)                        2
        sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x)
                    cos(a x) + 1                cos(a x) + 1
   (1)  --------------------------------------------------------------------
                                      2
                                     a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      sin(a x)                        2
--R        sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x)
--R                    cos(a x) + 1                cos(a x) + 1
--R   (1)  --------------------------------------------------------------------
--R                                      2
--R                                     a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 42 of 55
bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))
 

        log(sin(a x)) - a x cot(a x)
   (2)  ----------------------------
                      2
                     a
                                                     Type: Expression Integer
--R
--R        log(sin(a x)) - a x cot(a x)
--R   (2)  ----------------------------
--R                      2
--R                     a
--R                                                     Type: Expression Integer
--E

--S 43 of 55
cc:=aa-bb
 

   (3)
                                               sin(a x)
       - sin(a x)log(sin(a x)) + sin(a x)log(------------)
                                             cos(a x) + 1
     + 
                           2
       - sin(a x)log(------------) + a x cot(a x)sin(a x) - a x cos(a x)
                     cos(a x) + 1
  /
      2
     a sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                               sin(a x)
--R       - sin(a x)log(sin(a x)) + sin(a x)log(------------)
--R                                             cos(a x) + 1
--R     + 
--R                           2
--R       - sin(a x)log(------------) + a x cot(a x)sin(a x) - a x cos(a x)
--R                     cos(a x) + 1
--R  /
--R      2
--R     a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 44 of 55
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 45 of 55
dd:=cotrule cc
 

                                sin(a x)                2
        - log(sin(a x)) + log(------------) - log(------------)
                              cos(a x) + 1        cos(a x) + 1
   (5)  -------------------------------------------------------
                                    2
                                   a
                                                     Type: Expression Integer
--R
--R                                sin(a x)                2
--R        - log(sin(a x)) + log(------------) - log(------------)
--R                              cos(a x) + 1        cos(a x) + 1
--R   (5)  -------------------------------------------------------
--R                                    2
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 46 of 55     14:468 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

          log(2)
   (6)  - ------
             2
            a
                                                     Type: Expression Integer
--R
--R          log(2)
--R   (6)  - ------
--R             2
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 47 of 55
aa:=integrate(1/(q+p*csc(a*x)),x)
 

   (1)
   [
           p
        *
           log
                                                          +-------+
                                    2    2             2  | 2    2
                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
                + 
                      2    3              3    2              3    2
                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
             /
                q sin(a x) + p
       + 
             +-------+
             | 2    2
         a x\|q  - p
    /
           +-------+
           | 2    2
       a q\|q  - p
     ,
                                          +---------+
                                          |   2    2         +---------+
            (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
    2p atan(-----------------------------------------) + a x\|- q  + p
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    --------------------------------------------------------------------]
                                   +---------+
                                   |   2    2
                               a q\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           p
--R        *
--R           log
--R                                                          +-------+
--R                                    2    2             2  | 2    2
--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R                + 
--R                      2    3              3    2              3    2
--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R             /
--R                q sin(a x) + p
--R       + 
--R             +-------+
--R             | 2    2
--R         a x\|q  - p
--R    /
--R           +-------+
--R           | 2    2
--R       a q\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2         +---------+
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
--R    2p atan(-----------------------------------------) + a x\|- q  + p
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    --------------------------------------------------------------------]
--R                                   +---------+
--R                                   |   2    2
--R                               a q\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 48 of 55
t1:=integrate(1/(p+q*sin(a*x)),x)
 

   (2)
   [
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
    /
         +-------+
         | 2    2
       a\|q  - p
     ,
                                          +---------+
                                          |   2    2
            (p sin(a x) + q cos(a x) + q)\|- q  + p
      2atan(-----------------------------------------)
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    - ------------------------------------------------]
                          +---------+
                          |   2    2
                        a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R    /
--R         +-------+
--R         | 2    2
--R       a\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
--R      2atan(-----------------------------------------)
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    - ------------------------------------------------]
--R                          +---------+
--R                          |   2    2
--R                        a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 49 of 55
bb1:=x/q-p/q*t1.1
 

   (3)
       -
            p
         *
            log
                                                           +-------+
                                     2    2             2  | 2    2
                   (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
                 + 
                         2    3                3    2              3    2
                   (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
              /
                 q sin(a x) + p
     + 
           +-------+
           | 2    2
       a x\|q  - p
  /
         +-------+
         | 2    2
     a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            p
--R         *
--R            log
--R                                                           +-------+
--R                                     2    2             2  | 2    2
--R                   (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R                 + 
--R                         2    3                3    2              3    2
--R                   (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R              /
--R                 q sin(a x) + p
--R     + 
--R           +-------+
--R           | 2    2
--R       a x\|q  - p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 50 of 55
bb2:=x/q-p/q*t1.2
 

                                              +---------+
                                              |   2    2         +---------+
                (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
        2p atan(-----------------------------------------) + a x\|- q  + p
                         2    2             2    2
                       (q  - p )cos(a x) + q  - p
   (4)  --------------------------------------------------------------------
                                       +---------+
                                       |   2    2
                                   a q\|- q  + p
                                                     Type: Expression Integer
--R
--R                                              +---------+
--R                                              |   2    2         +---------+
--R                (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
--R        2p atan(-----------------------------------------) + a x\|- q  + p
--R                         2    2             2    2
--R                       (q  - p )cos(a x) + q  - p
--R   (4)  --------------------------------------------------------------------
--R                                       +---------+
--R                                       |   2    2
--R                                   a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 51 of 55
cc1:=aa.1-bb1
 

   (5)
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
  /
         +-------+
         | 2    2
     a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 52 of 55
cc2:=aa.2-bb1
 

   (6)
           +---------+
           |   2    2
         p\|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                                                      +---------+
          +-------+                                   |   2    2
          | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       2p\|q  - p  atan(-----------------------------------------)
                                 2    2             2    2
                               (q  - p )cos(a x) + q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R           +---------+
--R           |   2    2
--R         p\|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                      +---------+
--R          +-------+                                   |   2    2
--R          | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       2p\|q  - p  atan(-----------------------------------------)
--R                                 2    2             2    2
--R                               (q  - p )cos(a x) + q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 53 of 55
cc3:=aa.1-bb2
 

   (7)
           +---------+
           |   2    2
         p\|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
                                                        +---------+
            +-------+                                   |   2    2
            | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       - 2p\|q  - p  atan(-----------------------------------------)
                                   2    2             2    2
                                 (q  - p )cos(a x) + q  - p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R           +---------+
--R           |   2    2
--R         p\|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                        +---------+
--R            +-------+                                   |   2    2
--R            | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       - 2p\|q  - p  atan(-----------------------------------------)
--R                                   2    2             2    2
--R                                 (q  - p )cos(a x) + q  - p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 54 of 55     14:469 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 55 of 55     14:470 Axiom cannot compute this integral
aa:=integrate(csc(a*x)^n,x)
 

           x
         ++           n
   (1)   |   csc(%P a) d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   csc(%H a) d%H
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to Stack.output (2010/3/27, 18:46:35).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 44
a:Stack INT:= stack [1,2,3,4,5]
 

   (1)  [1,2,3,4,5]
                                                          Type: Stack Integer
--R
--R   (1)  [1,2,3,4,5]
--R                                                          Type: Stack Integer
--E 1

--S 2 of 44
pop! a
 

   (2)  1
                                                        Type: PositiveInteger
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 44
a
 

   (3)  [2,3,4,5]
                                                          Type: Stack Integer
--R
--R   (3)  [2,3,4,5]
--R                                                          Type: Stack Integer
--E 3

--S 4 of 44
extract! a
 

   (4)  2
                                                        Type: PositiveInteger
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 44
a
 

   (5)  [3,4,5]
                                                          Type: Stack Integer
--R
--R   (5)  [3,4,5]
--R                                                          Type: Stack Integer
--E 5

--S 6 of 44
push!(9,a)
 

   (6)  9
                                                        Type: PositiveInteger
--R
--R   (6)  9
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 44
a
 

   (7)  [9,3,4,5]
                                                          Type: Stack Integer
--R
--R   (7)  [9,3,4,5]
--R                                                          Type: Stack Integer
--E 7

--S 8 of 44
insert!(8,a)
 

   (8)  [8,9,3,4,5]
                                                          Type: Stack Integer
--R
--R   (8)  [8,9,3,4,5]
--R                                                          Type: Stack Integer
--E 8

--S 9 of 44
a
 

   (9)  [8,9,3,4,5]
                                                          Type: Stack Integer
--R
--R   (9)  [8,9,3,4,5]
--R                                                          Type: Stack Integer
--E 9

--S 10 of 44
inspect a
 

   (10)  8
                                                        Type: PositiveInteger
--R
--R   (10)  8
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 44
empty? a
 

   (11)  false
                                                                Type: Boolean
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 44
top a
 

   (12)  8
                                                        Type: PositiveInteger
--R
--R   (12)  8
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 44
depth a
 

   (13)  5
                                                        Type: PositiveInteger
--R
--R   (13)  5
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 44
#a
 

   (14)  5
                                                        Type: PositiveInteger
--R
--R   (14)  5
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 44
less?(a,9)
 

   (15)  true
                                                                Type: Boolean
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 44
more?(a,9)
 

   (16)  false
                                                                Type: Boolean
--R
--R   (16)  false
--R                                                                Type: Boolean
--E 16

--S 17 of 44
size?(a,#a)
 

   (17)  true
                                                                Type: Boolean
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 44
size?(a,9)
 

   (18)  false
                                                                Type: Boolean
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 44
parts a
 

   (19)  [8,9,3,4,5]
                                                           Type: List Integer
--R
--R   (19)  [8,9,3,4,5]
--R                                                           Type: List Integer
--E 19

--S 20 of 44
bag([1,2,3,4,5])$Stack(INT)
 

   (20)  [5,4,3,2,1]
                                                          Type: Stack Integer
--R
--R   (20)  [5,4,3,2,1]
--R                                                          Type: Stack Integer
--E 20

--S 21 of 44
b:=empty()$(Stack INT)
 

   (21)  []
                                                          Type: Stack Integer
--R
--R   (21)  []
--R                                                          Type: Stack Integer
--E 21

--S 22 of 44
empty? b
 

   (22)  true
                                                                Type: Boolean
--R
--R   (22)  true
--R                                                                Type: Boolean
--E 22

--S 23 of 44
sample()$Stack(INT)
 

   (23)  []
                                                          Type: Stack Integer
--R
--R   (23)  []
--R                                                          Type: Stack Integer
--E 23

--S 24 of 44
c:=copy a
 

   (24)  [8,9,3,4,5]
                                                          Type: Stack Integer
--R
--R   (24)  [8,9,3,4,5]
--R                                                          Type: Stack Integer
--E 24

--S 25 of 44
eq?(a,c)
 

   (25)  false
                                                                Type: Boolean
--R
--R   (25)  false
--R                                                                Type: Boolean
--E 25

--S 26 of 44
eq?(a,a)
 

   (26)  true
                                                                Type: Boolean
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26

--S 27 of 44
(a=c)@Boolean
 

   (27)  true
                                                                Type: Boolean
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 44
(a=a)@Boolean
 

   (28)  true
                                                                Type: Boolean
--R
--R   (28)  true
--R                                                                Type: Boolean
--E 28

--S 29 of 44
a~=c
 

   (29)  false
                                                                Type: Boolean
--R
--R   (29)  false
--R                                                                Type: Boolean
--E 29

--S 30 of 44
any?(x+->(x=4),a)
 

   (30)  true
                                                                Type: Boolean
--R
--R   (30)  true
--R                                                                Type: Boolean
--E 30

--S 31 of 44
any?(x+->(x=11),a)
 

   (31)  false
                                                                Type: Boolean
--R
--R   (31)  false
--R                                                                Type: Boolean
--E 31

--S 32 of 44
every?(x+->(x=11),a)
 

   (32)  false
                                                                Type: Boolean
--R
--R   (32)  false
--R                                                                Type: Boolean
--E 32

--S 33 of 44
count(4,a)
 

   (33)  1
                                                        Type: PositiveInteger
--R
--R   (33)  1
--R                                                        Type: PositiveInteger
--E 33

--S 34 of 44
count(x+->(x>2),a)
 

   (34)  5
                                                        Type: PositiveInteger
--R
--R   (34)  5
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 44
map(x+->x+10,a)
 

   (35)  [18,19,13,14,15]
                                                          Type: Stack Integer
--R
--R   (35)  [18,19,13,14,15]
--R                                                          Type: Stack Integer
--E 35

--S 36 of 44
a
 

   (36)  [8,9,3,4,5]
                                                          Type: Stack Integer
--R
--R   (36)  [8,9,3,4,5]
--R                                                          Type: Stack Integer
--E 36

--S 37 of 44
map!(x+->x+10,a)
 

   (37)  [18,19,13,14,15]
                                                          Type: Stack Integer
--R
--R   (37)  [18,19,13,14,15]
--R                                                          Type: Stack Integer
--E 37

--S 38 of 44
a
 

   (38)  [18,19,13,14,15]
                                                          Type: Stack Integer
--R
--R   (38)  [18,19,13,14,15]
--R                                                          Type: Stack Integer
--E 38

--S 39 of 44
members a
 

   (39)  [18,19,13,14,15]
                                                           Type: List Integer
--R
--R   (39)  [18,19,13,14,15]
--R                                                           Type: List Integer
--E 39

--S 40 of 44
member?(14,a)
 

   (40)  true
                                                                Type: Boolean
--R
--R   (40)  true
--R                                                                Type: Boolean
--E 40

--S 41 of 44
coerce a
 

   (41)  [18,19,13,14,15]
                                                             Type: OutputForm
--R 
--R
--R   (41)  [18,19,13,14,15]
--R                                                             Type: OutputForm
--E 41

--S 42 of 44
hash a
 

   (42)  4999539
                                                          Type: SingleInteger
--R 
--R
--I   (42)  4999539
--R                                                          Type: SingleInteger
--E 42

--S 43 of 44
latex a
 

   (43)  "\mbox{\bf Unimplemented}"
                                                                 Type: String
--R 
--R
--R   (43)  "\mbox{\bf Unimplemented}"
--R                                                                 Type: String
--E 43

--S 44 of 44
)show Stack
 
 Stack S: SetCategory  is a domain constructor
 Abbreviation for Stack is STACK 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for STACK 

------------------------------- Operations --------------------------------
 bag : List S -> %                     copy : % -> %
 depth : % -> NonNegativeInteger       empty : () -> %
 empty? : % -> Boolean                 eq? : (%,%) -> Boolean
 extract! : % -> S                     insert! : (S,%) -> %
 inspect : % -> S                      map : ((S -> S),%) -> %
 pop! : % -> S                         push! : (S,%) -> S
 sample : () -> %                      stack : List S -> %
 top : % -> S                         
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?=? : (%,%) -> Boolean if S has SETCAT
 any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 coerce : % -> OutputForm if S has SETCAT
 count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
 count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
 every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 hash : % -> SingleInteger if S has SETCAT
 latex : % -> String if S has SETCAT
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((S -> S),%) -> % if $ has shallowlyMutable
 member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
 members : % -> List S if $ has finiteAggregate
 more? : (%,NonNegativeInteger) -> Boolean
 parts : % -> List S if $ has finiteAggregate
 size? : (%,NonNegativeInteger) -> Boolean
 ?~=? : (%,%) -> Boolean if S has SETCAT

--R Stack S: SetCategory  is a domain constructor
--R Abbreviation for Stack is STACK 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for STACK 
--R
--R------------------------------- Operations --------------------------------
--R bag : List S -> %                     copy : % -> %
--R depth : % -> NonNegativeInteger       empty : () -> %
--R empty? : % -> Boolean                 eq? : (%,%) -> Boolean
--R extract! : % -> S                     insert! : (S,%) -> %
--R inspect : % -> S                      map : ((S -> S),%) -> %
--R pop! : % -> S                         push! : (S,%) -> S
--R sample : () -> %                      stack : List S -> %
--R top : % -> S                         
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
--R members : % -> List S if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R parts : % -> List S if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
--E 44
)spool
 
Starts dribbling to string.output (2010/3/27, 18:41:8).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 35
hello := "Hello, I'm AXIOM!"
 

   (1)  "Hello, I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (1)  "Hello, I'm AXIOM!"
--R                                                                 Type: String
--E 1

--S 2 of 35
said  := "Jane said, _"Look!_""
 

   (2)  "Jane said, "Look!""
                                                                 Type: String
--R 
--R
--R   (2)  "Jane said, "Look!""
--R                                                                 Type: String
--E 2

--S 3 of 35
saw   := "She saw exactly one underscore: __."
 

   (3)  "She saw exactly one underscore: _."
                                                                 Type: String
--R 
--R
--R   (3)  "She saw exactly one underscore: _."
--R                                                                 Type: String
--E 3

--S 4 of 35
gasp: String := new(32, char "x")
 

   (4)  "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
                                                                 Type: String
--R 
--R
--R   (4)  "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
--R                                                                 Type: String
--E 4

--S 5 of 35
#gasp
 

   (5)  32
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  32
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 35
hello.2
 

   (6)  e
                                                              Type: Character
--R 
--R
--R   (6)  e
--R                                                              Type: Character
--E 6

--S 7 of 35
hello 2
 

   (7)  e
                                                              Type: Character
--R 
--R
--R   (7)  e
--R                                                              Type: Character
--E 7

--S 8 of 35
hello(2)
 

   (8)  e
                                                              Type: Character
--R 
--R
--R   (8)  e
--R                                                              Type: Character
--E 8

--S 9 of 35
hullo := copy hello
 

   (9)  "Hello, I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (9)  "Hello, I'm AXIOM!"
--R                                                                 Type: String
--E 9

--S 10 of 35
hullo.2 := char "u"; [hello, hullo]
 

   (10)  ["Hello, I'm AXIOM!","Hullo, I'm AXIOM!"]
                                                            Type: List String
--R 
--R
--R   (10)  ["Hello, I'm AXIOM!","Hullo, I'm AXIOM!"]
--R                                                            Type: List String
--E 10

--S 11 of 35
saidsaw := concat ["alpha","---","omega"]
 

   (11)  "alpha---omega"
                                                                 Type: String
--R 
--R
--R   (11)  "alpha---omega"
--R                                                                 Type: String
--E 11

--S 12 of 35
concat("hello ","goodbye")
 

   (12)  "hello goodbye"
                                                                 Type: String
--R 
--R
--R   (12)  "hello goodbye"
--R                                                                 Type: String
--E 12

--S 13 of 35
"This " "is " "several " "strings " "concatenated."
 

   (13)  "This is several strings concatenated."
                                                                 Type: String
--R 
--R
--R   (13)  "This is several strings concatenated."
--R                                                                 Type: String
--E 13

--S 14 of 35
hello(1..5)
 

   (14)  "Hello"
                                                                 Type: String
--R 
--R
--R   (14)  "Hello"
--R                                                                 Type: String
--E 14

--S 15 of 35
hello(8..)
 

   (15)  "I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (15)  "I'm AXIOM!"
--R                                                                 Type: String
--E 15

--S 16 of 35
split(hello, char " ")
 

   (16)  ["Hello,","I'm","AXIOM!"]
                                                            Type: List String
--R 
--R
--R   (16)  ["Hello,","I'm","AXIOM!"]
--R                                                            Type: List String
--E 16

--S 17 of 35
other := complement alphanumeric();
 

                                                         Type: CharacterClass
--R 
--R
--R                                                         Type: CharacterClass
--E 17

--S 18 of 35
split(saidsaw, other)
 

   (18)  ["alpha","omega"]
                                                            Type: List String
--R 
--R
--R   (18)  ["alpha","omega"]
--R                                                            Type: List String
--E 18

--S 19 of 35
trim     ("## ++ relax ++ ##", char "#")
 

   (19)  " ++ relax ++ "
                                                                 Type: String
--R 
--R
--R   (19)  " ++ relax ++ "
--R                                                                 Type: String
--E 19

--S 20 of 35
trim     ("## ++ relax ++ ##", other)
 

   (20)  "relax"
                                                                 Type: String
--R 
--R
--R   (20)  "relax"
--R                                                                 Type: String
--E 20

--S 21 of 35
leftTrim ("## ++ relax ++ ##", other)
 

   (21)  "relax ++ ##"
                                                                 Type: String
--R 
--R
--R   (21)  "relax ++ ##"
--R                                                                 Type: String
--E 21

--S 22 of 35
rightTrim("## ++ relax ++ ##", other)
 

   (22)  "## ++ relax"
                                                                 Type: String
--R 
--R
--R   (22)  "## ++ relax"
--R                                                                 Type: String
--E 22

--S 23 of 35
upperCase hello
 

   (23)  "HELLO, I'M AXIOM!"
                                                                 Type: String
--R 
--R
--R   (23)  "HELLO, I'M AXIOM!"
--R                                                                 Type: String
--E 23

--S 24 of 35
lowerCase hello
 

   (24)  "hello, i'm axiom!"
                                                                 Type: String
--R 
--R
--R   (24)  "hello, i'm axiom!"
--R                                                                 Type: String
--E 24

--S 25 of 35
prefix?("He", "Hello")
 

   (25)  true
                                                                Type: Boolean
--R 
--R
--R   (25)  true
--R                                                                Type: Boolean
--E 25

--S 26 of 35
prefix?("Her", "Hello")
 

   (26)  false
                                                                Type: Boolean
--R 
--R
--R   (26)  false
--R                                                                Type: Boolean
--E 26

--S 27 of 35
suffix?("", "Hello")
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 35
suffix?("LO", "Hello")
 

   (28)  false
                                                                Type: Boolean
--R 
--R
--R   (28)  false
--R                                                                Type: Boolean
--E 28

--S 29 of 35
substring?("ll", "Hello", 3)
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 35
substring?("ll", "Hello", 4)
 

   (30)  false
                                                                Type: Boolean
--R 
--R
--R   (30)  false
--R                                                                Type: Boolean
--E 30

--S 31 of 35
n := position("nd", "underground",   1)
 

   (31)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (31)  2
--R                                                        Type: PositiveInteger
--E 31

--S 32 of 35
n := position("nd", "underground", n+1)
 

   (32)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (32)  10
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 35
n := position("nd", "underground", n+1)
 

   (33)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (33)  0
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 35
position(char "d", "underground", 1)
 

   (34)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (34)  3
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 35
position(hexDigit(), "underground", 1)
 

   (35)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  3
--R                                                        Type: PositiveInteger
--E 35
)spool 
 
Starts dribbling to schaum15.output (2010/3/27, 18:37:55).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 65
aa:=integrate(1/(x^4+a^4),x)
 

   (1)
        +------+          +------+2            +------+
        |   1          8  |   1        4  +-+  |   1      2
        |------ log(16a   |------  + 4a x\|2   |------ + x )
       4|    12          4|    12             4|    12
       \|256a            \|256a               \|256a
     + 
          +------+          +------+2            +------+
          |   1          8  |   1        4  +-+  |   1      2
       -  |------ log(16a   |------  - 4a x\|2   |------ + x )
         4|    12          4|    12             4|    12
         \|256a            \|256a               \|256a
     + 
                              +------+                               +------+
                           4  |   1                               4  |   1
                         4a   |------                           4a   |------
        +------+             4|    12          +------+             4|    12
        |   1                \|256a            |   1                \|256a
     2  |------ atan(-------------------- - 2  |------ atan(--------------------)
       4|    12           +------+            4|    12           +------+
       \|256a          4  |   1       +-+     \|256a          4  |   1       +-+
                     4a   |------ - x\|2                    4a   |------ + x\|2
                         4|    12                               4|    12
                         \|256a                                 \|256a
  /
      +-+
     \|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R        +------+          +------+2            +------+
--R        |   1          8  |   1        4  +-+  |   1      2
--R        |------ log(16a   |------  + 4a x\|2   |------ + x )
--R       4|    12          4|    12             4|    12
--R       \|256a            \|256a               \|256a
--R     + 
--R          +------+          +------+2            +------+
--R          |   1          8  |   1        4  +-+  |   1      2
--R       -  |------ log(16a   |------  - 4a x\|2   |------ + x )
--R         4|    12          4|    12             4|    12
--R         \|256a            \|256a               \|256a
--R     + 
--R                              +------+                               +------+
--R                           4  |   1                               4  |   1
--R                         4a   |------                           4a   |------
--R        +------+             4|    12          +------+             4|    12
--R        |   1                \|256a            |   1                \|256a
--R     2  |------ atan(-------------------- - 2  |------ atan(--------------------)
--R       4|    12           +------+            4|    12           +------+
--R       \|256a          4  |   1       +-+     \|256a          4  |   1       +-+
--R                     4a   |------ - x\|2                    4a   |------ + x\|2
--R                         4|    12                               4|    12
--R                         \|256a                                 \|256a
--R  /
--R      +-+
--R     \|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 65
bb:=1/(4*a^3*sqrt(2))*log((x^2+a*x*sqrt(2)+a^2)/(x^2-a*x*sqrt(2)+a^2))-1/(2*a^3*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
 

                      +-+    2    2                  +-+
         +-+    - a x\|2  - x  - a       +-+     a x\|2
        \|2 log(-------------------) - 2\|2 atan(-------)
                     +-+    2    2                2    2
                 a x\|2  - x  - a                x  - a
   (2)  -------------------------------------------------
                                 3
                               8a
                                                     Type: Expression Integer
--R
--R                      +-+    2    2                  +-+
--R         +-+    - a x\|2  - x  - a       +-+     a x\|2
--R        \|2 log(-------------------) - 2\|2 atan(-------)
--R                     +-+    2    2                2    2
--R                 a x\|2  - x  - a                x  - a
--R   (2)  -------------------------------------------------
--R                                 3
--R                               8a
--R                                                     Type: Expression Integer
--E

--S 3 of 65
cc:=aa-bb
 

   (3)
            +------+          +------+2            +------+
         3  |   1          8  |   1        4  +-+  |   1      2
       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
           4|    12          4|    12             4|    12
           \|256a            \|256a               \|256a
     + 
              +------+          +------+2            +------+
           3  |   1          8  |   1        4  +-+  |   1      2
       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
             4|    12          4|    12             4|    12
             \|256a            \|256a               \|256a
     + 
                                  +------+
                               4  |   1
                             4a   |------
            +------+             4|    12
         3  |   1                \|256a
       8a   |------ atan(--------------------)
           4|    12           +------+
           \|256a          4  |   1       +-+
                         4a   |------ - x\|2
                             4|    12
                             \|256a
     + 
                                    +------+
                                 4  |   1
                               4a   |------
              +------+             4|    12                 +-+    2    2
           3  |   1                \|256a             - a x\|2  - x  - a
       - 8a   |------ atan(-------------------- - log(-------------------)
             4|    12           +------+                   +-+    2    2
             \|256a          4  |   1       +-+        a x\|2  - x  - a
                           4a   |------ + x\|2
                               4|    12
                               \|256a
     + 
                 +-+
             a x\|2
       2atan(-------)
              2    2
             x  - a
  /
       3 +-+
     4a \|2
                                                     Type: Expression Integer
--R
--R   (3)
--R            +------+          +------+2            +------+
--R         3  |   1          8  |   1        4  +-+  |   1      2
--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
--R           4|    12          4|    12             4|    12
--R           \|256a            \|256a               \|256a
--R     + 
--R              +------+          +------+2            +------+
--R           3  |   1          8  |   1        4  +-+  |   1      2
--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
--R             4|    12          4|    12             4|    12
--R             \|256a            \|256a               \|256a
--R     + 
--R                                  +------+
--R                               4  |   1
--R                             4a   |------
--R            +------+             4|    12
--R         3  |   1                \|256a
--R       8a   |------ atan(--------------------)
--R           4|    12           +------+
--R           \|256a          4  |   1       +-+
--R                         4a   |------ - x\|2
--R                             4|    12
--R                             \|256a
--R     + 
--R                                    +------+
--R                                 4  |   1
--R                               4a   |------
--R              +------+             4|    12                 +-+    2    2
--R           3  |   1                \|256a             - a x\|2  - x  - a
--R       - 8a   |------ atan(-------------------- - log(-------------------)
--R             4|    12           +------+                   +-+    2    2
--R             \|256a          4  |   1       +-+        a x\|2  - x  - a
--R                           4a   |------ + x\|2
--R                               4|    12
--R                               \|256a
--R     + 
--R                 +-+
--R             a x\|2
--R       2atan(-------)
--R              2    2
--R             x  - a
--R  /
--R       3 +-+
--R     4a \|2
--R                                                     Type: Expression Integer
--E

--S 4 of 65
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 5 of 65
dd:=atanrule cc
 

   (5)
            +------+          +------+2            +------+
         3  |   1          8  |   1        4  +-+  |   1      2
       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
           4|    12          4|    12             4|    12
           \|256a            \|256a               \|256a
     + 
              +------+          +------+2            +------+
           3  |   1          8  |   1        4  +-+  |   1      2
       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
             4|    12          4|    12             4|    12
             \|256a            \|256a               \|256a
     + 
                                          +------+
                                       4  |   1          +-+
                           (- 4 + 4%i)a   |------ + %i x\|2
               +------+                  4|    12
            3  |   1                     \|256a
       4%i a   |------ log(---------------------------------)
              4|    12                   +------+
              \|256a                  4  |   1          +-+
                            (4 + 4%i)a   |------ + %i x\|2
                                        4|    12
                                        \|256a
     + 
                                            +------+
                                         4  |   1          +-+
                             (- 4 + 4%i)a   |------ - %i x\|2
                 +------+                  4|    12
              3  |   1                     \|256a
       - 4%i a   |------ log(---------------------------------)
                4|    12                   +------+
                \|256a                  4  |   1          +-+
                              (4 + 4%i)a   |------ - %i x\|2
                                          4|    12
                                          \|256a
     + 
                      +-+       2       2              +-+    2    2
                - a x\|2  + %i x  - %i a         - a x\|2  - x  - a
       - %i log(-------------------------) - log(-------------------)
                     +-+       2       2              +-+    2    2
                 a x\|2  + %i x  - %i a           a x\|2  - x  - a
  /
       3 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (5)
--R            +------+          +------+2            +------+
--R         3  |   1          8  |   1        4  +-+  |   1      2
--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
--R           4|    12          4|    12             4|    12
--R           \|256a            \|256a               \|256a
--R     + 
--R              +------+          +------+2            +------+
--R           3  |   1          8  |   1        4  +-+  |   1      2
--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
--R             4|    12          4|    12             4|    12
--R             \|256a            \|256a               \|256a
--R     + 
--R                                          +------+
--R                                       4  |   1          +-+
--R                           (- 4 + 4%i)a   |------ + %i x\|2
--R               +------+                  4|    12
--R            3  |   1                     \|256a
--R       4%i a   |------ log(---------------------------------)
--R              4|    12                   +------+
--R              \|256a                  4  |   1          +-+
--R                            (4 + 4%i)a   |------ + %i x\|2
--R                                        4|    12
--R                                        \|256a
--R     + 
--R                                            +------+
--R                                         4  |   1          +-+
--R                             (- 4 + 4%i)a   |------ - %i x\|2
--R                 +------+                  4|    12
--R              3  |   1                     \|256a
--R       - 4%i a   |------ log(---------------------------------)
--R                4|    12                   +------+
--R                \|256a                  4  |   1          +-+
--R                              (4 + 4%i)a   |------ - %i x\|2
--R                                          4|    12
--R                                          \|256a
--R     + 
--R                      +-+       2       2              +-+    2    2
--R                - a x\|2  + %i x  - %i a         - a x\|2  - x  - a
--R       - %i log(-------------------------) - log(-------------------)
--R                     +-+       2       2              +-+    2    2
--R                 a x\|2  + %i x  - %i a           a x\|2  - x  - a
--R  /
--R       3 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 6 of 65
ee:=rootSimp dd
 

   (6)
                                         +-+
               +-+    2    2           x\|2  + (1 + %i)a
       log(a x\|2  + x  + a ) + %i log(-----------------)
                                         +-+
                                       x\|2  + (1 - %i)a
     + 
                  +-+                               +-+       2       2
                x\|2  + (- 1 - %i)a           - a x\|2  + %i x  - %i a
       - %i log(-------------------) - %i log(-------------------------)
                  +-+                              +-+       2       2
                x\|2  + (- 1 + %i)a            a x\|2  + %i x  - %i a
     + 
                   +-+    2    2
             - a x\|2  - x  - a               +-+    2    2
       - log(-------------------) - log(- a x\|2  + x  + a )
                  +-+    2    2
              a x\|2  - x  - a
  /
       3 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (6)
--R                                         +-+
--R               +-+    2    2           x\|2  + (1 + %i)a
--R       log(a x\|2  + x  + a ) + %i log(-----------------)
--R                                         +-+
--R                                       x\|2  + (1 - %i)a
--R     + 
--R                  +-+                               +-+       2       2
--R                x\|2  + (- 1 - %i)a           - a x\|2  + %i x  - %i a
--R       - %i log(-------------------) - %i log(-------------------------)
--R                  +-+                              +-+       2       2
--R                x\|2  + (- 1 + %i)a            a x\|2  + %i x  - %i a
--R     + 
--R                   +-+    2    2
--R             - a x\|2  - x  - a               +-+    2    2
--R       - log(-------------------) - log(- a x\|2  + x  + a )
--R                  +-+    2    2
--R              a x\|2  - x  - a
--R  /
--R       3 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 7 of 65
ff:=expandLog ee
 

   (7)
                  +-+       2       2               +-+       2       2
       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
     + 
                +-+                         +-+
       %i log(x\|2  + (1 + %i)a) - %i log(x\|2  + (1 - %i)a)
     + 
                +-+                           +-+
       %i log(x\|2  + (- 1 + %i)a) - %i log(x\|2  + (- 1 - %i)a)
     + 
       (- 2 - %i)log(- 1)
  /
       3 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                  +-+       2       2               +-+       2       2
--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
--R     + 
--R                +-+                         +-+
--R       %i log(x\|2  + (1 + %i)a) - %i log(x\|2  + (1 - %i)a)
--R     + 
--R                +-+                           +-+
--R       %i log(x\|2  + (- 1 + %i)a) - %i log(x\|2  + (- 1 - %i)a)
--R     + 
--R       (- 2 - %i)log(- 1)
--R  /
--R       3 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 8 of 65
gg:=complexNormalize ff
 

               %i             %i
        %i log(--) - %i log(- --) + (- 2 - %i)log(- 1)
                2              2
   (8)  ----------------------------------------------
                              3 +-+
                            4a \|2
                                             Type: Expression Complex Integer
--R
--R               %i             %i
--R        %i log(--) - %i log(- --) + (- 2 - %i)log(- 1)
--R                2              2
--R   (8)  ----------------------------------------------
--R                              3 +-+
--R                            4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 9 of 65      14:311 Schaums and Axiom differ by a constant
hh:=expandLog gg
 

        %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1)
   (9)  ----------------------------------------------
                              3 +-+
                            4a \|2
                                             Type: Expression Complex Integer
--R
--R        %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1)
--R   (9)  ----------------------------------------------
--R                              3 +-+
--R                            4a \|2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 10 of 65
aa:=integrate(x/(x^4+a^4),x)
 

              2
             x
        atan(--)
              2
             a
   (1)  --------
             2
           2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R             x
--R        atan(--)
--R              2
--R             a
--R   (1)  --------
--R             2
--R           2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 65
bb:=1/(2*a^2)*atan(x^2/a^2)
 

              2
             x
        atan(--)
              2
             a
   (2)  --------
             2
           2a
                                                     Type: Expression Integer
--R
--R              2
--R             x
--R        atan(--)
--R              2
--R             a
--R   (2)  --------
--R             2
--R           2a
--R                                                     Type: Expression Integer
--E

--S 12 of 65     14:312 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 65
aa:=integrate(x^2/(x^4+a^4),x)
 

   (1)
          +-----+               +-----+3        +-----+2
          |  1          4  +-+  |  1         4  |  1       2
       -  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
         4|    4               4|    4         4|    4
         \|256a                \|256a          \|256a
     + 
        +-----+                 +-----+3        +-----+2
        |  1            4  +-+  |  1         4  |  1       2
        |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
       4|    4                 4|    4         4|    4
       \|256a                  \|256a          \|256a
     + 
                              +-----+3                               +-----+3
                           4  |  1                                4  |  1
                        64a   |-----                           64a   |-----
        +-----+              4|    4           +-----+              4|    4
        |  1                 \|256a            |  1                 \|256a
     2  |----- atan(--------------------- - 2  |----- atan(---------------------)
       4|    4            +-----+3            4|    4            +-----+3
       \|256a          4  |  1        +-+     \|256a          4  |  1        +-+
                    64a   |-----  - x\|2                   64a   |-----  + x\|2
                         4|    4                                4|    4
                         \|256a                                 \|256a
  /
      +-+
     \|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R          +-----+               +-----+3        +-----+2
--R          |  1          4  +-+  |  1         4  |  1       2
--R       -  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R         4|    4               4|    4         4|    4
--R         \|256a                \|256a          \|256a
--R     + 
--R        +-----+                 +-----+3        +-----+2
--R        |  1            4  +-+  |  1         4  |  1       2
--R        |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
--R       4|    4                 4|    4         4|    4
--R       \|256a                  \|256a          \|256a
--R     + 
--R                              +-----+3                               +-----+3
--R                           4  |  1                                4  |  1
--R                        64a   |-----                           64a   |-----
--R        +-----+              4|    4           +-----+              4|    4
--R        |  1                 \|256a            |  1                 \|256a
--R     2  |----- atan(--------------------- - 2  |----- atan(---------------------)
--R       4|    4            +-----+3            4|    4            +-----+3
--R       \|256a          4  |  1        +-+     \|256a          4  |  1        +-+
--R                    64a   |-----  - x\|2                   64a   |-----  + x\|2
--R                         4|    4                                4|    4
--R                         \|256a                                 \|256a
--R  /
--R      +-+
--R     \|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 65
bb:=1/(4*a*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))-1/(2*a*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
 

                      +-+    2    2                  +-+
         +-+    - a x\|2  + x  + a       +-+     a x\|2
        \|2 log(-------------------) - 2\|2 atan(-------)
                     +-+    2    2                2    2
                 a x\|2  + x  + a                x  - a
   (2)  -------------------------------------------------
                                8a
                                                     Type: Expression Integer
--R
--R                      +-+    2    2                  +-+
--R         +-+    - a x\|2  + x  + a       +-+     a x\|2
--R        \|2 log(-------------------) - 2\|2 atan(-------)
--R                     +-+    2    2                2    2
--R                 a x\|2  + x  + a                x  - a
--R   (2)  -------------------------------------------------
--R                                8a
--R                                                     Type: Expression Integer
--E

--S 15 of 65
cc:=aa-bb
 

   (3)
             +-----+               +-----+3        +-----+2
             |  1          4  +-+  |  1         4  |  1       2
       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
            4|    4               4|    4         4|    4
            \|256a                \|256a          \|256a
     + 
           +-----+                 +-----+3        +-----+2
           |  1            4  +-+  |  1         4  |  1       2
       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
          4|    4                 4|    4         4|    4
          \|256a                  \|256a          \|256a
     + 
                                 +-----+3
                              4  |  1
                           64a   |-----
           +-----+              4|    4
           |  1                 \|256a
       8a  |----- atan(---------------------)
          4|    4            +-----+3
          \|256a          4  |  1        +-+
                       64a   |-----  - x\|2
                            4|    4
                            \|256a
     + 
                                   +-----+3
                                4  |  1
                             64a   |-----
             +-----+              4|    4                  +-+    2    2
             |  1                 \|256a             - a x\|2  + x  + a
       - 8a  |----- atan(--------------------- - log(-------------------)
            4|    4            +-----+3                   +-+    2    2
            \|256a          4  |  1        +-+        a x\|2  + x  + a
                         64a   |-----  + x\|2
                              4|    4
                              \|256a
     + 
                 +-+
             a x\|2
       2atan(-------)
              2    2
             x  - a
  /
        +-+
     4a\|2
                                                     Type: Expression Integer
--R
--R   (3)
--R             +-----+               +-----+3        +-----+2
--R             |  1          4  +-+  |  1         4  |  1       2
--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R            4|    4               4|    4         4|    4
--R            \|256a                \|256a          \|256a
--R     + 
--R           +-----+                 +-----+3        +-----+2
--R           |  1            4  +-+  |  1         4  |  1       2
--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
--R          4|    4                 4|    4         4|    4
--R          \|256a                  \|256a          \|256a
--R     + 
--R                                 +-----+3
--R                              4  |  1
--R                           64a   |-----
--R           +-----+              4|    4
--R           |  1                 \|256a
--R       8a  |----- atan(---------------------)
--R          4|    4            +-----+3
--R          \|256a          4  |  1        +-+
--R                       64a   |-----  - x\|2
--R                            4|    4
--R                            \|256a
--R     + 
--R                                   +-----+3
--R                                4  |  1
--R                             64a   |-----
--R             +-----+              4|    4                  +-+    2    2
--R             |  1                 \|256a             - a x\|2  + x  + a
--R       - 8a  |----- atan(--------------------- - log(-------------------)
--R            4|    4            +-----+3                   +-+    2    2
--R            \|256a          4  |  1        +-+        a x\|2  + x  + a
--R                         64a   |-----  + x\|2
--R                              4|    4
--R                              \|256a
--R     + 
--R                 +-+
--R             a x\|2
--R       2atan(-------)
--R              2    2
--R             x  - a
--R  /
--R        +-+
--R     4a\|2
--R                                                     Type: Expression Integer
--E

--S 16 of 65
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 17 of 65
dd:=atanrule cc
 

   (5)
             +-----+               +-----+3        +-----+2
             |  1          4  +-+  |  1         4  |  1       2
       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
            4|    4               4|    4         4|    4
            \|256a                \|256a          \|256a
     + 
                                          +-----+3
                                       4  |  1           +-+
                         (- 64 + 64%i)a   |-----  + %i x\|2
              +-----+                    4|    4
              |  1                       \|256a
       4%i a  |----- log(-----------------------------------)
             4|    4                     +-----+3
             \|256a                   4  |  1           +-+
                          (64 + 64%i)a   |-----  + %i x\|2
                                        4|    4
                                        \|256a
     + 
                                            +-----+3
                                         4  |  1           +-+
                           (- 64 + 64%i)a   |-----  - %i x\|2
                +-----+                    4|    4
                |  1                       \|256a
       - 4%i a  |----- log(-----------------------------------)
               4|    4                     +-----+3
               \|256a                   4  |  1           +-+
                            (64 + 64%i)a   |-----  - %i x\|2
                                          4|    4
                                          \|256a
     + 
           +-----+                 +-----+3        +-----+2
           |  1            4  +-+  |  1         4  |  1       2
       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
          4|    4                 4|    4         4|    4
          \|256a                  \|256a          \|256a
     + 
                   +-+    2    2                 +-+       2       2
             - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
       - log(-------------------) - %i log(-------------------------)
                  +-+    2    2                 +-+       2       2
              a x\|2  + x  + a              a x\|2  + %i x  - %i a
  /
        +-+
     4a\|2
                                             Type: Expression Complex Integer
--R
--R   (5)
--R             +-----+               +-----+3        +-----+2
--R             |  1          4  +-+  |  1         4  |  1       2
--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R            4|    4               4|    4         4|    4
--R            \|256a                \|256a          \|256a
--R     + 
--R                                          +-----+3
--R                                       4  |  1           +-+
--R                         (- 64 + 64%i)a   |-----  + %i x\|2
--R              +-----+                    4|    4
--R              |  1                       \|256a
--R       4%i a  |----- log(-----------------------------------)
--R             4|    4                     +-----+3
--R             \|256a                   4  |  1           +-+
--R                          (64 + 64%i)a   |-----  + %i x\|2
--R                                        4|    4
--R                                        \|256a
--R     + 
--R                                            +-----+3
--R                                         4  |  1           +-+
--R                           (- 64 + 64%i)a   |-----  - %i x\|2
--R                +-----+                    4|    4
--R                |  1                       \|256a
--R       - 4%i a  |----- log(-----------------------------------)
--R               4|    4                     +-----+3
--R               \|256a                   4  |  1           +-+
--R                            (64 + 64%i)a   |-----  - %i x\|2
--R                                          4|    4
--R                                          \|256a
--R     + 
--R           +-----+                 +-----+3        +-----+2
--R           |  1            4  +-+  |  1         4  |  1       2
--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
--R          4|    4                 4|    4         4|    4
--R          \|256a                  \|256a          \|256a
--R     + 
--R                   +-+    2    2                 +-+       2       2
--R             - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
--R       - log(-------------------) - %i log(-------------------------)
--R                  +-+    2    2                 +-+       2       2
--R              a x\|2  + x  + a              a x\|2  + %i x  - %i a
--R  /
--R        +-+
--R     4a\|2
--R                                             Type: Expression Complex Integer
--E

--S 18 of 65
ee:=expandLog dd
 

   (6)
             +-----+               +-----+3        +-----+2
             |  1          4  +-+  |  1         4  |  1       2
       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
            4|    4               4|    4         4|    4
            \|256a                \|256a          \|256a
     + 
           +-----+               +-----+3        +-----+2
           |  1          4  +-+  |  1         4  |  1       2
       4a  |----- log(64a x\|2   |-----  - 16a   |-----  - x )
          4|    4               4|    4         4|    4
          \|256a                \|256a          \|256a
     + 
              +-----+                   +-----+3
              |  1                   4  |  1        +-+
       4%i a  |----- log((64 + 64%i)a   |-----  + x\|2 )
             4|    4                   4|    4
             \|256a                    \|256a
     + 
                +-----+                   +-----+3
                |  1                   4  |  1           +-+
       - 4%i a  |----- log((64 + 64%i)a   |-----  + %i x\|2 )
               4|    4                   4|    4
               \|256a                    \|256a
     + 
              +-----+                   +-----+3
              |  1                   4  |  1           +-+
       4%i a  |----- log((64 + 64%i)a   |-----  - %i x\|2 )
             4|    4                   4|    4
             \|256a                    \|256a
     + 
                +-----+                   +-----+3                       +-----+
                |  1                   4  |  1        +-+                |  1
       - 4%i a  |----- log((64 + 64%i)a   |-----  - x\|2  + 4a log(- 1)  |-----
               4|    4                   4|    4                        4|    4
               \|256a                    \|256a                         \|256a
     + 
               +-+    2    2               +-+       2       2
       log(a x\|2  + x  + a ) + %i log(a x\|2  + %i x  - %i a )
     + 
                    +-+       2       2            +-+    2    2
       - %i log(a x\|2  - %i x  + %i a ) - log(a x\|2  - x  - a )
     + 
       (- 1 - %i)log(- 1)
  /
        +-+
     4a\|2
                                             Type: Expression Complex Integer
--R
--R   (6)
--R             +-----+               +-----+3        +-----+2
--R             |  1          4  +-+  |  1         4  |  1       2
--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
--R            4|    4               4|    4         4|    4
--R            \|256a                \|256a          \|256a
--R     + 
--R           +-----+               +-----+3        +-----+2
--R           |  1          4  +-+  |  1         4  |  1       2
--R       4a  |----- log(64a x\|2   |-----  - 16a   |-----  - x )
--R          4|    4               4|    4         4|    4
--R          \|256a                \|256a          \|256a
--R     + 
--R              +-----+                   +-----+3
--R              |  1                   4  |  1        +-+
--R       4%i a  |----- log((64 + 64%i)a   |-----  + x\|2 )
--R             4|    4                   4|    4
--R             \|256a                    \|256a
--R     + 
--R                +-----+                   +-----+3
--R                |  1                   4  |  1           +-+
--R       - 4%i a  |----- log((64 + 64%i)a   |-----  + %i x\|2 )
--R               4|    4                   4|    4
--R               \|256a                    \|256a
--R     + 
--R              +-----+                   +-----+3
--R              |  1                   4  |  1           +-+
--R       4%i a  |----- log((64 + 64%i)a   |-----  - %i x\|2 )
--R             4|    4                   4|    4
--R             \|256a                    \|256a
--R     + 
--R                +-----+                   +-----+3                       +-----+
--R                |  1                   4  |  1        +-+                |  1
--R       - 4%i a  |----- log((64 + 64%i)a   |-----  - x\|2  + 4a log(- 1)  |-----
--R               4|    4                   4|    4                        4|    4
--R               \|256a                    \|256a                         \|256a
--R     + 
--R               +-+    2    2               +-+       2       2
--R       log(a x\|2  + x  + a ) + %i log(a x\|2  + %i x  - %i a )
--R     + 
--R                    +-+       2       2            +-+    2    2
--R       - %i log(a x\|2  - %i x  + %i a ) - log(a x\|2  - x  - a )
--R     + 
--R       (- 1 - %i)log(- 1)
--R  /
--R        +-+
--R     4a\|2
--R                                             Type: Expression Complex Integer
--E

--S 19 of 65
ff:=rootSimp ee
 

   (7)
                  +-+       2       2               +-+       2       2
       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
     + 
                +-+                            +-+
       %i log(x\|2  + (1 + %i)a) - %i log(%i x\|2  + (1 + %i)a)
     + 
                   +-+                           +-+
     %i log(- %i x\|2  + (1 + %i)a) - %i log(- x\|2  + (1 + %i)a) - %i log(- 1)
  /
        +-+
     4a\|2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                  +-+       2       2               +-+       2       2
--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
--R     + 
--R                +-+                            +-+
--R       %i log(x\|2  + (1 + %i)a) - %i log(%i x\|2  + (1 + %i)a)
--R     + 
--R                   +-+                           +-+
--R     %i log(- %i x\|2  + (1 + %i)a) - %i log(- x\|2  + (1 + %i)a) - %i log(- 1)
--R  /
--R        +-+
--R     4a\|2
--R                                             Type: Expression Complex Integer
--E

--S 20 of 65     14:313 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

        %i log(2) - %i log(- 1) - %i log(- 2)
   (8)  -------------------------------------
                           +-+
                        4a\|2
                                             Type: Expression Complex Integer
--R
--R        %i log(2) - %i log(- 1) - %i log(- 2)
--R   (8)  -------------------------------------
--R                           +-+
--R                        4a\|2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 21 of 65
aa:=integrate(x^3/(x^4+a^4),x)
 

             4    4
        log(x  + a )
   (1)  ------------
              4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4    4
--R        log(x  + a )
--R   (1)  ------------
--R              4
--R                                          Type: Union(Expression Integer,...)
--E

--S 22 of 65
bb:=1/4*log(x^4+a^4)
 

             4    4
        log(x  + a )
   (2)  ------------
              4
                                                     Type: Expression Integer
--R
--R             4    4
--R        log(x  + a )
--R   (2)  ------------
--R              4
--R                                                     Type: Expression Integer
--E 

--S 23 of 65     14:314 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 24 of 65
aa:=integrate(1/(x*(x^4+a^4)),x)
 

               4    4
        - log(x  + a ) + 4log(x)
   (1)  ------------------------
                     4
                   4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               4    4
--R        - log(x  + a ) + 4log(x)
--R   (1)  ------------------------
--R                     4
--R                   4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25 of 65
bb:=1/(4*a^4)*log(x^4/(x^4+a^4))
 

                4
               x
        log(-------)
             4    4
            x  + a
   (2)  ------------
               4
             4a
                                                     Type: Expression Integer
--R
--R                4
--R               x
--R        log(-------)
--R             4    4
--R            x  + a
--R   (2)  ------------
--R               4
--R             4a
--R                                                     Type: Expression Integer
--E

--S 26 of 65
cc:=aa-bb
 

                                           4
               4    4                     x
        - log(x  + a ) + 4log(x) - log(-------)
                                        4    4
                                       x  + a
   (3)  ---------------------------------------
                            4
                          4a
                                                     Type: Expression Integer
--R
--R                                           4
--R               4    4                     x
--R        - log(x  + a ) + 4log(x) - log(-------)
--R                                        4    4
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            4
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 27 of 65     14:315 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 65
aa:=integrate(1/(x^2*(x^4+a^4)),x)
 

   (1)
            +------+                +------+3         +------+2
        4   |   1          16  +-+  |   1         12  |   1       2
       a x  |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
              +------+                  +------+3         +------+2
          4   |   1            16  +-+  |   1         12  |   1       2
       - a x  |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
             4|    20                  4|    20          4|    20
             \|256a                    \|256a            \|256a
     + 
                                       +------+3
                                   16  |   1
                                64a    |------
               +------+               4|    20
           4   |   1                  \|256a
       - 2a x  |------ atan(-----------------------)
              4|    20             +------+3
              \|256a           16  |   1        +-+
                            64a    |------  - x\|2
                                  4|    20
                                  \|256a
     + 
                                     +------+3
                                 16  |   1
                              64a    |------
             +------+               4|    20
         4   |   1                  \|256a           +-+
       2a x  |------ atan(----------------------- - \|2
            4|    20             +------+3
            \|256a           16  |   1        +-+
                          64a    |------  + x\|2
                                4|    20
                                \|256a
  /
      4  +-+
     a x\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +------+                +------+3         +------+2
--R        4   |   1          16  +-+  |   1         12  |   1       2
--R       a x  |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R              +------+                  +------+3         +------+2
--R          4   |   1            16  +-+  |   1         12  |   1       2
--R       - a x  |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
--R             4|    20                  4|    20          4|    20
--R             \|256a                    \|256a            \|256a
--R     + 
--R                                       +------+3
--R                                   16  |   1
--R                                64a    |------
--R               +------+               4|    20
--R           4   |   1                  \|256a
--R       - 2a x  |------ atan(-----------------------)
--R              4|    20             +------+3
--R              \|256a           16  |   1        +-+
--R                            64a    |------  - x\|2
--R                                  4|    20
--R                                  \|256a
--R     + 
--R                                     +------+3
--R                                 16  |   1
--R                              64a    |------
--R             +------+               4|    20
--R         4   |   1                  \|256a           +-+
--R       2a x  |------ atan(----------------------- - \|2
--R            4|    20             +------+3
--R            \|256a           16  |   1        +-+
--R                          64a    |------  + x\|2
--R                                4|    20
--R                                \|256a
--R  /
--R      4  +-+
--R     a x\|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29 of 65
bb:=-1/(a^4*x)-1/(4*a^5*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))+1/(2*a^5*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
 

                         +-+    2    2                   +-+
            +-+    - a x\|2  + x  + a        +-+     a x\|2
        - x\|2 log(-------------------) + 2x\|2 atan(-------) - 8a
                        +-+    2    2                 2    2
                    a x\|2  + x  + a                 x  - a
   (2)  ----------------------------------------------------------
                                     5
                                   8a x
                                                     Type: Expression Integer
--R
--R                         +-+    2    2                   +-+
--R            +-+    - a x\|2  + x  + a        +-+     a x\|2
--R        - x\|2 log(-------------------) + 2x\|2 atan(-------) - 8a
--R                        +-+    2    2                 2    2
--R                    a x\|2  + x  + a                 x  - a
--R   (2)  ----------------------------------------------------------
--R                                     5
--R                                   8a x
--R                                                     Type: Expression Integer
--E

--S 30 of 65
cc:=aa-bb
 

   (3)
            +------+                +------+3         +------+2
         5  |   1          16  +-+  |   1         12  |   1       2
       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
              +------+                  +------+3         +------+2
           5  |   1            16  +-+  |   1         12  |   1       2
       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
             4|    20                  4|    20          4|    20
             \|256a                    \|256a            \|256a
     + 
                                      +------+3
                                  16  |   1
                               64a    |------
              +------+               4|    20
           5  |   1                  \|256a
       - 8a   |------ atan(-----------------------)
             4|    20             +------+3
             \|256a           16  |   1        +-+
                           64a    |------  - x\|2
                                 4|    20
                                 \|256a
     + 
                                    +------+3
                                16  |   1
                             64a    |------
            +------+               4|    20                  +-+    2    2
         5  |   1                  \|256a              - a x\|2  + x  + a
       8a   |------ atan(----------------------- + log(-------------------)
           4|    20             +------+3                   +-+    2    2
           \|256a           16  |   1        +-+        a x\|2  + x  + a
                         64a    |------  + x\|2
                               4|    20
                               \|256a
     + 
                   +-+
               a x\|2
       - 2atan(-------)
                2    2
               x  - a
  /
       5 +-+
     4a \|2
                                                     Type: Expression Integer
--R
--R   (3)
--R            +------+                +------+3         +------+2
--R         5  |   1          16  +-+  |   1         12  |   1       2
--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R              +------+                  +------+3         +------+2
--R           5  |   1            16  +-+  |   1         12  |   1       2
--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
--R             4|    20                  4|    20          4|    20
--R             \|256a                    \|256a            \|256a
--R     + 
--R                                      +------+3
--R                                  16  |   1
--R                               64a    |------
--R              +------+               4|    20
--R           5  |   1                  \|256a
--R       - 8a   |------ atan(-----------------------)
--R             4|    20             +------+3
--R             \|256a           16  |   1        +-+
--R                           64a    |------  - x\|2
--R                                 4|    20
--R                                 \|256a
--R     + 
--R                                    +------+3
--R                                16  |   1
--R                             64a    |------
--R            +------+               4|    20                  +-+    2    2
--R         5  |   1                  \|256a              - a x\|2  + x  + a
--R       8a   |------ atan(----------------------- + log(-------------------)
--R           4|    20             +------+3                   +-+    2    2
--R           \|256a           16  |   1        +-+        a x\|2  + x  + a
--R                         64a    |------  + x\|2
--R                               4|    20
--R                               \|256a
--R     + 
--R                   +-+
--R               a x\|2
--R       - 2atan(-------)
--R                2    2
--R               x  - a
--R  /
--R       5 +-+
--R     4a \|2
--R                                                     Type: Expression Integer
--E

--S 31 of 65
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 32 of 65
dd:=atanrule cc
 

   (5)
            +------+                +------+3         +------+2
         5  |   1          16  +-+  |   1         12  |   1       2
       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
                                               +------+3
                                           16  |   1           +-+
                             (- 64 + 64%i)a    |------  + %i x\|2
                 +------+                     4|    20
              5  |   1                        \|256a
       - 4%i a   |------ log(-------------------------------------)
                4|    20                      +------+3
                \|256a                    16  |   1           +-+
                              (64 + 64%i)a    |------  + %i x\|2
                                             4|    20
                                             \|256a
     + 
                                             +------+3
                                         16  |   1           +-+
                           (- 64 + 64%i)a    |------  - %i x\|2
               +------+                     4|    20
            5  |   1                        \|256a
       4%i a   |------ log(-------------------------------------)
              4|    20                      +------+3
              \|256a                    16  |   1           +-+
                            (64 + 64%i)a    |------  - %i x\|2
                                           4|    20
                                           \|256a
     + 
              +------+                  +------+3         +------+2
           5  |   1            16  +-+  |   1         12  |   1       2
       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
             4|    20                  4|    20          4|    20
             \|256a                    \|256a            \|256a
     + 
                 +-+    2    2                 +-+       2       2
           - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
       log(-------------------) + %i log(-------------------------)
                +-+    2    2                 +-+       2       2
            a x\|2  + x  + a              a x\|2  + %i x  - %i a
  /
       5 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (5)
--R            +------+                +------+3         +------+2
--R         5  |   1          16  +-+  |   1         12  |   1       2
--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R                                               +------+3
--R                                           16  |   1           +-+
--R                             (- 64 + 64%i)a    |------  + %i x\|2
--R                 +------+                     4|    20
--R              5  |   1                        \|256a
--R       - 4%i a   |------ log(-------------------------------------)
--R                4|    20                      +------+3
--R                \|256a                    16  |   1           +-+
--R                              (64 + 64%i)a    |------  + %i x\|2
--R                                             4|    20
--R                                             \|256a
--R     + 
--R                                             +------+3
--R                                         16  |   1           +-+
--R                           (- 64 + 64%i)a    |------  - %i x\|2
--R               +------+                     4|    20
--R            5  |   1                        \|256a
--R       4%i a   |------ log(-------------------------------------)
--R              4|    20                      +------+3
--R              \|256a                    16  |   1           +-+
--R                            (64 + 64%i)a    |------  - %i x\|2
--R                                           4|    20
--R                                           \|256a
--R     + 
--R              +------+                  +------+3         +------+2
--R           5  |   1            16  +-+  |   1         12  |   1       2
--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
--R             4|    20                  4|    20          4|    20
--R             \|256a                    \|256a            \|256a
--R     + 
--R                 +-+    2    2                 +-+       2       2
--R           - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
--R       log(-------------------) + %i log(-------------------------)
--R                +-+    2    2                 +-+       2       2
--R            a x\|2  + x  + a              a x\|2  + %i x  - %i a
--R  /
--R       5 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 33 of 65
ee:=expandLog dd
 

   (6)
            +------+                +------+3         +------+2
         5  |   1          16  +-+  |   1         12  |   1       2
       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
           4|    20                4|    20          4|    20
           \|256a                  \|256a            \|256a
     + 
              +------+                +------+3         +------+2
           5  |   1          16  +-+  |   1         12  |   1       2
       - 4a   |------ log(64a  x\|2   |------  - 16a    |------  - x )
             4|    20                4|    20          4|    20
             \|256a                  \|256a            \|256a
     + 
                 +------+                    +------+3
              5  |   1                   16  |   1        +-+
       - 4%i a   |------ log((64 + 64%i)a    |------  + x\|2 )
                4|    20                    4|    20
                \|256a                      \|256a
     + 
               +------+                    +------+3
            5  |   1                   16  |   1           +-+
       4%i a   |------ log((64 + 64%i)a    |------  + %i x\|2 )
              4|    20                    4|    20
              \|256a                      \|256a
     + 
                 +------+                    +------+3
              5  |   1                   16  |   1           +-+
       - 4%i a   |------ log((64 + 64%i)a    |------  - %i x\|2 )
                4|    20                    4|    20
                \|256a                      \|256a
     + 
               +------+                    +------+3
            5  |   1                   16  |   1        +-+
       4%i a   |------ log((64 + 64%i)a    |------  - x\|2 )
              4|    20                    4|    20
              \|256a                      \|256a
     + 
                      +------+
           5          |   1             +-+    2    2
       - 4a log(- 1)  |------ - log(a x\|2  + x  + a )
                     4|    20
                     \|256a
     + 
                    +-+       2       2               +-+       2       2
       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
     + 
               +-+    2    2
       log(a x\|2  - x  - a ) + (1 + %i)log(- 1)
  /
       5 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (6)
--R            +------+                +------+3         +------+2
--R         5  |   1          16  +-+  |   1         12  |   1       2
--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
--R           4|    20                4|    20          4|    20
--R           \|256a                  \|256a            \|256a
--R     + 
--R              +------+                +------+3         +------+2
--R           5  |   1          16  +-+  |   1         12  |   1       2
--R       - 4a   |------ log(64a  x\|2   |------  - 16a    |------  - x )
--R             4|    20                4|    20          4|    20
--R             \|256a                  \|256a            \|256a
--R     + 
--R                 +------+                    +------+3
--R              5  |   1                   16  |   1        +-+
--R       - 4%i a   |------ log((64 + 64%i)a    |------  + x\|2 )
--R                4|    20                    4|    20
--R                \|256a                      \|256a
--R     + 
--R               +------+                    +------+3
--R            5  |   1                   16  |   1           +-+
--R       4%i a   |------ log((64 + 64%i)a    |------  + %i x\|2 )
--R              4|    20                    4|    20
--R              \|256a                      \|256a
--R     + 
--R                 +------+                    +------+3
--R              5  |   1                   16  |   1           +-+
--R       - 4%i a   |------ log((64 + 64%i)a    |------  - %i x\|2 )
--R                4|    20                    4|    20
--R                \|256a                      \|256a
--R     + 
--R               +------+                    +------+3
--R            5  |   1                   16  |   1        +-+
--R       4%i a   |------ log((64 + 64%i)a    |------  - x\|2 )
--R              4|    20                    4|    20
--R              \|256a                      \|256a
--R     + 
--R                      +------+
--R           5          |   1             +-+    2    2
--R       - 4a log(- 1)  |------ - log(a x\|2  + x  + a )
--R                     4|    20
--R                     \|256a
--R     + 
--R                    +-+       2       2               +-+       2       2
--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
--R     + 
--R               +-+    2    2
--R       log(a x\|2  - x  - a ) + (1 + %i)log(- 1)
--R  /
--R       5 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 34 of 65
ff:=rootSimp ee
 

   (7)
                    +-+       2       2               +-+       2       2
       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
     + 
                  +-+                            +-+
       - %i log(x\|2  + (1 + %i)a) + %i log(%i x\|2  + (1 + %i)a)
     + 
                       +-+                           +-+
       - %i log(- %i x\|2  + (1 + %i)a) + %i log(- x\|2  + (1 + %i)a)
     + 
       %i log(- 1)
  /
       5 +-+
     4a \|2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                    +-+       2       2               +-+       2       2
--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
--R     + 
--R                  +-+                            +-+
--R       - %i log(x\|2  + (1 + %i)a) + %i log(%i x\|2  + (1 + %i)a)
--R     + 
--R                       +-+                           +-+
--R       - %i log(- %i x\|2  + (1 + %i)a) + %i log(- x\|2  + (1 + %i)a)
--R     + 
--R       %i log(- 1)
--R  /
--R       5 +-+
--R     4a \|2
--R                                             Type: Expression Complex Integer
--E

--S 35 of 65     14:316 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

        - %i log(2) + %i log(- 1) + %i log(- 2)
   (8)  ---------------------------------------
                          5 +-+
                        4a \|2
                                             Type: Expression Complex Integer
--R
--R        - %i log(2) + %i log(- 1) + %i log(- 2)
--R   (8)  ---------------------------------------
--R                          5 +-+
--R                        4a \|2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 36 of 65
aa:=integrate(1/(x^3*(x^4+a^4)),x)
 

                  2
           2     x      2
        - x atan(--) - a
                  2
                 a
   (1)  -----------------
                6 2
              2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R           2     x      2
--R        - x atan(--) - a
--R                  2
--R                 a
--R   (1)  -----------------
--R                6 2
--R              2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37 of 65
bb:=-1/(2*a^4*x^2)-1/(2*a^6)*atan(x^2/a^2)
 

                  2
           2     x      2
        - x atan(--) - a
                  2
                 a
   (2)  -----------------
                6 2
              2a x
                                                     Type: Expression Integer
--R
--R                  2
--R           2     x      2
--R        - x atan(--) - a
--R                  2
--R                 a
--R   (2)  -----------------
--R                6 2
--R              2a x
--R                                                     Type: Expression Integer
--E

--S 38 of 65     14:317 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 65
aa:=integrate(1/(x^4-a^4),x)
 

                                          x
        - log(x + a) + log(x - a) - 2atan(-)
                                          a
   (1)  ------------------------------------
                           3
                         4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          x
--R        - log(x + a) + log(x - a) - 2atan(-)
--R                                          a
--R   (1)  ------------------------------------
--R                           3
--R                         4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40 of 65
bb:=1/(4*a^3)*log((x-a)/(x+a))-1/(2*a^3)*atan(x/a)
 

            x - a          x
        log(-----) - 2atan(-)
            x + a          a
   (2)  ---------------------
                   3
                 4a
                                                     Type: Expression Integer
--R
--R            x - a          x
--R        log(-----) - 2atan(-)
--R            x + a          a
--R   (2)  ---------------------
--R                   3
--R                 4a
--R                                                     Type: Expression Integer
--E

--S 41 of 65
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                            3
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                            3
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 42 of 65     14:318 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 43 of 65
aa:=integrate(x/(x^4-a^4),x)
 

               2    2         2    2
        - log(x  + a ) + log(x  - a )
   (1)  -----------------------------
                       2
                     4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2         2    2
--R        - log(x  + a ) + log(x  - a )
--R   (1)  -----------------------------
--R                       2
--R                     4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 44 of 65
bb:=1/(4*a^2)*log((x^2-a^2)/(x^2+a^2))
 

             2    2
            x  - a
        log(-------)
             2    2
            x  + a
   (2)  ------------
               2
             4a
                                                     Type: Expression Integer
--R
--R             2    2
--R            x  - a
--R        log(-------)
--R             2    2
--R            x  + a
--R   (2)  ------------
--R               2
--R             4a
--R                                                     Type: Expression Integer
--E

--S 45 of 65
cc:=aa-bb
 

                                             2    2
               2    2         2    2        x  - a
        - log(x  + a ) + log(x  - a ) - log(-------)
                                             2    2
                                            x  + a
   (3)  --------------------------------------------
                               2
                             4a
                                                     Type: Expression Integer
--R
--R                                             2    2
--R               2    2         2    2        x  - a
--R        - log(x  + a ) + log(x  - a ) - log(-------)
--R                                             2    2
--R                                            x  + a
--R   (3)  --------------------------------------------
--R                               2
--R                             4a
--R                                                     Type: Expression Integer
--E

--S 46 of 65     14:319 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 47 of 65
aa:=integrate(x^2/(x^4-a^4),x)
 

                                          x
        - log(x + a) + log(x - a) + 2atan(-)
                                          a
   (1)  ------------------------------------
                         4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          x
--R        - log(x + a) + log(x - a) + 2atan(-)
--R                                          a
--R   (1)  ------------------------------------
--R                         4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 48 of 65
bb:=1/(4*a)*log((x-a)/(x+a))+1/(2*a)*atan(x/a)
 

            x - a          x
        log(-----) + 2atan(-)
            x + a          a
   (2)  ---------------------
                  4a
                                                     Type: Expression Integer
--R
--R            x - a          x
--R        log(-----) + 2atan(-)
--R            x + a          a
--R   (2)  ---------------------
--R                  4a
--R                                                     Type: Expression Integer
--E 

--S 49 of 65
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 50 of 65     14:320 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 51 of 65
aa:=integrate(x^3/(x^4-a^4),x)
 

             4    4
        log(x  - a )
   (1)  ------------
              4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4    4
--R        log(x  - a )
--R   (1)  ------------
--R              4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 52 of 65
bb:=1/4*log(x^4-a^4)
 

             4    4
        log(x  - a )
   (2)  ------------
              4
                                                     Type: Expression Integer
--R
--R             4    4
--R        log(x  - a )
--R   (2)  ------------
--R              4
--R                                                     Type: Expression Integer
--E

--S 53 of 65     14:321 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 54 of 65
aa:=integrate(1/(x*(x^4-a^4)),x)
 

             4    4
        log(x  - a ) - 4log(x)
   (1)  ----------------------
                    4
                  4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4    4
--R        log(x  - a ) - 4log(x)
--R   (1)  ----------------------
--R                    4
--R                  4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 55 of 65
bb:=1/(4*a^4)*log((x^4-a^4)/x^4)
 

             4    4
            x  - a
        log(-------)
                4
               x
   (2)  ------------
               4
             4a
                                                     Type: Expression Integer
--R
--R             4    4
--R            x  - a
--R        log(-------)
--R                4
--R               x
--R   (2)  ------------
--R               4
--R             4a
--R                                                     Type: Expression Integer
--E 

--S 56 of 65
cc:=aa-bb
 

                                      4    4
             4    4                  x  - a
        log(x  - a ) - 4log(x) - log(-------)
                                         4
                                        x
   (3)  -------------------------------------
                           4
                         4a
                                                     Type: Expression Integer
--R
--R                                      4    4
--R             4    4                  x  - a
--R        log(x  - a ) - 4log(x) - log(-------)
--R                                         4
--R                                        x
--R   (3)  -------------------------------------
--R                           4
--R                         4a
--R                                                     Type: Expression Integer
--E

--S 57 of 65     14:322 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 58 of 65
aa:=integrate(1/(x^2*(x^4-a^4)),x)
 

                                                x
        - x log(x + a) + x log(x - a) + 2x atan(-) + 4a
                                                a
   (1)  -----------------------------------------------
                                5
                              4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                x
--R        - x log(x + a) + x log(x - a) + 2x atan(-) + 4a
--R                                                a
--R   (1)  -----------------------------------------------
--R                                5
--R                              4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 59 of 65
bb:=1/(a^4*x)+1/(4*a^5)*log((x-a)/(x+a))+1/(2*a^5)*atan(x/a)
 

              x - a            x
        x log(-----) + 2x atan(-) + 4a
              x + a            a
   (2)  ------------------------------
                       5
                     4a x
                                                     Type: Expression Integer
--R
--R              x - a            x
--R        x log(-----) + 2x atan(-) + 4a
--R              x + a            a
--R   (2)  ------------------------------
--R                       5
--R                     4a x
--R                                                     Type: Expression Integer
--E

--S 60 of 65
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                            5
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                            5
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 61 of 65     14:323 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 62 of 65
aa:=integrate(1/(x^3*(x^4-a^4)),x)
 

           2     2    2     2     2    2      2
        - x log(x  + a ) + x log(x  - a ) + 2a
   (1)  ---------------------------------------
                           6 2
                         4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2     2     2    2      2
--R        - x log(x  + a ) + x log(x  - a ) + 2a
--R   (1)  ---------------------------------------
--R                           6 2
--R                         4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63 of 65
bb:=1/(2*a^4*x^2)+1/(4*a^6)*log((x^2-a^2)/(x^2+a^2))
 

               2    2
         2    x  - a       2
        x log(-------) + 2a
               2    2
              x  + a
   (2)  --------------------
                  6 2
                4a x
                                                     Type: Expression Integer
--R
--R               2    2
--R         2    x  - a       2
--R        x log(-------) + 2a
--R               2    2
--R              x  + a
--R   (2)  --------------------
--R                  6 2
--R                4a x
--R                                                     Type: Expression Integer
--E

--S 64 of 65
cc:=aa-bb
 

                                             2    2
               2    2         2    2        x  - a
        - log(x  + a ) + log(x  - a ) - log(-------)
                                             2    2
                                            x  + a
   (3)  --------------------------------------------
                               6
                             4a
                                                     Type: Expression Integer
--R
--R                                             2    2
--R               2    2         2    2        x  - a
--R        - log(x  + a ) + log(x  - a ) - log(-------)
--R                                             2    2
--R                                            x  + a
--R   (3)  --------------------------------------------
--R                               6
--R                             4a
--R                                                     Type: Expression Integer
--E

--S 65 of 65     14:324 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)spool
 
Starts dribbling to uniseg.output (2010/3/27, 18:41:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
pints  := 1..
 

   (1)  1..
                                       Type: UniversalSegment PositiveInteger
--R 
--R
--R   (1)  1..
--R                                       Type: UniversalSegment PositiveInteger
--E 1

--S 2 of 9
nevens := (0..) by -2
 

   (2)  0.. by - 2
                                    Type: UniversalSegment NonNegativeInteger
--R 
--R
--R   (2)  0.. by - 2
--R                                    Type: UniversalSegment NonNegativeInteger
--E 2

--S 3 of 9
useg: UniversalSegment(Integer) := 3..10
 

   (3)  3..10
                                               Type: UniversalSegment Integer
--R 
--R
--R   (3)  3..10
--R                                               Type: UniversalSegment Integer
--E 3

--S 4 of 9
hasHi pints
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 9
hasHi nevens
 

   (5)  false
                                                                Type: Boolean
--R 
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 9
hasHi useg
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 9
expand pints
 

   (7)  [1,2,3,4,5,6,7,8,9,10,...]
                                                         Type: Stream Integer
--R 
--R
--R   (7)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                         Type: Stream Integer
--E 7

--S 8 of 9
expand nevens
 

   (8)  [0,- 2,- 4,- 6,- 8,- 10,- 12,- 14,- 16,- 18,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [0,- 2,- 4,- 6,- 8,- 10,- 12,- 14,- 16,- 18,...]
--R                                                         Type: Stream Integer
--E 8

--S 9 of 9
expand [1, 3, 10..15, 100..]
 

   (9)  [1,3,10,11,12,13,14,15,100,101,...]
                                                         Type: Stream Integer
--R 
--R
--R   (9)  [1,3,10,11,12,13,14,15,100,101,...]
--R                                                         Type: Stream Integer
--E 9
)spool 
 
Starts dribbling to schaum6.output (2010/3/27, 18:37:17).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 68
aa:=integrate(1/(x^2+a^2),x)
 

             x
        atan(-)
             a
   (1)  -------
           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R        atan(-)
--R             a
--R   (1)  -------
--R           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 68
bb:=(1/a)*atan(x/a)
 

             x
        atan(-)
             a
   (2)  -------
           a
                                                     Type: Expression Integer
--R
--R             x
--R        atan(-)
--R             a
--R   (2)  -------
--R           a
--R                                                     Type: Expression Integer
--E

--S 3 of 68      14:125 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 4 of 68
aa:=integrate(x/(x^2+a^2),x)
 

             2    2
        log(x  + a )
   (1)  ------------
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R        log(x  + a )
--R   (1)  ------------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 68
bb:=(1/2)*log(x^2+a^2)
 

             2    2
        log(x  + a )
   (2)  ------------
              2
                                                     Type: Expression Integer
--R
--R             2    2
--R        log(x  + a )
--R   (2)  ------------
--R              2
--R                                                     Type: Expression Integer
--E

--S 6 of 68      14:126 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 

--S 7 of 68
aa:=integrate(x^2/(x^2+a^2),x)
 

                 x
   (1)  - a atan(-) + x
                 a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 x
--R   (1)  - a atan(-) + x
--R                 a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 68
bb:=x-a*atan(x/a)
 

                 x
   (2)  - a atan(-) + x
                 a
                                                     Type: Expression Integer
--R
--R                 x
--R   (2)  - a atan(-) + x
--R                 a
--R                                                     Type: Expression Integer
--E

--S 9 of 68      14:127 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 10 of 68
aa:=integrate(x^3/(x^2+a^2),x)
 

           2     2    2     2
        - a log(x  + a ) + x
   (1)  ---------------------
                  2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2     2
--R        - a log(x  + a ) + x
--R   (1)  ---------------------
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 68
bb:=x^2/2-a^2/2*log(x^2+a^2)
 

           2     2    2     2
        - a log(x  + a ) + x
   (2)  ---------------------
                  2
                                                     Type: Expression Integer
--R
--R           2     2    2     2
--R        - a log(x  + a ) + x
--R   (2)  ---------------------
--R                  2
--R                                                     Type: Expression Integer
--E

--S 12 of 68     14:128 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 68
aa:=integrate(1/(x*(x^2+a^2)),x)
 

               2    2
        - log(x  + a ) + 2log(x)
   (1)  ------------------------
                     2
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R        - log(x  + a ) + 2log(x)
--R   (1)  ------------------------
--R                     2
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 68
bb:=1/(2*a^2)*log(x^2/(x^2+a^2))
 

                2
               x
        log(-------)
             2    2
            x  + a
   (2)  ------------
               2
             2a
                                                     Type: Expression Integer
--R
--R                2
--R               x
--R        log(-------)
--R             2    2
--R            x  + a
--R   (2)  ------------
--R               2
--R             2a
--R                                                     Type: Expression Integer
--E

--S 15 of 68
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  + a ) + 2log(x) - log(-------)
                                        2    2
                                       x  + a
   (3)  ---------------------------------------
                            2
                          2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  + a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            2
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 16 of 68
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 17 of 68
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  2
                2a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  2
--R                2a
--R                                                     Type: Expression Integer
--E

--S 18 of 68
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19 of 68     14:129 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 20 of 68
aa:=integrate(1/(x^2*(x^2+a^2)),x)
 

                 x
        - x atan(-) - a
                 a
   (1)  ---------------
               3
              a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 x
--R        - x atan(-) - a
--R                 a
--R   (1)  ---------------
--R               3
--R              a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21 of 68
bb:=-1/(a^2*x)-1/a^3*atan(x/a)
 

                 x
        - x atan(-) - a
                 a
   (2)  ---------------
               3
              a x
                                                     Type: Expression Integer
--R
--R                 x
--R        - x atan(-) - a
--R                 a
--R   (2)  ---------------
--R               3
--R              a x
--R                                                     Type: Expression Integer
--E

--S 22 of 68     14:130 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 23 of 68
aa:=integrate(1/(x^3*(x^2+a^2)),x)
 

         2     2    2      2          2
        x log(x  + a ) - 2x log(x) - a
   (1)  -------------------------------
                       4 2
                     2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         2     2    2      2          2
--R        x log(x  + a ) - 2x log(x) - a
--R   (1)  -------------------------------
--R                       4 2
--R                     2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 68
bb:=-1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2+a^2))
 

                    2
           2       x        2
        - x log(-------) - a
                 2    2
                x  + a
   (2)  ---------------------
                  4 2
                2a x
                                                     Type: Expression Integer
--R
--R                    2
--R           2       x        2
--R        - x log(-------) - a
--R                 2    2
--R                x  + a
--R   (2)  ---------------------
--R                  4 2
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 25 of 68
cc:=aa-bb
 

                                         2
             2    2                     x
        log(x  + a ) - 2log(x) + log(-------)
                                      2    2
                                     x  + a
   (3)  -------------------------------------
                           4
                         2a
                                                     Type: Expression Integer
--R
--R                                         2
--R             2    2                     x
--R        log(x  + a ) - 2log(x) + log(-------)
--R                                      2    2
--R                                     x  + a
--R   (3)  -------------------------------------
--R                           4
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 26 of 68
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27 of 68
dd:=divlog cc
 

             2
        log(x ) - 2log(x)
   (5)  -----------------
                 4
               2a
                                                     Type: Expression Integer
--R
--R             2
--R        log(x ) - 2log(x)
--R   (5)  -----------------
--R                 4
--R               2a
--R                                                     Type: Expression Integer
--E

--S 28 of 68
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29 of 68     14:131 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 30 of 68
aa:=integrate(1/((x^2+a^2)^2),x)
 

          2    2      x
        (x  + a )atan(-) + a x
                      a
   (1)  ----------------------
                3 2     5
              2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      x
--R        (x  + a )atan(-) + a x
--R                      a
--R   (1)  ----------------------
--R                3 2     5
--R              2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 31 of 68
bb:=x/(2*a^2*(x^2+a^2))+1/(2*a^3)*atan(x/a)
 

          2    2      x
        (x  + a )atan(-) + a x
                      a
   (2)  ----------------------
                3 2     5
              2a x  + 2a
                                                     Type: Expression Integer
--R
--R          2    2      x
--R        (x  + a )atan(-) + a x
--R                      a
--R   (2)  ----------------------
--R                3 2     5
--R              2a x  + 2a
--R                                                     Type: Expression Integer
--E

--S 32 of 68     14:132 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 33 of 68
aa:=integrate(x/((x^2+a^2)^2),x)
 

              1
   (1)  - ---------
            2     2
          2x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            2     2
--R          2x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34 of 68
bb:=-1/(2*(x^2+a^2))
 

              1
   (2)  - ---------
            2     2
          2x  + 2a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            2     2
--R          2x  + 2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 35 of 68     14:133 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 36 of 68
aa:=integrate(x^2/((x^2+a^2)^2),x)
 

          2    2      x
        (x  + a )atan(-) - a x
                      a
   (1)  ----------------------
                  2     3
              2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      x
--R        (x  + a )atan(-) - a x
--R                      a
--R   (1)  ----------------------
--R                  2     3
--R              2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37 of 68
bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a)
 

          2    2      x
        (x  + a )atan(-) - a x
                      a
   (2)  ----------------------
                  2     3
              2a x  + 2a
                                                     Type: Expression Integer
--R
--R          2    2      x
--R        (x  + a )atan(-) - a x
--R                      a
--R   (2)  ----------------------
--R                  2     3
--R              2a x  + 2a
--R                                                     Type: Expression Integer
--E

--S 38 of 68     14:134 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 68
aa:=integrate(x^3/((x^2+a^2)^2),x)
 

          2    2      2    2     2
        (x  + a )log(x  + a ) + a
   (1)  --------------------------
                   2     2
                 2x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      2    2     2
--R        (x  + a )log(x  + a ) + a
--R   (1)  --------------------------
--R                   2     2
--R                 2x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40 of 68
bb:=a^2/(2*(x^2+a^2))+1/2*log(x^2+a^2)
 

          2    2      2    2     2
        (x  + a )log(x  + a ) + a
   (2)  --------------------------
                   2     2
                 2x  + 2a
                                                     Type: Expression Integer
--R
--R          2    2      2    2     2
--R        (x  + a )log(x  + a ) + a
--R   (2)  --------------------------
--R                   2     2
--R                 2x  + 2a
--R                                                     Type: Expression Integer
--E

--S 41 of 68     14:135 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 42 of 68
aa:=integrate(1/(x*(x^2+a^2)^2),x)
 

            2    2      2    2       2     2           2
        (- x  - a )log(x  + a ) + (2x  + 2a )log(x) + a
   (1)  ------------------------------------------------
                             4 2     6
                           2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2      2    2       2     2           2
--R        (- x  - a )log(x  + a ) + (2x  + 2a )log(x) + a
--R   (1)  ------------------------------------------------
--R                             4 2     6
--R                           2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 43 of 68
bb:=1/(2*a^2*(x^2+a^2))+1/(2*a^4)*log(x^2/(x^2+a^2))
 

                         2
          2    2        x        2
        (x  + a )log(-------) + a
                      2    2
                     x  + a
   (2)  --------------------------
                  4 2     6
                2a x  + 2a
                                                     Type: Expression Integer
--R
--R                         2
--R          2    2        x        2
--R        (x  + a )log(-------) + a
--R                      2    2
--R                     x  + a
--R   (2)  --------------------------
--R                  4 2     6
--R                2a x  + 2a
--R                                                     Type: Expression Integer
--E

--S 44 of 68
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  + a ) + 2log(x) - log(-------)
                                        2    2
                                       x  + a
   (3)  ---------------------------------------
                            4
                          2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  + a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            4
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 45 of 68
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 46 of 68
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 47 of 68
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 48 of 68     14:136 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 49 of 68
aa:=integrate(1/(x^2*(x^2+a^2)^2),x)
 

             3     2       x        2     3
        (- 3x  - 3a x)atan(-) - 3a x  - 2a
                           a
   (1)  -----------------------------------
                      5 3     7
                    2a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R
--R             3     2       x        2     3
--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
--R                           a
--R   (1)  -----------------------------------
--R                      5 3     7
--R                    2a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E

--S 50 of 68
bb:=-1/(a^4*x)-x/(2*a^4*(x^2+a^2))-3/(2*a^5)*atan(x/a)
 

             3     2       x        2     3
        (- 3x  - 3a x)atan(-) - 3a x  - 2a
                           a
   (2)  -----------------------------------
                      5 3     7
                    2a x  + 2a x
                                                     Type: Expression Integer
--R
--R             3     2       x        2     3
--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
--R                           a
--R   (2)  -----------------------------------
--R                      5 3     7
--R                    2a x  + 2a x
--R                                                     Type: Expression Integer
--E

--S 51 of 68     14:137 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 52 of 68
aa:=integrate(1/(x^3*(x^2+a^2)^2),x)
 

           4     2 2      2    2         4     2 2            2 2    4
        (2x  + 2a x )log(x  + a ) + (- 4x  - 4a x )log(x) - 2a x  - a
   (1)  --------------------------------------------------------------
                                   6 4     8 2
                                 2a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           4     2 2      2    2         4     2 2            2 2    4
--R        (2x  + 2a x )log(x  + a ) + (- 4x  - 4a x )log(x) - 2a x  - a
--R   (1)  --------------------------------------------------------------
--R                                   6 4     8 2
--R                                 2a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53 of 68
bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2+a^2))-1/a^6*log(x^2/(x^2+a^2))
 

                               2
             4     2 2        x         2 2    4
        (- 2x  - 2a x )log(-------) - 2a x  - a
                            2    2
                           x  + a
   (2)  ----------------------------------------
                        6 4     8 2
                      2a x  + 2a x
                                                     Type: Expression Integer
--R
--R                               2
--R             4     2 2        x         2 2    4
--R        (- 2x  - 2a x )log(-------) - 2a x  - a
--R                            2    2
--R                           x  + a
--R   (2)  ----------------------------------------
--R                        6 4     8 2
--R                      2a x  + 2a x
--R                                                     Type: Expression Integer
--E

--S 54 of 68
cc:=aa-bb
 

                                         2
             2    2                     x
        log(x  + a ) - 2log(x) + log(-------)
                                      2    2
                                     x  + a
   (3)  -------------------------------------
                           6
                          a
                                                     Type: Expression Integer
--R
--R                                         2
--R             2    2                     x
--R        log(x  + a ) - 2log(x) + log(-------)
--R                                      2    2
--R                                     x  + a
--R   (3)  -------------------------------------
--R                           6
--R                          a
--R                                                     Type: Expression Integer
--E

--S 55 of 68
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 56 of 68
dd:=divlog cc
 

             2
        log(x ) - 2log(x)
   (5)  -----------------
                 6
                a
                                                     Type: Expression Integer
--R
--R             2
--R        log(x ) - 2log(x)
--R   (5)  -----------------
--R                 6
--R                a
--R                                                     Type: Expression Integer
--E

--S 57 of 68
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 58 of 68     14:138 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 59 of 68     14:139 Axiom cannot do this integral
aa:=integrate(1/((x^2+a^2)^n),x)
 

           x
         ++       1
   (1)   |   ----------- d%L
        ++     2     2 n
             (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 60 of 68
aa:=integrate(x/((x^2+a^2)^n),x)
 

                   2    2
                - x  - a
   (1)  ------------------------
                         2    2
                  n log(x  + a )
        (2n - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2    2
--R                - x  - a
--R   (1)  ------------------------
--R                         2    2
--R                  n log(x  + a )
--R        (2n - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 61 of 68
bb:=-1/(2*(n-1)*(x^2+a^2)^(n-1))
 

                     1
   (2)  - ----------------------
                    2    2 n - 1
          (2n - 2)(x  + a )
                                                     Type: Expression Integer
--R
--R                     1
--R   (2)  - ----------------------
--R                    2    2 n - 1
--R          (2n - 2)(x  + a )
--R                                                     Type: Expression Integer
--E

--S 62 of 68
cc:=aa-bb
 

                 2    2
          n log(x  + a )       2    2   2    2 n - 1
        %e               + (- x  - a )(x  + a )
   (3)  --------------------------------------------
                                          2    2
                     2    2 n - 1  n log(x  + a )
           (2n - 2)(x  + a )     %e
                                                     Type: Expression Integer
--R
--R                 2    2
--R          n log(x  + a )       2    2   2    2 n - 1
--R        %e               + (- x  - a )(x  + a )
--R   (3)  --------------------------------------------
--R                                          2    2
--R                     2    2 n - 1  n log(x  + a )
--R           (2n - 2)(x  + a )     %e
--R                                                     Type: Expression Integer
--E

--S 63 of 68
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 64 of 68
dd:=explog cc
 

          2    2 n       2    2   2    2 n - 1
        (x  + a )  + (- x  - a )(x  + a )
   (5)  --------------------------------------
                     2    2 n - 1  2    2 n
           (2n - 2)(x  + a )     (x  + a )
                                                     Type: Expression Integer
--R
--R          2    2 n       2    2   2    2 n - 1
--R        (x  + a )  + (- x  - a )(x  + a )
--R   (5)  --------------------------------------
--R                     2    2 n - 1  2    2 n
--R           (2n - 2)(x  + a )     (x  + a )
--R                                                     Type: Expression Integer
--E

--S 65 of 68     14:140 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 66 of 68     14:141 Axiom cannot do this integral
aa:=integrate(1/(x*(x^2+a^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++        2     2 n
             %L (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++        2     2 n
--I             %L (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 67 of 68     14:142 Axiom cannot do this integral
aa:=integrate(x^m/((x^2+a^2)^n),x)
 

           x       m
         ++      %L
   (1)   |   ----------- d%L
        ++     2     2 n
             (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %L
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 68 of 68     14:143 Axiom cannot do this integral
aa:=integrate(1/(x^m*(x^2+a^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++     m  2     2 n
             %L (a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++     m  2     2 n
--I             %L (a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to DistributedMultivariatePolynomial.output (2010/3/27, 18:41:57).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
(d1,d2,d3) : DMP([z,y,x],FRAC INT) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 10
d1 := -4*z + 4*y**2*x + 16*x**2 + 1 
 

                 2       2
   (2)  - 4z + 4y x + 16x  + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R                 2       2
--R   (2)  - 4z + 4y x + 16x  + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 2

--S 3 of 10
d2 := 2*z*y**2 + 4*x + 1 
 

            2
   (3)  2z y  + 4x + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (3)  2z y  + 4x + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 3

--S 4 of 10
d3 := 2*z*x**2 - 2*y**2 - x 
 

            2     2
   (4)  2z x  - 2y  - x
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (4)  2z x  - 2y  - x
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 4

--S 5 of 10
groebner [d1,d2,d3]
 

   (5)
        1568  6   1264  5    6   4   182  3   2047  2    103      2857
   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
        2745       305      305      549       610      2745     10980
     2    112  6    84  5   1264  4    13  3    84  2   1772       2
    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
         2745      305       305      549      305      2745     2745
     7   29  6   17  4   11  3    1  2   15     1
    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
          4      16       8      32      16     4
       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (5)
--R        1568  6   1264  5    6   4   182  3   2047  2    103      2857
--R   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
--R        2745       305      305      549       610      2745     10980
--R     2    112  6    84  5   1264  4    13  3    84  2   1772       2
--R    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
--R         2745      305       305      549      305      2745     2745
--R     7   29  6   17  4   11  3    1  2   15     1
--R    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
--R          4      16       8      32      16     4
--R       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 5

--S 6 of 10
(n1,n2,n3) : HDMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
n1 := d1
 

          2       2
   (7)  4y x + 16x  - 4z + 1
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R          2       2
--R   (7)  4y x + 16x  - 4z + 1
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 7

--S 8 of 10
n2 := d2
 

            2
   (8)  2z y  + 4x + 1
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (8)  2z y  + 4x + 1
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 8

--S 9 of 10
n3 := d3
 

            2     2
   (9)  2z x  - 2y  - x
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (9)  2z x  - 2y  - x
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 9

--S 10 of 10
groebner [n1,n2,n3]
 

   (10)
     4     3   3  2   1     1   4   29  3   1  2   7        9     1
   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
               2      2     8        4      8      4       16     4
       2        1   2      2       1     2    2   1
    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
                2                  4              2
     2     2     2   1     3
    z  - 4y  + 2x  - - z - - x]
                     4     2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (10)
--R     4     3   3  2   1     1   4   29  3   1  2   7        9     1
--R   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
--R               2      2     8        4      8      4       16     4
--R       2        1   2      2       1     2    2   1
--R    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
--R                2                  4              2
--R     2     2     2   1     3
--R    z  - 4y  + 2x  - - z - - x]
--R                     4     2
--RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 10
)spool
 
Starts dribbling to tbagg.output (2010/3/27, 18:41:14).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
R ==> Record(key: Symbol, entry: String)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 1

--S 2 of 7
T ==> AssociationList(Symbol, String)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 2

--S 3 of 7
t1:=construct([[x,"ix"]$R])$T
 

   (3)  table(x= "ix")
                                         Type: AssociationList(Symbol,String)
--R
--R   (3)  table(x= "ix")
--R                                         Type: AssociationList(Symbol,String)
--E 3

--S 4 of 7
t2:=construct([[y,"iy"]$R])$T
 

   (4)  table(y= "iy")
                                         Type: AssociationList(Symbol,String)
--R
--R   (4)  table(y= "iy")
--R                                         Type: AssociationList(Symbol,String)
--E 4

--S 5 of 7
(t1=t2)::Boolean
 

   (5)  false
                                                                Type: Boolean
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 7
t3:=construct([[y,"iy"]$R])$T
 

   (6)  table(y= "iy")
                                         Type: AssociationList(Symbol,String)
--R
--R   (6)  table(y= "iy")
--R                                         Type: AssociationList(Symbol,String)
--E 6

--S 7 of 7
(t3=t2)::Boolean
 

   (7)  true
                                                                Type: Boolean
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7
)spool 
 
Starts dribbling to Dequeue.output (2010/3/27, 18:41:56).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 63
a:Dequeue INT:= dequeue [1,2,3,4,5]
 

   (1)  [1,2,3,4,5]
                                                        Type: Dequeue Integer
--R 
--R
--R   (1)  [1,2,3,4,5]
--R                                                        Type: Dequeue Integer
--E 1

--S 2 of 63
dequeue! a
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 63
a
 

   (3)  [2,3,4,5]
                                                        Type: Dequeue Integer
--R 
--R
--R   (3)  [2,3,4,5]
--R                                                        Type: Dequeue Integer
--E 3

--S 4 of 63
extract! a
 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 63
a
 

   (5)  [3,4,5]
                                                        Type: Dequeue Integer
--R 
--R
--R   (5)  [3,4,5]
--R                                                        Type: Dequeue Integer
--E 5

--S 6 of 63
enqueue!(9,a)
 

   (6)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  9
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 63
a
 

   (7)  [3,4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (7)  [3,4,5,9]
--R                                                        Type: Dequeue Integer
--E 7

--S 8 of 63
insert!(8,a)
 

   (8)  [3,4,5,9,8]
                                                        Type: Dequeue Integer
--R 
--R
--R   (8)  [3,4,5,9,8]
--R                                                        Type: Dequeue Integer
--E 8

--S 9 of 63
a
 

   (9)  [3,4,5,9,8]
                                                        Type: Dequeue Integer
--R 
--R
--R   (9)  [3,4,5,9,8]
--R                                                        Type: Dequeue Integer
--E 9

--S 10 of 63
front a
 

   (10)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  3
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 63
back a
 

   (11)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  8
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 63
bottom! a
 

   (12)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  8
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 63
a
 

   (13)  [3,4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (13)  [3,4,5,9]
--R                                                        Type: Dequeue Integer
--E 13

--S 14 of 63
depth a
 

   (14)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  4
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 63
height a
 

   (15)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  4
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 63
insertBottom!(6,a)
 

   (16)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  6
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 63
a
 

   (17)  [3,4,5,9,6]
                                                        Type: Dequeue Integer
--R 
--R
--R   (17)  [3,4,5,9,6]
--R                                                        Type: Dequeue Integer
--E 17

--S 18 of 63
extractBottom! a
 

   (18)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  6
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 63
a
 

   (19)  [3,4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (19)  [3,4,5,9]
--R                                                        Type: Dequeue Integer
--E 19

--S 20 of 63
insertTop!(7,a)
 

   (20)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  7
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 63
a
 

   (21)  [7,3,4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (21)  [7,3,4,5,9]
--R                                                        Type: Dequeue Integer
--E 21

--S 22 of 63
extractTop! a
 

   (22)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  7
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 63
a
 

   (23)  [3,4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (23)  [3,4,5,9]
--R                                                        Type: Dequeue Integer
--E 23

--S 24 of 63
top a
 

   (24)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (24)  3
--R                                                        Type: PositiveInteger
--E 24

--S 25 of 63
a
 

   (25)  [3,4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (25)  [3,4,5,9]
--R                                                        Type: Dequeue Integer
--E 25

--S 26 of 63
top! a
 

   (26)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  3
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 63
a
 

   (27)  [4,5,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (27)  [4,5,9]
--R                                                        Type: Dequeue Integer
--E 27

--S 28 of 63
reverse! a
 

   (28)  [9,5,4]
                                                        Type: Dequeue Integer
--R 
--R
--R   (28)  [9,5,4]
--R                                                        Type: Dequeue Integer
--E 28

--S 29 of 63
rotate! a
 

   (29)  [5,4,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (29)  [5,4,9]
--R                                                        Type: Dequeue Integer
--E 29

--S 30 of 63
inspect a
 

   (30)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  5
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 63
empty? a
 

   (31)  false
                                                                Type: Boolean
--R 
--R
--R   (31)  false
--R                                                                Type: Boolean
--E 31

--S 32 of 63
#a
 

   (32)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (32)  3
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 63
length a
 

   (33)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (33)  3
--R                                                        Type: PositiveInteger
--E 33

--S 34 of 63
less?(a,9)
 

   (34)  true
                                                                Type: Boolean
--R 
--R
--R   (34)  true
--R                                                                Type: Boolean
--E 34

--S 35 of 63
more?(a,9)
 

   (35)  false
                                                                Type: Boolean
--R 
--R
--R   (35)  false
--R                                                                Type: Boolean
--E 35

--S 36 of 63
size?(a,#a)
 

   (36)  true
                                                                Type: Boolean
--R 
--R
--R   (36)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 63
size?(a,9)
 

   (37)  false
                                                                Type: Boolean
--R 
--R
--R   (37)  false
--R                                                                Type: Boolean
--E 37

--S 38 of 63
parts a
 

   (38)  [5,4,9]
                                                           Type: List Integer
--R 
--R
--R   (38)  [5,4,9]
--R                                                           Type: List Integer
--E 38

--S 39 of 63
bag([1,2,3,4,5])$Dequeue(INT)
 

   (39)  [1,2,3,4,5]
                                                        Type: Dequeue Integer
--R 
--R
--R   (39)  [1,2,3,4,5]
--R                                                        Type: Dequeue Integer
--E 39

--S 40 of 63
b:=empty()$(Dequeue INT)
 

   (40)  []
                                                        Type: Dequeue Integer
--R 
--R
--R   (40)  []
--R                                                        Type: Dequeue Integer
--E 40

--S 41 of 63
empty? b
 

   (41)  true
                                                                Type: Boolean
--R 
--R
--R   (41)  true
--R                                                                Type: Boolean
--E 41

--S 42 of 63
sample()$Dequeue(INT)
 

   (42)  []
                                                        Type: Dequeue Integer
--R 
--R
--R   (42)  []
--R                                                        Type: Dequeue Integer
--E 42

--S 43 of 63
c:=copy a
 

   (43)  [5,4,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (43)  [5,4,9]
--R                                                        Type: Dequeue Integer
--E 43

--S 44 of 63
eq?(a,c)
 

   (44)  false
                                                                Type: Boolean
--R 
--R
--R   (44)  false
--R                                                                Type: Boolean
--E 44

--S 45 of 63
eq?(a,a)
 

   (45)  true
                                                                Type: Boolean
--R 
--R
--R   (45)  true
--R                                                                Type: Boolean
--E 45

--S 46 of 63
(a=c)@Boolean
 

   (46)  true
                                                                Type: Boolean
--R 
--R
--R   (46)  true
--R                                                                Type: Boolean
--E 46

--S 47 of 63
(a=a)@Boolean
 

   (47)  true
                                                                Type: Boolean
--R 
--R
--R   (47)  true
--R                                                                Type: Boolean
--E 47

--S 48 of 63
a~=c
 

   (48)  false
                                                                Type: Boolean
--R 
--R
--R   (48)  false
--R                                                                Type: Boolean
--E 48

--S 49 of 63
any?(x+->(x=4),a)
 

   (49)  true
                                                                Type: Boolean
--R 
--R
--R   (49)  true
--R                                                                Type: Boolean
--E 49

--S 50 of 63
any?(x+->(x=11),a)
 

   (50)  false
                                                                Type: Boolean
--R 
--R
--R   (50)  false
--R                                                                Type: Boolean
--E 50

--S 51 of 63
every?(x+->(x=11),a)
 

   (51)  false
                                                                Type: Boolean
--R 
--R
--R   (51)  false
--R                                                                Type: Boolean
--E 51

--S 52 of 63
count(4,a)
 

   (52)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (52)  1
--R                                                        Type: PositiveInteger
--E 52

--S 53 of 63
count(x+->(x>2),a)
 

   (53)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (53)  3
--R                                                        Type: PositiveInteger
--E 53

--S 54 of 63
map(x+->x+10,a)
 

   (54)  [15,14,19]
                                                        Type: Dequeue Integer
--R 
--R
--R   (54)  [15,14,19]
--R                                                        Type: Dequeue Integer
--E 54

--S 55 of 63
a
 

   (55)  [5,4,9]
                                                        Type: Dequeue Integer
--R 
--R
--R   (55)  [5,4,9]
--R                                                        Type: Dequeue Integer
--E 55

--S 56 of 63
map!(x+->x+10,a)
 

   (56)  [15,14,19]
                                                        Type: Dequeue Integer
--R 
--R
--R   (56)  [15,14,19]
--R                                                        Type: Dequeue Integer
--E 56

--S 57 of 63
a
 

   (57)  [15,14,19]
                                                        Type: Dequeue Integer
--R 
--R
--R   (57)  [15,14,19]
--R                                                        Type: Dequeue Integer
--E 57

--S 58 of 63
members a
 

   (58)  [15,14,19]
                                                           Type: List Integer
--R 
--R
--R   (58)  [15,14,19]
--R                                                           Type: List Integer
--E 58

--S 59 of 63
member?(14,a)
 

   (59)  true
                                                                Type: Boolean
--R 
--R
--R   (59)  true
--R                                                                Type: Boolean
--E 59

--S 60 of 63
coerce a
 

   (60)  [15,14,19]
                                                             Type: OutputForm
--R 
--R
--R   (60)  [15,14,19]
--R                                                             Type: OutputForm
--E 60

--S 61 of 63
hash a
 

   (61)  4999531
                                                          Type: SingleInteger
--R 
--R
--I   (61)  4999531
--R                                                          Type: SingleInteger
--E 61

--S 62 of 63
latex a
 

   (62)  "\mbox{\bf Unimplemented}"
                                                                 Type: String
--R 
--R
--R   (62)  "\mbox{\bf Unimplemented}"
--R                                                                 Type: String
--E 62

--S 63 of 63
)show Dequeue
 
 Dequeue S: SetCategory  is a domain constructor
 Abbreviation for Dequeue is DEQUEUE 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for DEQUEUE 

------------------------------- Operations --------------------------------
 back : % -> S                         bag : List S -> %
 bottom! : % -> S                      copy : % -> %
 depth : % -> NonNegativeInteger       dequeue : List S -> %
 dequeue : () -> %                     dequeue! : % -> S
 empty : () -> %                       empty? : % -> Boolean
 enqueue! : (S,%) -> S                 eq? : (%,%) -> Boolean
 extract! : % -> S                     extractBottom! : % -> S
 extractTop! : % -> S                  front : % -> S
 height : % -> NonNegativeInteger      insert! : (S,%) -> %
 insertBottom! : (S,%) -> S            insertTop! : (S,%) -> S
 inspect : % -> S                      length : % -> NonNegativeInteger
 map : ((S -> S),%) -> %               pop! : % -> S
 push! : (S,%) -> S                    reverse! : % -> %
 rotate! : % -> %                      sample : () -> %
 top : % -> S                          top! : % -> S
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?=? : (%,%) -> Boolean if S has SETCAT
 any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 coerce : % -> OutputForm if S has SETCAT
 count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
 count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
 every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 hash : % -> SingleInteger if S has SETCAT
 latex : % -> String if S has SETCAT
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((S -> S),%) -> % if $ has shallowlyMutable
 member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
 members : % -> List S if $ has finiteAggregate
 more? : (%,NonNegativeInteger) -> Boolean
 parts : % -> List S if $ has finiteAggregate
 size? : (%,NonNegativeInteger) -> Boolean
 ?~=? : (%,%) -> Boolean if S has SETCAT

--R 
--R Dequeue S: SetCategory  is a domain constructor
--R Abbreviation for Dequeue is DEQUEUE 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for DEQUEUE 
--R
--R------------------------------- Operations --------------------------------
--R back : % -> S                         bag : List S -> %
--R bottom! : % -> S                      copy : % -> %
--R depth : % -> NonNegativeInteger       dequeue : List S -> %
--R dequeue : () -> %                     dequeue! : % -> S
--R empty : () -> %                       empty? : % -> Boolean
--R enqueue! : (S,%) -> S                 eq? : (%,%) -> Boolean
--R extract! : % -> S                     extractBottom! : % -> S
--R extractTop! : % -> S                  front : % -> S
--R height : % -> NonNegativeInteger      insert! : (S,%) -> %
--R insertBottom! : (S,%) -> S            insertTop! : (S,%) -> S
--R inspect : % -> S                      length : % -> NonNegativeInteger
--R map : ((S -> S),%) -> %               pop! : % -> S
--R push! : (S,%) -> S                    reverse! : % -> %
--R rotate! : % -> %                      sample : () -> %
--R top : % -> S                          top! : % -> S
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
--R members : % -> List S if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R parts : % -> List S if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
--E 63

)spool
 
Starts dribbling to RomanNumeral.output (2010/3/27, 18:46:32).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 15
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 1

--S 2 of 15
D(f x,x,7)
 

         (vii)
   (2)  f     (x)

                                                     Type: Expression Integer
--R 
--R
--R         (vii)
--R   (2)  f     (x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 15
a := roman(1978 - 1965)
 

   (3)  XIII
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XIII
--R                                                           Type: RomanNumeral
--E 3

--S 4 of 15
x : UTS(ROMAN,'x,0) := x
 

   (4)  x
                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--R 
--R
--R   (4)  x
--R                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--E 4

--S 5 of 15
recip(1 - x - x**2)
 

   (5)
                 2        3      4         5         6        7          8
     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
   + 
         9           10      11
     LV x  + LXXXIX x   + O(x  )
                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--R 
--R
--R   (5)
--R                 2        3      4         5         6        7          8
--R     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
--R   + 
--R         9           10      11
--R     LV x  + LXXXIX x   + O(x  )
--R                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--E 5

--S 6 of 15
m : MATRIX FRAC ROMAN
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 15
m := matrix [ [1/(i + j) for i in 1..3] for j in 1..3]
 

        + I    I    I+
        |--   ---  --|
        |II   III  IV|
        |            |
        | I    I   I |
   (7)  |---  --   - |
        |III  IV   V |
        |            |
        | I    I    I|
        |--    -   --|
        +IV    V   VI+
                                           Type: Matrix Fraction RomanNumeral
--R 
--R
--R        + I    I    I+
--R        |--   ---  --|
--R        |II   III  IV|
--R        |            |
--R        | I    I   I |
--R   (7)  |---  --   - |
--R        |III  IV   V |
--R        |            |
--R        | I    I    I|
--R        |--    -   --|
--R        +IV    V   VI+
--R                                           Type: Matrix Fraction RomanNumeral
--E 7

--S 8 of 15
inverse m
 

        +LXXII   - CCXL    CLXXX +
        |                        |
   (8)  |- CCXL    CM     - DCCXX|
        |                        |
        +CLXXX   - DCCXX    DC   +
                                Type: Union(Matrix Fraction RomanNumeral,...)
--R 
--R
--R        +LXXII   - CCXL    CLXXX +
--R        |                        |
--R   (8)  |- CCXL    CM     - DCCXX|
--R        |                        |
--R        +CLXXX   - DCCXX    DC   +
--R                                Type: Union(Matrix Fraction RomanNumeral,...)
--E 8

--S 9 of 15
y := factorial 10
 

   (9)  3628800
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  3628800
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 15
roman y
 

   (10)
  ((((I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))(
  (I)) MMMMMMMMDCCC
                                                           Type: RomanNumeral
--R 
--R
--R   (10)
--R  ((((I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))(
--R  (I)) MMMMMMMMDCCC
--R                                                           Type: RomanNumeral
--E 10

--S 11 of 15
a := roman(78)
 

   (11)  LXXVIII
                                                           Type: RomanNumeral
--R 
--R
--R   (11)  LXXVIII
--R                                                           Type: RomanNumeral
--E 11

--S 12 of 15
b := roman(87)
 

   (12)  LXXXVII
                                                           Type: RomanNumeral
--R 
--R
--R   (12)  LXXXVII
--R                                                           Type: RomanNumeral
--E 12

--S 13 of 15
a + b 
 

   (13)  CLXV
                                                           Type: RomanNumeral
--R 
--R
--R   (13)  CLXV
--R                                                           Type: RomanNumeral
--E 13

--S 14 of 15
a * b
 

   (14)  MMMMMMDCCLXXXVI
                                                           Type: RomanNumeral
--R 
--R
--R   (14)  MMMMMMDCCLXXXVI
--R                                                           Type: RomanNumeral
--E 14

--S 15 of 15
b rem a 
 

   (15)  IX
                                                           Type: RomanNumeral
--R 
--R
--R   (15)  IX
--R                                                           Type: RomanNumeral
--E 15
)spool
 
Starts dribbling to file.output (2010/3/27, 18:25:58).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 12
ifile:File List Integer:=open("/tmp/jazz1","output")
 

   (1)  "/tmp/jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (1)  "/tmp/jazz1"
--R                                                      Type: File List Integer
--E 1

--S 2 of 12
write!(ifile, [-1,2,3])
 

   (2)  [- 1,2,3]
                                                           Type: List Integer
--R 
--R
--R   (2)  [- 1,2,3]
--R                                                           Type: List Integer
--E 2

--S 3 of 12
write!(ifile, [10,-10,0,111])
 

   (3)  [10,- 10,0,111]
                                                           Type: List Integer
--R 
--R
--R   (3)  [10,- 10,0,111]
--R                                                           Type: List Integer
--E 3

--S 4 of 12
write!(ifile, [7])
 

   (4)  [7]
                                                           Type: List Integer
--R 
--R
--R   (4)  [7]
--R                                                           Type: List Integer
--E 4

--S 5 of 12
reopen!(ifile, "input")
 

   (5)  "/tmp/jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (5)  "/tmp/jazz1"
--R                                                      Type: File List Integer
--E 5

--S 6 of 12
read! ifile
 

   (6)  [- 1,2,3]
                                                           Type: List Integer
--R 
--R
--R   (6)  [- 1,2,3]
--R                                                           Type: List Integer
--E 6

--S 7 of 12
read! ifile
 

   (7)  [10,- 10,0,111]
                                                           Type: List Integer
--R 
--R
--R   (7)  [10,- 10,0,111]
--R                                                           Type: List Integer
--E 7

--S 8 of 12
readIfCan! ifile
 

   (8)  [7]
                                                Type: Union(List Integer,...)
--R 
--R
--R   (8)  [7]
--R                                                Type: Union(List Integer,...)
--E 8

--S 9 of 12
readIfCan! ifile
 

   (9)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (9)  "failed"
--R                                                    Type: Union("failed",...)
--E 9

--S 10 of 12
iomode ifile
 

   (10)  "input"
                                                                 Type: String
--R 
--R
--R   (10)  "input"
--R                                                                 Type: String
--E 10

--S 11 of 12
name ifile
 

   (11)  "/tmp/jazz1"
                                                               Type: FileName
--R 
--R
--R   (11)  "/tmp/jazz1"
--R                                                               Type: FileName
--E 11

--S 12 of 12
close! ifile
 

   (12)  "/tmp/jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (12)  "/tmp/jazz1"
--R                                                      Type: File List Integer
--E 12
)spool 
 
Starts dribbling to kernel.output (2010/3/27, 18:28:31).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 19
x :: Expression Integer
 

   (1)  x
                                                     Type: Expression Integer
--R 
--R
--R   (1)  x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 19
kernel x
 

   (2)  x
                                              Type: Kernel Expression Integer
--R 
--R
--R   (2)  x
--R                                              Type: Kernel Expression Integer
--E 2

--S 3 of 19
sin(x) + cos(x)
 

   (3)  sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 19
kernels %
 

   (4)  [sin(x),cos(x)]
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (4)  [sin(x),cos(x)]
--R                                         Type: List Kernel Expression Integer
--E 4

--S 5 of 19
sin(x)**2 + sin(x) + cos(x)
 

              2
   (5)  sin(x)  + sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R              2
--R   (5)  sin(x)  + sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 19
kernels %
 

   (6)  [sin(x),cos(x)]
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (6)  [sin(x),cos(x)]
--R                                         Type: List Kernel Expression Integer
--E 6

--S 7 of 19
kernels(1 :: Expression Integer)
 

   (7)  []
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (7)  []
--R                                         Type: List Kernel Expression Integer
--E 7

--S 8 of 19
mainKernel(cos(x) + tan(x))
 

   (8)  tan(x)
                                   Type: Union(Kernel Expression Integer,...)
--R 
--R
--R   (8)  tan(x)
--R                                   Type: Union(Kernel Expression Integer,...)
--E 8

--S 9 of 19
height kernel x
 

   (9)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  1
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 19
height mainKernel(sin x)
 

   (10)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  2
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 19
height mainKernel(sin cos x)
 

   (11)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  3
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 19
height mainKernel(sin cos (tan x + sin x))
 

   (12)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 19
operator mainKernel(sin cos (tan x + sin x))
 

   (13)  sin
                                                          Type: BasicOperator
--R 
--R
--R   (13)  sin
--R                                                          Type: BasicOperator
--E 13

--S 14 of 19
name mainKernel(sin cos (tan x + sin x))
 

   (14)  sin
                                                                 Type: Symbol
--R 
--R
--R   (14)  sin
--R                                                                 Type: Symbol
--E 14

--S 15 of 19
f := operator 'f
 

   (15)  f
                                                          Type: BasicOperator
--R 
--R
--R   (15)  f
--R                                                          Type: BasicOperator
--E 15

--S 16 of 19
e := f(x, y, 10)
 

   (16)  f(x,y,10)
                                                     Type: Expression Integer
--R 
--R
--R   (16)  f(x,y,10)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 19
is?(e, f)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 19
is?(e, 'f)
 

   (18)  true
                                                                Type: Boolean
--R 
--R
--R   (18)  true
--R                                                                Type: Boolean
--E 18

--S 19 of 19
argument mainKernel e
 

   (19)  [x,y,10]
                                                Type: List Expression Integer
--R 
--R
--R   (19)  [x,y,10]
--R                                                Type: List Expression Integer
--E 19
)spool 
 
Starts dribbling to MappingPackage1.output (2010/3/27, 18:46:4).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 26
power(q: FRAC INT, n: INT): FRAC INT == q**n
 
   Function declaration power : (Fraction Integer,Integer) -> Fraction 
      Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration power : (Fraction Integer,Integer) -> Fraction 
--R      Integer has been added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 26
power(2,3)
 
   Compiling function power with type (Fraction Integer,Integer) -> 
      Fraction Integer 

   (2)  8
                                                       Type: Fraction Integer
--R 
--R   Compiling function power with type (Fraction Integer,Integer) -> 
--R      Fraction Integer 
--R
--R   (2)  8
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 26
rewop := twist power
 

   (3)  theMap(MAPPKG3;twist;MM;5!0)
                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--I   (3)  theMap(MAPPKG3;twist;MM;5!0)
--R                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--E 3

--S 4 of 26
rewop(3, 2)
 

   (4)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (4)  8
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 26
square: FRAC INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 26
square:= curryRight(power, 2)
 

   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--I   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 6

--S 7 of 26
square 4
 

   (7)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (7)  16
--R                                                       Type: Fraction Integer
--E 7

--S 8 of 26
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
 

   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--I   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
--R              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--E 8

--S 9 of 26
squirrel(1/2, 1/3)
 

        1
   (9)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (9)  -
--R        4
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 26
sixteen := curry(square, 4/1)
 

   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                               Type: (() -> Fraction Integer)
--R 
--R
--I   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                               Type: (() -> Fraction Integer)
--E 10

--S 11 of 26
sixteen()
 

   (11)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  16
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 26
square2:=square*square
 

   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--I   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 12

--S 13 of 26
square2 3
 

   (13)  81
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  81
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 26
sc(x: FRAC INT): FRAC INT == x + 1
 
   Function declaration sc : Fraction Integer -> Fraction Integer has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration sc : Fraction Integer -> Fraction Integer has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 14

--S 15 of 26
incfns := [sc**i for i in 0..10]
 
   Compiling function sc with type Fraction Integer -> Fraction Integer
      

   (15)
   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0)]
                            Type: List (Fraction Integer -> Fraction Integer)
--R 
--R   Compiling function sc with type Fraction Integer -> Fraction Integer
--R      
--R
--R   (15)
--I   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0)]
--R                            Type: List (Fraction Integer -> Fraction Integer)
--E 15

--S 16 of 26
[f 4 for f in incfns]
 

   (16)  [4,5,6,7,8,9,10,11,12,13,14]
                                                  Type: List Fraction Integer
--R 
--R
--R   (16)  [4,5,6,7,8,9,10,11,12,13,14]
--R                                                  Type: List Fraction Integer
--E 16

--S 17 of 26
times(n:NNI, i:INT):INT == n*i
 
   Function declaration times : (NonNegativeInteger,Integer) -> Integer
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration times : (NonNegativeInteger,Integer) -> Integer
--R      has been added to workspace.
--R                                                                   Type: Void
--E 17

--S 18 of 26
r := recur(times)
 
   Compiling function times with type (NonNegativeInteger,Integer) -> 
      Integer 

   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
                              Type: ((NonNegativeInteger,Integer) -> Integer)
--R 
--R   Compiling function times with type (NonNegativeInteger,Integer) -> 
--R      Integer 
--R
--I   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
--R                              Type: ((NonNegativeInteger,Integer) -> Integer)
--E 18

--S 19 of 26
fact := curryRight(r, 1)
 

   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                        Type: (NonNegativeInteger -> Integer)
--R 
--R
--I   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                        Type: (NonNegativeInteger -> Integer)
--E 19

--S 20 of 26
fact 4
 

   (20)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  24
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 26
mto2ton(m, n) ==
  raiser := square^n
  raiser m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 26
mto2ton(3, 3)
 
   Compiling function mto2ton with type (PositiveInteger,
      PositiveInteger) -> Fraction Integer 

   (22)  6561
                                                       Type: Fraction Integer
--R 
--R   Compiling function mto2ton with type (PositiveInteger,
--R      PositiveInteger) -> Fraction Integer 
--R
--R   (22)  6561
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 26
shiftfib(r: List INT) : INT ==
  t := r.1
  r.1 := r.2
  r.2 := r.2 + t
  t
 
   Function declaration shiftfib : List Integer -> Integer has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration shiftfib : List Integer -> Integer has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 23

--S 24 of 26
fibinit: List INT := [0, 1]
 

   (24)  [0,1]
                                                           Type: List Integer
--R 
--R
--R   (24)  [0,1]
--R                                                           Type: List Integer
--E 24

--S 25 of 26
fibs := curry(shiftfib, fibinit)
 
   Compiling function shiftfib with type List Integer -> Integer 

   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                                        Type: (() -> Integer)
--R 
--R   Compiling function shiftfib with type List Integer -> Integer 
--R
--I   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                                        Type: (() -> Integer)
--E 25

--S 26 of 26
[fibs() for i in 0..30]
 

   (26)
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
    317811, 514229, 832040]
                                                           Type: List Integer
--R 
--R
--R   (26)
--R   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
--R    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
--R    317811, 514229, 832040]
--R                                                           Type: List Integer
--E 26
 
)spool 
 
Starts dribbling to Product.output (2010/3/27, 18:46:16).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 6
f:=(x:INT):INT +-> 3*x
 

   (1)  theMap(Closure)
                                                   Type: (Integer -> Integer)
--R 
--R
--R   (1)  theMap(Closure)
--R                                                   Type: (Integer -> Integer)
--E 1

--S 2 of 6
f(3)
 

   (2)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  9
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 6
g:=(x:INT):INT +-> x^3
 

   (3)  theMap(Closure)
                                                   Type: (Integer -> Integer)
--R 
--R
--R   (3)  theMap(Closure)
--R                                                   Type: (Integer -> Integer)
--E 3

--S 4 of 6
g(3)
 

   (4)  27
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  27
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 6
h(x:INT):Product(INT,INT) == makeprod(f x, g x)
 
   Function declaration h : Integer -> Product(Integer,Integer) has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration h : Integer -> Product(Integer,Integer) has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 5

--S 6 of 6
h(3)
 
   Compiling function h with type Integer -> Product(Integer,Integer) 

   (6)  (9,27)
                                               Type: Product(Integer,Integer)
--R 
--R   Compiling function h with type Integer -> Product(Integer,Integer) 
--R
--R   (6)  (9,27)
--R                                               Type: Product(Integer,Integer)
--E 6

)spool
 
Starts dribbling to fname1.output (2010/3/27, 18:26:16).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 18
fn: FileName
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
fn := "/spad/src/input/fname.input"
 

   (2)  "/spad/src/input/fname.input"
                                                               Type: FileName
--R 
--R
--R   (2)  "/spad/src/input/fname.input"
--R                                                               Type: FileName
--E 2

--S 3 of 18
directory fn
 

   (3)  "/spad/src/input"
                                                                 Type: String
--R 
--R
--R   (3)  "/spad/src/input"
--R                                                                 Type: String
--E 3

--S 4 of 18
name fn
 

   (4)  "fname"
                                                                 Type: String
--R 
--R
--R   (4)  "fname"
--R                                                                 Type: String
--E 4

--S 5 of 18
extension fn
 

   (5)  "input"
                                                                 Type: String
--R 
--R
--R   (5)  "input"
--R                                                                 Type: String
--E 5

--S 6 of 18
fn := filename("/u/smwatt/work", "fname", "input")
 

   (6)  "/u/smwatt/work/fname.input"
                                                               Type: FileName
--R 
--R
--R   (6)  "/u/smwatt/work/fname.input"
--R                                                               Type: FileName
--E 6

--S 7 of 18
objdir := "/tmp"
 

   (7)  "/tmp"
                                                                 Type: String
--R 
--R
--R   (7)  "/tmp"
--R                                                                 Type: String
--E 7

--S 8 of 18
fn := filename(objdir, "table", "spad")
 

   (8)  "/tmp/table.spad"
                                                               Type: FileName
--R 
--R
--R   (8)  "/tmp/table.spad"
--R                                                               Type: FileName
--E 8

--S 9 of 18
fn := filename("", "letter", "")
 

   (9)  "letter"
                                                               Type: FileName
--R 
--R
--R   (9)  "letter"
--R                                                               Type: FileName
--E 9

--S 10 of 18
exists? "/etc/passwd"
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 18
readable? "/etc/passwd"
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 18
readable? "/etc/security/passwd"
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 18
readable? "/ect/passwd"
 

   (13)  false
                                                                Type: Boolean
--R 
--R
--R   (13)  false
--R                                                                Type: Boolean
--E 13

--S 14 of 18
writable? "/etc/passwd"
 

   (14)  false
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 18
writable? "/dev/null"
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 18
writable? "/etc/DoesNotExist"
 

   (16)  false
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 18
writable? "/tmp/DoesNotExist"
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 18
fn := new(objdir, "xxx", "yy")
 

   (18)  "NIL"
                                                               Type: FileName
--R 
--R
--I   (18)  "/tmp/xxx1420.yy"
--R                                                               Type: FileName
--E 18
)spool 
 
Starts dribbling to kamke1.output (2010/3/27, 18:27:23).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 120
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 120
f := operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 120
g := operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

--S 4 of 120
h := operator 'h
 

   (4)  h
                                                          Type: BasicOperator
--R
--R   (4)  h
--R                                                          Type: BasicOperator
--E 4

--S 5 of 120
ode51 := D(y(x),x) - (y(x)-f(x))*(y(x)-g(x))*(y(x)-(a*f(x)+b*g(x))/(a+b))*h(x)_
           - D(f(x),x)*(y(x)-g(x))/(f(x)-g(x)) _
           - D(g(x),x)*(y(x)-f(x))/(g(x)-f(x))
 

   (5)
                                     ,                                    ,
       ((b + a)g(x) + (- b - a)f(x))y (x) + ((- b - a)y(x) + (b + a)f(x))g (x)

     + 
                                     ,
       ((b + a)y(x) + (- b - a)g(x))f (x)

     + 
                                            3
       ((- b - a)g(x) + (b + a)f(x))h(x)y(x)
     + 
                    2                                     2         2
       ((2b + a)g(x)  + (- b + a)f(x)g(x) + (- b - 2a)f(x) )h(x)y(x)
     + 
                3                     2               2             3
       (- b g(x)  + (- b - 2a)f(x)g(x)  + (2b + a)f(x) g(x) + a f(x) )h(x)y(x)
     + 
                  3                2    2         3
       (b f(x)g(x)  + (- b + a)f(x) g(x)  - a f(x) g(x))h(x)
  /
     (b + a)g(x) + (- b - a)f(x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                     ,                                    ,
--R       ((b + a)g(x) + (- b - a)f(x))y (x) + ((- b - a)y(x) + (b + a)f(x))g (x)
--R
--R     + 
--R                                     ,
--R       ((b + a)y(x) + (- b - a)g(x))f (x)
--R
--R     + 
--R                                            3
--R       ((- b - a)g(x) + (b + a)f(x))h(x)y(x)
--R     + 
--R                    2                                     2         2
--R       ((2b + a)g(x)  + (- b + a)f(x)g(x) + (- b - 2a)f(x) )h(x)y(x)
--R     + 
--R                3                     2               2             3
--R       (- b g(x)  + (- b - 2a)f(x)g(x)  + (2b + a)f(x) g(x) + a f(x) )h(x)y(x)
--R     + 
--R                  3                2    2         3
--R       (b f(x)g(x)  + (- b + a)f(x) g(x)  - a f(x) g(x))h(x)
--R  /
--R     (b + a)g(x) + (- b - a)f(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 120
ode51a:=solve(ode51,y,x)
 

   (6)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (6)  "failed"
--R                                                    Type: Union("failed",...)
--E 6

--S 7 of 120
ode52 := D(y(x),x) - a*y(x)**n - b*x**(n/(1-n))
 

                                 n
                             - -----
         ,            n        n - 1
   (7)  y (x) - a y(x)  - b x

                                                     Type: Expression Integer
--R
--R                                 n
--R                             - -----
--R         ,            n        n - 1
--R   (7)  y (x) - a y(x)  - b x
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 120
ode52a:=solve(ode52,y,x)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8

--S 9 of 120
ode53 := D(y(x),x) - f(x)**(1-n)*D(g(x),x)*y(x)**n/(a*g(x)+b)**n _
           - D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x)
 

   (9)
                       n ,
       f(x)(a g(x) + b) y (x)

     + 
                - n + 1    n       2            n  ,                      n ,
     (- f(x)f(x)       y(x)  - f(x) (a g(x) + b) )g (x) - y(x)(a g(x) + b) f (x)

  /
                     n
     f(x)(a g(x) + b)
                                                     Type: Expression Integer
--R
--R   (9)
--R                       n ,
--R       f(x)(a g(x) + b) y (x)
--R
--R     + 
--R                - n + 1    n       2            n  ,                      n ,
--R     (- f(x)f(x)       y(x)  - f(x) (a g(x) + b) )g (x) - y(x)(a g(x) + b) f (x)
--R
--R  /
--R                     n
--R     f(x)(a g(x) + b)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 120
ode53a:=solve(ode53,y,x)
 

   (10)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (10)  "failed"
--R                                                    Type: Union("failed",...)
--E 10

--S 11 of 120
ode54 := D(y(x),x) - a**n*f(x)**(1-n)*D(g(x),x)*y(x)**n - _
          D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x)
 

              ,              n    - n + 1    n       2  ,           ,
         f(x)y (x) + (- f(x)a f(x)       y(x)  - f(x) )g (x) - y(x)f (x)

   (11)  ---------------------------------------------------------------
                                       f(x)
                                                     Type: Expression Integer
--R
--R              ,              n    - n + 1    n       2  ,           ,
--R         f(x)y (x) + (- f(x)a f(x)       y(x)  - f(x) )g (x) - y(x)f (x)
--R
--R   (11)  ---------------------------------------------------------------
--R                                       f(x)
--R                                                     Type: Expression Integer
--E 11

--S 12 of 120
ode54a:=solve(ode54,y,x)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 120
ode55 := D(y(x),x) - f(x)*y(x)**n - g(x)*y(x) - h(x)
 

          ,              n
   (13)  y (x) - f(x)y(x)  - g(x)y(x) - h(x)

                                                     Type: Expression Integer
--R
--R          ,              n
--R   (13)  y (x) - f(x)y(x)  - g(x)y(x) - h(x)
--R
--R                                                     Type: Expression Integer
--E 13

--S 14 of 120
ode55a:=solve(ode55,y,x)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 14

--S 15 of 120
ode56 := D(y(x),x) - f(x)*y(x)**a - g(x)*y(x)**b
 

          ,              b           a
   (15)  y (x) - g(x)y(x)  - f(x)y(x)

                                                     Type: Expression Integer
--R
--R          ,              b           a
--R   (15)  y (x) - g(x)y(x)  - f(x)y(x)
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 120
ode5a:=solve(ode56,y,x)
 

   (16)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (16)  "failed"
--R                                                    Type: Union("failed",...)
--E 16

--S 17 of 120
ode57 := D(y(x),x) - sqrt(abs(y(x)))
 

            +---------+    ,
   (17)  - \|abs(y(x))  + y (x)

                                                     Type: Expression Integer
--R
--R            +---------+    ,
--R   (17)  - \|abs(y(x))  + y (x)
--R
--R                                                     Type: Expression Integer
--E 17

--S 18 of 120
yx:=solve(ode57,y,x)
 

             +---------+
         - x\|abs(y(x))  + 2y(x)
   (18)  -----------------------
                  +----+
                 \|y(x)
                                          Type: Union(Expression Integer,...)
--R
--R             +---------+
--R         - x\|abs(y(x))  + 2y(x)
--R   (18)  -----------------------
--R                  +----+
--R                 \|y(x)
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 120
ode57expr := D(yx,x) - sqrt(abs(yx))
 

   (19)
                             +--------------------------+
                             |      +---------+
          +----+ +---------+ |    x\|abs(y(x))  - 2y(x)      ,    +---------+
       - \|y(x) \|abs(y(x))  |abs(---------------------)  + y (x)\|abs(y(x))
                             |            +----+
                            \|           \|y(x)
     + 
       - abs(y(x))
  /
      +----+ +---------+
     \|y(x) \|abs(y(x))
                                                     Type: Expression Integer
--R
--R   (19)
--R                             +--------------------------+
--R                             |      +---------+
--R          +----+ +---------+ |    x\|abs(y(x))  - 2y(x)      ,    +---------+
--R       - \|y(x) \|abs(y(x))  |abs(---------------------)  + y (x)\|abs(y(x))
--R                             |            +----+
--R                            \|           \|y(x)
--R     + 
--R       - abs(y(x))
--R  /
--R      +----+ +---------+
--R     \|y(x) \|abs(y(x))
--R                                                     Type: Expression Integer
--E 19

--S 20 of 120
ode58 := D(y(x),x) - a*sqrt(y(x)) - b*x
 

          ,        +----+
   (20)  y (x) - a\|y(x)  - b x

                                                     Type: Expression Integer
--R
--R          ,        +----+
--R   (20)  y (x) - a\|y(x)  - b x
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 120
ode58a:=solve(ode58,y,x)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--  this never finishes
--  ode59 := D(y(x),x) - a*sqrt(y(x)**2+1) - b
--

--S 22 of 120
ode60 := D(y(x),x) - sqrt(y(x)**2-1)/sqrt(x**2-1)
 

          +------+         +---------+
          | 2      ,       |    2
         \|x  - 1 y (x) - \|y(x)  - 1

   (22)  -----------------------------
                    +------+
                    | 2
                   \|x  - 1
                                                     Type: Expression Integer
--R
--R          +------+         +---------+
--R          | 2      ,       |    2
--R         \|x  - 1 y (x) - \|y(x)  - 1
--R
--R   (22)  -----------------------------
--R                    +------+
--R                    | 2
--R                   \|x  - 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 120
ode60a:=solve(ode60,y,x)
 

   (23)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (23)  "failed"
--R                                                    Type: Union("failed",...)
--E 23

--S 24 of 120
ode61 := D(y(x),x) - sqrt(x**2-1)/sqrt(y(x)**2-1)
 

          +---------+         +------+
          |    2      ,       | 2
         \|y(x)  - 1 y (x) - \|x  - 1

   (24)  -----------------------------
                   +---------+
                   |    2
                  \|y(x)  - 1
                                                     Type: Expression Integer
--R
--R          +---------+         +------+
--R          |    2      ,       | 2
--R         \|y(x)  - 1 y (x) - \|x  - 1
--R
--R   (24)  -----------------------------
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R                                                     Type: Expression Integer
--E 24

--S 25 of 120
yx:=solve(ode61,y,x)
 

   (25)
                    +------+                    +---------+
                    | 2             2           |    2
           (4x y(x)\|x  - 1  + (- 4x  + 2)y(x))\|y(x)  - 1
         + 
                             +------+
                     2       | 2           2         2     2
           (- 4x y(x)  + 2x)\|x  - 1  + (4x  - 2)y(x)  - 2x  + 1
      *
              +---------+
              |    2
         log(\|y(x)  - 1  - y(x))
     + 
                      +------+                      +------+
                      | 2           2               | 2
           (- 4x y(x)\|x  - 1  + (4x  - 2)y(x))log(\|x  - 1  - x)
         + 
                                  +------+
                     3     3      | 2           2         3
           (- 4x y(x)  + 4x y(x))\|x  - 1  + (4x  - 2)y(x)
         + 
                4     2
           (- 4x  + 2x  + 1)y(x)
      *
          +---------+
          |    2
         \|y(x)  - 1
     + 
                        +------+                                   +------+
                2       | 2             2         2     2          | 2
       ((4x y(x)  - 2x)\|x  - 1  + (- 4x  + 2)y(x)  + 2x  - 1)log(\|x  - 1  - x)
     + 
                                                +------+
               4        3          2     3      | 2             2         4
       (4x y(x)  + (- 4x  - 2x)y(x)  + 2x  - x)\|x  - 1  + (- 4x  + 2)y(x)
     + 
          4         2     4     2
       (4x  - 2)y(x)  - 2x  + 2x
  /
                +------+                    +---------+
                | 2             2           |    2
       (8x y(x)\|x  - 1  + (- 8x  + 4)y(x))\|y(x)  - 1
     + 
                         +------+
                 2       | 2           2         2     2
       (- 8x y(x)  + 4x)\|x  - 1  + (8x  - 4)y(x)  - 4x  + 2
                                          Type: Union(Expression Integer,...)
--R
--R   (25)
--R                    +------+                    +---------+
--R                    | 2             2           |    2
--R           (4x y(x)\|x  - 1  + (- 4x  + 2)y(x))\|y(x)  - 1
--R         + 
--R                             +------+
--R                     2       | 2           2         2     2
--R           (- 4x y(x)  + 2x)\|x  - 1  + (4x  - 2)y(x)  - 2x  + 1
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  - 1  - y(x))
--R     + 
--R                      +------+                      +------+
--R                      | 2           2               | 2
--R           (- 4x y(x)\|x  - 1  + (4x  - 2)y(x))log(\|x  - 1  - x)
--R         + 
--R                                  +------+
--R                     3     3      | 2           2         3
--R           (- 4x y(x)  + 4x y(x))\|x  - 1  + (4x  - 2)y(x)
--R         + 
--R                4     2
--R           (- 4x  + 2x  + 1)y(x)
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                        +------+                                   +------+
--R                2       | 2             2         2     2          | 2
--R       ((4x y(x)  - 2x)\|x  - 1  + (- 4x  + 2)y(x)  + 2x  - 1)log(\|x  - 1  - x)
--R     + 
--R                                                +------+
--R               4        3          2     3      | 2             2         4
--R       (4x y(x)  + (- 4x  - 2x)y(x)  + 2x  - x)\|x  - 1  + (- 4x  + 2)y(x)
--R     + 
--R          4         2     4     2
--R       (4x  - 2)y(x)  - 2x  + 2x
--R  /
--R                +------+                    +---------+
--R                | 2             2           |    2
--R       (8x y(x)\|x  - 1  + (- 8x  + 4)y(x))\|y(x)  - 1
--R     + 
--R                         +------+
--R                 2       | 2           2         2     2
--R       (- 8x y(x)  + 4x)\|x  - 1  + (8x  - 4)y(x)  - 4x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 25

--S 26 of 120
ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1)
 

   (26)
                             4      2         5       4      2          3
                       (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
                     + 
                             4      2
                       (- 32x  + 32x  - 4)y(x)
                  *
                      +------+
                      | 2
                     \|x  - 1
                 + 
                       5      3           5         5       3           3
                   (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
                 + 
                       5      3
                   (32x  - 48x  + 16x)y(x)
              *
                  +---------+
                  |    2
                 \|y(x)  - 1
             + 
                       4      2         6          4       2          4
                   (64x  - 64x  + 8)y(x)  + (- 128x  + 128x  - 16)y(x)
                 + 
                       4      2         2     4     2
                   (72x  - 72x  + 9)y(x)  - 8x  + 8x  - 1
              *
                  +------+
                  | 2
                 \|x  - 1
             + 
                     5      3           6        5       3           4
               (- 64x  + 96x  - 32x)y(x)  + (128x  - 192x  + 64x)y(x)
             + 
                     5       3           2     5      3
               (- 72x  + 108x  - 36x)y(x)  + 8x  - 12x  + 4x
          *
              ,
             y (x)

         + 
                       5      3           4         5      3           2     5
                   (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
                 + 
                        3
                   - 12x  + 4x
              *
                  +------+
                  | 2
                 \|x  - 1
             + 
                     6       4      2         4       6       4      2         2
               (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
             + 
                   6      4     2
               - 8x  + 16x  - 9x  + 1
          *
              +---------+
              |    2
             \|y(x)  - 1
         + 
                     5      3           5       5       3           3
               (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
             + 
                     5      3
               (- 32x  + 48x  - 16x)y(x)
          *
              +------+
              | 2
             \|x  - 1
         + 
               6       4      2         5         6       4       2          3
           (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
         + 
               6      4      2
           (32x  - 64x  + 36x  - 4)y(x)
      *
         ROOT
                                                                 +------+
                             3           3         3             | 2
                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                      + 
                              4      2         3       4      2
                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                   *
                       +---------+
                       |    2
                      \|y(x)  - 1
                  + 
                             3           4       3           2     3
                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                        4      2         4         4      2         2     4
                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
                  + 
                        2
                    - 8x  + 1
               *
                       +---------+        2
                       |    2
                  log(\|y(x)  - 1  - y(x))
              + 
                                                                      +------+
                                    3           3       3             | 2
                            ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
                          + 
                                 4       2          3         4      2
                            (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
                       *
                               +------+
                               | 2
                          log(\|x  - 1  - x)
                      + 
                                   3           5        5           3
                            (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
                          + 
                                  5      3
                            (- 64x  + 48x )y(x)
                       *
                           +------+
                           | 2
                          \|x  - 1
                      + 
                             4       2          5
                        (128x  - 128x  + 16)y(x)
                      + 
                               6      4      2          3
                        (- 128x  + 64x  + 64x  - 16)y(x)
                      + 
                            6      4      2
                        (64x  - 80x  + 16x  + 2)y(x)
                   *
                       +---------+
                       |    2
                      \|y(x)  - 1
                  + 
                                   3           4          3           2      3
                              (128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x
                            + 
                              - 8x
                       *
                           +------+
                           | 2
                          \|x  - 1
                      + 
                               4       2          4        4       2          2
                        (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
                      + 
                             4      2
                        - 16x  + 16x  - 2
                   *
                           +------+
                           | 2
                      log(\|x  - 1  - x)
                  + 
                             3           6          5      3           4
                        (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
                      + 
                             5      3           2      5      3
                        (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                           4       2          6        6       2          4
                    (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
                  + 
                           6       4         2      6      4     2
                    (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
               *
                       +---------+
                       |    2
                  log(\|y(x)  - 1  - y(x))
              + 
                                                                 +------+
                             3           3         3             | 2
                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                      + 
                              4      2         3       4      2
                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                   *
                           +------+     2
                           | 2
                      log(\|x  - 1  - x)
                  + 
                                 3           5          5           3
                            (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
                          + 
                                5      3
                            (64x  - 48x )y(x)
                       *
                           +------+
                           | 2
                          \|x  - 1
                      + 
                               4       2          5
                        (- 128x  + 128x  - 16)y(x)
                      + 
                             6      4      2          3
                        (128x  - 64x  - 64x  + 16)y(x)
                      + 
                              6      4      2
                        (- 64x  + 80x  - 16x  - 2)y(x)
                   *
                           +------+
                           | 2
                      log(\|x  - 1  - x)
                  + 
                            3           7          5      3           5
                        (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
                      + 
                            7      5       3            3
                        (64x  + 32x  - 320x  + 128x)y(x)
                      + 
                              7      5       3
                        (- 32x  + 32x  + 128x  - 66x)y(x)
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                          4      2         7        6      4      2          5
                    (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
                  + 
                          8       4       2          3
                    (- 64x  + 344x  - 280x  + 28)y(x)
                  + 
                        8      6       4       2
                    (32x  - 48x  - 116x  + 132x  - 16)y(x)
               *
                   +---------+
                   |    2
                  \|y(x)  - 1
              + 
                             3           4       3           2     3
                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                        4      2         4         4      2         2     4
                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
                  + 
                        2
                    - 8x  + 1
               *
                       +------+     2
                       | 2
                  log(\|x  - 1  - x)
              + 
                               3           6        5      3           4
                        (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
                      + 
                               5      3           2      5      3
                        (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
                   *
                       +------+
                       | 2
                      \|x  - 1
                  + 
                         4       2          6          6       2          4
                    (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
                  + 
                         6       4         2      6      4     2
                    (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
               *
                       +------+
                       | 2
                  log(\|x  - 1  - x)
              + 
                          3           8        5           6
                    (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
                  + 
                          7      5       3            4
                    (- 64x  - 96x  + 344x  - 116x)y(x)
                  + 
                        7      5       3            2     7      5      3
                    (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
               *
                   +------+
                   | 2
                  \|x  - 1
              + 
                    4      2         8          6      4      2          6
                (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
              + 
                    8      6       4       2          4
                (64x  + 64x  - 400x  + 272x  - 23)y(x)
              + 
                      8      6       4       2          2     8      6      4
                (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
              + 
                   2
                31x  - 4
           /
                                                                +------+
                          3            3          3             | 2
                    ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
                  + 
                           4       2          3        4       2
                    (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
               *
                   +---------+
                   |    2
                  \|y(x)  - 1
              + 
                          3            4        3            2      3
                  ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
               *
                   +------+
                   | 2
                  \|x  - 1
              + 
                     4       2          4          4       2          2      4
                (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
              + 
                     2
                - 32x  + 4
     + 
                   5      3           4         5      3           2     5
               (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
             + 
                    3
               - 12x  + 4x
          *
              +------+
              | 2
             \|x  - 1
         + 
                 6       4      2         4       6       4      2         2
           (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
         + 
               6      4     2
           - 8x  + 16x  - 9x  + 1
      *
          +---------+
          |    2
         \|y(x)  - 1
     + 
                 5      3           5       5       3           3
           (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
         + 
                 5      3
           (- 32x  + 48x  - 16x)y(x)
      *
          +------+
          | 2
         \|x  - 1
     + 
           6       4      2         5         6       4       2          3
       (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
     + 
           6      4      2
       (32x  - 64x  + 36x  - 4)y(x)
  /
                       4      2         4         4      2         2     4     2
                   (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
                 + 
                   1
            *
                +------+
                | 2
               \|x  - 1
           + 
                   5      3           4       5      3           2     5      3
             (- 64x  + 96x  - 32x)y(x)  + (64x  - 96x  + 32x)y(x)  - 8x  + 12x
           + 
             - 4x
        *
            +---------+
            |    2
           \|y(x)  - 1
       + 
                   4      2         5       4      2          3
             (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
           + 
                   4      2
             (- 32x  + 32x  - 4)y(x)
        *
            +------+
            | 2
           \|x  - 1
       + 
             5      3           5         5       3           3
         (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
       + 
             5      3
         (32x  - 48x  + 16x)y(x)
    *
       ROOT
                                                               +------+
                           3           3         3             | 2
                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                    + 
                            4      2         3       4      2
                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                 *
                     +---------+
                     |    2
                    \|y(x)  - 1
                + 
                                                                       +------+
                         3           4       3           2     3       | 2
                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
                + 
                      4      2         4         4      2         2     4     2
                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
                + 
                  1
             *
                     +---------+        2
                     |    2
                log(\|y(x)  - 1  - y(x))
            + 
                                                                    +------+
                                  3           3       3             | 2
                          ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
                        + 
                               4       2          3         4      2
                          (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
                     *
                             +------+
                             | 2
                        log(\|x  - 1  - x)
                    + 
                                 3           5        5           3
                          (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
                        + 
                                5      3
                          (- 64x  + 48x )y(x)
                     *
                         +------+
                         | 2
                        \|x  - 1
                    + 
                           4       2          5
                      (128x  - 128x  + 16)y(x)
                    + 
                             6      4      2          3
                      (- 128x  + 64x  + 64x  - 16)y(x)
                    + 
                          6      4      2
                      (64x  - 80x  + 16x  + 2)y(x)
                 *
                     +---------+
                     |    2
                    \|y(x)  - 1
                + 
                              3           4          3           2      3
                        ((128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x  - 8x)
                     *
                         +------+
                         | 2
                        \|x  - 1
                    + 
                             4       2          4        4       2          2
                      (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
                    + 
                           4      2
                      - 16x  + 16x  - 2
                 *
                         +------+
                         | 2
                    log(\|x  - 1  - x)
                + 
                           3           6          5      3           4
                      (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
                    + 
                           5      3           2      5      3
                      (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
                 *
                     +------+
                     | 2
                    \|x  - 1
                + 
                         4       2          6        6       2          4
                  (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
                + 
                         6       4         2      6      4     2
                  (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
             *
                     +---------+
                     |    2
                log(\|y(x)  - 1  - y(x))
            + 
                                                               +------+
                           3           3         3             | 2
                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
                    + 
                            4      2         3       4      2
                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
                 *
                         +------+     2
                         | 2
                    log(\|x  - 1  - x)
                + 
                               3           5          5           3
                          (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
                        + 
                              5      3
                          (64x  - 48x )y(x)
                     *
                         +------+
                         | 2
                        \|x  - 1
                    + 
                             4       2          5
                      (- 128x  + 128x  - 16)y(x)
                    + 
                           6      4      2          3
                      (128x  - 64x  - 64x  + 16)y(x)
                    + 
                            6      4      2
                      (- 64x  + 80x  - 16x  - 2)y(x)
                 *
                         +------+
                         | 2
                    log(\|x  - 1  - x)
                + 
                          3           7          5      3           5
                      (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
                    + 
                          7      5       3            3
                      (64x  + 32x  - 320x  + 128x)y(x)
                    + 
                            7      5       3
                      (- 32x  + 32x  + 128x  - 66x)y(x)
                 *
                     +------+
                     | 2
                    \|x  - 1
                + 
                        4      2         7        6      4      2          5
                  (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
                + 
                        8       4       2          3
                  (- 64x  + 344x  - 280x  + 28)y(x)
                + 
                      8      6       4       2
                  (32x  - 48x  - 116x  + 132x  - 16)y(x)
             *
                 +---------+
                 |    2
                \|y(x)  - 1
            + 
                                                                       +------+
                         3           4       3           2     3       | 2
                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
                + 
                      4      2         4         4      2         2     4     2
                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
                + 
                  1
             *
                     +------+     2
                     | 2
                log(\|x  - 1  - x)
            + 
                             3           6        5      3           4
                      (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
                    + 
                             5      3           2      5      3
                      (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
                 *
                     +------+
                     | 2
                    \|x  - 1
                + 
                       4       2          6          6       2          4
                  (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
                + 
                       6       4         2      6      4     2
                  (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
             *
                     +------+
                     | 2
                log(\|x  - 1  - x)
            + 
                        3           8        5           6
                  (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
                + 
                        7      5       3            4
                  (- 64x  - 96x  + 344x  - 116x)y(x)
                + 
                      7      5       3            2     7      5      3
                  (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
             *
                 +------+
                 | 2
                \|x  - 1
            + 
                  4      2         8          6      4      2          6
              (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
            + 
                  8      6       4       2          4
              (64x  + 64x  - 400x  + 272x  - 23)y(x)
            + 
                    8      6       4       2          2     8      6      4
              (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
            + 
                 2
              31x  - 4
         /
                                                              +------+
                        3            3          3             | 2
                  ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
                + 
                         4       2          3        4       2
                  (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
             *
                 +---------+
                 |    2
                \|y(x)  - 1
            + 
                        3            4        3            2      3
                ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
             *
                 +------+
                 | 2
                \|x  - 1
            + 
                   4       2          4          4       2          2      4
              (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
            + 
                   2
              - 32x  + 4
                                                     Type: Expression Integer
--R
--R   (26)
--R                             4      2         5       4      2          3
--R                       (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R                     + 
--R                             4      2
--R                       (- 32x  + 32x  - 4)y(x)
--R                  *
--R                      +------+
--R                      | 2
--R                     \|x  - 1
--R                 + 
--R                       5      3           5         5       3           3
--R                   (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R                 + 
--R                       5      3
--R                   (32x  - 48x  + 16x)y(x)
--R              *
--R                  +---------+
--R                  |    2
--R                 \|y(x)  - 1
--R             + 
--R                       4      2         6          4       2          4
--R                   (64x  - 64x  + 8)y(x)  + (- 128x  + 128x  - 16)y(x)
--R                 + 
--R                       4      2         2     4     2
--R                   (72x  - 72x  + 9)y(x)  - 8x  + 8x  - 1
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     5      3           6        5       3           4
--R               (- 64x  + 96x  - 32x)y(x)  + (128x  - 192x  + 64x)y(x)
--R             + 
--R                     5       3           2     5      3
--R               (- 72x  + 108x  - 36x)y(x)  + 8x  - 12x  + 4x
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                       5      3           4         5      3           2     5
--R                   (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R                 + 
--R                        3
--R                   - 12x  + 4x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     6       4      2         4       6       4      2         2
--R               (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R             + 
--R                   6      4     2
--R               - 8x  + 16x  - 9x  + 1
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  - 1
--R         + 
--R                     5      3           5       5       3           3
--R               (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R             + 
--R                     5      3
--R               (- 32x  + 48x  - 16x)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R               6       4      2         5         6       4       2          3
--R           (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R         + 
--R               6      4      2
--R           (32x  - 64x  + 36x  - 4)y(x)
--R      *
--R         ROOT
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +---------+        2
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                      +------+
--R                                    3           3       3             | 2
--R                            ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
--R                          + 
--R                                 4       2          3         4      2
--R                            (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
--R                       *
--R                               +------+
--R                               | 2
--R                          log(\|x  - 1  - x)
--R                      + 
--R                                   3           5        5           3
--R                            (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
--R                          + 
--R                                  5      3
--R                            (- 64x  + 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                             4       2          5
--R                        (128x  - 128x  + 16)y(x)
--R                      + 
--R                               6      4      2          3
--R                        (- 128x  + 64x  + 64x  - 16)y(x)
--R                      + 
--R                            6      4      2
--R                        (64x  - 80x  + 16x  + 2)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                                   3           4          3           2      3
--R                              (128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x
--R                            + 
--R                              - 8x
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          4        4       2          2
--R                        (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
--R                      + 
--R                             4      2
--R                        - 16x  + 16x  - 2
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                             3           6          5      3           4
--R                        (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
--R                      + 
--R                             5      3           2      5      3
--R                        (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                           4       2          6        6       2          4
--R                    (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
--R                  + 
--R                           6       4         2      6      4     2
--R                    (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
--R               *
--R                       +---------+
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                           +------+     2
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                                 3           5          5           3
--R                            (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
--R                          + 
--R                                5      3
--R                            (64x  - 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  + 128x  - 16)y(x)
--R                      + 
--R                             6      4      2          3
--R                        (128x  - 64x  - 64x  + 16)y(x)
--R                      + 
--R                              6      4      2
--R                        (- 64x  + 80x  - 16x  - 2)y(x)
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                            3           7          5      3           5
--R                        (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
--R                      + 
--R                            7      5       3            3
--R                        (64x  + 32x  - 320x  + 128x)y(x)
--R                      + 
--R                              7      5       3
--R                        (- 32x  + 32x  + 128x  - 66x)y(x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                          4      2         7        6      4      2          5
--R                    (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
--R                  + 
--R                          8       4       2          3
--R                    (- 64x  + 344x  - 280x  + 28)y(x)
--R                  + 
--R                        8      6       4       2
--R                    (32x  - 48x  - 116x  + 132x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +------+     2
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                               3           6        5      3           4
--R                        (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
--R                      + 
--R                               5      3           2      5      3
--R                        (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                         4       2          6          6       2          4
--R                    (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
--R                  + 
--R                         6       4         2      6      4     2
--R                    (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
--R               *
--R                       +------+
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                          3           8        5           6
--R                    (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
--R                  + 
--R                          7      5       3            4
--R                    (- 64x  - 96x  + 344x  - 116x)y(x)
--R                  + 
--R                        7      5       3            2     7      5      3
--R                    (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                    4      2         8          6      4      2          6
--R                (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
--R              + 
--R                    8      6       4       2          4
--R                (64x  + 64x  - 400x  + 272x  - 23)y(x)
--R              + 
--R                      8      6       4       2          2     8      6      4
--R                (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
--R              + 
--R                   2
--R                31x  - 4
--R           /
--R                                                                +------+
--R                          3            3          3             | 2
--R                    ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
--R                  + 
--R                           4       2          3        4       2
--R                    (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                          3            4        3            2      3
--R                  ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                     4       2          4          4       2          2      4
--R                (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
--R              + 
--R                     2
--R                - 32x  + 4
--R     + 
--R                   5      3           4         5      3           2     5
--R               (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R             + 
--R                    3
--R               - 12x  + 4x
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R                 6       4      2         4       6       4      2         2
--R           (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R         + 
--R               6      4     2
--R           - 8x  + 16x  - 9x  + 1
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                 5      3           5       5       3           3
--R           (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R         + 
--R                 5      3
--R           (- 32x  + 48x  - 16x)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  - 1
--R     + 
--R           6       4      2         5         6       4       2          3
--R       (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R     + 
--R           6      4      2
--R       (32x  - 64x  + 36x  - 4)y(x)
--R  /
--R                       4      2         4         4      2         2     4     2
--R                   (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
--R                 + 
--R                   1
--R            *
--R                +------+
--R                | 2
--R               \|x  - 1
--R           + 
--R                   5      3           4       5      3           2     5      3
--R             (- 64x  + 96x  - 32x)y(x)  + (64x  - 96x  + 32x)y(x)  - 8x  + 12x
--R           + 
--R             - 4x
--R        *
--R            +---------+
--R            |    2
--R           \|y(x)  - 1
--R       + 
--R                   4      2         5       4      2          3
--R             (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R           + 
--R                   4      2
--R             (- 32x  + 32x  - 4)y(x)
--R        *
--R            +------+
--R            | 2
--R           \|x  - 1
--R       + 
--R             5      3           5         5       3           3
--R         (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R       + 
--R             5      3
--R         (32x  - 48x  + 16x)y(x)
--R    *
--R       ROOT
--R                                                               +------+
--R                           3           3         3             | 2
--R                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                    + 
--R                            4      2         3       4      2
--R                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                 *
--R                     +---------+
--R                     |    2
--R                    \|y(x)  - 1
--R                + 
--R                                                                       +------+
--R                         3           4       3           2     3       | 2
--R                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
--R                + 
--R                      4      2         4         4      2         2     4     2
--R                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
--R                + 
--R                  1
--R             *
--R                     +---------+        2
--R                     |    2
--R                log(\|y(x)  - 1  - y(x))
--R            + 
--R                                                                    +------+
--R                                  3           3       3             | 2
--R                          ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
--R                        + 
--R                               4       2          3         4      2
--R                          (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
--R                     *
--R                             +------+
--R                             | 2
--R                        log(\|x  - 1  - x)
--R                    + 
--R                                 3           5        5           3
--R                          (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
--R                        + 
--R                                5      3
--R                          (- 64x  + 48x )y(x)
--R                     *
--R                         +------+
--R                         | 2
--R                        \|x  - 1
--R                    + 
--R                           4       2          5
--R                      (128x  - 128x  + 16)y(x)
--R                    + 
--R                             6      4      2          3
--R                      (- 128x  + 64x  + 64x  - 16)y(x)
--R                    + 
--R                          6      4      2
--R                      (64x  - 80x  + 16x  + 2)y(x)
--R                 *
--R                     +---------+
--R                     |    2
--R                    \|y(x)  - 1
--R                + 
--R                              3           4          3           2      3
--R                        ((128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x  - 8x)
--R                     *
--R                         +------+
--R                         | 2
--R                        \|x  - 1
--R                    + 
--R                             4       2          4        4       2          2
--R                      (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
--R                    + 
--R                           4      2
--R                      - 16x  + 16x  - 2
--R                 *
--R                         +------+
--R                         | 2
--R                    log(\|x  - 1  - x)
--R                + 
--R                           3           6          5      3           4
--R                      (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
--R                    + 
--R                           5      3           2      5      3
--R                      (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
--R                 *
--R                     +------+
--R                     | 2
--R                    \|x  - 1
--R                + 
--R                         4       2          6        6       2          4
--R                  (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
--R                + 
--R                         6       4         2      6      4     2
--R                  (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
--R             *
--R                     +---------+
--R                     |    2
--R                log(\|y(x)  - 1  - y(x))
--R            + 
--R                                                               +------+
--R                           3           3         3             | 2
--R                      ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                    + 
--R                            4      2         3       4      2
--R                      (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                 *
--R                         +------+     2
--R                         | 2
--R                    log(\|x  - 1  - x)
--R                + 
--R                               3           5          5           3
--R                          (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
--R                        + 
--R                              5      3
--R                          (64x  - 48x )y(x)
--R                     *
--R                         +------+
--R                         | 2
--R                        \|x  - 1
--R                    + 
--R                             4       2          5
--R                      (- 128x  + 128x  - 16)y(x)
--R                    + 
--R                           6      4      2          3
--R                      (128x  - 64x  - 64x  + 16)y(x)
--R                    + 
--R                            6      4      2
--R                      (- 64x  + 80x  - 16x  - 2)y(x)
--R                 *
--R                         +------+
--R                         | 2
--R                    log(\|x  - 1  - x)
--R                + 
--R                          3           7          5      3           5
--R                      (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
--R                    + 
--R                          7      5       3            3
--R                      (64x  + 32x  - 320x  + 128x)y(x)
--R                    + 
--R                            7      5       3
--R                      (- 32x  + 32x  + 128x  - 66x)y(x)
--R                 *
--R                     +------+
--R                     | 2
--R                    \|x  - 1
--R                + 
--R                        4      2         7        6      4      2          5
--R                  (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
--R                + 
--R                        8       4       2          3
--R                  (- 64x  + 344x  - 280x  + 28)y(x)
--R                + 
--R                      8      6       4       2
--R                  (32x  - 48x  - 116x  + 132x  - 16)y(x)
--R             *
--R                 +---------+
--R                 |    2
--R                \|y(x)  - 1
--R            + 
--R                                                                       +------+
--R                         3           4       3           2     3       | 2
--R                  ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)\|x  - 1
--R                + 
--R                      4      2         4         4      2         2     4     2
--R                  (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x
--R                + 
--R                  1
--R             *
--R                     +------+     2
--R                     | 2
--R                log(\|x  - 1  - x)
--R            + 
--R                             3           6        5      3           4
--R                      (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
--R                    + 
--R                             5      3           2      5      3
--R                      (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
--R                 *
--R                     +------+
--R                     | 2
--R                    \|x  - 1
--R                + 
--R                       4       2          6          6       2          4
--R                  (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
--R                + 
--R                       6       4         2      6      4     2
--R                  (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
--R             *
--R                     +------+
--R                     | 2
--R                log(\|x  - 1  - x)
--R            + 
--R                        3           8        5           6
--R                  (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
--R                + 
--R                        7      5       3            4
--R                  (- 64x  - 96x  + 344x  - 116x)y(x)
--R                + 
--R                      7      5       3            2     7      5      3
--R                  (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
--R             *
--R                 +------+
--R                 | 2
--R                \|x  - 1
--R            + 
--R                  4      2         8          6      4      2          6
--R              (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
--R            + 
--R                  8      6       4       2          4
--R              (64x  + 64x  - 400x  + 272x  - 23)y(x)
--R            + 
--R                    8      6       4       2          2     8      6      4
--R              (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
--R            + 
--R                 2
--R              31x  - 4
--R         /
--R                                                              +------+
--R                        3            3          3             | 2
--R                  ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
--R                + 
--R                         4       2          3        4       2
--R                  (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
--R             *
--R                 +---------+
--R                 |    2
--R                \|y(x)  - 1
--R            + 
--R                        3            4        3            2      3
--R                ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
--R             *
--R                 +------+
--R                 | 2
--R                \|x  - 1
--R            + 
--R                   4       2          4          4       2          2      4
--R              (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
--R            + 
--R                   2
--R              - 32x  + 4
--R                                                     Type: Expression Integer
--E 26

--S 27 of 120
ode62 := D(y(x),x) - (y(x)-x**2*sqrt(x**2-y(x)**2))/_
                      (x*y(x)*sqrt(x**2-y(x)**2)+x)
 

                 +------------+                +------------+
                 |      2    2       ,       2 |      2    2
         (x y(x)\|- y(x)  + x   + x)y (x) + x \|- y(x)  + x   - y(x)

   (27)  -----------------------------------------------------------
                                 +------------+
                                 |      2    2
                          x y(x)\|- y(x)  + x   + x
                                                     Type: Expression Integer
--R
--R                 +------------+                +------------+
--R                 |      2    2       ,       2 |      2    2
--R         (x y(x)\|- y(x)  + x   + x)y (x) + x \|- y(x)  + x   - y(x)
--R
--R   (27)  -----------------------------------------------------------
--R                                 +------------+
--R                                 |      2    2
--R                          x y(x)\|- y(x)  + x   + x
--R                                                     Type: Expression Integer
--E 27

--S 28 of 120
ode62a:=solve(ode62,y,x)
 

   (28)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (28)  "failed"
--R                                                    Type: Union("failed",...)
--E 28

--S 29 of 120
ode63 := D(y(x),x) - (1+ y(x)**2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)**3)
 

                 +-----+ ,        +--------+               2
         (x + 1)\|x + 1 y (x)abs(\|y(x) + 1  + y(x)) - y(x)  - 1

   (29)  -------------------------------------------------------
                          +-----+     +--------+
                  (x + 1)\|x + 1 abs(\|y(x) + 1  + y(x))
                                                     Type: Expression Integer
--R
--R                 +-----+ ,        +--------+               2
--R         (x + 1)\|x + 1 y (x)abs(\|y(x) + 1  + y(x)) - y(x)  - 1
--R
--R   (29)  -------------------------------------------------------
--R                          +-----+     +--------+
--R                  (x + 1)\|x + 1 abs(\|y(x) + 1  + y(x))
--R                                                     Type: Expression Integer
--E 29

--S 30 of 120
ode63a:=solve(ode63,y,x)
 

   (30)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (30)  "failed"
--R                                                    Type: Union("failed",...)
--E 30

--S 31 of 120
ode64 := D(y(x),x) - sqrt((a*y(x)**2+b*y(x)+c)/(a*x**2+b*x+c))
 

                  +--------------------+
                  |      2
          ,       |a y(x)  + b y(x) + c
   (31)  y (x) -  |--------------------
                  |      2
                 \|   a x  + b x + c
                                                     Type: Expression Integer
--R
--R                  +--------------------+
--R                  |      2
--R          ,       |a y(x)  + b y(x) + c
--R   (31)  y (x) -  |--------------------
--R                  |      2
--R                 \|   a x  + b x + c
--R                                                     Type: Expression Integer
--E 31

--S 32 of 120
yx:=solve(ode64,y,x)
 

   (32)
       log
                                                +--------------------+
                                                |      2
                       2 2                  +-+ |a y(x)  + b y(x) + c
                    (2a x  + 2a b x + 2a c)\|a  |--------------------
                                                |      2
                                               \|   a x  + b x + c
                 *
                     +--------------------+
                     |      2
                    \|a y(x)  + b y(x) + c
                + 
                       3 3     2   2     2        2
                  (- 2a x  - 2a b x  - 2a c x)y(x)
                + 
                       2   3       2 2                     2   3           2
                  (- 2a b x  - 2a b x  - 2a b c x)y(x) - 2a c x  - 2a b c x
                + 
                        2
                  - 2a c x
             *
                 +-------------------------+
                 |        2               2
                \|a c y(x)  + b c y(x) + c
            + 
                      3 4    2   3     2   2                2    3     2
                  (- a x  - a b x  - 2a c x  - a b c x - a c  - a )y(x)
                + 
                      2   4      2 3           2    2         2    2
                  (- a b x  - a b x  - 2a b c x  - b c x - b c  - a b)y(x)
                + 
                     2   4          3       2 2      2     3    2
                  - a c x  - a b c x  - 2a c x  - b c x - c  - a c
             *
                     +--------------------+
                 +-+ |      2
                \|a \|a y(x)  + b y(x) + c
            + 
                     4 3     3   2     3        2
                  (2a x  + 2a b x  + 2a c x)y(x)
                + 
                     3   3     2 2 2     2               3   3     2     2
                  (2a b x  + 2a b x  + 2a b c x)y(x) + 2a c x  + 2a b c x
                + 
                    2 2
                  2a c x
             *
                 +--------------------+
                 |      2
                 |a y(x)  + b y(x) + c
                 |--------------------
                 |      2
                \|   a x  + b x + c
         /
                                        +--------------------+
                                        |      2
                   2 2                  |a y(x)  + b y(x) + c
                (2a x  + 2a b x + 2a c) |--------------------
                                        |      2
                                       \|   a x  + b x + c
             *
                 +-------------------------+
                 |        2               2
                \|a c y(x)  + b c y(x) + c
            + 
                3 4    2   3                2    3     2
              (a x  + a b x  - a b c x - a c  - a )y(x)
            + 
                2   4      2 3    2         2    2          2   4          3
              (a b x  + a b x  - b c x - b c  - a b)y(x) + a c x  + a b c x
            + 
                   2     3    2
              - b c x - c  - a c
     + 
       log
                                    +--------------------+
                 +-+ +-+            |      2                         +-+
              (2\|a \|c  - 2a y(x))\|a y(x)  + b y(x) + c  + 2a y(x)\|c
            + 
                        2                +-+
              (- 2a y(x)  - b y(x) - 2c)\|a
         /
                  +--------------------+
              +-+ |      2
            2\|c \|a y(x)  + b y(x) + c  - b y(x) - 2c
  /
      +-+
     \|a
                                          Type: Union(Expression Integer,...)
--R
--R   (32)
--R       log
--R                                                +--------------------+
--R                                                |      2
--R                       2 2                  +-+ |a y(x)  + b y(x) + c
--R                    (2a x  + 2a b x + 2a c)\|a  |--------------------
--R                                                |      2
--R                                               \|   a x  + b x + c
--R                 *
--R                     +--------------------+
--R                     |      2
--R                    \|a y(x)  + b y(x) + c
--R                + 
--R                       3 3     2   2     2        2
--R                  (- 2a x  - 2a b x  - 2a c x)y(x)
--R                + 
--R                       2   3       2 2                     2   3           2
--R                  (- 2a b x  - 2a b x  - 2a b c x)y(x) - 2a c x  - 2a b c x
--R                + 
--R                        2
--R                  - 2a c x
--R             *
--R                 +-------------------------+
--R                 |        2               2
--R                \|a c y(x)  + b c y(x) + c
--R            + 
--R                      3 4    2   3     2   2                2    3     2
--R                  (- a x  - a b x  - 2a c x  - a b c x - a c  - a )y(x)
--R                + 
--R                      2   4      2 3           2    2         2    2
--R                  (- a b x  - a b x  - 2a b c x  - b c x - b c  - a b)y(x)
--R                + 
--R                     2   4          3       2 2      2     3    2
--R                  - a c x  - a b c x  - 2a c x  - b c x - c  - a c
--R             *
--R                     +--------------------+
--R                 +-+ |      2
--R                \|a \|a y(x)  + b y(x) + c
--R            + 
--R                     4 3     3   2     3        2
--R                  (2a x  + 2a b x  + 2a c x)y(x)
--R                + 
--R                     3   3     2 2 2     2               3   3     2     2
--R                  (2a b x  + 2a b x  + 2a b c x)y(x) + 2a c x  + 2a b c x
--R                + 
--R                    2 2
--R                  2a c x
--R             *
--R                 +--------------------+
--R                 |      2
--R                 |a y(x)  + b y(x) + c
--R                 |--------------------
--R                 |      2
--R                \|   a x  + b x + c
--R         /
--R                                        +--------------------+
--R                                        |      2
--R                   2 2                  |a y(x)  + b y(x) + c
--R                (2a x  + 2a b x + 2a c) |--------------------
--R                                        |      2
--R                                       \|   a x  + b x + c
--R             *
--R                 +-------------------------+
--R                 |        2               2
--R                \|a c y(x)  + b c y(x) + c
--R            + 
--R                3 4    2   3                2    3     2
--R              (a x  + a b x  - a b c x - a c  - a )y(x)
--R            + 
--R                2   4      2 3    2         2    2          2   4          3
--R              (a b x  + a b x  - b c x - b c  - a b)y(x) + a c x  + a b c x
--R            + 
--R                   2     3    2
--R              - b c x - c  - a c
--R     + 
--R       log
--R                                    +--------------------+
--R                 +-+ +-+            |      2                         +-+
--R              (2\|a \|c  - 2a y(x))\|a y(x)  + b y(x) + c  + 2a y(x)\|c
--R            + 
--R                        2                +-+
--R              (- 2a y(x)  - b y(x) - 2c)\|a
--R         /
--R                  +--------------------+
--R              +-+ |      2
--R            2\|c \|a y(x)  + b y(x) + c  - b y(x) - 2c
--R  /
--R      +-+
--R     \|a
--R                                          Type: Union(Expression Integer,...)
--E 32

--S 33 of 120
ode64expr := D(yx,x) - sqrt((a*yx**2+b*yx+c)/(a*x**2+b*x+c));
 

                                                     Type: Expression Integer
--E 33

--S 34 of 120
ode65 := D(y(x),x) - sqrt((y(x)**3+1)/(x**3+1))
 

                  +---------+
                  |    3
          ,       |y(x)  + 1
   (34)  y (x) -  |---------
                  |   3
                 \|  x  + 1
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |    3
--R          ,       |y(x)  + 1
--R   (34)  y (x) -  |---------
--R                  |   3
--R                 \|  x  + 1
--R                                                     Type: Expression Integer
--E 34

--S 35 of 120
ode65a:=solve(ode65,y,x)
 

                 +---------+
                 |    3
                 |y(x)  + 1
                 |---------
            x    |   3                 y(x)
          ++    \| %S  + 1           ++          1
   (35)   |   - ------------ d%S  +  |      ---------- d%S
         ++      +---------+        ++       +-------+
                 |    3                      |  3
                \|y(x)  + 1                 \|%S  + 1
                                          Type: Union(Expression Integer,...)
--R
--R                 +---------+
--R                 |    3
--R                 |y(x)  + 1
--R                 |---------
--R            x    |   3                 y(x)
--I          ++    \| %P  + 1           ++          1
--I   (35)   |   - ------------ d%P  +  |      ---------- d%P
--R         ++      +---------+        ++       +-------+
--R                 |    3                      |  3
--I                \|y(x)  + 1                 \|%P  + 1
--R                                          Type: Union(Expression Integer,...)
--E 35

--S 36 of 120
ode66 := D(y(x),x) - sqrt(abs(y(x)*(1-y(x))*(1-a*y(x))))/_
               sqrt(abs(x*(1-x)*(1-a*x)))
 

   (36)
          +------------------------------------+
          |          3                2
       - \|abs(a y(x)  + (- a - 1)y(x)  + y(x))
     + 
        +---------------------------+
        |       3             2       ,
       \|abs(a x  + (- a - 1)x  + x) y (x)

  /
      +---------------------------+
      |       3             2
     \|abs(a x  + (- a - 1)x  + x)
                                                     Type: Expression Integer
--R
--R   (36)
--R          +------------------------------------+
--R          |          3                2
--R       - \|abs(a y(x)  + (- a - 1)y(x)  + y(x))
--R     + 
--R        +---------------------------+
--R        |       3             2       ,
--R       \|abs(a x  + (- a - 1)x  + x) y (x)
--R
--R  /
--R      +---------------------------+
--R      |       3             2
--R     \|abs(a x  + (- a - 1)x  + x)
--R                                                     Type: Expression Integer
--E 36

--S 37 of 120
ode66a:=solve(ode66,y,x)
 

   (37)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (37)  "failed"
--R                                                    Type: Union("failed",...)
--E 37

--S 38 of 120
ode67 := D(y(x),x) - sqrt(1-y(x)**4)/sqrt(1-x**4)
 

          +--------+         +-----------+
          |   4      ,       |      4
         \|- x  + 1 y (x) - \|- y(x)  + 1

   (38)  ---------------------------------
                     +--------+
                     |   4
                    \|- x  + 1
                                                     Type: Expression Integer
--R
--R          +--------+         +-----------+
--R          |   4      ,       |      4
--R         \|- x  + 1 y (x) - \|- y(x)  + 1
--R
--R   (38)  ---------------------------------
--R                     +--------+
--R                     |   4
--R                    \|- x  + 1
--R                                                     Type: Expression Integer
--E 38

--S 39 of 120
ode67a:=solve(ode67,y,x)
 

   (39)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (39)  "failed"
--R                                                    Type: Union("failed",...)
--E 39

--S 40 of 120
ode68 := D(y(x),x) - sqrt((a*y(x)**4+b*y(x)**2+1)/(a*x**4+b*x**2+1))
 

                  +---------------------+
                  |      4         2
          ,       |a y(x)  + b y(x)  + 1
   (40)  y (x) -  |---------------------
                  |      4      2
                 \|   a x  + b x  + 1
                                                     Type: Expression Integer
--R
--R                  +---------------------+
--R                  |      4         2
--R          ,       |a y(x)  + b y(x)  + 1
--R   (40)  y (x) -  |---------------------
--R                  |      4      2
--R                 \|   a x  + b x  + 1
--R                                                     Type: Expression Integer
--E 40

--S 41 of 120
ode68a:=solve(ode68,y,x)
 

   (41)
           +---------------------+
           |      4         2
           |a y(x)  + b y(x)  + 1
           |---------------------
      x    |     2      4                    y(x)
    ++    \|   %S b + %S a + 1             ++              1
    |   - ------------------------ d%S  +  |      ------------------ d%S
   ++      +---------------------+        ++       +---------------+
           |      4         2                      |  2      4
          \|a y(x)  + b y(x)  + 1                 \|%S b + %S a + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (41)
--R           +---------------------+
--R           |      4         2
--R           |a y(x)  + b y(x)  + 1
--R           |---------------------
--R      x    |     2      4                    y(x)
--I    ++    \|   %N b + %N a + 1             ++              1
--I    |   - ------------------------ d%N  +  |      ------------------ d%N
--R   ++      +---------------------+        ++       +---------------+
--R           |      4         2                      |  2      4
--I          \|a y(x)  + b y(x)  + 1                 \|%N b + %N a + 1
--R                                          Type: Union(Expression Integer,...)
--E 41

--S 42 of 120
ode69 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)*_
                           (a4*x**4+a3*x**3+a2*x**2+a1*x+a0))
 

   (42)
      ,
     y (x)

   + 
     -
        ROOT
                     4          3          2                       4
             (a4 b4 x  + a3 b4 x  + a2 b4 x  + a1 b4 x + a0 b4)y(x)
           + 
                     4          3          2                       3
             (a4 b3 x  + a3 b3 x  + a2 b3 x  + a1 b3 x + a0 b3)y(x)
           + 
                     4          3          2                       2
             (a4 b2 x  + a3 b2 x  + a2 b2 x  + a1 b2 x + a0 b2)y(x)
           + 
                     4          3          2                                 4
             (a4 b1 x  + a3 b1 x  + a2 b1 x  + a1 b1 x + a0 b1)y(x) + a4 b0 x
           + 
                    3          2
             a3 b0 x  + a2 b0 x  + a1 b0 x + a0 b0
                                                     Type: Expression Integer
--R 
--R
--R   (42)
--R      ,
--R     y (x)
--R
--R   + 
--R     -
--R        ROOT
--R                     4          3          2                       4
--R             (a4 b4 x  + a3 b4 x  + a2 b4 x  + a1 b4 x + a0 b4)y(x)
--R           + 
--R                     4          3          2                       3
--R             (a4 b3 x  + a3 b3 x  + a2 b3 x  + a1 b3 x + a0 b3)y(x)
--R           + 
--R                     4          3          2                       2
--R             (a4 b2 x  + a3 b2 x  + a2 b2 x  + a1 b2 x + a0 b2)y(x)
--R           + 
--R                     4          3          2                                 4
--R             (a4 b1 x  + a3 b1 x  + a2 b1 x  + a1 b1 x + a0 b1)y(x) + a4 b0 x
--R           + 
--R                    3          2
--R             a3 b0 x  + a2 b0 x  + a1 b0 x + a0 b0
--R                                                     Type: Expression Integer
--E 42

--S 43 of 120
ode69a:=solve(ode69,y,x)
 
 
   >> Error detected within library code:
   PFO::possibleOrder: more than 1 algebraic constant

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   PFO::possibleOrder: more than 1 algebraic constant
--R
--R   Continuing to read the file...
--R
--E 43

--S 44 of 120
ode70 := D(y(x),x) - sqrt((a4*x**4+a3*x**3+a2*x**2+a1*x+a0)/_
                        (b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0))
 

                  +---------------------------------------------+
                  |          4       3       2
          ,       |      a4 x  + a3 x  + a2 x  + a1 x + a0
   (43)  y (x) -  |---------------------------------------------
                  |       4          3          2
                 \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
                                                     Type: Expression Integer
--R
--R                  +---------------------------------------------+
--R                  |          4       3       2
--R          ,       |      a4 x  + a3 x  + a2 x  + a1 x + a0
--R   (43)  y (x) -  |---------------------------------------------
--R                  |       4          3          2
--R                 \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R                                                     Type: Expression Integer
--E 44

--S 45 of 120
ode70a:=solve(ode70,y,x)
 
 
   >> Error detected within library code:
   PFO::possibleOrder: more than 1 algebraic constant

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   PFO::possibleOrder: more than 1 algebraic constant
--R
--R   Continuing to read the file...
--R
--E 45

--S 46 of 120
ode71 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)/_
                       (a4*x**4+a3*x**3+a2*x**2+a1*x+a0))
 

                  +---------------------------------------------+
                  |       4          3          2
          ,       |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
   (44)  y (x) -  |---------------------------------------------
                  |          4       3       2
                 \|      a4 x  + a3 x  + a2 x  + a1 x + a0
                                                     Type: Expression Integer
--R
--R                  +---------------------------------------------+
--R                  |       4          3          2
--R          ,       |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R   (44)  y (x) -  |---------------------------------------------
--R                  |          4       3       2
--R                 \|      a4 x  + a3 x  + a2 x  + a1 x + a0
--R                                                     Type: Expression Integer
--E 46

--S 47 of 120
ode71a:=solve(ode71,y,x)
 

   (45)
             +---------------------------------------------+
             |       4          3          2
             |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
             |---------------------------------------------
        x    |        4       3       2
      ++    \|      %S a4 + %S a3 + %S a2 + %S a1 + a0
      |   - ------------------------------------------------ d%S
     ++      +---------------------------------------------+
             |       4          3          2
            \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
   + 
        y(x)
      ++                       1
      |      ------------------------------------- d%S
     ++       +----------------------------------+
              |  4       3       2
             \|%S b4 + %S b3 + %S b2 + %S b1 + b0
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (45)
--R             +---------------------------------------------+
--R             |       4          3          2
--R             |b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R             |---------------------------------------------
--R        x    |        4       3       2
--I      ++    \|      %N a4 + %N a3 + %N a2 + %N a1 + a0
--I      |   - ------------------------------------------------ d%N
--R     ++      +---------------------------------------------+
--R             |       4          3          2
--R            \|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0
--R   + 
--R        y(x)
--R      ++                       1
--I      |      ------------------------------------- d%N
--R     ++       +----------------------------------+
--R              |  4       3       2
--I             \|%N b4 + %N b3 + %N b2 + %N b1 + b0
--R                                          Type: Union(Expression Integer,...)
--E 47

--S 48 of 120
R1:=operator 'R1
 

   (46)  R1
                                                          Type: BasicOperator
--R
--R   (46)  R1
--R                                                          Type: BasicOperator
--E 48

--S 49 of 120
R2:=operator 'R2
 

   (47)  R2
                                                          Type: BasicOperator
--R
--R   (47)  R2
--R                                                          Type: BasicOperator
--E 49

--S 50 of 120
ode72 := D(y(x),x) - R1(x,sqrt(a4*x**4+a3*x**3+a2*x**2+a1*x+a0))*_
             R2(y(x),sqrt(b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0))
 

   (48)
     -
                +---------------------------------+
                |    4       3       2
          R1(x,\|a4 x  + a3 x  + a2 x  + a1 x + a0 )
       *
                   +---------------------------------------------+
                   |       4          3          2
          R2(y(x),\|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0 )
   + 
      ,
     y (x)

                                                     Type: Expression Integer
--R
--R   (48)
--R     -
--R                +---------------------------------+
--R                |    4       3       2
--R          R1(x,\|a4 x  + a3 x  + a2 x  + a1 x + a0 )
--R       *
--R                   +---------------------------------------------+
--R                   |       4          3          2
--R          R2(y(x),\|b4 y(x)  + b3 y(x)  + b2 y(x)  + b1 y(x) + b0 )
--R   + 
--R      ,
--R     y (x)
--R
--R                                                     Type: Expression Integer
--E 50

--S 51 of 120
ode72a:=solve(ode72,y,x)
 
 
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 51

--S 52 of 120
ode73 := D(y(x),x) - ((a3*x**3+a2*x**2+a1*x+a0)/_
           (a3*y(x)**3+a2*y(x)**2+a1*y(x)+a0))**(2/3)
 

                  +----------------------------------+2
                  |         3       2
          ,       |     a3 x  + a2 x  + a1 x + a0
   (49)  y (x) -  |----------------------------------
                 3|       3          2
                 \|a3 y(x)  + a2 y(x)  + a1 y(x) + a0
                                                     Type: Expression Integer
--R
--R                  +----------------------------------+2
--R                  |         3       2
--R          ,       |     a3 x  + a2 x  + a1 x + a0
--R   (49)  y (x) -  |----------------------------------
--R                 3|       3          2
--R                 \|a3 y(x)  + a2 y(x)  + a1 y(x) + a0
--R                                                     Type: Expression Integer
--E 52


--S 53 of 120
ode74 := D(y(x),x) - f(x)*(y(x)-g(x))*sqrt((y(x)-a)*(y(x)-b))
 

                                         +---------------------------+
          ,                              |    2
   (50)  y (x) + (- f(x)y(x) + f(x)g(x))\|y(x)  + (- b - a)y(x) + a b

                                                     Type: Expression Integer
--R
--R                                         +---------------------------+
--R          ,                              |    2
--R   (50)  y (x) + (- f(x)y(x) + f(x)g(x))\|y(x)  + (- b - a)y(x) + a b
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 120
ode74a:=solve(ode74,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 54

--S 55 of 120
ode75 := D(y(x),x) - exp(x-y(x)) + exp(x)
 

          ,        - y(x) + x     x
   (52)  y (x) - %e           + %e

                                                     Type: Expression Integer
--R
--R          ,        - y(x) + x     x
--R   (52)  y (x) - %e           + %e
--R
--R                                                     Type: Expression Integer
--E 55

--S 56 of 120
ode75a:=solve(ode75,y,x)
 

   (53)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (53)  "failed"
--R                                                    Type: Union("failed",...)
--E 56

--S 57 of 120
ode76 := D(y(x),x) - a*cos(y(x)) + b
 

          ,
   (54)  y (x) - a cos(y(x)) + b

                                                     Type: Expression Integer
--R
--R          ,
--R   (54)  y (x) - a cos(y(x)) + b
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 120
yx:=solve(ode76,y,x)
 

   (55)
                                    +---------+              +---------+
               2    2               |   2    2               |   2    2
           (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
       log(-------------------------------------------------------------)
                                  a cos(y(x)) - b
     + 
         +---------+
         |   2    2
       x\|- b  + a
  /
      +---------+
      |   2    2
     \|- b  + a
                                          Type: Union(Expression Integer,...)
--R
--R   (55)
--R                                    +---------+              +---------+
--R               2    2               |   2    2               |   2    2
--R           (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
--R       log(-------------------------------------------------------------)
--R                                  a cos(y(x)) - b
--R     + 
--R         +---------+
--R         |   2    2
--R       x\|- b  + a
--R  /
--R      +---------+
--R      |   2    2
--R     \|- b  + a
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 120
ode76expr := D(yx,x) - a*cos(yx) + b
 

   (56)
                2 2    4                3    3
           ((- a b  + a )cos(y(x)) + a b  - a b)sin(y(x))
         + 
               +---------+                           +---------+
            2  |   2    2          2         2    3  |   2    2
           a b\|- b  + a  cos(y(x))  + (- a b  - a )\|- b  + a  cos(y(x))
         + 
               +---------+
            2  |   2    2
           a b\|- b  + a
      *
         cos
                log
                                            +---------+              +---------+
                       2    2               |   2    2               |   2    2
                   (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
                   -------------------------------------------------------------
                                          a cos(y(x)) - b
              + 
                  +---------+
                  |   2    2
                x\|- b  + a
           /
               +---------+
               |   2    2
              \|- b  + a
     + 
               +---------+
               |   2    2          2       2    2
           - a\|- b  + a  sin(y(x))  + (- b  + a )sin(y(x))
         + 
               +---------+               +---------+
               |   2    2          2     |   2    2
           - a\|- b  + a  cos(y(x))  + b\|- b  + a  cos(y(x))
      *
          ,
         y (x)

     + 
            3      2    3     3              4    3    2 2    2
       ((a b  + a b  - a b - a )cos(y(x)) - b  - b  + a b  + a b)sin(y(x))
     + 
                      +---------+
             2        |   2    2          2
       (- a b  - a b)\|- b  + a  cos(y(x))
     + 
                            +---------+                           +---------+
         3    2    2     2  |   2    2                   2        |   2    2
       (b  + b  + a b + a )\|- b  + a  cos(y(x)) + (- a b  - a b)\|- b  + a
  /
                                                        +---------+
            2    3              3    2                  |   2    2          2
       ((a b  - a )cos(y(x)) - b  + a b)sin(y(x)) - a b\|- b  + a  cos(y(x))
     + 
                 +---------+                +---------+
         2    2  |   2    2                 |   2    2
       (b  + a )\|- b  + a  cos(y(x)) - a b\|- b  + a
                                                     Type: Expression Integer
--R
--R   (56)
--R                2 2    4                3    3
--R           ((- a b  + a )cos(y(x)) + a b  - a b)sin(y(x))
--R         + 
--R               +---------+                           +---------+
--R            2  |   2    2          2         2    3  |   2    2
--R           a b\|- b  + a  cos(y(x))  + (- a b  - a )\|- b  + a  cos(y(x))
--R         + 
--R               +---------+
--R            2  |   2    2
--R           a b\|- b  + a
--R      *
--R         cos
--R                log
--R                                            +---------+              +---------+
--R                       2    2               |   2    2               |   2    2
--R                   (- b  + a )sin(y(x)) + b\|- b  + a  cos(y(x)) - a\|- b  + a
--R                   -------------------------------------------------------------
--R                                          a cos(y(x)) - b
--R              + 
--R                  +---------+
--R                  |   2    2
--R                x\|- b  + a
--R           /
--R               +---------+
--R               |   2    2
--R              \|- b  + a
--R     + 
--R               +---------+
--R               |   2    2          2       2    2
--R           - a\|- b  + a  sin(y(x))  + (- b  + a )sin(y(x))
--R         + 
--R               +---------+               +---------+
--R               |   2    2          2     |   2    2
--R           - a\|- b  + a  cos(y(x))  + b\|- b  + a  cos(y(x))
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R            3      2    3     3              4    3    2 2    2
--R       ((a b  + a b  - a b - a )cos(y(x)) - b  - b  + a b  + a b)sin(y(x))
--R     + 
--R                      +---------+
--R             2        |   2    2          2
--R       (- a b  - a b)\|- b  + a  cos(y(x))
--R     + 
--R                            +---------+                           +---------+
--R         3    2    2     2  |   2    2                   2        |   2    2
--R       (b  + b  + a b + a )\|- b  + a  cos(y(x)) + (- a b  - a b)\|- b  + a
--R  /
--R                                                        +---------+
--R            2    3              3    2                  |   2    2          2
--R       ((a b  - a )cos(y(x)) - b  + a b)sin(y(x)) - a b\|- b  + a  cos(y(x))
--R     + 
--R                 +---------+                +---------+
--R         2    2  |   2    2                 |   2    2
--R       (b  + a )\|- b  + a  cos(y(x)) - a b\|- b  + a
--R                                                     Type: Expression Integer
--E 59

--S 60 of 120
ode77 := D(y(x),x) - cos(a*y(x)+b*x)
 

          ,
   (57)  y (x) - cos(a y(x) + b x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (57)  y (x) - cos(a y(x) + b x)
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 120
ode77a:=solve(ode77,y,x)
 

   (58)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (58)  "failed"
--R                                                    Type: Union("failed",...)
--E 61

--S 62 of 120
ode78 := D(y(x),x) + a*sin(alpha*y(x)+beta*x) + b
 

          ,
   (59)  y (x) + a sin(alpha y(x) + beta x) + b

                                                     Type: Expression Integer
--R
--R          ,
--R   (59)  y (x) + a sin(alpha y(x) + beta x) + b
--R
--R                                                     Type: Expression Integer
--E 62

--S 63 of 120
ode78a:=solve(ode78,y,x)
 

   (60)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (60)  "failed"
--R                                                    Type: Union("failed",...)
--E 63

--S 64 of 120
ode79 := D(y(x),x) + f(x)*cos(a*y(x)) + g(x)*sin(a*y(x)) + h(x)
 

          ,
   (61)  y (x) + g(x)sin(a y(x)) + f(x)cos(a y(x)) + h(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (61)  y (x) + g(x)sin(a y(x)) + f(x)cos(a y(x)) + h(x)
--R
--R                                                     Type: Expression Integer
--E 64

--S 65 of 120
ode79a:=solve(ode79,y,x)
 

   (62)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (62)  "failed"
--R                                                    Type: Union("failed",...)
--E 65

--S 66 of 120
ode80 := D(y(x),x) + f(x)*sin(y(x)) + (1-D(f(x),x))*cos(y(x)) - D(f(x),x) - 1
 

          ,                        ,
   (63)  y (x) + (- cos(y(x)) - 1)f (x) + f(x)sin(y(x)) + cos(y(x)) - 1

                                                     Type: Expression Integer
--R
--R          ,                        ,
--R   (63)  y (x) + (- cos(y(x)) - 1)f (x) + f(x)sin(y(x)) + cos(y(x)) - 1
--R
--R                                                     Type: Expression Integer
--E 66

--S 67 of 120
ode80a:=solve(ode80,y,x)
 

   (64)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (64)  "failed"
--R                                                    Type: Union("failed",...)
--E 67

--S 68 of 120
ode81 := D(y(x),x) + 2*tan(y(x))*tan(x) - 1
 

          ,
   (65)  y (x) + 2tan(x)tan(y(x)) - 1

                                                     Type: Expression Integer
--R
--R          ,
--R   (65)  y (x) + 2tan(x)tan(y(x)) - 1
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 120
ode81a:=solve(ode81,y,x)
 

   (66)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (66)  "failed"
--R                                                    Type: Union("failed",...)
--E 69

--S 70 of 120
ode82 := D(y(x),x) - a*(1+tan(y(x))**2) + tan(y(x))*tan(x)
 

          ,                 2
   (67)  y (x) - a tan(y(x))  + tan(x)tan(y(x)) - a

                                                     Type: Expression Integer
--R
--R          ,                 2
--R   (67)  y (x) - a tan(y(x))  + tan(x)tan(y(x)) - a
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 120
ode82a:=solve(ode82,y,x)
 

   (68)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (68)  "failed"
--R                                                    Type: Union("failed",...)
--E 71

--S 72 of 120
ode83 := D(y(x),x) - tan(x*y(x))
 

          ,
   (69)  y (x) - tan(x y(x))

                                                     Type: Expression Integer
--R
--R          ,
--R   (69)  y (x) - tan(x y(x))
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 120
ode83a:=solve(ode83,y,x)
 

   (70)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (70)  "failed"
--R                                                    Type: Union("failed",...)
--E 73

--S 74 of 120
ode84 := D(y(x),x) - f(a*x + b*y(x))
 

          ,
   (71)  y (x) - f(b y(x) + a x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (71)  y (x) - f(b y(x) + a x)
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 120
ode84a:=solve(ode84,y,x)
 

   (72)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (72)  "failed"
--R                                                    Type: Union("failed",...)
--E 75

--S 76 of 120
ode85 := D(y(x),x) - x**(a-1)*y(x)**(1-b)*f(x**a/a + y(x)**b/b)
 

                                    b      a
            a - 1    - b + 1  a y(x)  + b x      ,
   (73)  - x     y(x)       f(--------------) + y (x)
                                    a b
                                                     Type: Expression Integer
--R
--R                                    b      a
--R            a - 1    - b + 1  a y(x)  + b x      ,
--R   (73)  - x     y(x)       f(--------------) + y (x)
--R                                    a b
--R                                                     Type: Expression Integer
--E 76

--S 77 of 120
ode85a:=solve(ode85,y,x)
 

   (74)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (74)  "failed"
--R                                                    Type: Union("failed",...)
--E 77

--S 78 of 120
ode86 := D(y(x),x) - (y(x)-x*f(x**2+a*y(x)**2))/(x+a*y(x)*f(x**2+a*y(x)**2))
 

                        2    2       ,                2    2
         (a y(x)f(a y(x)  + x ) + x)y (x) + x f(a y(x)  + x ) - y(x)

   (75)  -----------------------------------------------------------
                                        2    2
                          a y(x)f(a y(x)  + x ) + x
                                                     Type: Expression Integer
--R
--R                        2    2       ,                2    2
--R         (a y(x)f(a y(x)  + x ) + x)y (x) + x f(a y(x)  + x ) - y(x)
--R
--R   (75)  -----------------------------------------------------------
--R                                        2    2
--R                          a y(x)f(a y(x)  + x ) + x
--R                                                     Type: Expression Integer
--E 78

--S 79 of 120
ode86a:=solve(ode86,y,x)
 

   (76)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (76)  "failed"
--R                                                    Type: Union("failed",...)
--E 79

--S 80 of 120
ode87 := D(y(x),x) - (y(x)*a*f(x**c*y(x))+c*x**a*y(x)**b)/_
            (x*b*f(x**c*y(x))-x**a*y(x)**b)
 

           a    b              c   ,         a    b                c
         (x y(x)  - b x f(y(x)x ))y (x) + c x y(x)  + a y(x)f(y(x)x )

   (77)  ------------------------------------------------------------
                             a    b              c
                            x y(x)  - b x f(y(x)x )
                                                     Type: Expression Integer
--R
--R           a    b              c   ,         a    b                c
--R         (x y(x)  - b x f(y(x)x ))y (x) + c x y(x)  + a y(x)f(y(x)x )
--R
--R   (77)  ------------------------------------------------------------
--R                             a    b              c
--R                            x y(x)  - b x f(y(x)x )
--R                                                     Type: Expression Integer
--E 80

--S 81 of 120
ode87a:=solve(ode87,y,x)
 

   (78)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (78)  "failed"
--R                                                    Type: Union("failed",...)
--E 81

--S 82 of 120
ode88 := 2*D(y(x),x) - 3*y(x)**2 - 4*a*y(x) - b - c*exp(-2*a*x)
 

           ,          - 2a x        2
   (79)  2y (x) - c %e       - 3y(x)  - 4a y(x) - b

                                                     Type: Expression Integer
--R
--R           ,          - 2a x        2
--R   (79)  2y (x) - c %e       - 3y(x)  - 4a y(x) - b
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 120
ode88a:=solve(ode88,y,x)
 

   (80)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (80)  "failed"
--R                                                    Type: Union("failed",...)
--E 83

--S 84 of 120
ode89 := x*D(y(x),x) - sqrt(a**2 - x**2)
 

                   +---------+
           ,       |   2    2
   (81)  xy (x) - \|- x  + a

                                                     Type: Expression Integer
--R
--R                   +---------+
--R           ,       |   2    2
--R   (81)  xy (x) - \|- x  + a
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 120
ode89a:=solve(ode89,y,x)
 

   (82)
                                         +---------+
                   +---------+           |   2    2
                   |   2    2     2     \|- x  + a   - a     2
                (a\|- x  + a   - a )log(----------------) - x
                                                x
   [particular= ----------------------------------------------,basis= [1]]
                                +---------+
                                |   2    2
                               \|- x  + a   - a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (82)
--R                                         +---------+
--R                   +---------+           |   2    2
--R                   |   2    2     2     \|- x  + a   - a     2
--R                (a\|- x  + a   - a )log(----------------) - x
--R                                                x
--R   [particular= ----------------------------------------------,basis= [1]]
--R                                +---------+
--R                                |   2    2
--R                               \|- x  + a   - a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 85

--S 86 of 120
yx:=ode89a.particular
 

                                  +---------+
            +---------+           |   2    2
            |   2    2     2     \|- x  + a   - a     2
         (a\|- x  + a   - a )log(----------------) - x
                                         x
   (83)  ----------------------------------------------
                         +---------+
                         |   2    2
                        \|- x  + a   - a
                                                     Type: Expression Integer
--R
--R                                  +---------+
--R            +---------+           |   2    2
--R            |   2    2     2     \|- x  + a   - a     2
--R         (a\|- x  + a   - a )log(----------------) - x
--R                                         x
--R   (83)  ----------------------------------------------
--R                         +---------+
--R                         |   2    2
--R                        \|- x  + a   - a
--R                                                     Type: Expression Integer
--E 86

--S 87 of 120
ode89expr := x*D(yx,x) - sqrt(a**2 - x**2)
 

   (84)  0
                                                     Type: Expression Integer
--R
--R   (84)  0
--R                                                     Type: Expression Integer
--E 87

--S 88 of 120
ode90 := x*D(y(x),x) + y(x) - x*sin(x)
 

           ,
   (85)  xy (x) - x sin(x) + y(x)

                                                     Type: Expression Integer
--R
--R           ,
--R   (85)  xy (x) - x sin(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 88

--S 89 of 120
ode90a:=solve(ode90,y,x)
 

                      sin(x) - x cos(x)         1
   (86)  [particular= -----------------,basis= [-]]
                              x                 x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                      sin(x) - x cos(x)         1
--R   (86)  [particular= -----------------,basis= [-]]
--R                              x                 x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 89

--S 90 of 120
yx:=ode90a.particular
 

         sin(x) - x cos(x)
   (87)  -----------------
                 x
                                                     Type: Expression Integer
--R
--R         sin(x) - x cos(x)
--R   (87)  -----------------
--R                 x
--R                                                     Type: Expression Integer
--E 90

--S 91 of 120
ode90expr := x*D(yx,x) + yx - x*sin(x)
 

   (88)  0
                                                     Type: Expression Integer
--R
--R   (88)  0
--R                                                     Type: Expression Integer
--E 91

--S 92 of 120
ode91 := x*D(y(x),x) - y(x) - x/log(x)
 

                  ,
         x log(x)y (x) - y(x)log(x) - x

   (89)  ------------------------------
                     log(x)
                                                     Type: Expression Integer
--R
--R                  ,
--R         x log(x)y (x) - y(x)log(x) - x
--R
--R   (89)  ------------------------------
--R                     log(x)
--R                                                     Type: Expression Integer
--E 92

--S 93 of 120
ode91a:=solve(ode91,y,x)
 

   (90)  [particular= x log(log(x)),basis= [x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (90)  [particular= x log(log(x)),basis= [x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 93

--S 94 of 120
yx:=ode91a.particular
 

   (91)  x log(log(x))
                                                     Type: Expression Integer
--R
--R   (91)  x log(log(x))
--R                                                     Type: Expression Integer
--E 94

--S 95 of 120
ode91expr := x*D(yx,x) - yx - x/log(x)
 

   (92)  0
                                                     Type: Expression Integer
--R
--R   (92)  0
--R                                                     Type: Expression Integer
--E 95

--S 96 of 120
ode92 := x*D(y(x),x) - y(x) - x**2*sin(x)
 

           ,       2
   (93)  xy (x) - x sin(x) - y(x)

                                                     Type: Expression Integer
--R
--R           ,       2
--R   (93)  xy (x) - x sin(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 120
ode92a:=solve(ode92,y,x)
 

   (94)  [particular= - x cos(x),basis= [x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (94)  [particular= - x cos(x),basis= [x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 97

--S 98 of 120
yx:=ode92a.particular
 

   (95)  - x cos(x)
                                                     Type: Expression Integer
--R
--R   (95)  - x cos(x)
--R                                                     Type: Expression Integer
--E 98

--S 99 of 120
ode92expr := x*D(yx,x) - yx - x**2*sin(x)
 

   (96)  0
                                                     Type: Expression Integer
--R
--R   (96)  0
--R                                                     Type: Expression Integer
--E 99


--S 100 of 120
ode93 := x*D(y(x),x) - y(x) - x*cos(log(log(x)))/log(x)
 

                                         ,
         - x cos(log(log(x))) + x log(x)y (x) - y(x)log(x)

   (97)  -------------------------------------------------
                               log(x)
                                                     Type: Expression Integer
--R
--R                                         ,
--R         - x cos(log(log(x))) + x log(x)y (x) - y(x)log(x)
--R
--R   (97)  -------------------------------------------------
--R                               log(x)
--R                                                     Type: Expression Integer
--E 100

--S 101 of 120
ode93a:=solve(ode93,y,x)
 

   (98)  [particular= x sin(log(log(x))),basis= [x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (98)  [particular= x sin(log(log(x))),basis= [x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 101

--S 102 of 120
yx:=ode93a.particular
 

   (99)  x sin(log(log(x)))
                                                     Type: Expression Integer
--R
--R   (99)  x sin(log(log(x)))
--R                                                     Type: Expression Integer
--E 102

--S 103 of 120
ode93 := x*D(yx,x) - yx - x*cos(log(log(x)))/log(x)
 

   (100)  0
                                                     Type: Expression Integer
--R
--R   (100)  0
--R                                                     Type: Expression Integer
--E 103

--S 104 of 120
ode94 := x*D(y(x),x) +a*y(x) + b*x**n
 

            ,         n
   (101)  xy (x) + b x  + a y(x)

                                                     Type: Expression Integer
--R
--R            ,         n
--R   (101)  xy (x) + b x  + a y(x)
--R
--R                                                     Type: Expression Integer
--E 104

--S 105 of 120
ode94a:=solve(ode94,y,x)
 

                             n log(x)
                         b %e                   - a log(x)
   (102)  [particular= - ------------,basis= [%e          ]]
                             n + a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                             n log(x)
--R                         b %e                   - a log(x)
--R   (102)  [particular= - ------------,basis= [%e          ]]
--R                             n + a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 105

--S 106 of 120
yx:=ode94a.particular
 

                n log(x)
            b %e
   (103)  - ------------
                n + a
                                                     Type: Expression Integer
--R
--R                n log(x)
--R            b %e
--R   (103)  - ------------
--R                n + a
--R                                                     Type: Expression Integer
--E 106

--S 107 of 120
ode94expr := x*D(yx,x) +a*yx + b*x**n
 

                n log(x)      n
   (104)  - b %e         + b x
                                                     Type: Expression Integer
--R
--R                n log(x)      n
--R   (104)  - b %e         + b x
--R                                                     Type: Expression Integer
--E 107

--S 108 of 120
exprule := rule x^n == %e^(n*log(x))
 

           n      n log(x)
   (105)  x  == %e
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           n      n log(x)
--R   (105)  x  == %e
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 108

--S 109 of 120
exprule ode94expr
 

   (106)  0
                                                     Type: Expression Integer
--R
--R   (106)  0
--R                                                     Type: Expression Integer
--E 109

--S 110 of 120
ode95 := x*D(y(x),x) + y(x)**2 + x**2
 

            ,          2    2
   (107)  xy (x) + y(x)  + x

                                                     Type: Expression Integer
--R
--R            ,          2    2
--R   (107)  xy (x) + y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 110

--S 111 of 120
ode95a:=solve(ode95,y,x)
 

   (108)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (108)  "failed"
--R                                                    Type: Union("failed",...)
--E 111

--S 112 of 120
ode96 := x*D(y(x),x) - y(x)**2 + 1
 

            ,          2
   (109)  xy (x) - y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R            ,          2
--R   (109)  xy (x) - y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 112

--S 113 of 120
yx:=solve(ode96,y,x)
 

               - x y(x) - x
   (110)  ----------------------
           +--------+ +--------+
          \|y(x) - 1 \|y(x) + 1
                                          Type: Union(Expression Integer,...)
--R
--R               - x y(x) - x
--R   (110)  ----------------------
--R           +--------+ +--------+
--R          \|y(x) - 1 \|y(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 113

--S 114 of 120
ode96expr := x*D(yx,x) - yx**2 + 1
 

   (111)
    2 ,           2             2      +--------+ +--------+         2
   x y (x) + ((- x  + 1)y(x) - x  - 1)\|y(x) - 1 \|y(x) + 1  - x y(x)  + x

   -----------------------------------------------------------------------
                                  +--------+ +--------+
                       (y(x) - 1)\|y(x) - 1 \|y(x) + 1
                                                     Type: Expression Integer
--R
--R   (111)
--R    2 ,           2             2      +--------+ +--------+         2
--R   x y (x) + ((- x  + 1)y(x) - x  - 1)\|y(x) - 1 \|y(x) + 1  - x y(x)  + x
--R
--R   -----------------------------------------------------------------------
--R                                  +--------+ +--------+
--R                       (y(x) - 1)\|y(x) - 1 \|y(x) + 1
--R                                                     Type: Expression Integer
--E 114

--S 115 of 120
ode98 := x*D(y(x),x) + a*y(x)**2 - b*y(x) + c*x**(2*b)
 

            ,         2b         2
   (112)  xy (x) + c x   + a y(x)  - b y(x)

                                                     Type: Expression Integer
--R 
--R
--R            ,         2b         2
--R   (112)  xy (x) + c x   + a y(x)  - b y(x)
--R
--R                                                     Type: Expression Integer
--E 115

--S 116 of 120
ode98a:=solve(ode98,y,x)
 

   (113)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (113)  "failed"
--R                                                    Type: Union("failed",...)
--E 116

--S 117 of 120
ode99 := x*D(y(x),x) + a*y(x)**2 - b*y(x) - c*x**beta
 

            ,         beta         2
   (114)  xy (x) - c x     + a y(x)  - b y(x)

                                                     Type: Expression Integer
--R 
--R
--R            ,         beta         2
--R   (114)  xy (x) - c x     + a y(x)  - b y(x)
--R
--R                                                     Type: Expression Integer
--E 117

--S 118 of 120
ode99a:=solve(ode99,y,x)
 

   (115)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (115)  "failed"
--R                                                    Type: Union("failed",...)
--E 118

--S 119 of 120
ode100 := x*D(y(x),x) + x*y(x)**2 + a
 

            ,            2
   (116)  xy (x) + x y(x)  + a

                                                     Type: Expression Integer
--R 
--R
--R            ,            2
--R   (116)  xy (x) + x y(x)  + a
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 120
ode100a:=solve(ode100,y,x)
 

   (117)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (117)  "failed"
--R                                                    Type: Union("failed",...)
--E 120
)spool
 
Starts dribbling to HomogeneousDistributedMultivariatePolynomial.output (2010/3/27, 18:42:10).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
(d1,d2,d3) : DMP([z,y,x],FRAC INT) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 10
d1 := -4*z + 4*y**2*x + 16*x**2 + 1 
 

                 2       2
   (2)  - 4z + 4y x + 16x  + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R                 2       2
--R   (2)  - 4z + 4y x + 16x  + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 2

--S 3 of 10
d2 := 2*z*y**2 + 4*x + 1 
 

            2
   (3)  2z y  + 4x + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (3)  2z y  + 4x + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 3

--S 4 of 10
d3 := 2*z*x**2 - 2*y**2 - x 
 

            2     2
   (4)  2z x  - 2y  - x
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (4)  2z x  - 2y  - x
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 4

--S 5 of 10
groebner [d1,d2,d3]
 

   (5)
        1568  6   1264  5    6   4   182  3   2047  2    103      2857
   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
        2745       305      305      549       610      2745     10980
     2    112  6    84  5   1264  4    13  3    84  2   1772       2
    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
         2745      305       305      549      305      2745     2745
     7   29  6   17  4   11  3    1  2   15     1
    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
          4      16       8      32      16     4
       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (5)
--R        1568  6   1264  5    6   4   182  3   2047  2    103      2857
--R   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
--R        2745       305      305      549       610      2745     10980
--R     2    112  6    84  5   1264  4    13  3    84  2   1772       2
--R    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
--R         2745      305       305      549      305      2745     2745
--R     7   29  6   17  4   11  3    1  2   15     1
--R    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
--R          4      16       8      32      16     4
--R       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 5

--S 6 of 10
(n1,n2,n3) : HDMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
n1 := d1
 

          2       2
   (7)  4y x + 16x  - 4z + 1
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R          2       2
--R   (7)  4y x + 16x  - 4z + 1
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 7

--S 8 of 10
n2 := d2
 

            2
   (8)  2z y  + 4x + 1
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (8)  2z y  + 4x + 1
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 8

--S 9 of 10
n3 := d3
 

            2     2
   (9)  2z x  - 2y  - x
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (9)  2z x  - 2y  - x
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 9

--S 10 of 10
groebner [n1,n2,n3]
 

   (10)
     4     3   3  2   1     1   4   29  3   1  2   7        9     1
   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
               2      2     8        4      8      4       16     4
       2        1   2      2       1     2    2   1
    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
                2                  4              2
     2     2     2   1     3
    z  - 4y  + 2x  - - z - - x]
                     4     2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (10)
--R     4     3   3  2   1     1   4   29  3   1  2   7        9     1
--R   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
--R               2      2     8        4      8      4       16     4
--R       2        1   2      2       1     2    2   1
--R    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
--R                2                  4              2
--R     2     2     2   1     3
--R    z  - 4y  + 2x  - - z - - x]
--R                     4     2
--RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 10
)spool
 
Starts dribbling to BinaryExpansion.output (2010/3/27, 18:41:45).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
r := binary(22/7)
 

           ___
   (1)  11.001
                                                        Type: BinaryExpansion
--R 
--R
--R           ___
--R   (1)  11.001
--R                                                        Type: BinaryExpansion
--E 1

--S 2 of 7
r + binary(6/7)
 

   (2)  100
                                                        Type: BinaryExpansion
--R 
--R
--R   (2)  100
--R                                                        Type: BinaryExpansion
--E 2

--S 3 of 7
[binary(1/i) for i in 102..106]
 

   (3)
       ________    ___________________________________________________
   [0.000000101, 0.000000100111110001000101100101111001110010010101001,
         ____________    ____________
    0.000000100111011, 0.000000100111,
       ____________________________________________________
    0.00000010011010100100001110011111011001010110111100011]
                                                   Type: List BinaryExpansion
--R 
--R
--R   (3)
--R       ________    ___________________________________________________
--R   [0.000000101, 0.000000100111110001000101100101111001110010010101001,
--R         ____________    ____________
--R    0.000000100111011, 0.000000100111,
--R       ____________________________________________________
--R    0.00000010011010100100001110011111011001010110111100011]
--R                                                   Type: List BinaryExpansion
--E 3

--S 4 of 7
binary(1/1007)
 

   (4)
   0.
     OVERBAR
        00000000010000010001010010010111100000111111000010111111001011000111110
          100010011100100110011000110010010101011110110100110000000011000011001
          111011100011010001011110100100011110110000101011101110011101010111001
          100101001011100000001110001111001000000100100100110111001010100111010
          001101110110101110001001000001100101101100000010110010111110001010000
          010101010110101100000110110111010010101111111010111010100110010000101
          0011011000100110001000100001000011000111010011110001
                                                        Type: BinaryExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        00000000010000010001010010010111100000111111000010111111001011000111110
--R          100010011100100110011000110010010101011110110100110000000011000011001
--R          111011100011010001011110100100011110110000101011101110011101010111001
--R          100101001011100000001110001111001000000100100100110111001010100111010
--R          001101110110101110001001000001100101101100000010110010111110001010000
--R          010101010110101100000110110111010010101111111010111010100110010000101
--R          0011011000100110001000100001000011000111010011110001
--R                                                        Type: BinaryExpansion
--E 4

--S 5 of 7
p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9)
 

             2     __      ______
   (5)  0.01x  + 0.10x + 0.011100
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R             2     __      ______
--R   (5)  0.01x  + 0.10x + 0.011100
--R                                             Type: Polynomial BinaryExpansion
--E 5

--S 6 of 7
q := D(p, x)
 

                 __
   (6)  0.1x + 0.10
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R                 __
--R   (6)  0.1x + 0.10
--R                                             Type: Polynomial BinaryExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              __
   (7)  x + 1.01
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R              __
--R   (7)  x + 1.01
--R                                             Type: Polynomial BinaryExpansion
--E 7
)spool
 
Starts dribbling to exsum.output (2010/3/27, 18:25:47).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 13
sum(k * x**k,k = 1..n)
 

            2               n
        (n x  + (- n - 1)x)x  + x
   (1)  -------------------------
                2
               x  - 2x + 1
                                                     Type: Expression Integer
--R 
--R
--R            2               n
--R        (n x  + (- n - 1)x)x  + x
--R   (1)  -------------------------
--R                2
--R               x  - 2x + 1
--R                                                     Type: Expression Integer
--E 1

)clear all
 

--S 2 of 13
limit( sum(1/(k * (k + 2)),k = 1..n) ,n = %plusInfinity)
 

        3
   (1)  -
        4
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R        3
--R   (1)  -
--R        4
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 2

)clear all
 

--S 3 of 13
s := sum(k**2,k = a..b)
 

          3     2         3     2
        2b  + 3b  + b - 2a  + 3a  - a
   (1)  -----------------------------
                      6
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          3     2         3     2
--R        2b  + 3b  + b - 2a  + 3a  - a
--R   (1)  -----------------------------
--R                      6
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 13
eval(s,[a,b],[1,25])
 

   (2)  5525
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (2)  5525
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 13
reduce(+,[i**2 for i in 1..25])
 

   (3)  5525
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  5525
--R                                                        Type: PositiveInteger
--E 5

)clear all
 

--S 6 of 13
sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))
 

   (1)
            3      2           3      2               2             2        2
       (128b  + 48b  + 4b - 54a  + 27a  - 3a)d + (192b  + 48b - 108a  + 36a)c
     + 
           2             2
       192b  + 48b - 108a  + 36a
  /
        2
     (2c  + 2)d
                                 Type: Union(Fraction Polynomial Integer,...)
--R 
--R
--R   (1)
--R            3      2           3      2               2             2        2
--R       (128b  + 48b  + 4b - 54a  + 27a  - 3a)d + (192b  + 48b - 108a  + 36a)c
--R     + 
--R           2             2
--R       192b  + 48b - 108a  + 36a
--R  /
--R        2
--R     (2c  + 2)d
--R                                 Type: Union(Fraction Polynomial Integer,...)
--E 6

)clear all
 

--S 7 of 13
[i for i in 1..15]
 

   (1)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
--R                                                   Type: List PositiveInteger
--E 7

--S 8 of 13
reduce(+,[i for i in 1..15])
 

   (2)  120
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  120
--R                                                        Type: PositiveInteger
--E 8

)clear all
 

--S 9 of 13
reduce(+,[1.0/factorial(n) for n in 0..20])
 

   (1)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (1)  2.7182818284 590452354
--R                                                                  Type: Float
--E 9

)clear all
 

--S 10 of 13
[n**2 for n in 5..20]
 

   (1)  [25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400]
--R                                                   Type: List PositiveInteger
--E 10

--S 11 of 13
reduce(+,[n**2 for n in 5..20])
 

   (2)  2840
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  2840
--R                                                        Type: PositiveInteger
--E 11

)clear all
 

--S 12 of 13
sum(k**3,k = 1..n)
 

         4     3    2
        n  + 2n  + n
   (1)  -------------
              4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         4     3    2
--R        n  + 2n  + n
--R   (1)  -------------
--R              4
--R                                            Type: Fraction Polynomial Integer
--E 12

--S 13 of 13
sum(k,k = 1..n) ** 2
 

         4     3    2
        n  + 2n  + n
   (2)  -------------
              4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         4     3    2
--R        n  + 2n  + n
--R   (2)  -------------
--R              4
--R                                            Type: Fraction Polynomial Integer
--E 13
)spool 
 
Starts dribbling to IntegerNumberTheoryFunctions.output (2010/3/27, 18:42:13).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 30
div144 := divisors(144)
 

   (1)  [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144]
--R                                                           Type: List Integer
--E 1

--S 2 of 30
#(div144)
 

   (2)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  15
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 30
reduce(+,div144)
 

   (3)  403
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  403
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 30
numberOfDivisors(144)
 

   (4)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  15
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 30
sumOfDivisors(144)
 

   (5)  403
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  403
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 30
f1(n)==reduce(+,[moebiusMu(d)*numberOfDivisors(quo(n,d))_
     for d in divisors(n)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 30
f1(200)
 
   Compiling function f1 with type PositiveInteger -> Integer 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling function f1 with type PositiveInteger -> Integer 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 30
f1(846)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 30
f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d))_
     for d in divisors(n)]) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 30
f2(200)
 
   Compiling function f2 with type PositiveInteger -> Integer 

   (10)  200
                                                        Type: PositiveInteger
--R 
--R   Compiling function f2 with type PositiveInteger -> Integer 
--R
--R   (10)  200
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 30
f2(846)
 

   (11)  846
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  846
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 30
fibonacci(25)
 

   (12)  75025
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  75025
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 30
[fibonacci(n) for n in 1..15]
 

   (13)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
                                                           Type: List Integer
--R 
--R
--R   (13)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
--R                                                           Type: List Integer
--E 13

--S 14 of 30
fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 30
fib(25)
 
   Compiling function fib with type PositiveInteger -> Integer 

   (15)  75025
                                                        Type: PositiveInteger
--R 
--R   Compiling function fib with type PositiveInteger -> Integer 
--R
--R   (15)  75025
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 30
[fib(n) for n in 1..15]
 

   (16)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
                                                           Type: List Integer
--R 
--R
--R   (16)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
--R                                                           Type: List Integer
--E 16

--S 17 of 30
legendre(3,5)
 

   (17)  - 1
                                                                Type: Integer
--R 
--R
--R   (17)  - 1
--R                                                                Type: Integer
--E 17

--S 18 of 30
legendre(23,691)
 

   (18)  - 1
                                                                Type: Integer
--R 
--R
--R   (18)  - 1
--R                                                                Type: Integer
--E 18

--S 19 of 30
h(d) == quo(reduce(+,[jacobi(d,k) for k in 1..quo(-d, 2)]),2-jacobi(d,2))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 30
h(-163)
 
   Compiling function h with type Integer -> Integer 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling function h with type Integer -> Integer 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 30
h(-499)
 

   (21)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  3
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 30
h(-1832)
 

   (22)  26
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  26
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 30
inverse:(INT,INT)->INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 30
inverse(a,b) ==
  borg:INT:=b
  c1:INT := 1
  d1:INT := 0
  while b ~= 0 repeat
    q := a quo b
    r := a-q*b
    print [a, "=", q, "*(", b, ")+", r]
    (a,b):=(b,r)
    (c1,d1):=(d1,c1-q*d1)
  a ~= 1 => error("moduli are not relatively prime")
  positiveRemainder(c1,borg)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 30
inverse(15,26)
 
   Compiling function inverse with type (Integer,Integer) -> Integer 
   [15,"=",0,"*(",26,")+",15]
   [26,"=",1,"*(",15,")+",11]
   [15,"=",1,"*(",11,")+",4]
   [11,"=",2,"*(",4,")+",3]
   [4,"=",1,"*(",3,")+",1]
   [3,"=",3,"*(",1,")+",0]

   (25)  7
                                                        Type: PositiveInteger
--R 
--R   Compiling function inverse with type (Integer,Integer) -> Integer 
--R   [15,"=",0,"*(",26,")+",15]
--R   [26,"=",1,"*(",15,")+",11]
--R   [15,"=",1,"*(",11,")+",4]
--R   [11,"=",2,"*(",4,")+",3]
--R   [4,"=",1,"*(",3,")+",1]
--R   [3,"=",3,"*(",1,")+",0]
--R
--R   (25)  7
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 30
x1:=4
 

   (26)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  4
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 30
m1:=5
 

   (27)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  5
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 30
x2:=2
 

   (28)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  2
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 30
m2:=3
 

   (29)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (29)  3
--R                                                        Type: PositiveInteger
--E 29

--S 30 of 30
result:=chineseRemainder(x1,m1,x2,m2)
 

   (30)  14
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  14
--R                                                        Type: PositiveInteger
--E 30

)spool
 
Starts dribbling to farray.output (2010/3/27, 18:25:49).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 16
flexibleArray [i for i in 1..6]
 

   (1)  [1,2,3,4,5,6]
                                          Type: FlexibleArray PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6]
--R                                          Type: FlexibleArray PositiveInteger
--E 1

--S 2 of 16
f : FARRAY INT := new(6,0)
 

   (2)  [0,0,0,0,0,0]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0]
--R                                                  Type: FlexibleArray Integer
--E 2

--S 3 of 16
for i in 1..6 repeat f.i := i; f
 

   (3)  [1,2,3,4,5,6]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6]
--R                                                  Type: FlexibleArray Integer
--E 3

--S 4 of 16
physicalLength f
 

   (4)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  6
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 16
concat!(f,11)
 

   (5)  [1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (5)  [1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 5

--S 6 of 16
physicalLength f
 

   (6)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  10
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 16
physicalLength!(f,15)
 

   (7)  [1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (7)  [1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 7

--S 8 of 16
concat!(f,f)
 

   (8)  [1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (8)  [1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 8

--S 9 of 16
insert!(22,f,1)
 

   (9)  [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (9)  [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 9

--S 10 of 16
g := f(10..)
 

   (10)  [2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (10)  [2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 10

--S 11 of 16
insert!(g,f,1)
 

   (11)  [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (11)  [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 11

--S 12 of 16
merge!(sort! f, sort! g)
 

   (12)  [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (12)  [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22]
--R                                                  Type: FlexibleArray Integer
--E 12

--S 13 of 16
removeDuplicates! f
 

   (13)  [1,2,3,4,5,6,11,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (13)  [1,2,3,4,5,6,11,22]
--R                                                  Type: FlexibleArray Integer
--E 13

--S 14 of 16
select!(i +-> even? i,f)
 

   (14)  [2,4,6,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (14)  [2,4,6,22]
--R                                                  Type: FlexibleArray Integer
--E 14

--S 15 of 16
physicalLength f
 

   (15)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  8
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 16
shrinkable(false)$FlexibleArray(Integer)
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16
)spool 
 
Starts dribbling to fixed.output (2010/3/27, 18:25:58).
)set message test on
 
)set message auto off
 
)set break resume
 
)set expose add constructor SquareMatrix
 
   SquareMatrix is now explicitly exposed in frame initial 

)clear all
 

--S 1 of 267
t1:=series(x/(x+log(x)))
 

   (1)
        1          1     2      1     3      1     4      1     5      1     6
     ------ x - ------- x  + ------- x  - ------- x  + ------- x  - ------- x
     log(x)           2            3            4            5            6
                log(x)       log(x)       log(x)       log(x)       log(x)
   + 
      1     7      1     8      1     9       1     10       1     11      12
   ------- x  - ------- x  + ------- x  - -------- x   + -------- x   + O(x  )
         7            8            9            10             11
   log(x)       log(x)       log(x)       log(x)         log(x)
                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--R
--R   (1)
--R        1          1     2      1     3      1     4      1     5      1     6
--R     ------ x - ------- x  + ------- x  - ------- x  + ------- x  - ------- x
--R     log(x)           2            3            4            5            6
--R                log(x)       log(x)       log(x)       log(x)       log(x)
--R   + 
--R      1     7      1     8      1     9       1     10       1     11      12
--R   ------- x  - ------- x  + ------- x  - -------- x   + -------- x   + O(x  )
--R         7            8            9            10             11
--R   log(x)       log(x)       log(x)       log(x)         log(x)
--R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--E


--S 2 of 267
integrate(t1)
 
 
Daly Bug
   >> Error detected within library code:
   "'integrate' unavailable on this domain;  use 'approximate' first"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   "'integrate' unavailable on this domain;  use 'approximate' first"
--R
--R   Continuing to read the file...
--R
--E

)clear all
 

--S 3 of 267
t1:=2*sin(t)*sqrt(1+cos(t))
 

                +----------+
   (1)  2sin(t)\|cos(t) + 1
                                                     Type: Expression Integer
--R
--R                +----------+
--R   (1)  2sin(t)\|cos(t) + 1
--R                                                     Type: Expression Integer
--E


--S 4 of 267
integrate(t1,t)
 

                        +----------+
        (- 4cos(t) - 4)\|cos(t) + 1
   (2)  ----------------------------
                      3
                                          Type: Union(Expression Integer,...)
--R
--R                        +----------+
--R        (- 4cos(t) - 4)\|cos(t) + 1
--R   (2)  ----------------------------
--R                      3
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 5 of 267
n:Complex ?
 
                                                                   Type: Void
--R                                                                   Type: Void
--E


--S 6 of 267
n:=x/y+%i
 

        x
   (2)  - + %i
        y
                                    Type: Complex Fraction Polynomial Integer
--R
--R        x
--R   (2)  - + %i
--R        y
--R                                    Type: Complex Fraction Polynomial Integer
--E

)clear all
 

--S 7 of 267
f:=(a-b-c-d)**2::EXPR INT
 

         2                      2                 2           2
   (1)  d  + (2c + 2b - 2a)d + c  + (2b - 2a)c + b  - 2a b + a
                                                     Type: Expression Integer
--R
--R         2                      2                 2           2
--R   (1)  d  + (2c + 2b - 2a)d + c  + (2b - 2a)c + b  - 2a b + a
--R                                                     Type: Expression Integer
--E

--S 8 of 267
t1:=f::DMP(['a,'b],EXPR INT)
 

         2                          2                 2           2
   (2)  a  - 2a b + (- 2d - 2c)a + b  + (2d + 2c)b + d  + 2c d + c
            Type: DistributedMultivariatePolynomial([a,b],Expression Integer)
--R
--R         2                          2                 2           2
--R   (2)  a  - 2a b + (- 2d - 2c)a + b  + (2d + 2c)b + d  + 2c d + c
--R            Type: DistributedMultivariatePolynomial([a,b],Expression Integer)
--E

--S 9 of 267
degree t1
 

   (3)  [2,0]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R
--R   (3)  [2,0]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E

)clear all
 

--S 10 of 267
integrate(sqrt(1+cos(x)),x)
 

                +----------+
        2sin(x)\|cos(x) + 1
   (1)  --------------------
             cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R
--R                +----------+
--R        2sin(x)\|cos(x) + 1
--R   (1)  --------------------
--R             cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 11 of 267
integrate(exp(x**2),x)
 

           x     2
         ++    %K
   (1)   |   %e   d%K
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x     2
--I         ++    %K
--I   (1)   |   %e   d%K
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 12 of 267
f:=log(1-(b*x/(a+c*x**2)))/x
 

               2
            c x  - b x + a
        log(--------------)
                  2
               c x  + a
   (1)  -------------------
                 x
                                                     Type: Expression Integer
--R
--R               2
--R            c x  - b x + a
--R        log(--------------)
--R                  2
--R               c x  + a
--R   (1)  -------------------
--R                 x
--R                                                     Type: Expression Integer
--E

--S 13 of 267
integrate(f,x)
 

                   2
                 %K c - %K b + a
             log(---------------)
           x           2
         ++          %K c + a
   (2)   |   -------------------- d%K
        ++            %K
                                          Type: Union(Expression Integer,...)
--R
--R                   2
--I                 %K c - %K b + a
--R             log(---------------)
--R           x           2
--I         ++          %K c + a
--I   (2)   |   -------------------- d%K
--I        ++            %K
--R                                          Type: Union(Expression Integer,...)
--E

--S 14 of 267
g:=expand f
 

                 2               2
        - log(c x  + a) + log(c x  - b x + a)
   (3)  -------------------------------------
                          x
                                                     Type: Expression Integer
--R
--R                 2               2
--R        - log(c x  + a) + log(c x  - b x + a)
--R   (3)  -------------------------------------
--R                          x
--R                                                     Type: Expression Integer
--E

--S 15 of 267
integrate(g,x)
 

           x         2               2
         ++  - log(%K c + a) + log(%K c - %K b + a)
   (4)   |   -------------------------------------- d%K
        ++                     %K
                                          Type: Union(Expression Integer,...)
--R
--R           x         2               2
--I         ++  - log(%K c + a) + log(%K c - %K b + a)
--I   (4)   |   -------------------------------------- d%K
--I        ++                     %K
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 16 of 267
%i/m*sqrt(m) 
 

           +-+
        %i\|m
   (1)  ------
           m
                                             Type: Expression Complex Integer
--R
--R           +-+
--R        %i\|m
--R   (1)  ------
--R           m
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 17 of 267
foo n == matrix[[i for i in 1..n] for j in 1..n]
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 18 of 267
foo
 

   (2)  foo n == [[i for i in 1..n] for j in 1..n]
                                                     Type: FunctionCalled foo
--R
--R   (2)  foo n == [[i for i in 1..n] for j in 1..n]
--R                                                     Type: FunctionCalled foo
--E

)clear all
 

msq := Matrix SquareMatrix(2,POLY INT)
 

   (1)  Matrix SquareMatrix(2,Polynomial Integer)
                                                                 Type: Domain

)clear all
 

--S 19 of 267
msq := Matrix SquareMatrix(2,POLY INT)
 

   (1)  Matrix SquareMatrix(2,Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Matrix SquareMatrix(2,Polynomial Integer)
--R                                                                 Type: Domain
--E

--S 20 of 267
m : msq := zero(2,2)
 

        ++0  0+  +0  0++
        ||    |  |    ||
        |+0  0+  +0  0+|
   (2)  |              |
        |+0  0+  +0  0+|
        ||    |  |    ||
        ++0  0+  +0  0++
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R        ++0  0+  +0  0++
--R        ||    |  |    ||
--R        |+0  0+  +0  0+|
--R   (2)  |              |
--R        |+0  0+  +0  0+|
--R        ||    |  |    ||
--R        ++0  0+  +0  0++
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 21 of 267
m(1,1) := matrix([[1,2],[a,b]])
 

        +1  2+
   (3)  |    |
        +a  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R
--R        +1  2+
--R   (3)  |    |
--R        +a  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E

--S 22 of 267
m(1,2) := matrix([[a,b],[2,b]])
 

        +a  b+
   (4)  |    |
        +2  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R
--R        +a  b+
--R   (4)  |    |
--R        +2  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E

--S 23 of 267
m(2,2) := matrix([[1,2],[2,b]])
 

        +1  2+
   (5)  |    |
        +2  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R
--R        +1  2+
--R   (5)  |    |
--R        +2  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E

--S 24 of 267
m
 

        ++1  2+  +a  b++
        ||    |  |    ||
        |+a  b+  +2  b+|
   (6)  |              |
        |+0  0+  +1  2+|
        ||    |  |    ||
        ++0  0+  +2  b++
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R        ++1  2+  +a  b++
--R        ||    |  |    ||
--R        |+a  b+  +2  b+|
--R   (6)  |              |
--R        |+0  0+  +1  2+|
--R        ||    |  |    ||
--R        ++0  0+  +2  b++
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 25 of 267
m*m
 

        +                    +              2           ++
        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
        ||                |  |                          ||
        ||          2     |  |      2        2          ||
   (7)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
        |                                                |
        |      +0  0+              +  5     2b + 2+      |
        |      |    |              |              |      |
        |      +0  0+              |         2    |      |
        +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R        +                    +              2           ++
--R        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R        ||                |  |                          ||
--R        ||          2     |  |      2        2          ||
--R   (7)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R        |                                                |
--R        |      +0  0+              +  5     2b + 2+      |
--R        |      |    |              |              |      |
--R        |      +0  0+              |         2    |      |
--R        +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 26 of 267
m**2
 

        +                    +              2           ++
        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
        ||                |  |                          ||
        ||          2     |  |      2        2          ||
   (8)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
        |                                                |
        |      +0  0+              +  5     2b + 2+      |
        |      |    |              |              |      |
        |      +0  0+              |         2    |      |
        +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R        +                    +              2           ++
--R        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R        ||                |  |                          ||
--R        ||          2     |  |      2        2          ||
--R   (8)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R        |                                                |
--R        |      +0  0+              +  5     2b + 2+      |
--R        |      |    |              |              |      |
--R        |      +0  0+              |         2    |      |
--R        +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 27 of 267
m**3
 

        +matrix1  matrix2+
   (9)  |                |
        +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R        +matrix1  matrix2+
--R   (9)  |                |
--R        +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 28 of 267
(m*m)*m
 

         +matrix1  matrix2+
   (10)  |                |
         +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R         +matrix1  matrix2+
--R   (10)  |                |
--R         +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 29 of 267
mm:=m*m
 

         +                    +              2           ++
         |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
         ||                |  |                          ||
         ||          2     |  |      2        2          ||
   (11)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
         |                                                |
         |      +0  0+              +  5     2b + 2+      |
         |      |    |              |              |      |
         |      +0  0+              |         2    |      |
         +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R         +                    +              2           ++
--R         |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R         ||                |  |                          ||
--R         ||          2     |  |      2        2          ||
--R   (11)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R         |                                                |
--R         |      +0  0+              +  5     2b + 2+      |
--R         |      |    |              |              |      |
--R         |      +0  0+              |         2    |      |
--R         +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

--S 30 of 267
mm*m
 

         +matrix1  matrix2+
   (12)  |                |
         +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R
--R         +matrix1  matrix2+
--R   (12)  |                |
--R         +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E

)clear all
 
--S 31 of 267
eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x)
 

            3      2         4
   (1)  - 6x  + 13x  + 4= - x  + 12x
                                            Type: Equation Polynomial Integer
--R
--R            3      2         4
--R   (1)  - 6x  + 13x  + 4= - x  + 12x
--R                                            Type: Equation Polynomial Integer
--E

--S 32 of 267
eq2 := x**4+13*x**2-12*x = 6*x**3-4
 

         4      2          3
   (2)  x  + 13x  - 12x= 6x  - 4
                                            Type: Equation Polynomial Integer
--R
--R         4      2          3
--R   (2)  x  + 13x  - 12x= 6x  - 4
--R                                            Type: Equation Polynomial Integer
--E

--S 33 of 267
eq := eq1*y**2+eq2
 

             3      2      2    4      2            4        2     3
   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
                                            Type: Equation Polynomial Integer
--R
--R             3      2      2    4      2            4        2     3
--R   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
--R                                            Type: Equation Polynomial Integer
--E

--S 34 of 267
t1:=swap eq
 

            4        2     3           3      2      2    4      2
   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
                                            Type: Equation Polynomial Integer
--R
--R            4        2     3           3      2      2    4      2
--R   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
--R                                            Type: Equation Polynomial Integer
--E

--S 35 of 267
t2:=t1 + 4
 

            4        2     3       3      2      2    4      2
   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R
--R            4        2     3       3      2      2    4      2
--R   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E

--S 36 of 267
t3:=t2-6*x**3
 

            4        2       3      2      2    4     3      2
   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R
--R            4        2       3      2      2    4     3      2
--R   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E

--S 37 of 267
t4:=leftZero t3
 

             4     3      2            2    4     3      2
   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R
--R             4     3      2            2    4     3      2
--R   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E

--S 38 of 267
t5:=swap t4
 

          4     3      2            2    4     3      2
   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
                                            Type: Equation Polynomial Integer
--R
--R          4     3      2            2    4     3      2
--R   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
--R                                            Type: Equation Polynomial Integer
--E

--S 39 of 267
t6:=factor lhs t5
 

               2       2  2
   (9)  (x - 2) (x - 1) (y  + 1)
                                            Type: Factored Polynomial Integer
--R
--R               2       2  2
--R   (9)  (x - 2) (x - 1) (y  + 1)
--R                                            Type: Factored Polynomial Integer
--E

--S 40 of 267
t7:=factorAndSplit eq
 

                             2
   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
                                       Type: List Equation Polynomial Integer
--R
--R                             2
--R   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
--R                                       Type: List Equation Polynomial Integer
--E

--S 41 of 267
t8:=inv (eq :: EQ FRAC POLY INT)
 

                             1                                1
   (11)  - ------------------------------------= - ----------------------
              3      2      2    4      2            4        2     3
           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
                                   Type: Equation Fraction Polynomial Integer
--R
--R                             1                                1
--R   (11)  - ------------------------------------= - ----------------------
--R              3      2      2    4      2            4        2     3
--R           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
--R                                   Type: Equation Fraction Polynomial Integer
--E

--S 42 of 267
- t8
 

                           1                              1
   (12)  ------------------------------------= ----------------------
            3      2      2    4      2          4        2     3
         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
                                   Type: Equation Fraction Polynomial Integer
--R
--R                           1                              1
--R   (12)  ------------------------------------= ----------------------
--R            3      2      2    4      2          4        2     3
--R         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
--R                                   Type: Equation Fraction Polynomial Integer
--E

)clear all
 

--S 43 of 267
(p1,p2):UP(x,INT)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 44 of 267
p1:=3*x**4+11*x**2-4
 

          4      2
   (2)  3x  + 11x  - 4
                                        Type: UnivariatePolynomial(x,Integer)
--R
--R          4      2
--R   (2)  3x  + 11x  - 4
--R                                        Type: UnivariatePolynomial(x,Integer)
--E

--S 45 of 267
p2:=9*x**4+9*x**2-4
 

          4     2
   (3)  9x  + 9x  - 4
                                        Type: UnivariatePolynomial(x,Integer)
--R
--R          4     2
--R   (3)  9x  + 9x  - 4
--R                                        Type: UnivariatePolynomial(x,Integer)
--E

--S 46 of 267
myNextPrime: (INT,NNI) -> INT
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 47 of 267
myNextPrime(x,n)==nextPrime(x)$PRIMES(INT)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 48 of 267
modularGcd([p1,p2])$InnerModularGcd(INT,UP(x,INT),67108859,myNextPrime)
 
   Compiling function myNextPrime with type (Integer,NonNegativeInteger
      ) -> Integer 

          2
   (6)  3x  - 1
                                        Type: UnivariatePolynomial(x,Integer)
--R   Compiling function myNextPrime with type (Integer,NonNegativeInteger
--R      ) -> Integer 
--R
--R          2
--R   (6)  3x  - 1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E

)clear all
 

--S 49 of 267
numeric(%e ** %pi)
 

   (1)  23.1406926327 79269006
                                                                  Type: Float
--R
--R   (1)  23.1406926327 79269006
--R                                                                  Type: Float
--E

)clear all
 

--S 50 of 267
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E

--S 51 of 267
deqx:=differentiate(y(x),x,2)+differentiate(y(x),x)+y(x)
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E

--S 52 of 267
solve(deqx,y,x)
 

                                             x     x
                                     +-+   - -   - -      +-+
                                   x\|3      2     2    x\|3
   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                             x     x
--R                                     +-+   - -   - -      +-+
--R                                   x\|3      2     2    x\|3
--R   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E

--S 53 of 267
solve(deqx,y,x=0,[1])
 

                      x
              +-+   - -
            x\|3      2
   (4)  cos(-----)%e
              2
                                          Type: Union(Expression Integer,...)
--R
--R                      x
--R              +-+   - -
--R            x\|3      2
--R   (4)  cos(-----)%e
--R              2
--R                                          Type: Union(Expression Integer,...)
--E

--S 54 of 267
deqt:=differentiate(y(t),t,2)+differentiate(y(t),t)+y(t)
 

         ,,       ,
   (5)  y  (t) + y (t) + y(t)

                                                     Type: Expression Integer
--R
--R         ,,       ,
--R   (5)  y  (t) + y (t) + y(t)
--R
--R                                                     Type: Expression Integer
--E

--S 55 of 267
solve(deqt,y,t)
 

                                             t     t
                                     +-+   - -   - -      +-+
                                   t\|3      2     2    t\|3
   (6)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                             t     t
--R                                     +-+   - -   - -      +-+
--R                                   t\|3      2     2    t\|3
--R   (6)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E

--S 56 of 267
solve(deqt,y,t=0,[1]) -- bug
 

                      t
              +-+   - -
            t\|3      2
   (7)  cos(-----)%e
              2
                                          Type: Union(Expression Integer,...)
--R
--R                      t
--R              +-+   - -
--R            t\|3      2
--R   (7)  cos(-----)%e
--R              2
--R                                          Type: Union(Expression Integer,...)
--E

--S 57 of 267
deqz:=differentiate(y(z),z,2)+differentiate(y(z),z)+y(z)
 

         ,,       ,
   (8)  y  (z) + y (z) + y(z)

                                                     Type: Expression Integer
--R
--R         ,,       ,
--R   (8)  y  (z) + y (z) + y(z)
--R
--R                                                     Type: Expression Integer
--E

--S 58 of 267
solve(deqz,y,z)
 

                                             z     z
                                     +-+   - -   - -      +-+
                                   z\|3      2     2    z\|3
   (9)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                             z     z
--R                                     +-+   - -   - -      +-+
--R                                   z\|3      2     2    z\|3
--R   (9)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E

--S 59 of 267
solve(deqz,y,z=0,[1]) --bug
 

                       z
               +-+   - -
             z\|3      2
   (10)  cos(-----)%e
               2
                                          Type: Union(Expression Integer,...)
--R
--R                       z
--R               +-+   - -
--R             z\|3      2
--R   (10)  cos(-----)%e
--R               2
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 60 of 267
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E

--S 61 of 267
deq:=D(y(x),x)+x**2=(y x)/x-(y x)**2
 

                            2
         ,       2  - x y(x)  + y(x)
   (2)  y (x) + x = ----------------
                            x
                                            Type: Equation Expression Integer
--R
--R                            2
--R         ,       2  - x y(x)  + y(x)
--R   (2)  y (x) + x = ----------------
--R                            x
--R                                            Type: Equation Expression Integer
--E

)clear all
 

--S 62 of 267
laplace(exp(-x**3)*x**7,x,s) 
 

                       3
                 7  - x
   (1)  laplace(x %e    ,x,s)
                                                     Type: Expression Integer
--R
--R                       3
--R                 7  - x
--R   (1)  laplace(x %e    ,x,s)
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 63 of 267
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E

--S 64 of 267
x**2 * D(y x, x) + 2*x*(y x) - (y x)**3 = 0
 

         2 ,          3
   (2)  x y (x) - y(x)  + 2x y(x)= 0

                                            Type: Equation Expression Integer
--R
--R         2 ,          3
--R   (2)  x y (x) - y(x)  + 2x y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E

--S 65 of 267
solve(%,y,x)
 

             5         2
        (- 3x  - 2)y(x)  + 5x
   (3)  ---------------------
                 5    2
               5x y(x)
                                          Type: Union(Expression Integer,...)
--R
--R             5         2
--R        (- 3x  - 2)y(x)  + 5x
--R   (3)  ---------------------
--R                 5    2
--R               5x y(x)
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 66 of 267
p:POLY FRAC INT := 3*(x+1)
 

   (1)  3x + 3
                                            Type: Polynomial Fraction Integer
--R
--R   (1)  3x + 3
--R                                            Type: Polynomial Fraction Integer
--E


--S 67 of 267
factor(p)**2 
 

                2
   (2)  9(x + 1)
                                   Type: Factored Polynomial Fraction Integer
--R
--R                2
--R   (2)  9(x + 1)
--R                                   Type: Factored Polynomial Fraction Integer
--E

)clear all
 

--S 68 of 267
fout:TextFile:=open("/tmp/foo","output")
 

   (1)  "/tmp/foo"
                                                               Type: TextFile
--R
--R   (1)  "/tmp/foo"
--R                                                               Type: TextFile
--E

--S 69 of 267
write!(fout,"foo")
 

   (2)  "foo"
                                                                 Type: String
--R
--R   (2)  "foo"
--R                                                                 Type: String
--E

--S 70 of 267
close!(fout)
 

   (3)  "/tmp/foo"
                                                               Type: TextFile
--R
--R   (3)  "/tmp/foo"
--R                                                               Type: TextFile
--E

--S 71 of 267
fin:TextFile:=open("/tmp/foo","input")
 

   (4)  "/tmp/foo"
                                                               Type: TextFile
--R
--R   (4)  "/tmp/foo"
--R                                                               Type: TextFile
--E

--S 72 of 267
readLineIfCan!(fin)
 

   (5)  "foo"
                                                      Type: Union(String,...)
--R
--R   (5)  "foo"
--R                                                      Type: Union(String,...)
--E

--S 73 of 267
readLineIfCan!(fin)
 

   (6)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (6)  "failed"
--R                                                    Type: Union("failed",...)
--E

--S 74 of 267
close!(fin)
 

   (7)  "/tmp/foo"
                                                               Type: TextFile
--R
--R   (7)  "/tmp/foo"
--R                                                               Type: TextFile
--E

--S 75 of 267
)lis (system "rm /tmp/foo")
 
Value = 0
--R 
--RValue = 0
--E

)clear all
 

--S 76 of 267
a | a**2+1
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
   a : SAEa := a

   (1)  a
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R   a : SAEa := a
--R
--R   (1)  a
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--E

--S 77 of 267
t1:=(x+a)*(x+a+1)
 

         2
   (2)  x  + (2a + 1)x + a - 1
Type: Polynomial SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R
--R         2
--R   (2)  x  + (2a + 1)x + a - 1
--RType: Polynomial SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--E

--S 78 of 267
factor t1
 

   (3)  (x + a + 1)(x + a)
Type: Factored Polynomial SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R
--R   (3)  (x + a + 1)(x + a)
--RType: Factored Polynomial SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--E

)clear all
 

)set expose add constructor SquareMatrix
 
   SquareMatrix is already explicitly exposed in frame initial 

--S 79 of 267
S2:= SquareMatrix(2,FRAC POLY INT);
 

                                                                 Type: Domain
--R
--R                                                                 Type: Domain
--E

--S 80 of 267
V2: S2 := matrix([[v,-v],[-v,v]])
 

        + v   - v+
   (2)  |        |
        +- v   v +
                            Type: SquareMatrix(2,Fraction Polynomial Integer)
--R
--R        + v   - v+
--R   (2)  |        |
--R        +- v   v +
--R                            Type: SquareMatrix(2,Fraction Polynomial Integer)
--E

--S 81 of 267
I2: S2 := 1
 

        +1  0+
   (3)  |    |
        +0  1+
                            Type: SquareMatrix(2,Fraction Polynomial Integer)
--R
--R        +1  0+
--R   (3)  |    |
--R        +0  1+
--R                            Type: SquareMatrix(2,Fraction Polynomial Integer)
--E

--S 82 of 267
m:=5
 

   (4)  5
                                                        Type: PositiveInteger
--R
--R   (4)  5
--R                                                        Type: PositiveInteger
--E

--S 83 of 267
l: List(S2) := append(cons(V2+h*I2,_
            [(V2+2*h*I2) for i in 2 .. (m-1)]),_
             [V2+h*I2])
 

   (5)
    +v + h   - v +  +v + 2h   - v  +  +v + 2h   - v  +  +v + 2h   - v  +
   [|            |, |              |, |              |, |              |,
    + - v   v + h+  + - v    v + 2h+  + - v    v + 2h+  + - v    v + 2h+
    +v + h   - v +
    |            |]
    + - v   v + h+
                       Type: List SquareMatrix(2,Fraction Polynomial Integer)
--R 
--R
--R   (5)
--R    +v + h   - v +  +v + 2h   - v  +  +v + 2h   - v  +  +v + 2h   - v  +
--R   [|            |, |              |, |              |, |              |,
--R    + - v   v + h+  + - v    v + 2h+  + - v    v + 2h+  + - v    v + 2h+
--R    +v + h   - v +
--R    |            |]
--R    + - v   v + h+
--R                       Type: List SquareMatrix(2,Fraction Polynomial Integer)
--E

--S 84 of 267
A: SquareMatrix(m, S2) := diagonalMatrix(l)
 

        +matrix1  matrix2  matrix2  matrix2  matrix2+
        |                                           |
        |matrix2  matrix3  matrix2  matrix2  matrix2|
        |                                           |
   (6)  |matrix2  matrix2  matrix3  matrix2  matrix2|
        |                                           |
        |matrix2  matrix2  matrix2  matrix3  matrix2|
        |                                           |
        +matrix2  matrix2  matrix2  matrix2  matrix1+



                  +v + h   - v +
   where matrix1= |            |
                  + - v   v + h+

                +0  0+
   and matrix2= |    |
                +0  0+

                +v + 2h   - v  +
   and matrix3= |              |
                + - v    v + 2h+
            Type: SquareMatrix(5,SquareMatrix(2,Fraction Polynomial Integer))
--R
--R        +matrix1  matrix2  matrix2  matrix2  matrix2+
--R        |                                           |
--R        |matrix2  matrix3  matrix2  matrix2  matrix2|
--R        |                                           |
--R   (6)  |matrix2  matrix2  matrix3  matrix2  matrix2|
--R        |                                           |
--R        |matrix2  matrix2  matrix2  matrix3  matrix2|
--R        |                                           |
--R        +matrix2  matrix2  matrix2  matrix2  matrix1+
--R
--R
--R
--R                  +v + h   - v +
--R   where matrix1= |            |
--R                  + - v   v + h+
--R
--R                +0  0+
--R   and matrix2= |    |
--R                +0  0+
--R
--R                +v + 2h   - v  +
--R   and matrix3= |              |
--R                + - v    v + 2h+
--R            Type: SquareMatrix(5,SquareMatrix(2,Fraction Polynomial Integer))
--E

)clear all
 

--S 85 of 267
squareFree((2*x*y+1)*(x*y+1)**2)
 

                 2
   (1)  (x y + 1) (2x y + 1)
                                            Type: Factored Polynomial Integer
--R
--R                 2
--R   (1)  (x y + 1) (2x y + 1)
--R                                            Type: Factored Polynomial Integer
--E

)clear all
 

--S 86 of 267
limit(atan(1/sin(x)),x=0)
 

                          %pi                 %pi
   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R
--R                          %pi                 %pi
--R   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E

)clear all
 

--S 87 of 267
limit(atan(-sin(x)/(cos(x)+e)),x=acos(-e))
 

                          %pi                 %pi
   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R
--R                          %pi                 %pi
--R   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E

--S 88 of 267
limit(atan(1/(cos(x)+e)),x=acos(-e))
 

                        %pi                   %pi
   (2)  [leftHandLimit= ---,rightHandLimit= - ---]
                         2                     2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R
--R                        %pi                   %pi
--R   (2)  [leftHandLimit= ---,rightHandLimit= - ---]
--R                         2                     2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E

)clear all
 

--S 89 of 267
D := MATRIX FRAC(POLY INT)
 

   (1)  Matrix Fraction Polynomial Integer
                                                                 Type: Domain
--R
--R   (1)  Matrix Fraction Polynomial Integer
--R                                                                 Type: Domain
--E

--S 90 of 267
d : (INT, Boolean) -> POLY INT
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 91 of 267
d(i,ss)  ==
  ex := i rem 4
  if ex < 0 then ex := ex+4
  ss =>
    ex = 0 => 's
    ex = 1 => 'sd
    ex = 2 => 'sdd
    'sddd
  ex = 0 => 1
  ex = 1 => 'd
  ex = 2 => 'dd
  'ddd
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E

-- 1,d,dd,ddd,s,sd,sdd,sddd

--S 92 of 267
mTV4 : D := new(8,8,0)
 

        +0  0  0  0  0  0  0  0+
        |                      |
        |0  0  0  0  0  0  0  0|
        |                      |
        |0  0  0  0  0  0  0  0|
        |                      |
        |0  0  0  0  0  0  0  0|
   (4)  |                      |
        |0  0  0  0  0  0  0  0|
        |                      |
        |0  0  0  0  0  0  0  0|
        |                      |
        |0  0  0  0  0  0  0  0|
        |                      |
        +0  0  0  0  0  0  0  0+
                                     Type: Matrix Fraction Polynomial Integer
--R
--R        +0  0  0  0  0  0  0  0+
--R        |                      |
--R        |0  0  0  0  0  0  0  0|
--R        |                      |
--R        |0  0  0  0  0  0  0  0|
--R        |                      |
--R        |0  0  0  0  0  0  0  0|
--R   (4)  |                      |
--R        |0  0  0  0  0  0  0  0|
--R        |                      |
--R        |0  0  0  0  0  0  0  0|
--R        |                      |
--R        |0  0  0  0  0  0  0  0|
--R        |                      |
--R        +0  0  0  0  0  0  0  0+
--R                                     Type: Matrix Fraction Polynomial Integer
--E

--S 93 of 267
for i in 1..8 repeat
  for j in 1..8 repeat
    mTV4(i,j) :=
      i <= 4 =>
        j <= 4 => d(i+j-2, false)
        d(-i+j,true)
      j <= 4 => d(i+j-2,true)
      d(-i+j,false)
 
   Compiling function d with type (Integer,Boolean) -> Polynomial 
      Integer 
                                                                   Type: Void
--R 
--R   Compiling function d with type (Integer,Boolean) -> Polynomial 
--R      Integer 
--R                                                                   Type: Void
--E

--S 94 of 267
mTV4
 

        + 1     d     dd   ddd    s     sd   sdd   sddd+
        |                                              |
        | d     dd   ddd    1    sddd   s     sd   sdd |
        |                                              |
        | dd   ddd    1     d    sdd   sddd   s     sd |
        |                                              |
        |ddd    1     d     dd    sd   sdd   sddd   s  |
   (6)  |                                              |
        | s     sd   sdd   sddd   1     d     dd   ddd |
        |                                              |
        | sd   sdd   sddd   s    ddd    1     d     dd |
        |                                              |
        |sdd   sddd   s     sd    dd   ddd    1     d  |
        |                                              |
        +sddd   s     sd   sdd    d     dd   ddd    1  +
                                     Type: Matrix Fraction Polynomial Integer
--R
--R        + 1     d     dd   ddd    s     sd   sdd   sddd+
--R        |                                              |
--R        | d     dd   ddd    1    sddd   s     sd   sdd |
--R        |                                              |
--R        | dd   ddd    1     d    sdd   sddd   s     sd |
--R        |                                              |
--R        |ddd    1     d     dd    sd   sdd   sddd   s  |
--R   (6)  |                                              |
--R        | s     sd   sdd   sddd   1     d     dd   ddd |
--R        |                                              |
--R        | sd   sdd   sddd   s    ddd    1     d     dd |
--R        |                                              |
--R        |sdd   sddd   s     sd    dd   ddd    1     d  |
--R        |                                              |
--R        +sddd   s     sd   sdd    d     dd   ddd    1  +
--R                                     Type: Matrix Fraction Polynomial Integer
--E

--S 95 of 267
gdd4 := determinant mTV4
 

   (7)
           8                2       2      2     2         6
     - sddd  + (8s sdd + 4sd  + 4ddd  + 4dd  + 4d  + 4)sddd
   + 
                  2
         - 8sd sdd  + ((- 8dd - 8)ddd - 8d dd - 8d)sdd
       + 
              2
         (- 8s  - 16d ddd - 16dd)sd + ((- 8dd - 8)ddd - 8d dd - 8d)s
    *
           5
       sddd
   + 
             4         2       2                2            2        2
         2sdd  + (- 20s  + 4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sdd
       + 
                    2
             - 8s sd  + ((24dd + 24)ddd + 24d dd + 24d)sd
           + 
                     2                 2             2
             (- 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)s
        *
           sdd
       + 
              4          2      2     2       2
         - 6sd  + (- 4ddd  - 4dd  - 4d  - 4)sd
       + 
                                                 4
         ((24dd + 24)ddd + 24d dd + 24d)s sd + 2s
       + 
              2                2            2      2       4
         (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s  - 6ddd
       + 
               2           2        2         2                        4
         (- 8dd  + 8dd - 4d  - 8)ddd  + (8d dd  + 32d dd + 8d)ddd - 6dd
       + 
              2       2     2       4     2
         (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
    *
           4
       sddd
   + 
                                                      3
         (32s sd + (- 16dd - 16)ddd - 16d dd - 16d)sdd
       + 
              3                                                              2
         (16sd  + (- 32d ddd - 32dd)sd + ((16dd + 16)ddd + 16d dd + 16d)s)sdd
       + 
                                                2
             ((- 16dd - 16)ddd - 16d dd - 16d)sd
           + 
                 3           2       2      2
             (32s  + (- 32ddd  - 32dd  - 32d  - 32)s)sd
           + 
                                             2                 3
             ((16dd + 16)ddd + 16d dd + 16d)s  + (16dd + 16)ddd
           + 
                                2
             (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
           sdd
       + 
             2                    3                                        2
         (16s  + 32d ddd + 32dd)sd  + ((- 16dd - 16)ddd - 16d dd - 16d)s sd
       + 
                                2          3          2         2
             (- 32d ddd - 32dd)s  + 32d ddd  + (- 16dd  - 16)ddd
           + 
                            3           3      2  2             2
             (- 64d dd + 32d )ddd + 32dd  - 16d dd  + 32dd - 16d
        *
           sd
       + 
                                           3
         ((- 16dd - 16)ddd - 16d dd - 16d)s
       + 
                           3                      2
             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
           s
    *
           3
       sddd
   + 
                 5          2       2                2            2        4
         - 8s sdd  + (- 20sd  + 4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sdd
       + 
                                                 3                          3
         (((16dd + 16)ddd + 16d dd + 16d)sd + 16s  + (- 32d ddd - 32dd)s)sdd
       + 
                   2        2                 2             2        2
             (- 56s  + 24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)sd
           + 
             ((- 16dd - 16)ddd - 16d dd - 16d)s sd
           + 
                   2                 2             2       2       4          3
             (24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)s  - 8ddd  - 16d ddd
           + 
                   2      2        2                3          4       3
             (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd - 8dd  - 16dd
           + 
                  2        2            4     2
             (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
        *
              2
           sdd
       + 
                    4                                      3
             - 8s sd  + ((- 16dd - 16)ddd - 16d dd - 16d)sd
           + 
                   2                 2             2          2
             (32ddd  + 96d ddd + 32dd  + 96dd + 32d  + 32)s sd
           + 
                                                   2                   3
                 ((- 16dd - 16)ddd - 16d dd - 16d)s  + (- 16dd - 16)ddd
               + 
                                  2
                 (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
               sd
           + 
                 5                      3
             - 8s  + (- 32d ddd - 32dd)s
           + 
                     4                2    2            2                4
                 8ddd  + (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd
               + 
                     2      2       4
                 48dd  - 32d dd + 8d  + 8
            *
               s
        *
           sdd
       + 
            6          2      2     2       4
         4sd  + (- 4ddd  - 4dd  - 4d  - 4)sd
       + 
                                              3
         ((- 16dd - 16)ddd - 16d dd - 16d)s sd
       + 
                  4         2                 2             2       2       4
             - 20s  + (24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)s  - 4ddd
           + 
                  2             2         2          2                         4
             (16dd  + 48dd - 88d  + 16)ddd  + (48d dd  - 64d dd + 48d)ddd - 4dd
           + 
                 2        2      2       4      2
             (16d  - 88)dd  + 48d dd - 4d  + 16d  - 4
        *
             2
           sd
       + 
                                             3
             ((16dd + 16)ddd + 16d dd + 16d)s
           + 
                                 3                    2
                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
               s
        *
           sd
       + 
              2                2            2      4
         (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s
       + 
                   4          3         2      2        2                3
             - 8ddd  - 16d ddd  + (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd
           + 
                  4       3        2        2            4     2
             - 8dd  - 16dd  + (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
        *
            2
           s
       + 
             6       2            2        4             3
         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
       + 
             4       2        2      2       4      2        2
         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
       + 
                  4         3         2         3                         6
         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
       + 
            2       4      4      2       2      4       6     4     2
         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
    *
           2
       sddd
   + 
                6                                   5
         8sd sdd  + ((- 8dd - 8)ddd - 8d dd - 8d)sdd
       + 
                  2        2                 2             2
             (- 8s  - 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)sd
           + 
             ((24dd + 24)ddd + 24d dd + 24d)s
        *
              4
           sdd
       + 
                   3                                    2
             32s sd  + ((16dd + 16)ddd + 16d dd + 16d)sd
           + 
                     2       2      2
             (- 32ddd  - 32dd  - 32d  - 32)s sd
           + 
                                               2                 3
             ((- 16dd - 16)ddd - 16d dd - 16d)s  + (16dd + 16)ddd
           + 
                                2
             (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
              3
           sdd
       + 
                  5                       3
             - 8sd  + (- 32d ddd - 32dd)sd
           + 
                                                  2
             ((- 16dd - 16)ddd - 16d dd - 16d)s sd
           + 
                     4         2                 2             2       2       4
                 - 8s  + (32ddd  + 96d ddd + 32dd  + 96dd + 32d  + 32)s  + 8ddd
               + 
                              2    2            2                4       2
                 (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd  + 48dd
               + 
                      2       4
                 - 32d dd + 8d  + 8
            *
               sd
           + 
                                               3
             ((- 16dd - 16)ddd - 16d dd - 16d)s
           + 
                                 3                    2
                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
               s
        *
              2
           sdd
       + 
                                              4
             ((24dd + 24)ddd + 24d dd + 24d)sd
           + 
                 3           2       2      2          3
             (32s  + (- 32ddd  - 32dd  - 32d  - 32)s)sd
           + 
                                                   2                   3
                 ((- 16dd - 16)ddd - 16d dd - 16d)s  + (- 16dd - 16)ddd
               + 
                                  2
                 (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
                 2
               sd
           + 
                         2       2      2       3
                 (- 32ddd  - 32dd  - 32d  - 32)s
               + 
                          4          3        2      2         2
                     32ddd  - 64d ddd  + (96dd  - 64d  + 96)ddd
                   + 
                                     3           4       3       2        2
                     (- 128d dd - 64d )ddd + 32dd  - 64dd  + (96d  - 64)dd
                   + 
                                 4      2
                     - 64dd + 32d  + 96d  + 32
                *
                   s
            *
               sd
           + 
                                             4
             ((24dd + 24)ddd + 24d dd + 24d)s
           + 
                                 3                    2
                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
                2
               s
           + 
                           5                    4
             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
           + 
                    3       2         2              2         3
             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
           + 
                    3         2         3               3          2
             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
           + 
                      5       4       2        3         2        2
                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
               + 
                     4      2              4      2
                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
            *
               ddd
           + 
                    5         4         3         3       3         2
             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
           + 
                  5      3              5      3
             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
        *
           sdd
       + 
              2                    5                                      4
         (- 8s  - 16d ddd - 16dd)sd  + ((24dd + 24)ddd + 24d dd + 24d)s sd
       + 
                                2          3          2         2
             (- 32d ddd - 32dd)s  + 32d ddd  + (- 16dd  - 16)ddd
           + 
                            3           3      2  2             2
             (- 64d dd + 32d )ddd + 32dd  - 16d dd  + 32dd - 16d
        *
             3
           sd
       + 
                                             3
             ((16dd + 16)ddd + 16d dd + 16d)s
           + 
                                 3                    2
                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
               s
        *
             2
           sd
       + 
               6           2                 2             2       4
             8s  + (- 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)s
           + 
                     4                2    2            2                4
                 8ddd  + (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd
               + 
                     2      2       4
                 48dd  - 32d dd + 8d  + 8
            *
                2
               s
           + 
                      5        2                4            2      3          3
             - 16d ddd  + (16dd  + 16dd + 16)ddd  + (- 32d dd  + 32d  - 32d)ddd
           + 
                  4       3         2        2       2              2         2
             (16dd  - 32dd  + (- 32d  - 32)dd  + (96d  - 32)dd - 32d  + 16)ddd
           + 
                    4         3         2      5      3                 5
             (16d dd  + (- 32d  + 96d)dd  - 16d  - 32d  + 16d)ddd - 16dd
           + 
                2  4         2        3       4      2   2
             16d dd  + (- 32d  + 32)dd  + (16d  - 32d )dd
           + 
                 4      2              4      2
             (16d  - 32d  - 16)dd + 16d  + 16d
        *
           sd
       + 
                                       5
         ((- 8dd - 8)ddd - 8d dd - 8d)s
       + 
                           3                      2
             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
            3
           s
       + 
                           5                    4
             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
           + 
                    3       2         2              2         3
             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
           + 
                    3         2         3               3          2
             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
           + 
                      5       4       2        3         2        2
                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
               + 
                     4      2              4      2
                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
            *
               ddd
           + 
                    5         4         3         3       3         2
             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
           + 
                  5      3              5      3
             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
        *
           s
    *
       sddd
   + 
          8      2       2      2     2        6
     - sdd  + (4s  + 4ddd  + 4dd  + 4d  + 4)sdd
   + 
             2                                                            5
     (- 8s sd  + ((- 8dd - 8)ddd - 8d dd - 8d)sd + (- 16d ddd - 16dd)s)sdd
   + 
            4        2                2            2       2
         2sd  + (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sd
       + 
                                                 4
         ((24dd + 24)ddd + 24d dd + 24d)s sd - 6s
       + 
                2      2     2      2       4         2           2        2
         (- 4ddd  - 4dd  - 4d  - 4)s  - 6ddd  + (- 8dd  + 8dd - 4d  - 8)ddd
       + 
             2                        4        2       2     2       4     2
       (8d dd  + 32d dd + 8d)ddd - 6dd  + (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
    *
          4
       sdd
   + 
                                            3       3                         2
         ((- 16dd - 16)ddd - 16d dd - 16d)sd  + (16s  + (- 32d ddd - 32dd)s)sd
       + 
                                               2                 3
             ((- 16dd - 16)ddd - 16d dd - 16d)s  + (16dd + 16)ddd
           + 
                                2
             (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
           sd
       + 
                          3
         (32d ddd + 32dd)s
       + 
                    3          2         2                  3           3
             32d ddd  + (- 16dd  - 16)ddd  + (- 64d dd + 32d )ddd + 32dd
           + 
                  2  2             2
             - 16d dd  + 32dd - 16d
        *
           s
    *
          3
       sdd
   + 
               2       2                2            2       4
         (- 20s  + 4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sd
       + 
                                            3
         ((16dd + 16)ddd + 16d dd + 16d)s sd
       + 
                   2                 2             2       2       4          3
             (24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)s  - 8ddd  - 16d ddd
           + 
                   2      2        2                3          4       3
             (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd - 8dd  - 16dd
           + 
                  2        2            4     2
             (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
        *
             2
           sd
       + 
                                               3
             ((- 16dd - 16)ddd - 16d dd - 16d)s
           + 
                                 3                    2
                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
               s
        *
           sd
       + 
           6          2      2     2      4
         4s  + (- 4ddd  - 4dd  - 4d  - 4)s
       + 
                   4        2             2         2
             - 4ddd  + (16dd  + 48dd - 88d  + 16)ddd
           + 
                    2                         4       2        2      2       4
             (48d dd  - 64d dd + 48d)ddd - 4dd  + (16d  - 88)dd  + 48d dd - 4d
           + 
                2
             16d  - 4
        *
            2
           s
       + 
             6       2            2        4             3
         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
       + 
             4       2        2      2       4      2        2
         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
       + 
                  4         3         2         3                         6
         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
       + 
            2       4      4      2       2      4       6     4     2
         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
    *
          2
       sdd
   + 
              6                                  5
         8s sd  + ((- 8dd - 8)ddd - 8d dd - 8d)sd
       + 
                 2                 2             2          4
         (- 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)s sd
       + 
                                             2                 3
             ((16dd + 16)ddd + 16d dd + 16d)s  + (16dd + 16)ddd
           + 
                                2
             (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
             3
           sd
       + 
                 5                      3
             - 8s  + (- 32d ddd - 32dd)s
           + 
                     4                2    2            2                4
                 8ddd  + (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd
               + 
                     2      2       4
                 48dd  - 32d dd + 8d  + 8
            *
               s
        *
             2
           sd
       + 
                                             4
             ((24dd + 24)ddd + 24d dd + 24d)s
           + 
                                 3                    2
                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
               + 
                        3       2       2              2                  3
                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
               + 
                       2         3               3
                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
            *
                2
               s
           + 
                           5                    4
             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
           + 
                    3       2         2              2         3
             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
           + 
                    3         2         3               3          2
             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
           + 
                      5       4       2        3         2        2
                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
               + 
                     4      2              4      2
                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
            *
               ddd
           + 
                    5         4         3         3       3         2
             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
           + 
                  5      3              5      3
             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
        *
           sd
       + 
                            5
         (- 16d ddd - 16dd)s
       + 
                    3          2         2                  3           3
             32d ddd  + (- 16dd  - 16)ddd  + (- 64d dd + 32d )ddd + 32dd
           + 
                  2  2             2
             - 16d dd  + 32dd - 16d
        *
            3
           s
       + 
                      5        2                4            2      3          3
             - 16d ddd  + (16dd  + 16dd + 16)ddd  + (- 32d dd  + 32d  - 32d)ddd
           + 
                  4       3         2        2       2              2         2
             (16dd  - 32dd  + (- 32d  - 32)dd  + (96d  - 32)dd - 32d  + 16)ddd
           + 
                    4         3         2      5      3                 5
             (16d dd  + (- 32d  + 96d)dd  - 16d  - 32d  + 16d)ddd - 16dd
           + 
                2  4         2        3       4      2   2
             16d dd  + (- 32d  + 32)dd  + (16d  - 32d )dd
           + 
                 4      2              4      2
             (16d  - 32d  - 16)dd + 16d  + 16d
        *
           s
    *
       sdd
   + 
         8        2      2     2       6                                    5
     - sd  + (4ddd  + 4dd  + 4d  + 4)sd  + ((- 8dd - 8)ddd - 8d dd - 8d)s sd
   + 
           4        2                2            2      2       4
         2s  + (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s  - 6ddd
       + 
               2           2        2         2                        4
         (- 8dd  + 8dd - 4d  - 8)ddd  + (8d dd  + 32d dd + 8d)ddd - 6dd
       + 
              2       2     2       4     2
         (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
    *
         4
       sd
   + 
                                           3
         ((- 16dd - 16)ddd - 16d dd - 16d)s
       + 
                           3                      2
             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
           s
    *
         3
       sd
   + 
              2                2            2      4
         (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s
       + 
                   4          3         2      2        2                3
             - 8ddd  - 16d ddd  + (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd
           + 
                  4       3        2        2            4     2
             - 8dd  - 16dd  + (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
        *
            2
           s
       + 
             6       2            2        4             3
         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
       + 
             4       2        2      2       4      2        2
         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
       + 
                  4         3         2         3                         6
         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
       + 
            2       4      4      2       2      4       6     4     2
         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
    *
         2
       sd
   + 
                                       5
         ((- 8dd - 8)ddd - 8d dd - 8d)s
       + 
                           3                      2
             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
           + 
                  3       2         2              2                  3
             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
           + 
                     2       3               3
             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
        *
            3
           s
       + 
                           5                    4
             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
           + 
                    3       2         2              2         3
             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
           + 
                    3         2         3               3          2
             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
           + 
                      5       4       2        3         2        2
                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
               + 
                     4      2              4      2
                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
            *
               ddd
           + 
                    5         4         3         3       3         2
             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
           + 
                  5      3              5      3
             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
        *
           s
    *
       sd
   + 
        8        2      2     2      6
     - s  + (4ddd  + 4dd  + 4d  + 4)s
   + 
               4         2           2        2         2
         - 6ddd  + (- 8dd  + 8dd - 4d  - 8)ddd  + (8d dd  + 32d dd + 8d)ddd
       + 
              4        2       2     2       4     2
         - 6dd  + (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
    *
        4
       s
   + 
             6       2            2        4             3
         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
       + 
             4       2        2      2       4      2        2
         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
       + 
                  4         3         2         3                         6
         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
       + 
            2       4      4      2       2      4       6     4     2
         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
    *
        2
       s
   + 
          8            2    6           2         5
     - ddd  + (8dd + 4d )ddd  + (- 8d dd  - 8d)ddd
   + 
         4       2     2       4        4
     (2dd  - 20dd  - 8d dd - 6d  + 2)ddd
   + 
            3      3  2               3    3
     (32d dd  + 16d dd  + 32d dd + 16d )ddd
   + 
           5      2  4       3      2  2        4            6      2    2
     (- 8dd  - 20d dd  + 16dd  - 56d dd  + (- 8d  - 8)dd + 4d  - 20d )ddd
   + 
           6        4      3  3        5        2      3       5              8
     (8d dd  - 8d dd  + 32d dd  + (- 8d  - 8d)dd  + 32d dd - 8d  + 8d)ddd - dd
   + 
        6     2  5      4       4      2  3         4       2      6     2
     4dd  - 8d dd  + (2d  - 6)dd  + 16d dd  + (- 20d  + 4)dd  + (8d  - 8d )dd
   + 
        8     4
     - d  + 2d  - 1
                                            Type: Fraction Polynomial Integer
--R
--R   (7)
--R           8                2       2      2     2         6
--R     - sddd  + (8s sdd + 4sd  + 4ddd  + 4dd  + 4d  + 4)sddd
--R   + 
--R                  2
--R         - 8sd sdd  + ((- 8dd - 8)ddd - 8d dd - 8d)sdd
--R       + 
--R              2
--R         (- 8s  - 16d ddd - 16dd)sd + ((- 8dd - 8)ddd - 8d dd - 8d)s
--R    *
--R           5
--R       sddd
--R   + 
--R             4         2       2                2            2        2
--R         2sdd  + (- 20s  + 4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sdd
--R       + 
--R                    2
--R             - 8s sd  + ((24dd + 24)ddd + 24d dd + 24d)sd
--R           + 
--R                     2                 2             2
--R             (- 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)s
--R        *
--R           sdd
--R       + 
--R              4          2      2     2       2
--R         - 6sd  + (- 4ddd  - 4dd  - 4d  - 4)sd
--R       + 
--R                                                 4
--R         ((24dd + 24)ddd + 24d dd + 24d)s sd + 2s
--R       + 
--R              2                2            2      2       4
--R         (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s  - 6ddd
--R       + 
--R               2           2        2         2                        4
--R         (- 8dd  + 8dd - 4d  - 8)ddd  + (8d dd  + 32d dd + 8d)ddd - 6dd
--R       + 
--R              2       2     2       4     2
--R         (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
--R    *
--R           4
--R       sddd
--R   + 
--R                                                      3
--R         (32s sd + (- 16dd - 16)ddd - 16d dd - 16d)sdd
--R       + 
--R              3                                                              2
--R         (16sd  + (- 32d ddd - 32dd)sd + ((16dd + 16)ddd + 16d dd + 16d)s)sdd
--R       + 
--R                                                2
--R             ((- 16dd - 16)ddd - 16d dd - 16d)sd
--R           + 
--R                 3           2       2      2
--R             (32s  + (- 32ddd  - 32dd  - 32d  - 32)s)sd
--R           + 
--R                                             2                 3
--R             ((16dd + 16)ddd + 16d dd + 16d)s  + (16dd + 16)ddd
--R           + 
--R                                2
--R             (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R           sdd
--R       + 
--R             2                    3                                        2
--R         (16s  + 32d ddd + 32dd)sd  + ((- 16dd - 16)ddd - 16d dd - 16d)s sd
--R       + 
--R                                2          3          2         2
--R             (- 32d ddd - 32dd)s  + 32d ddd  + (- 16dd  - 16)ddd
--R           + 
--R                            3           3      2  2             2
--R             (- 64d dd + 32d )ddd + 32dd  - 16d dd  + 32dd - 16d
--R        *
--R           sd
--R       + 
--R                                           3
--R         ((- 16dd - 16)ddd - 16d dd - 16d)s
--R       + 
--R                           3                      2
--R             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R           s
--R    *
--R           3
--R       sddd
--R   + 
--R                 5          2       2                2            2        4
--R         - 8s sdd  + (- 20sd  + 4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sdd
--R       + 
--R                                                 3                          3
--R         (((16dd + 16)ddd + 16d dd + 16d)sd + 16s  + (- 32d ddd - 32dd)s)sdd
--R       + 
--R                   2        2                 2             2        2
--R             (- 56s  + 24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)sd
--R           + 
--R             ((- 16dd - 16)ddd - 16d dd - 16d)s sd
--R           + 
--R                   2                 2             2       2       4          3
--R             (24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)s  - 8ddd  - 16d ddd
--R           + 
--R                   2      2        2                3          4       3
--R             (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd - 8dd  - 16dd
--R           + 
--R                  2        2            4     2
--R             (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
--R        *
--R              2
--R           sdd
--R       + 
--R                    4                                      3
--R             - 8s sd  + ((- 16dd - 16)ddd - 16d dd - 16d)sd
--R           + 
--R                   2                 2             2          2
--R             (32ddd  + 96d ddd + 32dd  + 96dd + 32d  + 32)s sd
--R           + 
--R                                                   2                   3
--R                 ((- 16dd - 16)ddd - 16d dd - 16d)s  + (- 16dd - 16)ddd
--R               + 
--R                                  2
--R                 (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R               sd
--R           + 
--R                 5                      3
--R             - 8s  + (- 32d ddd - 32dd)s
--R           + 
--R                     4                2    2            2                4
--R                 8ddd  + (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd
--R               + 
--R                     2      2       4
--R                 48dd  - 32d dd + 8d  + 8
--R            *
--R               s
--R        *
--R           sdd
--R       + 
--R            6          2      2     2       4
--R         4sd  + (- 4ddd  - 4dd  - 4d  - 4)sd
--R       + 
--R                                              3
--R         ((- 16dd - 16)ddd - 16d dd - 16d)s sd
--R       + 
--R                  4         2                 2             2       2       4
--R             - 20s  + (24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)s  - 4ddd
--R           + 
--R                  2             2         2          2                         4
--R             (16dd  + 48dd - 88d  + 16)ddd  + (48d dd  - 64d dd + 48d)ddd - 4dd
--R           + 
--R                 2        2      2       4      2
--R             (16d  - 88)dd  + 48d dd - 4d  + 16d  - 4
--R        *
--R             2
--R           sd
--R       + 
--R                                             3
--R             ((16dd + 16)ddd + 16d dd + 16d)s
--R           + 
--R                                 3                    2
--R                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R               s
--R        *
--R           sd
--R       + 
--R              2                2            2      4
--R         (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s
--R       + 
--R                   4          3         2      2        2                3
--R             - 8ddd  - 16d ddd  + (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd
--R           + 
--R                  4       3        2        2            4     2
--R             - 8dd  - 16dd  + (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
--R        *
--R            2
--R           s
--R       + 
--R             6       2            2        4             3
--R         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
--R       + 
--R             4       2        2      2       4      2        2
--R         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
--R       + 
--R                  4         3         2         3                         6
--R         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
--R       + 
--R            2       4      4      2       2      4       6     4     2
--R         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
--R    *
--R           2
--R       sddd
--R   + 
--R                6                                   5
--R         8sd sdd  + ((- 8dd - 8)ddd - 8d dd - 8d)sdd
--R       + 
--R                  2        2                 2             2
--R             (- 8s  - 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)sd
--R           + 
--R             ((24dd + 24)ddd + 24d dd + 24d)s
--R        *
--R              4
--R           sdd
--R       + 
--R                   3                                    2
--R             32s sd  + ((16dd + 16)ddd + 16d dd + 16d)sd
--R           + 
--R                     2       2      2
--R             (- 32ddd  - 32dd  - 32d  - 32)s sd
--R           + 
--R                                               2                 3
--R             ((- 16dd - 16)ddd - 16d dd - 16d)s  + (16dd + 16)ddd
--R           + 
--R                                2
--R             (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R              3
--R           sdd
--R       + 
--R                  5                       3
--R             - 8sd  + (- 32d ddd - 32dd)sd
--R           + 
--R                                                  2
--R             ((- 16dd - 16)ddd - 16d dd - 16d)s sd
--R           + 
--R                     4         2                 2             2       2       4
--R                 - 8s  + (32ddd  + 96d ddd + 32dd  + 96dd + 32d  + 32)s  + 8ddd
--R               + 
--R                              2    2            2                4       2
--R                 (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd  + 48dd
--R               + 
--R                      2       4
--R                 - 32d dd + 8d  + 8
--R            *
--R               sd
--R           + 
--R                                               3
--R             ((- 16dd - 16)ddd - 16d dd - 16d)s
--R           + 
--R                                 3                    2
--R                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R               s
--R        *
--R              2
--R           sdd
--R       + 
--R                                              4
--R             ((24dd + 24)ddd + 24d dd + 24d)sd
--R           + 
--R                 3           2       2      2          3
--R             (32s  + (- 32ddd  - 32dd  - 32d  - 32)s)sd
--R           + 
--R                                                   2                   3
--R                 ((- 16dd - 16)ddd - 16d dd - 16d)s  + (- 16dd - 16)ddd
--R               + 
--R                                  2
--R                 (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R                 2
--R               sd
--R           + 
--R                         2       2      2       3
--R                 (- 32ddd  - 32dd  - 32d  - 32)s
--R               + 
--R                          4          3        2      2         2
--R                     32ddd  - 64d ddd  + (96dd  - 64d  + 96)ddd
--R                   + 
--R                                     3           4       3       2        2
--R                     (- 128d dd - 64d )ddd + 32dd  - 64dd  + (96d  - 64)dd
--R                   + 
--R                                 4      2
--R                     - 64dd + 32d  + 96d  + 32
--R                *
--R                   s
--R            *
--R               sd
--R           + 
--R                                             4
--R             ((24dd + 24)ddd + 24d dd + 24d)s
--R           + 
--R                                 3                    2
--R                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R                2
--R               s
--R           + 
--R                           5                    4
--R             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
--R           + 
--R                    3       2         2              2         3
--R             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
--R           + 
--R                    3         2         3               3          2
--R             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
--R           + 
--R                      5       4       2        3         2        2
--R                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
--R               + 
--R                     4      2              4      2
--R                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
--R            *
--R               ddd
--R           + 
--R                    5         4         3         3       3         2
--R             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
--R           + 
--R                  5      3              5      3
--R             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
--R        *
--R           sdd
--R       + 
--R              2                    5                                      4
--R         (- 8s  - 16d ddd - 16dd)sd  + ((24dd + 24)ddd + 24d dd + 24d)s sd
--R       + 
--R                                2          3          2         2
--R             (- 32d ddd - 32dd)s  + 32d ddd  + (- 16dd  - 16)ddd
--R           + 
--R                            3           3      2  2             2
--R             (- 64d dd + 32d )ddd + 32dd  - 16d dd  + 32dd - 16d
--R        *
--R             3
--R           sd
--R       + 
--R                                             3
--R             ((16dd + 16)ddd + 16d dd + 16d)s
--R           + 
--R                                 3                    2
--R                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R               s
--R        *
--R             2
--R           sd
--R       + 
--R               6           2                 2             2       4
--R             8s  + (- 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)s
--R           + 
--R                     4                2    2            2                4
--R                 8ddd  + (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd
--R               + 
--R                     2      2       4
--R                 48dd  - 32d dd + 8d  + 8
--R            *
--R                2
--R               s
--R           + 
--R                      5        2                4            2      3          3
--R             - 16d ddd  + (16dd  + 16dd + 16)ddd  + (- 32d dd  + 32d  - 32d)ddd
--R           + 
--R                  4       3         2        2       2              2         2
--R             (16dd  - 32dd  + (- 32d  - 32)dd  + (96d  - 32)dd - 32d  + 16)ddd
--R           + 
--R                    4         3         2      5      3                 5
--R             (16d dd  + (- 32d  + 96d)dd  - 16d  - 32d  + 16d)ddd - 16dd
--R           + 
--R                2  4         2        3       4      2   2
--R             16d dd  + (- 32d  + 32)dd  + (16d  - 32d )dd
--R           + 
--R                 4      2              4      2
--R             (16d  - 32d  - 16)dd + 16d  + 16d
--R        *
--R           sd
--R       + 
--R                                       5
--R         ((- 8dd - 8)ddd - 8d dd - 8d)s
--R       + 
--R                           3                      2
--R             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R            3
--R           s
--R       + 
--R                           5                    4
--R             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
--R           + 
--R                    3       2         2              2         3
--R             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
--R           + 
--R                    3         2         3               3          2
--R             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
--R           + 
--R                      5       4       2        3         2        2
--R                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
--R               + 
--R                     4      2              4      2
--R                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
--R            *
--R               ddd
--R           + 
--R                    5         4         3         3       3         2
--R             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
--R           + 
--R                  5      3              5      3
--R             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
--R        *
--R           s
--R    *
--R       sddd
--R   + 
--R          8      2       2      2     2        6
--R     - sdd  + (4s  + 4ddd  + 4dd  + 4d  + 4)sdd
--R   + 
--R             2                                                            5
--R     (- 8s sd  + ((- 8dd - 8)ddd - 8d dd - 8d)sd + (- 16d ddd - 16dd)s)sdd
--R   + 
--R            4        2                2            2       2
--R         2sd  + (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sd
--R       + 
--R                                                 4
--R         ((24dd + 24)ddd + 24d dd + 24d)s sd - 6s
--R       + 
--R                2      2     2      2       4         2           2        2
--R         (- 4ddd  - 4dd  - 4d  - 4)s  - 6ddd  + (- 8dd  + 8dd - 4d  - 8)ddd
--R       + 
--R             2                        4        2       2     2       4     2
--R       (8d dd  + 32d dd + 8d)ddd - 6dd  + (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
--R    *
--R          4
--R       sdd
--R   + 
--R                                            3       3                         2
--R         ((- 16dd - 16)ddd - 16d dd - 16d)sd  + (16s  + (- 32d ddd - 32dd)s)sd
--R       + 
--R                                               2                 3
--R             ((- 16dd - 16)ddd - 16d dd - 16d)s  + (16dd + 16)ddd
--R           + 
--R                                2
--R             (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R           sd
--R       + 
--R                          3
--R         (32d ddd + 32dd)s
--R       + 
--R                    3          2         2                  3           3
--R             32d ddd  + (- 16dd  - 16)ddd  + (- 64d dd + 32d )ddd + 32dd
--R           + 
--R                  2  2             2
--R             - 16d dd  + 32dd - 16d
--R        *
--R           s
--R    *
--R          3
--R       sdd
--R   + 
--R               2       2                2            2       4
--R         (- 20s  + 4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)sd
--R       + 
--R                                            3
--R         ((16dd + 16)ddd + 16d dd + 16d)s sd
--R       + 
--R                   2                 2             2       2       4          3
--R             (24ddd  - 32d ddd + 24dd  - 32dd + 24d  + 24)s  - 8ddd  - 16d ddd
--R           + 
--R                   2      2        2                3          4       3
--R             (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd - 8dd  - 16dd
--R           + 
--R                  2        2            4     2
--R             (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
--R        *
--R             2
--R           sd
--R       + 
--R                                               3
--R             ((- 16dd - 16)ddd - 16d dd - 16d)s
--R           + 
--R                                 3                    2
--R                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R               s
--R        *
--R           sd
--R       + 
--R           6          2      2     2      4
--R         4s  + (- 4ddd  - 4dd  - 4d  - 4)s
--R       + 
--R                   4        2             2         2
--R             - 4ddd  + (16dd  + 48dd - 88d  + 16)ddd
--R           + 
--R                    2                         4       2        2      2       4
--R             (48d dd  - 64d dd + 48d)ddd - 4dd  + (16d  - 88)dd  + 48d dd - 4d
--R           + 
--R                2
--R             16d  - 4
--R        *
--R            2
--R           s
--R       + 
--R             6       2            2        4             3
--R         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
--R       + 
--R             4       2        2      2       4      2        2
--R         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
--R       + 
--R                  4         3         2         3                         6
--R         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
--R       + 
--R            2       4      4      2       2      4       6     4     2
--R         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
--R    *
--R          2
--R       sdd
--R   + 
--R              6                                  5
--R         8s sd  + ((- 8dd - 8)ddd - 8d dd - 8d)sd
--R       + 
--R                 2                 2             2          4
--R         (- 16ddd  + 16d ddd - 16dd  + 16dd - 16d  - 16)s sd
--R       + 
--R                                             2                 3
--R             ((16dd + 16)ddd + 16d dd + 16d)s  + (16dd + 16)ddd
--R           + 
--R                                2
--R             (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R             3
--R           sd
--R       + 
--R                 5                      3
--R             - 8s  + (- 32d ddd - 32dd)s
--R           + 
--R                     4                2    2            2                4
--R                 8ddd  + (- 32dd + 48d )ddd  + (- 32d dd  - 32d)ddd + 8dd
--R               + 
--R                     2      2       4
--R                 48dd  - 32d dd + 8d  + 8
--R            *
--R               s
--R        *
--R             2
--R           sd
--R       + 
--R                                             4
--R             ((24dd + 24)ddd + 24d dd + 24d)s
--R           + 
--R                                 3                    2
--R                 (- 16dd - 16)ddd  + (16d dd + 16d)ddd
--R               + 
--R                        3       2       2              2                  3
--R                 (- 16dd  + 16dd  + (16d  + 16)dd + 16d  - 16)ddd - 16d dd
--R               + 
--R                       2         3               3
--R                 16d dd  + (- 16d  + 16d)dd - 16d  - 16d
--R            *
--R                2
--R               s
--R           + 
--R                           5                    4
--R             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
--R           + 
--R                    3       2         2              2         3
--R             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
--R           + 
--R                    3         2         3               3          2
--R             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
--R           + 
--R                      5       4       2        3         2        2
--R                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
--R               + 
--R                     4      2              4      2
--R                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
--R            *
--R               ddd
--R           + 
--R                    5         4         3         3       3         2
--R             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
--R           + 
--R                  5      3              5      3
--R             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
--R        *
--R           sd
--R       + 
--R                            5
--R         (- 16d ddd - 16dd)s
--R       + 
--R                    3          2         2                  3           3
--R             32d ddd  + (- 16dd  - 16)ddd  + (- 64d dd + 32d )ddd + 32dd
--R           + 
--R                  2  2             2
--R             - 16d dd  + 32dd - 16d
--R        *
--R            3
--R           s
--R       + 
--R                      5        2                4            2      3          3
--R             - 16d ddd  + (16dd  + 16dd + 16)ddd  + (- 32d dd  + 32d  - 32d)ddd
--R           + 
--R                  4       3         2        2       2              2         2
--R             (16dd  - 32dd  + (- 32d  - 32)dd  + (96d  - 32)dd - 32d  + 16)ddd
--R           + 
--R                    4         3         2      5      3                 5
--R             (16d dd  + (- 32d  + 96d)dd  - 16d  - 32d  + 16d)ddd - 16dd
--R           + 
--R                2  4         2        3       4      2   2
--R             16d dd  + (- 32d  + 32)dd  + (16d  - 32d )dd
--R           + 
--R                 4      2              4      2
--R             (16d  - 32d  - 16)dd + 16d  + 16d
--R        *
--R           s
--R    *
--R       sdd
--R   + 
--R         8        2      2     2       6                                    5
--R     - sd  + (4ddd  + 4dd  + 4d  + 4)sd  + ((- 8dd - 8)ddd - 8d dd - 8d)s sd
--R   + 
--R           4        2                2            2      2       4
--R         2s  + (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s  - 6ddd
--R       + 
--R               2           2        2         2                        4
--R         (- 8dd  + 8dd - 4d  - 8)ddd  + (8d dd  + 32d dd + 8d)ddd - 6dd
--R       + 
--R              2       2     2       4     2
--R         (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
--R    *
--R         4
--R       sd
--R   + 
--R                                           3
--R         ((- 16dd - 16)ddd - 16d dd - 16d)s
--R       + 
--R                           3                      2
--R             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R           s
--R    *
--R         3
--R       sd
--R   + 
--R              2                2            2      4
--R         (4ddd  + 16d ddd + 4dd  + 16dd + 4d  + 4)s
--R       + 
--R                   4          3         2      2        2                3
--R             - 8ddd  - 16d ddd  + (- 8dd  + 16d  - 8)ddd  + (96d dd - 16d )ddd
--R           + 
--R                  4       3        2        2            4     2
--R             - 8dd  - 16dd  + (- 8d  + 16)dd  - 16dd - 8d  - 8d  - 8
--R        *
--R            2
--R           s
--R       + 
--R             6       2            2        4             3
--R         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
--R       + 
--R             4       2        2      2       4      2        2
--R         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
--R       + 
--R                  4         3         2         3                         6
--R         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
--R       + 
--R            2       4      4      2       2      4       6     4     2
--R         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
--R    *
--R         2
--R       sd
--R   + 
--R                                       5
--R         ((- 8dd - 8)ddd - 8d dd - 8d)s
--R       + 
--R                           3                      2
--R             (16dd + 16)ddd  + (- 16d dd - 16d)ddd
--R           + 
--R                  3       2         2              2                  3
--R             (16dd  - 16dd  + (- 16d  - 16)dd - 16d  + 16)ddd + 16d dd
--R           + 
--R                     2       3               3
--R             - 16d dd  + (16d  - 16d)dd + 16d  + 16d
--R        *
--R            3
--R           s
--R       + 
--R                           5                    4
--R             (- 8dd - 8)ddd  + (24d dd + 24d)ddd
--R           + 
--R                    3       2         2              2         3
--R             (- 16dd  + 16dd  + (- 16d  + 16)dd - 16d  - 16)ddd
--R           + 
--R                    3         2         3               3          2
--R             (16d dd  - 16d dd  + (- 16d  - 16d)dd - 16d  + 16d)ddd
--R           + 
--R                      5       4       2        3         2        2
--R                 - 8dd  + 24dd  + (16d  - 16)dd  + (- 16d  - 16)dd
--R               + 
--R                     4      2              4      2
--R                 (24d  - 16d  + 24)dd + 24d  + 16d  - 8
--R            *
--R               ddd
--R           + 
--R                    5         4         3         3       3         2
--R             - 8d dd  + 24d dd  + (- 16d  - 16d)dd  + (16d  - 16d)dd
--R           + 
--R                  5      3              5      3
--R             (- 8d  + 16d  + 24d)dd - 8d  - 16d  - 8d
--R        *
--R           s
--R    *
--R       sd
--R   + 
--R        8        2      2     2      6
--R     - s  + (4ddd  + 4dd  + 4d  + 4)s
--R   + 
--R               4         2           2        2         2
--R         - 6ddd  + (- 8dd  + 8dd - 4d  - 8)ddd  + (8d dd  + 32d dd + 8d)ddd
--R       + 
--R              4        2       2     2       4     2
--R         - 6dd  + (- 8d  - 4)dd  + 8d dd - 6d  - 8d  - 6
--R    *
--R        4
--R       s
--R   + 
--R             6       2            2        4             3
--R         4ddd  + (4dd  - 16dd - 4d  + 4)ddd  - 32d dd ddd
--R       + 
--R             4       2        2      2       4      2        2
--R         (4dd  + (24d  + 24)dd  + 32d dd - 4d  + 24d  + 4)ddd
--R       + 
--R                  4         3         2         3                         6
--R         (- 16d dd  - 32d dd  + 32d dd  + (- 32d  - 32d)dd - 16d)ddd + 4dd
--R       + 
--R            2       4      4      2       2      4       6     4     2
--R         (4d  - 4)dd  + (4d  + 24d  - 4)dd  - 16d dd + 4d  + 4d  + 4d  + 4
--R    *
--R        2
--R       s
--R   + 
--R          8            2    6           2         5
--R     - ddd  + (8dd + 4d )ddd  + (- 8d dd  - 8d)ddd
--R   + 
--R         4       2     2       4        4
--R     (2dd  - 20dd  - 8d dd - 6d  + 2)ddd
--R   + 
--R            3      3  2               3    3
--R     (32d dd  + 16d dd  + 32d dd + 16d )ddd
--R   + 
--R           5      2  4       3      2  2        4            6      2    2
--R     (- 8dd  - 20d dd  + 16dd  - 56d dd  + (- 8d  - 8)dd + 4d  - 20d )ddd
--R   + 
--R           6        4      3  3        5        2      3       5              8
--R     (8d dd  - 8d dd  + 32d dd  + (- 8d  - 8d)dd  + 32d dd - 8d  + 8d)ddd - dd
--R   + 
--R        6     2  5      4       4      2  3         4       2      6     2
--R     4dd  - 8d dd  + (2d  - 6)dd  + 16d dd  + (- 20d  + 4)dd  + (8d  - 8d )dd
--R   + 
--R        8     4
--R     - d  + 2d  - 1
--R                                            Type: Fraction Polynomial Integer
--E

)clear all
 

--S 96 of 267
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E

--S 97 of 267
dx:=operator("D")::OP(POLY FRAC INT)
 

   (2)  D
                                   Type: Operator Polynomial Fraction Integer
--R
--R   (2)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E

--S 98 of 267
evaluate(dx,p+-> differentiate(p,'x))
 
   There are 4 exposed and 1 unexposed library operations named 
      evaluate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op evaluate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      evaluate with argument type(s) 
                    Operator Polynomial Fraction Integer
                              AnonymousFunction
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 4 exposed and 1 unexposed library operations named 
--R      evaluate having 2 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op evaluate
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      evaluate with argument type(s) 
--R                    Operator Polynomial Fraction Integer
--R                              AnonymousFunction
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E

--S 99 of 267
E n == (1-x**2)*dx**2-2*x*dx+n*(n+1)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 100 of 267
L 15
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

   (4)
     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
       2048          2048           2048           2048          2048
   + 
       2909907  5   255255  3   6435
     - ------- x  + ------ x  - ---- x
         2048        2048       2048
                                            Type: Polynomial Fraction Integer
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R   (4)
--R     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
--R     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       2909907  5   255255  3   6435
--R     - ------- x  + ------ x  - ---- x
--R         2048        2048       2048
--R                                            Type: Polynomial Fraction Integer
--E


--S 101 of 267
E 15
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                       2      2
   (5)  240 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                       2      2
--R   (5)  240 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E

)clear all
 

--S 102 of 267
bug:=(1+x**(1/4))**(1/3)/(x**(1/2))
 

         +--------+
        3|4+-+
        \|\|x  + 1
   (1)  -----------
             +-+
            \|x
                                                     Type: Expression Integer
--R
--R         +--------+
--R        3|4+-+
--R        \|\|x  + 1
--R   (1)  -----------
--R             +-+
--R            \|x
--R                                                     Type: Expression Integer
--E

--S 103 of 267
integrate(bug,x)
 

                              +--------+
           4+-+2    4+-+     3|4+-+
        (12\|x   + 3\|x  - 9)\|\|x  + 1
   (2)  --------------------------------
                        7
                                          Type: Union(Expression Integer,...)
--R
--R                              +--------+
--R           4+-+2    4+-+     3|4+-+
--R        (12\|x   + 3\|x  - 9)\|\|x  + 1
--R   (2)  --------------------------------
--R                        7
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 104 of 267
g::ROMAN
 
 
Daly Bug
   >> Error detected within library code:
   Improper character in Roman numeral: 
   #\G

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   Improper character in Roman numeral: 
--R   #\G
--R
--R   Continuing to read the file...
--R
--E

)clear all
 

--S 105 of 267
factor 1068303355883998767544567663620885466990173600
 

         5 7 2 4  2  2  2
   (1)  2 3 5 7 17 19 23 3343 4219 326705949951846198203
                                                       Type: Factored Integer
--R
--R         5 7 2 4  2  2  2
--R   (1)  2 3 5 7 17 19 23 3343 4219 326705949951846198203
--R                                                       Type: Factored Integer
--E

--S 106 of 267
sqrt 1068303355883998767544567663620885466990173600
 

                  +-----------------------------+
   (2)  196571340\|27647393656301898872761810506
                                                        Type: AlgebraicNumber
--R
--R                  +-----------------------------+
--R   (2)  196571340\|27647393656301898872761810506
--R                                                        Type: AlgebraicNumber
--E

)clear all
 
--      REAL T7,T6,T5,T4,T3,T2,T1
--      T1=x*x
--      T2=2.*y**5
--      T3=4.*T1
--      T4=y**3
--      T5=2.*T7
--      T6=x**3
--      T7=x**4
--      R46=((T2+(T3+8.*x+8.)*T4+(T5+8.*T6+(-40.*T1))*y)*SIN(x)+(-T2+(-T3+
--     &16.*x)*T4+(-T5+16.*T6)*y)*COS(x))/(y**8+4.*T1*y**6+6.*T7*y**4+4.*x
--     &**6*y*y+x**8)
-- T7 is referenced before it is defined

--S 107 of 267
a1:=sin(x)/(x**2+y**2)
 

         sin(x)
   (1)  -------
         2    2
        y  + x
                                                     Type: Expression Integer
--R
--R         sin(x)
--R   (1)  -------
--R         2    2
--R        y  + x
--R                                                     Type: Expression Integer
--E

--S 108 of 267
a2:=D(a1,[x,y])
 

                           3     2
        8x y sin(x) + (- 2y  - 2x y)cos(x)
   (2)  ----------------------------------
               6     2 4     4 2    6
              y  + 3x y  + 3x y  + x
                                                     Type: Expression Integer
--R
--R                           3     2
--R        8x y sin(x) + (- 2y  - 2x y)cos(x)
--R   (2)  ----------------------------------
--R               6     2 4     4 2    6
--R              y  + 3x y  + 3x y  + x
--R                                                     Type: Expression Integer
--E

--S 109 of 267
a2+D(a2,x)
 

   (3)
          5      2           3      4     3      2
       (2y  + (4x  + 8x + 8)y  + (2x  + 8x  - 40x )y)sin(x)
     + 
            5        2        3        4      3
       (- 2y  + (- 4x  + 16x)y  + (- 2x  + 16x )y)cos(x)
  /
      8     2 6     4 4     6 2    8
     y  + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R
--R   (3)
--R          5      2           3      4     3      2
--R       (2y  + (4x  + 8x + 8)y  + (2x  + 8x  - 40x )y)sin(x)
--R     + 
--R            5        2        3        4      3
--R       (- 2y  + (- 4x  + 16x)y  + (- 2x  + 16x )y)cos(x)
--R  /
--R      8     2 6     4 4     6 2    8
--R     y  + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 110 of 267
R := FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E

--S 111 of 267
lpx : List POLY R := [x1+x2+x3, x1*x2+x1*x3+x2*x3,x1*x2*x3]
 

   (2)  [x3 + x2 + x1,(x2 + x1)x3 + x1 x2,x1 x2 x3]
                                       Type: List Polynomial Fraction Integer
--R
--R   (2)  [x3 + x2 + x1,(x2 + x1)x3 + x1 x2,x1 x2 x3]
--R                                       Type: List Polynomial Fraction Integer
--E

--S 112 of 267
lip := [lpx.1-e3, lpx.2-e2, lpx.3-e1]--R
 

   (3)  [x3 + x2 + x1 - e3,(x2 + x1)x3 + x1 x2 - e2,x1 x2 x3 - e1]
                                       Type: List Polynomial Fraction Integer
--R
--R   (3)  [x3 + x2 + x1 - e3,(x2 + x1)x3 + x1 x2 - e2,x1 x2 x3 - e1]
--R                                       Type: List Polynomial Fraction Integer
--E

--S 113 of 267
gbp := groebner lip
 

   (4)
                         2                   2
   [x3 + x2 + x1 - e3, x2  + (x1 - e3)x2 + x1  - e3 x1 + e2,
      3        2
    x1  - e3 x1  + e2 x1 - e1]
                                       Type: List Polynomial Fraction Integer
--R
--R   (4)
--R                         2                   2
--R   [x3 + x2 + x1 - e3, x2  + (x1 - e3)x2 + x1  - e3 x1 + e2,
--R      3        2
--R    x1  - e3 x1  + e2 x1 - e1]
--R                                       Type: List Polynomial Fraction Integer
--E

--S 114 of 267
normalForm(x1**2+x2**2+x3**2,gbp)
 

          2
   (5)  e3  - 2e2
                                            Type: Polynomial Fraction Integer
--R
--R          2
--R   (5)  e3  - 2e2
--R                                            Type: Polynomial Fraction Integer
--E

--S 115 of 267
dmp := DMP([x1,x2,x3,e1,e2,e3],INT)
 

   (6)  DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
                                                                 Type: Domain
--R
--R   (6)  DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--R                                                                 Type: Domain
--E

--S 116 of 267
li : List dmp := [lpx.1-e1, lpx.2-e2, lpx.3-e3]
 

   (7)  [x1 + x2 + x3 - e1,x1 x2 + x1 x3 + x2 x3 - e2,x1 x2 x3 - e3]
    Type: List DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--R
--R   (7)  [x1 + x2 + x3 - e1,x1 x2 + x1 x3 + x2 x3 - e2,x1 x2 x3 - e3]
--R    Type: List DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--E

--S 117 of 267
gb := groebner li
 

   (8)
                         2                     2
   [x1 + x2 + x3 - e1, x2  + x2 x3 - x2 e1 + x3  - x3 e1 + e2,
      3     2
    x3  - x3 e1 + x3 e2 - e3]
    Type: List DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--R
--R   (8)
--R                         2                     2
--R   [x1 + x2 + x3 - e1, x2  + x2 x3 - x2 e1 + x3  - x3 e1 + e2,
--R      3     2
--R    x3  - x3 e1 + x3 e2 - e3]
--R    Type: List DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--E

--S 118 of 267
p:dmp:=(x1**2+x2**2+x3**2)
 

          2     2     2
   (9)  x1  + x2  + x3
         Type: DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--R
--R          2     2     2
--R   (9)  x1  + x2  + x3
--R         Type: DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Integer)
--E

--S 119 of 267
normalForm(p,gb)
 

           2
   (10)  e1  - 2e2
Type: DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Fraction Integer)
--R
--R           2
--R   (10)  e1  - 2e2
--RType: DistributedMultivariatePolynomial([x1,x2,x3,e1,e2,e3],Fraction Integer)
--E

--S 120 of 267
normalForm(x1**2+x2**2+x3**2,gb)
 

            2                      2              2
   (11)  2x2  + (2x1 - 2e1)x2 + 2x1  - 2e1 x1 + e1
                                            Type: Polynomial Fraction Integer
--R
--R            2                      2              2
--R   (11)  2x2  + (2x1 - 2e1)x2 + 2x1  - 2e1 x1 + e1
--R                                            Type: Polynomial Fraction Integer
--E

)clear all
 

--S 121 of 267
integrate(normalize(sqrt(1+cos(x)),x),x)
 

                +--------+
             x  |     x 2
        2sin(-) |2cos(-)
             2 \|     2
   (1)  ------------------
                  x
              cos(-)
                  2
                                          Type: Union(Expression Integer,...)
--R
--R                +--------+
--R             x  |     x 2
--R        2sin(-) |2cos(-)
--R             2 \|     2
--R   (1)  ------------------
--R                  x
--R              cos(-)
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 122 of 267
integrate(((-x-1)*log((x**2+x))**2+2*log(x))/(x+1),x)
 

           x                 2      2
         ++  (- %K - 1)log(%K  + %K)  + 2log(%K)
   (1)   |   ----------------------------------- d%K
        ++                  %K + 1
                                          Type: Union(Expression Integer,...)
--R
--R           x                 2      2
--I         ++  (- %K - 1)log(%K  + %K)  + 2log(%K)
--I   (1)   |   ----------------------------------- d%K
--I        ++                  %K + 1
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 123 of 267
t1:=i::POLY INT
 

   (1)  i
                                                     Type: Polynomial Integer
--R
--R   (1)  i
--R                                                     Type: Polynomial Integer
--E

--S 124 of 267
t2:=t1::Union(s:Symbol, p:POLY INT)
 

   (2)  i
                                       Type: Union(p: Polynomial Integer,...)
--R
--R   (2)  i
--R                                       Type: Union(p: Polynomial Integer,...)
--E

--S 125 of 267
list t2
 

   (3)  [i]
                            Type: List Union(s: Symbol,p: Polynomial Integer)
--R
--R   (3)  [i]
--R                            Type: List Union(s: Symbol,p: Polynomial Integer)
--E

)clear all
 

--S 126 of 267
I:=operator 'I
 

   (1)  I
                                                          Type: BasicOperator
--R
--R   (1)  I
--R                                                          Type: BasicOperator
--E

--S 127 of 267
J:=operator 'J
 

   (2)  J
                                                          Type: BasicOperator
--R
--R   (2)  J
--R                                                          Type: BasicOperator
--E

--S 128 of 267
eq := mu * D(I x,x) = - (K + S) * I(x) + S*J(x)
 

           ,
   (3)  muI (x)= S J(x) + (- S - K)I(x)

                                            Type: Equation Expression Integer
--R
--R           ,
--R   (3)  muI (x)= S J(x) + (- S - K)I(x)
--R
--R                                            Type: Equation Expression Integer
--E

--S 129 of 267
solve(eq,I,x)
 

   (4)
                  (- S - K)x                                       (- S - K)x
                  ----------   x                                   ----------
                      mu     ++        S J(%K)                         mu
   [particular= %e           |   ------------------ d%K ,basis= [%e          ]]
                            ++        - %K S - %K K
                                      -------------
                                            mu
                                 mu %e
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (4)
--R                  (- S - K)x                                       (- S - K)x
--R                  ----------   x                                   ----------
--I                      mu     ++        S J(%K)                         mu
--I   [particular= %e           |   ------------------ d%K ,basis= [%e          ]]
--I                            ++        - %K S - %K K
--R                                      -------------
--R                                            mu
--R                                 mu %e
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E

)clear all
 

--S 130 of 267
ofile: File String := open("/tmp/test","output")
 

   (1)  "/tmp/test"
                                                            Type: File String
--R
--R   (1)  "/tmp/test"
--R                                                            Type: File String
--E


--S 131 of 267
write!(ofile,"\\test"::String)
 

   (2)  "\\test"
                                                                 Type: String
--R
--R   (2)  "\\test"
--R                                                                 Type: String
--E

--S 132 of 267
close! ofile
 

   (3)  "/tmp/test"
                                                            Type: File String
--R
--R   (3)  "/tmp/test"
--R                                                            Type: File String
--E

)clear all
 

--S 133 of 267
pol:DMP([x,y,z],PF(2)):=x**2*y**2+x**2*y*z+x**2*z**2+x*y*z**2+y**3*z+y*z**3
 

         2 2    2       2 2        2    3       3
   (1)  x y  + x y z + x z  + x y z  + y z + y z
                Type: DistributedMultivariatePolynomial([x,y,z],PrimeField 2)
--R
--R         2 2    2       2 2        2    3       3
--R   (1)  x y  + x y z + x z  + x y z  + y z + y z
--R                Type: DistributedMultivariatePolynomial([x,y,z],PrimeField 2)
--E

--S 134 of 267
factor pol
 

         2 2    2       2 2        2    3       3
   (2)  x y  + x y z + x z  + x y z  + y z + y z
       Type: Factored DistributedMultivariatePolynomial([x,y,z],PrimeField 2)
--R
--R         2 2    2       2 2        2    3       3
--R   (2)  x y  + x y z + x z  + x y z  + y z + y z
--R       Type: Factored DistributedMultivariatePolynomial([x,y,z],PrimeField 2)
--E

)clear all
 

--S 135 of 267
up := UP('w,FRAC INT)
 

   (1)  UnivariatePolynomial(w,Fraction Integer)
                                                                 Type: Domain
--R
--R   (1)  UnivariatePolynomial(w,Fraction Integer)
--R                                                                 Type: Domain
--E

--S 136 of 267
p : up := w**4 + w**3 + w**2 + w + 1
 

         4    3    2
   (2)  w  + w  + w  + w + 1
                               Type: UnivariatePolynomial(w,Fraction Integer)
--R
--R         4    3    2
--R   (2)  w  + w  + w  + w + 1
--R                               Type: UnivariatePolynomial(w,Fraction Integer)
--E

--S 137 of 267
sae := SAE(FRAC INT,up,p)
 

   (3)
  SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Int
  eger),w**4+w**3+w*w+w+1)
                                                                 Type: Domain
--R
--R   (3)
--R  SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Int
--R  eger),w**4+w**3+w*w+w+1)
--R                                                                 Type: Domain
--E

--S 138 of 267
q : UP('x,sae) := x**5 - 1
 

         5
   (4)  x  - 1
Type: UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1))
--R
--R         5
--R   (4)  x  - 1
--RType: UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1))
--E

--S 139 of 267
factor q 
 

                            2       3       3    2
   (5)  (x - 1)(x - w)(x - w )(x - w )(x + w  + w  + w + 1)
Type: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1))
--R
--R                            2       3       3    2
--R   (5)  (x - 1)(x - w)(x - w )(x - w )(x + w  + w  + w + 1)
--RType: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1))
--E

--S 140 of 267
saefact := SAEFACT(up,sae,UP('x,sae))
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R
--R   (6)
--R  SimpleAlgebraicExtensionAlgFactor(UnivariatePolynomial(w,Fraction Integer),Si
--R  mpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integ
--R  er),w**4+w**3+w*w+w+1),UnivariatePolynomial(x,SimpleAlgebraicExtension(Fracti
--R  on Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1)))
--R                                                                 Type: Domain
--E

--S 141 of 267
factor(q)$saefact
 

                            2       3       3    2
   (6)  (x - 1)(x - w)(x - w )(x - w )(x + w  + w  + w + 1)
Type: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1))
--R
--R                            2       3       3    2
--R   (7)  (x - 1)(x - w)(x - w )(x - w )(x + w  + w  + w + 1)
--RType: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(w,Fraction Integer),w**4+w**3+w*w+w+1))
--E

)clear all
 

--S 142 of 267
10::RadixExpansion(16)
 

   (1)  A
                                                      Type: RadixExpansion 16
--R
--R   (1)  A
--R                                                      Type: RadixExpansion 16
--E

)clear all
 

--S 143 of 267
r:=rule 'x == 1
 

   (1)  x == 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (1)  x == 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 144 of 267
r x
 

   (2)  1
                                                     Type: Expression Integer
--R
--R   (2)  1
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 145 of 267
t1:=factor(-12)
 

           2
   (1)  - 2 3
                                                       Type: Factored Integer
--R
--R           2
--R   (1)  - 2 3
--R                                                       Type: Factored Integer
--E

--S 146 of 267
t1**2
 

         4 2
   (2)  2 3
                                                       Type: Factored Integer
--R
--R         4 2
--R   (2)  2 3
--R                                                       Type: Factored Integer
--E

)clear all
 

--S 147 of 267
complexNumeric(log(sqrt(-3)))
 

   (1)  0.5493061443 340548457 + 1.5707963267 948966192 %i
                                                          Type: Complex Float
--R
--R   (1)  0.5493061443 340548457 + 1.5707963267 948966192 %i
--R                                                          Type: Complex Float
--E

\begin{verbatim}
 
   There are no library operations named begin 
      Use HyperDoc Browse or issue
                               )what op begin
      to learn if there is any operation containing " begin " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named begin
      with argument type(s) 
                              Variable verbatim
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
)clear all
 
)sys rm -f /tmp/tpd.spad
 
)lisp (setq ofile (open "/tmp/tpd.spad" :direction :output))
 
Value = #<output stream "/tmp/tpd.spad">
)lisp (format ofile ")abbreviation package TPD Tpd~%")
 
Value = NIL
)lisp (format ofile "Tpd() : with~%")
 
Value = NIL
)lisp (format ofile "   leftProductBy : Integer -> (Integer -> Integer)~%")
 
Value = NIL
)lisp (format ofile "   rightProductBy : Integer -> Mapping(Integer, Integer)~%")
 
Value = NIL
)lisp (format ofile "  == add~%")
 
Value = NIL
)lisp (format ofile "   leftProductBy(n) == n * #1~%")
 
Value = NIL
)lisp (format ofile "   rightProductBy(n : Integer) : Mapping(Integer, Integer) == #1 * n~%")
 
Value = NIL
)lisp (close ofile)
 
Value = T
)compile /tmp/tpd.spad
 
   Compiling AXIOM source code from file /tmp/tpd.spad using old system
      compiler.
   TPD abbreviates package Tpd 
------------------------------------------------------------------------
   initializing nrlib TPD for Tpd 
   compiling into nrlib TPD 
   compiling exported leftProductBy : Integer -> Integer -> Integer
Time: 0 SEC.

   compiling exported rightProductBy : Integer -> Integer -> Integer
Time: 0 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |Tpd| REDEFINED

;;;     ***       |Tpd| REDEFINED
Time: 0.04 SEC.


   Cumulative Statistics for Constructor Tpd
      Time: 0.04 seconds
 
   finalizing nrlib TPD 
   Processing Tpd for Browser database:
--->-->Tpd((leftProductBy ((Mapping (Integer) (Integer)) (Integer)))): Not documented!!!!
--->-->Tpd((rightProductBy ((Mapping (Integer) (Integer)) (Integer)))): Not documented!!!!
--->-->Tpd(constructor): Not documented!!!!
--->-->Tpd(): Missing Description
------------------------------------------------------------------------
   Tpd is now explicitly exposed in frame initial 
   Tpd will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/TPD.nrlib/code

)sys rm -f /tmp/tpd.spad
 
)sys rm -rf /tmp/TPD.nrlib
 

)clear all
 

--S 148 of 267
sqrt(-1::EXPR FLOAT)
 

         +-----+
   (1)  \|- 1.0
                                                       Type: Expression Float
--R
--R         +-----+
--R   (1)  \|- 1.0
--R                                                       Type: Expression Float
--E

--S 149 of 267
sqrt(2::EXPR FLOAT)
 

   (2)  1.4142135623 730950488
                                                       Type: Expression Float
--R 
--R
--R   (2)  1.4142135623 730950488
--R                                                       Type: Expression Float
--E

--S 150 of 267
nthRoot(-2::EXPR FLOAT, 3)
 

   (3)  - 1.2599210498 948731648
                                                       Type: Expression Float
--R
--R   (3)  - 1.2599210498 948731648
--R                                                       Type: Expression Float
--E

--S 151 of 267
nthRoot(-2::EXPR FLOAT, 4)
 

        4+-----+
   (4)  \|- 2.0
                                                       Type: Expression Float
--R
--R        4+-----+
--R   (4)  \|- 2.0
--R                                                       Type: Expression Float
--E

)clear all
 

--S 152 of 267
real abs(4 + %i * 5)
 

         +--+
   (1)  \|41
                                                     Type: Expression Integer
--R
--R         +--+
--R   (1)  \|41
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 153 of 267
exp(5/3*%i*%pi)
 

             +-+
        - %i\|3  + 1
   (1)  ------------
              2
                                             Type: Expression Complex Integer
--R
--R             +-+
--R        - %i\|3  + 1
--R   (1)  ------------
--R              2
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 154 of 267
exp(log(-1))
 

   (1)  - 1
                                                     Type: Expression Integer
--R
--R   (1)  - 1
--R                                                     Type: Expression Integer
--E

--S 155 of 267
sum((-1)**k * (k+m),k=0..n)
 

                          n
        (2n + 2m + 1)(- 1)  + 2m - 1
   (2)  ----------------------------
                      4
                                                     Type: Expression Integer
--R
--R                          n
--R        (2n + 2m + 1)(- 1)  + 2m - 1
--R   (2)  ----------------------------
--R                      4
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 156 of 267
abs((1/2)::EXPR(INT))
 

        1
   (1)  -
        2
                                                     Type: Expression Integer
--R
--R        1
--R   (1)  -
--R        2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 157 of 267
integrate(1/(x**2 + %i*a),x)
 

         +--+         +--+         +--+           +--+
         |%i          |%i          |%i            |%i
         |-- log(%i a |--  + x) -  |-- log(- %i a |--  + x)
        \| a         \| a         \| a           \| a
   (1)  ---------------------------------------------------
                                 2
                                  Type: Union(Expression Complex Integer,...)
--R
--R         +--+         +--+         +--+           +--+
--R         |%i          |%i          |%i            |%i
--R         |-- log(%i a |--  + x) -  |-- log(- %i a |--  + x)
--R        \| a         \| a         \| a           \| a
--R   (1)  ---------------------------------------------------
--R                                 2
--R                                  Type: Union(Expression Complex Integer,...)
--E

)clear all
 

--S 158 of 267
limit(1/2**n,n=%plusInfinity)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E

)clear all
 

--S 159 of 267
x := sqrt(-3) + sqrt 2 + sqrt(- exp a) + log(-a**2-1)
 

         +-----+
         |    a           2         +-+    +---+
   (1)  \|- %e   + log(- a  - 1) + \|2  + \|- 3
                                                     Type: Expression Integer
--R
--R         +-----+
--R         |    a           2         +-+    +---+
--R   (1)  \|- %e   + log(- a  - 1) + \|2  + \|- 3
--R                                                     Type: Expression Integer
--E

--S 160 of 267
real? x
 

   (2)  false
                                                                Type: Boolean
--R
--R   (2)  false
--R                                                                Type: Boolean
--E

--S 161 of 267
real x
 

             2         +-+
   (3)  log(a  + 1) + \|2
                                                     Type: Expression Integer
--R
--R             2         +-+
--R   (3)  log(a  + 1) + \|2
--R                                                     Type: Expression Integer
--E

--S 162 of 267
imag x
 

         +---+
         |  a     +-+
   (4)  \|%e   + \|3  + %pi
                                                     Type: Expression Integer
--R
--R         +---+
--R         |  a     +-+
--R   (4)  \|%e   + \|3  + %pi
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 163 of 267
haha := rule x*x == z
 

         2
   (1)  x  == z
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R         2
--R   (1)  x  == z
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 164 of 267
haha 4
 

   (2)  z
                                                     Type: Expression Integer
--R
--R   (2)  z
--R                                                     Type: Expression Integer
--E

--S 165 of 267
haha 3
 

   (3)  3
                                                     Type: Expression Integer
--R
--R   (3)  3
--R                                                     Type: Expression Integer
--E

--S 166 of 267
haha(4*z)
 

   (4)  z
                                                     Type: Expression Integer
--R
--R   (4)  z
--R                                                     Type: Expression Integer
--E

--S 167 of 267
haha(3*z)
 

   (5)  3z
                                                     Type: Expression Integer
--R
--R   (5)  3z
--R                                                     Type: Expression Integer
--E


--S 168 of 267
t1:=a*a + b*b + c**2 + d*d
 

         2    2    2    2
   (6)  d  + c  + b  + a
                                                     Type: Polynomial Integer
--R
--R         2    2    2    2
--R   (6)  d  + c  + b  + a
--R                                                     Type: Polynomial Integer
--E

--S 169 of 267
t2:=applyRules([haha], t1, 1)$APPRULE(INT,INT,EXPR INT)
 

   (7)  4z
                                                     Type: Expression Integer
--R
--R   (7)  4z
--R                                                     Type: Expression Integer
--E

--S 170 of 267
t3:=applyRules([haha], t2, 1)$APPRULE(INT,INT,EXPR INT)
 

         2
   (8)  z
                                                     Type: Expression Integer
--R
--R         2
--R   (8)  z
--R                                                     Type: Expression Integer
--E

--S 171 of 267
t4:=applyRules([haha], t3, 1)$APPRULE(INT,INT,EXPR INT)
 

   (9)  z
                                                     Type: Expression Integer
--R
--R   (9)  z
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 172 of 267
harm(1) == 1
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 173 of 267
harm(n) == harm(n-1) + 1/n
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 174 of 267
harm : Integer -> Fraction Integer
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

--S 175 of 267
harm(1023)
 
   Compiling function harm with type Integer -> Fraction Integer 
   Compiling function harm as a recurrence relation.

   (4)
    56918929836783747778186562994910417364284519936484803738256503363047591584_
     2733402533503384016070102378254838554019021072460441324115730731899754524_
     3051637047716166927952839924926898113855910441901034429495456850574721819_
     0959291999714039498339199810512595613399980225816207570338522992407348206_
     8458996501642275777927445608416707051265982507444007863105751583310646982_
     3197880912123301992627534179914738912810939235218743092316208657821544413_
     7507111
  /
    75809030906834453523777687598142141106414192506285711254121803198491495253_
     8828569124484088941284219071465702944545255084351101237230340026626588247_
     6367291194600696876416243191521584529737974727209031624214028323361847170_
     9764957043186933388156027004157275042770718773974970630837005685761111898_
     3824612373575784564285126841732340269099782510311467722310664215128464192_
     0090417465131869897386008931792841181410706392968052396422445537614139284_
     160000
                                                       Type: Fraction Integer
--R   Compiling function harm with type Integer -> Fraction Integer 
--R   Compiling function harm as a recurrence relation.
--R
--R   (4)
--R    56918929836783747778186562994910417364284519936484803738256503363047591584_
--R     2733402533503384016070102378254838554019021072460441324115730731899754524_
--R     3051637047716166927952839924926898113855910441901034429495456850574721819_
--R     0959291999714039498339199810512595613399980225816207570338522992407348206_
--R     8458996501642275777927445608416707051265982507444007863105751583310646982_
--R     3197880912123301992627534179914738912810939235218743092316208657821544413_
--R     7507111
--R  /
--R    75809030906834453523777687598142141106414192506285711254121803198491495253_
--R     8828569124484088941284219071465702944545255084351101237230340026626588247_
--R     6367291194600696876416243191521584529737974727209031624214028323361847170_
--R     9764957043186933388156027004157275042770718773974970630837005685761111898_
--R     3824612373575784564285126841732340269099782510311467722310664215128464192_
--R     0090417465131869897386008931792841181410706392968052396422445537614139284_
--R     160000
--R                                                       Type: Fraction Integer
--E

--S 176 of 267
harm(1024)
 

   (5)
    11385266612491648666057698881942984686550388639494349140449232739078238853_
     8713454502191389383076154933054707275314439864005454497269185801458595955_
     4127443958199377930451435489735214028719028533199097687298001800355635024_
     8967439746760057644460577384504944069458175160764295712712838133748769663_
     0859452124788876557627760315566968995024077356615956093475101696822581124_
     2802077948390776255359440156469896861491512274902986275736609357453715408_
     90803597
  /
    15161806181366890704755537519628428221282838501257142250824360639698299050_
     7765713824896817788256843814293140588909051016870220247446068005325317649_
     5273458238920139375283248638304316905947594945441806324842805664672369434_
     1952991408637386677631205400831455008554143754794994126167401137152222379_
     6764922474715156912857025368346468053819956502062293544462132843025692838_
     4018083493026373979477201786358568236282141278593610479284489107522827856_
     8320000
                                                       Type: Fraction Integer
--R
--R   (5)
--R    11385266612491648666057698881942984686550388639494349140449232739078238853_
--R     8713454502191389383076154933054707275314439864005454497269185801458595955_
--R     4127443958199377930451435489735214028719028533199097687298001800355635024_
--R     8967439746760057644460577384504944069458175160764295712712838133748769663_
--R     0859452124788876557627760315566968995024077356615956093475101696822581124_
--R     2802077948390776255359440156469896861491512274902986275736609357453715408_
--R     90803597
--R  /
--R    15161806181366890704755537519628428221282838501257142250824360639698299050_
--R     7765713824896817788256843814293140588909051016870220247446068005325317649_
--R     5273458238920139375283248638304316905947594945441806324842805664672369434_
--R     1952991408637386677631205400831455008554143754794994126167401137152222379_
--R     6764922474715156912857025368346468053819956502062293544462132843025692838_
--R     4018083493026373979477201786358568236282141278593610479284489107522827856_
--R     8320000
--R                                                       Type: Fraction Integer
--E

)clear all
 

--S 177 of 267
t1:=series(x**x,x=0)
 

   (1)
                         2            3            4            5
                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
                      2            6            24          120
   + 
           6            7            8            9            10
     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
       720          5040        40320        362880       3628800
                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--R
--R   (1)
--R                         2            3            4            5
--R                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
--R     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
--R                      2            6            24          120
--R   + 
--R           6            7            8            9            10
--R     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
--R     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
--R       720          5040        40320        362880       3628800
--R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--E


--S 178 of 267
differentiate t1
 
   >> Error detected within library code:
   "'differentiate' unavailable on this domain;  use 'approximate' first"
 
  Line2689: --R
  Line2690: --R   (1)
  Line2691: --R                         2            3            4            5
  Line2692: --R                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
  Line2693: --R     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
  Line2694: --R                      2            6            24          120
  Line2695: --R   + 
  Line2696: --R           6            7            8            9            10
  Line2697: --R     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
  Line2698: --R     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
  Line2699: --R       720          5040        40320        362880       3628800
  Line2700: --R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
  Line2701: --E
  Line2702: 
  Line2703: 
  Line2704: --S 178 of 267
  Line2705: differentiate t1
  Line2706:  
  Line2707:    >> Error detected within library code:
           ...A....................................B
  Error  A: (from #\A up to #\B) Ignored.
  Error  B: Improper syntax.
  Line2708:    "'differentiate' unavailable on this domain;  use 'approximate' first"
   2 error(s) parsing 

--E

)clear all
 

--S 179 of 267
t1:=laurent(cos(a+x)/x,x=0)
 

   (1)
            - 1            cos(a)     sin(a)  2   cos(a)  3   sin(a)  4
     cos(a)x    - sin(a) - ------ x + ------ x  + ------ x  - ------ x
                              2          6          24          120
   + 
       cos(a)  5   sin(a)  6   cos(a)  7   sin(a)  8    cos(a)  9      10
     - ------ x  + ------ x  + ------ x  - ------ x  - ------- x  + O(x  )
         720        5040        40320      362880      3628800
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R
--R   (1)
--R            - 1            cos(a)     sin(a)  2   cos(a)  3   sin(a)  4
--R     cos(a)x    - sin(a) - ------ x + ------ x  + ------ x  - ------ x
--R                              2          6          24          120
--R   + 
--R       cos(a)  5   sin(a)  6   cos(a)  7   sin(a)  8    cos(a)  9      10
--R     - ------ x  + ------ x  + ------ x  - ------ x  - ------- x  + O(x  )
--R         720        5040        40320      362880      3628800
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E

--S 180 of 267
approximate(t1,3)
 

           3                  4      2
        (4x  - 24x)sin(a) + (x  - 12x  + 24)cos(a)
   (2)  ------------------------------------------
                            24x
                                                     Type: Expression Integer
--R
--R           3                  4      2
--R        (4x  - 24x)sin(a) + (x  - 12x  + 24)cos(a)
--R   (2)  ------------------------------------------
--R                            24x
--R                                                     Type: Expression Integer
--E


--S 181 of 267
t2:=puiseux(cos(a+x)/x,x=0)
 

   (3)
            - 1            cos(a)     sin(a)  2   cos(a)  3   sin(a)  4
     cos(a)x    - sin(a) - ------ x + ------ x  + ------ x  - ------ x
                              2          6          24          120
   + 
       cos(a)  5   sin(a)  6   cos(a)  7   sin(a)  8    cos(a)  9      10
     - ------ x  + ------ x  + ------ x  - ------ x  - ------- x  + O(x  )
         720        5040        40320      362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R
--R   (3)
--R            - 1            cos(a)     sin(a)  2   cos(a)  3   sin(a)  4
--R     cos(a)x    - sin(a) - ------ x + ------ x  + ------ x  - ------ x
--R                              2          6          24          120
--R   + 
--R       cos(a)  5   sin(a)  6   cos(a)  7   sin(a)  8    cos(a)  9      10
--R     - ------ x  + ------ x  + ------ x  - ------ x  - ------- x  + O(x  )
--R         720        5040        40320      362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E

--S 182 of 267
approximate(t2,3)
 

           3                  4      2
        (4x  - 24x)sin(a) + (x  - 12x  + 24)cos(a)
   (4)  ------------------------------------------
                            24x
                                                     Type: Expression Integer
--R
--R           3                  4      2
--R        (4x  - 24x)sin(a) + (x  - 12x  + 24)cos(a)
--R   (4)  ------------------------------------------
--R                            24x
--R                                                     Type: Expression Integer
--E

--S 183 of 267
t3:=series(cos(x**(2/3) + a),x=0)
 

   (5)
                   2           4                       8           10      11
                   -           -                       -           --      --
                   3   cos(a)  3   sin(a)  2   cos(a)  3   sin(a)   3       3
   cos(a) - sin(a)x  - ------ x  + ------ x  + ------ x  - ------ x   + O(x  )
                          2           6          24          120
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R
--R   (5)
--R                   2           4                       8           10      11
--R                   -           -                       -           --      --
--R                   3   cos(a)  3   sin(a)  2   cos(a)  3   sin(a)   3       3
--R   cos(a) - sin(a)x  - ------ x  + ------ x  + ------ x  - ------ x   + O(x  )
--R                          2           6          24          120
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E

--S 184 of 267
approximate(t3,2)
 

                 3+-+2            3+-+    2
        - 6sin(a)\|x   - 3x cos(a)\|x  + x sin(a) + 6cos(a)
   (6)  ---------------------------------------------------
                                 6
                                                     Type: Expression Integer
--R
--R                 3+-+2            3+-+    2
--R        - 6sin(a)\|x   - 3x cos(a)\|x  + x sin(a) + 6cos(a)
--R   (6)  ---------------------------------------------------
--R                                 6
--R                                                     Type: Expression Integer
--E

--S 185 of 267
approximate(t1,7)
 

   (7)
          7       5        3
       (8x  - 336x  + 6720x  - 40320x)sin(a)
     + 
         8      6        4         2
       (x  - 56x  + 1680x  - 20160x  + 40320)cos(a)
  /
     40320x
                                                     Type: Expression Integer
--R
--R   (7)
--R          7       5        3
--R       (8x  - 336x  + 6720x  - 40320x)sin(a)
--R     + 
--R         8      6        4         2
--R       (x  - 56x  + 1680x  - 20160x  + 40320)cos(a)
--R  /
--R     40320x
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 186 of 267
sqrt(-1::EXPR FLOAT)
 

         +-----+
   (1)  \|- 1.0
                                                       Type: Expression Float
--R
--R         +-----+
--R   (1)  \|- 1.0
--R                                                       Type: Expression Float
--E

--S 187 of 267
sqrt(2::EXPR FLOAT)
 

   (2)  1.4142135623 730950488
                                                       Type: Expression Float
--R
--R   (2)  1.4142135623 730950488
--R                                                       Type: Expression Float
--E

--S 188 of 267
nthRoot(-2::EXPR FLOAT, 3)
 

   (3)  - 1.2599210498 948731648
                                                       Type: Expression Float
--R
--R   (3)  - 1.2599210498 948731648
--R                                                       Type: Expression Float
--E

--S 189 of 267
nthRoot(-2::EXPR FLOAT, 4)
 

        4+-----+
   (4)  \|- 2.0
                                                       Type: Expression Float
--R
--R        4+-----+
--R   (4)  \|- 2.0
--R                                                       Type: Expression Float
--E

)clear all
 

--S 190 of 267
integrate(1/(x*(log(x)**2+a**2-1)),x)
 

   (1)
                           +--------+                                +------+
               2    2      |   2           2                         | 2
        (log(x)  - a  + 1)\|- a  + 1  + (2a  - 2)log(x)       log(x)\|a  - 1
    log(-----------------------------------------------) atan(---------------)
                              2    2                                2
                        log(x)  + a  - 1                           a  - 1
   [----------------------------------------------------,---------------------]
                          +--------+                            +------+
                          |   2                                 | 2
                        2\|- a  + 1                            \|a  - 1
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R                           +--------+                                +------+
--R               2    2      |   2           2                         | 2
--R        (log(x)  - a  + 1)\|- a  + 1  + (2a  - 2)log(x)       log(x)\|a  - 1
--R    log(-----------------------------------------------) atan(---------------)
--R                              2    2                                2
--R                        log(x)  + a  - 1                           a  - 1
--R   [----------------------------------------------------,---------------------]
--R                          +--------+                            +------+
--R                          |   2                                 | 2
--R                        2\|- a  + 1                            \|a  - 1
--R                                     Type: Union(List Expression Integer,...)
--E

)clear all
 

--S 191 of 267
normalize(2**(1/2) + 2**(1/4)) 
 

        4+-+2   4+-+
   (1)  \|2   + \|2
                                                     Type: Expression Integer
--R
--R        4+-+2   4+-+
--R   (1)  \|2   + \|2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 912 of 267
integrate(%e**x,x=0..1)
 

   (1)  %e - 1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R   (1)  %e - 1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E

--S 913 of 267
integrate(log(x),x=1..2)
 

   (2)  log(4) - 1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R   (2)  log(4) - 1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E

)clear all
 

--S 194 of 267
simplify(2**(1/3)*2**(1/2)) -- 
 

        6+-+5
   (1)  \|2
                                                     Type: Expression Integer
--R
--R        6+-+5
--R   (1)  \|2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 195 of 267
integrate(1/sqrt(1+cos(x)), x)
 

                  +-+       +----------+         2
         +-+    2\|2 sin(x)\|cos(x) + 1  - cos(x)  + 2cos(x) + 3
        \|2 log(------------------------------------------------)
                                    2
                              cos(x)  + 2cos(x) + 1
   (1)  ---------------------------------------------------------
                                    2
                                          Type: Union(Expression Integer,...)
--R
--R                  +-+       +----------+         2
--R         +-+    2\|2 sin(x)\|cos(x) + 1  - cos(x)  + 2cos(x) + 3
--R        \|2 log(------------------------------------------------)
--R                                    2
--R                              cos(x)  + 2cos(x) + 1
--R   (1)  ---------------------------------------------------------
--R                                    2
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 196 of 267
normalize atan(cos(x)/sin(x))
 

        - 2x + %pi
   (1)  ----------
             2
                                                     Type: Expression Integer
--R
--R        - 2x + %pi
--R   (1)  ----------
--R             2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 197 of 267
a := 2**(1/6)
 

        6+-+
   (1)  \|2
                                                        Type: AlgebraicNumber
--R
--R        6+-+
--R   (1)  \|2
--R                                                        Type: AlgebraicNumber
--E

--S 198 of 267
[a**n for n in 2..13]
 

         6+-+2 6+-+3 6+-+4 6+-+5    6+-+  6+-+2  6+-+3  6+-+4  6+-+5    6+-+
   (2)  [\|2  ,\|2  ,\|2  ,\|2  ,2,2\|2 ,2\|2  ,2\|2  ,2\|2  ,2\|2  ,4,4\|2 ]
                                                   Type: List AlgebraicNumber
--R
--R         6+-+2 6+-+3 6+-+4 6+-+5    6+-+  6+-+2  6+-+3  6+-+4  6+-+5    6+-+
--R   (2)  [\|2  ,\|2  ,\|2  ,\|2  ,2,2\|2 ,2\|2  ,2\|2  ,2\|2  ,2\|2  ,4,4\|2 ]
--R                                                   Type: List AlgebraicNumber
--E

)clear all
 

--S 199 of 267
int:=sqrt(a*(1-u**2)/(1+u**2))/u
 

         +----------+
         |     2
         |- a u  + a
         |----------
         |   2
        \|  u  + 1
   (1)  -------------
              u
                                                     Type: Expression Integer
--R
--R         +----------+
--R         |     2
--R         |- a u  + a
--R         |----------
--R         |   2
--R        \|  u  + 1
--R   (1)  -------------
--R              u
--R                                                     Type: Expression Integer
--E

--S 200 of 267
integrate(eval(int,a=1),u) 
 

                     +--------+                       +--------+
                     |   2                            |   2
              2      |- u  + 1                 2      |- u  + 1
            (u  + 1) |--------  - 1          (u  + 1) |--------  - 1
                     |  2                             |  2
                    \| u  + 1                        \| u  + 1
        log(-----------------------) + 2atan(-----------------------)
                        2                                2
                       u                                u
   (2)  -------------------------------------------------------------
                                      2
                                          Type: Union(Expression Integer,...)
--R
--R                     +--------+                       +--------+
--R                     |   2                            |   2
--R              2      |- u  + 1                 2      |- u  + 1
--R            (u  + 1) |--------  - 1          (u  + 1) |--------  - 1
--R                     |  2                             |  2
--R                    \| u  + 1                        \| u  + 1
--R        log(-----------------------) + 2atan(-----------------------)
--R                        2                                2
--R                       u                                u
--R   (2)  -------------------------------------------------------------
--R                                      2
--R                                          Type: Union(Expression Integer,...)
--E

--S 201 of 267
integrate(eval(int,a=sqrt(-1)),u)
 

   (3)
             +---+      +-+
         (- \|- 1  + 1)\|2
      *
                                +----------------+
                                |    2      +---+
               2      +---+ +-+ |(- u  + 1)\|- 1       2      +---+    2
             (u  + 1)\|- 1 \|2  |----------------  + (u  - 1)\|- 1  + u  + 1
                                |      2
                               \|     u  + 1
         log(---------------------------------------------------------------)
                                        2 +---+ +-+
                                       u \|- 1 \|2
     + 
                                              +----------------+
                                              |    2      +---+
                             2      +---+ +-+ |(- u  + 1)\|- 1      +---+
                           (u  + 1)\|- 1 \|2  |----------------  - \|- 1  + 1
                                              |      2
         +---+      +-+                      \|     u  + 1
       (\|- 1  + 1)\|2 log(--------------------------------------------------)
                                               2 +---+ +-+
                                              u \|- 1 \|2
     + 
           +---+      +-+
         (\|- 1  - 1)\|2
      *
                                +----------------+
                                |    2      +---+
               2      +---+ +-+ |(- u  + 1)\|- 1         2      +---+    2
             (u  + 1)\|- 1 \|2  |----------------  + (- u  - 1)\|- 1  - u  + 1
                                |      2
                               \|     u  + 1
         log(-----------------------------------------------------------------)
                                         2 +---+ +-+
                                        u \|- 1 \|2
  /
     4
                                          Type: Union(Expression Integer,...)
--R
--R   (3)
--R             +---+      +-+
--R         (- \|- 1  + 1)\|2
--R      *
--R                                +----------------+
--R                                |    2      +---+
--R               2      +---+ +-+ |(- u  + 1)\|- 1       2      +---+    2
--R             (u  + 1)\|- 1 \|2  |----------------  + (u  - 1)\|- 1  + u  + 1
--R                                |      2
--R                               \|     u  + 1
--R         log(---------------------------------------------------------------)
--R                                        2 +---+ +-+
--R                                       u \|- 1 \|2
--R     + 
--R                                              +----------------+
--R                                              |    2      +---+
--R                             2      +---+ +-+ |(- u  + 1)\|- 1      +---+
--R                           (u  + 1)\|- 1 \|2  |----------------  - \|- 1  + 1
--R                                              |      2
--R         +---+      +-+                      \|     u  + 1
--R       (\|- 1  + 1)\|2 log(--------------------------------------------------)
--R                                               2 +---+ +-+
--R                                              u \|- 1 \|2
--R     + 
--R           +---+      +-+
--R         (\|- 1  - 1)\|2
--R      *
--R                                +----------------+
--R                                |    2      +---+
--R               2      +---+ +-+ |(- u  + 1)\|- 1         2      +---+    2
--R             (u  + 1)\|- 1 \|2  |----------------  + (- u  - 1)\|- 1  - u  + 1
--R                                |      2
--R                               \|     u  + 1
--R         log(-----------------------------------------------------------------)
--R                                         2 +---+ +-+
--R                                        u \|- 1 \|2
--R  /
--R     4
--R                                          Type: Union(Expression Integer,...)
--E

--S 202 of 267
integrate(eval(int,a=1)*(-1)**(1/4),u)
 

   (4)
                                            +--------+
                                            |   2
                               2      +---+ |- u  + 1     +---+    2
                             (u  + 1)\|- 1  |--------  - \|- 1  + u
                                            |  2
           +---+      +-+                  \| u  + 1
       (- \|- 1  + 1)\|2 log(---------------------------------------)
                                              2 +---+
                                             u \|- 1
     + 
                                    +--------+
                                    |   2
                             2      |- u  + 1
                           (u  + 1) |--------  - 1
                                    |  2
         +---+      +-+            \| u  + 1
       (\|- 1  + 1)\|2 log(-----------------------)
                                       2
                                      u
     + 
                                          +--------+
                                          |   2
                             2      +---+ |- u  + 1     +---+    2
                           (u  + 1)\|- 1  |--------  - \|- 1  - u
                                          |  2
         +---+      +-+                  \| u  + 1
       (\|- 1  - 1)\|2 log(---------------------------------------)
                                            2 +---+
                                           u \|- 1
  /
     4
                                          Type: Union(Expression Integer,...)
--R
--R   (4)
--R                                            +--------+
--R                                            |   2
--R                               2      +---+ |- u  + 1     +---+    2
--R                             (u  + 1)\|- 1  |--------  - \|- 1  + u
--R                                            |  2
--R           +---+      +-+                  \| u  + 1
--R       (- \|- 1  + 1)\|2 log(---------------------------------------)
--R                                              2 +---+
--R                                             u \|- 1
--R     + 
--R                                    +--------+
--R                                    |   2
--R                             2      |- u  + 1
--R                           (u  + 1) |--------  - 1
--R                                    |  2
--R         +---+      +-+            \| u  + 1
--R       (\|- 1  + 1)\|2 log(-----------------------)
--R                                       2
--R                                      u
--R     + 
--R                                          +--------+
--R                                          |   2
--R                             2      +---+ |- u  + 1     +---+    2
--R                           (u  + 1)\|- 1  |--------  - \|- 1  - u
--R                                          |  2
--R         +---+      +-+                  \| u  + 1
--R       (\|- 1  - 1)\|2 log(---------------------------------------)
--R                                            2 +---+
--R                                           u \|- 1
--R  /
--R     4
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 203 of 267
t1:=sqrt((1-x**2)*(1-k**2*x**2))
 

         +-----------------------+
         | 2 4       2      2
   (1)  \|k x  + (- k  - 1)x  + 1
                                                     Type: Expression Integer
--R
--R         +-----------------------+
--R         | 2 4       2      2
--R   (1)  \|k x  + (- k  - 1)x  + 1
--R                                                     Type: Expression Integer
--E

--S 204 of 267
integrate(x/t1,x)
 

                 +-----------------------+
                 | 2 4       2      2          2 2    2
          log(2k\|k x  + (- k  - 1)x  + 1  - 2k x  + k  + 1)
   (2)  - --------------------------------------------------
                                  2k
                                          Type: Union(Expression Integer,...)
--R
--R                 +-----------------------+
--R                 | 2 4       2      2          2 2    2
--R          log(2k\|k x  + (- k  - 1)x  + 1  - 2k x  + k  + 1)
--R   (2)  - --------------------------------------------------
--R                                  2k
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 205 of 267
t1:=last zerosOf((2+y)**8-3,y)
 

           +-------------+
           |    +-------+
           |    |    +-+
        - \|- 2\|- 4\|3    - 4
   (1)  ----------------------
                   2
                                                     Type: Expression Integer
--R
--R           +-------------+
--R           |    +-------+
--R           |    |    +-+
--R        - \|- 2\|- 4\|3    - 4
--R   (1)  ----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 206 of 267
k:=first kernels t1
 

         +-------------+
         |    +-------+
         |    |    +-+
   (2)  \|- 2\|- 4\|3
                                              Type: Kernel Expression Integer
--R
--R         +-------------+
--R         |    +-------+
--R         |    |    +-+
--R   (2)  \|- 2\|- 4\|3
--R                                              Type: Kernel Expression Integer
--E

--S 207 of 267
eval(t1,k,t1)
 

         +-------------+
         |    +-------+
         |    |    +-+
        \|- 2\|- 4\|3    - 4
   (3)  --------------------
                  4
                                                     Type: Expression Integer
--R
--R         +-------------+
--R         |    +-------+
--R         |    |    +-+
--R        \|- 2\|- 4\|3    - 4
--R   (3)  --------------------
--R                  4
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 208 of 267
f := (x - y) / (x + y)
 

        - y + x
   (1)  -------
         y + x
                                            Type: Fraction Polynomial Integer
--R
--R        - y + x
--R   (1)  -------
--R         y + x
--R                                            Type: Fraction Polynomial Integer
--E

--S 209 of 267
eval(f,x=1/x)
 

        - x y + 1
   (2)  ---------
         x y + 1
                                            Type: Fraction Polynomial Integer
--R
--R        - x y + 1
--R   (2)  ---------
--R         x y + 1
--R                                            Type: Fraction Polynomial Integer
--E

)clear all
 

--S 210 of 267
digits 200
 

   (1)  20
                                                        Type: PositiveInteger
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E

--S 211 of 267
a:=4*sin(2*%pi/9)*sin(5*%pi/9)/sqrt(3)
 

             2%pi     5%pi
        4sin(----)sin(----)
               9        9
   (2)  -------------------
                 +-+
                \|3
                                                     Type: Expression Integer
--R
--R             2%pi     5%pi
--R        4sin(----)sin(----)
--R               9        9
--R   (2)  -------------------
--R                 +-+
--R                \|3
--R                                                     Type: Expression Integer
--E

--S 212 of 267
b:=1/(2*sin(%pi/9))
 

            1
   (3)  ---------
             %pi
        2sin(---)
              9
                                                     Type: Expression Integer
--R
--R            1
--R   (3)  ---------
--R             %pi
--R        2sin(---)
--R              9
--R                                                     Type: Expression Integer
--E

--S 213 of 267
a::EXPR FLOAT
 

   (4)
  1.4619022000 8154362611 6377206683 1458519367 5283075946 2240855318 493177672
  5 8139967590 4919627790 5155131563 5927196029 5136978338 4351923544 366777748
  4 3145835284 9347399264 0517928099 4530246377 7454860377 762537213
                                                       Type: Expression Float
--R
--R   (4)
--R  1.4619022000 8154362611 6377206683 1458519367 5283075946 2240855318 493177672
--R  5 8139967590 4919627790 5155131563 5927196029 5136978338 4351923544 366777748
--R  4 3145835284 9347399264 0517928099 4530246377 7454860377 762537213
--R                                                       Type: Expression Float
--E

--S 214 of 267
b::EXPR FLOAT
 

   (5)
  1.4619022000 8154362611 6377206683 1458519367 5283075946 2240855318 493177672
  5 8139967590 4919627790 5155131563 5927196029 5136978338 4351923544 366777748
  4 3145835284 9347399264 0517928099 4530246377 7454860377 762537213
                                                       Type: Expression Float
--R
--R   (5)
--R  1.4619022000 8154362611 6377206683 1458519367 5283075946 2240855318 493177672
--R  5 8139967590 4919627790 5155131563 5927196029 5136978338 4351923544 366777748
--R  4 3145835284 9347399264 0517928099 4530246377 7454860377 762537213
--R                                                       Type: Expression Float
--E

--S 215 of 267
digits 20
 

   (6)  200
                                                        Type: PositiveInteger
--R
--R   (6)  200
--R                                                        Type: PositiveInteger
--E
)clear all
 

--S 216 of 267
limit(tanh(x),x=%plusInfinity)
 

   (1)  1
                        Type: Union(OrderedCompletion Expression Integer,...)
--R
--R   (1)  1
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E

)clear all
 

--S 217 of 267
a := x::EXPR INT
 

   (1)  x
                                                     Type: Expression Integer
--R
--R   (1)  x
--R                                                     Type: Expression Integer
--E

--S 218 of 267
b := x::EXPR COMPLEX INT
 

   (2)  x
                                             Type: Expression Complex Integer
--R
--R   (2)  x
--R                                             Type: Expression Complex Integer
--E

--S 219 of 267
zeroOf(a**4+1,x)
 

         +---+
        \|- 1  + 1
   (3)  ----------
            +-+
           \|2
                                                     Type: Expression Integer
--R
--R         +---+
--R        \|- 1  + 1
--R   (3)  ----------
--R            +-+
--R           \|2
--R                                                     Type: Expression Integer
--E

--S 220 of 267
zeroOf(b**4+1,x)
 

        1 + %i
   (4)  ------
          +-+
         \|2
                                             Type: Expression Complex Integer
--R
--R        1 + %i
--R   (4)  ------
--R          +-+
--R         \|2
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 221 of 267
normalize(0**a)
 

   (1)  0
                                                     Type: Expression Integer
--R
--R   (1)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 222 of 267
t1:=log(a+%i * b)
 

   (1)  log(%i b + a)
                                             Type: Expression Complex Integer
--R
--R   (1)  log(%i b + a)
--R                                             Type: Expression Complex Integer
--E

--S 223 of 267
complexForm t1
 

             2    2
        log(b  + a )        b
   (2)  ------------ + atan(-)%i
              2             a
                                             Type: Complex Expression Integer
--R
--R             2    2
--R        log(b  + a )        b
--R   (2)  ------------ + atan(-)%i
--R              2             a
--R                                             Type: Complex Expression Integer
--E

--S 224 of 267
t2:=complexIntegrate(1/(x-%i),x)
 

   (3)  log(x - %i)
                                             Type: Expression Complex Integer
--R
--R   (3)  log(x - %i)
--R                                             Type: Expression Complex Integer
--E

--S 225 of 267
complexForm t2
 

             2
        log(x  + 1)        1
   (4)  ----------- - atan(-)%i
             2             x
                                             Type: Complex Expression Integer
--R
--R             2
--R        log(x  + 1)        1
--R   (4)  ----------- - atan(-)%i
--R             2             x
--R                                             Type: Complex Expression Integer
--E

)clear all
 

--S 226 of 267
D:=DMP([a,b],INT)
 

   (1)  DistributedMultivariatePolynomial([a,b],Integer)
                                                                 Type: Domain
--R
--R   (1)  DistributedMultivariatePolynomial([a,b],Integer)
--R                                                                 Type: Domain
--E

--S 227 of 267
l:List D:=[2*a-1,b-a]
 

   (2)  [2a - 1,- a + b]
                  Type: List DistributedMultivariatePolynomial([a,b],Integer)
--R
--R   (2)  [2a - 1,- a + b]
--R                  Type: List DistributedMultivariatePolynomial([a,b],Integer)
--E

--S 228 of 267
g:=groebner l
 

   (3)  [2a - 1,2b - 1]
                  Type: List DistributedMultivariatePolynomial([a,b],Integer)
--R
--R   (3)  [2a - 1,2b - 1]
--R                  Type: List DistributedMultivariatePolynomial([a,b],Integer)
--E

--S 229 of 267
p:D:=a
 

   (4)  a
                       Type: DistributedMultivariatePolynomial([a,b],Integer)
--R
--R   (4)  a
--R                       Type: DistributedMultivariatePolynomial([a,b],Integer)
--E

--S 230 of 267
normalForm(p,g)
 

        1
   (5)  -
        2
              Type: DistributedMultivariatePolynomial([a,b],Fraction Integer)
--R
--R        1
--R   (5)  -
--R        2
--R              Type: DistributedMultivariatePolynomial([a,b],Fraction Integer)
--E

)clear all
 

--S 231 of 267
squareFreePart(50)
 

   (1)  10
                                                        Type: PositiveInteger
--R
--R   (1)  10
--R                                                        Type: PositiveInteger
--E

)clear all
 

--S 232 of 267
f:=complexIntegrate(1/((x-%i)*(x-2*%i)),x)
 

   (1)  %i log(x - %i) - %i log(x - 2%i)
                                             Type: Expression Complex Integer
--R
--R   (1)  %i log(x - %i) - %i log(x - 2%i)
--R                                             Type: Expression Complex Integer
--E

--S 233 of 267
g:=subst(f,x=1)
 

   (2)  %i log(1 - %i) - %i log(1 - 2%i)
                                             Type: Expression Complex Integer
--R
--R   (2)  %i log(1 - %i) - %i log(1 - 2%i)
--R                                             Type: Expression Complex Integer
--E

--S 234 of 267
imag g
 

        - log(5) + log(2)
   (3)  -----------------
                2
                                                     Type: Expression Integer
--R
--R        - log(5) + log(2)
--R   (3)  -----------------
--R                2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 235 of 267
primes(1,10)
 

   (1)  [2,7,5,3]
                                                           Type: List Integer
--R
--R   (1)  [2,7,5,3]
--R                                                           Type: List Integer
--E

)clear all
 

--S 236 of 267
m:=matrix[[1,a,0],[b,0,a],[0,b,c]]
 

        +1  a  0+
        |       |
   (1)  |b  0  a|
        |       |
        +0  b  c+
                                              Type: Matrix Polynomial Integer
--R
--R        +1  a  0+
--R        |       |
--R   (1)  |b  0  a|
--R        |       |
--R        +0  b  c+
--R                                              Type: Matrix Polynomial Integer
--E

--S 237 of 267
ll:=radicalEigenvectors m
 

   (2)
   [
     [
       radval =
               9
            *
                 ROOT
                          9
                       *
                          ROOT
                                            4              3
                               (- 4a b - 1)c  + (6a b + 2)c
                             + 
                                     2 2             2       2 2
                               (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c
                             + 
                                    3 3      2 2
                               - 32a b  - 13a b  - 4a b
                      + 
                           3     2                             +-+
                        (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                   /
                         +-+
                      54\|3
                ,
                    3
              **
                 2
           + 
               (3c + 3)
            *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
           + 
              2
             c  - c + 6a b + 1
        /
             9
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
       ,
      radmult= 1,

       radvect =
         [
   [
     [
                                  +-+
             (- 18c + 18a b + 18)\|3
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                 9
              *
                 ROOT
                                   4              3         2 2             2
                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                    + 
                          2 2               3 3      2 2
                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
             + 
                  2                               +-+
               (3c  + (- 21a b - 9)c + 15a b + 6)\|3
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
             (- 3c + 6)
          *
             ROOT
                               4              3         2 2             2
                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                + 
                      2 2               3 3      2 2
                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
         + 
             3               2                       2 2             +-+
           (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|3
      /
              2 +-+
           54b \|3
        *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
          **
             2
       ]
     ,

     [
             9
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
             (- 6c + 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
            2
           c  - c + 6a b + 1
      /
           9b
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
       ]
     ,
    [1]]
           ]
       ]
     ,

     [
       radval =
                    +---+
               (- 9\|- 3  - 9)
            *
                 ROOT
                          9
                       *
                          ROOT
                                            4              3
                               (- 4a b - 1)c  + (6a b + 2)c
                             + 
                                     2 2             2       2 2
                               (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c
                             + 
                                    3 3      2 2
                               - 32a b  - 13a b  - 4a b
                      + 
                           3     2                             +-+
                        (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                   /
                         +-+
                      54\|3
                ,
                    3
              **
                 2
           + 
                         +---+
               ((3c + 3)\|- 3  - 3c - 3)
            *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
           + 
               2
             2c  - 2c + 12a b + 2
        /
                +---+
             (9\|- 3  - 9)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
       ,
      radmult= 1,

       radvect =
         [
   [
     [
                                  +-+
             (- 36c + 36a b + 36)\|3
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                      +---+
                 (- 9\|- 3  - 9)
              *
                 ROOT
                                   4              3         2 2             2
                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                    + 
                          2 2               3 3      2 2
                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
             + 
                        2                             +---+     2
                   (- 3c  + (21a b + 9)c - 15a b - 6)\|- 3  - 3c  + (21a b + 9)c
                 + 
                   - 15a b - 6
              *
                  +-+
                 \|3
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
                         +---+
             ((- 3c + 6)\|- 3  + 3c - 6)
          *
             ROOT
                               4              3         2 2             2
                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                + 
                      2 2               3 3      2 2
                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
         + 
                 3               2                       2 2             +---+
               (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|- 3
             + 
                  3                 2                     2 2
               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
          *
              +-+
             \|3
      /
               2 +-+
           108b \|3
        *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
          **
             2
       ]
     ,

     [
                  +---+
             (- 9\|- 3  - 9)
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                         +---+
             ((- 6c + 3)\|- 3  + 6c - 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
             2
           2c  - 2c + 12a b + 2
      /
               +---+
           (9b\|- 3  - 9b)
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
       ]
     ,
    [1]]
           ]
       ]
     ,

     [
       radval =
                    +---+
               (- 9\|- 3  + 9)
            *
                 ROOT
                          9
                       *
                          ROOT
                                            4              3
                               (- 4a b - 1)c  + (6a b + 2)c
                             + 
                                     2 2             2       2 2
                               (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c
                             + 
                                    3 3      2 2
                               - 32a b  - 13a b  - 4a b
                      + 
                           3     2                             +-+
                        (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                   /
                         +-+
                      54\|3
                ,
                    3
              **
                 2
           + 
                         +---+
               ((3c + 3)\|- 3  + 3c + 3)
            *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
           + 
                 2
             - 2c  + 2c - 12a b - 2
        /
                +---+
             (9\|- 3  + 9)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
       ,
      radmult= 1,

       radvect =
         [
   [
     [
                                  +-+
             (- 36c + 36a b + 36)\|3
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                    +---+
                 (9\|- 3  - 9)
              *
                 ROOT
                                   4              3         2 2             2
                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                    + 
                          2 2               3 3      2 2
                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
             + 
                      2                               +---+     2
                   (3c  + (- 21a b - 9)c + 15a b + 6)\|- 3  - 3c  + (21a b + 9)c
                 + 
                   - 15a b - 6
              *
                  +-+
                 \|3
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
                       +---+
             ((3c - 6)\|- 3  + 3c - 6)
          *
             ROOT
                               4              3         2 2             2
                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                + 
                      2 2               3 3      2 2
                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
         + 
                   3                 2                     2 2             +---+
               (- c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2)\|- 3
             + 
                  3                 2                     2 2
               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
          *
              +-+
             \|3
      /
               2 +-+
           108b \|3
        *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
          **
             2
       ]
     ,

     [
                  +---+
             (- 9\|- 3  + 9)
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                         +---+
             ((- 6c + 3)\|- 3  - 6c + 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
               2
           - 2c  + 2c - 12a b - 2
      /
               +---+
           (9b\|- 3  + 9b)
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
       ]
     ,
    [1]]
           ]
       ]
     ]
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R
--R   (2)
--R   [
--R     [
--R       radval =
--R               9
--R            *
--R                 ROOT
--R                          9
--R                       *
--R                          ROOT
--R                                            4              3
--R                               (- 4a b - 1)c  + (6a b + 2)c
--R                             + 
--R                                     2 2             2       2 2
--R                               (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c
--R                             + 
--R                                    3 3      2 2
--R                               - 32a b  - 13a b  - 4a b
--R                      + 
--R                           3     2                             +-+
--R                        (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                   /
--R                         +-+
--R                      54\|3
--R                ,
--R                    3
--R              **
--R                 2
--R           + 
--R               (3c + 3)
--R            *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R           + 
--R              2
--R             c  - c + 6a b + 1
--R        /
--R             9
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R       ,
--R      radmult= 1,
--R
--R       radvect =
--R         [
--R   [
--R     [
--R                                  +-+
--R             (- 18c + 18a b + 18)\|3
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                 9
--R              *
--R                 ROOT
--R                                   4              3         2 2             2
--R                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                    + 
--R                          2 2               3 3      2 2
--R                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R             + 
--R                  2                               +-+
--R               (3c  + (- 21a b - 9)c + 15a b + 6)\|3
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R             (- 3c + 6)
--R          *
--R             ROOT
--R                               4              3         2 2             2
--R                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                + 
--R                      2 2               3 3      2 2
--R                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R         + 
--R             3               2                       2 2             +-+
--R           (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|3
--R      /
--R              2 +-+
--R           54b \|3
--R        *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R          **
--R             2
--R       ]
--R     ,
--R
--R     [
--R             9
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R             (- 6c + 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R            2
--R           c  - c + 6a b + 1
--R      /
--R           9b
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R       ]
--R     ,
--R    [1]]
--R           ]
--R       ]
--R     ,
--R
--R     [
--R       radval =
--R                    +---+
--R               (- 9\|- 3  - 9)
--R            *
--R                 ROOT
--R                          9
--R                       *
--R                          ROOT
--R                                            4              3
--R                               (- 4a b - 1)c  + (6a b + 2)c
--R                             + 
--R                                     2 2             2       2 2
--R                               (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c
--R                             + 
--R                                    3 3      2 2
--R                               - 32a b  - 13a b  - 4a b
--R                      + 
--R                           3     2                             +-+
--R                        (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                   /
--R                         +-+
--R                      54\|3
--R                ,
--R                    3
--R              **
--R                 2
--R           + 
--R                         +---+
--R               ((3c + 3)\|- 3  - 3c - 3)
--R            *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R           + 
--R               2
--R             2c  - 2c + 12a b + 2
--R        /
--R                +---+
--R             (9\|- 3  - 9)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R       ,
--R      radmult= 1,
--R
--R       radvect =
--R         [
--R   [
--R     [
--R                                  +-+
--R             (- 36c + 36a b + 36)\|3
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                      +---+
--R                 (- 9\|- 3  - 9)
--R              *
--R                 ROOT
--R                                   4              3         2 2             2
--R                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                    + 
--R                          2 2               3 3      2 2
--R                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R             + 
--R                        2                             +---+     2
--R                   (- 3c  + (21a b + 9)c - 15a b - 6)\|- 3  - 3c  + (21a b + 9)c
--R                 + 
--R                   - 15a b - 6
--R              *
--R                  +-+
--R                 \|3
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R                         +---+
--R             ((- 3c + 6)\|- 3  + 3c - 6)
--R          *
--R             ROOT
--R                               4              3         2 2             2
--R                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                + 
--R                      2 2               3 3      2 2
--R                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R         + 
--R                 3               2                       2 2             +---+
--R               (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|- 3
--R             + 
--R                  3                 2                     2 2
--R               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
--R          *
--R              +-+
--R             \|3
--R      /
--R               2 +-+
--R           108b \|3
--R        *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R          **
--R             2
--R       ]
--R     ,
--R
--R     [
--R                  +---+
--R             (- 9\|- 3  - 9)
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                         +---+
--R             ((- 6c + 3)\|- 3  + 6c - 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R             2
--R           2c  - 2c + 12a b + 2
--R      /
--R               +---+
--R           (9b\|- 3  - 9b)
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R       ]
--R     ,
--R    [1]]
--R           ]
--R       ]
--R     ,
--R
--R     [
--R       radval =
--R                    +---+
--R               (- 9\|- 3  + 9)
--R            *
--R                 ROOT
--R                          9
--R                       *
--R                          ROOT
--R                                            4              3
--R                               (- 4a b - 1)c  + (6a b + 2)c
--R                             + 
--R                                     2 2             2       2 2
--R                               (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c
--R                             + 
--R                                    3 3      2 2
--R                               - 32a b  - 13a b  - 4a b
--R                      + 
--R                           3     2                             +-+
--R                        (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                   /
--R                         +-+
--R                      54\|3
--R                ,
--R                    3
--R              **
--R                 2
--R           + 
--R                         +---+
--R               ((3c + 3)\|- 3  + 3c + 3)
--R            *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R           + 
--R                 2
--R             - 2c  + 2c - 12a b - 2
--R        /
--R                +---+
--R             (9\|- 3  + 9)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R       ,
--R      radmult= 1,
--R
--R       radvect =
--R         [
--R   [
--R     [
--R                                  +-+
--R             (- 36c + 36a b + 36)\|3
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                    +---+
--R                 (9\|- 3  - 9)
--R              *
--R                 ROOT
--R                                   4              3         2 2             2
--R                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                    + 
--R                          2 2               3 3      2 2
--R                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R             + 
--R                      2                               +---+     2
--R                   (3c  + (- 21a b - 9)c + 15a b + 6)\|- 3  - 3c  + (21a b + 9)c
--R                 + 
--R                   - 15a b - 6
--R              *
--R                  +-+
--R                 \|3
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R                       +---+
--R             ((3c - 6)\|- 3  + 3c - 6)
--R          *
--R             ROOT
--R                               4              3         2 2             2
--R                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                + 
--R                      2 2               3 3      2 2
--R                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R         + 
--R                   3                 2                     2 2             +---+
--R               (- c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2)\|- 3
--R             + 
--R                  3                 2                     2 2
--R               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
--R          *
--R              +-+
--R             \|3
--R      /
--R               2 +-+
--R           108b \|3
--R        *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R          **
--R             2
--R       ]
--R     ,
--R
--R     [
--R                  +---+
--R             (- 9\|- 3  + 9)
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                         +---+
--R             ((- 6c + 3)\|- 3  - 6c + 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R               2
--R           - 2c  + 2c - 12a b - 2
--R      /
--R               +---+
--R           (9b\|- 3  + 9b)
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R       ]
--R     ,
--R    [1]]
--R           ]
--R       ]
--R     ]
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E


--S 238 of 267
ll 1
 

   (3)
   [
     radval =
             9
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
             (3c + 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
            2
           c  - c + 6a b + 1
      /
           9
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
     ,
    radmult= 1,

     radvect =
       [
   [
     [
                                  +-+
             (- 18c + 18a b + 18)\|3
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                 9
              *
                 ROOT
                                   4              3         2 2             2
                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                    + 
                          2 2               3 3      2 2
                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
             + 
                  2                               +-+
               (3c  + (- 21a b - 9)c + 15a b + 6)\|3
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
             (- 3c + 6)
          *
             ROOT
                               4              3         2 2             2
                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                + 
                      2 2               3 3      2 2
                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
         + 
             3               2                       2 2             +-+
           (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|3
      /
              2 +-+
           54b \|3
        *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
          **
             2
       ]
     ,

     [
             9
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
             (- 6c + 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
            2
           c  - c + 6a b + 1
      /
           9b
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
       ]
     ,
    [1]]
         ]
     ]
Type: Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R
--R   (3)
--R   [
--R     radval =
--R             9
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R             (3c + 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R            2
--R           c  - c + 6a b + 1
--R      /
--R           9
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R     ,
--R    radmult= 1,
--R
--R     radvect =
--R       [
--R   [
--R     [
--R                                  +-+
--R             (- 18c + 18a b + 18)\|3
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                 9
--R              *
--R                 ROOT
--R                                   4              3         2 2             2
--R                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                    + 
--R                          2 2               3 3      2 2
--R                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R             + 
--R                  2                               +-+
--R               (3c  + (- 21a b - 9)c + 15a b + 6)\|3
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R             (- 3c + 6)
--R          *
--R             ROOT
--R                               4              3         2 2             2
--R                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                + 
--R                      2 2               3 3      2 2
--R                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R         + 
--R             3               2                       2 2             +-+
--R           (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|3
--R      /
--R              2 +-+
--R           54b \|3
--R        *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R          **
--R             2
--R       ]
--R     ,
--R
--R     [
--R             9
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R             (- 6c + 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R            2
--R           c  - c + 6a b + 1
--R      /
--R           9b
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R       ]
--R     ,
--R    [1]]
--R         ]
--R     ]
--RType: Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E

--S 239 of 267
ll 2
 

   (4)
   [
     radval =
                  +---+
             (- 9\|- 3  - 9)
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                       +---+
             ((3c + 3)\|- 3  - 3c - 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
             2
           2c  - 2c + 12a b + 2
      /
              +---+
           (9\|- 3  - 9)
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
     ,
    radmult= 1,

     radvect =
       [
   [
     [
                                  +-+
             (- 36c + 36a b + 36)\|3
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                      +---+
                 (- 9\|- 3  - 9)
              *
                 ROOT
                                   4              3         2 2             2
                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                    + 
                          2 2               3 3      2 2
                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
             + 
                        2                             +---+     2
                   (- 3c  + (21a b + 9)c - 15a b - 6)\|- 3  - 3c  + (21a b + 9)c
                 + 
                   - 15a b - 6
              *
                  +-+
                 \|3
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
                         +---+
             ((- 3c + 6)\|- 3  + 3c - 6)
          *
             ROOT
                               4              3         2 2             2
                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                + 
                      2 2               3 3      2 2
                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
         + 
                 3               2                       2 2             +---+
               (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|- 3
             + 
                  3                 2                     2 2
               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
          *
              +-+
             \|3
      /
               2 +-+
           108b \|3
        *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
          **
             2
       ]
     ,

     [
                  +---+
             (- 9\|- 3  - 9)
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                         +---+
             ((- 6c + 3)\|- 3  + 6c - 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
             2
           2c  - 2c + 12a b + 2
      /
               +---+
           (9b\|- 3  - 9b)
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
       ]
     ,
    [1]]
         ]
     ]
Type: Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R
--R   (4)
--R   [
--R     radval =
--R                  +---+
--R             (- 9\|- 3  - 9)
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                       +---+
--R             ((3c + 3)\|- 3  - 3c - 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R             2
--R           2c  - 2c + 12a b + 2
--R      /
--R              +---+
--R           (9\|- 3  - 9)
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R     ,
--R    radmult= 1,
--R
--R     radvect =
--R       [
--R   [
--R     [
--R                                  +-+
--R             (- 36c + 36a b + 36)\|3
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                      +---+
--R                 (- 9\|- 3  - 9)
--R              *
--R                 ROOT
--R                                   4              3         2 2             2
--R                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                    + 
--R                          2 2               3 3      2 2
--R                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R             + 
--R                        2                             +---+     2
--R                   (- 3c  + (21a b + 9)c - 15a b - 6)\|- 3  - 3c  + (21a b + 9)c
--R                 + 
--R                   - 15a b - 6
--R              *
--R                  +-+
--R                 \|3
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R                         +---+
--R             ((- 3c + 6)\|- 3  + 3c - 6)
--R          *
--R             ROOT
--R                               4              3         2 2             2
--R                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                + 
--R                      2 2               3 3      2 2
--R                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R         + 
--R                 3               2                       2 2             +---+
--R               (c  + (11a b + 1)c  + (- 11a b - 4)c + 24a b  + 2a b + 2)\|- 3
--R             + 
--R                  3                 2                     2 2
--R               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
--R          *
--R              +-+
--R             \|3
--R      /
--R               2 +-+
--R           108b \|3
--R        *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R          **
--R             2
--R       ]
--R     ,
--R
--R     [
--R                  +---+
--R             (- 9\|- 3  - 9)
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                         +---+
--R             ((- 6c + 3)\|- 3  + 6c - 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R             2
--R           2c  - 2c + 12a b + 2
--R      /
--R               +---+
--R           (9b\|- 3  - 9b)
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R       ]
--R     ,
--R    [1]]
--R         ]
--R     ]
--RType: Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E

--S 240 of 267
ll 3
 

   (5)
   [
     radval =
                  +---+
             (- 9\|- 3  + 9)
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                       +---+
             ((3c + 3)\|- 3  + 3c + 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
               2
           - 2c  + 2c - 12a b - 2
      /
              +---+
           (9\|- 3  + 9)
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
     ,
    radmult= 1,

     radvect =
       [
   [
     [
                                  +-+
             (- 36c + 36a b + 36)\|3
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                    +---+
                 (9\|- 3  - 9)
              *
                 ROOT
                                   4              3         2 2             2
                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                    + 
                          2 2               3 3      2 2
                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
             + 
                      2                               +---+     2
                   (3c  + (- 21a b - 9)c + 15a b + 6)\|- 3  - 3c  + (21a b + 9)c
                 + 
                   - 15a b - 6
              *
                  +-+
                 \|3
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
                       +---+
             ((3c - 6)\|- 3  + 3c - 6)
          *
             ROOT
                               4              3         2 2             2
                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                + 
                      2 2               3 3      2 2
                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
         + 
                   3                 2                     2 2             +---+
               (- c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2)\|- 3
             + 
                  3                 2                     2 2
               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
          *
              +-+
             \|3
      /
               2 +-+
           108b \|3
        *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
          **
             2
       ]
     ,

     [
                  +---+
             (- 9\|- 3  + 9)
          *
               ROOT
                        9
                     *
                        ROOT
                                          4              3
                             (- 4a b - 1)c  + (6a b + 2)c
                           + 
                                   2 2             2       2 2               3 3
                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                           + 
                                  2 2
                             - 13a b  - 4a b
                    + 
                         3     2                             +-+
                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
                 /
                       +-+
                    54\|3
              ,
                  3
            **
               2
         + 
                         +---+
             ((- 6c + 3)\|- 3  - 6c + 3)
          *
             ROOT
                      9
                   *
                      ROOT
                                        4              3
                           (- 4a b - 1)c  + (6a b + 2)c
                         + 
                                 2 2             2       2 2               3 3
                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
                         + 
                                2 2
                           - 13a b  - 4a b
                  + 
                       3     2                             +-+
                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
               /
                     +-+
                  54\|3
            ,
                3
         + 
               2
           - 2c  + 2c - 12a b - 2
      /
               +---+
           (9b\|- 3  + 9b)
        *
           ROOT
                    9
                 *
                    ROOT
                                      4              3         2 2             2
                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
                       + 
                             2 2               3 3      2 2
                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
                + 
                     3     2                             +-+
                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
             /
                   +-+
                54\|3
          ,
              3
       ]
     ,
    [1]]
         ]
     ]
Type: Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R
--R   (5)
--R   [
--R     radval =
--R                  +---+
--R             (- 9\|- 3  + 9)
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                       +---+
--R             ((3c + 3)\|- 3  + 3c + 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R               2
--R           - 2c  + 2c - 12a b - 2
--R      /
--R              +---+
--R           (9\|- 3  + 9)
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R     ,
--R    radmult= 1,
--R
--R     radvect =
--R       [
--R   [
--R     [
--R                                  +-+
--R             (- 36c + 36a b + 36)\|3
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                    +---+
--R                 (9\|- 3  - 9)
--R              *
--R                 ROOT
--R                                   4              3         2 2             2
--R                      (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                    + 
--R                          2 2               3 3      2 2
--R                      (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R             + 
--R                      2                               +---+     2
--R                   (3c  + (- 21a b - 9)c + 15a b + 6)\|- 3  - 3c  + (21a b + 9)c
--R                 + 
--R                   - 15a b - 6
--R              *
--R                  +-+
--R                 \|3
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R                       +---+
--R             ((3c - 6)\|- 3  + 3c - 6)
--R          *
--R             ROOT
--R                               4              3         2 2             2
--R                  (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                + 
--R                      2 2               3 3      2 2
--R                  (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R         + 
--R                   3                 2                     2 2             +---+
--R               (- c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2)\|- 3
--R             + 
--R                  3                 2                     2 2
--R               - c  + (- 11a b - 1)c  + (11a b + 4)c - 24a b  - 2a b - 2
--R          *
--R              +-+
--R             \|3
--R      /
--R               2 +-+
--R           108b \|3
--R        *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R          **
--R             2
--R       ]
--R     ,
--R
--R     [
--R                  +---+
--R             (- 9\|- 3  + 9)
--R          *
--R               ROOT
--R                        9
--R                     *
--R                        ROOT
--R                                          4              3
--R                             (- 4a b - 1)c  + (6a b + 2)c
--R                           + 
--R                                   2 2             2       2 2               3 3
--R                             (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                           + 
--R                                  2 2
--R                             - 13a b  - 4a b
--R                    + 
--R                         3     2                             +-+
--R                      (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R                 /
--R                       +-+
--R                    54\|3
--R              ,
--R                  3
--R            **
--R               2
--R         + 
--R                         +---+
--R             ((- 6c + 3)\|- 3  - 6c + 3)
--R          *
--R             ROOT
--R                      9
--R                   *
--R                      ROOT
--R                                        4              3
--R                           (- 4a b - 1)c  + (6a b + 2)c
--R                         + 
--R                                 2 2             2       2 2               3 3
--R                           (- 13a b  - 4a b - 1)c  + (22a b  + 6a b)c - 32a b
--R                         + 
--R                                2 2
--R                           - 13a b  - 4a b
--R                  + 
--R                       3     2                             +-+
--R                    (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R               /
--R                     +-+
--R                  54\|3
--R            ,
--R                3
--R         + 
--R               2
--R           - 2c  + 2c - 12a b - 2
--R      /
--R               +---+
--R           (9b\|- 3  + 9b)
--R        *
--R           ROOT
--R                    9
--R                 *
--R                    ROOT
--R                                      4              3         2 2             2
--R                         (- 4a b - 1)c  + (6a b + 2)c  + (- 13a b  - 4a b - 1)c
--R                       + 
--R                             2 2               3 3      2 2
--R                         (22a b  + 6a b)c - 32a b  - 13a b  - 4a b
--R                + 
--R                     3     2                             +-+
--R                  (2c  - 3c  + (- 9a b - 3)c - 9a b + 2)\|3
--R             /
--R                   +-+
--R                54\|3
--R          ,
--R              3
--R       ]
--R     ,
--R    [1]]
--R         ]
--R     ]
--RType: Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E

)clear all
 

--S 241 of 267
qrimes : Stream Integer := generate(nextPrime,2**512-5000)
 

   (1)
   [
    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06079096
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06079203
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06079443
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06079621
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06080091
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06080203
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06080427
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06080637
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06080953
     ,

    13407807929942597099574024998205846127479365820592393377723561443721764030_
     0735469768018742981669034276900318581864860508537538828119465699464336490_
     06081129
     ,
    ...]
                                                         Type: Stream Integer
--R
--R   (1)
--R   [
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06079096
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06079203
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06079443
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06079621
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06080091
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06080203
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06080427
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06080637
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06080953
--R     ,
--R
--R    13407807929942597099574024998205846127479365820592393377723561443721764030_
--R     0735469768018742981669034276900318581864860508537538828119465699464336490_
--R     06081129
--R     ,
--R    ...]
--R                                                         Type: Stream Integer
--E

--S 242 of 267
rrimes := [ 2**512-p for p in qrimes while p < 2**512 ]
 

   (2)  [5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...]
                                                         Type: Stream Integer
--R
--R   (2)  [5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...]
--R                                                         Type: Stream Integer
--E

--S 243 of 267
srimes := complete rrimes
 

   (3)  [5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...]
                                                         Type: Stream Integer
--R
--R   (3)  [5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...]
--R                                                         Type: Stream Integer
--E

--S 244 of 267
[srimes.i for i in [1..18]]
 

   (4)  [[5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...]]
                                                    Type: List Stream Integer
--R
--R   (4)  [[5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...]]
--R                                                    Type: List Stream Integer
--E

--S 245 of 267
[srimes.i for i in [10..18]]
 

   (5)  [[2967,2807,2529,1827,1695,975,875,629,569]]
                                                    Type: List Stream Integer
--R
--R   (5)  [[2967,2807,2529,1827,1695,975,875,629,569]]
--R                                                    Type: List Stream Integer
--E

)clear all
 

--S 246 of 267
X := log(0.7*%i*x)
 

   (1)  log(0.7 %i x)
                                               Type: Expression Complex Float
--R
--R   (1)  log(0.7 %i x)
--R                                               Type: Expression Complex Float
--E

)clear all
 

--S 247 of 267
log2() --> Float
 

   (1)  0.6931471805 5994530942
                                                                  Type: Float
--R 
--R
--R   (1)  0.6931471805 5994530942
--R                                                                  Type: Float
--E

--S 248 of 267
exp1() --> DoubleFLoat ???
 

   (2)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (2)  2.7182818284 590452354
--R                                                                  Type: Float
--E

)clear all
 

--S 249 of 267
L : List(String) := ["There is", "it seems", "a real bug", "here"]
 

   (1)  ["There is","it seems","a real bug","here"]
                                                            Type: List String
--R
--R   (1)  ["There is","it seems","a real bug","here"]
--R                                                            Type: List String
--E

--S 250 of 267
L1 := delete!(L, 1)
 

   (2)  ["it seems","a real bug","here"]
                                                            Type: List String
--R
--R   (2)  ["it seems","a real bug","here"]
--R                                                            Type: List String
--E

--S 251 of 267
L
 

   (3)  ["There is","it seems","a real bug","here"]
                                                            Type: List String
--R
--R   (3)  ["There is","it seems","a real bug","here"]
--R                                                            Type: List String
--E

--S 252 of 267
L2 := delete!(L, 2)
 

   (4)  ["There is","a real bug","here"]
                                                            Type: List String
--R
--R   (4)  ["There is","a real bug","here"]
--R                                                            Type: List String
--E

--S 253 of 267
L
 

   (5)  ["There is","a real bug","here"]
                                                            Type: List String
--R
--R   (5)  ["There is","a real bug","here"]
--R                                                            Type: List String
--E

)clear all
 

--S 254 of 267
K := Fraction(Integer)   
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E

--S 255 of 267
PolK := UP('X, K) 
 

   (2)  UnivariatePolynomial(X,Fraction Integer)
                                                                 Type: Domain
--R
--R   (2)  UnivariatePolynomial(X,Fraction Integer)
--R                                                                 Type: Domain
--E

--S 256 of 267
X : PolK := monomial(1, 1) 
 

   (3)  X
                               Type: UnivariatePolynomial(X,Fraction Integer)
--R
--R   (3)  X
--R                               Type: UnivariatePolynomial(X,Fraction Integer)
--E

--S 257 of 267
n : PositiveInteger := 15 
 

   (4)  15
                                                        Type: PositiveInteger
--R
--R   (4)  15
--R                                                        Type: PositiveInteger
--E

--S 258 of 267
E := SimpleAlgebraicExtension(K, PolK, X**n + X**(n-3) -1) 
 

   (5)
  SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(X,Fraction Int
  eger),X**15+X**12-1)
                                                                 Type: Domain
--R
--R   (5)
--R  SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(X,Fraction Int
--R  eger),X**15+X**12-1)
--R                                                                 Type: Domain
--E

--S 259 of 267
y : E := X::E
 

   (6)  X
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(X,Fraction Integer),X**15+X**12-1)
--R
--R   (6)  X
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(X,Fraction Integer),X**15+X**12-1)
--E

--S 260 of 267
minimalPolynomial(y)$E
 

         15    12
   (7)  X   + X   - 1
                               Type: UnivariatePolynomial(X,Fraction Integer)
--R
--R         15    12
--R   (7)  X   + X   - 1
--R                               Type: UnivariatePolynomial(X,Fraction Integer)
--E

)clear all
 

--S 261 of 267
tr := rule cos(x)**(n | integer? n and even? n)==(1-sin(x)**2)**(n/2)
 

                                  n
                                  -
              n             2     2
   (1)  cos(x)  == (- sin(x)  + 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                  n
--R                                  -
--R              n             2     2
--R   (1)  cos(x)  == (- sin(x)  + 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

)clear all
 

--S 262 of 267
sqrt(2)*2.0 -- fails
 

   (1)  2.8284271247 461900976
                                                       Type: Expression Float
--R 
--R
--R   (1)  2.8284271247 461900976
--R                                                       Type: Expression Float
--E

--S 263 of 267
sqrt(2)::EXPR INT * 2.0 -- works
 

   (2)  2.8284271247 461900976
                                                       Type: Expression Float
--R 
--R
--R   (2)  2.8284271247 461900976
--R                                                       Type: Expression Float
--E

)clear all
 

--S 264 of 267
f := exp(exp(x)*exp(1/exp(x))) / exp exp x
 

                1
               ---
                 x
            x  %e
          %e %e
        %e
   (1)  ----------
               x
             %e
           %e
                                                     Type: Expression Integer
--R
--R                1
--R               ---
--R                 x
--R            x  %e
--R          %e %e
--R        %e
--R   (1)  ----------
--R               x
--R             %e
--R           %e
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 265 of 267
[1,2,3] :: DirectProduct(3, Fraction Integer)
 

   (1)  [1,2,3]
                                      Type: DirectProduct(3,Fraction Integer)
--R
--R   (1)  [1,2,3]
--R                                      Type: DirectProduct(3,Fraction Integer)
--E

)clear all
 

--S 266 of 267
x**10+1::Polynomial PrimeField 2
 

         10
   (1)  x   + 1
                                                Type: Polynomial PrimeField 2
--R
--R         10
--R   (1)  x   + 1
--R                                                Type: Polynomial PrimeField 2
--E

)clear all
 

--S 267 of 267
f(x)==x**2
 
                                                                   Type: Void
--R                                                                   Type: Void
--E

)spool
 
Starts dribbling to FlexibleArray.output (2010/3/27, 18:42:3).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
flexibleArray [i for i in 1..6]
 

   (1)  [1,2,3,4,5,6]
                                          Type: FlexibleArray PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6]
--R                                          Type: FlexibleArray PositiveInteger
--E 1

--S 2 of 16
f : FARRAY INT := new(6,0)
 

   (2)  [0,0,0,0,0,0]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0]
--R                                                  Type: FlexibleArray Integer
--E 2

--S 3 of 16
for i in 1..6 repeat f.i := i; f
 

   (3)  [1,2,3,4,5,6]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6]
--R                                                  Type: FlexibleArray Integer
--E 3

--S 4 of 16
physicalLength f
 

   (4)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  6
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 16
concat!(f,11)
 

   (5)  [1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (5)  [1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 5

--S 6 of 16
physicalLength f
 

   (6)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  10
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 16
physicalLength!(f,15)
 

   (7)  [1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (7)  [1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 7

--S 8 of 16
concat!(f,f)
 

   (8)  [1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (8)  [1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 8

--S 9 of 16
insert!(22,f,1)
 

   (9)  [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (9)  [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 9

--S 10 of 16
g := f(10..)
 

   (10)  [2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (10)  [2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 10

--S 11 of 16
insert!(g,f,1)
 

   (11)  [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (11)  [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11]
--R                                                  Type: FlexibleArray Integer
--E 11

--S 12 of 16
merge!(sort! f, sort! g)
 

   (12)  [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (12)  [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22]
--R                                                  Type: FlexibleArray Integer
--E 12

--S 13 of 16
removeDuplicates! f
 

   (13)  [1,2,3,4,5,6,11,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (13)  [1,2,3,4,5,6,11,22]
--R                                                  Type: FlexibleArray Integer
--E 13

--S 14 of 16
select!(i +-> even? i,f)
 

   (14)  [2,4,6,22]
                                                  Type: FlexibleArray Integer
--R 
--R
--R   (14)  [2,4,6,22]
--R                                                  Type: FlexibleArray Integer
--E 14

--S 15 of 16
physicalLength f
 

   (15)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  8
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 16
shrinkable(false)$FlexibleArray(Integer)
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16
)spool
 
Starts dribbling to op.output (2010/3/27, 18:30:34).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 2
abs(x)
 

   (1)  abs(x)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  abs(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 2
eval(%,x=-3.4)
 

   (2)  3.4
                                                       Type: Expression Float
--R 
--R
--R   (2)  3.4
--R                                                       Type: Expression Float
--E 2
)spool 
 
Starts dribbling to unit-i-funsel.output (2010/3/27, 18:41:35).
)set message test on
 
)set message auto off
 
)clear all
 
)lisp (setq *print-level* 3)
 
Value = 3

-- these do not have unit tests yet
)lisp (trace |sayFunctionSelection|)
 
Value = (|sayFunctionSelection|)
)lisp (trace |sayFunctionSelectionResult|)
 
Value = (|sayFunctionSelectionResult|)
)lisp (trace |selectMostGeneralMm|)
 
Value = (|selectMostGeneralMm|)
)lisp (trace |evalMmFreeFunction|)
 
Value = (|evalMmFreeFunction|)
)lisp (trace |printMms|)
 
Value = (|printMms|)

)lisp (trace |allOrMatchingMms|)
 
Value = (|allOrMatchingMms|)
)lisp (trace |constructSubst|)
 
Value = (|constructSubst|)
)lisp (trace |findFunctionInDomain|)
 
Value = (|findFunctionInDomain|)
)lisp (trace |findFunctionInDomain1|)
 
Value = (|findFunctionInDomain1|)
)lisp (trace |hasCaty|)
 
Value = (|hasCaty|)
)lisp (trace |isEqualOrSubDomain|)
 
Value = (|isEqualOrSubDomain|)
)lisp (trace |isHomogeneousList|)
 
Value = (|isHomogeneousList|)
)lisp (trace |isPartialMode|)
 
Value = (|isPartialMode|)
)lisp (trace |matchMmCond|)
 
Value = (|matchMmCond|)
)lisp (trace |matchMmSig|)
 
Value = (|matchMmSig|)
)lisp (trace |matchMmSigTar|)
 
Value = (|matchMmSigTar|)
)lisp (trace |ofCategory|)
 
Value = (|ofCategory|)
)lisp (trace |selectMms2|)
 
Value = (|selectMms2|)

--S 1 of 31
l := [1,4,2,-6,0,3,5,4,2,3]
 
  1> (|isPartialMode| NIL)
  <1 (|isPartialMode| NIL)
  1> (|ofCategory| (|Integer|) (|Ring|))
    2> (|hasCaty| (|Integer|) (|Ring|) NIL)
    <2 (|hasCaty| NIL)
  <1 (|ofCategory| T)
  1> (|ofCategory| (|Integer|) (|Ring|))
    2> (|hasCaty| (|Integer|) (|Ring|) NIL)
    <2 (|hasCaty| NIL)
  <1 (|ofCategory| T)
  1> (|ofCategory| (|Integer|) (|Ring|))
    2> (|hasCaty| (|Integer|) (|Ring|) NIL)
    <2 (|hasCaty| NIL)
  <1 (|ofCategory| T)
  1> (|isPartialMode| NIL)
  <1 (|isPartialMode| NIL)
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|NonNegativeInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|NonNegativeInteger| |PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
  <1 (|isEqualOrSubDomain| (|PositiveInteger|))

  1> (|isEqualOrSubDomain| (|List| (|Integer|)) (|OutputForm|))
  <1 (|isEqualOrSubDomain| NIL)
  1> (|selectMms2| |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) NIL)
    2> (|isPartialMode| (|OutputForm|))
    <2 (|isPartialMode| NIL)
    2> (|isPartialMode| (|OutputForm|))
    <2 (|isPartialMode| NIL)
    2> (|findFunctionInDomain| |coerce| (|List| (|Integer|)) (|OutputForm|) ((|List| #)) ((|List| #)) NIL NIL)
      3> (|constructSubst| (|List| (|Integer|)))
      <3 (|constructSubst| ((|#1| |Integer|) ($ |List| #)))
      3> (|isHomogeneousList| ((|List| #)))
      <3 (|isHomogeneousList| T)
      3> (|isHomogeneousList| ($))
      <3 (|isHomogeneousList| T)
      3> (|allOrMatchingMms| ((# NIL # ELT)) ((|List| #)) (|OutputForm|) (|List| (|Integer|)))
      <3 (|allOrMatchingMms| ((# NIL # ELT)))
      3> (|findFunctionInDomain1| ((# $) NIL (|has| |#1| #) ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) ((|#1| |Integer|) ($ |List| #)))
        4> (|matchMmCond| (|has| (|Integer|) (|SetCategory|)))
          5> (|hasCaty| (|Integer|) (|SetCategory|) NIL)
          <5 (|hasCaty| NIL)
        <4 (|matchMmCond| T)
        4> (|matchMmSig| ((# #) NIL (|has| # #) ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|List| (|Integer|)))
          <5 (|isEqualOrSubDomain| T)
          5> (|matchMmSigTar| (|OutputForm|) (|OutputForm|))
            6> (|isEqualOrSubDomain| (|OutputForm|) (|OutputForm|))
            <6 (|isEqualOrSubDomain| T)
          <5 (|matchMmSigTar| T)
        <4 (|matchMmSig| T)
      <3 (|findFunctionInDomain1| ((# # #)))
      3> (|allOrMatchingMms| NIL ((|List| #)) (|OutputForm|) (|List| (|Integer|)))
      <3 (|allOrMatchingMms| NIL)
    <2 (|findFunctionInDomain| ((# # #)))
    2> (|findFunctionInDomain| |coerce| (|OutputForm|) (|OutputForm|) ((|List| #)) ((|List| #)) NIL NIL)
      3> (|constructSubst| (|OutputForm|))
      <3 (|constructSubst| (($ |OutputForm|)))
      3> (|isHomogeneousList| ((|List| #)))
      <3 (|isHomogeneousList| T)
      3> (|isHomogeneousList| ($))
      <3 (|isHomogeneousList| T)
      3> (|allOrMatchingMms| ((# 18 T ELT)) ((|List| #)) (|OutputForm|) (|OutputForm|))
      <3 (|allOrMatchingMms| ((# 18 T ELT)))
      3> (|findFunctionInDomain1| ((# $) 18 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |OutputForm|)))
        4> (|matchMmCond| T)
        <4 (|matchMmCond| T)
        4> (|matchMmSig| ((# #) 18 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|OutputForm|))
          <5 (|isEqualOrSubDomain| NIL)
        <4 (|matchMmSig| NIL)
      <3 (|findFunctionInDomain1| NIL)
      3> (|allOrMatchingMms| NIL ((|List| #)) (|OutputForm|) (|OutputForm|))
      <3 (|allOrMatchingMms| NIL)
    <2 (|findFunctionInDomain| NIL)
    2> (|findFunctionInDomain| |coerce| (|Integer|) (|OutputForm|) ((|List| #)) ((|List| #)) NIL NIL)
      3> (|constructSubst| (|Integer|))
      <3 (|constructSubst| (($ |Integer|)))
      3> (|isHomogeneousList| ((|List| #)))
      <3 (|isHomogeneousList| T)
      3> (|isHomogeneousList| ($))
      <3 (|isHomogeneousList| T)
      3> (|isHomogeneousList| ((|Integer|)))
      <3 (|isHomogeneousList| T)
      3> (|isHomogeneousList| ($))
      <3 (|isHomogeneousList| T)
      3> (|isHomogeneousList| ((|Integer|)))
      <3 (|isHomogeneousList| T)
      3> (|allOrMatchingMms| ((# 38 T ELT) (# NIL T ELT) (# 38 T ELT) (# 37 T ELT)) ((|List| #)) (|OutputForm|) (|Integer|))
      <3 (|allOrMatchingMms| ((# 38 T ELT) (# NIL T ELT) (# 38 T ELT) (# 37 T ELT)))
      3> (|findFunctionInDomain1| (($ #) 38 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
        4> (|matchMmCond| T)
        <4 (|matchMmCond| T)
        4> (|matchMmSig| ((# #) 38 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
          <5 (|isEqualOrSubDomain| NIL)
        <4 (|matchMmSig| NIL)
      <3 (|findFunctionInDomain1| NIL)
      3> (|findFunctionInDomain1| (($ $) NIL T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
        4> (|matchMmCond| T)
        <4 (|matchMmCond| T)
        4> (|matchMmSig| ((# #) NIL T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
          <5 (|isEqualOrSubDomain| NIL)
        <4 (|matchMmSig| NIL)
      <3 (|findFunctionInDomain1| NIL)
      3> (|findFunctionInDomain1| (($ #) 38 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
        4> (|matchMmCond| T)
        <4 (|matchMmCond| T)
        4> (|matchMmSig| ((# #) 38 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
          <5 (|isEqualOrSubDomain| NIL)
        <4 (|matchMmSig| NIL)
      <3 (|findFunctionInDomain1| NIL)
      3> (|findFunctionInDomain1| ((# $) 37 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
        4> (|matchMmCond| T)
        <4 (|matchMmCond| T)
        4> (|matchMmSig| ((# #) 37 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
          <5 (|isEqualOrSubDomain| NIL)
        <4 (|matchMmSig| NIL)
      <3 (|findFunctionInDomain1| NIL)
      3> (|allOrMatchingMms| NIL ((|List| #)) (|OutputForm|) (|Integer|))
      <3 (|allOrMatchingMms| NIL)
    <2 (|findFunctionInDomain| NIL)
  <1 (|selectMms2| ((# # #)))
   (1)  [1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R  1> (|isPartialMode| NIL)
--R  <1 (|isPartialMode| NIL)
--R  1> (|ofCategory| (|Integer|) (|Ring|))
--R    2> (|hasCaty| (|Integer|) (|Ring|) NIL)
--R    <2 (|hasCaty| NIL)
--R  <1 (|ofCategory| T)
--R  1> (|ofCategory| (|Integer|) (|Ring|))
--R    2> (|hasCaty| (|Integer|) (|Ring|) NIL)
--R    <2 (|hasCaty| NIL)
--R  <1 (|ofCategory| T)
--R  1> (|ofCategory| (|Integer|) (|Ring|))
--R    2> (|hasCaty| (|Integer|) (|Ring|) NIL)
--R    <2 (|hasCaty| NIL)
--R  <1 (|ofCategory| T)
--R  1> (|isPartialMode| NIL)
--R  <1 (|isPartialMode| NIL)
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|NonNegativeInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|NonNegativeInteger| |PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R  1> (|isEqualOrSubDomain| (|PositiveInteger|) (|Integer|))
--R  <1 (|isEqualOrSubDomain| (|PositiveInteger|))
--R
--R  1> (|isEqualOrSubDomain| (|List| (|Integer|)) (|OutputForm|))
--R  <1 (|isEqualOrSubDomain| NIL)
--R  1> (|selectMms2| |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) NIL)
--R    2> (|isPartialMode| (|OutputForm|))
--R    <2 (|isPartialMode| NIL)
--R    2> (|isPartialMode| (|OutputForm|))
--R    <2 (|isPartialMode| NIL)
--R    2> (|findFunctionInDomain| |coerce| (|List| (|Integer|)) (|OutputForm|) ((|List| #)) ((|List| #)) NIL NIL)
--R      3> (|constructSubst| (|List| (|Integer|)))
--R      <3 (|constructSubst| ((|#1| |Integer|) ($ |List| #)))
--R      3> (|isHomogeneousList| ((|List| #)))
--R      <3 (|isHomogeneousList| T)
--R      3> (|isHomogeneousList| ($))
--R      <3 (|isHomogeneousList| T)
--R      3> (|allOrMatchingMms| ((# NIL # ELT)) ((|List| #)) (|OutputForm|) (|List| (|Integer|)))
--R      <3 (|allOrMatchingMms| ((# NIL # ELT)))
--R      3> (|findFunctionInDomain1| ((# $) NIL (|has| |#1| #) ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) ((|#1| |Integer|) ($ |List| #)))
--R        4> (|matchMmCond| (|has| (|Integer|) (|SetCategory|)))
--R          5> (|hasCaty| (|Integer|) (|SetCategory|) NIL)
--R          <5 (|hasCaty| NIL)
--R        <4 (|matchMmCond| T)
--R        4> (|matchMmSig| ((# #) NIL (|has| # #) ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
--R          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|List| (|Integer|)))
--R          <5 (|isEqualOrSubDomain| T)
--R          5> (|matchMmSigTar| (|OutputForm|) (|OutputForm|))
--R            6> (|isEqualOrSubDomain| (|OutputForm|) (|OutputForm|))
--R            <6 (|isEqualOrSubDomain| T)
--R          <5 (|matchMmSigTar| T)
--R        <4 (|matchMmSig| T)
--R      <3 (|findFunctionInDomain1| ((# # #)))
--R      3> (|allOrMatchingMms| NIL ((|List| #)) (|OutputForm|) (|List| (|Integer|)))
--R      <3 (|allOrMatchingMms| NIL)
--R    <2 (|findFunctionInDomain| ((# # #)))
--R    2> (|findFunctionInDomain| |coerce| (|OutputForm|) (|OutputForm|) ((|List| #)) ((|List| #)) NIL NIL)
--R      3> (|constructSubst| (|OutputForm|))
--R      <3 (|constructSubst| (($ |OutputForm|)))
--R      3> (|isHomogeneousList| ((|List| #)))
--R      <3 (|isHomogeneousList| T)
--R      3> (|isHomogeneousList| ($))
--R      <3 (|isHomogeneousList| T)
--R      3> (|allOrMatchingMms| ((# 18 T ELT)) ((|List| #)) (|OutputForm|) (|OutputForm|))
--R      <3 (|allOrMatchingMms| ((# 18 T ELT)))
--R      3> (|findFunctionInDomain1| ((# $) 18 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |OutputForm|)))
--R        4> (|matchMmCond| T)
--R        <4 (|matchMmCond| T)
--R        4> (|matchMmSig| ((# #) 18 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
--R          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|OutputForm|))
--R          <5 (|isEqualOrSubDomain| NIL)
--R        <4 (|matchMmSig| NIL)
--R      <3 (|findFunctionInDomain1| NIL)
--R      3> (|allOrMatchingMms| NIL ((|List| #)) (|OutputForm|) (|OutputForm|))
--R      <3 (|allOrMatchingMms| NIL)
--R    <2 (|findFunctionInDomain| NIL)
--R    2> (|findFunctionInDomain| |coerce| (|Integer|) (|OutputForm|) ((|List| #)) ((|List| #)) NIL NIL)
--R      3> (|constructSubst| (|Integer|))
--R      <3 (|constructSubst| (($ |Integer|)))
--R      3> (|isHomogeneousList| ((|List| #)))
--R      <3 (|isHomogeneousList| T)
--R      3> (|isHomogeneousList| ($))
--R      <3 (|isHomogeneousList| T)
--R      3> (|isHomogeneousList| ((|Integer|)))
--R      <3 (|isHomogeneousList| T)
--R      3> (|isHomogeneousList| ($))
--R      <3 (|isHomogeneousList| T)
--R      3> (|isHomogeneousList| ((|Integer|)))
--R      <3 (|isHomogeneousList| T)
--R      3> (|allOrMatchingMms| ((# 38 T ELT) (# NIL T ELT) (# 38 T ELT) (# 37 T ELT)) ((|List| #)) (|OutputForm|) (|Integer|))
--R      <3 (|allOrMatchingMms| ((# 38 T ELT) (# NIL T ELT) (# 38 T ELT) (# 37 T ELT)))
--R      3> (|findFunctionInDomain1| (($ #) 38 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
--R        4> (|matchMmCond| T)
--R        <4 (|matchMmCond| T)
--R        4> (|matchMmSig| ((# #) 38 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
--R          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
--R          <5 (|isEqualOrSubDomain| NIL)
--R        <4 (|matchMmSig| NIL)
--R      <3 (|findFunctionInDomain1| NIL)
--R      3> (|findFunctionInDomain1| (($ $) NIL T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
--R        4> (|matchMmCond| T)
--R        <4 (|matchMmCond| T)
--R        4> (|matchMmSig| ((# #) NIL T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
--R          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
--R          <5 (|isEqualOrSubDomain| NIL)
--R        <4 (|matchMmSig| NIL)
--R      <3 (|findFunctionInDomain1| NIL)
--R      3> (|findFunctionInDomain1| (($ #) 38 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
--R        4> (|matchMmCond| T)
--R        <4 (|matchMmCond| T)
--R        4> (|matchMmSig| ((# #) 38 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
--R          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
--R          <5 (|isEqualOrSubDomain| NIL)
--R        <4 (|matchMmSig| NIL)
--R      <3 (|findFunctionInDomain1| NIL)
--R      3> (|findFunctionInDomain1| ((# $) 37 T ELT) |coerce| (|OutputForm|) ((|List| #)) ((|List| #)) (($ |Integer|)))
--R        4> (|matchMmCond| T)
--R        <4 (|matchMmCond| T)
--R        4> (|matchMmSig| ((# #) 37 T ELT) (|OutputForm|) ((|List| #)) ((|List| #)))
--R          5> (|isEqualOrSubDomain| (|List| (|Integer|)) (|Integer|))
--R          <5 (|isEqualOrSubDomain| NIL)
--R        <4 (|matchMmSig| NIL)
--R      <3 (|findFunctionInDomain1| NIL)
--R      3> (|allOrMatchingMms| NIL ((|List| #)) (|OutputForm|) (|Integer|))
--R      <3 (|allOrMatchingMms| NIL)
--R    <2 (|findFunctionInDomain| NIL)
--R  <1 (|selectMms2| ((# # #)))
--R   (1)  [1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 1

)lisp (untrace)
 
Value = (|selectMms2| |ofCategory| |matchMmSigTar| |matchMmSig| |matchMmCond| |isPartialMode| |isHomogeneousList| |isEqualOrSubDomain| |hasCaty| |findFunctionInDomain1| |findFunctionInDomain| |constructSubst| |allOrMatchingMms| |printMms| |evalMmFreeFunction| |selectMostGeneralMm| |sayFunctionSelectionResult| |sayFunctionSelection|)
 
)lisp (trace |altTypeOf|)
 
Value = (|altTypeOf|)
)lisp (trace |argCouldBelongToSubdomain|)
 
Value = (|argCouldBelongToSubdomain|)
)lisp (trace |CONTAINEDisDomain|)
 
Value = (|CONTAINEDisDomain|)
)lisp (trace |defaultTarget|)
 
Value = (|defaultTarget|)
)lisp (trace |getLocalMms|)
 
Value = (|getLocalMms|)
)lisp (trace |getOpArgTypes|)
 
Value = (|getOpArgTypes|)
)lisp (trace |getOpArgTypes1|)
 
Value = (|getOpArgTypes1|)
)lisp (trace |orderMms|)
 
Value = (|orderMms|)
)lisp (trace |selectLocalMms|)
 
Value = (|selectLocalMms|)
)lisp (trace |selectMms|)
 
Value = (|selectMms|)

--S 2 of 31
m := list 555555
 
  1> (|selectMms| #<vector 08d6c32c> (#<vector 08d6c310>) NIL)
    2> (|getOpArgTypes| |list| (#<vector 08d6c310>))
      3> (|getOpArgTypes1| |list| (#<vector 08d6c310>))
        4> (|argCouldBelongToSubdomain| |list| 1)
          5> (|CONTAINEDisDomain| *1 (AND (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|CONTAINEDisDomain| *1 (|isDomain| *2 (|List| #)))
            <6 (|CONTAINEDisDomain| NIL)
            6> (|CONTAINEDisDomain| *1 (|isDomain| *1 (|Symbol|)))
            <6 (|CONTAINEDisDomain| NIL)
          <5 (|CONTAINEDisDomain| NIL)
          5> (|CONTAINEDisDomain| *2 (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|CONTAINEDisDomain| *2 (|ofCategory| *1 (|ListAggregate| *2)))
            <6 (|CONTAINEDisDomain| NIL)
            6> (|CONTAINEDisDomain| *2 (|ofCategory| *2 (|Type|)))
            <6 (|CONTAINEDisDomain| NIL)
          <5 (|CONTAINEDisDomain| NIL)
        <4 (|argCouldBelongToSubdomain| #<vector 08d6c2f4>)
      <3 (|getOpArgTypes1| ((|PositiveInteger|)))
    <2 (|getOpArgTypes| ((|PositiveInteger|)))
    2> (|altTypeOf| (|PositiveInteger|) #<vector 08d6c310> (|PositiveInteger|))
    <2 (|altTypeOf| (|Integer|))
    2> (|defaultTarget| #<vector 08d6c32c> |list| 1 ((|PositiveInteger|)))
    <2 (|defaultTarget| (|List| (|PositiveInteger|)))
    2> (|selectLocalMms| #<vector 08d6c32c> |list| ((|PositiveInteger|)) (|List| (|PositiveInteger|)))
      3> (|getLocalMms| |list| ((|PositiveInteger|)) (|List| (|PositiveInteger|)))
      <3 (|getLocalMms| NIL)
    <2 (|selectLocalMms| NIL)
    2> (|orderMms| |list| ((# # #)) ((|PositiveInteger|)) ((|Integer|)) (|List| (|PositiveInteger|)))
    <2 (|orderMms| ((# # #)))
  <1 (|selectMms| ((# # #)))

  1> (|orderMms| |coerce| ((# # #)) ((|List| #)) ((|List| #)) (|OutputForm|))
  <1 (|orderMms| ((# # #)))
   (2)  [555555]
                                                   Type: List PositiveInteger
--R 
--I  1> (|selectMms| #<vector 086b116c> (#<vector 086b1134>) NIL)
--I    2> (|getOpArgTypes| |list| (#<vector 086b1134>))
--I      3> (|getOpArgTypes1| |list| (#<vector 086b1134>))
--R        4> (|argCouldBelongToSubdomain| |list| 1)
--R          5> (|CONTAINEDisDomain| *1 (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|CONTAINEDisDomain| *1 (|isDomain| *2 (|List| #)))
--R            <6 (|CONTAINEDisDomain| NIL)
--R            6> (|CONTAINEDisDomain| *1 (|isDomain| *1 (|Symbol|)))
--R            <6 (|CONTAINEDisDomain| NIL)
--R          <5 (|CONTAINEDisDomain| NIL)
--R          5> (|CONTAINEDisDomain| *2 (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|CONTAINEDisDomain| *2 (|ofCategory| *1 (|ListAggregate| *2)))
--R            <6 (|CONTAINEDisDomain| NIL)
--R            6> (|CONTAINEDisDomain| *2 (|ofCategory| *2 (|Type|)))
--R            <6 (|CONTAINEDisDomain| NIL)
--R          <5 (|CONTAINEDisDomain| NIL)
--I        <4 (|argCouldBelongToSubdomain| #<vector 086b1118>)
--R      <3 (|getOpArgTypes1| ((|PositiveInteger|)))
--R    <2 (|getOpArgTypes| ((|PositiveInteger|)))
--I    2> (|altTypeOf| (|PositiveInteger|) #<vector 086b1134> (|PositiveInteger|))
--R    <2 (|altTypeOf| (|Integer|))
--I    2> (|defaultTarget| #<vector 086b116c> |list| 1 ((|PositiveInteger|)))
--R    <2 (|defaultTarget| (|List| (|PositiveInteger|)))
--I    2> (|selectLocalMms| #<vector 086b116c> |list| ((|PositiveInteger|)) (|List| (|PositiveInteger|)))
--R      3> (|getLocalMms| |list| ((|PositiveInteger|)) (|List| (|PositiveInteger|)))
--R      <3 (|getLocalMms| NIL)
--R    <2 (|selectLocalMms| NIL)
--R    2> (|orderMms| |list| ((# # #)) ((|PositiveInteger|)) ((|Integer|)) (|List| (|PositiveInteger|)))
--R    <2 (|orderMms| ((# # #)))
--R  <1 (|selectMms| ((# # #)))
--R
--R  1> (|orderMms| |coerce| ((# # #)) ((|List| #)) ((|List| #)) (|OutputForm|))
--R  <1 (|orderMms| ((# # #)))
--R   (2)  [555555]
--R                                                   Type: List PositiveInteger
--E 2

)lisp (untrace)
 
Value = (|selectMms| |selectLocalMms| |orderMms| |getOpArgTypes1| |getOpArgTypes| |getLocalMms| |defaultTarget| |CONTAINEDisDomain| |argCouldBelongToSubdomain| |altTypeOf|)
 
)lisp (trace |getOpArgTypes,f|)
 
Value = (|getOpArgTypes,f|)

--S 3 of 31
concat(5,l)
 
  1> (|getOpArgTypes,f| (|PositiveInteger|) |concat|)
  <1 (|getOpArgTypes,f| (|PositiveInteger|))
  1> (|getOpArgTypes,f| (|List| (|Integer|)) |concat|)
  <1 (|getOpArgTypes,f| (|List| (|Integer|)))

   (3)  [5,1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R  1> (|getOpArgTypes,f| (|PositiveInteger|) |concat|)
--R  <1 (|getOpArgTypes,f| (|PositiveInteger|))
--R  1> (|getOpArgTypes,f| (|List| (|Integer|)) |concat|)
--R  <1 (|getOpArgTypes,f| (|List| (|Integer|)))
--R
--R   (3)  [5,1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 3

)lisp (untrace)
 
Value = (|getOpArgTypes,f|)
 
)lisp (trace |coerceTypeArgs|)
 
Value = (|coerceTypeArgs|)
)lisp (trace |containsVars|)
 
Value = (|containsVars|)
)lisp (trace |containsVars1|)
 
Value = (|containsVars1|)
)lisp (trace |defaultTypeForCategory|)
 
Value = (|defaultTypeForCategory|)
)lisp (trace |domArg2|)
 
Value = (|domArg2|)
)lisp (trace |evalMm|)
 
Value = (|evalMm|)
)lisp (trace |evalMmCat|)
 
Value = (|evalMmCat|)
)lisp (trace |evalMmCat1|)
 
Value = (|evalMmCat1|)
)lisp (trace |evalMmCond|)
 
Value = (|evalMmCond|)
)lisp (trace |evalMmCond0|)
 
Value = (|evalMmCond0|)
)lisp (trace |evalMmDom|)
 
Value = (|evalMmDom|)
)lisp (trace |evalMmStack|)
 
Value = (|evalMmStack|)
)lisp (trace |evalMmStackInner|)
 
Value = (|evalMmStackInner|)
)lisp (trace |fixUpTypeArgs|)
 
Value = (|fixUpTypeArgs|)
)lisp (trace |hasCate|)
 
Value = (|hasCate|)
)lisp (trace |hasCate1|)
 
Value = (|hasCate1|)
)lisp (trace |hasCateSpecial|)
 
Value = (|hasCateSpecial|)
)lisp (trace |hasCateSpecialNew|)
 
Value = (|hasCateSpecialNew|)
)lisp (trace |matchTypes|)
 
Value = (|matchTypes|)
)lisp (trace |mkDomPvar|)
 
Value = (|mkDomPvar|)
)lisp (trace |mmCatComp|)
 
Value = (|mmCatComp|)
)lisp (trace |noSharpCallsHere|)
 
Value = (|noSharpCallsHere|)
)lisp (trace |orderMmCatStack|)
 
Value = (|orderMmCatStack|)
)lisp (trace |replaceSharpCalls|)
 
Value = (|replaceSharpCalls|)
)lisp (trace |selectMmsGen|)
 
Value = (|selectMmsGen|)
)lisp (trace |selectMmsGen,exact?|)
 
Value = (|selectMmsGen,exact?|)
)lisp (trace |selectMmsGen,matchMms|)
 
Value = (|selectMmsGen,matchMms|)
)lisp (trace |filterModemapsFromPackages|)
 
Value = (|filterModemapsFromPackages|)
)lisp (trace |unifyStruct|)
 
Value = (|unifyStruct|)
)lisp (trace |unifyStructVar|)
 
Value = (|unifyStructVar|)

--S 4 of 31
concat(m,l)
 
  1> (|selectMmsGen| |coerce| (|List| (|Integer|)) ((|PositiveInteger|)) ((|PositiveInteger|)))
    2> (|filterModemapsFromPackages| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) ("PositiveInteger" "List") |coerce|)
    <2 (|filterModemapsFromPackages| ((# #) (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
    2> (|selectMmsGen,exact?| ((# #) (# #)) (|List| (|Integer|)) ((|PositiveInteger|)))
    <2 (|selectMmsGen,exact?| (NIL (# #)))
    2> (|selectMmsGen,matchMms| ((# #) (# #)) |coerce| (|List| (|Integer|)) ((|PositiveInteger|)) ((|PositiveInteger|)))
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList|))
              7> (|containsVars1| (|DataList|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList|))
              7> (|containsVars1| (|DataList|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
    <2 (|selectMmsGen,matchMms| NIL)
    2> (|selectMmsGen,exact?| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) (|List| (|Integer|)) ((|PositiveInteger|)))
    <2 (|selectMmsGen,exact?| (NIL (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
    2> (|selectMmsGen,matchMms| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) |coerce| (|List| (|Integer|)) ((|PositiveInteger|)) ((|PositiveInteger|)))
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) |coerce| NIL)
                8> (|hasCate| *1 (|XFreeAlgebra| *2 *3) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|XFreeAlgebra| *2 *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
                8> (|hasCate| *2 (|OrderedSet|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|OrderedSet|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|OrderedSet|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *3 (|Ring|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) NIL)
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|)))
          <5 (|evalMmCond0| ((*3 |Integer|)))
        <4 (|evalMmCond| ((*3 |Integer|)))
        4> (|fixUpTypeArgs| ((*3 |Integer|)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|XAlgebra| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|XAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|XAlgebra| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|XAlgebra| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|XAlgebra| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|XAlgebra| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|XAlgebra| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|XAlgebra| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *2 (|Ring|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|Ring|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|Ring|) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|Ring|) NIL)
                    10> (|hasCate| (|Integer|) (|Ring|) ((*2 |Integer|)))
                    <10 (|hasCate| ((*2 |Integer|)))
                  <9 (|hasCateSpecial| ((*2 |Integer|)))
                <8 (|hasCate| ((*2 |Integer|)))
              <7 (|evalMmCat1| ((*2 |Integer|)))
            <6 (|evalMmCat| ((*2 |Integer|)))
          <5 (|evalMmCond0| ((*2 |Integer|)))
        <4 (|evalMmCond| ((*2 |Integer|)))
        4> (|fixUpTypeArgs| ((*2 |Integer|)))
          5> (|coerceTypeArgs| (|PositiveInteger|) (|Integer|) ((*2 |Integer|)))
          <5 (|coerceTypeArgs| (|Integer|))
        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Void|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Void|) (*2 |OutputForm|)))
            6> (|containsVars| (|Void|))
              7> (|containsVars1| (|Void|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) |coerce| NIL)
                8> (|hasCate| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) |coerce| NIL)
                8> (|hasCate| *2 (|UnivariateLaurentSeriesCategory| *3) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL)
                    10> (|hasCate| (|Integer|) (|UnivariateLaurentSeriesCategory| *3) ((*2 |Integer|)))
                    <10 (|hasCate| |failed|)
                    10> (|hasCateSpecialNew| *2 (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesCategory| *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *3 (|Ring|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) NIL)
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|)))
          <5 (|evalMmCond0| ((*3 |Integer|)))
        <4 (|evalMmCond| ((*3 |Integer|)))
        4> (|fixUpTypeArgs| ((*3 |Integer|)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariatePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            <6 (|evalMmDom| ((*1 |UnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariatePolynomial| *3))
              7> (|containsVars1| (|UnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Segment| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|UniversalSegment| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |UniversalSegment| *3) (*2 |Segment| *3)))
            6> (|containsVars| (|UniversalSegment| *3))
              7> (|containsVars1| (|UniversalSegment| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UniversalSegment| *3))
              7> (|containsVars1| (|UniversalSegment| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UniversalSegment|))
              7> (|containsVars1| (|UniversalSegment|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) |coerce| NIL)
                8> (|hasCate| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) |coerce| NIL)
                8> (|hasCate| *2 (|UnivariateTaylorSeriesCategory| *3) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL)
                    10> (|hasCate| (|Integer|) (|UnivariateTaylorSeriesCategory| *3) ((*2 |Integer|)))
                    <10 (|hasCate| |failed|)
                    10> (|hasCateSpecialNew| *2 (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariateTaylorSeriesCategory| *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *3 (|Ring|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) NIL)
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|)))
          <5 (|evalMmCond0| ((*3 |Integer|)))
        <4 (|evalMmCond| ((*3 |Integer|)))
        4> (|fixUpTypeArgs| ((*3 |Integer|)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePolynomial| # *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |UnivariatePolynomial| # *3)))
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries|))
              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |Variable| #)))
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries|))
              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Symbol|)))
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries|))
              7> (|containsVars1| (|TaylorSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Polynomial| *3)))
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries|))
              7> (|containsVars1| (|TaylorSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |TexFormat|) (*2 |OutputForm|)))
            6> (|containsVars| (|TexFormat|))
              7> (|containsVars1| (|TexFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|TexFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |TexFormat1| *3) (*2 |TexFormat|)))
            6> (|containsVars| (|TexFormat|))
              7> (|containsVars1| (|TexFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Tableau| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Tableau| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Tableau| *3))
              7> (|containsVars1| (|Tableau| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Tableau| *3))
              7> (|containsVars1| (|Tableau| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Tableau|))
              7> (|containsVars1| (|Tableau|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Table| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|SymbolTable|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |SymbolTable|) (*2 |Table| # #)))
            6> (|containsVars| (|SymbolTable|))
              7> (|containsVars1| (|SymbolTable|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Symbol|) (*2 |String|)))
            6> (|containsVars| (|Symbol|))
              7> (|containsVars1| (|Symbol|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Switch|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Switch|) (*2 |Symbol|)))
            6> (|containsVars| (|Switch|))
              7> (|containsVars1| (|Switch|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Stream| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Stream| *3) (*2 |List| *3)))
            6> (|containsVars| (|Stream| *3))
              7> (|containsVars1| (|Stream| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stream| *3))
              7> (|containsVars1| (|Stream| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stream|))
              7> (|containsVars1| (|Stream|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Stack| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Stack| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Stack| *3))
              7> (|containsVars1| (|Stack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stack| *3))
              7> (|containsVars1| (|Stack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stack|))
              7> (|containsVars1| (|Stack|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Character|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|StringAggregate|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Character|)))
            6> (|containsVars| (|Character|))
              7> (|containsVars1| (|Character|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|ThreeSpaceCategory| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |OutputForm|)))
            6> (|containsVars| (|OutputForm|))
              7> (|containsVars1| (|OutputForm|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Integer|)))
            6> (|containsVars| (|Integer|))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|RationalFunction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |RationalFunction| *3) (*2 |Fraction| #)))
            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
                8> (|containsVars1| (|Polynomial| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
                8> (|containsVars1| (|Polynomial| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction|))
              7> (|containsVars1| (|Fraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|RetractableTo| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|RetractableTo| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|RetractableTo| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|RetractableTo| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|RetractableTo| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|RetractableTo| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|RetractableTo| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
                8> (|hasCate| *2 (|Type|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|Type|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|Type|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Exit|)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *2) (*3 |Exit|)))
            6> (|containsVars| (|Exit|))
              7> (|containsVars1| (|Exit|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Void|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *3) (*2 |Void|)))
            6> (|containsVars| (|Void|))
              7> (|containsVars1| (|Void|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|RadixExpansion| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |RadixExpansion| *3) (*2 |Fraction| #)))
            6> (|containsVars| (|RadixExpansion| *3))
              7> (|containsVars1| (|RadixExpansion| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|RadixExpansion| *3))
              7> (|containsVars1| (|RadixExpansion| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|RadixExpansion| *3))
              7> (|containsVars1| (|RadixExpansion| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Queue| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Queue| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Queue| *3))
              7> (|containsVars1| (|Queue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Queue| *3))
              7> (|containsVars1| (|Queue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Queue|))
              7> (|containsVars1| (|Queue|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Pi|)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PiCoercions| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
        <4 (|evalMmStack| ((# # # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
            <6 (|evalMmDom| ((*1 |PiCoercions| *4) (*2 |Expression| *4) (*3 |Pi|)))
            6> (|containsVars| (|Expression| *4))
              7> (|containsVars1| (|Expression| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Expression| *4))
              7> (|containsVars1| (|Expression| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Expression|))
              7> (|containsVars1| (|Expression|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| *3)))
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction|))
              7> (|containsVars1| (|PartialFraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| #)))
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction|))
              7> (|containsVars1| (|PartialFraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| #)))
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation|))
              7> (|containsVars1| (|Permutation|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| *3)))
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation|))
              7> (|containsVars1| (|Permutation|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup|))
              7> (|containsVars1| (|PermutationGroup|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup|))
              7> (|containsVars1| (|PermutationGroup|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Tree| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PendantTree| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |PendantTree| *3) (*2 |Tree| *3)))
            6> (|containsVars| (|PendantTree| *3))
              7> (|containsVars1| (|PendantTree| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PendantTree| *3))
              7> (|containsVars1| (|PendantTree| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PendantTree|))
              7> (|containsVars1| (|PendantTree|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalPDEProblem|))
              7> (|containsVars1| (|NumericalPDEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |Record| # # # # #)))
            6> (|containsVars| (|NumericalPDEProblem|))
              7> (|containsVars1| (|NumericalPDEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Fraction| #)))
            6> (|containsVars| (|Expression| (|Integer|)))
              7> (|containsVars1| (|Expression| (|Integer|)))
                8> (|containsVars1| (|Integer|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Polynomial| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Polynomial| #)))
            6> (|containsVars| (|Expression| (|Integer|)))
              7> (|containsVars1| (|Expression| (|Integer|)))
                8> (|containsVars1| (|Integer|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Color|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Palette|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Palette|) (*2 |Color|)))
            6> (|containsVars| (|Palette|))
              7> (|containsVars1| (|Palette|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|OrdSetInts|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |OrdSetInts|) (*2 |Integer|)))
            6> (|containsVars| (|OrdSetInts|))
              7> (|containsVars1| (|OrdSetInts|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # # # # #)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # #)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Union| # #)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|OpenMathErrorKind|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |OpenMathErrorKind|) (*2 |Symbol|)))
            6> (|containsVars| (|OpenMathErrorKind|))
              7> (|containsVars1| (|OpenMathErrorKind|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *4 *3))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
        4> (|evalMmStack| (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *4 *3))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalODEProblem|))
              7> (|containsVars1| (|NumericalODEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |Record| # # # # # # # #)))
            6> (|containsVars| (|NumericalODEProblem|))
              7> (|containsVars1| (|NumericalODEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|None|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NoneFunctions1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |NoneFunctions1| *3) (*2 |None|)))
            6> (|containsVars| (|None|))
              7> (|containsVars1| (|None|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # # #)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # #)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Union| # #)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|NonAssociativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Integer|)))
            6> (|containsVars| (|Integer|))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *2)))
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Polynomial| *4)))
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MyExpression| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MyExpression| *3 *4) (*2 |Fraction| #)))
            6> (|containsVars| (|MyExpression| *3 *4))
              7> (|containsVars1| (|MyExpression| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyExpression| *3 *4))
              7> (|containsVars1| (|MyExpression| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyExpression| *3))
              7> (|containsVars1| (|MyExpression| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MathMLFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MathMLFormat|) (*2 |String|) (*3 |OutputForm|)))
            6> (|containsVars| (|String|))
              7> (|containsVars1| (|String|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineInteger|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineInteger|) (*2 |Expression| #) (*3 |Expression| #)))
            6> (|containsVars| (|Expression| (|MachineInteger|)))
              7> (|containsVars1| (|Expression| (|MachineInteger|)))
                8> (|containsVars1| (|MachineInteger|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Float|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |Float|)))
            6> (|containsVars| (|MachineFloat|))
              7> (|containsVars1| (|MachineFloat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|MachineInteger|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |MachineInteger|)))
            6> (|containsVars| (|MachineFloat|))
              7> (|containsVars1| (|MachineFloat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *4 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) |coerce| NIL)
                8> (|hasCate| *1 (|MatrixCategory| *3 *4 *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|MatrixCategory| *3 *4 *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) |coerce| NIL)
                8> (|hasCate| *2 (|FiniteLinearAggregate| *3) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL)
                    10> (|hasCate| (|Integer|) (|FiniteLinearAggregate| *3) ((*2 |Integer|)))
                    <10 (|hasCate| |failed|)
                    10> (|hasCateSpecialNew| *2 (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
                <8 (|defaultTypeForCategory| (|Vector| *3))
                8> (|containsVars| (|Vector| *3))
                  9> (|containsVars1| (|Vector| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars| T)
                8> (|containsVars| (|Vector| *3))
                  9> (|containsVars1| (|Vector| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars| T)
                8> (|containsVars| (|Vector|))
                  9> (|containsVars1| (|Vector|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| (|Integer|))
                  9> (|containsVars1| (|Integer|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| *3)
                <8 (|containsVars| T)
                8> (|containsVars| (|Vector|))
                  9> (|containsVars1| (|Vector|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| ((|Integer|)))
                  9> (|containsVars1| ((|Integer|)))
                    10> (|containsVars1| (|Integer|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) |coerce| NIL)
                8> (|hasCate| *4 (|FiniteLinearAggregate| *3) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
                <8 (|defaultTypeForCategory| (|Vector| *3))
              <7 (|evalMmCat1| ((*4 |Vector| *3)))
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| ((*4 |Vector| *3)))
                8> (|hasCate| *3 (|Ring|) ((*4 |Vector| *3)))
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) ((*4 |Vector| *3)))
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|) (*4 |Vector| *3)))
          <5 (|evalMmCond0| ((*3 |Integer|) (*4 |Vector| *3)))
        <4 (|evalMmCond| ((*3 |Integer|) (*4 |Vector| *3)))
        4> (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
          5> (|replaceSharpCalls| (|Vector| *3))
            6> (|noSharpCallsHere| (|Vector| *3))
              7> (|noSharpCallsHere| *3)
              <7 (|noSharpCallsHere| T)
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Vector| *3))
        <4 (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Mapping| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MappingPackage1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |MappingPackage1| *3) (*2 |Mapping| *3)))
            6> (|containsVars| (|Mapping| *3))
              7> (|containsVars1| (|Mapping| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Mapping| *3))
              7> (|containsVars1| (|Mapping| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Mapping| *3))
              7> (|containsVars1| (|Mapping| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix|))
              7> (|containsVars1| (|ThreeDimensionalMatrix|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix|))
              7> (|containsVars1| (|ThreeDimensionalMatrix|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |AssociatedLieAlgebra| *3 *2)))
            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedLieAlgebra|))
              7> (|containsVars1| (|AssociatedLieAlgebra|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|LeftAlgebra| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|LeftAlgebra| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|LeftAlgebra| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|LeftAlgebra| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|LeftAlgebra| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *2 (|Ring|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|Ring|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|Ring|) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|Ring|) NIL)
                    10> (|hasCate| (|Integer|) (|Ring|) ((*2 |Integer|)))
                    <10 (|hasCate| ((*2 |Integer|)))
                  <9 (|hasCateSpecial| ((*2 |Integer|)))
                <8 (|hasCate| ((*2 |Integer|)))
              <7 (|evalMmCat1| ((*2 |Integer|)))
            <6 (|evalMmCat| ((*2 |Integer|)))
          <5 (|evalMmCond0| ((*2 |Integer|)))
        <4 (|evalMmCond| ((*2 |Integer|)))
        4> (|fixUpTypeArgs| ((*2 |Integer|)))
          5> (|coerceTypeArgs| (|PositiveInteger|) (|Integer|) ((*2 |Integer|)))
          <5 (|coerceTypeArgs| (|Integer|))
        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|CoercibleTo| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|CoercibleTo| *2)) (|ofCategory| *2 (|Type|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|CoercibleTo| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|CoercibleTo| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|CoercibleTo| *2) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|CoercibleTo| *2) NIL *1)
                    10> (|hasCate| (|PositiveInteger|) (|CoercibleTo| *2) NIL)
                    11> (|mkDomPvar| $ (|PositiveInteger|) ((|OutputForm|)) (*2))
                    <11 (|mkDomPvar| (|PositiveInteger|))
                    11> (|domArg2| (|OutputForm|) (($ |PositiveInteger|)) (($ |PositiveInteger|)))
                    <11 (|domArg2| (|OutputForm|))
                    11> (|unifyStruct| (*2) ((|OutputForm|)) ((*1 |PositiveInteger|)))
                    12> (|unifyStruct| *2 (|OutputForm|) ((*1 |PositiveInteger|)))
                    13> (|unifyStructVar| *2 (|OutputForm|) ((*1 |PositiveInteger|)))
                    14> (|unifyStruct| (|List| (|Integer|)) (|OutputForm|) ((*1 |PositiveInteger|)))
                    15> (|unifyStruct| |List| |OutputForm| ((*1 |PositiveInteger|)))
                    <15 (|unifyStruct| |failed|)
                    <14 (|unifyStruct| |failed|)
                    <13 (|unifyStructVar| |failed|)
                    <12 (|unifyStruct| |failed|)
                    <11 (|unifyStruct| |failed|)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|PositiveInteger|) (|CoercibleTo| *2) NIL)
                    10> (|hasCate| (|Integer|) (|CoercibleTo| *2) ((*1 |Integer|)))
                    11> (|mkDomPvar| $ (|Integer|) ((|OutputForm|)) (*2))
                    <11 (|mkDomPvar| (|Integer|))
                    11> (|domArg2| (|OutputForm|) (($ |Integer|)) (($ |Integer|)))
                    <11 (|domArg2| (|OutputForm|))
                    11> (|unifyStruct| (*2) ((|OutputForm|)) ((*1 |Integer|)))
                    12> (|unifyStruct| *2 (|OutputForm|) ((*1 |Integer|)))
                    13> (|unifyStructVar| *2 (|OutputForm|) ((*1 |Integer|)))
                    14> (|unifyStruct| (|List| (|Integer|)) (|OutputForm|) ((*1 |Integer|)))
                    15> (|unifyStruct| |List| |OutputForm| ((*1 |Integer|)))
                    <15 (|unifyStruct| |failed|)
                    <14 (|unifyStruct| |failed|)
                    <13 (|unifyStructVar| |failed|)
                    <12 (|unifyStruct| |failed|)
                    <11 (|unifyStruct| |failed|)
                    <10 (|hasCate| |failed|)
                    10> (|hasCateSpecialNew| *1 (|PositiveInteger|) (|CoercibleTo| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|CoercibleTo| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
                8> (|hasCate| *2 (|Type|) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|Type|) NIL *2)
                    10> (|hasCate| (|List| (|Integer|)) (|Type|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|PositiveInteger|) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|PositiveInteger|) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |AssociatedJordanAlgebra| *3 *2)))
            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedJordanAlgebra|))
              7> (|containsVars1| (|AssociatedJordanAlgebra|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *6)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|ofCategory| *6 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|OrderedAbelianMonoidSup|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *5 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PolynomialIdeals| *3 *4 *5 *6) (*2 |List| *6)))
            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PolynomialIdeals|))
              7> (|containsVars1| (|PolynomialIdeals|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|IndexCard|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |IndexCard|) (*2 |String|)))
            6> (|containsVars| (|IndexCard|))
              7> (|containsVars1| (|IndexCard|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |Fraction| #)))
            6> (|containsVars| (|HexadecimalExpansion|))
              7> (|containsVars1| (|HexadecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 16)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |RadixExpansion| 16)))
            6> (|containsVars| (|HexadecimalExpansion|))
              7> (|containsVars1| (|HexadecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Heap| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Heap| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Heap| *3))
              7> (|containsVars1| (|Heap| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Heap| *3))
              7> (|containsVars1| (|Heap| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Heap|))
              7> (|containsVars1| (|Heap|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *5 *3))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |Variable| *4)))
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 *3))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |UnivariatePuiseuxSeries| *3 *4 *5)))
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Vector| #)))
            6> (|containsVars| (|Vector| (|MachineFloat|)))
              7> (|containsVars1| (|Vector| (|MachineFloat|)))
                8> (|containsVars1| (|MachineFloat|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |OutputForm|)))
            6> (|containsVars| (|FortranType|))
              7> (|containsVars1| (|FortranType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |FortranScalarType|)))
            6> (|containsVars| (|FortranType|))
              7> (|containsVars1| (|FortranType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |String|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SExpression|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |SExpression|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| *3 #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |SparseMultivariatePolynomial| *3 #)))
            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|SparseMultivariatePolynomial|))
              7> (|containsVars1| (|SparseMultivariatePolynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Fraction| *3)))
            6> (|containsVars| (|Fraction| *3))
              7> (|containsVars1| (|Fraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction| *3))
              7> (|containsVars1| (|Fraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction|))
              7> (|containsVars1| (|Fraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Polynomial| #)))
            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                8> (|containsVars1| (|Fraction| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                8> (|containsVars1| (|Fraction| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Polynomial|))
              7> (|containsVars1| (|Polynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Fraction| #)))
            6> (|containsVars| (|Fraction| (|Polynomial| #)))
              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                  9> (|containsVars1| (|Fraction| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction| (|Polynomial| #)))
              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                  9> (|containsVars1| (|Fraction| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction|))
              7> (|containsVars1| (|Fraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *2 *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FourierSeries| *2 *3)))
            6> (|containsVars| (|FourierSeries| *2 *3))
              7> (|containsVars1| (|FourierSeries| *2 *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries| *2 *3))
              7> (|containsVars1| (|FourierSeries| *2 *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries|))
              7> (|containsVars1| (|FourierSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FourierComponent| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FourierSeries| *3 *4) (*2 |FourierComponent| *4)))
            6> (|containsVars| (|FourierSeries| *3 *4))
              7> (|containsVars1| (|FourierSeries| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries| *3 *4))
              7> (|containsVars1| (|FourierSeries| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries|))
              7> (|containsVars1| (|FourierSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |FortranCode|)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |List| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Record| # #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat|) (*2 |OutputForm|)))
            6> (|containsVars| (|ScriptFormulaFormat|))
              7> (|containsVars1| (|ScriptFormulaFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|ScriptFormulaFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat1| *3) (*2 |ScriptFormulaFormat|)))
            6> (|containsVars| (|ScriptFormulaFormat|))
              7> (|containsVars1| (|ScriptFormulaFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |String|)))
            6> (|containsVars| (|String|))
              7> (|containsVars1| (|String|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |String|)))
            6> (|containsVars| (|String|))
              7> (|containsVars1| (|String|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Matrix| #)))
            6> (|containsVars| (|Matrix| (|MachineFloat|)))
              7> (|containsVars1| (|Matrix| (|MachineFloat|)))
                8> (|containsVars1| (|MachineFloat|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) |coerce| NIL)
                8> (|hasCate| *1 (|FreeLieAlgebra| *2 *3) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FreeLieAlgebra| *2 *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
                8> (|hasCate| *2 (|OrderedSet|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|OrderedSet|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|OrderedSet|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|CommutativeRing|)) |coerce| NIL)
                8> (|hasCate| *3 (|CommutativeRing|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|CommutativeRing|) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|XDistributedPolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |XDistributedPolynomial| *3 *4)))
            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XDistributedPolynomial|))
              7> (|containsVars1| (|XDistributedPolynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|XRecursivePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |XRecursivePolynomial| *3 *4)))
            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XRecursivePolynomial|))
              7> (|containsVars1| (|XRecursivePolynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *2)
                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                  9> (|hasCate1| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *3)
                    10> (|hasCate| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*3 |Integer|) (*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCate| |failed|)
                    10> (|hasCateSpecialNew| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *2 *4 *3))
              7> (|noSharpCallsHere| *2)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *4)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *3)
              <7 (|noSharpCallsHere| T)
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|List| #) *4 (|PositiveInteger|)))
              7> (|containsVars1| (|List| (|Integer|)))
                8> (|containsVars1| (|Integer|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| T)
          <5 (|containsVars1| T)
        <4 (|containsVars| T)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *2)
                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                  9> (|hasCate1| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *3)
                    10> (|hasCate| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*3 |Integer|) (*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCate| |failed|)
                    10> (|hasCateSpecialNew| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *3 *4 *2))
              7> (|noSharpCallsHere| *3)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *4)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *2)
              <7 (|noSharpCallsHere| T)
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|PositiveInteger|) *4 (|List| #)))
              7> (|containsVars1| (|PositiveInteger|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| T)
          <5 (|containsVars1| T)
        <4 (|containsVars| T)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranExpression| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|FortranMachineTypeCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            <6 (|evalMmDom| ((*1 |FortranExpression| *3 *4 *5) (*2 |Expression| *5)))
            6> (|containsVars| (|FortranExpression| *3 *4 *5))
              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranExpression| *3 *4 *5))
              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranExpression| *3 *4))
              7> (|containsVars1| (|FortranExpression| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranCode|) (*2 |OutputForm|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|DifferentialVariableCategory| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|DifferentialVariableCategory| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
                8> (|hasCate| *2 (|OrderedSet|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|OrderedSet|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|OrderedSet|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|PositiveInteger|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|SegmentBinding| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SegmentBinding| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DrawNumericHack| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DrawNumericHack| *4) (*2 |SegmentBinding| #) (*3 |SegmentBinding| #)))
            6> (|containsVars| (|SegmentBinding| (|Float|)))
              7> (|containsVars1| (|SegmentBinding| (|Float|)))
                8> (|containsVars1| (|Float|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Dequeue| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Dequeue| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Dequeue| *3))
              7> (|containsVars1| (|Dequeue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Dequeue| *3))
              7> (|containsVars1| (|Dequeue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Dequeue|))
              7> (|containsVars1| (|Dequeue|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |Fraction| #)))
            6> (|containsVars| (|DecimalExpansion|))
              7> (|containsVars1| (|DecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 10)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |RadixExpansion| 10)))
            6> (|containsVars| (|DecimalExpansion|))
              7> (|containsVars1| (|DecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Database| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Database| *3) (*2 |List| *3)))
            6> (|containsVars| (|Database| *3))
              7> (|containsVars1| (|Database| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Database| *3))
              7> (|containsVars1| (|Database| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Database|))
              7> (|containsVars1| (|Database|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|DirectProduct| *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |DirectProduct| *4 *5)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SquareMatrix| *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |SquareMatrix| *4 *5)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| *5)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| #)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |Fraction| #)))
            6> (|containsVars| (|BinaryExpansion|))
              7> (|containsVars1| (|BinaryExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 2)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |RadixExpansion| 2)))
            6> (|containsVars| (|BinaryExpansion|))
              7> (|containsVars1| (|BinaryExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ArrayStack| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ArrayStack| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|ArrayStack| *3))
              7> (|containsVars1| (|ArrayStack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ArrayStack| *3))
              7> (|containsVars1| (|ArrayStack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ArrayStack|))
              7> (|containsVars1| (|ArrayStack|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp9| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp9| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp9| *3))
              7> (|containsVars1| (|Asp9| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp9| *3))
              7> (|containsVars1| (|Asp9| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp9| *3))
              7> (|containsVars1| (|Asp9| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp80| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp80| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp80| *3))
              7> (|containsVars1| (|Asp80| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp80| *3))
              7> (|containsVars1| (|Asp80| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp80| *3))
              7> (|containsVars1| (|Asp80| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp7| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp7| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp7| *3))
              7> (|containsVars1| (|Asp7| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp7| *3))
              7> (|containsVars1| (|Asp7| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp7| *3))
              7> (|containsVars1| (|Asp7| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp78| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp78| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp78| *3))
              7> (|containsVars1| (|Asp78| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp78| *3))
              7> (|containsVars1| (|Asp78| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp78| *3))
              7> (|containsVars1| (|Asp78| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp77| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp77| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp77| *3))
              7> (|containsVars1| (|Asp77| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp77| *3))
              7> (|containsVars1| (|Asp77| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp77| *3))
              7> (|containsVars1| (|Asp77| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp74| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp74| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp74| *3))
              7> (|containsVars1| (|Asp74| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp74| *3))
              7> (|containsVars1| (|Asp74| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp74| *3))
              7> (|containsVars1| (|Asp74| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp73| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp73| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp73| *3))
              7> (|containsVars1| (|Asp73| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp73| *3))
              7> (|containsVars1| (|Asp73| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp73| *3))
              7> (|containsVars1| (|Asp73| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp6| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp6| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp6| *3))
              7> (|containsVars1| (|Asp6| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp6| *3))
              7> (|containsVars1| (|Asp6| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp6| *3))
              7> (|containsVars1| (|Asp6| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp55| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp55| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp55| *3))
              7> (|containsVars1| (|Asp55| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp55| *3))
              7> (|containsVars1| (|Asp55| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp55| *3))
              7> (|containsVars1| (|Asp55| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp50| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp50| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp50| *3))
              7> (|containsVars1| (|Asp50| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp50| *3))
              7> (|containsVars1| (|Asp50| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp50| *3))
              7> (|containsVars1| (|Asp50| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp4| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp4| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp4| *3))
              7> (|containsVars1| (|Asp4| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp4| *3))
              7> (|containsVars1| (|Asp4| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp4| *3))
              7> (|containsVars1| (|Asp4| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp49| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp49| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp49| *3))
              7> (|containsVars1| (|Asp49| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp49| *3))
              7> (|containsVars1| (|Asp49| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp49| *3))
              7> (|containsVars1| (|Asp49| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp42| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp42| *3 *4 *5) (*2 |Vector| #)))
            6> (|containsVars| (|Asp42| *3 *4 *5))
              7> (|containsVars1| (|Asp42| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp42| *3 *4 *5))
              7> (|containsVars1| (|Asp42| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp42| *3 *4 *5))
              7> (|containsVars1| (|Asp42| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp41| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp41| *3 *4 *5) (*2 |Vector| #)))
            6> (|containsVars| (|Asp41| *3 *4 *5))
              7> (|containsVars1| (|Asp41| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp41| *3 *4 *5))
              7> (|containsVars1| (|Asp41| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp41| *3 *4 *5))
              7> (|containsVars1| (|Asp41| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp35| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp35| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp35| *3))
              7> (|containsVars1| (|Asp35| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp35| *3))
              7> (|containsVars1| (|Asp35| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp35| *3))
              7> (|containsVars1| (|Asp35| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp31| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp31| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp31| *3))
              7> (|containsVars1| (|Asp31| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp31| *3))
              7> (|containsVars1| (|Asp31| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp31| *3))
              7> (|containsVars1| (|Asp31| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp24| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp24| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp24| *3))
              7> (|containsVars1| (|Asp24| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp24| *3))
              7> (|containsVars1| (|Asp24| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp24| *3))
              7> (|containsVars1| (|Asp24| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp20| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp20| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp20| *3))
              7> (|containsVars1| (|Asp20| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp20| *3))
              7> (|containsVars1| (|Asp20| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp20| *3))
              7> (|containsVars1| (|Asp20| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp1| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp1| *3))
              7> (|containsVars1| (|Asp1| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp1| *3))
              7> (|containsVars1| (|Asp1| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp1| *3))
              7> (|containsVars1| (|Asp1| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp19| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp19| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp19| *3))
              7> (|containsVars1| (|Asp19| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp19| *3))
              7> (|containsVars1| (|Asp19| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp19| *3))
              7> (|containsVars1| (|Asp19| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp10| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp10| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp10| *3))
              7> (|containsVars1| (|Asp10| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp10| *3))
              7> (|containsVars1| (|Asp10| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp10| *3))
              7> (|containsVars1| (|Asp10| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Any|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AnyFunctions1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |AnyFunctions1| *3) (*2 |Any|)))
            6> (|containsVars| (|Any|))
              7> (|containsVars1| (|Any|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraicNumber|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |AlgebraicNumber|) (*2 |SparseMultivariatePolynomial| # #)))
            6> (|containsVars| (|AlgebraicNumber|))
              7> (|containsVars1| (|AlgebraicNumber|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *6 (|Vector| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|PositiveInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |AlgebraGivenByStructuralConstants| *3 *4 *5 *6) (*2 |Vector| *3)))
            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|Algebra| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|Algebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|Algebra| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|Algebra| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|Algebra| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|Algebra| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|Algebra| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Algebra| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|CommutativeRing|)) |coerce| NIL)
                8> (|hasCate| *2 (|CommutativeRing|) NIL)
                  9> (|hasCate1| (|PositiveInteger|) (|CommutativeRing|) NIL *2)
                    10> (|hasCate| (|PositiveInteger|) (|CommutativeRing|) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|CommutativeRing|) NIL)
                    10> (|hasCate| (|Integer|) (|CommutativeRing|) ((*2 |Integer|)))
                    <10 (|hasCate| ((*2 |Integer|)))
                  <9 (|hasCateSpecial| ((*2 |Integer|)))
                <8 (|hasCate| ((*2 |Integer|)))
              <7 (|evalMmCat1| ((*2 |Integer|)))
            <6 (|evalMmCat| ((*2 |Integer|)))
          <5 (|evalMmCond0| ((*2 |Integer|)))
        <4 (|evalMmCond| ((*2 |Integer|)))
        4> (|fixUpTypeArgs| ((*2 |Integer|)))
          5> (|coerceTypeArgs| (|PositiveInteger|) (|Integer|) ((*2 |Integer|)))
          <5 (|coerceTypeArgs| (|Integer|))
        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
    <2 (|selectMmsGen,matchMms| NIL)
  <1 (|selectMmsGen| NIL)
  1> (|selectMmsGen| |coerce| (|List| (|Integer|)) ((|Integer|)) ((|Integer|)))
    2> (|filterModemapsFromPackages| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) ("Integer" "List") |coerce|)
    <2 (|filterModemapsFromPackages| ((# # #) (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
    2> (|selectMmsGen,exact?| ((# #) (# #) (# #)) (|List| (|Integer|)) ((|Integer|)))
    <2 (|selectMmsGen,exact?| (NIL (# # #)))
    2> (|selectMmsGen,matchMms| ((# #) (# #) (# #)) |coerce| (|List| (|Integer|)) ((|Integer|)) ((|Integer|)))
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineInteger|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineInteger|) (*2 |Expression| #) (*3 |Expression| #)))
            6> (|containsVars| (|Expression| (|MachineInteger|)))
              7> (|containsVars1| (|Expression| (|MachineInteger|)))
                8> (|containsVars1| (|MachineInteger|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList|))
              7> (|containsVars1| (|DataList|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList| *3))
              7> (|containsVars1| (|DataList| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|DataList|))
              7> (|containsVars1| (|DataList|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
    <2 (|selectMmsGen,matchMms| NIL)
    2> (|selectMmsGen,exact?| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) (|List| (|Integer|)) ((|Integer|)))
    <2 (|selectMmsGen,exact?| (NIL (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
    2> (|selectMmsGen,matchMms| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) |coerce| (|List| (|Integer|)) ((|Integer|)) ((|Integer|)))
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) |coerce| NIL)
                8> (|hasCate| *1 (|XFreeAlgebra| *2 *3) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|XFreeAlgebra| *2 *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
                8> (|hasCate| *2 (|OrderedSet|) NIL)
                  9> (|hasCate1| (|Integer|) (|OrderedSet|) NIL *2)
                    10> (|hasCate| (|Integer|) (|OrderedSet|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *3 (|Ring|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) NIL)
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|)))
          <5 (|evalMmCond0| ((*3 |Integer|)))
        <4 (|evalMmCond| ((*3 |Integer|)))
        4> (|fixUpTypeArgs| ((*3 |Integer|)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|XAlgebra| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|XAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|XAlgebra| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|XAlgebra| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|XAlgebra| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|XAlgebra| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|XAlgebra| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|XAlgebra| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *2 (|Ring|) NIL)
                  9> (|hasCate1| (|Integer|) (|Ring|) NIL *2)
                    10> (|hasCate| (|Integer|) (|Ring|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Void|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Void|) (*2 |OutputForm|)))
            6> (|containsVars| (|Void|))
              7> (|containsVars1| (|Void|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) |coerce| NIL)
                8> (|hasCate| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) |coerce| NIL)
                8> (|hasCate| *2 (|UnivariateLaurentSeriesCategory| *3) NIL)
                  9> (|hasCate1| (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL *2)
                    10> (|hasCate| (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL)
                    10> (|hasCateSpecialNew| *2 (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesCategory| *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *3 (|Ring|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) NIL)
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|)))
          <5 (|evalMmCond0| ((*3 |Integer|)))
        <4 (|evalMmCond| ((*3 |Integer|)))
        4> (|fixUpTypeArgs| ((*3 |Integer|)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariatePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            <6 (|evalMmDom| ((*1 |UnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariatePolynomial| *3))
              7> (|containsVars1| (|UnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Segment| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|UniversalSegment| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |UniversalSegment| *3) (*2 |Segment| *3)))
            6> (|containsVars| (|UniversalSegment| *3))
              7> (|containsVars1| (|UniversalSegment| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UniversalSegment| *3))
              7> (|containsVars1| (|UniversalSegment| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UniversalSegment|))
              7> (|containsVars1| (|UniversalSegment|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) |coerce| NIL)
                8> (|hasCate| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) |coerce| NIL)
                8> (|hasCate| *2 (|UnivariateTaylorSeriesCategory| *3) NIL)
                  9> (|hasCate1| (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL *2)
                    10> (|hasCate| (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL)
                    10> (|hasCateSpecialNew| *2 (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|UnivariateTaylorSeriesCategory| *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *3 (|Ring|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) NIL)
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|)))
          <5 (|evalMmCond0| ((*3 |Integer|)))
        <4 (|evalMmCond| ((*3 |Integer|)))
        4> (|fixUpTypeArgs| ((*3 |Integer|)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePolynomial| # *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |UnivariatePolynomial| # *3)))
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries|))
              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |Variable| #)))
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|UnivariateFormalPowerSeries|))
              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Symbol|)))
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries|))
              7> (|containsVars1| (|TaylorSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Polynomial| *3)))
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries| *3))
              7> (|containsVars1| (|TaylorSeries| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|TaylorSeries|))
              7> (|containsVars1| (|TaylorSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |TexFormat|) (*2 |OutputForm|)))
            6> (|containsVars| (|TexFormat|))
              7> (|containsVars1| (|TexFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|TexFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |TexFormat1| *3) (*2 |TexFormat|)))
            6> (|containsVars| (|TexFormat|))
              7> (|containsVars1| (|TexFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Tableau| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Tableau| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Tableau| *3))
              7> (|containsVars1| (|Tableau| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Tableau| *3))
              7> (|containsVars1| (|Tableau| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Tableau|))
              7> (|containsVars1| (|Tableau|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Table| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|SymbolTable|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |SymbolTable|) (*2 |Table| # #)))
            6> (|containsVars| (|SymbolTable|))
              7> (|containsVars1| (|SymbolTable|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Symbol|) (*2 |String|)))
            6> (|containsVars| (|Symbol|))
              7> (|containsVars1| (|Symbol|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Switch|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Switch|) (*2 |Symbol|)))
            6> (|containsVars| (|Switch|))
              7> (|containsVars1| (|Switch|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Stream| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Stream| *3) (*2 |List| *3)))
            6> (|containsVars| (|Stream| *3))
              7> (|containsVars1| (|Stream| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stream| *3))
              7> (|containsVars1| (|Stream| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stream|))
              7> (|containsVars1| (|Stream|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Stack| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Stack| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Stack| *3))
              7> (|containsVars1| (|Stack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stack| *3))
              7> (|containsVars1| (|Stack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Stack|))
              7> (|containsVars1| (|Stack|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Character|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|StringAggregate|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Character|)))
            6> (|containsVars| (|Character|))
              7> (|containsVars1| (|Character|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|ThreeSpaceCategory| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |OutputForm|)))
            6> (|containsVars| (|OutputForm|))
              7> (|containsVars1| (|OutputForm|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Integer|)))
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)) ((*2 |Integer|)))
              7> (|orderMmCatStack| ((|ofCategory| *1 #)))
              <7 (|orderMmCatStack| ((|ofCategory| *1 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|Ring|)) |coerce| ((*2 |Integer|)))
                8> (|hasCate| *1 (|Ring|) ((*2 |Integer|)))
                  9> (|hasCate1| (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)) *1)
                    10> (|hasCate| (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)))
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) ((*2 |Integer|)))
                <8 (|defaultTypeForCategory| (|Integer|))
                8> (|containsVars| (|Integer|))
                  9> (|containsVars1| (|Integer|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| ((*2 |Integer|)))
          <5 (|evalMmCond0| ((*2 |Integer|)))
        <4 (|evalMmCond| ((*2 |Integer|)))
        4> (|fixUpTypeArgs| ((*2 |Integer|)))
          5> (|coerceTypeArgs| (|Integer|) (|Integer|) ((*2 |Integer|)))
          <5 (|coerceTypeArgs| (|Integer|))
        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|RationalFunction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |RationalFunction| *3) (*2 |Fraction| #)))
            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
                8> (|containsVars1| (|Polynomial| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
                8> (|containsVars1| (|Polynomial| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction|))
              7> (|containsVars1| (|Fraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|RetractableTo| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|RetractableTo| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|RetractableTo| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|RetractableTo| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|RetractableTo| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|RetractableTo| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|RetractableTo| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
                8> (|hasCate| *2 (|Type|) NIL)
                  9> (|hasCate1| (|Integer|) (|Type|) NIL *2)
                    10> (|hasCate| (|Integer|) (|Type|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Exit|)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *2) (*3 |Exit|)))
            6> (|containsVars| (|Exit|))
              7> (|containsVars1| (|Exit|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Void|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *3) (*2 |Void|)))
            6> (|containsVars| (|Void|))
              7> (|containsVars1| (|Void|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|RadixExpansion| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |RadixExpansion| *3) (*2 |Fraction| #)))
            6> (|containsVars| (|RadixExpansion| *3))
              7> (|containsVars1| (|RadixExpansion| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|RadixExpansion| *3))
              7> (|containsVars1| (|RadixExpansion| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|RadixExpansion| *3))
              7> (|containsVars1| (|RadixExpansion| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Queue| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Queue| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Queue| *3))
              7> (|containsVars1| (|Queue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Queue| *3))
              7> (|containsVars1| (|Queue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Queue|))
              7> (|containsVars1| (|Queue|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Pi|)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PiCoercions| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
        <4 (|evalMmStack| ((# # # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
            <6 (|evalMmDom| ((*1 |PiCoercions| *4) (*2 |Expression| *4) (*3 |Pi|)))
            6> (|containsVars| (|Expression| *4))
              7> (|containsVars1| (|Expression| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Expression| *4))
              7> (|containsVars1| (|Expression| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Expression|))
              7> (|containsVars1| (|Expression|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| *3)))
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction|))
              7> (|containsVars1| (|PartialFraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| #)))
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction| *3))
              7> (|containsVars1| (|PartialFraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PartialFraction|))
              7> (|containsVars1| (|PartialFraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| #)))
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation|))
              7> (|containsVars1| (|Permutation|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| *3)))
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation| *3))
              7> (|containsVars1| (|Permutation| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Permutation|))
              7> (|containsVars1| (|Permutation|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup|))
              7> (|containsVars1| (|PermutationGroup|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup| *3))
              7> (|containsVars1| (|PermutationGroup| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PermutationGroup|))
              7> (|containsVars1| (|PermutationGroup|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Tree| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PendantTree| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |PendantTree| *3) (*2 |Tree| *3)))
            6> (|containsVars| (|PendantTree| *3))
              7> (|containsVars1| (|PendantTree| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PendantTree| *3))
              7> (|containsVars1| (|PendantTree| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PendantTree|))
              7> (|containsVars1| (|PendantTree|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalPDEProblem|))
              7> (|containsVars1| (|NumericalPDEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |Record| # # # # #)))
            6> (|containsVars| (|NumericalPDEProblem|))
              7> (|containsVars1| (|NumericalPDEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Fraction| #)))
            6> (|containsVars| (|Expression| (|Integer|)))
              7> (|containsVars1| (|Expression| (|Integer|)))
                8> (|containsVars1| (|Integer|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|Polynomial| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Polynomial| #)))
            6> (|containsVars| (|Expression| (|Integer|)))
              7> (|containsVars1| (|Expression| (|Integer|)))
                8> (|containsVars1| (|Integer|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Color|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Palette|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Palette|) (*2 |Color|)))
            6> (|containsVars| (|Palette|))
              7> (|containsVars1| (|Palette|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|OrdSetInts|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |OrdSetInts|) (*2 |Integer|)))
            6> (|containsVars| (|OrdSetInts|))
              7> (|containsVars1| (|OrdSetInts|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # # # # #)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # #)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Union| # #)))
            6> (|containsVars| (|NumericalOptimizationProblem|))
              7> (|containsVars1| (|NumericalOptimizationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|OpenMathErrorKind|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |OpenMathErrorKind|) (*2 |Symbol|)))
            6> (|containsVars| (|OpenMathErrorKind|))
              7> (|containsVars1| (|OpenMathErrorKind|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *4 *3))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
        4> (|evalMmStack| (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *4 *3))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalODEProblem|))
              7> (|containsVars1| (|NumericalODEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |Record| # # # # # # # #)))
            6> (|containsVars| (|NumericalODEProblem|))
              7> (|containsVars1| (|NumericalODEProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|None|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NoneFunctions1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |NoneFunctions1| *3) (*2 |None|)))
            6> (|containsVars| (|None|))
              7> (|containsVars1| (|None|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |OutputForm|)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # # #)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # #)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Union| # #)))
            6> (|containsVars| (|NumericalIntegrationProblem|))
              7> (|containsVars1| (|NumericalIntegrationProblem|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|NonAssociativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Integer|)))
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)) ((*2 |Integer|)))
              7> (|orderMmCatStack| ((|ofCategory| *1 #)))
              <7 (|orderMmCatStack| ((|ofCategory| *1 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|NonAssociativeRing|)) |coerce| ((*2 |Integer|)))
                8> (|hasCate| *1 (|NonAssociativeRing|) ((*2 |Integer|)))
                  9> (|hasCate1| (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)) *1)
                    10> (|hasCate| (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)))
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|NonAssociativeRing|) ((*2 |Integer|)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| ((*2 |Integer|)))
          <5 (|evalMmCond0| ((*2 |Integer|)))
        <4 (|evalMmCond| ((*2 |Integer|)))
        4> (|fixUpTypeArgs| ((*2 |Integer|)))
          5> (|coerceTypeArgs| (|Integer|) (|Integer|) ((*2 |Integer|)))
          <5 (|coerceTypeArgs| (|Integer|))
        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *2)))
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Polynomial| *4)))
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyUnivariatePolynomial| *3))
              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MyExpression| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MyExpression| *3 *4) (*2 |Fraction| #)))
            6> (|containsVars| (|MyExpression| *3 *4))
              7> (|containsVars1| (|MyExpression| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyExpression| *3 *4))
              7> (|containsVars1| (|MyExpression| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|MyExpression| *3))
              7> (|containsVars1| (|MyExpression| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MathMLFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MathMLFormat|) (*2 |String|) (*3 |OutputForm|)))
            6> (|containsVars| (|String|))
              7> (|containsVars1| (|String|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Float|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |Float|)))
            6> (|containsVars| (|MachineFloat|))
              7> (|containsVars1| (|MachineFloat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|MachineInteger|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |MachineInteger|)))
            6> (|containsVars| (|MachineFloat|))
              7> (|containsVars1| (|MachineFloat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
            6> (|containsVars| (|MachineComplex|))
              7> (|containsVars1| (|MachineComplex|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *4 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) |coerce| NIL)
                8> (|hasCate| *1 (|MatrixCategory| *3 *4 *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|MatrixCategory| *3 *4 *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) |coerce| NIL)
                8> (|hasCate| *2 (|FiniteLinearAggregate| *3) NIL)
                  9> (|hasCate1| (|Integer|) (|FiniteLinearAggregate| *3) NIL *2)
                    10> (|hasCate| (|Integer|) (|FiniteLinearAggregate| *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|Integer|) (|FiniteLinearAggregate| *3) NIL)
                    10> (|hasCateSpecialNew| *2 (|Integer|) (|FiniteLinearAggregate| *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
                <8 (|defaultTypeForCategory| (|Vector| *3))
                8> (|containsVars| (|Vector| *3))
                  9> (|containsVars1| (|Vector| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars| T)
                8> (|containsVars| (|Vector| *3))
                  9> (|containsVars1| (|Vector| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars| T)
                8> (|containsVars| (|Vector|))
                  9> (|containsVars1| (|Vector|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| (|Integer|))
                  9> (|containsVars1| (|Integer|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| *3)
                <8 (|containsVars| T)
                8> (|containsVars| (|Vector|))
                  9> (|containsVars1| (|Vector|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
                8> (|containsVars| ((|Integer|)))
                  9> (|containsVars1| ((|Integer|)))
                    10> (|containsVars1| (|Integer|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) |coerce| NIL)
                8> (|hasCate| *4 (|FiniteLinearAggregate| *3) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
                <8 (|defaultTypeForCategory| (|Vector| *3))
              <7 (|evalMmCat1| ((*4 |Vector| *3)))
              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| ((*4 |Vector| *3)))
                8> (|hasCate| *3 (|Ring|) ((*4 |Vector| *3)))
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Ring|) ((*4 |Vector| *3)))
                <8 (|defaultTypeForCategory| (|Integer|))
              <7 (|evalMmCat1| ((*3 |Integer|)))
            <6 (|evalMmCat| ((*3 |Integer|) (*4 |Vector| *3)))
          <5 (|evalMmCond0| ((*3 |Integer|) (*4 |Vector| *3)))
        <4 (|evalMmCond| ((*3 |Integer|) (*4 |Vector| *3)))
        4> (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
          5> (|replaceSharpCalls| (|Integer|))
            6> (|noSharpCallsHere| (|Integer|))
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Integer|))
          5> (|replaceSharpCalls| (|Vector| *3))
            6> (|noSharpCallsHere| (|Vector| *3))
              7> (|noSharpCallsHere| *3)
              <7 (|noSharpCallsHere| T)
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|Vector| *3))
        <4 (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Mapping| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|MappingPackage1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |MappingPackage1| *3) (*2 |Mapping| *3)))
            6> (|containsVars| (|Mapping| *3))
              7> (|containsVars1| (|Mapping| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Mapping| *3))
              7> (|containsVars1| (|Mapping| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Mapping| *3))
              7> (|containsVars1| (|Mapping| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix|))
              7> (|containsVars1| (|ThreeDimensionalMatrix|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ThreeDimensionalMatrix|))
              7> (|containsVars1| (|ThreeDimensionalMatrix|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |AssociatedLieAlgebra| *3 *2)))
            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedLieAlgebra|))
              7> (|containsVars1| (|AssociatedLieAlgebra|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|LeftAlgebra| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|LeftAlgebra| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|LeftAlgebra| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|LeftAlgebra| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|LeftAlgebra| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
                8> (|hasCate| *2 (|Ring|) NIL)
                  9> (|hasCate1| (|Integer|) (|Ring|) NIL *2)
                    10> (|hasCate| (|Integer|) (|Ring|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|CoercibleTo| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|CoercibleTo| *2)) (|ofCategory| *2 (|Type|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|CoercibleTo| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|CoercibleTo| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|CoercibleTo| *2) NIL)
                  9> (|hasCate1| (|Integer|) (|CoercibleTo| *2) NIL *1)
                    10> (|hasCate| (|Integer|) (|CoercibleTo| *2) NIL)
                    11> (|mkDomPvar| $ (|Integer|) ((|OutputForm|)) (*2))
                    <11 (|mkDomPvar| (|Integer|))
                    11> (|domArg2| (|OutputForm|) (($ |Integer|)) (($ |Integer|)))
                    <11 (|domArg2| (|OutputForm|))
                    11> (|unifyStruct| (*2) ((|OutputForm|)) ((*1 |Integer|)))
                    12> (|unifyStruct| *2 (|OutputForm|) ((*1 |Integer|)))
                    13> (|unifyStructVar| *2 (|OutputForm|) ((*1 |Integer|)))
                    14> (|unifyStruct| (|List| (|Integer|)) (|OutputForm|) ((*1 |Integer|)))
                    15> (|unifyStruct| |List| |OutputForm| ((*1 |Integer|)))
                    <15 (|unifyStruct| |failed|)
                    <14 (|unifyStruct| |failed|)
                    <13 (|unifyStructVar| |failed|)
                    <12 (|unifyStruct| |failed|)
                    <11 (|unifyStruct| |failed|)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|Integer|) (|CoercibleTo| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|Integer|) (|CoercibleTo| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|CoercibleTo| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
                8> (|hasCate| *2 (|Type|) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|Type|) NIL *2)
                    10> (|hasCate| (|List| (|Integer|)) (|Type|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|Integer|) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|Integer|) (|List| #) (|Integer|)))
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| ((*1 |AssociatedJordanAlgebra| *3 *2)))
            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AssociatedJordanAlgebra|))
              7> (|containsVars1| (|AssociatedJordanAlgebra|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *6)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|ofCategory| *6 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|OrderedAbelianMonoidSup|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *5 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |PolynomialIdeals| *3 *4 *5 *6) (*2 |List| *6)))
            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|PolynomialIdeals|))
              7> (|containsVars1| (|PolynomialIdeals|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|IndexCard|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |IndexCard|) (*2 |String|)))
            6> (|containsVars| (|IndexCard|))
              7> (|containsVars1| (|IndexCard|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |Fraction| #)))
            6> (|containsVars| (|HexadecimalExpansion|))
              7> (|containsVars1| (|HexadecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 16)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |RadixExpansion| 16)))
            6> (|containsVars| (|HexadecimalExpansion|))
              7> (|containsVars1| (|HexadecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Heap| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Heap| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Heap| *3))
              7> (|containsVars1| (|Heap| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Heap| *3))
              7> (|containsVars1| (|Heap| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Heap|))
              7> (|containsVars1| (|Heap|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *5 *3))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |Variable| *4)))
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 *3))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |UnivariatePuiseuxSeries| *3 *4 *5)))
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Vector| #)))
            6> (|containsVars| (|Vector| (|MachineFloat|)))
              7> (|containsVars1| (|Vector| (|MachineFloat|)))
                8> (|containsVars1| (|MachineFloat|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |OutputForm|)))
            6> (|containsVars| (|FortranType|))
              7> (|containsVars1| (|FortranType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |FortranScalarType|)))
            6> (|containsVars| (|FortranType|))
              7> (|containsVars1| (|FortranType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |String|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SExpression|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |SExpression|)))
            6> (|containsVars| (|FortranScalarType|))
              7> (|containsVars1| (|FortranScalarType|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| *3 #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |SparseMultivariatePolynomial| *3 #)))
            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|SparseMultivariatePolynomial|))
              7> (|containsVars1| (|SparseMultivariatePolynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Fraction| *3)))
            6> (|containsVars| (|Fraction| *3))
              7> (|containsVars1| (|Fraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction| *3))
              7> (|containsVars1| (|Fraction| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction|))
              7> (|containsVars1| (|Fraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Polynomial| #)))
            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                8> (|containsVars1| (|Fraction| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                8> (|containsVars1| (|Fraction| *3))
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Polynomial|))
              7> (|containsVars1| (|Polynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Fraction| #)))
            6> (|containsVars| (|Fraction| (|Polynomial| #)))
              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                  9> (|containsVars1| (|Fraction| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction| (|Polynomial| #)))
              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
                  9> (|containsVars1| (|Fraction| *3))
                  <9 (|containsVars1| T)
                <8 (|containsVars1| T)
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Fraction|))
              7> (|containsVars1| (|Fraction|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *2 *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FourierSeries| *2 *3)))
            6> (|containsVars| (|FourierSeries| *2 *3))
              7> (|containsVars1| (|FourierSeries| *2 *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries| *2 *3))
              7> (|containsVars1| (|FourierSeries| *2 *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries|))
              7> (|containsVars1| (|FourierSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FourierComponent| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FourierSeries| *3 *4) (*2 |FourierComponent| *4)))
            6> (|containsVars| (|FourierSeries| *3 *4))
              7> (|containsVars1| (|FourierSeries| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries| *3 *4))
              7> (|containsVars1| (|FourierSeries| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FourierSeries|))
              7> (|containsVars1| (|FourierSeries|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |FortranCode|)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |List| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Record| # #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat|) (*2 |OutputForm|)))
            6> (|containsVars| (|ScriptFormulaFormat|))
              7> (|containsVars1| (|ScriptFormulaFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|ScriptFormulaFormat|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat1| *3) (*2 |ScriptFormulaFormat|)))
            6> (|containsVars| (|ScriptFormulaFormat|))
              7> (|containsVars1| (|ScriptFormulaFormat|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |String|)))
            6> (|containsVars| (|String|))
              7> (|containsVars1| (|String|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |String|)))
            6> (|containsVars| (|String|))
              7> (|containsVars1| (|String|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Matrix| #)))
            6> (|containsVars| (|Matrix| (|MachineFloat|)))
              7> (|containsVars1| (|Matrix| (|MachineFloat|)))
                8> (|containsVars1| (|MachineFloat|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |List| #)))
            6> (|containsVars| (|List| (|FortranCode|)))
              7> (|containsVars1| (|List| (|FortranCode|)))
                8> (|containsVars1| (|FortranCode|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |FortranCode|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
            <6 (|evalMmDom| ((*2 |Record| # #)))
            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
                  9> (|containsVars1| (|SymbolTable|))
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
                8> (|containsVars1| (|:| |code| (|List| #)))
                  9> (|containsVars1| (|List| (|FortranCode|)))
                    10> (|containsVars1| (|FortranCode|))
                    <10 (|containsVars1| NIL)
                  <9 (|containsVars1| NIL)
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) |coerce| NIL)
                8> (|hasCate| *1 (|FreeLieAlgebra| *2 *3) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FreeLieAlgebra| *2 *3) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
                8> (|hasCate| *2 (|OrderedSet|) NIL)
                  9> (|hasCate1| (|Integer|) (|OrderedSet|) NIL *2)
                    10> (|hasCate| (|Integer|) (|OrderedSet|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|CommutativeRing|)) |coerce| NIL)
                8> (|hasCate| *3 (|CommutativeRing|) NIL)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|CommutativeRing|) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|XDistributedPolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |XDistributedPolynomial| *3 *4)))
            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XDistributedPolynomial|))
              7> (|containsVars1| (|XDistributedPolynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|XRecursivePolynomial| *3 *4)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
            <6 (|evalMmDom| ((*2 |XRecursivePolynomial| *3 *4)))
            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|XRecursivePolynomial|))
              7> (|containsVars1| (|XRecursivePolynomial|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *2)
                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                  9> (|hasCate1| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *3)
                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    10> (|hasCateSpecialNew| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *2 *4 *3))
              7> (|noSharpCallsHere| *2)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *4)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *3)
              <7 (|noSharpCallsHere| T)
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|List| #) *4 (|Integer|)))
              7> (|containsVars1| (|List| (|Integer|)))
                8> (|containsVars1| (|Integer|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| T)
          <5 (|containsVars1| T)
        <4 (|containsVars| T)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
                <8 (|mmCatComp| T)
                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *2)
                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                  9> (|hasCate1| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *3)
                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    10> (|hasCateSpecialNew| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *3 *4 *2))
              7> (|noSharpCallsHere| *3)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *4)
              <7 (|noSharpCallsHere| T)
              7> (|noSharpCallsHere| *2)
              <7 (|noSharpCallsHere| T)
            <6 (|noSharpCallsHere| T)
          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|Integer|) *4 (|List| #)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| T)
          <5 (|containsVars1| T)
        <4 (|containsVars| T)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranExpression| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|List| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|FortranMachineTypeCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            <6 (|evalMmDom| ((*1 |FortranExpression| *3 *4 *5) (*2 |Expression| *5)))
            6> (|containsVars| (|FortranExpression| *3 *4 *5))
              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranExpression| *3 *4 *5))
              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|FortranExpression| *3 *4))
              7> (|containsVars1| (|FortranExpression| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|FortranCode|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |FortranCode|) (*2 |OutputForm|)))
            6> (|containsVars| (|FortranCode|))
              7> (|containsVars1| (|FortranCode|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|DifferentialVariableCategory| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|DifferentialVariableCategory| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
                8> (|hasCate| *2 (|OrderedSet|) NIL)
                  9> (|hasCate1| (|Integer|) (|OrderedSet|) NIL *2)
                    10> (|hasCate| (|Integer|) (|OrderedSet|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *3 (|SegmentBinding| #)))
          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SegmentBinding| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DrawNumericHack| *4)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DrawNumericHack| *4) (*2 |SegmentBinding| #) (*3 |SegmentBinding| #)))
            6> (|containsVars| (|SegmentBinding| (|Float|)))
              7> (|containsVars1| (|SegmentBinding| (|Float|)))
                8> (|containsVars1| (|Float|))
                <8 (|containsVars1| NIL)
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Dequeue| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |Dequeue| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|Dequeue| *3))
              7> (|containsVars1| (|Dequeue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Dequeue| *3))
              7> (|containsVars1| (|Dequeue| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Dequeue|))
              7> (|containsVars1| (|Dequeue|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |Fraction| #)))
            6> (|containsVars| (|DecimalExpansion|))
              7> (|containsVars1| (|DecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 10)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |RadixExpansion| 10)))
            6> (|containsVars| (|DecimalExpansion|))
              7> (|containsVars1| (|DecimalExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Database| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Database| *3) (*2 |List| *3)))
            6> (|containsVars| (|Database| *3))
              7> (|containsVars1| (|Database| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Database| *3))
              7> (|containsVars1| (|Database| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Database|))
              7> (|containsVars1| (|Database|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|DirectProduct| *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |DirectProduct| *4 *5)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SquareMatrix| *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |SquareMatrix| *4 *5)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| *5)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| *5)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| #)))
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|CartesianTensor| *3 *4))
              7> (|containsVars1| (|CartesianTensor| *3 *4))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |Fraction| #)))
            6> (|containsVars| (|BinaryExpansion|))
              7> (|containsVars1| (|BinaryExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 2)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |RadixExpansion| 2)))
            6> (|containsVars| (|BinaryExpansion|))
              7> (|containsVars1| (|BinaryExpansion|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|ArrayStack| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |ArrayStack| *3) (*2 |OutputForm|)))
            6> (|containsVars| (|ArrayStack| *3))
              7> (|containsVars1| (|ArrayStack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ArrayStack| *3))
              7> (|containsVars1| (|ArrayStack| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|ArrayStack|))
              7> (|containsVars1| (|ArrayStack|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp9| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp9| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp9| *3))
              7> (|containsVars1| (|Asp9| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp9| *3))
              7> (|containsVars1| (|Asp9| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp9| *3))
              7> (|containsVars1| (|Asp9| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp80| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp80| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp80| *3))
              7> (|containsVars1| (|Asp80| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp80| *3))
              7> (|containsVars1| (|Asp80| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp80| *3))
              7> (|containsVars1| (|Asp80| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp7| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp7| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp7| *3))
              7> (|containsVars1| (|Asp7| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp7| *3))
              7> (|containsVars1| (|Asp7| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp7| *3))
              7> (|containsVars1| (|Asp7| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp78| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp78| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp78| *3))
              7> (|containsVars1| (|Asp78| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp78| *3))
              7> (|containsVars1| (|Asp78| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp78| *3))
              7> (|containsVars1| (|Asp78| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp77| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp77| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp77| *3))
              7> (|containsVars1| (|Asp77| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp77| *3))
              7> (|containsVars1| (|Asp77| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp77| *3))
              7> (|containsVars1| (|Asp77| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp74| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp74| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp74| *3))
              7> (|containsVars1| (|Asp74| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp74| *3))
              7> (|containsVars1| (|Asp74| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp74| *3))
              7> (|containsVars1| (|Asp74| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp73| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp73| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp73| *3))
              7> (|containsVars1| (|Asp73| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp73| *3))
              7> (|containsVars1| (|Asp73| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp73| *3))
              7> (|containsVars1| (|Asp73| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp6| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp6| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp6| *3))
              7> (|containsVars1| (|Asp6| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp6| *3))
              7> (|containsVars1| (|Asp6| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp6| *3))
              7> (|containsVars1| (|Asp6| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp55| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp55| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp55| *3))
              7> (|containsVars1| (|Asp55| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp55| *3))
              7> (|containsVars1| (|Asp55| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp55| *3))
              7> (|containsVars1| (|Asp55| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp50| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp50| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp50| *3))
              7> (|containsVars1| (|Asp50| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp50| *3))
              7> (|containsVars1| (|Asp50| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp50| *3))
              7> (|containsVars1| (|Asp50| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp4| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp4| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp4| *3))
              7> (|containsVars1| (|Asp4| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp4| *3))
              7> (|containsVars1| (|Asp4| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp4| *3))
              7> (|containsVars1| (|Asp4| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp49| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp49| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp49| *3))
              7> (|containsVars1| (|Asp49| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp49| *3))
              7> (|containsVars1| (|Asp49| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp49| *3))
              7> (|containsVars1| (|Asp49| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp42| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp42| *3 *4 *5) (*2 |Vector| #)))
            6> (|containsVars| (|Asp42| *3 *4 *5))
              7> (|containsVars1| (|Asp42| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp42| *3 *4 *5))
              7> (|containsVars1| (|Asp42| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp42| *3 *4 *5))
              7> (|containsVars1| (|Asp42| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp41| *3 *4 *5)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp41| *3 *4 *5) (*2 |Vector| #)))
            6> (|containsVars| (|Asp41| *3 *4 *5))
              7> (|containsVars1| (|Asp41| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp41| *3 *4 *5))
              7> (|containsVars1| (|Asp41| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp41| *3 *4 *5))
              7> (|containsVars1| (|Asp41| *3 *4 *5))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp35| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp35| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp35| *3))
              7> (|containsVars1| (|Asp35| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp35| *3))
              7> (|containsVars1| (|Asp35| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp35| *3))
              7> (|containsVars1| (|Asp35| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp31| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp31| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp31| *3))
              7> (|containsVars1| (|Asp31| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp31| *3))
              7> (|containsVars1| (|Asp31| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp31| *3))
              7> (|containsVars1| (|Asp31| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp24| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp24| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp24| *3))
              7> (|containsVars1| (|Asp24| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp24| *3))
              7> (|containsVars1| (|Asp24| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp24| *3))
              7> (|containsVars1| (|Asp24| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp20| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp20| *3) (*2 |Matrix| #)))
            6> (|containsVars| (|Asp20| *3))
              7> (|containsVars1| (|Asp20| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp20| *3))
              7> (|containsVars1| (|Asp20| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp20| *3))
              7> (|containsVars1| (|Asp20| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp1| *3) (*2 |FortranExpression| # # #)))
            6> (|containsVars| (|Asp1| *3))
              7> (|containsVars1| (|Asp1| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp1| *3))
              7> (|containsVars1| (|Asp1| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp1| *3))
              7> (|containsVars1| (|Asp1| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp19| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp19| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp19| *3))
              7> (|containsVars1| (|Asp19| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp19| *3))
              7> (|containsVars1| (|Asp19| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp19| *3))
              7> (|containsVars1| (|Asp19| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|Asp10| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |Asp10| *3) (*2 |Vector| #)))
            6> (|containsVars| (|Asp10| *3))
              7> (|containsVars1| (|Asp10| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp10| *3))
              7> (|containsVars1| (|Asp10| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|Asp10| *3))
              7> (|containsVars1| (|Asp10| *3))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Any|)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AnyFunctions1| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
            <6 (|evalMmDom| ((*1 |AnyFunctions1| *3) (*2 |Any|)))
            6> (|containsVars| (|Any|))
              7> (|containsVars1| (|Any|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| # #)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraicNumber|)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |AlgebraicNumber|) (*2 |SparseMultivariatePolynomial| # #)))
            6> (|containsVars| (|AlgebraicNumber|))
              7> (|containsVars1| (|AlgebraicNumber|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars| NIL)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| *3)))
          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
          5> (|evalMmStackInner| (|ofType| *6 (|Vector| #)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)))
          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
          5> (|evalMmStackInner| (|ofType| *4 (|PositiveInteger|)))
          <5 (|evalMmStackInner| NIL)
          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
          <5 (|evalMmStackInner| NIL)
        <4 (|evalMmStack| ((# # #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
            <6 (|evalMmDom| ((*1 |AlgebraGivenByStructuralConstants| *3 *4 *5 *6) (*2 |Vector| *3)))
            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
              <7 (|containsVars1| T)
            <6 (|containsVars| T)
          <5 (|evalMmCond0| |failed|)
        <4 (|evalMmCond| |failed|)
      <3 (|evalMm| NIL)
      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
      <3 (|matchTypes| NIL)
      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmStackInner| (|ofCategory| *1 (|Algebra| *2)))
          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
          5> (|evalMmStackInner| (|ofCategory| *2 (|CommutativeRing|)))
          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
        <4 (|evalMmStack| ((# #)))
        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
            <6 (|evalMmDom| NIL)
            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
                8> (|mmCatComp| (|ofCategory| *1 (|Algebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))
                <8 (|mmCatComp| NIL)
                8> (|mmCatComp| (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|Algebra| *2)))
                <8 (|mmCatComp| NIL)
              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
              7> (|evalMmCat1| (|ofCategory| *1 (|Algebra| *2)) |coerce| NIL)
                8> (|hasCate| *1 (|Algebra| *2) NIL)
                  9> (|hasCate1| (|List| (|Integer|)) (|Algebra| *2) NIL *1)
                    10> (|hasCate| (|List| (|Integer|)) (|Algebra| *2) NIL)
                    <10 (|hasCate| |failed|)
                  <9 (|hasCate1| |failed|)
                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
                    <10 (|hasCateSpecialNew| |failed|)
                  <9 (|hasCateSpecial| |failed|)
                <8 (|hasCate| |failed|)
                8> (|defaultTypeForCategory| (|Algebra| *2) NIL)
                <8 (|defaultTypeForCategory| NIL)
              <7 (|evalMmCat1| NIL)
              7> (|evalMmCat1| (|ofCategory| *2 (|CommutativeRing|)) |coerce| NIL)
                8> (|hasCate| *2 (|CommutativeRing|) NIL)
                  9> (|hasCate1| (|Integer|) (|CommutativeRing|) NIL *2)
                    10> (|hasCate| (|Integer|) (|CommutativeRing|) NIL)
                    <10 (|hasCate| NIL)
                  <9 (|hasCate1| NIL)
                <8 (|hasCate| NIL)
              <7 (|evalMmCat1| NIL)
            <6 (|evalMmCat| NIL)
          <5 (|evalMmCond0| NIL)
        <4 (|evalMmCond| NIL)
        4> (|fixUpTypeArgs| NIL)
        <4 (|fixUpTypeArgs| NIL)
        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|List| (|Integer|)))
              7> (|containsVars1| (|Integer|))
              <7 (|containsVars1| NIL)
            <6 (|containsVars1| NIL)
            6> (|containsVars1| (|Integer|))
            <6 (|containsVars1| NIL)
          <5 (|containsVars1| NIL)
        <4 (|containsVars| NIL)
      <3 (|evalMm| NIL)
    <2 (|selectMmsGen,matchMms| NIL)
  <1 (|selectMmsGen| NIL)

   (4)  [555555,1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R  1> (|selectMmsGen| |coerce| (|List| (|Integer|)) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R    2> (|filterModemapsFromPackages| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) ("PositiveInteger" "List") |coerce|)
--R    <2 (|filterModemapsFromPackages| ((# #) (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
--R    2> (|selectMmsGen,exact?| ((# #) (# #)) (|List| (|Integer|)) ((|PositiveInteger|)))
--R    <2 (|selectMmsGen,exact?| (NIL (# #)))
--R    2> (|selectMmsGen,matchMms| ((# #) (# #)) |coerce| (|List| (|Integer|)) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList|))
--R              7> (|containsVars1| (|DataList|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList|))
--R              7> (|containsVars1| (|DataList|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R    <2 (|selectMmsGen,matchMms| NIL)
--R    2> (|selectMmsGen,exact?| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) (|List| (|Integer|)) ((|PositiveInteger|)))
--R    <2 (|selectMmsGen,exact?| (NIL (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
--R    2> (|selectMmsGen,matchMms| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) |coerce| (|List| (|Integer|)) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) |coerce| NIL)
--R                8> (|hasCate| *1 (|XFreeAlgebra| *2 *3) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|XFreeAlgebra| *2 *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|OrderedSet|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|OrderedSet|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|OrderedSet|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|Ring|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) NIL)
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|)))
--R          <5 (|evalMmCond0| ((*3 |Integer|)))
--R        <4 (|evalMmCond| ((*3 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|XAlgebra| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|XAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|XAlgebra| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|XAlgebra| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|XAlgebra| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|XAlgebra| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|XAlgebra| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|XAlgebra| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Ring|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|Ring|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|Ring|) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|Ring|) NIL)
--R                    10> (|hasCate| (|Integer|) (|Ring|) ((*2 |Integer|)))
--R                    <10 (|hasCate| ((*2 |Integer|)))
--R                  <9 (|hasCateSpecial| ((*2 |Integer|)))
--R                <8 (|hasCate| ((*2 |Integer|)))
--R              <7 (|evalMmCat1| ((*2 |Integer|)))
--R            <6 (|evalMmCat| ((*2 |Integer|)))
--R          <5 (|evalMmCond0| ((*2 |Integer|)))
--R        <4 (|evalMmCond| ((*2 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*2 |Integer|)))
--R          5> (|coerceTypeArgs| (|PositiveInteger|) (|Integer|) ((*2 |Integer|)))
--R          <5 (|coerceTypeArgs| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Void|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Void|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Void|))
--R              7> (|containsVars1| (|Void|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) |coerce| NIL)
--R                8> (|hasCate| *2 (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                    10> (|hasCate| (|Integer|) (|UnivariateLaurentSeriesCategory| *3) ((*2 |Integer|)))
--R                    <10 (|hasCate| |failed|)
--R                    10> (|hasCateSpecialNew| *2 (|PositiveInteger|) (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|Ring|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) NIL)
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|)))
--R          <5 (|evalMmCond0| ((*3 |Integer|)))
--R        <4 (|evalMmCond| ((*3 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariatePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            <6 (|evalMmDom| ((*1 |UnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
--R            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariatePolynomial| *3))
--R              7> (|containsVars1| (|UnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Segment| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UniversalSegment| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |UniversalSegment| *3) (*2 |Segment| *3)))
--R            6> (|containsVars| (|UniversalSegment| *3))
--R              7> (|containsVars1| (|UniversalSegment| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UniversalSegment| *3))
--R              7> (|containsVars1| (|UniversalSegment| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UniversalSegment|))
--R              7> (|containsVars1| (|UniversalSegment|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) |coerce| NIL)
--R                8> (|hasCate| *2 (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                    10> (|hasCate| (|Integer|) (|UnivariateTaylorSeriesCategory| *3) ((*2 |Integer|)))
--R                    <10 (|hasCate| |failed|)
--R                    10> (|hasCateSpecialNew| *2 (|PositiveInteger|) (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|Ring|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) NIL)
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|)))
--R          <5 (|evalMmCond0| ((*3 |Integer|)))
--R        <4 (|evalMmCond| ((*3 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePolynomial| # *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |UnivariatePolynomial| # *3)))
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries|))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |Variable| #)))
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries|))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Symbol|)))
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries|))
--R              7> (|containsVars1| (|TaylorSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Polynomial| *3)))
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries|))
--R              7> (|containsVars1| (|TaylorSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |TexFormat|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|TexFormat|))
--R              7> (|containsVars1| (|TexFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|TexFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |TexFormat1| *3) (*2 |TexFormat|)))
--R            6> (|containsVars| (|TexFormat|))
--R              7> (|containsVars1| (|TexFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Tableau| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Tableau| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Tableau| *3))
--R              7> (|containsVars1| (|Tableau| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Tableau| *3))
--R              7> (|containsVars1| (|Tableau| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Tableau|))
--R              7> (|containsVars1| (|Tableau|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Table| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |SymbolTable|) (*2 |Table| # #)))
--R            6> (|containsVars| (|SymbolTable|))
--R              7> (|containsVars1| (|SymbolTable|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Symbol|) (*2 |String|)))
--R            6> (|containsVars| (|Symbol|))
--R              7> (|containsVars1| (|Symbol|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Switch|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Switch|) (*2 |Symbol|)))
--R            6> (|containsVars| (|Switch|))
--R              7> (|containsVars1| (|Switch|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Stream| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Stream| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|Stream| *3))
--R              7> (|containsVars1| (|Stream| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stream| *3))
--R              7> (|containsVars1| (|Stream| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stream|))
--R              7> (|containsVars1| (|Stream|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Stack| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Stack| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Stack| *3))
--R              7> (|containsVars1| (|Stack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stack| *3))
--R              7> (|containsVars1| (|Stack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stack|))
--R              7> (|containsVars1| (|Stack|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Character|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|StringAggregate|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Character|)))
--R            6> (|containsVars| (|Character|))
--R              7> (|containsVars1| (|Character|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|ThreeSpaceCategory| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |OutputForm|)))
--R            6> (|containsVars| (|OutputForm|))
--R              7> (|containsVars1| (|OutputForm|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Integer|)))
--R            6> (|containsVars| (|Integer|))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|RationalFunction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |RationalFunction| *3) (*2 |Fraction| #)))
--R            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
--R                8> (|containsVars1| (|Polynomial| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
--R                8> (|containsVars1| (|Polynomial| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction|))
--R              7> (|containsVars1| (|Fraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|RetractableTo| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|RetractableTo| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|RetractableTo| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|RetractableTo| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|RetractableTo| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|RetractableTo| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|RetractableTo| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Type|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|Type|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|Type|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Exit|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *2) (*3 |Exit|)))
--R            6> (|containsVars| (|Exit|))
--R              7> (|containsVars1| (|Exit|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Void|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *3) (*2 |Void|)))
--R            6> (|containsVars| (|Void|))
--R              7> (|containsVars1| (|Void|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|RadixExpansion| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |RadixExpansion| *3) (*2 |Fraction| #)))
--R            6> (|containsVars| (|RadixExpansion| *3))
--R              7> (|containsVars1| (|RadixExpansion| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|RadixExpansion| *3))
--R              7> (|containsVars1| (|RadixExpansion| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|RadixExpansion| *3))
--R              7> (|containsVars1| (|RadixExpansion| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Queue| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Queue| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Queue| *3))
--R              7> (|containsVars1| (|Queue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Queue| *3))
--R              7> (|containsVars1| (|Queue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Queue|))
--R              7> (|containsVars1| (|Queue|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Pi|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PiCoercions| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
--R        <4 (|evalMmStack| ((# # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R            <6 (|evalMmDom| ((*1 |PiCoercions| *4) (*2 |Expression| *4) (*3 |Pi|)))
--R            6> (|containsVars| (|Expression| *4))
--R              7> (|containsVars1| (|Expression| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Expression| *4))
--R              7> (|containsVars1| (|Expression| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Expression|))
--R              7> (|containsVars1| (|Expression|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| *3)))
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction|))
--R              7> (|containsVars1| (|PartialFraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| #)))
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction|))
--R              7> (|containsVars1| (|PartialFraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| #)))
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation|))
--R              7> (|containsVars1| (|Permutation|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation|))
--R              7> (|containsVars1| (|Permutation|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup|))
--R              7> (|containsVars1| (|PermutationGroup|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup|))
--R              7> (|containsVars1| (|PermutationGroup|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Tree| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PendantTree| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |PendantTree| *3) (*2 |Tree| *3)))
--R            6> (|containsVars| (|PendantTree| *3))
--R              7> (|containsVars1| (|PendantTree| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PendantTree| *3))
--R              7> (|containsVars1| (|PendantTree| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PendantTree|))
--R              7> (|containsVars1| (|PendantTree|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalPDEProblem|))
--R              7> (|containsVars1| (|NumericalPDEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |Record| # # # # #)))
--R            6> (|containsVars| (|NumericalPDEProblem|))
--R              7> (|containsVars1| (|NumericalPDEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Fraction| #)))
--R            6> (|containsVars| (|Expression| (|Integer|)))
--R              7> (|containsVars1| (|Expression| (|Integer|)))
--R                8> (|containsVars1| (|Integer|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Polynomial| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Polynomial| #)))
--R            6> (|containsVars| (|Expression| (|Integer|)))
--R              7> (|containsVars1| (|Expression| (|Integer|)))
--R                8> (|containsVars1| (|Integer|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Color|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Palette|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Palette|) (*2 |Color|)))
--R            6> (|containsVars| (|Palette|))
--R              7> (|containsVars1| (|Palette|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OrdSetInts|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |OrdSetInts|) (*2 |Integer|)))
--R            6> (|containsVars| (|OrdSetInts|))
--R              7> (|containsVars1| (|OrdSetInts|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # # # # #)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # #)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Union| # #)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OpenMathErrorKind|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |OpenMathErrorKind|) (*2 |Symbol|)))
--R            6> (|containsVars| (|OpenMathErrorKind|))
--R              7> (|containsVars1| (|OpenMathErrorKind|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 *3))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
--R        4> (|evalMmStack| (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 *3))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalODEProblem|))
--R              7> (|containsVars1| (|NumericalODEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |Record| # # # # # # # #)))
--R            6> (|containsVars| (|NumericalODEProblem|))
--R              7> (|containsVars1| (|NumericalODEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|None|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NoneFunctions1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |NoneFunctions1| *3) (*2 |None|)))
--R            6> (|containsVars| (|None|))
--R              7> (|containsVars1| (|None|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # # #)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # #)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Union| # #)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|NonAssociativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Integer|)))
--R            6> (|containsVars| (|Integer|))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *2)))
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Polynomial| *4)))
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyExpression| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MyExpression| *3 *4) (*2 |Fraction| #)))
--R            6> (|containsVars| (|MyExpression| *3 *4))
--R              7> (|containsVars1| (|MyExpression| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyExpression| *3 *4))
--R              7> (|containsVars1| (|MyExpression| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyExpression| *3))
--R              7> (|containsVars1| (|MyExpression| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MathMLFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MathMLFormat|) (*2 |String|) (*3 |OutputForm|)))
--R            6> (|containsVars| (|String|))
--R              7> (|containsVars1| (|String|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineInteger|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineInteger|) (*2 |Expression| #) (*3 |Expression| #)))
--R            6> (|containsVars| (|Expression| (|MachineInteger|)))
--R              7> (|containsVars1| (|Expression| (|MachineInteger|)))
--R                8> (|containsVars1| (|MachineInteger|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Float|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |Float|)))
--R            6> (|containsVars| (|MachineFloat|))
--R              7> (|containsVars1| (|MachineFloat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|MachineInteger|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |MachineInteger|)))
--R            6> (|containsVars| (|MachineFloat|))
--R              7> (|containsVars1| (|MachineFloat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *4 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|MatrixCategory| *3 *4 *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|MatrixCategory| *3 *4 *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) |coerce| NIL)
--R                8> (|hasCate| *2 (|FiniteLinearAggregate| *3) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL)
--R                    10> (|hasCate| (|Integer|) (|FiniteLinearAggregate| *3) ((*2 |Integer|)))
--R                    <10 (|hasCate| |failed|)
--R                    10> (|hasCateSpecialNew| *2 (|PositiveInteger|) (|FiniteLinearAggregate| *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
--R                <8 (|defaultTypeForCategory| (|Vector| *3))
--R                8> (|containsVars| (|Vector| *3))
--R                  9> (|containsVars1| (|Vector| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars| T)
--R                8> (|containsVars| (|Vector| *3))
--R                  9> (|containsVars1| (|Vector| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars| T)
--R                8> (|containsVars| (|Vector|))
--R                  9> (|containsVars1| (|Vector|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| (|Integer|))
--R                  9> (|containsVars1| (|Integer|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| *3)
--R                <8 (|containsVars| T)
--R                8> (|containsVars| (|Vector|))
--R                  9> (|containsVars1| (|Vector|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| ((|Integer|)))
--R                  9> (|containsVars1| ((|Integer|)))
--R                    10> (|containsVars1| (|Integer|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) |coerce| NIL)
--R                8> (|hasCate| *4 (|FiniteLinearAggregate| *3) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
--R                <8 (|defaultTypeForCategory| (|Vector| *3))
--R              <7 (|evalMmCat1| ((*4 |Vector| *3)))
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| ((*4 |Vector| *3)))
--R                8> (|hasCate| *3 (|Ring|) ((*4 |Vector| *3)))
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) ((*4 |Vector| *3)))
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|) (*4 |Vector| *3)))
--R          <5 (|evalMmCond0| ((*3 |Integer|) (*4 |Vector| *3)))
--R        <4 (|evalMmCond| ((*3 |Integer|) (*4 |Vector| *3)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R          5> (|replaceSharpCalls| (|Vector| *3))
--R            6> (|noSharpCallsHere| (|Vector| *3))
--R              7> (|noSharpCallsHere| *3)
--R              <7 (|noSharpCallsHere| T)
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Vector| *3))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Mapping| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MappingPackage1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |MappingPackage1| *3) (*2 |Mapping| *3)))
--R            6> (|containsVars| (|Mapping| *3))
--R              7> (|containsVars1| (|Mapping| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Mapping| *3))
--R              7> (|containsVars1| (|Mapping| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Mapping| *3))
--R              7> (|containsVars1| (|Mapping| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix|))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix|))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |AssociatedLieAlgebra| *3 *2)))
--R            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedLieAlgebra|))
--R              7> (|containsVars1| (|AssociatedLieAlgebra|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|LeftAlgebra| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|LeftAlgebra| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|LeftAlgebra| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|LeftAlgebra| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|LeftAlgebra| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Ring|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|Ring|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|Ring|) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|Ring|) NIL)
--R                    10> (|hasCate| (|Integer|) (|Ring|) ((*2 |Integer|)))
--R                    <10 (|hasCate| ((*2 |Integer|)))
--R                  <9 (|hasCateSpecial| ((*2 |Integer|)))
--R                <8 (|hasCate| ((*2 |Integer|)))
--R              <7 (|evalMmCat1| ((*2 |Integer|)))
--R            <6 (|evalMmCat| ((*2 |Integer|)))
--R          <5 (|evalMmCond0| ((*2 |Integer|)))
--R        <4 (|evalMmCond| ((*2 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*2 |Integer|)))
--R          5> (|coerceTypeArgs| (|PositiveInteger|) (|Integer|) ((*2 |Integer|)))
--R          <5 (|coerceTypeArgs| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|CoercibleTo| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|CoercibleTo| *2)) (|ofCategory| *2 (|Type|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|CoercibleTo| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|CoercibleTo| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|CoercibleTo| *2) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|CoercibleTo| *2) NIL *1)
--R                    10> (|hasCate| (|PositiveInteger|) (|CoercibleTo| *2) NIL)
--R                    11> (|mkDomPvar| $ (|PositiveInteger|) ((|OutputForm|)) (*2))
--R                    <11 (|mkDomPvar| (|PositiveInteger|))
--R                    11> (|domArg2| (|OutputForm|) (($ |PositiveInteger|)) (($ |PositiveInteger|)))
--R                    <11 (|domArg2| (|OutputForm|))
--R                    11> (|unifyStruct| (*2) ((|OutputForm|)) ((*1 |PositiveInteger|)))
--R                    12> (|unifyStruct| *2 (|OutputForm|) ((*1 |PositiveInteger|)))
--R                    13> (|unifyStructVar| *2 (|OutputForm|) ((*1 |PositiveInteger|)))
--R                    14> (|unifyStruct| (|List| (|Integer|)) (|OutputForm|) ((*1 |PositiveInteger|)))
--R                    15> (|unifyStruct| |List| |OutputForm| ((*1 |PositiveInteger|)))
--R                    <15 (|unifyStruct| |failed|)
--R                    <14 (|unifyStruct| |failed|)
--R                    <13 (|unifyStructVar| |failed|)
--R                    <12 (|unifyStruct| |failed|)
--R                    <11 (|unifyStruct| |failed|)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|PositiveInteger|) (|CoercibleTo| *2) NIL)
--R                    10> (|hasCate| (|Integer|) (|CoercibleTo| *2) ((*1 |Integer|)))
--R                    11> (|mkDomPvar| $ (|Integer|) ((|OutputForm|)) (*2))
--R                    <11 (|mkDomPvar| (|Integer|))
--R                    11> (|domArg2| (|OutputForm|) (($ |Integer|)) (($ |Integer|)))
--R                    <11 (|domArg2| (|OutputForm|))
--R                    11> (|unifyStruct| (*2) ((|OutputForm|)) ((*1 |Integer|)))
--R                    12> (|unifyStruct| *2 (|OutputForm|) ((*1 |Integer|)))
--R                    13> (|unifyStructVar| *2 (|OutputForm|) ((*1 |Integer|)))
--R                    14> (|unifyStruct| (|List| (|Integer|)) (|OutputForm|) ((*1 |Integer|)))
--R                    15> (|unifyStruct| |List| |OutputForm| ((*1 |Integer|)))
--R                    <15 (|unifyStruct| |failed|)
--R                    <14 (|unifyStruct| |failed|)
--R                    <13 (|unifyStructVar| |failed|)
--R                    <12 (|unifyStruct| |failed|)
--R                    <11 (|unifyStruct| |failed|)
--R                    <10 (|hasCate| |failed|)
--R                    10> (|hasCateSpecialNew| *1 (|PositiveInteger|) (|CoercibleTo| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|CoercibleTo| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Type|) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|Type|) NIL *2)
--R                    10> (|hasCate| (|List| (|Integer|)) (|Type|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|PositiveInteger|) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|PositiveInteger|) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |AssociatedJordanAlgebra| *3 *2)))
--R            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedJordanAlgebra|))
--R              7> (|containsVars1| (|AssociatedJordanAlgebra|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *6 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|OrderedAbelianMonoidSup|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PolynomialIdeals| *3 *4 *5 *6) (*2 |List| *6)))
--R            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
--R              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
--R              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PolynomialIdeals|))
--R              7> (|containsVars1| (|PolynomialIdeals|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|IndexCard|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |IndexCard|) (*2 |String|)))
--R            6> (|containsVars| (|IndexCard|))
--R              7> (|containsVars1| (|IndexCard|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |Fraction| #)))
--R            6> (|containsVars| (|HexadecimalExpansion|))
--R              7> (|containsVars1| (|HexadecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 16)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |RadixExpansion| 16)))
--R            6> (|containsVars| (|HexadecimalExpansion|))
--R              7> (|containsVars1| (|HexadecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Heap| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Heap| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Heap| *3))
--R              7> (|containsVars1| (|Heap| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Heap| *3))
--R              7> (|containsVars1| (|Heap| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Heap|))
--R              7> (|containsVars1| (|Heap|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *5 *3))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |Variable| *4)))
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 *3))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |UnivariatePuiseuxSeries| *3 *4 *5)))
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Vector| #)))
--R            6> (|containsVars| (|Vector| (|MachineFloat|)))
--R              7> (|containsVars1| (|Vector| (|MachineFloat|)))
--R                8> (|containsVars1| (|MachineFloat|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|FortranType|))
--R              7> (|containsVars1| (|FortranType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |FortranScalarType|)))
--R            6> (|containsVars| (|FortranType|))
--R              7> (|containsVars1| (|FortranType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |String|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SExpression|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |SExpression|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| *3 #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |SparseMultivariatePolynomial| *3 #)))
--R            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|SparseMultivariatePolynomial|))
--R              7> (|containsVars1| (|SparseMultivariatePolynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Fraction| *3)))
--R            6> (|containsVars| (|Fraction| *3))
--R              7> (|containsVars1| (|Fraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction| *3))
--R              7> (|containsVars1| (|Fraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction|))
--R              7> (|containsVars1| (|Fraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Polynomial| #)))
--R            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
--R              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                8> (|containsVars1| (|Fraction| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
--R              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                8> (|containsVars1| (|Fraction| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Polynomial|))
--R              7> (|containsVars1| (|Polynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Fraction| #)))
--R            6> (|containsVars| (|Fraction| (|Polynomial| #)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
--R                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                  9> (|containsVars1| (|Fraction| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction| (|Polynomial| #)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
--R                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                  9> (|containsVars1| (|Fraction| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction|))
--R              7> (|containsVars1| (|Fraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *2 *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FourierSeries| *2 *3)))
--R            6> (|containsVars| (|FourierSeries| *2 *3))
--R              7> (|containsVars1| (|FourierSeries| *2 *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries| *2 *3))
--R              7> (|containsVars1| (|FourierSeries| *2 *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries|))
--R              7> (|containsVars1| (|FourierSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FourierComponent| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FourierSeries| *3 *4) (*2 |FourierComponent| *4)))
--R            6> (|containsVars| (|FourierSeries| *3 *4))
--R              7> (|containsVars1| (|FourierSeries| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries| *3 *4))
--R              7> (|containsVars1| (|FourierSeries| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries|))
--R              7> (|containsVars1| (|FourierSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |List| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Record| # #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|ScriptFormulaFormat|))
--R              7> (|containsVars1| (|ScriptFormulaFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|ScriptFormulaFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat1| *3) (*2 |ScriptFormulaFormat|)))
--R            6> (|containsVars| (|ScriptFormulaFormat|))
--R              7> (|containsVars1| (|ScriptFormulaFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |String|)))
--R            6> (|containsVars| (|String|))
--R              7> (|containsVars1| (|String|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |String|)))
--R            6> (|containsVars| (|String|))
--R              7> (|containsVars1| (|String|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Matrix| #)))
--R            6> (|containsVars| (|Matrix| (|MachineFloat|)))
--R              7> (|containsVars1| (|Matrix| (|MachineFloat|)))
--R                8> (|containsVars1| (|MachineFloat|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) |coerce| NIL)
--R                8> (|hasCate| *1 (|FreeLieAlgebra| *2 *3) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FreeLieAlgebra| *2 *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|OrderedSet|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|OrderedSet|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|OrderedSet|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|CommutativeRing|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|CommutativeRing|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|CommutativeRing|) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|XDistributedPolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |XDistributedPolynomial| *3 *4)))
--R            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
--R              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
--R              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XDistributedPolynomial|))
--R              7> (|containsVars1| (|XDistributedPolynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|XRecursivePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |XRecursivePolynomial| *3 *4)))
--R            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
--R              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
--R              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XRecursivePolynomial|))
--R              7> (|containsVars1| (|XRecursivePolynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
--R              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *2)
--R                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                  9> (|hasCate1| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *3)
--R                    10> (|hasCate| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*3 |Integer|) (*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCate| |failed|)
--R                    10> (|hasCateSpecialNew| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
--R            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *2 *4 *3))
--R              7> (|noSharpCallsHere| *2)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *4)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *3)
--R              <7 (|noSharpCallsHere| T)
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
--R        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|List| #) *4 (|PositiveInteger|)))
--R              7> (|containsVars1| (|List| (|Integer|)))
--R                8> (|containsVars1| (|Integer|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| T)
--R          <5 (|containsVars1| T)
--R        <4 (|containsVars| T)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
--R              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *2)
--R                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                  9> (|hasCate1| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *3)
--R                    10> (|hasCate| (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*3 |Integer|) (*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCate| |failed|)
--R                    10> (|hasCateSpecialNew| *3 (|PositiveInteger|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
--R            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *3 *4 *2))
--R              7> (|noSharpCallsHere| *3)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *4)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *2)
--R              <7 (|noSharpCallsHere| T)
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
--R        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|PositiveInteger|) *4 (|List| #)))
--R              7> (|containsVars1| (|PositiveInteger|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| T)
--R          <5 (|containsVars1| T)
--R        <4 (|containsVars| T)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranExpression| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|FortranMachineTypeCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            <6 (|evalMmDom| ((*1 |FortranExpression| *3 *4 *5) (*2 |Expression| *5)))
--R            6> (|containsVars| (|FortranExpression| *3 *4 *5))
--R              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranExpression| *3 *4 *5))
--R              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranExpression| *3 *4))
--R              7> (|containsVars1| (|FortranExpression| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranCode|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|DifferentialVariableCategory| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|DifferentialVariableCategory| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|OrderedSet|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|OrderedSet|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|OrderedSet|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|PositiveInteger|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|PositiveInteger|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|PositiveInteger|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|SegmentBinding| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SegmentBinding| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DrawNumericHack| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DrawNumericHack| *4) (*2 |SegmentBinding| #) (*3 |SegmentBinding| #)))
--R            6> (|containsVars| (|SegmentBinding| (|Float|)))
--R              7> (|containsVars1| (|SegmentBinding| (|Float|)))
--R                8> (|containsVars1| (|Float|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Dequeue| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Dequeue| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Dequeue| *3))
--R              7> (|containsVars1| (|Dequeue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Dequeue| *3))
--R              7> (|containsVars1| (|Dequeue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Dequeue|))
--R              7> (|containsVars1| (|Dequeue|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |Fraction| #)))
--R            6> (|containsVars| (|DecimalExpansion|))
--R              7> (|containsVars1| (|DecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 10)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |RadixExpansion| 10)))
--R            6> (|containsVars| (|DecimalExpansion|))
--R              7> (|containsVars1| (|DecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Database| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Database| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|Database| *3))
--R              7> (|containsVars1| (|Database| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Database| *3))
--R              7> (|containsVars1| (|Database| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Database|))
--R              7> (|containsVars1| (|Database|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|DirectProduct| *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |DirectProduct| *4 *5)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SquareMatrix| *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |SquareMatrix| *4 *5)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| *5)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| #)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |Fraction| #)))
--R            6> (|containsVars| (|BinaryExpansion|))
--R              7> (|containsVars1| (|BinaryExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |RadixExpansion| 2)))
--R            6> (|containsVars| (|BinaryExpansion|))
--R              7> (|containsVars1| (|BinaryExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ArrayStack| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ArrayStack| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|ArrayStack| *3))
--R              7> (|containsVars1| (|ArrayStack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ArrayStack| *3))
--R              7> (|containsVars1| (|ArrayStack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ArrayStack|))
--R              7> (|containsVars1| (|ArrayStack|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp9| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp9| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp9| *3))
--R              7> (|containsVars1| (|Asp9| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp9| *3))
--R              7> (|containsVars1| (|Asp9| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp9| *3))
--R              7> (|containsVars1| (|Asp9| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp80| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp80| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp80| *3))
--R              7> (|containsVars1| (|Asp80| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp80| *3))
--R              7> (|containsVars1| (|Asp80| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp80| *3))
--R              7> (|containsVars1| (|Asp80| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp7| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp7| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp7| *3))
--R              7> (|containsVars1| (|Asp7| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp7| *3))
--R              7> (|containsVars1| (|Asp7| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp7| *3))
--R              7> (|containsVars1| (|Asp7| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp78| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp78| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp78| *3))
--R              7> (|containsVars1| (|Asp78| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp78| *3))
--R              7> (|containsVars1| (|Asp78| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp78| *3))
--R              7> (|containsVars1| (|Asp78| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp77| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp77| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp77| *3))
--R              7> (|containsVars1| (|Asp77| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp77| *3))
--R              7> (|containsVars1| (|Asp77| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp77| *3))
--R              7> (|containsVars1| (|Asp77| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp74| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp74| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp74| *3))
--R              7> (|containsVars1| (|Asp74| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp74| *3))
--R              7> (|containsVars1| (|Asp74| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp74| *3))
--R              7> (|containsVars1| (|Asp74| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp73| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp73| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp73| *3))
--R              7> (|containsVars1| (|Asp73| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp73| *3))
--R              7> (|containsVars1| (|Asp73| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp73| *3))
--R              7> (|containsVars1| (|Asp73| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp6| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp6| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp6| *3))
--R              7> (|containsVars1| (|Asp6| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp6| *3))
--R              7> (|containsVars1| (|Asp6| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp6| *3))
--R              7> (|containsVars1| (|Asp6| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp55| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp55| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp55| *3))
--R              7> (|containsVars1| (|Asp55| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp55| *3))
--R              7> (|containsVars1| (|Asp55| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp55| *3))
--R              7> (|containsVars1| (|Asp55| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp50| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp50| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp50| *3))
--R              7> (|containsVars1| (|Asp50| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp50| *3))
--R              7> (|containsVars1| (|Asp50| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp50| *3))
--R              7> (|containsVars1| (|Asp50| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp4| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp4| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp4| *3))
--R              7> (|containsVars1| (|Asp4| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp4| *3))
--R              7> (|containsVars1| (|Asp4| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp4| *3))
--R              7> (|containsVars1| (|Asp4| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp49| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp49| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp49| *3))
--R              7> (|containsVars1| (|Asp49| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp49| *3))
--R              7> (|containsVars1| (|Asp49| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp49| *3))
--R              7> (|containsVars1| (|Asp49| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp42| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp42| *3 *4 *5) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp42| *3 *4 *5))
--R              7> (|containsVars1| (|Asp42| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp42| *3 *4 *5))
--R              7> (|containsVars1| (|Asp42| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp42| *3 *4 *5))
--R              7> (|containsVars1| (|Asp42| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp41| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp41| *3 *4 *5) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp41| *3 *4 *5))
--R              7> (|containsVars1| (|Asp41| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp41| *3 *4 *5))
--R              7> (|containsVars1| (|Asp41| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp41| *3 *4 *5))
--R              7> (|containsVars1| (|Asp41| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp35| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp35| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp35| *3))
--R              7> (|containsVars1| (|Asp35| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp35| *3))
--R              7> (|containsVars1| (|Asp35| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp35| *3))
--R              7> (|containsVars1| (|Asp35| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp31| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp31| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp31| *3))
--R              7> (|containsVars1| (|Asp31| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp31| *3))
--R              7> (|containsVars1| (|Asp31| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp31| *3))
--R              7> (|containsVars1| (|Asp31| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp24| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp24| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp24| *3))
--R              7> (|containsVars1| (|Asp24| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp24| *3))
--R              7> (|containsVars1| (|Asp24| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp24| *3))
--R              7> (|containsVars1| (|Asp24| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp20| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp20| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp20| *3))
--R              7> (|containsVars1| (|Asp20| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp20| *3))
--R              7> (|containsVars1| (|Asp20| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp20| *3))
--R              7> (|containsVars1| (|Asp20| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp1| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp1| *3))
--R              7> (|containsVars1| (|Asp1| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp1| *3))
--R              7> (|containsVars1| (|Asp1| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp1| *3))
--R              7> (|containsVars1| (|Asp1| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp19| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp19| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp19| *3))
--R              7> (|containsVars1| (|Asp19| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp19| *3))
--R              7> (|containsVars1| (|Asp19| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp19| *3))
--R              7> (|containsVars1| (|Asp19| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp10| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp10| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp10| *3))
--R              7> (|containsVars1| (|Asp10| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp10| *3))
--R              7> (|containsVars1| (|Asp10| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp10| *3))
--R              7> (|containsVars1| (|Asp10| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Any|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AnyFunctions1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |AnyFunctions1| *3) (*2 |Any|)))
--R            6> (|containsVars| (|Any|))
--R              7> (|containsVars1| (|Any|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraicNumber|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |AlgebraicNumber|) (*2 |SparseMultivariatePolynomial| # #)))
--R            6> (|containsVars| (|AlgebraicNumber|))
--R              7> (|containsVars1| (|AlgebraicNumber|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *6 (|Vector| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|PositiveInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |AlgebraGivenByStructuralConstants| *3 *4 *5 *6) (*2 |Vector| *3)))
--R            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
--R              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|PositiveInteger|)) ((|PositiveInteger|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|Algebra| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|Algebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|Algebra| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|Algebra| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|Algebra| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|Algebra| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|Algebra| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Algebra| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|CommutativeRing|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|CommutativeRing|) NIL)
--R                  9> (|hasCate1| (|PositiveInteger|) (|CommutativeRing|) NIL *2)
--R                    10> (|hasCate| (|PositiveInteger|) (|CommutativeRing|) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|PositiveInteger|) (|CommutativeRing|) NIL)
--R                    10> (|hasCate| (|Integer|) (|CommutativeRing|) ((*2 |Integer|)))
--R                    <10 (|hasCate| ((*2 |Integer|)))
--R                  <9 (|hasCateSpecial| ((*2 |Integer|)))
--R                <8 (|hasCate| ((*2 |Integer|)))
--R              <7 (|evalMmCat1| ((*2 |Integer|)))
--R            <6 (|evalMmCat| ((*2 |Integer|)))
--R          <5 (|evalMmCond0| ((*2 |Integer|)))
--R        <4 (|evalMmCond| ((*2 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*2 |Integer|)))
--R          5> (|coerceTypeArgs| (|PositiveInteger|) (|Integer|) ((*2 |Integer|)))
--R          <5 (|coerceTypeArgs| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R    <2 (|selectMmsGen,matchMms| NIL)
--R  <1 (|selectMmsGen| NIL)
--R  1> (|selectMmsGen| |coerce| (|List| (|Integer|)) ((|Integer|)) ((|Integer|)))
--R    2> (|filterModemapsFromPackages| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) ("Integer" "List") |coerce|)
--R    <2 (|filterModemapsFromPackages| ((# # #) (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
--R    2> (|selectMmsGen,exact?| ((# #) (# #) (# #)) (|List| (|Integer|)) ((|Integer|)))
--R    <2 (|selectMmsGen,exact?| (NIL (# # #)))
--R    2> (|selectMmsGen,matchMms| ((# #) (# #) (# #)) |coerce| (|List| (|Integer|)) ((|Integer|)) ((|Integer|)))
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineInteger|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineInteger|) (*2 |Expression| #) (*3 |Expression| #)))
--R            6> (|containsVars| (|Expression| (|MachineInteger|)))
--R              7> (|containsVars1| (|Expression| (|MachineInteger|)))
--R                8> (|containsVars1| (|MachineInteger|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList|))
--R              7> (|containsVars1| (|DataList|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DataList| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |DataList| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList| *3))
--R              7> (|containsVars1| (|DataList| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|DataList|))
--R              7> (|containsVars1| (|DataList|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R    <2 (|selectMmsGen,matchMms| NIL)
--R    2> (|selectMmsGen,exact?| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) (|List| (|Integer|)) ((|Integer|)))
--R    <2 (|selectMmsGen,exact?| (NIL (# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #)))
--R    2> (|selectMmsGen,matchMms| ((# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #) (# #)) |coerce| (|List| (|Integer|)) ((|Integer|)) ((|Integer|)))
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|XFreeAlgebra| *2 *3)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) |coerce| NIL)
--R                8> (|hasCate| *1 (|XFreeAlgebra| *2 *3) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XFreeAlgebra| *2 *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|XFreeAlgebra| *2 *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|OrderedSet|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|OrderedSet|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|OrderedSet|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|Ring|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) NIL)
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|)))
--R          <5 (|evalMmCond0| ((*3 |Integer|)))
--R        <4 (|evalMmCond| ((*3 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|XAlgebra| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|XAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|XAlgebra| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|XAlgebra| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|XAlgebra| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|XAlgebra| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|XAlgebra| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|XAlgebra| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|XAlgebra| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Ring|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|Ring|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|Ring|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Void|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Void|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Void|))
--R              7> (|containsVars1| (|Void|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)) |coerce| NIL)
--R                8> (|hasCate| *2 (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                  9> (|hasCate1| (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                    10> (|hasCateSpecialNew| *2 (|Integer|) (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesCategory| *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|Ring|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) NIL)
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|)))
--R          <5 (|evalMmCond0| ((*3 |Integer|)))
--R        <4 (|evalMmCond| ((*3 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariatePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            <6 (|evalMmDom| ((*1 |UnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
--R            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|UnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariatePolynomial| *3))
--R              7> (|containsVars1| (|UnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Segment| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UniversalSegment| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |UniversalSegment| *3) (*2 |Segment| *3)))
--R            6> (|containsVars| (|UniversalSegment| *3))
--R              7> (|containsVars1| (|UniversalSegment| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UniversalSegment| *3))
--R              7> (|containsVars1| (|UniversalSegment| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UniversalSegment|))
--R              7> (|containsVars1| (|UniversalSegment|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariateLaurentSeriesConstructorCategory| *3 *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)) |coerce| NIL)
--R                8> (|hasCate| *2 (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                  9> (|hasCate1| (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                    10> (|hasCateSpecialNew| *2 (|Integer|) (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|UnivariateTaylorSeriesCategory| *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|Ring|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) NIL)
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|)))
--R          <5 (|evalMmCond0| ((*3 |Integer|)))
--R        <4 (|evalMmCond| ((*3 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePolynomial| # *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |UnivariatePolynomial| # *3)))
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries|))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |UnivariateFormalPowerSeries| *3) (*2 |Variable| #)))
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries| *3))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|UnivariateFormalPowerSeries|))
--R              7> (|containsVars1| (|UnivariateFormalPowerSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Symbol|)))
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries|))
--R              7> (|containsVars1| (|TaylorSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TaylorSeries| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |TaylorSeries| *3) (*2 |Polynomial| *3)))
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries| *3))
--R              7> (|containsVars1| (|TaylorSeries| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|TaylorSeries|))
--R              7> (|containsVars1| (|TaylorSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |TexFormat|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|TexFormat|))
--R              7> (|containsVars1| (|TexFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|TexFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|TexFormat1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |TexFormat1| *3) (*2 |TexFormat|)))
--R            6> (|containsVars| (|TexFormat|))
--R              7> (|containsVars1| (|TexFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Tableau| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Tableau| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Tableau| *3))
--R              7> (|containsVars1| (|Tableau| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Tableau| *3))
--R              7> (|containsVars1| (|Tableau| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Tableau|))
--R              7> (|containsVars1| (|Tableau|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Table| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |SymbolTable|) (*2 |Table| # #)))
--R            6> (|containsVars| (|SymbolTable|))
--R              7> (|containsVars1| (|SymbolTable|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Symbol|) (*2 |String|)))
--R            6> (|containsVars| (|Symbol|))
--R              7> (|containsVars1| (|Symbol|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Switch|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Switch|) (*2 |Symbol|)))
--R            6> (|containsVars| (|Switch|))
--R              7> (|containsVars1| (|Switch|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Stream| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Stream| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|Stream| *3))
--R              7> (|containsVars1| (|Stream| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stream| *3))
--R              7> (|containsVars1| (|Stream| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stream|))
--R              7> (|containsVars1| (|Stream|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Stack| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Stack| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Stack| *3))
--R              7> (|containsVars1| (|Stack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stack| *3))
--R              7> (|containsVars1| (|Stack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Stack|))
--R              7> (|containsVars1| (|Stack|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Character|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|StringAggregate|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Character|)))
--R            6> (|containsVars| (|Character|))
--R              7> (|containsVars1| (|Character|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|ThreeSpaceCategory| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |OutputForm|)))
--R            6> (|containsVars| (|OutputForm|))
--R              7> (|containsVars1| (|OutputForm|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Integer|)))
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)) ((*2 |Integer|)))
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #)))
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|Ring|)) |coerce| ((*2 |Integer|)))
--R                8> (|hasCate| *1 (|Ring|) ((*2 |Integer|)))
--R                  9> (|hasCate1| (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)) *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)))
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|Ring|) ((*2 |Integer|)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) ((*2 |Integer|)))
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R                8> (|containsVars| (|Integer|))
--R                  9> (|containsVars1| (|Integer|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| ((*2 |Integer|)))
--R          <5 (|evalMmCond0| ((*2 |Integer|)))
--R        <4 (|evalMmCond| ((*2 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*2 |Integer|)))
--R          5> (|coerceTypeArgs| (|Integer|) (|Integer|) ((*2 |Integer|)))
--R          <5 (|coerceTypeArgs| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|RationalFunction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |RationalFunction| *3) (*2 |Fraction| #)))
--R            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
--R                8> (|containsVars1| (|Polynomial| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction| (|Polynomial| *3)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| *3)))
--R                8> (|containsVars1| (|Polynomial| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction|))
--R              7> (|containsVars1| (|Fraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|RetractableTo| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|RetractableTo| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|RetractableTo| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|RetractableTo| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|RetractableTo| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|RetractableTo| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|RetractableTo| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|RetractableTo| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Type|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|Type|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|Type|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Exit|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *2) (*3 |Exit|)))
--R            6> (|containsVars| (|Exit|))
--R              7> (|containsVars1| (|Exit|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Void|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ResolveLatticeCompletion| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ResolveLatticeCompletion| *3) (*2 |Void|)))
--R            6> (|containsVars| (|Void|))
--R              7> (|containsVars1| (|Void|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|RadixExpansion| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |RadixExpansion| *3) (*2 |Fraction| #)))
--R            6> (|containsVars| (|RadixExpansion| *3))
--R              7> (|containsVars1| (|RadixExpansion| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|RadixExpansion| *3))
--R              7> (|containsVars1| (|RadixExpansion| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|RadixExpansion| *3))
--R              7> (|containsVars1| (|RadixExpansion| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Queue| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Queue| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Queue| *3))
--R              7> (|containsVars1| (|Queue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Queue| *3))
--R              7> (|containsVars1| (|Queue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Queue|))
--R              7> (|containsVars1| (|Queue|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Pi|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PiCoercions| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
--R        <4 (|evalMmStack| ((# # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R            <6 (|evalMmDom| ((*1 |PiCoercions| *4) (*2 |Expression| *4) (*3 |Pi|)))
--R            6> (|containsVars| (|Expression| *4))
--R              7> (|containsVars1| (|Expression| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Expression| *4))
--R              7> (|containsVars1| (|Expression| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Expression|))
--R              7> (|containsVars1| (|Expression|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| *3)))
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction|))
--R              7> (|containsVars1| (|PartialFraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|EuclideanDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PartialFraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PartialFraction| *3) (*2 |Fraction| #)))
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction| *3))
--R              7> (|containsVars1| (|PartialFraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PartialFraction|))
--R              7> (|containsVars1| (|PartialFraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| #)))
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation|))
--R              7> (|containsVars1| (|Permutation|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Permutation| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Permutation| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation| *3))
--R              7> (|containsVars1| (|Permutation| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Permutation|))
--R              7> (|containsVars1| (|Permutation|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup|))
--R              7> (|containsVars1| (|PermutationGroup|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PermutationGroup| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PermutationGroup| *3) (*2 |List| #)))
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup| *3))
--R              7> (|containsVars1| (|PermutationGroup| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PermutationGroup|))
--R              7> (|containsVars1| (|PermutationGroup|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Tree| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PendantTree| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |PendantTree| *3) (*2 |Tree| *3)))
--R            6> (|containsVars| (|PendantTree| *3))
--R              7> (|containsVars1| (|PendantTree| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PendantTree| *3))
--R              7> (|containsVars1| (|PendantTree| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PendantTree|))
--R              7> (|containsVars1| (|PendantTree|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalPDEProblem|))
--R              7> (|containsVars1| (|NumericalPDEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalPDEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalPDEProblem|) (*2 |Record| # # # # #)))
--R            6> (|containsVars| (|NumericalPDEProblem|))
--R              7> (|containsVars1| (|NumericalPDEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Fraction| #)))
--R            6> (|containsVars| (|Expression| (|Integer|)))
--R              7> (|containsVars1| (|Expression| (|Integer|)))
--R                8> (|containsVars1| (|Integer|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|Polynomial| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialAN2Expression|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PolynomialAN2Expression|) (*2 |Expression| #) (*3 |Polynomial| #)))
--R            6> (|containsVars| (|Expression| (|Integer|)))
--R              7> (|containsVars1| (|Expression| (|Integer|)))
--R                8> (|containsVars1| (|Integer|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Color|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Palette|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Palette|) (*2 |Color|)))
--R            6> (|containsVars| (|Palette|))
--R              7> (|containsVars1| (|Palette|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OrdSetInts|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |OrdSetInts|) (*2 |Integer|)))
--R            6> (|containsVars| (|OrdSetInts|))
--R              7> (|containsVars1| (|OrdSetInts|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # # # # #)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Record| # #)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalOptimizationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalOptimizationProblem|) (*2 |Union| # #)))
--R            6> (|containsVars| (|NumericalOptimizationProblem|))
--R              7> (|containsVars1| (|NumericalOptimizationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OpenMathErrorKind|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |OpenMathErrorKind|) (*2 |Symbol|)))
--R            6> (|containsVars| (|OpenMathErrorKind|))
--R              7> (|containsVars1| (|OpenMathErrorKind|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofType| *4 *3) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 *3))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
--R        4> (|evalMmStack| (AND (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *4 *3)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|PartialDifferentialRing| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 *3))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |OrdinaryDifferentialRing| *3 *2 *4)))
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *3 *2 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|OrdinaryDifferentialRing| *4))
--R              7> (|containsVars1| (|OrdinaryDifferentialRing| *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalODEProblem|))
--R              7> (|containsVars1| (|NumericalODEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalODEProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalODEProblem|) (*2 |Record| # # # # # # # #)))
--R            6> (|containsVars| (|NumericalODEProblem|))
--R              7> (|containsVars1| (|NumericalODEProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|None|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NoneFunctions1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |NoneFunctions1| *3) (*2 |None|)))
--R            6> (|containsVars| (|None|))
--R              7> (|containsVars1| (|None|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # # #)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Record| # # # #)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Union| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|NumericalIntegrationProblem|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |NumericalIntegrationProblem|) (*2 |Union| # #)))
--R            6> (|containsVars| (|NumericalIntegrationProblem|))
--R              7> (|containsVars1| (|NumericalIntegrationProblem|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Integer|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|NonAssociativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Integer|)))
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)) ((*2 |Integer|)))
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #)))
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|NonAssociativeRing|)) |coerce| ((*2 |Integer|)))
--R                8> (|hasCate| *1 (|NonAssociativeRing|) ((*2 |Integer|)))
--R                  9> (|hasCate1| (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)) *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)))
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|NonAssociativeRing|) ((*2 |Integer|)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|NonAssociativeRing|) ((*2 |Integer|)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| ((*2 |Integer|)))
--R          <5 (|evalMmCond0| ((*2 |Integer|)))
--R        <4 (|evalMmCond| ((*2 |Integer|)))
--R        4> (|fixUpTypeArgs| ((*2 |Integer|)))
--R          5> (|coerceTypeArgs| (|Integer|) (|Integer|) ((*2 |Integer|)))
--R          <5 (|coerceTypeArgs| (|Integer|))
--R        <4 (|fixUpTypeArgs| ((*2 |Integer|)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofType| *3 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *2)))
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *2))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *4 #)))
--R            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Variable| *3)))
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MyUnivariatePolynomial| *3 *4) (*2 |Polynomial| *4)))
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3 *4))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyUnivariatePolynomial| *3))
--R              7> (|containsVars1| (|MyUnivariatePolynomial| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *3 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MyExpression| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MyExpression| *3 *4) (*2 |Fraction| #)))
--R            6> (|containsVars| (|MyExpression| *3 *4))
--R              7> (|containsVars1| (|MyExpression| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyExpression| *3 *4))
--R              7> (|containsVars1| (|MyExpression| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|MyExpression| *3))
--R              7> (|containsVars1| (|MyExpression| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MathMLFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MathMLFormat|) (*2 |String|) (*3 |OutputForm|)))
--R            6> (|containsVars| (|String|))
--R              7> (|containsVars1| (|String|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Float|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |Float|)))
--R            6> (|containsVars| (|MachineFloat|))
--R              7> (|containsVars1| (|MachineFloat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|MachineInteger|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineFloat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineFloat|) (*2 |MachineInteger|)))
--R            6> (|containsVars| (|MachineFloat|))
--R              7> (|containsVars1| (|MachineFloat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Complex| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MachineComplex|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |MachineComplex|) (*2 |Complex| #)))
--R            6> (|containsVars| (|MachineComplex|))
--R              7> (|containsVars1| (|MachineComplex|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *3 #) (|ofCategory| *1 #) (|ofCategory| *4 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Ring|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *4 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|MatrixCategory| *3 *4 *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|MatrixCategory| *3 *4 *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|MatrixCategory| *3 *4 *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteLinearAggregate| *3)) |coerce| NIL)
--R                8> (|hasCate| *2 (|FiniteLinearAggregate| *3) NIL)
--R                  9> (|hasCate1| (|Integer|) (|FiniteLinearAggregate| *3) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|FiniteLinearAggregate| *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|Integer|) (|FiniteLinearAggregate| *3) NIL)
--R                    10> (|hasCateSpecialNew| *2 (|Integer|) (|FiniteLinearAggregate| *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
--R                <8 (|defaultTypeForCategory| (|Vector| *3))
--R                8> (|containsVars| (|Vector| *3))
--R                  9> (|containsVars1| (|Vector| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars| T)
--R                8> (|containsVars| (|Vector| *3))
--R                  9> (|containsVars1| (|Vector| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars| T)
--R                8> (|containsVars| (|Vector|))
--R                  9> (|containsVars1| (|Vector|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| (|Integer|))
--R                  9> (|containsVars1| (|Integer|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| *3)
--R                <8 (|containsVars| T)
--R                8> (|containsVars| (|Vector|))
--R                  9> (|containsVars1| (|Vector|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R                8> (|containsVars| ((|Integer|)))
--R                  9> (|containsVars1| ((|Integer|)))
--R                    10> (|containsVars1| (|Integer|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteLinearAggregate| *3)) |coerce| NIL)
--R                8> (|hasCate| *4 (|FiniteLinearAggregate| *3) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteLinearAggregate| *3) NIL)
--R                <8 (|defaultTypeForCategory| (|Vector| *3))
--R              <7 (|evalMmCat1| ((*4 |Vector| *3)))
--R              7> (|evalMmCat1| (|ofCategory| *3 (|Ring|)) |coerce| ((*4 |Vector| *3)))
--R                8> (|hasCate| *3 (|Ring|) ((*4 |Vector| *3)))
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Ring|) ((*4 |Vector| *3)))
--R                <8 (|defaultTypeForCategory| (|Integer|))
--R              <7 (|evalMmCat1| ((*3 |Integer|)))
--R            <6 (|evalMmCat| ((*3 |Integer|) (*4 |Vector| *3)))
--R          <5 (|evalMmCond0| ((*3 |Integer|) (*4 |Vector| *3)))
--R        <4 (|evalMmCond| ((*3 |Integer|) (*4 |Vector| *3)))
--R        4> (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
--R          5> (|replaceSharpCalls| (|Integer|))
--R            6> (|noSharpCallsHere| (|Integer|))
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Integer|))
--R          5> (|replaceSharpCalls| (|Vector| *3))
--R            6> (|noSharpCallsHere| (|Vector| *3))
--R              7> (|noSharpCallsHere| *3)
--R              <7 (|noSharpCallsHere| T)
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|Vector| *3))
--R        <4 (|fixUpTypeArgs| ((*3 |Integer|) (*4 |Vector| *3)))
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Mapping| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|MappingPackage1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |MappingPackage1| *3) (*2 |Mapping| *3)))
--R            6> (|containsVars| (|Mapping| *3))
--R              7> (|containsVars1| (|Mapping| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Mapping| *3))
--R              7> (|containsVars1| (|Mapping| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Mapping| *3))
--R              7> (|containsVars1| (|Mapping| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix|))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|PrimitiveArray| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ThreeDimensionalMatrix| *3) (*2 |PrimitiveArray| #)))
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix| *3))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ThreeDimensionalMatrix|))
--R              7> (|containsVars1| (|ThreeDimensionalMatrix|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |AssociatedLieAlgebra| *3 *2)))
--R            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedLieAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedLieAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedLieAlgebra|))
--R              7> (|containsVars1| (|AssociatedLieAlgebra|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|LeftAlgebra| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|LeftAlgebra| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|LeftAlgebra| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|LeftAlgebra| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|LeftAlgebra| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|LeftAlgebra| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Ring|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Ring|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|Ring|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|Ring|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|CoercibleTo| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|CoercibleTo| *2)) (|ofCategory| *2 (|Type|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|Type|)) (|ofCategory| *1 (|CoercibleTo| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|CoercibleTo| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|CoercibleTo| *2) NIL)
--R                  9> (|hasCate1| (|Integer|) (|CoercibleTo| *2) NIL *1)
--R                    10> (|hasCate| (|Integer|) (|CoercibleTo| *2) NIL)
--R                    11> (|mkDomPvar| $ (|Integer|) ((|OutputForm|)) (*2))
--R                    <11 (|mkDomPvar| (|Integer|))
--R                    11> (|domArg2| (|OutputForm|) (($ |Integer|)) (($ |Integer|)))
--R                    <11 (|domArg2| (|OutputForm|))
--R                    11> (|unifyStruct| (*2) ((|OutputForm|)) ((*1 |Integer|)))
--R                    12> (|unifyStruct| *2 (|OutputForm|) ((*1 |Integer|)))
--R                    13> (|unifyStructVar| *2 (|OutputForm|) ((*1 |Integer|)))
--R                    14> (|unifyStruct| (|List| (|Integer|)) (|OutputForm|) ((*1 |Integer|)))
--R                    15> (|unifyStruct| |List| |OutputForm| ((*1 |Integer|)))
--R                    <15 (|unifyStruct| |failed|)
--R                    <14 (|unifyStruct| |failed|)
--R                    <13 (|unifyStructVar| |failed|)
--R                    <12 (|unifyStruct| |failed|)
--R                    <11 (|unifyStruct| |failed|)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|Integer|) (|CoercibleTo| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|Integer|) (|CoercibleTo| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|CoercibleTo| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|Type|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|Type|) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|Type|) NIL *2)
--R                    10> (|hasCate| (|List| (|Integer|)) (|Type|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|Integer|) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|Integer|) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *3 #) (|isDomain| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| ((*1 |AssociatedJordanAlgebra| *3 *2)))
--R            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedJordanAlgebra| *3 *2))
--R              7> (|containsVars1| (|AssociatedJordanAlgebra| *3 *2))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AssociatedJordanAlgebra|))
--R              7> (|containsVars1| (|AssociatedJordanAlgebra|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *6 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|OrderedAbelianMonoidSup|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *6 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |PolynomialIdeals| *3 *4 *5 *6) (*2 |List| *6)))
--R            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
--R              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PolynomialIdeals| *3 *4 *5 *6))
--R              7> (|containsVars1| (|PolynomialIdeals| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|PolynomialIdeals|))
--R              7> (|containsVars1| (|PolynomialIdeals|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|IndexCard|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |IndexCard|) (*2 |String|)))
--R            6> (|containsVars| (|IndexCard|))
--R              7> (|containsVars1| (|IndexCard|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |Fraction| #)))
--R            6> (|containsVars| (|HexadecimalExpansion|))
--R              7> (|containsVars1| (|HexadecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 16)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|HexadecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |HexadecimalExpansion|) (*2 |RadixExpansion| 16)))
--R            6> (|containsVars| (|HexadecimalExpansion|))
--R              7> (|containsVars1| (|HexadecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Heap| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Heap| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Heap| *3))
--R              7> (|containsVars1| (|Heap| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Heap| *3))
--R              7> (|containsVars1| (|Heap| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Heap|))
--R              7> (|containsVars1| (|Heap|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofType| *5 *3)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Variable| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *5 *3))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |Variable| *4)))
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *4 #) (|ofType| *5 *3) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 *3))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |GeneralUnivariatePowerSeries| *3 *4 *5) (*2 |UnivariatePuiseuxSeries| *3 *4 *5)))
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|GeneralUnivariatePowerSeries| *4 *5))
--R              7> (|containsVars1| (|GeneralUnivariatePowerSeries| *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Vector| #)))
--R            6> (|containsVars| (|Vector| (|MachineFloat|)))
--R              7> (|containsVars1| (|Vector| (|MachineFloat|)))
--R                8> (|containsVars1| (|MachineFloat|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranVectorCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|FortranType|))
--R              7> (|containsVars1| (|FortranType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranType|) (*2 |FortranScalarType|)))
--R            6> (|containsVars| (|FortranType|))
--R              7> (|containsVars1| (|FortranType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |String|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Symbol|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |Symbol|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SExpression|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranScalarType|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranScalarType|) (*2 |SExpression|)))
--R            6> (|containsVars| (|FortranScalarType|))
--R              7> (|containsVars1| (|FortranScalarType|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| *3 #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Ring|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |SparseMultivariatePolynomial| *3 #)))
--R            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              7> (|containsVars1| (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|SparseMultivariatePolynomial|))
--R              7> (|containsVars1| (|SparseMultivariatePolynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Fraction| *3)))
--R            6> (|containsVars| (|Fraction| *3))
--R              7> (|containsVars1| (|Fraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction| *3))
--R              7> (|containsVars1| (|Fraction| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction|))
--R              7> (|containsVars1| (|Fraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Polynomial| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Polynomial| #)))
--R            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
--R              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                8> (|containsVars1| (|Fraction| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Polynomial| (|Fraction| *3)))
--R              7> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                8> (|containsVars1| (|Fraction| *3))
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Polynomial|))
--R              7> (|containsVars1| (|Polynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|IntegralDomain|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FunctionSpace| *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Fraction| #)))
--R            6> (|containsVars| (|Fraction| (|Polynomial| #)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
--R                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                  9> (|containsVars1| (|Fraction| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction| (|Polynomial| #)))
--R              7> (|containsVars1| (|Fraction| (|Polynomial| #)))
--R                8> (|containsVars1| (|Polynomial| (|Fraction| *3)))
--R                  9> (|containsVars1| (|Fraction| *3))
--R                  <9 (|containsVars1| T)
--R                <8 (|containsVars1| T)
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Fraction|))
--R              7> (|containsVars1| (|Fraction|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *2 *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *1 #) (|ofCategory| *2 #) (|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FourierSeries| *2 *3)))
--R            6> (|containsVars| (|FourierSeries| *2 *3))
--R              7> (|containsVars1| (|FourierSeries| *2 *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries| *2 *3))
--R              7> (|containsVars1| (|FourierSeries| *2 *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries|))
--R              7> (|containsVars1| (|FourierSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FourierComponent| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FourierSeries| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FourierSeries| *3 *4) (*2 |FourierComponent| *4)))
--R            6> (|containsVars| (|FourierSeries| *3 *4))
--R              7> (|containsVars1| (|FourierSeries| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries| *3 *4))
--R              7> (|containsVars1| (|FourierSeries| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FourierSeries|))
--R              7> (|containsVars1| (|FourierSeries|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |List| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Record| # #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Expression| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #) (|ofType| *6 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Equation| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Union| # #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *6 (|SymbolTable|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranProgram| *3 *4 *5 *6) (*2 |Equation| #)))
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranProgram| *3 *4 *5 *6))
--R              7> (|containsVars1| (|FortranProgram| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|ScriptFormulaFormat|))
--R              7> (|containsVars1| (|ScriptFormulaFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|ScriptFormulaFormat|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ScriptFormulaFormat1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ScriptFormulaFormat1| *3) (*2 |ScriptFormulaFormat|)))
--R            6> (|containsVars| (|ScriptFormulaFormat|))
--R              7> (|containsVars1| (|ScriptFormulaFormat|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |String|)))
--R            6> (|containsVars| (|String|))
--R              7> (|containsVars1| (|String|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FileNameCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|String|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |String|)))
--R            6> (|containsVars| (|String|))
--R              7> (|containsVars1| (|String|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Matrix| #)))
--R            6> (|containsVars| (|Matrix| (|MachineFloat|)))
--R              7> (|containsVars1| (|Matrix| (|MachineFloat|)))
--R                8> (|containsVars1| (|MachineFloat|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |List| #)))
--R            6> (|containsVars| (|List| (|FortranCode|)))
--R              7> (|containsVars1| (|List| (|FortranCode|)))
--R                8> (|containsVars1| (|FortranCode|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |FortranCode|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Record| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FortranMatrixCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *1 #)))
--R            <6 (|evalMmDom| ((*2 |Record| # #)))
--R            6> (|containsVars| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R              7> (|containsVars1| (|Record| (|:| |localSymbols| #) (|:| |code| #)))
--R                8> (|containsVars1| (|:| |localSymbols| (|SymbolTable|)))
--R                  9> (|containsVars1| (|SymbolTable|))
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R                8> (|containsVars1| (|:| |code| (|List| #)))
--R                  9> (|containsVars1| (|List| (|FortranCode|)))
--R                    10> (|containsVars1| (|FortranCode|))
--R                    <10 (|containsVars1| NIL)
--R                  <9 (|containsVars1| NIL)
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) |coerce| NIL)
--R                8> (|hasCate| *1 (|FreeLieAlgebra| *2 *3) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|FreeLieAlgebra| *2 *3) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FreeLieAlgebra| *2 *3) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|OrderedSet|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|OrderedSet|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|OrderedSet|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|CommutativeRing|)) |coerce| NIL)
--R                8> (|hasCate| *3 (|CommutativeRing|) NIL)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|CommutativeRing|) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|XDistributedPolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |XDistributedPolynomial| *3 *4)))
--R            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
--R              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XDistributedPolynomial| *3 *4))
--R              7> (|containsVars1| (|XDistributedPolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XDistributedPolynomial|))
--R              7> (|containsVars1| (|XDistributedPolynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|XRecursivePolynomial| *3 *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #)))
--R            <6 (|evalMmDom| ((*2 |XRecursivePolynomial| *3 *4)))
--R            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
--R              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XRecursivePolynomial| *3 *4))
--R              7> (|containsVars1| (|XRecursivePolynomial| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|XRecursivePolynomial|))
--R              7> (|containsVars1| (|XRecursivePolynomial|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
--R              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *2)
--R                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                  9> (|hasCate1| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)) *3)
--R                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    10> (|hasCateSpecialNew| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
--R            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *2 *4 *3))
--R              7> (|noSharpCallsHere| *2)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *4)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *3)
--R              <7 (|noSharpCallsHere| T)
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *2 *4 *3))
--R        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|List| #) *4 (|Integer|)))
--R              7> (|containsVars1| (|List| (|Integer|)))
--R                8> (|containsVars1| (|Integer|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| T)
--R          <5 (|containsVars1| T)
--R        <4 (|containsVars| T)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|FiniteFieldCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R            6> (|evalMmCat| |coerce| (*1 *2 *3) ((|ofCategory| *4 #) (|ofCategory| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R              7> (|orderMmCatStack| ((|ofCategory| *4 #) (|ofCategory| *2 #) (|ofCategory| *3 #)))
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))
--R                <8 (|mmCatComp| T)
--R                8> (|mmCatComp| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *2 #) (|ofCategory| *3 #) (|ofCategory| *4 #)))
--R              7> (|evalMmCat1| (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                8> (|hasCate| *2 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                  9> (|hasCate1| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *2)
--R                    10> (|hasCate| (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    10> (|hasCateSpecialNew| *2 (|List| (|Integer|)) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                8> (|hasCate| *3 (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                  9> (|hasCate1| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)) *3)
--R                    10> (|hasCate| (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    10> (|hasCateSpecialNew| *3 (|Integer|) (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteAlgebraicExtensionField| *4) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *4 (|FiniteFieldCategory|)) |coerce| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                8> (|hasCate| *4 (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|FiniteFieldCategory|) ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R          <5 (|evalMmCond0| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R        <4 (|evalMmCond| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R        4> (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R          5> (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
--R            6> (|noSharpCallsHere| (|FiniteFieldHomomorphisms| *3 *4 *2))
--R              7> (|noSharpCallsHere| *3)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *4)
--R              <7 (|noSharpCallsHere| T)
--R              7> (|noSharpCallsHere| *2)
--R              <7 (|noSharpCallsHere| T)
--R            <6 (|noSharpCallsHere| T)
--R          <5 (|replaceSharpCalls| (|FiniteFieldHomomorphisms| *3 *4 *2))
--R        <4 (|fixUpTypeArgs| ((*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R        4> (|containsVars| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|FiniteFieldHomomorphisms| # *4 #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|FiniteFieldHomomorphisms| (|Integer|) *4 (|List| #)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| T)
--R          <5 (|containsVars1| T)
--R        <4 (|containsVars| T)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Expression| *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranExpression| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|FortranMachineTypeCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            <6 (|evalMmDom| ((*1 |FortranExpression| *3 *4 *5) (*2 |Expression| *5)))
--R            6> (|containsVars| (|FortranExpression| *3 *4 *5))
--R              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranExpression| *3 *4 *5))
--R              7> (|containsVars1| (|FortranExpression| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|FortranExpression| *3 *4))
--R              7> (|containsVars1| (|FortranExpression| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|FortranCode|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |FortranCode|) (*2 |OutputForm|)))
--R            6> (|containsVars| (|FortranCode|))
--R              7> (|containsVars1| (|FortranCode|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|OrderedSet|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|DifferentialVariableCategory| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|DifferentialVariableCategory| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|DifferentialVariableCategory| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|DifferentialVariableCategory| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|OrderedSet|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|OrderedSet|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|OrderedSet|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|OrderedSet|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *3 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *3 (|SegmentBinding| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *4 (|Join| # # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SegmentBinding| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DrawNumericHack| *4)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *3 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|ofCategory| *4 #) (|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DrawNumericHack| *4) (*2 |SegmentBinding| #) (*3 |SegmentBinding| #)))
--R            6> (|containsVars| (|SegmentBinding| (|Float|)))
--R              7> (|containsVars1| (|SegmentBinding| (|Float|)))
--R                8> (|containsVars1| (|Float|))
--R                <8 (|containsVars1| NIL)
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Dequeue| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |Dequeue| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|Dequeue| *3))
--R              7> (|containsVars1| (|Dequeue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Dequeue| *3))
--R              7> (|containsVars1| (|Dequeue| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Dequeue|))
--R              7> (|containsVars1| (|Dequeue|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |Fraction| #)))
--R            6> (|containsVars| (|DecimalExpansion|))
--R              7> (|containsVars1| (|DecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 10)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|DecimalExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |DecimalExpansion|) (*2 |RadixExpansion| 10)))
--R            6> (|containsVars| (|DecimalExpansion|))
--R              7> (|containsVars1| (|DecimalExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Join| # #)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Database| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Database| *3) (*2 |List| *3)))
--R            6> (|containsVars| (|Database| *3))
--R              7> (|containsVars1| (|Database| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Database| *3))
--R              7> (|containsVars1| (|Database| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Database|))
--R              7> (|containsVars1| (|Database|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|DirectProduct| *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |DirectProduct| *4 *5)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofType| *4 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SquareMatrix| *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |SquareMatrix| *4 *5)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *5 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| *5)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofCategory| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|List| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|CartesianTensor| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Integer|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|NonNegativeInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofCategory| *5 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *5 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *5 #)))
--R            <6 (|evalMmDom| ((*1 |CartesianTensor| *3 *4 *5) (*2 |List| #)))
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4 *5))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|CartesianTensor| *3 *4))
--R              7> (|containsVars1| (|CartesianTensor| *3 *4))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Fraction| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |Fraction| #)))
--R            6> (|containsVars| (|BinaryExpansion|))
--R              7> (|containsVars1| (|BinaryExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|RadixExpansion| 2)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|BinaryExpansion|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |BinaryExpansion|) (*2 |RadixExpansion| 2)))
--R            6> (|containsVars| (|BinaryExpansion|))
--R              7> (|containsVars1| (|BinaryExpansion|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*1) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *1) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|OutputForm|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|ArrayStack| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|SetCategory|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *1) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |ArrayStack| *3) (*2 |OutputForm|)))
--R            6> (|containsVars| (|ArrayStack| *3))
--R              7> (|containsVars1| (|ArrayStack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ArrayStack| *3))
--R              7> (|containsVars1| (|ArrayStack| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|ArrayStack|))
--R              7> (|containsVars1| (|ArrayStack|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp9| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp9| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp9| *3))
--R              7> (|containsVars1| (|Asp9| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp9| *3))
--R              7> (|containsVars1| (|Asp9| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp9| *3))
--R              7> (|containsVars1| (|Asp9| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp80| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp80| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp80| *3))
--R              7> (|containsVars1| (|Asp80| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp80| *3))
--R              7> (|containsVars1| (|Asp80| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp80| *3))
--R              7> (|containsVars1| (|Asp80| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp7| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp7| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp7| *3))
--R              7> (|containsVars1| (|Asp7| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp7| *3))
--R              7> (|containsVars1| (|Asp7| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp7| *3))
--R              7> (|containsVars1| (|Asp7| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp78| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp78| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp78| *3))
--R              7> (|containsVars1| (|Asp78| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp78| *3))
--R              7> (|containsVars1| (|Asp78| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp78| *3))
--R              7> (|containsVars1| (|Asp78| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp77| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp77| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp77| *3))
--R              7> (|containsVars1| (|Asp77| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp77| *3))
--R              7> (|containsVars1| (|Asp77| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp77| *3))
--R              7> (|containsVars1| (|Asp77| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp74| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp74| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp74| *3))
--R              7> (|containsVars1| (|Asp74| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp74| *3))
--R              7> (|containsVars1| (|Asp74| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp74| *3))
--R              7> (|containsVars1| (|Asp74| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp73| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp73| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp73| *3))
--R              7> (|containsVars1| (|Asp73| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp73| *3))
--R              7> (|containsVars1| (|Asp73| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp73| *3))
--R              7> (|containsVars1| (|Asp73| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp6| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp6| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp6| *3))
--R              7> (|containsVars1| (|Asp6| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp6| *3))
--R              7> (|containsVars1| (|Asp6| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp6| *3))
--R              7> (|containsVars1| (|Asp6| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp55| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp55| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp55| *3))
--R              7> (|containsVars1| (|Asp55| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp55| *3))
--R              7> (|containsVars1| (|Asp55| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp55| *3))
--R              7> (|containsVars1| (|Asp55| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp50| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp50| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp50| *3))
--R              7> (|containsVars1| (|Asp50| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp50| *3))
--R              7> (|containsVars1| (|Asp50| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp50| *3))
--R              7> (|containsVars1| (|Asp50| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp4| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp4| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp4| *3))
--R              7> (|containsVars1| (|Asp4| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp4| *3))
--R              7> (|containsVars1| (|Asp4| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp4| *3))
--R              7> (|containsVars1| (|Asp4| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp49| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp49| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp49| *3))
--R              7> (|containsVars1| (|Asp49| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp49| *3))
--R              7> (|containsVars1| (|Asp49| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp49| *3))
--R              7> (|containsVars1| (|Asp49| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp42| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp42| *3 *4 *5) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp42| *3 *4 *5))
--R              7> (|containsVars1| (|Asp42| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp42| *3 *4 *5))
--R              7> (|containsVars1| (|Asp42| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp42| *3 *4 *5))
--R              7> (|containsVars1| (|Asp42| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #) (|ofType| *4 #) (|ofType| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp41| *3 *4 *5)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *4 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp41| *3 *4 *5) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp41| *3 *4 *5))
--R              7> (|containsVars1| (|Asp41| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp41| *3 *4 *5))
--R              7> (|containsVars1| (|Asp41| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp41| *3 *4 *5))
--R              7> (|containsVars1| (|Asp41| *3 *4 *5))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp35| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp35| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp35| *3))
--R              7> (|containsVars1| (|Asp35| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp35| *3))
--R              7> (|containsVars1| (|Asp35| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp35| *3))
--R              7> (|containsVars1| (|Asp35| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp31| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp31| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp31| *3))
--R              7> (|containsVars1| (|Asp31| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp31| *3))
--R              7> (|containsVars1| (|Asp31| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp31| *3))
--R              7> (|containsVars1| (|Asp31| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp24| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp24| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp24| *3))
--R              7> (|containsVars1| (|Asp24| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp24| *3))
--R              7> (|containsVars1| (|Asp24| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp24| *3))
--R              7> (|containsVars1| (|Asp24| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Matrix| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp20| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp20| *3) (*2 |Matrix| #)))
--R            6> (|containsVars| (|Asp20| *3))
--R              7> (|containsVars1| (|Asp20| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp20| *3))
--R              7> (|containsVars1| (|Asp20| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp20| *3))
--R              7> (|containsVars1| (|Asp20| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|FortranExpression| # # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp1| *3) (*2 |FortranExpression| # # #)))
--R            6> (|containsVars| (|Asp1| *3))
--R              7> (|containsVars1| (|Asp1| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp1| *3))
--R              7> (|containsVars1| (|Asp1| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp1| *3))
--R              7> (|containsVars1| (|Asp1| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp19| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp19| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp19| *3))
--R              7> (|containsVars1| (|Asp19| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp19| *3))
--R              7> (|containsVars1| (|Asp19| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp19| *3))
--R              7> (|containsVars1| (|Asp19| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofType| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|Asp10| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *3 (|Symbol|)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |Asp10| *3) (*2 |Vector| #)))
--R            6> (|containsVars| (|Asp10| *3))
--R              7> (|containsVars1| (|Asp10| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp10| *3))
--R              7> (|containsVars1| (|Asp10| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|Asp10| *3))
--R              7> (|containsVars1| (|Asp10| *3))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*3) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *2 *3) (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Any|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AnyFunctions1| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Type|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *2 *3) ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #) (|ofCategory| *3 #)))
--R            <6 (|evalMmDom| ((*1 |AnyFunctions1| *3) (*2 |Any|)))
--R            6> (|containsVars| (|Any|))
--R              7> (|containsVars1| (|Any|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|SparseMultivariatePolynomial| # #)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraicNumber|)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |AlgebraicNumber|) (*2 |SparseMultivariatePolynomial| # #)))
--R            6> (|containsVars| (|AlgebraicNumber|))
--R              7> (|containsVars1| (|AlgebraicNumber|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars| NIL)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
--R        4> (|evalMmStack| (AND (|isDomain| *2 #) (|ofCategory| *3 #) (|ofType| *6 #) (|isDomain| *1 #) (|ofType| *4 #) (|ofType| *5 #)))
--R          5> (|evalMmStackInner| (|isDomain| *2 (|Vector| *3)))
--R          <5 (|evalMmStackInner| ((|isDomain| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *3 (|Field|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *3 #)))
--R          5> (|evalMmStackInner| (|ofType| *6 (|Vector| #)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)))
--R          <5 (|evalMmStackInner| ((|isDomain| *1 #)))
--R          5> (|evalMmStackInner| (|ofType| *4 (|PositiveInteger|)))
--R          <5 (|evalMmStackInner| NIL)
--R          5> (|evalMmStackInner| (|ofType| *5 (|List| #)))
--R          <5 (|evalMmStackInner| NIL)
--R        <4 (|evalMmStack| ((# # #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            6> (|evalMmDom| ((|isDomain| *2 #) (|ofCategory| *3 #) (|isDomain| *1 #)))
--R            <6 (|evalMmDom| ((*1 |AlgebraGivenByStructuralConstants| *3 *4 *5 *6) (*2 |Vector| *3)))
--R            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R            6> (|containsVars| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
--R              7> (|containsVars1| (|AlgebraGivenByStructuralConstants| *4 *5 *6))
--R              <7 (|containsVars1| T)
--R            <6 (|containsVars| T)
--R          <5 (|evalMmCond0| |failed|)
--R        <4 (|evalMmCond| |failed|)
--R      <3 (|evalMm| NIL)
--R      3> (|matchTypes| (*2) ((|Integer|)) ((|Integer|)))
--R      <3 (|matchTypes| NIL)
--R      3> (|evalMm| |coerce| (|List| (|Integer|)) (*1 *1 *2) (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R        4> (|evalMmStack| (AND (|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *1 (|Algebra| *2)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *1 #)))
--R          5> (|evalMmStackInner| (|ofCategory| *2 (|CommutativeRing|)))
--R          <5 (|evalMmStackInner| ((|ofCategory| *2 #)))
--R        <4 (|evalMmStack| ((# #)))
--R        4> (|evalMmCond| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R          5> (|evalMmCond0| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            6> (|evalMmDom| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R            <6 (|evalMmDom| NIL)
--R            6> (|evalMmCat| |coerce| (*1 *1 *2) ((|ofCategory| *1 #) (|ofCategory| *2 #)) NIL)
--R              7> (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R                8> (|mmCatComp| (|ofCategory| *1 (|Algebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))
--R                <8 (|mmCatComp| NIL)
--R                8> (|mmCatComp| (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|Algebra| *2)))
--R                <8 (|mmCatComp| NIL)
--R              <7 (|orderMmCatStack| ((|ofCategory| *1 #) (|ofCategory| *2 #)))
--R              7> (|evalMmCat1| (|ofCategory| *1 (|Algebra| *2)) |coerce| NIL)
--R                8> (|hasCate| *1 (|Algebra| *2) NIL)
--R                  9> (|hasCate1| (|List| (|Integer|)) (|Algebra| *2) NIL *1)
--R                    10> (|hasCate| (|List| (|Integer|)) (|Algebra| *2) NIL)
--R                    <10 (|hasCate| |failed|)
--R                  <9 (|hasCate1| |failed|)
--R                  9> (|hasCateSpecial| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
--R                    10> (|hasCateSpecialNew| *1 (|List| (|Integer|)) (|Algebra| *2) NIL)
--R                    <10 (|hasCateSpecialNew| |failed|)
--R                  <9 (|hasCateSpecial| |failed|)
--R                <8 (|hasCate| |failed|)
--R                8> (|defaultTypeForCategory| (|Algebra| *2) NIL)
--R                <8 (|defaultTypeForCategory| NIL)
--R              <7 (|evalMmCat1| NIL)
--R              7> (|evalMmCat1| (|ofCategory| *2 (|CommutativeRing|)) |coerce| NIL)
--R                8> (|hasCate| *2 (|CommutativeRing|) NIL)
--R                  9> (|hasCate1| (|Integer|) (|CommutativeRing|) NIL *2)
--R                    10> (|hasCate| (|Integer|) (|CommutativeRing|) NIL)
--R                    <10 (|hasCate| NIL)
--R                  <9 (|hasCate1| NIL)
--R                <8 (|hasCate| NIL)
--R              <7 (|evalMmCat1| NIL)
--R            <6 (|evalMmCat| NIL)
--R          <5 (|evalMmCond0| NIL)
--R        <4 (|evalMmCond| NIL)
--R        4> (|fixUpTypeArgs| NIL)
--R        <4 (|fixUpTypeArgs| NIL)
--R        4> (|containsVars| ((|List| #) (|List| #) (|Integer|)))
--R          5> (|containsVars1| ((|List| #) (|List| #) (|Integer|)))
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|List| (|Integer|)))
--R              7> (|containsVars1| (|Integer|))
--R              <7 (|containsVars1| NIL)
--R            <6 (|containsVars1| NIL)
--R            6> (|containsVars1| (|Integer|))
--R            <6 (|containsVars1| NIL)
--R          <5 (|containsVars1| NIL)
--R        <4 (|containsVars| NIL)
--R      <3 (|evalMm| NIL)
--R    <2 (|selectMmsGen,matchMms| NIL)
--R  <1 (|selectMmsGen| NIL)
--R
--R   (4)  [555555,1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 4

)lisp (untrace)
 
Value = (|unifyStructVar| |unifyStruct| |filterModemapsFromPackages| |selectMmsGen,matchMms| |selectMmsGen,exact?| |selectMmsGen| |replaceSharpCalls| |orderMmCatStack| |noSharpCallsHere| |mmCatComp| |mkDomPvar| |matchTypes| |hasCateSpecialNew| |hasCateSpecial| |hasCate1| |hasCate| |fixUpTypeArgs| |evalMmStackInner| |evalMmStack| |evalMmDom| |evalMmCond0| |evalMmCond| |evalMmCat1| |evalMmCat| |evalMm| |domArg2| |defaultTypeForCategory| |containsVars1| |containsVars| |coerceTypeArgs|)
 
)lisp (trace |hasAtt|)
 
Value = (|hasAtt|)

--S 5 of 31
removeDuplicates l
 
  1> (|hasAtt| (|List| (|Integer|)) |finiteAggregate| NIL)
  <1 (|hasAtt| NIL)

   (5)  [1,4,2,- 6,0,3,5]
                                                           Type: List Integer
--R 
--R  1> (|hasAtt| (|List| (|Integer|)) |finiteAggregate| NIL)
--R  <1 (|hasAtt| NIL)
--R
--R   (5)  [1,4,2,- 6,0,3,5]
--R                                                           Type: List Integer
--E 5

)lisp (untrace)
 
Value = (|hasAtt|)
 
)lisp (trace |defaultTargetFE|)
 
Value = (|defaultTargetFE|)
)lisp (trace |domArg|)
 
Value = (|domArg|)
)lisp (trace |domainDepth|)
 
Value = (|domainDepth|)
)lisp (trace |hasCaty1|)
 
Value = (|hasCaty1|)
)lisp (trace |hitListOfTarget|)
 
Value = (|hitListOfTarget|)
)lisp (trace |mmCost|)
 
Value = (|mmCost|)
)lisp (trace |mmCost0|)
 
Value = (|mmCost0|)

--S 6 of 31
p := numeric %pi
 
  1> (|defaultTargetFE| (|Pi|))
  <1 (|defaultTargetFE| (|Expression| (|Integer|)))
  1> (|hasCaty1| (OR (|has| # #) (|has| # #) (|has| # #) (|has| # #) (|has| # #)) NIL)
  <1 (|hasCaty1| NIL)
  1> (|defaultTargetFE| (|Integer|))
  <1 (|defaultTargetFE| (|Expression| (|Integer|)))
  1> (|hasCaty1| (OR (|has| # #) (|has| # #) (|has| # #)) NIL)
  <1 (|hasCaty1| NIL)
  1> (|domArg| (|Pi|) 0 ((|Fraction| #)) ((|Symbol|)))
  <1 (|domArg| (|Pi|))
  1> (|domArg| (|Pi|) 0 ((|Integer|)) ((|Symbol|)))
  <1 (|domArg| (|Pi|))
  1> (|domArg| (|Pi|) 0 (|#1|) ((|Symbol|)))
  <1 (|domArg| (|Symbol|))
  1> (|domArg| (|Pi|) 0 ((|Symbol|)) ((|Symbol|)))
  <1 (|domArg| (|Pi|))
  1> (|mmCost| |numeric| ((|Numeric| #) (|Float|) (|Fraction| #)) (NIL) NIL ((|Pi|)) (NIL))
    2> (|mmCost0| |numeric| ((|Numeric| #) (|Float|) (|Fraction| #)) (NIL) NIL ((|Pi|)) (NIL))
      3> (|domainDepth| (|Float|))
        4> (|domainDepth| |Float|)
        <4 (|domainDepth| 0)
        4> (|domainDepth| NIL)
        <4 (|domainDepth| 0)
      <3 (|domainDepth| 1)
      3> (|hitListOfTarget| (|Float|))
      <3 (|hitListOfTarget| 500)
    <2 (|mmCost0| 51500)
  <1 (|mmCost| 51500)
  1> (|mmCost| |numeric| ((|Numeric| #) (|Float|) (|Pi|)) (NIL) NIL ((|Pi|)) (NIL))
    2> (|mmCost0| |numeric| ((|Numeric| #) (|Float|) (|Pi|)) (NIL) NIL ((|Pi|)) (NIL))
      3> (|domainDepth| (|Float|))
        4> (|domainDepth| |Float|)
        <4 (|domainDepth| 0)
        4> (|domainDepth| NIL)
        <4 (|domainDepth| 0)
      <3 (|domainDepth| 1)
      3> (|hitListOfTarget| (|Float|))
      <3 (|hitListOfTarget| 500)
    <2 (|mmCost0| 11500)
  <1 (|mmCost| 11500)
  1> (|mmCost| |numeric| ((|Numeric| #) (|Float|) (|Polynomial| #)) (NIL) NIL ((|Pi|)) (NIL))
    2> (|mmCost0| |numeric| ((|Numeric| #) (|Float|) (|Polynomial| #)) (NIL) NIL ((|Pi|)) (NIL))
      3> (|domainDepth| (|Float|))
        4> (|domainDepth| |Float|)
        <4 (|domainDepth| 0)
        4> (|domainDepth| NIL)
        <4 (|domainDepth| 0)
      <3 (|domainDepth| 1)
      3> (|hitListOfTarget| (|Float|))
      <3 (|hitListOfTarget| 500)
    <2 (|mmCost0| 51500)
  <1 (|mmCost| 51500)

   (6)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R  1> (|defaultTargetFE| (|Pi|))
--R  <1 (|defaultTargetFE| (|Expression| (|Integer|)))
--R  1> (|hasCaty1| (OR (|has| # #) (|has| # #) (|has| # #) (|has| # #) (|has| # #)) NIL)
--R  <1 (|hasCaty1| NIL)
--R  1> (|defaultTargetFE| (|Integer|))
--R  <1 (|defaultTargetFE| (|Expression| (|Integer|)))
--R  1> (|hasCaty1| (OR (|has| # #) (|has| # #) (|has| # #)) NIL)
--R  <1 (|hasCaty1| NIL)
--R  1> (|domArg| (|Pi|) 0 ((|Fraction| #)) ((|Symbol|)))
--R  <1 (|domArg| (|Pi|))
--R  1> (|domArg| (|Pi|) 0 ((|Integer|)) ((|Symbol|)))
--R  <1 (|domArg| (|Pi|))
--R  1> (|domArg| (|Pi|) 0 (|#1|) ((|Symbol|)))
--R  <1 (|domArg| (|Symbol|))
--R  1> (|domArg| (|Pi|) 0 ((|Symbol|)) ((|Symbol|)))
--R  <1 (|domArg| (|Pi|))
--R  1> (|mmCost| |numeric| ((|Numeric| #) (|Float|) (|Fraction| #)) (NIL) NIL ((|Pi|)) (NIL))
--R    2> (|mmCost0| |numeric| ((|Numeric| #) (|Float|) (|Fraction| #)) (NIL) NIL ((|Pi|)) (NIL))
--R      3> (|domainDepth| (|Float|))
--R        4> (|domainDepth| |Float|)
--R        <4 (|domainDepth| 0)
--R        4> (|domainDepth| NIL)
--R        <4 (|domainDepth| 0)
--R      <3 (|domainDepth| 1)
--R      3> (|hitListOfTarget| (|Float|))
--R      <3 (|hitListOfTarget| 500)
--R    <2 (|mmCost0| 51500)
--R  <1 (|mmCost| 51500)
--R  1> (|mmCost| |numeric| ((|Numeric| #) (|Float|) (|Pi|)) (NIL) NIL ((|Pi|)) (NIL))
--R    2> (|mmCost0| |numeric| ((|Numeric| #) (|Float|) (|Pi|)) (NIL) NIL ((|Pi|)) (NIL))
--R      3> (|domainDepth| (|Float|))
--R        4> (|domainDepth| |Float|)
--R        <4 (|domainDepth| 0)
--R        4> (|domainDepth| NIL)
--R        <4 (|domainDepth| 0)
--R      <3 (|domainDepth| 1)
--R      3> (|hitListOfTarget| (|Float|))
--R      <3 (|hitListOfTarget| 500)
--R    <2 (|mmCost0| 11500)
--R  <1 (|mmCost| 11500)
--R  1> (|mmCost| |numeric| ((|Numeric| #) (|Float|) (|Polynomial| #)) (NIL) NIL ((|Pi|)) (NIL))
--R    2> (|mmCost0| |numeric| ((|Numeric| #) (|Float|) (|Polynomial| #)) (NIL) NIL ((|Pi|)) (NIL))
--R      3> (|domainDepth| (|Float|))
--R        4> (|domainDepth| |Float|)
--R        <4 (|domainDepth| 0)
--R        4> (|domainDepth| NIL)
--R        <4 (|domainDepth| 0)
--R      <3 (|domainDepth| 1)
--R      3> (|hitListOfTarget| (|Float|))
--R      <3 (|hitListOfTarget| 500)
--R    <2 (|mmCost0| 51500)
--R  <1 (|mmCost| 51500)
--R
--R   (6)  3.1415926535 897932385
--R                                                                  Type: Float
--E 6

)lisp (untrace)
 
Value = (|mmCost0| |mmCost| |hitListOfTarget| |hasCaty1| |domainDepth| |domArg| |defaultTargetFE|)
 
)lisp (trace |findCommonSigInDomain|)
 
Value = (|findCommonSigInDomain|)
)lisp (trace |isOpInDomain|)
 
Value = (|isOpInDomain|)
)lisp (trace |selectDollarMms|)
 
Value = (|selectDollarMms|)

--S 7 of 31
a := 163.0
 
  1> (|isOpInDomain| |float| (|Float|) 1)
  <1 (|isOpInDomain| NIL)
  1> (|isOpInDomain| |float| (|Float|) 3)
  <1 (|isOpInDomain| ((# 107 T ELT)))
  1> (|findCommonSigInDomain| |float| (|Float|) 3)
  <1 (|findCommonSigInDomain| ((|Float|) (|Integer|) (|Integer|) (|PositiveInteger|)))
  1> (|selectDollarMms| (|Float|) |float| ((|Integer|) (|Integer|) (|PositiveInteger|)) (NIL NIL (|Integer|)))
  <1 (|selectDollarMms| ((# # #)))

   (7)  163.0
                                                                  Type: Float
--R 
--R  1> (|isOpInDomain| |float| (|Float|) 1)
--R  <1 (|isOpInDomain| NIL)
--R  1> (|isOpInDomain| |float| (|Float|) 3)
--R  <1 (|isOpInDomain| ((# 107 T ELT)))
--R  1> (|findCommonSigInDomain| |float| (|Float|) 3)
--R  <1 (|findCommonSigInDomain| ((|Float|) (|Integer|) (|Integer|) (|PositiveInteger|)))
--R  1> (|selectDollarMms| (|Float|) |float| ((|Integer|) (|Integer|) (|PositiveInteger|)) (NIL NIL (|Integer|)))
--R  <1 (|selectDollarMms| ((# # #)))
--R
--R   (7)  163.0
--R                                                                  Type: Float
--E 7

)lisp (untrace)
 
Value = (|selectDollarMms| |isOpInDomain| |findCommonSigInDomain|)
 
)lisp (trace |isAVariableType|)
 
Value = (|isAVariableType|)

--S 8 of 31
16*c**4 - 16*c**2 + 1
 
  1> (|isAVariableType| (|Variable| |c|))
  <1 (|isAVariableType| T)
  1> (|isAVariableType| (|Variable| |c|))
  <1 (|isAVariableType| T)

           4      2
   (8)  16c  - 16c  + 1
                                                     Type: Polynomial Integer
--R 
--R  1> (|isAVariableType| (|Variable| |c|))
--R  <1 (|isAVariableType| T)
--R  1> (|isAVariableType| (|Variable| |c|))
--R  <1 (|isAVariableType| T)
--R
--R           4      2
--R   (8)  16c  - 16c  + 1
--R                                                     Type: Polynomial Integer
--E 8

)lisp (untrace)
 
Value = (|isAVariableType|)
 
)lisp (trace |hasAttSig|)
 
Value = (|hasAttSig|)
)lisp (trace |hasSig|)
 
Value = (|hasSig|)

--S 9 of 31
u := factor (x**4 - y**4)
 
  1> (|hasAttSig| (|Symbol|) ((SIGNATURE |convert| #)) ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
    2> (|hasSig| (|Symbol|) |convert| ((|Symbol|) (|Symbol|)) ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
    <2 (|hasSig| ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
  <1 (|hasAttSig| ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
  1> (|hasAttSig| (|Symbol|) ((SIGNATURE |convert| #)) NIL)
    2> (|hasSig| (|Symbol|) |convert| ((|Symbol|) (|Symbol|)) NIL)
    <2 (|hasSig| NIL)
  <1 (|hasAttSig| NIL)

                          2    2
   (9)  - (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R  1> (|hasAttSig| (|Symbol|) ((SIGNATURE |convert| #)) ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
--R    2> (|hasSig| (|Symbol|) |convert| ((|Symbol|) (|Symbol|)) ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
--R    <2 (|hasSig| ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
--R  <1 (|hasAttSig| ((*5 |Symbol|) (*4 |IndexedExponents| #) (*3 |Polynomial| #) (*1 |MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3) (*2 |Factored| *3)))
--R  1> (|hasAttSig| (|Symbol|) ((SIGNATURE |convert| #)) NIL)
--R    2> (|hasSig| (|Symbol|) |convert| ((|Symbol|) (|Symbol|)) NIL)
--R    <2 (|hasSig| NIL)
--R  <1 (|hasAttSig| NIL)
--R
--R                          2    2
--R   (9)  - (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 9

)lisp (untrace)
 
Value = (|hasSig| |hasAttSig|)
 
)lisp (trace |getSymbolType|)
 
Value = (|getSymbolType|)

--S 10 of 31
v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1)
 
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *2)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *2)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
  1> (|getSymbolType| *1)
  <1 (|getSymbolType| (|Polynomial| (|Integer|)))

                2       2  2    2
   (10)  (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *2)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *2)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R  1> (|getSymbolType| *1)
--R  <1 (|getSymbolType| (|Polynomial| (|Integer|)))
--R
--R                2       2  2    2
--R   (10)  (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 10

)lisp (untrace)
 
Value = (|getSymbolType|)
 
)lisp (trace |constrArg|)
 
Value = (|constrArg|)
)lisp (trace |makeConstrArg|)
 
Value = (|makeConstrArg|)

--S 11 of 31
ux:UP(x,PF(19)) :=3*x**4+2*x**2+15*x+18
 
  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
  <1 (|constrArg| (|PositiveInteger|))
  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
  <1 (|constrArg| (|PositiveInteger|))
  1> (|makeConstrArg| 19 19 (|PositiveInteger|) (|PositiveInteger|) NIL)
  <1 (|makeConstrArg| 19)
  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
  <1 (|constrArg| (|PositiveInteger|))
  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
  <1 (|constrArg| (|PositiveInteger|))
  1> (|makeConstrArg| 19 19 (|PositiveInteger|) (|PositiveInteger|) NIL)
  <1 (|makeConstrArg| 19)

           4     2
   (11)  3x  + 2x  + 15x + 18
                                  Type: UnivariatePolynomial(x,PrimeField 19)
--R 
--R  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R  <1 (|constrArg| (|PositiveInteger|))
--R  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *2 *4 *3)))
--R  <1 (|constrArg| (|PositiveInteger|))
--R  1> (|makeConstrArg| 19 19 (|PositiveInteger|) (|PositiveInteger|) NIL)
--R  <1 (|makeConstrArg| 19)
--R  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R  <1 (|constrArg| (|PositiveInteger|))
--R  1> (|constrArg| (|PositiveInteger|) ((|#1| . 19) ($ |PrimeField| 19)) ((*4 . *3) (*3 |PrimeField| 19) (*1 |FiniteFieldHomomorphisms| *3 *4 *2)))
--R  <1 (|constrArg| (|PositiveInteger|))
--R  1> (|makeConstrArg| 19 19 (|PositiveInteger|) (|PositiveInteger|) NIL)
--R  <1 (|makeConstrArg| 19)
--R
--R           4     2
--R   (11)  3x  + 2x  + 15x + 18
--R                                  Type: UnivariatePolynomial(x,PrimeField 19)
--E 11

)lisp (untrace)
 
Value = (|makeConstrArg| |constrArg|)
 
)lisp (trace |getFunctionFromDomain|)
 
Value = (|getFunctionFromDomain|)
)lisp (trace |isTowerWithSubdomain|)
 
Value = (|isTowerWithSubdomain|)

--S 12 of 31
f:MPOLY([x,y,z],FRAC INT) :=(4/9*x**2-1/16)*(x**3/27+125)
 
  1> (|isTowerWithSubdomain| (|Fraction| (|Integer|)) (|Integer|))
  <1 (|isTowerWithSubdomain| (|Fraction| (|Integer|)))
  1> (|getFunctionFromDomain| |ground?| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;ground?;$B;16|> . #<vector 09943ccc>))
  1> (|getFunctionFromDomain| |leadingMonomial| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;leadingMonomial;2$;78|> . #<vector 09943ccc>))
  1> (|getFunctionFromDomain| |leadingCoefficient| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;leadingCoefficient;$R;77|> . #<vector 09943ccc>))
  1> (|isTowerWithSubdomain| (|Fraction| (|Integer|)) (|Integer|))
  <1 (|isTowerWithSubdomain| (|Fraction| (|Integer|)))
  1> (|getFunctionFromDomain| |primitiveMonomials| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |POLYCAT-;primitiveMonomials;SL;12|> . #<vector 09b8a578>))
  1> (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) (|Fraction| (|Integer|)))
  <1 (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)))
  1> (|getFunctionFromDomain| |reductum| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;reductum;2$;79|> . #<vector 09943ccc>))
  1> (|getFunctionFromDomain| |ground?| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;ground?;$B;16|> . #<vector 09943ccc>))
  1> (|getFunctionFromDomain| |ground| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |FAMR-;ground;SR;4|> . #<vector 09bf1fdc>))
  1> (|getFunctionFromDomain| + (|Fraction| (|MultivariatePolynomial| # #)) ((|Fraction| #) (|Fraction| #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |FRAC;+;3$;21|> . #<vector 08bf416c>))
  1> (|getFunctionFromDomain| * (|Fraction| (|MultivariatePolynomial| # #)) ((|Fraction| #) (|Fraction| #)))
  <1 (|getFunctionFromDomain| (#<compiled-function |FRAC;*;3$;23|> . #<vector 08bf416c>))
  1> (|isTowerWithSubdomain| (|Fraction| (|MultivariatePolynomial| # #)) (|MultivariatePolynomial| (|x| |y| |z|) (|Integer|)))
  <1 (|isTowerWithSubdomain| (|Fraction| (|MultivariatePolynomial| # #)))
  1> (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Integer|)) (|Integer|))
  <1 (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Integer|)))

          4   5    1   3   500  2   125
   (12)  --- x  - --- x  + --- x  - ---
         243      432       9        16
                       Type: MultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R  1> (|isTowerWithSubdomain| (|Fraction| (|Integer|)) (|Integer|))
--R  <1 (|isTowerWithSubdomain| (|Fraction| (|Integer|)))
--R  1> (|getFunctionFromDomain| |ground?| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;ground?;$B;16|> . #<vector 09454d58>))
--R  1> (|getFunctionFromDomain| |leadingMonomial| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;leadingMonomial;2$;78|> . #<vector 09454d58>))
--R  1> (|getFunctionFromDomain| |leadingCoefficient| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;leadingCoefficient;$R;77|> . #<vector 09454d58>))
--R  1> (|isTowerWithSubdomain| (|Fraction| (|Integer|)) (|Integer|))
--R  <1 (|isTowerWithSubdomain| (|Fraction| (|Integer|)))
--R  1> (|getFunctionFromDomain| |primitiveMonomials| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |POLYCAT-;primitiveMonomials;SL;12|> . #<vector 093c071c>))
--R  1> (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) (|Fraction| (|Integer|)))
--R  <1 (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)))
--R  1> (|getFunctionFromDomain| |reductum| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;reductum;2$;79|> . #<vector 09454d58>))
--R  1> (|getFunctionFromDomain| |ground?| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |SMP;ground?;$B;16|> . #<vector 09454d58>))
--R  1> (|getFunctionFromDomain| |ground| (|MultivariatePolynomial| (|x| |y| |z|) (|Fraction| #)) ((|MultivariatePolynomial| # #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |FAMR-;ground;SR;4|> . #<vector 09151e70>))
--R  1> (|getFunctionFromDomain| + (|Fraction| (|MultivariatePolynomial| # #)) ((|Fraction| #) (|Fraction| #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |FRAC;+;3$;21|> . #<vector 093c0e54>))
--R  1> (|getFunctionFromDomain| * (|Fraction| (|MultivariatePolynomial| # #)) ((|Fraction| #) (|Fraction| #)))
--I  <1 (|getFunctionFromDomain| (#<compiled-function |FRAC;*;3$;23|> . #<vector 093c0e54>))
--R  1> (|isTowerWithSubdomain| (|Fraction| (|MultivariatePolynomial| # #)) (|MultivariatePolynomial| (|x| |y| |z|) (|Integer|)))
--R  <1 (|isTowerWithSubdomain| (|Fraction| (|MultivariatePolynomial| # #)))
--R  1> (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Integer|)) (|Integer|))
--R  <1 (|isTowerWithSubdomain| (|MultivariatePolynomial| (|x| |y| |z|) (|Integer|)))
--R
--R          4   5    1   3   500  2   125
--R   (12)  --- x  - --- x  + --- x  - ---
--R         243      432       9        16
--R                       Type: MultivariatePolynomial([x,y,z],Fraction Integer)
--E 12

)lisp (untrace)
 
Value = (|isTowerWithSubdomain| |getFunctionFromDomain|)
 
)lisp (trace |doReplaceSharpCalls|)
 
Value = (|doReplaceSharpCalls|)

--S 13 of 31
g:DMP([x,y],FRAC POLY INT):=a**2*x**2/b**2 -c**2*y**2/d**2
 
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
    <2 (|doReplaceSharpCalls| 2)
    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))

                     2
         26569  2   c   2
   (13)  ----- x  - -- y
            2        2
           b        d
   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R  1> (|doReplaceSharpCalls| (|DirectProduct| (|#| #) (|NonNegativeInteger|)))
--R    2> (|doReplaceSharpCalls| (|#| (|x| |y|)))
--R    <2 (|doReplaceSharpCalls| 2)
--R    2> (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R    <2 (|doReplaceSharpCalls| (|NonNegativeInteger|))
--R  <1 (|doReplaceSharpCalls| (|DirectProduct| 2 (|NonNegativeInteger|)))
--R
--R                     2
--R         26569  2   c   2
--R   (13)  ----- x  - -- y
--R            2        2
--R           b        d
--R   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 13

)lisp (untrace)
 
Value = (|doReplaceSharpCalls|)
 
)lisp (trace |getLocalMms,f|)
 
Value = (|getLocalMms,f|)

--S 14 of 31
fib(n | n = 0) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 31
fib(n | n = 1) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 31
fib(n | n > 1) == fib(n-1) + fib(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 31
fib 5
 
  1> (|getLocalMms,f| (|Integer|) (|Integer|) T)
  <1 (|getLocalMms,f| T)
  1> (|getLocalMms,f| (|Integer|) (|Integer|) T)
  <1 (|getLocalMms,f| T)
   Compiling function fib with type Integer -> PositiveInteger 
   Compiling function fib as a recurrence relation.
  1> (|getLocalMms,f| (|PositiveInteger|) (|Integer|) T)
  <1 (|getLocalMms,f| (|PositiveInteger|))

   (17)  8
                                                        Type: PositiveInteger
--R 
--R  1> (|getLocalMms,f| (|Integer|) (|Integer|) T)
--R  <1 (|getLocalMms,f| T)
--R  1> (|getLocalMms,f| (|Integer|) (|Integer|) T)
--R  <1 (|getLocalMms,f| T)
--R   Compiling function fib with type Integer -> PositiveInteger 
--R   Compiling function fib as a recurrence relation.
--R  1> (|getLocalMms,f| (|PositiveInteger|) (|Integer|) T)
--R  <1 (|getLocalMms,f| (|PositiveInteger|))
--R
--R   (17)  8
--R                                                        Type: PositiveInteger
--E 17

)clear all
 
 
)lisp (untrace)
 
Value = (|getLocalMms,f|)
 
)lisp (trace |mkRationalFunction|)
 
Value = (|mkRationalFunction|)

--S 18 of 31
laplace(2/t * (1 - cos(a*t)), t, s)
 
  1> (|mkRationalFunction| (|Integer|))
  <1 (|mkRationalFunction| (|Fraction| (|Polynomial| #)))

             2    2
   (1)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R  1> (|mkRationalFunction| (|Integer|))
--R  <1 (|mkRationalFunction| (|Fraction| (|Polynomial| #)))
--R
--R             2    2
--R   (1)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 18

)lisp (untrace)
 
Value = (|mkRationalFunction|)
 
)lisp (trace |hasSigAnd|)
 
Value = (|hasSigAnd|)

--S 19 of 31
rootSimp(normalize(z))
 
  1> (|hasSigAnd| ((|has| |#1| #) (|has| |#1| #)) ((|#1| . *3) ($ |Expression| *3)) ((*3 |Integer|) (*3 |Integer|) (*3 |Integer|) (*2 |Expression| *3) (*1 |AlgebraicManipulations| *3 *2)))
  <1 (|hasSigAnd| ((*3 |Integer|) (*3 |Integer|) (*3 |Integer|) (*2 |Expression| *3) (*1 |AlgebraicManipulations| *3 *2)))
  1> (|hasSigAnd| ((|has| |#1| #) (|has| |#1| #)) ((|#1| |Integer|) ($ |Expression| #)) NIL)
  <1 (|hasSigAnd| NIL)

   (2)  z
                                                     Type: Expression Integer
--R 
--R  1> (|hasSigAnd| ((|has| |#1| #) (|has| |#1| #)) ((|#1| . *3) ($ |Expression| *3)) ((*3 |Integer|) (*3 |Integer|) (*3 |Integer|) (*2 |Expression| *3) (*1 |AlgebraicManipulations| *3 *2)))
--R  <1 (|hasSigAnd| ((*3 |Integer|) (*3 |Integer|) (*3 |Integer|) (*2 |Expression| *3) (*1 |AlgebraicManipulations| *3 *2)))
--R  1> (|hasSigAnd| ((|has| |#1| #) (|has| |#1| #)) ((|#1| |Integer|) ($ |Expression| #)) NIL)
--R  <1 (|hasSigAnd| NIL)
--R
--R   (2)  z
--R                                                     Type: Expression Integer
--E 19

)lisp (untrace)
 
Value = (|hasSigAnd|)
 
)lisp (trace |findFunctionInCategory|)
 
Value = (|findFunctionInCategory|)

--S 20 of 31
a : UP('X,IntegerMod(4)) := 2 * X**2
 

          2
   (3)  2X
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R          2
--R   (3)  2X
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 20

--S 21 of 31
b : UP('X,IntegerMod(4)) := X**2 + 2*X + 1
 

         2
   (4)  X  + 2X + 1
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R         2
--R   (4)  X  + 2X + 1
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 21

--S 22 of 31
qr := monicDivide(a, b)
 

   (5)  [quotient= 2,remainder= 2]
Type: Record(quotient: UnivariatePolynomial(X,IntegerMod 4),remainder: UnivariatePolynomial(X,IntegerMod 4))
--R 
--R
--R   (5)  [quotient= 2,remainder= 2]
--RType: Record(quotient: UnivariatePolynomial(X,IntegerMod 4),remainder: UnivariatePolynomial(X,IntegerMod 4))
--E 22

--S 23 of 31
a - (qr.quotient * b + qr.remainder)
 
  1> (|findFunctionInCategory| |elt| (|Record| (|:| |quotient| #) (|:| |remainder| #)) NIL ((|Record| # #) (|Variable| |quotient|)) (NIL (|Symbol|)) NIL NIL)
  <1 (|findFunctionInCategory| ((# # #)))
  1> (|findFunctionInCategory| |elt| (|Record| (|:| |quotient| #) (|:| |remainder| #)) NIL ((|Record| # #) (|Variable| |remainder|)) (NIL (|Symbol|)) NIL NIL)
  <1 (|findFunctionInCategory| ((# # #)))

   (6)  0
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R  1> (|findFunctionInCategory| |elt| (|Record| (|:| |quotient| #) (|:| |remainder| #)) NIL ((|Record| # #) (|Variable| |quotient|)) (NIL (|Symbol|)) NIL NIL)
--R  <1 (|findFunctionInCategory| ((# # #)))
--R  1> (|findFunctionInCategory| |elt| (|Record| (|:| |quotient| #) (|:| |remainder| #)) NIL ((|Record| # #) (|Variable| |remainder|)) (NIL (|Symbol|)) NIL NIL)
--R  <1 (|findFunctionInCategory| ((# # #)))
--R
--R   (6)  0
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 23

)clear all
 
 
)lisp (untrace)
 
Value = (|findFunctionInCategory|)
 
)lisp (trace |findUniqueOpInDomain|)
 
Value = (|findUniqueOpInDomain|)

--S 24 of 31
bar?(n:INT):BOOLEAN == prime? n and is?(n, m**2 + 1)
 
   Function declaration bar? : Integer -> Boolean has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration bar? : Integer -> Boolean has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 24

--S 25 of 31
myprimes := [i for i in 1.. | bar? i]
 
  1> (|findUniqueOpInDomain| #<vector 09fc42f4> |incrementBy| (|IncrementingMaps| (|PositiveInteger|)))
  <1 (|findUniqueOpInDomain| ((|Mapping| # #)))
   Compiling function bar? with type Integer -> Boolean 

   (2)  [5,17,37,101,197,257,401,577,677,1297,...]
                                                 Type: Stream PositiveInteger
--R 
--I  1> (|findUniqueOpInDomain| #<vector 099f9150> |incrementBy| (|IncrementingMaps| (|PositiveInteger|)))
--R  <1 (|findUniqueOpInDomain| ((|Mapping| # #)))
--R   Compiling function bar? with type Integer -> Boolean 
--R
--R   (2)  [5,17,37,101,197,257,401,577,677,1297,...]
--R                                                 Type: Stream PositiveInteger
--E 25

)lisp (untrace)
 
Value = (|findUniqueOpInDomain|)
 
)lisp (trace |hasCatExpression|)
 
Value = (|hasCatExpression|)

--S 26 of 31
m5 : MATRIX POLY INT := new(4,4,1)
 

        +1  1  1  1+
        |          |
        |1  1  1  1|
   (3)  |          |
        |1  1  1  1|
        |          |
        +1  1  1  1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  1  1  1+
--R        |          |
--R        |1  1  1  1|
--R   (3)  |          |
--R        |1  1  1  1|
--R        |          |
--R        +1  1  1  1+
--R                                              Type: Matrix Polynomial Integer
--E 26

--S 27 of 31
vars : LIST POLY INT := [x,y,z,u]
 

   (4)  [x,y,z,u]
                                                Type: List Polynomial Integer
--R 
--R
--R   (4)  [x,y,z,u]
--R                                                Type: List Polynomial Integer
--E 27

--S 28 of 31
for i in 1..4 repeat for j in 1..3 repeat m5(i,j + 1) := (vars.i)**j
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 31
det := determinant(m5)
 
  1> (|hasCatExpression| (|has| (|Integer|) (|CommutativeRing|)) NIL)
  <1 (|hasCatExpression| NIL)

   (6)
                2     2    2        2    2   3
     ((- x + u)y  + (x  - u )y - u x  + u x)z
   + 
              3       3    3        3    3   2
     ((x - u)y  + (- x  + u )y + u x  - u x)z
   + 
          2    2  3     3    3  2    2 3    3 2         2    2   3
     ((- x  + u )y  + (x  - u )y  - u x  + u x )z + (u x  - u x)y
   + 
           3    3   2     2 3    3 2
     (- u x  + u x)y  + (u x  - u x )y
                                                     Type: Polynomial Integer
--R 
--R  1> (|hasCatExpression| (|has| (|Integer|) (|CommutativeRing|)) NIL)
--R  <1 (|hasCatExpression| NIL)
--R
--R   (6)
--R                2     2    2        2    2   3
--R     ((- x + u)y  + (x  - u )y - u x  + u x)z
--R   + 
--R              3       3    3        3    3   2
--R     ((x - u)y  + (- x  + u )y + u x  - u x)z
--R   + 
--R          2    2  3     3    3  2    2 3    3 2         2    2   3
--R     ((- x  + u )y  + (x  - u )y  - u x  + u x )z + (u x  - u x)y
--R   + 
--R           3    3   2     2 3    3 2
--R     (- u x  + u x)y  + (u x  - u x )y
--R                                                     Type: Polynomial Integer
--E 29

)lisp (untrace)
 
Value = (|hasCatExpression|)
 
)lisp (trace |hasSigOr|)
 
Value = (|hasSigOr|)

--S 30 of 31
t1:=laurent(cos(a+x)/x,x=0)
 

   (7)
            - 1            cos(a)     sin(a)  2   cos(a)  3   sin(a)  4
     cos(a)x    - sin(a) - ------ x + ------ x  + ------ x  - ------ x
                              2          6          24          120
   + 
       cos(a)  5   sin(a)  6   cos(a)  7   sin(a)  8    cos(a)  9      10
     - ------ x  + ------ x  + ------ x  - ------ x  - ------- x  + O(x  )
         720        5040        40320      362880      3628800
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R   (7)
--R            - 1            cos(a)     sin(a)  2   cos(a)  3   sin(a)  4
--R     cos(a)x    - sin(a) - ------ x + ------ x  + ------ x  - ------ x
--R                              2          6          24          120
--R   + 
--R       cos(a)  5   sin(a)  6   cos(a)  7   sin(a)  8    cos(a)  9      10
--R     - ------ x  + ------ x  + ------ x  - ------ x  - ------- x  + O(x  )
--R         720        5040        40320      362880      3628800
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 30

--S 31 of 31
approximate(t1,3)
 
  1> (|hasSigOr| ((|has| |#1| #) (|has| |#1| #)) ((|#1| |Integer|) ($ |Expression| #)) NIL)
  <1 (|hasSigOr| NIL)

           3                  4      2
        (4x  - 24x)sin(a) + (x  - 12x  + 24)cos(a)
   (8)  ------------------------------------------
                            24x
                                                     Type: Expression Integer
--R 
--R  1> (|hasSigOr| ((|has| |#1| #) (|has| |#1| #)) ((|#1| |Integer|) ($ |Expression| #)) NIL)
--R  <1 (|hasSigOr| NIL)
--R
--R           3                  4      2
--R        (4x  - 24x)sin(a) + (x  - 12x  + 24)cos(a)
--R   (8)  ------------------------------------------
--R                            24x
--R                                                     Type: Expression Integer
--E 31

 
)spool 
 
Starts dribbling to triglim.output (2010/3/27, 18:41:30).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 6
limit(atan(1/sin(x)),x = 0)
 

                          %pi                 %pi
   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (1)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 1

--S 2 of 6
limit(atan(sqrt(1 - x**2)/x),x = 0)
 

                          %pi                 %pi
   (2)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (2)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 2

--S 3 of 6
limit(atan(-sin(x)/(cos(x) + a)),x = acos(-a))
 

                          %pi                 %pi
   (3)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (3)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 3

--S 4 of 6
limit(atan(sin(x)/(cos(x) + a)),x = acos(-a))
 

                        %pi                   %pi
   (4)  [leftHandLimit= ---,rightHandLimit= - ---]
                         2                     2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                        %pi                   %pi
--R   (4)  [leftHandLimit= ---,rightHandLimit= - ---]
--R                         2                     2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 4

--S 5 of 6
limit(atan(1/(cos(x) + a)),x = acos(-a))
 

                        %pi                   %pi
   (5)  [leftHandLimit= ---,rightHandLimit= - ---]
                         2                     2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                        %pi                   %pi
--R   (5)  [leftHandLimit= ---,rightHandLimit= - ---]
--R                         2                     2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 5

--S 6 of 6
limit(atan(1/(sin(x) + a)),x = asin(-a))
 

                          %pi                 %pi
   (6)  [leftHandLimit= - ---,rightHandLimit= ---]
                           2                   2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                          %pi                 %pi
--R   (6)  [leftHandLimit= - ---,rightHandLimit= ---]
--R                           2                   2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 6
)spool 
 
Starts dribbling to lodo3.output (2010/3/27, 18:28:46).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
Dx: LODO(EXPR INT, f +-> D(f, x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 16
Dx := D()
 

   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1679 envArg,SPADCALL(G1679,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R   (2)  D
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1405 envArg,SPADCALL(G1405,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 2

--S 3 of 16
Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1
 

                       3
         3    G     - x  + H
   (3)  D  + -- D + --------
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1679 envArg,SPADCALL(G1679,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R                       3
--R         3    G     - x  + H
--R   (3)  D  + -- D + --------
--R              2         3
--R             x         x
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1405 envArg,SPADCALL(G1405,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 3

--S 4 of 16
n == 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 16
phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 16
phi1 ==  Dop(phi) / exp x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 16
phi2 == phi1 *x**(n+3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 16
phi3 == retract(phi2)@(POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 16
pans == phi3 ::UP(x,POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 16
pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 16
leq == solve(pans1,[subscript(s,[i]) for i in 1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling function G1805 with type Integer -> Boolean 

   (12)
                           2                                3        2
         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
          0        0     0       0         0       0      0        0        0
   [[s = ---,s = ------------------,s = --------------------------------------]]
      1   3   2          18          3                    162
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--I   Compiling function G3350 with type Integer -> Boolean 
--R
--R   (12)
--R                           2                                3        2
--R         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
--R          0        0     0       0         0       0      0        0        0
--R   [[s = ---,s = ------------------,s = --------------------------------------]]
--R      1   3   2          18          3                    162
--R                         Type: List List Equation Fraction Polynomial Integer
--E 12

--S 13 of 16
n==4
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 13

--S 14 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (14)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 14

--S 15 of 16
n==7
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 15

--S 16 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ,

       s  =
        5
                               2         3          2
             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
                  0         0          0          0           0          0
           + 
                5        4          3          2
             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
              0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                   4          3           2                                6
             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
                 0          0           0            0            0      0
           + 
                  5          4           3           2
             90s G  + 2628s G  + 27864s G  + 90720s G
                0          0           0           0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                    3           2                            2
             (945s G  + 81648s G  + 2082996s G + 14171760s )H
                  0           0             0             0
           + 
                   5          4            3             2
             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
                 0          0            0             0              0
           + 
                7         6          5           4             3              2
             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
              0         0          0           0             0              0
           + 
             - 97977600s G
                        0
        /
           11022480
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (16)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ,
--R
--R       s  =
--R        5
--R                               2         3          2
--R             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
--R                  0         0          0          0           0          0
--R           + 
--R                5        4          3          2
--R             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
--R              0        0          0          0           0
--R        /
--R           29160
--R       ,
--R
--R       s  =
--R        6
--R                   3          2                        2
--R             405s H  + (405s G  + 18468s G + 174960s )H
--R                 0          0           0           0
--R           + 
--R                   4          3           2                                6
--R             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
--R                 0          0           0            0            0      0
--R           + 
--R                  5          4           3           2
--R             90s G  + 2628s G  + 27864s G  + 90720s G
--R                0          0           0           0
--R        /
--R           524880
--R       ,
--R
--R       s  =
--R        7
--R                                 3
--R             (2835s G + 91854s )H
--R                   0          0
--R           + 
--R                    3           2                            2
--R             (945s G  + 81648s G  + 2082996s G + 14171760s )H
--R                  0           0             0             0
--R           + 
--R                   5          4            3             2
--R             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
--R                 0          0            0             0              0
--R           + 
--R                7         6          5           4             3              2
--R             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
--R              0         0          0           0             0              0
--R           + 
--R             - 97977600s G
--R                        0
--R        /
--R           11022480
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 16
)spool 
 
Starts dribbling to array1.output (2010/3/27, 18:23:7).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 9
oneDimensionalArray [i**2 for i in 1..10]
 

   (1)  [1,4,9,16,25,36,49,64,81,100]
                                    Type: OneDimensionalArray PositiveInteger
--R 
--R
--R   (1)  [1,4,9,16,25,36,49,64,81,100]
--R                                    Type: OneDimensionalArray PositiveInteger
--E 1

--S 2 of 9
a : ARRAY1 INT := new(10,0)
 

   (2)  [0,0,0,0,0,0,0,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0,0,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 2

--S 3 of 9
for i in 1..10 repeat a.i := i; a
 

   (3)  [1,2,3,4,5,6,7,8,9,10]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10]
--R                                            Type: OneDimensionalArray Integer
--E 3

--S 4 of 9
map!(i +-> i ** 2,a); a
 

   (4)  [1,4,9,16,25,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (4)  [1,4,9,16,25,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 4

--S 5 of 9
reverse! a
 

   (5)  [100,81,64,49,36,25,16,9,4,1]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (5)  [100,81,64,49,36,25,16,9,4,1]
--R                                            Type: OneDimensionalArray Integer
--E 5

--S 6 of 9
swap!(a,4,5); a
 

   (6)  [100,81,64,36,49,25,16,9,4,1]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (6)  [100,81,64,36,49,25,16,9,4,1]
--R                                            Type: OneDimensionalArray Integer
--E 6

--S 7 of 9
sort! a
 

   (7)  [1,4,9,16,25,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (7)  [1,4,9,16,25,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 7

--S 8 of 9
b := a(6..10)
 

   (8)  [36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (8)  [36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 8

--S 9 of 9
copyInto!(a,b,1)
 

   (9)  [36,49,64,81,100,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (9)  [36,49,64,81,100,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 9
)spool
 
Starts dribbling to Permanent.output (2010/3/27, 18:46:14).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
kn n ==
  r : MATRIX INT := new(n,n,1)
  for i in 1..n repeat
    r.i.i := 0
  r
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 3
permanent(kn(5) :: SQMATRIX(5,INT))
 
   Compiling function kn with type PositiveInteger -> Matrix Integer 

   (2)  44
                                                        Type: PositiveInteger
--R 
--R   Compiling function kn with type PositiveInteger -> Matrix Integer 
--R
--R   (2)  44
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 3
[permanent(kn(n) :: SQMATRIX(n,INT)) for n in 1..13]
 
   Cannot compile conversion for types involving local variables. In 
      particular, could not compile the expression involving :: 
      SQMATRIX(n,INT) 
   AXIOM will attempt to step through and interpret the code.

   (3)
   [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932]
                                                Type: List NonNegativeInteger
--R 
--R   Cannot compile conversion for types involving local variables. In 
--R      particular, could not compile the expression involving :: 
--R      SQMATRIX(n,INT) 
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (3)
--R   [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932]
--R                                                Type: List NonNegativeInteger
--E 3
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read ffrac
 
--Copyright The Numerical Algorithms Group Limited 1994.

)lib ffrac
 
   )library cannot find the file ffrac.

f1 : FormalFraction Integer
 
 
Daly Bug
   Category, domain or package constructor FormalFraction is not 
      available.
f1 := 6/3
 

   (1)  2
                                                       Type: Fraction Integer

--       6
--       -
--       3

f2 := (3.6/2.4)$FormalFraction Float
 
 
Daly Bug
   Category, domain or package constructor FormalFraction is not 
      available.

--       3.6
--       ---
--       2.4

numer f1
 

   (2)  2
                                                        Type: PositiveInteger

--       6

denom f2
 

   (3)  1
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)

--       2.4

f1 :: FRAC INT
 

   (4)  2
                                                       Type: Fraction Integer

--       2

% :: FormalFraction Integer      
 
 
Daly Bug
   Category, domain or package constructor FormalFraction is not 
      available.

--       2
--       -
--       1

f2 :: Float
 
 
Daly Bug
   Cannot convert from type Variable f2 to Float for value
   f2


--       1.5

output "End of tests"
 
   End of tests
                                                                   Type: Void
)lisp (bye)
 
Starts dribbling to mpoly.output (2010/3/27, 18:30:0).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
m : MPOLY([x,y],INT) := (x**2 - x*y**3 +3*y)**2
 

         4     3 3     6       2     4      2
   (1)  x  - 2y x  + (y  + 6y)x  - 6y x + 9y
                                  Type: MultivariatePolynomial([x,y],Integer)
--R 
--R
--R         4     3 3     6       2     4      2
--R   (1)  x  - 2y x  + (y  + 6y)x  - 6y x + 9y
--R                                  Type: MultivariatePolynomial([x,y],Integer)
--E 1

--S 2 of 10
m :: MPOLY([y,x],INT)
 

         2 6       4     3 3     2     2     4
   (2)  x y  - 6x y  - 2x y  + 9y  + 6x y + x
                                  Type: MultivariatePolynomial([y,x],Integer)
--R 
--R
--R         2 6       4     3 3     2     2     4
--R   (2)  x y  - 6x y  - 2x y  + 9y  + 6x y + x
--R                                  Type: MultivariatePolynomial([y,x],Integer)
--E 2

--S 3 of 10
p : MPOLY([x,y],POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 10
p := (a**2*x - b*y**2 + 1)**2
 

         4 2        2   2     2      2 4       2
   (4)  a x  + (- 2a b y  + 2a )x + b y  - 2b y  + 1
                       Type: MultivariatePolynomial([x,y],Polynomial Integer)
--R 
--R
--R         4 2        2   2     2      2 4       2
--R   (4)  a x  + (- 2a b y  + 2a )x + b y  - 2b y  + 1
--R                       Type: MultivariatePolynomial([x,y],Polynomial Integer)
--E 4

--S 5 of 10
p :: POLY INT
 

         2 4        2          2    4 2     2
   (5)  b y  + (- 2a b x - 2b)y  + a x  + 2a x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2 4        2          2    4 2     2
--R   (5)  b y  + (- 2a b x - 2b)y  + a x  + 2a x + 1
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 10
% :: MPOLY([a,b],POLY INT)
 

         2 4          2        2    4 2     2
   (6)  x a  + (- 2x y b + 2x)a  + y b  - 2y b + 1
                       Type: MultivariatePolynomial([a,b],Polynomial Integer)
--R 
--R
--R         2 4          2        2    4 2     2
--R   (6)  x a  + (- 2x y b + 2x)a  + y b  - 2y b + 1
--R                       Type: MultivariatePolynomial([a,b],Polynomial Integer)
--E 6

--S 7 of 10
q : UP(x, FRAC MPOLY([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 10
q := (x**2 - x*(z+1)/y +2)**2
 

                             2    2
         4   - 2z - 2  3   4y  + z  + 2z + 1  2   - 4z - 4
   (8)  x  + -------- x  + ----------------- x  + -------- x + 4
                 y                  2                 y
                                   y
 Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer))
--R 
--R
--R                             2    2
--R         4   - 2z - 2  3   4y  + z  + 2z + 1  2   - 4z - 4
--R   (8)  x  + -------- x  + ----------------- x  + -------- x + 4
--R                 y                  2                 y
--R                                   y
--R Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer))
--E 8

--S 9 of 10
q :: UP(z, FRAC MPOLY([x,y],INT))
 

   (9)
    2            3     2             2 4       3      2      2            2
   x   2   - 2y x  + 2x  - 4y x     y x  - 2y x  + (4y  + 1)x  - 4y x + 4y
   -- z  + -------------------- z + ---------------------------------------
    2                2                                  2
   y                y                                  y
 Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer))
--R 
--R
--R   (9)
--R    2            3     2             2 4       3      2      2            2
--R   x   2   - 2y x  + 2x  - 4y x     y x  - 2y x  + (4y  + 1)x  - 4y x + 4y
--R   -- z  + -------------------- z + ---------------------------------------
--R    2                2                                  2
--R   y                y                                  y
--R Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer))
--E 9

--S 10 of 10
q :: MPOLY([x,z], FRAC UP(y,INT))
 

                                                2
          4      2     2  3     1  2    2     4y  + 1  2      4     4
   (10)  x  + (- - z - -)x  + (-- z  + -- z + -------)x  + (- - z - -)x + 4
                 y     y        2       2         2           y     y
                               y       y         y
 Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer))
--R 
--R
--R                                                2
--R          4      2     2  3     1  2    2     4y  + 1  2      4     4
--R   (10)  x  + (- - z - -)x  + (-- z  + -- z + -------)x  + (- - z - -)x + 4
--R                 y     y        2       2         2           y     y
--R                               y       y         y
--R Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer))
--E 10
)spool 
 
Starts dribbling to summation.output (2010/3/27, 18:41:9).
)set message test on
 
)set output mathml on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
summation(i^2,i=a..b)^(d-c)
 

         b      d - c
        --+    2
   (1)  >     i
        --+
        i= a
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>)</mo></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         b      d - c
--R        --+    2
--R   (1)  >     i
--R        --+
--R        i= a
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow><mo>)</mo></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 1
--S 2 of 5
summation(i^2^(d-c),i=a..b)
 

         b      d - c
        --+    2
   (2)  >     i
        --+
        i= a
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow></mrow></msup></mrow></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         b      d - c
--R        --+    2
--R   (2)  >     i
--R        --+
--R        i= a
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mi>a</mi></mrow></mrow></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msup><mrow><mi>i</mi></mrow><mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mrow></msup></mrow></mrow></msup></mrow></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 2
--S 3 of 5
sum(operator(f) (i)+1,i=1..n)
 

         n
        --+
   (3)  >     f(i) + 1
        --+
        i= 1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         n
--R        --+
--R   (3)  >     f(i) + 1
--R        --+
--R        i= 1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 3
--S 4 of 5
sum(operator(f) (i),i=1..n)+1
 

         n
        --+
   (4)  >     f(i) + 1
        --+
        i= 1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo><mo>+</mo><mn>1</mn></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         n
--R        --+
--R   (4)  >     f(i) + 1
--R        --+
--R        i= 1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo><mo>+</mo><mn>1</mn></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 4
--S 5 of 5
sum(operator(f) (i)+1,i=1..n)^3
 

         n            3
        --+
   (5)  >     f(i) + 1
        --+
        i= 1
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow>
</math>

                                                     Type: Expression Integer
--R
--R         n            3
--R        --+
--R   (5)  >     f(i) + 1
--R        --+
--R        i= 1
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>&#x02211;</mo><mrow><mrow><mrow><mi>i</mi></mrow><mo>=</mo><mrow><mn>1</mn></mrow></mrow></mrow><mrow><mi>n</mi></mrow></munderover><mo>(</mo><mrow><mrow><mo><mi>f</mi></mo><mo>(</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow>
--R</math>
--R
--R                                                     Type: Expression Integer
--E 5
)spool 
 
Starts dribbling to MathMLFormat.output (2010/3/27, 18:46:2).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 5
)set output mathml on
 
 
--R 
--E 1 
 
--S 2 of 5
1/2
 

        1
   (1)  -
        2
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow>
</math>

                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (1)  -
--R        2
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow>
--R</math>
--R
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 5
1/(x+5)
 

          1
   (2)  -----
        x + 5
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mrow></mfrac></mrow>
</math>

                                            Type: Fraction Polynomial Integer
--R 
--R
--R          1
--R   (2)  -----
--R        x + 5
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mrow></mfrac></mrow>
--R</math>
--R
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 5
(x+3)/(y-5)
 

        x + 3
   (3)  -----
        y - 5
<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
<mrow><mfrac><mrow><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mrow><mrow><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mrow></mfrac></mrow>
</math>

                                            Type: Fraction Polynomial Integer
--R 
--R
--R        x + 3
--R   (3)  -----
--R        y - 5
--R<math xmlns="http://www.w3.org/1998/Math/MathML" mathsize="big" display="block">
--R<mrow><mfrac><mrow><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mrow><mrow><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mrow></mfrac></mrow>
--R</math>
--R
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 5
)show MathMLFormat
 
 MathMLFormat  is a domain constructor
 Abbreviation for MathMLFormat is MMLFORM 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for MMLFORM 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                coerce : OutputForm -> String
 coerce : % -> OutputForm              coerceL : OutputForm -> String
 coerceS : OutputForm -> String        display : String -> Void
 exprex : OutputForm -> String         hash : % -> SingleInteger
 latex : % -> String                   ?~=? : (%,%) -> Boolean

--R MathMLFormat  is a domain constructor
--R Abbreviation for MathMLFormat is MMLFORM 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for MMLFORM 
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean                coerce : OutputForm -> String
--R coerce : % -> OutputForm              coerceL : OutputForm -> String
--R coerceS : OutputForm -> String        display : String -> Void
--R exprex : OutputForm -> String         hash : % -> SingleInteger
--R latex : % -> String                   ?~=? : (%,%) -> Boolean
--R
--E 5

)spool 
 
Starts dribbling to intdeq.output (2010/3/27, 18:26:59).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 7
deq := differentiate(y x, x, 2) + 2*w[0]*differentiate(y x, x) + w[0]**2*y x
 

         ,,          ,        2
   (2)  y  (x) + 2w y (x) + w  y(x)
                   0         0
                                                     Type: Expression Integer
--R 
--R
--R         ,,          ,        2
--R   (2)  y  (x) + 2w y (x) + w  y(x)
--R                   0         0
--R                                                     Type: Expression Integer
--E 2

--S 3 of 7
sol:= solve(deq = sin (w*x), y, x=0,[0,0])
 

                                                      - w x
            2     2               3     2                0
        (- w  + w  )sin(w x) + ((w  + w  w)x + 2w w)%e      - 2w w cos(w x)
                 0                     0         0              0
   (3)  -------------------------------------------------------------------
                                  4      2 2     4
                                 w  + 2w  w  + w
                                        0       0
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                      - w x
--R            2     2               3     2                0
--R        (- w  + w  )sin(w x) + ((w  + w  w)x + 2w w)%e      - 2w w cos(w x)
--R                 0                     0         0              0
--R   (3)  -------------------------------------------------------------------
--R                                  4      2 2     4
--R                                 w  + 2w  w  + w
--R                                        0       0
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 7
work:= sol *sin(w*x)
 

   (4)
           2     2         2
       (- w  + w  )sin(w x)
                0
     + 
                               - w x
           3     2                0
       (((w  + w  w)x + 2w w)%e      - 2w w cos(w x))sin(w x)
                0         0              0
  /
      4      2 2     4
     w  + 2w  w  + w
            0       0
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R           2     2         2
--R       (- w  + w  )sin(w x)
--R                0
--R     + 
--R                               - w x
--R           3     2                0
--R       (((w  + w  w)x + 2w w)%e      - 2w w cos(w x))sin(w x)
--R                0         0              0
--R  /
--R      4      2 2     4
--R     w  + 2w  w  + w
--R            0       0
--R                                                     Type: Expression Integer
--E 4

--S 5 of 7
integrate(work,x)
 

   (5)
                                                - w x
                  4      3 2       4      2 2      0      4     4
         (((- 2w w  - 2w  w )x + 2w  - 6w  w )%e      + (w  - w  )cos(w x))
                0       0                0                     0
      *
         sin(w x)
     + 
                                            - w x
             5      2 3         3              0         3      3          2
       ((- 2w  - 2w  w )x - 8w w )cos(w x)%e      + (2w w  + 2w  w)cos(w x)
                   0          0                        0       0
     + 
           5     4
       (- w  + w  w)x
                0
  /
       7      2 5      4 3      6
     2w  + 6w  w  + 6w  w  + 2w  w
             0        0        0
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)
--R                                                - w x
--R                  4      3 2       4      2 2      0      4     4
--R         (((- 2w w  - 2w  w )x + 2w  - 6w  w )%e      + (w  - w  )cos(w x))
--R                0       0                0                     0
--R      *
--R         sin(w x)
--R     + 
--R                                            - w x
--R             5      2 3         3              0         3      3          2
--R       ((- 2w  - 2w  w )x - 8w w )cos(w x)%e      + (2w w  + 2w  w)cos(w x)
--R                   0          0                        0       0
--R     + 
--R           5     4
--R       (- w  + w  w)x
--R                0
--R  /
--R       7      2 5      4 3      6
--R     2w  + 6w  w  + 6w  w  + 2w  w
--R             0        0        0
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 7
D(%,x)-work
 

          2     2         2     2     2         2    2     2
        (w  - w  )sin(w x)  + (w  - w  )cos(w x)  - w  + w
               0                     0                    0
   (6)  ----------------------------------------------------
                           4      2 2      4
                         2w  + 4w  w  + 2w
                                 0        0
                                                     Type: Expression Integer
--R 
--R
--R          2     2         2     2     2         2    2     2
--R        (w  - w  )sin(w x)  + (w  - w  )cos(w x)  - w  + w
--R               0                     0                    0
--R   (6)  ----------------------------------------------------
--R                           4      2 2      4
--R                         2w  + 4w  w  + 2w
--R                                 0        0
--R                                                     Type: Expression Integer
--E 6

--S 7 of 7
simplify %
 

   (7)  0
                                                     Type: Expression Integer
--R 
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E 7
)spool 
 
Starts dribbling to Any.output (2010/3/27, 18:41:42).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 18
a:Any := [1,2]
 

   (1)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 18
b:Any := [1,2]
 

   (2)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1,2]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 18
(a = b)@Boolean
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 18
c := [1,2]
 

   (4)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [1,2]
--R                                                   Type: List PositiveInteger
--E 4

--S 5 of 18
typeOf a
 

   (5)  Any
                                                                 Type: Domain
--R 
--R
--R   (5)  Any
--R                                                                 Type: Domain
--E 5

--S 6 of 18
typeOf c
 

   (6)  List PositiveInteger
                                                                 Type: Domain
--R 
--R
--R   (6)  List PositiveInteger
--R                                                                 Type: Domain
--E 6

--S 7 of 18
(a = c)@Boolean
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 18
b := [1,3]
 

   (8)  [1,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (8)  [1,3]
--R                                                   Type: List PositiveInteger
--E 8

--S 9 of 18
(a = b)@Boolean
 

   (9)  false
                                                                Type: Boolean
--R 
--R
--R   (9)  false
--R                                                                Type: Boolean
--E 9

--S 10 of 18
a := "A"
 

   (10)  "A"
                                                                 Type: String
--R 
--R
--R   (10)  "A"
--R                                                                 Type: String
--E 10

--S 11 of 18
(a = b)@Boolean
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 18
b := "A"
 

   (12)  "A"
                                                                 Type: String
--R 
--R
--R   (12)  "A"
--R                                                                 Type: String
--E 12

--S 13 of 18
(a = b)@Boolean
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 18
Sae := SAE(FRAC INT, UP(x, FRAC INT), x^2-3)
 

   (14)
  SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Int
  eger),x*x-3)
                                                                 Type: Domain
--R 
--R
--R   (14)
--R  SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Int
--R  eger),x*x-3)
--R                                                                 Type: Domain
--E 14

--S 15 of 18
a := generator()$Sae
 

   (15)  x
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),x*x-3)
--R 
--R
--R   (15)  x
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),x*x-3)
--E 15

--S 16 of 18
b := generator()$Sae
 

   (16)  x
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),x*x-3)
--R 
--R
--R   (16)  x
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),x*x-3)
--E 16

--S 17 of 18
(a = b)@Boolean
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 18
)show Any
 
 Any  is a domain constructor
 Abbreviation for Any is ANY 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for ANY 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                any : (SExpression,None) -> %
 coerce : % -> OutputForm              dom : % -> SExpression
 domainOf : % -> OutputForm            hash : % -> SingleInteger
 latex : % -> String                   obj : % -> None
 objectOf : % -> OutputForm            ?~=? : (%,%) -> Boolean
 showTypeInOutput : Boolean -> String

--R 
--R Any  is a domain constructor
--R Abbreviation for Any is ANY 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for ANY 
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean                any : (SExpression,None) -> %
--R coerce : % -> OutputForm              dom : % -> SExpression
--R domainOf : % -> OutputForm            hash : % -> SingleInteger
--R latex : % -> String                   obj : % -> None
--R objectOf : % -> OutputForm            ?~=? : (%,%) -> Boolean
--R showTypeInOutput : Boolean -> String
--R
--E 18

)spool
 
Starts dribbling to poly1.output (2010/3/27, 18:30:49).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 46
x + 1
 

   (1)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  x + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 46
z - 2.3
 

   (2)  z - 2.3
                                                       Type: Polynomial Float
--R 
--R
--R   (2)  z - 2.3
--R                                                       Type: Polynomial Float
--E 2

--S 3 of 46
y**2 - z + 3/4
 

               2   3
   (3)  - z + y  + -
                   4
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2   3
--R   (3)  - z + y  + -
--R                   4
--R                                            Type: Polynomial Fraction Integer
--E 3

--S 4 of 46
y **2 + x*y + y
 

         2
   (4)  y  + (x + 1)y
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (4)  y  + (x + 1)y
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 46
% :: DMP([y,x],INT)
 

         2
   (5)  y  + y x + y
                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--R 
--R
--R         2
--R   (5)  y  + y x + y
--R                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--E 5

--S 6 of 46
p := (y-1)**2 * x * z
 

            2
   (6)  (x y  - 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (6)  (x y  - 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 46
q := (y-1) * x * (z+5)
 

   (7)  (x y - x)z + 5x y - 5x
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  (x y - x)z + 5x y - 5x
--R                                                     Type: Polynomial Integer
--E 7

--S 8 of 46
factor(q)
 

   (8)  x(y - 1)(z + 5)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (8)  x(y - 1)(z + 5)
--R                                            Type: Factored Polynomial Integer
--E 8

--S 9 of 46
p - q**2
 

   (9)
         2 2     2     2  2          2      2       2             2
     (- x y  + 2x y - x )z  + ((- 10x  + x)y  + (20x  - 2x)y - 10x  + x)z
   + 
          2 2      2       2
     - 25x y  + 50x y - 25x
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)
--R         2 2     2     2  2          2      2       2             2
--R     (- x y  + 2x y - x )z  + ((- 10x  + x)y  + (20x  - 2x)y - 10x  + x)z
--R   + 
--R          2 2      2       2
--R     - 25x y  + 50x y - 25x
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 46
gcd(p,q)
 

   (10)  x y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)  x y - x
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 46
factor %
 

   (11)  x(y - 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (11)  x(y - 1)
--R                                            Type: Factored Polynomial Integer
--E 11

--S 12 of 46
lcm(p,q)
 

             2             2        2
   (12)  (x y  - 2x y + x)z  + (5x y  - 10x y + 5x)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2             2        2
--R   (12)  (x y  - 2x y + x)z  + (5x y  - 10x y + 5x)z
--R                                                     Type: Polynomial Integer
--E 12

--S 13 of 46
content p
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 46
resultant(p,q,z)
 

           2 3      2 2      2      2
   (14)  5x y  - 15x y  + 15x y - 5x
                                                     Type: Polynomial Integer
--R 
--R
--R           2 3      2 2      2      2
--R   (14)  5x y  - 15x y  + 15x y - 5x
--R                                                     Type: Polynomial Integer
--E 14

--S 15 of 46
resultant(p,q,x)
 

   (15)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  0
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 46
mainVariable p
 

   (16)  z
                                                      Type: Union(Symbol,...)
--R 
--R
--R   (16)  z
--R                                                      Type: Union(Symbol,...)
--E 16

--S 17 of 46
mainVariable(1 :: POLY INT)
 

   (17)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (17)  "failed"
--R                                                    Type: Union("failed",...)
--E 17

--S 18 of 46
ground? p
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 46
ground?(1 :: POLY INT)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19

--S 20 of 46
variables p
 

   (20)  [z,y,x]
                                                            Type: List Symbol
--R 
--R
--R   (20)  [z,y,x]
--R                                                            Type: List Symbol
--E 20

--S 21 of 46
degree(p,x)
 

   (21)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  1
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 46
degree(p,y)
 

   (22)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  2
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 46
degree(p,z)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 46
degree(p,[x,y,z])
 

   (24)  [1,2,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (24)  [1,2,1]
--R                                                Type: List NonNegativeInteger
--E 24

--S 25 of 46
minimumDegree(p,z)
 

   (25)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  1
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 46
totalDegree p
 

   (26)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  4
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 46
leadingMonomial p
 

            2
   (27)  x y z
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (27)  x y z
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 46
reductum p
 

   (28)  (- 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R   (28)  (- 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 28

--S 29 of 46
p - leadingMonomial p - reductum p
 

   (29)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (29)  0
--R                                                     Type: Polynomial Integer
--E 29

--S 30 of 46
leadingCoefficient p
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 46
p
 

             2
   (31)  (x y  - 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (31)  (x y  - 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 46
eval(p,x,w)
 

             2
   (32)  (w y  - 2w y + w)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (32)  (w y  - 2w y + w)z
--R                                                     Type: Polynomial Integer
--E 32

--S 33 of 46
eval(p,x,1)
 

           2
   (33)  (y  - 2y + 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (33)  (y  - 2y + 1)z
--R                                                     Type: Polynomial Integer
--E 33

--S 34 of 46
eval(p,x,y**2 - 1)
 

           4     3
   (34)  (y  - 2y  + 2y - 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           4     3
--R   (34)  (y  - 2y  + 2y - 1)z
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 46
D(p,x)
 

           2
   (35)  (y  - 2y + 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (35)  (y  - 2y + 1)z
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 46
D(p,y)
 

   (36)  (2x y - 2x)z
                                                     Type: Polynomial Integer
--R 
--R
--R   (36)  (2x y - 2x)z
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 46
D(p,z)
 

            2
   (37)  x y  - 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (37)  x y  - 2x y + x
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 46
integrate(p,y)
 

          1    3      2
   (38)  (- x y  - x y  + x y)z
          3
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1    3      2
--R   (38)  (- x y  - x y  + x y)z
--R          3
--R                                            Type: Polynomial Fraction Integer
--E 38

--S 39 of 46
qr := monicDivide(p,x+1,x)
 

                      2                           2
   (39)  [quotient= (y  - 2y + 1)z,remainder= (- y  + 2y - 1)z]
     Type: Record(quotient: Polynomial Integer,remainder: Polynomial Integer)
--R 
--R
--R                      2                           2
--R   (39)  [quotient= (y  - 2y + 1)z,remainder= (- y  + 2y - 1)z]
--R     Type: Record(quotient: Polynomial Integer,remainder: Polynomial Integer)
--E 39

--S 40 of 46
qr.remainder
 

             2
   (40)  (- y  + 2y - 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (40)  (- y  + 2y - 1)z
--R                                                     Type: Polynomial Integer
--E 40

--S 41 of 46
p - ((x+1) * qr.quotient + qr.remainder)
 

   (41)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (41)  0
--R                                                     Type: Polynomial Integer
--E 41

--S 42 of 46
p/q
 

         (y - 1)z
   (42)  --------
           z + 5
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         (y - 1)z
--R   (42)  --------
--R           z + 5
--R                                            Type: Fraction Polynomial Integer
--E 42

--S 43 of 46
(2/3) * x**2 - y + 4/5
 

               2  2   4
   (43)  - y + - x  + -
               3      5
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2  2   4
--R   (43)  - y + - x  + -
--R               3      5
--R                                            Type: Polynomial Fraction Integer
--E 43

--S 44 of 46
% :: FRAC POLY INT
 

                    2
         - 15y + 10x  + 12
   (44)  -----------------
                 15
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                    2
--R         - 15y + 10x  + 12
--R   (44)  -----------------
--R                 15
--R                                            Type: Fraction Polynomial Integer
--E 44

--S 45 of 46
% :: POLY FRAC INT
 

               2  2   4
   (45)  - y + - x  + -
               3      5
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2  2   4
--R   (45)  - y + - x  + -
--R               3      5
--R                                            Type: Polynomial Fraction Integer
--E 45

--S 46 of 46
map(numeric,%)
 

                                            2
   (46)  - 1.0 y + 0.6666666666 6666666667 x  + 0.8
                                                       Type: Polynomial Float
--R 
--R
--R                                            2
--R   (46)  - 1.0 y + 0.6666666666 6666666667 x  + 0.8
--R                                                       Type: Polynomial Float
--E 46
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read tsetcatchemical
 
-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [x4,x3,x2,x1,t];
 

                                                            Type: List Symbol
V := OVAR(ls);
 

                                                                 Type: Domain
R := Integer;
 

                                                                 Type: Domain
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x4,x3,x2,x1,t]
                                                                 Type: Domain
P := NSMP(R, V);
 

                                                                 Type: Domain
LP := List(P);
 

                                                                 Type: Domain

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x1: P := 'x1;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
x2: P := 'x2;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
x3: P := 'x3;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
x4: P := 'x4;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
t: P := 't;
 
  Line  21: t: P := 't;
  Error   : The character #\Tab is not an AXIOM character.
   1 error(s) parsing 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
	
 
  Line  22: 	
           A
  Error  A: Improper syntax.
   1 error(s) parsing 

p1 := 2 - 7 * x1 + x1 ** 2 * x2 + t * (x3 - x1) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
p2 := 6 * x1 - x1 ** 2 * x2 + 10 * t * (x4 - x2) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
p3 := 2 - 7 * x3 + x3 ** 2 * x4 + t * (x1 - x3) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])
p4 := 6 * x3 - x3 **2 * x4  + 1 - t * (x2 - x4) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])

lp := [p1,p2,p3,p4];
 

Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])


-----------------------------------------------------------------------------
--% Computations
-----------------------------------------------------------------------------

T := WUTSET(R,E,V,P)
 

   (17)
  WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2
  ,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(In
  teger,OrderedVariableList [x4,x3,x2,x1,t]))
                                                                 Type: Domain

medialSet(lp)$T
 

   (18)
   {
            11       10      9    8   9          11       10       9      8   8
       (242t   + 165t   + 24t  + t )x1  + (- 605t   + 880t   + 679t  + 54t )x1
     + 
             12        11        10       9       8   7
       (2178t   - 5445t   - 9794t   - 574t  + 672t )x1
     + 
               12         11        10         9        8   6
       (- 6776t   + 26840t   + 8126t   - 17620t  - 1568t )x1
     + 
                11         10         9   5            10         9   4
       (- 30800t   + 52304t   + 53760t )x1  + (- 39200t   - 15680t )x1
     ,
        3      2   2           3      2         3      2
    (11t  + 10t )x1 x2 + (- 86t  - 70t )x1 + 50t  + 20t ,
             2                                    2
    t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])),...)

characteristicSet(lp)$T
 

   (19)
   {
            11       10      9    8   9          11       10       9      8   8
       (242t   + 165t   + 24t  + t )x1  + (- 605t   + 880t   + 679t  + 54t )x1
     + 
             12        11        10       9       8   7
       (2178t   - 5445t   - 9794t   - 574t  + 672t )x1
     + 
               12         11        10         9        8   6
       (- 6776t   + 26840t   + 8126t   - 17620t  - 1568t )x1
     + 
                11         10         9   5            10         9   4
       (- 30800t   + 52304t   + 53760t )x1  + (- 39200t   - 15680t )x1
     ,
        3      2   2           3      2         3      2
    (11t  + 10t )x1 x2 + (- 86t  - 70t )x1 + 50t  + 20t ,
             2                                    2
    t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t])),...)

characteristicSerie(lp)$T
 

   (20)
   [
                             3        2
     {11t + 10, 900x1 + 6655t  + 2662t ,

                      3
         38971649024x2
       + 
                                            5               4
             (- 1414695942t - 14146959420)x1  + 2829391884x1
           + 
                            2                  3                  2
             (- 14146959420t  - 99028715940t)x1  + 28293918840t x1
        *
             2
           x2
       + 
                        2                                4
             (707347971t  + 18391047246t + 94077280143)x1
           + 
                                            3
             (- 2829391884t - 36782094492)x1
           + 
                         3               2                                 2
             (7073479710t  + 99028715940t  + 352446356790t + 43750348884)x1
           + 
                            2
             (- 28293918840t  - 198057431880t)x1 + 28293918840t
        *
           x2
       + 
                       2                                 3
         (- 4244087826t  - 59417229564t - 207960303474)x1
       + 
                                        2
         (16976351304t + 118834459128)x1
       + 
                       2
         (- 5845851000t  - 87156324000t - 303423050304)x1 + 11691702000t
       + 
         71213094000
       ,
                 2                                     2
      10x3 - 11x1 x2 + (11t + 77)x1 - 22, 100x4 + (11x1  + 110t)x2 - 66x1}
     ,

         3      2
     {55t  + 72t  + 20t, (11t + 10)x1,

                          2
         (465452061949952t  + 423138238136320t)x2
       + 
                                 12                      11
             - 30395419454296875t   - 701857867399218750t
           + 
                                   10                        9
             - 6488291645330859375t   - 32105875440117187500t
           + 
                                    8                         7
             - 98115068719335937500t  - 200070637593750000000t
           + 
                                     6                         5
             - 283812925429687500000t  - 285360368906250000000t
           + 
                                     4                         3
             - 203392019531250000000t  - 100776328125000000000t
           + 
                                  2
           - 33082617187500000000t  - 6480468750000000000t - 574218750000000000
        *
             3
           x1
       + 
                                11                       10
             121581677817187500t   + 1956359724876562500t
           + 
                                  9                        8
             12258648507187500000t  + 42612962210156250000t
           + 
                                  7                         6
             94169539406250000000t  + 141095774531250000000t
           + 
                                   5                         4
             147581280000000000000t  + 108372515625000000000t
           + 
                                  3                        2
             54960468750000000000t  + 18382031250000000000t
           + 
             3656250000000000000t + 328125000000000000
        *
             2
           x1
       + 
                                  13                       12
             - 709226453933593750t   - 8929805806345703125t
           + 
                                    11                         10
             - 48942486697070312500t   - 156380528045981250000t
           + 
                                     9                         8
             - 326629621730156250000t  - 471538077372656250000t
           + 
                                     7                         6
             - 483442617281250000000t  - 355362026250000000000t
           + 
                                     5                        4
             - 186769852500000000000t  - 69530398437500000000t
           + 
                                    3                       2
             - 18287656250000000000t  - 3509375000000000000t
           + 
             - 515625000000000000t - 46875000000000000
        *
           x1
       + 
                            13                       12
         202636129695312500t   + 2551373087527343750t
       + 
                              11                        10
         13983567627734375000t   + 44645413248046875000t
       + 
                              9                         8
         93006952500000000000t  + 133433269921875000000t
       + 
                               7                        6
         134994595312500000000t  + 96549492187500000000t
       + 
                              5                        4                       3
         47927343750000000000t  + 15748046875000000000t  + 3085937500000000000t
       + 
                            2
         273437500000000000t
       ,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ,

     {11t + 1,

                3         2               3            2               3
         78345x1  + 9722x1  + (- 89741344t  - 73045280t )x1 + 52175200t
       + 
                  2
         20870080t
       ,
         2              3        2           3        2
      9x1 x2 + (- 10406t  - 8470t )x1 + 6050t  + 2420t ,
               2                                    2
      x3 - 11x1 x2 + (11t + 77)x1 - 22, 10x4 + (11x1  + 110t)x2 - 66x1}
     ,

         2
     {22t  + 13t + 1,

                    8
         (99t + 9)x1
       + 
                    12           11            10          9          8   7
         (- 2230272t   + 5575680t   + 10029056t   + 587776t  - 688128t )x1
       + 
                  12            11           10            9           8   6
         (6938624t   - 27484160t   - 8321024t   + 18042880t  + 1605632t )x1
       + 
                   11            10            9   5
         (31539200t   - 53559296t   - 55050240t )x1
       + 
                   10            9   4
         (40140800t   + 16056320t )x1
       ,
                  2           3        2           3       2
      (113t + 7)x1 x2 + (3784t  + 3080t )x1 - 2200t  - 880t ,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ,
    {t,x1 - 2,4x2 + (- t - 7)x1 + 2,x3 - 3,9x4 + (- t - 7)x3 + t x1 + 2},

     {
              11       10      9    8   9
         (242t   + 165t   + 24t  + t )x1
       + 
                11       10       9      8   8
         (- 605t   + 880t   + 679t  + 54t )x1
       + 
               12        11        10       9       8   7
         (2178t   - 5445t   - 9794t   - 574t  + 672t )x1
       + 
                 12         11        10         9        8   6
         (- 6776t   + 26840t   + 8126t   - 17620t  - 1568t )x1
       + 
                  11         10         9   5            10         9   4
         (- 30800t   + 52304t   + 53760t )x1  + (- 39200t   - 15680t )x1
       ,
          3      2   2           3      2         3      2
      (11t  + 10t )x1 x2 + (- 86t  - 70t )x1 + 50t  + 20t ,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t]))

zeroSetSplit(lp)$T
 

   (21)
   [{t,x1 - 2,4x2 + (- t - 7)x1 + 2,x3 - 3,9x4 + (- t - 7)x3 + 2},

                             3        2
     {11t + 10, 900x1 + 6655t  + 2662t ,

                      3
         38971649024x2
       + 
                                            5               4
             (- 1414695942t - 14146959420)x1  + 2829391884x1
           + 
                            2                  3                  2
             (- 14146959420t  - 99028715940t)x1  + 28293918840t x1
        *
             2
           x2
       + 
                        2                                4
             (707347971t  + 18391047246t + 94077280143)x1
           + 
                                            3
             (- 2829391884t - 36782094492)x1
           + 
                         3               2                                 2
             (7073479710t  + 99028715940t  + 352446356790t + 43750348884)x1
           + 
                            2
             (- 28293918840t  - 198057431880t)x1 + 28293918840t
        *
           x2
       + 
                       2                                 3
         (- 4244087826t  - 59417229564t - 207960303474)x1
       + 
                                        2
         (16976351304t + 118834459128)x1
       + 
                       2
         (- 5845851000t  - 87156324000t - 303423050304)x1 + 11691702000t
       + 
         71213094000
       ,
                 2                                     2
      10x3 - 11x1 x2 + (11t + 77)x1 - 22, 100x4 + (11x1  + 110t)x2 - 66x1}
     ,

     {11t + 1,

                3         2               3            2               3
         78345x1  + 9722x1  + (- 89741344t  - 73045280t )x1 + 52175200t
       + 
                  2
         20870080t
       ,
         2              3        2           3        2
      9x1 x2 + (- 10406t  - 8470t )x1 + 6050t  + 2420t ,
               2                                    2
      x3 - 11x1 x2 + (11t + 77)x1 - 22, 10x4 + (11x1  + 110t)x2 - 66x1}
     ,

         2
     {22t  + 13t + 1,

                    5
         (99t + 9)x1
       + 
                    12           11            10          9          8   4
         (- 2230272t   + 5575680t   + 10029056t   + 587776t  - 688128t )x1
       + 
                  12            11           10            9           8   3
         (6938624t   - 27484160t   - 8321024t   + 18042880t  + 1605632t )x1
       + 
                   11            10            9   2
         (31539200t   - 53559296t   - 55050240t )x1
       + 
                   10            9
         (40140800t   + 16056320t )x1
       ,
                  2           3        2           3       2
      (113t + 7)x1 x2 + (3784t  + 3080t )x1 - 2200t  - 880t ,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ,

         3      2
     {55t  + 72t  + 20t, (11t + 10)x1,

                          2
         (465452061949952t  + 423138238136320t)x2
       + 
                                 12                      11
             - 30395419454296875t   - 701857867399218750t
           + 
                                   10                        9
             - 6488291645330859375t   - 32105875440117187500t
           + 
                                    8                         7
             - 98115068719335937500t  - 200070637593750000000t
           + 
                                     6                         5
             - 283812925429687500000t  - 285360368906250000000t
           + 
                                     4                         3
             - 203392019531250000000t  - 100776328125000000000t
           + 
                                  2
           - 33082617187500000000t  - 6480468750000000000t - 574218750000000000
        *
             3
           x1
       + 
                                11                       10
             121581677817187500t   + 1956359724876562500t
           + 
                                  9                        8
             12258648507187500000t  + 42612962210156250000t
           + 
                                  7                         6
             94169539406250000000t  + 141095774531250000000t
           + 
                                   5                         4
             147581280000000000000t  + 108372515625000000000t
           + 
                                  3                        2
             54960468750000000000t  + 18382031250000000000t
           + 
             3656250000000000000t + 328125000000000000
        *
             2
           x1
       + 
                                  13                       12
             - 709226453933593750t   - 8929805806345703125t
           + 
                                    11                         10
             - 48942486697070312500t   - 156380528045981250000t
           + 
                                     9                         8
             - 326629621730156250000t  - 471538077372656250000t
           + 
                                     7                         6
             - 483442617281250000000t  - 355362026250000000000t
           + 
                                     5                        4
             - 186769852500000000000t  - 69530398437500000000t
           + 
                                    3                       2
             - 18287656250000000000t  - 3509375000000000000t
           + 
             - 515625000000000000t - 46875000000000000
        *
           x1
       + 
                            13                       12
         202636129695312500t   + 2551373087527343750t
       + 
                              11                        10
         13983567627734375000t   + 44645413248046875000t
       + 
                              9                         8
         93006952500000000000t  + 133433269921875000000t
       + 
                               7                        6
         134994595312500000000t  + 96549492187500000000t
       + 
                              5                        4                       3
         47927343750000000000t  + 15748046875000000000t  + 3085937500000000000t
       + 
                            2
         273437500000000000t
       ,
                                            2
      t x3 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2}
     ,

     {
              4       3      2       6          4       3       2         5
         (242t  + 165t  + 24t  + t)x1  + (- 605t  + 880t  + 679t  + 54t)x1
       + 
               5        4        3       2          4
         (2178t  - 5445t  - 9794t  - 574t  + 672t)x1
       + 
                 5         4        3         2           3
         (- 6776t  + 26840t  + 8126t  - 17620t  - 1568t)x1
       + 
                  4         3         2   2            3         2
         (- 30800t  + 52304t  + 53760t )x1  + (- 39200t  - 15680t )x1
       ,
          2         2           2               2
      (11t  + 10t)x1 x2 + (- 86t  - 70t)x1 + 50t  + 20t,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t]))


T := REGSET(R,E,V,P)
 

   (22)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x
  1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Inte
  ger,OrderedVariableList [x4,x3,x2,x1,t]))
                                                                 Type: Domain

zeroSetSplit(lp)$T
 

   (23)
   [
     {
              3       2             5          3       2               4
         (242t  + 165t  + 24t + 1)x1  + (- 605t  + 880t  + 679t + 54)x1
       + 
               4        3        2                3
         (2178t  - 5445t  - 9794t  - 574t + 672)x1
       + 
                 4         3        2                   2
         (- 6776t  + 26840t  + 8126t  - 17620t - 1568)x1
       + 
                  3         2                     2
         (- 30800t  + 52304t  + 53760t)x1 - 39200t  - 15680t
       ,
                  2
      (11t + 10)x1 x2 + (- 86t - 70)x1 + 50t + 20,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t]))

zeroSetSplit(lp,false)$T
 

   (24)
   [
     {
              3       2             5          3       2               4
         (242t  + 165t  + 24t + 1)x1  + (- 605t  + 880t  + 679t + 54)x1
       + 
               4        3        2                3
         (2178t  - 5445t  - 9794t  - 574t + 672)x1
       + 
                 4         3        2                   2
         (- 6776t  + 26840t  + 8126t  - 17620t - 1568)x1
       + 
                  3         2                     2
         (- 30800t  + 52304t  + 53760t)x1 - 39200t  - 15680t
       ,
                  2
      (11t + 10)x1 x2 + (- 86t - 70)x1 + 50t + 20,
               2                                    2
      t x3 + x1 x2 + (- t - 7)x1 + 2, 10t x4 + (- x1  - 10t)x2 + 6x1}
     ,

                      3         2                          2
     {11t + 1, 78345x1  + 9722x1  - 536256x1 + 133280, 99x1 x2 - 684x1 + 170,
      9x3 - 28, 9x4 - 9x2 + 9x1 - 17}
     ,

                  4         3          2                       2
     {2t + 1, 81x1  - 5382x1  + 43960x1  - 79632x1 - 15680, 9x1 x2 - 54x1 - 10,
      9x3 + 9x1 - 56, 9x4 - 9x2 + 2}
     ,

     {11t + 10, 9x1 - 28,
                  3                2
      2435728064x2  - 85841821296x2  + 299777296923x2 - 274523632083,
      405x3 - 4312x2 + 7551, 2025x4 + 131x2 - 4158}
     ,
    {5t + 2,x1,25x2 - 31,x3 - 5,25x4 - 31}, {t,x1 - 2,x2 - 3,x3 - 3,9x4 - 19}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x4,x3,x2,x1,t],OrderedVariableList [x4,x3,x2,x1,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x4,x3,x2,x1,t]))
)lisp (bye)
 
Starts dribbling to fib.output (2010/3/27, 18:25:57).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 4
fib(n | n=0)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 4
fib(n | n=1)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
fib(n | n>1)==fib(n-1)+fib(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
fibs == [fib i for i in 0..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
)spool 
 
Starts dribbling to grpthry.output (2010/3/27, 18:26:42).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 68
x : PERM INT := [[1,3,5],[7,11,9]]
 

   (1)  (1 3 5)(7 11 9)
                                                    Type: Permutation Integer
--R 
--R
--R   (1)  (1 3 5)(7 11 9)
--R                                                    Type: Permutation Integer
--E 1

--S 2 of 68
y : PERM INT := [[3,5,7,9]]
 

   (2)  (3 5 7 9)
                                                    Type: Permutation Integer
--R 
--R
--R   (2)  (3 5 7 9)
--R                                                    Type: Permutation Integer
--E 2

--S 3 of 68
z : PERM INT := [1,3,11]
 

   (3)  (1 3 11)
                                                    Type: Permutation Integer
--R 
--R
--R   (3)  (1 3 11)
--R                                                    Type: Permutation Integer
--E 3

--S 4 of 68
g1 : PERMGRP INT := [ x , y ]
 

   (4)  <(1 3 5)(7 11 9),(3 5 7 9)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (4)  <(1 3 5)(7 11 9),(3 5 7 9)>
--R                                               Type: PermutationGroup Integer
--E 4

--S 5 of 68
g2 : PERMGRP INT := [ x , z ]
 

   (5)  <(1 3 5)(7 11 9),(1 3 11)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (5)  <(1 3 5)(7 11 9),(1 3 11)>
--R                                               Type: PermutationGroup Integer
--E 5

--S 6 of 68
g3 : PERMGRP INT := [ y , z ]
 

   (6)  <(3 5 7 9),(1 3 11)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (6)  <(3 5 7 9),(1 3 11)>
--R                                               Type: PermutationGroup Integer
--E 6

--S 7 of 68
order g1
 

   (7)  720
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  720
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 68
degree g3
 

   (8)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  6
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 68
movedPoints g2
 

   (9)  {1,3,5,7,9,11}
                                                            Type: Set Integer
--R 
--R
--R   (9)  {1,3,5,7,9,11}
--R                                                            Type: Set Integer
--E 9

--S 10 of 68
orbit (g1, 3)
 

   (10)  {1,3,5,7,9,11}
                                                            Type: Set Integer
--R 
--R
--R   (10)  {1,3,5,7,9,11}
--R                                                            Type: Set Integer
--E 10

--S 11 of 68
orbits g3
 

   (11)  {{1,3,5,7,9,11}}
                                                        Type: Set Set Integer
--R 
--R
--R   (11)  {{1,3,5,7,9,11}}
--R                                                        Type: Set Set Integer
--E 11

--S 12 of 68
member? ( y , g2 )
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 68
)sh PERMGRP
 
 PermutationGroup S: SetCategory  is a domain constructor
 Abbreviation for PermutationGroup is PERMGRP 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for PERMGRP 

------------------------------- Operations --------------------------------
 ?<? : (%,%) -> Boolean                ?<=? : (%,%) -> Boolean
 ?=? : (%,%) -> Boolean                base : % -> List S
 coerce : List Permutation S -> %      coerce : % -> List Permutation S
 coerce : % -> OutputForm              degree : % -> NonNegativeInteger
 hash : % -> SingleInteger             latex : % -> String
 movedPoints : % -> Set S              orbit : (%,List S) -> Set List S
 orbit : (%,Set S) -> Set Set S        orbit : (%,S) -> Set S
 orbits : % -> Set Set S               order : % -> NonNegativeInteger
 random : % -> Permutation S           ?~=? : (%,%) -> Boolean
 ?.? : (%,NonNegativeInteger) -> Permutation S
 generators : % -> List Permutation S
 initializeGroupForWordProblem : (%,Integer,Integer) -> Void
 initializeGroupForWordProblem : % -> Void
 member? : (Permutation S,%) -> Boolean
 permutationGroup : List Permutation S -> %
 random : (%,Integer) -> Permutation S
 strongGenerators : % -> List Permutation S
 wordInGenerators : (Permutation S,%) -> List NonNegativeInteger
 wordInStrongGenerators : (Permutation S,%) -> List NonNegativeInteger
 wordsForStrongGenerators : % -> List List NonNegativeInteger

--R 
--R PermutationGroup S: SetCategory  is a domain constructor
--R Abbreviation for PermutationGroup is PERMGRP 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for PERMGRP 
--R
--R------------------------------- Operations --------------------------------
--R ?<? : (%,%) -> Boolean                ?<=? : (%,%) -> Boolean
--R ?=? : (%,%) -> Boolean                base : % -> List S
--R coerce : List Permutation S -> %      coerce : % -> List Permutation S
--R coerce : % -> OutputForm              degree : % -> NonNegativeInteger
--R hash : % -> SingleInteger             latex : % -> String
--R movedPoints : % -> Set S              orbit : (%,List S) -> Set List S
--R orbit : (%,Set S) -> Set Set S        orbit : (%,S) -> Set S
--R orbits : % -> Set Set S               order : % -> NonNegativeInteger
--R random : % -> Permutation S           ?~=? : (%,%) -> Boolean
--R ?.? : (%,NonNegativeInteger) -> Permutation S
--R generators : % -> List Permutation S
--R initializeGroupForWordProblem : (%,Integer,Integer) -> Void
--R initializeGroupForWordProblem : % -> Void
--R member? : (Permutation S,%) -> Boolean
--R permutationGroup : List Permutation S -> %
--R random : (%,Integer) -> Permutation S
--R strongGenerators : % -> List Permutation S
--R wordInGenerators : (Permutation S,%) -> List NonNegativeInteger
--R wordInStrongGenerators : (Permutation S,%) -> List NonNegativeInteger
--R wordsForStrongGenerators : % -> List List NonNegativeInteger
--R
--E 13

)clear all
 

--S 14 of 68
ptn9 := partitions 9
 

   (1)
   [[9],[8,1],[7,2],[7,1,1],[6,3],[6,2,1],[6,1,1,1],[5,4],[5,3,1],[5,2,2],...]
                                                    Type: Stream List Integer
--R 
--R
--R   (1)
--R   [[9],[8,1],[7,2],[7,1,1],[6,3],[6,2,1],[6,1,1,1],[5,4],[5,3,1],[5,2,2],...]
--R                                                    Type: Stream List Integer
--E 14

--S 15 of 68
map(dimensionOfIrreducibleRepresentation, ptn9)
 

   (2)  [1,8,27,28,48,105,56,42,162,120,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (2)  [1,8,27,28,48,105,56,42,162,120,...]
--R                                              Type: Stream NonNegativeInteger
--E 15

--S 16 of 68
yt := listYoungTableaus [4,2]
 

   (3)
    +0  2  4  5+  +0  2  3  5+  +0  2  3  4+  +0  1  4  5+  +0  1  3  5+
   [|          |, |          |, |          |, |          |, |          |,
    +1  3  0  0+  +1  4  0  0+  +1  5  0  0+  +2  3  0  0+  +2  4  0  0+
    +0  1  3  4+  +0  1  2  5+  +0  1  2  4+  +0  1  2  3+
    |          |, |          |, |          |, |          |]
    +2  5  0  0+  +3  4  0  0+  +3  5  0  0+  +4  5  0  0+
                                                    Type: List Matrix Integer
--R 
--R
--R   (3)
--R    +0  2  4  5+  +0  2  3  5+  +0  2  3  4+  +0  1  4  5+  +0  1  3  5+
--R   [|          |, |          |, |          |, |          |, |          |,
--R    +1  3  0  0+  +1  4  0  0+  +1  5  0  0+  +2  3  0  0+  +2  4  0  0+
--R    +0  1  3  4+  +0  1  2  5+  +0  1  2  4+  +0  1  2  3+
--R    |          |, |          |, |          |, |          |]
--R    +2  5  0  0+  +3  4  0  0+  +3  5  0  0+  +4  5  0  0+
--R                                                    Type: List Matrix Integer
--E 16

--S 17 of 68
r1 := irreducibleRepresentation([4,2],[1,2,4,5,3,6])
 

        + 0   - 1  - 1   0    0    0    0    0    1 +
        |                                           |
        |- 1   0    0    0    0    0    0    0    0 |
        |                                           |
        | 1    1    1    0    0    0    0    0    0 |
        |                                           |
        | 0    1    0    0    0    0    0    0   - 1|
        |                                           |
   (4)  | 0    0    0    0    0    0    1    0    0 |
        |                                           |
        | 0    0    0    0    1    0    0    0    0 |
        |                                           |
        | 1    0    0    0    0    0   - 1  - 1   0 |
        |                                           |
        |- 1  - 1  - 1  - 1  - 1  - 1   0    0    0 |
        |                                           |
        + 0    0    0    1    0    0    0    0    0 +
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   - 1  - 1   0    0    0    0    0    1 +
--R        |                                           |
--R        |- 1   0    0    0    0    0    0    0    0 |
--R        |                                           |
--R        | 1    1    1    0    0    0    0    0    0 |
--R        |                                           |
--R        | 0    1    0    0    0    0    0    0   - 1|
--R        |                                           |
--R   (4)  | 0    0    0    0    0    0    1    0    0 |
--R        |                                           |
--R        | 0    0    0    0    1    0    0    0    0 |
--R        |                                           |
--R        | 1    0    0    0    0    0   - 1  - 1   0 |
--R        |                                           |
--R        |- 1  - 1  - 1  - 1  - 1  - 1   0    0    0 |
--R        |                                           |
--R        + 0    0    0    1    0    0    0    0    0 +
--R                                                         Type: Matrix Integer
--E 17

--S 18 of 68
r2 := irreducibleRepresentation([4,2],[3,2,1,5,6,4])
 

        + 0    0   - 1   0    0    0    0   - 1   0 +
        |                                           |
        | 1    0    1    0   - 1   0   - 1   0    0 |
        |                                           |
        | 0    0    0    0    1    0    0    0    0 |
        |                                           |
        | 0    0    0    0    0    0    0    1    0 |
        |                                           |
   (5)  |- 1   0    0   - 1   0    0    0    0    0 |
        |                                           |
        | 0    0    0    0    0    0    1    0    0 |
        |                                           |
        | 0    0   - 1   0    0   - 1   0   - 1  - 1|
        |                                           |
        | 0    0    0    0    0    0    0    0    1 |
        |                                           |
        + 0   - 1   0    0   - 1   0   - 1   0    0 +
                                                         Type: Matrix Integer
--R 
--R
--R        + 0    0   - 1   0    0    0    0   - 1   0 +
--R        |                                           |
--R        | 1    0    1    0   - 1   0   - 1   0    0 |
--R        |                                           |
--R        | 0    0    0    0    1    0    0    0    0 |
--R        |                                           |
--R        | 0    0    0    0    0    0    0    1    0 |
--R        |                                           |
--R   (5)  |- 1   0    0   - 1   0    0    0    0    0 |
--R        |                                           |
--R        | 0    0    0    0    0    0    1    0    0 |
--R        |                                           |
--R        | 0    0   - 1   0    0   - 1   0   - 1  - 1|
--R        |                                           |
--R        | 0    0    0    0    0    0    0    0    1 |
--R        |                                           |
--R        + 0   - 1   0    0   - 1   0   - 1   0    0 +
--R                                                         Type: Matrix Integer
--E 18

--S 19 of 68
r3 := irreducibleRepresentation([4,2],[4,2,1,3,6,5])
 

        +0   0    0   0   1    0    1    0    1 +
        |                                       |
        |0   0    0   0   0    1    0    1    0 |
        |                                       |
        |0   0    0   1   0    0    0    0    0 |
        |                                       |
        |0  - 1   0   0  - 1   0   - 1   0    0 |
        |                                       |
   (6)  |0   0   - 1  0   0   - 1   0   - 1  - 1|
        |                                       |
        |1   1    1   0   0    0    0    0    0 |
        |                                       |
        |0   0    0   0   0    0    0    0    1 |
        |                                       |
        |0   0    0   0   1    0    0    0    0 |
        |                                       |
        +0   0    0   0   0    1    0    0    0 +
                                                         Type: Matrix Integer
--R 
--R
--R        +0   0    0   0   1    0    1    0    1 +
--R        |                                       |
--R        |0   0    0   0   0    1    0    1    0 |
--R        |                                       |
--R        |0   0    0   1   0    0    0    0    0 |
--R        |                                       |
--R        |0  - 1   0   0  - 1   0   - 1   0    0 |
--R        |                                       |
--R   (6)  |0   0   - 1  0   0   - 1   0   - 1  - 1|
--R        |                                       |
--R        |1   1    1   0   0    0    0    0    0 |
--R        |                                       |
--R        |0   0    0   0   0    0    0    0    1 |
--R        |                                       |
--R        |0   0    0   0   1    0    0    0    0 |
--R        |                                       |
--R        +0   0    0   0   0    1    0    0    0 +
--R                                                         Type: Matrix Integer
--E 19

--S 20 of 68
(r3 = r1*r2) :: Boolean
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 20

--S 21 of 68
irreducibleRepresentation [4,4,1]
 

   (8)
   [
   [
     [- 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 0, - 1,
      0, - 1, - 1, - 1, 0, 1, 1, 0, 0, 0, 0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 1, 0,
      1, 1, 0, - 1, - 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1, 0, 1,
      0, 0, 1, 1, 0, 0, - 1, 0, - 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1,
      - 1, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, - 1,
      - 1, - 1, 0, 0, 1, 0, 0, 0, 0, 0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 1, 1, 0, 0, 0,
      0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 1, 0,
      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1,
      0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0,
      - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
      0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
      0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
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      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, - 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, - 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, - 1, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0,
      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
      0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
     ,

     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
      0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
     ]
     ]
                                                    Type: List Matrix Integer
--R 
--R
--R   (8)
--R   [
--R   [
--R     [- 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 0, - 1,
--R      0, - 1, - 1, - 1, 0, 1, 1, 0, 0, 0, 0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, 0, 0, 1, 1, 0,
--R      1, 1, 0, - 1, - 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1, 0, 1,
--R      0, 0, 1, 1, 0, 0, - 1, 0, - 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 1, 0, - 1,
--R      - 1, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      - 1, - 1, 0, 0, 1, 0, 0, 0, 0, 0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 1, 1, 0, 0, 0,
--R      0, - 1, 0, - 1, 1, - 1, - 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 1, 0,
--R      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0, - 1,
--R      0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 1, 0,
--R      - 1, - 1, 0, 0, 0, - 1, 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
--R      0, - 1, - 1, - 1, 1, - 1, - 1, - 1, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
--R      0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
--R      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
--R      0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, - 1, - 1, - 1]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
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--R     ,
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--R      - 1, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0,
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--R     ,
--R
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--R      - 1, 0, 1, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 1, - 1, 0, 0, 0, - 1, - 1, - 1, 0]
--R     ,
--R
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--R      1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
--R     ,
--R
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--R      1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,
--R      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
--R      0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [- 1, 0, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, - 1, 0, - 1,
--R      0, 0, - 1, - 1, 0, 0, 0, 0, - 1, - 1, - 1, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, - 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R      - 1, - 1, 0, - 1, - 1, 0, 0, 0, 0, - 1, - 1, - 1, - 1, 0, - 1, - 1, 0, 0,
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--R     ,
--R
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--R      0, - 1, - 1, - 1, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
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--R
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--R
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--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
--R      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      - 1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0,
--R      1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0,
--R      - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, - 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, - 1, - 1, 0, 0, 0, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, - 1, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, - 1, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, - 1, 0,
--R      0, 0, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1, 0,
--R      0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0, 0]
--R     ,
--R
--R     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
--R      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 1,
--R      0, 0, - 1, 0, 0, 0, - 1, 0, 0, 0, - 1, 0]
--R     ]
--R     ]
--R                                                    Type: List Matrix Integer
--E 21

)clear all
 

--S 22 of 68
permutationRepresentation [2,3,1,4,6,5,11,10,7,8,9]
 

        +0  0  1  0  0  0  0  0  0  0  0+
        |                               |
        |1  0  0  0  0  0  0  0  0  0  0|
        |                               |
        |0  1  0  0  0  0  0  0  0  0  0|
        |                               |
        |0  0  0  1  0  0  0  0  0  0  0|
        |                               |
        |0  0  0  0  0  1  0  0  0  0  0|
        |                               |
   (1)  |0  0  0  0  1  0  0  0  0  0  0|
        |                               |
        |0  0  0  0  0  0  0  0  1  0  0|
        |                               |
        |0  0  0  0  0  0  0  0  0  1  0|
        |                               |
        |0  0  0  0  0  0  0  0  0  0  1|
        |                               |
        |0  0  0  0  0  0  0  1  0  0  0|
        |                               |
        +0  0  0  0  0  0  1  0  0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  0  1  0  0  0  0  0  0  0  0+
--R        |                               |
--R        |1  0  0  0  0  0  0  0  0  0  0|
--R        |                               |
--R        |0  1  0  0  0  0  0  0  0  0  0|
--R        |                               |
--R        |0  0  0  1  0  0  0  0  0  0  0|
--R        |                               |
--R        |0  0  0  0  0  1  0  0  0  0  0|
--R        |                               |
--R   (1)  |0  0  0  0  1  0  0  0  0  0  0|
--R        |                               |
--R        |0  0  0  0  0  0  0  0  1  0  0|
--R        |                               |
--R        |0  0  0  0  0  0  0  0  0  1  0|
--R        |                               |
--R        |0  0  0  0  0  0  0  0  0  0  1|
--R        |                               |
--R        |0  0  0  0  0  0  0  1  0  0  0|
--R        |                               |
--R        +0  0  0  0  0  0  1  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 68
gm2 := createGenericMatrix 2
 

        +x     x   +
        | 1,1   1,2|
   (2)  |          |
        |x     x   |
        + 2,1   2,2+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x     x   +
--R        | 1,1   1,2|
--R   (2)  |          |
--R        |x     x   |
--R        + 2,1   2,2+
--R                                              Type: Matrix Polynomial Integer
--E 23

--S 24 of 68
symmetricTensors (gm2,2)
 

        +      2          2                       +
        |  x          x             x   x         |
        |   1,1        1,2           1,1 1,2      |
        |                                         |
   (3)  |      2          2                       |
        |  x          x             x   x         |
        |   2,1        2,2           2,1 2,2      |
        |                                         |
        |2x   x     2x   x     x   x    + x   x   |
        +  1,1 2,1    1,2 2,2   1,1 2,2    1,2 2,1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +      2          2                       +
--R        |  x          x             x   x         |
--R        |   1,1        1,2           1,1 1,2      |
--R        |                                         |
--R   (3)  |      2          2                       |
--R        |  x          x             x   x         |
--R        |   2,1        2,2           2,1 2,2      |
--R        |                                         |
--R        |2x   x     2x   x     x   x    + x   x   |
--R        +  1,1 2,1    1,2 2,2   1,1 2,2    1,2 2,1+
--R                                              Type: Matrix Polynomial Integer
--E 24

--S 25 of 68
gm3 := createGenericMatrix 3
 

        +x     x     x   +
        | 1,1   1,2   1,3|
        |                |
   (4)  |x     x     x   |
        | 2,1   2,2   2,3|
        |                |
        |x     x     x   |
        + 3,1   3,2   3,3+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x     x     x   +
--R        | 1,1   1,2   1,3|
--R        |                |
--R   (4)  |x     x     x   |
--R        | 2,1   2,2   2,3|
--R        |                |
--R        |x     x     x   |
--R        + 3,1   3,2   3,3+
--R                                              Type: Matrix Polynomial Integer
--E 25

--S 26 of 68
antisymmetricTensors (gm3,2)
 

        +x   x    - x   x     x   x    - x   x     x   x    - x   x   +
        | 1,1 2,2    1,2 2,1   1,1 2,3    1,3 2,1   1,2 2,3    1,3 2,2|
        |                                                             |
   (5)  |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
        | 1,1 3,2    1,2 3,1   1,1 3,3    1,3 3,1   1,2 3,3    1,3 3,2|
        |                                                             |
        |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
        + 2,1 3,2    2,2 3,1   2,1 3,3    2,3 3,1   2,2 3,3    2,3 3,2+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x   x    - x   x     x   x    - x   x     x   x    - x   x   +
--R        | 1,1 2,2    1,2 2,1   1,1 2,3    1,3 2,1   1,2 2,3    1,3 2,2|
--R        |                                                             |
--R   (5)  |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
--R        | 1,1 3,2    1,2 3,1   1,1 3,3    1,3 3,1   1,2 3,3    1,3 3,2|
--R        |                                                             |
--R        |x   x    - x   x     x   x    - x   x     x   x    - x   x   |
--R        + 2,1 3,2    2,2 3,1   2,1 3,3    2,3 3,1   2,2 3,3    2,3 3,2+
--R                                              Type: Matrix Polynomial Integer
--E 26

--S 27 of 68
tensorProduct(gm2,gm2)
 

        +     2                             2  +
        | x        x   x     x   x      x      |
        |  1,1      1,1 1,2   1,1 1,2    1,2   |
        |                                      |
        |x   x     x   x     x   x     x   x   |
        | 1,1 2,1   1,1 2,2   1,2 2,1   1,2 2,2|
   (6)  |                                      |
        |x   x     x   x     x   x     x   x   |
        | 1,1 2,1   1,2 2,1   1,1 2,2   1,2 2,2|
        |                                      |
        |     2                             2  |
        | x        x   x     x   x      x      |
        +  2,1      2,1 2,2   2,1 2,2    2,2   +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +     2                             2  +
--R        | x        x   x     x   x      x      |
--R        |  1,1      1,1 1,2   1,1 1,2    1,2   |
--R        |                                      |
--R        |x   x     x   x     x   x     x   x   |
--R        | 1,1 2,1   1,1 2,2   1,2 2,1   1,2 2,2|
--R   (6)  |                                      |
--R        |x   x     x   x     x   x     x   x   |
--R        | 1,1 2,1   1,2 2,1   1,1 2,2   1,2 2,2|
--R        |                                      |
--R        |     2                             2  |
--R        | x        x   x     x   x      x      |
--R        +  2,1      2,1 2,2   2,1 2,2    2,2   +
--R                                              Type: Matrix Polynomial Integer
--E 27

--S 28 of 68
)sh REP1
 
 RepresentationPackage1 R: Ring  is a package constructor
 Abbreviation for RepresentationPackage1 is REP1 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for REP1 

------------------------------- Operations --------------------------------
 antisymmetricTensors : (Matrix R,PositiveInteger) -> Matrix R if R has commutative *
 antisymmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R if R has commutative *
 createGenericMatrix : NonNegativeInteger -> Matrix Polynomial R
 permutationRepresentation : (Permutation Integer,Integer) -> Matrix Integer
 permutationRepresentation : List Integer -> Matrix Integer
 permutationRepresentation : (List Permutation Integer,Integer) -> List Matrix Integer
 permutationRepresentation : List List Integer -> List Matrix Integer
 symmetricTensors : (Matrix R,PositiveInteger) -> Matrix R
 symmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R
 tensorProduct : (Matrix R,Matrix R) -> Matrix R
 tensorProduct : (List Matrix R,List Matrix R) -> List Matrix R
 tensorProduct : Matrix R -> Matrix R
 tensorProduct : List Matrix R -> List Matrix R

--R 
--R RepresentationPackage1 R: Ring  is a package constructor
--R Abbreviation for RepresentationPackage1 is REP1 
--R This constructor is exposed in this frame.
--I Issue )edit /research/research/s2/mnt/fedora5/../../src/algebra/REP1.spad to see algebra source code for REP1 
--R
--R------------------------------- Operations --------------------------------
--R antisymmetricTensors : (Matrix R,PositiveInteger) -> Matrix R if R has commutative *
--R antisymmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R if R has commutative *
--R createGenericMatrix : NonNegativeInteger -> Matrix Polynomial R
--R permutationRepresentation : (Permutation Integer,Integer) -> Matrix Integer
--R permutationRepresentation : List Integer -> Matrix Integer
--R permutationRepresentation : (List Permutation Integer,Integer) -> List Matrix Integer
--R permutationRepresentation : List List Integer -> List Matrix Integer
--R symmetricTensors : (Matrix R,PositiveInteger) -> Matrix R
--R symmetricTensors : (List Matrix R,PositiveInteger) -> List Matrix R
--R tensorProduct : (Matrix R,Matrix R) -> Matrix R
--R tensorProduct : (List Matrix R,List Matrix R) -> List Matrix R
--R tensorProduct : Matrix R -> Matrix R
--R tensorProduct : List Matrix R -> List Matrix R
--R
--E 28

)clear all
 

--S 29 of 68
r0 := irreducibleRepresentation [2,2,2,1,1];
 

                                                    Type: List Matrix Integer
--R 
--R
--R                                                    Type: List Matrix Integer
--E 29

--S 30 of 68
r28 := meatAxe (r0::(LIST MATRIX PF 2))
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (2)
   [
      +0  1  1  1  1  1  1  0  0  1  1  1  0  0+
      |                                        |
      |1  0  1  1  1  0  0  1  1  1  0  0  1  1|
      |                                        |
      |1  1  0  1  0  1  0  0  1  0  1  0  0  1|
      |                                        |
      |1  1  1  0  0  0  1  1  0  0  0  1  1  0|
      |                                        |
      |1  1  0  0  0  1  1  1  1  1  1  1  1  1|
      |                                        |
      |1  0  1  0  1  0  1  0  1  1  1  1  0  1|
      |                                        |
      |1  0  0  1  1  1  0  1  0  1  1  1  1  0|
     [|                                        |,
      |0  1  1  0  1  1  0  1  0  1  1  0  0  0|
      |                                        |
      |0  1  0  1  1  0  1  0  1  1  0  1  0  0|
      |                                        |
      |1  1  0  0  1  0  0  0  0  0  0  0  0  0|
      |                                        |
      |1  0  1  0  0  1  0  0  0  0  0  0  0  0|
      |                                        |
      |1  0  0  1  0  0  1  0  0  0  0  0  0  0|
      |                                        |
      |0  1  1  0  0  0  0  1  0  0  0  0  0  0|
      |                                        |
      +0  1  0  1  0  0  0  0  1  0  0  0  0  0+
      +1  1  1  1  0  0  0  0  0  0  0  0  0  0+
      |                                        |
      |1  1  1  0  0  0  1  0  0  1  1  0  0  0|
      |                                        |
      |1  1  1  0  0  0  0  0  1  1  0  0  1  0|
      |                                        |
      |1  1  1  0  0  0  0  1  1  0  1  0  1  0|
      |                                        |
      |1  1  1  0  0  0  0  1  0  1  1  1  1  0|
      |                                        |
      |1  1  1  0  0  1  0  0  0  1  1  0  1  1|
      |                                        |
      |1  1  1  0  1  0  0  0  0  1  1  0  0  1|
      |                                        |]
      |1  1  0  0  0  0  0  0  0  0  1  1  1  1|
      |                                        |
      |1  0  1  0  0  0  0  0  0  1  0  1  0  1|
      |                                        |
      |0  0  0  1  0  0  1  0  0  1  1  1  1  0|
      |                                        |
      |0  0  0  1  0  0  0  0  1  1  1  0  1  1|
      |                                        |
      |0  0  0  1  0  0  0  1  1  1  1  0  0  1|
      |                                        |
      |0  0  0  0  0  0  1  0  1  0  1  1  1  1|
      |                                        |
      +0  0  0  0  0  0  1  1  1  1  0  1  0  1+
     ,

      +1  0  0  0  0  0  0  0  1  1  1  1  1  1+
      |                                        |
      |0  1  0  0  0  0  0  0  1  1  1  0  0  0|
      |                                        |
      |0  0  1  0  0  1  1  0  1  0  0  1  0  0|
      |                                        |
      |0  0  0  1  0  1  0  1  0  1  0  0  1  0|
      |                                        |
      |0  0  0  0  1  0  1  1  1  1  0  0  0  1|
      |                                        |
      |0  0  0  0  0  1  1  1  1  1  0  1  1  0|
      |                                        |
      |0  0  0  0  0  1  1  1  1  0  1  1  0  1|
     [|                                        |,
      |0  0  0  0  0  1  1  1  0  1  1  0  1  1|
      |                                        |
      |0  0  0  0  0  1  1  0  1  1  1  1  0  0|
      |                                        |
      |0  0  0  0  0  1  0  1  1  1  1  0  1  0|
      |                                        |
      |0  0  0  0  0  0  1  1  1  1  1  1  1  0|
      |                                        |
      |0  0  0  0  0  0  0  0  0  0  0  0  1  1|
      |                                        |
      |0  0  0  0  0  0  0  0  0  0  0  1  0  1|
      |                                        |
      +0  0  0  0  0  0  0  0  0  0  0  0  0  1+
      +0  0  1  1  1  1  1  0  1  0  0  0  0  0+
      |                                        |
      |0  0  1  0  0  0  0  0  0  0  0  0  1  1|
      |                                        |
      |0  0  0  0  0  0  0  1  0  1  0  0  1  0|
      |                                        |
      |0  0  0  0  0  0  0  1  0  0  1  0  0  1|
      |                                        |
      |0  0  1  0  0  0  0  0  0  1  1  0  1  1|
      |                                        |
      |0  0  0  0  0  0  0  1  1  0  0  1  0  0|
      |                                        |
      |0  0  0  0  0  0  1  0  0  1  0  1  0  0|
      |                                        |]
      |1  1  0  0  0  1  0  0  0  0  1  1  0  0|
      |                                        |
      |0  0  1  1  0  0  1  0  1  0  0  0  1  0|
      |                                        |
      |1  0  1  0  1  1  0  0  1  0  0  0  0  1|
      |                                        |
      |1  0  1  1  1  0  0  0  1  0  0  0  1  1|
      |                                        |
      |0  0  1  1  0  0  1  1  1  1  0  1  1  0|
      |                                        |
      |0  1  1  0  1  1  0  1  1  0  1  1  0  1|
      |                                        |
      +0  1  1  1  1  0  0  0  1  1  1  1  1  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (2)
--R   [
--R      +0  1  1  1  1  1  1  0  0  1  1  1  0  0+
--R      |                                        |
--R      |1  0  1  1  1  0  0  1  1  1  0  0  1  1|
--R      |                                        |
--R      |1  1  0  1  0  1  0  0  1  0  1  0  0  1|
--R      |                                        |
--R      |1  1  1  0  0  0  1  1  0  0  0  1  1  0|
--R      |                                        |
--R      |1  1  0  0  0  1  1  1  1  1  1  1  1  1|
--R      |                                        |
--R      |1  0  1  0  1  0  1  0  1  1  1  1  0  1|
--R      |                                        |
--R      |1  0  0  1  1  1  0  1  0  1  1  1  1  0|
--R     [|                                        |,
--R      |0  1  1  0  1  1  0  1  0  1  1  0  0  0|
--R      |                                        |
--R      |0  1  0  1  1  0  1  0  1  1  0  1  0  0|
--R      |                                        |
--R      |1  1  0  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |1  0  1  0  0  1  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |1  0  0  1  0  0  1  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  1  1  0  0  0  0  1  0  0  0  0  0  0|
--R      |                                        |
--R      +0  1  0  1  0  0  0  0  1  0  0  0  0  0+
--R      +1  1  1  1  0  0  0  0  0  0  0  0  0  0+
--R      |                                        |
--R      |1  1  1  0  0  0  1  0  0  1  1  0  0  0|
--R      |                                        |
--R      |1  1  1  0  0  0  0  0  1  1  0  0  1  0|
--R      |                                        |
--R      |1  1  1  0  0  0  0  1  1  0  1  0  1  0|
--R      |                                        |
--R      |1  1  1  0  0  0  0  1  0  1  1  1  1  0|
--R      |                                        |
--R      |1  1  1  0  0  1  0  0  0  1  1  0  1  1|
--R      |                                        |
--R      |1  1  1  0  1  0  0  0  0  1  1  0  0  1|
--R      |                                        |]
--R      |1  1  0  0  0  0  0  0  0  0  1  1  1  1|
--R      |                                        |
--R      |1  0  1  0  0  0  0  0  0  1  0  1  0  1|
--R      |                                        |
--R      |0  0  0  1  0  0  1  0  0  1  1  1  1  0|
--R      |                                        |
--R      |0  0  0  1  0  0  0  0  1  1  1  0  1  1|
--R      |                                        |
--R      |0  0  0  1  0  0  0  1  1  1  1  0  0  1|
--R      |                                        |
--R      |0  0  0  0  0  0  1  0  1  0  1  1  1  1|
--R      |                                        |
--R      +0  0  0  0  0  0  1  1  1  1  0  1  0  1+
--R     ,
--R
--R      +1  0  0  0  0  0  0  0  1  1  1  1  1  1+
--R      |                                        |
--R      |0  1  0  0  0  0  0  0  1  1  1  0  0  0|
--R      |                                        |
--R      |0  0  1  0  0  1  1  0  1  0  0  1  0  0|
--R      |                                        |
--R      |0  0  0  1  0  1  0  1  0  1  0  0  1  0|
--R      |                                        |
--R      |0  0  0  0  1  0  1  1  1  1  0  0  0  1|
--R      |                                        |
--R      |0  0  0  0  0  1  1  1  1  1  0  1  1  0|
--R      |                                        |
--R      |0  0  0  0  0  1  1  1  1  0  1  1  0  1|
--R     [|                                        |,
--R      |0  0  0  0  0  1  1  1  0  1  1  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  1  1  0  1  1  1  1  0  0|
--R      |                                        |
--R      |0  0  0  0  0  1  0  1  1  1  1  0  1  0|
--R      |                                        |
--R      |0  0  0  0  0  0  1  1  1  1  1  1  1  0|
--R      |                                        |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R      |                                        |
--R      +0  0  0  0  0  0  0  0  0  0  0  0  0  1+
--R      +0  0  1  1  1  1  1  0  1  0  0  0  0  0+
--R      |                                        |
--R      |0  0  1  0  0  0  0  0  0  0  0  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  0  1  0  0  1  0|
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  0  0  1  0  0  1|
--R      |                                        |
--R      |0  0  1  0  0  0  0  0  0  1  1  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  1  0  0  1  0  0|
--R      |                                        |
--R      |0  0  0  0  0  0  1  0  0  1  0  1  0  0|
--R      |                                        |]
--R      |1  1  0  0  0  1  0  0  0  0  1  1  0  0|
--R      |                                        |
--R      |0  0  1  1  0  0  1  0  1  0  0  0  1  0|
--R      |                                        |
--R      |1  0  1  0  1  1  0  0  1  0  0  0  0  1|
--R      |                                        |
--R      |1  0  1  1  1  0  0  0  1  0  0  0  1  1|
--R      |                                        |
--R      |0  0  1  1  0  0  1  1  1  1  0  1  1  0|
--R      |                                        |
--R      |0  1  1  0  1  1  0  1  1  0  1  1  0  1|
--R      |                                        |
--R      +0  1  1  1  1  0  0  0  1  1  1  1  1  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 30

--S 31 of 68
areEquivalent? (r28.1, r28.2)
 
   Dimensions of kernels differ

   Representations are not equivalent.

   (3)  [0]
                                                    Type: Matrix PrimeField 2
--R 
--R   Dimensions of kernels differ
--R
--R   Representations are not equivalent.
--R
--R   (3)  [0]
--R                                                    Type: Matrix PrimeField 2
--E 31

--S 32 of 68
meatAxe r28.2
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is irreducible, but we don't know
       whether it is absolutely irreducible

   (4)
   [
      +1  0  0  0  0  0  0  0  0  0  0  0  0  0+
      |                                        |
      |0  1  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  1  0  0  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  0  1  0  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  0  0  1  0  0  0  0  0  0  0  0  0|
      |                                        |
      |0  0  1  1  0  1  1  1  1  1  0  0  0  0|
      |                                        |
      |0  0  1  0  1  1  1  1  1  0  1  0  0  0|
     [|                                        |,
      |0  0  0  1  1  1  1  1  0  1  1  0  0  0|
      |                                        |
      |1  1  1  0  1  1  1  0  1  1  1  0  0  0|
      |                                        |
      |1  1  0  1  1  1  0  1  1  1  1  0  0  0|
      |                                        |
      |1  1  0  0  0  0  1  1  1  1  1  0  0  0|
      |                                        |
      |1  0  1  0  0  1  1  0  1  0  1  0  1  0|
      |                                        |
      |1  0  0  1  0  1  0  1  0  1  1  1  0  0|
      |                                        |
      +1  0  0  0  1  0  1  1  0  0  0  1  1  1+
      +0  0  0  0  0  0  0  1  0  1  1  0  0  0+
      |                                        |
      |0  0  0  0  0  0  0  1  0  0  0  0  1  1|
      |                                        |
      |1  1  0  0  1  0  0  0  1  1  1  1  1  1|
      |                                        |
      |1  0  0  0  0  0  0  0  1  0  1  1  0  1|
      |                                        |
      |1  0  0  0  0  0  0  0  0  1  1  0  1  1|
      |                                        |
      |1  0  0  0  0  0  0  1  0  1  0  0  1  0|
      |                                        |
      |1  0  0  0  0  0  1  0  1  0  0  1  0  0|
      |                                        |]
      |0  0  1  1  0  1  0  0  0  0  0  1  1  0|
      |                                        |
      |1  0  0  0  0  1  0  0  1  1  1  1  1  1|
      |                                        |
      |0  0  1  0  1  0  1  0  0  0  0  1  0  1|
      |                                        |
      |0  0  0  1  1  0  0  1  0  0  0  0  1  1|
      |                                        |
      |0  0  0  0  0  1  1  1  0  0  0  1  1  1|
      |                                        |
      |0  1  1  0  1  0  0  0  1  0  1  1  0  1|
      |                                        |
      +0  1  0  1  1  0  0  0  0  1  1  0  1  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is irreducible, but we don't know
--R       whether it is absolutely irreducible
--R
--R   (4)
--R   [
--R      +1  0  0  0  0  0  0  0  0  0  0  0  0  0+
--R      |                                        |
--R      |0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                        |
--R      |0  0  1  1  0  1  1  1  1  1  0  0  0  0|
--R      |                                        |
--R      |0  0  1  0  1  1  1  1  1  0  1  0  0  0|
--R     [|                                        |,
--R      |0  0  0  1  1  1  1  1  0  1  1  0  0  0|
--R      |                                        |
--R      |1  1  1  0  1  1  1  0  1  1  1  0  0  0|
--R      |                                        |
--R      |1  1  0  1  1  1  0  1  1  1  1  0  0  0|
--R      |                                        |
--R      |1  1  0  0  0  0  1  1  1  1  1  0  0  0|
--R      |                                        |
--R      |1  0  1  0  0  1  1  0  1  0  1  0  1  0|
--R      |                                        |
--R      |1  0  0  1  0  1  0  1  0  1  1  1  0  0|
--R      |                                        |
--R      +1  0  0  0  1  0  1  1  0  0  0  1  1  1+
--R      +0  0  0  0  0  0  0  1  0  1  1  0  0  0+
--R      |                                        |
--R      |0  0  0  0  0  0  0  1  0  0  0  0  1  1|
--R      |                                        |
--R      |1  1  0  0  1  0  0  0  1  1  1  1  1  1|
--R      |                                        |
--R      |1  0  0  0  0  0  0  0  1  0  1  1  0  1|
--R      |                                        |
--R      |1  0  0  0  0  0  0  0  0  1  1  0  1  1|
--R      |                                        |
--R      |1  0  0  0  0  0  0  1  0  1  0  0  1  0|
--R      |                                        |
--R      |1  0  0  0  0  0  1  0  1  0  0  1  0  0|
--R      |                                        |]
--R      |0  0  1  1  0  1  0  0  0  0  0  1  1  0|
--R      |                                        |
--R      |1  0  0  0  0  1  0  0  1  1  1  1  1  1|
--R      |                                        |
--R      |0  0  1  0  1  0  1  0  0  0  0  1  0  1|
--R      |                                        |
--R      |0  0  0  1  1  0  0  1  0  0  0  0  1  1|
--R      |                                        |
--R      |0  0  0  0  0  1  1  1  0  0  0  1  1  1|
--R      |                                        |
--R      |0  1  1  0  1  0  0  0  1  0  1  1  0  1|
--R      |                                        |
--R      +0  1  0  1  1  0  0  0  0  1  1  0  1  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 32

--S 33 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? r28.2
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (5)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 33

--S 34 of 68
ma := meatAxe r28.1
 
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (6)
     +0  0  0  0  1  0  1  1+ +1  1  1  1  1  1  0  0+
     |                      | |                      |
     |0  0  0  0  0  1  0  1| |1  0  0  1  1  0  1  0|
     |                      | |                      |
     |0  0  0  0  0  0  1  1| |0  0  1  1  0  0  1  0|
     |                      | |                      |
     |0  0  0  0  0  0  0  1| |1  1  0  1  1  1  1  1|
   [[|                      |,|                      |],
     |1  0  1  0  0  0  0  0| |1  1  1  1  0  0  1  0|
     |                      | |                      |
     |0  1  0  1  0  0  0  0| |1  0  0  1  1  1  1  1|
     |                      | |                      |
     |0  0  1  1  0  0  0  0| |0  1  1  0  1  0  1  1|
     |                      | |                      |
     +0  0  0  1  0  0  0  0+ +1  0  0  1  0  1  0  1+
     +0  1  1  0  0  1+ +1  1  0  0  0  0+
     |                | |                |
     |1  0  1  0  0  1| |1  0  1  1  0  0|
     |                | |                |
     |1  1  0  0  0  1| |1  0  0  1  0  1|
    [|                |,|                |]]
     |0  0  0  1  0  0| |1  0  1  1  1  0|
     |                | |                |
     |0  0  0  0  1  0| |1  0  0  0  1  1|
     |                | |                |
     +1  1  1  0  0  0+ +0  1  1  1  0  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (6)
--R     +0  0  0  0  1  0  1  1+ +1  1  1  1  1  1  0  0+
--R     |                      | |                      |
--R     |0  0  0  0  0  1  0  1| |1  0  0  1  1  0  1  0|
--R     |                      | |                      |
--R     |0  0  0  0  0  0  1  1| |0  0  1  1  0  0  1  0|
--R     |                      | |                      |
--R     |0  0  0  0  0  0  0  1| |1  1  0  1  1  1  1  1|
--R   [[|                      |,|                      |],
--R     |1  0  1  0  0  0  0  0| |1  1  1  1  0  0  1  0|
--R     |                      | |                      |
--R     |0  1  0  1  0  0  0  0| |1  0  0  1  1  1  1  1|
--R     |                      | |                      |
--R     |0  0  1  1  0  0  0  0| |0  1  1  0  1  0  1  1|
--R     |                      | |                      |
--R     +0  0  0  1  0  0  0  0+ +1  0  0  1  0  1  0  1+
--R     +0  1  1  0  0  1+ +1  1  0  0  0  0+
--R     |                | |                |
--R     |1  0  1  0  0  1| |1  0  1  1  0  0|
--R     |                | |                |
--R     |1  1  0  0  0  1| |1  0  0  1  0  1|
--R    [|                |,|                |]]
--R     |0  0  0  1  0  0| |1  0  1  1  1  0|
--R     |                | |                |
--R     |0  0  0  0  1  0| |1  0  0  0  1  1|
--R     |                | |                |
--R     +1  1  1  0  0  0+ +0  1  1  1  0  1+
--R                                          Type: List List Matrix PrimeField 2
--E 34

--S 35 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? ma.1
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (7)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 35

--S 36 of 68
isAbsolutelyIrreducible? ma.2
 
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (8)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 36

)clear all
 

--S 37 of 68
px : PERM PF 29 := cycles [[1,3,5],[7,11,9]]
 

   (1)  (1 3 5)(7 11 9)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (1)  (1 3 5)(7 11 9)
--R                                              Type: Permutation PrimeField 29
--E 37

--S 38 of 68
py : PERM PF 29 := cycles [[3,5,7,9]]
 

   (2)  (3 5 7 9)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (2)  (3 5 7 9)
--R                                              Type: Permutation PrimeField 29
--E 38

--S 39 of 68
pz : PERM PF 29 := cycle [1,3,11]
 

   (3)  (1 3 11)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (3)  (1 3 11)
--R                                              Type: Permutation PrimeField 29
--E 39

--S 40 of 68
px * pz
 

   (4)  (1 5)(3 9 7 11)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (4)  (1 5)(3 9 7 11)
--R                                              Type: Permutation PrimeField 29
--E 40

--S 41 of 68
py ** 3
 

   (5)  (3 9 7 5)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (5)  (3 9 7 5)
--R                                              Type: Permutation PrimeField 29
--E 41

--S 42 of 68
inv px
 

   (6)  (1 5 3)(7 9 11)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (6)  (1 5 3)(7 9 11)
--R                                              Type: Permutation PrimeField 29
--E 42

--S 43 of 68
order px
 

   (7)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  3
--R                                                        Type: PositiveInteger
--E 43

--S 44 of 68
movedPoints py
 

   (8)  {3,5,7,9}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (8)  {3,5,7,9}
--R                                                      Type: Set PrimeField 29
--E 44

--S 45 of 68
orbit ( pz , 3 )
 

   (9)  {3,11,1}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (9)  {3,11,1}
--R                                                      Type: Set PrimeField 29
--E 45

--S 46 of 68
eval ( py , 7 )
 

   (10)  9
                                                          Type: PrimeField 29
--R 
--R
--R   (10)  9
--R                                                          Type: PrimeField 29
--E 46

--S 47 of 68
)sh PERM
 
 Permutation S: SetCategory  is a domain constructor
 Abbreviation for Permutation is PERM 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for PERM 

------------------------------- Operations --------------------------------
 ?*? : (%,%) -> %                      ?**? : (%,Integer) -> %
 ?**? : (%,PositiveInteger) -> %       ?/? : (%,%) -> %
 ?<? : (%,%) -> Boolean                ?=? : (%,%) -> Boolean
 1 : () -> %                           ?^? : (%,Integer) -> %
 ?^? : (%,PositiveInteger) -> %        coerce : List S -> %
 coerce : List List S -> %             coerce : % -> OutputForm
 coerceImages : List S -> %            commutator : (%,%) -> %
 conjugate : (%,%) -> %                cycle : List S -> %
 cyclePartition : % -> Partition       cycles : List List S -> %
 degree : % -> NonNegativeInteger      ?.? : (%,S) -> S
 eval : (%,S) -> S                     even? : % -> Boolean
 hash : % -> SingleInteger             inv : % -> %
 latex : % -> String                   movedPoints : % -> Set S
 odd? : % -> Boolean                   one? : % -> Boolean
 orbit : (%,S) -> Set S                order : % -> NonNegativeInteger
 recip : % -> Union(%,"failed")        sample : () -> %
 sign : % -> Integer                   sort : List % -> List %
 ?~=? : (%,%) -> Boolean              
 ?**? : (%,NonNegativeInteger) -> %
 ?<=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
 ?>? : (%,%) -> Boolean if S has FINITE or S has ORDSET
 ?>=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
 ?^? : (%,NonNegativeInteger) -> %
 coerceListOfPairs : List List S -> %
 coercePreimagesImages : List List S -> %
 fixedPoints : % -> Set S if S has FINITE
 listRepresentation : % -> Record(preimage: List S,image: List S)
 max : (%,%) -> % if S has FINITE or S has ORDSET
 min : (%,%) -> % if S has FINITE or S has ORDSET
 numberOfCycles : % -> NonNegativeInteger

--R 
--R Permutation S: SetCategory  is a domain constructor
--R Abbreviation for Permutation is PERM 
--R This constructor is exposed in this frame.
--I Issue )edit /research/research/s2/mnt/fedora5/../../src/algebra/PERM.spad to see algebra source code for PERM 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (%,%) -> %                      ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> %       ?/? : (%,%) -> %
--R ?<? : (%,%) -> Boolean                ?=? : (%,%) -> Boolean
--R 1 : () -> %                           ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> %        coerce : List S -> %
--R coerce : List List S -> %             coerce : % -> OutputForm
--R coerceImages : List S -> %            commutator : (%,%) -> %
--R conjugate : (%,%) -> %                cycle : List S -> %
--R cyclePartition : % -> Partition       cycles : List List S -> %
--R degree : % -> NonNegativeInteger      ?.? : (%,S) -> S
--R eval : (%,S) -> S                     even? : % -> Boolean
--R hash : % -> SingleInteger             inv : % -> %
--R latex : % -> String                   movedPoints : % -> Set S
--R odd? : % -> Boolean                   one? : % -> Boolean
--R orbit : (%,S) -> Set S                order : % -> NonNegativeInteger
--R recip : % -> Union(%,"failed")        sample : () -> %
--R sign : % -> Integer                   sort : List % -> List %
--R ?~=? : (%,%) -> Boolean              
--R ?**? : (%,NonNegativeInteger) -> %
--R ?<=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
--R ?>? : (%,%) -> Boolean if S has FINITE or S has ORDSET
--R ?>=? : (%,%) -> Boolean if S has FINITE or S has ORDSET
--R ?^? : (%,NonNegativeInteger) -> %
--R coerceListOfPairs : List List S -> %
--R coercePreimagesImages : List List S -> %
--R fixedPoints : % -> Set S if S has FINITE
--R listRepresentation : % -> Record(preimage: List S,image: List S)
--R max : (%,%) -> % if S has FINITE or S has ORDSET
--R min : (%,%) -> % if S has FINITE or S has ORDSET
--R numberOfCycles : % -> NonNegativeInteger
--R
--E 47

)clear all
 

--S 48 of 68
genA6 : List PERM INT := [cycle [1,2,3],cycle [2,3,4,5,6]]
 

   (1)  [(1 2 3),(2 3 4 5 6)]
                                               Type: List Permutation Integer
--R 
--R
--R   (1)  [(1 2 3),(2 3 4 5 6)]
--R                                               Type: List Permutation Integer
--E 48

--S 49 of 68
pRA6 := permutationRepresentation (genA6,6)
 

         +0  0  1  0  0  0+ +1  0  0  0  0  0+
         |                | |                |
         |1  0  0  0  0  0| |0  0  0  0  0  1|
         |                | |                |
         |0  1  0  0  0  0| |0  1  0  0  0  0|
   (2)  [|                |,|                |]
         |0  0  0  1  0  0| |0  0  1  0  0  0|
         |                | |                |
         |0  0  0  0  1  0| |0  0  0  1  0  0|
         |                | |                |
         +0  0  0  0  0  1+ +0  0  0  0  1  0+
                                                    Type: List Matrix Integer
--R 
--R
--R         +0  0  1  0  0  0+ +1  0  0  0  0  0+
--R         |                | |                |
--R         |1  0  0  0  0  0| |0  0  0  0  0  1|
--R         |                | |                |
--R         |0  1  0  0  0  0| |0  1  0  0  0  0|
--R   (2)  [|                |,|                |]
--R         |0  0  0  1  0  0| |0  0  1  0  0  0|
--R         |                | |                |
--R         |0  0  0  0  1  0| |0  0  0  1  0  0|
--R         |                | |                |
--R         +0  0  0  0  0  1+ +0  0  0  0  1  0+
--R                                                    Type: List Matrix Integer
--E 49

--S 50 of 68
sp0 := meatAxe (pRA6::(List Matrix PF 2))
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

          +0  0  1  0  0+ +1  0  0  0  0+
          |             | |             |
          |1  0  0  0  0| |1  1  1  1  1|
          |             | |             |
   (3)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
          |             | |             |
          |0  0  0  1  0| |0  0  1  0  0|
          |             | |             |
          +0  0  0  0  1+ +0  0  0  1  0+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R          +0  0  1  0  0+ +1  0  0  0  0+
--R          |             | |             |
--R          |1  0  0  0  0| |1  1  1  1  1|
--R          |             | |             |
--R   (3)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
--R          |             | |             |
--R          |0  0  0  1  0| |0  0  1  0  0|
--R          |             | |             |
--R          +0  0  0  0  1+ +0  0  0  1  0+
--R                                          Type: List List Matrix PrimeField 2
--E 50

--S 51 of 68
sp1 := meatAxe sp0.1
 
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices
     Representation is not irreducible and it will be split:

                    +0  1  0  0+ +0  1  1  1+
                    |          | |          |
                    |0  0  1  0| |1  1  0  1|
   (4)  [[[1],[1]],[|          |,|          |]]
                    |1  0  0  0| |1  1  1  0|
                    |          | |          |
                    +0  0  0  1+ +1  1  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R     Representation is not irreducible and it will be split:
--R
--R                    +0  1  0  0+ +0  1  1  1+
--R                    |          | |          |
--R                    |0  0  1  0| |1  1  0  1|
--R   (4)  [[[1],[1]],[|          |,|          |]]
--R                    |1  0  0  0| |1  1  1  0|
--R                    |          | |          |
--R                    +0  0  0  1+ +1  1  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 51

--S 52 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp1.2
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (5)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--I   (5)  true
--R                                                                Type: Boolean
--E 52

--S 53 of 68
d2211 := irreducibleRepresentation ([2,2,1,1],genA6)
 

   (6)
    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
    |                                     | |                                 |
    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
    |                                     | |                                 |
    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
    |                                     | |                                 |
   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
    |                                     | |                                 |
    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
    |                                     | |                                 |
    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
    |                                     | |                                 |
    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
                                                    Type: List Matrix Integer
--R 
--R
--R   (6)
--R    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
--R    |                                     | |                                 |
--R    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
--R    |                                     | |                                 |
--R   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
--R    |                                     | |                                 |
--R    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
--R                                                    Type: List Matrix Integer
--E 53

--S 54 of 68
d2211m2 := (d2211::(List Matrix PF 2)); sp2 := meatAxe d2211m2
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

                                      +1  0  0  0  0+ +1  1  1  0  0+
          +1  0  1  1+ +0  0  1  0+   |             | |             |
          |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
          |0  1  0  1| |1  1  1  1|   |             | |             |
   (7)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
          |1  1  0  0| |1  0  1  1|   |             | |             |
          |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
          +0  1  0  0+ +0  1  0  1+   |             | |             |
                                      +0  1  1  1  0+ +1  0  0  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R                                      +1  0  0  0  0+ +1  1  1  0  0+
--R          +1  0  1  1+ +0  0  1  0+   |             | |             |
--R          |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
--R          |0  1  0  1| |1  1  1  1|   |             | |             |
--R   (7)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
--R          |1  1  0  0| |1  0  1  1|   |             | |             |
--R          |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
--R          +0  1  0  0+ +0  1  0  1+   |             | |             |
--R                                      +0  1  1  1  0+ +1  0  0  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 54

--S 55 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp2.1
 
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (8)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 55

--S 56 of 68 random generation, FAILURE OK.
areEquivalent? (sp2.1, sp1.2)
 
   Dimensions of kernels differ

   Representations are not equivalent.

   (9)  [0]
                                                    Type: Matrix PrimeField 2
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Dimensions of kernels differ
--R
--R   Representations are not equivalent.
--R
--R   (9)  [0]
--R                                                    Type: Matrix PrimeField 2
--E 56

--S 57 of 68
dA6d16 := tensorProduct(sp2.1,sp1.2); meatAxe dA6d16
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is irreducible, but we don't know
       whether it is absolutely irreducible

   (10)
   [
      +0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0+
      |                                              |
      |1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
      |                                              |
      |0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
      |                                              |
      |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0|
      |                                              |
      |0  0  0  0  1  0  0  0  1  0  0  0  1  0  0  0|
      |                                              |
      |0  0  0  0  0  1  0  0  0  1  0  0  0  1  0  0|
      |                                              |
      |0  0  0  0  0  0  0  1  0  0  0  1  0  0  0  1|
     [|                                              |,
      |0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      +0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0+
      +0  0  0  0  0  1  1  1  0  1  1  1  0  0  0  0+
      |                                              |
      |0  0  0  0  1  1  1  1  1  1  1  1  0  0  0  0|
      |                                              |
      |0  0  0  0  1  0  1  1  1  0  1  1  0  0  0  0|
      |                                              |
      |0  0  0  0  1  1  0  1  1  1  0  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
      |                                              |
      |0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1|
      |                                              |
      |0  0  0  0  1  0  1  1  0  0  0  0  1  0  1  1|
      |                                              |
      |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
      |                                              |]
      |0  1  1  1  0  1  1  1  0  1  1  1  0  0  0  0|
      |                                              |
      |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
      |                                              |
      |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
      |                                              |
      |1  1  0  1  1  1  0  1  1  1  0  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
      |                                              |
      |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
      |                                              |
      |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
      |                                              |
      +0  0  0  0  1  1  0  1  1  1  0  1  1  1  0  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is irreducible, but we don't know
--R       whether it is absolutely irreducible
--R
--R   (10)
--R   [
--R      +0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0+
--R      |                                              |
--R      |1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R      |                                              |
--R      |0  0  0  0  1  0  0  0  1  0  0  0  1  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  0  0  0  1  0  0  0  1  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  1  0  0  0  1  0  0  0  1|
--R     [|                                              |,
--R      |0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      +0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0+
--R      +0  0  0  0  0  1  1  1  0  1  1  1  0  0  0  0+
--R      |                                              |
--R      |0  0  0  0  1  1  1  1  1  1  1  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  0  1  1  1  0  1  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  1  0  1  1  1  0  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  0  1  1  0  0  0  0  1  0  1  1|
--R      |                                              |
--R      |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
--R      |                                              |]
--R      |0  1  1  1  0  1  1  1  0  1  1  1  0  0  0  0|
--R      |                                              |
--R      |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R      |                                              |
--R      |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R      |                                              |
--R      |1  1  0  1  1  1  0  1  1  1  0  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R      |                                              |
--R      |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R      |                                              |
--R      +0  0  0  0  1  1  0  1  1  1  0  1  1  1  0  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 57

--S 58 of 68
isAbsolutelyIrreducible? dA6d16
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   We have not found a one-dimensional kernel so far,
     as we do a random search you could try again

   (11)  false
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   We have not found a one-dimensional kernel so far,
--R     as we do a random search you could try again
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 58

--S 59 of 68
sp3 := meatAxe (dA6d16 :: (List Matrix FF(2,2)))
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (12)
   [
      +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
      |                                                              |
      |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
      |                                                              |
      |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
      |                                                              |
      |  0       %A    %A + 1    %A      0       1       1       0   |
     [|                                                              |,
      |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
      |                                                              |
      |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
      |                                                              |
      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
      |                                                              |
      +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
      +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
      |                                                          |
      |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
      |                                                          |
      |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
      |                                                          |
      |  %A      1       0       %A    %A    0       1       %A  |
      |                                                          |]
      |  1       1       0     %A + 1  0     1       1       0   |
      |                                                          |
      |  1       %A      1       0     1     0       0       %A  |
      |                                                          |
      |%A + 1    0       1       1     0     %A    %A + 1    1   |
      |                                                          |
      +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
     ,

      +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
      |                                                              |
      |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
      |                                                              |
      |  1       1       %A      %A      1       %A      1     %A + 1|
      |                                                              |
      |  1       0       1     %A + 1  %A + 1    0       %A      1   |
     [|                                                              |,
      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
      |                                                              |
      |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
      |                                                              |
      |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
      |                                                              |
      +  %A      0     %A + 1    0       1       0       1       %A  +
      +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
      |                                                          |
      |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
      |                                                          |
      |  %A    0     1       0     %A + 1    0     %A + 1    1   |
      |                                                          |
      |  1     1   %A + 1    %A      %A      %A      1       0   |
      |                                                          |]
      |  1     %A    0       1       1       %A      1       0   |
      |                                                          |
      |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
      |                                                          |
      |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
      |                                                          |
      +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
     ]
                                      Type: List List Matrix FiniteField(2,2)
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (12)
--R   [
--R      +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
--R      |                                                              |
--R      |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
--R      |                                                              |
--R      |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
--R      |                                                              |
--R      |  0       %A    %A + 1    %A      0       1       1       0   |
--R     [|                                                              |,
--R      |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
--R      |                                                              |
--R      |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
--R      |                                                              |
--R      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R      |                                                              |
--R      +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
--R      +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
--R      |                                                          |
--R      |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
--R      |                                                          |
--R      |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
--R      |                                                          |
--R      |  %A      1       0       %A    %A    0       1       %A  |
--R      |                                                          |]
--R      |  1       1       0     %A + 1  0     1       1       0   |
--R      |                                                          |
--R      |  1       %A      1       0     1     0       0       %A  |
--R      |                                                          |
--R      |%A + 1    0       1       1     0     %A    %A + 1    1   |
--R      |                                                          |
--R      +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
--R     ,
--R
--R      +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
--R      |                                                              |
--R      |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
--R      |                                                              |
--R      |  1       1       %A      %A      1       %A      1     %A + 1|
--R      |                                                              |
--R      |  1       0       1     %A + 1  %A + 1    0       %A      1   |
--R     [|                                                              |,
--R      |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R      |                                                              |
--R      |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
--R      |                                                              |
--R      |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
--R      |                                                              |
--R      +  %A      0     %A + 1    0       1       0       1       %A  +
--R      +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
--R      |                                                          |
--R      |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
--R      |                                                          |
--R      |  %A    0     1       0     %A + 1    0     %A + 1    1   |
--R      |                                                          |
--R      |  1     1   %A + 1    %A      %A      %A      1       0   |
--R      |                                                          |]
--R      |  1     %A    0       1       1       %A      1       0   |
--R      |                                                          |
--R      |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
--R      |                                                          |
--R      |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
--R      |                                                          |
--R      +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
--R     ]
--R                                      Type: List List Matrix FiniteField(2,2)
--E 59

--S 60 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp3.1
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (13)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 60

--S 61 of 68 random generation, FAILURE OK.
isAbsolutelyIrreducible? sp3.2
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (14)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 61

--S 62 of 68 random generation, FAILURE OK.
areEquivalent? (sp3.1,sp3.2)
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     There is no isomorphism, as the only possible one
       fails to do the necessary base change

   Representations are not equivalent.

   (15)  [0]
                                                Type: Matrix FiniteField(2,2)
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     There is no isomorphism, as the only possible one
--R       fails to do the necessary base change
--R
--R   Representations are not equivalent.
--R
--R   (15)  [0]
--R                                                Type: Matrix FiniteField(2,2)
--E 62

--S 63 of 68
sp0.2
 

   (16)  [[1],[1]]
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (16)  [[1],[1]]
--R                                               Type: List Matrix PrimeField 2
--E 63

--S 64 of 68
sp1.2
 

          +0  1  0  0+ +0  1  1  1+
          |          | |          |
          |0  0  1  0| |1  1  0  1|
   (17)  [|          |,|          |]
          |1  0  0  0| |1  1  1  0|
          |          | |          |
          +0  0  0  1+ +1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +0  1  0  0+ +0  1  1  1+
--R          |          | |          |
--R          |0  0  1  0| |1  1  0  1|
--R   (17)  [|          |,|          |]
--R          |1  0  0  0| |1  1  1  0|
--R          |          | |          |
--R          +0  0  0  1+ +1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 64

--S 65 of 68
sp2.1
 

          +1  0  1  1+ +0  0  1  0+
          |          | |          |
          |0  1  0  1| |1  1  1  1|
   (18)  [|          |,|          |]
          |1  1  0  0| |1  0  1  1|
          |          | |          |
          +0  1  0  0+ +0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  1  1+ +0  0  1  0+
--R          |          | |          |
--R          |0  1  0  1| |1  1  1  1|
--R   (18)  [|          |,|          |]
--R          |1  1  0  0| |1  0  1  1|
--R          |          | |          |
--R          +0  1  0  0+ +0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 65

--S 66 of 68
sp3.1
 

   (19)
    +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
    |                                                              |
    |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
    |                                                              |
    |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
    |                                                              |
    |  0       %A    %A + 1    %A      0       1       1       0   |
   [|                                                              |,
    |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
    |                                                              |
    |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
    |                                                              |
    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
    |                                                              |
    +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
    +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
    |                                                          |
    |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
    |                                                          |
    |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
    |                                                          |
    |  %A      1       0       %A    %A    0       1       %A  |
    |                                                          |]
    |  1       1       0     %A + 1  0     1       1       0   |
    |                                                          |
    |  1       %A      1       0     1     0       0       %A  |
    |                                                          |
    |%A + 1    0       1       1     0     %A    %A + 1    1   |
    |                                                          |
    +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (19)
--R    +%A + 1  %A + 1    0       %A      1       %A      %A    %A + 1+
--R    |                                                              |
--R    |  %A      0     %A + 1  %A + 1    1     %A + 1  %A + 1    %A  |
--R    |                                                              |
--R    |  %A    %A + 1    %A      0       1       %A    %A + 1    0   |
--R    |                                                              |
--R    |  0       %A    %A + 1    %A      0       1       1       0   |
--R   [|                                                              |,
--R    |  %A      %A    %A + 1    1     %A + 1    %A      0       %A  |
--R    |                                                              |
--R    |%A + 1    %A    %A + 1    1       %A      0       %A    %A + 1|
--R    |                                                              |
--R    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R    |                                                              |
--R    +  0     %A + 1    %A      0       0       %A    %A + 1  %A + 1+
--R    +  0     %A + 1  %A + 1    %A    1     1       0       %A  +
--R    |                                                          |
--R    |%A + 1  %A + 1    1       0     1   %A + 1    1     %A + 1|
--R    |                                                          |
--R    |  %A      0       1       1     %A  %A + 1  %A + 1    0   |
--R    |                                                          |
--R    |  %A      1       0       %A    %A    0       1       %A  |
--R    |                                                          |]
--R    |  1       1       0     %A + 1  0     1       1       0   |
--R    |                                                          |
--R    |  1       %A      1       0     1     0       0       %A  |
--R    |                                                          |
--R    |%A + 1    0       1       1     0     %A    %A + 1    1   |
--R    |                                                          |
--R    +%A + 1    %A      %A    %A + 1  0   %A + 1    %A      0   +
--R                                           Type: List Matrix FiniteField(2,2)
--E 66

--S 67 of 68
sp3.2
 

   (20)
    +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
    |                                                              |
    |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
    |                                                              |
    |  1       1       %A      %A      1       %A      1     %A + 1|
    |                                                              |
    |  1       0       1     %A + 1  %A + 1    0       %A      1   |
   [|                                                              |,
    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
    |                                                              |
    |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
    |                                                              |
    |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
    |                                                              |
    +  %A      0     %A + 1    0       1       0       1       %A  +
    +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
    |                                                          |
    |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
    |                                                          |
    |  %A    0     1       0     %A + 1    0     %A + 1    1   |
    |                                                          |
    |  1     1   %A + 1    %A      %A      %A      1       0   |
    |                                                          |]
    |  1     %A    0       1       1       %A      1       0   |
    |                                                          |
    |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
    |                                                          |
    |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
    |                                                          |
    +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (20)
--R    +%A + 1    %A      %A      0       %A      1     %A + 1    0   +
--R    |                                                              |
--R    |%A + 1    1       0     %A + 1    1     %A + 1    1       %A  |
--R    |                                                              |
--R    |  1       1       %A      %A      1       %A      1     %A + 1|
--R    |                                                              |
--R    |  1       0       1     %A + 1  %A + 1    0       %A      1   |
--R   [|                                                              |,
--R    |  1       1       1       0     %A + 1  %A + 1    %A      0   |
--R    |                                                              |
--R    |%A + 1    %A      %A      1     %A + 1    1       1     %A + 1|
--R    |                                                              |
--R    |%A + 1  %A + 1    %A      1       0       1       %A      %A  |
--R    |                                                              |
--R    +  %A      0     %A + 1    0       1       0       1       %A  +
--R    +  1     1     %A    %A + 1    0       %A    %A + 1  %A + 1+
--R    |                                                          |
--R    |%A + 1  0     0       1     %A + 1    1       1     %A + 1|
--R    |                                                          |
--R    |  %A    0     1       0     %A + 1    0     %A + 1    1   |
--R    |                                                          |
--R    |  1     1   %A + 1    %A      %A      %A      1       0   |
--R    |                                                          |]
--R    |  1     %A    0       1       1       %A      1       0   |
--R    |                                                          |
--R    |  1     0     1     %A + 1    0     %A + 1    1     %A + 1|
--R    |                                                          |
--R    |  0     1   %A + 1    1       1     %A + 1  %A + 1    1   |
--R    |                                                          |
--R    +  %A    %A  %A + 1  %A + 1    %A      %A      0       1   +
--R                                           Type: List Matrix FiniteField(2,2)
--E 67

--S 68 of 68
dA6d16
 

   (21)
    +0  1  0  0  0  0  0  0  0  1  0  0  0  1  0  0+
    |                                              |
    |0  0  1  0  0  0  0  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  0  0  0  0  0  0  0  1  0  0  0  1  0  0  0|
    |                                              |
    |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  1|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  1  0  0|
    |                                              |
    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |0  0  0  0  1  0  0  0  0  0  0  0  1  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  1|
   [|                                              |,
    |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    +0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0+
    +0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0+
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  1  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  1  1  0  0  0  0|
    |                                              |
    |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
    |                                              |
    |1  1  0  1  1  1  0  1  1  1  0  1  1  1  0  1|
    |                                              |
    |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |]
    |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
    |                                              |
    |1  1  0  1  0  0  0  0  1  1  0  1  1  1  0  1|
    |                                              |
    |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
    |                                              |
    |1  1  1  1  0  0  0  0  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
    |                                              |
    |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
    |                                              |
    |0  0  0  0  1  1  1  0  0  0  0  0  1  1  1  0|
    |                                              |
    +0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (21)
--R    +0  1  0  0  0  0  0  0  0  1  0  0  0  1  0  0+
--R    |                                              |
--R    |0  0  1  0  0  0  0  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  0  0  0  0  0  0  0  1  0  0  0  1  0  0  0|
--R    |                                              |
--R    |0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  1  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |0  0  0  0  1  0  0  0  0  0  0  0  1  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  1|
--R   [|                                              |,
--R    |0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0+
--R    +0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  1  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
--R    |                                              |
--R    |1  1  0  1  1  1  0  1  1  1  0  1  1  1  0  1|
--R    |                                              |
--R    |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |]
--R    |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
--R    |                                              |
--R    |1  1  0  1  0  0  0  0  1  1  0  1  1  1  0  1|
--R    |                                              |
--R    |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
--R    |                                              |
--R    |1  1  1  1  0  0  0  0  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  1  1  0  0  0  0  0  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  1  0  1  0  0  0  0  1  1  0  1|
--R    |                                              |
--R    |0  0  0  0  1  1  1  0  0  0  0  0  1  1  1  0|
--R    |                                              |
--R    +0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 68
)spool 
 
Starts dribbling to operator.output (2010/3/27, 18:30:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
dx := operator("D") :: OP(POLY FRAC INT)
 

   (2)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (2)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 2

--S 3 of 6
evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT)
 

   (3)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (3)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 3

--S 4 of 6
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 6
L 15
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

   (5)
     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
       2048          2048           2048           2048          2048
   + 
       2909907  5   255255  3   6435
     - ------- x  + ------ x  - ---- x
         2048        2048       2048
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R   (5)
--R     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
--R     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       2909907  5   255255  3   6435
--R     - ------- x  + ------ x  - ---- x
--R         2048        2048       2048
--R                                            Type: Polynomial Fraction Integer
--E 5

--S 6 of 6
E 15
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                       2      2
   (6)  240 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                       2      2
--R   (6)  240 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 6
)spool 
 
Starts dribbling to mfinfact.output (2010/3/27, 18:29:55).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 13
p:POLY PF 7 :=6*x +6*y +6*z +x^49+y^49+z^49
 

         49         49         49
   (1)  z   + 6z + y   + 6y + x   + 6x
                                                Type: Polynomial PrimeField 7
--R 
--R
--R         49         49         49
--R   (1)  z   + 6z + y   + 6y + x   + 6x
--R                                                Type: Polynomial PrimeField 7
--E 1

--S 2 of 13
factor p
 

   (2)
     (z + y + x + 1)(z + y + x + 2)(z + y + x + 3)(z + y + x + 4)(z + y + x + 5)
  *
     (z + y + x + 6)(z + y + x)
  *
       2                     2                2
     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 4)
  *
       2                     2                2
     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 6)
  *
       2                     2                2
     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 2)
  *
       2                     2                2
     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 1)
  *
       2                     2                2
     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 6)
  *
       2                     2                2
     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 1)
  *
       2                     2                2
     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 6)
  *
       2                     2                2
     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 2)
  *
       2                     2                2
     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 5)
  *
       2                     2                2
     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 3)
  *
       2                     2                2
     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 4)
  *
       2                     2                2
     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 6)
  *
       2                 2           2
     (z  + (2y + 2x)z + y  + 2x y + x  + 1)
  *
     2                 2           2       2                 2           2
   (z  + (2y + 2x)z + y  + 2x y + x  + 2)(z  + (2y + 2x)z + y  + 2x y + x  + 4)
                                       Type: Factored Polynomial PrimeField 7
--R 
--R
--R   (2)
--R     (z + y + x + 1)(z + y + x + 2)(z + y + x + 3)(z + y + x + 4)(z + y + x + 5)
--R  *
--R     (z + y + x + 6)(z + y + x)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 4)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 1)z + y  + (2x + 1)y + x  + x + 6)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 2)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 2)z + y  + (2x + 2)y + x  + 2x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 1)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 3)z + y  + (2x + 3)y + x  + 3x + 6)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 1)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 4)z + y  + (2x + 4)y + x  + 4x + 6)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 2)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 5)z + y  + (2x + 5)y + x  + 5x + 5)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 3)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 4)
--R  *
--R       2                     2                2
--R     (z  + (2y + 2x + 6)z + y  + (2x + 6)y + x  + 6x + 6)
--R  *
--R       2                 2           2
--R     (z  + (2y + 2x)z + y  + 2x y + x  + 1)
--R  *
--R     2                 2           2       2                 2           2
--R   (z  + (2y + 2x)z + y  + 2x y + x  + 2)(z  + (2y + 2x)z + y  + 2x y + x  + 4)
--R                                       Type: Factored Polynomial PrimeField 7
--E 2

--S 3 of 13
p:POLY PF 7:=(x+3*y+z)*(w*x+y)*(x*y+w**3)
 

   (3)
         2       2    3      4          3             2     3  2
     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
   + 
         3      4    3        4 2
     (w x  + (3w  + w )x)y + w x
                                                Type: Polynomial PrimeField 7
--R 
--R
--R   (3)
--R         2       2    3      4          3             2     3  2
--R     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
--R   + 
--R         3      4    3        4 2
--R     (w x  + (3w  + w )x)y + w x
--R                                                Type: Polynomial PrimeField 7
--E 3

--S 4 of 13
factor p
 

                         3
   (4)  (y + w x)(x y + w )(z + 3y + x)
                                       Type: Factored Polynomial PrimeField 7
--R 
--R
--R                         3
--R   (4)  (y + w x)(x y + w )(z + 3y + x)
--R                                       Type: Factored Polynomial PrimeField 7
--E 4

--S 5 of 13
pp:=p**2
 

   (5)
            2 4        3     3   3     2 4     4 2    6  2      5 3     7
           x y  + (2w x  + 2w x)y  + (w x  + 4w x  + w )y  + (2w x  + 2w x)y
         + 
            8 2
           w x
    *
        2
       z
   + 
           2 5             3     3   4       2       4      4     3  2     6  3
         6x y  + ((5w + 2)x  + 5w x)y  + ((6w  + 4w)x  + (3w  + 4w )x  + 6w )y
       + 
            2 5      5    4  3      7     6    2      5 4      8     7  2
         (2w x  + (5w  + w )x  + (5w  + 2w )x)y  + (4w x  + (6w  + 4w )x )y
       + 
           8 3
         2w x
    *
       z
   + 
       2 6             3     3   5       2           4     4     3  2     6  4
     2x y  + ((4w + 6)x  + 4w x)y  + ((2w  + 5w + 1)x  + (w  + 5w )x  + 2w )y
   + 
         2       5      5     4     3  3      7     6    3
     ((6w  + 2w)x  + (4w  + 3w  + 2w )x  + (4w  + 6w )x)y
   + 
       2 6      5     4  4      8     7    6  2  2      5 5      8     7  3
     (w x  + (5w  + 4w )x  + (2w  + 5w  + w )x )y  + (2w x  + (6w  + 2w )x )y
   + 
      8 4
     w x
                                                Type: Polynomial PrimeField 7
--R 
--R
--R   (5)
--R            2 4        3     3   3     2 4     4 2    6  2      5 3     7
--R           x y  + (2w x  + 2w x)y  + (w x  + 4w x  + w )y  + (2w x  + 2w x)y
--R         + 
--R            8 2
--R           w x
--R    *
--R        2
--R       z
--R   + 
--R           2 5             3     3   4       2       4      4     3  2     6  3
--R         6x y  + ((5w + 2)x  + 5w x)y  + ((6w  + 4w)x  + (3w  + 4w )x  + 6w )y
--R       + 
--R            2 5      5    4  3      7     6    2      5 4      8     7  2
--R         (2w x  + (5w  + w )x  + (5w  + 2w )x)y  + (4w x  + (6w  + 4w )x )y
--R       + 
--R           8 3
--R         2w x
--R    *
--R       z
--R   + 
--R       2 6             3     3   5       2           4     4     3  2     6  4
--R     2x y  + ((4w + 6)x  + 4w x)y  + ((2w  + 5w + 1)x  + (w  + 5w )x  + 2w )y
--R   + 
--R         2       5      5     4     3  3      7     6    3
--R     ((6w  + 2w)x  + (4w  + 3w  + 2w )x  + (4w  + 6w )x)y
--R   + 
--R       2 6      5     4  4      8     7    6  2  2      5 5      8     7  3
--R     (w x  + (5w  + 4w )x  + (2w  + 5w  + w )x )y  + (2w x  + (6w  + 2w )x )y
--R   + 
--R      8 4
--R     w x
--R                                                Type: Polynomial PrimeField 7
--E 5

--S 6 of 13
gcd(p,differentiate(p,x))
 

   (6)  1
                                                Type: Polynomial PrimeField 7
--R 
--R
--R   (6)  1
--R                                                Type: Polynomial PrimeField 7
--E 6

--S 7 of 13
p23:POLY PF 23:=(x+3*y+z)*(w*x+y)*(x*y+w**3)
 

   (7)
         2       2    3      4          3             2     3  2
     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
   + 
         3      4    3        4 2
     (w x  + (3w  + w )x)y + w x
                                               Type: Polynomial PrimeField 23
--R 
--R
--R   (7)
--R         2       2    3      4          3             2     3  2
--R     (x y  + (w x  + w )y + w x)z + 3x y  + ((3w + 1)x  + 3w )y
--R   + 
--R         3      4    3        4 2
--R     (w x  + (3w  + w )x)y + w x
--R                                               Type: Polynomial PrimeField 23
--E 7

--S 8 of 13
factor(p23)
 

                         3
   (8)  (y + w x)(x y + w )(z + 3y + x)
                                      Type: Factored Polynomial PrimeField 23
--R 
--R
--R                         3
--R   (8)  (y + w x)(x y + w )(z + 3y + x)
--R                                      Type: Factored Polynomial PrimeField 23
--E 8

--S 9 of 13
q: POLY PF 2 := y**4 + y**3 + x**4 + x**2
 

         4    3    4    2
   (9)  y  + y  + x  + x
                                                Type: Polynomial PrimeField 2
--R 
--R
--R         4    3    4    2
--R   (9)  y  + y  + x  + x
--R                                                Type: Polynomial PrimeField 2
--E 9

--S 10 of 13
factor q
 

          4    3    4    2
   (10)  y  + y  + x  + x
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R          4    3    4    2
--R   (10)  y  + y  + x  + x
--R                                       Type: Factored Polynomial PrimeField 2
--E 10

--S 11 of 13
factor(q*(q+1))
 

           4    3    4    2       4    3    4    2
   (11)  (y  + y  + x  + x  + 1)(y  + y  + x  + x )
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R           4    3    4    2       4    3    4    2
--R   (11)  (y  + y  + x  + x  + 1)(y  + y  + x  + x )
--R                                       Type: Factored Polynomial PrimeField 2
--E 11

--S 12 of 13
q:=x**2*y**2+z
 

              2 2
   (12)  z + x y
                                                Type: Polynomial PrimeField 2
--R 
--R
--R              2 2
--R   (12)  z + x y
--R                                                Type: Polynomial PrimeField 2
--E 12

--S 13 of 13
factor(q*(1+q))
 

               2 2           2 2
   (13)  (z + x y  + 1)(z + x y )
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R               2 2           2 2
--R   (13)  (z + x y  + 1)(z + x y )
--R                                       Type: Factored Polynomial PrimeField 2
--E 13
)spool 
 
Starts dribbling to cycles1.output (2010/3/27, 18:24:40).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from CycleIndicatorsXmpPage

)expose EVALCYC
 
   EvaluateCycleIndicators is now explicitly exposed in frame initial 
 
--S 1 of 46
complete 1
 

   (1)  (1)
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (1)  (1)
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 1

--S 2 of 46
complete 2
 

        1       1   2
   (2)  - (2) + - (1 )
        2       2
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1   2
--R   (2)  - (2) + - (1 )
--R        2       2
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 2

--S 3 of 46
complete 3
 

        1       1         1   3
   (3)  - (3) + - (2 1) + - (1 )
        3       2         6
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1         1   3
--R   (3)  - (3) + - (2 1) + - (1 )
--R        3       2         6
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 3

--S 4 of 46
complete 7
 

   (4)
     1       1          1          1     2     1         1            1     3
     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
      1      5      1    7
     --- (2 1 ) + ---- (1 )
     240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (4)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R      1      5      1    7
--R     --- (2 1 ) + ---- (1 )
--R     240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 4

--S 5 of 46
elementary 7
 

   (5)
     1       1          1          1     2     1         1            1     3
     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
        1      5      1    7
     - --- (2 1 ) + ---- (1 )
       240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (5)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R        1      5      1    7
--R     - --- (2 1 ) + ---- (1 )
--R       240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 5

--S 6 of 46
alternating 7
 

   (6)
     2       1     2    1           1   2      1     2     1     4     1   2 3
     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
     7       5          4           9         12          36          24
   + 
       1    7
     ---- (1 )
     2520
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (6)
--R     2       1     2    1           1   2      1     2     1     4     1   2 3
--R     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
--R     7       5          4           9         12          36          24
--R   + 
--R       1    7
--R     ---- (1 )
--R     2520
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 6

--S 7 of 46
cyclic 7
 

        6       1   7
   (7)  - (7) + - (1 )
        7       7
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        6       1   7
--R   (7)  - (7) + - (1 )
--R        7       7
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 7

--S 8 of 46
dihedral 7
 

        3       1   3      1   7
   (8)  - (7) + - (2 1) + -- (1 )
        7       2         14
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        3       1   3      1   7
--R   (8)  - (7) + - (2 1) + -- (1 )
--R        7       2         14
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 8

--S 9 of 46
graphs 5
 

   (9)
   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
   6           5        4         6         8          12          120
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (9)
--R   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
--R   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
--R   6           5        4         6         8          12          120
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 9

--S 10 of 46
cap(complete 2**2, complete 2*complete 1**2)
 

   (10)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (10)  4
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 46
cap(elementary 2**2, complete 2*complete 1**2)
 

   (11)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  2
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 46
cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)
 

   (12)  24
                                                       Type: Fraction Integer
--R 
--R
--R   (12)  24
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 46
cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)
 

   (13)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  8
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 46
cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)
 

   (14)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (14)  8
--R                                                       Type: Fraction Integer
--E 14

--S 15 of 46
eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))
 

   (15)  1500
                                                       Type: Fraction Integer
--R 
--R
--R   (15)  1500
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 46
square:=dihedral 4
 

         1       3   2    1     2    1   4
   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
         4       8        4          8
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1       3   2    1     2    1   4
--R   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
--R         4       8        4          8
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 16

--S 17 of 46
cap(complete 2**2,square)
 

   (17)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  2
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 46
cap(complete 3*complete 2**2,dihedral 7)
 

   (18)  18
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  18
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 46
cap(graphs 5,complete 7*complete 3)
 

   (19)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (19)  4
--R                                                       Type: Fraction Integer
--E 19

--S 20 of 46
s(x) == powerSum(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 46
cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)
 
   Compiling function s with type PositiveInteger -> 
      SymmetricPolynomial Fraction Integer 

         1   2    1   2 2    3   4     1   8
   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
         4        3          8        24
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R   Compiling function s with type PositiveInteger -> 
--R      SymmetricPolynomial Fraction Integer 
--R
--R         1   2    1   2 2    3   4     1   8
--R   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
--R         4        3          8        24
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 21

--S 22 of 46
cap(complete 4**2,cube)
 

   (22)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  7
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))
 

   (23)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (23)  7
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))
 

   (24)  17
                                                       Type: Fraction Integer
--R 
--R
--R   (24)  17
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))
 

   (25)  10
                                                       Type: Fraction Integer
--R 
--R
--R   (25)  10
--R                                                       Type: Fraction Integer
--E 25

--S 26 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))
 

   (26)  23
                                                       Type: Fraction Integer
--R 
--R
--R   (26)  23
--R                                                       Type: Fraction Integer
--E 26

--S 27 of 46
x: ULS(FRAC INT,'x,0) := 'x
 

   (27)  x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (27)  x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 27

--S 28 of 46
ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 46
Integers: INT -> ULS(FRAC INT, 'x, 0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 46
ZeroOrOne n == 1+x**n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 46
ZeroOrOne 5
 
   Compiling function ZeroOrOne with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5
   (31)  1 + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function ZeroOrOne with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5
--R   (31)  1 + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 31

--S 32 of 46
Integers n == 1/(1-x**n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 46
Integers 5
 
   Compiling function Integers with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5    10      11
   (33)  1 + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function Integers with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5    10      11
--R   (33)  1 + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 33

--S 34 of 46
eval(ZeroOrOne, graphs 5)
 

                   2     3     4     5     6     7     8    9    10      11
   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6     7     8    9    10      11
--R   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 34

--S 35 of 46
eval(ZeroOrOne,dihedral 8)
 

                   2     3     4     5     6    7    8
   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 35

--S 36 of 46
eval(Integers,complete 4)
 

   (36)
             2     3     4     5     6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (36)
--R             2     3     4     5     6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 36

--S 37 of 46
eval(Integers,elementary 4)
 

   (37)
      6    7     8     9     10     11     12      13      14      15      16
     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
   + 
        17
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (37)
--R      6    7     8     9     10     11     12      13      14      15      16
--R     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
--R   + 
--R        17
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 37

--S 38 of 46
eval(ZeroOrOne,cube)
 

                   2     3     4     5     6    7    8
   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 38

--S 39 of 46
eval(Integers,cube)
 

   (39)
               2     3      4      5      6       7       8       9       10
     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (39)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 39

--S 40 of 46
eval(Integers,graphs 5)
 

   (40)
               2     3      4      5      6       7       8       9       10
     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (40)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 40

--S 41 of 46
eval(ZeroOrOne ,graphs 15)
 

   (41)
               2     3      4      5      6       7       8        9        10
     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (41)
--R               2     3      4      5      6       7       8        9        10
--R     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 41

--S 42 of 46
cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)
 

   (42)  49958972383320
                                                       Type: Fraction Integer
--R 
--R
--R   (42)  49958972383320
--R                                                       Type: Fraction Integer
--E 42

--S 43 of 46
sf3221:= SFunction [3,2,2,1]
 

   (43)
      1          1     2     1   2     1            1     4     1   2
     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
     12         12          16        12           24          36
   + 
      1   2 2     1     2      1       3     1     5     1    4     1   3 2
     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
     36          24           36            72          192        48
   + 
      1   2 4     1      6     1    8
     -- (2 1 ) - --- (2 1 ) + --- (1 )
     96          144          576
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (43)
--R      1          1     2     1   2     1            1     4     1   2
--R     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
--R     12         12          16        12           24          36
--R   + 
--R      1   2 2     1     2      1       3     1     5     1    4     1   3 2
--R     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
--R     36          24           36            72          192        48
--R   + 
--R      1   2 4     1      6     1    8
--R     -- (2 1 ) - --- (2 1 ) + --- (1 )
--R     96          144          576
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 43

--S 44 of 46
cap(sf3221,complete 2**4)
 

   (44)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (44)  3
--R                                                       Type: Fraction Integer
--E 44

--S 45 of 46
cap(sf3221, powerSum 1**8)
 

   (45)  70
                                                       Type: Fraction Integer
--R 
--R
--R   (45)  70
--R                                                       Type: Fraction Integer
--E 45

--S 46 of 46
eval(Integers, sf3221)
 

   (46)
      9     10     11      12      13      14      15       16       17       18
     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
   + 
         19      20
     432x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (46)
--R      9     10     11      12      13      14      15       16       17       18
--R     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
--R   + 
--R         19      20
--R     432x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 46
)spool
 
Starts dribbling to tutchap1.output (2010/3/27, 18:41:32).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 19
1+1
 

   (1)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 19
123^45
 

   (2)
  1111040818513195628591079058717645191855915321226802182362907319986611100124_
   2743283966127048043
                                                        Type: PositiveInteger
--R 
--R
--R   (2)
--R  1111040818513195628591079058717645191855915321226802182362907319986611100124_
--R   2743283966127048043
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 19
2^(3+4)
 

   (3)  128
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  128
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 19
4/3
 

        4
   (4)  -
        3
                                                       Type: Fraction Integer
--R 
--R
--R        4
--R   (4)  -
--R        3
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 19
2/2
 

   (5)  1
                                                       Type: Fraction Integer
--R 
--R
--R   (5)  1
--R                                                       Type: Fraction Integer
--E 5

--S 6 of 19
a := 2
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 19
b := a
 

   (7)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  2
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 19
a := 3
 

   (8)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  3
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 19
b
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 19
i : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 19
i := 2/3
 
 
Daly Bug
   Cannot convert right-hand side of assignment
   2
   -
   3

      to an object of the type Integer of the left-hand side.
--R 
--R 
--RDaly Bug
--R   Cannot convert right-hand side of assignment
--R   2
--R   -
--R   3
--R
--R      to an object of the type Integer of the left-hand side.
--E 11

--S 12 of 19
i := 4/2
 

   (11)  2
                                                                Type: Integer
--R 
--R
--R   (11)  2
--R                                                                Type: Integer
--E 12

--S 13 of 19
c : PositiveInteger := 3
 

   (12)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  3
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 19
(j, k, l) : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 19
)display names
 

Names of User-Defined Objects in the Workspace:

%    a    b    c    i    j    k    l    

Names of System-Defined Objects in the Workspace:

%e                %i                %infinity         %minusInfinity    
%pi               %plusInfinity     SF                
--R 
--R
--RNames of User-Defined Objects in the Workspace:
--R
--R%    a    b    c    i    j    k    l    
--R
--RNames of System-Defined Objects in the Workspace:
--R
--R%e                %i                %infinity         %minusInfinity    
--R%pi               %plusInfinity     SF                
--E 15

)clear properties c i
 

--S 16 of 19
%%(1)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 19
1 + %%(-3)
 

   (15)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  4
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 19
1 _
  +_
  2
 

   (16)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  3
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 19
7 * 8 -- In the next chapter we shall move beyond elementary arithmetic.
 

   (17)  56
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  56
--R                                                        Type: PositiveInteger
--E 19
)spool 
 
Starts dribbling to algaggr.output (2010/3/27, 18:22:59).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 28
l := [1,4,2,-6,0,3,5,4,2,3]
 

   (1)  [1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 1

--S 2 of 28
m := list 555555
 

   (2)  [555555]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [555555]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 28
concat(5,l)
 

   (3)  [5,1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (3)  [5,1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 3

--S 4 of 28
concat(m,l)
 

   (4)  [555555,1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (4)  [555555,1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 4

--S 5 of 28
removeDuplicates l
 

   (5)  [1,4,2,- 6,0,3,5]
                                                           Type: List Integer
--R 
--R
--R   (5)  [1,4,2,- 6,0,3,5]
--R                                                           Type: List Integer
--E 5

--S 6 of 28
first l
 

   (6)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  1
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 28
rest l
 

   (7)  [4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (7)  [4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 7

--S 8 of 28
last l
 

   (8)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  3
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 28
#l
 

   (9)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  10
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 28
l
 

   (10)  [1,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (10)  [1,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 10

--S 11 of 28
first(l,3)
 

   (11)  [1,4,2]
                                                           Type: List Integer
--R 
--R
--R   (11)  [1,4,2]
--R                                                           Type: List Integer
--E 11

--S 12 of 28
rest(l,3)
 

   (12)  [- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (12)  [- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 12

--S 13 of 28
l.1
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 28
l.2
 

   (14)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  4
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 28
l.(#l)
 

   (15)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  3
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 28
l.1 := 1000000000
 

   (16)  1000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  1000000000
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 28
l
 

   (17)  [1000000000,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (17)  [1000000000,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 17

--S 18 of 28
insert(10,l,4)
 

   (18)  [1000000000,4,2,10,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (18)  [1000000000,4,2,10,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 18

--S 19 of 28
insert(2,l,1)
 

   (19)  [2,1000000000,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (19)  [2,1000000000,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 19

--S 20 of 28
position(-6,l)
 

   (20)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  4
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 28
reverse l
 

   (21)  [3,2,4,5,3,0,- 6,2,4,1000000000]
                                                           Type: List Integer
--R 
--R
--R   (21)  [3,2,4,5,3,0,- 6,2,4,1000000000]
--R                                                           Type: List Integer
--E 21

--S 22 of 28
l
 

   (22)  [1000000000,4,2,- 6,0,3,5,4,2,3]
                                                           Type: List Integer
--R 
--R
--R   (22)  [1000000000,4,2,- 6,0,3,5,4,2,3]
--R                                                           Type: List Integer
--E 22

--S 23 of 28
m := [4,2,3,6,5,7,-9,1,2,3,2]
 

   (23)  [4,2,3,6,5,7,- 9,1,2,3,2]
                                                           Type: List Integer
--R 
--R
--R   (23)  [4,2,3,6,5,7,- 9,1,2,3,2]
--R                                                           Type: List Integer
--E 23

--S 24 of 28
sl:SET(INT) := brace l
 

   (24)  {- 6,0,2,3,4,5,1000000000}
                                                            Type: Set Integer
--R 
--R
--R   (24)  {- 6,0,2,3,4,5,1000000000}
--R                                                            Type: Set Integer
--E 24

--S 25 of 28
sm:SET(INT) := brace m
 

   (25)  {- 9,1,2,3,4,5,6,7}
                                                            Type: Set Integer
--R 
--R
--R   (25)  {- 9,1,2,3,4,5,6,7}
--R                                                            Type: Set Integer
--E 25

--S 26 of 28
difference(sl, sm)
 

   (26)  {- 6,0,1000000000}
                                                            Type: Set Integer
--R 
--R
--R   (26)  {- 6,0,1000000000}
--R                                                            Type: Set Integer
--E 26

--S 27 of 28
intersect(sl,sm)
 

   (27)  {2,3,4,5}
                                                            Type: Set Integer
--R 
--R
--R   (27)  {2,3,4,5}
--R                                                            Type: Set Integer
--E 27

--S 28 of 28
union(sl,sm)
 

   (28)  {- 9,- 6,0,1,2,3,4,5,6,7,1000000000}
                                                            Type: Set Integer
--R 
--R
--R   (28)  {- 9,- 6,0,1,2,3,4,5,6,7,1000000000}
--R                                                            Type: Set Integer
--E 28
)spool 
 
Starts dribbling to lodo1.output (2010/3/27, 18:28:45).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
RFZ := Fraction UnivariatePolynomial('x, Integer)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 20
x : RFZ := 'x
 

   (2)  x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (2)  x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 2

--S 3 of 20
Dx : LODO1 RFZ := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 3

--S 4 of 20
b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 4

--S 5 of 20
a : LODO1 RFZ := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 5

--S 6 of 20
p := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 6

--S 7 of 20
(a*b - b*a) p
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 20
ld := leftDivide(a,b)
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 8

--S 9 of 20
a = b * ld.quotient + ld.remainder
 

           3 3       2        2         7     3 3       2        2         7
   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
                                        x                                  x
Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7     3 3       2        2         7
--R   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                        x                                  x
--RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 9

--S 10 of 20
rd := rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 10

--S 11 of 20
a = rd.quotient * b + rd.remainder
 

            3 3       2        2         7     3 3       2        2         7
   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
                                         x                                  x
Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7     3 3       2        2         7
--R   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                         x                                  x
--RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 11

--S 12 of 20
rightQuotient(a,b)
 

   (12)  5x D + 7
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (12)  5x D + 7
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 12

--S 13 of 20
rightRemainder(a,b)
 

               5
   (13)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (13)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 20
leftExactQuotient(a,b)
 

   (14)  5x D + 7
Type: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...)
--R 
--R
--R   (14)  5x D + 7
--RType: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...)
--E 14

--S 15 of 20
e := leftGcd(a,b)
 

           2 2        1
   (15)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (15)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 20
leftRemainder(a, e)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 20
rightRemainder(a, e)
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18 of 20
f := rightLcm(a,b)
 

            3 3       2        2         7
   (18)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (18)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 18

--S 19 of 20
rightRemainder(f, b)
 

               5
   (19)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (19)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 20
leftRemainder(f, b)
 

   (20)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (20)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 20
)spool 
 
Starts dribbling to schaum26.output (2010/3/27, 18:38:33).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 43
aa:=integrate(log(x),x)
 

   (1)  x log(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  x log(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 43
bb:=x*log(x)-x
 

   (2)  x log(x) - x
                                                     Type: Expression Integer
--R
--R   (2)  x log(x) - x
--R                                                     Type: Expression Integer
--E

--S 3 of 43      14:525 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 43
aa:=integrate(x*log(x),x)
 

          2          2
        2x log(x) - x
   (1)  --------------
               4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2          2
--R        2x log(x) - x
--R   (1)  --------------
--R               4
--R                                          Type: Union(Expression Integer,...)
--E

--S 5 of 43
bb:=x^2/2*(log(x)-1/2)
 

          2          2
        2x log(x) - x
   (2)  --------------
               4
                                                     Type: Expression Integer
--R
--R          2          2
--R        2x log(x) - x
--R   (2)  --------------
--R               4
--R                                                     Type: Expression Integer
--E 

--S 6 of 43      14:526 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 43
aa:=integrate(x^m*log(x),x)
 

                               m log(x)
        ((m + 1)x log(x) - x)%e
   (1)  -------------------------------
                   2
                  m  + 2m + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               m log(x)
--R        ((m + 1)x log(x) - x)%e
--R   (1)  -------------------------------
--R                   2
--R                  m  + 2m + 1
--R                                          Type: Union(Expression Integer,...)
--E

--S 8 of 43
bb:=x^(m+1)/(m+1)*(log(x)-1/(m+1))
 

                            m + 1
        ((m + 1)log(x) - 1)x
   (2)  -------------------------
                2
               m  + 2m + 1
                                                     Type: Expression Integer
--R
--R                            m + 1
--R        ((m + 1)log(x) - 1)x
--R   (2)  -------------------------
--R                2
--R               m  + 2m + 1
--R                                                     Type: Expression Integer
--E

--S 9 of 43
cc:=aa-bb
 

                               m log(x)                         m + 1
        ((m + 1)x log(x) - x)%e         + ((- m - 1)log(x) + 1)x
   (3)  -------------------------------------------------------------
                                  2
                                 m  + 2m + 1
                                                     Type: Expression Integer
--R
--R                               m log(x)                         m + 1
--R        ((m + 1)x log(x) - x)%e         + ((- m - 1)log(x) + 1)x
--R   (3)  -------------------------------------------------------------
--R                                  2
--R                                 m  + 2m + 1
--R                                                     Type: Expression Integer
--E

--S 10 of 43
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 11 of 43
dd:=explog cc
 

                              m + 1                         m
        ((- m - 1)log(x) + 1)x      + ((m + 1)x log(x) - x)x
   (5)  -----------------------------------------------------
                              2
                             m  + 2m + 1
                                                     Type: Expression Integer
--R
--R                              m + 1                         m
--R        ((- m - 1)log(x) + 1)x      + ((m + 1)x log(x) - x)x
--R   (5)  -----------------------------------------------------
--R                              2
--R                             m  + 2m + 1
--R                                                     Type: Expression Integer
--E

--S 12 of 43     14:527 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 43
aa:=integrate(log(x)/x,x)
 

              2
        log(x)
   (1)  -------
           2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2
--R        log(x)
--R   (1)  -------
--R           2
--R                                          Type: Union(Expression Integer,...)
--E

--S 14 of 43
bb:=1/2*log(x)^2
 

              2
        log(x)
   (2)  -------
           2
                                                     Type: Expression Integer
--R
--R              2
--R        log(x)
--R   (2)  -------
--R           2
--R                                                     Type: Expression Integer
--E 

--S 15 of 43     14:528 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 43
aa:=integrate(log(x)/x^2,x)
 

        - log(x) - 1
   (1)  ------------
              x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(x) - 1
--R   (1)  ------------
--R              x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17 of 43
bb:=-log(x)/x-1/x
 

        - log(x) - 1
   (2)  ------------
              x
                                                     Type: Expression Integer
--R
--R        - log(x) - 1
--R   (2)  ------------
--R              x
--R                                                     Type: Expression Integer
--E

--S 18 of 43     14:529 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 43
aa:=integrate(log(x)^2,x)
 

                2
   (1)  x log(x)  - 2x log(x) + 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R   (1)  x log(x)  - 2x log(x) + 2x
--R                                          Type: Union(Expression Integer,...)
--E

--S 20 of 43
bb:=x*log(x)^2-2*x*log(x)+2*x
 

                2
   (2)  x log(x)  - 2x log(x) + 2x
                                                     Type: Expression Integer
--R
--R                2
--R   (2)  x log(x)  - 2x log(x) + 2x
--R                                                     Type: Expression Integer
--E 

--S 21 of 43     14:530 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 22 of 43
aa:=integrate(log(x)^n/x,x)
 

                n log(log(x))
        log(x)%e
   (1)  ---------------------
                n + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                n log(log(x))
--R        log(x)%e
--R   (1)  ---------------------
--R                n + 1
--R                                          Type: Union(Expression Integer,...)
--E

--S 23 of 43
bb:=log(x)^(n+1)/(n+1)
 

              n + 1
        log(x)
   (2)  -----------
           n + 1
                                                     Type: Expression Integer
--R
--R              n + 1
--R        log(x)
--R   (2)  -----------
--R           n + 1
--R                                                     Type: Expression Integer
--E 

--S 24 of 43
cc:=aa-bb
 

                n log(log(x))         n + 1
        log(x)%e              - log(x)
   (3)  -----------------------------------
                       n + 1
                                                     Type: Expression Integer
--R
--R                n log(log(x))         n + 1
--R        log(x)%e              - log(x)
--R   (3)  -----------------------------------
--R                       n + 1
--R                                                     Type: Expression Integer
--E

--S 25 of 43
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26 of 43
dd:=explog cc
 

                n + 1               n
        - log(x)      + log(x)log(x)
   (5)  -----------------------------
                    n + 1
                                                     Type: Expression Integer
--R
--R                n + 1               n
--R        - log(x)      + log(x)log(x)
--R   (5)  -----------------------------
--R                    n + 1
--R                                                     Type: Expression Integer
--E

--S 27 of 43     14:531 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 43
aa:=integrate(1/(x*log(x)),x)
 

   (1)  log(log(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  log(log(x))
--R                                          Type: Union(Expression Integer,...)
--E

--S 29 of 43
bb:=log(log(x))
 

   (2)  log(log(x))
                                                     Type: Expression Integer
--R
--R   (2)  log(log(x))
--R                                                     Type: Expression Integer
--E

--S 30 of 43     14:532 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 31 of 43     14:533 Schaums and Axiom agree by definition
aa:=integrate(1/log(x),x)
 

   (1)  li(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  li(x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 32 of 43     14:534 Axiom cannot compute this integral
aa:=integrate(x^m/log(x),x)
 

           x     m
         ++    %J
   (1)   |   ------- d%J
        ++   log(%J)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x     m
--I         ++    %I
--I   (1)   |   ------- d%I
--I        ++   log(%I)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 33 of 43     14:535 Axiom cannot compute this integral
aa:=integrate(log(x)^n,x)
 

           x
         ++         n
   (1)   |   log(%J) d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         n
--I   (1)   |   log(%I) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 34 of 43     14:536 Axiom cannot compute this integral
aa:=integrate(x^m*log(x)^n,x)
 

           x
         ++    m       n
   (1)   |   %J log(%J) d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    m       n
--I   (1)   |   %I log(%I) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 35 of 43
aa:=integrate(log(x^2+a^2),x)
 

               2    2            x
   (1)  x log(x  + a ) + 2a atan(-) - 2x
                                 a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2            x
--R   (1)  x log(x  + a ) + 2a atan(-) - 2x
--R                                 a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36 of 43
bb:=x*log(x^2+a^2)-2*x+2*a*atan(x/a)
 

               2    2            x
   (2)  x log(x  + a ) + 2a atan(-) - 2x
                                 a
                                                     Type: Expression Integer
--R
--R               2    2            x
--R   (2)  x log(x  + a ) + 2a atan(-) - 2x
--R                                 a
--R                                                     Type: Expression Integer
--E

--S 37 of 43     14:537 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 38 of 43
aa:=integrate(log(x^2-a^2),x)
 

               2    2
   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 39 of 43
bb:=x*log(x^2-a^2)-2*x+a*log((x+a)/(x-a))
 

               2    2          x + a
   (2)  x log(x  - a ) + a log(-----) - 2x
                               x - a
                                                     Type: Expression Integer
--R
--R               2    2          x + a
--R   (2)  x log(x  - a ) + a log(-----) - 2x
--R                               x - a
--R                                                     Type: Expression Integer
--E

--S 40 of 43
cc:=aa-bb
 

                                            x + a
   (3)  a log(x + a) - a log(x - a) - a log(-----)
                                            x - a
                                                     Type: Expression Integer
--R
--R                                            x + a
--R   (3)  a log(x + a) - a log(x - a) - a log(-----)
--R                                            x - a
--R                                                     Type: Expression Integer
--E

--S 41 of 43     14:538 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 42 of 43
aa:=integrate(x^m*log(x^2+a^2),x)
 

           x
         ++       2     2   m
   (1)   |   log(a  + %J )%J d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       2     2   m
--I   (1)   |   log(a  + %I )%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 43 of 43     14:539 Axiom cannot compute this integral
aa:=integrate(x^m*log(x^2-a^2),x)
 

           x
         ++         2     2   m
   (1)   |   log(- a  + %J )%J d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         2     2   m
--I   (1)   |   log(- a  + %I )%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to quat.output (2010/3/27, 18:30:52).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 25
q := quatern(2/11,-8,3/4,1)
 

         2        3
   (1)  -- - 8i + - j + k
        11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         2        3
--R   (1)  -- - 8i + - j + k
--R        11        4
--R                                            Type: Quaternion Fraction Integer
--E 1

--S 2 of 25
real q
 

         2
   (2)  --
        11
                                                       Type: Fraction Integer
--R 
--R
--R         2
--R   (2)  --
--R        11
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 25
imagI q
 

   (3)  - 8
                                                       Type: Fraction Integer
--R 
--R
--R   (3)  - 8
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 25
imagJ q
 

        3
   (4)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (4)  -
--R        4
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 25
imagK q
 

   (5)  1
                                                       Type: Fraction Integer
--R 
--R
--R   (5)  1
--R                                                       Type: Fraction Integer
--E 5

--S 6 of 25
inv q
 

          352     15488      484       1936
   (6)  ------ + ------ i - ----- j - ------ k
        126993   126993     42331     126993
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          352     15488      484       1936
--R   (6)  ------ + ------ i - ----- j - ------ k
--R        126993   126993     42331     126993
--R                                            Type: Quaternion Fraction Integer
--E 6
 
--S 7 of 25
q**6
 

          2029490709319345   48251690851     144755072553     48251690851
   (7)  - ---------------- - ----------- i + ------------ j + ----------- k
             7256313856        1288408         41229056         10307264
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2029490709319345   48251690851     144755072553     48251690851
--R   (7)  - ---------------- - ----------- i + ------------ j + ----------- k
--R             7256313856        1288408         41229056         10307264
--R                                            Type: Quaternion Fraction Integer
--E 7

--S 8 of 25
r := quatern(-2,3,23/9,-89)
 

                   23
   (8)  - 2 + 3i + -- j - 89k
                    9
                                            Type: Quaternion Fraction Integer
--R 
--R
--R                   23
--R   (8)  - 2 + 3i + -- j - 89k
--R                    9
--R                                            Type: Quaternion Fraction Integer
--E 8

--S 9 of 25
q + r
 

          20        119
   (9)  - -- - 5i + --- j - 88k
          11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          20        119
--R   (9)  - -- - 5i + --- j - 88k
--R          11         36
--R                                            Type: Quaternion Fraction Integer
--E 9

--S 10 of 25
q - r
 

         24         65
   (10)  -- - 11i - -- j + 90k
         11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         24         65
--R   (10)  -- - 11i - -- j + 90k
--R         11         36
--R                                            Type: Quaternion Fraction Integer
--E 10

--S 11 of 25
q * r
 

         14615   20893     140587     16187
   (11)  ----- - ----- i - ------ j - ----- k
          132     396        198       396
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         14615   20893     140587     16187
--R   (11)  ----- - ----- i - ------ j - ----- k
--R          132     396        198       396
--R                                            Type: Quaternion Fraction Integer
--E 11

--S 12 of 25
r * q
 

         14615   33997     140177     1787
   (12)  ----- + ----- i + ------ j + ---- k
          132     396        198       396
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         14615   33997     140177     1787
--R   (12)  ----- + ----- i + ------ j + ---- k
--R          132     396        198       396
--R                                            Type: Quaternion Fraction Integer
--E 12

--S 13 of 25
i := quatern(0,1,0,0)
 

   (13)  i
                                                     Type: Quaternion Integer
--R 
--R
--R   (13)  i
--R                                                     Type: Quaternion Integer
--E 13

--S 14 of 25
j := quatern(0,0,1,0)
 

   (14)  j
                                                     Type: Quaternion Integer
--R 
--R
--R   (14)  j
--R                                                     Type: Quaternion Integer
--E 14

--S 15 of 25
k := quatern(0,0,0,1)
 

   (15)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (15)  k
--R                                                     Type: Quaternion Integer
--E 15

--S 16 of 25
i*i
 

   (16)  - 1
                                                     Type: Quaternion Integer
--R 
--R
--R   (16)  - 1
--R                                                     Type: Quaternion Integer
--E 16

--S 17 of 25
j*j
 

   (17)  - 1
                                                     Type: Quaternion Integer
--R 
--R
--R   (17)  - 1
--R                                                     Type: Quaternion Integer
--E 17

--S 18 of 25
k*k
 

   (18)  - 1
                                                     Type: Quaternion Integer
--R 
--R
--R   (18)  - 1
--R                                                     Type: Quaternion Integer
--E 18

--S 19 of 25
i*j
 

   (19)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (19)  k
--R                                                     Type: Quaternion Integer
--E 19

--S 20 of 25
j*k
 

   (20)  i
                                                     Type: Quaternion Integer
--R 
--R
--R   (20)  i
--R                                                     Type: Quaternion Integer
--E 20

--S 21 of 25
k*i
 

   (21)  j
                                                     Type: Quaternion Integer
--R 
--R
--R   (21)  j
--R                                                     Type: Quaternion Integer
--E 21

--S 22 of 25
q * i
 

              2         3
   (22)  8 + -- i + j - - k
             11         4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R              2         3
--R   (22)  8 + -- i + j - - k
--R             11         4
--R                                            Type: Quaternion Fraction Integer
--E 22

--S 23 of 25
norm q
 

         126993
   (23)  ------
          1936
                                                       Type: Fraction Integer
--R 
--R
--R         126993
--R   (23)  ------
--R          1936
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 25
conjugate q
 

          2        3
   (24)  -- + 8i - - j - k
         11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2        3
--R   (24)  -- + 8i - - j - k
--R         11        4
--R                                            Type: Quaternion Fraction Integer
--E 24

--S 25 of 25
q * %
 

         126993
   (25)  ------
          1936
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         126993
--R   (25)  ------
--R          1936
--R                                            Type: Quaternion Fraction Integer
--E 25
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read xpr
 
)cl all
 

Word := OrderedFreeMonoid(Symbol)
 

   (1)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
poly:= XPR(Integer,Word)
 

   (2)  XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
                                                                 Type: Domain
p:poly := 2 * x - 3 * y + 1
 

   (3)  1 + 2x - 3y
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
q:poly := 2 * x + 1
 

   (4)  1 + 2x
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
p + q
 

   (5)  2 + 4x - 3y
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
p * q
 

                        2
   (6)  1 + 4x - 3y + 4x  - 6y x
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
(p +q)^2 -p^2 -q^2 - 2*p*q
 

   (7)  - 6x y + 6y x
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
M := SquareMatrix(2,Fraction Integer)
 

   (8)  SquareMatrix(2,Fraction Integer)
                                                                 Type: Domain
poly1:= XPR(M,Word)
 

   (9)
   XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
                                                                 Type: Domain
m1:M := matrix [[i*j**2 for i in 1..2] for j in 1..2]
 

         +1  2+
   (10)  |    |
         +4  8+
                                       Type: SquareMatrix(2,Fraction Integer)
m2:M := m1 - 5/4
 

         +  1    +
         |- -  2 |
         |  4    |
   (11)  |       |
         |     27|
         | 4   --|
         +      4+
                                       Type: SquareMatrix(2,Fraction Integer)
m3: M := m2**2
 

         +129     +
         |---  13 |
         | 16     |
   (12)  |        |
         |     857|
         |26   ---|
         +      16+
                                       Type: SquareMatrix(2,Fraction Integer)
pm:poly1   := m1*x + m2*y + m3*z - 2/3
 

         +  2     +             +  1    +    +129     +
         |- -   0 |             |- -  2 |    |---  13 |
         |  3     |   +1  2+    |  4    |    | 16     |
   (13)  |        | + |    |x + |       |y + |        |z
         |       2|   +4  8+    |     27|    |     857|
         | 0   - -|             | 4   --|    |26   ---|
         +       3+             +      4+    +      16+
Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
qm:poly1 := pm - m1*x
 

         +  2     +   +  1    +    +129     +
         |- -   0 |   |- -  2 |    |---  13 |
         |  3     |   |  4    |    | 16     |
   (14)  |        | + |       |y + |        |z
         |       2|   |     27|    |     857|
         | 0   - -|   | 4   --|    |26   ---|
         +       3+   +      4+    +      16+
Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
qm**3
 

   (15)
     +   8      +   +  1  8+    +43   52 +    +  129       +
     |- --   0  |   |- -  -|    |--   -- |    |- ---  - 26 |
     |  27      |   |  3  3|    | 4    3 |    |   8        | 2
     |          | + |      |y + |        |z + |            |y
     |         8|   |16    |    |104  857|    |         857|
     | 0    - --|   |--   9|    |---  ---|    |- 52   - ---|
     +        27+   + 3    +    + 3    12+    +          8 +
   + 
     +  3199     831 +      +  3199     831 +      +  103169     6409 +
     |- ----   - --- |      |- ----   - --- |      |- ------   - ---- |
     |   32       4  |      |   32       4  |      |    128        4  | 2
     |               |y z + |               |z y + |                  |z
     |  831     26467|      |  831     26467|      |   6409     820977|
     |- ---   - -----|      |- ---   - -----|      | - ----   - ------|
     +   2        32 +      +   2        32 +      +     2        128 +
   + 
     +3199   831 +     +103169   6409 +      +103169   6409 +
     |----   --- |     |------   ---- |      |------   ---- |
     | 64     8  | 3   |  256      8  | 2    |  256      8  |
     |           |y  + |              |y z + |              |y z y
     |831   26467|     | 6409   820977|      | 6409   820977|
     |---   -----|     | ----   ------|      | ----   ------|
     + 4      64 +     +   4      256 +      +   4      256 +
   + 
     +3178239   795341 +       +103169   6409 +       +3178239   795341 +
     |-------   ------ |       |------   ---- |       |-------   ------ |
     |  1024      128  |   2   |  256      8  |   2   |  1024      128  |
     |                 |y z  + |              |z y  + |                 |z y z
     |795341   25447787|       | 6409   820977|       |795341   25447787|
     |------   --------|       | ----   ------|       |------   --------|
     +  64       1024  +       +   4      256 +       +  64       1024  +
   + 
     +3178239   795341 +      +98625409  12326223 +
     |-------   ------ |      |--------  -------- |
     |  1024      128  | 2    |  4096       256   | 3
     |                 |z y + |                   |z
     |795341   25447787|      |12326223  788893897|
     |------   --------|      |--------  ---------|
     +  64       1024  +      +   128       4096  +
Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
)lisp (bye)
 
Starts dribbling to arrows.output (2010/3/27, 18:23:7).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 3
arrowAngle:=%pi-%pi/10.0@SF
 

   (1)  2.8274333882308138
                                                            Type: DoubleFloat
--R 
--R
--R   (1)  2.8274333882308138
--R                                                            Type: DoubleFloat
--E 1

--S 2 of 3
arrowScale:=0.2@SF
 

   (2)  0.20000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  0.20000000000000001
--R                                                            Type: DoubleFloat
--E 2

--S 3 of 3
makeArrow(p1,p2) ==
    delta    :=p2 -p1
    len      := arrowScale * length delta
    theta := atan(delta.1, delta.2)
    c1:= len*cos(theta+arrowAngle)
    s1:= len*sin(theta+arrowAngle)
    c2:= len*cos(theta-arrowAngle)
    s2:= len*sin(theta-arrowAngle)
    z:= p2.3*(1-arrowScale)
    p3:=point[p2.1+c1,p2.2+s1,z,p2.4]
    p4:=point[p2.1+c2,p2.2+s2,z,p2.4]
    [[p1,p2,p3],[p2,p4]]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3
)spool
 
Starts dribbling to schaum29.output (2010/3/27, 18:38:40).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 81
aa:=integrate(sinh(a*x)*cosh(a*x),x)
 

                 2            2
        sinh(a x)  + cosh(a x)
   (1)  -----------------------
                   4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2            2
--R        sinh(a x)  + cosh(a x)
--R   (1)  -----------------------
--R                   4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 81
bb:=sinh(a*x)^2/(2*a)
 

                 2
        sinh(a x)
   (2)  ----------
            2a
                                                     Type: Expression Integer
--R
--R                 2
--R        sinh(a x)
--R   (2)  ----------
--R            2a
--R                                                     Type: Expression Integer
--E

--S 3 of 81
cc:=aa-bb
 

                   2            2
        - sinh(a x)  + cosh(a x)
   (3)  -------------------------
                    4a
                                                     Type: Expression Integer
--R
--R                   2            2
--R        - sinh(a x)  + cosh(a x)
--R   (3)  -------------------------
--R                    4a
--R                                                     Type: Expression Integer
--E

--S 4 of 81
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 81
dd:=sinhsqrrule cc
 

                                 2
        - cosh(2a x) + 2cosh(a x)  + 1
   (5)  ------------------------------
                      8a
                                                     Type: Expression Integer
--R
--R                                 2
--R        - cosh(2a x) + 2cosh(a x)  + 1
--R   (5)  ------------------------------
--R                      8a
--R                                                     Type: Expression Integer
--E

--S 6 of 81
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 7 of 81      14:590 Schaums and Axiom differ by a constant
ee:=coshsqrrule dd
 

         1
   (7)  --
        4a
                                                     Type: Expression Integer
--R
--R         1
--R   (7)  --
--R        4a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 8 of 81
aa:=integrate(sinh(p*x)*cosh(q*x),x)
 

        - q sinh(p x)sinh(q x) + p cosh(p x)cosh(q x)
   (1)  ---------------------------------------------
           2    2          2       2    2          2
         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - q sinh(p x)sinh(q x) + p cosh(p x)cosh(q x)
--R   (1)  ---------------------------------------------
--R           2    2          2       2    2          2
--R         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 81
bb:=(cosh(p+q)*x)/(2*(p+q))+(cosh(p-q)*x)/(2*(p-q))
 

        (q - p)x cosh(q + p) + (- q - p)x cosh(q - p)
   (2)  ---------------------------------------------
                            2     2
                          2q  - 2p
                                                     Type: Expression Integer
--R
--R        (q - p)x cosh(q + p) + (- q - p)x cosh(q - p)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 10 of 81     14:591 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       - 2q sinh(p x)sinh(q x)
     + 
                                                               2
       ((- q + p)x cosh(q + p) + (q + p)x cosh(q - p))sinh(p x)
     + 
       2p cosh(p x)cosh(q x)
     + 
                                                               2
       ((q - p)x cosh(q + p) + (- q - p)x cosh(q - p))cosh(p x)
  /
        2     2          2        2     2          2
     (2q  - 2p )sinh(p x)  + (- 2q  + 2p )cosh(p x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - 2q sinh(p x)sinh(q x)
--R     + 
--R                                                               2
--R       ((- q + p)x cosh(q + p) + (q + p)x cosh(q - p))sinh(p x)
--R     + 
--R       2p cosh(p x)cosh(q x)
--R     + 
--R                                                               2
--R       ((q - p)x cosh(q + p) + (- q - p)x cosh(q - p))cosh(p x)
--R  /
--R        2     2          2        2     2          2
--R     (2q  - 2p )sinh(p x)  + (- 2q  + 2p )cosh(p x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 11 of 81
aa:=integrate(sinh(a*x)^n*cosh(a*x),x)
 

        - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
   (1)  -------------------------------------------------------------------
                                      2                       2
                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
--R   (1)  -------------------------------------------------------------------
--R                                      2                       2
--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12 of 81
bb:=sinh(a*x)/((n+1)*a)
 

        sinh(a x)
   (2)  ---------
         a n + a
                                                     Type: Expression Integer
--R
--R        sinh(a x)
--R   (2)  ---------
--R         a n + a
--R                                                     Type: Expression Integer
--E

--S 13 of 81     14:592 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
     + 
                  3            2
       - sinh(a x)  + cosh(a x) sinh(a x)
  /
                       2                       2
     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
--R     + 
--R                  3            2
--R       - sinh(a x)  + cosh(a x) sinh(a x)
--R  /
--R                       2                       2
--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 14 of 81
aa:=integrate(cosh(a*x)^n*sinh(a*x),x)
 

        - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
   (1)  -------------------------------------------------------------------
                                      2                       2
                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
--R   (1)  -------------------------------------------------------------------
--R                                      2                       2
--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 15 of 81
bb:=cosh(a*x)^(n+1)/((n+1)*a)
 

                 n + 1
        cosh(a x)
   (2)  --------------
            a n + a
                                                     Type: Expression Integer
--R
--R                 n + 1
--R        cosh(a x)
--R   (2)  --------------
--R            a n + a
--R                                                     Type: Expression Integer
--E

--S 16 of 81     14:593 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
     + 
                   2            2          n + 1
       (- sinh(a x)  + cosh(a x) )cosh(a x)
  /
                       2                       2
     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
--R     + 
--R                   2            2          n + 1
--R       (- sinh(a x)  + cosh(a x) )cosh(a x)
--R  /
--R                       2                       2
--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 17 of 81
aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
 

                          3            3
        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
   (1)  -----------------------------------------------
                               8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          3            3
--R        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
--R   (1)  -----------------------------------------------
--R                               8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 18 of 81
bb:=sinh(4*a*x)/(32*a)-x/8
 

        sinh(4a x) - 4a x
   (2)  -----------------
               32a
                                                     Type: Expression Integer
--R
--R        sinh(4a x) - 4a x
--R   (2)  -----------------
--R               32a
--R                                                     Type: Expression Integer
--E

--S 19 of 81     14:594 Schaums and Axiom agree
cc:=complexNormalize(aa-bb)
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 20 of 81
aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x)
 

                      2cosh(a x)                     2sinh(a x)
        - log(- ---------------------) + log(- ---------------------)
                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   (1)  -------------------------------------------------------------
                                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2cosh(a x)                     2sinh(a x)
--R        - log(- ---------------------) + log(- ---------------------)
--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   (1)  -------------------------------------------------------------
--R                                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21 of 81
bb:=1/a*log(tanh(a*x))
 

        log(tanh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(tanh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 22 of 81
cc:=aa-bb
 

   (3)
                                      2cosh(a x)
       - log(tanh(a x)) - log(- ---------------------)
                                sinh(a x) - cosh(a x)
     + 
                   2sinh(a x)
       log(- ---------------------)
             sinh(a x) - cosh(a x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      2cosh(a x)
--R       - log(tanh(a x)) - log(- ---------------------)
--R                                sinh(a x) - cosh(a x)
--R     + 
--R                   2sinh(a x)
--R       log(- ---------------------)
--R             sinh(a x) - cosh(a x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 23 of 81
dd:=expandLog cc
 

        - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x))
   (4)  --------------------------------------------------
                                 a
                                                     Type: Expression Integer
--R
--R        - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x))
--R   (4)  --------------------------------------------------
--R                                 a
--R                                                     Type: Expression Integer
--E

--S 24 of 81
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (5)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (5)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25 of 81
ee:=tanhrule dd
 

                             sinh(a x)
        log(sinh(a x)) - log(---------) - log(cosh(a x))
                             cosh(a x)
   (6)  ------------------------------------------------
                                a
                                                     Type: Expression Integer
--R
--R                             sinh(a x)
--R        log(sinh(a x)) - log(---------) - log(cosh(a x))
--R                             cosh(a x)
--R   (6)  ------------------------------------------------
--R                                a
--R                                                     Type: Expression Integer
--E

--S 26 of 81     14:595 Schaums and Axiom agree
ff:=expandLog ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 81
aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)),x)
 

   (1)
                      2                                   2
         (- 2sinh(a x)  - 4cosh(a x)sinh(a x) - 2cosh(a x)  + 2)
      *
         atan(sinh(a x) + cosh(a x))
     + 
       - 2sinh(a x) - 2cosh(a x)
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                      2                                   2
--R         (- 2sinh(a x)  - 4cosh(a x)sinh(a x) - 2cosh(a x)  + 2)
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R       - 2sinh(a x) - 2cosh(a x)
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28 of 81
bb:=-1/a*atan(sinh(a*x)-csch(a*x))/a
 

          atan(sinh(a x) - csch(a x))
   (2)  - ---------------------------
                        2
                       a
                                                     Type: Expression Integer
--R
--R          atan(sinh(a x) - csch(a x))
--R   (2)  - ---------------------------
--R                        2
--R                       a
--R                                                     Type: Expression Integer
--E

--S 29 of 81     14:596 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                        2                                       2
         (- 2a sinh(a x)  - 4a cosh(a x)sinh(a x) - 2a cosh(a x)  + 2a)
      *
         atan(sinh(a x) + cosh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
         atan(sinh(a x) - csch(a x))
     + 
       - 2a sinh(a x) - 2a cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                        2                                       2
--R         (- 2a sinh(a x)  - 4a cosh(a x)sinh(a x) - 2a cosh(a x)  + 2a)
--R      *
--R         atan(sinh(a x) + cosh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R         atan(sinh(a x) - csch(a x))
--R     + 
--R       - 2a sinh(a x) - 2a cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 30 of 81
aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x)
 

   (1)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
       2sinh(a x) + 2cosh(a x)
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       2sinh(a x) + 2cosh(a x)
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 31 of 81
bb:=sech(a*x)/a+1/a*log(tanh((a*x)/2))
 

                 a x
        log(tanh(---)) + sech(a x)
                  2
   (2)  --------------------------
                     a
                                                     Type: Expression Integer
--R
--R                 a x
--R        log(tanh(---)) + sech(a x)
--R                  2
--R   (2)  --------------------------
--R                     a
--R                                                     Type: Expression Integer
--E

--S 32 of 81
cc:=aa-bb
 

   (3)
                   2                                  2              a x
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(tanh(---))
                                                                      2
     + 
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                           2
       - sech(a x)sinh(a x)  + (- 2cosh(a x)sech(a x) + 2)sinh(a x)
     + 
                   2
       (- cosh(a x)  - 1)sech(a x) + 2cosh(a x)
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2              a x
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(tanh(---))
--R                                                                      2
--R     + 
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                           2
--R       - sech(a x)sinh(a x)  + (- 2cosh(a x)sech(a x) + 2)sinh(a x)
--R     + 
--R                   2
--R       (- cosh(a x)  - 1)sech(a x) + 2cosh(a x)
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 33 of 81
sechrule:=rule(sech(x) == 1/cosh(x))
 

                      1
   (4)  sech(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (4)  sech(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34 of 81
dd:=sechrule cc
 

   (5)
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
                  a x
         log(tanh(---))
                   2
     + 
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                            2             2                     3
         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                  2            2
       - sinh(a x)  + cosh(a x)  - 1
  /
                         2               2                       3
     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                            2             2                     3
--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  2            2
--R       - sinh(a x)  + cosh(a x)  - 1
--R  /
--R                         2               2                       3
--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 35 of 81
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (6)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (6)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36 of 81
ee:=tanhrule dd
 

   (7)
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                            2             2                     3
         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                              2             2                     3
         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
      *
                  a x
             sinh(---)
                   2
         log(---------)
                  a x
             cosh(---)
                   2
     + 
                  2            2
       - sinh(a x)  + cosh(a x)  - 1
  /
                         2               2                       3
     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (7)
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                            2             2                     3
--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                              2             2                     3
--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
--R      *
--R                  a x
--R             sinh(---)
--R                   2
--R         log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R     + 
--R                  2            2
--R       - sinh(a x)  + cosh(a x)  - 1
--R  /
--R                         2               2                       3
--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 37 of 81
coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
 

               3    cosh(3x) - 3cosh(x)
   (8)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) - 3cosh(x)
--R   (8)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38 of 81
ff:=coshcuberule ee
 

   (9)
                                  2             2
             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
           + 
             - cosh(a x)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                             2             2
         (4cosh(a x)sinh(a x)  + 8cosh(a x) sinh(a x) + cosh(3a x) + cosh(a x))
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                  2             2
             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
           + 
             - cosh(a x)
      *
                  a x
             sinh(---)
                   2
         log(---------)
                  a x
             cosh(---)
                   2
     + 
                   2             2
       - 4sinh(a x)  + 4cosh(a x)  - 4
  /
                            2               2
       4a cosh(a x)sinh(a x)  + 8a cosh(a x) sinh(a x) + a cosh(3a x)
     + 
       a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (9)
--R                                  2             2
--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
--R           + 
--R             - cosh(a x)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                             2             2
--R         (4cosh(a x)sinh(a x)  + 8cosh(a x) sinh(a x) + cosh(3a x) + cosh(a x))
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                  2             2
--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
--R           + 
--R             - cosh(a x)
--R      *
--R                  a x
--R             sinh(---)
--R                   2
--R         log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R     + 
--R                   2             2
--R       - 4sinh(a x)  + 4cosh(a x)  - 4
--R  /
--R                            2               2
--R       4a cosh(a x)sinh(a x)  + 8a cosh(a x) sinh(a x) + a cosh(3a x)
--R     + 
--R       a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 39 of 81
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

                2    cosh(2x) + 1
   (10)  cosh(x)  == ------------
                           2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                2    cosh(2x) + 1
--R   (10)  cosh(x)  == ------------
--R                           2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 40 of 81
gg:=coshsqrrule ff
 

   (11)
                                2
           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
         + 
           - cosh(a x)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                              2
           4cosh(a x)sinh(a x)  + (4cosh(2a x) + 4)sinh(a x) + cosh(3a x)
         + 
           cosh(a x)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                2
           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
         + 
           - cosh(a x)
      *
                  a x
             sinh(---)
                   2
         log(---------)
                  a x
             cosh(---)
                   2
     + 
                   2
       - 4sinh(a x)  + 2cosh(2a x) - 2
  /
                            2
       4a cosh(a x)sinh(a x)  + (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x)
     + 
       a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (11)
--R                                2
--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
--R         + 
--R           - cosh(a x)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                              2
--R           4cosh(a x)sinh(a x)  + (4cosh(2a x) + 4)sinh(a x) + cosh(3a x)
--R         + 
--R           cosh(a x)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                2
--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
--R         + 
--R           - cosh(a x)
--R      *
--R                  a x
--R             sinh(---)
--R                   2
--R         log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R     + 
--R                   2
--R       - 4sinh(a x)  + 2cosh(2a x) - 2
--R  /
--R                            2
--R       4a cosh(a x)sinh(a x)  + (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x)
--R     + 
--R       a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 41 of 81
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

                2    cosh(2x) - 1
   (12)  sinh(x)  == ------------
                           2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                2    cosh(2x) - 1
--R   (12)  sinh(x)  == ------------
--R                           2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 42 of 81
hh:=sinhsqrrule gg
 

   (13)
       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
     + 
                  a x
             sinh(---)
                   2
       - log(---------)
                  a x
             cosh(---)
                   2
  /
     a
                                                     Type: Expression Integer
--R
--R   (13)
--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  a x
--R             sinh(---)
--R                   2
--R       - log(---------)
--R                  a x
--R             cosh(---)
--R                   2
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 43 of 81
ii:=expandLog hh
 

   (14)
       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
     + 
                  a x              a x
       - log(sinh(---)) + log(cosh(---))
                   2                2
  /
     a
                                                     Type: Expression Integer
--R
--R   (14)
--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  a x              a x
--R       - log(sinh(---)) + log(cosh(---))
--R                   2                2
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 44 of 81     14:597 Schaums and Axiom agree
jj:=complexNormalize ii
 

   (15)  0
                                                     Type: Expression Integer
--R
--R   (15)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 45 of 81
aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x)
 

   (1)
   -
        4
     /
                     4                        3               2         2
          a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
        + 
                      3                       4
          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R   -
--R        4
--R     /
--R                     4                        3               2         2
--R          a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
--R        + 
--R                      3                       4
--R          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 46 of 81
bb:=-(2*coth(2*a*x))/a
 

          2coth(2a x)
   (2)  - -----------
               a
                                                     Type: Expression Integer
--R
--R          2coth(2a x)
--R   (2)  - -----------
--R               a
--R                                                     Type: Expression Integer
--E

--S 47 of 81     14:598 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                           4                                3
       2coth(2a x)sinh(a x)  + 8cosh(a x)coth(2a x)sinh(a x)
     + 
                  2                   2             3
       12cosh(a x) coth(2a x)sinh(a x)  + 8cosh(a x) coth(2a x)sinh(a x)
     + 
                  4
       (2cosh(a x)  - 2)coth(2a x) - 4
  /
                  4                        3               2         2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
     + 
                   3                       4
       4a cosh(a x) sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                           4                                3
--R       2coth(2a x)sinh(a x)  + 8cosh(a x)coth(2a x)sinh(a x)
--R     + 
--R                  2                   2             3
--R       12cosh(a x) coth(2a x)sinh(a x)  + 8cosh(a x) coth(2a x)sinh(a x)
--R     + 
--R                  4
--R       (2cosh(a x)  - 2)coth(2a x) - 4
--R  /
--R                  4                        3               2         2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
--R     + 
--R                   3                       4
--R       4a cosh(a x) sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 48 of 81
aa:=integrate(sinh(a*x)^2/cosh(a*x),x)
 

   (1)
                                                                         2
       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x)) + sinh(a x)
     + 
                                      2
       2cosh(a x)sinh(a x) + cosh(a x)  - 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                         2
--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x)) + sinh(a x)
--R     + 
--R                                      2
--R       2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49 of 81
bb:=sinh(a*x)/a-1/a*atan(sinh(a*x))
 

        - atan(sinh(a x)) + sinh(a x)
   (2)  -----------------------------
                      a
                                                     Type: Expression Integer
--R
--R        - atan(sinh(a x)) + sinh(a x)
--R   (2)  -----------------------------
--R                      a
--R                                                     Type: Expression Integer
--E

--S 50 of 81     14:599 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x))
     + 
                                                           2            2
       (2sinh(a x) + 2cosh(a x))atan(sinh(a x)) - sinh(a x)  + cosh(a x)  - 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x))
--R     + 
--R                                                           2            2
--R       (2sinh(a x) + 2cosh(a x))atan(sinh(a x)) - sinh(a x)  + cosh(a x)  - 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 51 of 81
aa:=integrate(cosh(a*x)^2/sinh(a*x),x)
 

   (1)
       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
     + 
                                                                          2
       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
     + 
                                      2
       2cosh(a x)sinh(a x) + cosh(a x)  + 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                                                          2
--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
--R     + 
--R                                      2
--R       2cosh(a x)sinh(a x) + cosh(a x)  + 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 52 of 81
bb:=cosh(a*x)/a+1/a*log(tanh((a*x)/2))
 

                 a x
        log(tanh(---)) + cosh(a x)
                  2
   (2)  --------------------------
                     a
                                                     Type: Expression Integer
--R
--R                 a x
--R        log(tanh(---)) + cosh(a x)
--R                  2
--R   (2)  --------------------------
--R                     a
--R                                                     Type: Expression Integer
--E

--S 53 of 81     14:600 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                                           a x
       (- 2sinh(a x) - 2cosh(a x))log(tanh(---))
                                            2
     + 
       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
     + 
                                                                          2
       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
     + 
                  2
       - cosh(a x)  + 1
  /
     2a sinh(a x) + 2a cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           a x
--R       (- 2sinh(a x) - 2cosh(a x))log(tanh(---))
--R                                            2
--R     + 
--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                                                          2
--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
--R     + 
--R                  2
--R       - cosh(a x)  + 1
--R  /
--R     2a sinh(a x) + 2a cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 54 of 81
aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x)
 

   (1)
                     2cosh(a x)                - 2sinh(a x) - 2
       - log(- ---------------------) + log(---------------------)
               sinh(a x) - cosh(a x)        sinh(a x) - cosh(a x)
     + 
       2atan(sinh(a x) + cosh(a x))
  /
     2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     2cosh(a x)                - 2sinh(a x) - 2
--R       - log(- ---------------------) + log(---------------------)
--R               sinh(a x) - cosh(a x)        sinh(a x) - cosh(a x)
--R     + 
--R       2atan(sinh(a x) + cosh(a x))
--R  /
--R     2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 55 of 81
bb:=1/(2*a)*log((1+sinh(a*x))/cosh(a*x))+1/a*atan(%e^(a*x))
 

            sinh(a x) + 1            a x
        log(-------------) + 2atan(%e   )
              cosh(a x)
   (2)  ---------------------------------
                        2a
                                                     Type: Expression Integer
--R
--R            sinh(a x) + 1            a x
--R        log(-------------) + 2atan(%e   )
--R              cosh(a x)
--R   (2)  ---------------------------------
--R                        2a
--R                                                     Type: Expression Integer
--E

--S 56 of 81
cc:=aa-bb
 

   (3)
             sinh(a x) + 1                2cosh(a x)
       - log(-------------) - log(- ---------------------)
               cosh(a x)            sinh(a x) - cosh(a x)
     + 
              - 2sinh(a x) - 2                                             a x
       log(---------------------) + 2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
           sinh(a x) - cosh(a x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R             sinh(a x) + 1                2cosh(a x)
--R       - log(-------------) - log(- ---------------------)
--R               cosh(a x)            sinh(a x) - cosh(a x)
--R     + 
--R              - 2sinh(a x) - 2                                             a x
--R       log(---------------------) + 2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
--R           sinh(a x) - cosh(a x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 57 of 81
dd:=expandLog cc
 

                                             a x
        atan(sinh(a x) + cosh(a x)) - atan(%e   )
   (4)  -----------------------------------------
                            a
                                                     Type: Expression Integer
--R
--R                                             a x
--R        atan(sinh(a x) + cosh(a x)) - atan(%e   )
--R   (4)  -----------------------------------------
--R                            a
--R                                                     Type: Expression Integer
--E

--S 58 of 81
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (5)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (5)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 59 of 81
ee:=atanrule dd
 

                   a x
               - %e    + %i           - sinh(a x) - cosh(a x) + %i
        %i log(------------) - %i log(----------------------------)
                  a x                  sinh(a x) + cosh(a x) + %i
                %e    + %i
   (6)  -----------------------------------------------------------
                                     2a
                                             Type: Expression Complex Integer
--R
--R                   a x
--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
--R        %i log(------------) - %i log(----------------------------)
--R                  a x                  sinh(a x) + cosh(a x) + %i
--R                %e    + %i
--R   (6)  -----------------------------------------------------------
--R                                     2a
--R                                             Type: Expression Complex Integer
--E

--S 60 of 81
ff:=expandLog ee
 

   (7)
       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
     + 
                  a x                  a x
       - %i log(%e    + %i) + %i log(%e    - %i)
  /
     2a
                                             Type: Expression Complex Integer
--R
--R   (7)
--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
--R     + 
--R                  a x                  a x
--R       - %i log(%e    + %i) + %i log(%e    - %i)
--R  /
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 61 of 81     14:601 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 62 of 81
aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x)
 

   (1)
                      2                                          2
           - sinh(a x)  + (- 2cosh(a x) - 2)sinh(a x) - cosh(a x)  - 2cosh(a x)
         + 
           - 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                   2                                        2
         (sinh(a x)  + (2cosh(a x) + 2)sinh(a x) + cosh(a x)  + 2cosh(a x) + 1)
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
       2sinh(a x) + 2cosh(a x)
  /
                   2                                              2
       2a sinh(a x)  + (4a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
     + 
       4a cosh(a x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                      2                                          2
--R           - sinh(a x)  + (- 2cosh(a x) - 2)sinh(a x) - cosh(a x)  - 2cosh(a x)
--R         + 
--R           - 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                   2                                        2
--R         (sinh(a x)  + (2cosh(a x) + 2)sinh(a x) + cosh(a x)  + 2cosh(a x) + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       2sinh(a x) + 2cosh(a x)
--R  /
--R                   2                                              2
--R       2a sinh(a x)  + (4a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R       4a cosh(a x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63 of 81
bb:=1/(2*a)*log(tanh((a*x)/2))+1/(2*a*(cosh(a*x)+1))
 

                                a x
        (cosh(a x) + 1)log(tanh(---)) + 1
                                 2
   (2)  ---------------------------------
                2a cosh(a x) + 2a
                                                     Type: Expression Integer
--R
--R                                a x
--R        (cosh(a x) + 1)log(tanh(---)) + 1
--R                                 2
--R   (2)  ---------------------------------
--R                2a cosh(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 64 of 81
cc:=aa-bb
 

   (3)
                                     2
           (- cosh(a x) - 1)sinh(a x)
         + 
                        2                                       3             2
           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
         + 
           - 3cosh(a x) - 1
      *
                  a x
         log(tanh(---))
                   2
     + 
                                     2
           (- cosh(a x) - 1)sinh(a x)
         + 
                        2                                       3             2
           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
         + 
           - 3cosh(a x) - 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                   2              2
           (cosh(a x) + 1)sinh(a x)  + (2cosh(a x)  + 4cosh(a x) + 2)sinh(a x)
         + 
                    3             2
           cosh(a x)  + 3cosh(a x)  + 3cosh(a x) + 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                  2            2
       - sinh(a x)  + cosh(a x)  - 1
  /
                                   2
       (2a cosh(a x) + 2a)sinh(a x)
     + 
                    2                                             3
       (4a cosh(a x)  + 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
     + 
                   2
       6a cosh(a x)  + 6a cosh(a x) + 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                     2
--R           (- cosh(a x) - 1)sinh(a x)
--R         + 
--R                        2                                       3             2
--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
--R         + 
--R           - 3cosh(a x) - 1
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                     2
--R           (- cosh(a x) - 1)sinh(a x)
--R         + 
--R                        2                                       3             2
--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
--R         + 
--R           - 3cosh(a x) - 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                   2              2
--R           (cosh(a x) + 1)sinh(a x)  + (2cosh(a x)  + 4cosh(a x) + 2)sinh(a x)
--R         + 
--R                    3             2
--R           cosh(a x)  + 3cosh(a x)  + 3cosh(a x) + 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                  2            2
--R       - sinh(a x)  + cosh(a x)  - 1
--R  /
--R                                   2
--R       (2a cosh(a x) + 2a)sinh(a x)
--R     + 
--R                    2                                             3
--R       (4a cosh(a x)  + 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R                   2
--R       6a cosh(a x)  + 6a cosh(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 65 of 81
coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
 

               3    cosh(3x) - 3cosh(x)
   (4)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) - 3cosh(x)
--R   (4)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 66 of 81
dd:=coshcuberule cc
 

   (5)
                                      2
           (- 4cosh(a x) - 4)sinh(a x)
         + 
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                        2
           - 12cosh(a x)  - 9cosh(a x) - 4
      *
                  a x
         log(tanh(---))
                   2
     + 
                                      2
           (- 4cosh(a x) - 4)sinh(a x)
         + 
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                        2
           - 12cosh(a x)  - 9cosh(a x) - 4
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                    2              2
           (4cosh(a x) + 4)sinh(a x)  + (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x)
         + 
                                   2
           cosh(3a x) + 12cosh(a x)  + 9cosh(a x) + 4
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                   2             2
       - 4sinh(a x)  + 4cosh(a x)  - 4
  /
                                   2
       (8a cosh(a x) + 8a)sinh(a x)
     + 
                     2
       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                    2
       24a cosh(a x)  + 18a cosh(a x) + 8a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                      2
--R           (- 4cosh(a x) - 4)sinh(a x)
--R         + 
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                        2
--R           - 12cosh(a x)  - 9cosh(a x) - 4
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                      2
--R           (- 4cosh(a x) - 4)sinh(a x)
--R         + 
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                        2
--R           - 12cosh(a x)  - 9cosh(a x) - 4
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                    2              2
--R           (4cosh(a x) + 4)sinh(a x)  + (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x)
--R         + 
--R                                   2
--R           cosh(3a x) + 12cosh(a x)  + 9cosh(a x) + 4
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                   2             2
--R       - 4sinh(a x)  + 4cosh(a x)  - 4
--R  /
--R                                   2
--R       (8a cosh(a x) + 8a)sinh(a x)
--R     + 
--R                     2
--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                    2
--R       24a cosh(a x)  + 18a cosh(a x) + 8a
--R                                                     Type: Expression Integer
--E

--S 67 of 81
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 68 of 81
ee:=sinhsqrrule dd
 

   (7)
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                                                     2
           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
      *
                  a x
         log(tanh(---))
                   2
     + 
                        2
           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                                                     2
           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      2
           (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
         + 
                                                   2
           (2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  + 7cosh(a x) + 2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                 2
       - 2cosh(2a x) + 4cosh(a x)  - 2
  /
                     2
       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                                                    2
       (4a cosh(a x) + 4a)cosh(2a x) + 24a cosh(a x)  + 14a cosh(a x) + 4a
                                                     Type: Expression Integer
--R
--R   (7)
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                                                     2
--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                        2
--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                                                     2
--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      2
--R           (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
--R         + 
--R                                                   2
--R           (2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  + 7cosh(a x) + 2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                 2
--R       - 2cosh(2a x) + 4cosh(a x)  - 2
--R  /
--R                     2
--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                                                    2
--R       (4a cosh(a x) + 4a)cosh(2a x) + 24a cosh(a x)  + 14a cosh(a x) + 4a
--R                                                     Type: Expression Integer
--E

--S 69 of 81
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (8)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (8)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 70 of 81
ff:=coshsqrrule ee
 

   (9)
                  a x
       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
                   2
     + 
       log(sinh(a x) + cosh(a x) - 1)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (9)
--R                  a x
--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
--R                   2
--R     + 
--R       log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 71 of 81     14:602 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (10)  0
                                                     Type: Expression Integer
--R
--R   (10)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 72 of 81
aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x)
 

   (1)
                   2                                        2
         (sinh(a x)  + (2cosh(a x) - 2)sinh(a x) + cosh(a x)  - 2cosh(a x) + 1)
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      2                                          2
           - sinh(a x)  + (- 2cosh(a x) + 2)sinh(a x) - cosh(a x)  + 2cosh(a x)
         + 
           - 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
       - 2sinh(a x) - 2cosh(a x)
  /
                   2                                              2
       2a sinh(a x)  + (4a cosh(a x) - 4a)sinh(a x) + 2a cosh(a x)
     + 
       - 4a cosh(a x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   2                                        2
--R         (sinh(a x)  + (2cosh(a x) - 2)sinh(a x) + cosh(a x)  - 2cosh(a x) + 1)
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      2                                          2
--R           - sinh(a x)  + (- 2cosh(a x) + 2)sinh(a x) - cosh(a x)  + 2cosh(a x)
--R         + 
--R           - 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       - 2sinh(a x) - 2cosh(a x)
--R  /
--R                   2                                              2
--R       2a sinh(a x)  + (4a cosh(a x) - 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R       - 4a cosh(a x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 73 of 81
bb:=-1/(2*a)*log(tanh((a*x)/2))-1/(2*a*(cosh(a*x)-1))
 

                                  a x
        (- cosh(a x) + 1)log(tanh(---)) - 1
                                   2
   (2)  -----------------------------------
                 2a cosh(a x) - 2a
                                                     Type: Expression Integer
--R
--R                                  a x
--R        (- cosh(a x) + 1)log(tanh(---)) - 1
--R                                   2
--R   (2)  -----------------------------------
--R                 2a cosh(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 74 of 81
cc:=aa-bb
 

   (3)
                                   2              2
           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
         + 
                    3             2
           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
      *
                  a x
         log(tanh(---))
                   2
     + 
                                   2              2
           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
         + 
                    3             2
           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                     2
           (- cosh(a x) + 1)sinh(a x)
         + 
                        2                                       3             2
           (- 2cosh(a x)  + 4cosh(a x) - 2)sinh(a x) - cosh(a x)  + 3cosh(a x)
         + 
           - 3cosh(a x) + 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                2            2
       sinh(a x)  - cosh(a x)  + 1
  /
                                   2
       (2a cosh(a x) - 2a)sinh(a x)
     + 
                    2                                             3
       (4a cosh(a x)  - 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
     + 
                     2
       - 6a cosh(a x)  + 6a cosh(a x) - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                   2              2
--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
--R         + 
--R                    3             2
--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                   2              2
--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
--R         + 
--R                    3             2
--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                     2
--R           (- cosh(a x) + 1)sinh(a x)
--R         + 
--R                        2                                       3             2
--R           (- 2cosh(a x)  + 4cosh(a x) - 2)sinh(a x) - cosh(a x)  + 3cosh(a x)
--R         + 
--R           - 3cosh(a x) + 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                2            2
--R       sinh(a x)  - cosh(a x)  + 1
--R  /
--R                                   2
--R       (2a cosh(a x) - 2a)sinh(a x)
--R     + 
--R                    2                                             3
--R       (4a cosh(a x)  - 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
--R     + 
--R                     2
--R       - 6a cosh(a x)  + 6a cosh(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 75 of 81
coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
 

               3    cosh(3x) - 3cosh(x)
   (4)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) - 3cosh(x)
--R   (4)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 76 of 81
dd:=coshcuberule cc
 

   (5)
                                    2              2
           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
         + 
                                   2
           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
      *
                  a x
         log(tanh(---))
                   2
     + 
                                    2              2
           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
         + 
                                   2
           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                                      2
           (- 4cosh(a x) + 4)sinh(a x)
         + 
                        2
           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                      2
           12cosh(a x)  - 9cosh(a x) + 4
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                 2             2
       4sinh(a x)  - 4cosh(a x)  + 4
  /
                                   2
       (8a cosh(a x) - 8a)sinh(a x)
     + 
                     2
       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                      2
       - 24a cosh(a x)  + 18a cosh(a x) - 8a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                    2              2
--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
--R         + 
--R                                   2
--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                                    2              2
--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
--R         + 
--R                                   2
--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                      2
--R           (- 4cosh(a x) + 4)sinh(a x)
--R         + 
--R                        2
--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                      2
--R           12cosh(a x)  - 9cosh(a x) + 4
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                 2             2
--R       4sinh(a x)  - 4cosh(a x)  + 4
--R  /
--R                                   2
--R       (8a cosh(a x) - 8a)sinh(a x)
--R     + 
--R                     2
--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                      2
--R       - 24a cosh(a x)  + 18a cosh(a x) - 8a
--R                                                     Type: Expression Integer
--E

--S 77 of 81
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 78 of 81
ee:=sinhsqrrule dd
 

   (7)
                      2
           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
         + 
                                                   2
           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
      *
                  a x
         log(tanh(---))
                   2
     + 
                      2
           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
         + 
                                                   2
           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                        2
           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
         + 
                                                     2
           (- 2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  - 7cosh(a x) + 2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                               2
       2cosh(2a x) - 4cosh(a x)  + 2
  /
                     2
       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
     + 
                                                    2
       (4a cosh(a x) - 4a)cosh(2a x) - 24a cosh(a x)  + 14a cosh(a x) - 4a
                                                     Type: Expression Integer
--R
--R   (7)
--R                      2
--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
--R         + 
--R                                                   2
--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                      2
--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
--R         + 
--R                                                   2
--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                        2
--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
--R         + 
--R                                                     2
--R           (- 2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  - 7cosh(a x) + 2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                               2
--R       2cosh(2a x) - 4cosh(a x)  + 2
--R  /
--R                     2
--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
--R     + 
--R                                                    2
--R       (4a cosh(a x) - 4a)cosh(2a x) - 24a cosh(a x)  + 14a cosh(a x) - 4a
--R                                                     Type: Expression Integer
--E

--S 79 of 81
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (8)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (8)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 80 of 81
ff:=coshsqrrule ee
 

   (9)
                a x
       log(tanh(---)) + log(sinh(a x) + cosh(a x) + 1)
                 2
     + 
       - log(sinh(a x) + cosh(a x) - 1)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (9)
--R                a x
--R       log(tanh(---)) + log(sinh(a x) + cosh(a x) + 1)
--R                 2
--R     + 
--R       - log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 81 of 81     14:603 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (10)  0
                                                     Type: Expression Integer
--R
--R   (10)  0
--R                                                     Type: Expression Integer
--E

)spool
 
Starts dribbling to Character.output (2010/3/27, 18:41:47).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 13
chars := [char "a", char "A", char "X", char "8", char "+"]
 

   (1)  [a,A,X,8,+]
                                                         Type: List Character
--R 
--R
--R   (1)  [a,A,X,8,+]
--R                                                         Type: List Character
--E 1

--S 2 of 13
space()
 

   (2)
                                                              Type: Character
--R 
--R
--R   (2)
--R                                                              Type: Character
--E 2

--S 3 of 13
quote()
 

   (3)  "
                                                              Type: Character
--R 
--R
--R   (3)  "
--R                                                              Type: Character
--E 3

--S 4 of 13
escape()
 

   (4)  _
                                                              Type: Character
--R 
--R
--R   (4)  _
--R                                                              Type: Character
--E 4

--S 5 of 13
[ord c for c in chars]
 

   (5)  [97,65,88,56,43]
                                                           Type: List Integer
--R 
--R
--R   (5)  [97,65,88,56,43]
--R                                                           Type: List Integer
--E 5

--S 6 of 13
[upperCase c for c in chars]
 

   (6)  [A,A,X,8,+]
                                                         Type: List Character
--R 
--R
--R   (6)  [A,A,X,8,+]
--R                                                         Type: List Character
--E 6

--S 7 of 13
[lowerCase c for c in chars]
 

   (7)  [a,a,x,8,+]
                                                         Type: List Character
--R 
--R
--R   (7)  [a,a,x,8,+]
--R                                                         Type: List Character
--E 7

--S 8 of 13
[alphabetic? c for c in chars]
 

   (8)  [true,true,true,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,true,true,false,false]
--R                                                           Type: List Boolean
--E 8

--S 9 of 13
[upperCase? c for c in chars]
 

   (9)  [false,true,true,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [false,true,true,false,false]
--R                                                           Type: List Boolean
--E 9

--S 10 of 13
[lowerCase? c for c in chars]
 

   (10)  [true,false,false,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (10)  [true,false,false,false,false]
--R                                                           Type: List Boolean
--E 10

--S 11 of 13
[digit? c for c in chars]
 

   (11)  [false,false,false,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (11)  [false,false,false,true,false]
--R                                                           Type: List Boolean
--E 11

--S 12 of 13
[hexDigit? c for c in chars]
 

   (12)  [true,true,false,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (12)  [true,true,false,true,false]
--R                                                           Type: List Boolean
--E 12

--S 13 of 13
[alphanumeric? c for c in chars]
 

   (13)  [true,true,true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (13)  [true,true,true,true,false]
--R                                                           Type: List Boolean
--E 13
)spool
 
Starts dribbling to calculus2.output (2010/3/27, 18:24:20).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input for page FormalDerivativePage

--S 1 of 112
differentiate(f, x)
 

   (1)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  0
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 112
f := operator f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 112
x := operator x
 

   (3)  x
                                                          Type: BasicOperator
--R 
--R
--R   (3)  x
--R                                                          Type: BasicOperator
--E 3

--S 4 of 112
y := operator y
 

   (4)  y
                                                          Type: BasicOperator
--R 
--R
--R   (4)  y
--R                                                          Type: BasicOperator
--E 4

--S 5 of 112
a := f(x z, y z, z**2) + x y(z+1)
 

                                   2
   (5)  x(y(z + 1)) + f(x(z),y(z),z )
                                                     Type: Expression Integer
--R 
--R
--R                                   2
--R   (5)  x(y(z + 1)) + f(x(z),y(z),z )
--R                                                     Type: Expression Integer
--E 5

--S 6 of 112
dadz := differentiate(a, z)
 

   (6)
                      2     ,                  2     ,                  2
     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
        ,3                       ,2                       ,1
   + 
      ,           ,
     x (y(z + 1))y (z + 1)

                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                      2     ,                  2     ,                  2
--R     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
--R        ,3                       ,2                       ,1
--R   + 
--R      ,           ,
--R     x (y(z + 1))y (z + 1)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 112
eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

   (7)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 112
eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

            z             2
   (8)  f(%e ,log(z + 1),z ) + z + 2
                                                     Type: Expression Integer
--R 
--R
--R            z             2
--R   (8)  f(%e ,log(z + 1),z ) + z + 2
--R                                                     Type: Expression Integer
--E 8

--S 9 of 112
differentiate(%, z)
 

   (9)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (9)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 9

-- Input for page SeriesArithmeticPage
)clear all
 

--S 10 of 112
x := series x
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 10

--S 11 of 112
num := 3 + x
 

   (2)  3 + x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)  3 + x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11

--S 12 of 112
den := 1 + 7 * x
 

   (3)  1 + 7x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)  1 + 7x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 12

--S 13 of 112
num / den
 

   (4)
                   2       3        4         5          6           7
     3 - 20x + 140x  - 980x  + 6860x  - 48020x  + 336140x  - 2352980x
   + 
              8             9             10      11
     16470860x  - 115296020x  + 807072140x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (4)
--R                   2       3        4         5          6           7
--R     3 - 20x + 140x  - 980x  + 6860x  - 48020x  + 336140x  - 2352980x
--R   + 
--R              8             9             10      11
--R     16470860x  - 115296020x  + 807072140x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 13

--S 14 of 112
base := 1 / (1 - x)
 

                 2    3    4    5    6    7    8    9    10      11
   (5)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (5)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 14

--S 15 of 112
expon := x * base
 

             2    3    4    5    6    7    8    9    10    11      12
   (6)  x + x  + x  + x  + x  + x  + x  + x  + x  + x   + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             2    3    4    5    6    7    8    9    10    11      12
--R   (6)  x + x  + x  + x  + x  + x  + x  + x  + x  + x   + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 15

--S 16 of 112
base ** expon
 

   (7)
          2   3  3   7  4   43  5   649  6   241  7   3706  8   85763  9
     1 + x  + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
              2      3      12      120       30       315       5040
   + 
     245339  10      11
     ------ x   + O(x  )
      10080
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (7)
--R          2   3  3   7  4   43  5   649  6   241  7   3706  8   85763  9
--R     1 + x  + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R              2      3      12      120       30       315       5040
--R   + 
--R     245339  10      11
--R     ------ x   + O(x  )
--R      10080
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 16

-- Input for page SeriesConversionPage
)clear all
 

--S 17 of 112
f := sin(a*x)
 

   (1)  sin(a x)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  sin(a x)
--R                                                     Type: Expression Integer
--E 17

--S 18 of 112
series(f,x = 0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (2)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (2)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 18

--S 19 of 112
g := y / (exp(y) - 1)
 

           y
   (3)  -------
          y
        %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R           y
--R   (3)  -------
--R          y
--R        %e  - 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 112
series(g)
 

   (4)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - y + -- y  - --- y  + ----- y  - ------- y  + -------- y   + O(y  )
       2     12      720      30240      1209600      47900160
                        Type: UnivariatePuiseuxSeries(Expression Integer,y,0)
--R 
--R
--R   (4)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - y + -- y  - --- y  + ----- y  - ------- y  + -------- y   + O(y  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,y,0)
--E 20

--S 21 of 112
h := sin(3*x)
 

   (5)  sin(3x)
                                                     Type: Expression Integer
--R 
--R
--R   (5)  sin(3x)
--R                                                     Type: Expression Integer
--E 21

--S 22 of 112
series(h,x,x = %pi/12)
 

   (6)
                %pi               %pi 2              %pi 3               %pi 4
     sin(3)(x - ---) + sin(6)(x - ---)  + sin(9)(x - ---)  + sin(12)(x - ---)
                 12                12                 12                  12
   + 
                 %pi 5               %pi 6               %pi 7
     sin(15)(x - ---)  + sin(18)(x - ---)  + sin(21)(x - ---)
                  12                  12                  12
   + 
                 %pi 8               %pi 9               %pi 10
     sin(24)(x - ---)  + sin(27)(x - ---)  + sin(30)(x - ---)
                  12                  12                  12
   + 
                 %pi 11          %pi 12
     sin(33)(x - ---)   + O((x - ---)  )
                  12              12
                    Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/12)
--R 
--R
--R   (6)
--R                %pi               %pi 2              %pi 3               %pi 4
--R     sin(3)(x - ---) + sin(6)(x - ---)  + sin(9)(x - ---)  + sin(12)(x - ---)
--R                 12                12                 12                  12
--R   + 
--R                 %pi 5               %pi 6               %pi 7
--R     sin(15)(x - ---)  + sin(18)(x - ---)  + sin(21)(x - ---)
--R                  12                  12                  12
--R   + 
--R                 %pi 8               %pi 9               %pi 10
--R     sin(24)(x - ---)  + sin(27)(x - ---)  + sin(30)(x - ---)
--R                  12                  12                  12
--R   + 
--R                 %pi 11          %pi 12
--R     sin(33)(x - ---)   + O((x - ---)  )
--R                  12              12
--R                    Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/12)
--E 22

--S 23 of 112
series(sqrt(tan(a*x)),x = 0)
 

             1           5             9
             -    2 +-+  -      4 +-+  -
         +-+ 2   a \|a   2   19a \|a   2      6
   (7)  \|a x  + ------ x  + -------- x  + O(x )
                    6           360
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1           5             9
--R             -    2 +-+  -      4 +-+  -
--R         +-+ 2   a \|a   2   19a \|a   2      6
--R   (7)  \|a x  + ------ x  + -------- x  + O(x )
--R                    6           360
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 23

--S 24 of 112
series(sec(x) ** 2,x = %pi/2)
 

   (8)
          %pi - 2   1    1      %pi 2    2       %pi 4    1       %pi 6
     (x - ---)    + - + -- (x - ---)  + --- (x - ---)  + --- (x - ---)
           2        3   15       2      189       2      675       2
   + 
       2        %pi 8          %pi 9
     ----- (x - ---)  + O((x - ---) )
     10395       2              2
                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--R 
--R
--R   (8)
--R          %pi - 2   1    1      %pi 2    2       %pi 4    1       %pi 6
--R     (x - ---)    + - + -- (x - ---)  + --- (x - ---)  + --- (x - ---)
--R           2        3   15       2      189       2      675       2
--R   + 
--R       2        %pi 8          %pi 9
--R     ----- (x - ---)  + O((x - ---) )
--R     10395       2              2
--R                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--E 24

--S 25 of 112
bern := t * exp(t*x) / (exp(t) - 1)
 

            t x
        t %e
   (9)  -------
          t
        %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R            t x
--R        t %e
--R   (9)  -------
--R          t
--R        %e  - 1
--R                                                     Type: Expression Integer
--E 25

--S 26 of 112
series(bern,t = 0)
 

   (10)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
     ---------------------- t  + --------------------- t
               720                        720
   + 
        6       5       4      2            7      6      5     3
     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
     ------------------------------- t  + --------------------------- t
                  30240                              30240
   + 
        8       7       6      4      2
     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
     -------------------------------------- t
                     1209600
   + 
        9      8      7      5      3
     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
     ------------------------------------- t
                    3628800
   + 
        10       9       8       6       4      2
     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
     ------------------------------------------------ t   + O(t  )
                         239500800
                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--R 
--R
--R   (10)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
--R     ---------------------- t  + --------------------- t
--R               720                        720
--R   + 
--R        6       5       4      2            7      6      5     3
--R     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
--R     ------------------------------- t  + --------------------------- t
--R                  30240                              30240
--R   + 
--R        8       7       6      4      2
--R     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
--R     -------------------------------------- t
--R                     1209600
--R   + 
--R        9      8      7      5      3
--R     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
--R     ------------------------------------- t
--R                    3628800
--R   + 
--R        10       9       8       6       4      2
--R     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
--R     ------------------------------------------------ t   + O(t  )
--R                         239500800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 26

-- Input for page SeriesDifferentialEquationPage
)clear all
 

)set streams calculate 7
 
 
--S 27 of 112
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 27

--S 28 of 112
eq := differentiate(y(x), x, 3) - sin(differentiate(y(x), x, 2)) * exp(y(x)) = cos(x)
 

         ,,,        y(x)     ,,
   (2)  y   (x) - %e    sin(y  (x))= cos(x)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,,        y(x)     ,,
--R   (2)  y   (x) - %e    sin(y  (x))= cos(x)
--R
--R                                            Type: Equation Expression Integer
--E 28

--S 29 of 112
seriesSolve(eq, y, x = 0, [1, 0, 0])
 
   Compiling function %B with type List UnivariateTaylorSeries(
      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
      Integer,x,0) 

   (3)
                          2            3              4      2
         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
         6      24        120           720                 5040
   + 
        8
     O(x )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--I   Compiling function %B with type List UnivariateTaylorSeries(
--R      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,0) 
--R
--R   (3)
--R                          2            3              4      2
--R         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
--R     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
--R         6      24        120           720                 5040
--R   + 
--R        8
--R     O(x )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 29

--S 30 of 112
x := operator 'x
 
   Compiled code for %B has been cleared.

   (4)  x
                                                          Type: BasicOperator
--R 
--I   Compiled code for %B has been cleared.
--R
--R   (4)  x
--R                                                          Type: BasicOperator
--E 30

--S 31 of 112
eq1 := differentiate(x(t), t) = 1 + x(t)**2
 

         ,         2
   (5)  x (t)= x(t)  + 1

                                            Type: Equation Expression Integer
--R 
--R
--R         ,         2
--R   (5)  x (t)= x(t)  + 1
--R
--R                                            Type: Equation Expression Integer
--E 31

--S 32 of 112
eq2 := differentiate(y(t), t) = x(t) * y(t)
 

         ,
   (6)  y (t)= x(t)y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,
--R   (6)  y (t)= x(t)y(t)
--R
--R                                            Type: Equation Expression Integer
--E 32

--S 33 of 112
seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])
 
   Compiling function %D with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 
   Compiling function %E with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 

             1  3    2  5    17  7      8      1  2    5  4    61  6      8
   (7)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
             3      15      315                2      24      720
                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--I   Compiling function %D with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--I   Compiling function %E with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R
--R             1  3    2  5    17  7      8      1  2    5  4    61  6      8
--R   (7)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
--R             3      15      315                2      24      720
--R                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--E 33

-- Input for page LaplacePage
)clear all
 

--S 34 of 112
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
 

   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
--R                                                     Type: Expression Integer
--E 34

--S 35 of 112
laplace(%, t, s)
 

             3
           4a
   (2)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R             3
--R           4a
--R   (2)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 35

--S 36 of 112
laplace((exp(a*t) - exp(b*t))/t, t, s)
 

   (3)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 36

--S 37 of 112
laplace(2/t * (1 - cos(a*t)), t, s)
 

             2    2
   (4)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R             2    2
--R   (4)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 37

--S 38 of 112
laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
 

                    1
   (5)  ------------------------
           2             3    2
        b s  + 2a b s + b  + a b
                                                     Type: Expression Integer
--R 
--R
--R                    1
--R   (5)  ------------------------
--R           2             3    2
--R        b s  + 2a b s + b  + a b
--R                                                     Type: Expression Integer
--E 38

--S 39 of 112
laplace((cos(a*t) - cos(b*t))/t, t, s)
 

             2    2         2    2
        log(s  + b ) - log(s  + a )
   (6)  ---------------------------
                     2
                                                     Type: Expression Integer
--R 
--R
--R             2    2         2    2
--R        log(s  + b ) - log(s  + a )
--R   (6)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 39

--S 40 of 112
laplace(exp(a*t+b)*Ei(c*t), t, s)
 

          b    s + c - a
        %e log(---------)
                   c
   (7)  -----------------
              s - a
                                                     Type: Expression Integer
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (7)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 40

--S 41 of 112
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
 

               2    2
              s  + b             d
        a log(-------) + 2c atan(-)
                  2              s
                 b
   (8)  ---------------------------
                     2s
                                                     Type: Expression Integer
--R
--R               2    2
--R              s  + b             d
--R        a log(-------) + 2c atan(-)
--R                  2              s
--R                 b
--R   (8)  ---------------------------
--R                     2s
--R                                                     Type: Expression Integer
--E 41

--S 42 of 112
laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
 

                                    2
          4     2 2    4           t           3
        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
   (9)  ----------------------------------------
                      4     2 2    4
                     s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                                    2
--R          4     2 2    4           t           3
--R        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
--R   (9)  ----------------------------------------
--R                      4     2 2    4
--R                     s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 42

-- Input for page SeriesCoefficientPage
)clear all
 

--S 43 of 112
x := series(x)
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 43

--S 44 of 112
y := exp(x) * sin(x)
 

             2   1  3    1  5    1  6    1   7      9
   (2)  x + x  + - x  - -- x  - -- x  - --- x  + O(x )
                 3      30      90      630
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             2   1  3    1  5    1  6    1   7      9
--R   (2)  x + x  + - x  - -- x  - -- x  - --- x  + O(x )
--R                 3      30      90      630
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 44

--S 45 of 112
coefficient(y,6)
 

           1
   (3)  - --
          90
                                                     Type: Expression Integer
--R 
--R
--R           1
--R   (3)  - --
--R          90
--R                                                     Type: Expression Integer
--E 45

--S 46 of 112
coefficient(y,15)
 

               1
   (4)  - -----------
          10216206000
                                                     Type: Expression Integer
--R 
--R
--R               1
--R   (4)  - -----------
--R          10216206000
--R                                                     Type: Expression Integer
--E 46

--S 47 of 112
y
 

   (5)
          2   1  3    1  5    1  6    1   7     1    9      1    10
     x + x  + - x  - -- x  - -- x  - --- x  + ----- x  + ------ x
              3      30      90      630      22680      113400
   + 
        1     11       1     13       1      14        1       15      16
     ------- x   - -------- x   - --------- x   - ----------- x   + O(x  )
     1247400       97297200       681080400       10216206000
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (5)
--R          2   1  3    1  5    1  6    1   7     1    9      1    10
--R     x + x  + - x  - -- x  - -- x  - --- x  + ----- x  + ------ x
--R              3      30      90      630      22680      113400
--R   + 
--R        1     11       1     13       1      14        1       15      16
--R     ------- x   - -------- x   - --------- x   - ----------- x   + O(x  )
--R     1247400       97297200       681080400       10216206000
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 47

-- Input for page SymbolicIntegrationPage
)clear all
 

--S 48 of 112
f := (x**2+2*x+1) / (x**6+6*x**5+15*x**4+20*x**3+15*x**2+6*x+2)
 

                       2
                      x  + 2x + 1
   (1)  --------------------------------------
         6     5      4      3      2
        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                       2
--R                      x  + 2x + 1
--R   (1)  --------------------------------------
--R         6     5      4      3      2
--R        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
--R                                            Type: Fraction Polynomial Integer
--E 48

--S 49 of 112
integrate(f, x)
 

              3     2
        atan(x  + 3x  + 3x + 1)
   (2)  -----------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2
--R        atan(x  + 3x  + 3x + 1)
--R   (2)  -----------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 112
g := log(1 + sqrt(a * x + b)) / x
 

             +-------+
        log(\|a x + b  + 1)
   (3)  -------------------
                 x
                                                     Type: Expression Integer
--R 
--R
--R             +-------+
--R        log(\|a x + b  + 1)
--R   (3)  -------------------
--R                 x
--R                                                     Type: Expression Integer
--E 50

--S 51 of 112
integrate(g, x)
 

           x      +--------+
         ++  log(\|b + %J a  + 1)
   (4)   |   -------------------- d%J
        ++            %J
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x      +--------+
--I         ++  log(\|b + %G a  + 1)
--I   (4)   |   -------------------- d%G
--I        ++            %G
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 112
integrate(1/(x**2 - 2),x)
 

              2      +-+
            (x  + 2)\|2  - 4x
        log(-----------------)
                   2
                  x  - 2
   (5)  ----------------------
                   +-+
                 2\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2      +-+
--R            (x  + 2)\|2  - 4x
--R        log(-----------------)
--R                   2
--R                  x  - 2
--R   (5)  ----------------------
--R                   +-+
--R                 2\|2
--R                                          Type: Union(Expression Integer,...)
--E 52

--S 53 of 112
integrate(1/(x**2 + 2),x)
 

               +-+
             x\|2
        atan(-----)
               2
   (6)  -----------
             +-+
            \|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-+
--R             x\|2
--R        atan(-----)
--R               2
--R   (6)  -----------
--R             +-+
--R            \|2
--R                                          Type: Union(Expression Integer,...)
--E 53

--S 54 of 112
h := x**2 / (x**4 - a**2)
 

            2
           x
   (7)  -------
         4    2
        x  - a
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            2
--R           x
--R   (7)  -------
--R         4    2
--R        x  - a
--R                                            Type: Fraction Polynomial Integer
--E 54

--S 55 of 112
integrate(h, x)
 

   (8)
          2      +-+                   +-+
        (x  + a)\|a  - 2a x          x\|a
    log(-------------------) + 2atan(-----)
                2                      a
               x  - a
   [---------------------------------------,
                       +-+
                     4\|a
          2      +---+                   +---+
        (x  - a)\|- a  + 2a x          x\|- a
    log(---------------------) - 2atan(-------)
                 2                        a
                x  + a
    -------------------------------------------]
                        +---+
                      4\|- a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (8)
--R          2      +-+                   +-+
--R        (x  + a)\|a  - 2a x          x\|a
--R    log(-------------------) + 2atan(-----)
--R                2                      a
--R               x  - a
--R   [---------------------------------------,
--R                       +-+
--R                     4\|a
--R          2      +---+                   +---+
--R        (x  - a)\|- a  + 2a x          x\|- a
--R    log(---------------------) - 2atan(-------)
--R                 2                        a
--R                x  + a
--R    -------------------------------------------]
--R                        +---+
--R                      4\|- a
--R                                     Type: Union(List Expression Integer,...)
--E 55

--S 56 of 112
complexIntegrate(h, x)
 

   (9)
          +--+       +--+         +----+       +----+
          | 1        | 1          |   1        |   1
       -  |-- log(2a |--  + x) +  |- -- log(2a |- --  + x)
         \|4a       \|4a         \|  4a       \|  4a
     + 
          +----+         +----+         +--+         +--+
          |   1          |   1          | 1          | 1
       -  |- -- log(- 2a |- --  + x) +  |-- log(- 2a |--  + x)
         \|  4a         \|  4a         \|4a         \|4a
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (9)
--R          +--+       +--+         +----+       +----+
--R          | 1        | 1          |   1        |   1
--R       -  |-- log(2a |--  + x) +  |- -- log(2a |- --  + x)
--R         \|4a       \|4a         \|  4a       \|  4a
--R     + 
--R          +----+         +----+         +--+         +--+
--R          |   1          |   1          | 1          | 1
--R       -  |- -- log(- 2a |- --  + x) +  |-- log(- 2a |--  + x)
--R         \|  4a         \|  4a         \|4a         \|4a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 56

--S 57 of 112
expandLog %
 

   (10)
          +--+       +--+         +--+       +--+
          | 1        | 1          | 1        | 1
       -  |-- log(2a |--  + x) +  |-- log(2a |--  - x)
         \|4a       \|4a         \|4a       \|4a
     + 
        +----+       +----+         +----+       +----+                 +--+
        |   1        |   1          |   1        |   1                  | 1
        |- -- log(2a |- --  + x) -  |- -- log(2a |- --  - x) + log(- 1) |--
       \|  4a       \|  4a         \|  4a       \|  4a                 \|4a
     + 
                  +----+
                  |   1
       - log(- 1) |- --
                 \|  4a
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (10)
--R          +--+       +--+         +--+       +--+
--R          | 1        | 1          | 1        | 1
--R       -  |-- log(2a |--  + x) +  |-- log(2a |--  - x)
--R         \|4a       \|4a         \|4a       \|4a
--R     + 
--R        +----+       +----+         +----+       +----+                 +--+
--R        |   1        |   1          |   1        |   1                  | 1
--R        |- -- log(2a |- --  + x) -  |- -- log(2a |- --  - x) + log(- 1) |--
--R       \|  4a       \|  4a         \|  4a       \|  4a                 \|4a
--R     + 
--R                  +----+
--R                  |   1
--R       - log(- 1) |- --
--R                 \|  4a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 57

--S 58 of 112
rootSimp %
 

   (11)
                 +---+                    +-+                    +---+
        +-+    x\|- a  + a     +---+    x\|a  + a     +-+    - x\|- a  + a
       \|a log(-----------) - \|- a log(---------) - \|a log(-------------)
                   +---+                    +-+                   +---+
                  \|- a                    \|a                   \|- a
     + 
                     +-+
        +---+    - x\|a  + a             +-+            +---+
       \|- a log(-----------) - log(- 1)\|a  + log(- 1)\|- a
                      +-+
                     \|a
  /
       +---+ +-+
     4\|- a \|a
                                                     Type: Expression Integer
--R 
--R
--R   (11)
--R                 +---+                    +-+                    +---+
--R        +-+    x\|- a  + a     +---+    x\|a  + a     +-+    - x\|- a  + a
--R       \|a log(-----------) - \|- a log(---------) - \|a log(-------------)
--R                   +---+                    +-+                   +---+
--R                  \|- a                    \|a                   \|- a
--R     + 
--R                     +-+
--R        +---+    - x\|a  + a             +-+            +---+
--R       \|- a log(-----------) - log(- 1)\|a  + log(- 1)\|- a
--R                      +-+
--R                     \|a
--R  /
--R       +---+ +-+
--R     4\|- a \|a
--R                                                     Type: Expression Integer
--E 58

--S 59 of 112
ratForm %
 
   There are no library operations named ratForm 
      Use HyperDoc Browse or issue
                              )what op ratForm
      to learn if there is any operation containing " ratForm " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      ratForm with argument type(s) 
                             Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named ratForm 
--R      Use HyperDoc Browse or issue
--R                              )what op ratForm
--R      to learn if there is any operation containing " ratForm " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      ratForm with argument type(s) 
--R                             Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 59

-- Input for page DerivativePage
)clear all
 

--S 60 of 112
f := exp exp x
 

            x
          %e
   (1)  %e
                                                     Type: Expression Integer
--R 
--R
--R            x
--R          %e
--R   (1)  %e
--R                                                     Type: Expression Integer
--E 60

--S 61 of 112
differentiate(f, x)
 

               x
          x  %e
   (2)  %e %e
                                                     Type: Expression Integer
--R 
--R
--R               x
--R          x  %e
--R   (2)  %e %e
--R                                                     Type: Expression Integer
--E 61

--S 62 of 112
differentiate(f, x, 4)
 

                                              x
            x 4       x 3       x 2     x   %e
   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
                                                     Type: Expression Integer
--R 
--R
--R                                              x
--R            x 4       x 3       x 2     x   %e
--R   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
--R                                                     Type: Expression Integer
--E 62

--S 63 of 112
g := sin(x**2 + y)
 

                 2
   (4)  sin(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (4)  sin(y + x )
--R                                                     Type: Expression Integer
--E 63

--S 64 of 112
differentiate(g, y)
 

                 2
   (5)  cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (5)  cos(y + x )
--R                                                     Type: Expression Integer
--E 64

--S 65 of 112
differentiate(g, [y, y, x, x])
 

          2         2              2
   (6)  4x sin(y + x ) - 2cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R          2         2              2
--R   (6)  4x sin(y + x ) - 2cos(y + x )
--R                                                     Type: Expression Integer
--E 65

-- Input for page SeriesFormulaPage
)clear all
 

--S 66 of 112
taylor(n +-> 1/factorial(n),x = 0)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (1)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
                2      6      24      120      720      5040
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (1)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
--R                2      6      24      120      720      5040
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 66

--S 67 of 112
taylor(n +-> (-1)**(n-1)/n,x = 1,1..)
 

   (2)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7            8
     - (x - 1)  + O((x - 1) )
     7
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (2)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7            8
--R     - (x - 1)  + O((x - 1) )
--R     7
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 67

--S 68 of 112
taylor(n +-> (-1)**(n-1)/n,x = 1,1..7)
 

   (3)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7
     - (x - 1)
     7
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (3)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7
--R     - (x - 1)
--R     7
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 68

--S 69 of 112
laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..)
 

   (4)
            - 1   1   1           1        2   1        3   1        4
     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
                  2   3           4            5            6
   + 
     1        5   1        6            7
     - (x - 1)  - - (x - 1)  + O((x - 1) )
     7            8
                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--R 
--R
--R   (4)
--R            - 1   1   1           1        2   1        3   1        4
--R     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
--R                  2   3           4            5            6
--R   + 
--R     1        5   1        6            7
--R     - (x - 1)  - - (x - 1)  + O((x - 1) )
--R     7            8
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--E 69

--S 70 of 112
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)
 

            1  3    1   5     1   7      9
   (5)  x - - x  + --- x  - ---- x  + O(x )
            6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      9
--R   (5)  x - - x  + --- x  - ---- x  + O(x )
--R            6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 70

--S 71 of 112
puiseux(j +-> j**2,x = 8,-4/3..,1/2)
 

                    4               5              1
                  - -             - -            - -
        16          3   25          6   1          3            0
   (6)  -- (x - 8)    + -- (x - 8)    + - (x - 8)    + O((x - 8) )
         9              36              9
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                    4               5              1
--R                  - -             - -            - -
--R        16          3   25          6   1          3            0
--R   (6)  -- (x - 8)    + -- (x - 8)    + - (x - 8)    + O((x - 8) )
--R         9              36              9
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 71

--S 72 of 112
series(n +-> 1/factorial(n),x = 0)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (7)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
                2      6      24      120      720      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (7)  1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + O(x )
--R                2      6      24      120      720      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 72

--S 73 of 112
series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..)
 

   (8)
            - 1   1   1           1        2   1        3   1        4
     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
                  2   3           4            5            6
   + 
     1        5   1        6            7
     - (x - 1)  - - (x - 1)  + O((x - 1) )
     7            8
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (8)
--R            - 1   1   1           1        2   1        3   1        4
--R     (x - 1)    - - + - (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)
--R                  2   3           4            5            6
--R   + 
--R     1        5   1        6            7
--R     - (x - 1)  - - (x - 1)  + O((x - 1) )
--R     7            8
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 73

--S 74 of 112
series(i +-> (-1)**((i - 1)/2)/factorial(i),x = 0,1..,2)
 

            1  3    1   5     1   7      9
   (9)  x - - x  + --- x  - ---- x  + O(x )
            6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      9
--R   (9)  x - - x  + --- x  - ---- x  + O(x )
--R            6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 74

-- Input for page SeriesCreationPage
)clear all
 

--S 75 of 112
x := series x
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 75

--S 76 of 112
1/(1 - x - x**2)
 

                  2     3     4     5      6      7      8
   (2)  1 + x + 2x  + 3x  + 5x  + 8x  + 13x  + 21x  + O(x )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                  2     3     4     5      6      7      8
--R   (2)  1 + x + 2x  + 3x  + 5x  + 8x  + 13x  + 21x  + O(x )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 76

--S 77 of 112
sin(x)
 

            1  3    1   5     1   7      9
   (3)  x - - x  + --- x  - ---- x  + O(x )
            6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      9
--R   (3)  x - - x  + --- x  - ---- x  + O(x )
--R            6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 77

--S 78 of 112
sin(1 + x)
 

   (4)
                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
                           2           6          24          120
   + 
       sin(1)  6   cos(1)  7      8
     - ------ x  - ------ x  + O(x )
         720        5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (4)
--R                        sin(1)  2   cos(1)  3   sin(1)  4   cos(1)  5
--R     sin(1) + cos(1)x - ------ x  - ------ x  + ------ x  + ------ x
--R                           2           6          24          120
--R   + 
--R       sin(1)  6   cos(1)  7      8
--R     - ------ x  - ------ x  + O(x )
--R         720        5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 78

--S 79 of 112
sin(a * x)
 

               3        5        7
              a   3    a   5    a    7      9
   (5)  a x - -- x  + --- x  - ---- x  + O(x )
               6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7
--R              a   3    a   5    a    7      9
--R   (5)  a x - -- x  + --- x  - ---- x  + O(x )
--R               6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 79

--S 80 of 112
series(1/log(y),y = 1)
 

   (6)
            - 1   1    1            1        2    19        3    3         4
     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
                  2   12           24            720            160
   + 
        863         5    275         6            7
     - ----- (y - 1)  + ----- (y - 1)  + O((y - 1) )
       60480            24192
                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--R 
--R
--R   (6)
--R            - 1   1    1            1        2    19        3    3         4
--R     (y - 1)    + - - -- (y - 1) + -- (y - 1)  - --- (y - 1)  + --- (y - 1)
--R                  2   12           24            720            160
--R   + 
--R        863         5    275         6            7
--R     - ----- (y - 1)  + ----- (y - 1)  + O((y - 1) )
--R       60480            24192
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,y,1)
--E 80

--S 81 of 112
f : UTS(FLOAT,z,0) := exp(z)
 

   (7)
                    2                            3
     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
   + 
                                4                               5
     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
   + 
                                 6                               7      8
     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z  + O(z )
                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--R 
--R
--R   (7)
--R                    2                            3
--R     1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
--R   + 
--R                                 6                               7      8
--R     0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z  + O(z )
--R                                    Type: UnivariateTaylorSeries(Float,z,0.0)
--E 81

--S 82 of 112
series(1/factorial(n),n,w = 0)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (8)  1 + w + - w  + - w  + -- w  + --- w  + --- w  + ---- w  + O(w )
                2      6      24      120      720      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,w,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (8)  1 + w + - w  + - w  + -- w  + --- w  + --- w  + ---- w  + O(w )
--R                2      6      24      120      720      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,w,0)
--E 82

-- Input for page SeriesFunctionPage
)clear all
 

--S 83 of 112
x := series x
 

   (1)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 83

--S 84 of 112
rat := x**2 / (1 - 6*x + x**2)
 

   (2)
    2     3      4       5        6        7         8          9      10
   x  + 6x  + 35x  + 204x  + 1189x  + 6930x  + 40391x  + 235416x  + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R    2     3      4       5        6        7         8          9      10
--R   x  + 6x  + 35x  + 204x  + 1189x  + 6930x  + 40391x  + 235416x  + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 84

--S 85 of 112
sin(rat)
 

   (3)
    2     3      4       5   7133  6        7   80711  8          9      10
   x  + 6x  + 35x  + 204x  + ---- x  + 6927x  + ----- x  + 235068x  + O(x  )
                               6                  2
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)
--R    2     3      4       5   7133  6        7   80711  8          9      10
--R   x  + 6x  + 35x  + 204x  + ---- x  + 6927x  + ----- x  + 235068x  + O(x  )
--R                               6                  2
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 85

--S 86 of 112
y : UTS(FRAC INT,y,0) := y
 

   (4)  y
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R   (4)  y
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 86

--S 87 of 112
exp(y)
 

                1  2   1  3    1  4    1   5    1   6     1   7      8
   (5)  1 + y + - y  + - y  + -- y  + --- y  + --- y  + ---- y  + O(y )
                2      6      24      120      720      5040
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R                1  2   1  3    1  4    1   5    1   6     1   7      8
--R   (5)  1 + y + - y  + - y  + -- y  + --- y  + --- y  + ---- y  + O(y )
--R                2      6      24      120      720      5040
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 87

--S 88 of 112
tan(y**2)
 

         2   1  6      8
   (6)  y  + - y  + O(y )
             3
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R         2   1  6      8
--R   (6)  y  + - y  + O(y )
--R             3
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 88

--S 89 of 112
cos(y + y**5)
 

            1  2    1  4   721  6      8
   (7)  1 - - y  + -- y  - --- y  + O(y )
            2      24      720
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R            1  2    1  4   721  6      8
--R   (7)  1 - - y  + -- y  - --- y  + O(y )
--R            2      24      720
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 89

--S 90 of 112
log(1 + sin(y))
 

            1  2   1  3    1  4    1  5    1  6    61   7      8
   (8)  y - - y  + - y  - -- y  + -- y  - -- y  + ---- y  + O(y )
            2      6      12      24      45      5040
                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--R 
--R
--R            1  2   1  3    1  4    1  5    1  6    61   7      8
--R   (8)  y - - y  + - y  - -- y  + -- y  - -- y  + ---- y  + O(y )
--R            2      6      12      24      45      5040
--R                           Type: UnivariateTaylorSeries(Fraction Integer,y,0)
--E 90

--S 91 of 112
z : UTS(EXPR INT,z,0) := z
 

   (9)  z
                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--R 
--R
--R   (9)  z
--R                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--E 91

--S 92 of 112
exp(2 + tan(z))
 

   (10)
                    2        2         2          2          2           2
       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
     %e  + %e z + --- z  + --- z  + ---- z  + ----- z  + ----- z  + ------ z
                   2        2         8        120        240         720
   + 
        8
     O(z )
                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--R 
--R
--R   (10)
--R                    2        2         2          2          2           2
--R       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
--R     %e  + %e z + --- z  + --- z  + ---- z  + ----- z  + ----- z  + ------ z
--R                   2        2         8        120        240         720
--R   + 
--R        8
--R     O(z )
--R                         Type: UnivariateTaylorSeries(Expression Integer,z,0)
--E 92

--S 93 of 112
w := taylor w
 

   (11)  w
                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--R 
--R
--R   (11)  w
--R                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--E 93

--S 94 of 112
exp(2 + tan(w))
 

   (12)
                    2        2         2          2          2           2
       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
     %e  + %e w + --- w  + --- w  + ---- w  + ----- w  + ----- w  + ------ w
                   2        2         8        120        240         720
   + 
        8
     O(w )
                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--R 
--R
--R   (12)
--R                    2        2         2          2          2           2
--R       2     2    %e   2   %e   3   3%e   4   37%e   5   59%e   6   137%e   7
--R     %e  + %e w + --- w  + --- w  + ---- w  + ----- w  + ----- w  + ------ w
--R                   2        2         8        120        240         720
--R   + 
--R        8
--R     O(w )
--R                         Type: UnivariateTaylorSeries(Expression Integer,w,0)
--E 94

-- Input for page LimitPage
)clear all
 

--S 95 of 112
f := sin(a*x) / tan(b*x)
 

        sin(a x)
   (1)  --------
        tan(b x)
                                                     Type: Expression Integer
--R 
--R
--R        sin(a x)
--R   (1)  --------
--R        tan(b x)
--R                                                     Type: Expression Integer
--E 95

--S 96 of 112
limit(f,x=0)
 

        a
   (2)  -
        b
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        a
--R   (2)  -
--R        b
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 96

--S 97 of 112
g := csc(a*x) / csch(b*x)
 

         csc(a x)
   (3)  ---------
        csch(b x)
                                                     Type: Expression Integer
--R 
--R
--R         csc(a x)
--R   (3)  ---------
--R        csch(b x)
--R                                                     Type: Expression Integer
--E 97

--S 98 of 112
limit(g,x=0)
 

        b
   (4)  -
        a
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        b
--R   (4)  -
--R        a
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 98

--S 99 of 112
h := (1 + k/x)**x
 

         x + k x
   (5)  (-----)
           x
                                                     Type: Expression Integer
--R 
--R
--R         x + k x
--R   (5)  (-----)
--R           x
--R                                                     Type: Expression Integer
--E 99

--S 100 of 112
limit(h,x=%plusInfinity)
 

          k
   (6)  %e
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R          k
--R   (6)  %e
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 100

-- Input for page SeriesBernoulliPage
)clear all
 

--S 101 of 112
reduce(+,[m**4 for m in 1..10])
 

   (1)  25333
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  25333
--R                                                        Type: PositiveInteger
--E 101

--S 102 of 112
sum4 := sum(m**4, m = 1..k)
 

          5      4      3
        6k  + 15k  + 10k  - k
   (2)  ---------------------
                  30
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          5      4      3
--R        6k  + 15k  + 10k  - k
--R   (2)  ---------------------
--R                  30
--R                                            Type: Fraction Polynomial Integer
--E 102

--S 103 of 112
eval(sum4, k = 10)
 

   (3)  25333
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (3)  25333
--R                                            Type: Fraction Polynomial Integer
--E 103

--S 104 of 112
f := t*exp(x*t) / (exp(t) - 1)
 

            t x
        t %e
   (4)  -------
          t
        %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R            t x
--R        t %e
--R   (4)  -------
--R          t
--R        %e  - 1
--R                                                     Type: Expression Integer
--E 104

)set streams calculate 5
 
 
--S 105 of 112
ff := taylor(f,t = 0)
 

   (5)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5      6
     ---------------------- t  + --------------------- t  + O(t )
               720                        720
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (5)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5      6
--R     ---------------------- t  + --------------------- t  + O(t )
--R               720                        720
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 105

--S 106 of 112
factorial(6) * coefficient(ff,6)
 

           6       5       4      2
        42x  - 126x  + 105x  - 21x  + 1
   (6)  -------------------------------
                       42
                                                     Type: Expression Integer
--R 
--R
--R           6       5       4      2
--R        42x  - 126x  + 105x  - 21x  + 1
--R   (6)  -------------------------------
--R                       42
--R                                                     Type: Expression Integer
--E 106

--S 107 of 112
g := eval(f, x = x + 1) - f
 

            t x + t       t x
        t %e        - t %e
   (7)  ---------------------
                 t
               %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R            t x + t       t x
--R        t %e        - t %e
--R   (7)  ---------------------
--R                 t
--R               %e  - 1
--R                                                     Type: Expression Integer
--E 107

--S 108 of 112
normalize(g)
 

            t x
   (8)  t %e
                                                     Type: Expression Integer
--R 
--R
--R            t x
--R   (8)  t %e
--R                                                     Type: Expression Integer
--E 108

--S 109 of 112
taylor(g,t = 0)
 

                    2       3       4
               2   x   3   x   4   x   5      6
   (9)  t + x t  + -- t  + -- t  + -- t  + O(t )
                    2       6      24
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R                    2       3       4
--R               2   x   3   x   4   x   5      6
--R   (9)  t + x t  + -- t  + -- t  + -- t  + O(t )
--R                    2       6      24
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 109

--S 110 of 112
B5 := factorial(5) * coefficient(ff,5)
 

           5      4      3
         6x  - 15x  + 10x  - x
   (10)  ---------------------
                   6
                                                     Type: Expression Integer
--R 
--R
--R           5      4      3
--R         6x  - 15x  + 10x  - x
--R   (10)  ---------------------
--R                   6
--R                                                     Type: Expression Integer
--E 110

--S 111 of 112
1/5 * (eval(B5, x = k + 1) - eval(B5, x = 1))
 

           5      4      3
         6k  + 15k  + 10k  - k
   (11)  ---------------------
                   30
                                                     Type: Expression Integer
--R 
--R
--R           5      4      3
--R         6k  + 15k  + 10k  - k
--R   (11)  ---------------------
--R                   30
--R                                                     Type: Expression Integer
--E 111

--S 112 of 112
sum4
 

           5      4      3
         6k  + 15k  + 10k  - k
   (12)  ---------------------
                   30
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           5      4      3
--R         6k  + 15k  + 10k  - k
--R   (12)  ---------------------
--R                   30
--R                                            Type: Fraction Polynomial Integer
--E 112
)spool
 
Starts dribbling to cycles.output (2010/3/27, 18:24:44).
)set message test on
 
)set message auto off
 
)clear all
 


)clear all
 

)expose EVALCYC
 
   EvaluateCycleIndicators is now explicitly exposed in frame initial 

--S 1 of 46
complete 1
 

   (1)  (1)
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (1)  (1)
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 1

--S 2 of 46
complete 2
 

        1       1   2
   (2)  - (2) + - (1 )
        2       2
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1   2
--R   (2)  - (2) + - (1 )
--R        2       2
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 2

--S 3 of 46
complete 3
 

        1       1         1   3
   (3)  - (3) + - (2 1) + - (1 )
        3       2         6
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        1       1         1   3
--R   (3)  - (3) + - (2 1) + - (1 )
--R        3       2         6
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 3

--S 4 of 46
complete 7
 

   (4)
     1       1          1          1     2     1         1            1     3
     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
      1      5      1    7
     --- (2 1 ) + ---- (1 )
     240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (4)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) + - (6 1) + -- (5 2) + -- (5 1 ) + -- (4 3) + - (4 2 1) + -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) + -- (3 2 1 ) + -- (3 1 ) + -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R      1      5      1    7
--R     --- (2 1 ) + ---- (1 )
--R     240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 4

--S 5 of 46
elementary 7
 

   (5)
     1       1          1          1     2     1         1            1     3
     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
     7       6         10         10          12         8           24
   + 
      1   2      1     2     1       2     1     4     1   3      1   2 3
     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
     18         24          12            72          48         48
   + 
        1      5      1    7
     - --- (2 1 ) + ---- (1 )
       240          5040
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (5)
--R     1       1          1          1     2     1         1            1     3
--R     - (7) - - (6 1) - -- (5 2) + -- (5 1 ) - -- (4 3) + - (4 2 1) - -- (4 1 )
--R     7       6         10         10          12         8           24
--R   + 
--R      1   2      1     2     1       2     1     4     1   3      1   2 3
--R     -- (3 1) + -- (3 2 ) - -- (3 2 1 ) + -- (3 1 ) - -- (2 1) + -- (2 1 )
--R     18         24          12            72          48         48
--R   + 
--R        1      5      1    7
--R     - --- (2 1 ) + ---- (1 )
--R       240          5040
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 5

--S 6 of 46
alternating 7
 

   (6)
     2       1     2    1           1   2      1     2     1     4     1   2 3
     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
     7       5          4           9         12          36          24
   + 
       1    7
     ---- (1 )
     2520
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (6)
--R     2       1     2    1           1   2      1     2     1     4     1   2 3
--R     - (7) + - (5 1 ) + - (4 2 1) + - (3 1) + -- (3 2 ) + -- (3 1 ) + -- (2 1 )
--R     7       5          4           9         12          36          24
--R   + 
--R       1    7
--R     ---- (1 )
--R     2520
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 6

--S 7 of 46
cyclic 7
 

        6       1   7
   (7)  - (7) + - (1 )
        7       7
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        6       1   7
--R   (7)  - (7) + - (1 )
--R        7       7
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 7

--S 8 of 46
dihedral 7
 

        3       1   3      1   7
   (8)  - (7) + - (2 1) + -- (1 )
        7       2         14
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R        3       1   3      1   7
--R   (8)  - (7) + - (2 1) + -- (1 )
--R        7       2         14
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 8

--S 9 of 46
graphs 5
 

   (9)
   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
   6           5        4         6         8          12          120
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (9)
--R   1           1   2    1   2     1   3     1   4 2     1   3 4     1    10
--R   - (6 3 1) + - (5 ) + - (4 2) + - (3 1) + - (2 1 ) + -- (2 1 ) + --- (1  )
--R   6           5        4         6         8          12          120
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 9

--S 10 of 46
cap(complete 2**2,complete 2*complete 1**2)
 

   (10)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (10)  4
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 46
cap(elementary 2**2,complete 2*complete 1**2)
 

   (11)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  2
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 46
cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)
 

   (12)  24
                                                       Type: Fraction Integer
--R 
--R
--R   (12)  24
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 46
cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)
 

   (13)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  8
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 46
cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)
 

   (14)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (14)  8
--R                                                       Type: Fraction Integer
--E 14

--S 15 of 46
eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))
 

   (15)  1500
                                                       Type: Fraction Integer
--R 
--R
--R   (15)  1500
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 46
square:=dihedral 4
 

         1       3   2    1     2    1   4
   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
         4       8        4          8
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1       3   2    1     2    1   4
--R   (16)  - (4) + - (2 ) + - (2 1 ) + - (1 )
--R         4       8        4          8
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 16

--S 17 of 46
cap(complete 2**2,square)
 

   (17)  2
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  2
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 46
cap(complete 3*complete 2**2,dihedral 7)
 

   (18)  18
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  18
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 46
cap(graphs 5,complete 7*complete 3)
 

   (19)  4
                                                       Type: Fraction Integer
--R 
--R
--R   (19)  4
--R                                                       Type: Fraction Integer
--E 19

--S 20 of 46
macro s == powerSum
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 46
cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)
 

         1   2    1   2 2    3   4     1   8
   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
         4        3          8        24
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R         1   2    1   2 2    3   4     1   8
--R   (21)  - (4 ) + - (3 1 ) + - (2 ) + -- (1 )
--R         4        3          8        24
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 21

--S 22 of 46
cap(complete 4**2,cube)
 

   (22)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  7
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))
 

   (23)  7
                                                       Type: Fraction Integer
--R 
--R
--R   (23)  7
--R                                                       Type: Fraction Integer
--E 23

--S 24 of 46
cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))
 

   (24)  17
                                                       Type: Fraction Integer
--R 
--R
--R   (24)  17
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))
 

   (25)  10
                                                       Type: Fraction Integer
--R 
--R
--R   (25)  10
--R                                                       Type: Fraction Integer
--E 25

--S 26 of 46
cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))
 

   (26)  23
                                                       Type: Fraction Integer
--R 
--R
--R   (26)  23
--R                                                       Type: Fraction Integer
--E 26

--S 27 of 46
x:ULS(FRAC INT,'x,0):=x
 

   (27)  x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (27)  x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 27

--S 28 of 46
ZeroOrOne:INT->ULS(FRAC INT,'x,0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 46
Integers:INT->ULS(FRAC INT,'x,0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 46
ZeroOrOne n == 1+x**n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E

--S 31 of 46
ZeroOrOne 5
 
   Compiling function ZeroOrOne with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5
   (31)  1 + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function ZeroOrOne with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5
--R   (31)  1 + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 31

--S 32 of 46
Integers n == 1/(1-x**n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 46
Integers 5
 
   Compiling function Integers with type Integer -> 
      UnivariateLaurentSeries(Fraction Integer,x,0) 

              5    10      11
   (33)  1 + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R   Compiling function Integers with type Integer -> 
--R      UnivariateLaurentSeries(Fraction Integer,x,0) 
--R
--R              5    10      11
--R   (33)  1 + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 33

--S 34 of 46
eval(ZeroOrOne,graphs 5)
 

                   2     3     4     5     6     7     8    9    10      11
   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6     7     8    9    10      11
--R   (34)  1 + x + 2x  + 4x  + 6x  + 6x  + 6x  + 4x  + 2x  + x  + x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 34

--S 35 of 46
eval(ZeroOrOne,dihedral 8)
 

                   2     3     4     5     6    7    8
   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (35)  1 + x + 4x  + 5x  + 8x  + 5x  + 4x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 35

--S 36 of 46
eval(Integers,complete 4)
 

   (36)
             2     3     4     5     6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (36)
--R             2     3     4     5     6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 6x  + 9x  + 11x  + 15x  + 18x  + 23x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 36

--S 37 of 46
eval(Integers,elementary 4)
 

   (37)
      6    7     8     9     10     11     12      13      14      15      16
     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
   + 
        17
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (37)
--R      6    7     8     9     10     11     12      13      14      15      16
--R     x  + x  + 2x  + 3x  + 5x   + 6x   + 9x   + 11x   + 15x   + 18x   + 23x
--R   + 
--R        17
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 37

--S 38 of 46
eval(ZeroOrOne,cube)
 

                   2     3     4     5     6    7    8
   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R                   2     3     4     5     6    7    8
--R   (38)  1 + x + 3x  + 3x  + 7x  + 3x  + 3x  + x  + x
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 38

--S 39 of 46
eval(Integers,cube)
 

   (39)
               2     3      4      5      6       7       8       9       10
     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (39)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 4x  + 7x  + 21x  + 37x  + 85x  + 151x  + 292x  + 490x  + 848x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 39

--S 40 of 46
eval(Integers,graphs 5)
 

   (40)
               2     3      4      5      6       7       8       9       10
     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (40)
--R               2     3      4      5      6       7       8       9       10
--R     1 + x + 3x  + 7x  + 17x  + 35x  + 76x  + 149x  + 291x  + 539x  + 974x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 40

--S 41 of 46
eval(ZeroOrOne ,graphs 15)
 

   (41)
               2     3      4      5      6       7       8        9        10
     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
   + 
        11
     O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (41)
--R               2     3      4      5      6       7       8        9        10
--R     1 + x + 2x  + 5x  + 11x  + 26x  + 68x  + 177x  + 496x  + 1471x  + 4583x
--R   + 
--R        11
--R     O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 41

--S 42 of 46
cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)
 

   (42)  49958972383320
                                                       Type: Fraction Integer
--R 
--R
--R   (42)  49958972383320
--R                                                       Type: Fraction Integer
--E 42

--S 43 of 46
sf3221:= SFunction [3,2,2,1]
 

   (43)
      1          1     2     1   2     1            1     4     1   2
     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
     12         12          16        12           24          36
   + 
      1   2 2     1     2      1       3     1     5     1    4     1   3 2
     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
     36          24           36            72          192        48
   + 
      1   2 4     1      6     1    8
     -- (2 1 ) - --- (2 1 ) + --- (1 )
     96          144          576
                                   Type: SymmetricPolynomial Fraction Integer
--R 
--R
--R   (43)
--R      1          1     2     1   2     1            1     4     1   2
--R     -- (6 2) - -- (6 1 ) - -- (4 ) + -- (4 3 1) + -- (4 1 ) - -- (3 2)
--R     12         12          16        12           24          36
--R   + 
--R      1   2 2     1     2      1       3     1     5     1    4     1   3 2
--R     -- (3 1 ) - -- (3 2 1) - -- (3 2 1 ) - -- (3 1 ) - --- (2 ) + -- (2 1 )
--R     36          24           36            72          192        48
--R   + 
--R      1   2 4     1      6     1    8
--R     -- (2 1 ) - --- (2 1 ) + --- (1 )
--R     96          144          576
--R                                   Type: SymmetricPolynomial Fraction Integer
--E 43

--S 44 of 46
cap(sf3221,complete 2**4)
 

   (44)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (44)  3
--R                                                       Type: Fraction Integer
--E 44

--S 45 of 46
cap(sf3221,powerSum 1**8)
 

   (45)  70
                                                       Type: Fraction Integer
--R 
--R
--R   (45)  70
--R                                                       Type: Fraction Integer
--E 45

--S 46 of 46
eval(Integers,sf3221)
 

   (46)
      9     10     11      12      13      14      15       16       17       18
     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
   + 
         19      20
     432x   + O(x  )
                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--R 
--R
--R   (46)
--R      9     10     11      12      13      14      15       16       17       18
--R     x  + 3x   + 7x   + 14x   + 27x   + 47x   + 79x   + 126x   + 196x   + 294x
--R   + 
--R         19      20
--R     432x   + O(x  )
--R                          Type: UnivariateLaurentSeries(Fraction Integer,x,0)
--E 46
)spool
 
Starts dribbling to XPolynomialRing.output (2010/3/27, 18:46:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 15
Word := OrderedFreeMonoid(Symbol)
 

   (1)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (1)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 1

--S 2 of 15
poly:= XPR(Integer,Word)
 

   (2)  XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
                                                                 Type: Domain
--R 
--R
--R   (2)  XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--R                                                                 Type: Domain
--E 2

--S 3 of 15
p:poly := 2 * x - 3 * y + 1
 

   (3)  1 + 2x - 3y
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--R 
--R
--R   (3)  1 + 2x - 3y
--R                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--E 3

--S 4 of 15
q:poly := 2 * x + 1
 

   (4)  1 + 2x
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--R 
--R
--R   (4)  1 + 2x
--R                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--E 4

--S 5 of 15
p + q
 

   (5)  2 + 4x - 3y
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--R 
--R
--R   (5)  2 + 4x - 3y
--R                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--E 5

--S 6 of 15
p * q
 

                        2
   (6)  1 + 4x - 3y + 4x  - 6y x
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--R 
--R
--R                        2
--R   (6)  1 + 4x - 3y + 4x  - 6y x
--R                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--E 6

--S 7 of 15
(p+q)**2-p**2-q**2-2*p*q
 

   (7)  - 6x y + 6y x
                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--R 
--R
--R   (7)  - 6x y + 6y x
--R                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
--E 7

--S 8 of 15
M := SquareMatrix(2,Fraction Integer)
 

   (8)  SquareMatrix(2,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (8)  SquareMatrix(2,Fraction Integer)
--R                                                                 Type: Domain
--E 8

--S 9 of 15
poly1:= XPR(M,Word)
 

   (9)
   XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
                                                                 Type: Domain
--R 
--R
--R   (9)
--R   XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--R                                                                 Type: Domain
--E 9

--S 10 of 15
m1:M := matrix [ [i*j**2 for i in 1..2] for j in 1..2]
 

         +1  2+
   (10)  |    |
         +4  8+
                                       Type: SquareMatrix(2,Fraction Integer)
--R 
--R
--R         +1  2+
--R   (10)  |    |
--R         +4  8+
--R                                       Type: SquareMatrix(2,Fraction Integer)
--E 10

--S 11 of 15
m2:M := m1 - 5/4
 

         +  1    +
         |- -  2 |
         |  4    |
   (11)  |       |
         |     27|
         | 4   --|
         +      4+
                                       Type: SquareMatrix(2,Fraction Integer)
--R 
--R
--R         +  1    +
--R         |- -  2 |
--R         |  4    |
--R   (11)  |       |
--R         |     27|
--R         | 4   --|
--R         +      4+
--R                                       Type: SquareMatrix(2,Fraction Integer)
--E 11

--S 12 of 15
m3: M := m2**2
 

         +129     +
         |---  13 |
         | 16     |
   (12)  |        |
         |     857|
         |26   ---|
         +      16+
                                       Type: SquareMatrix(2,Fraction Integer)
--R 
--R
--R         +129     +
--R         |---  13 |
--R         | 16     |
--R   (12)  |        |
--R         |     857|
--R         |26   ---|
--R         +      16+
--R                                       Type: SquareMatrix(2,Fraction Integer)
--E 12

--S 13 of 15
pm:poly1   := m1*x + m2*y + m3*z - 2/3 
 

         +  2     +             +  1    +    +129     +
         |- -   0 |             |- -  2 |    |---  13 |
         |  3     |   +1  2+    |  4    |    | 16     |
   (13)  |        | + |    |x + |       |y + |        |z
         |       2|   +4  8+    |     27|    |     857|
         | 0   - -|             | 4   --|    |26   ---|
         +       3+             +      4+    +      16+
Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--R 
--R
--R         +  2     +             +  1    +    +129     +
--R         |- -   0 |             |- -  2 |    |---  13 |
--R         |  3     |   +1  2+    |  4    |    | 16     |
--R   (13)  |        | + |    |x + |       |y + |        |z
--R         |       2|   +4  8+    |     27|    |     857|
--R         | 0   - -|             | 4   --|    |26   ---|
--R         +       3+             +      4+    +      16+
--RType: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--E 13

--S 14 of 15
qm:poly1 := pm - m1*x
 

         +  2     +   +  1    +    +129     +
         |- -   0 |   |- -  2 |    |---  13 |
         |  3     |   |  4    |    | 16     |
   (14)  |        | + |       |y + |        |z
         |       2|   |     27|    |     857|
         | 0   - -|   | 4   --|    |26   ---|
         +       3+   +      4+    +      16+
Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--R 
--R
--R         +  2     +   +  1    +    +129     +
--R         |- -   0 |   |- -  2 |    |---  13 |
--R         |  3     |   |  4    |    | 16     |
--R   (14)  |        | + |       |y + |        |z
--R         |       2|   |     27|    |     857|
--R         | 0   - -|   | 4   --|    |26   ---|
--R         +       3+   +      4+    +      16+
--RType: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--E 14

--S 15 of 15
qm**3
 

   (15)
     +   8      +   +  1  8+    +43   52 +    +  129       +
     |- --   0  |   |- -  -|    |--   -- |    |- ---  - 26 |
     |  27      |   |  3  3|    | 4    3 |    |   8        | 2
     |          | + |      |y + |        |z + |            |y
     |         8|   |16    |    |104  857|    |         857|
     | 0    - --|   |--   9|    |---  ---|    |- 52   - ---|
     +        27+   + 3    +    + 3    12+    +          8 +
   + 
     +  3199     831 +      +  3199     831 +      +  103169     6409 +
     |- ----   - --- |      |- ----   - --- |      |- ------   - ---- |
     |   32       4  |      |   32       4  |      |    128        4  | 2
     |               |y z + |               |z y + |                  |z
     |  831     26467|      |  831     26467|      |   6409     820977|
     |- ---   - -----|      |- ---   - -----|      | - ----   - ------|
     +   2        32 +      +   2        32 +      +     2        128 +
   + 
     +3199   831 +     +103169   6409 +      +103169   6409 +
     |----   --- |     |------   ---- |      |------   ---- |
     | 64     8  | 3   |  256      8  | 2    |  256      8  |
     |           |y  + |              |y z + |              |y z y
     |831   26467|     | 6409   820977|      | 6409   820977|
     |---   -----|     | ----   ------|      | ----   ------|
     + 4      64 +     +   4      256 +      +   4      256 +
   + 
     +3178239   795341 +       +103169   6409 +       +3178239   795341 +
     |-------   ------ |       |------   ---- |       |-------   ------ |
     |  1024      128  |   2   |  256      8  |   2   |  1024      128  |
     |                 |y z  + |              |z y  + |                 |z y z
     |795341   25447787|       | 6409   820977|       |795341   25447787|
     |------   --------|       | ----   ------|       |------   --------|
     +  64       1024  +       +   4      256 +       +  64       1024  +
   + 
     +3178239   795341 +      +98625409  12326223 +
     |-------   ------ |      |--------  -------- |
     |  1024      128  | 2    |  4096       256   | 3
     |                 |z y + |                   |z
     |795341   25447787|      |12326223  788893897|
     |------   --------|      |--------  ---------|
     +  64       1024  +      +   128       4096  +
Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--R 
--R
--R   (15)
--R     +   8      +   +  1  8+    +43   52 +    +  129       +
--R     |- --   0  |   |- -  -|    |--   -- |    |- ---  - 26 |
--R     |  27      |   |  3  3|    | 4    3 |    |   8        | 2
--R     |          | + |      |y + |        |z + |            |y
--R     |         8|   |16    |    |104  857|    |         857|
--R     | 0    - --|   |--   9|    |---  ---|    |- 52   - ---|
--R     +        27+   + 3    +    + 3    12+    +          8 +
--R   + 
--R     +  3199     831 +      +  3199     831 +      +  103169     6409 +
--R     |- ----   - --- |      |- ----   - --- |      |- ------   - ---- |
--R     |   32       4  |      |   32       4  |      |    128        4  | 2
--R     |               |y z + |               |z y + |                  |z
--R     |  831     26467|      |  831     26467|      |   6409     820977|
--R     |- ---   - -----|      |- ---   - -----|      | - ----   - ------|
--R     +   2        32 +      +   2        32 +      +     2        128 +
--R   + 
--R     +3199   831 +     +103169   6409 +      +103169   6409 +
--R     |----   --- |     |------   ---- |      |------   ---- |
--R     | 64     8  | 3   |  256      8  | 2    |  256      8  |
--R     |           |y  + |              |y z + |              |y z y
--R     |831   26467|     | 6409   820977|      | 6409   820977|
--R     |---   -----|     | ----   ------|      | ----   ------|
--R     + 4      64 +     +   4      256 +      +   4      256 +
--R   + 
--R     +3178239   795341 +       +103169   6409 +       +3178239   795341 +
--R     |-------   ------ |       |------   ---- |       |-------   ------ |
--R     |  1024      128  |   2   |  256      8  |   2   |  1024      128  |
--R     |                 |y z  + |              |z y  + |                 |z y z
--R     |795341   25447787|       | 6409   820977|       |795341   25447787|
--R     |------   --------|       | ----   ------|       |------   --------|
--R     +  64       1024  +       +   4      256 +       +  64       1024  +
--R   + 
--R     +3178239   795341 +      +98625409  12326223 +
--R     |-------   ------ |      |--------  -------- |
--R     |  1024      128  | 2    |  4096       256   | 3
--R     |                 |z y + |                   |z
--R     |795341   25447787|      |12326223  788893897|
--R     |------   --------|      |--------  ---------|
--R     +  64       1024  +      +   128       4096  +
--RType: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
--E 15
)spool
 
Starts dribbling to pfaffian.output (2010/3/27, 18:30:45).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 26
B0 n == matrix [[(if i=j+1 and odd? j then -1 else _
                   if i=j-1 and odd? i then 1 else 0) _
                     for j in 1..n] for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1
--S 2 of 26
B0 1
 
   Compiling function B0 with type PositiveInteger -> Matrix Integer 

   (2)  [0]
                                                         Type: Matrix Integer
--R 
--R   Compiling function B0 with type PositiveInteger -> Matrix Integer 
--R
--R   (2)  [0]
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 26
B0 2
 

        + 0   1+
   (3)  |      |
        +- 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1+
--R   (3)  |      |
--R        +- 1  0+
--R                                                         Type: Matrix Integer
--E 3

--S 4 of 26
B0 3
 

        + 0   1  0+
        |         |
   (4)  |- 1  0  0|
        |         |
        + 0   0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1  0+
--R        |         |
--R   (4)  |- 1  0  0|
--R        |         |
--R        + 0   0  0+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 26
B0 4
 

        + 0   1   0   0+
        |              |
        |- 1  0   0   0|
   (5)  |              |
        | 0   0   0   1|
        |              |
        + 0   0  - 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0+
--R        |              |
--R        |- 1  0   0   0|
--R   (5)  |              |
--R        | 0   0   0   1|
--R        |              |
--R        + 0   0  - 1  0+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 26
B0 5
 

        + 0   1   0   0  0+
        |                 |
        |- 1  0   0   0  0|
        |                 |
   (6)  | 0   0   0   1  0|
        |                 |
        | 0   0  - 1  0  0|
        |                 |
        + 0   0   0   0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0  0+
--R        |                 |
--R        |- 1  0   0   0  0|
--R        |                 |
--R   (6)  | 0   0   0   1  0|
--R        |                 |
--R        | 0   0  - 1  0  0|
--R        |                 |
--R        + 0   0   0   0  0+
--R                                                         Type: Matrix Integer
--E 6

--S 7 of 26
B0 6
 

        + 0   1   0   0   0   0+
        |                      |
        |- 1  0   0   0   0   0|
        |                      |
        | 0   0   0   1   0   0|
   (7)  |                      |
        | 0   0  - 1  0   0   0|
        |                      |
        | 0   0   0   0   0   1|
        |                      |
        + 0   0   0   0  - 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0   0   0+
--R        |                      |
--R        |- 1  0   0   0   0   0|
--R        |                      |
--R        | 0   0   0   1   0   0|
--R   (7)  |                      |
--R        | 0   0  - 1  0   0   0|
--R        |                      |
--R        | 0   0   0   0   0   1|
--R        |                      |
--R        + 0   0   0   0  - 1  0+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 26
B0 7
 

        + 0   1   0   0   0   0  0+
        |                         |
        |- 1  0   0   0   0   0  0|
        |                         |
        | 0   0   0   1   0   0  0|
        |                         |
   (8)  | 0   0  - 1  0   0   0  0|
        |                         |
        | 0   0   0   0   0   1  0|
        |                         |
        | 0   0   0   0  - 1  0  0|
        |                         |
        + 0   0   0   0   0   0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0   0   0  0+
--R        |                         |
--R        |- 1  0   0   0   0   0  0|
--R        |                         |
--R        | 0   0   0   1   0   0  0|
--R        |                         |
--R   (8)  | 0   0  - 1  0   0   0  0|
--R        |                         |
--R        | 0   0   0   0   0   1  0|
--R        |                         |
--R        | 0   0   0   0  - 1  0  0|
--R        |                         |
--R        + 0   0   0   0   0   0  0+
--R                                                         Type: Matrix Integer
--E 8

--S 9 of 26
B0 8
 

        + 0   1   0   0   0   0   0   0+
        |                              |
        |- 1  0   0   0   0   0   0   0|
        |                              |
        | 0   0   0   1   0   0   0   0|
        |                              |
        | 0   0  - 1  0   0   0   0   0|
   (9)  |                              |
        | 0   0   0   0   0   1   0   0|
        |                              |
        | 0   0   0   0  - 1  0   0   0|
        |                              |
        | 0   0   0   0   0   0   0   1|
        |                              |
        + 0   0   0   0   0   0  - 1  0+
                                                         Type: Matrix Integer
--R 
--R
--R        + 0   1   0   0   0   0   0   0+
--R        |                              |
--R        |- 1  0   0   0   0   0   0   0|
--R        |                              |
--R        | 0   0   0   1   0   0   0   0|
--R        |                              |
--R        | 0   0  - 1  0   0   0   0   0|
--R   (9)  |                              |
--R        | 0   0   0   0   0   1   0   0|
--R        |                              |
--R        | 0   0   0   0  - 1  0   0   0|
--R        |                              |
--R        | 0   0   0   0   0   0   0   1|
--R        |                              |
--R        + 0   0   0   0   0   0  - 1  0+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 26
PfChar(lambda, A) ==
    n := nrows A
    odd? n => 0
    (n = 2) => lambda^2 + A.(1,2)
    M := subMatrix(A, 3, n, 3, n)
    r := subMatrix(A, 1, 1, 3, n)
    s := subMatrix(A, 3, n, 2, 2)

    p := PfChar(lambda, M)
    d := degree(p, lambda)

    B := B0(n-2)
    C := r*B
    g := [(C*s).(1,1), A.(1,2), 1]
    if d >= 4 then 
        B := M*B
        for i in 4..d by 2 repeat
            C := C*B
            g := cons((C*s).(1,1), g)
    g := reverse! g

    res := 0
    for i in 0..d by 2 for j in 2..d+2 repeat
        c := coefficient(p, lambda, i)
        for e in first(g, j) for k in 2..-d by -2 repeat
            res := res +  c * e * lambda^(k+i)

    res
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 26
pfaffian A == eval(PfChar(l, A), l=0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 26
m:Matrix(Integer):=[[0,15],[-15,0]]
 

         + 0    15+
   (12)  |        |
         +- 15  0 +
                                                         Type: Matrix Integer
--R 
--R
--R         + 0    15+
--R   (12)  |        |
--R         +- 15  0 +
--R                                                         Type: Matrix Integer
--E 12

--S 13 of 26
pfaffian m
 
   Compiling function B0 with type Integer -> Matrix Integer 
   The type of the local variable res has changed in the computation.
   We will attempt to interpret the code.
   Cannot compile map: PfChar 
   We will attempt to interpret the code.

   (13)  15
                                                     Type: Polynomial Integer
--R 
--R   Compiling function B0 with type Integer -> Matrix Integer 
--R   The type of the local variable res has changed in the computation.
--R   We will attempt to interpret the code.
--R   Cannot compile map: PfChar 
--R   We will attempt to interpret the code.
--R
--R   (13)  15
--R                                                     Type: Polynomial Integer
--E 13

--S 14 of 26
m1:Matrix(Polynomial(Integer)):=[[0,a,b,c],[-a,0,d,e],[-b,-d,0,f],[-c,-e,-f,0]]
 

         + 0    a    b   c+
         |                |
         |- a   0    d   e|
   (14)  |                |
         |- b  - d   0   f|
         |                |
         +- c  - e  - f  0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         + 0    a    b   c+
--R         |                |
--R         |- a   0    d   e|
--R   (14)  |                |
--R         |- b  - d   0   f|
--R         |                |
--R         +- c  - e  - f  0+
--R                                              Type: Matrix Polynomial Integer
--E 14

--S 15 of 26
pfaffian m1
 

   (15)  a f - b e + c d
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  a f - b e + c d
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 26
(a,b,c,d,e,f):=(3,5,7,11,13,17)
 

   (16)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  17
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 26
m1
 

         + 0    a    b   c+
         |                |
         |- a   0    d   e|
   (17)  |                |
         |- b  - d   0   f|
         |                |
         +- c  - e  - f  0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         + 0    a    b   c+
--R         |                |
--R         |- a   0    d   e|
--R   (17)  |                |
--R         |- b  - d   0   f|
--R         |                |
--R         +- c  - e  - f  0+
--R                                              Type: Matrix Polynomial Integer
--E 17

--S 18 of 26
a*f-b*e+d*c
 

   (18)  63
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  63
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 26
n:=pfaffian m1
 

   (19)  a f - b e + c d
                                                     Type: Polynomial Integer
--R 
--R
--R   (19)  a f - b e + c d
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 26
eval(n,['a,'b,'c,'d,'e,'f]::List(Symbol),[a,b,c,d,e,f])
 

   (20)  63
                                                     Type: Polynomial Integer
--R 
--R
--R   (20)  63
--R                                                     Type: Polynomial Integer
--E 20


)clear properties z
 
)clear properties d
 
)clear properties v
 

--S 21 of 26
z:SQMATRIX(2,INT):=[[0,0],[0,0]]
 

         +0  0+
   (21)  |    |
         +0  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +0  0+
--R   (21)  |    |
--R         +0  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 21

--S 22 of 26
d:SQMATRIX(2,INT):=[[0,1],[-1,0]]
 

         + 0   1+
   (22)  |      |
         +- 1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         + 0   1+
--R   (22)  |      |
--R         +- 1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 22

--S 23 of 26
v:SQMATRIX(4,SQMATRIX(2,INT)):=[[z,d,d,d],[-d,z,d,d],[-d,-d,z,d],[-d,-d,-d,z]]
 

         + +0  0+   + 0   1+  + 0   1+  + 0   1++
         | |    |   |      |  |      |  |      ||
         | +0  0+   +- 1  0+  +- 1  0+  +- 1  0+|
         |                                      |
         |+0  - 1+   +0  0+   + 0   1+  + 0   1+|
         ||      |   |    |   |      |  |      ||
         |+1   0 +   +0  0+   +- 1  0+  +- 1  0+|
   (23)  |                                      |
         |+0  - 1+  +0  - 1+   +0  0+   + 0   1+|
         ||      |  |      |   |    |   |      ||
         |+1   0 +  +1   0 +   +0  0+   +- 1  0+|
         |                                      |
         |+0  - 1+  +0  - 1+  +0  - 1+   +0  0+ |
         ||      |  |      |  |      |   |    | |
         ++1   0 +  +1   0 +  +1   0 +   +0  0+ +
                                Type: SquareMatrix(4,SquareMatrix(2,Integer))
--R 
--R
--R         + +0  0+   + 0   1+  + 0   1+  + 0   1++
--R         | |    |   |      |  |      |  |      ||
--R         | +0  0+   +- 1  0+  +- 1  0+  +- 1  0+|
--R         |                                      |
--R         |+0  - 1+   +0  0+   + 0   1+  + 0   1+|
--R         ||      |   |    |   |      |  |      ||
--R         |+1   0 +   +0  0+   +- 1  0+  +- 1  0+|
--R   (23)  |                                      |
--R         |+0  - 1+  +0  - 1+   +0  0+   + 0   1+|
--R         ||      |  |      |   |    |   |      ||
--R         |+1   0 +  +1   0 +   +0  0+   +- 1  0+|
--R         |                                      |
--R         |+0  - 1+  +0  - 1+  +0  - 1+   +0  0+ |
--R         ||      |  |      |  |      |   |    | |
--R         ++1   0 +  +1   0 +  +1   0 +   +0  0+ +
--R                                Type: SquareMatrix(4,SquareMatrix(2,Integer))
--E 23

--S 24 of 26
pfaffian v
 
   There are 1 exposed and 0 unexposed library operations named 
      subMatrix having 5 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op subMatrix
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      subMatrix with argument type(s) 
                   SquareMatrix(4,SquareMatrix(2,Integer))
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      subMatrix having 5 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op subMatrix
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      subMatrix with argument type(s) 
--R                   SquareMatrix(4,SquareMatrix(2,Integer))
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24

--S 25 of 26
mypf(m) ==
 nr:= nrows m
 odd? nr => 0
-- not zero? (nr mod 2)
 not square? m => 0
 not antisymmetric? m => 0
 nr = 2 => m.(1,2)
 nr = 4 => m.(1,2)*m.(3,4)-m.(1,3)*m.(2,4)+m.(2,3)*m.(1,4)
 0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 26
antisymmetric(seq,n) == 
  m:= matrix [[(if i<j then (seq.(j-i)) _
                 else if i>j then -(seq.(i-j))    
                  else 0) for j in 1..n] for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

)spool 
 
Starts dribbling to Queue.output (2010/3/27, 18:46:18).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 46
a:Queue INT:= queue [1,2,3,4,5]
 

   (1)  [1,2,3,4,5]
                                                          Type: Queue Integer
--R 
--R
--R   (1)  [1,2,3,4,5]
--R                                                          Type: Queue Integer
--E 1

--S 2 of 46
dequeue! a
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 46
a
 

   (3)  [2,3,4,5]
                                                          Type: Queue Integer
--R 
--R
--R   (3)  [2,3,4,5]
--R                                                          Type: Queue Integer
--E 3

--S 4 of 46
extract! a
 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 46
a
 

   (5)  [3,4,5]
                                                          Type: Queue Integer
--R 
--R
--R   (5)  [3,4,5]
--R                                                          Type: Queue Integer
--E 5

--S 6 of 46
enqueue!(9,a)
 

   (6)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  9
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 46
a
 

   (7)  [3,4,5,9]
                                                          Type: Queue Integer
--R 
--R
--R   (7)  [3,4,5,9]
--R                                                          Type: Queue Integer
--E 7

--S 8 of 46
insert!(8,a)
 

   (8)  [3,4,5,9,8]
                                                          Type: Queue Integer
--R 
--R
--R   (8)  [3,4,5,9,8]
--R                                                          Type: Queue Integer
--E 8

--S 9 of 46
a
 

   (9)  [3,4,5,9,8]
                                                          Type: Queue Integer
--R 
--R
--R   (9)  [3,4,5,9,8]
--R                                                          Type: Queue Integer
--E 9

--S 10 of 46
inspect a
 

   (10)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  3
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 46
empty? a
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 46
front a
 

   (12)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  3
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 46
back a
 

   (13)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  8
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 46
rotate! a
 

   (14)  [4,5,9,8,3]
                                                          Type: Queue Integer
--R 
--R
--R   (14)  [4,5,9,8,3]
--R                                                          Type: Queue Integer
--E 14

--S 15 of 46
#a
 

   (15)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  5
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 46
length a
 

   (16)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  5
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 46
less?(a,9)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 46
more?(a,9)
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 46
size?(a,#a)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19

--S 20 of 46
size?(a,9)
 

   (20)  false
                                                                Type: Boolean
--R 
--R
--R   (20)  false
--R                                                                Type: Boolean
--E 20

--S 21 of 46
parts a
 

   (21)  [4,5,9,8,3]
                                                           Type: List Integer
--R 
--R
--R   (21)  [4,5,9,8,3]
--R                                                           Type: List Integer
--E 21

--S 22 of 46
bag([1,2,3,4,5])$Queue(INT)
 

   (22)  [1,2,3,4,5]
                                                          Type: Queue Integer
--R 
--R
--R   (22)  [1,2,3,4,5]
--R                                                          Type: Queue Integer
--E 22

--S 23 of 46
b:=empty()$(Queue INT)
 

   (23)  []
                                                          Type: Queue Integer
--R 
--R
--R   (23)  []
--R                                                          Type: Queue Integer
--E 23

--S 24 of 46
empty? b
 

   (24)  true
                                                                Type: Boolean
--R 
--R
--R   (24)  true
--R                                                                Type: Boolean
--E 24

--S 25 of 46
sample()$Queue(INT)
 

   (25)  []
                                                          Type: Queue Integer
--R 
--R
--R   (25)  []
--R                                                          Type: Queue Integer
--E 25

--S 26 of 46
c:=copy a
 

   (26)  [4,5,9,8,3]
                                                          Type: Queue Integer
--R 
--R
--R   (26)  [4,5,9,8,3]
--R                                                          Type: Queue Integer
--E 26

--S 27 of 46
eq?(a,c)
 

   (27)  false
                                                                Type: Boolean
--R 
--R
--R   (27)  false
--R                                                                Type: Boolean
--E 27

--S 28 of 46
eq?(a,a)
 

   (28)  true
                                                                Type: Boolean
--R 
--R
--R   (28)  true
--R                                                                Type: Boolean
--E 28

--S 29 of 46
(a=c)@Boolean
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 46
(a=a)@Boolean
 

   (30)  true
                                                                Type: Boolean
--R 
--R
--R   (30)  true
--R                                                                Type: Boolean
--E 30

--S 31 of 46
a~=c
 

   (31)  false
                                                                Type: Boolean
--R 
--R
--R   (31)  false
--R                                                                Type: Boolean
--E 31

--S 32 of 46
any?(x+->(x=4),a)
 

   (32)  true
                                                                Type: Boolean
--R 
--R
--R   (32)  true
--R                                                                Type: Boolean
--E 32

--S 33 of 46
any?(x+->(x=11),a)
 

   (33)  false
                                                                Type: Boolean
--R 
--R
--R   (33)  false
--R                                                                Type: Boolean
--E 33

--S 34 of 46
every?(x+->(x=11),a)
 

   (34)  false
                                                                Type: Boolean
--R 
--R
--R   (34)  false
--R                                                                Type: Boolean
--E 34

--S 35 of 46
count(4,a)
 

   (35)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  1
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 46
count(x+->(x>2),a)
 

   (36)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (36)  5
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 46
map(x+->x+10,a)
 

   (37)  [14,15,19,18,13]
                                                          Type: Queue Integer
--R 
--R
--R   (37)  [14,15,19,18,13]
--R                                                          Type: Queue Integer
--E 37

--S 38 of 46
a
 

   (38)  [4,5,9,8,3]
                                                          Type: Queue Integer
--R 
--R
--R   (38)  [4,5,9,8,3]
--R                                                          Type: Queue Integer
--E 38

--S 39 of 46
map!(x+->x+10,a)
 

   (39)  [14,15,19,18,13]
                                                          Type: Queue Integer
--R 
--R
--R   (39)  [14,15,19,18,13]
--R                                                          Type: Queue Integer
--E 39

--S 40 of 46
a
 

   (40)  [14,15,19,18,13]
                                                          Type: Queue Integer
--R 
--R
--R   (40)  [14,15,19,18,13]
--R                                                          Type: Queue Integer
--E 40

--S 41 of 46
members a
 

   (41)  [14,15,19,18,13]
                                                           Type: List Integer
--R 
--R
--R   (41)  [14,15,19,18,13]
--R                                                           Type: List Integer
--E 41

--S 42 of 46
member?(14,a)
 

   (42)  true
                                                                Type: Boolean
--R 
--R
--R   (42)  true
--R                                                                Type: Boolean
--E 42

--S 43 of 46
coerce a
 

   (43)  [14,15,19,18,13]
                                                             Type: OutputForm
--R 
--R
--R   (43)  [14,15,19,18,13]
--R                                                             Type: OutputForm
--E 43

--S 44 of 46
hash a
 

   (44)  4999531
                                                          Type: SingleInteger
--R 
--R
--I   (44)  4999531
--R                                                          Type: SingleInteger
--E 44

--S 45 of 46
latex a
 

   (45)  "\mbox{\bf Unimplemented}"
                                                                 Type: String
--R 
--R
--R   (45)  "\mbox{\bf Unimplemented}"
--R                                                                 Type: String
--E 45

--S 46 of 46
)show Queue
 
 Queue S: SetCategory  is a domain constructor
 Abbreviation for Queue is QUEUE 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for QUEUE 

------------------------------- Operations --------------------------------
 back : % -> S                         bag : List S -> %
 copy : % -> %                         dequeue! : % -> S
 empty : () -> %                       empty? : % -> Boolean
 enqueue! : (S,%) -> S                 eq? : (%,%) -> Boolean
 extract! : % -> S                     front : % -> S
 insert! : (S,%) -> %                  inspect : % -> S
 length : % -> NonNegativeInteger      map : ((S -> S),%) -> %
 queue : List S -> %                   rotate! : % -> %
 sample : () -> %                     
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?=? : (%,%) -> Boolean if S has SETCAT
 any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 coerce : % -> OutputForm if S has SETCAT
 count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
 count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
 every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 hash : % -> SingleInteger if S has SETCAT
 latex : % -> String if S has SETCAT
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((S -> S),%) -> % if $ has shallowlyMutable
 member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
 members : % -> List S if $ has finiteAggregate
 more? : (%,NonNegativeInteger) -> Boolean
 parts : % -> List S if $ has finiteAggregate
 size? : (%,NonNegativeInteger) -> Boolean
 ?~=? : (%,%) -> Boolean if S has SETCAT

--R 
--R Queue S: SetCategory  is a domain constructor
--R Abbreviation for Queue is QUEUE 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for QUEUE 
--R
--R------------------------------- Operations --------------------------------
--R back : % -> S                         bag : List S -> %
--R copy : % -> %                         dequeue! : % -> S
--R empty : () -> %                       empty? : % -> Boolean
--R enqueue! : (S,%) -> S                 eq? : (%,%) -> Boolean
--R extract! : % -> S                     front : % -> S
--R insert! : (S,%) -> %                  inspect : % -> S
--R length : % -> NonNegativeInteger      map : ((S -> S),%) -> %
--R queue : List S -> %                   rotate! : % -> %
--R sample : () -> %                     
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
--R members : % -> List S if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R parts : % -> List S if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
--E 46
 

)spool
 
Starts dribbling to scope.output (2010/3/27, 18:38:52).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
showbug1():Void ==
 for i in 1..1 repeat
  z:="I'm OK"
  print(z)
  showbug2()
  print(z)
 
   Function declaration showbug1 : () -> Void has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration showbug1 : () -> Void has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 3
showbug2():Void ==
 for i in 1..1 repeat
  z:="I'm nasty"
 
   Function declaration showbug2 : () -> Void has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration showbug2 : () -> Void has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 2
-- used to print:
-- I'm OK
-- I'm nasty

--S 3 of 3
showbug1()
 
   Compiling function showbug2 with type () -> Void 
   Compiling function showbug1 with type () -> Void 
   "I'm OK"
   "I'm OK"
                                                                   Type: Void
--R 
--R   Compiling function showbug2 with type () -> Void 
--R   Compiling function showbug1 with type () -> Void 
--R   "I'm OK"
--R   "I'm OK"
--R                                                                   Type: Void
--E 3
)spool 
 
Starts dribbling to matrix.output (2010/3/27, 18:29:54).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 42
mat : MATRIX FRAC INT := matrix [[1/(i + j) for i in 1..5] for j in 1..5]
 

        +1  1  1  1  1 +
        |-  -  -  -  - |
        |2  3  4  5  6 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |3  4  5  6  7 |
        |              |
        |1  1  1  1  1 |
   (1)  |-  -  -  -  - |
        |4  5  6  7  8 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |5  6  7  8  9 |
        |              |
        |1  1  1  1   1|
        |-  -  -  -  --|
        +6  7  8  9  10+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +1  1  1  1  1 +
--R        |-  -  -  -  - |
--R        |2  3  4  5  6 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |3  4  5  6  7 |
--R        |              |
--R        |1  1  1  1  1 |
--R   (1)  |-  -  -  -  - |
--R        |4  5  6  7  8 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |5  6  7  8  9 |
--R        |              |
--R        |1  1  1  1   1|
--R        |-  -  -  -  --|
--R        +6  7  8  9  10+
--R                                                Type: Matrix Fraction Integer
--E 1

--S 2 of 42
matinv := inverse mat
 

        +  450     - 4200    12600    - 15120     6300  +
        |                                               |
        |- 4200    44100    - 141120   176400   - 75600 |
        |                                               |
   (2)  | 12600   - 141120   470400   - 604800   264600 |
        |                                               |
        |- 15120   176400   - 604800   793800   - 352800|
        |                                               |
        + 6300    - 75600    264600   - 352800   158760 +
                                     Type: Union(Matrix Fraction Integer,...)
--R 
--R
--R        +  450     - 4200    12600    - 15120     6300  +
--R        |                                               |
--R        |- 4200    44100    - 141120   176400   - 75600 |
--R        |                                               |
--R   (2)  | 12600   - 141120   470400   - 604800   264600 |
--R        |                                               |
--R        |- 15120   176400   - 604800   793800   - 352800|
--R        |                                               |
--R        + 6300    - 75600    264600   - 352800   158760 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 2

--S 3 of 42
mat * matinv
 

        +1  0  0  0  0+
        |             |
        |0  1  0  0  0|
        |             |
   (3)  |0  0  1  0  0|
        |             |
        |0  0  0  1  0|
        |             |
        +0  0  0  0  1+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +1  0  0  0  0+
--R        |             |
--R        |0  1  0  0  0|
--R        |             |
--R   (3)  |0  0  1  0  0|
--R        |             |
--R        |0  0  0  1  0|
--R        |             |
--R        +0  0  0  0  1+
--R                                                Type: Matrix Fraction Integer
--E 3

--S 4 of 42
mat1 : IMATRIX(FRAC INT,-3,47) := _
   matrix [[1/(i + j) for i in 1..5] for j in 1..5]
 

        +1  1  1  1  1 +
        |-  -  -  -  - |
        |2  3  4  5  6 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |3  4  5  6  7 |
        |              |
        |1  1  1  1  1 |
   (4)  |-  -  -  -  - |
        |4  5  6  7  8 |
        |              |
        |1  1  1  1  1 |
        |-  -  -  -  - |
        |5  6  7  8  9 |
        |              |
        |1  1  1  1   1|
        |-  -  -  -  --|
        +6  7  8  9  10+
                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--R 
--R
--R        +1  1  1  1  1 +
--R        |-  -  -  -  - |
--R        |2  3  4  5  6 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |3  4  5  6  7 |
--R        |              |
--R        |1  1  1  1  1 |
--R   (4)  |-  -  -  -  - |
--R        |4  5  6  7  8 |
--R        |              |
--R        |1  1  1  1  1 |
--R        |-  -  -  -  - |
--R        |5  6  7  8  9 |
--R        |              |
--R        |1  1  1  1   1|
--R        |-  -  -  -  --|
--R        +6  7  8  9  10+
--R                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--E 4

--S 5 of 42
mat1inv := inverse mat1
 

        +  450     - 4200    12600    - 15120     6300  +
        |                                               |
        |- 4200    44100    - 141120   176400   - 75600 |
        |                                               |
   (5)  | 12600   - 141120   470400   - 604800   264600 |
        |                                               |
        |- 15120   176400   - 604800   793800   - 352800|
        |                                               |
        + 6300    - 75600    264600   - 352800   158760 +
                       Type: Union(IndexedMatrix(Fraction Integer,-3,47),...)
--R 
--R
--R        +  450     - 4200    12600    - 15120     6300  +
--R        |                                               |
--R        |- 4200    44100    - 141120   176400   - 75600 |
--R        |                                               |
--R   (5)  | 12600   - 141120   470400   - 604800   264600 |
--R        |                                               |
--R        |- 15120   176400   - 604800   793800   - 352800|
--R        |                                               |
--R        + 6300    - 75600    264600   - 352800   158760 +
--R                       Type: Union(IndexedMatrix(Fraction Integer,-3,47),...)
--E 5

--S 6 of 42
mat1 * mat1inv
 

        +1  0  0  0  0+
        |             |
        |0  1  0  0  0|
        |             |
   (6)  |0  0  1  0  0|
        |             |
        |0  0  0  1  0|
        |             |
        +0  0  0  0  1+
                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--R 
--R
--R        +1  0  0  0  0+
--R        |             |
--R        |0  1  0  0  0|
--R        |             |
--R   (6)  |0  0  1  0  0|
--R        |             |
--R        |0  0  0  1  0|
--R        |             |
--R        +0  0  0  0  1+
--R                                  Type: IndexedMatrix(Fraction Integer,-3,47)
--E 6
 
--S 7 of 42
mat2 : MATRIX INT := matrix [[j**i for i in 0..4] for j in 1..5]
 

        +1  1  1    1    1 +
        |                  |
        |1  2  4    8   16 |
        |                  |
   (7)  |1  3  9   27   81 |
        |                  |
        |1  4  16  64   256|
        |                  |
        +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  1  1    1    1 +
--R        |                  |
--R        |1  2  4    8   16 |
--R        |                  |
--R   (7)  |1  3  9   27   81 |
--R        |                  |
--R        |1  4  16  64   256|
--R        |                  |
--R        +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 42
rowEchelon  mat2
 

        +1  0  0  0  0 +
        |              |
        |0  1  1  1  1 |
        |              |
   (8)  |0  0  2  0  2 |
        |              |
        |0  0  0  6  12|
        |              |
        +0  0  0  0  24+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  0  0  0  0 +
--R        |              |
--R        |0  1  1  1  1 |
--R        |              |
--R   (8)  |0  0  2  0  2 |
--R        |              |
--R        |0  0  0  6  12|
--R        |              |
--R        +0  0  0  0  24+
--R                                                         Type: Matrix Integer
--E 8

--S 9 of 42
determinant mat2
 

   (9)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  288
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 42
minordet    mat2
 

   (10)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  288
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 42
mat3 : IMATRIX(INT,13,-7) := _
   matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (11)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                           Type: IndexedMatrix(Integer,13,-7)
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (11)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                           Type: IndexedMatrix(Integer,13,-7)
--E 11

--S 12 of 42
rowEchelon  mat3
 

         +1  0  0  0  0 +
         |              |
         |0  1  1  1  1 |
         |              |
   (12)  |0  0  2  0  2 |
         |              |
         |0  0  0  6  12|
         |              |
         +0  0  0  0  24+
                                           Type: IndexedMatrix(Integer,13,-7)
--R 
--R
--R         +1  0  0  0  0 +
--R         |              |
--R         |0  1  1  1  1 |
--R         |              |
--R   (12)  |0  0  2  0  2 |
--R         |              |
--R         |0  0  0  6  12|
--R         |              |
--R         +0  0  0  0  24+
--R                                           Type: IndexedMatrix(Integer,13,-7)
--E 12

--S 13 of 42
determinant mat3
 

   (13)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  288
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 42
minordet    mat3
 

   (14)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  288
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 42
mat4 : MATRIX FRAC INT := matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (15)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (15)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                Type: Matrix Fraction Integer
--E 15

--S 16 of 42
rowEchelon  mat4
 

         +1  0  0  0  0+
         |             |
         |0  1  0  0  0|
         |             |
   (16)  |0  0  1  0  0|
         |             |
         |0  0  0  1  0|
         |             |
         +0  0  0  0  1+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  0  0  0  0+
--R         |             |
--R         |0  1  0  0  0|
--R         |             |
--R   (16)  |0  0  1  0  0|
--R         |             |
--R         |0  0  0  1  0|
--R         |             |
--R         +0  0  0  0  1+
--R                                                Type: Matrix Fraction Integer
--E 16

--S 17 of 42
determinant mat4
 

   (17)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (17)  288
--R                                                       Type: Fraction Integer
--E 17

--S 18 of 42
minordet    mat4
 

   (18)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (18)  288
--R                                                       Type: Fraction Integer
--E 18

--S 19 of 42
mat5 : IMATRIX(FRAC INT,-113,37) := _
   matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (19)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                Type: IndexedMatrix(Fraction Integer,-113,37)
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (19)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                Type: IndexedMatrix(Fraction Integer,-113,37)
--E 19

--S 20 of 42
rowEchelon  mat5
 

         +1  0  0  0  0+
         |             |
         |0  1  0  0  0|
         |             |
   (20)  |0  0  1  0  0|
         |             |
         |0  0  0  1  0|
         |             |
         +0  0  0  0  1+
                                Type: IndexedMatrix(Fraction Integer,-113,37)
--R 
--R
--R         +1  0  0  0  0+
--R         |             |
--R         |0  1  0  0  0|
--R         |             |
--R   (20)  |0  0  1  0  0|
--R         |             |
--R         |0  0  0  1  0|
--R         |             |
--R         +0  0  0  0  1+
--R                                Type: IndexedMatrix(Fraction Integer,-113,37)
--E 20

--S 21 of 42
determinant mat5
 

   (21)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (21)  288
--R                                                       Type: Fraction Integer
--E 21

--S 22 of 42
minordet    mat5
 

   (22)  288
                                                       Type: Fraction Integer
--R 
--R
--R   (22)  288
--R                                                       Type: Fraction Integer
--E 22
 
--S 23 of 42
mat6 : MATRIX INT := matrix [[1,2,3],[4,5,6],[7,8,9]]
 

         +1  2  3+
         |       |
   (23)  |4  5  6|
         |       |
         +7  8  9+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (23)  |4  5  6|
--R         |       |
--R         +7  8  9+
--R                                                         Type: Matrix Integer
--E 23

--S 24 of 42
rowEchelon mat6
 

         +1  2  3+
         |       |
   (24)  |0  3  6|
         |       |
         +0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (24)  |0  3  6|
--R         |       |
--R         +0  0  0+
--R                                                         Type: Matrix Integer
--E 24

--S 25 of 42
rank       mat6
 

   (25)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  2
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 42
nullity    mat6
 

   (26)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  1
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 42
nullSpace  mat6
 

   (27)  [[1,- 2,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (27)  [[1,- 2,1]]
--R                                                    Type: List Vector Integer
--E 27
 
--S 28 of 42
mat7 : IMATRIX(FRAC INT,163,61657) := matrix [[1,2,3],[4,5,6],[7,8,9]]
 

         +1  2  3+
         |       |
   (28)  |4  5  6|
         |       |
         +7  8  9+
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (28)  |4  5  6|
--R         |       |
--R         +7  8  9+
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 28

--S 29 of 42
rowEchelon mat7
 

         +1  0  - 1+
         |         |
   (29)  |0  1   2 |
         |         |
         +0  0   0 +
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         +1  0  - 1+
--R         |         |
--R   (29)  |0  1   2 |
--R         |         |
--R         +0  0   0 +
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 29

--S 30 of 42
rank       mat7
 

   (30)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  2
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 42
nullity    mat7
 

   (31)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (31)  1
--R                                                        Type: PositiveInteger
--E 31

--S 32 of 42
nullSpace  mat7
 

   (32)  [[1,- 2,1]]
                               Type: List IndexedVector(Fraction Integer,163)
--R 
--R
--R   (32)  [[1,- 2,1]]
--R                               Type: List IndexedVector(Fraction Integer,163)
--E 32

--S 33 of 42
mat8 : MATRIX INT := _
 matrix [[1,-2,13,0,5,-47],[-4,15,0,16,-2,1],[-7,0,8,-11,9,0]]
 

         + 1   - 2  13   0     5   - 47+
         |                             |
   (33)  |- 4  15   0    16   - 2   1  |
         |                             |
         +- 7   0   8   - 11   9    0  +
                                                         Type: Matrix Integer
--R 
--R
--R         + 1   - 2  13   0     5   - 47+
--R         |                             |
--R   (33)  |- 4  15   0    16   - 2   1  |
--R         |                             |
--R         +- 7   0   8   - 11   9    0  +
--R                                                         Type: Matrix Integer
--E 33

--S 34 of 42
rowEchelon mat8
 

         +1  5  65   16  23  - 234+
         |                        |
   (34)  |0  7  52   16  18  - 187|
         |                        |
         +0  0  203  21  80  - 703+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  5  65   16  23  - 234+
--R         |                        |
--R   (34)  |0  7  52   16  18  - 187|
--R         |                        |
--R         +0  0  203  21  80  - 703+
--R                                                         Type: Matrix Integer
--E 34

--S 35 of 42
rank       mat8
 

   (35)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  3
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 42
nullity    mat8
 

   (36)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (36)  3
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 42
nullSpace  mat8
 

   (37)
   [[- 49,- 44,- 3,29,0,0],[1187,506,- 560,0,1421,0],[5624,1405,4921,0,0,1421]]
                                                    Type: List Vector Integer
--R 
--R
--R   (37)
--R   [[- 49,- 44,- 3,29,0,0],[1187,506,- 560,0,1421,0],[5624,1405,4921,0,0,1421]]
--R                                                    Type: List Vector Integer
--E 37
 
--S 38 of 42
mat9 : IMATRIX(FRAC INT,163,61657) := _
 matrix [[1,-2,13,0,5,-47],[-4,15,0,16,-2,1],[-7,0,8,-11,9,0]]
 

         + 1   - 2  13   0     5   - 47+
         |                             |
   (38)  |- 4  15   0    16   - 2   1  |
         |                             |
         +- 7   0   8   - 11   9    0  +
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         + 1   - 2  13   0     5   - 47+
--R         |                             |
--R   (38)  |- 4  15   0    16   - 2   1  |
--R         |                             |
--R         +- 7   0   8   - 11   9    0  +
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 38

--S 39 of 42
rowEchelon mat9
 

         +         49    1187    5624+
         |1  0  0  --  - ----  - ----|
         |         29    1421    1421|
         |                           |
         |         44     506    1405|
   (39)  |0  1  0  --  - ----  - ----|
         |         29    1421    1421|
         |                           |
         |          3    80      703 |
         |0  0  1  --   ---    - --- |
         +         29   203      203 +
                              Type: IndexedMatrix(Fraction Integer,163,61657)
--R 
--R
--R         +         49    1187    5624+
--R         |1  0  0  --  - ----  - ----|
--R         |         29    1421    1421|
--R         |                           |
--R         |         44     506    1405|
--R   (39)  |0  1  0  --  - ----  - ----|
--R         |         29    1421    1421|
--R         |                           |
--R         |          3    80      703 |
--R         |0  0  1  --   ---    - --- |
--R         +         29   203      203 +
--R                              Type: IndexedMatrix(Fraction Integer,163,61657)
--E 39

--S 40 of 42
rank       mat9
 

   (40)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (40)  3
--R                                                        Type: PositiveInteger
--E 40

--S 41 of 42
nullity    mat9
 

   (41)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (41)  3
--R                                                        Type: PositiveInteger
--E 41

--S 42 of 42
nullSpace  mat9
 

   (42)
       49   44    3         1187  506    80         5624 1405 703
   [[- --,- --,- --,1,0,0],[----,----,- ---,0,1,0],[----,----,---,0,0,1]]
       29   29   29         1421 1421   203         1421 1421 203
                               Type: List IndexedVector(Fraction Integer,163)
--R 
--R
--R   (42)
--R       49   44    3         1187  506    80         5624 1405 703
--R   [[- --,- --,- --,1,0,0],[----,----,- ---,0,1,0],[----,----,---,0,0,1]]
--R       29   29   29         1421 1421   203         1421 1421 203
--R                               Type: List IndexedVector(Fraction Integer,163)
--E 42
)spool 
 
Starts dribbling to NottinghamGroup.output (2010/3/27, 18:46:8).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 8
x:=monomial(1,1)$UFPS PF 1783
 

   (1)  x
                            Type: UnivariateFormalPowerSeries PrimeField 1783
--R 
--R
--R   (1)  x
--R                            Type: UnivariateFormalPowerSeries PrimeField 1783
--E 1

--S 2 of 8
s:=retract(sin x)$NOTTING PF 1783
 

                3        5       7       9      11
   (2)  x + 297x  + 1679x  + 427x  + 316x  + O(x  )
                                        Type: NottinghamGroup PrimeField 1783
--R 
--R
--R                3        5       7       9      11
--R   (2)  x + 297x  + 1679x  + 427x  + 316x  + O(x  )
--R                                        Type: NottinghamGroup PrimeField 1783
--E 2

--S 3 of 8
s^2
 

                3       5        7        9      11
   (3)  x + 594x  + 535x  + 1166x  + 1379x  + O(x  )
                                        Type: NottinghamGroup PrimeField 1783
--R 
--R
--R                3       5        7        9      11
--R   (3)  x + 594x  + 535x  + 1166x  + 1379x  + O(x  )
--R                                        Type: NottinghamGroup PrimeField 1783
--E 3

--S 4 of 8
s^-1
 

                 3       5       7        9      11
   (4)  x + 1486x  + 847x  + 207x  + 1701x  + O(x  )
                                        Type: NottinghamGroup PrimeField 1783
--R 
--R
--R                 3       5       7        9      11
--R   (4)  x + 1486x  + 847x  + 207x  + 1701x  + O(x  )
--R                                        Type: NottinghamGroup PrimeField 1783
--E 4

--S 5 of 8
s^-1*s
 

               11
   (5)  x + O(x  )
                                        Type: NottinghamGroup PrimeField 1783
--R 
--R
--R               11
--R   (5)  x + O(x  )
--R                                        Type: NottinghamGroup PrimeField 1783
--E 5

--S 6 of 8
s*s^-1
 

               11
   (6)  x + O(x  )
                                        Type: NottinghamGroup PrimeField 1783
--R 
--R
--R               11
--R   (6)  x + O(x  )
--R                                        Type: NottinghamGroup PrimeField 1783
--E 6

--S 7 of 8
sample()$NOTTING(PF(1783))
 

   (7)  x
                                        Type: NottinghamGroup PrimeField 1783
--R
--R   (7)  x
--R                                        Type: NottinghamGroup PrimeField 1783
--E 7

--S 8 of 8
)show NottinghamGroup
 
 NottinghamGroup F: FiniteFieldCategory  is a domain constructor
 Abbreviation for NottinghamGroup is NOTTING 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for NOTTING 

------------------------------- Operations --------------------------------
 ?*? : (%,%) -> %                      ?**? : (%,Integer) -> %
 ?**? : (%,PositiveInteger) -> %       ?/? : (%,%) -> %
 ?=? : (%,%) -> Boolean                1 : () -> %
 ?^? : (%,Integer) -> %                ?^? : (%,PositiveInteger) -> %
 coerce : % -> OutputForm              commutator : (%,%) -> %
 conjugate : (%,%) -> %                hash : % -> SingleInteger
 inv : % -> %                          latex : % -> String
 one? : % -> Boolean                   recip : % -> Union(%,"failed")
 sample : () -> %                      ?~=? : (%,%) -> Boolean
 ?**? : (%,NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %
 retract : UnivariateFormalPowerSeries F -> %

--R 
--R NottinghamGroup F: FiniteFieldCategory  is a domain constructor
--R Abbreviation for NottinghamGroup is NOTTING 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for NOTTING 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (%,%) -> %                      ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> %       ?/? : (%,%) -> %
--R ?=? : (%,%) -> Boolean                1 : () -> %
--R ?^? : (%,Integer) -> %                ?^? : (%,PositiveInteger) -> %
--R coerce : % -> OutputForm              commutator : (%,%) -> %
--R conjugate : (%,%) -> %                hash : % -> SingleInteger
--R inv : % -> %                          latex : % -> String
--R one? : % -> Boolean                   recip : % -> Union(%,"failed")
--R sample : () -> %                      ?~=? : (%,%) -> Boolean
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R retract : UnivariateFormalPowerSeries F -> %
--R
--E 8

)spool
 
Starts dribbling to float2.output (2010/3/27, 18:26:16).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 41
f := 2.0/3
 

   (1)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (1)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 1

--S 2 of 41
log exp f
 

   (2)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (2)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 2

--S 3 of 41
asin sin f
 

   (3)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (3)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 3

--S 4 of 41
acos cos f
 

   (4)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (4)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 4

--S 5 of 41
atan tan f
 

   (5)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (5)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 5

--S 6 of 41
asinh sinh f
 

   (6)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (6)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 6

--S 7 of 41
acosh cosh f
 

   (7)  0.6666666666 6666666666
                                                                  Type: Float
--R 
--R
--R   (7)  0.6666666666 6666666666
--R                                                                  Type: Float
--E 7

--S 8 of 41
atanh tanh f
 

   (8)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (8)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 8

--S 9 of 41
sqrt(f**2)
 

   (9)  0.6666666666 6666666667
                                                                  Type: Float
--R 
--R
--R   (9)  0.6666666666 6666666667
--R                                                                  Type: Float
--E 9

--S 10 of 41
4*atan(1.0)-%pi
 

   (10)  0.0
                                                                  Type: Float
--R 
--R
--R   (10)  0.0
--R                                                                  Type: Float
--E 10

--S 11 of 41
log exp1()
 

   (11)  1.0
                                                                  Type: Float
--R 
--R
--R   (11)  1.0
--R                                                                  Type: Float
--E 11

--S 12 of 41
exp log2()
 

   (12)  2.0
                                                                  Type: Float
--R 
--R
--R   (12)  2.0
--R                                                                  Type: Float
--E 12

--S 13 of 41
exp log10()
 

   (13)  10.0
                                                                  Type: Float
--R 
--R
--R   (13)  10.0
--R                                                                  Type: Float
--E 13
 
--S 14 of 41
f := 100.0/7
 

   (14)  14.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (14)  14.2857142857 14285714
--R                                                                  Type: Float
--E 14

--S 15 of 41
exp log f
 

   (15)  14.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (15)  14.2857142857 14285714
--R                                                                  Type: Float
--E 15

--S 16 of 41
sqrt(f**2)
 

   (16)  14.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (16)  14.2857142857 14285714
--R                                                                  Type: Float
--E 16

--S 17 of 41
sin(f)**2+cos(f)**2
 

   (17)  1.0
                                                                  Type: Float
--R 
--R
--R   (17)  1.0
--R                                                                  Type: Float
--E 17

--S 18 of 41
sinh(f)**2-cosh(f)**2
 

   (18)  - 1.0
                                                                  Type: Float
--R 
--R
--R   (18)  - 1.0
--R                                                                  Type: Float
--E 18

--S 19 of 41
truncate f
 

   (19)  14.0
                                                                  Type: Float
--R 
--R
--R   (19)  14.0
--R                                                                  Type: Float
--E 19

--S 20 of 41
round f
 

   (20)  14.0
                                                                  Type: Float
--R 
--R
--R   (20)  14.0
--R                                                                  Type: Float
--E 20

--S 21 of 41
fractionPart f
 

   (21)  0.2857142857 14285714
                                                                  Type: Float
--R 
--R
--R   (21)  0.2857142857 14285714
--R                                                                  Type: Float
--E 21

--S 22 of 41
ceiling f
 

   (22)  15.0
                                                                  Type: Float
--R 
--R
--R   (22)  15.0
--R                                                                  Type: Float
--E 22

--S 23 of 41
floor f
 

   (23)  14.0
                                                                  Type: Float
--R 
--R
--R   (23)  14.0
--R                                                                  Type: Float
--E 23

--S 24 of 41
wholePart f
 

   (24)  14
                                                        Type: PositiveInteger
--R 
--R
--R   (24)  14
--R                                                        Type: PositiveInteger
--E 24
 
--S 25 of 41
digits 50
 

   (25)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  20
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 41
f := 1.0/3
 

   (26)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (26)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 26

--S 27 of 41
exp log f
 

   (27)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (27)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 27

--S 28 of 41
asin sin f
 

   (28)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (28)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 28

--S 29 of 41
acos cos f
 

   (29)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (29)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 29

--S 30 of 41
atan tan f
 

   (30)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (30)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 30

--S 31 of 41
asinh sinh f
 

   (31)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (31)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 31

--S 32 of 41
acosh cosh f
 

   (32)  0.3333333333 3333333333 3333333333 3333333333 3333333334
                                                                  Type: Float
--R 
--R
--R   (32)  0.3333333333 3333333333 3333333333 3333333333 3333333334
--R                                                                  Type: Float
--E 32

--S 33 of 41
atanh tanh f
 

   (33)  0.3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (33)  0.3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 33

--S 34 of 41
log exp1()
 

   (34)  1.0
                                                                  Type: Float
--R 
--R
--R   (34)  1.0
--R                                                                  Type: Float
--E 34

--S 35 of 41
sin numeric %pi
 

   (35)  - 0.6356225157 7200746034 5144300600 8220509036 2417341559 E -50
                                                                  Type: Float
--R 
--R
--R   (35)  - 0.6356225157 7200746034 5144300600 8220509036 2417341559 E -50
--R                                                                  Type: Float
--E 35

--S 36 of 41
exp log2()
 

   (36)  2.0
                                                                  Type: Float
--R 
--R
--R   (36)  2.0
--R                                                                  Type: Float
--E 36

--S 37 of 41
exp log10()
 

   (37)  10.0
                                                                  Type: Float
--R 
--R
--R   (37)  10.0
--R                                                                  Type: Float
--E 37

--S 38 of 41
f := 1024.0
 

   (38)  1024.0
                                                                  Type: Float
--R 
--R
--R   (38)  1024.0
--R                                                                  Type: Float
--E 38

--S 39 of 41
log2 f
 

   (39)  10.0
                                                                  Type: Float
--R 
--R
--R   (39)  10.0
--R                                                                  Type: Float
--E 39

--S 40 of 41
f := 1000.0
 

   (40)  1000.0
                                                                  Type: Float
--R 
--R
--R   (40)  1000.0
--R                                                                  Type: Float
--E 40

--S 41 of 41
log10 f
 

   (41)  3.0
                                                                  Type: Float
--R 
--R
--R   (41)  3.0
--R                                                                  Type: Float
--E 41
)spool 
 
Starts dribbling to chtheorem.output (2010/3/27, 18:24:28).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 28
D:=FFP(PF 2,x^4+x+1)
 

   (1)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
                                                                 Type: Domain
--R 
--R
--R   (1)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--R                                                                 Type: Domain
--E 1

--S 2 of 28
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +       3                3                     3     2    +
        |     %A  + %A         %A  + %A       %A     %A  + %A  + 1|
        |                                                         |
        |  3     2             3     2        3                   |
        |%A  + %A  + %A + 1  %A  + %A  + 1  %A  + 1     %A + 1    |
   (2)  |                                                         |
        |       2                3                                |
        |     %A  + %A         %A  + %A        1           1      |
        |                                                         |
        |                           3                    3     2  |
        +        %A               %A        %A + 1     %A  + %A   +
         Type: Matrix FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--R 
--R
--R        +      3     2                                           3     2+
--R        |    %A  + %A                0                1        %A  + %A |
--R        |                                                               |
--R        |  3     2                  2                             2     |
--R        |%A  + %A  + %A + 1       %A  + %A            1         %A  + 1 |
--R   (2)  |                                                               |
--R        |      3     2            3                                     |
--R        |    %A  + %A           %A  + %A + 1          0         %A + 1  |
--R        |                                                               |
--R        |                      3     2             2             3     2|
--R        +        0           %A  + %A  + %A + 1  %A  + %A + 1  %A  + %A +
--R         Type: Matrix FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--E 2

--S 3 of 28
p:=characteristicPolynomial(M,y)
 

         4      3       3      2       2      3     2           3     2
   (3)  y  + (%A  + %A)y  + (%A  + %A)y  + (%A  + %A  + 1)y + %A  + %A  + %A
     Type: Polynomial FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--R 
--R
--R         4      2       3      2           2            3     2
--R   (3)  y  + (%A  + %A)y  + (%A  + %A + 1)y  + %A y + %A  + %A  + %A
--R     Type: Polynomial FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--E 3

--S 4 of 28
SM:=SquareMatrix(4,D)
 

   (4)
   SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
                                                                 Type: Domain
--R 
--R
--R   (4)
--R   SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R                                                                 Type: Domain
--E 4

--S 5 of 28
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

   (5)
          +  3                                   +
          |%A  + %A     0         0         0    |
          |                                      |
          |            3                         |
      4   |   0      %A  + %A     0         0    | 3
     y  + |                                      |y
          |                      3               |
          |   0         0      %A  + %A     0    |
          |                                      |
          |                                3     |
          +   0         0         0      %A  + %A+
   + 
     +  2                                   +
     |%A  + %A     0         0         0    |
     |                                      |
     |            2                         |
     |   0      %A  + %A     0         0    | 2
     |                                      |y
     |                      2               |
     |   0         0      %A  + %A     0    |
     |                                      |
     |                                2     |
     +   0         0         0      %A  + %A+
   + 
     +  3     2                                                 +
     |%A  + %A  + 1        0              0              0      |
     |                                                          |
     |                 3     2                                  |
     |      0        %A  + %A  + 1        0              0      |
     |                                                          |y
     |                                3     2                   |
     |      0              0        %A  + %A  + 1        0      |
     |                                                          |
     |                                               3     2    |
     +      0              0              0        %A  + %A  + 1+
   + 
     +  3     2                                                     +
     |%A  + %A  + %A        0               0               0       |
     |                                                              |
     |                  3     2                                     |
     |      0         %A  + %A  + %A        0               0       |
     |                                                              |
     |                                  3     2                     |
     |      0               0         %A  + %A  + %A        0       |
     |                                                              |
     |                                                  3     2     |
     +      0               0               0         %A  + %A  + %A+
Type: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R 
--R
--R   (5)
--R          +  2                                   +
--R          |%A  + %A     0         0         0    |
--R          |                                      |
--R          |            2                         |
--R      4   |   0      %A  + %A     0         0    | 3
--R     y  + |                                      |y
--R          |                      2               |
--R          |   0         0      %A  + %A     0    |
--R          |                                      |
--R          |                                2     |
--R          +   0         0         0      %A  + %A+
--R   + 
--R     +  2                                                   +
--R     |%A  + %A + 1       0             0             0      |
--R     |                                                      |
--R     |                2                                     |
--R     |     0        %A  + %A + 1       0             0      | 2
--R     |                                                      |y
--R     |                              2                       |
--R     |     0             0        %A  + %A + 1       0      |
--R     |                                                      |
--R     |                                            2         |
--R     +     0             0             0        %A  + %A + 1+
--R   + 
--R     +%A  0   0   0 +
--R     |              |
--R     |0   %A  0   0 |
--R     |              |y
--R     |0   0   %A  0 |
--R     |              |
--R     +0   0   0   %A+
--R   + 
--R     +  3     2                                                     +
--R     |%A  + %A  + %A        0               0               0       |
--R     |                                                              |
--R     |                  3     2                                     |
--R     |      0         %A  + %A  + %A        0               0       |
--R     |                                                              |
--R     |                                  3     2                     |
--R     |      0               0         %A  + %A  + %A        0       |
--R     |                                                              |
--R     |                                                  3     2     |
--R     +      0               0               0         %A  + %A  + %A+
--RType: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--E 5

--S 6 of 28
sm:=squareMatrix(M)$SM
 

        +       3                3                     3     2    +
        |     %A  + %A         %A  + %A       %A     %A  + %A  + 1|
        |                                                         |
        |  3     2             3     2        3                   |
        |%A  + %A  + %A + 1  %A  + %A  + 1  %A  + 1     %A + 1    |
   (6)  |                                                         |
        |       2                3                                |
        |     %A  + %A         %A  + %A        1           1      |
        |                                                         |
        |                           3                    3     2  |
        +        %A               %A        %A + 1     %A  + %A   +
Type: SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R 
--R
--R        +      3     2                                           3     2+
--R        |    %A  + %A                0                1        %A  + %A |
--R        |                                                               |
--R        |  3     2                  2                             2     |
--R        |%A  + %A  + %A + 1       %A  + %A            1         %A  + 1 |
--R   (6)  |                                                               |
--R        |      3     2            3                                     |
--R        |    %A  + %A           %A  + %A + 1          0         %A + 1  |
--R        |                                                               |
--R        |                      3     2             2             3     2|
--R        +        0           %A  + %A  + %A + 1  %A  + %A + 1  %A  + %A +
--RType: SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--E 6

--S 7 of 28
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
Type: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--RType: Polynomial SquareMatrix(4,FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--E 7

)clear all
 
 
--S 8 of 28
D:=INT
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 8

--S 9 of 28
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +56219635  21520321  17671881  41363951+
        |                                      |
        |38951340  26503261  29446612  34537765|
   (2)  |                                      |
        |11865529  60517533  40101650  28928862|
        |                                      |
        +24944857  63097921  7357765   39633500+
                                                         Type: Matrix Integer
--R 
--R
--R        +23884875  62211449  24992607  36817117+
--R        |                                      |
--R        |11791443  2792865   1578023   13067461|
--R   (2)  |                                      |
--R        |24115163  48682825  18166895  38340141|
--R        |                                      |
--R        +63446755  11508337  5309495   33821973+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 28
p:=characteristicPolynomial(M,y)
 

   (3)
      4             3                    2
     y  - 162458046y  + 3421396277430748y  + 42605859051460526429870y
   + 
     - 247807886119855992129747147845
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)
--R      4            3                    2
--R     y  - 78666608y  - 2034871330953280y  - 37379714246895929917440y
--R   + 
--R     - 43330011013671754134127116288
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 28
SM:=SquareMatrix(4,D)
 

   (4)  SquareMatrix(4,Integer)
                                                                 Type: Domain
--R 
--R
--R   (4)  SquareMatrix(4,Integer)
--R                                                                 Type: Domain
--E 11

--S 12 of 28
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

   (5)
          +- 162458046       0            0            0     +
          |                                                  |
      4   |     0       - 162458046       0            0     | 3
     y  + |                                                  |y
          |     0            0       - 162458046       0     |
          |                                                  |
          +     0            0            0       - 162458046+
   + 
     +3421396277430748         0                 0                 0        +
     |                                                                      |
     |       0          3421396277430748         0                 0        | 2
     |                                                                      |y
     |       0                 0          3421396277430748         0        |
     |                                                                      |
     +       0                 0                 0          3421396277430748+
   + 
   [[42605859051460526429870,0,0,0], [0,42605859051460526429870,0,0],
    [0,0,42605859051460526429870,0], [0,0,0,42605859051460526429870]]
    *
       y
   + 
   [[- 247807886119855992129747147845,0,0,0],
    [0,- 247807886119855992129747147845,0,0],
    [0,0,- 247807886119855992129747147845,0],
    [0,0,0,- 247807886119855992129747147845]]
                                     Type: Polynomial SquareMatrix(4,Integer)
--R 
--R
--R   (5)
--R          +- 78666608      0           0           0     +
--R          |                                              |
--R      4   |    0       - 78666608      0           0     | 3
--R     y  + |                                              |y
--R          |    0           0       - 78666608      0     |
--R          |                                              |
--R          +    0           0           0       - 78666608+
--R   + 
--R   [[- 2034871330953280,0,0,0], [0,- 2034871330953280,0,0],
--R    [0,0,- 2034871330953280,0], [0,0,0,- 2034871330953280]]
--R    *
--R        2
--R       y
--R   + 
--R   [[- 37379714246895929917440,0,0,0], [0,- 37379714246895929917440,0,0],
--R    [0,0,- 37379714246895929917440,0], [0,0,0,- 37379714246895929917440]]
--R    *
--R       y
--R   + 
--R   [[- 43330011013671754134127116288,0,0,0],
--R    [0,- 43330011013671754134127116288,0,0],
--R    [0,0,- 43330011013671754134127116288,0],
--R    [0,0,0,- 43330011013671754134127116288]]
--R                                     Type: Polynomial SquareMatrix(4,Integer)
--E 12

--S 13 of 28
sm:=squareMatrix(M)$SM
 

        +56219635  21520321  17671881  41363951+
        |                                      |
        |38951340  26503261  29446612  34537765|
   (6)  |                                      |
        |11865529  60517533  40101650  28928862|
        |                                      |
        +24944857  63097921  7357765   39633500+
                                                Type: SquareMatrix(4,Integer)
--R 
--R
--R        +23884875  62211449  24992607  36817117+
--R        |                                      |
--R        |11791443  2792865   1578023   13067461|
--R   (6)  |                                      |
--R        |24115163  48682825  18166895  38340141|
--R        |                                      |
--R        +63446755  11508337  5309495   33821973+
--R                                                Type: SquareMatrix(4,Integer)
--E 13

--S 14 of 28
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                     Type: Polynomial SquareMatrix(4,Integer)
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                     Type: Polynomial SquareMatrix(4,Integer)
--E 14

)clear all
 
 
--S 15 of 28
D:=PF 7
 

   (1)  PrimeField 7
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 7
--R                                                                 Type: Domain
--E 15

--S 16 of 28
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +1  6  5  0+
        |          |
        |6  5  6  4|
   (2)  |          |
        |2  6  1  2|
        |          |
        +5  2  6  3+
                                                    Type: Matrix PrimeField 7
--R 
--R
--R        +0  0  4  6+
--R        |          |
--R        |4  1  2  6|
--R   (2)  |          |
--R        |1  5  4  1|
--R        |          |
--R        +1  1  2  0+
--R                                                    Type: Matrix PrimeField 7
--E 16

--S 17 of 28
p:=characteristicPolynomial(M,y)
 

         4     3
   (3)  y  + 4y  + 3y + 5
                                                Type: Polynomial PrimeField 7
--R 
--R
--R         4     3     2
--R   (3)  y  + 2y  + 4y  + 4y + 1
--R                                                Type: Polynomial PrimeField 7
--E 17

--S 18 of 28
SM:=SquareMatrix(4,D)
 

   (4)  SquareMatrix(4,PrimeField 7)
                                                                 Type: Domain
--R 
--R
--R   (4)  SquareMatrix(4,PrimeField 7)
--R                                                                 Type: Domain
--E 18

--S 19 of 28
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

             +4  0  0  0+     +3  0  0  0+    +5  0  0  0+
             |          |     |          |    |          |
         4   |0  4  0  0| 3   |0  3  0  0|    |0  5  0  0|
   (5)  y  + |          |y  + |          |y + |          |
             |0  0  4  0|     |0  0  3  0|    |0  0  5  0|
             |          |     |          |    |          |
             +0  0  0  4+     +0  0  0  3+    +0  0  0  5+
                                Type: Polynomial SquareMatrix(4,PrimeField 7)
--R 
--R
--R             +2  0  0  0+     +4  0  0  0+     +4  0  0  0+    +1  0  0  0+
--R             |          |     |          |     |          |    |          |
--R         4   |0  2  0  0| 3   |0  4  0  0| 2   |0  4  0  0|    |0  1  0  0|
--R   (5)  y  + |          |y  + |          |y  + |          |y + |          |
--R             |0  0  2  0|     |0  0  4  0|     |0  0  4  0|    |0  0  1  0|
--R             |          |     |          |     |          |    |          |
--R             +0  0  0  2+     +0  0  0  4+     +0  0  0  4+    +0  0  0  1+
--R                                Type: Polynomial SquareMatrix(4,PrimeField 7)
--E 19

--S 20 of 28
sm:=squareMatrix(M)$SM
 

        +1  6  5  0+
        |          |
        |6  5  6  4|
   (6)  |          |
        |2  6  1  2|
        |          |
        +5  2  6  3+
                                           Type: SquareMatrix(4,PrimeField 7)
--R 
--R
--R        +0  0  4  6+
--R        |          |
--R        |4  1  2  6|
--R   (6)  |          |
--R        |1  5  4  1|
--R        |          |
--R        +1  1  2  0+
--R                                           Type: SquareMatrix(4,PrimeField 7)
--E 20

--S 21 of 28
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                Type: Polynomial SquareMatrix(4,PrimeField 7)
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                Type: Polynomial SquareMatrix(4,PrimeField 7)
--E 21

)clear all
 
 
--S 22 of 28
D:=FF(2,4)
 

   (1)  FiniteField(2,4)
                                                                 Type: Domain
--R 
--R
--R   (1)  FiniteField(2,4)
--R                                                                 Type: Domain
--E 22

--S 23 of 28
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
 

        +  2             3     2                3                3     2     +
        |%A  + %A + 1  %A  + %A  + %A + 1     %A  + %A + 1     %A  + %A  + 1 |
        |                                                                    |
        |                  3     2           3     2                2        |
        |   %A + 1       %A  + %A  + %A    %A  + %A  + %A + 1     %A  + 1    |
   (2)  |                                                                    |
        |                     3                 3                3     2     |
        |     1             %A  + %A          %A  + %A + 1     %A  + %A  + %A|
        |                                                                    |
        |    2                                    2                          |
        +  %A  + 1             1                %A  + %A             0       +
                                                Type: Matrix FiniteField(2,4)
--R 
--R
--R        +                      2            2       3     2         +
--R        |        %A          %A  + %A     %A      %A  + %A  + %A + 1|
--R        |                                                           |
--R        |  3     2             3     2    3              3          |
--R        |%A  + %A  + %A + 1  %A  + %A   %A  + %A       %A  + %A     |
--R   (2)  |                                                           |
--R        |  3     2             3          3                         |
--R        |%A  + %A  + %A + 1  %A  + %A   %A  + %A          %A        |
--R        |                                                           |
--R        |     3                 2           2         3     2       |
--R        +   %A  + %A + 1      %A  + 1     %A        %A  + %A  + %A  +
--R                                                Type: Matrix FiniteField(2,4)
--E 23

--S 24 of 28
p:=characteristicPolynomial(M,y)
 

         4       3      3     2       2      3     2            3     2
   (3)  y  + %A y  + (%A  + %A  + %A)y  + (%A  + %A  + %A)y + %A  + %A  + %A
                                            Type: Polynomial FiniteField(2,4)
--R 
--R
--R         4      3       3      3       2         3
--R   (3)  y  + (%A  + %A)y  + (%A  + %A)y  + y + %A  + 1
--R                                            Type: Polynomial FiniteField(2,4)
--E 24

--S 25 of 28
SM:=SquareMatrix(4,D)
 

   (4)  SquareMatrix(4,FiniteField(2,4))
                                                                 Type: Domain
--R 
--R
--R   (4)  SquareMatrix(4,FiniteField(2,4))
--R                                                                 Type: Domain
--E 25

--S 26 of 28
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
 

   (5)
          +%A  0   0   0 +
          |              |
      4   |0   %A  0   0 | 3
     y  + |              |y
          |0   0   %A  0 |
          |              |
          +0   0   0   %A+
   + 
     +  3     2                                                     +
     |%A  + %A  + %A        0               0               0       |
     |                                                              |
     |                  3     2                                     |
     |      0         %A  + %A  + %A        0               0       | 2
     |                                                              |y
     |                                  3     2                     |
     |      0               0         %A  + %A  + %A        0       |
     |                                                              |
     |                                                  3     2     |
     +      0               0               0         %A  + %A  + %A+
   + 
     +  3     2                                                     +
     |%A  + %A  + %A        0               0               0       |
     |                                                              |
     |                  3     2                                     |
     |      0         %A  + %A  + %A        0               0       |
     |                                                              |y
     |                                  3     2                     |
     |      0               0         %A  + %A  + %A        0       |
     |                                                              |
     |                                                  3     2     |
     +      0               0               0         %A  + %A  + %A+
   + 
     +  3     2                                                     +
     |%A  + %A  + %A        0               0               0       |
     |                                                              |
     |                  3     2                                     |
     |      0         %A  + %A  + %A        0               0       |
     |                                                              |
     |                                  3     2                     |
     |      0               0         %A  + %A  + %A        0       |
     |                                                              |
     |                                                  3     2     |
     +      0               0               0         %A  + %A  + %A+
                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
--R 
--R
--R   (5)
--R          +  3                                   +
--R          |%A  + %A     0         0         0    |
--R          |                                      |
--R          |            3                         |
--R      4   |   0      %A  + %A     0         0    | 3
--R     y  + |                                      |y
--R          |                      3               |
--R          |   0         0      %A  + %A     0    |
--R          |                                      |
--R          |                                3     |
--R          +   0         0         0      %A  + %A+
--R   + 
--R     +  3                                   +
--R     |%A  + %A     0         0         0    |
--R     |                                      |
--R     |            3                         |
--R     |   0      %A  + %A     0         0    | 2
--R     |                                      |y  + y
--R     |                      3               |
--R     |   0         0      %A  + %A     0    |
--R     |                                      |
--R     |                                3     |
--R     +   0         0         0      %A  + %A+
--R   + 
--R     +  3                               +
--R     |%A  + 1     0        0        0   |
--R     |                                  |
--R     |           3                      |
--R     |   0     %A  + 1     0        0   |
--R     |                                  |
--R     |                    3             |
--R     |   0        0     %A  + 1     0   |
--R     |                                  |
--R     |                             3    |
--R     +   0        0        0     %A  + 1+
--R                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
--E 26

--S 27 of 28
sm:=squareMatrix(M)$SM
 

        +  2             3     2                3                3     2     +
        |%A  + %A + 1  %A  + %A  + %A + 1     %A  + %A + 1     %A  + %A  + 1 |
        |                                                                    |
        |                  3     2           3     2                2        |
        |   %A + 1       %A  + %A  + %A    %A  + %A  + %A + 1     %A  + 1    |
   (6)  |                                                                    |
        |                     3                 3                3     2     |
        |     1             %A  + %A          %A  + %A + 1     %A  + %A  + %A|
        |                                                                    |
        |    2                                    2                          |
        +  %A  + 1             1                %A  + %A             0       +
                                       Type: SquareMatrix(4,FiniteField(2,4))
--R 
--R
--R        +                      2            2       3     2         +
--R        |        %A          %A  + %A     %A      %A  + %A  + %A + 1|
--R        |                                                           |
--R        |  3     2             3     2    3              3          |
--R        |%A  + %A  + %A + 1  %A  + %A   %A  + %A       %A  + %A     |
--R   (6)  |                                                           |
--R        |  3     2             3          3                         |
--R        |%A  + %A  + %A + 1  %A  + %A   %A  + %A          %A        |
--R        |                                                           |
--R        |     3                 2           2         3     2       |
--R        +   %A  + %A + 1      %A  + 1     %A        %A  + %A  + %A  +
--R                                       Type: SquareMatrix(4,FiniteField(2,4))
--E 27

--S 28 of 28
eval(sp,y=sm)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
   (7)  |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R   (7)  |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                            Type: Polynomial SquareMatrix(4,FiniteField(2,4))
--E 28

)spool 
 
Starts dribbling to besselk.output (2010/3/27, 18:23:11).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
D(besselK(a,x),x)
 

        - besselK(a + 1,x) - besselK(a - 1,x)
   (1)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R
--R        - besselK(a + 1,x) - besselK(a - 1,x)
--R   (1)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E 1

--S 2 of 6
D(besselK(a,x),a)
 

   (2)  besselK  (a,x)
               ,1
                                                     Type: Expression Integer
--R
--R   (2)  besselK  (a,x)
--R               ,1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
integrate(D(besselK(a,x),a),a)
 

   (3)  besselK(a,x)
                                          Type: Union(Expression Integer,...)
--R
--R   (3)  besselK(a,x)
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 6
limit(D(besselK(a,x),a),a=1/2)
 

   (4)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (4)  "failed"
--R                                                    Type: Union("failed",...)
--E 4

--S 5 of 6
stegun(x)== %e^x * besselK(1,x)
 
                                                                   Type: Void
--E 5

--S 6 of 6
[[0.1, 10.890182683 , stegun(0.1),  stegun(0.1)- 10.890182683 ],_
 [0.2,  5.833386037 , stegun(0.2),  stegun(0.2)-  5.833386037 ],_
 [0.3,  4.125157762 , stegun(0.3),  stegun(0.3)-  4.125157762 ],_
 [0.4,  3.258673880 , stegun(0.4),  stegun(0.4)-  3.258673880 ],_
 [0.5,  2.7310097082, stegun(0.5),  stegun(0.5)-  2.7310097082],_
 [0.6,  2.3739200376, stegun(0.6),  stegun(0.6)-  2.3739200376],_
 [0.7,  2.1150113128, stegun(0.7),  stegun(0.7)-  2.1150113128],_
 [0.8,  1.9179302990, stegun(0.8),  stegun(0.8)-  1.9179302990],_
 [0.9,  1.7623882197, stegun(0.9),  stegun(0.9)-  1.7623882197],_
 [1.0,  1.6361534863, stegun(1.0),  stegun(1.0)-  1.6361534863],_
 [1.1,  1.5314037541, stegun(1.1),  stegun(1.1)-  1.5314037541],_
 [1.2,  1.4428975522, stegun(1.2),  stegun(1.2)-  1.4428975522],_
 [1.3,  1.3669872841, stegun(1.3),  stegun(1.3)-  1.3669872841],_
 [1.4,  1.3010537400, stegun(1.4),  stegun(1.4)-  1.3010537400],_
 [1.5,  1.2431658736, stegun(1.5),  stegun(1.5)-  1.2431658736],_
 [1.6,  1.1918675654, stegun(1.6),  stegun(1.6)-  1.1918675654],_
 [1.7,  1.1460392462, stegun(1.7),  stegun(1.7)-  1.1460392462],_
 [1.8,  1.1048053726, stegun(1.8),  stegun(1.8)-  1.1048053726],_
 [1.9,  1.0674709298, stegun(1.9),  stegun(1.9)-  1.0674709298],_
 [2.0,  1.0334768471, stegun(2.0),  stegun(2.0)-  1.0334768471],_
 [2.1,  1.0023680527, stegun(2.1),  stegun(2.1)-  1.0023680527],_
 [2.2,  0.9737701679, stegun(2.2),  stegun(2.2)-  0.9737701679],_
 [2.3,  0.9473722250, stegun(2.3),  stegun(2.3)-  0.9473722250],_
 [2.4,  0.9229136650, stegun(2.4),  stegun(2.4)-  0.9229136650],_
 [2.5,  0.9001744239, stegun(2.5),  stegun(2.5)-  0.9001744239],_
 [2.6,  0.8789672806, stegun(2.6),  stegun(2.6)-  0.8789672806],_
 [2.7,  0.8591318867, stegun(2.7),  stegun(2.7)-  0.8591318867],_
 [2.8,  0.8405300604, stegun(2.8),  stegun(2.8)-  0.8405300604],_
 [2.9,  0.8230420403, stegun(2.9),  stegun(2.9)-  0.8230420403],_
 [3.0,  0.8065634800, stegun(3.0),  stegun(3.0)-  0.8065634800],_
 [3.1,  0.7910030157, stegun(3.1),  stegun(3.1)-  0.7910030157],_
 [3.2,  0.7762802824, stegun(3.2),  stegun(3.2)-  0.7762802824],_
 [3.3,  0.7623242864, stegun(3.3),  stegun(3.3)-  0.7623242864],_
 [3.4,  0.7490720613, stegun(3.4),  stegun(3.4)-  0.7490720613],_
 [3.5,  0.7364675480, stegun(3.5),  stegun(3.5)-  0.7364675480],_
 [3.6,  0.7244606608, stegun(3.6),  stegun(3.6)-  0.7244606608],_
 [3.7,  0.7130065010, stegun(3.7),  stegun(3.7)-  0.7130065010],_
 [3.8,  0.7020646931, stegun(3.8),  stegun(3.8)-  0.7020646931],_
 [3.9,  0.6915988206, stegun(3.9),  stegun(3.9)-  0.6915988206],_
 [4.0,  0.6815759452, stegun(4.0),  stegun(4.0)-  0.6815759452],_
 [4.1,  0.6719661952, stegun(4.1),  stegun(4.1)-  0.6719661952],_
 [4.2,  0.6627424110, stegun(4.2),  stegun(4.2)-  0.6627424110],_
 [4.3,  0.6538798395, stegun(4.3),  stegun(4.3)-  0.6538798395],_
 [4.4,  0.6453558689, stegun(4.4),  stegun(4.4)-  0.6453558689],_
 [4.5,  0.6371497988, stegun(4.5),  stegun(4.5)-  0.6371497988],_
 [4.6,  0.6292426383, stegun(4.6),  stegun(4.6)-  0.6292426383],_
 [4.7,  0.6216169312, stegun(4.7),  stegun(4.7)-  0.6216169312],_
 [4.8,  0.6142566003, stegun(4.8),  stegun(4.8)-  0.6142566003],_
 [4.9,  0.6071468131, stegun(4.9),  stegun(4.9)-  0.6071468131],_
 [5.0,  0.6002738587, stegun(5.0),  stegun(5.0)-  0.6002738587],_
 [5.1,  0.5936250463, stegun(5.1),  stegun(5.1)-  0.5936250463],_
 [5.2,  0.5871886062, stegun(5.2),  stegun(5.2)-  0.5871886062],_
 [5.3,  0.5809536085, stegun(5.3),  stegun(5.3)-  0.5809536085],_
 [5.4,  0.5749098871, stegun(5.4),  stegun(5.4)-  0.5749098871],_
 [5.5,  0.5690479741, stegun(5.5),  stegun(5.5)-  0.5690479741],_
 [5.6,  0.5633590393, stegun(5.6),  stegun(5.6)-  0.5633590393],_
 [5.7,  0.5578348348, stegun(5.7),  stegun(5.7)-  0.5578348348],_
 [5.8,  0.5524676495, stegun(5.8),  stegun(5.8)-  0.5524676495],_
 [5.9,  0.5472502639, stegun(5.9),  stegun(5.9)-  0.5472502639],_
 [6.0,  0.5421759104, stegun(6.0),  stegun(6.0)-  0.5421759104],_
 [6.1,  0.5372382386, stegun(6.1),  stegun(6.1)-  0.5372382386],_
 [6.2,  0.5324312833, stegun(6.2),  stegun(6.2)-  0.5324312833],_
 [6.3,  0.5277494344, stegun(6.3),  stegun(6.3)-  0.5277494344],_
 [6.4,  0.5231874101, stegun(6.4),  stegun(6.4)-  0.5231874101],_
 [6.5,  0.5187402336, stegun(6.5),  stegun(6.5)-  0.5187402336],_
 [6.6,  0.5144032108, stegun(6.6),  stegun(6.6)-  0.5144032108],_
 [6.7,  0.5101719097, stegun(6.7),  stegun(6.7)-  0.5101719097],_
 [6.8,  0.5060421421, stegun(6.8),  stegun(6.8)-  0.5060421421],_
 [6.9,  0.5020099471, stegun(6.9),  stegun(6.9)-  0.5020099471],_
 [7.0,  0.4980715749, stegun(7.0),  stegun(7.0)-  0.4980715749],_
 [7.1,  0.4942234737, stegun(7.1),  stegun(7.1)-  0.4942234737],_
 [7.2,  0.4904622755, stegun(7.2),  stegun(7.2)-  0.4904622755],_
 [7.3,  0.4867847842, stegun(7.3),  stegun(7.3)-  0.4867847842],_
 [7.4,  0.4831879648, stegun(7.4),  stegun(7.4)-  0.4831879648],_
 [7.5,  0.4796689336, stegun(7.5),  stegun(7.5)-  0.4796689336],_
 [7.6,  0.4762249486, stegun(7.6),  stegun(7.6)-  0.4762249486],_
 [7.7,  0.4728533995, stegun(7.7),  stegun(7.7)-  0.4728533995],_
 [7.8,  0.4695518010, stegun(7.8),  stegun(7.8)-  0.4695518010],_
 [7.9,  0.4663177847, stegun(7.9),  stegun(7.9)-  0.4663177847],_
 [8.0,  0.4631490928, stegun(8.0),  stegun(8.0)-  0.4631490928],_
 [8.1,  0.4600435709, stegun(8.1),  stegun(8.1)-  0.4600435709],_
 [8.2,  0.4569991615, stegun(8.2),  stegun(8.2)-  0.4569991615],_
 [8.3,  0.4540139001, stegun(8.3),  stegun(8.3)-  0.4540139001],_
 [8.4,  0.4510859089, stegun(8.4),  stegun(8.4)-  0.4510859089],_
 [8.5,  0.4482133915, stegun(8.5),  stegun(8.5)-  0.4482133915],_
 [8.6,  0.4453946295, stegun(8.6),  stegun(8.6)-  0.4453946295],_
 [8.7,  0.4426279775, stegun(8.7),  stegun(8.7)-  0.4426279775],_
 [8.8,  0.4399118594, stegun(8.8),  stegun(8.8)-  0.4399118594],_
 [8.9,  0.4372447648, stegun(8.9),  stegun(8.9)-  0.4372447648],_
 [9.0,  0.4346252454, stegun(9.0),  stegun(9.0)-  0.4346252454],_
 [9.1,  0.4320519116, stegun(9.1),  stegun(9.1)-  0.4320519116],_
 [9.2,  0.4295234301, stegun(9.2),  stegun(9.2)-  0.4295234301],_
 [9.3,  0.4270385204, stegun(9.3),  stegun(9.3)-  0.4270385204],_
 [9.4,  0.4245959520, stegun(9.4),  stegun(9.4)-  0.4245959520],_
 [9.5,  0.4221945430, stegun(9.5),  stegun(9.5)-  0.4221945430],_
 [9.6,  0.4198331565, stegun(9.6),  stegun(9.6)-  0.4198331565],_
 [9.7,  0.4175106989, stegun(9.7),  stegun(9.7)-  0.4175106989],_
 [9.8,  0.4152261179, stegun(9.8),  stegun(9.8)-  0.4152261179],_
 [9.9,  0.4129784003, stegun(9.9),  stegun(9.9)-  0.4129784003],_
 [10.0, 0.4107665704, stegun(10.0), stegun(10.0)- 0.4107665704]]
 
   Compiling function stegun with type Float -> Expression DoubleFloat 

   (6)
   [
     [0.10000000000000001, 10.890182682999999, 10.890319022557506,
      1.3633955750691484E-4]
     ,

     [0.20000000000000001, 5.8333860370000004, 5.8336819371503417,
      2.9590015034131056E-4]
     ,

     [0.29999999999999999, 4.1251577619999997, 4.1255945522062101,
      4.3679020621034681E-4]
     ,

     [0.40000000000000002, 3.2586738799999999, 3.2593701943917295,
      6.9631439172956888E-4]
     ,
    [0.5,2.7310097082000002,2.731886965647174,8.7725744717381815E-4],

     [0.59999999999999998, 2.3739200375999996, 2.374756542488131,
      8.3650488813136192E-4]
     ,

     [0.69999999999999996, 2.1150113128000001, 2.1152292590263659,
      2.1794622636583938E-4]
     ,
    [0.80000000000000004,1.917930299,1.9212801731849565,3.3498741849564695E-3],
    [0.89999999999999991,1.7623882197,1.7648211448559692,2.4329251559691567E-3],
    [1.,1.6361534863,1.6442713513080276,8.1178650080275805E-3],

     [1.1000000000000001, 1.5314037540999998, 1.5236186717580464,
      - 7.7850823419534088E-3]
     ,
    [1.2,1.4428975521999998,1.4371532138071441,- 5.7443383928557079E-3],

     [1.2999999999999998, 1.3669872840999999, 1.3784285159502272,
      1.1441231850227274E-2]
     ,
    [1.3999999999999999,1.30105374,1.2939838727691517,- 7.0698672308482369E-3],
    [1.5,1.2431658736,1.2416298871516902,- 1.5359864483097674E-3],

     [1.6000000000000001, 1.1918675653999999, 1.2192304384913151,
      2.7362873091315132E-2]
     ,
    [1.7,1.1460392462,1.1715529109616845,2.5513664761684485E-2],
    [1.7999999999999998,1.1048053726,1.0740259687380604,- 3.0779403861939558E-2]
     ,

     [1.8999999999999999, 1.0674709297999998, 1.1502695453127476,
      8.2798615512747809E-2]
     ,
    [2.,1.0334768471,1.1432923484271666,0.10981550132716666],

     [2.0999999999999996, 1.0023680527000001, 1.1037861331103433,
      0.10141808041034328]
     ,

     [2.2000000000000002, 0.97377016789999993, 0.95805766496233935,
      - 1.5712502937660577E-2]
     ,

     [2.2999999999999998, 0.94737222499999996, 1.2112893246589573,
      0.26391709965895738]
     ,

     [2.3999999999999999, 0.92291366500000005, - 0.51967642905672573,
      - 1.4425900940567258]
     ,
    [2.5,0.90017442390000002,1.2002778272528141,0.30010340335281405],

     [2.5999999999999996, 0.87896728059999996, - 0.39468573407023966,
      - 1.2736530146702396]
     ,

     [2.7000000000000002, 0.85913188669999996, 0.48509647462255634,
      - 0.37403541207744362]
     ,

     [2.7999999999999998, 0.84053006039999989, - 1.9342117634624107,
      - 2.7747418238624109]
     ,

     [2.8999999999999999, 0.82304204030000006, 0.40630327883074574,
      - 0.41673876146925432]
     ,
    [3.,0.80656348,- 10.876871938559711,- 11.683435418559711],

     [3.0999999999999996, 0.79100301569999998, 1.3116492298713476,
      0.5206462141713476]
     ,

     [3.2000000000000002, 0.77628028239999991, 8.0781790384939089,
      7.3018987560939088]
     ,

     [3.2999999999999998, 0.76232428639999994, 1.0349106313808072,
      0.27258634498080725]
     ,

     [3.3999999999999999, 0.74907206129999993, 1.139352728906901,
      0.39028066760690105]
     ,
    [3.5,0.73646754800000003,- 5.2569081315720521,- 5.9933756795720523],

     [3.5999999999999996, 0.72446066079999993, - 36.818666980943973,
      - 37.543127641743972]
     ,

     [3.7000000000000002, 0.71300650099999996, - 19.744563220721343,
      - 20.457569721721342]
     ,

     [3.7999999999999998, 0.70206469309999997, 164.75115684991093,
      164.04909215681093]
     ,
    [3.8999999999999999,0.6915988206,15.439012540683065,14.747413720083065],
    [4.,0.68157594519999998,140.04378623941682,139.36221029421682],
    [4.0999999999999996,0.6719661952,- 191.76189667462589,- 192.4338628698259],

     [4.1999999999999993, 0.66274241099999998, 27.589639470521707,
      26.926897059521707]
     ,

     [4.2999999999999998, 0.65387983949999995, 316.45036140633619,
      315.79648156683618]
     ,

     [4.4000000000000004, 0.64535586889999996, - 1256.4908007120307,
      - 1257.1361565809307]
     ,
    [4.5,0.63714979879999989,- 1499.8587600704061,- 1500.4959098692061],

     [4.5999999999999996, 0.62924263830000005, 312.36454149821105,
      311.73529885991104]
     ,

     [4.6999999999999993, 0.62161693119999994, 2959.902042500421,
      2959.2804255692208]
     ,

     [4.7999999999999998, 0.61425660029999996, 4411.9496555704291,
      4411.3353989701291]
     ,

     [4.9000000000000004, 0.60714681309999996, - 2015.6628980205714,
      - 2016.2700448336714]
     ,
    [5.,0.60027385870000005,5354.1644760481649,5353.5642021894646],

     [5.0999999999999996, 0.5936250462999999, - 9844.8175435093763,
      - 9845.4111685556763]
     ,

     [5.1999999999999993, 0.58718860620000002, - 8685.3869160682698,
      - 8685.9741046744693]
     ,
    [5.2999999999999998,0.5809536085,3726.2767503831265,3725.6957967746266],

     [5.4000000000000004, 0.57490988710000002, 3756.3505421043819,
      3755.7756322172818]
     ,
    [5.5,0.56904797409999996,27311.41679377839,27310.847745804291],

     [5.5999999999999996, 0.56335903929999998, 21037.772051995871,
      21037.20869295657]
     ,

     [5.6999999999999993, 0.55783483479999996, 41867.350637025193,
      41866.792802190394]
     ,

     [5.7999999999999998, 0.55246764950000005, - 61855.345973813441,
      - 61855.898441462938]
     ,

     [5.9000000000000004, 0.54725026389999998, - 100911.09568283817,
      - 100911.64293310208]
     ,
    [6.,0.54217591039999991,- 157208.07753263818,- 157208.61970854859],

     [6.0999999999999996, 0.53723823859999997, - 312575.12039718224,
      - 312575.65763542085]
     ,
    [6.1999999999999993,0.5324312833,244352.1468130147,244351.6143817314],

     [6.2999999999999998, 0.52774943439999999, - 242662.08665637492,
      - 242662.61440580932]
     ,

     [6.4000000000000004, 0.52318741010000003, 613229.36836314097,
      613228.84517573088]
     ,
    [6.5,0.51874023359999999,638739.50261170371,638738.98387147009],

     [6.5999999999999996, 0.51440321079999995, - 660105.2135660986,
      - 660105.72796930943]
     ,

     [6.6999999999999993, 0.51017190969999993, - 1820675.3976876703,
      - 1820675.9078595799]
     ,

     [6.7999999999999998, 0.50604214209999998, 1217376.6837833647,
      1217376.1777412225]
     ,

     [6.9000000000000004, 0.50200994709999991, 710753.45019748132,
      710752.94818753423]
     ,
    [7.,0.49807157489999998,5408624.9820442246,5408624.48397265],

     [7.0999999999999996, 0.49422347369999997, - 11831626.770237859,
      - 11831627.264461333]
     ,

     [7.1999999999999993, 0.49046227549999999, - 2084367.1455923028,
      - 2084367.6360545782]
     ,

     [7.2999999999999998, 0.48678478419999999, - 1795630.3917610554,
      - 1795630.8785458396]
     ,

     [7.4000000000000004, 0.48318796479999998, - 20143898.366605397,
      - 20143898.849793363]
     ,
    [7.5,0.47966893359999996,- 39167730.517877236,- 39167730.997546166],

     [7.5999999999999996, 0.47622494859999998, - 22924081.053716745,
      - 22924081.529941693]
     ,

     [7.6999999999999993, 0.47285339949999999, - 70209184.511092067,
      - 70209184.983945459]
     ,

     [7.7999999999999998, 0.46955180099999999, - 65786321.971720159,
      - 65786322.441271961]
     ,

     [7.9000000000000004, 0.46631778469999996, 82915526.820476264,
      82915526.354158476]
     ,
    [8.,0.4631490928,47517980.680922575,47517980.217773482],

     [8.0999999999999996, 0.46004357089999998, - 249874912.50967234,
      - 249874912.96971592]
     ,

     [8.1999999999999993, 0.45699916149999997, 346570801.44758362,
      346570800.99058443]
     ,

     [8.3000000000000007, 0.45401390009999998, - 221829478.78925869,
      - 221829479.2432726]
     ,
    [8.3999999999999986,0.4510859089,98011755.921689853,98011755.470603943],
    [8.5,0.44821339149999995,648624945.52613997,648624945.07792664],

     [8.5999999999999996, 0.44539462949999997, - 673892935.65853786,
      - 673892936.1039325]
     ,

     [8.6999999999999993, 0.44262797749999999, 308596985.6075266,
      308596985.16489863]
     ,

     [8.8000000000000007, 0.43991185939999999, - 3255255823.7619305,
      - 3255255824.2018423]
     ,

     [8.8999999999999986, 0.43724476479999996, 594981570.79734111,
      594981570.36009634]
     ,
    [9.,0.43462524540000003,1735724420.9596174,1735724420.5249922],
    [9.0999999999999996,0.4320519116,2236290078.2552886,2236290077.8232365],

     [9.1999999999999993, 0.42952343009999999, 608399367.03416002,
      608399366.60463655]
     ,

     [9.3000000000000007, 0.42703852040000001, - 11199155560.514084,
      - 11199155560.941122]
     ,
    [9.3999999999999986,0.424595952,- 12762104068.83704,- 12762104069.261637],
    [9.5,0.42219454299999998,- 32818948767.798557,- 32818948768.220753],

     [9.5999999999999996, 0.41983315649999997, - 26100466231.101562,
      - 26100466231.521397]
     ,

     [9.6999999999999993, 0.41751069889999998, 59418330763.052277,
      59418330762.634766]
     ,

     [9.8000000000000007, 0.41522611789999997, - 74333139139.499191,
      - 74333139139.914413]
     ,

     [9.8999999999999986, 0.41297840029999999, - 22853087574.401817,
      - 22853087574.814796]
     ,
    [10.,0.41076657039999998,43444307295.047157,43444307294.636391]]
                                       Type: List List Expression DoubleFloat
--E 6

)spool 
 
Starts dribbling to MakeFunction.output (2010/3/27, 18:46:2).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
expr := (x - exp x + 1)^2 * (sin(x^2) * x + 1)^3
 

   (1)
       3   x 2        4     3   x    5     4    3      2 3
     (x (%e )  + (- 2x  - 2x )%e  + x  + 2x  + x )sin(x )
   + 
        2   x 2        3     2   x     4     3     2      2 2
     (3x (%e )  + (- 6x  - 6x )%e  + 3x  + 6x  + 3x )sin(x )
   + 
            x 2        2        x     3     2           2       x 2
     (3x (%e )  + (- 6x  - 6x)%e  + 3x  + 6x  + 3x)sin(x ) + (%e )
   + 
                 x    2
     (- 2x - 2)%e  + x  + 2x + 1
                                                     Type: Expression Integer
--R 
--R
--R   (1)
--R       3   x 2        4     3   x    5     4    3      2 3
--R     (x (%e )  + (- 2x  - 2x )%e  + x  + 2x  + x )sin(x )
--R   + 
--R        2   x 2        3     2   x     4     3     2      2 2
--R     (3x (%e )  + (- 6x  - 6x )%e  + 3x  + 6x  + 3x )sin(x )
--R   + 
--R            x 2        2        x     3     2           2       x 2
--R     (3x (%e )  + (- 6x  - 6x)%e  + 3x  + 6x  + 3x)sin(x ) + (%e )
--R   + 
--R                 x    2
--R     (- 2x - 2)%e  + x  + 2x + 1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 9
function(expr, f, x)
 

   (2)  f
                                                                 Type: Symbol
--R 
--R
--R   (2)  f
--R                                                                 Type: Symbol
--E 2

--S 3 of 9
tbl := [f(0.1 * i - 1) for i in 0..20]
 
   Compiling function f with type Float -> Float 

   (3)
   [0.0005391844 0362701574, 0.0039657551 1844206653,
    0.0088545187 4833983689 2, 0.0116524883 0907069695,
    0.0108618220 9245751364 5, 0.0076366823 2120869965 06,
    0.0040584985 7597822062 55, 0.0015349542 8910500836 48,
    0.0003424903 1549879905 716, 0.0000233304 8276098819 6001, 0.0,
    0.0000268186 8782862599 4229, 0.0004691571 3720051642 621,
    0.0026924576 5968519586 08, 0.0101486881 7369135148 8,
    0.0313833725 8543810564 3, 0.0876991144 5154615297 9,
    0.2313019789 3439968362, 0.5843743955 958098772, 1.4114930171 992819197,
    3.2216948276 75164252]
                                                             Type: List Float
--R 
--R   Compiling function f with type Float -> Float 
--R
--R   (3)
--R   [0.0005391844 0362701574, 0.0039657551 1844206653,
--R    0.0088545187 4833983689 2, 0.0116524883 0907069695,
--R    0.0108618220 9245751364 5, 0.0076366823 2120869965 06,
--R    0.0040584985 7597822062 55, 0.0015349542 8910500836 48,
--R    0.0003424903 1549879905 716, 0.0000233304 8276098819 6001, 0.0,
--R    0.0000268186 8782862599 4229, 0.0004691571 3720051642 621,
--R    0.0026924576 5968519586 08, 0.0101486881 7369135148 8,
--R    0.0313833725 8543810564 3, 0.0876991144 5154615297 9,
--R    0.2313019789 3439968362, 0.5843743955 958098772, 1.4114930171 992819197,
--R    3.2216948276 75164252]
--R                                                             Type: List Float
--E 3

--S 4 of 9
e := (x - y + 1)^2 * (x^2 * y + 1)^2 
 

   (4)
      4 4        5     4     2  3     6     5    4     3     2      2
     x y  + (- 2x  - 2x  + 2x )y  + (x  + 2x  + x  - 4x  - 4x  + 1)y
   + 
        4     3     2               2
     (2x  + 4x  + 2x  - 2x - 2)y + x  + 2x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)
--R      4 4        5     4     2  3     6     5    4     3     2      2
--R     x y  + (- 2x  - 2x  + 2x )y  + (x  + 2x  + x  - 4x  - 4x  + 1)y
--R   + 
--R        4     3     2               2
--R     (2x  + 4x  + 2x  - 2x - 2)y + x  + 2x + 1
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 9
function(e, g, [x, y])
 

   (5)  g
                                                                 Type: Symbol
--R 
--R
--R   (5)  g
--R                                                                 Type: Symbol
--E 5

--S 6 of 9
function(e, h, x, y)
 

   (6)  h
                                                                 Type: Symbol
--R 
--R
--R   (6)  h
--R                                                                 Type: Symbol
--E 6

--S 7 of 9
m1 := squareMatrix [ [1, 2], [3, 4] ]
 

        +1  2+
   (7)  |    |
        +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 7

--S 8 of 9
m2 := squareMatrix [ [1, 0], [-1, 1] ]
 

        + 1   0+
   (8)  |      |
        +- 1  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        + 1   0+
--R   (8)  |      |
--R        +- 1  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 9
h(m1, m2)
 
   Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix
      (2,Integer)) -> SquareMatrix(2,Integer) 

        +- 7836   8960 +
   (9)  |              |
        +- 17132  19588+
                                                Type: SquareMatrix(2,Integer)
--R 
--R   Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix
--R      (2,Integer)) -> SquareMatrix(2,Integer) 
--R
--R        +- 7836   8960 +
--R   (9)  |              |
--R        +- 17132  19588+
--R                                                Type: SquareMatrix(2,Integer)
--E 9
)spool
 
Starts dribbling to donsimple.output (2010/3/27, 18:25:1).
)set message test on
 
)set message auto off
 
)clear all
 
)sys cp $AXIOM/../../src/input/donsimple.input.pamphlet .
 
)lisp (tangle "donsimple.input.pamphlet" "donsimp.spad" "donsimp.spad")
 
Value = NIL
)co donsimp
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/donsimp.spad 
      using old system compiler.
   DONSIMP abbreviates package donSimple 
   processing macro definition F ==> Float 
   processing macro definition SF ==> Segment Float 
   processing macro definition EF ==> Expression Float 
   processing macro definition SBF ==> SegmentBinding Float 
   processing macro definition Exports ==> -- the constructor category 
   processing macro definition Implementation ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing nrlib DONSIMP for donSimple 
   compiling into nrlib DONSIMP 
   compiling exported simple : (Float -> Float,Segment Float) -> Float
Time: 0.01 SEC.

   compiling exported simple : (Expression Float,SegmentBinding Float) -> Expression Float
Time: 0.09 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |donSimple| REDEFINED

;;;     ***       |donSimple| REDEFINED
Time: 0 SEC.

 
   Warnings: 
      [1] simple: not known that (OrderedSet) is of mode (CATEGORY package (SIGNATURE simple ((Float) (Mapping (Float) (Float)) (Segment (Float)))) (SIGNATURE simple ((Expression (Float)) (Expression (Float)) (SegmentBinding (Float)))))
 

   Cumulative Statistics for Constructor donSimple
      Time: 0.10 seconds
 
   finalizing nrlib DONSIMP 
   Processing donSimple for Browser database:
--------(simple (F (Mapping F F) SF))---------
--->-->donSimple((simple (F (Mapping F F) SF))): Improper first word in comments: 
"\\indented{1}{simple(a,{}\\spad{b})} \\blankline \\spad{X} simple(\\spad{x+}-\\spad{>x^2},{}1..2)"
--------(simple (EF EF SBF))---------
--->-->donSimple((simple (EF EF SBF))): Improper first word in comments: 
"\\indented{1}{simple(a,{}\\spad{b})} \\blankline \\spad{X} simple(\\spad{x^2},{}\\spad{x=1}..2)"
--->-->donSimple(constructor): Not documented!!!!
--->-->donSimple(): Missing Description
------------------------------------------------------------------------
   donSimple is now explicitly exposed in frame initial 
   donSimple will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/DONSIMP.nrlib/code


--S 1 of 2
simple(1/x,x=2..3)
 

   (1)  - 0.1666666666 666666667
                                                       Type: Expression Float
--R
--R   (1)  - 0.1666666666 666666667
--R                                                       Type: Expression Float
--E 1

--S 2 of 2
simple(x+->1/x,2..3)
 

   (2)  - 0.1666666666 666666667
                                                                  Type: Float
--R
--R   (2)  - 0.1666666666 666666667
--R                                                                  Type: Float
--E 2

)spool 
 
Starts dribbling to ZeroDimensionalSolvePackage.output (2010/3/27, 18:46:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 28
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 28
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 28
ls2 : List Symbol := [x,y,z,t,new()$Symbol]
 

   (3)  [x,y,z,t,%A]
                                                            Type: List Symbol
--R 
--R
--R   (3)  [x,y,z,t,%A]
--R                                                            Type: List Symbol
--E 3

--S 4 of 28
pack := ZDSOLVE(R,ls,ls2)
 

   (4)  ZeroDimensionalSolvePackage(Integer,[x,y,z,t],[x,y,z,t,%A])
                                                                 Type: Domain
--R 
--R
--R   (4)  ZeroDimensionalSolvePackage(Integer,[x,y,z,t],[x,y,z,t,%A])
--R                                                                 Type: Domain
--E 4

--S 5 of 28
p1 := x**2*y*z + x*y**2*z + x*y*z**2 + x*y*z + x*y + x*z + y*z
 

             2       2     2
   (5)  x y z  + (x y  + (x  + x + 1)y + x)z + x y
                                                     Type: Polynomial Integer
--R 
--R
--R             2       2     2
--R   (5)  x y z  + (x y  + (x  + x + 1)y + x)z + x y
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 28
p2 := x**2*y**2*z + x*y**2*z**2 + x**2*y*z + x*y*z + y*z + x + z
 

           2 2     2 2     2
   (6)  x y z  + (x y  + (x  + x + 1)y + 1)z + x
                                                     Type: Polynomial Integer
--R 
--R
--R           2 2     2 2     2
--R   (6)  x y z  + (x y  + (x  + x + 1)y + 1)z + x
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 28
p3 := x**2*y**2*z**2 + x**2*y**2*z + x*y**2*z + x*y*z + x*z + z + 1
 

         2 2 2      2      2
   (7)  x y z  + ((x  + x)y  + x y + x + 1)z + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2 2 2      2      2
--R   (7)  x y z  + ((x  + x)y  + x y + x + 1)z + 1
--R                                                     Type: Polynomial Integer
--E 7

--S 8 of 28
lp := [p1, p2, p3]
 

   (8)
         2       2     2
   [x y z  + (x y  + (x  + x + 1)y + x)z + x y,
       2 2     2 2     2
    x y z  + (x y  + (x  + x + 1)y + 1)z + x,
     2 2 2      2      2
    x y z  + ((x  + x)y  + x y + x + 1)z + 1]
                                                Type: List Polynomial Integer
--R 
--R
--R   (8)
--R         2       2     2
--R   [x y z  + (x y  + (x  + x + 1)y + x)z + x y,
--R       2 2     2 2     2
--R    x y z  + (x y  + (x  + x + 1)y + 1)z + x,
--R     2 2 2      2      2
--R    x y z  + ((x  + x)y  + x y + x + 1)z + 1]
--R                                                Type: List Polynomial Integer
--E 8

--S 9 of 28
triangSolve(lp)$pack
 

   (9)
   [
     {
          20     19      18      17       16      15       14       13       12
         z   - 6z   - 41z   + 71z   + 106z   + 92z   + 197z   + 145z   + 257z
       + 
             11       10       9       8       7       6      5       4      3
         278z   + 201z   + 278z  + 257z  + 145z  + 197z  + 92z  + 106z  + 71z
       + 
              2
         - 41z  - 6z + 1
       ,

                      19            18             17             16
             14745844z   + 50357474z   - 130948857z   - 185261586z
           + 
                         15             14             13             12
             - 180077775z   - 338007307z   - 275379623z   - 453190404z
           + 
                         11             10             9             8
             - 474597456z   - 366147695z   - 481433567z  - 430613166z
           + 
                         7             6             5             4
             - 261878358z  - 326073537z  - 163008796z  - 177213227z
           + 
                         3            2
             - 104356755z  + 65241699z  + 9237732z - 1567348
        *
           y
       + 
                 19           18            17            16            15
         1917314z   + 6508991z   - 16973165z   - 24000259z   - 23349192z
       + 
                    14            13            12            11            10
         - 43786426z   - 35696474z   - 58724172z   - 61480792z   - 47452440z
       + 
                    9            8            7            6            5
         - 62378085z  - 55776527z  - 33940618z  - 42233406z  - 21122875z
       + 
                    4            3           2
         - 22958177z  - 13504569z  + 8448317z  + 1195888z - 202934
       ,
         3       2       3    2               2              2
      ((z  - 2z)y  + (- z  - z  - 2z - 1)y - z  - z + 1)x + z  - 1}
     ]
                                   Type: List RegularChain(Integer,[x,y,z,t])
--R 
--R
--R   (9)
--R   [
--R     {
--R          20     19      18      17       16      15       14       13       12
--R         z   - 6z   - 41z   + 71z   + 106z   + 92z   + 197z   + 145z   + 257z
--R       + 
--R             11       10       9       8       7       6      5       4      3
--R         278z   + 201z   + 278z  + 257z  + 145z  + 197z  + 92z  + 106z  + 71z
--R       + 
--R              2
--R         - 41z  - 6z + 1
--R       ,
--R
--R                      19            18             17             16
--R             14745844z   + 50357474z   - 130948857z   - 185261586z
--R           + 
--R                         15             14             13             12
--R             - 180077775z   - 338007307z   - 275379623z   - 453190404z
--R           + 
--R                         11             10             9             8
--R             - 474597456z   - 366147695z   - 481433567z  - 430613166z
--R           + 
--R                         7             6             5             4
--R             - 261878358z  - 326073537z  - 163008796z  - 177213227z
--R           + 
--R                         3            2
--R             - 104356755z  + 65241699z  + 9237732z - 1567348
--R        *
--R           y
--R       + 
--R                 19           18            17            16            15
--R         1917314z   + 6508991z   - 16973165z   - 24000259z   - 23349192z
--R       + 
--R                    14            13            12            11            10
--R         - 43786426z   - 35696474z   - 58724172z   - 61480792z   - 47452440z
--R       + 
--R                    9            8            7            6            5
--R         - 62378085z  - 55776527z  - 33940618z  - 42233406z  - 21122875z
--R       + 
--R                    4            3           2
--R         - 22958177z  - 13504569z  + 8448317z  + 1195888z - 202934
--R       ,
--R         3       2       3    2               2              2
--R      ((z  - 2z)y  + (- z  - z  - 2z - 1)y - z  - z + 1)x + z  - 1}
--R     ]
--R                                   Type: List RegularChain(Integer,[x,y,z,t])
--E 9

--S 10 of 28
univariateSolve(lp)$pack
 

   (10)
   [
     [
       complexRoots =
            12      11      10     9     8      7      6      5     4     3
           ?   - 12?   + 24?   + 4?  - 9?  + 27?  - 21?  + 27?  - 9?  + 4?
         + 
              2
           24?  - 12? + 1
       ,

       coordinates =
         [
                       11        10         9        8        7         6
             63x + 62%A   - 721%A   + 1220%A  + 705%A  - 285%A  + 1512%A
           + 
                    5         4       3        2
             - 735%A  + 1401%A  - 21%A  + 215%A  + 1577%A - 142
           ,

                       11        10         9        8        7         6
             63y - 75%A   + 890%A   - 1682%A  - 516%A  + 588%A  - 1953%A
           + 
                   5         4        3        2
             1323%A  - 1815%A  + 426%A  - 243%A  - 1801%A + 679
           ,
          z - %A]
       ]
     ,

                     6    5    4    3    2
     [complexRoots= ?  + ?  + ?  + ?  + ?  + ? + 1,
                          5       3
      coordinates= [x - %A ,y - %A ,z - %A]]
     ,
                    2
    [complexRoots= ?  + 5? + 1,coordinates= [x - 1,y - 1,z - %A]]]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--R 
--R
--R   (10)
--R   [
--R     [
--R       complexRoots =
--R            12      11      10     9     8      7      6      5     4     3
--R           ?   - 12?   + 24?   + 4?  - 9?  + 27?  - 21?  + 27?  - 9?  + 4?
--R         + 
--R              2
--R           24?  - 12? + 1
--R       ,
--R
--R       coordinates =
--R         [
--R                       11        10         9        8        7         6
--R             63x + 62%A   - 721%A   + 1220%A  + 705%A  - 285%A  + 1512%A
--R           + 
--R                    5         4       3        2
--R             - 735%A  + 1401%A  - 21%A  + 215%A  + 1577%A - 142
--R           ,
--R
--R                       11        10         9        8        7         6
--R             63y - 75%A   + 890%A   - 1682%A  - 516%A  + 588%A  - 1953%A
--R           + 
--R                   5         4        3        2
--R             1323%A  - 1815%A  + 426%A  - 243%A  - 1801%A + 679
--R           ,
--R          z - %A]
--R       ]
--R     ,
--R
--R                     6    5    4    3    2
--R     [complexRoots= ?  + ?  + ?  + ?  + ?  + ? + 1,
--R                          5       3
--R      coordinates= [x - %A ,y - %A ,z - %A]]
--R     ,
--R                    2
--R    [complexRoots= ?  + 5? + 1,coordinates= [x - 1,y - 1,z - %A]]]
--RType: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--E 10

--S 11 of 28
lr := realSolve(lp)$pack
 

   (11)
   [
     [%B1,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B1   - ------- %B1   - ------- %B1   + -------- %B1
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B1   + -------- %B1   + ------ %B1   + --------- %B1
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B1   + --------- %B1   + --------- %B1  + --------- %B1
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B1  + ------- %B1  + ------ %B1  + ------- %B1
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B1  + -------- %B1  - ---- %B1 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B1   + ------ %B1   + ------- %B1   - ------- %B1
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B1   - -------- %B1   - -------- %B1   - ------ %B1
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B1   - -------- %B1   - -------- %B1  - ------- %B1
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B1  - -------- %B1  - -------- %B1  - -------- %B1
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B1  - -------- %B1  - ------- %B1 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B2,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B2   - ------- %B2   - ------- %B2   + -------- %B2
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B2   + -------- %B2   + ------ %B2   + --------- %B2
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B2   + --------- %B2   + --------- %B2  + --------- %B2
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B2  + ------- %B2  + ------ %B2  + ------- %B2
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B2  + -------- %B2  - ---- %B2 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B2   + ------ %B2   + ------- %B2   - ------- %B2
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B2   - -------- %B2   - -------- %B2   - ------ %B2
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B2   - -------- %B2   - -------- %B2  - ------- %B2
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B2  - -------- %B2  - -------- %B2  - -------- %B2
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B2  - -------- %B2  - ------- %B2 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B3,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B3   - ------- %B3   - ------- %B3   + -------- %B3
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B3   + -------- %B3   + ------ %B3   + --------- %B3
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B3   + --------- %B3   + --------- %B3  + --------- %B3
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B3  + ------- %B3  + ------ %B3  + ------- %B3
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B3  + -------- %B3  - ---- %B3 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B3   + ------ %B3   + ------- %B3   - ------- %B3
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B3   - -------- %B3   - -------- %B3   - ------ %B3
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B3   - -------- %B3   - -------- %B3  - ------- %B3
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B3  - -------- %B3  - -------- %B3  - -------- %B3
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B3  - -------- %B3  - ------- %B3 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B4,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B4   - ------- %B4   - ------- %B4   + -------- %B4
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B4   + -------- %B4   + ------ %B4   + --------- %B4
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B4   + --------- %B4   + --------- %B4  + --------- %B4
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B4  + ------- %B4  + ------ %B4  + ------- %B4
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B4  + -------- %B4  - ---- %B4 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B4   + ------ %B4   + ------- %B4   - ------- %B4
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B4   - -------- %B4   - -------- %B4   - ------ %B4
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B4   - -------- %B4   - -------- %B4  - ------- %B4
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B4  - -------- %B4  - -------- %B4  - -------- %B4
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B4  - -------- %B4  - ------- %B4 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B5,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B5   - ------- %B5   - ------- %B5   + -------- %B5
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B5   + -------- %B5   + ------ %B5   + --------- %B5
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B5   + --------- %B5   + --------- %B5  + --------- %B5
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B5  + ------- %B5  + ------ %B5  + ------- %B5
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B5  + -------- %B5  - ---- %B5 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B5   + ------ %B5   + ------- %B5   - ------- %B5
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B5   - -------- %B5   - -------- %B5   - ------ %B5
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B5   - -------- %B5   - -------- %B5  - ------- %B5
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B5  - -------- %B5  - -------- %B5  - -------- %B5
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B5  - -------- %B5  - ------- %B5 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B6,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B6   - ------- %B6   - ------- %B6   + -------- %B6
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B6   + -------- %B6   + ------ %B6   + --------- %B6
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B6   + --------- %B6   + --------- %B6  + --------- %B6
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B6  + ------- %B6  + ------ %B6  + ------- %B6
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B6  + -------- %B6  - ---- %B6 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B6   + ------ %B6   + ------- %B6   - ------- %B6
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B6   - -------- %B6   - -------- %B6   - ------ %B6
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B6   - -------- %B6   - -------- %B6  - ------- %B6
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B6  - -------- %B6  - -------- %B6  - -------- %B6
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B6  - -------- %B6  - ------- %B6 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B7,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B7   - ------- %B7   - ------- %B7   + -------- %B7
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B7   + -------- %B7   + ------ %B7   + --------- %B7
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B7   + --------- %B7   + --------- %B7  + --------- %B7
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B7  + ------- %B7  + ------ %B7  + ------- %B7
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B7  + -------- %B7  - ---- %B7 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B7   + ------ %B7   + ------- %B7   - ------- %B7
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B7   - -------- %B7   - -------- %B7   - ------ %B7
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B7   - -------- %B7   - -------- %B7  - ------- %B7
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B7  - -------- %B7  - -------- %B7  - -------- %B7
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B7  - -------- %B7  - ------- %B7 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B8,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B8   - ------- %B8   - ------- %B8   + -------- %B8
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B8   + -------- %B8   + ------ %B8   + --------- %B8
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B8   + --------- %B8   + --------- %B8  + --------- %B8
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B8  + ------- %B8  + ------ %B8  + ------- %B8
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B8  + -------- %B8  - ---- %B8 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B8   + ------ %B8   + ------- %B8   - ------- %B8
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B8   - -------- %B8   - -------- %B8   - ------ %B8
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B8   - -------- %B8   - -------- %B8  - ------- %B8
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B8  - -------- %B8  - -------- %B8  - -------- %B8
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B8  - -------- %B8  - ------- %B8 + ------
            26117         705159          705159       705159
       ]
     ]
                                 Type: List List RealClosure Fraction Integer
--R 
--R
--R   (11)
--R   [
--R     [%B1,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B1   - ------- %B1   - ------- %B1   + -------- %B1
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B1   + -------- %B1   + ------ %B1   + --------- %B1
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B1   + --------- %B1   + --------- %B1  + --------- %B1
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B1  + ------- %B1  + ------ %B1  + ------- %B1
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B1  + -------- %B1  - ---- %B1 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B1   + ------ %B1   + ------- %B1   - ------- %B1
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B1   - -------- %B1   - -------- %B1   - ------ %B1
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B1   - -------- %B1   - -------- %B1  - ------- %B1
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B1  - -------- %B1  - -------- %B1  - -------- %B1
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B1  - -------- %B1  - ------- %B1 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B2,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B2   - ------- %B2   - ------- %B2   + -------- %B2
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B2   + -------- %B2   + ------ %B2   + --------- %B2
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B2   + --------- %B2   + --------- %B2  + --------- %B2
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B2  + ------- %B2  + ------ %B2  + ------- %B2
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B2  + -------- %B2  - ---- %B2 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B2   + ------ %B2   + ------- %B2   - ------- %B2
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B2   - -------- %B2   - -------- %B2   - ------ %B2
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B2   - -------- %B2   - -------- %B2  - ------- %B2
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B2  - -------- %B2  - -------- %B2  - -------- %B2
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B2  - -------- %B2  - ------- %B2 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B3,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B3   - ------- %B3   - ------- %B3   + -------- %B3
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B3   + -------- %B3   + ------ %B3   + --------- %B3
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B3   + --------- %B3   + --------- %B3  + --------- %B3
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B3  + ------- %B3  + ------ %B3  + ------- %B3
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B3  + -------- %B3  - ---- %B3 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B3   + ------ %B3   + ------- %B3   - ------- %B3
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B3   - -------- %B3   - -------- %B3   - ------ %B3
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B3   - -------- %B3   - -------- %B3  - ------- %B3
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B3  - -------- %B3  - -------- %B3  - -------- %B3
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B3  - -------- %B3  - ------- %B3 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B4,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B4   - ------- %B4   - ------- %B4   + -------- %B4
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B4   + -------- %B4   + ------ %B4   + --------- %B4
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B4   + --------- %B4   + --------- %B4  + --------- %B4
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B4  + ------- %B4  + ------ %B4  + ------- %B4
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B4  + -------- %B4  - ---- %B4 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B4   + ------ %B4   + ------- %B4   - ------- %B4
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B4   - -------- %B4   - -------- %B4   - ------ %B4
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B4   - -------- %B4   - -------- %B4  - ------- %B4
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B4  - -------- %B4  - -------- %B4  - -------- %B4
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B4  - -------- %B4  - ------- %B4 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B5,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B5   - ------- %B5   - ------- %B5   + -------- %B5
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B5   + -------- %B5   + ------ %B5   + --------- %B5
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B5   + --------- %B5   + --------- %B5  + --------- %B5
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B5  + ------- %B5  + ------ %B5  + ------- %B5
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B5  + -------- %B5  - ---- %B5 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B5   + ------ %B5   + ------- %B5   - ------- %B5
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B5   - -------- %B5   - -------- %B5   - ------ %B5
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B5   - -------- %B5   - -------- %B5  - ------- %B5
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B5  - -------- %B5  - -------- %B5  - -------- %B5
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B5  - -------- %B5  - ------- %B5 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B6,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B6   - ------- %B6   - ------- %B6   + -------- %B6
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B6   + -------- %B6   + ------ %B6   + --------- %B6
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B6   + --------- %B6   + --------- %B6  + --------- %B6
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B6  + ------- %B6  + ------ %B6  + ------- %B6
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B6  + -------- %B6  - ---- %B6 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B6   + ------ %B6   + ------- %B6   - ------- %B6
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B6   - -------- %B6   - -------- %B6   - ------ %B6
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B6   - -------- %B6   - -------- %B6  - ------- %B6
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B6  - -------- %B6  - -------- %B6  - -------- %B6
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B6  - -------- %B6  - ------- %B6 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B7,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B7   - ------- %B7   - ------- %B7   + -------- %B7
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B7   + -------- %B7   + ------ %B7   + --------- %B7
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B7   + --------- %B7   + --------- %B7  + --------- %B7
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B7  + ------- %B7  + ------ %B7  + ------- %B7
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B7  + -------- %B7  - ---- %B7 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B7   + ------ %B7   + ------- %B7   - ------- %B7
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B7   - -------- %B7   - -------- %B7   - ------ %B7
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B7   - -------- %B7   - -------- %B7  - ------- %B7
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B7  - -------- %B7  - -------- %B7  - -------- %B7
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B7  - -------- %B7  - ------- %B7 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ,
--R
--R     [%B8,
--R
--R         1184459    19   2335702    18   5460230    17   79900378    16
--R         ------- %B8   - ------- %B8   - ------- %B8   + -------- %B8
--R         1645371          548457          182819          1645371
--R       + 
--R         43953929    15   13420192    14   553986    13   193381378    12
--R         -------- %B8   + -------- %B8   + ------ %B8   + --------- %B8
--R          548457           182819           3731           1645371
--R       + 
--R         35978916    11   358660781    10   271667666    9   118784873    8
--R         -------- %B8   + --------- %B8   + --------- %B8  + --------- %B8
--R          182819           1645371           1645371           548457
--R       + 
--R         337505020    7   1389370    6   688291    5   3378002    4
--R         --------- %B8  + ------- %B8  + ------ %B8  + ------- %B8
--R          1645371          11193          4459          42189
--R       + 
--R         140671876    3   32325724    2   8270       9741532
--R         --------- %B8  + -------- %B8  - ---- %B8 - -------
--R          1645371          548457          343       1645371
--R       ,
--R
--R            91729    19   487915    18   4114333    17   1276987    16
--R         - ------ %B8   + ------ %B8   + ------- %B8   - ------- %B8
--R           705159         705159          705159          235053
--R       + 
--R           13243117    15   16292173    14   26536060    13   722714    12
--R         - -------- %B8   - -------- %B8   - -------- %B8   - ------ %B8
--R            705159           705159           705159           18081
--R       + 
--R           5382578    11   15449995    10   14279770    9   6603890    8
--R         - ------- %B8   - -------- %B8   - -------- %B8  - ------- %B8
--R            100737          235053           235053          100737
--R       + 
--R           409930    7   37340389    6   34893715    5   26686318    4
--R         - ------ %B8  - -------- %B8  - -------- %B8  - -------- %B8
--R            6027          705159          705159          705159
--R       + 
--R           801511    3   17206178    2   4406102       377534
--R         - ------ %B8  - -------- %B8  - ------- %B8 + ------
--R            26117         705159          705159       705159
--R       ]
--R     ]
--R                                 Type: List List RealClosure Fraction Integer
--E 11

--S 12 of 28
# lr
 

   (12)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  8
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 28
[ [approximate(r,1/1000000) for r in point] for point in lr]
 

   (13)
   [
        10048059
     [- --------,
         2097152

        4503057316985387943524397913838966414596731976211768219335881208385516_
         314058924567176091423629695777403099833360761048898228916578137094309_
         838597331137202584846939132376157019506760357601165917454986815382098_
         789094851523420392811293126141329856546977145464661495487825919941188_
         447041722440491921567263542158028061437758844364634410045253024786561_
         923163288214175
      /
        4503057283025245488516511806985826635083100693757320465280554706865644_
         949577509916867201889438090408354817931718593862797624551518983570793_
         048774424291488708829840324189200301436123314860200821443733790755311_
         243632919864895421704228949571290016119498807957023663865443069392027_
         148979688266712323356043491523434068924275280417338574817381189277066_
         143312396681216
       ,

        2106260768823475073894798680486016596249607148690685538763683715020639_
         680858649650790055889505646893309447097099937802187329095325898785247_
         249020717504983660482075156618738724514685333060011202964635166381351_
         543255982200250305283981086837110614842307026091211297929876896285681_
         830479054760056380762664905618462055306047816191782011588703789138988_
         1895
      /
        2106260609498464192472113804816474175341962953296434102413903142368757_
         967685273888585590975965211778862189872881953943640246297357061959812_
         326103659799025126863258676567202342106877031710184247484181423288921_
         837681237062708470295706218485928867400771937828499200923760593314168_
         901000666373896347598118228556731037072026474496776228383762993923280_
         0768
       ]
     ,

        2563013
     [- -------,
        2097152

       -
           2611346176791927789698617693237757719238259963063541781922752330440_
            189899668072928338490768623593207442125925986733815932243504809294_
            837523030237337236806668167446173001727271353311571242897
         /
           1165225400505222530583981916004589143757226610276858990008790134819_
            914940922413753983971394019523433320408139928153188829495755455163_
            963417619308395977544797140231469234269034921938055593984
       ,

        3572594550275917221096588729615788272998517054675603239578198141006034_
         091735282826590621902304466963941971038923304526273329316373757450061_
         9789892286110976997087250466235373
      /
        1039548269345598936877071244834026055800814551120170592200522366591759_
         409659486442339141029452950265179989960104811875822530205346505131581_
         2439017247289173865014702966308864
       ]
     ,

        1715967
     [- -------,
        2097152

       -
           4213093533784303521084839517977082390377261503969586224828998436606_
            030656076359374564813773498376603121267822565801436206939519951465_
            18222580524697287410022543952491
         /
           9441814144185374458649692034349224052436597470966253663930641960795_
            805882585493199840191699917659443264824641135187383583888147867340_
            19307857605820364195856822304768
       ,

        7635833347112644222515625424410831225347475669008589338834162172501904_
         994376346730876809042845208919919925302105720971453918982731389072591_
         4035
      /
        2624188764086097199784297610478066633934230467895851602278580978503784_
         549205788499019640602266966026891580103543567625039018629887141284916_
         75648
       ]
     ,

         437701
     [- -------,
        2097152

        1683106908638349588322172332654225913562986313181951031452750161441497_
         473455328150721364868355579646781603507777199075077835213366484533654_
         91383623741304759
      /
        1683106868095213389001709982705913638963077668731226111167785188004907_
         425226298680325887810962614140298597366984264887998908377068799998454_
         23381649008099328
       ,

        4961550109835010186422681013422108735958714801003760639707968096646912_
         82670847283444311723917219104249213450966312411133
      /
        4961549872757738315509192078210209029852897118611097126236384040829376_
         59261914313170254867464792718363492160482442215424
       ]
     ,

       222801
     [-------,
      2097152

       -
           8994884880402428265107595121970691427136045692541978275573001865213_
            759921588137716696126349101655220195142994932299137183241705867672_
            383477
         /
           1167889998665026372177765100691888582708969960229934769690835752457_
            077779416435209473767866507769405888942764587718542434255625992456_
            372224
       ,

       -
           2389704888133156878320801544373808395612771509208491019847452991885_
            509546519525467839016613593999693886640036283570552321155037871291_
            458703265
         /
           5355487273645096326090403286689931905988225444685411433221593833681_
            192957562833671468654290340746993656285925599117602120446183443145_
            479421952
       ]
     ,

       765693
     [-------,
      2097152

        8558969219816716267873244761178198088724698958616670140213765754322002_
         303251685786118678330840203328837654339523418704917749518340772512899_
         000391009630373148561
      /
        2941442445533010790976428411376393499815580215945856917906452535495723_
         013856818941702330228779890141296236721138154231997238917322156711965_
         2444639331719460159488
       ,

       -
           2057618230582572101247650324860242561111302581543588808843923662767_
            549382241659362712290777612800192921420574408948085193743688582762_
            2246433251878894899015
         /
           2671598203325735538097952353501450220576313759890835097091722520642_
            710198771902667183948906289863714759678360292483949204616471537777_
            775324180661095366656
       ]
     ,

      5743879
     [-------,
      2097152

        1076288816968906847955546394773570208171456724942618614023663123574768_
         960850434263971398072546592772662158833449797698617455397887562900072_
         984768000608343553189801693408727205047612559889232757563830528688953_
         535421809482771058917542602890060941949620874083007858366669453501766_
         24841488732463225
      /
        3131768957080317946648461940023552044190376613458584986228549631916196_
         601616219781765615532532294746529648276430583810894079374566460757823_
         146888581195556029208515218838883200318658407469399426063260589828612_
         309231596669129707986481319851571942927230340622934023923486703042068_
         1530440845099008
       ,

       -
           2113286699185750918364120475565458437870172489865485994389828135335_
            264444665284557526492734931691731407872701432935503473348172076098_
            720545849008780077564160534317894688366119529739980502944162668550_
            098127961950496210221942878089359674925850594427768502251789758706_
            752831632503615
         /
           1627615584937987580242906624347104580889144466168459718043153839408_
            372525533309808070363699585502216011211087103263609551026027769414_
            087391148126221168139781682587438075322591466131939975457200522349_
            838568964285634448018562038272378787354460106106141518010935617205_
            1706396253618176
       ]
     ,

      19739877
     [--------,
       2097152

       -
           2997249936832703303799015804861520949215040387500707177701285766720_
            192530579422478953566024359860143101547801638082771611160372212874_
            847778035809872843149225484238365858013629341705321702582333350918_
            009601789937023985935304900460493389873837030853410347089908880814_
            853981132018464582458800615394770741699487295875960210750215891948_
            814476854871031530931295467332190133702671098200902282300510751860_
            7185928457030277807397796525813862762239286996106809728023675
         /
           2308433274852278590728910081191811023906504141321432646123936794873_
            933319270608960702138193417647898360620229519176632937631786851455_
            014766027206259022252505551741823688896883806636602574431760472240_
            292093196729475160247268834121141893318848728661844434927287285112_
            897080767552864895056585864033178565910387065006112801516403522741_
            037360990556054476949527059227070809593049491257519554708879259595_
            52929920110858560812556635485429471554031675979542656381353984
       ,

       -
           5128189263548228489096276397868940080600938410663080459407966335845_
            009264109490520459825316250084723010047035024497436523038925818959_
            289312931584701353927621435434398674263047293909122850133851990696_
            490231566094371994333795070782624011727587749989296611277318372294_
            624207116537910436554574146082884701305543912620419354885410735940_
            157775896602822364575864611831512943973974715166920465061850603762_
            87516256195847052412587282839139194642913955
         /
           2288281939778439330531208793181290471183631092455368990386390824243_
            509463644236249773080647438987739144921607794682653851741189091711_
            741868145114978337284191822497675868358729486644730856622552687209_
            203724411800481405702837198310642291275676195774614443815996713502_
            629391749783590041470860127752372996488627742672487622480063268808_
            889324891850842494934347337603075939980268208482904859678177751444_
            65749979827872616963053217673201717237252096
       ]
     ]
                                             Type: List List Fraction Integer
--R 
--R
--R   (13)
--R   [
--R        10048059
--R     [- --------,
--R         2097152
--R
--R        4503057316985387943524397913838966414596731976211768219335881208385516_
--R         314058924567176091423629695777403099833360761048898228916578137094309_
--R         838597331137202584846939132376157019506760357601165917454986815382098_
--R         789094851523420392811293126141329856546977145464661495487825919941188_
--R         447041722440491921567263542158028061437758844364634410045253024786561_
--R         923163288214175
--R      /
--R        4503057283025245488516511806985826635083100693757320465280554706865644_
--R         949577509916867201889438090408354817931718593862797624551518983570793_
--R         048774424291488708829840324189200301436123314860200821443733790755311_
--R         243632919864895421704228949571290016119498807957023663865443069392027_
--R         148979688266712323356043491523434068924275280417338574817381189277066_
--R         143312396681216
--R       ,
--R
--R        2106260768823475073894798680486016596249607148690685538763683715020639_
--R         680858649650790055889505646893309447097099937802187329095325898785247_
--R         249020717504983660482075156618738724514685333060011202964635166381351_
--R         543255982200250305283981086837110614842307026091211297929876896285681_
--R         830479054760056380762664905618462055306047816191782011588703789138988_
--R         1895
--R      /
--R        2106260609498464192472113804816474175341962953296434102413903142368757_
--R         967685273888585590975965211778862189872881953943640246297357061959812_
--R         326103659799025126863258676567202342106877031710184247484181423288921_
--R         837681237062708470295706218485928867400771937828499200923760593314168_
--R         901000666373896347598118228556731037072026474496776228383762993923280_
--R         0768
--R       ]
--R     ,
--R
--R        2563013
--R     [- -------,
--R        2097152
--R
--R       -
--R           2611346176791927789698617693237757719238259963063541781922752330440_
--R            189899668072928338490768623593207442125925986733815932243504809294_
--R            837523030237337236806668167446173001727271353311571242897
--R         /
--R           1165225400505222530583981916004589143757226610276858990008790134819_
--R            914940922413753983971394019523433320408139928153188829495755455163_
--R            963417619308395977544797140231469234269034921938055593984
--R       ,
--R
--R        3572594550275917221096588729615788272998517054675603239578198141006034_
--R         091735282826590621902304466963941971038923304526273329316373757450061_
--R         9789892286110976997087250466235373
--R      /
--R        1039548269345598936877071244834026055800814551120170592200522366591759_
--R         409659486442339141029452950265179989960104811875822530205346505131581_
--R         2439017247289173865014702966308864
--R       ]
--R     ,
--R
--R        1715967
--R     [- -------,
--R        2097152
--R
--R       -
--R           4213093533784303521084839517977082390377261503969586224828998436606_
--R            030656076359374564813773498376603121267822565801436206939519951465_
--R            18222580524697287410022543952491
--R         /
--R           9441814144185374458649692034349224052436597470966253663930641960795_
--R            805882585493199840191699917659443264824641135187383583888147867340_
--R            19307857605820364195856822304768
--R       ,
--R
--R        7635833347112644222515625424410831225347475669008589338834162172501904_
--R         994376346730876809042845208919919925302105720971453918982731389072591_
--R         4035
--R      /
--R        2624188764086097199784297610478066633934230467895851602278580978503784_
--R         549205788499019640602266966026891580103543567625039018629887141284916_
--R         75648
--R       ]
--R     ,
--R
--R         437701
--R     [- -------,
--R        2097152
--R
--R        1683106908638349588322172332654225913562986313181951031452750161441497_
--R         473455328150721364868355579646781603507777199075077835213366484533654_
--R         91383623741304759
--R      /
--R        1683106868095213389001709982705913638963077668731226111167785188004907_
--R         425226298680325887810962614140298597366984264887998908377068799998454_
--R         23381649008099328
--R       ,
--R
--R        4961550109835010186422681013422108735958714801003760639707968096646912_
--R         82670847283444311723917219104249213450966312411133
--R      /
--R        4961549872757738315509192078210209029852897118611097126236384040829376_
--R         59261914313170254867464792718363492160482442215424
--R       ]
--R     ,
--R
--R       222801
--R     [-------,
--R      2097152
--R
--R       -
--R           8994884880402428265107595121970691427136045692541978275573001865213_
--R            759921588137716696126349101655220195142994932299137183241705867672_
--R            383477
--R         /
--R           1167889998665026372177765100691888582708969960229934769690835752457_
--R            077779416435209473767866507769405888942764587718542434255625992456_
--R            372224
--R       ,
--R
--R       -
--R           2389704888133156878320801544373808395612771509208491019847452991885_
--R            509546519525467839016613593999693886640036283570552321155037871291_
--R            458703265
--R         /
--R           5355487273645096326090403286689931905988225444685411433221593833681_
--R            192957562833671468654290340746993656285925599117602120446183443145_
--R            479421952
--R       ]
--R     ,
--R
--R       765693
--R     [-------,
--R      2097152
--R
--R        8558969219816716267873244761178198088724698958616670140213765754322002_
--R         303251685786118678330840203328837654339523418704917749518340772512899_
--R         000391009630373148561
--R      /
--R        2941442445533010790976428411376393499815580215945856917906452535495723_
--R         013856818941702330228779890141296236721138154231997238917322156711965_
--R         2444639331719460159488
--R       ,
--R
--R       -
--R           2057618230582572101247650324860242561111302581543588808843923662767_
--R            549382241659362712290777612800192921420574408948085193743688582762_
--R            2246433251878894899015
--R         /
--R           2671598203325735538097952353501450220576313759890835097091722520642_
--R            710198771902667183948906289863714759678360292483949204616471537777_
--R            775324180661095366656
--R       ]
--R     ,
--R
--R      5743879
--R     [-------,
--R      2097152
--R
--R        1076288816968906847955546394773570208171456724942618614023663123574768_
--R         960850434263971398072546592772662158833449797698617455397887562900072_
--R         984768000608343553189801693408727205047612559889232757563830528688953_
--R         535421809482771058917542602890060941949620874083007858366669453501766_
--R         24841488732463225
--R      /
--R        3131768957080317946648461940023552044190376613458584986228549631916196_
--R         601616219781765615532532294746529648276430583810894079374566460757823_
--R         146888581195556029208515218838883200318658407469399426063260589828612_
--R         309231596669129707986481319851571942927230340622934023923486703042068_
--R         1530440845099008
--R       ,
--R
--R       -
--R           2113286699185750918364120475565458437870172489865485994389828135335_
--R            264444665284557526492734931691731407872701432935503473348172076098_
--R            720545849008780077564160534317894688366119529739980502944162668550_
--R            098127961950496210221942878089359674925850594427768502251789758706_
--R            752831632503615
--R         /
--R           1627615584937987580242906624347104580889144466168459718043153839408_
--R            372525533309808070363699585502216011211087103263609551026027769414_
--R            087391148126221168139781682587438075322591466131939975457200522349_
--R            838568964285634448018562038272378787354460106106141518010935617205_
--R            1706396253618176
--R       ]
--R     ,
--R
--R      19739877
--R     [--------,
--R       2097152
--R
--R       -
--R           2997249936832703303799015804861520949215040387500707177701285766720_
--R            192530579422478953566024359860143101547801638082771611160372212874_
--R            847778035809872843149225484238365858013629341705321702582333350918_
--R            009601789937023985935304900460493389873837030853410347089908880814_
--R            853981132018464582458800615394770741699487295875960210750215891948_
--R            814476854871031530931295467332190133702671098200902282300510751860_
--R            7185928457030277807397796525813862762239286996106809728023675
--R         /
--R           2308433274852278590728910081191811023906504141321432646123936794873_
--R            933319270608960702138193417647898360620229519176632937631786851455_
--R            014766027206259022252505551741823688896883806636602574431760472240_
--R            292093196729475160247268834121141893318848728661844434927287285112_
--R            897080767552864895056585864033178565910387065006112801516403522741_
--R            037360990556054476949527059227070809593049491257519554708879259595_
--R            52929920110858560812556635485429471554031675979542656381353984
--R       ,
--R
--R       -
--R           5128189263548228489096276397868940080600938410663080459407966335845_
--R            009264109490520459825316250084723010047035024497436523038925818959_
--R            289312931584701353927621435434398674263047293909122850133851990696_
--R            490231566094371994333795070782624011727587749989296611277318372294_
--R            624207116537910436554574146082884701305543912620419354885410735940_
--R            157775896602822364575864611831512943973974715166920465061850603762_
--R            87516256195847052412587282839139194642913955
--R         /
--R           2288281939778439330531208793181290471183631092455368990386390824243_
--R            509463644236249773080647438987739144921607794682653851741189091711_
--R            741868145114978337284191822497675868358729486644730856622552687209_
--R            203724411800481405702837198310642291275676195774614443815996713502_
--R            629391749783590041470860127752372996488627742672487622480063268808_
--R            889324891850842494934347337603075939980268208482904859678177751444_
--R            65749979827872616963053217673201717237252096
--R       ]
--R     ]
--R                                             Type: List List Fraction Integer
--E 13

--S 14 of 28
lpr := positiveSolve(lp)$pack
 

   (14)  []
                                 Type: List List RealClosure Fraction Integer
--R 
--R
--R   (14)  []
--R                                 Type: List List RealClosure Fraction Integer
--E 14

--S 15 of 28
f0 := x**3 + y + z + t- 1
 

                  3
   (15)  z + y + x  + t - 1
                                                     Type: Polynomial Integer
--R 
--R
--R                  3
--R   (15)  z + y + x  + t - 1
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 28
f1 := x + y**3 + z + t -1
 

              3
   (16)  z + y  + x + t - 1
                                                     Type: Polynomial Integer
--R 
--R
--R              3
--R   (16)  z + y  + x + t - 1
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 28
f2 := x + y + z**3 + t-1
 

          3
   (17)  z  + y + x + t - 1
                                                     Type: Polynomial Integer
--R 
--R
--R          3
--R   (17)  z  + y + x + t - 1
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 28
f3 := x + y + z + t**3 -1
 

                      3
   (18)  z + y + x + t  - 1
                                                     Type: Polynomial Integer
--R 
--R
--R                      3
--R   (18)  z + y + x + t  - 1
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 28
lf := [f0, f1, f2, f3]
 

   (19)
             3              3              3                              3
   [z + y + x  + t - 1,z + y  + x + t - 1,z  + y + x + t - 1,z + y + x + t  - 1]
                                                Type: List Polynomial Integer
--R 
--R
--R   (19)
--R             3              3              3                              3
--R   [z + y + x  + t - 1,z + y  + x + t - 1,z  + y + x + t - 1,z + y + x + t  - 1]
--R                                                Type: List Polynomial Integer
--E 19

--S 20 of 28
lts := triangSolve(lf)$pack
 

   (20)
   [
       2           3        3
     {t  + t + 1, z  - z - t  + t,

                 3      2      2      3           6     3            3      2
         (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
       + 
            6     3          9     6     3
         (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
       ,
      x + y + z}
     ,

       16     13     10     7      4      2
     {t   - 6t   + 9t   + 4t  + 15t  - 54t  + 27,

                     15            14             13            12            11
             4907232t   + 40893984t   - 115013088t   + 22805712t   + 36330336t
           + 
                       10             9             8             7
             162959040t   - 159859440t  - 156802608t  + 117168768t
           + 
                       6             5             4             3
             126282384t  - 129351600t  + 306646992t  + 475302816t
           + 
                          2
             - 1006837776t  - 237269088t + 480716208
        *
           z
       + 
            54       51        48      46         45        43          42
         48t   - 912t   + 8232t   - 72t   - 46848t   + 1152t   + 186324t
       + 
                40          39        38         37           36         35
         - 3780t   - 543144t   - 3168t   - 21384t   + 1175251t   + 41184t
       + 
                34           33          32           31           30
         278003t   - 1843242t   - 301815t   - 1440726t   + 1912012t
       + 
                 29           28          27           26            25
         1442826t   + 4696262t   - 922481t   - 4816188t   - 10583524t
       + 
                  24            23            22          21            20
         - 208751t   + 11472138t   + 16762859t   - 857663t   - 19328175t
       + 
                    19           18            17            16           15
         - 18270421t   + 4914903t   + 22483044t   + 12926517t   - 8605511t
       + 
                    14           13           12           11          10
         - 17455518t   - 5014597t   + 8108814t   + 8465535t   + 190542t
       + 
                   9           8          7           6          5          4
         - 4305624t  - 2226123t  + 661905t  + 1169775t  + 226260t  - 209952t
       + 
                  3
         - 141183t  + 27216t
       ,

                 3      2      2      3           6     3            3      2
         (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
       + 
            6     3          9     6     3
         (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
       ,
                   3
      x + y + z + t  - 1}
     ,
              2                       2                     2
    {t,z - 1,y  - 1,x + y}, {t - 1,z,y  - 1,x + y}, {t - 1,z  - 1,z y + 1,x},

       16     13     10     7      4      2
     {t   - 6t   + 9t   + 4t  + 15t  - 54t  + 27,

                     29            28             27           26             25
             4907232t   + 40893984t   - 115013088t   - 1730448t   - 168139584t
           + 
                       24             23             22              21
             738024480t   - 195372288t   + 315849456t   - 2567279232t
           + 
                       20              19              18              17
             937147968t   + 1026357696t   + 4780488240t   - 2893767696t
           + 
                          16              15              14              13
             - 5617160352t   - 3427651728t   + 5001100848t   + 8720098416t
           + 
                        12             11               10              9
             2331732960t   - 499046544t   - 16243306272t   - 9748123200t
           + 
                        8               7               6               5
             3927244320t  + 25257280896t  + 10348032096t  - 17128672128t
           + 
                           4             3               2
             - 14755488768t  + 544086720t  + 10848188736t  + 1423614528t
           + 
             - 2884297248
        *
           z
       + 
              68        65         62       60          59        57          56
         - 48t   + 1152t   - 13560t   + 360t   + 103656t   - 7560t   - 572820t
       + 
               54           53        52          51           50         49
         71316t   + 2414556t   + 2736t   - 402876t   - 7985131t   - 49248t
       + 
                 48            47          46           45            44
         1431133t   + 20977409t   + 521487t   - 2697635t   - 43763654t
       + 
                   43           42            41            40            39
         - 3756573t   - 2093410t   + 71546495t   + 19699032t   + 35025028t
       + 
                    38            37             36            35             34
         - 89623786t   - 77798760t   - 138654191t   + 87596128t   + 235642497t
       + 
                   33            32             31             30             29
         349607642t   - 93299834t   - 551563167t   - 630995176t   + 186818962t
       + 
                   28             27             26              25
         995427468t   + 828416204t   - 393919231t   - 1076617485t
       + 
                      24             23              22              21
         - 1609479791t   + 595738126t   + 1198787136t   + 4342832069t
       + 
                      20              19              18              17
         - 2075938757t   - 4390835799t   - 4822843033t   + 6932747678t
       + 
                    16              15              14              13
         6172196808t   + 1141517740t   - 4981677585t   - 9819815280t
       + 
                      12             11               10               9
         - 7404299976t   - 157295760t   + 29124027630t   + 14856038208t
       + 
                       8               7              6               5
         - 16184101410t  - 26935440354t  - 3574164258t  + 10271338974t
       + 
                     4              3              2
         11191425264t  + 6869861262t  - 9780477840t  - 3586674168t + 2884297248
       ,

            3      3      2      6      3           9     6    3
         (3z  + (6t  - 6)z  + (6t  - 12t  + 3)z + 2t  - 6t  + t  + 3t)y
       + 
            3      3      6      3      2      9      6      3          12     9
         (3t  - 3)z  + (6t  - 12t  + 6)z  + (4t  - 12t  + 11t  - 3)z + t   - 4t
       + 
           6     3
         5t  - 2t
       ,
                   3
      x + y + z + t  - 1}
     ,
            2
    {t - 1,z  - 1,y,x + z},

       8    7    6     5     4     3      2
     {t  + t  + t  - 2t  - 2t  - 2t  + 19t  + 19t - 8,

                     7           6           5            4           3
             2395770t  + 3934440t  - 3902067t  - 10084164t  - 1010448t
           + 
                      2
             32386932t  + 22413225t - 10432368
        *
           z
       + 
                  7           6           5           4            3
         - 463519t  + 3586833t  + 9494955t  - 8539305t  - 33283098t
       + 
                  2
         35479377t  + 46263256t - 17419896
       ,

               4      3      3       6      3      2          3
             3z  + (9t  - 9)z  + (12t  - 24t  + 9)z  + (- 152t  + 219t - 67)z
           + 
                  6      4      3
             - 41t  + 57t  + 25t  - 57t + 16
        *
           y
       + 
            3      4      6      3      3          3              2
         (3t  - 3)z  + (9t  - 18t  + 9)z  + (- 181t  + 270t - 89)z
       + 
               6       4      3                    7      6      4       3
         (- 92t  + 135t  + 49t  - 135t + 43)z + 27t  - 27t  - 54t  + 396t
       + 
         - 486t + 144
       ,
                   3
      x + y + z + t  - 1}
     ,
            3
    {t,z - t  + 1,y - 1,x - 1}, {t - 1,z,y,x}, {t,z - 1,y,x}, {t,z,y - 1,x},
    {t,z,y,x - 1}]
                                   Type: List RegularChain(Integer,[x,y,z,t])
--R 
--R
--R   (20)
--R   [
--R       2           3        3
--R     {t  + t + 1, z  - z - t  + t,
--R
--R                 3      2      2      3           6     3            3      2
--R         (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
--R       + 
--R            6     3          9     6     3
--R         (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
--R       ,
--R      x + y + z}
--R     ,
--R
--R       16     13     10     7      4      2
--R     {t   - 6t   + 9t   + 4t  + 15t  - 54t  + 27,
--R
--R                     15            14             13            12            11
--R             4907232t   + 40893984t   - 115013088t   + 22805712t   + 36330336t
--R           + 
--R                       10             9             8             7
--R             162959040t   - 159859440t  - 156802608t  + 117168768t
--R           + 
--R                       6             5             4             3
--R             126282384t  - 129351600t  + 306646992t  + 475302816t
--R           + 
--R                          2
--R             - 1006837776t  - 237269088t + 480716208
--R        *
--R           z
--R       + 
--R            54       51        48      46         45        43          42
--R         48t   - 912t   + 8232t   - 72t   - 46848t   + 1152t   + 186324t
--R       + 
--R                40          39        38         37           36         35
--R         - 3780t   - 543144t   - 3168t   - 21384t   + 1175251t   + 41184t
--R       + 
--R                34           33          32           31           30
--R         278003t   - 1843242t   - 301815t   - 1440726t   + 1912012t
--R       + 
--R                 29           28          27           26            25
--R         1442826t   + 4696262t   - 922481t   - 4816188t   - 10583524t
--R       + 
--R                  24            23            22          21            20
--R         - 208751t   + 11472138t   + 16762859t   - 857663t   - 19328175t
--R       + 
--R                    19           18            17            16           15
--R         - 18270421t   + 4914903t   + 22483044t   + 12926517t   - 8605511t
--R       + 
--R                    14           13           12           11          10
--R         - 17455518t   - 5014597t   + 8108814t   + 8465535t   + 190542t
--R       + 
--R                   9           8          7           6          5          4
--R         - 4305624t  - 2226123t  + 661905t  + 1169775t  + 226260t  - 209952t
--R       + 
--R                  3
--R         - 141183t  + 27216t
--R       ,
--R
--R                 3      2      2      3           6     3            3      2
--R         (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
--R       + 
--R            6     3          9     6     3
--R         (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
--R       ,
--R                   3
--R      x + y + z + t  - 1}
--R     ,
--R              2                       2                     2
--R    {t,z - 1,y  - 1,x + y}, {t - 1,z,y  - 1,x + y}, {t - 1,z  - 1,z y + 1,x},
--R
--R       16     13     10     7      4      2
--R     {t   - 6t   + 9t   + 4t  + 15t  - 54t  + 27,
--R
--R                     29            28             27           26             25
--R             4907232t   + 40893984t   - 115013088t   - 1730448t   - 168139584t
--R           + 
--R                       24             23             22              21
--R             738024480t   - 195372288t   + 315849456t   - 2567279232t
--R           + 
--R                       20              19              18              17
--R             937147968t   + 1026357696t   + 4780488240t   - 2893767696t
--R           + 
--R                          16              15              14              13
--R             - 5617160352t   - 3427651728t   + 5001100848t   + 8720098416t
--R           + 
--R                        12             11               10              9
--R             2331732960t   - 499046544t   - 16243306272t   - 9748123200t
--R           + 
--R                        8               7               6               5
--R             3927244320t  + 25257280896t  + 10348032096t  - 17128672128t
--R           + 
--R                           4             3               2
--R             - 14755488768t  + 544086720t  + 10848188736t  + 1423614528t
--R           + 
--R             - 2884297248
--R        *
--R           z
--R       + 
--R              68        65         62       60          59        57          56
--R         - 48t   + 1152t   - 13560t   + 360t   + 103656t   - 7560t   - 572820t
--R       + 
--R               54           53        52          51           50         49
--R         71316t   + 2414556t   + 2736t   - 402876t   - 7985131t   - 49248t
--R       + 
--R                 48            47          46           45            44
--R         1431133t   + 20977409t   + 521487t   - 2697635t   - 43763654t
--R       + 
--R                   43           42            41            40            39
--R         - 3756573t   - 2093410t   + 71546495t   + 19699032t   + 35025028t
--R       + 
--R                    38            37             36            35             34
--R         - 89623786t   - 77798760t   - 138654191t   + 87596128t   + 235642497t
--R       + 
--R                   33            32             31             30             29
--R         349607642t   - 93299834t   - 551563167t   - 630995176t   + 186818962t
--R       + 
--R                   28             27             26              25
--R         995427468t   + 828416204t   - 393919231t   - 1076617485t
--R       + 
--R                      24             23              22              21
--R         - 1609479791t   + 595738126t   + 1198787136t   + 4342832069t
--R       + 
--R                      20              19              18              17
--R         - 2075938757t   - 4390835799t   - 4822843033t   + 6932747678t
--R       + 
--R                    16              15              14              13
--R         6172196808t   + 1141517740t   - 4981677585t   - 9819815280t
--R       + 
--R                      12             11               10               9
--R         - 7404299976t   - 157295760t   + 29124027630t   + 14856038208t
--R       + 
--R                       8               7              6               5
--R         - 16184101410t  - 26935440354t  - 3574164258t  + 10271338974t
--R       + 
--R                     4              3              2
--R         11191425264t  + 6869861262t  - 9780477840t  - 3586674168t + 2884297248
--R       ,
--R
--R            3      3      2      6      3           9     6    3
--R         (3z  + (6t  - 6)z  + (6t  - 12t  + 3)z + 2t  - 6t  + t  + 3t)y
--R       + 
--R            3      3      6      3      2      9      6      3          12     9
--R         (3t  - 3)z  + (6t  - 12t  + 6)z  + (4t  - 12t  + 11t  - 3)z + t   - 4t
--R       + 
--R           6     3
--R         5t  - 2t
--R       ,
--R                   3
--R      x + y + z + t  - 1}
--R     ,
--R            2
--R    {t - 1,z  - 1,y,x + z},
--R
--R       8    7    6     5     4     3      2
--R     {t  + t  + t  - 2t  - 2t  - 2t  + 19t  + 19t - 8,
--R
--R                     7           6           5            4           3
--R             2395770t  + 3934440t  - 3902067t  - 10084164t  - 1010448t
--R           + 
--R                      2
--R             32386932t  + 22413225t - 10432368
--R        *
--R           z
--R       + 
--R                  7           6           5           4            3
--R         - 463519t  + 3586833t  + 9494955t  - 8539305t  - 33283098t
--R       + 
--R                  2
--R         35479377t  + 46263256t - 17419896
--R       ,
--R
--R               4      3      3       6      3      2          3
--R             3z  + (9t  - 9)z  + (12t  - 24t  + 9)z  + (- 152t  + 219t - 67)z
--R           + 
--R                  6      4      3
--R             - 41t  + 57t  + 25t  - 57t + 16
--R        *
--R           y
--R       + 
--R            3      4      6      3      3          3              2
--R         (3t  - 3)z  + (9t  - 18t  + 9)z  + (- 181t  + 270t - 89)z
--R       + 
--R               6       4      3                    7      6      4       3
--R         (- 92t  + 135t  + 49t  - 135t + 43)z + 27t  - 27t  - 54t  + 396t
--R       + 
--R         - 486t + 144
--R       ,
--R                   3
--R      x + y + z + t  - 1}
--R     ,
--R            3
--R    {t,z - t  + 1,y - 1,x - 1}, {t - 1,z,y,x}, {t,z - 1,y,x}, {t,z,y - 1,x},
--R    {t,z,y,x - 1}]
--R                                   Type: List RegularChain(Integer,[x,y,z,t])
--E 20

--S 21 of 28
univariateSolve(lf)$pack
 

   (21)
   [[complexRoots= ?,coordinates= [x - 1,y - 1,z + 1,t - %A]],
    [complexRoots= ?,coordinates= [x,y - 1,z,t - %A]],
    [complexRoots= ? - 1,coordinates= [x,y,z,t - %A]],
    [complexRoots= ?,coordinates= [x - 1,y,z,t - %A]],
    [complexRoots= ?,coordinates= [x,y,z - 1,t - %A]],
    [complexRoots= ? - 2,coordinates= [x - 1,y + 1,z,t - 1]],
    [complexRoots= ?,coordinates= [x + 1,y - 1,z,t - 1]],
    [complexRoots= ? - 1,coordinates= [x - 1,y + 1,z - 1,t]],
    [complexRoots= ? + 1,coordinates= [x + 1,y - 1,z - 1,t]],

                     6     3     2
     [complexRoots= ?  - 2?  + 3?  - 3,
                           3                 3
      coordinates= [2x + %A  + %A - 1,2y + %A  + %A - 1,z - %A,t - %A]]
     ,

                     5     3     2
     [complexRoots= ?  + 3?  - 2?  + 3? - 3,
                                        3
      coordinates= [x - %A,y - %A,z + %A  + 2%A - 1,t - %A]]
     ,

                     4    3     2
     [complexRoots= ?  - ?  - 2?  + 3,
                          3                3                3
      coordinates= [x + %A  - %A - 1,y + %A  - %A - 1,z - %A  + 2%A + 1,t - %A]]
     ,
    [complexRoots= ? + 1,coordinates= [x - 1,y - 1,z,t - %A]],

                     6     3     2
     [complexRoots= ?  + 2?  + 3?  - 3,
                           3                        3
      coordinates= [2x - %A  - %A - 1,y + %A,2z - %A  - %A - 1,t + %A]]
     ,

                     6      4      3      2
     [complexRoots= ?  + 12?  + 20?  - 45?  - 42? - 953,

       coordinates =
                       5       4       3        2
         [12609x + 23%A  + 49%A  - 46%A  + 362%A  - 5015%A - 8239,
                       5       4       3        2
          25218y + 23%A  + 49%A  - 46%A  + 362%A  + 7594%A - 8239,
                       5       4       3        2
          25218z + 23%A  + 49%A  - 46%A  + 362%A  + 7594%A - 8239,
                       5       4       3        2
          12609t + 23%A  + 49%A  - 46%A  + 362%A  - 5015%A - 8239]
       ]
     ,

                     5      3      2
     [complexRoots= ?  + 12?  - 16?  + 48? - 96,
                           3
      coordinates= [8x + %A  + 8%A - 8,2y - %A,2z - %A,2t - %A]]
     ,

                     5    4     3     2
     [complexRoots= ?  + ?  - 5?  - 3?  + 9? + 3,

       coordinates =
                 3                   3                   3
         [2x - %A  + 2%A - 1, 2y + %A  - 4%A + 1, 2z - %A  + 2%A - 1,
                 3
          2t - %A  + 2%A - 1]
       ]
     ,

                     4     3     2
     [complexRoots= ?  - 3?  + 4?  - 6? + 13,

       coordinates =
                  3      2                  3      2
         [9x - 2%A  + 4%A  - %A + 2, 9y + %A  - 2%A  + 5%A - 1,
                 3      2                   3      2
          9z + %A  - 2%A  + 5%A - 1, 9t + %A  - 2%A  - 4%A - 1]
       ]
     ,

                     4      2
     [complexRoots= ?  - 11?  + 37,

       coordinates =
                 2            2                  2            2
         [3x - %A  + 7,6y + %A  + 3%A - 7,3z - %A  + 7,6t + %A  - 3%A - 7]
       ]
     ,
    [complexRoots= ? + 1,coordinates= [x - 1,y,z - 1,t + 1]],
    [complexRoots= ? + 2,coordinates= [x,y - 1,z - 1,t + 1]],
    [complexRoots= ? - 2,coordinates= [x,y - 1,z + 1,t - 1]],
    [complexRoots= ?,coordinates= [x,y + 1,z - 1,t - 1]],
    [complexRoots= ? - 2,coordinates= [x - 1,y,z + 1,t - 1]],
    [complexRoots= ?,coordinates= [x + 1,y,z - 1,t - 1]],

                     4     3      2
     [complexRoots= ?  + 5?  + 16?  + 30? + 57,

       coordinates =
                     3       2                          3       2
         [151x + 15%A  + 54%A  + 104%A + 93, 151y - 10%A  - 36%A  - 19%A - 62,
                    3       2                        3       2
          151z - 5%A  - 18%A  - 85%A - 31, 151t - 5%A  - 18%A  - 85%A - 31]
       ]
     ,

                     4    3     2
     [complexRoots= ?  - ?  - 2?  + 3,
                          3                 3                       3
      coordinates= [x - %A  + 2%A + 1,y + %A  - %A - 1,z - %A,t + %A  - %A - 1]]
     ,

                     4     3     2
     [complexRoots= ?  + 2?  - 8?  + 48,

       coordinates =
                 3                          3                  3
         [8x - %A  + 4%A - 8,2y + %A,8z + %A  - 8%A + 8,8t - %A  + 4%A - 8]
       ]
     ,

                     5    4     3     2
     [complexRoots= ?  + ?  - 2?  - 4?  + 5? + 8,
                           3            3            3
      coordinates= [3x + %A  - 1,3y + %A  - 1,3z + %A  - 1,t - %A]]
     ,
                    3
    [complexRoots= ?  + 3? - 1,coordinates= [x - %A,y - %A,z - %A,t - %A]]]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--R 
--R
--R   (21)
--R   [[complexRoots= ?,coordinates= [x - 1,y - 1,z + 1,t - %A]],
--R    [complexRoots= ?,coordinates= [x,y - 1,z,t - %A]],
--R    [complexRoots= ? - 1,coordinates= [x,y,z,t - %A]],
--R    [complexRoots= ?,coordinates= [x - 1,y,z,t - %A]],
--R    [complexRoots= ?,coordinates= [x,y,z - 1,t - %A]],
--R    [complexRoots= ? - 2,coordinates= [x - 1,y + 1,z,t - 1]],
--R    [complexRoots= ?,coordinates= [x + 1,y - 1,z,t - 1]],
--R    [complexRoots= ? - 1,coordinates= [x - 1,y + 1,z - 1,t]],
--R    [complexRoots= ? + 1,coordinates= [x + 1,y - 1,z - 1,t]],
--R
--R                     6     3     2
--R     [complexRoots= ?  - 2?  + 3?  - 3,
--R                           3                 3
--R      coordinates= [2x + %A  + %A - 1,2y + %A  + %A - 1,z - %A,t - %A]]
--R     ,
--R
--R                     5     3     2
--R     [complexRoots= ?  + 3?  - 2?  + 3? - 3,
--R                                        3
--R      coordinates= [x - %A,y - %A,z + %A  + 2%A - 1,t - %A]]
--R     ,
--R
--R                     4    3     2
--R     [complexRoots= ?  - ?  - 2?  + 3,
--R                          3                3                3
--R      coordinates= [x + %A  - %A - 1,y + %A  - %A - 1,z - %A  + 2%A + 1,t - %A]]
--R     ,
--R    [complexRoots= ? + 1,coordinates= [x - 1,y - 1,z,t - %A]],
--R
--R                     6     3     2
--R     [complexRoots= ?  + 2?  + 3?  - 3,
--R                           3                        3
--R      coordinates= [2x - %A  - %A - 1,y + %A,2z - %A  - %A - 1,t + %A]]
--R     ,
--R
--R                     6      4      3      2
--R     [complexRoots= ?  + 12?  + 20?  - 45?  - 42? - 953,
--R
--R       coordinates =
--R                       5       4       3        2
--R         [12609x + 23%A  + 49%A  - 46%A  + 362%A  - 5015%A - 8239,
--R                       5       4       3        2
--R          25218y + 23%A  + 49%A  - 46%A  + 362%A  + 7594%A - 8239,
--R                       5       4       3        2
--R          25218z + 23%A  + 49%A  - 46%A  + 362%A  + 7594%A - 8239,
--R                       5       4       3        2
--R          12609t + 23%A  + 49%A  - 46%A  + 362%A  - 5015%A - 8239]
--R       ]
--R     ,
--R
--R                     5      3      2
--R     [complexRoots= ?  + 12?  - 16?  + 48? - 96,
--R                           3
--R      coordinates= [8x + %A  + 8%A - 8,2y - %A,2z - %A,2t - %A]]
--R     ,
--R
--R                     5    4     3     2
--R     [complexRoots= ?  + ?  - 5?  - 3?  + 9? + 3,
--R
--R       coordinates =
--R                 3                   3                   3
--R         [2x - %A  + 2%A - 1, 2y + %A  - 4%A + 1, 2z - %A  + 2%A - 1,
--R                 3
--R          2t - %A  + 2%A - 1]
--R       ]
--R     ,
--R
--R                     4     3     2
--R     [complexRoots= ?  - 3?  + 4?  - 6? + 13,
--R
--R       coordinates =
--R                  3      2                  3      2
--R         [9x - 2%A  + 4%A  - %A + 2, 9y + %A  - 2%A  + 5%A - 1,
--R                 3      2                   3      2
--R          9z + %A  - 2%A  + 5%A - 1, 9t + %A  - 2%A  - 4%A - 1]
--R       ]
--R     ,
--R
--R                     4      2
--R     [complexRoots= ?  - 11?  + 37,
--R
--R       coordinates =
--R                 2            2                  2            2
--R         [3x - %A  + 7,6y + %A  + 3%A - 7,3z - %A  + 7,6t + %A  - 3%A - 7]
--R       ]
--R     ,
--R    [complexRoots= ? + 1,coordinates= [x - 1,y,z - 1,t + 1]],
--R    [complexRoots= ? + 2,coordinates= [x,y - 1,z - 1,t + 1]],
--R    [complexRoots= ? - 2,coordinates= [x,y - 1,z + 1,t - 1]],
--R    [complexRoots= ?,coordinates= [x,y + 1,z - 1,t - 1]],
--R    [complexRoots= ? - 2,coordinates= [x - 1,y,z + 1,t - 1]],
--R    [complexRoots= ?,coordinates= [x + 1,y,z - 1,t - 1]],
--R
--R                     4     3      2
--R     [complexRoots= ?  + 5?  + 16?  + 30? + 57,
--R
--R       coordinates =
--R                     3       2                          3       2
--R         [151x + 15%A  + 54%A  + 104%A + 93, 151y - 10%A  - 36%A  - 19%A - 62,
--R                    3       2                        3       2
--R          151z - 5%A  - 18%A  - 85%A - 31, 151t - 5%A  - 18%A  - 85%A - 31]
--R       ]
--R     ,
--R
--R                     4    3     2
--R     [complexRoots= ?  - ?  - 2?  + 3,
--R                          3                 3                       3
--R      coordinates= [x - %A  + 2%A + 1,y + %A  - %A - 1,z - %A,t + %A  - %A - 1]]
--R     ,
--R
--R                     4     3     2
--R     [complexRoots= ?  + 2?  - 8?  + 48,
--R
--R       coordinates =
--R                 3                          3                  3
--R         [8x - %A  + 4%A - 8,2y + %A,8z + %A  - 8%A + 8,8t - %A  + 4%A - 8]
--R       ]
--R     ,
--R
--R                     5    4     3     2
--R     [complexRoots= ?  + ?  - 2?  - 4?  + 5? + 8,
--R                           3            3            3
--R      coordinates= [3x + %A  - 1,3y + %A  - 1,3z + %A  - 1,t - %A]]
--R     ,
--R                    3
--R    [complexRoots= ?  + 3? - 1,coordinates= [x - %A,y - %A,z - %A,t - %A]]]
--RType: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--E 21

--S 22 of 28
ts := lts.1
 

   (22)
     2           3        3
   {t  + t + 1, z  - z - t  + t,

               3      2      2      3           6     3            3      2
       (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
     + 
          6     3          9     6     3
       (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
     ,
    x + y + z}
                                        Type: RegularChain(Integer,[x,y,z,t])
--R 
--R
--R   (22)
--R     2           3        3
--R   {t  + t + 1, z  - z - t  + t,
--R
--R               3      2      2      3           6     3            3      2
--R       (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
--R     + 
--R          6     3          9     6     3
--R       (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
--R     ,
--R    x + y + z}
--R                                        Type: RegularChain(Integer,[x,y,z,t])
--E 22

univariateSolve(ts)$pack
 

   (23)
   [
                     4     3      2
     [complexRoots= ?  + 5?  + 16?  + 30? + 57,

       coordinates =
                     3       2                          3       2
         [151x + 15%A  + 54%A  + 104%A + 93, 151y - 10%A  - 36%A  - 19%A - 62,
                    3       2                        3       2
          151z - 5%A  - 18%A  - 85%A - 31, 151t - 5%A  - 18%A  - 85%A - 31]
       ]
     ,

                     4    3     2
     [complexRoots= ?  - ?  - 2?  + 3,
                          3                 3                       3
      coordinates= [x - %A  + 2%A + 1,y + %A  - %A - 1,z - %A,t + %A  - %A - 1]]
     ,

                     4     3     2
     [complexRoots= ?  + 2?  - 8?  + 48,

       coordinates =
                 3                          3                  3
         [8x - %A  + 4%A - 8,2y + %A,8z + %A  - 8%A + 8,8t - %A  + 4%A - 8]
       ]
     ]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--S 23 of 28
--R 
--R
--R   (23)
--R   [
--R                     4     3      2
--R     [complexRoots= ?  + 5?  + 16?  + 30? + 57,
--R
--R       coordinates =
--R                     3       2                          3       2
--R         [151x + 15%A  + 54%A  + 104%A + 93, 151y - 10%A  - 36%A  - 19%A - 62,
--R                    3       2                        3       2
--R          151z - 5%A  - 18%A  - 85%A - 31, 151t - 5%A  - 18%A  - 85%A - 31]
--R       ]
--R     ,
--R
--R                     4    3     2
--R     [complexRoots= ?  - ?  - 2?  + 3,
--R                          3                 3                       3
--R      coordinates= [x - %A  + 2%A + 1,y + %A  - %A - 1,z - %A,t + %A  - %A - 1]]
--R     ,
--R
--R                     4     3     2
--R     [complexRoots= ?  + 2?  - 8?  + 48,
--R
--R       coordinates =
--R                 3                          3                  3
--R         [8x - %A  + 4%A - 8,2y + %A,8z + %A  - 8%A + 8,8t - %A  + 4%A - 8]
--R       ]
--R     ]
--RType: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--E 23

--S 24 of 28
realSolve(ts)$pack
 

   (24)  []
                                 Type: List List RealClosure Fraction Integer
--R 
--R
--R   (24)  []
--R                                 Type: List List RealClosure Fraction Integer
--E 24

--S 25 of 28
lr2 := realSolve(lf)$pack
 

   (25)
   [[0,- 1,1,1], [0,0,1,0], [1,0,0,0], [0,0,0,1], [0,1,0,0], [1,0,%B37,- %B37],
    [1,0,%B38,- %B38], [0,1,%B35,- %B35], [0,1,%B36,- %B36], [- 1,0,1,1],

     [%B32,

          1     15    2     14    1     13    4     12   11     11    4     10
         -- %B32   + -- %B32   + -- %B32   - -- %B32   - -- %B32   - -- %B32
         27          27          27          27          27          27
       + 
          1     9   14     8    1     7   2     6   1     5   2     4       3
         -- %B32  + -- %B32  + -- %B32  + - %B32  + - %B32  + - %B32  + %B32
         27         27         27         9         3         9
       + 
         4     2
         - %B32  - %B32 - 2
         3
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B32   - -- %B32   - -- %B32   + -- %B32   + -- %B32   + -- %B32
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B32  - -- %B32  - -- %B32  - - %B32  - - %B32  - - %B32  - %B32
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B32  + - %B32 + -
           3         2        2
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B32   - -- %B32   - -- %B32   + -- %B32   + -- %B32   + -- %B32
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B32  - -- %B32  - -- %B32  - - %B32  - - %B32  - - %B32  - %B32
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B32  + - %B32 + -
           3         2        2
       ]
     ,

     [%B33,

          1     15    2     14    1     13    4     12   11     11    4     10
         -- %B33   + -- %B33   + -- %B33   - -- %B33   - -- %B33   - -- %B33
         27          27          27          27          27          27
       + 
          1     9   14     8    1     7   2     6   1     5   2     4       3
         -- %B33  + -- %B33  + -- %B33  + - %B33  + - %B33  + - %B33  + %B33
         27         27         27         9         3         9
       + 
         4     2
         - %B33  - %B33 - 2
         3
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B33   - -- %B33   - -- %B33   + -- %B33   + -- %B33   + -- %B33
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B33  - -- %B33  - -- %B33  - - %B33  - - %B33  - - %B33  - %B33
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B33  + - %B33 + -
           3         2        2
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B33   - -- %B33   - -- %B33   + -- %B33   + -- %B33   + -- %B33
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B33  - -- %B33  - -- %B33  - - %B33  - - %B33  - - %B33  - %B33
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B33  + - %B33 + -
           3         2        2
       ]
     ,

     [%B34,

          1     15    2     14    1     13    4     12   11     11    4     10
         -- %B34   + -- %B34   + -- %B34   - -- %B34   - -- %B34   - -- %B34
         27          27          27          27          27          27
       + 
          1     9   14     8    1     7   2     6   1     5   2     4       3
         -- %B34  + -- %B34  + -- %B34  + - %B34  + - %B34  + - %B34  + %B34
         27         27         27         9         3         9
       + 
         4     2
         - %B34  - %B34 - 2
         3
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B34   - -- %B34   - -- %B34   + -- %B34   + -- %B34   + -- %B34
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B34  - -- %B34  - -- %B34  - - %B34  - - %B34  - - %B34  - %B34
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B34  + - %B34 + -
           3         2        2
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B34   - -- %B34   - -- %B34   + -- %B34   + -- %B34   + -- %B34
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B34  - -- %B34  - -- %B34  - - %B34  - - %B34  - - %B34  - %B34
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B34  + - %B34 + -
           3         2        2
       ]
     ,
    [- 1,1,0,1], [- 1,1,1,0],

     [%B23,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B23   - -- %B23   - -- %B23   + -- %B23   + -- %B23   + -- %B23
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B23  - -- %B23  - -- %B23  - - %B23  - - %B23  - - %B23  - %B23
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B23  + - %B23 + -
           3         2        2
       ,
      %B30,

                   1     15    1     14    1     13    2     12   11     11
         - %B30 + -- %B23   + -- %B23   + -- %B23   - -- %B23   - -- %B23
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B23   + -- %B23  + -- %B23  + -- %B23  + - %B23  + - %B23
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B23  + - %B23  - - %B23 - -
         9         3         2        2
       ]
     ,

     [%B23,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B23   - -- %B23   - -- %B23   + -- %B23   + -- %B23   + -- %B23
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B23  - -- %B23  - -- %B23  - - %B23  - - %B23  - - %B23  - %B23
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B23  + - %B23 + -
           3         2        2
       ,
      %B31,

                   1     15    1     14    1     13    2     12   11     11
         - %B31 + -- %B23   + -- %B23   + -- %B23   - -- %B23   - -- %B23
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B23   + -- %B23  + -- %B23  + -- %B23  + - %B23  + - %B23
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B23  + - %B23  - - %B23 - -
         9         3         2        2
       ]
     ,

     [%B24,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B24   - -- %B24   - -- %B24   + -- %B24   + -- %B24   + -- %B24
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B24  - -- %B24  - -- %B24  - - %B24  - - %B24  - - %B24  - %B24
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B24  + - %B24 + -
           3         2        2
       ,
      %B28,

                   1     15    1     14    1     13    2     12   11     11
         - %B28 + -- %B24   + -- %B24   + -- %B24   - -- %B24   - -- %B24
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B24   + -- %B24  + -- %B24  + -- %B24  + - %B24  + - %B24
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B24  + - %B24  - - %B24 - -
         9         3         2        2
       ]
     ,

     [%B24,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B24   - -- %B24   - -- %B24   + -- %B24   + -- %B24   + -- %B24
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B24  - -- %B24  - -- %B24  - - %B24  - - %B24  - - %B24  - %B24
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B24  + - %B24 + -
           3         2        2
       ,
      %B29,

                   1     15    1     14    1     13    2     12   11     11
         - %B29 + -- %B24   + -- %B24   + -- %B24   - -- %B24   - -- %B24
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B24   + -- %B24  + -- %B24  + -- %B24  + - %B24  + - %B24
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B24  + - %B24  - - %B24 - -
         9         3         2        2
       ]
     ,

     [%B25,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B25   - -- %B25   - -- %B25   + -- %B25   + -- %B25   + -- %B25
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B25  - -- %B25  - -- %B25  - - %B25  - - %B25  - - %B25  - %B25
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B25  + - %B25 + -
           3         2        2
       ,
      %B26,

                   1     15    1     14    1     13    2     12   11     11
         - %B26 + -- %B25   + -- %B25   + -- %B25   - -- %B25   - -- %B25
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B25   + -- %B25  + -- %B25  + -- %B25  + - %B25  + - %B25
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B25  + - %B25  - - %B25 - -
         9         3         2        2
       ]
     ,

     [%B25,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B25   - -- %B25   - -- %B25   + -- %B25   + -- %B25   + -- %B25
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B25  - -- %B25  - -- %B25  - - %B25  - - %B25  - - %B25  - %B25
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B25  + - %B25 + -
           3         2        2
       ,
      %B27,

                   1     15    1     14    1     13    2     12   11     11
         - %B27 + -- %B25   + -- %B25   + -- %B25   - -- %B25   - -- %B25
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B25   + -- %B25  + -- %B25  + -- %B25  + - %B25  + - %B25
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B25  + - %B25  - - %B25 - -
         9         3         2        2
       ]
     ,
    [1,%B21,- %B21,0], [1,%B22,- %B22,0], [1,%B19,0,- %B19], [1,%B20,0,- %B20],
            1     3   1   1     3   1   1     3   1
    [%B17,- - %B17  + -,- - %B17  + -,- - %B17  + -],
            3         3   3         3   3         3
            1     3   1   1     3   1   1     3   1
    [%B18,- - %B18  + -,- - %B18  + -,- - %B18  + -]]
            3         3   3         3   3         3
                                 Type: List List RealClosure Fraction Integer
--R 
--R
--R   (25)
--R   [[0,- 1,1,1], [0,0,1,0], [1,0,0,0], [0,0,0,1], [0,1,0,0], [1,0,%B37,- %B37],
--R    [1,0,%B38,- %B38], [0,1,%B35,- %B35], [0,1,%B36,- %B36], [- 1,0,1,1],
--R
--R     [%B32,
--R
--R          1     15    2     14    1     13    4     12   11     11    4     10
--R         -- %B32   + -- %B32   + -- %B32   - -- %B32   - -- %B32   - -- %B32
--R         27          27          27          27          27          27
--R       + 
--R          1     9   14     8    1     7   2     6   1     5   2     4       3
--R         -- %B32  + -- %B32  + -- %B32  + - %B32  + - %B32  + - %B32  + %B32
--R         27         27         27         9         3         9
--R       + 
--R         4     2
--R         - %B32  - %B32 - 2
--R         3
--R       ,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B32   - -- %B32   - -- %B32   + -- %B32   + -- %B32   + -- %B32
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B32  - -- %B32  - -- %B32  - - %B32  - - %B32  - - %B32  - %B32
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B32  + - %B32 + -
--R           3         2        2
--R       ,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B32   - -- %B32   - -- %B32   + -- %B32   + -- %B32   + -- %B32
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B32  - -- %B32  - -- %B32  - - %B32  - - %B32  - - %B32  - %B32
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B32  + - %B32 + -
--R           3         2        2
--R       ]
--R     ,
--R
--R     [%B33,
--R
--R          1     15    2     14    1     13    4     12   11     11    4     10
--R         -- %B33   + -- %B33   + -- %B33   - -- %B33   - -- %B33   - -- %B33
--R         27          27          27          27          27          27
--R       + 
--R          1     9   14     8    1     7   2     6   1     5   2     4       3
--R         -- %B33  + -- %B33  + -- %B33  + - %B33  + - %B33  + - %B33  + %B33
--R         27         27         27         9         3         9
--R       + 
--R         4     2
--R         - %B33  - %B33 - 2
--R         3
--R       ,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B33   - -- %B33   - -- %B33   + -- %B33   + -- %B33   + -- %B33
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B33  - -- %B33  - -- %B33  - - %B33  - - %B33  - - %B33  - %B33
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B33  + - %B33 + -
--R           3         2        2
--R       ,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B33   - -- %B33   - -- %B33   + -- %B33   + -- %B33   + -- %B33
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B33  - -- %B33  - -- %B33  - - %B33  - - %B33  - - %B33  - %B33
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B33  + - %B33 + -
--R           3         2        2
--R       ]
--R     ,
--R
--R     [%B34,
--R
--R          1     15    2     14    1     13    4     12   11     11    4     10
--R         -- %B34   + -- %B34   + -- %B34   - -- %B34   - -- %B34   - -- %B34
--R         27          27          27          27          27          27
--R       + 
--R          1     9   14     8    1     7   2     6   1     5   2     4       3
--R         -- %B34  + -- %B34  + -- %B34  + - %B34  + - %B34  + - %B34  + %B34
--R         27         27         27         9         3         9
--R       + 
--R         4     2
--R         - %B34  - %B34 - 2
--R         3
--R       ,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B34   - -- %B34   - -- %B34   + -- %B34   + -- %B34   + -- %B34
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B34  - -- %B34  - -- %B34  - - %B34  - - %B34  - - %B34  - %B34
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B34  + - %B34 + -
--R           3         2        2
--R       ,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B34   - -- %B34   - -- %B34   + -- %B34   + -- %B34   + -- %B34
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B34  - -- %B34  - -- %B34  - - %B34  - - %B34  - - %B34  - %B34
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B34  + - %B34 + -
--R           3         2        2
--R       ]
--R     ,
--R    [- 1,1,0,1], [- 1,1,1,0],
--R
--R     [%B23,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B23   - -- %B23   - -- %B23   + -- %B23   + -- %B23   + -- %B23
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B23  - -- %B23  - -- %B23  - - %B23  - - %B23  - - %B23  - %B23
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B23  + - %B23 + -
--R           3         2        2
--R       ,
--R      %B30,
--R
--R                   1     15    1     14    1     13    2     12   11     11
--R         - %B30 + -- %B23   + -- %B23   + -- %B23   - -- %B23   - -- %B23
--R                  54          27          54          27          54
--R       + 
--R            2     10    1     9    7     8    1     7   1     6   1     5
--R         - -- %B23   + -- %B23  + -- %B23  + -- %B23  + - %B23  + - %B23
--R           27          54         27         54         9         6
--R       + 
--R         1     4   2     2   1        1
--R         - %B23  + - %B23  - - %B23 - -
--R         9         3         2        2
--R       ]
--R     ,
--R
--R     [%B23,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B23   - -- %B23   - -- %B23   + -- %B23   + -- %B23   + -- %B23
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B23  - -- %B23  - -- %B23  - - %B23  - - %B23  - - %B23  - %B23
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B23  + - %B23 + -
--R           3         2        2
--R       ,
--R      %B31,
--R
--R                   1     15    1     14    1     13    2     12   11     11
--R         - %B31 + -- %B23   + -- %B23   + -- %B23   - -- %B23   - -- %B23
--R                  54          27          54          27          54
--R       + 
--R            2     10    1     9    7     8    1     7   1     6   1     5
--R         - -- %B23   + -- %B23  + -- %B23  + -- %B23  + - %B23  + - %B23
--R           27          54         27         54         9         6
--R       + 
--R         1     4   2     2   1        1
--R         - %B23  + - %B23  - - %B23 - -
--R         9         3         2        2
--R       ]
--R     ,
--R
--R     [%B24,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B24   - -- %B24   - -- %B24   + -- %B24   + -- %B24   + -- %B24
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B24  - -- %B24  - -- %B24  - - %B24  - - %B24  - - %B24  - %B24
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B24  + - %B24 + -
--R           3         2        2
--R       ,
--R      %B28,
--R
--R                   1     15    1     14    1     13    2     12   11     11
--R         - %B28 + -- %B24   + -- %B24   + -- %B24   - -- %B24   - -- %B24
--R                  54          27          54          27          54
--R       + 
--R            2     10    1     9    7     8    1     7   1     6   1     5
--R         - -- %B24   + -- %B24  + -- %B24  + -- %B24  + - %B24  + - %B24
--R           27          54         27         54         9         6
--R       + 
--R         1     4   2     2   1        1
--R         - %B24  + - %B24  - - %B24 - -
--R         9         3         2        2
--R       ]
--R     ,
--R
--R     [%B24,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B24   - -- %B24   - -- %B24   + -- %B24   + -- %B24   + -- %B24
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B24  - -- %B24  - -- %B24  - - %B24  - - %B24  - - %B24  - %B24
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B24  + - %B24 + -
--R           3         2        2
--R       ,
--R      %B29,
--R
--R                   1     15    1     14    1     13    2     12   11     11
--R         - %B29 + -- %B24   + -- %B24   + -- %B24   - -- %B24   - -- %B24
--R                  54          27          54          27          54
--R       + 
--R            2     10    1     9    7     8    1     7   1     6   1     5
--R         - -- %B24   + -- %B24  + -- %B24  + -- %B24  + - %B24  + - %B24
--R           27          54         27         54         9         6
--R       + 
--R         1     4   2     2   1        1
--R         - %B24  + - %B24  - - %B24 - -
--R         9         3         2        2
--R       ]
--R     ,
--R
--R     [%B25,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B25   - -- %B25   - -- %B25   + -- %B25   + -- %B25   + -- %B25
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B25  - -- %B25  - -- %B25  - - %B25  - - %B25  - - %B25  - %B25
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B25  + - %B25 + -
--R           3         2        2
--R       ,
--R      %B26,
--R
--R                   1     15    1     14    1     13    2     12   11     11
--R         - %B26 + -- %B25   + -- %B25   + -- %B25   - -- %B25   - -- %B25
--R                  54          27          54          27          54
--R       + 
--R            2     10    1     9    7     8    1     7   1     6   1     5
--R         - -- %B25   + -- %B25  + -- %B25  + -- %B25  + - %B25  + - %B25
--R           27          54         27         54         9         6
--R       + 
--R         1     4   2     2   1        1
--R         - %B25  + - %B25  - - %B25 - -
--R         9         3         2        2
--R       ]
--R     ,
--R
--R     [%B25,
--R
--R            1     15    1     14    1     13    2     12   11     11    2     10
--R         - -- %B25   - -- %B25   - -- %B25   + -- %B25   + -- %B25   + -- %B25
--R           54          27          54          27          54          27
--R       + 
--R            1     9    7     8    1     7   1     6   1     5   1     4       3
--R         - -- %B25  - -- %B25  - -- %B25  - - %B25  - - %B25  - - %B25  - %B25
--R           54         27         54         9         6         9
--R       + 
--R           2     2   1        3
--R         - - %B25  + - %B25 + -
--R           3         2        2
--R       ,
--R      %B27,
--R
--R                   1     15    1     14    1     13    2     12   11     11
--R         - %B27 + -- %B25   + -- %B25   + -- %B25   - -- %B25   - -- %B25
--R                  54          27          54          27          54
--R       + 
--R            2     10    1     9    7     8    1     7   1     6   1     5
--R         - -- %B25   + -- %B25  + -- %B25  + -- %B25  + - %B25  + - %B25
--R           27          54         27         54         9         6
--R       + 
--R         1     4   2     2   1        1
--R         - %B25  + - %B25  - - %B25 - -
--R         9         3         2        2
--R       ]
--R     ,
--R    [1,%B21,- %B21,0], [1,%B22,- %B22,0], [1,%B19,0,- %B19], [1,%B20,0,- %B20],
--R            1     3   1   1     3   1   1     3   1
--R    [%B17,- - %B17  + -,- - %B17  + -,- - %B17  + -],
--R            3         3   3         3   3         3
--R            1     3   1   1     3   1   1     3   1
--R    [%B18,- - %B18  + -,- - %B18  + -,- - %B18  + -]]
--R            3         3   3         3   3         3
--R                                 Type: List List RealClosure Fraction Integer
--E 25

--S 26 of 28
#lr2
 

   (26)  27
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  27
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 28
lpr2 := positiveSolve(lf)$pack
 

                  1     3   1   1     3   1   1     3   1
   (27)  [[%B40,- - %B40  + -,- - %B40  + -,- - %B40  + -]]
                  3         3   3         3   3         3
                                 Type: List List RealClosure Fraction Integer
--R 
--R
--R                  1     3   1   1     3   1   1     3   1
--R   (27)  [[%B40,- - %B40  + -,- - %B40  + -,- - %B40  + -]]
--R                  3         3   3         3   3         3
--R                                 Type: List List RealClosure Fraction Integer
--E 27

--S 28 of 28
[approximate(r,1/10**21)::Float for r in lpr2.1]
 

   (28)
   [0.3221853546 2608559291, 0.3221853546 2608559291, 0.3221853546 2608559291,
    0.3221853546 2608559291]
                                                             Type: List Float
--R 
--R
--R   (28)
--R   [0.3221853546 2608559291, 0.3221853546 2608559291, 0.3221853546 2608559291,
--R    0.3221853546 2608559291]
--R                                                             Type: List Float
--E 28
)spool
 
Starts dribbling to intef.output (2010/3/27, 18:27:0).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 16
(a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x)
 

                        a x + b
   (1)  --------------------------------------
         2        2         2          2 3
        b x log(x)  + 2a b x log(x) + a x  + x
                                                     Type: Expression Integer
--R 
--R
--R                        a x + b
--R   (1)  --------------------------------------
--R         2        2         2          2 3
--R        b x log(x)  + 2a b x log(x) + a x  + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 16
integrate(%,x)
 

   (2)  atan(b log(x) + a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)  atan(b log(x) + a x)
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 16
((exp(x)-x**2+2*x)/(x**2*(exp(x)+x)**2))*exp((x**2-1)/x+1/(exp(x)+x))
 

                           2       x    3
                         (x  - 1)%e  + x
                         ----------------
                                x    2
           x    2           x %e  + x
        (%e  - x  + 2x)%e
   (3)  ---------------------------------
               2   x 2     3  x    4
              x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R                           2       x    3
--R                         (x  - 1)%e  + x
--R                         ----------------
--R                                x    2
--R           x    2           x %e  + x
--R        (%e  - x  + 2x)%e
--R   (3)  ---------------------------------
--R               2   x 2     3  x    4
--R              x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 3

--S 4 of 16
integrate(%,x)
 

            2       x    3
          (x  - 1)%e  + x
          ----------------
                 x    2
             x %e  + x
        %e
   (4)  ------------------
                  x
                %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2       x    3
--R          (x  - 1)%e  + x
--R          ----------------
--R                 x    2
--R             x %e  + x
--R        %e
--R   (4)  ------------------
--R                  x
--R                %e
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 16
sin(x)/x
 

        sin(x)
   (5)  ------
           x
                                                     Type: Expression Integer
--R 
--R
--R        sin(x)
--R   (5)  ------
--R           x
--R                                                     Type: Expression Integer
--E 5

--S 6 of 16
integrate(%,x)
 

   (6)  Si(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (6)  Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 16
x * cot x
 

   (7)  x cot(x)
                                                     Type: Expression Integer
--R 
--R
--R   (7)  x cot(x)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 16
integrate(%,x)
 

           x
         ++
   (8)   |   %J cot(%J)d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--R   (8)   |   %J cot(%J)d%J
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 16
(2 * log(x)**2 - log x - x**2) / (log(x)**3 - x**2 * log x)
 

               2             2
        2log(x)  - log(x) - x
   (9)  ----------------------
                3    2
          log(x)  - x log(x)
                                                     Type: Expression Integer
--R 
--R
--R               2             2
--R        2log(x)  - log(x) - x
--R   (9)  ----------------------
--R                3    2
--R          log(x)  - x log(x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 16
integrate(%,x)
 

         log(log(x) + x) - log(log(x) - x) + 2li(x)
   (10)  ------------------------------------------
                              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         log(log(x) + x) - log(log(x) - x) + 2li(x)
--R   (10)  ------------------------------------------
--R                              2
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 16
cos(a * x) / (1 + cos(a * x))
 

           cos(a x)
   (11)  ------------
         cos(a x) + 1
                                                     Type: Expression Integer
--R 
--R
--R           cos(a x)
--R   (11)  ------------
--R         cos(a x) + 1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 16
integrate(%,x)
 

         - sin(a x) + a x cos(a x) + a x
   (12)  -------------------------------
                  a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - sin(a x) + a x cos(a x) + a x
--R   (12)  -------------------------------
--R                  a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 16
cos(3*x)*sin(2*x)
 

   (13)  cos(3x)sin(2x)
                                                     Type: Expression Integer
--R 
--R
--R   (13)  cos(3x)sin(2x)
--R                                                     Type: Expression Integer
--E 13

--S 14 of 16
integrate(%,x)
 

                  5           3
         - 8cos(x)  + 10cos(x)
   (14)  ----------------------
                    5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  5           3
--R         - 8cos(x)  + 10cos(x)
--R   (14)  ----------------------
--R                    5
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 16
cosh(a*x)*sinh(a*x)
 

   (15)  cosh(a x)sinh(a x)
                                                     Type: Expression Integer
--R 
--R
--R   (15)  cosh(a x)sinh(a x)
--R                                                     Type: Expression Integer
--E 15

--S 16 of 16
integrate(%,x)
 

                  2            2
         sinh(a x)  + cosh(a x)
   (16)  -----------------------
                    4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2            2
--R         sinh(a x)  + cosh(a x)
--R   (16)  -----------------------
--R                    4a
--R                                          Type: Union(Expression Integer,...)
--E 16
)spool 
 
Starts dribbling to skew.output (2010/3/27, 18:40:44).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 36
lv:List Symbol := [x,y,z]
 

   (1)  [x,y,z]
                                                            Type: List Symbol
--R 
--R
--R   (1)  [x,y,z]
--R                                                            Type: List Symbol
--E 1

--S 2 of 36
macro coefRing == Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 36
R := Expression coefRing
 

   (3)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (3)  Expression Integer
--R                                                                 Type: Domain
--E 3

--S 4 of 36
der := DERHAM(coefRing,lv)
 

   (4)  DeRhamComplex(Integer,[x,y,z])
                                                                 Type: Domain
--R 
--R
--R   (4)  DeRhamComplex(Integer,[x,y,z])
--R                                                                 Type: Domain
--E 4


--S 5 of 36
f:R:=x**2*y*z-5*x**3*y**2*z**5
 

            3 2 5    2
   (5)  - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3 2 5    2
--R   (5)  - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 5

--S 6 of 36
g:R:=z**2*y*cos(z)-7*sin(x**3*y**2)*z**2
 

            2     3 2       2
   (6)  - 7z sin(x y ) + y z cos(z)
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2
--R   (6)  - 7z sin(x y ) + y z cos(z)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 36
h:R:=x*y*z-2*x**3*y*z**2
 

            3   2
   (7)  - 2x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3   2
--R   (7)  - 2x y z  + x y z
--R                                                     Type: Expression Integer
--E 7


--S 8 of 36
dx :der := generator(1)
 

   (8)  dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (8)  dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 8

--S 9 of 36
dy :der := generator(2)
 

   (9)  dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (9)  dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 9

--S 10 of 36
dz :der := generator(3)
 

   (10)  dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (10)  dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 10

--S 11 of 36
[dx,dy,dz] := [generator(i)$der for i in 1..3]
 

   (11)  [dx,dy,dz]
                                    Type: List DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (11)  [dx,dy,dz]
--R                                    Type: List DeRhamComplex(Integer,[x,y,z])
--E 11

--S 12 of 36
alpha:der := f*dx + g*dy + h*dz
 

   (12)
          3   2                   2     3 2       2
     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
   + 
          3 2 5    2
     (- 5x y z  + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (12)
--R          3   2                   2     3 2       2
--R     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
--R   + 
--R          3 2 5    2
--R     (- 5x y z  + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 12

--S 13 of 36
beta:der  := cos(tan(x*y*z)+x*y*z)*dx + x*dy 
 

   (13)  x dy + cos(tan(x y z) + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (13)  x dy + cos(tan(x y z) + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 13

--S 14 of 36
exteriorDifferential alpha
 

   (14)
         2                  3 2                    3 2
     (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)dy dz
   + 
         3 2 4     2   2          2
     (25x y z  - 6x y z  + y z - x y)dx dz
   + 
           2 2 2     3 2       3   5    2
     (- 21x y z cos(x y ) + 10x y z  - x z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (14)
--R         2                  3 2                    3 2
--R     (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)dy dz
--R   + 
--R         3 2 4     2   2          2
--R     (25x y z  - 6x y z  + y z - x y)dx dz
--R   + 
--R           2 2 2     3 2       3   5    2
--R     (- 21x y z cos(x y ) + 10x y z  - x z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 14

--S 15 of 36
exteriorDifferential %
 

   (15)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (15)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 15

--S 16 of 36
macro exD == exteriorDifferential
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 36
gamma := alpha * beta
 

   (17)
        4   2    2               3   2
     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
   + 
       2     3 2       2                                   4 2 5    3
   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (17)
--R        4   2    2               3   2
--R     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
--R   + 
--R       2     3 2       2                                   4 2 5    3
--R   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 17

--S 18 of 36
delta := exD gamma
 

   (18)
                    2     3 2       2 2           4   3    2   2           2
           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
         + 
                    2     3 2        2 2           4   3     2   2
           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
      *
         sin(tan(x y z) + x y z)
     + 
             2                  3 2                    3 2
         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
      *
         cos(tan(x y z) + x y z)
     + 
            4 2 4     3   2             3
       - 25x y z  + 8x y z  - 2x y z + x y
  *
     dx dy dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (18)
--R                    2     3 2       2 2           4   3    2   2           2
--R           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
--R         + 
--R                    2     3 2        2 2           4   3     2   2
--R           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
--R      *
--R         sin(tan(x y z) + x y z)
--R     + 
--R             2                  3 2                    3 2
--R         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
--R      *
--R         cos(tan(x y z) + x y z)
--R     + 
--R            4 2 4     3   2             3
--R       - 25x y z  + 8x y z  - 2x y z + x y
--R  *
--R     dx dy dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 18

--S 19 of 36
epsilon := exD(alpha)*beta - alpha * exD(beta)
 

   (19)
                    2     3 2       2 2           4   3    2   2           2
           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
         + 
                    2     3 2        2 2           4   3     2   2
           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
      *
         sin(tan(x y z) + x y z)
     + 
             2                  3 2                    3 2
         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
      *
         cos(tan(x y z) + x y z)
     + 
            4 2 4     3   2             3
       - 25x y z  + 8x y z  - 2x y z + x y
  *
     dx dy dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (19)
--R                    2     3 2       2 2           4   3    2   2           2
--R           (- 7x y z sin(x y ) + x y z cos(z) + 2x y z  - x y z )tan(x y z)
--R         + 
--R                    2     3 2        2 2           4   3     2   2
--R           - 14x y z sin(x y ) + 2x y z cos(z) + 4x y z  - 2x y z
--R      *
--R         sin(tan(x y z) + x y z)
--R     + 
--R             2                  3 2                    3 2
--R         (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)
--R      *
--R         cos(tan(x y z) + x y z)
--R     + 
--R            4 2 4     3   2             3
--R       - 25x y z  + 8x y z  - 2x y z + x y
--R  *
--R     dx dy dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 19

--S 20 of 36
delta - epsilon 
 

   (20)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (20)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 20

--S 21 of 36
a:BOP := operator('a)
 

   (21)  a
                                                          Type: BasicOperator
--R 
--R
--R   (21)  a
--R                                                          Type: BasicOperator
--E 21

--S 22 of 36
b:BOP := operator('b)
 

   (22)  b
                                                          Type: BasicOperator
--R 
--R
--R   (22)  b
--R                                                          Type: BasicOperator
--E 22

--S 23 of 36
c:BOP := operator('c)
 

   (23)  c
                                                          Type: BasicOperator
--R 
--R
--R   (23)  c
--R                                                          Type: BasicOperator
--E 23

--S 24 of 36
alpha := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz
 

   (24)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (24)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 24

--S 25 of 36
beta  := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz
 

   (25)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (25)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 25

--S 26 of 36
totalDifferential(a(x,y,z))$der
 

   (26)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
          ,3             ,2             ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (26)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
--R          ,3             ,2             ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 26

--S 27 of 36
exD alpha
 

   (27)
     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
       ,2           ,3                  ,1           ,3
   + 
     (b  (x,y,z) - a  (x,y,z))dx dy
       ,1           ,2
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (27)
--R     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
--R       ,2           ,3                  ,1           ,3
--R   + 
--R     (b  (x,y,z) - a  (x,y,z))dx dy
--R       ,1           ,2
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 27

--S 28 of 36
exD beta
 

   (28)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
           ,1           ,2           ,3
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (28)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
--R           ,1           ,2           ,3
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 28

--S 29 of 36
id:der := 1
 

   (29)  1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (29)  1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 29

--S 30 of 36
g1:der := a([x,t,y,u,v,z,e]) * id
 

   (30)  a(x,t,y,u,v,z,e)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (30)  a(x,t,y,u,v,z,e)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 30

--S 31 of 36
h1:der := a([x,y,x,t,x,z,y,r,u,x]) * id
 

   (31)  a(x,y,x,t,x,z,y,r,u,x)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (31)  a(x,y,x,t,x,z,y,r,u,x)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 31

--S 32 of 36
exD g1
 

   (32)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
          ,6                     ,3                     ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (32)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
--R          ,6                     ,3                     ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 32

--S 33 of 36
exD h1
 

   (33)
     a  (x,y,x,t,x,z,y,r,u,x)dz
      ,6
   + 
     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
       ,7                         ,2
   + 
         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,10                         ,5
       + 
         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,3                         ,1
    *
       dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (33)
--R     a  (x,y,x,t,x,z,y,r,u,x)dz
--R      ,6
--R   + 
--R     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
--R       ,7                         ,2
--R   + 
--R         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,10                         ,5
--R       + 
--R         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,3                         ,1
--R    *
--R       dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 33

--S 34 of 36
coefficient(gamma, dx*dy)
 

            2     3 2       2                                   4 2 5    3
   (34)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2                                   4 2 5    3
--R   (34)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 34

--S 35 of 36
coefficient(gamma, id)
 

   (35)  0
                                                     Type: Expression Integer
--R 
--R
--R   (35)  0
--R                                                     Type: Expression Integer
--E 35

--S 36 of 36
coefficient(g1,id)
 

   (36)  a(x,t,y,u,v,z,e)
                                                     Type: Expression Integer
--R 
--R
--R   (36)  a(x,t,y,u,v,z,e)
--R                                                     Type: Expression Integer
--E 36
)spool 
 
Starts dribbling to leg.output (2010/3/27, 18:28:37).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 4
p(n | n=0) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 4
p(n | n=1) == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
p(n | n>1) == ((2*n-1)*x*p(n-1)-(n-1)*p(n-2))/n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
p 3
 
   Compiling function p with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function p as a recurrence relation.

        5  3   3
   (4)  - x  - - x
        2      2
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function p with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function p as a recurrence relation.
--R
--R        5  3   3
--R   (4)  - x  - - x
--R        2      2
--R                                            Type: Polynomial Fraction Integer
--E 4
)spool 
 
Starts dribbling to sincos.output (2010/3/27, 18:40:42).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 2
[[0.01,0.00999983333416666468254,sin(0.01),sin(0.01)-(0.00999983333416666468254)],_
[0.02,0.01999866669333307936649,sin(0.02),sin(0.02)-(0.01999866669333307936649)],_
[0.03,0.02999550020249566076853,sin(0.03),sin(0.03)-(0.02999550020249566076853)],_
[0.04,0.03998933418663415945255,sin(0.04),sin(0.04)-(0.03998933418663415945255)],_
[0.05,0.04997916927067832879487,sin(0.05),sin(0.05)-(0.04997916927067832879487)],_
[0.06,0.05996400647944459919909,sin(0.06),sin(0.06)-(0.05996400647944459919909)],_
[0.07,0.06994284733753276397655,sin(0.07),sin(0.07)-(0.06994284733753276397655)],_
[0.08,0.07991469396917268730688,sin(0.08),sin(0.08)-(0.07991469396917268730688)],_
[0.09,0.08987854919801104969125,sin(0.09),sin(0.09)-(0.08987854919801104969125)],_
[0.10,0.09983341664682815230681,sin(0.10),sin(0.10)-(0.09983341664682815230681)],_
[0.11,0.10977830083717480866495,sin(0.11),sin(0.11)-(0.10977830083717480866495)],_
[0.12,0.11971220728891935996735,sin(0.12),sin(0.12)-(0.11971220728891935996735)],_
[0.13,0.12963414261969485954121,sin(0.13),sin(0.13)-(0.12963414261969485954121)],_
[0.14,0.13954311464423648171799,sin(0.14),sin(0.14)-(0.13954311464423648171799)],_
[0.15,0.14943813247359922149773,sin(0.15),sin(0.15)-(0.14943813247359922149773)],_
[0.16,0.15931820661424596331146,sin(0.16),sin(0.16)-(0.15931820661424596331146)],_
[0.17,0.16918234906699601015762,sin(0.17),sin(0.17)-(0.16918234906699601015762)],_
[0.18,0.17902957342582417834180,sin(0.18),sin(0.18)-(0.17902957342582417834180)],_
[0.19,0.18885889497650057799285,sin(0.19),sin(0.19)-(0.18885889497650057799285)],_
[0.20,0.19866933079506121545941,sin(0.20),sin(0.20)-(0.19866933079506121545941)],_
[0.21,0.20845989984609957060871,sin(0.21),sin(0.21)-(0.20845989984609957060871)],_
[0.22,0.21822962308086931995179,sin(0.22),sin(0.22)-(0.21822962308086931995179)],_
[0.23,0.22797752353518839540462,sin(0.23),sin(0.23)-(0.22797752353518839540462)],_
[0.24,0.23770262642713458836079,sin(0.24),sin(0.24)-(0.23770262642713458836079)],_
[0.25,0.24740395925452292959685,sin(0.25),sin(0.25)-(0.24740395925452292959685)],_
[0.26,0.25708055189215509735339,sin(0.26),sin(0.26)-(0.25708055189215509735339)],_
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   (1)
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                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.01,0.0099998333 3416666468 26,0.0099998333 3416666468 26,0.0],
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--R    [1.09,0.8866269144 4948723161,0.8866269144 4948723161,0.0],
--R    [1.1,0.8912073600 6143533995,0.8912073600 6143533995,0.3 E -20],
--R    [1.11,0.8956986856 8004762924,0.8956986856 8004762924,0.0],
--R    [1.12,0.9001004421 7650499712,0.9001004421 7650499712,0.0],
--R    [1.13,0.9044121893 7882591604,0.9044121893 7882591604,0.0],
--R    [1.14,0.9086334961 1588326459,0.9086334961 1588326459,0.0],
--R    [1.15,0.9127639402 6052108094,0.9127639402 6052108094,0.0],
--R    [1.16,0.9168031087 7176692662,0.9168031087 7176692662,- 0.3 E -20],
--R    [1.17,0.9207505977 3613563957,0.9207505977 3613563958,0.3 E -20],
--R    [1.18,0.9246060124 0802034611,0.9246060124 0802034611,0.0],
--R    [1.19,0.9283689672 491666926,0.9283689672 491666926,0.0],
--R    [1.2,0.9320390859 6722634967,0.9320390859 6722634967,0.3 E -20],
--R    [1.21,0.9356160015 5338593342,0.9356160015 5338593342,0.0],
--R    [1.22,0.9390993563 1906758094,0.9390993563 1906758094,0.0],
--R    [1.23,0.9424888019 3169751002,0.9424888019 3169751002,0.0],
--R    [1.24,0.9457839994 4953898629,0.9457839994 4953898629,0.0],
--R    [1.25,0.9489846193 5558621435,0.9489846193 5558621435,0.0],
--R    [1.26,0.9520903415 9051576386,0.9520903415 9051576386,0.0],
--R    [1.27,0.9551008555 8469223509,0.9551008555 8469223509,0.0],
--R    [1.28,0.9580158602 892249637,0.9580158602 892249637,0.0],
--R    [1.29,0.9608350642 0607265891,0.9608350642 0607265891,0.0],
--R    [1.3,0.9635581854 171929647,0.9635581854 171929647,- 0.3 E -20],
--R    [1.31,0.9661849516 1273402917,0.9661849516 1273402917,0.0],
--R    [1.32,0.9687151001 1826526273,0.9687151001 1826526273,0.0],
--R    [1.33,0.9711483779 2104456234,0.9711483779 2104456234,0.0],
--R    [1.34,0.9734845416 9531937479,0.9734845416 9531937479,0.0],
--R    [1.35,0.9757233578 2665906926,0.9757233578 2665906926,0.0],
--R    [1.36,0.9778646024 3531618568,0.9778646024 3531618568,0.0],
--R    [1.37,0.9799080613 9861422289,0.9799080613 9861422289,0.0],
--R    [1.38,0.9818535303 7235972788,0.9818535303 7235972788,0.0],
--R    [1.39,0.9837008148 1127654484,0.9837008148 1127654484,0.0],
--R    [1.4,0.9854497299 8846018066,0.9854497299 8846018066,0.0],
--R    [1.41,0.9871001010 1385034143,0.9871001010 1385034143,0.0],
--R    [1.42,0.9886517628 5171979274,0.9886517628 5171979274,0.0],
--R    [1.43,0.9901045603 3717779486,0.9901045603 3717779486,0.0],
--R    [1.44,0.9914583481 9168646253,0.9914583481 9168646253,0.0],
--R    [1.45,0.9927129910 3758849767,0.9927129910 3758849767,0.0],
--R    [1.46,0.9938683634 1164484229,0.9938683634 1164484229,0.0],
--R    [1.47,0.9949243497 7758089786,0.9949243497 7758089786,0.0],
--R    [1.48,0.9958808445 3764005648,0.9958808445 3764005648,0.0],
--R    [1.49,0.9967377520 4314338855,0.9967377520 4314338855,0.0],
--R    [1.5,0.9974949866 0405443094,0.9974949866 0405443094,0.0],
--R    [1.51,0.9981524724 9754811924,0.9981524724 9754811924,0.0],
--R    [1.52,0.9987101439 7558300717,0.9987101439 7558300717,0.0],
--R    [1.53,0.9991679452 7147601592,0.9991679452 7147601592,0.0],
--R    [1.54,0.9995258306 0547905601,0.9995258306 0547905601,0.0],
--R    [1.55,0.9997837641 893569639,0.9997837641 893569639,0.0],
--R    [1.56,0.9999417202 2996629574,0.9999417202 2996629574,0.0],
--R    [1.57,0.9999996829 3183462021,0.9999996829 3183462021,0.0],
--R    [1.58,0.9999576464 9874005255,0.9999576464 9874005255,0.0],
--R    [1.59,0.9998156151 3429087198,0.9998156151 3429087198,0.0],
--R    [1.6,0.9995736030 4150516434,0.9995736030 4150516434,0.0]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
[[0.01,0.99995000041666527778026,cos(0.01),cos(0.01)-(0.99995000041666527778026)],_
[0.02,0.99980000666657777841270,cos(0.02),cos(0.02)-(0.99980000666657777841270)],_
[0.03,0.99955003374898751627216,cos(0.03),cos(0.03)-(0.99955003374898751627216)],_
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[0.08,0.99680170630261938497771,cos(0.08),cos(0.08)-(0.99680170630261938497771)],_
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   (2)
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                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,0.9999500004 1666527778,0.9999500004 1666527778,0.0],
--R    [0.02,0.9998000066 6657777841,0.9998000066 6657777841,0.0],
--R    [0.03,0.9995500337 4898751627,0.9995500337 4898751627,0.0],
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--R    [0.05,0.9987502603 9496624656,0.9987502603 9496624656,0.0],
--R    [0.06,0.9982005399 3520416555,0.9982005399 3520416555,0.0],
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--R    [0.09,0.9959527330 1199425309,0.9959527330 1199425309,0.0],
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--R    [0.12,0.9928086358 5386625225,0.9928086358 5386625225,0.0],
--R    [0.13,0.9915618937 1478803959,0.9915618937 1478803959,0.0],
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--R    [0.16,0.9872272833 7562694904,0.9872272833 7562694904,0.0],
--R    [0.17,0.9855847669 0956070917,0.9855847669 0956070917,0.0],
--R    [0.18,0.9838436927 8812141459,0.9838436927 8812141459,0.0],
--R    [0.19,0.9820042351 1727031897,0.9820042351 1727031897,0.0],
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--R    [0.26,0.9663899781 3451322556,0.9663899781 3451322556,0.0],
--R    [0.27,0.9637708963 6589051302,0.9637708963 6589051302,0.0],
--R    [0.28,0.9610554383 1077094792,0.9610554383 1077094792,0.0],
--R    [0.29,0.9582438755 1269716807,0.9582438755 1269716807,0.0],
--R    [0.3,0.9553364891 2560601964,0.9553364891 2560601964,0.0],
--R    [0.31,0.9523335698 8571339784,0.9523335698 8571339784,0.0],
--R    [0.32,0.9492354180 8244086758,0.9492354180 8244086758,0.0],
--R    [0.33,0.9460423435 2838697153,0.9460423435 2838697153,0.0],
--R    [0.34,0.9427546655 283462285,0.9427546655 283462285,0.0],
--R    [0.35,0.9393727128 4737892004,0.9393727128 4737892004,0.0],
--R    [0.36,0.9358968236 7793485835,0.9358968236 7793485835,0.0],
--R    [0.37,0.9323273456 060344232,0.9323273456 060344232,0.0],
--R    [0.38,0.9286646355 7651024949,0.9286646355 7651024949,0.0],
--R    [0.39,0.9249090598 5731304145,0.9249090598 5731304145,0.0],
--R    [0.4,0.9210609940 028850828,0.9210609940 028850828,0.0],
--R    [0.41,0.9171208228 1660510548,0.9171208228 1660510548,0.0],
--R    [0.42,0.9130889403 1230827244,0.9130889403 1230827244,0.0],
--R    [0.43,0.9089657496 7488512248,0.9089657496 7488512248,0.0],
--R    [0.44,0.9047516632 1996341716,0.9047516632 1996341717,0.3 E -20],
--R    [0.45,0.9004471023 5267692167,0.9004471023 5267692167,0.0],
--R    [0.46,0.8960524975 2552524254,0.8960524975 2552524254,0.0],
--R    [0.47,0.8915682881 9532893645,0.8915682881 9532893645,0.0],
--R    [0.48,0.8869949227 792841944,0.8869949227 792841944,0.0],
--R    [0.49,0.8823328586 101214957,0.8823328586 101214957,0.0],
--R    [0.5,0.8775825618 9037271612,0.8775825618 9037271612,0.0],
--R    [0.51,0.8727445076 457512631,0.8727445076 457512631,0.0],
--R    [0.52,0.8678191796 7764990039,0.8678191796 7764990039,0.0],
--R    [0.53,0.8628070705 1476101181,0.8628070705 1476101181,0.0],
--R    [0.54,0.8577086813 6382414254,0.8577086813 6382414254,0.0],
--R    [0.55,0.8525245220 595057428,0.8525245220 595057428,0.0],
--R    [0.56,0.8472551110 1341612609,0.8472551110 1341612609,0.0],
--R    [0.57,0.8419009751 6226874013,0.8419009751 6226874013,0.0],
--R    [0.58,0.8364626499 1518693466,0.8364626499 1518693466,0.0],
--R    [0.59,0.8309406791 0016349525,0.8309406791 0016349525,0.0],
--R    [0.6,0.8253356149 0967829724,0.8253356149 0967829724,0.0],
--R    [0.61,0.8196480178 454795179,0.8196480178 454795179,0.0],
--R    [0.62,0.8138784566 6253392868,0.8138784566 6253392868,0.0],
--R    [0.63,0.8080275083 1215187252,0.8080275083 1215187253,0.3 E -20],
--R    [0.64,0.8020957578 8429261359,0.8020957578 8429261358,- 0.3 E -20],
--R    [0.65,0.7960837985 4905582892,0.7960837985 4905582892,0.0],
--R    [0.66,0.7899922314 9736509279,0.7899922314 9736509279,0.0],
--R    [0.67,0.7838216658 808492853,0.7838216658 808492853,0.0],
--R    [0.68,0.7775727187 5092793718,0.7775727187 5092793718,0.0],
--R    [0.69,0.7712460149 9710660197,0.7712460149 9710660197,0.0],
--R    [0.7,0.7648421872 8448842626,0.7648421872 8448842626,0.0],
--R    [0.71,0.7583618759 9050816654,0.7583618759 9050816654,- 0.3 E -20],
--R    [0.72,0.7518057291 4089497945,0.7518057291 4089497945,0.0],
--R    [0.73,0.7451744023 4487038879,0.7451744023 4487038879,0.0],
--R    [0.74,0.7384685587 2958790979,0.7384685587 2958790979,0.3 E -20],
--R    [0.75,0.7316888688 7382088631,0.7316888688 7382088631,0.0],
--R    [0.76,0.7248360107 4090517234,0.7248360107 4090517234,0.0],
--R    [0.77,0.7179106696 1094336337,0.7179106696 1094336337,0.0],
--R    [0.78,0.7109135380 1227735722,0.7109135380 1227735722,0.0],
--R    [0.79,0.7038453156 5223609691,0.7038453156 5223609691,0.0],
--R    [0.8,0.6967067093 4716542092,0.6967067093 4716542092,- 0.3 E -20],
--R    [0.81,0.6894984329 5174701755,0.6894984329 5174701755,0.0],
--R    [0.82,0.6822212072 8761355167,0.6822212072 8761355167,0.0],
--R    [0.83,0.6748757600 7126710211,0.6748757600 7126710211,0.3 E -20],
--R    [0.84,0.6674628258 4130811792,0.6674628258 4130811792,0.0],
--R    [0.85,0.6599831458 8498217039,0.6599831458 8498217039,0.0],
--R    [0.86,0.6524374681 6405184627,0.6524374681 6405184627,0.0],
--R    [0.87,0.6448265472 4000119478,0.6448265472 4000119478,- 0.3 E -20],
--R    [0.88,0.6371511441 9858020802,0.6371511441 9858020802,0.0],
--R    [0.89,0.6294120265 736968802,0.6294120265 736968802,0.0],
--R    [0.9,0.6216099682 7066445648,0.6216099682 7066445648,0.0],
--R    [0.91,0.6137457494 8881154652,0.6137457494 8881154652,0.0],
--R    [0.92,0.6058201566 434628418,0.6058201566 434628418,0.0],
--R    [0.93,0.5978339822 872982385,0.5978339822 872982385,0.0],
--R    [0.94,0.5897880250 3109822996,0.5897880250 3109822996,- 0.3 E -20],
--R    [0.95,0.5816830894 6388349417,0.5816830894 6388349417,0.0],
--R    [0.96,0.5735199860 7245666213,0.5735199860 7245666212,- 0.3 E -20],
--R    [0.97,0.5652995311 6035431304,0.5652995311 6035431304,0.0],
--R    [0.98,0.5570225467 6621730088,0.5570225467 6621730087,- 0.3 E -20],
--R    [0.99,0.5486898605 8158757534,0.5486898605 8158757535,0.3 E -20],
--R    [1.0,0.5403023058 681397174,0.5403023058 681397174,0.0],
--R    [1.01,0.5318607213 7435546621,0.5318607213 7435546621,0.0],
--R    [1.02,0.5233659512 5164956989,0.5233659512 5164956989,- 0.3 E -20],
--R    [1.03,0.5148188449 6995534753,0.5148188449 6995534753,0.0],
--R    [1.04,0.5062202572 3277840374,0.5062202572 3277840374,0.0],
--R    [1.05,0.4975710478 9172699029,0.4975710478 9172699029,0.3 E -20],
--R    [1.06,0.4888720818 6052756192,0.4888720818 6052756192,- 0.2 E -20],
--R    [1.07,0.4801242290 2853412436,0.4801242290 2853412437,0.2 E -20],
--R    [1.08,0.4713283641 7374002391,0.4713283641 7374002391,0.0],
--R    [1.09,0.4624853668 7530087703,0.4624853668 7530087702,- 0.3 E -20],
--R    [1.1,0.4535961214 2557738777,0.4535961214 2557738777,- 0.2 E -20],
--R    [1.11,0.4446615167 4170684864,0.4446615167 4170684864,0.0],
--R    [1.12,0.4356824462 7671216761,0.4356824462 7671216762,0.2 E -20],
--R    [1.13,0.4266598079 3015731037,0.4266598079 3015731037,- 0.3 E -20],
--R    [1.14,0.4175945039 5835809217,0.4175945039 5835809217,0.0],
--R    [1.15,0.4084874408 8415729815,0.4084874408 8415729815,0.0],
--R    [1.16,0.3993395294 0627315445,0.3993395294 0627315445,0.3 E -20],
--R    [1.17,0.3901516843 0823021533,0.3901516843 0823021533,- 0.2 E -20],
--R    [1.18,0.3809248243 6688177303,0.3809248243 6688177303,0.0],
--R    [1.19,0.3716598722 6053293807,0.3716598722 6053293807,0.2 E -20],
--R    [1.2,0.3623577544 7667357764,0.3623577544 7667357763,- 0.3 E -20],
--R    [1.21,0.3530194012 193303387,0.3530194012 193303387,- 0.2 E -20],
--R    [1.22,0.3436457463 1604702048,0.3436457463 1604702048,0.0],
--R    [1.23,0.3342377271 2450259824,0.3342377271 2450259824,0.2 E -20],
--R    [1.24,0.3247962844 3877623658,0.3247962844 3877623657,- 0.3 E -20],
--R    [1.25,0.3153223623 9526866545,0.3153223623 9526866545,0.0],
--R    [1.26,0.3058169083 7828932689,0.3058169083 7828932689,0.2 E -20],
--R    [1.27,0.2962808729 2531873355,0.2962808729 2531873355,- 0.3 E -20],
--R    [1.28,0.2867152096 3195551278,0.2867152096 3195551278,- 0.2 E -20],
--R    [1.29,0.2771208750 5655764139,0.2771208750 5655764139,0.0],
--R    [1.3,0.2674988286 24587407,0.2674988286 24587407,0.2 E -20],
--R    [1.31,0.2578500325 3266966134,0.2578500325 3266966134,- 0.3 E -20],
--R    [1.32,0.2481754516 5237295957,0.2481754516 5237295957,0.0],
--R    [1.33,0.2384760534 3372320752,0.2384760534 3372320752,0.8 E -21],
--R    [1.34,0.2287528078 0845946523,0.2287528078 0845946523,- 0.3 E -20],
--R    [1.35,0.2190066870 9304158142,0.2190066870 9304158142,- 0.2 E -20],
--R    [1.36,0.2092386658 9141935768,0.2092386658 9141935768,0.0],
--R    [1.37,0.1994497209 9757296569,0.1994497209 9757296569,0.2 E -20],
--R    [1.38,0.1896408312 9783436321,0.1896408312 9783436321,- 0.3 E -20],
--R    [1.39,0.1798129776 729994766,0.1798129776 729994766,- 0.8 E -21],
--R    [1.4,0.1699671429 0024093862,0.1699671429 0024093862,0.8 E -21],
--R    [1.41,0.1601043115 5483119016,0.1601043115 5483119017,0.3 E -20],
--R    [1.42,0.1502254699 1168577349,0.1502254699 1168577349,- 0.2 E -20],
--R    [1.43,0.1403316058 4673666253,0.1403316058 4673666253,0.0],
--R    [1.44,0.1304237087 3814549298,0.1304237087 3814549298,0.2 E -20],
--R    [1.45,0.1205027693 6736657053,0.1205027693 6736657053,- 0.3 E -20],
--R    [1.46,0.1105697798 2006955117,0.1105697798 2006955117,- 0.8 E -21],
--R    [1.47,0.1006257333 8693170091,0.1006257333 8693170091,0.8 E -21],
--R    [1.48,0.0906716244 6430965577 6,0.0906716244 6430965577 9,0.3 E -20],
--R    [1.49,0.0807084484 5480061486 8,0.0807084484 5480061486 6,- 0.2 E -20],
--R    [1.5,0.0707372016 6770291008 8,0.0707372016 6770291008 8,0.0],
--R    [1.51,0.0607588812 1938590658 2,0.0607588812 1938590658 3,0.2 E -20],
--R    [1.52,0.0507744849 3357919672 6,0.0507744849 3357919672 3,- 0.3 E -20],
--R    [1.53,0.0407850112 4159105868 9,0.0407850112 4159105868 8,- 0.1 E -20],
--R    [1.54,0.0307914590 8246615762 2,0.0307914590 8246615762 3,0.8 E -21],
--R    [1.55,0.0207948278 0309247364 4,0.0207948278 0309247364 7,0.3 E -20],
--R    [1.56,0.0107961170 5826744582 4,0.0107961170 5826744582 2,- 0.2 E -20],
--R    [1.57,0.0007963267 1073332548 541,0.0007963267 1073332548 514,- 0.3 E -21],
--R    [1.58,- 0.0092035432 6880826480 54,- 0.0092035432 6880826480 38,0.2 E -20],
--R    [1.59,- 0.0192024929 0169256809 5,- 0.0192024929 0169256809 8,- 0.3 E -20],
--R    [1.6,- 0.0291995223 0128872620 6,- 0.0291995223 0128872620 7,- 0.1 E -20]]
--R                                                        Type: List List Float
--E 2
 
)spool 
 
Starts dribbling to tanatan.output (2010/3/27, 18:41:13).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 9
eq:=2*tan(x)+2*tan(2*x)
 

   (1)  2tan(2x) + 2tan(x)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  2tan(2x) + 2tan(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 9
thesols:=solve(eq,x)
 

                 2%pi      2%pi    %pi      %pi
   (2)  [x= 0,x= ----,x= - ----,x= ---,x= - ---]
                   3         3      3        3
                                       Type: List Equation Expression Integer
--R 
--R
--R                 2%pi      2%pi    %pi      %pi
--R   (2)  [x= 0,x= ----,x= - ----,x= ---,x= - ---]
--R                   3         3      3        3
--R                                       Type: List Equation Expression Integer
--E 2

--S 3 of 9
theproofs:=[eval(eq,i) for i in thesols]
 

   (3)  [0,0,0,0,0]
                                                Type: List Expression Integer
--R 
--R
--R   (3)  [0,0,0,0,0]
--R                                                Type: List Expression Integer
--E 3

--S 4 of 9
thetowers:=[tower i for i in theproofs];
 

                                    Type: List List Kernel Expression Integer
--R 
--R
--R                                    Type: List List Kernel Expression Integer
--E 4

--S 5 of 9
thesubs:LIST Record (a:LIST KERNEL EXPR INT ,b:LIST EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 9
thetans:LIST LIST Record(i:INT,k:KERNEL EXPR INT,z:List Equation EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 9
thetans:=_
 [[construct(j,i.j,Is(argument(i.j).1,n * atan(y))) for j in 1..#i_
      |is?(i.j,tan) and is?(argument(i.j).1,n * atan(y))] _
          for i in thetowers] ;
 

Type: List List Record(i: Integer,k: Kernel Expression Integer,z: List Equation Expression Integer)
--R 
--R
--RType: List List Record(i: Integer,k: Kernel Expression Integer,z: List Equation Expression Integer)
--E 7

--S 8 of 9
thesubs:=_
  [construct([j.k for j in thetans.i],_
             [tanNa(rhs(j.z.2),rhs(j.z.1) ::INT)$TangentExpansions(EXPR INT)_
                        for j in thetans.i]) _
            for i in 1..#theproofs];
 

Type: List Record(a: List Kernel Expression Integer,b: List Expression Integer)
--R 
--R
--RType: List Record(a: List Kernel Expression Integer,b: List Expression Integer)
--E 8

--S 9 of 9
thezeros:=[eval(i,j.a,j.b) for i in theproofs for j in thesubs]
 

   (9)  [0,0,0,0,0]
                                                Type: List Expression Integer
--R 
--R
--R   (9)  [0,0,0,0,0]
--R                                                Type: List Expression Integer
--E 9
)spool 
 
Starts dribbling to SquareMatrix.output (2010/3/27, 18:46:34).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
)set expose add constructor SquareMatrix
 
   SquareMatrix is now explicitly exposed in frame initial 
--R 
--I   SquareMatrix is now explicitly exposed in frame frame0 
--E 1 

--S 2 of 6
m := squareMatrix [ [1,-%i],[%i,4] ]
 

        +1   - %i+
   (1)  |        |
        +%i   4  +
                                        Type: SquareMatrix(2,Complex Integer)
--R 
--R
--R        +1   - %i+
--R   (1)  |        |
--R        +%i   4  +
--R                                        Type: SquareMatrix(2,Complex Integer)
--E 2

--S 3 of 6
m*m - m
 

        + 1   - 4%i+
   (2)  |          |
        +4%i   13  +
                                        Type: SquareMatrix(2,Complex Integer)
--R 
--R
--R        + 1   - 4%i+
--R   (2)  |          |
--R        +4%i   13  +
--R                                        Type: SquareMatrix(2,Complex Integer)
--E 3

--S 4 of 6
mm := squareMatrix [ [m, 1], [1-m, m**2] ]
 

        ++1   - %i+      +1  0+   +
        ||        |      |    |   |
        |+%i   4  +      +0  1+   |
   (3)  |                         |
        |+ 0    %i +  + 2   - 5%i+|
        ||         |  |          ||
        ++- %i  - 3+  +5%i   17  ++
                        Type: SquareMatrix(2,SquareMatrix(2,Complex Integer))
--R 
--R
--R        ++1   - %i+      +1  0+   +
--R        ||        |      |    |   |
--R        |+%i   4  +      +0  1+   |
--R   (3)  |                         |
--R        |+ 0    %i +  + 2   - 5%i+|
--R        ||         |  |          ||
--R        ++- %i  - 3+  +5%i   17  ++
--R                        Type: SquareMatrix(2,SquareMatrix(2,Complex Integer))
--E 4

--S 5 of 6
p := (x + m)**2
 

         2   + 2   - 2%i+    + 2   - 5%i+
   (4)  x  + |          |x + |          |
             +2%i    8  +    +5%i   17  +
                             Type: Polynomial SquareMatrix(2,Complex Integer)
--R 
--R
--R         2   + 2   - 2%i+    + 2   - 5%i+
--R   (4)  x  + |          |x + |          |
--R             +2%i    8  +    +5%i   17  +
--R                             Type: Polynomial SquareMatrix(2,Complex Integer)
--E 5

--S 6 of 6
p::SquareMatrix(2, ?)
 

        + 2                        +
        |x  + 2x + 2  - 2%i x - 5%i|
   (5)  |                          |
        |              2           |
        +2%i x + 5%i  x  + 8x + 17 +
                             Type: SquareMatrix(2,Polynomial Complex Integer)
--R 
--R
--R        + 2                        +
--R        |x  + 2x + 2  - 2%i x - 5%i|
--R   (5)  |                          |
--R        |              2           |
--R        +2%i x + 5%i  x  + 8x + 17 +
--R                             Type: SquareMatrix(2,Polynomial Complex Integer)
--E 6
)spool
 
Starts dribbling to divisor.output (2010/3/27, 18:25:0).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 18
P0 := UP(x, FRAC INT)
 

   (1)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 18
P1 := UP(y, FRAC P0)
 

   (2)
   UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer))
                                                                 Type: Domain
--R 
--R
--R   (2)
--R   UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer))
--R                                                                 Type: Domain
--E 2

--S 3 of 18
R := RADFF(FRAC INT, P0, P1, 1 + x**8, 2)
 

   (3)
  RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer
  ),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x
  **8+1,2)
                                                                 Type: Domain
--R 
--R
--R   (3)
--R  RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer
--R  ),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x
--R  **8+1,2)
--R                                                                 Type: Domain
--E 3

--S 4 of 18
genus()$R
 

   (4)  3
                                                     Type: NonNegativeInteger
--R 
--R
--R   (4)  3
--R                                                     Type: NonNegativeInteger
--E 4

--S 5 of 18
fd := FDIV(FRAC INT, P0, P1, R)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R 
--R
--R   (5)
--R  FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),Univa
--R  riatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalF
--R  unctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),Univar
--R  iatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R  )
--R                                                                 Type: Domain
--E 5

--S 6 of 18
d1 := divisor(0, 1)$fd
 

   (5)  (x,y - 1)
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R   (6)  (x,y - 1)
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 6

--S 7 of 18
d2 := divisor(0, -1)$fd
 

   (6)  (x,y + 1)
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R   (7)  (x,y + 1)
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 7

--S 8 of 18
d  := d1 - d2
 

        1     2         8
   (7)  - (- x ,- 2y + x  + 2)
        x
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R        1     2         8
--R   (8)  - (- x ,- 2y + x  + 2)
--R        x
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 8

--S 9 of 18
d  := reduce d
 

        1     2         8
   (8)  - (- x ,- 2y + x  + 2)
        x
Type: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--R 
--R
--R        1     2         8
--R   (9)  - (- x ,- 2y + x  + 2)
--R        x
--RType: FiniteDivisor(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2))
--E 9

--S 10 of 18
generator d
 

   (9)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (10)  "failed"
--R                                                    Type: Union("failed",...)
--E 10

--S 11 of 18
generator reduce(2 * d)
 

   (10)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (11)  "failed"
--R                                                    Type: Union("failed",...)
--E 11

--S 12 of 18
generator reduce(3 * d)
 

   (11)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 18
generator reduce(4 * d)
 

            1      1
   (12)  - -- y + --
            4      4
           x      x
Type: Union(RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2),...)
--R 
--R
--R            1      1
--R   (13)  - -- y + --
--R            4      4
--R           x      x
--RType: Union(RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2),...)
--E 13

--S 14 of 18
lSpaceBasis d1
 

   (13)  [- 1]
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R   (14)  [- 1]
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 14

--S 15 of 18
lSpaceBasis(2 * d1)
 

   (14)  [- 1]
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R   (15)  [- 1]
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 15

--S 16 of 18
lSpaceBasis(3 * d1)
 

   (15)  [- 1]
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R   (16)  [- 1]
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 16

--S 17 of 18
lSpaceBasis(4 * d1)
 

           1      1
   (16)  [-- y + --,- 1]
           4      4
          x      x
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R           1      1
--R   (17)  [-- y + --,- 1]
--R           4      4
--R          x      x
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 17

--S 18 of 18
lSpaceBasis(5 * d1)
 

           1      1  1      1
   (17)  [-- y + --,-- y + --,- 1]
           5      5  4      4
          x      x  x      x
Type: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--R 
--R
--R           1      1  1      1
--R   (18)  [-- y + --,-- y + --,- 1]
--R           5      5  4      4
--R          x      x  x      x
--RType: Vector RadicalFunctionField(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),UnivariatePolynomial(y,Fraction UnivariatePolynomial(x,Fraction Integer)),x**8+1,2)
--E 18
)spool
 
Starts dribbling to lodof.output (2010/3/27, 18:28:49).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
)expose LODOF 
 
   LinearOrdinaryDifferentialOperatorFactorizer is now explicitly 
      exposed in frame initial 
--R 
--R   LinearOrdinaryDifferentialOperatorFactorizer is now explicitly 
--R      exposed in frame initial 
--E 1

--S 2 of 16
P := UP(t, AN)
 

   (1)  UnivariatePolynomial(t,AlgebraicNumber)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(t,AlgebraicNumber)
--R                                                                 Type: Domain
--E 2

--S 3 of 16
Q := FRAC P
 

   (2)  Fraction UnivariatePolynomial(t,AlgebraicNumber)
                                                                 Type: Domain
--R 
--R
--R   (2)  Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R                                                                 Type: Domain
--E 3

--S 4 of 16
L := LODO1 Q
 

   (3)
  LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,Algebraic
  Number)
                                                                 Type: Domain
--R 
--R
--R   (3)
--R  LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,Algebraic
--R  Number)
--R                                                                 Type: Domain
--E 4

--S 5 of 16
d := D()$L
 

   (4)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (4)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 5

--S 6 of 16
t := t::P::Q
 

   (5)  t
                       Type: Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (5)  t
--R                       Type: Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 6

--S 7 of 16
op := d**2 + t * d + 1
 

         2
   (6)  D  + t D + 1
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R         2
--R   (6)  D  + t D + 1
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 7

--S 8 of 16
factor op
 

   (7)  [D,D + t]
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (7)  [D,D + t]
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 8

--S 9 of 16
op := 2*t**3 * d**2 + 3*t**2 * d - 2
 

          3 2     2
   (8)  2t D  + 3t D - 2
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R          3 2     2
--R   (8)  2t D  + 3t D - 2
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 9

--S 10 of 16
factor op
 

           3 2     2
   (9)  [2t D  + 3t D - 2]
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           3 2     2
--R   (9)  [2t D  + 3t D - 2]
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 10

--S 11 of 16
op := 2*t**3 * d**3 - (2*t**4 - 9*t**2) * d**2 - (3*t**3 - 6*t + 2) * d + 2*t
 

           3 3        4     2  2        3
   (10)  2t D  + (- 2t  + 9t )D  + (- 3t  + 6t - 2)D + 2t
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           3 3        4     2  2        3
--R   (10)  2t D  + (- 2t  + 9t )D  + (- 3t  + 6t - 2)D + 2t
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 11

--S 12 of 16
factor op
 

                      3 2        4     2       5      3
   (11)  [- D + t,- 2t D  + (- 8t  - 3t )D - 8t  - 10t  + 2]
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R                      3 2        4     2       5      3
--R   (11)  [- D + t,- 2t D  + (- 8t  - 3t )D - 8t  - 10t  + 2]
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 12

--S 13 of 16
op := (t**9 + t**3) * d**3 + 18 * t**8 * d**2 - 90 * t * d - 30 * (11*t**6-3)
 

           9    3  3      8 2               6
   (12)  (t  + t )D  + 18t D  - 90t D - 330t  + 90
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           9    3  3      8 2               6
--R   (12)  (t  + t )D  + 18t D  - 90t D - 330t  + 90
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 13

--S 14 of 16
factor op
 

   (13)
                                                          +--+      6    +--+
      9    3         +--+      8       +--+      2      (\|91  + 6)t  + \|91
   [(t  + t )D + (- \|91  + 7)t  + (- \|91  + 1)t , D + ---------------------,
                                                                 7
                                                                t  + t
          6
        5t  - 1
    D + -------]
          7
         t  + t
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R   (13)
--R                                                          +--+      6    +--+
--R      9    3         +--+      8       +--+      2      (\|91  + 6)t  + \|91
--R   [(t  + t )D + (- \|91  + 7)t  + (- \|91  + 1)t , D + ---------------------,
--R                                                                 7
--R                                                                t  + t
--R          6
--R        5t  - 1
--R    D + -------]
--R          7
--R         t  + t
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 14

--S 15 of 16
op := d**3 + 2 * d**2 + 5 / t * d + 7 / t**2
 

          3     2   5      7
   (14)  D  + 2D  + - D + --
                    t      2
                          t
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R          3     2   5      7
--R   (14)  D  + 2D  + - D + --
--R                    t      2
--R                          t
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 15

--S 16 of 16
factor op
 

           3     2   5      7
   (15)  [D  + 2D  + - D + --]
                     t      2
                           t
Type: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--R 
--R
--R           3     2   5      7
--R   (15)  [D  + 2D  + - D + --]
--R                     t      2
--R                           t
--RType: List LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(t,AlgebraicNumber)
--E 16
)spool 
 
Starts dribbling to schaum24.output (2010/3/27, 18:38:27).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 146
aa:=integrate(asin(x/a),x)
 

                    +---------+
                    |   2    2       +---------+
                 2x\|- x  + a        |   2    2
        - x atan(--------------) + 2\|- x  + a
                      2    2
                    2x  - a
   (1)  ----------------------------------------
                            2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +---------+
--R                    |   2    2       +---------+
--R                 2x\|- x  + a        |   2    2
--R        - x atan(--------------) + 2\|- x  + a
--R                      2    2
--R                    2x  - a
--R   (1)  ----------------------------------------
--R                            2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 146
bb:=s+asin(x/a)+sqrt(a^2-x^2)
 

         +---------+
         |   2    2         x
   (2)  \|- x  + a   + asin(-) + s
                            a
                                                     Type: Expression Integer
--R
--R         +---------+
--R         |   2    2         x
--R   (2)  \|- x  + a   + asin(-) + s
--R                            a
--R                                                     Type: Expression Integer
--E

--S 3 of 146      14:471 Axiom cannot simplify this expression
cc:=aa-bb
 

                    +---------+
                    |   2    2
                 2x\|- x  + a            x
        - x atan(--------------) - 2asin(-) - 2s
                      2    2             a
                    2x  - a
   (3)  ----------------------------------------
                            2
                                                     Type: Expression Integer
--R
--R                    +---------+
--R                    |   2    2
--R                 2x\|- x  + a            x
--R        - x atan(--------------) - 2asin(-) - 2s
--R                      2    2             a
--R                    2x  - a
--R   (3)  ----------------------------------------
--R                            2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 4 of 146
aa:=integrate(x*asin(x/a),x)
 

                            +---------+
                            |   2    2        +---------+
             2    2      2x\|- x  + a         |   2    2
        (- 2x  + a )atan(--------------) + 2x\|- x  + a
                              2    2
                            2x  - a
   (1)  -------------------------------------------------
                                8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            +---------+
--R                            |   2    2        +---------+
--R             2    2      2x\|- x  + a         |   2    2
--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
--R                              2    2
--R                            2x  - a
--R   (1)  -------------------------------------------------
--R                                8
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 146
bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
 

          +---------+
          |   2    2       2    2      x
        x\|- x  + a   + (2x  - a )asin(-)
                                       a
   (2)  ---------------------------------
                        4
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2       2    2      x
--R        x\|- x  + a   + (2x  - a )asin(-)
--R                                       a
--R   (2)  ---------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E

--S 6 of 146
cc:=aa-bb
 

                            +---------+
                            |   2    2
             2    2      2x\|- x  + a           2     2      x
        (- 2x  + a )atan(--------------) + (- 4x  + 2a )asin(-)
                              2    2                         a
                            2x  - a
   (3)  -------------------------------------------------------
                                   8
                                                     Type: Expression Integer
--R
--R                            +---------+
--R                            |   2    2
--R             2    2      2x\|- x  + a           2     2      x
--R        (- 2x  + a )atan(--------------) + (- 4x  + 2a )asin(-)
--R                              2    2                         a
--R                            2x  - a
--R   (3)  -------------------------------------------------------
--R                                   8
--R                                                     Type: Expression Integer
--E

)clear all
 
--S 7 of 146
t1:=x*asin(x/a)
 

               x
   (1)  x asin(-)
               a
                                                     Type: Expression Integer
--R
--R               x
--R   (1)  x asin(-)
--R               a
--R                                                     Type: Expression Integer
--E
--S 8 of 146
t2:=integrate(t1,x)
 

                            +---------+
                            |   2    2        +---------+
             2    2      2x\|- x  + a         |   2    2
        (- 2x  + a )atan(--------------) + 2x\|- x  + a
                              2    2
                            2x  - a
   (2)  -------------------------------------------------
                                8
                                          Type: Union(Expression Integer,...)
--R
--R                            +---------+
--R                            |   2    2        +---------+
--R             2    2      2x\|- x  + a         |   2    2
--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
--R                              2    2
--R                            2x  - a
--R   (2)  -------------------------------------------------
--R                                8
--R                                          Type: Union(Expression Integer,...)
--E
--S 9 of 146
t3:=D(t2,x)
 

                    +---------+
                    |   2    2
                 2x\|- x  + a
          x atan(--------------)
                      2    2
                    2x  - a
   (3)  - ----------------------
                     2
                                                     Type: Expression Integer
--R
--R                    +---------+
--R                    |   2    2
--R                 2x\|- x  + a
--R          x atan(--------------)
--R                      2    2
--R                    2x  - a
--R   (3)  - ----------------------
--R                     2
--R                                                     Type: Expression Integer
--E
--S 10 of 146
t4:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
 

          +---------+
          |   2    2       2    2      x
        x\|- x  + a   + (2x  - a )asin(-)
                                       a
   (4)  ---------------------------------
                        4
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2       2    2      x
--R        x\|- x  + a   + (2x  - a )asin(-)
--R                                       a
--R   (4)  ---------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E
--S 11 of 146
t5:=D(t4,x)
 

   (5)
                                           +---------+
                 +---------+               |   2    2               +---------+
              x  |   2    2        2    3  |- x  + a        2    2  |   2    2
   (4a x asin(-)\|- x  + a   - 2a x  + a ) |---------  + (2x  - a )\|- x  + a
              a                            |     2
                                          \|    a
   ----------------------------------------------------------------------------
                                           +---------+
                               +---------+ |   2    2
                               |   2    2  |- x  + a
                            4a\|- x  + a   |---------
                                           |     2
                                          \|    a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                           +---------+
--R                 +---------+               |   2    2               +---------+
--R              x  |   2    2        2    3  |- x  + a        2    2  |   2    2
--R   (4a x asin(-)\|- x  + a   - 2a x  + a ) |---------  + (2x  - a )\|- x  + a
--R              a                            |     2
--R                                          \|    a
--R   ----------------------------------------------------------------------------
--R                                           +---------+
--R                               +---------+ |   2    2
--R                               |   2    2  |- x  + a
--R                            4a\|- x  + a   |---------
--R                                           |     2
--R                                          \|    a
--R                                                     Type: Expression Integer
--E
--S 12 of 146
f:=makeFloatFunction(t1,x,a)
 
   Compiling function %V with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 

   (6)  theMap(MKBCFUNC;binaryFunction;SM;2!0,0)
                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--I   Compiling function %BF with type (DoubleFloat,DoubleFloat) -> 
--R      DoubleFloat 
--R
--I   (6)  theMap(MKBCFUNC;binaryFunction;SM;2!0,120)
--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--E
--S 13 of 146
axiom:=makeFloatFunction(t3,x,a)
 
   Compiling function %X with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 

   (7)  theMap(MKBCFUNC;binaryFunction;SM;2!0,0)
                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--I   Compiling function %BJ with type (DoubleFloat,DoubleFloat) -> 
--R      DoubleFloat 
--R
--I   (7)  theMap(MKBCFUNC;binaryFunction;SM;2!0,996)
--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--E
--S 14 of 146
schaums:=makeFloatFunction(t5,x,a)
 
   Compiling function %Y with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 

   (8)  theMap(MKBCFUNC;binaryFunction;SM;2!0,0)
                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--I   Compiling function %BK with type (DoubleFloat,DoubleFloat) -> 
--R      DoubleFloat 
--R
--I   (8)  theMap(MKBCFUNC;binaryFunction;SM;2!0,62)
--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
--E
--S 15 of 146     14:472 Schaums and Axiom agree (modulo branch cuts)
[ [f(i::Float,i::Float+1.0::Float)::Float,axiom(i::Float,i::Float+1.0::Float)::Float,schaums(i::Float,i::Float+1.0::Float)::Float] for i in 1..4]
 

   (9)
   [[0.5235987755 9829892668,0.5235987755 9829892668,0.5235987755 9829881566],
    [1.4594553124 539326738,1.4594553124 539326738,1.4594553124 539324518],
    [2.5441862369 444430136,- 2.1682027434 402466604,2.5441862369 444430136],
    [3.7091808720 064496363,- 2.5740044351 731374839,3.7091808720 064500804]]
                                                        Type: List List Float
--R
--R   (9)
--R   [[0.5235987755 9829892668,0.5235987755 9829892668,0.5235987755 9829881566],
--R    [1.4594553124 539326738,1.4594553124 539326738,1.4594553124 539324518],
--R    [2.5441862369 444430136,- 2.1682027434 402466604,2.5441862369 444430136],
--R    [3.7091808720 064496363,- 2.5740044351 731374839,3.7091808720 064500804]]
--R                                                        Type: List List Float
--E
)clear all
 

--S 16 of 146
aa:=integrate(x^2*asin(x/a),x)
 

                     +---------+
                     |   2    2                 +---------+
            3     2x\|- x  + a         2     2  |   2    2
        - 3x atan(--------------) + (2x  + 4a )\|- x  + a
                       2    2
                     2x  - a
   (1)  ---------------------------------------------------
                                 18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +---------+
--R                     |   2    2                 +---------+
--R            3     2x\|- x  + a         2     2  |   2    2
--R        - 3x atan(--------------) + (2x  + 4a )\|- x  + a
--R                       2    2
--R                     2x  - a
--R   (1)  ---------------------------------------------------
--R                                 18
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17 of 146
bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9
 

                   +---------+
          2     2  |   2    2      3     x
        (x  + 2a )\|- x  + a   + 3x asin(-)
                                         a
   (2)  -----------------------------------
                         9
                                                     Type: Expression Integer
--R
--R                   +---------+
--R          2     2  |   2    2      3     x
--R        (x  + 2a )\|- x  + a   + 3x asin(-)
--R                                         a
--R   (2)  -----------------------------------
--R                         9
--R                                                     Type: Expression Integer
--E

--S 18 of 146     14:473 Axiom cannot simplify this expression
cc:=aa-bb
 

                    +---------+
                    |   2    2
           3     2x\|- x  + a        3     x
        - x atan(--------------) - 2x asin(-)
                      2    2               a
                    2x  - a
   (3)  -------------------------------------
                          6
                                                     Type: Expression Integer
--R
--R                    +---------+
--R                    |   2    2
--R           3     2x\|- x  + a        3     x
--R        - x atan(--------------) - 2x asin(-)
--R                      2    2               a
--R                    2x  - a
--R   (3)  -------------------------------------
--R                          6
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 146     14:474 Axiom cannot compute this integral
aa:=integrate(asin(x/a)/x,x)
 

                  %K
           x asin(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x asin(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 20 of 146
aa:=integrate(asin(x/a)/x^2,x)
 

   (1)
                                                                   +---------+
            +---------+               +---------+                  |   2    2
            |   2    2                |   2    2                2x\|- x  + a
   - x log(\|- x  + a   + a) + x log(\|- x  + a   - a) + a atan(--------------)
                                                                     2    2
                                                                   2x  - a
   ----------------------------------------------------------------------------
                                       2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                   +---------+
--R            +---------+               +---------+                  |   2    2
--R            |   2    2                |   2    2                2x\|- x  + a
--R   - x log(\|- x  + a   + a) + x log(\|- x  + a   - a) + a atan(--------------)
--R                                                                     2    2
--R                                                                   2x  - a
--R   ----------------------------------------------------------------------------
--R                                       2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21 of 146
bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x)
 

                 +---------+
                 |   2    2
                \|- x  + a   + a           x
        - x log(----------------) - a asin(-)
                        x                  a
   (2)  -------------------------------------
                         a x
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   + a           x
--R        - x log(----------------) - a asin(-)
--R                        x                  a
--R   (2)  -------------------------------------
--R                         a x
--R                                                     Type: Expression Integer
--E

--S 22 of 146     14:475 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                +---------+               +---------+
                |   2    2                |   2    2
       - x log(\|- x  + a   + a) + x log(\|- x  + a   - a)
     + 
               +---------+                  +---------+
               |   2    2                   |   2    2
              \|- x  + a   + a           2x\|- x  + a              x
       2x log(----------------) + a atan(--------------) + 2a asin(-)
                      x                       2    2               a
                                            2x  - a
  /
     2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                +---------+               +---------+
--R                |   2    2                |   2    2
--R       - x log(\|- x  + a   + a) + x log(\|- x  + a   - a)
--R     + 
--R               +---------+                  +---------+
--R               |   2    2                   |   2    2
--R              \|- x  + a   + a           2x\|- x  + a              x
--R       2x log(----------------) + a atan(--------------) + 2a asin(-)
--R                      x                       2    2               a
--R                                            2x  - a
--R  /
--R     2a x
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 23 of 146
aa:=integrate(asin(x/a)^2,x)
 

                  +---------+ 2                        +---------+
                  |   2    2        +---------+        |   2    2
               2x\|- x  + a         |   2    2      2x\|- x  + a
        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
                    2    2                               2    2
                  2x  - a                              2x  - a
   (1)  ----------------------------------------------------------------
                                        4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+ 2                        +---------+
--R                  |   2    2        +---------+        |   2    2
--R               2x\|- x  + a         |   2    2      2x\|- x  + a
--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
--R                    2    2                               2    2
--R                  2x  - a                              2x  - a
--R   (1)  ----------------------------------------------------------------
--R                                        4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 146
bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a)
 

                 +---------+
              x  |   2    2           x 2
   (2)  2asin(-)\|- x  + a   + x asin(-)  - 2x
              a                       a
                                                     Type: Expression Integer
--R
--R                 +---------+
--R              x  |   2    2           x 2
--R   (2)  2asin(-)\|- x  + a   + x asin(-)  - 2x
--R              a                       a
--R                                                     Type: Expression Integer
--E

--S 25 of 146     14:476 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                 +---------+ 2                        +---------+
                 |   2    2        +---------+        |   2    2
              2x\|- x  + a         |   2    2      2x\|- x  + a
       x atan(--------------)  - 4\|- x  + a  atan(--------------)
                   2    2                               2    2
                 2x  - a                              2x  - a
     + 
                  +---------+
               x  |   2    2            x 2
       - 8asin(-)\|- x  + a   - 4x asin(-)
               a                        a
  /
     4
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +---------+ 2                        +---------+
--R                 |   2    2        +---------+        |   2    2
--R              2x\|- x  + a         |   2    2      2x\|- x  + a
--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
--R                   2    2                               2    2
--R                 2x  - a                              2x  - a
--R     + 
--R                  +---------+
--R               x  |   2    2            x 2
--R       - 8asin(-)\|- x  + a   - 4x asin(-)
--R               a                        a
--R  /
--R     4
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 26 of 146
aa:=integrate(acos(x/a),x)
 

                  +---------+
                  |   2    2       +---------+
               2x\|- x  + a        |   2    2
        x atan(--------------) - 2\|- x  + a
                    2    2
                  2x  - a
   (1)  --------------------------------------
                           2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+
--R                  |   2    2       +---------+
--R               2x\|- x  + a        |   2    2
--R        x atan(--------------) - 2\|- x  + a
--R                    2    2
--R                  2x  - a
--R   (1)  --------------------------------------
--R                           2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27 of 146
bb:=x*acos(x/a)-sqrt(a^2-x^2)
 

           +---------+
           |   2    2           x
   (2)  - \|- x  + a   + x acos(-)
                                a
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2           x
--R   (2)  - \|- x  + a   + x acos(-)
--R                                a
--R                                                     Type: Expression Integer
--E

--S 28 of 146     14:477 Axiom cannot simplify this expression
cc:=aa-bb
 

                  +---------+
                  |   2    2
               2x\|- x  + a              x
        x atan(--------------) - 2x acos(-)
                    2    2               a
                  2x  - a
   (3)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2
--R               2x\|- x  + a              x
--R        x atan(--------------) - 2x acos(-)
--R                    2    2               a
--R                  2x  - a
--R   (3)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 29 of 146
aa:=integrate(x*acos(x/a),x)
 

                          +---------+
                          |   2    2        +---------+
           2    2      2x\|- x  + a         |   2    2
        (2x  - a )atan(--------------) - 2x\|- x  + a
                            2    2
                          2x  - a
   (1)  -----------------------------------------------
                               8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +---------+
--R                          |   2    2        +---------+
--R           2    2      2x\|- x  + a         |   2    2
--R        (2x  - a )atan(--------------) - 2x\|- x  + a
--R                            2    2
--R                          2x  - a
--R   (1)  -----------------------------------------------
--R                               8
--R                                          Type: Union(Expression Integer,...)
--E

--S 30 of 146
bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4
 

            +---------+
            |   2    2       2    2      x
        - x\|- x  + a   + (2x  - a )acos(-)
                                         a
   (2)  -----------------------------------
                         4
                                                     Type: Expression Integer
--R
--R            +---------+
--R            |   2    2       2    2      x
--R        - x\|- x  + a   + (2x  - a )acos(-)
--R                                         a
--R   (2)  -----------------------------------
--R                         4
--R                                                     Type: Expression Integer
--E

--S 31 of 146     14:478 Axiom cannot simplify this expression
cc:=aa-bb
 

                          +---------+
                          |   2    2
           2    2      2x\|- x  + a           2     2      x
        (2x  - a )atan(--------------) + (- 4x  + 2a )acos(-)
                            2    2                         a
                          2x  - a
   (3)  -----------------------------------------------------
                                  8
                                                     Type: Expression Integer
--R
--R                          +---------+
--R                          |   2    2
--R           2    2      2x\|- x  + a           2     2      x
--R        (2x  - a )atan(--------------) + (- 4x  + 2a )acos(-)
--R                            2    2                         a
--R                          2x  - a
--R   (3)  -----------------------------------------------------
--R                                  8
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 32 of 146
aa:=integrate(x^2*acos(x/a),x)
 

                   +---------+
                   |   2    2                   +---------+
          3     2x\|- x  + a           2     2  |   2    2
        3x atan(--------------) + (- 2x  - 4a )\|- x  + a
                     2    2
                   2x  - a
   (1)  ---------------------------------------------------
                                 18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +---------+
--R                   |   2    2                   +---------+
--R          3     2x\|- x  + a           2     2  |   2    2
--R        3x atan(--------------) + (- 2x  - 4a )\|- x  + a
--R                     2    2
--R                   2x  - a
--R   (1)  ---------------------------------------------------
--R                                 18
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33 of 146
bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9
 

                     +---------+
            2     2  |   2    2      3     x
        (- x  - 2a )\|- x  + a   + 3x acos(-)
                                           a
   (2)  -------------------------------------
                          9
                                                     Type: Expression Integer
--R
--R                     +---------+
--R            2     2  |   2    2      3     x
--R        (- x  - 2a )\|- x  + a   + 3x acos(-)
--R                                           a
--R   (2)  -------------------------------------
--R                          9
--R                                                     Type: Expression Integer
--E

--S 34 of 146     14:479 Axiom cannot simplify this expression
cc:=aa-bb
 

                  +---------+
                  |   2    2
         3     2x\|- x  + a        3     x
        x atan(--------------) - 2x acos(-)
                    2    2               a
                  2x  - a
   (3)  -----------------------------------
                         6
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2
--R         3     2x\|- x  + a        3     x
--R        x atan(--------------) - 2x acos(-)
--R                    2    2               a
--R                  2x  - a
--R   (3)  -----------------------------------
--R                         6
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 35 of 146     14:480 Axiom cannot compute this integral
aa:=integrate(acos(x/a)/x,x)
 

                  %K
           x acos(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x acos(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 36 of 146
aa:=integrate(acos(x/a)/x^2,x)
 

   (1)
                                                                 +---------+
          +---------+               +---------+                  |   2    2
          |   2    2                |   2    2                2x\|- x  + a
   x log(\|- x  + a   + a) - x log(\|- x  + a   - a) - a atan(--------------)
                                                                   2    2
                                                                 2x  - a
   --------------------------------------------------------------------------
                                      2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                 +---------+
--R          +---------+               +---------+                  |   2    2
--R          |   2    2                |   2    2                2x\|- x  + a
--R   x log(\|- x  + a   + a) - x log(\|- x  + a   - a) - a atan(--------------)
--R                                                                   2    2
--R                                                                 2x  - a
--R   --------------------------------------------------------------------------
--R                                      2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37 of 146
bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x)
 

               +---------+
               |   2    2
              \|- x  + a   + a           x
        x log(----------------) - a acos(-)
                      x                  a
   (2)  -----------------------------------
                        a x
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   + a           x
--R        x log(----------------) - a acos(-)
--R                      x                  a
--R   (2)  -----------------------------------
--R                        a x
--R                                                     Type: Expression Integer
--E

--S 38 of 146     14:481 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
              +---------+               +---------+
              |   2    2                |   2    2
       x log(\|- x  + a   + a) - x log(\|- x  + a   - a)
     + 
                 +---------+                  +---------+
                 |   2    2                   |   2    2
                \|- x  + a   + a           2x\|- x  + a              x
       - 2x log(----------------) - a atan(--------------) + 2a acos(-)
                        x                       2    2               a
                                              2x  - a
  /
     2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R              +---------+               +---------+
--R              |   2    2                |   2    2
--R       x log(\|- x  + a   + a) - x log(\|- x  + a   - a)
--R     + 
--R                 +---------+                  +---------+
--R                 |   2    2                   |   2    2
--R                \|- x  + a   + a           2x\|- x  + a              x
--R       - 2x log(----------------) - a atan(--------------) + 2a acos(-)
--R                        x                       2    2               a
--R                                              2x  - a
--R  /
--R     2a x
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 146
aa:=integrate(acos(x/a)^2,x)
 

                  +---------+ 2                        +---------+
                  |   2    2        +---------+        |   2    2
               2x\|- x  + a         |   2    2      2x\|- x  + a
        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
                    2    2                               2    2
                  2x  - a                              2x  - a
   (1)  ----------------------------------------------------------------
                                        4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +---------+ 2                        +---------+
--R                  |   2    2        +---------+        |   2    2
--R               2x\|- x  + a         |   2    2      2x\|- x  + a
--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
--R                    2    2                               2    2
--R                  2x  - a                              2x  - a
--R   (1)  ----------------------------------------------------------------
--R                                        4
--R                                          Type: Union(Expression Integer,...)
--E

--S 40 of 146
bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a)
 

                   +---------+
                x  |   2    2           x 2
   (2)  - 2acos(-)\|- x  + a   + x acos(-)  - 2x
                a                       a
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                x  |   2    2           x 2
--R   (2)  - 2acos(-)\|- x  + a   + x acos(-)  - 2x
--R                a                       a
--R                                                     Type: Expression Integer
--E

--S 41 of 146     14:482 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                 +---------+ 2                        +---------+
                 |   2    2        +---------+        |   2    2
              2x\|- x  + a         |   2    2      2x\|- x  + a
       x atan(--------------)  - 4\|- x  + a  atan(--------------)
                   2    2                               2    2
                 2x  - a                              2x  - a
     + 
                +---------+
             x  |   2    2            x 2
       8acos(-)\|- x  + a   - 4x acos(-)
             a                        a
  /
     4
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +---------+ 2                        +---------+
--R                 |   2    2        +---------+        |   2    2
--R              2x\|- x  + a         |   2    2      2x\|- x  + a
--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
--R                   2    2                               2    2
--R                 2x  - a                              2x  - a
--R     + 
--R                +---------+
--R             x  |   2    2            x 2
--R       8acos(-)\|- x  + a   - 4x acos(-)
--R             a                        a
--R  /
--R     4
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 42 of 146
aa:=integrate(atan(x/a),x)
 

                 2    2             2a x
        - a log(x  + a ) - x atan(-------)
                                   2    2
                                  x  - a
   (1)  ----------------------------------
                         2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2             2a x
--R        - a log(x  + a ) - x atan(-------)
--R                                   2    2
--R                                  x  - a
--R   (1)  ----------------------------------
--R                         2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 43 of 146
bb:=x*atan(x/a)-a/2*log(x^2+a^2)
 

                 2    2            x
        - a log(x  + a ) + 2x atan(-)
                                   a
   (2)  -----------------------------
                      2
                                                     Type: Expression Integer
--R
--R                 2    2            x
--R        - a log(x  + a ) + 2x atan(-)
--R                                   a
--R   (2)  -----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 44 of 146
cc:=aa-bb
 

                  x             2a x
        - 2x atan(-) - x atan(-------)
                  a            2    2
                              x  - a
   (3)  ------------------------------
                       2
                                                     Type: Expression Integer
--R
--R                  x             2a x
--R        - 2x atan(-) - x atan(-------)
--R                  a            2    2
--R                              x  - a
--R   (3)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E

--S 45 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 46 of 146
dd:=atanrule cc
 

                  2              2
                 x  + 2%i a x - a               - x + %i a
        %i x log(-----------------) + 2%i x log(----------)
                  2              2               x + %i a
                 x  - 2%i a x - a
   (5)  ---------------------------------------------------
                                 4
                                             Type: Expression Complex Integer
--R
--R                  2              2
--R                 x  + 2%i a x - a               - x + %i a
--R        %i x log(-----------------) + 2%i x log(----------)
--R                  2              2               x + %i a
--R                 x  - 2%i a x - a
--R   (5)  ---------------------------------------------------
--R                                 4
--R                                             Type: Expression Complex Integer
--E

--S 47 of 146     14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
ee:=expandLog dd
 

        %i x log(- 1)
   (6)  -------------
              2
                                             Type: Expression Complex Integer
--R
--R        %i x log(- 1)
--R   (6)  -------------
--R              2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 48 of 146     14:484 Axiom cannot compute this integral
aa:=integrate(x*tan(x/a),x)
 

           x
         ++         %K
   (1)   |   %K tan(--)d%K
        ++           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++         %H
--I   (1)   |   %H tan(--)d%H
--R        ++           a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 49 of 146
aa:=integrate(x^2*atan(x/a),x)
 

         3     2    2     3       2a x        2
        a log(x  + a ) - x atan(-------) - a x
                                 2    2
                                x  - a
   (1)  ---------------------------------------
                           6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         3     2    2     3       2a x        2
--R        a log(x  + a ) - x atan(-------) - a x
--R                                 2    2
--R                                x  - a
--R   (1)  ---------------------------------------
--R                           6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50 of 146
bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2)
 

         3     2    2      3     x       2
        a log(x  + a ) + 3x atan(-) - a x
                                 a
   (2)  ----------------------------------
                         6
                                                     Type: Expression Integer
--R
--R         3     2    2      3     x       2
--R        a log(x  + a ) + 3x atan(-) - a x
--R                                 a
--R   (2)  ----------------------------------
--R                         6
--R                                                     Type: Expression Integer
--E

--S 51 of 146     14:485 Axiom cannot simplify this expression
cc:=aa-bb
 

            3     x     3       2a x
        - 3x atan(-) - x atan(-------)
                  a            2    2
                              x  - a
   (3)  ------------------------------
                       6
                                                     Type: Expression Integer
--R
--R            3     x     3       2a x
--R        - 3x atan(-) - x atan(-------)
--R                  a            2    2
--R                              x  - a
--R   (3)  ------------------------------
--R                       6
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 52 of 146     14:486 Axiom cannot compute this integral
aa:=integrate(atan(x/a)/x,x)
 

                  %K
           x atan(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x atan(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 53 of 146
aa:=integrate(atan(x/a)/x^2,x)
 

                 2    2                         2a x
        - x log(x  + a ) + 2x log(x) + a atan(-------)
                                               2    2
                                              x  - a
   (1)  ----------------------------------------------
                             2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2                         2a x
--R        - x log(x  + a ) + 2x log(x) + a atan(-------)
--R                                               2    2
--R                                              x  - a
--R   (1)  ----------------------------------------------
--R                             2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54 of 146
bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2)
 

                 2    2
                x  + a             x
        - x log(-------) - 2a atan(-)
                    2              a
                   x
   (2)  -----------------------------
                     2a x
                                                     Type: Expression Integer
--R
--R                 2    2
--R                x  + a             x
--R        - x log(-------) - 2a atan(-)
--R                    2              a
--R                   x
--R   (2)  -----------------------------
--R                     2a x
--R                                                     Type: Expression Integer
--E

--S 55 of 146
cc:=aa-bb
 

   (3)
                                         2    2
            2    2                      x  + a             x             2a x
   - x log(x  + a ) + 2x log(x) + x log(-------) + 2a atan(-) + a atan(-------)
                                            2              a            2    2
                                           x                           x  - a
   ----------------------------------------------------------------------------
                                       2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                         2    2
--R            2    2                      x  + a             x             2a x
--R   - x log(x  + a ) + 2x log(x) + x log(-------) + 2a atan(-) + a atan(-------)
--R                                            2              a            2    2
--R                                           x                           x  - a
--R   ----------------------------------------------------------------------------
--R                                       2a x
--R                                                     Type: Expression Integer
--E

--S 56 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 57 of 146
dd:=atanrule cc
 

   (5)
                                                 2              2
                 2    2                         x  + 2%i a x - a
       - 2x log(x  + a ) + 4x log(x) - %i a log(-----------------)
                                                 2              2
                                                x  - 2%i a x - a
     + 
               2    2
              x  + a               - x + %i a
       2x log(-------) - 2%i a log(----------)
                  2                 x + %i a
                 x
  /
     4a x
                                             Type: Expression Complex Integer
--R
--R   (5)
--R                                                 2              2
--R                 2    2                         x  + 2%i a x - a
--R       - 2x log(x  + a ) + 4x log(x) - %i a log(-----------------)
--R                                                 2              2
--R                                                x  - 2%i a x - a
--R     + 
--R               2    2
--R              x  + a               - x + %i a
--R       2x log(-------) - 2%i a log(----------)
--R                  2                 x + %i a
--R                 x
--R  /
--R     4a x
--R                                             Type: Expression Complex Integer
--E

--S 58 of 146     14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
ee:=expandLog dd
 

          %i log(- 1)
   (6)  - -----------
               2x
                                             Type: Expression Complex Integer
--R
--R          %i log(- 1)
--R   (6)  - -----------
--R               2x
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 59 of 146
aa:=integrate(acot(x/a),x)
 

               2    2             2a x
        a log(x  + a ) + x atan(-------)
                                 2    2
                                x  - a
   (1)  --------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2             2a x
--R        a log(x  + a ) + x atan(-------)
--R                                 2    2
--R                                x  - a
--R   (1)  --------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E

--S 60 of 146
bb:=x*acot(x/a)+a/2*log(x^2+a^2)
 

               2    2            x
        a log(x  + a ) + 2x acot(-)
                                 a
   (2)  ---------------------------
                     2
                                                     Type: Expression Integer
--R
--R               2    2            x
--R        a log(x  + a ) + 2x acot(-)
--R                                 a
--R   (2)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 

--S 61 of 146
cc:=aa-bb
 

                 2a x             x
        x atan(-------) - 2x acot(-)
                2    2            a
               x  - a
   (3)  ----------------------------
                      2
                                                     Type: Expression Integer
--R
--R                 2a x             x
--R        x atan(-------) - 2x acot(-)
--R                2    2            a
--R               x  - a
--R   (3)  ----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 62 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 63 of 146
dd:=atanrule cc
 

                    2              2
                   x  + 2%i a x - a             x
        - %i x log(-----------------) - 4x acot(-)
                    2              2            a
                   x  - 2%i a x - a
   (5)  ------------------------------------------
                             4
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R                   x  + 2%i a x - a             x
--R        - %i x log(-----------------) - 4x acot(-)
--R                    2              2            a
--R                   x  - 2%i a x - a
--R   (5)  ------------------------------------------
--R                             4
--R                                             Type: Expression Complex Integer
--E

--S 64 of 146
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (6)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (6)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 65 of 146
ee:=acotrule dd
 

                    2              2
                   x  + 2%i a x - a               x + %i a
        - %i x log(-----------------) + 2%i x log(--------)
                    2              2              x - %i a
                   x  - 2%i a x - a
   (7)  ---------------------------------------------------
                                 4
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R                   x  + 2%i a x - a               x + %i a
--R        - %i x log(-----------------) + 2%i x log(--------)
--R                    2              2              x - %i a
--R                   x  - 2%i a x - a
--R   (7)  ---------------------------------------------------
--R                                 4
--R                                             Type: Expression Complex Integer
--E

--S 66 of 146     14:488 Axiom and Schaums agree
ff:=expandLog %
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 67 of 146
aa:=integrate(x*acot(x/a),x)
 

          2    2        2a x
        (x  + a )atan(-------) + 2a x
                       2    2
                      x  - a
   (1)  -----------------------------
                      4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2        2a x
--R        (x  + a )atan(-------) + 2a x
--R                       2    2
--R                      x  - a
--R   (1)  -----------------------------
--R                      4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68 of 146
bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2
 

          2    2      x
        (x  + a )acot(-) + a x
                      a
   (2)  ----------------------
                   2
                                                     Type: Expression Integer
--R
--R          2    2      x
--R        (x  + a )acot(-) + a x
--R                      a
--R   (2)  ----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 69 of 146
cc:=aa-bb
 

          2    2        2a x          2     2      x
        (x  + a )atan(-------) + (- 2x  - 2a )acot(-)
                       2    2                      a
                      x  - a
   (3)  ---------------------------------------------
                              4
                                                     Type: Expression Integer
--R
--R          2    2        2a x          2     2      x
--R        (x  + a )atan(-------) + (- 2x  - 2a )acot(-)
--R                       2    2                      a
--R                      x  - a
--R   (3)  ---------------------------------------------
--R                              4
--R                                                     Type: Expression Integer
--E

--S 70 of 146
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (4)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (4)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 71 of 146
dd:=acotrule cc
 

             2       2     x + %i a      2    2        2a x
        (%i x  + %i a )log(--------) + (x  + a )atan(-------)
                           x - %i a                   2    2
                                                     x  - a
   (5)  -----------------------------------------------------
                                  4
                                             Type: Expression Complex Integer
--R
--R             2       2     x + %i a      2    2        2a x
--R        (%i x  + %i a )log(--------) + (x  + a )atan(-------)
--R                           x - %i a                   2    2
--R                                                     x  - a
--R   (5)  -----------------------------------------------------
--R                                  4
--R                                             Type: Expression Complex Integer
--E

--S 72 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 73 of 146
ee:=atanrule dd
 

   (7)
                         2              2
          2       2     x  + 2%i a x - a           2        2     x + %i a
   (- %i x  - %i a )log(-----------------) + (2%i x  + 2%i a )log(--------)
                         2              2                         x - %i a
                        x  - 2%i a x - a
   ------------------------------------------------------------------------
                                       8
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                         2              2
--R          2       2     x  + 2%i a x - a           2        2     x + %i a
--R   (- %i x  - %i a )log(-----------------) + (2%i x  + 2%i a )log(--------)
--R                         2              2                         x - %i a
--R                        x  - 2%i a x - a
--R   ------------------------------------------------------------------------
--R                                       8
--R                                             Type: Expression Complex Integer
--E

--S 74 of 146     14:489 Axiom and Schaums agree
ff:=expandLog ee
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 75 of 146
aa:=integrate(x^2*acot(x/a),x)
 

           3     2    2     3       2a x        2
        - a log(x  + a ) + x atan(-------) + a x
                                   2    2
                                  x  - a
   (1)  -----------------------------------------
                            6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           3     2    2     3       2a x        2
--R        - a log(x  + a ) + x atan(-------) + a x
--R                                   2    2
--R                                  x  - a
--R   (1)  -----------------------------------------
--R                            6
--R                                          Type: Union(Expression Integer,...)
--E

--S 76 of 146
bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2)
 

           3     2    2      3     x       2
        - a log(x  + a ) + 2x acot(-) + a x
                                   a
   (2)  ------------------------------------
                          6
                                                     Type: Expression Integer
--R
--R           3     2    2      3     x       2
--R        - a log(x  + a ) + 2x acot(-) + a x
--R                                   a
--R   (2)  ------------------------------------
--R                          6
--R                                                     Type: Expression Integer
--E 

--S 77 of 146
cc:=aa-bb
 

         3       2a x       3     x
        x atan(-------) - 2x acot(-)
                2    2            a
               x  - a
   (3)  ----------------------------
                      6
                                                     Type: Expression Integer
--R
--R         3       2a x       3     x
--R        x atan(-------) - 2x acot(-)
--R                2    2            a
--R               x  - a
--R   (3)  ----------------------------
--R                      6
--R                                                     Type: Expression Integer
--E

--S 78 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 79 of 146
dd:=atanrule cc
 

                    2              2
              3    x  + 2%i a x - a       3     x
        - %i x log(-----------------) - 4x acot(-)
                    2              2            a
                   x  - 2%i a x - a
   (5)  ------------------------------------------
                            12
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R              3    x  + 2%i a x - a       3     x
--R        - %i x log(-----------------) - 4x acot(-)
--R                    2              2            a
--R                   x  - 2%i a x - a
--R   (5)  ------------------------------------------
--R                            12
--R                                             Type: Expression Complex Integer
--E

--S 80 of 146
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (6)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (6)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 81 of 146
ee:=acotrule dd
 

                    2              2
              3    x  + 2%i a x - a          3    x + %i a
        - %i x log(-----------------) + 2%i x log(--------)
                    2              2              x - %i a
                   x  - 2%i a x - a
   (7)  ---------------------------------------------------
                                 12
                                             Type: Expression Complex Integer
--R
--R                    2              2
--R              3    x  + 2%i a x - a          3    x + %i a
--R        - %i x log(-----------------) + 2%i x log(--------)
--R                    2              2              x - %i a
--R                   x  - 2%i a x - a
--R   (7)  ---------------------------------------------------
--R                                 12
--R                                             Type: Expression Complex Integer
--E

--S 82 of 146     14:490 Axiom and Schaums agree
ff:=expandLog ee
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 83 of 146     14:491 Axiom cannot compute this integral
aa:=integrate(acot(x/a)/x,x)
 

                  %K
           x acot(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x acot(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 84 of 146
aa:=integrate(acot(x/a)/x^2,x)
 

               2    2                         2a x
        x log(x  + a ) - 2x log(x) - a atan(-------)
                                             2    2
                                            x  - a
   (1)  --------------------------------------------
                            2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2                         2a x
--R        x log(x  + a ) - 2x log(x) - a atan(-------)
--R                                             2    2
--R                                            x  - a
--R   (1)  --------------------------------------------
--R                            2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 85 of 146
bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2)
 

               2    2
              x  + a             x
        x log(-------) - 2a acot(-)
                  2              a
                 x
   (2)  ---------------------------
                    2a x
                                                     Type: Expression Integer
--R
--R               2    2
--R              x  + a             x
--R        x log(-------) - 2a acot(-)
--R                  2              a
--R                 x
--R   (2)  ---------------------------
--R                    2a x
--R                                                     Type: Expression Integer
--E

--S 86 of 146
cc:=aa-bb
 

   (3)
                                       2    2
          2    2                      x  + a              2a x             x
   x log(x  + a ) - 2x log(x) - x log(-------) - a atan(-------) + 2a acot(-)
                                          2              2    2            a
                                         x              x  - a
   --------------------------------------------------------------------------
                                      2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                       2    2
--R          2    2                      x  + a              2a x             x
--R   x log(x  + a ) - 2x log(x) - x log(-------) - a atan(-------) + 2a acot(-)
--R                                          2              2    2            a
--R                                         x              x  - a
--R   --------------------------------------------------------------------------
--R                                      2a x
--R                                                     Type: Expression Integer
--E

--S 87 of 146
acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 

                            x + %i
                     %i log(------)
                            x - %i
   (4)  acot(x) == - --------------
                            2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            x + %i
--R                     %i log(------)
--R                            x - %i
--R   (4)  acot(x) == - --------------
--R                            2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 88 of 146
dd:=acotrule cc
 

   (5)
                                                                2    2
              2    2                         x + %i a          x  + a
       x log(x  + a ) - 2x log(x) - %i a log(--------) - x log(-------)
                                             x - %i a              2
                                                                  x
     + 
                  2a x
       - a atan(-------)
                 2    2
                x  - a
  /
     2a x
                                             Type: Expression Complex Integer
--R
--R   (5)
--R                                                                2    2
--R              2    2                         x + %i a          x  + a
--R       x log(x  + a ) - 2x log(x) - %i a log(--------) - x log(-------)
--R                                             x - %i a              2
--R                                                                  x
--R     + 
--R                  2a x
--R       - a atan(-------)
--R                 2    2
--R                x  - a
--R  /
--R     2a x
--R                                             Type: Expression Complex Integer
--E

--S 89 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 90 of 146
ee:=atanrule dd
 

   (7)
                                               2              2
               2    2                         x  + 2%i a x - a
       2x log(x  + a ) - 4x log(x) + %i a log(-----------------)
                                               2              2
                                              x  - 2%i a x - a
     + 
                                       2    2
                   x + %i a           x  + a
       - 2%i a log(--------) - 2x log(-------)
                   x - %i a               2
                                         x
  /
     4a x
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                                               2              2
--R               2    2                         x  + 2%i a x - a
--R       2x log(x  + a ) - 4x log(x) + %i a log(-----------------)
--R                                               2              2
--R                                              x  - 2%i a x - a
--R     + 
--R                                       2    2
--R                   x + %i a           x  + a
--R       - 2%i a log(--------) - 2x log(-------)
--R                   x - %i a               2
--R                                         x
--R  /
--R     4a x
--R                                             Type: Expression Complex Integer
--E

--S 91 of 146     14:492 Schaums and Axiom agree
ff:=expandLog ee
 

   (8)  0
                                             Type: Expression Complex Integer
--R
--R   (8)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 92 of 146
aa:=integrate(asec(x/a),x)
 

   (1)
                          +---------+              +---------+
                      +-+ |   2    2               |   2    2
           +-+     2x\|2 \|- x  + a             2a\|- x  + a
       - a\|2 atan(------------------) + x atan(--------------)
                          2     2                      2
                        3x  - 2a                      x
     + 
                       x
       - 2a atan(------------)
                  +---------+
                  |   2    2
                 \|- x  + a
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                          +---------+              +---------+
--R                      +-+ |   2    2               |   2    2
--R           +-+     2x\|2 \|- x  + a             2a\|- x  + a
--R       - a\|2 atan(------------------) + x atan(--------------)
--R                          2     2                      2
--R                        3x  - 2a                      x
--R     + 
--R                       x
--R       - 2a atan(------------)
--R                  +---------+
--R                  |   2    2
--R                 \|- x  + a
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 93 of 146
bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2))
 

                 +-------+
                 | 2    2                x
   (2)  - a log(\|x  - a   + x) + x asec(-)
                                         a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2                x
--R   (2)  - a log(\|x  - a   + x) + x asec(-)
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 94 of 146
bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2))
 

               +-------+
               | 2    2                x
   (3)  a log(\|x  - a   + x) + x asec(-)
                                       a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2                x
--R   (3)  a log(\|x  - a   + x) + x asec(-)
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 95 of 146
cc1:=aa-bb1
 

   (4)
                                                 +---------+
               +-------+                     +-+ |   2    2
               | 2    2           +-+     2x\|2 \|- x  + a
       2a log(\|x  - a   + x) - a\|2 atan(------------------)
                                                 2     2
                                               3x  - 2a
     + 
                 +---------+
                 |   2    2
              2a\|- x  + a                    x                 x
       x atan(--------------) - 2a atan(------------) - 2x asec(-)
                     2                   +---------+            a
                    x                    |   2    2
                                        \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                 +---------+
--R               +-------+                     +-+ |   2    2
--R               | 2    2           +-+     2x\|2 \|- x  + a
--R       2a log(\|x  - a   + x) - a\|2 atan(------------------)
--R                                                 2     2
--R                                               3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2
--R              2a\|- x  + a                    x                 x
--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
--R                     2                   +---------+            a
--R                    x                    |   2    2
--R                                        \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 96 of 146     14:493 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                                   +---------+
                 +-------+                     +-+ |   2    2
                 | 2    2           +-+     2x\|2 \|- x  + a
       - 2a log(\|x  - a   + x) - a\|2 atan(------------------)
                                                   2     2
                                                 3x  - 2a
     + 
                 +---------+
                 |   2    2
              2a\|- x  + a                    x                 x
       x atan(--------------) - 2a atan(------------) - 2x asec(-)
                     2                   +---------+            a
                    x                    |   2    2
                                        \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                   +---------+
--R                 +-------+                     +-+ |   2    2
--R                 | 2    2           +-+     2x\|2 \|- x  + a
--R       - 2a log(\|x  - a   + x) - a\|2 atan(------------------)
--R                                                   2     2
--R                                                 3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2
--R              2a\|- x  + a                    x                 x
--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
--R                     2                   +---------+            a
--R                    x                    |   2    2
--R                                        \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 97 of 146
aa:=integrate(x*asec(x/a),x)
 

                          +---------+
                          |   2    2        +---------+
          2     2      2a\|- x  + a         |   2    2
        (x  - 2a )atan(--------------) + 2a\|- x  + a
                              2
                             x
   (1)  -----------------------------------------------
                               4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +---------+
--R                          |   2    2        +---------+
--R          2     2      2a\|- x  + a         |   2    2
--R        (x  - 2a )atan(--------------) + 2a\|- x  + a
--R                              2
--R                             x
--R   (1)  -----------------------------------------------
--R                               4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 98 of 146
bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2
 

            +-------+
            | 2    2     2     x
        - a\|x  - a   + x asec(-)
                               a
   (2)  -------------------------
                    2
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2     x
--R        - a\|x  - a   + x asec(-)
--R                               a
--R   (2)  -------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 99 of 146
bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2
 

          +-------+
          | 2    2     2     x
        a\|x  - a   + x asec(-)
                             a
   (3)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2     x
--R        a\|x  - a   + x asec(-)
--R                             a
--R   (3)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 100 of 146
cc1:=aa-bb1
 

   (4)
                     +---------+
                     |   2    2        +-------+      +---------+
     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (x  - 2a )atan(--------------) + 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
                         2                                                  a
                        x
   ---------------------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R   (4)
--R                     +---------+
--R                     |   2    2        +-------+      +---------+
--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (x  - 2a )atan(--------------) + 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
--R                         2                                                  a
--R                        x
--R   ---------------------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 101 of 146    14:494 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                     +---------+
                     |   2    2        +-------+      +---------+
     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (x  - 2a )atan(--------------) - 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
                         2                                                  a
                        x
   ---------------------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R   (5)
--R                     +---------+
--R                     |   2    2        +-------+      +---------+
--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (x  - 2a )atan(--------------) - 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
--R                         2                                                  a
--R                        x
--R   ---------------------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 102 of 146
aa:=integrate(x^2*asec(x/a),x)
 

   (1)
                            +---------+              +---------+
                        +-+ |   2    2               |   2    2
           3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
       - 2a \|2 atan(------------------) + x atan(--------------)
                            2     2                      2
                          3x  - 2a                      x
     + 
                                     +---------+
           3           x             |   2    2
       - 5a atan(------------) + a x\|- x  + a
                  +---------+
                  |   2    2
                 \|- x  + a
  /
     6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                            +---------+              +---------+
--R                        +-+ |   2    2               |   2    2
--R           3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
--R       - 2a \|2 atan(------------------) + x atan(--------------)
--R                            2     2                      2
--R                          3x  - 2a                      x
--R     + 
--R                                     +---------+
--R           3           x             |   2    2
--R       - 5a atan(------------) + a x\|- x  + a
--R                  +---------+
--R                  |   2    2
--R                 \|- x  + a
--R  /
--R     6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103 of 146
bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 

                 +-------+            +-------+
           3     | 2    2             | 2    2      3     x
        - a log(\|x  - a   + x) - a x\|x  - a   + 2x asec(-)
                                                          a
   (2)  ----------------------------------------------------
                                  6
                                                     Type: Expression Integer
--R
--R                 +-------+            +-------+
--R           3     | 2    2             | 2    2      3     x
--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x asec(-)
--R                                                          a
--R   (2)  ----------------------------------------------------
--R                                  6
--R                                                     Type: Expression Integer
--E

--S 104 of 146
bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 

               +-------+            +-------+
         3     | 2    2             | 2    2      3     x
        a log(\|x  - a   + x) + a x\|x  - a   + 2x asec(-)
                                                        a
   (3)  --------------------------------------------------
                                 6
                                                     Type: Expression Integer
--R
--R               +-------+            +-------+
--R         3     | 2    2             | 2    2      3     x
--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x asec(-)
--R                                                        a
--R   (3)  --------------------------------------------------
--R                                 6
--R                                                     Type: Expression Integer
--E

--S 105 of 146
cc1:=aa-bb1
 

   (4)
                                                  +---------+
              +-------+                       +-+ |   2    2
        3     | 2    2           3 +-+     2x\|2 \|- x  + a
       a log(\|x  - a   + x) - 2a \|2 atan(------------------)
                                                  2     2
                                                3x  - 2a
     + 
                 +---------+
                 |   2    2                                 +-------+
        3     2a\|- x  + a        3           x             | 2    2
       x atan(--------------) - 5a atan(------------) + a x\|x  - a
                     2                   +---------+
                    x                    |   2    2
                                        \|- x  + a
     + 
           +---------+
           |   2    2      3     x
       a x\|- x  + a   - 2x asec(-)
                                 a
  /
     6
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                  +---------+
--R              +-------+                       +-+ |   2    2
--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       a log(\|x  - a   + x) - 2a \|2 atan(------------------)
--R                                                  2     2
--R                                                3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2                                 +-------+
--R        3     2a\|- x  + a        3           x             | 2    2
--R       x atan(--------------) - 5a atan(------------) + a x\|x  - a
--R                     2                   +---------+
--R                    x                    |   2    2
--R                                        \|- x  + a
--R     + 
--R           +---------+
--R           |   2    2      3     x
--R       a x\|- x  + a   - 2x asec(-)
--R                                 a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E

--S 106 of 146     14:495 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                                    +---------+
                +-------+                       +-+ |   2    2
          3     | 2    2           3 +-+     2x\|2 \|- x  + a
       - a log(\|x  - a   + x) - 2a \|2 atan(------------------)
                                                    2     2
                                                  3x  - 2a
     + 
                 +---------+
                 |   2    2                                 +-------+
        3     2a\|- x  + a        3           x             | 2    2
       x atan(--------------) - 5a atan(------------) - a x\|x  - a
                     2                   +---------+
                    x                    |   2    2
                                        \|- x  + a
     + 
           +---------+
           |   2    2      3     x
       a x\|- x  + a   - 2x asec(-)
                                 a
  /
     6
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                    +---------+
--R                +-------+                       +-+ |   2    2
--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       - a log(\|x  - a   + x) - 2a \|2 atan(------------------)
--R                                                    2     2
--R                                                  3x  - 2a
--R     + 
--R                 +---------+
--R                 |   2    2                                 +-------+
--R        3     2a\|- x  + a        3           x             | 2    2
--R       x atan(--------------) - 5a atan(------------) - a x\|x  - a
--R                     2                   +---------+
--R                    x                    |   2    2
--R                                        \|- x  + a
--R     + 
--R           +---------+
--R           |   2    2      3     x
--R       a x\|- x  + a   - 2x asec(-)
--R                                 a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 107 of 146    14:496 Axiom cannot compute this integral
aa:=integrate(asec(x/a)/x,x)
 

                  %K
           x asec(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x asec(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 108 of 146
aa:=integrate(asec(x/a)/x^2,x)
 

                      +---------+                 +---------+
                  +-+ |   2    2                  |   2    2
               2x\|2 \|- x  + a        +-+     2a\|- x  + a
        x atan(------------------) - a\|2 atan(--------------)
                      2     2                         2
                    3x  - 2a                         x
   (1)  ------------------------------------------------------
                                    +-+
                               2a x\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      +---------+                 +---------+
--R                  +-+ |   2    2                  |   2    2
--R               2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R        x atan(------------------) - a\|2 atan(--------------)
--R                      2     2                         2
--R                    3x  - 2a                         x
--R   (1)  ------------------------------------------------------
--R                                    +-+
--R                               2a x\|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 109 of 146
bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x)
 

         +-------+
         | 2    2           x
        \|x  - a   - a asec(-)
                            a
   (2)  ----------------------
                  a x
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2           x
--R        \|x  - a   - a asec(-)
--R                            a
--R   (2)  ----------------------
--R                  a x
--R                                                     Type: Expression Integer
--E

--S 110 of 146
bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x)
 

           +-------+
           | 2    2           x
        - \|x  - a   - a asec(-)
                              a
   (3)  ------------------------
                   a x
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2           x
--R        - \|x  - a   - a asec(-)
--R                              a
--R   (3)  ------------------------
--R                   a x
--R                                                     Type: Expression Integer
--E

--S 111 of 146
cc1:=aa-bb1
 

   (4)
                     +---------+                 +---------+
                 +-+ |   2    2                  |   2    2           +-------+
              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
       x atan(------------------) - a\|2 atan(--------------) - 2\|2 \|x  - a
                     2     2                         2
                   3x  - 2a                         x
     + 
          +-+     x
       2a\|2 asec(-)
                  a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (4)
--R                     +---------+                 +---------+
--R                 +-+ |   2    2                  |   2    2           +-------+
--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
--R       x atan(------------------) - a\|2 atan(--------------) - 2\|2 \|x  - a
--R                     2     2                         2
--R                   3x  - 2a                         x
--R     + 
--R          +-+     x
--R       2a\|2 asec(-)
--R                  a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E

--S 112 of 146    14:497 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                     +---------+                 +---------+
                 +-+ |   2    2                  |   2    2           +-------+
              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
       x atan(------------------) - a\|2 atan(--------------) + 2\|2 \|x  - a
                     2     2                         2
                   3x  - 2a                         x
     + 
          +-+     x
       2a\|2 asec(-)
                  a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (5)
--R                     +---------+                 +---------+
--R                 +-+ |   2    2                  |   2    2           +-------+
--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
--R       x atan(------------------) - a\|2 atan(--------------) + 2\|2 \|x  - a
--R                     2     2                         2
--R                   3x  - 2a                         x
--R     + 
--R          +-+     x
--R       2a\|2 asec(-)
--R                  a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 113 of 146
aa:=integrate(acsc(x/a),x)
 

   (1)
                        +---------+              +---------+
                    +-+ |   2    2               |   2    2
         +-+     2x\|2 \|- x  + a             2a\|- x  + a
       a\|2 atan(------------------) - x atan(--------------)
                        2     2                      2
                      3x  - 2a                      x
     + 
                     x
       2a atan(------------)
                +---------+
                |   2    2
               \|- x  + a
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                        +---------+              +---------+
--R                    +-+ |   2    2               |   2    2
--R         +-+     2x\|2 \|- x  + a             2a\|- x  + a
--R       a\|2 atan(------------------) - x atan(--------------)
--R                        2     2                      2
--R                      3x  - 2a                      x
--R     + 
--R                     x
--R       2a atan(------------)
--R                +---------+
--R                |   2    2
--R               \|- x  + a
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 114 of 146
bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2))
 

               +-------+
               | 2    2                x
   (2)  a log(\|x  - a   + x) + x acsc(-)
                                       a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2                x
--R   (2)  a log(\|x  - a   + x) + x acsc(-)
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 115 of 146
bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2))
 

                 +-------+
                 | 2    2                x
   (3)  - a log(\|x  - a   + x) + x acsc(-)
                                         a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2                x
--R   (3)  - a log(\|x  - a   + x) + x acsc(-)
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 116 of 146
cc1:=aa-bb1
 

   (4)
                                                   +---------+
                 +-------+                     +-+ |   2    2
                 | 2    2           +-+     2x\|2 \|- x  + a
       - 2a log(\|x  - a   + x) + a\|2 atan(------------------)
                                                   2     2
                                                 3x  - 2a
     + 
                   +---------+
                   |   2    2
                2a\|- x  + a                    x                 x
       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
                       2                   +---------+            a
                      x                    |   2    2
                                          \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                   +---------+
--R                 +-------+                     +-+ |   2    2
--R                 | 2    2           +-+     2x\|2 \|- x  + a
--R       - 2a log(\|x  - a   + x) + a\|2 atan(------------------)
--R                                                   2     2
--R                                                 3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2
--R                2a\|- x  + a                    x                 x
--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
--R                       2                   +---------+            a
--R                      x                    |   2    2
--R                                          \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 117 of 146    14:498 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                                 +---------+
               +-------+                     +-+ |   2    2
               | 2    2           +-+     2x\|2 \|- x  + a
       2a log(\|x  - a   + x) + a\|2 atan(------------------)
                                                 2     2
                                               3x  - 2a
     + 
                   +---------+
                   |   2    2
                2a\|- x  + a                    x                 x
       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
                       2                   +---------+            a
                      x                    |   2    2
                                          \|- x  + a
  /
     2
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                 +---------+
--R               +-------+                     +-+ |   2    2
--R               | 2    2           +-+     2x\|2 \|- x  + a
--R       2a log(\|x  - a   + x) + a\|2 atan(------------------)
--R                                                 2     2
--R                                               3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2
--R                2a\|- x  + a                    x                 x
--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
--R                       2                   +---------+            a
--R                      x                    |   2    2
--R                                          \|- x  + a
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 118 of 146
aa:=integrate(x*acsc(x/a),x)
 

                            +---------+
                            |   2    2        +---------+
            2     2      2a\|- x  + a         |   2    2
        (- x  + 2a )atan(--------------) - 2a\|- x  + a
                                2
                               x
   (1)  -------------------------------------------------
                                4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            +---------+
--R                            |   2    2        +---------+
--R            2     2      2a\|- x  + a         |   2    2
--R        (- x  + 2a )atan(--------------) - 2a\|- x  + a
--R                                2
--R                               x
--R   (1)  -------------------------------------------------
--R                                4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 119 of 146
bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2
 

          +-------+
          | 2    2     2     x
        a\|x  - a   + x acsc(-)
                             a
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2     x
--R        a\|x  - a   + x acsc(-)
--R                             a
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 120 of 146
bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2
 

            +-------+
            | 2    2     2     x
        - a\|x  - a   + x acsc(-)
                               a
   (3)  -------------------------
                    2
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2     x
--R        - a\|x  - a   + x acsc(-)
--R                               a
--R   (3)  -------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 121 of 146
cc1:=aa-bb1
 

   (4)
                       +---------+
                       |   2    2        +-------+      +---------+
       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (- x  + 2a )atan(--------------) - 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
                           2                                                  a
                          x
   -----------------------------------------------------------------------------
                                         4
                                                     Type: Expression Integer
--R
--R   (4)
--R                       +---------+
--R                       |   2    2        +-------+      +---------+
--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (- x  + 2a )atan(--------------) - 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
--R                           2                                                  a
--R                          x
--R   -----------------------------------------------------------------------------
--R                                         4
--R                                                     Type: Expression Integer
--E

--S 122 of 146    14:499 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                       +---------+
                       |   2    2        +-------+      +---------+
       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
   (- x  + 2a )atan(--------------) + 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
                           2                                                  a
                          x
   -----------------------------------------------------------------------------
                                         4
                                                     Type: Expression Integer
--R
--R   (5)
--R                       +---------+
--R                       |   2    2        +-------+      +---------+
--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
--R   (- x  + 2a )atan(--------------) + 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
--R                           2                                                  a
--R                          x
--R   -----------------------------------------------------------------------------
--R                                         4
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 123 of 146
aa:=integrate(x^2*acsc(x/a),x)
 

   (1)
                          +---------+              +---------+
                      +-+ |   2    2               |   2    2
         3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
       2a \|2 atan(------------------) - x atan(--------------)
                          2     2                      2
                        3x  - 2a                      x
     + 
                                   +---------+
         3           x             |   2    2
       5a atan(------------) - a x\|- x  + a
                +---------+
                |   2    2
               \|- x  + a
  /
     6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                          +---------+              +---------+
--R                      +-+ |   2    2               |   2    2
--R         3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
--R       2a \|2 atan(------------------) - x atan(--------------)
--R                          2     2                      2
--R                        3x  - 2a                      x
--R     + 
--R                                   +---------+
--R         3           x             |   2    2
--R       5a atan(------------) - a x\|- x  + a
--R                +---------+
--R                |   2    2
--R               \|- x  + a
--R  /
--R     6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 124 of 146
bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 

               +-------+            +-------+
         3     | 2    2             | 2    2      3     x
        a log(\|x  - a   + x) + a x\|x  - a   + 2x acsc(-)
                                                        a
   (2)  --------------------------------------------------
                                 6
                                                     Type: Expression Integer
--R
--R               +-------+            +-------+
--R         3     | 2    2             | 2    2      3     x
--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x acsc(-)
--R                                                        a
--R   (2)  --------------------------------------------------
--R                                 6
--R                                                     Type: Expression Integer
--E

--S 125 of 146
bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 

                 +-------+            +-------+
           3     | 2    2             | 2    2      3     x
        - a log(\|x  - a   + x) - a x\|x  - a   + 2x acsc(-)
                                                          a
   (3)  ----------------------------------------------------
                                  6
                                                     Type: Expression Integer
--R
--R                 +-------+            +-------+
--R           3     | 2    2             | 2    2      3     x
--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x acsc(-)
--R                                                          a
--R   (3)  ----------------------------------------------------
--R                                  6
--R                                                     Type: Expression Integer
--E

--S 126 of 146
cc1:=aa-bb1
 

   (4)
                                                    +---------+
                +-------+                       +-+ |   2    2
          3     | 2    2           3 +-+     2x\|2 \|- x  + a
       - a log(\|x  - a   + x) + 2a \|2 atan(------------------)
                                                    2     2
                                                  3x  - 2a
     + 
                   +---------+
                   |   2    2                                 +-------+
          3     2a\|- x  + a        3           x             | 2    2
       - x atan(--------------) + 5a atan(------------) - a x\|x  - a
                       2                   +---------+
                      x                    |   2    2
                                          \|- x  + a
     + 
             +---------+
             |   2    2      3     x
       - a x\|- x  + a   - 2x acsc(-)
                                   a
  /
     6
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                    +---------+
--R                +-------+                       +-+ |   2    2
--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       - a log(\|x  - a   + x) + 2a \|2 atan(------------------)
--R                                                    2     2
--R                                                  3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2                                 +-------+
--R          3     2a\|- x  + a        3           x             | 2    2
--R       - x atan(--------------) + 5a atan(------------) - a x\|x  - a
--R                       2                   +---------+
--R                      x                    |   2    2
--R                                          \|- x  + a
--R     + 
--R             +---------+
--R             |   2    2      3     x
--R       - a x\|- x  + a   - 2x acsc(-)
--R                                   a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E

--S 127 of 146    14:500 Axiom cannot simplify this expression
cc2:=aa-bb2
 

   (5)
                                                  +---------+
              +-------+                       +-+ |   2    2
        3     | 2    2           3 +-+     2x\|2 \|- x  + a
       a log(\|x  - a   + x) + 2a \|2 atan(------------------)
                                                  2     2
                                                3x  - 2a
     + 
                   +---------+
                   |   2    2                                 +-------+
          3     2a\|- x  + a        3           x             | 2    2
       - x atan(--------------) + 5a atan(------------) + a x\|x  - a
                       2                   +---------+
                      x                    |   2    2
                                          \|- x  + a
     + 
             +---------+
             |   2    2      3     x
       - a x\|- x  + a   - 2x acsc(-)
                                   a
  /
     6
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                  +---------+
--R              +-------+                       +-+ |   2    2
--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
--R       a log(\|x  - a   + x) + 2a \|2 atan(------------------)
--R                                                  2     2
--R                                                3x  - 2a
--R     + 
--R                   +---------+
--R                   |   2    2                                 +-------+
--R          3     2a\|- x  + a        3           x             | 2    2
--R       - x atan(--------------) + 5a atan(------------) + a x\|x  - a
--R                       2                   +---------+
--R                      x                    |   2    2
--R                                          \|- x  + a
--R     + 
--R             +---------+
--R             |   2    2      3     x
--R       - a x\|- x  + a   - 2x acsc(-)
--R                                   a
--R  /
--R     6
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 128 of 146    14:501 Axiom cannot compute this integral
aa:=integrate(acsc(x/a)/x,x)
 

                  %K
           x acsc(--)
         ++        a
   (1)   |   -------- d%K
        ++      %K
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                  %H
--R           x acsc(--)
--R         ++        a
--I   (1)   |   -------- d%H
--I        ++      %H
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 129 of 146
aa:=integrate(acsc(x/a)/x^2,x)
 

                        +---------+                 +---------+
                    +-+ |   2    2                  |   2    2
                 2x\|2 \|- x  + a        +-+     2a\|- x  + a
        - x atan(------------------) + a\|2 atan(--------------)
                        2     2                         2
                      3x  - 2a                         x
   (1)  --------------------------------------------------------
                                     +-+
                                2a x\|2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        +---------+                 +---------+
--R                    +-+ |   2    2                  |   2    2
--R                 2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R        - x atan(------------------) + a\|2 atan(--------------)
--R                        2     2                         2
--R                      3x  - 2a                         x
--R   (1)  --------------------------------------------------------
--R                                     +-+
--R                                2a x\|2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 130 of 146
bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x)
 

           +-------+
           | 2    2           x
        - \|x  - a   - a acsc(-)
                              a
   (2)  ------------------------
                   a x
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2           x
--R        - \|x  - a   - a acsc(-)
--R                              a
--R   (2)  ------------------------
--R                   a x
--R                                                     Type: Expression Integer
--E

--S 131 of 146
bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x)
 

         +-------+
         | 2    2           x
        \|x  - a   - a acsc(-)
                            a
   (3)  ----------------------
                  a x
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2           x
--R        \|x  - a   - a acsc(-)
--R                            a
--R   (3)  ----------------------
--R                  a x
--R                                                     Type: Expression Integer
--E

--S 132 of 146
cc1:=aa-bb1
 

   (4)
                       +---------+                 +---------+
                   +-+ |   2    2                  |   2    2
                2x\|2 \|- x  + a        +-+     2a\|- x  + a
       - x atan(------------------) + a\|2 atan(--------------)
                       2     2                         2
                     3x  - 2a                         x
     + 
             +-------+
         +-+ | 2    2       +-+     x
       2\|2 \|x  - a   + 2a\|2 acsc(-)
                                    a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (4)
--R                       +---------+                 +---------+
--R                   +-+ |   2    2                  |   2    2
--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R       - x atan(------------------) + a\|2 atan(--------------)
--R                       2     2                         2
--R                     3x  - 2a                         x
--R     + 
--R             +-------+
--R         +-+ | 2    2       +-+     x
--R       2\|2 \|x  - a   + 2a\|2 acsc(-)
--R                                    a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E

--S 133 of 146    14:502 Axiom cannot simplify this expression
cc2:=aa-bb2
 

   (5)
                       +---------+                 +---------+
                   +-+ |   2    2                  |   2    2
                2x\|2 \|- x  + a        +-+     2a\|- x  + a
       - x atan(------------------) + a\|2 atan(--------------)
                       2     2                         2
                     3x  - 2a                         x
     + 
               +-------+
           +-+ | 2    2       +-+     x
       - 2\|2 \|x  - a   + 2a\|2 acsc(-)
                                      a
  /
          +-+
     2a x\|2
                                                     Type: Expression Integer
--R
--R   (5)
--R                       +---------+                 +---------+
--R                   +-+ |   2    2                  |   2    2
--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
--R       - x atan(------------------) + a\|2 atan(--------------)
--R                       2     2                         2
--R                     3x  - 2a                         x
--R     + 
--R               +-------+
--R           +-+ | 2    2       +-+     x
--R       - 2\|2 \|x  - a   + 2a\|2 acsc(-)
--R                                      a
--R  /
--R          +-+
--R     2a x\|2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 134 of 146    14:503 Axiom cannot compute this integral
aa:=integrate(x^m*asin(x/a),x)
 

           x
         ++       %K   m
   (1)   |   asin(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   asin(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 135 of 146    14:504 Axiom cannot compute this integral
aa:=integrate(x^m*acos(x/a),x)
 

           x
         ++       %K   m
   (1)   |   acos(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   acos(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 136 of 146
aa:=integrate(x*m*atan(x/a),x)
 

              2    2         2a x
        (- m x  - a m)atan(-------) - 2a m x
                            2    2
                           x  - a
   (1)  ------------------------------------
                          4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2    2         2a x
--R        (- m x  - a m)atan(-------) - 2a m x
--R                            2    2
--R                           x  - a
--R   (1)  ------------------------------------
--R                          4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 137 of 146
t1:=integrate(x^(m+1)/(x^2+a^2),x)
 

           x    m + 1
         ++   %K
   (2)   |   -------- d%K
        ++    2     2
             a  + %K
                                          Type: Union(Expression Integer,...)
--E

--S 138 of 146
bb:=D(aa,x)
 

                     2a x
          m x atan(-------)
                    2    2
                   x  - a
   (3)  - -----------------
                  2
                                                     Type: Expression Integer
--R
--R                     2a x
--R          m x atan(-------)
--R                    2    2
--R                   x  - a
--R   (3)  - -----------------
--R                  2
--R                                                     Type: Expression Integer
--E
--S 139 of 146
aa1:=x*m*atan(x/a)
 

                 x
   (4)  m x atan(-)
                 a
                                                     Type: Expression Integer
--R
--R                 x
--R   (4)  m x atan(-)
--R                 a
--R                                                     Type: Expression Integer
--E
--S 140 of 146
dd:=aa1-bb
 

                  x               2a x
        2m x atan(-) + m x atan(-------)
                  a              2    2
                                x  - a
   (5)  --------------------------------
                        2
                                                     Type: Expression Integer
--R
--R                  x               2a x
--R        2m x atan(-) + m x atan(-------)
--R                  a              2    2
--R                                x  - a
--R   (5)  --------------------------------
--R                        2
--R                                                     Type: Expression Integer
--E
--S 141 of 146
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E
--S 142 of 146
ee:=atanrule dd
 

                      2              2
                     x  + 2%i a x - a                 - x + %i a
        - %i m x log(-----------------) - 2%i m x log(----------)
                      2              2                 x + %i a
                     x  - 2%i a x - a
   (7)  ---------------------------------------------------------
                                    4
                                             Type: Expression Complex Integer
--R
--R                      2              2
--R                     x  + 2%i a x - a                 - x + %i a
--R        - %i m x log(-----------------) - 2%i m x log(----------)
--R                      2              2                 x + %i a
--R                     x  - 2%i a x - a
--R   (7)  ---------------------------------------------------------
--R                                    4
--R                                             Type: Expression Complex Integer
--E
--S 143 of 146    14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
ff:=expandLog ee
 

          %i m x log(- 1)
   (8)  - ---------------
                 2
                                             Type: Expression Complex Integer
--R
--R          %i m x log(- 1)
--R   (8)  - ---------------
--R                 2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 144 of 146    14:506 Axiom cannot compute this integral
aa:=integrate(x^m*acot(x/a),x)
 

           x
         ++       %K   m
   (1)   |   acot(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   acot(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 145 of 146    14:507 Axiom cannot compute this integral
aa:=integrate(x^m*asec(x/a),x)
 

           x
         ++       %K   m
   (1)   |   asec(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   asec(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 146 of 146    14:508 Axiom cannot compute this integral
aa:=integrate(x^m*acsc(x/a),x)
 

           x
         ++       %K   m
   (1)   |   acsc(--)%K d%K
        ++         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %H   m
--I   (1)   |   acsc(--)%H d%H
--R        ++         a
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to tanhcoth.output (2010/3/27, 18:41:12).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.00,0.00000000,tanh(0.00),tanh(0.00)-0.00000000],_
[0.01,0.00999967,tanh(0.01),tanh(0.01)-0.00999967],_
[0.02,0.01999733,tanh(0.02),tanh(0.02)-0.01999733],_
[0.03,0.02999100,tanh(0.03),tanh(0.03)-0.02999100],_
[0.04,0.03997868,tanh(0.04),tanh(0.04)-0.03997868],_
[0.05,0.04995838,tanh(0.05),tanh(0.05)-0.04995838],_
[0.06,0.05992810,tanh(0.06),tanh(0.06)-0.05992810],_
[0.07,0.06988589,tanh(0.07),tanh(0.07)-0.06988589],_
[0.08,0.07982977,tanh(0.08),tanh(0.08)-0.07982977],_
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R    [1.39,0.88317089,0.8831708889 1520749667,- 0.1084792503 3 E -8],
--R    [1.4,0.88535165,0.8853516482 0226250758,- 0.1797737492 4 E -8],
--R    [1.41,0.88749413,0.8874941328 5366526128,0.2853665261 3 E -8],
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--R    [1.57,0.91702576,0.9170257613 9660829878,0.1396608298 8 E -8],
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--R    [1.81,0.94783185,0.9478318497 0723412158,- 0.2927658784 E -9],
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--R    [1.84,0.95079514,0.9507951431 9452112204,0.3194521122 E -8],
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--R    [1.86,0.95267884,0.9526788436 8907758132,0.3689077581 3 E -8],
--R    [1.87,0.95359412,0.9535941237 0871183917,0.3708711839 2 E -8],
--R    [1.88,0.95449211,0.9544921130 7439201893,0.3074392018 9 E -8],
--R    [1.89,0.95537312,0.9553731226 0193552915,0.2601935529 1 E -8],
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--R    [1.93,0.95873341,0.9587334055 4618760356,- 0.4453812396 44 E -8],
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--R    [1.95,0.96031939,0.9603193885 3184498689,- 0.1468155013 1 E -8],
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--R    [1.97,0.96184561,0.9618456053 6948368021,- 0.4630516319 79 E -8],
--R    [1.98,0.96258698,0.9625869800 9129079438,0.9129079438 E -10],
--R    [1.99,0.96331422,0.9633142186 0451342618,- 0.1395486573 8 E -8],
--R    [2.0,0.96402758,0.9640275800 7581688395,0.7581688395 E -10]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
[[0.01,100.0033333,coth(0.01),coth(0.01)-100.003333],_
[0.02,50.0066665,coth(0.02),coth(0.02)-50.0066665],_
[0.03,33.3433327,coth(0.03),coth(0.03)-33.3433327],_
[0.04,25.0133319,coth(0.04),coth(0.04)-25.0133319],_
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[0.08,12.5266553,coth(0.08),coth(0.08)-12.5266553],_
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[0.10,10.0333111,coth(0.10),coth(0.10)-10.0333111],_
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[0.31,3.3284838,coth(0.31),coth(0.31)-3.3284838],_
[0.32,3.2309455,coth(0.32),coth(0.32)-3.2309455],_
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[0.40,2.6319324,coth(0.40),coth(0.40)-2.6319324],_
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[0.44,2.4175352,coth(0.44),coth(0.44)-2.4175352],_
[0.45,2.3702355,coth(0.45),coth(0.45)-2.3702355],_
[0.46,2.3251260,coth(0.46),coth(0.46)-2.3251260],_
[0.47,2.2820666,coth(0.47),coth(0.47)-2.2820666],_
[0.48,2.2409284,coth(0.48),coth(0.48)-2.2409284],_
[0.49,2.2015936,coth(0.49),coth(0.49)-2.2015936],_
[0.50,2.1639534,coth(0.50),coth(0.50)-2.1639534],_
[0.51,2.1279077,coth(0.51),coth(0.51)-2.1279077],_
[0.52,2.0933640,coth(0.52),coth(0.52)-2.0933640],_
[0.53,2.0602368,coth(0.53),coth(0.53)-2.0602368],_
[0.54,2.0284471,coth(0.54),coth(0.54)-2.0284471],_
[0.55,1.9979213,coth(0.55),coth(0.55)-1.9979213],_
[0.56,1.9685914,coth(0.56),coth(0.56)-1.9685914],_
[0.57,1.9403939,coth(0.57),coth(0.57)-1.9403939],_
[0.58,1.9132698,coth(0.58),coth(0.58)-1.9132698],_
[0.59,1.8871642,coth(0.59),coth(0.59)-1.8871642],_
[0.60,1.8620255,coth(0.60),coth(0.60)-1.8620255],_
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   (2)
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    [1.75,1.0622753,1.0622753185 155995724,0.1851559957 24 E -7],
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    [1.77,1.0597605,1.0597605052 49804028,0.5249804028 E -8],
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    [1.86,1.0496717,1.0496716775 274233515,- 0.2247257664 85 E -7],
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    [1.88,1.0476776,1.0476775934 575597155,- 0.6542440284 5 E -8],
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    [1.92,1.0439314,1.0439314477 1385408,0.4771385408 E -7],
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    [1.96,1.0404855,1.0404854654 443926981,- 0.3455560730 19 E -7],
    [1.97,1.0396679,1.0396678993 151501465,- 0.6848498535 E -9],
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    [1.99,1.0380829,1.0380828816 672411665,- 0.1833275883 35 E -7],
    [2.0,1.0373147,1.0373147207 275480959,0.2072754809 59 E -7]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,100.0033333,100.0033333111 1132275,0.3111113227 5 E -6],
--R    [0.02,50.0066665,50.0066664888 95661105,- 0.111043389 E -7],
--R    [0.03,33.3433327,33.3433327333 84757277,0.3338475727 7 E -7],
--R    [0.04,25.0133319,25.0133319113 27796018,0.1132779602 E -7],
--R    [0.05,20.0166639,20.0166638895 50099248,- 0.1044990075 E -7],
--R    [0.06,16.6866619,16.6866618683 11788711,- 0.3168821128 9 E -7],
--R    [0.07,14.30904,14.3090400003 80691777,0.380691777 E -9],
--R    [0.08,12.5266553,12.5266552958 19479794,- 0.4180520206 E -8],
--R    [0.09,11.1410949,11.1410949235 98139558,0.2359813955 8 E -7],
--R    [0.1,10.0333111,10.0333111322 5398961,0.3225398961 E -7],
--R    [0.11,9.1275462,9.1275462138 41655179,0.1384165517 9 E -7],
--R    [0.12,8.373295,8.3732949859 20466106,- 0.1407953389 4 E -7],
--R    [0.13,7.7355923,7.7355922818 667577388,- 0.1813324226 1 E -7],
--R    [0.14,7.1894629,7.1894629453 485603813,0.4534856038 12 E -7],
--R    [0.15,6.7165918,6.7165918270 201652046,0.2702016520 5 E -7],
--R    [0.16,6.3032425,6.3032425324 653055781,0.3246530557 81 E -7],
--R    [0.17,5.9389107,5.9389107296 982815716,0.2969828157 2 E -7],
--R    [0.18,5.6154264,5.6154263541 72649833,- 0.4582735016 7 E -7],
--R    [0.19,5.3263393,5.3263393280 051508097,0.2800515081 E -7],
--R    [0.2,5.0664896,5.0664895634 394727136,- 0.3656052728 64 E -7],
--R    [0.21,4.8316998,4.8316998224 69838787,0.2246983878 7 E -7],
--R    [0.22,4.6185523,4.6185523420 28042354,0.4202804235 4 E -7],
--R    [0.23,4.4242237,4.4242237308 667251076,0.3086672510 75 E -7],
--R    [0.24,4.2463611,4.2463611422 274259979,0.4222742599 79 E -7],
--R    [0.25,4.0829882,4.0829881650 735965683,- 0.3492640343 17 E -7],
--R    [0.26,3.9324324,3.9324324327 36408036,0.3273640803 6 E -7],
--R    [0.27,3.7932693,3.7932693185 329284388,0.1853292843 88 E -7],
--R    [0.28,3.6642777,3.6642776966 135092065,- 0.3386490793 5 E -8],
--R    [0.29,3.5444049,3.5444048557 416074988,- 0.4425839250 12 E -7],
--R    [0.3,3.4327384,3.4327384303 217415894,0.3032174158 94 E -7],
--R    [0.31,3.3284838,3.3284837641 356108564,- 0.3586438914 36 E -7],
--R    [0.32,3.2309455,3.2309455183 814022485,0.1838140224 85 E -7],
--R    [0.33,3.1395126,3.1395126237 094799327,0.2370947993 27 E -7],
--R    [0.34,3.0536459,3.0536458877 845481399,- 0.1221545186 E -7],
--R    [0.35,2.9728677,2.9728677272 689265964,0.2726892659 64 E -7],
--R    [0.36,2.8967536,2.8967536111 449900164,0.1114499001 6 E -7],
--R    [0.37,2.8249249,2.8249248916 098377328,- 0.8390162267 1 E -8],
--R    [0.38,2.7570428,2.7570427669 367181087,- 0.3306328189 13 E -7],
--R    [0.39,2.6928032,2.6928031731 296236301,- 0.2687037636 99 E -7],
--R    [0.4,2.6319324,2.6319324418 321883572,0.4183218835 72 E -7],
--R    [0.41,2.5741836,2.5741835936 66919577,- 0.6333080423 E -8],
--R    [0.42,2.5193332,2.5193331610 996456868,- 0.3890035431 32 E -7],
--R    [0.43,2.4671785,2.4671784546 273392718,- 0.4537266072 82 E -7],
--R    [0.44,2.4175352,2.4175352017 605355925,0.1760535592 E -8],
--R    [0.45,2.3702355,2.3702355008 100157433,0.8100157433 E -9],
--R    [0.46,2.325126,2.3251260415 726980245,0.4157269802 45 E -7],
--R    [0.47,2.2820666,2.2820665531 657326625,- 0.4683426733 75 E -7],
--R    [0.48,2.2409284,2.2409284458 829619758,0.4588296197 58 E -7],
--R    [0.49,2.2015936,2.2015936193 562076931,0.1935620769 3 E -7],
--R    [0.5,2.1639534,2.1639534137 386528488,0.1373865284 9 E -7],
--R    [0.51,2.1279077,2.1279076842 79778673,- 0.1572022132 7 E -7],
--R    [0.52,2.093364,2.0933639826 813995967,- 0.1731860040 33 E -7],
--R    [0.53,2.0602368,2.0602368311 315780091,0.3113157800 91 E -7],
--R    [0.54,2.0284471,2.0284470770 025658705,- 0.2299743412 95 E -7],
--R    [0.55,1.9979213,1.9979213179 463896248,0.1794638962 48 E -7],
--R    [0.56,1.9685914,1.9685913885 883209462,- 0.1141167905 38 E -7],
--R    [0.57,1.9403939,1.9403939012 535294422,0.1253529442 2 E -8],
--R    [0.58,1.9132698,1.9132698342 056208124,0.3420562081 24 E -7],
--R    [0.59,1.8871642,1.8871641617 600075376,- 0.3823999246 24 E -7],
--R    [0.6,1.8620255,1.8620255213 866662476,0.2138666624 76 E -7],
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--R    [0.62,1.8144604,1.8144604306 416324911,0.3064163249 11 E -7],
--R    [0.63,1.791947,1.7919470116 200198016,0.1162001980 16 E -7],
--R    [0.64,1.7702262,1.7702262197 970203553,0.1979702035 53 E -7],
--R    [0.65,1.749261,1.7492610410 306350676,0.4103063506 76 E -7],
--R    [0.66,1.7290167,1.7290167003 061253871,0.3061253871 E -9],
--R    [0.67,1.7094605,1.7094604947 361744339,- 0.5263825566 1 E -8],
--R    [0.68,1.6905616,1.6905616412 966267409,0.4129662674 09 E -7],
--R    [0.69,1.6722911,1.6722911378 028518669,0.3780285186 7 E -7],
--R    [0.7,1.6546216,1.6546216358 026294047,0.3580262940 47 E -7],
--R    [0.71,1.6375273,1.6375273242 106478561,0.2421064785 61 E -7],
--R    [0.72,1.6209838,1.6209838226 402554549,0.2264025545 49 E -7],
--R    [0.73,1.6049681,1.6049680835 025519782,- 0.1649744802 18 E -7],
--R    [0.74,1.5894583,1.5894583020 434418638,0.2043441863 8 E -8],
--R    [0.75,1.5744338,1.5744338335 777364887,0.3357773648 87 E -7],
--R    [0.76,1.5598751,1.5598751172 573846082,0.1725738460 82 E -7],
--R    [0.77,1.5457636,1.5457636057 797852649,0.5779785264 9 E -8],
--R    [0.78,1.5320817,1.5320817005 030656562,0.5030656562 E -9],
--R    [0.79,1.5188127,1.5188126914 891934625,- 0.8510806537 49 E -8],
--R    [0.8,1.5059407,1.5059407020 437066212,0.2043706621 2 E -8],
--R    [0.81,1.4934506,1.4934506373 634333213,0.3736343332 13 E -7],
--R    [0.82,1.4813281,1.4813281369 414902969,0.3694149029 69 E -7],
--R    [0.83,1.4695595,1.4695595304 126515262,0.3041265152 62 E -7],
--R    [0.84,1.4581318,1.4581317965 523616189,- 0.3447638381 1 E -8],
--R    [0.85,1.4470325,1.4470325251 696546055,0.2516965460 55 E -7],
--R    [0.86,1.4362499,1.4362498816 584011227,- 0.1834159887 73 E -7],
--R    [0.87,1.4257726,1.4257725739 929697346,- 0.2600703026 54 E -7],
--R    [0.88,1.4155898,1.4155898219 738353763,0.2197383537 63 E -7],
--R    [0.89,1.4056913,1.4056913285 461485888,0.2854614858 88 E -7],
--R    [0.9,1.3960673,1.3960672530 300118351,- 0.4696998816 49 E -7],
--R    [0.91,1.3867082,1.3867081861 153858453,- 0.1388461415 47 E -7],
--R    [0.92,1.3776051,1.3776051264 873387552,0.2648733875 52 E -7],
--R    [0.93,1.3687495,1.3687494589 589029032,- 0.4104109709 68 E -7],
--R    [0.94,1.3601329,1.3601329339 992502041,0.3399925020 41 E -7],
--R    [0.95,1.3517476,1.3517476485 543534541,0.4855435345 41 E -7],
--R    [0.96,1.343586,1.3435860280 658708165,0.2806587081 65 E -7],
--R    [0.97,1.3356408,1.3356408096 017654982,0.9601765498 2 E -8],
--R    [0.98,1.327905,1.3279050260 192333791,0.2601923337 91 E -7],
--R    [0.99,1.320372,1.3203719910 869302267,- 0.8913069773 26 E -8],
--R    [1.0,1.3130353,1.3130352854 993313036,- 0.1450066869 64 E -7],
--R    [1.01,1.3058887,1.3058887437 213768521,0.4372137685 21 E -7],
--R    [1.02,1.2989264,1.2989264416 064081471,0.4160640814 71 E -7],
--R    [1.03,1.2921427,1.2921426847 348261269,- 0.1526517387 31 E -7],
--R    [1.04,1.285532,1.2855319974 249487926,- 0.2575051207 4 E -8],
--R    [1.05,1.2790891,1.2790891123 712411139,0.1237124111 39 E -7],
--R    [1.06,1.272809,1.2728089608 684747719,- 0.3913152522 81 E -7],
--R    [1.07,1.2666867,1.2666866635 834740719,- 0.3641652592 81 E -7],
--R    [1.08,1.2607175,1.2607175218 389451031,0.2183894510 31 E -7],
--R    [1.09,1.254897,1.2548970093 764914129,0.9376491412 86 E -8],
--R    [1.1,1.2492208,1.2492207645 683124166,- 0.3543168758 34 E -7],
--R    [1.11,1.2436846,1.2436845830 492796933,- 0.1695072030 67 E -7],
--R    [1.12,1.2382844,1.2382844107 43108546,0.1074310854 6 E -7],
--R    [1.13,1.2330163,1.2330163372 582033675,0.3725820336 75 E -7],
--R    [1.14,1.2278766,1.2278765896 304695801,- 0.1036953041 99 E -7],
--R    [1.15,1.2228615,1.2228615263 919649847,0.2639196498 47 E -7],
--R    [1.16,1.2179676,1.2179676319 457208259,0.3194572082 59 E -7],
--R    [1.17,1.2131915,1.2131915112 284082387,0.1122840823 87 E -7],
--R    [1.18,1.2085299,1.2085298846 437684793,- 0.1535623152 07 E -7],
--R    [1.19,1.2039796,1.2039795832 508740941,- 0.1674912590 59 E -7],
--R    [1.2,1.1995375,1.1995375441 923507667,0.4419235076 67 E -7],
--R    [1.21,1.1952008,1.1952008063 486731313,0.6348673131 3 E -8],
--R    [1.22,1.1909665,1.1909665062 055588292,0.6205558829 2 E -8],
--R    [1.23,1.1868319,1.1868318739 22329409,- 0.2607767059 1 E -7],
--R    [1.24,1.1827942,1.1827942295 898897106,0.2958988971 06 E -7],
--R    [1.25,1.178851,1.1788509796 677040268,- 0.2033229597 32 E -7],
--R    [1.26,1.1749996,1.1749996135 898220841,0.1358982208 41 E -7],
--R    [1.27,1.1712377,1.1712377005 306348077,0.5306348077 E -9],
--R    [1.28,1.1675629,1.1675628863 216226741,- 0.1367837732 59 E -7],
--R    [1.29,1.1639729,1.1639728905 10901625,- 0.9489098374 98 E -8],
--R    [1.3,1.1604655,1.1604655035 578761464,0.3557876146 4 E -8],
--R    [1.31,1.1570386,1.1570385841 557790704,- 0.1584422092 96 E -7],
--R    [1.32,1.1536901,1.1536900566 75315566,- 0.4332468443 4 E -7],
--R    [1.33,1.1504179,1.1504179087 23037052,0.8723037051 99 E -8],
--R    [1.34,1.1472202,1.1472201888 084516077,- 0.1119154839 23 E -7],
--R    [1.35,1.144095,1.1440950041 142329045,0.4114232904 5 E -8],
--R    [1.36,1.1410405,1.1410405183 642215979,0.1836422159 79 E -7],
--R    [1.37,1.138055,1.1380549497 842232286,- 0.5021577677 14 E -7],
--R    [1.38,1.1351366,1.1351365691 508965597,- 0.3084910344 03 E -7],
--R    [1.39,1.1322837,1.1322836979 242973771,- 0.2075702622 9 E -8],
--R    [1.4,1.1294947,1.1294947064 598964505,0.6459896450 5 E -8],
--R    [1.41,1.126768,1.1267680122 961278243,0.1229612782 43 E -7],
--R    [1.42,1.1241021,1.1241020785 137460187,- 0.2148625398 13 E -7],
--R    [1.43,1.1214954,1.1214954121 634791355,0.1216347913 55 E -7],
--R    [1.44,1.1189466,1.1189465627 586602379,- 0.3724133976 21 E -7],
--R    [1.45,1.1164541,1.1164541208 297026222,0.2082970262 22 E -7],
--R    [1.46,1.1140167,1.1140167165 374565427,0.1653745654 27 E -7],
--R    [1.47,1.111633,1.1116330183 426463597,0.1834264635 97 E -7],
--R    [1.48,1.1093017,1.1093017317 287386746,0.3172873867 46 E -7],
--R    [1.49,1.1070216,1.1070215979 757344389,- 0.2024265561 1 E -8],
--R    [1.5,1.1047914,1.1047913929 825119039,- 0.7017488096 1 E -8],
--R    [1.51,1.1026099,1.1026099261 354731665,0.2613547316 65 E -7],
--R    [1.52,1.100476,1.1004760392 213654987,0.3922136549 87 E -7],
--R    [1.53,1.0983886,1.0983886053 822601088,0.5382260108 8 E -8],
--R    [1.54,1.0963465,1.0963465281 107759211,0.2811077592 11 E -7],
--R    [1.55,1.0943487,1.0943487402 837348018,0.4028373480 18 E -7],
--R    [1.56,1.0923942,1.0923942032 325277949,0.3232527794 9 E -8],
--R    [1.57,1.0904819,1.0904819058 485597183,0.5848559718 3 E -8],
--R    [1.58,1.0886109,1.0886108637 222222566,- 0.3627777774 34 E -7],
--R    [1.59,1.0867801,1.0867801183 139237769,0.1831392377 69 E -7],
--R    [1.6,1.0849887,1.0849887361 557777925,0.3615577779 25 E -7],
--R    [1.61,1.0832358,1.0832358080 826215661,0.8082621566 08 E -8],
--R    [1.62,1.0815204,1.0815204484 911020471,0.4849110204 71 E -7],
--R    [1.63,1.0798418,1.0798417946 256284042,- 0.5374371595 8 E -8],
--R    [1.64,1.078199,1.0781990058 90049072,0.5890049072 E -8],
--R    [1.65,1.0765913,1.0765912631 839666847,- 0.3681603331 53 E -7],
--R    [1.66,1.0750178,1.0750177682 626567093,- 0.3173734329 07 E -7],
--R    [1.67,1.0734777,1.0734777431 19605205,0.4311960520 5 E -7],
--R    [1.68,1.0719704,1.0719704293 907280832,0.2939072808 32 E -7],
--R    [1.69,1.0704951,1.0704950877 793786871,- 0.1222062131 29 E -7],
--R    [1.7,1.069051,1.0690509975 012925984,- 0.2498707401 6 E -8],
--R    [1.71,1.0676375,1.0676374557 486584477,- 0.4425134155 23 E -7],
--R    [1.72,1.0662538,1.0662537771 725412807,- 0.2282745871 93 E -7],
--R    [1.73,1.0648993,1.0648992933 829208457,- 0.6617079154 3 E -8],
--R    [1.74,1.0635734,1.0635733524 656411166,- 0.4753435888 34 E -7],
--R    [1.75,1.0622753,1.0622753185 155995724,0.1851559957 24 E -7],
--R    [1.76,1.0610046,1.0610045711 855353057,- 0.2881446469 43 E -7],
--R    [1.77,1.0597605,1.0597605052 49804028,0.5249804028 E -8],
--R    [1.78,1.0585425,1.0585425301 825555676,0.3018255556 76 E -7],
--R    [1.79,1.0573501,1.0573500697 497555933,- 0.3025024440 67 E -7],
--R    [1.8,1.0561826,1.0561825616 145181279,- 0.3838548187 21 E -7],
--R    [1.81,1.0550395,1.0550394569 552390051,- 0.4304476099 49 E -7],
--R    [1.82,1.0539202,1.0539202200 960428446,0.2009604284 46 E -7],
--R    [1.83,1.0528243,1.0528243281 490774395,0.2814907743 95 E -7],
--R    [1.84,1.0517513,1.0517512706 682097163,- 0.2933179028 37 E -7],
--R    [1.85,1.0507005,1.0507005493 136967107,0.4931369671 07 E -7],
--R    [1.86,1.0496717,1.0496716775 274233515,- 0.2247257664 85 E -7],
--R    [1.87,1.0486642,1.0486641802 183162995,- 0.1978168370 05 E -7],
--R    [1.88,1.0476776,1.0476775934 575597155,- 0.6542440284 5 E -8],
--R    [1.89,1.0467115,1.0467114641 832546561,- 0.3581674534 39 E -7],
--R    [1.9,1.0457653,1.0457653499 141788749,0.4991417887 49 E -7],
--R    [1.91,1.0448388,1.0448388184 72318166,0.1847231816 6 E -7],
--R    [1.92,1.0439314,1.0439314477 1385408,0.4771385408 E -7],
--R    [1.93,1.0430428,1.0430428252 683058841,0.2526830588 41 E -7],
--R    [1.94,1.0421725,1.0421725482 855370847,0.4828553708 47 E -7],
--R    [1.95,1.0413202,1.0413202231 90348688,0.2319034868 8 E -7],
--R    [1.96,1.0404855,1.0404854654 443926981,- 0.3455560730 19 E -7],
--R    [1.97,1.0396679,1.0396678993 151501465,- 0.6848498535 E -9],
--R    [1.98,1.0388672,1.0388671576 517282541,- 0.4234827174 59 E -7],
--R    [1.99,1.0380829,1.0380828816 672411665,- 0.1833275883 35 E -7],
--R    [2.0,1.0373147,1.0373147207 275480959,0.2072754809 59 E -7]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to BinarySearchTree.output (2010/3/27, 18:41:46).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
lv := [8,3,5,4,6,2,1,5,7]
 

   (1)  [8,3,5,4,6,2,1,5,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [8,3,5,4,6,2,1,5,7]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 12
t := binarySearchTree lv
 

   (2)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
                                       Type: BinarySearchTree PositiveInteger
--R 
--R
--R   (2)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
--R                                       Type: BinarySearchTree PositiveInteger
--E 2

--S 3 of 12
emptybst := empty()$BSTREE(INT)
 

   (3)  []
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (3)  []
--R                                               Type: BinarySearchTree Integer
--E 3

--S 4 of 12
t1 := insert!(8,emptybst)
 

   (4)  8
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (4)  8
--R                                               Type: BinarySearchTree Integer
--E 4

--S 5 of 12
insert!(3,t1)
 

   (5)  [3,8,.]
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (5)  [3,8,.]
--R                                               Type: BinarySearchTree Integer
--E 5

--S 6 of 12
leaves t
 

   (6)  [1,4,5,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (6)  [1,4,5,7]
--R                                                   Type: List PositiveInteger
--E 6

--S 7 of 12
split(3,t)
 

   (7)  [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]]
Type: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger)
--R 
--R
--R   (7)  [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]]
--RType: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger)
--E 7

--S 8 of 12
insertRoot: (INT,BSTREE INT) -> BSTREE INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 12
insertRoot(x, t) ==
    a := split(x, t)
    node(a.less, x, a.greater)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 12
buildFromRoot ls == reduce(insertRoot,ls,emptybst)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 12
rt := buildFromRoot reverse lv
 
   Compiling function buildFromRoot with type List PositiveInteger -> 
      BinarySearchTree Integer 
   Compiling function insertRoot with type (Integer,BinarySearchTree 
      Integer) -> BinarySearchTree Integer 

   (11)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
                                               Type: BinarySearchTree Integer
--R 
--R   Compiling function buildFromRoot with type List PositiveInteger -> 
--R      BinarySearchTree Integer 
--R   Compiling function insertRoot with type (Integer,BinarySearchTree 
--R      Integer) -> BinarySearchTree Integer 
--R
--R   (11)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
--R                                               Type: BinarySearchTree Integer
--E 11

--S 12 of 12
(t = rt)@Boolean
 

   (12)  true
                                                                Type: Boolean
--R 
--R
--R   (12)  true
--R                                                                Type: Boolean
--E 12
)spool
 
Starts dribbling to exlap.output (2010/3/27, 18:25:39).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
laplace(2/t * (1 - cos(a*t)), t, s)
 

             2    2
   (1)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R             2    2
--R   (1)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 6
laplace((exp(a*t) - exp(b*t))/t, t, s)
 

   (2)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
laplace(exp(a*t+b)*Ei(c*t), t, s)
 

          b    s + c - a
        %e log(---------)
                   c
   (3)  -----------------
              s - a
                                                     Type: Expression Integer
--R 
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (3)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 3

)clear all
 

--S 4 of 6
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
 

               2    2
              s  + b             d
        a log(-------) + 2c atan(-)
                  2              s
                 b
   (1)  ---------------------------
                     2s
                                                     Type: Expression Integer
--R 
--R
--R               2    2
--R              s  + b             d
--R        a log(-------) + 2c atan(-)
--R                  2              s
--R                 b
--R   (1)  ---------------------------
--R                     2s
--R                                                     Type: Expression Integer
--E 4

)clear all
 

--S 5 of 6
laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s)
 

             3
           4a
   (1)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R             3
--R           4a
--R   (1)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 5

)clear all
 

--S 6 of 6
laplace(t**4 * exp(-a*t) / factorial(4), t, s)
 

                            1
   (1)  ----------------------------------------
         5       4      2 3      3 2     4     5
        s  + 5a s  + 10a s  + 10a s  + 5a s + a
                                                     Type: Expression Integer
--R 
--R
--R                            1
--R   (1)  ----------------------------------------
--R         5       4      2 3      3 2     4     5
--R        s  + 5a s  + 10a s  + 10a s  + 5a s + a
--R                                                     Type: Expression Integer
--E 6
)spool 
 
Starts dribbling to Multiset.output (2010/3/27, 18:46:7).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 14
s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10]
 

   (1)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (1)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 1

--S 2 of 14
insert!(3,s)
 

   (2)  {1,2: 2,4: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (2)  {1,2: 2,4: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 2

--S 3 of 14
remove!(3,s,1)
 

   (3)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (3)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 3

--S 4 of 14
s
 

   (4)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (4)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 4

--S 5 of 14
remove!(5,s)
 

   (5)  {1,2: 2,3: 3,4: 4,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (5)  {1,2: 2,3: 3,4: 4,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 5

--S 6 of 14
s
 

   (6)  {1,2: 2,3: 3,4: 4,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (6)  {1,2: 2,3: 3,4: 4,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 6

--S 7 of 14
count(5,s)
 

   (7)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (7)  0
--R                                                     Type: NonNegativeInteger
--E 7

--S 8 of 14
t := multiset [2,2,2,-9]
 

   (8)  {3: 2,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (8)  {3: 2,- 9}
--R                                                       Type: Multiset Integer
--E 8

--S 9 of 14
U := union(s,t)
 

   (9)  {1,5: 2,3: 3,4: 4,6,7,10,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (9)  {1,5: 2,3: 3,4: 4,6,7,10,- 9}
--R                                                       Type: Multiset Integer
--E 9

--S 10 of 14
I := intersect(s,t)
 

   (10)  {5: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {5: 2}
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 14
difference(s,t)
 

   (11)  {1,3: 3,4: 4,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (11)  {1,3: 3,4: 4,6,7,10}
--R                                                       Type: Multiset Integer
--E 11

--S 12 of 14
S := symmetricDifference(s,t)
 

   (12)  {1,3: 3,4: 4,6,7,10,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (12)  {1,3: 3,4: 4,6,7,10,- 9}
--R                                                       Type: Multiset Integer
--E 12

--S 13 of 14
(U = union(S,I))@Boolean
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 14
t1 := multiset [1,2,2,3]; [t1 < t, t1 < s, t < s, t1 <= s]
 

   (14)  [false,true,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (14)  [false,true,false,true]
--R                                                           Type: List Boolean
--E 14
)spool
 
Starts dribbling to intg0.output (2010/3/27, 18:27:1).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 25
y := sqrt(a * x + b)
 

         +-------+
   (1)  \|a x + b
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R   (1)  \|a x + b
--R                                                     Type: Expression Integer
--E 1

--S 2 of 25
integrate(y,x)
 

                    +-------+
        (2a x + 2b)\|a x + b
   (2)  ---------------------
                  3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-------+
--R        (2a x + 2b)\|a x + b
--R   (2)  ---------------------
--R                  3a
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 25
t1:=x * y
 

          +-------+
   (3)  x\|a x + b
                                                     Type: Expression Integer
--R 
--R
--R          +-------+
--R   (3)  x\|a x + b
--R                                                     Type: Expression Integer
--E 3

--S 4 of 25
integrate(t1,x)
 

           2 2              2  +-------+
        (6a x  + 2a b x - 4b )\|a x + b
   (4)  --------------------------------
                         2
                      15a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2              2  +-------+
--R        (6a x  + 2a b x - 4b )\|a x + b
--R   (4)  --------------------------------
--R                         2
--R                      15a
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 25
z := sqrt(a**2 - x**2)
 

         +---------+
         |   2    2
   (5)  \|- x  + a
                                                     Type: Expression Integer
--R 
--R
--R         +---------+
--R         |   2    2
--R   (5)  \|- x  + a
--R                                                     Type: Expression Integer
--E 5

--S 6 of 25
t2:=1 / z
 

              1
   (6)  ------------
         +---------+
         |   2    2
        \|- x  + a
                                                     Type: Expression Integer
--R 
--R
--R              1
--R   (6)  ------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a
--R                                                     Type: Expression Integer
--E 6

--S 7 of 25
integrate(t2,x)
 

                 +---------+
                 |   2    2
                \|- x  + a   - a
   (7)  - 2atan(----------------)
                        x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   - a
--R   (7)  - 2atan(----------------)
--R                        x
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 25
t3:=x**2 * z
 

           +---------+
         2 |   2    2
   (8)  x \|- x  + a
                                                     Type: Expression Integer
--R 
--R
--R           +---------+
--R         2 |   2    2
--R   (8)  x \|- x  + a
--R                                                     Type: Expression Integer
--E 8

--S 9 of 25
integrate(t3,x)
 

   (9)
                           +---------+
               5 2      7  |   2    2      4 4      6 2      8
         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                    +---------+
        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
  /
                     +---------+
           2      3  |   2    2      4      2 2      4
     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (9)
--R                           +---------+
--R               5 2      7  |   2    2      4 4      6 2      8
--R         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                    +---------+
--R        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
--R     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
--R  /
--R                     +---------+
--R           2      3  |   2    2      4      2 2      4
--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 25
t4:=x**3 / (a+b*x)**(1/3)
 

              3
             x
   (10)  ----------
         3+-------+
         \|b x + a
                                                     Type: Expression Integer
--R 
--R
--R              3
--R             x
--R   (10)  ----------
--R         3+-------+
--R         \|b x + a
--R                                                     Type: Expression Integer
--E 10

--S 11 of 25
integrate(t4,x)
 

              3 3         2 2       2          3 3+-------+2
         (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
   (11)  ---------------------------------------------------
                                    4
                                440b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3 3         2 2       2          3 3+-------+2
--R         (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
--R   (11)  ---------------------------------------------------
--R                                    4
--R                                440b
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 25
t5:=1 / (x**3 * (a+b*x)**(1/3))
 

               1
   (12)  ------------
          3 3+-------+
         x  \|b x + a
                                                     Type: Expression Integer
--R 
--R
--R               1
--R   (12)  ------------
--R          3 3+-------+
--R         x  \|b x + a
--R                                                     Type: Expression Integer
--E 12

--S 13 of 25
integrate(t5,x)
 

   (13)
           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
     + 
         2 2 +-+    3+-+2 3+-------+
       4b x \|3 log(\|a   \|b x + a - a)
     + 
                  +-+3+-+2 3+-------+    +-+
        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
                             3a
  /
        2 2 +-+3+-+
     18a x \|3 \|a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (13)
--R           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
--R       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
--R     + 
--R         2 2 +-+    3+-+2 3+-------+
--R       4b x \|3 log(\|a   \|b x + a - a)
--R     + 
--R                  +-+3+-+2 3+-------+    +-+
--R        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
--R     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
--R                             3a
--R  /
--R        2 2 +-+3+-+
--R     18a x \|3 \|a
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 25
t6:=x / (y + y**2) + log(y + 1)
 

           +-------+                +-------+
         (\|a x + b  + a x + b)log(\|a x + b  + 1) + x
   (14)  ---------------------------------------------
                       +-------+
                      \|a x + b  + a x + b
                                                     Type: Expression Integer
--R 
--R
--R           +-------+                +-------+
--R         (\|a x + b  + a x + b)log(\|a x + b  + 1) + x
--R   (14)  ---------------------------------------------
--R                       +-------+
--R                      \|a x + b  + a x + b
--R                                                     Type: Expression Integer
--E 14

--S 15 of 25
integrate(t6,x)
 

   (15)
          2                            +-------+                 +-------+
       (2a x + (2a - 4)b - 2a + 4)log(\|a x + b  + 1) + (2a - 4)\|a x + b
     + 
           2
       (- a  + 2a)x
  /
       2
     2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (15)
--R          2                            +-------+                 +-------+
--R       (2a x + (2a - 4)b - 2a + 4)log(\|a x + b  + 1) + (2a - 4)\|a x + b
--R     + 
--R           2
--R       (- a  + 2a)x
--R  /
--R       2
--R     2a
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 25
t7:=(2 + 1/sqrt(x)) * cos(x + sqrt x)
 

            +-+          +-+
         (2\|x  + 1)cos(\|x  + x)
   (16)  ------------------------
                    +-+
                   \|x
                                                     Type: Expression Integer
--R 
--R
--R            +-+          +-+
--R         (2\|x  + 1)cos(\|x  + x)
--R   (16)  ------------------------
--R                    +-+
--R                   \|x
--R                                                     Type: Expression Integer
--E 16

--S 17 of 25
integrate(t7,x)
 

               +-+
   (17)  2sin(\|x  + x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-+
--R   (17)  2sin(\|x  + x)
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 25
t8:=log(1 + y) / x
 

              +-------+
         log(\|a x + b  + 1)
   (18)  -------------------
                  x
                                                     Type: Expression Integer
--R 
--R
--R              +-------+
--R         log(\|a x + b  + 1)
--R   (18)  -------------------
--R                  x
--R                                                     Type: Expression Integer
--E 18

--S 19 of 25
integrate(t8,x)
 

            x      +--------+
          ++  log(\|b + %N a  + 1)
   (19)   |   -------------------- d%N
         ++            %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x      +--------+
--I          ++  log(\|b + %K a  + 1)
--I   (19)   |   -------------------- d%K
--I         ++            %K
--R                                          Type: Union(Expression Integer,...)
--E 19

--S 20 of 25
t9:=(sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b))))
 

                   +-----+          +-----+
             sinh(\|x + b  + 1) + 2\|x + b
   (20)  --------------------------------------
          +-----+      +-----+          +-----+
         \|x + b cosh(\|x + b  + 1) + x\|x + b
                                                     Type: Expression Integer
--R 
--R
--R                   +-----+          +-----+
--R             sinh(\|x + b  + 1) + 2\|x + b
--R   (20)  --------------------------------------
--R          +-----+      +-----+          +-----+
--R         \|x + b cosh(\|x + b  + 1) + x\|x + b
--R                                                     Type: Expression Integer
--E 20

--S 21 of 25
integrate(t9,x)
 

                              +-----+
                     - 2cosh(\|x + b  + 1) - 2x            +-----+
   (21)  2log(---------------------------------------) - 2\|x + b
                    +-----+              +-----+
              sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              +-----+
--R                     - 2cosh(\|x + b  + 1) - 2x            +-----+
--R   (21)  2log(---------------------------------------) - 2\|x + b
--R                    +-----+              +-----+
--R              sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
--R                                          Type: Union(Expression Integer,...)
--E 21

--S 22 of 25
t10:=tan(atan(x)/2)
 

             atan(x)
   (22)  tan(-------)
                2
                                                     Type: Expression Integer
--R 
--R
--R             atan(x)
--R   (22)  tan(-------)
--R                2
--R                                                     Type: Expression Integer
--E 22

--S 23 of 25
integrate(t10,x)
 

   (23)
           +------+          +------+
           | 2               | 2
       (- \|x  + 1  + x)log(\|x  + 1  - x + 1)
     + 
         +------+          +------+                           +------+
         | 2               | 2                                | 2
       (\|x  + 1  - x)log(\|x  + 1  - x - 1) + (- log(x) - x)\|x  + 1
     + 
                   2
       x log(x) + x  + 1
  /
      +------+
      | 2
     \|x  + 1  - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (23)
--R           +------+          +------+
--R           | 2               | 2
--R       (- \|x  + 1  + x)log(\|x  + 1  - x + 1)
--R     + 
--R         +------+          +------+                           +------+
--R         | 2               | 2                                | 2
--R       (\|x  + 1  - x)log(\|x  + 1  - x - 1) + (- log(x) - x)\|x  + 1
--R     + 
--R                   2
--R       x log(x) + x  + 1
--R  /
--R      +------+
--R      | 2
--R     \|x  + 1  - x
--R                                          Type: Union(Expression Integer,...)
--E 23

--S 24 of 25
t11:=tan(atan(x)/3)
 

             atan(x)
   (24)  tan(-------)
                3
                                                     Type: Expression Integer
--R 
--R
--R             atan(x)
--R   (24)  tan(-------)
--R                3
--R                                                     Type: Expression Integer
--E 24

--S 25 of 25
integrate(t11,x)
 

                   atan(x) 2             atan(x) 2           atan(x)
         8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
                      3                     3                   3
   (25)  ------------------------------------------------------------
                                      18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   atan(x) 2             atan(x) 2           atan(x)
--R         8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
--R                      3                     3                   3
--R   (25)  ------------------------------------------------------------
--R                                      18
--R                                          Type: Union(Expression Integer,...)
--E 25
)spool 
 
Starts dribbling to tpiezas002.output (2010/3/27, 18:41:29).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 71
c:=sqrt(a^2+b^2)
 

         +-------+
         | 2    2
   (1)  \|b  + a
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         | 2    2
--R   (1)  \|b  + a
--R                                                     Type: Expression Integer
--E 1

--S 2 of 71
t1:=(a+2*b+2*c)^2
 

                  +-------+
                  | 2    2      2            2
   (2)  (8b + 4a)\|b  + a   + 8b  + 4a b + 5a
                                                     Type: Expression Integer
--R 
--R
--R                  +-------+
--R                  | 2    2      2            2
--R   (2)  (8b + 4a)\|b  + a   + 8b  + 4a b + 5a
--R                                                     Type: Expression Integer
--E 2

--S 3 of 71
t2:=(2*a+b+2*c)^2
 

                  +-------+
                  | 2    2      2            2
   (3)  (4b + 8a)\|b  + a   + 5b  + 4a b + 8a
                                                     Type: Expression Integer
--R 
--R
--R                  +-------+
--R                  | 2    2      2            2
--R   (3)  (4b + 8a)\|b  + a   + 5b  + 4a b + 8a
--R                                                     Type: Expression Integer
--E 3

--S 4 of 71
t3:=(2*a+2*b+3*c)^2
 

                    +-------+
                    | 2    2       2             2
   (4)  (12b + 12a)\|b  + a   + 13b  + 8a b + 13a
                                                     Type: Expression Integer
--R 
--R
--R                    +-------+
--R                    | 2    2       2             2
--R   (4)  (12b + 12a)\|b  + a   + 13b  + 8a b + 13a
--R                                                     Type: Expression Integer
--E 4

--S 5 of 71
t1+t2-t3
 

   (5)  0
                                                     Type: Expression Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E 5

)clear all
 

--S 6 of 71
f(a,b,c)==[(a+2*b+2*c),(2*a+b+2*c),(2*a+2*b+3*c)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 71
f(5,12,13)
 
   Compiling function f with type (PositiveInteger,PositiveInteger,
      PositiveInteger) -> List PositiveInteger 

   (2)  [55,48,73]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function f with type (PositiveInteger,PositiveInteger,
--R      PositiveInteger) -> List PositiveInteger 
--R
--R   (2)  [55,48,73]
--R                                                   Type: List PositiveInteger
--E 7

--S 8 of 71
f(-5,12,13)
 
   Compiling function f with type (Integer,PositiveInteger,
      PositiveInteger) -> List Integer 

   (3)  [45,28,53]
                                                           Type: List Integer
--R 
--R   Compiling function f with type (Integer,PositiveInteger,
--R      PositiveInteger) -> List Integer 
--R
--R   (3)  [45,28,53]
--R                                                           Type: List Integer
--E 8

--S 9 of 71
f(5,-12,13)
 
   Compiling function f with type (PositiveInteger,Integer,
      PositiveInteger) -> List Integer 

   (4)  [7,24,25]
                                                           Type: List Integer
--R 
--R   Compiling function f with type (PositiveInteger,Integer,
--R      PositiveInteger) -> List Integer 
--R
--R   (4)  [7,24,25]
--R                                                           Type: List Integer
--E 9

--S 10 of 71
f(-5,-12,13)
 
   Compiling function f with type (Integer,Integer,PositiveInteger) -> 
      List Integer 

   (5)  [- 3,4,5]
                                                           Type: List Integer
--R 
--R   Compiling function f with type (Integer,Integer,PositiveInteger) -> 
--R      List Integer 
--R
--R   (5)  [- 3,4,5]
--R                                                           Type: List Integer
--E 10

)clear all
 

--S 11 of 71
x:=(a^2-b^2)
 

           2    2
   (1)  - b  + a
                                                     Type: Polynomial Integer
--R 
--R
--R           2    2
--R   (1)  - b  + a
--R                                                     Type: Polynomial Integer
--E 11

--S 12 of 71
y:=(2*a*b)
 

   (2)  2a b
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  2a b
--R                                                     Type: Polynomial Integer
--E 12

--S 13 of 71
z:=(a^2+b^2)
 

         2    2
   (3)  b  + a
                                                     Type: Polynomial Integer
--R 
--R
--R         2    2
--R   (3)  b  + a
--R                                                     Type: Polynomial Integer
--E 13

--S 14 of 71
x^2+y^2-z^2
 

   (4)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Polynomial Integer
--E 14

)clear all
 

--S 15 of 71
(60*v)^2+(900*v^2-1)^2 - (900*v^2+1)^2
 

   (1)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  0
--R                                                     Type: Polynomial Integer
--E 15

)clear all
 

--S 16 of 71
n:=2*(m^2+m)
 

          2
   (1)  2m  + 2m
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (1)  2m  + 2m
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 71
(2*m+1)^2 + n^2 - (n+1)^2
 

   (2)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Polynomial Integer
--E 17

)clear all
 

--S 18 of 71
n:=4*m^2-1
 

          2
   (1)  4m  - 1
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (1)  4m  - 1
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 71
(4*m)^2 + n^2 - (n+2)^2
 

   (2)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 71
(a^2-b^2)^2+(2*a*b)^2-(a^2+b^2)^2
 

   (3)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Polynomial Integer
--E 20

--S 21 of 71
(a^3-3*a*b^2)^2 + (3*a^2*b-b^3)^2 - (a^2+b^2)^3
 

   (4)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Polynomial Integer
--E 21

)clear all
 

--S 22 of 71
t0:=quatern(a,b,c,d)^3
 

   (1)
           2       2       2    3         2      2    3     2
     - 3a d  - 3a c  - 3a b  + a  + (- b d  - b c  - b  + 3a b)i
   + 
           2    3       2     2           3       2    2     2
     (- c d  - c  + (- b  + 3a )c)j + (- d  + (- c  - b  + 3a )d)k
                                          Type: Quaternion Polynomial Integer
--R 
--R
--R   (1)
--R           2       2       2    3         2      2    3     2
--R     - 3a d  - 3a c  - 3a b  + a  + (- b d  - b c  - b  + 3a b)i
--R   + 
--R           2    3       2     2           3       2    2     2
--R     (- c d  - c  + (- b  + 3a )c)j + (- d  + (- c  - b  + 3a )d)k
--R                                          Type: Quaternion Polynomial Integer
--E 22

--S 23 of 71
A:=real t0
 

              2       2       2    3
   (2)  - 3a d  - 3a c  - 3a b  + a
                                                     Type: Polynomial Integer
--R 
--R
--R              2       2       2    3
--R   (2)  - 3a d  - 3a c  - 3a b  + a
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 71
B:=imagI t0
 

             2      2    3     2
   (3)  - b d  - b c  - b  + 3a b
                                                     Type: Polynomial Integer
--R 
--R
--R             2      2    3     2
--R   (3)  - b d  - b c  - b  + 3a b
--R                                                     Type: Polynomial Integer
--E 24

--S 25 of 71
C:=imagJ t0
 

             2    3       2     2
   (4)  - c d  - c  + (- b  + 3a )c
                                                     Type: Polynomial Integer
--R 
--R
--R             2    3       2     2
--R   (4)  - c d  - c  + (- b  + 3a )c
--R                                                     Type: Polynomial Integer
--E 25

--S 26 of 71
D:=imagK t0
 

           3       2    2     2
   (5)  - d  + (- c  - b  + 3a )d
                                                     Type: Polynomial Integer
--R 
--R
--R           3       2    2     2
--R   (5)  - d  + (- c  - b  + 3a )d
--R                                                     Type: Polynomial Integer
--E 26

--S 27 of 71
A^2+B^2+C^2+D^2 - (a^2+b^2+c^2+d^2)^3
 

   (6)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  0
--R                                                     Type: Polynomial Integer
--E 27

)clear all
 

--S 28 of 71
d:=(b^2+3*c^2)/(2*c)
 

          2    2
        3c  + b
   (1)  --------
           2c
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          2    2
--R        3c  + b
--R   (1)  --------
--R           2c
--R                                            Type: Fraction Polynomial Integer
--E 28

--S 29 of 71
a:=sqrt(10*c^2+b^2)
 

         +---------+
         |   2    2
   (2)  \|10c  + b
                                                     Type: Expression Integer
--R 
--R
--R         +---------+
--R         |   2    2
--R   (2)  \|10c  + b
--R                                                     Type: Expression Integer
--E 29

--S 30 of 71
(a^2+b^2)^2 + (b^2+d^2)^2 - (b^2+8*c^2+d^2)^2
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 30

)clear all
 

--S 31 of 71
p:=2*n^2
 

          2
   (1)  2n
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (1)  2n
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 71
q:=n^2-1
 

         2
   (2)  n  - 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (2)  n  - 1
--R                                                     Type: Polynomial Integer
--E 32

--S 33 of 71
d:=(b^2+q*c^2)/(2*c)
 

         2 2    2    2
        c n  - c  + b
   (3)  --------------
              2c
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2 2    2    2
--R        c n  - c  + b
--R   (3)  --------------
--R              2c
--R                                            Type: Fraction Polynomial Integer
--E 33

--S 34 of 71
a:=sqrt(n*(n^2+1)*c^2 + (n-1)*b^2)
 

         +----------------------+
         | 2 3     2    2      2
   (4)  \|c n  + (c  + b )n - b
                                                     Type: Expression Integer
--R 
--R
--R         +----------------------+
--R         | 2 3     2    2      2
--R   (4)  \|c n  + (c  + b )n - b
--R                                                     Type: Expression Integer
--E 34

--S 35 of 71
(a^2+b^2)^2 + (b^2+d^2)^2-(b^2+p*c^2+d^2)^2
 

   (5)  0
                                                     Type: Expression Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E 35

)clear all
 

--S 36 of 71
a:=u^2-v^2-w^2
 

           2    2    2
   (1)  - w  - v  + u
                                                     Type: Polynomial Integer
--R 
--R
--R           2    2    2
--R   (1)  - w  - v  + u
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 71
b:=2*u*v
 

   (2)  2u v
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  2u v
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 71
p:=u^2+v^2+w^2
 

         2    2    2
   (3)  w  + v  + u
                                                     Type: Polynomial Integer
--R 
--R
--R         2    2    2
--R   (3)  w  + v  + u
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 71
q:=2*u*w
 

   (4)  2u w
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  2u w
--R                                                     Type: Polynomial Integer
--E 39

--S 40 of 71
c:=sqrt(4*u*w*(u^2+v^2+w^2)-d^2)
 

         +---------------------------+
         |    3        2     3      2
   (5)  \|4u w  + (4u v  + 4u )w - d
                                                     Type: Expression Integer
--R 
--R
--R         +---------------------------+
--R         |    3        2     3      2
--R   (5)  \|4u w  + (4u v  + 4u )w - d
--R                                                     Type: Expression Integer
--E 40

--S 41 of 71
(a^2+b^2)^2 + (c^2+d^2)^2 - (p^2+q^2)^2
 

   (6)  0
                                                     Type: Expression Integer
--R 
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E 41

)clear all
 

--S 42 of 71
q:=3*p+2*r+1
 

   (1)  2r + 3p + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  2r + 3p + 1
--R                                                     Type: Polynomial Integer
--E 42

--S 43 of 71
r:=sqrt(p^2+(p+1)^2)
 

         +------------+
         |  2
   (2)  \|2p  + 2p + 1
                                                     Type: Expression Integer
--R 
--R
--R         +------------+
--R         |  2
--R   (2)  \|2p  + 2p + 1
--R                                                     Type: Expression Integer
--E 43

--S 44 of 71
q^2 + (q+1)^2 - (p+q+r+1)^2
 

                        +------------+
                        |  2               2
   (3)  (- 4r - 8p - 4)\|2p  + 2p + 1  + 4r  + (8p + 4)r
                                                     Type: Expression Integer
--R 
--R
--R                        +------------+
--R                        |  2               2
--R   (3)  (- 4r - 8p - 4)\|2p  + 2p + 1  + 4r  + (8p + 4)r
--R                                                     Type: Expression Integer
--E 44

)clear all
 

--S 45 of 71
e:=sqrt(c^2+d^2)
 

         +-------+
         | 2    2
   (1)  \|d  + c
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         | 2    2
--R   (1)  \|d  + c
--R                                                     Type: Expression Integer
--E 45

--S 46 of 71
(a*c+b*d)^2 + (a*d-b*c)^2 - (a*e)^2 - (b*e)^2
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 46

)clear all
 

--S 47 of 71
a:=sqrt(c^2+d^2-b^2)
 

         +------------+
         | 2    2    2
   (1)  \|d  + c  - b
                                                     Type: Expression Integer
--R 
--R
--R         +------------+
--R         | 2    2    2
--R   (1)  \|d  + c  - b
--R                                                     Type: Expression Integer
--E 47

--S 48 of 71
(a*c+b*d)^2 + (a*d-b*c)^2 - (a^2 + b^2)^2
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 48

)clear all
 

--S 49 of 71
a:=sqrt(c^2+d^2-b^2)
 

         +------------+
         | 2    2    2
   (1)  \|d  + c  - b
                                                     Type: Expression Integer
--R 
--R
--R         +------------+
--R         | 2    2    2
--R   (1)  \|d  + c  - b
--R                                                     Type: Expression Integer
--E 49

--S 50 of 71
(a^2*c-b^2*c+2*a*b*d)^2 + (a^2*d-b^2*d-2*a*b*c)^2 - (a^2+b^2)^3
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 50

)clear all
 

--S 51 of 71
a:=sqrt(c^2+d^2-b^2)
 

         +------------+
         | 2    2    2
   (1)  \|d  + c  - b
                                                     Type: Expression Integer
--R 
--R
--R         +------------+
--R         | 2    2    2
--R   (1)  \|d  + c  - b
--R                                                     Type: Expression Integer
--E 51

--S 52 of 71
t1:=(a*c^3 - 3*b*c^2*d - 3*a*c*d^2 + b*d^3)^2
 

   (2)
                                     +------------+
              5        3 3       5   | 2    2    2       2    2  6
     (- 6b c d  + 20b c d  - 6b c d)\|d  + c  - b   + (9c  + b )d
   + 
        4      2 2  4        6      2 4  2    8    2 6
     (3c  - 15b c )d  + (- 5c  + 15b c )d  + c  - b c
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R                                     +------------+
--R              5        3 3       5   | 2    2    2       2    2  6
--R     (- 6b c d  + 20b c d  - 6b c d)\|d  + c  - b   + (9c  + b )d
--R   + 
--R        4      2 2  4        6      2 4  2    8    2 6
--R     (3c  - 15b c )d  + (- 5c  + 15b c )d  + c  - b c
--R                                                     Type: Expression Integer
--E 52

--S 53 of 71
t2:=(b*c^3 + 3*a*c^2*d - 3*b*c*d^2 - a*d^3)^2
 

   (3)
                                   +------------+
            5        3 3       5   | 2    2    2     8        2    2  6
     (6b c d  - 20b c d  + 6b c d)\|d  + c  - b   + d  + (- 5c  - b )d
   + 
        4      2 2  4      6      2 4  2    2 6
     (3c  + 15b c )d  + (9c  - 15b c )d  + b c
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                                   +------------+
--R            5        3 3       5   | 2    2    2     8        2    2  6
--R     (6b c d  - 20b c d  + 6b c d)\|d  + c  - b   + d  + (- 5c  - b )d
--R   + 
--R        4      2 2  4      6      2 4  2    2 6
--R     (3c  + 15b c )d  + (9c  - 15b c )d  + b c
--R                                                     Type: Expression Integer
--E 53

--S 54 of 71
t1+t2-(a^2+b^2)^4
 

   (4)  0
                                                     Type: Expression Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 54

)clear all
 

--S 55 of 71
a:=(p^2+q^2)*(r^2+s^2)
 

          2    2  2     2    2  2
   (1)  (q  + p )s  + (q  + p )r
                                                     Type: Polynomial Integer
--R 
--R
--R          2    2  2     2    2  2
--R   (1)  (q  + p )s  + (q  + p )r
--R                                                     Type: Polynomial Integer
--E 55

--S 56 of 71
b:=(p*r+q*s)^2 + (p*s-q*r)^2
 

          2    2  2     2    2  2
   (2)  (q  + p )s  + (q  + p )r
                                                     Type: Polynomial Integer
--R 
--R
--R          2    2  2     2    2  2
--R   (2)  (q  + p )s  + (q  + p )r
--R                                                     Type: Polynomial Integer
--E 56

--S 57 of 71
a-b
 

   (3)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Polynomial Integer
--E 57

--S 58 of 71
c:=(p*r-q*s)^2 + (p*s+q*r)^2
 

          2    2  2     2    2  2
   (4)  (q  + p )s  + (q  + p )r
                                                     Type: Polynomial Integer
--R 
--R
--R          2    2  2     2    2  2
--R   (4)  (q  + p )s  + (q  + p )r
--R                                                     Type: Polynomial Integer
--E 58

--S 59 of 71
a-c
 

   (5)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Polynomial Integer
--E 59

)clear all
 

--S 60 of 71
p:=sqrt(1+2*q^2)
 

         +-------+
         |  2
   (1)  \|2q  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         |  2
--R   (1)  \|2q  + 1
--R                                                     Type: Expression Integer
--E 60

--S 61 of 71
(q^2*(p^2-2))^2 + (2*q^2)^3 - (p*q)^4
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 61

)clear all
 

--S 62 of 71
p:=sqrt(-1+2*q^2)
 

         +-------+
         |  2
   (1)  \|2q  - 1
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         |  2
--R   (1)  \|2q  - 1
--R                                                     Type: Expression Integer
--E 62

--S 63 of 71
((p^4-p^2)/2)^2 + p^6 - (p*q)^4
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 63

)clear all
 

--S 64 of 71
p:=sqrt(1+d*q^2)
 

         +--------+
         |   2
   (1)  \|d q  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +--------+
--R         |   2
--R   (1)  \|d q  + 1
--R                                                     Type: Expression Integer
--E 64

--S 65 of 71
(4*q^2*d^4*(p^2-2))^2 + (4*q^2*d^3)^3 - (2*p*q*d^2)^4
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 65

)clear all
 

--S 66 of 71
p:=sqrt(-1+d*q^2)
 

         +--------+
         |   2
   (1)  \|d q  - 1
                                                     Type: Expression Integer
--R 
--R
--R         +--------+
--R         |   2
--R   (1)  \|d q  - 1
--R                                                     Type: Expression Integer
--E 66

--S 67 of 71
(4*p^2*d^3*(p^2-1))^2 + (2*p*d)^6 - (2*p*q*d^2)^4
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 67

)clear all
 

--S 68 of 71
p:=sqrt(1+3*q^2)
 

         +-------+
         |  2
   (1)  \|3q  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         |  2
--R   (1)  \|3q  + 1
--R                                                     Type: Expression Integer
--E 68

--S 69 of 71
p^4 + (q^2-1)^3 - (q^3+3*q)^2
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 69

)clear all
 

--S 70 of 71
p:=sqrt(1+3*d*q^2)
 

         +---------+
         |    2
   (1)  \|3d q  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +---------+
--R         |    2
--R   (1)  \|3d q  + 1
--R                                                     Type: Expression Integer
--E 70

--S 71 of 71
p^4 + (d*q^2-1)^3 - d*(d*q^3+3*q)^2
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 71

)spool 
 
Starts dribbling to typetower.output (2010/3/27, 18:41:33).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 17
F:=PrimeField 3
 

   (1)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 3
--R                                                                 Type: Domain
--E 1

--S 2 of 17
P:=UnivariatePolynomial(x,F)
 

   (2)  UnivariatePolynomial(x,PrimeField 3)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,PrimeField 3)
--R                                                                 Type: Domain
--E 2

--S 3 of 17
S:=SquareMatrix(2,P)
 

   (3)  SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
                                                                 Type: Domain
--R 
--R
--R   (3)  SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--R                                                                 Type: Domain
--E 3

--S 4 of 17
R:=UnivariatePolynomial(z,S)
 

   (4)
   UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
                                                                 Type: Domain
--R 
--R
--R   (4)
--R   UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R                                                                 Type: Domain
--E 4


--S 5 of 17
s1:S:=matrix [[2*x+1,x^2-1],[0,x-1]]
 

        +         2    +
   (5)  |2x + 1  x  + 2|
        |              |
        +  0     x + 2 +
                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--R 
--R
--R        +         2    +
--R   (5)  |2x + 1  x  + 2|
--R        |              |
--R        +  0     x + 2 +
--R                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--E 5

--S 6 of 17
s2:=transpose s1
 

        +2x + 1    0  +
   (6)  |             |
        | 2           |
        +x  + 2  x + 2+
                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--R 
--R
--R        +2x + 1    0  +
--R   (6)  |             |
--R        | 2           |
--R        +x  + 2  x + 2+
--R                   Type: SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3))
--E 6


--S 7 of 17
r:R:=z^2+s1*z+s2
 

         2   +         2    +    +2x + 1    0  +
   (7)  z  + |2x + 1  x  + 2|z + |             |
             |              |    | 2           |
             +  0     x + 2 +    +x  + 2  x + 2+
Type: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R 
--R
--R         2   +         2    +    +2x + 1    0  +
--R   (7)  z  + |2x + 1  x  + 2|z + |             |
--R             |              |    | 2           |
--R             +  0     x + 2 +    +x  + 2  x + 2+
--RType: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--E 7

--S 8 of 17
r+2*r
 

   (8)  0
Type: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R 
--R
--R   (8)  0
--RType: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--E 8


--S 9 of 17
degree r
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9


--S 10 of 17
r2:=r*r
 

   (10)
                               + 2             +     + 4              +
      4   +         2    + 3   |x  + 2x    0   | 2   |x  + 2x     0   |
     z  + |x + 2  2x  + 1|z  + |               |z  + |                |z
          |              |     |  2       2    |     |          4     |
          +  0    2x + 1 +     +2x  + 1  x  + 2+     +   0     x  + 2x+
   + 
     + 2                    +
     |x  + x + 1      0     |
     |                      |
     |             2        |
     +    0       x  + x + 1+
Type: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R 
--R
--R   (10)
--R                               + 2             +     + 4              +
--R      4   +         2    + 3   |x  + 2x    0   | 2   |x  + 2x     0   |
--R     z  + |x + 2  2x  + 1|z  + |               |z  + |                |z
--R          |              |     |  2       2    |     |          4     |
--R          +  0    2x + 1 +     +2x  + 1  x  + 2+     +   0     x  + 2x+
--R   + 
--R     + 2                    +
--R     |x  + x + 1      0     |
--R     |                      |
--R     |             2        |
--R     +    0       x  + x + 1+
--RType: UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--E 10


--S 11 of 17
gcd(r2,r)
 
   There are 4 exposed and 3 unexposed library operations named gcd 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op gcd
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named gcd 
      with argument type(s) 
UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
UnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 4 exposed and 3 unexposed library operations named gcd 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op gcd
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named gcd 
--R      with argument type(s) 
--RUnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--RUnivariatePolynomial(z,SquareMatrix(2,UnivariatePolynomial(x,PrimeField 3)))
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11


--S 12 of 17
p1:=s1(1,1)
 

   (11)  2x + 1
                                   Type: UnivariatePolynomial(x,PrimeField 3)
--R 
--R
--R   (11)  2x + 1
--R                                   Type: UnivariatePolynomial(x,PrimeField 3)
--E 12

--S 13 of 17
ps:=s1(1,2)
 

          2
   (12)  x  + 2
                                   Type: UnivariatePolynomial(x,PrimeField 3)
--R 
--R
--R          2
--R   (12)  x  + 2
--R                                   Type: UnivariatePolynomial(x,PrimeField 3)
--E 13

--S 14 of 17
gcd(p1,p2)
 

   (13)  1
          Type: UnivariatePolynomial(p2,UnivariatePolynomial(x,PrimeField 3))
--R 
--R
--R   (13)  1
--R          Type: UnivariatePolynomial(p2,UnivariatePolynomial(x,PrimeField 3))
--E 14


--S 15 of 17
q1:UP(x,INT):=2*x+1
 

   (14)  2x + 1
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (14)  2x + 1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 17
q2:UP(x,INT):=x^2+2
 

          2
   (15)  x  + 2
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R          2
--R   (15)  x  + 2
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 17
gcd(q1,q2)
 

   (16)  1
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 17


)spool 
 
Starts dribbling to fr1.output (2010/3/27, 18:26:20).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 1

--S 2 of 38
unit(g)
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 38
numberOfFactors(g)
 

   (3)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  3
--R                                                        Type: PositiveInteger
--E 4

--S 4 of 38
[nthFactor(g,i) for i in 1..numberOfFactors(g)]
 

   (4)  [2,7,11]
                                                           Type: List Integer
--R 
--R
--R   (4)  [2,7,11]
--R                                                           Type: List Integer
--E 4

--S 5 of 38
[nthExponent(g,i) for i in 1..numberOfFactors(g)]
 

   (5)  [3,2,1]
                                                           Type: List Integer
--R 
--R
--R   (5)  [3,2,1]
--R                                                           Type: List Integer
--E 5

--S 6 of 38
[nthFlag(g,i) for i in 1..numberOfFactors(g)]
 

   (6)  ["prime","prime","prime"]
                               Type: List Union("nil","sqfr","irred","prime")
--R 
--R
--R   (6)  ["prime","prime","prime"]
--R                               Type: List Union("nil","sqfr","irred","prime")
--E 6

--S 7 of 38
factorList(g)
 

   (7)
   [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2],
    [flg= "prime",fctr= 11,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--R 
--R
--R   (7)
--R   [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2],
--R    [flg= "prime",fctr= 11,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--E 7

--S 8 of 38
factors(g)
 

   (8)
   [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]]
                         Type: List Record(factor: Integer,exponent: Integer)
--R 
--R
--R   (8)
--R   [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]]
--R                         Type: List Record(factor: Integer,exponent: Integer)
--E 8

--S 9 of 38
first(%).factor
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9

)clear all
 

--S 10 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 10

--S 11 of 38
expand(g)
 

   (2)  4312
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  4312
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 38
reduce(*,[t.factor for t in factors(g)])
 

   (3)  154
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  154
--R                                                        Type: PositiveInteger
--E 12

)clear all
 

--S 13 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 13

--S 14 of 38
f := factor(246960)
 

         4 2   3
   (2)  2 3 5 7
                                                       Type: Factored Integer
--R 
--R
--R         4 2   3
--R   (2)  2 3 5 7
--R                                                       Type: Factored Integer
--E 14

--S 15 of 38
f * g
 

         7 2   5
   (3)  2 3 5 7 11
                                                       Type: Factored Integer
--R 
--R
--R         7 2   5
--R   (3)  2 3 5 7 11
--R                                                       Type: Factored Integer
--E 15

--S 16 of 38
f**500
 

         2000 1000 500 1500
   (4)  2    3    5   7
                                                       Type: Factored Integer
--R 
--R
--R         2000 1000 500 1500
--R   (4)  2    3    5   7
--R                                                       Type: Factored Integer
--E 16

--S 17 of 38
gcd(f,g)
 

         3 2
   (5)  2 7
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (5)  2 7
--R                                                       Type: Factored Integer
--E 17

--S 18 of 38
lcm(f,g)
 

         4 2   3
   (6)  2 3 5 7 11
                                                       Type: Factored Integer
--R 
--R
--R         4 2   3
--R   (6)  2 3 5 7 11
--R                                                       Type: Factored Integer
--E 18

--S 19 of 38
f + g
 

         3 2
   (7)  2 7 641
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (7)  2 7 641
--R                                                       Type: Factored Integer
--E 19

--S 20 of 38
f - g
 

         3 2
   (8)  2 7 619
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (8)  2 7 619
--R                                                       Type: Factored Integer
--E 20

--S 21 of 38
zero?(factor(0))
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 21

--S 22 of 38
zero?(g)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 22

--S 23 of 38
one?(factor(1))
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 23

--S 24 of 38
one?(f)
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 24

--S 25 of 38
0$Factored(Integer)
 

   (13)  0
                                                       Type: Factored Integer
--R 
--R
--R   (13)  0
--R                                                       Type: Factored Integer
--E 25

--S 26 of 38
1$Factored(Integer)
 

   (14)  1
                                                       Type: Factored Integer
--R 
--R
--R   (14)  1
--R                                                       Type: Factored Integer
--E 26

)clear all
 

--S 27 of 38
nilFactor(24,2)
 

          2
   (1)  24
                                                       Type: Factored Integer
--R 
--R
--R          2
--R   (1)  24
--R                                                       Type: Factored Integer
--E 27

--S 28 of 38
nthFlag(%,1)
 

   (2)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (2)  "nil"
--R                                                       Type: Union("nil",...)
--E 28

--S 29 of 38
sqfrFactor(30,2)
 

          2
   (3)  30
                                                       Type: Factored Integer
--R 
--R
--R          2
--R   (3)  30
--R                                                       Type: Factored Integer
--E 29

--S 30 of 38
irreducibleFactor(13,10)
 

          10
   (4)  13
                                                       Type: Factored Integer
--R 
--R
--R          10
--R   (4)  13
--R                                                       Type: Factored Integer
--E 30

--S 31 of 38
primeFactor(11,5)
 

          5
   (5)  11
                                                       Type: Factored Integer
--R 
--R
--R          5
--R   (5)  11
--R                                                       Type: Factored Integer
--E 31

--S 32 of 38
h := factor(-720)
 

           4 2
   (6)  - 2 3 5
                                                       Type: Factored Integer
--R 
--R
--R           4 2
--R   (6)  - 2 3 5
--R                                                       Type: Factored Integer
--E 32

--S 33 of 38
h - makeFR(unit(h),factorList(h))
 

   (7)  0
                                                       Type: Factored Integer
--R 
--R
--R   (7)  0
--R                                                       Type: Factored Integer
--E 33

)clear all
 

--S 34 of 38
p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63
 

           2            2      2                  2
   (1)  (4x  - 12x + 9)y  + (4x  - 12x + 9)y + 28x  - 84x + 63
                                                     Type: Polynomial Integer
--R 
--R
--R           2            2      2                  2
--R   (1)  (4x  - 12x + 9)y  + (4x  - 12x + 9)y + 28x  - 84x + 63
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 38
fp := factor(p)
 

                2  2
   (2)  (2x - 3) (y  + y + 7)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                2  2
--R   (2)  (2x - 3) (y  + y + 7)
--R                                            Type: Factored Polynomial Integer
--E 35

--S 36 of 38
D(p,x)
 

                  2
   (3)  (8x - 12)y  + (8x - 12)y + 56x - 84
                                                     Type: Polynomial Integer
--R 
--R
--R                  2
--R   (3)  (8x - 12)y  + (8x - 12)y + 56x - 84
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 38
D(fp,x)
 

                   2
   (4)  4(2x - 3)(y  + y + 7)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                   2
--R   (4)  4(2x - 3)(y  + y + 7)
--R                                            Type: Factored Polynomial Integer
--E 37

--S 38 of 38
numberOfFactors(%)
 

   (5)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  3
--R                                                        Type: PositiveInteger
--E 38
)spool 
 
Starts dribbling to tsetcatvermeer.output (2010/3/27, 18:41:31).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 21
ls : List Symbol := [w,v,u,y,x];
 

                                                            Type: List Symbol
--R 
--R
--R                                                            Type: List Symbol
--E 1

--S 2 of 21
V := OVAR(ls);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 2

--S 3 of 21
R := Integer;
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 3

--S 4 of 21
E := IndexedExponents V;
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 4

--S 5 of 21
P := NSMP(R, V);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 5

--S 6 of 21
LP := List(P);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 6

--S 7 of 21
x: P := 'x;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 7

--S 8 of 21
y: P := 'y;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 8

--S 9 of 21
u: P := 'u;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 9

--S 10 of 21
v: P := 'v;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 10

--S 11 of 21
w: P := 'w;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 11

--S 12 of 21
p1 := (x - u) ** 2 + (y - v) ** 2 - 1 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 12

--S 13 of 21
p2 := v ** 2 - u ** 3 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 13

--S 14 of 21
p3 := 2 * v * (x - u) + 3 * u ** 2 * (y - v) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 14

--S 15 of 21
f1 := (3 * w * u ** 2 - 1) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 15

--S 16 of 21
f2 := (2 * w * v - 1) ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 16

--S 17 of 21
p4 := f1 * f2 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 17

--S 18 of 21
lp := [p1,p2,p3,p4] ;
 

Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--R 
--R
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x])
--E 18

--S 19 of 21
T := REGSET(R,E,V,P)
 

   (19)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x]
  ,OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,Orde
  redVariableList [w,v,u,y,x]))
                                                                 Type: Domain
--R 
--R
--R   (19)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x]
--R  ,OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,Orde
--R  redVariableList [w,v,u,y,x]))
--R                                                                 Type: Domain
--E 19

--S 20 of 21
zeroSetSplit(lp)$T
 

   (20)
   [
     {
             6           3       2                 4
         729y  + (- 1458x  + 729x  - 4158x - 1685)y
       + 
              6        5        4        3       2                2       8
         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
       + 
             7        6        5        4        3        2
         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
       ,

                  4           3       2                  2        6        5
             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
           + 
                     4        3        2
             - 10125x  - 4800x  + 2501x  + 4968x - 1587
        *
           u
       + 
               3       2  2       6        5        4       3        2
         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
       ,
         2                   2                    2  2           2
      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--R 
--R
--R   (20)
--R   [
--R     {
--R             6           3       2                 4
--R         729y  + (- 1458x  + 729x  - 4158x - 1685)y
--R       + 
--R              6        5        4        3       2                2       8
--R         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
--R       + 
--R             7        6        5        4        3        2
--R         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
--R           + 
--R                     4        3        2
--R             - 10125x  - 4800x  + 2501x  + 4968x - 1587
--R        *
--R           u
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
--R       ,
--R         2                   2                    2  2           2
--R      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--E 20

--S 21 of 21
zeroSetSplit(lp,false)$T
 

   (21)
   [
     {
             6           3       2                 4
         729y  + (- 1458x  + 729x  - 4158x - 1685)y
       + 
              6        5        4        3       2                2       8
         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
       + 
             7        6        5        4        3        2
         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
       ,

                  4           3       2                  2        6        5
             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
           + 
                     4        3        2
             - 10125x  - 4800x  + 2501x  + 4968x - 1587
        *
           u
       + 
               3       2  2       6        5        4       3        2
         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
       ,
         2                   2                    2  2           2
      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
     ,

         4     3      2                               2
     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
        2          2
      6v  - 2u - 3x  + 2x + 3, 2v w - 1}
     ,

            6         5         4          3         2
     {59049x  + 91854x  - 45198x  + 145152x  + 63549x  + 60922x + 21420,

                            5                  4                  3
             31484448266904x  - 18316865522574x  + 23676995746098x
           + 
                           2
             6657857188965x  + 8904703998546x + 3890631403260
        *
            2
           y
       + 
                        5                  4                  3
         94262810316408x  - 82887296576616x  + 89801831438784x
       + 
                        2
         28141734167208x  + 38070359425432x + 16003865949120
       ,
           2             2         2       3      2                    3     2
      (243x  + 36x + 85)u  + (- 81y  - 162x  + 36x  + 154x + 72)u - 72x  + 4x ,
         2                   2                    2  2           2
      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
     ,

         4     3      2                               2
     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
        2          2             2
      6v  - 2u - 3x  + 2x + 3, 3u w - 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--R 
--R
--R   (21)
--R   [
--R     {
--R             6           3       2                 4
--R         729y  + (- 1458x  + 729x  - 4158x - 1685)y
--R       + 
--R              6        5        4        3       2                2       8
--R         (729x  - 1458x  - 2619x  - 4892x  - 297x  + 5814x + 427)y  + 729x
--R       + 
--R             7        6        5        4        3        2
--R         216x  - 2900x  - 2376x  + 3870x  + 4072x  - 1188x  - 1656x + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187y  + (- 4374x  - 972x  - 12474x - 2868)y  + 2187x  - 1944x
--R           + 
--R                     4        3        2
--R             - 10125x  - 4800x  + 2501x  + 4968x - 1587
--R        *
--R           u
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944x  - 108x )y  + 972x  + 3024x  - 1080x  + 496x  + 1116x
--R       ,
--R         2                   2                    2  2           2
--R      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
--R     ,
--R
--R         4     3      2                               2
--R     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
--R        2          2
--R      6v  - 2u - 3x  + 2x + 3, 2v w - 1}
--R     ,
--R
--R            6         5         4          3         2
--R     {59049x  + 91854x  - 45198x  + 145152x  + 63549x  + 60922x + 21420,
--R
--R                            5                  4                  3
--R             31484448266904x  - 18316865522574x  + 23676995746098x
--R           + 
--R                           2
--R             6657857188965x  + 8904703998546x + 3890631403260
--R        *
--R            2
--R           y
--R       + 
--R                        5                  4                  3
--R         94262810316408x  - 82887296576616x  + 89801831438784x
--R       + 
--R                        2
--R         28141734167208x  + 38070359425432x + 16003865949120
--R       ,
--R           2             2         2       3      2                    3     2
--R      (243x  + 36x + 85)u  + (- 81y  - 162x  + 36x  + 154x + 72)u - 72x  + 4x ,
--R         2                   2                    2  2           2
--R      (3u  + 2u - 2x)v - 3y u , ((4u - 4x)v - 6y u )w  + (2v + 3u )w - 1}
--R     ,
--R
--R         4     3      2                               2
--R     {27x  + 4x  - 54x  - 36x + 23, y, (12x + 2)u - 9x  - 2x + 9,
--R        2          2             2
--R      6v  - 2u - 3x  + 2x + 3, 3u w - 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [w,v,u,y,x],OrderedVariableList [w,v,u,y,x],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [w,v,u,y,x]))
--E 21
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read intlf
 
)set break resume
 
)spool intlf.output
 
 
Daly Bug
   >> System error:
   file intlf.output already exists

   Continuing to read the file...

)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 2
exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1)
 

                            2
                         - x
                 erf(x)%e
   (1)  ------------------------------
              3         2
        erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R                            2
--R                         - x
--R                 erf(x)%e
--R   (1)  ------------------------------
--R              3         2
--R        erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 2
integrate(%, x)
 

                     +---+    erf(x) - 1      +---+
        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
                              erf(x) + 1
   (2)  -------------------------------------------
                        8erf(x) - 8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +---+    erf(x) - 1      +---+
--R        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
--R                              erf(x) + 1
--R   (2)  -------------------------------------------
--R                        8erf(x) - 8
--R                                          Type: Union(Expression Integer,...)
--E 2
)spool 
 
 
Daly Bug
   >> System error:
   Not in dribble.

   Continuing to read the file...

)lisp (bye)
 
Starts dribbling to elemnum.output (2010/3/27, 18:25:23).
)set message test on
 
)set message auto off
 
)clear all
 
)set break resume
 

--S 1  of 50
x := 0.7::Float
 

   (1)  0.7
                                                                  Type: Float
--R 
--R
--R   (1)  0.7
--R                                                                  Type: Float
--E 1

--S 2 of 50
[exp log x]
 

   (2)  [0.7]
                                                             Type: List Float
--R 
--R
--R   (2)  [0.7]
--R                                                             Type: List Float
--E 2

--S 3 of 50
[log exp x]
 

   (3)  [0.7]
                                                             Type: List Float
--R 
--R
--R   (3)  [0.7]
--R                                                             Type: List Float
--E 3

--S 4 of 50
[sin asin x,  cos acos x,  tan atan x,  cot acot x]
 

   (4)  [0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (4)  [0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 4

--S 5 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (5)  [0.7,0.7,0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (5)  [0.7,0.7,0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 5

--S 6 of 50
[sinh asinh x,             tanh atanh x,             csch acsch x,sech asech x]
 

   (6)  [0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (6)  [0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 6

--S 7 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (7)  [0.7,0.7,0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R 
--R
--R   (7)  [0.7,0.7,0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 7

--should give errors:
--acsc  x
--asec  x 
--acosh x
--acoth x

--S 8 of 50
x := 1.1::Float
 

   (8)  1.1
                                                                  Type: Float
--R 
--R
--R   (8)  1.1
--R                                                                  Type: Float
--E 8

--S 9 of 50
[exp log x]
 

   (9)  [1.1]
                                                             Type: List Float
--R 
--R
--R   (9)  [1.1]
--R                                                             Type: List Float
--E 9

--S 10 of 50
[log exp x]
 

   (10)  [1.1]
                                                             Type: List Float
--R 
--R
--R   (10)  [1.1]
--R                                                             Type: List Float
--E 10

--S 11 of 50
[                          tan atan x,  cot acot x, csc acsc x,   sec asec x  ]
 

   (11)  [1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (11)  [1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 11

--S 12 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (12)  [1.1,1.1,1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (12)  [1.1,1.1,1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 12

--S 13 of 50
[sinh asinh x,cosh acosh x,             coth acoth x,csch acsch x             ]
 

   (13)  [1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (13)  [1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 13

--S 14 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (14)  [1.1,1.1,1.1,1.1,1.1,1.1]
                                                             Type: List Float
--R 
--R
--R   (14)  [1.1,1.1,1.1,1.1,1.1,1.1]
--R                                                             Type: List Float
--E 14

--should give errors: 
--asin x
--acos x
--atanh x
--asech x

--S 15 of 50
x := 0.7::DoubleFloat
 

   (15)  0.69999999999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (15)  0.69999999999999996
--R                                                            Type: DoubleFloat
--E 15

--S 16 of 50
[exp log x]
 

   (16)  [0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (16)  [0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 16

--S 17 of 50
[log exp x]
 

   (17)  [0.70000000000000007]
                                                       Type: List DoubleFloat
--R 
--R
--R   (17)  [0.70000000000000007]
--R                                                       Type: List DoubleFloat
--E 17

--S 18 of 50
[sin asin x,  cos acos x,  tan atan x,  cot acot x]
 

   (18)
   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,
    0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (18)
--R   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,
--R    0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 18

--S 19 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (19)
   [0.69999999999999996, 0.69999999999999996, 0.69999999999999996,
    0.69999999999999996, 0.69999999999999996, 0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (19)
--R   [0.69999999999999996, 0.69999999999999996, 0.69999999999999996,
--R    0.69999999999999996, 0.69999999999999996, 0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 19

--S 20 of 50
[sinh asinh x,             tanh atanh x,             csch acsch x,sech asech x]
 

   (20)
   [0.69999999999999996, 0.69999999999999996, 0.69999999999999984,
    0.69999999999999996]
                                                       Type: List DoubleFloat
--R 
--R
--R   (20)
--R   [0.69999999999999996, 0.69999999999999996, 0.69999999999999984,
--R    0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 20

--S 21 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (21)
   [0.70000000000000007, 0.70000000000000018, 0.70000000000000029,
    0.70000000000000029, 0.70000000000000007, 0.70000000000000018]
                                                       Type: List DoubleFloat
--R 
--R
--R   (21)
--R   [0.70000000000000007, 0.70000000000000018, 0.70000000000000029,
--R    0.70000000000000029, 0.70000000000000007, 0.70000000000000018]
--R                                                       Type: List DoubleFloat
--E 21

--should give errors: 
--acsc  x
--asec  x 
--acosh x
--acoth x

--S 22 of 50
x := 1.1::DoubleFloat
 

   (22)  1.1000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (22)  1.1000000000000001
--R                                                            Type: DoubleFloat
--E 22

--S 23 of 50
[exp log x]
 

   (23)  [1.1000000000000001]
                                                       Type: List DoubleFloat
--R 
--R
--R   (23)  [1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 23

--S 24 of 50
[log exp x]
 

   (24)  [1.1000000000000001]
                                                       Type: List DoubleFloat
--R 
--R
--R   (24)  [1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 24

--S 25 of 50
[                          tan atan x,  cot acot x, csc acsc x,   sec asec x  ]
 

   (25)
   [1.1000000000000001,1.0999999999999999,1.1000000000000001,1.1000000000000001]
                                                       Type: List DoubleFloat
--R 
--R
--R   (25)
--R   [1.1000000000000001,1.0999999999999999,1.1000000000000001,1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 25

--S 26 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (26)
   [1.1000000000000003, 1.1000000000000001, 1.1000000000000001,
    1.1000000000000001, 1.0999999999999999, 1.1000000000000001]
                                                       Type: List DoubleFloat
--R 
--R
--R   (26)
--R   [1.1000000000000003, 1.1000000000000001, 1.1000000000000001,
--R    1.1000000000000001, 1.0999999999999999, 1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 26

--S 27 of 50
[sinh asinh x,cosh acosh x,             coth acoth x,csch acsch x             ]
 

   (27)
   [1.1000000000000001,1.1000000000000001,1.1000000000000001,1.1000000000000001]
                                                       Type: List DoubleFloat
--R 
--R
--R   (27)
--R   [1.1000000000000001,1.1000000000000001,1.1000000000000001,1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 27

--S 28 of 50
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
 

   (28)
   [1.1000000000000001, 1.0999999999999999, 1.1000000000000001,
    1.1000000000000003, 1.1000000000000001, 1.0999999999999999]
                                                       Type: List DoubleFloat
--R 
--R
--R   (28)
--R   [1.1000000000000001, 1.0999999999999999, 1.1000000000000001,
--R    1.1000000000000003, 1.1000000000000001, 1.0999999999999999]
--R                                                       Type: List DoubleFloat
--E 28

--should give errors: 
--asin x
--acos x
--atanh x
--asech x

--S 29 of 50
qtest(a,b,n) ==
   m1 := if n = 1 or n = 4 then 0 else  1
   s1 := if n = 1 or n = 4 then 1 else -1
   s2 := if n = 1 or n = 2 then 1 else -1
   x := complex(s1*a, s2*b)
   [x- exp   log x, _
    x- sin   asin  x, x-    cos   acos  x, x- tan   atan  x , _
    x- csc   acsc  x, x-    sec   asec  x, x- cot   acot  x , _
    x- sinh  asinh x, x-    cosh  acosh x, x- tanh  atanh x , _
    x- csch  acsch x, x-    sech  asech x, x- coth  acoth x , _
    x- log   exp   x, _
    x- asin  sin   x, x- s1*acos  cos   x, x- atan  tan  x , _
    x- acsc  csc   x, x- s1*asec  sec   x, x- acot  cot  x + m1*%pi, _
    x- asinh sinh  x, x- s1*acosh cosh  x, x- atanh tanh x , _
    x- acsch csch  x, x- s1*asech sech  x, x- acoth coth x ]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 50
qerr(l) ==
    reduce(+, [norm v for v in l])/#l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 50
sa := 0.7::DoubleFloat
 

   (31)  0.69999999999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (31)  0.69999999999999996
--R                                                            Type: DoubleFloat
--E 31

--S 32 of 50
sb := 1.1::DoubleFloat
 

   (32)  1.1000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (32)  1.1000000000000001
--R                                                            Type: DoubleFloat
--E 32

--S 33 of 50
ba := 0.7::Float
 

   (33)  0.7
                                                                  Type: Float
--R 
--R
--R   (33)  0.7
--R                                                                  Type: Float
--E 33

--S 34 of 50
bb := 1.1::Float
 

   (34)  1.1
                                                                  Type: Float
--R 
--R
--R   (34)  1.1
--R                                                                  Type: Float
--E 34

--S 35 of 50
qtest(sa, sb, 1)
 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 

   (35)
   [1.1102230246251565E-16, 2.2204460492503131E-16 - 4.4408920985006262E-16 %i,
    - 2.2204460492503131E-16,
    - 4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
    4.4408920985006262E-16, - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
    1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
    1.1102230246251565E-16 - 2.2204460492503131E-16 %i, 0.,
    - 6.6613381477509392E-16 %i, - 1.1102230246251565E-16,
    - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
    - 3.3306690738754696E-16,
    - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
    - 5.5511151231257827E-16, - 2.2204460492503131E-16,
    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
                                               Type: List Complex DoubleFloat
--R 
--R   Compiling function qtest with type (DoubleFloat,DoubleFloat,
--R      PositiveInteger) -> List Complex DoubleFloat 
--R
--R   (35)
--R   [1.1102230246251565E-16, 2.2204460492503131E-16 - 4.4408920985006262E-16 %i,
--R    - 2.2204460492503131E-16,
--R    - 4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
--R    4.4408920985006262E-16, - 1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16 - 2.2204460492503131E-16 %i, 0.,
--R    - 6.6613381477509392E-16 %i, - 1.1102230246251565E-16,
--R    - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
--R    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
--R    - 3.3306690738754696E-16,
--R    - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
--R    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
--R    - 5.5511151231257827E-16, - 2.2204460492503131E-16,
--R    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.,
--R    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
--R                                               Type: List Complex DoubleFloat
--E 35

--S 36 of 50
qerr %
 
   Compiling function qerr with type List Complex DoubleFloat -> 
      DoubleFloat 

   (36)  1.2373359150401687E-31
                                                            Type: DoubleFloat
--R 
--R   Compiling function qerr with type List Complex DoubleFloat -> 
--R      DoubleFloat 
--R
--R   (36)  1.2373359150401687E-31
--R                                                            Type: DoubleFloat
--E 36

--S 37 of 50
qtest(ba, bb, 1)
 
   Compiling function qtest with type (Float,Float,PositiveInteger) -> 
      List Complex Float 

   (37)
   [- 0.3 E -20, 0.7 E -20, 0.7 E -20, 0.7 E -20 + 0.7 E -20 %i,
    - 0.7 E -20 %i, - 0.1 E -19, 0.3 E -20 - 0.7 E -20 %i,
    - 0.3 E -20 - 0.7 E -20 %i, 0.0, - 0.3 E -20, 0.1 E -19 %i,
    0.3 E -19 + 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19, - 0.3 E -20,
    - 0.7 E -20 - 0.1 E -19 %i, 0.2 E -19, - 0.2 E -19 - 0.7 E -20 %i,
    0.1 E -19 - 0.1 E -19 %i, - 0.7 E -20, - 0.7 E -20 - 0.7 E -20 %i, 0.0,
    - 0.7 E -20, 0.0, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R   Compiling function qtest with type (Float,Float,PositiveInteger) -> 
--R      List Complex Float 
--R
--R   (37)
--R   [- 0.3 E -20, 0.7 E -20, 0.7 E -20, 0.7 E -20 + 0.7 E -20 %i,
--R    - 0.7 E -20 %i, - 0.1 E -19, 0.3 E -20 - 0.7 E -20 %i,
--R    - 0.3 E -20 - 0.7 E -20 %i, 0.0, - 0.3 E -20, 0.1 E -19 %i,
--R    0.3 E -19 + 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19, - 0.3 E -20,
--R    - 0.7 E -20 - 0.1 E -19 %i, 0.2 E -19, - 0.2 E -19 - 0.7 E -20 %i,
--R    0.1 E -19 - 0.1 E -19 %i, - 0.7 E -20, - 0.7 E -20 - 0.7 E -20 %i, 0.0,
--R    - 0.7 E -20, 0.0, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 37

--S 38 of 50
qerr %
 
   Compiling function qerr with type List Complex Float -> Float 

   (38)  0.1355456601 9472741322 E -39
                                                                  Type: Float
--R 
--R   Compiling function qerr with type List Complex Float -> Float 
--R
--R   (38)  0.1355456601 9472741322 E -39
--R                                                                  Type: Float
--E 38

--S 39 of 50
qtest(sa, sb, 2)
 

   (39)
   [- 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 4.4408920985006262E-16 %i,
    - 3.3306690738754696E-16,
    4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
    - 4.4408920985006262E-16,
    1.1102230246251565E-16 - 2.2204460492503131E-16 %i,
    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
    - 1.1102230246251565E-16,
    4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 - 2.2204460492503131E-16 %i, 0.,
    4.4408920985006262E-16 - 4.4408920985006262E-16 %i, 0.,
    3.3306690738754696E-16, 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
    0., 8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
    3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
    2.2204460492503131E-16 - 2.2204460492503131E-16 %i]
                                               Type: List Complex DoubleFloat
--R 
--R
--R   (39)
--R   [- 1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 - 4.4408920985006262E-16 %i,
--R    - 3.3306690738754696E-16,
--R    4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
--R    - 4.4408920985006262E-16,
--R    1.1102230246251565E-16 - 2.2204460492503131E-16 %i,
--R    3.3306690738754696E-16 - 2.2204460492503131E-16 %i,
--R    - 1.1102230246251565E-16,
--R    4.4408920985006262E-16 - 2.2204460492503131E-16 %i,
--R    - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    - 1.1102230246251565E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i, 0.,
--R    4.4408920985006262E-16 - 4.4408920985006262E-16 %i, 0.,
--R    3.3306690738754696E-16, 4.4408920985006262E-16 - 4.4408920985006262E-16 %i,
--R    0., 8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
--R    3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i]
--R                                               Type: List Complex DoubleFloat
--E 39

--S 40 of 50
qerr %
 

   (40)  1.3985214365396544E-31
                                                            Type: DoubleFloat
--R 
--R
--R   (40)  1.3985214365396544E-31
--R                                                            Type: DoubleFloat
--E 40

--S 41 of 50
qtest(ba, bb, 2)
 

   (41)
   [0.3 E -20, - 0.7 E -20, - 0.3 E -20, - 0.7 E -20 + 0.7 E -20 %i,
    - 0.7 E -20 %i, - 0.3 E -20, - 0.7 E -20 %i, 0.1 E -19 + 0.1 E -19 %i,
    - 0.3 E -20, 0.0, 0.2 E -19 - 0.1 E -19 %i, - 0.2 E -19 + 0.7 E -20 %i,
    - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20, 0.7 E -20 - 0.1 E -19 %i,
    - 0.2 E -19, 0.2 E -19 - 0.7 E -20 %i, - 0.1 E -19 - 0.1 E -19 %i,
    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, 0.0,
    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R
--R   (41)
--R   [0.3 E -20, - 0.7 E -20, - 0.3 E -20, - 0.7 E -20 + 0.7 E -20 %i,
--R    - 0.7 E -20 %i, - 0.3 E -20, - 0.7 E -20 %i, 0.1 E -19 + 0.1 E -19 %i,
--R    - 0.3 E -20, 0.0, 0.2 E -19 - 0.1 E -19 %i, - 0.2 E -19 + 0.7 E -20 %i,
--R    - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20, 0.7 E -20 - 0.1 E -19 %i,
--R    - 0.2 E -19, 0.2 E -19 - 0.7 E -20 %i, - 0.1 E -19 - 0.1 E -19 %i,
--R    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, 0.0,
--R    0.3 E -20 - 0.7 E -20 %i, 0.7 E -20 - 0.7 E -20 %i, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 41

--S 42 of 50
qerr %
 

   (42)  0.1351041433 8627553239 E -39
                                                                  Type: Float
--R 
--R
--R   (42)  0.1351041433 8627553239 E -39
--R                                                                  Type: Float
--E 42

--S 43 of 50
qtest(sa, sb, 3)
 

   (43)
   [- 1.1102230246251565E-16, 0.,
    - 2.2204460492503131E-16 + 4.4408920985006262E-16 %i,
    - 2.2204460492503131E-16, 1.1102230246251565E-16, - 4.4408920985006262E-16,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16,
    4.4408920985006262E-16 + 2.2204460492503131E-16 %i,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 0., 0.,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 %i, 0.,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
    8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
    3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i]
                                               Type: List Complex DoubleFloat
--R 
--R
--R   (43)
--R   [- 1.1102230246251565E-16, 0.,
--R    - 2.2204460492503131E-16 + 4.4408920985006262E-16 %i,
--R    - 2.2204460492503131E-16, 1.1102230246251565E-16, - 4.4408920985006262E-16,
--R    - 1.1102230246251565E-16, - 1.1102230246251565E-16,
--R    4.4408920985006262E-16 + 2.2204460492503131E-16 %i,
--R    - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    - 1.1102230246251565E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 0., 0.,
--R    - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 %i, 0.,
--R    - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
--R    8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
--R    3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i]
--R                                               Type: List Complex DoubleFloat
--E 43

--S 44 of 50
qerr %
 

   (44)  1.0002983834232781E-31
                                                            Type: DoubleFloat
--R 
--R
--R   (44)  1.0002983834232781E-31
--R                                                            Type: DoubleFloat
--E 44

--S 45 of 50
qtest(ba, bb, 3)
 

   (45)
   [0.3 E -20, - 0.3 E -20, - 0.7 E -20, - 0.3 E -20 - 0.7 E -20 %i,
    - 0.3 E -20, 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i,
    0.1 E -19 - 0.1 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19 + 0.1 E -19 %i,
    - 0.2 E -19 - 0.7 E -20 %i, - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20,
    - 0.3 E -20 + 0.1 E -19 %i, - 0.1 E -19 + 0.7 E -20 %i,
    0.3 E -20 + 0.7 E -20 %i, 0.1 E -19 %i, 0.3 E -20 + 0.7 E -20 %i,
    0.7 E -20 + 0.7 E -20 %i, 0.0, 0.3 E -20 + 0.7 E -20 %i,
    0.7 E -20 + 0.7 E -20 %i, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R
--R   (45)
--R   [0.3 E -20, - 0.3 E -20, - 0.7 E -20, - 0.3 E -20 - 0.7 E -20 %i,
--R    - 0.3 E -20, 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i,
--R    0.1 E -19 - 0.1 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19 + 0.1 E -19 %i,
--R    - 0.2 E -19 - 0.7 E -20 %i, - 0.7 E -20, 0.0, - 0.2 E -19, 0.3 E -20,
--R    - 0.3 E -20 + 0.1 E -19 %i, - 0.1 E -19 + 0.7 E -20 %i,
--R    0.3 E -20 + 0.7 E -20 %i, 0.1 E -19 %i, 0.3 E -20 + 0.7 E -20 %i,
--R    0.7 E -20 + 0.7 E -20 %i, 0.0, 0.3 E -20 + 0.7 E -20 %i,
--R    0.7 E -20 + 0.7 E -20 %i, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 45

--S 46 of 50
qerr %
 

   (46)  0.1258322904 0878603507 E -39
                                                                  Type: Float
--R 
--R
--R   (46)  0.1258322904 0878603507 E -39
--R                                                                  Type: Float
--E 46

--S 47 of 50
qtest(sa, sb, 4)
 

   (47)
   [1.1102230246251565E-16, 0.,
    3.3306690738754696E-16 + 4.4408920985006262E-16 %i, 2.2204460492503131E-16,
    - 1.1102230246251565E-16,
    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 1.1102230246251565E-16,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
    1.1102230246251565E-16 + 2.2204460492503131E-16 %i, 0.,
    6.6613381477509392E-16 %i, - 1.1102230246251565E-16, 0., 0.,
    2.2204460492503131E-16 %i, 0., 0., - 6.6613381477509392E-16,
    - 2.2204460492503131E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
    0., - 1.1102230246251565E-16, - 1.1102230246251565E-16]
                                               Type: List Complex DoubleFloat
--R 
--R
--R   (47)
--R   [1.1102230246251565E-16, 0.,
--R    3.3306690738754696E-16 + 4.4408920985006262E-16 %i, 2.2204460492503131E-16,
--R    - 1.1102230246251565E-16,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 1.1102230246251565E-16,
--R    - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 - 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16 + 2.2204460492503131E-16 %i, 0.,
--R    6.6613381477509392E-16 %i, - 1.1102230246251565E-16, 0., 0.,
--R    2.2204460492503131E-16 %i, 0., 0., - 6.6613381477509392E-16,
--R    - 2.2204460492503131E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16,
--R    0., - 1.1102230246251565E-16, - 1.1102230246251565E-16]
--R                                               Type: List Complex DoubleFloat
--E 47

--S 48 of 50
qerr %
 

   (48)  7.3007559738002298E-32
                                                            Type: DoubleFloat
--R 
--R
--R   (48)  7.3007559738002298E-32
--R                                                            Type: DoubleFloat
--E 48

--S 49 of 50
qtest(ba, bb, 4)
 

   (49)
   [- 0.3 E -20, 0.3 E -20, 0.7 E -20, 0.3 E -20 - 0.7 E -20 %i, 0.3 E -20,
    - 0.3 E -20, 0.0, - 0.3 E -20 + 0.7 E -20 %i, 0.0, - 0.3 E -20,
    - 0.1 E -19 %i, 0.3 E -19 - 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19,
    - 0.3 E -20, 0.3 E -20 + 0.1 E -19 %i, 0.1 E -19 + 0.7 E -20 %i,
    - 0.3 E -20 + 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i, - 0.7 E -20,
    - 0.7 E -20 + 0.7 E -20 %i, 0.0, - 0.7 E -20, 0.0, - 0.3 E -20]
                                                     Type: List Complex Float
--R 
--R
--R   (49)
--R   [- 0.3 E -20, 0.3 E -20, 0.7 E -20, 0.3 E -20 - 0.7 E -20 %i, 0.3 E -20,
--R    - 0.3 E -20, 0.0, - 0.3 E -20 + 0.7 E -20 %i, 0.0, - 0.3 E -20,
--R    - 0.1 E -19 %i, 0.3 E -19 - 0.2 E -19 %i, - 0.3 E -20, 0.0, 0.2 E -19,
--R    - 0.3 E -20, 0.3 E -20 + 0.1 E -19 %i, 0.1 E -19 + 0.7 E -20 %i,
--R    - 0.3 E -20 + 0.7 E -20 %i, - 0.3 E -20 + 0.1 E -19 %i, - 0.7 E -20,
--R    - 0.7 E -20 + 0.7 E -20 %i, 0.0, - 0.7 E -20, 0.0, - 0.3 E -20]
--R                                                     Type: List Complex Float
--E 49

--S 50 of 50
qerr %
 

   (50)  0.1125867861 5522961033 E -39
                                                                  Type: Float
--R 
--R
--R   (50)  0.1125867861 5522961033 E -39
--R                                                                  Type: Float
--E 50
)spool
 
Starts dribbling to table.output (2010/3/27, 18:41:11).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 18
t: Table(Polynomial Integer, String) := table()
 

   (1)  table()
                                       Type: Table(Polynomial Integer,String)
--R 
--R
--R   (1)  table()
--R                                       Type: Table(Polynomial Integer,String)
--E 1

--S 2 of 18
setelt(t, x**2 - 1, "Easy to factor")
 

   (2)  "Easy to factor"
                                                                 Type: String
--R 
--R
--R   (2)  "Easy to factor"
--R                                                                 Type: String
--E 2

--S 3 of 18
t(x**3 + 1) := "Harder to factor"
 

   (3)  "Harder to factor"
                                                                 Type: String
--R 
--R
--R   (3)  "Harder to factor"
--R                                                                 Type: String
--E 3

--S 4 of 18
t(x)        := "The easiest to factor"
 

   (4)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (4)  "The easiest to factor"
--R                                                                 Type: String
--E 4

--S 5 of 18
elt(t, x)
 

   (5)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (5)  "The easiest to factor"
--R                                                                 Type: String
--E 5

--S 6 of 18
t.x
 

   (6)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (6)  "The easiest to factor"
--R                                                                 Type: String
--E 6

--S 7 of 18
t x
 

   (7)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (7)  "The easiest to factor"
--R                                                                 Type: String
--E 7

--S 8 of 18
t.(x**2 - 1)
 

   (8)  "Easy to factor"
                                                                 Type: String
--R 
--R
--R   (8)  "Easy to factor"
--R                                                                 Type: String
--E 8

--S 9 of 18
t (x**3 + 1)
 

   (9)  "Harder to factor"
                                                                 Type: String
--R 
--R
--R   (9)  "Harder to factor"
--R                                                                 Type: String
--E 9

--S 10 of 18
keys t
 

             3      2
   (10)  [x,x  + 1,x  - 1]
                                                Type: List Polynomial Integer
--R 
--R
--R             3      2
--R   (10)  [x,x  + 1,x  - 1]
--R                                                Type: List Polynomial Integer
--E 10

--S 11 of 18
search(x, t)
 

   (11)  "The easiest to factor"
                                                      Type: Union(String,...)
--R 
--R
--R   (11)  "The easiest to factor"
--R                                                      Type: Union(String,...)
--E 11

--S 12 of 18
search(x**2, t)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 18
search(x**2, t) case "failed"
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 18
remove!(x**2-1, t)
 

   (14)  "Easy to factor"
                                                      Type: Union(String,...)
--R 
--R
--R   (14)  "Easy to factor"
--R                                                      Type: Union(String,...)
--E 14

--S 15 of 18
remove!(x-1, t)
 

   (15)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (15)  "failed"
--R                                                    Type: Union("failed",...)
--E 15

--S 16 of 18
#t
 

   (16)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 18
members t
 

   (17)  ["The easiest to factor","Harder to factor"]
                                                            Type: List String
--R 
--R
--R   (17)  ["The easiest to factor","Harder to factor"]
--R                                                            Type: List String
--E 17

--S 18 of 18
count(s: String +-> prefix?("Hard", s), t)
 

   (18)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  1
--R                                                        Type: PositiveInteger
--E 18
)spool 
 
Starts dribbling to none.output (2010/3/27, 18:30:17).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
[]
 

   (1)  []
                                                              Type: List None
--R 
--R
--R   (1)  []
--R                                                              Type: List None
--E 1

--S 2 of 3
[] :: List Float
 

   (2)  []
                                                             Type: List Float
--R 
--R
--R   (2)  []
--R                                                             Type: List Float
--E 2

--S 3 of 3
[]$List(NonNegativeInteger)
 

   (3)  []
                                                Type: List NonNegativeInteger
--R 
--R
--R   (3)  []
--R                                                Type: List NonNegativeInteger
--E 3
)spool 
 
Starts dribbling to LinearOrdinaryDifferentialOperator.output (2010/3/27, 18:45:56).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
Dx: LODO(EXPR INT, f +-> D(f, x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 16
Dx := D()
 

   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1679 envArg,SPADCALL(G1679,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R   (2)  D
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1404 envArg,SPADCALL(G1404,QUOTE x,ELT(*1;anonymousFunction;0;frame0;internal;MV,0))))
--E 2

--S 3 of 16
Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1
 

                       3
         3    G     - x  + H
   (3)  D  + -- D + --------
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1679 envArg,SPADCALL(G1679,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R                       3
--R         3    G     - x  + H
--R   (3)  D  + -- D + --------
--R              2         3
--R             x         x
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1404 envArg,SPADCALL(G1404,QUOTE x,ELT(*1;anonymousFunction;0;frame0;internal;MV,0))))
--E 3

--S 4 of 16
n == 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 16
phi == reduce(+,[subscript(s,[i])*exp(x)/x^i for i in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 16
phi1 ==  Dop(phi) / exp x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 16
phi2 == phi1 *x**(n+3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 16
phi3 == retract(phi2)@(POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 16
pans == phi3 ::UP(x,POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 16
pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 16
leq == solve(pans1,[subscript(s,[i]) for i in 1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling function G1805 with type Integer -> Boolean 

   (12)
                           2                                3        2
         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
          0        0     0       0         0       0      0        0        0
   [[s = ---,s = ------------------,s = --------------------------------------]]
      1   3   2          18          3                    162
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--I   Compiling function G3349 with type Integer -> Boolean 
--R
--R   (12)
--R                           2                                3        2
--R         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
--R          0        0     0       0         0       0      0        0        0
--R   [[s = ---,s = ------------------,s = --------------------------------------]]
--R      1   3   2          18          3                    162
--R                         Type: List List Equation Fraction Polynomial Integer
--E 12

--S 13 of 16
n==4
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 13

--S 14 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (14)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 14

--S 15 of 16
n==7
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 15

--S 16 of 16
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ,

       s  =
        5
                               2         3          2
             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
                  0         0          0          0           0          0
           + 
                5        4          3          2
             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
              0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                   4          3           2                                6
             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
                 0          0           0            0            0      0
           + 
                  5          4           3           2
             90s G  + 2628s G  + 27864s G  + 90720s G
                0          0           0           0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                    3           2                            2
             (945s G  + 81648s G  + 2082996s G + 14171760s )H
                  0           0             0             0
           + 
                   5          4            3             2
             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
                 0          0            0             0              0
           + 
                7         6          5           4             3              2
             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
              0         0          0           0             0              0
           + 
             - 97977600s G
                        0
        /
           11022480
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (16)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ,
--R
--R       s  =
--R        5
--R                               2         3          2
--R             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
--R                  0         0          0          0           0          0
--R           + 
--R                5        4          3          2
--R             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
--R              0        0          0          0           0
--R        /
--R           29160
--R       ,
--R
--R       s  =
--R        6
--R                   3          2                        2
--R             405s H  + (405s G  + 18468s G + 174960s )H
--R                 0          0           0           0
--R           + 
--R                   4          3           2                                6
--R             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
--R                 0          0           0            0            0      0
--R           + 
--R                  5          4           3           2
--R             90s G  + 2628s G  + 27864s G  + 90720s G
--R                0          0           0           0
--R        /
--R           524880
--R       ,
--R
--R       s  =
--R        7
--R                                 3
--R             (2835s G + 91854s )H
--R                   0          0
--R           + 
--R                    3           2                            2
--R             (945s G  + 81648s G  + 2082996s G + 14171760s )H
--R                  0           0             0             0
--R           + 
--R                   5          4            3             2
--R             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
--R                 0          0            0             0              0
--R           + 
--R                7         6          5           4             3              2
--R             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
--R              0         0          0           0             0              0
--R           + 
--R             - 97977600s G
--R                        0
--R        /
--R           11022480
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 16
)spool
 
Starts dribbling to equation2.output (2010/3/27, 18:25:32).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 27
solve([3*x**3 + y + 1,y - 1],[x,y])
 

            3
   (1)  [[3x  + 2= 0,y= 1]]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R            3
--R   (1)  [[3x  + 2= 0,y= 1]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 1

--S 2 of 27
solve([x**3 + x - y**2 + 4,x*y + 2],[x,y],"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                           List Polynomial Integer
                       List OrderedVariableList [x,y]
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                           List Polynomial Integer
--R                       List OrderedVariableList [x,y]
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 2

--S 3 of 27
solve([x = y**2-19,y = z**2+x+3,z = 3*x],[x,y,z])
 

                    2
             z    3z  + z + 9   4     3      2
   (2)  [[x= -,y= -----------,9z  + 6z  + 55z  + 15z - 90= 0]]
             3         3
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R                    2
--R             z    3z  + z + 9   4     3      2
--R   (2)  [[x= -,y= -----------,9z  + 6z  + 55z  + 15z - 90= 0]]
--R             3         3
--R                         Type: List List Equation Fraction Polynomial Integer
--E 3

--S 4 of 27
solve([3*x + 2*y - z,x - 1/2*y + 1/3*z,4/5*x - 2/3*y - z])
 

   (3)  [[z= 0,y= 0,x= 0]]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R   (3)  [[z= 0,y= 0,x= 0]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 4

--S 5 of 27
solve([x**2*y - 1,x*y**2 - 2],[x,y],.01)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                           List Polynomial Integer
                       List OrderedVariableList [x,y]
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                           List Polynomial Integer
--R                       List OrderedVariableList [x,y]
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5

--S 6 of 27
solve([x**2/a = 1,a**2 - a*x = 0],[x,a],.001)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                  List Equation Fraction Polynomial Integer
                       List OrderedVariableList [x,a]
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                  List Equation Fraction Polynomial Integer
--R                       List OrderedVariableList [x,a]
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6

--S 7 of 27
solve([x**2/a + a + y**3 - 1,a*y + a + 1],[x,y])
 

           2 2    4     3     2                - a - 1
   (4)  [[a x  + a  - 2a  - 3a  - 3a - 1= 0,y= -------]]
                                                  a
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R           2 2    4     3     2                - a - 1
--R   (4)  [[a x  + a  - 2a  - 3a  - 3a - 1= 0,y= -------]]
--R                                                  a
--R                         Type: List List Equation Fraction Polynomial Integer
--E 7

)clear all
 

--S 8 of 27
solve(x**3 + 1 = 0,x)
 

                 2
   (1)  [x= - 1,x  - x + 1= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R                 2
--R   (1)  [x= - 1,x  - x + 1= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 8

--S 9 of 27
solve(x**3*y + x*y + 1,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9

--S 10 of 27
solve(3*x + 1/4*y = 1,x)
 

            - y + 4
   (2)  [x= -------]
               12
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R            - y + 4
--R   (2)  [x= -------]
--R               12
--R                              Type: List Equation Fraction Polynomial Integer
--E 10

--S 11 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                              Fraction Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                              Fraction Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11

--S 12 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12

--S 13 of 27
solve(x**3 - sqrt(2))
 

          3    +-+
   (3)  [x  - \|2 = 0]
                      Type: List Equation Fraction Polynomial AlgebraicNumber
--R 
--R
--R          3    +-+
--R   (3)  [x  - \|2 = 0]
--R                      Type: List Equation Fraction Polynomial AlgebraicNumber
--E 13

--S 14 of 27
solve(x**3/a + x/a + 1,x)
 

          3
   (4)  [x  + x + a= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R          3
--R   (4)  [x  + x + a= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 14

)clear all
 

--S 15 of 27
solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                    Equation Fraction Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                    Equation Fraction Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15

--S 16 of 27
solve(x**3 + 1 = 0,x)
 

                 2
   (1)  [x= - 1,x  - x + 1= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R                 2
--R   (1)  [x= - 1,x  - x + 1= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 16

--S 17 of 27
solve(x**3*y + x*y + 1,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17

--S 18 of 27
solve(3*x + 1/4*y = 1,x)
 

            - y + 4
   (2)  [x= -------]
               12
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R            - y + 4
--R   (2)  [x= -------]
--R               12
--R                              Type: List Equation Fraction Polynomial Integer
--E 18

--S 19 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000)
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                              Fraction Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                              Fraction Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 19

--S 20 of 27
solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                             Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20

--S 21 of 27
solve(x**3 - sqrt(2))
 

          3    +-+
   (3)  [x  - \|2 = 0]
                      Type: List Equation Fraction Polynomial AlgebraicNumber
--R 
--R
--R          3    +-+
--R   (3)  [x  - \|2 = 0]
--R                      Type: List Equation Fraction Polynomial AlgebraicNumber
--E 21

--S 22 of 27
solve(x**3/a + x/a + 1,x)
 

          3
   (4)  [x  + x + a= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R          3
--R   (4)  [x  + x + a= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 22

--S 23 of 27
solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym")
 
   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                    Equation Fraction Polynomial Integer
                                 Variable x
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 6 exposed and 1 unexposed library operations named solve 
--R      having 3 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op solve
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named solve
--R      with argument type(s) 
--R                    Equation Fraction Polynomial Integer
--R                                 Variable x
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23

)clear all
 

--S 24 of 27
solve([[1,1,1],[3,-2,1],[1,2,2]],[8,0,17])
 

   (1)  [particular= [- 1,2,7],basis= [[0,0,0]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (1)  [particular= [- 1,2,7],basis= [[0,0,0]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 24

--S 25 of 27
solve([[1,2,3],[2,3,4],[3,4,5]],[2,2,2])
 

   (2)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (2)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 25

--S 26 of 27
solve([[1,2,3],[2,3,4],[3,4,5]],[2,3,2])
 

   (3)  [particular= "failed",basis= [[1,- 2,1]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (3)  [particular= "failed",basis= [[1,- 2,1]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 26

--S 27 of 27
solve([[1,2,3],[2,3,4],[3,4,5]])
 

   (4)  solve
             [1,2,3],[2,3,4],[3,4,5]
                                                                 Type: Symbol
--R 
--R
--R   (4)  solve
--R             [1,2,3],[2,3,4],[3,4,5]
--R                                                                 Type: Symbol
--E 27
)spool
 
Starts dribbling to DeRhamComplex.output (2010/3/27, 18:41:54).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 34
coefRing := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 34
lv : List Symbol := [x,y,z] 
 

   (2)  [x,y,z]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z]
--R                                                            Type: List Symbol
--E 2

--S 3 of 34
der := DERHAM(coefRing,lv) 
 

   (3)  DeRhamComplex(Integer,[x,y,z])
                                                                 Type: Domain
--R 
--R
--R   (3)  DeRhamComplex(Integer,[x,y,z])
--R                                                                 Type: Domain
--E 3

--S 4 of 34
R := Expression coefRing
 

   (4)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (4)  Expression Integer
--R                                                                 Type: Domain
--E 4

--S 5 of 34
f : R := x**2*y*z-5*x**3*y**2*z**5
 

            3 2 5    2
   (5)  - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3 2 5    2
--R   (5)  - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 5

--S 6 of 34
g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 
 

            2     3 2       2
   (6)  - 7z sin(x y ) + y z cos(z)
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2
--R   (6)  - 7z sin(x y ) + y z cos(z)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 34
h : R :=x*y*z-2*x**3*y*z**2 
 

            3   2
   (7)  - 2x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            3   2
--R   (7)  - 2x y z  + x y z
--R                                                     Type: Expression Integer
--E 7

--S 8 of 34
dx : der := generator(1)
 

   (8)  dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (8)  dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 8

--S 9 of 34
dy : der := generator(2)
 

   (9)  dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (9)  dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 9

--S 10 of 34
dz : der := generator(3)
 

   (10)  dz
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (10)  dz
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 10

--S 11 of 34
[dx,dy,dz] := [generator(i)$der for i in 1..3]
 

   (11)  [dx,dy,dz]
                                    Type: List DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (11)  [dx,dy,dz]
--R                                    Type: List DeRhamComplex(Integer,[x,y,z])
--E 11

--S 12 of 34
alpha : der := f*dx + g*dy + h*dz
 

   (12)
          3   2                   2     3 2       2
     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
   + 
          3 2 5    2
     (- 5x y z  + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (12)
--R          3   2                   2     3 2       2
--R     (- 2x y z  + x y z)dz + (- 7z sin(x y ) + y z cos(z))dy
--R   + 
--R          3 2 5    2
--R     (- 5x y z  + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 12

--S 13 of 34
beta  : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy
 

   (13)  x dy + cos(tan(x y z) + x y z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (13)  x dy + cos(tan(x y z) + x y z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 13

--S 14 of 34
exteriorDifferential alpha
 

   (14)
         2                  3 2                    3 2
     (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)dy dz
   + 
         3 2 4     2   2          2
     (25x y z  - 6x y z  + y z - x y)dx dz
   + 
           2 2 2     3 2       3   5    2
     (- 21x y z cos(x y ) + 10x y z  - x z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (14)
--R         2                  3 2                    3 2
--R     (y z sin(z) + 14z sin(x y ) - 2y z cos(z) - 2x z  + x z)dy dz
--R   + 
--R         3 2 4     2   2          2
--R     (25x y z  - 6x y z  + y z - x y)dx dz
--R   + 
--R           2 2 2     3 2       3   5    2
--R     (- 21x y z cos(x y ) + 10x y z  - x z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 14

--S 15 of 34
exteriorDifferential %
 

   (15)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (15)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 15

--S 16 of 34
gamma := alpha * beta
 

   (16)
        4   2    2               3   2
     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
   + 
       2     3 2       2                                   4 2 5    3
   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (16)
--R        4   2    2               3   2
--R     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
--R   + 
--R       2     3 2       2                                   4 2 5    3
--R   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 16

--S 17 of 34
exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta)) 
 

   (17)  0
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (17)  0
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 17

--S 18 of 34
a : BOP := operator('a)
 

   (18)  a
                                                          Type: BasicOperator
--R 
--R
--R   (18)  a
--R                                                          Type: BasicOperator
--E 18

--S 19 of 34
b : BOP := operator('b)
 

   (19)  b
                                                          Type: BasicOperator
--R 
--R
--R   (19)  b
--R                                                          Type: BasicOperator
--E 19

--S 20 of 34
c : BOP := operator('c)
 

   (20)  c
                                                          Type: BasicOperator
--R 
--R
--R   (20)  c
--R                                                          Type: BasicOperator
--E 20

--S 21 of 34
sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz 
 

   (21)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (21)  c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 21

--S 22 of 34
theta  := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz 
 

   (22)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (22)  c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 22

--S 23 of 34
totalDifferential(a(x,y,z))$der 
 

   (23)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
          ,3             ,2             ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (23)  a  (x,y,z)dz + a  (x,y,z)dy + a  (x,y,z)dx
--R          ,3             ,2             ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 23

--S 24 of 34
exteriorDifferential sigma
 

   (24)
     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
       ,2           ,3                  ,1           ,3
   + 
     (b  (x,y,z) - a  (x,y,z))dx dy
       ,1           ,2
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (24)
--R     (c  (x,y,z) - b  (x,y,z))dy dz + (c  (x,y,z) - a  (x,y,z))dx dz
--R       ,2           ,3                  ,1           ,3
--R   + 
--R     (b  (x,y,z) - a  (x,y,z))dx dy
--R       ,1           ,2
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 24

--S 25 of 34
exteriorDifferential theta
 

   (25)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
           ,1           ,2           ,3
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (25)  (c  (x,y,z) - b  (x,y,z) + a  (x,y,z))dx dy dz
--R           ,1           ,2           ,3
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 25

--S 26 of 34
one : der := 1
 

   (26)  1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (26)  1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 26

--S 27 of 34
g1 : der := a([x,t,y,u,v,z,e]) * one 
 

   (27)  a(x,t,y,u,v,z,e)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (27)  a(x,t,y,u,v,z,e)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 27

--S 28 of 34
h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one 
 

   (28)  a(x,y,x,t,x,z,y,r,u,x)
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (28)  a(x,y,x,t,x,z,y,r,u,x)
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 28

--S 29 of 34
exteriorDifferential g1 
 

   (29)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
          ,6                     ,3                     ,1
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (29)  a  (x,t,y,u,v,z,e)dz + a  (x,t,y,u,v,z,e)dy + a  (x,t,y,u,v,z,e)dx
--R          ,6                     ,3                     ,1
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 29

--S 30 of 34
exteriorDifferential h1
 

   (30)
     a  (x,y,x,t,x,z,y,r,u,x)dz
      ,6
   + 
     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
       ,7                         ,2
   + 
         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,10                         ,5
       + 
         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
          ,3                         ,1
    *
       dx
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (30)
--R     a  (x,y,x,t,x,z,y,r,u,x)dz
--R      ,6
--R   + 
--R     (a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x))dy
--R       ,7                         ,2
--R   + 
--R         a   (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,10                         ,5
--R       + 
--R         a  (x,y,x,t,x,z,y,r,u,x) + a  (x,y,x,t,x,z,y,r,u,x)
--R          ,3                         ,1
--R    *
--R       dx
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 30

--S 31 of 34
coefficient(gamma, dx*dy)
 

            2     3 2       2                                   4 2 5    3
   (31)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
                                                     Type: Expression Integer
--R 
--R
--R            2     3 2       2                                   4 2 5    3
--R   (31)  (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z
--R                                                     Type: Expression Integer
--E 31

--S 32 of 34
coefficient(gamma, one)
 

   (32)  0
                                                     Type: Expression Integer
--R 
--R
--R   (32)  0
--R                                                     Type: Expression Integer
--E 32

--S 33 of 34
coefficient(g1,one)
 

   (33)  a(x,t,y,u,v,z,e)
                                                     Type: Expression Integer
--R 
--R
--R   (33)  a(x,t,y,u,v,z,e)
--R                                                     Type: Expression Integer
--E 33

--S 34 of 34
gamma := alpha * beta
 

   (34)
        4   2    2               3   2
     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
   + 
       2     3 2       2                                   4 2 5    3
   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
                                         Type: DeRhamComplex(Integer,[x,y,z])
--R 
--R
--R   (34)
--R        4   2    2               3   2
--R     (2x y z  - x y z)dy dz + (2x y z  - x y z)cos(tan(x y z) + x y z)dx dz
--R   + 
--R       2     3 2       2                                   4 2 5    3
--R   ((7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z  + x y z)dx dy
--R                                         Type: DeRhamComplex(Integer,[x,y,z])
--E 34
)spool
 
Starts dribbling to Fraction.output (2010/3/27, 18:42:4).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
a := 11/12
 

        11
   (1)  --
        12
                                                       Type: Fraction Integer
--R 
--R
--R        11
--R   (1)  --
--R        12
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 12
b := 23/24
 

        23
   (2)  --
        24
                                                       Type: Fraction Integer
--R 
--R
--R        23
--R   (2)  --
--R        24
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 12
3 - a*b**2 + a + b/a
 

        313271
   (3)  ------
         76032
                                                       Type: Fraction Integer
--R 
--R
--R        313271
--R   (3)  ------
--R         76032
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 12
numer(a)
 

   (4)  11
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  11
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 12
denom(b)
 

   (5)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  24
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 12
r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1)
 

         2
        x  + 2x + 1
   (6)  -----------
         2
        x  - 2x + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 2x + 1
--R   (6)  -----------
--R         2
--R        x  - 2x + 1
--R                                            Type: Fraction Polynomial Integer
--E 6

--S 7 of 12
factor(r)
 

         2
        x  + 2x + 1
   (7)  -----------
         2
        x  - 2x + 1
                                   Type: Factored Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 2x + 1
--R   (7)  -----------
--R         2
--R        x  - 2x + 1
--R                                   Type: Factored Fraction Polynomial Integer
--E 7

--S 8 of 12
map(factor,r)
 

               2
        (x + 1)
   (8)  --------
               2
        (x - 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R               2
--R        (x + 1)
--R   (8)  --------
--R               2
--R        (x - 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 8

--S 9 of 12
continuedFraction(7/12)
 

          1 |     1 |     1 |     1 |
   (9)  +---+ + +---+ + +---+ + +---+
        | 1     | 1     | 2     | 2
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1 |     1 |
--R   (9)  +---+ + +---+ + +---+ + +---+
--R        | 1     | 1     | 2     | 2
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 12
partialFraction(7,12)
 

              3   1
   (10)  1 - -- + -
              2   3
             2
                                                Type: PartialFraction Integer
--R 
--R
--R              3   1
--R   (10)  1 - -- + -
--R              2   3
--R             2
--R                                                Type: PartialFraction Integer
--E 10

--S 11 of 12
g := 2/3 + 4/5*%i
 

         2   4
   (11)  - + - %i
         3   5
                                               Type: Complex Fraction Integer
--R 
--R
--R         2   4
--R   (11)  - + - %i
--R         3   5
--R                                               Type: Complex Fraction Integer
--E 11

--S 12 of 12
g :: FRAC COMPLEX INT
 

         10 + 12%i
   (12)  ---------
             15
                                               Type: Fraction Complex Integer
--R 
--R
--R         10 + 12%i
--R   (12)  ---------
--R             15
--R                                               Type: Fraction Complex Integer
--E 12

)spool
 
Starts dribbling to ffdemo.output (2010/3/27, 18:25:49).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 350
p:=4817
 

   (1)  4817
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  4817
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 350
F:=PrimeField p
 

   (2)  PrimeField 4817
                                                                 Type: Domain
--R 
--R
--R   (2)  PrimeField 4817
--R                                                                 Type: Domain
--E 2

--S 3 of 350
size()$F
 

   (3)  4817
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  4817
--R                                                     Type: NonNegativeInteger
--E

--S 4 of 350
a:=index(size()$F quo 3)$F
 

   (4)  1605
                                                        Type: PrimeField 4817
--R 
--R
--R   (4)  1605
--R                                                        Type: PrimeField 4817
--E 4

--S 5 of 350
b:=index(size()$F quo 7)$F
 

   (5)  688
                                                        Type: PrimeField 4817
--R 
--R
--R   (5)  688
--R                                                        Type: PrimeField 4817
--E 5

--S 6 of 350
a+b
 

   (6)  2293
                                                        Type: PrimeField 4817
--R 
--R
--R   (6)  2293
--R                                                        Type: PrimeField 4817
--E 6

--S 7 of 350
a-b
 

   (7)  917
                                                        Type: PrimeField 4817
--R 
--R
--R   (7)  917
--R                                                        Type: PrimeField 4817
--E 7

--S 8 of 350
a*b
 

   (8)  1147
                                                        Type: PrimeField 4817
--R 
--R
--R   (8)  1147
--R                                                        Type: PrimeField 4817
--E 8

--S 9 of 350
a/b
 

   (9)  3216
                                                        Type: PrimeField 4817
--R 
--R
--R   (9)  3216
--R                                                        Type: PrimeField 4817
--E 9

--S 10 of 350
a**1234
 

   (10)  2068
                                                        Type: PrimeField 4817
--R 
--R
--R   (10)  2068
--R                                                        Type: PrimeField 4817
--E 10

--S 11 of 350
a**(-1)
 

   (11)  2407
                                                        Type: PrimeField 4817
--R 
--R
--R   (11)  2407
--R                                                        Type: PrimeField 4817
--E 11

--S 12 of 350
g := generator()$F
 

   (12)  1
                                                        Type: PrimeField 4817
--R 
--R
--R   (12)  1
--R                                                        Type: PrimeField 4817
--E 12

--S 13 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (13)  0
                                                        Type: PrimeField 4817
--R 
--R
--R   (13)  0
--R                                                        Type: PrimeField 4817
--E 13

--S 14 of 350
order(a)
 

   (14)  688
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  688
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 350
g:=primitiveElement()$F
 

   (15)  3
                                                        Type: PrimeField 4817
--R 
--R
--R   (15)  3
--R                                                        Type: PrimeField 4817
--E 15

--S 16 of 350
discreteLog(a)
 

   (16)  987
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  987
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 350
g**% - a
 

   (17)  0
                                                        Type: PrimeField 4817
--R 
--R
--R   (17)  0
--R                                                        Type: PrimeField 4817
--E 17

--S 18 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (18)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (18)  "failed"
--R                                                    Type: Union("failed",...)
--E 18

--S 19 of 350
extensionDegree()$F
 

   (19)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  1
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 350
degree(a)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 350
normalElement()$F
 

   (21)  1
                                                        Type: PrimeField 4817
--R 
--R
--R   (21)  1
--R                                                        Type: PrimeField 4817
--E 21

--S 22 of 350
definingPolynomial()$F
 

   (22)  ? + 4816
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (22)  ? + 4816
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 22

--S 23 of 350
minimalPolynomial(a)
 

   (23)  ? + 3212
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (23)  ? + 3212
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 23

--S 24 of 350
Frobenius(a)
 

   (24)  1605
                                                        Type: PrimeField 4817
--R 
--R
--R   (24)  1605
--R                                                        Type: PrimeField 4817
--E 24

--S 25 of 350
linearAssociatedOrder(a)
 

   (25)  ? + 4816
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (25)  ? + 4816
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 25

--S 26 of 350
linearAssociatedLog(a)
 

   (26)  1605
                             Type: SparseUnivariatePolynomial PrimeField 4817
--R 
--R
--R   (26)  1605
--R                             Type: SparseUnivariatePolynomial PrimeField 4817
--E 26

--S 27 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   Compiling function G1728 with type Integer -> Boolean 
   Compiling function G1742 with type NonNegativeInteger -> Boolean 
   1605
   1605
                                                                   Type: Void
--R 
--I   Compiling function G1462 with type Integer -> Boolean 
--I   Compiling function G1641 with type NonNegativeInteger -> Boolean 
--R   1605
--R   1605
--R                                                                   Type: Void
--E 27

--S 28 of 350
p:=7
 

   (28)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  7
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 350
P:=PrimeField p
 

   (29)  PrimeField 7
                                                                 Type: Domain
--R 
--R
--R   (29)  PrimeField 7
--R                                                                 Type: Domain
--E 29

--S 30 of 350
d:=6
 

   (30)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  6
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 350
f:=createIrreduciblePoly(d)$FFPOLY(P)
 

          6
   (31)  ?  + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6
--R   (31)  ?  + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 31

--S 32 of 350
F:=FFP(P,f)
 

   (32)  FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
                                                                 Type: Domain
--R 
--R
--R   (32)  FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R                                                                 Type: Domain
--E 32

--S 33 of 350
size()$F
 

   (33)  117649
                                                     Type: NonNegativeInteger
--R 
--R
--R   (33)  117649
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 350
a:=index(size()$F quo 3)$F
 

            5      4      3      2
   (34)  2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (34)  2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 34

--S 35 of 350
b:=index(size()$F quo 7)$F
 

           5
   (35)  %A
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R           5
--R   (35)  %A
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 35

--S 36 of 350
a+b
 

            5      4      3      2
   (36)  3%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (36)  3%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 36

--S 37 of 350
a-b
 

           5      4      3      2
   (37)  %A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R           5      4      3      2
--R   (37)  %A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 37

--S 38 of 350
a*b
 

            5      4      3      2
   (38)  2%A  + 3%A  + 3%A  + 3%A  + 3%A + 3
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (38)  2%A  + 3%A  + 3%A  + 3%A  + 3%A + 3
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 38

--S 39 of 350
a/b
 

            5      4      3      2
   (39)  6%A  + 6%A  + 6%A  + 6%A  + 6%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (39)  6%A  + 6%A  + 6%A  + 6%A  + 6%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 39

--S 40 of 350
a**1234
 

            5     4      3
   (40)  5%A  + %A  + 3%A  + 3%A + 4
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5     4      3
--R   (40)  5%A  + %A  + 3%A  + 3%A + 4
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 40

--S 41 of 350
a**(-1)
 

   (41)  %A + 6
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (41)  %A + 6
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 41

--S 42 of 350
g := generator()$F
 

   (42)  %A
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (42)  %A
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 42

--S 43 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (43)  0
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (43)  0
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 43

--S 44 of 350
order(a)
 

   (44)  117648
                                                        Type: PositiveInteger
--R 
--R
--R   (44)  117648
--R                                                        Type: PositiveInteger
--E 44

--S 45 of 350
g:=primitiveElement()$F
 

   (45)  %A + 1
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (45)  %A + 1
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 45

--S 46 of 350
discreteLog(a)
 

   (46)  58481
                                                        Type: PositiveInteger
--R 
--R
--R   (46)  58481
--R                                                        Type: PositiveInteger
--E 46

--S 47 of 350
g**% - a
 

   (47)  0
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R   (47)  0
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 47

--S 48 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (48)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (48)  "failed"
--R                                                    Type: Union("failed",...)
--E 48

--S 49 of 350
extensionDegree()$F
 

   (49)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (49)  6
--R                                                        Type: PositiveInteger
--E 49

--S 50 of 350
degree(a)
 

   (50)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (50)  6
--R                                                        Type: PositiveInteger
--E 50

--S 51 of 350
normalElement()$F
 

            5      4      3      2
   (51)  5%A  + 3%A  + 3%A  + 5%A  + %A + 5
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3      2
--R   (51)  5%A  + 3%A  + 3%A  + 5%A  + %A + 5
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 51

--S 52 of 350
definingPolynomial()$F
 

          6
   (52)  ?  + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6
--R   (52)  ?  + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 52

--S 53 of 350
minimalPolynomial(a)
 

          6     5     4     3     2
   (53)  ?  + 2?  + 5?  + 2?  + 5?  + 2? + 5
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6     5     4     3     2
--R   (53)  ?  + 2?  + 5?  + 2?  + 5?  + 2? + 5
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 53

--S 54 of 350
Frobenius(a)
 

            5      4      3     2
   (54)  6%A  + 4%A  + 5%A  + %A  + 3%A + 2
                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--R 
--R
--R            5      4      3     2
--R   (54)  6%A  + 4%A  + 5%A  + %A  + 3%A + 2
--R                  Type: FiniteFieldExtensionByPolynomial(PrimeField 7,?**6+2)
--E 54

--S 55 of 350
linearAssociatedOrder(a)
 

          6
   (55)  ?  + 6
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6
--R   (55)  ?  + 6
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 55

--S 56 of 350
linearAssociatedLog(a)
 

           5     4     3     2
   (56)  2?  + 3?  + 3?  + 3?  + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R           5     4     3     2
--R   (56)  2?  + 3?  + 3?  + 3?  + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 56

--S 57 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   5
   5
      3
   2%A  + 2
      3
   6%A  + 6
      4      2
   5%A  + 5%A  + 5
      4      2
   4%A  + 4%A  + 4
      5      4      3      2
   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
      5      4      3      2
   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
                                                                   Type: Void
--R 
--R   5
--R   5
--R      3
--R   2%A  + 2
--R      3
--R   6%A  + 6
--R      4      2
--R   5%A  + 5%A  + 5
--R      4      2
--R   4%A  + 4%A  + 4
--R      5      4      3      2
--R   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R      5      4      3      2
--R   2%A  + 2%A  + 2%A  + 2%A  + 2%A + 2
--R                                                                   Type: Void
--E 57

--S 58 of 350
f:=createNormalPoly(d)$FFPOLY(P)
 

          6     5
   (58)  ?  + 6?  + 2? + 4
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6     5
--R   (58)  ?  + 6?  + 2? + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 58

--S 59 of 350
F:=FFNBP(P,f)
 

   (59)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
                                                                 Type: Domain
--R 
--R
--R   (59)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R                                                                 Type: Domain
--E 59

--S 60 of 350
size()$F
 

   (60)  117649
                                                     Type: NonNegativeInteger
--R 
--R
--R   (60)  117649
--R                                                     Type: NonNegativeInteger
--E 60

--S 61 of 350
a:=index(size()$F quo 3)$F
 

             5       4       3       2
            q       q       q       q       q
   (61)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (61)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 61

--S 62 of 350
b:=index(size()$F quo 7)$F
 

            5
           q
   (62)  %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R            5
--R           q
--R   (62)  %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 62

--S 63 of 350
a+b
 

             5       4       3       2
            q       q       q       q       q
   (63)  3%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (63)  3%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 63

--S 64 of 350
a-b
 

            5       4       3       2
           q       q       q       q       q
   (64)  %B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R            5       4       3       2
--R           q       q       q       q       q
--R   (64)  %B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 64

--S 65 of 350
a*b
 

             5
            q
   (65)  2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5
--R            q
--R   (65)  2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 65

--S 66 of 350
a/b
 

             4       3       2
            q       q       q      q
   (66)  3%B   + 2%B   + 4%B   + %B  + 3%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             4       3       2
--R            q       q       q      q
--R   (66)  3%B   + 2%B   + 4%B   + %B  + 3%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 66

--S 67 of 350
a**1234
 

             5       4       3       2
            q       q       q       q       q
   (67)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (67)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 67

--S 68 of 350
a**(-1)
 

             5       4       3       2
            q       q       q       q       q
   (68)  4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (68)  4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 68

--S 69 of 350
g := generator()$F
 

   (69)  %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (69)  %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 69

--S 70 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (70)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (70)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 70

--S 71 of 350
order(a)
 

   (71)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (71)  3
--R                                                        Type: PositiveInteger
--E 71

--S 72 of 350
g:=primitiveElement()$F
 

            2
           q
   (72)  %B   + %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R            2
--R           q
--R   (72)  %B   + %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 72

--S 73 of 350
discreteLog(a)
 

   (73)  39216
                                                        Type: PositiveInteger
--R 
--R
--R   (73)  39216
--R                                                        Type: PositiveInteger
--E 73

--S 74 of 350
g**% - a
 

   (74)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (74)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 74

--S 75 of 350
discreteLog(b,a)
 

   (75)  9804
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (75)  9804
--R                                          Type: Union(NonNegativeInteger,...)
--E 75

--S 76 of 350
extensionDegree()$F
 

   (76)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (76)  6
--R                                                        Type: PositiveInteger
--E 76

--S 77 of 350
degree(a)
 

   (77)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (77)  1
--R                                                        Type: PositiveInteger
--E 77

--S 78 of 350
normalElement()$F
 

   (78)  %B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R   (78)  %B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 78

--S 79 of 350
definingPolynomial()$F
 

          6     5
   (79)  ?  + 6?  + 2? + 4
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R          6     5
--R   (79)  ?  + 6?  + 2? + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 79

--S 80 of 350
minimalPolynomial(a)
 

   (80)  ? + 5
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R   (80)  ? + 5
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 80

--S 81 of 350
Frobenius(a)
 

             5       4       3       2
            q       q       q       q       q
   (81)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--R 
--R
--R             5       4       3       2
--R            q       q       q       q       q
--R   (81)  2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 7,?**6+6*?**5+2*?+4)
--E 81

--S 82 of 350
linearAssociatedOrder(a)
 

   (82)  ? + 6
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R   (82)  ? + 6
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 82

--S 83 of 350
linearAssociatedLog(a)
 

           5     4     3     2
   (83)  2?  + 2?  + 2?  + 2?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R           5     4     3     2
--R   (83)  2?  + 2?  + 2?  + 2?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 83

--S 84 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
      5      4      3      2
     q      q      q      q      q
   %B   + %B   + %B   + %B   + %B  + %B
       5       4       3       2
      q       q       q       q       q
   5%B   + 5%B   + 5%B   + 5%B   + 5%B  + 5%B
      5      4      3      2
     q      q      q      q      q
   %B   + %B   + %B   + %B   + %B  + %B
       5       4       3       2
      q       q       q       q       q
   6%B   + 6%B   + 6%B   + 6%B   + 6%B  + 6%B
       5       4       3       2
      q       q       q       q       q
   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
       5       4       3       2
      q       q       q       q       q
   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
       5       4       3       2
      q       q       q       q       q
   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
       5       4       3       2
      q       q       q       q       q
   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
                                                                   Type: Void
--R 
--R      5      4      3      2
--R     q      q      q      q      q
--R   %B   + %B   + %B   + %B   + %B  + %B
--R       5       4       3       2
--R      q       q       q       q       q
--R   5%B   + 5%B   + 5%B   + 5%B   + 5%B  + 5%B
--R      5      4      3      2
--R     q      q      q      q      q
--R   %B   + %B   + %B   + %B   + %B  + %B
--R       5       4       3       2
--R      q       q       q       q       q
--R   6%B   + 6%B   + 6%B   + 6%B   + 6%B  + 6%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   4%B   + 4%B   + 4%B   + 4%B   + 4%B  + 4%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--R       5       4       3       2
--R      q       q       q       q       q
--R   2%B   + 2%B   + 2%B   + 2%B   + 2%B  + 2%B
--R                                                                   Type: Void
--E 84

--S 85 of 350
p:=5
 

   (85)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (85)  5
--R                                                        Type: PositiveInteger
--E 85

--S 86 of 350
P:=PrimeField p
 

   (86)  PrimeField 5
                                                                 Type: Domain
--R 
--R
--R   (86)  PrimeField 5
--R                                                                 Type: Domain
--E 86

--S 87 of 350
d:=4
 

   (87)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (87)  4
--R                                                        Type: PositiveInteger
--E 87

--S 88 of 350
f:=createPrimitivePoly(d)$FFPOLY(P)
 

          4    2
   (88)  ?  + ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R          4    2
--R   (88)  ?  + ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 88

--S 89 of 350
F:=FFCGP(P,f)
 

   (89)
   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
                                                                 Type: Domain
--R 
--R
--R   (89)
--R   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R                                                                 Type: Domain
--E 89

--S 90 of 350
size()$F
 

   (90)  625
                                                     Type: NonNegativeInteger
--R 
--R
--R   (90)  625
--R                                                     Type: NonNegativeInteger
--E 90

--S 91 of 350
a:=index(size()$F quo 3)$F
 

           207
   (91)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           207
--R   (91)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 91

--S 92 of 350
b:=index(size()$F quo 7)$F
 

           88
   (92)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           88
--R   (92)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 92

--S 93 of 350
a+b
 

           70
   (93)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           70
--R   (93)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 93

--S 94 of 350
a-b
 

           237
   (94)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           237
--R   (94)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 94

--S 95 of 350
a*b
 

           295
   (95)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           295
--R   (95)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 95

--S 96 of 350
a/b
 

           119
   (96)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           119
--R   (96)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 96

--S 97 of 350
a**1234
 

           222
   (97)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           222
--R   (97)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 97

--S 98 of 350
a**(-1)
 

           417
   (98)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           417
--R   (98)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 98

--S 99 of 350
g := generator()$F
 

           1
   (99)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R           1
--R   (99)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 99

--S 100 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (100)  0
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R   (100)  0
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 100

--S 101 of 350
order(a)
 

   (101)  208
                                                        Type: PositiveInteger
--R 
--R
--R   (101)  208
--R                                                        Type: PositiveInteger
--E 101

--S 102 of 350
g:=primitiveElement()$F
 

            1
   (102)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R            1
--R   (102)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 102

--S 103 of 350
discreteLog(a)
 

   (103)  207
                                                        Type: PositiveInteger
--R 
--R
--R   (103)  207
--R                                                        Type: PositiveInteger
--E 103

--S 104 of 350
g**% - a
 

   (104)  0
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R   (104)  0
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 104

--S 105 of 350
discreteLog(b,a)
 

   (105)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (105)  "failed"
--R                                                    Type: Union("failed",...)
--E 105

--S 106 of 350
extensionDegree()$F
 

   (106)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (106)  4
--R                                                        Type: PositiveInteger
--E 106

--S 107 of 350
degree(a)
 

   (107)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (107)  4
--R                                                        Type: PositiveInteger
--E 107

--S 108 of 350
normalElement()$F
 

            3
   (108)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R            3
--R   (108)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 108

--S 109 of 350
definingPolynomial()$F
 

           4    2
   (109)  ?  + ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R           4    2
--R   (109)  ?  + ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 109

--S 110 of 350
minimalPolynomial(a)
 

           4    3    2
   (110)  ?  + ?  + ?  + 3? + 3
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R           4    3    2
--R   (110)  ?  + ?  + ?  + 3? + 3
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 110

--S 111 of 350
Frobenius(a)
 

            411
   (111)  %C
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--R 
--R
--R            411
--R   (111)  %C
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 5,?**4+?*?+2*?+2)
--E 111

--S 112 of 350
linearAssociatedOrder(a)
 

           4
   (112)  ?  + 4
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R           4
--R   (112)  ?  + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 112

--S 113 of 350
linearAssociatedLog(a)
 

            3
   (113)  3?  + 4? + 4
                                Type: SparseUnivariatePolynomial PrimeField 5
--R 
--R
--R            3
--R   (113)  3?  + 4? + 4
--R                                Type: SparseUnivariatePolynomial PrimeField 5
--E 113

--S 114 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
     468
   %C
     312
   %C
     390
   %C
     416
   %C
     207
   %C
     207
   %C
                                                                   Type: Void
--R 
--R     468
--R   %C
--R     312
--R   %C
--R     390
--R   %C
--R     416
--R   %C
--R     207
--R   %C
--R     207
--R   %C
--R                                                                   Type: Void
--E 114

--S 115 of 350
p:=3
 

   (115)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (115)  3
--R                                                        Type: PositiveInteger
--E 115

--S 116 of 350
P:=PrimeField p
 

   (116)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (116)  PrimeField 3
--R                                                                 Type: Domain
--E 116

--S 117 of 350
d1:=2
 

   (117)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (117)  2
--R                                                        Type: PositiveInteger
--E 117

--S 118 of 350
d2:=3
 

   (118)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (118)  3
--R                                                        Type: PositiveInteger
--E 118

--S 119 of 350
f1:=createIrreduciblePoly(d1)$FFPOLY(P)
 

           2
   (119)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (119)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 119

--S 120 of 350
F1:=FFP(P,f1)
 

   (120)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (120)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R                                                                 Type: Domain
--E 120

--S 121 of 350
f2:=createIrreduciblePoly(d2)$FFPOLY(F1)
 

           3
   (121)  ?  + ? + %D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (121)  ?  + ? + %D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 121

--S 122 of 350
F:=FFP(F1,f2)
 

   (122)
  FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 
  3,?*?+1),?**3+?+D)
                                                                 Type: Domain
--R 
--R
--R   (122)
--R  FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 
--R  3,?*?+1),?**3+?+D)
--R                                                                 Type: Domain
--E 122

--S 123 of 350
size()$F
 

   (123)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (123)  729
--R                                                     Type: NonNegativeInteger
--E 123

--S 124 of 350
a:=index(size()$F quo 3)$F
 

               2
   (124)  %D %E
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R               2
--R   (124)  %D %E
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 124

--S 125 of 350
b:=index(size()$F quo 7)$F
 

            2
   (125)  %E  + 2%E + %D + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R            2
--R   (125)  %E  + 2%E + %D + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 125

--S 126 of 350
a+b
 

                    2
   (126)  (%D + 1)%E  + 2%E + %D + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                    2
--R   (126)  (%D + 1)%E  + 2%E + %D + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 126

--S 127 of 350
a-b
 

                    2
   (127)  (%D + 2)%E  + %E + 2%D + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                    2
--R   (127)  (%D + 2)%E  + %E + 2%D + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 127

--S 128 of 350
a*b
 

                    2
   (128)  (%D + 2)%E  + (%D + 1)%E + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                    2
--R   (128)  (%D + 2)%E  + (%D + 1)%E + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 128

--S 129 of 350
a/b
 

                2
   (129)  2%D %E  + 2%D + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R                2
--R   (129)  2%D %E  + 2%D + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 129

--S 130 of 350
a**1234
 

             2
   (130)  2%E  + %D %E + 2
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R             2
--R   (130)  2%E  + %D %E + 2
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 130

--S 131 of 350
a**(-1)
 

               2
   (131)  %D %E  + %E + %D
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R               2
--R   (131)  %D %E  + %E + %D
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 131

--S 132 of 350
g := generator()$F
 

   (132)  %E
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (132)  %E
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 132

--S 133 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (133)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (133)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 133

--S 134 of 350
order(a)
 

   (134)  52
                                                        Type: PositiveInteger
--R 
--R
--R   (134)  52
--R                                                        Type: PositiveInteger
--E 134

--S 135 of 350
g:=primitiveElement()$F
 

   (135)  %E + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (135)  %E + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 135

--S 136 of 350
discreteLog(a)
 

   (136)  462
                                                        Type: PositiveInteger
--R 
--R
--R   (136)  462
--R                                                        Type: PositiveInteger
--E 136

--S 137 of 350
g**% - a
 

   (137)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R   (137)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 137

--S 138 of 350
discreteLog(b,a)
 

   (138)  154
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (138)  154
--R                                          Type: Union(NonNegativeInteger,...)
--E 138

--S 139 of 350
extensionDegree()$F
 

   (139)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (139)  3
--R                                                        Type: PositiveInteger
--E 139

--S 140 of 350
degree(a)
 

   (140)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (140)  3
--R                                                        Type: PositiveInteger
--E 140

--S 141 of 350
normalElement()$F
 

            2
   (141)  %E  + %E
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R            2
--R   (141)  %E  + %E
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 141

--S 142 of 350
definingPolynomial()$F
 

           3
   (142)  ?  + ? + %D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (142)  ?  + ? + %D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 142

--S 143 of 350
minimalPolynomial(a)
 

           3        2
   (143)  ?  + 2%D ?  + 2? + 2%D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3        2
--R   (143)  ?  + 2%D ?  + 2? + 2%D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 143

--S 144 of 350
Frobenius(a)
 

               2
   (144)  %D %E  + 2%E + 2%D
Type: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--R 
--R
--R               2
--R   (144)  %D %E  + 2%E + 2%D
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+?+D)
--E 144

--S 145 of 350
linearAssociatedOrder(a)
 

           3
   (145)  ?  + 2
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (145)  ?  + 2
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 145

--S 146 of 350
linearAssociatedLog(a)
 

                    2
   (146)  (2%D + 2)?  + (2%D + 1)?
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R                    2
--R   (146)  (2%D + 2)?  + (2%D + 1)?
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 146

--S 147 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   %D
   %D
        2
   %D %E
        2
   %D %E
                                                                   Type: Void
--R 
--R   %D
--R   %D
--R        2
--R   %D %E
--R        2
--R   %D %E
--R                                                                   Type: Void
--E 147

--S 148 of 350
f1:=createNormalPoly(d1)$FFPOLY(P)
 

           2
   (148)  ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (148)  ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 148

--S 149 of 350
F1:=FFNBP(P,f1)
 

   (149)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
                                                                 Type: Domain
--R 
--R
--R   (149)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R                                                                 Type: Domain
--E 149

--S 150 of 350
f2:=createIrreduciblePoly(d2)$FFPOLY(F1)
 

           3
   (150)  ?  + ? + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3
--R   (150)  ?  + ? + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 150

--S 151 of 350
F:=FFP(F1,f2)
 

   (151)
  FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(
  PrimeField 3,?*?+2*?+2),?**3+?+F)
                                                                 Type: Domain
--R 
--R
--R   (151)
--R  FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(
--R  PrimeField 3,?*?+2*?+2),?**3+?+F)
--R                                                                 Type: Domain
--E 151 of 350

--S 152 of 250
size()$F
 

   (152)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (152)  729
--R                                                     Type: NonNegativeInteger
--E 152

--S 153 of 350
a:=index(size()$F quo 3)$F
 

            q  2
   (153)  %F %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2
--R   (153)  %F %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 153

--S 154 of 350
b:=index(size()$F quo 7)$F
 

               2              q
   (154)  %F %G  + 2%F %G + %F  + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R               2              q
--R   (154)  %F %G  + 2%F %G + %F  + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 154

--S 155 of 350
a+b
 

            2              q
   (155)  %G  + 2%F %G + %F  + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            2              q
--R   (155)  %G  + 2%F %G + %F  + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 155

--S 156 of 350
a-b
 

             q         2              q
   (156)  (%F  + 2%F)%G  + %F %G + 2%F  + %F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R             q         2              q
--R   (156)  (%F  + 2%F)%G  + %F %G + 2%F  + %F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 156

--S 157 of 350
a*b
 

            q  2      q
   (157)  %F %G  + 2%F %G + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2      q
--R   (157)  %F %G  + 2%F %G + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 157

--S 158 of 350
a/b
 

            2
   (158)  %G  + %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            2
--R   (158)  %G  + %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 158

--S 159 of 350
a**1234
 

            q  2             q
   (159)  %F %G  + %F %G + %F  + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2             q
--R   (159)  %F %G  + %F %G + %F  + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 159

--S 160 of 350
a**(-1)
 

            q  2          q
   (160)  %F %G  + %G + %F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2          q
--R   (160)  %F %G  + %G + %F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 160

--S 161 of 350
g := generator()$F
 

   (161)  %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (161)  %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 161

--S 162 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (162)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (162)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 162

--S 163 of 350
order(a)
 

   (163)  728
                                                        Type: PositiveInteger
--R 
--R
--R   (163)  728
--R                                                        Type: PositiveInteger
--E 163

--S 164 of 350
g:=primitiveElement()$F
 

   (164)  %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (164)  %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 164

--S 165 of 350
discreteLog(a)
 

   (165)  639
                                                        Type: PositiveInteger
--R 
--R
--R   (165)  639
--R                                                        Type: PositiveInteger
--E 165

--S 166 of 350
g**% - a
 

   (166)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R   (166)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 166

--S 167 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (167)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (167)  "failed"
--R                                                    Type: Union("failed",...)
--E 167

--S 168 of 350
extensionDegree()$F
 

   (168)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (168)  3
--R                                                        Type: PositiveInteger
--E 168

--S 169 of 350
degree(a)
 

   (169)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (169)  3
--R                                                        Type: PositiveInteger
--E 169

--S 170 of 350
normalElement()$F
 

            2
   (170)  %G
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            2
--R   (170)  %G
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 170

--S 171 of 350
definingPolynomial()$F
 

           3
   (171)  ?  + ? + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3
--R   (171)  ?  + ? + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 171

--S 172 of 350
minimalPolynomial(a)
 

           3      q 2       q             q
   (172)  ?  + 2%F ?  + (2%F  + %F)? + 2%F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q 2       q             q
--R   (172)  ?  + 2%F ?  + (2%F  + %F)? + 2%F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 172

--S 173 of 350
Frobenius(a)
 

            q  2               q
   (173)  %F %G  + 2%F %G + 2%F
Type: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--R 
--R
--R            q  2               q
--R   (173)  %F %G  + 2%F %G + 2%F
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+?+F)
--E 173

--S 174 of 350
linearAssociatedOrder(a)
 

           3      q
   (174)  ?  + 2%F  + 2%F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q
--R   (174)  ?  + 2%F  + 2%F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 174

--S 175 of 350
linearAssociatedLog(a)
 

            q
   (175)  %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R            q
--R   (175)  %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 175

--S 176 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
     q
   %F
     q
   %F
     q  2
   %F %G
     q  2
   %F %G
                                                                   Type: Void
--R 
--R     q
--R   %F
--R     q
--R   %F
--R     q  2
--R   %F %G
--R     q  2
--R   %F %G
--R                                                                   Type: Void
--E 176

--S 177 of 350
f1:=createPrimitivePoly(d1)$FFPOLY(P)
 

           2
   (177)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (177)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 177

--S 178 of 350
F1:=FFCGP(P,f1)
 

   (178)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
                                                                 Type: Domain
--R 
--R
--R   (178)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R                                                                 Type: Domain
--E 178

--S 179 of 350
f2:=createIrreduciblePoly(d2)$FFPOLY(F1)
 

           3         1
   (179)  ?  + ? + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3         1
--R   (179)  ?  + ? + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 179

--S 180 of 350
F:=FFP(F1,f2)
 

   (180)
  FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(
  PrimeField 3,?*?+?+2),?**3+?+H**1)
                                                                 Type: Domain
--R 
--R
--R   (180)
--R  FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(
--R  PrimeField 3,?*?+?+2),?**3+?+H**1)
--R                                                                 Type: Domain
--E 180

--S 181 of 350
size()$F
 

   (181)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (181)  729
--R                                                     Type: NonNegativeInteger
--E 181

--S 192 of 350
a:=index(size()$F quo 3)$F
 

            2  2
   (182)  %H %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2  2
--R   (182)  %H %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 182

--S 183 of 350
b:=index(size()$F quo 7)$F
 

            2     1       4
   (183)  %I  + %H %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2     1       4
--R   (183)  %I  + %H %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 183

--S 184 of 350
a+b
 

            3  2     1       4
   (184)  %H %I  + %H %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            3  2     1       4
--R   (184)  %H %I  + %H %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 184

--S 185 of 350
a-b
 

            5  2     5
   (185)  %H %I  + %H %I + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            5  2     5
--R   (185)  %H %I  + %H %I + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 185

--S 186 of 350
a*b
 

            2  2     3
   (186)  %H %I  + %H %I + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2  2     3
--R   (186)  %H %I  + %H %I + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 186

--S 187 of 350
a/b
 

            1  2     6
   (187)  %H %I  + %H %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            1  2     6
--R   (187)  %H %I  + %H %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 187

--S 188 of 350
a**1234
 

            5  2     7
   (188)  %H %I  + %H %I + 1
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            5  2     7
--R   (188)  %H %I  + %H %I + 1
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 188

--S 189 of 350
a**(-1)
 

            4  2     1       4
   (189)  %H %I  + %H %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            4  2     1       4
--R   (189)  %H %I  + %H %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 189

--S 190 of 350
g := generator()$F
 

   (190)  %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (190)  %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 190

--S 191 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (191)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (191)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 191

--S 192 of 350
order(a)
 

   (192)  91
                                                        Type: PositiveInteger
--R 
--R
--R   (192)  91
--R                                                        Type: PositiveInteger
--E 192

--S 193 of 350
g:=primitiveElement()$F
 

   (193)  %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (193)  %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 193

--S 194 of 350
discreteLog(a)
 

   (194)  184
                                                        Type: PositiveInteger
--R 
--R
--R   (194)  184
--R                                                        Type: PositiveInteger
--E 194

--S 195 of 350
g**% - a
 

   (195)  0
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R   (195)  0
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 195

--S 196 of 350
discreteLog(b,a)
 

   (196)  352
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (196)  352
--R                                          Type: Union(NonNegativeInteger,...)
--E 196

--S 197 of 350
extensionDegree()$F
 

   (197)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (197)  3
--R                                                        Type: PositiveInteger
--E 197

--S 198 of 350
degree(a)
 

   (198)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (198)  3
--R                                                        Type: PositiveInteger
--E 198

--S 199 of 350
normalElement()$F
 

            2
   (199)  %I
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2
--R   (199)  %I
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 199

--S 200 of 350
definingPolynomial()$F
 

           3         1
   (200)  ?  + ? + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3         1
--R   (200)  ?  + ? + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 200

--S 201 of 350
minimalPolynomial(a)
 

           3     6 2     4      4
   (201)  ?  + %H ?  + %H ? + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     6 2     4      4
--R   (201)  ?  + %H ?  + %H ? + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 201

--S 202 of 350
Frobenius(a)
 

            2  2          6
   (202)  %H %I  + %I + %H
Type: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--R 
--R
--R            2  2          6
--R   (202)  %H %I  + %I + %H
--RType: FiniteFieldExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+?+H**1)
--E 202

--S 203 of 350
linearAssociatedOrder(a)
 

           3     4
   (203)  ?  + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4
--R   (203)  ?  + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 203

--S 204 of 350
linearAssociatedLog(a)
 

            2
   (204)  %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R            2
--R   (204)  %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 204

--S 205 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
   1
     2
   %H
     2  2
   %H %I
     2  2
   %H %I
                                                                   Type: Void
--R 
--R   1
--R     2
--R   %H
--R     2  2
--R   %H %I
--R     2  2
--R   %H %I
--R                                                                   Type: Void
--E 205

--S 206 of 350
f1:=createIrreduciblePoly(d1)$FFPOLY(P)
 

           2
   (206)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (206)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 206

--S 207 of 350
F1:=FFP(P,f1)
 

   (207)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (207)  FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R                                                                 Type: Domain
--E 207

--S 208 of 350
f2:=createNormalPoly(d2)$FFPOLY(F1)
 

           3     2
   (208)  ?  + 2?  + 1
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3     2
--R   (208)  ?  + 2?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 208

--S 209 of 350
F:=FFNBP(F1,f2)
 

   (209)
  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(
  PrimeField 3,?*?+1),?**3+2*?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (209)
--R  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(
--R  PrimeField 3,?*?+1),?**3+2*?*?+1)
--R                                                                 Type: Domain
--E 209

--S 210 of 350
size()$F
 

   (210)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (210)  729
--R                                                     Type: NonNegativeInteger
--E 210

--S 211 of 350
a:=index(size()$F quo 3)$F
 

                2
               q
   (211)  %D %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                2
--R               q
--R   (211)  %D %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 211

--S 212 of 350
b:=index(size()$F quo 7)$F
 

             2
            q       q
   (212)  %J   + 2%J  + (%D + 2)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R             2
--R            q       q
--R   (212)  %J   + 2%J  + (%D + 2)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 212

--S 213 of 350
a+b
 

                     2
                    q       q
   (213)  (%D + 1)%J   + 2%J  + (%D + 2)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                     2
--R                    q       q
--R   (213)  (%D + 1)%J   + 2%J  + (%D + 2)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 213

--S 214 of 350
a-b
 

                     2
                    q      q
   (214)  (%D + 2)%J   + %J  + (2%D + 1)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                     2
--R                    q      q
--R   (214)  (%D + 2)%J   + %J  + (2%D + 1)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 214

--S 215 of 350
a*b
 

                     2
                    q         q
   (215)  (%D + 2)%J   + %D %J  + (2%D + 1)%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                     2
--R                    q         q
--R   (215)  (%D + 2)%J   + %D %J  + (2%D + 1)%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 215

--S 216 of 350
a/b
 

              2
             q         q
   (216)  2%J   + %D %J  + 2%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R              2
--R             q         q
--R   (216)  2%J   + %D %J  + 2%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 216

--S 217 of 350
a**1234
 

            q
   (217)  %J  + 2%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R            q
--R   (217)  %J  + 2%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 217

--S 218 of 350
a**(-1)
 

                q
   (218)  2%D %J  + %D %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                q
--R   (218)  2%D %J  + %D %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 218

--S 219 of 350
g := generator()$F
 

   (219)  %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (219)  %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 219

--S 220 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (220)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (220)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 220

--S 221 of 350
order(a)
 

   (221)  52
                                                        Type: PositiveInteger
--R 
--R
--R   (221)  52
--R                                                        Type: PositiveInteger
--E 221

--S 222 of 350
g:=primitiveElement()$F
 

                    q
   (222)  (%D + 1)%J  + 2%J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R                    q
--R   (222)  (%D + 1)%J  + 2%J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 222

--S 223 of 350
discreteLog(a)
 

   (223)  462
                                                        Type: PositiveInteger
--R 
--R
--R   (223)  462
--R                                                        Type: PositiveInteger
--E 223

--S 224 of 350
g**% - a
 

   (224)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (224)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 224

--S 225 of 350
discreteLog(b,a)
 

   (225)  70
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (225)  70
--R                                          Type: Union(NonNegativeInteger,...)
--E 225

--S 226 of 350
extensionDegree()$F
 

   (226)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (226)  3
--R                                                        Type: PositiveInteger
--E 226

--S 227 of 350
degree(a)
 

   (227)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (227)  3
--R                                                        Type: PositiveInteger
--E 227

--S 228 of 350
normalElement()$F
 

   (228)  %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (228)  %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 228

--S 229 of 350
definingPolynomial()$F
 

           3     2
   (229)  ?  + 2?  + 1
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3     2
--R   (229)  ?  + 2?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 229

--S 230 of 350
minimalPolynomial(a)
 

           3        2
   (230)  ?  + 2%D ?  + 2%D
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3        2
--R   (230)  ?  + 2%D ?  + 2%D
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 230

--S 231 of 350
Frobenius(a)
 

   (231)  %D %J
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--R 
--R
--R   (231)  %D %J
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1),?**3+2*?*?+1)
--E 231

--S 232 of 350
linearAssociatedOrder(a)
 

           3
   (232)  ?  + 2
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R           3
--R   (232)  ?  + 2
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 232

--S 233 of 350
linearAssociatedLog(a)
 

              2
   (233)  %D ?
Type: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--R 
--R
--R              2
--R   (233)  %D ?
--RType: SparseUnivariatePolynomial FiniteFieldExtensionByPolynomial(PrimeField 3,?*?+1)
--E 233

--S 234 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
         2
        q         q
   %D %J   + %D %J  + %D %J
         2
        q         q
   %D %J   + %D %J  + %D %J
         2
        q
   %D %J
         2
        q
   %D %J
                                                                   Type: Void
--R 
--R         2
--R        q         q
--R   %D %J   + %D %J  + %D %J
--R         2
--R        q         q
--R   %D %J   + %D %J  + %D %J
--R         2
--R        q
--R   %D %J
--R         2
--R        q
--R   %D %J
--R                                                                   Type: Void
--E 234

--S 235 of 350
f1:=createNormalPoly(d1)$FFPOLY(P)
 

           2
   (235)  ?  + 2? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (235)  ?  + 2? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 235

--S 236 of 350
F1:=FFNBP(P,f1)
 

   (236)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
                                                                 Type: Domain
--R 
--R
--R   (236)  FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R                                                                 Type: Domain
--E 236

--S 237 of 350
f2:=createNormalPoly(d2)$FFPOLY(F1)
 

           3       q        2     q
   (237)  ?  + (2%F  + 2%F)?  + %F  + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3       q        2     q
--R   (237)  ?  + (2%F  + 2%F)?  + %F  + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 237

--S 238 of 350
F:=FFNBP(F1,f2)
 

   (238)
  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionBy
  Polynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
                                                                 Type: Domain
--R 
--R
--R   (238)
--R  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionBy
--R  Polynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R                                                                 Type: Domain
--E 238

--S 239 of 350
size()$F
 

   (239)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (239)  729
--R                                                     Type: NonNegativeInteger
--E 239

--S 240 of 350
a:=index(size()$F quo 3)$F
 

                2
            q  q
   (240)  %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                2
--R            q  q
--R   (240)  %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 240

--S 241 of 350
b:=index(size()$F quo 7)$F
 

                2
               q          q      q
   (241)  %F %K   + 2%F %K  + (%F  + 2%F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                2
--R               q          q      q
--R   (241)  %F %K   + 2%F %K  + (%F  + 2%F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 241

--S 242 of 350
a+b
 

             2
            q          q      q
   (242)  %K   + 2%F %K  + (%F  + 2%F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R             2
--R            q          q      q
--R   (242)  %K   + 2%F %K  + (%F  + 2%F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 242

--S 243 of 350
a-b
 

                        2
             q         q         q       q
   (243)  (%F  + 2%F)%K   + %F %K  + (2%F  + %F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                        2
--R             q         q         q       q
--R   (243)  (%F  + 2%F)%K   + %F %K  + (2%F  + %F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 243

--S 244 of 350
a*b
 

                2
            q  q        q         q      q
   (244)  %F %K   + (2%F  + 2%F)%K  + 2%F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                2
--R            q  q        q         q      q
--R   (244)  %F %K   + (2%F  + 2%F)%K  + 2%F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 244

--S 245 of 350
a/b
 

                         2
              q         q       q         q       q
   (245)  (2%F  + 2%F)%K   + (%F  + 2%F)%K  + (2%F  + 2%F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                         2
--R              q         q       q         q       q
--R   (245)  (2%F  + 2%F)%K   + (%F  + 2%F)%K  + (2%F  + 2%F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 245

--S 246 of 350
a**1234
 

             q         q       q
   (246)  (%F  + 2%F)%K  + (2%F  + %F)%K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R             q         q       q
--R   (246)  (%F  + 2%F)%K  + (2%F  + %F)%K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 246

--S 247 of 350
a**(-1)
 

                q
   (247)  2%F %K  + %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R                q
--R   (247)  2%F %K  + %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 247

--S 248 of 350
g := generator()$F
 

   (248)  %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (248)  %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 248

--S 249 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (249)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (249)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 249

--S 250 of 350
order(a)
 

   (250)  104
                                                        Type: PositiveInteger
--R 
--R
--R   (250)  104
--R                                                        Type: PositiveInteger
--E 250

--S 251 of 350
g:=primitiveElement()$F
 

               q     q
   (251)  %F %K  + %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R               q     q
--R   (251)  %F %K  + %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 251

--S 252 of 350
discreteLog(a)
 

   (252)  343
                                                        Type: PositiveInteger
--R 
--R
--R   (252)  343
--R                                                        Type: PositiveInteger
--E 252

--S 253 of 350
g**% - a
 

   (253)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (253)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 253

--S 254 of 350
discreteLog(b,a)
 
   discreteLog: second argument not in cyclic group generated by first argument

   (254)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   discreteLog: second argument not in cyclic group generated by first argument
--R
--R   (254)  "failed"
--R                                                    Type: Union("failed",...)
--E 254

--S 255 of 350
extensionDegree()$F
 

   (255)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (255)  3
--R                                                        Type: PositiveInteger
--E 255

--S 256 of 350
degree(a)
 

   (256)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (256)  3
--R                                                        Type: PositiveInteger
--E 256

--S 257 of 350
normalElement()$F
 

   (257)  %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R   (257)  %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 257

--S 258 of 350
definingPolynomial()$F
 

           3       q        2     q
   (258)  ?  + (2%F  + 2%F)?  + %F  + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3       q        2     q
--R   (258)  ?  + (2%F  + 2%F)?  + %F  + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 258

--S 259 of 350
minimalPolynomial(a)
 

           3      q 2
   (259)  ?  + 2%F ?  + %F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q 2
--R   (259)  ?  + 2%F ?  + %F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 259

--S 260 of 350
Frobenius(a)
 

            q
   (260)  %F %K
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--R 
--R
--R            q
--R   (260)  %F %K
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2),?**3+(2*F**q+2*F)*?*?+F**q+F)
--E 260

--S 261 of 350
linearAssociatedOrder(a)
 

           3      q
   (261)  ?  + 2%F  + 2%F
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R           3      q
--R   (261)  ?  + 2%F  + 2%F
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 261

--S 262 of 350
linearAssociatedLog(a)
 

            q 2
   (262)  %F ?
Type: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--R 
--R
--R            q 2
--R   (262)  %F ?
--RType: SparseUnivariatePolynomial FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?*?+2*?+2)
--E 262

--S 263 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
          2
         q          q
   2%F %K   + 2%F %K  + 2%F %K
         2
     q  q      q  q     q
   %F %K   + %F %K  + %F %K
         2
     q  q
   %F %K
         2
     q  q
   %F %K
                                                                   Type: Void
--R 
--R          2
--R         q          q
--R   2%F %K   + 2%F %K  + 2%F %K
--R         2
--R     q  q      q  q     q
--R   %F %K   + %F %K  + %F %K
--R         2
--R     q  q
--R   %F %K
--R         2
--R     q  q
--R   %F %K
--R                                                                   Type: Void
--E 263

--S 264 of 350
f1:=createPrimitivePoly(d1)$FFPOLY(P)
 

           2
   (264)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           2
--R   (264)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 264

--S 265 of 350
F1:=FFCGP(P,f1)
 

   (265)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
                                                                 Type: Domain
--R 
--R
--R   (265)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R                                                                 Type: Domain
--E 265

--S 266 of 350
f2:=createNormalPoly(d2)$FFPOLY(F1)
 

           3     4 2
   (266)  ?  + %H ?  + 1
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4 2
--R   (266)  ?  + %H ?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 266

--S 267 of 350
F:=FFNBP(F1,f2)
 

   (267)
  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionBy
  Polynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (267)
--R  FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionBy
--R  Polynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R                                                                 Type: Domain
--E 267

--S 268 of 350
size()$F
 

   (268)  729
                                                     Type: NonNegativeInteger
--R 
--R
--R   (268)  729
--R                                                     Type: NonNegativeInteger
--E 268

--S 269 of 350
a:=index(size()$F quo 3)$F
 

                2
            2  q
   (269)  %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            2  q
--R   (269)  %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 269

--S 270 of 350
b:=index(size()$F quo 7)$F
 

             2
            q      1  q     4
   (270)  %L   + %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R             2
--R            q      1  q     4
--R   (270)  %L   + %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 270

--S 271 of 350
a+b
 

                2
            3  q      1  q     4
   (271)  %H %L   + %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            3  q      1  q     4
--R   (271)  %H %L   + %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 271

--S 272 of 350
a-b
 

                2
            5  q      5  q
   (272)  %H %L   + %H %L  + %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            5  q      5  q
--R   (272)  %H %L   + %H %L  + %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 272

--S 273 of 350
a*b
 

                2
            7  q      q     6
   (273)  %H %L   + %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            7  q      q     6
--R   (273)  %H %L   + %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 273

--S 274 of 350
a/b
 

                2
            2  q      5  q     6
   (274)  %H %L   + %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R                2
--R            2  q      5  q     6
--R   (274)  %H %L   + %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 274

--S 275 of 350
a**1234
 

            q     4
   (275)  %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            q     4
--R   (275)  %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 275

--S 276 of 350
a**(-1)
 

            6  q     2
   (276)  %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            6  q     2
--R   (276)  %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 276

--S 277 of 350
g := generator()$F
 

   (277)  %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (277)  %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 277

--S 278 of 350
(definingPolynomial()$F::SUP(F)).g
 

   (278)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (278)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 278

--S 279 of 350
order(a)
 

   (279)  52
                                                        Type: PositiveInteger
--R 
--R
--R   (279)  52
--R                                                        Type: PositiveInteger
--E 279

--S 280 of 350
g:=primitiveElement()$F
 

            1  q     2
   (280)  %H %L  + %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            1  q     2
--R   (280)  %H %L  + %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 280

--S 281 of 350
discreteLog(a)
 

   (281)  98
                                                        Type: PositiveInteger
--R 
--R
--R   (281)  98
--R                                                        Type: PositiveInteger
--E 281

--S 282 of 350
g**% - a
 

   (282)  0
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (282)  0
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 282

--S 283 of 350
discreteLog(b,a)
 

   (283)  574
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (283)  574
--R                                          Type: Union(NonNegativeInteger,...)
--E 283

--S 284 of 350
extensionDegree()$F
 

   (284)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (284)  3
--R                                                        Type: PositiveInteger
--E 284

--S 285 of 350
degree(a)
 

   (285)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (285)  3
--R                                                        Type: PositiveInteger
--E 285

--S 286 of 350
normalElement()$F
 

   (286)  %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R   (286)  %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 286

--S 287 of 350
definingPolynomial()$F
 

           3     4 2
   (287)  ?  + %H ?  + 1
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4 2
--R   (287)  ?  + %H ?  + 1
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 287

--S 288 of 350
minimalPolynomial(a)
 

           3     6 2     6
   (288)  ?  + %H ?  + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     6 2     6
--R   (288)  ?  + %H ?  + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 288

--S 289 of 350
Frobenius(a)
 

            2
   (289)  %H %L
Type: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--R 
--R
--R            2
--R   (289)  %H %L
--RType: FiniteFieldNormalBasisExtensionByPolynomial(FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2),?**3+H**4*?*?+1)
--E 289

--S 290 of 350
linearAssociatedOrder(a)
 

           3     4
   (290)  ?  + %H
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R           3     4
--R   (290)  ?  + %H
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 290 of 350

--S 291 of 350
linearAssociatedLog(a)
 

            2 2
   (291)  %H ?
Type: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--R 
--R
--R            2 2
--R   (291)  %H ?
--RType: SparseUnivariatePolynomial FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?*?+?+2)
--E 291

--S 292 of 350
for d in divisors extensionDegree()$F repeat
        print(norm(a,d::PI)::OUTFORM)
        print(trace(a,d::PI)::OUTFORM)
 
         2
     2  q      2  q     2
   %H %L   + %H %L  + %H %L
         2
     2  q      2  q     2
   %H %L   + %H %L  + %H %L
         2
     2  q
   %H %L
         2
     2  q
   %H %L
                                                                   Type: Void
--R 
--R         2
--R     2  q      2  q     2
--R   %H %L   + %H %L  + %H %L
--R         2
--R     2  q      2  q     2
--R   %H %L   + %H %L  + %H %L
--R         2
--R     2  q
--R   %H %L
--R         2
--R     2  q
--R   %H %L
--R                                                                   Type: Void
--E 292

--S 293 of 350
P3:= PF 3
 

   (293)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (293)  PrimeField 3
--R                                                                 Type: Domain
--E 293

--S 294 of 350
fi:=createIrreduciblePoly(6)$FFPOLY(P3)
 

           6
   (294)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           6
--R   (294)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 294

--S 295 of 350
fn:=createNormalPoly(6)$FFPOLY(P3)
 

           6     5    3
   (295)  ?  + 2?  + ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           6     5    3
--R   (295)  ?  + 2?  + ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 295

--S 296 of 350
fp:=createPrimitivePoly(3)$FFPOLY(P3)
 

           3
   (296)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           3
--R   (296)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 296

--S 297 of 350
F:=FFP(P3,fn)
 

   (297)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (297)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 297

--S 298 of 350
N:=FFNBP(P3,fn)
 

   (298)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (298)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 298

--S 299 of 350
a:=index(size()$F quo 3)$F
 

            5
   (299)  %M
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            5
--R   (299)  %M
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 299

--S 300 of 350
b:=index(size()$F quo 7)$F
 

            4      2
   (300)  %M  + 2%M  + %M + 2
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            4      2
--R   (300)  %M  + 2%M  + %M + 2
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 300

--S 301 of 350
an:=coerce(a)$FFHOM(F,P3,N)
 

             4      3
            q      q      q
   (301)  %N   + %N   + %N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R             4      3
--R            q      q      q
--R   (301)  %N   + %N   + %N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 301

--S 302 of 350
bn:=coerce(b)$FFHOM(F,P3,N)
 

             3      2
            q      q       q
   (302)  %N   + %N   + 2%N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R             3      2
--R            q      q       q
--R   (302)  %N   + %N   + 2%N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 302

--S 303 of 350
cn := an*bn
 

              5       4      3
             q       q      q      q
   (303)  2%N   + 2%N   + %N   + %N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5       4      3
--R             q       q      q      q
--R   (303)  2%N   + 2%N   + %N   + %N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 303

--S 304 of 350
coerce(cn)$FFHOM(F,P3,N)
 

            5      3      2
   (304)  %M  + 2%M  + 2%M
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            5      3      2
--R   (304)  %M  + 2%M  + 2%M
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 304

--S 305 of 350
c:=a*b
 

            5      3      2
   (305)  %M  + 2%M  + 2%M
      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R            5      3      2
--R   (305)  %M  + 2%M  + 2%M
--R      Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 305

--S 306 of 350
F:=FFP(P3,fi)
 

   (306)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
                                                                 Type: Domain
--R 
--R
--R   (306)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R                                                                 Type: Domain
--E 306

--S 307 of 350
N:=FFNBP(P3,fn)
 

   (307)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (307)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 307

--S 308 of 350
a:=index(size()$F quo 3)$F
 

            5
   (308)  %O
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R            5
--R   (308)  %O
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 308

--S 309 of 350
b:=index(size()$F quo 7)$F
 

            4      2
   (309)  %O  + 2%O  + %O + 2
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R            4      2
--R   (309)  %O  + 2%O  + %O + 2
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 309

--S 310 of 350
an:=coerce(a)$FFHOM(F,P3,N)
 

              5      4       3      2
             q      q       q      q      q
   (310)  2%N   + %N   + 2%N   + %N   + %N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5      4       3      2
--R             q      q       q      q      q
--R   (310)  2%N   + %N   + 2%N   + %N   + %N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 310

--S 311 of 350
bn:=coerce(b)$FFHOM(F,P3,N)
 

              3      2
             q      q
   (311)  2%N   + %N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              3      2
--R             q      q
--R   (311)  2%N   + %N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 311

--S 312 of 350
cn := an*bn
 

              5      4      3      2
             q      q      q      q      q
   (312)  2%N   + %N   + %N   + %N   + %N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5      4      3      2
--R             q      q      q      q      q
--R   (312)  2%N   + %N   + %N   + %N   + %N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 312

--S 313 of 350
coerce(cn)$FFHOM(F,P3,N)
 

             5      4     3     2
   (313)  2%O  + 2%O  + %O  + %O  + %O + 1
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R             5      4     3     2
--R   (313)  2%O  + 2%O  + %O  + %O  + %O + 1
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 313

--S 314 of 350
c:=a*b
 

             5      4     3     2
   (314)  2%O  + 2%O  + %O  + %O  + %O + 1
                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--R 
--R
--R             5      4     3     2
--R   (314)  2%O  + 2%O  + %O  + %O  + %O + 1
--R                Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**6+?+2)
--E 314

--S 315 of 350
C:=FFCGP(P3,fp)
 

   (315)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
                                                                 Type: Domain
--R 
--R
--R   (315)  FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R                                                                 Type: Domain
--E 315

--S 316 of 350
N:=FFNBP(P3,fn)
 

   (316)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
                                                                 Type: Domain
--R 
--R
--R   (316)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R                                                                 Type: Domain
--E 316

--S 317 of 350
a:=index(size()$C quo 3)$C
 

            8
   (317)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            8
--R   (317)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 317

--S 318 of 350
b:=index(size()$C quo 7)$C
 

            2
   (318)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            2
--R   (318)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 318

--S 319 of 350
an:=coerce(a)$FFHOM(C,P3,N)
 

              4       3
             q       q       q
   (319)  2%N   + 2%N   + 2%N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              4       3
--R             q       q       q
--R   (319)  2%N   + 2%N   + 2%N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 319

--S 320 of 350
bn:=coerce(b)$FFHOM(C,P3,N)
 

              5       2
             q       q
   (320)  2%N   + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5       2
--R             q       q
--R   (320)  2%N   + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 320

--S 321 of 350
cn := an+bn
 

              5       4       3       2
             q       q       q       q       q
   (321)  2%N   + 2%N   + 2%N   + 2%N   + 2%N  + 2%N
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--R 
--R
--R              5       4       3       2
--R             q       q       q       q       q
--R   (321)  2%N   + 2%N   + 2%N   + 2%N   + 2%N  + 2%N
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**6+2*?**5+?**3+1)
--E 321

--S 322 of 350
coerce(cn)$FFHOM(C,P3,N)
 

            13
   (322)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            13
--R   (322)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 322

--S 323 of 350
c:=a+b
 

            13
   (323)  %P
   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--R 
--R
--R            13
--R   (323)  %P
--R   Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**3+2*?+1)
--E 323

--S 324 of 350
f:=createPrimitiveNormalPoly(5)$FFPOLY(P3)
 

           5     4
   (324)  ?  + 2?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R           5     4
--R   (324)  ?  + 2?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 324

--S 325 of 350
FP:=FFP(P3,f)
 

   (325)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
                                                                 Type: Domain
--R 
--R
--R   (325)  FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R                                                                 Type: Domain
--E 325

--S 326 of 350
Fc:=FFCGP(P3,f)  -- FC is a domain abbreviation
 

   (326)
   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
                                                                 Type: Domain
--R 
--R
--R   (326)
--R   FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R                                                                 Type: Domain
--E 326

--S 328 of 350
FN:=FFNBP(P3,f)
 

   (327)
   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
                                                                 Type: Domain
--R 
--R
--R   (327)
--R   FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R                                                                 Type: Domain
--E 327

--S 328 of 350
ap:=index(size()$FP quo 3)$FP
 

            4
   (328)  %Q
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4
--R   (328)  %Q
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 328

--S 329 of 350
ac:=coerce(ap)$FFHOM(Fc,P3,FP)
 

            4
   (329)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4
--R   (329)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 329

--S 330 of 350
an:=coerce(ap)$FFHOM(FN,P3,FP)
 

              3       2
             q       q       q
   (330)  2%S   + 2%S   + 2%S  + %S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R              3       2
--R             q       q       q
--R   (330)  2%S   + 2%S   + 2%S  + %S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 330

--S 331 of 350
bp:=index(size()$FP quo 7)$FP
 

            3
   (331)  %Q  + 2%Q + 1
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            3
--R   (331)  %Q  + 2%Q + 1
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 331

--S 332 of 350
bc:=coerce(bp)$FFHOM(Fc,P3,FP)
 

            133
   (332)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            133
--R   (332)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 332

--S 333 of 350
bn:=coerce(bp)$FFHOM(FN,P3,FP)
 

             4      3      2
            q      q      q       q
   (333)  %S   + %S   + %S   + 2%S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4      3      2
--R            q      q      q       q
--R   (333)  %S   + %S   + %S   + 2%S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 333

--S 334 of 350
ac+bc
 

            187
   (334)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (334)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 334

--S 335 of 350
an*bn
 

             4      2
            q      q      q
   (335)  %S   + %S   + %S  + 2%S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4      2
--R            q      q      q
--R   (335)  %S   + %S   + %S  + 2%S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 335

--S 336 of 350
ap+bp
 

            4     3
   (336)  %Q  + %Q  + 2%Q + 1
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4     3
--R   (336)  %Q  + %Q  + 2%Q + 1
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 336

--S 337 of 350
an+bn
 

             4
            q      q
   (337)  %S   + %S  + %S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4
--R            q      q
--R   (337)  %S   + %S  + %S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 337

--S 338 of 350
ac+bc
 

            187
   (338)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (338)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 338

--S 339 of 350
ap*bp
 

            4      2
   (339)  %Q  + 2%Q  + 2%Q
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4      2
--R   (339)  %Q  + 2%Q  + 2%Q
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 339

--S 340 of 350
an*bn
 

             4      2
            q      q      q
   (340)  %S   + %S   + %S  + 2%S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4      2
--R            q      q      q
--R   (340)  %S   + %S   + %S  + 2%S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 340

--S 341 of 350
ac*bc
 

            137
   (341)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            137
--R   (341)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 341

--S 342 of 350
discreteLog(ap)
 

   (342)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (342)  4
--R                                                        Type: PositiveInteger
--E 342

--S 343 of 350
discreteLog(an)
 

   (343)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (343)  4
--R                                                        Type: PositiveInteger
--E 343

--S 344 of 350
discreteLog(ac)
 

   (344)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (344)  4
--R                                                        Type: PositiveInteger
--E 344

--S 345 of 350
ap**1234567
 

             4     2
   (345)  2%Q  + %Q  + %Q
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R             4     2
--R   (345)  2%Q  + %Q  + %Q
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 345

--S 346 of 350
an**1234567
 

              4       2
             q       q       q
   (346)  2%S   + 2%S   + 2%S  + %S
Type: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R              4       2
--R             q       q       q
--R   (346)  2%S   + 2%S   + 2%S  + %S
--RType: FiniteFieldNormalBasisExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 346

--S 347 of 350
ac**1234567
 

            16
   (347)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            16
--R   (347)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 347

--S 348 of 350
ap+bc
 

            187
   (348)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (348)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 348

--S 349 of 350
an+bc
 

            187
   (349)  %R
Type: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            187
--R   (349)  %R
--RType: FiniteFieldCyclicGroupExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 349

--S 350 of 350
an+bp
 

            4     3
   (350)  %Q  + %Q  + 2%Q + 1
           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--R 
--R
--R            4     3
--R   (350)  %Q  + %Q  + 2%Q + 1
--R           Type: FiniteFieldExtensionByPolynomial(PrimeField 3,?**5+2*?**4+1)
--E 350
)spool 
 
Starts dribbling to float1.output (2010/3/27, 18:26:15).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 37
1.234
 

   (1)  1.234
                                                                  Type: Float
--R 
--R
--R   (1)  1.234
--R                                                                  Type: Float
--E 1

--S 2 of 37
1.234E2
 

   (2)  123.4
                                                                  Type: Float
--R 
--R
--R   (2)  123.4
--R                                                                  Type: Float
--E 2

--S 3 of 37
sqrt(1.2 + 2.3 / 3.4 ** 4.5)
 

   (3)  1.0996972790 671286226
                                                                  Type: Float
--R 
--R
--R   (3)  1.0996972790 671286226
--R                                                                  Type: Float
--E 3

)clear all
 

--S 4 of 37
i := 3 :: Float
 

   (1)  3.0
                                                                  Type: Float
--R 
--R
--R   (1)  3.0
--R                                                                  Type: Float
--E 4

--S 5 of 37
i :: Integer
 

   (2)  3
                                                                Type: Integer
--R 
--R
--R   (2)  3
--R                                                                Type: Integer
--E 5

--S 6 of 37
i :: Fraction Integer
 

   (3)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (3)  3
--R                                                       Type: Fraction Integer
--E 6

--S 7 of 37
r := 3/7 :: Float
 

   (4)  0.4285714285 7142857143
                                                                  Type: Float
--R 
--R
--R   (4)  0.4285714285 7142857143
--R                                                                  Type: Float
--E 7

--S 8 of 37
r :: Fraction Integer
 

        3
   (5)  -
        7
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (5)  -
--R        7
--R                                                       Type: Fraction Integer
--E 8

--S 9 of 37
r :: Integer
 
 
Daly Bug
   Cannot convert from type Float to Integer for value
   0.4285714285 7142857143

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Float to Integer for value
--R   0.4285714285 7142857143
--R
--E 9

--S 10 of 37
truncate 3.6
 

   (6)  3.0
                                                                  Type: Float
--R 
--R
--R   (6)  3.0
--R                                                                  Type: Float
--E 10

--S 11 of 37
round 3.6
 

   (7)  4.0
                                                                  Type: Float
--R 
--R
--R   (7)  4.0
--R                                                                  Type: Float
--E 11

--S 21 of 37
truncate(-3.6)
 

   (8)  - 3.0
                                                                  Type: Float
--R 
--R
--R   (8)  - 3.0
--R                                                                  Type: Float
--E 12

--S 13 of 37
round(-3.6)
 

   (9)  - 4.0
                                                                  Type: Float
--R 
--R
--R   (9)  - 4.0
--R                                                                  Type: Float
--E 13

--S 14 of 37
fractionPart 3.6
 

   (10)  0.6
                                                                  Type: Float
--R 
--R
--R   (10)  0.6
--R                                                                  Type: Float
--E 14

--S 15 of 37
digits 40
 

   (11)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  20
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 37
sqrt 0.2
 

   (12)  0.4472135954 9995793928 1834733746 2552470881
                                                                  Type: Float
--R 
--R
--R   (12)  0.4472135954 9995793928 1834733746 2552470881
--R                                                                  Type: Float
--E 16

--S 17 of 37
pi()$Float
 

   (13)  3.1415926535 8979323846 2643383279 502884197
                                                                  Type: Float
--R 
--R
--R   (13)  3.1415926535 8979323846 2643383279 502884197
--R                                                                  Type: Float
--E 17

--S 18 of 37
digits 500
 

   (14)  40
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  40
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 37
pi()$Float
 

   (15)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (15)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 19

--S 20 of 37
digits 20
 

   (16)  500
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  500
--R                                                        Type: PositiveInteger
--E 20

)clear all
 

--S 21 of 37
outputSpacing 0; x := sqrt 0.2
 

   (1)  0.44721359549995793928
                                                                  Type: Float
--R 
--R
--R   (1)  0.44721359549995793928
--R                                                                  Type: Float
--E 21

--S 22 of 37
outputSpacing 5; x
 

   (2)  0.44721 35954 99957 93928
                                                                  Type: Float
--R 
--R
--R   (2)  0.44721 35954 99957 93928
--R                                                                  Type: Float
--E 22

--S 23 of 37
y := x/10**10
 

   (3)  0.44721 35954 99957 93928 E -10
                                                                  Type: Float
--R 
--R
--R   (3)  0.44721 35954 99957 93928 E -10
--R                                                                  Type: Float
--E 23

--S 24 of 37
outputFloating(); x
 

   (4)  0.44721 35954 99957 93928 E 0
                                                                  Type: Float
--R 
--R
--R   (4)  0.44721 35954 99957 93928 E 0
--R                                                                  Type: Float
--E 24

--S 25 of 37
outputFixed(); y
 

   (5)  0.00000 00000 44721 35954 99957 93928
                                                                  Type: Float
--R 
--R
--R   (5)  0.00000 00000 44721 35954 99957 93928
--R                                                                  Type: Float
--E 25

--S 26 of 37
outputFloating 2; y
 

   (6)  0.45 E -10
                                                                  Type: Float
--R 
--R
--R   (6)  0.45 E -10
--R                                                                  Type: Float
--E 26

--S 27 of 37
outputFixed 2; x
 

   (7)  0.45
                                                                  Type: Float
--R 
--R
--R   (7)  0.45
--R                                                                  Type: Float
--E 27

--S 28 of 37
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

)clear all
 

--S 29 of 37
a: Matrix Fraction Integer := matrix [[1/(i+j+1) for j in 0..9] for i in 0..9]
 

        +    1   1   1   1   1   1   1   1    1+
        |1   -   -   -   -   -   -   -   -   --|
        |    2   3   4   5   6   7   8   9   10|
        |                                      |
        |1   1   1   1   1   1   1   1    1   1|
        |-   -   -   -   -   -   -   -   --  --|
        |2   3   4   5   6   7   8   9   10  11|
        |                                      |
        |1   1   1   1   1   1   1    1   1   1|
        |-   -   -   -   -   -   -   --  --  --|
        |3   4   5   6   7   8   9   10  11  12|
        |                                      |
        |1   1   1   1   1   1    1   1   1   1|
        |-   -   -   -   -   -   --  --  --  --|
        |4   5   6   7   8   9   10  11  12  13|
        |                                      |
        |1   1   1   1   1    1   1   1   1   1|
        |-   -   -   -   -   --  --  --  --  --|
        |5   6   7   8   9   10  11  12  13  14|
   (1)  |                                      |
        |1   1   1   1    1   1   1   1   1   1|
        |-   -   -   -   --  --  --  --  --  --|
        |6   7   8   9   10  11  12  13  14  15|
        |                                      |
        |1   1   1    1   1   1   1   1   1   1|
        |-   -   -   --  --  --  --  --  --  --|
        |7   8   9   10  11  12  13  14  15  16|
        |                                      |
        |1   1    1   1   1   1   1   1   1   1|
        |-   -   --  --  --  --  --  --  --  --|
        |8   9   10  11  12  13  14  15  16  17|
        |                                      |
        |1    1   1   1   1   1   1   1   1   1|
        |-   --  --  --  --  --  --  --  --  --|
        |9   10  11  12  13  14  15  16  17  18|
        |                                      |
        | 1   1   1   1   1   1   1   1   1   1|
        |--  --  --  --  --  --  --  --  --  --|
        +10  11  12  13  14  15  16  17  18  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +    1   1   1   1   1   1   1   1    1+
--R        |1   -   -   -   -   -   -   -   -   --|
--R        |    2   3   4   5   6   7   8   9   10|
--R        |                                      |
--R        |1   1   1   1   1   1   1   1    1   1|
--R        |-   -   -   -   -   -   -   -   --  --|
--R        |2   3   4   5   6   7   8   9   10  11|
--R        |                                      |
--R        |1   1   1   1   1   1   1    1   1   1|
--R        |-   -   -   -   -   -   -   --  --  --|
--R        |3   4   5   6   7   8   9   10  11  12|
--R        |                                      |
--R        |1   1   1   1   1   1    1   1   1   1|
--R        |-   -   -   -   -   -   --  --  --  --|
--R        |4   5   6   7   8   9   10  11  12  13|
--R        |                                      |
--R        |1   1   1   1   1    1   1   1   1   1|
--R        |-   -   -   -   -   --  --  --  --  --|
--R        |5   6   7   8   9   10  11  12  13  14|
--R   (1)  |                                      |
--R        |1   1   1   1    1   1   1   1   1   1|
--R        |-   -   -   -   --  --  --  --  --  --|
--R        |6   7   8   9   10  11  12  13  14  15|
--R        |                                      |
--R        |1   1   1    1   1   1   1   1   1   1|
--R        |-   -   -   --  --  --  --  --  --  --|
--R        |7   8   9   10  11  12  13  14  15  16|
--R        |                                      |
--R        |1   1    1   1   1   1   1   1   1   1|
--R        |-   -   --  --  --  --  --  --  --  --|
--R        |8   9   10  11  12  13  14  15  16  17|
--R        |                                      |
--R        |1    1   1   1   1   1   1   1   1   1|
--R        |-   --  --  --  --  --  --  --  --  --|
--R        |9   10  11  12  13  14  15  16  17  18|
--R        |                                      |
--R        | 1   1   1   1   1   1   1   1   1   1|
--R        |--  --  --  --  --  --  --  --  --  --|
--R        +10  11  12  13  14  15  16  17  18  19+
--R                                                Type: Matrix Fraction Integer
--E 29

--S 30 of 37
d:= determinant a
 

                                  1
   (2)  -----------------------------------------------------
        46206893947914691316295628839036278726983680000000000
                                                       Type: Fraction Integer
--R 
--R
--R                                  1
--R   (2)  -----------------------------------------------------
--R        46206893947914691316295628839036278726983680000000000
--R                                                       Type: Fraction Integer
--E 30

--S 31 of 37
d :: Float
 

   (3)  0.21641 79226 43149 18691 E -52
                                                                  Type: Float
--R 
--R
--R   (3)  0.21641 79226 43149 18691 E -52
--R                                                                  Type: Float
--E 31

--S 32 of 37
b: Matrix DoubleFloat := matrix [[1/(i+j+1$DoubleFloat) for j in 0..9] for i in 0..9];
 

                                                     Type: Matrix DoubleFloat
--R 
--R
--R                                                     Type: Matrix DoubleFloat
--E 32

--S 33 of 37
determinant b
 

   (5)  2.1643677945721411E-53
                                                            Type: DoubleFloat
--R 
--R
--R   (5)  2.1643677945721411E-53
--R                                                            Type: DoubleFloat
--E 33

--S 34 of 37
digits 40
 

   (6)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  20
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 37
c: Matrix Float := matrix [[1/(i+j+1$Float) for j in 0..9] for i in 0..9];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 35

--S 36 of 37
determinant c
 

   (8)  0.21641 79226 43149 18690 60594 98362 26174 36159 E -52
                                                                  Type: Float
--R 
--R
--R   (8)  0.21641 79226 43149 18690 60594 98362 26174 36159 E -52
--R                                                                  Type: Float
--E 36

--S 37 of 37
digits 20
 

   (9)  40
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  40
--R                                                        Type: PositiveInteger
--E 37
)spool 
 
Starts dribbling to test.output (2010/3/27, 18:41:15).
)set message test on
 
)set message auto off
 
)set break resume
 

)clear all
 

--S 1 of 188
eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F
 

           2                   2
   (1)  C y  + (B x + E)y + A x  + D x + F
                                                     Type: Polynomial Integer
--R 
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 188
eq2:= eval(eq1,[x= xdot*cos(t) - ydot*sin(t), y=xdot*sin(t) + ydot*cos(t)])
 

   (2)
            2                       2       2
     (A ydot  - B xdot ydot + C xdot )sin(t)
   + 
               2                              2
     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
   + 
            2                       2       2
     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R            2                       2       2
--R     (A ydot  - B xdot ydot + C xdot )sin(t)
--R   + 
--R               2                              2
--R     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
--R   + 
--R            2                       2       2
--R     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
--R                                                     Type: Expression Integer
--E 2

)clear all
 

--S 3 of 188
taylor exp x
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 188
s := %
 

   (2)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 188
s::(UTS(EXPR FLOAT, x, 0))
 

   (3)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--R 
--R
--R   (3)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--E 5

--S 6 of 188
s::(UTS(FLOAT, x, 0))
 

   (4)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--R 
--R
--R   (4)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--E 6

--S 7 of 188
eval(s,1)
 

             5 8 65 163 1957 685 109601 98641
   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
             2 3 24  60  720 252  40320 36288
                                              Type: Stream Expression Integer
--R 
--R
--R             5 8 65 163 1957 685 109601 98641
--R   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
--R             2 3 24  60  720 252  40320 36288
--R                                              Type: Stream Expression Integer
--E 7

--S 8 of 188
%::(Stream Float)
 

   (6)
   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
    2.7182787698 412698413, 2.7182815255 731922399, ...]
                                                           Type: Stream Float
--R 
--R
--R   (6)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                           Type: Stream Float
--E 8

)clear all
 

--S 9 of 188
s := series(sin(a*x),x=0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 9

--S 10 of 188
eval(s, 1.0)
 

   (2)
                                          3
   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
                               3
    - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                      9                               7
       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
     + 
                                   5                            3
       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
     ,
    ...]
                                                Type: Stream Expression Float
--R 
--R
--R   (2)
--R                                          3
--R   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
--R                               3
--R    - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                      9                               7
--R       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
--R     + 
--R                                   5                            3
--R       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
--R     ,
--R    ...]
--R                                                Type: Stream Expression Float
--E 10

--S 11 of 188
s - a*x
 

   (3)
        3        5        7          9            11              13
       a   3    a   5    a    7     a     9      a      11       a       13
     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
        6      120      5040      362880      39916800       6227020800
   + 
        14
     O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (3)
--R        3        5        7          9            11              13
--R       a   3    a   5    a    7     a     9      a      11       a       13
--R     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
--R        6      120      5040      362880      39916800       6227020800
--R   + 
--R        14
--R     O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11


--S 12 of 188
eval(s, 1.0)
 

   (4)
                                          3
   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
                               3
    - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
                                5                            3
    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                     7                               5
       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
     + 
                                  3
       - 0.1666666666 6666666667 a  + a
     ,

                                      9                               7
       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
     + 
                                   5                            3
       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
     ,
    ...]
                                                Type: Stream Expression Float
--R 
--R
--R   (4)
--R                                          3
--R   [0.0, a, a, - 0.1666666666 6666666667 a  + a,
--R                               3
--R    - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R                                5                            3
--R    0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                     7                               5
--R       - 0.0001984126 9841269841 27 a  + 0.0083333333 3333333333 34 a
--R     + 
--R                                  3
--R       - 0.1666666666 6666666667 a  + a
--R     ,
--R
--R                                      9                               7
--R       0.0000027557 3192239858 90653 a  - 0.0001984126 9841269841 27 a
--R     + 
--R                                   5                            3
--R       0.0083333333 3333333333 34 a  - 0.1666666666 6666666667 a  + a
--R     ,
--R    ...]
--R                                                Type: Stream Expression Float
--E 12

)clear all
 

--S 13 of 188
v := vector [1,2,3]
 

   (1)  [1,2,3]
                                                 Type: Vector PositiveInteger
--R 
--R
--R   (1)  [1,2,3]
--R                                                 Type: Vector PositiveInteger
--E 13

--S 14 of 188
(1/2)*v
 

         1   3
   (2)  [-,1,-]
         2   2
                                                Type: Vector Fraction Integer
--R 
--R
--R         1   3
--R   (2)  [-,1,-]
--R         2   2
--R                                                Type: Vector Fraction Integer
--E 14

--S 15 of 188
eval(x**2, x=1/2)
 

        1
   (3)  -
        4
                                            Type: Polynomial Fraction Integer
--R 
--R
--R        1
--R   (3)  -
--R        4
--R                                            Type: Polynomial Fraction Integer
--E 15

--S 16 of 188
eval(x**2, x=0.5)
 

   (4)  0.25
                                                       Type: Polynomial Float
--R 
--R
--R   (4)  0.25
--R                                                       Type: Polynomial Float
--E 16

--S 17 of 188
eval(3**x, x=0.5)
 

   (5)  1.7320508075 688772935
                                                       Type: Expression Float
--R 
--R
--R   (5)  1.7320508075 688772935
--R                                                       Type: Expression Float
--E 17

)clear all
 

--S 18 of 188
f(x) == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 188
f(x,y) == x+y
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 188
f 3
 
   Compiling function f with type PositiveInteger -> PositiveInteger 

   (3)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (3)  4
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 188
f(3,4)
 
   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
      PositiveInteger 

   (4)  7
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
--R      PositiveInteger 
--R
--R   (4)  7
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 188
f(5)
 

   (5)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  6
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 188
f(1,x)
 
   Compiling function f with type (PositiveInteger,Variable x) -> 
      Polynomial Integer 

   (6)  x + 1
                                                     Type: Polynomial Integer
--R 
--R   Compiling function f with type (PositiveInteger,Variable x) -> 
--R      Polynomial Integer 
--R
--R   (6)  x + 1
--R                                                     Type: Polynomial Integer
--E 23

)clear all
 

--S 24 of 188
series(n +-> bernoulli(n)/factorial(n), t=0)
 

   (1)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--R 
--R
--R   (1)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 24

)clear all
 

--S 25 of 188
l := [1,2,-1]
 

   (1)  [1,2,- 1]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,- 1]
--R                                                           Type: List Integer
--E 25

--S 26 of 188
f : INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

--S 27 of 188
f x == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28 of 188
map(f, l)
 
   Compiling function f with type Integer -> Fraction Integer 

   (4)  [1,2,- 1]
                                                  Type: List Fraction Integer
--R 
--R   Compiling function f with type Integer -> Fraction Integer 
--R
--R   (4)  [1,2,- 1]
--R                                                  Type: List Fraction Integer
--E 28

)clear all
 

--S 29 of 188
f: INT -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 188
f x == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 188
u g == g 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 188
u f
 
   Compiling function u with type (Integer -> Integer) -> Integer 
   Compiling function f with type Integer -> Integer 

   (4)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function u with type (Integer -> Integer) -> Integer 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 32

)clear all
 

--S 33 of 188
groebner [x**2 - y, y**3+1]
 

              2  6
   (1)  [y - x ,x  + 1]
                                                Type: List Polynomial Integer
--R 
--R
--R              2  6
--R   (1)  [y - x ,x  + 1]
--R                                                Type: List Polynomial Integer
--E 33

)clear all
 

--S 34 of 188
factor x
 

   (1)  x
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (1)  x
--R                                            Type: Factored Polynomial Integer
--E 34

--draw(x, x=-1..1)

)clear all
 

--S 35 of 188
{}$(List INT)
 
 
Daly Bug
   The function SEQ is not implemented in List Integer .
--R 
--RDaly Bug
--R   The function SEQ is not implemented in List Integer .
--E 35

--S 36 of 188
brace []  -- {}
 

   (1)  {}
                                                               Type: Set None
--R
--R   (1)  {}
--R                                                               Type: Set None
--E 36

--S 37 of 188
brace [1] -- {1}
 

   (2)  {1}
                                                    Type: Set PositiveInteger
--R
--R   (2)  {1}
--R                                                    Type: Set PositiveInteger
--E 37

--S 38 of 188
union(brace [], brace [1,2])   -- union({}, {1,2})
 

   (3)  {1,2}
                                                    Type: Set PositiveInteger
--R
--R   (3)  {1,2}
--R                                                    Type: Set PositiveInteger
--E 38

)clear all
 

)set mes test off
 

--S 39 of 188
map(variable, [x,y])
 

   (1)  [x,y]
                         Type: List Union(OrderedVariableList [x,y],"failed")
--R 
--R
--R   (1)  [x,y]
--R                         Type: List Union(OrderedVariableList [x,y],"failed")
--E 39

)set mes test on
 

)clear all
 

)set fun recur off
 

--S 40 of 188
p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 40

--S 41 of 188
pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 41

--S 42 of 188
pp(-1,x) -- should be 1/(x-1)
 
   Compiling function p with type (Integer,Polynomial Integer) -> 
      Polynomial Integer 
   Compiling function p with type (Integer,Variable x) -> Polynomial 
      Integer 
   Compiling function pp with type (Integer,Variable x) -> Fraction 
      Polynomial Fraction Integer 

          1
   (3)  -----
        x - 1
                                   Type: Fraction Polynomial Fraction Integer
--R 
--R   Compiling function p with type (Integer,Polynomial Integer) -> 
--R      Polynomial Integer 
--R   Compiling function p with type (Integer,Variable x) -> Polynomial 
--R      Integer 
--R   Compiling function pp with type (Integer,Variable x) -> Fraction 
--R      Polynomial Fraction Integer 
--R
--R          1
--R   (3)  -----
--R        x - 1
--R                                   Type: Fraction Polynomial Fraction Integer
--E 42

)clear all
 

--S 43 of 188
f n ==
  for i in 1..n repeat
    j:=2*i
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 43

--S 44 of 188
g n ==
    j:=2*n
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 44

--S 45 of 188
g 3
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 45

--S 46 of 188
f 3
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0+
   |    |
   +0  1+
   +1  0  0  0+
   |          |
   |0  1  0  0|
   |          |
   |0  0  1  0|
   |          |
   +0  0  0  1+
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0+
--R   |    |
--R   +0  1+
--R   +1  0  0  0+
--R   |          |
--R   |0  1  0  0|
--R   |          |
--R   |0  0  1  0|
--R   |          |
--R   +0  0  0  1+
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 46

)clear all
 

--S 47 of 188
mp(x,l) ==
  l is [a,:b] =>
    a*x**(#b)+ mp(x,b)
  0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 47

--S 48 of 188
mp(x, [1,3,4, 2])
 
   Compiling function mp with type (Variable x,List PositiveInteger)
       -> Polynomial Integer 

         3     2
   (2)  x  + 3x  + 4x + 2
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List PositiveInteger)
--R       -> Polynomial Integer 
--R
--R         3     2
--R   (2)  x  + 3x  + 4x + 2
--R                                                     Type: Polynomial Integer
--E 48

--S 49 of 188
mp(x, [1,2,-3, 4])
 
   Compiling function mp with type (Variable x,List Integer) -> 
      Polynomial Integer 

         3     2
   (3)  x  + 2x  - 3x + 4
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List Integer) -> 
--R      Polynomial Integer 
--R
--R         3     2
--R   (3)  x  + 2x  - 3x + 4
--R                                                     Type: Polynomial Integer
--E 49

)clear all
 

--S 50 of 188
f1 n ==
  if n=0 then 1 else if n=1 then 1 else f1(n-1)+f1(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 50

--S 51 of 188
f2 n ==
  m:=n
  if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 51

--S 52 of 188
f3 n ==
  n=0 => 1
  n=1 => 1
  f3(n-1)+f3(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 52

--S 53 of 188
f4 n ==
  m:=n
  n=0 => 1
  n=1 => 1
  m:=n
  f4(n-1)+f4(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 53

--S 54 of 188
f5 n == if n=0 or n=1 then 1 else f5(n-1)+f5(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 54

--S 55 of 188
[f1 3,f2 3, f3 3,f4 3,f5 3]
 
   Compiling function f1 with type Integer -> PositiveInteger 
   Compiling function f2 with type Integer -> PositiveInteger 
   Compiling function f3 with type Integer -> PositiveInteger 
   Compiling function f4 with type Integer -> PositiveInteger 
   Compiling function f5 with type Integer -> PositiveInteger 

   (6)  [3,3,3,3,3]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function f1 with type Integer -> PositiveInteger 
--R   Compiling function f2 with type Integer -> PositiveInteger 
--R   Compiling function f3 with type Integer -> PositiveInteger 
--R   Compiling function f4 with type Integer -> PositiveInteger 
--R   Compiling function f5 with type Integer -> PositiveInteger 
--R
--R   (6)  [3,3,3,3,3]
--R                                                   Type: List PositiveInteger
--E 55

)clear all
 

--S 56 of 188
g: GDMP([x,y], INT, DIRPROD(2, NNI)) := x**2 + y
 

         2
   (1)  x  + y
Type: GeneralDistributedMultivariatePolynomial([x,y],Integer,DirectProduct(2,NonNegativeInteger))
--R 
--R
--R         2
--R   (1)  x  + y
--RType: GeneralDistributedMultivariatePolynomial([x,y],Integer,DirectProduct(2,NonNegativeInteger))
--E 56

)clear all
 

--S 57 of 188
i := INT
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 57

--S 58 of 188
i has Algebra(i)
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 58

)clear all
 

--S 59 of 188
f x == if x<0 then return x else x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 59

--S 60 of 188
f 2 -- should be 3
 
   Compiling function f with type PositiveInteger -> PositiveInteger 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 60

--S 61 of 188
f(-2) -- should be -2
 
   Compiling function f with type Integer -> Integer 

   (3)  - 2
                                                                Type: Integer
--R 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (3)  - 2
--R                                                                Type: Integer
--E 61

)clear all
 

--S 62 of 188
m = [[1,2],[2,3]]  -- Should return type EQ POLY SQMATRIX(2, INT)
 

           +1  2+
   (1)  m= |    |
           +2  3+
                            Type: Equation Polynomial SquareMatrix(2,Integer)
--R 
--R
--R           +1  2+
--R   (1)  m= |    |
--R           +2  3+
--R                            Type: Equation Polynomial SquareMatrix(2,Integer)
--E 62

--S 63 of 188
[1, "asd"]   -- Should be of type List Any
 

   (2)  [1,"asd"]
                                                               Type: List Any
--R 
--R
--R   (2)  [1,"asd"]
--R                                                               Type: List Any
--E 63

)set mes test off
 

--S 64 of 188
1+"asd"  -- These should both fail in the same way
 
   There are 12 exposed and 5 unexposed library operations named + 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op +
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named + 
      with argument type(s) 
                               PositiveInteger
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 12 exposed and 5 unexposed library operations named + 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                                )display op +
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named + 
--R      with argument type(s) 
--R                               PositiveInteger
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 64

--S 65 of 188
1/"asd"
 
   There are 14 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                               PositiveInteger
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 14 exposed and 12 unexposed library operations named / 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                                )display op /
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named / 
--R      with argument type(s) 
--R                               PositiveInteger
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 65

)set mes test on
 

)clear all
 

--S 66 of 188
t := MPOLY([x,y], INT)
 

   (1)  MultivariatePolynomial([x,y],Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  MultivariatePolynomial([x,y],Integer)
--R                                                                 Type: Domain
--E 66

--S 67 of 188
)show t
 
 MultivariatePolynomial([x,y],Integer) is a domain constructor.
 Abbreviation for MultivariatePolynomial is MPOLY 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for MPOLY 

------------------------------- Operations --------------------------------

 ?*? : (Fraction Integer,%) -> %       ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?*? : (%,Fraction Integer) -> %
 ?*? : (%,Integer) -> %                ?*? : (%,%) -> %
 ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
 ?-? : (%,%) -> %                      -? : % -> %
 ?/? : (%,Integer) -> %                ?<? : (%,%) -> Boolean
 ?<=? : (%,%) -> Boolean               ?=? : (%,%) -> Boolean
 ?>? : (%,%) -> Boolean                ?>=? : (%,%) -> Boolean
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        associates? : (%,%) -> Boolean
 coefficients : % -> List Integer      coerce : % -> OutputForm
 coerce : Fraction Integer -> %        coerce : Integer -> %
 coerce : % -> %                       content : % -> Integer
 convert : % -> InputForm              convert : % -> Pattern Float
 convert : % -> Pattern Integer        eval : (%,Equation %) -> %
 eval : (%,List Equation %) -> %       eval : (%,List %,List %) -> %
 eval : (%,%,%) -> %                   factor : % -> Factored %
 gcd : List % -> %                     gcd : (%,%) -> %
 ground : % -> Integer                 ground? : % -> Boolean
 hash : % -> SingleInteger             latex : % -> String
 lcm : List % -> %                     lcm : (%,%) -> %
 leadingCoefficient : % -> Integer     leadingMonomial : % -> %
 max : (%,%) -> %                      min : (%,%) -> %
 monomial? : % -> Boolean              monomials : % -> List %
 one? : % -> Boolean                   prime? : % -> Boolean
 primitiveMonomials : % -> List %      primitivePart : % -> %
 recip : % -> Union(%,"failed")        reductum : % -> %
 retract : % -> Fraction Integer       retract : % -> Integer
 sample : () -> %                      squareFree : % -> Factored %
 squareFreePart : % -> %               unit? : % -> Boolean
 unitCanonical : % -> %                zero? : % -> Boolean
 ?~=? : (%,%) -> Boolean              
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,NonNegativeInteger) -> %
 D : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 D : (%,List OrderedVariableList [x,y]) -> %
 D : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 D : (%,OrderedVariableList [x,y]) -> %
 ?^? : (%,NonNegativeInteger) -> %
 binomThmExpt : (%,%,NonNegativeInteger) -> %
 characteristic : () -> NonNegativeInteger
 charthRoot : % -> Union(%,"failed")
 coefficient : (%,IndexedExponents OrderedVariableList [x,y]) -> Integer
 coefficient : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 coefficient : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 coerce : OrderedVariableList [x,y] -> %
 conditionP : Matrix % -> Union(Vector %,"failed")
 content : (%,OrderedVariableList [x,y]) -> %
 degree : % -> IndexedExponents OrderedVariableList [x,y]
 degree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
 degree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
 differentiate : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 differentiate : (%,List OrderedVariableList [x,y]) -> %
 differentiate : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 differentiate : (%,OrderedVariableList [x,y]) -> %
 discriminant : (%,OrderedVariableList [x,y]) -> %
 eval : (%,List OrderedVariableList [x,y],List Integer) -> %
 eval : (%,List OrderedVariableList [x,y],List %) -> %
 eval : (%,OrderedVariableList [x,y],Integer) -> %
 eval : (%,OrderedVariableList [x,y],%) -> %
 exquo : (%,Integer) -> Union(%,"failed")
 exquo : (%,%) -> Union(%,"failed")
 factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
 factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
 gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
 isExpt : % -> Union(Record(var: OrderedVariableList [x,y],exponent: NonNegativeInteger),"failed")
 isPlus : % -> Union(List %,"failed")
 isTimes : % -> Union(List %,"failed")
 mainVariable : % -> Union(OrderedVariableList [x,y],"failed")
 map : ((Integer -> Integer),%) -> %
 mapExponents : ((IndexedExponents OrderedVariableList [x,y] -> IndexedExponents OrderedVariableList [x,y]),%) -> %
 minimumDegree : % -> IndexedExponents OrderedVariableList [x,y]
 minimumDegree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
 minimumDegree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
 monicDivide : (%,%,OrderedVariableList [x,y]) -> Record(quotient: %,remainder: %)
 monomial : (Integer,IndexedExponents OrderedVariableList [x,y]) -> %
 monomial : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
 monomial : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
 multivariate : (SparseUnivariatePolynomial Integer,OrderedVariableList [x,y]) -> %
 multivariate : (SparseUnivariatePolynomial %,OrderedVariableList [x,y]) -> %
 numberOfMonomials : % -> NonNegativeInteger
 patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
 patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
 pomopo! : (%,Integer,IndexedExponents OrderedVariableList [x,y],%) -> %
 primitivePart : (%,OrderedVariableList [x,y]) -> %
 reducedSystem : Matrix % -> Matrix Integer
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer)
 resultant : (%,%,OrderedVariableList [x,y]) -> %
 retract : % -> OrderedVariableList [x,y]
 retractIfCan : % -> Union(Fraction Integer,"failed")
 retractIfCan : % -> Union(Integer,"failed")
 retractIfCan : % -> Union(OrderedVariableList [x,y],"failed")
 solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed")
 squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
 subtractIfCan : (%,%) -> Union(%,"failed")
 totalDegree : (%,List OrderedVariableList [x,y]) -> NonNegativeInteger
 totalDegree : % -> NonNegativeInteger
 unitNormal : % -> Record(unit: %,canonical: %,associate: %)
 univariate : % -> SparseUnivariatePolynomial Integer
 univariate : (%,OrderedVariableList [x,y]) -> SparseUnivariatePolynomial %
 variables : % -> List OrderedVariableList [x,y]


--R 
--R MultivariatePolynomial([x,y],Integer) is a domain constructor.
--R Abbreviation for MultivariatePolynomial is MPOLY 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for MPOLY 
--R
--R------------------------------- Operations --------------------------------
--R
--R ?*? : (Fraction Integer,%) -> %       ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> %        ?*? : (%,Fraction Integer) -> %
--R ?*? : (%,Integer) -> %                ?*? : (%,%) -> %
--R ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
--R ?-? : (%,%) -> %                      -? : % -> %
--R ?/? : (%,Integer) -> %                ?<? : (%,%) -> Boolean
--R ?<=? : (%,%) -> Boolean               ?=? : (%,%) -> Boolean
--R ?>? : (%,%) -> Boolean                ?>=? : (%,%) -> Boolean
--R 1 : () -> %                           0 : () -> %
--R ?^? : (%,PositiveInteger) -> %        associates? : (%,%) -> Boolean
--R coefficients : % -> List Integer      coerce : % -> OutputForm
--R coerce : Fraction Integer -> %        coerce : Integer -> %
--R coerce : % -> %                       content : % -> Integer
--R convert : % -> InputForm              convert : % -> Pattern Float
--R convert : % -> Pattern Integer        eval : (%,Equation %) -> %
--R eval : (%,List Equation %) -> %       eval : (%,List %,List %) -> %
--R eval : (%,%,%) -> %                   factor : % -> Factored %
--R gcd : List % -> %                     gcd : (%,%) -> %
--R ground : % -> Integer                 ground? : % -> Boolean
--R hash : % -> SingleInteger             latex : % -> String
--R lcm : List % -> %                     lcm : (%,%) -> %
--R leadingCoefficient : % -> Integer     leadingMonomial : % -> %
--R max : (%,%) -> %                      min : (%,%) -> %
--R monomial? : % -> Boolean              monomials : % -> List %
--R one? : % -> Boolean                   prime? : % -> Boolean
--R primitiveMonomials : % -> List %      primitivePart : % -> %
--R recip : % -> Union(%,"failed")        reductum : % -> %
--R retract : % -> Fraction Integer       retract : % -> Integer
--R sample : () -> %                      squareFree : % -> Factored %
--R squareFreePart : % -> %               unit? : % -> Boolean
--R unitCanonical : % -> %                zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean              
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R D : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R D : (%,List OrderedVariableList [x,y]) -> %
--R D : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R D : (%,OrderedVariableList [x,y]) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R binomThmExpt : (%,%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed")
--R coefficient : (%,IndexedExponents OrderedVariableList [x,y]) -> Integer
--R coefficient : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R coefficient : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R coerce : OrderedVariableList [x,y] -> %
--R conditionP : Matrix % -> Union(Vector %,"failed")
--R content : (%,OrderedVariableList [x,y]) -> %
--R degree : % -> IndexedExponents OrderedVariableList [x,y]
--R degree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
--R degree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
--R differentiate : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R differentiate : (%,List OrderedVariableList [x,y]) -> %
--R differentiate : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R differentiate : (%,OrderedVariableList [x,y]) -> %
--R discriminant : (%,OrderedVariableList [x,y]) -> %
--R eval : (%,List OrderedVariableList [x,y],List Integer) -> %
--R eval : (%,List OrderedVariableList [x,y],List %) -> %
--R eval : (%,OrderedVariableList [x,y],Integer) -> %
--R eval : (%,OrderedVariableList [x,y],%) -> %
--R exquo : (%,Integer) -> Union(%,"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
--R isExpt : % -> Union(Record(var: OrderedVariableList [x,y],exponent: NonNegativeInteger),"failed")
--R isPlus : % -> Union(List %,"failed")
--R isTimes : % -> Union(List %,"failed")
--R mainVariable : % -> Union(OrderedVariableList [x,y],"failed")
--R map : ((Integer -> Integer),%) -> %
--R mapExponents : ((IndexedExponents OrderedVariableList [x,y] -> IndexedExponents OrderedVariableList [x,y]),%) -> %
--R minimumDegree : % -> IndexedExponents OrderedVariableList [x,y]
--R minimumDegree : (%,List OrderedVariableList [x,y]) -> List NonNegativeInteger
--R minimumDegree : (%,OrderedVariableList [x,y]) -> NonNegativeInteger
--R monicDivide : (%,%,OrderedVariableList [x,y]) -> Record(quotient: %,remainder: %)
--R monomial : (Integer,IndexedExponents OrderedVariableList [x,y]) -> %
--R monomial : (%,List OrderedVariableList [x,y],List NonNegativeInteger) -> %
--R monomial : (%,OrderedVariableList [x,y],NonNegativeInteger) -> %
--R multivariate : (SparseUnivariatePolynomial Integer,OrderedVariableList [x,y]) -> %
--R multivariate : (SparseUnivariatePolynomial %,OrderedVariableList [x,y]) -> %
--R numberOfMonomials : % -> NonNegativeInteger
--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
--R pomopo! : (%,Integer,IndexedExponents OrderedVariableList [x,y],%) -> %
--R primitivePart : (%,OrderedVariableList [x,y]) -> %
--R reducedSystem : Matrix % -> Matrix Integer
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer)
--R resultant : (%,%,OrderedVariableList [x,y]) -> %
--R retract : % -> OrderedVariableList [x,y]
--R retractIfCan : % -> Union(Fraction Integer,"failed")
--R retractIfCan : % -> Union(Integer,"failed")
--R retractIfCan : % -> Union(OrderedVariableList [x,y],"failed")
--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed")
--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R totalDegree : (%,List OrderedVariableList [x,y]) -> NonNegativeInteger
--R totalDegree : % -> NonNegativeInteger
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R univariate : % -> SparseUnivariatePolynomial Integer
--R univariate : (%,OrderedVariableList [x,y]) -> SparseUnivariatePolynomial %
--R variables : % -> List OrderedVariableList [x,y]
--R
--R
--E 67

)clear all
 

--S 68 of 188
)set fun cache all
 
   In general, interpreter functions will cache all values.
--R 
--R   In general, interpreter functions will cache all values.
--E 68

--S 69 of 188
u == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 69

--S 70 of 188
u
 
   Compiling body of rule u to compute value of type PositiveInteger 
   u will cache all previously computed values.

   (2)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule u to compute value of type PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 70

--S 71 of 188
)set fun cache 0
 
 In general, functions will cache no returned values.
--R 
--R In general, functions will cache no returned values.
--E 71

)clear all
 

--S 72 of 188
factorp: (UP(x,INT),PositiveInteger,PositiveInteger) -> List(UP(x,INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 72

--S 73 of 188
factorp(poly,p,e) ==
   ppoly:UP(x,PF p):=poly
   pl := [rec.factor for rec in factors factor ppoly]
   facl:=pl::List(UP(x,INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 73

--S 74 of 188
factorp(x**2+x+5,7,1)
 
   Cannot compile the declaration for ppoly because its (possible 
      partial) type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   Compiling function factorp with type (UnivariatePolynomial(x,Integer
      ),PositiveInteger,PositiveInteger) -> List UnivariatePolynomial(x
      ,Integer) 

   (3)  [x + 2,x + 6]
                                   Type: List UnivariatePolynomial(x,Integer)
--R 
--R   Cannot compile the declaration for ppoly because its (possible 
--R      partial) type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function factorp with type (UnivariatePolynomial(x,Integer
--R      ),PositiveInteger,PositiveInteger) -> List UnivariatePolynomial(x
--R      ,Integer) 
--R
--R   (3)  [x + 2,x + 6]
--R                                   Type: List UnivariatePolynomial(x,Integer)
--E 74

)clear all
 

--S 75 of 188
b:= 1..10
 

   (1)  1..10
                                                Type: Segment PositiveInteger
--R 
--R
--R   (1)  1..10
--R                                                Type: Segment PositiveInteger
--E 75

--S 76 of 188
for i in b by 2 repeat output i
 
   1
   3
   5
   7
   9
                                                                   Type: Void
--R 
--R   1
--R   3
--R   5
--R   7
--R   9
--R                                                                   Type: Void
--E 76

)clear all
 

--S 77 of 188
macro RN == FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 77

--S 78 of 188
a51:=x+y+z+t+u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 78

--S 79 of 188
a52:=x*y+y*z+z*t+x*u+t*u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 79

--S 80 of 188
a53:=x*y*z+y*z*t+x*y*u+x*t*u+z*t*u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 80

--S 81 of 188
a54:=x*y*z*t+x*y*z*u+x*y*t*u+x*z*t*u+y*z*t*u;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 81

--S 82 of 188
a55:=x*y*z*t*u-1;
 

                                                     Type: Polynomial Integer
--R 
--R
--R                                                     Type: Polynomial Integer
--E 82

--S 83 of 188
arnborg5: List HDMP([x,y,z,t,u],RN):=[a51,a52,a53,a54,a55];
 

Type: List HomogeneousDistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--R 
--R
--RType: List HomogeneousDistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--E 83

--S 84 of 188
arnborg5l: List DMP([x,y,z,t,u],RN):=[a51,a52,a53,a54,a55];
 

   Type: List DistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--R 
--R
--R   Type: List DistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer)
--E 84

)clear all
 

--S 85 of 188
factorp(poly,p,e) ==
   [rec.factor for rec in factors factor (poly::UP(x, PF p))]::List UP(x, INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 85

--S 86 of 188
factorp(x**2+x+5,7,1)
 
   Cannot compile conversion for types involving local variables. In 
      particular, could not compile the expression involving :: UP(x,PF
      #2) 
   AXIOM will attempt to step through and interpret the code.

   (2)  [x + 2,x + 6]
                                   Type: List UnivariatePolynomial(x,Integer)
--R 
--R   Cannot compile conversion for types involving local variables. In 
--R      particular, could not compile the expression involving :: UP(x,PF
--R      #2) 
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (2)  [x + 2,x + 6]
--R                                   Type: List UnivariatePolynomial(x,Integer)
--E 86

)clear all
 

--S 87 of 188
f (x) ==
  y: PF x := 1
  x = 3 => return x
  x = 4 => return(-x)
  (x+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 87

--S 88 of 188
f 3
 
   Cannot compile the declaration for y because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.

   (2)  3
                                                        Type: PositiveInteger
--R 
--R   Cannot compile the declaration for y because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 88

)clear all
 

--S 89 of 188
f (x) ==
  x = 3 => return x
  x = 4 => return(-x)
  return (x+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 89

--S 90 of 188
f 3
 
   Compiling function f with type PositiveInteger -> Integer 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> Integer 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 90

)clear all
 

--S 91 of 188
s:SQMATRIX(2, INT) := matrix [[1,2],[2,3]]
 

        +1  2+
   (1)  |    |
        +2  3+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (1)  |    |
--R        +2  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 91

--S 92 of 188
s::SQMATRIX(2, FRAC INT)
 

        +1  2+
   (2)  |    |
        +2  3+
                                       Type: SquareMatrix(2,Fraction Integer)
--R 
--R
--R        +1  2+
--R   (2)  |    |
--R        +2  3+
--R                                       Type: SquareMatrix(2,Fraction Integer)
--E 92

)clear all
 

--S 93 of 188
Mat := SquareMatrix(2, Polynomial Integer)
 

   (1)  SquareMatrix(2,Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  SquareMatrix(2,Polynomial Integer)
--R                                                                 Type: Domain
--E 93

--S 94 of 188
s:Mat := matrix [[ 2*x + 1, x], [x, 1]]
 

        +2x + 1  x+
   (2)  |         |
        +  x     1+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +2x + 1  x+
--R   (2)  |         |
--R        +  x     1+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 94

--S 95 of 188
s**3
 

        +   3      2             3     2     +
        |12x  + 15x  + 6x + 1  5x  + 6x  + 3x|
   (3)  |                                    |
        |     3     2            3     2     |
        +   5x  + 6x  + 3x     2x  + 3x  + 1 +
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +   3      2             3     2     +
--R        |12x  + 15x  + 6x + 1  5x  + 6x  + 3x|
--R   (3)  |                                    |
--R        |     3     2            3     2     |
--R        +   5x  + 6x  + 3x     2x  + 3x  + 1 +
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 95

--S 96 of 188
%::Polynomial(?)
 

        +12  5+ 3   +15  6+ 2   +6  3+    +1  0+
   (4)  |     |x  + |     |x  + |    |x + |    |
        +5   2+     +6   3+     +3  0+    +0  1+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R 
--R
--R        +12  5+ 3   +15  6+ 2   +6  3+    +1  0+
--R   (4)  |     |x  + |     |x  + |    |x + |    |
--R        +5   2+     +6   3+     +3  0+    +0  1+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 96

)clear all
 

--S 97 of 188
-2**2  -- Should return -4
 

   (1)  - 4
                                                                Type: Integer
--R 
--R
--R   (1)  - 4
--R                                                                Type: Integer
--E 97

)clear all
 

--S 98 of 188
f: DMP([x,y], INT) := x**2-y**2
 

         2    2
   (1)  x  - y
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R         2    2
--R   (1)  x  - y
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 98

--S 99 of 188
coefficient(f, degree f)
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 99

)clear all
 

--S 100 of 188
x+1::EXPR INT
 

   (1)  x + 1
                                                     Type: Expression Integer
--R 
--R
--R   (1)  x + 1
--R                                                     Type: Expression Integer
--E 100

--S 101 of 188
%::POLY INT
 

   (2)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  x + 1
--R                                                     Type: Polynomial Integer
--E 101

)clear all
 

--S 102 of 188
solve([[1,2],[2,3]],[-2,3])
 

   (1)  [particular= [12,- 7],basis= [[0,0]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R 
--R
--R   (1)  [particular= [12,- 7],basis= [[0,0]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 102

)clear all
 

--S 103 of 188
eval(m**2, m=[[1,2],[2,3]])
 

        +5  8 +
   (1)  |     |
        +8  13+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R 
--R
--R        +5  8 +
--R   (1)  |     |
--R        +8  13+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 103

)clear all
 

)set mes test off
 

--S 104 of 188
r: Ring
 
 
   Ring is a category, not a domain, and declarations require domains.
--R 
--R 
--R   Ring is a category, not a domain, and declarations require domains.
--E 104

--S 105 of 188
w: RF INT
 
 
   RationalFunction Integer is a package, not a domain, and 
      declarations require domains.
--R 
--R 
--R   RationalFunction Integer is a package, not a domain, and 
--R      declarations require domains.
--E 105

)set mes test on
 

)clear all
 

--S 106 of 188
r:Record(a: INT) := [1]
 

   (1)  [a= 1]
                                                     Type: Record(a: Integer)
--R 
--R
--R   (1)  [a= 1]
--R                                                     Type: Record(a: Integer)
--E 106

)clear all
 

--S 107 of 188
p: POLY FLOAT := (x-1)**30
 

   (1)
      30         29          28           27            26             25
     x   - 30.0 x   + 435.0 x   - 4060.0 x   + 27405.0 x   - 142506.0 x
   + 
               24              23              22               21
     593775.0 x   - 2035800.0 x   + 5852925.0 x   - 14307150.0 x
   + 
                 20               19               18                 17
     30045015.0 x   - 54627300.0 x   + 86493225.0 x   - 1 19759850.0 x
   + 
                   16                 15                 14                 13
     1 45422675.0 x   - 1 55117520.0 x   + 1 45422675.0 x   - 1 19759850.0 x
   + 
                 12               11               10               9
     86493225.0 x   - 54627300.0 x   + 30045015.0 x   - 14307150.0 x
   + 
                8              7             6             5            4
     5852925.0 x  - 2035800.0 x  + 593775.0 x  - 142506.0 x  + 27405.0 x
   + 
               3          2
     - 4060.0 x  + 435.0 x  - 30.0 x + 1.0
                                                       Type: Polynomial Float
--R 
--R
--R   (1)
--R      30         29          28           27            26             25
--R     x   - 30.0 x   + 435.0 x   - 4060.0 x   + 27405.0 x   - 142506.0 x
--R   + 
--R               24              23              22               21
--R     593775.0 x   - 2035800.0 x   + 5852925.0 x   - 14307150.0 x
--R   + 
--R                 20               19               18                 17
--R     30045015.0 x   - 54627300.0 x   + 86493225.0 x   - 1 19759850.0 x
--R   + 
--R                   16                 15                 14                 13
--R     1 45422675.0 x   - 1 55117520.0 x   + 1 45422675.0 x   - 1 19759850.0 x
--R   + 
--R                 12               11               10               9
--R     86493225.0 x   - 54627300.0 x   + 30045015.0 x   - 14307150.0 x
--R   + 
--R                8              7             6             5            4
--R     5852925.0 x  - 2035800.0 x  + 593775.0 x  - 142506.0 x  + 27405.0 x
--R   + 
--R               3          2
--R     - 4060.0 x  + 435.0 x  - 30.0 x + 1.0
--R                                                       Type: Polynomial Float
--E 107

--draw(p, x=-1..1)

)clear all
 

--S 108 of 188
sayBranch x == _
 if x case INT then output "Integer Branch" _
 else if x case STRING then output "String Branch" _
 else if x case FLOAT then output "Float Branch" _
 else output "don't know"
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 108

--S 109 of 188
x:Union(INT,STRING,FLOAT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 109

--S 110 of 188
x:=3
 

   (3)  3
                                                     Type: Union(Integer,...)
--R 
--R
--R   (3)  3
--R                                                     Type: Union(Integer,...)
--E 110

--S 111 of 188
sayBranch(x)
 
 
Daly Bug
   case is only used for Unions and the object on the left-hand side 
      does not belong to a union.
--R 
--R 
--RDaly Bug
--R   case is only used for Unions and the object on the left-hand side 
--R      does not belong to a union.
--E 111

)clear all
 

--S 112 of 188
RFI := FRAC POLY INT
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 112

--S 113 of 188
g:DMP([x,y], RFI) := a**2*x**2/b**2 - c**2*y**2/d**2
 

         2       2
        a   2   c   2
   (2)  -- x  - -- y
         2       2
        b       d
   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R         2       2
--R        a   2   c   2
--R   (2)  -- x  - -- y
--R         2       2
--R        b       d
--R   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 113

--S 114 of 188
factor g
 

         2
        a       b c        b c
   (3)  -- (x - --- y)(x + --- y)
         2      a d        a d
        b
Type: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R         2
--R        a       b c        b c
--R   (3)  -- (x - --- y)(x + --- y)
--R         2      a d        a d
--R        b
--RType: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 114

)clear all
 

--S 115 of 188
f(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+v
 
   Function declaration f : (DoubleFloat,DoubleFloat) -> DoubleFloat 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : (DoubleFloat,DoubleFloat) -> DoubleFloat 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 115

--S 116 of 188
g(u:DoubleFloat, v:DoubleFloat):DoubleFloat == sin(u+v)
 
   Function declaration g : (DoubleFloat,DoubleFloat) -> DoubleFloat 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration g : (DoubleFloat,DoubleFloat) -> DoubleFloat 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 116

--S 117 of 188
h(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+cos(v)
 
   Function declaration h : (DoubleFloat,DoubleFloat) -> DoubleFloat 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration h : (DoubleFloat,DoubleFloat) -> DoubleFloat 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 117

--draw(surface(f,g,h), 0..4, 0..2*%pi)

)clear all
 

)set mes test off
 

--S 118 of 188
(1+1)$Ring
 
 
   The right-hand side of the $ operator must be a package or domain 
      name, but Ring is a category.
--R 
--R 
--R   The right-hand side of the $ operator must be a package or domain 
--R      name, but Ring is a category.
--E 118

)set mes test on
 

)clear all
 

--S 119 of 188
s := series(sin(a*x), x=0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 119

--S 120 of 188
s - a*x
 

   (2)
        3        5        7          9            11              13
       a   3    a   5    a    7     a     9      a      11       a       13
     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
        6      120      5040      362880      39916800       6227020800
   + 
        14
     O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R        3        5        7          9            11              13
--R       a   3    a   5    a    7     a     9      a      11       a       13
--R     - -- x  + --- x  - ---- x  + ------ x  - -------- x   + ---------- x
--R        6      120      5040      362880      39916800       6227020800
--R   + 
--R        14
--R     O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 120

--S 121 of 188
s - sin(a*x)
 

           21
   (3)  O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R           21
--R   (3)  O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 121

)clear all
 

--S 122 of 188
sin %i
 

   (1)  sin(%i)
                                             Type: Expression Complex Integer
--R 
--R
--R   (1)  sin(%i)
--R                                             Type: Expression Complex Integer
--E 122

--S 123 of 188
sin sqrt 2
 

             +-+
   (2)  sin(\|2 )
                                                     Type: Expression Integer
--R 
--R
--R             +-+
--R   (2)  sin(\|2 )
--R                                                     Type: Expression Integer
--E 123

--S 124 of 188
%i*sqrt(2)
 

           +-+
   (3)  %i\|2
                                             Type: Expression Complex Integer
--R 
--R
--R           +-+
--R   (3)  %i\|2
--R                                             Type: Expression Complex Integer
--E 124

--S 125 of 188
sin(%i*sqrt 2)
 

               +-+
   (4)  sin(%i\|2 )
                                             Type: Expression Complex Integer
--R 
--R
--R               +-+
--R   (4)  sin(%i\|2 )
--R                                             Type: Expression Complex Integer
--E 125

--S 126 of 188
%i * sin(x)
 

   (5)  %i sin(x)
                                             Type: Expression Complex Integer
--R 
--R
--R   (5)  %i sin(x)
--R                                             Type: Expression Complex Integer
--E 126

--S 127 of 188
sin(x/sqrt(2))
 

              +-+
            x\|2
   (6)  sin(-----)
              2
                                                     Type: Expression Integer
--R 
--R
--R              +-+
--R            x\|2
--R   (6)  sin(-----)
--R              2
--R                                                     Type: Expression Integer
--E 127

)clear all
 

)set msg test off
 
   No option begins with msg .

--S 128 of 188
primaryDecomp xx
 
   There are 1 exposed and 0 unexposed library operations named 
      primaryDecomp having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                          )display op primaryDecomp
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      primaryDecomp with argument type(s) 
                                 Variable xx
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      primaryDecomp having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                          )display op primaryDecomp
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      primaryDecomp with argument type(s) 
--R                                 Variable xx
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 128

)set msg test on
 
   No option begins with msg .

)clear all
 

--S 129 of 188
f l ==
  reduce((x,y) +-> l.1 + x + y, l)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 129

--S 130 of 188
f [10,2,53]
 
   Compiling function f with type List PositiveInteger -> 
      PositiveInteger 

   (2)  85
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type List PositiveInteger -> 
--R      PositiveInteger 
--R
--R   (2)  85
--R                                                        Type: PositiveInteger
--E 130

--S 131 of 188
g l ==
  (x:INT):INT +-> l.x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 131

--S 132 of 188
w := g [23,1,341,12] ;
 
   Compiling function g with type List PositiveInteger -> (Integer -> 
      Integer) 

                                                   Type: (Integer -> Integer)
--R 
--R   Compiling function g with type List PositiveInteger -> (Integer -> 
--R      Integer) 
--R
--R                                                   Type: (Integer -> Integer)
--E 132

--S 133 of 188
w(1) + w(3)
 

   (5)  364
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  364
--R                                                        Type: PositiveInteger
--E 133

--S 134 of 188
w(-1) 
 
 
Daly Bug
   >> Error detected within library code:
   index out of range

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   index out of range
--R
--R   Continuing to read the file...
--R
--E 134

)clear all
 

--S 135 of 188
a := 2/3
 

        2
   (1)  -
        3
                                                       Type: Fraction Integer
--R 
--R
--R        2
--R   (1)  -
--R        3
--R                                                       Type: Fraction Integer
--E 135

)set mes test off
 

--S 136 of 188
a::PF 3
 
 
   Division by zero on conversion to GaloisField.
--R 
--R 
--R   Division by zero on conversion to GaloisField.
--E 136

)set mes test on
 

--S 137 of 188
b := x+1
 

   (2)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)  x + 1
--R                                                     Type: Polynomial Integer
--E 137

--S 138 of 188
b:: EXPR FLOAT
 

   (3)  x + 1.0
                                                       Type: Expression Float
--R 
--R
--R   (3)  x + 1.0
--R                                                       Type: Expression Float
--E 138

)clear all
 
 
--S 139 of 188
symbol(s:Symbol,i:Integer):Symbol ==
  st0:String:= convert(i)
  st0:= concat(string(s),st0)
  st0::Symbol
 
   Function declaration symbol : (Symbol,Integer) -> Symbol has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration symbol : (Symbol,Integer) -> Symbol has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 139

--S 140 of 188
f(a,b) == symbol(a,b)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 140

--S 141 of 188
f('abc,3)
 
   Compiling function symbol with type (Symbol,Integer) -> Symbol 
   Compiling function f with type (Variable abc,PositiveInteger) -> 
      Symbol 

   (3)  abc3
                                                                 Type: Symbol
--R 
--R   Compiling function symbol with type (Symbol,Integer) -> Symbol 
--R   Compiling function f with type (Variable abc,PositiveInteger) -> 
--R      Symbol 
--R
--R   (3)  abc3
--R                                                                 Type: Symbol
--E 141

)clear all
 

--S 142 of 188
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 412

--S 143 of 188
y := f(x)
 

   (2)  f(x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  f(x)
--R                                                     Type: Expression Integer
--E 143

--S 144 of 188
foo(u) == sin(u)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 144

--S 145 of 188
eval(y, 'f, foo)
 
   There are 2 exposed and 6 unexposed library operations named sin 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op sin
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Compiling function foo with type Expression Integer -> Expression 
      Integer 

   (4)  sin(x)
                                                     Type: Expression Integer
--R 
--R   There are 2 exposed and 6 unexposed library operations named sin 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op sin
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Compiling function foo with type Expression Integer -> Expression 
--R      Integer 
--R
--R   (4)  sin(x)
--R                                                     Type: Expression Integer
--E 145

)clear all
 

--S 146 of 188
init()$(PF 3)
 

   (1)  0
                                                           Type: PrimeField 3
--R 
--R
--R   (1)  0
--R                                                           Type: PrimeField 3
--E 146

)clear all
 

--draw((x,y) +-> x**2 - y**2, -1..1, -1..1)

)clear all
 

--S 147 of 188
dmp := DMP([u1,u2,u3],Fraction INT)
 

   (1)  DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
--R                                                                 Type: Domain
--E 147

--S 148 of 188
p : dmp := 2*u1**4*u2*u3
 

           4
   (2)  2u1 u2 u3
         Type: DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
--R 
--R
--R           4
--R   (2)  2u1 u2 u3
--R         Type: DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer)
--E 148

--S 149 of 188
e1 := degree p
 

   (3)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (3)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 149

--S 150 of 188
e2 : DirectProduct(3,NonNegativeInteger) := e1
 

   (4)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (4)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 150

--S 151 of 188
sup(e1,e1)
 

   (5)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (5)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 151


--S 152 of 188
sup(e1,e1)$DirectProduct(3,NonNegativeInteger)
 

   (6)  [4,1,1]
                                    Type: DirectProduct(3,NonNegativeInteger)
--R 
--R
--R   (6)  [4,1,1]
--R                                    Type: DirectProduct(3,NonNegativeInteger)
--E 152

)clear all
 

--S 153 of 188
sum:=0
 

   (1)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (1)  0
--R                                                     Type: NonNegativeInteger
--E 153

--S 154 of 188
m:=matrix [[1,2],[3,4]]
 

        +1  2+
   (2)  |    |
        +3  4+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2+
--R   (2)  |    |
--R        +3  4+
--R                                                         Type: Matrix Integer
--E 154

--S 155 of 188
lastcol:=ncols(m)
 

   (3)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  2
--R                                                        Type: PositiveInteger
--E 155

--S 156 of 188
for r in 1..nrows(m) repeat
 -- interpreter having a value for "row" would cause it to hide
 -- the system function
 Row:=row(m,r)
 for c in 1..lastcol repeat
  sum:=sum+Row.c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 156

--S 157 of 188
sum
 

   (5)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  10
--R                                                        Type: PositiveInteger
--E 157

)clear all
 

--S 158 of 188
splitPoly(f,var) ==
   map(g +-> multivariate(g,var),monomials univariate(f,var))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 158

--S 159 of 188
g:=sin(x)+cos(x)
 

   (2)  sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 159

--S 160 of 188
k:=kernels(g).1
 

   (3)  sin(x)
                                              Type: Kernel Expression Integer
--R 
--R
--R   (3)  sin(x)
--R                                              Type: Kernel Expression Integer
--E 160

)set mes test off
 

--S 161 of 188
splitPoly([g],k) -- this is an incorrect call
 
   There are 4 exposed and 1 unexposed library operations named 
      univariate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op univariate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      univariate with argument type(s) 
                           List Expression Integer
                          Kernel Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   There are 4 exposed and 1 unexposed library operations named 
      univariate having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op univariate
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named 
      univariate with argument type(s) 
                           List Expression Integer
                          Kernel Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 4 exposed and 1 unexposed library operations named 
--R      univariate having 2 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                           )display op univariate
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      univariate with argument type(s) 
--R                           List Expression Integer
--R                          Kernel Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   There are 4 exposed and 1 unexposed library operations named 
--R      univariate having 2 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                           )display op univariate
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named 
--R      univariate with argument type(s) 
--R                           List Expression Integer
--R                          Kernel Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 161

)set mes test on
 

--S 162 of 188
splitPoly(numer g,k) -- this is a correct call
 
   Compiling function splitPoly with type (SparseMultivariatePolynomial
      (Integer,Kernel Expression Integer),Kernel Expression Integer)
       -> List SparseMultivariatePolynomial(Integer,Kernel Expression 
      Integer) 

   (4)  [sin(x),cos(x)]
   Type: List SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R   Compiling function splitPoly with type (SparseMultivariatePolynomial
--R      (Integer,Kernel Expression Integer),Kernel Expression Integer)
--R       -> List SparseMultivariatePolynomial(Integer,Kernel Expression 
--R      Integer) 
--R
--R   (4)  [sin(x),cos(x)]
--R   Type: List SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 162

)clear all
 

--S 163 of 188
f x ==
  g := (y:DoubleFloat):DoubleFloat +-> y+x
  output(y+1)
  g(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 163

--S 164 of 188
f 3
 
   Compiling function f with type PositiveInteger -> DoubleFloat 
   y + 1

   (2)  6.
                                                            Type: DoubleFloat
--R 
--R   Compiling function f with type PositiveInteger -> DoubleFloat 
--R   y + 1
--R
--R   (2)  6.
--R                                                            Type: DoubleFloat
--E 164

)clear all
 

--S 165 of 188
f x == 1/factorial(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 165

--S 166 of 188
series(f, x=0)
 
   Compiling function f with type Integer -> Expression Integer 

   (2)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R   Compiling function f with type Integer -> Expression Integer 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 166

)clear all
 

--S 167 of 188
node_a == i1+i2+i3-i5+i6=0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 167

--S 168 of 188
node_b == -i2-i3+i4-i6=0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 168

--S 169 of 188
i1 == va/r1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 169

--S 170 of 188
i2 == (va-vb)/r2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 170

--S 171 of 188
i3 == (va-vb)/r3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 171

--S 172 of 188
i4 == vb/r4
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 172

--S 173 of 188
node_a
 
   Compiling body of rule i1 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule i2 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule i3 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule nodea to compute value of type Equation 
      Fraction Polynomial Integer 

        (- r1 r3 - r1 r2)vb + ((r2 + r1)r3 + r1 r2)va + (i6 - i5)r1 r2 r3
   (7)  -----------------------------------------------------------------= 0
                                     r1 r2 r3
                                   Type: Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule i1 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule i2 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule i3 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule nodea to compute value of type Equation 
--R      Fraction Polynomial Integer 
--R
--R        (- r1 r3 - r1 r2)vb + ((r2 + r1)r3 + r1 r2)va + (i6 - i5)r1 r2 r3
--R   (7)  -----------------------------------------------------------------= 0
--R                                     r1 r2 r3
--R                                   Type: Equation Fraction Polynomial Integer
--E 173

--S 174 of 188
node_b
 
   Compiling body of rule i4 to compute value of type Fraction 
      Polynomial Integer 
   Compiling body of rule nodeb to compute value of type Equation 
      Fraction Polynomial Integer 

        ((r3 + r2)r4 + r2 r3)vb + (- r3 - r2)r4 va - i6 r2 r3 r4
   (8)  --------------------------------------------------------= 0
                                r2 r3 r4
                                   Type: Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule i4 to compute value of type Fraction 
--R      Polynomial Integer 
--R   Compiling body of rule nodeb to compute value of type Equation 
--R      Fraction Polynomial Integer 
--R
--R        ((r3 + r2)r4 + r2 r3)vb + (- r3 - r2)r4 va - i6 r2 r3 r4
--R   (8)  --------------------------------------------------------= 0
--R                                r2 r3 r4
--R                                   Type: Equation Fraction Polynomial Integer
--E 174

--S 175 of 188
ans == solve([node_a,node_b],[va,vb]) -- (*)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 175

--S 176 of 188
x1 == rhs(ans.1.1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 176

--S 177 of 188
x2 == rhs(ans.1.2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 177

--S 178 of 188
x1       -- (**)
 
   Compiling body of rule ans to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling body of rule x1 to compute value of type Fraction 
      Polynomial Integer 

         (i5 r1 r3 + i5 r1 r2)r4 + (- i6 + i5)r1 r2 r3
   (12)  ---------------------------------------------
               (r3 + r2)r4 + (r2 + r1)r3 + r1 r2
                                            Type: Fraction Polynomial Integer
--R 
--R   Compiling body of rule ans to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R   Compiling body of rule x1 to compute value of type Fraction 
--R      Polynomial Integer 
--R
--R         (i5 r1 r3 + i5 r1 r2)r4 + (- i6 + i5)r1 r2 r3
--R   (12)  ---------------------------------------------
--R               (r3 + r2)r4 + (r2 + r1)r3 + r1 r2
--R                                            Type: Fraction Polynomial Integer
--E 178

--S 179 of 188
r1 == 2  -- (***)
 
   Compiled code for i1 has been cleared.
   Compiled code for nodea has been cleared.
   Compiled code for ans has been cleared.
   Compiled code for x1 has been cleared.
                                                                   Type: Void
--R 
--R   Compiled code for i1 has been cleared.
--R   Compiled code for nodea has been cleared.
--R   Compiled code for ans has been cleared.
--R   Compiled code for x1 has been cleared.
--R                                                                   Type: Void
--E 179

--S 180 of 188
x1       -- (****)
 
   Compiling body of rule r1 to compute value of type PositiveInteger 
   Compiling body of rule i1 to compute value of type Polynomial 
      Fraction Integer 
   Compiling body of rule nodea to compute value of type Equation 
      Fraction Polynomial Integer 
   Compiling body of rule ans to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling body of rule x1 to compute value of type Fraction 
      Polynomial Integer 

         (2i5 r3 + 2i5 r2)r4 + (- 2i6 + 2i5)r2 r3
   (14)  ----------------------------------------
              (r3 + r2)r4 + (r2 + 2)r3 + 2r2
                                            Type: Fraction Polynomial Integer
--R 
--R   Compiling body of rule r1 to compute value of type PositiveInteger 
--R   Compiling body of rule i1 to compute value of type Polynomial 
--R      Fraction Integer 
--R   Compiling body of rule nodea to compute value of type Equation 
--R      Fraction Polynomial Integer 
--R   Compiling body of rule ans to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R   Compiling body of rule x1 to compute value of type Fraction 
--R      Polynomial Integer 
--R
--R         (2i5 r3 + 2i5 r2)r4 + (- 2i6 + 2i5)r2 r3
--R   (14)  ----------------------------------------
--R              (r3 + r2)r4 + (r2 + 2)r3 + 2r2
--R                                            Type: Fraction Polynomial Integer
--E 180

)clear all
 

--S 181 of 188
"asd" "sdfsdf" "dfgdfg"
 

   (1)  "asdsdfsdfdfgdfg"
                                                                 Type: String
--R 
--R
--R   (1)  "asdsdfsdfdfgdfg"
--R                                                                 Type: String
--E 181

)clear all
 

--S 182 of 188
s := 3.4
 

   (1)  3.4
                                                                  Type: Float
--R 
--R
--R   (1)  3.4
--R                                                                  Type: Float
--E 182

--S 183 of 188
while s > 1.0 repeat (s := 1/2; print s)
 
   1
   -
   2
                                                                   Type: Void
--R 
--R   1
--R   -
--R   2
--R                                                                   Type: Void
--E 183

--S 184 of 188
s
 

        1
   (3)  -
        2
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (3)  -
--R        2
--R                                                       Type: Fraction Integer
--E 184

)clear all
 

--S 185 of 188
f x ==
  free s
  s := x
  while s > 1.0 repeat (s := 1/2; print s)
  s
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 185

--S 186 of 188
f(3.4)
 
   Compiling function f with type Float -> Float 
   Compiled code for f has been cleared.
   0.5

   (2)  0.5
                                                                  Type: Float
--R 
--R   Compiling function f with type Float -> Float 
--R   Compiled code for f has been cleared.
--R   0.5
--R
--R   (2)  0.5
--R                                                                  Type: Float
--E 186

)clear all
 

--S 187 of 188
t x ==
  if x = 1 then (1; return [x])
  return [2]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 187

--S 188 of 188
t 1
 
   Compiling function t with type PositiveInteger -> List 
      PositiveInteger 

   (2)  [1]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function t with type PositiveInteger -> List 
--R      PositiveInteger 
--R
--R   (2)  [1]
--R                                                   Type: List PositiveInteger
--E 188
)spool 
 
Starts dribbling to MatrixCategory.output (2010/3/27, 18:46:7).
)set message test on
 
)set message auto off
 
)clear all
 


--S 1 of 59
square? matrix [[j**i for i in 0..4] for j in 1..5]
 

   (1)  true
                                                                Type: Boolean
--R 
--R
--R   (1)  true
--R                                                                Type: Boolean
--E 1

--S 2 of 59
diagonal? matrix [[j**i for i in 0..4] for j in 1..5]
 

   (2)  false
                                                                Type: Boolean
--R 
--R
--R   (2)  false
--R                                                                Type: Boolean
--E 2

--S 3 of 59
symmetric? matrix [[j**i for i in 0..4] for j in 1..5]
 

   (3)  false
                                                                Type: Boolean
--R 
--R
--R   (3)  false
--R                                                                Type: Boolean
--E 3

--S 4 of 59
antisymmetric? matrix [[j**i for i in 0..4] for j in 1..5]
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 59
z:Matrix(INT):=zero(3,3)
 

        +0  0  0+
        |       |
   (5)  |0  0  0|
        |       |
        +0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  0  0+
--R        |       |
--R   (5)  |0  0  0|
--R        |       |
--R        +0  0  0+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 59
matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]]
 

        +1  2  3+
        |       |
        |4  5  6|
   (6)  |       |
        |7  8  9|
        |       |
        +1  1  1+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2  3+
--R        |       |
--R        |4  5  6|
--R   (6)  |       |
--R        |7  8  9|
--R        |       |
--R        +1  1  1+
--R                                                         Type: Matrix Integer
--E 6

--S 7 of 59
z:Matrix(INT):=scalarMatrix(3,5)
 

        +5  0  0+
        |       |
   (7)  |0  5  0|
        |       |
        +0  0  5+
                                                         Type: Matrix Integer
--R 
--R
--R        +5  0  0+
--R        |       |
--R   (7)  |0  5  0|
--R        |       |
--R        +0  0  5+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 59
diagonalMatrix [1,2,3]
 

        +1  0  0+
        |       |
   (8)  |0  2  0|
        |       |
        +0  0  3+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  0  0+
--R        |       |
--R   (8)  |0  2  0|
--R        |       |
--R        +0  0  3+
--R                                                         Type: Matrix Integer
--E 8

--S 9 of 59
diagonalMatrix [matrix [[1,2],[3,4]], matrix [[4,5],[6,7]]]
 

        +1  2  0  0+
        |          |
        |3  4  0  0|
   (9)  |          |
        |0  0  4  5|
        |          |
        +0  0  6  7+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2  0  0+
--R        |          |
--R        |3  4  0  0|
--R   (9)  |          |
--R        |0  0  4  5|
--R        |          |
--R        +0  0  6  7+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 59
coerce([1,2,3])@Matrix(INT)
 

         +1+
         | |
   (10)  |2|
         | |
         +3+
                                                         Type: Matrix Integer
--R 
--R
--R         +1+
--R         | |
--R   (10)  |2|
--R         | |
--R         +3+
--R                                                         Type: Matrix Integer
--E 10

--S 11 of 59
transpose([1,2,3])@Matrix(INT)
 

   (11)  [1  2  3]
                                                         Type: Matrix Integer
--R 
--R
--R   (11)  [1  2  3]
--R                                                         Type: Matrix Integer
--E 11

--S 12 of 59
transpose matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1   1    1    1 +
         |                   |
         |1  2   3    4    5 |
         |                   |
   (12)  |1  4   9   16   25 |
         |                   |
         |1  8   27  64   125|
         |                   |
         +1  16  81  256  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1   1    1    1 +
--R         |                   |
--R         |1  2   3    4    5 |
--R         |                   |
--R   (12)  |1  4   9   16   25 |
--R         |                   |
--R         |1  8   27  64   125|
--R         |                   |
--R         +1  16  81  256  625+
--R                                                         Type: Matrix Integer
--E 12

--S 13 of 59
squareTop matrix [[j**i for i in 0..2] for j in 1..5]
 

         +1  1  1+
         |       |
   (13)  |1  2  4|
         |       |
         +1  3  9+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1+
--R         |       |
--R   (13)  |1  2  4|
--R         |       |
--R         +1  3  9+
--R                                                         Type: Matrix Integer
--E 13

--S 14 of 59
t1:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (14)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (14)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 14

--S 15 of 59
horizConcat(t1,t1)
 

         +1  1  1    1    1   1  1  1    1    1 +
         |                                      |
         |1  2  4    8   16   1  2  4    8   16 |
         |                                      |
   (15)  |1  3  9   27   81   1  3  9   27   81 |
         |                                      |
         |1  4  16  64   256  1  4  16  64   256|
         |                                      |
         +1  5  25  125  625  1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1   1  1  1    1    1 +
--R         |                                      |
--R         |1  2  4    8   16   1  2  4    8   16 |
--R         |                                      |
--R   (15)  |1  3  9   27   81   1  3  9   27   81 |
--R         |                                      |
--R         |1  4  16  64   256  1  4  16  64   256|
--R         |                                      |
--R         +1  5  25  125  625  1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 15

--S 16 of 59
t2:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (16)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (16)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 16

--S 17 of 59
vertConcat(t2,t2)
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
         |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         |1  5  25  125  625|
   (17)  |                  |
         |1  1  1    1    1 |
         |                  |
         |1  2  4    8   16 |
         |                  |
         |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R         |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         |1  5  25  125  625|
--R   (17)  |                  |
--R         |1  1  1    1    1 |
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R         |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 17

--S 18 of 59
t3:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (18)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (18)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 18

--S 19 of 59
listOfLists t3
 

   (19)
   [[1,1,1,1,1],[1,2,4,8,16],[1,3,9,27,81],[1,4,16,64,256],[1,5,25,125,625]]
                                                      Type: List List Integer
--R 
--R
--R   (19)
--R   [[1,1,1,1,1],[1,2,4,8,16],[1,3,9,27,81],[1,4,16,64,256],[1,5,25,125,625]]
--R                                                      Type: List List Integer
--E 19

--S 20 of 59
t4:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (20)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (20)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 20

--S 21 of 59
elt(t4,3,3)
 

   (21)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  9
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 59
t5:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (22)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (22)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 59
setelt(t5,3,3,10)
 

   (23)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  10
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 59
t6:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (24)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (24)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 24

--S 25 of 59
swapRows!(t6,2,4)
 

         +1  1  1    1    1 +
         |                  |
         |1  4  16  64   256|
         |                  |
   (25)  |1  3  9   27   81 |
         |                  |
         |1  2  4    8   16 |
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R   (25)  |1  3  9   27   81 |
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 25

--S 26 of 59
t7:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (26)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (26)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 26

--S 27 of 59
swapColumns!(t7,2,4)
 

         +1   1   1   1   1 +
         |                  |
         |1   8   4   2  16 |
         |                  |
   (27)  |1  27   9   3  81 |
         |                  |
         |1  64   16  4  256|
         |                  |
         +1  125  25  5  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1   1   1   1   1 +
--R         |                  |
--R         |1   8   4   2  16 |
--R         |                  |
--R   (27)  |1  27   9   3  81 |
--R         |                  |
--R         |1  64   16  4  256|
--R         |                  |
--R         +1  125  25  5  625+
--R                                                         Type: Matrix Integer
--E 27

--S 28 of 59
t8:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (28)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (28)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 28

--S 29 of 59
subMatrix(t8,1,3,2,4)
 

         +1  1  1 +
         |        |
   (29)  |2  4  8 |
         |        |
         +3  9  27+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1 +
--R         |        |
--R   (29)  |2  4  8 |
--R         |        |
--R         +3  9  27+
--R                                                         Type: Matrix Integer
--E 29

--S 30 of 59
t9:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (30)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (30)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 30

--S 31 of 59
setsubMatrix!(t9,2,2,matrix [[3,3],[3,3]])
 

         +1  1  1    1    1 +
         |                  |
         |1  3  3    8   16 |
         |                  |
   (31)  |1  3  3   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  3  3    8   16 |
--R         |                  |
--R   (31)  |1  3  3   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 59
t0:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (32)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (32)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 32

--S 33 of 59
t0+t0
 

         +2  2   2    2    2  +
         |                    |
         |2  4   8   16    32 |
         |                    |
   (33)  |2  6   18  54   162 |
         |                    |
         |2  8   32  128  512 |
         |                    |
         +2  10  50  250  1250+
                                                         Type: Matrix Integer
--R 
--R
--R         +2  2   2    2    2  +
--R         |                    |
--R         |2  4   8   16    32 |
--R         |                    |
--R   (33)  |2  6   18  54   162 |
--R         |                    |
--R         |2  8   32  128  512 |
--R         |                    |
--R         +2  10  50  250  1250+
--R                                                         Type: Matrix Integer
--E 33

--S 34 of 59
t0-t0
 

         +0  0  0  0  0+
         |             |
         |0  0  0  0  0|
         |             |
   (34)  |0  0  0  0  0|
         |             |
         |0  0  0  0  0|
         |             |
         +0  0  0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R         +0  0  0  0  0+
--R         |             |
--R         |0  0  0  0  0|
--R         |             |
--R   (34)  |0  0  0  0  0|
--R         |             |
--R         |0  0  0  0  0|
--R         |             |
--R         +0  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 34

--S 35 of 59
-t0
 

         +- 1  - 1  - 1    - 1    - 1 +
         |                            |
         |- 1  - 2  - 4    - 8   - 16 |
         |                            |
   (35)  |- 1  - 3  - 9   - 27   - 81 |
         |                            |
         |- 1  - 4  - 16  - 64   - 256|
         |                            |
         +- 1  - 5  - 25  - 125  - 625+
                                                         Type: Matrix Integer
--R 
--R
--R         +- 1  - 1  - 1    - 1    - 1 +
--R         |                            |
--R         |- 1  - 2  - 4    - 8   - 16 |
--R         |                            |
--R   (35)  |- 1  - 3  - 9   - 27   - 81 |
--R         |                            |
--R         |- 1  - 4  - 16  - 64   - 256|
--R         |                            |
--R         +- 1  - 5  - 25  - 125  - 625+
--R                                                         Type: Matrix Integer
--E 35

--S 36 of 59
t0*t0
 

         + 5    15    55     225    979  +
         |                               |
         |31   129    573   2637   12405 |
         |                               |
   (36)  |121  547   2551   12121  58315 |
         |                               |
         |341  1593  7585   36561  177745|
         |                               |
         +781  3711  17871  86841  424731+
                                                         Type: Matrix Integer
--R 
--R
--R         + 5    15    55     225    979  +
--R         |                               |
--R         |31   129    573   2637   12405 |
--R         |                               |
--R   (36)  |121  547   2551   12121  58315 |
--R         |                               |
--R         |341  1593  7585   36561  177745|
--R         |                               |
--R         +781  3711  17871  86841  424731+
--R                                                         Type: Matrix Integer
--E 36

--S 37 of 59
1/3*t0
 

         +1  1  1    1    1 +
         |-  -  -    -    - |
         |3  3  3    3    3 |
         |                  |
         |1  2  4    8   16 |
         |-  -  -    -   -- |
         |3  3  3    3    3 |
         |                  |
         |1                 |
   (37)  |-  1  3    9   27 |
         |3                 |
         |                  |
         |1  4  16  64   256|
         |-  -  --  --   ---|
         |3  3   3   3    3 |
         |                  |
         |1  5  25  125  625|
         |-  -  --  ---  ---|
         +3  3   3   3    3 +
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |-  -  -    -    - |
--R         |3  3  3    3    3 |
--R         |                  |
--R         |1  2  4    8   16 |
--R         |-  -  -    -   -- |
--R         |3  3  3    3    3 |
--R         |                  |
--R         |1                 |
--R   (37)  |-  1  3    9   27 |
--R         |3                 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |-  -  --  --   ---|
--R         |3  3   3   3    3 |
--R         |                  |
--R         |1  5  25  125  625|
--R         |-  -  --  ---  ---|
--R         +3  3   3   3    3 +
--R                                                Type: Matrix Fraction Integer
--E 37

--S 38 of 59
m:=matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  1  1    1    1 +
         |                  |
         |1  2  4    8   16 |
         |                  |
   (38)  |1  3  9   27   81 |
         |                  |
         |1  4  16  64   256|
         |                  |
         +1  5  25  125  625+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |                  |
--R         |1  2  4    8   16 |
--R         |                  |
--R   (38)  |1  3  9   27   81 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |                  |
--R         +1  5  25  125  625+
--R                                                         Type: Matrix Integer
--E 38

--S 39 of 59
t0*1/3
 

         +1  1  1    1    1 +
         |-  -  -    -    - |
         |3  3  3    3    3 |
         |                  |
         |1  2  4    8   16 |
         |-  -  -    -   -- |
         |3  3  3    3    3 |
         |                  |
         |1                 |
   (39)  |-  1  3    9   27 |
         |3                 |
         |                  |
         |1  4  16  64   256|
         |-  -  --  --   ---|
         |3  3   3   3    3 |
         |                  |
         |1  5  25  125  625|
         |-  -  --  ---  ---|
         +3  3   3   3    3 +
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1    1    1 +
--R         |-  -  -    -    - |
--R         |3  3  3    3    3 |
--R         |                  |
--R         |1  2  4    8   16 |
--R         |-  -  -    -   -- |
--R         |3  3  3    3    3 |
--R         |                  |
--R         |1                 |
--R   (39)  |-  1  3    9   27 |
--R         |3                 |
--R         |                  |
--R         |1  4  16  64   256|
--R         |-  -  --  --   ---|
--R         |3  3   3   3    3 |
--R         |                  |
--R         |1  5  25  125  625|
--R         |-  -  --  ---  ---|
--R         +3  3   3   3    3 +
--R                                                Type: Matrix Fraction Integer
--E 39

--S 40 of 59
3*t0
 

         +3  3   3    3    3  +
         |                    |
         |3  6   12  24    48 |
         |                    |
   (40)  |3  9   27  81   243 |
         |                    |
         |3  12  48  192  768 |
         |                    |
         +3  15  75  375  1875+
                                                         Type: Matrix Integer
--R 
--R
--R         +3  3   3    3    3  +
--R         |                    |
--R         |3  6   12  24    48 |
--R         |                    |
--R   (40)  |3  9   27  81   243 |
--R         |                    |
--R         |3  12  48  192  768 |
--R         |                    |
--R         +3  15  75  375  1875+
--R                                                         Type: Matrix Integer
--E 40

--S 41 of 59
c:=coerce([1,2,3,4,5])@Matrix(INT)
 

         +1+
         | |
         |2|
         | |
   (41)  |3|
         | |
         |4|
         | |
         +5+
                                                         Type: Matrix Integer
--R 
--R
--R         +1+
--R         | |
--R         |2|
--R         | |
--R   (41)  |3|
--R         | |
--R         |4|
--R         | |
--R         +5+
--R                                                         Type: Matrix Integer
--E 41

--S 42 of 59
t0*c
 

         + 15 +
         |    |
         |129 |
         |    |
   (42)  |547 |
         |    |
         |1593|
         |    |
         +3711+
                                                         Type: Matrix Integer
--R 
--R
--R         + 15 +
--R         |    |
--R         |129 |
--R         |    |
--R   (42)  |547 |
--R         |    |
--R         |1593|
--R         |    |
--R         +3711+
--R                                                         Type: Matrix Integer
--E 42

--S 43 of 59
r:=transpose([1,2,3,4,5])@Matrix(INT)
 

   (43)  [1  2  3  4  5]
                                                         Type: Matrix Integer
--R 
--R
--R   (43)  [1  2  3  4  5]
--R                                                         Type: Matrix Integer
--E 43

--S 44 of 59
r*t0
 

   (44)  [15  55  225  979  4425]
                                                         Type: Matrix Integer
--R 
--R
--R   (44)  [15  55  225  979  4425]
--R                                                         Type: Matrix Integer
--E 44

--S 45 of 59
t0**3
 

         + 1279    5995     28635     138385    674175  +
         |                                              |
         |15775    74581    358021   1735927    8476705 |
         |                                              |
   (45)  |73655   348927   1677079   8138493   39765355 |
         |                                              |
         |223825  1061251  5103579   24775909  121090455|
         |                                              |
         +533935  2532835  12184195  59162185  289195879+
                                                         Type: Matrix Integer
--R 
--R
--R         + 1279    5995     28635     138385    674175  +
--R         |                                              |
--R         |15775    74581    358021   1735927    8476705 |
--R         |                                              |
--R   (45)  |73655   348927   1677079   8138493   39765355 |
--R         |                                              |
--R         |223825  1061251  5103579   24775909  121090455|
--R         |                                              |
--R         +533935  2532835  12184195  59162185  289195879+
--R                                                         Type: Matrix Integer
--E 45

--S 46 of 59
t10:=matrix [[2**i for i in 2..4] for j in 1..5]
 

         +4  8  16+
         |        |
         |4  8  16|
         |        |
   (46)  |4  8  16|
         |        |
         |4  8  16|
         |        |
         +4  8  16+
                                                         Type: Matrix Integer
--R 
--R
--R         +4  8  16+
--R         |        |
--R         |4  8  16|
--R         |        |
--R   (46)  |4  8  16|
--R         |        |
--R         |4  8  16|
--R         |        |
--R         +4  8  16+
--R                                                         Type: Matrix Integer
--E 46

--S 47 of 59
exquo(t10,2)
 

         +2  4  8+
         |       |
         |2  4  8|
         |       |
   (47)  |2  4  8|
         |       |
         |2  4  8|
         |       |
         +2  4  8+
                                              Type: Union(Matrix Integer,...)
--R 
--R
--R         +2  4  8+
--R         |       |
--R         |2  4  8|
--R         |       |
--R   (47)  |2  4  8|
--R         |       |
--R         |2  4  8|
--R         |       |
--R         +2  4  8+
--R                                              Type: Union(Matrix Integer,...)
--E 47

--S 48 of 59
t10/4
 

         +1  2  4+
         |       |
         |1  2  4|
         |       |
   (48)  |1  2  4|
         |       |
         |1  2  4|
         |       |
         +1  2  4+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  2  4+
--R         |       |
--R         |1  2  4|
--R         |       |
--R   (48)  |1  2  4|
--R         |       |
--R         |1  2  4|
--R         |       |
--R         +1  2  4+
--R                                                Type: Matrix Fraction Integer
--E 48

--S 49 of 59
rowEchelon matrix [[j**i for i in 0..4] for j in 1..5]
 

         +1  0  0  0  0 +
         |              |
         |0  1  1  1  1 |
         |              |
   (49)  |0  0  2  0  2 |
         |              |
         |0  0  0  6  12|
         |              |
         +0  0  0  0  24+
                                                         Type: Matrix Integer
--R 
--R
--R         +1  0  0  0  0 +
--R         |              |
--R         |0  1  1  1  1 |
--R         |              |
--R   (49)  |0  0  2  0  2 |
--R         |              |
--R         |0  0  0  6  12|
--R         |              |
--R         +0  0  0  0  24+
--R                                                         Type: Matrix Integer
--E 49

--S 50 of 59
columnSpace matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]]
 

   (50)  [[1,4,7,1],[2,5,8,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (50)  [[1,4,7,1],[2,5,8,1]]
--R                                                    Type: List Vector Integer
--E 50

--S 51 of 59
rank matrix [[1,2,3],[4,5,6],[7,8,9]]
 

   (51)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (51)  2
--R                                                        Type: PositiveInteger
--E 51

--S 52 of 59
nullity matrix [[1,2,3],[4,5,6],[7,8,9]]
 

   (52)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (52)  1
--R                                                        Type: PositiveInteger
--E 52

--S 53 of 59
nullSpace matrix [[1,2,3],[4,5,6],[7,8,9]]
 

   (53)  [[1,- 2,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (53)  [[1,- 2,1]]
--R                                                    Type: List Vector Integer
--E 53

--S 54 of 59
determinant matrix [[j**i for i in 0..4] for j in 1..5]
 

   (54)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (54)  288
--R                                                        Type: PositiveInteger
--E 54

--S 55 of 59
minordet matrix [[j**i for i in 0..4] for j in 1..5]
 

   (55)  288
                                                        Type: PositiveInteger
--R 
--R
--R   (55)  288
--R                                                        Type: PositiveInteger
--E 55

--S 56 of 59
pfaffian [[0,1,0,0],[-1,0,0,0],[0,0,0,1],[0,0,-1,0]]
 

   (56)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (56)  1
--R                                                        Type: PositiveInteger
--E 56

--S 57 of 59
inverse matrix [[j**i for i in 0..4] for j in 1..5]
 

         + 5    - 10   10   - 5    1  +
         |                            |
         |  77  107     39   61     25|
         |- --  ---   - --   --   - --|
         |  12   6       2    6     12|
         |                            |
         | 71     59   49     41   35 |
         | --   - --   --   - --   -- |
   (57)  | 24      6    4      6   24 |
         |                            |
         |   7   13          11      5|
         |- --   --   - 3    --   - --|
         |  12    6           6     12|
         |                            |
         |  1     1    1      1     1 |
         | --   - -    -    - -    -- |
         + 24     6    4      6    24 +
                                     Type: Union(Matrix Fraction Integer,...)
--R 
--R
--R         + 5    - 10   10   - 5    1  +
--R         |                            |
--R         |  77  107     39   61     25|
--R         |- --  ---   - --   --   - --|
--R         |  12   6       2    6     12|
--R         |                            |
--R         | 71     59   49     41   35 |
--R         | --   - --   --   - --   -- |
--R   (57)  | 24      6    4      6   24 |
--R         |                            |
--R         |   7   13          11      5|
--R         |- --   --   - 3    --   - --|
--R         |  12    6           6     12|
--R         |                            |
--R         |  1     1    1      1     1 |
--R         | --   - -    -    - -    -- |
--R         + 24     6    4      6    24 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 57

--S 58 of 59
(matrix [[j**i for i in 0..4] for j in 1..5]) ** 2
 

         + 5    15    55     225    979  +
         |                               |
         |31   129    573   2637   12405 |
         |                               |
   (58)  |121  547   2551   12121  58315 |
         |                               |
         |341  1593  7585   36561  177745|
         |                               |
         +781  3711  17871  86841  424731+
                                                         Type: Matrix Integer
--R 
--R
--R         + 5    15    55     225    979  +
--R         |                               |
--R         |31   129    573   2637   12405 |
--R         |                               |
--R   (58)  |121  547   2551   12121  58315 |
--R         |                               |
--R         |341  1593  7585   36561  177745|
--R         |                               |
--R         +781  3711  17871  86841  424731+
--R                                                         Type: Matrix Integer
--E 58

--S 59 of 59
)show MatrixCategory
 
 MatrixCategory(R: Ring,Row: FiniteLinearAggregate t#1,Col: FiniteLinearAggregate t#1)  is a category constructor
 Abbreviation for MatrixCategory is MATCAT 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.2.spad.pamphlet to see algebra source code for MATCAT 

------------------------------- Operations --------------------------------
 ?*? : (Row,%) -> Row                  ?*? : (%,Col) -> Col
 ?*? : (Integer,%) -> %                ?*? : (%,R) -> %
 ?*? : (R,%) -> %                      ?*? : (%,%) -> %
 ?+? : (%,%) -> %                      -? : % -> %
 ?-? : (%,%) -> %                      antisymmetric? : % -> Boolean
 coerce : Col -> %                     column : (%,Integer) -> Col
 copy : % -> %                         diagonal? : % -> Boolean
 diagonalMatrix : List % -> %          diagonalMatrix : List R -> %
 elt : (%,Integer,Integer,R) -> R      elt : (%,Integer,Integer) -> R
 empty : () -> %                       empty? : % -> Boolean
 eq? : (%,%) -> Boolean                fill! : (%,R) -> %
 horizConcat : (%,%) -> %              listOfLists : % -> List List R
 map : (((R,R) -> R),%,%,R) -> %       map : (((R,R) -> R),%,%) -> %
 map : ((R -> R),%) -> %               map! : ((R -> R),%) -> %
 matrix : List List R -> %             maxColIndex : % -> Integer
 maxRowIndex : % -> Integer            minColIndex : % -> Integer
 minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
 nrows : % -> NonNegativeInteger       parts : % -> List R
 qelt : (%,Integer,Integer) -> R       row : (%,Integer) -> Row
 sample : () -> %                      setRow! : (%,Integer,Row) -> %
 square? : % -> Boolean                squareTop : % -> %
 symmetric? : % -> Boolean             transpose : % -> %
 transpose : Row -> %                  vertConcat : (%,%) -> %
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?**? : (%,Integer) -> % if R has FIELD
 ?**? : (%,NonNegativeInteger) -> %
 ?/? : (%,R) -> % if R has FIELD
 ?=? : (%,%) -> Boolean if R has SETCAT
 any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 coerce : % -> OutputForm if R has SETCAT
 columnSpace : % -> List Col if R has EUCDOM
 count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
 count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 determinant : % -> R if R has commutative *
 elt : (%,List Integer,List Integer) -> %
 eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
 every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 exquo : (%,R) -> Union(%,"failed") if R has INTDOM
 hash : % -> SingleInteger if R has SETCAT
 inverse : % -> Union(%,"failed") if R has FIELD
 latex : % -> String if R has SETCAT
 less? : (%,NonNegativeInteger) -> Boolean
 member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
 members : % -> List R if $ has finiteAggregate
 minordet : % -> R if R has commutative *
 more? : (%,NonNegativeInteger) -> Boolean
 new : (NonNegativeInteger,NonNegativeInteger,R) -> %
 nullSpace : % -> List Col if R has INTDOM
 nullity : % -> NonNegativeInteger if R has INTDOM
 pfaffian : % -> R if R has COMRING
 qsetelt! : (%,Integer,Integer,R) -> R
 rank : % -> NonNegativeInteger if R has INTDOM
 rowEchelon : % -> % if R has EUCDOM
 scalarMatrix : (NonNegativeInteger,R) -> %
 setColumn! : (%,Integer,Col) -> %
 setelt : (%,List Integer,List Integer,%) -> %
 setelt : (%,Integer,Integer,R) -> R
 setsubMatrix! : (%,Integer,Integer,%) -> %
 size? : (%,NonNegativeInteger) -> Boolean
 subMatrix : (%,Integer,Integer,Integer,Integer) -> %
 swapColumns! : (%,Integer,Integer) -> %
 swapRows! : (%,Integer,Integer) -> %
 zero : (NonNegativeInteger,NonNegativeInteger) -> %
 ?~=? : (%,%) -> Boolean if R has SETCAT

--R 
--R MatrixCategory(R: Ring,Row: FiniteLinearAggregate t#1,Col: FiniteLinearAggregate t#1)  is a category constructor
--R Abbreviation for MatrixCategory is MATCAT 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.spad.pamphlet to see algebra source code for MATCAT 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (Row,%) -> Row                  ?*? : (%,Col) -> Col
--R ?*? : (Integer,%) -> %                ?*? : (%,R) -> %
--R ?*? : (R,%) -> %                      ?*? : (%,%) -> %
--R ?+? : (%,%) -> %                      -? : % -> %
--R ?-? : (%,%) -> %                      antisymmetric? : % -> Boolean
--R coerce : Col -> %                     column : (%,Integer) -> Col
--R copy : % -> %                         diagonal? : % -> Boolean
--R diagonalMatrix : List % -> %          diagonalMatrix : List R -> %
--R elt : (%,Integer,Integer,R) -> R      elt : (%,Integer,Integer) -> R
--R empty : () -> %                       empty? : % -> Boolean
--R eq? : (%,%) -> Boolean                fill! : (%,R) -> %
--R horizConcat : (%,%) -> %              listOfLists : % -> List List R
--R map : (((R,R) -> R),%,%,R) -> %       map : (((R,R) -> R),%,%) -> %
--R map : ((R -> R),%) -> %               map! : ((R -> R),%) -> %
--R matrix : List List R -> %             maxColIndex : % -> Integer
--R maxRowIndex : % -> Integer            minColIndex : % -> Integer
--R minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
--R nrows : % -> NonNegativeInteger       parts : % -> List R
--R qelt : (%,Integer,Integer) -> R       row : (%,Integer) -> Row
--R sample : () -> %                      setRow! : (%,Integer,Row) -> %
--R square? : % -> Boolean                squareTop : % -> %
--R symmetric? : % -> Boolean             transpose : % -> %
--R transpose : Row -> %                  vertConcat : (%,%) -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
--R ?=? : (%,%) -> Boolean if R has SETCAT
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if R has SETCAT
--R columnSpace : % -> List Col if R has EUCDOM
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R determinant : % -> R if R has commutative *
--R elt : (%,List Integer,List Integer) -> %
--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R hash : % -> SingleInteger if R has SETCAT
--R inverse : % -> Union(%,"failed") if R has FIELD
--R latex : % -> String if R has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
--R members : % -> List R if $ has finiteAggregate
--R minordet : % -> R if R has commutative *
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,NonNegativeInteger,R) -> %
--R nullSpace : % -> List Col if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
--R pfaffian : % -> R if R has COMRING
--R qsetelt! : (%,Integer,Integer,R) -> R
--R rank : % -> NonNegativeInteger if R has INTDOM
--R rowEchelon : % -> % if R has EUCDOM
--R scalarMatrix : (NonNegativeInteger,R) -> %
--R setColumn! : (%,Integer,Col) -> %
--R setelt : (%,List Integer,List Integer,%) -> %
--R setelt : (%,Integer,Integer,R) -> R
--R setsubMatrix! : (%,Integer,Integer,%) -> %
--R size? : (%,NonNegativeInteger) -> Boolean
--R subMatrix : (%,Integer,Integer,Integer,Integer) -> %
--R swapColumns! : (%,Integer,Integer) -> %
--R swapRows! : (%,Integer,Integer) -> %
--R zero : (NonNegativeInteger,NonNegativeInteger) -> %
--R ?~=? : (%,%) -> Boolean if R has SETCAT
--R
--E 59

)spool
 
Starts dribbling to BasicOperator.output (2010/3/27, 18:41:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 18
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 18
deq := D(y x, x, 2) + D(y x, x) + y x = 0
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 18
solve(deq, y, x)
 

                                             x     x
                                     +-+   - -   - -      +-+
                                   x\|3      2     2    x\|3
   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             x     x
--R                                     +-+   - -   - -      +-+
--R                                   x\|3      2     2    x\|3
--R   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 3

--S 4 of 18
nary? y
 

   (4)  true
                                                                Type: Boolean
--R 
--R
--R   (4)  true
--R                                                                Type: Boolean
--E 4

--S 5 of 18
unary? y
 

   (5)  false
                                                                Type: Boolean
--R 
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 18
opOne := operator('opOne, 1)
 

   (6)  opOne
                                                          Type: BasicOperator
--R 
--R
--R   (6)  opOne
--R                                                          Type: BasicOperator
--E 6

--S 7 of 18
nary? opOne
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 7

--S 8 of 18
unary? opOne
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 18
arity opOne
 

   (9)  1
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (9)  1
--R                                          Type: Union(NonNegativeInteger,...)
--E 9

--S 10 of 18
name opOne
 

   (10)  opOne
                                                                 Type: Symbol
--R 
--R
--R   (10)  opOne
--R                                                                 Type: Symbol
--E 10

--S 11 of 18
is?(opOne, 'z2)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 18
is?(opOne, "opOne")
 

   (12)  true
                                                                Type: Boolean
--R 
--R
--R   (12)  true
--R                                                                Type: Boolean
--E 12

--S 13 of 18
properties y
 

   (13)  table()
                                           Type: AssociationList(String,None)
--R 
--R
--R   (13)  table()
--R                                           Type: AssociationList(String,None)
--E 13

--S 14 of 18
setProperty(y, "use", "unknown function" :: None )
 

   (14)  y
                                                          Type: BasicOperator
--R 
--R
--R   (14)  y
--R                                                          Type: BasicOperator
--E 14

--S 15 of 18
properties y
 

   (15)  table("use"= NONE)
                                           Type: AssociationList(String,None)
--R 
--R
--R   (15)  table("use"= NONE)
--R                                           Type: AssociationList(String,None)
--E 15

--S 16 of 18
property(y, "use") :: None pretend String
 

   (16)  "unknown function"
                                                                 Type: String
--R 
--R
--R   (16)  "unknown function"
--R                                                                 Type: String
--E 16

--S 17 of 18
deleteProperty!(y, "use")
 

   (17)  y
                                                          Type: BasicOperator
--R 
--R
--R   (17)  y
--R                                                          Type: BasicOperator
--E 17

--S 18 of 18
properties y
 

   (18)  table()
                                           Type: AssociationList(String,None)
--R 
--R
--R   (18)  table()
--R                                           Type: AssociationList(String,None)
--E 18
)spool
 
Starts dribbling to dfloat.output (2010/3/27, 18:24:56).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 10
2.71828
 

   (1)  2.71828
                                                                  Type: Float
--R 
--R
--R   (1)  2.71828
--R                                                                  Type: Float
--E 1

--S 2 of 10
2.71828@DoubleFloat
 

   (2)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  2.71828
--R                                                            Type: DoubleFloat
--E 2

--S 3 of 10
2.71828 :: DoubleFloat
 

   (3)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (3)  2.71828
--R                                                            Type: DoubleFloat
--E 3

--S 4 of 10
eApprox : DoubleFloat := 2.71828
 

   (4)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (4)  2.71828
--R                                                            Type: DoubleFloat
--E 4

--S 5 of 10
avg : List DoubleFloat -> DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
avg l ==
  empty? l => 0 :: DoubleFloat
  reduce(_+,l) / #l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
avg []
 
   Compiling function avg with type List DoubleFloat -> DoubleFloat 

   (7)  0.
                                                            Type: DoubleFloat
--R 
--R   Compiling function avg with type List DoubleFloat -> DoubleFloat 
--R
--R   (7)  0.
--R                                                            Type: DoubleFloat
--E 7

--S 8 of 10
avg [3.4,9.7,-6.8]
 

   (8)  2.0999999999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (8)  2.1000000000000001
--R                                                            Type: DoubleFloat
--E 8

--S 9 of 10
cos(3.1415926)$DoubleFloat
 

   (9)  - 0.99999999999999856
                                                            Type: DoubleFloat
--R 
--R
--R   (9)  - 0.99999999999999856
--R                                                            Type: DoubleFloat
--E 9

--S 10 of 10
cos(3.1415926 :: DoubleFloat)
 

   (10)  - 0.99999999999999856
                                                            Type: DoubleFloat
--R 
--R
--R   (10)  - 0.99999999999999856
--R                                                            Type: DoubleFloat
--E 10
)spool
 
Starts dribbling to char.output (2010/3/27, 18:24:25).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from CharacterXmpPage

--S 1 of 13
chars := [char "a", char "A", char "X", char "8", char "+"]
 

   (1)  [a,A,X,8,+]
                                                         Type: List Character
--R 
--R
--R   (1)  [a,A,X,8,+]
--R                                                         Type: List Character
--E 1

--S 2 of 13
space()
 

   (2)
                                                              Type: Character
--R 
--R
--R   (2)
--R                                                              Type: Character
--E 2

--S 3 of 13
quote()
 

   (3)  "
                                                              Type: Character
--R 
--R
--R   (3)  "
--R                                                              Type: Character
--E 3

--S 4 of 13
escape()
 

   (4)  _
                                                              Type: Character
--R 
--R
--R   (4)  _
--R                                                              Type: Character
--E 4

--S 5 of 13
[ord c for c in chars]
 

   (5)  [97,65,88,56,43]
                                                           Type: List Integer
--R 
--R
--R   (5)  [97,65,88,56,43]
--R                                                           Type: List Integer
--E 5

--S 6 of 13
[upperCase c for c in chars]
 

   (6)  [A,A,X,8,+]
                                                         Type: List Character
--R 
--R
--R   (6)  [A,A,X,8,+]
--R                                                         Type: List Character
--E 6

--S 7 of 13
[lowerCase c for c in chars]
 

   (7)  [a,a,x,8,+]
                                                         Type: List Character
--R 
--R
--R   (7)  [a,a,x,8,+]
--R                                                         Type: List Character
--E 7

--S 8 of 13
[alphabetic? c for c in chars]
 

   (8)  [true,true,true,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,true,true,false,false]
--R                                                           Type: List Boolean
--E 8

--S 9 of 13
[upperCase? c for c in chars]
 

   (9)  [false,true,true,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [false,true,true,false,false]
--R                                                           Type: List Boolean
--E 9

--S 10 of 13
[lowerCase? c for c in chars]
 

   (10)  [true,false,false,false,false]
                                                           Type: List Boolean
--R 
--R
--R   (10)  [true,false,false,false,false]
--R                                                           Type: List Boolean
--E 10

--S 11 of 13
[digit? c for c in chars]
 

   (11)  [false,false,false,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (11)  [false,false,false,true,false]
--R                                                           Type: List Boolean
--E 11

--S 12 of 13
[hexDigit? c for c in chars]
 

   (12)  [true,true,false,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (12)  [true,true,false,true,false]
--R                                                           Type: List Boolean
--E 12

--S 13 of 13
[alphanumeric? c for c in chars]
 

   (13)  [true,true,true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (13)  [true,true,true,true,false]
--R                                                           Type: List Boolean
--E 13
)spool
 
Starts dribbling to pascal1.output (2010/3/27, 18:30:38).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
)set fun cache all
 
   In general, interpreter functions will cache all values.
--R 
--R   In general, interpreter functions will cache all values.
--E 1

--S 2 of 7
p(m,n | m = 1) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 7
p(m,n | m = n) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 7
p(i,n | 1 < i and i < n) == p(i-1,n-1)+p(i,n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 7
p(2,3)
 
   Compiling function p with type (Integer,Integer) -> PositiveInteger 
   p will cache all previously computed values.

   (4)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling function p with type (Integer,Integer) -> PositiveInteger 
--R   p will cache all previously computed values.
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 7
pr(n) == [p(i,n) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 7
l := [center blankSeparate [p(i,n)::OUTFORM for i in 1..n] for n in 1..10] ;
 

                                                        Type: List OutputForm
--R 
--R
--R                                                        Type: List OutputForm
--E 7
)spool 
 
Starts dribbling to TransSolvePackage.output (2010/3/27, 18:46:38).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 4
solve(1/2*v*v*cos(theta+phi)*cos(theta+phi)+g*l*cos(phi)=g*l,phi)
 

   (1)
   [phi= 2atan(%phi0) - theta, phi= 2atan(%phi1) - theta,

     phi =
           2
        *
           atan
                  ROOT
                               4    theta 4        4          2     theta 2
                           - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
                                      2                               2
                         + 
                               4          2      2 2
                           - 3v  + 24g l v  - 48g l
                      *
                              2
                         %phi1
                     + 
                                   4    theta 4        4          2     theta 2
                               - 2v tan(-----)  + (- 4v  + 16g l v )tan(-----)
                                          2                               2
                             + 
                                   4          2      2 2
                               - 2v  + 16g l v  - 32g l
                          *
                             %phi0
                         + 
                                  2    theta 3             2      2 2     theta
                         - 16g l v tan(-----)  + (- 16g l v  + 64g l )tan(-----)
                                         2                                  2
                      *
                         %phi1
                     + 
                               4    theta 4        4          2     theta 2
                           - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
                                      2                               2
                         + 
                               4          2      2 2
                           - 3v  + 24g l v  - 48g l
                      *
                              2
                         %phi0
                     + 
                                      2    theta 3
                             - 16g l v tan(-----)
                                             2
                           + 
                                       2      2 2     theta
                             (- 16g l v  + 64g l )tan(-----)
                                                        2
                      *
                         %phi0
                     + 
                          4          2     theta 4      4    theta 2     4
                       (8v  + 16g l v )tan(-----)  + 16v tan(-----)  + 8v
                                             2                 2
                     + 
                                2      2 2
                       - 16g l v  - 64g l
                + 
                      2    theta 2    2
                  (- v tan(-----)  - v  + 4g l)%phi1
                             2
                + 
                      2    theta 2    2                         theta
                  (- v tan(-----)  - v  + 4g l)%phi0 - 8g l tan(-----)
                             2                                    2
             /
                  2    theta 2     2
                2v tan(-----)  + 2v  - 8g l
                         2
       + 
         - theta
     ,

     phi =
         -
              2
           *
              atan
                     ROOT
                                  4    theta 4        4          2     theta 2
                              - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
                                         2                               2
                            + 
                                  4          2      2 2
                              - 3v  + 24g l v  - 48g l
                         *
                                 2
                            %phi1
                        + 
                                      4    theta 4
                                  - 2v tan(-----)
                                             2
                                + 
                                       4          2     theta 2     4          2
                                  (- 4v  + 16g l v )tan(-----)  - 2v  + 16g l v
                                                          2
                                + 
                                       2 2
                                  - 32g l
                             *
                                %phi0
                            + 
                                       2    theta 3
                              - 16g l v tan(-----)
                                              2
                            + 
                                        2      2 2     theta
                              (- 16g l v  + 64g l )tan(-----)
                                                         2
                         *
                            %phi1
                        + 
                                  4    theta 4        4          2     theta 2
                              - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
                                         2                               2
                            + 
                                  4          2      2 2
                              - 3v  + 24g l v  - 48g l
                         *
                                 2
                            %phi0
                        + 
                                       2    theta 3
                              - 16g l v tan(-----)
                                              2
                            + 
                                        2      2 2     theta
                              (- 16g l v  + 64g l )tan(-----)
                                                         2
                         *
                            %phi0
                        + 
                             4          2     theta 4      4    theta 2     4
                          (8v  + 16g l v )tan(-----)  + 16v tan(-----)  + 8v
                                                2                 2
                        + 
                                   2      2 2
                          - 16g l v  - 64g l
                   + 
                       2    theta 2    2
                     (v tan(-----)  + v  - 4g l)%phi1
                              2
                   + 
                       2    theta 2    2                         theta
                     (v tan(-----)  + v  - 4g l)%phi0 + 8g l tan(-----)
                              2                                    2
                /
                     2    theta 2     2
                   2v tan(-----)  + 2v  - 8g l
                            2
       + 
         - theta
     ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (1)
--R   [phi= 2atan(%phi0) - theta, phi= 2atan(%phi1) - theta,
--R
--R     phi =
--R           2
--R        *
--R           atan
--R                  ROOT
--R                               4    theta 4        4          2     theta 2
--R                           - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
--R                                      2                               2
--R                         + 
--R                               4          2      2 2
--R                           - 3v  + 24g l v  - 48g l
--R                      *
--R                              2
--R                         %phi1
--R                     + 
--R                                   4    theta 4        4          2     theta 2
--R                               - 2v tan(-----)  + (- 4v  + 16g l v )tan(-----)
--R                                          2                               2
--R                             + 
--R                                   4          2      2 2
--R                               - 2v  + 16g l v  - 32g l
--R                          *
--R                             %phi0
--R                         + 
--R                                  2    theta 3             2      2 2     theta
--R                         - 16g l v tan(-----)  + (- 16g l v  + 64g l )tan(-----)
--R                                         2                                  2
--R                      *
--R                         %phi1
--R                     + 
--R                               4    theta 4        4          2     theta 2
--R                           - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
--R                                      2                               2
--R                         + 
--R                               4          2      2 2
--R                           - 3v  + 24g l v  - 48g l
--R                      *
--R                              2
--R                         %phi0
--R                     + 
--R                                      2    theta 3
--R                             - 16g l v tan(-----)
--R                                             2
--R                           + 
--R                                       2      2 2     theta
--R                             (- 16g l v  + 64g l )tan(-----)
--R                                                        2
--R                      *
--R                         %phi0
--R                     + 
--R                          4          2     theta 4      4    theta 2     4
--R                       (8v  + 16g l v )tan(-----)  + 16v tan(-----)  + 8v
--R                                             2                 2
--R                     + 
--R                                2      2 2
--R                       - 16g l v  - 64g l
--R                + 
--R                      2    theta 2    2
--R                  (- v tan(-----)  - v  + 4g l)%phi1
--R                             2
--R                + 
--R                      2    theta 2    2                         theta
--R                  (- v tan(-----)  - v  + 4g l)%phi0 - 8g l tan(-----)
--R                             2                                    2
--R             /
--R                  2    theta 2     2
--R                2v tan(-----)  + 2v  - 8g l
--R                         2
--R       + 
--R         - theta
--R     ,
--R
--R     phi =
--R         -
--R              2
--R           *
--R              atan
--R                     ROOT
--R                                  4    theta 4        4          2     theta 2
--R                              - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
--R                                         2                               2
--R                            + 
--R                                  4          2      2 2
--R                              - 3v  + 24g l v  - 48g l
--R                         *
--R                                 2
--R                            %phi1
--R                        + 
--R                                      4    theta 4
--R                                  - 2v tan(-----)
--R                                             2
--R                                + 
--R                                       4          2     theta 2     4          2
--R                                  (- 4v  + 16g l v )tan(-----)  - 2v  + 16g l v
--R                                                          2
--R                                + 
--R                                       2 2
--R                                  - 32g l
--R                             *
--R                                %phi0
--R                            + 
--R                                       2    theta 3
--R                              - 16g l v tan(-----)
--R                                              2
--R                            + 
--R                                        2      2 2     theta
--R                              (- 16g l v  + 64g l )tan(-----)
--R                                                         2
--R                         *
--R                            %phi1
--R                        + 
--R                                  4    theta 4        4          2     theta 2
--R                              - 3v tan(-----)  + (- 6v  + 24g l v )tan(-----)
--R                                         2                               2
--R                            + 
--R                                  4          2      2 2
--R                              - 3v  + 24g l v  - 48g l
--R                         *
--R                                 2
--R                            %phi0
--R                        + 
--R                                       2    theta 3
--R                              - 16g l v tan(-----)
--R                                              2
--R                            + 
--R                                        2      2 2     theta
--R                              (- 16g l v  + 64g l )tan(-----)
--R                                                         2
--R                         *
--R                            %phi0
--R                        + 
--R                             4          2     theta 4      4    theta 2     4
--R                          (8v  + 16g l v )tan(-----)  + 16v tan(-----)  + 8v
--R                                                2                 2
--R                        + 
--R                                   2      2 2
--R                          - 16g l v  - 64g l
--R                   + 
--R                       2    theta 2    2
--R                     (v tan(-----)  + v  - 4g l)%phi1
--R                              2
--R                   + 
--R                       2    theta 2    2                         theta
--R                     (v tan(-----)  + v  - 4g l)%phi0 + 8g l tan(-----)
--R                              2                                    2
--R                /
--R                     2    theta 2     2
--R                   2v tan(-----)  + 2v  - 8g l
--R                            2
--R       + 
--R         - theta
--R     ]
--R                                       Type: List Equation Expression Integer
--E 1

--S 2 of 4
definingPolynomial %phi0
 

   (2)
              4         2      2            2             theta 2
       ((%phi0  - 2%phi0  + 1)v  + (- 4%phi0  - 4)g l)tan(-----)
                                                            2
     + 
              3                  theta          4         2      2
       (8%phi0  + 8%phi0)g l tan(-----) + (%phi0  - 2%phi0  + 1)v
                                   2
     + 
                4         2
       (- 4%phi0  - 4%phi0 )g l
  /
      2    theta 2    2
     v tan(-----)  + v  - 4g l
             2
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R              4         2      2            2             theta 2
--R       ((%phi0  - 2%phi0  + 1)v  + (- 4%phi0  - 4)g l)tan(-----)
--R                                                            2
--R     + 
--R              3                  theta          4         2      2
--R       (8%phi0  + 8%phi0)g l tan(-----) + (%phi0  - 2%phi0  + 1)v
--R                                   2
--R     + 
--R                4         2
--R       (- 4%phi0  - 4%phi0 )g l
--R  /
--R      2    theta 2    2
--R     v tan(-----)  + v  - 4g l
--R             2
--R                                                     Type: Expression Integer
--E 2

--S 3 of 4
definingPolynomial %phi1
 

   (3)
         2    theta 2    2             3
       (v tan(-----)  + v  - 4g l)%phi0
                2
     + 
               2    theta 2            theta           2                   2
       (%phi1 v tan(-----)  + 8g l tan(-----) + %phi1 v  - 4%phi1 g l)%phi0
                      2                  2
     + 
                  2      2            theta 2                  theta
           ((%phi1  - 2)v  - 4g l)tan(-----)  + 8%phi1 g l tan(-----)
                                        2                        2
         + 
                 2      2            2
           (%phi1  - 2)v  + (- 4%phi1  - 4)g l
      *
         %phi0
     + 
              3           2                  theta 2
       ((%phi1  - 2%phi1)v  - 4%phi1 g l)tan(-----)
                                               2
     + 
            2             theta          3           2            3
     (8%phi1  + 8)g l tan(-----) + (%phi1  - 2%phi1)v  + (- 4%phi1  - 4%phi1)g l
                            2
  /
      2    theta 2    2
     v tan(-----)  + v  - 4g l
             2
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R         2    theta 2    2             3
--R       (v tan(-----)  + v  - 4g l)%phi0
--R                2
--R     + 
--R               2    theta 2            theta           2                   2
--R       (%phi1 v tan(-----)  + 8g l tan(-----) + %phi1 v  - 4%phi1 g l)%phi0
--R                      2                  2
--R     + 
--R                  2      2            theta 2                  theta
--R           ((%phi1  - 2)v  - 4g l)tan(-----)  + 8%phi1 g l tan(-----)
--R                                        2                        2
--R         + 
--R                 2      2            2
--R           (%phi1  - 2)v  + (- 4%phi1  - 4)g l
--R      *
--R         %phi0
--R     + 
--R              3           2                  theta 2
--R       ((%phi1  - 2%phi1)v  - 4%phi1 g l)tan(-----)
--R                                               2
--R     + 
--R            2             theta          3           2            3
--R     (8%phi1  + 8)g l tan(-----) + (%phi1  - 2%phi1)v  + (- 4%phi1  - 4%phi1)g l
--R                            2
--R  /
--R      2    theta 2    2
--R     v tan(-----)  + v  - 4g l
--R             2
--R                                                     Type: Expression Integer
--E 3

--S 4 of 4
)show TransSolvePackage
 
 TransSolvePackage R: Join(OrderedSet,EuclideanDomain,RetractableTo Integer,LinearlyExplicitRingOver Integer,CharacteristicZero)  is a package constructor
 Abbreviation for TransSolvePackage is SOLVETRA 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for SOLVETRA 

------------------------------- Operations --------------------------------
 solve : Expression R -> List Equation Expression R
 solve : Equation Expression R -> List Equation Expression R
 solve : (Equation Expression R,Symbol) -> List Equation Expression R
 solve : (Expression R,Symbol) -> List Equation Expression R
 solve : (List Equation Expression R,List Symbol) -> List List Equation Expression R

--R 
--R TransSolvePackage R: Join(OrderedSet,EuclideanDomain,RetractableTo Integer,LinearlyExplicitRingOver Integer,CharacteristicZero)  is a package constructor
--R Abbreviation for TransSolvePackage is SOLVETRA 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for SOLVETRA 
--R
--R------------------------------- Operations --------------------------------
--R solve : Expression R -> List Equation Expression R
--R solve : Equation Expression R -> List Equation Expression R
--R solve : (Equation Expression R,Symbol) -> List Equation Expression R
--R solve : (Expression R,Symbol) -> List Equation Expression R
--R solve : (List Equation Expression R,List Symbol) -> List List Equation Expression R
--R
--E 4

)spool
 
Starts dribbling to FactoredFunctions2.output (2010/3/27, 18:42:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
double(x) == x + x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
f := factor(720) 
 

         4 2
   (2)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         4 2
--R   (2)  2 3 5
--R                                                       Type: Factored Integer
--E 2

--S 3 of 6
map(double,f) 
 
   Compiling function double with type Integer -> Integer 

           4 2
   (3)  2 4 6 10
                                                       Type: Factored Integer
--R 
--R   Compiling function double with type Integer -> Integer 
--R
--R           4 2
--R   (3)  2 4 6 10
--R                                                       Type: Factored Integer
--E 3

--S 4 of 6
makePoly(b) == x + b 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 6
g := map(makePoly,f) 
 
   Compiling function makePoly with type Integer -> Polynomial Integer 

                      4       2
   (5)  (x + 1)(x + 2) (x + 3) (x + 5)
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function makePoly with type Integer -> Polynomial Integer 
--R
--R                      4       2
--R   (5)  (x + 1)(x + 2) (x + 3) (x + 5)
--R                                            Type: Factored Polynomial Integer
--E 5

--S 6 of 6
nthFlag(g,1) 
 

   (6)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (6)  "nil"
--R                                                       Type: Union("nil",...)
--E 6
)spool
 
Starts dribbling to expexpan.output (2010/3/27, 18:25:42).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 18
xxp f == exprToXXP(f,true)$FS2EXPXP(INT,EXPR INT,x,0)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
f1 := (a**2 + 1) * exp(1/x**3 + 2/x**2) - exp(b) * exp(1/x**3 + 3/x**2)
 

            3x + 1                2x + 1
            ------                ------
               3                     3
              x     b     2         x
   (2)  - %e      %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R            3x + 1                2x + 1
--R            ------                ------
--R               3                     3
--R              x     b     2         x
--R   (2)  - %e      %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 2

--S 3 of 18
x1 := xxp f1
 
   Compiling function xxp with type Expression Integer -> Union(
      %expansion: ExponentialExpansion(Integer,Expression Integer,x,0),
      %problem: Record(func: String,prob: String)) 

                - 3     - 2              - 3     - 2
            b  x    + 3x        2       x    + 2x
   (3)  - %e %e             + (a  + 1)%e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R   Compiling function xxp with type Expression Integer -> Union(
--R      %expansion: ExponentialExpansion(Integer,Expression Integer,x,0),
--R      %problem: Record(func: String,prob: String)) 
--R
--R                - 3     - 2              - 3     - 2
--R            b  x    + 3x        2       x    + 2x
--R   (3)  - %e %e             + (a  + 1)%e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 3

--S 4 of 18
limitPlus x1   -- %minusInfinity
 

   (4)  - infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)  - infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 18
f2 := (a**2 + 1) * exp(1/x**3 + 2/x**2) - exp(b) * exp(-1/x**3 + 3/x**2)
 

            3x - 1                2x + 1
            ------                ------
               3                     3
              x     b     2         x
   (5)  - %e      %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R            3x - 1                2x + 1
--R            ------                ------
--R               3                     3
--R              x     b     2         x
--R   (5)  - %e      %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 5

--S 6 of 18
x2 := xxp f2
 

                   - 3     - 2           - 3     - 2
          2       x    + 2x        b  - x    + 3x
   (6)  (a  + 1)%e             - %e %e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R                   - 3     - 2           - 3     - 2
--R          2       x    + 2x        b  - x    + 3x
--R   (6)  (a  + 1)%e             - %e %e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 6

--S 7 of 18
limitPlus x2   -- %plusInfinity
 

   (7)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (7)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 7

--S 8 of 18
f3 := (a**2 + 1) * exp(1/x**3) - exp(b) * exp(c/x**2)
 

             c                 1
            --                --
             2                 3
            x   b     2       x
   (8)  - %e  %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R             c                 1
--R            --                --
--R             2                 3
--R            x   b     2       x
--R   (8)  - %e  %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 8

--S 9 of 18
x3 := xxp f3
 

                   - 3           - 2
          2       x        b  c x
   (9)  (a  + 1)%e     - %e %e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R                   - 3           - 2
--R          2       x        b  c x
--R   (9)  (a  + 1)%e     - %e %e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 9

--S 10 of 18
limitPlus x3   -- %plusInfinity
 

   (10)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (10)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 10

--S 11 of 18
f4 := (a**2 + 1) * exp(-1/x**3) - exp(b) * exp(c/x**2)
 

              c                   1
             --                - --
              2                   3
             x   b     2         x
   (11)  - %e  %e  + (a  + 1)%e
                                                     Type: Expression Integer
--R 
--R
--R              c                   1
--R             --                - --
--R              2                   3
--R             x   b     2         x
--R   (11)  - %e  %e  + (a  + 1)%e
--R                                                     Type: Expression Integer
--E 11

--S 12 of 18
x4 := xxp f4
 

                      - 3           - 2
           2       - x        b  c x
   (12)  (a  + 1)%e       - %e %e
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R                      - 3           - 2
--R           2       - x        b  c x
--R   (12)  (a  + 1)%e       - %e %e
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 12

--S 13 of 18
limitPlus x4   -- "failed"
 

   (13)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (13)  "failed"
--R                                                    Type: Union("failed",...)
--E 13

--S 14 of 18
p5 := tan(x) * exp(1/x**2) - tan(x) * exp(1/x**2 - 1/x) + sin(x) * exp(1/x)
 

             1     - x + 1
            --     -------            1
             2         2              -
            x         x               x
   (14)  (%e   - %e       )tan(x) + %e sin(x)
                                                     Type: Expression Integer
--R 
--R
--R             1     - x + 1
--R            --     -------            1
--R             2         2              -
--R            x         x               x
--R   (14)  (%e   - %e       )tan(x) + %e sin(x)
--R                                                     Type: Expression Integer
--E 14

--S 15 of 18
q5 := -4 * exp(-1/x**2 - 1/x) + sin(x) * exp(-1/x**2 + 1/x)
 

           x - 1            - x - 1
           -----            -------
              2                 2
             x                 x
   (15)  %e     sin(x) - 4%e
                                                     Type: Expression Integer
--R 
--R
--R           x - 1            - x - 1
--R           -----            -------
--R              2                 2
--R             x                 x
--R   (15)  %e     sin(x) - 4%e
--R                                                     Type: Expression Integer
--E 15

--S 16 of 18
f5 := p5 / q5
 

             1     - x + 1
            --     -------            1
             2         2              -
            x         x               x
         (%e   - %e       )tan(x) + %e sin(x)
   (16)  ------------------------------------
                x - 1            - x - 1
                -----            -------
                   2                 2
                  x                 x
              %e     sin(x) - 4%e
                                                     Type: Expression Integer
--R 
--R
--R             1     - x + 1
--R            --     -------            1
--R             2         2              -
--R            x         x               x
--R         (%e   - %e       )tan(x) + %e sin(x)
--R   (16)  ------------------------------------
--R                x - 1            - x - 1
--R                -----            -------
--R                   2                 2
--R                  x                 x
--R              %e     sin(x) - 4%e
--R                                                     Type: Expression Integer
--E 16

--S 17 of 18
x5 := xxp f5
 

   (17)
                1  3    1   5     1   7      1    9       1     11      12
         (- x + - x  - --- x  + ---- x  - ------ x  + -------- x   + O(x  ))
                6      120      5040      362880      39916800
      *
            - 2    - 1
           x    - x
         %e
     + 
                                                                           - 2
            1  3    1   5     1   7      1    9       1     11      12    x
       (x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  ))%e
            6      120      5040      362880      39916800
     + 
                                                                     - 1
            2  3    2  5    4   7     2   9      4    11      12    x
       (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))%e
            3      15      315      2835      155925
  /
              2  3    2  5    4   7     2   9      4    11      12
         (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))
              3      15      315      2835      155925
      *
              - 2    - 1
           - x    + x
         %e
     + 
                                                                      - 2    - 1
              2   1  4    1   6     1    8      1    10      11    - x    - x
     (- 4 + 2x  - - x  + --- x  - ----- x  + ------ x   + O(x  ))%e
                  6      180      10080      907200
Type: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--R 
--R
--R   (17)
--R                1  3    1   5     1   7      1    9       1     11      12
--R         (- x + - x  - --- x  + ---- x  - ------ x  + -------- x   + O(x  ))
--R                6      120      5040      362880      39916800
--R      *
--R            - 2    - 1
--R           x    - x
--R         %e
--R     + 
--R                                                                           - 2
--R            1  3    1   5     1   7      1    9       1     11      12    x
--R       (x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  ))%e
--R            6      120      5040      362880      39916800
--R     + 
--R                                                                     - 1
--R            2  3    2  5    4   7     2   9      4    11      12    x
--R       (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))%e
--R            3      15      315      2835      155925
--R  /
--R              2  3    2  5    4   7     2   9      4    11      12
--R         (x - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  ))
--R              3      15      315      2835      155925
--R      *
--R              - 2    - 1
--R           - x    + x
--R         %e
--R     + 
--R                                                                      - 2    - 1
--R              2   1  4    1   6     1    8      1    10      11    - x    - x
--R     (- 4 + 2x  - - x  + --- x  - ----- x  + ------ x   + O(x  ))%e
--R                  6      180      10080      907200
--RType: Union(%expansion: ExponentialExpansion(Integer,Expression Integer,x,0),...)
--E 17

--S 18 of 18
limitPlus x5   -- %plusInfinity
 

   (18)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (18)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 18
)spool 
 
Starts dribbling to EuclideanGroebnerBasisPackage.output (2010/3/27, 18:42:0).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 24
a1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1)
 

            2                2
   (1)  3y x  + 2y x + y + 9x  + 5x - 3
                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--R
--R            2                2
--R   (1)  3y x  + 2y x + y + 9x  + 5x - 3
--R                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--E 1

--S 2 of 24
a2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1)
 

            3               3     2
   (2)  2y x  - y x - y + 6x  - 2x  - 3x + 3
                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--R
--R            3               3     2
--R   (2)  2y x  - y x - y + 6x  - 2x  - 3x + 3
--R                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--E 2

--S 3 of 24
a3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2)
 

           3      2     3     2
   (3)  y x  + y x  + 3x  + 2x
                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--R
--R           3      2     3     2
--R   (3)  y x  + y x  + 3x  + 2x
--R                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--E 3

--S 4 of 24
an:=[a1,a2,a3]
 

   (4)
        2                2               3               3     2
   [3y x  + 2y x + y + 9x  + 5x - 3, 2y x  - y x - y + 6x  - 2x  - 3x + 3,
       3      2     3     2
    y x  + y x  + 3x  + 2x ]
                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--R
--R   (4)
--R        2                2               3               3     2
--R   [3y x  + 2y x + y + 9x  + 5x - 3, 2y x  - y x - y + 6x  - 2x  - 3x + 3,
--R       3      2     3     2
--R    y x  + y x  + 3x  + 2x ]
--R                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--E 4

--S 5 of 24
euclideanGroebner(an)
 

                                2            3     2
   (5)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--R
--R                                2            3     2
--R   (5)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--R                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--E 5

--S 6 of 24
euclideanGroebner(an,"redcrit")
 


    reduced Critpair - Polynom :


         2               2
   - 2y x  - y x - y - 6x  - 3x + 3




    reduced Critpair - Polynom :


   y x - y + x + 3




    reduced Critpair - Polynom :


          2
   4y + 4x  - 6x - 12




    reduced Critpair - Polynom :


       3      2
   - 4x  + 10x  + 10x




    reduced Critpair - Polynom :


          2
   2y + 2x  - 3x - 6




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


       3     2
   - 2x  + 5x  + 5x




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

                                2            3     2
   (6)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2               2
--R   - 2y x  - y x - y - 6x  - 3x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   y x - y + x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   4y + 4x  - 6x - 12
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3      2
--R   - 4x  + 10x  + 10x
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   2y + 2x  - 3x - 6
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3     2
--R   - 2x  + 5x  + 5x
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R                                2            3     2
--R   (6)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--R                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--E 6

--S 7 of 24
euclideanGroebner(an,"info")
 

   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





            3               3              2              2
   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]


            2               2
   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]


            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]


                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]


            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]


   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]


                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]


          3             3
   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]


            3                             2
   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]


                       3              2
   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]


     There are

   3

     Groebner Basis Polynomials.


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

                                2            3     2
   (7)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R            3               3              2              2
--R   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]
--R
--R
--R            2               2
--R   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]
--R
--R
--R   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R          3             3
--R   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]
--R
--R
--R            3                             2
--R   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]
--R
--R
--R                       3              2
--R   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]
--R
--R
--R     There are
--R
--R   3
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R                                2            3     2
--R   (7)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--R                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--E 7

--S 8 of 24
euclideanGroebner(an,"info","redcrit")
 


    reduced Critpair - Polynom :


         2               2
   - 2y x  - y x - y - 6x  - 3x + 3



   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





            3               3              2              2
   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


   y x - y + x + 3



            2               2
   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]



    reduced Critpair - Polynom :


          2
   4y + 4x  - 6x - 12



            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]



    reduced Critpair - Polynom :


       3      2
   - 4x  + 10x  + 10x



                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


          2
   2y + 2x  - 3x - 6



            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]



    reduced Critpair - Polynom :


   0



   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


       3     2
   - 2x  + 5x  + 5x



                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


   0



          3             3
   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]



    reduced Critpair - Polynom :


   0



            3                             2
   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]



    reduced Critpair - Polynom :


   0



                       3              2
   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]


     There are

   3

     Groebner Basis Polynomials.


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

                                2            3     2
   (8)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2               2
--R   - 2y x  - y x - y - 6x  - 3x + 3
--R
--R
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R            3               3              2              2
--R   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   y x - y + x + 3
--R
--R
--R
--R            2               2
--R   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   4y + 4x  - 6x - 12
--R
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3      2
--R   - 4x  + 10x  + 10x
--R
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   2y + 2x  - 3x - 6
--R
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3     2
--R   - 2x  + 5x  + 5x
--R
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          3             3
--R   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R            3                             2
--R   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                       3              2
--R   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]
--R
--R
--R     There are
--R
--R   3
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R                                2            3     2
--R   (8)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--R                  Type: List DistributedMultivariatePolynomial([y,x],Integer)
--E 8

--S 9 of 24
b1:HDMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1)
 

            2            2
   (9)  3y x  + 2y x + 9x  + y + 5x - 3
            Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R            2            2
--R   (9)  3y x  + 2y x + 9x  + y + 5x - 3
--R            Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 9

--S 10 of 24
b2:HDMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1)
 

             3     3           2
   (10)  2y x  + 6x  - y x - 2x  - y - 3x + 3
            Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R             3     3           2
--R   (10)  2y x  + 6x  - y x - 2x  - y - 3x + 3
--R            Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 10

--S 11 of 24
b3:HDMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2)
 

            3      2     3     2
   (11)  y x  + y x  + 3x  + 2x
            Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R            3      2     3     2
--R   (11)  y x  + y x  + 3x  + 2x
--R            Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 11

--S 12 of 24
bn:=[b1,b2,b3]
 

   (12)
        2            2                   3     3           2
   [3y x  + 2y x + 9x  + y + 5x - 3, 2y x  + 6x  - y x - 2x  - y - 3x + 3,
       3      2     3     2
    y x  + y x  + 3x  + 2x ]
       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R   (12)
--R        2            2                   3     3           2
--R   [3y x  + 2y x + 9x  + y + 5x - 3, 2y x  + 6x  - y x - 2x  - y - 3x + 3,
--R       3      2     3     2
--R    y x  + y x  + 3x  + 2x ]
--R       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 12

--S 13 of 24
euclideanGroebner(bn)
 

            2                                 2
   (13)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R            2                                 2
--R   (13)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
--R       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 13

--S 14 of 24
euclideanGroebner(bn,"redcrit")
 


    reduced Critpair - Polynom :


         2           2
   - 2y x  - y x - 6x  - y - 3x + 3




    reduced Critpair - Polynom :


   y x - y + x + 3




    reduced Critpair - Polynom :


     2
   4x  + 4y - 6x - 12




    reduced Critpair - Polynom :


     2
   2x  + 2y - 3x - 6




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


       2
   - 2y  + 5y + 8x + 3




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

            2                                 2
   (14)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2           2
--R   - 2y x  - y x - 6x  - y - 3x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   y x - y + x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R     2
--R   4x  + 4y - 6x - 12
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R     2
--R   2x  + 2y - 3x - 6
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       2
--R   - 2y  + 5y + 8x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R            2                                 2
--R   (14)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
--R       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 14

--S 15 of 24
euclideanGroebner(bn,"info")
 

   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





            3               3              2              2
   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]


            2               2
   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]


            2                                         2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]


            2                                         2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]


          2             2
   [[ci= x ,tci= 4,cj= x ,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 2,tD= 2]]


                         2            2            2
   [[ci= y x,tci= 4,cj= x ,tcj= 4,c= y ,tc= 5,rc= y ,trc= 4,tH= 3,tD= 2]]


                         2            2
   [[ci= y x,tci= 4,cj= y ,tcj= 4,c= y ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 1]]


            3                             2
   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 0]]


     There are

   3

     Groebner Basis Polynomials.


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

            2                                 2
   (15)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R            3               3              2              2
--R   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]
--R
--R
--R            2               2
--R   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]
--R
--R
--R            2                                         2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]
--R
--R
--R            2                                         2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]
--R
--R
--R          2             2
--R   [[ci= x ,tci= 4,cj= x ,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 2,tD= 2]]
--R
--R
--R                         2            2            2
--R   [[ci= y x,tci= 4,cj= x ,tcj= 4,c= y ,tc= 5,rc= y ,trc= 4,tH= 3,tD= 2]]
--R
--R
--R                         2            2
--R   [[ci= y x,tci= 4,cj= y ,tcj= 4,c= y ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 1]]
--R
--R
--R            3                             2
--R   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 0]]
--R
--R
--R     There are
--R
--R   3
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R            2                                 2
--R   (15)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
--R       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 15

--S 16 of 24
euclideanGroebner(bn,"info","redcrit")
 


    reduced Critpair - Polynom :


         2           2
   - 2y x  - y x - 6x  - y - 3x + 3



   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





            3               3              2              2
   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


   y x - y + x + 3



            2               2
   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]



    reduced Critpair - Polynom :


     2
   4x  + 4y - 6x - 12



            2                                         2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]



    reduced Critpair - Polynom :


     2
   2x  + 2y - 3x - 6



            2                                         2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]



    reduced Critpair - Polynom :


   0



          2             2
   [[ci= x ,tci= 4,cj= x ,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 2,tD= 2]]



    reduced Critpair - Polynom :


       2
   - 2y  + 5y + 8x + 3



                         2            2            2
   [[ci= y x,tci= 4,cj= x ,tcj= 4,c= y ,tc= 5,rc= y ,trc= 4,tH= 3,tD= 2]]



    reduced Critpair - Polynom :


   0



                         2            2
   [[ci= y x,tci= 4,cj= y ,tcj= 4,c= y ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 1]]



    reduced Critpair - Polynom :


   0



            3                             2
   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 0]]


     There are

   3

     Groebner Basis Polynomials.


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

            2                                 2
   (16)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2           2
--R   - 2y x  - y x - 6x  - y - 3x + 3
--R
--R
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R            3               3              2              2
--R   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   y x - y + x + 3
--R
--R
--R
--R            2               2
--R   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R     2
--R   4x  + 4y - 6x - 12
--R
--R
--R
--R            2                                         2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R     2
--R   2x  + 2y - 3x - 6
--R
--R
--R
--R            2                                         2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= x ,trc= 4,tH= 2,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          2             2
--R   [[ci= x ,tci= 4,cj= x ,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 2,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       2
--R   - 2y  + 5y + 8x + 3
--R
--R
--R
--R                         2            2            2
--R   [[ci= y x,tci= 4,cj= x ,tcj= 4,c= y ,tc= 5,rc= y ,trc= 4,tH= 3,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                         2            2
--R   [[ci= y x,tci= 4,cj= y ,tcj= 4,c= y ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R            3                             2
--R   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 0]]
--R
--R
--R     There are
--R
--R   3
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R            2                                 2
--R   (16)  [2y  - 5y - 8x - 3,y x - y + x + 3,2x  + 2y - 3x - 6]
--R       Type: List HomogeneousDistributedMultivariatePolynomial([y,x],Integer)
--E 16

--S 17 of 24
c1:GDMP([y,x],INT,DIRPROD(2,NNI)):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1)
 

             2                2
   (17)  3y x  + 2y x + y + 9x  + 5x - 3
Type: GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R             2                2
--R   (17)  3y x  + 2y x + y + 9x  + 5x - 3
--RType: GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 17

--S 18 of 24
c2:GDMP([y,x],INT,DIRPROD(2,NNI)):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1)
 

             3               3     2
   (18)  2y x  - y x - y + 6x  - 2x  - 3x + 3
Type: GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R             3               3     2
--R   (18)  2y x  - y x - y + 6x  - 2x  - 3x + 3
--RType: GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 18

--S 19 of 24
c3:GDMP([y,x],INT,DIRPROD(2,NNI)):= (3*x**3 + 2*x**2) + y*(x**3 + x**2)
 

            3      2     3     2
   (19)  y x  + y x  + 3x  + 2x
Type: GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R            3      2     3     2
--R   (19)  y x  + y x  + 3x  + 2x
--RType: GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 19

--S 20 of 24
cn:=[c1,c2,c3]
 

   (20)
        2                2               3               3     2
   [3y x  + 2y x + y + 9x  + 5x - 3, 2y x  - y x - y + 6x  - 2x  - 3x + 3,
       3      2     3     2
    y x  + y x  + 3x  + 2x ]
Type: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R   (20)
--R        2                2               3               3     2
--R   [3y x  + 2y x + y + 9x  + 5x - 3, 2y x  - y x - y + 6x  - 2x  - 3x + 3,
--R       3      2     3     2
--R    y x  + y x  + 3x  + 2x ]
--RType: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 20

--S 21 of 24
euclideanGroebner(cn)
 

                                 2            3     2
   (21)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
Type: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R                                 2            3     2
--R   (21)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--RType: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 21

--S 22 of 24
euclideanGroebner(cn,"redcrit")
 


    reduced Critpair - Polynom :


         2               2
   - 2y x  - y x - y - 6x  - 3x + 3




    reduced Critpair - Polynom :


   y x - y + x + 3




    reduced Critpair - Polynom :


          2
   4y + 4x  - 6x - 12




    reduced Critpair - Polynom :


       3      2
   - 4x  + 10x  + 10x




    reduced Critpair - Polynom :


          2
   2y + 2x  - 3x - 6




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


       3     2
   - 2x  + 5x  + 5x




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

                                 2            3     2
   (22)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
Type: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2               2
--R   - 2y x  - y x - y - 6x  - 3x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   y x - y + x + 3
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   4y + 4x  - 6x - 12
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3      2
--R   - 4x  + 10x  + 10x
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   2y + 2x  - 3x - 6
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3     2
--R   - 2x  + 5x  + 5x
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R                                 2            3     2
--R   (22)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--RType: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 22

--S 23 of 24
euclideanGroebner(cn,"info")
 

   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





            3               3              2              2
   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]


            2               2
   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]


            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]


                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]


            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]


   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]


                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]


          3             3
   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]


            3                             2
   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]


                       3              2
   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]


     There are

   3

     Groebner Basis Polynomials.


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

                                 2            3     2
   (23)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
Type: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R            3               3              2              2
--R   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]
--R
--R
--R            2               2
--R   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]
--R
--R
--R   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R          3             3
--R   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]
--R
--R
--R            3                             2
--R   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]
--R
--R
--R                       3              2
--R   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]
--R
--R
--R     There are
--R
--R   3
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R                                 2            3     2
--R   (23)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--RType: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 23

--S 24 of 24
euclideanGroebner(cn,"info","redcrit")
 


    reduced Critpair - Polynom :


         2               2
   - 2y x  - y x - y - 6x  - 3x + 3



   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





            3               3              2              2
   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


   y x - y + x + 3



            2               2
   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]



    reduced Critpair - Polynom :


          2
   4y + 4x  - 6x - 12



            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]



    reduced Critpair - Polynom :


       3      2
   - 4x  + 10x  + 10x



                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


          2
   2y + 2x  - 3x - 6



            2
   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]



    reduced Critpair - Polynom :


   0



   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


       3     2
   - 2x  + 5x  + 5x



                                                 3
   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]



    reduced Critpair - Polynom :


   0



          3             3
   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]



    reduced Critpair - Polynom :


   0



            3                             2
   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]



    reduced Critpair - Polynom :


   0



                       3              2
   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]


     There are

   3

     Groebner Basis Polynomials.


       THE GROEBNER BASIS over EUCLIDEAN DOMAIN

                                 2            3     2
   (24)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
Type: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2               2
--R   - 2y x  - y x - y - 6x  - 3x + 3
--R
--R
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R            3               3              2              2
--R   [[ci= y x ,tci= 7,cj= y x ,tcj= 4,c= y x ,tc= 6,rc= y x ,trc= 6,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   y x - y + x + 3
--R
--R
--R
--R            2               2
--R   [[ci= y x ,tci= 6,cj= y x ,tcj= 6,c= y x,tc= 4,rc= y x,trc= 4,tH= 1,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   4y + 4x  - 6x - 12
--R
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 2,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3      2
--R   - 4x  + 10x  + 10x
--R
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          2
--R   2y + 2x  - 3x - 6
--R
--R
--R
--R            2
--R   [[ci= y x ,tci= 6,cj= y x,tcj= 4,c= y x,tc= 5,rc= y,trc= 4,tH= 3,tD= 4]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R   [[ci= y,tci= 4,cj= y,tcj= 4,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       3     2
--R   - 2x  + 5x  + 5x
--R
--R
--R
--R                                                 3
--R   [[ci= y x,tci= 4,cj= y,tcj= 4,c= y,tc= 5,rc= x ,trc= 3,tH= 3,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          3             3
--R   [[ci= x ,tci= 3,cj= x ,tcj= 3,c= 0,tc= 0,rc= 0,trc= 0,tH= 3,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R            3                             2
--R   [[ci= y x ,tci= 4,cj= y x,tcj= 4,c= y x ,tc= 3,rc= 0,trc= 0,tH= 3,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                       3              2
--R   [[ci= y,tci= 4,cj= x ,tcj= 3,c= y x ,tc= 5,rc= 0,trc= 0,tH= 3,tD= 0]]
--R
--R
--R     There are
--R
--R   3
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS over EUCLIDEAN DOMAIN
--R
--R                                 2            3     2
--R   (24)  [y x - y + x + 3,2y + 2x  - 3x - 6,2x  - 5x  - 5x]
--RType: List GeneralDistributedMultivariatePolynomial([y,x],Integer,DirectProduct(2,NonNegativeInteger))
--E 24

)spool
 
Starts dribbling to conformal.output (2010/3/27, 18:24:35).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 18
C := Complex DoubleFloat                -- Complex Numbers
 

   (1)  Complex DoubleFloat
                                                                 Type: Domain
--R 
--R
--R   (1)  Complex DoubleFloat
--R                                                                 Type: Domain
--E 1

--S 2 of 18
S := Segment DoubleFloat                -- Draw ranges
 

   (2)  Segment DoubleFloat
                                                                 Type: Domain
--R 
--R
--R   (2)  Segment DoubleFloat
--R                                                                 Type: Domain
--E 2

--S 3 of 18
R3 := POINT DoubleFloat                         -- points in 3-space
 

   (3)  Point DoubleFloat
                                                                 Type: Domain
--R 
--R
--R   (3)  Point DoubleFloat
--R                                                                 Type: Domain
--E 3
--S 4 of 18
conformalDraw: (C -> C, S, S, PI, PI, String) -> VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 18
conformalDraw(f, rRange, tRange, rSteps, tSteps, coord) ==
  transformC :=
    coord = "polar" => polar2Complex
    cartesian2Complex
  cm := makeConformalMap(f, transformC)
  sp := createThreeSpace()
  adaptGrid(sp, cm, rRange, tRange, rSteps, tSteps)
  makeViewport3D(sp, "Conformal Map")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
--S 6 of 18
riemannConformalDraw: (C -> C, S, S, PI, PI, String) -> VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 18
riemannConformalDraw(f, rRange, tRange, rSteps, tSteps, coord) ==
  transformC :=
    coord = "polar" => polar2Complex
    cartesian2Complex
  sp := createThreeSpace()
  cm := makeRiemannConformalMap(f, transformC)
  adaptGrid(sp, cm, rRange, tRange, rSteps, tSteps)
  -- add an invisible point at the north pole for scaling
  curve(sp, [point [0,0,2.0@DoubleFloat,0], point [0,0, 2.0@DoubleFloat,0]])
  makeViewport3D(sp, "Conformal Map on the Riemann Sphere")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
--S 8 of 18
adaptGrid(sp, f, uRange, vRange,  uSteps, vSteps) ==
  delU := (hi(uRange) - lo(uRange))/uSteps
  delV := (hi(vRange) - lo(vRange))/vSteps
  uSteps := uSteps + 1; vSteps := vSteps + 1
  u := lo uRange
  -- draw the coodinate lines in the v direction
  for i in 1..uSteps repeat
    -- create a curve 'c' which fixes the current value of 'u'
    c := curryLeft(f,u)
    cf := (t:DoubleFloat):DoubleFloat +-> 0
    -- draw the 'v' coordinate line
    makeObject(c, vRange::Segment Float, colorFunction == cf, space == sp, _
               tubeRadius == 0.02,  tubePoints == 6)
    u := u + delU
  v := lo vRange
  -- draw the coodinate lines in the u direction
  for i in 1..vSteps repeat
    -- create a curve 'c' which fixes the current value of 'v'
    c := curryRight(f,v)
    cf := (t:DoubleFloat):DoubleFloat +-> 1
    -- draw the 'u' coordinate line
    makeObject(c, uRange::Segment Float, colorFunction == cf, space == sp, _
               tubeRadius == 0.02,  tubePoints == 6)
    v := v + delV
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8
--S 9 of 18
riemannTransform(z) ==
  r := sqrt norm z
  cosTheta := (real z)/r
  sinTheta := (imag z)/r
  cp := 4*r/(4+r**2)
  sp := sqrt(1-cp*cp)
  if r>2 then sp := -sp
  point [cosTheta*cp, sinTheta*cp, -sp + 1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9
--S 10 of 18
cartesian2Complex(r:DoubleFloat, i:DoubleFloat):C == complex(r, i)
 
   Function declaration cartesian2Complex : (DoubleFloat,DoubleFloat)
       -> Complex DoubleFloat has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration cartesian2Complex : (DoubleFloat,DoubleFloat)
--R       -> Complex DoubleFloat has been added to workspace.
--R                                                                   Type: Void
--E 10
--S 11 of 18
polar2Complex(r:DoubleFloat, th:DoubleFloat):C == complex(r*cos(th), r*sin(th))
 
   Function declaration polar2Complex : (DoubleFloat,DoubleFloat) -> 
      Complex DoubleFloat has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration polar2Complex : (DoubleFloat,DoubleFloat) -> 
--R      Complex DoubleFloat has been added to workspace.
--R                                                                   Type: Void
--E 11
--S 12 of 18
makeConformalMap(f, transformC) ==
  (u:DoubleFloat,v:DoubleFloat):R3 +->
    z := f transformC(u, v)
    point [real z, imag z, 0.0@DoubleFloat]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12
--S 13 of 18
makeRiemannConformalMap(f, transformC) ==
  (u:DoubleFloat, v:DoubleFloat):R3 +-> riemannTransform f transformC(u, v)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13
--S 14 of 18
riemannSphereDraw: (S, S, PI, PI, String) -> VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 18
riemannSphereDraw(rRange, tRange, rSteps, tSteps, coord) ==
  transformC :=
    coord = "polar" => polar2Complex
    cartesian2Complex
  grid := (u:DoubleFloat , v:DoubleFloat): R3 +->
    z1 := transformC(u, v)
    point [real z1, imag z1, 0]
  sp := createThreeSpace()
  adaptGrid(sp, grid, rRange, tRange, rSteps, tSteps)
  connectingLines(sp, grid, rRange, tRange, rSteps, tSteps)
  makeObject(riemannSphere, 0..2*%pi, 0..%pi, space == sp)
  f := (z:C):C +-> z
  cm := makeRiemannConformalMap(f, transformC)
  adaptGrid(sp, cm, rRange, tRange, rSteps, tSteps)
  makeViewport3D(sp, "Riemann Sphere")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15
--S 16 of 18
connectingLines(sp, f, uRange, vRange, uSteps, vSteps) ==
  delU := (hi(uRange) - lo(uRange))/uSteps
  delV := (hi(vRange) - lo(vRange))/vSteps
  uSteps := uSteps + 1; vSteps := vSteps + 1
  u := lo uRange
  -- for each grid point
  for i in 1..uSteps repeat
    v := lo vRange
    for j in 1..vSteps repeat
      p1 := f(u,v)
      p2 := riemannTransform complex(p1.1, p1.2)
      fun := lineFromTo(p1,p2)
      cf := (t:DoubleFloat):DoubleFloat +-> 3
      makeObject(fun, 0..1, space == sp, tubePoints == 4, tubeRadius == 0.01,
                 colorFunction == cf)
      v := v + delV
    u := u + delU
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 18
riemannSphere(u,v) ==
  sv := sin(v)
  0.99@DoubleFloat*(point [cos(u)*sv, sin(u)*sv, cos(v),0.0@DoubleFloat]) +
    point [0.0@DoubleFloat, 0.0@DoubleFloat, 1.0@DoubleFloat, 4.0@DoubleFloat]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17
--S 18 of 18
lineFromTo(p1, p2) ==
  d := p2 - p1
  (t:DoubleFloat):Point DoubleFloat +-> p1 + t*d
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18
)spool
 
Starts dribbling to sqrt3.output (2010/3/27, 18:40:59).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 23
t1:=(sqrt(3)-3)*(sqrt(3)+1)/6
 

           +-+
          \|3
   (1)  - ----
            3
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (1)  - ----
--R            3
--R                                                        Type: AlgebraicNumber
--E 1

--S 2 of 23
tt1:=-1/sqrt(3)
 

           +-+
          \|3
   (2)  - ----
            3
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (2)  - ----
--R            3
--R                                                        Type: AlgebraicNumber
--E 2

--S 3 of 23
t2:=sqrt(3)/6
 

         +-+
        \|3
   (3)  ----
          6
                                                        Type: AlgebraicNumber
--R 
--R
--R         +-+
--R        \|3
--R   (3)  ----
--R          6
--R                                                        Type: AlgebraicNumber
--E 3

--S 4 of 23
t1+t2
 

           +-+
          \|3
   (4)  - ----
            6
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (4)  - ----
--R            6
--R                                                        Type: AlgebraicNumber
--E 4

--S 5 of 23
tt1+t2
 

           +-+
          \|3
   (5)  - ----
            6
                                                        Type: AlgebraicNumber
--R 
--R
--R           +-+
--R          \|3
--R   (5)  - ----
--R            6
--R                                                        Type: AlgebraicNumber
--E 5

--S 6 of 23
RAN ==> RECLOS FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 23
x1:=(sqrt(3)$RAN-3)*(sqrt(3)$RAN+1)/6
 

         1  +-+   1  +-+   1  +-+   1
   (7)  (- \|3  - -)\|3  + - \|3  - -
         6        2        6        2
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         1  +-+   1  +-+   1  +-+   1
--R   (7)  (- \|3  - -)\|3  + - \|3  - -
--R         6        2        6        2
--R                                           Type: RealClosure Fraction Integer
--E 7

--S 8 of 23
xx1:=-1/sqrt(3)$RAN
 

          1  +-+
   (8)  - - \|3
          3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          1  +-+
--R   (8)  - - \|3
--R          3
--R                                           Type: RealClosure Fraction Integer
--E 8

--S 9 of 23
(x1=xx1)@Boolean
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 23
s3:=sqrt(3)$RAN
 

          +-+
   (10)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (10)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 10

--S 11 of 23
(s3-3)*(s3+1)/6
 

           1  +-+
   (11)  - - \|3
           3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           1  +-+
--R   (11)  - - \|3
--R           3
--R                                           Type: RealClosure Fraction Integer
--E 11

--S 12 of 23
f3:=sqrt(3,5)$RAN
 

         5+-+
   (12)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         5+-+
--R   (12)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 23
f25:=sqrt(1/25,5)$RAN
 

          +--+
          | 1
   (13)  5|--
         \|25
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          | 1
--R   (13)  5|--
--R         \|25
--R                                           Type: RealClosure Fraction Integer
--E 13

--S 14 of 23
f32:=sqrt(32/5,5)$RAN
 

          +--+
          |32
   (14)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |32
--R   (14)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 14

--S 15 of 23
f27:=sqrt(27/5,5)$RAN
 

          +--+
          |27
   (15)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |27
--R   (15)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 23
expr1:=sqrt(f32-f27,3)
 

          +---------------+
          |   +--+    +--+
          |   |27     |32
   (16)  3|- 5|--  + 5|--
         \|  \| 5    \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +---------------+
--R          |   +--+    +--+
--R          |   |27     |32
--R   (16)  3|- 5|--  + 5|--
--R         \|  \| 5    \| 5
--R                                           Type: RealClosure Fraction Integer
--E 16

--S 17 of 23
expr2:=(1+f3-f3^2)
 

           5+-+2   5+-+
   (17)  - \|3   + \|3  + 1
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           5+-+2   5+-+
--R   (17)  - \|3   + \|3  + 1
--R                                           Type: RealClosure Fraction Integer
--E 17

--S 18 of 23
expr1-f25*expr2
 

   (18)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (18)  0
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 23
s:=sqrt(190)$RAN+sqrt(1751)$RAN-sqrt(208)$RAN-sqrt(1698)$RAN
 

            +----+    +---+    +----+    +---+
   (19)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (19)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 19

--S 20 of 23
approximate(s,10^-15)::Float
 

   (20)  - 0.2341060678 6455900874 E -10
                                                                  Type: Float
--R 
--R
--R   (20)  - 0.2341060678 6455900874 E -10
--R                                                                  Type: Float
--E 20

--S 21 of 23
t:=sqrt(190)+sqrt(1751)-sqrt(208)-sqrt(1698)
 

          +----+    +----+    +---+     +--+
   (21)  \|1751  - \|1698  + \|190  - 4\|13
                                                        Type: AlgebraicNumber
--R 
--R
--R          +----+    +----+    +---+     +--+
--R   (21)  \|1751  - \|1698  + \|190  - 4\|13
--R                                                        Type: AlgebraicNumber
--E 21

--S 22 of 23
digits(30)
 

   (22)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  20
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 23
numeric t - approximate(s,10^-30)::Float
 

   (23)  - 0.5522026336 5 E -29
                                                                  Type: Float
--R 
--R
--R   (23)  - 0.5522026336 5 E -29
--R                                                                  Type: Float
--E 23

)spool 
 
Starts dribbling to SparseTable.output (2010/3/27, 18:46:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
t: SparseTable(Integer, String, "Try again!") := table()
 

   (1)  table()
                                 Type: SparseTable(Integer,String,Try again!)
--R 
--R
--R   (1)  table()
--R                                 Type: SparseTable(Integer,String,Try again!)
--E 1

--S 2 of 7
t.3 := "Number three"
 

   (2)  "Number three"
                                                                 Type: String
--R 
--R
--R   (2)  "Number three"
--R                                                                 Type: String
--E 2

--S 3 of 7
t.4 := "Number four"
 

   (3)  "Number four"
                                                                 Type: String
--R 
--R
--R   (3)  "Number four"
--R                                                                 Type: String
--E 3

--S 4 of 7
t.3
 

   (4)  "Number three"
                                                                 Type: String
--R 
--R
--R   (4)  "Number three"
--R                                                                 Type: String
--E 4

--S 5 of 7
t.2
 

   (5)  "Try again!"
                                                                 Type: String
--R 
--R
--R   (5)  "Try again!"
--R                                                                 Type: String
--E 5

--S 6 of 7
keys t
 

   (6)  [4,3]
                                                           Type: List Integer
--R 
--R
--R   (6)  [4,3]
--R                                                           Type: List Integer
--E 6

--S 7 of 7
entries t
 

   (7)  ["Number four","Number three"]
                                                            Type: List String
--R 
--R
--R   (7)  ["Number four","Number three"]
--R                                                            Type: List String
--E 7
)spool
 
Starts dribbling to assign.output (2010/3/27, 18:23:9).
)set message test on
 
)set message auto off
 
)clear all
 

-- This file shows the difference between assignments and rewrite
-- rules.
--S 1 of 11
a := 1
 

   (1)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 11
b := a         -- the value of b is now 1
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 11
b              -- see, told you
 

   (3)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 11
a := 2         -- what is the value of b?
 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 11
b              -- it is the value it had AT ASSIGNMENT
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 11
c == 1         -- c is a rule
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 11
c              -- it will evaluate to 1
 
   Compiling body of rule c to compute value of type PositiveInteger 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule c to compute value of type PositiveInteger 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 11
d == c         -- d is a rule that will evaluate to c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 11
d
 
   Compiling body of rule d to compute value of type PositiveInteger 

   (9)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule d to compute value of type PositiveInteger 
--R
--R   (9)  1
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 11
c == 2         -- we have changed the rule for c
 
   Compiled code for c has been cleared.
   Compiled code for d has been cleared.
   1 old definition(s) deleted for function or rule c 
                                                                   Type: Void
--R 
--R   Compiled code for c has been cleared.
--R   Compiled code for d has been cleared.
--R   1 old definition(s) deleted for function or rule c 
--R                                                                   Type: Void
--E 10

--S 11 of 11
d              -- and so the ultimate value computed from d will change
 
   Compiling body of rule c to compute value of type PositiveInteger 
   Compiling body of rule d to compute value of type PositiveInteger 

   (11)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling body of rule c to compute value of type PositiveInteger 
--R   Compiling body of rule d to compute value of type PositiveInteger 
--R
--R   (11)  2
--R                                                        Type: PositiveInteger
--E 11
)spool
 
Starts dribbling to Complex.output (2010/3/27, 18:41:50).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
a := complex(4/3,5/2)
 

        4   5
   (1)  - + - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (1)  - + - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 1

--S 2 of 16
b := complex(4/3,-5/2)
 

        4   5
   (2)  - - - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (2)  - - - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 2

--S 3 of 16
a + b
 

        8
   (3)  -
        3
                                               Type: Complex Fraction Integer
--R 
--R
--R        8
--R   (3)  -
--R        3
--R                                               Type: Complex Fraction Integer
--E 3

--S 4 of 16
a - b
 

   (4)  5%i
                                               Type: Complex Fraction Integer
--R 
--R
--R   (4)  5%i
--R                                               Type: Complex Fraction Integer
--E 4

--S 5 of 16
a * b
 

        289
   (5)  ---
         36
                                               Type: Complex Fraction Integer
--R 
--R
--R        289
--R   (5)  ---
--R         36
--R                                               Type: Complex Fraction Integer
--E 5

--S 6 of 16
a / b
 

          161   240
   (6)  - --- + --- %i
          289   289
                                               Type: Complex Fraction Integer
--R 
--R
--R          161   240
--R   (6)  - --- + --- %i
--R          289   289
--R                                               Type: Complex Fraction Integer
--E 6

--S 7 of 16
% :: Fraction Complex Integer
 

        - 15 + 8%i
   (7)  ----------
         15 + 8%i
                                               Type: Fraction Complex Integer
--R 
--R
--R        - 15 + 8%i
--R   (7)  ----------
--R         15 + 8%i
--R                                               Type: Fraction Complex Integer
--E 7

--S 8 of 16
3.4 + 6.7 * %i
 

   (8)  3.4 + 6.7 %i
                                                          Type: Complex Float
--R 
--R
--R   (8)  3.4 + 6.7 %i
--R                                                          Type: Complex Float
--E 8

--S 9 of 16
conjugate a
 

        4   5
   (9)  - - - %i
        3   2
                                               Type: Complex Fraction Integer
--R 
--R
--R        4   5
--R   (9)  - - - %i
--R        3   2
--R                                               Type: Complex Fraction Integer
--E 9

--S 10 of 16
norm a
 

         289
   (10)  ---
          36
                                                       Type: Fraction Integer
--R 
--R
--R         289
--R   (10)  ---
--R          36
--R                                                       Type: Fraction Integer
--E 10

--S 11 of 16
real a
 

         4
   (11)  -
         3
                                                       Type: Fraction Integer
--R 
--R
--R         4
--R   (11)  -
--R         3
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 16
imag a
 

         5
   (12)  -
         2
                                                       Type: Fraction Integer
--R 
--R
--R         5
--R   (12)  -
--R         2
--R                                                       Type: Fraction Integer
--E 12

--S 13 of 16
gcd(13 - 13*%i,31 + 27*%i)
 

   (13)  5 + %i
                                                        Type: Complex Integer
--R 
--R
--R   (13)  5 + %i
--R                                                        Type: Complex Integer
--E 13

--S 14 of 16
lcm(13 - 13*%i,31 + 27*%i)
 

   (14)  143 - 39%i
                                                        Type: Complex Integer
--R 
--R
--R   (14)  143 - 39%i
--R                                                        Type: Complex Integer
--E 14

--S 15 of 16
factor(13 - 13*%i)
 

   (15)  - (1 + %i)(2 + 3%i)(3 + 2%i)
                                               Type: Factored Complex Integer
--R 
--R
--R   (15)  - (1 + %i)(2 + 3%i)(3 + 2%i)
--R                                               Type: Factored Complex Integer
--E 15

--S 16 of 16
factor complex(2,0)
 

                      2
   (16)  - %i (1 + %i)
                                               Type: Factored Complex Integer
--R 
--R
--R                      2
--R   (16)  - %i (1 + %i)
--R                                               Type: Factored Complex Integer
--E 16
)spool
 
Starts dribbling to numbers.output (2010/3/27, 18:30:22).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 76
x := factorial(200)
 

   (1)
  7886578673647905035523632139321850622951359776871732632947425332443594499634_
   033429203042840119846239041772121389196388302576427902426371050619266249528_
   299311134628572707633172373969889439224456214516642402540332918641312274282_
   948532775242424075739032403212574055795686602260319041703240623517008587961_
   78922222789623703897374720000000000000000000000000000000000000000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (1)
--R  7886578673647905035523632139321850622951359776871732632947425332443594499634_
--R   033429203042840119846239041772121389196388302576427902426371050619266249528_
--R   299311134628572707633172373969889439224456214516642402540332918641312274282_
--R   948532775242424075739032403212574055795686602260319041703240623517008587961_
--R   78922222789623703897374720000000000000000000000000000000000000000000000000
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 76
y := 2**90 - 1
 

   (2)  1237940039285380274899124223
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1237940039285380274899124223
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 76
x + y
 

   (3)
  7886578673647905035523632139321850622951359776871732632947425332443594499634_
   033429203042840119846239041772121389196388302576427902426371050619266249528_
   299311134628572707633172373969889439224456214516642402540332918641312274282_
   948532775242424075739032403212574055795686602260319041703240623517008587961_
   78922222789623703897374720000000000000000000001237940039285380274899124223
                                                        Type: PositiveInteger
--R 
--R
--R   (3)
--R  7886578673647905035523632139321850622951359776871732632947425332443594499634_
--R   033429203042840119846239041772121389196388302576427902426371050619266249528_
--R   299311134628572707633172373969889439224456214516642402540332918641312274282_
--R   948532775242424075739032403212574055795686602260319041703240623517008587961_
--R   78922222789623703897374720000000000000000000001237940039285380274899124223
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 76
x - y
 

   (4)
  7886578673647905035523632139321850622951359776871732632947425332443594499634_
   033429203042840119846239041772121389196388302576427902426371050619266249528_
   299311134628572707633172373969889439224456214516642402540332918641312274282_
   948532775242424075739032403212574055795686602260319041703240623517008587961_
   78922222789623703897374719999999999999999999998762059960714619725100875777
                                                        Type: PositiveInteger
--R 
--R
--R   (4)
--R  7886578673647905035523632139321850622951359776871732632947425332443594499634_
--R   033429203042840119846239041772121389196388302576427902426371050619266249528_
--R   299311134628572707633172373969889439224456214516642402540332918641312274282_
--R   948532775242424075739032403212574055795686602260319041703240623517008587961_
--R   78922222789623703897374719999999999999999999998762059960714619725100875777
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 76
x * y
 

   (5)
  9763111513082929821843631196609502257766429667654140423707949648813338983407_
   032918809235547978281276568726017975734913119466356078732929100728088106228_
   471338396755093151069532609217447970141651251638848591388190535247585868963_
   019469887899504821090561806743717655381133973032509524956986554360537566475_
   497856969235918273095211823926950507033823968598425600000000000000000000000_
   00000000000000000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (5)
--R  9763111513082929821843631196609502257766429667654140423707949648813338983407_
--R   032918809235547978281276568726017975734913119466356078732929100728088106228_
--R   471338396755093151069532609217447970141651251638848591388190535247585868963_
--R   019469887899504821090561806743717655381133973032509524956986554360537566475_
--R   497856969235918273095211823926950507033823968598425600000000000000000000000_
--R   00000000000000000000000000
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 76
factor(x)
 

   (6)
      197 97 49 32  19  16  11  10  8  6  6  5  4  4  4  3  3  3  2  2  2  2  2
     2   3  5  7  11  13  17  19  23 29 31 37 41 43 47 53 59 61 67 71 73 79 83
  *
       2  2
     89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181
  *
     191 193 197 199
                                                       Type: Factored Integer
--R 
--R
--R   (6)
--R      197 97 49 32  19  16  11  10  8  6  6  5  4  4  4  3  3  3  2  2  2  2  2
--R     2   3  5  7  11  13  17  19  23 29 31 37 41 43 47 53 59 61 67 71 73 79 83
--R  *
--R       2  2
--R     89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181
--R  *
--R     191 193 197 199
--R                                                       Type: Factored Integer
--E 6

--S 7 of 76
factor(y)
 

         3
   (7)  3 7 11 19 31 73 151 331 631 23311 18837001
                                                       Type: Factored Integer
--R 
--R
--R         3
--R   (7)  3 7 11 19 31 73 151 331 631 23311 18837001
--R                                                       Type: Factored Integer
--E 7

)clear all
 

--S 8 of 76
sqrt(2.0)
 

   (1)  1.4142135623 730950488
                                                                  Type: Float
--R 
--R
--R   (1)  1.4142135623 730950488
--R                                                                  Type: Float
--E 8

--S 9 of 76
numeric %pi
 

   (2)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 897932385
--R                                                                  Type: Float
--E 9

--S 10 of 76
exp(1.0)
 

   (3)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (3)  2.7182818284 590452354
--R                                                                  Type: Float
--E 10

--S 11 of 76
exp(sqrt(163.0) * %pi)
 

   (4)  26253741 2640768743.97
                                                                  Type: Float
--R 
--R
--R   (4)  26253741 2640768743.97
--R                                                                  Type: Float
--E 11

--S 12 of 76
sin(%pi/6.)
 

   (5)  0.5
                                                                  Type: Float
--R 
--R
--R   (5)  0.5
--R                                                                  Type: Float
--E 12

)clear all
 

--S 13 of 76
1/4 - 1/5
 

         1
   (1)  --
        20
                                                       Type: Fraction Integer
--R 
--R
--R         1
--R   (1)  --
--R        20
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 76
f := (x**2 + 1)/(x - 1)
 

         2
        x  + 1
   (2)  ------
         x - 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 1
--R   (2)  ------
--R         x - 1
--R                                            Type: Fraction Polynomial Integer
--E 14

--S 15 of 76
g := (x**2 - 3*x + 2)/(x + 2)
 

         2
        x  - 3x + 2
   (3)  -----------
           x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  - 3x + 2
--R   (3)  -----------
--R           x + 2
--R                                            Type: Fraction Polynomial Integer
--E 15

--S 16 of 76
f * g
 

         3     2
        x  - 2x  + x - 2
   (4)  ----------------
              x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         3     2
--R        x  - 2x  + x - 2
--R   (4)  ----------------
--R              x + 2
--R                                            Type: Fraction Polynomial Integer
--E 16

)clear all
 

--S 17 of 76
numeric(%pi, 500)
 

   (1)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (1)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 17

--S 18 of 76
digits 500
 

   (2)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  20
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 76
numeric %pi
 

   (3)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (3)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 19

)clear all
 

--S 20 of 76
F7 := PF 7
 

   (1)  PrimeField 7
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 7
--R                                                                 Type: Domain
--E 20

--S 21 of 76
F49 := FF(7,2)
 

   (2)  FiniteField(7,2)
                                                                 Type: Domain
--R 
--R
--R   (2)  FiniteField(7,2)
--R                                                                 Type: Domain
--E 21

--S 22 of 76
definingPolynomial()$F49
 

         2
   (3)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R         2
--R   (3)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 22

--S 23 of 76
e := random()$F49 ; while e = 0 repeat e := random()$F49 ; e
 

   (4)  5
                                                       Type: FiniteField(7,2)
--R 
--R
--I   (4)  4%A + 3
--R                                                       Type: FiniteField(7,2)
--E 23

--S 24 of 76
norm e
 

   (5)  4
                                                           Type: PrimeField 7
--R 
--R
--I   (5)  4
--R                                                           Type: PrimeField 7
--E 24

--S 25 of 76
trace e
 

   (6)  3
                                                           Type: PrimeField 7
--R 
--R
--I   (6)  6
--R                                                           Type: PrimeField 7
--E 25

--S 26 of 76
order e
 

   (7)  6
                                                        Type: PositiveInteger
--R 
--R
--I   (7)  24
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 76
allElts := [index(i)$F49 for i in 1..48]
 

   (8)
   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
    6%A + 5, 6%A + 6]
                                                  Type: List FiniteField(7,2)
--R 
--R
--R   (8)
--R   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
--R    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
--R    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
--R    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
--R    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
--R    6%A + 5, 6%A + 6]
--R                                                  Type: List FiniteField(7,2)
--E 27

--S 28 of 76
reduce(+,allElts)
 

   (9)  0
                                                       Type: FiniteField(7,2)
--R 
--R
--R   (9)  0
--R                                                       Type: FiniteField(7,2)
--E 28

--S 29 of 76
[order e for e in allElts]
 

   (10)
   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
    48, 4, 24, 48, 48, 48, 48, 24]
                                                   Type: List PositiveInteger
--R 
--R
--R   (10)
--R   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
--R    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
--R    48, 4, 24, 48, 48, 48, 48, 24]
--R                                                   Type: List PositiveInteger
--E 29

--S 30 of 76
u:UP(x, F7) := x**2 + 1
 

          2
   (11)  x  + 1
                                   Type: UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R          2
--R   (11)  x  + 1
--R                                   Type: UnivariatePolynomial(x,PrimeField 7)
--E 30

--S 31 of 76
factor u
 

          2
   (12)  x  + 1
                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R          2
--R   (12)  x  + 1
--R                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--E 31

--S 32 of 76
u2:UP(x, F49) := u
 

          2
   (13)  x  + 1
                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R          2
--R   (13)  x  + 1
--R                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--E 32

--S 33 of 76
factor u2
 

   (14)  (x + %A)(x + 6%A)
                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R   (14)  (x + %A)(x + 6%A)
--R                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--E 33

)clear all
 
--S 34 of 76
f: NNI -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 76
f(n) == 2**n - 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 35

--S 36 of 76
factor f(7)
 
   Compiling function f with type NonNegativeInteger -> Integer 

   (3)  127
                                                       Type: Factored Integer
--R 
--R   Compiling function f with type NonNegativeInteger -> Integer 
--R
--R   (3)  127
--R                                                       Type: Factored Integer
--E 36

--S 37 of 76
ints := [n for n in 1..]
 

   (4)  [1,2,3,4,5,6,7,8,9,10,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (4)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                 Type: Stream PositiveInteger
--E 37

--S 28 of 76
primes := [x for x in ints | prime? x]
 

   (5)  [2,3,5,7,11,13,17,19,23,29,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (5)  [2,3,5,7,11,13,17,19,23,29,...]
--R                                                 Type: Stream PositiveInteger
--E 38

--S 39 of 76
primes.25
 

   (6)  97
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  97
--R                                                        Type: PositiveInteger
--E 39

--S 40 of 76
numbers := [f(n) for n in primes]
 

   (7)  [3,7,31,127,2047,8191,131071,524287,8388607,536870911,...]
                                                         Type: Stream Integer
--R 
--R
--R   (7)  [3,7,31,127,2047,8191,131071,524287,8388607,536870911,...]
--R                                                         Type: Stream Integer
--E 40

--S 41 of 76
factors := [factor n for n in numbers]
 

   (8)  [3,7,31,127,23 89,8191,131071,524287,47 178481,233 1103 2089,...]
                                                Type: Stream Factored Integer
--R 
--R
--R   (8)  [3,7,31,127,23 89,8191,131071,524287,47 178481,233 1103 2089,...]
--R                                                Type: Stream Factored Integer
--E 41

--S 42 of 76
nums := [x for x in numbers | not prime? x]
 

   (9)
   [2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207,
    140737488355327, 9007199254740991, 576460752303423487,
    147573952589676412927, ...]
                                                         Type: Stream Integer
--R 
--R
--R   (9)
--R   [2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207,
--R    140737488355327, 9007199254740991, 576460752303423487,
--R    147573952589676412927, ...]
--R                                                         Type: Stream Integer
--E 42

)clear all
 

--S 43 of 76
numbers := [n**2 - n + 41 for n in 0..40]
 

   (1)
   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
                                                           Type: List Integer
--R 
--R
--R   (1)
--R   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
--R    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
--R    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
--R                                                           Type: List Integer
--E 43

--S 44 of 76
[factor n for n in numbers]
 

   (2)
   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
                                                  Type: List Factored Integer
--R 
--R
--R   (2)
--R   [41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
--R    313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
--R    1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]
--R                                                  Type: List Factored Integer
--E 44

)clear all
 

--S 45 of 76
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 45

--S 46 of 76
differentiate(f x,x,7)
 

         (vii)
   (2)  f     (x)

                                                     Type: Expression Integer
--R 
--R
--R         (vii)
--R   (2)  f     (x)
--R
--R                                                     Type: Expression Integer
--E 46

--S 47 of 76
a := roman(1978 - 1965)
 

   (3)  XIII
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XIII
--R                                                           Type: RomanNumeral
--E 47

--S 48 of 76
x : UTS(ROMAN,'x,0) := x
 

   (4)  x
                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--R 
--R
--R   (4)  x
--R                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--E 48

--S 49 of 76
recip(1 - x - x**2)
 

   (5)
                 2        3      4         5         6        7          8
     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
   + 
         9           10      11
     LV x  + LXXXIX x   + O(x  )
                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--R 
--R
--R   (5)
--R                 2        3      4         5         6        7          8
--R     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
--R   + 
--R         9           10      11
--R     LV x  + LXXXIX x   + O(x  )
--R                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--E 49

--S 50 of 76
m : MATRIX FRAC ROMAN
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 50

--S 51 of 76
m := matrix [[1/(i + j) for i in 1..3] for j in 1..3]
 

        + I    I    I+
        |--   ---  --|
        |II   III  IV|
        |            |
        | I    I   I |
   (7)  |---  --   - |
        |III  IV   V |
        |            |
        | I    I    I|
        |--    -   --|
        +IV    V   VI+
                                           Type: Matrix Fraction RomanNumeral
--R 
--R
--R        + I    I    I+
--R        |--   ---  --|
--R        |II   III  IV|
--R        |            |
--R        | I    I   I |
--R   (7)  |---  --   - |
--R        |III  IV   V |
--R        |            |
--R        | I    I    I|
--R        |--    -   --|
--R        +IV    V   VI+
--R                                           Type: Matrix Fraction RomanNumeral
--E 51

--S 52 of 76
inverse m
 

        +LXXII   - CCXL    CLXXX +
        |                        |
   (8)  |- CCXL    CM     - DCCXX|
        |                        |
        +CLXXX   - DCCXX    DC   +
                                Type: Union(Matrix Fraction RomanNumeral,...)
--R 
--R
--R        +LXXII   - CCXL    CLXXX +
--R        |                        |
--R   (8)  |- CCXL    CM     - DCCXX|
--R        |                        |
--R        +CLXXX   - DCCXX    DC   +
--R                                Type: Union(Matrix Fraction RomanNumeral,...)
--E 52

--S 53 of 76
y := factorial 20
 

   (9)  2432902008176640000
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2432902008176640000
--R                                                        Type: PositiveInteger
--E 53

--S 54 of 76
roman y
 

   (10)
  ((((((((((((((((I))))))))))))))))((((((((((((((((I)))))))))))))))) ((((((((((
  (((((I)))))))))))))))(((((((((((((((I)))))))))))))))(((((((((((((((I)))))))))
  ))))))(((((((((((((((I))))))))))))))) ((((((((((((((I))))))))))))))((((((((((
  ((((I))))))))))))))((((((((((((((I)))))))))))))) (((((((((((((I)))))))))))))(
  ((((((((((((I))))))))))))) ((((((((((((I))))))))))))((((((((((((I))))))))))))
  ((((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((
  ((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((((
  ((((((((I)))))))))))) ((((((((((I))))))))))((((((((((I)))))))))) (((((((I))))
  )))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I))))))
  )(((((((I)))))))(((((((I))))))) ((((((I)))))) (((((I)))))(((((I)))))(((((I)))
  ))(((((I)))))(((((I)))))(((((I)))))(((((I))))) ((((I))))((((I))))((((I))))(((
  (I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))((I)
  )((I))((I))
                                                           Type: RomanNumeral
--R 
--R
--R   (10)
--R  ((((((((((((((((I))))))))))))))))((((((((((((((((I)))))))))))))))) ((((((((((
--R  (((((I)))))))))))))))(((((((((((((((I)))))))))))))))(((((((((((((((I)))))))))
--R  ))))))(((((((((((((((I))))))))))))))) ((((((((((((((I))))))))))))))((((((((((
--R  ((((I))))))))))))))((((((((((((((I)))))))))))))) (((((((((((((I)))))))))))))(
--R  ((((((((((((I))))))))))))) ((((((((((((I))))))))))))((((((((((((I))))))))))))
--R  ((((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((
--R  ((((((((((I))))))))))))((((((((((((I))))))))))))((((((((((((I))))))))))))((((
--R  ((((((((I)))))))))))) ((((((((((I))))))))))((((((((((I)))))))))) (((((((I))))
--R  )))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I)))))))(((((((I))))))
--R  )(((((((I)))))))(((((((I))))))) ((((((I)))))) (((((I)))))(((((I)))))(((((I)))
--R  ))(((((I)))))(((((I)))))(((((I)))))(((((I))))) ((((I))))((((I))))((((I))))(((
--R  (I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))((I)
--R  )((I))((I))
--R                                                           Type: RomanNumeral
--E 54

)clear all
 

--S 55 of 76
f: NNI -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 55

--S 56 of 76
f(n) == 2**(2**n) + 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 56

--S 57 of 76
factor f(1)
 
   Compiling function f with type NonNegativeInteger -> Integer 

   (3)  5
                                                       Type: Factored Integer
--R 
--R   Compiling function f with type NonNegativeInteger -> Integer 
--R
--R   (3)  5
--R                                                       Type: Factored Integer
--E 57

--S 58 of 76
factor f(2)
 

   (4)  17
                                                       Type: Factored Integer
--R 
--R
--R   (4)  17
--R                                                       Type: Factored Integer
--E 58

--S 59 of 76
for n in 1..6 repeat output factor f(n)
 
   5
   17
   257
   65537
   641 6700417
   274177 67280421310721
                                                                   Type: Void
--R 
--R   5
--R   17
--R   257
--R   65537
--R   641 6700417
--R   274177 67280421310721
--R                                                                   Type: Void
--E 59

)clear all
 

--S 60 of 76
exp(%pi * sqrt(163.0))
 

   (1)
  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 3733699086 27
  07537410 3782106479 1011860731 2951181346 1860645041 9308388794 9753864044 90
  57287144 7719681485 2322432039 1164782914 8864228272 0131178317 0650104522 26
  87801444 8417703469 6946335570 7681723887 6810009237 0653951938 6506362757 65
  78885582 2394811427 6912100830 8866511072 8471062346 5811298183 0124591328 36
  10006498 2665923651 7261788308 6371078645 2195528154 2746651096 1100147250 20
  97904639 3817787125 7500980365 7792230643 1216511310 8738059929 8242335584 94
  56123995 65
                                                                  Type: Float
--R 
--R
--R   (1)
--R  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 3733699086 27
--R  07537410 3782106479 1011860731 2951181346 1860645041 9308388794 9753864044 90
--R  57287144 7719681485 2322432039 1164782914 8864228272 0131178317 0650104522 26
--R  87801444 8417703469 6946335570 7681723887 6810009237 0653951938 6506362757 65
--R  78885582 2394811427 6912100830 8866511072 8471062346 5811298183 0124591328 36
--R  10006498 2665923651 7261788308 6371078645 2195528154 2746651096 1100147250 20
--R  97904639 3817787125 7500980365 7792230643 1216511310 8738059929 8242335584 94
--R  56123995 65
--R                                                                  Type: Float
--E 60

--S 61 of 76
digits 40
 

   (2)  500
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  500
--R                                                        Type: PositiveInteger
--E 61

--S 62 of 76
x := exp(%pi * sqrt(163.0))
 

   (3)  26253741 2640768743.9999999999 9925007259 76
                                                                  Type: Float
--R 
--R
--R   (3)  26253741 2640768743.9999999999 9925007259 76
--R                                                                  Type: Float
--E 62

--S 63 of 76
numeric(1/3, 5)
 

   (4)  0.33333
                                                                  Type: Float
--R 
--R
--R   (4)  0.33333
--R                                                                  Type: Float
--E 63

--S 64 of 76
numeric(1/3, 60)
 

   (5)  0.3333333333 3333333333 3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (5)  0.3333333333 3333333333 3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 64

--S 65 of 76
numeric(1/3)
 

   (6)  0.3333333333 3333333333 3333333333 3333333333
                                                                  Type: Float
--R 
--R
--R   (6)  0.3333333333 3333333333 3333333333 3333333333
--R                                                                  Type: Float
--E 65

)clear all
 

--S 66 of 76
61657 ** 10 / 999983 ** 12
 

   (1)
               794006207119672937688869745365148806136551203249
   ------------------------------------------------------------------------
   999796019072919181341770495558788771223957844095225846167460930641229761
                                                       Type: Fraction Integer
--R 
--R
--R   (1)
--R               794006207119672937688869745365148806136551203249
--R   ------------------------------------------------------------------------
--R   999796019072919181341770495558788771223957844095225846167460930641229761
--R                                                       Type: Fraction Integer
--E 66

--S 67 of 76
x := 104348/33215
 

        104348
   (2)  ------
         33215
                                                       Type: Fraction Integer
--R 
--R
--R        104348
--R   (2)  ------
--R         33215
--R                                                       Type: Fraction Integer
--E 67

--S 68 of 76
numeric x
 

   (3)  3.1415926539 2142104470 8715941592 653921421
                                                                  Type: Float
--R 
--R
--R   (3)  3.1415926539 2142104470 8715941592 653921421
--R                                                                  Type: Float
--E 68

--S 69 of 76
numer(x)
 

   (4)  104348
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  104348
--R                                                        Type: PositiveInteger
--E 69

--S 70 of 76
denom(x)
 

   (5)  33215
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  33215
--R                                                        Type: PositiveInteger
--E 70

--S 71 of 76
factor(numer x) / factor(denom x)
 

         2
        2 19 1373
   (6)  ---------
        5 7 13 73
                                              Type: Fraction Factored Integer
--R 
--R
--R         2
--R        2 19 1373
--R   (6)  ---------
--R        5 7 13 73
--R                                              Type: Fraction Factored Integer
--E 71

)clear all
 

--S 72 of 76
x := 2/7 :: DECIMAL
 

          ______
   (1)  0.285714
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (1)  0.285714
--R                                                       Type: DecimalExpansion
--E 72

--S 73 of 76
y := 13/17 :: DECIMAL
 

          ________________
   (2)  0.7647058823529411
                                                       Type: DecimalExpansion
--R 
--R
--R          ________________
--R   (2)  0.7647058823529411
--R                                                       Type: DecimalExpansion
--E 73

--S 74 of 76
x - y
 

            ________________________________________________
   (3)  - 0.478991596638655462184873949579831932773109243697
                                                       Type: DecimalExpansion
--R 
--R
--R            ________________________________________________
--R   (3)  - 0.478991596638655462184873949579831932773109243697
--R                                                       Type: DecimalExpansion
--E 74

--S 75 of 76
x + y
 

          ________________________________________________
   (4)  1.050420168067226890756302521008403361344537815126
                                                       Type: DecimalExpansion
--R 
--R
--R          ________________________________________________
--R   (4)  1.050420168067226890756302521008403361344537815126
--R                                                       Type: DecimalExpansion
--E 75

--S 76 of 76
x * y
 

          ________________________________________________
   (5)  0.218487394957983193277310924369747899159663865546
                                                       Type: DecimalExpansion
--R 
--R
--R          ________________________________________________
--R   (5)  0.218487394957983193277310924369747899159663865546
--R                                                       Type: DecimalExpansion
--E 76
)spool 
 
Starts dribbling to GroebnerFactorizationPackage.output (2010/3/27, 18:42:6).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  x  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  y|
        |            3   |
        |                |
   (1)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  x  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  y  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  x  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  y|
--R        |            3   |
--R        |                |
--R   (1)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  x  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  y  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 1

--S 2 of 3
eq := determinant mfzn
 

   (2)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (2)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 2

--S 3 of 3
groebnerFactorize [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])] 
 

   (3)
   [
                  22           22     22     121
     [x y + x z - -- x + y z - -- y - -- z + ---,
                   3            3      3      3
         2   22       25        2   22       25     22  2   388     250
      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
              3        9             3        9      3       9       27
       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
              3        9       3         9         27      9       27       81
     ,
             21994  2   21994     4427     463
    [x + y - -----,y  - ----- y + ----,z - ---],
              5625       5625      675      87
      2   1       11     5     265        2   38     265
    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
          2        2     6      18             3      9
         25     11     11        11     11     11        5     5     5
    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
          9      3      3         3      3      3        3     3     3
         19     5     5
    [x - --,y + -,z + -]]
          3     3     3
  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (3)
--R   [
--R                  22           22     22     121
--R     [x y + x z - -- x + y z - -- y - -- z + ---,
--R                   3            3      3      3
--R         2   22       25        2   22       25     22  2   388     250
--R      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
--R              3        9             3        9      3       9       27
--R       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
--R              3        9       3         9         27      9       27       81
--R     ,
--R             21994  2   21994     4427     463
--R    [x + y - -----,y  - ----- y + ----,z - ---],
--R              5625       5625      675      87
--R      2   1       11     5     265        2   38     265
--R    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
--R          2        2     6      18             3      9
--R         25     11     11        11     11     11        5     5     5
--R    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
--R          9      3      3         3      3      3        3     3     3
--R         19     5     5
--R    [x - --,y + -,z + -]]
--R          3     3     3
--R  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 3
)spool
 
Starts dribbling to matbug.output (2010/3/27, 18:29:52).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
msq := Matrix SquareMatrix(2,POLY INT)
 

   (1)  Matrix SquareMatrix(2,Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Matrix SquareMatrix(2,Polynomial Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 12
m : msq := zero(2,2)
 

        ++0  0+  +0  0++
        ||    |  |    ||
        |+0  0+  +0  0+|
   (2)  |              |
        |+0  0+  +0  0+|
        ||    |  |    ||
        ++0  0+  +0  0++
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        ++0  0+  +0  0++
--R        ||    |  |    ||
--R        |+0  0+  +0  0+|
--R   (2)  |              |
--R        |+0  0+  +0  0+|
--R        ||    |  |    ||
--R        ++0  0+  +0  0++
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 2

--S 3 of 12
m(1,1) := matrix([[1,2],[a,b]])
 

        +1  2+
   (3)  |    |
        +a  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +1  2+
--R   (3)  |    |
--R        +a  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 3

--S 4 of 12
m(1,2) := matrix([[a,b],[2,b]])
 

        +a  b+
   (4)  |    |
        +2  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +a  b+
--R   (4)  |    |
--R        +2  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 4

--S 5 of 12
m(2,2) := matrix([[1,2],[2,b]])
 

        +1  2+
   (5)  |    |
        +2  b+
                                     Type: SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +1  2+
--R   (5)  |    |
--R        +2  b+
--R                                     Type: SquareMatrix(2,Polynomial Integer)
--E 5

--S 6 of 12
m
 

        ++1  2+  +a  b++
        ||    |  |    ||
        |+a  b+  +2  b+|
   (6)  |              |
        |+0  0+  +1  2+|
        ||    |  |    ||
        ++0  0+  +2  b++
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        ++1  2+  +a  b++
--R        ||    |  |    ||
--R        |+a  b+  +2  b+|
--R   (6)  |              |
--R        |+0  0+  +1  2+|
--R        ||    |  |    ||
--R        ++0  0+  +2  b++
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 6

--S 7 of 12
m*m
 

        +                    +              2           ++
        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
        ||                |  |                          ||
        ||          2     |  |      2        2          ||
   (7)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
        |                                                |
        |      +0  0+              +  5     2b + 2+      |
        |      |    |              |              |      |
        |      +0  0+              |         2    |      |
        +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +                    +              2           ++
--R        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R        ||                |  |                          ||
--R        ||          2     |  |      2        2          ||
--R   (7)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R        |                                                |
--R        |      +0  0+              +  5     2b + 2+      |
--R        |      |    |              |              |      |
--R        |      +0  0+              |         2    |      |
--R        +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 7

--S 8 of 12
m**2
 

        +                    +              2           ++
        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
        ||                |  |                          ||
        ||          2     |  |      2        2          ||
   (8)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
        |                                                |
        |      +0  0+              +  5     2b + 2+      |
        |      |    |              |              |      |
        |      +0  0+              |         2    |      |
        +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +                    +              2           ++
--R        |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R        ||                |  |                          ||
--R        ||          2     |  |      2        2          ||
--R   (8)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R        |                                                |
--R        |      +0  0+              +  5     2b + 2+      |
--R        |      |    |              |              |      |
--R        |      +0  0+              |         2    |      |
--R        +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 8

--S 9 of 12
m**3
 

        +matrix1  matrix2+
   (9)  |                |
        +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R        +matrix1  matrix2+
--R   (9)  |                |
--R        +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 9

--S 10 of 12
(m*m)*m
 

         +matrix1  matrix2+
   (10)  |                |
         +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R         +matrix1  matrix2+
--R   (10)  |                |
--R         +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 10

--S 11 of 12
mm:=m*m
 

         +                    +              2           ++
         |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
         ||                |  |                          ||
         ||          2     |  |      2        2          ||
   (11)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
         |                                                |
         |      +0  0+              +  5     2b + 2+      |
         |      |    |              |              |      |
         |      +0  0+              |         2    |      |
         +                          +2b + 2  b  + 4+      +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R         +                    +              2           ++
--R         |+2a + 1   2b + 2 +  |2b + 2a + 4  b  + 3b + 2a ||
--R         ||                |  |                          ||
--R         ||          2     |  |      2        2          ||
--R   (11)  |+a b + a  b  + 2a+  +4b + a  + 2  2b  + a b + 4+|
--R         |                                                |
--R         |      +0  0+              +  5     2b + 2+      |
--R         |      |    |              |              |      |
--R         |      +0  0+              |         2    |      |
--R         +                          +2b + 2  b  + 4+      +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 11

--S 12 of 12
mm*m
 

         +matrix1  matrix2+
   (12)  |                |
         +matrix3  matrix4+



                  +                        2              +
                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
   where matrix1= |                                       |
                  |   2           2        3              |
                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +

   and matrix2 =
     +        2           2                    3     2                        +
     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
     |                                                                        |
     |  2     2                2              3       2                  2    |
     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+

                +0  0+
   and matrix3= |    |
                +0  0+

                +                 2          +
                |   4b + 9      2b  + 2b + 10|
   and matrix4= |                            |
                |  2              3          |
                +2b  + 2b + 10   b  + 8b + 4 +
                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--R 
--R
--R         +matrix1  matrix2+
--R   (12)  |                |
--R         +matrix3  matrix4+
--R
--R
--R
--R                  +                        2              +
--R                  |   2a b + 4a + 1      2b  + 2b + 4a + 2|
--R   where matrix1= |                                       |
--R                  |   2           2        3              |
--R                  +a b  + a b + 2a  + a   b  + 4a b + 2a  +
--R
--R   and matrix2 =
--R     +        2           2                    3     2                        +
--R     |      2b  + 12b + 2a  + 7a + 8          b  + 5b  + (4a + 7)b + 4a + 8   |
--R     |                                                                        |
--R     |  2     2                2              3       2                  2    |
--R     +6b  + (a  + 2a + 4)b + 2a  + 4a + 10  3b  + 2a b  + (3a + 12)b + 2a  + 4+
--R
--R                +0  0+
--R   and matrix3= |    |
--R                +0  0+
--R
--R                +                 2          +
--R                |   4b + 9      2b  + 2b + 10|
--R   and matrix4= |                            |
--R                |  2              3          |
--R                +2b  + 2b + 10   b  + 8b + 4 +
--R                              Type: Matrix SquareMatrix(2,Polynomial Integer)
--E 12
)spool 
 
Starts dribbling to herm.output (2010/3/27, 18:26:49).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 29
)lib $TEST_AXIOMXL/herm
 
   )library cannot find the file herm.
--R 
--R   )library cannot find the file herm.
--E 1

--S 2 of 29
h0 := pHS([] :: List INT)
 
   There are no library operations named pHS 
      Use HyperDoc Browse or issue
                                )what op pHS
      to learn if there is any operation containing " pHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named pHS 
      with argument type(s) 
                                List Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named pHS 
--R      Use HyperDoc Browse or issue
--R                                )what op pHS
--R      to learn if there is any operation containing " pHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named pHS 
--R      with argument type(s) 
--R                                List Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 2

--       []

--S 3 of 29
h1 := pHS [1]
 

   (1)  pHS
           1
                                                                 Type: Symbol
--R 
--R
--R   (1)  pHS
--R           1
--R                                                                 Type: Symbol
--E 3
--       [1]

--S 4 of 29
h2 := pHS [1,2]
 

   (2)  pHS
           1,2
                                                                 Type: Symbol
--R 
--R
--R   (2)  pHS
--R           1,2
--R                                                                 Type: Symbol
--E 4
--       [1,2]

--S 5 of 29
h3 := pHS [1,2,3]
 

   (3)  pHS
           1,2,3
                                                                 Type: Symbol
--R 
--R
--R   (3)  pHS
--R           1,2,3
--R                                                                 Type: Symbol
--E 5
--       [1,2,3]

--S 6 of 29
h4 := pHS [1,2,3,4]
 

   (4)  pHS
           1,2,3,4
                                                                 Type: Symbol
--R 
--R
--R   (4)  pHS
--R           1,2,3,4
--R                                                                 Type: Symbol
--E 6
--       [1,2,3,4]

--S 7 of 29
h5 := pHS [1,2,3,4,5]
 

   (5)  pHS
           1,2,3,4,5
                                                                 Type: Symbol
--R 
--R
--R   (5)  pHS
--R           1,2,3,4,5
--R                                                                 Type: Symbol
--E 7
--       [1,2,3,4,5]

--S 8 of 29
f0 := expand h0
 

   (6)  h0
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  h0
--R                                                     Type: Polynomial Integer
--E 8
--       []

--S 9 of 29
f1 := expand h1
 

   (7)  pHS
           1
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  pHS
--R           1
--R                                                     Type: Polynomial Integer
--E 9
--       [1]

--S 10 of 29
f2 := expand h2
 

   (8)  pHS
           1,2
                                                     Type: Polynomial Integer
--R 
--R
--R   (8)  pHS
--R           1,2
--R                                                     Type: Polynomial Integer
--E 10
--       [1,2]

--S 11 of 29
f3 := expand h3
 

   (9)  pHS
           1,2,3
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)  pHS
--R           1,2,3
--R                                                     Type: Polynomial Integer
--E 11
--       [1,2 + 3%i,2 - 3%i]

--S 12 of 29
f4 := expand h4
 

   (10)  pHS
            1,2,3,4
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)  pHS
--R            1,2,3,4
--R                                                     Type: Polynomial Integer
--E 12
--       [1,2 + 4%i,3,2 - 4%i]

--S 13 of 29
f5 := expand h5
 

   (11)  pHS
            1,2,3,4,5
                                                     Type: Polynomial Integer
--R 
--R
--R   (11)  pHS
--R            1,2,3,4,5
--R                                                     Type: Polynomial Integer
--E 13
--       [1,2 + 5%i,3 + 4%i,3 - 4%i,2 - 5%i]

--S 14 of 29
packHS f0
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 14
--       []

--S 15 of 29
packHS f1
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15
--       [1]

--S 16 of 29
packHS f2
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16
--       [1,2]

--S 17 of 29
packHS f3
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       [1,2,3]

--S 18 of 29
packHS f4
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18
--       [1,2,3,4]

--S 19 of 29
packHS f5
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 19
--       [1,2,3,4,5]

--S 20 of 29
packHS vector[%i,3,3,3]
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                           Vector Complex Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                           Vector Complex Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
-- Error signalled from user code:
--    The argument of packHS is not Hermitian - the first element must
--    be real.

--S 21 of 29
packHS vector [1, 3, 5, 7]
 
   There are no library operations named packHS 
      Use HyperDoc Browse or issue
                               )what op packHS
      to learn if there is any operation containing " packHS " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      packHS with argument type(s) 
                           Vector PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named packHS 
--R      Use HyperDoc Browse or issue
--R                               )what op packHS
--R      to learn if there is any operation containing " packHS " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      packHS with argument type(s) 
--R                           Vector PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21
-- Error signalled from user code:
--    The argument of packHS is not Hermitian - elements 2 and 4 are 
--    not conjugate.

--S 22 of 29
packHS [1, 3, %i, 3]
 

   (12)  packHS
               1,3,%i,3
                                                                 Type: Symbol
--R 
--R
--R   (12)  packHS
--R               1,3,%i,3
--R                                                                 Type: Symbol
--E 22
-- Error signalled from user code:
--    The argument of packHS is not Hermitian - element 3 must be real
--    to be self-conjugate.

--S 23 of 29
conjHerm h0
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                 Variable h0
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                 Variable h0
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23
--       []

--S 24 of 29
conjHerm h1
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24
--       [1]

--S 25 of 29
conjHerm h2
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25
--       [1,2]

--S 26 of 29
conjHerm h3
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 26
--       [1,2,- 3]

--S 27 of 29
conjHerm h4
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 27
--       [1,2,3,- 4]

--S 28 of 29
conjHerm h5
 
   There are no library operations named conjHerm 
      Use HyperDoc Browse or issue
                              )what op conjHerm
      to learn if there is any operation containing " conjHerm " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      conjHerm with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named conjHerm 
--R      Use HyperDoc Browse or issue
--R                              )what op conjHerm
--R      to learn if there is any operation containing " conjHerm " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      conjHerm with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 28
--       [1,2,3,- 4,- 5]

--S 29 of 29
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 29
)spool 
 
Starts dribbling to bouquet.output (2010/3/27, 18:23:19).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 4
arrowScale := 0.2@DFLOAT
 

   (1)  0.20000000000000001
                                                            Type: DoubleFloat
--R 
--R
--R   (1)  0.20000000000000001
--R                                                            Type: DoubleFloat
--E 1
--S 2 of 4
arrowAngle := %pi-%pi/10.0@DFLOAT
 

   (2)  2.8274333882308138
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  2.8274333882308138
--R                                                            Type: DoubleFloat
--E 2
--S 3 of 4
makeArrow(p1, p2) ==
  delta := p2 - p1
  len := arrowScale * length delta
  theta := atan(delta.1, delta.2)
  c1 := len * cos(theta + arrowAngle) 
  s1 := len * sin(theta + arrowAngle)
  c2 := len * cos(theta - arrowAngle) 
  s2 := len * sin(theta - arrowAngle)
  z  := p2.3*(1 - arrowScale)
  p3 := point [p2.1 + c1, p2.2 + s1, z, p2.4]
  p4 := point [p2.1 + c2, p2.2 + s2, z, p2.4]
  [[p1, p2, p3], [p2, p4]]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
drawBouquet(n,title) ==
  angle := 0.0@DFLOAT
  sp := create3Space()$ThreeSpace(DFLOAT)
  for i in 0..n-1 repeat
    start := point [0.0@DFLOAT,0.0@DFLOAT,0.0@DFLOAT,angle] 
    end   := point [cos angle, sin angle, 1.0@DFLOAT, angle]
    arrow := makeArrow(start, end)
    for a in arrow repeat curve(sp,a)
    angle := angle + 2*%pi/n
  makeViewport3D(sp,title)$VIEW3D
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
)spool
 
Starts dribbling to padic.output (2010/3/27, 18:30:36).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
root2 : PADIC 7 := sqrt(2,3)
 

   (1)
              2      3    4      5    6      7      8      9      10      11
   3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (1)
--R              2      3    4      5    6      7      8      9      10      11
--R   3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 1

--S 2 of 20
extend(root2,20)
 

   (2)
                2      3    4      5    6      7      8      9      10      11
     3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + 2 7
   + 
      12    13      15    16    17      18      19    20      21
     7   + 7   + 2 7   + 7   + 7   + 4 7   + 6 7   + 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (2)
--R                2      3    4      5    6      7      8      9      10      11
--R     3 + 7 + 2 7  + 6 7  + 7  + 2 7  + 7  + 2 7  + 4 7  + 6 7  + 6 7   + 2 7
--R   + 
--R      12    13      15    16    17      18      19    20      21
--R     7   + 7   + 2 7   + 7   + 7   + 4 7   + 6 7   + 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 2

--S 3 of 20
broot2 : BPADIC 7 := sqrt(2,3)
 

                   2    3      4      5    6      7      8      11
   (3)  3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                   2    3      4      5    6      7      8      11
--R   (3)  3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 3

--S 4 of 20
extend(broot2,20)
 

   (4)
                2    3      4      5    6      7      8      11    12    13
     3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + 3 7   + 7   + 7
   + 
        15    16    17      18      20      21
     2 7   + 7   + 7   - 3 7   + 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R   (4)
--R                2    3      4      5    6      7      8      11    12    13
--R     3 + 7 + 2 7  - 7  + 2 7  + 2 7  + 7  + 2 7  - 3 7  + 3 7   + 7   + 7
--R   + 
--R        15    16    17      18      20      21
--R     2 7   + 7   + 7   - 3 7   + 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 4

--S 5 of 20
xx : SUP INT := monomial(1,1)
 

   (5)  ?
                                     Type: SparseUnivariatePolynomial Integer
--R 
--R
--R   (5)  ?
--R                                     Type: SparseUnivariatePolynomial Integer
--E 5

--S 6 of 20
pp := xx^6 - 1
 

         6
   (6)  ?  - 1
                                     Type: SparseUnivariatePolynomial Integer
--R 
--R
--R         6
--R   (6)  ?  - 1
--R                                     Type: SparseUnivariatePolynomial Integer
--E 6

--S 7 of 20
r1 : PADIC 7 := root(pp,1)
 

               11
   (7)  1 + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R               11
--R   (7)  1 + O(7  )
--R                                                         Type: PAdicInteger 7
--E 7

--S 8 of 20
r2 : PADIC 7 := root(pp,2)
 

   (8)
                2      3      5      6      7      8      9      10      11
   2 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (8)
--R                2      3      5      6      7      8      9      10      11
--R   2 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 8

--S 9 of 20
r3 : PADIC 7 := root(pp,3)
 

   (9)
                2      3      5      6      7      8      9      10      11
   3 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (9)
--R                2      3      5      6      7      8      9      10      11
--R   3 + 4 7 + 6 7  + 3 7  + 2 7  + 6 7  + 2 7  + 4 7  + 3 7  + 4 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 9

--S 10 of 20
r4 : PADIC 7 := root(pp,4)
 

                      3      4      5      7      8      9      10      11
   (10)  4 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R                      3      4      5      7      8      9      10      11
--R   (10)  4 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 10

--S 11 of 20
r5 : PADIC 7 := root(pp,5)
 

                      3      4      5      7      8      9      10      11
   (11)  5 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R                      3      4      5      7      8      9      10      11
--R   (11)  5 + 2 7 + 3 7  + 6 7  + 4 7  + 4 7  + 2 7  + 3 7  + 2 7   + O(7  )
--R                                                         Type: PAdicInteger 7
--E 11

--S 12 of 20
r6 : PADIC 7 := root(pp,6)
 

   (12)
                  2      3      4      5      6      7      8      9      10
     6 + 6 7 + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7
   + 
        11
     O(7  )
                                                         Type: PAdicInteger 7
--R 
--R
--R   (12)
--R                  2      3      4      5      6      7      8      9      10
--R     6 + 6 7 + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7
--R   + 
--R        11
--R     O(7  )
--R                                                         Type: PAdicInteger 7
--E 12

--S 13 of 20
(x - r1) * (x - r2) * (x - r3) * (x - r4) * (x - r5) * (x - r6)
 

   (13)
      6      12  5      12  4      12  3      12  2      12                  2
     x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x + 6 + 6 7 + 6 7
   + 
        3      4      5      6      7      8      9      10      11
     6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7   + O(7  )
                                              Type: Polynomial PAdicInteger 7
--R 
--R
--R   (13)
--R      6      12  5      12  4      12  3      12  2      12                  2
--R     x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x + 6 + 6 7 + 6 7
--R   + 
--R        3      4      5      6      7      8      9      10      11
--R     6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7  + 6 7   + O(7  )
--R                                              Type: Polynomial PAdicInteger 7
--E 13

--S 14 of 20
rr1 : BPADIC 7 := root(pp,1)
 

                11
   (14)  1 + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                11
--R   (14)  1 + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 14

--S 15 of 20
rr2 : BPADIC 7 := root(pp,2)
 

                      3    4      5    6      7      8      9      10      11
   (15)  2 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                      3    4      5    6      7      8      9      10      11
--R   (15)  2 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 15

--S 16 of 20
rr3 : BPADIC 7 := root(pp,3)
 

                      3    4      5    6      7      8      9      10      11
   (16)  3 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                      3    4      5    6      7      8      9      10      11
--R   (16)  3 - 3 7 - 3 7  + 7  + 2 7  - 7  + 3 7  - 3 7  - 3 7  - 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 16

--S 17 of 20
rr4 : BPADIC 7 := root(pp,4)
 

   (17)
                  3    4      5    6      7      8      9      10      11
   - 3 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R   (17)
--R                  3    4      5    6      7      8      9      10      11
--R   - 3 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 17

--S 18 of 20
rr5 : BPADIC 7 := root(pp,5)
 

   (18)
                  3    4      5    6      7      8      9      10      11
   - 2 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R   (18)
--R                  3    4      5    6      7      8      9      10      11
--R   - 2 + 3 7 + 3 7  - 7  - 2 7  + 7  - 3 7  + 3 7  + 3 7  + 2 7   + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 18

--S 19 of 20
rr6 : BPADIC 7 := root(pp,6)
 

                  11
   (19)  - 1 + O(7  )
                                                 Type: BalancedPAdicInteger 7
--R 
--R
--R                  11
--R   (19)  - 1 + O(7  )
--R                                                 Type: BalancedPAdicInteger 7
--E 19

--S 20 of 20
(x - rr1) * (x - rr2) * (x - rr3) * (x - rr4) * (x - rr5) * (x - rr6)
 

          6      12  5      12  4      12  3      12  2      12            11
   (20)  x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x - 1 + O(7  )
                                      Type: Polynomial BalancedPAdicInteger 7
--R 
--R
--R          6      12  5      12  4      12  3      12  2      12            11
--R   (20)  x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x  + O(7  )x - 1 + O(7  )
--R                                      Type: Polynomial BalancedPAdicInteger 7
--E 20
)spool 
 
Starts dribbling to dhmatrix.output (2010/3/27, 18:24:56).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 16
t1:=DHMATRIX(DoubleFloat)
 

   (1)  DenavitHartenbergMatrix DoubleFloat
                                                                 Type: Domain
--R
--R   (1)  DenavitHartenbergMatrix DoubleFloat
--R                                                                 Type: Domain
--E 1

--S 2 of 16
t2:=identity()$t1
 

        +1.  0.  0.  0.+
        |              |
        |0.  1.  0.  0.|
   (2)  |              |
        |0.  0.  1.  0.|
        |              |
        +0.  0.  0.  1.+
                                    Type: DenavitHartenbergMatrix DoubleFloat
--R
--R        +1.  0.  0.  0.+
--R        |              |
--R        |0.  1.  0.  0.|
--R   (2)  |              |
--R        |0.  0.  1.  0.|
--R        |              |
--R        +0.  0.  0.  1.+
--R                                    Type: DenavitHartenbergMatrix DoubleFloat
--E 2

--S 3 of 16
t3:=rotatex(30)
 

        +1   0     0    0+
        |                |
        |    +-+         |
        |   \|3     1    |
        |0  ----  - -   0|
        |     2     2    |
   (3)  |                |
        |          +-+   |
        |    1    \|3    |
        |0   -    ----  0|
        |    2      2    |
        |                |
        +0   0     0    1+
                             Type: DenavitHartenbergMatrix Expression Integer
--R
--R        +1   0     0    0+
--R        |                |
--R        |    +-+         |
--R        |   \|3     1    |
--R        |0  ----  - -   0|
--R        |     2     2    |
--R   (3)  |                |
--R        |          +-+   |
--R        |    1    \|3    |
--R        |0   -    ----  0|
--R        |    2      2    |
--R        |                |
--R        +0   0     0    1+
--R                             Type: DenavitHartenbergMatrix Expression Integer
--E 3

--S 4 of 16
t4:=rotatey(30)
 

        + +-+            +
        |\|3       1     |
        |----  0   -    0|
        |  2       2     |
        |                |
        | 0    1   0    0|
   (4)  |                |
        |          +-+   |
        |  1      \|3    |
        |- -   0  ----  0|
        |  2        2    |
        |                |
        + 0    0   0    1+
                             Type: DenavitHartenbergMatrix Expression Integer
--R
--R        + +-+            +
--R        |\|3       1     |
--R        |----  0   -    0|
--R        |  2       2     |
--R        |                |
--R        | 0    1   0    0|
--R   (4)  |                |
--R        |          +-+   |
--R        |  1      \|3    |
--R        |- -   0  ----  0|
--R        |  2        2    |
--R        |                |
--R        + 0    0   0    1+
--R                             Type: DenavitHartenbergMatrix Expression Integer
--E 4

--S 5 of 16
t5:=rotatez(30)
 

        + +-+            +
        |\|3     1       |
        |----  - -   0  0|
        |  2     2       |
        |                |
        |       +-+      |
   (5)  | 1    \|3       |
        | -    ----  0  0|
        | 2      2       |
        |                |
        | 0     0    1  0|
        |                |
        + 0     0    0  1+
                             Type: DenavitHartenbergMatrix Expression Integer
--R
--R        + +-+            +
--R        |\|3     1       |
--R        |----  - -   0  0|
--R        |  2     2       |
--R        |                |
--R        |       +-+      |
--R   (5)  | 1    \|3       |
--R        | -    ----  0  0|
--R        | 2      2       |
--R        |                |
--R        | 0     0    1  0|
--R        |                |
--R        + 0     0    0  1+
--R                             Type: DenavitHartenbergMatrix Expression Integer
--E 5

--S 6 of 16
t6:=scale(0.5,0.5,0.5)
 

        +0.5  0.0  0.0  0.0+
        |                  |
        |0.0  0.5  0.0  0.0|
   (6)  |                  |
        |0.0  0.0  0.5  0.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                          Type: DenavitHartenbergMatrix Float
--R
--R        +0.5  0.0  0.0  0.0+
--R        |                  |
--R        |0.0  0.5  0.0  0.0|
--R   (6)  |                  |
--R        |0.0  0.0  0.5  0.0|
--R        |                  |
--R        +0.0  0.0  0.0  1.0+
--R                                          Type: DenavitHartenbergMatrix Float
--E 6

--S 7 of 16
t7:=translate(2.0,2.0,2.0)
 

        +1.0  0.0  0.0  2.0+
        |                  |
        |0.0  1.0  0.0  2.0|
   (7)  |                  |
        |0.0  0.0  1.0  2.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                          Type: DenavitHartenbergMatrix Float
--R
--R        +1.0  0.0  0.0  2.0+
--R        |                  |
--R        |0.0  1.0  0.0  2.0|
--R   (7)  |                  |
--R        |0.0  0.0  1.0  2.0|
--R        |                  |
--R        +0.0  0.0  0.0  1.0+
--R                                          Type: DenavitHartenbergMatrix Float
--E 7

--S 8 of 16
t8:Point(DoubleFloat):=[4.0,0.0,0.0]$List(DoubleFloat)
 

   (8)  [4.,0.,0.]
                                                      Type: Point DoubleFloat
--R
--R   (8)  [4.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 8

--S 9 of 16
t9:=translate(4.0,0.0,0.0)
 

        +1.0  0.0  0.0  4.0+
        |                  |
        |0.0  1.0  0.0  0.0|
   (9)  |                  |
        |0.0  0.0  1.0  0.0|
        |                  |
        +0.0  0.0  0.0  1.0+
                                          Type: DenavitHartenbergMatrix Float
--R
--R        +1.0  0.0  0.0  4.0+
--R        |                  |
--R        |0.0  1.0  0.0  0.0|
--R   (9)  |                  |
--R        |0.0  0.0  1.0  0.0|
--R        |                  |
--R        +0.0  0.0  0.0  1.0+
--R                                          Type: DenavitHartenbergMatrix Float
--E 9

--S 10 of 16
t10:=t9*t8
 

   (10)  [8.,0.,0.]
                                                      Type: Point DoubleFloat
--R
--R   (10)  [8.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 10

--S 11 of 16
t11:=rotatez(90)*t10
 

   (11)  [0.,8.,0.]
                                           Type: Point Expression DoubleFloat
--R
--R   (11)  [0.,8.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 11

--S 12 of 16
t12:=scale(0.0,0.5,0.0)*t11
 

   (12)  [0.,4.,0.]
                                           Type: Point Expression DoubleFloat
--R
--R   (12)  [0.,4.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 12

--S 13 of 16
t13:=rotatex(90)*t12
 

   (13)  [0.,0.,4.]
                                           Type: Point Expression DoubleFloat
--R
--R   (13)  [0.,0.,4.]
--R                                           Type: Point Expression DoubleFloat
--E 13

--S 14 of 16
t14:=rotatey(90)*t13
 

   (14)  [4.,0.,0.]
                                           Type: Point Expression DoubleFloat
--R
--R   (14)  [4.,0.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 14

--S 15 of 16
t15:=rotatey(90)*rotatex(90)*scale(0.0,0.5,0.0)*_
     rotatez(90)*translate(4.0,0.0,0.0)
 

         +0.5  0.0  0.0  2.0+
         |                  |
         |0.0  0.0  0.0  0.0|
   (15)  |                  |
         |0.0  0.0  0.0  0.0|
         |                  |
         +0.0  0.0  0.0  1.0+
                               Type: DenavitHartenbergMatrix Expression Float
--R
--R         +0.5  0.0  0.0  2.0+
--R         |                  |
--R         |0.0  0.0  0.0  0.0|
--R   (15)  |                  |
--R         |0.0  0.0  0.0  0.0|
--R         |                  |
--R         +0.0  0.0  0.0  1.0+
--R                               Type: DenavitHartenbergMatrix Expression Float
--E 15

--S 16 of 16
t16:=t15*t8
 

   (16)  [4.,0.,0.]
                                           Type: Point Expression DoubleFloat
--R
--R   (16)  [4.,0.,0.]
--R                                           Type: Point Expression DoubleFloat
--E 16

)spool 
 
Starts dribbling to bug103.output (2010/3/27, 18:23:22).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 1
solve(z=z,z)
 

   (1)  [0= 0]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R   (1)  [0= 0]
--R                              Type: List Equation Fraction Polynomial Integer
--E 1
)spool 
 
Starts dribbling to schaum9.output (2010/3/27, 18:37:23).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 110
aa:=integrate(1/(sqrt(x^2+a^2)),x)
 

               +-------+
               | 2    2
   (1)  - log(\|x  + a   - x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+
--R               | 2    2
--R   (1)  - log(\|x  + a   - x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 110
bb:=log(x+sqrt(x^2+a^2))
 

             +-------+
             | 2    2
   (2)  log(\|x  + a   + x)
                                                     Type: Expression Integer
--R
--R             +-------+
--R             | 2    2
--R   (2)  log(\|x  + a   + x)
--R                                                     Type: Expression Integer
--E

--S 3 of 110
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
--R                                                     Type: Expression Integer
--E

--S 4 of 110      14:182 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

               2
   (4)  - log(a )
                                                     Type: Expression Integer
--R
--R               2
--R   (4)  - log(a )
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 5 of 110
aa:=integrate(x/(sqrt(x^2+a^2)),x)
 

            +-------+
            | 2    2     2    2
        - x\|x  + a   + x  + a
   (1)  -----------------------
              +-------+
              | 2    2
             \|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +-------+
--R            | 2    2     2    2
--R        - x\|x  + a   + x  + a
--R   (1)  -----------------------
--R              +-------+
--R              | 2    2
--R             \|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 6 of 110
bb:=sqrt(x^2+a^2)
 

         +-------+
         | 2    2
   (2)  \|x  + a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2
--R   (2)  \|x  + a
--R                                                     Type: Expression Integer
--E

--S 7 of 110      14:183 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 8 of 110
aa:=integrate(x^2/sqrt(x^2+a^2),x)
 

   (1)
             +-------+                   +-------+
          2  | 2    2      2 2    4      | 2    2
       (2a x\|x  + a   - 2a x  - a )log(\|x  + a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  - a x)\|x  + a   + 2x  + 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  + a   - 4x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R             +-------+                   +-------+
--R          2  | 2    2      2 2    4      | 2    2
--R       (2a x\|x  + a   - 2a x  - a )log(\|x  + a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  - a x)\|x  + a   + 2x  + 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  + a   - 4x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 110
bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2))
 

                 +-------+          +-------+
           2     | 2    2           | 2    2
        - a log(\|x  + a   + x) + x\|x  + a
   (2)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R
--R                 +-------+          +-------+
--R           2     | 2    2           | 2    2
--R        - a log(\|x  + a   + x) + x\|x  + a
--R   (2)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E

--S 10 of 110
cc:=aa-bb
 

               +-------+               +-------+
         2     | 2    2          2     | 2    2
        a log(\|x  + a   + x) + a log(\|x  + a   - x)
   (3)  ---------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         2     | 2    2          2     | 2    2
--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
--R   (3)  ---------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 11 of 110
logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
 

   (4)  c log(b) + c log(a) + %H == c log(a b) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (4)  c log(b) + c log(a) + %K == c log(a b) + %K
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12 of 110     14:184 Schaums and Axiom differ by a constant
dd:=logmul1 cc
 

         2     2
        a log(a )
   (5)  ---------
            2
                                                     Type: Expression Integer
--R
--R         2     2
--R        a log(a )
--R   (5)  ---------
--R            2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 13 of 110
aa:=integrate(x^3/sqrt(x^2+a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2     6
        (- 4x  + 5a x  + 6a x)\|x  + a   + 4x  - 3a x  - 9a x  - 2a
   (1)  ------------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  + 3a )\|x  + a   - 12x  - 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2     6
--R        (- 4x  + 5a x  + 6a x)\|x  + a   + 4x  - 3a x  - 9a x  - 2a
--R   (1)  ------------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 110
bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2)
 

                   +-------+
          2     2  | 2    2
        (x  - 2a )\|x  + a
   (2)  --------------------
                  3
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2
--R        (x  - 2a )\|x  + a
--R   (2)  --------------------
--R                  3
--R                                                     Type: Expression Integer
--E

--S 15 of 110     14:185 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 110
aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
 

               +-------+                 +-------+
               | 2    2                  | 2    2
        - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
   (1)  ---------------------------------------------------
                                 a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+                 +-------+
--R               | 2    2                  | 2    2
--R        - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R   (1)  ---------------------------------------------------
--R                                 a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17 of 110
bb:=-1/a*log((a+sqrt(x^2+a^2))/x)
 

               +-------+
               | 2    2
              \|x  + a   + a
          log(--------------)
                     x
   (2)  - -------------------
                   a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  + a   + a
--R          log(--------------)
--R                     x
--R   (2)  - -------------------
--R                   a
--R                                                     Type: Expression Integer
--E

--S 18 of 110
cc:=aa-bb
 

   (3)
                                                              +-------+
          +-------+                 +-------+                 | 2    2
          | 2    2                  | 2    2                 \|x  + a   + a
   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
                                                                    x
   -------------------------------------------------------------------------
                                       a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                              +-------+
--R          +-------+                 +-------+                 | 2    2
--R          | 2    2                  | 2    2                 \|x  + a   + a
--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
--R                                                                    x
--R   -------------------------------------------------------------------------
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 19 of 110
dd:=expandLog cc
 

   (4)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 20 of 110     14:186 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 21 of 110
aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
 

                  1
   (1)  - ----------------
            +-------+
            | 2    2     2
          x\|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  1
--R   (1)  - ----------------
--R            +-------+
--R            | 2    2     2
--R          x\|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22 of 110
bb:=-sqrt(x^2+a^2)/(a^2*x)
 

           +-------+
           | 2    2
          \|x  + a
   (2)  - ----------
               2
              a x
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2
--R          \|x  + a
--R   (2)  - ----------
--R               2
--R              a x
--R                                                     Type: Expression Integer
--E

--S 23 of 110     14:187 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           1
   (3)  - --
           2
          a
                                                     Type: Expression Integer
--R
--R           1
--R   (3)  - --
--R           2
--R          a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 24 of 110
aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
 

   (1)
            +-------+                   +-------+
          3 | 2    2      4    2 2      | 2    2
       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x + a)
     + 
              +-------+                   +-------+
            3 | 2    2      4    2 2      | 2    2
       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x - a)
     + 
                    +-------+
            2    3  | 2    2        3     3
       (2a x  + a )\|x  + a   - 2a x  - 2a x
  /
           +-------+
       3 3 | 2    2      3 4     5 2
     4a x \|x  + a   - 4a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +-------+                   +-------+
--R          3 | 2    2      4    2 2      | 2    2
--R       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x + a)
--R     + 
--R              +-------+                   +-------+
--R            3 | 2    2      4    2 2      | 2    2
--R       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x - a)
--R     + 
--R                    +-------+
--R            2    3  | 2    2        3     3
--R       (2a x  + a )\|x  + a   - 2a x  - 2a x
--R  /
--R           +-------+
--R       3 3 | 2    2      3 4     5 2
--R     4a x \|x  + a   - 4a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25 of 110
bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x)
 

               +-------+
               | 2    2           +-------+
         2    \|x  + a   + a      | 2    2
        x log(--------------) - a\|x  + a
                     x
   (2)  -----------------------------------
                         3 2
                       2a x
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2           +-------+
--R         2    \|x  + a   + a      | 2    2
--R        x log(--------------) - a\|x  + a
--R                     x
--R   (2)  -----------------------------------
--R                         3 2
--R                       2a x
--R                                                     Type: Expression Integer
--E

--S 26 of 110
cc:=aa-bb
 

   (3)
                                                            +-------+
        +-------+                 +-------+                 | 2    2
        | 2    2                  | 2    2                 \|x  + a   + a
   log(\|x  + a   - x + a) - log(\|x  + a   - x - a) - log(--------------)
                                                                  x
   -----------------------------------------------------------------------
                                       3
                                     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                            +-------+
--R        +-------+                 +-------+                 | 2    2
--R        | 2    2                  | 2    2                 \|x  + a   + a
--R   log(\|x  + a   - x + a) - log(\|x  + a   - x - a) - log(--------------)
--R                                                                  x
--R   -----------------------------------------------------------------------
--R                                       3
--R                                     2a
--R                                                     Type: Expression Integer
--E

--S 27 of 110
dd:=expandLog cc
 

   (4)
              +-------+             +-------+                 +-------+
              | 2    2              | 2    2                  | 2    2
       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
     + 
       log(x)
  /
       3
     2a
                                                     Type: Expression Integer
--R
--R   (4)
--R              +-------+             +-------+                 +-------+
--R              | 2    2              | 2    2                  | 2    2
--R       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
--R     + 
--R       log(x)
--R  /
--R       3
--R     2a
--R                                                     Type: Expression Integer
--E

--S 28 of 110     14:188 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        log(- 1)
   (5)  --------
             3
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R             3
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 29 of 110
aa:=integrate(sqrt(x^2+a^2),x)
 

   (1)
               +-------+                   +-------+
            2  | 2    2      2 2    4      | 2    2
       (- 2a x\|x  + a   + 2a x  + a )log(\|x  + a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  - a x)\|x  + a   + 2x  + 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  + a   - 4x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               +-------+                   +-------+
--R            2  | 2    2      2 2    4      | 2    2
--R       (- 2a x\|x  + a   + 2a x  + a )log(\|x  + a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  - a x)\|x  + a   + 2x  + 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  + a   - 4x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 110
bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2))
 

               +-------+          +-------+
         2     | 2    2           | 2    2
        a log(\|x  + a   + x) + x\|x  + a
   (2)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R               +-------+          +-------+
--R         2     | 2    2           | 2    2
--R        a log(\|x  + a   + x) + x\|x  + a
--R   (2)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 31 of 110
cc:=aa-bb
 

                 +-------+               +-------+
           2     | 2    2          2     | 2    2
        - a log(\|x  + a   + x) - a log(\|x  + a   - x)
   (3)  -----------------------------------------------
                               2
                                                     Type: Expression Integer
--R
--R                 +-------+               +-------+
--R           2     | 2    2          2     | 2    2
--R        - a log(\|x  + a   + x) - a log(\|x  + a   - x)
--R   (3)  -----------------------------------------------
--R                               2
--R                                                     Type: Expression Integer
--E

--S 32 of 110     14:189 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           2     2
          a log(a )
   (4)  - ---------
              2
                                                     Type: Expression Integer
--R
--R           2     2
--R          a log(a )
--R   (4)  - ---------
--R              2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 33 of 110
aa:=integrate(x*sqrt(x^2+a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2    6
        (- 4x  - 7a x  - 3a x)\|x  + a   + 4x  + 9a x  + 6a x  + a
   (1)  -----------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  + 3a )\|x  + a   - 12x  - 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2    6
--R        (- 4x  - 7a x  - 3a x)\|x  + a   + 4x  + 9a x  + 6a x  + a
--R   (1)  -----------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34 of 110
bb:=(x^2+a^2)^(3/2)/3
 

                  +-------+
          2    2  | 2    2
        (x  + a )\|x  + a
   (2)  -------------------
                 3
                                                     Type: Expression Integer
--R
--R                  +-------+
--R          2    2  | 2    2
--R        (x  + a )\|x  + a
--R   (2)  -------------------
--R                 3
--R                                                     Type: Expression Integer
--E

--S 35 of 110     14:190 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 36 of 110
aa:=integrate(x^2*sqrt(x^2+a^2),x)
 

   (1)
                       +-------+                           +-------+
           4 3     6   | 2    2      4 4     6 2    8      | 2    2
       ((8a x  + 4a x)\|x  + a   - 8a x  - 8a x  - a )log(\|x  + a   - x)
     + 
                                      +-------+
           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
     (- 16x  - 24a x  - 10a x  - a x)\|x  + a   + 16x  + 32a x  + 20a x  + 4a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       +-------+                           +-------+
--R           4 3     6   | 2    2      4 4     6 2    8      | 2    2
--R       ((8a x  + 4a x)\|x  + a   - 8a x  - 8a x  - a )log(\|x  + a   - x)
--R     + 
--R                                      +-------+
--R           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
--R     (- 16x  - 24a x  - 10a x  - a x)\|x  + a   + 16x  + 32a x  + 20a x  + 4a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37 of 110
bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2))
 

                 +-------+                    +-------+
           4     | 2    2            3    2   | 2    2
        - a log(\|x  + a   + x) + (2x  + a x)\|x  + a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                 +-------+                    +-------+
--R           4     | 2    2            3    2   | 2    2
--R        - a log(\|x  + a   + x) + (2x  + a x)\|x  + a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 38 of 110
cc:=aa-bb
 

               +-------+               +-------+
         4     | 2    2          4     | 2    2
        a log(\|x  + a   + x) + a log(\|x  + a   - x)
   (3)  ---------------------------------------------
                              8
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         4     | 2    2          4     | 2    2
--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
--R   (3)  ---------------------------------------------
--R                              8
--R                                                     Type: Expression Integer
--E

--S 39 of 110     14:191 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

         4     2
        a log(a )
   (4)  ---------
            8
                                                     Type: Expression Integer
--R
--R         4     2
--R        a log(a )
--R   (4)  ---------
--R            8
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 40 of 110
aa:=integrate(x^3*sqrt(x^2+a^2),x)
 

   (1)
                                                  +-------+
             9      2 7     4 5      6 3      8   | 2    2       10       2 8
       (- 48x  - 76a x  - 3a x  + 35a x  + 10a x)\|x  + a   + 48x   + 100a x
     + 
          4 6      6 4      8 2     10
       35a x  - 40a x  - 25a x  - 2a
  /
                              +-------+
          4       2 2      4  | 2    2        5       2 3      4
     (240x  + 180a x  + 15a )\|x  + a   - 240x  - 300a x  - 75a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7     4 5      6 3      8   | 2    2       10       2 8
--R       (- 48x  - 76a x  - 3a x  + 35a x  + 10a x)\|x  + a   + 48x   + 100a x
--R     + 
--R          4 6      6 4      8 2     10
--R       35a x  - 40a x  - 25a x  - 2a
--R  /
--R                              +-------+
--R          4       2 2      4  | 2    2        5       2 3      4
--R     (240x  + 180a x  + 15a )\|x  + a   - 240x  - 300a x  - 75a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 41 of 110
bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3
 

                           +-------+
           4    2 2     4  | 2    2
        (3x  + a x  - 2a )\|x  + a
   (2)  ----------------------------
                     15
                                                     Type: Expression Integer
--R
--R                           +-------+
--R           4    2 2     4  | 2    2
--R        (3x  + a x  - 2a )\|x  + a
--R   (2)  ----------------------------
--R                     15
--R                                                     Type: Expression Integer
--E

--S 42 of 110     14:192 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 43 of 110
aa:=integrate(sqrt(x^2+a^2)/x,x)
 

   (1)
            +-------+            +-------+
            | 2    2             | 2    2
       (- a\|x  + a   + a x)log(\|x  + a   - x + a)
     + 
          +-------+            +-------+              +-------+
          | 2    2             | 2    2               | 2    2     2    2
       (a\|x  + a   - a x)log(\|x  + a   - x - a) - x\|x  + a   + x  + a
  /
      +-------+
      | 2    2
     \|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +-------+            +-------+
--R            | 2    2             | 2    2
--R       (- a\|x  + a   + a x)log(\|x  + a   - x + a)
--R     + 
--R          +-------+            +-------+              +-------+
--R          | 2    2             | 2    2               | 2    2     2    2
--R       (a\|x  + a   - a x)log(\|x  + a   - x - a) - x\|x  + a   + x  + a
--R  /
--R      +-------+
--R      | 2    2
--R     \|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 44 of 110
bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2          +-------+
                \|x  + a   + a     | 2    2
   (2)  - a log(--------------) + \|x  + a
                       x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2          +-------+
--R                \|x  + a   + a     | 2    2
--R   (2)  - a log(--------------) + \|x  + a
--R                       x
--R                                                     Type: Expression Integer
--E

--S 45 of 110
cc:=aa-bb
 

   (3)
              +-------+                   +-------+
              | 2    2                    | 2    2
     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
   + 
            +-------+
            | 2    2
           \|x  + a   + a
     a log(--------------)
                  x
                                                     Type: Expression Integer
--R
--R   (3)
--R              +-------+                   +-------+
--R              | 2    2                    | 2    2
--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
--R   + 
--R            +-------+
--R            | 2    2
--R           \|x  + a   + a
--R     a log(--------------)
--R                  x
--R                                                     Type: Expression Integer
--E

--S 46 of 110
dd:=expandLog cc
 

   (4)
            +-------+               +-------+
            | 2    2                | 2    2
     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
   + 
            +-------+
            | 2    2
     a log(\|x  + a   - x - a) - a log(x)
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+               +-------+
--R            | 2    2                | 2    2
--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
--R   + 
--R            +-------+
--R            | 2    2
--R     a log(\|x  + a   - x - a) - a log(x)
--R                                                     Type: Expression Integer
--E

--S 47 of 110     14:193 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

   (5)  - a log(- 1)
                                                     Type: Expression Integer
--R
--R   (5)  - a log(- 1)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 48 of 110
aa:=integrate(sqrt(x^2+a^2)/x^2,x)
 

             +-------+           +-------+
             | 2    2     2      | 2    2          2
        (- x\|x  + a   + x )log(\|x  + a   - x) - a
   (1)  --------------------------------------------
                        +-------+
                        | 2    2     2
                      x\|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+           +-------+
--R             | 2    2     2      | 2    2          2
--R        (- x\|x  + a   + x )log(\|x  + a   - x) - a
--R   (1)  --------------------------------------------
--R                        +-------+
--R                        | 2    2     2
--R                      x\|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49 of 110
bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2))
 

               +-------+         +-------+
               | 2    2          | 2    2
        x log(\|x  + a   + x) - \|x  + a
   (2)  ----------------------------------
                         x
                                                     Type: Expression Integer
--R
--R               +-------+         +-------+
--R               | 2    2          | 2    2
--R        x log(\|x  + a   + x) - \|x  + a
--R   (2)  ----------------------------------
--R                         x
--R                                                     Type: Expression Integer
--E

--S 50 of 110
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 51 of 110     14:194 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

               2
   (4)  - log(a ) - 1
                                                     Type: Expression Integer
--R
--R               2
--R   (4)  - log(a ) - 1
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 52 of 110
aa:=integrate(sqrt(x^2+a^2)/x^3,x)
 

   (1)
              +-------+                   +-------+
            3 | 2    2      4    2 2      | 2    2
       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x + a)
     + 
            +-------+                   +-------+
          3 | 2    2      4    2 2      | 2    2
       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x - a)
     + 
                    +-------+
            2    3  | 2    2        3     3
       (2a x  + a )\|x  + a   - 2a x  - 2a x
  /
           +-------+
         3 | 2    2        4     3 2
     4a x \|x  + a   - 4a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R              +-------+                   +-------+
--R            3 | 2    2      4    2 2      | 2    2
--R       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x + a)
--R     + 
--R            +-------+                   +-------+
--R          3 | 2    2      4    2 2      | 2    2
--R       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x - a)
--R     + 
--R                    +-------+
--R            2    3  | 2    2        3     3
--R       (2a x  + a )\|x  + a   - 2a x  - 2a x
--R  /
--R           +-------+
--R         3 | 2    2        4     3 2
--R     4a x \|x  + a   - 4a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53 of 110
bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2           +-------+
           2    \|x  + a   + a      | 2    2
        - x log(--------------) - a\|x  + a
                       x
   (2)  -------------------------------------
                            2
                        2a x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2           +-------+
--R           2    \|x  + a   + a      | 2    2
--R        - x log(--------------) - a\|x  + a
--R                       x
--R   (2)  -------------------------------------
--R                            2
--R                        2a x
--R                                                     Type: Expression Integer
--E

--S 54 of 110
cc:=aa-bb
 

   (3)
                                                              +-------+
          +-------+                 +-------+                 | 2    2
          | 2    2                  | 2    2                 \|x  + a   + a
   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
                                                                    x
   -------------------------------------------------------------------------
                                       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                              +-------+
--R          +-------+                 +-------+                 | 2    2
--R          | 2    2                  | 2    2                 \|x  + a   + a
--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
--R                                                                    x
--R   -------------------------------------------------------------------------
--R                                       2a
--R                                                     Type: Expression Integer
--E

--S 55 of 110
dd:=expandLog cc
 

   (4)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 56 of 110     14:195 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R             2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 57 of 110
aa:=integrate(1/(x^2+a^2)^(3/2),x)
 

                    1
   (1)  - ---------------------
            +-------+
            | 2    2     2    2
          x\|x  + a   - x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    1
--R   (1)  - ---------------------
--R            +-------+
--R            | 2    2     2    2
--R          x\|x  + a   - x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 58 of 110
bb:=x/(a^2*sqrt(x^2+a^2))
 

              x
   (2)  ------------
           +-------+
         2 | 2    2
        a \|x  + a
                                                     Type: Expression Integer
--R
--R              x
--R   (2)  ------------
--R           +-------+
--R         2 | 2    2
--R        a \|x  + a
--R                                                     Type: Expression Integer
--E

--S 59 of 110     14:196 Schaums and Axiom differ by a constant
cc:=aa-bb
 

         1
   (3)  --
         2
        a
                                                     Type: Expression Integer
--R
--R         1
--R   (3)  --
--R         2
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 60 of 110
aa:=integrate(x/(x^2+a^2)^(3/2),x)
 

             +-------+
             | 2    2
            \|x  + a   - x
   (1)  ---------------------
          +-------+
          | 2    2     2    2
        x\|x  + a   - x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+
--R             | 2    2
--R            \|x  + a   - x
--R   (1)  ---------------------
--R          +-------+
--R          | 2    2     2    2
--R        x\|x  + a   - x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 61 of 110
bb:=-1/sqrt(x^2+a^2)
 

               1
   (2)  - ----------
           +-------+
           | 2    2
          \|x  + a
                                                     Type: Expression Integer
--R
--R               1
--R   (2)  - ----------
--R           +-------+
--R           | 2    2
--R          \|x  + a
--R                                                     Type: Expression Integer
--E

--S 62 of 110     14:197 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 63 of 110
aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
 

             +-------+                +-------+
             | 2    2     2    2      | 2    2          2
        (- x\|x  + a   + x  + a )log(\|x  + a   - x) + a
   (1)  -------------------------------------------------
                        +-------+
                        | 2    2     2    2
                      x\|x  + a   - x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+                +-------+
--R             | 2    2     2    2      | 2    2          2
--R        (- x\|x  + a   + x  + a )log(\|x  + a   - x) + a
--R   (1)  -------------------------------------------------
--R                        +-------+
--R                        | 2    2     2    2
--R                      x\|x  + a   - x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 64 of 110
bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2))
 

         +-------+     +-------+
         | 2    2      | 2    2
        \|x  + a  log(\|x  + a   + x) - x
   (2)  ---------------------------------
                     +-------+
                     | 2    2
                    \|x  + a
                                                     Type: Expression Integer
--R
--R         +-------+     +-------+
--R         | 2    2      | 2    2
--R        \|x  + a  log(\|x  + a   + x) - x
--R   (2)  ---------------------------------
--R                     +-------+
--R                     | 2    2
--R                    \|x  + a
--R                                                     Type: Expression Integer
--E

--S 65 of 110
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 66 of 110     14:198 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

               2
   (4)  - log(a ) - 1
                                                     Type: Expression Integer
--R
--R               2
--R   (4)  - log(a ) - 1
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 67 of 110
aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
 

                       +-------+
             3     2   | 2    2      4     2 2     4
        (- 2x  - 4a x)\|x  + a   + 2x  + 5a x  + 2a
   (1)  --------------------------------------------
                         +-------+
                 2    2  | 2    2      3     2
              (2x  + a )\|x  + a   - 2x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       +-------+
--R             3     2   | 2    2      4     2 2     4
--R        (- 2x  - 4a x)\|x  + a   + 2x  + 5a x  + 2a
--R   (1)  --------------------------------------------
--R                         +-------+
--R                 2    2  | 2    2      3     2
--R              (2x  + a )\|x  + a   - 2x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68 of 110
bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2)
 

          2     2
         x  + 2a
   (2)  ----------
         +-------+
         | 2    2
        \|x  + a
                                                     Type: Expression Integer
--R
--R          2     2
--R         x  + 2a
--R   (2)  ----------
--R         +-------+
--R         | 2    2
--R        \|x  + a
--R                                                     Type: Expression Integer
--E

--S 69 of 110     14:199 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 70 of 110
aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
 

   (1)
            +-------+                +-------+
            | 2    2     2    2      | 2    2
       (- x\|x  + a   + x  + a )log(\|x  + a   - x + a)
     + 
          +-------+                +-------+              +-------+
          | 2    2     2    2      | 2    2               | 2    2
       (x\|x  + a   - x  - a )log(\|x  + a   - x - a) - a\|x  + a   + a x
  /
         +-------+
      3  | 2    2     3 2    5
     a x\|x  + a   - a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            +-------+                +-------+
--R            | 2    2     2    2      | 2    2
--R       (- x\|x  + a   + x  + a )log(\|x  + a   - x + a)
--R     + 
--R          +-------+                +-------+              +-------+
--R          | 2    2     2    2      | 2    2               | 2    2
--R       (x\|x  + a   - x  - a )log(\|x  + a   - x - a) - a\|x  + a   + a x
--R  /
--R         +-------+
--R      3  | 2    2     3 2    5
--R     a x\|x  + a   - a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 71 of 110
bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x)
 

                         +-------+
           +-------+     | 2    2
           | 2    2     \|x  + a   + a
        - \|x  + a  log(--------------) + a
                               x
   (2)  -----------------------------------
                       +-------+
                     3 | 2    2
                    a \|x  + a
                                                     Type: Expression Integer
--R
--R                         +-------+
--R           +-------+     | 2    2
--R           | 2    2     \|x  + a   + a
--R        - \|x  + a  log(--------------) + a
--R                               x
--R   (2)  -----------------------------------
--R                       +-------+
--R                     3 | 2    2
--R                    a \|x  + a
--R                                                     Type: Expression Integer
--E

--S 72 of 110
cc:=aa-bb
 

   (3)
                                                              +-------+
          +-------+                 +-------+                 | 2    2
          | 2    2                  | 2    2                 \|x  + a   + a
   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
                                                                    x
   -------------------------------------------------------------------------
                                        3
                                       a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                              +-------+
--R          +-------+                 +-------+                 | 2    2
--R          | 2    2                  | 2    2                 \|x  + a   + a
--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
--R                                                                    x
--R   -------------------------------------------------------------------------
--R                                        3
--R                                       a
--R                                                     Type: Expression Integer
--E

--S 73 of 110
dd:=expandLog cc
 

   (4)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
      3
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R      3
--R     a
--R                                                     Type: Expression Integer
--E

--S 74 of 110     14:200 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
              3
             a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R              3
--R             a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 75 of 110
aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
 

                           1
   (1)  - -----------------------------------
                      +-------+
             3    2   | 2    2      4     2 2
          (2x  + a x)\|x  + a   - 2x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           1
--R   (1)  - -----------------------------------
--R                      +-------+
--R             3    2   | 2    2      4     2 2
--R          (2x  + a x)\|x  + a   - 2x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 76 of 110
bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2))
 

              2    2
          - 2x  - a
   (2)  -------------
            +-------+
         4  | 2    2
        a x\|x  + a
                                                     Type: Expression Integer
--R
--R              2    2
--R          - 2x  - a
--R   (2)  -------------
--R            +-------+
--R         4  | 2    2
--R        a x\|x  + a
--R                                                     Type: Expression Integer
--E

--S 77 of 110     14:201 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           2
   (3)  - --
           4
          a
                                                     Type: Expression Integer
--R
--R           2
--R   (3)  - --
--R           4
--R          a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 78 of 110
aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
 

   (1)
                       +-------+                              +-------+
            5     2 3  | 2    2       6      2 4     4 2      | 2    2
       ((12x  + 9a x )\|x  + a   - 12x  - 15a x  - 3a x )log(\|x  + a   - x + a)
     + 
                           +-------+
                5     2 3  | 2    2       6      2 4     4 2
         ((- 12x  - 9a x )\|x  + a   + 12x  + 15a x  + 3a x )
      *
              +-------+
              | 2    2
         log(\|x  + a   - x - a)
     + 
                             +-------+
             4     3 2    5  | 2    2         5      3 3     5
       (12a x  + 7a x  + a )\|x  + a   - 12a x  - 13a x  - 3a x
  /
                     +-------+
        5 5     7 3  | 2    2      5 6      7 4     9 2
     (8a x  + 6a x )\|x  + a   - 8a x  - 10a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       +-------+                              +-------+
--R            5     2 3  | 2    2       6      2 4     4 2      | 2    2
--R       ((12x  + 9a x )\|x  + a   - 12x  - 15a x  - 3a x )log(\|x  + a   - x + a)
--R     + 
--R                           +-------+
--R                5     2 3  | 2    2       6      2 4     4 2
--R         ((- 12x  - 9a x )\|x  + a   + 12x  + 15a x  + 3a x )
--R      *
--R              +-------+
--R              | 2    2
--R         log(\|x  + a   - x - a)
--R     + 
--R                             +-------+
--R             4     3 2    5  | 2    2         5      3 3     5
--R       (12a x  + 7a x  + a )\|x  + a   - 12a x  - 13a x  - 3a x
--R  /
--R                     +-------+
--R        5 5     7 3  | 2    2      5 6      7 4     9 2
--R     (8a x  + 6a x )\|x  + a   - 8a x  - 10a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 79 of 110
bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x^2+a^2))/x)
 

                          +-------+
            +-------+     | 2    2
          2 | 2    2     \|x  + a   + a        2    3
        3x \|x  + a  log(--------------) - 3a x  - a
                                x
   (2)  ---------------------------------------------
                             +-------+
                         5 2 | 2    2
                       2a x \|x  + a
                                                     Type: Expression Integer
--R
--R                          +-------+
--R            +-------+     | 2    2
--R          2 | 2    2     \|x  + a   + a        2    3
--R        3x \|x  + a  log(--------------) - 3a x  - a
--R                                x
--R   (2)  ---------------------------------------------
--R                             +-------+
--R                         5 2 | 2    2
--R                       2a x \|x  + a
--R                                                     Type: Expression Integer
--E

--S 80 of 110
cc:=aa-bb
 

   (3)
                                                               +-------+
         +-------+                  +-------+                  | 2    2
         | 2    2                   | 2    2                  \|x  + a   + a
   3log(\|x  + a   - x + a) - 3log(\|x  + a   - x - a) - 3log(--------------)
                                                                     x
   --------------------------------------------------------------------------
                                         5
                                       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                               +-------+
--R         +-------+                  +-------+                  | 2    2
--R         | 2    2                   | 2    2                  \|x  + a   + a
--R   3log(\|x  + a   - x + a) - 3log(\|x  + a   - x - a) - 3log(--------------)
--R                                                                     x
--R   --------------------------------------------------------------------------
--R                                         5
--R                                       2a
--R                                                     Type: Expression Integer
--E

--S 81 of 110
dd:=expandLog cc
 

   (4)
               +-------+              +-------+
               | 2    2               | 2    2
       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
     + 
               +-------+
               | 2    2
       - 3log(\|x  + a   - x - a) + 3log(x)
  /
       5
     2a
                                                     Type: Expression Integer
--R
--R   (4)
--R               +-------+              +-------+
--R               | 2    2               | 2    2
--R       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
--R     + 
--R               +-------+
--R               | 2    2
--R       - 3log(\|x  + a   - x - a) + 3log(x)
--R  /
--R       5
--R     2a
--R                                                     Type: Expression Integer
--E

--S 82 of 110     14:202 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        3log(- 1)
   (5)  ---------
             5
           2a
                                                     Type: Expression Integer
--R
--R        3log(- 1)
--R   (5)  ---------
--R             5
--R           2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 83 of 110
aa:=integrate((x^2+a^2)^(3/2),x)
 

   (1)
                           +-------+                              +-------+
              4 3      6   | 2    2       4 4      6 2     8      | 2    2
       ((- 24a x  - 12a x)\|x  + a   + 24a x  + 24a x  + 3a )log(\|x  + a   - x)
     + 
                                         +-------+
             7      2 5      4 3     6   | 2    2       8      2 6      4 4
       (- 16x  - 56a x  - 42a x  - 5a x)\|x  + a   + 16x  + 64a x  + 68a x
     + 
          6 2
       20a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                           +-------+                              +-------+
--R              4 3      6   | 2    2       4 4      6 2     8      | 2    2
--R       ((- 24a x  - 12a x)\|x  + a   + 24a x  + 24a x  + 3a )log(\|x  + a   - x)
--R     + 
--R                                         +-------+
--R             7      2 5      4 3     6   | 2    2       8      2 6      4 4
--R       (- 16x  - 56a x  - 42a x  - 5a x)\|x  + a   + 16x  + 64a x  + 68a x
--R     + 
--R          6 2
--R       20a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84 of 110
bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2))
 

                +-------+                     +-------+
          4     | 2    2            3     2   | 2    2
        3a log(\|x  + a   + x) + (2x  + 5a x)\|x  + a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                +-------+                     +-------+
--R          4     | 2    2            3     2   | 2    2
--R        3a log(\|x  + a   + x) + (2x  + 5a x)\|x  + a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 85 of 110
cc:=aa-bb
 

                  +-------+                +-------+
            4     | 2    2           4     | 2    2
        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x)
   (3)  -------------------------------------------------
                                8
                                                     Type: Expression Integer
--R
--R                  +-------+                +-------+
--R            4     | 2    2           4     | 2    2
--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x)
--R   (3)  -------------------------------------------------
--R                                8
--R                                                     Type: Expression Integer
--E

--S 86 of 110     14:203 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

            4     2
          3a log(a )
   (4)  - ----------
               8
                                                     Type: Expression Integer
--R
--R            4     2
--R          3a log(a )
--R   (4)  - ----------
--R               8
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 87 of 110
aa:=integrate(x*(x^2+a^2)^(3/2),x)
 

   (1)
                                                  +-------+
             9      2 7      4 5      6 3     8   | 2    2       10      2 8
       (- 16x  - 52a x  - 61a x  - 30a x  - 5a x)\|x  + a   + 16x   + 60a x
     + 
          4 6      6 4      8 2    10
       85a x  + 55a x  + 15a x  + a
  /
                           +-------+
         4      2 2     4  | 2    2       5       2 3      4
     (80x  + 60a x  + 5a )\|x  + a   - 80x  - 100a x  - 25a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7      4 5      6 3     8   | 2    2       10      2 8
--R       (- 16x  - 52a x  - 61a x  - 30a x  - 5a x)\|x  + a   + 16x   + 60a x
--R     + 
--R          4 6      6 4      8 2    10
--R       85a x  + 55a x  + 15a x  + a
--R  /
--R                           +-------+
--R         4      2 2     4  | 2    2       5       2 3      4
--R     (80x  + 60a x  + 5a )\|x  + a   - 80x  - 100a x  - 25a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 88 of 110
bb:=(x^2+a^2)^(5/2)/5
 

                          +-------+
          4     2 2    4  | 2    2
        (x  + 2a x  + a )\|x  + a
   (2)  ---------------------------
                     5
                                                     Type: Expression Integer
--R
--R                          +-------+
--R          4     2 2    4  | 2    2
--R        (x  + 2a x  + a )\|x  + a
--R   (2)  ---------------------------
--R                     5
--R                                                     Type: Expression Integer
--E

--S 89 of 110     14:204 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 90 of 110
aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
 

   (1)
                                      +-------+
               6 5      8 3      10   | 2    2       6 6       8 4      10 2
           (96a x  + 96a x  + 18a  x)\|x  + a   - 96a x  - 144a x  - 54a  x
         + 
               12
           - 3a
      *
              +-------+
              | 2    2
         log(\|x  + a   - x)
     + 
                                                                 +-------+
              11       2 9       4 7       6 5      8 3     10   | 2    2
       (- 256x   - 832a x  - 912a x  - 404a x  - 68a x  - 3a  x)\|x  + a
     + 
           12       2 10        4 8       6 6       8 4      10 2
       256x   + 960a x   + 1296a x  + 772a x  + 198a x  + 18a  x
  /
                                  +-------+
           5        2 3       4   | 2    2         6        2 4       4 2      6
     (1536x  + 1536a x  + 288a x)\|x  + a   - 1536x  - 2304a x  - 864a x  - 48a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                      +-------+
--R               6 5      8 3      10   | 2    2       6 6       8 4      10 2
--R           (96a x  + 96a x  + 18a  x)\|x  + a   - 96a x  - 144a x  - 54a  x
--R         + 
--R               12
--R           - 3a
--R      *
--R              +-------+
--R              | 2    2
--R         log(\|x  + a   - x)
--R     + 
--R                                                                 +-------+
--R              11       2 9       4 7       6 5      8 3     10   | 2    2
--R       (- 256x   - 832a x  - 912a x  - 404a x  - 68a x  - 3a  x)\|x  + a
--R     + 
--R           12       2 10        4 8       6 6       8 4      10 2
--R       256x   + 960a x   + 1296a x  + 772a x  + 198a x  + 18a  x
--R  /
--R                                  +-------+
--R           5        2 3       4   | 2    2         6        2 4       4 2      6
--R     (1536x  + 1536a x  + 288a x)\|x  + a   - 1536x  - 2304a x  - 864a x  - 48a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91 of 110
bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^6/16*log(x+sqrt(x^2+a^2))
 

                  +-------+                              +-------+
            6     | 2    2            5      2 3     4   | 2    2
        - 3a log(\|x  + a   + x) + (8x  + 14a x  + 3a x)\|x  + a
   (2)  ----------------------------------------------------------
                                    48
                                                     Type: Expression Integer
--R
--R                  +-------+                              +-------+
--R            6     | 2    2            5      2 3     4   | 2    2
--R        - 3a log(\|x  + a   + x) + (8x  + 14a x  + 3a x)\|x  + a
--R   (2)  ----------------------------------------------------------
--R                                    48
--R                                                     Type: Expression Integer
--E

--S 92 of 110
cc:=aa-bb
 

               +-------+               +-------+
         6     | 2    2          6     | 2    2
        a log(\|x  + a   + x) + a log(\|x  + a   - x)
   (3)  ---------------------------------------------
                              16
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         6     | 2    2          6     | 2    2
--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
--R   (3)  ---------------------------------------------
--R                              16
--R                                                     Type: Expression Integer
--E

--S 93 of 110     14:205 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

         6     2
        a log(a )
   (4)  ---------
            16
                                                     Type: Expression Integer
--R
--R         6     2
--R        a log(a )
--R   (4)  ---------
--R            16
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 94 of 110
aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
 

   (1)
                   13        2 11        4 9       6 7       8 5       10 3
             - 320x   - 1072a x   - 1240a x  - 467a x  + 112a x  + 105a  x
           + 
                12
             14a  x
      *
          +-------+
          | 2    2
         \|x  + a
     + 
           14        2 12        4 10       6 8      8 6       10 4      12 2
       320x   + 1232a x   + 1736a x   + 973a x  + 21a x  - 175a  x  - 49a  x
     + 
           14
       - 2a
  /
                                            +-------+
             6        2 4       4 2      6  | 2    2         7        2 5
       (2240x  + 2800a x  + 840a x  + 35a )\|x  + a   - 2240x  - 3920a x
     + 
              4 3       6
       - 1960a x  - 245a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   13        2 11        4 9       6 7       8 5       10 3
--R             - 320x   - 1072a x   - 1240a x  - 467a x  + 112a x  + 105a  x
--R           + 
--R                12
--R             14a  x
--R      *
--R          +-------+
--R          | 2    2
--R         \|x  + a
--R     + 
--R           14        2 12        4 10       6 8      8 6       10 4      12 2
--R       320x   + 1232a x   + 1736a x   + 973a x  + 21a x  - 175a  x  - 49a  x
--R     + 
--R           14
--R       - 2a
--R  /
--R                                            +-------+
--R             6        2 4       4 2      6  | 2    2         7        2 5
--R       (2240x  + 2800a x  + 840a x  + 35a )\|x  + a   - 2240x  - 3920a x
--R     + 
--R              4 3       6
--R       - 1960a x  - 245a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 95 of 110
bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5
 

                                   +-------+
           6     2 4    4 2     6  | 2    2
        (5x  + 8a x  + a x  - 2a )\|x  + a
   (2)  ------------------------------------
                         35
                                                     Type: Expression Integer
--R
--R                                   +-------+
--R           6     2 4    4 2     6  | 2    2
--R        (5x  + 8a x  + a x  - 2a )\|x  + a
--R   (2)  ------------------------------------
--R                         35
--R                                                     Type: Expression Integer
--E

--S 96 of 110     14:206 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 97 of 110
aa:=integrate((x^2+a^2)^(3/2)/x,x)
 

   (1)
                         +-------+                      +-------+
              3 2     5  | 2    2       3 3     5       | 2    2
       ((- 12a x  - 3a )\|x  + a   + 12a x  + 9a x)log(\|x  + a   - x + a)
     + 
                       +-------+                      +-------+
            3 2     5  | 2    2       3 3     5       | 2    2
       ((12a x  + 3a )\|x  + a   - 12a x  - 9a x)log(\|x  + a   - x - a)
     + 
                                +-------+
            5      2 3      4   | 2    2      6      2 4      4 2     6
       (- 4x  - 19a x  - 12a x)\|x  + a   + 4x  + 21a x  + 21a x  + 4a
  /
                  +-------+
         2     2  | 2    2       3     2
     (12x  + 3a )\|x  + a   - 12x  - 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                         +-------+                      +-------+
--R              3 2     5  | 2    2       3 3     5       | 2    2
--R       ((- 12a x  - 3a )\|x  + a   + 12a x  + 9a x)log(\|x  + a   - x + a)
--R     + 
--R                       +-------+                      +-------+
--R            3 2     5  | 2    2       3 3     5       | 2    2
--R       ((12a x  + 3a )\|x  + a   - 12a x  - 9a x)log(\|x  + a   - x - a)
--R     + 
--R                                +-------+
--R            5      2 3      4   | 2    2      6      2 4      4 2     6
--R       (- 4x  - 19a x  - 12a x)\|x  + a   + 4x  + 21a x  + 21a x  + 4a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3     2
--R     (12x  + 3a )\|x  + a   - 12x  - 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 98 of 110
bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x)
 

                  +-------+
                  | 2    2                    +-------+
            3    \|x  + a   + a      2     2  | 2    2
        - 3a log(--------------) + (x  + 4a )\|x  + a
                        x
   (2)  -----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                  +-------+
--R                  | 2    2                    +-------+
--R            3    \|x  + a   + a      2     2  | 2    2
--R        - 3a log(--------------) + (x  + 4a )\|x  + a
--R                        x
--R   (2)  -----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 99 of 110
cc:=aa-bb
 

   (3)
              +-------+                   +-------+
        3     | 2    2              3     | 2    2
     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
   + 
            +-------+
            | 2    2
      3    \|x  + a   + a
     a log(--------------)
                  x
                                                     Type: Expression Integer
--R
--R   (3)
--R              +-------+                   +-------+
--R        3     | 2    2              3     | 2    2
--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
--R   + 
--R            +-------+
--R            | 2    2
--R      3    \|x  + a   + a
--R     a log(--------------)
--R                  x
--R                                                     Type: Expression Integer
--E

--S 100 of 110
dd:=expandLog cc
 

   (4)
            +-------+               +-------+
      3     | 2    2          3     | 2    2
     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
   + 
            +-------+
      3     | 2    2              3
     a log(\|x  + a   - x - a) - a log(x)
                                                     Type: Expression Integer
--R
--R   (4)
--R            +-------+               +-------+
--R      3     | 2    2          3     | 2    2
--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
--R   + 
--R            +-------+
--R      3     | 2    2              3
--R     a log(\|x  + a   - x - a) - a log(x)
--R                                                     Type: Expression Integer
--E

--S 101 of 110    14:207 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

           3
   (5)  - a log(- 1)
                                                     Type: Expression Integer
--R
--R           3
--R   (5)  - a log(- 1)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 102 of 110
aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
 

   (1)
                          +-------+                       +-------+
              2 3     4   | 2    2       2 4     4 2      | 2    2
       ((- 12a x  - 3a x)\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x)
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2     6
       (- 4x  - 3a x  + 4a x)\|x  + a   + 4x  + 5a x  - 3a x  - 2a
  /
                  +-------+
        3     2   | 2    2      4     2 2
     (8x  + 2a x)\|x  + a   - 8x  - 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                          +-------+                       +-------+
--R              2 3     4   | 2    2       2 4     4 2      | 2    2
--R       ((- 12a x  - 3a x)\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x)
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (- 4x  - 3a x  + 4a x)\|x  + a   + 4x  + 5a x  - 3a x  - 2a
--R  /
--R                  +-------+
--R        3     2   | 2    2      4     2 2
--R     (8x  + 2a x)\|x  + a   - 8x  - 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103 of 110
bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2))
 

                  +-------+                   +-------+
          2       | 2    2           2     2  | 2    2
        3a x log(\|x  + a   + x) + (x  - 2a )\|x  + a
   (2)  -----------------------------------------------
                               2x
                                                     Type: Expression Integer
--R
--R                  +-------+                   +-------+
--R          2       | 2    2           2     2  | 2    2
--R        3a x log(\|x  + a   + x) + (x  - 2a )\|x  + a
--R   (2)  -----------------------------------------------
--R                               2x
--R                                                     Type: Expression Integer
--E

--S 104 of 110
cc:=aa-bb
 

                  +-------+                +-------+
            2     | 2    2           2     | 2    2           2
        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x) - 2a
   (3)  -------------------------------------------------------
                                   2
                                                     Type: Expression Integer
--R
--R                  +-------+                +-------+
--R            2     | 2    2           2     | 2    2           2
--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x) - 2a
--R   (3)  -------------------------------------------------------
--R                                   2
--R                                                     Type: Expression Integer
--E

--S 105 of 110    14:208 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

            2     2      2
        - 3a log(a ) - 2a
   (4)  ------------------
                 2
                                                     Type: Expression Integer
--R
--R            2     2      2
--R        - 3a log(a ) - 2a
--R   (4)  ------------------
--R                 2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 106 of 110
aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
 

   (1)
                           +-------+                       +-------+
                4     3 2  | 2    2         5     3 3      | 2    2
       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
     + 
                         +-------+                       +-------+
              4     3 2  | 2    2         5     3 3      | 2    2
       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2    6
       (- 8x  - 2a x  + 3a x)\|x  + a   + 8x  + 6a x  - 3a x  - a
  /
                   +-------+
        4     2 2  | 2    2      5     2 3
     (8x  + 2a x )\|x  + a   - 8x  - 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +-------+                       +-------+
--R                4     3 2  | 2    2         5     3 3      | 2    2
--R       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
--R     + 
--R                         +-------+                       +-------+
--R              4     3 2  | 2    2         5     3 3      | 2    2
--R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2    6
--R       (- 8x  - 2a x  + 3a x)\|x  + a   + 8x  + 6a x  - 3a x  - a
--R  /
--R                   +-------+
--R        4     2 2  | 2    2      5     2 3
--R     (8x  + 2a x )\|x  + a   - 8x  - 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 107 of 110
bb:=-(x^2+a^2)^(3/2)/(2*x^2)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x)
 

                    +-------+
                    | 2    2                    +-------+
              2    \|x  + a   + a       2    2  | 2    2
        - 3a x log(--------------) + (2x  - a )\|x  + a
                          x
   (2)  -------------------------------------------------
                                 2
                               2x
                                                     Type: Expression Integer
--R
--R                    +-------+
--R                    | 2    2                    +-------+
--R              2    \|x  + a   + a       2    2  | 2    2
--R        - 3a x log(--------------) + (2x  - a )\|x  + a
--R                          x
--R   (2)  -------------------------------------------------
--R                                 2
--R                               2x
--R                                                     Type: Expression Integer
--E

--S 108 of 110
cc:=aa-bb
 

   (3)
                 +-------+                    +-------+
                 | 2    2                     | 2    2
       - 3a log(\|x  + a   - x + a) + 3a log(\|x  + a   - x - a)
     + 
               +-------+
               | 2    2
              \|x  + a   + a
       3a log(--------------)
                     x
  /
     2
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +-------+                    +-------+
--R                 | 2    2                     | 2    2
--R       - 3a log(\|x  + a   - x + a) + 3a log(\|x  + a   - x - a)
--R     + 
--R               +-------+
--R               | 2    2
--R              \|x  + a   + a
--R       3a log(--------------)
--R                     x
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 109 of 110
dd:=expandLog cc
 

   (4)
               +-------+                +-------+
               | 2    2                 | 2    2
       3a log(\|x  + a   + a) - 3a log(\|x  + a   - x + a)
     + 
               +-------+
               | 2    2
       3a log(\|x  + a   - x - a) - 3a log(x)
  /
     2
                                                     Type: Expression Integer
--R
--R   (4)
--R               +-------+                +-------+
--R               | 2    2                 | 2    2
--R       3a log(\|x  + a   + a) - 3a log(\|x  + a   - x + a)
--R     + 
--R               +-------+
--R               | 2    2
--R       3a log(\|x  + a   - x - a) - 3a log(x)
--R  /
--R     2
--R                                                     Type: Expression Integer
--E

--S 110 of 110    14:209 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          3a log(- 1)
   (5)  - -----------
               2
                                                     Type: Expression Integer
--R
--R          3a log(- 1)
--R   (5)  - -----------
--R               2
--R                                                     Type: Expression Integer
--E

)spool
 
Starts dribbling to arith.output (2010/3/27, 18:23:5).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 25
234+108
 

   (1)  342
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  342
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 25
234*108
 

   (2)  25272
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  25272
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 25
234**108
 

   (3)
  7504341690759264167679309791024278941530727955934090653805060111651544673126_
   088300475695723868519539237537191538150810021660251720209488577129906170829_
   305169117495939513626114577980010503744097313250953950814884553019803764362_
   781777309157631769660459319296
                                                        Type: PositiveInteger
--R 
--R
--R   (3)
--R  7504341690759264167679309791024278941530727955934090653805060111651544673126_
--R   088300475695723868519539237537191538150810021660251720209488577129906170829_
--R   305169117495939513626114577980010503744097313250953950814884553019803764362_
--R   781777309157631769660459319296
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 25
factor %
 

         108 216  108
   (4)  2   3   13
                                                       Type: Factored Integer
--R 
--R
--R         108 216  108
--R   (4)  2   3   13
--R                                                       Type: Factored Integer
--E 4

--S 5 of 25
z := 1/2
 

        1
   (5)  -
        2
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (5)  -
--R        2
--R                                                       Type: Fraction Integer
--E 5

--S 6 of 25
v := (z + 1) ** 10
 

        59049
   (6)  -----
         1024
                                                       Type: Fraction Integer
--R 
--R
--R        59049
--R   (6)  -----
--R         1024
--R                                                       Type: Fraction Integer
--E 6

--S 7 of 25
1024 * %
 

   (7)  59049
                                                       Type: Fraction Integer
--R 
--R
--R   (7)  59049
--R                                                       Type: Fraction Integer
--E 7

--S 8 of 25
u := (x+1)**6
 

         6     5      4      3      2
   (8)  x  + 6x  + 15x  + 20x  + 15x  + 6x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         6     5      4      3      2
--R   (8)  x  + 6x  + 15x  + 20x  + 15x  + 6x + 1
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 25
differentiate(u,x)
 

          5      4      3      2
   (9)  6x  + 30x  + 60x  + 60x  + 30x + 6
                                                     Type: Polynomial Integer
--R 
--R
--R          5      4      3      2
--R   (9)  6x  + 30x  + 60x  + 60x  + 30x + 6
--R                                                     Type: Polynomial Integer
--E 9

-- factor %
)clear all
 
 
-- compute Fibonacci numbers
--S 10 of 25
fib(n | n = 0)  == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 25
fib(n | n = 1)  == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 25
fib(n | n > 1)  == fib(n-1) + fib(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 25
fib 5
 
   Compiling function fib with type Integer -> PositiveInteger 
   Compiling function fib as a recurrence relation.

   (4)  8
                                                        Type: PositiveInteger
--R 
--R   Compiling function fib with type Integer -> PositiveInteger 
--R   Compiling function fib as a recurrence relation.
--R
--R   (4)  8
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 25
fib 20
 

   (5)  10946
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  10946
--R                                                        Type: PositiveInteger
--E 14

)clear all
 

-- compute Legendre polynomials
--S 15 of 25
leg(n | n = 0)  == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 25
leg(n | n = 1)  == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 25
leg(n | n > 1)  == ((2*n-1)*x*leg(n-1)-(n-1)*leg(n-2))/n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 25
leg 3
 
   Compiling function leg with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function leg as a recurrence relation.

        5  3   3
   (4)  - x  - - x
        2      2
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function leg with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function leg as a recurrence relation.
--R
--R        5  3   3
--R   (4)  - x  - - x
--R        2      2
--R                                            Type: Polynomial Fraction Integer
--E 18

--S 19 of 25
leg 14
 

   (5)
     5014575  14   16900975  12   22309287  10   14549535  8   4849845  6
     ------- x   - -------- x   + -------- x   - -------- x  + ------- x
       2048          2048           2048           2048          2048
   + 
       765765  4   45045  2    429
     - ------ x  + ----- x  - ----
        2048        2048      2048
                                            Type: Polynomial Fraction Integer
--R 
--R
--R   (5)
--R     5014575  14   16900975  12   22309287  10   14549535  8   4849845  6
--R     ------- x   - -------- x   + -------- x   - -------- x  + ------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       765765  4   45045  2    429
--R     - ------ x  + ----- x  - ----
--R        2048        2048      2048
--R                                            Type: Polynomial Fraction Integer
--E 19

-- look at it as a polynomial with rational number coefficients
--% :: POLY FRAC INT
)clear all
 
 
-- several flavors of computing factorial
--S 20 of 25
fac1(n | n=1)   == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 25
fac1(n | n > 1) == n*fac1(n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 25
fac2 n == if n = 1 then 1 else n*fac2(n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 25
fac3 n == reduce(*,[1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 25
fac1 10
 
   Compiling function fac1 with type Integer -> Integer 
   Compiling function fac1 as a recurrence relation.

   (5)  3628800
                                                        Type: PositiveInteger
--R 
--R   Compiling function fac1 with type Integer -> Integer 
--R   Compiling function fac1 as a recurrence relation.
--R
--R   (5)  3628800
--R                                                        Type: PositiveInteger
--E 24

--S 25 of 25
fac2 10
 
   Compiling function fac2 with type Integer -> Integer 
   Compiling function fac2 as a recurrence relation.

   (6)  3628800
                                                        Type: PositiveInteger
--R 
--R   Compiling function fac2 with type Integer -> Integer 
--R   Compiling function fac2 as a recurrence relation.
--R
--R   (6)  3628800
--R                                                        Type: PositiveInteger
--E 25
)spool
 
Starts dribbling to decimal.output (2010/3/27, 18:24:53).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from DecimalExpansionXmpPage

--S 1 of 7
r := decimal(22/7)
 

          ______
   (1)  3.142857
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (1)  3.142857
--R                                                       Type: DecimalExpansion
--E 1

--S 2 of 7
r + decimal(6/7)
 

   (2)  4
                                                       Type: DecimalExpansion
--R 
--R
--R   (2)  4
--R                                                       Type: DecimalExpansion
--E 2

--S 3 of 7
[decimal(1/i) for i in 350..354] 
 

   (3)
        ______    ______         __    ________________________________
   [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983,
       __________________________________________________________
    0.00282485875706214689265536723163841807909604519774011299435]
                                                  Type: List DecimalExpansion
--R 
--R
--R   (3)
--R        ______    ______         __    ________________________________
--R   [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983,
--R       __________________________________________________________
--R    0.00282485875706214689265536723163841807909604519774011299435]
--R                                                  Type: List DecimalExpansion
--E 3

--S 4 of 7
decimal(1/2049) 
 

   (4)
   0.
     OVERBAR
        00048804294777940458760370912640312347486578818936066373840897999023914
          104441190824792581747193753050268423621278672523182040019521717911176
          183504148365056124938994631527574426549536359199609565641776476329917
          032698877501220107369448511469009272816007808687164470473401659346022
          449975597852611029770619814543679843826256710590531966813079551
                                                       Type: DecimalExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        00048804294777940458760370912640312347486578818936066373840897999023914
--R          104441190824792581747193753050268423621278672523182040019521717911176
--R          183504148365056124938994631527574426549536359199609565641776476329917
--R          032698877501220107369448511469009272816007808687164470473401659346022
--R          449975597852611029770619814543679843826256710590531966813079551
--R                                                       Type: DecimalExpansion
--E 4

--S 5 of 7
p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9)
 

             2     _      _
   (5)  0.25x  + 0.6x + 0.4
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R             2     _      _
--R   (5)  0.25x  + 0.6x + 0.4
--R                                            Type: Polynomial DecimalExpansion
--E 5

--S 6 of 7
q := differentiate(p, x)
 

                 _
   (6)  0.5x + 0.6
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R                 _
--R   (6)  0.5x + 0.6
--R                                            Type: Polynomial DecimalExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              _
   (7)  x + 1.3
                                            Type: Polynomial DecimalExpansion
--R 
--R
--R              _
--R   (7)  x + 1.3
--R                                            Type: Polynomial DecimalExpansion
--E 7
)spool
 
Starts dribbling to nepip.output (2010/3/27, 18:30:4).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 27
outputGeneral 5
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 27
mA1 := matrix [[ 0.5 ,   1.5 ,   6.6 ,   4.8],  _
               [ 1.5 ,   6.5 ,  16.2 ,   8.6],  _
               [ 6.6 ,  16.2 ,  37.6 ,   9.8],  _
               [ 4.8 ,   8.6 ,   9.8 , -17.1]];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 2

--S 3 of 27
mB1 := matrix[[ 1 ,  3 ,   4 ,  1],  _
              [ 3 , 13 ,  16 , 11],  _
              [ 4 , 16 ,  24 , 18],  _
              [ 1 , 11 ,  18 , 27]];
 

                                                         Type: Matrix Integer
--R 
--R
--R                                                         Type: Matrix Integer
--E 3

--S 4 of 27
mA2 := matrix [[ 3.9 ,  12.5 , -34.5 ,  -0.5],  _
               [ 4.3 ,  21.5 , -47.5 ,   7.5],  _
               [ 4.3 ,  21.5 , -43.5 ,   3.5],  _
               [ 4.4 ,  26.0 , -46.0 ,   6.0]];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 4

--S 5 of 27
mB2 := matrix[[ 1 , 2 , -3 , 1],  _
              [ 1 , 3 , -5 , 4],  _
              [ 1 , 3 , -4 , 3],  _
              [ 1 , 3 , -4 , 4]];
 

                                                         Type: Matrix Integer
--R 
--R
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 27 used to work?
nagEigenvalues(mA1,mB1) :: List Float
 
   There are no library operations named nagEigenvalues 
      Use HyperDoc Browse or issue
                           )what op nagEigenvalues
      to learn if there is any operation containing " nagEigenvalues " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvalues with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvalues 
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvalues with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6
--       [- 3.0,- 1.0,2.0,4.0]

--S 7 of 27
vv1 := nagEigenvectors(mA1,mB1);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 7

--S 8 of 27 used to work?
(vv1.eigenvalues) :: List Float
 
   There are no library operations named vv1 
      Use HyperDoc Browse or issue
                                )what op vv1
      to learn if there is any operation containing " vv1 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv1 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv1 
--R      Use HyperDoc Browse or issue
--R                                )what op vv1
--R      to learn if there is any operation containing " vv1 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv1 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 8
--       [- 3.0,- 1.0,2.0,4.0]

--S 9 of 27 used to work?
(vv1.eigenvectors) :: List Vector Complex Float
 
   There are no library operations named vv1 
      Use HyperDoc Browse or issue
                                )what op vv1
      to learn if there is any operation containing " vv1 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv1 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv1 
--R      Use HyperDoc Browse or issue
--R                                )what op vv1
--R      to learn if there is any operation containing " vv1 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv1 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9
-- [[- 4.35,0.05,1.0,- 0.5], [- 2.05,0.15,0.5,- 0.5], [- 3.95,0.85,0.5,- 0.5],
--  [2.65,0.05,- 1.0,0.5]]

--S 10 of 27
nagEigenvalues(mA2,mB2)
 
   There are no library operations named nagEigenvalues 
      Use HyperDoc Browse or issue
                           )what op nagEigenvalues
      to learn if there is any operation containing " nagEigenvalues " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvalues with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvalues 
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvalues with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 10

--S 11 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Matrix Integer to List Complex Float for 
      value
   +1  2  - 3  1+
   |            |
   |1  3  - 5  4|
   |            |
   |1  3  - 4  3|
   |            |
   +1  3  - 4  4+

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Matrix Integer to List Complex Float for 
--R      value
--R   +1  2  - 3  1+
--R   |            |
--R   |1  3  - 5  4|
--R   |            |
--R   |1  3  - 4  3|
--R   |            |
--R   +1  3  - 4  4+
--R
--E 11
--       [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]

--S 12 of 27
vv2 := nagEigenvectors(mA2,mB2);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12

--S 13 of 27
vv2.eigenvalues
 
   There are no library operations named vv2 
      Use HyperDoc Browse or issue
                                )what op vv2
      to learn if there is any operation containing " vv2 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2
--R      to learn if there is any operation containing " vv2 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 13


--S 14 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Matrix Integer to List Complex Float for 
      value
   +1  2  - 3  1+
   |            |
   |1  3  - 5  4|
   |            |
   |1  3  - 4  3|
   |            |
   +1  3  - 4  4+

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Matrix Integer to List Complex Float for 
--R      value
--R   +1  2  - 3  1+
--R   |            |
--R   |1  3  - 5  4|
--R   |            |
--R   |1  3  - 4  3|
--R   |            |
--R   +1  3  - 4  4+
--R
--E 14
--       [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]

--S 15 of 27 used to work?
vv2.eigenvectors :: List Vector Complex Float
 
   There are no library operations named vv2 
      Use HyperDoc Browse or issue
                                )what op vv2
      to learn if there is any operation containing " vv2 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2
--R      to learn if there is any operation containing " vv2 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15

-- [[0.99606,0.0056917,0.062609,0.062609],
--
--   [0.94491, 0.18898 + 0.26077 E -14 %i, 0.11339 - 0.15119 %i,
--    0.11339 - 0.15119 %i]
--   ,
--
--   [0.94491, 0.18898 - 0.26077 E -14 %i, 0.11339 + 0.15119 %i,
--    0.11339 + 0.15119 %i]
--   ,
--  [0.98752,0.010972,- 0.032917,0.15361]]

-- The same call with eps=0.0001:
--S 16 of 27
vv2a := nagEigenvectors(mA2,mB2,0.0001);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16

--S 17 of 27 used to work?
vv2a.eigenvalues :: List Complex Float
 
   There are no library operations named vv2a 
      Use HyperDoc Browse or issue
                                )what op vv2a
      to learn if there is any operation containing " vv2a " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2a 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2a 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2a
--R      to learn if there is any operation containing " vv2a " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2a 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       [1.9989,3.0003 + 3.9994 %i,3.0003 - 3.9994 %i,4.0]

--S 18 of 27
vv2a.eigenvectors :: List Vector Complex Float
 
   There are no library operations named vv2a 
      Use HyperDoc Browse or issue
                                )what op vv2a
      to learn if there is any operation containing " vv2a " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv2a 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv2a 
--R      Use HyperDoc Browse or issue
--R                                )what op vv2a
--R      to learn if there is any operation containing " vv2a " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2a 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18
-- [[0.99605,0.0057355,0.062656,0.062656],
--
--   [0.94491, 0.18899 - 0.000048882 %i, 0.11336 - 0.15119 %i,
--    0.11336 - 0.15119 %i]
--   ,
--
--   [0.94491, 0.18899 + 0.000048882 %i, 0.11336 + 0.15119 %i,
--    0.11336 + 0.15119 %i]
--   ,
--  [0.98751,0.011031,- 0.032912,0.15367]]

--S 19 of 27
mB1(1,1) := -1;
 

                                                                Type: Integer
--R 
--R
--R                                                                Type: Integer
--E 19

--S 20 of 27
nagEigenvalues(mA1,mB1)
 
   There are no library operations named nagEigenvalues 
      Use HyperDoc Browse or issue
                           )what op nagEigenvalues
      to learn if there is any operation containing " nagEigenvalues " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvalues with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvalues 
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvalues with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20

--S 21 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Integer to List Complex Float for value
   - 1

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Integer to List Complex Float for value
--R   - 1
--R
--E 21
--       [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]

--S 22 of 27
vv3 := nagEigenvectors(mA1,mB1);
 
   There are no library operations named nagEigenvectors 
      Use HyperDoc Browse or issue
                          )what op nagEigenvectors
      to learn if there is any operation containing " nagEigenvectors "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEigenvectors with argument type(s) 
                                Matrix Float
                               Matrix Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEigenvectors 
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEigenvectors with argument type(s) 
--R                                Matrix Float
--R                               Matrix Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 22

--S 23 of 27
vv3.eigenvalues
 
   There are no library operations named vv3 
      Use HyperDoc Browse or issue
                                )what op vv3
      to learn if there is any operation containing " vv3 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv3 
      with argument type(s) 
                            Variable eigenvalues
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv3 
--R      Use HyperDoc Browse or issue
--R                                )what op vv3
--R      to learn if there is any operation containing " vv3 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv3 
--R      with argument type(s) 
--R                            Variable eigenvalues
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23


--S 24 of 27 used to work?
% :: List Complex Float
 
 
Daly Bug
   Cannot convert from type Integer to List Complex Float for value
   - 1

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Integer to List Complex Float for value
--R   - 1
--R
--E 24
--       [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]

--S 25 of 27 used to work?
vv3.eigenvectors :: List Vector Complex Float
 
   There are no library operations named vv3 
      Use HyperDoc Browse or issue
                                )what op vv3
      to learn if there is any operation containing " vv3 " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named vv3 
      with argument type(s) 
                            Variable eigenvectors
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named vv3 
--R      Use HyperDoc Browse or issue
--R                                )what op vv3
--R      to learn if there is any operation containing " vv3 " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv3 
--R      with argument type(s) 
--R                            Variable eigenvectors
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25
--  [[- 0.034577,0.63045,- 0.75202,0.1892],
--   [0.17876,- 0.73845,0.047413,0.64845],
--
--    [0.80838, - 0.00095133 + 0.47557 %i, - 0.20354 - 0.21737 %i,
--     0.15404 + 0.089179 %i]
--    ,
--
--    [0.80838, - 0.00095133 - 0.47557 %i, - 0.20354 + 0.21737 %i,
--     0.15404 - 0.089179 %i]
--   ]

--S 26 of 27
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

--S 27 of 27
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 27
)spool 
 
Starts dribbling to op1.output (2010/3/27, 18:30:31).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 21
R := SQMATRIX(2, INT)
 

   (1)  SquareMatrix(2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  SquareMatrix(2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 21
t := operator("tilde") :: OP(R)
 

   (2)  tilde
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R   (2)  tilde
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 2

--S 3 of 21
)set expose add constructor Operator
 
   Operator is now explicitly exposed in frame initial 
--R 
--R   Operator is now explicitly exposed in frame initial 
--E 3

--S 4 of 21
evaluate(t, m +-> transpose m)
 

   (3)  tilde
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R   (3)  tilde
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 4

--S 5 of 21
s : R := matrix [[0, 1], [1, 0]]
 

        +0  1+
   (4)  |    |
        +1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  1+
--R   (4)  |    |
--R        +1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 5

--S 6 of 21
rho := t * s
 

             +0  1+
   (5)  tilde|    |
             +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R             +0  1+
--R   (5)  tilde|    |
--R             +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 6

--S 7 of 21
z := rho**4 - 1
 

                   +0  1+     +0  1+     +0  1+     +0  1+
   (6)  - 1 + tilde|    |tilde|    |tilde|    |tilde|    |
                   +1  0+     +1  0+     +1  0+     +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R                   +0  1+     +0  1+     +0  1+     +0  1+
--R   (6)  - 1 + tilde|    |tilde|    |tilde|    |tilde|    |
--R                   +1  0+     +1  0+     +1  0+     +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 7

--S 8 of 21
m:R := matrix [[1, 2], [3, 4]]
 

        +1  2+
   (7)  |    |
        +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 21
z m
 

        +0  0+
   (8)  |    |
        +0  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  0+
--R   (8)  |    |
--R        +0  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 9

--S 10 of 21
rho m
 

        +3  1+
   (9)  |    |
        +4  2+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +3  1+
--R   (9)  |    |
--R        +4  2+
--R                                                Type: SquareMatrix(2,Integer)
--E 10

--S 11 of 21
rho rho m
 

         +4  3+
   (10)  |    |
         +2  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +4  3+
--R   (10)  |    |
--R         +2  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 11

--S 12 of 21
(rho**3) m
 

         +2  4+
   (11)  |    |
         +1  3+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +2  4+
--R   (11)  |    |
--R         +1  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 12

--S 13 of 21
b := t * s - s * t
 

           +0  1+             +0  1+
   (12)  - |    |tilde + tilde|    |
           +1  0+             +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R           +0  1+             +0  1+
--R   (12)  - |    |tilde + tilde|    |
--R           +1  0+             +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 13

--S 14 of 21
b m
 

         +1  - 3+
   (13)  |      |
         +3  - 1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +1  - 3+
--R   (13)  |      |
--R         +3  - 1+
--R                                                Type: SquareMatrix(2,Integer)
--E 14

--S 15 of 21
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 21
dx := operator("D") :: OP(POLY FRAC INT)
 

   (15)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (15)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 16

--S 17 of 21
evaluate(dx, p +-> D(p, 'x))
 

   (16)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (16)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 17

--S 18 of 21
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 21
L 15
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

   (18)
     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
       2048          2048           2048           2048          2048
   + 
       2909907  5   255255  3   6435
     - ------- x  + ------ x  - ---- x
         2048        2048       2048
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R   (18)
--R     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
--R     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       2909907  5   255255  3   6435
--R     - ------- x  + ------ x  - ---- x
--R         2048        2048       2048
--R                                            Type: Polynomial Fraction Integer
--E 18

--S 20 of 21
E 15
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                        2      2
   (19)  240 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                        2      2
--R   (19)  240 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 20

--S 21 of 21
(E 15)(L 15)
 

   (20)  0
                                            Type: Polynomial Fraction Integer
--R 
--R
--R   (20)  0
--R                                            Type: Polynomial Fraction Integer
--E 21
)spool 
 
Starts dribbling to kuipers.output (2010/3/27, 18:28:34).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 30
R1:=matrix([[cos a, sin a, 0],[-sin a, cos a, 0],[0, 0, 1]])
 

        + cos(a)   sin(a)  0+
        |                   |
   (1)  |- sin(a)  cos(a)  0|
        |                   |
        +   0        0     1+
                                              Type: Matrix Expression Integer
--R 
--R
--R        + cos(a)   sin(a)  0+
--R        |                   |
--R   (1)  |- sin(a)  cos(a)  0|
--R        |                   |
--R        +   0        0     1+
--R                                              Type: Matrix Expression Integer
--E 1

--S 2 of 30
R2:=matrix([[cos b, 0, -sin b],[0, 1, 0],[sin b, 0, cos b]])
 

        +cos(b)  0  - sin(b)+
        |                   |
   (2)  |  0     1     0    |
        |                   |
        +sin(b)  0   cos(b) +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +cos(b)  0  - sin(b)+
--R        |                   |
--R   (2)  |  0     1     0    |
--R        |                   |
--R        +sin(b)  0   cos(b) +
--R                                              Type: Matrix Expression Integer
--E 2

--S 3 of 30
R:=R2*R1
 

        +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
        |                                    |
   (3)  |  - sin(a)       cos(a)        0    |
        |                                    |
        +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
--R        |                                    |
--R   (3)  |  - sin(a)       cos(a)        0    |
--R        |                                    |
--R        +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
--R                                              Type: Matrix Expression Integer
--E 3

--S 4 of 30
V:=matrix([[x1],[y1],[z1]])
 

        +x1+
        |  |
   (4)  |y1|
        |  |
        +z1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +x1+
--R        |  |
--R   (4)  |y1|
--R        |  |
--R        +z1+
--R                                              Type: Matrix Polynomial Integer
--E 4

--S 5 of 30
E:=R*V=V
 

        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b)+  +x1+
        |                                               |  |  |
   (5)  |            - x1 sin(a) + y1 cos(a)            |= |y1|
        |                                               |  |  |
        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b)   +  +z1+
                                     Type: Equation Matrix Expression Integer
--R 
--R
--R        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b)+  +x1+
--R        |                                               |  |  |
--R   (5)  |            - x1 sin(a) + y1 cos(a)            |= |y1|
--R        |                                               |  |  |
--R        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b)   +  +z1+
--R                                     Type: Equation Matrix Expression Integer
--E 5

--S 6 of 30
F:=lhs(E)-rhs(E)
 

        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+
        |                                                    |
   (6)  |            - x1 sin(a) + y1 cos(a) - y1            |
        |                                                    |
        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+
--R        |                                                    |
--R   (6)  |            - x1 sin(a) + y1 cos(a) - y1            |
--R        |                                                    |
--R        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +
--R                                              Type: Matrix Expression Integer
--E 6

--S 7 of 30
G:=F=matrix([[0],[0],[0]])
 

        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+  +0+
        |                                                    |  | |
   (7)  |            - x1 sin(a) + y1 cos(a) - y1            |= |0|
        |                                                    |  | |
        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +  +0+
                                     Type: Equation Matrix Expression Integer
--R 
--R
--R        +- z1 sin(b) + y1 cos(b)sin(a) + x1 cos(a)cos(b) - x1+  +0+
--R        |                                                    |  | |
--R   (7)  |            - x1 sin(a) + y1 cos(a) - y1            |= |0|
--R        |                                                    |  | |
--R        +   (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1   +  +0+
--R                                     Type: Equation Matrix Expression Integer
--E 7

--S 8 of 30
H:=elt(F,2,1)
 

   (8)  - x1 sin(a) + y1 cos(a) - y1
                                                     Type: Expression Integer
--R 
--R
--R   (8)  - x1 sin(a) + y1 cos(a) - y1
--R                                                     Type: Expression Integer
--E 8

--S 9 of 30
x1:=k
 

   (9)  k
                                                             Type: Variable k
--R 
--R
--R   (9)  k
--R                                                             Type: Variable k
--E 9

--S 10 of 30
J:=subst(H,'x1=k)
 

   (10)  - k sin(a) + y1 cos(a) - y1
                                                     Type: Expression Integer
--R 
--R
--R   (10)  - k sin(a) + y1 cos(a) - y1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 30
L:=solve(J,y1)
 

               k sin(a)
   (11)  [y1= ----------]
              cos(a) - 1
                                       Type: List Equation Expression Integer
--R 
--R
--R               k sin(a)
--R   (11)  [y1= ----------]
--R              cos(a) - 1
--R                                       Type: List Equation Expression Integer
--E 11

--S 12 of 30
y1:=rhs(first(solve(J,y1)))
 

          k sin(a)
   (12)  ----------
         cos(a) - 1
                                                     Type: Expression Integer
--R 
--R
--R          k sin(a)
--R   (12)  ----------
--R         cos(a) - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 30
H1:=elt(F,3,1)
 

   (13)  (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1
                                                     Type: Expression Integer
--R 
--R
--R   (13)  (y1 sin(a) + x1 cos(a))sin(b) + z1 cos(b) - z1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 30
J1:=subst(H1,['x1=x1, 'y1=y1])
 

   (14)
                2           2
       (k sin(a)  + k cos(a)  - k cos(a))sin(b) + (z1 cos(a) - z1)cos(b)
     + 
       - z1 cos(a) + z1
  /
     cos(a) - 1
                                                     Type: Expression Integer
--R 
--R
--R   (14)
--R                2           2
--R       (k sin(a)  + k cos(a)  - k cos(a))sin(b) + (z1 cos(a) - z1)cos(b)
--R     + 
--R       - z1 cos(a) + z1
--R  /
--R     cos(a) - 1
--R                                                     Type: Expression Integer
--E 14

--S 15 of 30
z1:=simplify(rhs(first(solve(J1,z1))))
 

          k sin(b)
   (15)  ----------
         cos(b) - 1
                                                     Type: Expression Integer
--R 
--R
--R          k sin(b)
--R   (15)  ----------
--R         cos(b) - 1
--R                                                     Type: Expression Integer
--E 15

--S 16 of 30
[x1,y1,z1]
 

             k sin(a)   k sin(b)
   (16)  [k,----------,----------]
            cos(a) - 1 cos(b) - 1
                                                Type: List Expression Integer
--R 
--R
--R             k sin(a)   k sin(b)
--R   (16)  [k,----------,----------]
--R            cos(a) - 1 cos(b) - 1
--R                                                Type: List Expression Integer
--E 16

--S 17 of 30
y1:=eval(y1,[k=-1])
 

             sin(a)
   (17)  - ----------
           cos(a) - 1
                                                     Type: Expression Integer
--R 
--R
--R             sin(a)
--R   (17)  - ----------
--R           cos(a) - 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 30
z1:=eval(z1,[k=-1])
 

             sin(b)
   (18)  - ----------
           cos(b) - 1
                                                     Type: Expression Integer
--R 
--R
--R             sin(b)
--R   (18)  - ----------
--R           cos(b) - 1
--R                                                     Type: Expression Integer
--E 18

--S 19 of 30
[x1,y1,z1]
 

                sin(a)       sin(b)
   (19)  [k,- ----------,- ----------]
              cos(a) - 1   cos(b) - 1
                                                Type: List Expression Integer
--R 
--R
--R                sin(a)       sin(b)
--R   (19)  [k,- ----------,- ----------]
--R              cos(a) - 1   cos(b) - 1
--R                                                Type: List Expression Integer
--E 19

--S 20 of 30
RSQ:SQMATRIX(3,EXPR(INT)):=R
 

         +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
         |                                    |
   (20)  |  - sin(a)       cos(a)        0    |
         |                                    |
         +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
                                     Type: SquareMatrix(3,Expression Integer)
--R 
--R
--R         +cos(a)cos(b)  cos(b)sin(a)  - sin(b)+
--R         |                                    |
--R   (20)  |  - sin(a)       cos(a)        0    |
--R         |                                    |
--R         +cos(a)sin(b)  sin(a)sin(b)   cos(b) +
--R                                     Type: SquareMatrix(3,Expression Integer)
--E 20

--S 21 of 30
TR:=trace(RSQ)
 

   (21)  (cos(a) + 1)cos(b) + cos(a)
                                                     Type: Expression Integer
--R 
--R
--R   (21)  (cos(a) + 1)cos(b) + cos(a)
--R                                                     Type: Expression Integer
--E 21

--S 22 of 30
TREQ:=TR=1+2*cos(c)
 

   (22)  (cos(a) + 1)cos(b) + cos(a)= 2cos(c) + 1
                                            Type: Equation Expression Integer
--R 
--R
--R   (22)  (cos(a) + 1)cos(b) + cos(a)= 2cos(c) + 1
--R                                            Type: Equation Expression Integer
--E 22

--S 23 of 30
c:=rhs(first(solve(TREQ,c)))
 

              (cos(a) + 1)cos(b) + cos(a) - 1
   (23)  acos(-------------------------------)
                             2
                                                     Type: Expression Integer
--R 
--R
--R              (cos(a) + 1)cos(b) + cos(a) - 1
--R   (23)  acos(-------------------------------)
--R                             2
--R                                                     Type: Expression Integer
--E 23

--S 24 of 30
x1v:=eval(x1,k=-1)
 

   (24)  - 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (24)  - 1
--R                                                     Type: Polynomial Integer
--E 24

--S 25 of 30
y1v:=numeric(eval(y1,[a=%pi/6]))
 

   (25)  3.7320508075 688772936
                                                                  Type: Float
--R 
--R
--R   (25)  3.7320508075 688772936
--R                                                                  Type: Float
--E 25

--S 26 of 30
z1v:=numeric(eval(z1,[k=-1,b=%pi/3]))
 

   (26)  1.7320508075 688772935
                                                                  Type: Float
--R 
--R
--R   (26)  1.7320508075 688772935
--R                                                                  Type: Float
--E 26

--S 27 of 30
[x1v, y1v, z1v]
 

   (27)  [- 1.0,3.7320508075 688772936,1.7320508075 688772935]
                                                  Type: List Polynomial Float
--R 
--R
--R   (27)  [- 1.0,3.7320508075 688772936,1.7320508075 688772935]
--R                                                  Type: List Polynomial Float
--E 27

--S 28 of 30
c1v:=numeric(eval(c,[a=%pi/6,b=%pi/3]))
 

   (28)  1.1598041770 494147762
                                                                  Type: Float
--R 
--R
--R   (28)  1.1598041770 494147762
--R                                                                  Type: Float
--E 28

--S 29 of 30
c1v*180/%pi
 

   (29)  66.4518844065 75160021
                                                                  Type: Float
--R 
--R
--R   (29)  66.4518844065 75160021
--R                                                                  Type: Float
--E 29

--S 30 of 30
rv:=eval(R,[a=%pi/6,b=%pi/3])
 

         + +-+           +-++
         |\|3    1      \|3 |
         |----   -    - ----|
         |  4    4        2 |
         |                  |
         |       +-+        |
   (30)  |  1   \|3         |
         |- -   ----    0   |
         |  2     2         |
         |                  |
         |       +-+        |
         | 3    \|3     1   |
         | -    ----    -   |
         + 4      4     2   +
                                              Type: Matrix Expression Integer
--R 
--R
--R         + +-+           +-++
--R         |\|3    1      \|3 |
--R         |----   -    - ----|
--R         |  4    4        2 |
--R         |                  |
--R         |       +-+        |
--R   (30)  |  1   \|3         |
--R         |- -   ----    0   |
--R         |  2     2         |
--R         |                  |
--R         |       +-+        |
--R         | 3    \|3     1   |
--R         | -    ----    -   |
--R         + 4      4     2   +
--R                                              Type: Matrix Expression Integer
--E 30
)spool 
 
Starts dribbling to exlimit.output (2010/3/27, 18:25:40).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 13
limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)
 

          1
   (1)  - -
          2
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R          1
--R   (1)  - -
--R          2
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 1

)clear all
 

--S 2 of 13
complexLimit((2 + z)/(1 - z),z = %infinity)
 

   (1)  - 1
                         Type: OnePointCompletion Fraction Polynomial Integer
--R 
--R
--R   (1)  - 1
--R                         Type: OnePointCompletion Fraction Polynomial Integer
--E 2

--S 3 of 13
limit(sin(x)/x,x = %plusInfinity)
 

   (2)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (2)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 3

--S 4 of 13
complexLimit(sin(x)/x,x = %infinity)
 

   (3)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (3)  "failed"
--R                                                    Type: Union("failed",...)
--E 4

)clear all
 

--S 5 of 13
limit(x * log(x),x = 0,"right")
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 13
limit(x * log(x),x = 0)
 

   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 6

)clear all
 

--S 7 of 13
limit(sqrt(y**2)/y,y = 0)
 

   (1)  [leftHandLimit= - 1,rightHandLimit= 1]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (1)  [leftHandLimit= - 1,rightHandLimit= 1]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 7

--S 8 of 13
limit(sqrt(1 - cos(t))/t,t = 0)
 

                            1                    1
   (2)  [leftHandLimit= - ----,rightHandLimit= ----]
                           +-+                  +-+
                          \|2                  \|2
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R                            1                    1
--R   (2)  [leftHandLimit= - ----,rightHandLimit= ----]
--R                           +-+                  +-+
--R                          \|2                  \|2
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 8

)clear all
 

--S 9 of 13
limit(sqrt(3*x**2 + 1)/(5*x),x = %plusInfinity)
 

         +-+
        \|3
   (1)  ----
          5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         +-+
--R        \|3
--R   (1)  ----
--R          5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 9

--S 10 of 13
limit(sqrt(3*x**2 + 1)/(5*x),x = %minusInfinity)
 

           +-+
          \|3
   (2)  - ----
            5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R           +-+
--R          \|3
--R   (2)  - ----
--R            5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 10

)clear all
 

--S 11 of 13
limit(sinh(a*x)/tan(b*x),x = 0)
 

        a
   (1)  -
        b
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        a
--R   (1)  -
--R        b
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 11

)clear all
 

--S 12 of 13
limit(z * sin(1/z),z = 0)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 12

--S 13 of 13
complexLimit(z * sin(1/z),z = 0)
 

   (2)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (2)  "failed"
--R                                                    Type: Union("failed",...)
--E 13
)spool 
 
Starts dribbling to biquat.output (2010/3/27, 18:23:16).
)set message test on
 
)set message auto off
 
)clear all
 
 

--S 1 of 43
C:=Complex Expression Integer
 

   (1)  Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Complex Expression Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 43
Q:=Quaternion C
 

   (2)  Quaternion Complex Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (2)  Quaternion Complex Expression Integer
--R                                                                 Type: Domain
--E 2

--S 3 of 43
q:Q:=quatern(q0,q1,q2,q3)
 

   (3)  q0 + q1 i + q2 j + q3 k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (3)  q0 + q1 i + q2 j + q3 k
--R                                  Type: Quaternion Complex Expression Integer
--E 3


--S 4 of 43
qlist(l:List C):Q==quatern(1.1,1.2,1.3,1.4)
 
   Function declaration qlist : List Complex Expression Integer -> 
      Quaternion Complex Expression Integer has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration qlist : List Complex Expression Integer -> 
--R      Quaternion Complex Expression Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 4


--S 5 of 43
listq(x:Q):List C == [real x, imagI x, imagJ x, imagK x]
 
   Function declaration listq : Quaternion Complex Expression Integer
       -> List Complex Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration listq : Quaternion Complex Expression Integer
--R       -> List Complex Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 5


--S 6 of 43
matrixq(x:Q):Matrix C == matrix _
             [[real x + %i*imagI(x), imagJ x + %i*imagK(x)],_
             [-imagJ(x) + %i*imagK(x), real x - %i*imagI(x)]]
 
   Function declaration matrixq : Quaternion Complex Expression Integer
       -> Matrix Complex Expression Integer has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration matrixq : Quaternion Complex Expression Integer
--R       -> Matrix Complex Expression Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 6


--S 7 of 43
sig0:=quatern(1,0,0,0)::Q
 

   (7)  1
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (7)  1
--R                                  Type: Quaternion Complex Expression Integer
--E 7

--S 8 of 43
sig1:=%i*quatern(0,0,0,1)::Q
 

   (8)  %i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (8)  %i k
--R                                  Type: Quaternion Complex Expression Integer
--E 8

--S 9 of 43
sig2:=%i*quatern(0,0,1,0)::Q
 

   (9)  %i j
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (9)  %i j
--R                                  Type: Quaternion Complex Expression Integer
--E 9

--S 10 of 43
sig3:=-%i*quatern(0,1,0,0)::Q
 

   (10)  - %i i
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (10)  - %i i
--R                                  Type: Quaternion Complex Expression Integer
--E 10


--S 11 of 43
siglist(x:Q):List C == [real x, -imagK(x)*%i, -imagJ(x)*%i, %i*imagI(x)]
 
   Function declaration siglist : Quaternion Complex Expression Integer
       -> List Complex Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration siglist : Quaternion Complex Expression Integer
--R       -> List Complex Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 11


--S 12 of 43
D(q:Q,x:Symbol,y:Symbol,z:Symbol):Q==sig1*D(q,x)+sig2*D(q,y)+sig3*D(q,z)
 
   Function declaration D : (Quaternion Complex Expression Integer,
      Symbol,Symbol,Symbol) -> Quaternion Complex Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration D : (Quaternion Complex Expression Integer,
--R      Symbol,Symbol,Symbol) -> Quaternion Complex Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 12


--S 13 of 43
Ft:=operator 'Ft
 

   (13)  Ft
                                                          Type: BasicOperator
--R 
--R
--R   (13)  Ft
--R                                                          Type: BasicOperator
--E 13

--S 14 of 43
Fx:=operator 'Fx
 

   (14)  Fx
                                                          Type: BasicOperator
--R 
--R
--R   (14)  Fx
--R                                                          Type: BasicOperator
--E 14

--S 15 of 43
Fy:=operator 'Fy
 

   (15)  Fy
                                                          Type: BasicOperator
--R 
--R
--R   (15)  Fy
--R                                                          Type: BasicOperator
--E 15

--S 16 of 43
Fz:=operator 'Fz
 

   (16)  Fz
                                                          Type: BasicOperator
--R 
--R
--R   (16)  Fz
--R                                                          Type: BasicOperator
--E 16


--S 17 of 43
F:Q:=Ft(x,y,z)*sig0+Fx(x,y,z)*sig1+Fy(x,y,z)*sig2+Fz(x,y,z)*sig3
 

   (17)  Ft(x,y,z) - Fz(x,y,z)%i i + Fy(x,y,z)%i j + Fx(x,y,z)%i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (17)  Ft(x,y,z) - Fz(x,y,z)%i i + Fy(x,y,z)%i j + Fx(x,y,z)%i k
--R                                  Type: Quaternion Complex Expression Integer
--E 17


--S 18 of 43
siglist(D(F,x,y,z))
 
   Compiling function D with type (Quaternion Complex Expression 
      Integer,Symbol,Symbol,Symbol) -> Quaternion Complex Expression 
      Integer 
   Compiling function siglist with type Quaternion Complex Expression 
      Integer -> List Complex Expression Integer 

   (18)
   [Fz  (x,y,z) + Fy  (x,y,z) + Fx  (x,y,z),
      ,3            ,2            ,1
    Ft  (x,y,z) + (Fz  (x,y,z) - Fy  (x,y,z))%i,
      ,1             ,2            ,3
    Ft  (x,y,z) + (- Fz  (x,y,z) + Fx  (x,y,z))%i,
      ,2               ,1            ,3
    Ft  (x,y,z) + (Fy  (x,y,z) - Fx  (x,y,z))%i]
      ,3             ,1            ,2
                                        Type: List Complex Expression Integer
--R 
--R   Compiling function D with type (Quaternion Complex Expression 
--R      Integer,Symbol,Symbol,Symbol) -> Quaternion Complex Expression 
--R      Integer 
--R   Compiling function siglist with type Quaternion Complex Expression 
--R      Integer -> List Complex Expression Integer 
--R
--R   (18)
--R   [Fz  (x,y,z) + Fy  (x,y,z) + Fx  (x,y,z),
--R      ,3            ,2            ,1
--R    Ft  (x,y,z) + (Fz  (x,y,z) - Fy  (x,y,z))%i,
--R      ,1             ,2            ,3
--R    Ft  (x,y,z) + (- Fz  (x,y,z) + Fx  (x,y,z))%i,
--R      ,2               ,1            ,3
--R    Ft  (x,y,z) + (Fy  (x,y,z) - Fx  (x,y,z))%i]
--R      ,3             ,1            ,2
--R                                        Type: List Complex Expression Integer
--E 18


--S 19 of 43
rot(theta:Expression Integer,q:Q):Q==cos(theta/2)-%i::Q*q*sin(theta/2)
 
   Function declaration rot : (Expression Integer,Quaternion Complex 
      Expression Integer) -> Quaternion Complex Expression Integer has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration rot : (Expression Integer,Quaternion Complex 
--R      Expression Integer) -> Quaternion Complex Expression Integer has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 19


--S 20 of 43
((x:Q)/(y:Q)):Q == x*inv(y)
 
   Function declaration ?/? : (Quaternion Complex Expression Integer,
      Quaternion Complex Expression Integer) -> Quaternion Complex 
      Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration ?/? : (Quaternion Complex Expression Integer,
--R      Quaternion Complex Expression Integer) -> Quaternion Complex 
--R      Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 20

--S 21 of 43
abs(q:Q):C == sqrt((q*conjugate(q))::C)
 
   Function declaration abs : Quaternion Complex Expression Integer -> 
      Complex Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration abs : Quaternion Complex Expression Integer -> 
--R      Complex Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 21

--S 22 of 43
exp(q:Q):Q == (_
  q-conjugate(q)=0 => exp( (q+conjugate(q))::C/2)$C * sig0; _
  exp( (q+conjugate(q))::C/2)$C * (sig0*cos(abs(q)) +_
  (q-conjugate(q))/abs(q-conjugate(q))*sin(abs(q))) )
 
   Function declaration exp : Quaternion Complex Expression Integer -> 
      Quaternion Complex Expression Integer has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration exp : Quaternion Complex Expression Integer -> 
--R      Quaternion Complex Expression Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 22


--S 23 of 43
qx:=sig1
 

   (23)  %i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R   (23)  %i k
--R                                  Type: Quaternion Complex Expression Integer
--E 23

--S 24 of 43
mm:=siglist(rot(2,qx))
 
   Compiling function / with type (Quaternion Complex Expression 
      Integer,Quaternion Complex Expression Integer) -> Quaternion 
      Complex Expression Integer 
   There are 2 exposed and 6 unexposed library operations named cos 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op cos
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named cos 
      with argument type(s) 
                    Quaternion Complex Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function rot with type (Expression Integer,Quaternion 
      Complex Expression Integer) -> Quaternion Complex Expression 
      Integer 

   (24)
                2         3                  3          2
    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
   [-------------------------------- + ----------------------------- %i,
                  2          2                     2          2
           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
                  2         3                    3            2
    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
    ---------------------------------- + --------------------------------- %i,
                   2          2                        2          2
            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
    0, 0]
                                        Type: List Complex Expression Integer
--R 
--R   Compiling function / with type (Quaternion Complex Expression 
--R      Integer,Quaternion Complex Expression Integer) -> Quaternion 
--R      Complex Expression Integer 
--R   There are 2 exposed and 6 unexposed library operations named cos 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op cos
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named cos 
--R      with argument type(s) 
--R                    Quaternion Complex Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function rot with type (Expression Integer,Quaternion 
--R      Complex Expression Integer) -> Quaternion Complex Expression 
--R      Integer 
--R
--R   (24)
--R                2         3                  3          2
--R    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
--R   [-------------------------------- + ----------------------------- %i,
--R                  2          2                     2          2
--R           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
--R                  2         3                    3            2
--R    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
--R    ---------------------------------- + --------------------------------- %i,
--R                   2          2                        2          2
--R            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
--R    0, 0]
--R                                        Type: List Complex Expression Integer
--E 24

--S 25 of 43
nn:=siglist(exp(-%i::Q*qx))
 
   There are 2 exposed and 7 unexposed library operations named exp 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op exp
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named exp 
      with argument type(s) 
                    Quaternion Complex Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function exp with type Quaternion Complex Expression 
      Integer -> Quaternion Complex Expression Integer 
   Compiling function abs with type Quaternion Complex Expression 
      Integer -> Complex Expression Integer 

   (25)
                2         3                  3          2
    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
   [-------------------------------- + ----------------------------- %i,
                  2          2                     2          2
           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
                  2         3                    3            2
    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
    ---------------------------------- + --------------------------------- %i,
                   2          2                        2          2
            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
    0, 0]
                                        Type: List Complex Expression Integer
--R 
--R   There are 2 exposed and 7 unexposed library operations named exp 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op exp
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named exp 
--R      with argument type(s) 
--R                    Quaternion Complex Expression Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function exp with type Quaternion Complex Expression 
--R      Integer -> Quaternion Complex Expression Integer 
--R   Compiling function abs with type Quaternion Complex Expression 
--R      Integer -> Complex Expression Integer 
--R
--R   (25)
--R                2         3                  3          2
--R    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
--R   [-------------------------------- + ----------------------------- %i,
--R                  2          2                     2          2
--R           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
--R                  2         3                    3            2
--R    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
--R    ---------------------------------- + --------------------------------- %i,
--R                   2          2                        2          2
--R            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
--R    0, 0]
--R                                        Type: List Complex Expression Integer
--E 25

--S 26 of 43
(mm=nn)@Boolean
 

   (26)  true
                                                                Type: Boolean
--R 
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26


--S 27 of 43
qnv:=q1*sig1+q2*sig2+sqrt(1-q1^2-q2^2)*sig3
 

            +---------------+
            |    2     2
   (27)  - \|- q2  - q1  + 1 %i i + q2 %i j + q1 %i k
                                  Type: Quaternion Complex Expression Integer
--R 
--R
--R            +---------------+
--R            |    2     2
--R   (27)  - \|- q2  - q1  + 1 %i i + q2 %i j + q1 %i k
--R                                  Type: Quaternion Complex Expression Integer
--E 27


--S 28 of 43
theta:=_\theta
 

   (28)  \theta
                                                        Type: Variable \theta
--R 
--R
--R   (28)  \theta
--R                                                        Type: Variable \theta
--E 28

--S 29 of 43
testqeq:=map(simplify,siglist(rot(theta,qnv)-exp((-theta/2)*%i*qnv)))_
         ::List Expression Complex Integer
 

   (29)
           +-------+
           |      2
          \|\theta          \theta
   [- cos(----------) + cos(------),
               2               2
                        +-------+
          +-------+     |      2
          |      2     \|\theta                       \theta
    %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
                            2                            2
    ---------------------------------------------------------,
                              \theta
                        +-------+
          +-------+     |      2
          |      2     \|\theta                       \theta
    %i q2\|\theta  sin(----------) - %i \theta q2 sin(------)
                            2                            2
    ---------------------------------------------------------,
                              \theta

                                            +-------+
            +---------------+ +-------+     |      2
            |    2     2      |      2     \|\theta
         %i\|- q2  - q1  + 1 \|\theta  sin(----------)
                                                2
       + 
                                 +---------------+
                         \theta  |    2     2
         - %i \theta sin(------)\|- q2  - q1  + 1
                            2
    /
       \theta
     ]
                                        Type: List Expression Complex Integer
--R 
--R
--R   (29)
--R           +-------+
--R           |      2
--R          \|\theta          \theta
--R   [- cos(----------) + cos(------),
--R               2               2
--R                        +-------+
--R          +-------+     |      2
--R          |      2     \|\theta                       \theta
--R    %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
--R                            2                            2
--R    ---------------------------------------------------------,
--R                              \theta
--R                        +-------+
--R          +-------+     |      2
--R          |      2     \|\theta                       \theta
--R    %i q2\|\theta  sin(----------) - %i \theta q2 sin(------)
--R                            2                            2
--R    ---------------------------------------------------------,
--R                              \theta
--R
--R                                            +-------+
--R            +---------------+ +-------+     |      2
--R            |    2     2      |      2     \|\theta
--R         %i\|- q2  - q1  + 1 \|\theta  sin(----------)
--R                                                2
--R       + 
--R                                 +---------------+
--R                         \theta  |    2     2
--R         - %i \theta sin(------)\|- q2  - q1  + 1
--R                            2
--R    /
--R       \theta
--R     ]
--R                                        Type: List Expression Complex Integer
--E 29


--S 30 of 43
posthetaRule:=rule sqrt(theta^2)==theta
 

          +------+
          |     2
   (30)  \|theta   == theta
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R          +------+
--R          |     2
--R   (30)  \|theta   == theta
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 30


--S 31 of 43
map(x+->posthetaRule(x), [0,sqrt(theta^2),0,sqrt(theta^2)])
 

   (31)  [0,\theta,0,\theta]
                                                Type: List Expression Integer
--R 
--R
--R   (31)  [0,\theta,0,\theta]
--R                                                Type: List Expression Integer
--E 31


--S 32 of 43
posthetaRule testqeq.1
 
   There are no library operations named posthetaRule 
      Use HyperDoc Browse or issue
                            )what op posthetaRule
      to learn if there is any operation containing " posthetaRule " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      posthetaRule with argument type(s) 
                         Expression Complex Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named posthetaRule 
--R      Use HyperDoc Browse or issue
--R                            )what op posthetaRule
--R      to learn if there is any operation containing " posthetaRule " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      posthetaRule with argument type(s) 
--R                         Expression Complex Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 32


--S 33 of 43
[posthetaRule (testqeq.i::Expression Integer) for i in 1..1]
 

   (32)  [0]
                                                Type: List Expression Integer
--R 
--R
--R   (32)  [0]
--R                                                Type: List Expression Integer
--E 33


--S 34 of 43
[posthetaRule (testqeq.i::Expression Integer) for i in 1..4]
 
 
Daly Bug
   Cannot convert from type Expression Complex Integer to Expression 
      Integer for value
                       +-------+
         +-------+     |      2
         |      2     \|\theta                       \theta
   %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
                           2                            2
   ---------------------------------------------------------
                             \theta

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Expression Complex Integer to Expression 
--R      Integer for value
--R                       +-------+
--R         +-------+     |      2
--R         |      2     \|\theta                       \theta
--R   %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
--R                           2                            2
--R   ---------------------------------------------------------
--R                             \theta
--R
--E 34


--S 35 of 43
)show RewriteRule
 
 RewriteRule(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base))  is a domain constructor
 Abbreviation for RewriteRule is RULE 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for RULE 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                coerce : Equation F -> %
 coerce : % -> OutputForm              elt : (%,F,PositiveInteger) -> F
 ?.? : (%,F) -> F                      hash : % -> SingleInteger
 latex : % -> String                   lhs : % -> F
 pattern : % -> Pattern Base           retract : % -> Equation F
 rhs : % -> F                          rule : (F,F,List Symbol) -> %
 rule : (F,F) -> %                     ?~=? : (%,%) -> Boolean
 quotedOperators : % -> List Symbol
 retractIfCan : % -> Union(Equation F,"failed")
 suchThat : (%,List Symbol,(List F -> Boolean)) -> %

--R 
--R RewriteRule(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base))  is a domain constructor
--R Abbreviation for RewriteRule is RULE 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for RULE 
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean                coerce : Equation F -> %
--R coerce : % -> OutputForm              elt : (%,F,PositiveInteger) -> F
--R ?.? : (%,F) -> F                      hash : % -> SingleInteger
--R latex : % -> String                   lhs : % -> F
--R pattern : % -> Pattern Base           retract : % -> Equation F
--R rhs : % -> F                          rule : (F,F,List Symbol) -> %
--R rule : (F,F) -> %                     ?~=? : (%,%) -> Boolean
--R quotedOperators : % -> List Symbol
--R retractIfCan : % -> Union(Equation F,"failed")
--R suchThat : (%,List Symbol,(List F -> Boolean)) -> %
--R
--E 35


--S 36 of 43
Complex Integer has PatternMatchable Integer
 

   (33)  true
                                                                Type: Boolean
--R 
--R
--R   (33)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 43
Expression Complex Integer has FunctionSpace Complex Integer
 

   (34)  true
                                                                Type: Boolean
--R 
--R
--R   (34)  true
--R                                                                Type: Boolean
--E 37

--S 38 of 43
Expression Complex Integer has PatternMatchable Integer
 

   (35)  true
                                                                Type: Boolean
--R 
--R
--R   (35)  true
--R                                                                Type: Boolean
--E 38


--S 39 of 43
posxRule:=(rule sqrt('theta^2)==theta)$RewriteRule(Integer,Complex Integer,_
            Expression Complex Integer)
 

          +------+
          |     2
   (36)  \|theta   == theta
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R 
--R
--R          +------+
--R          |     2
--R   (36)  \|theta   == theta
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 39

--S 40 of 43
map(x+->posxRule x, testqeq)
 

   (37)  [0,0,0,0]
                                        Type: List Expression Complex Integer
--R 
--R
--R   (37)  [0,0,0,0]
--R                                        Type: List Expression Complex Integer
--E 40


--S 41 of 43
test (sqrt(x)^2=x)
 

   (38)  true
                                                                Type: Boolean
--R 
--R
--R   (38)  true
--R                                                                Type: Boolean
--E 41


--S 42 of 43
test (sqrt(sqrt(x)^2)=sqrt(x))
 

   (39)  true
                                                                Type: Boolean
--R 
--R
--R   (39)  true
--R                                                                Type: Boolean
--E 42


--S 43 of 43
eval(eval(testqeq,theta=sqrt(beta)),sqrt(beta)=theta)
 

   (40)  [0,0,0,0]
                                        Type: List Expression Complex Integer
--R 
--R
--R   (40)  [0,0,0,0]
--R                                        Type: List Expression Complex Integer
--E 43

)spool 
 
Starts dribbling to schaum25.output (2010/3/27, 18:38:32).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 40
aa:=integrate(%e^(a*x),x)
 

          a x
        %e
   (1)  -----
          a
                                          Type: Union(Expression Integer,...)
--R
--R          a x
--R        %e
--R   (1)  -----
--R          a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 40
bb:=%e^(a*x)/a
 

          a x
        %e
   (2)  -----
          a
                                                     Type: Expression Integer
--R
--R          a x
--R        %e
--R   (2)  -----
--R          a
--R                                                     Type: Expression Integer
--E

--S 3 of 40      14:509 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 40
aa:=integrate(x*%e^(a*x),x)
 

                   a x
        (a x - 1)%e
   (1)  --------------
               2
              a
                                          Type: Union(Expression Integer,...)
--R
--R                   a x
--R        (a x - 1)%e
--R   (1)  --------------
--R               2
--R              a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 40
bb:=%e^(a*x)/a*(x-1/a)
 

                   a x
        (a x - 1)%e
   (2)  --------------
               2
              a
                                                     Type: Expression Integer
--R
--R                   a x
--R        (a x - 1)%e
--R   (2)  --------------
--R               2
--R              a
--R                                                     Type: Expression Integer
--E

--S 6 of 40      14:510 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 40
aa:=integrate(x^2*%e^(a*x),x)
 

          2 2              a x
        (a x  - 2a x + 2)%e
   (1)  ----------------------
                   3
                  a
                                          Type: Union(Expression Integer,...)
--R
--R          2 2              a x
--R        (a x  - 2a x + 2)%e
--R   (1)  ----------------------
--R                   3
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 40
bb:=%e^(a*x)/a*(x^2-(2*x)/a+2/a^2)
 

          2 2              a x
        (a x  - 2a x + 2)%e
   (2)  ----------------------
                   3
                  a
                                                     Type: Expression Integer
--R
--R          2 2              a x
--R        (a x  - 2a x + 2)%e
--R   (2)  ----------------------
--R                   3
--R                  a
--R                                                     Type: Expression Integer
--E

--S 9 of 40      14:511 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 40     14:512 Axiom cannot compute this integral
aa:=integrate(x^n*%e^(a*x),x)
 

           x
         ++    %I a  n
   (1)   |   %e    %I d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++    %I a  n
--I   (1)   |   %e    %I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)clear all
 

--S 11 of 40     14:513 Schaums and Axiom agree by definition
aa:=integrate(%e^(a*x)/x,x)
 

   (1)  Ei(a x)
                                          Type: Union(Expression Integer,...)
--R
--R   (1)  Ei(a x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 12 of 40     14:514 Axiom cannot compute this integral
aa:=integrate(%e^(a*x)/x^n,x)
 

           x   %I a
         ++  %e
   (1)   |   ------ d%I
        ++       n
               %I
                                          Type: Union(Expression Integer,...)
--R
--I           x   %I a
--R         ++  %e
--I   (1)   |   ------ d%I
--R        ++       n
--I               %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 13 of 40
aa:=integrate(1/(p+q*%e^(a*x)),x)
 

                  a x
        - log(q %e    + p) + a x
   (1)  ------------------------
                   a p
                                          Type: Union(Expression Integer,...)
--R
--R                  a x
--R        - log(q %e    + p) + a x
--R   (1)  ------------------------
--R                   a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 40
bb:=x/p-1/(a*p)*log(p+q*%e^(a*x))
 

                  a x
        - log(q %e    + p) + a x
   (2)  ------------------------
                   a p
                                                     Type: Expression Integer
--R
--R                  a x
--R        - log(q %e    + p) + a x
--R   (2)  ------------------------
--R                   a p
--R                                                     Type: Expression Integer
--E

--S 15 of 40     14:515 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 40
aa:=integrate(1/(p+q*%e^(a*x))^2,x)
 

               a x             a x                a x
        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
   (1)  ---------------------------------------------------------
                               2    a x      3
                            a p q %e    + a p
                                          Type: Union(Expression Integer,...)
--R
--R               a x             a x                a x
--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
--R   (1)  ---------------------------------------------------------
--R                               2    a x      3
--R                            a p q %e    + a p
--R                                          Type: Union(Expression Integer,...)
--E

--S 17 of 40
bb:=x/p^2+1/(a*p*(p+q*%e^(a*x)))-1/(a*p^2)*log(p+q*%e^(a*x))
 

               a x             a x                a x
        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
   (2)  ---------------------------------------------------------
                               2    a x      3
                            a p q %e    + a p
                                                     Type: Expression Integer
--R
--R               a x             a x                a x
--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
--R   (2)  ---------------------------------------------------------
--R                               2    a x      3
--R                            a p q %e    + a p
--R                                                     Type: Expression Integer
--E

--S 18 of 40     14:516 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 40
aa:=integrate(1/(p*%e^(a*x)+q*%e^-(a*x)),x)
 

                   a x 2      +-----+          a x
             (p (%e   )  - q)\|- p q  + 2p q %e            a x +---+
         log(-------------------------------------)      %e   \|p q
                              a x 2                 atan(-----------)
                         p (%e   )  + q                       q
   (1)  [------------------------------------------,-----------------]
                            +-----+                        +---+
                         2a\|- p q                       a\|p q
                                     Type: Union(List Expression Integer,...)
--R
--R                   a x 2      +-----+          a x
--R             (p (%e   )  - q)\|- p q  + 2p q %e            a x +---+
--R         log(-------------------------------------)      %e   \|p q
--R                              a x 2                 atan(-----------)
--R                         p (%e   )  + q                       q
--R   (1)  [------------------------------------------,-----------------]
--R                            +-----+                        +---+
--R                         2a\|- p q                       a\|p q
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 20 of 40
bb1:=1/(a*sqrt(p*q))*atan(sqrt(p/q)*%e^(a*x))
 

                   +-+
               a x |p
        atan(%e    |- )
                  \|q
   (2)  ---------------
              +---+
            a\|p q
                                                     Type: Expression Integer
--R
--R                   +-+
--R               a x |p
--R        atan(%e    |- )
--R                  \|q
--R   (2)  ---------------
--R              +---+
--R            a\|p q
--R                                                     Type: Expression Integer
--E

--S 21 of 40
bb2:=1/(2*a*sqrt(-p*q))*log((%e^(a*x)-sqrt(-q/p))/(%e^(a*x)+sqrt(-q/p)))
 

               +---+
               |  q      a x
            -  |- -  + %e
              \|  p
        log(----------------)
              +---+
              |  q      a x
              |- -  + %e
             \|  p
   (3)  ---------------------
                 +-----+
              2a\|- p q
                                                     Type: Expression Integer
--R
--R               +---+
--R               |  q      a x
--R            -  |- -  + %e
--R              \|  p
--R        log(----------------)
--R              +---+
--R              |  q      a x
--R              |- -  + %e
--R             \|  p
--R   (3)  ---------------------
--R                 +-----+
--R              2a\|- p q
--R                                                     Type: Expression Integer
--E

--S 22 of 40
cc1:=aa.1-bb1
 

   (4)
                   a x 2      +-----+          a x                        +-+
    +---+    (p (%e   )  - q)\|- p q  + 2p q %e         +-----+       a x |p
   \|p q log(-------------------------------------) - 2\|- p q atan(%e    |- )
                              a x 2                                      \|q
                         p (%e   )  + q
   ---------------------------------------------------------------------------
                                    +-----+ +---+
                                 2a\|- p q \|p q
                                                     Type: Expression Integer
--R
--R   (4)
--R                   a x 2      +-----+          a x                        +-+
--R    +---+    (p (%e   )  - q)\|- p q  + 2p q %e         +-----+       a x |p
--R   \|p q log(-------------------------------------) - 2\|- p q atan(%e    |- )
--R                              a x 2                                      \|q
--R                         p (%e   )  + q
--R   ---------------------------------------------------------------------------
--R                                    +-----+ +---+
--R                                 2a\|- p q \|p q
--R                                                     Type: Expression Integer
--E

--S 23 of 40
cc2:=aa.2-bb1
 

               a x +---+               +-+
             %e   \|p q            a x |p
        atan(-----------) - atan(%e    |- )
                  q                   \|q
   (5)  -----------------------------------
                        +---+
                      a\|p q
                                                     Type: Expression Integer
--R
--R               a x +---+               +-+
--R             %e   \|p q            a x |p
--R        atan(-----------) - atan(%e    |- )
--R                  q                   \|q
--R   (5)  -----------------------------------
--R                        +---+
--R                      a\|p q
--R                                                     Type: Expression Integer
--E

--S 24 of 40
cc3:=aa.1-bb2
 

                                                            +---+
                                                            |  q      a x
                  a x 2      +-----+          a x        -  |- -  + %e
            (p (%e   )  - q)\|- p q  + 2p q %e             \|  p
        log(-------------------------------------) - log(----------------)
                             a x 2                         +---+
                        p (%e   )  + q                     |  q      a x
                                                           |- -  + %e
                                                          \|  p
   (6)  ------------------------------------------------------------------
                                       +-----+
                                    2a\|- p q
                                                     Type: Expression Integer
--R
--R                                                            +---+
--R                                                            |  q      a x
--R                  a x 2      +-----+          a x        -  |- -  + %e
--R            (p (%e   )  - q)\|- p q  + 2p q %e             \|  p
--R        log(-------------------------------------) - log(----------------)
--R                             a x 2                         +---+
--R                        p (%e   )  + q                     |  q      a x
--R                                                           |- -  + %e
--R                                                          \|  p
--R   (6)  ------------------------------------------------------------------
--R                                       +-----+
--R                                    2a\|- p q
--R                                                     Type: Expression Integer
--E

--S 25 of 40     14:517 Axiom cannot simplify these expressions
cc4:=aa.2-bb2
 

                       +---+
                       |  q      a x
                    -  |- -  + %e                       a x +---+
           +---+      \|  p               +-----+     %e   \|p q
        - \|p q log(----------------) + 2\|- p q atan(-----------)
                      +---+                                q
                      |  q      a x
                      |- -  + %e
                     \|  p
   (7)  ----------------------------------------------------------
                                +-----+ +---+
                             2a\|- p q \|p q
                                                     Type: Expression Integer
--R
--R                       +---+
--R                       |  q      a x
--R                    -  |- -  + %e                       a x +---+
--R           +---+      \|  p               +-----+     %e   \|p q
--R        - \|p q log(----------------) + 2\|- p q atan(-----------)
--R                      +---+                                q
--R                      |  q      a x
--R                      |- -  + %e
--R                     \|  p
--R   (7)  ----------------------------------------------------------
--R                                +-----+ +---+
--R                             2a\|- p q \|p q
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 26 of 40
aa:=integrate(%e^(a*x)*sin(b*x),x)
 

            a x                       a x
        a %e   sin(b x) - b cos(b x)%e
   (1)  ---------------------------------
                      2    2
                     b  + a
                                          Type: Union(Expression Integer,...)
--R
--R            a x                       a x
--R        a %e   sin(b x) - b cos(b x)%e
--R   (1)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27 of 40
bb:=((%e^(a*x))*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)
 

            a x                       a x
        a %e   sin(b x) - b cos(b x)%e
   (2)  ---------------------------------
                      2    2
                     b  + a
                                                     Type: Expression Integer
--R
--R            a x                       a x
--R        a %e   sin(b x) - b cos(b x)%e
--R   (2)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                                     Type: Expression Integer
--E

--S 28 of 40     14:518 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 29 of 40
aa:=integrate(%e^(a*x)*cos(b*x),x)
 

            a x                       a x
        b %e   sin(b x) + a cos(b x)%e
   (1)  ---------------------------------
                      2    2
                     b  + a
                                          Type: Union(Expression Integer,...)
--R
--R            a x                       a x
--R        b %e   sin(b x) + a cos(b x)%e
--R   (1)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 40
bb:=((%e^(a*x))*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)
 

            a x                       a x
        b %e   sin(b x) + a cos(b x)%e
   (2)  ---------------------------------
                      2    2
                     b  + a
                                                     Type: Expression Integer
--R
--R            a x                       a x
--R        b %e   sin(b x) + a cos(b x)%e
--R   (2)  ---------------------------------
--R                      2    2
--R                     b  + a
--R                                                     Type: Expression Integer
--E

--S 31 of 40     14:519 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 32 of 40
aa:=integrate(x*%e^(a*x)*sin(b*x),x)
 

   (1)
        2    3      2    2   a x                3    2                     a x
   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
   ---------------------------------------------------------------------------
                                  4     2 2    4
                                 b  + 2a b  + a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R        2    3      2    2   a x                3    2                     a x
--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
--R   ---------------------------------------------------------------------------
--R                                  4     2 2    4
--R                                 b  + 2a b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33 of 40
bb:=(x*%e^(a*x)*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*sin(b*x)-2*a*b*cos(b*x)))/(a^2+b^2)^2
 

   (2)
        2    3      2    2   a x                3    2                     a x
   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
   ---------------------------------------------------------------------------
                                  4     2 2    4
                                 b  + 2a b  + a
                                                     Type: Expression Integer
--R
--R   (2)
--R        2    3      2    2   a x                3    2                     a x
--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
--R   ---------------------------------------------------------------------------
--R                                  4     2 2    4
--R                                 b  + 2a b  + a
--R                                                     Type: Expression Integer
--E

--S 34 of 40     14:520 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 35 of 40
aa:=integrate(x*%e^(a*x)*cos(b*x),x)
 

   (1)
      3    2             a x                2    3      2    2           a x
   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
   -------------------------------------------------------------------------
                                 4     2 2    4
                                b  + 2a b  + a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R      3    2             a x                2    3      2    2           a x
--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
--R   -------------------------------------------------------------------------
--R                                 4     2 2    4
--R                                b  + 2a b  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36 of 40
bb:=(x*%e^(a*x)*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*cos(b*x)+2*a*b*sin(b*x)))/(a^2+b^2)^2
 

   (2)
      3    2             a x                2    3      2    2           a x
   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
   -------------------------------------------------------------------------
                                 4     2 2    4
                                b  + 2a b  + a
                                                     Type: Expression Integer
--R
--R   (2)
--R      3    2             a x                2    3      2    2           a x
--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
--R   -------------------------------------------------------------------------
--R                                 4     2 2    4
--R                                b  + 2a b  + a
--R                                                     Type: Expression Integer
--E

--S 37 of 40     14:521 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 38 of 40     14:522 Schaums and Axiom agree by definition
aa:=integrate(%e^(a*x)*log(x),x)
 

          a x
        %e   log(x) - Ei(a x)
   (1)  ---------------------
                  a
                                          Type: Union(Expression Integer,...)
--R
--R          a x
--R        %e   log(x) - Ei(a x)
--R   (1)  ---------------------
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 39 of 40     14:523 Axiom cannot compute this integral
aa:=integrate(%e^(a*x)*sin(b*x)^n,x)
 

           x
         ++    %I a         n
   (1)   |   %e    sin(%I b) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++    %I a         n
--I   (1)   |   %e    sin(%I b) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 40 of 40     14:524 Axiom cannot compute this integral
aa:=integrate(%e^(a*x)*cos(b*x)^n,x)
 

           x
         ++    %I a         n
   (1)   |   %e    cos(%I b) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++    %I a         n
--I   (1)   |   %e    cos(%I b) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to CardinalNumber.output (2010/3/27, 18:41:46).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
c0 := 0 :: CardinalNumber
 

   (1)  0
                                                         Type: CardinalNumber
--R 
--R
--R   (1)  0
--R                                                         Type: CardinalNumber
--E 1

--S 2 of 20
c1 := 1 :: CardinalNumber
 

   (2)  1
                                                         Type: CardinalNumber
--R 
--R
--R   (2)  1
--R                                                         Type: CardinalNumber
--E 2

--S 3 of 20
c2 := 2 :: CardinalNumber
 

   (3)  2
                                                         Type: CardinalNumber
--R 
--R
--R   (3)  2
--R                                                         Type: CardinalNumber
--E 3

--S 4 of 20
c3 := 3 :: CardinalNumber
 

   (4)  3
                                                         Type: CardinalNumber
--R 
--R
--R   (4)  3
--R                                                         Type: CardinalNumber
--E 4

--S 5 of 20
A0 := Aleph 0
 

   (5)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (5)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 5

--S 6 of 20
A1 := Aleph 1
 

   (6)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (6)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 6

--S 7 of 20
finite? c2
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 20
finite? A0
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 20
countable? c2
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 20
countable? A0
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 20
countable? A1
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 20
[c2 + c2, c2 + A1]
 

   (12)  [4,Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (12)  [4,Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 12

--S 13 of 20
[c0*c2, c1*c2, c2*c2, c0*A1, c1*A1, c2*A1, A0*A1]
 

   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 13

--S 14 of 20
[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]
 

   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 14

--S 15 of 20
[c2-c1, c2-c2, c2-c3, A1-c2, A1-A0, A1-A1]
 

   (15)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
                                    Type: List Union(CardinalNumber,"failed")
--R 
--R
--R   (15)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
--R                                    Type: List Union(CardinalNumber,"failed")
--E 15

--S 16 of 20
generalizedContinuumHypothesisAssumed true
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 20
[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1]
 

   (17)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (17)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
--R                                                    Type: List CardinalNumber
--E 17

--S 18 of 20
a := Aleph 0
 

   (18)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (18)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 18

--S 19 of 20
c := 2**a
 

   (19)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (19)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 19

--S 20 of 20
f := 2**c
 

   (20)  Aleph(2)
                                                         Type: CardinalNumber
--R 
--R
--R   (20)  Aleph(2)
--R                                                         Type: CardinalNumber
--E 20
)spool
 
Starts dribbling to SparseMultivariateTaylorSeries.output (2010/3/27, 18:46:34).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 10
xts:=x::TaylorSeries Fraction Integer
 

   (1)  x
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (1)  x
--R                                          Type: TaylorSeries Fraction Integer
--E 1

--S 2 of 10
yts:=y::TaylorSeries Fraction Integer
 

   (2)  y
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (2)  y
--R                                          Type: TaylorSeries Fraction Integer
--E 2

--S 3 of 10
zts:=z::TaylorSeries Fraction Integer
 

   (3)  z
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (3)  z
--R                                          Type: TaylorSeries Fraction Integer
--E 3

--S 4 of 10
t1:=sin(xts)
 

            1  3    1   5     1   7      1    9
   (4)  x - - x  + --- x  - ---- x  + ------ x  + O(11)
            6      120      5040      362880
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R            1  3    1   5     1   7      1    9
--R   (4)  x - - x  + --- x  - ---- x  + ------ x  + O(11)
--R            6      120      5040      362880
--R                                          Type: TaylorSeries Fraction Integer
--E 4

--S 5 of 10
coefficient(t1,3)
 

          1  3
   (5)  - - x
          6
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1  3
--R   (5)  - - x
--R          6
--R                                            Type: Polynomial Fraction Integer
--E 5

--S 6 of 10
coefficient(t1,monomial(3,x)$IndexedExponents Symbol)
 

          1
   (6)  - -
          6
                                                       Type: Fraction Integer
--R 
--R
--R          1
--R   (6)  - -
--R          6
--R                                                       Type: Fraction Integer
--E 6

--S 7 of 10
t2:=sin(xts + yts)
 

   (7)
                  1  3   1    2   1  2    1  3
     (y + x) + (- - y  - - x y  - - x y - - x )
                  6      2        2       6
   + 
       1   5    1    4    1  2 3    1  3 2    1  4     1   5
     (--- y  + -- x y  + -- x y  + -- x y  + -- x y + --- x )
      120      24        12        12        24       120
   + 
     PAREN
              1   7    1     6    1   2 5    1   3 4    1   4 3    1   5 2
          - ---- y  - --- x y  - --- x y  - --- x y  - --- x y  - --- x y
            5040      720        240        144        144        240
        + 
             1   6      1   7
          - --- x y - ---- x
            720       5040
   + 
     PAREN
             1    9     1      8     1    2 7     1   3 6     1   4 5
          ------ y  + ----- x y  + ----- x y  + ---- x y  + ---- x y
          362880      40320        10080        4320        2880
        + 
            1   5 4     1   6 3     1    7 2     1    8       1    9
          ---- x y  + ---- x y  + ----- x y  + ----- x y + ------ x
          2880        4320        10080        40320       362880
   + 
     O(11)
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (7)
--R                  1  3   1    2   1  2    1  3
--R     (y + x) + (- - y  - - x y  - - x y - - x )
--R                  6      2        2       6
--R   + 
--R       1   5    1    4    1  2 3    1  3 2    1  4     1   5
--R     (--- y  + -- x y  + -- x y  + -- x y  + -- x y + --- x )
--R      120      24        12        12        24       120
--R   + 
--R     PAREN
--R              1   7    1     6    1   2 5    1   3 4    1   4 3    1   5 2
--R          - ---- y  - --- x y  - --- x y  - --- x y  - --- x y  - --- x y
--R            5040      720        240        144        144        240
--R        + 
--R             1   6      1   7
--R          - --- x y - ---- x
--R            720       5040
--R   + 
--R     PAREN
--R             1    9     1      8     1    2 7     1   3 6     1   4 5
--R          ------ y  + ----- x y  + ----- x y  + ---- x y  + ---- x y
--R          362880      40320        10080        4320        2880
--R        + 
--R            1   5 4     1   6 3     1    7 2     1    8       1    9
--R          ---- x y  + ---- x y  + ----- x y  + ----- x y + ------ x
--R          2880        4320        10080        40320       362880
--R   + 
--R     O(11)
--R                                          Type: TaylorSeries Fraction Integer
--E 7

--S 8 of 10
coefficient(t2,3)
 

          1  3   1    2   1  2    1  3
   (8)  - - y  - - x y  - - x y - - x
          6      2        2       6
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1  3   1    2   1  2    1  3
--R   (8)  - - y  - - x y  - - x y - - x
--R          6      2        2       6
--R                                            Type: Polynomial Fraction Integer
--E 8

--S 9 of 10
coefficient(t2,monomial(3,x)$IndexedExponents Symbol)
 

          1
   (9)  - -
          6
                                                       Type: Fraction Integer
--R 
--R
--R          1
--R   (9)  - -
--R          6
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 10
polynomial(t2,5)
 

   (10)
      1   5    1    4     1  2   1  3     1  3   1    2     1  4   1  2
     --- y  + -- x y  + (-- x  - -)y  + (-- x  - - x)y  + (-- x  - - x  + 1)y
     120      24         12      6       12      2         24      2
   + 
      1   5   1  3
     --- x  - - x  + x
     120      6
                                            Type: Polynomial Fraction Integer
--R 
--R
--R   (10)
--R      1   5    1    4     1  2   1  3     1  3   1    2     1  4   1  2
--R     --- y  + -- x y  + (-- x  - -)y  + (-- x  - - x)y  + (-- x  - - x  + 1)y
--R     120      24         12      6       12      2         24      2
--R   + 
--R      1   5   1  3
--R     --- x  - - x  + x
--R     120      6
--R                                            Type: Polynomial Fraction Integer
--E 10

)spool
 
Starts dribbling to PlaneAlgebraicCurvePlot.output (2010/3/27, 18:46:15).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 5
sketch:=makeSketch(x+y,x,y,-1/2..1/2,-1/2..1/2)$ACPLOT
 

   (1)                    ACPLOT
                       1         1      1         1
        y + x = 0,   - - <= x <= -,   - - <= y <= -
                       2         2      2         2
                        [0.5,- 0.5]
                        [- 0.5,0.5]
                                                Type: PlaneAlgebraicCurvePlot
--R
--R   (1)                    ACPLOT
--R                       1         1      1         1
--R        y + x = 0,   - - <= x <= -,   - - <= y <= -
--R                       2         2      2         2
--R                        [0.5,- 0.5]
--R                        [- 0.5,0.5]
--R                                                Type: PlaneAlgebraicCurvePlot
--E 1

--S 2 of 5
refined:=refine(sketch,0.1)
 

   (2)                      ACPLOT
                         1         1      1         1
          y + x = 0,   - - <= x <= -,   - - <= y <= -
                         2         2      2         2
                          [0.5,- 0.5]
          [0.49600000000000083,- 0.49600000000000083]
          [0.49200000000000083,- 0.49200000000000083]
          [0.48800000000000082,- 0.48800000000000082]
          [0.48400000000000082,- 0.48400000000000082]
          [0.48000000000000081,- 0.48000000000000081]
          [0.47600000000000081,- 0.47600000000000081]
          [0.47200000000000081,- 0.47200000000000081]
           [0.4680000000000008,- 0.4680000000000008]
           [0.4640000000000008,- 0.4640000000000008]
           [0.4600000000000008,- 0.4600000000000008]
          [0.45600000000000079,- 0.45600000000000079]
          [0.45200000000000079,- 0.45200000000000079]
          [0.44800000000000079,- 0.44800000000000079]
          [0.44400000000000078,- 0.44400000000000078]
          [0.44000000000000078,- 0.44000000000000078]
          [0.43600000000000078,- 0.43600000000000078]
          [0.43200000000000077,- 0.43200000000000077]
          [0.42800000000000077,- 0.42800000000000077]
          [0.42400000000000077,- 0.42400000000000077]
          [0.42000000000000076,- 0.42000000000000076]
          [0.41600000000000076,- 0.41600000000000076]
          [0.41200000000000075,- 0.41200000000000075]
          [0.40800000000000075,- 0.40800000000000075]
          [0.40400000000000075,- 0.40400000000000075]
          [0.40000000000000074,- 0.40000000000000074]
          [0.39600000000000074,- 0.39600000000000074]
          [0.39200000000000074,- 0.39200000000000074]
          [0.38800000000000073,- 0.38800000000000073]
          [0.38400000000000073,- 0.38400000000000073]
          [0.38000000000000073,- 0.38000000000000073]
          [0.37600000000000072,- 0.37600000000000072]
          [0.37200000000000072,- 0.37200000000000072]
          [0.36800000000000072,- 0.36800000000000072]
          [0.36400000000000071,- 0.36400000000000071]
          [0.36000000000000071,- 0.36000000000000071]
           [0.3560000000000007,- 0.3560000000000007]
           [0.3520000000000007,- 0.3520000000000007]
           [0.3480000000000007,- 0.3480000000000007]
          [0.34400000000000069,- 0.34400000000000069]
          [0.34000000000000069,- 0.34000000000000069]
          [0.33600000000000069,- 0.33600000000000069]
          [0.33200000000000068,- 0.33200000000000068]
          [0.32800000000000068,- 0.32800000000000068]
          [0.32400000000000068,- 0.32400000000000068]
          [0.32000000000000067,- 0.32000000000000067]
          [0.31600000000000067,- 0.31600000000000067]
          [0.31200000000000067,- 0.31200000000000067]
          [0.30800000000000066,- 0.30800000000000066]
          [0.30400000000000066,- 0.30400000000000066]
          [0.30000000000000066,- 0.30000000000000066]
          [0.29600000000000065,- 0.29600000000000065]
          [0.29200000000000065,- 0.29200000000000065]
          [0.28800000000000064,- 0.28800000000000064]
          [0.28400000000000064,- 0.28400000000000064]
          [0.28000000000000064,- 0.28000000000000064]
          [0.27600000000000063,- 0.27600000000000063]
          [0.27200000000000063,- 0.27200000000000063]
          [0.26800000000000063,- 0.26800000000000063]
          [0.26400000000000062,- 0.26400000000000062]
          [0.26000000000000062,- 0.26000000000000062]
          [0.25600000000000062,- 0.25600000000000062]
          [0.25200000000000061,- 0.25200000000000061]
          [0.24800000000000061,- 0.24800000000000061]
          [0.24400000000000061,- 0.24400000000000061]
           [0.2400000000000006,- 0.2400000000000006]
           [0.2360000000000006,- 0.2360000000000006]
          [0.23200000000000059,- 0.23200000000000059]
          [0.22800000000000059,- 0.22800000000000059]
          [0.22400000000000059,- 0.22400000000000059]
          [0.22000000000000058,- 0.22000000000000058]
          [0.21600000000000058,- 0.21600000000000058]
          [0.21200000000000058,- 0.21200000000000058]
          [0.20800000000000057,- 0.20800000000000057]
          [0.20400000000000057,- 0.20400000000000057]
          [0.20000000000000057,- 0.20000000000000057]
          [0.19600000000000056,- 0.19600000000000056]
          [0.19200000000000056,- 0.19200000000000056]
          [0.18800000000000056,- 0.18800000000000056]
          [0.18400000000000055,- 0.18400000000000055]
          [0.18000000000000055,- 0.18000000000000055]
          [0.17600000000000054,- 0.17600000000000054]
          [0.17200000000000054,- 0.17200000000000054]
          [0.16800000000000054,- 0.16800000000000054]
          [0.16400000000000053,- 0.16400000000000053]
          [0.16000000000000053,- 0.16000000000000053]
          [0.15600000000000053,- 0.15600000000000053]
          [0.15200000000000052,- 0.15200000000000052]
          [0.14800000000000052,- 0.14800000000000052]
          [0.14400000000000052,- 0.14400000000000052]
          [0.14000000000000051,- 0.14000000000000051]
          [0.13600000000000051,- 0.13600000000000051]
          [0.13200000000000051,- 0.13200000000000051]
           [0.1280000000000005,- 0.1280000000000005]
           [0.1240000000000005,- 0.1240000000000005]
           [0.1200000000000005,- 0.1200000000000005]
          [0.11600000000000049,- 0.11600000000000049]
          [0.11200000000000049,- 0.11200000000000049]
          [0.10800000000000048,- 0.10800000000000048]
          [0.10400000000000048,- 0.10400000000000048]
          [0.10000000000000048,- 0.10000000000000048]
        [9.6000000000000474E-2,- 9.6000000000000474E-2]
         [9.200000000000047E-2,- 9.200000000000047E-2]
        [8.8000000000000467E-2,- 8.8000000000000467E-2]
        [8.4000000000000463E-2,- 8.4000000000000463E-2]
         [8.000000000000046E-2,- 8.000000000000046E-2]
        [7.6000000000000456E-2,- 7.6000000000000456E-2]
        [7.2000000000000453E-2,- 7.2000000000000453E-2]
        [6.8000000000000449E-2,- 6.8000000000000449E-2]
        [6.4000000000000445E-2,- 6.4000000000000445E-2]
        [6.0000000000000442E-2,- 6.0000000000000442E-2]
        [5.6000000000000438E-2,- 5.6000000000000438E-2]
        [5.2000000000000435E-2,- 5.2000000000000435E-2]
        [4.8000000000000431E-2,- 4.8000000000000431E-2]
        [4.4000000000000428E-2,- 4.4000000000000428E-2]
        [4.0000000000000424E-2,- 4.0000000000000424E-2]
        [3.6000000000000421E-2,- 3.6000000000000421E-2]
        [3.2000000000000417E-2,- 3.2000000000000417E-2]
        [2.8000000000000417E-2,- 2.8000000000000417E-2]
        [2.4000000000000417E-2,- 2.4000000000000417E-2]
        [2.0000000000000417E-2,- 2.0000000000000417E-2]
        [1.6000000000000417E-2,- 1.6000000000000417E-2]
        [1.2000000000000417E-2,- 1.2000000000000417E-2]
        [8.0000000000004165E-3,- 8.0000000000004165E-3]
        [4.0000000000004164E-3,- 4.0000000000004164E-3]
        [4.163336342344337E-16,- 4.163336342344337E-16]
        [- 3.9999999999995837E-3,3.9999999999995837E-3]
        [- 7.9999999999995838E-3,7.9999999999995838E-3]
        [- 1.1999999999999584E-2,1.1999999999999584E-2]
        [- 1.5999999999999584E-2,1.5999999999999584E-2]
        [- 1.9999999999999584E-2,1.9999999999999584E-2]
        [- 2.3999999999999584E-2,2.3999999999999584E-2]
        [- 2.7999999999999584E-2,2.7999999999999584E-2]
        [- 3.1999999999999584E-2,3.1999999999999584E-2]
        [- 3.5999999999999588E-2,3.5999999999999588E-2]
        [- 3.9999999999999591E-2,3.9999999999999591E-2]
        [- 4.3999999999999595E-2,4.3999999999999595E-2]
        [- 4.7999999999999599E-2,4.7999999999999599E-2]
        [- 5.1999999999999602E-2,5.1999999999999602E-2]
        [- 5.5999999999999606E-2,5.5999999999999606E-2]
        [- 5.9999999999999609E-2,5.9999999999999609E-2]
        [- 6.3999999999999613E-2,6.3999999999999613E-2]
        [- 6.7999999999999616E-2,6.7999999999999616E-2]
         [- 7.199999999999962E-2,7.199999999999962E-2]
        [- 7.5999999999999623E-2,7.5999999999999623E-2]
        [- 7.9999999999999627E-2,7.9999999999999627E-2]
        [- 8.3999999999999631E-2,8.3999999999999631E-2]
        [- 8.7999999999999634E-2,8.7999999999999634E-2]
        [- 9.1999999999999638E-2,9.1999999999999638E-2]
        [- 9.5999999999999641E-2,9.5999999999999641E-2]
        [- 9.9999999999999645E-2,9.9999999999999645E-2]
          [- 0.10399999999999965,0.10399999999999965]
          [- 0.10799999999999965,0.10799999999999965]
          [- 0.11199999999999966,0.11199999999999966]
          [- 0.11599999999999966,0.11599999999999966]
          [- 0.11999999999999966,0.11999999999999966]
          [- 0.12399999999999967,0.12399999999999967]
          [- 0.12799999999999967,0.12799999999999967]
          [- 0.13199999999999967,0.13199999999999967]
          [- 0.13599999999999968,0.13599999999999968]
          [- 0.13999999999999968,0.13999999999999968]
          [- 0.14399999999999968,0.14399999999999968]
          [- 0.14799999999999969,0.14799999999999969]
          [- 0.15199999999999969,0.15199999999999969]
          [- 0.15599999999999969,0.15599999999999969]
           [- 0.1599999999999997,0.1599999999999997]
           [- 0.1639999999999997,0.1639999999999997]
          [- 0.16799999999999971,0.16799999999999971]
          [- 0.17199999999999971,0.17199999999999971]
          [- 0.17599999999999971,0.17599999999999971]
          [- 0.17999999999999972,0.17999999999999972]
          [- 0.18399999999999972,0.18399999999999972]
          [- 0.18799999999999972,0.18799999999999972]
          [- 0.19199999999999973,0.19199999999999973]
          [- 0.19599999999999973,0.19599999999999973]
          [- 0.19999999999999973,0.19999999999999973]
          [- 0.20399999999999974,0.20399999999999974]
          [- 0.20799999999999974,0.20799999999999974]
          [- 0.21199999999999974,0.21199999999999974]
          [- 0.21599999999999975,0.21599999999999975]
          [- 0.21999999999999975,0.21999999999999975]
          [- 0.22399999999999975,0.22399999999999975]
          [- 0.22799999999999976,0.22799999999999976]
          [- 0.23199999999999976,0.23199999999999976]
          [- 0.23599999999999977,0.23599999999999977]
          [- 0.23999999999999977,0.23999999999999977]
          [- 0.24399999999999977,0.24399999999999977]
          [- 0.24799999999999978,0.24799999999999978]
          [- 0.25199999999999978,0.25199999999999978]
          [- 0.25599999999999978,0.25599999999999978]
          [- 0.25999999999999979,0.25999999999999979]
          [- 0.26399999999999979,0.26399999999999979]
          [- 0.26799999999999979,0.26799999999999979]
           [- 0.2719999999999998,0.2719999999999998]
           [- 0.2759999999999998,0.2759999999999998]
           [- 0.2799999999999998,0.2799999999999998]
          [- 0.28399999999999981,0.28399999999999981]
          [- 0.28799999999999981,0.28799999999999981]
          [- 0.29199999999999982,0.29199999999999982]
          [- 0.29599999999999982,0.29599999999999982]
          [- 0.29999999999999982,0.29999999999999982]
          [- 0.30399999999999983,0.30399999999999983]
          [- 0.30799999999999983,0.30799999999999983]
          [- 0.31199999999999983,0.31199999999999983]
          [- 0.31599999999999984,0.31599999999999984]
          [- 0.31999999999999984,0.31999999999999984]
          [- 0.32399999999999984,0.32399999999999984]
          [- 0.32799999999999985,0.32799999999999985]
          [- 0.33199999999999985,0.33199999999999985]
          [- 0.33599999999999985,0.33599999999999985]
          [- 0.33999999999999986,0.33999999999999986]
          [- 0.34399999999999986,0.34399999999999986]
          [- 0.34799999999999986,0.34799999999999986]
          [- 0.35199999999999987,0.35199999999999987]
          [- 0.35599999999999987,0.35599999999999987]
          [- 0.35999999999999988,0.35999999999999988]
          [- 0.36399999999999988,0.36399999999999988]
          [- 0.36799999999999988,0.36799999999999988]
          [- 0.37199999999999989,0.37199999999999989]
          [- 0.37599999999999989,0.37599999999999989]
          [- 0.37999999999999989,0.37999999999999989]
           [- 0.3839999999999999,0.3839999999999999]
           [- 0.3879999999999999,0.3879999999999999]
           [- 0.3919999999999999,0.3919999999999999]
          [- 0.39599999999999991,0.39599999999999991]
          [- 0.39999999999999991,0.39999999999999991]
          [- 0.40399999999999991,0.40399999999999991]
          [- 0.40799999999999992,0.40799999999999992]
          [- 0.41199999999999992,0.41199999999999992]
          [- 0.41599999999999993,0.41599999999999993]
          [- 0.41999999999999993,0.41999999999999993]
          [- 0.42399999999999993,0.42399999999999993]
          [- 0.42799999999999994,0.42799999999999994]
          [- 0.43199999999999994,0.43199999999999994]
          [- 0.43599999999999994,0.43599999999999994]
          [- 0.43999999999999995,0.43999999999999995]
          [- 0.44399999999999995,0.44399999999999995]
          [- 0.44799999999999995,0.44799999999999995]
          [- 0.45199999999999996,0.45199999999999996]
          [- 0.45599999999999996,0.45599999999999996]
          [- 0.45999999999999996,0.45999999999999996]
          [- 0.46399999999999997,0.46399999999999997]
          [- 0.46799999999999997,0.46799999999999997]
          [- 0.47199999999999998,0.47199999999999998]
          [- 0.47599999999999998,0.47599999999999998]
          [- 0.47999999999999998,0.47999999999999998]
          [- 0.48399999999999999,0.48399999999999999]
          [- 0.48799999999999999,0.48799999999999999]
          [- 0.49199999999999999,0.49199999999999999]
                        [- 0.496,0.496]
                          [- 0.5,0.5]
                                                Type: PlaneAlgebraicCurvePlot
--R
--R   (2)                      ACPLOT
--R                         1         1      1         1
--R          y + x = 0,   - - <= x <= -,   - - <= y <= -
--R                         2         2      2         2
--R                          [0.5,- 0.5]
--R          [0.49600000000000083,- 0.49600000000000083]
--R          [0.49200000000000083,- 0.49200000000000083]
--R          [0.48800000000000082,- 0.48800000000000082]
--R          [0.48400000000000082,- 0.48400000000000082]
--R          [0.48000000000000081,- 0.48000000000000081]
--R          [0.47600000000000081,- 0.47600000000000081]
--R          [0.47200000000000081,- 0.47200000000000081]
--R           [0.4680000000000008,- 0.4680000000000008]
--R           [0.4640000000000008,- 0.4640000000000008]
--R           [0.4600000000000008,- 0.4600000000000008]
--R          [0.45600000000000079,- 0.45600000000000079]
--R          [0.45200000000000079,- 0.45200000000000079]
--R          [0.44800000000000079,- 0.44800000000000079]
--R          [0.44400000000000078,- 0.44400000000000078]
--R          [0.44000000000000078,- 0.44000000000000078]
--R          [0.43600000000000078,- 0.43600000000000078]
--R          [0.43200000000000077,- 0.43200000000000077]
--R          [0.42800000000000077,- 0.42800000000000077]
--R          [0.42400000000000077,- 0.42400000000000077]
--R          [0.42000000000000076,- 0.42000000000000076]
--R          [0.41600000000000076,- 0.41600000000000076]
--R          [0.41200000000000075,- 0.41200000000000075]
--R          [0.40800000000000075,- 0.40800000000000075]
--R          [0.40400000000000075,- 0.40400000000000075]
--R          [0.40000000000000074,- 0.40000000000000074]
--R          [0.39600000000000074,- 0.39600000000000074]
--R          [0.39200000000000074,- 0.39200000000000074]
--R          [0.38800000000000073,- 0.38800000000000073]
--R          [0.38400000000000073,- 0.38400000000000073]
--R          [0.38000000000000073,- 0.38000000000000073]
--R          [0.37600000000000072,- 0.37600000000000072]
--R          [0.37200000000000072,- 0.37200000000000072]
--R          [0.36800000000000072,- 0.36800000000000072]
--R          [0.36400000000000071,- 0.36400000000000071]
--R          [0.36000000000000071,- 0.36000000000000071]
--R           [0.3560000000000007,- 0.3560000000000007]
--R           [0.3520000000000007,- 0.3520000000000007]
--R           [0.3480000000000007,- 0.3480000000000007]
--R          [0.34400000000000069,- 0.34400000000000069]
--R          [0.34000000000000069,- 0.34000000000000069]
--R          [0.33600000000000069,- 0.33600000000000069]
--R          [0.33200000000000068,- 0.33200000000000068]
--R          [0.32800000000000068,- 0.32800000000000068]
--R          [0.32400000000000068,- 0.32400000000000068]
--R          [0.32000000000000067,- 0.32000000000000067]
--R          [0.31600000000000067,- 0.31600000000000067]
--R          [0.31200000000000067,- 0.31200000000000067]
--R          [0.30800000000000066,- 0.30800000000000066]
--R          [0.30400000000000066,- 0.30400000000000066]
--R          [0.30000000000000066,- 0.30000000000000066]
--R          [0.29600000000000065,- 0.29600000000000065]
--R          [0.29200000000000065,- 0.29200000000000065]
--R          [0.28800000000000064,- 0.28800000000000064]
--R          [0.28400000000000064,- 0.28400000000000064]
--R          [0.28000000000000064,- 0.28000000000000064]
--R          [0.27600000000000063,- 0.27600000000000063]
--R          [0.27200000000000063,- 0.27200000000000063]
--R          [0.26800000000000063,- 0.26800000000000063]
--R          [0.26400000000000062,- 0.26400000000000062]
--R          [0.26000000000000062,- 0.26000000000000062]
--R          [0.25600000000000062,- 0.25600000000000062]
--R          [0.25200000000000061,- 0.25200000000000061]
--R          [0.24800000000000061,- 0.24800000000000061]
--R          [0.24400000000000061,- 0.24400000000000061]
--R           [0.2400000000000006,- 0.2400000000000006]
--R           [0.2360000000000006,- 0.2360000000000006]
--R          [0.23200000000000059,- 0.23200000000000059]
--R          [0.22800000000000059,- 0.22800000000000059]
--R          [0.22400000000000059,- 0.22400000000000059]
--R          [0.22000000000000058,- 0.22000000000000058]
--R          [0.21600000000000058,- 0.21600000000000058]
--R          [0.21200000000000058,- 0.21200000000000058]
--R          [0.20800000000000057,- 0.20800000000000057]
--R          [0.20400000000000057,- 0.20400000000000057]
--R          [0.20000000000000057,- 0.20000000000000057]
--R          [0.19600000000000056,- 0.19600000000000056]
--R          [0.19200000000000056,- 0.19200000000000056]
--R          [0.18800000000000056,- 0.18800000000000056]
--R          [0.18400000000000055,- 0.18400000000000055]
--R          [0.18000000000000055,- 0.18000000000000055]
--R          [0.17600000000000054,- 0.17600000000000054]
--R          [0.17200000000000054,- 0.17200000000000054]
--R          [0.16800000000000054,- 0.16800000000000054]
--R          [0.16400000000000053,- 0.16400000000000053]
--R          [0.16000000000000053,- 0.16000000000000053]
--R          [0.15600000000000053,- 0.15600000000000053]
--R          [0.15200000000000052,- 0.15200000000000052]
--R          [0.14800000000000052,- 0.14800000000000052]
--R          [0.14400000000000052,- 0.14400000000000052]
--R          [0.14000000000000051,- 0.14000000000000051]
--R          [0.13600000000000051,- 0.13600000000000051]
--R          [0.13200000000000051,- 0.13200000000000051]
--R           [0.1280000000000005,- 0.1280000000000005]
--R           [0.1240000000000005,- 0.1240000000000005]
--R           [0.1200000000000005,- 0.1200000000000005]
--R          [0.11600000000000049,- 0.11600000000000049]
--R          [0.11200000000000049,- 0.11200000000000049]
--R          [0.10800000000000048,- 0.10800000000000048]
--R          [0.10400000000000048,- 0.10400000000000048]
--R          [0.10000000000000048,- 0.10000000000000048]
--R        [9.6000000000000474E-2,- 9.6000000000000474E-2]
--R         [9.200000000000047E-2,- 9.200000000000047E-2]
--R        [8.8000000000000467E-2,- 8.8000000000000467E-2]
--R        [8.4000000000000463E-2,- 8.4000000000000463E-2]
--R         [8.000000000000046E-2,- 8.000000000000046E-2]
--R        [7.6000000000000456E-2,- 7.6000000000000456E-2]
--R        [7.2000000000000453E-2,- 7.2000000000000453E-2]
--R        [6.8000000000000449E-2,- 6.8000000000000449E-2]
--R        [6.4000000000000445E-2,- 6.4000000000000445E-2]
--R        [6.0000000000000442E-2,- 6.0000000000000442E-2]
--R        [5.6000000000000438E-2,- 5.6000000000000438E-2]
--R        [5.2000000000000435E-2,- 5.2000000000000435E-2]
--R        [4.8000000000000431E-2,- 4.8000000000000431E-2]
--R        [4.4000000000000428E-2,- 4.4000000000000428E-2]
--R        [4.0000000000000424E-2,- 4.0000000000000424E-2]
--R        [3.6000000000000421E-2,- 3.6000000000000421E-2]
--R        [3.2000000000000417E-2,- 3.2000000000000417E-2]
--R        [2.8000000000000417E-2,- 2.8000000000000417E-2]
--R        [2.4000000000000417E-2,- 2.4000000000000417E-2]
--R        [2.0000000000000417E-2,- 2.0000000000000417E-2]
--R        [1.6000000000000417E-2,- 1.6000000000000417E-2]
--R        [1.2000000000000417E-2,- 1.2000000000000417E-2]
--R        [8.0000000000004165E-3,- 8.0000000000004165E-3]
--R        [4.0000000000004164E-3,- 4.0000000000004164E-3]
--R        [4.163336342344337E-16,- 4.163336342344337E-16]
--R        [- 3.9999999999995837E-3,3.9999999999995837E-3]
--R        [- 7.9999999999995838E-3,7.9999999999995838E-3]
--R        [- 1.1999999999999584E-2,1.1999999999999584E-2]
--R        [- 1.5999999999999584E-2,1.5999999999999584E-2]
--R        [- 1.9999999999999584E-2,1.9999999999999584E-2]
--R        [- 2.3999999999999584E-2,2.3999999999999584E-2]
--R        [- 2.7999999999999584E-2,2.7999999999999584E-2]
--R        [- 3.1999999999999584E-2,3.1999999999999584E-2]
--R        [- 3.5999999999999588E-2,3.5999999999999588E-2]
--R        [- 3.9999999999999591E-2,3.9999999999999591E-2]
--R        [- 4.3999999999999595E-2,4.3999999999999595E-2]
--R        [- 4.7999999999999599E-2,4.7999999999999599E-2]
--R        [- 5.1999999999999602E-2,5.1999999999999602E-2]
--R        [- 5.5999999999999606E-2,5.5999999999999606E-2]
--R        [- 5.9999999999999609E-2,5.9999999999999609E-2]
--R        [- 6.3999999999999613E-2,6.3999999999999613E-2]
--R        [- 6.7999999999999616E-2,6.7999999999999616E-2]
--R         [- 7.199999999999962E-2,7.199999999999962E-2]
--R        [- 7.5999999999999623E-2,7.5999999999999623E-2]
--R        [- 7.9999999999999627E-2,7.9999999999999627E-2]
--R        [- 8.3999999999999631E-2,8.3999999999999631E-2]
--R        [- 8.7999999999999634E-2,8.7999999999999634E-2]
--R        [- 9.1999999999999638E-2,9.1999999999999638E-2]
--R        [- 9.5999999999999641E-2,9.5999999999999641E-2]
--R        [- 9.9999999999999645E-2,9.9999999999999645E-2]
--R          [- 0.10399999999999965,0.10399999999999965]
--R          [- 0.10799999999999965,0.10799999999999965]
--R          [- 0.11199999999999966,0.11199999999999966]
--R          [- 0.11599999999999966,0.11599999999999966]
--R          [- 0.11999999999999966,0.11999999999999966]
--R          [- 0.12399999999999967,0.12399999999999967]
--R          [- 0.12799999999999967,0.12799999999999967]
--R          [- 0.13199999999999967,0.13199999999999967]
--R          [- 0.13599999999999968,0.13599999999999968]
--R          [- 0.13999999999999968,0.13999999999999968]
--R          [- 0.14399999999999968,0.14399999999999968]
--R          [- 0.14799999999999969,0.14799999999999969]
--R          [- 0.15199999999999969,0.15199999999999969]
--R          [- 0.15599999999999969,0.15599999999999969]
--R           [- 0.1599999999999997,0.1599999999999997]
--R           [- 0.1639999999999997,0.1639999999999997]
--R          [- 0.16799999999999971,0.16799999999999971]
--R          [- 0.17199999999999971,0.17199999999999971]
--R          [- 0.17599999999999971,0.17599999999999971]
--R          [- 0.17999999999999972,0.17999999999999972]
--R          [- 0.18399999999999972,0.18399999999999972]
--R          [- 0.18799999999999972,0.18799999999999972]
--R          [- 0.19199999999999973,0.19199999999999973]
--R          [- 0.19599999999999973,0.19599999999999973]
--R          [- 0.19999999999999973,0.19999999999999973]
--R          [- 0.20399999999999974,0.20399999999999974]
--R          [- 0.20799999999999974,0.20799999999999974]
--R          [- 0.21199999999999974,0.21199999999999974]
--R          [- 0.21599999999999975,0.21599999999999975]
--R          [- 0.21999999999999975,0.21999999999999975]
--R          [- 0.22399999999999975,0.22399999999999975]
--R          [- 0.22799999999999976,0.22799999999999976]
--R          [- 0.23199999999999976,0.23199999999999976]
--R          [- 0.23599999999999977,0.23599999999999977]
--R          [- 0.23999999999999977,0.23999999999999977]
--R          [- 0.24399999999999977,0.24399999999999977]
--R          [- 0.24799999999999978,0.24799999999999978]
--R          [- 0.25199999999999978,0.25199999999999978]
--R          [- 0.25599999999999978,0.25599999999999978]
--R          [- 0.25999999999999979,0.25999999999999979]
--R          [- 0.26399999999999979,0.26399999999999979]
--R          [- 0.26799999999999979,0.26799999999999979]
--R           [- 0.2719999999999998,0.2719999999999998]
--R           [- 0.2759999999999998,0.2759999999999998]
--R           [- 0.2799999999999998,0.2799999999999998]
--R          [- 0.28399999999999981,0.28399999999999981]
--R          [- 0.28799999999999981,0.28799999999999981]
--R          [- 0.29199999999999982,0.29199999999999982]
--R          [- 0.29599999999999982,0.29599999999999982]
--R          [- 0.29999999999999982,0.29999999999999982]
--R          [- 0.30399999999999983,0.30399999999999983]
--R          [- 0.30799999999999983,0.30799999999999983]
--R          [- 0.31199999999999983,0.31199999999999983]
--R          [- 0.31599999999999984,0.31599999999999984]
--R          [- 0.31999999999999984,0.31999999999999984]
--R          [- 0.32399999999999984,0.32399999999999984]
--R          [- 0.32799999999999985,0.32799999999999985]
--R          [- 0.33199999999999985,0.33199999999999985]
--R          [- 0.33599999999999985,0.33599999999999985]
--R          [- 0.33999999999999986,0.33999999999999986]
--R          [- 0.34399999999999986,0.34399999999999986]
--R          [- 0.34799999999999986,0.34799999999999986]
--R          [- 0.35199999999999987,0.35199999999999987]
--R          [- 0.35599999999999987,0.35599999999999987]
--R          [- 0.35999999999999988,0.35999999999999988]
--R          [- 0.36399999999999988,0.36399999999999988]
--R          [- 0.36799999999999988,0.36799999999999988]
--R          [- 0.37199999999999989,0.37199999999999989]
--R          [- 0.37599999999999989,0.37599999999999989]
--R          [- 0.37999999999999989,0.37999999999999989]
--R           [- 0.3839999999999999,0.3839999999999999]
--R           [- 0.3879999999999999,0.3879999999999999]
--R           [- 0.3919999999999999,0.3919999999999999]
--R          [- 0.39599999999999991,0.39599999999999991]
--R          [- 0.39999999999999991,0.39999999999999991]
--R          [- 0.40399999999999991,0.40399999999999991]
--R          [- 0.40799999999999992,0.40799999999999992]
--R          [- 0.41199999999999992,0.41199999999999992]
--R          [- 0.41599999999999993,0.41599999999999993]
--R          [- 0.41999999999999993,0.41999999999999993]
--R          [- 0.42399999999999993,0.42399999999999993]
--R          [- 0.42799999999999994,0.42799999999999994]
--R          [- 0.43199999999999994,0.43199999999999994]
--R          [- 0.43599999999999994,0.43599999999999994]
--R          [- 0.43999999999999995,0.43999999999999995]
--R          [- 0.44399999999999995,0.44399999999999995]
--R          [- 0.44799999999999995,0.44799999999999995]
--R          [- 0.45199999999999996,0.45199999999999996]
--R          [- 0.45599999999999996,0.45599999999999996]
--R          [- 0.45999999999999996,0.45999999999999996]
--R          [- 0.46399999999999997,0.46399999999999997]
--R          [- 0.46799999999999997,0.46799999999999997]
--R          [- 0.47199999999999998,0.47199999999999998]
--R          [- 0.47599999999999998,0.47599999999999998]
--R          [- 0.47999999999999998,0.47999999999999998]
--R          [- 0.48399999999999999,0.48399999999999999]
--R          [- 0.48799999999999999,0.48799999999999999]
--R          [- 0.49199999999999999,0.49199999999999999]
--R                        [- 0.496,0.496]
--R                          [- 0.5,0.5]
--R                                                Type: PlaneAlgebraicCurvePlot
--E 2

--S 3 of 5
listBranches(sketch)
 

   (3)  [[[0.5,- 0.5],[- 0.5,0.5]]]
                                            Type: List List Point DoubleFloat
--R
--R   (3)  [[[0.5,- 0.5],[- 0.5,0.5]]]
--R                                            Type: List List Point DoubleFloat
--E 3

--S 4 of 5
listBranches(refined)
 

   (4)
   [
     [[0.5,- 0.5], [0.49600000000000083,- 0.49600000000000083],
      [0.49200000000000083,- 0.49200000000000083],
      [0.48800000000000082,- 0.48800000000000082],
      [0.48400000000000082,- 0.48400000000000082],
      [0.48000000000000081,- 0.48000000000000081],
      [0.47600000000000081,- 0.47600000000000081],
      [0.47200000000000081,- 0.47200000000000081],
      [0.4680000000000008,- 0.4680000000000008],
      [0.4640000000000008,- 0.4640000000000008],
      [0.4600000000000008,- 0.4600000000000008],
      [0.45600000000000079,- 0.45600000000000079],
      [0.45200000000000079,- 0.45200000000000079],
      [0.44800000000000079,- 0.44800000000000079],
      [0.44400000000000078,- 0.44400000000000078],
      [0.44000000000000078,- 0.44000000000000078],
      [0.43600000000000078,- 0.43600000000000078],
      [0.43200000000000077,- 0.43200000000000077],
      [0.42800000000000077,- 0.42800000000000077],
      [0.42400000000000077,- 0.42400000000000077],
      [0.42000000000000076,- 0.42000000000000076],
      [0.41600000000000076,- 0.41600000000000076],
      [0.41200000000000075,- 0.41200000000000075],
      [0.40800000000000075,- 0.40800000000000075],
      [0.40400000000000075,- 0.40400000000000075],
      [0.40000000000000074,- 0.40000000000000074],
      [0.39600000000000074,- 0.39600000000000074],
      [0.39200000000000074,- 0.39200000000000074],
      [0.38800000000000073,- 0.38800000000000073],
      [0.38400000000000073,- 0.38400000000000073],
      [0.38000000000000073,- 0.38000000000000073],
      [0.37600000000000072,- 0.37600000000000072],
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                                            Type: List List Point DoubleFloat
--R
--R   (4)
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--R      [- 0.19599999999999973,0.19599999999999973],
--R      [- 0.19999999999999973,0.19999999999999973],
--R      [- 0.20399999999999974,0.20399999999999974],
--R      [- 0.20799999999999974,0.20799999999999974],
--R      [- 0.21199999999999974,0.21199999999999974],
--R      [- 0.21599999999999975,0.21599999999999975],
--R      [- 0.21999999999999975,0.21999999999999975],
--R      [- 0.22399999999999975,0.22399999999999975],
--R      [- 0.22799999999999976,0.22799999999999976],
--R      [- 0.23199999999999976,0.23199999999999976],
--R      [- 0.23599999999999977,0.23599999999999977],
--R      [- 0.23999999999999977,0.23999999999999977],
--R      [- 0.24399999999999977,0.24399999999999977],
--R      [- 0.24799999999999978,0.24799999999999978],
--R      [- 0.25199999999999978,0.25199999999999978],
--R      [- 0.25599999999999978,0.25599999999999978],
--R      [- 0.25999999999999979,0.25999999999999979],
--R      [- 0.26399999999999979,0.26399999999999979],
--R      [- 0.26799999999999979,0.26799999999999979],
--R      [- 0.2719999999999998,0.2719999999999998],
--R      [- 0.2759999999999998,0.2759999999999998],
--R      [- 0.2799999999999998,0.2799999999999998],
--R      [- 0.28399999999999981,0.28399999999999981],
--R      [- 0.28799999999999981,0.28799999999999981],
--R      [- 0.29199999999999982,0.29199999999999982],
--R      [- 0.29599999999999982,0.29599999999999982],
--R      [- 0.29999999999999982,0.29999999999999982],
--R      [- 0.30399999999999983,0.30399999999999983],
--R      [- 0.30799999999999983,0.30799999999999983],
--R      [- 0.31199999999999983,0.31199999999999983],
--R      [- 0.31599999999999984,0.31599999999999984],
--R      [- 0.31999999999999984,0.31999999999999984],
--R      [- 0.32399999999999984,0.32399999999999984],
--R      [- 0.32799999999999985,0.32799999999999985],
--R      [- 0.33199999999999985,0.33199999999999985],
--R      [- 0.33599999999999985,0.33599999999999985],
--R      [- 0.33999999999999986,0.33999999999999986],
--R      [- 0.34399999999999986,0.34399999999999986],
--R      [- 0.34799999999999986,0.34799999999999986],
--R      [- 0.35199999999999987,0.35199999999999987],
--R      [- 0.35599999999999987,0.35599999999999987],
--R      [- 0.35999999999999988,0.35999999999999988],
--R      [- 0.36399999999999988,0.36399999999999988],
--R      [- 0.36799999999999988,0.36799999999999988],
--R      [- 0.37199999999999989,0.37199999999999989],
--R      [- 0.37599999999999989,0.37599999999999989],
--R      [- 0.37999999999999989,0.37999999999999989],
--R      [- 0.3839999999999999,0.3839999999999999],
--R      [- 0.3879999999999999,0.3879999999999999],
--R      [- 0.3919999999999999,0.3919999999999999],
--R      [- 0.39599999999999991,0.39599999999999991],
--R      [- 0.39999999999999991,0.39999999999999991],
--R      [- 0.40399999999999991,0.40399999999999991],
--R      [- 0.40799999999999992,0.40799999999999992],
--R      [- 0.41199999999999992,0.41199999999999992],
--R      [- 0.41599999999999993,0.41599999999999993],
--R      [- 0.41999999999999993,0.41999999999999993],
--R      [- 0.42399999999999993,0.42399999999999993],
--R      [- 0.42799999999999994,0.42799999999999994],
--R      [- 0.43199999999999994,0.43199999999999994],
--R      [- 0.43599999999999994,0.43599999999999994],
--R      [- 0.43999999999999995,0.43999999999999995],
--R      [- 0.44399999999999995,0.44399999999999995],
--R      [- 0.44799999999999995,0.44799999999999995],
--R      [- 0.45199999999999996,0.45199999999999996],
--R      [- 0.45599999999999996,0.45599999999999996],
--R      [- 0.45999999999999996,0.45999999999999996],
--R      [- 0.46399999999999997,0.46399999999999997],
--R      [- 0.46799999999999997,0.46799999999999997],
--R      [- 0.47199999999999998,0.47199999999999998],
--R      [- 0.47599999999999998,0.47599999999999998],
--R      [- 0.47999999999999998,0.47999999999999998],
--R      [- 0.48399999999999999,0.48399999999999999],
--R      [- 0.48799999999999999,0.48799999999999999],
--R      [- 0.49199999999999999,0.49199999999999999], [- 0.496,0.496],
--R      [- 0.5,0.5]]
--R     ]
--R                                            Type: List List Point DoubleFloat
--E 4

--S 5 of 5
)show ACPLOT
 
 PlaneAlgebraicCurvePlot  is a domain constructor
 Abbreviation for PlaneAlgebraicCurvePlot is ACPLOT 
 This constructor is not exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for ACPLOT 

------------------------------- Operations --------------------------------
 coerce : % -> OutputForm              refine : (%,DoubleFloat) -> %
 xRange : % -> Segment DoubleFloat     yRange : % -> Segment DoubleFloat
 listBranches : % -> List List Point DoubleFloat
 makeSketch : (Polynomial Integer,Symbol,Symbol,Segment Fraction Integer,Segment Fraction Integer) -> %

--R PlaneAlgebraicCurvePlot  is a domain constructor
--R Abbreviation for PlaneAlgebraicCurvePlot is ACPLOT 
--R This constructor is not exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for ACPLOT 
--R
--R------------------------------- Operations --------------------------------
--R coerce : % -> OutputForm              refine : (%,DoubleFloat) -> %
--R xRange : % -> Segment DoubleFloat     yRange : % -> Segment DoubleFloat
--R listBranches : % -> List List Point DoubleFloat
--R makeSketch : (Polynomial Integer,Symbol,Symbol,Segment Fraction Integer,Segment Fraction Integer) -> %
--R
--E 5

)spool
 
Starts dribbling to PartialFraction.output (2010/3/27, 18:46:13).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 22
partialFraction(1,factorial 10)
 

        159   23   12   1
   (1)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                                                Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (1)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                                                Type: PartialFraction Integer
--E 1

--S 2 of 22
f := padicFraction(%)
 

        1    1    1    1    1    1    2    1    2   2    2   1
   (2)  - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
        2    4    5    6    7    8    2    3    4   5    2   7
            2    2    2    2    2    3    3    3        5
                                                Type: PartialFraction Integer
--R 
--R
--R        1    1    1    1    1    1    2    1    2   2    2   1
--R   (2)  - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
--R        2    4    5    6    7    8    2    3    4   5    2   7
--R            2    2    2    2    2    3    3    3        5
--R                                                Type: PartialFraction Integer
--E 2

--S 3 of 22
compactFraction(f)
 

        159   23   12   1
   (3)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                                                Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (3)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                                                Type: PartialFraction Integer
--E 3

--S 4 of 22
numberOfFractionalTerms(f)
 

   (4)  12
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  12
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 22
nthFractionalTerm(f,3)
 

         1
   (5)  --
         5
        2
                                                Type: PartialFraction Integer
--R 
--R
--R         1
--R   (5)  --
--R         5
--R        2
--R                                                Type: PartialFraction Integer
--E 5

--S 6 of 22
partialFraction(1,- 13 + 14 * %i)
 

             1         4
   (6)  - ------- + -------
          1 + 2%i   3 + 8%i
                                        Type: PartialFraction Complex Integer
--R 
--R
--R             1         4
--R   (6)  - ------- + -------
--R          1 + 2%i   3 + 8%i
--R                                        Type: PartialFraction Complex Integer
--E 6

--S 7 of 22
% :: Fraction Complex Integer
 

              %i
   (7)  - ---------
          14 + 13%i
                                               Type: Fraction Complex Integer
--R 
--R
--R              %i
--R   (7)  - ---------
--R          14 + 13%i
--R                                               Type: Fraction Complex Integer
--E 7

--S 8 of 22
u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])
 

                      2       3       4
   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
                      Type: Factored UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                      2       3       4
--R   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
--R                      Type: Factored UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 22
partialFraction(1,u)
 

   (9)
     1     1      7     17  2         139   607  3   10115  2   391     44179
    ---    - x + --   - -- x  - 12x - ---   --- x  + ----- x  + --- x + -----
    648    4     16      8             8    324       432        4       324
   ----- + -------- + ------------------- + ---------------------------------
   x + 1          2                3                            4
           (x + 2)          (x + 3)                      (x + 4)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (9)
--R     1     1      7     17  2         139   607  3   10115  2   391     44179
--R    ---    - x + --   - -- x  - 12x - ---   --- x  + ----- x  + --- x + -----
--R    648    4     16      8             8    324       432        4       324
--R   ----- + -------- + ------------------- + ---------------------------------
--R   x + 1          2                3                            4
--R           (x + 2)          (x + 3)                      (x + 4)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 22
padicFraction %
 

   (10)
       1       1         1        17        3          1       607       403
      ---      -        --        --        -          -       ---       ---
      648      4        16         8        4          2       324       432
     ----- + ----- - -------- - ----- + -------- - -------- + ----- + --------
     x + 1   x + 2          2   x + 3          2          3   x + 4          2
                     (x + 2)            (x + 3)    (x + 3)            (x + 4)
   + 
        13          1
        --         --
        36         12
     -------- + --------
            3          4
     (x + 4)    (x + 4)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (10)
--R       1       1         1        17        3          1       607       403
--R      ---      -        --        --        -          -       ---       ---
--R      648      4        16         8        4          2       324       432
--R     ----- + ----- - -------- - ----- + -------- - -------- + ----- + --------
--R     x + 1   x + 2          2   x + 3          2          3   x + 4          2
--R                     (x + 2)            (x + 3)    (x + 3)            (x + 4)
--R   + 
--R        13          1
--R        --         --
--R        36         12
--R     -------- + --------
--R            3          4
--R     (x + 4)    (x + 4)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 10

--S 11 of 22
fraction:=Fraction(Polynomial(Integer))
 

   (11)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (11)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 11

--S 12 of 22
up:=UnivariatePolynomial(y,fraction)
 

   (12)  UnivariatePolynomial(y,Fraction Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (12)  UnivariatePolynomial(y,Fraction Polynomial Integer)
--R                                                                 Type: Domain
--E 12

--S 13 of 22
pfup:=PartialFraction(up)
 

   (13)  PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
                                                                 Type: Domain
--R 
--R
--R   (13)  PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--R                                                                 Type: Domain
--E 13

--S 14 of 22
a:=x+1/(y+1)
 

         x y + x + 1
   (14)  -----------
            y + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         x y + x + 1
--R   (14)  -----------
--R            y + 1
--R                                            Type: Fraction Polynomial Integer
--E 14

--S 15 of 22
b:=partialFraction(a,y)$PartialFractionPackage(Integer)
 

               1
   (15)  x + -----
             y + 1
    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--R 
--R
--R               1
--R   (15)  x + -----
--R             y + 1
--R    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--E 15

--S 16 of 22
c:=b::pfup
 

               1
   (16)  x + -----
             y + 1
    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--R 
--R
--R               1
--R   (16)  x + -----
--R             y + 1
--R    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--E 16

--S 17 of 22
cw:=(wholePart c)::Expression(Integer)
 

   (17)  x
                                                     Type: Expression Integer
--R 
--R
--R   (17)  x
--R                                                     Type: Expression Integer
--E 17

--S 18 of 22
m:=numberOfFractionalTerms(c)
 

   (18)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  1
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 22
crList:=[nthFractionalTerm(c,i) for i in 1..m]
 

            1
   (19)  [-----]
          y + 1
Type: List PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--R 
--R
--R            1
--R   (19)  [-----]
--R          y + 1
--RType: List PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--E 19

--S 20 of 22
cc:=reduce(+,crList)
 

           1
   (20)  -----
         y + 1
    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--R 
--R
--R           1
--R   (20)  -----
--R         y + 1
--R    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--E 20

--S 21 of 22
ccx:=cc::(Fraction(up))::(Expression(Integer))
 

           1
   (21)  -----
         y + 1
                                                     Type: Expression Integer
--R 
--R
--R           1
--R   (21)  -----
--R         y + 1
--R                                                     Type: Expression Integer
--E 21

--S 22 of 22
sin(cw)*cos(ccx)+sin(ccx)*cos(cw)
 

               1                        1
   (22)  cos(-----)sin(x) + cos(x)sin(-----)
             y + 1                    y + 1
                                                     Type: Expression Integer
--R 
--R
--R               1                        1
--R   (22)  cos(-----)sin(x) + cos(x)sin(-----)
--R             y + 1                    y + 1
--R                                                     Type: Expression Integer
--E 22

)spool
 
Starts dribbling to fr.output (2010/3/27, 18:26:23).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 55
(x,y,z,w): FR INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 55
x := 2**8 * 78**7 * 111**3 * 74534
 

         16 10  7  3
   (2)  2  3  13 37 83 449
                                                       Type: Factored Integer
--R 
--R
--R         16 10  7  3
--R   (2)  2  3  13 37 83 449
--R                                                       Type: Factored Integer
--E 2

--S 3 of 55
y := 2**4 * 45**3 * 162**6 * 774325
 

         10 30 5
   (3)  2  3  5 47 659
                                                       Type: Factored Integer
--R 
--R
--R         10 30 5
--R   (3)  2  3  5 47 659
--R                                                       Type: Factored Integer
--E 3

--S 4 of 55
z1 := factorial 50
 

   (4)  30414093201713378043612608166064768844377641568960512000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  30414093201713378043612608166064768844377641568960512000000000000
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 55
z := z1 :: (FR INT)
 

         47 22 12 8  4  3  2  2  2
   (5)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
                                                       Type: Factored Integer
--R 
--R
--R         47 22 12 8  4  3  2  2  2
--R   (5)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
--R                                                       Type: Factored Integer
--E 5

--S 6 of 55
nthFactor(z,1)
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 55
nthFlag(z,1)
 

   (7)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (7)  "prime"
--R                                                     Type: Union("prime",...)
--E 7

--S 8 of 55
nthExponent(z,1)
 

   (8)  47
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  47
--R                                                        Type: PositiveInteger
--E 8


--S 9 of 55
factorList z
 

   (9)
   [[flg= "prime",fctr= 2,xpnt= 47], [flg= "prime",fctr= 3,xpnt= 22],
    [flg= "prime",fctr= 5,xpnt= 12], [flg= "prime",fctr= 7,xpnt= 8],
    [flg= "prime",fctr= 11,xpnt= 4], [flg= "prime",fctr= 13,xpnt= 3],
    [flg= "prime",fctr= 17,xpnt= 2], [flg= "prime",fctr= 19,xpnt= 2],
    [flg= "prime",fctr= 23,xpnt= 2], [flg= "prime",fctr= 29,xpnt= 1],
    [flg= "prime",fctr= 31,xpnt= 1], [flg= "prime",fctr= 37,xpnt= 1],
    [flg= "prime",fctr= 41,xpnt= 1], [flg= "prime",fctr= 43,xpnt= 1],
    [flg= "prime",fctr= 47,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--R 
--R
--R   (9)
--R   [[flg= "prime",fctr= 2,xpnt= 47], [flg= "prime",fctr= 3,xpnt= 22],
--R    [flg= "prime",fctr= 5,xpnt= 12], [flg= "prime",fctr= 7,xpnt= 8],
--R    [flg= "prime",fctr= 11,xpnt= 4], [flg= "prime",fctr= 13,xpnt= 3],
--R    [flg= "prime",fctr= 17,xpnt= 2], [flg= "prime",fctr= 19,xpnt= 2],
--R    [flg= "prime",fctr= 23,xpnt= 2], [flg= "prime",fctr= 29,xpnt= 1],
--R    [flg= "prime",fctr= 31,xpnt= 1], [flg= "prime",fctr= 37,xpnt= 1],
--R    [flg= "prime",fctr= 41,xpnt= 1], [flg= "prime",fctr= 43,xpnt= 1],
--R    [flg= "prime",fctr= 47,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--E 9

--S 10 of 55
r:=reduce(*,[(nthFactor(z,i) :: (FR INT)) for i in 1..(numberOfFactors z)])
 

   (10)  2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
                                                       Type: Factored Integer
--R 
--R
--R   (10)  2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
--R                                                       Type: Factored Integer
--E 10

--S 11 of 55
exquo(z,r)
 

          46 21 11 7  3  2
   (11)  2  3  5  7 11 13 17 19 23
                                            Type: Union(Factored Integer,...)
--R 
--R
--R          46 21 11 7  3  2
--R   (11)  2  3  5  7 11 13 17 19 23
--R                                            Type: Union(Factored Integer,...)
--E 11

--S 12 of 55
x*y
 

          26 40 5  7  3
   (12)  2  3  5 13 37 47 83 449 659
                                                       Type: Factored Integer
--R 
--R
--R          26 40 5  7  3
--R   (12)  2  3  5 13 37 47 83 449 659
--R                                                       Type: Factored Integer
--E 12

--S 13 of 55
y*x
 

          26 40 5  7  3
   (13)  2  3  5 13 37 47 83 449 659
                                                       Type: Factored Integer
--R 
--R
--R          26 40 5  7  3
--R   (13)  2  3  5 13 37 47 83 449 659
--R                                                       Type: Factored Integer
--E 13

--S 14 of 55
(x*y = y*x) :: BOOLEAN
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 55
gcd(x,z)
 

          16 10  3
   (15)  2  3  13 37
                                                       Type: Factored Integer
--R 
--R
--R          16 10  3
--R   (15)  2  3  13 37
--R                                                       Type: Factored Integer
--E 15

--S 16 of 55
x+y
 

          10 10
   (16)  2  3  1109 3557 2007307818601
                                                       Type: Factored Integer
--R 
--R
--R          10 10
--R   (16)  2  3  1109 3557 2007307818601
--R                                                       Type: Factored Integer
--E 16

--S 17 of 55
expand(x+y)
 

   (17)  478786494447911114328204288
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  478786494447911114328204288
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 55
f := x/y
 

          6  7  3
         2 13 37 83 449
   (18)  --------------
            20 5
           3  5 47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R          6  7  3
--R         2 13 37 83 449
--R   (18)  --------------
--R            20 5
--R           3  5 47 659
--R                                              Type: Fraction Factored Integer
--E 18

--S 19 of 55
g := (x ** 9) / y
 

          134 60  63  27  9   9
         2   3  13  37  83 449
   (19)  ----------------------
                 5
                5 47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R          134 60  63  27  9   9
--R         2   3  13  37  83 449
--R   (19)  ----------------------
--R                 5
--R                5 47 659
--R                                              Type: Fraction Factored Integer
--E 19

--S 20 of 55
f * g
 

          140 40  70  30  10   10
         2   3  13  37  83  449
   (20)  ------------------------
                 10  2   2
                5  47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R          140 40  70  30  10   10
--R         2   3  13  37  83  449
--R   (20)  ------------------------
--R                 10  2   2
--R                5  47 659
--R                                              Type: Fraction Factored Integer
--E 20

--S 21 of 55
(f * g) / (g * primeFactor(2,200)) 
 

             7  3
           13 37 83 449
   (21)  ---------------
          194 20 5
         2   3  5 47 659
                                              Type: Fraction Factored Integer
--R 
--R
--R             7  3
--R           13 37 83 449
--R   (21)  ---------------
--R          194 20 5
--R         2   3  5 47 659
--R                                              Type: Fraction Factored Integer
--E 21

--S 22 of 55
(f * g) / (g * primeFactor(2,200)) * z
 

          2 7 8  4  10  2  2  2        4
         3 5 7 11 13  17 19 23 29 31 37 41 43 83 449
   (22)  -------------------------------------------
                            147
                           2   659
                                              Type: Fraction Factored Integer
--R 
--R
--R          2 7 8  4  10  2  2  2        4
--R         3 5 7 11 13  17 19 23 29 31 37 41 43 83 449
--R   (22)  -------------------------------------------
--R                            147
--R                           2   659
--R                                              Type: Fraction Factored Integer
--E 22 
 

)clear all
 
--S 23 of 55
(u,v,w): FR POLY INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23
 
--S 24 of 55
u := (x**4 - y**4) :: POLY INT
 

                          2    2
   (2)  - (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                          2    2
--R   (2)  - (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 24

--S 25 of 55
v := primeFactor(x-y,2) * primeFactor(x+y,2) * primeFactor(x**2 + y**2,1)
 

               2       2  2    2
   (3)  (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2       2  2    2
--R   (3)  (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 25

--S 26 of 55
w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * primeFactor(x-y,2)
 

               2           2
   (4)  (y - x) (y + x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2           2
--R   (4)  (y - x) (y + x + 1)
--R                                            Type: Factored Polynomial Integer
--E 26

--S 27 of 55
unit w
 

   (5)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)  1
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 55
l := factorList u
 

   (6)
   [[flg= "prime",fctr= y - x,xpnt= 1], [flg= "prime",fctr= y + x,xpnt= 1],
                         2    2
    [flg= "prime",fctr= y  + x ,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--R 
--R
--R   (6)
--R   [[flg= "prime",fctr= y - x,xpnt= 1], [flg= "prime",fctr= y + x,xpnt= 1],
--R                         2    2
--R    [flg= "prime",fctr= y  + x ,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--E 28

--S 29 of 55
factorList v
 

   (7)
   [[flg= "prime",fctr= y - x,xpnt= 2], [flg= "prime",fctr= y + x,xpnt= 2],
                         2    2
    [flg= "prime",fctr= y  + x ,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--R 
--R
--R   (7)
--R   [[flg= "prime",fctr= y - x,xpnt= 2], [flg= "prime",fctr= y + x,xpnt= 2],
--R                         2    2
--R    [flg= "prime",fctr= y  + x ,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--E 29

--S 30 of 55
factorList w
 

   (8)
   [[flg= "prime",fctr= y - x,xpnt= 2],[flg= "prime",fctr= y + x + 1,xpnt= 2]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--R 
--R
--R   (8)
--R   [[flg= "prime",fctr= y - x,xpnt= 2],[flg= "prime",fctr= y + x + 1,xpnt= 2]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Polynomial Integer,xpnt: Integer)
--E 30

--S 31 of 55
l.1.fctr
 

   (9)  y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)  y - x
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 55
l.1.xpnt
 

   (10)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  1
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 55
nthFactor(u,1)
 

   (11)  y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (11)  y - x
--R                                                     Type: Polynomial Integer
--E 33

--S 34 of 55
nthFactor(u,2)
 

   (12)  y + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (12)  y + x
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 55
nthFactor(u,3)
 

          2    2
   (13)  y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R          2    2
--R   (13)  y  + x
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 55
nthExponent(u,3)
 

   (14)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  1
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 55
nthFlag(u,3)
 

   (15)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (15)  "prime"
--R                                                     Type: Union("prime",...)
--E 37

--S 38 of 55
nthFactor(u,4)
 

   (16)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (16)  1
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 55
s:=reduce(*,[(nthFactor(v,i) :: FR POLY INT) for i in 1..(numberOfFactors v)])
 

                         2    2
   (17)  (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2
--R   (17)  (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 39

--S 40 of 55
exquo(v,s)
 

   (18)  (y - x)(y + x)
                                 Type: Union(Factored Polynomial Integer,...)
--R 
--R
--R   (18)  (y - x)(y + x)
--R                                 Type: Union(Factored Polynomial Integer,...)
--E 40

--S 41 of 55
gcd(u,v)
 

                         2    2
   (19)  (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2
--R   (19)  (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 41

--S 42 of 55
u + v
 

                         2    2       2    2
   (20)  (y - x)(y + x)(y  - x  - 1)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2       2    2
--R   (20)  (y - x)(y + x)(y  - x  - 1)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 42

--S 43 of 55
lcm(v,w)
 

                2       2           2  2    2
   (21)  (y - x) (y + x) (y + x + 1) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                2       2           2  2    2
--R   (21)  (y - x) (y + x) (y + x + 1) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 43

--S 44 of 55
u * v * w
 

                  5       3           2  2    2 2
   (22)  - (y - x) (y + x) (y + x + 1) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  5       3           2  2    2 2
--R   (22)  - (y - x) (y + x) (y + x + 1) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 44

--S 45 of 55
expand(u * v * w)
 

   (23)
        14     13      2           12      2       11       4     3  10
     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
   + 
        4     3  9        6     5     4  8        6     5  7      8     7  6
     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
   + 
        8     7  5     10     9     8  4      10     9  3        12     11  2
     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
   + 
          12     11      14     13    12
     (- 2x   - 2x  )y + x   + 2x   + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (23)
--R        14     13      2           12      2       11       4     3  10
--R     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
--R   + 
--R        4     3  9        6     5     4  8        6     5  7      8     7  6
--R     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
--R   + 
--R        8     7  5     10     9     8  4      10     9  3        12     11  2
--R     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
--R   + 
--R          12     11      14     13    12
--R     (- 2x   - 2x  )y + x   + 2x   + x
--R                                                     Type: Polynomial Integer
--E 45

--S 46 of 55
u/w
 

                      2    2
             (y + x)(y  + x )
   (24)  - -------------------
                             2
           (y - x)(y + x + 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                      2    2
--R             (y + x)(y  + x )
--R   (24)  - -------------------
--R                             2
--R           (y - x)(y + x + 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 46

--S 47 of 55
w/(u*v)
 

                             2
                  (y + x + 1)
   (25)  - -------------------------
                         3  2    2 2
           (y - x)(y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                             2
--R                  (y + x + 1)
--R   (25)  - -------------------------
--R                         3  2    2 2
--R           (y - x)(y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 47

--S 48 of 55
w/(u*v) * u/w
 

                     1
   (26)  -------------------------
                2       2  2    2
         (y - x) (y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                     1
--R   (26)  -------------------------
--R                2       2  2    2
--R         (y - x) (y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 48

--S 49 of 55
w/(u*v) + u/w
 

   (27)
   -
           10       9     2 8      3 7      4 6      5 5       6      4
          y   + 4x y  + 9x y  + 16x y  + 22x y  + 24x y  + (22x  + 1)y
        + 
              7           3      8     2            2
          (16x  + 4x + 4)y  + (9x  + 6x  + 12x + 6)y
        + 
             9     3      2                10    4     3     2
          (4x  + 4x  + 12x  + 12x + 4)y + x   + x  + 4x  + 6x  + 4x + 1
     /
                      3           2  2    2 2
        (y - x)(y + x) (y + x + 1) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R   (27)
--R   -
--R           10       9     2 8      3 7      4 6      5 5       6      4
--R          y   + 4x y  + 9x y  + 16x y  + 22x y  + 24x y  + (22x  + 1)y
--R        + 
--R              7           3      8     2            2
--R          (16x  + 4x + 4)y  + (9x  + 6x  + 12x + 6)y
--R        + 
--R             9     3      2                10    4     3     2
--R          (4x  + 4x  + 12x  + 12x + 4)y + x   + x  + 4x  + 6x  + 4x + 1
--R     /
--R                      3           2  2    2 2
--R        (y - x)(y + x) (y + x + 1) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 49

--S 50 of 55
differentiate(w,x)
 

   (28)  - 2(2x + 1)(y - x)(y + x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (28)  - 2(2x + 1)(y - x)(y + x + 1)
--R                                            Type: Factored Polynomial Integer
--E 50

--S 51 of 55
differentiate(w,y)
 

   (29)  2(y - x)(y + x + 1)(2y + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (29)  2(y - x)(y + x + 1)(2y + 1)
--R                                            Type: Factored Polynomial Integer
--E 51

--S 52 of 55
associates?(x,-x)
 

   (30)  true
                                                                Type: Boolean
--R 
--R
--R   (30)  true
--R                                                                Type: Boolean
--E 52

--S 53 of 55
characteristic()$FR POLY INT
 

   (31)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (31)  0
--R                                                     Type: NonNegativeInteger
--E 53

--S 54 of 55
1$FR POLY INT
 

   (32)  1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (32)  1
--R                                            Type: Factored Polynomial Integer
--E 54

--S 55 of 55
0$FR POLY INT
 

   (33)  0
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (33)  0
--R                                            Type: Factored Polynomial Integer
--E 55
)spool 
 
Starts dribbling to clif.output (2010/3/27, 18:24:32).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from ugxCliffordComplexPage
--S 1 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
m := matrix [[-1]]
 

   (2)  [- 1]
                                                         Type: Matrix Integer
--R 
--R
--R   (2)  [- 1]
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 36
C := CliffordAlgebra(1, K, quadraticForm m)
 

   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 3

--S 4 of 36
i: C := e(1)
 

   (4)  e
         1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 4

--S 5 of 36
x := a + b * i
 

   (5)  a + b e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  a + b e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 5

--S 6 of 36
y := c + d * i
 

   (6)  c + d e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  c + d e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 6

--S 7 of 36
x * y
 

   (7)  - b d + a c + (a d + b c)e
                                  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  - b d + a c + (a d + b c)e
--R                                  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 7

-- Input generated from ugxCliffordQuaternPage

)clear all
 

--S 8 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 8

--S 9 of 36
m := matrix [[-1,0],[0,-1]]
 

        +- 1   0 +
   (2)  |        |
        + 0   - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 1   0 +
--R   (2)  |        |
--R        + 0   - 1+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 36
H  := CliffordAlgebra(2, K, quadraticForm m)
 

   (3)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 10

--S 11 of 36
i: H  := e(1)
 

   (4)  e
         1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 11

--S 12 of 36
j: H  := e(2)
 

   (5)  e
         2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  e
--R         2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 12

--S 13 of 36
k: H  := i * j
 

   (6)  e e
         1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  e e
--R         1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 13

--S 14 of 36
x := a + b * i + c * j + d * k
 

   (7)  a + b e  + c e  + d e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  a + b e  + c e  + d e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 14

--S 15 of 36
y := e + f * i + g * j + h * k
 

   (8)  e + f e  + g e  + h e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (8)  e + f e  + g e  + h e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 15

--S 16 of 36
x + y
 

   (9)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
                        1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (9)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                        1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 16

--S 17 of 36
x * y
 

   (10)
     - d h - c g - b f + a e + (c h - d g + a f + b e)e
                                                       1
   + 
     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
                               2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (10)
--R     - d h - c g - b f + a e + (c h - d g + a f + b e)e
--R                                                       1
--R   + 
--R     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
--R                               2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 17

--S 18 of 36
y * x
 

   (11)
     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
                                                         1
   + 
     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (11)
--R     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
--R                                                         1
--R   + 
--R     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 18

-- Input generated from ugxCliffordExteriorPage
)clear all
 

--S 19 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 19

--S 20 of 36
Ext := CliffordAlgebra(3, K, quadraticForm 0)
 

   (2)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (2)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 20

--S 21 of 36
i: Ext := e(1)
 

   (3)  e
         1
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (3)  e
--R         1
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 21

--S 22 of 36
j: Ext := e(2)
 

   (4)  e
         2
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         2
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 22

--S 23 of 36
k: Ext := e(3)
 

   (5)  e
         3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  e
--R         3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 23

--S 24 of 36
x := x1*i + x2*j + x3*k
 

   (6)  x1 e  + x2 e  + x3 e
            1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  x1 e  + x2 e  + x3 e
--R            1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 24

--S 25 of 36
y := y1*i + y2*j + y3*k
 

   (7)  y1 e  + y2 e  + y3 e
            1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  y1 e  + y2 e  + y3 e
--R            1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 25

--S 26 of 36
x + y
 

   (8)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
                  1             2             3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (8)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
--R                  1             2             3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 26

--S 27 of 36
x * y + y * x
 

   (9)  0
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (9)  0
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 27

--S 28 of 36
dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 36
dual2(x*y)
 
   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) 

   (11)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
                         1                     2                   3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) 
--R
--R   (11)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
--R                         1                     2                   3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 29

-- Input generated from ugxCliffordDiracPage
)clear all
 

--S 30 of 36
K := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 30

--S 31 of 36
g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]
 

        +1   0    0    0 +
        |                |
        |0  - 1   0    0 |
   (2)  |                |
        |0   0   - 1   0 |
        |                |
        +0   0    0   - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +1   0    0    0 +
--R        |                |
--R        |0  - 1   0    0 |
--R   (2)  |                |
--R        |0   0   - 1   0 |
--R        |                |
--R        +0   0    0   - 1+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 36
D := CliffordAlgebra(4,K, quadraticForm g)
 

   (3)  CliffordAlgebra(4,Fraction Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(4,Fraction Integer,MATRIX)
--R                                                                 Type: Domain
--E 32

--S 33 of 36
gam := [e(i)$D for i in 1..4]
 

   (4)  [e ,e ,e ,e ]
          1  2  3  4
                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (4)  [e ,e ,e ,e ]
--R          1  2  3  4
--R                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 33

--S 34 of 36
m := 1; n:= 2; r := 3; s := 4;
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 36
lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4])
 

   (6)  - 4e e e e
            1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (6)  - 4e e e e
--R            1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 35

--S 36 of 36
rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)
 

   (7)  - 4e e e e
            1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (7)  - 4e e e e
--R            1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 36
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read tsetcatbutcher
 

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [b1,x,y,z,t,v,u,w];
 

                                                            Type: List Symbol
V := OVAR(ls);
 

                                                                 Type: Domain
R := Integer;
 

                                                                 Type: Domain
E := IndexedExponents V;
 

                                                                 Type: Domain
P := NSMP(R, V);
 

                                                                 Type: Domain
LP := List(P);
 

                                                                 Type: Domain

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

b1: P := 'b1;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
x: P := 'x;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
y: P := 'y;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
z: P := 'z;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
t: P := 't;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
u: P := 'u;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
v: P := 'v;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
w: P := 'w;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])

f0 := b1 + y + z - t - w;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w  ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w  ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1  ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1  ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
f7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 ;
 

Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])

lp := [f0,f1,f2,f3,f4,f5,f6,f7];
 

Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])

-----------------------------------------------------------------------------
--% Computations
-----------------------------------------------------------------------------

T := WUTSET(R,E,V,P);
 

                                                                 Type: Domain

medialSet(lp)$T
 

   (25)
   {
            10         9         8         7        6       5       4       3
       3456w   + 12960w  + 19872w  + 15912w  + 6732w  + 996w  - 337w  - 167w
     + 
            2
       - 23w  - w
     ,
        3      2                  6       5       4      3      2
    (12w  + 21w  + 10w + 1)u - 72w  - 180w  - 150w  - 51w  - 12w  - 3w,
        3      2                  5      4      3      2
    (12w  + 21w  + 10w + 1)v + 36w  + 90w  + 72w  + 18w ,
        3      2             4      3      2
    (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,

                 9          8          7          6          5          4
           82944w  + 323568w  + 536868w  + 501804w  + 291411w  + 106080w
         + 
                 3        2
           22458w  + 2316w  + 87w
      *
         z
     + 
                       10          9          8          7          6          5
               - 20736w   - 108864w  - 242352w  - 297756w  - 220104w  - 100116w
             + 
                       4        3       2
               - 27552w  - 4356w  - 360w  - 12w
          *
             v
         + 
                   11          10          9          8          7          6
           - 20736w   - 108864w   - 249264w  - 334044w  - 300888w  - 199368w
         + 
                    5         4        3        2
           - 100920w  - 37728w  - 9544w  - 1464w  - 120w - 4
      *
         t
     + 
                 11          10          9          8          7          6
           20736w   + 119232w   + 307152w  + 473364w  + 490158w  + 359046w
         + 
                  5         4         3        2
           187662w  + 68190w  + 16314w  + 2370w  + 186w + 6
      *
         v
     + 
             12          11          10          9          8          7
       20736w   + 129600w   + 378864w   + 685260w  + 840996w  + 717228w
     + 
              6          5         4        3       2
       421140w  + 165396w  + 41452w  + 6180w  + 492w  + 16w
     ,

           5       4       3      2           3      2
       (72w  + 180w  + 144w  + 36w )y + (- 24w  - 42w  - 20w - 2)u z
     + 
             4      3      2             5      4      3      2
       (- 24w  - 42w  - 20w  - 2w)t + 24w  + 54w  + 53w  + 33w  + 11w + 1
     ,

                     9             8              7              6             5
           177732288w  + 719015472w  + 1232091096w  + 1173573804w  + 679584244w
         + 
                     4            3           2
           241504763w  + 49510061w  + 5012029w  + 188379w
      *
         x
     + 
                       23                22                 21
           18345885696w   + 201804742656w   + 1034631512064w
         + 
                         20                 19                  18
           3285633466368w   + 7245828587520w   + 11794015715328w
         + 
                          17                  16                  15
           14705111236608w   + 14392584880128w   + 11248017481728w
         + 
                         14                 13                 12
           7106910658560w   + 3664870060032w   + 1553671950336w
         + 
                        11                10               9              8
           544159248384w   + 157668409344w   + 37615263744w  + 7285383168w
         + 
                      7             6            5          4         3
           1114865664w  + 128901120w  + 10481664w  + 528384w  + 12288w
      *
         t
     + 
                   23                22                 21                 20
       18345885696w   + 201422536704w   + 1030427246592w   + 3264142344192w
     + 
                     19                  18                  17
       7178014900224w   + 11646005796864w   + 14467760013312w
     + 
                      16                  15                 14
       14102539278336w   + 10971419618304w   + 6897670239744w
     + 
                     13                 12                11                10
       3537815786496w   + 1491187528704w   + 519099757056w   + 149437154304w
     + 
                   9              8              7             6           5
       35401691136w  + 6802421760w  + 1031325696w  + 117929472w  + 9464832w
     + 
              4         3
       470016w  + 10752w
     ,
    b1 + y + z - t - w}
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])),...)

characteristicSet(lp)$T
 

   (26)
   {
            10         9         8         7        6       5       4       3
       3456w   + 12960w  + 19872w  + 15912w  + 6732w  + 996w  - 337w  - 167w
     + 
            2
       - 23w  - w
     ,
        3      2                  6       5       4      3      2
    (12w  + 21w  + 10w + 1)u - 72w  - 180w  - 150w  - 51w  - 12w  - 3w,
        3      2                  5      4      3      2
    (12w  + 21w  + 10w + 1)v + 36w  + 90w  + 72w  + 18w ,
        3      2             4      3      2
    (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,

                 9          8          7          6          5          4
           82944w  + 323568w  + 536868w  + 501804w  + 291411w  + 106080w
         + 
                 3        2
           22458w  + 2316w  + 87w
      *
         z
     + 
                       10          9          8          7          6          5
               - 20736w   - 108864w  - 242352w  - 297756w  - 220104w  - 100116w
             + 
                       4        3       2
               - 27552w  - 4356w  - 360w  - 12w
          *
             v
         + 
                   11          10          9          8          7          6
           - 20736w   - 108864w   - 249264w  - 334044w  - 300888w  - 199368w
         + 
                    5         4        3        2
           - 100920w  - 37728w  - 9544w  - 1464w  - 120w - 4
      *
         t
     + 
                 11          10          9          8          7          6
           20736w   + 119232w   + 307152w  + 473364w  + 490158w  + 359046w
         + 
                  5         4         3        2
           187662w  + 68190w  + 16314w  + 2370w  + 186w + 6
      *
         v
     + 
             12          11          10          9          8          7
       20736w   + 129600w   + 378864w   + 685260w  + 840996w  + 717228w
     + 
              6          5         4        3       2
       421140w  + 165396w  + 41452w  + 6180w  + 492w  + 16w
     ,

           5       4       3      2           3      2
       (72w  + 180w  + 144w  + 36w )y + (- 24w  - 42w  - 20w - 2)u z
     + 
             4      3      2             5      4      3      2
       (- 24w  - 42w  - 20w  - 2w)t + 24w  + 54w  + 53w  + 33w  + 11w + 1
     ,

                     9             8              7              6             5
           177732288w  + 719015472w  + 1232091096w  + 1173573804w  + 679584244w
         + 
                     4            3           2
           241504763w  + 49510061w  + 5012029w  + 188379w
      *
         x
     + 
                       23                22                 21
           18345885696w   + 201804742656w   + 1034631512064w
         + 
                         20                 19                  18
           3285633466368w   + 7245828587520w   + 11794015715328w
         + 
                          17                  16                  15
           14705111236608w   + 14392584880128w   + 11248017481728w
         + 
                         14                 13                 12
           7106910658560w   + 3664870060032w   + 1553671950336w
         + 
                        11                10               9              8
           544159248384w   + 157668409344w   + 37615263744w  + 7285383168w
         + 
                      7             6            5          4         3
           1114865664w  + 128901120w  + 10481664w  + 528384w  + 12288w
      *
         t
     + 
                   23                22                 21                 20
       18345885696w   + 201422536704w   + 1030427246592w   + 3264142344192w
     + 
                     19                  18                  17
       7178014900224w   + 11646005796864w   + 14467760013312w
     + 
                      16                  15                 14
       14102539278336w   + 10971419618304w   + 6897670239744w
     + 
                     13                 12                11                10
       3537815786496w   + 1491187528704w   + 519099757056w   + 149437154304w
     + 
                   9              8              7             6           5
       35401691136w  + 6802421760w  + 1031325696w  + 117929472w  + 9464832w
     + 
              4         3
       470016w  + 10752w
     ,
    b1 + y + z - t - w}
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])),...)

characteristicSerie(lp)$T
 

   (27)
                       4      3      2
   [{w + 1,u,v,8t + 24w  + 36w  + 26w  + 7w + 1,z,b1 + y + z - t - w},

                        4      3      2
     {w + 1, u, 8t + 24w  + 36w  + 26w  + 7w + 1, z,
                             2
      2v y + 2u z + 2w t - 2w  - w - 1, b1 + y + z - t - w}
     ,

                    2          4      3      2               2     2
     {w + 1, u v - u , 8t + 24w  + 36w  + 26w  + 7w + 1, z, u y + u z,
      b1 + y + z - t - w}
     ,
                       4      3      2
    {w + 1,u,v,8t + 24w  + 36w  + 26w  + 7w + 1,b1 + y + z - t - w},

                        4      3      2
     {w + 1, u, 8t + 24w  + 36w  + 26w  + 7w + 1,
                             2
      2v y + 2u z + 2w t - 2w  - w - 1,
                    2                3     2
      6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w, b1 + y + z - t - w}
     ,

                    2          4      3      2            2     2    2
     {w + 1, u v - u , 8t + 24w  + 36w  + 26w  + 7w + 1, u y + u z, u z x,
      b1 + y + z - t - w}
     ,
                       4      3      2
    {w + 1,u,v,8t + 24w  + 36w  + 26w  + 7w + 1,b1 + y + z - t - w},

                        4      3      2                           2
     {w + 1, v, 8t + 24w  + 36w  + 26w  + 7w + 1, 2u z + 2w t - 2w  - w - 1,
      b1 + y + z - t - w}
     ,

                     4      3      2                   2
     {w + 1, 8t + 24w  + 36w  + 26w  + 7w + 1, (u v - u )z,
                             2
      2v y + 2u z + 2w t - 2w  - w - 1, b1 + y + z - t - w}
     ,

     {
              10         9         8         7        6       5       4       3
         3456w   + 12960w  + 19872w  + 15912w  + 6732w  + 996w  - 337w  - 167w
       + 
              2
         - 23w  - w
       ,
          3      2                  6       5       4      3      2
      (12w  + 21w  + 10w + 1)u - 72w  - 180w  - 150w  - 51w  - 12w  - 3w,
          3      2                  5      4      3      2
      (12w  + 21w  + 10w + 1)v + 36w  + 90w  + 72w  + 18w ,
          3      2             4      3      2
      (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,

                   9          8          7          6          5          4
             82944w  + 323568w  + 536868w  + 501804w  + 291411w  + 106080w
           + 
                   3        2
             22458w  + 2316w  + 87w
        *
           z
       + 
                         10          9          8          7          6
                 - 20736w   - 108864w  - 242352w  - 297756w  - 220104w
               + 
                          5         4        3       2
                 - 100116w  - 27552w  - 4356w  - 360w  - 12w
            *
               v
           + 
                     11          10          9          8          7          6
             - 20736w   - 108864w   - 249264w  - 334044w  - 300888w  - 199368w
           + 
                      5         4        3        2
             - 100920w  - 37728w  - 9544w  - 1464w  - 120w - 4
        *
           t
       + 
                   11          10          9          8          7          6
             20736w   + 119232w   + 307152w  + 473364w  + 490158w  + 359046w
           + 
                    5         4         3        2
             187662w  + 68190w  + 16314w  + 2370w  + 186w + 6
        *
           v
       + 
               12          11          10          9          8          7
         20736w   + 129600w   + 378864w   + 685260w  + 840996w  + 717228w
       + 
                6          5         4        3       2
         421140w  + 165396w  + 41452w  + 6180w  + 492w  + 16w
       ,

             5       4       3      2           3      2
         (72w  + 180w  + 144w  + 36w )y + (- 24w  - 42w  - 20w - 2)u z
       + 
               4      3      2             5      4      3      2
         (- 24w  - 42w  - 20w  - 2w)t + 24w  + 54w  + 53w  + 33w  + 11w + 1
       ,

                       9             8              7              6
             177732288w  + 719015472w  + 1232091096w  + 1173573804w
           + 
                       5             4            3           2
             679584244w  + 241504763w  + 49510061w  + 5012029w  + 188379w
        *
           x
       + 
                         23                22                 21
             18345885696w   + 201804742656w   + 1034631512064w
           + 
                           20                 19                  18
             3285633466368w   + 7245828587520w   + 11794015715328w
           + 
                            17                  16                  15
             14705111236608w   + 14392584880128w   + 11248017481728w
           + 
                           14                 13                 12
             7106910658560w   + 3664870060032w   + 1553671950336w
           + 
                          11                10               9              8
             544159248384w   + 157668409344w   + 37615263744w  + 7285383168w
           + 
                        7             6            5          4         3
             1114865664w  + 128901120w  + 10481664w  + 528384w  + 12288w
        *
           t
       + 
                     23                22                 21                 20
         18345885696w   + 201422536704w   + 1030427246592w   + 3264142344192w
       + 
                       19                  18                  17
         7178014900224w   + 11646005796864w   + 14467760013312w
       + 
                        16                  15                 14
         14102539278336w   + 10971419618304w   + 6897670239744w
       + 
                       13                 12                11                10
         3537815786496w   + 1491187528704w   + 519099757056w   + 149437154304w
       + 
                     9              8              7             6           5
         35401691136w  + 6802421760w  + 1031325696w  + 117929472w  + 9464832w
       + 
                4         3
         470016w  + 10752w
       ,
      b1 + y + z - t - w}
     ]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))

zeroSetSplit(lp)$T
 

   (28)
                       4      3      2
   [{w + 1,u,v,8t + 24w  + 36w  + 26w  + 7w + 1,z,b1 + y + z - t - w},
                       4      3      2
    {w + 1,u,v,8t + 24w  + 36w  + 26w  + 7w + 1,b1 + y + z - t - w},
                     4      3      2
    {w + 1,u,8t + 24w  + 36w  + 26w  + 7w + 1,z,v y,b1 + y + z - t - w},
                     4      3      2
    {w + 1,u,8t + 24w  + 36w  + 26w  + 7w + 1,v y,v z x,b1 + y + z - t - w},
                     4      3      2
    {w + 1,v,8t + 24w  + 36w  + 26w  + 7w + 1,u z,b1 + y + z - t - w},
                  2         4      3      2
    {w + 1,u v - u ,8t + 24w  + 36w  + 26w  + 7w + 1,z,u y,b1 + y + z - t - w},

                    2          4      3      2
     {w + 1, u v - u , 8t + 24w  + 36w  + 26w  + 7w + 1, u y + u z, u z x,
      b1 + y + z - t - w}
     ,
                   4      3      2                  2
    {w + 1,8t + 24w  + 36w  + 26w  + 7w + 1,(u v - u )z,v y,b1 + y + z - t - w},

     {
              10         9         8         7        6       5       4       3
         3456w   + 12960w  + 19872w  + 15912w  + 6732w  + 996w  - 337w  - 167w
       + 
              2
         - 23w  - w
       ,
          3      2                  6       5       4      3      2
      (12w  + 21w  + 10w + 1)u - 72w  - 180w  - 150w  - 51w  - 12w  - 3w,
          3      2                  5      4      3      2
      (12w  + 21w  + 10w + 1)v + 36w  + 90w  + 72w  + 18w ,
          3      2             4      3      2
      (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,

                   9          8          7          6          5          4
             82944w  + 323568w  + 536868w  + 501804w  + 291411w  + 106080w
           + 
                   3        2
             22458w  + 2316w  + 87w
        *
           z
       + 
                         10          9          8          7          6
                 - 20736w   - 108864w  - 242352w  - 297756w  - 220104w
               + 
                          5         4        3       2
                 - 100116w  - 27552w  - 4356w  - 360w  - 12w
            *
               v
           + 
                     11          10          9          8          7          6
             - 20736w   - 108864w   - 249264w  - 334044w  - 300888w  - 199368w
           + 
                      5         4        3        2
             - 100920w  - 37728w  - 9544w  - 1464w  - 120w - 4
        *
           t
       + 
                   11          10          9          8          7          6
             20736w   + 119232w   + 307152w  + 473364w  + 490158w  + 359046w
           + 
                    5         4         3        2
             187662w  + 68190w  + 16314w  + 2370w  + 186w + 6
        *
           v
       + 
               12          11          10          9          8          7
         20736w   + 129600w   + 378864w   + 685260w  + 840996w  + 717228w
       + 
                6          5         4        3       2
         421140w  + 165396w  + 41452w  + 6180w  + 492w  + 16w
       ,

             5       4       3      2           3      2
         (72w  + 180w  + 144w  + 36w )y + (- 24w  - 42w  - 20w - 2)u z
       + 
               4      3      2             5      4      3      2
         (- 24w  - 42w  - 20w  - 2w)t + 24w  + 54w  + 53w  + 33w  + 11w + 1
       ,

                       9             8              7              6
             177732288w  + 719015472w  + 1232091096w  + 1173573804w
           + 
                       5             4            3           2
             679584244w  + 241504763w  + 49510061w  + 5012029w  + 188379w
        *
           x
       + 
                         23                22                 21
             18345885696w   + 201804742656w   + 1034631512064w
           + 
                           20                 19                  18
             3285633466368w   + 7245828587520w   + 11794015715328w
           + 
                            17                  16                  15
             14705111236608w   + 14392584880128w   + 11248017481728w
           + 
                           14                 13                 12
             7106910658560w   + 3664870060032w   + 1553671950336w
           + 
                          11                10               9              8
             544159248384w   + 157668409344w   + 37615263744w  + 7285383168w
           + 
                        7             6            5          4         3
             1114865664w  + 128901120w  + 10481664w  + 528384w  + 12288w
        *
           t
       + 
                     23                22                 21                 20
         18345885696w   + 201422536704w   + 1030427246592w   + 3264142344192w
       + 
                       19                  18                  17
         7178014900224w   + 11646005796864w   + 14467760013312w
       + 
                        16                  15                 14
         14102539278336w   + 10971419618304w   + 6897670239744w
       + 
                       13                 12                11                10
         3537815786496w   + 1491187528704w   + 519099757056w   + 149437154304w
       + 
                     9              8              7             6           5
         35401691136w  + 6802421760w  + 1031325696w  + 117929472w  + 9464832w
       + 
                4         3
         470016w  + 10752w
       ,
      b1 + y + z - t - w}
     ]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))


T := REGSET(R,E,V,P)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

(29) -> 
Starts dribbling to galois.output (2010/3/27, 18:26:28).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 28
p := x**5 - 5*x + 12
 

         5
   (1)  x  - 5x + 12
                                                     Type: Polynomial Integer
--R 
--R
--R         5
--R   (1)  x  - 5x + 12
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 28
q := resultant(eval(p,x,y),-eval(p,x,y-x),y)
 

   (2)
      25      21        17         15        13           11          9
     x   - 50x   - 2375x   + 90000x   - 5000x   + 2700000x   + 250000x
   + 
              7            5
     18000000x  + 64000000x
                                                     Type: Polynomial Integer
--R 
--R
--R   (2)
--R      25      21        17         15        13           11          9
--R     x   - 50x   - 2375x   + 90000x   - 5000x   + 2700000x   + 250000x
--R   + 
--R              7            5
--R     18000000x  + 64000000x
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 28
q1 := exquo(q, x**5)
 

   (3)
      20      16        12         10        8           6          4
     x   - 50x   - 2375x   + 90000x   - 5000x  + 2700000x  + 250000x
   + 
              2
     18000000x  + 64000000
                                          Type: Union(Polynomial Integer,...)
--R 
--R
--R   (3)
--R      20      16        12         10        8           6          4
--R     x   - 50x   - 2375x   + 90000x   - 5000x  + 2700000x  + 250000x
--R   + 
--R              2
--R     18000000x  + 64000000
--R                                          Type: Union(Polynomial Integer,...)
--E 3

--S 4 of 28
factoredQ := factor q1
 

   (4)
       10      8      6        4        2
     (x   - 10x  - 75x  + 1500x  - 5500x  + 16000)
  *
       10      8       6       4        2
     (x   + 10x  + 125x  + 500x  + 2500x  + 4000)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (4)
--R       10      8      6        4        2
--R     (x   - 10x  - 75x  + 1500x  - 5500x  + 16000)
--R  *
--R       10      8       6       4        2
--R     (x   + 10x  + 125x  + 500x  + 2500x  + 4000)
--R                                            Type: Factored Polynomial Integer
--E 4

--S 5 of 28
r := nthFactor(factoredQ,1)
 

         10      8      6        4        2
   (5)  x   - 10x  - 75x  + 1500x  - 5500x  + 16000
                                                     Type: Polynomial Integer
--R 
--R
--R         10      8      6        4        2
--R   (5)  x   - 10x  - 75x  + 1500x  - 5500x  + 16000
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 28
beta := rootOf(eval(r,x,b))
 

   (6)  b
                                                        Type: AlgebraicNumber
--R 
--R
--R   (6)  b
--R                                                        Type: AlgebraicNumber
--E 6

--S 7 of 28
p := p::UP(x,INT)::UP(x,AN)
 

         5
   (7)  x  - 5x + 12
                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R         5
--R   (7)  x  - 5x + 12
--R                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--E 7

--S 8 of 28
algFactors := factor(p,[beta])
 

   (8)
       x
     + 
                9       8       7        6         5        4          3
           - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
         + 
                    2
           - 327000b  - 405200b + 2062400
      /
         1339200
  *
               8       6        4         2
          - 17b  + 156b  + 2979b  - 25410b  - 14080
     (x + -----------------------------------------)
                            66960
  *
              8        6         4          2
          143b  - 2100b  - 10485b  + 290550b  - 334800b - 960800
     (x + ------------------------------------------------------)
                                  669600
  *
              8        6         4          2
          143b  - 2100b  - 10485b  + 290550b  + 334800b - 960800
     (x + ------------------------------------------------------)
                                  669600
  *
       x
     + 
              9       8       7        6         5        4          3
           85b  - 116b  - 780b  + 2640b  - 14895b  - 8820b  + 127050b
         + 
                    2
           - 327000b  + 405200b + 2062400
      /
         1339200
                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R   (8)
--R       x
--R     + 
--R                9       8       7        6         5        4          3
--R           - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
--R         + 
--R                    2
--R           - 327000b  - 405200b + 2062400
--R      /
--R         1339200
--R  *
--R               8       6        4         2
--R          - 17b  + 156b  + 2979b  - 25410b  - 14080
--R     (x + -----------------------------------------)
--R                            66960
--R  *
--R              8        6         4          2
--R          143b  - 2100b  - 10485b  + 290550b  - 334800b - 960800
--R     (x + ------------------------------------------------------)
--R                                  669600
--R  *
--R              8        6         4          2
--R          143b  - 2100b  - 10485b  + 290550b  + 334800b - 960800
--R     (x + ------------------------------------------------------)
--R                                  669600
--R  *
--R       x
--R     + 
--R              9       8       7        6         5        4          3
--R           85b  - 116b  - 780b  + 2640b  - 14895b  - 8820b  + 127050b
--R         + 
--R                    2
--R           - 327000b  + 405200b + 2062400
--R      /
--R         1339200
--R                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--E 8

--S 9 of 28
factor(p)
 

         5
   (9)  x  - 5x + 12
                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R         5
--R   (9)  x  - 5x + 12
--R                       Type: Factored UnivariatePolynomial(x,AlgebraicNumber)
--E 9

--S 10 of 28
factor1 := nthFactor(algFactors,1)
 

   (10)
     x
   + 
              9       8       7        6         5        4          3
         - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
       + 
                  2
         - 327000b  - 405200b + 2062400
    /
       1339200
                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--R 
--R
--R   (10)
--R     x
--R   + 
--R              9       8       7        6         5        4          3
--R         - 85b  - 116b  + 780b  + 2640b  + 14895b  - 8820b  - 127050b
--R       + 
--R                  2
--R         - 327000b  - 405200b + 2062400
--R    /
--R       1339200
--R                                Type: UnivariatePolynomial(x,AlgebraicNumber)
--E 10

--S 11 of 28
root1 := -coefficient(factor1,0)
 

   (11)
          9       8       7        6         5        4          3          2
       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
     + 
       405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (11)
--R          9       8       7        6         5        4          3          2
--R       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
--R     + 
--R       405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 11

--S 12 of 28
roots := [-coefficient(nthFactor(algFactors,i),0) for i in 1..5]
 

   (12)
   [
            9       8       7        6         5        4          3          2
         85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
       + 
         405200b - 2062400
    /
       1339200
     ,
       8       6        4         2
    17b  - 156b  - 2979b  + 25410b  + 14080
    ---------------------------------------,
                     66960
          8        6         4          2
    - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
    --------------------------------------------------------,
                             669600
          8        6         4          2
    - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
    --------------------------------------------------------,
                             669600

              9       8       7        6         5        4          3
         - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b
       + 
                2
         327000b  - 405200b - 2062400
    /
       1339200
     ]
                                                   Type: List AlgebraicNumber
--R 
--R
--R   (12)
--R   [
--R            9       8       7        6         5        4          3          2
--R         85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
--R       + 
--R         405200b - 2062400
--R    /
--R       1339200
--R     ,
--R       8       6        4         2
--R    17b  - 156b  - 2979b  + 25410b  + 14080
--R    ---------------------------------------,
--R                     66960
--R          8        6         4          2
--R    - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
--R    --------------------------------------------------------,
--R                             669600
--R          8        6         4          2
--R    - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
--R    --------------------------------------------------------,
--R                             669600
--R
--R              9       8       7        6         5        4          3
--R         - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b
--R       + 
--R                2
--R         327000b  - 405200b - 2062400
--R    /
--R       1339200
--R     ]
--R                                                   Type: List AlgebraicNumber
--E 12

--S 13 of 28
(a1,a2,a3,a4,a5) := (roots.1,roots.2,roots.3,roots.4,roots.5)
 

   (13)
            9       8       7        6         5        4          3          2
       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
     + 
       - 405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (13)
--R            9       8       7        6         5        4          3          2
--R       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
--R     + 
--R       - 405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 13

--S 14 of 28
eval(r,x,a1 - a2)
 

   (14)  0
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (14)  0
--R                                             Type: Polynomial AlgebraicNumber
--E 14

--S 15 of 28
eval(r,x,a1 - a3)
 

   (15)
             9         8          7          6           5           4
       47905b  + 66920b  - 536100b  - 980400b  - 3345075b  - 5787000b
     + 
                3             2
       75572250b  + 161688000b  - 184600000b - 710912000
  /
     4464
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (15)
--R             9         8          7          6           5           4
--R       47905b  + 66920b  - 536100b  - 980400b  - 3345075b  - 5787000b
--R     + 
--R                3             2
--R       75572250b  + 161688000b  - 184600000b - 710912000
--R  /
--R     4464
--R                                             Type: Polynomial AlgebraicNumber
--E 15

--S 16 of 28
eval(r,x,a1 - a4)
 

   (16)  0
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (16)  0
--R                                             Type: Polynomial AlgebraicNumber
--E 16

--S 17 of 28
eval(r,x,a1 - a5)
 

             8        6         4          2
         405b  + 3450b  - 19875b  - 198000b  - 588000
   (17)  --------------------------------------------
                              31
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R             8        6         4          2
--R         405b  + 3450b  - 19875b  - 198000b  - 588000
--R   (17)  --------------------------------------------
--R                              31
--R                                             Type: Polynomial AlgebraicNumber
--E 17

--S 18 of 28
bb := a1 - a4
 

   (18)
          9       8       7        6         5         4          3          2
       85b  + 402b  - 780b  - 6840b  - 14895b  - 12150b  + 127050b  + 908100b
     + 
       1074800b - 3984000
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (18)
--R          9       8       7        6         5         4          3          2
--R       85b  + 402b  - 780b  - 6840b  - 14895b  - 12150b  + 127050b  + 908100b
--R     + 
--R       1074800b - 3984000
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 18

--S 19 of 28
aa1 := subst(a1,beta = bb)
 

               8        6         4          2
         - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
   (19)  --------------------------------------------------------
                                  669600
                                                        Type: AlgebraicNumber
--R 
--R
--R               8        6         4          2
--R         - 143b  + 2100b  + 10485b  - 290550b  + 334800b + 960800
--R   (19)  --------------------------------------------------------
--R                                  669600
--R                                                        Type: AlgebraicNumber
--E 19

--S 20 of 28
aa2 := subst(a2,beta = bb)
 

   (20)
            9       8       7        6         5        4          3          2
       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
     + 
       - 405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (20)
--R            9       8       7        6         5        4          3          2
--R       - 85b  + 116b  + 780b  - 2640b  + 14895b  + 8820b  - 127050b  + 327000b
--R     + 
--R       - 405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 20

--S 21 of 28
aa3 := subst(a3,beta = bb)
 

   (21)
          9       8       7        6         5        4          3          2
       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
     + 
       405200b - 2062400
  /
     1339200
                                                        Type: AlgebraicNumber
--R 
--R
--R   (21)
--R          9       8       7        6         5        4          3          2
--R       85b  + 116b  - 780b  - 2640b  - 14895b  + 8820b  + 127050b  + 327000b
--R     + 
--R       405200b - 2062400
--R  /
--R     1339200
--R                                                        Type: AlgebraicNumber
--E 21

--S 22 of 28
aa4 := subst(a4,beta = bb)
 

               8        6         4          2
         - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
   (22)  --------------------------------------------------------
                                  669600
                                                        Type: AlgebraicNumber
--R 
--R
--R               8        6         4          2
--R         - 143b  + 2100b  + 10485b  - 290550b  - 334800b + 960800
--R   (22)  --------------------------------------------------------
--R                                  669600
--R                                                        Type: AlgebraicNumber
--E 22

--S 23 of 28
aa5 := subst(a5,beta = bb)
 

            8       6        4         2
         17b  - 156b  - 2979b  + 25410b  + 14080
   (23)  ---------------------------------------
                          66960
                                                        Type: AlgebraicNumber
--R 
--R
--R            8       6        4         2
--R         17b  - 156b  - 2979b  + 25410b  + 14080
--R   (23)  ---------------------------------------
--R                          66960
--R                                                        Type: AlgebraicNumber
--E 23

--S 24 of 28
(aa1 = a1) :: Boolean
 

   (24)  false
                                                                Type: Boolean
--R 
--R
--R   (24)  false
--R                                                                Type: Boolean
--E 24

--S 25 of 28
(aa1 = a2) :: Boolean
 

   (25)  false
                                                                Type: Boolean
--R 
--R
--R   (25)  false
--R                                                                Type: Boolean
--E 25

--S 26 of 28
(aa1 = a3) :: Boolean
 

   (26)  true
                                                                Type: Boolean
--R 
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26

--S 27 of 28
(aa1 = a4) :: Boolean
 

   (27)  false
                                                                Type: Boolean
--R 
--R
--R   (27)  false
--R                                                                Type: Boolean
--E 27

--S 28 of 28
(aa1 = a5) :: Boolean
 

   (28)  false
                                                                Type: Boolean
--R 
--R
--R   (28)  false
--R                                                                Type: Boolean
--E 28
)spool 
 
Starts dribbling to dop.output (2010/3/27, 18:25:2).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 127
)d op binaryTree
 

There are 2 exposed functions called binaryTree :
   [1] (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from 
            BinaryTree D1
            if D1 has SETCAT
   [2] D1 -> BinaryTree D1 from BinaryTree D1 if D1 has SETCAT

Examples of binaryTree from BinaryTree

t1:=binaryTree([1,2,3]) 
t2:=binaryTree([4,5,6]) 
binaryTree(t1,[7,8,9],t2)

t1:=binaryTree([1,2,3])

--R 
--R
--RThere are 2 exposed functions called binaryTree :
--R   [1] (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from 
--R            BinaryTree D1
--R            if D1 has SETCAT
--R   [2] D1 -> BinaryTree D1 from BinaryTree D1 if D1 has SETCAT
--R
--RExamples of binaryTree from BinaryTree
--R
--Rt1:=binaryTree([1,2,3]) 
--Rt2:=binaryTree([4,5,6]) 
--RbinaryTree(t1,[7,8,9],t2)
--R
--Rt1:=binaryTree([1,2,3])
--R
--E 1

--S 2 of 127
)d op rationalPoint?
 

There is one exposed function called rationalPoint? :
   [1] (D2,D2) -> Boolean from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

There is one unexposed function called rationalPoint? :
   [1] (D2,D2) -> Boolean from FunctionFieldCategory&(D3,D2,D4,D5)
            if D2 has UFD and D4 has UPOLYC D2 and D5 has UPOLYC FRAC 
            D4 and D3 has FFCAT(D2,D4,D5)

Examples of rationalPoint? from FunctionFieldCategory&

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
rationalPoint?(0,0)$R 
R2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
rationalPoint?(0,0)$R2


Examples of rationalPoint? from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
rationalPoint?(0,0)$R 
R2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
rationalPoint?(0,0)$R2

--R 
--R
--RThere is one exposed function called rationalPoint? :
--R   [1] (D2,D2) -> Boolean from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RThere is one unexposed function called rationalPoint? :
--R   [1] (D2,D2) -> Boolean from FunctionFieldCategory&(D3,D2,D4,D5)
--R            if D2 has UFD and D4 has UPOLYC D2 and D5 has UPOLYC FRAC 
--R            D4 and D3 has FFCAT(D2,D4,D5)
--R
--RExamples of rationalPoint? from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RrationalPoint?(0,0)$R 
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
--RrationalPoint?(0,0)$R2
--R
--R
--RExamples of rationalPoint? from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RrationalPoint?(0,0)$R 
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
--RrationalPoint?(0,0)$R2
--R
--E 2

--S 3 of 127
)d op nthFactor
 

There are 2 exposed functions called nthFactor :
   [1] (D,Integer) -> D1 from D
            if D has FAMONC(D1,D3) and D3 has CABMON and D1 has SETCAT
            
   [2] (Factored D1,Integer) -> D1 from Factored D1 if D1 has INTDOM
         

There are 4 unexposed functions called nthFactor :
   [1] (FreeGroup D1,Integer) -> D1 from FreeGroup D1 if D1 has SETCAT
            
   [2] (FreeMonoid D1,Integer) -> D1 from FreeMonoid D1 if D1 has 
            SETCAT
   [3] (ListMonoidOps(D1,D3,D4),Integer) -> D1 from ListMonoidOps(D1,D3
            ,D4)
            if D1 has SETCAT and D3 has ABELMON and D4: D3
   [4] (OrderedFreeMonoid D1,Integer) -> D1 from OrderedFreeMonoid D1
            if D1 has ORDSET

Examples of nthFactor from FreeAbelianMonoidCategory


Examples of nthFactor from FreeGroup


Examples of nthFactor from FreeMonoid


Examples of nthFactor from Factored

a:=factor 9720000 
nthFactor(a,2)


Examples of nthFactor from ListMonoidOps


Examples of nthFactor from OrderedFreeMonoid

m1:=(x*y*y*z)$OFMONOID(Symbol) 
nthFactor(m1,2)

--R 
--R
--RThere are 2 exposed functions called nthFactor :
--R   [1] (D,Integer) -> D1 from D
--R            if D has FAMONC(D1,D3) and D3 has CABMON and D1 has SETCAT
--R            
--R   [2] (Factored D1,Integer) -> D1 from Factored D1 if D1 has INTDOM
--R         
--R
--RThere are 4 unexposed functions called nthFactor :
--R   [1] (FreeGroup D1,Integer) -> D1 from FreeGroup D1 if D1 has SETCAT
--R            
--R   [2] (FreeMonoid D1,Integer) -> D1 from FreeMonoid D1 if D1 has 
--R            SETCAT
--R   [3] (ListMonoidOps(D1,D3,D4),Integer) -> D1 from ListMonoidOps(D1,D3
--R            ,D4)
--R            if D1 has SETCAT and D3 has ABELMON and D4: D3
--R   [4] (OrderedFreeMonoid D1,Integer) -> D1 from OrderedFreeMonoid D1
--R            if D1 has ORDSET
--R
--RExamples of nthFactor from FreeAbelianMonoidCategory
--R
--R
--RExamples of nthFactor from FreeGroup
--R
--R
--RExamples of nthFactor from FreeMonoid
--R
--R
--RExamples of nthFactor from Factored
--R
--Ra:=factor 9720000 
--RnthFactor(a,2)
--R
--R
--RExamples of nthFactor from ListMonoidOps
--R
--R
--RExamples of nthFactor from OrderedFreeMonoid
--R
--E 3

--S 4 of 127
)d op qsetelt!
 

There are 2 exposed functions called qsetelt! :
   [1] (D,Integer,Integer,D1) -> D1 from D
            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
            D1 and D4 has FLAGG D1
   [2] (D,D2,D1) -> D1 from D
            if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2 
            has SETCAT and D1 has TYPE

Examples of qsetelt! from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,0) 
qsetelt!(arr,1,1,17)


Examples of qsetelt! from EltableAggregate

--R 
--R
--RThere are 2 exposed functions called qsetelt! :
--R   [1] (D,Integer,Integer,D1) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
--R            D1 and D4 has FLAGG D1
--R   [2] (D,D2,D1) -> D1 from D
--R            if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2 
--R            has SETCAT and D1 has TYPE
--R
--RExamples of qsetelt! from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0) 
--Rqsetelt!(arr,1,1,17)
--R
--R
--RExamples of qsetelt! from EltableAggregate
--R
--E 4

--S 5 of 127
)d op cycleElt
 

There is one unexposed function called cycleElt :
   [1] D1 -> Union(D1,"failed") from CyclicStreamTools(D2,D1)
            if D2 has TYPE and D1 has LZSTAGG D2

Examples of cycleElt from CyclicStreamTools

p:=repeating([1,2,3]) 
q:=cons(4,p) 
cycleElt q 
r:=[1,2,3]::Stream(Integer) 
cycleElt r

--R 
--R
--RThere is one unexposed function called cycleElt :
--R   [1] D1 -> Union(D1,"failed") from CyclicStreamTools(D2,D1)
--R            if D2 has TYPE and D1 has LZSTAGG D2
--R
--RExamples of cycleElt from CyclicStreamTools
--R
--Rp:=repeating([1,2,3]) 
--Rq:=cons(4,p) 
--RcycleElt q 
--Rr:=[1,2,3]::Stream(Integer) 
--RcycleElt r
--R
--E 5

--S 6 of 127
)d op cyclicEntries
 

There is one exposed function called cyclicEntries :
   [1] Tree D2 -> List Tree D2 from Tree D2 if D2 has SETCAT

Examples of cyclicEntries from Tree

t1:=tree [1,2,3,4] 
cyclicEntries t1

--R 
--R
--RThere is one exposed function called cyclicEntries :
--R   [1] Tree D2 -> List Tree D2 from Tree D2 if D2 has SETCAT
--R
--RExamples of cyclicEntries from Tree
--R
--Rt1:=tree [1,2,3,4] 
--RcyclicEntries t1
--R
--E 6

--S 7 of 127
)d op oneDimensionalArray
 

There are 2 exposed functions called oneDimensionalArray :
   [1] (NonNegativeInteger,D2) -> OneDimensionalArray D2
            from OneDimensionalArray D2 if D2 has TYPE
   [2] List D2 -> OneDimensionalArray D2 from OneDimensionalArray D2
            if D2 has TYPE

Examples of oneDimensionalArray from OneDimensionalArray

oneDimensionalArray(10,0.0)

oneDimensionalArray [i**2 for i in 1..10]

--R 
--R
--RThere are 2 exposed functions called oneDimensionalArray :
--R   [1] (NonNegativeInteger,D2) -> OneDimensionalArray D2
--R            from OneDimensionalArray D2 if D2 has TYPE
--R   [2] List D2 -> OneDimensionalArray D2 from OneDimensionalArray D2
--R            if D2 has TYPE
--R
--RExamples of oneDimensionalArray from OneDimensionalArray
--R
--RoneDimensionalArray(10,0.0)
--R
--RoneDimensionalArray [i**2 for i in 1..10]
--R
--E 7

--S 8 of 127
)d op alphanumeric?
 

There is one exposed function called alphanumeric? :
   [1] Character -> Boolean from Character

Examples of alphanumeric? from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[alphanumeric? c for c in chars]

--R 
--R
--RThere is one exposed function called alphanumeric? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of alphanumeric? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[alphanumeric? c for c in chars]
--R
--E 8

--S 9 of 127
)d op digit?
 

There is one exposed function called digit? :
   [1] Character -> Boolean from Character

Examples of digit? from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[digit? c for c in chars]

--R 
--R
--RThere is one exposed function called digit? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of digit? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[digit? c for c in chars]
--R
--E 9

--S 10 of 127
)d op sqfrFactor
 

There is one exposed function called sqfrFactor :
   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
         

Examples of sqfrFactor from Factored

a:=sqfrFactor(3,5) 
nthFlag(a,1)

--R 
--R
--RThere is one exposed function called sqfrFactor :
--R   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
--R         
--R
--RExamples of sqfrFactor from Factored
--R
--Ra:=sqfrFactor(3,5) 
--RnthFlag(a,1)
--R
--E 10

--S 11 of 127
)d op integralMatrix
 

There is one exposed function called integralMatrix :
   [1]  -> Matrix Fraction D3 from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

Examples of integralMatrix from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
integralMatrix()$R

--R 
--R
--RThere is one exposed function called integralMatrix :
--R   [1]  -> Matrix Fraction D3 from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RExamples of integralMatrix from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RintegralMatrix()$R
--R
--E 11

--S 12 of 127
)d op ptree
 

There are 2 exposed functions called ptree :
   [1] (PendantTree D1,PendantTree D1) -> PendantTree D1 from 
            PendantTree D1
            if D1 has SETCAT
   [2] D1 -> PendantTree D1 from PendantTree D1 if D1 has SETCAT

Examples of ptree from PendantTree

t1:=ptree([1,2,3]) 
ptree(t1,ptree([1,2,3]))

t1:=ptree([1,2,3])

--R 
--R
--RThere are 2 exposed functions called ptree :
--R   [1] (PendantTree D1,PendantTree D1) -> PendantTree D1 from 
--R            PendantTree D1
--R            if D1 has SETCAT
--R   [2] D1 -> PendantTree D1 from PendantTree D1 if D1 has SETCAT
--R
--RExamples of ptree from PendantTree
--R
--Rt1:=ptree([1,2,3]) 
--Rptree(t1,ptree([1,2,3]))
--R
--Rt1:=ptree([1,2,3])
--R
--E 12

--S 13 of 127
)d op insert!
 

There are 13 exposed functions called insert! :
   [1] (D1,ArrayStack D1) -> ArrayStack D1 from ArrayStack D1 if D1 has
            SETCAT
   [2] (D1,D) -> D from D if D has BGAGG D1 and D1 has TYPE
   [3] (D1,BinarySearchTree D1) -> BinarySearchTree D1
            from BinarySearchTree D1 if D1 has ORDSET
   [4] (D1,BinaryTournament D1) -> BinaryTournament D1
            from BinaryTournament D1 if D1 has ORDSET
   [5] (D1,Dequeue D1) -> Dequeue D1 from Dequeue D1 if D1 has SETCAT
         
   [6] (D,D,Integer) -> D from D if D has ELAGG D2 and D2 has TYPE
   [7] (D1,D,Integer) -> D from D if D has ELAGG D1 and D1 has TYPE
   [8] (D1,Heap D1) -> Heap D1 from Heap D1 if D1 has ORDSET
   [9] Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range
            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
            relerr: DoubleFloat),entry: Record(endPointContinuity: Union(
            continuous: Continuous at the end points,lowerSingular: 
            There is a singularity at the lower end point,upperSingular: 
            There is a singularity at the upper end point,bothSingular: 
            There are singularities at both end points,notEvaluated: 
            End point continuity not yet evaluated),singularitiesStream: 
            Union(str: Stream DoubleFloat,notEvaluated: 
            Internal singularities not yet evaluated),range: Union(finite: 
            The range is finite,lowerInfinite: 
            The bottom of range is infinite,upperInfinite: 
            The top of range is infinite,bothInfinite: 
            Both top and bottom points are infinite,notEvaluated: 
            Range not yet evaluated))) -> IntegrationFunctionsTable
            from IntegrationFunctionsTable
   [10] (D1,D,NonNegativeInteger) -> D from D
            if D has MDAGG D1 and D1 has SETCAT
   [11] Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: 
            Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: 
            List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,
            relerr: DoubleFloat),entry: Record(stiffness: Float,stability: 
            Float,expense: Float,accuracy: Float,intermediateResults: Float))
             -> ODEIntensityFunctionsTable
            from ODEIntensityFunctionsTable
   [12] (D1,Queue D1) -> Queue D1 from Queue D1 if D1 has SETCAT
   [13] (D1,Stack D1) -> Stack D1 from Stack D1 if D1 has SETCAT

There is one unexposed function called insert! :
   [1] (D2,D3) -> Void from TabulatedComputationPackage(D2,D3)
            if D2 has SETCAT and D3 has SETCAT

Examples of insert! from ArrayStack

a:ArrayStack INT:= arrayStack [1,2,3,4,5] 
insert!(8,a) 
a


Examples of insert! from BagAggregate


Examples of insert! from BinarySearchTree

t1:=binarySearchTree [1,2,3,4] 
insert!(5,t1)


Examples of insert! from BinaryTournament

t1:=binaryTournament [1,2,3,4] 
insert!(5,t1) 
t1


Examples of insert! from Dequeue

a:Dequeue INT:= dequeue [1,2,3,4,5] 
insert! (8,a) 
a


Examples of insert! from ExtensibleLinearAggregate


Examples of insert! from Heap

a:Heap INT:= heap [1,2,3,4,5] 
insert!(8,a) 
a


Examples of insert! from IntegrationFunctionsTable


Examples of insert! from MultiDictionary


Examples of insert! from ODEIntensityFunctionsTable


Examples of insert! from Queue

a:Queue INT:= queue [1,2,3,4,5] 
insert! (8,a) 
a


Examples of insert! from Stack

a:Stack INT:= stack [1,2,3,4,5] 
insert!(8,a) 
a


Examples of insert! from TabulatedComputationPackage

--R 
--R
--RThere are 13 exposed functions called insert! :
--R   [1] (D1,ArrayStack D1) -> ArrayStack D1 from ArrayStack D1 if D1 has
--R            SETCAT
--R   [2] (D1,D) -> D from D if D has BGAGG D1 and D1 has TYPE
--R   [3] (D1,BinarySearchTree D1) -> BinarySearchTree D1
--R            from BinarySearchTree D1 if D1 has ORDSET
--R   [4] (D1,BinaryTournament D1) -> BinaryTournament D1
--R            from BinaryTournament D1 if D1 has ORDSET
--R   [5] (D1,Dequeue D1) -> Dequeue D1 from Dequeue D1 if D1 has SETCAT
--R         
--R   [6] (D,D,Integer) -> D from D if D has ELAGG D2 and D2 has TYPE
--R   [7] (D1,D,Integer) -> D from D if D has ELAGG D1 and D1 has TYPE
--R   [8] (D1,Heap D1) -> Heap D1 from Heap D1 if D1 has ORDSET
--R   [9] Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range
--R            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
--R            relerr: DoubleFloat),entry: Record(endPointContinuity: Union(
--R            continuous: Continuous at the end points,lowerSingular: 
--R            There is a singularity at the lower end point,upperSingular: 
--R            There is a singularity at the upper end point,bothSingular: 
--R            There are singularities at both end points,notEvaluated: 
--R            End point continuity not yet evaluated),singularitiesStream: 
--R            Union(str: Stream DoubleFloat,notEvaluated: 
--R            Internal singularities not yet evaluated),range: Union(finite: 
--R            The range is finite,lowerInfinite: 
--R            The bottom of range is infinite,upperInfinite: 
--R            The top of range is infinite,bothInfinite: 
--R            Both top and bottom points are infinite,notEvaluated: 
--R            Range not yet evaluated))) -> IntegrationFunctionsTable
--R            from IntegrationFunctionsTable
--R   [10] (D1,D,NonNegativeInteger) -> D from D
--R            if D has MDAGG D1 and D1 has SETCAT
--R   [11] Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: 
--R            Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: 
--R            List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,
--R            relerr: DoubleFloat),entry: Record(stiffness: Float,stability: 
--R            Float,expense: Float,accuracy: Float,intermediateResults: Float))
--R             -> ODEIntensityFunctionsTable
--R            from ODEIntensityFunctionsTable
--R   [12] (D1,Queue D1) -> Queue D1 from Queue D1 if D1 has SETCAT
--R   [13] (D1,Stack D1) -> Stack D1 from Stack D1 if D1 has SETCAT
--R
--RThere is one unexposed function called insert! :
--R   [1] (D2,D3) -> Void from TabulatedComputationPackage(D2,D3)
--R            if D2 has SETCAT and D3 has SETCAT
--R
--RExamples of insert! from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] 
--Rinsert!(8,a) 
--Ra
--R
--R
--RExamples of insert! from BagAggregate
--R
--R
--RExamples of insert! from BinarySearchTree
--R
--Rt1:=binarySearchTree [1,2,3,4] 
--Rinsert!(5,t1)
--R
--R
--RExamples of insert! from BinaryTournament
--R
--Rt1:=binaryTournament [1,2,3,4] 
--Rinsert!(5,t1) 
--Rt1
--R
--R
--RExamples of insert! from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5] 
--Rinsert! (8,a) 
--Ra
--R
--R
--RExamples of insert! from ExtensibleLinearAggregate
--R
--R
--RExamples of insert! from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5] 
--Rinsert!(8,a) 
--Ra
--R
--R
--RExamples of insert! from IntegrationFunctionsTable
--R
--R
--RExamples of insert! from MultiDictionary
--R
--R
--RExamples of insert! from ODEIntensityFunctionsTable
--R
--R
--RExamples of insert! from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5] 
--Rinsert! (8,a) 
--Ra
--R
--R
--RExamples of insert! from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5] 
--Rinsert!(8,a) 
--Ra
--R
--R
--RExamples of insert! from TabulatedComputationPackage
--R
--E 13

--S 14 of 127
)d op genus
 

There is one exposed function called genus :
   [1]  -> NonNegativeInteger from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

There is one unexposed function called genus :
   [1]  -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC 
            D4 and D2 has FFCAT(D3,D4,D5)

Examples of genus from FunctionFieldCategory&

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
genus()$R


Examples of genus from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
genus()$R

--R 
--R
--RThere is one exposed function called genus :
--R   [1]  -> NonNegativeInteger from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RThere is one unexposed function called genus :
--R   [1]  -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
--R            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC 
--R            D4 and D2 has FFCAT(D3,D4,D5)
--R
--RExamples of genus from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--Rgenus()$R
--R
--R
--RExamples of genus from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--Rgenus()$R
--R
--E 14

--S 15 of 127
)d op hexDigit?
 

There is one exposed function called hexDigit? :
   [1] Character -> Boolean from Character

Examples of hexDigit? from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[hexDigit? c for c in chars]

--R 
--R
--RThere is one exposed function called hexDigit? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of hexDigit? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[hexDigit? c for c in chars]
--R
--E 15

--S 16 of 127
)d op computeCycleLength
 

There is one unexposed function called computeCycleLength :
   [1] D2 -> NonNegativeInteger from CyclicStreamTools(D3,D2)
            if D3 has TYPE and D2 has LZSTAGG D3

Examples of computeCycleLength from CyclicStreamTools

p:=repeating([1,2,3]) 
q:=cons(4,p) 
computeCycleLength(cycleElt(q))

--R 
--R
--RThere is one unexposed function called computeCycleLength :
--R   [1] D2 -> NonNegativeInteger from CyclicStreamTools(D3,D2)
--R            if D3 has TYPE and D2 has LZSTAGG D3
--R
--RExamples of computeCycleLength from CyclicStreamTools
--R
--Rp:=repeating([1,2,3]) 
--Rq:=cons(4,p) 
--RcomputeCycleLength(cycleElt(q))
--R
--E 16

--S 17 of 127
)d op findCycle
 

There is one exposed function called findCycle :
   [1] (NonNegativeInteger,Stream D3) -> Record(cycle?: Boolean,prefix
            : NonNegativeInteger,period: NonNegativeInteger)
            from Stream D3 if D3 has TYPE

Examples of findCycle from Stream

m:=[1,2,3] 
n:=repeating(m) 
findCycle(3,n) 
findCycle(2,n)

--R 
--R
--RThere is one exposed function called findCycle :
--R   [1] (NonNegativeInteger,Stream D3) -> Record(cycle?: Boolean,prefix
--R            : NonNegativeInteger,period: NonNegativeInteger)
--R            from Stream D3 if D3 has TYPE
--R
--RExamples of findCycle from Stream
--R
--Rm:=[1,2,3] 
--Rn:=repeating(m) 
--RfindCycle(3,n) 
--RfindCycle(2,n)
--R
--E 17

--S 18 of 127
)d op draw
 

There are 31 exposed functions called draw :
   [1] ((DoubleFloat -> DoubleFloat),Segment Float,List DrawOption) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [2] ((DoubleFloat -> DoubleFloat),Segment Float) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [3] (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
            ,List DrawOption) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [4] (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
            ) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [5] (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
            ,List DrawOption) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [6] (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
            ) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [7] ((DoubleFloat -> Point DoubleFloat),Segment Float,List 
            DrawOption) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [8] ((DoubleFloat -> Point DoubleFloat),Segment Float) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [9] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
            Segment Float,List DrawOption) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [10] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
            Segment Float) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [11] (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
            ,Segment Float,List DrawOption) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [12] (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
            ,Segment Float) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [13] (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
            Segment Float,Segment Float,List DrawOption) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [14] (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
            Segment Float,Segment Float) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [15] (Equation D6,Symbol,Symbol,List DrawOption) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForAlgebraicCurves(D5,D6)
            if D6 has FS D5 and D5 has Join(IntegralDomain,OrderedSet,
            RetractableTo Integer)
   [16] (D2,SegmentBinding Float,List DrawOption) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctions D2
            if D2 has Join(ConvertibleTo InputForm,SetCategory)
   [17] (D2,SegmentBinding Float) -> TwoDimensionalViewport
            from TopLevelDrawFunctions D2
            if D2 has Join(ConvertibleTo InputForm,SetCategory)
   [18] (ParametricPlaneCurve D5,SegmentBinding Float,List DrawOption)
             -> TwoDimensionalViewport
            from TopLevelDrawFunctions D5
            if D5 has Join(ConvertibleTo InputForm,SetCategory)
   [19] (ParametricPlaneCurve D4,SegmentBinding Float) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctions D4
            if D4 has Join(ConvertibleTo InputForm,SetCategory)
   [20] (ParametricSpaceCurve D5,SegmentBinding Float,List DrawOption)
             -> ThreeDimensionalViewport
            from TopLevelDrawFunctions D5
            if D5 has Join(ConvertibleTo InputForm,SetCategory)
   [21] (ParametricSpaceCurve D4,SegmentBinding Float) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctions D4
            if D4 has Join(ConvertibleTo InputForm,SetCategory)
   [22] (D2,SegmentBinding Float,SegmentBinding Float,List DrawOption)
             -> ThreeDimensionalViewport
            from TopLevelDrawFunctions D2
            if D2 has Join(ConvertibleTo InputForm,SetCategory)
   [23] (D2,SegmentBinding Float,SegmentBinding Float) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctions D2
            if D2 has Join(ConvertibleTo InputForm,SetCategory)
   [24] (ParametricSurface D5,SegmentBinding Float,SegmentBinding Float
            ,List DrawOption) -> ThreeDimensionalViewport
            from TopLevelDrawFunctions D5
            if D5 has Join(ConvertibleTo InputForm,SetCategory)
   [25] (ParametricSurface D4,SegmentBinding Float,SegmentBinding Float
            ) -> ThreeDimensionalViewport
            from TopLevelDrawFunctions D4
            if D4 has Join(ConvertibleTo InputForm,SetCategory)
   [26] (List DoubleFloat,List DoubleFloat) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [27] (List DoubleFloat,List DoubleFloat,List DrawOption) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [28] List Point DoubleFloat -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [29] (List Point DoubleFloat,List DrawOption) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [30] (List DoubleFloat,List DoubleFloat,List DoubleFloat) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [31] (List DoubleFloat,List DoubleFloat,List DoubleFloat,List 
            DrawOption) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForPoints

Examples of draw from TopLevelDrawFunctionsForCompiledFunctions


Examples of draw from TopLevelDrawFunctionsForAlgebraicCurves


Examples of draw from TopLevelDrawFunctions


Examples of draw from TopLevelDrawFunctionsForPoints

--R 
--R
--RThere are 31 exposed functions called draw :
--R   [1] ((DoubleFloat -> DoubleFloat),Segment Float,List DrawOption) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [2] ((DoubleFloat -> DoubleFloat),Segment Float) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [3] (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
--R            ,List DrawOption) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [4] (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
--R            ) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [5] (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
--R            ,List DrawOption) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [6] (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
--R            ) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [7] ((DoubleFloat -> Point DoubleFloat),Segment Float,List 
--R            DrawOption) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [8] ((DoubleFloat -> Point DoubleFloat),Segment Float) -> 
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [9] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
--R            Segment Float,List DrawOption) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [10] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
--R            Segment Float) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [11] (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
--R            ,Segment Float,List DrawOption) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [12] (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
--R            ,Segment Float) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [13] (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
--R            Segment Float,Segment Float,List DrawOption) -> 
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [14] (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
--R            Segment Float,Segment Float) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [15] (Equation D6,Symbol,Symbol,List DrawOption) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForAlgebraicCurves(D5,D6)
--R            if D6 has FS D5 and D5 has Join(IntegralDomain,OrderedSet,
--R            RetractableTo Integer)
--R   [16] (D2,SegmentBinding Float,List DrawOption) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctions D2
--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
--R   [17] (D2,SegmentBinding Float) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctions D2
--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
--R   [18] (ParametricPlaneCurve D5,SegmentBinding Float,List DrawOption)
--R             -> TwoDimensionalViewport
--R            from TopLevelDrawFunctions D5
--R            if D5 has Join(ConvertibleTo InputForm,SetCategory)
--R   [19] (ParametricPlaneCurve D4,SegmentBinding Float) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctions D4
--R            if D4 has Join(ConvertibleTo InputForm,SetCategory)
--R   [20] (ParametricSpaceCurve D5,SegmentBinding Float,List DrawOption)
--R             -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions D5
--R            if D5 has Join(ConvertibleTo InputForm,SetCategory)
--R   [21] (ParametricSpaceCurve D4,SegmentBinding Float) -> 
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctions D4
--R            if D4 has Join(ConvertibleTo InputForm,SetCategory)
--R   [22] (D2,SegmentBinding Float,SegmentBinding Float,List DrawOption)
--R             -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions D2
--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
--R   [23] (D2,SegmentBinding Float,SegmentBinding Float) -> 
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctions D2
--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
--R   [24] (ParametricSurface D5,SegmentBinding Float,SegmentBinding Float
--R            ,List DrawOption) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions D5
--R            if D5 has Join(ConvertibleTo InputForm,SetCategory)
--R   [25] (ParametricSurface D4,SegmentBinding Float,SegmentBinding Float
--R            ) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions D4
--R            if D4 has Join(ConvertibleTo InputForm,SetCategory)
--R   [26] (List DoubleFloat,List DoubleFloat) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [27] (List DoubleFloat,List DoubleFloat,List DrawOption) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [28] List Point DoubleFloat -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [29] (List Point DoubleFloat,List DrawOption) -> 
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [30] (List DoubleFloat,List DoubleFloat,List DoubleFloat) -> 
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [31] (List DoubleFloat,List DoubleFloat,List DoubleFloat,List 
--R            DrawOption) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R
--RExamples of draw from TopLevelDrawFunctionsForCompiledFunctions
--R
--R
--RExamples of draw from TopLevelDrawFunctionsForAlgebraicCurves
--R
--R
--RExamples of draw from TopLevelDrawFunctions
--R
--R
--RExamples of draw from TopLevelDrawFunctionsForPoints
--R
--E 18

--S 19 of 127
)d op repeating
 

There is one exposed function called repeating :
   [1] List D2 -> Stream D2 from Stream D2 if D2 has TYPE

Examples of repeating from Stream

m:=repeating([-1,0,1,2,3])

--R 
--R
--RThere is one exposed function called repeating :
--R   [1] List D2 -> Stream D2 from Stream D2 if D2 has TYPE
--R
--RExamples of repeating from Stream
--R
--Rm:=repeating([-1,0,1,2,3])
--R
--E 19

--S 20 of 127
)d op cons
 

There are 2 exposed functions called cons :
   [1] (D1,List D1) -> List D1 from List D1 if D1 has TYPE
   [2] (D1,Stream D1) -> Stream D1 from Stream D1 if D1 has TYPE

Examples of cons from List


Examples of cons from Stream

m:=[1,2,3] 
n:=repeating(m) 
cons(4,n)

--R 
--R
--RThere are 2 exposed functions called cons :
--R   [1] (D1,List D1) -> List D1 from List D1 if D1 has TYPE
--R   [2] (D1,Stream D1) -> Stream D1 from Stream D1 if D1 has TYPE
--R
--RExamples of cons from List
--R
--R
--RExamples of cons from Stream
--R
--Rm:=[1,2,3] 
--Rn:=repeating(m) 
--Rcons(4,n)
--R
--E 20

--S 21 of 127
)d op map
 

There are 86 exposed functions called map :
   [1] ((D2 -> D2),D) -> D from D
            if D has AMR(D2,D3) and D2 has RING and D3 has OAMON
   [2] (((D2,D2) -> D2),D,D,D2) -> D from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [3] (((D2,D2) -> D2),D,D) -> D from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [4] ((D2 -> D2),D) -> D from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [5] ((D4 -> D5),OneDimensionalArray D4) -> OneDimensionalArray D5
            from OneDimensionalArrayFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [6] ((D2 -> D2),ArrayStack D2) -> ArrayStack D2 from ArrayStack D2
            if D2 has SETCAT
   [7] ((D6 -> D7),CartesianTensor(D4,D5,D6)) -> CartesianTensor(D4,D5,
            D7)
            from CartesianTensorFunctions2(D4,D5,D6,D7)
            if D4: INT and D5: NNI and D6 has COMRING and D7 has 
            COMRING
   [8] ((D4 -> D5),Complex D4) -> Complex D5 from ComplexFunctions2(D4,
            D5)
            if D4 has COMRING and D5 has COMRING
   [9] ((D2 -> D2),Dequeue D2) -> Dequeue D2 from Dequeue D2 if D2 has 
            SETCAT
   [10] ((D5 -> D6),DirectProduct(D4,D5)) -> DirectProduct(D4,D6)
            from DirectProductFunctions2(D4,D5,D6)
            if D4: NNI and D5 has TYPE and D6 has TYPE
   [11] ((D4 -> D5),Equation D4) -> Equation D5 from EquationFunctions2
            (D4,D5)
            if D4 has TYPE and D5 has TYPE
   [12] ((D2 -> D2),Equation D2) -> Equation D2 from Equation D2 if D2 
            has TYPE
   [13] ((D4 -> D1),Kernel D4) -> D1 from ExpressionSpaceFunctions2(D4,
            D1)
            if D4 has ES and D1 has ES
   [14] ((D -> D),Kernel D) -> D from D if D has ES
   [15] ((D4 -> D5),Matrix D4) -> Matrix D5
            from ExpertSystemToolsPackage2(D4,D5)
            if D4 has RING and D5 has RING
   [16] ((D4 -> D5),Expression D4) -> Expression D5
            from ExpressionFunctions2(D4,D5)
            if D4 has ORDSET and D5 has ORDSET
   [17] ((D5 -> D6),D3) -> D1
            from FiniteAbelianMonoidRingFunctions2(D4,D5,D3,D6,D1)
            if D5 has RING and D6 has RING and D4 has OAMON and D1 has 
            FAMR(D6,D4) and D3 has FAMR(D5,D4)
   [18] ((D7 -> D11),FiniteDivisor(D7,D8,D9,D10)) -> FiniteDivisor(D11,
            D1,D2,D3)
            from FiniteDivisorFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
            if D7 has FIELD and D8 has UPOLYC D7 and D9 has UPOLYC FRAC
            D8 and D10 has FFCAT(D7,D8,D9) and D11 has FIELD and D1 has
            UPOLYC D11 and D2 has UPOLYC FRAC D1 and D3 has FFCAT(D11,
            D1,D2)
   [19] ((D2 -> D2),D) -> D from D if D has FEVALAB D2 and D2 has 
            SETCAT
   [20] ((D5 -> D8),D4) -> D2
            from FunctionFieldCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,
            D2)
            if D5 has UFD and D8 has UFD and D6 has UPOLYC D5 and D7 
            has UPOLYC FRAC D6 and D9 has UPOLYC D8 and D2 has FFCAT(D8
            ,D9,D1) and D4 has FFCAT(D5,D6,D7) and D1 has UPOLYC FRAC 
            D9
   [21] ((D4 -> D5),D3) -> D1 from FiniteLinearAggregateFunctions2(D4,
            D3,D5,D1)
            if D4 has TYPE and D5 has TYPE and D1 has FLAGG D5 and D3 
            has FLAGG D4
   [22] ((D2 -> D2),D) -> D from D
            if D has FMCAT(D2,D3) and D2 has RING and D3 has SETCAT
   [23] ((D4 -> D5),Factored D4) -> Factored D5 from FactoredFunctions2
            (D4,D5)
            if D4 has INTDOM and D5 has INTDOM
   [24] ((D4 -> D5),Fraction D4) -> Fraction D5 from FractionFunctions2
            (D4,D5)
            if D4 has INTDOM and D5 has INTDOM
   [25] ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal(
            D11,D1,D2,D3)
            from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
            if D7 has EUCDOM and D8 has QFCAT D7 and D9 has UPOLYC D8 
            and D10 has Join(FramedAlgebra(D8,D9),RetractableTo D8) and
            D11 has EUCDOM and D1 has QFCAT D11 and D2 has UPOLYC D1 
            and D3 has Join(FramedAlgebra(D1,D2),RetractableTo D1)
   [26] ((D4 -> D5),D3) -> D1
            from FramedNonAssociativeAlgebraFunctions2(D3,D4,D1,D5)
            if D4 has COMRING and D5 has COMRING and D1 has FRNAALG D5 
            and D3 has FRNAALG D4
   [27] ((D2 -> D2),Factored D2) -> Factored D2 from Factored D2
            if D2 has INTDOM
   [28] ((D4 -> D5),D3) -> D1 from FunctionSpaceFunctions2(D4,D3,D5,D1)
            if D4 has Join(Ring,OrderedSet) and D5 has Join(Ring,
            OrderedSet) and D1 has FS D5 and D3 has FS D4
   [29] ((D4 -> D5),D3) -> D1 from FiniteSetAggregateFunctions2(D4,D3,
            D5,D1)
            if D4 has SETCAT and D5 has SETCAT and D1 has FSAGG D5 and 
            D3 has FSAGG D4
   [30] ((D2 -> D2),Heap D2) -> Heap D2 from Heap D2 if D2 has ORDSET
         
   [31] ((D2 -> D2),D) -> D from D if D has HOAGG D2 and D2 has TYPE
         
   [32] ((D2 -> D2),D) -> D from D
            if D has IDPC(D2,D3) and D2 has SETCAT and D3 has ORDSET
         
   [33] ((D4 -> D5),IntegrationResult D4) -> IntegrationResult D5
            from IntegrationResultFunctions2(D4,D5)
            if D4 has FIELD and D5 has FIELD
   [34] ((D4 -> D5),Union(Record(ratpart: D4,coeff: D4),"failed")) -> 
            Union(Record(ratpart: D5,coeff: D5),"failed")
            from IntegrationResultFunctions2(D4,D5)
            if D4 has FIELD and D5 has FIELD
   [35] ((D4 -> D1),Union(D4,"failed")) -> Union(D1,"failed")
            from IntegrationResultFunctions2(D4,D1)
            if D4 has FIELD and D1 has FIELD
   [36] ((D4 -> D5),Union(Record(mainpart: D4,limitedlogs: List Record(
            coeff: D4,logand: D4)),"failed")) -> Union(Record(mainpart: D5,
            limitedlogs: List Record(coeff: D5,logand: D5)),"failed")
            from IntegrationResultFunctions2(D4,D5)
            if D4 has FIELD and D5 has FIELD
   [37] ((D4 -> D5),InfiniteTuple D4) -> InfiniteTuple D5
            from InfiniteTupleFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [38] (((D5,D6) -> D7),InfiniteTuple D5,InfiniteTuple D6) -> 
            InfiniteTuple D7
            from InfiniteTupleFunctions3(D5,D6,D7)
            if D5 has TYPE and D6 has TYPE and D7 has TYPE
   [39] (((D5,D6) -> D7),Stream D5,InfiniteTuple D6) -> Stream D7
            from InfiniteTupleFunctions3(D5,D6,D7)
            if D5 has TYPE and D6 has TYPE and D7 has TYPE
   [40] (((D5,D6) -> D7),InfiniteTuple D5,Stream D6) -> Stream D7
            from InfiniteTupleFunctions3(D5,D6,D7)
            if D5 has TYPE and D6 has TYPE and D7 has TYPE
   [41] ((D2 -> D2),InfiniteTuple D2) -> InfiniteTuple D2 from 
            InfiniteTuple D2
            if D2 has TYPE
   [42] ((D4 -> D5),List D4) -> List D5 from ListFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [43] (((D5,D6) -> D7),List D5,List D6) -> List D7
            from ListFunctions3(D5,D6,D7)
            if D5 has TYPE and D6 has TYPE and D7 has TYPE
   [44] (((D2,D2) -> D2),D,D) -> D from D if D has LNAGG D2 and D2 has 
            TYPE
   [45] ((D5 -> D8),D4) -> D2
            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
            if D5 has RING and D8 has RING and D6 has FLAGG D5 and D7 
            has FLAGG D5 and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT(
            D5,D6,D7) and D9 has FLAGG D8 and D1 has FLAGG D8
   [46] ((D5 -> Union(D8,"failed")),D4) -> Union(D2,"failed")
            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
            if D5 has RING and D8 has RING and D6 has FLAGG D5 and D7 
            has FLAGG D5 and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT(
            D5,D6,D7) and D9 has FLAGG D8 and D1 has FLAGG D8
   [47] ((D7 -> D8),D3) -> D1 from MPolyCatFunctions2(D4,D5,D6,D7,D8,D3
            ,D1)
            if D7 has RING and D8 has RING and D4 has ORDSET and D5 has
            OAMONS and D1 has POLYCAT(D8,D6,D4) and D6 has OAMONS and 
            D3 has POLYCAT(D7,D5,D4)
   [48] ((D4 -> D5),MonoidRing(D4,D6)) -> MonoidRing(D5,D6)
            from MonoidRingFunctions2(D4,D5,D6)
            if D4 has RING and D5 has RING and D6 has MONOID
   [49] ((D4 -> D5),D3) -> D1 from OctonionCategoryFunctions2(D3,D4,D1,
            D5)
            if D4 has COMRING and D5 has COMRING and D1 has OC D5 and 
            D3 has OC D4
   [50] ((D4 -> D5),OnePointCompletion D4) -> OnePointCompletion D5
            from OnePointCompletionFunctions2(D4,D5)
            if D4 has SETCAT and D5 has SETCAT
   [51] ((D4 -> D5),OnePointCompletion D4,OnePointCompletion D5) -> 
            OnePointCompletion D5
            from OnePointCompletionFunctions2(D4,D5)
            if D4 has SETCAT and D5 has SETCAT
   [52] ((D4 -> D5),OrderedCompletion D4) -> OrderedCompletion D5
            from OrderedCompletionFunctions2(D4,D5)
            if D4 has SETCAT and D5 has SETCAT
   [53] ((D4 -> D5),OrderedCompletion D4,OrderedCompletion D5,
            OrderedCompletion D5) -> OrderedCompletion D5
            from OrderedCompletionFunctions2(D4,D5)
            if D4 has SETCAT and D5 has SETCAT
   [54] ((D4 -> D5),ParametricPlaneCurve D4) -> ParametricPlaneCurve D5
            from ParametricPlaneCurveFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [55] ((D4 -> D5),ParametricSpaceCurve D4) -> ParametricSpaceCurve D5
            from ParametricSpaceCurveFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [56] ((D4 -> D5),ParametricSurface D4) -> ParametricSurface D5
            from ParametricSurfaceFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [57] ((D5 -> D6),PatternMatchResult(D4,D5)) -> PatternMatchResult(D4
            ,D6)
            from PatternMatchResultFunctions2(D4,D5,D6)
            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
   [58] ((D4 -> D5),Pattern D4) -> Pattern D5 from PatternFunctions2(D4
            ,D5)
            if D4 has SETCAT and D5 has SETCAT
   [59] ((D4 -> D5),Polynomial D4) -> Polynomial D5
            from PolynomialFunctions2(D4,D5)
            if D4 has RING and D5 has RING
   [60] ((D4 -> D5),PrimitiveArray D4) -> PrimitiveArray D5
            from PrimitiveArrayFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [61] ((D4 -> D5),Point D4) -> Point D5 from PointFunctions2(D4,D5)
            if D4 has RING and D5 has RING
   [62] ((D4 -> D5),D3) -> D1 from QuotientFieldCategoryFunctions2(D4,
            D5,D3,D1)
            if D4 has INTDOM and D5 has INTDOM and D1 has QFCAT D5 and 
            D3 has QFCAT D4
   [63] ((D4 -> D5),D3) -> D1 from QuaternionCategoryFunctions2(D3,D4,
            D1,D5)
            if D4 has COMRING and D5 has COMRING and D1 has QUATCAT D5 
            and D3 has QUATCAT D4
   [64] ((D2 -> D2),Queue D2) -> Queue D2 from Queue D2 if D2 has 
            SETCAT
   [65] (((D4,D4) -> D4),D,D) -> D from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
   [66] ((D4 -> D4),D) -> D from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
   [67] ((D9 -> D1),D6) -> D4
            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
            D6,D1,D2,D3,D4)
            if D9 has RING and D1 has RING and D7: NNI and D8: NNI and 
            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D4 
            has RMATCAT(D7,D8,D1,D2,D3) and D6 has RMATCAT(D7,D8,D9,D10
            ,D11) and D2 has DIRPCAT(D8,D1) and D3 has DIRPCAT(D7,D1)
         
   [68] ((D4 -> D5),Segment D4) -> Segment D5 from SegmentFunctions2(D4
            ,D5)
            if D4 has TYPE and D5 has TYPE
   [69] ((D4 -> D5),Segment D4) -> List D5 from SegmentFunctions2(D4,D5
            )
            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
   [70] ((D4 -> D5),SegmentBinding D4) -> SegmentBinding D5
            from SegmentBindingFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [71] ((D3 -> D3),D) -> D1 from D
            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
            D3
   [72] ((D2 -> D2),Stack D2) -> Stack D2 from Stack D2 if D2 has 
            SETCAT
   [73] ((D4 -> D5),Stream D4) -> Stream D5 from StreamFunctions2(D4,D5
            )
            if D4 has TYPE and D5 has TYPE
   [74] (((D5,D6) -> D7),Stream D5,Stream D6) -> Stream D7
            from StreamFunctions3(D5,D6,D7)
            if D5 has TYPE and D6 has TYPE and D7 has TYPE
   [75] ((D4 -> D5),SparseUnivariatePolynomial D4) -> 
            SparseUnivariatePolynomial D5
            from SparseUnivariatePolynomialFunctions2(D4,D5)
            if D4 has RING and D5 has RING
   [76] (((D3,D3) -> D3),D,D) -> D from D
            if D has TBAGG(D2,D3) and D2 has SETCAT and D3 has SETCAT
         
   [77] ((D5 -> D6),UnivariateLaurentSeries(D5,D7,D9)) -> 
            UnivariateLaurentSeries(D6,D8,D1)
            from UnivariateLaurentSeriesFunctions2(D5,D6,D7,D8,D9,D1)
            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5 
            and D1: D6 and D8: SYMBOL
   [78] ((D4 -> D5),UniversalSegment D4) -> UniversalSegment D5
            from UniversalSegmentFunctions2(D4,D5)
            if D4 has TYPE and D5 has TYPE
   [79] ((D4 -> D5),UniversalSegment D4) -> Stream D5
            from UniversalSegmentFunctions2(D4,D5)
            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
   [80] ((D5 -> D7),UnivariatePolynomial(D4,D5)) -> 
            UnivariatePolynomial(D6,D7)
            from UnivariatePolynomialFunctions2(D4,D5,D6,D7)
            if D4: SYMBOL and D5 has RING and D7 has RING and D6: 
            SYMBOL
   [81] ((D4 -> D5),D3) -> D1
            from UnivariatePolynomialCategoryFunctions2(D4,D3,D5,D1)
            if D4 has RING and D5 has RING and D1 has UPOLYC D5 and D3 
            has UPOLYC D4
   [82] ((D5 -> D6),UnivariatePuiseuxSeries(D5,D7,D9)) -> 
            UnivariatePuiseuxSeries(D6,D8,D1)
            from UnivariatePuiseuxSeriesFunctions2(D5,D6,D7,D8,D9,D1)
            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5 
            and D1: D6 and D8: SYMBOL
   [83] ((D4 -> D5),D3) -> D1
            from UnivariateTaylorSeriesFunctions2(D4,D5,D3,D1)
            if D4 has RING and D5 has RING and D1 has UTSCAT D5 and D3 
            has UTSCAT D4
   [84] ((D4 -> D5),Vector D4) -> Vector D5 from VectorFunctions2(D4,D5
            )
            if D4 has TYPE and D5 has TYPE
   [85] ((D4 -> Union(D5,"failed")),Vector D4) -> Union(Vector D5,
            "failed")
            from VectorFunctions2(D4,D5) if D4 has TYPE and D5 has TYPE
            
   [86] ((D3 -> D3),D) -> D from D
            if D has XFALG(D2,D3) and D2 has ORDSET and D3 has RING

There are 10 unexposed functions called map :
   [1] ((D2 -> D2),AntiSymm(D2,D3)) -> AntiSymm(D2,D3) from AntiSymm(D2
            ,D3)
            if D2 has RING and D3: LIST SYMBOL
   [2] ((Expression D2 -> Expression D2),DeRhamComplex(D2,D3)) -> 
            DeRhamComplex(D2,D3)
            from DeRhamComplex(D2,D3)
            if D2 has Join(Ring,OrderedSet) and D3: LIST SYMBOL
   [3] ((D5 -> D1),String,Kernel D5) -> D1
            from ExpressionSpaceFunctions1(D5,D1)
            if D5 has ES and D1 has TYPE
   [4] ((D4 -> D6),D3) -> D1 from MultipleMap(D4,D5,D3,D6,D7,D1)
            if D4 has INTDOM and D6 has INTDOM and D5 has UPOLYC D4 and
            D1 has UPOLYC FRAC D7 and D3 has UPOLYC FRAC D5 and D7 has 
            UPOLYC D6
   [5] ((D4 -> D5),D3) -> D1 from MPolyCatFunctions3(D4,D5,D6,D7,D8,D3,
            D1)
            if D4 has ORDSET and D5 has ORDSET and D6 has OAMONS and D8
            has RING and D1 has POLYCAT(D8,D7,D5) and D7 has OAMONS and
            D3 has POLYCAT(D8,D6,D4)
   [6] ((D2 -> D2),MonoidRing(D2,D3)) -> MonoidRing(D2,D3)
            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
   [7] ((D4 -> D5),NewSparseUnivariatePolynomial D4) -> 
            NewSparseUnivariatePolynomial D5
            from NewSparseUnivariatePolynomialFunctions2(D4,D5)
            if D4 has RING and D5 has RING
   [8] ((D7 -> D2),(D8 -> D2),D5) -> D2
            from PolynomialCategoryLifting(D6,D7,D8,D5,D2)
            if D7 has ORDSET and D8 has RING and D6 has OAMONS and D2 
            has SetCategory with 
               ?+? : (%,%) -> %
               ?*? : (%,%) -> %
               D : (%,NonNegativeInteger) -> % and D5 has POLYCAT(
            D8,D6,D7)
   [9] ((Polynomial D3 -> D1),D1) -> D1 from PushVariables(D3,D4,D5,D1)
            if D3 has RING and D1 has POLYCAT(POLY D3,D4,D5) and D4 has
            OAMONS and D5 has OrderedSet with 
               convert : % -> Symbol
               variable : Symbol -> Union(%,"failed")
   [10] ((D2 -> D2),XPolynomialRing(D2,D3)) -> XPolynomialRing(D2,D3)
            from XPolynomialRing(D2,D3) if D2 has RING and D3 has 
            ORDMON

Examples of map from AbelianMonoidRing


Examples of map from AntiSymm


Examples of map from TwoDimensionalArrayCategory

adder(a:Integer,b:Integer):Integer == a+b 
arr1 : ARRAY2 INT := new(5,4,10) 
arr2 : ARRAY2 INT := new(3,3,10) 
map(adder,arr1,arr2,17)

adder(a:Integer,b:Integer):Integer == a+b 
arr : ARRAY2 INT := new(5,4,10) 
map(adder,arr,arr)

arr : ARRAY2 INT := new(5,4,10) 
map(-,arr) 
map((x +-> x + x),arr)


Examples of map from OneDimensionalArrayFunctions2

T1:=OneDimensionalArrayFunctions2(Integer,Integer) 
map(x+->x+2,[i for i in 1..10])$T1


Examples of map from ArrayStack

a:ArrayStack INT:= arrayStack [1,2,3,4,5] 
map(x+->x+10,a) 
a


Examples of map from CartesianTensorFunctions2


Examples of map from ComplexFunctions2


Examples of map from Dequeue

a:Dequeue INT:= dequeue [1,2,3,4,5] 
map(x+->x+10,a) 
a


Examples of map from DeRhamComplex


Examples of map from DirectProductFunctions2


Examples of map from EquationFunctions2


Examples of map from Equation


Examples of map from ExpressionSpaceFunctions1


Examples of map from ExpressionSpaceFunctions2


Examples of map from ExpressionSpace


Examples of map from ExpertSystemToolsPackage2


Examples of map from ExpressionFunctions2


Examples of map from FiniteAbelianMonoidRingFunctions2


Examples of map from FiniteDivisorFunctions2


Examples of map from FullyEvalableOver


Examples of map from FunctionFieldCategoryFunctions2


Examples of map from FiniteLinearAggregateFunctions2


Examples of map from FreeModuleCat


Examples of map from FactoredFunctions2


Examples of map from FractionFunctions2


Examples of map from FractionalIdealFunctions2


Examples of map from FramedNonAssociativeAlgebraFunctions2


Examples of map from Factored

m(a:Factored Polynomial Integer):Factored Polynomial Integer == a^2 
f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 
map(m,f) 
g:=makeFR(z,factorList f) 
map(m,g)


Examples of map from FunctionSpaceFunctions2


Examples of map from FiniteSetAggregateFunctions2


Examples of map from Heap

a:Heap INT:= heap [1,2,3,4,5] 
map(x+->x+10,a) 
a


Examples of map from HomogeneousAggregate


Examples of map from IndexedDirectProductCategory


Examples of map from IntegrationResultFunctions2


Examples of map from InfiniteTupleFunctions2


Examples of map from InfiniteTupleFunctions3


Examples of map from InfiniteTuple


Examples of map from ListFunctions2


Examples of map from ListFunctions3


Examples of map from LinearAggregate


Examples of map from MatrixCategoryFunctions2


Examples of map from MultipleMap


Examples of map from MPolyCatFunctions2


Examples of map from MPolyCatFunctions3


Examples of map from MonoidRingFunctions2


Examples of map from MonoidRing


Examples of map from NewSparseUnivariatePolynomialFunctions2


Examples of map from OctonionCategoryFunctions2


Examples of map from OnePointCompletionFunctions2


Examples of map from OrderedCompletionFunctions2


Examples of map from ParametricPlaneCurveFunctions2


Examples of map from ParametricSpaceCurveFunctions2


Examples of map from ParametricSurfaceFunctions2


Examples of map from PatternMatchResultFunctions2


Examples of map from PatternFunctions2


Examples of map from PolynomialFunctions2


Examples of map from PolynomialCategoryLifting


Examples of map from PrimitiveArrayFunctions2

T1:=PrimitiveArrayFunctions2(Integer,Integer) 
map(x+->x+2,[i for i in 1..10])$T1


Examples of map from PointFunctions2


Examples of map from PushVariables


Examples of map from QuotientFieldCategoryFunctions2


Examples of map from QuaternionCategoryFunctions2

f(a:FRAC(INT)):COMPLEX(FRAC(INT)) == a::COMPLEX(FRAC(INT)) 
q:=quatern(2/11,-8,3/4,1) 
map(f,q)


Examples of map from Queue

a:Queue INT:= queue [1,2,3,4,5] 
map(x+->x+10,a) 
a


Examples of map from RectangularMatrixCategory


Examples of map from RectangularMatrixCategoryFunctions2


Examples of map from SegmentFunctions2


Examples of map from SegmentBindingFunctions2


Examples of map from SegmentExpansionCategory


Examples of map from Stack

a:Stack INT:= stack [1,2,3,4,5] 
map(x+->x+10,a) 
a


Examples of map from StreamFunctions2

m:=[i for i in 1..] 
f(i:PositiveInteger):PositiveInteger==i**2 
map(f,m)


Examples of map from StreamFunctions3

m:=[i for i in 1..]::Stream(Integer) 
n:=[i for i in 1..]::Stream(Integer) 
f(i:Integer,j:Integer):Integer == i+j 
map(f,m,n)


Examples of map from SparseUnivariatePolynomialFunctions2


Examples of map from TableAggregate


Examples of map from UnivariateLaurentSeriesFunctions2


Examples of map from UniversalSegmentFunctions2


Examples of map from UnivariatePolynomialFunctions2


Examples of map from UnivariatePolynomialCategoryFunctions2


Examples of map from UnivariatePuiseuxSeriesFunctions2


Examples of map from UnivariateTaylorSeriesFunctions2


Examples of map from VectorFunctions2


Examples of map from XFreeAlgebra


Examples of map from XPolynomialRing

--R 
--R
--RThere are 86 exposed functions called map :
--R   [1] ((D2 -> D2),D) -> D from D
--R            if D has AMR(D2,D3) and D2 has RING and D3 has OAMON
--R   [2] (((D2,D2) -> D2),D,D,D2) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [3] (((D2,D2) -> D2),D,D) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [4] ((D2 -> D2),D) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [5] ((D4 -> D5),OneDimensionalArray D4) -> OneDimensionalArray D5
--R            from OneDimensionalArrayFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [6] ((D2 -> D2),ArrayStack D2) -> ArrayStack D2 from ArrayStack D2
--R            if D2 has SETCAT
--R   [7] ((D6 -> D7),CartesianTensor(D4,D5,D6)) -> CartesianTensor(D4,D5,
--R            D7)
--R            from CartesianTensorFunctions2(D4,D5,D6,D7)
--R            if D4: INT and D5: NNI and D6 has COMRING and D7 has 
--R            COMRING
--R   [8] ((D4 -> D5),Complex D4) -> Complex D5 from ComplexFunctions2(D4,
--R            D5)
--R            if D4 has COMRING and D5 has COMRING
--R   [9] ((D2 -> D2),Dequeue D2) -> Dequeue D2 from Dequeue D2 if D2 has 
--R            SETCAT
--R   [10] ((D5 -> D6),DirectProduct(D4,D5)) -> DirectProduct(D4,D6)
--R            from DirectProductFunctions2(D4,D5,D6)
--R            if D4: NNI and D5 has TYPE and D6 has TYPE
--R   [11] ((D4 -> D5),Equation D4) -> Equation D5 from EquationFunctions2
--R            (D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [12] ((D2 -> D2),Equation D2) -> Equation D2 from Equation D2 if D2 
--R            has TYPE
--R   [13] ((D4 -> D1),Kernel D4) -> D1 from ExpressionSpaceFunctions2(D4,
--R            D1)
--R            if D4 has ES and D1 has ES
--R   [14] ((D -> D),Kernel D) -> D from D if D has ES
--R   [15] ((D4 -> D5),Matrix D4) -> Matrix D5
--R            from ExpertSystemToolsPackage2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [16] ((D4 -> D5),Expression D4) -> Expression D5
--R            from ExpressionFunctions2(D4,D5)
--R            if D4 has ORDSET and D5 has ORDSET
--R   [17] ((D5 -> D6),D3) -> D1
--R            from FiniteAbelianMonoidRingFunctions2(D4,D5,D3,D6,D1)
--R            if D5 has RING and D6 has RING and D4 has OAMON and D1 has 
--R            FAMR(D6,D4) and D3 has FAMR(D5,D4)
--R   [18] ((D7 -> D11),FiniteDivisor(D7,D8,D9,D10)) -> FiniteDivisor(D11,
--R            D1,D2,D3)
--R            from FiniteDivisorFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
--R            if D7 has FIELD and D8 has UPOLYC D7 and D9 has UPOLYC FRAC
--R            D8 and D10 has FFCAT(D7,D8,D9) and D11 has FIELD and D1 has
--R            UPOLYC D11 and D2 has UPOLYC FRAC D1 and D3 has FFCAT(D11,
--R            D1,D2)
--R   [19] ((D2 -> D2),D) -> D from D if D has FEVALAB D2 and D2 has 
--R            SETCAT
--R   [20] ((D5 -> D8),D4) -> D2
--R            from FunctionFieldCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,
--R            D2)
--R            if D5 has UFD and D8 has UFD and D6 has UPOLYC D5 and D7 
--R            has UPOLYC FRAC D6 and D9 has UPOLYC D8 and D2 has FFCAT(D8
--R            ,D9,D1) and D4 has FFCAT(D5,D6,D7) and D1 has UPOLYC FRAC 
--R            D9
--R   [21] ((D4 -> D5),D3) -> D1 from FiniteLinearAggregateFunctions2(D4,
--R            D3,D5,D1)
--R            if D4 has TYPE and D5 has TYPE and D1 has FLAGG D5 and D3 
--R            has FLAGG D4
--R   [22] ((D2 -> D2),D) -> D from D
--R            if D has FMCAT(D2,D3) and D2 has RING and D3 has SETCAT
--R   [23] ((D4 -> D5),Factored D4) -> Factored D5 from FactoredFunctions2
--R            (D4,D5)
--R            if D4 has INTDOM and D5 has INTDOM
--R   [24] ((D4 -> D5),Fraction D4) -> Fraction D5 from FractionFunctions2
--R            (D4,D5)
--R            if D4 has INTDOM and D5 has INTDOM
--R   [25] ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal(
--R            D11,D1,D2,D3)
--R            from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
--R            if D7 has EUCDOM and D8 has QFCAT D7 and D9 has UPOLYC D8 
--R            and D10 has Join(FramedAlgebra(D8,D9),RetractableTo D8) and
--R            D11 has EUCDOM and D1 has QFCAT D11 and D2 has UPOLYC D1 
--R            and D3 has Join(FramedAlgebra(D1,D2),RetractableTo D1)
--R   [26] ((D4 -> D5),D3) -> D1
--R            from FramedNonAssociativeAlgebraFunctions2(D3,D4,D1,D5)
--R            if D4 has COMRING and D5 has COMRING and D1 has FRNAALG D5 
--R            and D3 has FRNAALG D4
--R   [27] ((D2 -> D2),Factored D2) -> Factored D2 from Factored D2
--R            if D2 has INTDOM
--R   [28] ((D4 -> D5),D3) -> D1 from FunctionSpaceFunctions2(D4,D3,D5,D1)
--R            if D4 has Join(Ring,OrderedSet) and D5 has Join(Ring,
--R            OrderedSet) and D1 has FS D5 and D3 has FS D4
--R   [29] ((D4 -> D5),D3) -> D1 from FiniteSetAggregateFunctions2(D4,D3,
--R            D5,D1)
--R            if D4 has SETCAT and D5 has SETCAT and D1 has FSAGG D5 and 
--R            D3 has FSAGG D4
--R   [30] ((D2 -> D2),Heap D2) -> Heap D2 from Heap D2 if D2 has ORDSET
--R         
--R   [31] ((D2 -> D2),D) -> D from D if D has HOAGG D2 and D2 has TYPE
--R         
--R   [32] ((D2 -> D2),D) -> D from D
--R            if D has IDPC(D2,D3) and D2 has SETCAT and D3 has ORDSET
--R         
--R   [33] ((D4 -> D5),IntegrationResult D4) -> IntegrationResult D5
--R            from IntegrationResultFunctions2(D4,D5)
--R            if D4 has FIELD and D5 has FIELD
--R   [34] ((D4 -> D5),Union(Record(ratpart: D4,coeff: D4),"failed")) -> 
--R            Union(Record(ratpart: D5,coeff: D5),"failed")
--R            from IntegrationResultFunctions2(D4,D5)
--R            if D4 has FIELD and D5 has FIELD
--R   [35] ((D4 -> D1),Union(D4,"failed")) -> Union(D1,"failed")
--R            from IntegrationResultFunctions2(D4,D1)
--R            if D4 has FIELD and D1 has FIELD
--R   [36] ((D4 -> D5),Union(Record(mainpart: D4,limitedlogs: List Record(
--R            coeff: D4,logand: D4)),"failed")) -> Union(Record(mainpart: D5,
--R            limitedlogs: List Record(coeff: D5,logand: D5)),"failed")
--R            from IntegrationResultFunctions2(D4,D5)
--R            if D4 has FIELD and D5 has FIELD
--R   [37] ((D4 -> D5),InfiniteTuple D4) -> InfiniteTuple D5
--R            from InfiniteTupleFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [38] (((D5,D6) -> D7),InfiniteTuple D5,InfiniteTuple D6) -> 
--R            InfiniteTuple D7
--R            from InfiniteTupleFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [39] (((D5,D6) -> D7),Stream D5,InfiniteTuple D6) -> Stream D7
--R            from InfiniteTupleFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [40] (((D5,D6) -> D7),InfiniteTuple D5,Stream D6) -> Stream D7
--R            from InfiniteTupleFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [41] ((D2 -> D2),InfiniteTuple D2) -> InfiniteTuple D2 from 
--R            InfiniteTuple D2
--R            if D2 has TYPE
--R   [42] ((D4 -> D5),List D4) -> List D5 from ListFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [43] (((D5,D6) -> D7),List D5,List D6) -> List D7
--R            from ListFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [44] (((D2,D2) -> D2),D,D) -> D from D if D has LNAGG D2 and D2 has 
--R            TYPE
--R   [45] ((D5 -> D8),D4) -> D2
--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
--R            if D5 has RING and D8 has RING and D6 has FLAGG D5 and D7 
--R            has FLAGG D5 and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT(
--R            D5,D6,D7) and D9 has FLAGG D8 and D1 has FLAGG D8
--R   [46] ((D5 -> Union(D8,"failed")),D4) -> Union(D2,"failed")
--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
--R            if D5 has RING and D8 has RING and D6 has FLAGG D5 and D7 
--R            has FLAGG D5 and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT(
--R            D5,D6,D7) and D9 has FLAGG D8 and D1 has FLAGG D8
--R   [47] ((D7 -> D8),D3) -> D1 from MPolyCatFunctions2(D4,D5,D6,D7,D8,D3
--R            ,D1)
--R            if D7 has RING and D8 has RING and D4 has ORDSET and D5 has
--R            OAMONS and D1 has POLYCAT(D8,D6,D4) and D6 has OAMONS and 
--R            D3 has POLYCAT(D7,D5,D4)
--R   [48] ((D4 -> D5),MonoidRing(D4,D6)) -> MonoidRing(D5,D6)
--R            from MonoidRingFunctions2(D4,D5,D6)
--R            if D4 has RING and D5 has RING and D6 has MONOID
--R   [49] ((D4 -> D5),D3) -> D1 from OctonionCategoryFunctions2(D3,D4,D1,
--R            D5)
--R            if D4 has COMRING and D5 has COMRING and D1 has OC D5 and 
--R            D3 has OC D4
--R   [50] ((D4 -> D5),OnePointCompletion D4) -> OnePointCompletion D5
--R            from OnePointCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [51] ((D4 -> D5),OnePointCompletion D4,OnePointCompletion D5) -> 
--R            OnePointCompletion D5
--R            from OnePointCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [52] ((D4 -> D5),OrderedCompletion D4) -> OrderedCompletion D5
--R            from OrderedCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [53] ((D4 -> D5),OrderedCompletion D4,OrderedCompletion D5,
--R            OrderedCompletion D5) -> OrderedCompletion D5
--R            from OrderedCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [54] ((D4 -> D5),ParametricPlaneCurve D4) -> ParametricPlaneCurve D5
--R            from ParametricPlaneCurveFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [55] ((D4 -> D5),ParametricSpaceCurve D4) -> ParametricSpaceCurve D5
--R            from ParametricSpaceCurveFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [56] ((D4 -> D5),ParametricSurface D4) -> ParametricSurface D5
--R            from ParametricSurfaceFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [57] ((D5 -> D6),PatternMatchResult(D4,D5)) -> PatternMatchResult(D4
--R            ,D6)
--R            from PatternMatchResultFunctions2(D4,D5,D6)
--R            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
--R   [58] ((D4 -> D5),Pattern D4) -> Pattern D5 from PatternFunctions2(D4
--R            ,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [59] ((D4 -> D5),Polynomial D4) -> Polynomial D5
--R            from PolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [60] ((D4 -> D5),PrimitiveArray D4) -> PrimitiveArray D5
--R            from PrimitiveArrayFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [61] ((D4 -> D5),Point D4) -> Point D5 from PointFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [62] ((D4 -> D5),D3) -> D1 from QuotientFieldCategoryFunctions2(D4,
--R            D5,D3,D1)
--R            if D4 has INTDOM and D5 has INTDOM and D1 has QFCAT D5 and 
--R            D3 has QFCAT D4
--R   [63] ((D4 -> D5),D3) -> D1 from QuaternionCategoryFunctions2(D3,D4,
--R            D1,D5)
--R            if D4 has COMRING and D5 has COMRING and D1 has QUATCAT D5 
--R            and D3 has QUATCAT D4
--R   [64] ((D2 -> D2),Queue D2) -> Queue D2 from Queue D2 if D2 has 
--R            SETCAT
--R   [65] (((D4,D4) -> D4),D,D) -> D from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R   [66] ((D4 -> D4),D) -> D from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R   [67] ((D9 -> D1),D6) -> D4
--R            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
--R            D6,D1,D2,D3,D4)
--R            if D9 has RING and D1 has RING and D7: NNI and D8: NNI and 
--R            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D4 
--R            has RMATCAT(D7,D8,D1,D2,D3) and D6 has RMATCAT(D7,D8,D9,D10
--R            ,D11) and D2 has DIRPCAT(D8,D1) and D3 has DIRPCAT(D7,D1)
--R         
--R   [68] ((D4 -> D5),Segment D4) -> Segment D5 from SegmentFunctions2(D4
--R            ,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [69] ((D4 -> D5),Segment D4) -> List D5 from SegmentFunctions2(D4,D5
--R            )
--R            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
--R   [70] ((D4 -> D5),SegmentBinding D4) -> SegmentBinding D5
--R            from SegmentBindingFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [71] ((D3 -> D3),D) -> D1 from D
--R            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
--R            D3
--R   [72] ((D2 -> D2),Stack D2) -> Stack D2 from Stack D2 if D2 has 
--R            SETCAT
--R   [73] ((D4 -> D5),Stream D4) -> Stream D5 from StreamFunctions2(D4,D5
--R            )
--R            if D4 has TYPE and D5 has TYPE
--R   [74] (((D5,D6) -> D7),Stream D5,Stream D6) -> Stream D7
--R            from StreamFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [75] ((D4 -> D5),SparseUnivariatePolynomial D4) -> 
--R            SparseUnivariatePolynomial D5
--R            from SparseUnivariatePolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [76] (((D3,D3) -> D3),D,D) -> D from D
--R            if D has TBAGG(D2,D3) and D2 has SETCAT and D3 has SETCAT
--R         
--R   [77] ((D5 -> D6),UnivariateLaurentSeries(D5,D7,D9)) -> 
--R            UnivariateLaurentSeries(D6,D8,D1)
--R            from UnivariateLaurentSeriesFunctions2(D5,D6,D7,D8,D9,D1)
--R            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5 
--R            and D1: D6 and D8: SYMBOL
--R   [78] ((D4 -> D5),UniversalSegment D4) -> UniversalSegment D5
--R            from UniversalSegmentFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [79] ((D4 -> D5),UniversalSegment D4) -> Stream D5
--R            from UniversalSegmentFunctions2(D4,D5)
--R            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
--R   [80] ((D5 -> D7),UnivariatePolynomial(D4,D5)) -> 
--R            UnivariatePolynomial(D6,D7)
--R            from UnivariatePolynomialFunctions2(D4,D5,D6,D7)
--R            if D4: SYMBOL and D5 has RING and D7 has RING and D6: 
--R            SYMBOL
--R   [81] ((D4 -> D5),D3) -> D1
--R            from UnivariatePolynomialCategoryFunctions2(D4,D3,D5,D1)
--R            if D4 has RING and D5 has RING and D1 has UPOLYC D5 and D3 
--R            has UPOLYC D4
--R   [82] ((D5 -> D6),UnivariatePuiseuxSeries(D5,D7,D9)) -> 
--R            UnivariatePuiseuxSeries(D6,D8,D1)
--R            from UnivariatePuiseuxSeriesFunctions2(D5,D6,D7,D8,D9,D1)
--R            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5 
--R            and D1: D6 and D8: SYMBOL
--R   [83] ((D4 -> D5),D3) -> D1
--R            from UnivariateTaylorSeriesFunctions2(D4,D5,D3,D1)
--R            if D4 has RING and D5 has RING and D1 has UTSCAT D5 and D3 
--R            has UTSCAT D4
--R   [84] ((D4 -> D5),Vector D4) -> Vector D5 from VectorFunctions2(D4,D5
--R            )
--R            if D4 has TYPE and D5 has TYPE
--R   [85] ((D4 -> Union(D5,"failed")),Vector D4) -> Union(Vector D5,
--R            "failed")
--R            from VectorFunctions2(D4,D5) if D4 has TYPE and D5 has TYPE
--R            
--R   [86] ((D3 -> D3),D) -> D from D
--R            if D has XFALG(D2,D3) and D2 has ORDSET and D3 has RING
--R
--RThere are 10 unexposed functions called map :
--R   [1] ((D2 -> D2),AntiSymm(D2,D3)) -> AntiSymm(D2,D3) from AntiSymm(D2
--R            ,D3)
--R            if D2 has RING and D3: LIST SYMBOL
--R   [2] ((Expression D2 -> Expression D2),DeRhamComplex(D2,D3)) -> 
--R            DeRhamComplex(D2,D3)
--R            from DeRhamComplex(D2,D3)
--R            if D2 has Join(Ring,OrderedSet) and D3: LIST SYMBOL
--R   [3] ((D5 -> D1),String,Kernel D5) -> D1
--R            from ExpressionSpaceFunctions1(D5,D1)
--R            if D5 has ES and D1 has TYPE
--R   [4] ((D4 -> D6),D3) -> D1 from MultipleMap(D4,D5,D3,D6,D7,D1)
--R            if D4 has INTDOM and D6 has INTDOM and D5 has UPOLYC D4 and
--R            D1 has UPOLYC FRAC D7 and D3 has UPOLYC FRAC D5 and D7 has 
--R            UPOLYC D6
--R   [5] ((D4 -> D5),D3) -> D1 from MPolyCatFunctions3(D4,D5,D6,D7,D8,D3,
--R            D1)
--R            if D4 has ORDSET and D5 has ORDSET and D6 has OAMONS and D8
--R            has RING and D1 has POLYCAT(D8,D7,D5) and D7 has OAMONS and
--R            D3 has POLYCAT(D8,D6,D4)
--R   [6] ((D2 -> D2),MonoidRing(D2,D3)) -> MonoidRing(D2,D3)
--R            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
--R   [7] ((D4 -> D5),NewSparseUnivariatePolynomial D4) -> 
--R            NewSparseUnivariatePolynomial D5
--R            from NewSparseUnivariatePolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [8] ((D7 -> D2),(D8 -> D2),D5) -> D2
--R            from PolynomialCategoryLifting(D6,D7,D8,D5,D2)
--R            if D7 has ORDSET and D8 has RING and D6 has OAMONS and D2 
--R            has SetCategory with 
--R               ?+? : (%,%) -> %
--R               ?*? : (%,%) -> %
--R               D : (%,NonNegativeInteger) -> % and D5 has POLYCAT(
--R            D8,D6,D7)
--R   [9] ((Polynomial D3 -> D1),D1) -> D1 from PushVariables(D3,D4,D5,D1)
--R            if D3 has RING and D1 has POLYCAT(POLY D3,D4,D5) and D4 has
--R            OAMONS and D5 has OrderedSet with 
--R               convert : % -> Symbol
--R               variable : Symbol -> Union(%,"failed")
--R   [10] ((D2 -> D2),XPolynomialRing(D2,D3)) -> XPolynomialRing(D2,D3)
--R            from XPolynomialRing(D2,D3) if D2 has RING and D3 has 
--R            ORDMON
--R
--RExamples of map from AbelianMonoidRing
--R
--R
--RExamples of map from AntiSymm
--R
--R
--RExamples of map from TwoDimensionalArrayCategory
--R
--Radder(a:Integer,b:Integer):Integer == a+b 
--Rarr1 : ARRAY2 INT := new(5,4,10) 
--Rarr2 : ARRAY2 INT := new(3,3,10) 
--Rmap(adder,arr1,arr2,17)
--R
--Radder(a:Integer,b:Integer):Integer == a+b 
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rmap(adder,arr,arr)
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rmap(-,arr) 
--Rmap((x +-> x + x),arr)
--R
--R
--RExamples of map from OneDimensionalArrayFunctions2
--R
--RT1:=OneDimensionalArrayFunctions2(Integer,Integer) 
--Rmap(x+->x+2,[i for i in 1..10])$T1
--R
--R
--RExamples of map from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] 
--Rmap(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map from CartesianTensorFunctions2
--R
--R
--RExamples of map from ComplexFunctions2
--R
--R
--RExamples of map from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5] 
--Rmap(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map from DeRhamComplex
--R
--R
--RExamples of map from DirectProductFunctions2
--R
--R
--RExamples of map from EquationFunctions2
--R
--R
--RExamples of map from Equation
--R
--R
--RExamples of map from ExpressionSpaceFunctions1
--R
--R
--RExamples of map from ExpressionSpaceFunctions2
--R
--R
--RExamples of map from ExpressionSpace
--R
--R
--RExamples of map from ExpertSystemToolsPackage2
--R
--R
--RExamples of map from ExpressionFunctions2
--R
--R
--RExamples of map from FiniteAbelianMonoidRingFunctions2
--R
--R
--RExamples of map from FiniteDivisorFunctions2
--R
--R
--RExamples of map from FullyEvalableOver
--R
--R
--RExamples of map from FunctionFieldCategoryFunctions2
--R
--R
--RExamples of map from FiniteLinearAggregateFunctions2
--R
--R
--RExamples of map from FreeModuleCat
--R
--R
--RExamples of map from FactoredFunctions2
--R
--R
--RExamples of map from FractionFunctions2
--R
--R
--RExamples of map from FractionalIdealFunctions2
--R
--R
--RExamples of map from FramedNonAssociativeAlgebraFunctions2
--R
--R
--RExamples of map from Factored
--R
--Rm(a:Factored Polynomial Integer):Factored Polynomial Integer == a^2 
--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 
--Rmap(m,f) 
--Rg:=makeFR(z,factorList f) 
--Rmap(m,g)
--R
--R
--RExamples of map from FunctionSpaceFunctions2
--R
--R
--RExamples of map from FiniteSetAggregateFunctions2
--R
--R
--RExamples of map from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5] 
--Rmap(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map from HomogeneousAggregate
--R
--R
--RExamples of map from IndexedDirectProductCategory
--R
--R
--RExamples of map from IntegrationResultFunctions2
--R
--R
--RExamples of map from InfiniteTupleFunctions2
--R
--R
--RExamples of map from InfiniteTupleFunctions3
--R
--R
--RExamples of map from InfiniteTuple
--R
--R
--RExamples of map from ListFunctions2
--R
--R
--RExamples of map from ListFunctions3
--R
--R
--RExamples of map from LinearAggregate
--R
--R
--RExamples of map from MatrixCategoryFunctions2
--R
--R
--RExamples of map from MultipleMap
--R
--R
--RExamples of map from MPolyCatFunctions2
--R
--R
--RExamples of map from MPolyCatFunctions3
--R
--R
--RExamples of map from MonoidRingFunctions2
--R
--R
--RExamples of map from MonoidRing
--R
--R
--RExamples of map from NewSparseUnivariatePolynomialFunctions2
--R
--R
--RExamples of map from OctonionCategoryFunctions2
--R
--R
--RExamples of map from OnePointCompletionFunctions2
--R
--R
--RExamples of map from OrderedCompletionFunctions2
--R
--R
--RExamples of map from ParametricPlaneCurveFunctions2
--R
--R
--RExamples of map from ParametricSpaceCurveFunctions2
--R
--R
--RExamples of map from ParametricSurfaceFunctions2
--R
--R
--RExamples of map from PatternMatchResultFunctions2
--R
--R
--RExamples of map from PatternFunctions2
--R
--R
--RExamples of map from PolynomialFunctions2
--R
--R
--RExamples of map from PolynomialCategoryLifting
--R
--R
--RExamples of map from PrimitiveArrayFunctions2
--R
--RT1:=PrimitiveArrayFunctions2(Integer,Integer) 
--Rmap(x+->x+2,[i for i in 1..10])$T1
--R
--R
--RExamples of map from PointFunctions2
--R
--R
--RExamples of map from PushVariables
--R
--R
--RExamples of map from QuotientFieldCategoryFunctions2
--R
--R
--RExamples of map from QuaternionCategoryFunctions2
--R
--Rf(a:FRAC(INT)):COMPLEX(FRAC(INT)) == a::COMPLEX(FRAC(INT)) 
--Rq:=quatern(2/11,-8,3/4,1) 
--Rmap(f,q)
--R
--R
--RExamples of map from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5] 
--Rmap(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map from RectangularMatrixCategory
--R
--R
--RExamples of map from RectangularMatrixCategoryFunctions2
--R
--R
--RExamples of map from SegmentFunctions2
--R
--R
--RExamples of map from SegmentBindingFunctions2
--R
--R
--RExamples of map from SegmentExpansionCategory
--R
--R
--RExamples of map from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5] 
--Rmap(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map from StreamFunctions2
--R
--Rm:=[i for i in 1..] 
--Rf(i:PositiveInteger):PositiveInteger==i**2 
--Rmap(f,m)
--R
--R
--RExamples of map from StreamFunctions3
--R
--Rm:=[i for i in 1..]::Stream(Integer) 
--Rn:=[i for i in 1..]::Stream(Integer) 
--Rf(i:Integer,j:Integer):Integer == i+j 
--Rmap(f,m,n)
--R
--R
--RExamples of map from SparseUnivariatePolynomialFunctions2
--R
--R
--RExamples of map from TableAggregate
--R
--R
--RExamples of map from UnivariateLaurentSeriesFunctions2
--R
--R
--RExamples of map from UniversalSegmentFunctions2
--R
--R
--RExamples of map from UnivariatePolynomialFunctions2
--R
--R
--RExamples of map from UnivariatePolynomialCategoryFunctions2
--R
--R
--RExamples of map from UnivariatePuiseuxSeriesFunctions2
--R
--R
--RExamples of map from UnivariateTaylorSeriesFunctions2
--R
--R
--RExamples of map from VectorFunctions2
--R
--R
--RExamples of map from XFreeAlgebra
--R
--R
--RExamples of map from XPolynomialRing
--R
--E 21

--S 22 of 127
)d op complete
 

There are 5 exposed functions called complete :
   [1] ContinuedFraction D1 -> ContinuedFraction D1 from 
            ContinuedFraction D1
            if D1 has EUCDOM
   [2] Integer -> SymmetricPolynomial Fraction Integer from 
            CycleIndicators
   [3] D -> D from D if D has LZSTAGG D1 and D1 has TYPE
   [4] D -> D from D if D has PADICCT D1
   [5] D -> D from D
            if D has PSCAT(D1,D2,D3) and D1 has RING and D2 has OAMON 
            and D3 has ORDSET

Examples of complete from ContinuedFraction


Examples of complete from CycleIndicators


Examples of complete from LazyStreamAggregate

m:=[i for i in 1..] 
n:=filterUntil(i+->i>100,m) 
numberOfComputedEntries n 
complete n 
numberOfComputedEntries n


Examples of complete from PAdicIntegerCategory


Examples of complete from PowerSeriesCategory

--R 
--R
--RThere are 5 exposed functions called complete :
--R   [1] ContinuedFraction D1 -> ContinuedFraction D1 from 
--R            ContinuedFraction D1
--R            if D1 has EUCDOM
--R   [2] Integer -> SymmetricPolynomial Fraction Integer from 
--R            CycleIndicators
--R   [3] D -> D from D if D has LZSTAGG D1 and D1 has TYPE
--R   [4] D -> D from D if D has PADICCT D1
--R   [5] D -> D from D
--R            if D has PSCAT(D1,D2,D3) and D1 has RING and D2 has OAMON 
--R            and D3 has ORDSET
--R
--RExamples of complete from ContinuedFraction
--R
--R
--RExamples of complete from CycleIndicators
--R
--R
--RExamples of complete from LazyStreamAggregate
--R
--Rm:=[i for i in 1..] 
--Rn:=filterUntil(i+->i>100,m) 
--RnumberOfComputedEntries n 
--Rcomplete n 
--RnumberOfComputedEntries n
--R
--R
--RExamples of complete from PAdicIntegerCategory
--R
--R
--RExamples of complete from PowerSeriesCategory
--R
--E 22

--S 23 of 127
)d op cyclicEqual?
 

There is one exposed function called cyclicEqual? :
   [1] (Tree D2,Tree D2) -> Boolean from Tree D2 if D2 has SETCAT

Examples of cyclicEqual? from Tree

t1:=tree [1,2,3,4] 
t2:=tree [1,2,3,4] 
cyclicEqual?(t1,t2)

--R 
--R
--RThere is one exposed function called cyclicEqual? :
--R   [1] (Tree D2,Tree D2) -> Boolean from Tree D2 if D2 has SETCAT
--R
--RExamples of cyclicEqual? from Tree
--R
--Rt1:=tree [1,2,3,4] 
--Rt2:=tree [1,2,3,4] 
--RcyclicEqual?(t1,t2)
--R
--E 23

--S 24 of 127
)d op ncols
 

There are 2 exposed functions called ncols :
   [1] D -> NonNegativeInteger from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] D -> NonNegativeInteger from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

Examples of ncols from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
ncols(arr)


Examples of ncols from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called ncols :
--R   [1] D -> NonNegativeInteger from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] D -> NonNegativeInteger from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of ncols from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rncols(arr)
--R
--R
--RExamples of ncols from RectangularMatrixCategory
--R
--E 24

--S 25 of 127
)d op inverseIntegralMatrixAtInfinity
 

There is one exposed function called inverseIntegralMatrixAtInfinity :
   [1]  -> Matrix Fraction D3 from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

Examples of inverseIntegralMatrixAtInfinity from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
inverseIntegralMatrixAtInfinity()$R

--R 
--R
--RThere is one exposed function called inverseIntegralMatrixAtInfinity :
--R   [1]  -> Matrix Fraction D3 from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RExamples of inverseIntegralMatrixAtInfinity from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RinverseIntegralMatrixAtInfinity()$R
--R
--E 25

--S 26 of 127
)d op generalizedContinuumHypothesisAssumed
 

There is one exposed function called generalizedContinuumHypothesisAssumed :
   [1] Boolean -> Boolean from CardinalNumber

Examples of generalizedContinuumHypothesisAssumed from CardinalNumber

generalizedContinuumHypothesisAssumed true 
a:=Aleph 0 
c:=2**a 
f:=2**c

--R 
--R
--RThere is one exposed function called generalizedContinuumHypothesisAssumed :
--R   [1] Boolean -> Boolean from CardinalNumber
--R
--RExamples of generalizedContinuumHypothesisAssumed from CardinalNumber
--R
--RgeneralizedContinuumHypothesisAssumed true 
--Ra:=Aleph 0 
--Rc:=2**a 
--Rf:=2**c
--R
--E 26

--S 27 of 127
)d op cyclic?
 

There are 2 exposed functions called cyclic? :
   [1] D -> Boolean from D if D has RCAGG D2 and D2 has TYPE
   [2] Tree D2 -> Boolean from Tree D2 if D2 has SETCAT

Examples of cyclic? from RecursiveAggregate


Examples of cyclic? from Tree

t1:=tree [1,2,3,4] 
cyclic? t1

--R 
--R
--RThere are 2 exposed functions called cyclic? :
--R   [1] D -> Boolean from D if D has RCAGG D2 and D2 has TYPE
--R   [2] Tree D2 -> Boolean from Tree D2 if D2 has SETCAT
--R
--RExamples of cyclic? from RecursiveAggregate
--R
--R
--RExamples of cyclic? from Tree
--R
--Rt1:=tree [1,2,3,4] 
--Rcyclic? t1
--R
--E 27

--S 28 of 127
)d op nilFactor
 

There is one exposed function called nilFactor :
   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
         

Examples of nilFactor from Factored

nilFactor(24,2) 
nilFactor(x-y,3)

--R 
--R
--RThere is one exposed function called nilFactor :
--R   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
--R         
--R
--RExamples of nilFactor from Factored
--R
--RnilFactor(24,2) 
--RnilFactor(x-y,3)
--R
--E 28

--S 29 of 127
)d op quote
 

There is one exposed function called quote :
   [1]  -> Character from Character

There is one unexposed function called quote :
   [1] OutputForm -> OutputForm from OutputForm

Examples of quote from Character

quote()


Examples of quote from OutputForm

--R 
--R
--RThere is one exposed function called quote :
--R   [1]  -> Character from Character
--R
--RThere is one unexposed function called quote :
--R   [1] OutputForm -> OutputForm from OutputForm
--R
--RExamples of quote from Character
--R
--Rquote()
--R
--R
--RExamples of quote from OutputForm
--R
--E 29

--S 30 of 127
)d op balancedBinaryTree
 

There is one exposed function called balancedBinaryTree :
   [1] (NonNegativeInteger,D2) -> BalancedBinaryTree D2
            from BalancedBinaryTree D2 if D2 has SETCAT

Examples of balancedBinaryTree from BalancedBinaryTree

balancedBinaryTree(4, 0)

--R 
--R
--RThere is one exposed function called balancedBinaryTree :
--R   [1] (NonNegativeInteger,D2) -> BalancedBinaryTree D2
--R            from BalancedBinaryTree D2 if D2 has SETCAT
--R
--RExamples of balancedBinaryTree from BalancedBinaryTree
--R
--RbalancedBinaryTree(4, 0)
--R
--E 30

--S 31 of 127
)d op integralBasisAtInfinity
 

There is one exposed function called integralBasisAtInfinity :
   [1]  -> Vector D from D
            if D2 has UFD and D3 has UPOLYC D2 and D4 has UPOLYC FRAC 
            D3 and D has FFCAT(D2,D3,D4)

Examples of integralBasisAtInfinity from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
integralBasisAtInfinity()$R

--R 
--R
--RThere is one exposed function called integralBasisAtInfinity :
--R   [1]  -> Vector D from D
--R            if D2 has UFD and D3 has UPOLYC D2 and D4 has UPOLYC FRAC 
--R            D3 and D has FFCAT(D2,D3,D4)
--R
--RExamples of integralBasisAtInfinity from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RintegralBasisAtInfinity()$R
--R
--E 31

--S 32 of 127
)d op branchPointAtInfinity?
 

There is one exposed function called branchPointAtInfinity? :
   [1]  -> Boolean from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

Examples of branchPointAtInfinity? from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
branchPointAtInfinity?()$R 
R2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
branchPointAtInfinity?()$R

--R 
--R
--RThere is one exposed function called branchPointAtInfinity? :
--R   [1]  -> Boolean from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RExamples of branchPointAtInfinity? from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RbranchPointAtInfinity?()$R 
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
--RbranchPointAtInfinity?()$R
--R
--E 32

--S 33 of 127
)d op transpose
 

There are 4 exposed functions called transpose :
   [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
            D2,D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D2: INT and D3: NNI and D4 has COMRING
   [2] CartesianTensor(D1,D2,D3) -> CartesianTensor(D1,D2,D3)
            from CartesianTensor(D1,D2,D3)
            if D1: INT and D2: NNI and D3 has COMRING
   [3] D -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [4] D1 -> D from D
            if D2 has RING and D has MATCAT(D2,D1,D3) and D1 has FLAGG 
            D2 and D3 has FLAGG D2

There is one unexposed function called transpose :
   [1] SquareMatrix(D1,D2) -> SquareMatrix(D1,D2) from SquareMatrix(D1,
            D2)
            if D1: NNI and D2 has RING

Examples of transpose from CartesianTensor

m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
tm:CartesianTensor(1,2,Integer):=m 
tn:CartesianTensor(1,2,Integer):=[tm,tm] 
transpose(tn,1,2)

m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
Tm:CartesianTensor(1,2,Integer):=m 
transpose(Tm)


Examples of transpose from MatrixCategory

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
transpose m

transpose([1,2,3])@Matrix(INT)


Examples of transpose from SquareMatrix

--R 
--R
--RThere are 4 exposed functions called transpose :
--R   [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
--R            D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [2] CartesianTensor(D1,D2,D3) -> CartesianTensor(D1,D2,D3)
--R            from CartesianTensor(D1,D2,D3)
--R            if D1: INT and D2: NNI and D3 has COMRING
--R   [3] D -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [4] D1 -> D from D
--R            if D2 has RING and D has MATCAT(D2,D1,D3) and D1 has FLAGG 
--R            D2 and D3 has FLAGG D2
--R
--RThere is one unexposed function called transpose :
--R   [1] SquareMatrix(D1,D2) -> SquareMatrix(D1,D2) from SquareMatrix(D1,
--R            D2)
--R            if D1: NNI and D2 has RING
--R
--RExamples of transpose from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
--Rtm:CartesianTensor(1,2,Integer):=m 
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] 
--Rtranspose(tn,1,2)
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
--RTm:CartesianTensor(1,2,Integer):=m 
--Rtranspose(Tm)
--R
--R
--RExamples of transpose from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rtranspose m
--R
--Rtranspose([1,2,3])@Matrix(INT)
--R
--R
--RExamples of transpose from SquareMatrix
--R
--E 33

--S 34 of 127
)d op setrest!
 

There are 2 exposed functions called setrest! :
   [1] (Stream D2,Integer,Stream D2) -> Stream D2 from Stream D2 if D2 
            has TYPE
   [2] (D,D) -> D from D
            if D has shallowlyMutable and D has URAGG D1 and D1 has 
            TYPE

Examples of setrest! from Stream

p:=[i for i in 1..] 
q:=[i for i in 9..] 
setrest!(p,4,q) 
p


Examples of setrest! from UnaryRecursiveAggregate

--R 
--R
--RThere are 2 exposed functions called setrest! :
--R   [1] (Stream D2,Integer,Stream D2) -> Stream D2 from Stream D2 if D2 
--R            has TYPE
--R   [2] (D,D) -> D from D
--R            if D has shallowlyMutable and D has URAGG D1 and D1 has 
--R            TYPE
--R
--RExamples of setrest! from Stream
--R
--Rp:=[i for i in 1..] 
--Rq:=[i for i in 9..] 
--Rsetrest!(p,4,q) 
--Rp
--R
--R
--RExamples of setrest! from UnaryRecursiveAggregate
--R
--E 34

--S 35 of 127
)d op **
 

There are 21 exposed functions called ** :
   [1] (CardinalNumber,CardinalNumber) -> CardinalNumber from 
            CardinalNumber
   [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat
   [3] (D,Integer) -> D from D if D has DIVRING
   [4] (D,D) -> D from D if D has ELEMFUN
   [5] (Float,Float) -> Float from Float
   [6] (D,NonNegativeInteger) -> D from D
            if D has FS D2 and D2 has ORDSET and D2 has SGROUP
   [7] (D,Integer) -> D from D if D has GROUP
   [8] (PolynomialIdeals(D2,D3,D4,D5),NonNegativeInteger) -> 
            PolynomialIdeals(D2,D3,D4,D5)
            from PolynomialIdeals(D2,D3,D4,D5)
            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 
            has POLYCAT(D2,D3,D4)
   [9] ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from 
            MappingPackage1 D3
            if D3 has SETCAT
   [10] (D,Integer) -> D from D
            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
            D2 and D4 has FLAGG D2 and D2 has FIELD
   [11] (D,NonNegativeInteger) -> D from D
            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
            D2 and D4 has FLAGG D2
   [12] (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3)
            from ModuleOperator(D2,D3)
            if D2 has RING and D3 has LMODULE D2
   [13] (BasicOperator,Integer) -> ModuleOperator(D3,D4)
            from ModuleOperator(D3,D4)
            if D3 has RING and D4 has LMODULE D3
   [14] (D,PositiveInteger) -> D from D if D has MONAD
   [15] (D,NonNegativeInteger) -> D from D if D has MONADWU
   [16] (D,NonNegativeInteger) -> D from D if D has MONOID
   [17] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
            )
            from MyExpression(D1,D2)
            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
            IntegralDomain)
   [18] (D,Fraction Integer) -> D from D if D has RADCAT
   [19] (D,PositiveInteger) -> D from D if D has SGROUP
   [20] (D,Integer) -> D from D
            if D has SMATCAT(D2,D3,D4,D5) and D3 has RING and D4 has 
            DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) and D3 has FIELD
         
   [21] (D,D1) -> D from D
            if D has UTSCAT D1 and D1 has RING and D1 has FIELD

There are 18 unexposed functions called ** :
   [1] (D1,Fraction Integer) -> D1 from AlgebraicFunction(D3,D1)
            if D3 has RETRACT INT and D3 has Join(OrderedSet,
            IntegralDomain) and D1 has FS D3
   [2] (D1,D1) -> D1 from CombinatorialFunction(D2,D1)
            if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS D2
            
   [3] (D1,Fraction Integer) -> D1
            from ElementaryFunctionsUnivariateLaurentSeries(D3,D4,D1)
            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has 
            UTSCAT D3 and D1 has ULSCCAT(D3,D4)
   [4] (D1,Fraction Integer) -> D1
            from ElementaryFunctionsUnivariatePuiseuxSeries(D3,D4,D1,D5
            )
            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has 
            ULSCAT D3 and D1 has UPXSCCA(D3,D4) and D5 has PTRANFN D4
         
   [5] (D1,Integer) -> FreeGroup D1 from FreeGroup D1 if D1 has SETCAT
            
   [6] (D1,NonNegativeInteger) -> FreeMonoid D1 from FreeMonoid D1
            if D1 has SETCAT
   [7] (Vector D3,Integer) -> Vector D3 from 
            InnerNormalBasisFieldFunctions D3
            if D3 has FFIELDC
   [8] (InputForm,Integer) -> InputForm from InputForm
   [9] (InputForm,NonNegativeInteger) -> InputForm from InputForm
   [10] (Matrix D3,NonNegativeInteger) -> Matrix D3
            from StorageEfficientMatrixOperations D3 if D3 has RING
   [11] (D1,NonNegativeInteger) -> OrderedFreeMonoid D1
            from OrderedFreeMonoid D1 if D1 has ORDSET
   [12] (Operator D2,Integer) -> Operator D2 from Operator D2 if D2 has
            RING
   [13] (BasicOperator,Integer) -> Operator D3 from Operator D3 if D3 
            has RING
   [14] (OutputForm,OutputForm) -> OutputForm from OutputForm
   [15] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
            SETCAT
   [16] (Pattern D2,NonNegativeInteger) -> Pattern D2 from Pattern D2
            if D2 has SETCAT
   [17] (Stream D2,Stream D2) -> Stream D2
            from StreamTranscendentalFunctionsNonCommutative D2
            if D2 has ALGEBRA FRAC INT
   [18] (Stream D2,Stream D2) -> Stream D2
            from StreamTranscendentalFunctions D2 if D2 has ALGEBRA 
            FRAC INT

Examples of ** from AlgebraicFunction


Examples of ** from CardinalNumber

c2:=2::CardinalNumber 
c2**c2 
A1:=Aleph 1 
A1**c2 
generalizedContinuumHypothesisAssumed true 
A1**A1


Examples of ** from CombinatorialFunction


Examples of ** from DoubleFloat


Examples of ** from DivisionRing


Examples of ** from ElementaryFunctionsUnivariateLaurentSeries


Examples of ** from ElementaryFunctionsUnivariatePuiseuxSeries


Examples of ** from ElementaryFunctionCategory


Examples of ** from FreeGroup


Examples of ** from Float


Examples of ** from FreeMonoid


Examples of ** from FunctionSpace


Examples of ** from Group


Examples of ** from PolynomialIdeals


Examples of ** from InnerNormalBasisFieldFunctions


Examples of ** from InputForm


Examples of ** from MappingPackage1


Examples of ** from MatrixCategory

(matrix [[j**i for i in 0..4] for j in 1..5]) ** 2

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
m**3


Examples of ** from StorageEfficientMatrixOperations


Examples of ** from ModuleOperator


Examples of ** from Monad


Examples of ** from MonadWithUnit


Examples of ** from Monoid


Examples of ** from MyExpression


Examples of ** from OrderedFreeMonoid

m1:=(y**3)$OFMONOID(Symbol)


Examples of ** from Operator


Examples of ** from OutputForm


Examples of ** from Pattern


Examples of ** from RadicalCategory


Examples of ** from SemiGroup


Examples of ** from SquareMatrixCategory


Examples of ** from StreamTranscendentalFunctionsNonCommutative


Examples of ** from StreamTranscendentalFunctions


Examples of ** from UnivariateTaylorSeriesCategory

--R 
--R
--RThere are 21 exposed functions called ** :
--R   [1] (CardinalNumber,CardinalNumber) -> CardinalNumber from 
--R            CardinalNumber
--R   [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat
--R   [3] (D,Integer) -> D from D if D has DIVRING
--R   [4] (D,D) -> D from D if D has ELEMFUN
--R   [5] (Float,Float) -> Float from Float
--R   [6] (D,NonNegativeInteger) -> D from D
--R            if D has FS D2 and D2 has ORDSET and D2 has SGROUP
--R   [7] (D,Integer) -> D from D if D has GROUP
--R   [8] (PolynomialIdeals(D2,D3,D4,D5),NonNegativeInteger) -> 
--R            PolynomialIdeals(D2,D3,D4,D5)
--R            from PolynomialIdeals(D2,D3,D4,D5)
--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 
--R            has POLYCAT(D2,D3,D4)
--R   [9] ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from 
--R            MappingPackage1 D3
--R            if D3 has SETCAT
--R   [10] (D,Integer) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
--R            D2 and D4 has FLAGG D2 and D2 has FIELD
--R   [11] (D,NonNegativeInteger) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
--R            D2 and D4 has FLAGG D2
--R   [12] (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3)
--R            from ModuleOperator(D2,D3)
--R            if D2 has RING and D3 has LMODULE D2
--R   [13] (BasicOperator,Integer) -> ModuleOperator(D3,D4)
--R            from ModuleOperator(D3,D4)
--R            if D3 has RING and D4 has LMODULE D3
--R   [14] (D,PositiveInteger) -> D from D if D has MONAD
--R   [15] (D,NonNegativeInteger) -> D from D if D has MONADWU
--R   [16] (D,NonNegativeInteger) -> D from D if D has MONOID
--R   [17] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
--R            )
--R            from MyExpression(D1,D2)
--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [18] (D,Fraction Integer) -> D from D if D has RADCAT
--R   [19] (D,PositiveInteger) -> D from D if D has SGROUP
--R   [20] (D,Integer) -> D from D
--R            if D has SMATCAT(D2,D3,D4,D5) and D3 has RING and D4 has 
--R            DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) and D3 has FIELD
--R         
--R   [21] (D,D1) -> D from D
--R            if D has UTSCAT D1 and D1 has RING and D1 has FIELD
--R
--RThere are 18 unexposed functions called ** :
--R   [1] (D1,Fraction Integer) -> D1 from AlgebraicFunction(D3,D1)
--R            if D3 has RETRACT INT and D3 has Join(OrderedSet,
--R            IntegralDomain) and D1 has FS D3
--R   [2] (D1,D1) -> D1 from CombinatorialFunction(D2,D1)
--R            if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS D2
--R            
--R   [3] (D1,Fraction Integer) -> D1
--R            from ElementaryFunctionsUnivariateLaurentSeries(D3,D4,D1)
--R            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has 
--R            UTSCAT D3 and D1 has ULSCCAT(D3,D4)
--R   [4] (D1,Fraction Integer) -> D1
--R            from ElementaryFunctionsUnivariatePuiseuxSeries(D3,D4,D1,D5
--R            )
--R            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has 
--R            ULSCAT D3 and D1 has UPXSCCA(D3,D4) and D5 has PTRANFN D4
--R         
--R   [5] (D1,Integer) -> FreeGroup D1 from FreeGroup D1 if D1 has SETCAT
--R            
--R   [6] (D1,NonNegativeInteger) -> FreeMonoid D1 from FreeMonoid D1
--R            if D1 has SETCAT
--R   [7] (Vector D3,Integer) -> Vector D3 from 
--R            InnerNormalBasisFieldFunctions D3
--R            if D3 has FFIELDC
--R   [8] (InputForm,Integer) -> InputForm from InputForm
--R   [9] (InputForm,NonNegativeInteger) -> InputForm from InputForm
--R   [10] (Matrix D3,NonNegativeInteger) -> Matrix D3
--R            from StorageEfficientMatrixOperations D3 if D3 has RING
--R   [11] (D1,NonNegativeInteger) -> OrderedFreeMonoid D1
--R            from OrderedFreeMonoid D1 if D1 has ORDSET
--R   [12] (Operator D2,Integer) -> Operator D2 from Operator D2 if D2 has
--R            RING
--R   [13] (BasicOperator,Integer) -> Operator D3 from Operator D3 if D3 
--R            has RING
--R   [14] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [15] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
--R            SETCAT
--R   [16] (Pattern D2,NonNegativeInteger) -> Pattern D2 from Pattern D2
--R            if D2 has SETCAT
--R   [17] (Stream D2,Stream D2) -> Stream D2
--R            from StreamTranscendentalFunctionsNonCommutative D2
--R            if D2 has ALGEBRA FRAC INT
--R   [18] (Stream D2,Stream D2) -> Stream D2
--R            from StreamTranscendentalFunctions D2 if D2 has ALGEBRA 
--R            FRAC INT
--R
--RExamples of ** from AlgebraicFunction
--R
--R
--RExamples of ** from CardinalNumber
--R
--Rc2:=2::CardinalNumber 
--Rc2**c2 
--RA1:=Aleph 1 
--RA1**c2 
--RgeneralizedContinuumHypothesisAssumed true 
--RA1**A1
--R
--R
--RExamples of ** from CombinatorialFunction
--R
--R
--RExamples of ** from DoubleFloat
--R
--R
--RExamples of ** from DivisionRing
--R
--R
--RExamples of ** from ElementaryFunctionsUnivariateLaurentSeries
--R
--R
--RExamples of ** from ElementaryFunctionsUnivariatePuiseuxSeries
--R
--R
--RExamples of ** from ElementaryFunctionCategory
--R
--R
--RExamples of ** from FreeGroup
--R
--R
--RExamples of ** from Float
--R
--R
--RExamples of ** from FreeMonoid
--R
--R
--RExamples of ** from FunctionSpace
--R
--R
--RExamples of ** from Group
--R
--R
--RExamples of ** from PolynomialIdeals
--R
--R
--RExamples of ** from InnerNormalBasisFieldFunctions
--R
--R
--RExamples of ** from InputForm
--R
--R
--RExamples of ** from MappingPackage1
--R
--R
--RExamples of ** from MatrixCategory
--R
--R(matrix [[j**i for i in 0..4] for j in 1..5]) ** 2
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rm**3
--R
--R
--RExamples of ** from StorageEfficientMatrixOperations
--R
--R
--RExamples of ** from ModuleOperator
--R
--R
--RExamples of ** from Monad
--R
--R
--RExamples of ** from MonadWithUnit
--R
--R
--RExamples of ** from Monoid
--R
--R
--RExamples of ** from MyExpression
--R
--R
--RExamples of ** from OrderedFreeMonoid
--R
--R
--RExamples of ** from Operator
--R
--R
--RExamples of ** from OutputForm
--R
--R
--RExamples of ** from Pattern
--R
--R
--RExamples of ** from RadicalCategory
--R
--R
--RExamples of ** from SemiGroup
--R
--R
--RExamples of ** from SquareMatrixCategory
--R
--R
--RExamples of ** from StreamTranscendentalFunctionsNonCommutative
--R
--R
--RExamples of ** from StreamTranscendentalFunctions
--R
--R
--RExamples of ** from UnivariateTaylorSeriesCategory
--R
--E 35

--S 36 of 127
)d op plot
 

There are 12 unexposed functions called plot :
   [1] (D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1 D2
            if D2 has KONVERT INFORM
   [2] (D2,D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1 
            D2
            if D2 has KONVERT INFORM
   [3] (Plot3D,Segment DoubleFloat) -> Plot3D from Plot3D
   [4] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
            DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment 
            DoubleFloat,Segment DoubleFloat,Segment DoubleFloat,Segment 
            DoubleFloat) -> Plot3D
            from Plot3D
   [5] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
            DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment 
            DoubleFloat) -> Plot3D
            from Plot3D
   [6] (Plot,Segment DoubleFloat) -> Plot from Plot
   [7] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
            Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) -> 
            Plot
            from Plot
   [8] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
            Segment DoubleFloat) -> Plot
            from Plot
   [9] (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment 
            DoubleFloat) -> Plot
            from Plot
   [10] (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot
            from Plot
   [11] ((DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment 
            DoubleFloat) -> Plot
            from Plot
   [12] ((DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot from
            Plot

Examples of plot from PlotFunctions1


Examples of plot from Plot3D


Examples of plot from Plot

fp:=(t:DFLOAT):DFLOAT +-> sin(t) 
plot(fp,-1.0..1.0)$PLOT

--R 
--R
--RThere are 12 unexposed functions called plot :
--R   [1] (D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1 D2
--R            if D2 has KONVERT INFORM
--R   [2] (D2,D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1 
--R            D2
--R            if D2 has KONVERT INFORM
--R   [3] (Plot3D,Segment DoubleFloat) -> Plot3D from Plot3D
--R   [4] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
--R            DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment 
--R            DoubleFloat,Segment DoubleFloat,Segment DoubleFloat,Segment 
--R            DoubleFloat) -> Plot3D
--R            from Plot3D
--R   [5] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
--R            DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment 
--R            DoubleFloat) -> Plot3D
--R            from Plot3D
--R   [6] (Plot,Segment DoubleFloat) -> Plot from Plot
--R   [7] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
--R            Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) -> 
--R            Plot
--R            from Plot
--R   [8] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
--R            Segment DoubleFloat) -> Plot
--R            from Plot
--R   [9] (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment 
--R            DoubleFloat) -> Plot
--R            from Plot
--R   [10] (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot
--R            from Plot
--R   [11] ((DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment 
--R            DoubleFloat) -> Plot
--R            from Plot
--R   [12] ((DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot from
--R            Plot
--R
--RExamples of plot from PlotFunctions1
--R
--R
--RExamples of plot from Plot3D
--R
--R
--RExamples of plot from Plot
--R
--Rfp:=(t:DFLOAT):DFLOAT +-> sin(t) 
--Rplot(fp,-1.0..1.0)$PLOT
--R
--E 36

--S 37 of 127
)d op factorList
 

There is one exposed function called factorList :
   [1] Factored D2 -> List Record(flg: Union("nil","sqfr","irred",
            "prime"),fctr: D2,xpnt: Integer)
            from Factored D2 if D2 has INTDOM

There is one unexposed function called factorList :
   [1] (D2,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)
             -> List SparseUnivariatePolynomial D2
            from ChineseRemainderToolsForIntegralBases(D2,D4,D5)
            if D2 has FFIELDC and D4 has UPOLYC D2 and D5 has UPOLYC D4
            

Examples of factorList from Factored

f:=nilFactor(x-y,3) 
factorList f


Examples of factorList from ChineseRemainderToolsForIntegralBases

--R 
--R
--RThere is one exposed function called factorList :
--R   [1] Factored D2 -> List Record(flg: Union("nil","sqfr","irred",
--R            "prime"),fctr: D2,xpnt: Integer)
--R            from Factored D2 if D2 has INTDOM
--R
--RThere is one unexposed function called factorList :
--R   [1] (D2,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)
--R             -> List SparseUnivariatePolynomial D2
--R            from ChineseRemainderToolsForIntegralBases(D2,D4,D5)
--R            if D2 has FFIELDC and D4 has UPOLYC D2 and D5 has UPOLYC D4
--R            
--R
--RExamples of factorList from Factored
--R
--Rf:=nilFactor(x-y,3) 
--RfactorList f
--R
--R
--RExamples of factorList from ChineseRemainderToolsForIntegralBases
--R
--E 37

--S 38 of 127
)d op physicalLength
 

There is one exposed function called physicalLength :
   [1] FlexibleArray D2 -> NonNegativeInteger from FlexibleArray D2
            if D2 has TYPE

There is one unexposed function called physicalLength :
   [1] IndexedFlexibleArray(D2,D3) -> NonNegativeInteger
            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
            

Examples of physicalLength from FlexibleArray


Examples of physicalLength from IndexedFlexibleArray

T1:=IndexedFlexibleArray(Integer,20) 
t2:=flexibleArray([i for i in 1..10])$T1 
physicalLength t2

--R 
--R
--RThere is one exposed function called physicalLength :
--R   [1] FlexibleArray D2 -> NonNegativeInteger from FlexibleArray D2
--R            if D2 has TYPE
--R
--RThere is one unexposed function called physicalLength :
--R   [1] IndexedFlexibleArray(D2,D3) -> NonNegativeInteger
--R            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
--R            
--R
--RExamples of physicalLength from FlexibleArray
--R
--R
--RExamples of physicalLength from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20) 
--Rt2:=flexibleArray([i for i in 1..10])$T1 
--RphysicalLength t2
--R
--E 38

--S 39 of 127
)d op absolutelyIrreducible?
 

There is one exposed function called absolutelyIrreducible? :
   [1]  -> Boolean from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

There is one unexposed function called absolutelyIrreducible? :
   [1]  -> Boolean from FunctionFieldCategory&(D2,D3,D4,D5)
            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC 
            D4 and D2 has FFCAT(D3,D4,D5)

Examples of absolutelyIrreducible? from FunctionFieldCategory&

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
absolutelyIrreducible?()$R2


Examples of absolutelyIrreducible? from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
absolutelyIrreducible?()$R2

--R 
--R
--RThere is one exposed function called absolutelyIrreducible? :
--R   [1]  -> Boolean from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RThere is one unexposed function called absolutelyIrreducible? :
--R   [1]  -> Boolean from FunctionFieldCategory&(D2,D3,D4,D5)
--R            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC 
--R            D4 and D2 has FFCAT(D3,D4,D5)
--R
--RExamples of absolutelyIrreducible? from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
--RabsolutelyIrreducible?()$R2
--R
--R
--RExamples of absolutelyIrreducible? from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) 
--RabsolutelyIrreducible?()$R2
--R
--E 39

--S 40 of 127
)d op repeating?
 

There is one exposed function called repeating? :
   [1] (List D3,Stream D3) -> Boolean from Stream D3
            if D3 has SETCAT and D3 has TYPE

Examples of repeating? from Stream

m:=[1,2,3] 
n:=repeating(m) 
repeating?(m,n)

--R 
--R
--RThere is one exposed function called repeating? :
--R   [1] (List D3,Stream D3) -> Boolean from Stream D3
--R            if D3 has SETCAT and D3 has TYPE
--R
--RExamples of repeating? from Stream
--R
--Rm:=[1,2,3] 
--Rn:=repeating(m) 
--Rrepeating?(m,n)
--R
--E 40

--S 41 of 127
)d op lazy?
 

There is one exposed function called lazy? :
   [1] D -> Boolean from D if D has LZSTAGG D2 and D2 has TYPE

Examples of lazy? from LazyStreamAggregate

m:=[i for i in 0..] 
lazy? m

--R 
--R
--RThere is one exposed function called lazy? :
--R   [1] D -> Boolean from D if D has LZSTAGG D2 and D2 has TYPE
--R
--RExamples of lazy? from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--Rlazy? m
--R
--E 41

--S 42 of 127
)d op ord
 

There is one exposed function called ord :
   [1] Character -> Integer from Character

Examples of ord from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[ord c for c in chars]

--R 
--R
--RThere is one exposed function called ord :
--R   [1] Character -> Integer from Character
--R
--RExamples of ord from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[ord c for c in chars]
--R
--E 42

--S 43 of 127
)d op setColumn!
 

There is one exposed function called setColumn! :
   [1] (D,Integer,D2) -> D from D
            if D has ARR2CAT(D3,D4,D2) and D3 has TYPE and D4 has FLAGG
            D3 and D2 has FLAGG D3

Examples of setColumn! from TwoDimensionalArrayCategory

T1:=TwoDimensionalArray Integer 
arr:T1:= new(5,4,0) 
T2:=OneDimensionalArray Integer 
acol:=construct([1,2,3,4,5]::List(INT))$T2 
setColumn!(arr,1,acol)$T1

--R 
--R
--RThere is one exposed function called setColumn! :
--R   [1] (D,Integer,D2) -> D from D
--R            if D has ARR2CAT(D3,D4,D2) and D3 has TYPE and D4 has FLAGG
--R            D3 and D2 has FLAGG D3
--R
--RExamples of setColumn! from TwoDimensionalArrayCategory
--R
--RT1:=TwoDimensionalArray Integer 
--Rarr:T1:= new(5,4,0) 
--RT2:=OneDimensionalArray Integer 
--Racol:=construct([1,2,3,4,5]::List(INT))$T2 
--RsetColumn!(arr,1,acol)$T1
--R
--E 43

--S 44 of 127
)d op lowerCase?
 

There is one exposed function called lowerCase? :
   [1] Character -> Boolean from Character

Examples of lowerCase? from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[lowerCase? c for c in chars]

--R 
--R
--RThere is one exposed function called lowerCase? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of lowerCase? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[lowerCase? c for c in chars]
--R
--E 44

--S 45 of 127
)d op physicalLength!
 

There is one exposed function called physicalLength! :
   [1] (FlexibleArray D2,Integer) -> FlexibleArray D2 from 
            FlexibleArray D2
            if D2 has TYPE

There is one unexposed function called physicalLength! :
   [1] (IndexedFlexibleArray(D2,D3),Integer) -> IndexedFlexibleArray(D2
            ,D3)
            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
            

Examples of physicalLength! from FlexibleArray


Examples of physicalLength! from IndexedFlexibleArray

T1:=IndexedFlexibleArray(Integer,20) 
t2:=flexibleArray([i for i in 1..10])$T1 
physicalLength!(t2,15)

--R 
--R
--RThere is one exposed function called physicalLength! :
--R   [1] (FlexibleArray D2,Integer) -> FlexibleArray D2 from 
--R            FlexibleArray D2
--R            if D2 has TYPE
--R
--RThere is one unexposed function called physicalLength! :
--R   [1] (IndexedFlexibleArray(D2,D3),Integer) -> IndexedFlexibleArray(D2
--R            ,D3)
--R            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
--R            
--R
--RExamples of physicalLength! from FlexibleArray
--R
--R
--RExamples of physicalLength! from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20) 
--Rt2:=flexibleArray([i for i in 1..10])$T1 
--RphysicalLength!(t2,15)
--R
--E 45

--S 46 of 127
)d op countable?
 

There is one exposed function called countable? :
   [1] CardinalNumber -> Boolean from CardinalNumber

Examples of countable? from CardinalNumber

c2:=2::CardinalNumber 
countable? c2 
A0:=Aleph 0 
countable? A0 
A1:=Aleph 1 
countable? A1

--R 
--R
--RThere is one exposed function called countable? :
--R   [1] CardinalNumber -> Boolean from CardinalNumber
--R
--RExamples of countable? from CardinalNumber
--R
--Rc2:=2::CardinalNumber 
--Rcountable? c2 
--RA0:=Aleph 0 
--Rcountable? A0 
--RA1:=Aleph 1 
--Rcountable? A1
--R
--E 46

--S 47 of 127
)d op extend
 

There are 11 exposed functions called extend :
   [1] (ContinuedFraction D2,Integer) -> ContinuedFraction D2
            from ContinuedFraction D2 if D2 has EUCDOM
   [2] (D,Integer) -> D from D if D has LZSTAGG D2 and D2 has TYPE
   [3] (D,NonNegativeInteger) -> D from D
            if D has MTSCAT(D2,D3) and D2 has RING and D3 has ORDSET
         
   [4] (D,Integer) -> D from D if D has PADICCT D2
   [5] (D,List D2) -> D from D if D has PTCAT D2 and D2 has RING
   [6] (List D6,List D) -> List D from D
            if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 has 
            OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5)
   [7] (List D6,D) -> List D from D
            if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has 
            OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6)
   [8] (D2,List D) -> List D from D
            if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 has 
            OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5)
   [9] (D2,D) -> List D from D
            if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and D2
            has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2)
   [10] (D,D1) -> D from D
            if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 has 
            OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4)
   [11] (D,D1) -> D from D
            if D has UPSCAT(D2,D1) and D2 has RING and D1 has OAMON

Examples of extend from ContinuedFraction


Examples of extend from LazyStreamAggregate

m:=[i for i in 0..] 
numberOfComputedEntries m 
extend(m,20) 
numberOfComputedEntries m


Examples of extend from MultivariateTaylorSeriesCategory


Examples of extend from PAdicIntegerCategory


Examples of extend from PointCategory


Examples of extend from RegularTriangularSetCategory


Examples of extend from TriangularSetCategory


Examples of extend from UnivariatePowerSeriesCategory

--R 
--R
--RThere are 11 exposed functions called extend :
--R   [1] (ContinuedFraction D2,Integer) -> ContinuedFraction D2
--R            from ContinuedFraction D2 if D2 has EUCDOM
--R   [2] (D,Integer) -> D from D if D has LZSTAGG D2 and D2 has TYPE
--R   [3] (D,NonNegativeInteger) -> D from D
--R            if D has MTSCAT(D2,D3) and D2 has RING and D3 has ORDSET
--R         
--R   [4] (D,Integer) -> D from D if D has PADICCT D2
--R   [5] (D,List D2) -> D from D if D has PTCAT D2 and D2 has RING
--R   [6] (List D6,List D) -> List D from D
--R            if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 has 
--R            OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5)
--R   [7] (List D6,D) -> List D from D
--R            if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has 
--R            OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6)
--R   [8] (D2,List D) -> List D from D
--R            if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 has 
--R            OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5)
--R   [9] (D2,D) -> List D from D
--R            if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and D2
--R            has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2)
--R   [10] (D,D1) -> D from D
--R            if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 has 
--R            OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4)
--R   [11] (D,D1) -> D from D
--R            if D has UPSCAT(D2,D1) and D2 has RING and D1 has OAMON
--R
--RExamples of extend from ContinuedFraction
--R
--R
--RExamples of extend from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--RnumberOfComputedEntries m 
--Rextend(m,20) 
--RnumberOfComputedEntries m
--R
--R
--RExamples of extend from MultivariateTaylorSeriesCategory
--R
--R
--RExamples of extend from PAdicIntegerCategory
--R
--R
--RExamples of extend from PointCategory
--R
--R
--RExamples of extend from RegularTriangularSetCategory
--R
--R
--RExamples of extend from TriangularSetCategory
--R
--R
--RExamples of extend from UnivariatePowerSeriesCategory
--R
--E 47

--S 48 of 127
)d op length
 

There are 5 exposed functions called length :
   [1] Dequeue D2 -> NonNegativeInteger from Dequeue D2 if D2 has 
            SETCAT
   [2] D -> D from D if D has INS
   [3] D -> NonNegativeInteger from D if D has QUAGG D2 and D2 has TYPE
            
   [4] Queue D2 -> NonNegativeInteger from Queue D2 if D2 has SETCAT
         
   [5] D -> D1 from D
            if D has VECTCAT D1 and D1 has TYPE and D1 has RADCAT and 
            D1 has RING

There are 6 unexposed functions called length :
   [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1)
            if D3 has RING and D1 has Join(FloatingPointSystem,
            RetractableTo D3,Field,TranscendentalFunctionCategory,
            ElementaryFunctionCategory) and D2 has UPOLYC D3
   [2] LyndonWord D2 -> PositiveInteger from LyndonWord D2 if D2 has 
            ORDSET
   [3] Magma D2 -> PositiveInteger from Magma D2 if D2 has ORDSET
   [4] OrderedFreeMonoid D2 -> NonNegativeInteger from 
            OrderedFreeMonoid D2
            if D2 has ORDSET
   [5] PoincareBirkhoffWittLyndonBasis D2 -> NonNegativeInteger
            from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
         
   [6] Tuple D2 -> NonNegativeInteger from Tuple D2 if D2 has TYPE

Examples of length from Dequeue

a:Dequeue INT:= dequeue [1,2,3,4,5] 
length a


Examples of length from GaloisGroupFactorizationUtilities


Examples of length from IntegerNumberSystem


Examples of length from LyndonWord


Examples of length from Magma


Examples of length from OrderedFreeMonoid

m1:=(x*y*y*z)$OFMONOID(Symbol) 
length m1


Examples of length from PoincareBirkhoffWittLyndonBasis


Examples of length from QueueAggregate


Examples of length from Queue

a:Queue INT:= queue [1,2,3,4,5] 
length a


Examples of length from Tuple

t1:PrimitiveArray(Integer):= [i for i in 1..10] 
t2:=coerce(t1)$Tuple(Integer) 
length(t2)


Examples of length from VectorCategory

--R 
--R
--RThere are 5 exposed functions called length :
--R   [1] Dequeue D2 -> NonNegativeInteger from Dequeue D2 if D2 has 
--R            SETCAT
--R   [2] D -> D from D if D has INS
--R   [3] D -> NonNegativeInteger from D if D has QUAGG D2 and D2 has TYPE
--R            
--R   [4] Queue D2 -> NonNegativeInteger from Queue D2 if D2 has SETCAT
--R         
--R   [5] D -> D1 from D
--R            if D has VECTCAT D1 and D1 has TYPE and D1 has RADCAT and 
--R            D1 has RING
--R
--RThere are 6 unexposed functions called length :
--R   [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1)
--R            if D3 has RING and D1 has Join(FloatingPointSystem,
--R            RetractableTo D3,Field,TranscendentalFunctionCategory,
--R            ElementaryFunctionCategory) and D2 has UPOLYC D3
--R   [2] LyndonWord D2 -> PositiveInteger from LyndonWord D2 if D2 has 
--R            ORDSET
--R   [3] Magma D2 -> PositiveInteger from Magma D2 if D2 has ORDSET
--R   [4] OrderedFreeMonoid D2 -> NonNegativeInteger from 
--R            OrderedFreeMonoid D2
--R            if D2 has ORDSET
--R   [5] PoincareBirkhoffWittLyndonBasis D2 -> NonNegativeInteger
--R            from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
--R         
--R   [6] Tuple D2 -> NonNegativeInteger from Tuple D2 if D2 has TYPE
--R
--RExamples of length from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5] 
--Rlength a
--R
--R
--RExamples of length from GaloisGroupFactorizationUtilities
--R
--R
--RExamples of length from IntegerNumberSystem
--R
--R
--RExamples of length from LyndonWord
--R
--R
--RExamples of length from Magma
--R
--R
--RExamples of length from OrderedFreeMonoid
--R
--R
--RExamples of length from PoincareBirkhoffWittLyndonBasis
--R
--R
--RExamples of length from QueueAggregate
--R
--R
--RExamples of length from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5] 
--Rlength a
--R
--R
--RExamples of length from Tuple
--R
--Rt1:PrimitiveArray(Integer):= [i for i in 1..10] 
--Rt2:=coerce(t1)$Tuple(Integer) 
--Rlength(t2)
--R
--R
--RExamples of length from VectorCategory
--R
--E 48

--S 49 of 127
)d op viewPosDefault
 

There are 2 exposed functions called viewPosDefault :
   [1]  -> List NonNegativeInteger from ViewDefaultsPackage
   [2] List NonNegativeInteger -> List NonNegativeInteger
            from ViewDefaultsPackage

Examples of viewPosDefault from ViewDefaultsPackage

and Y position of a viewport window unless overriden explicityly, newly created viewports will have th 
and Y coordinates x, y.

and Y position of a viewport window unless overriden explicityly, newly created viewports will have this 
and Y coordinate.

--R 
--R
--RThere are 2 exposed functions called viewPosDefault :
--R   [1]  -> List NonNegativeInteger from ViewDefaultsPackage
--R   [2] List NonNegativeInteger -> List NonNegativeInteger
--R            from ViewDefaultsPackage
--R
--RExamples of viewPosDefault from ViewDefaultsPackage
--R
--Rand Y position of a viewport window unless overriden explicityly, newly created viewports will have th 
--Rand Y coordinates x, y.
--R
--Rand Y position of a viewport window unless overriden explicityly, newly created viewports will have this 
--Rand Y coordinate.
--R
--E 49

--S 50 of 127
)d op groebner
 

There are 4 exposed functions called groebner :
   [1] List D5 -> List D5 from GroebnerPackage(D2,D3,D4,D5)
            if D5 has POLYCAT(D2,D3,D4) and D2 has GCDDOM and D3 has 
            OAMONS and D4 has ORDSET
   [2] (List D6,String) -> List D6 from GroebnerPackage(D3,D4,D5,D6)
            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has 
            OAMONS and D5 has ORDSET
   [3] (List D6,String,String) -> List D6 from GroebnerPackage(D3,D4,D5
            ,D6)
            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has 
            OAMONS and D5 has ORDSET
   [4] PolynomialIdeals(D1,D2,D3,D4) -> PolynomialIdeals(D1,D2,D3,D4)
            from PolynomialIdeals(D1,D2,D3,D4)
            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
            has POLYCAT(D1,D2,D3)

There are 2 unexposed functions called groebner :
   [1] List Polynomial D2 -> List Polynomial D2 from FGLMIfCanPackage(
            D2,D3)
            if D2 has GCDDOM and D3: LIST SYMBOL
   [2] List NewSparseMultivariatePolynomial(D2,OrderedVariableList D3)
             -> List NewSparseMultivariatePolynomial(D2,OrderedVariableList 
            D3)
            from LexTriangularPackage(D2,D3)
            if D2 has GCDDOM and D3: LIST SYMBOL

Examples of groebner from FGLMIfCanPackage


Examples of groebner from GroebnerPackage

s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 
s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s 
s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 
s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s 
s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 
s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 
s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 
sn7:=[s1,s2,s3,s4,s5,s6,s7] 
groebner(sn7,"info","redcrit")

s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 
s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s 
s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 
s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s 
s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 
s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 
s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 
sn7:=[s1,s2,s3,s4,s5,s6,s7] 
groebner(sn7,"info") 
groebner(sn7,"redcrit")

s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 
s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s 
s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 
s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s 
s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 
s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 
s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 
sn7:=[s1,s2,s3,s4,s5,s6,s7] 
groebner(sn7)


Examples of groebner from PolynomialIdeals


Examples of groebner from LexTriangularPackage

--R 
--R
--RThere are 4 exposed functions called groebner :
--R   [1] List D5 -> List D5 from GroebnerPackage(D2,D3,D4,D5)
--R            if D5 has POLYCAT(D2,D3,D4) and D2 has GCDDOM and D3 has 
--R            OAMONS and D4 has ORDSET
--R   [2] (List D6,String) -> List D6 from GroebnerPackage(D3,D4,D5,D6)
--R            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has 
--R            OAMONS and D5 has ORDSET
--R   [3] (List D6,String,String) -> List D6 from GroebnerPackage(D3,D4,D5
--R            ,D6)
--R            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has 
--R            OAMONS and D5 has ORDSET
--R   [4] PolynomialIdeals(D1,D2,D3,D4) -> PolynomialIdeals(D1,D2,D3,D4)
--R            from PolynomialIdeals(D1,D2,D3,D4)
--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
--R            has POLYCAT(D1,D2,D3)
--R
--RThere are 2 unexposed functions called groebner :
--R   [1] List Polynomial D2 -> List Polynomial D2 from FGLMIfCanPackage(
--R            D2,D3)
--R            if D2 has GCDDOM and D3: LIST SYMBOL
--R   [2] List NewSparseMultivariatePolynomial(D2,OrderedVariableList D3)
--R             -> List NewSparseMultivariatePolynomial(D2,OrderedVariableList 
--R            D3)
--R            from LexTriangularPackage(D2,D3)
--R            if D2 has GCDDOM and D3: LIST SYMBOL
--R
--RExamples of groebner from FGLMIfCanPackage
--R
--R
--RExamples of groebner from GroebnerPackage
--R
--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 
--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s 
--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 
--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s 
--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 
--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 
--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 
--Rsn7:=[s1,s2,s3,s4,s5,s6,s7] 
--Rgroebner(sn7,"info","redcrit")
--R
--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 
--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s 
--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 
--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s 
--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 
--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 
--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 
--Rsn7:=[s1,s2,s3,s4,s5,s6,s7] 
--Rgroebner(sn7,"info") 
--Rgroebner(sn7,"redcrit")
--R
--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 
--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s 
--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 
--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s 
--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 
--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 
--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 
--Rsn7:=[s1,s2,s3,s4,s5,s6,s7] 
--Rgroebner(sn7)
--R
--R
--RExamples of groebner from PolynomialIdeals
--R
--R
--RExamples of groebner from LexTriangularPackage
--R
--E 50

--S 51 of 127
)d op primeFactor
 

There is one exposed function called primeFactor :
   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
         

Examples of primeFactor from Factored

a:=primeFactor(3,4) 
nthFlag(a,1)

--R 
--R
--RThere is one exposed function called primeFactor :
--R   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
--R         
--R
--RExamples of primeFactor from Factored
--R
--Ra:=primeFactor(3,4) 
--RnthFlag(a,1)
--R
--E 51

--S 52 of 127
)d op map!
 

There are 7 exposed functions called map! :
   [1] ((D2 -> D2),D) -> D from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] ((D2 -> D2),ArrayStack D2) -> ArrayStack D2 from ArrayStack D2
            if $ has shallowlyMutable and D2 has SETCAT
   [3] ((D2 -> D2),Dequeue D2) -> Dequeue D2 from Dequeue D2
            if $ has shallowlyMutable and D2 has SETCAT
   [4] ((D2 -> D2),Heap D2) -> Heap D2 from Heap D2
            if $ has shallowlyMutable and D2 has ORDSET
   [5] ((D2 -> D2),D) -> D from D
            if D has shallowlyMutable and D has HOAGG D2 and D2 has 
            TYPE
   [6] ((D2 -> D2),Queue D2) -> Queue D2 from Queue D2
            if $ has shallowlyMutable and D2 has SETCAT
   [7] ((D2 -> D2),Stack D2) -> Stack D2 from Stack D2
            if $ has shallowlyMutable and D2 has SETCAT

Examples of map! from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
map!(-,arr)


Examples of map! from ArrayStack

a:ArrayStack INT:= arrayStack [1,2,3,4,5] 
map!(x+->x+10,a) 
a


Examples of map! from Dequeue

a:Dequeue INT:= dequeue [1,2,3,4,5] 
map!(x+->x+10,a) 
a


Examples of map! from Heap

a:Heap INT:= heap [1,2,3,4,5] 
map!(x+->x+10,a) 
a


Examples of map! from HomogeneousAggregate


Examples of map! from Queue

a:Queue INT:= queue [1,2,3,4,5] 
map!(x+->x+10,a) 
a


Examples of map! from Stack

a:Stack INT:= stack [1,2,3,4,5] 
map!(x+->x+10,a) 
a

--R 
--R
--RThere are 7 exposed functions called map! :
--R   [1] ((D2 -> D2),D) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] ((D2 -> D2),ArrayStack D2) -> ArrayStack D2 from ArrayStack D2
--R            if $ has shallowlyMutable and D2 has SETCAT
--R   [3] ((D2 -> D2),Dequeue D2) -> Dequeue D2 from Dequeue D2
--R            if $ has shallowlyMutable and D2 has SETCAT
--R   [4] ((D2 -> D2),Heap D2) -> Heap D2 from Heap D2
--R            if $ has shallowlyMutable and D2 has ORDSET
--R   [5] ((D2 -> D2),D) -> D from D
--R            if D has shallowlyMutable and D has HOAGG D2 and D2 has 
--R            TYPE
--R   [6] ((D2 -> D2),Queue D2) -> Queue D2 from Queue D2
--R            if $ has shallowlyMutable and D2 has SETCAT
--R   [7] ((D2 -> D2),Stack D2) -> Stack D2 from Stack D2
--R            if $ has shallowlyMutable and D2 has SETCAT
--R
--RExamples of map! from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rmap!(-,arr)
--R
--R
--RExamples of map! from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] 
--Rmap!(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map! from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5] 
--Rmap!(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map! from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5] 
--Rmap!(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map! from HomogeneousAggregate
--R
--R
--RExamples of map! from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5] 
--Rmap!(x+->x+10,a) 
--Ra
--R
--R
--RExamples of map! from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5] 
--Rmap!(x+->x+10,a) 
--Ra
--R
--E 52

--S 53 of 127
)d op setleaves!
 

There is one exposed function called setleaves! :
   [1] (BalancedBinaryTree D2,List D2) -> BalancedBinaryTree D2
            from BalancedBinaryTree D2 if D2 has SETCAT

Examples of setleaves! from BalancedBinaryTree

t1:=balancedBinaryTree(4, 0) 
setleaves!(t1,[1,2,3,4])

--R 
--R
--RThere is one exposed function called setleaves! :
--R   [1] (BalancedBinaryTree D2,List D2) -> BalancedBinaryTree D2
--R            from BalancedBinaryTree D2 if D2 has SETCAT
--R
--RExamples of setleaves! from BalancedBinaryTree
--R
--Rt1:=balancedBinaryTree(4, 0) 
--Rsetleaves!(t1,[1,2,3,4])
--R
--E 53

--S 54 of 127
)d op scan
 

There are 8 exposed functions called scan :
   [1] (((D5,D4) -> D4),OneDimensionalArray D5,D4) -> 
            OneDimensionalArray D4
            from OneDimensionalArrayFunctions2(D5,D4)
            if D5 has TYPE and D4 has TYPE
   [2] (((D6,D4) -> D4),DirectProduct(D5,D6),D4) -> DirectProduct(D5,D4
            )
            from DirectProductFunctions2(D5,D6,D4)
            if D5: NNI and D6 has TYPE and D4 has TYPE
   [3] (((D5,D4) -> D4),D3,D4) -> D1
            from FiniteLinearAggregateFunctions2(D5,D3,D4,D1)
            if D5 has TYPE and D4 has TYPE and D1 has FLAGG D4 and D3 
            has FLAGG D5
   [4] (((D5,D4) -> D4),D3,D4) -> D1
            from FiniteSetAggregateFunctions2(D5,D3,D4,D1)
            if D5 has SETCAT and D4 has SETCAT and D1 has FSAGG D4 and 
            D3 has FSAGG D5
   [5] (((D5,D4) -> D4),List D5,D4) -> List D4 from ListFunctions2(D5,
            D4)
            if D5 has TYPE and D4 has TYPE
   [6] (((D5,D4) -> D4),PrimitiveArray D5,D4) -> PrimitiveArray D4
            from PrimitiveArrayFunctions2(D5,D4)
            if D5 has TYPE and D4 has TYPE
   [7] (D2,((D5,D2) -> D2),Stream D5) -> Stream D2
            from StreamFunctions2(D5,D2) if D5 has TYPE and D2 has TYPE
            
   [8] (((D5,D4) -> D4),Vector D5,D4) -> Vector D4
            from VectorFunctions2(D5,D4) if D5 has TYPE and D4 has TYPE
            

Examples of scan from OneDimensionalArrayFunctions2

T1:=OneDimensionalArrayFunctions2(Integer,Integer) 
adder(a:Integer,b:Integer):Integer == a+b 
scan(adder,[i for i in 1..10],0)$T1


Examples of scan from DirectProductFunctions2


Examples of scan from FiniteLinearAggregateFunctions2


Examples of scan from FiniteSetAggregateFunctions2


Examples of scan from ListFunctions2


Examples of scan from PrimitiveArrayFunctions2

T1:=PrimitiveArrayFunctions2(Integer,Integer) 
adder(a:Integer,b:Integer):Integer == a+b 
scan(adder,[i for i in 1..10],0)$T1


Examples of scan from StreamFunctions2

m:=[i for i in 1..]::Stream(Integer) 
f(i:Integer,j:Integer):Integer==i+j 
scan(1,f,m)


Examples of scan from VectorFunctions2

--R 
--R
--RThere are 8 exposed functions called scan :
--R   [1] (((D5,D4) -> D4),OneDimensionalArray D5,D4) -> 
--R            OneDimensionalArray D4
--R            from OneDimensionalArrayFunctions2(D5,D4)
--R            if D5 has TYPE and D4 has TYPE
--R   [2] (((D6,D4) -> D4),DirectProduct(D5,D6),D4) -> DirectProduct(D5,D4
--R            )
--R            from DirectProductFunctions2(D5,D6,D4)
--R            if D5: NNI and D6 has TYPE and D4 has TYPE
--R   [3] (((D5,D4) -> D4),D3,D4) -> D1
--R            from FiniteLinearAggregateFunctions2(D5,D3,D4,D1)
--R            if D5 has TYPE and D4 has TYPE and D1 has FLAGG D4 and D3 
--R            has FLAGG D5
--R   [4] (((D5,D4) -> D4),D3,D4) -> D1
--R            from FiniteSetAggregateFunctions2(D5,D3,D4,D1)
--R            if D5 has SETCAT and D4 has SETCAT and D1 has FSAGG D4 and 
--R            D3 has FSAGG D5
--R   [5] (((D5,D4) -> D4),List D5,D4) -> List D4 from ListFunctions2(D5,
--R            D4)
--R            if D5 has TYPE and D4 has TYPE
--R   [6] (((D5,D4) -> D4),PrimitiveArray D5,D4) -> PrimitiveArray D4
--R            from PrimitiveArrayFunctions2(D5,D4)
--R            if D5 has TYPE and D4 has TYPE
--R   [7] (D2,((D5,D2) -> D2),Stream D5) -> Stream D2
--R            from StreamFunctions2(D5,D2) if D5 has TYPE and D2 has TYPE
--R            
--R   [8] (((D5,D4) -> D4),Vector D5,D4) -> Vector D4
--R            from VectorFunctions2(D5,D4) if D5 has TYPE and D4 has TYPE
--R            
--R
--RExamples of scan from OneDimensionalArrayFunctions2
--R
--RT1:=OneDimensionalArrayFunctions2(Integer,Integer) 
--Radder(a:Integer,b:Integer):Integer == a+b 
--Rscan(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of scan from DirectProductFunctions2
--R
--R
--RExamples of scan from FiniteLinearAggregateFunctions2
--R
--R
--RExamples of scan from FiniteSetAggregateFunctions2
--R
--R
--RExamples of scan from ListFunctions2
--R
--R
--RExamples of scan from PrimitiveArrayFunctions2
--R
--RT1:=PrimitiveArrayFunctions2(Integer,Integer) 
--Radder(a:Integer,b:Integer):Integer == a+b 
--Rscan(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of scan from StreamFunctions2
--R
--Rm:=[i for i in 1..]::Stream(Integer) 
--Rf(i:Integer,j:Integer):Integer==i+j 
--Rscan(1,f,m)
--R
--R
--RExamples of scan from VectorFunctions2
--R
--E 54

--S 55 of 127
)d op alphabetic?
 

There is one exposed function called alphabetic? :
   [1] Character -> Boolean from Character

Examples of alphabetic? from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[alphabetic? c for c in chars]

--R 
--R
--RThere is one exposed function called alphabetic? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of alphabetic? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[alphabetic? c for c in chars]
--R
--E 55

--S 56 of 127
)d op +
 

There are 12 exposed functions called + :
   [1] (D,D) -> D from D if D has ABELSG
   [2] (Color,Color) -> Color from Color
   [3] (Database D1,Database D1) -> Database D1 from Database D1
            if D1 has OrderedSet with 
               ?.? : (%,Symbol) -> String
               display : % -> Void
               fullDisplay : % -> Void
   [4] (Equation D1,D1) -> Equation D1 from Equation D1
            if D1 has ABELSG and D1 has TYPE
   [5] (D1,Equation D1) -> Equation D1 from Equation D1
            if D1 has ABELSG and D1 has TYPE
   [6] (D1,D) -> D from D
            if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON
            
   [7] (D1,FullPartialFractionExpansion(D2,D1)) -> 
            FullPartialFractionExpansion(D2,D1)
            from FullPartialFractionExpansion(D2,D1)
            if D2 has Join(Field,CharacteristicZero) and D1 has UPOLYC 
            D2
   [8] (D,D) -> D from D
            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
            
   [9] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
             -> PolynomialIdeals(D1,D2,D3,D4)
            from PolynomialIdeals(D1,D2,D3,D4)
            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
            has POLYCAT(D1,D2,D3)
   [10] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
            D3)
            if D2 has SETCAT and D3 has RING
   [11] (D,D) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [12] (D,D) -> D from D
            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELSG

There are 5 unexposed functions called + :
   [1] (InputForm,InputForm) -> InputForm from InputForm
   [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
   [3] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has 
            SETCAT
   [4] (Stream D2,Stream D2) -> Stream D2 from 
            StreamTaylorSeriesOperations D2
            if D2 has RING
   [5] (Point DoubleFloat,Point DoubleFloat) -> Point DoubleFloat
            from TubePlotTools

Examples of + from AbelianSemiGroup


Examples of + from Color


Examples of + from Database


Examples of + from Equation


Examples of + from FreeAbelianMonoidCategory


Examples of + from FullPartialFractionExpansion


Examples of + from GradedModule


Examples of + from PolynomialIdeals


Examples of + from InputForm


Examples of + from MappingPackage4

f:=(x:INT):INT +-> 3*x 
g:=(x:INT):INT +-> 2*x+3 
(f+g)(4)


Examples of + from MatrixCategory

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
m+m


Examples of + from OutputForm


Examples of + from Pattern


Examples of + from StreamTaylorSeriesOperations


Examples of + from TubePlotTools


Examples of + from VectorCategory

--R 
--R
--RThere are 12 exposed functions called + :
--R   [1] (D,D) -> D from D if D has ABELSG
--R   [2] (Color,Color) -> Color from Color
--R   [3] (Database D1,Database D1) -> Database D1 from Database D1
--R            if D1 has OrderedSet with 
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [4] (Equation D1,D1) -> Equation D1 from Equation D1
--R            if D1 has ABELSG and D1 has TYPE
--R   [5] (D1,Equation D1) -> Equation D1 from Equation D1
--R            if D1 has ABELSG and D1 has TYPE
--R   [6] (D1,D) -> D from D
--R            if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON
--R            
--R   [7] (D1,FullPartialFractionExpansion(D2,D1)) -> 
--R            FullPartialFractionExpansion(D2,D1)
--R            from FullPartialFractionExpansion(D2,D1)
--R            if D2 has Join(Field,CharacteristicZero) and D1 has UPOLYC 
--R            D2
--R   [8] (D,D) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R            
--R   [9] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
--R             -> PolynomialIdeals(D1,D2,D3,D4)
--R            from PolynomialIdeals(D1,D2,D3,D4)
--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
--R            has POLYCAT(D1,D2,D3)
--R   [10] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
--R            D3)
--R            if D2 has SETCAT and D3 has RING
--R   [11] (D,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [12] (D,D) -> D from D
--R            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELSG
--R
--RThere are 5 unexposed functions called + :
--R   [1] (InputForm,InputForm) -> InputForm from InputForm
--R   [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [3] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has 
--R            SETCAT
--R   [4] (Stream D2,Stream D2) -> Stream D2 from 
--R            StreamTaylorSeriesOperations D2
--R            if D2 has RING
--R   [5] (Point DoubleFloat,Point DoubleFloat) -> Point DoubleFloat
--R            from TubePlotTools
--R
--RExamples of + from AbelianSemiGroup
--R
--R
--RExamples of + from Color
--R
--R
--RExamples of + from Database
--R
--R
--RExamples of + from Equation
--R
--R
--RExamples of + from FreeAbelianMonoidCategory
--R
--R
--RExamples of + from FullPartialFractionExpansion
--R
--R
--RExamples of + from GradedModule
--R
--R
--RExamples of + from PolynomialIdeals
--R
--R
--RExamples of + from InputForm
--R
--R
--RExamples of + from MappingPackage4
--R
--Rf:=(x:INT):INT +-> 3*x 
--Rg:=(x:INT):INT +-> 2*x+3 
--R(f+g)(4)
--R
--R
--RExamples of + from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rm+m
--R
--R
--RExamples of + from OutputForm
--R
--R
--RExamples of + from Pattern
--R
--R
--RExamples of + from StreamTaylorSeriesOperations
--R
--R
--RExamples of + from TubePlotTools
--R
--R
--RExamples of + from VectorCategory
--R
--E 56

--S 57 of 127
)d op -
 

There are 13 exposed functions called - :
   [1] (D,D) -> D from D if D has ABELGRP
   [2] D -> D from D if D has ABELGRP
   [3] (CardinalNumber,CardinalNumber) -> Union(CardinalNumber,"failed"
            )
            from CardinalNumber
   [4] (Database D1,Database D1) -> Database D1 from Database D1
            if D1 has OrderedSet with 
               ?.? : (%,Symbol) -> String
               display : % -> Void
               fullDisplay : % -> Void
   [5] (Equation D1,D1) -> Equation D1 from Equation D1
            if D1 has ABELGRP and D1 has TYPE
   [6] (D1,Equation D1) -> Equation D1 from Equation D1
            if D1 has ABELGRP and D1 has TYPE
   [7] (D,D) -> D from D
            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
            
   [8] D -> D from D
            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
            
   [9] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,D3
            )
            if D2 has SETCAT and D3 has RING
   [10] D -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [11] (D,D) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [12] (D,D) -> D from D
            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP
   [13] D -> D from D
            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP

There are 5 unexposed functions called - :
   [1] OutputForm -> OutputForm from OutputForm
   [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
   [3] (Stream D2,Stream D2) -> Stream D2 from 
            StreamTaylorSeriesOperations D2
            if D2 has RING
   [4] Stream D2 -> Stream D2 from StreamTaylorSeriesOperations D2
            if D2 has RING
   [5] (Point DoubleFloat,Point DoubleFloat) -> Point DoubleFloat
            from TubePlotTools

Examples of - from AbelianGroup


Examples of - from CardinalNumber

c2:=2::CardinalNumber 
c2-c2 
A1:=Aleph 1 
A1-c2


Examples of - from Database


Examples of - from Equation


Examples of - from GradedModule


Examples of - from MappingPackage4

f:=(x:INT):INT +-> 3*x 
g:=(x:INT):INT +-> 2*x+3 
(f-g)(4)


Examples of - from MatrixCategory

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
-m

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
m-m


Examples of - from OutputForm


Examples of - from StreamTaylorSeriesOperations


Examples of - from TubePlotTools


Examples of - from VectorCategory

--R 
--R
--RThere are 13 exposed functions called - :
--R   [1] (D,D) -> D from D if D has ABELGRP
--R   [2] D -> D from D if D has ABELGRP
--R   [3] (CardinalNumber,CardinalNumber) -> Union(CardinalNumber,"failed"
--R            )
--R            from CardinalNumber
--R   [4] (Database D1,Database D1) -> Database D1 from Database D1
--R            if D1 has OrderedSet with 
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [5] (Equation D1,D1) -> Equation D1 from Equation D1
--R            if D1 has ABELGRP and D1 has TYPE
--R   [6] (D1,Equation D1) -> Equation D1 from Equation D1
--R            if D1 has ABELGRP and D1 has TYPE
--R   [7] (D,D) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R            
--R   [8] D -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R            
--R   [9] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,D3
--R            )
--R            if D2 has SETCAT and D3 has RING
--R   [10] D -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [11] (D,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [12] (D,D) -> D from D
--R            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP
--R   [13] D -> D from D
--R            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP
--R
--RThere are 5 unexposed functions called - :
--R   [1] OutputForm -> OutputForm from OutputForm
--R   [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [3] (Stream D2,Stream D2) -> Stream D2 from 
--R            StreamTaylorSeriesOperations D2
--R            if D2 has RING
--R   [4] Stream D2 -> Stream D2 from StreamTaylorSeriesOperations D2
--R            if D2 has RING
--R   [5] (Point DoubleFloat,Point DoubleFloat) -> Point DoubleFloat
--R            from TubePlotTools
--R
--RExamples of - from AbelianGroup
--R
--R
--RExamples of - from CardinalNumber
--R
--Rc2:=2::CardinalNumber 
--Rc2-c2 
--RA1:=Aleph 1 
--RA1-c2
--R
--R
--RExamples of - from Database
--R
--R
--RExamples of - from Equation
--R
--R
--RExamples of - from GradedModule
--R
--R
--RExamples of - from MappingPackage4
--R
--Rf:=(x:INT):INT +-> 3*x 
--Rg:=(x:INT):INT +-> 2*x+3 
--R(f-g)(4)
--R
--R
--RExamples of - from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--R-m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rm-m
--R
--R
--RExamples of - from OutputForm
--R
--R
--RExamples of - from StreamTaylorSeriesOperations
--R
--R
--RExamples of - from TubePlotTools
--R
--R
--RExamples of - from VectorCategory
--R
--E 57

--S 58 of 127
)d op /
 

There are 14 exposed functions called / :
   [1] (D,D1) -> D from D
            if D has AMR(D1,D2) and D1 has RING and D2 has OAMON and D1
            has FIELD
   [2] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
   [3] (D,D) -> D from D
            if D = EQ D1 and D1 has FIELD and D1 has TYPE or D = EQ D1 
            and D1 has GROUP and D1 has TYPE
   [4] (D,D) -> D from D if D has FIELD
   [5] (Float,Integer) -> Float from Float
   [6] (SparseMultivariatePolynomial(D2,Kernel D),
            SparseMultivariatePolynomial(D2,Kernel D)) -> D
            from D if D2 has INTDOM and D2 has ORDSET and D has FS D2
         
   [7] (D,D) -> D from D if D has GROUP
   [8] (D,D1) -> D from D
            if D has LIECAT D1 and D1 has COMRING and D1 has FIELD
   [9] ((D2 -> Expression Integer),(D2 -> Expression Integer)) -> (D2
             -> Expression Integer)
            from MappingPackage4(D2,D3) if D2 has SETCAT and D3 has 
            RING
   [10] (D,D1) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1 and D1 has FIELD
   [11] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
            )
            from MyExpression(D1,D2)
            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
            IntegralDomain)
   [12] (D1,D1) -> D from D if D has QFCAT D1 and D1 has INTDOM
   [13] (D,D1) -> D from D
            if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has RING and D4 has
            DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1) and D1 has FIELD
         
   [14] (D,D1) -> D from D if D has VSPACE D1 and D1 has FIELD

There are 12 unexposed functions called / :
   [1] (Vector D2,Vector D2) -> Vector D2
            from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
         
   [2] (InputForm,InputForm) -> InputForm from InputForm
   [3] (D1,D2) -> LocalAlgebra(D1,D3,D2) from LocalAlgebra(D1,D3,D2)
            if D3 has COMRING and D1 has ALGEBRA D3 and D2 has 
            SubsetCategory(Monoid,D3)
   [4] (LocalAlgebra(D2,D3,D1),D1) -> LocalAlgebra(D2,D3,D1)
            from LocalAlgebra(D2,D3,D1)
            if D3 has COMRING and D2 has ALGEBRA D3 and D1 has 
            SubsetCategory(Monoid,D3)
   [5] (D1,D2) -> Localize(D1,D3,D2) from Localize(D1,D3,D2)
            if D3 has COMRING and D1 has MODULE D3 and D2 has 
            SubsetCategory(Monoid,D3)
   [6] (Localize(D2,D3,D1),D1) -> Localize(D2,D3,D1) from Localize(D2,
            D3,D1)
            if D3 has COMRING and D2 has MODULE D3 and D1 has 
            SubsetCategory(Monoid,D3)
   [7] (OutputForm,OutputForm) -> OutputForm from OutputForm
   [8] (OrdinaryWeightedPolynomials(D1,D2,D3,D4),
            OrdinaryWeightedPolynomials(D1,D2,D3,D4)) -> Union(
            OrdinaryWeightedPolynomials(D1,D2,D3,D4),"failed")
            from OrdinaryWeightedPolynomials(D1,D2,D3,D4)
            if D1 has FIELD and D1 has RING and D2: LIST SYMBOL and D3
            : LIST NNI and D4: NNI
   [9] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has 
            SETCAT
   [10] (Stream D2,Stream D2) -> Stream D2 from 
            StreamTaylorSeriesOperations D2
            if D2 has RING
   [11] (WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7),WeightedPolynomials(
            D1,D2,D3,D4,D5,D6,D7)) -> Union(WeightedPolynomials(D1,D2,D3,D4,
            D5,D6,D7),"failed")
            from WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7)
            if D1 has FIELD and D1 has RING and D2 has ORDSET and D3 
            has OAMONS and D5: LIST D2 and D4 has POLYCAT(D1,D3,D2) and
            D6: LIST NNI and D7: NNI
   [12] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
            from XPolynomialRing(D1,D2)
            if D1 has FIELD and D1 has RING and D2 has ORDMON

Examples of / from AbelianMonoidRing


Examples of / from DoubleFloat


Examples of / from Equation


Examples of / from Field


Examples of / from Float


Examples of / from FunctionSpace


Examples of / from Group


Examples of / from InnerNormalBasisFieldFunctions


Examples of / from InputForm


Examples of / from LocalAlgebra


Examples of / from LieAlgebra


Examples of / from Localize


Examples of / from MappingPackage4

p:=(x:EXPR(INT)):EXPR(INT)+->3*x 
q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 
(p/q)(4) 
(p/q)(x)


Examples of / from MatrixCategory

m:=matrix [[2**i for i in 2..4] for j in 1..5] 
m/4


Examples of / from MyExpression


Examples of / from OutputForm


Examples of / from OrdinaryWeightedPolynomials


Examples of / from Pattern


Examples of / from QuotientFieldCategory


Examples of / from RectangularMatrixCategory


Examples of / from StreamTaylorSeriesOperations


Examples of / from VectorSpace


Examples of / from WeightedPolynomials


Examples of / from XPolynomialRing

--R 
--R
--RThere are 14 exposed functions called / :
--R   [1] (D,D1) -> D from D
--R            if D has AMR(D1,D2) and D1 has RING and D2 has OAMON and D1
--R            has FIELD
--R   [2] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
--R   [3] (D,D) -> D from D
--R            if D = EQ D1 and D1 has FIELD and D1 has TYPE or D = EQ D1 
--R            and D1 has GROUP and D1 has TYPE
--R   [4] (D,D) -> D from D if D has FIELD
--R   [5] (Float,Integer) -> Float from Float
--R   [6] (SparseMultivariatePolynomial(D2,Kernel D),
--R            SparseMultivariatePolynomial(D2,Kernel D)) -> D
--R            from D if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R         
--R   [7] (D,D) -> D from D if D has GROUP
--R   [8] (D,D1) -> D from D
--R            if D has LIECAT D1 and D1 has COMRING and D1 has FIELD
--R   [9] ((D2 -> Expression Integer),(D2 -> Expression Integer)) -> (D2
--R             -> Expression Integer)
--R            from MappingPackage4(D2,D3) if D2 has SETCAT and D3 has 
--R            RING
--R   [10] (D,D1) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1 and D1 has FIELD
--R   [11] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
--R            )
--R            from MyExpression(D1,D2)
--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [12] (D1,D1) -> D from D if D has QFCAT D1 and D1 has INTDOM
--R   [13] (D,D1) -> D from D
--R            if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has RING and D4 has
--R            DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1) and D1 has FIELD
--R         
--R   [14] (D,D1) -> D from D if D has VSPACE D1 and D1 has FIELD
--R
--RThere are 12 unexposed functions called / :
--R   [1] (Vector D2,Vector D2) -> Vector D2
--R            from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
--R         
--R   [2] (InputForm,InputForm) -> InputForm from InputForm
--R   [3] (D1,D2) -> LocalAlgebra(D1,D3,D2) from LocalAlgebra(D1,D3,D2)
--R            if D3 has COMRING and D1 has ALGEBRA D3 and D2 has 
--R            SubsetCategory(Monoid,D3)
--R   [4] (LocalAlgebra(D2,D3,D1),D1) -> LocalAlgebra(D2,D3,D1)
--R            from LocalAlgebra(D2,D3,D1)
--R            if D3 has COMRING and D2 has ALGEBRA D3 and D1 has 
--R            SubsetCategory(Monoid,D3)
--R   [5] (D1,D2) -> Localize(D1,D3,D2) from Localize(D1,D3,D2)
--R            if D3 has COMRING and D1 has MODULE D3 and D2 has 
--R            SubsetCategory(Monoid,D3)
--R   [6] (Localize(D2,D3,D1),D1) -> Localize(D2,D3,D1) from Localize(D2,
--R            D3,D1)
--R            if D3 has COMRING and D2 has MODULE D3 and D1 has 
--R            SubsetCategory(Monoid,D3)
--R   [7] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [8] (OrdinaryWeightedPolynomials(D1,D2,D3,D4),
--R            OrdinaryWeightedPolynomials(D1,D2,D3,D4)) -> Union(
--R            OrdinaryWeightedPolynomials(D1,D2,D3,D4),"failed")
--R            from OrdinaryWeightedPolynomials(D1,D2,D3,D4)
--R            if D1 has FIELD and D1 has RING and D2: LIST SYMBOL and D3
--R            : LIST NNI and D4: NNI
--R   [9] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has 
--R            SETCAT
--R   [10] (Stream D2,Stream D2) -> Stream D2 from 
--R            StreamTaylorSeriesOperations D2
--R            if D2 has RING
--R   [11] (WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7),WeightedPolynomials(
--R            D1,D2,D3,D4,D5,D6,D7)) -> Union(WeightedPolynomials(D1,D2,D3,D4,
--R            D5,D6,D7),"failed")
--R            from WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7)
--R            if D1 has FIELD and D1 has RING and D2 has ORDSET and D3 
--R            has OAMONS and D5: LIST D2 and D4 has POLYCAT(D1,D3,D2) and
--R            D6: LIST NNI and D7: NNI
--R   [12] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
--R            from XPolynomialRing(D1,D2)
--R            if D1 has FIELD and D1 has RING and D2 has ORDMON
--R
--RExamples of / from AbelianMonoidRing
--R
--R
--RExamples of / from DoubleFloat
--R
--R
--RExamples of / from Equation
--R
--R
--RExamples of / from Field
--R
--R
--RExamples of / from Float
--R
--R
--RExamples of / from FunctionSpace
--R
--R
--RExamples of / from Group
--R
--R
--RExamples of / from InnerNormalBasisFieldFunctions
--R
--R
--RExamples of / from InputForm
--R
--R
--RExamples of / from LocalAlgebra
--R
--R
--RExamples of / from LieAlgebra
--R
--R
--RExamples of / from Localize
--R
--R
--RExamples of / from MappingPackage4
--R
--Rp:=(x:EXPR(INT)):EXPR(INT)+->3*x 
--Rq:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 
--R(p/q)(4) 
--R(p/q)(x)
--R
--R
--RExamples of / from MatrixCategory
--R
--Rm:=matrix [[2**i for i in 2..4] for j in 1..5] 
--Rm/4
--R
--R
--RExamples of / from MyExpression
--R
--R
--RExamples of / from OutputForm
--R
--R
--RExamples of / from OrdinaryWeightedPolynomials
--R
--R
--RExamples of / from Pattern
--R
--R
--RExamples of / from QuotientFieldCategory
--R
--R
--RExamples of / from RectangularMatrixCategory
--R
--R
--RExamples of / from StreamTaylorSeriesOperations
--R
--R
--RExamples of / from VectorSpace
--R
--R
--RExamples of / from WeightedPolynomials
--R
--R
--RExamples of / from XPolynomialRing
--R
--E 58

--S 59 of 127
)d op integralBasis
 

There is one exposed function called integralBasis :
   [1]  -> Vector D from D
            if D2 has UFD and D3 has UPOLYC D2 and D4 has UPOLYC FRAC 
            D3 and D has FFCAT(D2,D3,D4)

There are 4 unexposed functions called integralBasis :
   [1]  -> Record(basis: Matrix D2,basisDen: D2,basisInv: Matrix D2)
            from FunctionFieldIntegralBasis(D2,D3,D4)
            if D2 has EuclideanDomain with 
               squareFree : % -> Factored % and D3 has UPOLYC D2 
            and D4 has FRAMALG(D2,D3)
   [2]  -> Record(basis: Matrix Integer,basisDen: Integer,basisInv: 
            Matrix Integer)
            from NumberFieldIntegralBasis(D2,D3)
            if D2 has UPOLYC INT and D3 has FRAMALG(INT,D2)
   [3]  -> Record(basis: Matrix D3,basisDen: D3,basisInv: Matrix D3)
            from PAdicWildFunctionFieldIntegralBasis(D2,D3,D4,D5)
            if D2 has FFIELDC and D3 has UPOLYC D2 and D4 has UPOLYC D3
            and D5 has MONOGEN(D3,D4)
   [4]  -> Record(basis: Matrix D3,basisDen: D3,basisInv: Matrix D3)
            from WildFunctionFieldIntegralBasis(D2,D3,D4,D5)
            if D2 has FFIELDC and D3 has UPOLYC D2 and D4 has UPOLYC D3
            and D5 has FRAMALG(D3,D4)

Examples of integralBasis from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
integralBasis()$R


Examples of integralBasis from FunctionFieldIntegralBasis


Examples of integralBasis from NumberFieldIntegralBasis


Examples of integralBasis from PAdicWildFunctionFieldIntegralBasis


Examples of integralBasis from WildFunctionFieldIntegralBasis

--R 
--R
--RThere is one exposed function called integralBasis :
--R   [1]  -> Vector D from D
--R            if D2 has UFD and D3 has UPOLYC D2 and D4 has UPOLYC FRAC 
--R            D3 and D has FFCAT(D2,D3,D4)
--R
--RThere are 4 unexposed functions called integralBasis :
--R   [1]  -> Record(basis: Matrix D2,basisDen: D2,basisInv: Matrix D2)
--R            from FunctionFieldIntegralBasis(D2,D3,D4)
--R            if D2 has EuclideanDomain with 
--R               squareFree : % -> Factored % and D3 has UPOLYC D2 
--R            and D4 has FRAMALG(D2,D3)
--R   [2]  -> Record(basis: Matrix Integer,basisDen: Integer,basisInv: 
--R            Matrix Integer)
--R            from NumberFieldIntegralBasis(D2,D3)
--R            if D2 has UPOLYC INT and D3 has FRAMALG(INT,D2)
--R   [3]  -> Record(basis: Matrix D3,basisDen: D3,basisInv: Matrix D3)
--R            from PAdicWildFunctionFieldIntegralBasis(D2,D3,D4,D5)
--R            if D2 has FFIELDC and D3 has UPOLYC D2 and D4 has UPOLYC D3
--R            and D5 has MONOGEN(D3,D4)
--R   [4]  -> Record(basis: Matrix D3,basisDen: D3,basisInv: Matrix D3)
--R            from WildFunctionFieldIntegralBasis(D2,D3,D4,D5)
--R            if D2 has FFIELDC and D3 has UPOLYC D2 and D4 has UPOLYC D3
--R            and D5 has FRAMALG(D3,D4)
--R
--RExamples of integralBasis from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RintegralBasis()$R
--R
--R
--RExamples of integralBasis from FunctionFieldIntegralBasis
--R
--R
--RExamples of integralBasis from NumberFieldIntegralBasis
--R
--R
--RExamples of integralBasis from PAdicWildFunctionFieldIntegralBasis
--R
--R
--RExamples of integralBasis from WildFunctionFieldIntegralBasis
--R
--E 59

--S 60 of 127
)d op split
 

There are 8 exposed functions called split :
   [1] D2 -> Factored D2 from AlgFactor D2 if D2 has UPOLYC AN
   [2] (D2,BinarySearchTree D2) -> Record(less: BinarySearchTree D2,
            greater: BinarySearchTree D2)
            from BinarySearchTree D2 if D2 has ORDSET
   [3] IntegrationResult D3 -> IntegrationResult D3
            from IntegrationResultToFunction(D2,D3)
            if D3 has Join(AlgebraicallyClosedFunctionSpace D2,
            TranscendentalFunctionCategory) and D2 has Join(GcdDomain,
            RetractableTo Integer,OrderedSet,LinearlyExplicitRingOver 
            Integer)
   [4] IntegrationResult Fraction Polynomial D2 -> IntegrationResult 
            Fraction Polynomial D2
            from IntegrationResultRFToFunction D2
            if D2 has Join(GcdDomain,RetractableTo Integer,OrderedSet,
            LinearlyExplicitRingOver Integer)
   [5] (List Matrix D4,Vector D4) -> List List Matrix D4
            from RepresentationPackage2 D4 if D4 has FIELD and D4 has 
            RING
   [6] (List Matrix D4,Vector Vector D4) -> List List Matrix D4
            from RepresentationPackage2 D4 if D4 has FIELD and D4 has 
            RING
   [7] (D,CharacterClass) -> List D from D if D has SRAGG
   [8] (D,Character) -> List D from D if D has SRAGG

There is one unexposed function called split :
   [1] (D2,(D2 -> D2)) -> Record(normal: D2,special: D2)
            from MonomialExtensionTools(D4,D2)
            if D2 has UPOLYC D4 and D4 has FIELD

Examples of split from AlgFactor


Examples of split from BinarySearchTree

t1:=binarySearchTree [1,2,3,4] 
split(3,t1)


Examples of split from IntegrationResultToFunction


Examples of split from IntegrationResultRFToFunction


Examples of split from MonomialExtensionTools


Examples of split from RepresentationPackage2


Examples of split from StringAggregate

--R 
--R
--RThere are 8 exposed functions called split :
--R   [1] D2 -> Factored D2 from AlgFactor D2 if D2 has UPOLYC AN
--R   [2] (D2,BinarySearchTree D2) -> Record(less: BinarySearchTree D2,
--R            greater: BinarySearchTree D2)
--R            from BinarySearchTree D2 if D2 has ORDSET
--R   [3] IntegrationResult D3 -> IntegrationResult D3
--R            from IntegrationResultToFunction(D2,D3)
--R            if D3 has Join(AlgebraicallyClosedFunctionSpace D2,
--R            TranscendentalFunctionCategory) and D2 has Join(GcdDomain,
--R            RetractableTo Integer,OrderedSet,LinearlyExplicitRingOver 
--R            Integer)
--R   [4] IntegrationResult Fraction Polynomial D2 -> IntegrationResult 
--R            Fraction Polynomial D2
--R            from IntegrationResultRFToFunction D2
--R            if D2 has Join(GcdDomain,RetractableTo Integer,OrderedSet,
--R            LinearlyExplicitRingOver Integer)
--R   [5] (List Matrix D4,Vector D4) -> List List Matrix D4
--R            from RepresentationPackage2 D4 if D4 has FIELD and D4 has 
--R            RING
--R   [6] (List Matrix D4,Vector Vector D4) -> List List Matrix D4
--R            from RepresentationPackage2 D4 if D4 has FIELD and D4 has 
--R            RING
--R   [7] (D,CharacterClass) -> List D from D if D has SRAGG
--R   [8] (D,Character) -> List D from D if D has SRAGG
--R
--RThere is one unexposed function called split :
--R   [1] (D2,(D2 -> D2)) -> Record(normal: D2,special: D2)
--R            from MonomialExtensionTools(D4,D2)
--R            if D2 has UPOLYC D4 and D4 has FIELD
--R
--RExamples of split from AlgFactor
--R
--R
--RExamples of split from BinarySearchTree
--R
--Rt1:=binarySearchTree [1,2,3,4] 
--Rsplit(3,t1)
--R
--R
--RExamples of split from IntegrationResultToFunction
--R
--R
--RExamples of split from IntegrationResultRFToFunction
--R
--R
--RExamples of split from MonomialExtensionTools
--R
--R
--RExamples of split from RepresentationPackage2
--R
--R
--RExamples of split from StringAggregate
--R
--E 60

--S 61 of 127
)d op qelt
 

There are 3 exposed functions called qelt :
   [1] (D,Integer,Integer) -> D1 from D
            if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG D1 and D4 has 
            FLAGG D1 and D1 has TYPE
   [2] (D,D2) -> D1 from D
            if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
         
   [3] (D,Integer,Integer) -> D1 from D
            if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) 
            and D6 has DIRPCAT(D3,D1) and D1 has RING

Examples of qelt from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
qelt(arr,1,1)


Examples of qelt from EltableAggregate


Examples of qelt from RectangularMatrixCategory

--R 
--R
--RThere are 3 exposed functions called qelt :
--R   [1] (D,Integer,Integer) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG D1 and D4 has 
--R            FLAGG D1 and D1 has TYPE
--R   [2] (D,D2) -> D1 from D
--R            if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
--R         
--R   [3] (D,Integer,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) 
--R            and D6 has DIRPCAT(D3,D1) and D1 has RING
--R
--RExamples of qelt from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rqelt(arr,1,1)
--R
--R
--RExamples of qelt from EltableAggregate
--R
--R
--RExamples of qelt from RectangularMatrixCategory
--R
--E 61

--S 62 of 127
)d op mapUp!
 

There are 2 exposed functions called mapUp! :
   [1] (BalancedBinaryTree D2,BalancedBinaryTree D2,((D2,D2,D2,D2) -> 
            D2)) -> BalancedBinaryTree D2
            from BalancedBinaryTree D2 if D2 has SETCAT
   [2] (BalancedBinaryTree D1,((D1,D1) -> D1)) -> D1
            from BalancedBinaryTree D1 if D1 has SETCAT

Examples of mapUp! from BalancedBinaryTree

T1:=BalancedBinaryTree Integer 
t2:=balancedBinaryTree(4, 0)$T1 
setleaves!(t2,[1,2,3,4]::List(Integer)) 
adder4(i:INT,j:INT,k:INT,l:INT):INT == i+j+k+l 
mapUp!(t2,t2,adder4) 
t2

T1:=BalancedBinaryTree Integer 
t2:=balancedBinaryTree(4, 0)$T1 
setleaves!(t2,[1,2,3,4]::List(Integer)) 
adder(a:Integer,b:Integer):Integer == a+b 
mapUp!(t2,adder) 
t2

--R 
--R
--RThere are 2 exposed functions called mapUp! :
--R   [1] (BalancedBinaryTree D2,BalancedBinaryTree D2,((D2,D2,D2,D2) -> 
--R            D2)) -> BalancedBinaryTree D2
--R            from BalancedBinaryTree D2 if D2 has SETCAT
--R   [2] (BalancedBinaryTree D1,((D1,D1) -> D1)) -> D1
--R            from BalancedBinaryTree D1 if D1 has SETCAT
--R
--RExamples of mapUp! from BalancedBinaryTree
--R
--RT1:=BalancedBinaryTree Integer 
--Rt2:=balancedBinaryTree(4, 0)$T1 
--Rsetleaves!(t2,[1,2,3,4]::List(Integer)) 
--Radder4(i:INT,j:INT,k:INT,l:INT):INT == i+j+k+l 
--RmapUp!(t2,t2,adder4) 
--Rt2
--R
--RT1:=BalancedBinaryTree Integer 
--Rt2:=balancedBinaryTree(4, 0)$T1 
--Rsetleaves!(t2,[1,2,3,4]::List(Integer)) 
--Radder(a:Integer,b:Integer):Integer == a+b 
--RmapUp!(t2,adder) 
--Rt2
--R
--E 62

--S 63 of 127
)d op reindex
 

There is one exposed function called reindex :
   [1] (CartesianTensor(D2,D3,D4),List Integer) -> CartesianTensor(D2,
            D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D2: INT and D3: NNI and D4 has COMRING

Examples of reindex from CartesianTensor

n:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] 
tn:CartesianTensor(1,2,Integer):=n 
p:=product(tn,tn) 
reindex(p,[4,3,2,1])

--R 
--R
--RThere is one exposed function called reindex :
--R   [1] (CartesianTensor(D2,D3,D4),List Integer) -> CartesianTensor(D2,
--R            D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R
--RExamples of reindex from CartesianTensor
--R
--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] 
--Rtn:CartesianTensor(1,2,Integer):=n 
--Rp:=product(tn,tn) 
--Rreindex(p,[4,3,2,1])
--R
--E 63

--S 64 of 127
)d op mapDown!
 

There are 2 exposed functions called mapDown! :
   [1] (BalancedBinaryTree D1,D1,((D1,D1,D1) -> List D1)) -> 
            BalancedBinaryTree D1
            from BalancedBinaryTree D1 if D1 has SETCAT
   [2] (BalancedBinaryTree D1,D1,((D1,D1) -> D1)) -> BalancedBinaryTree
            D1
            from BalancedBinaryTree D1 if D1 has SETCAT

Examples of mapDown! from BalancedBinaryTree

T1:=BalancedBinaryTree Integer 
t2:=balancedBinaryTree(4, 0)$T1 
setleaves!(t2,[1,2,3,4]::List(Integer)) 
adder3(i:Integer,j:Integer,k:Integer):List Integer == [i+j,j+k] 
mapDown!(t2,4::INT,adder3) 
t2

T1:=BalancedBinaryTree Integer 
t2:=balancedBinaryTree(4, 0)$T1 
setleaves!(t2,[1,2,3,4]::List(Integer)) 
adder(i:Integer,j:Integer):Integer == i+j 
mapDown!(t2,4::INT,adder) 
t2

--R 
--R
--RThere are 2 exposed functions called mapDown! :
--R   [1] (BalancedBinaryTree D1,D1,((D1,D1,D1) -> List D1)) -> 
--R            BalancedBinaryTree D1
--R            from BalancedBinaryTree D1 if D1 has SETCAT
--R   [2] (BalancedBinaryTree D1,D1,((D1,D1) -> D1)) -> BalancedBinaryTree
--R            D1
--R            from BalancedBinaryTree D1 if D1 has SETCAT
--R
--RExamples of mapDown! from BalancedBinaryTree
--R
--RT1:=BalancedBinaryTree Integer 
--Rt2:=balancedBinaryTree(4, 0)$T1 
--Rsetleaves!(t2,[1,2,3,4]::List(Integer)) 
--Radder3(i:Integer,j:Integer,k:Integer):List Integer == [i+j,j+k] 
--RmapDown!(t2,4::INT,adder3) 
--Rt2
--R
--RT1:=BalancedBinaryTree Integer 
--Rt2:=balancedBinaryTree(4, 0)$T1 
--Rsetleaves!(t2,[1,2,3,4]::List(Integer)) 
--Radder(i:Integer,j:Integer):Integer == i+j 
--RmapDown!(t2,4::INT,adder) 
--Rt2
--R
--E 64

--S 65 of 127
)d op nrows
 

There are 2 exposed functions called nrows :
   [1] D -> NonNegativeInteger from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] D -> NonNegativeInteger from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

Examples of nrows from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
nrows(arr)


Examples of nrows from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called nrows :
--R   [1] D -> NonNegativeInteger from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] D -> NonNegativeInteger from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of nrows from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rnrows(arr)
--R
--R
--RExamples of nrows from RectangularMatrixCategory
--R
--E 65

--S 66 of 127
)d op row
 

There are 2 exposed functions called row :
   [1] (D,Integer) -> D1 from D
            if D has ARR2CAT(D3,D1,D4) and D3 has TYPE and D4 has FLAGG
            D3 and D1 has FLAGG D3
   [2] (D,Integer) -> D1 from D
            if D has RMATCAT(D3,D4,D5,D1,D6) and D5 has RING and D6 has
            DIRPCAT(D3,D5) and D1 has DIRPCAT(D4,D5)

Examples of row from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
row(arr,1)


Examples of row from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called row :
--R   [1] (D,Integer) -> D1 from D
--R            if D has ARR2CAT(D3,D1,D4) and D3 has TYPE and D4 has FLAGG
--R            D3 and D1 has FLAGG D3
--R   [2] (D,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D5,D1,D6) and D5 has RING and D6 has
--R            DIRPCAT(D3,D5) and D1 has DIRPCAT(D4,D5)
--R
--RExamples of row from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rrow(arr,1)
--R
--R
--RExamples of row from RectangularMatrixCategory
--R
--E 66

--S 67 of 127
)d op ravel
 

There is one exposed function called ravel :
   [1] CartesianTensor(D2,D3,D4) -> List D4 from CartesianTensor(D2,D3,
            D4)
            if D2: INT and D3: NNI and D4 has COMRING

Examples of ravel from CartesianTensor

n:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] 
tn:CartesianTensor(1,2,Integer):=n 
ravel tn

--R 
--R
--RThere is one exposed function called ravel :
--R   [1] CartesianTensor(D2,D3,D4) -> List D4 from CartesianTensor(D2,D3,
--R            D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R
--RExamples of ravel from CartesianTensor
--R
--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] 
--Rtn:CartesianTensor(1,2,Integer):=n 
--Rravel tn
--R
--E 67

--S 68 of 127
)d op inverseIntegralMatrix
 

There is one exposed function called inverseIntegralMatrix :
   [1]  -> Matrix Fraction D3 from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

Examples of inverseIntegralMatrix from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
inverseIntegralMatrix()$R

--R 
--R
--RThere is one exposed function called inverseIntegralMatrix :
--R   [1]  -> Matrix Fraction D3 from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RExamples of inverseIntegralMatrix from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RinverseIntegralMatrix()$R
--R
--E 68

--S 69 of 127
)d op coerce
 

There are 180 exposed functions called coerce :
   [1] D1 -> D from D if D has ALGEBRA D1 and D1 has COMRING
   [2] Vector D2 -> AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
            from AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
            if D2 has FIELD and D5: VECTOR MATRIX D2 and D3: PI and D4
            : LIST SYMBOL
   [3] SparseMultivariatePolynomial(Integer,Kernel AlgebraicNumber) -> 
            AlgebraicNumber
            from AlgebraicNumber
   [4] D2 -> Any from AnyFunctions1 D2 if D2 has TYPE
   [5] Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],
            [construct],MachineFloat) -> Asp10 D2
            from Asp10 D2 if D2: SYMBOL
   [6] Vector FortranExpression([construct],[construct,QUOTEXC],
            MachineFloat) -> Asp19 D2
            from Asp19 D2 if D2: SYMBOL
   [7] FortranExpression([construct,QUOTEX],[construct],MachineFloat)
             -> Asp1 D2
            from Asp1 D2 if D2: SYMBOL
   [8] Matrix FortranExpression([construct],[construct,QUOTEX,QUOTEHESS
            ],MachineFloat) -> Asp20 D2
            from Asp20 D2 if D2: SYMBOL
   [9] FortranExpression([construct],[construct,QUOTEXC],MachineFloat)
             -> Asp24 D2
            from Asp24 D2 if D2: SYMBOL
   [10] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
            MachineFloat) -> Asp31 D2
            from Asp31 D2 if D2: SYMBOL
   [11] Vector FortranExpression([construct],[construct,QUOTEX],
            MachineFloat) -> Asp35 D2
            from Asp35 D2 if D2: SYMBOL
   [12] Vector FortranExpression([construct,QUOTEX,QUOTEEPS],[construct
            ,QUOTEY],MachineFloat) -> Asp41(D2,D3,D4)
            from Asp41(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4: 
            SYMBOL
   [13] Vector FortranExpression([construct,QUOTEEPS],[construct,QUOTE
            YA,QUOTEYB],MachineFloat) -> Asp42(D2,D3,D4)
            from Asp42(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4: 
            SYMBOL
   [14] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
             -> Asp49 D2
            from Asp49 D2 if D2: SYMBOL
   [15] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
             -> Asp4 D2
            from Asp4 D2 if D2: SYMBOL
   [16] Vector FortranExpression([construct],[construct,QUOTEXC],
            MachineFloat) -> Asp50 D2
            from Asp50 D2 if D2: SYMBOL
   [17] Vector FortranExpression([construct],[construct,QUOTEX],
            MachineFloat) -> Asp55 D2
            from Asp55 D2 if D2: SYMBOL
   [18] Vector FortranExpression([construct],[construct,QUOTEX],
            MachineFloat) -> Asp6 D2
            from Asp6 D2 if D2: SYMBOL
   [19] Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],
            MachineFloat) -> Asp73 D2
            from Asp73 D2 if D2: SYMBOL
   [20] Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],
            MachineFloat) -> Asp74 D2
            from Asp74 D2 if D2: SYMBOL
   [21] Matrix FortranExpression([construct,QUOTEX],[construct],
            MachineFloat) -> Asp77 D2
            from Asp77 D2 if D2: SYMBOL
   [22] Vector FortranExpression([construct,QUOTEX],[construct],
            MachineFloat) -> Asp78 D2
            from Asp78 D2 if D2: SYMBOL
   [23] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
            MachineFloat) -> Asp7 D2
            from Asp7 D2 if D2: SYMBOL
   [24] Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],
            [construct],MachineFloat) -> Asp80 D2
            from Asp80 D2 if D2: SYMBOL
   [25] FortranExpression([construct,QUOTEX],[construct,QUOTEY],
            MachineFloat) -> Asp9 D2
            from Asp9 D2 if D2: SYMBOL
   [26] ArrayStack D2 -> OutputForm from ArrayStack D2
            if D2 has SETCAT and D2 has SETCAT
   [27] BinaryExpansion -> RadixExpansion 2 from BinaryExpansion
   [28] BinaryExpansion -> Fraction Integer from BinaryExpansion
   [29] List CartesianTensor(D2,D3,D4) -> CartesianTensor(D2,D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D2: INT and D3: NNI and D4 has COMRING
   [30] List D4 -> CartesianTensor(D2,D3,D4) from CartesianTensor(D2,D3
            ,D4)
            if D4 has COMRING and D2: INT and D3: NNI
   [31] SquareMatrix(D3,D4) -> CartesianTensor(D2,D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D3: NNI and D4 has COMRING and D2: INT
   [32] DirectProduct(D3,D4) -> CartesianTensor(D2,D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D3: NNI and D4 has COMRING and D2: INT
   [33] List D2 -> Database D2 from Database D2
            if D2 has OrderedSet with 
               ?.? : (%,Symbol) -> String
               display : % -> Void
               fullDisplay : % -> Void
   [34] DecimalExpansion -> RadixExpansion 10 from DecimalExpansion
   [35] DecimalExpansion -> Fraction Integer from DecimalExpansion
   [36] Dequeue D2 -> OutputForm from Dequeue D2
            if D2 has SETCAT and D2 has SETCAT
   [37] DataList D2 -> List D2 from DataList D2 if D2 has ORDSET
   [38] List D2 -> DataList D2 from DataList D2 if D2 has ORDSET
   [39] SegmentBinding Expression D3 -> SegmentBinding Float
            from DrawNumericHack D3
            if D3 has Join(OrderedSet,IntegralDomain,ConvertibleTo 
            Float)
   [40] D1 -> D from D if D has DVARCAT D1 and D1 has ORDSET
   [41] FortranCode -> OutputForm from FortranCode
   [42] FortranExpression(D2,D3,D4) -> Expression D4
            from FortranExpression(D2,D3,D4)
            if D2: LIST SYMBOL and D3: LIST SYMBOL and D4 has FMTC
   [43] D2 -> D1 from FiniteFieldHomomorphisms(D2,D3,D1)
            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
   [44] D2 -> D1 from FiniteFieldHomomorphisms(D1,D3,D2)
            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
   [45] D -> XRecursivePolynomial(D2,D3) from D
            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
            
   [46] D -> XDistributedPolynomial(D2,D3) from D
            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
            
   [47] D1 -> D from D
            if D has FLALG(D1,D2) and D1 has ORDSET and D2 has COMRING
            
   [48] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
            from D
            if D has FMC
   [49] FortranCode -> D from D if D has FMC
   [50] List FortranCode -> D from D if D has FMC
   [51] Matrix MachineFloat -> D from D if D has FMC
   [52] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
            from D
            if D has FMFUN
   [53] FortranCode -> D from D if D has FMFUN
   [54] List FortranCode -> D from D if D has FMFUN
   [55] D -> String from D if D has FNCAT
   [56] String -> D from D if D has FNCAT
   [57] D2 -> ScriptFormulaFormat from ScriptFormulaFormat1 D2 if D2 
            has SETCAT
   [58] OutputForm -> ScriptFormulaFormat from ScriptFormulaFormat
   [59] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
            from D
            if D has FORTFN
   [60] FortranCode -> D from D if D has FORTFN
   [61] List FortranCode -> D from D if D has FORTFN
   [62] Equation Expression Complex Float -> FortranProgram(D2,D3,D4,D5
            )
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [63] Equation Expression Float -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [64] Equation Expression Integer -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [65] Expression Complex Float -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [66] Expression Float -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [67] Expression Integer -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [68] Equation Expression MachineComplex -> FortranProgram(D2,D3,D4,
            D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [69] Equation Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [70] Equation Expression MachineInteger -> FortranProgram(D2,D3,D4,
            D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [71] Expression MachineComplex -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [72] Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [73] Expression MachineInteger -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [74] Record(localSymbols: SymbolTable,code: List FortranCode) -> 
            FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [75] List FortranCode -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [76] FortranCode -> FortranProgram(D2,D3,D4,D5)
            from FortranProgram(D2,D3,D4,D5)
            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
            void) and D4: LIST SYMBOL and D5: SYMTAB
   [77] FourierComponent D3 -> FourierSeries(D2,D3) from FourierSeries(
            D2,D3)
            if D3 has Join(OrderedSet,AbelianGroup) and D2 has Join(
            CommutativeRing,Algebra Fraction Integer)
   [78] D1 -> FourierSeries(D1,D2) from FourierSeries(D1,D2)
            if D1 has Join(CommutativeRing,Algebra Fraction Integer) 
            and D2 has Join(OrderedSet,AbelianGroup)
   [79] Fraction Polynomial Fraction D2 -> D from D
            if D2 has INTDOM and D2 has ORDSET and D has FS D2
   [80] Polynomial Fraction D2 -> D from D
            if D2 has INTDOM and D2 has ORDSET and D has FS D2
   [81] Fraction D2 -> D from D
            if D2 has INTDOM and D2 has ORDSET and D has FS D2
   [82] SparseMultivariatePolynomial(D2,Kernel D) -> D from D
            if D2 has RING and D2 has ORDSET and D has FS D2
   [83] FortranScalarType -> SExpression from FortranScalarType
   [84] FortranScalarType -> Symbol from FortranScalarType
   [85] Symbol -> FortranScalarType from FortranScalarType
   [86] String -> FortranScalarType from FortranScalarType
   [87] FortranScalarType -> FortranType from FortranType
   [88] FortranType -> OutputForm from FortranType
   [89] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
            from D
            if D has FVC
   [90] FortranCode -> D from D if D has FVC
   [91] List FortranCode -> D from D if D has FVC
   [92] Vector MachineFloat -> D from D if D has FVC
   [93] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
            from D
            if D has FVFUN
   [94] FortranCode -> D from D if D has FVFUN
   [95] List FortranCode -> D from D if D has FVFUN
   [96] UnivariatePuiseuxSeries(D2,D3,D4) -> 
            GeneralUnivariatePowerSeries(D2,D3,D4)
            from GeneralUnivariatePowerSeries(D2,D3,D4)
            if D2 has RING and D3: SYMBOL and D4: D2
   [97] Variable D3 -> GeneralUnivariatePowerSeries(D2,D3,D4)
            from GeneralUnivariatePowerSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [98] Heap D2 -> OutputForm from Heap D2
            if D2 has SETCAT and D2 has ORDSET
   [99] HexadecimalExpansion -> RadixExpansion 16 from 
            HexadecimalExpansion
   [100] HexadecimalExpansion -> Fraction Integer from 
            HexadecimalExpansion
   [101] String -> IndexCard from IndexCard
   [102] List D5 -> PolynomialIdeals(D2,D3,D4,D5)
            from PolynomialIdeals(D2,D3,D4,D5)
            if D5 has POLYCAT(D2,D3,D4) and D2 has FIELD and D3 has 
            OAMONS and D4 has ORDSET
   [103] D1 -> AssociatedJordanAlgebra(D2,D1)
            from AssociatedJordanAlgebra(D2,D1)
            if D2 has COMRING and D1 has NAALG D2
   [104] D -> D1 from D if D has KOERCE D1 and D1 has TYPE
   [105] D1 -> D from D if D has LALG D1 and D1 has RING
   [106] D1 -> AssociatedLieAlgebra(D2,D1) from AssociatedLieAlgebra(D2
            ,D1)
            if D2 has COMRING and D1 has NAALG D2
   [107] ThreeDimensionalMatrix D2 -> PrimitiveArray PrimitiveArray 
            PrimitiveArray D2
            from ThreeDimensionalMatrix D2 if D2 has SETCAT
   [108] PrimitiveArray PrimitiveArray PrimitiveArray D2 -> 
            ThreeDimensionalMatrix D2
            from ThreeDimensionalMatrix D2 if D2 has SETCAT
   [109] D2 -> (() -> D2) from MappingPackage1 D2 if D2 has SETCAT
   [110] D1 -> D from D
            if D2 has RING and D has MATCAT(D2,D3,D1) and D3 has FLAGG 
            D2 and D1 has FLAGG D2
   [111] MachineComplex -> Complex Float from MachineComplex
   [112] Complex MachineInteger -> MachineComplex from MachineComplex
         
   [113] Complex MachineFloat -> MachineComplex from MachineComplex
   [114] Complex Integer -> MachineComplex from MachineComplex
   [115] Complex Float -> MachineComplex from MachineComplex
   [116] MachineInteger -> MachineFloat from MachineFloat
   [117] MachineFloat -> Float from MachineFloat
   [118] Expression Integer -> Expression MachineInteger from 
            MachineInteger
   [119] OutputForm -> String from MathMLFormat
   [120] Fraction MyUnivariatePolynomial(D2,D3) -> MyExpression(D2,D3)
            from MyExpression(D2,D3)
            if D2: SYMBOL and D3 has Join(Ring,OrderedSet,
            IntegralDomain)
   [121] Polynomial D3 -> MyUnivariatePolynomial(D2,D3)
            from MyUnivariatePolynomial(D2,D3) if D3 has RING and D2: 
            SYMBOL
   [122] Variable D2 -> MyUnivariatePolynomial(D2,D3)
            from MyUnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
            RING
   [123] D1 -> MyUnivariatePolynomial(D2,D1) from 
            MyUnivariatePolynomial(D2,D1)
            if D2: SYMBOL and D1 has RING
   [124] Integer -> D from D if D has NASRING
   [125] Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range
            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
            relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,
            range: List Segment OrderedCompletion DoubleFloat,abserr: 
            DoubleFloat,relerr: DoubleFloat)) -> NumericalIntegrationProblem
            from NumericalIntegrationProblem
   [126] Record(fn: Expression DoubleFloat,range: List Segment 
            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: 
            DoubleFloat) -> NumericalIntegrationProblem
            from NumericalIntegrationProblem
   [127] Record(var: Symbol,fn: Expression DoubleFloat,range: Segment 
            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: 
            DoubleFloat) -> NumericalIntegrationProblem
            from NumericalIntegrationProblem
   [128] NumericalIntegrationProblem -> OutputForm
            from NumericalIntegrationProblem
   [129] D2 -> None from NoneFunctions1 D2 if D2 has TYPE
   [130] Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector 
            Expression DoubleFloat,yinit: List DoubleFloat,intvals: List 
            DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr
            : DoubleFloat) -> NumericalODEProblem
            from NumericalODEProblem
   [131] NumericalODEProblem -> OutputForm from NumericalODEProblem
   [132] OrdinaryDifferentialRing(D2,D1,D3) -> D1
            from OrdinaryDifferentialRing(D2,D1,D3)
            if D1 has PDRING D2 and D2 has SETCAT and D3: D2
   [133] D1 -> OrdinaryDifferentialRing(D2,D1,D3)
            from OrdinaryDifferentialRing(D2,D1,D3)
            if D2 has SETCAT and D3: D2 and D1 has PDRING D2
   [134] Symbol -> OpenMathErrorKind from OpenMathErrorKind
   [135] Union(noa: Record(fn: Expression DoubleFloat,init: List 
            DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List 
            Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),
            lsa: Record(lfn: List Expression DoubleFloat,init: List 
            DoubleFloat)) -> NumericalOptimizationProblem
            from NumericalOptimizationProblem
   [136] Record(lfn: List Expression DoubleFloat,init: List DoubleFloat
            ) -> NumericalOptimizationProblem
            from NumericalOptimizationProblem
   [137] Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: 
            List OrderedCompletion DoubleFloat,cf: List Expression 
            DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> 
            NumericalOptimizationProblem
            from NumericalOptimizationProblem
   [138] NumericalOptimizationProblem -> OutputForm
            from NumericalOptimizationProblem
   [139] Integer -> OrdSetInts from OrdSetInts
   [140] Color -> Palette from Palette
   [141] Polynomial AlgebraicNumber -> Expression Integer
            from PolynomialAN2Expression
   [142] Fraction Polynomial AlgebraicNumber -> Expression Integer
            from PolynomialAN2Expression
   [143] Record(pde: List Expression DoubleFloat,constraints: List 
            Record(start: DoubleFloat,finish: DoubleFloat,grid: 
            NonNegativeInteger,boundaryType: Integer,dStart: Matrix 
            DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression 
            DoubleFloat,st: String,tol: DoubleFloat) -> NumericalPDEProblem
            from NumericalPDEProblem
   [144] NumericalPDEProblem -> OutputForm from NumericalPDEProblem
   [145] PendantTree D2 -> Tree D2 from PendantTree D2 if D2 has SETCAT
            
   [146] List Permutation D2 -> PermutationGroup D2 from 
            PermutationGroup D2
            if D2 has SETCAT
   [147] PermutationGroup D2 -> List Permutation D2 from 
            PermutationGroup D2
            if D2 has SETCAT
   [148] List D2 -> Permutation D2 from Permutation D2 if D2 has SETCAT
            
   [149] List List D2 -> Permutation D2 from Permutation D2 if D2 has 
            SETCAT
   [150] Fraction Factored D2 -> PartialFraction D2 from 
            PartialFraction D2
            if D2 has EUCDOM
   [151] PartialFraction D2 -> Fraction D2 from PartialFraction D2
            if D2 has EUCDOM
   [152] Pi -> Expression D3 from PiCoercions D3
            if D3 has Join(OrderedSet,IntegralDomain)
   [153] Queue D2 -> OutputForm from Queue D2
            if D2 has SETCAT and D2 has SETCAT
   [154] RadixExpansion D2 -> Fraction Integer from RadixExpansion D2 
            if D2: INT
   [155] D2 -> Void from ResolveLatticeCompletion D2 if D2 has TYPE
   [156] Exit -> D1 from ResolveLatticeCompletion D1 if D1 has TYPE
   [157] D1 -> D from D if D has RETRACT D1 and D1 has TYPE
   [158] D2 -> Fraction Polynomial D2 from RationalFunction D2 if D2 
            has INTDOM
   [159] Integer -> D from D if D has RING
   [160] D -> OutputForm from D if D has SPACEC D2 and D2 has RING
   [161] Character -> D from D if D has SRAGG
   [162] Stack D2 -> OutputForm from Stack D2
            if D2 has SETCAT and D2 has SETCAT
   [163] List D2 -> Stream D2 from Stream D2 if D2 has TYPE
   [164] Symbol -> Switch from Switch
   [165] String -> Symbol from Symbol
   [166] SymbolTable -> Table(Symbol,FortranType) from SymbolTable
   [167] Tableau D2 -> OutputForm from Tableau D2 if D2 has SETCAT
   [168] D2 -> TexFormat from TexFormat1 D2 if D2 has SETCAT
   [169] OutputForm -> TexFormat from TexFormat
   [170] Polynomial D2 -> TaylorSeries D2 from TaylorSeries D2 if D2 
            has RING
   [171] Symbol -> TaylorSeries D2 from TaylorSeries D2 if D2 has RING
            
   [172] Variable QUOTE x -> UnivariateFormalPowerSeries D2
            from UnivariateFormalPowerSeries D2 if D2 has RING
   [173] UnivariatePolynomial(QUOTE x,D2) -> 
            UnivariateFormalPowerSeries D2
            from UnivariateFormalPowerSeries D2 if D2 has RING
   [174] D1 -> D from D
            if D2 has RING and D has ULSCCAT(D2,D1) and D1 has UTSCAT 
            D2
   [175] Segment D2 -> UniversalSegment D2 from UniversalSegment D2
            if D2 has TYPE
   [176] Variable D2 -> UnivariatePolynomial(D2,D3)
            from UnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has 
            RING
   [177] D1 -> D from D
            if D2 has RING and D has UPXSCCA(D2,D1) and D1 has ULSCAT 
            D2
   [178] Void -> OutputForm from Void
   [179] D1 -> D from D if D has XALG D1 and D1 has RING
   [180] D1 -> D from D
            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING

There are 50 unexposed functions called coerce :
   [1] Vector Matrix D3 -> Vector Matrix Fraction Polynomial D3
            from CoerceVectorMatrixPackage D3 if D3 has COMRING
   [2] List Integer -> ExtAlgBasis from ExtAlgBasis
   [3] EuclideanModularRing(D2,D1,D3,D4,D5,D6) -> D1
            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
            if D1 has UPOLYC D2 and D2 has COMRING and D3 has ABELMON 
            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
   [4] UnivariatePuiseuxSeries(D3,D4,D5) -> ExponentialExpansion(D2,D3,
            D4,D5)
            from ExponentialExpansion(D2,D3,D4,D5)
            if D3 has Join(AlgebraicallyClosedField,
            TranscendentalFunctionCategory,FunctionSpace D2) and D4: 
            SYMBOL and D5: D3 and D2 has Join(OrderedSet,RetractableTo 
            Integer,LinearlyExplicitRingOver Integer,GcdDomain)
   [5] Vector Fraction Polynomial D2 -> GenericNonAssociativeAlgebra(D2
            ,D3,D4,D5)
            from GenericNonAssociativeAlgebra(D2,D3,D4,D5)
            if D2 has COMRING and D5: VECTOR MATRIX D2 and D3: PI and 
            D4: LIST SYMBOL
   [6] List List Point DoubleFloat -> GraphImage from GraphImage
   [7] GraphImage -> OutputForm from GraphImage
   [8] SparseMultivariatePolynomial(Integer,Kernel InnerAlgebraicNumber
            ) -> InnerAlgebraicNumber
            from InnerAlgebraicNumber
   [9] LieExponentials(D2,D3,D4) -> XPBWPolynomial(D2,D3)
            from LieExponentials(D2,D3,D4)
            if D2 has ORDSET and D3 has Join(CommutativeRing,Module 
            Fraction Integer) and D4: PI
   [10] LieExponentials(D2,D3,D4) -> XDistributedPolynomial(D2,D3)
            from LieExponentials(D2,D3,D4)
            if D2 has ORDSET and D3 has Join(CommutativeRing,Module 
            Fraction Integer) and D4: PI
   [11] LyndonWord D2 -> Magma D2 from LyndonWord D2 if D2 has ORDSET
         
   [12] LyndonWord D2 -> OrderedFreeMonoid D2 from LyndonWord D2
            if D2 has ORDSET
   [13] Magma D2 -> OrderedFreeMonoid D2 from Magma D2 if D2 has ORDSET
            
   [14] D1 -> MakeCachableSet D1 from MakeCachableSet D1 if D1 has 
            SETCAT
   [15] ModularField(D1,D2,D3,D4,D5) -> D1 from ModularField(D1,D2,D3,
            D4,D5)
            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
            D2) -> Union(D1,"failed"))
   [16] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
            if D2 has RING and D1 has UPOLYC D2
   [17] ModuleMonomial(D2,D3,D4) -> Record(index: D2,exponent: D3)
            from ModuleMonomial(D2,D3,D4)
            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index: 
            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
            )
   [18] Record(index: D2,exponent: D3) -> ModuleMonomial(D2,D3,D4)
            from ModuleMonomial(D2,D3,D4)
            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index: 
            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
            )
   [19] ModularRing(D1,D2,D3,D4,D5) -> D1 from ModularRing(D1,D2,D3,D4,
            D5)
            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
            D2) -> Union(D1,"failed"))
   [20] List Record(coef: D2,monom: D3) -> MonoidRing(D2,D3)
            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
   [21] Variable D2 -> UnivariateSkewPolynomial(D2,D3,D4,D5)
            from UnivariateSkewPolynomial(D2,D3,D4,D5)
            if D2: SYMBOL and D3 has RING and D4: AUTOMOR D3 and D5: (
            D3 -> D3)
   [22] Polynomial D2 -> OrdinaryWeightedPolynomials(D2,D3,D4,D5)
            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
            : NNI
   [23] OrdinaryWeightedPolynomials(D2,D3,D4,D5) -> Polynomial D2
            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
            : NNI
   [24] D1 -> PoincareBirkhoffWittLyndonBasis D1
            from PoincareBirkhoffWittLyndonBasis D1 if D1 has ORDSET
         
   [25] PoincareBirkhoffWittLyndonBasis D2 -> OrderedFreeMonoid D2
            from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
         
   [26] Partition -> List Integer from Partition
   [27] D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
            D5)
            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1 
            has POLYCAT(D2,D3,D4) and D5: LIST D1
   [28] RectangularMatrix(D2,D3,D4) -> Matrix D4
            from RectangularMatrix(D2,D3,D4)
            if D2: NNI and D3: NNI and D4 has RING
   [29] D1 -> SparseMultivariateTaylorSeries(D2,D3,D1)
            from SparseMultivariateTaylorSeries(D2,D3,D1)
            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
            D3,D3)
   [30] D1 -> SparseMultivariateTaylorSeries(D2,D1,D3)
            from SparseMultivariateTaylorSeries(D2,D1,D3)
            if D2 has RING and D1 has ORDSET and D3 has POLYCAT(D2,INDE
            D1,D1)
   [31] SquareMatrix(D2,D3) -> Matrix D3 from SquareMatrix(D2,D3)
            if D2: NNI and D3 has RING
   [32] D2 -> Stream D2 from StreamTaylorSeriesOperations D2 if D2 has 
            RING
   [33] Variable D3 -> SparseUnivariateLaurentSeries(D2,D3,D4)
            from SparseUnivariateLaurentSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [34] Variable D3 -> SparseUnivariatePuiseuxSeries(D2,D3,D4)
            from SparseUnivariatePuiseuxSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [35] Variable D3 -> SparseUnivariateTaylorSeries(D2,D3,D4)
            from SparseUnivariateTaylorSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [36] UnivariatePolynomial(D3,D2) -> SparseUnivariateTaylorSeries(D2,
            D3,D4)
            from SparseUnivariateTaylorSeries(D2,D3,D4)
            if D2 has RING and D3: SYMBOL and D4: D2
   [37] PrimitiveArray D2 -> Tuple D2 from Tuple D2 if D2 has TYPE
   [38] Variable D3 -> UnivariateLaurentSeries(D2,D3,D4)
            from UnivariateLaurentSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [39] Variable D3 -> UnivariatePuiseuxSeries(D2,D3,D4)
            from UnivariatePuiseuxSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [40] Variable D3 -> UnivariateTaylorSeries(D2,D3,D4)
            from UnivariateTaylorSeries(D2,D3,D4)
            if D3: SYMBOL and D2 has RING and D4: D2
   [41] UnivariatePolynomial(D3,D2) -> UnivariateTaylorSeries(D2,D3,D4)
            from UnivariateTaylorSeries(D2,D3,D4)
            if D2 has RING and D3: SYMBOL and D4: D2
   [42] Variable D2 -> Symbol from Variable D2 if D2: SYMBOL
   [43] TwoDimensionalViewport -> OutputForm from 
            TwoDimensionalViewport
   [44] GraphImage -> TwoDimensionalViewport from ViewportPackage
   [45] D1 -> WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
            if D2 has RING and D3 has ORDSET and D4 has OAMONS and D5: 
            LIST D3 and D1 has POLYCAT(D2,D4,D3) and D6: LIST NNI and 
            D7: NNI
   [46] WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7) -> D1
            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
            if D1 has POLYCAT(D2,D4,D3) and D2 has RING and D3 has 
            ORDSET and D4 has OAMONS and D5: LIST D3 and D6: LIST NNI 
            and D7: NNI
   [47] XPBWPolynomial(D2,D3) -> XRecursivePolynomial(D2,D3)
            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
            COMRING
   [48] XPBWPolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
            COMRING
   [49] LiePolynomial(D2,D3) -> XPBWPolynomial(D2,D3)
            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
            COMRING
   [50] D1 -> XPolynomialRing(D2,D1) from XPolynomialRing(D2,D1)
            if D2 has RING and D1 has ORDMON

Examples of coerce from Algebra


Examples of coerce from AlgebraGivenByStructuralConstants


Examples of coerce from AlgebraicNumber


Examples of coerce from AnyFunctions1


Examples of coerce from Asp10


Examples of coerce from Asp19


Examples of coerce from Asp1


Examples of coerce from Asp20


Examples of coerce from Asp24


Examples of coerce from Asp31


Examples of coerce from Asp35


Examples of coerce from Asp41


Examples of coerce from Asp42


Examples of coerce from Asp49


Examples of coerce from Asp4


Examples of coerce from Asp50


Examples of coerce from Asp55


Examples of coerce from Asp6


Examples of coerce from Asp73


Examples of coerce from Asp74


Examples of coerce from Asp77


Examples of coerce from Asp78


Examples of coerce from Asp7


Examples of coerce from Asp80


Examples of coerce from Asp9


Examples of coerce from ArrayStack

a:ArrayStack INT:= arrayStack [1,2,3,4,5] 
coerce a


Examples of coerce from BinaryExpansion


Examples of coerce from CartesianTensor

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v 
tm:CartesianTensor(1,2,Integer):=[tv,tv]

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v

v:SquareMatrix(2,Integer):=[[1,2],[3,4]] 
tv:CartesianTensor(1,2,Integer):=v

v:DirectProduct(2,Integer):=directProduct [3,4] 
tv:CartesianTensor(1,2,Integer):=v


Examples of coerce from CoerceVectorMatrixPackage


Examples of coerce from Database


Examples of coerce from DecimalExpansion


Examples of coerce from Dequeue

a:Dequeue INT:= dequeue [1,2,3,4,5] 
coerce a


Examples of coerce from DataList


Examples of coerce from DrawNumericHack


Examples of coerce from DifferentialVariableCategory


Examples of coerce from ExtAlgBasis


Examples of coerce from EuclideanModularRing


Examples of coerce from ExponentialExpansion


Examples of coerce from FortranCode


Examples of coerce from FortranExpression


Examples of coerce from FiniteFieldHomomorphisms


Examples of coerce from FreeLieAlgebra


Examples of coerce from FortranMatrixCategory


Examples of coerce from FortranMatrixFunctionCategory


Examples of coerce from FileNameCategory


Examples of coerce from ScriptFormulaFormat1


Examples of coerce from ScriptFormulaFormat


Examples of coerce from FortranFunctionCategory


Examples of coerce from FortranProgram


Examples of coerce from FourierSeries


Examples of coerce from FunctionSpace


Examples of coerce from FortranScalarType


Examples of coerce from FortranType


Examples of coerce from FortranVectorCategory


Examples of coerce from FortranVectorFunctionCategory


Examples of coerce from GenericNonAssociativeAlgebra


Examples of coerce from GraphImage


Examples of coerce from GeneralUnivariatePowerSeries


Examples of coerce from Heap

a:Heap INT:= heap [1,2,3,4,5] 
coerce a


Examples of coerce from HexadecimalExpansion


Examples of coerce from InnerAlgebraicNumber


Examples of coerce from IndexCard


Examples of coerce from PolynomialIdeals


Examples of coerce from AssociatedJordanAlgebra


Examples of coerce from CoercibleTo


Examples of coerce from LeftAlgebra


Examples of coerce from LieExponentials


Examples of coerce from AssociatedLieAlgebra


Examples of coerce from LyndonWord


Examples of coerce from ThreeDimensionalMatrix


Examples of coerce from Magma


Examples of coerce from MappingPackage1


Examples of coerce from MatrixCategory

coerce([1,2,3])@Matrix(INT)


Examples of coerce from MachineComplex


Examples of coerce from MachineFloat


Examples of coerce from MachineInteger


Examples of coerce from MakeCachableSet


Examples of coerce from MathMLFormat


Examples of coerce from ModularField


Examples of coerce from ModMonic


Examples of coerce from ModuleMonomial


Examples of coerce from ModularRing


Examples of coerce from MonoidRing


Examples of coerce from MyExpression


Examples of coerce from MyUnivariatePolynomial


Examples of coerce from NonAssociativeRing


Examples of coerce from NumericalIntegrationProblem


Examples of coerce from NoneFunctions1


Examples of coerce from NumericalODEProblem


Examples of coerce from OrdinaryDifferentialRing


Examples of coerce from OpenMathErrorKind


Examples of coerce from NumericalOptimizationProblem


Examples of coerce from UnivariateSkewPolynomial


Examples of coerce from OrdSetInts


Examples of coerce from OrdinaryWeightedPolynomials


Examples of coerce from Palette


Examples of coerce from PolynomialAN2Expression


Examples of coerce from PoincareBirkhoffWittLyndonBasis


Examples of coerce from NumericalPDEProblem


Examples of coerce from PendantTree

t1:=ptree([1,2,3]) 
t2:=ptree(t1,ptree([1,2,3])) 
t2::Tree List PositiveInteger


Examples of coerce from PermutationGroup


Examples of coerce from Permutation


Examples of coerce from PartialFraction

(13/74)::PFR(INT)

a:=(13/74)::PFR(INT) 
a::FRAC(INT)


Examples of coerce from PiCoercions


Examples of coerce from Partition


Examples of coerce from Queue

a:Queue INT:= queue [1,2,3,4,5] 
coerce a


Examples of coerce from RadixExpansion


Examples of coerce from ResolveLatticeCompletion


Examples of coerce from ResidueRing


Examples of coerce from RetractableTo


Examples of coerce from RationalFunction


Examples of coerce from Ring


Examples of coerce from RectangularMatrix


Examples of coerce from SparseMultivariateTaylorSeries


Examples of coerce from ThreeSpaceCategory


Examples of coerce from SquareMatrix


Examples of coerce from StringAggregate


Examples of coerce from Stack

a:Stack INT:= stack [1,2,3,4,5] 
coerce a


Examples of coerce from Stream

m:=[1,2,3,4,5,6,7,8,9,10,11,12] 
coerce(m)@Stream(Integer) 
m::Stream(Integer)


Examples of coerce from StreamTaylorSeriesOperations


Examples of coerce from SparseUnivariateLaurentSeries


Examples of coerce from SparseUnivariatePuiseuxSeries


Examples of coerce from SparseUnivariateTaylorSeries


Examples of coerce from Switch


Examples of coerce from Symbol


Examples of coerce from SymbolTable


Examples of coerce from Tableau


Examples of coerce from TexFormat1


Examples of coerce from TexFormat


Examples of coerce from TaylorSeries


Examples of coerce from Tuple

t1:PrimitiveArray(Integer):= [i for i in 1..10] 
t2:=coerce(t1)$Tuple(Integer)


Examples of coerce from UnivariateFormalPowerSeries


Examples of coerce from UnivariateLaurentSeriesConstructorCategory


Examples of coerce from UnivariateLaurentSeries


Examples of coerce from UniversalSegment


Examples of coerce from UnivariatePolynomial


Examples of coerce from UnivariatePuiseuxSeriesConstructorCategory


Examples of coerce from UnivariatePuiseuxSeries


Examples of coerce from UnivariateTaylorSeries


Examples of coerce from Variable


Examples of coerce from TwoDimensionalViewport


Examples of coerce from ViewportPackage


Examples of coerce from Void


Examples of coerce from WeightedPolynomials


Examples of coerce from XAlgebra


Examples of coerce from XFreeAlgebra


Examples of coerce from XPBWPolynomial


Examples of coerce from XPolynomialRing

--R 
--R
--RThere are 180 exposed functions called coerce :
--R   [1] D1 -> D from D if D has ALGEBRA D1 and D1 has COMRING
--R   [2] Vector D2 -> AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
--R            from AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
--R            if D2 has FIELD and D5: VECTOR MATRIX D2 and D3: PI and D4
--R            : LIST SYMBOL
--R   [3] SparseMultivariatePolynomial(Integer,Kernel AlgebraicNumber) -> 
--R            AlgebraicNumber
--R            from AlgebraicNumber
--R   [4] D2 -> Any from AnyFunctions1 D2 if D2 has TYPE
--R   [5] Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],
--R            [construct],MachineFloat) -> Asp10 D2
--R            from Asp10 D2 if D2: SYMBOL
--R   [6] Vector FortranExpression([construct],[construct,QUOTEXC],
--R            MachineFloat) -> Asp19 D2
--R            from Asp19 D2 if D2: SYMBOL
--R   [7] FortranExpression([construct,QUOTEX],[construct],MachineFloat)
--R             -> Asp1 D2
--R            from Asp1 D2 if D2: SYMBOL
--R   [8] Matrix FortranExpression([construct],[construct,QUOTEX,QUOTEHESS
--R            ],MachineFloat) -> Asp20 D2
--R            from Asp20 D2 if D2: SYMBOL
--R   [9] FortranExpression([construct],[construct,QUOTEXC],MachineFloat)
--R             -> Asp24 D2
--R            from Asp24 D2 if D2: SYMBOL
--R   [10] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
--R            MachineFloat) -> Asp31 D2
--R            from Asp31 D2 if D2: SYMBOL
--R   [11] Vector FortranExpression([construct],[construct,QUOTEX],
--R            MachineFloat) -> Asp35 D2
--R            from Asp35 D2 if D2: SYMBOL
--R   [12] Vector FortranExpression([construct,QUOTEX,QUOTEEPS],[construct
--R            ,QUOTEY],MachineFloat) -> Asp41(D2,D3,D4)
--R            from Asp41(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4: 
--R            SYMBOL
--R   [13] Vector FortranExpression([construct,QUOTEEPS],[construct,QUOTE
--R            YA,QUOTEYB],MachineFloat) -> Asp42(D2,D3,D4)
--R            from Asp42(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4: 
--R            SYMBOL
--R   [14] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
--R             -> Asp49 D2
--R            from Asp49 D2 if D2: SYMBOL
--R   [15] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
--R             -> Asp4 D2
--R            from Asp4 D2 if D2: SYMBOL
--R   [16] Vector FortranExpression([construct],[construct,QUOTEXC],
--R            MachineFloat) -> Asp50 D2
--R            from Asp50 D2 if D2: SYMBOL
--R   [17] Vector FortranExpression([construct],[construct,QUOTEX],
--R            MachineFloat) -> Asp55 D2
--R            from Asp55 D2 if D2: SYMBOL
--R   [18] Vector FortranExpression([construct],[construct,QUOTEX],
--R            MachineFloat) -> Asp6 D2
--R            from Asp6 D2 if D2: SYMBOL
--R   [19] Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],
--R            MachineFloat) -> Asp73 D2
--R            from Asp73 D2 if D2: SYMBOL
--R   [20] Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],
--R            MachineFloat) -> Asp74 D2
--R            from Asp74 D2 if D2: SYMBOL
--R   [21] Matrix FortranExpression([construct,QUOTEX],[construct],
--R            MachineFloat) -> Asp77 D2
--R            from Asp77 D2 if D2: SYMBOL
--R   [22] Vector FortranExpression([construct,QUOTEX],[construct],
--R            MachineFloat) -> Asp78 D2
--R            from Asp78 D2 if D2: SYMBOL
--R   [23] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
--R            MachineFloat) -> Asp7 D2
--R            from Asp7 D2 if D2: SYMBOL
--R   [24] Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],
--R            [construct],MachineFloat) -> Asp80 D2
--R            from Asp80 D2 if D2: SYMBOL
--R   [25] FortranExpression([construct,QUOTEX],[construct,QUOTEY],
--R            MachineFloat) -> Asp9 D2
--R            from Asp9 D2 if D2: SYMBOL
--R   [26] ArrayStack D2 -> OutputForm from ArrayStack D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [27] BinaryExpansion -> RadixExpansion 2 from BinaryExpansion
--R   [28] BinaryExpansion -> Fraction Integer from BinaryExpansion
--R   [29] List CartesianTensor(D2,D3,D4) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [30] List D4 -> CartesianTensor(D2,D3,D4) from CartesianTensor(D2,D3
--R            ,D4)
--R            if D4 has COMRING and D2: INT and D3: NNI
--R   [31] SquareMatrix(D3,D4) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D3: NNI and D4 has COMRING and D2: INT
--R   [32] DirectProduct(D3,D4) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D3: NNI and D4 has COMRING and D2: INT
--R   [33] List D2 -> Database D2 from Database D2
--R            if D2 has OrderedSet with 
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [34] DecimalExpansion -> RadixExpansion 10 from DecimalExpansion
--R   [35] DecimalExpansion -> Fraction Integer from DecimalExpansion
--R   [36] Dequeue D2 -> OutputForm from Dequeue D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [37] DataList D2 -> List D2 from DataList D2 if D2 has ORDSET
--R   [38] List D2 -> DataList D2 from DataList D2 if D2 has ORDSET
--R   [39] SegmentBinding Expression D3 -> SegmentBinding Float
--R            from DrawNumericHack D3
--R            if D3 has Join(OrderedSet,IntegralDomain,ConvertibleTo 
--R            Float)
--R   [40] D1 -> D from D if D has DVARCAT D1 and D1 has ORDSET
--R   [41] FortranCode -> OutputForm from FortranCode
--R   [42] FortranExpression(D2,D3,D4) -> Expression D4
--R            from FortranExpression(D2,D3,D4)
--R            if D2: LIST SYMBOL and D3: LIST SYMBOL and D4 has FMTC
--R   [43] D2 -> D1 from FiniteFieldHomomorphisms(D2,D3,D1)
--R            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
--R   [44] D2 -> D1 from FiniteFieldHomomorphisms(D1,D3,D2)
--R            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
--R   [45] D -> XRecursivePolynomial(D2,D3) from D
--R            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
--R            
--R   [46] D -> XDistributedPolynomial(D2,D3) from D
--R            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
--R            
--R   [47] D1 -> D from D
--R            if D has FLALG(D1,D2) and D1 has ORDSET and D2 has COMRING
--R            
--R   [48] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
--R            from D
--R            if D has FMC
--R   [49] FortranCode -> D from D if D has FMC
--R   [50] List FortranCode -> D from D if D has FMC
--R   [51] Matrix MachineFloat -> D from D if D has FMC
--R   [52] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
--R            from D
--R            if D has FMFUN
--R   [53] FortranCode -> D from D if D has FMFUN
--R   [54] List FortranCode -> D from D if D has FMFUN
--R   [55] D -> String from D if D has FNCAT
--R   [56] String -> D from D if D has FNCAT
--R   [57] D2 -> ScriptFormulaFormat from ScriptFormulaFormat1 D2 if D2 
--R            has SETCAT
--R   [58] OutputForm -> ScriptFormulaFormat from ScriptFormulaFormat
--R   [59] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
--R            from D
--R            if D has FORTFN
--R   [60] FortranCode -> D from D if D has FORTFN
--R   [61] List FortranCode -> D from D if D has FORTFN
--R   [62] Equation Expression Complex Float -> FortranProgram(D2,D3,D4,D5
--R            )
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [63] Equation Expression Float -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [64] Equation Expression Integer -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [65] Expression Complex Float -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [66] Expression Float -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [67] Expression Integer -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [68] Equation Expression MachineComplex -> FortranProgram(D2,D3,D4,
--R            D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [69] Equation Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [70] Equation Expression MachineInteger -> FortranProgram(D2,D3,D4,
--R            D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [71] Expression MachineComplex -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [72] Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [73] Expression MachineInteger -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [74] Record(localSymbols: SymbolTable,code: List FortranCode) -> 
--R            FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [75] List FortranCode -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [76] FortranCode -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void: 
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [77] FourierComponent D3 -> FourierSeries(D2,D3) from FourierSeries(
--R            D2,D3)
--R            if D3 has Join(OrderedSet,AbelianGroup) and D2 has Join(
--R            CommutativeRing,Algebra Fraction Integer)
--R   [78] D1 -> FourierSeries(D1,D2) from FourierSeries(D1,D2)
--R            if D1 has Join(CommutativeRing,Algebra Fraction Integer) 
--R            and D2 has Join(OrderedSet,AbelianGroup)
--R   [79] Fraction Polynomial Fraction D2 -> D from D
--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R   [80] Polynomial Fraction D2 -> D from D
--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R   [81] Fraction D2 -> D from D
--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R   [82] SparseMultivariatePolynomial(D2,Kernel D) -> D from D
--R            if D2 has RING and D2 has ORDSET and D has FS D2
--R   [83] FortranScalarType -> SExpression from FortranScalarType
--R   [84] FortranScalarType -> Symbol from FortranScalarType
--R   [85] Symbol -> FortranScalarType from FortranScalarType
--R   [86] String -> FortranScalarType from FortranScalarType
--R   [87] FortranScalarType -> FortranType from FortranType
--R   [88] FortranType -> OutputForm from FortranType
--R   [89] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
--R            from D
--R            if D has FVC
--R   [90] FortranCode -> D from D if D has FVC
--R   [91] List FortranCode -> D from D if D has FVC
--R   [92] Vector MachineFloat -> D from D if D has FVC
--R   [93] Record(localSymbols: SymbolTable,code: List FortranCode) -> D 
--R            from D
--R            if D has FVFUN
--R   [94] FortranCode -> D from D if D has FVFUN
--R   [95] List FortranCode -> D from D if D has FVFUN
--R   [96] UnivariatePuiseuxSeries(D2,D3,D4) -> 
--R            GeneralUnivariatePowerSeries(D2,D3,D4)
--R            from GeneralUnivariatePowerSeries(D2,D3,D4)
--R            if D2 has RING and D3: SYMBOL and D4: D2
--R   [97] Variable D3 -> GeneralUnivariatePowerSeries(D2,D3,D4)
--R            from GeneralUnivariatePowerSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [98] Heap D2 -> OutputForm from Heap D2
--R            if D2 has SETCAT and D2 has ORDSET
--R   [99] HexadecimalExpansion -> RadixExpansion 16 from 
--R            HexadecimalExpansion
--R   [100] HexadecimalExpansion -> Fraction Integer from 
--R            HexadecimalExpansion
--R   [101] String -> IndexCard from IndexCard
--R   [102] List D5 -> PolynomialIdeals(D2,D3,D4,D5)
--R            from PolynomialIdeals(D2,D3,D4,D5)
--R            if D5 has POLYCAT(D2,D3,D4) and D2 has FIELD and D3 has 
--R            OAMONS and D4 has ORDSET
--R   [103] D1 -> AssociatedJordanAlgebra(D2,D1)
--R            from AssociatedJordanAlgebra(D2,D1)
--R            if D2 has COMRING and D1 has NAALG D2
--R   [104] D -> D1 from D if D has KOERCE D1 and D1 has TYPE
--R   [105] D1 -> D from D if D has LALG D1 and D1 has RING
--R   [106] D1 -> AssociatedLieAlgebra(D2,D1) from AssociatedLieAlgebra(D2
--R            ,D1)
--R            if D2 has COMRING and D1 has NAALG D2
--R   [107] ThreeDimensionalMatrix D2 -> PrimitiveArray PrimitiveArray 
--R            PrimitiveArray D2
--R            from ThreeDimensionalMatrix D2 if D2 has SETCAT
--R   [108] PrimitiveArray PrimitiveArray PrimitiveArray D2 -> 
--R            ThreeDimensionalMatrix D2
--R            from ThreeDimensionalMatrix D2 if D2 has SETCAT
--R   [109] D2 -> (() -> D2) from MappingPackage1 D2 if D2 has SETCAT
--R   [110] D1 -> D from D
--R            if D2 has RING and D has MATCAT(D2,D3,D1) and D3 has FLAGG 
--R            D2 and D1 has FLAGG D2
--R   [111] MachineComplex -> Complex Float from MachineComplex
--R   [112] Complex MachineInteger -> MachineComplex from MachineComplex
--R         
--R   [113] Complex MachineFloat -> MachineComplex from MachineComplex
--R   [114] Complex Integer -> MachineComplex from MachineComplex
--R   [115] Complex Float -> MachineComplex from MachineComplex
--R   [116] MachineInteger -> MachineFloat from MachineFloat
--R   [117] MachineFloat -> Float from MachineFloat
--R   [118] Expression Integer -> Expression MachineInteger from 
--R            MachineInteger
--R   [119] OutputForm -> String from MathMLFormat
--R   [120] Fraction MyUnivariatePolynomial(D2,D3) -> MyExpression(D2,D3)
--R            from MyExpression(D2,D3)
--R            if D2: SYMBOL and D3 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [121] Polynomial D3 -> MyUnivariatePolynomial(D2,D3)
--R            from MyUnivariatePolynomial(D2,D3) if D3 has RING and D2: 
--R            SYMBOL
--R   [122] Variable D2 -> MyUnivariatePolynomial(D2,D3)
--R            from MyUnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
--R            RING
--R   [123] D1 -> MyUnivariatePolynomial(D2,D1) from 
--R            MyUnivariatePolynomial(D2,D1)
--R            if D2: SYMBOL and D1 has RING
--R   [124] Integer -> D from D if D has NASRING
--R   [125] Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range
--R            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
--R            relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,
--R            range: List Segment OrderedCompletion DoubleFloat,abserr: 
--R            DoubleFloat,relerr: DoubleFloat)) -> NumericalIntegrationProblem
--R            from NumericalIntegrationProblem
--R   [126] Record(fn: Expression DoubleFloat,range: List Segment 
--R            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: 
--R            DoubleFloat) -> NumericalIntegrationProblem
--R            from NumericalIntegrationProblem
--R   [127] Record(var: Symbol,fn: Expression DoubleFloat,range: Segment 
--R            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: 
--R            DoubleFloat) -> NumericalIntegrationProblem
--R            from NumericalIntegrationProblem
--R   [128] NumericalIntegrationProblem -> OutputForm
--R            from NumericalIntegrationProblem
--R   [129] D2 -> None from NoneFunctions1 D2 if D2 has TYPE
--R   [130] Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector 
--R            Expression DoubleFloat,yinit: List DoubleFloat,intvals: List 
--R            DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr
--R            : DoubleFloat) -> NumericalODEProblem
--R            from NumericalODEProblem
--R   [131] NumericalODEProblem -> OutputForm from NumericalODEProblem
--R   [132] OrdinaryDifferentialRing(D2,D1,D3) -> D1
--R            from OrdinaryDifferentialRing(D2,D1,D3)
--R            if D1 has PDRING D2 and D2 has SETCAT and D3: D2
--R   [133] D1 -> OrdinaryDifferentialRing(D2,D1,D3)
--R            from OrdinaryDifferentialRing(D2,D1,D3)
--R            if D2 has SETCAT and D3: D2 and D1 has PDRING D2
--R   [134] Symbol -> OpenMathErrorKind from OpenMathErrorKind
--R   [135] Union(noa: Record(fn: Expression DoubleFloat,init: List 
--R            DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List 
--R            Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),
--R            lsa: Record(lfn: List Expression DoubleFloat,init: List 
--R            DoubleFloat)) -> NumericalOptimizationProblem
--R            from NumericalOptimizationProblem
--R   [136] Record(lfn: List Expression DoubleFloat,init: List DoubleFloat
--R            ) -> NumericalOptimizationProblem
--R            from NumericalOptimizationProblem
--R   [137] Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: 
--R            List OrderedCompletion DoubleFloat,cf: List Expression 
--R            DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> 
--R            NumericalOptimizationProblem
--R            from NumericalOptimizationProblem
--R   [138] NumericalOptimizationProblem -> OutputForm
--R            from NumericalOptimizationProblem
--R   [139] Integer -> OrdSetInts from OrdSetInts
--R   [140] Color -> Palette from Palette
--R   [141] Polynomial AlgebraicNumber -> Expression Integer
--R            from PolynomialAN2Expression
--R   [142] Fraction Polynomial AlgebraicNumber -> Expression Integer
--R            from PolynomialAN2Expression
--R   [143] Record(pde: List Expression DoubleFloat,constraints: List 
--R            Record(start: DoubleFloat,finish: DoubleFloat,grid: 
--R            NonNegativeInteger,boundaryType: Integer,dStart: Matrix 
--R            DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression 
--R            DoubleFloat,st: String,tol: DoubleFloat) -> NumericalPDEProblem
--R            from NumericalPDEProblem
--R   [144] NumericalPDEProblem -> OutputForm from NumericalPDEProblem
--R   [145] PendantTree D2 -> Tree D2 from PendantTree D2 if D2 has SETCAT
--R            
--R   [146] List Permutation D2 -> PermutationGroup D2 from 
--R            PermutationGroup D2
--R            if D2 has SETCAT
--R   [147] PermutationGroup D2 -> List Permutation D2 from 
--R            PermutationGroup D2
--R            if D2 has SETCAT
--R   [148] List D2 -> Permutation D2 from Permutation D2 if D2 has SETCAT
--R            
--R   [149] List List D2 -> Permutation D2 from Permutation D2 if D2 has 
--R            SETCAT
--R   [150] Fraction Factored D2 -> PartialFraction D2 from 
--R            PartialFraction D2
--R            if D2 has EUCDOM
--R   [151] PartialFraction D2 -> Fraction D2 from PartialFraction D2
--R            if D2 has EUCDOM
--R   [152] Pi -> Expression D3 from PiCoercions D3
--R            if D3 has Join(OrderedSet,IntegralDomain)
--R   [153] Queue D2 -> OutputForm from Queue D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [154] RadixExpansion D2 -> Fraction Integer from RadixExpansion D2 
--R            if D2: INT
--R   [155] D2 -> Void from ResolveLatticeCompletion D2 if D2 has TYPE
--R   [156] Exit -> D1 from ResolveLatticeCompletion D1 if D1 has TYPE
--R   [157] D1 -> D from D if D has RETRACT D1 and D1 has TYPE
--R   [158] D2 -> Fraction Polynomial D2 from RationalFunction D2 if D2 
--R            has INTDOM
--R   [159] Integer -> D from D if D has RING
--R   [160] D -> OutputForm from D if D has SPACEC D2 and D2 has RING
--R   [161] Character -> D from D if D has SRAGG
--R   [162] Stack D2 -> OutputForm from Stack D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [163] List D2 -> Stream D2 from Stream D2 if D2 has TYPE
--R   [164] Symbol -> Switch from Switch
--R   [165] String -> Symbol from Symbol
--R   [166] SymbolTable -> Table(Symbol,FortranType) from SymbolTable
--R   [167] Tableau D2 -> OutputForm from Tableau D2 if D2 has SETCAT
--R   [168] D2 -> TexFormat from TexFormat1 D2 if D2 has SETCAT
--R   [169] OutputForm -> TexFormat from TexFormat
--R   [170] Polynomial D2 -> TaylorSeries D2 from TaylorSeries D2 if D2 
--R            has RING
--R   [171] Symbol -> TaylorSeries D2 from TaylorSeries D2 if D2 has RING
--R            
--R   [172] Variable QUOTE x -> UnivariateFormalPowerSeries D2
--R            from UnivariateFormalPowerSeries D2 if D2 has RING
--R   [173] UnivariatePolynomial(QUOTE x,D2) -> 
--R            UnivariateFormalPowerSeries D2
--R            from UnivariateFormalPowerSeries D2 if D2 has RING
--R   [174] D1 -> D from D
--R            if D2 has RING and D has ULSCCAT(D2,D1) and D1 has UTSCAT 
--R            D2
--R   [175] Segment D2 -> UniversalSegment D2 from UniversalSegment D2
--R            if D2 has TYPE
--R   [176] Variable D2 -> UnivariatePolynomial(D2,D3)
--R            from UnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has 
--R            RING
--R   [177] D1 -> D from D
--R            if D2 has RING and D has UPXSCCA(D2,D1) and D1 has ULSCAT 
--R            D2
--R   [178] Void -> OutputForm from Void
--R   [179] D1 -> D from D if D has XALG D1 and D1 has RING
--R   [180] D1 -> D from D
--R            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
--R
--RThere are 50 unexposed functions called coerce :
--R   [1] Vector Matrix D3 -> Vector Matrix Fraction Polynomial D3
--R            from CoerceVectorMatrixPackage D3 if D3 has COMRING
--R   [2] List Integer -> ExtAlgBasis from ExtAlgBasis
--R   [3] EuclideanModularRing(D2,D1,D3,D4,D5,D6) -> D1
--R            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
--R            if D1 has UPOLYC D2 and D2 has COMRING and D3 has ABELMON 
--R            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
--R            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
--R   [4] UnivariatePuiseuxSeries(D3,D4,D5) -> ExponentialExpansion(D2,D3,
--R            D4,D5)
--R            from ExponentialExpansion(D2,D3,D4,D5)
--R            if D3 has Join(AlgebraicallyClosedField,
--R            TranscendentalFunctionCategory,FunctionSpace D2) and D4: 
--R            SYMBOL and D5: D3 and D2 has Join(OrderedSet,RetractableTo 
--R            Integer,LinearlyExplicitRingOver Integer,GcdDomain)
--R   [5] Vector Fraction Polynomial D2 -> GenericNonAssociativeAlgebra(D2
--R            ,D3,D4,D5)
--R            from GenericNonAssociativeAlgebra(D2,D3,D4,D5)
--R            if D2 has COMRING and D5: VECTOR MATRIX D2 and D3: PI and 
--R            D4: LIST SYMBOL
--R   [6] List List Point DoubleFloat -> GraphImage from GraphImage
--R   [7] GraphImage -> OutputForm from GraphImage
--R   [8] SparseMultivariatePolynomial(Integer,Kernel InnerAlgebraicNumber
--R            ) -> InnerAlgebraicNumber
--R            from InnerAlgebraicNumber
--R   [9] LieExponentials(D2,D3,D4) -> XPBWPolynomial(D2,D3)
--R            from LieExponentials(D2,D3,D4)
--R            if D2 has ORDSET and D3 has Join(CommutativeRing,Module 
--R            Fraction Integer) and D4: PI
--R   [10] LieExponentials(D2,D3,D4) -> XDistributedPolynomial(D2,D3)
--R            from LieExponentials(D2,D3,D4)
--R            if D2 has ORDSET and D3 has Join(CommutativeRing,Module 
--R            Fraction Integer) and D4: PI
--R   [11] LyndonWord D2 -> Magma D2 from LyndonWord D2 if D2 has ORDSET
--R         
--R   [12] LyndonWord D2 -> OrderedFreeMonoid D2 from LyndonWord D2
--R            if D2 has ORDSET
--R   [13] Magma D2 -> OrderedFreeMonoid D2 from Magma D2 if D2 has ORDSET
--R            
--R   [14] D1 -> MakeCachableSet D1 from MakeCachableSet D1 if D1 has 
--R            SETCAT
--R   [15] ModularField(D1,D2,D3,D4,D5) -> D1 from ModularField(D1,D2,D3,
--R            D4,D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [16] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
--R            if D2 has RING and D1 has UPOLYC D2
--R   [17] ModuleMonomial(D2,D3,D4) -> Record(index: D2,exponent: D3)
--R            from ModuleMonomial(D2,D3,D4)
--R            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index: 
--R            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
--R            )
--R   [18] Record(index: D2,exponent: D3) -> ModuleMonomial(D2,D3,D4)
--R            from ModuleMonomial(D2,D3,D4)
--R            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index: 
--R            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
--R            )
--R   [19] ModularRing(D1,D2,D3,D4,D5) -> D1 from ModularRing(D1,D2,D3,D4,
--R            D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [20] List Record(coef: D2,monom: D3) -> MonoidRing(D2,D3)
--R            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
--R   [21] Variable D2 -> UnivariateSkewPolynomial(D2,D3,D4,D5)
--R            from UnivariateSkewPolynomial(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3 has RING and D4: AUTOMOR D3 and D5: (
--R            D3 -> D3)
--R   [22] Polynomial D2 -> OrdinaryWeightedPolynomials(D2,D3,D4,D5)
--R            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
--R            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
--R            : NNI
--R   [23] OrdinaryWeightedPolynomials(D2,D3,D4,D5) -> Polynomial D2
--R            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
--R            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
--R            : NNI
--R   [24] D1 -> PoincareBirkhoffWittLyndonBasis D1
--R            from PoincareBirkhoffWittLyndonBasis D1 if D1 has ORDSET
--R         
--R   [25] PoincareBirkhoffWittLyndonBasis D2 -> OrderedFreeMonoid D2
--R            from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
--R         
--R   [26] Partition -> List Integer from Partition
--R   [27] D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
--R            D5)
--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1 
--R            has POLYCAT(D2,D3,D4) and D5: LIST D1
--R   [28] RectangularMatrix(D2,D3,D4) -> Matrix D4
--R            from RectangularMatrix(D2,D3,D4)
--R            if D2: NNI and D3: NNI and D4 has RING
--R   [29] D1 -> SparseMultivariateTaylorSeries(D2,D3,D1)
--R            from SparseMultivariateTaylorSeries(D2,D3,D1)
--R            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
--R            D3,D3)
--R   [30] D1 -> SparseMultivariateTaylorSeries(D2,D1,D3)
--R            from SparseMultivariateTaylorSeries(D2,D1,D3)
--R            if D2 has RING and D1 has ORDSET and D3 has POLYCAT(D2,INDE
--R            D1,D1)
--R   [31] SquareMatrix(D2,D3) -> Matrix D3 from SquareMatrix(D2,D3)
--R            if D2: NNI and D3 has RING
--R   [32] D2 -> Stream D2 from StreamTaylorSeriesOperations D2 if D2 has 
--R            RING
--R   [33] Variable D3 -> SparseUnivariateLaurentSeries(D2,D3,D4)
--R            from SparseUnivariateLaurentSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [34] Variable D3 -> SparseUnivariatePuiseuxSeries(D2,D3,D4)
--R            from SparseUnivariatePuiseuxSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [35] Variable D3 -> SparseUnivariateTaylorSeries(D2,D3,D4)
--R            from SparseUnivariateTaylorSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [36] UnivariatePolynomial(D3,D2) -> SparseUnivariateTaylorSeries(D2,
--R            D3,D4)
--R            from SparseUnivariateTaylorSeries(D2,D3,D4)
--R            if D2 has RING and D3: SYMBOL and D4: D2
--R   [37] PrimitiveArray D2 -> Tuple D2 from Tuple D2 if D2 has TYPE
--R   [38] Variable D3 -> UnivariateLaurentSeries(D2,D3,D4)
--R            from UnivariateLaurentSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [39] Variable D3 -> UnivariatePuiseuxSeries(D2,D3,D4)
--R            from UnivariatePuiseuxSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [40] Variable D3 -> UnivariateTaylorSeries(D2,D3,D4)
--R            from UnivariateTaylorSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [41] UnivariatePolynomial(D3,D2) -> UnivariateTaylorSeries(D2,D3,D4)
--R            from UnivariateTaylorSeries(D2,D3,D4)
--R            if D2 has RING and D3: SYMBOL and D4: D2
--R   [42] Variable D2 -> Symbol from Variable D2 if D2: SYMBOL
--R   [43] TwoDimensionalViewport -> OutputForm from 
--R            TwoDimensionalViewport
--R   [44] GraphImage -> TwoDimensionalViewport from ViewportPackage
--R   [45] D1 -> WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
--R            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
--R            if D2 has RING and D3 has ORDSET and D4 has OAMONS and D5: 
--R            LIST D3 and D1 has POLYCAT(D2,D4,D3) and D6: LIST NNI and 
--R            D7: NNI
--R   [46] WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7) -> D1
--R            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
--R            if D1 has POLYCAT(D2,D4,D3) and D2 has RING and D3 has 
--R            ORDSET and D4 has OAMONS and D5: LIST D3 and D6: LIST NNI 
--R            and D7: NNI
--R   [47] XPBWPolynomial(D2,D3) -> XRecursivePolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
--R            COMRING
--R   [48] XPBWPolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
--R            COMRING
--R   [49] LiePolynomial(D2,D3) -> XPBWPolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
--R            COMRING
--R   [50] D1 -> XPolynomialRing(D2,D1) from XPolynomialRing(D2,D1)
--R            if D2 has RING and D1 has ORDMON
--R
--RExamples of coerce from Algebra
--R
--R
--RExamples of coerce from AlgebraGivenByStructuralConstants
--R
--R
--RExamples of coerce from AlgebraicNumber
--R
--R
--RExamples of coerce from AnyFunctions1
--R
--R
--RExamples of coerce from Asp10
--R
--R
--RExamples of coerce from Asp19
--R
--R
--RExamples of coerce from Asp1
--R
--R
--RExamples of coerce from Asp20
--R
--R
--RExamples of coerce from Asp24
--R
--R
--RExamples of coerce from Asp31
--R
--R
--RExamples of coerce from Asp35
--R
--R
--RExamples of coerce from Asp41
--R
--R
--RExamples of coerce from Asp42
--R
--R
--RExamples of coerce from Asp49
--R
--R
--RExamples of coerce from Asp4
--R
--R
--RExamples of coerce from Asp50
--R
--R
--RExamples of coerce from Asp55
--R
--R
--RExamples of coerce from Asp6
--R
--R
--RExamples of coerce from Asp73
--R
--R
--RExamples of coerce from Asp74
--R
--R
--RExamples of coerce from Asp77
--R
--R
--RExamples of coerce from Asp78
--R
--R
--RExamples of coerce from Asp7
--R
--R
--RExamples of coerce from Asp80
--R
--R
--RExamples of coerce from Asp9
--R
--R
--RExamples of coerce from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] 
--Rcoerce a
--R
--R
--RExamples of coerce from BinaryExpansion
--R
--R
--RExamples of coerce from CartesianTensor
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v 
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v
--R
--Rv:SquareMatrix(2,Integer):=[[1,2],[3,4]] 
--Rtv:CartesianTensor(1,2,Integer):=v
--R
--Rv:DirectProduct(2,Integer):=directProduct [3,4] 
--Rtv:CartesianTensor(1,2,Integer):=v
--R
--R
--RExamples of coerce from CoerceVectorMatrixPackage
--R
--R
--RExamples of coerce from Database
--R
--R
--RExamples of coerce from DecimalExpansion
--R
--R
--RExamples of coerce from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5] 
--Rcoerce a
--R
--R
--RExamples of coerce from DataList
--R
--R
--RExamples of coerce from DrawNumericHack
--R
--R
--RExamples of coerce from DifferentialVariableCategory
--R
--R
--RExamples of coerce from ExtAlgBasis
--R
--R
--RExamples of coerce from EuclideanModularRing
--R
--R
--RExamples of coerce from ExponentialExpansion
--R
--R
--RExamples of coerce from FortranCode
--R
--R
--RExamples of coerce from FortranExpression
--R
--R
--RExamples of coerce from FiniteFieldHomomorphisms
--R
--R
--RExamples of coerce from FreeLieAlgebra
--R
--R
--RExamples of coerce from FortranMatrixCategory
--R
--R
--RExamples of coerce from FortranMatrixFunctionCategory
--R
--R
--RExamples of coerce from FileNameCategory
--R
--R
--RExamples of coerce from ScriptFormulaFormat1
--R
--R
--RExamples of coerce from ScriptFormulaFormat
--R
--R
--RExamples of coerce from FortranFunctionCategory
--R
--R
--RExamples of coerce from FortranProgram
--R
--R
--RExamples of coerce from FourierSeries
--R
--R
--RExamples of coerce from FunctionSpace
--R
--R
--RExamples of coerce from FortranScalarType
--R
--R
--RExamples of coerce from FortranType
--R
--R
--RExamples of coerce from FortranVectorCategory
--R
--R
--RExamples of coerce from FortranVectorFunctionCategory
--R
--R
--RExamples of coerce from GenericNonAssociativeAlgebra
--R
--R
--RExamples of coerce from GraphImage
--R
--R
--RExamples of coerce from GeneralUnivariatePowerSeries
--R
--R
--RExamples of coerce from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5] 
--Rcoerce a
--R
--R
--RExamples of coerce from HexadecimalExpansion
--R
--R
--RExamples of coerce from InnerAlgebraicNumber
--R
--R
--RExamples of coerce from IndexCard
--R
--R
--RExamples of coerce from PolynomialIdeals
--R
--R
--RExamples of coerce from AssociatedJordanAlgebra
--R
--R
--RExamples of coerce from CoercibleTo
--R
--R
--RExamples of coerce from LeftAlgebra
--R
--R
--RExamples of coerce from LieExponentials
--R
--R
--RExamples of coerce from AssociatedLieAlgebra
--R
--R
--RExamples of coerce from LyndonWord
--R
--R
--RExamples of coerce from ThreeDimensionalMatrix
--R
--R
--RExamples of coerce from Magma
--R
--R
--RExamples of coerce from MappingPackage1
--R
--R
--RExamples of coerce from MatrixCategory
--R
--Rcoerce([1,2,3])@Matrix(INT)
--R
--R
--RExamples of coerce from MachineComplex
--R
--R
--RExamples of coerce from MachineFloat
--R
--R
--RExamples of coerce from MachineInteger
--R
--R
--RExamples of coerce from MakeCachableSet
--R
--R
--RExamples of coerce from MathMLFormat
--R
--R
--RExamples of coerce from ModularField
--R
--R
--RExamples of coerce from ModMonic
--R
--R
--RExamples of coerce from ModuleMonomial
--R
--R
--RExamples of coerce from ModularRing
--R
--R
--RExamples of coerce from MonoidRing
--R
--R
--RExamples of coerce from MyExpression
--R
--R
--RExamples of coerce from MyUnivariatePolynomial
--R
--R
--RExamples of coerce from NonAssociativeRing
--R
--R
--RExamples of coerce from NumericalIntegrationProblem
--R
--R
--RExamples of coerce from NoneFunctions1
--R
--R
--RExamples of coerce from NumericalODEProblem
--R
--R
--RExamples of coerce from OrdinaryDifferentialRing
--R
--R
--RExamples of coerce from OpenMathErrorKind
--R
--R
--RExamples of coerce from NumericalOptimizationProblem
--R
--R
--RExamples of coerce from UnivariateSkewPolynomial
--R
--R
--RExamples of coerce from OrdSetInts
--R
--R
--RExamples of coerce from OrdinaryWeightedPolynomials
--R
--R
--RExamples of coerce from Palette
--R
--R
--RExamples of coerce from PolynomialAN2Expression
--R
--R
--RExamples of coerce from PoincareBirkhoffWittLyndonBasis
--R
--R
--RExamples of coerce from NumericalPDEProblem
--R
--R
--RExamples of coerce from PendantTree
--R
--Rt1:=ptree([1,2,3]) 
--Rt2:=ptree(t1,ptree([1,2,3])) 
--Rt2::Tree List PositiveInteger
--R
--R
--RExamples of coerce from PermutationGroup
--R
--R
--RExamples of coerce from Permutation
--R
--R
--RExamples of coerce from PartialFraction
--R
--R
--RExamples of coerce from PiCoercions
--R
--R
--RExamples of coerce from Partition
--R
--R
--RExamples of coerce from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5] 
--Rcoerce a
--R
--R
--RExamples of coerce from RadixExpansion
--R
--R
--RExamples of coerce from ResolveLatticeCompletion
--R
--R
--RExamples of coerce from ResidueRing
--R
--R
--RExamples of coerce from RetractableTo
--R
--R
--RExamples of coerce from RationalFunction
--R
--R
--RExamples of coerce from Ring
--R
--R
--RExamples of coerce from RectangularMatrix
--R
--R
--RExamples of coerce from SparseMultivariateTaylorSeries
--R
--R
--RExamples of coerce from ThreeSpaceCategory
--R
--R
--RExamples of coerce from SquareMatrix
--R
--R
--RExamples of coerce from StringAggregate
--R
--R
--RExamples of coerce from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5] 
--Rcoerce a
--R
--R
--RExamples of coerce from Stream
--R
--Rm:=[1,2,3,4,5,6,7,8,9,10,11,12] 
--Rcoerce(m)@Stream(Integer) 
--Rm::Stream(Integer)
--R
--R
--RExamples of coerce from StreamTaylorSeriesOperations
--R
--R
--RExamples of coerce from SparseUnivariateLaurentSeries
--R
--R
--RExamples of coerce from SparseUnivariatePuiseuxSeries
--R
--R
--RExamples of coerce from SparseUnivariateTaylorSeries
--R
--R
--RExamples of coerce from Switch
--R
--R
--RExamples of coerce from Symbol
--R
--R
--RExamples of coerce from SymbolTable
--R
--R
--RExamples of coerce from Tableau
--R
--R
--RExamples of coerce from TexFormat1
--R
--R
--RExamples of coerce from TexFormat
--R
--R
--RExamples of coerce from TaylorSeries
--R
--R
--RExamples of coerce from Tuple
--R
--Rt1:PrimitiveArray(Integer):= [i for i in 1..10] 
--Rt2:=coerce(t1)$Tuple(Integer)
--R
--R
--RExamples of coerce from UnivariateFormalPowerSeries
--R
--R
--RExamples of coerce from UnivariateLaurentSeriesConstructorCategory
--R
--R
--RExamples of coerce from UnivariateLaurentSeries
--R
--R
--RExamples of coerce from UniversalSegment
--R
--R
--RExamples of coerce from UnivariatePolynomial
--R
--R
--RExamples of coerce from UnivariatePuiseuxSeriesConstructorCategory
--R
--R
--RExamples of coerce from UnivariatePuiseuxSeries
--R
--R
--RExamples of coerce from UnivariateTaylorSeries
--R
--R
--RExamples of coerce from Variable
--R
--R
--RExamples of coerce from TwoDimensionalViewport
--R
--R
--RExamples of coerce from ViewportPackage
--R
--R
--RExamples of coerce from Void
--R
--R
--RExamples of coerce from WeightedPolynomials
--R
--R
--RExamples of coerce from XAlgebra
--R
--R
--RExamples of coerce from XFreeAlgebra
--R
--R
--RExamples of coerce from XPBWPolynomial
--R
--R
--RExamples of coerce from XPolynomialRing
--R
--E 69

--S 70 of 127
)d op contract
 

There are 3 exposed functions called contract :
   [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
            D2,D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D2: INT and D3: NNI and D4 has COMRING
   [2] (CartesianTensor(D2,D3,D4),Integer,CartesianTensor(D2,D3,D4),
            Integer) -> CartesianTensor(D2,D3,D4)
            from CartesianTensor(D2,D3,D4)
            if D2: INT and D3: NNI and D4 has COMRING
   [3] (PolynomialIdeals(Fraction Integer,DirectProduct(D4,
            NonNegativeInteger),OrderedVariableList D3,
            DistributedMultivariatePolynomial(D3,Fraction Integer)),List 
            OrderedVariableList D3) -> PolynomialIdeals(Fraction Integer,
            DirectProduct(D4,NonNegativeInteger),OrderedVariableList D3,
            DistributedMultivariatePolynomial(D3,Fraction Integer))
            from IdealDecompositionPackage(D3,D4)
            if D3: LIST SYMBOL and D4: NNI

Examples of contract from CartesianTensor

m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
Tm:CartesianTensor(1,2,Integer):=m 
v:DirectProduct(2,Integer):=directProduct [3,4] 
Tv:CartesianTensor(1,2,Integer):=v 
Tmv:=contract(Tm,2,1)

m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
Tm:CartesianTensor(1,2,Integer):=m 
v:DirectProduct(2,Integer):=directProduct [3,4] 
Tv:CartesianTensor(1,2,Integer):=v 
Tmv:=contract(Tm,2,Tv,1)


Examples of contract from IdealDecompositionPackage

--R 
--R
--RThere are 3 exposed functions called contract :
--R   [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
--R            D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [2] (CartesianTensor(D2,D3,D4),Integer,CartesianTensor(D2,D3,D4),
--R            Integer) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [3] (PolynomialIdeals(Fraction Integer,DirectProduct(D4,
--R            NonNegativeInteger),OrderedVariableList D3,
--R            DistributedMultivariatePolynomial(D3,Fraction Integer)),List 
--R            OrderedVariableList D3) -> PolynomialIdeals(Fraction Integer,
--R            DirectProduct(D4,NonNegativeInteger),OrderedVariableList D3,
--R            DistributedMultivariatePolynomial(D3,Fraction Integer))
--R            from IdealDecompositionPackage(D3,D4)
--R            if D3: LIST SYMBOL and D4: NNI
--R
--RExamples of contract from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
--RTm:CartesianTensor(1,2,Integer):=m 
--Rv:DirectProduct(2,Integer):=directProduct [3,4] 
--RTv:CartesianTensor(1,2,Integer):=v 
--RTmv:=contract(Tm,2,1)
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
--RTm:CartesianTensor(1,2,Integer):=m 
--Rv:DirectProduct(2,Integer):=directProduct [3,4] 
--RTv:CartesianTensor(1,2,Integer):=v 
--RTmv:=contract(Tm,2,Tv,1)
--R
--R
--RExamples of contract from IdealDecompositionPackage
--R
--E 70

--S 71 of 127
)d op irreducibleFactor
 

There is one exposed function called irreducibleFactor :
   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
         

Examples of irreducibleFactor from Factored

a:=irreducibleFactor(3,1) 
nthFlag(a,1)

--R 
--R
--RThere is one exposed function called irreducibleFactor :
--R   [1] (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
--R         
--R
--RExamples of irreducibleFactor from Factored
--R
--Ra:=irreducibleFactor(3,1) 
--RnthFlag(a,1)
--R
--E 71

--S 72 of 127
)d op concat
 

There are 10 exposed functions called concat :
   [1] (Result,Result) -> Result from ExpertSystemToolsPackage
   [2] List Result -> Result from ExpertSystemToolsPackage
   [3] List D -> D from D if D has LNAGG D2 and D2 has TYPE
   [4] (D,D) -> D from D if D has LNAGG D1 and D1 has TYPE
   [5] (D1,D) -> D from D if D has LNAGG D1 and D1 has TYPE
   [6] (D,D1) -> D from D if D has LNAGG D1 and D1 has TYPE
   [7] (RoutinesTable,RoutinesTable) -> RoutinesTable from 
            RoutinesTable
   [8] Stream Stream D3 -> Stream D3 from StreamFunctions1 D3 if D3 has
            TYPE
   [9] (D1,D) -> D from D if D has URAGG D1 and D1 has TYPE
   [10] (D,D) -> D from D if D has URAGG D1 and D1 has TYPE

Examples of concat from ExpertSystemToolsPackage


Examples of concat from LinearAggregate


Examples of concat from RoutinesTable


Examples of concat from StreamFunctions1

m:=[i for i in 10..] 
n:=[j for j in 1.. | prime? j] 
p:=[m,n]::Stream(Stream(PositiveInteger)) 
concat(p)


Examples of concat from UnaryRecursiveAggregate

--R 
--R
--RThere are 10 exposed functions called concat :
--R   [1] (Result,Result) -> Result from ExpertSystemToolsPackage
--R   [2] List Result -> Result from ExpertSystemToolsPackage
--R   [3] List D -> D from D if D has LNAGG D2 and D2 has TYPE
--R   [4] (D,D) -> D from D if D has LNAGG D1 and D1 has TYPE
--R   [5] (D1,D) -> D from D if D has LNAGG D1 and D1 has TYPE
--R   [6] (D,D1) -> D from D if D has LNAGG D1 and D1 has TYPE
--R   [7] (RoutinesTable,RoutinesTable) -> RoutinesTable from 
--R            RoutinesTable
--R   [8] Stream Stream D3 -> Stream D3 from StreamFunctions1 D3 if D3 has
--R            TYPE
--R   [9] (D1,D) -> D from D if D has URAGG D1 and D1 has TYPE
--R   [10] (D,D) -> D from D if D has URAGG D1 and D1 has TYPE
--R
--RExamples of concat from ExpertSystemToolsPackage
--R
--R
--RExamples of concat from LinearAggregate
--R
--R
--RExamples of concat from RoutinesTable
--R
--R
--RExamples of concat from StreamFunctions1
--R
--Rm:=[i for i in 10..] 
--Rn:=[j for j in 1.. | prime? j] 
--Rp:=[m,n]::Stream(Stream(PositiveInteger)) 
--Rconcat(p)
--R
--R
--RExamples of concat from UnaryRecursiveAggregate
--R
--E 72

--S 73 of 127
)d op binaryTournament
 

There is one exposed function called binaryTournament :
   [1] List D2 -> BinaryTournament D2 from BinaryTournament D2 if D2 
            has ORDSET

Examples of binaryTournament from BinaryTournament

binaryTournament [1,2,3,4]

--R 
--R
--RThere is one exposed function called binaryTournament :
--R   [1] List D2 -> BinaryTournament D2 from BinaryTournament D2 if D2 
--R            has ORDSET
--R
--RExamples of binaryTournament from BinaryTournament
--R
--RbinaryTournament [1,2,3,4]
--R
--E 73

--S 74 of 127
)d op upperCase
 

There are 3 exposed functions called upperCase :
   [1]  -> CharacterClass from CharacterClass
   [2] Character -> Character from Character
   [3] D -> D from D if D has SRAGG

Examples of upperCase from CharacterClass


Examples of upperCase from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[upperCase c for c in chars]


Examples of upperCase from StringAggregate

--R 
--R
--RThere are 3 exposed functions called upperCase :
--R   [1]  -> CharacterClass from CharacterClass
--R   [2] Character -> Character from Character
--R   [3] D -> D from D if D has SRAGG
--R
--RExamples of upperCase from CharacterClass
--R
--R
--RExamples of upperCase from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[upperCase c for c in chars]
--R
--R
--RExamples of upperCase from StringAggregate
--R
--E 74

--S 75 of 127
)d op exponent
 

There are 3 exposed functions called exponent :
   [1] D -> Integer from D if D has FPS
   [2] Factored D2 -> Integer from Factored D2 if D2 has INTDOM
   [3] MachineFloat -> Integer from MachineFloat

There are 2 unexposed functions called exponent :
   [1] ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) -> 
            UnivariatePuiseuxSeries(D2,D3,D4)
            from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4)
            if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2
            
   [2] ModuleMonomial(D2,D1,D3) -> D1 from ModuleMonomial(D2,D1,D3)
            if D1 has SETCAT and D2 has ORDSET and D3: ((Record(index: 
            D2,exponent: D1),Record(index: D2,exponent: D1)) -> Boolean
            )

Examples of exponent from ExponentialOfUnivariatePuiseuxSeries


Examples of exponent from FloatingPointSystem


Examples of exponent from Factored

f:=nilFactor(y-x,3) 
exponent(f)


Examples of exponent from MachineFloat


Examples of exponent from ModuleMonomial

--R 
--R
--RThere are 3 exposed functions called exponent :
--R   [1] D -> Integer from D if D has FPS
--R   [2] Factored D2 -> Integer from Factored D2 if D2 has INTDOM
--R   [3] MachineFloat -> Integer from MachineFloat
--R
--RThere are 2 unexposed functions called exponent :
--R   [1] ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) -> 
--R            UnivariatePuiseuxSeries(D2,D3,D4)
--R            from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4)
--R            if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2
--R            
--R   [2] ModuleMonomial(D2,D1,D3) -> D1 from ModuleMonomial(D2,D1,D3)
--R            if D1 has SETCAT and D2 has ORDSET and D3: ((Record(index: 
--R            D2,exponent: D1),Record(index: D2,exponent: D1)) -> Boolean
--R            )
--R
--RExamples of exponent from ExponentialOfUnivariatePuiseuxSeries
--R
--R
--RExamples of exponent from FloatingPointSystem
--R
--R
--RExamples of exponent from Factored
--R
--Rf:=nilFactor(y-x,3) 
--Rexponent(f)
--R
--R
--RExamples of exponent from MachineFloat
--R
--R
--RExamples of exponent from ModuleMonomial
--R
--E 75

--S 76 of 127
)d op setRow!
 

There is one exposed function called setRow! :
   [1] (D,Integer,D2) -> D from D
            if D has ARR2CAT(D3,D2,D4) and D3 has TYPE and D2 has FLAGG
            D3 and D4 has FLAGG D3

Examples of setRow! from TwoDimensionalArrayCategory

T1:=TwoDimensionalArray Integer 
arr:T1:= new(5,4,0) 
T2:=OneDimensionalArray Integer 
arow:=construct([1,2,3,4]::List(INT))$T2 
setRow!(arr,1,arow)$T1

--R 
--R
--RThere is one exposed function called setRow! :
--R   [1] (D,Integer,D2) -> D from D
--R            if D has ARR2CAT(D3,D2,D4) and D3 has TYPE and D2 has FLAGG
--R            D3 and D4 has FLAGG D3
--R
--RExamples of setRow! from TwoDimensionalArrayCategory
--R
--RT1:=TwoDimensionalArray Integer 
--Rarr:T1:= new(5,4,0) 
--RT2:=OneDimensionalArray Integer 
--Rarow:=construct([1,2,3,4]::List(INT))$T2 
--RsetRow!(arr,1,arow)$T1
--R
--E 76

--S 77 of 127
)d op generate
 

There are 4 exposed functions called generate :
   [1] (NonNegativeInteger,NonNegativeInteger) -> Vector List Integer
            from HallBasis
   [2] ((D2 -> D2),D2) -> InfiniteTuple D2 from InfiniteTuple D2 if D2 
            has TYPE
   [3] ((D2 -> D2),D2) -> Stream D2 from Stream D2 if D2 has TYPE
   [4] (() -> D2) -> Stream D2 from Stream D2 if D2 has TYPE

Examples of generate from HallBasis


Examples of generate from InfiniteTuple


Examples of generate from Stream

f(x:Integer):Integer == x+10 
generate(f,10)

f():Integer == 1 
generate(f)

--R 
--R
--RThere are 4 exposed functions called generate :
--R   [1] (NonNegativeInteger,NonNegativeInteger) -> Vector List Integer
--R            from HallBasis
--R   [2] ((D2 -> D2),D2) -> InfiniteTuple D2 from InfiniteTuple D2 if D2 
--R            has TYPE
--R   [3] ((D2 -> D2),D2) -> Stream D2 from Stream D2 if D2 has TYPE
--R   [4] (() -> D2) -> Stream D2 from Stream D2 if D2 has TYPE
--R
--RExamples of generate from HallBasis
--R
--R
--RExamples of generate from InfiniteTuple
--R
--R
--RExamples of generate from Stream
--R
--Rf(x:Integer):Integer == x+10 
--Rgenerate(f,10)
--R
--Rf():Integer == 1 
--Rgenerate(f)
--R
--E 77

--S 78 of 127
)d op gcd
 

There are 6 exposed functions called gcd :
   [1] List D -> D from D if D has GCDDOM
   [2] (D,D) -> D from D if D has GCDDOM
   [3] (D1,D1,Integer) -> D1 from ModularDistinctDegreeFactorizer D1
            if D1 has UPOLYC INT
   [4] (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger
            from NonNegativeInteger
   [5] (PositiveInteger,PositiveInteger) -> PositiveInteger
            from PositiveInteger
   [6] (D1,D) -> D1 from D
            if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has 
            OAMONS and D3 has ORDSET and D1 has GCDDOM

There are 6 unexposed functions called gcd :
   [1] List D1 -> D1 from HeuGcd D1 if D1 has UPOLYC INT
   [2] (D1,D1) -> D1 from PolynomialGcdPackage(D2,D3,D4,D1)
            if D2 has OAMONS and D3 has ORDSET and D4 has EUCDOM and D1
            has POLYCAT(D4,D2,D3)
   [3] List D1 -> D1 from PolynomialGcdPackage(D3,D4,D5,D1)
            if D1 has POLYCAT(D5,D3,D4) and D3 has OAMONS and D4 has 
            ORDSET and D5 has EUCDOM
   [4] (SparseUnivariatePolynomial D5,SparseUnivariatePolynomial D5)
             -> SparseUnivariatePolynomial D5
            from PolynomialGcdPackage(D2,D3,D4,D5)
            if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has 
            ORDSET and D4 has EUCDOM
   [5] List SparseUnivariatePolynomial D6 -> SparseUnivariatePolynomial
            D6
            from PolynomialGcdPackage(D3,D4,D5,D6)
            if D3 has OAMONS and D4 has ORDSET and D5 has EUCDOM and D6
            has POLYCAT(D5,D3,D4)
   [6] (D1,D1) -> D1 from PseudoRemainderSequence(D2,D1)
            if D2 has GCDDOM and D2 has INTDOM and D1 has UPOLYC D2

Examples of gcd from GcdDomain


Examples of gcd from HeuGcd

gcd([671*671*x^2-1,671*671*x^2+2*671*x+1]) 
gcd([7*x^2+1,(7*x^2+1)^2])


Examples of gcd from ModularDistinctDegreeFactorizer


Examples of gcd from NonNegativeInteger


Examples of gcd from PolynomialGcdPackage


Examples of gcd from PositiveInteger


Examples of gcd from PseudoRemainderSequence


Examples of gcd from RecursivePolynomialCategory

--R 
--R
--RThere are 6 exposed functions called gcd :
--R   [1] List D -> D from D if D has GCDDOM
--R   [2] (D,D) -> D from D if D has GCDDOM
--R   [3] (D1,D1,Integer) -> D1 from ModularDistinctDegreeFactorizer D1
--R            if D1 has UPOLYC INT
--R   [4] (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger
--R            from NonNegativeInteger
--R   [5] (PositiveInteger,PositiveInteger) -> PositiveInteger
--R            from PositiveInteger
--R   [6] (D1,D) -> D1 from D
--R            if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has 
--R            OAMONS and D3 has ORDSET and D1 has GCDDOM
--R
--RThere are 6 unexposed functions called gcd :
--R   [1] List D1 -> D1 from HeuGcd D1 if D1 has UPOLYC INT
--R   [2] (D1,D1) -> D1 from PolynomialGcdPackage(D2,D3,D4,D1)
--R            if D2 has OAMONS and D3 has ORDSET and D4 has EUCDOM and D1
--R            has POLYCAT(D4,D2,D3)
--R   [3] List D1 -> D1 from PolynomialGcdPackage(D3,D4,D5,D1)
--R            if D1 has POLYCAT(D5,D3,D4) and D3 has OAMONS and D4 has 
--R            ORDSET and D5 has EUCDOM
--R   [4] (SparseUnivariatePolynomial D5,SparseUnivariatePolynomial D5)
--R             -> SparseUnivariatePolynomial D5
--R            from PolynomialGcdPackage(D2,D3,D4,D5)
--R            if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has 
--R            ORDSET and D4 has EUCDOM
--R   [5] List SparseUnivariatePolynomial D6 -> SparseUnivariatePolynomial
--R            D6
--R            from PolynomialGcdPackage(D3,D4,D5,D6)
--R            if D3 has OAMONS and D4 has ORDSET and D5 has EUCDOM and D6
--R            has POLYCAT(D5,D3,D4)
--R   [6] (D1,D1) -> D1 from PseudoRemainderSequence(D2,D1)
--R            if D2 has GCDDOM and D2 has INTDOM and D1 has UPOLYC D2
--R
--RExamples of gcd from GcdDomain
--R
--R
--RExamples of gcd from HeuGcd
--R
--Rgcd([671*671*x^2-1,671*671*x^2+2*671*x+1]) 
--Rgcd([7*x^2+1,(7*x^2+1)^2])
--R
--R
--RExamples of gcd from ModularDistinctDegreeFactorizer
--R
--R
--RExamples of gcd from NonNegativeInteger
--R
--R
--RExamples of gcd from PolynomialGcdPackage
--R
--R
--RExamples of gcd from PositiveInteger
--R
--R
--RExamples of gcd from PseudoRemainderSequence
--R
--R
--RExamples of gcd from RecursivePolynomialCategory
--R
--E 78

--S 79 of 127
)d op binary
 

There is one exposed function called binary :
   [1] Fraction Integer -> BinaryExpansion from BinaryExpansion

There is one unexposed function called binary :
   [1] (InputForm,List InputForm) -> InputForm from InputForm

Examples of binary from BinaryExpansion

binary(22/7)


Examples of binary from InputForm

a:=[1,2,3]::List(InputForm) 
binary(_+::InputForm,a)

--R 
--R
--RThere is one exposed function called binary :
--R   [1] Fraction Integer -> BinaryExpansion from BinaryExpansion
--R
--RThere is one unexposed function called binary :
--R   [1] (InputForm,List InputForm) -> InputForm from InputForm
--R
--RExamples of binary from BinaryExpansion
--R
--Rbinary(22/7)
--R
--R
--RExamples of binary from InputForm
--R
--Ra:=[1,2,3]::List(InputForm) 
--Rbinary(_+::InputForm,a)
--R
--E 79

--S 80 of 127
)d op expand
 

There are 6 exposed functions called expand :
   [1] Factored D1 -> D1 from Factored D1 if D1 has INTDOM
   [2] IntegrationResult D4 -> List D4 from IntegrationResultToFunction
            (D3,D4)
            if D4 has Join(AlgebraicallyClosedFunctionSpace D3,
            TranscendentalFunctionCategory) and D3 has Join(GcdDomain,
            RetractableTo Integer,OrderedSet,LinearlyExplicitRingOver 
            Integer)
   [3] IntegrationResult Fraction Polynomial D3 -> List Expression D3
            from IntegrationResultRFToFunction D3
            if D3 has Join(GcdDomain,RetractableTo Integer,OrderedSet,
            LinearlyExplicitRingOver Integer)
   [4] D -> D1 from D
            if D has SEGXCAT(D2,D1) and D2 has ORDRING and D1 has STAGG
            D2
   [5] List D -> D1 from D
            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
            D3
   [6] D1 -> D1 from TranscendentalManipulations(D2,D1)
            if D2 has Join(OrderedSet,GcdDomain) and D1 has Join(
            FunctionSpace D2,TranscendentalFunctionCategory)

There are 3 unexposed functions called expand :
   [1] (Expression D5,PositiveInteger) -> List Expression D5
            from DegreeReductionPackage(D4,D5)
            if D5 has Join(IntegralDomain,OrderedSet) and D4 has RING
         
   [2] XPolynomial D2 -> XDistributedPolynomial(Symbol,D2) from 
            XPolynomial D2
            if D2 has RING
   [3] XRecursivePolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
            from XRecursivePolynomial(D2,D3)
            if D2 has ORDSET and D3 has RING

Examples of expand from DegreeReductionPackage


Examples of expand from Factored

f:=nilFactor(y-x,3) 
expand(f)


Examples of expand from IntegrationResultToFunction


Examples of expand from IntegrationResultRFToFunction


Examples of expand from SegmentExpansionCategory


Examples of expand from TranscendentalManipulations


Examples of expand from XPolynomial


Examples of expand from XRecursivePolynomial

--R 
--R
--RThere are 6 exposed functions called expand :
--R   [1] Factored D1 -> D1 from Factored D1 if D1 has INTDOM
--R   [2] IntegrationResult D4 -> List D4 from IntegrationResultToFunction
--R            (D3,D4)
--R            if D4 has Join(AlgebraicallyClosedFunctionSpace D3,
--R            TranscendentalFunctionCategory) and D3 has Join(GcdDomain,
--R            RetractableTo Integer,OrderedSet,LinearlyExplicitRingOver 
--R            Integer)
--R   [3] IntegrationResult Fraction Polynomial D3 -> List Expression D3
--R            from IntegrationResultRFToFunction D3
--R            if D3 has Join(GcdDomain,RetractableTo Integer,OrderedSet,
--R            LinearlyExplicitRingOver Integer)
--R   [4] D -> D1 from D
--R            if D has SEGXCAT(D2,D1) and D2 has ORDRING and D1 has STAGG
--R            D2
--R   [5] List D -> D1 from D
--R            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
--R            D3
--R   [6] D1 -> D1 from TranscendentalManipulations(D2,D1)
--R            if D2 has Join(OrderedSet,GcdDomain) and D1 has Join(
--R            FunctionSpace D2,TranscendentalFunctionCategory)
--R
--RThere are 3 unexposed functions called expand :
--R   [1] (Expression D5,PositiveInteger) -> List Expression D5
--R            from DegreeReductionPackage(D4,D5)
--R            if D5 has Join(IntegralDomain,OrderedSet) and D4 has RING
--R         
--R   [2] XPolynomial D2 -> XDistributedPolynomial(Symbol,D2) from 
--R            XPolynomial D2
--R            if D2 has RING
--R   [3] XRecursivePolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
--R            from XRecursivePolynomial(D2,D3)
--R            if D2 has ORDSET and D3 has RING
--R
--RExamples of expand from DegreeReductionPackage
--R
--R
--RExamples of expand from Factored
--R
--Rf:=nilFactor(y-x,3) 
--Rexpand(f)
--R
--R
--RExamples of expand from IntegrationResultToFunction
--R
--R
--RExamples of expand from IntegrationResultRFToFunction
--R
--R
--RExamples of expand from SegmentExpansionCategory
--R
--R
--RExamples of expand from TranscendentalManipulations
--R
--R
--RExamples of expand from XPolynomial
--R
--R
--RExamples of expand from XRecursivePolynomial
--R
--E 80

--S 81 of 127
)d op filterWhile
 

There are 2 exposed functions called filterWhile :
   [1] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
            from InfiniteTuple D2 if D2 has TYPE
   [2] ((D2 -> Boolean),Stream D2) -> Stream D2 from Stream D2 if D2 
            has TYPE

Examples of filterWhile from InfiniteTuple


Examples of filterWhile from Stream

m:=[i for i in 1..] 
f(x:PositiveInteger):Boolean == x < 5 
filterWhile(f,m)

--R 
--R
--RThere are 2 exposed functions called filterWhile :
--R   [1] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
--R            from InfiniteTuple D2 if D2 has TYPE
--R   [2] ((D2 -> Boolean),Stream D2) -> Stream D2 from Stream D2 if D2 
--R            has TYPE
--R
--RExamples of filterWhile from InfiniteTuple
--R
--R
--RExamples of filterWhile from Stream
--R
--Rm:=[i for i in 1..] 
--Rf(x:PositiveInteger):Boolean == x < 5 
--RfilterWhile(f,m)
--R
--E 81

--S 82 of 127
)d op filterUntil
 

There are 2 exposed functions called filterUntil :
   [1] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
            from InfiniteTuple D2 if D2 has TYPE
   [2] ((D2 -> Boolean),Stream D2) -> Stream D2 from Stream D2 if D2 
            has TYPE

Examples of filterUntil from InfiniteTuple


Examples of filterUntil from Stream

m:=[i for i in 1..] 
f(x:PositiveInteger):Boolean == x < 5 
filterUntil(f,m)

--R 
--R
--RThere are 2 exposed functions called filterUntil :
--R   [1] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
--R            from InfiniteTuple D2 if D2 has TYPE
--R   [2] ((D2 -> Boolean),Stream D2) -> Stream D2 from Stream D2 if D2 
--R            has TYPE
--R
--RExamples of filterUntil from InfiniteTuple
--R
--R
--RExamples of filterUntil from Stream
--R
--Rm:=[i for i in 1..] 
--Rf(x:PositiveInteger):Boolean == x < 5 
--RfilterUntil(f,m)
--R
--E 82

--S 83 of 127
)d op select
 

There are 4 exposed functions called select :
   [1] ((D2 -> Boolean),D) -> D from D
            if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE
            
   [2] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
            from InfiniteTuple D2 if D2 has TYPE
   [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has 
            TYPE
   [4] (D,D2) -> Union(D1,"failed") from D
            if D has TSETCAT(D3,D4,D2,D1) and D3 has INTDOM and D4 has 
            OAMONS and D2 has ORDSET and D1 has RPOLCAT(D3,D4,D2)

There is one unexposed function called select :
   [1] (Tuple D1,NonNegativeInteger) -> D1 from Tuple D1 if D1 has TYPE
            

Examples of select from Collection


Examples of select from InfiniteTuple


Examples of select from LazyStreamAggregate

m:=[i for i in 0..] 
select(x+->prime? x,m)


Examples of select from TriangularSetCategory


Examples of select from Tuple

t1:PrimitiveArray(Integer):= [i for i in 1..10] 
t2:=coerce(t1)$Tuple(Integer) 
select(t2,3)

--R 
--R
--RThere are 4 exposed functions called select :
--R   [1] ((D2 -> Boolean),D) -> D from D
--R            if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE
--R            
--R   [2] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
--R            from InfiniteTuple D2 if D2 has TYPE
--R   [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has 
--R            TYPE
--R   [4] (D,D2) -> Union(D1,"failed") from D
--R            if D has TSETCAT(D3,D4,D2,D1) and D3 has INTDOM and D4 has 
--R            OAMONS and D2 has ORDSET and D1 has RPOLCAT(D3,D4,D2)
--R
--RThere is one unexposed function called select :
--R   [1] (Tuple D1,NonNegativeInteger) -> D1 from Tuple D1 if D1 has TYPE
--R            
--R
--RExamples of select from Collection
--R
--R
--RExamples of select from InfiniteTuple
--R
--R
--RExamples of select from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--Rselect(x+->prime? x,m)
--R
--R
--RExamples of select from TriangularSetCategory
--R
--R
--RExamples of select from Tuple
--R
--Rt1:PrimitiveArray(Integer):= [i for i in 1..10] 
--Rt2:=coerce(t1)$Tuple(Integer) 
--Rselect(t2,3)
--R
--E 83

--S 84 of 127
)d op nthFlag
 

There is one exposed function called nthFlag :
   [1] (Factored D3,Integer) -> Union("nil","sqfr","irred","prime")
            from Factored D3 if D3 has INTDOM

Examples of nthFlag from Factored

a:=factor 9720000 
nthFlag(a,2)

--R 
--R
--RThere is one exposed function called nthFlag :
--R   [1] (Factored D3,Integer) -> Union("nil","sqfr","irred","prime")
--R            from Factored D3 if D3 has INTDOM
--R
--RExamples of nthFlag from Factored
--R
--Ra:=factor 9720000 
--RnthFlag(a,2)
--R
--E 84

--S 85 of 127
)d op makeFR
 

There is one exposed function called makeFR :
   [1] (D1,List Record(flg: Union("nil","sqfr","irred","prime"),fctr: 
            D1,xpnt: Integer)) -> Factored D1
            from Factored D1 if D1 has INTDOM

There is one unexposed function called makeFR :
   [1] Record(contp: Integer,factors: List Record(irr: D3,pow: Integer)
            ) -> Factored D3
            from GaloisGroupFactorizer D3 if D3 has UPOLYC INT

Examples of makeFR from Factored

f:=nilFactor(x-y,3) 
g:=factorList f 
makeFR(z,g)


Examples of makeFR from GaloisGroupFactorizer

--R 
--R
--RThere is one exposed function called makeFR :
--R   [1] (D1,List Record(flg: Union("nil","sqfr","irred","prime"),fctr: 
--R            D1,xpnt: Integer)) -> Factored D1
--R            from Factored D1 if D1 has INTDOM
--R
--RThere is one unexposed function called makeFR :
--R   [1] Record(contp: Integer,factors: List Record(irr: D3,pow: Integer)
--R            ) -> Factored D3
--R            from GaloisGroupFactorizer D3 if D3 has UPOLYC INT
--R
--RExamples of makeFR from Factored
--R
--Rf:=nilFactor(x-y,3) 
--Rg:=factorList f 
--RmakeFR(z,g)
--R
--R
--RExamples of makeFR from GaloisGroupFactorizer
--R
--E 85

--S 86 of 127
)d op *
 

There are 34 exposed functions called * :
   [1] (Integer,D) -> D from D if D has ABELGRP
   [2] (NonNegativeInteger,D) -> D from D if D has ABELMON
   [3] (PositiveInteger,D) -> D from D if D has ABELSG
   [4] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) -> 
            CartesianTensor(D1,D2,D3)
            from CartesianTensor(D1,D2,D3)
            if D1: INT and D2: NNI and D3 has COMRING
   [5] (DoubleFloat,Color) -> Color from Color
   [6] (PositiveInteger,Color) -> Color from Color
   [7] (DenavitHartenbergMatrix D2,Point D2) -> Point D2
            from DenavitHartenbergMatrix D2
            if D2 has Join(Field,TranscendentalFunctionCategory)
   [8] (D1,Equation D1) -> Equation D1 from Equation D1
            if D1 has SGROUP and D1 has TYPE
   [9] (Equation D1,D1) -> Equation D1 from Equation D1
            if D1 has SGROUP and D1 has TYPE
   [10] (D1,D2) -> D from D
            if D has FAMONC(D2,D1) and D2 has SETCAT and D1 has CABMON
            
   [11] (D1,D2) -> D from D
            if D has FMCAT(D1,D2) and D1 has RING and D2 has SETCAT
   [12] (D,D1) -> D from D
            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
            
   [13] (D1,D) -> D from D
            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
            
   [14] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
             -> PolynomialIdeals(D1,D2,D3,D4)
            from PolynomialIdeals(D1,D2,D3,D4)
            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
            has POLYCAT(D1,D2,D3)
   [15] (D1,D) -> D from D if D has LMODULE D1 and D1 has RNG
   [16] ((D5 -> D6),(D4 -> D5)) -> (D4 -> D6) from MappingPackage3(D4,
            D5,D6)
            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
   [17] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
            D3)
            if D2 has SETCAT and D3 has RING
   [18] (D1,D) -> D1 from D
            if D has MATCAT(D2,D1,D3) and D2 has RING and D1 has FLAGG 
            D2 and D3 has FLAGG D2
   [19] (D,D1) -> D1 from D
            if D has MATCAT(D2,D3,D1) and D2 has RING and D3 has FLAGG 
            D2 and D1 has FLAGG D2
   [20] (Integer,D) -> D from D
            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
            D2 and D4 has FLAGG D2
   [21] (D,D1) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [22] (D1,D) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [23] (D,D) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
            D1 and D3 has FLAGG D1
   [24] (D,D) -> D from D if D has MONAD
   [25] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
            )
            from MyExpression(D1,D2)
            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
            IntegralDomain)
   [26] (D,D1) -> D from D if D has RMODULE D1 and D1 has RNG
   [27] (D,D) -> D from D if D has SGROUP
   [28] (D1,D) -> D1 from D
            if D has SMATCAT(D2,D3,D1,D4) and D3 has RING and D1 has 
            DIRPCAT(D2,D3) and D4 has DIRPCAT(D2,D3)
   [29] (D,D1) -> D1 from D
            if D has SMATCAT(D2,D3,D4,D1) and D3 has RING and D4 has 
            DIRPCAT(D2,D3) and D1 has DIRPCAT(D2,D3)
   [30] (D,D1) -> D from D
            if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
   [31] (D1,D) -> D from D
            if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
   [32] (Integer,D) -> D from D
            if D has VECTCAT D2 and D2 has TYPE and D2 has ABELGRP
   [33] (D1,D) -> D from D
            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
   [34] (D,D1) -> D from D
            if D has XFALG(D2,D1) and D2 has ORDSET and D1 has RING

There are 23 unexposed functions called * :
   [1] (FreeGroup D1,D1) -> FreeGroup D1 from FreeGroup D1 if D1 has 
            SETCAT
   [2] (D1,FreeGroup D1) -> FreeGroup D1 from FreeGroup D1 if D1 has 
            SETCAT
   [3] (D1,D2) -> FreeModule1(D2,D1) from FreeModule1(D2,D1)
            if D2 has RING and D1 has ORDSET
   [4] (FreeMonoid D1,D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
            SETCAT
   [5] (D1,FreeMonoid D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
            SETCAT
   [6] (D1,GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)) -> 
            GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
            from GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
            if D2: LIST SYMBOL and D3 has COMRING and D5 has DIRPCAT(# 
            D2,NNI) and D6: ((Record(index: D4,exponent: D5),Record(
            index: D4,exponent: D5)) -> Boolean) and D4 has ORDSET and 
            D1 has POLYCAT(D3,D5,OVAR D2)
   [7] (Vector D2,Vector D2) -> Vector D2
            from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
         
   [8] (InputForm,InputForm) -> InputForm from InputForm
   [9] (InnerTaylorSeries D2,Integer) -> InnerTaylorSeries D2
            from InnerTaylorSeries D2 if D2 has RING
   [10] (InnerTaylorSeries D1,D1) -> InnerTaylorSeries D1
            from InnerTaylorSeries D1 if D1 has RING
   [11] (D1,InnerTaylorSeries D1) -> InnerTaylorSeries D1
            from InnerTaylorSeries D1 if D1 has RING
   [12] (Magma D1,Magma D1) -> Magma D1 from Magma D1 if D1 has ORDSET
            
   [13] (OrderedFreeMonoid D1,D1) -> OrderedFreeMonoid D1
            from OrderedFreeMonoid D1 if D1 has ORDSET
   [14] (D1,OrderedFreeMonoid D1) -> OrderedFreeMonoid D1
            from OrderedFreeMonoid D1 if D1 has ORDSET
   [15] (OutputForm,OutputForm) -> OutputForm from OutputForm
   [16] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
            SETCAT
   [17] (D2,Vector D3) -> Vector D3 from PseudoRemainderSequence(D2,D3)
            if D3 has UPOLYC D2 and D2 has INTDOM
   [18] (D1,SparseMultivariateTaylorSeries(D2,D3,D1)) -> 
            SparseMultivariateTaylorSeries(D2,D3,D1)
            from SparseMultivariateTaylorSeries(D2,D3,D1)
            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
            D3,D3)
   [19] (Stream D2,Stream D2) -> Stream D2 from 
            StreamTaylorSeriesOperations D2
            if D2 has RING
   [20] (D2,Stream D2) -> Stream D2 from StreamTaylorSeriesOperations 
            D2
            if D2 has RING
   [21] (Stream D2,D2) -> Stream D2 from StreamTaylorSeriesOperations 
            D2
            if D2 has RING
   [22] (DoubleFloat,Point DoubleFloat) -> Point DoubleFloat from 
            TubePlotTools
   [23] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
            from XPolynomialRing(D1,D2) if D1 has RING and D2 has 
            ORDMON

Examples of * from AbelianGroup


Examples of * from AbelianMonoid


Examples of * from AbelianSemiGroup


Examples of * from CartesianTensor

m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
Tm:CartesianTensor(1,2,Integer):=m 
v:DirectProduct(2,Integer):=directProduct [3,4] 
Tv:CartesianTensor(1,2,Integer):=v 
Tm*Tv


Examples of * from Color


Examples of * from DenavitHartenbergMatrix


Examples of * from Equation


Examples of * from FreeAbelianMonoidCategory


Examples of * from FreeGroup


Examples of * from FreeModule1


Examples of * from FreeModuleCat


Examples of * from FreeMonoid


Examples of * from GeneralModulePolynomial


Examples of * from GradedModule


Examples of * from PolynomialIdeals


Examples of * from InnerNormalBasisFieldFunctions


Examples of * from InputForm


Examples of * from InnerTaylorSeries


Examples of * from LeftModule


Examples of * from Magma


Examples of * from MappingPackage3


Examples of * from MappingPackage4

f:=(x:INT):INT +-> 3*x 
g:=(x:INT):INT +-> 2*x+3 
(f*g)(4)


Examples of * from MatrixCategory

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
r:=transpose([1,2,3,4,5])@Matrix(INT) 
r*m

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
c:=coerce([1,2,3,4,5])@Matrix(INT) 
m*c

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
3*m

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
m*1/3

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
1/3*m

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
m*m


Examples of * from Monad


Examples of * from MyExpression


Examples of * from OrderedFreeMonoid

m1:=(y**3)$OFMONOID(Symbol) 
m1*x

m1:=(x*y*y*z)$OFMONOID(Symbol) 
x*m1


Examples of * from OutputForm


Examples of * from Pattern


Examples of * from PseudoRemainderSequence


Examples of * from RightModule


Examples of * from SemiGroup


Examples of * from SquareMatrixCategory


Examples of * from SparseMultivariateTaylorSeries


Examples of * from StreamTaylorSeriesOperations


Examples of * from TubePlotTools


Examples of * from VectorCategory


Examples of * from XFreeAlgebra


Examples of * from XPolynomialRing

--R 
--R
--RThere are 34 exposed functions called * :
--R   [1] (Integer,D) -> D from D if D has ABELGRP
--R   [2] (NonNegativeInteger,D) -> D from D if D has ABELMON
--R   [3] (PositiveInteger,D) -> D from D if D has ABELSG
--R   [4] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) -> 
--R            CartesianTensor(D1,D2,D3)
--R            from CartesianTensor(D1,D2,D3)
--R            if D1: INT and D2: NNI and D3 has COMRING
--R   [5] (DoubleFloat,Color) -> Color from Color
--R   [6] (PositiveInteger,Color) -> Color from Color
--R   [7] (DenavitHartenbergMatrix D2,Point D2) -> Point D2
--R            from DenavitHartenbergMatrix D2
--R            if D2 has Join(Field,TranscendentalFunctionCategory)
--R   [8] (D1,Equation D1) -> Equation D1 from Equation D1
--R            if D1 has SGROUP and D1 has TYPE
--R   [9] (Equation D1,D1) -> Equation D1 from Equation D1
--R            if D1 has SGROUP and D1 has TYPE
--R   [10] (D1,D2) -> D from D
--R            if D has FAMONC(D2,D1) and D2 has SETCAT and D1 has CABMON
--R            
--R   [11] (D1,D2) -> D from D
--R            if D has FMCAT(D1,D2) and D1 has RING and D2 has SETCAT
--R   [12] (D,D1) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R            
--R   [13] (D1,D) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R            
--R   [14] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
--R             -> PolynomialIdeals(D1,D2,D3,D4)
--R            from PolynomialIdeals(D1,D2,D3,D4)
--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
--R            has POLYCAT(D1,D2,D3)
--R   [15] (D1,D) -> D from D if D has LMODULE D1 and D1 has RNG
--R   [16] ((D5 -> D6),(D4 -> D5)) -> (D4 -> D6) from MappingPackage3(D4,
--R            D5,D6)
--R            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
--R   [17] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
--R            D3)
--R            if D2 has SETCAT and D3 has RING
--R   [18] (D1,D) -> D1 from D
--R            if D has MATCAT(D2,D1,D3) and D2 has RING and D1 has FLAGG 
--R            D2 and D3 has FLAGG D2
--R   [19] (D,D1) -> D1 from D
--R            if D has MATCAT(D2,D3,D1) and D2 has RING and D3 has FLAGG 
--R            D2 and D1 has FLAGG D2
--R   [20] (Integer,D) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
--R            D2 and D4 has FLAGG D2
--R   [21] (D,D1) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [22] (D1,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [23] (D,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG 
--R            D1 and D3 has FLAGG D1
--R   [24] (D,D) -> D from D if D has MONAD
--R   [25] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
--R            )
--R            from MyExpression(D1,D2)
--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [26] (D,D1) -> D from D if D has RMODULE D1 and D1 has RNG
--R   [27] (D,D) -> D from D if D has SGROUP
--R   [28] (D1,D) -> D1 from D
--R            if D has SMATCAT(D2,D3,D1,D4) and D3 has RING and D1 has 
--R            DIRPCAT(D2,D3) and D4 has DIRPCAT(D2,D3)
--R   [29] (D,D1) -> D1 from D
--R            if D has SMATCAT(D2,D3,D4,D1) and D3 has RING and D4 has 
--R            DIRPCAT(D2,D3) and D1 has DIRPCAT(D2,D3)
--R   [30] (D,D1) -> D from D
--R            if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
--R   [31] (D1,D) -> D from D
--R            if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
--R   [32] (Integer,D) -> D from D
--R            if D has VECTCAT D2 and D2 has TYPE and D2 has ABELGRP
--R   [33] (D1,D) -> D from D
--R            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
--R   [34] (D,D1) -> D from D
--R            if D has XFALG(D2,D1) and D2 has ORDSET and D1 has RING
--R
--RThere are 23 unexposed functions called * :
--R   [1] (FreeGroup D1,D1) -> FreeGroup D1 from FreeGroup D1 if D1 has 
--R            SETCAT
--R   [2] (D1,FreeGroup D1) -> FreeGroup D1 from FreeGroup D1 if D1 has 
--R            SETCAT
--R   [3] (D1,D2) -> FreeModule1(D2,D1) from FreeModule1(D2,D1)
--R            if D2 has RING and D1 has ORDSET
--R   [4] (FreeMonoid D1,D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
--R            SETCAT
--R   [5] (D1,FreeMonoid D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
--R            SETCAT
--R   [6] (D1,GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)) -> 
--R            GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
--R            from GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
--R            if D2: LIST SYMBOL and D3 has COMRING and D5 has DIRPCAT(# 
--R            D2,NNI) and D6: ((Record(index: D4,exponent: D5),Record(
--R            index: D4,exponent: D5)) -> Boolean) and D4 has ORDSET and 
--R            D1 has POLYCAT(D3,D5,OVAR D2)
--R   [7] (Vector D2,Vector D2) -> Vector D2
--R            from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
--R         
--R   [8] (InputForm,InputForm) -> InputForm from InputForm
--R   [9] (InnerTaylorSeries D2,Integer) -> InnerTaylorSeries D2
--R            from InnerTaylorSeries D2 if D2 has RING
--R   [10] (InnerTaylorSeries D1,D1) -> InnerTaylorSeries D1
--R            from InnerTaylorSeries D1 if D1 has RING
--R   [11] (D1,InnerTaylorSeries D1) -> InnerTaylorSeries D1
--R            from InnerTaylorSeries D1 if D1 has RING
--R   [12] (Magma D1,Magma D1) -> Magma D1 from Magma D1 if D1 has ORDSET
--R            
--R   [13] (OrderedFreeMonoid D1,D1) -> OrderedFreeMonoid D1
--R            from OrderedFreeMonoid D1 if D1 has ORDSET
--R   [14] (D1,OrderedFreeMonoid D1) -> OrderedFreeMonoid D1
--R            from OrderedFreeMonoid D1 if D1 has ORDSET
--R   [15] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [16] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
--R            SETCAT
--R   [17] (D2,Vector D3) -> Vector D3 from PseudoRemainderSequence(D2,D3)
--R            if D3 has UPOLYC D2 and D2 has INTDOM
--R   [18] (D1,SparseMultivariateTaylorSeries(D2,D3,D1)) -> 
--R            SparseMultivariateTaylorSeries(D2,D3,D1)
--R            from SparseMultivariateTaylorSeries(D2,D3,D1)
--R            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
--R            D3,D3)
--R   [19] (Stream D2,Stream D2) -> Stream D2 from 
--R            StreamTaylorSeriesOperations D2
--R            if D2 has RING
--R   [20] (D2,Stream D2) -> Stream D2 from StreamTaylorSeriesOperations 
--R            D2
--R            if D2 has RING
--R   [21] (Stream D2,D2) -> Stream D2 from StreamTaylorSeriesOperations 
--R            D2
--R            if D2 has RING
--R   [22] (DoubleFloat,Point DoubleFloat) -> Point DoubleFloat from 
--R            TubePlotTools
--R   [23] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
--R            from XPolynomialRing(D1,D2) if D1 has RING and D2 has 
--R            ORDMON
--R
--RExamples of * from AbelianGroup
--R
--R
--RExamples of * from AbelianMonoid
--R
--R
--RExamples of * from AbelianSemiGroup
--R
--R
--RExamples of * from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
--RTm:CartesianTensor(1,2,Integer):=m 
--Rv:DirectProduct(2,Integer):=directProduct [3,4] 
--RTv:CartesianTensor(1,2,Integer):=v 
--RTm*Tv
--R
--R
--RExamples of * from Color
--R
--R
--RExamples of * from DenavitHartenbergMatrix
--R
--R
--RExamples of * from Equation
--R
--R
--RExamples of * from FreeAbelianMonoidCategory
--R
--R
--RExamples of * from FreeGroup
--R
--R
--RExamples of * from FreeModule1
--R
--R
--RExamples of * from FreeModuleCat
--R
--R
--RExamples of * from FreeMonoid
--R
--R
--RExamples of * from GeneralModulePolynomial
--R
--R
--RExamples of * from GradedModule
--R
--R
--RExamples of * from PolynomialIdeals
--R
--R
--RExamples of * from InnerNormalBasisFieldFunctions
--R
--R
--RExamples of * from InputForm
--R
--R
--RExamples of * from InnerTaylorSeries
--R
--R
--RExamples of * from LeftModule
--R
--R
--RExamples of * from Magma
--R
--R
--RExamples of * from MappingPackage3
--R
--R
--RExamples of * from MappingPackage4
--R
--Rf:=(x:INT):INT +-> 3*x 
--Rg:=(x:INT):INT +-> 2*x+3 
--R(f*g)(4)
--R
--R
--RExamples of * from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rr:=transpose([1,2,3,4,5])@Matrix(INT) 
--Rr*m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rc:=coerce([1,2,3,4,5])@Matrix(INT) 
--Rm*c
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--R3*m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rm*1/3
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--R1/3*m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rm*m
--R
--R
--RExamples of * from Monad
--R
--R
--RExamples of * from MyExpression
--R
--R
--RExamples of * from OrderedFreeMonoid
--R
--R
--RExamples of * from OutputForm
--R
--R
--RExamples of * from Pattern
--R
--R
--RExamples of * from PseudoRemainderSequence
--R
--R
--RExamples of * from RightModule
--R
--R
--RExamples of * from SemiGroup
--R
--R
--RExamples of * from SquareMatrixCategory
--R
--R
--RExamples of * from SparseMultivariateTaylorSeries
--R
--R
--RExamples of * from StreamTaylorSeriesOperations
--R
--R
--RExamples of * from TubePlotTools
--R
--R
--RExamples of * from VectorCategory
--R
--R
--RExamples of * from XFreeAlgebra
--R
--R
--RExamples of * from XPolynomialRing
--R
--E 86

--S 87 of 127
)d op numberOfComponents
 

There are 2 exposed functions called numberOfComponents :
   [1]  -> NonNegativeInteger from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3
   [2] D -> NonNegativeInteger from D if D has SPACEC D2 and D2 has 
            RING

There is one unexposed function called numberOfComponents :
   [1]  -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC 
            D4 and D2 has FFCAT(D3,D4,D5)

Examples of numberOfComponents from FunctionFieldCategory&

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
numberOfComponents()$R


Examples of numberOfComponents from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
numberOfComponents()$R


Examples of numberOfComponents from ThreeSpaceCategory

--R 
--R
--RThere are 2 exposed functions called numberOfComponents :
--R   [1]  -> NonNegativeInteger from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R   [2] D -> NonNegativeInteger from D if D has SPACEC D2 and D2 has 
--R            RING
--R
--RThere is one unexposed function called numberOfComponents :
--R   [1]  -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
--R            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC 
--R            D4 and D2 has FFCAT(D3,D4,D5)
--R
--RExamples of numberOfComponents from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RnumberOfComponents()$R
--R
--R
--RExamples of numberOfComponents from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RnumberOfComponents()$R
--R
--R
--RExamples of numberOfComponents from ThreeSpaceCategory
--R
--E 87

--S 88 of 127
)d op tree
 

There are 3 exposed functions called tree :
   [1] D1 -> Tree D1 from Tree D1 if D1 has SETCAT
   [2] List D2 -> Tree D2 from Tree D2 if D2 has SETCAT
   [3] (D1,List Tree D1) -> Tree D1 from Tree D1 if D1 has SETCAT

Examples of tree from Tree

tree 6

tree [1,2,3,4]

t1:=tree [1,2,3,4] 
tree(5,[t1])

--R 
--R
--RThere are 3 exposed functions called tree :
--R   [1] D1 -> Tree D1 from Tree D1 if D1 has SETCAT
--R   [2] List D2 -> Tree D2 from Tree D2 if D2 has SETCAT
--R   [3] (D1,List Tree D1) -> Tree D1 from Tree D1 if D1 has SETCAT
--R
--RExamples of tree from Tree
--R
--Rtree 6
--R
--Rtree [1,2,3,4]
--R
--Rt1:=tree [1,2,3,4] 
--Rtree(5,[t1])
--R
--E 88

--S 89 of 127
)d op Aleph
 

There is one exposed function called Aleph :
   [1] NonNegativeInteger -> CardinalNumber from CardinalNumber

Examples of Aleph from CardinalNumber

A0:=Aleph 0

--R 
--R
--RThere is one exposed function called Aleph :
--R   [1] NonNegativeInteger -> CardinalNumber from CardinalNumber
--R
--RExamples of Aleph from CardinalNumber
--R
--RA0:=Aleph 0
--R
--E 89

--S 90 of 127
)d op unit
 

There are 3 exposed functions called unit :
   [1] List Float -> DrawOption from DrawOption
   [2]  -> Union(D,"failed") from D
            if D has FINAALG D1 and D1 has INTDOM and D1 has COMRING
         
   [3] Factored D1 -> D1 from Factored D1 if D1 has INTDOM

Examples of unit from DrawOption


Examples of unit from FiniteRankNonAssociativeAlgebra


Examples of unit from Factored

f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 
unit f 
g:=makeFR(z,factorList f) 
unit g

--R 
--R
--RThere are 3 exposed functions called unit :
--R   [1] List Float -> DrawOption from DrawOption
--R   [2]  -> Union(D,"failed") from D
--R            if D has FINAALG D1 and D1 has INTDOM and D1 has COMRING
--R         
--R   [3] Factored D1 -> D1 from Factored D1 if D1 has INTDOM
--R
--RExamples of unit from DrawOption
--R
--R
--RExamples of unit from FiniteRankNonAssociativeAlgebra
--R
--R
--RExamples of unit from Factored
--R
--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 
--Runit f 
--Rg:=makeFR(z,factorList f) 
--Runit g
--R
--E 90

--S 91 of 127
)d op frst
 

There is one exposed function called frst :
   [1] D -> D1 from D if D has LZSTAGG D1 and D1 has TYPE

Examples of frst from LazyStreamAggregate

m:=[i for i in 0..] 
frst m

--R 
--R
--RThere is one exposed function called frst :
--R   [1] D -> D1 from D if D has LZSTAGG D1 and D1 has TYPE
--R
--RExamples of frst from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--Rfrst m
--R
--E 91

--S 92 of 127
)d op product
 

There are 4 exposed functions called product :
   [1] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) -> 
            CartesianTensor(D1,D2,D3)
            from CartesianTensor(D1,D2,D3)
            if D1: INT and D2: NNI and D3 has COMRING
   [2] (D,SegmentBinding D) -> D from D if D has COMBOPC
   [3] (D,Symbol) -> D from D if D has COMBOPC
   [4] (D,D) -> D from D
            if D has GRALG(D1,D2) and D1 has COMRING and D2 has ABELMON
            

There are 3 unexposed functions called product :
   [1] (D1,Symbol) -> D1 from CombinatorialFunction(D3,D1)
            if D3 has Join(OrderedSet,IntegralDomain) and D1 has FS D3
            
   [2] (D1,SegmentBinding D1) -> D1 from CombinatorialFunction(D3,D1)
            if D1 has FS D3 and D3 has Join(OrderedSet,IntegralDomain)
            
   [3] (XPBWPolynomial(D2,D3),XPBWPolynomial(D2,D3),NonNegativeInteger)
             -> XPBWPolynomial(D2,D3)
            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
            COMRING

Examples of product from CartesianTensor

m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
Tm:CartesianTensor(1,2,Integer):=m 
n:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] 
Tn:CartesianTensor(1,2,Integer):=n 
Tmn:=product(Tm,Tn)


Examples of product from CombinatorialFunction


Examples of product from CombinatorialOpsCategory


Examples of product from GradedAlgebra


Examples of product from XPBWPolynomial

--R 
--R
--RThere are 4 exposed functions called product :
--R   [1] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) -> 
--R            CartesianTensor(D1,D2,D3)
--R            from CartesianTensor(D1,D2,D3)
--R            if D1: INT and D2: NNI and D3 has COMRING
--R   [2] (D,SegmentBinding D) -> D from D if D has COMBOPC
--R   [3] (D,Symbol) -> D from D if D has COMBOPC
--R   [4] (D,D) -> D from D
--R            if D has GRALG(D1,D2) and D1 has COMRING and D2 has ABELMON
--R            
--R
--RThere are 3 unexposed functions called product :
--R   [1] (D1,Symbol) -> D1 from CombinatorialFunction(D3,D1)
--R            if D3 has Join(OrderedSet,IntegralDomain) and D1 has FS D3
--R            
--R   [2] (D1,SegmentBinding D1) -> D1 from CombinatorialFunction(D3,D1)
--R            if D1 has FS D3 and D3 has Join(OrderedSet,IntegralDomain)
--R            
--R   [3] (XPBWPolynomial(D2,D3),XPBWPolynomial(D2,D3),NonNegativeInteger)
--R             -> XPBWPolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has 
--R            COMRING
--R
--RExamples of product from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] 
--RTm:CartesianTensor(1,2,Integer):=m 
--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] 
--RTn:CartesianTensor(1,2,Integer):=n 
--RTmn:=product(Tm,Tn)
--R
--R
--RExamples of product from CombinatorialFunction
--R
--R
--RExamples of product from CombinatorialOpsCategory
--R
--R
--RExamples of product from GradedAlgebra
--R
--R
--RExamples of product from XPBWPolynomial
--R
--E 92

--S 93 of 127
)d op fill!
 

There are 2 exposed functions called fill! :
   [1] (D,D1) -> D from D
            if D has ARR2CAT(D1,D2,D3) and D1 has TYPE and D2 has FLAGG
            D1 and D3 has FLAGG D1
   [2] (D,D1) -> D from D
            if D has shallowlyMutable and D has IXAGG(D2,D1) and D2 has
            SETCAT and D1 has TYPE

Examples of fill! from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,0) 
fill!(arr,10)


Examples of fill! from IndexedAggregate

--R 
--R
--RThere are 2 exposed functions called fill! :
--R   [1] (D,D1) -> D from D
--R            if D has ARR2CAT(D1,D2,D3) and D1 has TYPE and D2 has FLAGG
--R            D1 and D3 has FLAGG D1
--R   [2] (D,D1) -> D from D
--R            if D has shallowlyMutable and D has IXAGG(D2,D1) and D2 has
--R            SETCAT and D1 has TYPE
--R
--RExamples of fill! from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0) 
--Rfill!(arr,10)
--R
--R
--RExamples of fill! from IndexedAggregate
--R
--E 93

--S 94 of 127
)d op upperCase?
 

There is one exposed function called upperCase? :
   [1] Character -> Boolean from Character

Examples of upperCase? from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[upperCase? c for c in chars]

--R 
--R
--RThere is one exposed function called upperCase? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of upperCase? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[upperCase? c for c in chars]
--R
--E 94

--S 95 of 127
)d op integralMatrixAtInfinity
 

There is one exposed function called integralMatrixAtInfinity :
   [1]  -> Matrix Fraction D3 from D
            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
            D2 and D4 has UPOLYC FRAC D3

Examples of integralMatrixAtInfinity from FunctionFieldCategory

P0 := UnivariatePolynomial(x, Integer) 
P1 := UnivariatePolynomial(y, Fraction P0) 
R := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
integralMatrixAtInfinity()$R

--R 
--R
--RThere is one exposed function called integralMatrixAtInfinity :
--R   [1]  -> Matrix Fraction D3 from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC 
--R            D2 and D4 has UPOLYC FRAC D3
--R
--RExamples of integralMatrixAtInfinity from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer) 
--RP1 := UnivariatePolynomial(y, Fraction P0) 
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) 
--RintegralMatrixAtInfinity()$R
--R
--E 95

--S 96 of 127
)d op finite?
 

There are 3 exposed functions called finite? :
   [1] CardinalNumber -> Boolean from CardinalNumber
   [2] OnePointCompletion D2 -> Boolean from OnePointCompletion D2
            if D2 has SETCAT
   [3] OrderedCompletion D2 -> Boolean from OrderedCompletion D2
            if D2 has SETCAT

Examples of finite? from CardinalNumber

c2:=2::CardinalNumber 
finite? c2 
A0:=Aleph 0 
finite? A0


Examples of finite? from OnePointCompletion


Examples of finite? from OrderedCompletion

--R 
--R
--RThere are 3 exposed functions called finite? :
--R   [1] CardinalNumber -> Boolean from CardinalNumber
--R   [2] OnePointCompletion D2 -> Boolean from OnePointCompletion D2
--R            if D2 has SETCAT
--R   [3] OrderedCompletion D2 -> Boolean from OrderedCompletion D2
--R            if D2 has SETCAT
--R
--RExamples of finite? from CardinalNumber
--R
--Rc2:=2::CardinalNumber 
--Rfinite? c2 
--RA0:=Aleph 0 
--Rfinite? A0
--R
--R
--RExamples of finite? from OnePointCompletion
--R
--R
--RExamples of finite? from OrderedCompletion
--R
--E 96

--S 97 of 127
)d op rank
 

There are 8 exposed functions called rank :
   [1] CartesianTensor(D2,D3,D4) -> NonNegativeInteger
            from CartesianTensor(D2,D3,D4)
            if D2: INT and D3: NNI and D4 has COMRING
   [2]  -> PositiveInteger from D if D has FINAALG D2 and D2 has 
            COMRING
   [3]  -> PositiveInteger from D
            if D has FINRALG(D2,D3) and D2 has COMRING and D3 has 
            UPOLYC D2
   [4] (Matrix D4,Vector D4) -> NonNegativeInteger
            from LinearSystemMatrixPackage1 D4 if D4 has FIELD
   [5] (D2,D3) -> NonNegativeInteger
            from LinearSystemMatrixPackage(D4,D5,D3,D2)
            if D4 has FIELD and D5 has FiniteLinearAggregate D4 with 
                 shallowlyMutable and D3 has FiniteLinearAggregate D4
            with 
                 shallowlyMutable and D2 has MATCAT(D4,D5,D3)
   [6] D -> NonNegativeInteger from D
            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
            D2 and D4 has FLAGG D2 and D2 has INTDOM
   [7] D2 -> NonNegativeInteger from MatrixLinearAlgebraFunctions(D3,D4
            ,D5,D2)
            if D3 has INTDOM and D3 has COMRING and D4 has FLAGG D3 and
            D5 has FLAGG D3 and D2 has MATCAT(D3,D4,D5)
   [8] D -> NonNegativeInteger from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) and D4 has INTDOM
            

There are 2 unexposed functions called rank :
   [1]  -> PositiveInteger from ComplexCategory&(D2,D3)
            if D3 has COMRING and D2 has COMPCAT D3
   [2] D2 -> NonNegativeInteger
            from InnerMatrixLinearAlgebraFunctions(D3,D4,D5,D2)
            if D3 has FIELD and D4 has FLAGG D3 and D5 has FLAGG D3 and
            D2 has MATCAT(D3,D4,D5)

Examples of rank from CartesianTensor

CT:=CARTEN(1,2,Integer) 
t0:CT:=8 
rank t0


Examples of rank from ComplexCategory&


Examples of rank from FiniteRankNonAssociativeAlgebra


Examples of rank from FiniteRankAlgebra


Examples of rank from InnerMatrixLinearAlgebraFunctions


Examples of rank from LinearSystemMatrixPackage1


Examples of rank from LinearSystemMatrixPackage


Examples of rank from MatrixCategory

rank matrix [[1,2,3],[4,5,6],[7,8,9]]


Examples of rank from MatrixLinearAlgebraFunctions


Examples of rank from RectangularMatrixCategory

--R 
--R
--RThere are 8 exposed functions called rank :
--R   [1] CartesianTensor(D2,D3,D4) -> NonNegativeInteger
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [2]  -> PositiveInteger from D if D has FINAALG D2 and D2 has 
--R            COMRING
--R   [3]  -> PositiveInteger from D
--R            if D has FINRALG(D2,D3) and D2 has COMRING and D3 has 
--R            UPOLYC D2
--R   [4] (Matrix D4,Vector D4) -> NonNegativeInteger
--R            from LinearSystemMatrixPackage1 D4 if D4 has FIELD
--R   [5] (D2,D3) -> NonNegativeInteger
--R            from LinearSystemMatrixPackage(D4,D5,D3,D2)
--R            if D4 has FIELD and D5 has FiniteLinearAggregate D4 with 
--R                 shallowlyMutable and D3 has FiniteLinearAggregate D4
--R            with 
--R                 shallowlyMutable and D2 has MATCAT(D4,D5,D3)
--R   [6] D -> NonNegativeInteger from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
--R            D2 and D4 has FLAGG D2 and D2 has INTDOM
--R   [7] D2 -> NonNegativeInteger from MatrixLinearAlgebraFunctions(D3,D4
--R            ,D5,D2)
--R            if D3 has INTDOM and D3 has COMRING and D4 has FLAGG D3 and
--R            D5 has FLAGG D3 and D2 has MATCAT(D3,D4,D5)
--R   [8] D -> NonNegativeInteger from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) and D4 has INTDOM
--R            
--R
--RThere are 2 unexposed functions called rank :
--R   [1]  -> PositiveInteger from ComplexCategory&(D2,D3)
--R            if D3 has COMRING and D2 has COMPCAT D3
--R   [2] D2 -> NonNegativeInteger
--R            from InnerMatrixLinearAlgebraFunctions(D3,D4,D5,D2)
--R            if D3 has FIELD and D4 has FLAGG D3 and D5 has FLAGG D3 and
--R            D2 has MATCAT(D3,D4,D5)
--R
--RExamples of rank from CartesianTensor
--R
--RCT:=CARTEN(1,2,Integer) 
--Rt0:CT:=8 
--Rrank t0
--R
--R
--RExamples of rank from ComplexCategory&
--R
--R
--RExamples of rank from FiniteRankNonAssociativeAlgebra
--R
--R
--RExamples of rank from FiniteRankAlgebra
--R
--R
--RExamples of rank from InnerMatrixLinearAlgebraFunctions
--R
--R
--RExamples of rank from LinearSystemMatrixPackage1
--R
--R
--RExamples of rank from LinearSystemMatrixPackage
--R
--R
--RExamples of rank from MatrixCategory
--R
--Rrank matrix [[1,2,3],[4,5,6],[7,8,9]]
--R
--R
--RExamples of rank from MatrixLinearAlgebraFunctions
--R
--R
--RExamples of rank from RectangularMatrixCategory
--R
--E 97

--S 98 of 127
)d op numberOfComputedEntries
 

There is one exposed function called numberOfComputedEntries :
   [1] D -> NonNegativeInteger from D if D has LZSTAGG D2 and D2 has 
            TYPE

Examples of numberOfComputedEntries from LazyStreamAggregate

m:=[i for i in 0..] 
numberOfComputedEntries m

--R 
--R
--RThere is one exposed function called numberOfComputedEntries :
--R   [1] D -> NonNegativeInteger from D if D has LZSTAGG D2 and D2 has 
--R            TYPE
--R
--RExamples of numberOfComputedEntries from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--RnumberOfComputedEntries m
--R
--E 98

--S 99 of 127
)d op groebnerFactorize
 

There are 4 exposed functions called groebnerFactorize :
   [1] (List D6,List D6) -> List List D6
            from GroebnerFactorizationPackage(D3,D4,D5,D6)
            if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 
            has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5)
         
   [2] (List D7,List D7,Boolean) -> List List D7
            from GroebnerFactorizationPackage(D4,D5,D6,D7)
            if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 
            has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6)
         
   [3] List D6 -> List List D6 from GroebnerFactorizationPackage(D3,D4,
            D5,D6)
            if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 
            has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5)
         
   [4] (List D7,Boolean) -> List List D7
            from GroebnerFactorizationPackage(D4,D5,D6,D7)
            if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 
            has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6)
         

Examples of groebnerFactorize from GroebnerFactorizationPackage

mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := ++X [ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], ++X [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ] 
eq := determinant mfzn 
groebnerFactorize ++X [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])]

--R 
--R
--RThere are 4 exposed functions called groebnerFactorize :
--R   [1] (List D6,List D6) -> List List D6
--R            from GroebnerFactorizationPackage(D3,D4,D5,D6)
--R            if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 
--R            has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5)
--R         
--R   [2] (List D7,List D7,Boolean) -> List List D7
--R            from GroebnerFactorizationPackage(D4,D5,D6,D7)
--R            if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 
--R            has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6)
--R         
--R   [3] List D6 -> List List D6 from GroebnerFactorizationPackage(D3,D4,
--R            D5,D6)
--R            if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 
--R            has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5)
--R         
--R   [4] (List D7,Boolean) -> List List D7
--R            from GroebnerFactorizationPackage(D4,D5,D6,D7)
--R            if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 
--R            has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6)
--R         
--R
--RExamples of groebnerFactorize from GroebnerFactorizationPackage
--R
--Rmfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := ++X [ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], ++X [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ] 
--Req := determinant mfzn 
--RgroebnerFactorize ++X [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])]
--R
--E 99

--S 100 of 127
)d op lowerCase
 

There are 3 exposed functions called lowerCase :
   [1]  -> CharacterClass from CharacterClass
   [2] Character -> Character from Character
   [3] D -> D from D if D has SRAGG

Examples of lowerCase from CharacterClass


Examples of lowerCase from Character

chars := [char "a", char "A", char "X", char "8", char "+"] 
[lowerCase c for c in chars]


Examples of lowerCase from StringAggregate

--R 
--R
--RThere are 3 exposed functions called lowerCase :
--R   [1]  -> CharacterClass from CharacterClass
--R   [2] Character -> Character from Character
--R   [3] D -> D from D if D has SRAGG
--R
--RExamples of lowerCase from CharacterClass
--R
--R
--RExamples of lowerCase from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"] 
--R[lowerCase c for c in chars]
--R
--R
--RExamples of lowerCase from StringAggregate
--R
--E 100

--S 101 of 127
)d op showAllElements
 

There is one exposed function called showAllElements :
   [1] Stream D2 -> OutputForm from Stream D2
            if D2 has SETCAT and D2 has TYPE

Examples of showAllElements from Stream

m:=[1,2,3,4,5,6,7,8,9,10,11,12] 
n:=m::Stream(PositiveInteger) 
showAllElements n

--R 
--R
--RThere is one exposed function called showAllElements :
--R   [1] Stream D2 -> OutputForm from Stream D2
--R            if D2 has SETCAT and D2 has TYPE
--R
--RExamples of showAllElements from Stream
--R
--Rm:=[1,2,3,4,5,6,7,8,9,10,11,12] 
--Rn:=m::Stream(PositiveInteger) 
--RshowAllElements n
--R
--E 101

--S 102 of 127
)d op maxColIndex
 

There are 2 exposed functions called maxColIndex :
   [1] D -> Integer from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] D -> Integer from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

Examples of maxColIndex from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
maxColIndex(arr)


Examples of maxColIndex from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called maxColIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of maxColIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--RmaxColIndex(arr)
--R
--R
--RExamples of maxColIndex from RectangularMatrixCategory
--R
--E 102

--S 103 of 127
)d op minRowIndex
 

There are 2 exposed functions called minRowIndex :
   [1] D -> Integer from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] D -> Integer from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

Examples of minRowIndex from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
minRowIndex(arr)


Examples of minRowIndex from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called minRowIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of minRowIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--RminRowIndex(arr)
--R
--R
--RExamples of minRowIndex from RectangularMatrixCategory
--R
--E 103

--S 104 of 127
)d op space
 

There are 2 exposed functions called space :
   [1]  -> Character from Character
   [2] ThreeSpace DoubleFloat -> DrawOption from DrawOption

There is one unexposed function called space :
   [1] List DrawOption -> ThreeSpace DoubleFloat from 
            DrawOptionFunctions0

Examples of space from Character

space()


Examples of space from DrawOptionFunctions0


Examples of space from DrawOption

--R 
--R
--RThere are 2 exposed functions called space :
--R   [1]  -> Character from Character
--R   [2] ThreeSpace DoubleFloat -> DrawOption from DrawOption
--R
--RThere is one unexposed function called space :
--R   [1] List DrawOption -> ThreeSpace DoubleFloat from 
--R            DrawOptionFunctions0
--R
--RExamples of space from Character
--R
--Rspace()
--R
--R
--RExamples of space from DrawOptionFunctions0
--R
--R
--RExamples of space from DrawOption
--R
--E 104

--S 105 of 127
)d op remove
 

There are 5 exposed functions called remove :
   [1] (D1,D) -> D from D
            if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
            and D1 has SETCAT
   [2] ((D2 -> Boolean),D) -> D from D
            if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE
            
   [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has 
            TYPE
   [4] ((D3 -> Boolean),Multiset D3,Integer) -> Multiset D3 from 
            Multiset D3
            if D3 has SETCAT
   [5] (D1,Multiset D1,Integer) -> Multiset D1 from Multiset D1
            if D1 has SETCAT

There is one unexposed function called remove :
   [1] (SplittingNode(D2,D3),SplittingTree(D2,D3)) -> SplittingTree(D2,
            D3)
            from SplittingTree(D2,D3)
            if D2 has Join(SetCategory,Aggregate) and D3 has Join(
            SetCategory,Aggregate)

Examples of remove from Collection


Examples of remove from LazyStreamAggregate

m:=[i for i in 1..] 
f(i:PositiveInteger):Boolean == even? i 
remove(f,m)


Examples of remove from Multiset


Examples of remove from SplittingTree

--R 
--R
--RThere are 5 exposed functions called remove :
--R   [1] (D1,D) -> D from D
--R            if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
--R            and D1 has SETCAT
--R   [2] ((D2 -> Boolean),D) -> D from D
--R            if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE
--R            
--R   [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has 
--R            TYPE
--R   [4] ((D3 -> Boolean),Multiset D3,Integer) -> Multiset D3 from 
--R            Multiset D3
--R            if D3 has SETCAT
--R   [5] (D1,Multiset D1,Integer) -> Multiset D1 from Multiset D1
--R            if D1 has SETCAT
--R
--RThere is one unexposed function called remove :
--R   [1] (SplittingNode(D2,D3),SplittingTree(D2,D3)) -> SplittingTree(D2,
--R            D3)
--R            from SplittingTree(D2,D3)
--R            if D2 has Join(SetCategory,Aggregate) and D3 has Join(
--R            SetCategory,Aggregate)
--R
--RExamples of remove from Collection
--R
--R
--RExamples of remove from LazyStreamAggregate
--R
--Rm:=[i for i in 1..] 
--Rf(i:PositiveInteger):Boolean == even? i 
--Rremove(f,m)
--R
--R
--RExamples of remove from Multiset
--R
--R
--RExamples of remove from SplittingTree
--R
--E 105

--S 106 of 127
)d op factors
 

There is one exposed function called factors :
   [1] Factored D2 -> List Record(factor: D2,exponent: Integer)
            from Factored D2 if D2 has INTDOM

There are 3 unexposed functions called factors :
   [1] FreeGroup D2 -> List Record(gen: D2,exp: Integer) from FreeGroup
            D2
            if D2 has SETCAT
   [2] FreeMonoid D2 -> List Record(gen: D2,exp: NonNegativeInteger)
            from FreeMonoid D2 if D2 has SETCAT
   [3] OrderedFreeMonoid D2 -> List Record(gen: D2,exp: 
            NonNegativeInteger)
            from OrderedFreeMonoid D2 if D2 has ORDSET

Examples of factors from FreeGroup


Examples of factors from FreeMonoid


Examples of factors from Factored

f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 
factors f 
g:=makeFR(z,factorList f) 
factors g


Examples of factors from OrderedFreeMonoid

m1:=(x*y*y*z)$OFMONOID(Symbol) 
factors m1

--R 
--R
--RThere is one exposed function called factors :
--R   [1] Factored D2 -> List Record(factor: D2,exponent: Integer)
--R            from Factored D2 if D2 has INTDOM
--R
--RThere are 3 unexposed functions called factors :
--R   [1] FreeGroup D2 -> List Record(gen: D2,exp: Integer) from FreeGroup
--R            D2
--R            if D2 has SETCAT
--R   [2] FreeMonoid D2 -> List Record(gen: D2,exp: NonNegativeInteger)
--R            from FreeMonoid D2 if D2 has SETCAT
--R   [3] OrderedFreeMonoid D2 -> List Record(gen: D2,exp: 
--R            NonNegativeInteger)
--R            from OrderedFreeMonoid D2 if D2 has ORDSET
--R
--RExamples of factors from FreeGroup
--R
--R
--RExamples of factors from FreeMonoid
--R
--R
--RExamples of factors from Factored
--R
--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 
--Rfactors f 
--Rg:=makeFR(z,factorList f) 
--Rfactors g
--R
--R
--RExamples of factors from OrderedFreeMonoid
--R
--E 106

--S 107 of 127
)d op output
 

There are 4 exposed functions called output :
   [1] String -> Void from OutputPackage
   [2] OutputForm -> Void from OutputPackage
   [3] (String,OutputForm) -> Void from OutputPackage
   [4] (Integer,Stream D3) -> Void from Stream D3
            if D3 has SETCAT and D3 has TYPE

Examples of output from OutputPackage


Examples of output from Stream

m:=[1,2,3] 
n:=repeating(m) 
output(5,n)

--R 
--R
--RThere are 4 exposed functions called output :
--R   [1] String -> Void from OutputPackage
--R   [2] OutputForm -> Void from OutputPackage
--R   [3] (String,OutputForm) -> Void from OutputPackage
--R   [4] (Integer,Stream D3) -> Void from Stream D3
--R            if D3 has SETCAT and D3 has TYPE
--R
--RExamples of output from OutputPackage
--R
--R
--RExamples of output from Stream
--R
--Rm:=[1,2,3] 
--Rn:=repeating(m) 
--Routput(5,n)
--R
--E 107

--S 108 of 127
)d op binarySearchTree
 

There is one exposed function called binarySearchTree :
   [1] List D2 -> BinarySearchTree D2 from BinarySearchTree D2 if D2 
            has ORDSET

Examples of binarySearchTree from BinarySearchTree

binarySearchTree [1,2,3,4]

--R 
--R
--RThere is one exposed function called binarySearchTree :
--R   [1] List D2 -> BinarySearchTree D2 from BinarySearchTree D2 if D2 
--R            has ORDSET
--R
--RExamples of binarySearchTree from BinarySearchTree
--R
--RbinarySearchTree [1,2,3,4]
--R
--E 108

--S 109 of 127
)d op char
 

There are 2 exposed functions called char :
   [1] String -> Character from Character
   [2] Integer -> Character from Character

Examples of char from Character

[char c for c in ["a","A","X","8","+"]]

[char c for c in [97,65,88,56,43]]

--R 
--R
--RThere are 2 exposed functions called char :
--R   [1] String -> Character from Character
--R   [2] Integer -> Character from Character
--R
--RExamples of char from Character
--R
--R[char c for c in ["a","A","X","8","+"]]
--R
--R[char c for c in [97,65,88,56,43]]
--R
--E 109

--S 110 of 127
)d op shrinkable
 

There is one exposed function called shrinkable :
   [1] Boolean -> Boolean from FlexibleArray D2 if D2 has TYPE

There is one unexposed function called shrinkable :
   [1] Boolean -> Boolean from IndexedFlexibleArray(D2,D3)
            if D2 has TYPE and D3: INT

Examples of shrinkable from FlexibleArray


Examples of shrinkable from IndexedFlexibleArray

T1:=IndexedFlexibleArray(Integer,20) 
shrinkable(false)$T1

--R 
--R
--RThere is one exposed function called shrinkable :
--R   [1] Boolean -> Boolean from FlexibleArray D2 if D2 has TYPE
--R
--RThere is one unexposed function called shrinkable :
--R   [1] Boolean -> Boolean from IndexedFlexibleArray(D2,D3)
--R            if D2 has TYPE and D3: INT
--R
--RExamples of shrinkable from FlexibleArray
--R
--R
--RExamples of shrinkable from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20) 
--Rshrinkable(false)$T1
--R
--E 110

--S 111 of 127
)d op rst
 

There is one exposed function called rst :
   [1] D -> D from D if D has LZSTAGG D1 and D1 has TYPE

Examples of rst from LazyStreamAggregate

m:=[i for i in 0..] 
rst m

--R 
--R
--RThere is one exposed function called rst :
--R   [1] D -> D from D if D has LZSTAGG D1 and D1 has TYPE
--R
--RExamples of rst from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--Rrst m
--R
--E 111

--S 112 of 127
)d op flexibleArray
 

There is one exposed function called flexibleArray :
   [1] List D2 -> FlexibleArray D2 from FlexibleArray D2 if D2 has TYPE
            

There is one unexposed function called flexibleArray :
   [1] List D2 -> IndexedFlexibleArray(D2,D3) from IndexedFlexibleArray
            (D2,D3)
            if D2 has TYPE and D3: INT

Examples of flexibleArray from FlexibleArray


Examples of flexibleArray from IndexedFlexibleArray

T1:=IndexedFlexibleArray(Integer,20) 
flexibleArray([i for i in 1..10])$T1

--R 
--R
--RThere is one exposed function called flexibleArray :
--R   [1] List D2 -> FlexibleArray D2 from FlexibleArray D2 if D2 has TYPE
--R            
--R
--RThere is one unexposed function called flexibleArray :
--R   [1] List D2 -> IndexedFlexibleArray(D2,D3) from IndexedFlexibleArray
--R            (D2,D3)
--R            if D2 has TYPE and D3: INT
--R
--RExamples of flexibleArray from FlexibleArray
--R
--R
--RExamples of flexibleArray from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20) 
--RflexibleArray([i for i in 1..10])$T1
--R
--E 112

--S 113 of 127
)d op setelt
 

There are 12 exposed functions called setelt :
   [1] (D,Integer,Integer,D1) -> D1 from D
            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
            D1 and D4 has FLAGG D1
   [2] (D,right,D) -> D from D
            if D has shallowlyMutable and D has BRAGG D2 and D2 has 
            TYPE
   [3] (D,left,D) -> D from D
            if D has shallowlyMutable and D has BRAGG D2 and D2 has 
            TYPE
   [4] (D,D2,D1) -> D1 from D
            if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2 
            has SETCAT and D1 has TYPE
   [5] (Library,Symbol,Any) -> Any from Library
   [6] (D,UniversalSegment Integer,D1) -> D1 from D
            if D has shallowlyMutable and D has LNAGG D1 and D1 has 
            TYPE
   [7] (D,List Integer,List Integer,D) -> D from D
            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
            D2 and D4 has FLAGG D2
   [8] (D,value,D1) -> D1 from D
            if D has shallowlyMutable and D has RCAGG D1 and D1 has 
            TYPE
   [9] (D,D2,D1) -> D1 from D
            if D has TBAGG(D2,D1) and D2 has SETCAT and D1 has SETCAT
         
   [10] (D,last,D1) -> D1 from D
            if D has shallowlyMutable and D has URAGG D1 and D1 has 
            TYPE
   [11] (D,rest,D) -> D from D
            if D has shallowlyMutable and D has URAGG D2 and D2 has 
            TYPE
   [12] (D,first,D1) -> D1 from D
            if D has shallowlyMutable and D has URAGG D1 and D1 has 
            TYPE

There is one unexposed function called setelt :
   [1] (Reference D1,D1) -> D1 from Reference D1 if D1 has TYPE

Examples of setelt from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,0) 
setelt(arr,1,1,17)


Examples of setelt from BinaryRecursiveAggregate


Examples of setelt from EltableAggregate


Examples of setelt from Library


Examples of setelt from LinearAggregate


Examples of setelt from MatrixCategory

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
setelt(m,3,3,10)


Examples of setelt from RecursiveAggregate


Examples of setelt from Reference


Examples of setelt from TableAggregate


Examples of setelt from UnaryRecursiveAggregate

--R 
--R
--RThere are 12 exposed functions called setelt :
--R   [1] (D,Integer,Integer,D1) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
--R            D1 and D4 has FLAGG D1
--R   [2] (D,right,D) -> D from D
--R            if D has shallowlyMutable and D has BRAGG D2 and D2 has 
--R            TYPE
--R   [3] (D,left,D) -> D from D
--R            if D has shallowlyMutable and D has BRAGG D2 and D2 has 
--R            TYPE
--R   [4] (D,D2,D1) -> D1 from D
--R            if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2 
--R            has SETCAT and D1 has TYPE
--R   [5] (Library,Symbol,Any) -> Any from Library
--R   [6] (D,UniversalSegment Integer,D1) -> D1 from D
--R            if D has shallowlyMutable and D has LNAGG D1 and D1 has 
--R            TYPE
--R   [7] (D,List Integer,List Integer,D) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
--R            D2 and D4 has FLAGG D2
--R   [8] (D,value,D1) -> D1 from D
--R            if D has shallowlyMutable and D has RCAGG D1 and D1 has 
--R            TYPE
--R   [9] (D,D2,D1) -> D1 from D
--R            if D has TBAGG(D2,D1) and D2 has SETCAT and D1 has SETCAT
--R         
--R   [10] (D,last,D1) -> D1 from D
--R            if D has shallowlyMutable and D has URAGG D1 and D1 has 
--R            TYPE
--R   [11] (D,rest,D) -> D from D
--R            if D has shallowlyMutable and D has URAGG D2 and D2 has 
--R            TYPE
--R   [12] (D,first,D1) -> D1 from D
--R            if D has shallowlyMutable and D has URAGG D1 and D1 has 
--R            TYPE
--R
--RThere is one unexposed function called setelt :
--R   [1] (Reference D1,D1) -> D1 from Reference D1 if D1 has TYPE
--R
--RExamples of setelt from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0) 
--Rsetelt(arr,1,1,17)
--R
--R
--RExamples of setelt from BinaryRecursiveAggregate
--R
--R
--RExamples of setelt from EltableAggregate
--R
--R
--RExamples of setelt from Library
--R
--R
--RExamples of setelt from LinearAggregate
--R
--R
--RExamples of setelt from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Rsetelt(m,3,3,10)
--R
--R
--RExamples of setelt from RecursiveAggregate
--R
--R
--RExamples of setelt from Reference
--R
--R
--RExamples of setelt from TableAggregate
--R
--R
--RExamples of setelt from UnaryRecursiveAggregate
--R
--E 113

--S 114 of 127
)d op cyclicParents
 

There is one exposed function called cyclicParents :
   [1] Tree D2 -> List Tree D2 from Tree D2 if D2 has SETCAT

Examples of cyclicParents from Tree

t1:=tree [1,2,3,4] 
cyclicParents t1

--R 
--R
--RThere is one exposed function called cyclicParents :
--R   [1] Tree D2 -> List Tree D2 from Tree D2 if D2 has SETCAT
--R
--RExamples of cyclicParents from Tree
--R
--Rt1:=tree [1,2,3,4] 
--RcyclicParents t1
--R
--E 114

--S 115 of 127
)d op explicitEntries?
 

There is one exposed function called explicitEntries? :
   [1] D -> Boolean from D if D has LZSTAGG D2 and D2 has TYPE

Examples of explicitEntries? from LazyStreamAggregate

m:=[i for i in 0..] 
explicitEntries? m

--R 
--R
--RThere is one exposed function called explicitEntries? :
--R   [1] D -> Boolean from D if D has LZSTAGG D2 and D2 has TYPE
--R
--RExamples of explicitEntries? from LazyStreamAggregate
--R
--Rm:=[i for i in 0..] 
--RexplicitEntries? m
--R
--E 115

--S 116 of 127
)d op column
 

There are 2 exposed functions called column :
   [1] (D,Integer) -> D1 from D
            if D has ARR2CAT(D3,D4,D1) and D3 has TYPE and D4 has FLAGG
            D3 and D1 has FLAGG D3
   [2] (D,Integer) -> D1 from D
            if D has RMATCAT(D3,D4,D5,D6,D1) and D5 has RING and D6 has
            DIRPCAT(D4,D5) and D1 has DIRPCAT(D3,D5)

Examples of column from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
column(arr,1)


Examples of column from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called column :
--R   [1] (D,Integer) -> D1 from D
--R            if D has ARR2CAT(D3,D4,D1) and D3 has TYPE and D4 has FLAGG
--R            D3 and D1 has FLAGG D3
--R   [2] (D,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D5,D6,D1) and D5 has RING and D6 has
--R            DIRPCAT(D4,D5) and D1 has DIRPCAT(D3,D5)
--R
--RExamples of column from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rcolumn(arr,1)
--R
--R
--RExamples of column from RectangularMatrixCategory
--R
--E 116

--S 117 of 127
)d op reduce
 

There are 19 exposed functions called reduce :
   [1] AlgebraicNumber -> AlgebraicNumber from AlgebraicNumber
   [2] (((D4,D1) -> D1),OneDimensionalArray D4,D1) -> D1
            from OneDimensionalArrayFunctions2(D4,D1)
            if D4 has TYPE and D1 has TYPE
   [3] (((D1,D1) -> D1),D,D1,D1) -> D1 from D
            if D1 has SETCAT and D has finiteAggregate and D has CLAGG 
            D1 and D1 has TYPE
   [4] (((D1,D1) -> D1),D,D1) -> D1 from D
            if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
            
   [5] (((D1,D1) -> D1),D) -> D1 from D
            if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
            
   [6] (((D5,D1) -> D1),DirectProduct(D4,D5),D1) -> D1
            from DirectProductFunctions2(D4,D5,D1)
            if D4: NNI and D5 has TYPE and D1 has TYPE
   [7] Expression D1 -> Expression D1 from Expression D1
            if D1 has INTDOM and D1 has ORDSET
   [8] D -> D from D
            if D has FDIVCAT(D1,D2,D3,D4) and D1 has FIELD and D2 has 
            UPOLYC D1 and D3 has UPOLYC FRAC D2 and D4 has FFCAT(D1,D2,
            D3)
   [9] (((D4,D1) -> D1),D3,D1) -> D1
            from FiniteLinearAggregateFunctions2(D4,D3,D1,D5)
            if D4 has TYPE and D1 has TYPE and D3 has FLAGG D4 and D5 
            has FLAGG D1
   [10] (((D4,D1) -> D1),D3,D1) -> D1
            from FiniteSetAggregateFunctions2(D4,D3,D1,D5)
            if D4 has SETCAT and D1 has SETCAT and D3 has FSAGG D4 and 
            D5 has FSAGG D1
   [11] (((D4,D1) -> D1),List D4,D1) -> D1 from ListFunctions2(D4,D1)
            if D4 has TYPE and D1 has TYPE
   [12] (((D5,D2) -> D2),D4,D2) -> D2
            from MatrixCategoryFunctions2(D5,D6,D7,D4,D2,D8,D9,D1)
            if D5 has RING and D2 has RING and D6 has FLAGG D5 and D7 
            has FLAGG D5 and D8 has FLAGG D2 and D9 has FLAGG D2 and D4
            has MATCAT(D5,D6,D7) and D1 has MATCAT(D2,D8,D9)
   [13] Fraction D3 -> Union(D,"failed") from D
            if D3 has UPOLYC D2 and D2 has FIELD and D2 has COMRING and
            D has MONOGEN(D2,D3)
   [14] D1 -> D from D
            if D2 has COMRING and D has MONOGEN(D2,D1) and D1 has 
            UPOLYC D2
   [15] (((D4,D1) -> D1),PrimitiveArray D4,D1) -> D1
            from PrimitiveArrayFunctions2(D4,D1)
            if D4 has TYPE and D1 has TYPE
   [16] (((D9,D4) -> D4),D6,D4) -> D4
            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
            D6,D4,D1,D2,D3)
            if D9 has RING and D4 has RING and D7: NNI and D8: NNI and 
            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D1 
            has DIRPCAT(D8,D4) and D2 has DIRPCAT(D7,D4) and D6 has 
            RMATCAT(D7,D8,D9,D10,D11) and D3 has RMATCAT(D7,D8,D4,D1,D2
            )
   [17] (D1,((D4,D1) -> D1),Stream D4) -> D1 from StreamFunctions2(D4,
            D1)
            if D4 has TYPE and D1 has TYPE
   [18] (D1,D,((D1,D1) -> D1),((D1,D1) -> Boolean)) -> D1 from D
            if D has TSETCAT(D4,D5,D6,D1) and D4 has INTDOM and D5 has 
            OAMONS and D6 has ORDSET and D1 has RPOLCAT(D4,D5,D6)
   [19] (((D4,D1) -> D1),Vector D4,D1) -> D1 from VectorFunctions2(D4,
            D1)
            if D4 has TYPE and D1 has TYPE

There are 7 unexposed functions called reduce :
   [1] SparseUnivariatePolynomial D3 -> Record(pol: 
            SparseUnivariatePolynomial D3,deg: PositiveInteger)
            from DegreeReductionPackage(D3,D4)
            if D3 has RING and D4 has Join(IntegralDomain,OrderedSet)
         
   [2] (D1,D2) -> EuclideanModularRing(D3,D1,D2,D4,D5,D6)
            from EuclideanModularRing(D3,D1,D2,D4,D5,D6)
            if D3 has COMRING and D1 has UPOLYC D3 and D2 has ABELMON 
            and D4: ((D1,D2) -> D1) and D5: ((D2,D2) -> Union(D2,
            "failed")) and D6: ((D1,D1,D2) -> Union(D1,"failed"))
   [3] InnerAlgebraicNumber -> InnerAlgebraicNumber from 
            InnerAlgebraicNumber
   [4] (D1,D2) -> ModularField(D1,D2,D3,D4,D5)
            from ModularField(D1,D2,D3,D4,D5)
            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
            D2) -> Union(D1,"failed"))
   [5] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
            if D2 has RING and D1 has UPOLYC D2
   [6] (D1,D2) -> ModularRing(D1,D2,D3,D4,D5) from ModularRing(D1,D2,D3
            ,D4,D5)
            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
            D2) -> Union(D1,"failed"))
   [7] D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
            D5)
            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1 
            has POLYCAT(D2,D3,D4) and D5: LIST D1

Examples of reduce from AlgebraicNumber


Examples of reduce from OneDimensionalArrayFunctions2

T1:=OneDimensionalArrayFunctions2(Integer,Integer) 
adder(a:Integer,b:Integer):Integer == a+b 
reduce(adder,[i for i in 1..10],0)$T1


Examples of reduce from Collection

reduce(+,[C[i]*x**i for i in 1..5])


Examples of reduce from DegreeReductionPackage


Examples of reduce from DirectProductFunctions2


Examples of reduce from EuclideanModularRing


Examples of reduce from Expression


Examples of reduce from FiniteDivisorCategory


Examples of reduce from FiniteLinearAggregateFunctions2


Examples of reduce from FiniteSetAggregateFunctions2


Examples of reduce from InnerAlgebraicNumber


Examples of reduce from ListFunctions2


Examples of reduce from MatrixCategoryFunctions2


Examples of reduce from ModularField


Examples of reduce from ModMonic


Examples of reduce from ModularRing


Examples of reduce from MonogenicAlgebra


Examples of reduce from PrimitiveArrayFunctions2

T1:=PrimitiveArrayFunctions2(Integer,Integer) 
adder(a:Integer,b:Integer):Integer == a+b 
reduce(adder,[i for i in 1..10],0)$T1


Examples of reduce from ResidueRing


Examples of reduce from RectangularMatrixCategoryFunctions2


Examples of reduce from StreamFunctions2

m:=[i for i in 1..300]::Stream(Integer) 
f(i:Integer,j:Integer):Integer==i+j 
reduce(1,f,m)


Examples of reduce from TriangularSetCategory


Examples of reduce from VectorFunctions2

--R 
--R
--RThere are 19 exposed functions called reduce :
--R   [1] AlgebraicNumber -> AlgebraicNumber from AlgebraicNumber
--R   [2] (((D4,D1) -> D1),OneDimensionalArray D4,D1) -> D1
--R            from OneDimensionalArrayFunctions2(D4,D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [3] (((D1,D1) -> D1),D,D1,D1) -> D1 from D
--R            if D1 has SETCAT and D has finiteAggregate and D has CLAGG 
--R            D1 and D1 has TYPE
--R   [4] (((D1,D1) -> D1),D,D1) -> D1 from D
--R            if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
--R            
--R   [5] (((D1,D1) -> D1),D) -> D1 from D
--R            if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
--R            
--R   [6] (((D5,D1) -> D1),DirectProduct(D4,D5),D1) -> D1
--R            from DirectProductFunctions2(D4,D5,D1)
--R            if D4: NNI and D5 has TYPE and D1 has TYPE
--R   [7] Expression D1 -> Expression D1 from Expression D1
--R            if D1 has INTDOM and D1 has ORDSET
--R   [8] D -> D from D
--R            if D has FDIVCAT(D1,D2,D3,D4) and D1 has FIELD and D2 has 
--R            UPOLYC D1 and D3 has UPOLYC FRAC D2 and D4 has FFCAT(D1,D2,
--R            D3)
--R   [9] (((D4,D1) -> D1),D3,D1) -> D1
--R            from FiniteLinearAggregateFunctions2(D4,D3,D1,D5)
--R            if D4 has TYPE and D1 has TYPE and D3 has FLAGG D4 and D5 
--R            has FLAGG D1
--R   [10] (((D4,D1) -> D1),D3,D1) -> D1
--R            from FiniteSetAggregateFunctions2(D4,D3,D1,D5)
--R            if D4 has SETCAT and D1 has SETCAT and D3 has FSAGG D4 and 
--R            D5 has FSAGG D1
--R   [11] (((D4,D1) -> D1),List D4,D1) -> D1 from ListFunctions2(D4,D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [12] (((D5,D2) -> D2),D4,D2) -> D2
--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D2,D8,D9,D1)
--R            if D5 has RING and D2 has RING and D6 has FLAGG D5 and D7 
--R            has FLAGG D5 and D8 has FLAGG D2 and D9 has FLAGG D2 and D4
--R            has MATCAT(D5,D6,D7) and D1 has MATCAT(D2,D8,D9)
--R   [13] Fraction D3 -> Union(D,"failed") from D
--R            if D3 has UPOLYC D2 and D2 has FIELD and D2 has COMRING and
--R            D has MONOGEN(D2,D3)
--R   [14] D1 -> D from D
--R            if D2 has COMRING and D has MONOGEN(D2,D1) and D1 has 
--R            UPOLYC D2
--R   [15] (((D4,D1) -> D1),PrimitiveArray D4,D1) -> D1
--R            from PrimitiveArrayFunctions2(D4,D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [16] (((D9,D4) -> D4),D6,D4) -> D4
--R            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
--R            D6,D4,D1,D2,D3)
--R            if D9 has RING and D4 has RING and D7: NNI and D8: NNI and 
--R            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D1 
--R            has DIRPCAT(D8,D4) and D2 has DIRPCAT(D7,D4) and D6 has 
--R            RMATCAT(D7,D8,D9,D10,D11) and D3 has RMATCAT(D7,D8,D4,D1,D2
--R            )
--R   [17] (D1,((D4,D1) -> D1),Stream D4) -> D1 from StreamFunctions2(D4,
--R            D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [18] (D1,D,((D1,D1) -> D1),((D1,D1) -> Boolean)) -> D1 from D
--R            if D has TSETCAT(D4,D5,D6,D1) and D4 has INTDOM and D5 has 
--R            OAMONS and D6 has ORDSET and D1 has RPOLCAT(D4,D5,D6)
--R   [19] (((D4,D1) -> D1),Vector D4,D1) -> D1 from VectorFunctions2(D4,
--R            D1)
--R            if D4 has TYPE and D1 has TYPE
--R
--RThere are 7 unexposed functions called reduce :
--R   [1] SparseUnivariatePolynomial D3 -> Record(pol: 
--R            SparseUnivariatePolynomial D3,deg: PositiveInteger)
--R            from DegreeReductionPackage(D3,D4)
--R            if D3 has RING and D4 has Join(IntegralDomain,OrderedSet)
--R         
--R   [2] (D1,D2) -> EuclideanModularRing(D3,D1,D2,D4,D5,D6)
--R            from EuclideanModularRing(D3,D1,D2,D4,D5,D6)
--R            if D3 has COMRING and D1 has UPOLYC D3 and D2 has ABELMON 
--R            and D4: ((D1,D2) -> D1) and D5: ((D2,D2) -> Union(D2,
--R            "failed")) and D6: ((D1,D1,D2) -> Union(D1,"failed"))
--R   [3] InnerAlgebraicNumber -> InnerAlgebraicNumber from 
--R            InnerAlgebraicNumber
--R   [4] (D1,D2) -> ModularField(D1,D2,D3,D4,D5)
--R            from ModularField(D1,D2,D3,D4,D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [5] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
--R            if D2 has RING and D1 has UPOLYC D2
--R   [6] (D1,D2) -> ModularRing(D1,D2,D3,D4,D5) from ModularRing(D1,D2,D3
--R            ,D4,D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [7] D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
--R            D5)
--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1 
--R            has POLYCAT(D2,D3,D4) and D5: LIST D1
--R
--RExamples of reduce from AlgebraicNumber
--R
--R
--RExamples of reduce from OneDimensionalArrayFunctions2
--R
--RT1:=OneDimensionalArrayFunctions2(Integer,Integer) 
--Radder(a:Integer,b:Integer):Integer == a+b 
--Rreduce(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of reduce from Collection
--R
--Rreduce(+,[C[i]*x**i for i in 1..5])
--R
--R
--RExamples of reduce from DegreeReductionPackage
--R
--R
--RExamples of reduce from DirectProductFunctions2
--R
--R
--RExamples of reduce from EuclideanModularRing
--R
--R
--RExamples of reduce from Expression
--R
--R
--RExamples of reduce from FiniteDivisorCategory
--R
--R
--RExamples of reduce from FiniteLinearAggregateFunctions2
--R
--R
--RExamples of reduce from FiniteSetAggregateFunctions2
--R
--R
--RExamples of reduce from InnerAlgebraicNumber
--R
--R
--RExamples of reduce from ListFunctions2
--R
--R
--RExamples of reduce from MatrixCategoryFunctions2
--R
--R
--RExamples of reduce from ModularField
--R
--R
--RExamples of reduce from ModMonic
--R
--R
--RExamples of reduce from ModularRing
--R
--R
--RExamples of reduce from MonogenicAlgebra
--R
--R
--RExamples of reduce from PrimitiveArrayFunctions2
--R
--RT1:=PrimitiveArrayFunctions2(Integer,Integer) 
--Radder(a:Integer,b:Integer):Integer == a+b 
--Rreduce(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of reduce from ResidueRing
--R
--R
--RExamples of reduce from RectangularMatrixCategoryFunctions2
--R
--R
--RExamples of reduce from StreamFunctions2
--R
--Rm:=[i for i in 1..300]::Stream(Integer) 
--Rf(i:Integer,j:Integer):Integer==i+j 
--Rreduce(1,f,m)
--R
--R
--RExamples of reduce from TriangularSetCategory
--R
--R
--RExamples of reduce from VectorFunctions2
--R
--E 117

--S 118 of 127
)d op new
 

There are 7 exposed functions called new :
   [1] (NonNegativeInteger,NonNegativeInteger,D2) -> D from D
            if D2 has TYPE and D has ARR2CAT(D2,D3,D4) and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] (String,String,String) -> D from D if D has FNCAT
   [3]  -> ScriptFormulaFormat from ScriptFormulaFormat
   [4] (NonNegativeInteger,D2) -> D from D
            if D has LNAGG D2 and D2 has TYPE
   [5] Symbol -> Symbol from Symbol
   [6]  -> Symbol from Symbol
   [7]  -> TexFormat from TexFormat

There are 4 unexposed functions called new :
   [1]  -> SubSpaceComponentProperty from SubSpaceComponentProperty
   [2]  -> PatternMatchListResult(D1,D2,D3)
            from PatternMatchListResult(D1,D2,D3)
            if D2 has SETCAT and D1 has SETCAT and D3 has LSAGG D2
   [3]  -> PatternMatchResult(D1,D2) from PatternMatchResult(D1,D2)
            if D1 has SETCAT and D2 has SETCAT
   [4]  -> SubSpace(D1,D2) from SubSpace(D1,D2) if D1: PI and D2 has 
            RING

Examples of new from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,0)


Examples of new from SubSpaceComponentProperty


Examples of new from FileNameCategory


Examples of new from ScriptFormulaFormat


Examples of new from LinearAggregate


Examples of new from PatternMatchListResult


Examples of new from PatternMatchResult


Examples of new from SubSpace


Examples of new from Symbol


Examples of new from TexFormat

--R 
--R
--RThere are 7 exposed functions called new :
--R   [1] (NonNegativeInteger,NonNegativeInteger,D2) -> D from D
--R            if D2 has TYPE and D has ARR2CAT(D2,D3,D4) and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] (String,String,String) -> D from D if D has FNCAT
--R   [3]  -> ScriptFormulaFormat from ScriptFormulaFormat
--R   [4] (NonNegativeInteger,D2) -> D from D
--R            if D has LNAGG D2 and D2 has TYPE
--R   [5] Symbol -> Symbol from Symbol
--R   [6]  -> Symbol from Symbol
--R   [7]  -> TexFormat from TexFormat
--R
--RThere are 4 unexposed functions called new :
--R   [1]  -> SubSpaceComponentProperty from SubSpaceComponentProperty
--R   [2]  -> PatternMatchListResult(D1,D2,D3)
--R            from PatternMatchListResult(D1,D2,D3)
--R            if D2 has SETCAT and D1 has SETCAT and D3 has LSAGG D2
--R   [3]  -> PatternMatchResult(D1,D2) from PatternMatchResult(D1,D2)
--R            if D1 has SETCAT and D2 has SETCAT
--R   [4]  -> SubSpace(D1,D2) from SubSpace(D1,D2) if D1: PI and D2 has 
--R            RING
--R
--RExamples of new from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0)
--R
--R
--RExamples of new from SubSpaceComponentProperty
--R
--R
--RExamples of new from FileNameCategory
--R
--R
--RExamples of new from ScriptFormulaFormat
--R
--R
--RExamples of new from LinearAggregate
--R
--R
--RExamples of new from PatternMatchListResult
--R
--R
--RExamples of new from PatternMatchResult
--R
--R
--RExamples of new from SubSpace
--R
--R
--RExamples of new from Symbol
--R
--R
--RExamples of new from TexFormat
--R
--E 118

--S 119 of 127
)d op insertRoot!
 

There is one exposed function called insertRoot! :
   [1] (D1,BinarySearchTree D1) -> BinarySearchTree D1
            from BinarySearchTree D1 if D1 has ORDSET

Examples of insertRoot! from BinarySearchTree

t1:=binarySearchTree [1,2,3,4] 
insertRoot!(5,t1)

--R 
--R
--RThere is one exposed function called insertRoot! :
--R   [1] (D1,BinarySearchTree D1) -> BinarySearchTree D1
--R            from BinarySearchTree D1 if D1 has ORDSET
--R
--RExamples of insertRoot! from BinarySearchTree
--R
--Rt1:=binarySearchTree [1,2,3,4] 
--RinsertRoot!(5,t1)
--R
--E 119

--S 120 of 127
)d op maxRowIndex
 

There are 2 exposed functions called maxRowIndex :
   [1] D -> Integer from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] D -> Integer from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

Examples of maxRowIndex from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
maxRowIndex(arr)


Examples of maxRowIndex from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called maxRowIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of maxRowIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--RmaxRowIndex(arr)
--R
--R
--RExamples of maxRowIndex from RectangularMatrixCategory
--R
--E 120

--S 121 of 127
)d op escape
 

There is one exposed function called escape :
   [1]  -> Character from Character

Examples of escape from Character

escape()

--R 
--R
--RThere is one exposed function called escape :
--R   [1]  -> Character from Character
--R
--RExamples of escape from Character
--R
--Rescape()
--R
--E 121

--S 122 of 127
)d op nthExponent
 

There is one exposed function called nthExponent :
   [1] (Factored D2,Integer) -> Integer from Factored D2 if D2 has 
            INTDOM

Examples of nthExponent from Factored

a:=factor 9720000 
nthExponent(a,2)

--R 
--R
--RThere is one exposed function called nthExponent :
--R   [1] (Factored D2,Integer) -> Integer from Factored D2 if D2 has 
--R            INTDOM
--R
--RExamples of nthExponent from Factored
--R
--Ra:=factor 9720000 
--RnthExponent(a,2)
--R
--E 122

--S 123 of 127
)d op parts
 

There are 7 exposed functions called parts :
   [1] D -> List D2 from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] ArrayStack D2 -> List D2 from ArrayStack D2
            if $ has finiteAggregate and D2 has SETCAT
   [3] Dequeue D2 -> List D2 from Dequeue D2
            if $ has finiteAggregate and D2 has SETCAT
   [4] Heap D2 -> List D2 from Heap D2
            if $ has finiteAggregate and D2 has ORDSET
   [5] D -> List D2 from D
            if D has finiteAggregate and D has HOAGG D2 and D2 has TYPE
            
   [6] Queue D2 -> List D2 from Queue D2
            if $ has finiteAggregate and D2 has SETCAT
   [7] Stack D2 -> List D2 from Stack D2
            if $ has finiteAggregate and D2 has SETCAT

Examples of parts from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
parts(arr)


Examples of parts from ArrayStack

a:ArrayStack INT:= arrayStack [1,2,3,4,5] 
parts a


Examples of parts from Dequeue

a:Dequeue INT:= dequeue [1,2,3,4,5] 
parts a


Examples of parts from Heap

a:Heap INT:= heap [1,2,3,4,5] 
parts a


Examples of parts from HomogeneousAggregate


Examples of parts from Queue

a:Queue INT:= queue [1,2,3,4,5] 
parts a


Examples of parts from Stack

a:Stack INT:= stack [1,2,3,4,5] 
parts a

--R 
--R
--RThere are 7 exposed functions called parts :
--R   [1] D -> List D2 from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] ArrayStack D2 -> List D2 from ArrayStack D2
--R            if $ has finiteAggregate and D2 has SETCAT
--R   [3] Dequeue D2 -> List D2 from Dequeue D2
--R            if $ has finiteAggregate and D2 has SETCAT
--R   [4] Heap D2 -> List D2 from Heap D2
--R            if $ has finiteAggregate and D2 has ORDSET
--R   [5] D -> List D2 from D
--R            if D has finiteAggregate and D has HOAGG D2 and D2 has TYPE
--R            
--R   [6] Queue D2 -> List D2 from Queue D2
--R            if $ has finiteAggregate and D2 has SETCAT
--R   [7] Stack D2 -> List D2 from Stack D2
--R            if $ has finiteAggregate and D2 has SETCAT
--R
--RExamples of parts from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Rparts(arr)
--R
--R
--RExamples of parts from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] 
--Rparts a
--R
--R
--RExamples of parts from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5] 
--Rparts a
--R
--R
--RExamples of parts from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5] 
--Rparts a
--R
--R
--RExamples of parts from HomogeneousAggregate
--R
--R
--RExamples of parts from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5] 
--Rparts a
--R
--R
--RExamples of parts from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5] 
--Rparts a
--R
--E 123

--S 124 of 127
)d op elt
 

There are 47 exposed functions called elt :
   [1] (D,Integer,Integer,D1) -> D1 from D
            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
            D1 and D4 has FLAGG D1
   [2] (D,Integer,Integer) -> D1 from D
            if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG D1 and D4 has 
            FLAGG D1 and D1 has TYPE
   [3] (D,right) -> D from D if D has BRAGG D2 and D2 has TYPE
   [4] (D,left) -> D from D if D has BRAGG D2 and D2 has TYPE
   [5] (CartesianTensor(D3,D4,D1),List Integer) -> D1
            from CartesianTensor(D3,D4,D1)
            if D1 has COMRING and D3: INT and D4: NNI
   [6] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer,Integer) -> 
            D1
            from CartesianTensor(D3,D4,D1)
            if D1 has COMRING and D3: INT and D4: NNI
   [7] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer) -> D1
            from CartesianTensor(D3,D4,D1)
            if D1 has COMRING and D3: INT and D4: NNI
   [8] (CartesianTensor(D3,D4,D1),Integer,Integer) -> D1
            from CartesianTensor(D3,D4,D1)
            if D1 has COMRING and D3: INT and D4: NNI
   [9] (CartesianTensor(D3,D4,D1),Integer) -> D1
            from CartesianTensor(D3,D4,D1)
            if D1 has COMRING and D3: INT and D4: NNI
   [10] CartesianTensor(D2,D3,D1) -> D1 from CartesianTensor(D2,D3,D1)
            if D1 has COMRING and D2: INT and D3: NNI
   [11] (Database D3,Symbol) -> DataList String from Database D3
            if D3 has OrderedSet with 
               ?.? : (%,Symbol) -> String
               display : % -> Void
               fullDisplay : % -> Void
   [12] (Database D2,QueryEquation) -> Database D2 from Database D2
            if D2 has OrderedSet with 
               ?.? : (%,Symbol) -> String
               display : % -> Void
               fullDisplay : % -> Void
   [13] (DataList D3,count) -> NonNegativeInteger from DataList D3
            if D3 has ORDSET
   [14] (DataList D2,sort) -> DataList D2 from DataList D2 if D2 has 
            ORDSET
   [15] (DataList D2,unique) -> DataList D2 from DataList D2 if D2 has 
            ORDSET
   [16] (D,D2) -> D1 from D
            if D has ELTAB(D2,D1) and D2 has SETCAT and D1 has TYPE
   [17] (D,D2,D1) -> D1 from D
            if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
         
   [18] (BasicOperator,List D) -> D from D if D has ES
   [19] (BasicOperator,D,D,D,D) -> D from D if D has ES
   [20] (BasicOperator,D,D,D) -> D from D if D has ES
   [21] (BasicOperator,D,D) -> D from D if D has ES
   [22] (BasicOperator,D) -> D from D if D has ES
   [23] (D,D1,D1) -> D1 from D
            if D has FFCAT(D1,D2,D3) and D1 has UFD and D2 has UPOLYC 
            D1 and D3 has UPOLYC FRAC D2
   [24] (D,Integer) -> D1 from D if D has FRNAALG D1 and D1 has COMRING
            
   [25] (IndexCard,Symbol) -> String from IndexCard
   [26] (Library,Symbol) -> Any from Library
   [27] (D,UniversalSegment Integer) -> D from D
            if D has LNAGG D2 and D2 has TYPE
   [28] (ThreeDimensionalMatrix D1,NonNegativeInteger,
            NonNegativeInteger,NonNegativeInteger) -> D1
            from ThreeDimensionalMatrix D1 if D1 has SETCAT
   [29] (D,List Integer,List Integer) -> D from D
            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
            D2 and D4 has FLAGG D2
   [30] (D,D1) -> D1 from D if D has PERMCAT D1 and D1 has SETCAT
   [31] (PermutationGroup D3,NonNegativeInteger) -> Permutation D3
            from PermutationGroup D3 if D3 has SETCAT
   [32] (QuadraticForm(D3,D1),DirectProduct(D3,D1)) -> D1
            from QuadraticForm(D3,D1) if D3: PI and D1 has FIELD
   [33] (D,value) -> D1 from D if D has RCAGG D1 and D1 has TYPE
   [34] (D,Integer,Integer,D1) -> D1 from D
            if D has RMATCAT(D3,D4,D1,D5,D6) and D1 has RING and D5 has
            DIRPCAT(D4,D1) and D6 has DIRPCAT(D3,D1)
   [35] (D,Integer,Integer) -> D1 from D
            if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) 
            and D6 has DIRPCAT(D3,D1) and D1 has RING
   [36] (RewriteRule(D3,D4,D1),D1,PositiveInteger) -> D1
            from RewriteRule(D3,D4,D1)
            if D3 has SETCAT and D4 has Join(Ring,PatternMatchable D3,
            OrderedSet,ConvertibleTo Pattern D3) and D1 has Join(
            FunctionSpace D4,PatternMatchable D3,ConvertibleTo Pattern 
            D3)
   [37] (Ruleset(D3,D4,D1),D1,PositiveInteger) -> D1 from Ruleset(D3,D4
            ,D1)
            if D3 has SETCAT and D4 has Join(Ring,PatternMatchable D3,
            OrderedSet,ConvertibleTo Pattern D3) and D1 has Join(
            FunctionSpace D4,PatternMatchable D3,ConvertibleTo Pattern 
            D3)
   [38] (D,List Integer) -> D from D
            if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 
            has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has 
            SETCAT
   [39] (D,Integer) -> D from D
            if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 
            has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has 
            SETCAT
   [40] (D,D) -> D from D if D has SRAGG
   [41] (Symbol,List OutputForm) -> Symbol from Symbol
   [42] (Fraction D,D1) -> D1 from D
            if D has UPOLYC D1 and D1 has RING and D1 has FIELD
   [43] (Fraction D,Fraction D) -> Fraction D from D
            if D has UPOLYC D2 and D2 has RING and D2 has INTDOM
   [44] (D,D2) -> D1 from D
            if D has UPSCAT(D1,D2) and D2 has OAMON and D1 has RING
   [45] (D,last) -> D1 from D if D has URAGG D1 and D1 has TYPE
   [46] (D,rest) -> D from D if D has URAGG D2 and D2 has TYPE
   [47] (D,first) -> D1 from D if D has URAGG D1 and D1 has TYPE

There are 4 unexposed functions called elt :
   [1] (EuclideanModularRing(D2,D1,D3,D4,D5,D6),D1) -> D1
            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
            if D2 has COMRING and D1 has UPOLYC D2 and D3 has ABELMON 
            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
   [2] (OutputForm,List OutputForm) -> OutputForm from OutputForm
   [3] (BasicOperator,List Pattern D3) -> Pattern D3 from Pattern D3
            if D3 has SETCAT
   [4] Reference D1 -> D1 from Reference D1 if D1 has TYPE

Examples of elt from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
elt(arr,1,1,6) 
elt(arr,1,10,6)

arr : ARRAY2 INT := new(5,4,10) 
elt(arr,1,1)


Examples of elt from BinaryRecursiveAggregate


Examples of elt from CartesianTensor

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v 
tm:CartesianTensor(1,2,Integer):=[tv,tv] 
tn:CartesianTensor(1,2,Integer):=[tm,tm] 
tp:CartesianTensor(1,2,Integer):=[tn,tn] 
tq:CartesianTensor(1,2,Integer):=[tp,tp] 
elt(tq,[2,2,2,2,2])

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v 
tm:CartesianTensor(1,2,Integer):=[tv,tv] 
tn:CartesianTensor(1,2,Integer):=[tm,tm] 
tp:CartesianTensor(1,2,Integer):=[tn,tn] 
elt(tp,2,2,2,2) 
tp[2,2,2,2]

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v 
tm:CartesianTensor(1,2,Integer):=[tv,tv] 
tn:CartesianTensor(1,2,Integer):=[tm,tm] 
elt(tn,2,2,2) 
tn[2,2,2]

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v 
tm:CartesianTensor(1,2,Integer):=[tv,tv] 
elt(tm,2,2) 
tm[2,2]

v:=[2,3] 
tv:CartesianTensor(1,2,Integer):=v 
elt(tv,2) 
tv[2]

tv:CartesianTensor(1,2,Integer):=8 
elt(tv) 
tv[]


Examples of elt from Database


Examples of elt from DataList


Examples of elt from Eltable


Examples of elt from EltableAggregate


Examples of elt from EuclideanModularRing


Examples of elt from ExpressionSpace


Examples of elt from FunctionFieldCategory


Examples of elt from FramedNonAssociativeAlgebra


Examples of elt from IndexCard


Examples of elt from Library


Examples of elt from LinearAggregate


Examples of elt from ThreeDimensionalMatrix


Examples of elt from MatrixCategory

m:=matrix [[j**i for i in 0..4] for j in 1..5] 
elt(m,3,3)


Examples of elt from OutputForm


Examples of elt from Pattern


Examples of elt from PermutationCategory


Examples of elt from PermutationGroup


Examples of elt from QuadraticForm


Examples of elt from RecursiveAggregate


Examples of elt from Reference


Examples of elt from RectangularMatrixCategory


Examples of elt from RewriteRule


Examples of elt from Ruleset


Examples of elt from SExpressionCategory


Examples of elt from StringAggregate


Examples of elt from Symbol


Examples of elt from UnivariatePolynomialCategory


Examples of elt from UnivariatePowerSeriesCategory


Examples of elt from UnaryRecursiveAggregate

--R 
--R
--RThere are 47 exposed functions called elt :
--R   [1] (D,Integer,Integer,D1) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
--R            D1 and D4 has FLAGG D1
--R   [2] (D,Integer,Integer) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG D1 and D4 has 
--R            FLAGG D1 and D1 has TYPE
--R   [3] (D,right) -> D from D if D has BRAGG D2 and D2 has TYPE
--R   [4] (D,left) -> D from D if D has BRAGG D2 and D2 has TYPE
--R   [5] (CartesianTensor(D3,D4,D1),List Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [6] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer,Integer) -> 
--R            D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [7] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [8] (CartesianTensor(D3,D4,D1),Integer,Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [9] (CartesianTensor(D3,D4,D1),Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [10] CartesianTensor(D2,D3,D1) -> D1 from CartesianTensor(D2,D3,D1)
--R            if D1 has COMRING and D2: INT and D3: NNI
--R   [11] (Database D3,Symbol) -> DataList String from Database D3
--R            if D3 has OrderedSet with 
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [12] (Database D2,QueryEquation) -> Database D2 from Database D2
--R            if D2 has OrderedSet with 
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [13] (DataList D3,count) -> NonNegativeInteger from DataList D3
--R            if D3 has ORDSET
--R   [14] (DataList D2,sort) -> DataList D2 from DataList D2 if D2 has 
--R            ORDSET
--R   [15] (DataList D2,unique) -> DataList D2 from DataList D2 if D2 has 
--R            ORDSET
--R   [16] (D,D2) -> D1 from D
--R            if D has ELTAB(D2,D1) and D2 has SETCAT and D1 has TYPE
--R   [17] (D,D2,D1) -> D1 from D
--R            if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
--R         
--R   [18] (BasicOperator,List D) -> D from D if D has ES
--R   [19] (BasicOperator,D,D,D,D) -> D from D if D has ES
--R   [20] (BasicOperator,D,D,D) -> D from D if D has ES
--R   [21] (BasicOperator,D,D) -> D from D if D has ES
--R   [22] (BasicOperator,D) -> D from D if D has ES
--R   [23] (D,D1,D1) -> D1 from D
--R            if D has FFCAT(D1,D2,D3) and D1 has UFD and D2 has UPOLYC 
--R            D1 and D3 has UPOLYC FRAC D2
--R   [24] (D,Integer) -> D1 from D if D has FRNAALG D1 and D1 has COMRING
--R            
--R   [25] (IndexCard,Symbol) -> String from IndexCard
--R   [26] (Library,Symbol) -> Any from Library
--R   [27] (D,UniversalSegment Integer) -> D from D
--R            if D has LNAGG D2 and D2 has TYPE
--R   [28] (ThreeDimensionalMatrix D1,NonNegativeInteger,
--R            NonNegativeInteger,NonNegativeInteger) -> D1
--R            from ThreeDimensionalMatrix D1 if D1 has SETCAT
--R   [29] (D,List Integer,List Integer) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG 
--R            D2 and D4 has FLAGG D2
--R   [30] (D,D1) -> D1 from D if D has PERMCAT D1 and D1 has SETCAT
--R   [31] (PermutationGroup D3,NonNegativeInteger) -> Permutation D3
--R            from PermutationGroup D3 if D3 has SETCAT
--R   [32] (QuadraticForm(D3,D1),DirectProduct(D3,D1)) -> D1
--R            from QuadraticForm(D3,D1) if D3: PI and D1 has FIELD
--R   [33] (D,value) -> D1 from D if D has RCAGG D1 and D1 has TYPE
--R   [34] (D,Integer,Integer,D1) -> D1 from D
--R            if D has RMATCAT(D3,D4,D1,D5,D6) and D1 has RING and D5 has
--R            DIRPCAT(D4,D1) and D6 has DIRPCAT(D3,D1)
--R   [35] (D,Integer,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) 
--R            and D6 has DIRPCAT(D3,D1) and D1 has RING
--R   [36] (RewriteRule(D3,D4,D1),D1,PositiveInteger) -> D1
--R            from RewriteRule(D3,D4,D1)
--R            if D3 has SETCAT and D4 has Join(Ring,PatternMatchable D3,
--R            OrderedSet,ConvertibleTo Pattern D3) and D1 has Join(
--R            FunctionSpace D4,PatternMatchable D3,ConvertibleTo Pattern 
--R            D3)
--R   [37] (Ruleset(D3,D4,D1),D1,PositiveInteger) -> D1 from Ruleset(D3,D4
--R            ,D1)
--R            if D3 has SETCAT and D4 has Join(Ring,PatternMatchable D3,
--R            OrderedSet,ConvertibleTo Pattern D3) and D1 has Join(
--R            FunctionSpace D4,PatternMatchable D3,ConvertibleTo Pattern 
--R            D3)
--R   [38] (D,List Integer) -> D from D
--R            if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 
--R            has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has 
--R            SETCAT
--R   [39] (D,Integer) -> D from D
--R            if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 
--R            has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has 
--R            SETCAT
--R   [40] (D,D) -> D from D if D has SRAGG
--R   [41] (Symbol,List OutputForm) -> Symbol from Symbol
--R   [42] (Fraction D,D1) -> D1 from D
--R            if D has UPOLYC D1 and D1 has RING and D1 has FIELD
--R   [43] (Fraction D,Fraction D) -> Fraction D from D
--R            if D has UPOLYC D2 and D2 has RING and D2 has INTDOM
--R   [44] (D,D2) -> D1 from D
--R            if D has UPSCAT(D1,D2) and D2 has OAMON and D1 has RING
--R   [45] (D,last) -> D1 from D if D has URAGG D1 and D1 has TYPE
--R   [46] (D,rest) -> D from D if D has URAGG D2 and D2 has TYPE
--R   [47] (D,first) -> D1 from D if D has URAGG D1 and D1 has TYPE
--R
--RThere are 4 unexposed functions called elt :
--R   [1] (EuclideanModularRing(D2,D1,D3,D4,D5,D6),D1) -> D1
--R            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
--R            if D2 has COMRING and D1 has UPOLYC D2 and D3 has ABELMON 
--R            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
--R            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
--R   [2] (OutputForm,List OutputForm) -> OutputForm from OutputForm
--R   [3] (BasicOperator,List Pattern D3) -> Pattern D3 from Pattern D3
--R            if D3 has SETCAT
--R   [4] Reference D1 -> D1 from Reference D1 if D1 has TYPE
--R
--RExamples of elt from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Relt(arr,1,1,6) 
--Relt(arr,1,10,6)
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--Relt(arr,1,1)
--R
--R
--RExamples of elt from BinaryRecursiveAggregate
--R
--R
--RExamples of elt from CartesianTensor
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v 
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] 
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] 
--Rtp:CartesianTensor(1,2,Integer):=[tn,tn] 
--Rtq:CartesianTensor(1,2,Integer):=[tp,tp] 
--Relt(tq,[2,2,2,2,2])
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v 
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] 
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] 
--Rtp:CartesianTensor(1,2,Integer):=[tn,tn] 
--Relt(tp,2,2,2,2) 
--Rtp[2,2,2,2]
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v 
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] 
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] 
--Relt(tn,2,2,2) 
--Rtn[2,2,2]
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v 
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] 
--Relt(tm,2,2) 
--Rtm[2,2]
--R
--Rv:=[2,3] 
--Rtv:CartesianTensor(1,2,Integer):=v 
--Relt(tv,2) 
--Rtv[2]
--R
--Rtv:CartesianTensor(1,2,Integer):=8 
--Relt(tv) 
--Rtv[]
--R
--R
--RExamples of elt from Database
--R
--R
--RExamples of elt from DataList
--R
--R
--RExamples of elt from Eltable
--R
--R
--RExamples of elt from EltableAggregate
--R
--R
--RExamples of elt from EuclideanModularRing
--R
--R
--RExamples of elt from ExpressionSpace
--R
--R
--RExamples of elt from FunctionFieldCategory
--R
--R
--RExamples of elt from FramedNonAssociativeAlgebra
--R
--R
--RExamples of elt from IndexCard
--R
--R
--RExamples of elt from Library
--R
--R
--RExamples of elt from LinearAggregate
--R
--R
--RExamples of elt from ThreeDimensionalMatrix
--R
--R
--RExamples of elt from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] 
--Relt(m,3,3)
--R
--R
--RExamples of elt from OutputForm
--R
--R
--RExamples of elt from Pattern
--R
--R
--RExamples of elt from PermutationCategory
--R
--R
--RExamples of elt from PermutationGroup
--R
--R
--RExamples of elt from QuadraticForm
--R
--R
--RExamples of elt from RecursiveAggregate
--R
--R
--RExamples of elt from Reference
--R
--R
--RExamples of elt from RectangularMatrixCategory
--R
--R
--RExamples of elt from RewriteRule
--R
--R
--RExamples of elt from Ruleset
--R
--R
--RExamples of elt from SExpressionCategory
--R
--R
--RExamples of elt from StringAggregate
--R
--R
--RExamples of elt from Symbol
--R
--R
--RExamples of elt from UnivariatePolynomialCategory
--R
--R
--RExamples of elt from UnivariatePowerSeriesCategory
--R
--R
--RExamples of elt from UnaryRecursiveAggregate
--R
--E 123

--S 125 of 127
)d op minColIndex
 

There are 2 exposed functions called minColIndex :
   [1] D -> Integer from D
            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
            D2 and D4 has FLAGG D2
   [2] D -> Integer from D
            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

Examples of minColIndex from TwoDimensionalArrayCategory

arr : ARRAY2 INT := new(5,4,10) 
minColIndex(arr)


Examples of minColIndex from RectangularMatrixCategory

--R 
--R
--RThere are 2 exposed functions called minColIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            D2 and D4 has FLAGG D2
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of minColIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10) 
--RminColIndex(arr)
--R
--R
--RExamples of minColIndex from RectangularMatrixCategory
--R
--E 125

--S 126 of 127
)d op numberOfFactors
 

There is one exposed function called numberOfFactors :
   [1] Factored D2 -> NonNegativeInteger from Factored D2 if D2 has 
            INTDOM

There is one unexposed function called numberOfFactors :
   [1] List Record(factor: D3,degree: Integer) -> NonNegativeInteger
            from GaloisGroupFactorizer D3 if D3 has UPOLYC INT

Examples of numberOfFactors from Factored

a:=factor 9720000 
numberOfFactors a


Examples of numberOfFactors from GaloisGroupFactorizer

--R 
--R
--RThere is one exposed function called numberOfFactors :
--R   [1] Factored D2 -> NonNegativeInteger from Factored D2 if D2 has 
--R            INTDOM
--R
--RThere is one unexposed function called numberOfFactors :
--R   [1] List Record(factor: D3,degree: Integer) -> NonNegativeInteger
--R            from GaloisGroupFactorizer D3 if D3 has UPOLYC INT
--R
--RExamples of numberOfFactors from Factored
--R
--Ra:=factor 9720000 
--RnumberOfFactors a
--R
--R
--RExamples of numberOfFactors from GaloisGroupFactorizer
--R
--E 126

--S 127 of 127
)d op cyclicCopy
 

There is one exposed function called cyclicCopy :
   [1] Tree D1 -> Tree D1 from Tree D1 if D1 has SETCAT

Examples of cyclicCopy from Tree

t1:=tree [1,2,3,4] 
cyclicCopy t1

--R 
--R
--RThere is one exposed function called cyclicCopy :
--R   [1] Tree D1 -> Tree D1 from Tree D1 if D1 has SETCAT
--R
--RExamples of cyclicCopy from Tree
--R
--Rt1:=tree [1,2,3,4] 
--RcyclicCopy t1
--R
--E 127

)spool 
 
Starts dribbling to gbf.output (2010/3/27, 18:26:38).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 3
mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [[0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  x  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  y|
        |            3   |
        |                |
   (1)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  x  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  y  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  x  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  y|
--R        |            3   |
--R        |                |
--R   (1)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  x  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  y  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 1

--S 2 of 3
eq := determinant mfzn
 

   (2)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (2)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 2

--S 3 of 3
groebnerFactorize [eq, eval(eq, [x,y,z], [y,z,x]), eval(eq, [x,y,z], [z,x,y])]
 

   (3)
   [
                  22           22     22     121
     [x y + x z - -- x + y z - -- y - -- z + ---,
                   3            3      3      3
         2   22       25        2   22       25     22  2   388     250
      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
              3        9             3        9      3       9       27
       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
              3        9       3         9         27      9       27       81
     ,
             21994  2   21994     4427     463
    [x + y - -----,y  - ----- y + ----,z - ---],
              5625       5625      675      87
      2   1       11     5     265        2   38     265
    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
          2        2     6      18             3      9
         25     11     11        11     11     11        5     5     5
    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
          9      3      3         3      3      3        3     3     3
         19     5     5
    [x - --,y + -,z + -]]
          3     3     3
  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (3)
--R   [
--R                  22           22     22     121
--R     [x y + x z - -- x + y z - -- y - -- z + ---,
--R                   3            3      3      3
--R         2   22       25        2   22       25     22  2   388     250
--R      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
--R              3        9             3        9      3       9       27
--R       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
--R              3        9       3         9         27      9       27       81
--R     ,
--R             21994  2   21994     4427     463
--R    [x + y - -----,y  - ----- y + ----,z - ---],
--R              5625       5625      675      87
--R      2   1       11     5     265        2   38     265
--R    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
--R          2        2     6      18             3      9
--R         25     11     11        11     11     11        5     5     5
--R    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
--R          9      3      3         3      3      3        3     3     3
--R         19     5     5
--R    [x - --,y + -,z + -]]
--R          3     3     3
--R  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 3
)spool 
 
Starts dribbling to GeneralSparseTable.output (2010/3/27, 18:42:5).
)set message test on
 
)set message auto off
 
)set break resume
 
)clear all
 
--S 1 of 7
patrons: GeneralSparseTable(String, Integer, KeyedAccessFile(Integer), 0) := table() ; 
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "kaf1680.sdata"

   Continuing to read the file...

--E 1

--S 2 of 7
patrons."Smith" := 10500 
 
 
Daly Bug
   patrons is declared as being in GeneralSparseTable(String,Integer,
      KeyedAccessFile Integer,0) but has not been given a value.
--E 2

--S 3 of 7
patrons."Jones" := 22000
 
 
Daly Bug
   patrons is declared as being in GeneralSparseTable(String,Integer,
      KeyedAccessFile Integer,0) but has not been given a value.
--E 3

--S 4 of 7
patrons."Jones" 
 
 
Daly Bug
   patrons is declared as being in GeneralSparseTable(String,Integer,
      KeyedAccessFile Integer,0) but has not been given a value.
--E 4

--S 5 of 7
patrons."Stingy"
 
 
Daly Bug
   patrons is declared as being in GeneralSparseTable(String,Integer,
      KeyedAccessFile Integer,0) but has not been given a value.
--E 5

--S 6 of 7
reduce(+, entries patrons) 
 
 
Daly Bug
   patrons is declared as being in GeneralSparseTable(String,Integer,
      KeyedAccessFile Integer,0) but has not been given a value.
--E 6

--S 7 of 7
)system rm -r kaf*.sdata
 
--E 7
)spool
 
Starts dribbling to ode.output (2010/3/27, 18:30:30).
)set message test on
 
)set message auto off
 
)clear all
 
 
)set break resume
 
--S 1 of 11
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 11
deqx:= differentiate(y x,x,2)+differentiate(y x,x) +y x
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 11
solve(deqx,y,x) --OK
 

                                             x     x
                                     +-+   - -   - -      +-+
                                   x\|3      2     2    x\|3
   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             x     x
--R                                     +-+   - -   - -      +-+
--R                                   x\|3      2     2    x\|3
--R   (3)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 3

--S 4 of 11
solve(deqx,y,x=0,[1]) --OK
 

                      x
              +-+   - -
            x\|3      2
   (4)  cos(-----)%e
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      x
--R              +-+   - -
--R            x\|3      2
--R   (4)  cos(-----)%e
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 11
deqt:= differentiate(y t,t,2)+differentiate(y t,t) +y t
 

         ,,       ,
   (5)  y  (t) + y (t) + y(t)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (5)  y  (t) + y (t) + y(t)
--R
--R                                                     Type: Expression Integer
--E 5

--S 6 of 11
solve(deqt,y,t) --OK
 

                                             t     t
                                     +-+   - -   - -      +-+
                                   t\|3      2     2    t\|3
   (6)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             t     t
--R                                     +-+   - -   - -      +-+
--R                                   t\|3      2     2    t\|3
--R   (6)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 6

--S 7 of 11
solve(deqt,y,t=0,[1]) -- BUG!
 

                      t
              +-+   - -
            t\|3      2
   (7)  cos(-----)%e
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      t
--R              +-+   - -
--R            t\|3      2
--R   (7)  cos(-----)%e
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 11
deqz:= differentiate(y z,z,2)+differentiate(y z,z) +y z
 

         ,,       ,
   (8)  y  (z) + y (z) + y(z)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (8)  y  (z) + y (z) + y(z)
--R
--R                                                     Type: Expression Integer
--E 8

--S 9 of 11
solve(deqz,y,z) --OK
 

                                             z     z
                                     +-+   - -   - -      +-+
                                   z\|3      2     2    z\|3
   (9)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                     2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                             z     z
--R                                     +-+   - -   - -      +-+
--R                                   z\|3      2     2    z\|3
--R   (9)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                     2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 9

--S 10 of 11
solve(deqz,y,z=0,[1]) -- BUG!
 

                       z
               +-+   - -
             z\|3      2
   (10)  cos(-----)%e
               2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       z
--R               +-+   - -
--R             z\|3      2
--R   (10)  cos(-----)%e
--R               2
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 11 needs fixing
solve(deqt,y,x=0,[1])
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseODE: equation has order 0
--R
--R   Continuing to read the file...
--R
--E 11
)spool 
 
Starts dribbling to bug6357.output (2010/3/27, 18:23:26).
)set message test on
 
)set message auto off
 
)clear all
 

-- The original author assumed (roughly) that sqrt(1/x)=1/sqrt(x),
-- which is wrong (for example,
-- sqrt(-1/2) = %i/sqrt(2) != 1/(%i*sqrt(2)) = -%i/sqrt(2)
--S 1 of 2
sqrt(-1/2)
 

         +---+
        \|- 1
   (1)  ------
          +-+
         \|2
                                                        Type: AlgebraicNumber
--R 
--R
--R         +---+
--R        \|- 1
--R   (1)  ------
--R          +-+
--R         \|2
--R                                                        Type: AlgebraicNumber
--E 1

--S 2 of 2
sqrt(-1/abs(x))-1/sqrt(-abs(x))
 

                    +--------+
         +--------+ |     1
        \|- abs(x)  |- ------  - 1
                   \|  abs(x)
   (2)  --------------------------
                 +--------+
                \|- abs(x)
                                                     Type: Expression Integer
--R 
--R
--R                    +--------+
--R         +--------+ |     1
--R        \|- abs(x)  |- ------  - 1
--R                   \|  abs(x)
--R   (2)  --------------------------
--R                 +--------+
--R                \|- abs(x)
--R                                                     Type: Expression Integer
--E 2
)spool
 
Starts dribbling to CartesianTensor.output (2010/3/27, 18:41:47).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 48
CT := CARTEN(i0 := 1, 2, Integer)
 

   (1)  CartesianTensor(1,2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  CartesianTensor(1,2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 48
t0: CT := 8
 

   (2)  8
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (2)  8
--R                                           Type: CartesianTensor(1,2,Integer)
--E 2

--S 3 of 48
rank t0
 

   (3)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  0
--R                                                     Type: NonNegativeInteger
--E 3

--S 4 of 48
v: DirectProduct(2, Integer) := directProduct [3,4]
 

   (4)  [3,4]
                                               Type: DirectProduct(2,Integer)
--R 
--R
--R   (4)  [3,4]
--R                                               Type: DirectProduct(2,Integer)
--E 4

--S 5 of 48
Tv: CT := v
 

   (5)  [3,4]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (5)  [3,4]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 5

--S 6 of 48
m: SquareMatrix(2, Integer) := matrix [ [1,2],[4,5] ]
 

        +1  2+
   (6)  |    |
        +4  5+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (6)  |    |
--R        +4  5+
--R                                                Type: SquareMatrix(2,Integer)
--E 6

--S 7 of 48
Tm: CT := m
 

        +1  2+
   (7)  |    |
        +4  5+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +4  5+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 7

--S 8 of 48
n: SquareMatrix(2, Integer) := matrix [ [2,3],[0,1] ]
 

        +2  3+
   (8)  |    |
        +0  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +2  3+
--R   (8)  |    |
--R        +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 48
Tn: CT := n
 

        +2  3+
   (9)  |    |
        +0  1+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R        +2  3+
--R   (9)  |    |
--R        +0  1+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 9

--S 10 of 48
t1: CT := [2, 3]
 

   (10)  [2,3]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (10)  [2,3]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 10

--S 11 of 48
rank t1
 

   (11)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  1
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 48
t2: CT := [t1, t1]
 

         +2  3+
   (12)  |    |
         +2  3+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  3+
--R   (12)  |    |
--R         +2  3+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 12

--S 13 of 48
t3: CT := [t2, t2]
 

          +2  3+ +2  3+
   (13)  [|    |,|    |]
          +2  3+ +2  3+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R          +2  3+ +2  3+
--R   (13)  [|    |,|    |]
--R          +2  3+ +2  3+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 13

--S 14 of 48
tt: CT := [t3, t3]; tt := [tt, tt]
 

          ++2  3+  +2  3++ ++2  3+  +2  3++
          ||    |  |    || ||    |  |    ||
          |+2  3+  +2  3+| |+2  3+  +2  3+|
   (14)  [|              |,|              |]
          |+2  3+  +2  3+| |+2  3+  +2  3+|
          ||    |  |    || ||    |  |    ||
          ++2  3+  +2  3++ ++2  3+  +2  3++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R          ++2  3+  +2  3++ ++2  3+  +2  3++
--R          ||    |  |    || ||    |  |    ||
--R          |+2  3+  +2  3+| |+2  3+  +2  3+|
--R   (14)  [|              |,|              |]
--R          |+2  3+  +2  3+| |+2  3+  +2  3+|
--R          ||    |  |    || ||    |  |    ||
--R          ++2  3+  +2  3++ ++2  3+  +2  3++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 14

--S 15 of 48
rank tt
 

   (15)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  5
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 48
Tmn := product(Tm, Tn)
 

         ++2  3+    +4  6+ +
         ||    |    |    | |
         |+0  1+    +0  2+ |
   (16)  |                 |
         |+8  12+  +10  15+|
         ||     |  |      ||
         ++0  4 +  +0   5 ++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  3+    +4  6+ +
--R         ||    |    |    | |
--R         |+0  1+    +0  2+ |
--R   (16)  |                 |
--R         |+8  12+  +10  15+|
--R         ||     |  |      ||
--R         ++0  4 +  +0   5 ++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 16

--S 17 of 48
Tmv := contract(Tm,2,Tv,1)
 

   (17)  [11,32]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (17)  [11,32]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 17

--S 18 of 48
Tm*Tv
 

   (18)  [11,32]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (18)  [11,32]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 18

--S 19 of 48
Tmv = m * v
 

   (19)  [11,32]= [11,32]
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R   (19)  [11,32]= [11,32]
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 19

--S 20 of 48
t0()
 

   (20)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  8
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 48
t1(1+1)
 

   (21)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  3
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 48
t2(2,1)
 

   (22)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  2
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 48
t3(2,1,2)
 

   (23)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  3
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 48
Tmn(2,1,2,1)
 

   (24)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (24)  0
--R                                                     Type: NonNegativeInteger
--E 24

--S 25 of 48
t0[]
 

   (25)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  8
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 48
t1[2]
 

   (26)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  3
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 48
t2[2,1]
 

   (27)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  2
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 48
t3[2,1,2]
 

   (28)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  3
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 48
Tmn[2,1,2,1]
 

   (29)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (29)  0
--R                                                     Type: NonNegativeInteger
--E 29

--S 30 of 48
cTmn := contract(Tmn,1,2)
 

         +12  18+
   (30)  |      |
         +0   6 +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +12  18+
--R   (30)  |      |
--R         +0   6 +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 30

--S 31 of 48
trace(m) * n
 

         +12  18+
   (31)  |      |
         +0   6 +
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +12  18+
--R   (31)  |      |
--R         +0   6 +
--R                                                Type: SquareMatrix(2,Integer)
--E 31

--S 32 of 48
contract(Tmn,1,2) = trace(m) * n
 

         +12  18+  +12  18+
   (32)  |      |= |      |
         +0   6 +  +0   6 +
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +12  18+  +12  18+
--R   (32)  |      |= |      |
--R         +0   6 +  +0   6 +
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 32

--S 33 of 48
contract(Tmn,1,3) = transpose(m) * n
 

         +2  7 +  +2  7 +
   (33)  |     |= |     |
         +4  11+  +4  11+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  7 +  +2  7 +
--R   (33)  |     |= |     |
--R         +4  11+  +4  11+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 33

--S 34 of 48
contract(Tmn,1,4) = transpose(m) * transpose(n)
 

         +14  4+  +14  4+
   (34)  |     |= |     |
         +19  5+  +19  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +14  4+  +14  4+
--R   (34)  |     |= |     |
--R         +19  5+  +19  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 34

--S 35 of 48
contract(Tmn,2,3) = m * n
 

         +2  5 +  +2  5 +
   (35)  |     |= |     |
         +8  17+  +8  17+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  5 +  +2  5 +
--R   (35)  |     |= |     |
--R         +8  17+  +8  17+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 35

--S 36 of 48
contract(Tmn,2,4) = m * transpose(n)
 

         +8   2+  +8   2+
   (36)  |     |= |     |
         +23  5+  +23  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +8   2+  +8   2+
--R   (36)  |     |= |     |
--R         +23  5+  +23  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 36

--S 37 of 48
contract(Tmn,3,4) = trace(n) * m
 

         +3   6 +  +3   6 +
   (37)  |      |= |      |
         +12  15+  +12  15+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +3   6 +  +3   6 +
--R   (37)  |      |= |      |
--R         +12  15+  +12  15+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 37

--S 38 of 48
tTmn := transpose(Tmn,1,3)
 

         ++2  3 +  +4   6 ++
         ||     |  |      ||
         |+8  12+  +10  15+|
   (38)  |                 |
         |+0  1+    +0  2+ |
         ||    |    |    | |
         ++0  4+    +0  5+ +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  3 +  +4   6 ++
--R         ||     |  |      ||
--R         |+8  12+  +10  15+|
--R   (38)  |                 |
--R         |+0  1+    +0  2+ |
--R         ||    |    |    | |
--R         ++0  4+    +0  5+ +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 38

--S 39 of 48
transpose Tmn
 

         ++2  8+   +4  10++
         ||    |   |     ||
         |+0  0+   +0  0 +|
   (39)  |                |
         |+3  12+  +6  15+|
         ||     |  |     ||
         ++1  4 +  +2  5 ++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  8+   +4  10++
--R         ||    |   |     ||
--R         |+0  0+   +0  0 +|
--R   (39)  |                |
--R         |+3  12+  +6  15+|
--R         ||     |  |     ||
--R         ++1  4 +  +2  5 ++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 39

--S 40 of 48
transpose Tm = transpose m
 

         +1  4+  +1  4+
   (40)  |    |= |    |
         +2  5+  +2  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +1  4+  +1  4+
--R   (40)  |    |= |    |
--R         +2  5+  +2  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 40

--S 41 of 48
rTmn := reindex(Tmn, [1,4,2,3])
 

         ++2  0+   +3  1+ +
         ||    |   |    | |
         |+4  0+   +6  2+ |
   (41)  |                |
         |+8   0+  +12  4+|
         ||     |  |     ||
         ++10  0+  +15  5++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  0+   +3  1+ +
--R         ||    |   |    | |
--R         |+4  0+   +6  2+ |
--R   (41)  |                |
--R         |+8   0+  +12  4+|
--R         ||     |  |     ||
--R         ++10  0+  +15  5++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 41

--S 42 of 48
tt := transpose(Tm)*Tn - Tn*transpose(Tm)
 

         +- 6  - 16+
   (42)  |         |
         + 2    6  +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +- 6  - 16+
--R   (42)  |         |
--R         + 2    6  +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 42

--S 43 of 48
Tv*(tt+Tn)
 

   (43)  [- 4,- 11]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (43)  [- 4,- 11]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 43

--S 44 of 48
reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm)
 

         ++46   84 +  +57   114++
         ||        |  |        ||
         |+174  212+  +228  285+|
   (44)  |                      |
         | +18  24+    +17  30+ |
         | |      |    |      | |
         + +57  63+    +63  76+ +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++46   84 +  +57   114++
--R         ||        |  |        ||
--R         |+174  212+  +228  285+|
--R   (44)  |                      |
--R         | +18  24+    +17  30+ |
--R         | |      |    |      | |
--R         + +57  63+    +63  76+ +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 44

--S 45 of 48
delta:  CT := kroneckerDelta()
 

         +1  0+
   (45)  |    |
         +0  1+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +1  0+
--R   (45)  |    |
--R         +0  1+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 45

--S 46 of 48
contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2])
 

         + +2  4+   +0  0++  + +2  4+   +0  0++
         | |    |   |    ||  | |    |   |    ||
         | +3  6+   +1  2+|  | +3  6+   +1  2+|
   (46)  |                |= |                |
         |+8   10+  +0  0+|  |+8   10+  +0  0+|
         ||      |  |    ||  ||      |  |    ||
         ++12  15+  +4  5++  ++12  15+  +4  5++
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         + +2  4+   +0  0++  + +2  4+   +0  0++
--R         | |    |   |    ||  | |    |   |    ||
--R         | +3  6+   +1  2+|  | +3  6+   +1  2+|
--R   (46)  |                |= |                |
--R         |+8   10+  +0  0+|  |+8   10+  +0  0+|
--R         ||      |  |    ||  ||      |  |    ||
--R         ++12  15+  +4  5++  ++12  15+  +4  5++
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 46

--S 47 of 48
epsilon:CT := leviCivitaSymbol()
 

         + 0   1+
   (47)  |      |
         +- 1  0+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         + 0   1+
--R   (47)  |      |
--R         +- 1  0+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 47

--S 48 of 48
contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m
 

   (48)  - 6= - 6
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R   (48)  - 6= - 6
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 48
)spool
 
Starts dribbling to IntegerCombinatoricFunctions.output (2010/3/27, 18:42:12).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 4
)set expose add constructor OutputForm
 
   OutputForm is now explicitly exposed in frame initial 
--R 
--I   OutputForm is already explicitly exposed in frame frame0 
--E 1

--S 2 of 4
pascalRow(n) == [right(binomial(n,i),4) for i in 0..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
displayRow(n)==output center blankSeparate pascalRow(n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
for i in 0..7 repeat displayRow i
 
   Compiling function pascalRow with type NonNegativeInteger -> List 
      OutputForm 
   Compiling function displayRow with type NonNegativeInteger -> Void 
                                     1
                                  1    1
                                1    2    1
                             1    3    3    1
                           1    4    6    4    1
                        1    5   10   10    5    1
                      1    6   15   20   15    6    1
                   1    7   21   35   35   21    7    1
                                                                   Type: Void
--R 
--R   Compiling function pascalRow with type NonNegativeInteger -> List 
--R      OutputForm 
--R   Compiling function displayRow with type NonNegativeInteger -> Void 
--R                                     1
--R                                  1    1
--R                                1    2    1
--R                             1    3    3    1
--R                           1    4    6    4    1
--R                        1    5   10   10    5    1
--R                      1    6   15   20   15    6    1
--R                   1    7   21   35   35   21    7    1
--R                                                                   Type: Void
--E 4

)spool
 
Starts dribbling to knot2.output (2010/3/27, 18:28:32).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
f(x:SF):SF == x
 
   Function declaration f : DoubleFloat -> DoubleFloat has been added 
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : DoubleFloat -> DoubleFloat has been added 
--R      to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 7
[p,q] := [3,5]
 

   (2)  [3,5]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [3,5]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 7
PQ    := p/q
 

        3
   (3)  -
        5
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (3)  -
--R        5
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 7
l := lcm(p, q) quo p
 

   (4)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  5
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 7
maxRange := (odd? l => l * %pi; 2 * l * %pi)  
 

   (5)  5%pi
                                                                     Type: Pi
--R 
--R
--R   (5)  5%pi
--R                                                                     Type: Pi
--E 5

--S 6 of 7
theRange := 0..maxRange
 

   (6)  0..(5%pi)
                                                             Type: Segment Pi
--R 
--R
--R   (6)  0..(5%pi)
--R                                                             Type: Segment Pi
--E 6

--S 7 of 7
v:=draw(curve(sin t * cos(PQ*t),cos t * cos(PQ*t),cos t * sin(PQ*t)), _
        t=theRange, tubeRadius==0.1)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Compiling function %F with type DoubleFloat -> DoubleFloat 
   Transmitting data...

   (7)  ThreeDimensionalViewport: "DCOS((3*t)/5)*DSIN(t)"
                                               Type: ThreeDimensionalViewport
--R 
--I   Compiling function %B with type DoubleFloat -> DoubleFloat 
--I   Compiling function %D with type DoubleFloat -> DoubleFloat 
--I   Compiling function %F with type DoubleFloat -> DoubleFloat 
--R   Transmitting data...
--R
--R   (7)  ThreeDimensionalViewport: "DCOS((3*t)/5)*DSIN(t)"
--R                                               Type: ThreeDimensionalViewport
--E 7


)spool 
 
Starts dribbling to frame.output (2010/3/27, 18:26:20).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 24
)frame new testframe
 
--R 
--E 1

--S 2 of 24
)frame names
 
   The names of the existing frames are:
            testframe 
            initial 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            testframe 
--R            initial 
--R      The current frame is the first one listed.
--E 2

--S 3 of 24
)frame next
 
--R 
--E 3

--S 4 of 24
)frame names
 
   The names of the existing frames are:
            initial 
            testframe 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            initial 
--R            testframe 
--R      The current frame is the first one listed.
--E 4

--S 5 of 24
)frame next
 
--R 
--E 5

--S 6 of 24
)frame names
 
   The names of the existing frames are:
            testframe 
            initial 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            testframe 
--R            initial 
--R      The current frame is the first one listed.
--E 6

--S 7 of 24
)frame next
 
--R 
--E 7

--S 8 of 24
)frame drop
 
--R 
--E 8

--S 9 of 24
)frame names
 
   The names of the existing frames are:
            testframe 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            testframe 
--R      The current frame is the first one listed.
--E 9

--S 10 of 24
)frame new testframe2
 
--R 
--E 10

--S 11 of 24
a:=1
 

   (1)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 24
)frame names
 
   The names of the existing frames are:
            testframe2 
            testframe 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            testframe2 
--R            testframe 
--R      The current frame is the first one listed.
--E 12

--S 13 of 24
)frame next
 
--R 
--E 13

--S 14 of 24
a
 

   (1)  a
                                                             Type: Variable a
--R 
--R
--R   (1)  a
--R                                                             Type: Variable a
--E 14

--S 15 of 24
)frame import testframe2 a
 
   Import from frame testframe2 is complete. Please issue )display all 
      if you wish to see the contents of the current frame.
--R 
--R   Import from frame testframe2 is complete. Please issue )display all 
--R      if you wish to see the contents of the current frame.
--E 15

--S 16 of 24
)display all
 
Properties of % :
   Value (has type Variable a):  a
Properties of %e :
   This is a system-defined macro.
   macro %e () == exp(1)
Properties of %i :
   This is a system-defined macro.
   macro %i () == complex(0,1)
Properties of %infinity :
   This is a system-defined macro.
   macro %infinity () == infinity()
Properties of %minusInfinity :
   This is a system-defined macro.
   macro %minusInfinity () == minusInfinity()
Properties of %pi :
   This is a system-defined macro.
   macro %pi () == pi()
Properties of %plusInfinity :
   This is a system-defined macro.
   macro %plusInfinity () == plusInfinity()
Properties of SF :
   This is a system-defined macro.
   macro SF () == DoubleFloat()
Properties of a :
   Value (has type PositiveInteger):  1
--R 
--RProperties of % :
--R   Value (has type Variable a):  a
--RProperties of %e :
--R   This is a system-defined macro.
--R   macro %e () == exp(1)
--RProperties of %i :
--R   This is a system-defined macro.
--R   macro %i () == complex(0,1)
--RProperties of %infinity :
--R   This is a system-defined macro.
--R   macro %infinity () == infinity()
--RProperties of %minusInfinity :
--R   This is a system-defined macro.
--R   macro %minusInfinity () == minusInfinity()
--RProperties of %pi :
--R   This is a system-defined macro.
--R   macro %pi () == pi()
--RProperties of %plusInfinity :
--R   This is a system-defined macro.
--R   macro %plusInfinity () == plusInfinity()
--RProperties of SF :
--R   This is a system-defined macro.
--R   macro SF () == DoubleFloat()
--RProperties of a :
--R   Value (has type PositiveInteger):  1
--E 16

--S 17 of 24
a
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 24
)set message prompt frame
 
--R 
--E 18

--S 19 of 24
)frame next
 
--R 
--E 19

--S 20 of 24
)frame next
 
--R 
--E 20

--S 21 of 24
)frame next
 
--R 
--E 21

--S 22 of 24
)frame names
 
   The names of the existing frames are:
            testframe2 
            testframe 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            testframe2 
--R            testframe 
--R      The current frame is the first one listed.
--E 22

--S 23 of 24
)frame drop testframe2
 
--R 
--E 23

--S 24 of 24
)frame names
 
   The names of the existing frames are:
            testframe 
      The current frame is the first one listed.
--R 
--R   The names of the existing frames are:
--R            testframe 
--R      The current frame is the first one listed.
--E 24

)spool 
 
Starts dribbling to UniversalSegment.output (2010/3/27, 18:46:42).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
pints := 1..
 

   (1)  1..
                                       Type: UniversalSegment PositiveInteger
--R 
--R
--R   (1)  1..
--R                                       Type: UniversalSegment PositiveInteger
--E 1

--S 2 of 9
nevens := (0..) by -2
 

   (2)  0.. by - 2
                                    Type: UniversalSegment NonNegativeInteger
--R 
--R
--R   (2)  0.. by - 2
--R                                    Type: UniversalSegment NonNegativeInteger
--E 2

--S 3 of 9
useg: UniversalSegment(Integer) := 3..10
 

   (3)  3..10
                                               Type: UniversalSegment Integer
--R 
--R
--R   (3)  3..10
--R                                               Type: UniversalSegment Integer
--E 3

--S 4 of 9
hasHi pints
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 9
hasHi nevens
 

   (5)  false
                                                                Type: Boolean
--R 
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 9
hasHi useg
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 9
expand pints
 

   (7)  [1,2,3,4,5,6,7,8,9,10,...]
                                                         Type: Stream Integer
--R 
--R
--R   (7)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                         Type: Stream Integer
--E 7

--S 8 of 9
expand nevens
 

   (8)  [0,- 2,- 4,- 6,- 8,- 10,- 12,- 14,- 16,- 18,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [0,- 2,- 4,- 6,- 8,- 10,- 12,- 14,- 16,- 18,...]
--R                                                         Type: Stream Integer
--E 8

--S 9 of 9
expand [1, 3, 10..15, 100..]
 

   (9)  [1,3,10,11,12,13,14,15,100,101,...]
                                                         Type: Stream Integer
--R 
--R
--R   (9)  [1,3,10,11,12,13,14,15,100,101,...]
--R                                                         Type: Stream Integer
--E 9
)spool
 
Starts dribbling to ideal.output (2010/3/27, 18:26:54).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 18
(n,m) : List DMP([x,y],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 18
m := [x**2+y**2-1]
 

          2    2
   (2)  [x  + y  - 1]
         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R          2    2
--R   (2)  [x  + y  - 1]
--R         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 2

--S 3 of 18
n := [x**2-y**2]
 

          2    2
   (3)  [x  - y ]
         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R          2    2
--R   (3)  [x  - y ]
--R         Type: List DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 3

--S 4 of 18
id := ideal m + ideal n
 

          2   1  2   1
   (4)  [x  - -,y  - -]
              2      2
Type: PolynomialIdeals(Fraction Integer,DirectProduct(2,NonNegativeInteger),OrderedVariableList [x,y],DistributedMultivariatePolynomial([x,y],Fraction Integer))
--R 
--R
--R          2   1  2   1
--R   (4)  [x  - -,y  - -]
--R              2      2
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(2,NonNegativeInteger),OrderedVariableList [x,y],DistributedMultivariatePolynomial([x,y],Fraction Integer))
--E 4

--S 5 of 18
zeroDim? id
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5

--S 6 of 18
zeroDim?(ideal m)
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 18
dimension ideal m
 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 18
(f,g):DMP([x,y],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 18
f := x**2-1
 

         2
   (9)  x  - 1
              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R         2
--R   (9)  x  - 1
--R              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 9

--S 10 of 18
g := x*(x**2-1)
 

          3
   (10)  x  - x
              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--R 
--R
--R          3
--R   (10)  x  - x
--R              Type: DistributedMultivariatePolynomial([x,y],Fraction Integer)
--E 10

--S 11 of 18
relationsIdeal [f,g]
 

              2     3     2          2          3
   (11)  [- %B  + %A  + %A ] | [%A= x  - 1,%B= x  - x]
Type: SuchThat(List Polynomial Fraction Integer,List Equation Polynomial Fraction Integer)
--R 
--R
--R              2     3     2          2          3
--R   (11)  [- %B  + %A  + %A ] | [%A= x  - 1,%B= x  - x]
--RType: SuchThat(List Polynomial Fraction Integer,List Equation Polynomial Fraction Integer)
--E 11

--S 12 of 18
l: List DMP([x,y,z],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 18
l:=[x**2+2*y**2,x*z**2-y*z,z**2-4]
 

           2     2    2        2
   (13)  [x  + 2y ,x z  - y z,z  - 4]
       Type: List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R           2     2    2        2
--R   (13)  [x  + 2y ,x z  - y z,z  - 4]
--R       Type: List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 13

--S 14 of 18
ld:=primaryDecomp ideal l
 

               1    2             1    2
   (14)  [[x + - y,y ,z + 2],[x - - y,y ,z - 2]]
               2                  2
Type: List PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               1    2             1    2
--R   (14)  [[x + - y,y ,z + 2],[x - - y,y ,z - 2]]
--R               2                  2
--RType: List PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 14

--S 15 of 18
reduce(intersect,ld)
 

              1      2  2
   (15)  [x - - y z,y ,z  - 4]
              4
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R              1      2  2
--R   (15)  [x - - y z,y ,z  - 4]
--R              4
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 15

--S 16 of 18
reduce(intersect,[radical ld.i for i in 1..2])
 

               2
   (16)  [x,y,z  - 4]
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               2
--R   (16)  [x,y,z  - 4]
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 16

--S 17 of 18
radical ideal l
 

               2
   (17)  [x,y,z  - 4]
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               2
--R   (17)  [x,y,z  - 4]
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 17

--S 18 of 18
quotient(ideal l,y)
 

               2
   (18)  [x,y,z  - 4]
Type: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R               2
--R   (18)  [x,y,z  - 4]
--RType: PolynomialIdeals(Fraction Integer,DirectProduct(3,NonNegativeInteger),OrderedVariableList [x,y,z],DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 18
)spool 
 
Starts dribbling to lode.output (2010/3/27, 18:28:42).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 15
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 15
deq := differentiate(y x, x, 2) + differentiate(y x, x) + y x
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 15
solve(deq, y, x).basis
 

                       x     x
               +-+   - -   - -      +-+
             x\|3      2     2    x\|3
   (3)  [cos(-----)%e   ,%e   sin(-----)]
               2                    2
                                                Type: List Expression Integer
--R 
--R
--R                       x     x
--R               +-+   - -   - -      +-+
--R             x\|3      2     2    x\|3
--R   (3)  [cos(-----)%e   ,%e   sin(-----)]
--R               2                    2
--R                                                Type: List Expression Integer
--E 3

--S 4 of 15
deq := differentiate(y x, x, 2) + y x
 

         ,,
   (4)  y  (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (4)  y  (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 15
solve(deq, y, x = 0, [1, 1])
 

   (5)  sin(x) + cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)  sin(x) + cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 15
solve(deq = sin x, y, x)
 

                       x cos(x)
   (6)  [particular= - --------,basis= [cos(x),sin(x)]]
                           2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                       x cos(x)
--R   (6)  [particular= - --------,basis= [cos(x),sin(x)]]
--R                           2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 6

--S 7 of 15
deq := x**3 * differentiate(y x, x, 3) + x**2 * differentiate(y x, x, 2) - _
2 * x * differentiate(y x, x) + 2 * y x = 2 * x**4
 

         3 ,,,       2 ,,         ,               4
   (7)  x y   (x) + x y  (x) - 2xy (x) + 2y(x)= 2x

                                            Type: Equation Expression Integer
--R 
--R
--R         3 ,,,       2 ,,         ,               4
--R   (7)  x y   (x) + x y  (x) - 2xy (x) + 2y(x)= 2x
--R
--R                                            Type: Equation Expression Integer
--E 7

--S 8 of 15
solve(deq, y, x)
 

   (8)
                 5      3      2               3     2      3      3     2
                x  - 10x  + 20x  + 4         2x  - 3x  + 1 x  - 1 x  - 3x  - 1
   [particular= --------------------,basis= [-------------,------,------------]]
                         15x                       x          x         x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (8)
--R                 5      3      2               3     2      3      3     2
--R                x  - 10x  + 20x  + 4         2x  - 3x  + 1 x  - 1 x  - 3x  - 1
--R   [particular= --------------------,basis= [-------------,------,------------]]
--R                         15x                       x          x         x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 8

--S 9 of 15
solve(deq, y, x = 1, [b, 0, a])
 

          5                      3                    2
        2x  + (- 10b + 10a - 10)x  + (30b - 15a + 10)x  + 10b + 5a - 2
   (9)  --------------------------------------------------------------
                                      30x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          5                      3                    2
--R        2x  + (- 10b + 10a - 10)x  + (30b - 15a + 10)x  + 10b + 5a - 2
--R   (9)  --------------------------------------------------------------
--R                                      30x
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 15
deq := (x**9 + x**3) * differentiate(y x, x, 3) + _
18 * x**8 * differentiate(y x, x,2) - 90 * x * differentiate(y x, x) - _
30 * (11*x**6-3) * y x
 

           9    3  ,,,         8 ,,          ,             6
   (10)  (x  + x )y   (x) + 18x y  (x) - 90xy (x) + (- 330x  + 90)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           9    3  ,,,         8 ,,          ,             6
--R   (10)  (x  + x )y   (x) + 18x y  (x) - 90xy (x) + (- 330x  + 90)y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 15
solve(deq, y, x).basis
 

                        +--+            +--+
                     - \|91 log(x)     \|91 log(x)
             x   x %e              x %e
   (11)  [------,-----------------,---------------]
           6            6                6
          x  + 1       x  + 1           x  + 1
                                                Type: List Expression Integer
--R 
--R
--R                        +--+            +--+
--R                     - \|91 log(x)     \|91 log(x)
--R             x   x %e              x %e
--R   (11)  [------,-----------------,---------------]
--R           6            6                6
--R          x  + 1       x  + 1           x  + 1
--R                                                Type: List Expression Integer
--E 11

--S 12 of 15
deq := (2*x+2)* differentiate(y x, x, 3) + 3* differentiate(y x, x, 2) + _
(2*x**2+2*x)* differentiate(y x,x) - sqrt(x+1) * y x = 2 * x**2 + x - 1
 

   (12)
            ,,,        ,,         2       ,           +-----+    2
   (2x + 2)y   (x) + 3y  (x) + (2x  + 2x)y (x) - y(x)\|x + 1 = 2x  + x - 1

                                            Type: Equation Expression Integer
--R 
--R
--R   (12)
--R            ,,,        ,,         2       ,           +-----+    2
--R   (2x + 2)y   (x) + 3y  (x) + (2x  + 2x)y (x) - y(x)\|x + 1 = 2x  + x - 1
--R
--R                                            Type: Equation Expression Integer
--E 12

--S 13 of 15
solve(deq, y, x).particular
 

          +-----+
   (13)  \|x + 1  + x
                                                     Type: Expression Integer
--R 
--R
--R          +-----+
--R   (13)  \|x + 1  + x
--R                                                     Type: Expression Integer
--E 13

--S 14 of 15
deq := 2*x**3*differentiate(y x,x,2) + 3*x**2*differentiate(y x,x) - 2*y x
 

           3 ,,        2 ,
   (14)  2x y  (x) + 3x y (x) - 2y(x)

                                                     Type: Expression Integer
--R 
--R
--R           3 ,,        2 ,
--R   (14)  2x y  (x) + 3x y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 15
solve(deq,y,x).basis
 

                2      2
            - ----   ----
               +-+    +-+
              \|x    \|x
   (15)  [%e      ,%e    ]
                                                Type: List Expression Integer
--R 
--R
--R                2      2
--R            - ----   ----
--R               +-+    +-+
--R              \|x    \|x
--R   (15)  [%e      ,%e    ]
--R                                                Type: List Expression Integer
--E 15
)spool 
 
Starts dribbling to pat.output (2010/3/27, 18:30:41).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 21
rule square(x) == x*x
 
   There are no library operations named square 
      Use HyperDoc Browse or issue
                               )what op square
      to learn if there is any operation containing " square " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      square with argument type(s) 
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named square 
--R      Use HyperDoc Browse or issue
--R                               )what op square
--R      to learn if there is any operation containing " square " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      square with argument type(s) 
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 1

--S 2 of 21
fact(n | n > 0) == n * fact(n - 1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 21
fact(0) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 21
f('A) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 21
f(0) == 0 otherwise
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 21
binary(true) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 21
binary(false) == 0
 
   1 old definition(s) deleted for function or rule binary 
                                                                   Type: Void
--R 
--R   1 old definition(s) deleted for function or rule binary 
--R                                                                   Type: Void
--E 7

--S 8 of 21
sinValues == rules
  sin(%pi) == 0
  sin(%pi/4) == sqrt(2)/2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 21
integrate(log(1 + tan(x)),x,0,%pi/4) == %pi/8*log(2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 21
powerOf(x,x) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 21
powerOf(x,x**n) == n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 21
powerOf(x,y) == 0 otherwise
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 21
powerOf(x,x**n%) == n%
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 21
powerOf(x,y) == 0 otherwise
 
   1 old definition(s) deleted for function or rule powerOf 
                                                                   Type: Void
--R 
--R   1 old definition(s) deleted for function or rule powerOf 
--R                                                                   Type: Void
--E 14

--S 15 of 21
linearExponent?(exp(%a*x+%b | freeOf?(%a,x) and freeOf?(%b,x)),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 21
linearExponent?(exp(a) | freeOf?(a,x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 21
linearExponent?(u,x) == false
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 21
linearExponent?(exp(x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 21
linearExponent?(exp(a*x) | freeOf?(a,x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 21
linearExponent?(exp(x+b) | freeOf?(b,x),x) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 21
linearExponent?(exp(a*x+b,x) | freeOf?(a,x) and freeOf?(b,x)) == true
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21
)spool 
 
Starts dribbling to Set.output (2010/3/27, 18:46:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
s := set [x**2-1, y**2-1, z**2-1]
 

          2      2      2
   (1)  {x  - 1,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      2      2
--R   (1)  {x  - 1,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 1

--S 2 of 20
t := set [x**i - i+1 for i in 2..10 | prime? i]
 

          2      3      5      7
   (2)  {x  - 1,x  - 2,x  - 4,x  - 6}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      3      5      7
--R   (2)  {x  - 1,x  - 2,x  - 4,x  - 6}
--R                                                 Type: Set Polynomial Integer
--E 2

--S 3 of 20
i := intersect(s,t)
 

          2
   (3)  {x  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2
--R   (3)  {x  - 1}
--R                                                 Type: Set Polynomial Integer
--E 3

--S 4 of 20
u := union(s,t)
 

          2      3      5      7      2      2
   (4)  {x  - 1,x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      3      5      7      2      2
--R   (4)  {x  - 1,x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 4

--S 5 of 20
difference(s,t)
 

          2      2
   (5)  {y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      2
--R   (5)  {y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 5

--S 6 of 20
symmetricDifference(s,t)
 

          3      5      7      2      2
   (6)  {x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          3      5      7      2      2
--R   (6)  {x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 6

--S 7 of 20
member?(y, s)
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 7

--S 8 of 20
member?((y+1)*(y-1), s)
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 20
subset?(i, s)
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 20
subset?(u, s)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 20
gs := set [g for i in 1..11 | primitive?(g := i::PF 11)] 
 

   (11)  {2,6,7,8}
                                                      Type: Set PrimeField 11
--R 
--R
--R   (11)  {2,6,7,8}
--R                                                      Type: Set PrimeField 11
--E 11

--S 12 of 20
complement gs 
 

   (12)  {1,3,4,5,9,10,0}
                                                      Type: Set PrimeField 11
--R 
--R
--R   (12)  {1,3,4,5,9,10,0}
--R                                                      Type: Set PrimeField 11
--E 12

--S 13 of 20
a := set [i**2 for i in 1..5]
 

   (13)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (13)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 13

--S 14 of 20
insert!(32, a)
 

   (14)  {1,4,9,16,25,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (14)  {1,4,9,16,25,32}
--R                                                    Type: Set PositiveInteger
--E 14

--S 15 of 20
remove!(25, a)
 

   (15)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (15)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 15

--S 16 of 20
a
 

   (16)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (16)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 16

--S 17 of 20
b := b0 := set [i**2 for i in 1..5]
 

   (17)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (17)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 17

--S 18 of 20
b := union(b, {32})
 

   (18)  {1,4,9,16,25,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (18)  {1,4,9,16,25,32}
--R                                                    Type: Set PositiveInteger
--E 18

--S 19 of 20
b := difference(b, {25})
 

   (19)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (19)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 19

--S 20 of 20
b0
 

   (20)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (20)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 20
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read synonym2
 
-- This file contains the standard system defined system command
-- synonyms for the Scratchpad II system. It is normally read into
-- the system by adding the line
--         )read synonym input )ifthere )quiet
-- to the start-up profile SPADPROF INPUT (on CMS) or spadprof.input
-- (on AIX).
 
-- If you wish to have a private list of synonyms, it is suggested
-- that you create a file MYSYNS INPUT (on CMS) or mysyns.input (on AIX).
-- This will also automatically be read into the system by the start-up
-- profile by the line
--         )read mysyns input )ifthere )quiet
 
)synonym  ?            what commands
 
)synonym  ap           what things
 
)synonym  apr          what things
 
)synonym  apropos      what things
 
--)synonym  bug          system spadnote
)synonym  cache        set functions cache
 
)synonym  cl           clear
 
)synonym  cls          zsystemdevelopment )cls
 
)synonym  cms          system
 
--)synonym  CMS          system
--)synonym  cp           system cp
--)synonym  CP           system cp
)synonym  co           compiler
 
)synonym  d            display
 
)synonym  dep          display dependents
 
)synonym  dependents   display dependents
 
)synonym  disc         system cp disc
 
)synonym  e            edit
 
--)synonym  exec         system exec
)synonym  fc           zsystemdevelopment )c
 
)synonym  fct          zsystemdevelopment )ct
 
)synonym  fe           zsystemdevelopment )e
 
)synonym  fec          zsystemdevelopment )ec
 
)synonym  fect         zsystemdevelopment )ect
 
)synonym  fns          exec spadfn
 
)synonym  fortran      set output fortran
 
--)synonym  glos         system exec getgloss
)synonym  h            help
 
)synonym  ht           system hypertex &
 
)synonym  include      compile
 
)synonym  kclam        boot clearClams ( )
 
)synonym  killcaches   boot clearConstructorAndLisplibCaches ( )
 
--)synonym  logoff       system cp logoff
--)synonym  note         system note
)synonym  patch        zsystemdevelopment )patch
 
)synonym  pause        zsystemdevelopment )pause
 
--)synonym  peek         system conpeek
)synonym  prompt       set message prompt
 
--)synonym  rdr          system checkrdr
)synonym  recurrence   set functions recurrence
 
)synonym  restore      history )restore
 
)synonym  save         history )save
 
)synonym  seq          set streams
 
)synonym  sequence     set streams
 
)synonym  storage      set message storage
 
)synonym  str          set streams
 
)synonym  streams      set streams
 
--)synonym  tell         system tell
)synonym  time         set message time
 
)synonym  type         set message type
 
)synonym  up           zsystemdevelopment )update
 
)synonym  version      zsystemdevelopment )version
 
)synonym  w            what
 
)synonym  wc           what categories
 
)synonym  wd           what domains
 
)synonym  wp           what packages
 
)synonym  ws           what synonyms
 
)lisp (bye)
 
Starts dribbling to Library.output (2010/3/27, 18:45:55).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
stuff := library "Neat.stuff"
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "Neat.stuff"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   File is not readable
--R   "Neat.stuff"
--R
--R   Continuing to read the file...
--R
--E 1

--S 2 of 7
stuff.int := 32**2
 
 
Daly Bug
   The form on the left hand side of an assignment must be a single 
      variable, a Tuple of variables or a reference to an entry in an 
      object supporting the setelt operation.
--R 
--R 
--RDaly Bug
--R   The form on the left hand side of an assignment must be a single 
--R      variable, a Tuple of variables or a reference to an entry in an 
--R      object supporting the setelt operation.
--E 2

--S 3 of 7
stuff."poly" := x**2 + 1
 
 
Daly Bug
   The form on the left hand side of an assignment must be a single 
      variable, a Tuple of variables or a reference to an entry in an 
      object supporting the setelt operation.
--R 
--R 
--RDaly Bug
--R   The form on the left hand side of an assignment must be a single 
--R      variable, a Tuple of variables or a reference to an entry in an 
--R      object supporting the setelt operation.
--E 3

--S 4 of 7
stuff.str := "Hello"
 
 
Daly Bug
   The form on the left hand side of an assignment must be a single 
      variable, a Tuple of variables or a reference to an entry in an 
      object supporting the setelt operation.
--R 
--R 
--RDaly Bug
--R   The form on the left hand side of an assignment must be a single 
--R      variable, a Tuple of variables or a reference to an entry in an 
--R      object supporting the setelt operation.
--E 4

--S 5 of 7
keys stuff
 
   There are 3 exposed and 0 unexposed library operations named keys 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op keys
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named keys 
      with argument type(s) 
                               Variable stuff
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 3 exposed and 0 unexposed library operations named keys 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                              )display op keys
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named keys 
--R      with argument type(s) 
--R                               Variable stuff
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5

--S 6 of 7
stuff.poly
 
   There are no library operations named stuff 
      Use HyperDoc Browse or issue
                               )what op stuff
      to learn if there is any operation containing " stuff " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named stuff
      with argument type(s) 
                                Variable poly
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named stuff 
--R      Use HyperDoc Browse or issue
--R                               )what op stuff
--R      to learn if there is any operation containing " stuff " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named stuff
--R      with argument type(s) 
--R                                Variable poly
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6

--S 7 of 7
stuff("poly")
 
   There are no library operations named stuff 
      Use HyperDoc Browse or issue
                               )what op stuff
      to learn if there is any operation containing " stuff " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named stuff
      with argument type(s) 
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named stuff 
--R      Use HyperDoc Browse or issue
--R                               )what op stuff
--R      to learn if there is any operation containing " stuff " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named stuff
--R      with argument type(s) 
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 7
)system rm -rf Neat.stuff
 
)spool
 
Starts dribbling to gonshor.output (2010/3/27, 18:26:41).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 98
R := FRAC POLY INT
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 98
(c100, c101, _
c200, c201, c202, c211, _
c300, c301, c302, c303, c311, c312, c322) : R
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 98
c100 :=  1 ;     c101 := -1 ;
 

                                            Type: Fraction Polynomial Integer
--R 
--R
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 98
c200 :=  0 ;     c201 :=  1 ;     c202 := -1 ;
                 c211 :=  2 ;
 

                                            Type: Fraction Polynomial Integer
--R 
--R
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 98
c300 :=  1 ;     c301 :=  0 ;     c302 := -1 ;     c303 :=  1 ;
                 c311 :=  1 ;     c312 :=  0 ;
                                  c322 :=  2 ;
 

                                            Type: Fraction Polynomial Integer
--R 
--R
--R                                            Type: Fraction Polynomial Integer
--E 5

--S 6 of 98
gonshor : List SquareMatrix(4,R) :=
  [matrix [ [1, 0, 0, 0], [0, 0, 0, 0],_
            [0, 0, 0, 0], [0, 0, 0, 0] ],_
   matrix [ [c100, c101, 0, 0], [c101, 0, 0, 0],_
            [0, 0, 0, 0], [0, 0, 0, 0] ],_
   matrix [ [c200, c201, c202, 0], [c201, c211, 0, 0],_
            [c202, 0, 0, 0], [0, 0, 0, 0] ],_
   matrix [ [c300, c301, c302, c303], [c301, c311, c312, 0],_
            [c302, c312, c322, 0], [c303, 0, 0, 0] ] ] ;
 

                       Type: List SquareMatrix(4,Fraction Polynomial Integer)
--R 
--R
--R                       Type: List SquareMatrix(4,Fraction Polynomial Integer)
--E 6

--S 7 of 98
basisSymbols : List Symbol := [subscript(e,[i]) for i in 0..3]
 

   (7)  [e ,e ,e ,e ]
          0  1  2  3
                                                            Type: List Symbol
--R 
--R
--R   (7)  [e ,e ,e ,e ]
--R          0  1  2  3
--R                                                            Type: List Symbol
--E 7

--S 8 of 98
GonshorGenetic := ALGSC(R, 4, basisSymbols, gonshor)
 

   (8)
  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
                                                                 Type: Domain
--R 
--R
--R   (8)
--R  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
--R  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R                                                                 Type: Domain
--E 8

--S 9 of 98
commutative?()$GonshorGenetic
 
   algebra is commutative

   (9)  true
                                                                Type: Boolean
--R 
--R   algebra is commutative
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 98
associative?()$GonshorGenetic
 
   algebra is not associative

   (10)  false
                                                                Type: Boolean
--R 
--R   algebra is not associative
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 98
e0 : GonshorGenetic := [1, 0, 0, 0] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 11

--S 12 of 98
e1 : GonshorGenetic := [0, 1, 0, 0] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 12

--S 13 of 98
e2 : GonshorGenetic := [0, 0, 1, 0] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 13

--S 14 of 98
e3 : GonshorGenetic := [0, 0, 0, 1] :: Vector R ;
 

Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 14

--S 15 of 98
x  : GonshorGenetic := x0*e0 + x1*e1 + x2*e2 + x3*e3
 

   (15)  x3 e  + x2 e  + x1 e  + x0 e
             3       2       1       0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (15)  x3 e  + x2 e  + x1 e  + x0 e
--R             3       2       1       0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 15

--S 16 of 98
Lx := leftRegularRepresentation x
 

         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
         |                                      |
         |0     - x0     2x1 + x0        x1     |
   (16)  |                                      |
         |0       0        - x0       2x2 - x0  |
         |                                      |
         +0       0          0           x0     +
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
--R         |                                      |
--R         |0     - x0     2x1 + x0        x1     |
--R   (16)  |                                      |
--R         |0       0        - x0       2x2 - x0  |
--R         |                                      |
--R         +0       0          0           x0     +
--R                                     Type: Matrix Fraction Polynomial Integer
--E 16

--S 17 of 98
p := characteristicPolynomial(Lx,Y)
 

           4     2  2    4
   (17)  x0  - 2Y x0  + Y
                                                     Type: Polynomial Integer
--R 
--R
--R           4     2  2    4
--R   (17)  x0  - 2Y x0  + Y
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 98
leftMinimalPolynomial x
 

          5      2 3     4
   (18)  ?  - 2x0 ?  + x0 ?
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--R
--R          5      2 3     4
--R   (18)  ?  - 2x0 ?  + x0 ?
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 18

)clear prop A a b c r s
 
 
--S 19 of 98
A := GonshorGenetic
 

   (19)
  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
                                                                 Type: Domain
--R 
--R
--R   (19)
--R  AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,
--R  *01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R                                                                 Type: Domain
--E 19

--S 20 of 98
a := x
 

   (20)  x3 e  + x2 e  + x1 e  + x0 e
             3       2       1       0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (20)  x3 e  + x2 e  + x1 e  + x0 e
--R             3       2       1       0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 20

--S 21 of 98
b := (1/4)*e1 + (1/5)*e2 + (3/20)*e3 + (2/5)*e0
 

          3      1      1      2
   (21)  -- e  + - e  + - e  + - e
         20  3   5  2   4  1   5  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          3      1      1      2
--R   (21)  -- e  + - e  + - e  + - e
--R         20  3   5  2   4  1   5  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 21

--S 22 of 98
c := (1/3)*e1 + (1/7)*e2 + (8/21)*e3 + (1/7)*e0
 

          8      1      1      1
   (22)  -- e  + - e  + - e  + - e
         21  3   7  2   3  1   7  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          8      1      1      1
--R   (22)  -- e  + - e  + - e  + - e
--R         21  3   7  2   3  1   7  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 22

--S 23 of 98
r  : R := r
 

   (23)  r
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (23)  r
--R                                            Type: Fraction Polynomial Integer
--E 23

--S 24 of 98
s  : R := s
 

   (24)  s
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (24)  s
--R                                            Type: Fraction Polynomial Integer
--E 24

--S 25 of 98
b*c
 

         2      1       47       2
   (25)  - e  + - e  - --- e  + -- e
         7  3   4  2   420  1   35  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         2      1       47       2
--R   (25)  - e  + - e  - --- e  + -- e
--R         7  3   4  2   420  1   35  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 25

--S 26 of 98
(b*c)*b
 

          893       277       4       4
   (26)  ---- e  - ---- e  + -- e  + --- e
         8400  3   1400  2   75  1   175  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          893       277       4       4
--R   (26)  ---- e  - ---- e  + -- e  + --- e
--R         8400  3   1400  2   75  1   175  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 26

--S 27 of 98
b*(c*b)
 

          893       277       4       4
   (27)  ---- e  - ---- e  + -- e  + --- e
         8400  3   1400  2   75  1   175  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R          893       277       4       4
--R   (27)  ---- e  - ---- e  + -- e  + --- e
--R         8400  3   1400  2   75  1   175  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 27


)clear prop AP
 
--S 28 of 98
AP := ALGPKG(R,A)
 

   (28)
  AlgebraPackage(Fraction Polynomial Integer,AlgebraGivenByStructuralConstants(
  Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX
  ,MATRIX]))
                                                                 Type: Domain
--R 
--R
--R   (28)
--R  AlgebraPackage(Fraction Polynomial Integer,AlgebraGivenByStructuralConstants(
--R  Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX
--R  ,MATRIX]))
--R                                                                 Type: Domain
--E 28

--S 29 of 98
r*a
 

   (29)  r x3 e  + r x2 e  + r x1 e  + r x0 e
               3         2         1         0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (29)  r x3 e  + r x2 e  + r x1 e  + r x0 e
--R               3         2         1         0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 29

--S 30 of 98
a*r
 

   (30)  r x3 e  + r x2 e  + r x1 e  + r x0 e
               3         2         1         0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (30)  r x3 e  + r x2 e  + r x1 e  + r x0 e
--R               3         2         1         0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 30

--S 31 of 98
a*b
 

         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      2x0
   (31)  --------------- e  + ----------------- e  + ----------- e  + --- e
                20        3           20         2        20      1    5   0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      2x0
--R   (31)  --------------- e  + ----------------- e  + ----------- e  + --- e
--R                20        3           20         2        20      1    5   0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 31

--S 32 of 98
b*c
 

         2      1       47       2
   (32)  - e  + - e  - --- e  + -- e
         7  3   4  2   420  1   35  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         2      1       47       2
--R   (32)  - e  + - e  - --- e  + -- e
--R         7  3   4  2   420  1   35  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 32

--S 33 of 98
12 * c
 

         32      12            12
   (33)  -- e  + -- e  + 4e  + -- e
          7  3    7  2     1    7  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         32      12            12
--R   (33)  -- e  + -- e  + 4e  + -- e
--R          7  3    7  2     1    7  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 32

--S 34 of 98
(-3) * a
 

   (34)  - 3x3 e  - 3x2 e  - 3x1 e  - 3x0 e
                3        2        1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (34)  - 3x3 e  - 3x2 e  - 3x1 e  - 3x0 e
--R                3        2        1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 34

--S 35 of 98
d  :=  a ** 12
 

   (35)
             11        10  2         9  2        10         11           8  4
         12x0  x3 + 4x0  x2  + (144x0 x1  + 144x0  x1 - 68x0  )x2 + 248x0 x1
       + 
                9  3       10  2        11         12
         - 784x0 x1  - 86x0  x1  + 204x0  x1 - 24x0
    *
       e
        3
   + 
         11         10  2       11            11       12        12
     (4x0  x2 - 92x0  x1  + 28x0  x1)e  + (4x0  x1 - x0  )e  + x0  e
                                      2                    1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (35)
--R             11        10  2         9  2        10         11           8  4
--R         12x0  x3 + 4x0  x2  + (144x0 x1  + 144x0  x1 - 68x0  )x2 + 248x0 x1
--R       + 
--R                9  3       10  2        11         12
--R         - 784x0 x1  - 86x0  x1  + 204x0  x1 - 24x0
--R    *
--R       e
--R        3
--R   + 
--R         11         10  2       11            11       12        12
--R     (4x0  x2 - 92x0  x1  + 28x0  x1)e  + (4x0  x1 - x0  )e  + x0  e
--R                                      2                    1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 35

--S 36 of 98
-d
 

   (36)
               11        10  2           9  2        10         11
         - 12x0  x3 - 4x0  x2  + (- 144x0 x1  - 144x0  x1 + 68x0  )x2
       + 
                8  4        9  3       10  2        11         12
         - 248x0 x1  + 784x0 x1  + 86x0  x1  - 204x0  x1 + 24x0
    *
       e
        3
   + 
           11         10  2       11              11       12        12
     (- 4x0  x2 + 92x0  x1  - 28x0  x1)e  + (- 4x0  x1 + x0  )e  - x0  e
                                        2                      1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (36)
--R               11        10  2           9  2        10         11
--R         - 12x0  x3 - 4x0  x2  + (- 144x0 x1  - 144x0  x1 + 68x0  )x2
--R       + 
--R                8  4        9  3       10  2        11         12
--R         - 248x0 x1  + 784x0 x1  + 86x0  x1  - 204x0  x1 + 24x0
--R    *
--R       e
--R        3
--R   + 
--R           11         10  2       11              11       12        12
--R     (- 4x0  x2 + 92x0  x1  - 28x0  x1)e  + (- 4x0  x1 + x0  )e  - x0  e
--R                                        2                      1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 36

--S 37 of 98
a + b
 

         20x3 + 3      5x2 + 1      4x1 + 1      5x0 + 2
   (37)  -------- e  + ------- e  + ------- e  + ------- e
            20     3      5     2      4     1      5     0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         20x3 + 3      5x2 + 1      4x1 + 1      5x0 + 2
--R   (37)  -------- e  + ------- e  + ------- e  + ------- e
--R            20     3      5     2      4     1      5     0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 37

--S 38 of 98
d-c
 

   (38)
                11         10  2          9  2         10           11
           252x0  x3 + 84x0  x2  + (3024x0 x1  + 3024x0  x1 - 1428x0  )x2
         + 
                 8  4          9  3         10  2         11          12
           5208x0 x1  - 16464x0 x1  - 1806x0  x1  + 4284x0  x1 - 504x0   - 8
      /
         21
    *
       e
        3
   + 
         11          10  2        11                11        12
     28x0  x2 - 644x0  x1  + 196x0  x1 - 1      12x0  x1 - 3x0   - 1
     ------------------------------------- e  + -------------------- e
                       7                    2             3           1
   + 
        12
     7x0   - 1
     --------- e
         7      0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (38)
--R                11         10  2          9  2         10           11
--R           252x0  x3 + 84x0  x2  + (3024x0 x1  + 3024x0  x1 - 1428x0  )x2
--R         + 
--R                 8  4          9  3         10  2         11          12
--R           5208x0 x1  - 16464x0 x1  - 1806x0  x1  + 4284x0  x1 - 504x0   - 8
--R      /
--R         21
--R    *
--R       e
--R        3
--R   + 
--R         11          10  2        11                11        12
--R     28x0  x2 - 644x0  x1  + 196x0  x1 - 1      12x0  x1 - 3x0   - 1
--R     ------------------------------------- e  + -------------------- e
--R                       7                    2             3           1
--R   + 
--R        12
--R     7x0   - 1
--R     --------- e
--R         7      0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 38

--S 39 of 98
(a*(a*a) = leftPower(a,3)) :: Boolean
 

   (39)  true
                                                                Type: Boolean
--R 
--R
--R   (39)  true
--R                                                                Type: Boolean
--E 39

--S 40 of 98
(a ** 11 =  (a**8 * a**2) * a) :: Boolean
 

   (40)  true
                                                                Type: Boolean
--R 
--R
--R   (40)  true
--R                                                                Type: Boolean
--E 40

--S 41 of 98
(a ** 11 =  a**8 * (a**2 * a)) :: Boolean
 

   (41)  false
                                                                Type: Boolean
--R 
--R
--R   (41)  false
--R                                                                Type: Boolean
--E 41

--S 42 of 98
zero := 0$A
 

   (42)  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (42)  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 42

--S 43 of 98
zero : A := 0
 

   (43)  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (43)  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 43

--S 44 of 98
alternative?()$A
 
   algebra is not left alternative

   (44)  false
                                                                Type: Boolean
--R 
--R   algebra is not left alternative
--R
--R   (44)  false
--R                                                                Type: Boolean
--E 44

--S 45 of 98
antiCommutative?()$A
 
   algebra is not anti-commutative

   (45)  false
                                                                Type: Boolean
--R 
--R   algebra is not anti-commutative
--R
--R   (45)  false
--R                                                                Type: Boolean
--E 45

--S 46 of 98
associative?()$A
 
   algebra is not associative

   (46)  false
                                                                Type: Boolean
--R 
--R   algebra is not associative
--R
--R   (46)  false
--R                                                                Type: Boolean
--E 46

--S 47 of 98
commutative?()$A
 
   algebra is commutative

   (47)  true
                                                                Type: Boolean
--R 
--R   algebra is commutative
--R
--R   (47)  true
--R                                                                Type: Boolean
--E 47

--S 48 of 98
commutator(a,b)
 

   (48)  0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (48)  0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 48

--S 49 of 98
antiCommutator(a,b)
 

         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      4x0
   (49)  --------------- e  + ----------------- e  + ----------- e  + --- e
                10        3           10         2        10      1    5   0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         8x3 + 5x1 + 7x0      - 8x2 + 18x1 + x0      - 8x1 + 3x0      4x0
--R   (49)  --------------- e  + ----------------- e  + ----------- e  + --- e
--R                10        3           10         2        10      1    5   0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 49

--S 50 of 98
associator(a,b,c)
 

         - 21x2 + 6x1 + 7x0      12x2 - 30x1 + 58x0      12x1 - 28x0
   (50)  ------------------ e  + ------------------ e  + ----------- e
                 42          3           105         2       105      1
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R         - 21x2 + 6x1 + 7x0      12x2 - 30x1 + 58x0      12x1 - 28x0
--R   (50)  ------------------ e  + ------------------ e  + ----------- e
--R                 42          3           105         2       105      1
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 50

--S 51 of 98
basis()$A
 

   (51)  [e ,e ,e ,e ]
           0  1  2  3
Type: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (51)  [e ,e ,e ,e ]
--R           0  1  2  3
--RType: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 51

--S 52 of 98
n := rank()$A
 

   (52)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (52)  4
--R                                                        Type: PositiveInteger
--E 52

--S 53 of 98
v : Vector R := [i for i in 1..n]
 

   (53)  [1,2,3,4]
                                     Type: Vector Fraction Polynomial Integer
--R 
--R
--R   (53)  [1,2,3,4]
--R                                     Type: Vector Fraction Polynomial Integer
--E 53

--S 54 of 98
g : A := represents  v
 

   (54)  4e  + 3e  + 2e  + e
           3     2     1    0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (54)  4e  + 3e  + 2e  + e
--R           3     2     1    0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 54

--S 55 of 98
coordinates a
 

   (55)  [x0,x1,x2,x3]
                                     Type: Vector Fraction Polynomial Integer
--R 
--R
--R   (55)  [x0,x1,x2,x3]
--R                                     Type: Vector Fraction Polynomial Integer
--E 55

--S 56 of 98
coordinates [a,b]
 

         +x0  x1  x2  x3+
         |              |
   (56)  |2   1   1    3|
         |-   -   -   --|
         +5   4   5   20+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  x1  x2  x3+
--R         |              |
--R   (56)  |2   1   1    3|
--R         |-   -   -   --|
--R         +5   4   5   20+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 56

--S 57 of 98
a.3
 

   (57)  x2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (57)  x2
--R                                            Type: Fraction Polynomial Integer
--E 57

--S 58 of 98
flexible?()$A
 
   algebra is flexible

   (58)  true
                                                                Type: Boolean
--R 
--R   algebra is flexible
--R
--R   (58)  true
--R                                                                Type: Boolean
--E 58

--S 59 of 98
leftAlternative?()$A
 
   algebra is not left alternative

   (59)  false
                                                                Type: Boolean
--R 
--R   algebra is not left alternative
--R
--R   (59)  false
--R                                                                Type: Boolean
--E 59

--S 60 of 98
rightAlternative?()$A
 
   algebra is not right alternative

   (60)  false
                                                                Type: Boolean
--R 
--R   algebra is not right alternative
--R
--R   (60)  false
--R                                                                Type: Boolean
--E 60

--S 61 of 98
sB := someBasis()$A
 

   (61)  [e ,e ,e ,e ]
           0  1  2  3
Type: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (61)  [e ,e ,e ,e ]
--R           0  1  2  3
--RType: Vector AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 61

--S 62 of 98
zero? a
 

   (62)  false
                                                                Type: Boolean
--R 
--R
--R   (62)  false
--R                                                                Type: Boolean
--E 62

--S 63 of 98
associatorDependence()$A
 

   (63)  [[1,1,1,0,0,0],[0,1,0,1,0,0],[1,0,0,0,1,0],[- 1,- 1,0,0,0,1]]
                                Type: List Vector Fraction Polynomial Integer
--R 
--R
--R   (63)  [[1,1,1,0,0,0],[0,1,0,1,0,0],[1,0,0,0,1,0],[- 1,- 1,0,0,0,1]]
--R                                Type: List Vector Fraction Polynomial Integer
--E 63

--S 64 of 98
jacobiIdentity?()$A
 
   Jacobi identity does not hold

   (64)  false
                                                                Type: Boolean
--R 
--R   Jacobi identity does not hold
--R
--R   (64)  false
--R                                                                Type: Boolean
--E 64

--S 65 of 98
jordanAlgebra?()$A
 
   algebra is commutative
   this is not a Jordan algebra

   (65)  false
                                                                Type: Boolean
--R 
--R   algebra is commutative
--R   this is not a Jordan algebra
--R
--R   (65)  false
--R                                                                Type: Boolean
--E 65

--S 66 of 98
jordanAdmissible?()$A
 
   algebra is not Jordan admissible

   (66)  false
                                                                Type: Boolean
--R 
--R   algebra is not Jordan admissible
--R
--R   (66)  false
--R                                                                Type: Boolean
--E 66

--S 67 of 98
lieAdmissible?()$A
 
   algebra is Lie admissible

   (67)  true
                                                                Type: Boolean
--R 
--R   algebra is Lie admissible
--R
--R   (67)  true
--R                                                                Type: Boolean
--E 67

--S 68 of 98
b2 := [reduce(+,[sB.i for i in 1..k]) for k in 1..n]
 

   (68)  [e ,e  + e ,e  + e  + e ,e  + e  + e  + e ]
           0  1    0  2    1    0  3    2    1    0
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (68)  [e ,e  + e ,e  + e  + e ,e  + e  + e  + e ]
--R           0  1    0  2    1    0  3    2    1    0
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 68

--S 69 of 98
coordinates  (a ,b2 :: Vector A)
 

   (69)  [- x1 + x0,- x2 + x1,- x3 + x2,x3]
                                     Type: Vector Fraction Polynomial Integer
--R 
--R
--R   (69)  [- x1 + x0,- x2 + x1,- x3 + x2,x3]
--R                                     Type: Vector Fraction Polynomial Integer
--E 69

--S 70 of 98
coordinates  ([a,b] ,bb := (b2 :: Vector A))
 

         +- x1 + x0  - x2 + x1  - x3 + x2  x3+
         |                                   |
   (70)  |    3          1          1       3|
         |   --         --         --      --|
         +   20         20         20      20+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +- x1 + x0  - x2 + x1  - x3 + x2  x3+
--R         |                                   |
--R   (70)  |    3          1          1       3|
--R         |   --         --         --      --|
--R         +   20         20         20      20+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 70

--S 71 of 98
leftMinimalPolynomial a
 

          5      2 3     4
   (71)  ?  - 2x0 ?  + x0 ?
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--R
--R          5      2 3     4
--R   (71)  ?  - 2x0 ?  + x0 ?
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 71

--S 72 of 98
leftPower (a,10)
 

   (72)
          9        8  2          7  2      8        9          8  2      10
     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
                                                                             3
   + 
           9         8  2      9        10            9       10        10
     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
                                            2                     1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (72)
--R          9        8  2          7  2      8        9          8  2      10
--R     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
--R                                                                             3
--R   + 
--R           9         8  2      9        10            9       10        10
--R     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
--R                                            2                     1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 72

--S 73 of 98
rightPower(a,10)
 

   (73)
          9        8  2          7  2      8        9          8  2      10
     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
                                                                             3
   + 
           9         8  2      9        10            9       10        10
     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
                                            2                     1        0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (73)
--R          9        8  2          7  2      8        9          8  2      10
--R     (10x0 x3 - 6x0 x2  + (- 32x0 x1  + 8x0 x1 + 2x0 )x2 + 13x0 x1  + 5x0  )e
--R                                                                             3
--R   + 
--R           9         8  2      9        10            9       10        10
--R     (- 2x0 x2 + 26x0 x1  + 6x0 x1 - 4x0  )e  + (- 2x0 x1 + x0  )e  + x0  e
--R                                            2                     1        0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 73

--S 74 of 98
leftRegularRepresentation a
 

         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
         |                                      |
         |0     - x0     2x1 + x0        x1     |
   (74)  |                                      |
         |0       0        - x0       2x2 - x0  |
         |                                      |
         +0       0          0           x0     +
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
--R         |                                      |
--R         |0     - x0     2x1 + x0        x1     |
--R   (74)  |                                      |
--R         |0       0        - x0       2x2 - x0  |
--R         |                                      |
--R         +0       0          0           x0     +
--R                                     Type: Matrix Fraction Polynomial Integer
--E 74

--S 75 of 98
leftRegularRepresentation (a,bb)
 

         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
         |                                                                |
         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
   (75)  |                                                                |
         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
         |                                                                |
         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
--R         |                                                                |
--R         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
--R   (75)  |                                                                |
--R         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
--R         |                                                                |
--R         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 75

--S 76 of 98
leftUnit()$A
 
   this algebra has no left unit

   (76)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   this algebra has no left unit
--R
--R   (76)  "failed"
--R                                                    Type: Union("failed",...)
--E 76

--S 77 of 98
represents (v,bb)
 

   (77)  4e  + 7e  + 9e  + 10e
           3     2     1      0
Type: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (77)  4e  + 7e  + 9e  + 10e
--R           3     2     1      0
--RType: AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 77

--S 78 of 98
rightMinimalPolynomial a
 

          5      2 3     4
   (78)  ?  - 2x0 ?  + x0 ?
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--R
--R          5      2 3     4
--R   (78)  ?  - 2x0 ?  + x0 ?
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 78

--S 79 of 98
rightRegularRepresentation a
 

         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
         |                                      |
         |0     - x0     2x1 + x0        x1     |
   (79)  |                                      |
         |0       0        - x0       2x2 - x0  |
         |                                      |
         +0       0          0           x0     +
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +x0  - x1 + x0  - x2 + x1  x3 - x2 + x0+
--R         |                                      |
--R         |0     - x0     2x1 + x0        x1     |
--R   (79)  |                                      |
--R         |0       0        - x0       2x2 - x0  |
--R         |                                      |
--R         +0       0          0           x0     +
--R                                     Type: Matrix Fraction Polynomial Integer
--E 79

--S 80 of 98
rightRegularRepresentation (a,bb)
 

         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
         |                                                                |
         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
   (80)  |                                                                |
         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
         |                                                                |
         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +  x1     x2 - 2x1 + x0     - x3 + x1 - x0        x3 - x2 + x0   +
--R         |                                                                |
--R         |x1 + x0  x2 - 4x1 - x0       - x3 + 2x1        x3 - x2 + x1 + x0|
--R   (80)  |                                                                |
--R         |x1 + x0    x2 - 4x1       - x3 - 2x2 + 2x1       x3 + x2 + x1   |
--R         |                                                                |
--R         +x1 + x0    x2 - 4x1     - x3 - 2x2 + 2x1 - x0  x3 + x2 + x1 + x0+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 80

--S 81 of 98
rightUnit()$A
 
   this algebra has no right unit

   (81)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   this algebra has no right unit
--R
--R   (81)  "failed"
--R                                                    Type: Union("failed",...)
--E 81

--S 82 of 98
structuralConstants()$A
 

          +1  0  0  0+ + 1   - 1  0  0+ + 0   1  - 1  0+ + 1   0  - 1  1+
          |          | |              | |              | |              |
          |0  0  0  0| |- 1   0   0  0| | 1   2   0   0| | 0   1   0   0|
   (82)  [|          |,|              |,|              |,|              |]
          |0  0  0  0| | 0    0   0  0| |- 1  0   0   0| |- 1  0   2   0|
          |          | |              | |              | |              |
          +0  0  0  0+ + 0    0   0  0+ + 0   0   0   0+ + 1   0   0   0+
                              Type: Vector Matrix Fraction Polynomial Integer
--R 
--R
--R          +1  0  0  0+ + 1   - 1  0  0+ + 0   1  - 1  0+ + 1   0  - 1  1+
--R          |          | |              | |              | |              |
--R          |0  0  0  0| |- 1   0   0  0| | 1   2   0   0| | 0   1   0   0|
--R   (82)  [|          |,|              |,|              |,|              |]
--R          |0  0  0  0| | 0    0   0  0| |- 1  0   0   0| |- 1  0   2   0|
--R          |          | |              | |              | |              |
--R          +0  0  0  0+ + 0    0   0  0+ + 0   0   0   0+ + 1   0   0   0+
--R                              Type: Vector Matrix Fraction Polynomial Integer
--E 82

--S 83 of 98
structuralConstants(bb)
 

          +0  1  1  1+ + 1   - 1   0    0 + +- 1  0   0   - 1+ +1  1  0  1+
          |          | |                  | |                | |          |
          |1  2  2  2| |- 1  - 5  - 4  - 4| | 0   2   2    1 | |1  2  1  2|
   (83)  [|          |,|                  |,|                |,|          |]
          |1  2  2  2| | 0   - 4  - 3  - 3| | 0   2   0   - 1| |0  1  2  3|
          |          | |                  | |                | |          |
          +1  2  2  2+ + 0   - 4  - 3  - 3+ +- 1  1  - 1  - 2+ +1  2  3  4+
                              Type: Vector Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  1  1  1+ + 1   - 1   0    0 + +- 1  0   0   - 1+ +1  1  0  1+
--R          |          | |                  | |                | |          |
--R          |1  2  2  2| |- 1  - 5  - 4  - 4| | 0   2   2    1 | |1  2  1  2|
--R   (83)  [|          |,|                  |,|                |,|          |]
--R          |1  2  2  2| | 0   - 4  - 3  - 3| | 0   2   0   - 1| |0  1  2  3|
--R          |          | |                  | |                | |          |
--R          +1  2  2  2+ + 0   - 4  - 3  - 3+ +- 1  1  - 1  - 2+ +1  2  3  4+
--R                              Type: Vector Matrix Fraction Polynomial Integer
--E 83

--S 84 of 98
unit()$A
 
   this algebra has no unit

   (84)  "failed"
                                                    Type: Union("failed",...)
--R 
--R   this algebra has no unit
--R
--R   (84)  "failed"
--R                                                    Type: Union("failed",...)
--E 84

--S 85 of 98
biRank  a
 

   (85)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (85)  4
--R                                                        Type: PositiveInteger
--E 85

--S 86 of 98
leftRank a
 

   (86)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (86)  4
--R                                                        Type: PositiveInteger
--E 86

--S 87 of 98
doubleRank a
 

   (87)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (87)  4
--R                                                        Type: PositiveInteger
--E 87

--S 88 of 98
rightRank a
 

   (88)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (88)  4
--R                                                        Type: PositiveInteger
--E 88

--S 89 of 98
weakBiRank a
 

   (89)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (89)  4
--R                                                        Type: PositiveInteger
--E 89

--S 90 of 98
basisOfCenter()$AP
 

   (90)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (90)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 90

--S 91 of 98
basisOfLeftNucleus()$AP
 

   (91)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (91)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 91

--S 92 of 98
basisOfNucleus()$AP
 

   (92)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (92)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 92

--S 93 of 98
basisOfRightNucleus()$AP
 

   (93)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (93)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 93

--S 94 of 98
basisOfCentroid()$AP
 

          +0  0  0  0+ +1  0  0  0+
          |          | |          |
          |0  0  0  0| |0  1  0  0|
   (94)  [|          |,|          |]
          |0  0  0  0| |0  0  1  0|
          |          | |          |
          +1  0  0  0+ +0  0  0  1+
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  0  0  0+ +1  0  0  0+
--R          |          | |          |
--R          |0  0  0  0| |0  1  0  0|
--R   (94)  [|          |,|          |]
--R          |0  0  0  0| |0  0  1  0|
--R          |          | |          |
--R          +1  0  0  0+ +0  0  0  1+
--R                                Type: List Matrix Fraction Polynomial Integer
--E 94

--S 95 of 98
basisOfCommutingElements()$AP
 

   (95)  [e ,e ,e ,e ]
           3  2  1  0
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (95)  [e ,e ,e ,e ]
--R           3  2  1  0
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 95

--S 96 of 98
basisOfLeftNucloid()$AP
 

          +0  0  0  0+ +1  0  0  0+
          |          | |          |
          |0  0  0  0| |0  1  0  0|
   (96)  [|          |,|          |]
          |0  0  0  0| |0  0  1  0|
          |          | |          |
          +1  0  0  0+ +0  0  0  1+
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  0  0  0+ +1  0  0  0+
--R          |          | |          |
--R          |0  0  0  0| |0  1  0  0|
--R   (96)  [|          |,|          |]
--R          |0  0  0  0| |0  0  1  0|
--R          |          | |          |
--R          +1  0  0  0+ +0  0  0  1+
--R                                Type: List Matrix Fraction Polynomial Integer
--E 96

--S 97 of 98
basisOfMiddleNucleus()$AP
 

   (97)  [e ]
           3
Type: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--R 
--R
--R   (97)  [e ]
--R           3
--RType: List AlgebraGivenByStructuralConstants(Fraction Polynomial Integer,4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])
--E 97

--S 98 of 98
basisOfRightNucloid()$AP
 

          +0  0  0  0+ +1  0  0  0+
          |          | |          |
          |0  0  0  0| |0  1  0  0|
   (98)  [|          |,|          |]
          |0  0  0  0| |0  0  1  0|
          |          | |          |
          +1  0  0  0+ +0  0  0  1+
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +0  0  0  0+ +1  0  0  0+
--R          |          | |          |
--R          |0  0  0  0| |0  1  0  0|
--R   (98)  [|          |,|          |]
--R          |0  0  0  0| |0  0  1  0|
--R          |          | |          |
--R          +1  0  0  0+ +0  0  0  1+
--R                                Type: List Matrix Fraction Polynomial Integer
--E 98
)spool 
 
Starts dribbling to algbrbf.output (2010/3/27, 18:22:59).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 13
digits 20
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 13
p := numeric %pi
 

   (2)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 897932385
--R                                                                  Type: Float
--E 2

--S 3 of 13
a := 163.0
 

   (3)  163.0
                                                                  Type: Float
--R 
--R
--R   (3)  163.0
--R                                                                  Type: Float
--E 3

--S 4 of 13
b := sqrt a
 

   (4)  12.7671453348 03704662
                                                                  Type: Float
--R 
--R
--R   (4)  12.7671453348 03704662
--R                                                                  Type: Float
--E 4

--S 5 of 13
exp(p * b)
 

   (5)  26253741 2640768743.97
                                                                  Type: Float
--R 
--R
--R   (5)  26253741 2640768743.97
--R                                                                  Type: Float
--E 5

--S 6 of 13
digits 60
 

   (6)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  20
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 13
p := numeric %pi
 

   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
                                                                  Type: Float
--R 
--R
--R   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
--R                                                                  Type: Float
--E 7

--S 8 of 13
a := 163.0
 

   (8)  163.0
                                                                  Type: Float
--R 
--R
--R   (8)  163.0
--R                                                                  Type: Float
--E 8

--S 9 of 13
b := sqrt a
 

   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
                                                                  Type: Float
--R 
--R
--R   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
--R                                                                  Type: Float
--E 9

--S 10 of 13
exp(p * b)
 

   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
                                                                  Type: Float
--R 
--R
--R   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
--R                                                                  Type: Float
--E 10

--S 11 of 13
c := cos(p/12)
 

   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
                                                                  Type: Float
--R 
--R
--R   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
--R                                                                  Type: Float
--E 11

--S 12 of 13
16*c**4 - 16*c**2 + 1
 

   (12)  0.0
                                                                  Type: Float
--R 
--R
--R   (12)  0.0
--R                                                                  Type: Float
--E 12

--S 13 of 13
numeric(%pi, 500)
 

   (13)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (13)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 13
)spool
 
Starts dribbling to mset.output (2010/3/27, 18:30:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 17
macro I == Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 17
macro symdif == symmetricDifference
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 17
s:Multiset I
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 17
t:Multiset I
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 17
t1:Multiset I
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 17
s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10]
 

   (6)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (6)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                                       Type: Multiset Integer
--E 6

--S 7 of 17
t := multiset [2,2,2,9]
 

   (7)  {3: 2,9}
                                                       Type: Multiset Integer
--R 
--R
--R   (7)  {3: 2,9}
--R                                                       Type: Multiset Integer
--E 7

--S 8 of 17
union(s,t)
 

   (8)  {1,5: 2,3: 3,4: 4,2: 5,6,7,9,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (8)  {1,5: 2,3: 3,4: 4,2: 5,6,7,9,10}
--R                                                       Type: Multiset Integer
--E 8

--S 9 of 17
union(s,s)
 

   (9)  {2: 1,4: 2,6: 3,8: 4,4: 5,2: 6,2: 7,2: 10}
                                                       Type: Multiset Integer
--R 
--R
--R   (9)  {2: 1,4: 2,6: 3,8: 4,4: 5,2: 6,2: 7,2: 10}
--R                                                       Type: Multiset Integer
--E 9

--S 10 of 17
intersect(s,t)
 

   (10)  {5: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {5: 2}
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 17
difference(s,t)
 

   (11)  {1,3: 3,4: 4,2: 5,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (11)  {1,3: 3,4: 4,2: 5,6,7,10}
--R                                                       Type: Multiset Integer
--E 11

--S 12 of 17
symdif(s,t)
 

   (12)  {1,3: 3,4: 4,2: 5,6,7,9,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (12)  {1,3: 3,4: 4,2: 5,6,7,9,10}
--R                                                       Type: Multiset Integer
--E 12

--S 13 of 17
symdif(s,s)
 

   (13)  {}
                                                       Type: Multiset Integer
--R 
--R
--R   (13)  {}
--R                                                       Type: Multiset Integer
--E 13

--S 14 of 17
t1 := multiset [2,2]
 

   (14)  {2: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (14)  {2: 2}
--R                                                       Type: Multiset Integer
--E 14

--S 15 of 17
[t1 < t, t1 < s, t1 <= t, t1 <= s]
 

   (15)  [true,true,true,true]
                                                           Type: List Boolean
--R 
--R
--R   (15)  [true,true,true,true]
--R                                                           Type: List Boolean
--E 15

--S 16 of 17
t1 := multiset [2,2,2]
 

   (16)  {3: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (16)  {3: 2}
--R                                                       Type: Multiset Integer
--E 16

--S 17 of 17
[t1 < t, t1 < s, t1 <= t, t1 <= s]
 

   (17)  [true,false,true,true]
                                                           Type: List Boolean
--R 
--R
--R   (17)  [true,false,true,true]
--R                                                           Type: List Boolean
--E 17
)spool 
 
Starts dribbling to symbol.output (2010/3/27, 18:41:9).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 24
X: Symbol := 'x
 

   (1)  x
                                                                 Type: Symbol
--R 
--R
--R   (1)  x
--R                                                                 Type: Symbol
--E 1

--S 2 of 24
XX: Symbol := x
 

   (2)  x
                                                                 Type: Symbol
--R 
--R
--R   (2)  x
--R                                                                 Type: Symbol
--E 2

--S 3 of 24
A := 'a
 

   (3)  a
                                                             Type: Variable a
--R 
--R
--R   (3)  a
--R                                                             Type: Variable a
--E 3

--S 4 of 24
B := b
 

   (4)  b
                                                             Type: Variable b
--R 
--R
--R   (4)  b
--R                                                             Type: Variable b
--E 4

--S 5 of 24
x**2 + 1
 

         2
   (5)  x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (5)  x  + 1
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 24
"Hello"::Symbol
 

   (6)  Hello
                                                                 Type: Symbol
--R 
--R
--R   (6)  Hello
--R                                                                 Type: Symbol
--E 6

--S 7 of 24
new()$Symbol
 

   (7)  %A
                                                                 Type: Symbol
--R 
--R
--R   (7)  %A
--R                                                                 Type: Symbol
--E 7

--S 8 of 24
new()$Symbol
 

   (8)  %B
                                                                 Type: Symbol
--R 
--R
--R   (8)  %B
--R                                                                 Type: Symbol
--E 8

--S 9 of 24
new("xyz")$Symbol
 

   (9)  %xyz0
                                                                 Type: Symbol
--R 
--R
--R   (9)  %xyz0
--R                                                                 Type: Symbol
--E 9

--S 10 of 24
X[i,j]
 

   (10)  x
          i,j
                                                                 Type: Symbol
--R 
--R
--R   (10)  x
--R          i,j
--R                                                                 Type: Symbol
--E 10

--S 11 of 24
U := subscript(u, [1,2,1,2])
 

   (11)  u
          1,2,1,2
                                                                 Type: Symbol
--R 
--R
--R   (11)  u
--R          1,2,1,2
--R                                                                 Type: Symbol
--E 11

--S 12 of 24
V := superscript(v, [n])
 

          n
   (12)  v
                                                                 Type: Symbol
--R 
--R
--R          n
--R   (12)  v
--R                                                                 Type: Symbol
--E 12

--S 13 of 24
P := argscript(p, [t])
 

   (13)  p(t)
                                                                 Type: Symbol
--R 
--R
--R   (13)  p(t)
--R                                                                 Type: Symbol
--E 13

--S 14 of 24
scripted? U
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 24
scripted? X
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 24
string X
 

   (16)  "x"
                                                                 Type: String
--R 
--R
--R   (16)  "x"
--R                                                                 Type: String
--E 16

--S 17 of 24
name U
 

   (17)  u
                                                                 Type: Symbol
--R 
--R
--R   (17)  u
--R                                                                 Type: Symbol
--E 17

--S 18 of 24
scripts U
 

   (18)  [sub= [1,2,1,2],sup= [],presup= [],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (18)  [sub= [1,2,1,2],sup= [],presup= [],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 18

--S 19 of 24
name X
 

   (19)  x
                                                                 Type: Symbol
--R 
--R
--R   (19)  x
--R                                                                 Type: Symbol
--E 19

--S 20 of 24
scripts X
 

   (20)  [sub= [],sup= [],presup= [],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (20)  [sub= [],sup= [],presup= [],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 20

--S 21 of 24
M := script(Mammoth, [[i,j],[k,l],[0,1],[2],[u,v,w]])
 

         0,1       k,l
   (21)     Mammoth   (u,v,w)
           2       i,j
                                                                 Type: Symbol
--R 
--R
--R         0,1       k,l
--R   (21)     Mammoth   (u,v,w)
--R           2       i,j
--R                                                                 Type: Symbol
--E 21

--S 22 of 24
scripts M
 

   (22)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [2],args= [u,v,w]]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (22)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [2],args= [u,v,w]]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 22

--S 23 of 24
N := script(Nut, [[i,j],[k,l],[0,1]])
 

         0,1   k,l
   (23)     Nut
               i,j
                                                                 Type: Symbol
--R 
--R
--R         0,1   k,l
--R   (23)     Nut
--R               i,j
--R                                                                 Type: Symbol
--E 23

--S 24 of 24
scripts N
 

   (24)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (24)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 24
)spool 
 
Starts dribbling to matrix1.output (2010/3/27, 18:29:53).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 38
m : Matrix(Integer) := new(3,3,0)
 

        +0  0  0+
        |       |
   (1)  |0  0  0|
        |       |
        +0  0  0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  0  0+
--R        |       |
--R   (1)  |0  0  0|
--R        |       |
--R        +0  0  0+
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 38
setelt(m,2,3,5)
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 38
m(1,2) := 10
 

   (3)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  10
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 38
m
 

        +0  10  0+
        |        |
   (4)  |0  0   5|
        |        |
        +0  0   0+
                                                         Type: Matrix Integer
--R 
--R
--R        +0  10  0+
--R        |        |
--R   (4)  |0  0   5|
--R        |        |
--R        +0  0   0+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 38
matrix [[1,2,3,4],[0,9,8,7]]
 

        +1  2  3  4+
   (5)  |          |
        +0  9  8  7+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2  3  4+
--R   (5)  |          |
--R        +0  9  8  7+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 38
dm := diagonalMatrix [1,x**2,x**3,x**4,x**5]
 

        +1  0   0   0   0 +
        |                 |
        |    2            |
        |0  x   0   0   0 |
        |                 |
        |        3        |
   (6)  |0  0   x   0   0 |
        |                 |
        |            4    |
        |0  0   0   x   0 |
        |                 |
        |                5|
        +0  0   0   0   x +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  0   0   0   0 +
--R        |                 |
--R        |    2            |
--R        |0  x   0   0   0 |
--R        |                 |
--R        |        3        |
--R   (6)  |0  0   x   0   0 |
--R        |                 |
--R        |            4    |
--R        |0  0   0   x   0 |
--R        |                 |
--R        |                5|
--R        +0  0   0   0   x +
--R                                              Type: Matrix Polynomial Integer
--E 6

--S 7 of 38
setRow!(dm,5,vector [1,1,1,1,1])
 

        +1  0   0   0   0+
        |                |
        |    2           |
        |0  x   0   0   0|
        |                |
   (7)  |        3       |
        |0  0   x   0   0|
        |                |
        |            4   |
        |0  0   0   x   0|
        |                |
        +1  1   1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  0   0   0   0+
--R        |                |
--R        |    2           |
--R        |0  x   0   0   0|
--R        |                |
--R   (7)  |        3       |
--R        |0  0   x   0   0|
--R        |                |
--R        |            4   |
--R        |0  0   0   x   0|
--R        |                |
--R        +1  1   1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 7

--S 8 of 38
setColumn!(dm,2,vector [y,y,y,y,y])
 

        +1  y  0   0   0+
        |               |
        |0  y  0   0   0|
        |               |
        |       3       |
   (8)  |0  y  x   0   0|
        |               |
        |           4   |
        |0  y  0   x   0|
        |               |
        +1  y  1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  y  0   0   0+
--R        |               |
--R        |0  y  0   0   0|
--R        |               |
--R        |       3       |
--R   (8)  |0  y  x   0   0|
--R        |               |
--R        |           4   |
--R        |0  y  0   x   0|
--R        |               |
--R        +1  y  1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 8

--S 9 of 38
cdm := copy(dm)
 

        +1  y  0   0   0+
        |               |
        |0  y  0   0   0|
        |               |
        |       3       |
   (9)  |0  y  x   0   0|
        |               |
        |           4   |
        |0  y  0   x   0|
        |               |
        +1  y  1   1   1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +1  y  0   0   0+
--R        |               |
--R        |0  y  0   0   0|
--R        |               |
--R        |       3       |
--R   (9)  |0  y  x   0   0|
--R        |               |
--R        |           4   |
--R        |0  y  0   x   0|
--R        |               |
--R        +1  y  1   1   1+
--R                                              Type: Matrix Polynomial Integer
--E 9

--S 10 of 38
setelt(dm,4,1,1-x**7)
 

            7
   (10)  - x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R            7
--R   (10)  - x  + 1
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 38
[dm,cdm]
 

          +   1      y  0   0   0+ +1  y  0   0   0+
          |                      | |               |
          |   0      y  0   0   0| |0  y  0   0   0|
          |                      | |               |
          |              3       | |       3       |
   (11)  [|   0      y  x   0   0|,|0  y  x   0   0|]
          |                      | |               |
          |   7              4   | |           4   |
          |- x  + 1  y  0   x   0| |0  y  0   x   0|
          |                      | |               |
          +   1      y  1   1   1+ +1  y  1   1   1+
                                         Type: List Matrix Polynomial Integer
--R 
--R
--R          +   1      y  0   0   0+ +1  y  0   0   0+
--R          |                      | |               |
--R          |   0      y  0   0   0| |0  y  0   0   0|
--R          |                      | |               |
--R          |              3       | |       3       |
--R   (11)  [|   0      y  x   0   0|,|0  y  x   0   0|]
--R          |                      | |               |
--R          |   7              4   | |           4   |
--R          |- x  + 1  y  0   x   0| |0  y  0   x   0|
--R          |                      | |               |
--R          +   1      y  1   1   1+ +1  y  1   1   1+
--R                                         Type: List Matrix Polynomial Integer
--E 11

--S 12 of 38
subMatrix(dm,2,3,2,4)
 

         +y  0   0+
   (12)  |        |
         |    3   |
         +y  x   0+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +y  0   0+
--R   (12)  |        |
--R         |    3   |
--R         +y  x   0+
--R                                              Type: Matrix Polynomial Integer
--E 12

--S 13 of 38
d := diagonalMatrix [1.2,-1.3,1.4,-1.5]
 

         +1.2   0.0   0.0   0.0 +
         |                      |
         |0.0  - 1.3  0.0   0.0 |
   (13)  |                      |
         |0.0   0.0   1.4   0.0 |
         |                      |
         +0.0   0.0   0.0  - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2   0.0   0.0   0.0 +
--R         |                      |
--R         |0.0  - 1.3  0.0   0.0 |
--R   (13)  |                      |
--R         |0.0   0.0   1.4   0.0 |
--R         |                      |
--R         +0.0   0.0   0.0  - 1.5+
--R                                                           Type: Matrix Float
--E 13

--S 14 of 38
e := matrix [[6.7,9.11],[-31.33,67.19]]
 

         +  6.7    9.11 +
   (14)  |              |
         +- 31.33  67.19+
                                                           Type: Matrix Float
--R 
--R
--R         +  6.7    9.11 +
--R   (14)  |              |
--R         +- 31.33  67.19+
--R                                                           Type: Matrix Float
--E 14

--S 15 of 38
setsubMatrix!(d,1,2,e)
 

         +1.2    6.7    9.11    0.0 +
         |                          |
         |0.0  - 31.33  67.19   0.0 |
   (15)  |                          |
         |0.0    0.0     1.4    0.0 |
         |                          |
         +0.0    0.0     0.0   - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2    6.7    9.11    0.0 +
--R         |                          |
--R         |0.0  - 31.33  67.19   0.0 |
--R   (15)  |                          |
--R         |0.0    0.0     1.4    0.0 |
--R         |                          |
--R         +0.0    0.0     0.0   - 1.5+
--R                                                           Type: Matrix Float
--E 15

--S 16 of 38
d
 

         +1.2    6.7    9.11    0.0 +
         |                          |
         |0.0  - 31.33  67.19   0.0 |
   (16)  |                          |
         |0.0    0.0     1.4    0.0 |
         |                          |
         +0.0    0.0     0.0   - 1.5+
                                                           Type: Matrix Float
--R 
--R
--R         +1.2    6.7    9.11    0.0 +
--R         |                          |
--R         |0.0  - 31.33  67.19   0.0 |
--R   (16)  |                          |
--R         |0.0    0.0     1.4    0.0 |
--R         |                          |
--R         +0.0    0.0     0.0   - 1.5+
--R                                                           Type: Matrix Float
--E 16

--S 17 of 38
a := matrix [[1/2,1/3,1/4],[1/5,1/6,1/7]]
 

         +1  1  1+
         |-  -  -|
         |2  3  4|
   (17)  |       |
         |1  1  1|
         |-  -  -|
         +5  6  7+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1+
--R         |-  -  -|
--R         |2  3  4|
--R   (17)  |       |
--R         |1  1  1|
--R         |-  -  -|
--R         +5  6  7+
--R                                                Type: Matrix Fraction Integer
--E 17

--S 18 of 38
b := matrix [[3/5,3/7,3/11],[3/13,3/17,3/19]]
 

         +3   3    3+
         |-   -   --|
         |5   7   11|
   (18)  |          |
         | 3   3   3|
         |--  --  --|
         +13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +3   3    3+
--R         |-   -   --|
--R         |5   7   11|
--R   (18)  |          |
--R         | 3   3   3|
--R         |--  --  --|
--R         +13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 18

--S 19 of 38
horizConcat(a,b)
 

         +1  1  1  3   3    3+
         |-  -  -  -   -   --|
         |2  3  4  5   7   11|
   (19)  |                   |
         |1  1  1   3   3   3|
         |-  -  -  --  --  --|
         +5  6  7  13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  1  3   3    3+
--R         |-  -  -  -   -   --|
--R         |2  3  4  5   7   11|
--R   (19)  |                   |
--R         |1  1  1   3   3   3|
--R         |-  -  -  --  --  --|
--R         +5  6  7  13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 19

--S 20 of 38
vab := vertConcat(a,b)
 

         +1   1   1 +
         |-   -   - |
         |2   3   4 |
         |          |
         |1   1   1 |
         |-   -   - |
         |5   6   7 |
   (20)  |          |
         |3   3    3|
         |-   -   --|
         |5   7   11|
         |          |
         | 3   3   3|
         |--  --  --|
         +13  17  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1   1   1 +
--R         |-   -   - |
--R         |2   3   4 |
--R         |          |
--R         |1   1   1 |
--R         |-   -   - |
--R         |5   6   7 |
--R   (20)  |          |
--R         |3   3    3|
--R         |-   -   --|
--R         |5   7   11|
--R         |          |
--R         | 3   3   3|
--R         |--  --  --|
--R         +13  17  19+
--R                                                Type: Matrix Fraction Integer
--E 20

--S 21 of 38
transpose vab
 

         +1  1  3    3+
         |-  -  -   --|
         |2  5  5   13|
         |            |
         |1  1  3    3|
   (21)  |-  -  -   --|
         |3  6  7   17|
         |            |
         |1  1   3   3|
         |-  -  --  --|
         +4  7  11  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  1  3    3+
--R         |-  -  -   --|
--R         |2  5  5   13|
--R         |            |
--R         |1  1  3    3|
--R   (21)  |-  -  -   --|
--R         |3  6  7   17|
--R         |            |
--R         |1  1   3   3|
--R         |-  -  --  --|
--R         +4  7  11  19+
--R                                                Type: Matrix Fraction Integer
--E 21

)clear all
 

--S 22 of 38
m := matrix [[1,2],[3,4]]
 

        +1  2+
   (1)  |    |
        +3  4+
                                                         Type: Matrix Integer
--R 
--R
--R        +1  2+
--R   (1)  |    |
--R        +3  4+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 38
4 * m * (-5)
 

        +- 20  - 40+
   (2)  |          |
        +- 60  - 80+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 20  - 40+
--R   (2)  |          |
--R        +- 60  - 80+
--R                                                         Type: Matrix Integer
--E 23

--S 24 of 38
n := matrix([[1,0,-2],[-3,5,1]])
 

        + 1   0  - 2+
   (3)  |           |
        +- 3  5   1 +
                                                         Type: Matrix Integer
--R 
--R
--R        + 1   0  - 2+
--R   (3)  |           |
--R        +- 3  5   1 +
--R                                                         Type: Matrix Integer
--E 24

--S 25 of 38
m * n
 

        +- 5  10   0 +
   (4)  |            |
        +- 9  20  - 2+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 5  10   0 +
--R   (4)  |            |
--R        +- 9  20  - 2+
--R                                                         Type: Matrix Integer
--E 25

--S 26 of 38
vec := column(n,3)
 

   (5)  [- 2,1]
                                                         Type: Vector Integer
--R 
--R
--R   (5)  [- 2,1]
--R                                                         Type: Vector Integer
--E 26

--S 27 of 38
vec * m
 

   (6)  [1,0]
                                                         Type: Vector Integer
--R 
--R
--R   (6)  [1,0]
--R                                                         Type: Vector Integer
--E 27

--S 28 of 38
m * vec
 

   (7)  [0,- 2]
                                                         Type: Vector Integer
--R 
--R
--R   (7)  [0,- 2]
--R                                                         Type: Vector Integer
--E 28

--S 29 of 38
hilb := matrix([[1/(i + j) for i in 1..3] for j in 1..3])
 

        +1  1  1+
        |-  -  -|
        |2  3  4|
        |       |
        |1  1  1|
   (8)  |-  -  -|
        |3  4  5|
        |       |
        |1  1  1|
        |-  -  -|
        +4  5  6+
                                                Type: Matrix Fraction Integer
--R 
--R
--R        +1  1  1+
--R        |-  -  -|
--R        |2  3  4|
--R        |       |
--R        |1  1  1|
--R   (8)  |-  -  -|
--R        |3  4  5|
--R        |       |
--R        |1  1  1|
--R        |-  -  -|
--R        +4  5  6+
--R                                                Type: Matrix Fraction Integer
--E 29

--S 30 of 38
inverse(hilb)
 

        + 72    - 240   180 +
        |                   |
   (9)  |- 240   900   - 720|
        |                   |
        + 180   - 720   600 +
                                     Type: Union(Matrix Fraction Integer,...)
--R 
--R
--R        + 72    - 240   180 +
--R        |                   |
--R   (9)  |- 240   900   - 720|
--R        |                   |
--R        + 180   - 720   600 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 30

--S 31 of 38
mm := matrix([[1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16]])
 

         +1   2   3   4 +
         |              |
         |5   6   7   8 |
   (10)  |              |
         |9   10  11  12|
         |              |
         +13  14  15  16+
                                                         Type: Matrix Integer
--R 
--R
--R         +1   2   3   4 +
--R         |              |
--R         |5   6   7   8 |
--R   (10)  |              |
--R         |9   10  11  12|
--R         |              |
--R         +13  14  15  16+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 38
inverse(mm)
 

   (11)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (11)  "failed"
--R                                                    Type: Union("failed",...)
--E 32

--S 33 of 38
determinant(mm)
 

   (12)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (12)  0
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 38
trace(mm)
 

   (13)  34
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  34
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 38
rank(mm)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 38
nullity(mm)
 

   (15)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  2
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 38
nullSpace(mm)
 

   (16)  [[1,- 2,1,0],[2,- 3,0,1]]
                                                    Type: List Vector Integer
--R 
--R
--R   (16)  [[1,- 2,1,0],[2,- 3,0,1]]
--R                                                    Type: List Vector Integer
--E 37

--S 38 of 38
rowEchelon(mm)
 

         +1  2  3  4 +
         |           |
         |0  4  8  12|
   (17)  |           |
         |0  0  0  0 |
         |           |
         +0  0  0  0 +
                                                         Type: Matrix Integer
--R 
--R
--R         +1  2  3  4 +
--R         |           |
--R         |0  4  8  12|
--R   (17)  |           |
--R         |0  0  0  0 |
--R         |           |
--R         +0  0  0  0 +
--R                                                         Type: Matrix Integer
--E 38
)spool 
 
Starts dribbling to kafile.output (2010/3/27, 18:27:19).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 5
ey: KeyedAccessFile(Integer) := open("/tmp/editor.year", "output")
 

   (1)  "/tmp/editor.year"
                                                Type: KeyedAccessFile Integer
--R 
--R
--R   (1)  "/tmp/editor.year"
--R                                                Type: KeyedAccessFile Integer
--E 1

--S 2 of 5
ey."Char"     := 1986
 

   (2)  1986
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1986
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 5
ey."Caviness" := 1985
 

   (3)  1985
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1985
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 5
ey."Fitch"    := 1984
 

   (4)  1984
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  1984
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 5
ey."Char"
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "/tmp/editor.year"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   File is not readable
--R   "/tmp/editor.year"
--R
--R   Continuing to read the file...
--R
--E 5
)spool 
 
Starts dribbling to schaum3.output (2010/3/27, 18:37:12).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 28
aa:=integrate(1/((a*x+b)*(p*x+q)),x)
 

        - log(p x + q) + log(a x + b)
   (1)  -----------------------------
                  a q - b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(p x + q) + log(a x + b)
--R   (1)  -----------------------------
--R                  a q - b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 28
bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b))
 

              p x + q
          log(-------)
              a x + b
   (2)  - ------------
            a q - b p
                                                     Type: Expression Integer
--R 
--R
--R              p x + q
--R          log(-------)
--R              a x + b
--R   (2)  - ------------
--R            a q - b p
--R                                                     Type: Expression Integer
--E

--S 3 of 28
cc:=aa-bb
 

                                            p x + q
        - log(p x + q) + log(a x + b) + log(-------)
                                            a x + b
   (3)  --------------------------------------------
                          a q - b p
                                                     Type: Expression Integer
--R 
--R
--R                                            p x + q
--R        - log(p x + q) + log(a x + b) + log(-------)
--R                                            a x + b
--R   (3)  --------------------------------------------
--R                          a q - b p
--R                                                     Type: Expression Integer
--E

--S 4 of 28
logdiv:=rule(log(a)-log(b) == log(a/b))
 

                                      a
   (4)  - log(b) + log(a) + %G == log(-) + %G
                                      b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                      a
--I   (4)  - log(b) + log(a) + %I == log(-) + %I
--R                                      b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 28
dd:=logdiv cc
 

                              1
        log(a x + b) + log(-------)
                           a x + b
   (5)  ---------------------------
                 a q - b p
                                                     Type: Expression Integer
--R
--R                              1
--R        log(a x + b) + log(-------)
--R                           a x + b
--R   (5)  ---------------------------
--R                 a q - b p
--R                                                     Type: Expression Integer
--E

--S 6 of 28
logmul:=rule(log(a)+log(b) == log(a*b))
 

   (6)  log(b) + log(a) + %H == log(a b) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(b) + log(a) + %J == log(a b) + %J
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 7 of 28      14:105 Schaums and Axiom agree
ee:=logmul dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 8 of 28
aa:=integrate(x/((a*x+b)*(p*x+q)),x)
 

        a q log(p x + q) - b p log(a x + b)
   (1)  -----------------------------------
                    2           2
                   a p q - a b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a q log(p x + q) - b p log(a x + b)
--R   (1)  -----------------------------------
--R                    2           2
--R                   a p q - a b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 28
bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q))
 

        a q log(p x + q) - b p log(a x + b)
   (2)  -----------------------------------
                    2           2
                   a p q - a b p
                                                     Type: Expression Integer
--R 
--R
--R        a q log(p x + q) - b p log(a x + b)
--R   (2)  -----------------------------------
--R                    2           2
--R                   a p q - a b p
--R                                                     Type: Expression Integer
--E

--S 10 of 28     14:106 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 11 of 28
aa:=integrate(1/((a*x+b)^2*(p*x+q)),x)
 

        (a p x + b p)log(p x + q) + (- a p x - b p)log(a x + b) - a q + b p
   (1)  -------------------------------------------------------------------
                 3 2     2           2 2      2   2       2       3 2
               (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        (a p x + b p)log(p x + q) + (- a p x - b p)log(a x + b) - a q + b p
--R   (1)  -------------------------------------------------------------------
--R                 3 2     2           2 2      2   2       2       3 2
--R               (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12 of 28
bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b)))
 

                                  p x + q
                 (a p x + b p)log(-------) - a q + b p
                                  a x + b
   (2)  ------------------------------------------------------
          3 2     2           2 2      2   2       2       3 2
        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
                                                     Type: Expression Integer
--R 
--R
--R                                  p x + q
--R                 (a p x + b p)log(-------) - a q + b p
--R                                  a x + b
--R   (2)  ------------------------------------------------------
--R          3 2     2           2 2      2   2       2       3 2
--R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
--R                                                     Type: Expression Integer
--E

--S 13 of 28
cc:=aa-bb
 

                                                p x + q
        p log(p x + q) - p log(a x + b) - p log(-------)
                                                a x + b
   (3)  ------------------------------------------------
                      2 2               2 2
                     a q  - 2a b p q + b p
                                                     Type: Expression Integer
--R 
--R
--R                                                p x + q
--R        p log(p x + q) - p log(a x + b) - p log(-------)
--R                                                a x + b
--R   (3)  ------------------------------------------------
--R                      2 2               2 2
--R                     a q  - 2a b p q + b p
--R                                                     Type: Expression Integer
--E

--S 14 of 28
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 15 of 28     14:107 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 16 of 28
aa:=integrate(x/((a*x+b)^2*(p*x+q)),x)
 

   (1)
       2                             2                                    2
   (- a q x - a b q)log(p x + q) + (a q x + a b q)log(a x + b) + a b q - b p
   -------------------------------------------------------------------------
              4 2     3         2 2 2      3   2     2 2         3 2
            (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       2                             2                                    2
--R   (- a q x - a b q)log(p x + q) + (a q x + a b q)log(a x + b) + a b q - b p
--R   -------------------------------------------------------------------------
--R              4 2     3         2 2 2      3   2     2 2         3 2
--R            (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17 of 28
bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b)))
 

                  2                a x + b             2
                (a q x + a b q)log(-------) + a b q - b p
                                   p x + q
   (2)  --------------------------------------------------------
          4 2     3         2 2 2      3   2     2 2         3 2
        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
                                                     Type: Expression Integer
--R 
--R
--R                  2                a x + b             2
--R                (a q x + a b q)log(-------) + a b q - b p
--R                                   p x + q
--R   (2)  --------------------------------------------------------
--R          4 2     3         2 2 2      3   2     2 2         3 2
--R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
--R                                                     Type: Expression Integer
--E

--S 18 of 28
cc:=aa-bb
 

                                                  a x + b
        - q log(p x + q) + q log(a x + b) - q log(-------)
                                                  p x + q
   (3)  --------------------------------------------------
                       2 2               2 2
                      a q  - 2a b p q + b p
                                                     Type: Expression Integer
--R 
--R
--R                                                  a x + b
--R        - q log(p x + q) + q log(a x + b) - q log(-------)
--R                                                  p x + q
--R   (3)  --------------------------------------------------
--R                       2 2               2 2
--R                      a q  - 2a b p q + b p
--R                                                     Type: Expression Integer
--E

--S 19 of 28
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20 of 28     14:108 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 21 of 28
aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x)
 

   (1)
         3 2     2   2
       (a q x + a b q )log(p x + q)
     + 
             2           2 2         2       3 2                   2       3 2
       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
  /
       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R         3 2     2   2
--R       (a q x + a b q )log(p x + q)
--R     + 
--R             2           2 2         2       3 2                   2       3 2
--R       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
--R  /
--R       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
--R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22 of 28
bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_
     1/(b*p-a*q)^2*(q^2/p*log(p*x+q)+((b*(b*p-2*a*q))/a^2)*log(a*x+b))
 

   (2)
         3 2     2   2
       (a q x + a b q )log(p x + q)
     + 
             2           2 2         2       3 2                   2       3 2
       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
  /
       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R         3 2     2   2
--R       (a q x + a b q )log(p x + q)
--R     + 
--R             2           2 2         2       3 2                   2       3 2
--R       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
--R  /
--R       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
--R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
--R                                                     Type: Expression Integer
--E

--S 23 of 28     14:109 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 24 of 28     14:110 Axiom cannot do this integral
aa:=integrate(1/((a*x+b)^m*(p*x+q)^n),x)
 

           x
         ++             1
   (1)   |   ---------------------- d%N
        ++             m          n
             (b + %N a) (q + %N p)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             1
--I   (1)   |   ---------------------- d%L
--R        ++             m          n
--I             (b + %L a) (q + %L p)
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 25 of 28
aa:=integrate((a*x+b)/(p*x+q),x)
 

        (- a q + b p)log(p x + q) + a p x
   (1)  ---------------------------------
                         2
                        p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        (- a q + b p)log(p x + q) + a p x
--R   (1)  ---------------------------------
--R                         2
--R                        p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 26 of 28
bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q)
 

        (- a q + b p)log(p x + q) + a p x
   (2)  ---------------------------------
                         2
                        p
                                                     Type: Expression Integer
--R 
--R
--R        (- a q + b p)log(p x + q) + a p x
--R   (2)  ---------------------------------
--R                         2
--R                        p
--R                                                     Type: Expression Integer
--E

--S 27 of 28     14:111 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 28     14:112 Axiom cannot do this integral
aa:=integrate((a*x+b)^m/(p*x+q)^n,x)
 

           x           m
         ++  (b + %N a)
   (1)   |   ----------- d%N
        ++             n
             (q + %N p)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           m
--I         ++  (b + %L a)
--I   (1)   |   ----------- d%L
--R        ++             n
--I             (q + %L p)
--R                                          Type: Union(Expression Integer,...)
--E
)spool
 
Starts dribbling to robidoux.output (2010/3/27, 18:36:55).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 15
X1:=operator 'X1
 

   (1)  X1
                                                          Type: BasicOperator
--R 
--R
--R   (1)  X1
--R                                                          Type: BasicOperator
--E 1

--S 2 of 15
deq1:=D(X1 t,t)=(1+ cos t /(2+sin t)) * X1 t
 

          ,     X1(t)sin(t) + X1(t)cos(t) + 2X1(t)
   (2)  X1 (t)= ----------------------------------
                            sin(t) + 2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,     X1(t)sin(t) + X1(t)cos(t) + 2X1(t)
--R   (2)  X1 (t)= ----------------------------------
--R                            sin(t) + 2
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 15
solve(deq1,X1,t)
 

                                 t            t
   (3)  [particular= 0,basis= [%e sin(t) + 2%e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                 t            t
--R   (3)  [particular= 0,basis= [%e sin(t) + 2%e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 3

--S 4 of 15
C1*%.basis.1
 

             t               t
   (4)  C1 %e sin(t) + 2C1 %e
                                                     Type: Expression Integer
--R 
--R
--R             t               t
--R   (4)  C1 %e sin(t) + 2C1 %e
--R                                                     Type: Expression Integer
--E 4

--S 5 of 15
function(%,'x1,'t)
 

   (5)  x1
                                                                 Type: Symbol
--R 
--R
--R   (5)  x1
--R                                                                 Type: Symbol
--E 5

--S 6 of 15
x1
 

   (6)  x1 t == C1 exp(t)sin(t) + 2C1 exp(t)
                                                      Type: FunctionCalled x1
--R 
--R
--R   (6)  x1 t == C1 exp(t)sin(t) + 2C1 exp(t)
--R                                                      Type: FunctionCalled x1
--E 6

--S 7 of 15
X2:=operator 'X2
 

   (7)  X2
                                                          Type: BasicOperator
--R 
--R
--R   (7)  X2
--R                                                          Type: BasicOperator
--E 7

--S 8 of 15
deq2:=D(X2 t,t)=x1 t - X2 t
 
   Compiling function x1 with type Variable t -> Expression Integer 

          ,          t               t
   (8)  X2 (t)= C1 %e sin(t) + 2C1 %e  - X2(t)

                                            Type: Equation Expression Integer
--R 
--R   Compiling function x1 with type Variable t -> Expression Integer 
--R
--R          ,          t               t
--R   (8)  X2 (t)= C1 %e sin(t) + 2C1 %e  - X2(t)
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 15
solve(deq2,X2,t)
 

   (9)
                      - t   t 2                              - t   t 2
                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
   [particular= ------------------------------------------------------,
                                           5
              - t
    basis= [%e   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (9)
--R                      - t   t 2                              - t   t 2
--R                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
--R   [particular= ------------------------------------------------------,
--R                                           5
--R              - t
--R    basis= [%e   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 9

--S 10 of 15
%.particular
 

               - t   t 2                              - t   t 2
         2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
   (10)  ------------------------------------------------------
                                    5
                                                     Type: Expression Integer
--R 
--R
--R               - t   t 2                              - t   t 2
--R         2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
--R   (10)  ------------------------------------------------------
--R                                    5
--R                                                     Type: Expression Integer
--E 10

--S 11 of 15
simplify %
 

               t                              t
         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e
   (11)  --------------------------------------
                            5
                                                     Type: Expression Integer
--R 
--R
--R               t                              t
--R         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e
--R   (11)  --------------------------------------
--R                            5
--R                                                     Type: Expression Integer
--E 11

--S 12 of 15
%+C2*%%(-3).basis.1
 

               t                              t         - t
         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
   (12)  --------------------------------------------------
                                  5
                                                     Type: Expression Integer
--R 
--R
--R               t                              t         - t
--R         2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
--R   (12)  --------------------------------------------------
--R                                  5
--R                                                     Type: Expression Integer
--E 12

--S 13 of 15
function(%,'x2,'t)
 

   (13)  x2
                                                                 Type: Symbol
--R 
--R
--R   (13)  x2
--R                                                                 Type: Symbol
--E 13

--S 14 of 15
x2
 

                 2C1 exp(t)sin(t) + (- C1 cos(t) + 5C1)exp(t) + 5C2 exp(- t)
   (14)  x2 t == -----------------------------------------------------------
                                              5
                                                      Type: FunctionCalled x2
--R 
--R
--R                 2C1 exp(t)sin(t) + (- C1 cos(t) + 5C1)exp(t) + 5C2 exp(- t)
--R   (14)  x2 t == -----------------------------------------------------------
--R                                              5
--R                                                      Type: FunctionCalled x2
--E 14

--S 15 of 15
x1 t
 

              t               t
   (15)  C1 %e sin(t) + 2C1 %e
                                                     Type: Expression Integer
--R 
--R
--R              t               t
--R   (15)  C1 %e sin(t) + 2C1 %e
--R                                                     Type: Expression Integer
--E 15
)spool 
 
Starts dribbling to intrf.output (2010/3/27, 18:27:15).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 14
x + y/x
 

             2
        y + x
   (1)  ------
           x
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             2
--R        y + x
--R   (1)  ------
--R           x
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 14
integrate(%,x)
 

                     2
        2y log(x) + x
   (2)  --------------
               2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R        2y log(x) + x
--R   (2)  --------------
--R               2
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 14
(x+1)**2/((x+1)**6+1)
 

                       2
                      x  + 2x + 1
   (3)  --------------------------------------
         6     5      4      3      2
        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                       2
--R                      x  + 2x + 1
--R   (3)  --------------------------------------
--R         6     5      4      3      2
--R        x  + 6x  + 15x  + 20x  + 15x  + 6x + 2
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 14
integrate(%,x)
 

              3     2
        atan(x  + 3x  + 3x + 1)
   (4)  -----------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2
--R        atan(x  + 3x  + 3x + 1)
--R   (4)  -----------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 14
(2*x**2+4)**4/(x**2-2)**5
 

            8       6       4       2
         16x  + 128x  + 384x  + 512x  + 256
   (5)  ------------------------------------
         10      8      6      4      2
        x   - 10x  + 40x  - 80x  + 80x  - 32
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            8       6       4       2
--R         16x  + 128x  + 384x  + 512x  + 256
--R   (5)  ------------------------------------
--R         10      8      6      4      2
--R        x   - 10x  + 40x  - 80x  + 80x  - 32
--R                                            Type: Fraction Polynomial Integer
--E 5

--S 6 of 14
integrate(%,x)
 

   (6)
                                                   +-+    2
          8      6      4      2       +-+    - 2x\|2  + x  + 2       7      5
       (3x  - 24x  + 72x  - 96x  + 48)\|2 log(-----------------) - 20x  - 24x
                                                     2
                                                    x  - 2
     + 
            3
       - 48x  - 160x
  /
       8      6      4      2
     2x  - 16x  + 48x  - 64x  + 32
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (6)
--R                                                   +-+    2
--R          8      6      4      2       +-+    - 2x\|2  + x  + 2       7      5
--R       (3x  - 24x  + 72x  - 96x  + 48)\|2 log(-----------------) - 20x  - 24x
--R                                                     2
--R                                                    x  - 2
--R     + 
--R            3
--R       - 48x  - 160x
--R  /
--R       8      6      4      2
--R     2x  - 16x  + 48x  - 64x  + 32
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 14
x**5/(x**4+x**2+1)**2
 

                    5
                   x
   (7)  ------------------------
         8     6     4     2
        x  + 2x  + 3x  + 2x  + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                    5
--R                   x
--R   (7)  ------------------------
--R         8     6     4     2
--R        x  + 2x  + 3x  + 2x  + 1
--R                                            Type: Fraction Polynomial Integer
--E 7

--S 8 of 14
integrate(%,x)
 

                               2      +-+
           4     2          (2x  + 1)\|3         2      +-+
        (4x  + 4x  + 4)atan(-------------) + (- x  + 1)\|3
                                  3
   (8)  ---------------------------------------------------
                           4     2      +-+
                        (6x  + 6x  + 6)\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               2      +-+
--R           4     2          (2x  + 1)\|3         2      +-+
--R        (4x  + 4x  + 4)atan(-------------) + (- x  + 1)\|3
--R                                  3
--R   (8)  ---------------------------------------------------
--R                           4     2      +-+
--R                        (6x  + 6x  + 6)\|3
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 14
1/(x**2 + a)
 

           1
   (9)  ------
         2
        x  + a
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           1
--R   (9)  ------
--R         2
--R        x  + a
--R                                            Type: Fraction Polynomial Integer
--E 9

--S 10 of 14
integrate(%,x)
 

                2      +---+
              (x  - a)\|- a  + 2a x         +-+
          log(---------------------)      x\|a
                       2             atan(-----)
                      x  + a                a
   (10)  [--------------------------,-----------]
                      +---+               +-+
                    2\|- a               \|a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                2      +---+
--R              (x  - a)\|- a  + 2a x         +-+
--R          log(---------------------)      x\|a
--R                       2             atan(-----)
--R                      x  + a                a
--R   (10)  [--------------------------,-----------]
--R                      +---+               +-+
--R                    2\|- a               \|a
--R                                     Type: Union(List Expression Integer,...)
--E 10

--S 11 of 14
x**2/(x**4-a**2)
 

             2
            x
   (11)  -------
          4    2
         x  - a
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             2
--R            x
--R   (11)  -------
--R          4    2
--R         x  - a
--R                                            Type: Fraction Polynomial Integer
--E 11

--S 12 of 14
integrate(%,x)
 

   (12)
          2      +-+                   +-+
        (x  + a)\|a  - 2a x          x\|a
    log(-------------------) + 2atan(-----)
                2                      a
               x  - a
   [---------------------------------------,
                       +-+
                     4\|a
          2      +---+                   +---+
        (x  - a)\|- a  + 2a x          x\|- a
    log(---------------------) - 2atan(-------)
                 2                        a
                x  + a
    -------------------------------------------]
                        +---+
                      4\|- a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (12)
--R          2      +-+                   +-+
--R        (x  + a)\|a  - 2a x          x\|a
--R    log(-------------------) + 2atan(-----)
--R                2                      a
--R               x  - a
--R   [---------------------------------------,
--R                       +-+
--R                     4\|a
--R          2      +---+                   +---+
--R        (x  - a)\|- a  + 2a x          x\|- a
--R    log(---------------------) - 2atan(-------)
--R                 2                        a
--R                x  + a
--R    -------------------------------------------]
--R                        +---+
--R                      4\|- a
--R                                     Type: Union(List Expression Integer,...)
--E 12

--S 13 of 14
x/(1-x**3)
 

              x
   (13)  - ------
            3
           x  - 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R              x
--R   (13)  - ------
--R            3
--R           x  - 1
--R                                            Type: Fraction Polynomial Integer
--E 13

--S 14 of 14
integrate(%,x)
 

                                                                +-+
          +-+     2              +-+                   (2x + 1)\|3
         \|3 log(x  + x + 1) - 2\|3 log(x - 1) - 6atan(------------)
                                                             3
   (14)  -----------------------------------------------------------
                                      +-+
                                    6\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                +-+
--R          +-+     2              +-+                   (2x + 1)\|3
--R         \|3 log(x  + x + 1) - 2\|3 log(x - 1) - 6atan(------------)
--R                                                             3
--R   (14)  -----------------------------------------------------------
--R                                      +-+
--R                                    6\|3
--R                                          Type: Union(Expression Integer,...)
--E 14
)spool 
 
Starts dribbling to intheory.output (2010/3/27, 18:27:3).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
div144 := divisors(144)
 

   (1)  [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144]
--R                                                           Type: List Integer
--E 1

--S 2 of 22
#(div144)
 

   (2)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  15
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 22
reduce(+,div144)
 

   (3)  403
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  403
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 22
numberOfDivisors(144)
 

   (4)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  15
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 22
sumOfDivisors(144)
 

   (5)  403
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  403
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 22
f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 22
f1(200)
 
   Compiling function f1 with type PositiveInteger -> Integer 

   (7)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling function f1 with type PositiveInteger -> Integer 
--R
--R   (7)  1
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 22
f1(846)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 22
f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 22
f2(200)
 
   Compiling function f2 with type PositiveInteger -> Integer 

   (10)  200
                                                        Type: PositiveInteger
--R 
--R   Compiling function f2 with type PositiveInteger -> Integer 
--R
--R   (10)  200
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 22
f2(846)
 

   (11)  846
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  846
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 22
fibonacci(25)
 

   (12)  75025
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  75025
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 22
[fibonacci(n) for n in 1..15]
 

   (13)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
                                                           Type: List Integer
--R 
--R
--R   (13)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
--R                                                           Type: List Integer
--E 13

--S 14 of 22
fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 22
fib(25)
 
   Compiling function fib with type PositiveInteger -> Integer 

   (15)  75025
                                                        Type: PositiveInteger
--R 
--R   Compiling function fib with type PositiveInteger -> Integer 
--R
--R   (15)  75025
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 22
[fib(n) for n in 1..15]
 

   (16)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
                                                           Type: List Integer
--R 
--R
--R   (16)  [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]
--R                                                           Type: List Integer
--E 16

--S 17 of 22
legendre(3,5)
 

   (17)  - 1
                                                                Type: Integer
--R 
--R
--R   (17)  - 1
--R                                                                Type: Integer
--E 17

--S 18 of 22
legendre(23,691)
 

   (18)  - 1
                                                                Type: Integer
--R 
--R
--R   (18)  - 1
--R                                                                Type: Integer
--E 18

--S 19 of 22
h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 22
h(-163)
 
   Compiling function h with type Integer -> Integer 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R   Compiling function h with type Integer -> Integer 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 22
h(-499)
 

   (21)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  3
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 22
h(-1832)
 

   (22)  26
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  26
--R                                                        Type: PositiveInteger
--E 22
)spool 
 
Starts dribbling to kamke5.output (2010/3/27, 18:28:27).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 130
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 130
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 130
f0:=operator 'f0
 

   (3)  f0
                                                          Type: BasicOperator
--R 
--R
--R   (3)  f0
--R                                                          Type: BasicOperator
--E 3

--S 4 of 130
f1:=operator 'f1
 

   (4)  f1
                                                          Type: BasicOperator
--R 
--R
--R   (4)  f1
--R                                                          Type: BasicOperator
--E 4

--S 5 of 130
f2:=operator 'f2
 

   (5)  f2
                                                          Type: BasicOperator
--R 
--R
--R   (5)  f2
--R                                                          Type: BasicOperator
--E 5

--S 6 of 130
f3:=operator 'f3
 

   (6)  f3
                                                          Type: BasicOperator
--R 
--R
--R   (6)  f3
--R                                                          Type: BasicOperator
--E 6

--S 7 of 130
g:=operator 'g
 

   (7)  g
                                                          Type: BasicOperator
--R 
--R
--R   (7)  g
--R                                                          Type: BasicOperator
--E 7

--S 8 of 130
g0:=operator 'g0
 

   (8)  g0
                                                          Type: BasicOperator
--R 
--R
--R   (8)  g0
--R                                                          Type: BasicOperator
--E 8

--S 9 of 130
g1:=operator 'g1
 

   (9)  g1
                                                          Type: BasicOperator
--R 
--R
--R   (9)  g1
--R                                                          Type: BasicOperator
--E 9

--S 10 of 130
h:=operator 'h
 

   (10)  h
                                                          Type: BasicOperator
--R 
--R
--R   (10)  h
--R                                                          Type: BasicOperator
--E 10

--S 11 of 130
ode251 := (x**2*y(x)-1)*D(y(x),x)+x*y(x)**2-1
 

           2          ,            2
   (11)  (x y(x) - 1)y (x) + x y(x)  - 1

                                                     Type: Expression Integer
--R 
--R
--R           2          ,            2
--R   (11)  (x y(x) - 1)y (x) + x y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 11

--S 12 of 130
yx:=solve(ode251,y,x)
 

          2    2
         x y(x)  - 2y(x) - 2x
   (12)  --------------------
                   2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2
--R         x y(x)  - 2y(x) - 2x
--R   (12)  --------------------
--R                   2
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 130
ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1
 

   (13)
          6    3     4    2     5         3      ,        5    4     3    3
       (2x y(x)  - 6x y(x)  - 4x y(x) + 4x  + 4)y (x) + 3x y(x)  - 8x y(x)

     + 
            4    2      2         3
       - 10x y(x)  + 12x y(x) + 8x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R          6    3     4    2     5         3      ,        5    4     3    3
--R       (2x y(x)  - 6x y(x)  - 4x y(x) + 4x  + 4)y (x) + 3x y(x)  - 8x y(x)
--R
--R     + 
--R            4    2      2         3
--R       - 10x y(x)  + 12x y(x) + 8x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 13

--S 14 of 130
ode252 := (x**2*y(x)-1)*D(y(x),x)-(x*y(x)**2-1)
 

           2          ,            2
   (14)  (x y(x) - 1)y (x) - x y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R           2          ,            2
--R   (14)  (x y(x) - 1)y (x) - x y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 130
solve(ode252,y,x)
 

   (15)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (15)  "failed"
--R                                                    Type: Union("failed",...)
--E 15

--S 16 of 130
ode253 := (x**2*y(x)-1)*D(y(x),x)+8*(x*y(x)**2-1)
 

           2          ,             2
   (16)  (x y(x) - 1)y (x) + 8x y(x)  - 8

                                                     Type: Expression Integer
--R 
--R
--R           2          ,             2
--R   (16)  (x y(x) - 1)y (x) + 8x y(x)  - 8
--R
--R                                                     Type: Expression Integer
--E 16

--S 17 of 130
solve(ode253,y,x)
 

   (17)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (17)  "failed"
--R                                                    Type: Union("failed",...)
--E 17

--S 18 of 130
ode254 := x*(x*y(x)-2)*D(y(x),x)+x**2*y(x)**3+x*y(x)**2-2*y(x)
 

           2           ,       2    3         2
   (18)  (x y(x) - 2x)y (x) + x y(x)  + x y(x)  - 2y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2           ,       2    3         2
--R   (18)  (x y(x) - 2x)y (x) + x y(x)  + x y(x)  - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 130
solve(ode254,y,x)
 

   (19)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (19)  "failed"
--R                                                    Type: Union("failed",...)
--E 19

--S 20 of 130
ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)**2-y(x)
 

           2           ,            2
   (20)  (x y(x) - 3x)y (x) + x y(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2           ,            2
--R   (20)  (x y(x) - 3x)y (x) + x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 130
solve(ode255,y,x)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--S 22 of 130
ode256 := x**2*(y(x)-1)*D(y(x),x)+(x-1)*y(x)
 

           2        2  ,
   (22)  (x y(x) - x )y (x) + (x - 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2        2  ,
--R   (22)  (x y(x) - x )y (x) + (x - 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 22

--S 23 of 130
solve(ode256,y,x)
 

   (23)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (23)  "failed"
--R                                                    Type: Union("failed",...)
--E 23

--S 24 of 130
ode257 := x*(x*y(x)+x**4-1)*D(y(x),x)-y(x)*(x*y(x)-x**4-1)
 

           2        5      ,            2     4
   (24)  (x y(x) + x  - x)y (x) - x y(x)  + (x  + 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2        5      ,            2     4
--R   (24)  (x y(x) + x  - x)y (x) - x y(x)  + (x  + 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 24

--S 25 of 130
solve(ode257,y,x)
 

   (25)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (25)  "failed"
--R                                                    Type: Union("failed",...)
--E 25

--S 26 of 130
ode258 := 2*x**2*y(x)*D(y(x),x)+y(x)**2-2*x**3-x**2
 

           2     ,          2     3    2
   (26)  2x y(x)y (x) + y(x)  - 2x  - x

                                                     Type: Expression Integer
--R 
--R
--R           2     ,          2     3    2
--R   (26)  2x y(x)y (x) + y(x)  - 2x  - x
--R
--R                                                     Type: Expression Integer
--E 26

--S 27 of 130
yx:=solve(ode258,y,x)
 

                         1
                       - -
              2    2     x
   (27)  (y(x)  - x )%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         1
--R                       - -
--R              2    2     x
--R   (27)  (y(x)  - x )%e
--R                                          Type: Union(Expression Integer,...)
--E 27

--S 28 of 130
ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2
 

   (28)
                              1 2
                            - -
        2    3     4          x   ,
     (4x y(x)  - 4x y(x))(%e   ) y (x)

   + 
                                                   1 2
                                                 - -
           4        3     2     2     5     4      x       3    2
     (3y(x)  + (- 4x  - 6x )y(x)  + 4x  + 3x )(%e   )  - 2x  - x
                                                     Type: Expression Integer
--R 
--R
--R   (28)
--R                              1 2
--R                            - -
--R        2    3     4          x   ,
--R     (4x y(x)  - 4x y(x))(%e   ) y (x)
--R
--R   + 
--R                                                   1 2
--R                                                 - -
--R           4        3     2     2     5     4      x       3    2
--R     (3y(x)  + (- 4x  - 6x )y(x)  + 4x  + 3x )(%e   )  - 2x  - x
--R                                                     Type: Expression Integer
--E 28

--S 29 of 130
ode259 := 2*x**2*y(x)*D(y(x),x)-y(x)**2-x**2*exp(x-1/x)
 

                             2
                            x  - 1
                            ------
           2     ,       2     x         2
   (29)  2x y(x)y (x) - x %e       - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                             2
--R                            x  - 1
--R                            ------
--R           2     ,       2     x         2
--R   (29)  2x y(x)y (x) - x %e       - y(x)
--R
--R                                                     Type: Expression Integer
--E 29

--S 30 of 130
yx:=solve(ode259,y,x)
 

                 2
             1  x  - 1          1
             -  ------          -
             x     x         2  x
   (30)  - %e %e       + y(x) %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2
--R             1  x  - 1          1
--R             -  ------          -
--R             x     x         2  x
--R   (30)  - %e %e       + y(x) %e
--R                                          Type: Union(Expression Integer,...)
--E 30

--S 31 of 130
ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x)
 

   (31)
                        2
                  1 2  x  - 1              1 2
                  -    ------              -
          2       x       x       2    3   x    ,
     (- 4x y(x)(%e ) %e       + 4x y(x) (%e ) )y (x)

   + 
                        2     2                                   2
                 1 2   x  - 1                         1 2        x  - 1
                 -     ------                         -          ------
        2        x        x             2         2   x      2      x
     (2x  - 1)(%e ) (%e      )  + ((- 2x  + 4)y(x) (%e )  - x )%e
   + 
                1 2
                -
            4   x
     - 3y(x) (%e )
                                                     Type: Expression Integer
--R 
--R
--R   (31)
--R                        2
--R                  1 2  x  - 1              1 2
--R                  -    ------              -
--R          2       x       x       2    3   x    ,
--R     (- 4x y(x)(%e ) %e       + 4x y(x) (%e ) )y (x)
--R
--R   + 
--R                        2     2                                   2
--R                 1 2   x  - 1                         1 2        x  - 1
--R                 -     ------                         -          ------
--R        2        x        x             2         2   x      2      x
--R     (2x  - 1)(%e ) (%e      )  + ((- 2x  + 4)y(x) (%e )  - x )%e
--R   + 
--R                1 2
--R                -
--R            4   x
--R     - 3y(x) (%e )
--R                                                     Type: Expression Integer
--E 31

--S 32 of 130
ode260 := (2*x**2*y(x)+x)*D(y(x),x)-x**2*y(x)**3+2*x*y(x)**2+y(x)
 

            2          ,       2    3          2
   (32)  (2x y(x) + x)y (x) - x y(x)  + 2x y(x)  + y(x)

                                                     Type: Expression Integer
--R 
--R
--R            2          ,       2    3          2
--R   (32)  (2x y(x) + x)y (x) - x y(x)  + 2x y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 32

--S 33 of 130
solve(ode260,y,x)
 

   (33)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (33)  "failed"
--R                                                    Type: Union("failed",...)
--E 33

--S 34 of 130
ode261 := (2*x**2*y(x)-x)*D(y(x),x)-2*x*y(x)**2-y(x)
 

            2          ,             2
   (34)  (2x y(x) - x)y (x) - 2x y(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R            2          ,             2
--R   (34)  (2x y(x) - x)y (x) - 2x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 34

--S 35 of 130
solve(ode261,y,x)
 

   (35)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (35)  "failed"
--R                                                    Type: Union("failed",...)
--E 35

--S 36 of 130
ode262 := (2*x**2*y(x)-x**3)*D(y(x),x)+y(x)**3-4*x*y(x)**2+2*x**3
 

            2        3  ,          3          2     3
   (36)  (2x y(x) - x )y (x) + y(x)  - 4x y(x)  + 2x

                                                     Type: Expression Integer
--R 
--R
--R            2        3  ,          3          2     3
--R   (36)  (2x y(x) - x )y (x) + y(x)  - 4x y(x)  + 2x
--R
--R                                                     Type: Expression Integer
--E 36

--S 37 of 130
solve(ode262,y,x)
 

   (37)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (37)  "failed"
--R                                                    Type: Union("failed",...)
--E 37

--S 38 of 130
ode263 := 2*x**3+y(x)*D(y(x),x)+3*x**2*y(x)**2+7
 

              ,        2    2     3
   (38)  y(x)y (x) + 3x y(x)  + 2x  + 7

                                                     Type: Expression Integer
--R 
--R
--R              ,        2    2     3
--R   (38)  y(x)y (x) + 3x y(x)  + 2x  + 7
--R
--R                                                     Type: Expression Integer
--E 38

--S 39 of 130
solve(ode263,y,x)
 

            x                            3
          ++      2    2      3       2%K
   (39)   |   (3%K y(x)  + 2%K  + 7)%e    d%K
         ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x                            3
--I          ++      2    2      3       2%K
--I   (39)   |   (3%K y(x)  + 2%K  + 7)%e    d%K
--R         ++
--R                                          Type: Union(Expression Integer,...)
--E 39

--S 40 of 130
ode264 := 2*x*(x**3*y(x)+1)*D(y(x),x)+(3*x**3*y(x)-1)*y(x)
 

            4           ,        3    2
   (40)  (2x y(x) + 2x)y (x) + 3x y(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R            4           ,        3    2
--R   (40)  (2x y(x) + 2x)y (x) + 3x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 40

--S 41 of 130
solve(ode264,y,x)
 

   (41)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (41)  "failed"
--R                                                    Type: Union("failed",...)
--E 41

--S 42 of 130
ode265 := (x**(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)**2*x**(n-1)_
            *(x**(n**2)*y(x)**2-1)
 

   (42)
            2                                            2
           n  + n      ,         2              2 n - 1 n
     (y(x)x       - 1)y (x) + (2n  + 4n + 2)y(x) x     x

   + 
          2           n - 1
     (- 2n  - 4n - 2)x
                                                     Type: Expression Integer
--R 
--R
--R   (42)
--R            2                                            2
--R           n  + n      ,         2              2 n - 1 n
--R     (y(x)x       - 1)y (x) + (2n  + 4n + 2)y(x) x     x
--R
--R   + 
--R          2           n - 1
--R     (- 2n  - 4n - 2)x
--R                                                     Type: Expression Integer
--E 42

--S 43 of 130
solve(ode265,y,x)
 

   (43)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (43)  "failed"
--R                                                    Type: Union("failed",...)
--E 43

--S 44 of 130
ode266 := (y(x)-x)*sqrt(x**2+1)*D(y(x),x)-a*sqrt((y(x)**2+1)**3)
 

                    +------+          +---------------------------+
                    | 2      ,        |    6        4        2
   (44)  (y(x) - x)\|x  + 1 y (x) - a\|y(x)  + 3y(x)  + 3y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R                    +------+          +---------------------------+
--R                    | 2      ,        |    6        4        2
--R   (44)  (y(x) - x)\|x  + 1 y (x) - a\|y(x)  + 3y(x)  + 3y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 44

--S 45 of 130
solve(ode266,y,x)
 

   (45)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (45)  "failed"
--R                                                    Type: Union("failed",...)
--E 45

--S 46 of 130
ode267 := y(x)*D(y(x),x)*sin(x)**2+y(x)**2*cos(x)*sin(x)-1
 

                   2 ,          2
   (46)  y(x)sin(x) y (x) + y(x) cos(x)sin(x) - 1

                                                     Type: Expression Integer
--R 
--R
--R                   2 ,          2
--R   (46)  y(x)sin(x) y (x) + y(x) cos(x)sin(x) - 1
--R
--R                                                     Type: Expression Integer
--E 46

--S 47 of 130
yx:=solve(ode267,y,x)
 

             2      2
         y(x) sin(x)  - 2x
   (47)  -----------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2      2
--R         y(x) sin(x)  - 2x
--R   (47)  -----------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 47

--S 48 of 130
ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1
 

   (48)
             3      6                4  ,           4            5
       (2y(x) sin(x)  - 4x y(x)sin(x) )y (x) + 3y(x) cos(x)sin(x)

     + 
            2      4          2            3            2     2
     - 2y(x) sin(x)  - 8x y(x) cos(x)sin(x)  + 4x sin(x)  + 4x cos(x)sin(x) - 4
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (48)
--R             3      6                4  ,           4            5
--R       (2y(x) sin(x)  - 4x y(x)sin(x) )y (x) + 3y(x) cos(x)sin(x)
--R
--R     + 
--R            2      4          2            3            2     2
--R     - 2y(x) sin(x)  - 8x y(x) cos(x)sin(x)  + 4x sin(x)  + 4x cos(x)sin(x) - 4
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 48

--S 49 of 130
ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)**2+h(x)
 

                  ,              2
   (49)  f(x)y(x)y (x) + g(x)y(x)  + h(x)

                                                     Type: Expression Integer
--R 
--R
--R                  ,              2
--R   (49)  f(x)y(x)y (x) + g(x)y(x)  + h(x)
--R
--R                                                     Type: Expression Integer
--E 49

--S 50 of 130
solve(ode268,y,x)
 
 
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 50

--S 51 of 130
ode269 := (g1(x)*y(x)+g0(x))*D(y(x),x)-f1(x)*y(x)-_
              f2(x)*y(x)**2-f3(x)*y(x)**3-f0(x)
 

   (50)
                       ,               3            2
   (g1(x)y(x) + g0(x))y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)

                                                     Type: Expression Integer
--R 
--R
--R   (50)
--R                       ,               3            2
--R   (g1(x)y(x) + g0(x))y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)
--R
--R                                                     Type: Expression Integer
--E 51

--S 52 of 130
solve(ode269,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 52

--S 53 of 130
ode270 := (y(x)**2-x)*D(y(x),x)-y(x)+x**2
 

              2      ,              2
   (52)  (y(x)  - x)y (x) - y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              2      ,              2
--R   (52)  (y(x)  - x)y (x) - y(x) + x
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 130
yx:=solve(ode270,y,x)
 

             3              3
         y(x)  - 3x y(x) + x
   (53)  --------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3              3
--R         y(x)  - 3x y(x) + x
--R   (53)  --------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 54

--S 55 of 130
ode270expr := (yx**2-x)*D(yx,x)-yx+x**2
 

   (54)
               8          6     3    5      2    4     4    3
           y(x)  - 7x y(x)  + 2x y(x)  + 15x y(x)  - 8x y(x)
         + 
             6     3          2     5        7     2
           (x  - 9x  - 9x)y(x)  + 6x y(x) - x  + 9x
      *
          ,
         y (x)

     + 
             7    2    6          5     3    4      5     2         3
       - y(x)  + x y(x)  + 6x y(x)  - 8x y(x)  + (2x  - 9x  - 3)y(x)
     + 
          4    2        6               8      3     2
       15x y(x)  + (- 7x  + 18x)y(x) + x  - 12x  + 9x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (54)
--R               8          6     3    5      2    4     4    3
--R           y(x)  - 7x y(x)  + 2x y(x)  + 15x y(x)  - 8x y(x)
--R         + 
--R             6     3          2     5        7     2
--R           (x  - 9x  - 9x)y(x)  + 6x y(x) - x  + 9x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             7    2    6          5     3    4      5     2         3
--R       - y(x)  + x y(x)  + 6x y(x)  - 8x y(x)  + (2x  - 9x  - 3)y(x)
--R     + 
--R          4    2        6               8      3     2
--R       15x y(x)  + (- 7x  + 18x)y(x) + x  - 12x  + 9x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 55

--S 56 of 130
ode271 := (y(x)**2+x**2)*D(y(x),x)+2*x*(y(x)+2*x)
 

              2    2  ,                  2
   (55)  (y(x)  + x )y (x) + 2x y(x) + 4x

                                                     Type: Expression Integer
--R 
--R
--R              2    2  ,                  2
--R   (55)  (y(x)  + x )y (x) + 2x y(x) + 4x
--R
--R                                                     Type: Expression Integer
--E 56

--S 57 of 130
yx:=solve(ode271,y,x)
 

             3     2         3
         y(x)  + 3x y(x) + 4x
   (56)  ---------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3     2         3
--R         y(x)  + 3x y(x) + 4x
--R   (56)  ---------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 57

--S 58 of 130
ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x)
 

   (57)
               8     2    6     3    5      4    4      5    3
           y(x)  + 7x y(x)  + 8x y(x)  + 15x y(x)  + 32x y(x)
         + 
               6     2     2      7          8     4
           (25x  + 9x )y(x)  + 24x y(x) + 16x  + 9x
      *
          ,
         y (x)

     + 
              7     2    6      3    5      4    4       5          3
       2x y(x)  + 4x y(x)  + 12x y(x)  + 40x y(x)  + (50x  + 6x)y(x)
     + 
          6    2        7      3           8      4      2
       84x y(x)  + (128x  + 36x )y(x) + 64x  + 60x  + 36x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (57)
--R               8     2    6     3    5      4    4      5    3
--R           y(x)  + 7x y(x)  + 8x y(x)  + 15x y(x)  + 32x y(x)
--R         + 
--R               6     2     2      7          8     4
--R           (25x  + 9x )y(x)  + 24x y(x) + 16x  + 9x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R              7     2    6      3    5      4    4       5          3
--R       2x y(x)  + 4x y(x)  + 12x y(x)  + 40x y(x)  + (50x  + 6x)y(x)
--R     + 
--R          6    2        7      3           8      4      2
--R       84x y(x)  + (128x  + 36x )y(x) + 64x  + 60x  + 36x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 58

--S 59 of 130
ode272 := (y(x)**2+x**2)*D(y(x),x)-y(x)**2
 

              2    2  ,          2
   (58)  (y(x)  + x )y (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2  ,          2
--R   (58)  (y(x)  + x )y (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 59

--S 60 of 130
solve(ode272,y,x)
 

   (59)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (59)  "failed"
--R                                                    Type: Union("failed",...)
--E 60

--S 61 of 130
ode273 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)
 

              2    2      ,
   (60)  (y(x)  + x  + a)y (x) + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2      ,
--R   (60)  (y(x)  + x  + a)y (x) + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 61

--S 62 of 130
yx:=solve(ode273,y,x)
 

             3      2
         y(x)  + (3x  + 3a)y(x)
   (61)  ----------------------
                    3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3      2
--R         y(x)  + (3x  + 3a)y(x)
--R   (61)  ----------------------
--R                    3
--R                                          Type: Union(Expression Integer,...)
--E 62

--S 63 of 130
ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx
 

   (62)
               8      2          6       4        2      2     4
           y(x)  + (7x  + 7a)y(x)  + (15x  + 30a x  + 15a )y(x)
         + 
              6        4       2      2     3          2     4        2     2
           (9x  + 27a x  + (27a  + 9)x  + 9a  + 9a)y(x)  + 9x  + 18a x  + 9a
      *
          ,
         y (x)

     + 
              7       3             5       5        3       2           3
       2x y(x)  + (12x  + 12a x)y(x)  + (18x  + 36a x  + (18a  + 6)x)y(x)
     + 
           3
       (36x  + 36a x)y(x)
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (62)
--R               8      2          6       4        2      2     4
--R           y(x)  + (7x  + 7a)y(x)  + (15x  + 30a x  + 15a )y(x)
--R         + 
--R              6        4       2      2     3          2     4        2     2
--R           (9x  + 27a x  + (27a  + 9)x  + 9a  + 9a)y(x)  + 9x  + 18a x  + 9a
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R              7       3             5       5        3       2           3
--R       2x y(x)  + (12x  + 12a x)y(x)  + (18x  + 36a x  + (18a  + 6)x)y(x)
--R     + 
--R           3
--R       (36x  + 36a x)y(x)
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 63

--S 64 of 130
ode274 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)+x**2+b
 

              2    2      ,                 2
   (63)  (y(x)  + x  + a)y (x) + 2x y(x) + x  + b

                                                     Type: Expression Integer
--R 
--R
--R              2    2      ,                 2
--R   (63)  (y(x)  + x  + a)y (x) + 2x y(x) + x  + b
--R
--R                                                     Type: Expression Integer
--E 64

--S 65 of 130
yx:=solve(ode274,y,x)
 

             3      2              3
         y(x)  + (3x  + 3a)y(x) + x  + 3b x
   (64)  ----------------------------------
                          3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3      2              3
--R         y(x)  + (3x  + 3a)y(x) + x  + 3b x
--R   (64)  ----------------------------------
--R                          3
--R                                          Type: Union(Expression Integer,...)
--E 65

--S 66 of 130
ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b
 

   (65)
               8      2          6      3            5
           y(x)  + (7x  + 7a)y(x)  + (2x  + 6b x)y(x)
         + 
               4        2      2     4      5              3               3
           (15x  + 30a x  + 15a )y(x)  + (8x  + (24b + 8a)x  + 24a b x)y(x)
         + 
               6              4      2      2      2     3          2
           (10x  + (6b + 27a)x  + (9b  + 27a  + 9)x  + 9a  + 9a)y(x)
         + 
              7               5              2  3      2            8
           (6x  + (18b + 12a)x  + (36a b + 6a )x  + 18a b x)y(x) + x
         + 
                    6      2             4        2        2     2
           (6b + a)x  + (9b  + 6a b + 9)x  + (9a b  + 18a)x  + 9a
      *
          ,
         y (x)

     + 
              7     2         6       3             5
       2x y(x)  + (x  + b)y(x)  + (12x  + 12a x)y(x)
     + 
           4              2            4
       (10x  + (18b + 6a)x  + 6a b)y(x)
     + 
           5              3      2      2           3
       (20x  + (8b + 36a)x  + (6b  + 18a  + 6)x)y(x)
     + 
           6               4              2  2     2      2
       (21x  + (45b + 30a)x  + (54a b + 9a )x  + 9a b)y(x)
     + 
          7              5       2               3         2                 8
       (8x  + (36b + 6a)x  + (36b  + 24a b + 36)x  + (18a b  + 36a)x)y(x) + x
     + 
           6       2       4      3                 2
       7b x  + (15b  + 15)x  + (9b  + 27b + 9a + 9)x  + (9a + 9)b
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (65)
--R               8      2          6      3            5
--R           y(x)  + (7x  + 7a)y(x)  + (2x  + 6b x)y(x)
--R         + 
--R               4        2      2     4      5              3               3
--R           (15x  + 30a x  + 15a )y(x)  + (8x  + (24b + 8a)x  + 24a b x)y(x)
--R         + 
--R               6              4      2      2      2     3          2
--R           (10x  + (6b + 27a)x  + (9b  + 27a  + 9)x  + 9a  + 9a)y(x)
--R         + 
--R              7               5              2  3      2            8
--R           (6x  + (18b + 12a)x  + (36a b + 6a )x  + 18a b x)y(x) + x
--R         + 
--R                    6      2             4        2        2     2
--R           (6b + a)x  + (9b  + 6a b + 9)x  + (9a b  + 18a)x  + 9a
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R              7     2         6       3             5
--R       2x y(x)  + (x  + b)y(x)  + (12x  + 12a x)y(x)
--R     + 
--R           4              2            4
--R       (10x  + (18b + 6a)x  + 6a b)y(x)
--R     + 
--R           5              3      2      2           3
--R       (20x  + (8b + 36a)x  + (6b  + 18a  + 6)x)y(x)
--R     + 
--R           6               4              2  2     2      2
--R       (21x  + (45b + 30a)x  + (54a b + 9a )x  + 9a b)y(x)
--R     + 
--R          7              5       2               3         2                 8
--R       (8x  + (36b + 6a)x  + (36b  + 24a b + 36)x  + (18a b  + 36a)x)y(x) + x
--R     + 
--R           6       2       4      3                 2
--R       7b x  + (15b  + 15)x  + (9b  + 27b + 9a + 9)x  + (9a + 9)b
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 66

--S 67 of 130
ode275 := (y(x)**2+x**2+x)*D(y(x),x)-y(x)
 

              2    2      ,
   (66)  (y(x)  + x  + x)y (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2      ,
--R   (66)  (y(x)  + x  + x)y (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 67

--S 68 of 130
solve(ode275,y,x)
 

   (67)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (67)  "failed"
--R                                                    Type: Union("failed",...)
--E 68

--S 69 of 130
ode276 := (y(x)**2-x**2)*D(y(x),x)+2*x*y(x)
 

              2    2  ,
   (68)  (y(x)  - x )y (x) + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    2  ,
--R   (68)  (y(x)  - x )y (x) + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 69

--S 70 of 130
yx:=solve(ode276,y,x)
 

             2    2
         y(x)  + x
   (69)  ----------
            y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R         y(x)  + x
--R   (69)  ----------
--R            y(x)
--R                                          Type: Union(Expression Integer,...)
--E 70

--S 71 of 130
ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx
 

              6    6  ,             5     3    3     5
         (y(x)  - x )y (x) + 4x y(x)  + 4x y(x)  + 2x y(x)

   (70)  -------------------------------------------------
                                   4
                               y(x)
                                                     Type: Expression Integer
--R 
--R
--R              6    6  ,             5     3    3     5
--R         (y(x)  - x )y (x) + 4x y(x)  + 4x y(x)  + 2x y(x)
--R
--R   (70)  -------------------------------------------------
--R                                   4
--R                               y(x)
--R                                                     Type: Expression Integer
--E 71

--S 72 of 130
ode277 := (y(x)**2+x**4)*D(y(x),x)-4*x**3*y(x)
 

              2    4  ,        3
   (71)  (y(x)  + x )y (x) - 4x y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2    4  ,        3
--R   (71)  (y(x)  + x )y (x) - 4x y(x)
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 130
yx:=solve(ode277,y,x)
 

             2    4
         y(x)  - x
   (72)  ----------
            y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    4
--R         y(x)  - x
--R   (72)  ----------
--R            y(x)
--R                                          Type: Union(Expression Integer,...)
--E 73

--S 74 of 130
ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx
 

              6    12  ,        3    5     7    3     11
         (y(x)  + x  )y (x) - 8x y(x)  + 8x y(x)  - 4x  y(x)

   (73)  ---------------------------------------------------
                                    4
                                y(x)
                                                     Type: Expression Integer
--R 
--R
--R              6    12  ,        3    5     7    3     11
--R         (y(x)  + x  )y (x) - 8x y(x)  + 8x y(x)  - 4x  y(x)
--R
--R   (73)  ---------------------------------------------------
--R                                    4
--R                                y(x)
--R                                                     Type: Expression Integer
--E 74

--S 75 of 130
ode278 := (y(x)**2+4*sin(x))*D(y(x),x)-cos(x)
 

                        2  ,
   (74)  (4sin(x) + y(x) )y (x) - cos(x)

                                                     Type: Expression Integer
--R 
--R
--R                        2  ,
--R   (74)  (4sin(x) + y(x) )y (x) - cos(x)
--R
--R                                                     Type: Expression Integer
--E 75

--S 76 of 130
yx:=solve(ode278,y,x)
 

                            2               - 4y(x)
         (- 32sin(x) - 8y(x)  - 4y(x) - 1)%e
   (75)  ------------------------------------------
                             32
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            2               - 4y(x)
--R         (- 32sin(x) - 8y(x)  - 4y(x) - 1)%e
--R   (75)  ------------------------------------------
--R                             32
--R                                          Type: Union(Expression Integer,...)
--E 76

--S 77 of 130
ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x)
 

   (76)
                         3            2                        2
               4096sin(x)  + (3072y(x)  + 1024y(x) + 256)sin(x)
             + 
                       4          3          2                             6
               (768y(x)  + 512y(x)  + 192y(x)  + 32y(x) + 4)sin(x) + 64y(x)
             + 
                     5         4        3       2
               64y(x)  + 32y(x)  + 8y(x)  + y(x)
          *
                - 4y(x) 3
             (%e       )
         + 
                       2           2         - 4y(x)
           (16384sin(x)  + 4096y(x) sin(x))%e
      *
          ,
         y (x)

     + 
                             2             2
           - 1024cos(x)sin(x)  + (- 512y(x)  - 256y(x) - 64)cos(x)sin(x)
         + 
                    4         3         2
           (- 64y(x)  - 64y(x)  - 32y(x)  - 8y(x) - 1)cos(x)
      *
            - 4y(x) 3
         (%e       )
     + 
                           - 4y(x)
       - 4096cos(x)sin(x)%e        - 1024cos(x)
  /
     1024
                                                     Type: Expression Integer
--R 
--R
--R   (76)
--R                         3            2                        2
--R               4096sin(x)  + (3072y(x)  + 1024y(x) + 256)sin(x)
--R             + 
--R                       4          3          2                             6
--R               (768y(x)  + 512y(x)  + 192y(x)  + 32y(x) + 4)sin(x) + 64y(x)
--R             + 
--R                     5         4        3       2
--R               64y(x)  + 32y(x)  + 8y(x)  + y(x)
--R          *
--R                - 4y(x) 3
--R             (%e       )
--R         + 
--R                       2           2         - 4y(x)
--R           (16384sin(x)  + 4096y(x) sin(x))%e
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                             2             2
--R           - 1024cos(x)sin(x)  + (- 512y(x)  - 256y(x) - 64)cos(x)sin(x)
--R         + 
--R                    4         3         2
--R           (- 64y(x)  - 64y(x)  - 32y(x)  - 8y(x) - 1)cos(x)
--R      *
--R            - 4y(x) 3
--R         (%e       )
--R     + 
--R                           - 4y(x)
--R       - 4096cos(x)sin(x)%e        - 1024cos(x)
--R  /
--R     1024
--R                                                     Type: Expression Integer
--E 77

--S 78 of 130
ode279 := (y(x)**2+2*y(x)+x)*D(y(x),x)+(y(x)+x)**2*y(x)**2+y(x)*(y(x)+1)
 

              2              ,          4          3     2         2
   (77)  (y(x)  + 2y(x) + x)y (x) + y(x)  + 2x y(x)  + (x  + 1)y(x)  + y(x)

                                                     Type: Expression Integer
--R 
--R
--R              2              ,          4          3     2         2
--R   (77)  (y(x)  + 2y(x) + x)y (x) + y(x)  + 2x y(x)  + (x  + 1)y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 78

--S 79 of 130
solve(ode279,y,x)
 

   (78)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (78)  "failed"
--R                                                    Type: Union("failed",...)
--E 79

--S 80 of 130
ode280 := (y(x)+x)**2*D(y(x),x)-a**2
 

              2              2  ,       2
   (79)  (y(x)  + 2x y(x) + x )y (x) - a

                                                     Type: Expression Integer
--R 
--R
--R              2              2  ,       2
--R   (79)  (y(x)  + 2x y(x) + x )y (x) - a
--R
--R                                                     Type: Expression Integer
--E 80

--S 81 of 130
solve(ode280,y,x)
 

   (80)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (80)  "failed"
--R                                                    Type: Union("failed",...)
--E 81

--S 82 of 130
ode281 := (y(x)**2+2*x*y(x)-x**2)*D(y(x),x)-_
            y(x)**2+2*x*y(x)+x**2
 

              2              2  ,          2              2
   (81)  (y(x)  + 2x y(x) - x )y (x) - y(x)  + 2x y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              2              2  ,          2              2
--R   (81)  (y(x)  + 2x y(x) - x )y (x) - y(x)  + 2x y(x) + x
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 130
solve(ode281,y,x)
 

   (82)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (82)  "failed"
--R                                                    Type: Union("failed",...)
--E 83

--S 84 of 130
ode282 := (y(x)+3*x-1)**2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3)
 

   (83)
          2                    2           ,           2
     (y(x)  + (6x - 2)y(x) + 9x  - 6x + 1)y (x) - 8y(x)  + (- 12x + 10)y(x) + 6x

   + 
     - 3
                                                     Type: Expression Integer
--R 
--R
--R   (83)
--R          2                    2           ,           2
--R     (y(x)  + (6x - 2)y(x) + 9x  - 6x + 1)y (x) - 8y(x)  + (- 12x + 10)y(x) + 6x
--R
--R   + 
--R     - 3
--R                                                     Type: Expression Integer
--E 84

--S 85 of 130
solve(ode282,y,x)
 

   (84)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (84)  "failed"
--R                                                    Type: Union("failed",...)
--E 85

--S 86 of 130
ode283 := 3*(y(x)**2-x**2)*D(y(x),x)+2*y(x)**3-6*x*(x+1)*y(x)-3*exp(x)
 

               2     2  ,         x        3        2
   (85)  (3y(x)  - 3x )y (x) - 3%e  + 2y(x)  + (- 6x  - 6x)y(x)

                                                     Type: Expression Integer
--R 
--R
--R               2     2  ,         x        3        2
--R   (85)  (3y(x)  - 3x )y (x) - 3%e  + 2y(x)  + (- 6x  - 6x)y(x)
--R
--R                                                     Type: Expression Integer
--E 86

--S 87 of 130
yx:=solve(ode283,y,x)
 

              x 3        3     2        x 2
   (86)  - (%e )  + (y(x)  - 3x y(x))(%e )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              x 3        3     2        x 2
--R   (86)  - (%e )  + (y(x)  - 3x y(x))(%e )
--R                                          Type: Union(Expression Integer,...)
--E 87

--S 88 of 130
ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x)
 

   (87)
               2     2    x 8            5      2    3      4        x 7
         (9y(x)  - 9x )(%e )  + (- 18y(x)  + 72x y(x)  - 54x y(x))(%e )
       + 
               8      2    6       4    4      6    2    x 6
         (9y(x)  - 63x y(x)  + 135x y(x)  - 81x y(x) )(%e )
       + 
              2    2     4    x 2
         (- 9x y(x)  + 9x )(%e )
    *
        ,
       y (x)

   + 
            x 9          3         2               x 8
     - 11(%e )  + (30y(x)  + (- 90x  - 18x)y(x))(%e )
   + 
              6        2           4          4       3     2    x 7
     (- 27y(x)  + (162x  + 36x)y(x)  + (- 243x  - 108x )y(x) )(%e )
   + 
              9         2           7        4       3     5
         8y(x)  + (- 72x  - 18x)y(x)  + (216x  + 108x )y(x)
       + 
                6       5     3
         (- 216x  - 162x )y(x)
    *
          x 6
       (%e )
   + 
         2         x 3          2          3       4      3         x 2      x
     (15x  + 6x)(%e )  + ((- 12x  - 6x)y(x)  + (36x  + 36x )y(x))(%e )  - 3%e
                                                     Type: Expression Integer
--R 
--R
--R   (87)
--R               2     2    x 8            5      2    3      4        x 7
--R         (9y(x)  - 9x )(%e )  + (- 18y(x)  + 72x y(x)  - 54x y(x))(%e )
--R       + 
--R               8      2    6       4    4      6    2    x 6
--R         (9y(x)  - 63x y(x)  + 135x y(x)  - 81x y(x) )(%e )
--R       + 
--R              2    2     4    x 2
--R         (- 9x y(x)  + 9x )(%e )
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R            x 9          3         2               x 8
--R     - 11(%e )  + (30y(x)  + (- 90x  - 18x)y(x))(%e )
--R   + 
--R              6        2           4          4       3     2    x 7
--R     (- 27y(x)  + (162x  + 36x)y(x)  + (- 243x  - 108x )y(x) )(%e )
--R   + 
--R              9         2           7        4       3     5
--R         8y(x)  + (- 72x  - 18x)y(x)  + (216x  + 108x )y(x)
--R       + 
--R                6       5     3
--R         (- 216x  - 162x )y(x)
--R    *
--R          x 6
--R       (%e )
--R   + 
--R         2         x 3          2          3       4      3         x 2      x
--R     (15x  + 6x)(%e )  + ((- 12x  - 6x)y(x)  + (36x  + 36x )y(x))(%e )  - 3%e
--R                                                     Type: Expression Integer
--E 88

--S 89 of 130
ode284 := (4*y(x)**2+x**2)*D(y(x),x)-x*y(x)
 

               2    2  ,
   (88)  (4y(x)  + x )y (x) - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R               2    2  ,
--R   (88)  (4y(x)  + x )y (x) - x y(x)
--R
--R                                                     Type: Expression Integer
--E 89

--S 90 of 130
yx:=solve(ode284,y,x)
 

              2             2
         8y(x) log(y(x)) - x
   (89)  --------------------
                     2
                2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2             2
--R         8y(x) log(y(x)) - x
--R   (89)  --------------------
--R                     2
--R                2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 90

--S 91 of 130
ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx
 

   (90)
                   6       2    4          2
           (512y(x)  + 128x y(x) )log(y(x))
         + 
                  2    4      4    2               2    6     4    4     4    2
           (- 128x y(x)  - 32x y(x) )log(y(x)) + 8x y(x)  + 2x y(x)  + 8x y(x)
         + 
             6
           2x
      *
          ,
         y (x)

     + 
                  5         2             7      3    3              3    5
       - 128x y(x) log(y(x))  + (- 8x y(x)  + 32x y(x) )log(y(x)) - x y(x)
     + 
           5
       - 2x y(x)
  /
          7
     2y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (90)
--R                   6       2    4          2
--R           (512y(x)  + 128x y(x) )log(y(x))
--R         + 
--R                  2    4      4    2               2    6     4    4     4    2
--R           (- 128x y(x)  - 32x y(x) )log(y(x)) + 8x y(x)  + 2x y(x)  + 8x y(x)
--R         + 
--R             6
--R           2x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                  5         2             7      3    3              3    5
--R       - 128x y(x) log(y(x))  + (- 8x y(x)  + 32x y(x) )log(y(x)) - x y(x)
--R     + 
--R           5
--R       - 2x y(x)
--R  /
--R          7
--R     2y(x)
--R                                                     Type: Expression Integer
--E 91

--S 92 of 130
ode285 := (4*y(x)**2+2*x*y(x)+3*x**2)*D(y(x),x)+y(x)**2+6*x*y(x)+2*x**2
 

               2               2  ,          2               2
   (91)  (4y(x)  + 2x y(x) + 3x )y (x) + y(x)  + 6x y(x) + 2x

                                                     Type: Expression Integer
--R 
--R
--R               2               2  ,          2               2
--R   (91)  (4y(x)  + 2x y(x) + 3x )y (x) + y(x)  + 6x y(x) + 2x
--R
--R                                                     Type: Expression Integer
--E 92

--S 93 of 130
yx:=solve(ode285,y,x)
 

              3          2     2         3
         4y(x)  + 3x y(x)  + 9x y(x) + 2x
   (92)  ---------------------------------
                         3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3          2     2         3
--R         4y(x)  + 3x y(x)  + 9x y(x) + 2x
--R   (92)  ---------------------------------
--R                         3
--R                                          Type: Union(Expression Integer,...)
--E 93

--S 94 of 130
ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2
 

   (93)
                  8            7        2    6         3           5
           256y(x)  + 512x y(x)  + 1680x y(x)  + (2056x  + 96x)y(x)
         + 
                 4       2     4         5       3     3
           (3020x  + 120x )y(x)  + (2160x  + 324x )y(x)
         + 
                 6       4       2     2        7       5      3           8
           (1468x  + 210x  + 108x )y(x)  + (464x  + 186x  + 54x )y(x) + 48x
         + 
              6      4
           36x  + 81x
      *
          ,
         y (x)

     + 
             8            7         2          6         3           5
       64y(x)  + 480x y(x)  + (1028x  + 16)y(x)  + (2416x  + 48x)y(x)
     + 
             4       2     4         5       3           3
       (2700x  + 243x )y(x)  + (2936x  + 280x  + 72x)y(x)
     + 
             6       4      2     2        7       5       3           8      6
       (1624x  + 465x  + 81x )y(x)  + (384x  + 216x  + 324x )y(x) + 32x  + 28x
     + 
          4      2
       90x  + 18x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (93)
--R                  8            7        2    6         3           5
--R           256y(x)  + 512x y(x)  + 1680x y(x)  + (2056x  + 96x)y(x)
--R         + 
--R                 4       2     4         5       3     3
--R           (3020x  + 120x )y(x)  + (2160x  + 324x )y(x)
--R         + 
--R                 6       4       2     2        7       5      3           8
--R           (1468x  + 210x  + 108x )y(x)  + (464x  + 186x  + 54x )y(x) + 48x
--R         + 
--R              6      4
--R           36x  + 81x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             8            7         2          6         3           5
--R       64y(x)  + 480x y(x)  + (1028x  + 16)y(x)  + (2416x  + 48x)y(x)
--R     + 
--R             4       2     4         5       3           3
--R       (2700x  + 243x )y(x)  + (2936x  + 280x  + 72x)y(x)
--R     + 
--R             6       4      2     2        7       5       3           8      6
--R       (1624x  + 465x  + 81x )y(x)  + (384x  + 216x  + 324x )y(x) + 32x  + 28x
--R     + 
--R          4      2
--R       90x  + 18x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 94

--S 95 of 130
ode286 := (2*y(x)-3*x+1)**2*D(y(x),x)-(3*y(x)-2*x-4)**2
 

   (94)
           2                       2           ,           2
     (4y(x)  + (- 12x + 4)y(x) + 9x  - 6x + 1)y (x) - 9y(x)  + (12x + 24)y(x)

   + 
         2
     - 4x  - 16x - 16
                                                     Type: Expression Integer
--R 
--R
--R   (94)
--R           2                       2           ,           2
--R     (4y(x)  + (- 12x + 4)y(x) + 9x  - 6x + 1)y (x) - 9y(x)  + (12x + 24)y(x)
--R
--R   + 
--R         2
--R     - 4x  - 16x - 16
--R                                                     Type: Expression Integer
--E 95

--S 96 of 130
solve(ode286,y,x)
 

   (95)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (95)  "failed"
--R                                                    Type: Union("failed",...)
--E 96

--S 97 of 130
ode287 := (2*y(x)-4*x+1)**2*D(y(x),x)-(y(x)-2*x)**2
 

   (96)
         2                        2           ,          2               2
   (4y(x)  + (- 16x + 4)y(x) + 16x  - 8x + 1)y (x) - y(x)  + 4x y(x) - 4x

                                                     Type: Expression Integer
--R 
--R
--R   (96)
--R         2                        2           ,          2               2
--R   (4y(x)  + (- 16x + 4)y(x) + 16x  - 8x + 1)y (x) - y(x)  + 4x y(x) - 4x
--R
--R                                                     Type: Expression Integer
--E 97

--S 98 of 130
solve(ode287,y,x)
 

   (97)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (97)  "failed"
--R                                                    Type: Union("failed",...)
--E 98

--S 99 of 130
ode288 := (6*y(x)**2-3*x**2*y(x)+1)*D(y(x),x)-3*x*y(x)**2+x
 

               2     2          ,             2
   (98)  (6y(x)  - 3x y(x) + 1)y (x) - 3x y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R               2     2          ,             2
--R   (98)  (6y(x)  - 3x y(x) + 1)y (x) - 3x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 99

--S 100 of 130
yx:=solve(ode288,y,x)
 

              3     2    2            2
         4y(x)  - 3x y(x)  + 2y(x) + x
   (99)  ------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2    2            2
--R         4y(x)  - 3x y(x)  + 2y(x) + x
--R   (99)  ------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 100

--S 101 of 130
ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x
 

   (100)
                  8        2    7        4           6          6       2     5
           576y(x)  - 1152x y(x)  + (756x  + 672)y(x)  + (- 162x  - 720x )y(x)
         + 
               4           4       6      2     3         4          2
           (90x  + 240)y(x)  + (54x  - 48x )y(x)  + (- 54x  + 48)y(x)  + 4
      *
          ,
         y (x)

     + 
                  8       3    7          5            6      3    5
       - 288x y(x)  + 432x y(x)  + (- 162x  - 240x)y(x)  + 72x y(x)
     + 
           5           4      3    3     5
       (81x  - 24x)y(x)  - 72x y(x)  - 3x  + 8x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (100)
--R                  8        2    7        4           6          6       2     5
--R           576y(x)  - 1152x y(x)  + (756x  + 672)y(x)  + (- 162x  - 720x )y(x)
--R         + 
--R               4           4       6      2     3         4          2
--R           (90x  + 240)y(x)  + (54x  - 48x )y(x)  + (- 54x  + 48)y(x)  + 4
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                  8       3    7          5            6      3    5
--R       - 288x y(x)  + 432x y(x)  + (- 162x  - 240x)y(x)  + 72x y(x)
--R     + 
--R           5           4      3    3     5
--R       (81x  - 24x)y(x)  - 72x y(x)  - 3x  + 8x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 101

--S 102 of 130
ode289 := (6*y(x)-x)**2*D(y(x),x)-6*y(x)**2+2*x*y(x)+a
 

                 2               2  ,           2
   (101)  (36y(x)  - 12x y(x) + x )y (x) - 6y(x)  + 2x y(x) + a

                                                     Type: Expression Integer
--R 
--R
--R                 2               2  ,           2
--R   (101)  (36y(x)  - 12x y(x) + x )y (x) - 6y(x)  + 2x y(x) + a
--R
--R                                                     Type: Expression Integer
--E 102

--S 103 of 130
yx:=solve(ode289,y,x)
 

                3          2    2
   (102)  12y(x)  - 6x y(x)  + x y(x) + a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3          2    2
--R   (102)  12y(x)  - 6x y(x)  + x y(x) + a x
--R                                          Type: Union(Expression Integer,...)
--E 103

--S 104 of 130
ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a
 

   (103)
                   8               7          2    6
         186624y(x)  - 248832x y(x)  + 145152x y(x)
       + 
                  3                        5
         (- 46656x  + (31104a - 5184)x)y(x)
       + 
               4                     2     4          5                  3     3
         (8640x  + (- 25920a + 4320)x )y(x)  + (- 864x  + (8640a - 1440)x )y(x)
       + 
             6                   4         2              2     2
         (36x  + (- 1296a + 216)x  + (1296a  - 432a + 36)x )y(x)
       + 
                     5          2              3            2            4
         ((72a - 12)x  + (- 432a  + 144a - 12)x )y(x) + (36a  - 12a + 1)x
    *
        ,
       y (x)

   + 
                8              7            2                   6
     - 31104y(x)  + 41472x y(x)  + (- 23328x  + 5184a - 864)y(x)
   + 
           3                          5           4                  2     4
     (6912x  + (- 10368a + 1728)x)y(x)  + (- 1080x  + (6480a - 1080)x )y(x)
   + 
         5                   3        2                   3
     (72x  + (- 1728a + 288)x  + (864a  - 288a + 24)x)y(x)
   + 
                  4          2              2     2        2            3
     ((180a - 30)x  + (- 648a  + 216a - 18)x )y(x)  + (144a  - 48a + 4)x y(x)
   + 
         3      2       2
     (36a  - 18a  + 3a)x  + a
                                                     Type: Expression Integer
--R 
--R
--R   (103)
--R                   8               7          2    6
--R         186624y(x)  - 248832x y(x)  + 145152x y(x)
--R       + 
--R                  3                        5
--R         (- 46656x  + (31104a - 5184)x)y(x)
--R       + 
--R               4                     2     4          5                  3     3
--R         (8640x  + (- 25920a + 4320)x )y(x)  + (- 864x  + (8640a - 1440)x )y(x)
--R       + 
--R             6                   4         2              2     2
--R         (36x  + (- 1296a + 216)x  + (1296a  - 432a + 36)x )y(x)
--R       + 
--R                     5          2              3            2            4
--R         ((72a - 12)x  + (- 432a  + 144a - 12)x )y(x) + (36a  - 12a + 1)x
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R                8              7            2                   6
--R     - 31104y(x)  + 41472x y(x)  + (- 23328x  + 5184a - 864)y(x)
--R   + 
--R           3                          5           4                  2     4
--R     (6912x  + (- 10368a + 1728)x)y(x)  + (- 1080x  + (6480a - 1080)x )y(x)
--R   + 
--R         5                   3        2                   3
--R     (72x  + (- 1728a + 288)x  + (864a  - 288a + 24)x)y(x)
--R   + 
--R                  4          2              2     2        2            3
--R     ((180a - 30)x  + (- 648a  + 216a - 18)x )y(x)  + (144a  - 48a + 4)x y(x)
--R   + 
--R         3      2       2
--R     (36a  - 18a  + 3a)x  + a
--R                                                     Type: Expression Integer
--E 104

--S 105 of 130
ode290 := (a*y(x)**2+2*b*x*y(x)+c*x**2)*D(y(x),x)+b*y(x)**2+2*c*x*y(x)+d*x**2
 

                 2                  2  ,            2                  2
   (104)  (a y(x)  + 2b x y(x) + c x )y (x) + b y(x)  + 2c x y(x) + d x

                                                     Type: Expression Integer
--R 
--R
--R                 2                  2  ,            2                  2
--R   (104)  (a y(x)  + 2b x y(x) + c x )y (x) + b y(x)  + 2c x y(x) + d x
--R
--R                                                     Type: Expression Integer
--E 105

--S 106 of 130
yx:=solve(ode290,y,x)
 

                3            2       2          3
          a y(x)  + 3b x y(x)  + 3c x y(x) + d x
   (105)  ---------------------------------------
                             3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3            2       2          3
--R          a y(x)  + 3b x y(x)  + 3c x y(x) + d x
--R   (105)  ---------------------------------------
--R                             3
--R                                          Type: Union(Expression Integer,...)
--E 106

--S 107 of 130
ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2
 

   (106)
            4    8     3        7      3       2 2  2    6
           a y(x)  + 8a b x y(x)  + (7a c + 21a b )x y(x)
         + 
               3       2           3  3     2        5
           ((2a d + 36a b c + 18a b )x  + 6a b x)y(x)
         + 
                2         2 2        2   4        2 2     4
           ((10a b d + 15a c  + 45a b c)x  + 30a b x )y(x)
         + 
                2         2            2  5                 3  3     3
           (((8a c + 12a b )d + 36a b c )x  + (24a b c + 36b )x )y(x)
         + 
              2 2                   3  6                2   4         2     2
           ((a d  + 18a b c d + 9a c )x  + (6a b d + 54b c)x  + 9a c x )y(x)
         + 
                   2       2   7       2         2  5          3             2 8
           ((2a b d  + 6a c d)x  + (12b d + 18b c )x  + 18b c x )y(x) + a c d x
         + 
                   6     2 4
           6b c d x  + 9c x
      *
          ,
         y (x)

     + 
        3      8      3      2 2       7
       a b y(x)  + (2a c + 6a b )x y(x)
     + 
          3       2          3  2    2      6
       ((a d + 18a b c + 9a b )x  + a b)y(x)
     + 
           2         2 2        2   3        2      5
       ((8a b d + 12a c  + 36a b c)x  + 12a b x)y(x)
     + 
             2         2            2  4                 3  2     4
       (((10a c + 15a b )d + 45a b c )x  + (18a b c + 27b )x )y(x)
     + 
           2 2                    3  5                2   3              3
       ((2a d  + 36a b c d + 18a c )x  + (8a b d + 72b c)x  + 6a c x)y(x)
     + 
               2        2   6       2         2  4          2     2
       ((7a b d  + 21a c d)x  + (30b d + 45b c )x  + 27b c x )y(x)
     + 
            2 7            5      2 3           3 8       2 6          4       2
     (8a c d x  + 36b c d x  + 36c x )y(x) + a d x  + 7b d x  + 15c d x  + 9d x
  /
     9
                                                     Type: Expression Integer
--R 
--R
--R   (106)
--R            4    8     3        7      3       2 2  2    6
--R           a y(x)  + 8a b x y(x)  + (7a c + 21a b )x y(x)
--R         + 
--R               3       2           3  3     2        5
--R           ((2a d + 36a b c + 18a b )x  + 6a b x)y(x)
--R         + 
--R                2         2 2        2   4        2 2     4
--R           ((10a b d + 15a c  + 45a b c)x  + 30a b x )y(x)
--R         + 
--R                2         2            2  5                 3  3     3
--R           (((8a c + 12a b )d + 36a b c )x  + (24a b c + 36b )x )y(x)
--R         + 
--R              2 2                   3  6                2   4         2     2
--R           ((a d  + 18a b c d + 9a c )x  + (6a b d + 54b c)x  + 9a c x )y(x)
--R         + 
--R                   2       2   7       2         2  5          3             2 8
--R           ((2a b d  + 6a c d)x  + (12b d + 18b c )x  + 18b c x )y(x) + a c d x
--R         + 
--R                   6     2 4
--R           6b c d x  + 9c x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R        3      8      3      2 2       7
--R       a b y(x)  + (2a c + 6a b )x y(x)
--R     + 
--R          3       2          3  2    2      6
--R       ((a d + 18a b c + 9a b )x  + a b)y(x)
--R     + 
--R           2         2 2        2   3        2      5
--R       ((8a b d + 12a c  + 36a b c)x  + 12a b x)y(x)
--R     + 
--R             2         2            2  4                 3  2     4
--R       (((10a c + 15a b )d + 45a b c )x  + (18a b c + 27b )x )y(x)
--R     + 
--R           2 2                    3  5                2   3              3
--R       ((2a d  + 36a b c d + 18a c )x  + (8a b d + 72b c)x  + 6a c x)y(x)
--R     + 
--R               2        2   6       2         2  4          2     2
--R       ((7a b d  + 21a c d)x  + (30b d + 45b c )x  + 27b c x )y(x)
--R     + 
--R            2 7            5      2 3           3 8       2 6          4       2
--R     (8a c d x  + 36b c d x  + 36c x )y(x) + a d x  + 7b d x  + 15c d x  + 9d x
--R  /
--R     9
--R                                                     Type: Expression Integer
--E 107

--S 108 of 130
ode291 := (b*(beta*y(x)+alpha*x)**2-beta*(b*y(x)+a*x))*D(y(x),x)+_
              a*(beta*y(x)+alpha*x)**2-alpha*(b*y(x)+a*x)
 

   (107)
              2    2                                         2   2
       (b beta y(x)  + (2alpha b beta x - b beta)y(x) + alpha b x  - a beta x)
    *
        ,
       y (x)

   + 
           2    2                                            2 2
     a beta y(x)  + (2a alpha beta x - alpha b)y(x) + a alpha x  - a alpha x
                                                     Type: Expression Integer
--R 
--R
--R   (107)
--R              2    2                                         2   2
--R       (b beta y(x)  + (2alpha b beta x - b beta)y(x) + alpha b x  - a beta x)
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R           2    2                                            2 2
--R     a beta y(x)  + (2a alpha beta x - alpha b)y(x) + a alpha x  - a alpha x
--R                                                     Type: Expression Integer
--E 108

--S 109 of 130
solve(ode291,y,x)
 

   (108)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (108)  "failed"
--R                                                    Type: Union("failed",...)
--E 109

--S 110 of 130
ode292 := (a*y(x)+b*x+c)**2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)**2
 

   (109)
       2    2                          2 2             2  ,           2    2
     (a y(x)  + (2a b x + 2a c)y(x) + b x  + 2b c x + c )y (x) + alpha y(x)

   + 
                                              2 2                        2
     (2alpha beta x + 2alpha gamma)y(x) + beta x  + 2beta gamma x + gamma
                                                     Type: Expression Integer
--R 
--R
--R   (109)
--R       2    2                          2 2             2  ,           2    2
--R     (a y(x)  + (2a b x + 2a c)y(x) + b x  + 2b c x + c )y (x) + alpha y(x)
--R
--R   + 
--R                                              2 2                        2
--R     (2alpha beta x + 2alpha gamma)y(x) + beta x  + 2beta gamma x + gamma
--R                                                     Type: Expression Integer
--E 110

--S 111 of 130
solve(ode292,y,x)
 

   (110)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (110)  "failed"
--R                                                    Type: Union("failed",...)
--E 111

--S 112 of 130
ode293 := x*(y(x)**2-3*x)*D(y(x),x)+2*y(x)**3-5*x*y(x)
 

                 2     2  ,           3
   (111)  (x y(x)  - 3x )y (x) + 2y(x)  - 5x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 2     2  ,           3
--R   (111)  (x y(x)  - 3x )y (x) + 2y(x)  - 5x y(x)
--R
--R                                                     Type: Expression Integer
--E 112

--S 113 of 130
solve(ode293,y,x)
 

   (112)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (112)  "failed"
--R                                                    Type: Union("failed",...)
--E 113

--S 114 of 130
ode294 := x*(y(x)**2+x**2-a)*D(y(x),x)-y(x)*(y(x)**2+x**2+a)
 

                 2    3        ,          3       2
   (113)  (x y(x)  + x  - a x)y (x) - y(x)  + (- x  - a)y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 2    3        ,          3       2
--R   (113)  (x y(x)  + x  - a x)y (x) - y(x)  + (- x  - a)y(x)
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 130
solve(ode294,y,x)
 

   (114)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (114)  "failed"
--R                                                    Type: Union("failed",...)
--E 115

--S 116 of 130
ode295 := x*(y(x)**2+x*y(x)-x**2)*D(y(x),x)-y(x)**3+x*y(x)**2+x**2*y(x)
 

                 2    2        3  ,          3         2    2
   (115)  (x y(x)  + x y(x) - x )y (x) - y(x)  + x y(x)  + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 2    2        3  ,          3         2    2
--R   (115)  (x y(x)  + x y(x) - x )y (x) - y(x)  + x y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 116

--S 117 of 130
solve(ode295,y,x)
 

   (116)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (116)  "failed"
--R                                                    Type: Union("failed",...)
--E 117

--S 118 of 130
ode296 := x*(y(x)**2+x**2*y(x)+x**2)*D(y(x),x)-2*y(x)**3-2*x**2*y(x)**2+x**4
 

                 2    3        3  ,           3     2    2    4
   (117)  (x y(x)  + x y(x) + x )y (x) - 2y(x)  - 2x y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R                 2    3        3  ,           3     2    2    4
--R   (117)  (x y(x)  + x y(x) + x )y (x) - 2y(x)  - 2x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 118

--S 119 of 130
solve(ode296,y,x)
 

   (118)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (118)  "failed"
--R                                                    Type: Union("failed",...)
--E 119

--S 120 of 130
ode297 := 2*x*(y(x)**2+5*x**2)*D(y(x),x)+y(x)**3-x**2*y(x)
 

                  2      3  ,          3    2
   (119)  (2x y(x)  + 10x )y (x) + y(x)  - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                  2      3  ,          3    2
--R   (119)  (2x y(x)  + 10x )y (x) + y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 130
solve(ode297,y,x)
 

   (120)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (120)  "failed"
--R                                                    Type: Union("failed",...)
--E 121

--S 122 of 130
ode298 := 3*x*y(x)**2*D(y(x),x)+y(x)**3-2*x
 

                 2 ,          3
   (121)  3x y(x) y (x) + y(x)  - 2x

                                                     Type: Expression Integer
--R 
--R
--R                 2 ,          3
--R   (121)  3x y(x) y (x) + y(x)  - 2x
--R
--R                                                     Type: Expression Integer
--E 122

--S 123 of 130
yx:=solve(ode298,y,x)
 

                3    2
   (122)  x y(x)  - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3    2
--R   (122)  x y(x)  - x
--R                                          Type: Union(Expression Integer,...)
--E 123

--S 124 of 130
ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x
 

   (123)
        4    8      5    5     6    2  ,        3    9      4    6      5    3
     (9x y(x)  - 18x y(x)  + 9x y(x) )y (x) + 4x y(x)  - 15x y(x)  + 18x y(x)

   + 
         6
     - 7x  - 2x
                                                     Type: Expression Integer
--R 
--R
--R   (123)
--R        4    8      5    5     6    2  ,        3    9      4    6      5    3
--R     (9x y(x)  - 18x y(x)  + 9x y(x) )y (x) + 4x y(x)  - 15x y(x)  + 18x y(x)
--R
--R   + 
--R         6
--R     - 7x  - 2x
--R                                                     Type: Expression Integer
--E 124

--S 125 of 130
ode299 := (3*x*y(x)**2-x**2)*D(y(x),x)+y(x)**3-2*x*y(x)
 

                  2    2  ,          3
   (124)  (3x y(x)  - x )y (x) + y(x)  - 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                  2    2  ,          3
--R   (124)  (3x y(x)  - x )y (x) + y(x)  - 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 125

--S 126 of 130
yx:=solve(ode299,y,x)
 

                3    2
   (125)  x y(x)  - x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3    2
--R   (125)  x y(x)  - x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 126

--S 127 of 130
ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx
 

   (126)
        4    8      5    6      6    4        7     3     2    4  ,
     (9x y(x)  - 21x y(x)  + 15x y(x)  + (- 3x  - 3x )y(x)  + x )y (x)

   + 
       3    9      4    7      5    5        6     2     3     3
     4x y(x)  - 15x y(x)  + 18x y(x)  + (- 7x  - 3x )y(x)  + 4x y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (126)
--R        4    8      5    6      6    4        7     3     2    4  ,
--R     (9x y(x)  - 21x y(x)  + 15x y(x)  + (- 3x  - 3x )y(x)  + x )y (x)
--R
--R   + 
--R       3    9      4    7      5    5        6     2     3     3
--R     4x y(x)  - 15x y(x)  + 18x y(x)  + (- 7x  - 3x )y(x)  + 4x y(x)
--R                                                     Type: Expression Integer
--E 127

--S 128 of 130
ode300 := 6*x*y(x)**2*D(y(x),x)+2*y(x)**3+x
 

                 2 ,           3
   (127)  6x y(x) y (x) + 2y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R                 2 ,           3
--R   (127)  6x y(x) y (x) + 2y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 128

--S 129 of 130
yx:=solve(ode300,y,x)
 

                 3    2
          4x y(x)  + x
   (128)  -------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 3    2
--R          4x y(x)  + x
--R   (128)  -------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 129

--S 130 of 130
ode300expr := 6*x*yx**2*D(yx,x)+2*yx**3+x
 

   (129)
            4    8       5    5      6    2  ,          3    9       4    6
       (576x y(x)  + 288x y(x)  + 36x y(x) )y (x) + 256x y(x)  + 240x y(x)

     + 
          5    3     6
       72x y(x)  + 7x  + 4x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (129)
--R            4    8       5    5      6    2  ,          3    9       4    6
--R       (576x y(x)  + 288x y(x)  + 36x y(x) )y (x) + 256x y(x)  + 240x y(x)
--R
--R     + 
--R          5    3     6
--R       72x y(x)  + 7x  + 4x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 130

)spool
 
Starts dribbling to newton.output (2010/3/27, 18:30:8).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
newtonStep(f) ==
  fun  := complexNumericFunction f
  deriv := complexDerivativeFunction(f,1)
  (b:Complex DoubleFloat):Complex DoubleFloat +->
    b - fun(b)/deriv(b)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 5
complexFunPack := MakeUnaryCompiledFunction(EXPR INT, Complex DoubleFloat, Complex DoubleFloat)
 

   (2)
  MakeUnaryCompiledFunction(Expression Integer,Complex DoubleFloat,Complex Doub
  leFloat)
                                                                 Type: Domain
--R 
--R
--R   (2)
--R  MakeUnaryCompiledFunction(Expression Integer,Complex DoubleFloat,Complex Doub
--R  leFloat)
--R                                                                 Type: Domain
--E 2

--S 3 of 5
complexNumericFunction x ==
  v := theVariable x
  compiledFunction(x, v)$complexFunPack
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
complexDerivativeFunction(x,n) ==
  v := theVariable x
  df := differentiate(x,v,n)
  compiledFunction(df, v)$complexFunPack
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
theVariable x ==
  vl := variables x
  nv := # vl
  nv > 1 => error "Expression is not univariate."
  nv = 0 => 'x
  first vl
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
)spool 
 
Starts dribbling to branchcut.output (2010/3/27, 18:23:20).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
t1:=integrate(a/(a*x+b),x=0..1,"noPole")
 

             2           2         2
        log(b  + 2a b + a ) - log(b )
   (1)  -----------------------------
                      2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R             2           2         2
--R        log(b  + 2a b + a ) - log(b )
--R   (1)  -----------------------------
--R                      2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 1

--S 2 of 5
t2:=(1/a)*log((a+b)/b)
 

            b + a
        log(-----)
              b
   (2)  ----------
             a
                                                     Type: Expression Integer
--R 
--R
--R            b + a
--R        log(-----)
--R              b
--R   (2)  ----------
--R             a
--R                                                     Type: Expression Integer
--E 2

--S 3 of 5
complexNormalize t1-t2
 

               2           2           2         b + a
        a log(b  + 2a b + a ) - a log(b ) - 2log(-----)
                                                   b
   (3)  -----------------------------------------------
                               2a
                                                     Type: Expression Integer
--R 
--R
--R               2           2           2         b + a
--R        a log(b  + 2a b + a ) - a log(b ) - 2log(-----)
--R                                                   b
--R   (3)  -----------------------------------------------
--R                               2a
--R                                                     Type: Expression Integer
--E 3

--S 4 of 5
t3:=log(a+b)/a-log(b)/a
 

        log(b + a) - log(b)
   (4)  -------------------
                 a
                                                     Type: Expression Integer
--R 
--R
--R        log(b + a) - log(b)
--R   (4)  -------------------
--R                 a
--R                                                     Type: Expression Integer
--E 4

--S 5 of 5
complexNormalize t1-t3
 

               2           2           2
        a log(b  + 2a b + a ) - a log(b ) - 2log(b + a) + 2log(b)
   (5)  ---------------------------------------------------------
                                    2a
                                                     Type: Expression Integer
--R 
--R
--R               2           2           2
--R        a log(b  + 2a b + a ) - a log(b ) - 2log(b + a) + 2log(b)
--R   (5)  ---------------------------------------------------------
--R                                    2a
--R                                                     Type: Expression Integer
--E 5

)spool 
 
Starts dribbling to RadicalSolvePackage.output (2010/3/27, 18:46:18).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 14
b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13)
 

           3
         3x  + 7
   (1)  --------
          2
        5x  - 13
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           3
--R         3x  + 7
--R   (1)  --------
--R          2
--R        5x  - 13
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 14
radicalSolve(b,x)
 

   (2)
       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
   [x= ------,x= -------------------------,x= ---------------------------]
        3+-+                3+-+                          3+-+
        \|3                2\|3                          2\|3
                                       Type: List Equation Expression Integer
--R 
--R
--R   (2)
--R       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
--R       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
--R   [x= ------,x= -------------------------,x= ---------------------------]
--R        3+-+                3+-+                          3+-+
--R        \|3                2\|3                          2\|3
--R                                       Type: List Equation Expression Integer
--E 2

--S 3 of 14
radicalSolve(b)
 

   (3)
       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
   [x= ------,x= -------------------------,x= ---------------------------]
        3+-+                3+-+                          3+-+
        \|3                2\|3                          2\|3
                                       Type: List Equation Expression Integer
--R 
--R
--R   (3)
--R       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
--R       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
--R   [x= ------,x= -------------------------,x= ---------------------------]
--R        3+-+                3+-+                          3+-+
--R        \|3                2\|3                          2\|3
--R                                       Type: List Equation Expression Integer
--E 3

--S 4 of 14
radicalSolve(b=0,x)
 

   (4)
       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
   [x= ------,x= -------------------------,x= ---------------------------]
        3+-+                3+-+                          3+-+
        \|3                2\|3                          2\|3
                                       Type: List Equation Expression Integer
--R 
--R
--R   (4)
--R       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
--R       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
--R   [x= ------,x= -------------------------,x= ---------------------------]
--R        3+-+                3+-+                          3+-+
--R        \|3                2\|3                          2\|3
--R                                       Type: List Equation Expression Integer
--E 4

--S 5 of 14
radicalSolve(b=0)
 

   (5)
       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
   [x= ------,x= -------------------------,x= ---------------------------]
        3+-+                3+-+                          3+-+
        \|3                2\|3                          2\|3
                                       Type: List Equation Expression Integer
--R 
--R
--R   (5)
--R       3+---+    3+---+ +---+ +-+   3+---+      3+---+ +---+ +-+   3+---+
--R       \|- 7     \|- 7 \|- 1 \|3  - \|- 7     - \|- 7 \|- 1 \|3  - \|- 7
--R   [x= ------,x= -------------------------,x= ---------------------------]
--R        3+-+                3+-+                          3+-+
--R        \|3                2\|3                          2\|3
--R                                       Type: List Equation Expression Integer
--E 5

--S 6 of 14
radicalRoots(b,x)
 

         3+---+ 3+---+ +---+ +-+   3+---+   3+---+ +---+ +-+   3+---+
         \|- 7  \|- 7 \|- 1 \|3  - \|- 7  - \|- 7 \|- 1 \|3  - \|- 7
   (6)  [------,-------------------------,---------------------------]
          3+-+             3+-+                       3+-+
          \|3             2\|3                       2\|3
                                                Type: List Expression Integer
--R 
--R
--R         3+---+ 3+---+ +---+ +-+   3+---+   3+---+ +---+ +-+   3+---+
--R         \|- 7  \|- 7 \|- 1 \|3  - \|- 7  - \|- 7 \|- 1 \|3  - \|- 7
--R   (6)  [------,-------------------------,---------------------------]
--R          3+-+             3+-+                       3+-+
--R          \|3             2\|3                       2\|3
--R                                                Type: List Expression Integer
--E 6

--S 7 of 14
contractSolve(b=0,x)
 

                 +---+ +-+     3+--+     +---+ +-+     3+--+
         3+--+ (\|- 1 \|3  - 1)\|%A  (- \|- 1 \|3  - 1)\|%A            7
   (7)  [\|%A ,---------------------,-----------------------] | [%A= - -]
                         2                      2                      3
     Type: SuchThat(List Expression Integer,List Equation Expression Integer)
--R 
--R
--R                 +---+ +-+     3+--+     +---+ +-+     3+--+
--R         3+--+ (\|- 1 \|3  - 1)\|%A  (- \|- 1 \|3  - 1)\|%A            7
--R   (7)  [\|%A ,---------------------,-----------------------] | [%A= - -]
--R                         2                      2                      3
--R     Type: SuchThat(List Expression Integer,List Equation Expression Integer)
--E 7

--S 8 of 14
contractSolve(b,x)
 

                 +---+ +-+     3+--+     +---+ +-+     3+--+
         3+--+ (\|- 1 \|3  - 1)\|%B  (- \|- 1 \|3  - 1)\|%B            7
   (8)  [\|%B ,---------------------,-----------------------] | [%B= - -]
                         2                      2                      3
     Type: SuchThat(List Expression Integer,List Equation Expression Integer)
--R 
--R
--R                 +---+ +-+     3+--+     +---+ +-+     3+--+
--R         3+--+ (\|- 1 \|3  - 1)\|%B  (- \|- 1 \|3  - 1)\|%B            7
--R   (8)  [\|%B ,---------------------,-----------------------] | [%B= - -]
--R                         2                      2                      3
--R     Type: SuchThat(List Expression Integer,List Equation Expression Integer)
--E 8

--S 9 of 14
c:Fraction(Polynomial(Integer)):=(y^2+4)/(y+1)
 

         2
        y  + 4
   (9)  ------
         y + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        y  + 4
--R   (9)  ------
--R         y + 1
--R                                            Type: Fraction Polynomial Integer
--E 9

--S 10 of 14
radicalSolve([b,c],[x,y])
 

   (10)
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7         +---+
   [[x= ---------------------------,y= - 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                    3+---+
        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
                   3+-+                               3+-+
                  2\|3                                \|3
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7       +---+
    [x= ---------------------------,y= 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                  3+---+
        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
                   3+-+                             3+-+
                  2\|3                              \|3
                                  Type: List List Equation Expression Integer
--R 
--R
--R   (10)
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7         +---+
--R   [[x= ---------------------------,y= - 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                    3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
--R    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
--R                   3+-+                               3+-+
--R                  2\|3                                \|3
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7       +---+
--R    [x= ---------------------------,y= 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                  3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
--R    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
--R                   3+-+                             3+-+
--R                  2\|3                              \|3
--R                                  Type: List List Equation Expression Integer
--E 10

--S 11 of 14
radicalSolve([b,c])
 

   (11)
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7         +---+
   [[x= ---------------------------,y= - 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                    3+---+
        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
                   3+-+                               3+-+
                  2\|3                                \|3
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7       +---+
    [x= ---------------------------,y= 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                  3+---+
        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
                   3+-+                             3+-+
                  2\|3                              \|3
                                  Type: List List Equation Expression Integer
--R 
--R
--R   (11)
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7         +---+
--R   [[x= ---------------------------,y= - 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                    3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
--R    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
--R                   3+-+                               3+-+
--R                  2\|3                                \|3
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7       +---+
--R    [x= ---------------------------,y= 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                  3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
--R    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
--R                   3+-+                             3+-+
--R                  2\|3                              \|3
--R                                  Type: List List Equation Expression Integer
--E 11

--S 12 of 14
radicalSolve([b=0,c=0],[x,y])
 

   (12)
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7         +---+
   [[x= ---------------------------,y= - 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                    3+---+
        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
                   3+-+                               3+-+
                  2\|3                                \|3
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7       +---+
    [x= ---------------------------,y= 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                  3+---+
        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
                   3+-+                             3+-+
                  2\|3                              \|3
                                  Type: List List Equation Expression Integer
--R 
--R
--R   (12)
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7         +---+
--R   [[x= ---------------------------,y= - 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                    3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
--R    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
--R                   3+-+                               3+-+
--R                  2\|3                                \|3
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7       +---+
--R    [x= ---------------------------,y= 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                  3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
--R    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
--R                   3+-+                             3+-+
--R                  2\|3                              \|3
--R                                  Type: List List Equation Expression Integer
--E 12

--S 13 of 14
radicalSolve([b=0,c=0])
 

   (13)
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7         +---+
   [[x= ---------------------------,y= - 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                    3+---+
        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
                   3+-+                               3+-+
                  2\|3                                \|3
          3+---+ +---+ +-+   3+---+
        - \|- 7 \|- 1 \|3  - \|- 7       +---+
    [x= ---------------------------,y= 2\|- 1 ],
                    3+-+
                   2\|3
        3+---+ +---+ +-+   3+---+                  3+---+
        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
                   3+-+                             3+-+
                  2\|3                              \|3
                                  Type: List List Equation Expression Integer
--R 
--R
--R   (13)
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7         +---+
--R   [[x= ---------------------------,y= - 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                    3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7         +---+       \|- 7         +---+
--R    [x= -------------------------,y= - 2\|- 1 ], [x= ------,y= - 2\|- 1 ],
--R                   3+-+                               3+-+
--R                  2\|3                                \|3
--R          3+---+ +---+ +-+   3+---+
--R        - \|- 7 \|- 1 \|3  - \|- 7       +---+
--R    [x= ---------------------------,y= 2\|- 1 ],
--R                    3+-+
--R                   2\|3
--R        3+---+ +---+ +-+   3+---+                  3+---+
--R        \|- 7 \|- 1 \|3  - \|- 7       +---+       \|- 7       +---+
--R    [x= -------------------------,y= 2\|- 1 ], [x= ------,y= 2\|- 1 ]]
--R                   3+-+                             3+-+
--R                  2\|3                              \|3
--R                                  Type: List List Equation Expression Integer
--E 13

--S 14 of 14
radicalRoots([b,c],[x,y])
 

   (14)
       3+---+ +---+ +-+   3+---+
     - \|- 7 \|- 1 \|3  - \|- 7      +---+
   [[---------------------------,- 2\|- 1 ],
                 3+-+
                2\|3
     3+---+ +---+ +-+   3+---+              3+---+
     \|- 7 \|- 1 \|3  - \|- 7      +---+    \|- 7      +---+
    [-------------------------,- 2\|- 1 ], [------,- 2\|- 1 ],
                3+-+                         3+-+
               2\|3                          \|3
       3+---+ +---+ +-+   3+---+            3+---+ +---+ +-+   3+---+
     - \|- 7 \|- 1 \|3  - \|- 7    +---+    \|- 7 \|- 1 \|3  - \|- 7    +---+
    [---------------------------,2\|- 1 ], [-------------------------,2\|- 1 ],
                 3+-+                                  3+-+
                2\|3                                  2\|3
     3+---+
     \|- 7    +---+
    [------,2\|- 1 ]]
      3+-+
      \|3
                                           Type: List List Expression Integer
--R 
--R
--R   (14)
--R       3+---+ +---+ +-+   3+---+
--R     - \|- 7 \|- 1 \|3  - \|- 7      +---+
--R   [[---------------------------,- 2\|- 1 ],
--R                 3+-+
--R                2\|3
--R     3+---+ +---+ +-+   3+---+              3+---+
--R     \|- 7 \|- 1 \|3  - \|- 7      +---+    \|- 7      +---+
--R    [-------------------------,- 2\|- 1 ], [------,- 2\|- 1 ],
--R                3+-+                         3+-+
--R               2\|3                          \|3
--R       3+---+ +---+ +-+   3+---+            3+---+ +---+ +-+   3+---+
--R     - \|- 7 \|- 1 \|3  - \|- 7    +---+    \|- 7 \|- 1 \|3  - \|- 7    +---+
--R    [---------------------------,2\|- 1 ], [-------------------------,2\|- 1 ],
--R                 3+-+                                  3+-+
--R                2\|3                                  2\|3
--R     3+---+
--R     \|- 7    +---+
--R    [------,2\|- 1 ]]
--R      3+-+
--R      \|3
--R                                           Type: List List Expression Integer
--E 14

)spool
 
Starts dribbling to bbtree.output (2010/3/27, 18:23:11).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 10
lm := [3,5,7,11]
 

   (1)  [3,5,7,11]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [3,5,7,11]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 10
modTree(12,lm)
 

   (2)  [0,2,5,1]
                                                           Type: List Integer
--R 
--R
--R   (2)  [0,2,5,1]
--R                                                           Type: List Integer
--E 2

--S 3 of 10
t := balancedBinaryTree(#lm, 0)
 

   (3)  [[0,0,0],0,[0,0,0]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (3)  [[0,0,0],0,[0,0,0]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 3

--S 4 of 10
setleaves!(t,lm)
 

   (4)  [[3,0,5],0,[7,0,11]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (4)  [[3,0,5],0,[7,0,11]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 4

--S 5 of 10
mapUp!(t,_*)
 

   (5)  1155
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1155
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
t
 

   (6)  [[3,15,5],1155,[7,77,11]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (6)  [[3,15,5],1155,[7,77,11]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 6

--S 7 of 10
mapDown!(t,12,_rem)
 

   (7)  [[0,12,2],12,[5,12,1]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--R 
--R
--R   (7)  [[0,12,2],12,[5,12,1]]
--R                                  Type: BalancedBinaryTree NonNegativeInteger
--E 7

--S 8 of 10
leaves %
 

   (8)  [0,2,5,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (8)  [0,2,5,1]
--R                                                Type: List NonNegativeInteger
--E 8

--S 9 of 10
squares := [x**2 rem m for x in % for m in lm]
 

   (9)  [0,4,4,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (9)  [0,4,4,1]
--R                                                Type: List NonNegativeInteger
--E 9

--S 10 of 10
chineseRemainder(%,lm)
 

   (10)  144
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  144
--R                                                        Type: PositiveInteger
--E 10
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read vector
 

-- Input generated from VectorXmpPage
)clear all
 

u : VECTOR INT := new(5,12)
 

   (1)  [12,12,12,12,12]
                                                         Type: Vector Integer
v : VECTOR INT := vector([1,2,3,4,5])
 

   (2)  [1,2,3,4,5]
                                                         Type: Vector Integer
#(v)
 

   (3)  5
                                                        Type: PositiveInteger
v.2
 

   (4)  2
                                                        Type: PositiveInteger
v.3 := 99
 

   (5)  99
                                                        Type: PositiveInteger
v
 

   (6)  [1,2,99,4,5]
                                                         Type: Vector Integer
5 * v
 

   (7)  [5,10,495,20,25]
                                                         Type: Vector Integer
v * 7
 

   (8)  [7,14,693,28,35]
                                                         Type: Vector Integer
w : VECTOR INT := vector([2,3,4,5,6])
 

   (9)  [2,3,4,5,6]
                                                         Type: Vector Integer
v + w
 

   (10)  [3,5,103,9,11]
                                                         Type: Vector Integer
v - w
 

   (11)  [- 1,- 1,95,- 1,- 1]
                                                         Type: Vector Integer
)lisp (bye)
 
Starts dribbling to bugs.output (2010/3/27, 18:23:22).
)set message test on
 
)set message auto off
 
)clear all
 

-- File of Currently active and recently fixed interpreter bugs

--- eval a polynomial with EXPR substitution values
--- Fixed by SCM, verified on 10/30/90

)clear all
 

--S 1 of 44 
eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F
 

           2                   2
   (1)  C y  + (B x + E)y + A x  + D x + F
                                                     Type: Polynomial Integer
--R 
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 44 
eq2:= eval(eq1,[x= xdot*cos(t) - ydot*sin(t), y=xdot*sin(t) + ydot*cos(t)])
 

   (2)
            2                       2       2
     (A ydot  - B xdot ydot + C xdot )sin(t)
   + 
               2                              2
     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
   + 
            2                       2       2
     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R            2                       2       2
--R     (A ydot  - B xdot ydot + C xdot )sin(t)
--R   + 
--R               2                              2
--R     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
--R   + 
--R            2                       2       2
--R     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
--R                                                     Type: Expression Integer
--E 2

-- UTS coercions.  Fixed by SCM, verified on 10/30/90

)clear all
 

--S 3 of 44 
taylor exp x
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 44 
s := %
 

   (2)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 44 
s::(UTS(EXPR FLOAT, x, 0))
 

   (3)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--R 
--R
--R   (3)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--E 5

--S 6 of 44 
s::(UTS(FLOAT, x, 0))
 

   (4)
                    2                            3
     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
   + 
                                4                               5
     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
   + 
                                 6                               7
     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
   + 
                                   8                                  9
     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
   + 
                                   10      11
     0.2755731922 3985890653 E -6 x   + O(x  )
                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--R 
--R
--R   (4)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--E 6

--S 7 of 44 
eval(s,1)
 

             5 8 65 163 1957 685 109601 98641
   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
             2 3 24  60  720 252  40320 36288
                                              Type: Stream Expression Integer
--R 
--R
--R             5 8 65 163 1957 685 109601 98641
--R   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
--R             2 3 24  60  720 252  40320 36288
--R                                              Type: Stream Expression Integer
--E 7

--S 8 of 44 
%::(Stream Float)
 

   (6)
   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
    2.7182787698 412698413, 2.7182815255 731922399, ...]
                                                           Type: Stream Float
--R 
--R
--R   (6)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                           Type: Stream Float
--E 8

-- overloading interpreter maps on arity
--- Fixed by SCM, verified on 10/30/90

)clear all
 

--S 9 of 44 
f(x) == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 44 
f(x,y) == x+y
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 44 
f 3
 
   Compiling function f with type PositiveInteger -> PositiveInteger 

   (3)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (3)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 44 
f(3,4)
 
   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
      PositiveInteger 

   (4)  7
                                                        Type: PositiveInteger
--R 
--R   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
--R      PositiveInteger 
--R
--R   (4)  7
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 44 
f(5)
 

   (5)  6
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  6
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 44 
f(1,x)
 
   Compiling function f with type (PositiveInteger,Variable x) -> 
      Polynomial Integer 

   (6)  x + 1
                                                     Type: Polynomial Integer
--R 
--R   Compiling function f with type (PositiveInteger,Variable x) -> 
--R      Polynomial Integer 
--R
--R   (6)  x + 1
--R                                                     Type: Polynomial Integer
--E 14

-- targetted function requiring a coercion
--- Fixed by SCM, verified on 10/30/90

)clear all
 

--S 15 of 44 
series(n +-> bernoulli(n)/factorial(n), t=0)
 

   (1)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--R 
--R
--R   (1)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 15

-- in-homogeneous list mapping
--- Fixed by SCM, verified on 10/30/90

)clear all
 

--S 16 of 44 
l := [1,2,-1]
 

   (1)  [1,2,- 1]
                                                           Type: List Integer
--R 
--R
--R   (1)  [1,2,- 1]
--R                                                           Type: List Integer
--E 16

--S 17 of 44 
f : INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 44 
f x == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 44 
map(f, l)
 
   Compiling function f with type Integer -> Fraction Integer 

   (4)  [1,2,- 1]
                                                  Type: List Fraction Integer
--R 
--R   Compiling function f with type Integer -> Fraction Integer 
--R
--R   (4)  [1,2,- 1]
--R                                                  Type: List Fraction Integer
--E 19

-- Function args to interpreter functions
--- Fixed by SCM, verified on 10/30/90

)clear all
 
 
--S 20 of 44 
f: INT -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 44 
f x == x+1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 44 
u g == g 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 44 
u f
 
   Compiling function u with type (Integer -> Integer) -> Integer 
   Compiling function f with type Integer -> Integer 

   (4)  4
                                                        Type: PositiveInteger
--R 
--R   Compiling function u with type (Integer -> Integer) -> Integer 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 23

-- category modemap requiring a field to be constructed
--- Fixed by SCM, verified on 10/30/90

)clear all
 

--S 24 of 44 
groebner [x**2 - y, y**3+1]
 

              2  6
   (1)  [y - x ,x  + 1]
                                                Type: List Polynomial Integer
--R 
--R
--R              2  6
--R   (1)  [y - x ,x  + 1]
--R                                                Type: List Polynomial Integer
--E 24

-- operations requiring polynomials, passed variables
--- Fixed by SCM, verified on 10/30/90

)clear all
 

--S 25 of 44 
factor x
 

   (1)  x
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (1)  x
--R                                            Type: Factored Polynomial Integer
--E 25

-- bracket parsing and empty-set types
--- Fixed by SCM, verified on 10/30/90

)clear all
 
 
--S 26 of 44 
{}$(List INT)
 
 
Daly Bug
   The function SEQ is not implemented in List Integer .
--R 
--R 
--RDaly Bug
--R   The function SEQ is not implemented in List Integer .
--E 26

--S 27 of 44 
{1}
 

   (1)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 27

-- Shouldn't work, but no longer bombs the interpreter
--- Fixed by SCM, verified on 10/30/90

)clear all
 
 
--S 28 of 44 
map(variable, [x,y])
 

   (1)  [x,y]
                         Type: List Union(OrderedVariableList [x,y],"failed")
--R 
--R
--R   (1)  [x,y]
--R                         Type: List Union(OrderedVariableList [x,y],"failed")
--E 28

-- Recursive map type analysis bug
--- Fixed by SCM, verified on 10/30/90
)set fun recur off
 
 
)clear all
 
 
--S 29 of 44 
p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 44 
pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 44 
pp(-1,x) -- should be 1/(x-1)
 
   Compiling function p with type (Integer,Polynomial Integer) -> 
      Polynomial Integer 
   Compiling function p with type (Integer,Variable x) -> Polynomial 
      Integer 
   Compiling function pp with type (Integer,Variable x) -> Fraction 
      Polynomial Fraction Integer 

          1
   (3)  -----
        x - 1
                                   Type: Fraction Polynomial Fraction Integer
--R 
--R   Compiling function p with type (Integer,Polynomial Integer) -> 
--R      Polynomial Integer 
--R   Compiling function p with type (Integer,Variable x) -> Polynomial 
--R      Integer 
--R   Compiling function pp with type (Integer,Variable x) -> Fraction 
--R      Polynomial Fraction Integer 
--R
--R          1
--R   (3)  -----
--R        x - 1
--R                                   Type: Fraction Polynomial Fraction Integer
--E 31

-- interpret-code mode for iterators is broken

)clear all
 

--S 32 of 44 
f n ==
  for i in 1..n repeat
    j:=2*i
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 44 
g n ==
    j:=2*n
    m:SQMATRIX(j,?):=1
    print m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 44 
g 3 -- Should work
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 34

--S 35 of 44 
f 3 -- Bombs
 
   Cannot compile the declaration for m because its (possible partial) 
      type contains a local variable.
   AXIOM will attempt to step through and interpret the code.
   +1  0+
   |    |
   +0  1+
   +1  0  0  0+
   |          |
   |0  1  0  0|
   |          |
   |0  0  1  0|
   |          |
   +0  0  0  1+
   +1  0  0  0  0  0+
   |                |
   |0  1  0  0  0  0|
   |                |
   |0  0  1  0  0  0|
   |                |
   |0  0  0  1  0  0|
   |                |
   |0  0  0  0  1  0|
   |                |
   +0  0  0  0  0  1+
                                                                   Type: Void
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0+
--R   |    |
--R   +0  1+
--R   +1  0  0  0+
--R   |          |
--R   |0  1  0  0|
--R   |          |
--R   |0  0  1  0|
--R   |          |
--R   +0  0  0  1+
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 35

-- Test interpreter list destructuring

)clear all
 
 
--S 36 of 44 
mp(x,l) ==
  l is [a,:b] =>
    a*x**(#b)+ mp(x,b)
  0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 44 
mp(x, [1,3,4, 2])
 
   Compiling function mp with type (Variable x,List PositiveInteger)
       -> Polynomial Integer 

         3     2
   (2)  x  + 3x  + 4x + 2
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List PositiveInteger)
--R       -> Polynomial Integer 
--R
--R         3     2
--R   (2)  x  + 3x  + 4x + 2
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 44 
mp(x, [1,2,-3, 4])
 
   Compiling function mp with type (Variable x,List Integer) -> 
      Polynomial Integer 

         3     2
   (3)  x  + 2x  - 3x + 4
                                                     Type: Polynomial Integer
--R 
--R   Compiling function mp with type (Variable x,List Integer) -> 
--R      Polynomial Integer 
--R
--R         3     2
--R   (3)  x  + 2x  - 3x + 4
--R                                                     Type: Polynomial Integer
--E 38

-- Tests compilation of recursive functions

)clear all
 
 
--S 39 of 44 
f1 n ==
  if n=0 then 1 else if n=1 then 1 else f1(n-1)+f1(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 39

--S 40 of 44 
f2 n ==
  m:=n
  if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 40

--S 41 of 44 
f3 n ==
  n=0 => 1
  n=1 => 1
  f3(n-1)+f3(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 41

--S 42 of 44 
f4 n ==
  m:=n
  n=0 => 1
  n=1 => 1
  m:=n
  f4(n-1)+f4(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 42

--S 43 of 44 
f5 n == if n=0 or n=1 then 1 else f5(n-1)+f5(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 43

--S 44 of 44 
[f1 3,f2 3, f3 3,f4 3,f5 3]
 
   Compiling function f1 with type Integer -> PositiveInteger 
   Compiling function f2 with type Integer -> PositiveInteger 
   Compiling function f3 with type Integer -> PositiveInteger 
   Compiling function f4 with type Integer -> PositiveInteger 
   Compiling function f5 with type Integer -> PositiveInteger 

   (6)  [3,3,3,3,3]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function f1 with type Integer -> PositiveInteger 
--R   Compiling function f2 with type Integer -> PositiveInteger 
--R   Compiling function f3 with type Integer -> PositiveInteger 
--R   Compiling function f4 with type Integer -> PositiveInteger 
--R   Compiling function f5 with type Integer -> PositiveInteger 
--R
--R   (6)  [3,3,3,3,3]
--R                                                   Type: List PositiveInteger
--E 44
)spool
 
Starts dribbling to kamke0.output (2010/3/27, 18:27:20).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 134
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 134
f := operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 134
g := operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

--S 4 of 134
ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2)
 

         +---------------------------------+
         |    4       3       2              ,
        \|a4 x  + a3 x  + a2 x  + a1 x + a0 y (x) - 1

   (4)  ---------------------------------------------
              +---------------------------------+
              |    4       3       2
             \|a4 x  + a3 x  + a2 x  + a1 x + a0
                                                     Type: Expression Integer
--R 
--R
--R         +---------------------------------+
--R         |    4       3       2              ,
--R        \|a4 x  + a3 x  + a2 x  + a1 x + a0 y (x) - 1
--R
--R   (4)  ---------------------------------------------
--R              +---------------------------------+
--R              |    4       3       2
--R             \|a4 x  + a3 x  + a2 x  + a1 x + a0
--R                                                     Type: Expression Integer
--E 4

--S 5 of 134
ode1a:=solve(ode1,y,x)
 

   (5)
                   x
                 ++                    1
   [particular=  |   ------------------------------------- d%N ,basis= [1]]
                ++    +----------------------------------+
                      |  4       3       2
                     \|%N a4 + %N a3 + %N a2 + %N a1 + a0
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (5)
--R                   x
--R                 ++                    1
--I   [particular=  |   ------------------------------------- d%N ,basis= [1]]
--R                ++    +----------------------------------+
--R                      |  4       3       2
--I                     \|%N a4 + %N a3 + %N a2 + %N a1 + a0
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 5

--S 6 of 134
ode2 := D(y(x),x) + a*y(x) - c*exp(b*x)
 

         ,          b x
   (6)  y (x) - c %e    + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,          b x
--R   (6)  y (x) - c %e    + a y(x)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 134
ode2a:=solve(ode2,y,x)
 

                         b x
                     c %e              - a x
   (7)  [particular= -------,basis= [%e     ]]
                      b + a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                         b x
--R                     c %e              - a x
--R   (7)  [particular= -------,basis= [%e     ]]
--R                      b + a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 7

--S 8 of 134
yx:=ode2a.particular
 

            b x
        c %e
   (8)  -------
         b + a
                                                     Type: Expression Integer
--R
--R            b x
--R        c %e
--R   (8)  -------
--R         b + a
--R                                                     Type: Expression Integer
--E 8

--S 9 of 134
ode2expr:=D(yx,x) + a*yx -c*exp(b*x)
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E 9

--S 10 of 134
ode3 := D(y(x),x) + a*y(x) - b*sin(c*x)
 

          ,
   (10)  y (x) - b sin(c x) + a y(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (10)  y (x) - b sin(c x) + a y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 134
ode3a:=solve(ode3,y,x)
 

                      a b sin(c x) - b c cos(c x)           - a x
   (11)  [particular= ---------------------------,basis= [%e     ]]
                                 2    2
                                c  + a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                      a b sin(c x) - b c cos(c x)           - a x
--R   (11)  [particular= ---------------------------,basis= [%e     ]]
--R                                 2    2
--R                                c  + a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 11

--S 12 of 134
yx:=ode3a.particular
 

         a b sin(c x) - b c cos(c x)
   (12)  ---------------------------
                    2    2
                   c  + a
                                                     Type: Expression Integer
--R
--R         a b sin(c x) - b c cos(c x)
--R   (12)  ---------------------------
--R                    2    2
--R                   c  + a
--R                                                     Type: Expression Integer
--E 12

--S 13 of 134
ode3expr:=D(yx,x) + a*yx - b*sin(c*x)
 

   (13)  0
                                                     Type: Expression Integer
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 134
ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2)
 

                        2
          ,          - x
   (14)  y (x) - x %e     + 2x y(x)

                                                     Type: Expression Integer
--R
--R                        2
--R          ,          - x
--R   (14)  y (x) - x %e     + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 134
ode4a:=solve(ode4,y,x)
 

                             2
                       2  - x               2
                      x %e               - x
   (15)  [particular= --------,basis= [%e    ]]
                          2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                             2
--R                       2  - x               2
--R                      x %e               - x
--R   (15)  [particular= --------,basis= [%e    ]]
--R                          2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 15

--S 16 of 134
yx:=ode4a.particular
 

                2
          2  - x
         x %e
   (16)  --------
             2
                                                     Type: Expression Integer
--R
--R                2
--R          2  - x
--R         x %e
--R   (16)  --------
--R             2
--R                                                     Type: Expression Integer
--E 16

--S 17 of 134
ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2)
 

   (17)  0
                                                     Type: Expression Integer
--R
--R   (17)  0
--R                                                     Type: Expression Integer
--E 17

--S 18 of 134
ode5 := D(y(x),x) + y(x)*cos(x) - exp(2*x)
 

          ,        2x
   (18)  y (x) - %e   + y(x)cos(x)

                                                     Type: Expression Integer
--R
--R          ,        2x
--R   (18)  y (x) - %e   + y(x)cos(x)
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 134
ode5a:=solve(ode5,y,x)
 

                                   x      2%N
                        - sin(x) ++     %e                      - sin(x)
   (19)  [particular= %e         |   ----------- d%N ,basis= [%e        ]]
                                ++     - sin(%N)
                                     %e
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--I                                   x      2%H
--R                        - sin(x) ++     %e                      - sin(x)
--I   (19)  [particular= %e         |   ----------- d%H ,basis= [%e        ]]
--I                                ++     - sin(%H)
--R                                     %e
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 19

--S 20 of 134
ode6 := D(y(x),x) + y(x)*cos(x) - sin(2*x)/2
 

           ,
         2y (x) - sin(2x) + 2y(x)cos(x)

   (20)  ------------------------------
                        2
                                                     Type: Expression Integer
--R
--R           ,
--R         2y (x) - sin(2x) + 2y(x)cos(x)
--R
--R   (20)  ------------------------------
--R                        2
--R                                                     Type: Expression Integer
--E 20

--S 21 of 134
ode6a:=solve(ode6,y,x)
 

                                           - sin(x)
   (21)  [particular= sin(x) - 1,basis= [%e        ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                           - sin(x)
--R   (21)  [particular= sin(x) - 1,basis= [%e        ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 21

--S 22 of 134
yx:=ode6a.particular
 

   (22)  sin(x) - 1
                                                     Type: Expression Integer
--R
--R   (22)  sin(x) - 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 134
ode6expr:=D(yx,x) + yx*cos(x) - sin(2*x)/2
 

         - sin(2x) + 2cos(x)sin(x)
   (23)  -------------------------
                     2
                                                     Type: Expression Integer
--R
--R         - sin(2x) + 2cos(x)sin(x)
--R   (23)  -------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 23

--S 24 of 134
sin2rule := rule 2*cos(x)*sin(x) == sin(2*x)
 

   (24)  2%BJ cos(x)sin(x) == %BJ sin(2x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (24)  2%Y cos(x)sin(x) == %Y sin(2x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 24

--S 25 of 134
sin2rule ode6expr
 

   (25)  0
                                                     Type: Expression Integer
--R
--R   (25)  0
--R                                                     Type: Expression Integer
--E 25

--S 26 of 134
ode7 := D(y(x),x) + y(x)*cos(x) - exp(-sin(x))
 

          ,        - sin(x)
   (26)  y (x) - %e         + y(x)cos(x)

                                                     Type: Expression Integer
--R
--R          ,        - sin(x)
--R   (26)  y (x) - %e         + y(x)cos(x)
--R
--R                                                     Type: Expression Integer
--E 26

--S 27 of 134
ode7a:=solve(ode7,y,x)
 

                          - sin(x)           - sin(x)
   (27)  [particular= x %e        ,basis= [%e        ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                          - sin(x)           - sin(x)
--R   (27)  [particular= x %e        ,basis= [%e        ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 27

--S 28 of 134
yx:=ode7a.particular
 

             - sin(x)
   (28)  x %e
                                                     Type: Expression Integer
--R
--R             - sin(x)
--R   (28)  x %e
--R                                                     Type: Expression Integer
--E 28

--S 29 of 134
ode7expr := D(yx,x) + yx*cos(x) - exp(-sin(x))
 

   (29)  0
                                                     Type: Expression Integer
--R
--R   (29)  0
--R                                                     Type: Expression Integer
--E 29

--S 30 of 134
ode8 := D(y(x),x) + y(x)*tan(x) - sin(2*x)
 

          ,
   (30)  y (x) + y(x)tan(x) - sin(2x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (30)  y (x) + y(x)tan(x) - sin(2x)
--R
--R                                                     Type: Expression Integer
--E 30

--S 31 of 134
ode8a:=solve(ode8,y,x)
 

   (31)
                                        +-------+
                          2             |   1
                (- 2cos(x)  + 2cos(x))  |-------
                                       4|      4
                                       \|cos(x)                 1
   [particular= --------------------------------,basis= [--------------]]
                          +-----------+                   +-----------+
                          |      2                        |      2
                         \|tan(x)  + 1                   \|tan(x)  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R   (31)
--R                                        +-------+
--R                          2             |   1
--R                (- 2cos(x)  + 2cos(x))  |-------
--R                                       4|      4
--R                                       \|cos(x)                 1
--R   [particular= --------------------------------,basis= [--------------]]
--R                          +-----------+                   +-----------+
--R                          |      2                        |      2
--R                         \|tan(x)  + 1                   \|tan(x)  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 31

--S 32 of 134
yx:=ode8a.particular
 

                                 +-------+
                   2             |   1
         (- 2cos(x)  + 2cos(x))  |-------
                                4|      4
                                \|cos(x)
   (32)  --------------------------------
                   +-----------+
                   |      2
                  \|tan(x)  + 1
                                                     Type: Expression Integer
--R
--R                                 +-------+
--R                   2             |   1
--R         (- 2cos(x)  + 2cos(x))  |-------
--R                                4|      4
--R                                \|cos(x)
--R   (32)  --------------------------------
--R                   +-----------+
--R                   |      2
--R                  \|tan(x)  + 1
--R                                                     Type: Expression Integer
--E 32

--S 33 of 134
ode8expr:=D(yx,x) + yx*tan(x) - sin(2*x)
 

                           +-------+3 +-----------+
                 3         |   1      |      2
         - cos(x) sin(2x)  |-------  \|tan(x)  + 1 + 2sin(x)
                          4|      4
                          \|cos(x)
   (33)  ---------------------------------------------------
                            +-------+3 +-----------+
                         3  |   1      |      2
                   cos(x)   |-------  \|tan(x)  + 1
                           4|      4
                           \|cos(x)
                                                     Type: Expression Integer
--R
--R                           +-------+3 +-----------+
--R                 3         |   1      |      2
--R         - cos(x) sin(2x)  |-------  \|tan(x)  + 1 + 2sin(x)
--R                          4|      4
--R                          \|cos(x)
--R   (33)  ---------------------------------------------------
--R                            +-------+3 +-----------+
--R                         3  |   1      |      2
--R                   cos(x)   |-------  \|tan(x)  + 1
--R                           4|      4
--R                           \|cos(x)
--R                                                     Type: Expression Integer
--E 33

--S 34 of 134
ode9 := D(y(x),x) - (sin(log(x)) + cos(log(x)) +a)*y(x)
 

          ,
   (34)  y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (34)  y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x)
--R
--R                                                     Type: Expression Integer
--E 34

--S 35 of 134
ode9a:=solve(ode9,y,x)
 

                                  x sin(log(x)) + a x
   (35)  [particular= 0,basis= [%e                   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                  x sin(log(x)) + a x
--R   (35)  [particular= 0,basis= [%e                   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 35

--S 36 of 134
yx:=ode9a.particular
 

   (36)  0
                                                     Type: Expression Integer
--R
--R   (36)  0
--R                                                     Type: Expression Integer
--E 36

--S 37 of 134
ode9expr:=D(yx,x) - (sin(log(x)) + cos(log(x)) +a)*yx
 

   (37)  0
                                                     Type: Expression Integer
--R
--R   (37)  0
--R                                                     Type: Expression Integer
--E 37

--S 38 of 134
ode10 := D(y(x),x) + D(f(x),x)*y(x) - f(x)*D(f(x),x)
 

          ,                    ,
   (38)  y (x) + (y(x) - f(x))f (x)

                                                     Type: Expression Integer
--R
--R          ,                    ,
--R   (38)  y (x) + (y(x) - f(x))f (x)
--R
--R                                                     Type: Expression Integer
--E 38

--S 39 of 134
ode10a:=solve(ode10,y,x)
 
 
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 39

--S 40 of 134
ode11 := D(y(x),x)  + f(x)*y(x) - g(x)
 

          ,
   (39)  y (x) + f(x)y(x) - g(x)

                                                     Type: Expression Integer
--R
--R          ,
--R   (39)  y (x) + f(x)y(x) - g(x)
--R
--R                                                     Type: Expression Integer
--E 40

--S 41 of 134
ode11a:=solve(ode11,y,x)
 
 
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 41

--S 42 of 134
ode12 := D(y(x),x) + y(x)**2 - 1
 

          ,          2
   (40)  y (x) + y(x)  - 1

                                                     Type: Expression Integer
--R
--R          ,          2
--R   (40)  y (x) + y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 134
yx:=solve(ode12,y,x)
 

         - log(y(x) + 1) + log(y(x) - 1) + 2x
   (41)  ------------------------------------
                           2
                                          Type: Union(Expression Integer,...)
--R
--R         - log(y(x) + 1) + log(y(x) - 1) + 2x
--R   (41)  ------------------------------------
--R                           2
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 134
ode12expr:=D(yx,x) + yx**2 - 1
 

   (42)
         ,           2                  2
       4y (x) + (y(x)  - 1)log(y(x) + 1)

     + 
                2                            2
       ((- 2y(x)  + 2)log(y(x) - 1) - 4x y(x)  + 4x)log(y(x) + 1)
     + 
          2                  2           2                        2    2     2
     (y(x)  - 1)log(y(x) - 1)  + (4x y(x)  - 4x)log(y(x) - 1) + 4x y(x)  - 4x
  /
          2
     4y(x)  - 4
                                                     Type: Expression Integer
--R
--R   (42)
--R         ,           2                  2
--R       4y (x) + (y(x)  - 1)log(y(x) + 1)
--R
--R     + 
--R                2                            2
--R       ((- 2y(x)  + 2)log(y(x) - 1) - 4x y(x)  + 4x)log(y(x) + 1)
--R     + 
--R          2                  2           2                        2    2     2
--R     (y(x)  - 1)log(y(x) - 1)  + (4x y(x)  - 4x)log(y(x) - 1) + 4x y(x)  - 4x
--R  /
--R          2
--R     4y(x)  - 4
--R                                                     Type: Expression Integer
--E 44

--S 45 of 134
ode13 := D(y(x),x) + y(x)**2 - a*x - b
 

          ,          2
   (43)  y (x) + y(x)  - a x - b

                                                     Type: Expression Integer
--R
--R          ,          2
--R   (43)  y (x) + y(x)  - a x - b
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 134
ode13a:=solve(ode13,y,x)
 

   (44)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (44)  "failed"
--R                                                    Type: Union("failed",...)
--E 46

--S 47 of 134
ode14 := D(y(x),x) + y(x)**2 + a*x**m
 

          ,         m       2
   (45)  y (x) + a x  + y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,         m       2
--R   (45)  y (x) + a x  + y(x)
--R
--R                                                     Type: Expression Integer
--E 47

--S 48 of 134
ode14a:=solve(ode14,y,x)
 

   (46)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (46)  "failed"
--R                                                    Type: Union("failed",...)
--E 48

--S 49 of 134
ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1
 

          ,          2     2        4
   (47)  y (x) + y(x)  - 2x y(x) + x  - 2x - 1

                                                     Type: Expression Integer
--R 
--R
--R          ,          2     2        4
--R   (47)  y (x) + y(x)  - 2x y(x) + x  - 2x - 1
--R
--R                                                     Type: Expression Integer
--E 49

--S 50 of 134
yx:=solve(ode15,y,x)
 

                     2
             y(x) - x  + 1
   (48)  ---------------------
                    2       2x
         (2y(x) - 2x  - 2)%e
                                          Type: Union(Expression Integer,...)
--R
--R                     2
--R             y(x) - x  + 1
--R   (48)  ---------------------
--R                    2       2x
--R         (2y(x) - 2x  - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 50

--S 51 of 134
ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1
 

   (49)
            2x ,
       - 4%e  y (x)

     + 
              4              2        6     4      3     2                    8
           (4x  - 8x - 4)y(x)  + (- 8x  - 8x  + 16x  + 8x  + 16x + 8)y(x) + 4x
         + 
             6     5      3     2
           8x  - 8x  - 16x  - 8x  - 8x - 4
      *
            2x 2
         (%e  )
     + 
             2         2      4     2          6     4     2            2x
       ((- 4x  - 4)y(x)  + (8x  + 8x )y(x) - 4x  - 4x  + 4x  + 8x + 4)%e
     + 
           2        2             4     2
       y(x)  + (- 2x  + 2)y(x) + x  - 2x  + 1
  /
           2        2              4     2        2x 2
     (4y(x)  + (- 8x  - 8)y(x) + 4x  + 8x  + 4)(%e  )
                                                     Type: Expression Integer
--R
--R   (49)
--R            2x ,
--R       - 4%e  y (x)
--R
--R     + 
--R              4              2        6     4      3     2                    8
--R           (4x  - 8x - 4)y(x)  + (- 8x  - 8x  + 16x  + 8x  + 16x + 8)y(x) + 4x
--R         + 
--R             6     5      3     2
--R           8x  - 8x  - 16x  - 8x  - 8x - 4
--R      *
--R            2x 2
--R         (%e  )
--R     + 
--R             2         2      4     2          6     4     2            2x
--R       ((- 4x  - 4)y(x)  + (8x  + 8x )y(x) - 4x  - 4x  + 4x  + 8x + 4)%e
--R     + 
--R           2        2             4     2
--R       y(x)  + (- 2x  + 2)y(x) + x  - 2x  + 1
--R  /
--R           2        2              4     2        2x 2
--R     (4y(x)  + (- 8x  - 8)y(x) + 4x  + 8x  + 4)(%e  )
--R                                                     Type: Expression Integer
--E 51

--S 52 of 134
ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x)
 

          ,          2
   (50)  y (x) + y(x)  + x f(x)y(x) - f(x)

                                                     Type: Expression Integer
--R
--R          ,          2
--R   (50)  y (x) + y(x)  + x f(x)y(x) - f(x)
--R
--R                                                     Type: Expression Integer
--E 52

--S 53 of 134
ode16a:=solve(ode16,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 53

--S 54 of 134
ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4 
 

          ,          2
   (52)  y (x) - y(x)  - 3y(x) + 4

                                                     Type: Expression Integer
--R 
--R
--R          ,          2
--R   (52)  y (x) - y(x)  - 3y(x) + 4
--R
--R                                                     Type: Expression Integer
--E 54

--S 55 of 134
yx:=solve(ode17,y,x)
 

         - log(y(x) + 4) + log(y(x) - 1) - 5x
   (53)  ------------------------------------
                           5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - log(y(x) + 4) + log(y(x) - 1) - 5x
--R   (53)  ------------------------------------
--R                           5
--R                                          Type: Union(Expression Integer,...)
--E 55

--S 56 of 134
ode17expr:=D(yx,x) - yx**2 -3*yx + 4 
 

   (54)
          ,             2                          2
       25y (x) + (- y(x)  - 3y(x) + 4)log(y(x) + 4)

     + 
                 2                                             2
           (2y(x)  + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x)
         + 
           (- 30x + 45)y(x) + 40x - 60
      *
         log(y(x) + 4)
     + 
              2                          2
       (- y(x)  - 3y(x) + 4)log(y(x) - 1)
     + 
                      2
       ((10x - 15)y(x)  + (30x - 45)y(x) - 40x + 60)log(y(x) - 1)
     + 
           2                2         2                         2
     (- 25x  + 75x + 75)y(x)  + (- 75x  + 225x + 225)y(x) + 100x  - 300x - 300
  /
           2
     25y(x)  + 75y(x) - 100
                                                     Type: Expression Integer
--R
--R   (54)
--R          ,             2                          2
--R       25y (x) + (- y(x)  - 3y(x) + 4)log(y(x) + 4)
--R
--R     + 
--R                 2                                             2
--R           (2y(x)  + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x)
--R         + 
--R           (- 30x + 45)y(x) + 40x - 60
--R      *
--R         log(y(x) + 4)
--R     + 
--R              2                          2
--R       (- y(x)  - 3y(x) + 4)log(y(x) - 1)
--R     + 
--R                      2
--R       ((10x - 15)y(x)  + (30x - 45)y(x) - 40x + 60)log(y(x) - 1)
--R     + 
--R           2                2         2                         2
--R     (- 25x  + 75x + 75)y(x)  + (- 75x  + 225x + 225)y(x) + 100x  - 300x - 300
--R  /
--R           2
--R     25y(x)  + 75y(x) - 100
--R                                                     Type: Expression Integer
--E 56

--S 57 of 134
ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1 
 

          ,          2
   (55)  y (x) - y(x)  - x y(x) - x + 1

                                                     Type: Expression Integer
--R 
--R
--R          ,          2
--R   (55)  y (x) - y(x)  - x y(x) - x + 1
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 134
yx:=solve(ode18,y,x)
 

                          2
                       - x  + 4x
                       ---------   x
                           2     ++          1
         (- y(x) - 1)%e          |   - ------------- d%N  + 1
                                ++           2
                                         - %N  + 4%N
                                         -----------
                                              2
                                       %e
   (56)  ----------------------------------------------------
                                        2
                                     - x  + 4x
                                     ---------
                                         2
                         (y(x) + 1)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2
--R                       - x  + 4x
--R                       ---------   x
--R                           2     ++          1
--I         (- y(x) - 1)%e          |   - ------------- d%N  + 1
--R                                ++           2
--I                                         - %N  + 4%N
--R                                         -----------
--R                                              2
--R                                       %e
--R   (56)  ----------------------------------------------------
--R                                        2
--R                                     - x  + 4x
--R                                     ---------
--R                                         2
--R                         (y(x) + 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 134
ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 
 

   (57)
                                  2      2
                               - x  + 4x
                               ---------     x                     2
              2                    2       ++          1
       (- y(x)  - 2y(x) - 1)(%e         )  |   - ------------- d%N
                                          ++           2
                                                   - %N  + 4%N
                                                   -----------
                                                        2
                                                 %e
     + 
                                       2      2                   2
                                    - x  + 4x                  - x  + 4x
                                    ---------                  ---------
                 2                      2                          2
         ((x y(x)  + 2x y(x) + x)(%e         )  + (2y(x) + 2)%e         )
      *
            x
          ++          1
          |   - ------------- d%N
         ++           2
                  - %N  + 4%N
                  -----------
                       2
                %e
     + 
              2
           - x  + 4x
           ---------
               2     ,
       - %e         y (x)

     + 
                                                      2      2
                                                   - x  + 4x
                                                   ---------
                     2                                 2
       ((- x + 1)y(x)  + (- 2x + 2)y(x) - x + 1)(%e         )
     + 
                       2
                    - x  + 4x
                    ---------
            2           2
       (y(x)  - 1)%e          - 1
  /
                              2      2
                           - x  + 4x
                           ---------
          2                    2
     (y(x)  + 2y(x) + 1)(%e         )
                                                     Type: Expression Integer
--R   (57)
--R                                  2      2
--R                               - x  + 4x
--R                               ---------     x                     2
--R              2                    2       ++          1
--I       (- y(x)  - 2y(x) - 1)(%e         )  |   - ------------- d%H
--R                                          ++           2
--I                                                   - %H  + 4%H
--R                                                   -----------
--R                                                        2
--R                                                 %e
--R     + 
--R                                       2      2                   2
--R                                    - x  + 4x                  - x  + 4x
--R                                    ---------                  ---------
--R                 2                      2                          2
--R         ((x y(x)  + 2x y(x) + x)(%e         )  + (2y(x) + 2)%e         )
--R      *
--R            x
--R          ++          1
--I          |   - ------------- d%H
--R         ++           2
--I                  - %H  + 4%H
--R                  -----------
--R                       2
--R                %e
--R     + 
--R              2
--R           - x  + 4x
--R           ---------
--R               2     ,
--R       - %e         y (x)
--R
--R     + 
--R                                                      2      2
--R                                                   - x  + 4x
--R                                                   ---------
--R                     2                                 2
--R       ((- x + 1)y(x)  + (- 2x + 2)y(x) - x + 1)(%e         )
--R     + 
--R                       2
--R                    - x  + 4x
--R                    ---------
--R            2           2
--R       (y(x)  - 1)%e          - 1
--R  /
--R                              2      2
--R                           - x  + 4x
--R                           ---------
--R          2                    2
--R     (y(x)  + 2y(x) + 1)(%e         )
--R                                                     Type: Expression Integer
--E 59

--S 60 of 134
ode19 := D(y(x),x) - (y(x) + x)**2
 

          ,          2              2
   (58)  y (x) - y(x)  - 2x y(x) - x

                                                     Type: Expression Integer
--R 
--R
--R          ,          2              2
--R   (58)  y (x) - y(x)  - 2x y(x) - x
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 134
yx:=solve(ode19,y,x)
 

                             +---+
                   - y(x) + \|- 1  - x
   (59)  --------------------------------------
                                          +---+
            +---+          +---+       2x\|- 1
         (2\|- 1 y(x) + 2x\|- 1  - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             +---+
--R                   - y(x) + \|- 1  - x
--R   (59)  --------------------------------------
--R                                          +---+
--R            +---+          +---+       2x\|- 1
--R         (2\|- 1 y(x) + 2x\|- 1  - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 134
ode19expr := D(yx,x) - (yx + x)**2
 

   (60)
               +---+
            2x\|- 1  ,
       - 4%e        y (x)

     + 
              2    2        2 +---+     3          3 +---+     4     2
         (- 4x y(x)  + (- 8x \|- 1  - 8x )y(x) - 8x \|- 1  - 4x  + 4x )
      *
               +---+ 2
            2x\|- 1
         (%e        )
     + 
                 +---+         2        2 +---+                  3       +---+
           (- 4x\|- 1  + 4)y(x)  + (- 8x \|- 1  + 8x)y(x) + (- 4x  - 4x)\|- 1
         + 
             2
           4x
      *
              +---+
           2x\|- 1
         %e
     + 
           2        +---+                +---+    2
       y(x)  + (- 2\|- 1  + 2x)y(x) - 2x\|- 1  + x  - 1
  /
                                                             +---+ 2
           2      +---+                +---+     2        2x\|- 1
     (4y(x)  + (8\|- 1  + 8x)y(x) + 8x\|- 1  + 4x  - 4)(%e        )
                                                     Type: Expression Integer
--R
--R   (60)
--R               +---+
--R            2x\|- 1  ,
--R       - 4%e        y (x)
--R
--R     + 
--R              2    2        2 +---+     3          3 +---+     4     2
--R         (- 4x y(x)  + (- 8x \|- 1  - 8x )y(x) - 8x \|- 1  - 4x  + 4x )
--R      *
--R               +---+ 2
--R            2x\|- 1
--R         (%e        )
--R     + 
--R                 +---+         2        2 +---+                  3       +---+
--R           (- 4x\|- 1  + 4)y(x)  + (- 8x \|- 1  + 8x)y(x) + (- 4x  - 4x)\|- 1
--R         + 
--R             2
--R           4x
--R      *
--R              +---+
--R           2x\|- 1
--R         %e
--R     + 
--R           2        +---+                +---+    2
--R       y(x)  + (- 2\|- 1  + 2x)y(x) - 2x\|- 1  + x  - 1
--R  /
--R                                                             +---+ 2
--R           2      +---+                +---+     2        2x\|- 1
--R     (4y(x)  + (8\|- 1  + 8x)y(x) + 8x\|- 1  + 4x  - 4)(%e        )
--R                                                     Type: Expression Integer
--E 62

--S 63 of 134
ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x 
 

          ,          2     2
   (61)  y (x) - y(x)  + (x  + 1)y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R          ,          2     2
--R   (61)  y (x) - y(x)  + (x  + 1)y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 63

--S 64 of 134
yx:=solve(ode20,y,x)
 

                               3
                            - x  - 3x
                            ---------   x
                    2           3     ++          1
         (- y(x) + x  + 1)%e          |   - ------------- d%N  + 1
                                     ++           3
                                              - %N  - 3%N
                                              -----------
                                                   3
                                            %e
   (62)  ---------------------------------------------------------
                                             3
                                          - x  - 3x
                                          ---------
                                  2           3
                         (y(x) - x  - 1)%e
                                          Type: Union(Expression Integer,...)
--R
--R                               3
--R                            - x  - 3x
--R                            ---------   x
--R                    2           3     ++          1
--I         (- y(x) + x  + 1)%e          |   - ------------- d%H  + 1
--R                                     ++           3
--I                                              - %H  - 3%H
--R                                              -----------
--R                                                   3
--R                                            %e
--R   (62)  ---------------------------------------------------------
--R                                             3
--R                                          - x  - 3x
--R                                          ---------
--R                                  2           3
--R                         (y(x) - x  - 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 64

--S 65 of 134
ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x 
 

   (63)
                                                       3      2
                                                    - x  - 3x
                                                    ---------
                2      2             4     2            3
         (- y(x)  + (2x  + 2)y(x) - x  - 2x  - 1)(%e         )
      *
            x                     2
          ++          1
          |   - ------------- d%N
         ++           3
                  - %N  - 3%N
                  -----------
                       3
                %e
     + 
                  2         2      4     2             6     4     2
             ((- x  - 1)y(x)  + (2x  + 4x  + 2)y(x) - x  - 3x  - 3x  - 1)
          *
                   3      2
                - x  - 3x
                ---------
                    3
             (%e         )
         + 
                                 3
                              - x  - 3x
                              ---------
                      2           3
           (2y(x) - 2x  - 2)%e
      *
            x
          ++          1
          |   - ------------- d%N
         ++           3
                  - %N  - 3%N
                  -----------
                       3
                %e
     + 
              3
           - x  - 3x
           ---------
               3     ,
       - %e         y (x)

     + 
                                                           3      2
                                                        - x  - 3x
                                                        ---------
                 2      3               5     3             3
       (- 2x y(x)  + (4x  + 4x)y(x) - 2x  - 4x  - 2x)(%e         )
     + 
                                       3
                                    - x  - 3x
                                    ---------
            2    4     2                3
       (y(x)  - x  - 2x  + 2x - 1)%e          - 1
  /
                                                   3      2
                                                - x  - 3x
                                                ---------
          2        2             4     2            3
     (y(x)  + (- 2x  - 2)y(x) + x  + 2x  + 1)(%e         )
                                                     Type: Expression Integer
--R
--R   (63)
--R                                                       3      2
--R                                                    - x  - 3x
--R                                                    ---------
--R                2      2             4     2            3
--R         (- y(x)  + (2x  + 2)y(x) - x  - 2x  - 1)(%e         )
--R      *
--R            x                     2
--R          ++          1
--I          |   - ------------- d%H
--R         ++           3
--I                  - %H  - 3%H
--R                  -----------
--R                       3
--R                %e
--R     + 
--R                  2         2      4     2             6     4     2
--R             ((- x  - 1)y(x)  + (2x  + 4x  + 2)y(x) - x  - 3x  - 3x  - 1)
--R          *
--R                   3      2
--R                - x  - 3x
--R                ---------
--R                    3
--R             (%e         )
--R         + 
--R                                 3
--R                              - x  - 3x
--R                              ---------
--R                      2           3
--R           (2y(x) - 2x  - 2)%e
--R      *
--R            x
--R          ++          1
--I          |   - ------------- d%H
--R         ++           3
--I                  - %H  - 3%H
--R                  -----------
--R                       3
--R                %e
--R     + 
--R              3
--R           - x  - 3x
--R           ---------
--R               3     ,
--R       - %e         y (x)
--R
--R     + 
--R                                                           3      2
--R                                                        - x  - 3x
--R                                                        ---------
--R                 2      3               5     3             3
--R       (- 2x y(x)  + (4x  + 4x)y(x) - 2x  - 4x  - 2x)(%e         )
--R     + 
--R                                       3
--R                                    - x  - 3x
--R                                    ---------
--R            2    4     2                3
--R       (y(x)  - x  - 2x  + 2x - 1)%e          - 1
--R  /
--R                                                   3      2
--R                                                - x  - 3x
--R                                                ---------
--R          2        2             4     2            3
--R     (y(x)  + (- 2x  - 2)y(x) + x  + 2x  + 1)(%e         )
--R                                                     Type: Expression Integer
--E 65

--S 66 of 134
ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x) 
 

          ,                                2
   (64)  y (x) + y(x)sin(x) - cos(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,                                2
--R   (64)  y (x) + y(x)sin(x) - cos(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 66

--S 67 of 134
ode21a:=solve(ode21,y,x)
 

   (65)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (65)  "failed"
--R                                                    Type: Union("failed",...)
--E 67

--S 68 of 134
ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x) 
 

          ,                                  2
   (66)  y (x) - y(x)sin(2x) - cos(2x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,                                  2
--R   (66)  y (x) - y(x)sin(2x) - cos(2x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 134
ode22a:=solve(ode22,y,x)
 

   (67)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (67)  "failed"
--R                                                    Type: Union("failed",...)
--E 69

--S 70 of 134
ode23 := D(y(x),x) + a*y(x)**2 - b
 

          ,            2
   (68)  y (x) + a y(x)  - b

                                                     Type: Expression Integer
--R 
--R
--R          ,            2
--R   (68)  y (x) + a y(x)  - b
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 134
yx:=solve(ode23,y,x)
 

                    2      +---+
             (a y(x)  + b)\|a b  - 2a b y(x)       +---+
         log(-------------------------------) + 2x\|a b
                             2
                       a y(x)  - b
   (69)  -----------------------------------------------
                               +---+
                             2\|a b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2      +---+
--R             (a y(x)  + b)\|a b  - 2a b y(x)       +---+
--R         log(-------------------------------) + 2x\|a b
--R                             2
--R                       a y(x)  - b
--R   (69)  -----------------------------------------------
--R                               +---+
--R                             2\|a b
--R                                          Type: Union(Expression Integer,...)
--E 71

--S 72 of 134
ode23expr := D(yx,x) + a*yx**2 - b
 

   (70)
                                         2      +---+             2
          ,             2         (a y(x)  + b)\|a b  - 2a b y(x)
       4by (x) + (a y(x)  - b)log(-------------------------------)
                                                  2
                                            a y(x)  - b
     + 
                                           2      +---+
                 2         +---+    (a y(x)  + b)\|a b  - 2a b y(x)
       (4a x y(x)  - 4b x)\|a b log(-------------------------------)
                                                    2
                                              a y(x)  - b
     + 
          2   2       2            2       2 2     3     2
       (4a b x  - 4a b  + 4a b)y(x)  - 4a b x  + 4b  - 4b
  /
              2     2
     4a b y(x)  - 4b
                                                     Type: Expression Integer
--R
--R   (70)
--R                                         2      +---+             2
--R          ,             2         (a y(x)  + b)\|a b  - 2a b y(x)
--R       4by (x) + (a y(x)  - b)log(-------------------------------)
--R                                                  2
--R                                            a y(x)  - b
--R     + 
--R                                           2      +---+
--R                 2         +---+    (a y(x)  + b)\|a b  - 2a b y(x)
--R       (4a x y(x)  - 4b x)\|a b log(-------------------------------)
--R                                                    2
--R                                              a y(x)  - b
--R     + 
--R          2   2       2            2       2 2     3     2
--R       (4a b x  - 4a b  + 4a b)y(x)  - 4a b x  + 4b  - 4b
--R  /
--R              2     2
--R     4a b y(x)  - 4b
--R                                                     Type: Expression Integer
--E 72

--S 73 of 134
ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu
 

          ,         nu         2
   (71)  y (x) - b x   + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,         nu         2
--R   (71)  y (x) - b x   + a y(x)
--R
--R                                                     Type: Expression Integer
--E 73

--S 74 of 134
ode24a:=solve(ode24,y,x)
 

   (72)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (72)  "failed"
--R                                                    Type: Union("failed",...)
--E 74

--S 75 of 134
ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1)
 

          ,         2nu      nu - 1         2
   (73)  y (x) - b x    - c x       + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,         2nu      nu - 1         2
--R   (73)  y (x) - b x    - c x       + a y(x)
--R
--R                                                     Type: Expression Integer
--E 75

--S 76 of 134
ode25expr:=solve(ode25,y,x)
 

   (74)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (74)  "failed"
--R                                                    Type: Union("failed",...)
--E 76

--S 77 of 134
ode26 := D(y(x),x) - (A*y(x) - a)*(B*y(x) - b)
 

          ,              2
   (75)  y (x) - A B y(x)  + (A b + B a)y(x) - a b

                                                     Type: Expression Integer
--R 
--R
--R          ,              2
--R   (75)  y (x) - A B y(x)  + (A b + B a)y(x) - a b
--R
--R                                                     Type: Expression Integer
--E 77

--S 78 of 134
yx:=solve(ode26,y,x)
 

         log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x
   (76)  --------------------------------------------------
                              A b - B a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x
--R   (76)  --------------------------------------------------
--R                              A b - B a
--R                                          Type: Union(Expression Integer,...)
--E 78

--S 79 of 134
ode26expr := D(yx,x) - (A*yx - a)*(B*yx - b)
 

   (77)
         2 2               2 2  ,
       (A b  - 2A B a b + B a )y (x)

     + 
           2 2    2     2         2                                2
       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(B y(x) - b)
     + 
              2 2    2        2          2
           (2A B y(x)  + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a)
         + 
               3 2      2 3       3   2      3 2     2
           ((2A B b - 2A B a)x + A B b  - A B a )y(x)
         + 
                 3   2       3 2      3 3    2     2      2 2     3 3
           ((- 2A B b  + 2A B a )x - A b  - A B a b  + A B a b + B a )y(x)
         + 
              2     2       2 2       2   3    2 3
           (2A B a b  - 2A B a b)x + A a b  - B a b
      *
         log(B y(x) - b)
     + 
           2 2    2     2         2                                2
       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(A y(x) - a)
     + 
                 3 2      2 3       3   2      3 2     2
           ((- 2A B b + 2A B a)x - A B b  + A B a )y(x)
         + 
               3   2       3 2      3 3    2     2      2 2     3 3
           ((2A B b  - 2A B a )x + A b  + A B a b  - A B a b - B a )y(x)
         + 
                2     2       2 2       2   3    2 3
           (- 2A B a b  + 2A B a b)x - A a b  + B a b
      *
         log(A y(x) - a)
     + 
               4 2 2     3 3       2 4 2  2
           (- A B b  + 2A B a b - A B a )x
         + 
               4   3    3 2   2    2 3 2       4 3      3     3
           (- A B b  + A B a b  + A B a b - A B a )x - A B a b
         + 
              2 2 2    3   2         3 3     2 2         3 2
           (2A B a  - A B)b  + (- A B a  + 2A B a)b - A B a
      *
             2
         y(x)
     + 
             4   3    3 2   2    2 3 2       4 3  2     4 4     2 2 2 2    4 4
           (A B b  - A B a b  - A B a b + A B a )x  + (A b  - 2A B a b  + B a )x
         + 
            3   4       2   2    3  3         2 3    2     2     3 4      2 2
           A a b  + (- A B a  + A )b  + (- A B a  - A B a)b  + (B a  - A B a )b
         + 
            3 3
           B a
      *
         y(x)
     + 
           3     3     2 2 2 2      3 3   2
       (- A B a b  + 2A B a b  - A B a b)x
     + 
           3   4    2   2 3      2 3 2    3 4       2 2 4          3    2   3
       (- A a b  + A B a b  + A B a b  - B a b)x - A a b  + (2A B a  - A a)b
     + 
           2 4         2  2    2 3
       (- B a  + 2A B a )b  - B a b
  /
         3   2     2 2         3 2     2
       (A B b  - 2A B a b + A B a )y(x)
     + 
           3 3    2     2      2 2     3 3         2   3         2 2    2 3
       (- A b  + A B a b  + A B a b - B a )y(x) + A a b  - 2A B a b  + B a b
                                                     Type: Expression Integer
--R
--R   (77)
--R         2 2               2 2  ,
--R       (A b  - 2A B a b + B a )y (x)
--R
--R     + 
--R           2 2    2     2         2                                2
--R       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(B y(x) - b)
--R     + 
--R              2 2    2        2          2
--R           (2A B y(x)  + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a)
--R         + 
--R               3 2      2 3       3   2      3 2     2
--R           ((2A B b - 2A B a)x + A B b  - A B a )y(x)
--R         + 
--R                 3   2       3 2      3 3    2     2      2 2     3 3
--R           ((- 2A B b  + 2A B a )x - A b  - A B a b  + A B a b + B a )y(x)
--R         + 
--R              2     2       2 2       2   3    2 3
--R           (2A B a b  - 2A B a b)x + A a b  - B a b
--R      *
--R         log(B y(x) - b)
--R     + 
--R           2 2    2     2         2                                2
--R       (- A B y(x)  + (A B b + A B a)y(x) - A B a b)log(A y(x) - a)
--R     + 
--R                 3 2      2 3       3   2      3 2     2
--R           ((- 2A B b + 2A B a)x - A B b  + A B a )y(x)
--R         + 
--R               3   2       3 2      3 3    2     2      2 2     3 3
--R           ((2A B b  - 2A B a )x + A b  + A B a b  - A B a b - B a )y(x)
--R         + 
--R                2     2       2 2       2   3    2 3
--R           (- 2A B a b  + 2A B a b)x - A a b  + B a b
--R      *
--R         log(A y(x) - a)
--R     + 
--R               4 2 2     3 3       2 4 2  2
--R           (- A B b  + 2A B a b - A B a )x
--R         + 
--R               4   3    3 2   2    2 3 2       4 3      3     3
--R           (- A B b  + A B a b  + A B a b - A B a )x - A B a b
--R         + 
--R              2 2 2    3   2         3 3     2 2         3 2
--R           (2A B a  - A B)b  + (- A B a  + 2A B a)b - A B a
--R      *
--R             2
--R         y(x)
--R     + 
--R             4   3    3 2   2    2 3 2       4 3  2     4 4     2 2 2 2    4 4
--R           (A B b  - A B a b  - A B a b + A B a )x  + (A b  - 2A B a b  + B a )x
--R         + 
--R            3   4       2   2    3  3         2 3    2     2     3 4      2 2
--R           A a b  + (- A B a  + A )b  + (- A B a  - A B a)b  + (B a  - A B a )b
--R         + 
--R            3 3
--R           B a
--R      *
--R         y(x)
--R     + 
--R           3     3     2 2 2 2      3 3   2
--R       (- A B a b  + 2A B a b  - A B a b)x
--R     + 
--R           3   4    2   2 3      2 3 2    3 4       2 2 4          3    2   3
--R       (- A a b  + A B a b  + A B a b  - B a b)x - A a b  + (2A B a  - A a)b
--R     + 
--R           2 4         2  2    2 3
--R       (- B a  + 2A B a )b  - B a b
--R  /
--R         3   2     2 2         3 2     2
--R       (A B b  - 2A B a b + A B a )y(x)
--R     + 
--R           3 3    2     2      2 2     3 3         2   3         2 2    2 3
--R       (- A b  + A B a b  + A B a b - B a )y(x) + A a b  - 2A B a b  + B a b
--R                                                     Type: Expression Integer
--E 79

--S 80 of 134
ode27 := D(y(x),x) + a*y(x)*(y(x)-x) - 1
 

          ,            2
   (78)  y (x) + a y(x)  - a x y(x) - 1

                                                     Type: Expression Integer
--R 
--R
--R          ,            2
--R   (78)  y (x) + a y(x)  - a x y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 80

--S 81 of 134
ode27a:=solve(ode27,y,x)
 

                          2
                       a x
                       ----   x
                         2  ++     a
         (- y(x) + x)%e     |   ------ d%N  + 1
                           ++       2
                                  %N a
                                  ----
                                    2
                                %e
   (79)  --------------------------------------
                                   2
                                a x
                                ----
                                  2
                    (y(x) - x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2
--R                       a x
--R                       ----   x
--R                         2  ++     a
--I         (- y(x) + x)%e     |   ------ d%N  + 1
--R                           ++       2
--I                                  %N a
--R                                  ----
--R                                    2
--R                                %e
--R   (79)  --------------------------------------
--R                                   2
--R                                a x
--R                                ----
--R                                  2
--R                    (y(x) - x)%e
--R                                          Type: Union(Expression Integer,...)
--E 81

--S 82 of 134
ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x 
 

          ,            2    3
   (80)  y (x) + x y(x)  - x y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R          ,            2    3
--R   (80)  y (x) + x y(x)  - x y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 134
ode28a:=solve(ode28,y,x)
 

                         4
                        x
                        --   x
                    2    4 ++    %N
         (- y(x) + x )%e   |   ----- d%N  + 1
                          ++       4
                                 %N
                                 ---
                                  4
                               %e
   (81)  ------------------------------------
                                  4
                                 x
                                 --
                             2    4
                    (y(x) - x )%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                         4
--R                        x
--R                        --   x
--I                    2    4 ++    %N
--I         (- y(x) + x )%e   |   ----- d%N  + 1
--R                          ++       4
--I                                 %N
--R                                 ---
--R                                  4
--R                               %e
--R   (81)  ------------------------------------
--R                                  4
--R                                 x
--R                                 --
--R                             2    4
--R                    (y(x) - x )%e
--R                                          Type: Union(Expression Integer,...)
--E 83

--S 84 of 134
ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x) 
 

          ,            2
   (82)  y (x) - x y(x)  - 3x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,            2
--R   (82)  y (x) - x y(x)  - 3x y(x)
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 134
yx:=solve(ode29,y,x)
 

                                           2
         - 2log(y(x) + 3) + 2log(y(x)) - 3x
   (83)  -----------------------------------
                          6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                           2
--R         - 2log(y(x) + 3) + 2log(y(x)) - 3x
--R   (83)  -----------------------------------
--R                          6
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 134
ode29expr := D(yx,x) - x*yx**2 - 3*x*yx 
 

   (84)
          ,                2                         2
       36y (x) + (- 4x y(x)  - 12x y(x))log(y(x) + 3)

     + 
                   2                              3           2
           (8x y(x)  + 24x y(x))log(y(x)) + (- 12x  + 36x)y(x)
         + 
                 3
           (- 36x  + 108x)y(x)
      *
         log(y(x) + 3)
     + 
                 2                     2
       (- 4x y(x)  - 12x y(x))log(y(x))
     + 
            3           2       3
       ((12x  - 36x)y(x)  + (36x  - 108x)y(x))log(y(x))
     + 
            5      3           2         5       3
       (- 9x  + 54x  - 36x)y(x)  + (- 27x  + 162x  - 108x)y(x)
  /
           2
     36y(x)  + 108y(x)
                                                     Type: Expression Integer
--R
--R   (84)
--R          ,                2                         2
--R       36y (x) + (- 4x y(x)  - 12x y(x))log(y(x) + 3)
--R
--R     + 
--R                   2                              3           2
--R           (8x y(x)  + 24x y(x))log(y(x)) + (- 12x  + 36x)y(x)
--R         + 
--R                 3
--R           (- 36x  + 108x)y(x)
--R      *
--R         log(y(x) + 3)
--R     + 
--R                 2                     2
--R       (- 4x y(x)  - 12x y(x))log(y(x))
--R     + 
--R            3           2       3
--R       ((12x  - 36x)y(x)  + (36x  - 108x)y(x))log(y(x))
--R     + 
--R            5      3           2         5       3
--R       (- 9x  + 54x  - 36x)y(x)  + (- 27x  + 162x  - 108x)y(x)
--R  /
--R           2
--R     36y(x)  + 108y(x)
--R                                                     Type: Expression Integer
--E 86

--S 87 of 134
ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a
 

          ,       a       2 - a - 1
   (85)  y (x) - x  + y(x) x

                                                     Type: Expression Integer
--R 
--R
--R          ,       a       2 - a - 1
--R   (85)  y (x) - x  + y(x) x
--R
--R                                                     Type: Expression Integer
--E 87

--S 88 of 134
ode30a:=solve(ode30,y,x)
 

   (86)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (86)  "failed"
--R                                                    Type: Union("failed",...)
--E 88

--S 89 of 134
ode31 := D(y(x),x) - a*x**n*(y(x)**2+1) 
 

          ,               2      n
   (87)  y (x) + (- a y(x)  - a)x

                                                     Type: Expression Integer
--R 
--R
--R          ,               2      n
--R   (87)  y (x) + (- a y(x)  - a)x
--R
--R                                                     Type: Expression Integer
--E 89

--S 90 of 134
yx:=solve(ode31,y,x)
 

                 n log(x)
         - a x %e         + (n + 1)atan(y(x))
   (88)  ------------------------------------
                         n + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 n log(x)
--R         - a x %e         + (n + 1)atan(y(x))
--R   (88)  ------------------------------------
--R                         n + 1
--R                                          Type: Union(Expression Integer,...)
--E 90

--S 91 of 134
ode31expr := D(yx,x) - a*x**n*(yx**2+1) 
 

   (89)
         2           ,          3 2    2    3 2  n   n log(x) 2
       (n  + 2n + 1)y (x) + (- a x y(x)  - a x )x (%e        )

     + 
               2      2       2      2      2    n
           ((2a n + 2a )x y(x)  + (2a n + 2a )x)x atan(y(x))
         + 
                 2                2      2
           (- a n  - 2a n - a)y(x)  - a n  - 2a n - a
      *
           n log(x)
         %e
     + 
              2                2      2             n          2
       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x atan(y(x))
     + 
              2                2      2             n
       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x
  /
       2              2    2
     (n  + 2n + 1)y(x)  + n  + 2n + 1
                                                     Type: Expression Integer
--R
--R   (89)
--R         2           ,          3 2    2    3 2  n   n log(x) 2
--R       (n  + 2n + 1)y (x) + (- a x y(x)  - a x )x (%e        )
--R
--R     + 
--R               2      2       2      2      2    n
--R           ((2a n + 2a )x y(x)  + (2a n + 2a )x)x atan(y(x))
--R         + 
--R                 2                2      2
--R           (- a n  - 2a n - a)y(x)  - a n  - 2a n - a
--R      *
--R           n log(x)
--R         %e
--R     + 
--R              2                2      2             n          2
--R       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x atan(y(x))
--R     + 
--R              2                2      2             n
--R       ((- a n  - 2a n - a)y(x)  - a n  - 2a n - a)x
--R  /
--R       2              2    2
--R     (n  + 2n + 1)y(x)  + n  + 2n + 1
--R                                                     Type: Expression Integer
--E 91

--S 92 of 134
ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2
 

               2 ,           2      2
         cos(x) y (x) + (y(x) cos(x)  - 2)sin(x)

   (90)  ---------------------------------------
                               2
                         cos(x)
                                                     Type: Expression Integer
--R 
--R
--R               2 ,           2      2
--R         cos(x) y (x) + (y(x) cos(x)  - 2)sin(x)
--R
--R   (90)  ---------------------------------------
--R                               2
--R                         cos(x)
--R                                                     Type: Expression Integer
--E 92

--S 93 of 134
yx:=solve(ode32,y,x)
 

   (91)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (91)  "failed"
--R                                                    Type: Union("failed",...)
--E 93

--S 94 of 134
ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x)
 

                  ,           ,              2 ,
         f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x)

   (92)  ------------------------------------------
                          f(x)g(x)
                                                     Type: Expression Integer
--R
--R                  ,           ,              2 ,
--R         f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x)
--R
--R   (92)  ------------------------------------------
--R                          f(x)g(x)
--R                                                     Type: Expression Integer
--E 94

--S 95 of 134
ode33a:=solve(ode33,y,x)
 

   (93)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (93)  "failed"
--R                                                    Type: Union("failed",...)
--E 95

--S 96 of 134
ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x) 
 

          ,              2
   (94)  y (x) + f(x)y(x)  + g(x)y(x)

                                                     Type: Expression Integer
--R
--R          ,              2
--R   (94)  y (x) + f(x)y(x)  + g(x)y(x)
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 134
ode34a:=solve(ode34,y,x)
 
 
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 97

--S 98 of 134
ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b) 
 

          ,              2
   (95)  y (x) + f(x)y(x)  + 2a f(x)y(x) + b f(x)

                                                     Type: Expression Integer
--R
--R          ,              2
--R   (95)  y (x) + f(x)y(x)  + 2a f(x)y(x) + b f(x)
--R
--R                                                     Type: Expression Integer
--E 98

--S 99 of 134
yx:=solve(ode35,y,x)
 

   (96)
         +--------+   x
         |       2  ++
       2\|- b + a   |   f(%N)d%N
                   ++
     + 
                                     +--------+
              2                   2  |       2            2                 3
         (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
     log(--------------------------------------------------------------------)
                                      2
                                  y(x)  + 2a y(x) + b
  /
       +--------+
       |       2
     2\|- b + a
                                          Type: Union(Expression Integer,...)
--R
--R   (96)
--R         +--------+   x
--R         |       2  ++
--I       2\|- b + a   |   f(%H)d%H
--R                   ++
--R     + 
--R                                     +--------+
--R              2                   2  |       2            2                 3
--R         (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
--R     log(--------------------------------------------------------------------)
--R                                      2
--R                                  y(x)  + 2a y(x) + b
--R  /
--R       +--------+
--R       |       2
--R     2\|- b + a
--R                                          Type: Union(Expression Integer,...)
--E 99

--S 100 of 134
ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) 
 

   (97)
                  2         2             3               2     2
         ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
      *
          +--------+   x          2
          |       2  ++
         \|- b + a   |   f(%N)d%N
                    ++
     + 
                      2         2             3               2     2
             ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
          *
             log
                                                +--------+
                         2                   2  |       2            2
                    (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x)
                  + 
                             3
                    2a b - 2a
               /
                      2
                  y(x)  + 2a y(x) + b
         + 
                           3         2       2       4
                 (8a b - 8a )f(x)y(x)  + (16a b - 16a )f(x)y(x)
               + 
                      2     3
                 (8a b  - 8a b)f(x)
          *
              +--------+
              |       2
             \|- b + a
      *
            x
          ++
          |   f(%N)d%N
         ++
     + 
                  +--------+
               2  |       2  ,
       (4b - 4a )\|- b + a  y (x)

     + 
                                              +--------+
                    2                         |       2
         (- f(x)y(x)  - 2a f(x)y(x) - b f(x))\|- b + a
      *
           log
                                              +--------+
                       2                   2  |       2            2
                  (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b
                + 
                      3
                  - 2a
             /
                    2
                y(x)  + 2a y(x) + b
        **
           2
     + 
                    3         2      2      4                 2     3
         ((4a b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4a b  - 4a b)f(x))
      *
                                       +--------+
                2                   2  |       2            2                 3
           (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
       log(--------------------------------------------------------------------)
                                        2
                                    y(x)  + 2a y(x) + b
     + 
              2        2           2         2
           (4b  + (- 4a  + 4)b - 4a )f(x)y(x)
         + 
                2        3            3
           (8a b  + (- 8a  + 8a)b - 8a )f(x)y(x)
         + 
              3        2      2     2
           (4b  + (- 4a  + 4)b  - 4a b)f(x)
      *
          +--------+
          |       2
         \|- b + a
  /
                                                       +--------+
              2     2             3          2     2   |       2
     ((4b - 4a )y(x)  + (8a b - 8a )y(x) + 4b  - 4a b)\|- b + a
                                                     Type: Expression Integer
--R
--R   (97)
--R                  2         2             3               2     2
--R         ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
--R      *
--R          +--------+   x          2
--R          |       2  ++
--I         \|- b + a   |   f(%H)d%H
--R                    ++
--R     + 
--R                      2         2             3               2     2
--R             ((4b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4b  - 4a b)f(x))
--R          *
--R             log
--R                                                +--------+
--R                         2                   2  |       2            2
--R                    (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x)
--R                  + 
--R                             3
--R                    2a b - 2a
--R               /
--R                      2
--R                  y(x)  + 2a y(x) + b
--R         + 
--R                           3         2       2       4
--R                 (8a b - 8a )f(x)y(x)  + (16a b - 16a )f(x)y(x)
--R               + 
--R                      2     3
--R                 (8a b  - 8a b)f(x)
--R          *
--R              +--------+
--R              |       2
--R             \|- b + a
--R      *
--R            x
--R          ++
--I          |   f(%H)d%H
--R         ++
--R     + 
--R                  +--------+
--R               2  |       2  ,
--R       (4b - 4a )\|- b + a  y (x)
--R
--R     + 
--R                                              +--------+
--R                    2                         |       2
--R         (- f(x)y(x)  - 2a f(x)y(x) - b f(x))\|- b + a
--R      *
--R           log
--R                                              +--------+
--R                       2                   2  |       2            2
--R                  (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b
--R                + 
--R                      3
--R                  - 2a
--R             /
--R                    2
--R                y(x)  + 2a y(x) + b
--R        **
--R           2
--R     + 
--R                    3         2      2      4                 2     3
--R         ((4a b - 4a )f(x)y(x)  + (8a b - 8a )f(x)y(x) + (4a b  - 4a b)f(x))
--R      *
--R                                       +--------+
--R                2                   2  |       2            2                 3
--R           (y(x)  + 2a y(x) - b + 2a )\|- b + a   + (2b - 2a )y(x) + 2a b - 2a
--R       log(--------------------------------------------------------------------)
--R                                        2
--R                                    y(x)  + 2a y(x) + b
--R     + 
--R              2        2           2         2
--R           (4b  + (- 4a  + 4)b - 4a )f(x)y(x)
--R         + 
--R                2        3            3
--R           (8a b  + (- 8a  + 8a)b - 8a )f(x)y(x)
--R         + 
--R              3        2      2     2
--R           (4b  + (- 4a  + 4)b  - 4a b)f(x)
--R      *
--R          +--------+
--R          |       2
--R         \|- b + a
--R  /
--R                                                       +--------+
--R              2     2             3          2     2   |       2
--R     ((4b - 4a )y(x)  + (8a b - 8a )y(x) + 4b  - 4a b)\|- b + a
--R                                                     Type: Expression Integer
--E 100

--S 101 of 134
ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2 
 

          ,          3           2
   (98)  y (x) + y(x)  + a x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,          3           2
--R   (98)  y (x) + y(x)  + a x y(x)
--R
--R                                                     Type: Expression Integer
--E 101

--S 102 of 134
ode36a:=solve(ode36,y,x)
 

   (99)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (99)  "failed"
--R                                                    Type: Union("failed",...)
--E 102

--S 103 of 134
ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2
 

           ,            2  x       3
   (100)  y (x) - a y(x) %e  - y(x)

                                                     Type: Expression Integer
--R
--R           ,            2  x       3
--R   (100)  y (x) - a y(x) %e  - y(x)
--R
--R                                                     Type: Expression Integer
--E 103

--S 104 of 134
ode37a:=solve(ode37,y,x)
 

   (101)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (101)  "failed"
--R                                                    Type: Union("failed",...)
--E 104

--S 105 of 134
ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2)
 

           ,          +-+         3
   (102)  y (x) - b x\|x  - a y(x)

                                                     Type: Expression Integer
--R
--R           ,          +-+         3
--R   (102)  y (x) - b x\|x  - a y(x)
--R
--R                                                     Type: Expression Integer
--E 105

--S 106 of 134
ode38a:=solve(ode38,y,x)
 

   (103)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (103)  "failed"
--R                                                    Type: Union("failed",...)
--E 106

--S 107 of 134
ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0
 

           ,             3          2
   (104)  y (x) - a3 y(x)  - a2 y(x)  - a1 y(x) - a0

                                                     Type: Expression Integer
--R
--R           ,             3          2
--R   (104)  y (x) - a3 y(x)  - a2 y(x)  - a1 y(x) - a0
--R
--R                                                     Type: Expression Integer
--E 107

--S 108 of 134
yx:=solve(ode39,y,x)
 

   (105)
           ROOT
                           2  2                     3             3      2  2
                    (- 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2  + 3a1 a2 )
                 *
                         2
                    %%CR0
                + 
                               2
                  12a1 a3 - 4a2
             /
                    2  2                      3            3     2  2
                27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
         + 
           - %%CR0
      *
         log
                           2     3          2  2           2         4   2
                      162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
                    + 
                                 3       3  2            5      2  4
                      (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
                 *
                    %%CR0
                + 
                      2  3                       3   2           3      2  2
                  81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3
             *
                ROOT
                                 2  2                     3             3
                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
                         + 
                              2  2
                           3a1 a2
                      *
                              2
                         %%CR0
                     + 
                                    2
                       12a1 a3 - 4a2
                  /
                         2  2                      3            3     2  2
                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
            + 
                       2     3          2  2           2         4   2
                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
                + 
                             3       3  2            5      2  4
                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
             *
                     2
                %%CR0
            + 
                          2  3                     3   2
                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
                  + 
                              3      2  2
                    (- 12a0 a2  + 3a1 a2 )a3
             *
                %%CR0
            + 
                      3             2      3                         2   2
              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
            + 
                    2
              2a1 a2 a3
     + 
           -
              ROOT
                                 2  2                     3             3
                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
                         + 
                              2  2
                           3a1 a2
                    *
                            2
                       %%CR0
                   + 
                                  2
                     12a1 a3 - 4a2
                /
                       2  2                      3            3     2  2
                   27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
         + 
           - %%CR0
      *
         log
                             2     3        2  2           2         4   2
                      - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
                    + 
                                   3       3  2            5      2  4
                      (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
                 *
                    %%CR0
                + 
                      2  3                     3   2             3      2  2
                - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3  + (- 12a0 a2  + 3a1 a2 )a3
             *
                ROOT
                                 2  2                     3             3
                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
                         + 
                              2  2
                           3a1 a2
                      *
                              2
                         %%CR0
                     + 
                                    2
                       12a1 a3 - 4a2
                  /
                         2  2                      3            3     2  2
                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
            + 
                       2     3          2  2           2         4   2
                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
                + 
                             3       3  2            5      2  4
                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
             *
                     2
                %%CR0
            + 
                          2  3                     3   2
                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
                  + 
                              3      2  2
                    (- 12a0 a2  + 3a1 a2 )a3
             *
                %%CR0
            + 
                      3             2      3                         2   2
              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
            + 
                    2
              2a1 a2 a3
     + 
         2%%CR0
      *
         log
                         2     3        2  2           2         4   2
                  - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
                + 
                               3       3  2            5      2  4
                  (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
             *
                     2
                %%CR0
            + 
                     2  3                       3   2           3      2  2
                (81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3)
             *
                %%CR0
            + 
                      3            2      3                        2   2
              (27a0 a3  - 9a1 a2 a3  + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3
            + 
                       2        4
              - 11a1 a2 a3 + 2a2
     + 
       - 2x
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (105)
--R           ROOT
--R                           2  2                     3             3      2  2
--R                    (- 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2  + 3a1 a2 )
--R                 *
--R                         2
--I                    %%CK0
--R                + 
--R                               2
--R                  12a1 a3 - 4a2
--R             /
--R                    2  2                      3            3     2  2
--R                27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R         + 
--I           - %%CK0
--R      *
--R         log
--R                           2     3          2  2           2         4   2
--R                      162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
--R                    + 
--R                                 3       3  2            5      2  4
--R                      (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
--R                 *
--I                    %%CK0
--R                + 
--R                      2  3                       3   2           3      2  2
--R                  81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3
--R             *
--R                ROOT
--R                                 2  2                     3             3
--R                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
--R                         + 
--R                              2  2
--R                           3a1 a2
--R                      *
--R                              2
--I                         %%CK0
--R                     + 
--R                                    2
--R                       12a1 a3 - 4a2
--R                  /
--R                         2  2                      3            3     2  2
--R                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R            + 
--R                       2     3          2  2           2         4   2
--R                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
--R                + 
--R                             3       3  2            5      2  4
--R                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
--R             *
--R                     2
--I                %%CK0
--R            + 
--R                          2  3                     3   2
--R                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
--R                  + 
--R                              3      2  2
--R                    (- 12a0 a2  + 3a1 a2 )a3
--R             *
--I                %%CK0
--R            + 
--R                      3             2      3                         2   2
--R              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
--R            + 
--R                    2
--R              2a1 a2 a3
--R     + 
--R           -
--R              ROOT
--R                                 2  2                     3             3
--R                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
--R                         + 
--R                              2  2
--R                           3a1 a2
--R                    *
--R                            2
--I                       %%CK0
--R                   + 
--R                                  2
--R                     12a1 a3 - 4a2
--R                /
--R                       2  2                      3            3     2  2
--R                   27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R         + 
--I           - %%CK0
--R      *
--R         log
--R                             2     3        2  2           2         4   2
--R                      - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
--R                    + 
--R                                   3       3  2            5      2  4
--R                      (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
--R                 *
--I                    %%CK0
--R                + 
--R                      2  3                     3   2             3      2  2
--R                - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3  + (- 12a0 a2  + 3a1 a2 )a3
--R             *
--R                ROOT
--R                                 2  2                     3             3
--R                           - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
--R                         + 
--R                              2  2
--R                           3a1 a2
--R                      *
--R                              2
--I                         %%CK0
--R                     + 
--R                                    2
--R                       12a1 a3 - 4a2
--R                  /
--R                         2  2                      3            3     2  2
--R                     27a0 a3  + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2  - a1 a2
--R            + 
--R                       2     3          2  2           2         4   2
--R                  162a0 a1 a3  + (- 54a0 a2  - 108a0 a1 a2 + 24a1 )a3
--R                + 
--R                             3       3  2            5      2  4
--R                  (60a0 a1 a2  - 14a1 a2 )a3 - 8a0 a2  + 2a1 a2
--R             *
--R                     2
--I                %%CK0
--R            + 
--R                          2  3                     3   2
--R                    - 81a0 a3  + (54a0 a1 a2 - 12a1 )a3
--R                  + 
--R                              3      2  2
--R                    (- 12a0 a2  + 3a1 a2 )a3
--R             *
--I                %%CK0
--R            + 
--R                      3             2      3                         2   2
--R              (54a0 a3  - 18a1 a2 a3  + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
--R            + 
--R                    2
--R              2a1 a2 a3
--R     + 
--I         2%%CK0
--R      *
--R         log
--R                         2     3        2  2           2         4   2
--R                  - 162a0 a1 a3  + (54a0 a2  + 108a0 a1 a2 - 24a1 )a3
--R                + 
--R                               3       3  2            5      2  4
--R                  (- 60a0 a1 a2  + 14a1 a2 )a3 + 8a0 a2  - 2a1 a2
--R             *
--R                     2
--I                %%CK0
--R            + 
--R                     2  3                       3   2           3      2  2
--R                (81a0 a3  + (- 54a0 a1 a2 + 12a1 )a3  + (12a0 a2  - 3a1 a2 )a3)
--R             *
--I                %%CK0
--R            + 
--R                      3            2      3                        2   2
--R              (27a0 a3  - 9a1 a2 a3  + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3
--R            + 
--R                       2        4
--R              - 11a1 a2 a3 + 2a2
--R     + 
--R       - 2x
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 108

--S 109 of 134
ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2
 

           ,             3            2
   (106)  y (x) + 3a y(x)  + 6a x y(x)

                                                     Type: Expression Integer
--R
--R           ,             3            2
--R   (106)  y (x) + 3a y(x)  + 6a x y(x)
--R
--R                                                     Type: Expression Integer
--E 109

--S 110 of 134
ode40a:=solve(ode40,y,x)
 

   (107)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (107)  "failed"
--R                                                    Type: Union("failed",...)
--E 110

--S 111 of 134
ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2
 

           ,              3         2
   (108)  y (x) + a x y(x)  + b y(x)

                                                     Type: Expression Integer
--R
--R           ,              3         2
--R   (108)  y (x) + a x y(x)  + b y(x)
--R
--R                                                     Type: Expression Integer
--E 111

--S 112 of 134
ode41a:=solve(ode41,y,x)
 

   (109)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (109)  "failed"
--R                                                    Type: Union("failed",...)
--E 112

--S 113 of 134
ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2
 

           ,          2          3                2
   (110)  y (x) + (- x  - 2x)y(x)  + (- x - 3)y(x)

                                                     Type: Expression Integer
--R
--R           ,          2          3                2
--R   (110)  y (x) + (- x  - 2x)y(x)  + (- x - 3)y(x)
--R
--R                                                     Type: Expression Integer
--E 113

--S 114 of 134
ode42a:=solve(ode42,y,x)
 

   (111)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (111)  "failed"
--R                                                    Type: Union("failed",...)
--E 114

--S 115 of 134
ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2
 

           ,           2     2          3          2
   (112)  y (x) + (3a x  + 4a x + b)y(x)  + 3x y(x)

                                                     Type: Expression Integer
--R
--R           ,           2     2          3          2
--R   (112)  y (x) + (3a x  + 4a x + b)y(x)  + 3x y(x)
--R
--R                                                     Type: Expression Integer
--E 115

--S 116 of 134
ode43a:=solve(ode43,y,x)
 

   (113)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (113)  "failed"
--R                                                    Type: Union("failed",...)
--E 116

--S 117 of 134
ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x)
 

           ,          3    3
   (114)  y (x) + 2a x y(x)  + 2x y(x)

                                                     Type: Expression Integer
--R
--R           ,          3    3
--R   (114)  y (x) + 2a x y(x)  + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 117

--S 118 of 134
yx:=solve(ode44,y,x)
 

               2         2
          (2a x  + a)y(x)  + 2
   (115)  --------------------
                         2
                    2  2x
               2y(x) %e
                                          Type: Union(Expression Integer,...)
--R
--R               2         2
--R          (2a x  + a)y(x)  + 2
--R   (115)  --------------------
--R                         2
--R                    2  2x
--R               2y(x) %e
--R                                          Type: Union(Expression Integer,...)
--E 118

--S 119 of 134
ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx
 

   (116)
                    2 2                                               2 2
              3   2x    ,              3            6          4    2x
       - 8y(x) (%e   ) y (x) + ((- 8a x  + 4a x)y(x)  - 8x y(x) )(%e   )

     + 
          4 9      4 7     4 5    4 3     6       3 7      3 5     3 3     4
       (8a x  + 12a x  + 6a x  + a x )y(x)  + (24a x  + 24a x  + 6a x )y(x)
     + 
           2 5      2 3     2       3
       (24a x  + 12a x )y(x)  + 8a x
  /
                2 3
          6   2x
     4y(x) (%e   )
                                                     Type: Expression Integer
--R
--R   (116)
--R                    2 2                                               2 2
--R              3   2x    ,              3            6          4    2x
--R       - 8y(x) (%e   ) y (x) + ((- 8a x  + 4a x)y(x)  - 8x y(x) )(%e   )
--R
--R     + 
--R          4 9      4 7     4 5    4 3     6       3 7      3 5     3 3     4
--R       (8a x  + 12a x  + 6a x  + a x )y(x)  + (24a x  + 24a x  + 6a x )y(x)
--R     + 
--R           2 5      2 3     2       3
--R       (24a x  + 12a x )y(x)  + 8a x
--R  /
--R                2 3
--R          6   2x
--R     4y(x) (%e   )
--R                                                     Type: Expression Integer
--E 119

--S 120 of 134
ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2
 

           ,         2 3     2      3          2
   (117)  y (x) + (2a x  - 2b x)y(x)  + 3b y(x)

                                                     Type: Expression Integer
--R
--R           ,         2 3     2      3          2
--R   (117)  y (x) + (2a x  - 2b x)y(x)  + 3b y(x)
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 134
ode45a:=solve(ode45,y,x)
 

   (118)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (118)  "failed"
--R                                                    Type: Union("failed",...)
--E 121

--S 122 of 134
ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _
              -x**(-2*a) + a*x**(-a-1)
 

           ,          3 a        - a      - a - 1    - 2a        2
   (119)  y (x) - y(x) x  - y(x)x    + a x        - x     + 3y(x)

                                                     Type: Expression Integer
--R
--R           ,          3 a        - a      - a - 1    - 2a        2
--R   (119)  y (x) - y(x) x  - y(x)x    + a x        - x     + 3y(x)
--R
--R                                                     Type: Expression Integer
--E 122

--S 123 of 134
ode46a:=solve(ode46,y,x)
 

   (120)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (120)  "failed"
--R                                                    Type: Union("failed",...)
--E 123

--S 124 of 134
ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2
 

           ,            3 n           3       2
   (121)  y (x) - a y(x) x  + a x y(x)  - y(x)

                                                     Type: Expression Integer
--R
--R           ,            3 n           3       2
--R   (121)  y (x) - a y(x) x  + a x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 124

--S 125 of 134
ode47a:=solve(ode47,y,x)
 

   (122)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (122)  "failed"
--R                                                    Type: Union("failed",...)
--E 125

--S 126 of 134
ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2
 

           ,            3 n           3         2
   (123)  y (x) - a y(x) x  - b x y(x)  - c y(x)

                                                     Type: Expression Integer
--R
--R           ,            3 n           3         2
--R   (123)  y (x) - a y(x) x  - b x y(x)  - c y(x)
--R
--R                                                     Type: Expression Integer
--E 126

--S 127 of 134
ode48a:=solve(ode48,y,x)
 

   (124)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (124)  "failed"
--R                                                    Type: Union("failed",...)
--E 127

--S 128 of 134
ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _
          (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1)
 
   There are no library operations named phi 
      Use HyperDoc Browse or issue
                                )what op phi
      to learn if there is any operation containing " phi " in its 
      name.
 
   Cannot find a definition or applicable library operation named phi 
      with argument type(s) 
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named phi 
--R      Use HyperDoc Browse or issue
--R                                )what op phi
--R      to learn if there is any operation containing " phi " in its 
--R      name.
--R 
--R   Cannot find a definition or applicable library operation named phi 
--R      with argument type(s) 
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 128

--S 129 of 134
f1 := operator 'f1
 

   (125)  f1
                                                          Type: BasicOperator
--R
--R   (125)  f1
--R                                                          Type: BasicOperator
--E 129

--S 130 of 134
f2 := operator 'f2
 

   (126)  f2
                                                          Type: BasicOperator
--R
--R   (126)  f2
--R                                                          Type: BasicOperator
--E 130

--S 131 of 134
f3 := operator 'f3
 

   (127)  f3
                                                          Type: BasicOperator
--R
--R   (127)  f3
--R                                                          Type: BasicOperator
--E 131

--S 132 of 134
f0 := operator 'f0
 

   (128)  f0
                                                          Type: BasicOperator
--R
--R   (128)  f0
--R                                                          Type: BasicOperator
--E 132

--S 133 of 134
ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x)
 

           ,               3            2
   (129)  y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)

                                                     Type: Expression Integer
--R
--R           ,               3            2
--R   (129)  y (x) - f3(x)y(x)  - f2(x)y(x)  - f1(x)y(x) - f0(x)
--R
--R                                                     Type: Expression Integer
--E 133

--S 134 of 134
ode50a:=solve(ode50,y,x)
 

   (130)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (130)  "failed"
--R                                                    Type: Union("failed",...)
--E 134

)spool
 
Starts dribbling to schaum10.output (2010/3/27, 18:37:27).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 150
aa:=integrate(1/(sqrt(x^2-a^2)),x)
 

               +-------+
               | 2    2
   (1)  - log(\|x  - a   - x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+
--R               | 2    2
--R   (1)  - log(\|x  - a   - x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 150
bb:=log(x+sqrt(x^2-a^2))
 

             +-------+
             | 2    2
   (2)  log(\|x  - a   + x)
                                                     Type: Expression Integer
--R
--R             +-------+
--R             | 2    2
--R   (2)  log(\|x  - a   + x)
--R                                                     Type: Expression Integer
--E

--S 3 of 150
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x)
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x)
--R                                                     Type: Expression Integer
--E

--S 4 of 150
logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
 

   (4)  c log(b) + c log(a) + %H == c log(a b) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (4)  c log(b) + c log(a) + %I == c log(a b) + %I
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 150      14:210 Schaums and Axiom differ by a constant
dd:=logmul1 cc
 

                 2
   (5)  - log(- a )
                                                     Type: Expression Integer
--R
--R                 2
--R   (5)  - log(- a )
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 6 of 150
aa:=integrate(x/(sqrt(x^2-a^2)),x)
 

            +-------+
            | 2    2     2    2
        - x\|x  - a   + x  - a
   (1)  -----------------------
              +-------+
              | 2    2
             \|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +-------+
--R            | 2    2     2    2
--R        - x\|x  - a   + x  - a
--R   (1)  -----------------------
--R              +-------+
--R              | 2    2
--R             \|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7 of 150
bb:=sqrt(x^2-a^2)
 

         +-------+
         | 2    2
   (2)  \|x  - a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2
--R   (2)  \|x  - a
--R                                                     Type: Expression Integer
--E

--S 8 of 150      14:xxx Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 9 of 150
aa:=integrate(x^2/sqrt(x^2-a^2),x)
 

   (1)
               +-------+                   +-------+
            2  | 2    2      2 2    4      | 2    2
       (- 2a x\|x  - a   + 2a x  - a )log(\|x  - a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  + a x)\|x  - a   + 2x  - 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  - a   - 4x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               +-------+                   +-------+
--R            2  | 2    2      2 2    4      | 2    2
--R       (- 2a x\|x  - a   + 2a x  - a )log(\|x  - a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  + a x)\|x  - a   + 2x  - 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  - a   - 4x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 10 of 150
bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2))
 

               +-------+          +-------+
         2     | 2    2           | 2    2
        a log(\|x  - a   + x) + x\|x  - a
   (2)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R               +-------+          +-------+
--R         2     | 2    2           | 2    2
--R        a log(\|x  - a   + x) + x\|x  - a
--R   (2)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 11 of 150
cc:=aa-bb
 

                 +-------+               +-------+
           2     | 2    2          2     | 2    2
        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
   (3)  -----------------------------------------------
                               2
                                                     Type: Expression Integer
--R
--R                 +-------+               +-------+
--R           2     | 2    2          2     | 2    2
--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
--R   (3)  -----------------------------------------------
--R                               2
--R                                                     Type: Expression Integer
--E

--S 12 of 150     14:211 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           2       2
          a log(- a )
   (4)  - -----------
               2
                                                     Type: Expression Integer
--R
--R           2       2
--R          a log(- a )
--R   (4)  - -----------
--R               2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 13 of 150
aa:=integrate(x^3/sqrt(x^2-a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2     6
        (- 4x  - 5a x  + 6a x)\|x  - a   + 4x  + 3a x  - 9a x  + 2a
   (1)  ------------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  - 3a )\|x  - a   - 12x  + 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2     6
--R        (- 4x  - 5a x  + 6a x)\|x  - a   + 4x  + 3a x  - 9a x  + 2a
--R   (1)  ------------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 150
bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2)
 

                   +-------+
          2     2  | 2    2
        (x  + 2a )\|x  - a
   (2)  --------------------
                  3
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2
--R        (x  + 2a )\|x  - a
--R   (2)  --------------------
--R                  3
--R                                                     Type: Expression Integer
--E

--S 15 of 150     14:212 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 150
aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
 

               +-------+
               | 2    2
              \|x  - a   - x
        2atan(--------------)
                     a
   (1)  ---------------------
                  a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x
--R        2atan(--------------)
--R                     a
--R   (1)  ---------------------
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 17 of 150
bb:=1/a*asec(x/a)
 

             x
        asec(-)
             a
   (2)  -------
           a
                                                     Type: Expression Integer
--R
--R             x
--R        asec(-)
--R             a
--R   (2)  -------
--R           a
--R                                                     Type: Expression Integer
--E

--S 18 of 150
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  - a   - x         x
        2atan(--------------) - asec(-)
                     a               a
   (3)  -------------------------------
                       a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x         x
--R        2atan(--------------) - asec(-)
--R                     a               a
--R   (3)  -------------------------------
--R                       a
--R                                                     Type: Expression Integer
--E

--S 19 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (4)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (4)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 20 of 150
dd:=asecrule cc
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a           +-------+
                    |    2                     | 2    2
                   \|   x                     \|x  - a   - x
        - 2%i log(------------------) + 4atan(--------------) - %pi
                           x                         a
   (5)  -----------------------------------------------------------
                                     2a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a           +-------+
--R                    |    2                     | 2    2
--R                   \|   x                     \|x  - a   - x
--R        - 2%i log(------------------) + 4atan(--------------) - %pi
--R                           x                         a
--R   (5)  -----------------------------------------------------------
--R                                     2a
--R                                             Type: Expression Complex Integer
--E

--S 21 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 22 of 150
ee:=atanrule dd
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a               +-------+
                    |    2                         | 2    2
                   \|   x                       - \|x  - a   + x + %i a
        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
                           x                      +-------+
                                                  | 2    2
                                                 \|x  - a   - x + %i a
   (7)  ----------------------------------------------------------------------
                                          2a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a               +-------+
--R                    |    2                         | 2    2
--R                   \|   x                       - \|x  - a   + x + %i a
--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
--R                           x                      +-------+
--R                                                  | 2    2
--R                                                 \|x  - a   - x + %i a
--R   (7)  ----------------------------------------------------------------------
--R                                          2a
--R                                             Type: Expression Complex Integer
--E

--S 23 of 150
ff:=expandLog ee
 

   (8)
                +-------+                        +-------+
                | 2    2                         | 2    2
       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
                   |    2
                  \|   x
  /
     2a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                +-------+                        +-------+
--R                | 2    2                         | 2    2
--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R                   |    2
--R                  \|   x
--R  /
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 24 of 150
gg:=rootSimp ff
 

   (9)
                  +-------+                    +-------+
                  | 2    2                     | 2    2
       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
  /
     2a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                    +-------+
--R                  | 2    2                     | 2    2
--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R  /
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 25 of 150     14:213 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

           %pi
   (10)  - ---
            2a
                                             Type: Expression Complex Integer
--R
--R           %pi
--R   (10)  - ---
--R            2a
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 26 of 150
aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
 

                  1
   (1)  - ----------------
            +-------+
            | 2    2     2
          x\|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  1
--R   (1)  - ----------------
--R            +-------+
--R            | 2    2     2
--R          x\|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27 of 150
bb:=sqrt(x^2-a^2)/(a^2*x)
 

         +-------+
         | 2    2
        \|x  - a
   (2)  ----------
             2
            a x
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2
--R        \|x  - a
--R   (2)  ----------
--R             2
--R            a x
--R                                                     Type: Expression Integer
--E

--S 28 of 150     14:214 Schaums and Axiom differ by a constant
cc:=aa-bb
 

         1
   (3)  --
         2
        a
                                                     Type: Expression Integer
--R
--R         1
--R   (3)  --
--R         2
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 29 of 150
aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
 

   (1)
                                          +-------+
            +-------+                     | 2    2
          3 | 2    2      4     2 2      \|x  - a   - x
       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
                                                a
     + 
                      +-------+
              2    3  | 2    2        3     3
       (- 2a x  + a )\|x  - a   + 2a x  - 2a x
  /
           +-------+
       3 3 | 2    2      3 4     5 2
     4a x \|x  - a   - 4a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                          +-------+
--R            +-------+                     | 2    2
--R          3 | 2    2      4     2 2      \|x  - a   - x
--R       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
--R                                                a
--R     + 
--R                      +-------+
--R              2    3  | 2    2        3     3
--R       (- 2a x  + a )\|x  - a   + 2a x  - 2a x
--R  /
--R           +-------+
--R       3 3 | 2    2      3 4     5 2
--R     4a x \|x  - a   - 4a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 150
bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a)
 

          +-------+
          | 2    2     2     x
        a\|x  - a   + x asec(-)
                             a
   (2)  -----------------------
                   3 2
                 2a x
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2     x
--R        a\|x  - a   + x asec(-)
--R                             a
--R   (2)  -----------------------
--R                   3 2
--R                 2a x
--R                                                     Type: Expression Integer
--E

--S 31 of 150
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  - a   - x         x
        2atan(--------------) - asec(-)
                     a               a
   (3)  -------------------------------
                        3
                      2a
                                                     Type: Expression Integer
--R 
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x         x
--R        2atan(--------------) - asec(-)
--R                     a               a
--R   (3)  -------------------------------
--R                        3
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 32 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 33 of 150
dd:=atanrule cc
 

                    +-------+
                    | 2    2
                 - \|x  - a   + x + %i a         x
        - %i log(-----------------------) - asec(-)
                   +-------+                     a
                   | 2    2
                  \|x  - a   - x + %i a
   (5)  -------------------------------------------
                              3
                            2a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                 - \|x  - a   + x + %i a         x
--R        - %i log(-----------------------) - asec(-)
--R                   +-------+                     a
--R                   | 2    2
--R                  \|x  - a   - x + %i a
--R   (5)  -------------------------------------------
--R                              3
--R                            2a
--R                                             Type: Expression Complex Integer
--E

--S 34 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 35 of 150
ee:=asecrule dd
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a               +-------+
                    |    2                         | 2    2
                   \|   x                       - \|x  - a   + x + %i a
        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
                           x                      +-------+
                                                  | 2    2
                                                 \|x  - a   - x + %i a
   (7)  ----------------------------------------------------------------------
                                            3
                                          4a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a               +-------+
--R                    |    2                         | 2    2
--R                   \|   x                       - \|x  - a   + x + %i a
--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
--R                           x                      +-------+
--R                                                  | 2    2
--R                                                 \|x  - a   - x + %i a
--R   (7)  ----------------------------------------------------------------------
--R                                            3
--R                                          4a
--R                                             Type: Expression Complex Integer
--E

--S 36 of 150
ff:=expandLog ee
 

   (8)
                +-------+                        +-------+
                | 2    2                         | 2    2
       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
                   |    2
                  \|   x
  /
       3
     4a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                +-------+                        +-------+
--R                | 2    2                         | 2    2
--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R                   |    2
--R                  \|   x
--R  /
--R       3
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 37 of 150
gg:=rootSimp ff
 

   (9)
                  +-------+                    +-------+
                  | 2    2                     | 2    2
       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
  /
       3
     4a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                    +-------+
--R                  | 2    2                     | 2    2
--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R  /
--R       3
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 38 of 150     14:215 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

           %pi
   (10)  - ---
             3
           4a
                                             Type: Expression Complex Integer
--R
--R           %pi
--R   (10)  - ---
--R             3
--R           4a
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 39 of 150
aa:=integrate(sqrt(x^2-a^2),x)
 

   (1)
             +-------+                   +-------+
          2  | 2    2      2 2    4      | 2    2
       (2a x\|x  - a   - 2a x  + a )log(\|x  - a   - x)
     + 
                     +-------+
            3    2   | 2    2      4     2 2
       (- 2x  + a x)\|x  - a   + 2x  - 2a x
  /
        +-------+
        | 2    2      2     2
     4x\|x  - a   - 4x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R             +-------+                   +-------+
--R          2  | 2    2      2 2    4      | 2    2
--R       (2a x\|x  - a   - 2a x  + a )log(\|x  - a   - x)
--R     + 
--R                     +-------+
--R            3    2   | 2    2      4     2 2
--R       (- 2x  + a x)\|x  - a   + 2x  - 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     4x\|x  - a   - 4x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40 of 150
bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2))
 

                 +-------+          +-------+
           2     | 2    2           | 2    2
        - a log(\|x  - a   + x) + x\|x  - a
   (2)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R
--R                 +-------+          +-------+
--R           2     | 2    2           | 2    2
--R        - a log(\|x  - a   + x) + x\|x  - a
--R   (2)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E

--S 41 of 150
cc:=aa-bb
 

               +-------+               +-------+
         2     | 2    2          2     | 2    2
        a log(\|x  - a   + x) + a log(\|x  - a   - x)
   (3)  ---------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         2     | 2    2          2     | 2    2
--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
--R   (3)  ---------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 42 of 150     14:216 Schaums and Axiom differ by a constant 
dd:=complexNormalize cc
 

         2       2
        a log(- a )
   (4)  -----------
             2
                                                     Type: Expression Integer
--R
--R         2       2
--R        a log(- a )
--R   (4)  -----------
--R             2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 43 of 150
aa:=integrate(x*sqrt(x^2-a^2),x)
 

                               +-------+
             5     2 3     4   | 2    2      6     2 4     4 2    6
        (- 4x  + 7a x  - 3a x)\|x  - a   + 4x  - 9a x  + 6a x  - a
   (1)  -----------------------------------------------------------
                                 +-------+
                        2     2  | 2    2       3     2
                    (12x  - 3a )\|x  - a   - 12x  + 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R             5     2 3     4   | 2    2      6     2 4     4 2    6
--R        (- 4x  + 7a x  - 3a x)\|x  - a   + 4x  - 9a x  + 6a x  - a
--R   (1)  -----------------------------------------------------------
--R                                 +-------+
--R                        2     2  | 2    2       3     2
--R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
--R                                          Type: Union(Expression Integer,...)
--E

--S 44 of 150
bb:=(x^2-a^2)^(3/2)/3
 

                  +-------+
          2    2  | 2    2
        (x  - a )\|x  - a
   (2)  -------------------
                 3
                                                     Type: Expression Integer
--R
--R                  +-------+
--R          2    2  | 2    2
--R        (x  - a )\|x  - a
--R   (2)  -------------------
--R                 3
--R                                                     Type: Expression Integer
--E

--S 45 of 150     14:217 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 46 of 150
aa:=integrate(x^2*sqrt(x^2-a^2),x)
 

   (1)
                       +-------+                           +-------+
           4 3     6   | 2    2      4 4     6 2    8      | 2    2
       ((8a x  - 4a x)\|x  - a   - 8a x  + 8a x  - a )log(\|x  - a   - x)
     + 
                                      +-------+
           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
     (- 16x  + 24a x  - 10a x  + a x)\|x  - a   + 16x  - 32a x  + 20a x  - 4a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       +-------+                           +-------+
--R           4 3     6   | 2    2      4 4     6 2    8      | 2    2
--R       ((8a x  - 4a x)\|x  - a   - 8a x  + 8a x  - a )log(\|x  - a   - x)
--R     + 
--R                                      +-------+
--R           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
--R     (- 16x  + 24a x  - 10a x  + a x)\|x  - a   + 16x  - 32a x  + 20a x  - 4a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 47 of 150
bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2))
 

                 +-------+                    +-------+
           4     | 2    2            3    2   | 2    2
        - a log(\|x  - a   + x) + (2x  - a x)\|x  - a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                 +-------+                    +-------+
--R           4     | 2    2            3    2   | 2    2
--R        - a log(\|x  - a   + x) + (2x  - a x)\|x  - a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 48 of 150
cc:=aa-bb
 

               +-------+               +-------+
         4     | 2    2          4     | 2    2
        a log(\|x  - a   + x) + a log(\|x  - a   - x)
   (3)  ---------------------------------------------
                              8
                                                     Type: Expression Integer
--R
--R               +-------+               +-------+
--R         4     | 2    2          4     | 2    2
--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
--R   (3)  ---------------------------------------------
--R                              8
--R                                                     Type: Expression Integer
--E

--S 49 of 150     14:218 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

         4       2
        a log(- a )
   (4)  -----------
             8
                                                     Type: Expression Integer
--R
--R         4       2
--R        a log(- a )
--R   (4)  -----------
--R             8
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 50 of 150
aa:=integrate(x^3*sqrt(x^2-a^2),x)
 

   (1)
                                                  +-------+
             9      2 7     4 5      6 3      8   | 2    2       10       2 8
       (- 48x  + 76a x  - 3a x  - 35a x  + 10a x)\|x  - a   + 48x   - 100a x
     + 
          4 6      6 4      8 2     10
       35a x  + 40a x  - 25a x  + 2a
  /
                              +-------+
          4       2 2      4  | 2    2        5       2 3      4
     (240x  - 180a x  + 15a )\|x  - a   - 240x  + 300a x  - 75a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7     4 5      6 3      8   | 2    2       10       2 8
--R       (- 48x  + 76a x  - 3a x  - 35a x  + 10a x)\|x  - a   + 48x   - 100a x
--R     + 
--R          4 6      6 4      8 2     10
--R       35a x  + 40a x  - 25a x  + 2a
--R  /
--R                              +-------+
--R          4       2 2      4  | 2    2        5       2 3      4
--R     (240x  - 180a x  + 15a )\|x  - a   - 240x  + 300a x  - 75a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 51 of 150
bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3
 

                           +-------+
           4    2 2     4  | 2    2
        (3x  - a x  - 2a )\|x  - a
   (2)  ----------------------------
                     15
                                                     Type: Expression Integer
--R
--R                           +-------+
--R           4    2 2     4  | 2    2
--R        (3x  - a x  - 2a )\|x  - a
--R   (2)  ----------------------------
--R                     15
--R                                                     Type: Expression Integer
--E

--S 52 of 150     14:219 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 53 of 150
aa:=integrate(sqrt(x^2-a^2)/x,x)
 

                                     +-------+
              +-------+              | 2    2           +-------+
              | 2    2              \|x  - a   - x      | 2    2     2    2
        (- 2a\|x  - a   + 2a x)atan(--------------) - x\|x  - a   + x  - a
                                           a
   (1)  -------------------------------------------------------------------
                                    +-------+
                                    | 2    2
                                   \|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     +-------+
--R              +-------+              | 2    2           +-------+
--R              | 2    2              \|x  - a   - x      | 2    2     2    2
--R        (- 2a\|x  - a   + 2a x)atan(--------------) - x\|x  - a   + x  - a
--R                                           a
--R   (1)  -------------------------------------------------------------------
--R                                    +-------+
--R                                    | 2    2
--R                                   \|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54 of 150
bb:=sqrt(x^2-a^2)-a*asec(x/a)
 

         +-------+
         | 2    2           x
   (2)  \|x  - a   - a asec(-)
                            a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2           x
--R   (2)  \|x  - a   - a asec(-)
--R                            a
--R                                                     Type: Expression Integer
--E

--S 55 of 150
cc:=aa-bb
 

                   +-------+
                   | 2    2
                  \|x  - a   - x           x
   (3)  - 2a atan(--------------) + a asec(-)
                         a                 a
                                                     Type: Expression Integer
--R
--R                   +-------+
--R                   | 2    2
--R                  \|x  - a   - x           x
--R   (3)  - 2a atan(--------------) + a asec(-)
--R                         a                 a
--R                                                     Type: Expression Integer
--E

--S 56 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 57 of 150
dd:=atanrule cc
 

                    +-------+
                    | 2    2
                 - \|x  - a   + x + %i a           x
   (5)  %i a log(-----------------------) + a asec(-)
                   +-------+                       a
                   | 2    2
                  \|x  - a   - x + %i a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                 - \|x  - a   + x + %i a           x
--R   (5)  %i a log(-----------------------) + a asec(-)
--R                   +-------+                       a
--R                   | 2    2
--R                  \|x  - a   - x + %i a
--R                                             Type: Expression Complex Integer
--E

--S 58 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 59 of 150
ee:=asecrule dd
 

   (7)
               +-------+
               | 2    2
               |x  - a
             x |-------  + %i a                 +-------+
               |    2                           | 2    2
              \|   x                         - \|x  - a   + x + %i a
   2%i a log(------------------) + 2%i a log(-----------------------) + a %pi
                      x                        +-------+
                                               | 2    2
                                              \|x  - a   - x + %i a
   --------------------------------------------------------------------------
                                        2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R               +-------+
--R               | 2    2
--R               |x  - a
--R             x |-------  + %i a                 +-------+
--R               |    2                           | 2    2
--R              \|   x                         - \|x  - a   + x + %i a
--R   2%i a log(------------------) + 2%i a log(-----------------------) + a %pi
--R                      x                        +-------+
--R                                               | 2    2
--R                                              \|x  - a   - x + %i a
--R   --------------------------------------------------------------------------
--R                                        2
--R                                             Type: Expression Complex Integer
--E

--S 60 of 150
ff:=expandLog ee
 

   (8)
                    +-------+                          +-------+
                    | 2    2                           | 2    2
       - 2%i a log(\|x  - a   - x + %i a) + 2%i a log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       2%i a log(x |-------  + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
                   |    2
                  \|   x
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +-------+                          +-------+
--R                    | 2    2                           | 2    2
--R       - 2%i a log(\|x  - a   - x + %i a) + 2%i a log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       2%i a log(x |-------  + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
--R                   |    2
--R                  \|   x
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 61 of 150
gg:=rootSimp ff
 

   (9)
                  +-------+                      +-------+
                  | 2    2                       | 2    2
       2%i a log(\|x  - a   + %i a) - 2%i a log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       2%i a log(\|x  - a   - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                      +-------+
--R                  | 2    2                       | 2    2
--R       2%i a log(\|x  - a   + %i a) - 2%i a log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       2%i a log(\|x  - a   - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 62 of 150     14:220 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         a %pi
   (10)  -----
           2
                                             Type: Expression Complex Integer
--R
--R         a %pi
--R   (10)  -----
--R           2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 63 of 150
aa:=integrate(sqrt(x^2-a^2)/x^2,x)
 

             +-------+           +-------+
             | 2    2     2      | 2    2          2
        (- x\|x  - a   + x )log(\|x  - a   - x) + a
   (1)  --------------------------------------------
                        +-------+
                        | 2    2     2
                      x\|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+           +-------+
--R             | 2    2     2      | 2    2          2
--R        (- x\|x  - a   + x )log(\|x  - a   - x) + a
--R   (1)  --------------------------------------------
--R                        +-------+
--R                        | 2    2     2
--R                      x\|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 64 of 150
bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2))
 

               +-------+         +-------+
               | 2    2          | 2    2
        x log(\|x  - a   + x) - \|x  - a
   (2)  ----------------------------------
                         x
                                                     Type: Expression Integer
--R
--R               +-------+         +-------+
--R               | 2    2          | 2    2
--R        x log(\|x  - a   + x) - \|x  - a
--R   (2)  ----------------------------------
--R                         x
--R                                                     Type: Expression Integer
--E

--S 65 of 150
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 66 of 150     14:221 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

                 2
   (4)  - log(- a ) - 1
                                                     Type: Expression Integer
--R
--R                 2
--R   (4)  - log(- a ) - 1
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 67 of 150
aa:=integrate(sqrt(x^2-a^2)/x^3,x)
 

   (1)
                                          +-------+
            +-------+                     | 2    2
          3 | 2    2      4     2 2      \|x  - a   - x
       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
                                                a
     + 
                    +-------+
            2    3  | 2    2        3     3
       (2a x  - a )\|x  - a   - 2a x  + 2a x
  /
           +-------+
         3 | 2    2        4     3 2
     4a x \|x  - a   - 4a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                          +-------+
--R            +-------+                     | 2    2
--R          3 | 2    2      4     2 2      \|x  - a   - x
--R       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
--R                                                a
--R     + 
--R                    +-------+
--R            2    3  | 2    2        3     3
--R       (2a x  - a )\|x  - a   - 2a x  + 2a x
--R  /
--R           +-------+
--R         3 | 2    2        4     3 2
--R     4a x \|x  - a   - 4a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68 of 150
bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a)
 

            +-------+
            | 2    2     2     x
        - a\|x  - a   + x asec(-)
                               a
   (2)  -------------------------
                      2
                  2a x
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2     x
--R        - a\|x  - a   + x asec(-)
--R                               a
--R   (2)  -------------------------
--R                      2
--R                  2a x
--R                                                     Type: Expression Integer
--E

--S 69 of 150
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  - a   - x         x
        2atan(--------------) - asec(-)
                     a               a
   (3)  -------------------------------
                       2a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   - x         x
--R        2atan(--------------) - asec(-)
--R                     a               a
--R   (3)  -------------------------------
--R                       2a
--R                                                     Type: Expression Integer
--E

--S 70 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (4)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (4)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 71 of 150
dd:=asecrule cc
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a           +-------+
                    |    2                     | 2    2
                   \|   x                     \|x  - a   - x
        - 2%i log(------------------) + 4atan(--------------) - %pi
                           x                         a
   (5)  -----------------------------------------------------------
                                     4a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a           +-------+
--R                    |    2                     | 2    2
--R                   \|   x                     \|x  - a   - x
--R        - 2%i log(------------------) + 4atan(--------------) - %pi
--R                           x                         a
--R   (5)  -----------------------------------------------------------
--R                                     4a
--R                                             Type: Expression Complex Integer
--E

--S 72 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 73 of 150
ee:=atanrule dd
 

                    +-------+
                    | 2    2
                    |x  - a
                  x |-------  + %i a               +-------+
                    |    2                         | 2    2
                   \|   x                       - \|x  - a   + x + %i a
        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
                           x                      +-------+
                                                  | 2    2
                                                 \|x  - a   - x + %i a
   (7)  ----------------------------------------------------------------------
                                          4a
                                             Type: Expression Complex Integer
--R
--R                    +-------+
--R                    | 2    2
--R                    |x  - a
--R                  x |-------  + %i a               +-------+
--R                    |    2                         | 2    2
--R                   \|   x                       - \|x  - a   + x + %i a
--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
--R                           x                      +-------+
--R                                                  | 2    2
--R                                                 \|x  - a   - x + %i a
--R   (7)  ----------------------------------------------------------------------
--R                                          4a
--R                                             Type: Expression Complex Integer
--E

--S 74 of 150
ff:=expandLog ee
 

   (8)
                +-------+                        +-------+
                | 2    2                         | 2    2
       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
                   |    2
                  \|   x
  /
     4a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                +-------+                        +-------+
--R                | 2    2                         | 2    2
--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R                   |    2
--R                  \|   x
--R  /
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 75 of 150
gg:=rootSimp ff
 

   (9)
                  +-------+                    +-------+
                  | 2    2                     | 2    2
       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
     + 
                  +-------+
                  | 2    2
       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
  /
     4a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                    +-------+
--R                  | 2    2                     | 2    2
--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R                  | 2    2
--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
--R  /
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 76 of 150     14:222 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

           %pi
   (10)  - ---
            4a
                                             Type: Expression Complex Integer
--R
--R           %pi
--R   (10)  - ---
--R            4a
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 77 of 150
aa:=integrate(1/(x^2-a^2)^(3/2),x)
 

                    1
   (1)  - ---------------------
            +-------+
            | 2    2     2    2
          x\|x  - a   - x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    1
--R   (1)  - ---------------------
--R            +-------+
--R            | 2    2     2    2
--R          x\|x  - a   - x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 78 of 150
bb:=-x/(a^2*sqrt(x^2-a^2))
 

                x
   (2)  - ------------
             +-------+
           2 | 2    2
          a \|x  - a
                                                     Type: Expression Integer
--R
--R                x
--R   (2)  - ------------
--R             +-------+
--R           2 | 2    2
--R          a \|x  - a
--R                                                     Type: Expression Integer
--E

--S 79 of 150     14:223 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           1
   (3)  - --
           2
          a
                                                     Type: Expression Integer
--R
--R           1
--R   (3)  - --
--R           2
--R          a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 80 of 150
aa:=integrate(x/(x^2-a^2)^(3/2),x)
 

             +-------+
             | 2    2
            \|x  - a   - x
   (1)  ---------------------
          +-------+
          | 2    2     2    2
        x\|x  - a   - x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+
--R             | 2    2
--R            \|x  - a   - x
--R   (1)  ---------------------
--R          +-------+
--R          | 2    2     2    2
--R        x\|x  - a   - x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 81 of 150
bb:=-1/sqrt(x^2-a^2)
 

               1
   (2)  - ----------
           +-------+
           | 2    2
          \|x  - a
                                                     Type: Expression Integer
--R
--R               1
--R   (2)  - ----------
--R           +-------+
--R           | 2    2
--R          \|x  - a
--R                                                     Type: Expression Integer
--E

--S 82 of 150     14:224 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 83 of 150
aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
 

             +-------+                +-------+
             | 2    2     2    2      | 2    2          2
        (- x\|x  - a   + x  - a )log(\|x  - a   - x) - a
   (1)  -------------------------------------------------
                        +-------+
                        | 2    2     2    2
                      x\|x  - a   - x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +-------+                +-------+
--R             | 2    2     2    2      | 2    2          2
--R        (- x\|x  - a   + x  - a )log(\|x  - a   - x) - a
--R   (1)  -------------------------------------------------
--R                        +-------+
--R                        | 2    2     2    2
--R                      x\|x  - a   - x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84 of 150
bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2))
 

         +-------+     +-------+
         | 2    2      | 2    2
        \|x  - a  log(\|x  - a   + x) - x
   (2)  ---------------------------------
                     +-------+
                     | 2    2
                    \|x  - a
                                                     Type: Expression Integer
--R
--R         +-------+     +-------+
--R         | 2    2      | 2    2
--R        \|x  - a  log(\|x  - a   + x) - x
--R   (2)  ---------------------------------
--R                     +-------+
--R                     | 2    2
--R                    \|x  - a
--R                                                     Type: Expression Integer
--E

--S 85      of 150
cc:=aa-bb
 

               +-------+             +-------+
               | 2    2              | 2    2
   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
                                                     Type: Expression Integer
--R
--R               +-------+             +-------+
--R               | 2    2              | 2    2
--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
--R                                                     Type: Expression Integer
--E

--S 86 of 150     14:225 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

                 2
   (4)  - log(- a ) - 1
                                                     Type: Expression Integer
--R
--R                 2
--R   (4)  - log(- a ) - 1
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 87 of 150
aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
 

                       +-------+
             3     2   | 2    2      4     2 2     4
        (- 2x  + 4a x)\|x  - a   + 2x  - 5a x  + 2a
   (1)  --------------------------------------------
                         +-------+
                 2    2  | 2    2      3     2
              (2x  - a )\|x  - a   - 2x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       +-------+
--R             3     2   | 2    2      4     2 2     4
--R        (- 2x  + 4a x)\|x  - a   + 2x  - 5a x  + 2a
--R   (1)  --------------------------------------------
--R                         +-------+
--R                 2    2  | 2    2      3     2
--R              (2x  - a )\|x  - a   - 2x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 88 of 150
bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2)
 

          2     2
         x  - 2a
   (2)  ----------
         +-------+
         | 2    2
        \|x  - a
                                                     Type: Expression Integer
--R
--R          2     2
--R         x  - 2a
--R   (2)  ----------
--R         +-------+
--R         | 2    2
--R        \|x  - a
--R                                                     Type: Expression Integer
--E

--S 89 of 150     14:226 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 90 of 150
aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
 

                                          +-------+
              +-------+                   | 2    2           +-------+
              | 2    2      2     2      \|x  - a   - x      | 2    2
        (- 2x\|x  - a   + 2x  - 2a )atan(--------------) + a\|x  - a   - a x
                                                a
   (1)  --------------------------------------------------------------------
                                  +-------+
                               3  | 2    2     3 2    5
                              a x\|x  - a   - a x  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          +-------+
--R              +-------+                   | 2    2           +-------+
--R              | 2    2      2     2      \|x  - a   - x      | 2    2
--R        (- 2x\|x  - a   + 2x  - 2a )atan(--------------) + a\|x  - a   - a x
--R                                                a
--R   (1)  --------------------------------------------------------------------
--R                                  +-------+
--R                               3  | 2    2     3 2    5
--R                              a x\|x  - a   - a x  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91 of 150
bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a)
 

                  +-------+
               x  | 2    2
        - asec(-)\|x  - a   - a
               a
   (2)  -----------------------
                 +-------+
               3 | 2    2
              a \|x  - a
                                                     Type: Expression Integer
--R
--R                  +-------+
--R               x  | 2    2
--R        - asec(-)\|x  - a   - a
--R               a
--R   (2)  -----------------------
--R                 +-------+
--R               3 | 2    2
--R              a \|x  - a
--R                                                     Type: Expression Integer
--E

--S 92 of 150
cc:=aa-bb
 

                 +-------+
                 | 2    2
                \|x  - a   - x         x
        - 2atan(--------------) + asec(-)
                       a               a
   (3)  ---------------------------------
                         3
                        a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  - a   - x         x
--R        - 2atan(--------------) + asec(-)
--R                       a               a
--R   (3)  ---------------------------------
--R                         3
--R                        a
--R                                                     Type: Expression Integer
--E

--S 93 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 94 of 150
dd:=atanrule cc
 

                  +-------+
                  | 2    2
               - \|x  - a   + x + %i a         x
        %i log(-----------------------) + asec(-)
                 +-------+                     a
                 | 2    2
                \|x  - a   - x + %i a
   (5)  -----------------------------------------
                             3
                            a
                                             Type: Expression Complex Integer
--R
--R                  +-------+
--R                  | 2    2
--R               - \|x  - a   + x + %i a         x
--R        %i log(-----------------------) + asec(-)
--R                 +-------+                     a
--R                 | 2    2
--R                \|x  - a   - x + %i a
--R   (5)  -----------------------------------------
--R                             3
--R                            a
--R                                             Type: Expression Complex Integer
--E

--S 95 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 96 of 150
ee:=asecrule dd
 

                  +-------+
                  | 2    2
                  |x  - a
                x |-------  + %i a               +-------+
                  |    2                         | 2    2
                 \|   x                       - \|x  - a   + x + %i a
        2%i log(------------------) + 2%i log(-----------------------) + %pi
                         x                      +-------+
                                                | 2    2
                                               \|x  - a   - x + %i a
   (7)  --------------------------------------------------------------------
                                           3
                                         2a
                                             Type: Expression Complex Integer
--R
--R                  +-------+
--R                  | 2    2
--R                  |x  - a
--R                x |-------  + %i a               +-------+
--R                  |    2                         | 2    2
--R                 \|   x                       - \|x  - a   + x + %i a
--R        2%i log(------------------) + 2%i log(-----------------------) + %pi
--R                         x                      +-------+
--R                                                | 2    2
--R                                               \|x  - a   - x + %i a
--R   (7)  --------------------------------------------------------------------
--R                                           3
--R                                         2a
--R                                             Type: Expression Complex Integer
--E

--S 97 of 150
ff:=expandLog ee
 

   (8)
                  +-------+                        +-------+
                  | 2    2                         | 2    2
       - 2%i log(\|x  - a   - x + %i a) + 2%i log(\|x  - a   - x - %i a)
     + 
                 +-------+
                 | 2    2
                 |x  - a
       2%i log(x |-------  + %i a) - 2%i log(x) + 2%i log(- 1) + %pi
                 |    2
                \|   x
  /
       3
     2a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                  +-------+                        +-------+
--R                  | 2    2                         | 2    2
--R       - 2%i log(\|x  - a   - x + %i a) + 2%i log(\|x  - a   - x - %i a)
--R     + 
--R                 +-------+
--R                 | 2    2
--R                 |x  - a
--R       2%i log(x |-------  + %i a) - 2%i log(x) + 2%i log(- 1) + %pi
--R                 |    2
--R                \|   x
--R  /
--R       3
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 98 of 150
gg:=rootSimp ff
 

   (9)
                +-------+                    +-------+
                | 2    2                     | 2    2
       2%i log(\|x  - a   + %i a) - 2%i log(\|x  - a   - x + %i a)
     + 
                +-------+
                | 2    2
       2%i log(\|x  - a   - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi
  /
       3
     2a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                +-------+                    +-------+
--R                | 2    2                     | 2    2
--R       2%i log(\|x  - a   + %i a) - 2%i log(\|x  - a   - x + %i a)
--R     + 
--R                +-------+
--R                | 2    2
--R       2%i log(\|x  - a   - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi
--R  /
--R       3
--R     2a
--R                                             Type: Expression Complex Integer
--E

--S 99 of 150     14:227 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         %pi
   (10)  ---
           3
         2a
                                             Type: Expression Complex Integer
--R
--R         %pi
--R   (10)  ---
--R           3
--R         2a
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 100 of 150
aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
 

                           1
   (1)  - -----------------------------------
                      +-------+
             3    2   | 2    2      4     2 2
          (2x  - a x)\|x  - a   - 2x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           1
--R   (1)  - -----------------------------------
--R                      +-------+
--R             3    2   | 2    2      4     2 2
--R          (2x  - a x)\|x  - a   - 2x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 101 of 150
bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2))
 

              2    2
          - 2x  + a
   (2)  -------------
            +-------+
         4  | 2    2
        a x\|x  - a
                                                     Type: Expression Integer
--R
--R              2    2
--R          - 2x  + a
--R   (2)  -------------
--R            +-------+
--R         4  | 2    2
--R        a x\|x  - a
--R                                                     Type: Expression Integer
--E

--S 102 of 150    14:228 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           2
   (3)  - --
           4
          a
                                                     Type: Expression Integer
--R
--R           2
--R   (3)  - --
--R           4
--R          a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 103 of 150
aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
 

   (1)
                                                                  +-------+
                          +-------+                               | 2    2
              5      2 3  | 2    2       6      2 4     4 2      \|x  - a   - x
       ((- 24x  + 18a x )\|x  - a   + 24x  - 30a x  + 6a x )atan(--------------)
                                                                        a
     + 
                             +-------+
             4     3 2    5  | 2    2         5      3 3     5
       (12a x  - 7a x  + a )\|x  - a   - 12a x  + 13a x  - 3a x
  /
                     +-------+
        5 5     7 3  | 2    2      5 6      7 4     9 2
     (8a x  - 6a x )\|x  - a   - 8a x  + 10a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                  +-------+
--R                          +-------+                               | 2    2
--R              5      2 3  | 2    2       6      2 4     4 2      \|x  - a   - x
--R       ((- 24x  + 18a x )\|x  - a   + 24x  - 30a x  + 6a x )atan(--------------)
--R                                                                        a
--R     + 
--R                             +-------+
--R             4     3 2    5  | 2    2         5      3 3     5
--R       (12a x  - 7a x  + a )\|x  - a   - 12a x  + 13a x  - 3a x
--R  /
--R                     +-------+
--R        5 5     7 3  | 2    2      5 6      7 4     9 2
--R     (8a x  - 6a x )\|x  - a   - 8a x  + 10a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 104 of 150
bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a)
 

                     +-------+
            2     x  | 2    2        2    3
        - 3x asec(-)\|x  - a   - 3a x  + a
                  a
   (2)  -----------------------------------
                        +-------+
                    5 2 | 2    2
                  2a x \|x  - a
                                                     Type: Expression Integer
--R
--R                     +-------+
--R            2     x  | 2    2        2    3
--R        - 3x asec(-)\|x  - a   - 3a x  + a
--R                  a
--R   (2)  -----------------------------------
--R                        +-------+
--R                    5 2 | 2    2
--R                  2a x \|x  - a
--R                                                     Type: Expression Integer
--E

--S 105 of 150
cc:=aa-bb
 

                 +-------+
                 | 2    2
                \|x  - a   - x          x
        - 6atan(--------------) + 3asec(-)
                       a                a
   (3)  ----------------------------------
                          5
                        2a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  - a   - x          x
--R        - 6atan(--------------) + 3asec(-)
--R                       a                a
--R   (3)  ----------------------------------
--R                          5
--R                        2a
--R                                                     Type: Expression Integer
--E

--S 106 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 107 of 150
dd:=atanrule cc
 

                   +-------+
                   | 2    2
                - \|x  - a   + x + %i a          x
        3%i log(-----------------------) + 3asec(-)
                  +-------+                      a
                  | 2    2
                 \|x  - a   - x + %i a
   (5)  -------------------------------------------
                              5
                            2a
                                             Type: Expression Complex Integer
--R
--R                   +-------+
--R                   | 2    2
--R                - \|x  - a   + x + %i a          x
--R        3%i log(-----------------------) + 3asec(-)
--R                  +-------+                      a
--R                  | 2    2
--R                 \|x  - a   - x + %i a
--R   (5)  -------------------------------------------
--R                              5
--R                            2a
--R                                             Type: Expression Complex Integer
--E

--S 108 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 109 of 150
ee:=asecrule dd
 

                  +-------+
                  | 2    2
                  |x  - a
                x |-------  + %i a               +-------+
                  |    2                         | 2    2
                 \|   x                       - \|x  - a   + x + %i a
        6%i log(------------------) + 6%i log(-----------------------) + 3%pi
                         x                      +-------+
                                                | 2    2
                                               \|x  - a   - x + %i a
   (7)  ---------------------------------------------------------------------
                                           5
                                         4a
                                             Type: Expression Complex Integer
--R
--R                  +-------+
--R                  | 2    2
--R                  |x  - a
--R                x |-------  + %i a               +-------+
--R                  |    2                         | 2    2
--R                 \|   x                       - \|x  - a   + x + %i a
--R        6%i log(------------------) + 6%i log(-----------------------) + 3%pi
--R                         x                      +-------+
--R                                                | 2    2
--R                                               \|x  - a   - x + %i a
--R   (7)  ---------------------------------------------------------------------
--R                                           5
--R                                         4a
--R                                             Type: Expression Complex Integer
--E

--S 110 of 150
ff:=expandLog ee
 

   (8)
                  +-------+                        +-------+
                  | 2    2                         | 2    2
       - 6%i log(\|x  - a   - x + %i a) + 6%i log(\|x  - a   - x - %i a)
     + 
                 +-------+
                 | 2    2
                 |x  - a
       6%i log(x |-------  + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
                 |    2
                \|   x
  /
       5
     4a
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                  +-------+                        +-------+
--R                  | 2    2                         | 2    2
--R       - 6%i log(\|x  - a   - x + %i a) + 6%i log(\|x  - a   - x - %i a)
--R     + 
--R                 +-------+
--R                 | 2    2
--R                 |x  - a
--R       6%i log(x |-------  + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
--R                 |    2
--R                \|   x
--R  /
--R       5
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 111 of 150
gg:=rootSimp ff
 

   (9)
                +-------+                    +-------+
                | 2    2                     | 2    2
       6%i log(\|x  - a   + %i a) - 6%i log(\|x  - a   - x + %i a)
     + 
                +-------+
                | 2    2
       6%i log(\|x  - a   - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
  /
       5
     4a
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                +-------+                    +-------+
--R                | 2    2                     | 2    2
--R       6%i log(\|x  - a   + %i a) - 6%i log(\|x  - a   - x + %i a)
--R     + 
--R                +-------+
--R                | 2    2
--R       6%i log(\|x  - a   - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
--R  /
--R       5
--R     4a
--R                                             Type: Expression Complex Integer
--E

--S 112 of 150    14:229 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         3%pi
   (10)  ----
            5
          4a
                                             Type: Expression Complex Integer
--R
--R         3%pi
--R   (10)  ----
--R            5
--R          4a
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 113 of 150
aa:=integrate((x^2-a^2)^(3/2),x)
 

   (1)
                           +-------+                              +-------+
              4 3      6   | 2    2       4 4      6 2     8      | 2    2
       ((- 24a x  + 12a x)\|x  - a   + 24a x  - 24a x  + 3a )log(\|x  - a   - x)
     + 
                                         +-------+
             7      2 5      4 3     6   | 2    2       8      2 6      4 4
       (- 16x  + 56a x  - 42a x  + 5a x)\|x  - a   + 16x  - 64a x  + 68a x
     + 
            6 2
       - 20a x
  /
                    +-------+
         3      2   | 2    2       4      2 2     4
     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +-------+                              +-------+
--R              4 3      6   | 2    2       4 4      6 2     8      | 2    2
--R       ((- 24a x  + 12a x)\|x  - a   + 24a x  - 24a x  + 3a )log(\|x  - a   - x)
--R     + 
--R                                         +-------+
--R             7      2 5      4 3     6   | 2    2       8      2 6      4 4
--R       (- 16x  + 56a x  - 42a x  + 5a x)\|x  - a   + 16x  - 64a x  + 68a x
--R     + 
--R            6 2
--R       - 20a x
--R  /
--R                    +-------+
--R         3      2   | 2    2       4      2 2     4
--R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 114 of 150
bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2))
 

                +-------+                     +-------+
          4     | 2    2            3     2   | 2    2
        3a log(\|x  - a   + x) + (2x  - 5a x)\|x  - a
   (2)  -----------------------------------------------
                               8
                                                     Type: Expression Integer
--R
--R                +-------+                     +-------+
--R          4     | 2    2            3     2   | 2    2
--R        3a log(\|x  - a   + x) + (2x  - 5a x)\|x  - a
--R   (2)  -----------------------------------------------
--R                               8
--R                                                     Type: Expression Integer
--E

--S 115 of 150
cc:=aa-bb
 

                  +-------+                +-------+
            4     | 2    2           4     | 2    2
        - 3a log(\|x  - a   + x) - 3a log(\|x  - a   - x)
   (3)  -------------------------------------------------
                                8
                                                     Type: Expression Integer
--R
--R                  +-------+                +-------+
--R            4     | 2    2           4     | 2    2
--R        - 3a log(\|x  - a   + x) - 3a log(\|x  - a   - x)
--R   (3)  -------------------------------------------------
--R                                8
--R                                                     Type: Expression Integer
--E

--S 116 of 150    14:230 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

            4       2
          3a log(- a )
   (4)  - ------------
                8
                                                     Type: Expression Integer
--R
--R            4       2
--R          3a log(- a )
--R   (4)  - ------------
--R                8
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 117 of 150
aa:=integrate(x*(x^2-a^2)^(3/2),x)
 

   (1)
                                                  +-------+
             9      2 7      4 5      6 3     8   | 2    2       10      2 8
       (- 16x  + 52a x  - 61a x  + 30a x  - 5a x)\|x  - a   + 16x   - 60a x
     + 
          4 6      6 4      8 2    10
       85a x  - 55a x  + 15a x  - a
  /
                           +-------+
         4      2 2     4  | 2    2       5       2 3      4
     (80x  - 60a x  + 5a )\|x  - a   - 80x  + 100a x  - 25a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                  +-------+
--R             9      2 7      4 5      6 3     8   | 2    2       10      2 8
--R       (- 16x  + 52a x  - 61a x  + 30a x  - 5a x)\|x  - a   + 16x   - 60a x
--R     + 
--R          4 6      6 4      8 2    10
--R       85a x  - 55a x  + 15a x  - a
--R  /
--R                           +-------+
--R         4      2 2     4  | 2    2       5       2 3      4
--R     (80x  - 60a x  + 5a )\|x  - a   - 80x  + 100a x  - 25a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 118 of 150
bb:=(x^2-a^2)^(5/2)/5
 

                          +-------+
          4     2 2    4  | 2    2
        (x  - 2a x  + a )\|x  - a
   (2)  ---------------------------
                     5
                                                     Type: Expression Integer
--R
--R                          +-------+
--R          4     2 2    4  | 2    2
--R        (x  - 2a x  + a )\|x  - a
--R   (2)  ---------------------------
--R                     5
--R                                                     Type: Expression Integer
--E

--S 119 of 150    14:231 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 120 of 150
aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
 

   (1)
                                        +-------+
                 6 5      8 3      10   | 2    2       6 6       8 4      10 2
           (- 96a x  + 96a x  - 18a  x)\|x  - a   + 96a x  - 144a x  + 54a  x
         + 
               12
           - 3a
      *
              +-------+
              | 2    2
         log(\|x  - a   - x)
     + 
                                                                 +-------+
              11       2 9       4 7       6 5      8 3     10   | 2    2
       (- 256x   + 832a x  - 912a x  + 404a x  - 68a x  + 3a  x)\|x  - a
     + 
           12       2 10        4 8       6 6       8 4      10 2
       256x   - 960a x   + 1296a x  - 772a x  + 198a x  - 18a  x
  /
                                  +-------+
           5        2 3       4   | 2    2         6        2 4       4 2      6
     (1536x  - 1536a x  + 288a x)\|x  - a   - 1536x  + 2304a x  - 864a x  + 48a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                        +-------+
--R                 6 5      8 3      10   | 2    2       6 6       8 4      10 2
--R           (- 96a x  + 96a x  - 18a  x)\|x  - a   + 96a x  - 144a x  + 54a  x
--R         + 
--R               12
--R           - 3a
--R      *
--R              +-------+
--R              | 2    2
--R         log(\|x  - a   - x)
--R     + 
--R                                                                 +-------+
--R              11       2 9       4 7       6 5      8 3     10   | 2    2
--R       (- 256x   + 832a x  - 912a x  + 404a x  - 68a x  + 3a  x)\|x  - a
--R     + 
--R           12       2 10        4 8       6 6       8 4      10 2
--R       256x   - 960a x   + 1296a x  - 772a x  + 198a x  - 18a  x
--R  /
--R                                  +-------+
--R           5        2 3       4   | 2    2         6        2 4       4 2      6
--R     (1536x  - 1536a x  + 288a x)\|x  - a   - 1536x  + 2304a x  - 864a x  + 48a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 121 of 150
bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2))
 

                +-------+                              +-------+
          6     | 2    2            5      2 3     4   | 2    2
        3a log(\|x  - a   + x) + (8x  - 14a x  + 3a x)\|x  - a
   (2)  --------------------------------------------------------
                                   48
                                                     Type: Expression Integer
--R
--R                +-------+                              +-------+
--R          6     | 2    2            5      2 3     4   | 2    2
--R        3a log(\|x  - a   + x) + (8x  - 14a x  + 3a x)\|x  - a
--R   (2)  --------------------------------------------------------
--R                                   48
--R                                                     Type: Expression Integer
--E

--S 122 of 150
cc:=aa-bb
 

                 +-------+               +-------+
           6     | 2    2          6     | 2    2
        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
   (3)  -----------------------------------------------
                               16
                                                     Type: Expression Integer
--R
--R                 +-------+               +-------+
--R           6     | 2    2          6     | 2    2
--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
--R   (3)  -----------------------------------------------
--R                               16
--R                                                     Type: Expression Integer
--E

--S 123 of 150    14:232 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           6       2
          a log(- a )
   (4)  - -----------
               16
                                                     Type: Expression Integer
--R
--R           6       2
--R          a log(- a )
--R   (4)  - -----------
--R               16
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 124 of 150
aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
 

   (1)
                   13        2 11        4 9       6 7       8 5       10 3
             - 320x   + 1072a x   - 1240a x  + 467a x  + 112a x  - 105a  x
           + 
                12
             14a  x
      *
          +-------+
          | 2    2
         \|x  - a
     + 
           14        2 12        4 10       6 8      8 6       10 4      12 2
       320x   - 1232a x   + 1736a x   - 973a x  + 21a x  + 175a  x  - 49a  x
     + 
         14
       2a
  /
                                            +-------+
             6        2 4       4 2      6  | 2    2         7        2 5
       (2240x  - 2800a x  + 840a x  - 35a )\|x  - a   - 2240x  + 3920a x
     + 
              4 3       6
       - 1960a x  + 245a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   13        2 11        4 9       6 7       8 5       10 3
--R             - 320x   + 1072a x   - 1240a x  + 467a x  + 112a x  - 105a  x
--R           + 
--R                12
--R             14a  x
--R      *
--R          +-------+
--R          | 2    2
--R         \|x  - a
--R     + 
--R           14        2 12        4 10       6 8      8 6       10 4      12 2
--R       320x   - 1232a x   + 1736a x   - 973a x  + 21a x  + 175a  x  - 49a  x
--R     + 
--R         14
--R       2a
--R  /
--R                                            +-------+
--R             6        2 4       4 2      6  | 2    2         7        2 5
--R       (2240x  - 2800a x  + 840a x  - 35a )\|x  - a   - 2240x  + 3920a x
--R     + 
--R              4 3       6
--R       - 1960a x  + 245a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 125 of 150
bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5
 

                                   +-------+
           6     2 4    4 2     6  | 2    2
        (5x  - 8a x  + a x  + 2a )\|x  - a
   (2)  ------------------------------------
                         35
                                                     Type: Expression Integer
--R
--R                                   +-------+
--R           6     2 4    4 2     6  | 2    2
--R        (5x  - 8a x  + a x  + 2a )\|x  - a
--R   (2)  ------------------------------------
--R                         35
--R                                                     Type: Expression Integer
--E

--S 126 of 150    14:233 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 127 of 150
aa:=integrate((x^2-a^2)^(3/2)/x,x)
 

   (1)
                                                        +-------+
                       +-------+                        | 2    2
            3 2     5  | 2    2       3 3      5       \|x  - a   - x
       ((24a x  - 6a )\|x  - a   - 24a x  + 18a x)atan(--------------)
                                                              a
     + 
                                +-------+
            5      2 3      4   | 2    2      6      2 4      4 2     6
       (- 4x  + 19a x  - 12a x)\|x  - a   + 4x  - 21a x  + 21a x  - 4a
  /
                  +-------+
         2     2  | 2    2       3     2
     (12x  - 3a )\|x  - a   - 12x  + 9a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                        +-------+
--R                       +-------+                        | 2    2
--R            3 2     5  | 2    2       3 3      5       \|x  - a   - x
--R       ((24a x  - 6a )\|x  - a   - 24a x  + 18a x)atan(--------------)
--R                                                              a
--R     + 
--R                                +-------+
--R            5      2 3      4   | 2    2      6      2 4      4 2     6
--R       (- 4x  + 19a x  - 12a x)\|x  - a   + 4x  - 21a x  + 21a x  - 4a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3     2
--R     (12x  - 3a )\|x  - a   - 12x  + 9a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 128 of 150
bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a)
 

                   +-------+
          2     2  | 2    2      3     x
        (x  - 4a )\|x  - a   + 3a asec(-)
                                       a
   (2)  ---------------------------------
                        3
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2      3     x
--R        (x  - 4a )\|x  - a   + 3a asec(-)
--R                                       a
--R   (2)  ---------------------------------
--R                        3
--R                                                     Type: Expression Integer
--E

--S 129 of 150
cc:=aa-bb
 

                 +-------+
                 | 2    2
          3     \|x  - a   - x     3     x
   (3)  2a atan(--------------) - a asec(-)
                       a                 a
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R          3     \|x  - a   - x     3     x
--R   (3)  2a atan(--------------) - a asec(-)
--R                       a                 a
--R                                                     Type: Expression Integer
--E

--S 130 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (4)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (4)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 131 of 150
dd:=asecrule cc
 

                      +-------+
                      | 2    2
                      |x  - a
                    x |-------  + %i a             +-------+
                      |    2                       | 2    2
               3     \|   x                 3     \|x  - a   - x     3
        - 2%i a log(------------------) + 4a atan(--------------) - a %pi
                             x                           a
   (5)  -----------------------------------------------------------------
                                        2
                                             Type: Expression Complex Integer
--R
--R                      +-------+
--R                      | 2    2
--R                      |x  - a
--R                    x |-------  + %i a             +-------+
--R                      |    2                       | 2    2
--R               3     \|   x                 3     \|x  - a   - x     3
--R        - 2%i a log(------------------) + 4a atan(--------------) - a %pi
--R                             x                           a
--R   (5)  -----------------------------------------------------------------
--R                                        2
--R                                             Type: Expression Complex Integer
--E

--S 132 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 133 of 150
ee:=atanrule dd
 

   (7)
                 +-------+
                 | 2    2
                 |x  - a
               x |-------  + %i a                 +-------+
                 |    2                           | 2    2
          3     \|   x                    3    - \|x  - a   + x + %i a     3
   - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi
                        x                        +-------+
                                                 | 2    2
                                                \|x  - a   - x + %i a
   ----------------------------------------------------------------------------
                                         2
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                 +-------+
--R                 | 2    2
--R                 |x  - a
--R               x |-------  + %i a                 +-------+
--R                 |    2                           | 2    2
--R          3     \|   x                    3    - \|x  - a   + x + %i a     3
--R   - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi
--R                        x                        +-------+
--R                                                 | 2    2
--R                                                \|x  - a   - x + %i a
--R   ----------------------------------------------------------------------------
--R                                         2
--R                                             Type: Expression Complex Integer
--E

--S 134 of 150
ff:=expandLog ee
 

   (8)
                  +-------+                          +-------+
            3     | 2    2                     3     | 2    2
       2%i a log(\|x  - a   - x + %i a) - 2%i a log(\|x  - a   - x - %i a)
     + 
                     +-------+
                     | 2    2
              3      |x  - a                  3              3            3
       - 2%i a log(x |-------  + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
                     |    2
                    \|   x
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                  +-------+                          +-------+
--R            3     | 2    2                     3     | 2    2
--R       2%i a log(\|x  - a   - x + %i a) - 2%i a log(\|x  - a   - x - %i a)
--R     + 
--R                     +-------+
--R                     | 2    2
--R              3      |x  - a                  3              3            3
--R       - 2%i a log(x |-------  + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
--R                     |    2
--R                    \|   x
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 135 of 150
gg:=rootSimp ff
 

   (9)
                    +-------+                      +-------+
              3     | 2    2                 3     | 2    2
       - 2%i a log(\|x  - a   + %i a) + 2%i a log(\|x  - a   - x + %i a)
     + 
                  +-------+
            3     | 2    2                     3              3            3
     - 2%i a log(\|x  - a   - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                    +-------+                      +-------+
--R              3     | 2    2                 3     | 2    2
--R       - 2%i a log(\|x  - a   + %i a) + 2%i a log(\|x  - a   - x + %i a)
--R     + 
--R                  +-------+
--R            3     | 2    2                     3              3            3
--R     - 2%i a log(\|x  - a   - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 136 of 150    14:234 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

            3
           a %pi
   (10)  - -----
             2
                                             Type: Expression Complex Integer
--R
--R            3
--R           a %pi
--R   (10)  - -----
--R             2
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 137 of 150
aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
 

   (1)
                        +-------+                       +-------+
            2 3     4   | 2    2       2 4     4 2      | 2    2
       ((12a x  - 3a x)\|x  - a   - 12a x  + 9a x )log(\|x  - a   - x)
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2     6
       (- 4x  + 3a x  + 4a x)\|x  - a   + 4x  - 5a x  - 3a x  + 2a
  /
                  +-------+
        3     2   | 2    2      4     2 2
     (8x  - 2a x)\|x  - a   - 8x  + 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                        +-------+                       +-------+
--R            2 3     4   | 2    2       2 4     4 2      | 2    2
--R       ((12a x  - 3a x)\|x  - a   - 12a x  + 9a x )log(\|x  - a   - x)
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (- 4x  + 3a x  + 4a x)\|x  - a   + 4x  - 5a x  - 3a x  + 2a
--R  /
--R                  +-------+
--R        3     2   | 2    2      4     2 2
--R     (8x  - 2a x)\|x  - a   - 8x  + 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 138 of 150
bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2))
 

                    +-------+                   +-------+
            2       | 2    2           2     2  | 2    2
        - 3a x log(\|x  - a   + x) + (x  + 2a )\|x  - a
   (2)  -------------------------------------------------
                                2x
                                                     Type: Expression Integer
--R
--R                    +-------+                   +-------+
--R            2       | 2    2           2     2  | 2    2
--R        - 3a x log(\|x  - a   + x) + (x  + 2a )\|x  - a
--R   (2)  -------------------------------------------------
--R                                2x
--R                                                     Type: Expression Integer
--E

--S 139 of 150
cc:=aa-bb
 

                +-------+                +-------+
          2     | 2    2           2     | 2    2           2
        3a log(\|x  - a   + x) + 3a log(\|x  - a   - x) + 2a
   (3)  -----------------------------------------------------
                                  2
                                                     Type: Expression Integer
--R
--R                +-------+                +-------+
--R          2     | 2    2           2     | 2    2           2
--R        3a log(\|x  - a   + x) + 3a log(\|x  - a   - x) + 2a
--R   (3)  -----------------------------------------------------
--R                                  2
--R                                                     Type: Expression Integer
--E

--S 140 of 150    14:235 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

          2       2      2
        3a log(- a ) + 2a
   (4)  ------------------
                 2
                                                     Type: Expression Integer
--R
--R          2       2      2
--R        3a log(- a ) + 2a
--R   (4)  ------------------
--R                 2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 141 of 150
aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
 

   (1)
                                                             +-------+
                           +-------+                         | 2    2
                4     3 2  | 2    2         5      3 3      \|x  - a   - x
       ((- 24a x  + 6a x )\|x  - a   + 24a x  - 18a x )atan(--------------)
                                                                   a
     + 
                              +-------+
            5     2 3     4   | 2    2      6     2 4     4 2    6
       (- 8x  + 2a x  + 3a x)\|x  - a   + 8x  - 6a x  - 3a x  + a
  /
                   +-------+
        4     2 2  | 2    2      5     2 3
     (8x  - 2a x )\|x  - a   - 8x  + 6a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                             +-------+
--R                           +-------+                         | 2    2
--R                4     3 2  | 2    2         5      3 3      \|x  - a   - x
--R       ((- 24a x  + 6a x )\|x  - a   + 24a x  - 18a x )atan(--------------)
--R                                                                   a
--R     + 
--R                              +-------+
--R            5     2 3     4   | 2    2      6     2 4     4 2    6
--R       (- 8x  + 2a x  + 3a x)\|x  - a   + 8x  - 6a x  - 3a x  + a
--R  /
--R                   +-------+
--R        4     2 2  | 2    2      5     2 3
--R     (8x  - 2a x )\|x  - a   - 8x  + 6a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 142 of 150
bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a)
 

                   +-------+
           2    2  | 2    2        2     x
        (2x  + a )\|x  - a   - 3a x asec(-)
                                         a
   (2)  -----------------------------------
                          2
                        2x
                                                     Type: Expression Integer
--R
--R                   +-------+
--R           2    2  | 2    2        2     x
--R        (2x  + a )\|x  - a   - 3a x asec(-)
--R                                         a
--R   (2)  -----------------------------------
--R                          2
--R                        2x
--R                                                     Type: Expression Integer
--E

--S 143 of 150
cc:=aa-bb
 

                   +-------+
                   | 2    2
                  \|x  - a   - x            x
        - 6a atan(--------------) + 3a asec(-)
                         a                  a
   (3)  --------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                   +-------+
--R                   | 2    2
--R                  \|x  - a   - x            x
--R        - 6a atan(--------------) + 3a asec(-)
--R                         a                  a
--R   (3)  --------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 144 of 150
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 145 of 150
dd:=atanrule cc
 

                     +-------+
                     | 2    2
                  - \|x  - a   + x + %i a            x
        3%i a log(-----------------------) + 3a asec(-)
                    +-------+                        a
                    | 2    2
                   \|x  - a   - x + %i a
   (5)  -----------------------------------------------
                               2
                                             Type: Expression Complex Integer
--R
--R                     +-------+
--R                     | 2    2
--R                  - \|x  - a   + x + %i a            x
--R        3%i a log(-----------------------) + 3a asec(-)
--R                    +-------+                        a
--R                    | 2    2
--R                   \|x  - a   - x + %i a
--R   (5)  -----------------------------------------------
--R                               2
--R                                             Type: Expression Complex Integer
--E

--S 146 of 150
asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
 

                             +------+
                             | 2
                             |x  - 1
                           x |------  + %i
                             |   2
                            \|  x
                   2%i log(---------------) + %pi
                                  x
   (6)  asec(x) == ------------------------------
                                  2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             +------+
--R                             | 2
--R                             |x  - 1
--R                           x |------  + %i
--R                             |   2
--R                            \|  x
--R                   2%i log(---------------) + %pi
--R                                  x
--R   (6)  asec(x) == ------------------------------
--R                                  2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 147 of 150
ee:=asecrule dd
 

   (7)
               +-------+
               | 2    2
               |x  - a
             x |-------  + %i a                 +-------+
               |    2                           | 2    2
              \|   x                         - \|x  - a   + x + %i a
   6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi
                      x                        +-------+
                                               | 2    2
                                              \|x  - a   - x + %i a
   ---------------------------------------------------------------------------
                                        4
                                             Type: Expression Complex Integer
--R
--R   (7)
--R               +-------+
--R               | 2    2
--R               |x  - a
--R             x |-------  + %i a                 +-------+
--R               |    2                           | 2    2
--R              \|   x                         - \|x  - a   + x + %i a
--R   6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi
--R                      x                        +-------+
--R                                               | 2    2
--R                                              \|x  - a   - x + %i a
--R   ---------------------------------------------------------------------------
--R                                        4
--R                                             Type: Expression Complex Integer
--E

--S 148 of 150
ff:=expandLog ee
 

   (8)
                    +-------+                          +-------+
                    | 2    2                           | 2    2
       - 6%i a log(\|x  - a   - x + %i a) + 6%i a log(\|x  - a   - x - %i a)
     + 
                   +-------+
                   | 2    2
                   |x  - a
       6%i a log(x |-------  + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
                   |    2
                  \|   x
  /
     4
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +-------+                          +-------+
--R                    | 2    2                           | 2    2
--R       - 6%i a log(\|x  - a   - x + %i a) + 6%i a log(\|x  - a   - x - %i a)
--R     + 
--R                   +-------+
--R                   | 2    2
--R                   |x  - a
--R       6%i a log(x |-------  + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
--R                   |    2
--R                  \|   x
--R  /
--R     4
--R                                             Type: Expression Complex Integer
--E

--S 149 of 150
gg:=rootSimp ff
 

   (9)
                  +-------+                      +-------+
                  | 2    2                       | 2    2
       6%i a log(\|x  - a   + %i a) - 6%i a log(\|x  - a   - x + %i a)
     + 
                +-------+
                | 2    2
     6%i a log(\|x  - a   - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
  /
     4
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                  +-------+                      +-------+
--R                  | 2    2                       | 2    2
--R       6%i a log(\|x  - a   + %i a) - 6%i a log(\|x  - a   - x + %i a)
--R     + 
--R                +-------+
--R                | 2    2
--R     6%i a log(\|x  - a   - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
--R  /
--R     4
--R                                             Type: Expression Complex Integer
--E

--S 150 of 150    14:236 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         3a %pi
   (10)  ------
            4
                                             Type: Expression Complex Integer
--R
--R         3a %pi
--R   (10)  ------
--R            4
--R                                             Type: Expression Complex Integer
--E

)spool
 
Starts dribbling to ArrayStack.output (2010/3/27, 18:41:43).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 44
a:ArrayStack INT:= arrayStack [1,2,3,4,5]
 

   (1)  [1,2,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (1)  [1,2,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 1

--S 2 of 44
pop! a
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 44
a
 

   (3)  [2,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (3)  [2,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 3

--S 4 of 44
extract! a
 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 44
a
 

   (5)  [3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (5)  [3,4,5]
--R                                                     Type: ArrayStack Integer
--E 5

--S 6 of 44
push!(9,a)
 

   (6)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  9
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 44
a
 

   (7)  [9,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (7)  [9,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 7

--S 8 of 44
insert!(8,a)
 

   (8)  [8,9,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (8)  [8,9,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 8

--S 9 of 44
a
 

   (9)  [8,9,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (9)  [8,9,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 9

--S 10 of 44
inspect a
 

   (10)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  8
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 44
empty? a
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 44
top a
 

   (12)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  8
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 44
depth a
 

   (13)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  5
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 44
#a
 

   (14)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  5
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 44
less?(a,9)
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 44
more?(a,9)
 

   (16)  false
                                                                Type: Boolean
--R 
--R
--R   (16)  false
--R                                                                Type: Boolean
--E 16

--S 17 of 44
size?(a,#a)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 44
size?(a,9)
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 44
parts a
 

   (19)  [8,9,3,4,5]
                                                           Type: List Integer
--R 
--R
--R   (19)  [8,9,3,4,5]
--R                                                           Type: List Integer
--E 19

--S 20 of 44
bag([1,2,3,4,5])$ArrayStack(INT)
 

   (20)  [5,4,3,2,1]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (20)  [5,4,3,2,1]
--R                                                     Type: ArrayStack Integer
--E 20

--S 21 of 44
b:=empty()$(ArrayStack INT)
 

   (21)  []
                                                     Type: ArrayStack Integer
--R 
--R
--R   (21)  []
--R                                                     Type: ArrayStack Integer
--E 21

--S 22 of 44
empty? b
 

   (22)  true
                                                                Type: Boolean
--R 
--R
--R   (22)  true
--R                                                                Type: Boolean
--E 22

--S 23 of 44
sample()$ArrayStack(INT)
 

   (23)  []
                                                     Type: ArrayStack Integer
--R 
--R
--R   (23)  []
--R                                                     Type: ArrayStack Integer
--E 23

--S 24 of 44
c:=copy a
 

   (24)  [8,9,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (24)  [8,9,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 24

--S 25 of 44
eq?(a,c)
 

   (25)  false
                                                                Type: Boolean
--R 
--R
--R   (25)  false
--R                                                                Type: Boolean
--E 25

--S 26 of 44
eq?(a,a)
 

   (26)  true
                                                                Type: Boolean
--R 
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26

--S 27 of 44
(a=c)@Boolean
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 44
(a=a)@Boolean
 

   (28)  true
                                                                Type: Boolean
--R 
--R
--R   (28)  true
--R                                                                Type: Boolean
--E 28

--S 29 of 44
a~=c
 

   (29)  false
                                                                Type: Boolean
--R 
--R
--R   (29)  false
--R                                                                Type: Boolean
--E 29

--S 30 of 44
any?(x+->(x=4),a)
 

   (30)  true
                                                                Type: Boolean
--R 
--R
--R   (30)  true
--R                                                                Type: Boolean
--E 30

--S 31 of 44
any?(x+->(x=11),a)
 

   (31)  false
                                                                Type: Boolean
--R 
--R
--R   (31)  false
--R                                                                Type: Boolean
--E 31

--S 32 of 44
every?(x+->(x=11),a)
 

   (32)  false
                                                                Type: Boolean
--R 
--R
--R   (32)  false
--R                                                                Type: Boolean
--E 32

--S 33 of 44
count(4,a)
 

   (33)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (33)  1
--R                                                        Type: PositiveInteger
--E 33

--S 34 of 44
count(x+->(x>2),a)
 

   (34)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (34)  5
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 44
map(x+->x+10,a)
 

   (35)  [18,19,13,14,15]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (35)  [18,19,13,14,15]
--R                                                     Type: ArrayStack Integer
--E 35

--S 36 of 44
a
 

   (36)  [8,9,3,4,5]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (36)  [8,9,3,4,5]
--R                                                     Type: ArrayStack Integer
--E 36

--S 37 of 44
map!(x+->x+10,a)
 

   (37)  [18,19,13,14,15]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (37)  [18,19,13,14,15]
--R                                                     Type: ArrayStack Integer
--E 37

--S 38 of 44
a
 

   (38)  [18,19,13,14,15]
                                                     Type: ArrayStack Integer
--R 
--R
--R   (38)  [18,19,13,14,15]
--R                                                     Type: ArrayStack Integer
--E 38

--S 39 of 44
members a
 

   (39)  [18,19,13,14,15]
                                                           Type: List Integer
--R 
--R
--R   (39)  [18,19,13,14,15]
--R                                                           Type: List Integer
--E 39

--S 40 of 44
member?(14,a)
 

   (40)  true
                                                                Type: Boolean
--R 
--R
--R   (40)  true
--R                                                                Type: Boolean
--E 40

--S 41 of 44
coerce a
 

   (41)  [18,19,13,14,15]
                                                             Type: OutputForm
--R 
--R
--R   (41)  [18,19,13,14,15]
--R                                                             Type: OutputForm
--E 41

--S 42 of 44
hash a
 

   (42)  36688306
                                                          Type: SingleInteger
--R 
--R
--I   (42)  36310821
--R                                                          Type: SingleInteger
--E 42

--S 43 of 44
latex a
 

   (43)  "\mbox{\bf Unimplemented}"
                                                                 Type: String
--R 
--R
--R   (43)  "\mbox{\bf Unimplemented}"
--R                                                                 Type: String
--E 43

--S 44 of 44
)show ArrayStack
 
 ArrayStack S: SetCategory  is a domain constructor
 Abbreviation for ArrayStack is ASTACK 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for ASTACK 

------------------------------- Operations --------------------------------
 arrayStack : List S -> %              bag : List S -> %
 copy : % -> %                         depth : % -> NonNegativeInteger
 empty : () -> %                       empty? : % -> Boolean
 eq? : (%,%) -> Boolean                extract! : % -> S
 insert! : (S,%) -> %                  inspect : % -> S
 map : ((S -> S),%) -> %               pop! : % -> S
 push! : (S,%) -> S                    sample : () -> %
 top : % -> S                         
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?=? : (%,%) -> Boolean if S has SETCAT
 any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 coerce : % -> OutputForm if S has SETCAT
 count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
 count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
 every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 hash : % -> SingleInteger if S has SETCAT
 latex : % -> String if S has SETCAT
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((S -> S),%) -> % if $ has shallowlyMutable
 member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
 members : % -> List S if $ has finiteAggregate
 more? : (%,NonNegativeInteger) -> Boolean
 parts : % -> List S if $ has finiteAggregate
 size? : (%,NonNegativeInteger) -> Boolean
 ?~=? : (%,%) -> Boolean if S has SETCAT

--R 
--R ArrayStack S: SetCategory  is a domain constructor
--R Abbreviation for ArrayStack is ASTACK 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for ASTACK 
--R
--R------------------------------- Operations --------------------------------
--R arrayStack : List S -> %              bag : List S -> %
--R copy : % -> %                         depth : % -> NonNegativeInteger
--R empty : () -> %                       empty? : % -> Boolean
--R eq? : (%,%) -> Boolean                extract! : % -> S
--R insert! : (S,%) -> %                  inspect : % -> S
--R map : ((S -> S),%) -> %               pop! : % -> S
--R push! : (S,%) -> S                    sample : () -> %
--R top : % -> S                         
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
--R members : % -> List S if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R parts : % -> List S if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
--E 44

)spool
 
Starts dribbling to File.output (2010/3/27, 18:42:2).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
ifile:File List Integer:=open("jazz1","output") 
 

   (1)  "jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (1)  "jazz1"
--R                                                      Type: File List Integer
--E 1

--S 2 of 12
write!(ifile, [-1,2,3])
 

   (2)  [- 1,2,3]
                                                           Type: List Integer
--R 
--R
--R   (2)  [- 1,2,3]
--R                                                           Type: List Integer
--E 2

--S 3 of 12
write!(ifile, [10,-10,0,111])
 

   (3)  [10,- 10,0,111]
                                                           Type: List Integer
--R 
--R
--R   (3)  [10,- 10,0,111]
--R                                                           Type: List Integer
--E 3

--S 4 of 12
write!(ifile, [7])
 

   (4)  [7]
                                                           Type: List Integer
--R 
--R
--R   (4)  [7]
--R                                                           Type: List Integer
--E 4

--S 5 of 12
reopen!(ifile, "input")
 

   (5)  "jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (5)  "jazz1"
--R                                                      Type: File List Integer
--E 5

--S 6 of 12
read! ifile
 

   (6)  [- 1,2,3]
                                                           Type: List Integer
--R 
--R
--R   (6)  [- 1,2,3]
--R                                                           Type: List Integer
--E 6

--S 7 of 12
read! ifile
 

   (7)  [10,- 10,0,111]
                                                           Type: List Integer
--R 
--R
--R   (7)  [10,- 10,0,111]
--R                                                           Type: List Integer
--E 7

--S 8 of 12
readIfCan! ifile 
 

   (8)  [7]
                                                Type: Union(List Integer,...)
--R 
--R
--R   (8)  [7]
--R                                                Type: Union(List Integer,...)
--E 8

--S 9 of 12
readIfCan! ifile
 

   (9)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (9)  "failed"
--R                                                    Type: Union("failed",...)
--E 9

--S 10 of 12
iomode ifile
 

   (10)  "input"
                                                                 Type: String
--R 
--R
--R   (10)  "input"
--R                                                                 Type: String
--E 10

--S 11 of 12
name ifile
 

   (11)  "jazz1"
                                                               Type: FileName
--R 
--R
--R   (11)  "jazz1"
--R                                                               Type: FileName
--E 11

--S 12 of 12
close! ifile
 

   (12)  "jazz1"
                                                      Type: File List Integer
--R 
--R
--R   (12)  "jazz1"
--R                                                      Type: File List Integer
--E 12
)system rm jazz1
 
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read wutset
 

-- Input generated from WuWenTsunTriangularSetXmpPage
)clear all
 

R := Integer
 

   (1)  Integer
                                                                 Type: Domain
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
T := WUTSET(R,E,V,P)
 

   (10)
  WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t]
  ,OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,Ordere
  dVariableList [x,y,z,t]))
                                                                 Type: Domain
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
characteristicSet(lp)$T
 

   (15)
     5    4  4 2 2     3 4        7     4      6    6    3      3     3     3
   {z  - t ,t z y  + 2t z y + (- t  + 2t  - t)z  + t z,(t  - 1)z x - z y - t }
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])),...)
zeroSetSplit(lp)$T
 

   (16)
                 3      5    4  3     3    2
   [{t,z,y,x}, {t  - 1,z  - t ,z y + t ,z x  - t},
      5    4  4 2 2     3 4        7     4      6    6    3      3     3     3
    {z  - t ,t z y  + 2t z y + (- t  + 2t  - t)z  + t z,(t  - 1)z x - z y - t }]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
)lisp (bye)
 
Starts dribbling to mapleok.output (2010/3/27, 18:28:59).
)set message test on
 
)set message auto off
 
)clear all
 
)set break resume
 
--S 1 of 224
in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 

            +-+
        %pi\|3
   (1)  -------
           3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            +-+
--R        %pi\|3
--R   (1)  -------
--R           3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 1

--S 2 of 224
in101a:=integrate((sqrt(z)^%i)^%i, z= 0..1,"noPole")
 

   (2)  2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (2)  2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 2

--S 3 of 224
in108a:=integrate(sqrt((1 + cos(z))*(1 + sin(z))),z=0..%plusInfinity,"noPole")
 

   (3)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (3)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 3

--S 4 of 224
in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole")
 

   (4)
              +-+              +-+                 +-+
       3log(2\|2  + 3) + 2log(\|2  + 1) - 3log(- 2\|2  + 3)
     + 
                     +-+       +-+      +-+
        +-+    (- 32\|2  - 30)\|5  + 48\|2  + 102           +-+
       \|5 log(----------------------------------) - log(4)\|5
                              +-+
                            2\|2  + 3
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)
--R              +-+              +-+                 +-+
--R       3log(2\|2  + 3) + 2log(\|2  + 1) - 3log(- 2\|2  + 3)
--R     + 
--R                     +-+       +-+      +-+
--R        +-+    (- 32\|2  - 30)\|5  + 48\|2  + 102           +-+
--R       \|5 log(----------------------------------) - log(4)\|5
--R                              +-+
--R                            2\|2  + 3
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 224
in120a:=integrate(1/(1+1/z^6), z=0..%plusInfinity)
 

   (5)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (5)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 224
in1030a:=integrate(%i*z/(%i*z+1), z= 0..%plusInfinity,"noPole")
 

   (6)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (6)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 6

--S 7 of 224
in1066a:=integrate(acoth(z)*real(z), z= 0..1,"noPole")
 

        1
   (7)  -
        2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R        1
--R   (7)  -
--R        2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 7

--S 8 of 224
in1067a:=integrate(acoth(z)*z^(1/2), z= 0..1,"noPole")
 

        - 2log(2) - %pi + 8
   (8)  -------------------
                 6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R        - 2log(2) - %pi + 8
--R   (8)  -------------------
--R                 6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 8

--S 9 of 224
in1076a:=integrate(sin(z)*(1-cos(z)/(1-sin(z)^2)^(1/2))^2, z= 0..1,"noPole")
 

   (9)  - 4cos(1) + 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (9)  - 4cos(1) + 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 9

--S 10 of 224
in1084a:=integrate(atan(sin(z))+atan(1/sin(z)), z= 0..1,"noPole")
 

           %pi
   (10)  - ---
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           %pi
--R   (10)  - ---
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 10

--S 11 of 224
in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole")
 

   (11)
               +--------+              +-------+
               |2%pi - 1               |%pi - 1
       - 2log( |--------  + 1) + 2log( |-------  + 1)
              \|  2%pi                \|  %pi
     + 
                    +-------+                          +--------+
                    |%pi - 1                           |2%pi - 1
             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
                   \|  %pi                            \|  2%pi
       - log(---------------------------) + log(----------------------------)
                         %pi                                2%pi
     + 
            +--------+        +-------+
            |2%pi - 1         |%pi - 1
       8%pi |--------  - 4%pi |-------
           \|  2%pi          \|  %pi
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (11)
--R               +--------+              +-------+
--R               |2%pi - 1               |%pi - 1
--R       - 2log( |--------  + 1) + 2log( |-------  + 1)
--R              \|  2%pi                \|  %pi
--R     + 
--R                    +-------+                          +--------+
--R                    |%pi - 1                           |2%pi - 1
--R             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
--R                   \|  %pi                            \|  2%pi
--R       - log(---------------------------) + log(----------------------------)
--R                         %pi                                2%pi
--R     + 
--R            +--------+        +-------+
--R            |2%pi - 1         |%pi - 1
--R       8%pi |--------  - 4%pi |-------
--R           \|  2%pi          \|  %pi
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 11

--S 12 of 224
in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*%i*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole")
 

   (12)  - infinity
   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--R 
--R
--R   (12)  - infinity
--R   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--E 12

--S 13 of 224
in1118:=integrate(acot(z), z= 0..1/2*%i)
 

         1     3    1     1
   (13)  - log(-) - - log(-)
         2     4    8     9
   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--R 
--R
--R         1     3    1     1
--R   (13)  - log(-) - - log(-)
--R         2     4    8     9
--R   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
--E 13

--S 14 of 224
in1120a:=integrate((z^2)^(1/2), z= 1..2,"noPole")
 

         3
   (14)  -
         2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         3
--R   (14)  -
--R         2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 14

--S 15 of 224
in1130a:=integrate(3^log(z), z= -%i..%i,"noPole")
 

              log(%i)log(3)        log(- %i)log(3)
         %i %e              + %i %e
   (15)  -----------------------------------------
                         log(3) + 1
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              log(%i)log(3)        log(- %i)log(3)
--R         %i %e              + %i %e
--R   (15)  -----------------------------------------
--R                         log(3) + 1
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 15

--S 16 of 224
in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i)
 

   (16)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (16)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 16

--S 17 of 224
in1150a:=integrate(1/z^(1/2), z= -%i..%i,"noPole")
 

           +--+     +----+
   (17)  2\|%i  - 2\|- %i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R           +--+     +----+
--R   (17)  2\|%i  - 2\|- %i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 17

--S 18 of 224
in1161a:=integrate(hermiteH(1, z), z= -%i..%i)
 

   (18)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (18)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 18

--S 19 of 224
in1160:=integrate(hermiteH(2, z), z= -%i..%i)
 

           20%i
   (19)  - ----
             3
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R           20%i
--R   (19)  - ----
--R             3
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 19

--S 20 of 224
in1162:=integrate(laguerreL(1, z), z= -%i..%i)
 

   (20)  2%i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (20)  2%i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 20

--S 21 of 224
in1163:=integrate(legendreP(3, z), z= -%i..%i)
 

   (21)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (21)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 21

--S 22 of 224
in1164:=integrate(legendreP(2, z), z= -%i..%i)
 

   (22)  - 2%i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (22)  - 2%i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 22

--S 23 of 224
in1167a:=integrate((z^2)^(1/6), z= -3..-1,"noPole")
 

            3+---+    3+---+
         - 3\|- 1  + 9\|- 3
   (23)  -------------------
                  4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            3+---+    3+---+
--R         - 3\|- 1  + 9\|- 3
--R   (23)  -------------------
--R                  4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 23

--S 24 of 224
in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
 

   (24)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (24)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 24

--S 25 of 224
in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,"noPole")
 

   (25)
         3
      *
         log
               999999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
                99999999999999999999999999999999999999999999999999999999999999_
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                3+--+2
                \|10
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             *
                3+--+
                \|10
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              -
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     + 
       -
            12
         *
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                *
                   3+--+2
                   \|10
               + 
                 1
     + 
            +-+
         12\|3
      *
         atan
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               *
                  3+--+2
                  \|10
              + 
                - 1
           /
               +-+
              \|3
     + 
            +-+
       2%pi\|3
  /
     24
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (25)
--R         3
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--R               999999999999999999999999999999999999999999999999999999999999999_
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--R                3+--+2
--R                \|10
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--R                3+--+
--R                \|10
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--R       -
--R            12
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--R                  100000000000000000000000000000000000000000000000000000000000_
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--R                *
--R                   3+--+2
--R                   \|10
--R               + 
--R                 1
--R     + 
--R            +-+
--R         12\|3
--R      *
--R         atan
--R                 2000000000000000000000000000000000000000000000000000000000000_
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--R               *
--R                  3+--+2
--R                  \|10
--R              + 
--R                - 1
--R           /
--R               +-+
--R              \|3
--R     + 
--R            +-+
--R       2%pi\|3
--R  /
--R     24
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 25

--S 26 of 224
in1183a:=integrate(csc(z), z= 1-%i..1+%i,"noPole")
 

   (26)
                            2                                      2
                 sin(1 + %i)                            sin(1 - %i)
   log(-------------------------------) - log(-------------------------------)
                  2                                      2
       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
   ---------------------------------------------------------------------------
                                        2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (26)
--R                            2                                      2
--R                 sin(1 + %i)                            sin(1 - %i)
--R   log(-------------------------------) - log(-------------------------------)
--R                  2                                      2
--R       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
--R   ---------------------------------------------------------------------------
--R                                        2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 26

--S 27 of 224
in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 

   (27)
         ROOT
                 +-----------------------------------------+
                 |         2                          2          +-+
                \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                              +-+            +-+             +-+           +-+
                      ((24576\|2 %%CC0 - 768\|2 )%%CC1 - 768\|2 %%CC0 - 48\|2 )
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                                             2               2
                    (196608%%CC0 - 6144)%%CC1  + (196608%%CC0  + 384)%%CC1
                  + 
                               2
                    - 6144%%CC0  + 384%%CC0 + 48
               *
                  ROOT
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                60\|2
           /
               +-+
              \|2
     + 
       -
            ROOT
                    +-----------------------------------------+
                    |         2                          2          +-+
                   \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                         ((24576%%CC0 - 768)%%CC1 - 768%%CC0 - 48)
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                              +-+             +-+      2
                       (98304\|2 %%CC0 - 3072\|2 )%%CC1
                     + 
                              +-+     2       +-+              +-+     2
                       (98304\|2 %%CC0  + 192\|2 )%%CC1 - 3072\|2 %%CC0
                     + 
                           +-+           +-+
                       192\|2 %%CC0 + 24\|2
                  *
                     ROOT
                             +-----------------------------------------+
                             |         2                          2
                            \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 42\|2
              /
                  +-+
                 \|2
     + 
       -
            ROOT
                      +-----------------------------------------+
                      |         2                          2          +-+
                   - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                                    +-+            +-+             +-+
                             (24576\|2 %%CC0 - 768\|2 )%%CC1 - 768\|2 %%CC0
                           + 
                                  +-+
                             - 48\|2
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                                                  2
                       (- 196608%%CC0 + 6144)%%CC1
                     + 
                                     2                        2
                       (- 196608%%CC0  - 384)%%CC1 + 6144%%CC0  - 384%%CC0 - 48
                  *
                     ROOT
                               +-----------------------------------------+
                               |         2                          2
                            - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 60\|2
              /
                  +-+
                 \|2
     + 
         ROOT
                   +-----------------------------------------+
                   |         2                          2          +-+
                - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                      ((24576%%CC0 - 768)%%CC1 - 768%%CC0 - 48)
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                             +-+             +-+      2
                    (- 98304\|2 %%CC0 + 3072\|2 )%%CC1
                  + 
                             +-+     2       +-+              +-+     2
                    (- 98304\|2 %%CC0  - 192\|2 )%%CC1 + 3072\|2 %%CC0
                  + 
                          +-+           +-+
                    - 192\|2 %%CC0 - 24\|2
               *
                  ROOT
                            +-----------------------------------------+
                            |         2                          2
                         - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                42\|2
           /
               +-+
              \|2
     + 
       -
            ROOT
                      +-----------------------------------------+
                      |         2                          2          +-+
                   - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                         ((- 24576%%CC0 + 768)%%CC1 + 768%%CC0 + 48)
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                              +-+             +-+      2
                       (98304\|2 %%CC0 - 3072\|2 )%%CC1
                     + 
                              +-+     2       +-+              +-+     2
                       (98304\|2 %%CC0  + 192\|2 )%%CC1 - 3072\|2 %%CC0
                     + 
                           +-+           +-+
                       192\|2 %%CC0 + 24\|2
                  *
                     ROOT
                               +-----------------------------------------+
                               |         2                          2
                            - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 42\|2
              /
                  +-+
                 \|2
     + 
         ROOT
                   +-----------------------------------------+
                   |         2                          2          +-+
                - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                                   +-+            +-+             +-+
                          (- 24576\|2 %%CC0 + 768\|2 )%%CC1 + 768\|2 %%CC0
                        + 
                             +-+
                          48\|2
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                                             2               2
                    (196608%%CC0 - 6144)%%CC1  + (196608%%CC0  + 384)%%CC1
                  + 
                               2
                    - 6144%%CC0  + 384%%CC0 + 48
               *
                  ROOT
                            +-----------------------------------------+
                            |         2                          2
                         - \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((3072%%CC0 - 384)%%CC1 - 384%%CC0 + 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                60\|2
           /
               +-+
              \|2
     + 
         ROOT
                 +-----------------------------------------+
                 |         2                          2          +-+
                \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
              + 
                    +-+
                - 4\|2 %%CC0
           /
                +-+
              2\|2
      *
         log
                      ((- 24576%%CC0 + 768)%%CC1 + 768%%CC0 + 48)
                   *
                       +-----------------------------------------+
                       |         2                          2
                      \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                  + 
                             +-+             +-+      2
                    (- 98304\|2 %%CC0 + 3072\|2 )%%CC1
                  + 
                             +-+     2       +-+              +-+     2
                    (- 98304\|2 %%CC0  - 192\|2 )%%CC1 + 3072\|2 %%CC0
                  + 
                          +-+           +-+
                    - 192\|2 %%CC0 - 24\|2
               *
                  ROOT
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                       + 
                             +-+          +-+
                         - 4\|2 %%CC1 - 4\|2 %%CC0
                    /
                         +-+
                       2\|2
              + 
                  ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
               *
                   +-----------------------------------------+
                   |         2                          2
                  \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
              + 
                         +-+             +-+      2
                (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
              + 
                         +-+     2      +-+              +-+     2      +-+
                (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0  + 48\|2 %%CC0
              + 
                   +-+
                42\|2
           /
               +-+
              \|2
     + 
       -
            ROOT
                    +-----------------------------------------+
                    |         2                          2          +-+
                   \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1  - 4\|2 %%CC1
                 + 
                       +-+
                   - 4\|2 %%CC0
              /
                   +-+
                 2\|2
         *
            log
                                    +-+            +-+             +-+
                           (- 24576\|2 %%CC0 + 768\|2 )%%CC1 + 768\|2 %%CC0
                         + 
                              +-+
                           48\|2
                      *
                          +-----------------------------------------+
                          |         2                          2
                         \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                     + 
                                                  2
                       (- 196608%%CC0 + 6144)%%CC1
                     + 
                                     2                        2
                       (- 196608%%CC0  - 384)%%CC1 + 6144%%CC0  - 384%%CC0 - 48
                  *
                     ROOT
                             +-----------------------------------------+
                             |         2                          2
                            \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                          + 
                                +-+          +-+
                            - 4\|2 %%CC1 - 4\|2 %%CC0
                       /
                            +-+
                          2\|2
                 + 
                     ((- 3072%%CC0 + 384)%%CC1 + 384%%CC0 - 12)
                  *
                      +-----------------------------------------+
                      |         2                          2
                     \|- 96%%CC1  - 64%%CC0 %%CC1 - 96%%CC0  - 1
                 + 
                            +-+             +-+      2
                   (- 12288\|2 %%CC0 + 1536\|2 )%%CC1
                 + 
                            +-+     2      +-+              +-+     2
                   (- 12288\|2 %%CC0  + 48\|2 )%%CC1 + 1536\|2 %%CC0
                 + 
                      +-+           +-+
                   48\|2 %%CC0 + 60\|2
              /
                  +-+
                 \|2
     + 
       -
             +------+
            \|4%%CC1
         *
            log
                            +-+             +-+      2
                     (98304\|2 %%CC0 - 3072\|2 )%%CC1
                   + 
                            +-+     2       +-+               +-+     3
                     (98304\|2 %%CC0  + 192\|2 )%%CC1 + 98304\|2 %%CC0
                   + 
                         +-+           +-+
                     768\|2 %%CC0 - 36\|2
                *
                    +------+
                   \|4%%CC1
               + 
                                         2              2
                 (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1
               + 
                           3
                 12288%%CC0  + 96%%CC0 + 18
     + 
          +------+
         \|4%%CC1
      *
         log
                                          2              2
                  (98304%%CC0 - 3072)%%CC1  + (98304%%CC0  + 192)%%CC1
                + 
                            3
                  98304%%CC0  + 768%%CC0 - 36
             *
                 +------+
                \|4%%CC1
            + 
                                      2              2                        3
              (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1 + 12288%%CC0
            + 
              96%%CC0 + 9
     + 
       -
             +------+
            \|4%%CC1
         *
            log
                                               2                2
                     (- 98304%%CC0 + 3072)%%CC1  + (- 98304%%CC0  - 192)%%CC1
                   + 
                                 3
                     - 98304%%CC0  - 768%%CC0 + 36
                *
                    +------+
                   \|4%%CC1
               + 
                                         2              2
                 (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1
               + 
                           3
                 12288%%CC0  + 96%%CC0 + 9
     + 
          +------+
         \|4%%CC1
      *
         log
                           +-+             +-+      2
                  (- 98304\|2 %%CC0 + 3072\|2 )%%CC1
                + 
                           +-+     2       +-+               +-+     3
                  (- 98304\|2 %%CC0  - 192\|2 )%%CC1 - 98304\|2 %%CC0
                + 
                        +-+           +-+
                  - 768\|2 %%CC0 + 36\|2
             *
                 +------+
                \|4%%CC1
            + 
                                      2              2                        3
              (12288%%CC0 - 1536)%%CC1  + (12288%%CC0  - 48)%%CC1 + 12288%%CC0
            + 
              96%%CC0 + 18
     + 
          +------+
         \|4%%CC0
      *
         log
                       +-+     3        +-+     2       +-+           +-+
                (98304\|2 %%CC0  + 3072\|2 %%CC0  + 576\|2 %%CC0 - 60\|2 )
             *
                 +------+
                \|4%%CC0
            + 
                          3            2
              - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 30
     + 
       -
             +------+
            \|4%%CC0
         *
            log
                            3            2                  +------+
                 (98304%%CC0  + 3072%%CC0  + 576%%CC0 - 60)\|4%%CC0
               + 
                             3            2
                 - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 21
     + 
          +------+
         \|4%%CC0
      *
         log
                           3            2                  +------+
              (- 98304%%CC0  - 3072%%CC0  - 576%%CC0 + 60)\|4%%CC0
            + 
                          3            2
              - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 21
     + 
       -
             +------+
            \|4%%CC0
         *
            log
                            +-+     3        +-+     2       +-+           +-+
                   (- 98304\|2 %%CC0  - 3072\|2 %%CC0  - 576\|2 %%CC0 + 60\|2 )
                *
                    +------+
                   \|4%%CC0
               + 
                             3            2
                 - 12288%%CC0  - 1536%%CC0  - 144%%CC0 + 30
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (27)
--R         ROOT
--R                 +-----------------------------------------+
--R                 |         2                          2          +-+
--I                \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--R                              +-+            +-+             +-+           +-+
--I                      ((24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0 - 48\|2 )
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                                             2               2
--I                    (196608%%BQ0 - 6144)%%BQ1  + (196608%%BQ0  + 384)%%BQ1
--R                  + 
--R                               2
--I                    - 6144%%BQ0  + 384%%BQ0 + 48
--R               *
--R                  ROOT
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                60\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R            ROOT
--R                    +-----------------------------------------+
--R                    |         2                          2          +-+
--I                   \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--I                         ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48)
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                              +-+             +-+      2
--I                       (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
--R                     + 
--R                              +-+     2       +-+              +-+     2
--I                       (98304\|2 %%BQ0  + 192\|2 )%%BQ1 - 3072\|2 %%BQ0
--R                     + 
--R                           +-+           +-+
--I                       192\|2 %%BQ0 + 24\|2
--R                  *
--R                     ROOT
--R                             +-----------------------------------------+
--R                             |         2                          2
--I                            \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 42\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R       -
--R            ROOT
--R                      +-----------------------------------------+
--R                      |         2                          2          +-+
--I                   - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--R                                    +-+            +-+             +-+
--I                             (24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0
--R                           + 
--R                                  +-+
--R                             - 48\|2
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                                                  2
--I                       (- 196608%%BQ0 + 6144)%%BQ1
--R                     + 
--R                                     2                        2
--I                       (- 196608%%BQ0  - 384)%%BQ1 + 6144%%BQ0  - 384%%BQ0 - 48
--R                  *
--R                     ROOT
--R                               +-----------------------------------------+
--R                               |         2                          2
--I                            - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 60\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R         ROOT
--R                   +-----------------------------------------+
--R                   |         2                          2          +-+
--I                - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--I                      ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48)
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                             +-+             +-+      2
--I                    (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
--R                  + 
--R                             +-+     2       +-+              +-+     2
--I                    (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 + 3072\|2 %%BQ0
--R                  + 
--R                          +-+           +-+
--I                    - 192\|2 %%BQ0 - 24\|2
--R               *
--R                  ROOT
--R                            +-----------------------------------------+
--R                            |         2                          2
--I                         - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                42\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R            ROOT
--R                      +-----------------------------------------+
--R                      |         2                          2          +-+
--I                   - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--I                         ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48)
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                              +-+             +-+      2
--I                       (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
--R                     + 
--R                              +-+     2       +-+              +-+     2
--I                       (98304\|2 %%BQ0  + 192\|2 )%%BQ1 - 3072\|2 %%BQ0
--R                     + 
--R                           +-+           +-+
--I                       192\|2 %%BQ0 + 24\|2
--R                  *
--R                     ROOT
--R                               +-----------------------------------------+
--R                               |         2                          2
--I                            - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 42\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R         ROOT
--R                   +-----------------------------------------+
--R                   |         2                          2          +-+
--I                - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--R                                   +-+            +-+             +-+
--I                          (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0
--R                        + 
--R                             +-+
--R                          48\|2
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                                             2               2
--I                    (196608%%BQ0 - 6144)%%BQ1  + (196608%%BQ0  + 384)%%BQ1
--R                  + 
--R                               2
--I                    - 6144%%BQ0  + 384%%BQ0 + 48
--R               *
--R                  ROOT
--R                            +-----------------------------------------+
--R                            |         2                          2
--I                         - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                60\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R         ROOT
--R                 +-----------------------------------------+
--R                 |         2                          2          +-+
--I                \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R              + 
--R                    +-+
--I                - 4\|2 %%BQ0
--R           /
--R                +-+
--R              2\|2
--R      *
--R         log
--I                      ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48)
--R                   *
--R                       +-----------------------------------------+
--R                       |         2                          2
--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                  + 
--R                             +-+             +-+      2
--I                    (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
--R                  + 
--R                             +-+     2       +-+              +-+     2
--I                    (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 + 3072\|2 %%BQ0
--R                  + 
--R                          +-+           +-+
--I                    - 192\|2 %%BQ0 - 24\|2
--R               *
--R                  ROOT
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                       + 
--R                             +-+          +-+
--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                    /
--R                         +-+
--R                       2\|2
--R              + 
--I                  ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R               *
--R                   +-----------------------------------------+
--R                   |         2                          2
--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R              + 
--R                         +-+             +-+      2
--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R              + 
--R                         +-+     2      +-+              +-+     2      +-+
--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
--R              + 
--R                   +-+
--R                42\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R            ROOT
--R                    +-----------------------------------------+
--R                    |         2                          2          +-+
--I                   \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
--R                 + 
--R                       +-+
--I                   - 4\|2 %%BQ0
--R              /
--R                   +-+
--R                 2\|2
--R         *
--R            log
--R                                    +-+            +-+             +-+
--I                           (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0
--R                         + 
--R                              +-+
--R                           48\|2
--R                      *
--R                          +-----------------------------------------+
--R                          |         2                          2
--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                     + 
--R                                                  2
--I                       (- 196608%%BQ0 + 6144)%%BQ1
--R                     + 
--R                                     2                        2
--I                       (- 196608%%BQ0  - 384)%%BQ1 + 6144%%BQ0  - 384%%BQ0 - 48
--R                  *
--R                     ROOT
--R                             +-----------------------------------------+
--R                             |         2                          2
--I                            \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                          + 
--R                                +-+          +-+
--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
--R                       /
--R                            +-+
--R                          2\|2
--R                 + 
--I                     ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
--R                  *
--R                      +-----------------------------------------+
--R                      |         2                          2
--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
--R                 + 
--R                            +-+             +-+      2
--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
--R                 + 
--R                            +-+     2      +-+              +-+     2
--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
--R                 + 
--R                      +-+           +-+
--I                   48\|2 %%BQ0 + 60\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ1
--R         *
--R            log
--R                            +-+             +-+      2
--I                     (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
--R                   + 
--R                            +-+     2       +-+               +-+     3
--I                     (98304\|2 %%BQ0  + 192\|2 )%%BQ1 + 98304\|2 %%BQ0
--R                   + 
--R                         +-+           +-+
--I                     768\|2 %%BQ0 - 36\|2
--R                *
--R                    +------+
--I                   \|4%%BQ1
--R               + 
--R                                         2              2
--I                 (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1
--R               + 
--R                           3
--I                 12288%%BQ0  + 96%%BQ0 + 18
--R     + 
--R          +------+
--I         \|4%%BQ1
--R      *
--R         log
--R                                          2              2
--I                  (98304%%BQ0 - 3072)%%BQ1  + (98304%%BQ0  + 192)%%BQ1
--R                + 
--R                            3
--I                  98304%%BQ0  + 768%%BQ0 - 36
--R             *
--R                 +------+
--I                \|4%%BQ1
--R            + 
--R                                      2              2                        3
--I              (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1 + 12288%%BQ0
--R            + 
--I              96%%BQ0 + 9
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ1
--R         *
--R            log
--R                                               2                2
--I                     (- 98304%%BQ0 + 3072)%%BQ1  + (- 98304%%BQ0  - 192)%%BQ1
--R                   + 
--R                                 3
--I                     - 98304%%BQ0  - 768%%BQ0 + 36
--R                *
--R                    +------+
--I                   \|4%%BQ1
--R               + 
--R                                         2              2
--I                 (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1
--R               + 
--R                           3
--I                 12288%%BQ0  + 96%%BQ0 + 9
--R     + 
--R          +------+
--I         \|4%%BQ1
--R      *
--R         log
--R                           +-+             +-+      2
--I                  (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
--R                + 
--R                           +-+     2       +-+               +-+     3
--I                  (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 - 98304\|2 %%BQ0
--R                + 
--R                        +-+           +-+
--I                  - 768\|2 %%BQ0 + 36\|2
--R             *
--R                 +------+
--I                \|4%%BQ1
--R            + 
--R                                      2              2                        3
--I              (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1 + 12288%%BQ0
--R            + 
--I              96%%BQ0 + 18
--R     + 
--R          +------+
--I         \|4%%BQ0
--R      *
--R         log
--R                       +-+     3        +-+     2       +-+           +-+
--I                (98304\|2 %%BQ0  + 3072\|2 %%BQ0  + 576\|2 %%BQ0 - 60\|2 )
--R             *
--R                 +------+
--I                \|4%%BQ0
--R            + 
--R                          3            2
--I              - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 30
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ0
--R         *
--R            log
--R                            3            2                  +------+
--I                 (98304%%BQ0  + 3072%%BQ0  + 576%%BQ0 - 60)\|4%%BQ0
--R               + 
--R                             3            2
--I                 - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 21
--R     + 
--R          +------+
--I         \|4%%BQ0
--R      *
--R         log
--R                           3            2                  +------+
--I              (- 98304%%BQ0  - 3072%%BQ0  - 576%%BQ0 + 60)\|4%%BQ0
--R            + 
--R                          3            2
--I              - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 21
--R     + 
--R       -
--R             +------+
--I            \|4%%BQ0
--R         *
--R            log
--R                            +-+     3        +-+     2       +-+           +-+
--I                   (- 98304\|2 %%BQ0  - 3072\|2 %%BQ0  - 576\|2 %%BQ0 + 60\|2 )
--R                *
--R                    +------+
--I                   \|4%%BQ0
--R               + 
--R                             3            2
--I                 - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 30
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 27

--S 28 of 224
in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole")
 

   (28)
             +-+      4+-+    %pi
         (17\|2  - 24)\|2 cos(---)
                               8
      *
         log
                   %pi 4     +-+4+-+3    %pi 3
              2sin(---)  + 2\|2 \|2  sin(---)
                    8                     8
            + 
                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
              (4cos(---)  - 2\|2 \|2  cos(---) + 4\|2  )sin(---)
                     8                     8                 8
            + 
                 +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
              (2\|2 \|2  cos(---)  - 4\|2  cos(---) + 2\|2 \|2 )sin(---)
                              8                 8                    8
            + 
                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
              2cos(---)  - 2\|2 \|2  cos(---)  + 4\|2  cos(---)
                    8                     8                 8
            + 
                  +-+4+-+    %pi
              - 2\|2 \|2 cos(---) + 1
                              8
     + 
               +-+      4+-+    %pi
         (- 17\|2  + 24)\|2 cos(---)
                                 8
      *
         log
                   %pi 4    4+-+3    %pi 3
              2sin(---)  + 4\|2  sin(---)
                    8                 8
            + 
                      %pi 2        +-+     4+-+3    %pi         +-+      4+-+2
                (4cos(---)  + (- 4\|2  + 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
                       8                             8
             *
                    %pi 2
                sin(---)
                     8
            + 
                   4+-+3    %pi 2        +-+     4+-+2    %pi
                  4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
                             8                             8
                + 
                       +-+      4+-+
                  (- 8\|2  + 16)\|2
             *
                    %pi
                sin(---)
                     8
            + 
                   %pi 4        +-+     4+-+3    %pi 3
              2cos(---)  + (- 4\|2  + 4)\|2  cos(---)
                    8                             8
            + 
                    +-+      4+-+2    %pi 2         +-+      4+-+    %pi
              (- 12\|2  + 20)\|2  cos(---)  + (- 24\|2  + 32)\|2 cos(---)
                                       8                              8
            + 
                   +-+
              - 16\|2  + 24
     + 
             +-+      4+-+    %pi
         (17\|2  - 24)\|2 cos(---)
                               8
      *
         log
                   %pi 4    4+-+3    %pi 3
              2sin(---)  - 4\|2  sin(---)
                    8                 8
            + 
                      %pi 2      +-+     4+-+3    %pi         +-+      4+-+2
                (4cos(---)  + (4\|2  - 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
                       8                           8
             *
                    %pi 2
                sin(---)
                     8
            + 
                     4+-+3    %pi 2        +-+     4+-+2    %pi
                  - 4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
                               8                             8
                + 
                     +-+      4+-+
                  (8\|2  - 16)\|2
             *
                    %pi
                sin(---)
                     8
            + 
                   %pi 4      +-+     4+-+3    %pi 3
              2cos(---)  + (4\|2  - 4)\|2  cos(---)
                    8                           8
            + 
                    +-+      4+-+2    %pi 2       +-+      4+-+    %pi       +-+
              (- 12\|2  + 20)\|2  cos(---)  + (24\|2  - 32)\|2 cos(---) - 16\|2
                                       8                            8
            + 
              24
     + 
               +-+      4+-+    %pi
         (- 17\|2  + 24)\|2 cos(---)
                                 8
      *
         log
                   %pi 4     +-+4+-+3    %pi 3
              2sin(---)  - 2\|2 \|2  sin(---)
                    8                     8
            + 
                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
              (4cos(---)  + 2\|2 \|2  cos(---) + 4\|2  )sin(---)
                     8                     8                 8
            + 
                   +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
              (- 2\|2 \|2  cos(---)  - 4\|2  cos(---) - 2\|2 \|2 )sin(---)
                                8                 8                    8
            + 
                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
              2cos(---)  + 2\|2 \|2  cos(---)  + 4\|2  cos(---)
                    8                     8                 8
            + 
                +-+4+-+    %pi
              2\|2 \|2 cos(---) + 1
                            8
     + 
                                       4+-+    %pi    4+-+    %pi     +-+
                                       \|2 sin(---) - \|2 cos(---) + \|2
           +-+      4+-+    %pi                 8              8
       (68\|2  - 96)\|2 sin(---)atan(--------------------------------------)
                             8       4+-+    %pi    4+-+    %pi     +-+
                                     \|2 sin(---) + \|2 cos(---) - \|2  + 2
                                              8              8
     + 
                                       4+-+    %pi    4+-+    %pi     +-+
                                       \|2 sin(---) - \|2 cos(---) + \|2
             +-+      4+-+    %pi               8              8
       (- 68\|2  + 96)\|2 sin(---)atan(----------------------------------)
                               8           4+-+    %pi    4+-+    %pi
                                           \|2 sin(---) + \|2 cos(---)
                                                    8              8
     + 
                                     4+-+    %pi    4+-+    %pi     +-+
                                     \|2 sin(---) - \|2 cos(---) - \|2
           +-+      4+-+    %pi               8              8
       (68\|2  - 96)\|2 sin(---)atan(----------------------------------)
                             8           4+-+    %pi    4+-+    %pi
                                         \|2 sin(---) + \|2 cos(---)
                                                  8              8
     + 
                                         4+-+    %pi    4+-+    %pi     +-+
                                         \|2 sin(---) - \|2 cos(---) - \|2
             +-+      4+-+    %pi                 8              8
       (- 68\|2  + 96)\|2 sin(---)atan(--------------------------------------)
                               8       4+-+    %pi    4+-+    %pi     +-+
                                       \|2 sin(---) + \|2 cos(---) + \|2  - 2
                                                8              8
     + 
             +-+
       - 136\|2  + 192
  /
         +-+
     384\|2  - 544
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (28)
--R             +-+      4+-+    %pi
--R         (17\|2  - 24)\|2 cos(---)
--R                               8
--R      *
--R         log
--R                   %pi 4     +-+4+-+3    %pi 3
--R              2sin(---)  + 2\|2 \|2  sin(---)
--R                    8                     8
--R            + 
--R                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
--R              (4cos(---)  - 2\|2 \|2  cos(---) + 4\|2  )sin(---)
--R                     8                     8                 8
--R            + 
--R                 +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
--R              (2\|2 \|2  cos(---)  - 4\|2  cos(---) + 2\|2 \|2 )sin(---)
--R                              8                 8                    8
--R            + 
--R                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
--R              2cos(---)  - 2\|2 \|2  cos(---)  + 4\|2  cos(---)
--R                    8                     8                 8
--R            + 
--R                  +-+4+-+    %pi
--R              - 2\|2 \|2 cos(---) + 1
--R                              8
--R     + 
--R               +-+      4+-+    %pi
--R         (- 17\|2  + 24)\|2 cos(---)
--R                                 8
--R      *
--R         log
--R                   %pi 4    4+-+3    %pi 3
--R              2sin(---)  + 4\|2  sin(---)
--R                    8                 8
--R            + 
--R                      %pi 2        +-+     4+-+3    %pi         +-+      4+-+2
--R                (4cos(---)  + (- 4\|2  + 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
--R                       8                             8
--R             *
--R                    %pi 2
--R                sin(---)
--R                     8
--R            + 
--R                   4+-+3    %pi 2        +-+     4+-+2    %pi
--R                  4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
--R                             8                             8
--R                + 
--R                       +-+      4+-+
--R                  (- 8\|2  + 16)\|2
--R             *
--R                    %pi
--R                sin(---)
--R                     8
--R            + 
--R                   %pi 4        +-+     4+-+3    %pi 3
--R              2cos(---)  + (- 4\|2  + 4)\|2  cos(---)
--R                    8                             8
--R            + 
--R                    +-+      4+-+2    %pi 2         +-+      4+-+    %pi
--R              (- 12\|2  + 20)\|2  cos(---)  + (- 24\|2  + 32)\|2 cos(---)
--R                                       8                              8
--R            + 
--R                   +-+
--R              - 16\|2  + 24
--R     + 
--R             +-+      4+-+    %pi
--R         (17\|2  - 24)\|2 cos(---)
--R                               8
--R      *
--R         log
--R                   %pi 4    4+-+3    %pi 3
--R              2sin(---)  - 4\|2  sin(---)
--R                    8                 8
--R            + 
--R                      %pi 2      +-+     4+-+3    %pi         +-+      4+-+2
--R                (4cos(---)  + (4\|2  - 4)\|2  cos(---) + (- 4\|2  + 12)\|2  )
--R                       8                           8
--R             *
--R                    %pi 2
--R                sin(---)
--R                     8
--R            + 
--R                     4+-+3    %pi 2        +-+     4+-+2    %pi
--R                  - 4\|2  cos(---)  + (- 8\|2  + 8)\|2  cos(---)
--R                               8                             8
--R                + 
--R                     +-+      4+-+
--R                  (8\|2  - 16)\|2
--R             *
--R                    %pi
--R                sin(---)
--R                     8
--R            + 
--R                   %pi 4      +-+     4+-+3    %pi 3
--R              2cos(---)  + (4\|2  - 4)\|2  cos(---)
--R                    8                           8
--R            + 
--R                    +-+      4+-+2    %pi 2       +-+      4+-+    %pi       +-+
--R              (- 12\|2  + 20)\|2  cos(---)  + (24\|2  - 32)\|2 cos(---) - 16\|2
--R                                       8                            8
--R            + 
--R              24
--R     + 
--R               +-+      4+-+    %pi
--R         (- 17\|2  + 24)\|2 cos(---)
--R                                 8
--R      *
--R         log
--R                   %pi 4     +-+4+-+3    %pi 3
--R              2sin(---)  - 2\|2 \|2  sin(---)
--R                    8                     8
--R            + 
--R                    %pi 2     +-+4+-+3    %pi     4+-+2     %pi 2
--R              (4cos(---)  + 2\|2 \|2  cos(---) + 4\|2  )sin(---)
--R                     8                     8                 8
--R            + 
--R                   +-+4+-+3    %pi 2    4+-+2    %pi      +-+4+-+     %pi
--R              (- 2\|2 \|2  cos(---)  - 4\|2  cos(---) - 2\|2 \|2 )sin(---)
--R                                8                 8                    8
--R            + 
--R                   %pi 4     +-+4+-+3    %pi 3    4+-+2    %pi 2
--R              2cos(---)  + 2\|2 \|2  cos(---)  + 4\|2  cos(---)
--R                    8                     8                 8
--R            + 
--R                +-+4+-+    %pi
--R              2\|2 \|2 cos(---) + 1
--R                            8
--R     + 
--R                                       4+-+    %pi    4+-+    %pi     +-+
--R                                       \|2 sin(---) - \|2 cos(---) + \|2
--R           +-+      4+-+    %pi                 8              8
--R       (68\|2  - 96)\|2 sin(---)atan(--------------------------------------)
--R                             8       4+-+    %pi    4+-+    %pi     +-+
--R                                     \|2 sin(---) + \|2 cos(---) - \|2  + 2
--R                                              8              8
--R     + 
--R                                       4+-+    %pi    4+-+    %pi     +-+
--R                                       \|2 sin(---) - \|2 cos(---) + \|2
--R             +-+      4+-+    %pi               8              8
--R       (- 68\|2  + 96)\|2 sin(---)atan(----------------------------------)
--R                               8           4+-+    %pi    4+-+    %pi
--R                                           \|2 sin(---) + \|2 cos(---)
--R                                                    8              8
--R     + 
--R                                     4+-+    %pi    4+-+    %pi     +-+
--R                                     \|2 sin(---) - \|2 cos(---) - \|2
--R           +-+      4+-+    %pi               8              8
--R       (68\|2  - 96)\|2 sin(---)atan(----------------------------------)
--R                             8           4+-+    %pi    4+-+    %pi
--R                                         \|2 sin(---) + \|2 cos(---)
--R                                                  8              8
--R     + 
--R                                         4+-+    %pi    4+-+    %pi     +-+
--R                                         \|2 sin(---) - \|2 cos(---) - \|2
--R             +-+      4+-+    %pi                 8              8
--R       (- 68\|2  + 96)\|2 sin(---)atan(--------------------------------------)
--R                               8       4+-+    %pi    4+-+    %pi     +-+
--R                                       \|2 sin(---) + \|2 cos(---) + \|2  - 2
--R                                                8              8
--R     + 
--R             +-+
--R       - 136\|2  + 192
--R  /
--R         +-+
--R     384\|2  - 544
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 28

--S 29 of 224
in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole")
 

   (29)
                                                                   +------+
                     3                             4            2  |sin(1)
           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
                                                                  \|cos(1)
         + 
                                       4           2      +-+
           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                                                                   +------+
                     3                             4            2  |sin(1)
           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
                                                                  \|cos(1)
         + 
                                       4           2      +-+
           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                                                                     +------+
                      3                              4            2  |sin(1)
           ((384cos(1)  + 96cos(1))sin(1) - 384cos(1)  + 480cos(1) ) |------
                                                                    \|cos(1)
         + 
                                         4            2       +-+
           (- 192cos(1)sin(1) + 384cos(1)  - 384cos(1)  - 12)\|2
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
                                                                      \|cos(1)
         + 
                                       4            2       +-+
           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
                                                                      \|cos(1)
         + 
                                       4            2       +-+
           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                          3                               5
               (- 96cos(1)  - 24cos(1))log(4) - 1024cos(1)
             + 
                                   3
               (96%pi + 1024)cos(1)  + (24%pi + 32)cos(1)
          *
             sin(1)
         + 
                    4            2                               4
           (96cos(1)  - 120cos(1) )log(4) + (- 96%pi - 512)cos(1)
         + 
                               2
           (120%pi + 512)cos(1)
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                        5            3
             (48cos(1)log(4) + 512cos(1)  - 384cos(1)  + (- 48%pi - 128)cos(1))
          *
             sin(1)
         + 
                      4           2                       6
           (- 96cos(1)  + 96cos(1)  + 3)log(4) - 512cos(1)
         + 
                               4                        2
           (96%pi + 1152)cos(1)  + (- 96%pi - 640)cos(1)  - 3%pi
      *
          +-+
         \|2
  /
                     3                                4             2  +-+
         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                      4             2
       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (29)
--R                                                                   +------+
--R                     3                             4            2  |sin(1)
--R           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                       4           2      +-+
--R           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                                                                   +------+
--R                     3                             4            2  |sin(1)
--R           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                       4           2      +-+
--R           (- 48cos(1)sin(1) + 96cos(1)  - 96cos(1)  - 3)\|2
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                                                                     +------+
--R                      3                              4            2  |sin(1)
--R           ((384cos(1)  + 96cos(1))sin(1) - 384cos(1)  + 480cos(1) ) |------
--R                                                                    \|cos(1)
--R         + 
--R                                         4            2       +-+
--R           (- 192cos(1)sin(1) + 384cos(1)  - 384cos(1)  - 12)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                       4            2       +-+
--R           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 384cos(1)  - 96cos(1))sin(1) + 384cos(1)  - 480cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                       4            2       +-+
--R           (192cos(1)sin(1) - 384cos(1)  + 384cos(1)  + 12)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                          3                               5
--R               (- 96cos(1)  - 24cos(1))log(4) - 1024cos(1)
--R             + 
--R                                   3
--R               (96%pi + 1024)cos(1)  + (24%pi + 32)cos(1)
--R          *
--R             sin(1)
--R         + 
--R                    4            2                               4
--R           (96cos(1)  - 120cos(1) )log(4) + (- 96%pi - 512)cos(1)
--R         + 
--R                               2
--R           (120%pi + 512)cos(1)
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                        5            3
--R             (48cos(1)log(4) + 512cos(1)  - 384cos(1)  + (- 48%pi - 128)cos(1))
--R          *
--R             sin(1)
--R         + 
--R                      4           2                       6
--R           (- 96cos(1)  + 96cos(1)  + 3)log(4) - 512cos(1)
--R         + 
--R                               4                        2
--R           (96%pi + 1152)cos(1)  + (- 96%pi - 640)cos(1)  - 3%pi
--R      *
--R          +-+
--R         \|2
--R  /
--R                     3                                4             2  +-+
--R         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                      4             2
--R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 29

--S 30 of 224
in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole")
 

   (30)
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                                                                     +------+
                      3                              4            2  |sin(1)
           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
                                                                    \|cos(1)
         + 
                                        4            2      +-+
           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                       3                                       3
             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
          *
             sin(1)
         + 
                      4           2                    6
           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
         + 
                                 4                     2
           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                        5            3
           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
         + 
                    4           2                       6                      4
           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
         + 
                                2
           (- 32%pi - 128)cos(1)  - %pi
      *
          +-+
         \|2
  /
                     3                                4             2  +-+
         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                      4             2
       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (30)
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                                                                     +------+
--R                      3                              4            2  |sin(1)
--R           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
--R                                                                    \|cos(1)
--R         + 
--R                                        4            2      +-+
--R           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                       3                                       3
--R             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
--R          *
--R             sin(1)
--R         + 
--R                      4           2                    6
--R           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
--R         + 
--R                                 4                     2
--R           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                        5            3
--R           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
--R         + 
--R                    4           2                       6                      4
--R           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
--R         + 
--R                                2
--R           (- 32%pi - 128)cos(1)  - %pi
--R      *
--R          +-+
--R         \|2
--R  /
--R                     3                                4             2  +-+
--R         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                      4             2
--R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 30

--S 31 of 224
in1193a:=integrate(-sin(z)^2*cot(z-1), z= 0..1,"noPole")
 

   (31)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (31)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 31

--S 32 of 224
in1207:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1)
 

   (32)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (32)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 32

--S 33 of 224
in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (33)
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                                                                   +------+
                       3                            4           2  |sin(1)
           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
                                                                  \|cos(1)
         + 
                                     4           2      +-+
           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                                                                     +------+
                      3                              4            2  |sin(1)
           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
                                                                    \|cos(1)
         + 
                                        4            2      +-+
           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                                                                       +------+
                        3                              4            2  |sin(1)
           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
                                                                      \|cos(1)
         + 
                                      4            2      +-+
           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                       3                                       3
             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
          *
             sin(1)
         + 
                      4           2                    6
           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
         + 
                                 4                     2
           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                        5            3
           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
         + 
                    4           2                       6                      4
           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
         + 
                                2
           (- 32%pi - 128)cos(1)  - %pi
      *
          +-+
         \|2
  /
                     3                                4             2  +-+
         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
      *
          +------+
          |sin(1)
          |------
         \|cos(1)
     + 
                                      4             2
       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (33)
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                                                                   +------+
--R                       3                            4           2  |sin(1)
--R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
--R                                                                  \|cos(1)
--R         + 
--R                                     4           2      +-+
--R           (16cos(1)sin(1) - 32cos(1)  + 32cos(1)  + 1)\|2
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                                                                     +------+
--R                      3                              4            2  |sin(1)
--R           ((128cos(1)  + 32cos(1))sin(1) - 128cos(1)  + 160cos(1) ) |------
--R                                                                    \|cos(1)
--R         + 
--R                                        4            2      +-+
--R           (- 64cos(1)sin(1) + 128cos(1)  - 128cos(1)  - 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                                                                       +------+
--R                        3                              4            2  |sin(1)
--R           ((- 128cos(1)  - 32cos(1))sin(1) + 128cos(1)  - 160cos(1) ) |------
--R                                                                      \|cos(1)
--R         + 
--R                                      4            2      +-+
--R           (64cos(1)sin(1) - 128cos(1)  + 128cos(1)  + 4)\|2
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                       3                                       3
--R             ((32cos(1)  + 8cos(1))log(4) + (32%pi + 512)cos(1)  + 8%pi cos(1))
--R          *
--R             sin(1)
--R         + 
--R                      4           2                    6
--R           (- 32cos(1)  + 40cos(1) )log(4) - 1024cos(1)
--R         + 
--R                                 4                     2
--R           (- 32%pi + 1024)cos(1)  + (40%pi + 32)cos(1)
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                        5            3
--R           (- 16cos(1)log(4) + 512cos(1)  - 640cos(1)  - 16%pi cos(1))sin(1)
--R         + 
--R                    4           2                       6                      4
--R           (32cos(1)  - 32cos(1)  - 1)log(4) + 512cos(1)  + (32%pi - 384)cos(1)
--R         + 
--R                                2
--R           (- 32%pi - 128)cos(1)  - %pi
--R      *
--R          +-+
--R         \|2
--R  /
--R                     3                                4             2  +-+
--R         ((1024cos(1)  + 256cos(1))sin(1) - 1024cos(1)  + 1280cos(1) )\|2
--R      *
--R          +------+
--R          |sin(1)
--R          |------
--R         \|cos(1)
--R     + 
--R                                      4             2
--R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 33

--S 34 of 224
in1210a:=integrate(-sin(z)*cos(z)*cot(z-1), z= 0..1,"noPole")
 

   (34)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (34)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 34

--S 35 of 224
in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole")
 

   (35)
              1 2    1 2
         4cos(-) sin(-)
              2      2
      *
         log
                     1 4        1 2    1 2       1 4       2
                (sin(-)  - 2cos(-) sin(-)  + cos(-) )sin(1)
                     2          2      2         2
              + 
                      1           1 3        1 3          1
                (4cos(-)cos(1)sin(-)  - 4cos(-) cos(1)sin(-))sin(1)
                      2           2          2            2
              + 
                     1 2      2    1 2
                4cos(-) cos(1) sin(-)
                     2             2
           /
                  1 4      2        1 4             1 4
              cos(-) cos(1)  + 2cos(-) cos(1) + cos(-)
                  2                 2               2
     + 
                                1 2
                            sin(-)
              1 2    1 2        2
       - 4cos(-) sin(-) log(-------)
              2      2          1 2
                            cos(-)
                                2
     + 
                                                                2
              1 4        1 2    1 2       1 4            4cos(1)
       (- sin(-)  - 2cos(-) sin(-)  - cos(-) )log(---------------------)
              2          2      2         2             2
                                                  cos(1)  + 2cos(1) + 1
     + 
            1 4        1 2    1 2       1 4               4
       (sin(-)  - 2cos(-) sin(-)  + cos(-) )log(---------------------)
            2          2      2         2             2
                                                cos(1)  + 2cos(1) + 1
     + 
              1     1 3        1 3    1
       - 4cos(-)sin(-)  + 4cos(-) sin(-)
              2     2          2      2
  /
          1 4        1 4
     2sin(-)  - 2cos(-)
          2          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (35)
--R              1 2    1 2
--R         4cos(-) sin(-)
--R              2      2
--R      *
--R         log
--R                     1 4        1 2    1 2       1 4       2
--R                (sin(-)  - 2cos(-) sin(-)  + cos(-) )sin(1)
--R                     2          2      2         2
--R              + 
--R                      1           1 3        1 3          1
--R                (4cos(-)cos(1)sin(-)  - 4cos(-) cos(1)sin(-))sin(1)
--R                      2           2          2            2
--R              + 
--R                     1 2      2    1 2
--R                4cos(-) cos(1) sin(-)
--R                     2             2
--R           /
--R                  1 4      2        1 4             1 4
--R              cos(-) cos(1)  + 2cos(-) cos(1) + cos(-)
--R                  2                 2               2
--R     + 
--R                                1 2
--R                            sin(-)
--R              1 2    1 2        2
--R       - 4cos(-) sin(-) log(-------)
--R              2      2          1 2
--R                            cos(-)
--R                                2
--R     + 
--R                                                                2
--R              1 4        1 2    1 2       1 4            4cos(1)
--R       (- sin(-)  - 2cos(-) sin(-)  - cos(-) )log(---------------------)
--R              2          2      2         2             2
--R                                                  cos(1)  + 2cos(1) + 1
--R     + 
--R            1 4        1 2    1 2       1 4               4
--R       (sin(-)  - 2cos(-) sin(-)  + cos(-) )log(---------------------)
--R            2          2      2         2             2
--R                                                cos(1)  + 2cos(1) + 1
--R     + 
--R              1     1 3        1 3    1
--R       - 4cos(-)sin(-)  + 4cos(-) sin(-)
--R              2     2          2      2
--R  /
--R          1 4        1 4
--R     2sin(-)  - 2cos(-)
--R          2          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 35

--S 36 of 224
in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (36)
                  +------+
                  |sin(1)                        +-+
         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
                 \|cos(1)
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                  +------+
                  |sin(1)                        +-+
         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
                 \|cos(1)
      *
         log
                              2      2              3
                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
                  + 
                              2
                    - 16cos(1)
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                            3            2      2            3
              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
            + 
              4
     + 
                    +------+
                    |sin(1)                        +-+
         (- 8cos(1) |------  + (4sin(1) + 4cos(1))\|2 )
                   \|cos(1)
      *
                            +------+
                            |sin(1)                            2      +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
                           \|cos(1)
         atan(-----------------------------------------------------------)
                            +------+
                          2 |sin(1)                            2  +-+
                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                           \|cos(1)
     + 
                  +------+
                  |sin(1)                          +-+
         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
                 \|cos(1)
      *
                            +------+
                            |sin(1)                              2      +-+
              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                           \|cos(1)
         atan(-------------------------------------------------------------)
                          +------+
                        2 |sin(1)                              2      +-+
                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                         \|cos(1)
     + 
                  +------+
                  |sin(1)                          +-+
         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
                 \|cos(1)
      *
                            +------+
                            |sin(1)                            2  +-+
              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
                           \|cos(1)
         atan(-------------------------------------------------------)
                        +------+
                      2 |sin(1)                            2      +-+
               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                       \|cos(1)
     + 
                                                          +------+
                                                          |sin(1)
       (- 32sin(1) - 2cos(1)log(4) + (- 2%pi - 32)cos(1)) |------
                                                         \|cos(1)
     + 
                                                               +-+
       ((log(4) + %pi + 32)sin(1) + cos(1)log(4) + %pi cos(1))\|2
  /
                  +------+
              +-+ |sin(1)
     16cos(1)\|2  |------  - 16sin(1) - 16cos(1)
                 \|cos(1)
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (36)
--R                  +------+
--R                  |sin(1)                        +-+
--R         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                  +------+
--R                  |sin(1)                        +-+
--R         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R         log
--R                              2      2              3
--R                    - 64cos(1) sin(1)  + (- 64cos(1)  - 16cos(1))sin(1)
--R                  + 
--R                              2
--R                    - 16cos(1)
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                            3            2      2            3
--R              32cos(1)sin(1)  + 128cos(1) sin(1)  + (32cos(1)  + 32cos(1))sin(1)
--R            + 
--R              4
--R     + 
--R                    +------+
--R                    |sin(1)                        +-+
--R         (- 8cos(1) |------  + (4sin(1) + 4cos(1))\|2 )
--R                   \|cos(1)
--R      *
--R                            +------+
--R                            |sin(1)                            2      +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-----------------------------------------------------------)
--R                            +------+
--R                          2 |sin(1)                            2  +-+
--R                   2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                           \|cos(1)
--R     + 
--R                  +------+
--R                  |sin(1)                          +-+
--R         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R                            +------+
--R                            |sin(1)                              2      +-+
--R              4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------------)
--R                          +------+
--R                        2 |sin(1)                              2      +-+
--R                 4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                         \|cos(1)
--R     + 
--R                  +------+
--R                  |sin(1)                          +-+
--R         (8cos(1) |------  + (- 4sin(1) - 4cos(1))\|2 )
--R                 \|cos(1)
--R      *
--R                            +------+
--R                            |sin(1)                            2  +-+
--R              2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R                           \|cos(1)
--R         atan(-------------------------------------------------------)
--R                        +------+
--R                      2 |sin(1)                            2      +-+
--R               2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                       \|cos(1)
--R     + 
--R                                                          +------+
--R                                                          |sin(1)
--R       (- 32sin(1) - 2cos(1)log(4) + (- 2%pi - 32)cos(1)) |------
--R                                                         \|cos(1)
--R     + 
--R                                                               +-+
--R       ((log(4) + %pi + 32)sin(1) + cos(1)log(4) + %pi cos(1))\|2
--R  /
--R                  +------+
--R              +-+ |sin(1)
--R     16cos(1)\|2  |------  - 16sin(1) - 16cos(1)
--R                 \|cos(1)
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 36

--S 37 of 224
in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole")
 

   (37)
           +-+
         2\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                               +------+
                               |sin(1)                            2      +-+
                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
         +-+                  \|cos(1)
       4\|2 atan(-----------------------------------------------------------)
                               +------+
                             2 |sin(1)                            2  +-+
                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                              \|cos(1)
     + 
       -
              +-+
            4\|2
         *
                               +------+
                               |sin(1)                              2      +-+
                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                              \|cos(1)
            atan(-------------------------------------------------------------)
                             +------+
                           2 |sin(1)                              2      +-+
                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                            \|cos(1)
     + 
                                 +------+
                                 |sin(1)                            2  +-+
                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
           +-+                  \|cos(1)
       - 4\|2 atan(-------------------------------------------------------)
                             +------+
                           2 |sin(1)                            2      +-+
                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                            \|cos(1)
     + 
           +-+
       %pi\|2
  /
     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (37)
--R           +-+
--R         2\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                               +------+
--R                               |sin(1)                            2      +-+
--R                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R         +-+                  \|cos(1)
--R       4\|2 atan(-----------------------------------------------------------)
--R                               +------+
--R                             2 |sin(1)                            2  +-+
--R                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                              \|cos(1)
--R     + 
--R       -
--R              +-+
--R            4\|2
--R         *
--R                               +------+
--R                               |sin(1)                              2      +-+
--R                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                              \|cos(1)
--R            atan(-------------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                              2      +-+
--R                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R                                 +------+
--R                                 |sin(1)                            2  +-+
--R                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R           +-+                  \|cos(1)
--R       - 4\|2 atan(-------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                            2      +-+
--R                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R           +-+
--R       %pi\|2
--R  /
--R     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 37

--S 38 of 224
in1a:=integrate(log(abs(z^2-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 

   (38)  1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (38)  1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 38

--S 39 of 224
in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole")
 

   (39)
              %pi
         6cos(---)
               9
      *
         log
                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
                  2sin(---)  + 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
                        9                9       9            9        9
                + 
                    +-+    %pi 3    %pi 3           %pi 4          %pi 2
                  8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
                            9        9               9              9
                + 
                     +-+    %pi 5      +-+    %pi      %pi         %pi 6
                  (4\|3 cos(---)  + 4a\|3 cos(---))sin(---) - 2cos(---)
                             9                 9        9           9
                + 
                           %pi 2
                  - 2a cos(---)
                            9
             *
                 +-+
                \|a
            + 
                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
                   9            9        9             9              9
            + 
                 +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
              4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
                         9       9             9               9         9
            + 
                   +-+    %pi 3    %pi        %pi 8          %pi 4    2
              - 4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
                           9        9          9              9
     + 
              +-+    %pi         %pi
         (- 3\|3 sin(---) - 3cos(---))
                      9           9
      *
         log
                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
                  2sin(---)  - 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
                        9                9       9            9        9
                + 
                      +-+    %pi 3    %pi 3           %pi 4          %pi 2
                  - 8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
                              9        9               9              9
                + 
                       +-+    %pi 5      +-+    %pi      %pi         %pi 6
                  (- 4\|3 cos(---)  - 4a\|3 cos(---))sin(---) - 2cos(---)
                               9                 9        9           9
                + 
                           %pi 2
                  - 2a cos(---)
                            9
             *
                 +-+
                \|a
            + 
                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
                   9            9        9             9              9
            + 
                   +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
              - 4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
                           9       9             9               9         9
            + 
                 +-+    %pi 3    %pi        %pi 8          %pi 4    2
              4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
                         9        9          9              9
     + 
                5 +-+    10               +-+
       6a log(2a \|a  + a   + a) - 12log(\|a  + 1)
     + 
                       +-+    2
       3log((- 2a - 2)\|a  + a  + 3a + 1)
     + 
            +-+    %pi         %pi
         (3\|3 sin(---) - 3cos(---))
                    9           9
      *
         log
                         %pi 6        %pi 2    %pi 4
                  - 4sin(---)  - 4cos(---) sin(---)
                          9            9        9
                + 
                        %pi 4          %pi 2        %pi 6          %pi 2
                  (4cos(---)  - 4a)sin(---)  + 4cos(---)  + 4a cos(---)
                         9              9            9              9
             *
                 +-+
                \|a
            + 
                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 6a)sin(---)
                   9            9        9             9              9
            + 
                  %pi 6          %pi 2     %pi 2       %pi 8          %pi 4    2
            (4cos(---)  - 4a cos(---) )sin(---)  + cos(---)  + 6a cos(---)  + a
                   9              9         9           9              9
     + 
                %pi       +-+    %pi
         (12sin(---) - 12\|3 cos(---))
                 9                9
      *
               +-+    %pi 2        %pi     %pi     +-+    %pi 2
              \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
                       9            9       9              9
         atan(-------------------------------------------------)
                    %pi 2     +-+    %pi     %pi        %pi 2
                sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
                     9                9       9          9
     + 
                   +-+ +-+    +-+
         +-+     2\|3 \|a  - \|3
       6\|3 atan(----------------)
                    +-+
                  2\|a  - 2a + 1
     + 
                       +-+    %pi 2        %pi     %pi     +-+    %pi 2
                      \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
             %pi               9            9       9              9
       24sin(---)atan(-------------------------------------------------)
              9             %pi 2     +-+    %pi     %pi        %pi 2
                        sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
                             9                9       9          9
     + 
                                                %pi     %pi
                                           2cos(---)sin(---)
              %pi       +-+    %pi               9       9
       (12sin(---) + 12\|3 cos(---))atan(---------------------)
               9                9            %pi 2       %pi 2
                                         sin(---)  - cos(---)
                                              9           9
     + 
                  %pi       +-+    %pi
         (- 12sin(---) + 12\|3 cos(---))
                   9                9
      *
                 +-+    %pi 2        %pi     %pi     +-+    %pi 2
                \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
                         9            9       9              9
         atan(-----------------------------------------------------)
                +-+       %pi 2     +-+    %pi     %pi        %pi 2
              2\|a  + sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
                           9                9       9          9
     + 
                           +-+    %pi 2        %pi     %pi     +-+    %pi 2
                          \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
               %pi                 9            9       9              9
       - 24sin(---)atan(-----------------------------------------------------)
                9         +-+       %pi 2     +-+    %pi     %pi        %pi 2
                        2\|a  + sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
                                     9                9       9          9
     + 
                                                    %pi     %pi
                                               2cos(---)sin(---)
              %pi       +-+    %pi                   9       9
       (12sin(---) + 12\|3 cos(---))atan(----------------------------)
               9                9         +-+       %pi 2       %pi 2
                                         \|a  - sin(---)  + cos(---)
                                                     9           9
     + 
            +-+
       2%pi\|3  - 60a
  /
     12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (39)
--R              %pi
--R         6cos(---)
--R               9
--R      *
--R         log
--R                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
--R                  2sin(---)  + 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
--R                        9                9       9            9        9
--R                + 
--R                    +-+    %pi 3    %pi 3           %pi 4          %pi 2
--R                  8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
--R                            9        9               9              9
--R                + 
--R                     +-+    %pi 5      +-+    %pi      %pi         %pi 6
--R                  (4\|3 cos(---)  + 4a\|3 cos(---))sin(---) - 2cos(---)
--R                             9                 9        9           9
--R                + 
--R                           %pi 2
--R                  - 2a cos(---)
--R                            9
--R             *
--R                 +-+
--R                \|a
--R            + 
--R                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
--R              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
--R                   9            9        9             9              9
--R            + 
--R                 +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
--R              4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
--R                         9       9             9               9         9
--R            + 
--R                   +-+    %pi 3    %pi        %pi 8          %pi 4    2
--R              - 4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
--R                           9        9          9              9
--R     + 
--R              +-+    %pi         %pi
--R         (- 3\|3 sin(---) - 3cos(---))
--R                      9           9
--R      *
--R         log
--R                       %pi 6     +-+    %pi     %pi 5        %pi 2    %pi 4
--R                  2sin(---)  - 4\|3 cos(---)sin(---)  + 2cos(---) sin(---)
--R                        9                9       9            9        9
--R                + 
--R                      +-+    %pi 3    %pi 3           %pi 4          %pi 2
--R                  - 8\|3 cos(---) sin(---)  + (- 2cos(---)  + 2a)sin(---)
--R                              9        9               9              9
--R                + 
--R                       +-+    %pi 5      +-+    %pi      %pi         %pi 6
--R                  (- 4\|3 cos(---)  - 4a\|3 cos(---))sin(---) - 2cos(---)
--R                               9                 9        9           9
--R                + 
--R                           %pi 2
--R                  - 2a cos(---)
--R                            9
--R             *
--R                 +-+
--R                \|a
--R            + 
--R                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
--R              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 3a)sin(---)
--R                   9            9        9             9              9
--R            + 
--R                   +-+    %pi     %pi 3         %pi 6           %pi 2     %pi 2
--R              - 4a\|3 cos(---)sin(---)  + (4cos(---)  + 14a cos(---) )sin(---)
--R                           9       9             9               9         9
--R            + 
--R                 +-+    %pi 3    %pi        %pi 8          %pi 4    2
--R              4a\|3 cos(---) sin(---) + cos(---)  + 3a cos(---)  + a
--R                         9        9          9              9
--R     + 
--R                5 +-+    10               +-+
--R       6a log(2a \|a  + a   + a) - 12log(\|a  + 1)
--R     + 
--R                       +-+    2
--R       3log((- 2a - 2)\|a  + a  + 3a + 1)
--R     + 
--R            +-+    %pi         %pi
--R         (3\|3 sin(---) - 3cos(---))
--R                    9           9
--R      *
--R         log
--R                         %pi 6        %pi 2    %pi 4
--R                  - 4sin(---)  - 4cos(---) sin(---)
--R                          9            9        9
--R                + 
--R                        %pi 4          %pi 2        %pi 6          %pi 2
--R                  (4cos(---)  - 4a)sin(---)  + 4cos(---)  + 4a cos(---)
--R                         9              9            9              9
--R             *
--R                 +-+
--R                \|a
--R            + 
--R                  %pi 8        %pi 2    %pi 6         %pi 4          %pi 4
--R              sin(---)  + 4cos(---) sin(---)  + (6cos(---)  + 6a)sin(---)
--R                   9            9        9             9              9
--R            + 
--R                  %pi 6          %pi 2     %pi 2       %pi 8          %pi 4    2
--R            (4cos(---)  - 4a cos(---) )sin(---)  + cos(---)  + 6a cos(---)  + a
--R                   9              9         9           9              9
--R     + 
--R                %pi       +-+    %pi
--R         (12sin(---) - 12\|3 cos(---))
--R                 9                9
--R      *
--R               +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R              \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
--R                       9            9       9              9
--R         atan(-------------------------------------------------)
--R                    %pi 2     +-+    %pi     %pi        %pi 2
--R                sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
--R                     9                9       9          9
--R     + 
--R                   +-+ +-+    +-+
--R         +-+     2\|3 \|a  - \|3
--R       6\|3 atan(----------------)
--R                    +-+
--R                  2\|a  - 2a + 1
--R     + 
--R                       +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R                      \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
--R             %pi               9            9       9              9
--R       24sin(---)atan(-------------------------------------------------)
--R              9             %pi 2     +-+    %pi     %pi        %pi 2
--R                        sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
--R                             9                9       9          9
--R     + 
--R                                                %pi     %pi
--R                                           2cos(---)sin(---)
--R              %pi       +-+    %pi               9       9
--R       (12sin(---) + 12\|3 cos(---))atan(---------------------)
--R               9                9            %pi 2       %pi 2
--R                                         sin(---)  - cos(---)
--R                                              9           9
--R     + 
--R                  %pi       +-+    %pi
--R         (- 12sin(---) + 12\|3 cos(---))
--R                   9                9
--R      *
--R                 +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R                \|3 sin(---)  + 2cos(---)sin(---) - \|3 cos(---)
--R                         9            9       9              9
--R         atan(-----------------------------------------------------)
--R                +-+       %pi 2     +-+    %pi     %pi        %pi 2
--R              2\|a  + sin(---)  - 2\|3 cos(---)sin(---) - cos(---)
--R                           9                9       9          9
--R     + 
--R                           +-+    %pi 2        %pi     %pi     +-+    %pi 2
--R                          \|3 sin(---)  - 2cos(---)sin(---) - \|3 cos(---)
--R               %pi                 9            9       9              9
--R       - 24sin(---)atan(-----------------------------------------------------)
--R                9         +-+       %pi 2     +-+    %pi     %pi        %pi 2
--R                        2\|a  + sin(---)  + 2\|3 cos(---)sin(---) - cos(---)
--R                                     9                9       9          9
--R     + 
--R                                                    %pi     %pi
--R                                               2cos(---)sin(---)
--R              %pi       +-+    %pi                   9       9
--R       (12sin(---) + 12\|3 cos(---))atan(----------------------------)
--R               9                9         +-+       %pi 2       %pi 2
--R                                         \|a  - sin(---)  + cos(---)
--R                                                     9           9
--R     + 
--R            +-+
--R       2%pi\|3  - 60a
--R  /
--R     12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 39

--S 40 of 224
in20a:=integrate(log(sin(z)^2+cos(z)^2), z= 0..1,"noPole")
 

   (40)  0
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (40)  0
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 40

--S 41 of 224
in126a:=integrate(atan(1/cot(z)), z= 0..2*%pi,"noPole")
 

             2
   (41)  2%pi
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R             2
--R   (41)  2%pi
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 41

--S 42 of 224
in128a:=integrate(atan(sqrt(1-cos(z)^2)/(1+cos(z))), z= 0..1,"noPole")
 

         1
   (42)  -
         4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         1
--R   (42)  -
--R         4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 42

--S 43 of 224
in134a:=integrate(log(exp(z)), z= -%i..%i)
 

   (43)  0
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (43)  0
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 43

--S 44 of 224
in1221a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole")
 

         log(4)
   (44)  ------
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(4)
--R   (44)  ------
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 44

--S 45 of 224
in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (45)
           +-+
         2\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                               +------+
                               |sin(1)                            2      +-+
                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
         +-+                  \|cos(1)
       4\|2 atan(-----------------------------------------------------------)
                               +------+
                             2 |sin(1)                            2  +-+
                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                              \|cos(1)
     + 
       -
              +-+
            4\|2
         *
                               +------+
                               |sin(1)                              2      +-+
                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                              \|cos(1)
            atan(-------------------------------------------------------------)
                             +------+
                           2 |sin(1)                              2      +-+
                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                            \|cos(1)
     + 
                                 +------+
                                 |sin(1)                            2  +-+
                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
           +-+                  \|cos(1)
       - 4\|2 atan(-------------------------------------------------------)
                             +------+
                           2 |sin(1)                            2      +-+
                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                            \|cos(1)
     + 
           +-+
       %pi\|2
  /
     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (45)
--R           +-+
--R         2\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                               +------+
--R                               |sin(1)                            2      +-+
--R                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R         +-+                  \|cos(1)
--R       4\|2 atan(-----------------------------------------------------------)
--R                               +------+
--R                             2 |sin(1)                            2  +-+
--R                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                              \|cos(1)
--R     + 
--R       -
--R              +-+
--R            4\|2
--R         *
--R                               +------+
--R                               |sin(1)                              2      +-+
--R                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                              \|cos(1)
--R            atan(-------------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                              2      +-+
--R                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R                                 +------+
--R                                 |sin(1)                            2  +-+
--R                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R           +-+                  \|cos(1)
--R       - 4\|2 atan(-------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                            2      +-+
--R                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R           +-+
--R       %pi\|2
--R  /
--R     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 45

--S 46 of 224
in1241a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole")
 

         log(4)
   (46)  ------
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(4)
--R   (46)  ------
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 46

--S 47 of 224
in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 

   (47)
           +-+
         2\|2
      *
         log
                           2      2              3                           2
                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
             *
                     +------+
                 +-+ |sin(1)
                \|2  |------
                    \|cos(1)
            + 
                         3           2      2           3
            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
     + 
                               +------+
                               |sin(1)                            2      +-+
                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
         +-+                  \|cos(1)
       4\|2 atan(-----------------------------------------------------------)
                               +------+
                             2 |sin(1)                            2  +-+
                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
                              \|cos(1)
     + 
       -
              +-+
            4\|2
         *
                               +------+
                               |sin(1)                              2      +-+
                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
                              \|cos(1)
            atan(-------------------------------------------------------------)
                             +------+
                           2 |sin(1)                              2      +-+
                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
                            \|cos(1)
     + 
                                 +------+
                                 |sin(1)                            2  +-+
                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
           +-+                  \|cos(1)
       - 4\|2 atan(-------------------------------------------------------)
                             +------+
                           2 |sin(1)                            2      +-+
                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
                            \|cos(1)
     + 
           +-+
       %pi\|2
  /
     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (47)
--R           +-+
--R         2\|2
--R      *
--R         log
--R                           2      2              3                           2
--R                (- 16cos(1) sin(1)  + (- 16cos(1)  - 4cos(1))sin(1) - 4cos(1) )
--R             *
--R                     +------+
--R                 +-+ |sin(1)
--R                \|2  |------
--R                    \|cos(1)
--R            + 
--R                         3           2      2           3
--R            8cos(1)sin(1)  + 32cos(1) sin(1)  + (8cos(1)  + 8cos(1))sin(1) + 1
--R     + 
--R                               +------+
--R                               |sin(1)                            2      +-+
--R                 2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1)  - 1)\|2
--R         +-+                  \|cos(1)
--R       4\|2 atan(-----------------------------------------------------------)
--R                               +------+
--R                             2 |sin(1)                            2  +-+
--R                      2cos(1)  |------  + (- cos(1)sin(1) - cos(1) )\|2
--R                              \|cos(1)
--R     + 
--R       -
--R              +-+
--R            4\|2
--R         *
--R                               +------+
--R                               |sin(1)                              2      +-+
--R                 4cos(1)sin(1) |------  + (- 2cos(1)sin(1) + 2cos(1)  - 1)\|2
--R                              \|cos(1)
--R            atan(-------------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                              2      +-+
--R                    4cos(1)  |------  + (- 2cos(1)sin(1) - 2cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R                                 +------+
--R                                 |sin(1)                            2  +-+
--R                   2cos(1)sin(1) |------  + (- cos(1)sin(1) + cos(1) )\|2
--R           +-+                  \|cos(1)
--R       - 4\|2 atan(-------------------------------------------------------)
--R                             +------+
--R                           2 |sin(1)                            2      +-+
--R                    2cos(1)  |------  + (- cos(1)sin(1) - cos(1)  + 1)\|2
--R                            \|cos(1)
--R     + 
--R           +-+
--R       %pi\|2
--R  /
--R     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 47

--S 48 of 224
in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole")
 

   (48)
                  2         2
         (- sin(1)  + cos(1)  + 2cos(1) + 1)
      *
         log
                              2                                   2
                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
               *
                   +-+
                  \|3
              + 
                      2                                     2
              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
           /
                     2
              4sin(1)  - 4sin(1) + 1
     + 
                2         2
         (sin(1)  - cos(1)  - 2cos(1) - 1)
      *
         log
                              2                                     2
                    - 12sin(1)  + (- 42cos(1) - 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
               *
                   +-+
                  \|3
              + 
                        2                                   2
                21sin(1)  + (72cos(1) + 84)sin(1) + 63cos(1)  + 144cos(1) + 84
           /
                     2
              4sin(1)  + 4sin(1) + 1
     + 
                             +-+
       (- 4cos(1) - 4)sin(1)\|3
  /
             2          2                +-+
     (3sin(1)  - 3cos(1)  - 6cos(1) - 3)\|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (48)
--R                  2         2
--R         (- sin(1)  + cos(1)  + 2cos(1) + 1)
--R      *
--R         log
--R                              2                                   2
--R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R               *
--R                   +-+
--R                  \|3
--R              + 
--R                      2                                     2
--R              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R           /
--R                     2
--R              4sin(1)  - 4sin(1) + 1
--R     + 
--R                2         2
--R         (sin(1)  - cos(1)  - 2cos(1) - 1)
--R      *
--R         log
--R                              2                                     2
--R                    - 12sin(1)  + (- 42cos(1) - 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R               *
--R                   +-+
--R                  \|3
--R              + 
--R                        2                                   2
--R                21sin(1)  + (72cos(1) + 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R           /
--R                     2
--R              4sin(1)  + 4sin(1) + 1
--R     + 
--R                             +-+
--R       (- 4cos(1) - 4)sin(1)\|3
--R  /
--R             2          2                +-+
--R     (3sin(1)  - 3cos(1)  - 6cos(1) - 3)\|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 48

--S 49 of 224
in1273a:=integrate((1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole")
 

   (49)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (49)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 49

--S 50 of 224
in1274a:=integrate(1/(1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole")
 

   (50)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (50)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 50

--S 51 of 224
in1284a:=integrate(log(1+2^(1/2)/z^(1/4)-1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (51)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (51)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 51

--S 52 of 224
in1314a:=integrate(log(1-z)*atanh(z^(1/2)), z= 0..1,"noPole")
 

         log(16) - 6
   (52)  -----------
              2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(16) - 6
--R   (52)  -----------
--R              2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 52

--S 53 of 224
in1359a:=integrate((%i*z)^(1/2)*(-%i*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole")
 

   (53)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (53)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 53

--S 54 of 224
in1376a:=integrate(z*acoth(z^(1/2)), z= 0..1,"noPole")
 

         2
   (54)  -
         3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         2
--R   (54)  -
--R         3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 54

--S 55 of 224
in1377a:=integrate(z*acoth(1-z), z= 0..1,"noPole")
 

         log(4) - 1
   (55)  ----------
              2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         log(4) - 1
--R   (55)  ----------
--R              2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 55

--S 56 of 224
in1378a:=integrate(z*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole")
 

         - 3log(4) + 5
   (56)  -------------
               3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         - 3log(4) + 5
--R   (56)  -------------
--R               3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 56

--S 57 of 224
in1392a:=integrate(acoth(z^(1/2)), z= 0..1,"noPole")
 

   (57)  1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (57)  1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 57

--S 58 of 224
in1397a:=integrate(1/(-1+z^(1/2))^(1/2), z= 1..2,"noPole")
 

                     +--------+
            +-+      | +-+
         (4\|2  + 8)\|\|2  - 1
   (58)  ----------------------
                    3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                     +--------+
--R            +-+      | +-+
--R         (4\|2  + 8)\|\|2  - 1
--R   (58)  ----------------------
--R                    3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 58

--S 59 of 224
in1398a:=integrate(acoth(1/z), z= 1..2,"noPole")
 

         3log(9) - 2log(4)
   (59)  -----------------
                 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         3log(9) - 2log(4)
--R   (59)  -----------------
--R                 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 59

--S 60 of 224
in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole")
 

                 +-+
             - 2\|2  - 3      +-+
         log(-----------) + 4\|2  - 4
                +-+
              2\|2  - 3
   (60)  ----------------------------
                       4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 +-+
--R             - 2\|2  - 3      +-+
--R         log(-----------) + 4\|2  - 4
--R                +-+
--R              2\|2  - 3
--R   (60)  ----------------------------
--R                       4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 60

--S 61 of 224
in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole")
 

   (61)
         4+-+    %pi
         \|2 cos(---)
                  8
      *
         log
                   %pi 4     +-+4+-+3    %pi 3         %pi 2     4+-+2     %pi 2
              2sin(---)  + 4\|2 \|2  sin(---)  + (4cos(---)  + 12\|2  )sin(---)
                    8                     8             8                   8
            + 
                 +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
              (4\|2 \|2  cos(---)  + 8\|2 \|2 )sin(---) + 2cos(---)
                              8                     8           8
            + 
               4+-+2    %pi 2
              4\|2  cos(---)  + 4
                         8
     + 
       -
            4+-+    %pi
            \|2 cos(---)
                     8
         *
            log
                      %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
                 2sin(---)  + 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
                       8                 8             8                  8
               + 
                   4+-+3    %pi 2    4+-+     %pi         %pi 4
                 (4\|2  cos(---)  + 4\|2 )sin(---) + 2cos(---)
                             8                 8           8
               + 
                  4+-+2    %pi 2
                 2\|2  cos(---)  + 1
                            8
     + 
         4+-+    %pi
         \|2 cos(---)
                  8
      *
         log
                   %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
              2sin(---)  - 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
                    8                 8             8                  8
            + 
                  4+-+3    %pi 2    4+-+     %pi         %pi 4    4+-+2    %pi 2
              (- 4\|2  cos(---)  - 4\|2 )sin(---) + 2cos(---)  + 2\|2  cos(---)
                            8                 8           8                 8
            + 
              1
     + 
       -
            4+-+    %pi
            \|2 cos(---)
                     8
         *
            log
                      %pi 4     +-+4+-+3    %pi 3
                 2sin(---)  - 4\|2 \|2  sin(---)
                       8                     8
               + 
                       %pi 2     4+-+2     %pi 2
                 (4cos(---)  + 12\|2  )sin(---)
                        8                   8
               + 
                      +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
                 (- 4\|2 \|2  cos(---)  - 8\|2 \|2 )sin(---) + 2cos(---)
                                   8                     8           8
               + 
                  4+-+2    %pi 2
                 4\|2  cos(---)  + 4
                            8
     + 
                               4+-+    %pi
                               \|2 cos(---)
          4+-+    %pi                   8
       - 4\|2 sin(---)atan(-------------------)
                   8       4+-+    %pi     +-+
                           \|2 sin(---) - \|2
                                    8
     + 
                           4+-+    %pi                           4+-+    %pi
                           \|2 cos(---)                          \|2 cos(---)
        4+-+    %pi                 8         4+-+    %pi                 8
       4\|2 sin(---)atan(----------------) - 4\|2 sin(---)atan(----------------)
                 8       4+-+    %pi                   8       4+-+    %pi
                         \|2 sin(---) - 1                      \|2 sin(---) + 1
                                  8                                     8
     + 
                             4+-+    %pi
                             \|2 cos(---)
        4+-+    %pi                   8
       4\|2 sin(---)atan(-------------------)
                 8       4+-+    %pi     +-+
                         \|2 sin(---) + \|2
                                  8
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (61)
--R         4+-+    %pi
--R         \|2 cos(---)
--R                  8
--R      *
--R         log
--R                   %pi 4     +-+4+-+3    %pi 3         %pi 2     4+-+2     %pi 2
--R              2sin(---)  + 4\|2 \|2  sin(---)  + (4cos(---)  + 12\|2  )sin(---)
--R                    8                     8             8                   8
--R            + 
--R                 +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
--R              (4\|2 \|2  cos(---)  + 8\|2 \|2 )sin(---) + 2cos(---)
--R                              8                     8           8
--R            + 
--R               4+-+2    %pi 2
--R              4\|2  cos(---)  + 4
--R                         8
--R     + 
--R       -
--R            4+-+    %pi
--R            \|2 cos(---)
--R                     8
--R         *
--R            log
--R                      %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
--R                 2sin(---)  + 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
--R                       8                 8             8                  8
--R               + 
--R                   4+-+3    %pi 2    4+-+     %pi         %pi 4
--R                 (4\|2  cos(---)  + 4\|2 )sin(---) + 2cos(---)
--R                             8                 8           8
--R               + 
--R                  4+-+2    %pi 2
--R                 2\|2  cos(---)  + 1
--R                            8
--R     + 
--R         4+-+    %pi
--R         \|2 cos(---)
--R                  8
--R      *
--R         log
--R                   %pi 4    4+-+3    %pi 3         %pi 2    4+-+2     %pi 2
--R              2sin(---)  - 4\|2  sin(---)  + (4cos(---)  + 6\|2  )sin(---)
--R                    8                 8             8                  8
--R            + 
--R                  4+-+3    %pi 2    4+-+     %pi         %pi 4    4+-+2    %pi 2
--R              (- 4\|2  cos(---)  - 4\|2 )sin(---) + 2cos(---)  + 2\|2  cos(---)
--R                            8                 8           8                 8
--R            + 
--R              1
--R     + 
--R       -
--R            4+-+    %pi
--R            \|2 cos(---)
--R                     8
--R         *
--R            log
--R                      %pi 4     +-+4+-+3    %pi 3
--R                 2sin(---)  - 4\|2 \|2  sin(---)
--R                       8                     8
--R               + 
--R                       %pi 2     4+-+2     %pi 2
--R                 (4cos(---)  + 12\|2  )sin(---)
--R                        8                   8
--R               + 
--R                      +-+4+-+3    %pi 2     +-+4+-+     %pi         %pi 4
--R                 (- 4\|2 \|2  cos(---)  - 8\|2 \|2 )sin(---) + 2cos(---)
--R                                   8                     8           8
--R               + 
--R                  4+-+2    %pi 2
--R                 4\|2  cos(---)  + 4
--R                            8
--R     + 
--R                               4+-+    %pi
--R                               \|2 cos(---)
--R          4+-+    %pi                   8
--R       - 4\|2 sin(---)atan(-------------------)
--R                   8       4+-+    %pi     +-+
--R                           \|2 sin(---) - \|2
--R                                    8
--R     + 
--R                           4+-+    %pi                           4+-+    %pi
--R                           \|2 cos(---)                          \|2 cos(---)
--R        4+-+    %pi                 8         4+-+    %pi                 8
--R       4\|2 sin(---)atan(----------------) - 4\|2 sin(---)atan(----------------)
--R                 8       4+-+    %pi                   8       4+-+    %pi
--R                         \|2 sin(---) - 1                      \|2 sin(---) + 1
--R                                  8                                     8
--R     + 
--R                             4+-+    %pi
--R                             \|2 cos(---)
--R        4+-+    %pi                   8
--R       4\|2 sin(---)atan(-------------------)
--R                 8       4+-+    %pi     +-+
--R                         \|2 sin(---) + \|2
--R                                  8
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 61

--S 62 of 224
in144:=integrate(1, z= %i*infinity..%plusInfinity)
 

   (62)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (62)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 62

--S 63 of 224
in146a:=integrate(csc(z), z= 1-%i..1+%i,"noPole")
 

   (63)
                            2                                      2
                 sin(1 + %i)                            sin(1 - %i)
   log(-------------------------------) - log(-------------------------------)
                  2                                      2
       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
   ---------------------------------------------------------------------------
                                        2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (63)
--R                            2                                      2
--R                 sin(1 + %i)                            sin(1 - %i)
--R   log(-------------------------------) - log(-------------------------------)
--R                  2                                      2
--R       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
--R   ---------------------------------------------------------------------------
--R                                        2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 63

--S 64 of 224
in148:=integrate(min(1,z), z= 0..2)
 

   (64)  2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (64)  2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 64

--S 65 of 224
in156a:=integrate(z^(2/3), z= 1..10,"noPole")
 

           3+--+2
         30\|10   - 3
   (65)  ------------
               5
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           3+--+2
--R         30\|10   - 3
--R   (65)  ------------
--R               5
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 65

--S 66 of 224
in1425a:=integrate(-(z^2+%i*z+3)/(z^2+%i*z+2), z= 0..%plusInfinity,"noPole")
 

   (66)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (66)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 66

--S 67 of 224
in1426a:=integrate(-%i/(1+%i*z^3)*z^3, z= 0..%plusInfinity,"noPole")
 

   (67)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (67)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 67

--S 68 of 224
in1428a:=integrate(-%i/(1+%i*z)*z, z= 0..%plusInfinity,"noPole")
 

   (68)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (68)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 68

--S 69 of 224
in1432:=integrate(-(z+%i)*(-1+1/(z+%i)), z= 0..%plusInfinity)
 

   (69)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (69)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 69

--S 70 of 224
in1434a:=integrate(-(1+(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (70)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (70)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 70

--S 71 of 224
in1440a:=integrate((1-(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (71)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (71)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 71

--S 72 of 224
in1460:=integrate(z^2+%i*z+3, z= 0..%plusInfinity)
 

   (72)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (72)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 72

--S 73 of 224
in1464a:=integrate(1+1/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (73)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (73)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 73

--S 74 of 224
in2045:=integrate(atan(1/tan(z)), z= 0..2*%pi,"noPole")
 

               2
   (74)  - 3%pi
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R               2
--R   (74)  - 3%pi
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 74

--S 75 of 224
in1502a:=integrate(log(z)^2*log(-z), z= 0..%plusInfinity,"noPole")
 

   (75)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (75)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 75

--S 76 of 224
in1512a:=integrate(log(z)*(1/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole")
 

   (76)  [ + infinity, + infinity]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (76)  [ + infinity, + infinity]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 76

--S 77 of 224
in1513a:=integrate(log(z)*(1/(z+%i))^(1/2), z= 1..%plusInfinity,"noPole")
 

   (77)  [ + infinity, + infinity]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (77)  [ + infinity, + infinity]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 77

--S 78 of 224
in1514a:=integrate(log(z)/(%i/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole")
 

   (78)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (78)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 78

--S 79 of 224
in161:=integrate((-z^2)^(1/3), z)
 

            +----+
           3|   2
         3z\|- z
   (79)  ---------
             5
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +----+
--R           3|   2
--R         3z\|- z
--R   (79)  ---------
--R             5
--R                                          Type: Union(Expression Integer,...)
--E 79

--S 80 of 224
in179:=integrate(1/(1+(3*z+1)^2), z)
 

         atan(3z + 1)
   (80)  ------------
               3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         atan(3z + 1)
--R   (80)  ------------
--R               3
--R                                          Type: Union(Expression Integer,...)
--E 80

--S 81 of 224
in1636a:=integrate(-z/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (81)
   [ + infinity,

                               +------+                           +----+
           +---------+        \|1 - %i        +---------+       2\|- %i
         3\|- 4 + 4%i log(- ------------) - 3\|- 4 + 4%i atan(------------)
                             +---------+                       +---------+
                            \|- 4 + 4%i                       \|- 4 + 4%i
       + 
                     +------+             +----+
         (- 8 + 2%i)\|1 - %i  + (6 - 2%i)\|- %i
    /
       3
     ]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (81)
--R   [ + infinity,
--R
--R                               +------+                           +----+
--R           +---------+        \|1 - %i        +---------+       2\|- %i
--R         3\|- 4 + 4%i log(- ------------) - 3\|- 4 + 4%i atan(------------)
--R                             +---------+                       +---------+
--R                            \|- 4 + 4%i                       \|- 4 + 4%i
--R       + 
--R                     +------+             +----+
--R         (- 8 + 2%i)\|1 - %i  + (6 - 2%i)\|- %i
--R    /
--R       3
--R     ]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 81

--S 82 of 224
in1639a:=integrate(-z/(z-1)/(1-%i*z^2)^(1/2), z= 0..1,"noPole")
 

   (82)
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  + 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                        +------+         +-+               +----+ +------+
                    (16\|1 - %i  - 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
                  + 
                                  +----+
                    (- 16 + 16%i)\|- %i
               *
                   +------------------------+
                   |          +-+     +----+
                   |(1 + 3%i)\|2  + 2\|- %i
                   |------------------------
                   |           +-+
                  \|          \|2
              + 
                      +------+              +-+               +----+ +------+
                (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  + 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                                                 +------------------------+
                                                 |          +-+     +----+
                                +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
                   ((16 - 16%i)\|2  + 32\|- %i ) |------------------------
                                                 |           +-+
                                                \|          \|2
                 + 
                               +-+               +----+
                   (32 - 32%i)\|2  + (32 + 32%i)\|- %i
              /
                  +-+
                 \|2
     + 
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  - 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                        +------+         +-+                 +----+ +------+
                    (16\|1 - %i  - 16%i)\|2  + (- 48 + 16%i)\|- %i \|1 - %i
                  + 
                                +----+
                    (16 - 16%i)\|- %i
               *
                   +------------------------+
                   |          +-+     +----+
                   |(1 + 3%i)\|2  - 2\|- %i
                   |------------------------
                   |           +-+
                  \|          \|2
              + 
                      +------+              +-+                 +----+ +------+
                (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  - 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                                                 +------------------------+
                                                 |          +-+     +----+
                                +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
                   ((16 - 16%i)\|2  - 32\|- %i ) |------------------------
                                                 |           +-+
                                                \|          \|2
                 + 
                               +-+                 +----+
                   (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
              /
                  +-+
                 \|2
     + 
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  - 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                                                +------------------------+
                                                |          +-+     +----+
                               +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
                ((- 16 + 16%i)\|2  + 32\|- %i ) |------------------------
                                                |           +-+
                                               \|          \|2
              + 
                            +-+                 +----+
                (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  - 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                             +------+         +-+               +----+ +------+
                       (- 16\|1 - %i  + 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
                     + 
                                     +----+
                       (- 16 + 16%i)\|- %i
                  *
                      +------------------------+
                      |          +-+     +----+
                      |(1 + 3%i)\|2  - 2\|- %i
                      |------------------------
                      |           +-+
                     \|          \|2
                 + 
                       +------+              +-+                 +----+ +------+
                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
              /
                  +-+
                 \|2
     + 
          +------------------------+
          |          +-+     +----+
          |(1 + 3%i)\|2  + 2\|- %i
          |------------------------
          |           +-+
         \|          \|2
      *
         log
                                                +------------------------+
                                                |          +-+     +----+
                               +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
                ((- 16 + 16%i)\|2  - 32\|- %i ) |------------------------
                                                |           +-+
                                               \|          \|2
              + 
                            +-+               +----+
                (32 - 32%i)\|2  + (32 + 32%i)\|- %i
           /
               +-+
              \|2
     + 
       -
             +------------------------+
             |          +-+     +----+
             |(1 + 3%i)\|2  + 2\|- %i
             |------------------------
             |           +-+
            \|          \|2
         *
            log
                             +------+         +-+
                       (- 16\|1 - %i  + 16%i)\|2
                     + 
                                     +----+ +------+               +----+
                       (- 48 + 16%i)\|- %i \|1 - %i  + (16 - 16%i)\|- %i
                  *
                      +------------------------+
                      |          +-+     +----+
                      |(1 + 3%i)\|2  + 2\|- %i
                      |------------------------
                      |           +-+
                     \|          \|2
                 + 
                       +------+              +-+               +----+ +------+
                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
              /
                  +-+
                 \|2
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (82)
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  + 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                        +------+         +-+               +----+ +------+
--R                    (16\|1 - %i  - 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
--R                  + 
--R                                  +----+
--R                    (- 16 + 16%i)\|- %i
--R               *
--R                   +------------------------+
--R                   |          +-+     +----+
--R                   |(1 + 3%i)\|2  + 2\|- %i
--R                   |------------------------
--R                   |           +-+
--R                  \|          \|2
--R              + 
--R                      +------+              +-+               +----+ +------+
--R                (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  + 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                                                 +------------------------+
--R                                                 |          +-+     +----+
--R                                +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
--R                   ((16 - 16%i)\|2  + 32\|- %i ) |------------------------
--R                                                 |           +-+
--R                                                \|          \|2
--R                 + 
--R                               +-+               +----+
--R                   (32 - 32%i)\|2  + (32 + 32%i)\|- %i
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  - 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                        +------+         +-+                 +----+ +------+
--R                    (16\|1 - %i  - 16%i)\|2  + (- 48 + 16%i)\|- %i \|1 - %i
--R                  + 
--R                                +----+
--R                    (16 - 16%i)\|- %i
--R               *
--R                   +------------------------+
--R                   |          +-+     +----+
--R                   |(1 + 3%i)\|2  - 2\|- %i
--R                   |------------------------
--R                   |           +-+
--R                  \|          \|2
--R              + 
--R                      +------+              +-+                 +----+ +------+
--R                (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  - 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                                                 +------------------------+
--R                                                 |          +-+     +----+
--R                                +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
--R                   ((16 - 16%i)\|2  - 32\|- %i ) |------------------------
--R                                                 |           +-+
--R                                                \|          \|2
--R                 + 
--R                               +-+                 +----+
--R                   (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  - 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                                                +------------------------+
--R                                                |          +-+     +----+
--R                               +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
--R                ((- 16 + 16%i)\|2  + 32\|- %i ) |------------------------
--R                                                |           +-+
--R                                               \|          \|2
--R              + 
--R                            +-+                 +----+
--R                (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  - 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                             +------+         +-+               +----+ +------+
--R                       (- 16\|1 - %i  + 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
--R                     + 
--R                                     +----+
--R                       (- 16 + 16%i)\|- %i
--R                  *
--R                      +------------------------+
--R                      |          +-+     +----+
--R                      |(1 + 3%i)\|2  - 2\|- %i
--R                      |------------------------
--R                      |           +-+
--R                     \|          \|2
--R                 + 
--R                       +------+              +-+                 +----+ +------+
--R                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +------------------------+
--R          |          +-+     +----+
--R          |(1 + 3%i)\|2  + 2\|- %i
--R          |------------------------
--R          |           +-+
--R         \|          \|2
--R      *
--R         log
--R                                                +------------------------+
--R                                                |          +-+     +----+
--R                               +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
--R                ((- 16 + 16%i)\|2  - 32\|- %i ) |------------------------
--R                                                |           +-+
--R                                               \|          \|2
--R              + 
--R                            +-+               +----+
--R                (32 - 32%i)\|2  + (32 + 32%i)\|- %i
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +------------------------+
--R             |          +-+     +----+
--R             |(1 + 3%i)\|2  + 2\|- %i
--R             |------------------------
--R             |           +-+
--R            \|          \|2
--R         *
--R            log
--R                             +------+         +-+
--R                       (- 16\|1 - %i  + 16%i)\|2
--R                     + 
--R                                     +----+ +------+               +----+
--R                       (- 48 + 16%i)\|- %i \|1 - %i  + (16 - 16%i)\|- %i
--R                  *
--R                      +------------------------+
--R                      |          +-+     +----+
--R                      |(1 + 3%i)\|2  + 2\|- %i
--R                      |------------------------
--R                      |           +-+
--R                     \|          \|2
--R                 + 
--R                       +------+              +-+               +----+ +------+
--R                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
--R              /
--R                  +-+
--R                 \|2
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 82

--S 83 of 224
in1712a:=integrate(-log(-z)*(-%i*z)^(1/2), z= 0..1,"noPole")
 

           +----+
         4\|- %i
   (83)  --------
             9
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R           +----+
--R         4\|- %i
--R   (83)  --------
--R             9
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 83

--S 84 of 224
in1720a:=integrate(-z^2/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (84)
            +------+              +------+
            |   1                 |   1    +------+
       - %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
           \|1 + %i              \|1 + %i
     + 
        +------+              +------+
        |  %i                 |  %i    +------+
        |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
       \|1 + %i              \|1 + %i
     + 
          +------+                     +------+
          |   1                 +----+ |   1
       %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
         \|1 + %i                     \|1 + %i
     + 
          +------+              +------+
          |  %i                 |  %i    +----+
       -  |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
         \|1 + %i              \|1 + %i
     + 
        +------+                +------+
        |  %i                   |  %i    +----+
        |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
       \|1 + %i                \|1 + %i
     + 
            +------+                       +------+
            |   1                   +----+ |   1
       - %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
           \|1 + %i                       \|1 + %i
     + 
          +------+                +------+
          |  %i                   |  %i    +------+
       -  |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
         \|1 + %i                \|1 + %i
     + 
        +------+                +------+
        |   1                   |   1    +------+            +------+     +----+
     %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i) - 8\|1 - %i  + 8\|- %i
       \|1 + %i                \|1 + %i
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (84)
--R            +------+              +------+
--R            |   1                 |   1    +------+
--R       - %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
--R           \|1 + %i              \|1 + %i
--R     + 
--R        +------+              +------+
--R        |  %i                 |  %i    +------+
--R        |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
--R       \|1 + %i              \|1 + %i
--R     + 
--R          +------+                     +------+
--R          |   1                 +----+ |   1
--R       %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
--R         \|1 + %i                     \|1 + %i
--R     + 
--R          +------+              +------+
--R          |  %i                 |  %i    +----+
--R       -  |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
--R         \|1 + %i              \|1 + %i
--R     + 
--R        +------+                +------+
--R        |  %i                   |  %i    +----+
--R        |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
--R       \|1 + %i                \|1 + %i
--R     + 
--R            +------+                       +------+
--R            |   1                   +----+ |   1
--R       - %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
--R           \|1 + %i                       \|1 + %i
--R     + 
--R          +------+                +------+
--R          |  %i                   |  %i    +------+
--R       -  |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
--R         \|1 + %i                \|1 + %i
--R     + 
--R        +------+                +------+
--R        |   1                   |   1    +------+            +------+     +----+
--R     %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i) - 8\|1 - %i  + 8\|- %i
--R       \|1 + %i                \|1 + %i
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 84

--S 85 of 224
in1721a:=integrate(-z^2/(z^2-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (85)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (85)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 85

--S 86 of 224
in1723a:=integrate(-z^2/(z^2-1)*(1+%i/z)^(1/2), z= 0..1,"noPole")
 

   (86)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (86)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 86

--S 87 of 224
in1731:=integrate(-log(1-z^2)*atanh(z), z= 0..1)
 

                 2
         - log(4)  + 4log(4)
   (87)  -------------------
                  4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 2
--R         - log(4)  + 4log(4)
--R   (87)  -------------------
--R                  4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 87

--S 88 of 224
in1793a:=integrate((1-z^(1/2))^(1/2)*acoth(z^(1/2)), z= 0..1,"noPole")
 

             +-+       +-+
         - 2\|2 log(12\|2  + 17) + 16
   (88)  ----------------------------
                      15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R             +-+       +-+
--R         - 2\|2 log(12\|2  + 17) + 16
--R   (88)  ----------------------------
--R                      15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 88

--S 89 of 224
in1794a:=integrate((1-z^(1/2))^(1/2)*acoth(1-z^(1/2)), z= 0..1,"noPole")
 

         - 4log(2) - 8%pi + 32
   (89)  ---------------------
                   15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         - 4log(2) - 8%pi + 32
--R   (89)  ---------------------
--R                   15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 89

--S 90 of 224
in1796a:=integrate((1+(1-z)^(1/2))^(1/2), z= 0..1,"noPole")
 

           +-+
         8\|2  + 8
   (90)  ---------
             15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           +-+
--R         8\|2  + 8
--R   (90)  ---------
--R             15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 90

--S 91 of 224
in184:=integrate(exp(%i*z), z= %i..2*%i)
 

              2
         %i %e  - %i %e
   (91)  --------------
                  2
             %e %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              2
--R         %i %e  - %i %e
--R   (91)  --------------
--R                  2
--R             %e %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 91

--S 92 of 224
in184a:=integrate(exp(%i*z), z= %i..2*%i)
 

              2
         %i %e  - %i %e
   (92)  --------------
                  2
             %e %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              2
--R         %i %e  - %i %e
--R   (92)  --------------
--R                  2
--R             %e %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 92

--S 93 of 224
in187a:=integrate(2^log(z), z= -%i..%i,"noPole")
 

              log(%i)log(2)        log(- %i)log(2)
         %i %e              + %i %e
   (93)  -----------------------------------------
                         log(2) + 1
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              log(%i)log(2)        log(- %i)log(2)
--R         %i %e              + %i %e
--R   (93)  -----------------------------------------
--R                         log(2) + 1
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 93

--S 94 of 224
in187a:=integrate(2^log(z), z= -%i..%i,"noPole")
 

              log(%i)log(2)        log(- %i)log(2)
         %i %e              + %i %e
   (94)  -----------------------------------------
                         log(2) + 1
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              log(%i)log(2)        log(- %i)log(2)
--R         %i %e              + %i %e
--R   (94)  -----------------------------------------
--R                         log(2) + 1
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 94

--S 95 of 224
in194a:=integrate(sqrt(z^2), z= 1..2,"noPole")
 

         3
   (95)  -
         2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         3
--R   (95)  -
--R         2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 95

--S 96 of 224
in1854a:=integrate(1/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (96)
   [ + infinity,

                              +------+                          +----+
          +---------+        \|1 - %i       +---------+       2\|- %i
       - \|- 4 + 4%i log(- ------------) + \|- 4 + 4%i atan(------------)
                            +---------+                      +---------+
                           \|- 4 + 4%i                      \|- 4 + 4%i
     + 
         +------+     +----+
       2\|1 - %i  - 2\|- %i
     ]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (96)
--R   [ + infinity,
--R
--R                              +------+                          +----+
--R          +---------+        \|1 - %i       +---------+       2\|- %i
--R       - \|- 4 + 4%i log(- ------------) + \|- 4 + 4%i atan(------------)
--R                            +---------+                      +---------+
--R                           \|- 4 + 4%i                      \|- 4 + 4%i
--R     + 
--R         +------+     +----+
--R       2\|1 - %i  - 2\|- %i
--R     ]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 96

--S 97 of 224
in1856a:=integrate(1/(z-1)/(1-%i*z)^(1/2), z= 0..1,"noPole")
 

   (97)
   [ + infinity,
                                +------+
       +---------+           %i\|1 - %i          +---------+        1 + %i
    - \|- 2 - 2%i log(- --------------------) + \|- 2 - 2%i atan(------------)]
                                 +---------+                      +---------+
                        (1 + %i)\|- 2 - 2%i                      \|- 2 - 2%i
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (97)
--R   [ + infinity,
--R                                +------+
--R       +---------+           %i\|1 - %i          +---------+        1 + %i
--R    - \|- 2 - 2%i log(- --------------------) + \|- 2 - 2%i atan(------------)]
--R                                 +---------+                      +---------+
--R                        (1 + %i)\|- 2 - 2%i                      \|- 2 - 2%i
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 97

--S 98 of 224
in1863a:=integrate(1/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole")
 

   (98)
          +------+              +------+
          |   1                 |   1    +------+
       %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
         \|1 + %i              \|1 + %i
     + 
          +------+              +------+
          |  %i                 |  %i    +------+
       -  |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
         \|1 + %i              \|1 + %i
     + 
            +------+                     +------+
            |   1                 +----+ |   1
       - %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
           \|1 + %i                     \|1 + %i
     + 
        +------+              +------+
        |  %i                 |  %i    +----+
        |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
       \|1 + %i              \|1 + %i
     + 
          +------+                +------+
          |  %i                   |  %i    +----+
       -  |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
         \|1 + %i                \|1 + %i
     + 
          +------+                       +------+
          |   1                   +----+ |   1
       %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
         \|1 + %i                       \|1 + %i
     + 
        +------+                +------+
        |  %i                   |  %i    +------+
        |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
       \|1 + %i                \|1 + %i
     + 
            +------+                +------+
            |   1                   |   1    +------+
       - %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i)
           \|1 + %i                \|1 + %i
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (98)
--R          +------+              +------+
--R          |   1                 |   1    +------+
--R       %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
--R         \|1 + %i              \|1 + %i
--R     + 
--R          +------+              +------+
--R          |  %i                 |  %i    +------+
--R       -  |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
--R         \|1 + %i              \|1 + %i
--R     + 
--R            +------+                     +------+
--R            |   1                 +----+ |   1
--R       - %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
--R           \|1 + %i                     \|1 + %i
--R     + 
--R        +------+              +------+
--R        |  %i                 |  %i    +----+
--R        |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
--R       \|1 + %i              \|1 + %i
--R     + 
--R          +------+                +------+
--R          |  %i                   |  %i    +----+
--R       -  |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
--R         \|1 + %i                \|1 + %i
--R     + 
--R          +------+                       +------+
--R          |   1                   +----+ |   1
--R       %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
--R         \|1 + %i                       \|1 + %i
--R     + 
--R        +------+                +------+
--R        |  %i                   |  %i    +------+
--R        |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
--R       \|1 + %i                \|1 + %i
--R     + 
--R            +------+                +------+
--R            |   1                   |   1    +------+
--R       - %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i)
--R           \|1 + %i                \|1 + %i
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 98

--S 99 of 224
in1864a:=integrate(1/(z^2-1)*((1+z)/(z-1))^(1/3), z= 0..1,"noPole")
 

   (99)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (99)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 99

--S 100 of 224
in1866a:=integrate(1/(z^2-1)*(1-%i/z)^(1/2), z= 0..1,"noPole")
 

   (100)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (100)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 100

--S 101 of 224
in1870a:=integrate(1/(z^2-1)/(1+(%i*z)^(1/2))^(1/2), z= 0..1,"noPole")
 

   (101)
       -
             +-------------------+
             |    +---------+
             |    |  +-+
             |    |3\|2  + 4
             |4%i |---------  + 1
             |    |     +-+
            \|   \|  16\|2
         *
            log
                                    +---------+
                                    |  +-+                 +---------+
                          +-+       |3\|2  + 4        +-+  | +--+
                     ((48\|2  - 64) |---------  - 4%i\|2 )\|\|%i  + 1
                                    |     +-+
                                   \|  16\|2
                  *
                      +-------------------+
                      |    +---------+
                      |    |  +-+
                      |    |3\|2  + 4
                      |4%i |---------  + 1
                      |    |     +-+
                     \|   \|  16\|2
                 + 
                                       +---------+
                                       |  +-+
                           +-+         |3\|2  + 4       +--+      +-+
                   (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                       |     +-+
                                      \|  16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |    +---------+
          |    |  +-+
          |    |3\|2  + 4
          |4%i |---------  + 1
          |    |     +-+
         \|   \|  16\|2
      *
         log
                                                      +-------------------+
                               +---------+            |    +---------+
                               |  +-+                 |    |  +-+
                     +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
                ((48\|2  - 64) |---------  - 4%i\|2 ) |4%i |---------  + 1
                               |     +-+              |    |     +-+
                              \|  16\|2              \|   \|  16\|2
              + 
                                    +---------+
                                    |  +-+
                        +-+         |3\|2  + 4      +-+
                (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
                                    |     +-+
                                   \|  16\|2
           /
               +-+
              \|2
     + 
       -
             +-------------------+
             |  +-----------+
             |  |    +-+
             |  |- 3\|2  + 4
             |4 |-----------  + 1
             |  |      +-+
            \| \|   16\|2
         *
            log
                                        +-----------+
                                        |    +-+                 +---------+
                            +-+         |- 3\|2  + 4        +-+  | +--+
                     ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
                                        |      +-+
                                       \|   16\|2
                  *
                      +-------------------+
                      |  +-----------+
                      |  |    +-+
                      |  |- 3\|2  + 4
                      |4 |-----------  + 1
                      |  |      +-+
                     \| \|   16\|2
                 + 
                                   +-----------+
                                   |    +-+
                         +-+       |- 3\|2  + 4       +--+      +-+
                   (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
                                   |      +-+
                                  \|   16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |  +-----------+
          |  |    +-+
          |  |- 3\|2  + 4
          |4 |-----------  + 1
          |  |      +-+
         \| \|   16\|2
      *
         log
                                     +-----------+
                                     |    +-+
                         +-+         |- 3\|2  + 4        +-+
                  ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )
                                     |      +-+
                                    \|   16\|2
               *
                   +-------------------+
                   |  +-----------+
                   |  |    +-+
                   |  |- 3\|2  + 4
                   |4 |-----------  + 1
                   |  |      +-+
                  \| \|   16\|2
              + 
                                +-----------+
                                |    +-+
                      +-+       |- 3\|2  + 4      +-+
                (- 16\|2  - 16) |-----------  + 8\|2  + 4
                                |      +-+
                               \|   16\|2
           /
               +-+
              \|2
     + 
          +---------------------+
          |    +-----------+
          |    |    +-+
          |    |- 3\|2  + 4
          |- 4 |-----------  + 1
          |    |      +-+
         \|   \|   16\|2
      *
         log
                                     +-----------+
                                     |    +-+                 +---------+
                         +-+         |- 3\|2  + 4        +-+  | +--+
                  ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
                                     |      +-+
                                    \|   16\|2
               *
                   +---------------------+
                   |    +-----------+
                   |    |    +-+
                   |    |- 3\|2  + 4
                   |- 4 |-----------  + 1
                   |    |      +-+
                  \|   \|   16\|2
              + 
                              +-----------+
                              |    +-+
                    +-+       |- 3\|2  + 4       +--+      +-+
                (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
                              |      +-+
                             \|   16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |    +-----------+
             |    |    +-+
             |    |- 3\|2  + 4
             |- 4 |-----------  + 1
             |    |      +-+
            \|   \|   16\|2
         *
            log
                                        +-----------+
                                        |    +-+
                            +-+         |- 3\|2  + 4        +-+
                     ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )
                                        |      +-+
                                       \|   16\|2
                  *
                      +---------------------+
                      |    +-----------+
                      |    |    +-+
                      |    |- 3\|2  + 4
                      |- 4 |-----------  + 1
                      |    |      +-+
                     \|   \|   16\|2
                 + 
                                 +-----------+
                                 |    +-+
                       +-+       |- 3\|2  + 4      +-+
                   (16\|2  + 16) |-----------  + 8\|2  + 4
                                 |      +-+
                                \|   16\|2
              /
                  +-+
                 \|2
     + 
          +---------------------+
          |      +---------+
          |      |  +-+
          |      |3\|2  + 4
          |- 4%i |---------  + 1
          |      |     +-+
         \|     \|  16\|2
      *
         log
                                 +---------+
                                 |  +-+                 +---------+
                       +-+       |3\|2  + 4        +-+  | +--+
                  ((48\|2  - 64) |---------  + 4%i\|2 )\|\|%i  + 1
                                 |     +-+
                                \|  16\|2
               *
                   +---------------------+
                   |      +---------+
                   |      |  +-+
                   |      |3\|2  + 4
                   |- 4%i |---------  + 1
                   |      |     +-+
                  \|     \|  16\|2
              + 
                                  +---------+
                                  |  +-+
                      +-+         |3\|2  + 4       +--+      +-+
                (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                  |     +-+
                                 \|  16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |      +---------+
             |      |  +-+
             |      |3\|2  + 4
             |- 4%i |---------  + 1
             |      |     +-+
            \|     \|  16\|2
         *
            log
                                                         +---------------------+
                                  +---------+            |      +---------+
                                  |  +-+                 |      |  +-+
                        +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
                   ((48\|2  - 64) |---------  + 4%i\|2 ) |- 4%i |---------  + 1
                                  |     +-+              |      |     +-+
                                 \|  16\|2              \|     \|  16\|2
                 + 
                                     +---------+
                                     |  +-+
                         +-+         |3\|2  + 4      +-+
                   (16%i\|2  - 16%i) |---------  + 8\|2  - 4
                                     |     +-+
                                    \|  16\|2
              /
                  +-+
                 \|2
     + 
          +---------------------+
          |      +---------+
          |      |  +-+
          |      |3\|2  + 4
          |- 4%i |---------  + 1
          |      |     +-+
         \|     \|  16\|2
      *
         log
                                                        +---------------------+
                                 +---------+            |      +---------+
                                 |  +-+                 |      |  +-+
                       +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
                ((- 48\|2  + 64) |---------  - 4%i\|2 ) |- 4%i |---------  + 1
                                 |     +-+              |      |     +-+
                                \|  16\|2              \|     \|  16\|2
              + 
                                  +---------+
                                  |  +-+
                      +-+         |3\|2  + 4      +-+
                (16%i\|2  - 16%i) |---------  + 8\|2  - 4
                                  |     +-+
                                 \|  16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |      +---------+
             |      |  +-+
             |      |3\|2  + 4
             |- 4%i |---------  + 1
             |      |     +-+
            \|     \|  16\|2
         *
            log
                                      +---------+
                                      |  +-+                 +---------+
                            +-+       |3\|2  + 4        +-+  | +--+
                     ((- 48\|2  + 64) |---------  - 4%i\|2 )\|\|%i  + 1
                                      |     +-+
                                     \|  16\|2
                  *
                      +---------------------+
                      |      +---------+
                      |      |  +-+
                      |      |3\|2  + 4
                      |- 4%i |---------  + 1
                      |      |     +-+
                     \|     \|  16\|2
                 + 
                                     +---------+
                                     |  +-+
                         +-+         |3\|2  + 4       +--+      +-+
                   (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                     |     +-+
                                    \|  16\|2
              /
                  +-+
                 \|2
     + 
          +---------------------+
          |    +-----------+
          |    |    +-+
          |    |- 3\|2  + 4
          |- 4 |-----------  + 1
          |    |      +-+
         \|   \|   16\|2
      *
         log
                                       +-----------+
                                       |    +-+
                           +-+         |- 3\|2  + 4        +-+
                  ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )
                                       |      +-+
                                      \|   16\|2
               *
                   +---------------------+
                   |    +-----------+
                   |    |    +-+
                   |    |- 3\|2  + 4
                   |- 4 |-----------  + 1
                   |    |      +-+
                  \|   \|   16\|2
              + 
                              +-----------+
                              |    +-+
                    +-+       |- 3\|2  + 4      +-+
                (16\|2  + 16) |-----------  + 8\|2  + 4
                              |      +-+
                             \|   16\|2
           /
               +-+
              \|2
     + 
       -
             +---------------------+
             |    +-----------+
             |    |    +-+
             |    |- 3\|2  + 4
             |- 4 |-----------  + 1
             |    |      +-+
            \|   \|   16\|2
         *
            log
                                          +-----------+
                                          |    +-+                 +---------+
                              +-+         |- 3\|2  + 4        +-+  | +--+
                     ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
                                          |      +-+
                                         \|   16\|2
                  *
                      +---------------------+
                      |    +-----------+
                      |    |    +-+
                      |    |- 3\|2  + 4
                      |- 4 |-----------  + 1
                      |    |      +-+
                     \|   \|   16\|2
                 + 
                                 +-----------+
                                 |    +-+
                       +-+       |- 3\|2  + 4       +--+      +-+
                   (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
                                 |      +-+
                                \|   16\|2
              /
                  +-+
                 \|2
     + 
       -
             +-------------------+
             |  +-----------+
             |  |    +-+
             |  |- 3\|2  + 4
             |4 |-----------  + 1
             |  |      +-+
            \| \|   16\|2
         *
            log
                                          +-----------+
                                          |    +-+
                              +-+         |- 3\|2  + 4        +-+
                     ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )
                                          |      +-+
                                         \|   16\|2
                  *
                      +-------------------+
                      |  +-----------+
                      |  |    +-+
                      |  |- 3\|2  + 4
                      |4 |-----------  + 1
                      |  |      +-+
                     \| \|   16\|2
                 + 
                                   +-----------+
                                   |    +-+
                         +-+       |- 3\|2  + 4      +-+
                   (- 16\|2  - 16) |-----------  + 8\|2  + 4
                                   |      +-+
                                  \|   16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |  +-----------+
          |  |    +-+
          |  |- 3\|2  + 4
          |4 |-----------  + 1
          |  |      +-+
         \| \|   16\|2
      *
         log
                                       +-----------+
                                       |    +-+                 +---------+
                           +-+         |- 3\|2  + 4        +-+  | +--+
                  ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
                                       |      +-+
                                      \|   16\|2
               *
                   +-------------------+
                   |  +-----------+
                   |  |    +-+
                   |  |- 3\|2  + 4
                   |4 |-----------  + 1
                   |  |      +-+
                  \| \|   16\|2
              + 
                                +-----------+
                                |    +-+
                      +-+       |- 3\|2  + 4       +--+      +-+
                (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
                                |      +-+
                               \|   16\|2
           /
               +-+
              \|2
     + 
       -
             +-------------------+
             |    +---------+
             |    |  +-+
             |    |3\|2  + 4
             |4%i |---------  + 1
             |    |     +-+
            \|   \|  16\|2
         *
            log
                                                           +-------------------+
                                    +---------+            |    +---------+
                                    |  +-+                 |    |  +-+
                          +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
                   ((- 48\|2  + 64) |---------  + 4%i\|2 ) |4%i |---------  + 1
                                    |     +-+              |    |     +-+
                                   \|  16\|2              \|   \|  16\|2
                 + 
                                       +---------+
                                       |  +-+
                           +-+         |3\|2  + 4      +-+
                   (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
                                       |     +-+
                                      \|  16\|2
              /
                  +-+
                 \|2
     + 
          +-------------------+
          |    +---------+
          |    |  +-+
          |    |3\|2  + 4
          |4%i |---------  + 1
          |    |     +-+
         \|   \|  16\|2
      *
         log
                                   +---------+
                                   |  +-+                 +---------+
                         +-+       |3\|2  + 4        +-+  | +--+
                  ((- 48\|2  + 64) |---------  + 4%i\|2 )\|\|%i  + 1
                                   |     +-+
                                  \|  16\|2
               *
                   +-------------------+
                   |    +---------+
                   |    |  +-+
                   |    |3\|2  + 4
                   |4%i |---------  + 1
                   |    |     +-+
                  \|   \|  16\|2
              + 
                                    +---------+
                                    |  +-+
                        +-+         |3\|2  + 4       +--+      +-+
                (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
                                    |     +-+
                                   \|  16\|2
           /
               +-+
              \|2
  /
       +-+
     4\|2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (101)
--R       -
--R             +-------------------+
--R             |    +---------+
--R             |    |  +-+
--R             |    |3\|2  + 4
--R             |4%i |---------  + 1
--R             |    |     +-+
--R            \|   \|  16\|2
--R         *
--R            log
--R                                    +---------+
--R                                    |  +-+                 +---------+
--R                          +-+       |3\|2  + 4        +-+  | +--+
--R                     ((48\|2  - 64) |---------  - 4%i\|2 )\|\|%i  + 1
--R                                    |     +-+
--R                                   \|  16\|2
--R                  *
--R                      +-------------------+
--R                      |    +---------+
--R                      |    |  +-+
--R                      |    |3\|2  + 4
--R                      |4%i |---------  + 1
--R                      |    |     +-+
--R                     \|   \|  16\|2
--R                 + 
--R                                       +---------+
--R                                       |  +-+
--R                           +-+         |3\|2  + 4       +--+      +-+
--R                   (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                       |     +-+
--R                                      \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |    +---------+
--R          |    |  +-+
--R          |    |3\|2  + 4
--R          |4%i |---------  + 1
--R          |    |     +-+
--R         \|   \|  16\|2
--R      *
--R         log
--R                                                      +-------------------+
--R                               +---------+            |    +---------+
--R                               |  +-+                 |    |  +-+
--R                     +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
--R                ((48\|2  - 64) |---------  - 4%i\|2 ) |4%i |---------  + 1
--R                               |     +-+              |    |     +-+
--R                              \|  16\|2              \|   \|  16\|2
--R              + 
--R                                    +---------+
--R                                    |  +-+
--R                        +-+         |3\|2  + 4      +-+
--R                (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
--R                                    |     +-+
--R                                   \|  16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +-------------------+
--R             |  +-----------+
--R             |  |    +-+
--R             |  |- 3\|2  + 4
--R             |4 |-----------  + 1
--R             |  |      +-+
--R            \| \|   16\|2
--R         *
--R            log
--R                                        +-----------+
--R                                        |    +-+                 +---------+
--R                            +-+         |- 3\|2  + 4        +-+  | +--+
--R                     ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
--R                                        |      +-+
--R                                       \|   16\|2
--R                  *
--R                      +-------------------+
--R                      |  +-----------+
--R                      |  |    +-+
--R                      |  |- 3\|2  + 4
--R                      |4 |-----------  + 1
--R                      |  |      +-+
--R                     \| \|   16\|2
--R                 + 
--R                                   +-----------+
--R                                   |    +-+
--R                         +-+       |- 3\|2  + 4       +--+      +-+
--R                   (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                                   |      +-+
--R                                  \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |  +-----------+
--R          |  |    +-+
--R          |  |- 3\|2  + 4
--R          |4 |-----------  + 1
--R          |  |      +-+
--R         \| \|   16\|2
--R      *
--R         log
--R                                     +-----------+
--R                                     |    +-+
--R                         +-+         |- 3\|2  + 4        +-+
--R                  ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )
--R                                     |      +-+
--R                                    \|   16\|2
--R               *
--R                   +-------------------+
--R                   |  +-----------+
--R                   |  |    +-+
--R                   |  |- 3\|2  + 4
--R                   |4 |-----------  + 1
--R                   |  |      +-+
--R                  \| \|   16\|2
--R              + 
--R                                +-----------+
--R                                |    +-+
--R                      +-+       |- 3\|2  + 4      +-+
--R                (- 16\|2  - 16) |-----------  + 8\|2  + 4
--R                                |      +-+
--R                               \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R          +---------------------+
--R          |    +-----------+
--R          |    |    +-+
--R          |    |- 3\|2  + 4
--R          |- 4 |-----------  + 1
--R          |    |      +-+
--R         \|   \|   16\|2
--R      *
--R         log
--R                                     +-----------+
--R                                     |    +-+                 +---------+
--R                         +-+         |- 3\|2  + 4        +-+  | +--+
--R                  ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
--R                                     |      +-+
--R                                    \|   16\|2
--R               *
--R                   +---------------------+
--R                   |    +-----------+
--R                   |    |    +-+
--R                   |    |- 3\|2  + 4
--R                   |- 4 |-----------  + 1
--R                   |    |      +-+
--R                  \|   \|   16\|2
--R              + 
--R                              +-----------+
--R                              |    +-+
--R                    +-+       |- 3\|2  + 4       +--+      +-+
--R                (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                              |      +-+
--R                             \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |    +-----------+
--R             |    |    +-+
--R             |    |- 3\|2  + 4
--R             |- 4 |-----------  + 1
--R             |    |      +-+
--R            \|   \|   16\|2
--R         *
--R            log
--R                                        +-----------+
--R                                        |    +-+
--R                            +-+         |- 3\|2  + 4        +-+
--R                     ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )
--R                                        |      +-+
--R                                       \|   16\|2
--R                  *
--R                      +---------------------+
--R                      |    +-----------+
--R                      |    |    +-+
--R                      |    |- 3\|2  + 4
--R                      |- 4 |-----------  + 1
--R                      |    |      +-+
--R                     \|   \|   16\|2
--R                 + 
--R                                 +-----------+
--R                                 |    +-+
--R                       +-+       |- 3\|2  + 4      +-+
--R                   (16\|2  + 16) |-----------  + 8\|2  + 4
--R                                 |      +-+
--R                                \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +---------------------+
--R          |      +---------+
--R          |      |  +-+
--R          |      |3\|2  + 4
--R          |- 4%i |---------  + 1
--R          |      |     +-+
--R         \|     \|  16\|2
--R      *
--R         log
--R                                 +---------+
--R                                 |  +-+                 +---------+
--R                       +-+       |3\|2  + 4        +-+  | +--+
--R                  ((48\|2  - 64) |---------  + 4%i\|2 )\|\|%i  + 1
--R                                 |     +-+
--R                                \|  16\|2
--R               *
--R                   +---------------------+
--R                   |      +---------+
--R                   |      |  +-+
--R                   |      |3\|2  + 4
--R                   |- 4%i |---------  + 1
--R                   |      |     +-+
--R                  \|     \|  16\|2
--R              + 
--R                                  +---------+
--R                                  |  +-+
--R                      +-+         |3\|2  + 4       +--+      +-+
--R                (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                  |     +-+
--R                                 \|  16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |      +---------+
--R             |      |  +-+
--R             |      |3\|2  + 4
--R             |- 4%i |---------  + 1
--R             |      |     +-+
--R            \|     \|  16\|2
--R         *
--R            log
--R                                                         +---------------------+
--R                                  +---------+            |      +---------+
--R                                  |  +-+                 |      |  +-+
--R                        +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
--R                   ((48\|2  - 64) |---------  + 4%i\|2 ) |- 4%i |---------  + 1
--R                                  |     +-+              |      |     +-+
--R                                 \|  16\|2              \|     \|  16\|2
--R                 + 
--R                                     +---------+
--R                                     |  +-+
--R                         +-+         |3\|2  + 4      +-+
--R                   (16%i\|2  - 16%i) |---------  + 8\|2  - 4
--R                                     |     +-+
--R                                    \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +---------------------+
--R          |      +---------+
--R          |      |  +-+
--R          |      |3\|2  + 4
--R          |- 4%i |---------  + 1
--R          |      |     +-+
--R         \|     \|  16\|2
--R      *
--R         log
--R                                                        +---------------------+
--R                                 +---------+            |      +---------+
--R                                 |  +-+                 |      |  +-+
--R                       +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
--R                ((- 48\|2  + 64) |---------  - 4%i\|2 ) |- 4%i |---------  + 1
--R                                 |     +-+              |      |     +-+
--R                                \|  16\|2              \|     \|  16\|2
--R              + 
--R                                  +---------+
--R                                  |  +-+
--R                      +-+         |3\|2  + 4      +-+
--R                (16%i\|2  - 16%i) |---------  + 8\|2  - 4
--R                                  |     +-+
--R                                 \|  16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |      +---------+
--R             |      |  +-+
--R             |      |3\|2  + 4
--R             |- 4%i |---------  + 1
--R             |      |     +-+
--R            \|     \|  16\|2
--R         *
--R            log
--R                                      +---------+
--R                                      |  +-+                 +---------+
--R                            +-+       |3\|2  + 4        +-+  | +--+
--R                     ((- 48\|2  + 64) |---------  - 4%i\|2 )\|\|%i  + 1
--R                                      |     +-+
--R                                     \|  16\|2
--R                  *
--R                      +---------------------+
--R                      |      +---------+
--R                      |      |  +-+
--R                      |      |3\|2  + 4
--R                      |- 4%i |---------  + 1
--R                      |      |     +-+
--R                     \|     \|  16\|2
--R                 + 
--R                                     +---------+
--R                                     |  +-+
--R                         +-+         |3\|2  + 4       +--+      +-+
--R                   (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                     |     +-+
--R                                    \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +---------------------+
--R          |    +-----------+
--R          |    |    +-+
--R          |    |- 3\|2  + 4
--R          |- 4 |-----------  + 1
--R          |    |      +-+
--R         \|   \|   16\|2
--R      *
--R         log
--R                                       +-----------+
--R                                       |    +-+
--R                           +-+         |- 3\|2  + 4        +-+
--R                  ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )
--R                                       |      +-+
--R                                      \|   16\|2
--R               *
--R                   +---------------------+
--R                   |    +-----------+
--R                   |    |    +-+
--R                   |    |- 3\|2  + 4
--R                   |- 4 |-----------  + 1
--R                   |    |      +-+
--R                  \|   \|   16\|2
--R              + 
--R                              +-----------+
--R                              |    +-+
--R                    +-+       |- 3\|2  + 4      +-+
--R                (16\|2  + 16) |-----------  + 8\|2  + 4
--R                              |      +-+
--R                             \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +---------------------+
--R             |    +-----------+
--R             |    |    +-+
--R             |    |- 3\|2  + 4
--R             |- 4 |-----------  + 1
--R             |    |      +-+
--R            \|   \|   16\|2
--R         *
--R            log
--R                                          +-----------+
--R                                          |    +-+                 +---------+
--R                              +-+         |- 3\|2  + 4        +-+  | +--+
--R                     ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
--R                                          |      +-+
--R                                         \|   16\|2
--R                  *
--R                      +---------------------+
--R                      |    +-----------+
--R                      |    |    +-+
--R                      |    |- 3\|2  + 4
--R                      |- 4 |-----------  + 1
--R                      |    |      +-+
--R                     \|   \|   16\|2
--R                 + 
--R                                 +-----------+
--R                                 |    +-+
--R                       +-+       |- 3\|2  + 4       +--+      +-+
--R                   (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                                 |      +-+
--R                                \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R       -
--R             +-------------------+
--R             |  +-----------+
--R             |  |    +-+
--R             |  |- 3\|2  + 4
--R             |4 |-----------  + 1
--R             |  |      +-+
--R            \| \|   16\|2
--R         *
--R            log
--R                                          +-----------+
--R                                          |    +-+
--R                              +-+         |- 3\|2  + 4        +-+
--R                     ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )
--R                                          |      +-+
--R                                         \|   16\|2
--R                  *
--R                      +-------------------+
--R                      |  +-----------+
--R                      |  |    +-+
--R                      |  |- 3\|2  + 4
--R                      |4 |-----------  + 1
--R                      |  |      +-+
--R                     \| \|   16\|2
--R                 + 
--R                                   +-----------+
--R                                   |    +-+
--R                         +-+       |- 3\|2  + 4      +-+
--R                   (- 16\|2  - 16) |-----------  + 8\|2  + 4
--R                                   |      +-+
--R                                  \|   16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |  +-----------+
--R          |  |    +-+
--R          |  |- 3\|2  + 4
--R          |4 |-----------  + 1
--R          |  |      +-+
--R         \| \|   16\|2
--R      *
--R         log
--R                                       +-----------+
--R                                       |    +-+                 +---------+
--R                           +-+         |- 3\|2  + 4        +-+  | +--+
--R                  ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
--R                                       |      +-+
--R                                      \|   16\|2
--R               *
--R                   +-------------------+
--R                   |  +-----------+
--R                   |  |    +-+
--R                   |  |- 3\|2  + 4
--R                   |4 |-----------  + 1
--R                   |  |      +-+
--R                  \| \|   16\|2
--R              + 
--R                                +-----------+
--R                                |    +-+
--R                      +-+       |- 3\|2  + 4       +--+      +-+
--R                (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
--R                                |      +-+
--R                               \|   16\|2
--R           /
--R               +-+
--R              \|2
--R     + 
--R       -
--R             +-------------------+
--R             |    +---------+
--R             |    |  +-+
--R             |    |3\|2  + 4
--R             |4%i |---------  + 1
--R             |    |     +-+
--R            \|   \|  16\|2
--R         *
--R            log
--R                                                           +-------------------+
--R                                    +---------+            |    +---------+
--R                                    |  +-+                 |    |  +-+
--R                          +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
--R                   ((- 48\|2  + 64) |---------  + 4%i\|2 ) |4%i |---------  + 1
--R                                    |     +-+              |    |     +-+
--R                                   \|  16\|2              \|   \|  16\|2
--R                 + 
--R                                       +---------+
--R                                       |  +-+
--R                           +-+         |3\|2  + 4      +-+
--R                   (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
--R                                       |     +-+
--R                                      \|  16\|2
--R              /
--R                  +-+
--R                 \|2
--R     + 
--R          +-------------------+
--R          |    +---------+
--R          |    |  +-+
--R          |    |3\|2  + 4
--R          |4%i |---------  + 1
--R          |    |     +-+
--R         \|   \|  16\|2
--R      *
--R         log
--R                                   +---------+
--R                                   |  +-+                 +---------+
--R                         +-+       |3\|2  + 4        +-+  | +--+
--R                  ((- 48\|2  + 64) |---------  + 4%i\|2 )\|\|%i  + 1
--R                                   |     +-+
--R                                  \|  16\|2
--R               *
--R                   +-------------------+
--R                   |    +---------+
--R                   |    |  +-+
--R                   |    |3\|2  + 4
--R                   |4%i |---------  + 1
--R                   |    |     +-+
--R                  \|   \|  16\|2
--R              + 
--R                                    +---------+
--R                                    |  +-+
--R                        +-+         |3\|2  + 4       +--+      +-+
--R                (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
--R                                    |     +-+
--R                                   \|  16\|2
--R           /
--R               +-+
--R              \|2
--R  /
--R       +-+
--R     4\|2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 101

--S 102 of 224
in1872a:=integrate(1/(z^2-1)/(%i/(z+%i))^(1/2), z= 0..1,"noPole")
 

   (102)
                              +------+
        +------+              |  %i    +------+
       \|1 + %i log((2 + 2%i) |------ \|1 + %i  + 2%i)
                             \|1 + %i
     + 
          +------+              +------+
       - \|1 + %i log((2 + 2%i)\|1 + %i  + 1 + 3%i)
     + 
                              +------+
        +------+              |  %i    +------+
       \|1 - %i log((2 - 2%i) |------ \|1 - %i  - 2 + 2%i)
                             \|1 + %i
     + 
          +------+              +------+
       - \|1 - %i log((2 - 2%i)\|1 - %i  - 1 + 3%i)
     + 
        +------+                +------+
       \|1 - %i log((- 2 + 2%i)\|1 - %i  - 1 + 3%i)
     + 
                                  +------+
          +------+                |  %i    +------+
       - \|1 - %i log((- 2 + 2%i) |------ \|1 - %i  - 2 + 2%i)
                                 \|1 + %i
     + 
        +------+                +------+
       \|1 + %i log((- 2 - 2%i)\|1 + %i  + 1 + 3%i)
     + 
                                  +------+
          +------+                |  %i    +------+
       - \|1 + %i log((- 2 - 2%i) |------ \|1 + %i  + 2%i)
                                 \|1 + %i
  /
     4
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (102)
--R                              +------+
--R        +------+              |  %i    +------+
--R       \|1 + %i log((2 + 2%i) |------ \|1 + %i  + 2%i)
--R                             \|1 + %i
--R     + 
--R          +------+              +------+
--R       - \|1 + %i log((2 + 2%i)\|1 + %i  + 1 + 3%i)
--R     + 
--R                              +------+
--R        +------+              |  %i    +------+
--R       \|1 - %i log((2 - 2%i) |------ \|1 - %i  - 2 + 2%i)
--R                             \|1 + %i
--R     + 
--R          +------+              +------+
--R       - \|1 - %i log((2 - 2%i)\|1 - %i  - 1 + 3%i)
--R     + 
--R        +------+                +------+
--R       \|1 - %i log((- 2 + 2%i)\|1 - %i  - 1 + 3%i)
--R     + 
--R                                  +------+
--R          +------+                |  %i    +------+
--R       - \|1 - %i log((- 2 + 2%i) |------ \|1 - %i  - 2 + 2%i)
--R                                 \|1 + %i
--R     + 
--R        +------+                +------+
--R       \|1 + %i log((- 2 - 2%i)\|1 + %i  + 1 + 3%i)
--R     + 
--R                                  +------+
--R          +------+                |  %i    +------+
--R       - \|1 + %i log((- 2 - 2%i) |------ \|1 + %i  + 2%i)
--R                                 \|1 + %i
--R  /
--R     4
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 102

--S 103 of 224
in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole")
 

   (103)
           +-+     4+-+    %pi
         (\|2  - 1)\|2 cos(---)
                            8
      *
              4+-+2    %pi 2     4+-+3    4+-+     %pi     4+-+2
         log(4\|2  sin(---)  + (4\|2   + 4\|2 )sin(---) + 2\|2   + 3)
                        8                           8
     + 
             +-+     4+-+    %pi
         (- \|2  + 1)\|2 cos(---)
                              8
      *
              4+-+2    %pi 2       4+-+3    4+-+     %pi     4+-+2
         log(4\|2  sin(---)  + (- 4\|2   - 4\|2 )sin(---) + 2\|2   + 3)
                        8                             8
     + 
             +-+     4+-+    %pi
         (- \|2  + 1)\|2 cos(---)
                              8
      *
         log
               4+-+2    %pi 2
              4\|2  sin(---)
                         8
            + 
                    +-+     4+-+2    %pi     4+-+3        +-+      4+-+     %pi
              ((- 8\|2  + 8)\|2  cos(---) + 4\|2   + (- 8\|2  + 16)\|2 )sin(---)
                                      8                                      8
            + 
                   +-+      4+-+2    %pi 2
              (- 8\|2  + 12)\|2  cos(---)
                                      8
            + 
                    +-+     4+-+3         +-+      4+-+     %pi
              ((- 4\|2  + 4)\|2   + (- 24\|2  + 32)\|2 )cos(---)
                                                             8
            + 
                   +-+     4+-+2      +-+
              (- 4\|2  + 8)\|2   - 16\|2  + 26
     + 
           +-+     4+-+    %pi
         (\|2  - 1)\|2 cos(---)
                            8
      *
         log
               4+-+2    %pi 2
              4\|2  sin(---)
                         8
            + 
                    +-+     4+-+2    %pi     4+-+3      +-+      4+-+     %pi
              ((- 8\|2  + 8)\|2  cos(---) - 4\|2   + (8\|2  - 16)\|2 )sin(---)
                                      8                                    8
            + 
                   +-+      4+-+2    %pi 2
              (- 8\|2  + 12)\|2  cos(---)
                                      8
            + 
                  +-+     4+-+3       +-+      4+-+     %pi
              ((4\|2  - 4)\|2   + (24\|2  - 32)\|2 )cos(---)
                                                         8
            + 
                   +-+     4+-+2      +-+
              (- 4\|2  + 8)\|2   - 16\|2  + 26
     + 
                                       4+-+    %pi
                                       \|2 sin(---) + 1
          +-+     4+-+    %pi                   8
       (4\|2  - 4)\|2 sin(---)atan(-----------------------)
                           8       4+-+    %pi     +-+
                                   \|2 cos(---) - \|2  + 1
                                            8
     + 
                                     4+-+    %pi
                                     \|2 sin(---) + 1
            +-+     4+-+    %pi               8
       (- 4\|2  + 4)\|2 sin(---)atan(----------------)
                             8         4+-+    %pi
                                       \|2 cos(---)
                                                8
     + 
                                   4+-+    %pi
                                   \|2 sin(---) - 1
          +-+     4+-+    %pi               8
       (4\|2  - 4)\|2 sin(---)atan(----------------)
                           8         4+-+    %pi
                                     \|2 cos(---)
                                              8
     + 
                                         4+-+    %pi
                                         \|2 sin(---) - 1
            +-+     4+-+    %pi                   8                 +-+
       (- 4\|2  + 4)\|2 sin(---)atan(-----------------------) + %pi\|2  - 2%pi
                             8       4+-+    %pi     +-+
                                     \|2 cos(---) + \|2  - 1
                                              8
  /
       +-+
     2\|2  - 2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (103)
--R           +-+     4+-+    %pi
--R         (\|2  - 1)\|2 cos(---)
--R                            8
--R      *
--R              4+-+2    %pi 2     4+-+3    4+-+     %pi     4+-+2
--R         log(4\|2  sin(---)  + (4\|2   + 4\|2 )sin(---) + 2\|2   + 3)
--R                        8                           8
--R     + 
--R             +-+     4+-+    %pi
--R         (- \|2  + 1)\|2 cos(---)
--R                              8
--R      *
--R              4+-+2    %pi 2       4+-+3    4+-+     %pi     4+-+2
--R         log(4\|2  sin(---)  + (- 4\|2   - 4\|2 )sin(---) + 2\|2   + 3)
--R                        8                             8
--R     + 
--R             +-+     4+-+    %pi
--R         (- \|2  + 1)\|2 cos(---)
--R                              8
--R      *
--R         log
--R               4+-+2    %pi 2
--R              4\|2  sin(---)
--R                         8
--R            + 
--R                    +-+     4+-+2    %pi     4+-+3        +-+      4+-+     %pi
--R              ((- 8\|2  + 8)\|2  cos(---) + 4\|2   + (- 8\|2  + 16)\|2 )sin(---)
--R                                      8                                      8
--R            + 
--R                   +-+      4+-+2    %pi 2
--R              (- 8\|2  + 12)\|2  cos(---)
--R                                      8
--R            + 
--R                    +-+     4+-+3         +-+      4+-+     %pi
--R              ((- 4\|2  + 4)\|2   + (- 24\|2  + 32)\|2 )cos(---)
--R                                                             8
--R            + 
--R                   +-+     4+-+2      +-+
--R              (- 4\|2  + 8)\|2   - 16\|2  + 26
--R     + 
--R           +-+     4+-+    %pi
--R         (\|2  - 1)\|2 cos(---)
--R                            8
--R      *
--R         log
--R               4+-+2    %pi 2
--R              4\|2  sin(---)
--R                         8
--R            + 
--R                    +-+     4+-+2    %pi     4+-+3      +-+      4+-+     %pi
--R              ((- 8\|2  + 8)\|2  cos(---) - 4\|2   + (8\|2  - 16)\|2 )sin(---)
--R                                      8                                    8
--R            + 
--R                   +-+      4+-+2    %pi 2
--R              (- 8\|2  + 12)\|2  cos(---)
--R                                      8
--R            + 
--R                  +-+     4+-+3       +-+      4+-+     %pi
--R              ((4\|2  - 4)\|2   + (24\|2  - 32)\|2 )cos(---)
--R                                                         8
--R            + 
--R                   +-+     4+-+2      +-+
--R              (- 4\|2  + 8)\|2   - 16\|2  + 26
--R     + 
--R                                       4+-+    %pi
--R                                       \|2 sin(---) + 1
--R          +-+     4+-+    %pi                   8
--R       (4\|2  - 4)\|2 sin(---)atan(-----------------------)
--R                           8       4+-+    %pi     +-+
--R                                   \|2 cos(---) - \|2  + 1
--R                                            8
--R     + 
--R                                     4+-+    %pi
--R                                     \|2 sin(---) + 1
--R            +-+     4+-+    %pi               8
--R       (- 4\|2  + 4)\|2 sin(---)atan(----------------)
--R                             8         4+-+    %pi
--R                                       \|2 cos(---)
--R                                                8
--R     + 
--R                                   4+-+    %pi
--R                                   \|2 sin(---) - 1
--R          +-+     4+-+    %pi               8
--R       (4\|2  - 4)\|2 sin(---)atan(----------------)
--R                           8         4+-+    %pi
--R                                     \|2 cos(---)
--R                                              8
--R     + 
--R                                         4+-+    %pi
--R                                         \|2 sin(---) - 1
--R            +-+     4+-+    %pi                   8                 +-+
--R       (- 4\|2  + 4)\|2 sin(---)atan(-----------------------) + %pi\|2  - 2%pi
--R                             8       4+-+    %pi     +-+
--R                                     \|2 cos(---) + \|2  - 1
--R                                              8
--R  /
--R       +-+
--R     2\|2  - 2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 103

--S 104 of 224
in1945a:=integrate(acoth((1-z)/(1+z)), z= 0..1,"noPole")
 

          1
   (104)  -
          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (104)  -
--R          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 104

--S 105 of 224
in1946a:=integrate(acoth((1-z)/(1+z))*z, z= 0..1,"noPole")
 

          1
   (105)  -
          8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (105)  -
--R          8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 105

--S 106 of 224
in1947a:=integrate(acoth((1-z)/(1+z))*z^(1/2), z= 0..1,"noPole")
 

          2
   (106)  -
          9
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          2
--R   (106)  -
--R          9
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 106

--S 107 of 224
in1950a:=integrate(acoth((1-z)/(1+z))/(1-z)^(1/2), z= 0..1,"noPole")
 

          - log(4) - 2log(2) + 4
   (107)  ----------------------
                     2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - log(4) - 2log(2) + 4
--R   (107)  ----------------------
--R                     2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 107

--S 108 of 224
in1952a:=integrate(acoth((1-z)/(1+z))*(%i*z)^(1/2), z= 0..1,"noPole")
 

            +--+
          2\|%i
   (108)  ------
             9
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R            +--+
--R          2\|%i
--R   (108)  ------
--R             9
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 108

--S 109 of 224
in1954a:=integrate(acoth((1-z)/(1+z))/(%i*z)^(1/2), z= 0..1,"noPole")
 

                +--+
   (109)  - 2%i\|%i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                +--+
--R   (109)  - 2%i\|%i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 109

--S 110 of 224
in202a:=integrate(acsc(z), z= 0..1/2,"noPole")
 

                        +-+ +-+
              +-+     2\|2 \|3             +-+
          - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi
                          5
   (110)  --------------------------------------------
                               12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                        +-+ +-+
--R              +-+     2\|2 \|3             +-+
--R          - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi
--R                          5
--R   (110)  --------------------------------------------
--R                               12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 110

--S 111 of 224
in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole")
 

   (111)
               +--------+              +-------+
               |2%pi - 1               |%pi - 1
       - 2log( |--------  + 1) + 2log( |-------  + 1)
              \|  2%pi                \|  %pi
     + 
                    +-------+                          +--------+
                    |%pi - 1                           |2%pi - 1
             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
                   \|  %pi                            \|  2%pi
       - log(---------------------------) + log(----------------------------)
                         %pi                                2%pi
     + 
            +--------+        +-------+
            |2%pi - 1         |%pi - 1
       8%pi |--------  - 4%pi |-------
           \|  2%pi          \|  %pi
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (111)
--R               +--------+              +-------+
--R               |2%pi - 1               |%pi - 1
--R       - 2log( |--------  + 1) + 2log( |-------  + 1)
--R              \|  2%pi                \|  %pi
--R     + 
--R                    +-------+                          +--------+
--R                    |%pi - 1                           |2%pi - 1
--R             - 2%pi |-------  + 2%pi - 1        - 4%pi |--------  + 4%pi - 1
--R                   \|  %pi                            \|  2%pi
--R       - log(---------------------------) + log(----------------------------)
--R                         %pi                                2%pi
--R     + 
--R            +--------+        +-------+
--R            |2%pi - 1         |%pi - 1
--R       8%pi |--------  - 4%pi |-------
--R           \|  2%pi          \|  %pi
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 111

--S 112 of 224
in211:=integrate(acos(sin(2*z))*cos(z), z= 0..4*%pi/3)
 

                +-+
          13%pi\|3  + 36
   (112)  --------------
                12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+
--R          13%pi\|3  + 36
--R   (112)  --------------
--R                12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 112

--S 113 of 224
in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole")
 

   (113)
                                      3+---+2    3+---+
         3+---+2    3+---+            \|- 1   + 2\|- 1  + 1    3+---+2    3+---+
   - log(\|- 1   + 2\|- 1  + 1) + log(---------------------) - \|- 1   + 2\|- 1
                                             3+---+2
                                             \|- 1
   -----------------------------------------------------------------------------
                                         2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (113)
--R                                      3+---+2    3+---+
--R         3+---+2    3+---+            \|- 1   + 2\|- 1  + 1    3+---+2    3+---+
--R   - log(\|- 1   + 2\|- 1  + 1) + log(---------------------) - \|- 1   + 2\|- 1
--R                                             3+---+2
--R                                             \|- 1
--R   -----------------------------------------------------------------------------
--R                                         2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 113

--S 114 of 224
in216a:=integrate(1/(1/z-1)^(1/3), z= 0..1,"noPole")
 

           2%pi
   (114)  -----
            +-+
          3\|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R           2%pi
--R   (114)  -----
--R            +-+
--R          3\|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 114

--S 115 of 224
in2023a:=integrate((1-z)/(-1+z^(1/2)), z= 1..2,"noPole")
 

              +-+
          - 4\|2  - 1
   (115)  -----------
               3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R              +-+
--R          - 4\|2  - 1
--R   (115)  -----------
--R               3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 115

--S 116 of 224
in2024a:=integrate(log(1-1/z)+csc(z-1), z= 0..1,"noPole")
 

   (116)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (116)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 116

--S 117 of 224
in2032a:=integrate(acoth(z)/z^(1/2), z= 0..1,"noPole")
 

          - 2log(2) + %pi
   (117)  ---------------
                 2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - 2log(2) + %pi
--R   (117)  ---------------
--R                 2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 117

--S 118 of 224
in2040a:=integrate(log(1-1/z^4)+cot(z), z= -1..1,"noPole")
 

   (118)  log(16) + log(4) + %pi
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (118)  log(16) + log(4) + %pi
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 118

--S 119 of 224
in2050a:=integrate(-csc(z-1)-1/z^(1/3), z= -1..1,"noPole")
 

   (119)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (119)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 119

--S 120 of 224
in2051a:=integrate((z^2+%i*z-1)^(1/2)*z, z= -1..1,"noPole")
 

   (120)
                    +----+                  +--+                   +----+
           (12132%i\|- %i  + 8550 + 8460%i)\|%i  + (8550 - 8460%i)\|- %i
         + 
           - 11925%i
      *
                       +----+
         log((8 - 4%i)\|- %i  + 3 - 8%i)
     + 
                      +----+                  +--+                     +----+
           (- 12132%i\|- %i  - 8550 - 8460%i)\|%i  + (- 8550 + 8460%i)\|- %i
         + 
           11925%i
      *
                         +--+
         log((- 8 - 4%i)\|%i  + 3 + 8%i)
     + 
               +----+                  +--+                   +----+
       (- 7360\|- %i  - 5116 + 5576%i)\|%i  + (5116 + 5576%i)\|- %i  + 7760
  /
               +----+                    +--+                       +----+
       (129408\|- %i  + 90240 - 91200%i)\|%i  + (- 90240 - 91200%i)\|- %i
     + 
       - 127200
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (120)
--R                    +----+                  +--+                   +----+
--R           (12132%i\|- %i  + 8550 + 8460%i)\|%i  + (8550 - 8460%i)\|- %i
--R         + 
--R           - 11925%i
--R      *
--R                       +----+
--R         log((8 - 4%i)\|- %i  + 3 - 8%i)
--R     + 
--R                      +----+                  +--+                     +----+
--R           (- 12132%i\|- %i  - 8550 - 8460%i)\|%i  + (- 8550 + 8460%i)\|- %i
--R         + 
--R           11925%i
--R      *
--R                         +--+
--R         log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R     + 
--R               +----+                  +--+                   +----+
--R       (- 7360\|- %i  - 5116 + 5576%i)\|%i  + (5116 + 5576%i)\|- %i  + 7760
--R  /
--R               +----+                    +--+                       +----+
--R       (129408\|- %i  + 90240 - 91200%i)\|%i  + (- 90240 - 91200%i)\|- %i
--R     + 
--R       - 127200
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 120

--S 121 of 224
in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole")
 

   (121)
                      4            3            2
       - log(4infinity  - 8infinity  + 8infinity  - 4infinity + 1)
     + 
                                  2infinity - 1
       (- 4infinity + 2)atan(----------------------) - %pi
                                      2
                             2infinity  - 2infinity
  /
     8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (121)
--R                      4            3            2
--R       - log(4infinity  - 8infinity  + 8infinity  - 4infinity + 1)
--R     + 
--R                                  2infinity - 1
--R       (- 4infinity + 2)atan(----------------------) - %pi
--R                                      2
--R                             2infinity  - 2infinity
--R  /
--R     8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 121

--S 122 of 224
in2054:=integrate(atan(1/z^(1/2))+1, z= -1..1)
 

   (122)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (122)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 122

--S 123 of 224
in2056a:=integrate(z^(1/2)-acoth(1-z), z= 0..1,"noPole")
 

          - 3log(4) + 4
   (123)  -------------
                6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - 3log(4) + 4
--R   (123)  -------------
--R                6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 123

--S 124 of 224
in2058a:=integrate((z^2+%i*z-3)^(1/2)+z, z= -1..1,"noPole")
 

   (124)
                  +--------+               +--------+
           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
         + 
                          +--------+
           (- 88 + 924%i)\|- 2 - %i  + 979
      *
                       +--------+
         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                +--------+               +--------+                +--------+
           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
         + 
           - 979
      *
                         +--------+
         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                 +--------+                 +--------+
       (- 1280%i\|- 2 - %i  - 2312 - 356%i)\|- 2 + %i
     + 
                        +--------+
       (- 2312 + 356%i)\|- 2 - %i  + 3360%i
  /
             +--------+                 +--------+                  +--------+
       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
     + 
       - 1424
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (124)
--R                  +--------+               +--------+
--R           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
--R         + 
--R                          +--------+
--R           (- 88 + 924%i)\|- 2 - %i  + 979
--R      *
--R                       +--------+
--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                +--------+               +--------+                +--------+
--R           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
--R         + 
--R           - 979
--R      *
--R                         +--------+
--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                 +--------+                 +--------+
--R       (- 1280%i\|- 2 - %i  - 2312 - 356%i)\|- 2 + %i
--R     + 
--R                        +--------+
--R       (- 2312 + 356%i)\|- 2 - %i  + 3360%i
--R  /
--R             +--------+                 +--------+                  +--------+
--R       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
--R     + 
--R       - 1424
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 124

--S 125 of 224
in2068a:=integrate(1/(%i*z)^(1/2)-csch(z), z= 0..1,"noPole")
 

   (125)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (125)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 125

--S 126 of 224
in2071a:=integrate(1/(3+z)^3*acoth(z), z= -1..1,"noPole")
 

          - 3log(16) + 3log(4) - 2
   (126)  ------------------------
                     128
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - 3log(16) + 3log(4) - 2
--R   (126)  ------------------------
--R                     128
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 126

--S 127 of 224
in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole")
 

   (127)
                                         3+---+2
         13467752003249079711273325865856\|- 1
       + 
                                           3+---+
         - 27601768453337700619258203429120\|- 1
       + 
         30944953633416008247597858726912
    *
         3+---+
         \|- 1
       %e
   + 
     - 9746099248106233432776547720320%e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (127)
--R                                         3+---+2
--R         13467752003249079711273325865856\|- 1
--R       + 
--R                                           3+---+
--R         - 27601768453337700619258203429120\|- 1
--R       + 
--R         30944953633416008247597858726912
--R    *
--R         3+---+
--R         \|- 1
--R       %e
--R   + 
--R     - 9746099248106233432776547720320%e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 127

--S 128 of 224
in2094a:=integrate(asinh(z)-acoth(z), z= -1..1,"noPole")
 

                +-+                +-+
          log(2\|2  + 3) + log(- 2\|2  + 3)
   (128)  ---------------------------------
                          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+                +-+
--R          log(2\|2  + 3) + log(- 2\|2  + 3)
--R   (128)  ---------------------------------
--R                          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 128

--S 129 of 224
in2096a:=integrate(log(z)^2, z= %minusInfinity..%plusInfinity,"noPole")
 

   (129)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (129)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 129

--S 130 of 224
in2098a:=integrate(1/z^(1/3)-z^2/(z-1)^2, z= -1..1,"noPole")
 

   (130)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (130)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 130

--S 131 of 224
in2105a:=integrate(-1/(z^2-%i*z+2)^(1/2)/z, z= 0..1,"noPole")
 

   (131)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (131)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 131

--S 132 of 224
in2106a:=integrate(acos(z)+acoth(1-z), z= 0..1,"noPole")
 

          log(4) + 2
   (132)  ----------
               2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(4) + 2
--R   (132)  ----------
--R               2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 132

--S 133 of 224
in2112a:=integrate(-cot(z-1)+log(1-1/z^4), z= -1..1,"noPole")
 

   (133)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (133)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 133

--S 134 of 224
in2115a:=integrate(-z/(z-1)+log(1-z^(1/3)), z= -1..1,"noPole")
 

   (134)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (134)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 134

--S 135 of 224
in2120a:=integrate(-z+1/(z^2+%i*z-3)^(1/2), z= -1..1,"noPole")
 

   (135)
                 +--------+                              +--------+
   log((8 - 4%i)\|- 2 - %i  - 5 - 8%i) - log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
   ---------------------------------------------------------------------------
                                        2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (135)
--R                 +--------+                              +--------+
--R   log((8 - 4%i)\|- 2 - %i  - 5 - 8%i) - log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R   ---------------------------------------------------------------------------
--R                                        2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 135

--S 136 of 224
in25:=integrate(cos(z), z= %i..a)
 

   (136)  sin(a) - sin(%i)
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (136)  sin(a) - sin(%i)
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 136

--S 137 of 224
in25a:=integrate(cos(z), z= %i..a)
 

   (137)  sin(a) - sin(%i)
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (137)  sin(a) - sin(%i)
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 137

--S 138 of 224
in25b:=integrate(exp(%i*z), z= %i..%i*infinity)
 

                    - infinity
          - %i %e %e           + %i
   (138)  -------------------------
                      %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                    - infinity
--R          - %i %e %e           + %i
--R   (138)  -------------------------
--R                      %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 138

--S 139 of 224
in25c:=integrate(exp(%i*z), z= %i..%i*infinity)
 

                    - infinity
          - %i %e %e           + %i
   (139)  -------------------------
                      %e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                    - infinity
--R          - %i %e %e           + %i
--R   (139)  -------------------------
--R                      %e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 139

--S 140 of 224
in28a:=integrate(1/z, z=1..z,"noPole")
 

               2
          log(z )
   (140)  -------
             2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R               2
--R          log(z )
--R   (140)  -------
--R             2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 140

--S 141 of 224
in30:=integrate(sin(3*asin(1/(1+z^2))), z= 0..%plusInfinity)
 

          3%pi
   (141)  ----
            4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          3%pi
--R   (141)  ----
--R            4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 141

--S 142 of 224
in32:=integrate(exp(-z), z= 0..%plusInfinity)
 

   (142)  1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (142)  1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 142

--S 143 of 224
in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 

   (143)
       log
                              2                                   2
                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
             *
                 +-+
                \|3
            + 
                      2                                     2
              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
         /
                   2
            4sin(1)  - 4sin(1) + 1
     + 
                   +-+
       - log(- 168\|3  + 291)
  /
      +-+
     \|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (143)
--R       log
--R                              2                                   2
--R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R             *
--R                 +-+
--R                \|3
--R            + 
--R                      2                                     2
--R              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R         /
--R                   2
--R            4sin(1)  - 4sin(1) + 1
--R     + 
--R                   +-+
--R       - log(- 168\|3  + 291)
--R  /
--R      +-+
--R     \|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 143

--S 144 of 224
in37:=integrate(atan(tan(1/z)), z= 0..1)
 

   (144)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (144)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 144

--S 145 of 224
in40:=integrate(atan(tan(z)), z= 0..%plusInfinity)
 

   (145)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (145)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 145

--S 146 of 224
in2157a:=integrate(acoth(z)-1/(1+z^(1/2)), z= 0..1,"noPole")
 

          log(4) + 10log(2) - 8
   (146)  ---------------------
                    4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(4) + 10log(2) - 8
--R   (146)  ---------------------
--R                    4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 146

--S 147 of 224
in2158a:=integrate(2*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole")
 

   (147)  2log(4) - 2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (147)  2log(4) - 2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 147

--S 148 of 224
in2168a:=integrate(-csch(z-1)-(1+%i*z)^(1/2), z= 0..1,"noPole")
 

   (148)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (148)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 148

--S 149 of 224
in2185a:=integrate(csch(z)+(z^2-%i*z+1)^(1/2), z= 0..1,"noPole")
 

   (149)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (149)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 149

--S 150 of 224
in2195a:=integrate(1-acoth(1-(1-z)^(1/2)), z= -1..1,"noPole")
 

   (150)
         +-+            +-+                 +-+          +-+
   2log(\|2 ) - log(- 2\|2  + 3) + 3log(- 4\|2  + 6) + 4\|2  - 4log(4) + 8
   -----------------------------------------------------------------------
                                      4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (150)
--R         +-+            +-+                 +-+          +-+
--R   2log(\|2 ) - log(- 2\|2  + 3) + 3log(- 4\|2  + 6) + 4\|2  - 4log(4) + 8
--R   -----------------------------------------------------------------------
--R                                      4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 150

--S 151 of 224
in2201a:=integrate(acoth(z)+%pi-asec(z-1), z= 0..1,"noPole")
 

                +-+
          - %pi\|2  + log(4) + 2%pi
   (151)  -------------------------
                      2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+
--R          - %pi\|2  + log(4) + 2%pi
--R   (151)  -------------------------
--R                      2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 151

--S 152 of 224
in221:=integrate(log(z+sqrt(z^2-1)), z)
 

             +------+           +------+          +------+
             | 2         2      | 2               | 2         2
          (z\|z  - 1  - z )log(\|z  - 1  + z) + z\|z  - 1  - z  + 1
   (152)  ---------------------------------------------------------
                                 +------+
                                 | 2
                                \|z  - 1  - z
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +------+           +------+          +------+
--R             | 2         2      | 2               | 2         2
--R          (z\|z  - 1  - z )log(\|z  - 1  + z) + z\|z  - 1  - z  + 1
--R   (152)  ---------------------------------------------------------
--R                                 +------+
--R                                 | 2
--R                                \|z  - 1  - z
--R                                          Type: Union(Expression Integer,...)
--E 152

--S 153 of 224
in227a:=integrate(atan(sin(z))+atan(1/(sin(z))), z= 0..1,"noPole")
 

            %pi
   (153)  - ---
             2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            %pi
--R   (153)  - ---
--R             2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 153

--S 154 of 224
in237a:=integrate(sin(z)*(1-cos(z)/sqrt(1-sin(z)^2))^2, z= 0..1,"noPole")
 

   (154)  - 4cos(1) + 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (154)  - 4cos(1) + 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 154

--S 155 of 224
in2221:=integrate((z-%i)*(-1+1/(z-%i)), z= 0..%plusInfinity)
 

   (155)  - infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (155)  - infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 155

--S 156 of 224
in2243a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..1,"noPole")
 

   (156)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (156)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 156

--S 157 of 224
in2254a:=integrate(cosh(z^(1/2))-acoth(1-z), z= 0..1,"noPole")
 

          - %e log(4) + 4%e - 4
   (157)  ---------------------
                   2%e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - %e log(4) + 4%e - 4
--R   (157)  ---------------------
--R                   2%e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 157

--S 158 of 224
in2270a:=integrate(log(z)*log(1/z)*(%i*z)^(1/3), z= -1..1,"noPole")
 

              3+--+     3+----+
          - 27\|%i  - 27\|- %i
   (158)  ---------------------
                    32
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              3+--+     3+----+
--R          - 27\|%i  - 27\|- %i
--R   (158)  ---------------------
--R                    32
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 158

--S 159 of 224
in2274a:=integrate(acoth(1-z)-acosh(1/z), z= -1..1,"noPole")
 

          3log(9) - 4%pi
   (159)  --------------
                 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          3log(9) - 4%pi
--R   (159)  --------------
--R                 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 159

--S 160 of 224
in2275a:=integrate((z^2+%i*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole")
 

   (160)
                       +--------+                          +--------+
           (- 51691200\|- 2 - %i  - 26455440 + 73601880%i)\|- 2 + %i
         + 
                                   +--------+
           (26455440 + 73601880%i)\|- 2 - %i  + 118339815
      *
                       +--------+
         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                     +--------+                          +--------+
           (51691200\|- 2 - %i  + 26455440 - 73601880%i)\|- 2 + %i
         + 
                                     +--------+
           (- 26455440 - 73601880%i)\|- 2 - %i  - 118339815
      *
                         +--------+
         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                      +--------+                           +--------+
       (- 123056128%i\|- 2 - %i  - 167267016 - 40872532%i)\|- 2 + %i
     + 
                                  +--------+
       (- 167267016 + 40872532%i)\|- 2 - %i  + 236452160%i
  /
                 +--------+                          +--------+
       (21872640\|- 2 - %i  + 11194368 - 31143936%i)\|- 2 + %i
     + 
                                 +--------+
       (- 11194368 - 31143936%i)\|- 2 - %i  - 50074368
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (160)
--R                       +--------+                          +--------+
--R           (- 51691200\|- 2 - %i  - 26455440 + 73601880%i)\|- 2 + %i
--R         + 
--R                                   +--------+
--R           (26455440 + 73601880%i)\|- 2 - %i  + 118339815
--R      *
--R                       +--------+
--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                     +--------+                          +--------+
--R           (51691200\|- 2 - %i  + 26455440 - 73601880%i)\|- 2 + %i
--R         + 
--R                                     +--------+
--R           (- 26455440 - 73601880%i)\|- 2 - %i  - 118339815
--R      *
--R                         +--------+
--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                      +--------+                           +--------+
--R       (- 123056128%i\|- 2 - %i  - 167267016 - 40872532%i)\|- 2 + %i
--R     + 
--R                                  +--------+
--R       (- 167267016 + 40872532%i)\|- 2 - %i  + 236452160%i
--R  /
--R                 +--------+                          +--------+
--R       (21872640\|- 2 - %i  + 11194368 - 31143936%i)\|- 2 + %i
--R     + 
--R                                 +--------+
--R       (- 11194368 - 31143936%i)\|- 2 - %i  - 50074368
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 160

--S 161 of 224
in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole")
 

   (161)
                3+---+2          3+---+                3+---+
       (- 918750\|- 1   + 1200000\|- 1  + 2100000)atan(\|- 1  + 1)
     + 
                               3+---+2                              3+---+
       (918750atan(2) - 466984)\|- 1   + (- 1200000atan(2) - 364526)\|- 1
     + 
       - 2100000atan(2) + 96142
  /
          3+---+2        3+---+
     30625\|- 1   - 40000\|- 1  - 70000
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (161)
--R                3+---+2          3+---+                3+---+
--R       (- 918750\|- 1   + 1200000\|- 1  + 2100000)atan(\|- 1  + 1)
--R     + 
--R                               3+---+2                              3+---+
--R       (918750atan(2) - 466984)\|- 1   + (- 1200000atan(2) - 364526)\|- 1
--R     + 
--R       - 2100000atan(2) + 96142
--R  /
--R          3+---+2        3+---+
--R     30625\|- 1   - 40000\|- 1  - 70000
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 161

--S 162 of 224
in2278a:=integrate(acoth(1-z)+log(abs(z-1)/z), z= 0..1,"noPole")
 

          log(4)
   (162)  ------
             2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(4)
--R   (162)  ------
--R             2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 162

--S 163 of 224
in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole")
 

   (163)
                                                                     +-+
               +-+               +-+               +-+            - \|3  - 2
       2log(12\|3  + 21) + log(6\|3  + 12) - log(2\|3  + 4) + log(----------)
                                                                    +-+
                                                                   \|3  - 2
     + 
       log(16) - 2log(4)
  /
     4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (163)
--R                                                                     +-+
--R               +-+               +-+               +-+            - \|3  - 2
--R       2log(12\|3  + 21) + log(6\|3  + 12) - log(2\|3  + 4) + log(----------)
--R                                                                    +-+
--R                                                                   \|3  - 2
--R     + 
--R       log(16) - 2log(4)
--R  /
--R     4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 163

--S 164 of 224
in2311a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..%pi,"noPole")
 

   (164)
              %pi - 1 2      %pi - 1               %pi - 1 2      %pi - 1
       log((%e       )  + 2%e        + 1) - log((%e       )  - 2%e        + 1)
     + 
                              2                    2
             +------+       %e  + 2%e + 1        %e  - 2%e + 1
       - 4%i\|%i %pi  - log(-------------) + log(-------------)
                                   2                    2
                                 %e                   %e
  /
     2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (164)
--R              %pi - 1 2      %pi - 1               %pi - 1 2      %pi - 1
--R       log((%e       )  + 2%e        + 1) - log((%e       )  - 2%e        + 1)
--R     + 
--R                              2                    2
--R             +------+       %e  + 2%e + 1        %e  - 2%e + 1
--R       - 4%i\|%i %pi  - log(-------------) + log(-------------)
--R                                   2                    2
--R                                 %e                   %e
--R  /
--R     2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 164

--S 165 of 224
in2312:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1)
 

   (165)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (165)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 165

--S 166 of 224
in2312a:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole")
 

                          +----+                              +--+
          - log((8 - 4%i)\|- %i  + 3 - 8%i) + log((- 8 - 4%i)\|%i  + 3 + 8%i)
   (166)  -------------------------------------------------------------------
                                           2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R                          +----+                              +--+
--R          - log((8 - 4%i)\|- %i  + 3 - 8%i) + log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R   (166)  -------------------------------------------------------------------
--R                                           2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 166

--S 167 of 224
in2324a:=integrate(cosh(z^(1/2)-1)+acoth(1-z), z= 0..1,"noPole")
 

                         2
          %e log(4) + 2%e  - 4%e + 2
   (167)  --------------------------
                      2%e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                         2
--R          %e log(4) + 2%e  - 4%e + 2
--R   (167)  --------------------------
--R                      2%e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 167

--S 168 of 224
in2330a:=integrate(exp(-z)+1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole")
 

   (168)
                        +----+                                 +--+
       %e log((8 - 4%i)\|- %i  + 3 - 8%i) - %e log((- 8 - 4%i)\|%i  + 3 + 8%i)
     + 
          2
       2%e  - 2
  /
     2%e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (168)
--R                        +----+                                 +--+
--R       %e log((8 - 4%i)\|- %i  + 3 - 8%i) - %e log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R     + 
--R          2
--R       2%e  - 2
--R  /
--R     2%e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 168

--S 169 of 224
in2332a:=integrate(acoth(z^(1/2))*(1-z^(1/2)), z= 0..1,"noPole")
 

          log(16) - log(4) - 10log(2) + 8
   (169)  -------------------------------
                         12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(16) - log(4) - 10log(2) + 8
--R   (169)  -------------------------------
--R                         12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 169

--S 170 of 224
in2333a:=integrate(acoth(z)+1/(z^2+z+2)^(1/2), z= 0..1,"noPole")
 

                  +-+
          log(- 4\|2  + 9) + log(4)
   (170)  -------------------------
                      2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                  +-+
--R          log(- 4\|2  + 9) + log(4)
--R   (170)  -------------------------
--R                      2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 170

--S 171 of 224
in2360a:=integrate(1/(1-%i*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole")
 

   (171)  [ + infinity, + infinity]
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (171)  [ + infinity, + infinity]
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 171

--S 172 of 224
in2367a:=integrate(log(1-z^2)-1/(%i/(z-%i))^(1/2), z= -1..1,"noPole")
 

   (172)
                                         %i           %i
             (6log(4) + 3log(2%i) - 3log(--) - 3log(- --) + 3log(- 2%i) - 24)
                                          2            2
          *
              +--------+
              |    %i
              |- ------
             \|  1 + %i
         + 
           - 4 - 4%i
      *
          +------+
          |   1
          |------
         \|1 + %i
     + 
                 +--------+
                 |    %i
       (4 + 4%i) |- ------
                \|  1 + %i
  /
        +--------+ +------+
        |    %i    |   1
     6  |- ------  |------
       \|  1 + %i \|1 + %i
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (172)
--R                                         %i           %i
--R             (6log(4) + 3log(2%i) - 3log(--) - 3log(- --) + 3log(- 2%i) - 24)
--R                                          2            2
--R          *
--R              +--------+
--R              |    %i
--R              |- ------
--R             \|  1 + %i
--R         + 
--R           - 4 - 4%i
--R      *
--R          +------+
--R          |   1
--R          |------
--R         \|1 + %i
--R     + 
--R                 +--------+
--R                 |    %i
--R       (4 + 4%i) |- ------
--R                \|  1 + %i
--R  /
--R        +--------+ +------+
--R        |    %i    |   1
--R     6  |- ------  |------
--R       \|  1 + %i \|1 + %i
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 172

--S 173 of 224
in2375a:=integrate(acoth(1-z^(1/2))+1/z^(1/3), z= 0..1,"noPole")
 

          2log(4) + 1
   (173)  -----------
               2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          2log(4) + 1
--R   (173)  -----------
--R               2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 173

--S 174 of 224
in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole")
 

   (174)
           +-+
         3\|5
      *
         log
                      +-+      3+--------+2
                (- 12\|5  - 36)\|infinity
              + 
                      +-+                  3+--------+                     +-+
                (- 16\|5  - 4infinity - 32)\|infinity  + (- 8infinity - 6)\|5
              + 
                - 8infinity - 14
           /
              3+--------+2                   3+--------+
              \|infinity   + (- infinity + 2)\|infinity  - 2infinity - 1
     + 
         (3infinity + 6)
      *
               3+--------+2                 3+--------+
         log(- \|infinity   + (infinity - 2)\|infinity  + 2infinity + 1)
     + 
        3+--------+2     3+--------+     +-+      +-+
       3\|infinity   - 18\|infinity  - 3\|5 log(6\|5  + 14) - 4infinity
  /
     6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (174)
--R           +-+
--R         3\|5
--R      *
--R         log
--R                      +-+      3+--------+2
--R                (- 12\|5  - 36)\|infinity
--R              + 
--R                      +-+                  3+--------+                     +-+
--R                (- 16\|5  - 4infinity - 32)\|infinity  + (- 8infinity - 6)\|5
--R              + 
--R                - 8infinity - 14
--R           /
--R              3+--------+2                   3+--------+
--R              \|infinity   + (- infinity + 2)\|infinity  - 2infinity - 1
--R     + 
--R         (3infinity + 6)
--R      *
--R               3+--------+2                 3+--------+
--R         log(- \|infinity   + (infinity - 2)\|infinity  + 2infinity + 1)
--R     + 
--R        3+--------+2     3+--------+     +-+      +-+
--R       3\|infinity   - 18\|infinity  - 3\|5 log(6\|5  + 14) - 4infinity
--R  /
--R     6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 174

--S 175 of 224
in2378a:=integrate((z^2+%i*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole")
 

   (175)
                  +--------+               +--------+
           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
         + 
                          +--------+
           (- 88 + 924%i)\|- 2 - %i  + 979
      *
                       +--------+
         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                +--------+               +--------+                +--------+
           (640\|- 2 - %i  - 64 - 672%i)\|- 2 + %i  + (64 - 672%i)\|- 2 - %i
         + 
           - 712
      *
                2 4       2 2
             (%e )  + 2(%e )  + 1
         log(--------------------)
                       2 4
                    (%e )
     + 
                +--------+               +--------+                +--------+
           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
         + 
           - 979
      *
                         +--------+
         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                                         +--------+
           (- 640log(4) + 2560 - 1280%i)\|- 2 - %i  + (64 + 672%i)log(4) - 2568
         + 
           - 3044%i
      *
          +--------+
         \|- 2 + %i
     + 
                                              +--------+
       ((- 64 + 672%i)log(4) - 2056 - 2332%i)\|- 2 - %i  + 712log(4) - 2848
     + 
       3360%i
  /
             +--------+                 +--------+                  +--------+
       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
     + 
       - 1424
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (175)
--R                  +--------+               +--------+
--R           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
--R         + 
--R                          +--------+
--R           (- 88 + 924%i)\|- 2 - %i  + 979
--R      *
--R                       +--------+
--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                +--------+               +--------+                +--------+
--R           (640\|- 2 - %i  - 64 - 672%i)\|- 2 + %i  + (64 - 672%i)\|- 2 - %i
--R         + 
--R           - 712
--R      *
--R                2 4       2 2
--R             (%e )  + 2(%e )  + 1
--R         log(--------------------)
--R                       2 4
--R                    (%e )
--R     + 
--R                +--------+               +--------+                +--------+
--R           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
--R         + 
--R           - 979
--R      *
--R                         +--------+
--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                                         +--------+
--R           (- 640log(4) + 2560 - 1280%i)\|- 2 - %i  + (64 + 672%i)log(4) - 2568
--R         + 
--R           - 3044%i
--R      *
--R          +--------+
--R         \|- 2 + %i
--R     + 
--R                                              +--------+
--R       ((- 64 + 672%i)log(4) - 2056 - 2332%i)\|- 2 - %i  + 712log(4) - 2848
--R     + 
--R       3360%i
--R  /
--R             +--------+                 +--------+                  +--------+
--R       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
--R     + 
--R       - 1424
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 175

--S 176 of 224
in2386a:=integrate(acoth(1-z)-(z^2-z+2)^(1/2), z= 0..1,"noPole")
 

                   +-+                 +-+          +-+
          - 7log(4\|2  + 9) + 7log(- 4\|2  + 9) - 8\|2  + 8log(4)
   (176)  -------------------------------------------------------
                                     16
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                   +-+                 +-+          +-+
--R          - 7log(4\|2  + 9) + 7log(- 4\|2  + 9) - 8\|2  + 8log(4)
--R   (176)  -------------------------------------------------------
--R                                     16
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 176

--S 177 of 224
in2390a:=integrate((z^2-%i*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole")
 

   (177)
                   2%i +--------+                  2%i  +--------+
           (- 560%e   \|- 1 - %i  + (168 - 476%i)%e   )\|- 1 + %i
         + 
                            2%i +--------+        2%i
           (- 168 - 476%i)%e   \|- 1 - %i  + 455%e
      *
                       +--------+
         log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
     + 
                 2%i +--------+                    2%i  +--------+
           (560%e   \|- 1 - %i  + (- 168 + 476%i)%e   )\|- 1 + %i
         + 
                          2%i +--------+        2%i
           (168 + 476%i)%e   \|- 1 - %i  - 455%e
      *
                         +--------+
         log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i)
     + 
                       2%i 2            2%i          +--------+
           (- 640%i (%e   )  + 1280%i %e    + 640%i)\|- 1 - %i
         + 
                           2%i 2                     2%i
           (544 + 192%i)(%e   )  + (- 1480 - 580%i)%e    - 544 - 192%i
      *
          +--------+
         \|- 1 + %i
     + 
                        2%i 2                     2%i                +--------+
       ((544 - 192%i)(%e   )  + (- 1480 + 580%i)%e    - 544 + 192%i)\|- 1 - %i
     + 
                2%i 2            2%i
       520%i (%e   )  - 1824%i %e    - 520%i
  /
              2%i +--------+                     2%i  +--------+
       (1280%e   \|- 1 - %i  + (- 384 + 1088%i)%e   )\|- 1 + %i
     + 
                       2%i +--------+         2%i
       (384 + 1088%i)%e   \|- 1 - %i  - 1040%e
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (177)
--R                   2%i +--------+                  2%i  +--------+
--R           (- 560%e   \|- 1 - %i  + (168 - 476%i)%e   )\|- 1 + %i
--R         + 
--R                            2%i +--------+        2%i
--R           (- 168 - 476%i)%e   \|- 1 - %i  + 455%e
--R      *
--R                       +--------+
--R         log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
--R     + 
--R                 2%i +--------+                    2%i  +--------+
--R           (560%e   \|- 1 - %i  + (- 168 + 476%i)%e   )\|- 1 + %i
--R         + 
--R                          2%i +--------+        2%i
--R           (168 + 476%i)%e   \|- 1 - %i  - 455%e
--R      *
--R                         +--------+
--R         log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i)
--R     + 
--R                       2%i 2            2%i          +--------+
--R           (- 640%i (%e   )  + 1280%i %e    + 640%i)\|- 1 - %i
--R         + 
--R                           2%i 2                     2%i
--R           (544 + 192%i)(%e   )  + (- 1480 - 580%i)%e    - 544 - 192%i
--R      *
--R          +--------+
--R         \|- 1 + %i
--R     + 
--R                        2%i 2                     2%i                +--------+
--R       ((544 - 192%i)(%e   )  + (- 1480 + 580%i)%e    - 544 + 192%i)\|- 1 - %i
--R     + 
--R                2%i 2            2%i
--R       520%i (%e   )  - 1824%i %e    - 520%i
--R  /
--R              2%i +--------+                     2%i  +--------+
--R       (1280%e   \|- 1 - %i  + (- 384 + 1088%i)%e   )\|- 1 + %i
--R     + 
--R                       2%i +--------+         2%i
--R       (384 + 1088%i)%e   \|- 1 - %i  - 1040%e
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 177

--S 178 of 224
in2392a:=integrate(1/sec(z-1)+acoth(1-z^(1/2)), z= 0..1,"noPole")
 

   (178)  sin(1) + log(4) - 1
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (178)  sin(1) + log(4) - 1
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 178

--S 179 of 224
in2404a:=integrate(1/(1+%i*z^2)^(1/2)+acoth(z), z= -1..1,"noPole")
 

   (179)
   [
            +-----+
           \|- 4%i
        *
           log
                             +-----+             +------+               +-----+
                  ((4 - 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i  + (- 8 + 8%i)\|- 4%i
                + 
                  - 20%i
             /
                  +------+
                2\|1 + %i  - 2 - %i
       + 
         -
               +-----+
              \|- 4%i
           *
              log
                                  +-----+             +------+
                     ((- 4 + 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i
                   + 
                               +-----+
                     (8 - 8%i)\|- 4%i  - 20%i
                /
                     +------+
                   2\|1 + %i  - 2 - %i
    /
       4
     ,
                      +------+
        +---+     2%i\|1 + %i  - 2%i
    - 2\|4%i atan(------------------)]
                         +---+
                        \|4%i
       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (179)
--R   [
--R            +-----+
--R           \|- 4%i
--R        *
--R           log
--R                             +-----+             +------+               +-----+
--R                  ((4 - 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i  + (- 8 + 8%i)\|- 4%i
--R                + 
--R                  - 20%i
--R             /
--R                  +------+
--R                2\|1 + %i  - 2 - %i
--R       + 
--R         -
--R               +-----+
--R              \|- 4%i
--R           *
--R              log
--R                                  +-----+             +------+
--R                     ((- 4 + 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i
--R                   + 
--R                               +-----+
--R                     (8 - 8%i)\|- 4%i  - 20%i
--R                /
--R                     +------+
--R                   2\|1 + %i  - 2 - %i
--R    /
--R       4
--R     ,
--R                      +------+
--R        +---+     2%i\|1 + %i  - 2%i
--R    - 2\|4%i atan(------------------)]
--R                         +---+
--R                        \|4%i
--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
--E 179

--S 180 of 224
in2409a:=integrate(tan(z)+1/(%i/(z+%i))^(1/2), z= 0..1/2*%pi,"noPole")
 

   (180)   + infinity
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (180)   + infinity
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 180

--S 181 of 224
in248a:=integrate(log(z^%i)^2, z= 0..1,"noPole")
 

   (181)  - 2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (181)  - 2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 181

--S 182 of 224
in248b:=integrate(log(z^%i)^2, z= 0..1,"noPole")
 

   (182)  - 2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (182)  - 2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 182

--S 183 of 224
in249a:=integrate((sin(z)/(cos(z)-1))^(1/3), z= 0..%pi,"noPole")
 

                 3+-+           3+-+         +-+
          3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3
   (183)  --------------------------------------
                            24
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 3+-+           3+-+         +-+
--R          3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3
--R   (183)  --------------------------------------
--R                            24
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 183

--S 184 of 224
in251a:=integrate((-1)^z*exp(-z)*sin(z), z= 0..%plusInfinity,"noPole")
 

               2
          - %pi  + 2
   (184)  ----------
              4
           %pi  + 4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R               2
--R          - %pi  + 2
--R   (184)  ----------
--R              4
--R           %pi  + 4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 184

--S 185 of 224
in2434a:=integrate(acoth(z^(1/2))+log(abs(z-1)), z= 0..1,"noPole")
 

          log(16) + log(4) - 6log(2)
   (185)  --------------------------
                       4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(16) + log(4) - 6log(2)
--R   (185)  --------------------------
--R                       4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 185

--S 186 of 224
in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole")
 

   (186)
                                        3+---+2    3+---+
           3+---+2    3+---+            \|- 1   - 2\|- 1  + 1
       log(\|- 1   - 2\|- 1  + 1) + log(---------------------) + 4atan(%e)
                                               3+---+2
                                               \|- 1
     + 
                1    3+---+2    3+---+
       - 4atan(--) + \|- 1   + 2\|- 1  - 3
               %e
  /
     2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (186)
--R                                        3+---+2    3+---+
--R           3+---+2    3+---+            \|- 1   - 2\|- 1  + 1
--R       log(\|- 1   - 2\|- 1  + 1) + log(---------------------) + 4atan(%e)
--R                                               3+---+2
--R                                               \|- 1
--R     + 
--R                1    3+---+2    3+---+
--R       - 4atan(--) + \|- 1   + 2\|- 1  - 3
--R               %e
--R  /
--R     2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 186

--S 187 of 224
in2462a:=integrate(log((1+(1-z)^(1/2))/z)+csch(z), z= -1..0,"noPole")
 

   (187)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (187)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 187

--S 188 of 224
in2469a:=integrate(1/(2+z)^2+1/(z^2-%i*z-2)^(1/2), z= -1..1,"noPole")
 

   (188)
                      +--------+
       3log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
     + 
                          +--------+
       - 3log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i) + 4
  /
     6
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (188)
--R                      +--------+
--R       3log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
--R     + 
--R                          +--------+
--R       - 3log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i) + 4
--R  /
--R     6
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 188

--S 189 of 224
in2484a:=integrate(log(1-z^2)+sinh(z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (189)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (189)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 189

--S 190 of 224
in2485a:=integrate(log(1-z^(1/2))-acoth(z^(1/2)), z= 0..1,"noPole")
 

          - log(16) + log(4) + 2log(2) - 10
   (190)  ---------------------------------
                          4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          - log(16) + log(4) + 2log(2) - 10
--R   (190)  ---------------------------------
--R                          4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 190

--S 191 of 224
in2521a:=integrate(acoth(z^(1/2))+cos(z^(1/2)-1), z= 0..1,"noPole")
 

   (191)  - 2cos(1) + 3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (191)  - 2cos(1) + 3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 191

--S 192 of 224
in2524a:=integrate(log(abs(1+1/z^(1/3)))+log(1+1/z), z= -1..0,"noPole")
 

   (192)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (192)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 192

--S 193 of 224
in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole")
 

   (193)
                                          3+---+2    3+---+
              3+---+2   3+---+            \|- 1   - 2\|- 1  + 1    3+---+2
       - log(3\|- 1   + \|- 1  - 1) + log(---------------------) + \|- 1
                                                 3+---+2
                                                 \|- 1
     + 
        3+---+
       2\|- 1  - log(4)
  /
     2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (193)
--R                                          3+---+2    3+---+
--R              3+---+2   3+---+            \|- 1   - 2\|- 1  + 1    3+---+2
--R       - log(3\|- 1   + \|- 1  - 1) + log(---------------------) + \|- 1
--R                                                 3+---+2
--R                                                 \|- 1
--R     + 
--R        3+---+
--R       2\|- 1  - log(4)
--R  /
--R     2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 193

--S 194 of 224
in2566a:=integrate(log(1+(1-z)^(1/2))+acoth(1-z), z= -1..1,"noPole")
 

                +-+          +-+
          4log(\|2  + 1) + 4\|2  + 3log(9) - 4
   (194)  ------------------------------------
                            4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                +-+          +-+
--R          4log(\|2  + 1) + 4\|2  + 3log(9) - 4
--R   (194)  ------------------------------------
--R                            4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 194

--S 195 of 224
in2586a:=integrate(acoth(z^(1/2))+atan(z^(1/2)), z= 0..1,"noPole")
 

          log(16) - log(4) - 2log(2) + 2%pi
   (195)  ---------------------------------
                          4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(16) - log(4) - 2log(2) + 2%pi
--R   (195)  ---------------------------------
--R                          4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 195

--S 196 of 224
in2591a:=integrate(log(z)/(1-z^(1/2))^3-log(z)*log(-z), z= 0..1,"noPole")
 

   (196)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (196)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 196

--S 197 of 224
in2598a:=integrate(exp(-z^(1/2))+acoth(1-z^(1/2)), z= 0..1,"noPole")
 

          %e log(4) + %e - 4
   (197)  ------------------
                  %e
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          %e log(4) + %e - 4
--R   (197)  ------------------
--R                  %e
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 197

--S 198 of 224
in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole")
 

   (198)
             6+-+2                6+-+3                6+-+3         6+-+4
       18log(\|2   + 1) + 3log(- 2\|2   + 3) - 6log(- 4\|2   + 6) + 3\|2
     + 
          6+-+3    6+-+2
       - 6\|2   - 6\|2   - 12log(2) + 7
  /
     6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (198)
--R             6+-+2                6+-+3                6+-+3         6+-+4
--R       18log(\|2   + 1) + 3log(- 2\|2   + 3) - 6log(- 4\|2   + 6) + 3\|2
--R     + 
--R          6+-+3    6+-+2
--R       - 6\|2   - 6\|2   - 12log(2) + 7
--R  /
--R     6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 198

--S 199 of 224
in271a:=integrate(1/sqrt((z^2-1)*(z^2-1)), z= 2..%plusInfinity,"noPole")
 

          log(9)
   (199)  ------
             4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          log(9)
--R   (199)  ------
--R             4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 199

--S 200 of 224
in275c:=integrate(sqrt(z), z= -%i..%i,"noPole")
 

              +--+       +----+
          2%i\|%i  + 2%i\|- %i
   (200)  ---------------------
                    3
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R              +--+       +----+
--R          2%i\|%i  + 2%i\|- %i
--R   (200)  ---------------------
--R                    3
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 200

--S 201 of 224
in275a:=integrate(1/(1+z), z= -%i..%i,"noPole")
 

          log(2%i) - log(- 2%i)
   (201)  ---------------------
                    2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R          log(2%i) - log(- 2%i)
--R   (201)  ---------------------
--R                    2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 201

--S 202 of 224
in275b:=integrate(1/(1+z), z= -%i..%i,"noPole")
 

          log(2%i) - log(- 2%i)
   (202)  ---------------------
                    2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R          log(2%i) - log(- 2%i)
--R   (202)  ---------------------
--R                    2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 202

--S 203 of 224
in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole")
 

   (203)
           +-+
         3\|5
      *
         log
                                +--------+2                   +--------+
                      +-+      3| +-+               +-+      3| +-+          +-+
                (- 12\|5  - 36)\|\|5  - 2   + (- 20\|5  - 24)\|\|5  - 2  + 2\|5
              + 
                - 38
           /
               +--------+2                +--------+
              3| +-+             +-+     3| +-+          +-+
              \|\|5  - 2   + (- \|5  + 4)\|\|5  - 2  - 2\|5  + 3
     + 
                   +--------+2              +--------+
         +-+      3| +-+           +-+     3| +-+          +-+
       3\|5 log(- \|\|5  - 2   + (\|5  - 4)\|\|5  - 2  + 2\|5  - 3)
     + 
         +--------+2      +--------+
        3| +-+           3| +-+          +-+      +-+           +-+
       3\|\|5  - 2   - 18\|\|5  - 2  - 3\|5 log(6\|5  + 14) - 4\|5  + 8
  /
     6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (203)
--R           +-+
--R         3\|5
--R      *
--R         log
--R                                +--------+2                   +--------+
--R                      +-+      3| +-+               +-+      3| +-+          +-+
--R                (- 12\|5  - 36)\|\|5  - 2   + (- 20\|5  - 24)\|\|5  - 2  + 2\|5
--R              + 
--R                - 38
--R           /
--R               +--------+2                +--------+
--R              3| +-+             +-+     3| +-+          +-+
--R              \|\|5  - 2   + (- \|5  + 4)\|\|5  - 2  - 2\|5  + 3
--R     + 
--R                   +--------+2              +--------+
--R         +-+      3| +-+           +-+     3| +-+          +-+
--R       3\|5 log(- \|\|5  - 2   + (\|5  - 4)\|\|5  - 2  + 2\|5  - 3)
--R     + 
--R         +--------+2      +--------+
--R        3| +-+           3| +-+          +-+      +-+           +-+
--R       3\|\|5  - 2   - 18\|\|5  - 2  - 3\|5 log(6\|5  + 14) - 4\|5  + 8
--R  /
--R     6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 203

--S 204 of 224
in2634a:=integrate(1/(z^2+%i*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole")
 

   (204)
                     +----+                              +--+
       log((8 - 4%i)\|- %i  + 3 - 8%i) - log((- 8 - 4%i)\|%i  + 3 + 8%i)
     + 
       2log(4) - 4
  /
     2
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (204)
--R                     +----+                              +--+
--R       log((8 - 4%i)\|- %i  + 3 - 8%i) - log((- 8 - 4%i)\|%i  + 3 + 8%i)
--R     + 
--R       2log(4) - 4
--R  /
--R     2
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 204

--S 205 of 224
in2656a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole")
 

   (205)
            +-+            +-+                 +-+          +-+
   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
   ----------------------------------------------------------------------
                                      4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (205)
--R            +-+            +-+                 +-+          +-+
--R   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
--R   ----------------------------------------------------------------------
--R                                      4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 205

--S 206 of 224
in2676a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole")
 

   (206)
            +-+            +-+                 +-+          +-+
   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
   ----------------------------------------------------------------------
                                      4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (206)
--R            +-+            +-+                 +-+          +-+
--R   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
--R   ----------------------------------------------------------------------
--R                                      4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 206

--S 207 of 224
in2664aa:=integrate(atanh(1/z)+(1+z^2)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (207)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (207)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 207

--S 208 of 224
in2681a:=integrate((z^2-%i*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole")
 

   (208)
                  +--------+               +--------+                +--------+
           (- 880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
         + 
           979
      *
                       +--------+
         log((8 + 4%i)\|- 2 + %i  - 5 + 8%i)
     + 
                +--------+               +--------+                  +--------+
           (880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i  + (- 88 + 924%i)\|- 2 - %i
         + 
           - 979
      *
                         +--------+
         log((- 8 + 4%i)\|- 2 - %i  - 5 - 8%i)
     + 
                                   - 4 + 3%i                      +--------+
           (320log(25) - 640%i log(---------) + 2560%pi + 1280%i)\|- 2 - %i
                                    4 + 3%i
         + 
                                                 - 4 + 3%i
           (32 + 336%i)log(25) + (672 - 64%i)log(---------) + (256 + 2688%i)%pi
                                                  4 + 3%i
         + 
           - 2312 - 356%i
      *
          +--------+
         \|- 2 + %i
     + 
                                                   - 4 + 3%i
           (- 32 + 336%i)log(25) + (672 + 64%i)log(---------)
                                                    4 + 3%i
         + 
           (- 256 + 2688%i)%pi - 2312 + 356%i
      *
          +--------+
         \|- 2 - %i
     + 
                                - 4 + 3%i
       - 356log(25) + 712%i log(---------) - 2848%pi - 3360%i
                                 4 + 3%i
  /
             +--------+                 +--------+                    +--------+
       (1280\|- 2 - %i  + 128 + 1344%i)\|- 2 + %i  + (- 128 + 1344%i)\|- 2 - %i
     + 
       - 1424
            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--R 
--R
--R   (208)
--R                  +--------+               +--------+                +--------+
--R           (- 880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
--R         + 
--R           979
--R      *
--R                       +--------+
--R         log((8 + 4%i)\|- 2 + %i  - 5 + 8%i)
--R     + 
--R                +--------+               +--------+                  +--------+
--R           (880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i  + (- 88 + 924%i)\|- 2 - %i
--R         + 
--R           - 979
--R      *
--R                         +--------+
--R         log((- 8 + 4%i)\|- 2 - %i  - 5 - 8%i)
--R     + 
--R                                   - 4 + 3%i                      +--------+
--R           (320log(25) - 640%i log(---------) + 2560%pi + 1280%i)\|- 2 - %i
--R                                    4 + 3%i
--R         + 
--R                                                 - 4 + 3%i
--R           (32 + 336%i)log(25) + (672 - 64%i)log(---------) + (256 + 2688%i)%pi
--R                                                  4 + 3%i
--R         + 
--R           - 2312 - 356%i
--R      *
--R          +--------+
--R         \|- 2 + %i
--R     + 
--R                                                   - 4 + 3%i
--R           (- 32 + 336%i)log(25) + (672 + 64%i)log(---------)
--R                                                    4 + 3%i
--R         + 
--R           (- 256 + 2688%i)%pi - 2312 + 356%i
--R      *
--R          +--------+
--R         \|- 2 - %i
--R     + 
--R                                - 4 + 3%i
--R       - 356log(25) + 712%i log(---------) - 2848%pi - 3360%i
--R                                 4 + 3%i
--R  /
--R             +--------+                 +--------+                    +--------+
--R       (1280\|- 2 - %i  + 128 + 1344%i)\|- 2 + %i  + (- 128 + 1344%i)\|- 2 - %i
--R     + 
--R       - 1424
--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
--E 208

--S 209 of 224
in2720a:=integrate(acoth(1-(1-z)^(1/2))+atan(z-1), z= 0..1,"noPole")
 

          5log(4) - %pi - 4
   (209)  -----------------
                  4
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          5log(4) - %pi - 4
--R   (209)  -----------------
--R                  4
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 209

--S 210 of 224
in2724a:=integrate(log(1-1/z^3)-(1+1/z^2)^(1/2), z= 0..%plusInfinity,"noPole")
 

   (210)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (210)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 210

--S 211 of 224
in2732:=integrate(atan(1/3*3^(1/2)*(2*z-1)), z= 0..%plusInfinity)
 

   (211)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (211)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 211

--S 212 of 224
in2783a:=integrate(1/z^(1/3)+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (212)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (212)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 212

--S 213 of 224
in285:=integrate(sqrt(1+sqrt(z-1)), z)
 

                                 +------------+
             +-----+             | +-----+
          (4\|z - 1  + 12z - 20)\|\|z - 1  + 1
   (213)  -------------------------------------
                            15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 +------------+
--R             +-----+             | +-----+
--R          (4\|z - 1  + 12z - 20)\|\|z - 1  + 1
--R   (213)  -------------------------------------
--R                            15
--R                                          Type: Union(Expression Integer,...)
--E 213

--S 214 of 224
in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z)
 

                                  +-------------+
             +------+             | +------+
             | 2          2       | | 2
          (2\|z  - 1  + 6z  - 10)\|\|z  - 1  + 1
   (214)  ---------------------------------------
                             15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                  +-------------+
--R             +------+             | +------+
--R             | 2          2       | | 2
--R          (2\|z  - 1  + 6z  - 10)\|\|z  - 1  + 1
--R   (214)  ---------------------------------------
--R                             15
--R                                          Type: Union(Expression Integer,...)
--E 214

--S 215 of 224
in295ba:=integrate(z*sqrt(1+sqrt(z^2-1)), z= 1..sqrt(2),"noPole")
 

            +-+
          4\|2  + 4
   (215)  ---------
              15
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            +-+
--R          4\|2  + 4
--R   (215)  ---------
--R              15
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 215

--S 216 of 224
integrate(1/sqrt(20+x^2+y^2), x = -5..5,"noPole")
 

                 +-------+                       +-------+
                 | 2          2                  | 2          2
          log(10\|y  + 45  + y  + 70) - log(- 10\|y  + 45  + y  + 70)
   (216)  -----------------------------------------------------------
                                       2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                 +-------+                       +-------+
--R                 | 2          2                  | 2          2
--R          log(10\|y  + 45  + y  + 70) - log(- 10\|y  + 45  + y  + 70)
--R   (216)  -----------------------------------------------------------
--R                                       2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 216

--S 217 of 224
in291:=integrate(cos(2*atan(z-sqrt(2)))-sin(2*atan(z-sqrt(2))), z = 0..%plusInfinity)
 

   (217)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (217)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 217

--S 218 of 224
in2992a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..%plusInfinity,"noPole")
 

   (218)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (218)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 218

--S 219 of 224
in2997a:=integrate(log(1+1/z^3)-log(abs(1+z)), z= %minusInfinity..%plusInfinity,"noPole")
 

   (219)  - infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (219)  - infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 219

--S 220 of 224
in3008a:=integrate(exp(-z^(1/3))+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 

   (220)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (220)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 220

--S 221 of 224
in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole")
 

   (221)
       log
                     +-+           - n 8          +-+          - n 6
              (- 816\|2  + 1154)(%e   )  + (- 560\|2  + 792)(%e   )
            + 
                     +-+          - n 4         +-+         - n 2
              (- 144\|2  + 204)(%e   )  + (- 16\|2  + 24)(%e   )  + 2
         /
               - n 8        - n 6        - n 4        - n 2
            (%e   )  + 12(%e   )  + 38(%e   )  + 12(%e   )  + 1
     + 
                  +-+
       - log(- 24\|2  + 34)
  /
        +-+
     4n\|2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (221)
--R       log
--R                     +-+           - n 8          +-+          - n 6
--R              (- 816\|2  + 1154)(%e   )  + (- 560\|2  + 792)(%e   )
--R            + 
--R                     +-+          - n 4         +-+         - n 2
--R              (- 144\|2  + 204)(%e   )  + (- 16\|2  + 24)(%e   )  + 2
--R         /
--R               - n 8        - n 6        - n 4        - n 2
--R            (%e   )  + 12(%e   )  + 38(%e   )  + 12(%e   )  + 1
--R     + 
--R                  +-+
--R       - log(- 24\|2  + 34)
--R  /
--R        +-+
--R     4n\|2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 221

--S 222 of 224
in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 

   (222)
       log
                              2                                   2
                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
                  + 
                    - 48
             *
                 +-+
                \|3
            + 
                      2                                     2
              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
         /
                   2
            4sin(1)  - 4sin(1) + 1
     + 
                   +-+
       - log(- 168\|3  + 291)
  /
      +-+
     \|3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (222)
--R       log
--R                              2                                   2
--R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
--R                  + 
--R                    - 48
--R             *
--R                 +-+
--R                \|3
--R            + 
--R                      2                                     2
--R              21sin(1)  + (- 72cos(1) - 84)sin(1) + 63cos(1)  + 144cos(1) + 84
--R         /
--R                   2
--R            4sin(1)  - 4sin(1) + 1
--R     + 
--R                   +-+
--R       - log(- 168\|3  + 291)
--R  /
--R      +-+
--R     \|3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 222

--S 223 of 224
in317:=integrate((cos(z)^a)^(1/a), z= 0..%pi)
 

   (223)  0
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (223)  0
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 223

--S 224 of 224
in319a:=integrate(exp(-z)*atan(sin(z)/(1+cos(z))), z=0..%plusInfinity,"noPole")
 

          1
   (224)  -
          2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (224)  -
--R          2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 224
)spool 
 
Starts dribbling to XPBWPolynomial.output (2010/3/27, 18:46:43).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 39
a:Symbol := 'a
 

   (1)  a
                                                                 Type: Symbol
--R 
--R
--R   (1)  a
--R                                                                 Type: Symbol
--E 1

--S 2 of 39
b:Symbol := 'b
 

   (2)  b
                                                                 Type: Symbol
--R 
--R
--R   (2)  b
--R                                                                 Type: Symbol
--E 2

--S 3 of 39
RN := Fraction(Integer)
 

   (3)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (3)  Fraction Integer
--R                                                                 Type: Domain
--E 3

--S 4 of 39
word := OrderedFreeMonoid Symbol
 

   (4)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 39
lword := LyndonWord(Symbol)
 

   (5)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 39
base := PoincareBirkhoffWittLyndonBasis Symbol
 

   (6)  PoincareBirkhoffWittLyndonBasis Symbol
                                                                 Type: Domain
--R 
--R
--R   (6)  PoincareBirkhoffWittLyndonBasis Symbol
--R                                                                 Type: Domain
--E 6

--S 7 of 39
dpoly := XDistributedPolynomial(Symbol, RN)
 

   (7)  XDistributedPolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (7)  XDistributedPolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 7

--S 8 of 39
rpoly := XRecursivePolynomial(Symbol, RN)
 

   (8)  XRecursivePolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (8)  XRecursivePolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 8

--S 9 of 39
lpoly := LiePolynomial(Symbol, RN)
 

   (9)  LiePolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (9)  LiePolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 9

--S 10 of 39
poly  := XPBWPolynomial(Symbol, RN)
 

   (10)  XPBWPolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (10)  XPBWPolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 10

--S 11 of 39
liste : List lword := LyndonWordsList([a,b], 6)
 

   (11)
                       2        2     3      2 2       3     4      3 2
   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
      2          2 3           2       4     5      4 2     3          3 3
    [a b a b], [a b ], [a b a b ], [a b ], [a b], [a b ], [a b a b], [a b ],
      2     2     2 2        2 4           3       5
    [a b a b ], [a b a b], [a b ], [a b a b ], [a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (11)
--R                       2        2     3      2 2       3     4      3 2
--R   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
--R      2          2 3           2       4     5      4 2     3          3 3
--R    [a b a b], [a b ], [a b a b ], [a b ], [a b], [a b ], [a b a b], [a b ],
--R      2     2     2 2        2 4           3       5
--R    [a b a b ], [a b a b], [a b ], [a b a b ], [a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 11

--S 12 of 39
0$poly
 

   (12)  0
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (12)  0
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 12

--S 13 of 39
1$poly
 

   (13)  1
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (13)  1
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 13

--S 14 of 39
p : poly := a
 

   (14)  [a]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (14)  [a]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 14

--S 15 of 39
q : poly := b
 

   (15)  [b]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (15)  [b]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 15

--S 16 of 39
pq: poly := p*q
 

   (16)  [a b] + [b][a]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (16)  [a b] + [b][a]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 16

--S 17 of 39
pq :: dpoly
 

   (17)  a b
                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (17)  a b
--R                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--E 17

--S 18 of 39
mirror pq
 

   (18)  [b][a]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (18)  [b][a]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 18

--S 19 of 39
listOfTerms pq
 

   (19)  [[k= [b][a],c= 1],[k= [a b],c= 1]]
Type: List Record(k: PoincareBirkhoffWittLyndonBasis Symbol,c: Fraction Integer)
--R 
--R
--R   (19)  [[k= [b][a],c= 1],[k= [a b],c= 1]]
--RType: List Record(k: PoincareBirkhoffWittLyndonBasis Symbol,c: Fraction Integer)
--E 19

--S 20 of 39
reductum pq
 

   (20)  [a b]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (20)  [a b]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 20

--S 21 of 39
leadingMonomial pq
 

   (21)  [b][a]
                                 Type: PoincareBirkhoffWittLyndonBasis Symbol
--R 
--R
--R   (21)  [b][a]
--R                                 Type: PoincareBirkhoffWittLyndonBasis Symbol
--E 21

--S 22 of 39
coefficients pq
 

   (22)  [1,1]
                                                  Type: List Fraction Integer
--R 
--R
--R   (22)  [1,1]
--R                                                  Type: List Fraction Integer
--E 22

--S 23 of 39
leadingTerm pq
 

   (23)  [k= [b][a],c= 1]
  Type: Record(k: PoincareBirkhoffWittLyndonBasis Symbol,c: Fraction Integer)
--R 
--R
--R   (23)  [k= [b][a],c= 1]
--R  Type: Record(k: PoincareBirkhoffWittLyndonBasis Symbol,c: Fraction Integer)
--E 23

--S 24 of 39
degree pq
 

   (24)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (24)  2
--R                                                        Type: PositiveInteger
--E 24

--S 25 of 39
pq4:=exp(pq,4)
 

   (25)
                          1              1     2       1      2
     1 + [a b] + [b][a] + - [a b][a b] + - [a b ][a] + - [b][a b]
                          2              2             2
   + 
     3               1
     - [b][a b][a] + - [b][b][a][a]
     2               2
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (25)
--R                          1              1     2       1      2
--R     1 + [a b] + [b][a] + - [a b][a b] + - [a b ][a] + - [b][a b]
--R                          2              2             2
--R   + 
--R     3               1
--R     - [b][a b][a] + - [b][b][a][a]
--R     2               2
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 25

--S 26 of 39
log(pq4,4) - pq
 

   (26)  0
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (26)  0
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 26

--S 27 of 39
lp1 :lpoly := LiePoly liste.10
 

           3 2
   (27)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R           3 2
--R   (27)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 27

--S 28 of 39
lp2 :lpoly := LiePoly liste.11
 

           2
   (28)  [a b a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R           2
--R   (28)  [a b a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 28

--S 29 of 39
lp :lpoly := [lp1, lp2]
 

           3 2 2
   (29)  [a b a b a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R           3 2 2
--R   (29)  [a b a b a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 29

--S 30 of 39
lpd1: dpoly := lp1
 

          3 2     2         2 2                    2 2           2    2 3
   (30)  a b  - 2a b a b - a b a + 4a b a b a - a b a  - 2b a b a  + b a
                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--R 
--R
--R          3 2     2         2 2                    2 2           2    2 3
--R   (30)  a b  - 2a b a b - a b a + 4a b a b a - a b a  - 2b a b a  + b a
--R                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--E 30

--S 31 of 39
lpd2: dpoly := lp2
 

   (31)
      2         2 2          2                    2 2       3        2
     a b a b - a b a - 3a b a b + 4a b a b a - a b a  + 2b a b - 3b a b a
   + 
            2
     b a b a
                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (31)
--R      2         2 2          2                    2 2       3        2
--R     a b a b - a b a - 3a b a b + 4a b a b a - a b a  + 2b a b - 3b a b a
--R   + 
--R            2
--R     b a b a
--R                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--E 31

--S 32 of 39
lpd : dpoly := lpd1 * lpd2 - lpd2 * lpd1
 

   (32)
      3 2 2         3 2 2 2      3 2     2      3 2             3 2   2 2
     a b a b a b - a b a b a - 3a b a b a b + 4a b a b a b a - a b a b a
   + 
       3 3 3      3 3 2       3 3     2    2       3 2     2       2 2
     2a b a b - 3a b a b a + a b a b a  - a b a b a b  + 3a b a b a b a
   + 
       2           2       2                    2         2 2     2     2 3
     6a b a b a b a b - 12a b a b a b a b a + 3a b a b a b a  - 4a b a b a b
   + 
       2     2 2       2     3 3    2 2 4 2     2 2 3          2 2 2   2
     6a b a b a b a - a b a b a  + a b a b  - 3a b a b a b + 3a b a b a b
   + 
         2 2     3      2 2     2        2 2         2    2 2   2 3
     - 2a b a b a b + 3a b a b a b a - 3a b a b a b a  + a b a b a
   + 
           2   3 2         2   2              2   2 2           2
     3a b a b a b  - 6a b a b a b a b - 3a b a b a b a + 12a b a b a b a b a
   + 
             2     2 2         2 2     2         2 3 3             4 2
     - 3a b a b a b a  - 6a b a b a b a  + 3a b a b a  - 4a b a b a b
   + 
                3                   2   2                  3
     12a b a b a b a b - 12a b a b a b a b + 8a b a b a b a b
   + 
                      2                         2               2 3      2 5 2
     - 12a b a b a b a b a + 12a b a b a b a b a  - 4a b a b a b a  + a b a b
   + 
           2 4            2 3   2        2 2   3        2 2   2
     - 3a b a b a b + 3a b a b a b - 2a b a b a b + 3a b a b a b a
   + 
           2 2       2      2 2 2 3       3   3 2       3   2
     - 3a b a b a b a  + a b a b a  - 2b a b a b  + 4b a b a b a b
   + 
         3   2 2        3                  3     2 2       3 2     2       3 3 3
     2b a b a b a - 8b a b a b a b a + 2b a b a b a  + 4b a b a b a  - 2b a b a
   + 
         2   4 2       2   3            2   3 2         2   2
     3b a b a b  - 6b a b a b a b - 3b a b a b a + 12b a b a b a b a
   + 
           2   2 2 2       2           2       2     2 3          5 2
     - 3b a b a b a  - 6b a b a b a b a  + 3b a b a b a  - b a b a b
   + 
             4 2            3   2             3                  3 2 2
     3b a b a b a + 6b a b a b a b - 12b a b a b a b a + 3b a b a b a
   + 
               2   3            2   2             2 2 3    2 5         2 5 2
     - 4b a b a b a b + 6b a b a b a b a - b a b a b a  + b a b a b - b a b a
   + 
         2 4   2      2 4           2 4 2 2     2 3   3      2 3   2
     - 3b a b a b + 4b a b a b a - b a b a  + 2b a b a b - 3b a b a b a
   + 
      2 3       2
     b a b a b a
                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (32)
--R      3 2 2         3 2 2 2      3 2     2      3 2             3 2   2 2
--R     a b a b a b - a b a b a - 3a b a b a b + 4a b a b a b a - a b a b a
--R   + 
--R       3 3 3      3 3 2       3 3     2    2       3 2     2       2 2
--R     2a b a b - 3a b a b a + a b a b a  - a b a b a b  + 3a b a b a b a
--R   + 
--R       2           2       2                    2         2 2     2     2 3
--R     6a b a b a b a b - 12a b a b a b a b a + 3a b a b a b a  - 4a b a b a b
--R   + 
--R       2     2 2       2     3 3    2 2 4 2     2 2 3          2 2 2   2
--R     6a b a b a b a - a b a b a  + a b a b  - 3a b a b a b + 3a b a b a b
--R   + 
--R         2 2     3      2 2     2        2 2         2    2 2   2 3
--R     - 2a b a b a b + 3a b a b a b a - 3a b a b a b a  + a b a b a
--R   + 
--R           2   3 2         2   2              2   2 2           2
--R     3a b a b a b  - 6a b a b a b a b - 3a b a b a b a + 12a b a b a b a b a
--R   + 
--R             2     2 2         2 2     2         2 3 3             4 2
--R     - 3a b a b a b a  - 6a b a b a b a  + 3a b a b a  - 4a b a b a b
--R   + 
--R                3                   2   2                  3
--R     12a b a b a b a b - 12a b a b a b a b + 8a b a b a b a b
--R   + 
--R                      2                         2               2 3      2 5 2
--R     - 12a b a b a b a b a + 12a b a b a b a b a  - 4a b a b a b a  + a b a b
--R   + 
--R           2 4            2 3   2        2 2   3        2 2   2
--R     - 3a b a b a b + 3a b a b a b - 2a b a b a b + 3a b a b a b a
--R   + 
--R           2 2       2      2 2 2 3       3   3 2       3   2
--R     - 3a b a b a b a  + a b a b a  - 2b a b a b  + 4b a b a b a b
--R   + 
--R         3   2 2        3                  3     2 2       3 2     2       3 3 3
--R     2b a b a b a - 8b a b a b a b a + 2b a b a b a  + 4b a b a b a  - 2b a b a
--R   + 
--R         2   4 2       2   3            2   3 2         2   2
--R     3b a b a b  - 6b a b a b a b - 3b a b a b a + 12b a b a b a b a
--R   + 
--R           2   2 2 2       2           2       2     2 3          5 2
--R     - 3b a b a b a  - 6b a b a b a b a  + 3b a b a b a  - b a b a b
--R   + 
--R             4 2            3   2             3                  3 2 2
--R     3b a b a b a + 6b a b a b a b - 12b a b a b a b a + 3b a b a b a
--R   + 
--R               2   3            2   2             2 2 3    2 5         2 5 2
--R     - 4b a b a b a b + 6b a b a b a b a - b a b a b a  + b a b a b - b a b a
--R   + 
--R         2 4   2      2 4           2 4 2 2     2 3   3      2 3   2
--R     - 3b a b a b + 4b a b a b a - b a b a  + 2b a b a b - 3b a b a b a
--R   + 
--R      2 3       2
--R     b a b a b a
--R                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--E 32

--S 33 of 39
lp :: dpoly - lpd
 

   (33)  0
                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (33)  0
--R                        Type: XDistributedPolynomial(Symbol,Fraction Integer)
--E 33

--S 34 of 39
p := 3 * lp
 

            3 2 2
   (34)  3[a b a b a b]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R            3 2 2
--R   (34)  3[a b a b a b]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 34

--S 35 of 39
q := lp1
 

           3 2
   (35)  [a b ]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R           3 2
--R   (35)  [a b ]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 35

--S 36 of 39
pq:= p * q
 

            3 2 2        3 2
   (36)  3[a b a b a b][a b ]
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R            3 2 2        3 2
--R   (36)  3[a b a b a b][a b ]
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 36

--S 37 of 39
pr:rpoly := p :: rpoly
 

   (37)
       a
    *
           a
        *
               a b b
            *
                 a(a b(a b 3 + b a(- 3)) + b(a(a b(- 9) + b a 12) + b a a(- 3)))
               + 
                 b a(a(a b 6 + b a(- 9)) + b a a 3)
           + 
               b
            *
                   a b
                *
                       a
                    *
                         a(a b b(- 3) + b b a 9)
                       + 
                         b(a(a b 18 + b a(- 36)) + b a a 9)
                   + 
                     b(a a(a b(- 12) + b a 18) + b a a a(- 3))
               + 
                   b a
                *
                     a(a(a b b 3 + b a b(- 9)) + b a a b 9)
                   + 
                     b(a(a(a b(- 6) + b a 9) + b a a(- 9)) + b a a a 3)
       + 
           b
        *
               a
            *
                   a b
                *
                       a
                    *
                         a(a b b 9 + b(a b(- 18) + b a(- 9)))
                       + 
                         b(a b a 36 + b a a(- 9))
                   + 
                     b(a b a a(- 18) + b a a a 9)
               + 
                   b a
                *
                     a(a(a b b(- 12) + b a b 36) + b a a b(- 36))
                   + 
                     b(a(a(a b 24 + b a(- 36)) + b a a 36) + b a a a(- 12))
           + 
               b a a
            *
                 a(a(a b b 3 + b a b(- 9)) + b a a b 9)
               + 
                 b(a(a(a b(- 6) + b a 9) + b a a(- 9)) + b a a a 3)
   + 
       b
    *
           a
        *
               a
            *
                   a b
                *
                       a
                    *
                         a(a b b(- 6) + b(a b 12 + b a 6))
                       + 
                         b(a b a(- 24) + b a a 6)
                   + 
                     b(a b a a 12 + b a a a(- 6))
               + 
                   b a
                *
                       a
                    *
                         a(a b b 9 + b(a b(- 18) + b a(- 9)))
                       + 
                         b(a b a 36 + b a a(- 9))
                   + 
                     b(a b a a(- 18) + b a a a 9)
           + 
               b a a
            *
                 a(a(a b b(- 3) + b b a 9) + b(a(a b 18 + b a(- 36)) + b a a 9))
               + 
                 b(a a(a b(- 12) + b a 18) + b a a a(- 3))
       + 
           b a a a
        *
             a(a b(a b 3 + b a(- 3)) + b(a(a b(- 9) + b a 12) + b a a(- 3)))
           + 
             b a(a(a b 6 + b a(- 9)) + b a a 3)
                          Type: XRecursivePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (37)
--R       a
--R    *
--R           a
--R        *
--R               a b b
--R            *
--R                 a(a b(a b 3 + b a(- 3)) + b(a(a b(- 9) + b a 12) + b a a(- 3)))
--R               + 
--R                 b a(a(a b 6 + b a(- 9)) + b a a 3)
--R           + 
--R               b
--R            *
--R                   a b
--R                *
--R                       a
--R                    *
--R                         a(a b b(- 3) + b b a 9)
--R                       + 
--R                         b(a(a b 18 + b a(- 36)) + b a a 9)
--R                   + 
--R                     b(a a(a b(- 12) + b a 18) + b a a a(- 3))
--R               + 
--R                   b a
--R                *
--R                     a(a(a b b 3 + b a b(- 9)) + b a a b 9)
--R                   + 
--R                     b(a(a(a b(- 6) + b a 9) + b a a(- 9)) + b a a a 3)
--R       + 
--R           b
--R        *
--R               a
--R            *
--R                   a b
--R                *
--R                       a
--R                    *
--R                         a(a b b 9 + b(a b(- 18) + b a(- 9)))
--R                       + 
--R                         b(a b a 36 + b a a(- 9))
--R                   + 
--R                     b(a b a a(- 18) + b a a a 9)
--R               + 
--R                   b a
--R                *
--R                     a(a(a b b(- 12) + b a b 36) + b a a b(- 36))
--R                   + 
--R                     b(a(a(a b 24 + b a(- 36)) + b a a 36) + b a a a(- 12))
--R           + 
--R               b a a
--R            *
--R                 a(a(a b b 3 + b a b(- 9)) + b a a b 9)
--R               + 
--R                 b(a(a(a b(- 6) + b a 9) + b a a(- 9)) + b a a a 3)
--R   + 
--R       b
--R    *
--R           a
--R        *
--R               a
--R            *
--R                   a b
--R                *
--R                       a
--R                    *
--R                         a(a b b(- 6) + b(a b 12 + b a 6))
--R                       + 
--R                         b(a b a(- 24) + b a a 6)
--R                   + 
--R                     b(a b a a 12 + b a a a(- 6))
--R               + 
--R                   b a
--R                *
--R                       a
--R                    *
--R                         a(a b b 9 + b(a b(- 18) + b a(- 9)))
--R                       + 
--R                         b(a b a 36 + b a a(- 9))
--R                   + 
--R                     b(a b a a(- 18) + b a a a 9)
--R           + 
--R               b a a
--R            *
--R                 a(a(a b b(- 3) + b b a 9) + b(a(a b 18 + b a(- 36)) + b a a 9))
--R               + 
--R                 b(a a(a b(- 12) + b a 18) + b a a a(- 3))
--R       + 
--R           b a a a
--R        *
--R             a(a b(a b 3 + b a(- 3)) + b(a(a b(- 9) + b a 12) + b a a(- 3)))
--R           + 
--R             b a(a(a b 6 + b a(- 9)) + b a a 3)
--R                          Type: XRecursivePolynomial(Symbol,Fraction Integer)
--E 37

--S 38 of 39
qr:rpoly := q :: rpoly
 

   (38)
     a(a(a b b 1 + b(a b(- 2) + b a(- 1))) + b(a b a 4 + b a a(- 1)))
   + 
     b(a b a a(- 2) + b a a a 1)
                          Type: XRecursivePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (38)
--R     a(a(a b b 1 + b(a b(- 2) + b a(- 1))) + b(a b a 4 + b a a(- 1)))
--R   + 
--R     b(a b a a(- 2) + b a a a 1)
--R                          Type: XRecursivePolynomial(Symbol,Fraction Integer)
--E 38

--S 39 of 39
pq :: rpoly - pr*qr
 

   (39)  0
                          Type: XRecursivePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (39)  0
--R                          Type: XRecursivePolynomial(Symbol,Fraction Integer)
--E 39
)spool
 
Starts dribbling to scherk.output (2010/3/27, 18:38:52).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 7
(xOffset, yOffset):DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 7
drawScherk(m,n) ==
  free xOffset, yOffset
  space := create3Space()$ThreeSpace(DoubleFloat)
  for i in 0..m-1 repeat
    xOffset := i*%pi
    for j in 0 .. n-1 repeat
      rem(i+j, 2) = 0 => 'iter
      yOffset := j*%pi
      drawOneScherk(space)
  makeViewport3D(space, "Scherk's Minimal Surface")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 7
scherk1(u,v) ==
  x := cos(u)/exp(v)
  point [xOffset + acos(x), yOffset + u, v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 7
scherk2(u,v) ==
  x := cos(u)/exp(v)
  point [xOffset - acos(x), yOffset + u, v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 7
scherk3(u,v) ==
  x := exp(v) * cos(u)
  point [xOffset + u, yOffset + acos(x), v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 7
scherk4(u,v) ==
  x := exp(v) * cos(u)
  point [xOffset + u, yOffset - acos(x), v, abs(v)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 7
drawOneScherk(s) ==
  makeObject(scherk1, -%pi/2..%pi/2, 0..%pi/2,  space == s, _
             var1Steps == 28, var2Steps == 28)
  makeObject(scherk2, -%pi/2..%pi/2, 0..%pi/2,  space == s, _
             var1Steps == 28, var2Steps == 28)
  makeObject(scherk3, -%pi/2..%pi/2, -%pi/2..0, space == s, _
             var1Steps == 28, var2Steps == 28)
  makeObject(scherk4, -%pi/2..%pi/2, -%pi/2..0, space == s, _
             var1Steps == 28, var2Steps == 28)
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
)spool 
 
Starts dribbling to fnla.output (2010/3/27, 18:26:17).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
fnl := FNLA(4,4,INT)
 

   (1)  FreeNilpotentLie(4,4,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  FreeNilpotentLie(4,4,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 7
dimension()$fnl
 

   (2)  90
                                                     Type: NonNegativeInteger
--R 
--R
--R   (2)  90
--R                                                     Type: NonNegativeInteger
--E 2
 
--S 3 of 7
x:fnl := generator(1)
 

   (3)  e
         1
                                          Type: FreeNilpotentLie(4,4,Integer)
--R 
--R
--R   (3)  e
--R         1
--R                                          Type: FreeNilpotentLie(4,4,Integer)
--E 3

--S 4 of 7
y:fnl := generator(17)
 

   (4)  e
         17
                                          Type: FreeNilpotentLie(4,4,Integer)
--R 
--R
--R   (4)  e
--R         17
--R                                          Type: FreeNilpotentLie(4,4,Integer)
--E 4

--S 5 of 7
z:=x*y
 

   (5)  2e   - e   + e
          78    45    38
                                          Type: FreeNilpotentLie(4,4,Integer)
--R 
--R
--R   (5)  2e   - e   + e
--R          78    45    38
--R                                          Type: FreeNilpotentLie(4,4,Integer)
--E 5

--S 6 of 7
deepExpand z
 

   (6)  2[[e ,e ],[e ,e ]] - [e ,[e ,[e ,e ]]] + [e ,[e ,[e ,e ]]]
            1  2    2  3       3   2   1  2        2   2   1  3
                                                             Type: OutputForm
--R 
--R
--R   (6)  2[[e ,e ],[e ,e ]] - [e ,[e ,[e ,e ]]] + [e ,[e ,[e ,e ]]]
--R            1  2    2  3       3   2   1  2        2   2   1  3
--R                                                             Type: OutputForm
--E 6

--S 7 of 7
shallowExpand z
 

   (7)  2[e ,e ] - [e ,e  ] + [e ,e  ]
           5  8      3  14      2  15
                                                             Type: OutputForm
--R 
--R
--R   (7)  2[e ,e ] - [e ,e  ] + [e ,e  ]
--R           5  8      3  14      2  15
--R                                                             Type: OutputForm
--E 7
)spool 
 
Starts dribbling to strtbl.output (2010/3/27, 18:41:9).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
t: StringTable(Integer) := table()
 

   (1)  table()
                                                    Type: StringTable Integer
--R 
--R
--R   (1)  table()
--R                                                    Type: StringTable Integer
--E 1

--S 2 of 3
for s in split("My name is Ian Watt.",char " ")
  repeat
    t.s := #s
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 3
for key in keys t repeat output [key, t.key]
 
   ["Watt.",5]
   ["Ian",3]
   ["is",2]
   ["name",4]
   ["My",2]
                                                                   Type: Void
--R 
--R   ["Watt.",5]
--R   ["Ian",3]
--R   ["is",2]
--R   ["name",4]
--R   ["My",2]
--R                                                                   Type: Void
--E 3
)spool 
 
Starts dribbling to lword.output (2010/3/27, 18:28:57).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
a:Symbol :='a
 

   (1)  a
                                                                 Type: Symbol
--R 
--R
--R   (1)  a
--R                                                                 Type: Symbol
--E 1

--S 2 of 22
b:Symbol :='b
 

   (2)  b
                                                                 Type: Symbol
--R 
--R
--R   (2)  b
--R                                                                 Type: Symbol
--E 2

--S 3 of 22
c:Symbol :='c
 

   (3)  c
                                                                 Type: Symbol
--R 
--R
--R   (3)  c
--R                                                                 Type: Symbol
--E 3

--S 4 of 22
lword:= LyndonWord(Symbol)
 

   (4)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 22
magma := Magma(Symbol)
 

   (5)  Magma Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  Magma Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 22
word   := OrderedFreeMonoid(Symbol)
 

   (6)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (6)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 6

--S 7 of 22
LyndonWordsList1([a,b,c],3)$lword
 

   (7)
   [[[a],[b],[c]], [[a b],[a c],[b c]],
       2     2       2                      2    2       2
    [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]]
                             Type: OneDimensionalArray List LyndonWord Symbol
--R 
--R
--R   (7)
--R   [[[a],[b],[c]], [[a b],[a c],[b c]],
--R       2     2       2                      2    2       2
--R    [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]]
--R                             Type: OneDimensionalArray List LyndonWord Symbol
--E 7

--S 8 of 22
LyndonWordsList([a,b,c],3)$lword
 

   (8)
                                          2      2        2
   [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b],
        2     2        2
    [a c ], [b c], [b c ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (8)
--R                                          2      2        2
--R   [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b],
--R        2     2        2
--R    [a c ], [b c], [b c ]]
--R                                                 Type: List LyndonWord Symbol
--E 8

--S 9 of 22
lw := LyndonWordsList([a,b],5)$lword
 

   (9)
                       2        2     3      2 2       3     4      3 2
   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
      2          2 3           2       4
    [a b a b], [a b ], [a b a b ], [a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (9)
--R                       2        2     3      2 2       3     4      3 2
--R   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
--R      2          2 3           2       4
--R    [a b a b], [a b ], [a b a b ], [a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 9

--S 10 of 22
w1 : word := lw.4 :: word
 

          2
   (10)  a b
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R          2
--R   (10)  a b
--R                                               Type: OrderedFreeMonoid Symbol
--E 10

--S 11 of 22
w2 : word := lw.5 :: word
 

            2
   (11)  a b
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R            2
--R   (11)  a b
--R                                               Type: OrderedFreeMonoid Symbol
--E 11

--S 12 of 22
factor(a::word)$lword
 

   (12)  [[a]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (12)  [[a]]
--R                                                 Type: List LyndonWord Symbol
--E 12

--S 13 of 22
factor(w1*w2)$lword
 

            2     2
   (13)  [[a b a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R            2     2
--R   (13)  [[a b a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 13

--S 14 of 22
factor(w2*w2)$lword
 

              2      2
   (14)  [[a b ],[a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R              2      2
--R   (14)  [[a b ],[a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 14

--S 15 of 22
factor(w2*w1)$lword
 

              2    2
   (15)  [[a b ],[a b]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R              2    2
--R   (15)  [[a b ],[a b]]
--R                                                 Type: List LyndonWord Symbol
--E 15

--S 16 of 22
lyndon?(w1)$lword
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 22
lyndon?(w1*w2)$lword
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 22
lyndon?(w2*w1)$lword
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 22
lyndonIfCan(w1)$lword
 

           2
   (19)  [a b]
                                           Type: Union(LyndonWord Symbol,...)
--R 
--R
--R           2
--R   (19)  [a b]
--R                                           Type: Union(LyndonWord Symbol,...)
--E 19

--S 20 of 22
lyndonIfCan(w2*w1)$lword
 

   (20)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (20)  "failed"
--R                                                    Type: Union("failed",...)
--E 20

--S 21 of 22
lyndon(w1)$lword
 

           2
   (21)  [a b]
                                                      Type: LyndonWord Symbol
--R 
--R
--R           2
--R   (21)  [a b]
--R                                                      Type: LyndonWord Symbol
--E 21

--S 22 of 22
lyndon(w1*w2)$lword
 

           2     2
   (22)  [a b a b ]
                                                      Type: LyndonWord Symbol
--R 
--R
--R           2     2
--R   (22)  [a b a b ]
--R                                                      Type: LyndonWord Symbol
--E 22
)spool 
 
Starts dribbling to calculus.output (2010/3/27, 18:24:23).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input for page FormalDerivativePage

--S 1 of 24
differentiate(f, x)
 

   (1)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  0
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 24
f := operator f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 24
x := operator x
 

   (3)  x
                                                          Type: BasicOperator
--R 
--R
--R   (3)  x
--R                                                          Type: BasicOperator
--E 3

--S 4 of 24
y := operator y
 

   (4)  y
                                                          Type: BasicOperator
--R 
--R
--R   (4)  y
--R                                                          Type: BasicOperator
--E 4

--S 5 of 24
a := f(x z, y z, z**2) + x y(z+1)
 

                                   2
   (5)  x(y(z + 1)) + f(x(z),y(z),z )
                                                     Type: Expression Integer
--R 
--R
--R                                   2
--R   (5)  x(y(z + 1)) + f(x(z),y(z),z )
--R                                                     Type: Expression Integer
--E 5

--S 6 of 24
dadz := differentiate(a, z)
 

   (6)
                      2     ,                  2     ,                  2
     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
        ,3                       ,2                       ,1
   + 
      ,           ,
     x (y(z + 1))y (z + 1)

                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                      2     ,                  2     ,                  2
--R     2zf  (x(z),y(z),z ) + y (z)f  (x(z),y(z),z ) + x (z)f  (x(z),y(z),z )
--R        ,3                       ,2                       ,1
--R   + 
--R      ,           ,
--R     x (y(z + 1))y (z + 1)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 24
eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

   (7)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 24
eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
 

            z             2
   (8)  f(%e ,log(z + 1),z ) + z + 2
                                                     Type: Expression Integer
--R 
--R
--R            z             2
--R   (8)  f(%e ,log(z + 1),z ) + z + 2
--R                                                     Type: Expression Integer
--E 8

--S 9 of 24
differentiate(%, z)
 

   (9)
          2            z             2          z             2
       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
                  ,3                       ,2
     + 
                z      z             2
       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
                  ,1
  /
     z + 1
                                                     Type: Expression Integer
--R 
--R
--R   (9)
--R          2            z             2          z             2
--R       (2z  + 2z)f  (%e ,log(z + 1),z ) + f  (%e ,log(z + 1),z )
--R                  ,3                       ,2
--R     + 
--R                z      z             2
--R       (z + 1)%e f  (%e ,log(z + 1),z ) + z + 1
--R                  ,1
--R  /
--R     z + 1
--R                                                     Type: Expression Integer
--E 9

-- Input for page LaplacePage
)clear all
 

--S 10 of 24
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
 

   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
--R                                                     Type: Expression Integer
--E 10

--S 11 of 24
laplace(%, t, s)
 

             3
           4a
   (2)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R             3
--R           4a
--R   (2)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 11

--S 12 of 24
laplace((exp(a*t) - exp(b*t))/t, t, s)
 

   (3)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 12

--S 13 of 24
laplace(2/t * (1 - cos(a*t)), t, s)
 

             2    2
   (4)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R             2    2
--R   (4)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 13

--S 14 of 24
laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
 

                    1
   (5)  ------------------------
           2             3    2
        b s  + 2a b s + b  + a b
                                                     Type: Expression Integer
--R 
--R
--R                    1
--R   (5)  ------------------------
--R           2             3    2
--R        b s  + 2a b s + b  + a b
--R                                                     Type: Expression Integer
--E 14

--S 15 of 24
laplace((cos(a*t) - cos(b*t))/t, t, s)
 

             2    2         2    2
        log(s  + b ) - log(s  + a )
   (6)  ---------------------------
                     2
                                                     Type: Expression Integer
--R 
--R
--R             2    2         2    2
--R        log(s  + b ) - log(s  + a )
--R   (6)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 15

--S 16 of 24
laplace(exp(a*t+b)*Ei(c*t), t, s)
 

          b    s + c - a
        %e log(---------)
                   c
   (7)  -----------------
              s - a
                                                     Type: Expression Integer
--R 
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (7)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 16

--S 17 of 24
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
 

               2    2
              s  + b             d
        a log(-------) + 2c atan(-)
                  2              s
                 b
   (8)  ---------------------------
                     2s
                                                     Type: Expression Integer
--R 
--R
--R               2    2
--R              s  + b             d
--R        a log(-------) + 2c atan(-)
--R                  2              s
--R                 b
--R   (8)  ---------------------------
--R                     2s
--R                                                     Type: Expression Integer
--E 17

--S 18 of 24
laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
 

                                    2
          4     2 2    4           t           3
        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
   (9)  ----------------------------------------
                      4     2 2    4
                     s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                                    2
--R          4     2 2    4           t           3
--R        (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
--R   (9)  ----------------------------------------
--R                      4     2 2    4
--R                     s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 18

-- Input for page DerivativePage
)clear all
 

--S 19 of 24
f := exp exp x
 

            x
          %e
   (1)  %e
                                                     Type: Expression Integer
--R 
--R
--R            x
--R          %e
--R   (1)  %e
--R                                                     Type: Expression Integer
--E 19

--S 20 of 24
differentiate(f, x)
 

               x
          x  %e
   (2)  %e %e
                                                     Type: Expression Integer
--R 
--R
--R               x
--R          x  %e
--R   (2)  %e %e
--R                                                     Type: Expression Integer
--E 20

--S 21 of 24
differentiate(f, x, 4)
 

                                              x
            x 4       x 3       x 2     x   %e
   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
                                                     Type: Expression Integer
--R 
--R
--R                                              x
--R            x 4       x 3       x 2     x   %e
--R   (3)  ((%e )  + 6(%e )  + 7(%e )  + %e )%e
--R                                                     Type: Expression Integer
--E 21

--S 22 of 24
g := sin(x**2 + y)
 

                 2
   (4)  sin(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (4)  sin(y + x )
--R                                                     Type: Expression Integer
--E 22

--S 23 of 24
differentiate(g, y)
 

                 2
   (5)  cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R   (5)  cos(y + x )
--R                                                     Type: Expression Integer
--E 23

--S 24 of 24
differentiate(g, [y, y, x, x])
 

          2         2              2
   (6)  4x sin(y + x ) - 2cos(y + x )
                                                     Type: Expression Integer
--R 
--R
--R          2         2              2
--R   (6)  4x sin(y + x ) - 2cos(y + x )
--R                                                     Type: Expression Integer
--E 24
 
)spool
 
Starts dribbling to gamma.output (2010/3/27, 18:26:31).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 12
[[1.000,1.0000000000,Gamma(1.000),Gamma(1.000)-1.0000000000],_
 [1.005,0.9971385354,Gamma(1.005),Gamma(1.005)-0.9971385354],_
 [1.010,0.9943258512,Gamma(1.010),Gamma(1.010)-0.9943258512],_
 [1.015,0.9915612888,Gamma(1.015),Gamma(1.015)-0.9915612888],_
 [1.020,0.9888442033,Gamma(1.020),Gamma(1.020)-0.9888442033],_
 [1.025,0.9861739633,Gamma(1.025),Gamma(1.025)-0.9861739633],_
 [1.030,0.9835499506,Gamma(1.030),Gamma(1.030)-0.9835499506],_
 [1.035,0.9809715606,Gamma(1.035),Gamma(1.035)-0.9809715606],_
 [1.040,0.9784382009,Gamma(1.040),Gamma(1.040)-0.9784382009],_
 [1.045,0.9759492919,Gamma(1.045),Gamma(1.045)-0.9759492919],_
 [1.050,0.9735042656,Gamma(1.050),Gamma(1.050)-0.9735042656],_
 [1.055,0.9711025663,Gamma(1.055),Gamma(1.055)-0.9711025663],_
 [1.060,0.9687436495,Gamma(1.060),Gamma(1.060)-0.9687436495],_
 [1.065,0.9664269823,Gamma(1.065),Gamma(1.065)-0.9664269823],_
 [1.070,0.9641520425,Gamma(1.070),Gamma(1.070)-0.9641520425],_
 [1.075,0.9619183189,Gamma(1.075),Gamma(1.075)-0.9619183189],_
 [1.080,0.9597253107,Gamma(1.080),Gamma(1.080)-0.9597253107],_
 [1.085,0.9575725273,Gamma(1.085),Gamma(1.085)-0.9575725273],_
 [1.090,0.9554594882,Gamma(1.090),Gamma(1.090)-0.9554594882],_
 [1.095,0.9533857227,Gamma(1.095),Gamma(1.095)-0.9533857227],_
 [1.100,0.9513507699,Gamma(1.100),Gamma(1.100)-0.9513507699],_
 [1.105,0.9493541778,Gamma(1.105),Gamma(1.105)-0.9493541778],_
 [1.110,0.9473955040,Gamma(1.110),Gamma(1.110)-0.9473955040],_
 [1.115,0.9454743149,Gamma(1.115),Gamma(1.115)-0.9454743149],_
 [1.120,0.9435901856,Gamma(1.120),Gamma(1.120)-0.9435901856],_
 [1.125,0.9417426997,Gamma(1.125),Gamma(1.125)-0.9417426997],_
 [1.130,0.9399314497,Gamma(1.130),Gamma(1.130)-0.9399314497],_
 [1.135,0.9381560356,Gamma(1.135),Gamma(1.135)-0.9381560356],_
 [1.140,0.9364160657,Gamma(1.140),Gamma(1.140)-0.9364160657],_
 [1.145,0.9347111562,Gamma(1.145),Gamma(1.145)-0.9347111562],_
 [1.150,0.9330409311,Gamma(1.150),Gamma(1.150)-0.9330409311],_
 [1.155,0.9314050217,Gamma(1.155),Gamma(1.155)-0.9314050217],_
 [1.160,0.9298030666,Gamma(1.160),Gamma(1.160)-0.9298030666],_
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   (1)
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     [1.9199999999999999, 0.96877430899999994, 0.96877430902597383,
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     ,

     [1.9350000000000001, 0.9742379672, 0.97423796711012756,
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     ,

     [1.9399999999999999, 0.97609890749999995, 0.97609890747260597,
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     [1.9449999999999998, 0.97797978609999991, 0.9779797860816809,
      - 1.831901297322247E-11]
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    [1.9550000000000001,0.9818015524,0.98180155250325418,1.032541829815159E-10],
    [1.96,0.98374254039999998,0.98374254035288666,- 4.711331325069068E-11],

     [1.9649999999999999, 0.98570366639999996, 0.98570366652054975,
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     [1.9750000000000001, 0.98968654619999996, 0.98968654619855956,
      - 1.4404033521486781E-12]
     ,
    [1.98,0.99170840869999999,0.99170840869626087,- 3.7391201246350647E-12],

     [1.9849999999999999, 0.99375062739999998, 0.99375062748495291,
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     ,
    [1.99,0.99581325980000002,0.995813259847667,4.7666981473071246E-11],

     [1.9950000000000001, 0.99789636429999995, 0.99789636418206007,
      - 1.1793988008435008E-10]
     ]
                                                  Type: List List DoubleFloat
--R 
--R
--R   (1)
--R   [[1.,1.,1.,0.],
--R
--R     [1.0049999999999999, 0.99713853539999997, 0.99713853525101781,
--R      - 1.4898215994207931E-10]
--R     ,
--R    [1.01,0.99432585120000005,0.99432585119150585,- 8.4942053391046102E-12],
--R
--R     [1.0149999999999999, 0.99156128880000005, 0.99156128884897066,
--R      4.8970605348586105E-11]
--R     ,
--R    [1.02,0.9888442033,0.98884420326391309,- 3.6086911237021013E-11],
--R
--R     [1.0249999999999999, 0.98617396329999996, 0.98617396314825367,
--R      - 1.5174628220648856E-10]
--R     ,
--R    [1.03,0.98354995059999994,0.98354995055382399,- 4.6175951950999661E-11],
--R
--R     [1.0349999999999999, 0.98097156060000001, 0.98097156055058576,
--R      - 4.9414250469226317E-11]
--R     ,
--R    [1.04,0.9784382009,0.97843820091424472,1.4244716517453071E-11],
--R
--R     [1.0449999999999999, 0.97594929190000002, 0.97594929182295154,
--R      - 7.7048478708263701E-11]
--R     ,
--R    [1.05,0.97350426560000003,0.97350426556277558,- 3.7224445748051949E-11],
--R
--R     [1.0549999999999999, 0.97110256630000003, 0.97110256624166991,
--R      - 5.8330118513083562E-11]
--R     ,
--R
--R     [1.0600000000000001, 0.96874364950000003, 0.9687436495116386,
--R      1.1638578989447979E-11]
--R     ,
--R
--R     [1.0649999999999999, 0.96642698230000001, 0.96642698229884005,
--R      - 1.1599610161283636E-12]
--R     ,
--R
--R     [1.0700000000000001, 0.96415204249999997, 0.96415204254136644,
--R      4.1366465808323483E-11]
--R     ,
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--R      6.1954885666182236E-12]
--R     ,
--R    [1.855,0.94713946370000002,0.94713946380763558,1.0763556712589661E-10],
--R
--R     [1.8600000000000001, 0.94868704169999996, 0.94868704167794815,
--R      - 2.2051804826617172E-11]
--R     ,
--R    [1.865,0.95025393889999998,0.95025393889642473,- 3.5752512062003916E-12],
--R
--R     [1.8700000000000001, 0.95184018550000005, 0.95184018551317828,
--R      1.3178236279998146E-11]
--R     ,
--R    [1.875,0.95344581269999995,0.95344581274503493,4.5034975748592387E-11],
--R
--R     [1.8799999999999999, 0.95507085300000005, 0.95507085297159322,
--R      - 2.840683244187403E-11]
--R     ,
--R    [1.885,0.95671533980000001,0.95671533973145539,- 6.8544614428844852E-11],
--R
--R     [1.8899999999999999, 0.95837930770000002, 0.95837930771862279,
--R      1.8622769992759913E-11]
--R     ,
--R    [1.895,0.96006279269999995,0.96006279277905426,7.9054318646853972E-11],
--R
--R     [1.8999999999999999, 0.96176583189999998, 0.96176583190738751,
--R      7.3875350281582541E-12]
--R     ,
--R    [1.905,0.96348846320000003,0.96348846324382054,4.3820502781954929E-11],
--R
--R     [1.9099999999999999, 0.96523072610000005, 0.96523072607114846,
--R      - 2.8851587785538868E-11]
--R     ,
--R    [1.915,0.96699266080000001,0.96699266081195756,1.1957546064422786E-11],
--R
--R     [1.9199999999999999, 0.96877430899999994, 0.96877430902597383,
--R      2.5973889705710462E-11]
--R     ,
--R    [1.925,0.97057571340000004,0.97057571340755988,7.5598416415800784E-12],
--R
--R     [1.9299999999999999, 0.97239691780000004, 0.97239691778336623,
--R      - 1.6633805444143945E-11]
--R     ,
--R
--R     [1.9350000000000001, 0.9742379672, 0.97423796711012756,
--R      - 8.9872442821103959E-11]
--R     ,
--R
--R     [1.9399999999999999, 0.97609890749999995, 0.97609890747260597,
--R      - 2.73939759765085E-11]
--R     ,
--R
--R     [1.9450000000000001, 0.97797978610000003, 0.97797978608168112,
--R      - 1.8318901950920008E-11]
--R     ,
--R    [1.95,0.97988065130000002,0.97988065127258051,- 2.7419511106074879E-11],
--R    [1.9550000000000001,0.9818015524,0.98180155250325418,1.032541829815159E-10],
--R    [1.96,0.98374254039999998,0.98374254035288666,- 4.711331325069068E-11],
--R
--R     [1.9650000000000001, 0.98570366639999996, 0.98570366652054964,
--R      1.2054968134833643E-10]
--R     ,
--R    [1.97,0.98768498380000003,0.98768498382399139,2.399136445063732E-11],
--R
--R     [1.9750000000000001, 0.98968654619999996, 0.98968654619855956,
--R      - 1.4404033521486781E-12]
--R     ,
--R    [1.98,0.99170840869999999,0.99170840869626087,- 3.7391201246350647E-12],
--R
--R     [1.9850000000000001, 0.99375062739999998, 0.99375062748495313,
--R      8.4953155621292353E-11]
--R     ,
--R    [1.99,0.99581325980000002,0.995813259847667,4.7666981473071246E-11],
--R
--R     [1.9950000000000001, 0.99789636429999995, 0.99789636418206007,
--R      - 1.1793988008435008E-10]
--R     ]
--R                                                  Type: List List DoubleFloat
--E 1

--S 2 of 12
Psi(x:DFLOAT):DFLOAT==polygamma(0,x)
 
   Function declaration Psi : DoubleFloat -> DoubleFloat has been added
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration Psi : DoubleFloat -> DoubleFloat has been added
--R      to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 12
[[1.000, -0.5772156649, Psi(1.000), Psi(1.000)- -0.5772156649],_
 [1.005, -0.5690209113, Psi(1.005), Psi(1.005)- -0.5690209113],_
 [1.010, -0.5608854579, Psi(1.010), Psi(1.010)- -0.5608854579],_
 [1.015, -0.5528085156, Psi(1.015), Psi(1.015)- -0.5528085156],_
 [1.020, -0.5447893105, Psi(1.020), Psi(1.020)- -0.5447893105],_
 [1.025, -0.5368270828, Psi(1.025), Psi(1.025)- -0.5368270828],_
 [1.030, -0.5289210873, Psi(1.030), Psi(1.030)- -0.5289210873],_
 [1.035, -0.5210705921, Psi(1.035), Psi(1.035)- -0.5210705921],_
 [1.040, -0.5132748789, Psi(1.040), Psi(1.040)- -0.5132748789],_
 [1.045, -0.5055332428, Psi(1.045), Psi(1.045)- -0.5055332428],_
 [1.050, -0.4978449913, Psi(1.050), Psi(1.050)- -0.4978449913],_
 [1.055, -0.4902094448, Psi(1.055), Psi(1.055)- -0.4902094448],_
 [1.060, -0.4826259358, Psi(1.060), Psi(1.060)- -0.4826259358],_
 [1.065, -0.4750938088, Psi(1.065), Psi(1.065)- -0.4750938088],_
 [1.070, -0.4676124199, Psi(1.070), Psi(1.070)- -0.4676124199],_
 [1.075, -0.4601811367, Psi(1.075), Psi(1.075)- -0.4601811367],_
 [1.080, -0.4527993380, Psi(1.080), Psi(1.080)- -0.4527993380],_
 [1.085, -0.4454664135, Psi(1.085), Psi(1.085)- -0.4454664135],_
 [1.090, -0.4381817635, Psi(1.090), Psi(1.090)- -0.4381817635],_
 [1.095, -0.4309447988, Psi(1.095), Psi(1.095)- -0.4309447988],_
 [1.100, -0.4237549404, Psi(1.100), Psi(1.100)- -0.4237549404],_
 [1.105, -0.4166116193, Psi(1.105), Psi(1.105)- -0.4166116193],_
 [1.110, -0.4095142761, Psi(1.110), Psi(1.110)- -0.4095142761],_
 [1.115, -0.4024623611, Psi(1.115), Psi(1.115)- -0.4024623611],_
 [1.120, -0.3954553339, Psi(1.120), Psi(1.120)- -0.3954553339],_
 [1.125, -0.3884926633, Psi(1.125), Psi(1.125)- -0.3884926633],_
 [1.130, -0.3815738268, Psi(1.130), Psi(1.130)- -0.3815738268],_
 [1.135, -0.3746983110, Psi(1.135), Psi(1.135)- -0.3746983110],_
 [1.140, -0.3678656106, Psi(1.140), Psi(1.140)- -0.3678656106],_
 [1.145, -0.3610752291, Psi(1.145), Psi(1.145)- -0.3610752291],_
 [1.150, -0.3543266780, Psi(1.150), Psi(1.150)- -0.3543266780],_
 [1.155, -0.3476194768, Psi(1.155), Psi(1.155)- -0.3476194768],_
 [1.160, -0.3409531528, Psi(1.160), Psi(1.160)- -0.3409531528],_
 [1.165, -0.3343272413, Psi(1.165), Psi(1.165)- -0.3343272413],_
 [1.170, -0.3277412847, Psi(1.170), Psi(1.170)- -0.3277412847],_
 [1.175, -0.3211948332, Psi(1.175), Psi(1.175)- -0.3211948332],_
 [1.180, -0.3146874438, Psi(1.180), Psi(1.180)- -0.3146874438],_
 [1.185, -0.3082186809, Psi(1.185), Psi(1.185)- -0.3082186809],_
 [1.190, -0.3017881156, Psi(1.190), Psi(1.190)- -0.3017881156],_
 [1.195, -0.2953953259, Psi(1.195), Psi(1.195)- -0.2953953259],_
 [1.200, -0.2890398966, Psi(1.200), Psi(1.200)- -0.2890398966],_
 [1.205, -0.2827214187, Psi(1.205), Psi(1.205)- -0.2827214187],_
 [1.210, -0.2764394897, Psi(1.210), Psi(1.210)- -0.2764394897],_
 [1.215, -0.2701937135, Psi(1.215), Psi(1.215)- -0.2701937135],_
 [1.220, -0.2639837000, Psi(1.220), Psi(1.220)- -0.2639837000],_
 [1.225, -0.2578090652, Psi(1.225), Psi(1.225)- -0.2578090652],_
 [1.230, -0.2516694307, Psi(1.230), Psi(1.230)- -0.2516694307],_
 [1.235, -0.2455644243, Psi(1.235), Psi(1.235)- -0.2455644243],_
 [1.240, -0.2394936791, Psi(1.240), Psi(1.240)- -0.2394936791],_
 [1.245, -0.2334568341, Psi(1.245), Psi(1.245)- -0.2334568341],_
 [1.250, -0.2274535334, Psi(1.250), Psi(1.250)- -0.2274535334],_
 [1.255, -0.2214834266, Psi(1.255), Psi(1.255)- -0.2214834266],_
 [1.260, -0.2155461686, Psi(1.260), Psi(1.260)- -0.2155461686],_
 [1.265, -0.2096414193, Psi(1.265), Psi(1.265)- -0.2096414193],_
 [1.270, -0.2037688437, Psi(1.270), Psi(1.270)- -0.2037688437],_
 [1.275, -0.1979281118, Psi(1.275), Psi(1.275)- -0.1979281118],_
 [1.280, -0.1921188983, Psi(1.280), Psi(1.280)- -0.1921188983],_
 [1.285, -0.1863408828, Psi(1.285), Psi(1.285)- -0.1863408828],_
 [1.290, -0.1805937494, Psi(1.290), Psi(1.290)- -0.1805937494],_
 [1.295, -0.1748771870, Psi(1.295), Psi(1.295)- -0.1748771870],_
 [1.300, -0.1691908889, Psi(1.300), Psi(1.300)- -0.1691908889],_
 [1.305, -0.1635345526, Psi(1.305), Psi(1.305)- -0.1635345526],_
 [1.310, -0.1579078803, Psi(1.310), Psi(1.310)- -0.1579078803],_
 [1.315, -0.1523105782, Psi(1.315), Psi(1.315)- -0.1523105782],_
 [1.320, -0.1467423568, Psi(1.320), Psi(1.320)- -0.1467423568],_
 [1.325, -0.1412029305, Psi(1.325), Psi(1.325)- -0.1412029305],_
 [1.330, -0.1356920180, Psi(1.330), Psi(1.330)- -0.1356920180],_
 [1.335, -0.1302093416, Psi(1.335), Psi(1.335)- -0.1302093416],_
 [1.340, -0.1247546279, Psi(1.340), Psi(1.340)- -0.1247546279],_
 [1.345, -0.1193276069, Psi(1.345), Psi(1.345)- -0.1193276069],_
 [1.350, -0.1139280127, Psi(1.350), Psi(1.350)- -0.1139280127],_
 [1.355, -0.1085555827, Psi(1.355), Psi(1.355)- -0.1085555827],_
 [1.360, -0.1032100582, Psi(1.360), Psi(1.360)- -0.1032100582],_
 [1.365, -0.0978911840, Psi(1.365), Psi(1.365)- -0.0978911840],_
 [1.370, -0.0925987082, Psi(1.370), Psi(1.370)- -0.0925987082],_
 [1.375, -0.0873323825, Psi(1.375), Psi(1.375)- -0.0873323825],_
 [1.380, -0.0820919619, Psi(1.380), Psi(1.380)- -0.0820919619],_
 [1.385, -0.0768772046, Psi(1.385), Psi(1.385)- -0.0768772046],_
 [1.390, -0.0716878723, Psi(1.390), Psi(1.390)- -0.0716878723],_
 [1.395, -0.0665237297, Psi(1.395), Psi(1.395)- -0.0665237297],_
 [1.400, -0.0613845446, Psi(1.400), Psi(1.400)- -0.0613845446],_
 [1.405, -0.0562700879, Psi(1.405), Psi(1.405)- -0.0562700879],_
 [1.410, -0.0511801337, Psi(1.410), Psi(1.410)- -0.0511801337],_
 [1.415, -0.0461144589, Psi(1.415), Psi(1.415)- -0.0461144589],_
 [1.420, -0.0410728433, Psi(1.420), Psi(1.420)- -0.0410728433],_
 [1.425, -0.0360550697, Psi(1.425), Psi(1.425)- -0.0360550697],_
 [1.430, -0.0310609237, Psi(1.430), Psi(1.430)- -0.0310609237],_
 [1.435, -0.0260901935, Psi(1.435), Psi(1.435)- -0.0260901935],_
 [1.440, -0.0211426703, Psi(1.440), Psi(1.440)- -0.0211426703],_
 [1.445, -0.0162181479, Psi(1.445), Psi(1.445)- -0.0162181479],_
 [1.450, -0.0113164226, Psi(1.450), Psi(1.450)- -0.0113164226],_
 [1.455, -0.0064372934, Psi(1.455), Psi(1.455)- -0.0064372934],_
 [1.460, -0.0015805620, Psi(1.460), Psi(1.460)- -0.0015805620],_
 [1.465,  0.0032539677, Psi(1.465), Psi(1.465)-  0.0032539677],_
 [1.470,  0.0080664890, Psi(1.470), Psi(1.470)-  0.0080664890],_
 [1.475,  0.0128571930, Psi(1.475), Psi(1.475)-  0.0128571930],_
 [1.480,  0.0176262684, Psi(1.480), Psi(1.480)-  0.0176262684],_
 [1.485,  0.0223739013, Psi(1.485), Psi(1.485)-  0.0223739013],_
 [1.490,  0.0271002758, Psi(1.490), Psi(1.490)-  0.0271002758],_
 [1.495,  0.0318055736, Psi(1.495), Psi(1.495)-  0.0318055736],_
 [1.500,  0.0364899740, Psi(1.500), Psi(1.500)-  0.0364899740],_
 [1.505,  0.0411536543, Psi(1.505), Psi(1.505)-  0.0411536543],_
 [1.510,  0.0457967896, Psi(1.510), Psi(1.510)-  0.0457967896],_
 [1.515,  0.0504195527, Psi(1.515), Psi(1.515)-  0.0504195527],_
 [1.520,  0.0550221146, Psi(1.520), Psi(1.520)-  0.0550221146],_
 [1.525,  0.0596046439, Psi(1.525), Psi(1.525)-  0.0596046439],_
 [1.530,  0.0641673074, Psi(1.530), Psi(1.530)-  0.0641673074],_
 [1.535,  0.0687102697, Psi(1.535), Psi(1.535)-  0.0687102697],_
 [1.540,  0.0732336936, Psi(1.540), Psi(1.540)-  0.0732336936],_
 [1.545,  0.0777377300, Psi(1.545), Psi(1.545)-  0.0777377300],_
 [1.550,  0.0822225675, Psi(1.550), Psi(1.550)-  0.0822225675],_
 [1.555,  0.0866883334, Psi(1.555), Psi(1.555)-  0.0866883334],_
 [1.560,  0.0911351925, Psi(1.560), Psi(1.560)-  0.0911351925],_
 [1.565,  0.0955632984, Psi(1.565), Psi(1.565)-  0.0955632984],_
 [1.570,  0.0999728024, Psi(1.570), Psi(1.570)-  0.0999728024],_
 [1.575,  0.1043638544, Psi(1.575), Psi(1.575)-  0.1043638544],_
 [1.580,  0.1087366023, Psi(1.580), Psi(1.580)-  0.1087366023],_
 [1.585,  0.1130911923, Psi(1.585), Psi(1.585)-  0.1130911923],_
 [1.590,  0.1174277690, Psi(1.590), Psi(1.590)-  0.1174277690],_
 [1.595,  0.1217464754, Psi(1.595), Psi(1.595)-  0.1217464754],_
 [1.600,  0.1260474528, Psi(1.600), Psi(1.600)-  0.1260474528],_
 [1.605,  0.1303308407, Psi(1.605), Psi(1.605)-  0.1303308407],_
 [1.610,  0.1345967772, Psi(1.610), Psi(1.610)-  0.1345967772],_
 [1.615,  0.1388453988, Psi(1.615), Psi(1.615)-  0.1388453988],_
 [1.620,  0.1430768404, Psi(1.620), Psi(1.620)-  0.1430768404],_
 [1.625,  0.1472912354, Psi(1.625), Psi(1.625)-  0.1472912354],_
 [1.630,  0.1514887158, Psi(1.630), Psi(1.630)-  0.1514887158],_
 [1.635,  0.1556694120, Psi(1.635), Psi(1.635)-  0.1556694120],_
 [1.640,  0.1598334529, Psi(1.640), Psi(1.640)-  0.1598334529],_
 [1.645,  0.1639809660, Psi(1.645), Psi(1.645)-  0.1639809660],_
 [1.650,  0.1681120776, Psi(1.650), Psi(1.650)-  0.1681120776],_
 [1.655,  0.1722269122, Psi(1.655), Psi(1.655)-  0.1722269122],_
 [1.660,  0.1763255933, Psi(1.660), Psi(1.660)-  0.1763255933],_
 [1.665,  0.1804082427, Psi(1.665), Psi(1.665)-  0.1804082427],_
 [1.670,  0.1844749813, Psi(1.670), Psi(1.670)-  0.1844749813],_
 [1.675,  0.1885259282, Psi(1.675), Psi(1.675)-  0.1885259282],_
 [1.680,  0.1925612015, Psi(1.680), Psi(1.680)-  0.1925612015],_
 [1.685,  0.1965809180, Psi(1.685), Psi(1.685)-  0.1965809180],_
 [1.690,  0.2005851931, Psi(1.690), Psi(1.690)-  0.2005851931],_
 [1.695,  0.2045741410, Psi(1.695), Psi(1.695)-  0.2045741410],_
 [1.700,  0.2085478749, Psi(1.700), Psi(1.700)-  0.2085478749],_
 [1.705,  0.2125065064, Psi(1.705), Psi(1.705)-  0.2125065064],_
 [1.710,  0.2164501462, Psi(1.710), Psi(1.710)-  0.2164501462],_
 [1.715,  0.2203789037, Psi(1.715), Psi(1.715)-  0.2203789037],_
 [1.720,  0.2242928871, Psi(1.720), Psi(1.720)-  0.2242928871],_
 [1.725,  0.2281922037, Psi(1.725), Psi(1.725)-  0.2281922037],_
 [1.730,  0.2320769593, Psi(1.730), Psi(1.730)-  0.2320769593],_
 [1.735,  0.2359472589, Psi(1.735), Psi(1.735)-  0.2359472589],_
 [1.740,  0.2398032061, Psi(1.740), Psi(1.740)-  0.2398032061],_
 [1.745,  0.2436449038, Psi(1.745), Psi(1.745)-  0.2436449038],_
 [1.750,  0.2474724535, Psi(1.750), Psi(1.750)-  0.2474724535],_
 [1.755,  0.2512859559, Psi(1.755), Psi(1.755)-  0.2512859559],_
 [1.760,  0.2550855103, Psi(1.760), Psi(1.760)-  0.2550855103],_
 [1.765,  0.2588712154, Psi(1.765), Psi(1.765)-  0.2588712154],_
 [1.770,  0.2626431686, Psi(1.770), Psi(1.770)-  0.2626431686],_
 [1.775,  0.2664014664, Psi(1.775), Psi(1.775)-  0.2664014664],_
 [1.780,  0.2701462043, Psi(1.780), Psi(1.780)-  0.2701462043],_
 [1.785,  0.2738774769, Psi(1.785), Psi(1.785)-  0.2738774769],_
 [1.790,  0.2775953776, Psi(1.790), Psi(1.790)-  0.2775953776],_
 [1.795,  0.2812999992, Psi(1.795), Psi(1.795)-  0.2812999992],_
 [1.800,  0.2849914333, Psi(1.800), Psi(1.800)-  0.2849914333],_
 [1.805,  0.2886697707, Psi(1.805), Psi(1.805)-  0.2886697707],_
 [1.810,  0.2923351012, Psi(1.810), Psi(1.810)-  0.2923351012],_
 [1.815,  0.2959875138, Psi(1.815), Psi(1.815)-  0.2959875138],_
 [1.820,  0.2996270966, Psi(1.820), Psi(1.820)-  0.2996270966],_
 [1.825,  0.3032539367, Psi(1.825), Psi(1.825)-  0.3032539367],_
 [1.830,  0.3068681205, Psi(1.830), Psi(1.830)-  0.3068681205],_
 [1.835,  0.3104697335, Psi(1.835), Psi(1.835)-  0.3104697335],_
 [1.840,  0.3140588602, Psi(1.840), Psi(1.840)-  0.3140588602],_
 [1.845,  0.3176355846, Psi(1.845), Psi(1.845)-  0.3176355846],_
 [1.850,  0.3211999895, Psi(1.850), Psi(1.850)-  0.3211999895],_
 [1.855,  0.3247521572, Psi(1.855), Psi(1.855)-  0.3247521572],_
 [1.860,  0.3282921691, Psi(1.860), Psi(1.860)-  0.3282921691],_
 [1.865,  0.3318201056, Psi(1.865), Psi(1.865)-  0.3318201056],_
 [1.870,  0.3353360467, Psi(1.870), Psi(1.870)-  0.3353360467],_
 [1.875,  0.3388400713, Psi(1.875), Psi(1.875)-  0.3388400713],_
 [1.880,  0.3423322577, Psi(1.880), Psi(1.880)-  0.3423322577],_
 [1.885,  0.3458126835, Psi(1.885), Psi(1.885)-  0.3458126835],_
 [1.890,  0.3492814255, Psi(1.890), Psi(1.890)-  0.3492814255],_
 [1.895,  0.3527385596, Psi(1.895), Psi(1.895)-  0.3527385596],_
 [1.900,  0.3561841612, Psi(1.900), Psi(1.900)-  0.3561841612],_
 [1.905,  0.3596183049, Psi(1.905), Psi(1.905)-  0.3596183049],_
 [1.910,  0.3630410646, Psi(1.910), Psi(1.910)-  0.3630410646],_
 [1.915,  0.3664525136, Psi(1.915), Psi(1.915)-  0.3664525136],_
 [1.920,  0.3698527244, Psi(1.920), Psi(1.920)-  0.3698527244],_
 [1.925,  0.3732417688, Psi(1.925), Psi(1.925)-  0.3732417688],_
 [1.930,  0.3766197179, Psi(1.930), Psi(1.930)-  0.3766197179],_
 [1.935,  0.3799866424, Psi(1.935), Psi(1.935)-  0.3799866424],_
 [1.940,  0.3833426119, Psi(1.940), Psi(1.940)-  0.3833426119],_
 [1.945,  0.3866876959, Psi(1.945), Psi(1.945)-  0.3866876959],_
 [1.950,  0.3900219627, Psi(1.950), Psi(1.950)-  0.3900219627],_
 [1.955,  0.3933454805, Psi(1.955), Psi(1.955)-  0.3933454805],_
 [1.960,  0.3966583163, Psi(1.960), Psi(1.960)-  0.3966583163],_
 [1.965,  0.3999605371, Psi(1.965), Psi(1.965)-  0.3999605371],_
 [1.970,  0.4032522088, Psi(1.970), Psi(1.970)-  0.4032522088],_
 [1.975,  0.4065333970, Psi(1.975), Psi(1.975)-  0.4065333970],_
 [1.980,  0.4098041664, Psi(1.980), Psi(1.980)-  0.4098041664],_
 [1.985,  0.4130645816, Psi(1.985), Psi(1.985)-  0.4130645816],_
 [1.990,  0.4163147060, Psi(1.990), Psi(1.990)-  0.4163147060],_
 [1.995,  0.4195546030, Psi(1.995), Psi(1.995)-  0.4195546030],_
 [2.000,  0.4227843351, Psi(2.000), Psi(2.000)-  0.4227843351]]
 
   Compiling function Psi with type DoubleFloat -> DoubleFloat 

   (3)
   [[1.,- 0.57721566489999998,- 0.57721566490153275,- 1.5327739077974911E-12],

     [1.0049999999999999, - 0.56902091129999999, - 0.56902091134438304,
      - 4.4383052788532495E-11]
     ,

     [1.0099999999999998, - 0.5608854579, - 0.56088545786867494,
      3.1325053662101254E-11]
     ,

     [1.0149999999999999, - 0.55280851559999999, - 0.55280851559434629,
      5.6536997306011472E-12]
     ,
    [1.02,- 0.5447893104999999,- 0.54478931045617984,4.3820058692745079E-11],

     [1.0249999999999999, - 0.53682708279999991, - 0.53682708284938863,
      - 4.9388715339659939E-11]
     ,

     [1.0299999999999998, - 0.52892108730000009, - 0.52892108728543108,
      1.4569012662946079E-11]
     ,

     [1.0349999999999999, - 0.52107059210000006, - 0.52107059205771,
      4.229006034250915E-11]
     ,
    [1.04,- 0.5132748788999999,- 0.51327487891683021,- 1.6830314919502598E-11],

     [1.0449999999999999, - 0.50553324279999989, - 0.50553324275508449,
      4.4915404728840258E-11]
     ,

     [1.0499999999999998, - 0.49784499130000004, - 0.49784499129987053,
      1.2950751582252451E-13]
     ,

     [1.0549999999999999, - 0.49020944479999995, - 0.49020944481574569,
      - 1.5745738046746283E-11]
     ,

     [1.0600000000000001, - 0.48262593579999996, - 0.48262593581482538,
      - 1.4825418670483259E-11]
     ,

     [1.0649999999999999, - 0.47509380879999996, - 0.47509380877526647,
      2.4733493031448006E-11]
     ,

     [1.0699999999999998, - 0.46761241989999996, - 0.46761241986755375,
      3.2446212383518969E-11]
     ,
    [1.075,- 0.46018113670000005,- 0.4601811366883593,1.1640743924345998E-11],

     [1.0800000000000001, - 0.45279933800000005, - 0.45279933800171246,
      - 1.7124079931818414E-12]
     ,
    [1.085,- 0.44546641350000005,- 0.44546641348725191,1.274813588025836E-11],

     [1.0899999999999999, - 0.43818176350000004, - 0.43818176349533511,
      4.6649351048699828E-12]
     ,
    [1.095,- 0.43094479880000003,- 0.43094479880878706,- 8.7870266618494952E-12]
     ,

     [1.1000000000000001, - 0.42375494039999995, - 0.42375494041107653,
      - 1.1076584094382724E-11]
     ,
    [1.105,- 0.41661161929999996,- 0.41661161926071655,3.9283409858370533E-11],

     [1.1099999999999999, - 0.40951427609999996, - 0.40951427607169422,
      2.830574663548191E-11]
     ,
    [1.115,- 0.4024623611,- 0.40246236109974648,2.535194276731545E-13],

     [1.1200000000000001, - 0.39545533389999998, - 0.39545533393429283,
      - 3.4292846340377992E-11]
     ,
    [1.125,- 0.38849266329999999,- 0.38849266329585463,4.1453507293454095E-12],

     [1.1299999999999999, - 0.38157382679999996, - 0.38157382683879215,
      - 3.8792191681125132E-11]
     ,

     [1.1349999999999998, - 0.37469831099999995, - 0.37469831095919104,
      4.0808911805356729E-11]
     ,

     [1.1399999999999999, - 0.36786561059999995, - 0.36786561060774969,
      - 7.7497452899422115E-12]
     ,
    [1.145,- 0.36107522909999995,- 0.361075229107509,- 7.5090489382034775E-12],

     [1.1499999999999999, - 0.35432667799999995, - 0.35432667797627904,
      2.3720914121838632E-11]
     ,

     [1.1549999999999998, - 0.34761947680000005, - 0.34761947675362392,
      4.6376125162339576E-11]
     ,

     [1.1599999999999999, - 0.34095315280000005, - 0.34095315283226135,
      - 3.2261304738767649E-11]
     ,
    [1.165,- 0.33432724129999997,- 0.3343272412937619,6.2380656196125983E-12],

     [1.1699999999999999, - 0.32774128469999997, - 0.3277412847483927,
      - 4.8392734264268711E-11]
     ,

     [1.1749999999999998, - 0.32119483319999997, - 0.32119483317900821,
      2.0991763882705072E-11]
     ,

     [1.1799999999999999, - 0.31468744379999997, - 0.31468744378886082,
      1.1139145161820352E-11]
     ,

     [1.1850000000000001, - 0.30821868090000004, - 0.30821868085320625,
      4.679379106420356E-11]
     ,

     [1.1899999999999999, - 0.30178811559999996, - 0.30178811557461016,
      2.5389801372455167E-11]
     ,

     [1.1949999999999998, - 0.29539532589999995, - 0.29539532594182993,
      - 4.1829983921104485E-11]
     ,
    [1.2,- 0.28903989659999996,- 0.28903989659218843,7.8115292012626014E-12],

     [1.2050000000000001, - 0.28272141869999995, - 0.28272141867731704,
      2.2682911104965342E-11]
     ,
    [1.21,- 0.27643948969999999,- 0.2764394897321919,- 3.2191915799728577E-11],

     [1.2149999999999999, - 0.27019371349999999, - 0.27019371354735267,
      - 4.7352677334799864E-11]
     ,
    [1.22,- 0.26398370000000004,- 0.26398370004422023,- 4.4220183070819985E-11],

     [1.2250000000000001, - 0.25780906519999996, - 0.25780906515343338,
      4.6566583922214022E-11]
     ,
    [1.23,- 0.25166943070000003,- 0.25166943069609982,3.9002134855081749E-12],

     [1.2349999999999999, - 0.24556442429999997, - 0.24556442426789804,
      3.2101932223582708E-11]
     ,
    [1.24,- 0.23949367910000002,- 0.23949367912593666,- 2.5936641723234288E-11],

     [1.2450000000000001, - 0.23345683409999998, - 0.23345683407831253,
      2.1687457385510811E-11]
     ,
    [1.25,- 0.22745353340000002,- 0.22745353337626528,2.3734736398495215E-11],

     [1.2549999999999999, - 0.22148342659999998, - 0.22148342660888165,
      - 8.8816731746987898E-12]
     ,

     [1.2599999999999998, - 0.21554616859999998, - 0.21554616860026543,
      - 2.6545432518787493E-13]
     ,

     [1.2649999999999999, - 0.20964141930000002, - 0.20964141930911384,
      - 9.11382080914791E-12]
     ,
    [1.27,- 0.20376884369999998,- 0.20376884373062343,- 3.0623448221689387E-11],

     [1.2749999999999999, - 0.19792811179999997, - 0.19792811180067393,
      - 6.7396088709870128E-13]
     ,

     [1.2799999999999998, - 0.19211889829999998, - 0.19211889830222206,
      - 2.2220836282116352E-12]
     ,

     [1.2849999999999999, - 0.1863408828, - 0.18634088277384209,
      2.6157909172042082E-11]
     ,
    [1.29,- 0.18059374939999998,- 0.1805937494203691,- 2.0369123054919669E-11],

     [1.2949999999999999, - 0.17487718699999999, - 0.17487718702556942,
      - 2.5569435457839518E-11]
     ,

     [1.2999999999999998, - 0.16919088889999997, - 0.16919088886679956,
      3.3200414639722453E-11]
     ,

     [1.3049999999999999, - 0.16353455259999999, - 0.163534552631597,
      - 3.1597002791983186E-11]
     ,

     [1.3100000000000001, - 0.15790788030000003, - 0.15790788033614178,
      - 3.6141756254437496E-11]
     ,

     [1.3149999999999999, - 0.15231057819999999, - 0.15231057824555994,
      - 4.5559944705786393E-11]
     ,

     [1.3199999999999998, - 0.14674235679999997, - 0.14674235679599612,
      4.0038528048569333E-12]
     ,
    [1.325,- 0.14120293049999999,- 0.14120293051842803,- 1.8428036874240661E-11]
     ,

     [1.3300000000000001, - 0.13569201800000003, - 0.13569201796416941,
      3.5830616251786296E-11]
     ,
    [1.335,- 0.13020934159999997,- 0.13020934163201769,- 3.2017721807164889E-11]
     ,

     [1.3399999999999999, - 0.1247546279, - 0.12475462789700387,
      2.9961311209802943E-12]
     ,
    [1.345,- 0.11932760689999999,- 0.11932760694070754,- 4.0707548443208452E-11]
     ,

     [1.3500000000000001, - 0.1139280127, - 0.11392801268308839,
      1.6911611000480775E-11]
     ,
    [1.355,- 0.10855558269999999,- 0.10855558271580501,- 1.5805023956261266E-11]
     ,

     [1.3599999999999999, - 0.10321005820000001, - 0.10321005823697749,
      - 3.6977476636224083E-11]
     ,

     [1.365, - 9.7891183999999992E-2, - 9.7891183987354968E-2,
      1.2645023916846299E-11]
     ,

     [1.3700000000000001, - 9.2598708199999991E-2, - 9.2598708187860979E-2,
      1.2139012017797768E-11]
     ,
    [1.375,- 8.73323825E-2,- 8.7332382478473081E-2,2.1526919136150013E-11],

     [1.3799999999999999, - 8.209196190000001E-2, - 8.2091961858406615E-2,
      4.1593395394556865E-11]
     ,

     [1.3849999999999998, - 7.6877204599999999E-2, - 7.6877204627574636E-2,
      - 2.7574637018190629E-11]
     ,

     [1.3899999999999999, - 7.1687872300000011E-2, - 7.1687872329281643E-2,
      - 2.9281632674127422E-11]
     ,

     [1.395, - 6.6523729699999992E-2, - 6.6523729694132228E-2,
      5.8677646075366852E-12]
     ,

     [1.3999999999999999, - 6.1384544599999993E-2, - 6.1384544585116108E-2,
      1.4883885790517581E-11]
     ,

     [1.4049999999999998, - 5.6270087899999995E-2, - 5.6270087943842473E-2,
      - 4.3842478258948603E-11]
     ,

     [1.4099999999999999, - 5.1180133700000005E-2, - 5.1180133737897426E-2,
      - 3.7897421312216295E-11]
     ,

     [1.415, - 4.6114458899999995E-2, - 4.6114458909301992E-2,
      - 9.3019966729279702E-12]
     ,

     [1.4199999999999999, - 4.1072843299999995E-2, - 4.1072843324024277E-2,
      - 2.4024282563317456E-11]
     ,

     [1.4249999999999998, - 3.6055069699999998E-2, - 3.6055069722548017E-2,
      - 2.2548019007473385E-11]
     ,

     [1.4299999999999999, - 3.10609237E-2, - 3.1060923671447194E-2,
      2.8552805952930527E-11]
     ,

     [1.4350000000000001, - 2.6090193499999997E-2, - 2.609019351596098E-2,
      - 1.5960982535645485E-11]
     ,

     [1.4399999999999999, - 2.1142670299999999E-2, - 2.1142670333530678E-2,
      - 3.3530678233972822E-11]
     ,

     [1.4449999999999998, - 1.6218147899999997E-2, - 1.6218147888283796E-2,
      1.1716200926104037E-11]
     ,

     [1.45, - 1.1316422599999999E-2, - 1.1316422586445718E-2,
      1.3554280961503018E-11]
     ,

     [1.4550000000000001, - 6.4372933999999995E-3, - 6.4372934326406561E-3,
      - 3.2640656670579471E-11]
     ,

     [1.46, - 1.5805620000000002E-3, - 1.5805619870833398E-3,
      1.2916660362821686E-11]
     ,

     [1.4649999999999999, 3.2539676999999998E-3, 3.2539676763744252E-3,
      - 2.3625574586960685E-11]
     ,
    [1.47,8.0664889999999996E-3,8.0664890113649745E-3,1.1364974933369965E-11],

     [1.4750000000000001, 1.2857192999999999E-2, 1.2857193039295334E-2,
      3.9295334347544397E-11]
     ,
    [1.48,1.7626268399999999E-2,1.7626268388849287E-2,- 1.1150712297958165E-11],

     [1.4849999999999999, 2.2373901299999999E-2, 2.2373901334705293E-2,
      3.4705294194026237E-11]
     ,
    [1.49,2.7100275799999997E-2,2.7100275835486465E-2,3.5486467930834209E-11],

     [1.4950000000000001, 3.1805573599999998E-2, 3.1805573570971468E-2,
      - 2.9028529580088502E-11]
     ,
    [1.5,3.6489973999999994E-2,3.6489973978576673E-2,- 2.1423321450164678E-11],

     [1.5049999999999999, 4.1153654299999995E-2, 4.1153654289123542E-2,
      - 1.0876452516406232E-11]
     ,

     [1.5099999999999998, 4.5796789599999999E-2, 4.5796789561914686E-2,
      - 3.8085312681346295E-11]
     ,

     [1.5149999999999999, 5.0419552699999995E-2, 5.0419552719128236E-2,
      1.9128240658083939E-11]
     ,
    [1.52,5.5022114599999998E-2,5.5022114579551307E-2,- 2.0448691351315773E-11],

     [1.5249999999999999, 5.9604643899999997E-2, 5.960464389166209E-2,
      - 8.3379067539190999E-12]
     ,

     [1.5299999999999998, 6.4167307399999998E-2, 6.4167307366077009E-2,
      - 3.3922989417511928E-11]
     ,

     [1.5349999999999999, 6.8710269699999993E-2, 6.8710269707385141E-2,
      7.38514804865531E-12]
     ,
    [1.54,7.3233693599999997E-2,7.3233693645366138E-2,4.5366141399050264E-11],

     [1.5449999999999999, 7.7737730000000005E-2, 7.7737739965624497E-2,
      9.9656244922918802E-9]
     ,

     [1.5499999999999998, 8.2222567499999996E-2, 8.222256753964452E-2,
      3.9644523774917673E-11]
     ,

     [1.5549999999999999, 8.6688333399999998E-2, 8.6688333354268288E-2,
      - 4.5731710085483712E-11]
     ,

     [1.5600000000000001, 9.113519249999999E-2, 9.1135192540635401E-2,
      4.0635411702183433E-11]
     ,

     [1.5649999999999999, 9.5563298399999996E-2, 9.5563298402570163E-2,
      2.5701663020072374E-12]
     ,

     [1.5699999999999998, 9.9972802400000005E-2, 9.9972802444444619E-2,
      4.444461465524796E-11]
     ,
    [1.575,0.1043638544,0.10436385439851947,- 1.4805240367010697E-12],

     [1.5800000000000001, 0.1087366023, 0.10873660225178161,
      - 4.8218387616039138E-11]
     ,
    [1.585,0.1130911923,0.11309119227228603,- 2.7713970007781086E-11],

     [1.5899999999999999, 0.11742776899999999, 0.11742776903501084,
      3.5010855325978696E-11]
     ,
    [1.595,0.1217464754,0.12174647544723916,4.7239157030531942E-11],

     [1.6000000000000001, 0.12604745279999999, 0.12604745277347584,
      - 2.6524143992290306E-11]
     ,
    [1.605,0.13033084070000001,0.13033084065991318,- 4.0086822750140527E-11],

     [1.6099999999999999, 0.13459677719999999, 0.1345967771584452,
      - 4.1554787388875525E-11]
     ,
    [1.615,0.13884539879999999,0.13884539875025736,- 4.9742626684334823E-11],

     [1.6200000000000001, 0.14307684039999999, 0.14307684036898005,
      - 3.1019936619358646E-11]
     ,
    [1.625,0.1472912354,0.14729123542343325,2.3433255336158254E-11],

     [1.6299999999999999, 0.15148871580000001, 0.15148871581995815,
      1.9958146246779052E-11]
     ,

     [1.6349999999999998, 0.15566941200000001, 0.15566941198435291,
      - 1.5647094731008337E-11]
     ,

     [1.6399999999999999, 0.15983345290000001, 0.15983345288341522,
      - 1.6584789097606745E-11]
     ,
    [1.645,0.16398096600000001,0.16398096604610457,4.6104564610516263E-11],

     [1.6499999999999999, 0.16811207759999999, 0.16811207758432767,
      - 1.5672324549242944E-11]
     ,
    [1.6549999999999998,0.1722269122,0.17222691221335718,1.3357176475992105E-11]
     ,

     [1.6599999999999999, 0.1763255933, 0.17632559327189457,
      - 2.8105434646263916E-11]
     ,
    [1.665,0.1804082427,0.18040824274177392,4.1773917658360915E-11],

     [1.6699999999999999, 0.18447498130000001, 0.1844749812673292,
      - 3.2670810501400638E-11]
     ,

     [1.6749999999999998, 0.1885259282, 0.18852592817442237,
      - 2.5577623352646128E-11]
     ,

     [1.6799999999999999, 0.1925612015, 0.19256120148913258,
      - 1.0867418076543345E-11]
     ,

     [1.6850000000000001, 0.19658091799999999, 0.19658091795613342,
      - 4.3866577037476873E-11]
     ,

     [1.6899999999999999, 0.2005851931, 0.20058519305674649,
      - 4.3253511883278861E-11]
     ,

     [1.6949999999999998, 0.20457414099999999, 0.20457414102668592,
      2.6685931242553806E-11]
     ,
    [1.7,0.20854787489999999,0.20854787487349435,- 2.6505631023354681E-11],

     [1.7050000000000001, 0.21250650639999999, 0.21250650639368796,
      - 6.3120342286282494E-12]
     ,
    [1.71,0.2164501462,0.21645014618960501,- 1.0394990423989725E-11],

     [1.7149999999999999, 0.22037890369999999, 0.22037890368596569,
      - 1.4034301498710988E-11]
     ,
    [1.72,0.2242928871,0.22429288714615725,4.6157244693034727E-11],

     [1.7250000000000001, 0.22819220369999998, 0.22819220368823745,
      - 1.1762535390147377E-11]
     ,
    [1.73,0.2320769593,0.23207695930067274,6.7273964177161361E-13],

     [1.7349999999999999, 0.23594725890000001, 0.23594725885781098,
      - 4.2189030047268261E-11]
     ,
    [1.74,0.2398032061,0.23980320613509676,3.5096758832509067E-11],

     [1.7450000000000001, 0.24364490379999998, 0.24364490382402559,
      2.4025614830947006E-11]
     ,
    [1.75,0.24747245349999999,0.2474724535468612,4.6861209357373923E-11],

     [1.7549999999999999, 0.25128595590000002, 0.25128595587109781,
      - 2.8902213955461775E-11]
     ,

     [1.7599999999999998, 0.25508551029999998, 0.25508551032368809,
      2.3688107031460959E-11]
     ,

     [1.7649999999999999, 0.25887121540000002, 0.25887121540503744,
      5.0374149296317228E-12]
     ,
    [1.77,0.26264316859999998,0.26264316860276249,2.7625124410235458E-12],

     [1.7749999999999999, 0.26640146639999995, 0.2664014664052331,
      5.2331472488731379E-12]
     ,

     [1.7799999999999998, 0.27014620430000003, 0.27014620431488345,
      1.4883427823519924E-11]
     ,

     [1.7849999999999999, 0.27387747689999997, 0.27387747686131236,
      - 3.8687608672205442E-11]
     ,
    [1.79,0.27759537759999997,0.27759537761416786,1.416788908414901E-11],

     [1.7949999999999999, 0.28129999919999998, 0.2812999991958266,
      - 4.1733838607171947E-12]
     ,

     [1.7999999999999998, 0.28499143329999999, 0.2849914332938619,
      - 6.138090036245103E-12]
     ,

     [1.8049999999999999, 0.28866977069999999, 0.28866977067331689,
      - 2.6683100173841012E-11]
     ,

     [1.8100000000000001, 0.29233510119999995, 0.29233510118877948,
      - 1.1220468998374145E-11]
     ,

     [1.8149999999999999, 0.29598751379999999, 0.29598751379626109,
      - 3.7388980800301397E-12]
     ,

     [1.8199999999999998, 0.29962709659999998, 0.29962709656488751,
      - 3.5112468488307513E-11]
     ,
    [1.825,0.3032539367,0.30325393668840539,- 1.1594614157672822E-11],

     [1.8300000000000001, 0.30686812050000001, 0.30686812049650136,
      - 3.4986458175012558E-12]
     ,
    [1.835,0.31046973349999996,0.31046973346594764,- 3.4052316522092951E-11],

     [1.8399999999999999, 0.31405886019999996, 0.31405886023156848,
      3.1568525571401551E-11]
     ,
    [1.845,0.31763558459999996,0.31763558459703256,- 2.9674041002181184E-12],

     [1.8500000000000001, 0.32119998949999995, 0.32119998954547946,
      4.54795090476523E-11]
     ,
    [1.855,0.32475215719999995,0.32475215724997797,4.9978021721130972E-11],

     [1.8599999999999999, 0.32829216909999998, 0.32829216908382031,
      - 1.6179668715921025E-11]
     ,
    [1.865,0.33182010559999997,0.33182010563065989,3.0659919048048323E-11],

     [1.8700000000000001, 0.33533604669999995, 0.33533604669448569,
      - 5.5142557187082275E-12]
     ,
    [1.875,0.33884007129999999,0.33884007130944738,9.4473873168965383E-12],

     [1.8799999999999999, 0.34233225769999998, 0.34233225774952925,
      4.9529269574577484E-11]
     ,
    [1.8849999999999998,0.3458126835,0.34581268353806771,3.8067715646405986E-11]
     ,

     [1.8899999999999999, 0.34928142549999996, 0.34928142545713492,
      - 4.2865044846962519E-11]
     ,
    [1.895,0.3527385596,0.35273855955676792,- 4.3232084578903596E-11],

     [1.8999999999999999, 0.35618416119999996, 0.35618416116406026,
      - 3.5939695663955717E-11]
     ,

     [1.9049999999999998, 0.35961830490000002, 0.35961830489211777,
      - 7.8822504079312239E-12]
     ,

     [1.9099999999999999, 0.36304106459999996, 0.36304106464888108,
      4.8881121372801317E-11]
     ,
    [1.915,0.36645251359999997,0.36645251364580167,4.580169576939852E-11],
    [1.9199999999999999,0.3698527244,0.36985272440640171,6.4017124934423464E-12]
     ,

     [1.9249999999999998, 0.37324176879999998, 0.37324176877469784,
      - 2.5302149264661011E-11]
     ,

     [1.9299999999999999, 0.37661971789999998, 0.37661971792349891,
      2.3498925028064832E-11]
     ,

     [1.9350000000000001, 0.37998664240000002, 0.37998664236258128,
      - 3.7418734777361351E-11]
     ,

     [1.9399999999999999, 0.38334261189999996, 0.38334261194674013,
      4.6740167292114165E-11]
     ,

     [1.9449999999999998, 0.38668769589999996, 0.38668769588372276,
      - 1.6277201808634345E-11]
     ,
    [1.95,0.3900219627,0.39002196274204304,4.2043035719530053E-11],

     [1.9550000000000001, 0.39334548049999996, 0.39334548045868012,
      - 4.1319836441289226E-11]
     ,
    [1.96,0.39665831629999998,0.39665831634666171,4.6661730035424398E-11],

     [1.9649999999999999, 0.39996053710000001, 0.39996053710254509,
      2.5450752616507089E-12]
     ,
    [1.97,0.40325220880000001,0.40325220881377177,1.3771761508962754E-11],

     [1.9750000000000001, 0.40653339700000002, 0.40653339696592627,
      - 3.4073743826468217E-11]
     ,
    [1.98,0.40980416639999995,0.40980416644989071,4.9890758191395435E-11],

     [1.9849999999999999, 0.41306458159999998, 0.41306458156888604,
      - 3.1113944753968781E-11]
     ,
    [1.99,0.41631470599999998,0.41631470604541487,4.5414894067619116E-11],

     [1.9950000000000001, 0.41955460300000003, 0.41955460302810832,
      2.8108293470552326E-11]
     ,
    [2.,0.42278433510000002,0.42278433509846725,- 1.5327739077974911E-12]]
                                                  Type: List List DoubleFloat
--R 
--R   Compiling function Psi with type DoubleFloat -> DoubleFloat 
--R
--R   (3)
--R   [[1.,- 0.57721566489999998,- 0.57721566490153275,- 1.5327739077974911E-12],
--R
--R     [1.0049999999999999, - 0.56902091129999999, - 0.56902091134438304,
--R      - 4.4383052788532495E-11]
--R     ,
--R    [1.01,- 0.5608854579,- 0.56088545786867472,3.1325275706706179E-11],
--R
--R     [1.0149999999999999, - 0.55280851559999999, - 0.55280851559434629,
--R      5.6536997306011472E-12]
--R     ,
--R    [1.02,- 0.54478931050000001,- 0.54478931045617984,4.3820169715047541E-11],
--R
--R     [1.0249999999999999, - 0.53682708280000002, - 0.53682708284938863,
--R      - 4.9388604317357476E-11]
--R     ,
--R    [1.03,- 0.52892108729999998,- 0.5289210872854303,1.4569678796760854E-11],
--R
--R     [1.0349999999999999, - 0.52107059209999995, - 0.52107059205771,
--R      4.2289949320206688E-11]
--R     ,
--R    [1.04,- 0.51327487890000001,- 0.51327487891683021,- 1.6830203897200136E-11],
--R
--R     [1.0449999999999999, - 0.5055332428, - 0.50553324275508449,
--R      4.4915515751142721E-11]
--R     ,
--R    [1.05,- 0.49784499129999998,- 0.49784499129987031,1.2967404927621828E-13],
--R
--R     [1.0549999999999999, - 0.4902094448, - 0.49020944481574569,
--R      - 1.5745682535595051E-11]
--R     ,
--R
--R     [1.0600000000000001, - 0.48262593580000002, - 0.48262593581482538,
--R      - 1.4825363159332028E-11]
--R     ,
--R
--R     [1.0649999999999999, - 0.47509380880000002, - 0.47509380877526647,
--R      2.4733548542599237E-11]
--R     ,
--R
--R     [1.0700000000000001, - 0.46761241990000002, - 0.46761241986755342,
--R      3.2446600961577587E-11]
--R     ,
--R    [1.075,- 0.46018113669999999,- 0.4601811366883593,1.1640688413194766E-11],
--R
--R     [1.0800000000000001, - 0.452799338, - 0.45279933800171246,
--R      - 1.7124635043330727E-12]
--R     ,
--R    [1.085,- 0.44546641349999999,- 0.44546641348725191,1.2748080369107129E-11],
--R
--R     [1.0900000000000001, - 0.43818176349999999, - 0.43818176349533489,
--R      4.6651016383236765E-12]
--R     ,
--R    [1.095,- 0.43094479879999997,- 0.43094479880878706,- 8.7870821730007265E-12]
--R     ,
--R
--R     [1.1000000000000001, - 0.4237549404, - 0.42375494041107653,
--R      - 1.1076528583231493E-11]
--R     ,
--R    [1.105,- 0.41661161930000001,- 0.41661161926071655,3.9283465369521764E-11],
--R
--R     [1.1100000000000001, - 0.40951427610000002, - 0.40951427607169383,
--R      2.830619072469176E-11]
--R     ,
--R    [1.115,- 0.4024623611,- 0.40246236109974648,2.535194276731545E-13],
--R
--R     [1.1200000000000001, - 0.39545533389999998, - 0.39545533393429283,
--R      - 3.4292846340377992E-11]
--R     ,
--R    [1.125,- 0.38849266329999999,- 0.38849266329585463,4.1453507293454095E-12],
--R
--R     [1.1299999999999999, - 0.38157382680000002, - 0.38157382683879215,
--R      - 3.8792136169973901E-11]
--R     ,
--R    [1.135,- 0.37469831100000001,- 0.37469831095919082,4.0809189361112885E-11],
--R
--R     [1.1399999999999999, - 0.3678656106, - 0.36786561060774969,
--R      - 7.7496897787909802E-12]
--R     ,
--R    [1.145,- 0.36107522910000001,- 0.361075229107509,- 7.5089934270522463E-12],
--R
--R     [1.1499999999999999, - 0.35432667800000001, - 0.35432667797627904,
--R      2.3720969632989863E-11]
--R     ,
--R    [1.155,- 0.34761947679999999,- 0.34761947675362337,4.6376624762700658E-11],
--R
--R     [1.1599999999999999, - 0.34095315279999999, - 0.34095315283226135,
--R      - 3.226136024991888E-11]
--R     ,
--R    [1.165,- 0.33432724130000002,- 0.3343272412937619,6.2381211307638296E-12],
--R
--R     [1.1699999999999999, - 0.32774128470000002, - 0.3277412847483927,
--R      - 4.839267875311748E-11]
--R     ,
--R    [1.175,- 0.32119483319999997,- 0.3211948331790081,2.0991874905007535E-11],
--R
--R     [1.1799999999999999, - 0.31468744380000002, - 0.31468744378886082,
--R      1.1139200672971583E-11]
--R     ,
--R
--R     [1.1850000000000001, - 0.30821868089999999, - 0.30821868085320625,
--R      4.6793735553052329E-11]
--R     ,
--R
--R     [1.1899999999999999, - 0.30178811560000002, - 0.30178811557461016,
--R      2.5389856883606399E-11]
--R     ,
--R
--R     [1.1950000000000001, - 0.29539532590000001, - 0.2953953259418296,
--R      - 4.1829595343045867E-11]
--R     ,
--R    [1.2,- 0.28903989660000001,- 0.28903989659218843,7.8115847124138327E-12],
--R
--R     [1.2050000000000001, - 0.2827214187, - 0.28272141867731704,
--R      2.2682966616116573E-11]
--R     ,
--R    [1.21,- 0.27643948969999999,- 0.2764394897321919,- 3.2191915799728577E-11],
--R
--R     [1.2150000000000001, - 0.27019371349999999, - 0.27019371354735244,
--R      - 4.7352455290194939E-11]
--R     ,
--R    [1.22,- 0.26398369999999999,- 0.26398370004422023,- 4.4220238581971216E-11],
--R
--R     [1.2250000000000001, - 0.25780906520000002, - 0.25780906515343338,
--R      4.6566639433365253E-11]
--R     ,
--R    [1.23,- 0.25166943069999997,- 0.25166943069609982,3.9001579743569437E-12],
--R
--R     [1.2350000000000001, - 0.2455644243, - 0.24556442426789726,
--R      3.2102737135275561E-11]
--R     ,
--R    [1.24,- 0.2394936791,- 0.23949367912593666,- 2.5936669478809904E-11],
--R
--R     [1.2450000000000001, - 0.23345683410000001, - 0.23345683407831253,
--R      2.1687485141086427E-11]
--R     ,
--R    [1.25,- 0.22745353339999999,- 0.22745353337626528,2.37347086429196E-11],
--R
--R     [1.2549999999999999, - 0.22148342660000001, - 0.22148342660888165,
--R      - 8.8816454191231742E-12]
--R     ,
--R    [1.26,- 0.2155461686,- 0.21554616860026521,- 2.6520452500733427E-13],
--R
--R     [1.2649999999999999, - 0.20964141929999999, - 0.20964141930911384,
--R      - 9.1138485647235257E-12]
--R     ,
--R    [1.27,- 0.20376884370000001,- 0.20376884373062343,- 3.0623420466113771E-11],
--R
--R     [1.2749999999999999, - 0.1979281118, - 0.19792811180067393,
--R      - 6.7393313152308565E-13]
--R     ,
--R    [1.28,- 0.19211889830000001,- 0.19211889830222173,- 2.221722805728632E-12],
--R
--R     [1.2849999999999999, - 0.1863408828, - 0.18634088277384209,
--R      2.6157909172042082E-11]
--R     ,
--R    [1.29,- 0.1805937494,- 0.1805937494203691,- 2.0369095299344053E-11],
--R
--R     [1.2949999999999999, - 0.17487718699999999, - 0.17487718702556942,
--R      - 2.5569435457839518E-11]
--R     ,
--R    [1.3,- 0.1691908889,- 0.16919088886679934,3.3200664439902994E-11],
--R
--R     [1.3049999999999999, - 0.16353455259999999, - 0.163534552631597,
--R      - 3.1597002791983186E-11]
--R     ,
--R
--R     [1.3100000000000001, - 0.1579078803, - 0.15790788033614178,
--R      - 3.6141784010013112E-11]
--R     ,
--R
--R     [1.3149999999999999, - 0.15231057819999999, - 0.15231057824555994,
--R      - 4.5559944705786393E-11]
--R     ,
--R
--R     [1.3200000000000001, - 0.1467423568, - 0.1467423567959959,
--R      4.0041026050374739E-12]
--R     ,
--R    [1.325,- 0.14120293049999999,- 0.14120293051842803,- 1.8428036874240661E-11]
--R     ,
--R
--R     [1.3300000000000001, - 0.135692018, - 0.13569201796416941,
--R      3.583058849621068E-11]
--R     ,
--R    [1.335,- 0.1302093416,- 0.13020934163201769,- 3.2017694051589274E-11],
--R
--R     [1.3400000000000001, - 0.1247546279, - 0.12475462789700376,
--R      2.9962421432827568E-12]
--R     ,
--R    [1.345,- 0.11932760689999999,- 0.11932760694070754,- 4.0707548443208452E-11]
--R     ,
--R
--R     [1.3500000000000001, - 0.1139280127, - 0.11392801268308839,
--R      1.6911611000480775E-11]
--R     ,
--R    [1.355,- 0.1085555827,- 0.10855558271580501,- 1.5805010078473458E-11],
--R
--R     [1.3600000000000001, - 0.1032100582, - 0.10321005823697738,
--R      - 3.6977379491709428E-11]
--R     ,
--R
--R     [1.365, - 9.7891184000000006E-2, - 9.7891183987354968E-2,
--R      1.2645037794634106E-11]
--R     ,
--R
--R     [1.3700000000000001, - 9.2598708200000004E-2, - 9.2598708187860979E-2,
--R      1.2139025895585576E-11]
--R     ,
--R    [1.375,- 8.73323825E-2,- 8.7332382478473081E-2,2.1526919136150013E-11],
--R
--R     [1.3799999999999999, - 8.2091961899999996E-2, - 8.2091961858406615E-2,
--R      4.1593381516769057E-11]
--R     ,
--R
--R     [1.385, - 7.6877204599999999E-2, - 7.6877204627574525E-2,
--R      - 2.7574525995888166E-11]
--R     ,
--R
--R     [1.3899999999999999, - 7.1687872299999997E-2, - 7.1687872329281643E-2,
--R      - 2.928164655191523E-11]
--R     ,
--R
--R     [1.395, - 6.6523729700000006E-2, - 6.6523729694132228E-2,
--R      5.867778485324493E-12]
--R     ,
--R
--R     [1.3999999999999999, - 6.13845446E-2, - 6.1384544585116108E-2,
--R      1.4883892729411485E-11]
--R     ,
--R
--R     [1.405, - 5.6270087900000001E-2, - 5.6270087943841696E-2,
--R      - 4.3841694163937461E-11]
--R     ,
--R
--R     [1.4099999999999999, - 5.1180133699999998E-2, - 5.1180133737897426E-2,
--R      - 3.7897428251110199E-11]
--R     ,
--R
--R     [1.415, - 4.6114458900000002E-2, - 4.6114458909301992E-2,
--R      - 9.3019897340340663E-12]
--R     ,
--R
--R     [1.4199999999999999, - 4.1072843300000002E-2, - 4.1072843324024277E-2,
--R      - 2.4024275624423552E-11]
--R     ,
--R
--R     [1.425, - 3.6055069699999998E-2, - 3.6055069722547906E-2,
--R      - 2.2547907985170923E-11]
--R     ,
--R
--R     [1.4299999999999999, - 3.10609237E-2, - 3.1060923671447194E-2,
--R      2.8552805952930527E-11]
--R     ,
--R
--R     [1.4350000000000001, - 2.6090193500000001E-2, - 2.609019351596098E-2,
--R      - 1.5960979066198533E-11]
--R     ,
--R
--R     [1.4399999999999999, - 2.1142670299999999E-2, - 2.1142670333530678E-2,
--R      - 3.3530678233972822E-11]
--R     ,
--R
--R     [1.4450000000000001, - 1.62181479E-2, - 1.6218147888283685E-2,
--R      1.1716315417853451E-11]
--R     ,
--R
--R     [1.45, - 1.1316422600000001E-2, - 1.1316422586445718E-2,
--R      1.3554282696226494E-11]
--R     ,
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--R                                                  Type: List List DoubleFloat
--E 3
--S 4 of 12
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   (4)
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     ]
                                          Type: List List Complex DoubleFloat
--R 
--R
--R   (4)
--R   [[1.,0.,0.,0.],
--R
--R     [1. + 0.10000000000000001 %i,
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--R
--R     [1. + 7.5999999999999996 %i, - 10.005039426790001 + 8.5883535709619991 %i,
--R      - 10.005039426790399 + 2.3051682637825208 %i,
--R      - 3.979039320256561E-13 - 6.2831853071794779 %i]
--R     ,
--R
--R     [1. + 7.7000000000000002 %i, - 10.155583018686 + 8.7919660705869997 %i,
--R      - 10.155583018686212 + 2.5087807634076618 %i,
--R      - 2.1138646388862981E-13 - 6.2831853071793375 %i]
--R     ,
--R
--R     [1. + 7.7999999999999998 %i, - 10.306210948947999 + 8.9968736442289998 %i,
--R      - 10.306210948947749 + 2.7136883370494931 %i,
--R      2.5046631435543532E-13 - 6.2831853071795063 %i]
--R     ,
--R
--R     [1. + 7.9000000000000004 %i, - 10.456921068739 + 9.2030597799250007 %i,
--R      - 10.456921068738524 + 2.9198744727458439 %i,
--R      4.7606363295926712E-13 - 6.2831853071791564 %i]
--R     ,
--R
--R     [1. + 8. %i, - 10.607711310315 + 9.4105083803120007 %i,
--R      - 10.607711310314581 + 3.1273230731320214 %i,
--R      4.1922021409845911E-13 - 6.2831853071799788 %i]
--R     ,
--R
--R     [1. + 8.0999999999999996 %i, - 10.758579682995 + 9.6192037472420004 %i,
--R      - 10.758579682994794 - 2.9471668671170055 %i,
--R      2.0605739337042905E-13 - 12.566370614359005 %i]
--R     ,
--R
--R     [1. + 8.1999999999999993 %i, - 10.909524269378 + 9.8291305671620002 %i,
--R      - 10.909524269378373 - 2.7372400471974712 %i,
--R      - 3.730349362740526E-13 - 12.566370614359471 %i]
--R     ,
--R
--R     [1. + 8.3000000000000007 %i, - 11.060543221792001 + 10.040273897180001 %i,
--R      - 11.060543221791693 - 2.5260967171793411 %i,
--R      3.0730973321624333E-13 - 12.566370614359341 %i]
--R     ,
--R
--R     [1. + 8.4000000000000004 %i, - 11.211634758948 + 10.252619151809 %i,
--R      - 11.211634758947826 - 2.3137514625505582 %i,
--R      1.7408297026122455E-13 - 12.566370614359558 %i]
--R     ,
--R
--R     [1. + 8.5 %i, - 11.362797162804 + 10.466152090324 %i,
--R      - 11.362797162803814 - 2.100218524035578 %i,
--R      1.865174681370263E-13 - 12.566370614359577 %i]
--R     ,
--R
--R     [1. + 8.5999999999999996 %i, - 11.514028775602 + 10.680858804712001 %i,
--R      - 11.514028775601707 - 1.8855118096468773 %i,
--R      2.9309887850104133E-13 - 12.566370614358878 %i]
--R     ,
--R
--R     [1. + 8.6999999999999993 %i, - 11.665327997081 + 10.896725708177 %i,
--R      - 11.665327997080658 - 1.6696449061826013 %i,
--R      3.4283687000424834E-13 - 12.566370614359601 %i]
--R     ,
--R
--R     [1. + 8.8000000000000007 %i, - 11.816693281848 + 11.113739524156999 %i,
--R      - 11.816693281848337 - 1.452631090201765 %i,
--R      - 3.3750779948604759E-13 - 12.566370614358764 %i]
--R     ,
--R
--R     [1. + 8.9000000000000004 %i, - 11.968123136900999 + 11.331887275852999 %i,
--R      - 11.968123136900861 - 1.2344833385062608 %i,
--R      1.3855583347321954E-13 - 12.56637061435926 %i]
--R     ,
--R
--R     [1. + 9. %i, - 12.119616119281 + 11.551156276202001 %i,
--R      - 12.119616119281286 - 1.0152143381569982 %i,
--R      - 2.8599345114344032E-13 - 12.566370614358998 %i]
--R     ,
--R
--R     [1. + 9.0999999999999996 %i, - 12.271170833867 + 11.771534118309001 %i,
--R      - 12.271170833867483 - 0.79483649604973161 %i,
--R      - 4.8316906031686813E-13 - 12.566370614358732 %i]
--R     ,
--R
--R     [1. + 9.1999999999999993 %i, - 12.422785931281 + 11.993008666285 %i,
--R      - 12.422785931280877 - 0.5733619480744393 %i,
--R      1.2256862191861728E-13 - 12.566370614359439 %i]
--R     ,
--R
--R     [1. + 9.3000000000000007 %i, - 12.574460105908001 + 12.215568046479 %i,
--R      - 12.574460105908262 - 0.35080256788055886 %i,
--R      - 2.6112445539183682E-13 - 12.566370614359558 %i]
--R     ,
--R
--R     [1. + 9.4000000000000004 %i, - 12.726192094029001 + 12.43920063909 %i,
--R      - 12.726192094029377 - 0.12716997526913024 %i,
--R      - 3.765876499528531E-13 - 12.56637061435913 %i]
--R     ,
--R
--R     [1. + 9.5 %i, - 12.877980672044 + 12.663895070128 %i,
--R      - 12.877980672043599 + 9.7524455768741289E-2 %i,
--R      4.0145664570445661E-13 - 12.566370614359258 %i]
--R     ,
--R
--R     [1. + 9.5999999999999996 %i, - 13.029824654789 + 12.889640203708 %i,
--R      - 13.02982465478944 + 0.32326958934851951 %i,
--R      - 4.4053649617126212E-13 - 12.56637061435948 %i]
--R     ,
--R
--R     [1. + 9.6999999999999993 %i, - 13.181722893950999 + 13.116425134666001 %i,
--R      - 13.181722893951155 + 0.55005452030683832 %i,
--R      - 1.5631940186722204E-13 - 12.566370614359162 %i]
--R     ,
--R
--R     [1. + 9.8000000000000007 %i, - 13.333674276547001 + 13.344239181477 %i,
--R      - 13.333674276547052 + 0.77786856711780805 %i,
--R      - 5.1514348342607263E-14 - 12.566370614359192 %i]
--R     ,
--R
--R     [1. + 9.9000000000000004 %i, - 13.485677723495 + 13.573071879455 %i,
--R      - 13.485677723494533 + 1.0067012650958465 %i,
--R      4.6718184876226587E-13 - 12.566370614359153 %i]
--R     ,
--R
--R     [1. + 10. %i, - 13.637732188247 + 13.802912974230001 %i,
--R      - 13.637732188247268 + 1.2365423598707301 %i,
--R      - 2.6822988274943782E-13 - 12.56637061435927 %i]
--R     ]
--R                                          Type: List List Complex DoubleFloat
--E 4

--S 5 of 12
halfLog2Pi:=log(2.0*%pi)/2
 

   (5)  0.9189385332 0467274178
                                                                  Type: Float
--R 
--R
--R   (5)  0.9189385332 0467274178
--R                                                                  Type: Float
--E 5

--S 6 of 12
inner(k,n)==reduce(+,[(-1)^r*binomial(k,r)*r^n for r in 0..k])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 12
B(n)==reduce(+,[(inner(k,n)/(k+1)) for k in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 12
Z(m,z)==B(2*m)/((2*m*(2*m-1))*z^(2*m-1))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 12
H(z)==(z-1/2)*log(z)-z+halfLog2Pi+reduce(+,[Z(m,z) for m in 1..5]) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 12
[[1. + 0.0 * %i,0.,H(1. + 0.0 * %i),H(1. + 0.0 * %i)-0.0],_
[1. + 0.1 * %i, -0.008197780565 - 0.057322940417 * %i,_
H(1. + 0.1 * %i),_
H(1. + 0.1 * %i)-( -0.008197780565 - 0.057322940417 * %i)],_
[1. + 0.2 * %i, -0.032476292318 - 0.112302222644 * %i,_
H(1. + 0.2 * %i),_
H(1. + 0.2 * %i)-( -0.032476292318 - 0.112302222644 * %i)],_
[1. + 0.3 * %i, -0.071946250900 - 0.162820672168 * %i,_
H(1. + 0.3 * %i),_
H(1. + 0.3 * %i)-( -0.071946250900 - 0.162820672168 * %i)],_
[1. + 0.4 * %i, -0.125289374821 - 0.207155826316 * %i,_
H(1. + 0.4 * %i),_
H(1. + 0.4 * %i)-( -0.125289374821 - 0.207155826316 * %i)],_
[1. + 0.5 * %i,- 0.190945499187 - 0.244058298905 * %i,_
H(1. + 0.5 * %i),_
H(1. + 0.5 * %i)-(- 0.190945499187 - 0.244058298905 * %i)],_
[1. + 0.6 * %i,- 0.267290068214 - 0.272743810491 * %i,_
H(1. + 0.6 * %i),_
H(1. + 0.6 * %i)-(- 0.267290068214 - 0.272743810491 * %i)],_
[1. + 0.7 * %i,- 0.352768690860 - 0.292826351187 * %i,_
H(1. + 0.7 * %i),_
H(1. + 0.7 * %i)-(- 0.352768690860 - 0.292826351187 * %i)],_
[1. + 0.8 * %i,- 0.445978783549 - 0.304225602976 * %i,_
H(1. + 0.8 * %i),_
H(1. + 0.8 * %i)-(- 0.445978783549 - 0.304225602976 * %i)],_
[1. + 0.9 * %i,- 0.545705128605 - 0.307074375642 * %i,_
H(1. + 0.9 * %i),_
H(1. + 0.9 * %i)-(- 0.545705128605 - 0.307074375642 * %i)],_
[1. + 1.0 * %i,- 0.650923199302 - 0.301640320468 * %i,_
H(1. + 1.0 * %i),_
H(1. + 1.0 * %i)-(- 0.650923199302 - 0.301640320468 * %i)],_
[1. + 1.1 * %i,- 0.760783958841 - 0.288266614239 * %i,_
H(1. + 1.1 * %i),_
H(1. + 1.1 * %i)-(- 0.760783958841 - 0.288266614239 * %i)],_
[1. + 1.2 * %i,- 0.874590463895 - 0.267330580581 * %i,_
H(1. + 1.2 * %i),_
H(1. + 1.2 * %i)-(- 0.874590463895 - 0.267330580581 * %i)],_
[1. + 1.3 * %i,- 0.991772766959 - 0.239216784465 * %i,_
H(1. + 1.3 * %i),_
H(1. + 1.3 * %i)-(- 0.991772766959 - 0.239216784465 * %i)],_
[1. + 1.4 * %i,- 1.111864566426 - 0.204300724149 * %i,_
H(1. + 1.4 * %i),_
H(1. + 1.4 * %i)-(- 1.111864566426 - 0.204300724149 * %i)],_
[1. + 1.5 * %i,- 1.234483051547 - 0.162939769480 * %i,_
H(1. + 1.5 * %i),_
H(1. + 1.5 * %i)-(- 1.234483051547 - 0.162939769480 * %i)],_
[1. + 1.6 * %i,- 1.359312248465 - 0.115468793589 * %i,_
H(1. + 1.6 * %i),_
H(1. + 1.6 * %i)-(- 1.359312248465 - 0.115468793589 * %i)],_
[1. + 1.7 * %i,- 1.486089612757 - 0.062198698329 * %i,_
H(1. + 1.7 * %i),_
H(1. + 1.7 * %i)-(- 1.486089612757 - 0.062198698329 * %i)],_
[1. + 1.8 * %i,- 1.614595396000 - 0.003416631477 * %i,_
H(1. + 1.8 * %i),_
H(1. + 1.8 * %i)-(- 1.614595396000 - 0.003416631477 * %i)],_
[1. + 1.9 * %i,- 1.744644276174 + 0.060612874295 * %i,_
H(1. + 1.9 * %i),_
H(1. + 1.9 * %i)-(- 1.744644276174 + 0.060612874295 * %i)],_
[1. + 2.0 * %i,- 1.876078786431 + 0.129646316310 * %i,_
H(1. + 2.0 * %i),_
H(1. + 2.0 * %i)-(- 1.876078786431 + 0.129646316310 * %i)],_
[1. + 2.1 * %i,- 2.008764150471 + 0.203459473833 * %i,_
H(1. + 2.1 * %i),_
H(1. + 2.1 * %i)-(- 2.008764150471 + 0.203459473833 * %i)],_
[1. + 2.2 * %i,- 2.142584209296 + 0.281845658426 * %i,_
H(1. + 2.2 * %i),_
H(1. + 2.2 * %i)-(- 2.142584209296 + 0.281845658426 * %i)],_
[1. + 2.3 * %i,- 2.277438192204 + 0.364614048950 * %i,_
H(1. + 2.3 * %i),_
H(1. + 2.3 * %i)-(- 2.277438192204 + 0.364614048950 * %i)],_
[1. + 2.4 * %i,- 2.413238141184 + 0.451588152441 * %i,_
H(1. + 2.4 * %i),_
H(1. + 2.4 * %i)-(- 2.413238141184 + 0.451588152441 * %i)],_
[1. + 2.5 * %i,- 2.549906842495 + 0.542604405852 * %i,_
H(1. + 2.5 * %i),_
H(1. + 2.5 * %i)-(- 2.549906842495 + 0.542604405852 * %i)],_
[1. + 2.6 * %i,- 2.687376153750 + 0.637510919046 * %i,_
H(1. + 2.6 * %i),_
H(1. + 2.6 * %i)-(- 2.687376153750 + 0.637510919046 * %i)],_
[1. + 2.7 * %i,- 2.825585641191 + 0.736166351679 * %i,_
H(1. + 2.7 * %i),_
H(1. + 2.7 * %i)-(- 2.825585641191 + 0.736166351679 * %i)],_
[1. + 2.8 * %i,- 2.964481461789 + 0.838438913096 * %i,_
H(1. + 2.8 * %i),_
H(1. + 2.8 * %i)-(- 2.964481461789 + 0.838438913096 * %i)],_
[1. + 2.9 * %i,- 3.104015439901 + 0.944205473039 * %i,_
H(1. + 2.9 * %i),_
H(1. + 2.9 * %i)-(- 3.104015439901 + 0.944205473039 * %i)],_
[1. + 3.0 * %i,- 3.244144299590 + 1.053350771069 * %i,_
H(1. + 3.0 * %i),_
H(1. + 3.0 * %i)-(- 3.244144299590 + 1.053350771069 * %i)],_
[1. + 3.1 * %i,- 3.384829022377 + 1.165766713286 * %i,_
H(1. + 3.1 * %i),_
H(1. + 3.1 * %i)-(- 3.384829022377 + 1.165766713286 * %i)],_
[1. + 3.2 * %i,- 3.526034306709 + 1.281351745932 * %i,_
H(1. + 3.2 * %i),_
H(1. + 3.2 * %i)-(- 3.526034306709 + 1.281351745932 * %i)],_
[1. + 3.3 * %i,- 3.667728110488 + 1.400010296576 * %i,_
H(1. + 3.3 * %i),_
H(1. + 3.3 * %i)-(- 3.667728110488 + 1.400010296576 * %i)],_
[1. + 3.4 * %i,- 3.809881261823 + 1.521652274673 * %i,_
H(1. + 3.4 * %i),_
H(1. + 3.4 * %i)-(- 3.809881261823 + 1.521652274673 * %i)],_
[1. + 3.5 * %i,- 3.952467126189 + 1.646192624269 * %i,_
H(1. + 3.5 * %i),_
H(1. + 3.5 * %i)-(- 3.952467126189 + 1.646192624269 * %i)],_
[1. + 3.6 * %i,- 4.095461320451 + 1.773550922591 * %i,_
H(1. + 3.6 * %i),_
H(1. + 3.6 * %i)-(- 4.095461320451 + 1.773550922591 * %i)],_
[1. + 3.7 * %i,- 4.238841466071 + 1.903651019019 * %i,_
H(1. + 3.7 * %i),_
H(1. + 3.7 * %i)-(- 4.238841466071 + 1.903651019019 * %i)],_
[1. + 3.8 * %i,- 4.382586975228 + 2.036420709693 * %i,_
H(1. + 3.8 * %i),_
H(1. + 3.8 * %i)-(- 4.382586975228 + 2.036420709693 * %i)],_
[1. + 3.9 * %i,- 4.526678864716 + 2.171791443605 * %i,_
H(1. + 3.9 * %i),_
H(1. + 3.9 * %i)-(- 4.526678864716 + 2.171791443605 * %i)],_
[1. + 4.0 * %i,- 4.671099593409 + 2.309698056573 * %i,_
H(1. + 4.0 * %i),_
H(1. + 4.0 * %i)-(- 4.671099593409 + 2.309698056573 * %i)],_
[1. + 4.1 * %i,- 4.815832919796 + 2.450078529947 * %i,_
H(1. + 4.1 * %i),_
H(1. + 4.1 * %i)-(- 4.815832919796 + 2.450078529947 * %i)],_
[1. + 4.2 * %i,- 4.960863776687 + 2.592873771319 * %i,_
H(1. + 4.2 * %i),_
H(1. + 4.2 * %i)-(- 4.960863776687 + 2.592873771319 * %i)],_
[1. + 4.3 * %i,- 5.106178160663 + 2.738027414820 * %i,_
H(1. + 4.3 * %i),_
H(1. + 4.3 * %i)-(- 5.106178160663 + 2.738027414820 * %i)],_
[1. + 4.4 * %i,- 5.251763034230 + 2.885485638927 * %i,_
H(1. + 4.4 * %i),_
H(1. + 4.4 * %i)-(- 5.251763034230 + 2.885485638927 * %i)],_
[1. + 4.5 * %i,- 5.397606238984 + 3.035196999922 * %i,_
H(1. + 4.5 * %i),_
H(1. + 4.5 * %i)-(- 5.397606238984 + 3.035196999922 * %i)],_
[1. + 4.6 * %i,- 5.543696418304 + 3.187112279389 * %i,_
H(1. + 4.6 * %i),_
H(1. + 4.6 * %i)-(- 5.543696418304 + 3.187112279389 * %i)],_
[1. + 4.7 * %i,- 5.690022948373 + 3.341184344327 * %i,_
H(1. + 4.7 * %i),_
H(1. + 4.7 * %i)-(- 5.690022948373 + 3.341184344327 * %i)],_
[1. + 4.8 * %i,- 5.836575876454 + 3.497368018615 * %i,_
H(1. + 4.8 * %i),_
H(1. + 4.8 * %i)-(- 5.836575876454 + 3.497368018615 * %i)],_
[1. + 4.9 * %i,- 5.983345865532 + 3.655619964712 * %i,_
H(1. + 4.9 * %i),_
H(1. + 4.9 * %i)-(- 5.983345865532 + 3.655619964712 * %i)],_
[1. + 5.0 * %i,- 6.130324144553 + 3.815898574615 * %i,_
H(1. + 5.0 * %i),_
H(1. + 5.0 * %i)-(- 6.130324144553 + 3.815898574615 * %i)],_
[1. + 5.1 * %i,- 6.277502463584 + 3.978163869188 * %i,_
H(1. + 5.1 * %i),_
H(1. + 5.1 * %i)-(- 6.277502463584 + 3.978163869188 * %i)],_
[1. + 5.2 * %i,- 6.424873053335 + 4.142377405086 * %i,_
H(1. + 5.2 * %i),_
H(1. + 5.2 * %i)-(- 6.424873053335 + 4.142377405086 * %i)],_
[1. + 5.3 * %i,- 6.572428588529 + 4.308502188583 * %i,_
H(1. + 5.3 * %i),_
H(1. + 5.3 * %i)-(- 6.572428588529 + 4.308502188583 * %i)],_
[1. + 5.4 * %i,- 6.720162154703 + 4.476502595668 * %i,_
H(1. + 5.4 * %i),_
H(1. + 5.4 * %i)-(- 6.720162154703 + 4.476502595668 * %i)],_
[1. + 5.5 * %i,- 6.868067218048 + 4.646344297870 * %i,_
H(1. + 5.5 * %i),_
H(1. + 5.5 * %i)-(- 6.868067218048 + 4.646344297870 * %i)],_
[1. + 5.6 * %i,- 7.016137597976 + 4.817994193305 * %i,_
H(1. + 5.6 * %i),_
H(1. + 5.6 * %i)-(- 7.016137597976 + 4.817994193305 * %i)],_
[1. + 5.7 * %i,- 7.164367442106 + 4.991420342489 * %i,_
H(1. + 5.7 * %i),_
H(1. + 5.7 * %i)-(- 7.164367442106 + 4.991420342489 * %i)],_
[1. + 5.8 * %i,- 7.312751203430 + 5.166591908537 * %i,_
H(1. + 5.8 * %i),_
H(1. + 5.8 * %i)-(- 7.312751203430 + 5.166591908537 * %i)],_
[1. + 5.9 * %i,- 7.461283619429 + 5.343479101353 * %i,_
H(1. + 5.9 * %i),_
H(1. + 5.9 * %i)-(- 7.461283619429 + 5.343479101353 * %i)],_
[1. + 6.0 * %i,- 7.609959692951 + 5.522053125515 * %i,_
H(1. + 6.0 * %i),_
H(1. + 6.0 * %i)-(- 7.609959692951 + 5.522053125515 * %i)],_
[1. + 6.1 * %i,- 7.758774674655 + 5.702286131535 * %i,_
H(1. + 6.1 * %i),_
H(1. + 6.1 * %i)-(- 7.758774674655 + 5.702286131535 * %i)],_
[1. + 6.2 * %i,- 7.907724046898 + 5.884151170239 * %i,_
H(1. + 6.2 * %i),_
H(1. + 6.2 * %i)-(- 7.907724046898 + 5.884151170239 * %i)],_
[1. + 6.3 * %i,- 8.056803508904 + 6.067622150013 * %i,_
H(1. + 6.3 * %i),_
H(1. + 6.3 * %i)-(- 8.056803508904 + 6.067622150013 * %i)],_
[1. + 6.4 * %i,- 8.206008963100 + 6.252673796705 * %i,_
H(1. + 6.4 * %i),_
H(1. + 6.4 * %i)-(- 8.206008963100 + 6.252673796705 * %i)],_
[1. + 6.5 * %i,- 8.355336502511 + 6.439281615976 * %i,_
H(1. + 6.5 * %i),_
H(1. + 6.5 * %i)-(- 8.355336502511 + 6.439281615976 * %i)],_
[1. + 6.6 * %i,- 8.504782399125 + 6.627421857912 * %i,_
H(1. + 6.6 * %i),_
H(1. + 6.6 * %i)-(- 8.504782399125 + 6.627421857912 * %i)],_
[1. + 6.7 * %i,- 8.654343093123 + 6.817071483744 * %i,_
H(1. + 6.7 * %i),_
H(1. + 6.7 * %i)-(- 8.654343093123 + 6.817071483744 * %i)],_
[1. + 6.8 * %i,- 8.804015182910 + 7.008208134502 * %i,_
H(1. + 6.8 * %i),_
H(1. + 6.8 * %i)-(- 8.804015182910 + 7.008208134502 * %i)],_
[1. + 6.9 * %i,- 8.953795415879 + 7.200810101493 * %i,_
H(1. + 6.9 * %i),_
H(1. + 6.9 * %i)-(- 8.953795415879 + 7.200810101493 * %i)],_
[1. + 7.0 * %i,- 9.103680679832 + 7.394856298436 * %i,_
H(1. + 7.0 * %i),_
H(1. + 7.0 * %i)-(- 9.103680679832 + 7.394856298436 * %i)],_
[1. + 7.1 * %i,- 9.253667995015 + 7.590326235184 * %i,_
H(1. + 7.1 * %i),_
H(1. + 7.1 * %i)-(- 9.253667995015 + 7.590326235184 * %i)],_
[1. + 7.2 * %i,- 9.403754506708 + 7.787199992877 * %i,_
H(1. + 7.2 * %i),_
H(1. + 7.2 * %i)-(- 9.403754506708 + 7.787199992877 * %i)],_
[1. + 7.3 * %i,- 9.553937478321 + 7.985458200468 * %i,_
H(1. + 7.3 * %i),_
H(1. + 7.3 * %i)-(- 9.553937478321 + 7.985458200468 * %i)],_
[1. + 7.4 * %i,- 9.704214284972 + 8.185082012503 * %i,_
H(1. + 7.4 * %i),_
H(1. + 7.4 * %i)-(- 9.704214284972 + 8.185082012503 * %i)],_
[1. + 7.5 * %i,- 9.854582407486 + 8.386053088089 * %i,_
H(1. + 7.5 * %i),_
H(1. + 7.5 * %i)-(- 9.854582407486 + 8.386053088089 * %i)],_
[1. + 7.6 * %i,- 10.005039426790 + 8.588353570962 * %i,_
H(1. + 7.6 * %i),_
H(1. + 7.6 * %i)-(- 10.005039426790 + 8.588353570962 * %i)],_
[1. + 7.7 * %i,- 10.155583018686 + 8.791966070587 * %i,_
H(1. + 7.7 * %i),_
H(1. + 7.7 * %i)-(- 10.155583018686 + 8.791966070587 * %i)],_
[1. + 7.8 * %i,- 10.306210948948 + 8.996873644229 * %i,_
H(1. + 7.8 * %i),_
H(1. + 7.8 * %i)-(- 10.306210948948 + 8.996873644229 * %i)],_
[1. + 7.9 * %i,- 10.456921068739 + 9.203059779925 * %i,_
H(1. + 7.9 * %i),_
H(1. + 7.9 * %i)-(- 10.456921068739 + 9.203059779925 * %i)],_
[1. + 8.0 * %i,- 10.607711310315 + 9.410508380312 * %i,_
H(1. + 8.0 * %i),_
H(1. + 8.0 * %i)-(- 10.607711310315 + 9.410508380312 * %i)],_
[1. + 8.1 * %i,- 10.758579682995 + 9.619203747242 * %i,_
H(1. + 8.1 * %i),_
H(1. + 8.1 * %i)-(- 10.758579682995 + 9.619203747242 * %i)],_
[1. + 8.2 * %i,- 10.909524269378 + 9.829130567162 * %i,_
H(1. + 8.2 * %i),_
H(1. + 8.2 * %i)-(- 10.909524269378 + 9.829130567162 * %i)],_
[1. + 8.3 * %i,- 11.060543221792 + 10.040273897180 * %i,_
H(1. + 8.3 * %i),_
H(1. + 8.3 * %i)-(- 11.060543221792 + 10.040273897180 * %i)],_
[1. + 8.4 * %i,- 11.211634758948 + 10.252619151809 * %i,_
H(1. + 8.4 * %i),_
H(1. + 8.4 * %i)-(- 11.211634758948 + 10.252619151809 * %i)],_
[1. + 8.5 * %i,- 11.362797162804 + 10.466152090324 * %i,_
H(1. + 8.5 * %i),_
H(1. + 8.5 * %i)-(- 11.362797162804 + 10.466152090324 * %i)],_
[1. + 8.6 * %i,- 11.514028775602 + 10.680858804712 * %i,_
H(1. + 8.6 * %i),_
H(1. + 8.6 * %i)-(- 11.514028775602 + 10.680858804712 * %i)],_
[1. + 8.7 * %i,- 11.665327997081 + 10.896725708177 * %i,_
H(1. + 8.7 * %i),_
H(1. + 8.7 * %i)-(- 11.665327997081 + 10.896725708177 * %i)],_
[1. + 8.8 * %i,- 11.816693281848 + 11.113739524157 * %i,_
H(1. + 8.8 * %i),_
H(1. + 8.8 * %i)-(- 11.816693281848 + 11.113739524157 * %i)],_
[1. + 8.9 * %i,- 11.968123136901 + 11.331887275853 * %i,_
H(1. + 8.9 * %i),_
H(1. + 8.9 * %i)-(- 11.968123136901 + 11.331887275853 * %i)],_
[1. + 9.0 * %i,- 12.119616119281 + 11.551156276202 * %i,_
H(1. + 9.0 * %i),_
H(1. + 9.0 * %i)-(- 12.119616119281 + 11.551156276202 * %i)],_
[1. + 9.1 * %i,- 12.271170833867 + 11.771534118309 * %i,_
H(1. + 9.1 * %i),_
H(1. + 9.1 * %i)-(- 12.271170833867 + 11.771534118309 * %i)],_
[1. + 9.2 * %i,- 12.422785931281 + 11.993008666285 * %i,_
H(1. + 9.2 * %i),_
H(1. + 9.2 * %i)-(- 12.422785931281 + 11.993008666285 * %i)],_
[1. + 9.3 * %i,- 12.574460105908 + 12.215568046479 * %i,_
H(1. + 9.3 * %i),_
H(1. + 9.3 * %i)-(- 12.574460105908 + 12.215568046479 * %i)],_
[1. + 9.4 * %i,- 12.726192094029 + 12.439200639090 * %i,_
H(1. + 9.4 * %i),_
H(1. + 9.4 * %i)-(- 12.726192094029 + 12.439200639090 * %i)],_
[1. + 9.5 * %i,- 12.877980672044 + 12.663895070128 * %i,_
H(1. + 9.5 * %i),_
H(1. + 9.5 * %i)-(- 12.877980672044 + 12.663895070128 * %i)],_
[1. + 9.6 * %i,- 13.029824654789 + 12.889640203708 * %i,_
H(1. + 9.6 * %i),_
H(1. + 9.6 * %i)-(- 13.029824654789 + 12.889640203708 * %i)],_
[1. + 9.7 * %i,- 13.181722893951 + 13.116425134666 * %i,_
H(1. + 9.7 * %i),_
H(1. + 9.7 * %i)-(- 13.181722893951 + 13.116425134666 * %i)],_
[1. + 9.8 * %i,- 13.333674276547 + 13.344239181477 * %i,_
H(1. + 9.8 * %i),_
H(1. + 9.8 * %i)-(- 13.333674276547 + 13.344239181477 * %i)],_
[1. + 9.9 * %i,- 13.485677723495 + 13.573071879455 * %i,_
H(1. + 9.9 * %i),_
H(1. + 9.9 * %i)-(- 13.485677723495 + 13.573071879455 * %i)],_
[1. + 10.0 * %i,- 13.637732188247 + 13.802912974230 * %i,_
H(1. + 10.0 * %i),_
H(1. + 10.0 * %i)-(- 13.637732188247 + 13.802912974230 * %i)]]
 
   Compiling function inner with type (NonNegativeInteger,
      PositiveInteger) -> Integer 
   Compiling function B with type PositiveInteger -> Fraction Integer 
   Compiling function Z with type (PositiveInteger,Complex Float) -> 
      Complex Float 
   Compiling function H with type Complex Float -> Complex Float 

   (10)
   [[1.0,0.0,0.0005342523 0039183749 9,0.0005342523 0039183749 9],

     [1.0 + 0.1 %i, - 0.0081977805 65 - 0.0573229404 17 %i,
      - 0.0079060360 5641775235 1 - 0.0577425561 880608609 %i,
      0.0002917445 0858224764 9 - 0.0004196157 710608609 %i]
     ,

     [1.0 + 0.2 %i, - 0.0324762923 18 - 0.1123022226 44 %i,
      - 0.0326253424 137575225 - 0.1127252606 10617179 %i,
      - 0.0001490500 957575225 - 0.0004230379 66617179 %i]
     ,

     [1.0 + 0.3 %i, - 0.0719462509 - 0.1628206721 68 %i,
      - 0.0722917796 3325300528 - 0.1629343118 0182595104 %i,
      - 0.0003455287 3325300528 - 0.0001136396 33825951 %i]
     ,

     [1.0 + 0.4 %i, - 0.1252893748 21 - 0.2071558263 16 %i,
      - 0.1255237832 8903895364 - 0.2070111768 1461131296 %i,
      - 0.0002344084 6803895364 + 0.0001446495 0138868704 %i]
     ,

     [1.0 + 0.5 %i, - 0.1909454991 87 - 0.2440582989 05 %i,
      - 0.1909844153 9406580427 - 0.2438650024 4353127544 %i,
      - 0.0000389162 0706580427 + 0.0001932964 6146872456 %i]
     ,

     [1.0 + 0.6 %i, - 0.2672900682 14 - 0.2727438104 91 %i,
      - 0.2672177072 7708327583 - 0.2726297345 2049521095 %i,
      0.0000723609 3691672417 + 0.0001140759 70504789 %i]
     ,

     [1.0 + 0.7 %i, - 0.3527686908 6 - 0.2928263511 87 %i,
      - 0.3526830217 4071123327 - 0.2928000766 8168133466 %i,
      0.0000856691 1928876673 + 0.0000262745 053186653 %i]
     ,

     [1.0 + 0.8 %i, - 0.4459787835 49 - 0.3042256029 76 %i,
      - 0.4459243064 600936154 - 0.3042458540 6494479039 %i,
      0.0000544770 889063846 - 0.0000202510 889447904 %i]
     ,

     [1.0 + 0.9 %i, - 0.5457051286 05 - 0.3070743756 42 %i,
      - 0.5456837564 2266021862 - 0.3071047743 7404541115 %i,
      0.0000213721 823397814 - 0.0000303987 320454111 %i]
     ,

     [1.0 + %i, - 0.6509231993 02 - 0.3016403204 68 %i,
      - 0.6509218279 5803214573 - 0.3016638509 8907615826 %i,
      0.0000013713 439678543 - 0.0000235305 210761583 %i]
     ,

     [1.0 + 1.1 %i, - 0.7607839588 41 - 0.2882666142 39 %i,
      - 0.7607904806 1959258337 - 0.2882800153 6783960204 %i,
      - 0.0000065217 7859258337 - 0.0000134011 28839602 %i]
     ,

     [1.0 + 1.2 %i, - 0.8745904638 95 - 0.2673305805 81 %i,
      - 0.8745979912 3533931918 - 0.2673362568 721629649 %i,
      - 0.0000075273 4033931918 - 0.0000056762 911629649 %i]
     ,

     [1.0 + 1.3 %i, - 0.9917727669 59 - 0.2392167844 65 %i,
      - 0.9917786169 8448669121 - 0.2392180306 8558905783 %i,
      - 0.0000058500 2548669121 - 0.0000012462 2058905783 %i]
     ,

     [1.0 + 1.4 %i, - 1.1118645664 26 - 0.2043007241 49 %i,
      - 1.1118683074 739622893 - 0.2042999880 7236175351 %i,
      - 0.0000037410 479622893 + 0.7360766382 4649 E -6 %i]
     ,

     [1.0 + 1.5 %i, - 1.2344830515 47 - 0.1629397694 8 %i,
      - 1.2344851106 088582896 - 0.1629384511 4283237552 %i,
      - 0.0000020590 618582896 + 0.0000013183 3716762448 %i]
     ,

     [1.0 + 1.6 %i, - 1.3593122484 65 - 0.1154687935 89 %i,
      - 1.3593132065 575271954 - 0.1154675392 0060867755 %i,
      - 0.9580925271 9539 E -6 + 0.0000012543 8839132245 %i]
     ,

     [1.0 + 1.7 %i, - 1.4860896127 57 - 0.0621986983 29 %i,
      - 1.4860899424 768375682 - 0.0621977263 0645742299 5 %i,
      - 0.3297198375 682 E -6 + 0.9720225425 77005 E -6 %i]
     ,

     [1.0 + 1.8 %i, - 1.614595396 - 0.0034166314 77 %i,
      - 1.6145954117 853473727 - 0.0034159591 4562980466 %i,
      - 0.1578534737 27 E -7 + 0.6723313701 953421 E -6 %i]
     ,

     [1.0 + 1.9 %i, - 1.7446442761 74 + 0.0606128742 95 %i,
      - 1.7446441619 196944916 + 0.0606133033 8564864100 7 %i,
      0.1142543055 08 E -6 + 0.4290906486 41007 E -6 %i]
     ,

     [1.0 + 2.0 %i, - 1.8760787864 31 + 0.1296463163 1 %i,
      - 1.8760786381 585810542 + 0.1296465718 833341783 %i,
      0.1482724189 458 E -6 + 0.2555733341 783 E -6 %i]
     ,

     [1.0 + 2.1 %i, - 2.0087641504 71 + 0.2034594738 33 %i,
      - 2.0087640119 218530981 + 0.2034596154 799745979 %i,
      0.1385491469 02 E -6 + 0.1416469745 979 E -6 %i]
     ,

     [1.0 + 2.2 %i, - 2.1425842092 96 + 0.2818456584 26 %i,
      - 2.1425840960 876952162 + 0.2818457299 3685319226 %i,
      0.1132083047 84 E -6 + 0.7151085319 226 E -7 %i]
     ,

     [1.0 + 2.3 %i, - 2.2774381922 04 + 0.3646140489 5 %i,
      - 2.2774381063 831111412 + 0.3646140797 7055414725 %i,
      0.8582088885 88 E -7 + 0.3082055414 725 E -7 %i]
     ,

     [1.0 + 2.4 %i, - 2.4132381411 84 + 0.4515881524 41 %i,
      - 2.4132380792 215488516 + 0.4515881611 4945339852 %i,
      0.6196245114 84 E -7 + 0.8708453398 52 E -8 %i]
     ,

     [1.0 + 2.5 %i, - 2.5499068424 95 + 0.5426044058 52 %i,
      - 2.5499067992 955284158 + 0.5426044035 6280478379 %i,
      0.4319947158 42 E -7 - 0.2289195216 2 E -8 %i]
     ,

     [1.0 + 2.6 %i, - 2.6873761537 5 + 0.6375109190 46 %i,
      - 2.6873761244 380686304 + 0.6375109120 6490899231 %i,
      0.2931193136 96 E -7 - 0.6981091007 69 E -8 %i]
     ,

     [1.0 + 2.7 %i, - 2.8255856411 91 + 0.7361663516 79 %i,
      - 2.8255856217 482878084 + 0.7361663433 7467081169 %i,
      0.1944271219 16 E -7 - 0.8304329188 32 E -8 %i]
     ,

     [1.0 + 2.8 %i, - 2.9644814617 89 + 0.8384389130 96 %i,
      - 2.9644814491 554295115 + 0.8384389051 1754275168 %i,
      0.1263357048 8 E -7 - 0.7978457248 32 E -8 %i]
     ,

     [1.0 + 2.9 %i, - 3.1040154399 01 + 0.9442054730 39 %i,
      - 3.1040154318 565321996 + 0.9442054660 7862553084 %i,
      0.8044467800 4 E -8 - 0.6960374469 16 E -8 %i]
     ,

     [1.0 + 3.0 %i, - 3.2441442995 9 + 1.0533507710 69 %i,
      - 3.2441442945 809249541 + 1.0533507653 179013667 %i,
      0.5009075046 E -8 - 0.5751098633 3 E -8 %i]
     ,

     [1.0 + 3.1 %i, - 3.3848290223 77 + 1.1657667132 86 %i,
      - 3.3848290193 409889189 + 1.1657667086 926332139 %i,
      0.3036011081 1 E -8 - 0.4593366786 1 E -8 %i]
     ,

     [1.0 + 3.2 %i, - 3.5260343067 09 + 1.2813517459 32 %i,
      - 3.5260343049 347826646 + 1.2813517423 440037128 %i,
      0.1774217335 E -8 - 0.3587996287 2 E -8 %i]
     ,

     [1.0 + 3.3 %i, - 3.6677281104 88 + 1.4000102965 76 %i,
      - 3.6677281095 052040502 + 1.4000102938 163542918 %i,
      0.9827959498 E -9 - 0.2759645708 2 E -8 %i]
     ,

     [1.0 + 3.4 %i, - 3.8098812618 23 + 1.5216522746 73 %i,
      - 3.8098812613 276184867 + 1.5216522725 71566048 %i,
      0.4953815133 E -9 - 0.2101433952 E -8 %i]
     ,

     [1.0 + 3.5 %i, - 3.9524671261 89 + 1.6461926242 69 %i,
      - 3.9524671259 853198893 + 1.6461926226 807455415 %i,
      0.203680111 E -9 - 0.1588254458 5 E -8 %i]
     ,

     [1.0 + 3.6 %i, - 4.0954613204 51 + 1.7735509225 91 %i,
      - 4.0954613204 155384205 + 1.7735509213 962023574 %i,
      0.354615795 E -10 - 0.1194797642 6 E -8 %i]
     ,

     [1.0 + 3.7 %i, - 4.2388414660 71 + 1.9036510190 19 %i,
      - 4.2388414661 27781932 + 1.9036510181 226951001 %i,
      - 0.56781932 E -10 - 0.8963048999 E -9 %i]
     ,

     [1.0 + 3.8 %i, - 4.3825869752 28 + 2.0364207096 93 %i,
      - 4.3825869753 299956382 + 2.0364207090 215572509 %i,
      - 0.101995638 E -9 - 0.6714427491 E -9 %i]
     ,

     [1.0 + 3.9 %i, - 4.5266788647 16 + 2.1717914436 05 %i,
      - 4.5266788648 352793739 + 2.1717914431 026276223 %i,
      - 0.119279374 E -9 - 0.5023723777 E -9 %i]
     ,

     [1.0 + 4.0 %i, - 4.6710995934 09 + 2.3096980565 73 %i,
      - 4.6710995935 296268252 + 2.3096980561 967129493 %i,
      - 0.120626825 E -9 - 0.3762870507 E -9 %i]
     ,

     [1.0 + 4.1 %i, - 4.8158329197 96 + 2.4500785299 47 %i,
      - 4.8158329199 100070487 + 2.4500785296 656839327 %i,
      - 0.114007049 E -9 - 0.2813160673 E -9 %i]
     ,

     [1.0 + 4.2 %i, - 4.9608637766 87 + 2.5928737713 19 %i,
      - 4.9608637767 906961011 + 2.5928737711 078289946 %i,
      - 0.103696101 E -9 - 0.211171005 E -9 %i]
     ,

     [1.0 + 4.3 %i, - 5.1061781606 63 + 2.7380274148 2 %i,
      - 5.1061781607 536849241 + 2.7380274146 614806809 %i,
      - 0.906849241 E -10 - 0.158519319 E -9 %i]
     ,

     [1.0 + 4.4 %i, - 5.2517630342 3 + 2.8854856389 27 %i,
      - 5.2517630343 090783839 + 2.8854856388 07923102 %i,
      - 0.790783839 E -10 - 0.119076898 E -9 %i]
     ,

     [1.0 + 4.5 %i, - 5.3976062389 84 + 3.0351969999 22 %i,
      - 5.3976062390 513914695 + 3.0351969998 31937613 %i,
      - 0.673914695 E -10 - 0.90062387 E -10 %i]
     ,

     [1.0 + 4.6 %i, - 5.5436964183 04 + 3.1871122793 89 %i,
      - 5.5436964183 61390699 + 3.1871122793 208820187 %i,
      - 0.57390699 E -10 - 0.681179813 E -10 %i]
     ,

     [1.0 + 4.7 %i, - 5.6900229483 73 + 3.3411843443 27 %i,
      - 5.6900229484 214997719 + 3.3411843442 759324334 %i,
      - 0.484997719 E -10 - 0.510675666 E -10 %i]
     ,

     [1.0 + 4.8 %i, - 5.8365758764 54 + 3.4973680186 15 %i,
      - 5.8365758764 943805837 + 3.4973680185 763247957 %i,
      - 0.403805838 E -10 - 0.386752043 E -10 %i]
     ,

     [1.0 + 4.9 %i, - 5.9833458655 32 + 3.6556199647 12 %i,
      - 5.9833458655 659367284 + 3.6556199646 827616217 %i,
      - 0.339367284 E -10 - 0.292383783 E -10 %i]
     ,

     [1.0 + 5.0 %i, - 6.1303241445 53 + 3.8158985746 15 %i,
      - 6.1303241445 811123102 + 3.8158985745 927031289 %i,
      - 0.2811231 E -10 - 0.222968711 E -10 %i]
     ,

     [1.0 + 5.1 %i, - 6.2775024635 84 + 3.9781638691 88 %i,
      - 6.2775024636 078422767 + 3.9781638691 706816787 %i,
      - 0.23842277 E -10 - 0.173183213 E -10 %i]
     ,

     [1.0 + 5.2 %i, - 6.4248730533 35 + 4.1423774050 86 %i,
      - 6.4248730533 548717638 + 4.1423774050 733123933 %i,
      - 0.19871764 E -10 - 0.12687607 E -10 %i]
     ,

     [1.0 + 5.3 %i, - 6.5724285885 29 + 4.3085021885 83 %i,
      - 6.5724285885 457509092 + 4.3085021885 732350035 %i,
      - 0.16750909 E -10 - 0.97649965 E -11 %i]
     ,

     [1.0 + 5.4 %i, - 6.7201621547 03 + 4.4765025956 68 %i,
      - 6.7201621547 164454344 + 4.4765025956 6044423 %i,
      - 0.13445434 E -10 - 0.75557699 E -11 %i]
     ,

     [1.0 + 5.5 %i, - 6.8680672180 48 + 4.6463442978 7 %i,
      - 6.8680672180 595740196 + 4.6463442978 647410058 %i,
      - 0.1157402 E -10 - 0.52589942 E -11 %i]
     ,

     [1.0 + 5.6 %i, - 7.0161375979 76 + 4.8179941933 05 %i,
      - 7.0161375979 858421857 + 4.8179941933 005550433 %i,
      - 0.98421857 E -11 - 0.44449567 E -11 %i]
     ,

     [1.0 + 5.7 %i, - 7.1643674421 06 + 4.9914203424 89 %i,
      - 7.1643674421 140655762 + 4.9914203424 861697905 %i,
      - 0.80655762 E -11 - 0.2830209 E -11 %i]
     ,

     [1.0 + 5.8 %i, - 7.3127512034 3 + 5.1665919085 37 %i,
      - 7.3127512034 36317679 + 5.1665919085 342976767 %i,
      - 0.6317679 E -11 - 0.2702323 E -11 %i]
     ,

     [1.0 + 5.9 %i, - 7.4612836194 29 + 5.3434791013 53 %i,
      - 7.4612836194 350723482 + 5.3434791013 5075755 %i,
      - 0.60723482 E -11 - 0.224245 E -11 %i]
     ,

     [1.0 + 6.0 %i, - 7.6099596929 51 + 5.5220531255 15 %i,
      - 7.6099596929 554672207 + 5.5220531255 133435246 %i,
      - 0.44672207 E -11 - 0.1656475 E -11 %i]
     ,

     [1.0 + 6.1 %i, - 7.7587746746 55 + 5.7022861315 35 %i,
      - 7.7587746746 585972836 + 5.7022861315 344022325 %i,
      - 0.3597284 E -11 - 0.5977675 E -12 %i]
     ,

     [1.0 + 6.2 %i, - 7.9077240468 98 + 5.8841511702 39 %i,
      - 7.9077240469 015667429 + 5.8841511702 386349799 %i,
      - 0.3566743 E -11 - 0.36502 E -12 %i]
     ,

     [1.0 + 6.3 %i, - 8.0568035089 04 + 6.0676221500 13 %i,
      - 8.0568035089 073088969 + 6.0676221500 126290404 %i,
      - 0.3308897 E -11 - 0.37096 E -12 %i]
     ,

     [1.0 + 6.4 %i, - 8.2060089631 + 6.2526737967 05 %i,
      - 8.2060089631 022876515 + 6.2526737967 049593955 %i,
      - 0.2287651 E -11 - 0.406045 E -13 %i]
     ,

     [1.0 + 6.5 %i, - 8.3553365025 11 + 6.4392816159 76 %i,
      - 8.3553365025 134245282 + 6.4392816159 757023231 %i,
      - 0.2424528 E -11 - 0.297677 E -12 %i]
     ,

     [1.0 + 6.6 %i, - 8.5047823991 25 + 6.6274218579 12 %i,
      - 8.5047823991 272090321 + 6.6274218579 121383093 %i,
      - 0.2209032 E -11 + 0.138309 E -12 %i]
     ,

     [1.0 + 6.7 %i, - 8.6543430931 23 + 6.8170714837 44 %i,
      - 8.6543430931 241668318 + 6.8170714837 435317714 %i,
      - 0.1166832 E -11 - 0.4682286 E -12 %i]
     ,

     [1.0 + 6.8 %i, - 8.8040151829 1 + 7.0082081345 02 %i,
      - 8.8040151829 108657274 + 7.0082081345 023668668 %i,
      - 0.865727 E -12 + 0.366867 E -12 %i]
     ,

     [1.0 + 6.9 %i, - 8.9537954158 79 + 7.2008101014 93 %i,
      - 8.9537954158 795929843 + 7.2008101014 924740199 %i,
      - 0.592984 E -12 - 0.5259801 E -12 %i]
     ,

     [1.0 + 7.0 %i, - 9.1036806798 32 + 7.3948562984 36 %i,
      - 9.1036806798 328755451 + 7.3948562984 362601022 %i,
      - 0.875545 E -12 + 0.260102 E -12 %i]
     ,

     [1.0 + 7.1 %i, - 9.2536679950 15 + 7.5903262351 84 %i,
      - 9.2536679950 162537946 + 7.5903262351 838962951 %i,
      - 0.1253795 E -11 - 0.103705 E -12 %i]
     ,

     [1.0 + 7.2 %i, - 9.4037545067 08 + 7.7871999928 77 %i,
      - 9.4037545067 082605399 + 7.7871999928 769445859 %i,
      - 0.26054 E -12 - 0.554141 E -13 %i]
     ,

     [1.0 + 7.3 %i, - 9.5539374783 21 + 7.9854582004 68 %i,
      - 9.5539374783 214863185 + 7.9854582004 676249208 %i,
      - 0.486319 E -12 - 0.375079 E -12 %i]
     ,

     [1.0 + 7.4 %i, - 9.7042142849 72 + 8.1850820125 03 %i,
      - 9.7042142849 730050014 + 8.1850820125 028358342 %i,
      - 0.1005001 E -11 - 0.164166 E -12 %i]
     ,

     [1.0 + 7.5 %i, - 9.8545824074 86 + 8.3860530880 89 %i,
      - 9.8545824074 863547157 + 8.3860530880 892263646 %i,
      - 0.354716 E -12 + 0.226365 E -12 %i]
     ,

     [1.0 + 7.6 %i, - 10.0050394267 9 + 8.5883535709 62 %i,
      - 10.0050394267 9077464 + 8.5883535709 621509583 %i,
      - 0.77464 E -12 + 0.150958 E -12 %i]
     ,

     [1.0 + 7.7 %i, - 10.1555830186 86 + 8.7919660705 87 %i,
      - 10.1555830186 86537113 + 8.7919660705 872881232 %i,
      - 0.537113 E -12 + 0.288123 E -12 %i]
     ,

     [1.0 + 7.8 %i, - 10.3062109489 48 + 8.9968736442 29 %i,
      - 10.3062109489 48029324 + 8.9968736442 291265808 %i,
      - 0.29324 E -13 + 0.126581 E -12 %i]
     ,

     [1.0 + 7.9 %i, - 10.4569210687 39 + 9.2030597799 25 %i,
      - 10.4569210687 38766792 + 9.2030597799 254718746 %i,
      0.233208 E -12 + 0.471875 E -12 %i]
     ,

     [1.0 + 8.0 %i, - 10.6077113103 15 + 9.4105083803 12 %i,
      - 10.6077113103 1479434 + 9.4105083803 116483136 %i,
      0.20566 E -12 - 0.351686 E -12 %i]
     ,

     [1.0 + 8.1 %i, - 10.7585796829 95 + 9.6192037472 42 %i,
      - 10.7585796829 94977847 + 9.6192037472 422072521 %i,
      0.22153 E -13 + 0.207252 E -12 %i]
     ,

     [1.0 + 8.2 %i, - 10.9095242693 78 + 9.8291305671 62 %i,
      - 10.9095242693 78536574 + 9.8291305671 617400305 %i,
      - 0.536574 E -12 - 0.25997 E -12 %i]
     ,

     [1.0 + 8.3 %i, - 11.0605432217 92 + 10.0402738971 8 %i,
      - 11.0605432217 91833327 + 10.0402738971 79865529 %i,
      0.166673 E -12 - 0.134471 E -12 %i]
     ,

     [1.0 + 8.4 %i, - 11.2116347589 48 + 10.2526191518 09 %i,
      - 11.2116347589 47947425 + 10.2526191518 08647801 %i,
      0.52575 E -13 - 0.352199 E -12 %i]
     ,

     [1.0 + 8.5 %i, - 11.3627971628 04 + 10.4661520903 24 %i,
      - 11.3627971628 03920333 + 10.4661520903 23625234 %i,
      0.796669 E -13 - 0.374766 E -12 %i]
     ,

     [1.0 + 8.6 %i, - 11.5140287756 02 + 10.6808588047 12 %i,
      - 11.5140287756 01801068 + 10.6808588047 12322866 %i,
      0.198932 E -12 + 0.322866 E -12 %i]
     ,

     [1.0 + 8.7 %i, - 11.6653279970 81 + 10.8967257081 77 %i,
      - 11.6653279970 80741204 + 10.8967257081 76595379 %i,
      0.258796 E -12 - 0.404621 E -12 %i]
     ,

     [1.0 + 8.8 %i, - 11.8166932818 48 + 11.1137395241 57 %i,
      - 11.8166932818 48409467 + 11.1137395241 57428959 %i,
      - 0.409467 E -12 + 0.428959 E -12 %i]
     ,

     [1.0 + 8.9 %i, - 11.9681231369 01 + 11.3318872758 53 %i,
      - 11.9681231369 00923725 + 11.3318872758 52933183 %i,
      0.762754 E -13 - 0.668174 E -13 %i]
     ,

     [1.0 + 9.0 %i, - 12.1196161192 81 + 11.5511562762 02 %i,
      - 12.1196161192 81343173 + 11.5511562762 02194801 %i,
      - 0.343173 E -12 + 0.194801 E -12 %i]
     ,

     [1.0 + 9.1 %i, - 12.2711708338 67 + 11.7715341183 09 %i,
      - 12.2711708338 67533716 + 11.7715341183 09457939 %i,
      - 0.533716 E -12 + 0.457939 E -12 %i]
     ,

     [1.0 + 9.2 %i, - 12.4227859312 81 + 11.9930086662 85 %i,
      - 12.4227859312 80922451 + 11.9930086662 84752568 %i,
      0.775495 E -13 - 0.247432 E -12 %i]
     ,

     [1.0 + 9.3 %i, - 12.5744601059 08 + 12.2155680464 79 %i,
      - 12.5744601059 08299231 + 12.2155680464 7862654 %i,
      - 0.299231 E -12 - 0.37346 E -12 %i]
     ,

     [1.0 + 9.4 %i, - 12.7261920940 29 + 12.4392006390 9 %i,
      - 12.7261920940 29410474 + 12.4392006390 90056598 %i,
      - 0.410474 E -12 + 0.56598 E -13 %i]
     ,

     [1.0 + 9.5 %i, - 12.8779806720 44 + 12.6638950701 28 %i,
      - 12.8779806720 43627774 + 12.6638950701 27929907 %i,
      0.372226 E -12 - 0.70093 E -13 %i]
     ,

     [1.0 + 9.6 %i, - 13.0298246547 89 + 12.8896402037 08 %i,
      - 13.0298246547 89466317 + 12.8896402037 07708444 %i,
      - 0.466316 E -12 - 0.291556 E -12 %i]
     ,

     [1.0 + 9.7 %i, - 13.1817228939 51 + 13.1164251346 66 %i,
      - 13.1817228939 51179682 + 13.1164251346 66021834 %i,
      - 0.179682 E -12 + 0.21834 E -13 %i]
     ,

     [1.0 + 9.8 %i, - 13.3336742765 47 + 13.3442391814 77 %i,
      - 13.3336742765 47072151 + 13.3442391814 7698698 %i,
      - 0.721508 E -13 - 0.1302 E -13 %i]
     ,

     [1.0 + 9.9 %i, - 13.4856777234 95 + 13.5730718794 55 %i,
      - 13.4856777234 94550479 + 13.5730718794 5503157 %i,
      0.449521 E -12 + 0.3157 E -13 %i]
     ,

     [1.0 + 10.0 %i, - 13.6377321882 47 + 13.8029129742 3 %i,
      - 13.6377321882 47287365 + 13.8029129742 29909153 %i,
      - 0.287365 E -12 - 0.908474 E -13 %i]
     ]
                                                Type: List List Complex Float
--R 
--R   Compiling function inner with type (NonNegativeInteger,
--R      PositiveInteger) -> Integer 
--R   Compiling function B with type PositiveInteger -> Fraction Integer 
--R   Compiling function Z with type (PositiveInteger,Complex Float) -> 
--R      Complex Float 
--R   Compiling function H with type Complex Float -> Complex Float 
--R
--R   (10)
--R   [[1.0,0.0,0.0005342523 0039183749 9,0.0005342523 0039183749 9],
--R
--R     [1.0 + 0.1 %i, - 0.0081977805 65 - 0.0573229404 17 %i,
--R      - 0.0079060360 5641775235 1 - 0.0577425561 880608609 %i,
--R      0.0002917445 0858224764 9 - 0.0004196157 710608609 %i]
--R     ,
--R
--R     [1.0 + 0.2 %i, - 0.0324762923 18 - 0.1123022226 44 %i,
--R      - 0.0326253424 137575225 - 0.1127252606 10617179 %i,
--R      - 0.0001490500 957575225 - 0.0004230379 66617179 %i]
--R     ,
--R
--R     [1.0 + 0.3 %i, - 0.0719462509 - 0.1628206721 68 %i,
--R      - 0.0722917796 3325300528 - 0.1629343118 0182595104 %i,
--R      - 0.0003455287 3325300528 - 0.0001136396 33825951 %i]
--R     ,
--R
--R     [1.0 + 0.4 %i, - 0.1252893748 21 - 0.2071558263 16 %i,
--R      - 0.1255237832 8903895364 - 0.2070111768 1461131296 %i,
--R      - 0.0002344084 6803895364 + 0.0001446495 0138868704 %i]
--R     ,
--R
--R     [1.0 + 0.5 %i, - 0.1909454991 87 - 0.2440582989 05 %i,
--R      - 0.1909844153 9406580427 - 0.2438650024 4353127544 %i,
--R      - 0.0000389162 0706580427 + 0.0001932964 6146872456 %i]
--R     ,
--R
--R     [1.0 + 0.6 %i, - 0.2672900682 14 - 0.2727438104 91 %i,
--R      - 0.2672177072 7708327583 - 0.2726297345 2049521095 %i,
--R      0.0000723609 3691672417 + 0.0001140759 70504789 %i]
--R     ,
--R
--R     [1.0 + 0.7 %i, - 0.3527686908 6 - 0.2928263511 87 %i,
--R      - 0.3526830217 4071123327 - 0.2928000766 8168133466 %i,
--R      0.0000856691 1928876673 + 0.0000262745 053186653 %i]
--R     ,
--R
--R     [1.0 + 0.8 %i, - 0.4459787835 49 - 0.3042256029 76 %i,
--R      - 0.4459243064 600936154 - 0.3042458540 6494479039 %i,
--R      0.0000544770 889063846 - 0.0000202510 889447904 %i]
--R     ,
--R
--R     [1.0 + 0.9 %i, - 0.5457051286 05 - 0.3070743756 42 %i,
--R      - 0.5456837564 2266021862 - 0.3071047743 7404541115 %i,
--R      0.0000213721 823397814 - 0.0000303987 320454111 %i]
--R     ,
--R
--R     [1.0 + %i, - 0.6509231993 02 - 0.3016403204 68 %i,
--R      - 0.6509218279 5803214573 - 0.3016638509 8907615826 %i,
--R      0.0000013713 439678543 - 0.0000235305 210761583 %i]
--R     ,
--R
--R     [1.0 + 1.1 %i, - 0.7607839588 41 - 0.2882666142 39 %i,
--R      - 0.7607904806 1959258337 - 0.2882800153 6783960204 %i,
--R      - 0.0000065217 7859258337 - 0.0000134011 28839602 %i]
--R     ,
--R
--R     [1.0 + 1.2 %i, - 0.8745904638 95 - 0.2673305805 81 %i,
--R      - 0.8745979912 3533931918 - 0.2673362568 721629649 %i,
--R      - 0.0000075273 4033931918 - 0.0000056762 911629649 %i]
--R     ,
--R
--R     [1.0 + 1.3 %i, - 0.9917727669 59 - 0.2392167844 65 %i,
--R      - 0.9917786169 8448669121 - 0.2392180306 8558905783 %i,
--R      - 0.0000058500 2548669121 - 0.0000012462 2058905783 %i]
--R     ,
--R
--R     [1.0 + 1.4 %i, - 1.1118645664 26 - 0.2043007241 49 %i,
--R      - 1.1118683074 739622893 - 0.2042999880 7236175351 %i,
--R      - 0.0000037410 479622893 + 0.7360766382 4649 E -6 %i]
--R     ,
--R
--R     [1.0 + 1.5 %i, - 1.2344830515 47 - 0.1629397694 8 %i,
--R      - 1.2344851106 088582896 - 0.1629384511 4283237552 %i,
--R      - 0.0000020590 618582896 + 0.0000013183 3716762448 %i]
--R     ,
--R
--R     [1.0 + 1.6 %i, - 1.3593122484 65 - 0.1154687935 89 %i,
--R      - 1.3593132065 575271954 - 0.1154675392 0060867755 %i,
--R      - 0.9580925271 9539 E -6 + 0.0000012543 8839132245 %i]
--R     ,
--R
--R     [1.0 + 1.7 %i, - 1.4860896127 57 - 0.0621986983 29 %i,
--R      - 1.4860899424 768375682 - 0.0621977263 0645742299 5 %i,
--R      - 0.3297198375 682 E -6 + 0.9720225425 77005 E -6 %i]
--R     ,
--R
--R     [1.0 + 1.8 %i, - 1.614595396 - 0.0034166314 77 %i,
--R      - 1.6145954117 853473727 - 0.0034159591 4562980466 %i,
--R      - 0.1578534737 27 E -7 + 0.6723313701 953421 E -6 %i]
--R     ,
--R
--R     [1.0 + 1.9 %i, - 1.7446442761 74 + 0.0606128742 95 %i,
--R      - 1.7446441619 196944916 + 0.0606133033 8564864100 7 %i,
--R      0.1142543055 08 E -6 + 0.4290906486 41007 E -6 %i]
--R     ,
--R
--R     [1.0 + 2.0 %i, - 1.8760787864 31 + 0.1296463163 1 %i,
--R      - 1.8760786381 585810542 + 0.1296465718 833341783 %i,
--R      0.1482724189 458 E -6 + 0.2555733341 783 E -6 %i]
--R     ,
--R
--R     [1.0 + 2.1 %i, - 2.0087641504 71 + 0.2034594738 33 %i,
--R      - 2.0087640119 218530981 + 0.2034596154 799745979 %i,
--R      0.1385491469 02 E -6 + 0.1416469745 979 E -6 %i]
--R     ,
--R
--R     [1.0 + 2.2 %i, - 2.1425842092 96 + 0.2818456584 26 %i,
--R      - 2.1425840960 876952162 + 0.2818457299 3685319226 %i,
--R      0.1132083047 84 E -6 + 0.7151085319 226 E -7 %i]
--R     ,
--R
--R     [1.0 + 2.3 %i, - 2.2774381922 04 + 0.3646140489 5 %i,
--R      - 2.2774381063 831111412 + 0.3646140797 7055414725 %i,
--R      0.8582088885 88 E -7 + 0.3082055414 725 E -7 %i]
--R     ,
--R
--R     [1.0 + 2.4 %i, - 2.4132381411 84 + 0.4515881524 41 %i,
--R      - 2.4132380792 215488516 + 0.4515881611 4945339852 %i,
--R      0.6196245114 84 E -7 + 0.8708453398 52 E -8 %i]
--R     ,
--R
--R     [1.0 + 2.5 %i, - 2.5499068424 95 + 0.5426044058 52 %i,
--R      - 2.5499067992 955284158 + 0.5426044035 6280478379 %i,
--R      0.4319947158 42 E -7 - 0.2289195216 2 E -8 %i]
--R     ,
--R
--R     [1.0 + 2.6 %i, - 2.6873761537 5 + 0.6375109190 46 %i,
--R      - 2.6873761244 380686304 + 0.6375109120 6490899231 %i,
--R      0.2931193136 96 E -7 - 0.6981091007 69 E -8 %i]
--R     ,
--R
--R     [1.0 + 2.7 %i, - 2.8255856411 91 + 0.7361663516 79 %i,
--R      - 2.8255856217 482878084 + 0.7361663433 7467081169 %i,
--R      0.1944271219 16 E -7 - 0.8304329188 32 E -8 %i]
--R     ,
--R
--R     [1.0 + 2.8 %i, - 2.9644814617 89 + 0.8384389130 96 %i,
--R      - 2.9644814491 554295115 + 0.8384389051 1754275168 %i,
--R      0.1263357048 8 E -7 - 0.7978457248 32 E -8 %i]
--R     ,
--R
--R     [1.0 + 2.9 %i, - 3.1040154399 01 + 0.9442054730 39 %i,
--R      - 3.1040154318 565321996 + 0.9442054660 7862553084 %i,
--R      0.8044467800 4 E -8 - 0.6960374469 16 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.0 %i, - 3.2441442995 9 + 1.0533507710 69 %i,
--R      - 3.2441442945 809249541 + 1.0533507653 179013667 %i,
--R      0.5009075046 E -8 - 0.5751098633 3 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.1 %i, - 3.3848290223 77 + 1.1657667132 86 %i,
--R      - 3.3848290193 409889189 + 1.1657667086 926332139 %i,
--R      0.3036011081 1 E -8 - 0.4593366786 1 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.2 %i, - 3.5260343067 09 + 1.2813517459 32 %i,
--R      - 3.5260343049 347826646 + 1.2813517423 440037128 %i,
--R      0.1774217335 E -8 - 0.3587996287 2 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.3 %i, - 3.6677281104 88 + 1.4000102965 76 %i,
--R      - 3.6677281095 052040502 + 1.4000102938 163542918 %i,
--R      0.9827959498 E -9 - 0.2759645708 2 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.4 %i, - 3.8098812618 23 + 1.5216522746 73 %i,
--R      - 3.8098812613 276184867 + 1.5216522725 71566048 %i,
--R      0.4953815133 E -9 - 0.2101433952 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.5 %i, - 3.9524671261 89 + 1.6461926242 69 %i,
--R      - 3.9524671259 853198893 + 1.6461926226 807455415 %i,
--R      0.203680111 E -9 - 0.1588254458 5 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.6 %i, - 4.0954613204 51 + 1.7735509225 91 %i,
--R      - 4.0954613204 155384205 + 1.7735509213 962023574 %i,
--R      0.354615795 E -10 - 0.1194797642 6 E -8 %i]
--R     ,
--R
--R     [1.0 + 3.7 %i, - 4.2388414660 71 + 1.9036510190 19 %i,
--R      - 4.2388414661 27781932 + 1.9036510181 226951001 %i,
--R      - 0.56781932 E -10 - 0.8963048999 E -9 %i]
--R     ,
--R
--R     [1.0 + 3.8 %i, - 4.3825869752 28 + 2.0364207096 93 %i,
--R      - 4.3825869753 299956382 + 2.0364207090 215572509 %i,
--R      - 0.101995638 E -9 - 0.6714427491 E -9 %i]
--R     ,
--R
--R     [1.0 + 3.9 %i, - 4.5266788647 16 + 2.1717914436 05 %i,
--R      - 4.5266788648 352793739 + 2.1717914431 026276223 %i,
--R      - 0.119279374 E -9 - 0.5023723777 E -9 %i]
--R     ,
--R
--R     [1.0 + 4.0 %i, - 4.6710995934 09 + 2.3096980565 73 %i,
--R      - 4.6710995935 296268252 + 2.3096980561 967129493 %i,
--R      - 0.120626825 E -9 - 0.3762870507 E -9 %i]
--R     ,
--R
--R     [1.0 + 4.1 %i, - 4.8158329197 96 + 2.4500785299 47 %i,
--R      - 4.8158329199 100070487 + 2.4500785296 656839327 %i,
--R      - 0.114007049 E -9 - 0.2813160673 E -9 %i]
--R     ,
--R
--R     [1.0 + 4.2 %i, - 4.9608637766 87 + 2.5928737713 19 %i,
--R      - 4.9608637767 906961011 + 2.5928737711 078289946 %i,
--R      - 0.103696101 E -9 - 0.211171005 E -9 %i]
--R     ,
--R
--R     [1.0 + 4.3 %i, - 5.1061781606 63 + 2.7380274148 2 %i,
--R      - 5.1061781607 536849241 + 2.7380274146 614806809 %i,
--R      - 0.906849241 E -10 - 0.158519319 E -9 %i]
--R     ,
--R
--R     [1.0 + 4.4 %i, - 5.2517630342 3 + 2.8854856389 27 %i,
--R      - 5.2517630343 090783839 + 2.8854856388 07923102 %i,
--R      - 0.790783839 E -10 - 0.119076898 E -9 %i]
--R     ,
--R
--R     [1.0 + 4.5 %i, - 5.3976062389 84 + 3.0351969999 22 %i,
--R      - 5.3976062390 513914695 + 3.0351969998 31937613 %i,
--R      - 0.673914695 E -10 - 0.90062387 E -10 %i]
--R     ,
--R
--R     [1.0 + 4.6 %i, - 5.5436964183 04 + 3.1871122793 89 %i,
--R      - 5.5436964183 61390699 + 3.1871122793 208820187 %i,
--R      - 0.57390699 E -10 - 0.681179813 E -10 %i]
--R     ,
--R
--R     [1.0 + 4.7 %i, - 5.6900229483 73 + 3.3411843443 27 %i,
--R      - 5.6900229484 214997719 + 3.3411843442 759324334 %i,
--R      - 0.484997719 E -10 - 0.510675666 E -10 %i]
--R     ,
--R
--R     [1.0 + 4.8 %i, - 5.8365758764 54 + 3.4973680186 15 %i,
--R      - 5.8365758764 943805837 + 3.4973680185 763247957 %i,
--R      - 0.403805838 E -10 - 0.386752043 E -10 %i]
--R     ,
--R
--R     [1.0 + 4.9 %i, - 5.9833458655 32 + 3.6556199647 12 %i,
--R      - 5.9833458655 659367284 + 3.6556199646 827616217 %i,
--R      - 0.339367284 E -10 - 0.292383783 E -10 %i]
--R     ,
--R
--R     [1.0 + 5.0 %i, - 6.1303241445 53 + 3.8158985746 15 %i,
--R      - 6.1303241445 811123102 + 3.8158985745 927031289 %i,
--R      - 0.2811231 E -10 - 0.222968711 E -10 %i]
--R     ,
--R
--R     [1.0 + 5.1 %i, - 6.2775024635 84 + 3.9781638691 88 %i,
--R      - 6.2775024636 078422767 + 3.9781638691 706816787 %i,
--R      - 0.23842277 E -10 - 0.173183213 E -10 %i]
--R     ,
--R
--R     [1.0 + 5.2 %i, - 6.4248730533 35 + 4.1423774050 86 %i,
--R      - 6.4248730533 548717638 + 4.1423774050 733123933 %i,
--R      - 0.19871764 E -10 - 0.12687607 E -10 %i]
--R     ,
--R
--R     [1.0 + 5.3 %i, - 6.5724285885 29 + 4.3085021885 83 %i,
--R      - 6.5724285885 457509092 + 4.3085021885 732350035 %i,
--R      - 0.16750909 E -10 - 0.97649965 E -11 %i]
--R     ,
--R
--R     [1.0 + 5.4 %i, - 6.7201621547 03 + 4.4765025956 68 %i,
--R      - 6.7201621547 164454344 + 4.4765025956 6044423 %i,
--R      - 0.13445434 E -10 - 0.75557699 E -11 %i]
--R     ,
--R
--R     [1.0 + 5.5 %i, - 6.8680672180 48 + 4.6463442978 7 %i,
--R      - 6.8680672180 595740196 + 4.6463442978 647410058 %i,
--R      - 0.1157402 E -10 - 0.52589942 E -11 %i]
--R     ,
--R
--R     [1.0 + 5.6 %i, - 7.0161375979 76 + 4.8179941933 05 %i,
--R      - 7.0161375979 858421857 + 4.8179941933 005550433 %i,
--R      - 0.98421857 E -11 - 0.44449567 E -11 %i]
--R     ,
--R
--R     [1.0 + 5.7 %i, - 7.1643674421 06 + 4.9914203424 89 %i,
--R      - 7.1643674421 140655762 + 4.9914203424 861697905 %i,
--R      - 0.80655762 E -11 - 0.2830209 E -11 %i]
--R     ,
--R
--R     [1.0 + 5.8 %i, - 7.3127512034 3 + 5.1665919085 37 %i,
--R      - 7.3127512034 36317679 + 5.1665919085 342976767 %i,
--R      - 0.6317679 E -11 - 0.2702323 E -11 %i]
--R     ,
--R
--R     [1.0 + 5.9 %i, - 7.4612836194 29 + 5.3434791013 53 %i,
--R      - 7.4612836194 350723482 + 5.3434791013 5075755 %i,
--R      - 0.60723482 E -11 - 0.224245 E -11 %i]
--R     ,
--R
--R     [1.0 + 6.0 %i, - 7.6099596929 51 + 5.5220531255 15 %i,
--R      - 7.6099596929 554672207 + 5.5220531255 133435246 %i,
--R      - 0.44672207 E -11 - 0.1656475 E -11 %i]
--R     ,
--R
--R     [1.0 + 6.1 %i, - 7.7587746746 55 + 5.7022861315 35 %i,
--R      - 7.7587746746 585972836 + 5.7022861315 344022325 %i,
--R      - 0.3597284 E -11 - 0.5977675 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.2 %i, - 7.9077240468 98 + 5.8841511702 39 %i,
--R      - 7.9077240469 015667429 + 5.8841511702 386349799 %i,
--R      - 0.3566743 E -11 - 0.36502 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.3 %i, - 8.0568035089 04 + 6.0676221500 13 %i,
--R      - 8.0568035089 073088969 + 6.0676221500 126290404 %i,
--R      - 0.3308897 E -11 - 0.37096 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.4 %i, - 8.2060089631 + 6.2526737967 05 %i,
--R      - 8.2060089631 022876515 + 6.2526737967 049593955 %i,
--R      - 0.2287651 E -11 - 0.406045 E -13 %i]
--R     ,
--R
--R     [1.0 + 6.5 %i, - 8.3553365025 11 + 6.4392816159 76 %i,
--R      - 8.3553365025 134245282 + 6.4392816159 757023231 %i,
--R      - 0.2424528 E -11 - 0.297677 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.6 %i, - 8.5047823991 25 + 6.6274218579 12 %i,
--R      - 8.5047823991 272090321 + 6.6274218579 121383093 %i,
--R      - 0.2209032 E -11 + 0.138309 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.7 %i, - 8.6543430931 23 + 6.8170714837 44 %i,
--R      - 8.6543430931 241668318 + 6.8170714837 435317714 %i,
--R      - 0.1166832 E -11 - 0.4682286 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.8 %i, - 8.8040151829 1 + 7.0082081345 02 %i,
--R      - 8.8040151829 108657274 + 7.0082081345 023668668 %i,
--R      - 0.865727 E -12 + 0.366867 E -12 %i]
--R     ,
--R
--R     [1.0 + 6.9 %i, - 8.9537954158 79 + 7.2008101014 93 %i,
--R      - 8.9537954158 795929843 + 7.2008101014 924740199 %i,
--R      - 0.592984 E -12 - 0.5259801 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.0 %i, - 9.1036806798 32 + 7.3948562984 36 %i,
--R      - 9.1036806798 328755451 + 7.3948562984 362601022 %i,
--R      - 0.875545 E -12 + 0.260102 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.1 %i, - 9.2536679950 15 + 7.5903262351 84 %i,
--R      - 9.2536679950 162537946 + 7.5903262351 838962951 %i,
--R      - 0.1253795 E -11 - 0.103705 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.2 %i, - 9.4037545067 08 + 7.7871999928 77 %i,
--R      - 9.4037545067 082605399 + 7.7871999928 769445859 %i,
--R      - 0.26054 E -12 - 0.554141 E -13 %i]
--R     ,
--R
--R     [1.0 + 7.3 %i, - 9.5539374783 21 + 7.9854582004 68 %i,
--R      - 9.5539374783 214863185 + 7.9854582004 676249208 %i,
--R      - 0.486319 E -12 - 0.375079 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.4 %i, - 9.7042142849 72 + 8.1850820125 03 %i,
--R      - 9.7042142849 730050014 + 8.1850820125 028358342 %i,
--R      - 0.1005001 E -11 - 0.164166 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.5 %i, - 9.8545824074 86 + 8.3860530880 89 %i,
--R      - 9.8545824074 863547157 + 8.3860530880 892263646 %i,
--R      - 0.354716 E -12 + 0.226365 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.6 %i, - 10.0050394267 9 + 8.5883535709 62 %i,
--R      - 10.0050394267 9077464 + 8.5883535709 621509583 %i,
--R      - 0.77464 E -12 + 0.150958 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.7 %i, - 10.1555830186 86 + 8.7919660705 87 %i,
--R      - 10.1555830186 86537113 + 8.7919660705 872881232 %i,
--R      - 0.537113 E -12 + 0.288123 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.8 %i, - 10.3062109489 48 + 8.9968736442 29 %i,
--R      - 10.3062109489 48029324 + 8.9968736442 291265808 %i,
--R      - 0.29324 E -13 + 0.126581 E -12 %i]
--R     ,
--R
--R     [1.0 + 7.9 %i, - 10.4569210687 39 + 9.2030597799 25 %i,
--R      - 10.4569210687 38766792 + 9.2030597799 254718746 %i,
--R      0.233208 E -12 + 0.471875 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.0 %i, - 10.6077113103 15 + 9.4105083803 12 %i,
--R      - 10.6077113103 1479434 + 9.4105083803 116483136 %i,
--R      0.20566 E -12 - 0.351686 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.1 %i, - 10.7585796829 95 + 9.6192037472 42 %i,
--R      - 10.7585796829 94977847 + 9.6192037472 422072521 %i,
--R      0.22153 E -13 + 0.207252 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.2 %i, - 10.9095242693 78 + 9.8291305671 62 %i,
--R      - 10.9095242693 78536574 + 9.8291305671 617400305 %i,
--R      - 0.536574 E -12 - 0.25997 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.3 %i, - 11.0605432217 92 + 10.0402738971 8 %i,
--R      - 11.0605432217 91833327 + 10.0402738971 79865529 %i,
--R      0.166673 E -12 - 0.134471 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.4 %i, - 11.2116347589 48 + 10.2526191518 09 %i,
--R      - 11.2116347589 47947425 + 10.2526191518 08647801 %i,
--R      0.52575 E -13 - 0.352199 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.5 %i, - 11.3627971628 04 + 10.4661520903 24 %i,
--R      - 11.3627971628 03920333 + 10.4661520903 23625234 %i,
--R      0.796669 E -13 - 0.374766 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.6 %i, - 11.5140287756 02 + 10.6808588047 12 %i,
--R      - 11.5140287756 01801068 + 10.6808588047 12322866 %i,
--R      0.198932 E -12 + 0.322866 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.7 %i, - 11.6653279970 81 + 10.8967257081 77 %i,
--R      - 11.6653279970 80741204 + 10.8967257081 76595379 %i,
--R      0.258796 E -12 - 0.404621 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.8 %i, - 11.8166932818 48 + 11.1137395241 57 %i,
--R      - 11.8166932818 48409467 + 11.1137395241 57428959 %i,
--R      - 0.409467 E -12 + 0.428959 E -12 %i]
--R     ,
--R
--R     [1.0 + 8.9 %i, - 11.9681231369 01 + 11.3318872758 53 %i,
--R      - 11.9681231369 00923725 + 11.3318872758 52933183 %i,
--R      0.762754 E -13 - 0.668174 E -13 %i]
--R     ,
--R
--R     [1.0 + 9.0 %i, - 12.1196161192 81 + 11.5511562762 02 %i,
--R      - 12.1196161192 81343173 + 11.5511562762 02194801 %i,
--R      - 0.343173 E -12 + 0.194801 E -12 %i]
--R     ,
--R
--R     [1.0 + 9.1 %i, - 12.2711708338 67 + 11.7715341183 09 %i,
--R      - 12.2711708338 67533716 + 11.7715341183 09457939 %i,
--R      - 0.533716 E -12 + 0.457939 E -12 %i]
--R     ,
--R
--R     [1.0 + 9.2 %i, - 12.4227859312 81 + 11.9930086662 85 %i,
--R      - 12.4227859312 80922451 + 11.9930086662 84752568 %i,
--R      0.775495 E -13 - 0.247432 E -12 %i]
--R     ,
--R
--R     [1.0 + 9.3 %i, - 12.5744601059 08 + 12.2155680464 79 %i,
--R      - 12.5744601059 08299231 + 12.2155680464 7862654 %i,
--R      - 0.299231 E -12 - 0.37346 E -12 %i]
--R     ,
--R
--R     [1.0 + 9.4 %i, - 12.7261920940 29 + 12.4392006390 9 %i,
--R      - 12.7261920940 29410474 + 12.4392006390 90056598 %i,
--R      - 0.410474 E -12 + 0.56598 E -13 %i]
--R     ,
--R
--R     [1.0 + 9.5 %i, - 12.8779806720 44 + 12.6638950701 28 %i,
--R      - 12.8779806720 43627774 + 12.6638950701 27929907 %i,
--R      0.372226 E -12 - 0.70093 E -13 %i]
--R     ,
--R
--R     [1.0 + 9.6 %i, - 13.0298246547 89 + 12.8896402037 08 %i,
--R      - 13.0298246547 89466317 + 12.8896402037 07708444 %i,
--R      - 0.466316 E -12 - 0.291556 E -12 %i]
--R     ,
--R
--R     [1.0 + 9.7 %i, - 13.1817228939 51 + 13.1164251346 66 %i,
--R      - 13.1817228939 51179682 + 13.1164251346 66021834 %i,
--R      - 0.179682 E -12 + 0.21834 E -13 %i]
--R     ,
--R
--R     [1.0 + 9.8 %i, - 13.3336742765 47 + 13.3442391814 77 %i,
--R      - 13.3336742765 47072151 + 13.3442391814 7698698 %i,
--R      - 0.721508 E -13 - 0.1302 E -13 %i]
--R     ,
--R
--R     [1.0 + 9.9 %i, - 13.4856777234 95 + 13.5730718794 55 %i,
--R      - 13.4856777234 94550479 + 13.5730718794 5503157 %i,
--R      0.449521 E -12 + 0.3157 E -13 %i]
--R     ,
--R
--R     [1.0 + 10.0 %i, - 13.6377321882 47 + 13.8029129742 3 %i,
--R      - 13.6377321882 47287365 + 13.8029129742 29909153 %i,
--R      - 0.287365 E -12 - 0.908474 E -13 %i]
--R     ]
--R                                                Type: List List Complex Float
--E 10
--S 11 of 12
lng2(xx:COMPLEX(DFLOAT)):COMPLEX(DFLOAT)==
  y:COMPLEX(DFLOAT):=xx;
  x:COMPLEX(DFLOAT):=xx;
  t1:COMPLEX(DFLOAT):=x+5.5-(x+0.5)*log(x+5.5)
  ser:COMPLEX(DFLOAT):=1.000000000190015
  y:=y+1;
  ser:=ser+(76.18009172947146/y)
  y:=y+1;
  ser:=ser+(-86.50532032941677/y)
  y:=y+1;
  ser:=ser+(24.01409824083091/y)
  y:=y+1;
  ser:=ser+(-1.231739572450155/y)
  y:=y+1;
  ser:=ser+(0.1208650973866179E-2/y)
  y:=y+1;
  ser:=ser+(-0.5395239384953E-5/y)
  result:COMPLEX(DFLOAT):=log(2.5066282746310005*ser/x)-t1
  result
 
   Function declaration lng2 : Complex DoubleFloat -> Complex 
      DoubleFloat has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration lng2 : Complex DoubleFloat -> Complex 
--R      DoubleFloat has been added to workspace.
--R                                                                   Type: Void
--E 11

--S 12 of 12
[[1. + 0.0 * %i,0.,lng2(1. + 0.0 * %i),lng2(1. + 0.0 * %i)-0.0],_
[1. + 0.1 * %i, -0.008197780565 - 0.057322940417 * %i,_
lng2(1. + 0.1 * %i),log(Gamma(1. + 0.1 * %i)),_
lng2(1. + 0.1 * %i)-log(Gamma(1. + 0.1 * %i)),_
lng2(1. + 0.1 * %i),logGamma(1. + 0.1 * %i),_
lng2(1. + 0.1 * %i)-logGamma(1. + 0.1 * %i),_
lng2(1. + 0.1 * %i)-( -0.008197780565 - 0.057322940417 * %i)],_
[1. + 0.2 * %i, -0.032476292318 - 0.112302222644 * %i,_
lng2(1. + 0.2 * %i),log(Gamma(1. + 0.2 * %i)),_
lng2(1. + 0.2 * %i)-log(Gamma(1. + 0.2 * %i)),_
lng2(1. + 0.2 * %i),logGamma(1. + 0.2 * %i),_
lng2(1. + 0.2 * %i)-logGamma(1. + 0.2 * %i),_
lng2(1. + 0.2 * %i)-( -0.032476292318 - 0.112302222644 * %i)],_
[1. + 0.3 * %i, -0.071946250900 - 0.162820672168 * %i,_
lng2(1. + 0.3 * %i),log(Gamma(1. + 0.3 * %i)),_
lng2(1. + 0.3 * %i)-log(Gamma(1. + 0.3 * %i)),_
lng2(1. + 0.3 * %i),logGamma(1. + 0.3 * %i),_
lng2(1. + 0.3 * %i)-logGamma(1. + 0.3 * %i),_
lng2(1. + 0.3 * %i)-( -0.071946250900 - 0.162820672168 * %i)],_
[1. + 0.4 * %i, -0.125289374821 - 0.207155826316 * %i,_
lng2(1. + 0.4 * %i),log(Gamma(1. + 0.4 * %i)),_
lng2(1. + 0.4 * %i)-log(Gamma(1. + 0.4 * %i)),_
lng2(1. + 0.4 * %i),logGamma(1. + 0.4 * %i),_
lng2(1. + 0.4 * %i)-logGamma(1. + 0.4 * %i),_
lng2(1. + 0.4 * %i)-( -0.125289374821 - 0.207155826316 * %i)],_
[1. + 0.5 * %i,- 0.190945499187 - 0.244058298905 * %i,_
lng2(1. + 0.5 * %i),log(Gamma(1. + 0.5 * %i)),_
lng2(1. + 0.5 * %i)-log(Gamma(1. + 0.5 * %i)),_
lng2(1. + 0.5 * %i),logGamma(1. + 0.5 * %i),_
lng2(1. + 0.5 * %i)-logGamma(1. + 0.5 * %i),_
lng2(1. + 0.5 * %i)-(- 0.190945499187 - 0.244058298905 * %i)],_
[1. + 0.6 * %i,- 0.267290068214 - 0.272743810491 * %i,_
lng2(1. + 0.6 * %i),log(Gamma(1. + 0.6 * %i)),_
lng2(1. + 0.6 * %i)-log(Gamma(1. + 0.6 * %i)),_
lng2(1. + 0.6 * %i),logGamma(1. + 0.6 * %i),_
lng2(1. + 0.6 * %i)-logGamma(1. + 0.6 * %i),_
lng2(1. + 0.6 * %i)-(- 0.267290068214 - 0.272743810491 * %i)],_
[1. + 0.7 * %i,- 0.352768690860 - 0.292826351187 * %i,_
lng2(1. + 0.7 * %i),log(Gamma(1. + 0.7 * %i)),_
lng2(1. + 0.7 * %i)-log(Gamma(1. + 0.7 * %i)),_
lng2(1. + 0.7 * %i),logGamma(1. + 0.7 * %i),_
lng2(1. + 0.7 * %i)-logGamma(1. + 0.7 * %i),_
lng2(1. + 0.7 * %i)-(- 0.352768690860 - 0.292826351187 * %i)],_
[1. + 0.8 * %i,- 0.445978783549 - 0.304225602976 * %i,_
lng2(1. + 0.8 * %i),log(Gamma(1. + 0.8 * %i)),_
lng2(1. + 0.8 * %i)-log(Gamma(1. + 0.8 * %i)),_
lng2(1. + 0.8 * %i),logGamma(1. + 0.8 * %i),_
lng2(1. + 0.8 * %i)-logGamma(1. + 0.8 * %i),_
lng2(1. + 0.8 * %i)-(- 0.445978783549 - 0.304225602976 * %i)],_
[1. + 0.9 * %i,- 0.545705128605 - 0.307074375642 * %i,_
lng2(1. + 0.9 * %i),log(Gamma(1. + 0.9 * %i)),_
lng2(1. + 0.9 * %i)-log(Gamma(1. + 0.9 * %i)),_
lng2(1. + 0.9 * %i),logGamma(1. + 0.9 * %i),_
lng2(1. + 0.9 * %i)-logGamma(1. + 0.9 * %i),_
lng2(1. + 0.9 * %i)-(- 0.545705128605 - 0.307074375642 * %i)],_
[1. + 1.0 * %i,- 0.650923199302 - 0.301640320468 * %i,_
lng2(1. + 1.0 * %i),log(Gamma(1. + 1.0 * %i)),_
lng2(1. + 1.0 * %i)-log(Gamma(1. + 1.0 * %i)),_
lng2(1. + 1.0 * %i),logGamma(1. + 1.0 * %i),_
lng2(1. + 1.0 * %i)-logGamma(1. + 1.0 * %i),_
lng2(1. + 1.0 * %i)-(- 0.650923199302 - 0.301640320468 * %i)],_
[1. + 1.1 * %i,- 0.760783958841 - 0.288266614239 * %i,_
lng2(1. + 1.1 * %i),log(Gamma(1. + 1.1 * %i)),_
lng2(1. + 1.1 * %i)-log(Gamma(1. + 1.1 * %i)),_
lng2(1. + 1.1 * %i),logGamma(1. + 1.1 * %i),_
lng2(1. + 1.1 * %i)-logGamma(1. + 1.1 * %i),_
lng2(1. + 1.1 * %i)-(- 0.760783958841 - 0.288266614239 * %i)],_
[1. + 1.2 * %i,- 0.874590463895 - 0.267330580581 * %i,_
lng2(1. + 1.2 * %i),log(Gamma(1. + 1.2 * %i)),_
lng2(1. + 1.2 * %i)-log(Gamma(1. + 1.2 * %i)),_
lng2(1. + 1.2 * %i),logGamma(1. + 1.2 * %i),_
lng2(1. + 1.2 * %i)-logGamma(1. + 1.2 * %i),_
lng2(1. + 1.2 * %i)-(- 0.874590463895 - 0.267330580581 * %i)],_
[1. + 1.3 * %i,- 0.991772766959 - 0.239216784465 * %i,_
lng2(1. + 1.3 * %i),log(Gamma(1. + 1.3 * %i)),_
lng2(1. + 1.3 * %i)-log(Gamma(1. + 1.3 * %i)),_
lng2(1. + 1.3 * %i),logGamma(1. + 1.3 * %i),_
lng2(1. + 1.3 * %i)-logGamma(1. + 1.3 * %i),_
lng2(1. + 1.3 * %i)-(- 0.991772766959 - 0.239216784465 * %i)],_
[1. + 1.4 * %i,- 1.111864566426 - 0.204300724149 * %i,_
lng2(1. + 1.4 * %i),log(Gamma(1. + 1.4 * %i)),_
lng2(1. + 1.4 * %i)-log(Gamma(1. + 1.4 * %i)),_
lng2(1. + 1.4 * %i),logGamma(1. + 1.4 * %i),_
lng2(1. + 1.4 * %i)-logGamma(1. + 1.4 * %i),_
lng2(1. + 1.4 * %i)-(- 1.111864566426 - 0.204300724149 * %i)],_
[1. + 1.5 * %i,- 1.234483051547 - 0.162939769480 * %i,_
lng2(1. + 1.5 * %i),log(Gamma(1. + 1.5 * %i)),_
lng2(1. + 1.5 * %i)-log(Gamma(1. + 1.5 * %i)),_
lng2(1. + 1.5 * %i),logGamma(1. + 1.5 * %i),_
lng2(1. + 1.5 * %i)-logGamma(1. + 1.5 * %i),_
lng2(1. + 1.5 * %i)-(- 1.234483051547 - 0.162939769480 * %i)],_
[1. + 1.6 * %i,- 1.359312248465 - 0.115468793589 * %i,_
lng2(1. + 1.6 * %i),log(Gamma(1. + 1.6 * %i)),_
lng2(1. + 1.6 * %i)-log(Gamma(1. + 1.6 * %i)),_
lng2(1. + 1.6 * %i),logGamma(1. + 1.6 * %i),_
lng2(1. + 1.6 * %i)-logGamma(1. + 1.6 * %i),_
lng2(1. + 1.6 * %i)-(- 1.359312248465 - 0.115468793589 * %i)],_
[1. + 1.7 * %i,- 1.486089612757 - 0.062198698329 * %i,_
lng2(1. + 1.7 * %i),log(Gamma(1. + 1.7 * %i)),_
lng2(1. + 1.7 * %i)-log(Gamma(1. + 1.7 * %i)),_
lng2(1. + 1.7 * %i),logGamma(1. + 1.7 * %i),_
lng2(1. + 1.7 * %i)-logGamma(1. + 1.7 * %i),_
lng2(1. + 1.7 * %i)-(- 1.486089612757 - 0.062198698329 * %i)],_
[1. + 1.8 * %i,- 1.614595396000 - 0.003416631477 * %i,_
lng2(1. + 1.8 * %i),log(Gamma(1. + 1.8 * %i)),_
lng2(1. + 1.8 * %i)-log(Gamma(1. + 1.8 * %i)),_
lng2(1. + 1.8 * %i),logGamma(1. + 1.8 * %i),_
lng2(1. + 1.8 * %i)-logGamma(1. + 1.8 * %i),_
lng2(1. + 1.8 * %i)-(- 1.614595396000 - 0.003416631477 * %i)],_
[1. + 1.9 * %i,- 1.744644276174 + 0.060612874295 * %i,_
lng2(1. + 1.9 * %i),log(Gamma(1. + 1.9 * %i)),_
lng2(1. + 1.9 * %i)-log(Gamma(1. + 1.9 * %i)),_
lng2(1. + 1.9 * %i),logGamma(1. + 1.9 * %i),_
lng2(1. + 1.9 * %i)-logGamma(1. + 1.9 * %i),_
lng2(1. + 1.9 * %i)-(- 1.744644276174 + 0.060612874295 * %i)],_
[1. + 2.0 * %i,- 1.876078786431 + 0.129646316310 * %i,_
lng2(1. + 2.0 * %i),log(Gamma(1. + 2.0 * %i)),_
lng2(1. + 2.0 * %i)-log(Gamma(1. + 2.0 * %i)),_
lng2(1. + 2.0 * %i),logGamma(1. + 2.0 * %i),_
lng2(1. + 2.0 * %i)-logGamma(1. + 2.0 * %i),_
lng2(1. + 2.0 * %i)-(- 1.876078786431 + 0.129646316310 * %i)],_
[1. + 2.1 * %i,- 2.008764150471 + 0.203459473833 * %i,_
lng2(1. + 2.1 * %i),log(Gamma(1. + 2.1 * %i)),_
lng2(1. + 2.1 * %i)-log(Gamma(1. + 2.1 * %i)),_
lng2(1. + 2.1 * %i),logGamma(1. + 2.1 * %i),_
lng2(1. + 2.1 * %i)-logGamma(1. + 2.1 * %i),_
lng2(1. + 2.1 * %i)-(- 2.008764150471 + 0.203459473833 * %i)],_
[1. + 2.2 * %i,- 2.142584209296 + 0.281845658426 * %i,_
lng2(1. + 2.2 * %i),log(Gamma(1. + 2.2 * %i)),_
lng2(1. + 2.2 * %i)-log(Gamma(1. + 2.2 * %i)),_
lng2(1. + 2.2 * %i),logGamma(1. + 2.2 * %i),_
lng2(1. + 2.2 * %i)-logGamma(1. + 2.2 * %i),_
lng2(1. + 2.2 * %i)-(- 2.142584209296 + 0.281845658426 * %i)],_
[1. + 2.3 * %i,- 2.277438192204 + 0.364614048950 * %i,_
lng2(1. + 2.3 * %i),log(Gamma(1. + 2.3 * %i)),_
lng2(1. + 2.3 * %i)-log(Gamma(1. + 2.3 * %i)),_
lng2(1. + 2.3 * %i),logGamma(1. + 2.3 * %i),_
lng2(1. + 2.3 * %i)-logGamma(1. + 2.3 * %i),_
lng2(1. + 2.3 * %i)-(- 2.277438192204 + 0.364614048950 * %i)],_
[1. + 2.4 * %i,- 2.413238141184 + 0.451588152441 * %i,_
lng2(1. + 2.4 * %i),log(Gamma(1. + 2.4 * %i)),_
lng2(1. + 2.4 * %i)-log(Gamma(1. + 2.4 * %i)),_
lng2(1. + 2.4 * %i),logGamma(1. + 2.4 * %i),_
lng2(1. + 2.4 * %i)-logGamma(1. + 2.4 * %i),_
lng2(1. + 2.4 * %i)-(- 2.413238141184 + 0.451588152441 * %i)],_
[1. + 2.5 * %i,- 2.549906842495 + 0.542604405852 * %i,_
lng2(1. + 2.5 * %i),log(Gamma(1. + 2.5 * %i)),_
lng2(1. + 2.5 * %i)-log(Gamma(1. + 2.5 * %i)),_
lng2(1. + 2.5 * %i),logGamma(1. + 2.5 * %i),_
lng2(1. + 2.5 * %i)-logGamma(1. + 2.5 * %i),_
lng2(1. + 2.5 * %i)-(- 2.549906842495 + 0.542604405852 * %i)],_
[1. + 2.6 * %i,- 2.687376153750 + 0.637510919046 * %i,_
lng2(1. + 2.6 * %i),log(Gamma(1. + 2.6 * %i)),_
lng2(1. + 2.6 * %i)-log(Gamma(1. + 2.6 * %i)),_
lng2(1. + 2.6 * %i),logGamma(1. + 2.6 * %i),_
lng2(1. + 2.6 * %i)-logGamma(1. + 2.6 * %i),_
lng2(1. + 2.6 * %i)-(- 2.687376153750 + 0.637510919046 * %i)],_
[1. + 2.7 * %i,- 2.825585641191 + 0.736166351679 * %i,_
lng2(1. + 2.7 * %i),log(Gamma(1. + 2.7 * %i)),_
lng2(1. + 2.7 * %i)-log(Gamma(1. + 2.7 * %i)),_
lng2(1. + 2.7 * %i),logGamma(1. + 2.7 * %i),_
lng2(1. + 2.7 * %i)-logGamma(1. + 2.7 * %i),_
lng2(1. + 2.7 * %i)-(- 2.825585641191 + 0.736166351679 * %i)],_
[1. + 2.8 * %i,- 2.964481461789 + 0.838438913096 * %i,_
lng2(1. + 2.8 * %i),log(Gamma(1. + 2.8 * %i)),_
lng2(1. + 2.8 * %i)-log(Gamma(1. + 2.8 * %i)),_
lng2(1. + 2.8 * %i),logGamma(1. + 2.8 * %i),_
lng2(1. + 2.8 * %i)-logGamma(1. + 2.8 * %i),_
lng2(1. + 2.8 * %i)-(- 2.964481461789 + 0.838438913096 * %i)],_
[1. + 2.9 * %i,- 3.104015439901 + 0.944205473039 * %i,_
lng2(1. + 2.9 * %i),log(Gamma(1. + 2.9 * %i)),_
lng2(1. + 2.9 * %i)-log(Gamma(1. + 2.9 * %i)),_
lng2(1. + 2.9 * %i),logGamma(1. + 2.9 * %i),_
lng2(1. + 2.9 * %i)-logGamma(1. + 2.9 * %i),_
lng2(1. + 2.9 * %i)-(- 3.104015439901 + 0.944205473039 * %i)],_
[1. + 3.0 * %i,- 3.244144299590 + 1.053350771069 * %i,_
lng2(1. + 3.0 * %i),log(Gamma(1. + 3.0 * %i)),_
lng2(1. + 3.0 * %i)-log(Gamma(1. + 3.0 * %i)),_
lng2(1. + 3.0 * %i),logGamma(1. + 3.0 * %i),_
lng2(1. + 3.0 * %i)-logGamma(1. + 3.0 * %i),_
lng2(1. + 3.0 * %i)-(- 3.244144299590 + 1.053350771069 * %i)],_
[1. + 3.1 * %i,- 3.384829022377 + 1.165766713286 * %i,_
lng2(1. + 3.1 * %i),log(Gamma(1. + 3.1 * %i)),_
lng2(1. + 3.1 * %i)-log(Gamma(1. + 3.1 * %i)),_
lng2(1. + 3.1 * %i),logGamma(1. + 3.1 * %i),_
lng2(1. + 3.1 * %i)-logGamma(1. + 3.1 * %i),_
lng2(1. + 3.1 * %i)-(- 3.384829022377 + 1.165766713286 * %i)],_
[1. + 3.2 * %i,- 3.526034306709 + 1.281351745932 * %i,_
lng2(1. + 3.2 * %i),log(Gamma(1. + 3.2 * %i)),_
lng2(1. + 3.2 * %i)-log(Gamma(1. + 3.2 * %i)),_
lng2(1. + 3.2 * %i),logGamma(1. + 3.2 * %i),_
lng2(1. + 3.2 * %i)-logGamma(1. + 3.2 * %i),_
lng2(1. + 3.2 * %i)-(- 3.526034306709 + 1.281351745932 * %i)],_
[1. + 3.3 * %i,- 3.667728110488 + 1.400010296576 * %i,_
lng2(1. + 3.3 * %i),log(Gamma(1. + 3.3 * %i)),_
lng2(1. + 3.3 * %i)-log(Gamma(1. + 3.3 * %i)),_
lng2(1. + 3.3 * %i),logGamma(1. + 3.3 * %i),_
lng2(1. + 3.3 * %i)-logGamma(1. + 3.3 * %i),_
lng2(1. + 3.3 * %i)-(- 3.667728110488 + 1.400010296576 * %i)],_
[1. + 3.4 * %i,- 3.809881261823 + 1.521652274673 * %i,_
lng2(1. + 3.4 * %i),log(Gamma(1. + 3.4 * %i)),_
lng2(1. + 3.4 * %i)-log(Gamma(1. + 3.4 * %i)),_
lng2(1. + 3.4 * %i),logGamma(1. + 3.4 * %i),_
lng2(1. + 3.4 * %i)-logGamma(1. + 3.4 * %i),_
lng2(1. + 3.4 * %i)-(- 3.809881261823 + 1.521652274673 * %i)],_
[1. + 3.5 * %i,- 3.952467126189 + 1.646192624269 * %i,_
lng2(1. + 3.5 * %i),log(Gamma(1. + 3.5 * %i)),_
lng2(1. + 3.5 * %i)-log(Gamma(1. + 3.5 * %i)),_
lng2(1. + 3.5 * %i),logGamma(1. + 3.5 * %i),_
lng2(1. + 3.5 * %i)-logGamma(1. + 3.5 * %i),_
lng2(1. + 3.5 * %i)-(- 3.952467126189 + 1.646192624269 * %i)],_
[1. + 3.6 * %i,- 4.095461320451 + 1.773550922591 * %i,_
lng2(1. + 3.6 * %i),log(Gamma(1. + 3.6 * %i)),_
lng2(1. + 3.6 * %i)-log(Gamma(1. + 3.6 * %i)),_
lng2(1. + 3.6 * %i),logGamma(1. + 3.6 * %i),_
lng2(1. + 3.6 * %i)-logGamma(1. + 3.6 * %i),_
lng2(1. + 3.6 * %i)-(- 4.095461320451 + 1.773550922591 * %i)],_
[1. + 3.7 * %i,- 4.238841466071 + 1.903651019019 * %i,_
lng2(1. + 3.7 * %i),log(Gamma(1. + 3.7 * %i)),_
lng2(1. + 3.7 * %i)-log(Gamma(1. + 3.7 * %i)),_
lng2(1. + 3.7 * %i),logGamma(1. + 3.7 * %i),_
lng2(1. + 3.7 * %i)-logGamma(1. + 3.7 * %i),_
lng2(1. + 3.7 * %i)-(- 4.238841466071 + 1.903651019019 * %i)],_
[1. + 3.8 * %i,- 4.382586975228 + 2.036420709693 * %i,_
lng2(1. + 3.8 * %i),log(Gamma(1. + 3.8 * %i)),_
lng2(1. + 3.8 * %i)-log(Gamma(1. + 3.8 * %i)),_
lng2(1. + 3.8 * %i),logGamma(1. + 3.8 * %i),_
lng2(1. + 3.8 * %i)-logGamma(1. + 3.8 * %i),_
lng2(1. + 3.8 * %i)-(- 4.382586975228 + 2.036420709693 * %i)],_
[1. + 3.9 * %i,- 4.526678864716 + 2.171791443605 * %i,_
lng2(1. + 3.9 * %i),log(Gamma(1. + 3.9 * %i)),_
lng2(1. + 3.9 * %i)-log(Gamma(1. + 3.9 * %i)),_
lng2(1. + 3.9 * %i),logGamma(1. + 3.9 * %i),_
lng2(1. + 3.9 * %i)-logGamma(1. + 3.9 * %i),_
lng2(1. + 3.9 * %i)-(- 4.526678864716 + 2.171791443605 * %i)],_
[1. + 4.0 * %i,- 4.671099593409 + 2.309698056573 * %i,_
lng2(1. + 4.0 * %i),log(Gamma(1. + 4.0 * %i)),_
lng2(1. + 4.0 * %i)-log(Gamma(1. + 4.0 * %i)),_
lng2(1. + 4.0 * %i),logGamma(1. + 4.0 * %i),_
lng2(1. + 4.0 * %i)-logGamma(1. + 4.0 * %i),_
lng2(1. + 4.0 * %i)-(- 4.671099593409 + 2.309698056573 * %i)],_
[1. + 4.1 * %i,- 4.815832919796 + 2.450078529947 * %i,_
lng2(1. + 4.1 * %i),log(Gamma(1. + 4.1 * %i)),_
lng2(1. + 4.1 * %i)-log(Gamma(1. + 4.1 * %i)),_
lng2(1. + 4.1 * %i),logGamma(1. + 4.1 * %i),_
lng2(1. + 4.1 * %i)-logGamma(1. + 4.1 * %i),_
lng2(1. + 4.1 * %i)-(- 4.815832919796 + 2.450078529947 * %i)],_
[1. + 4.2 * %i,- 4.960863776687 + 2.592873771319 * %i,_
lng2(1. + 4.2 * %i),log(Gamma(1. + 4.2 * %i)),_
lng2(1. + 4.2 * %i)-log(Gamma(1. + 4.2 * %i)),_
lng2(1. + 4.2 * %i),logGamma(1. + 4.2 * %i),_
lng2(1. + 4.2 * %i)-logGamma(1. + 4.2 * %i),_
lng2(1. + 4.2 * %i)-(- 4.960863776687 + 2.592873771319 * %i)],_
[1. + 4.3 * %i,- 5.106178160663 + 2.738027414820 * %i,_
lng2(1. + 4.3 * %i),log(Gamma(1. + 4.3 * %i)),_
lng2(1. + 4.3 * %i)-log(Gamma(1. + 4.3 * %i)),_
lng2(1. + 4.3 * %i),logGamma(1. + 4.3 * %i),_
lng2(1. + 4.3 * %i)-logGamma(1. + 4.3 * %i),_
lng2(1. + 4.3 * %i)-(- 5.106178160663 + 2.738027414820 * %i)],_
[1. + 4.4 * %i,- 5.251763034230 + 2.885485638927 * %i,_
lng2(1. + 4.4 * %i),log(Gamma(1. + 4.4 * %i)),_
lng2(1. + 4.4 * %i)-log(Gamma(1. + 4.4 * %i)),_
lng2(1. + 4.4 * %i),logGamma(1. + 4.4 * %i),_
lng2(1. + 4.4 * %i)-logGamma(1. + 4.4 * %i),_
lng2(1. + 4.4 * %i)-(- 5.251763034230 + 2.885485638927 * %i)],_
[1. + 4.5 * %i,- 5.397606238984 + 3.035196999922 * %i,_
lng2(1. + 4.5 * %i),log(Gamma(1. + 4.5 * %i)),_
lng2(1. + 4.5 * %i)-log(Gamma(1. + 4.5 * %i)),_
lng2(1. + 4.5 * %i),logGamma(1. + 4.5 * %i),_
lng2(1. + 4.5 * %i)-logGamma(1. + 4.5 * %i),_
lng2(1. + 4.5 * %i)-(- 5.397606238984 + 3.035196999922 * %i)],_
[1. + 4.6 * %i,- 5.543696418304 + 3.187112279389 * %i,_
lng2(1. + 4.6 * %i),log(Gamma(1. + 4.6 * %i)),_
lng2(1. + 4.6 * %i)-log(Gamma(1. + 4.6 * %i)),_
lng2(1. + 4.6 * %i),logGamma(1. + 4.6 * %i),_
lng2(1. + 4.6 * %i)-logGamma(1. + 4.6 * %i),_
lng2(1. + 4.6 * %i)-(- 5.543696418304 + 3.187112279389 * %i)],_
[1. + 4.7 * %i,- 5.690022948373 + 3.341184344327 * %i,_
lng2(1. + 4.7 * %i),log(Gamma(1. + 4.7 * %i)),_
lng2(1. + 4.7 * %i)-log(Gamma(1. + 4.7 * %i)),_
lng2(1. + 4.7 * %i),logGamma(1. + 4.7 * %i),_
lng2(1. + 4.7 * %i)-logGamma(1. + 4.7 * %i),_
lng2(1. + 4.7 * %i)-(- 5.690022948373 + 3.341184344327 * %i)],_
[1. + 4.8 * %i,- 5.836575876454 + 3.497368018615 * %i,_
lng2(1. + 4.8 * %i),log(Gamma(1. + 4.8 * %i)),_
lng2(1. + 4.8 * %i)-log(Gamma(1. + 4.8 * %i)),_
lng2(1. + 4.8 * %i),logGamma(1. + 4.8 * %i),_
lng2(1. + 4.8 * %i)-logGamma(1. + 4.8 * %i),_
lng2(1. + 4.8 * %i)-(- 5.836575876454 + 3.497368018615 * %i)],_
[1. + 4.9 * %i,- 5.983345865532 + 3.655619964712 * %i,_
lng2(1. + 4.9 * %i),log(Gamma(1. + 4.9 * %i)),_
lng2(1. + 4.9 * %i)-log(Gamma(1. + 4.9 * %i)),_
lng2(1. + 4.9 * %i),logGamma(1. + 4.9 * %i),_
lng2(1. + 4.9 * %i)-logGamma(1. + 4.9 * %i),_
lng2(1. + 4.9 * %i)-(- 5.983345865532 + 3.655619964712 * %i)],_
[1. + 5.0 * %i,- 6.130324144553 + 3.815898574615 * %i,_
lng2(1. + 5.0 * %i),log(Gamma(1. + 5.0 * %i)),_
lng2(1. + 5.0 * %i)-log(Gamma(1. + 5.0 * %i)),_
lng2(1. + 5.0 * %i),logGamma(1. + 5.0 * %i),_
lng2(1. + 5.0 * %i)-logGamma(1. + 5.0 * %i),_
lng2(1. + 5.0 * %i)-(- 6.130324144553 + 3.815898574615 * %i)],_
[1. + 5.1 * %i,- 6.277502463584 + 3.978163869188 * %i,_
lng2(1. + 5.1 * %i),log(Gamma(1. + 5.1 * %i)),_
lng2(1. + 5.1 * %i)-log(Gamma(1. + 5.1 * %i)),_
lng2(1. + 5.1 * %i),logGamma(1. + 5.1 * %i),_
lng2(1. + 5.1 * %i)-logGamma(1. + 5.1 * %i),_
lng2(1. + 5.1 * %i)-(- 6.277502463584 + 3.978163869188 * %i)],_
[1. + 5.2 * %i,- 6.424873053335 + 4.142377405086 * %i,_
lng2(1. + 5.2 * %i),log(Gamma(1. + 5.2 * %i)),_
lng2(1. + 5.2 * %i)-log(Gamma(1. + 5.2 * %i)),_
lng2(1. + 5.2 * %i),logGamma(1. + 5.2 * %i),_
lng2(1. + 5.2 * %i)-logGamma(1. + 5.2 * %i),_
lng2(1. + 5.2 * %i)-(- 6.424873053335 + 4.142377405086 * %i)],_
[1. + 5.3 * %i,- 6.572428588529 + 4.308502188583 * %i,_
lng2(1. + 5.3 * %i),log(Gamma(1. + 5.3 * %i)),_
lng2(1. + 5.3 * %i)-log(Gamma(1. + 5.3 * %i)),_
lng2(1. + 5.3 * %i),logGamma(1. + 5.3 * %i),_
lng2(1. + 5.3 * %i)-logGamma(1. + 5.3 * %i),_
lng2(1. + 5.3 * %i)-(- 6.572428588529 + 4.308502188583 * %i)],_
[1. + 5.4 * %i,- 6.720162154703 + 4.476502595668 * %i,_
lng2(1. + 5.4 * %i),log(Gamma(1. + 5.4 * %i)),_
lng2(1. + 5.4 * %i)-log(Gamma(1. + 5.4 * %i)),_
lng2(1. + 5.4 * %i),logGamma(1. + 5.4 * %i),_
lng2(1. + 5.4 * %i)-logGamma(1. + 5.4 * %i),_
lng2(1. + 5.4 * %i)-(- 6.720162154703 + 4.476502595668 * %i)],_
[1. + 5.5 * %i,- 6.868067218048 + 4.646344297870 * %i,_
lng2(1. + 5.5 * %i),log(Gamma(1. + 5.5 * %i)),_
lng2(1. + 5.5 * %i)-log(Gamma(1. + 5.5 * %i)),_
lng2(1. + 5.5 * %i),logGamma(1. + 5.5 * %i),_
lng2(1. + 5.5 * %i)-logGamma(1. + 5.5 * %i),_
lng2(1. + 5.5 * %i)-(- 6.868067218048 + 4.646344297870 * %i)],_
[1. + 5.6 * %i,- 7.016137597976 + 4.817994193305 * %i,_
lng2(1. + 5.6 * %i),log(Gamma(1. + 5.6 * %i)),_
lng2(1. + 5.6 * %i)-log(Gamma(1. + 5.6 * %i)),_
lng2(1. + 5.6 * %i),logGamma(1. + 5.6 * %i),_
lng2(1. + 5.6 * %i)-logGamma(1. + 5.6 * %i),_
lng2(1. + 5.6 * %i)-(- 7.016137597976 + 4.817994193305 * %i)],_
[1. + 5.7 * %i,- 7.164367442106 + 4.991420342489 * %i,_
lng2(1. + 5.7 * %i),log(Gamma(1. + 5.7 * %i)),_
lng2(1. + 5.7 * %i)-log(Gamma(1. + 5.7 * %i)),_
lng2(1. + 5.7 * %i),logGamma(1. + 5.7 * %i),_
lng2(1. + 5.7 * %i)-logGamma(1. + 5.7 * %i),_
lng2(1. + 5.7 * %i)-(- 7.164367442106 + 4.991420342489 * %i)],_
[1. + 5.8 * %i,- 7.312751203430 + 5.166591908537 * %i,_
lng2(1. + 5.8 * %i),log(Gamma(1. + 5.8 * %i)),_
lng2(1. + 5.8 * %i)-log(Gamma(1. + 5.8 * %i)),_
lng2(1. + 5.8 * %i),logGamma(1. + 5.8 * %i),_
lng2(1. + 5.8 * %i)-logGamma(1. + 5.8 * %i),_
lng2(1. + 5.8 * %i)-(- 7.312751203430 + 5.166591908537 * %i)],_
[1. + 5.9 * %i,- 7.461283619429 + 5.343479101353 * %i,_
lng2(1. + 5.9 * %i),log(Gamma(1. + 5.9 * %i)),_
lng2(1. + 5.9 * %i)-log(Gamma(1. + 5.9 * %i)),_
lng2(1. + 5.9 * %i),logGamma(1. + 5.9 * %i),_
lng2(1. + 5.9 * %i)-logGamma(1. + 5.9 * %i),_
lng2(1. + 5.9 * %i)-(- 7.461283619429 + 5.343479101353 * %i)],_
[1. + 6.0 * %i,- 7.609959692951 + 5.522053125515 * %i,_
lng2(1. + 6.0 * %i),log(Gamma(1. + 6.0 * %i)),_
lng2(1. + 6.0 * %i)-log(Gamma(1. + 6.0 * %i)),_
lng2(1. + 6.0 * %i),logGamma(1. + 6.0 * %i),_
lng2(1. + 6.0 * %i)-logGamma(1. + 6.0 * %i),_
lng2(1. + 6.0 * %i)-(- 7.609959692951 + 5.522053125515 * %i)],_
[1. + 6.1 * %i,- 7.758774674655 + 5.702286131535 * %i,_
lng2(1. + 6.1 * %i),log(Gamma(1. + 6.1 * %i)),_
lng2(1. + 6.1 * %i)-log(Gamma(1. + 6.1 * %i)),_
lng2(1. + 6.1 * %i),logGamma(1. + 6.1 * %i),_
lng2(1. + 6.1 * %i)-logGamma(1. + 6.1 * %i),_
lng2(1. + 6.1 * %i)-(- 7.758774674655 + 5.702286131535 * %i)],_
[1. + 6.2 * %i,- 7.907724046898 + 5.884151170239 * %i,_
lng2(1. + 6.2 * %i),log(Gamma(1. + 6.2 * %i)),_
lng2(1. + 6.2 * %i)-log(Gamma(1. + 6.2 * %i)),_
lng2(1. + 6.2 * %i),logGamma(1. + 6.2 * %i),_
lng2(1. + 6.2 * %i)-logGamma(1. + 6.2 * %i),_
lng2(1. + 6.2 * %i)-(- 7.907724046898 + 5.884151170239 * %i)],_
[1. + 6.3 * %i,- 8.056803508904 + 6.067622150013 * %i,_
lng2(1. + 6.3 * %i),log(Gamma(1. + 6.3 * %i)),_
lng2(1. + 6.3 * %i)-log(Gamma(1. + 6.3 * %i)),_
lng2(1. + 6.3 * %i),logGamma(1. + 6.3 * %i),_
lng2(1. + 6.3 * %i)-logGamma(1. + 6.3 * %i),_
lng2(1. + 6.3 * %i)-(- 8.056803508904 + 6.067622150013 * %i)],_
[1. + 6.4 * %i,- 8.206008963100 + 6.252673796705 * %i,_
lng2(1. + 6.4 * %i),log(Gamma(1. + 6.4 * %i)),_
lng2(1. + 6.4 * %i)-log(Gamma(1. + 6.4 * %i)),_
lng2(1. + 6.4 * %i),logGamma(1. + 6.4 * %i),_
lng2(1. + 6.4 * %i)-logGamma(1. + 6.4 * %i),_
lng2(1. + 6.4 * %i)-(- 8.206008963100 + 6.252673796705 * %i)],_
[1. + 6.5 * %i,- 8.355336502511 + 6.439281615976 * %i,_
lng2(1. + 6.5 * %i),log(Gamma(1. + 6.5 * %i)),_
lng2(1. + 6.5 * %i)-log(Gamma(1. + 6.5 * %i)),_
lng2(1. + 6.5 * %i),logGamma(1. + 6.5 * %i),_
lng2(1. + 6.5 * %i)-logGamma(1. + 6.5 * %i),_
lng2(1. + 6.5 * %i)-(- 8.355336502511 + 6.439281615976 * %i)],_
[1. + 6.6 * %i,- 8.504782399125 + 6.627421857912 * %i,_
lng2(1. + 6.6 * %i),log(Gamma(1. + 6.6 * %i)),_
lng2(1. + 6.6 * %i)-log(Gamma(1. + 6.6 * %i)),_
lng2(1. + 6.6 * %i),logGamma(1. + 6.6 * %i),_
lng2(1. + 6.6 * %i)-logGamma(1. + 6.6 * %i),_
lng2(1. + 6.6 * %i)-(- 8.504782399125 + 6.627421857912 * %i)],_
[1. + 6.7 * %i,- 8.654343093123 + 6.817071483744 * %i,_
lng2(1. + 6.7 * %i),log(Gamma(1. + 6.7 * %i)),_
lng2(1. + 6.7 * %i)-log(Gamma(1. + 6.7 * %i)),_
lng2(1. + 6.7 * %i),logGamma(1. + 6.7 * %i),_
lng2(1. + 6.7 * %i)-logGamma(1. + 6.7 * %i),_
lng2(1. + 6.7 * %i)-(- 8.654343093123 + 6.817071483744 * %i)],_
[1. + 6.8 * %i,- 8.804015182910 + 7.008208134502 * %i,_
lng2(1. + 6.8 * %i),log(Gamma(1. + 6.8 * %i)),_
lng2(1. + 6.8 * %i)-log(Gamma(1. + 6.8 * %i)),_
lng2(1. + 6.8 * %i),logGamma(1. + 6.8 * %i),_
lng2(1. + 6.8 * %i)-logGamma(1. + 6.8 * %i),_
lng2(1. + 6.8 * %i)-(- 8.804015182910 + 7.008208134502 * %i)],_
[1. + 6.9 * %i,- 8.953795415879 + 7.200810101493 * %i,_
lng2(1. + 6.9 * %i),log(Gamma(1. + 6.9 * %i)),_
lng2(1. + 6.9 * %i)-log(Gamma(1. + 6.9 * %i)),_
lng2(1. + 6.9 * %i),logGamma(1. + 6.9 * %i),_
lng2(1. + 6.9 * %i)-logGamma(1. + 6.9 * %i),_
lng2(1. + 6.9 * %i)-(- 8.953795415879 + 7.200810101493 * %i)],_
[1. + 7.0 * %i,- 9.103680679832 + 7.394856298436 * %i,_
lng2(1. + 7.0 * %i),log(Gamma(1. + 7.0 * %i)),_
lng2(1. + 7.0 * %i)-log(Gamma(1. + 7.0 * %i)),_
lng2(1. + 7.0 * %i),logGamma(1. + 7.0 * %i),_
lng2(1. + 7.0 * %i)-logGamma(1. + 7.0 * %i),_
lng2(1. + 7.0 * %i)-(- 9.103680679832 + 7.394856298436 * %i)],_
[1. + 7.1 * %i,- 9.253667995015 + 7.590326235184 * %i,_
lng2(1. + 7.1 * %i),log(Gamma(1. + 7.1 * %i)),_
lng2(1. + 7.1 * %i)-log(Gamma(1. + 7.1 * %i)),_
lng2(1. + 7.1 * %i),logGamma(1. + 7.1 * %i),_
lng2(1. + 7.1 * %i)-logGamma(1. + 7.1 * %i),_
lng2(1. + 7.1 * %i)-(- 9.253667995015 + 7.590326235184 * %i)],_
[1. + 7.2 * %i,- 9.403754506708 + 7.787199992877 * %i,_
lng2(1. + 7.2 * %i),log(Gamma(1. + 7.2 * %i)),_
lng2(1. + 7.2 * %i)-log(Gamma(1. + 7.2 * %i)),_
lng2(1. + 7.2 * %i),logGamma(1. + 7.2 * %i),_
lng2(1. + 7.2 * %i)-logGamma(1. + 7.2 * %i),_
lng2(1. + 7.2 * %i)-(- 9.403754506708 + 7.787199992877 * %i)],_
[1. + 7.3 * %i,- 9.553937478321 + 7.985458200468 * %i,_
lng2(1. + 7.3 * %i),log(Gamma(1. + 7.3 * %i)),_
lng2(1. + 7.3 * %i)-log(Gamma(1. + 7.3 * %i)),_
lng2(1. + 7.3 * %i),logGamma(1. + 7.3 * %i),_
lng2(1. + 7.3 * %i)-logGamma(1. + 7.3 * %i),_
lng2(1. + 7.3 * %i)-(- 9.553937478321 + 7.985458200468 * %i)],_
[1. + 7.4 * %i,- 9.704214284972 + 8.185082012503 * %i,_
lng2(1. + 7.4 * %i),log(Gamma(1. + 7.4 * %i)),_
lng2(1. + 7.4 * %i)-log(Gamma(1. + 7.4 * %i)),_
lng2(1. + 7.4 * %i),logGamma(1. + 7.4 * %i),_
lng2(1. + 7.4 * %i)-logGamma(1. + 7.4 * %i),_
lng2(1. + 7.4 * %i)-(- 9.704214284972 + 8.185082012503 * %i)],_
[1. + 7.5 * %i,- 9.854582407486 + 8.386053088089 * %i,_
lng2(1. + 7.5 * %i),log(Gamma(1. + 7.5 * %i)),_
lng2(1. + 7.5 * %i)-log(Gamma(1. + 7.5 * %i)),_
lng2(1. + 7.5 * %i),logGamma(1. + 7.5 * %i),_
lng2(1. + 7.5 * %i)-logGamma(1. + 7.5 * %i),_
lng2(1. + 7.5 * %i)-(- 9.854582407486 + 8.386053088089 * %i)],_
[1. + 7.6 * %i,- 10.005039426790 + 8.588353570962 * %i,_
lng2(1. + 7.6 * %i),log(Gamma(1. + 7.6 * %i)),_
lng2(1. + 7.6 * %i)-log(Gamma(1. + 7.6 * %i)),_
lng2(1. + 7.6 * %i),logGamma(1. + 7.6 * %i),_
lng2(1. + 7.6 * %i)-logGamma(1. + 7.6 * %i),_
lng2(1. + 7.6 * %i)-(- 10.005039426790 + 8.588353570962 * %i)],_
[1. + 7.7 * %i,- 10.155583018686 + 8.791966070587 * %i,_
lng2(1. + 7.7 * %i),log(Gamma(1. + 7.7 * %i)),_
lng2(1. + 7.7 * %i)-log(Gamma(1. + 7.7 * %i)),_
lng2(1. + 7.7 * %i),logGamma(1. + 7.7 * %i),_
lng2(1. + 7.7 * %i)-logGamma(1. + 7.7 * %i),_
lng2(1. + 7.7 * %i)-(- 10.155583018686 + 8.791966070587 * %i)],_
[1. + 7.8 * %i,- 10.306210948948 + 8.996873644229 * %i,_
lng2(1. + 7.8 * %i),log(Gamma(1. + 7.8 * %i)),_
lng2(1. + 7.8 * %i)-log(Gamma(1. + 7.8 * %i)),_
lng2(1. + 7.8 * %i),logGamma(1. + 7.8 * %i),_
lng2(1. + 7.8 * %i)-logGamma(1. + 7.8 * %i),_
lng2(1. + 7.8 * %i)-(- 10.306210948948 + 8.996873644229 * %i)],_
[1. + 7.9 * %i,- 10.456921068739 + 9.203059779925 * %i,_
lng2(1. + 7.9 * %i),log(Gamma(1. + 7.9 * %i)),_
lng2(1. + 7.9 * %i)-log(Gamma(1. + 7.9 * %i)),_
lng2(1. + 7.9 * %i),logGamma(1. + 7.9 * %i),_
lng2(1. + 7.9 * %i)-logGamma(1. + 7.9 * %i),_
lng2(1. + 7.9 * %i)-(- 10.456921068739 + 9.203059779925 * %i)],_
[1. + 8.0 * %i,- 10.607711310315 + 9.410508380312 * %i,_
lng2(1. + 8.0 * %i),log(Gamma(1. + 8.0 * %i)),_
lng2(1. + 8.0 * %i)-log(Gamma(1. + 8.0 * %i)),_
lng2(1. + 8.0 * %i),logGamma(1. + 8.0 * %i),_
lng2(1. + 8.0 * %i)-logGamma(1. + 8.0 * %i),_
lng2(1. + 8.0 * %i)-(- 10.607711310315 + 9.410508380312 * %i)],_
[1. + 8.1 * %i,- 10.758579682995 + 9.619203747242 * %i,_
lng2(1. + 8.1 * %i),log(Gamma(1. + 8.1 * %i)),_
lng2(1. + 8.1 * %i)-log(Gamma(1. + 8.1 * %i)),_
lng2(1. + 8.1 * %i),logGamma(1. + 8.1 * %i),_
lng2(1. + 8.1 * %i)-logGamma(1. + 8.1 * %i),_
lng2(1. + 8.1 * %i)-(- 10.758579682995 + 9.619203747242 * %i)],_
[1. + 8.2 * %i,- 10.909524269378 + 9.829130567162 * %i,_
lng2(1. + 8.2 * %i),log(Gamma(1. + 8.2 * %i)),_
lng2(1. + 8.2 * %i)-log(Gamma(1. + 8.2 * %i)),_
lng2(1. + 8.2 * %i),logGamma(1. + 8.2 * %i),_
lng2(1. + 8.2 * %i)-logGamma(1. + 8.2 * %i),_
lng2(1. + 8.2 * %i)-(- 10.909524269378 + 9.829130567162 * %i)],_
[1. + 8.3 * %i,- 11.060543221792 + 10.040273897180 * %i,_
lng2(1. + 8.3 * %i),log(Gamma(1. + 8.3 * %i)),_
lng2(1. + 8.3 * %i)-log(Gamma(1. + 8.3 * %i)),_
lng2(1. + 8.3 * %i),logGamma(1. + 8.3 * %i),_
lng2(1. + 8.3 * %i)-logGamma(1. + 8.3 * %i),_
lng2(1. + 8.3 * %i)-(- 11.060543221792 + 10.040273897180 * %i)],_
[1. + 8.4 * %i,- 11.211634758948 + 10.252619151809 * %i,_
lng2(1. + 8.4 * %i),log(Gamma(1. + 8.4 * %i)),_
lng2(1. + 8.4 * %i)-log(Gamma(1. + 8.4 * %i)),_
lng2(1. + 8.4 * %i),logGamma(1. + 8.4 * %i),_
lng2(1. + 8.4 * %i)-logGamma(1. + 8.4 * %i),_
lng2(1. + 8.4 * %i)-(- 11.211634758948 + 10.252619151809 * %i)],_
[1. + 8.5 * %i,- 11.362797162804 + 10.466152090324 * %i,_
lng2(1. + 8.5 * %i),log(Gamma(1. + 8.5 * %i)),_
lng2(1. + 8.5 * %i)-log(Gamma(1. + 8.5 * %i)),_
lng2(1. + 8.5 * %i),logGamma(1. + 8.5 * %i),_
lng2(1. + 8.5 * %i)-logGamma(1. + 8.5 * %i),_
lng2(1. + 8.5 * %i)-(- 11.362797162804 + 10.466152090324 * %i)],_
[1. + 8.6 * %i,- 11.514028775602 + 10.680858804712 * %i,_
lng2(1. + 8.6 * %i),log(Gamma(1. + 8.6 * %i)),_
lng2(1. + 8.6 * %i)-log(Gamma(1. + 8.6 * %i)),_
lng2(1. + 8.6 * %i),logGamma(1. + 8.6 * %i),_
lng2(1. + 8.6 * %i)-logGamma(1. + 8.6 * %i),_
lng2(1. + 8.6 * %i)-(- 11.514028775602 + 10.680858804712 * %i)],_
[1. + 8.7 * %i,- 11.665327997081 + 10.896725708177 * %i,_
lng2(1. + 8.7 * %i),log(Gamma(1. + 8.7 * %i)),_
lng2(1. + 8.7 * %i)-log(Gamma(1. + 8.7 * %i)),_
lng2(1. + 8.7 * %i),logGamma(1. + 8.7 * %i),_
lng2(1. + 8.7 * %i)-logGamma(1. + 8.7 * %i),_
lng2(1. + 8.7 * %i)-(- 11.665327997081 + 10.896725708177 * %i)],_
[1. + 8.8 * %i,- 11.816693281848 + 11.113739524157 * %i,_
lng2(1. + 8.8 * %i),log(Gamma(1. + 8.8 * %i)),_
lng2(1. + 8.8 * %i)-log(Gamma(1. + 8.8 * %i)),_
lng2(1. + 8.8 * %i),logGamma(1. + 8.8 * %i),_
lng2(1. + 8.8 * %i)-logGamma(1. + 8.8 * %i),_
lng2(1. + 8.8 * %i)-(- 11.816693281848 + 11.113739524157 * %i)],_
[1. + 8.9 * %i,- 11.968123136901 + 11.331887275853 * %i,_
lng2(1. + 8.9 * %i),log(Gamma(1. + 8.9 * %i)),_
lng2(1. + 8.9 * %i)-log(Gamma(1. + 8.9 * %i)),_
lng2(1. + 8.9 * %i),logGamma(1. + 8.9 * %i),_
lng2(1. + 8.9 * %i)-logGamma(1. + 8.9 * %i),_
lng2(1. + 8.9 * %i)-(- 11.968123136901 + 11.331887275853 * %i)],_
[1. + 9.0 * %i,- 12.119616119281 + 11.551156276202 * %i,_
lng2(1. + 9.0 * %i),log(Gamma(1. + 9.0 * %i)),_
lng2(1. + 9.0 * %i)-log(Gamma(1. + 9.0 * %i)),_
lng2(1. + 9.0 * %i),logGamma(1. + 9.0 * %i),_
lng2(1. + 9.0 * %i)-logGamma(1. + 9.0 * %i),_
lng2(1. + 9.0 * %i)-(- 12.119616119281 + 11.551156276202 * %i)],_
[1. + 9.1 * %i,- 12.271170833867 + 11.771534118309 * %i,_
lng2(1. + 9.1 * %i),log(Gamma(1. + 9.1 * %i)),_
lng2(1. + 9.1 * %i)-log(Gamma(1. + 9.1 * %i)),_
lng2(1. + 9.1 * %i),logGamma(1. + 9.1 * %i),_
lng2(1. + 9.1 * %i)-logGamma(1. + 9.1 * %i),_
lng2(1. + 9.1 * %i)-(- 12.271170833867 + 11.771534118309 * %i)],_
[1. + 9.2 * %i,- 12.422785931281 + 11.993008666285 * %i,_
lng2(1. + 9.2 * %i),log(Gamma(1. + 9.2 * %i)),_
lng2(1. + 9.2 * %i)-log(Gamma(1. + 9.2 * %i)),_
lng2(1. + 9.2 * %i),logGamma(1. + 9.2 * %i),_
lng2(1. + 9.2 * %i)-logGamma(1. + 9.2 * %i),_
lng2(1. + 9.2 * %i)-(- 12.422785931281 + 11.993008666285 * %i)],_
[1. + 9.3 * %i,- 12.574460105908 + 12.215568046479 * %i,_
lng2(1. + 9.3 * %i),log(Gamma(1. + 9.3 * %i)),_
lng2(1. + 9.3 * %i)-log(Gamma(1. + 9.3 * %i)),_
lng2(1. + 9.3 * %i),logGamma(1. + 9.3 * %i),_
lng2(1. + 9.3 * %i)-logGamma(1. + 9.3 * %i),_
lng2(1. + 9.3 * %i)-(- 12.574460105908 + 12.215568046479 * %i)],_
[1. + 9.4 * %i,- 12.726192094029 + 12.439200639090 * %i,_
lng2(1. + 9.4 * %i),log(Gamma(1. + 9.4 * %i)),_
lng2(1. + 9.4 * %i)-log(Gamma(1. + 9.4 * %i)),_
lng2(1. + 9.4 * %i),logGamma(1. + 9.4 * %i),_
lng2(1. + 9.4 * %i)-logGamma(1. + 9.4 * %i),_
lng2(1. + 9.4 * %i)-(- 12.726192094029 + 12.439200639090 * %i)],_
[1. + 9.5 * %i,- 12.877980672044 + 12.663895070128 * %i,_
lng2(1. + 9.5 * %i),log(Gamma(1. + 9.5 * %i)),_
lng2(1. + 9.5 * %i)-log(Gamma(1. + 9.5 * %i)),_
lng2(1. + 9.5 * %i),logGamma(1. + 9.5 * %i),_
lng2(1. + 9.5 * %i)-logGamma(1. + 9.5 * %i),_
lng2(1. + 9.5 * %i)-(- 12.877980672044 + 12.663895070128 * %i)],_
[1. + 9.6 * %i,- 13.029824654789 + 12.889640203708 * %i,_
lng2(1. + 9.6 * %i),log(Gamma(1. + 9.6 * %i)),_
lng2(1. + 9.6 * %i)-log(Gamma(1. + 9.6 * %i)),_
lng2(1. + 9.6 * %i),logGamma(1. + 9.6 * %i),_
lng2(1. + 9.6 * %i)-logGamma(1. + 9.6 * %i),_
lng2(1. + 9.6 * %i)-(- 13.029824654789 + 12.889640203708 * %i)],_
[1. + 9.7 * %i,- 13.181722893951 + 13.116425134666 * %i,_
lng2(1. + 9.7 * %i),log(Gamma(1. + 9.7 * %i)),_
lng2(1. + 9.7 * %i)-log(Gamma(1. + 9.7 * %i)),_
lng2(1. + 9.7 * %i),logGamma(1. + 9.7 * %i),_
lng2(1. + 9.7 * %i)-logGamma(1. + 9.7 * %i),_
lng2(1. + 9.7 * %i)-(- 13.181722893951 + 13.116425134666 * %i)],_
[1. + 9.8 * %i,- 13.333674276547 + 13.344239181477 * %i,_
lng2(1. + 9.8 * %i),log(Gamma(1. + 9.8 * %i)),_
lng2(1. + 9.8 * %i)-log(Gamma(1. + 9.8 * %i)),_
lng2(1. + 9.8 * %i),logGamma(1. + 9.8 * %i),_
lng2(1. + 9.8 * %i)-logGamma(1. + 9.8 * %i),_
lng2(1. + 9.8 * %i)-(- 13.333674276547 + 13.344239181477 * %i)],_
[1. + 9.9 * %i,- 13.485677723495 + 13.573071879455 * %i,_
lng2(1. + 9.9 * %i),log(Gamma(1. + 9.9 * %i)),_
lng2(1. + 9.9 * %i)-log(Gamma(1. + 9.9 * %i)),_
lng2(1. + 9.9 * %i),logGamma(1. + 9.9 * %i),_
lng2(1. + 9.9 * %i)-logGamma(1. + 9.9 * %i),_
lng2(1. + 9.9 * %i)-(- 13.485677723495 + 13.573071879455 * %i)],_
[1. + 10.0 * %i,- 13.637732188247 + 13.802912974230 * %i,_
lng2(1. + 10.0 * %i),log(Gamma(1. + 10.0 * %i)),_
lng2(1. + 10.0 * %i)-log(Gamma(1. + 10.0 * %i)),_
lng2(1. + 10.0 * %i),logGamma(1. + 10.0 * %i),_
lng2(1. + 10.0 * %i)-logGamma(1. + 10.0 * %i),_
lng2(1. + 10.0 * %i)-(- 13.637732188247 + 13.802912974230 * %i)]]
 
   Compiling function lng2 with type Complex DoubleFloat -> Complex 
      DoubleFloat 

   (12)
   [[1.,0.,0.,0.],

     [1. + 0.10000000000000001 %i,
      - 8.1977805649999999E-3 - 5.7322940417000007E-2 %i,
      - 8.1977805654074309E-3 - 5.732294041672345E-2 %i,
      - 8.1977805654051359E-3 - 5.7322940416719675E-2 %i,
      - 2.2950391587173158E-15 - 3.7747582837255322E-15 %i,
      - 8.1977805654074309E-3 - 5.732294041672345E-2 %i,
      - 8.1977805654052105E-3 - 5.7322940416719675E-2 %i,
      - 2.2204460492503131E-15 - 3.7747582837255322E-15 %i,
      - 4.0743103335572073E-13 + 2.7655655543412649E-13 %i]
     ,

     [1. + 0.20000000000000001 %i, - 3.2476292318000005E-2 - 0.112302222644 %i,
      - 3.2476292318133204E-2 - 0.11230222264419082 %i,
      - 3.2476292318128805E-2 - 0.11230222264418371 %i,
      - 4.3992587350771828E-15 - 7.1054273576010019E-15 %i,
      - 3.2476292318133204E-2 - 0.11230222264419082 %i,
      - 3.2476292318128763E-2 - 0.11230222264418371 %i,
      - 4.4408920985006262E-15 - 7.1054273576010019E-15 %i,
      - 1.3319900737940316E-13 - 1.9081958235744878E-13 %i]
     ,

     [1. + 0.29999999999999999 %i,
      - 7.1946250900000008E-2 - 0.16282067216799997 %i,
      - 7.1946250899646902E-2 - 0.16282067216786528 %i,
      - 7.1946250899640213E-2 - 0.16282067216785573 %i,
      - 6.6890937233665682E-15 - 9.5479180117763462E-15 %i,
      - 7.1946250899646902E-2 - 0.16282067216786528 %i,
      - 7.1946250899640241E-2 - 0.16282067216785573 %i,
      - 6.6613381477509392E-15 - 9.5479180117763462E-15 %i,
      3.5310643298203104E-13 + 1.3469780846264712E-13 %i]
     ,

     [1. + 0.40000000000000002 %i, - 0.125289374821 - 0.20715582631599999 %i,
      - 0.12528937482072333 - 0.20715582631567919 %i,
      - 0.12528937482070648 - 0.20715582631566853 %i,
      - 1.6847634398686751E-14 - 1.0658141036401503E-14 %i,
      - 0.12528937482072333 - 0.20715582631567919 %i,
      - 0.12528937482070646 - 0.20715582631566853 %i,
      - 1.6875389974302379E-14 - 1.0658141036401503E-14 %i,
      2.7666757773658901E-13 + 3.2079894296543898E-13 %i]
     ,

     [1. + 0.5 %i, - 0.19094549918699999 - 0.24405829890500003 %i,
      - 0.19094549918680226 - 0.24405829890543784 %i,
      - 0.19094549918678008 - 0.24405829890542749 %i,
      - 2.2176704916887502E-14 - 1.0352829704629585E-14 %i,
      - 0.19094549918680226 - 0.24405829890543784 %i,
      - 0.19094549918678005 - 0.24405829890542752 %i,
      - 2.2204460492503131E-14 - 1.0325074129013956E-14 %i,
      1.9773072068574038E-13 - 4.3781644976093048E-13 %i]
     ,

     [1. + 0.59999999999999998 %i,
      - 0.26729006821400003 - 0.27274381049100005 %i,
      - 0.26729006821416545 - 0.27274381049105989 %i,
      - 0.2672900682141322 - 0.27274381049105378 %i,
      - 3.3251179587523438E-14 - 6.106226635438361E-15 %i,
      - 0.26729006821416545 - 0.27274381049105989 %i,
      - 0.26729006821413215 - 0.27274381049105378 %i,
      - 3.3306690738754696E-14 - 6.106226635438361E-15 %i,
      - 1.6542323066914832E-13 - 5.9841021027295938E-14 %i]
     ,

     [1. + 0.69999999999999996 %i,
      - 0.35276869085999996 - 0.29282635118699996 %i,
      - 0.35276869085965368 - 0.29282635118686051 %i,
      - 0.3527686908596116 - 0.29282635118686201 %i,
      - 4.2077452633293433E-14 + 1.4988010832439613E-15 %i,
      - 0.35276869085965368 - 0.29282635118686051 %i,
      - 0.35276869085961149 - 0.29282635118686196 %i,
      - 4.2188474935755949E-14 + 1.4432899320127035E-15 %i,
      3.4627856138058632E-13 + 1.3944401189291966E-13 %i]
     ,

     [1. + 0.80000000000000004 %i,
      - 0.44597878354899995 - 0.30422560297599999 %i,
      - 0.4459787835488167 - 0.30422560297617007 %i,
      - 0.4459787835487648 - 0.30422560297618323 %i,
      - 5.1902926401226068E-14 + 1.3156142841808105E-14 %i,
      - 0.4459787835488167 - 0.30422560297617007 %i,
      - 0.44597878354876475 - 0.30422560297618317 %i,
      - 5.1958437552457326E-14 + 1.3100631690576847E-14 %i,
      1.8324231021438209E-13 - 1.7008616737257398E-13 %i]
     ,

     [1. + 0.89999999999999991 %i,
      - 0.54570512860500009 - 0.30707437564199996 %i,
      - 0.54570512860503806 - 0.30707437564241991 %i,
      - 0.54570512860497644 - 0.30707437564245171 %i,
      - 6.1617377866696188E-14 + 3.1807889655510735E-14 %i,
      - 0.54570512860503806 - 0.30707437564241991 %i,
      - 0.54570512860497633 - 0.30707437564245166 %i,
      - 6.1728400169158704E-14 + 3.1752378504279477E-14 %i,
      - 3.7969627442180354E-14 - 4.1994185906446546E-13 %i]
     ,

     [1. + %i, - 0.65092319930199993 - 0.30164032046800004 %i,
      - 0.65092319930192311 - 0.30164032046747735 %i,
      - 0.65092319930185472 - 0.30164032046753331 %i,
      - 6.8389738316909643E-14 + 5.595524044110789E-14 %i,
      - 0.65092319930192311 - 0.30164032046747735 %i,
      - 0.65092319930185472 - 0.30164032046753331 %i,
      - 6.8389738316909643E-14 + 5.595524044110789E-14 %i,
      7.6827433304060833E-14 + 5.226929999935237E-13 %i]
     ,

     [1. + 1.1000000000000001 %i,
      - 0.76078395884099992 - 0.28826661423899996 %i,
      - 0.76078395884088268 - 0.28826661423897093 %i,
      - 0.76078395884081551 - 0.28826661423905575 %i,
      - 6.7168492989821971E-14 + 8.482103908136196E-14 %i,
      - 0.76078395884088268 - 0.28826661423897093 %i,
      - 0.76078395884081562 - 0.28826661423905575 %i,
      - 6.7057470687359455E-14 + 8.482103908136196E-14 %i,
      1.1723955140041653E-13 + 2.9032332093947844E-14 %i]
     ,

     [1. + 1.2 %i, - 0.87459046389499995 - 0.26733058058099995 %i,
      - 0.87459046389477102 - 0.2673305805810684 %i,
      - 0.87459046389471329 - 0.26733058058118808 %i,
      - 5.773159728050814E-14 + 1.1968204205459188E-13 %i,
      - 0.87459046389477102 - 0.2673305805810684 %i,
      - 0.87459046389471329 - 0.26733058058118808 %i,
      - 5.773159728050814E-14 + 1.1968204205459188E-13 %i,
      2.2892798767770728E-13 - 6.8445249468140901E-14 %i]
     ,

     [1. + 1.2999999999999998 %i, - 0.99177276695899996 - 0.239216784465 %i,
      - 0.99177276695938321 - 0.23921678446488515 %i,
      - 0.99177276695934236 - 0.2392167844650448 %i,
      - 4.0856207306205761E-14 + 1.5965007094109751E-13 %i,
      - 0.99177276695938321 - 0.23921678446488515 %i,
      - 0.99177276695934236 - 0.2392167844650448 %i,
      - 4.0856207306205761E-14 + 1.5965007094109751E-13 %i,
      - 3.8324898810060404E-13 + 1.1485257189747244E-13 %i]
     ,

     [1. + 1.3999999999999999 %i,
      - 1.1118645664259998 - 0.20430072414900002 %i,
      - 1.1118645664255413 - 0.20430072414906242 %i,
      - 1.1118645664255329 - 0.20430072414926384 %i,
      - 8.4376949871511897E-15 + 2.0142221224261903E-13 %i,
      - 1.1118645664255413 - 0.20430072414906242 %i,
      - 1.1118645664255329 - 0.20430072414926381 %i,
      - 8.4376949871511897E-15 + 2.013944566670034E-13 %i,
      4.5852210917018965E-13 - 6.2394533983933798E-14 %i]
     ,

     [1. + 1.5 %i, - 1.234483051547 - 0.16293976948 %i,
      - 1.2344830515465768 - 0.16293976947988265 %i,
      - 1.2344830515466152 - 0.16293976948012379 %i,
      3.8413716652030416E-14 + 2.41140440948584E-13 %i,
      - 1.2344830515465768 - 0.16293976947988265 %i,
      - 1.234483051546615 - 0.16293976948012379 %i,
      3.8191672047105385E-14 + 2.41140440948584E-13 %i,
      4.2321701698710967E-13 + 1.1735057370287905E-13 %i]
     ,

     [1. + 1.6000000000000001 %i,
      - 1.3593122484650002 - 0.11546879358899999 %i,
      - 1.3593122484650171 - 0.11546879358852835 %i,
      - 1.3593122484651154 - 0.11546879358880435 %i,
      9.8365759981788869E-14 + 2.7600144392181392E-13 %i,
      - 1.3593122484650171 - 0.11546879358852835 %i,
      - 1.3593122484651152 - 0.11546879358880435 %i,
      9.8143715376863838E-14 + 2.7600144392181392E-13 %i,
      - 1.6875389974302379E-14 + 4.7163661864857431E-13 %i]
     ,

     [1. + 1.7 %i, - 1.4860896127569998 - 6.2198698329000005E-2 %i,
      - 1.4860896127570808 - 6.2198698328699953E-2 %i,
      - 1.4860896127572634 - 6.2198698328999047E-2 %i,
      1.8252066524837574E-13 + 2.9909408283401717E-13 %i,
      - 1.4860896127570808 - 6.2198698328699953E-2 %i,
      - 1.4860896127572634 - 6.2198698328999047E-2 %i,
      1.8252066524837574E-13 + 2.9909408283401717E-13 %i,
      - 8.1046280797636427E-14 + 3.0005165019275637E-13 %i]
     ,

     [1. + 1.7999999999999998 %i,
      - 1.6145953959999999 - 3.4166314769999997E-3 %i,
      - 1.6145953959992845 - 3.4166314766119754E-3 %i,
      - 1.6145953959995614 - 3.4166314769201729E-3 %i,
      2.7688962234151404E-13 + 3.0819747795507446E-13 %i,
      - 1.6145953959992845 - 3.4166314766119754E-3 %i,
      - 1.6145953959995616 - 3.4166314769201733E-3 %i,
      2.7711166694643907E-13 + 3.0819791163594346E-13 %i,
      7.1542771706845087E-13 + 3.8802424814909919E-13 %i]
     ,

     [1. + 1.8999999999999999 %i,
      - 1.7446442761740002 + 6.0612874294999994E-2 %i,
      - 1.7446442761733065 + 6.0612874295708608E-2 %i,
      - 1.7446442761736973 + 6.0612874295411963E-2 %i,
      3.907985046680551E-13 + 2.9664465328593792E-13 %i,
      - 1.7446442761733065 + 6.0612874295708608E-2 %i,
      - 1.7446442761736973 + 6.0612874295411956E-2 %i,
      3.907985046680551E-13 + 2.9665159217984183E-13 %i,
      6.9366734578579781E-13 + 7.0861372325481398E-13 %i]
     ,

     [1. + 2. %i, - 1.8760787864309998 + 0.12964631631000001 %i,
      - 1.8760787864304147 + 0.12964631631004808 %i,
      - 1.8760787864309298 + 0.12964631630978829 %i,
      5.1514348342607263E-13 + 2.5979218776228663E-13 %i,
      - 1.8760787864304147 + 0.12964631631004808 %i,
      - 1.8760787864309298 + 0.12964631630978829 %i,
      5.1514348342607263E-13 + 2.5979218776228663E-13 %i,
      5.850875339774575E-13 + 4.8072656966269278E-14 %i]
     ,

     [1. + 2.0999999999999996 %i, - 2.0087641504710003 + 0.203459473833 %i,
      - 2.0087641504706006 + 0.20345947383285434 %i,
      - 2.0087641504712481 + 0.20345947383266205 %i,
      6.4748206796139129E-13 + 1.9229062786507711E-13 %i,
      - 2.0087641504706006 + 0.20345947383285434 %i,
      - 2.0087641504712481 + 0.20345947383266205 %i,
      6.4748206796139129E-13 + 1.9229062786507711E-13 %i,
      3.9968028886505635E-13 - 1.4566126083082054E-13 %i]
     ,

     [1. + 2.2000000000000002 %i,
      - 2.1425842092960004 + 0.28184565842599996 %i,
      - 2.1425842092954812 + 0.28184565842572962 %i,
      - 2.1425842092962588 + 0.28184565842564124 %i,
      7.7760020644745964E-13 + 8.8373752760162461E-14 %i,
      - 2.1425842092954812 + 0.28184565842572962 %i,
      - 2.1425842092962588 + 0.28184565842564124 %i,
      7.7760020644745964E-13 + 8.8373752760162461E-14 %i,
      5.191402863147232E-13 - 2.7033930649622562E-13 %i]
     ,

     [1. + 2.2999999999999998 %i,
      - 2.2774381922040003 + 0.36461404894999999 %i,
      - 2.2774381922033489 + 0.36461404895011906 %i,
      - 2.2774381922042544 + 0.36461404895017457 %i,
      9.0549789888427767E-13 - 5.5511151231257827E-14 %i,
      - 2.2774381922033489 + 0.36461404895011906 %i,
      - 2.2774381922042544 + 0.36461404895017457 %i,
      9.0549789888427767E-13 - 5.5511151231257827E-14 %i,
      6.5147887085004186E-13 + 1.1907141939104804E-13 %i]
     ,

     [1. + 2.3999999999999999 %i,
      - 2.4132381411840003 + 0.45158815244099998 %i,
      - 2.4132381411832058 + 0.45158815244041817 %i,
      - 2.4132381411842241 + 0.45158815244065842 %i,
      1.0182965581861936E-12 - 2.4025226252888388E-13 %i,
      - 2.4132381411832058 + 0.45158815244041817 %i,
      - 2.4132381411842241 + 0.45158815244065842 %i,
      1.0182965581861936E-12 - 2.4025226252888388E-13 %i,
      7.9447559642176202E-13 - 5.8181237605481329E-13 %i]
     ,

     [1. + 2.5 %i, - 2.549906842495 + 0.54260440585199998 %i,
      - 2.5499068424935154 + 0.54260440585197189 %i,
      - 2.5499068424946199 + 0.54260440585243641 %i,
      1.1044498648971057E-12 - 4.645173135031655E-13 %i,
      - 2.5499068424935154 + 0.54260440585197189 %i,
      - 2.5499068424946199 + 0.54260440585243641 %i,
      1.1044498648971057E-12 - 4.645173135031655E-13 %i,
      1.4845902285287593E-12 - 2.808864252301646E-14 %i]
     ,

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      5.1613824325613678E-11 - 3.4852121189032914E-11 %i,
      5.2015280971318134E-11 - 3.4937386317324126E-11 %i]
     ,

     [1. + 9.5999999999999996 %i, - 13.029824654789 + 12.889640203708 %i,
      - 13.029824654738606 + 12.889640203669721 %i,
      - 13.02982465478944 + 0.32326958934851951 %i,
      5.0834003673116968E-11 + 12.566370614321201 %i,
      - 13.029824654738606 + 12.889640203669721 %i,
      - 13.02982465478944 + 12.889640203707692 %i,
      5.0834003673116968E-11 - 3.7971403799019754E-11 %i,
      5.0393467176945705E-11 - 3.8278713532235997E-11 %i]
     ,

     [1. + 9.6999999999999993 %i, - 13.181722893951001 + 13.116425134665999 %i,
      - 13.181722893901259 + 13.116425134624947 %i,
      - 13.181722893951155 + 0.55005452030683832 %i,
      4.9896087261913635E-11 + 12.566370614318108 %i,
      - 13.181722893901259 + 13.116425134624947 %i,
      - 13.181722893951155 + 13.116425134666011 %i,
      4.9896087261913635E-11 - 4.106404105641559E-11 %i,
      4.9741544216885814E-11 - 4.1051606558539788E-11 %i]
     ,

     [1. + 9.8000000000000007 %i, - 13.333674276546999 + 13.344239181477 %i,
      - 13.33367427649825 + 13.344239181432879 %i,
      - 13.333674276547052 + 0.77786856711780805 %i,
      4.8801851448843081E-11 + 12.566370614315071 %i,
      - 13.33367427649825 + 13.344239181432879 %i,
      - 13.333674276547052 + 13.344239181476981 %i,
      4.8801851448843081E-11 - 4.4101611251790018E-11 %i,
      4.8748560743661074E-11 - 4.4121151177023421E-11 %i]
     ,

     [1. + 9.8999999999999986 %i, - 13.485677723495002 + 13.573071879455 %i,
      - 13.485677723446965 + 13.573071879407928 %i,
      - 13.485677723494529 + 1.0067012650958449 %i,
      4.7563730731781106E-11 + 12.566370614312083 %i,
      - 13.485677723446965 + 13.573071879407928 %i,
      - 13.485677723494529 + 13.573071879455018 %i,
      4.7563730731781106E-11 - 4.708944345566124E-11 %i,
      4.8036241651061573E-11 - 4.7071679887267237E-11 %i]
     ,

     [1. + 10. %i, - 13.637732188247 + 13.802912974230001 %i,
      - 13.637732188201092 + 13.802912974179876 %i,
      - 13.637732188247268 + 1.2365423598707301 %i,
      4.6176396040209511E-11 + 12.566370614309145 %i,
      - 13.637732188201092 + 13.802912974179876 %i,
      - 13.637732188247268 + 13.802912974229903 %i,
      4.6176396040209511E-11 - 5.0027537668029254E-11 %i,
      4.5908166157460073E-11 - 5.0125237294196268E-11 %i]
     ]
                                          Type: List List Complex DoubleFloat
--R 
--R   Compiling function lng2 with type Complex DoubleFloat -> Complex 
--R      DoubleFloat 
--R
--R   (12)
--R   [[1.,0.,0.,0.],
--R
--R     [1. + 0.10000000000000001 %i,
--R      - 8.1977805649999999E-3 - 5.7322940417E-2 %i,
--R      - 8.1977805654074309E-3 - 5.732294041672345E-2 %i,
--R      - 8.1977805654051359E-3 - 5.7322940416719675E-2 %i,
--R      - 2.2950391587173158E-15 - 3.7747582837255322E-15 %i,
--R      - 8.1977805654074309E-3 - 5.732294041672345E-2 %i,
--R      - 8.1977805654052105E-3 - 5.7322940416719675E-2 %i,
--R      - 2.2204460492503131E-15 - 3.7747582837255322E-15 %i,
--R      - 4.0743103335572073E-13 + 2.7654961654022259E-13 %i]
--R     ,
--R
--R     [1. + 0.20000000000000001 %i, - 3.2476292317999998E-2 - 0.112302222644 %i,
--R      - 3.2476292318133204E-2 - 0.11230222264419082 %i,
--R      - 3.2476292318128805E-2 - 0.11230222264418371 %i,
--R      - 4.3992587350771828E-15 - 7.1054273576010019E-15 %i,
--R      - 3.2476292318133204E-2 - 0.11230222264419082 %i,
--R      - 3.2476292318128763E-2 - 0.11230222264418371 %i,
--R      - 4.4408920985006262E-15 - 7.1054273576010019E-15 %i,
--R      - 1.3320594627330706E-13 - 1.9081958235744878E-13 %i]
--R     ,
--R
--R     [1. + 0.29999999999999999 %i, - 7.1946250899999994E-2 - 0.162820672168 %i,
--R      - 7.1946250899646902E-2 - 0.16282067216786528 %i,
--R      - 7.1946250899640213E-2 - 0.16282067216785573 %i,
--R      - 6.6890937233665682E-15 - 9.5479180117763462E-15 %i,
--R      - 7.1946250899646902E-2 - 0.16282067216786528 %i,
--R      - 7.1946250899640241E-2 - 0.16282067216785573 %i,
--R      - 6.6613381477509392E-15 - 9.5479180117763462E-15 %i,
--R      3.5309255519422322E-13 + 1.3472556403826275E-13 %i]
--R     ,
--R
--R     [1. + 0.40000000000000002 %i, - 0.125289374821 - 0.20715582631599999 %i,
--R      - 0.12528937482072333 - 0.20715582631567919 %i,
--R      - 0.12528937482070648 - 0.20715582631566853 %i,
--R      - 1.6847634398686751E-14 - 1.0658141036401503E-14 %i,
--R      - 0.12528937482072333 - 0.20715582631567919 %i,
--R      - 0.12528937482070646 - 0.20715582631566853 %i,
--R      - 1.6875389974302379E-14 - 1.0658141036401503E-14 %i,
--R      2.7666757773658901E-13 + 3.2079894296543898E-13 %i]
--R     ,
--R
--R     [1. + 0.5 %i, - 0.19094549918699999 - 0.244058298905 %i,
--R      - 0.19094549918680226 - 0.24405829890543784 %i,
--R      - 0.19094549918678008 - 0.24405829890542749 %i,
--R      - 2.2176704916887502E-14 - 1.0352829704629585E-14 %i,
--R      - 0.19094549918680226 - 0.24405829890543784 %i,
--R      - 0.19094549918678005 - 0.24405829890542752 %i,
--R      - 2.2204460492503131E-14 - 1.0325074129013956E-14 %i,
--R      1.9773072068574038E-13 - 4.3784420533654611E-13 %i]
--R     ,
--R
--R     [1. + 0.59999999999999998 %i,
--R      - 0.26729006821399998 - 0.27274381049099999 %i,
--R      - 0.26729006821416545 - 0.27274381049105989 %i,
--R      - 0.2672900682141322 - 0.27274381049105378 %i,
--R      - 3.3251179587523438E-14 - 6.106226635438361E-15 %i,
--R      - 0.26729006821416545 - 0.27274381049105989 %i,
--R      - 0.26729006821413215 - 0.27274381049105378 %i,
--R      - 3.3306690738754696E-14 - 6.106226635438361E-15 %i,
--R      - 1.6547874182037958E-13 - 5.9896532178527195E-14 %i]
--R     ,
--R
--R     [1. + 0.69999999999999996 %i,
--R      - 0.35276869086000001 - 0.29282635118700001 %i,
--R      - 0.35276869085965368 - 0.29282635118686051 %i,
--R      - 0.3527686908596116 - 0.29282635118686201 %i,
--R      - 4.2077452633293433E-14 + 1.4988010832439613E-15 %i,
--R      - 0.35276869085965368 - 0.29282635118686051 %i,
--R      - 0.35276869085961149 - 0.29282635118686196 %i,
--R      - 4.2188474935755949E-14 + 1.4432899320127035E-15 %i,
--R      3.4633407253181758E-13 + 1.3949952304415092E-13 %i]
--R     ,
--R
--R     [1. + 0.80000000000000004 %i, - 0.445978783549 - 0.30422560297599999 %i,
--R      - 0.4459787835488167 - 0.30422560297617007 %i,
--R      - 0.4459787835487648 - 0.30422560297618323 %i,
--R      - 5.1902926401226068E-14 + 1.3156142841808105E-14 %i,
--R      - 0.4459787835488167 - 0.30422560297617007 %i,
--R      - 0.44597878354876475 - 0.30422560297618317 %i,
--R      - 5.1958437552457326E-14 + 1.3100631690576847E-14 %i,
--R      1.8329782136561334E-13 - 1.7008616737257398E-13 %i]
--R     ,
--R
--R     [1. + 0.90000000000000002 %i,
--R      - 0.54570512860499998 - 0.30707437564200002 %i,
--R      - 0.54570512860503806 - 0.30707437564241957 %i,
--R      - 0.54570512860497633 - 0.30707437564245121 %i,
--R      - 6.1728400169158704E-14 + 3.1641356201816961E-14 %i,
--R      - 0.54570512860503806 - 0.30707437564241957 %i,
--R      - 0.54570512860497633 - 0.30707437564245121 %i,
--R      - 6.1728400169158704E-14 + 3.1641356201816961E-14 %i,
--R      - 3.8080649744642869E-14 - 4.1955328100584666E-13 %i]
--R     ,
--R
--R     [1. + %i, - 0.65092319930200004 - 0.30164032046799999 %i,
--R      - 0.65092319930192311 - 0.30164032046747735 %i,
--R      - 0.65092319930185472 - 0.30164032046753331 %i,
--R      - 6.8389738316909643E-14 + 5.595524044110789E-14 %i,
--R      - 0.65092319930192311 - 0.30164032046747735 %i,
--R      - 0.65092319930185472 - 0.30164032046753331 %i,
--R      - 6.8389738316909643E-14 + 5.595524044110789E-14 %i,
--R      7.6938455606523348E-14 + 5.2263748884229244E-13 %i]
--R     ,
--R
--R     [1. + 1.1000000000000001 %i,
--R      - 0.76078395884100003 - 0.28826661423900002 %i,
--R      - 0.76078395884088268 - 0.28826661423897093 %i,
--R      - 0.76078395884081551 - 0.28826661423905575 %i,
--R      - 6.7168492989821971E-14 + 8.482103908136196E-14 %i,
--R      - 0.76078395884088268 - 0.28826661423897093 %i,
--R      - 0.76078395884081562 - 0.28826661423905575 %i,
--R      - 6.7057470687359455E-14 + 8.482103908136196E-14 %i,
--R      1.1735057370287905E-13 + 2.9087843245179101E-14 %i]
--R     ,
--R
--R     [1. + 1.2 %i, - 0.87459046389499995 - 0.26733058058100001 %i,
--R      - 0.87459046389477102 - 0.2673305805810684 %i,
--R      - 0.87459046389471329 - 0.26733058058118808 %i,
--R      - 5.773159728050814E-14 + 1.1968204205459188E-13 %i,
--R      - 0.87459046389477102 - 0.2673305805810684 %i,
--R      - 0.87459046389471329 - 0.26733058058118808 %i,
--R      - 5.773159728050814E-14 + 1.1968204205459188E-13 %i,
--R      2.2892798767770728E-13 - 6.8389738316909643E-14 %i]
--R     ,
--R
--R     [1. + 1.3 %i, - 0.99177276695899996 - 0.239216784465 %i,
--R      - 0.99177276695938366 - 0.23921678446488515 %i,
--R      - 0.99177276695934224 - 0.23921678446504457 %i,
--R      - 4.1411318818518339E-14 + 1.5942802633617248E-13 %i,
--R      - 0.99177276695938366 - 0.23921678446488515 %i,
--R      - 0.99177276695934236 - 0.23921678446504457 %i,
--R      - 4.1300296516055823E-14 + 1.5942802633617248E-13 %i,
--R      - 3.836930773104541E-13 + 1.1485257189747244E-13 %i]
--R     ,
--R
--R     [1. + 1.3999999999999999 %i, - 1.1118645664260001 - 0.204300724149 %i,
--R      - 1.1118645664255413 - 0.20430072414906242 %i,
--R      - 1.1118645664255329 - 0.20430072414926384 %i,
--R      - 8.4376949871511897E-15 + 2.0142221224261903E-13 %i,
--R      - 1.1118645664255413 - 0.20430072414906242 %i,
--R      - 1.1118645664255329 - 0.20430072414926381 %i,
--R      - 8.4376949871511897E-15 + 2.013944566670034E-13 %i,
--R      4.5874415377511468E-13 - 6.2422289559549426E-14 %i]
--R     ,
--R
--R     [1. + 1.5 %i, - 1.234483051547 - 0.16293976948 %i,
--R      - 1.2344830515465768 - 0.16293976947988265 %i,
--R      - 1.2344830515466152 - 0.16293976948012379 %i,
--R      3.8413716652030416E-14 + 2.41140440948584E-13 %i,
--R      - 1.2344830515465768 - 0.16293976947988265 %i,
--R      - 1.234483051546615 - 0.16293976948012379 %i,
--R      3.8191672047105385E-14 + 2.41140440948584E-13 %i,
--R      4.2321701698710967E-13 + 1.1735057370287905E-13 %i]
--R     ,
--R
--R     [1. + 1.6000000000000001 %i, - 1.359312248465 - 0.115468793589 %i,
--R      - 1.3593122484650171 - 0.11546879358852835 %i,
--R      - 1.3593122484651154 - 0.11546879358880435 %i,
--R      9.8365759981788869E-14 + 2.7600144392181392E-13 %i,
--R      - 1.3593122484650171 - 0.11546879358852835 %i,
--R      - 1.3593122484651152 - 0.11546879358880435 %i,
--R      9.8143715376863838E-14 + 2.7600144392181392E-13 %i,
--R      - 1.7097434579227411E-14 + 4.7165049643638213E-13 %i]
--R     ,
--R
--R     [1. + 1.7 %i, - 1.486089612757 - 6.2198698328999998E-2 %i,
--R      - 1.4860896127570808 - 6.2198698328699953E-2 %i,
--R      - 1.4860896127572634 - 6.2198698328999047E-2 %i,
--R      1.8252066524837574E-13 + 2.9909408283401717E-13 %i,
--R      - 1.4860896127570808 - 6.2198698328699953E-2 %i,
--R      - 1.4860896127572634 - 6.2198698328999047E-2 %i,
--R      1.8252066524837574E-13 + 2.9909408283401717E-13 %i,
--R      - 8.0824236192711396E-14 + 3.0004471129885246E-13 %i]
--R     ,
--R
--R     [1. + 1.8 %i, - 1.6145953959999999 - 3.4166314770000001E-3 %i,
--R      - 1.6145953959992845 - 3.4166314766115313E-3 %i,
--R      - 1.6145953959995625 - 3.4166314769192847E-3 %i,
--R      2.779998453661392E-13 + 3.077533887452244E-13 %i,
--R      - 1.6145953959992845 - 3.4166314766115313E-3 %i,
--R      - 1.6145953959995625 - 3.4166314769192851E-3 %i,
--R      2.779998453661392E-13 + 3.0775382242609339E-13 %i,
--R      7.1542771706845087E-13 + 3.8846877103981825E-13 %i]
--R     ,
--R
--R     [1. + 1.8999999999999999 %i, - 1.744644276174 + 6.0612874295000001E-2 %i,
--R      - 1.7446442761733065 + 6.0612874295708608E-2 %i,
--R      - 1.7446442761736973 + 6.0612874295411963E-2 %i,
--R      3.907985046680551E-13 + 2.9664465328593792E-13 %i,
--R      - 1.7446442761733065 + 6.0612874295708608E-2 %i,
--R      - 1.7446442761736973 + 6.0612874295411956E-2 %i,
--R      3.907985046680551E-13 + 2.9665159217984183E-13 %i,
--R      6.9344530118087278E-13 + 7.0860678436091007E-13 %i]
--R     ,
--R
--R     [1. + 2. %i, - 1.876078786431 + 0.12964631631000001 %i,
--R      - 1.8760787864304147 + 0.12964631631004808 %i,
--R      - 1.8760787864309298 + 0.12964631630978829 %i,
--R      5.1514348342607263E-13 + 2.5979218776228663E-13 %i,
--R      - 1.8760787864304147 + 0.12964631631004808 %i,
--R      - 1.8760787864309298 + 0.12964631630978829 %i,
--R      5.1514348342607263E-13 + 2.5979218776228663E-13 %i,
--R      5.8530957858238253E-13 + 4.8072656966269278E-14 %i]
--R     ,
--R
--R     [1. + 2.1000000000000001 %i, - 2.0087641504709999 + 0.203459473833 %i,
--R      - 2.008764150470602 + 0.20345947383285479 %i,
--R      - 2.008764150471249 + 0.20345947383266247 %i,
--R      6.4703797875154123E-13 + 1.9231838344069274E-13 %i,
--R      - 2.008764150470602 + 0.20345947383285479 %i,
--R      - 2.008764150471249 + 0.2034594738326625 %i,
--R      6.4703797875154123E-13 + 1.9229062786507711E-13 %i,
--R      3.979039320256561E-13 - 1.4521717162097048E-13 %i]
--R     ,
--R
--R     [1. + 2.2000000000000002 %i,
--R      - 2.1425842092959999 + 0.28184565842600001 %i,
--R      - 2.1425842092954812 + 0.28184565842572962 %i,
--R      - 2.1425842092962588 + 0.28184565842564124 %i,
--R      7.7760020644745964E-13 + 8.8373752760162461E-14 %i,
--R      - 2.1425842092954812 + 0.28184565842572962 %i,
--R      - 2.1425842092962588 + 0.28184565842564124 %i,
--R      7.7760020644745964E-13 + 8.8373752760162461E-14 %i,
--R      5.1869619710487314E-13 - 2.7039481764745688E-13 %i]
--R     ,
--R
--R     [1. + 2.2999999999999998 %i,
--R      - 2.2774381922039999 + 0.36461404894999999 %i,
--R      - 2.2774381922033489 + 0.36461404895011906 %i,
--R      - 2.2774381922042544 + 0.36461404895017457 %i,
--R      9.0549789888427767E-13 - 5.5511151231257827E-14 %i,
--R      - 2.2774381922033489 + 0.36461404895011906 %i,
--R      - 2.2774381922042544 + 0.36461404895017457 %i,
--R      9.0549789888427767E-13 - 5.5511151231257827E-14 %i,
--R      6.510347816401918E-13 + 1.1907141939104804E-13 %i]
--R     ,
--R
--R     [1. + 2.3999999999999999 %i,
--R      - 2.4132381411839998 + 0.45158815244099998 %i,
--R      - 2.4132381411832058 + 0.45158815244041817 %i,
--R      - 2.4132381411842241 + 0.45158815244065842 %i,
--R      1.0182965581861936E-12 - 2.4025226252888388E-13 %i,
--R      - 2.4132381411832058 + 0.45158815244041817 %i,
--R      - 2.4132381411842241 + 0.45158815244065842 %i,
--R      1.0182965581861936E-12 - 2.4025226252888388E-13 %i,
--R      7.9403150721191196E-13 - 5.8181237605481329E-13 %i]
--R     ,
--R
--R     [1. + 2.5 %i, - 2.549906842495 + 0.54260440585199998 %i,
--R      - 2.5499068424935154 + 0.54260440585197189 %i,
--R      - 2.5499068424946199 + 0.54260440585243641 %i,
--R      1.1044498648971057E-12 - 4.645173135031655E-13 %i,
--R      - 2.5499068424935154 + 0.54260440585197189 %i,
--R      - 2.5499068424946199 + 0.54260440585243641 %i,
--R      1.1044498648971057E-12 - 4.645173135031655E-13 %i,
--R      1.4845902285287593E-12 - 2.808864252301646E-14 %i]
--R     ,
--R
--R     [1. + 2.6000000000000001 %i,
--R      - 2.6873761537499998 + 0.63751091904599999 %i,
--R      - 2.68737615374839 + 0.63751091904501767 %i,
--R      - 2.6873761537495495 + 0.63751091904574642 %i,
--R      1.1595169269185135E-12 - 7.2875039336395275E-13 %i,
--R      - 2.68737615374839 + 0.63751091904501767 %i,
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--R      5.3033133440294478E-11 + 12.566370614340155 %i,
--R      - 12.119616119228253 + 11.551156276183157 %i,
--R      - 12.119616119281286 + 11.551156276202175 %i,
--R      5.3033133440294478E-11 - 1.9017676322619081E-11 %i,
--R      5.2747139989151037E-11 - 1.8843593352357857E-11 %i]
--R     ,
--R
--R     [1. + 9.0999999999999996 %i, - 12.271170833867 + 11.771534118309001 %i,
--R      - 12.271170833814395 + 11.77153411828726 %i,
--R      - 12.271170833867483 - 0.79483649604973161 %i,
--R      5.3088200502315885E-11 + 12.566370614336991 %i,
--R      - 12.271170833814395 + 11.77153411828726 %i,
--R      - 12.271170833867483 + 11.771534118309441 %i,
--R      5.3088200502315885E-11 - 2.2181367853590928E-11 %i,
--R      5.2605031441999017E-11 - 2.1740831357419665E-11 %i]
--R     ,
--R
--R     [1. + 9.1999999999999993 %i, - 12.422785931281 + 11.993008666285 %i,
--R      - 12.422785931227907 + 11.993008666259376 %i,
--R      - 12.422785931280877 - 0.5733619480744393 %i,
--R      5.2970960950915469E-11 + 12.566370614333815 %i,
--R      - 12.422785931227907 + 11.993008666259376 %i,
--R      - 12.422785931280877 + 11.993008666284734 %i,
--R      5.2970960950915469E-11 - 2.5357493882438575E-11 %i,
--R      5.3093529572834086E-11 - 2.5623947408348613E-11 %i]
--R     ,
--R
--R     [1. + 9.3000000000000007 %i, - 12.574460105908001 + 12.215568046479 %i,
--R      - 12.574460105855573 + 12.215568046450077 %i,
--R      - 12.574460105908262 - 0.35080256788055886 %i,
--R      5.2688520213450829E-11 + 12.566370614330635 %i,
--R      - 12.574460105855573 + 12.215568046450077 %i,
--R      - 12.574460105908262 + 12.215568046478614 %i,
--R      5.2688520213450829E-11 - 2.8537172624965024E-11 %i,
--R      5.2427395758058992E-11 - 2.8922642059114878E-11 %i]
--R     ,
--R
--R     [1. + 9.4000000000000004 %i, - 12.726192094029001 + 12.43920063909 %i,
--R      - 12.726192093977144 + 12.43920063905834 %i,
--R      - 12.726192094029377 - 0.12716997526913024 %i,
--R      5.2233772862564365E-11 + 12.56637061432747 %i,
--R      - 12.726192093977144 + 12.43920063905834 %i,
--R      - 12.726192094029377 + 12.439200639090043 %i,
--R      5.2233772862564365E-11 - 3.170264051277627E-11 %i,
--R      5.1857185212611512E-11 - 3.1660007948630664E-11 %i]
--R     ,
--R
--R     [1. + 9.5 %i, - 12.877980672044 + 12.663895070128 %i,
--R      - 12.877980671991985 + 12.663895070093062 %i,
--R      - 12.877980672043599 + 9.7524455768741289E-2 %i,
--R      5.1613824325613678E-11 + 12.56637061432432 %i,
--R      - 12.877980671991985 + 12.663895070093062 %i,
--R      - 12.877980672043599 + 12.663895070127914 %i,
--R      5.1613824325613678E-11 - 3.4852121189032914E-11 %i,
--R      5.2015280971318134E-11 - 3.4937386317324126E-11 %i]
--R     ,
--R
--R     [1. + 9.5999999999999996 %i, - 13.029824654789 + 12.889640203708 %i,
--R      - 13.029824654738606 + 12.889640203669721 %i,
--R      - 13.02982465478944 + 0.32326958934851951 %i,
--R      5.0834003673116968E-11 + 12.566370614321201 %i,
--R      - 13.029824654738606 + 12.889640203669721 %i,
--R      - 13.02982465478944 + 12.889640203707692 %i,
--R      5.0834003673116968E-11 - 3.7971403799019754E-11 %i,
--R      5.0393467176945705E-11 - 3.8278713532235997E-11 %i]
--R     ,
--R
--R     [1. + 9.6999999999999993 %i, - 13.181722893950999 + 13.116425134666001 %i,
--R      - 13.181722893901259 + 13.116425134624947 %i,
--R      - 13.181722893951155 + 0.55005452030683832 %i,
--R      4.9896087261913635E-11 + 12.566370614318108 %i,
--R      - 13.181722893901259 + 13.116425134624947 %i,
--R      - 13.181722893951155 + 13.116425134666011 %i,
--R      4.9896087261913635E-11 - 4.106404105641559E-11 %i,
--R      4.9739767860046413E-11 - 4.1053382915379188E-11 %i]
--R     ,
--R
--R     [1. + 9.8000000000000007 %i, - 13.333674276547001 + 13.344239181477 %i,
--R      - 13.33367427649825 + 13.344239181432879 %i,
--R      - 13.333674276547052 + 0.77786856711780805 %i,
--R      4.8801851448843081E-11 + 12.566370614315071 %i,
--R      - 13.33367427649825 + 13.344239181432879 %i,
--R      - 13.333674276547052 + 13.344239181476981 %i,
--R      4.8801851448843081E-11 - 4.4101611251790018E-11 %i,
--R      4.8750337100500474E-11 - 4.4121151177023421E-11 %i]
--R     ,
--R
--R     [1. + 9.9000000000000004 %i, - 13.485677723495 + 13.573071879455 %i,
--R      - 13.485677723446969 + 13.573071879407928 %i,
--R      - 13.485677723494533 + 1.0067012650958465 %i,
--R      4.7563730731781106E-11 + 12.566370614312081 %i,
--R      - 13.485677723446969 + 13.573071879407928 %i,
--R      - 13.485677723494533 + 13.57307187945502 %i,
--R      4.7563730731781106E-11 - 4.709121981250064E-11 %i,
--R      4.8030912580543372E-11 - 4.7071679887267237E-11 %i]
--R     ,
--R
--R     [1. + 10. %i, - 13.637732188247 + 13.802912974230001 %i,
--R      - 13.637732188201092 + 13.802912974179876 %i,
--R      - 13.637732188247268 + 1.2365423598707301 %i,
--R      4.6176396040209511E-11 + 12.566370614309145 %i,
--R      - 13.637732188201092 + 13.802912974179876 %i,
--R      - 13.637732188247268 + 13.802912974229903 %i,
--R      4.6176396040209511E-11 - 5.0027537668029254E-11 %i,
--R      4.5908166157460073E-11 - 5.0125237294196268E-11 %i]
--R     ]
--R                                          Type: List List Complex DoubleFloat
--E 12
)spool 
 
Starts dribbling to ovar.output (2010/3/27, 18:30:34).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 5
ls:List Symbol:=['x,'a,'z]
 

   (1)  [x,a,z]
                                                            Type: List Symbol
--R 
--R
--R   (1)  [x,a,z]
--R                                                            Type: List Symbol
--E 1

--S 2 of 5
Z:=OVAR ls
 

   (2)  OrderedVariableList [x,a,z]
                                                                 Type: Domain
--R 
--R
--R   (2)  OrderedVariableList [x,a,z]
--R                                                                 Type: Domain
--E 2

--S 3 of 5
size()$Z
 

   (3)  3
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  3
--R                                                     Type: NonNegativeInteger
--E 3

--S 4 of 5
lv:=[index(i::PI)$Z for i in 1..size()$Z]
 
   Compiling function G1683 with type Integer -> Boolean 
   Compiling function G1697 with type NonNegativeInteger -> Boolean 

   (4)  [x,a,z]
                                       Type: List OrderedVariableList [x,a,z]
--R 
--I   Compiling function G1409 with type Integer -> Boolean 
--I   Compiling function G1573 with type NonNegativeInteger -> Boolean 
--R
--R   (4)  [x,a,z]
--R                                       Type: List OrderedVariableList [x,a,z]
--E 4

--S 5 of 5
sorted?(>,lv)
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5
)spool 
 
Starts dribbling to schaum20.output (2010/3/27, 18:38:20).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 56
aa:=integrate(tan(a*x),x)
 

                    2
        log(tan(a x)  + 1)
   (1)  ------------------
                2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2
--R        log(tan(a x)  + 1)
--R   (1)  ------------------
--R                2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 56
bb1:=-1/a*log(cos(a*x))
 

          log(cos(a x))
   (2)  - -------------
                a
                                                     Type: Expression Integer
--R
--R          log(cos(a x))
--R   (2)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 3 of 56
bb2:=1/a*log(sec(a*x))
 

        log(sec(a x))
   (3)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(sec(a x))
--R   (3)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 4 of 56
cc1:=aa-bb1
 

                    2
        log(tan(a x)  + 1) + 2log(cos(a x))
   (4)  -----------------------------------
                         2a
                                                     Type: Expression Integer
--R
--R                    2
--R        log(tan(a x)  + 1) + 2log(cos(a x))
--R   (4)  -----------------------------------
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 5 of 56
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (5)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (5)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 6 of 56
dd1:=tanrule cc1
 

                    2           2
            sin(a x)  + cos(a x)
        log(---------------------) + 2log(cos(a x))
                          2
                  cos(a x)
   (6)  -------------------------------------------
                             2a
                                                     Type: Expression Integer
--R
--R                    2           2
--R            sin(a x)  + cos(a x)
--R        log(---------------------) + 2log(cos(a x))
--R                          2
--R                  cos(a x)
--R   (6)  -------------------------------------------
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 7 of 56
ee1:=expandLog dd1
 

                    2           2
        log(sin(a x)  + cos(a x) )
   (7)  --------------------------
                    2a
                                                     Type: Expression Integer
--R
--R                    2           2
--R        log(sin(a x)  + cos(a x) )
--R   (7)  --------------------------
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 8 of 56
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (8)  sin(a)  + cos(a)  + %K == %K + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (8)  sin(a)  + cos(a)  + %K == %K + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 9 of 56      14:429 Schaums and Axiom agree
ff1:=sincossqrrule ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 56
aa:=integrate(tan(a*x)^2,x)
 

        tan(a x) - a x
   (1)  --------------
               a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        tan(a x) - a x
--R   (1)  --------------
--R               a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 56
bb:=tan(a*x)/a-x
 

        tan(a x) - a x
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        tan(a x) - a x
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 12 of 56     14:430 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 56
aa:=integrate(tan(a*x)^3,x)
 

                      2                2
        - log(tan(a x)  + 1) + tan(a x)
   (1)  --------------------------------
                       2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2                2
--R        - log(tan(a x)  + 1) + tan(a x)
--R   (1)  --------------------------------
--R                       2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 56
bb:=tan(a*x)^2/(2*a)+1/a*log(cos(a*x))
 

                                 2
        2log(cos(a x)) + tan(a x)
   (2)  --------------------------
                    2a
                                                     Type: Expression Integer
--R
--R                                 2
--R        2log(cos(a x)) + tan(a x)
--R   (2)  --------------------------
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 15 of 56
cc:=aa-bb
 

                      2
        - log(tan(a x)  + 1) - 2log(cos(a x))
   (3)  -------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                      2
--R        - log(tan(a x)  + 1) - 2log(cos(a x))
--R   (3)  -------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 16 of 56
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 17 of 56
dd:=tanrule cc
 

                      2           2
              sin(a x)  + cos(a x)
        - log(---------------------) - 2log(cos(a x))
                            2
                    cos(a x)
   (5)  ---------------------------------------------
                              2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R              sin(a x)  + cos(a x)
--R        - log(---------------------) - 2log(cos(a x))
--R                            2
--R                    cos(a x)
--R   (5)  ---------------------------------------------
--R                              2a
--R                                                     Type: Expression Integer
--E

--S 18 of 56
ee:=expandLog dd
 

                      2           2
          log(sin(a x)  + cos(a x) )
   (6)  - --------------------------
                      2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R          log(sin(a x)  + cos(a x) )
--R   (6)  - --------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 19 of 56
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (7)  sin(a)  + cos(a)  + %L == %L + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (7)  sin(a)  + cos(a)  + %L == %L + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20 of 56     14:431 Schaums and Axiom agree
ff:=sincossqrrule ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 21 of 56
aa:=integrate(tan(a*x)^n*sec(a*x)^2,x)
 

                        sin(a x)
                  n log(--------)
                        cos(a x)
        sin(a x)%e
   (1)  -------------------------
            (a n + a)cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        sin(a x)
--R                  n log(--------)
--R                        cos(a x)
--R        sin(a x)%e
--R   (1)  -------------------------
--R            (a n + a)cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 22 of 56
bb:=tan(a*x)^(n+1)/((n+1)*a)
 

                n + 1
        tan(a x)
   (2)  -------------
           a n + a
                                                     Type: Expression Integer
--R
--R                n + 1
--R        tan(a x)
--R   (2)  -------------
--R           a n + a
--R                                                     Type: Expression Integer
--E

--S 23 of 56
cc:=aa-bb
 

                        sin(a x)
                  n log(--------)
                        cos(a x)                    n + 1
        sin(a x)%e                - cos(a x)tan(a x)
   (3)  -------------------------------------------------
                        (a n + a)cos(a x)
                                                     Type: Expression Integer
--R
--R                        sin(a x)
--R                  n log(--------)
--R                        cos(a x)                    n + 1
--R        sin(a x)%e                - cos(a x)tan(a x)
--R   (3)  -------------------------------------------------
--R                        (a n + a)cos(a x)
--R                                                     Type: Expression Integer
--E

--S 24 of 56
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25 of 56
dd:=explog cc
 

                          n + 1            sin(a x) n
        - cos(a x)tan(a x)      + sin(a x)(--------)
                                           cos(a x)
   (5)  ---------------------------------------------
                      (a n + a)cos(a x)
                                                     Type: Expression Integer
--R
--R                          n + 1            sin(a x) n
--R        - cos(a x)tan(a x)      + sin(a x)(--------)
--R                                           cos(a x)
--R   (5)  ---------------------------------------------
--R                      (a n + a)cos(a x)
--R                                                     Type: Expression Integer
--E

--S 26 of 56
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (6)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (6)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27 of 56
ee:=tanrule dd
 

                   sin(a x) n + 1            sin(a x) n
        - cos(a x)(--------)      + sin(a x)(--------)
                   cos(a x)                  cos(a x)
   (7)  -----------------------------------------------
                       (a n + a)cos(a x)
                                                     Type: Expression Integer
--R
--R                   sin(a x) n + 1            sin(a x) n
--R        - cos(a x)(--------)      + sin(a x)(--------)
--R                   cos(a x)                  cos(a x)
--R   (7)  -----------------------------------------------
--R                       (a n + a)cos(a x)
--R                                                     Type: Expression Integer
--E

--S 28 of 56     14:432 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 29 of 56
aa:=integrate(sec(a*x)^2/tan(a*x),x)
 

              sin(a x)              2cos(a x)
        log(------------) - log(- ------------)
            cos(a x) + 1          cos(a x) + 1
   (1)  ---------------------------------------
                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)              2cos(a x)
--R        log(------------) - log(- ------------)
--R            cos(a x) + 1          cos(a x) + 1
--R   (1)  ---------------------------------------
--R                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 56
bb:=1/a*log(tan(a*x))
 

        log(tan(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(tan(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 31 of 56
cc:=aa-bb
 

                                sin(a x)              2cos(a x)
        - log(tan(a x)) + log(------------) - log(- ------------)
                              cos(a x) + 1          cos(a x) + 1
   (3)  ---------------------------------------------------------
                                    a
                                                     Type: Expression Integer
--R
--R                                sin(a x)              2cos(a x)
--R        - log(tan(a x)) + log(------------) - log(- ------------)
--R                              cos(a x) + 1          cos(a x) + 1
--R   (3)  ---------------------------------------------------------
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 32 of 56
dd:=expandLog cc
 

        - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2)
   (4)  ----------------------------------------------------------
                                     a
                                                     Type: Expression Integer
--R
--R        - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2)
--R   (4)  ----------------------------------------------------------
--R                                     a
--R                                                     Type: Expression Integer
--E

--S 33 of 56     14:433 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

          log(- 2)
   (5)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 2)
--R   (5)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 34 of 56
aa:=integrate(1/tan(a*x),x)
 

                      2
        - log(tan(a x)  + 1) + 2log(tan(a x))
   (1)  -------------------------------------
                          2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2
--R        - log(tan(a x)  + 1) + 2log(tan(a x))
--R   (1)  -------------------------------------
--R                          2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 35 of 56
bb:=1/a*log(sin(a*x))
 

        log(sin(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(sin(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 36 of 56
cc:=aa-bb
 

                      2
        - log(tan(a x)  + 1) + 2log(tan(a x)) - 2log(sin(a x))
   (3)  ------------------------------------------------------
                                  2a
                                                     Type: Expression Integer
--R
--R                      2
--R        - log(tan(a x)  + 1) + 2log(tan(a x)) - 2log(sin(a x))
--R   (3)  ------------------------------------------------------
--R                                  2a
--R                                                     Type: Expression Integer
--E

--S 37 of 56
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 38 of 56     14:435 Axiom cannot compute this integral
aa:=integrate(x*tan(a*x),x)
 

           x
         ++
   (1)   |   %T tan(%T a)d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %I tan(%I a)d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 39 of 56     14:436 Axiom cannot compute this integral
aa:=integrate(tan(a*x)/x,x)
 

           x
         ++  tan(%T a)
   (1)   |   --------- d%T
        ++       %T
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  tan(%I a)
--I   (1)   |   --------- d%I
--I        ++       %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 40 of 56
aa:=integrate(x*tan(a*x)^2,x)
 

                      2                         2 2
        - log(tan(a x)  + 1) + 2a x tan(a x) - a x
   (1)  -------------------------------------------
                              2
                            2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2                         2 2
--R        - log(tan(a x)  + 1) + 2a x tan(a x) - a x
--R   (1)  -------------------------------------------
--R                              2
--R                            2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 41 of 56
bb:=(x*tan(a*x))/a+1/a^2*log(cos(a*x))-x^2/2
 

                                          2 2
        2log(cos(a x)) + 2a x tan(a x) - a x
   (2)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                                          2 2
--R        2log(cos(a x)) + 2a x tan(a x) - a x
--R   (2)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 42 of 56
cc:=aa-bb
 

                      2
        - log(tan(a x)  + 1) - 2log(cos(a x))
   (3)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                      2
--R        - log(tan(a x)  + 1) - 2log(cos(a x))
--R   (3)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 43 of 56
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 44 of 56
dd:=tanrule cc
 

                      2           2
              sin(a x)  + cos(a x)
        - log(---------------------) - 2log(cos(a x))
                            2
                    cos(a x)
   (5)  ---------------------------------------------
                               2
                             2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R              sin(a x)  + cos(a x)
--R        - log(---------------------) - 2log(cos(a x))
--R                            2
--R                    cos(a x)
--R   (5)  ---------------------------------------------
--R                               2
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 45 of 56
ee:=expandLog dd
 

                      2           2
          log(sin(a x)  + cos(a x) )
   (6)  - --------------------------
                        2
                      2a
                                                     Type: Expression Integer
--R
--R                      2           2
--R          log(sin(a x)  + cos(a x) )
--R   (6)  - --------------------------
--R                        2
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 46 of 56
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (7)  sin(a)  + cos(a)  + %BB == %BB + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (7)  sin(a)  + cos(a)  + %R == %R + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 47 of 56     14:437 Schaums and Axiom agree
ff:=sincossqrrule ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 48 of 56
aa:=integrate(1/(p+q*tan(a*x)),x)
 

                        2
        - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p) + 2a p x
   (1)  --------------------------------------------------------
                                  2       2
                              2a q  + 2a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2
--R        - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p) + 2a p x
--R   (1)  --------------------------------------------------------
--R                                  2       2
--R                              2a q  + 2a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49 of 56
bb:=(p*x)/(p^2+q^2)+q/(a*(p^2+q^2))*log(q*sin(a*x)+p*cos(a*x))
 

        q log(q sin(a x) + p cos(a x)) + a p x
   (2)  --------------------------------------
                         2      2
                      a q  + a p
                                                     Type: Expression Integer
--R
--R        q log(q sin(a x) + p cos(a x)) + a p x
--R   (2)  --------------------------------------
--R                         2      2
--R                      a q  + a p
--R                                                     Type: Expression Integer
--E

--S 50 of 56
cc:=aa-bb
 

   (3)
                       2
       - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p)
     + 
       - 2q log(q sin(a x) + p cos(a x))
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                       2
--R       - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p)
--R     + 
--R       - 2q log(q sin(a x) + p cos(a x))
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 51 of 56
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 52 of 56
dd:=tanrule cc
 

   (5)
                       2           2
               sin(a x)  + cos(a x)
       - q log(---------------------) - 2q log(q sin(a x) + p cos(a x))
                             2
                     cos(a x)
     + 
              q sin(a x) + p cos(a x)
       2q log(-----------------------)
                      cos(a x)
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (5)
--R                       2           2
--R               sin(a x)  + cos(a x)
--R       - q log(---------------------) - 2q log(q sin(a x) + p cos(a x))
--R                             2
--R                     cos(a x)
--R     + 
--R              q sin(a x) + p cos(a x)
--R       2q log(-----------------------)
--R                      cos(a x)
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 53 of 56
ee:=expandLog dd
 

                        2           2
          q log(sin(a x)  + cos(a x) )
   (6)  - ----------------------------
                      2       2
                  2a q  + 2a p
                                                     Type: Expression Integer
--R
--R                        2           2
--R          q log(sin(a x)  + cos(a x) )
--R   (6)  - ----------------------------
--R                      2       2
--R                  2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 54 of 56
sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
 

              2         2
   (7)  sin(a)  + cos(a)  + %BC == %BC + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2         2
--I   (7)  sin(a)  + cos(a)  + %S == %S + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 55 of 56     14:438 Schaums and Axiom agree
ff:=sincossqrrule ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 56 of 56     14:439 Axiom cannot compute this integral
aa:=integrate(tan(a*x)^n,x)
 

           x
         ++           n
   (1)   |   tan(%T a) d%T
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   tan(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to Float.output (2010/3/27, 18:42:3).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 64
1.234
 

   (1)  1.234
                                                                  Type: Float
--R 
--R
--R   (1)  1.234
--R                                                                  Type: Float
--E 1

--S 2 of 64
1.234E2
 

   (2)  123.4
                                                                  Type: Float
--R 
--R
--R   (2)  123.4
--R                                                                  Type: Float
--E 2

--S 3 of 64
sqrt(1.2 + 2.3 / 3.4 ** 4.5)
 

   (3)  1.0996972790 671286226
                                                                  Type: Float
--R 
--R
--R   (3)  1.0996972790 671286226
--R                                                                  Type: Float
--E 3

--S 4 of 64
i := 3 :: Float
 

   (4)  3.0
                                                                  Type: Float
--R 
--R
--R   (4)  3.0
--R                                                                  Type: Float
--E 4

--S 5 of 64
i :: Integer
 

   (5)  3
                                                                Type: Integer
--R 
--R
--R   (5)  3
--R                                                                Type: Integer
--E 5

--S 6 of 64
i :: Fraction Integer 
 

   (6)  3
                                                       Type: Fraction Integer
--R 
--R
--R   (6)  3
--R                                                       Type: Fraction Integer
--E 6

--S 7 of 64
r := 3/7 :: Float 
 

   (7)  0.4285714285 7142857143
                                                                  Type: Float
--R 
--R
--R   (7)  0.4285714285 7142857143
--R                                                                  Type: Float
--E 7

--S 8 of 64
r :: Fraction Integer
 

        3
   (8)  -
        7
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (8)  -
--R        7
--R                                                       Type: Fraction Integer
--E 8

--S 9 of 64
r :: Integer
 
 
Daly Bug
   Cannot convert from type Float to Integer for value
   0.4285714285 7142857143

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Float to Integer for value
--R   0.4285714285 7142857143
--R
--E 9

--S 10 of 64
truncate 3.6
 

   (9)  3.0
                                                                  Type: Float
--R 
--R
--R   (9)  3.0
--R                                                                  Type: Float
--E 10

--S 11 of 64
round 3.6
 

   (10)  4.0
                                                                  Type: Float
--R 
--R
--R   (10)  4.0
--R                                                                  Type: Float
--E 11

--S 12 of 64
truncate(-3.6)
 

   (11)  - 3.0
                                                                  Type: Float
--R 
--R
--R   (11)  - 3.0
--R                                                                  Type: Float
--E 12

--S 13 of 64
round(-3.6)
 

   (12)  - 4.0
                                                                  Type: Float
--R 
--R
--R   (12)  - 4.0
--R                                                                  Type: Float
--E 13

--S 14 of 64
fractionPart 3.6
 

   (13)  0.6
                                                                  Type: Float
--R 
--R
--R   (13)  0.6
--R                                                                  Type: Float
--E 14

--S 15 of 64
digits 40 
 

   (14)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  20
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 64
sqrt 0.2
 

   (15)  0.4472135954 9995793928 1834733746 2552470881
                                                                  Type: Float
--R 
--R
--R   (15)  0.4472135954 9995793928 1834733746 2552470881
--R                                                                  Type: Float
--E 16

--S 17 of 64
pi()$Float
 

   (16)  3.1415926535 8979323846 2643383279 502884197
                                                                  Type: Float
--R 
--R
--R   (16)  3.1415926535 8979323846 2643383279 502884197
--R                                                                  Type: Float
--E 17

--S 18 of 64
digits 500
 

   (17)  40
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  40
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 64
pi()$Float
 

   (18)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
  1 830119491
                                                                  Type: Float
--R 
--R
--R   (18)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881097
--R  5 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 454326648
--R  2 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 917153643
--R  6 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 575959195
--R  3 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 891227938
--R  1 830119491
--R                                                                  Type: Float
--E 19

--S 20 of 64
digits 20
 

   (19)  500
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  500
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 64
outputSpacing 0; x := sqrt 0.2
 

   (20)  0.44721359549995793928
                                                                  Type: Float
--R 
--R
--R   (20)  0.44721359549995793928
--R                                                                  Type: Float
--E 21

--S 22 of 64
outputSpacing 5; x
 

   (21)  0.44721 35954 99957 93928
                                                                  Type: Float
--R 
--R
--R   (21)  0.44721 35954 99957 93928
--R                                                                  Type: Float
--E 22

--S 23 of 64
y := x/10**10
 

   (22)  0.44721 35954 99957 93928 E -10
                                                                  Type: Float
--R 
--R
--R   (22)  0.44721 35954 99957 93928 E -10
--R                                                                  Type: Float
--E 23

--S 24 of 64
outputFloating(); x 
 

   (23)  0.44721 35954 99957 93928 E 0
                                                                  Type: Float
--R 
--R
--R   (23)  0.44721 35954 99957 93928 E 0
--R                                                                  Type: Float
--E 24

--S 25 of 64
outputFixed(); y 
 

   (24)  0.00000 00000 44721 35954 99957 93928
                                                                  Type: Float
--R 
--R
--R   (24)  0.00000 00000 44721 35954 99957 93928
--R                                                                  Type: Float
--E 25

--S 26 of 64
outputFloating 2; y 
 

   (25)  0.45 E -10
                                                                  Type: Float
--R 
--R
--R   (25)  0.45 E -10
--R                                                                  Type: Float
--E 26

--S 27 of 64
outputFixed 2; x 
 

   (26)  0.45
                                                                  Type: Float
--R 
--R
--R   (26)  0.45
--R                                                                  Type: Float
--E 27

--S 28 of 64
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 64
a: Matrix Fraction Integer := matrix [ [1/(i+j+1) for j in 0..9] for i in 0..9]
 

         +    1   1   1   1   1   1   1   1    1+
         |1   -   -   -   -   -   -   -   -   --|
         |    2   3   4   5   6   7   8   9   10|
         |                                      |
         |1   1   1   1   1   1   1   1    1   1|
         |-   -   -   -   -   -   -   -   --  --|
         |2   3   4   5   6   7   8   9   10  11|
         |                                      |
         |1   1   1   1   1   1   1    1   1   1|
         |-   -   -   -   -   -   -   --  --  --|
         |3   4   5   6   7   8   9   10  11  12|
         |                                      |
         |1   1   1   1   1   1    1   1   1   1|
         |-   -   -   -   -   -   --  --  --  --|
         |4   5   6   7   8   9   10  11  12  13|
         |                                      |
         |1   1   1   1   1    1   1   1   1   1|
         |-   -   -   -   -   --  --  --  --  --|
         |5   6   7   8   9   10  11  12  13  14|
   (28)  |                                      |
         |1   1   1   1    1   1   1   1   1   1|
         |-   -   -   -   --  --  --  --  --  --|
         |6   7   8   9   10  11  12  13  14  15|
         |                                      |
         |1   1   1    1   1   1   1   1   1   1|
         |-   -   -   --  --  --  --  --  --  --|
         |7   8   9   10  11  12  13  14  15  16|
         |                                      |
         |1   1    1   1   1   1   1   1   1   1|
         |-   -   --  --  --  --  --  --  --  --|
         |8   9   10  11  12  13  14  15  16  17|
         |                                      |
         |1    1   1   1   1   1   1   1   1   1|
         |-   --  --  --  --  --  --  --  --  --|
         |9   10  11  12  13  14  15  16  17  18|
         |                                      |
         | 1   1   1   1   1   1   1   1   1   1|
         |--  --  --  --  --  --  --  --  --  --|
         +10  11  12  13  14  15  16  17  18  19+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +    1   1   1   1   1   1   1   1    1+
--R         |1   -   -   -   -   -   -   -   -   --|
--R         |    2   3   4   5   6   7   8   9   10|
--R         |                                      |
--R         |1   1   1   1   1   1   1   1    1   1|
--R         |-   -   -   -   -   -   -   -   --  --|
--R         |2   3   4   5   6   7   8   9   10  11|
--R         |                                      |
--R         |1   1   1   1   1   1   1    1   1   1|
--R         |-   -   -   -   -   -   -   --  --  --|
--R         |3   4   5   6   7   8   9   10  11  12|
--R         |                                      |
--R         |1   1   1   1   1   1    1   1   1   1|
--R         |-   -   -   -   -   -   --  --  --  --|
--R         |4   5   6   7   8   9   10  11  12  13|
--R         |                                      |
--R         |1   1   1   1   1    1   1   1   1   1|
--R         |-   -   -   -   -   --  --  --  --  --|
--R         |5   6   7   8   9   10  11  12  13  14|
--R   (28)  |                                      |
--R         |1   1   1   1    1   1   1   1   1   1|
--R         |-   -   -   -   --  --  --  --  --  --|
--R         |6   7   8   9   10  11  12  13  14  15|
--R         |                                      |
--R         |1   1   1    1   1   1   1   1   1   1|
--R         |-   -   -   --  --  --  --  --  --  --|
--R         |7   8   9   10  11  12  13  14  15  16|
--R         |                                      |
--R         |1   1    1   1   1   1   1   1   1   1|
--R         |-   -   --  --  --  --  --  --  --  --|
--R         |8   9   10  11  12  13  14  15  16  17|
--R         |                                      |
--R         |1    1   1   1   1   1   1   1   1   1|
--R         |-   --  --  --  --  --  --  --  --  --|
--R         |9   10  11  12  13  14  15  16  17  18|
--R         |                                      |
--R         | 1   1   1   1   1   1   1   1   1   1|
--R         |--  --  --  --  --  --  --  --  --  --|
--R         +10  11  12  13  14  15  16  17  18  19+
--R                                                Type: Matrix Fraction Integer
--E 29

--S 30 of 64
d:= determinant a
 

                                   1
   (29)  -----------------------------------------------------
         46206893947914691316295628839036278726983680000000000
                                                       Type: Fraction Integer
--R 
--R
--R                                   1
--R   (29)  -----------------------------------------------------
--R         46206893947914691316295628839036278726983680000000000
--R                                                       Type: Fraction Integer
--E 30

--S 31 of 64
d :: Float
 

   (30)  0.21641 79226 43149 18691 E -52
                                                                  Type: Float
--R 
--R
--R   (30)  0.21641 79226 43149 18691 E -52
--R                                                                  Type: Float
--E 31

--S 32 of 64
b: Matrix DoubleFloat := matrix [ [1/(i+j+1$DoubleFloat) for j in 0..9] for i in 0..9]
 

   (31)
   [
     [1., 0.5, 0.33333333333333331, 0.25, 0.20000000000000001,
      0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111,
      0.10000000000000001]
     ,

     [0.5, 0.33333333333333331, 0.25, 0.20000000000000001, 0.16666666666666666,
      0.14285714285714285, 0.125, 0.1111111111111111, 0.10000000000000001,
      9.0909090909090912E-2]
     ,

     [0.33333333333333331, 0.25, 0.20000000000000001, 0.16666666666666666,
      0.14285714285714285, 0.125, 0.1111111111111111, 0.10000000000000001,
      9.0909090909090912E-2, 8.3333333333333329E-2]
     ,

     [0.25, 0.20000000000000001, 0.16666666666666666, 0.14285714285714285,
      0.125, 0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
      8.3333333333333329E-2, 7.6923076923076927E-2]
     ,

     [0.20000000000000001, 0.16666666666666666, 0.14285714285714285, 0.125,
      0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
      8.3333333333333329E-2, 7.6923076923076927E-2, 7.1428571428571425E-2]
     ,

     [0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111,
      0.10000000000000001, 9.0909090909090912E-2, 8.3333333333333329E-2,
      7.6923076923076927E-2, 7.1428571428571425E-2, 6.6666666666666666E-2]
     ,

     [0.14285714285714285, 0.125, 0.1111111111111111, 0.10000000000000001,
      9.0909090909090912E-2, 8.3333333333333329E-2, 7.6923076923076927E-2,
      7.1428571428571425E-2, 6.6666666666666666E-2, 6.25E-2]
     ,

     [0.125, 0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
      8.3333333333333329E-2, 7.6923076923076927E-2, 7.1428571428571425E-2,
      6.6666666666666666E-2, 6.25E-2, 5.8823529411764705E-2]
     ,

     [0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
      8.3333333333333329E-2, 7.6923076923076927E-2, 7.1428571428571425E-2,
      6.6666666666666666E-2, 6.25E-2, 5.8823529411764705E-2,
      5.5555555555555552E-2]
     ,

     [0.10000000000000001, 9.0909090909090912E-2, 8.3333333333333329E-2,
      7.6923076923076927E-2, 7.1428571428571425E-2, 6.6666666666666666E-2,
      6.25E-2, 5.8823529411764705E-2, 5.5555555555555552E-2,
      5.2631578947368418E-2]
     ]
                                                     Type: Matrix DoubleFloat
--R 
--R
--R   (31)
--R   [
--R     [1., 0.5, 0.33333333333333331, 0.25, 0.20000000000000001,
--R      0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111,
--R      0.10000000000000001]
--R     ,
--R
--R     [0.5, 0.33333333333333331, 0.25, 0.20000000000000001, 0.16666666666666666,
--R      0.14285714285714285, 0.125, 0.1111111111111111, 0.10000000000000001,
--R      9.0909090909090912E-2]
--R     ,
--R
--R     [0.33333333333333331, 0.25, 0.20000000000000001, 0.16666666666666666,
--R      0.14285714285714285, 0.125, 0.1111111111111111, 0.10000000000000001,
--R      9.0909090909090912E-2, 8.3333333333333329E-2]
--R     ,
--R
--R     [0.25, 0.20000000000000001, 0.16666666666666666, 0.14285714285714285,
--R      0.125, 0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
--R      8.3333333333333329E-2, 7.6923076923076927E-2]
--R     ,
--R
--R     [0.20000000000000001, 0.16666666666666666, 0.14285714285714285, 0.125,
--R      0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
--R      8.3333333333333329E-2, 7.6923076923076927E-2, 7.1428571428571425E-2]
--R     ,
--R
--R     [0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111,
--R      0.10000000000000001, 9.0909090909090912E-2, 8.3333333333333329E-2,
--R      7.6923076923076927E-2, 7.1428571428571425E-2, 6.6666666666666666E-2]
--R     ,
--R
--R     [0.14285714285714285, 0.125, 0.1111111111111111, 0.10000000000000001,
--R      9.0909090909090912E-2, 8.3333333333333329E-2, 7.6923076923076927E-2,
--R      7.1428571428571425E-2, 6.6666666666666666E-2, 6.25E-2]
--R     ,
--R
--R     [0.125, 0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
--R      8.3333333333333329E-2, 7.6923076923076927E-2, 7.1428571428571425E-2,
--R      6.6666666666666666E-2, 6.25E-2, 5.8823529411764705E-2]
--R     ,
--R
--R     [0.1111111111111111, 0.10000000000000001, 9.0909090909090912E-2,
--R      8.3333333333333329E-2, 7.6923076923076927E-2, 7.1428571428571425E-2,
--R      6.6666666666666666E-2, 6.25E-2, 5.8823529411764705E-2,
--R      5.5555555555555552E-2]
--R     ,
--R
--R     [0.10000000000000001, 9.0909090909090912E-2, 8.3333333333333329E-2,
--R      7.6923076923076927E-2, 7.1428571428571425E-2, 6.6666666666666666E-2,
--R      6.25E-2, 5.8823529411764705E-2, 5.5555555555555552E-2,
--R      5.2631578947368418E-2]
--R     ]
--R                                                     Type: Matrix DoubleFloat
--E 32

--S 33 of 64
determinant b
 

   (32)  2.1643677945721411E-53
                                                            Type: DoubleFloat
--R 
--R
--R   (32)  2.1643677945721411E-53
--R                                                            Type: DoubleFloat
--E 33

--S 34 of 64
digits 40 
 

   (33)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (33)  20
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 64
c: Matrix Float := matrix [ [1/(i+j+1$Float) for j in 0..9] for i in 0..9]
 

   (34)
   [
     [1.0, 0.5, 0.33333 33333 33333 33333 33333 33333 33333 33333, 0.25, 0.2,
      0.16666 66666 66666 66666 66666 66666 66666 66667,
      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1]
     ,

     [0.5, 0.33333 33333 33333 33333 33333 33333 33333 33333, 0.25, 0.2,
      0.16666 66666 66666 66666 66666 66666 66666 66667,
      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1]
     ,

     [0.33333 33333 33333 33333 33333 33333 33333 33333, 0.25, 0.2,
      0.16666 66666 66666 66666 66666 66666 66666 66667,
      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4]
     ,

     [0.25, 0.2, 0.16666 66666 66666 66666 66666 66666 66666 66667,
      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2]
     ,

     [0.2, 0.16666 66666 66666 66666 66666 66666 66666 66667,
      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
      0.07142 85714 28571 42857 14285 71428 57142 85714 3]
     ,

     [0.16666 66666 66666 66666 66666 66666 66666 66667,
      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
      0.06666 66666 66666 66666 66666 66666 66666 66666 7]
     ,

     [0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625]
     ,

     [0.125, 0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625,
      0.05882 35294 11764 70588 23529 41176 47058 82352 9]
     ,

     [0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625,
      0.05882 35294 11764 70588 23529 41176 47058 82352 9,
      0.05555 55555 55555 55555 55555 55555 55555 55555 6]
     ,

     [0.1, 0.09090 90909 09090 90909 09090 90909 09090 90909 1,
      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625,
      0.05882 35294 11764 70588 23529 41176 47058 82352 9,
      0.05555 55555 55555 55555 55555 55555 55555 55555 6,
      0.05263 15789 47368 42105 26315 78947 36842 10526 3]
     ]
                                                           Type: Matrix Float
--R 
--R
--R   (34)
--R   [
--R     [1.0, 0.5, 0.33333 33333 33333 33333 33333 33333 33333 33333, 0.25, 0.2,
--R      0.16666 66666 66666 66666 66666 66666 66666 66667,
--R      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1]
--R     ,
--R
--R     [0.5, 0.33333 33333 33333 33333 33333 33333 33333 33333, 0.25, 0.2,
--R      0.16666 66666 66666 66666 66666 66666 66666 66667,
--R      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1]
--R     ,
--R
--R     [0.33333 33333 33333 33333 33333 33333 33333 33333, 0.25, 0.2,
--R      0.16666 66666 66666 66666 66666 66666 66666 66667,
--R      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4]
--R     ,
--R
--R     [0.25, 0.2, 0.16666 66666 66666 66666 66666 66666 66666 66667,
--R      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2]
--R     ,
--R
--R     [0.2, 0.16666 66666 66666 66666 66666 66666 66666 66667,
--R      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
--R      0.07142 85714 28571 42857 14285 71428 57142 85714 3]
--R     ,
--R
--R     [0.16666 66666 66666 66666 66666 66666 66666 66667,
--R      0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
--R      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
--R      0.06666 66666 66666 66666 66666 66666 66666 66666 7]
--R     ,
--R
--R     [0.14285 71428 57142 85714 28571 42857 14285 71429, 0.125,
--R      0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
--R      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
--R      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625]
--R     ,
--R
--R     [0.125, 0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
--R      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
--R      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625,
--R      0.05882 35294 11764 70588 23529 41176 47058 82352 9]
--R     ,
--R
--R     [0.11111 11111 11111 11111 11111 11111 11111 11111, 0.1,
--R      0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
--R      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
--R      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625,
--R      0.05882 35294 11764 70588 23529 41176 47058 82352 9,
--R      0.05555 55555 55555 55555 55555 55555 55555 55555 6]
--R     ,
--R
--R     [0.1, 0.09090 90909 09090 90909 09090 90909 09090 90909 1,
--R      0.08333 33333 33333 33333 33333 33333 33333 33333 4,
--R      0.07692 30769 23076 92307 69230 76923 07692 30769 2,
--R      0.07142 85714 28571 42857 14285 71428 57142 85714 3,
--R      0.06666 66666 66666 66666 66666 66666 66666 66666 7, 0.0625,
--R      0.05882 35294 11764 70588 23529 41176 47058 82352 9,
--R      0.05555 55555 55555 55555 55555 55555 55555 55555 6,
--R      0.05263 15789 47368 42105 26315 78947 36842 10526 3]
--R     ]
--R                                                           Type: Matrix Float
--E 35

--S 36 of 64
determinant c
 

   (35)  0.21641 79226 43149 18690 60594 98362 26174 36159 E -52
                                                                  Type: Float
--R 
--R
--R   (35)  0.21641 79226 43149 18690 60594 98362 26174 36159 E -52
--R                                                                  Type: Float
--E 36

--S 37 of 64
digits 20
 

   (36)  40
                                                        Type: PositiveInteger
--R 
--R
--R   (36)  40
--R                                                        Type: PositiveInteger
--E 37

)clear all
 

--S 38 of 64
outputFixed()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 38

--S 39 of 64
a:=3.0
 

   (2)  3.0
                                                                  Type: Float
--R 
--R
--R   (2)  3.0
--R                                                                  Type: Float
--E 39

--S 40 of 64
b:=3.1
 

   (3)  3.1
                                                                  Type: Float
--R 
--R
--R   (3)  3.1
--R                                                                  Type: Float
--E 40

--S 41 of 64
c:=numeric pi()
 

   (4)  3.14159 26535 89793 2385
                                                                  Type: Float
--R 
--R
--R   (4)  3.14159 26535 89793 2385
--R                                                                  Type: Float
--E 41

--S 42 of 64
d:=0.0
 

   (5)  0.0
                                                                  Type: Float
--R 
--R
--R   (5)  0.0
--R                                                                  Type: Float
--E 42

--S 43 of 64
outputFixed 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 43

--S 44 of 64
a
 

   (7)  3.00
                                                                  Type: Float
--R 
--R
--R   (7)  3.00
--R                                                                  Type: Float
--E 44

--S 45 of 64
b
 

   (8)  3.10
                                                                  Type: Float
--R 
--R
--R   (8)  3.10
--R                                                                  Type: Float
--E 45

--S 46 of 64
c
 

   (9)  3.14
                                                                  Type: Float
--R 
--R
--R   (9)  3.14
--R                                                                  Type: Float
--E 46

--S 47 of 64
d
 

   (10)  0.00
                                                                  Type: Float
--R 
--R
--R   (10)  0.00
--R                                                                  Type: Float
--E 47

--S 48 of 64
outputFixed 0
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 48

--S 49 of 64
a
 

   (12)  3.0
                                                                  Type: Float
--R 
--R
--R   (12)  3.0
--R                                                                  Type: Float
--E 49

--S 50 of 64
b
 

   (13)  3.
                                                                  Type: Float
--R 
--R
--R   (13)  3.
--R                                                                  Type: Float
--E 50

--S 51 of 64
c
 

   (14)  3.
                                                                  Type: Float
--R 
--R
--R   (14)  3.
--R                                                                  Type: Float
--E 51

--S 52 of 64
31.1
 

   (15)  31.
                                                                  Type: Float
--R 
--R
--R   (15)  31.
--R                                                                  Type: Float
--E 52

--S 53 of 64
310.1
 

   (16)  310.
                                                                  Type: Float
--R 
--R
--R   (16)  310.
--R                                                                  Type: Float
--E 53

--S 54 of 64
d
 

   (17)  0.0
                                                                  Type: Float
--R 
--R
--R   (17)  0.0
--R                                                                  Type: Float
--E 54

--S 55 of 64
outputFixed(0)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 55

--S 56 of 64
1.1
 

   (19)  1.
                                                                  Type: Float
--R
--R   (19)  1.
--R                                                                  Type: Float
--E 56

--S 57 of 64
3111.1
 

   (20)  3111.
                                                                  Type: Float
--R
--R   (20)  3111.
--R                                                                  Type: Float
--E 57

--S 58 of 64
1234567890.1
 

   (21)  12345 67890.
                                                                  Type: Float
--R
--R   (21)  12345 67890.
--R                                                                  Type: Float
--E 58

--S 59 of 64
outputFixed(12)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 59

--S 60 of 64
1234567890.1
 

   (23)  12345 67890.09999 99999 99
                                                                  Type: Float
--R
--R   (23)  12345 67890.09999 99999 99
--R                                                                  Type: Float
--E 60

--S 61 of 64
outputFixed(15)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 61

--S 62 of 64
1234567890.1
 

   (25)  12345 67890.09999 99999 98545
                                                                  Type: Float
--R
--R   (25)  12345 67890.09999 99999 98545
--R                                                                  Type: Float
--E 62

--S 63 of 64
outputFixed(2)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 63

--S 64 of 64
1234567890.1
 

   (27)  12345 67890.10
                                                                  Type: Float
--R
--R   (27)  12345 67890.10
--R                                                                  Type: Float
--E 64

)spool
 
Starts dribbling to space3.output (2010/3/27, 18:40:58).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 1

--S 2 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 2

--S 3 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 3

--S 4 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 4

--S 5 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 5

--S 6 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 6

--S 7 of 185
closedCurve(space,[[1,1,1],[1,0,0],[0,0,0],[0,1,1]])
 

   (7)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 7

--S 8 of 185
cspace := closedCurve([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (8)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 8

--S 9 of 185
closedCurve cspace
 

   (9)  [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (9)  [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 9

)clear all
 

--S 10 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 10

--S 11 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 11

--S 12 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 12

--S 13 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 13

--S 14 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 14

--S 15 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 15

--S 16 of 185
closedCurve? space
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 185
curve(space,[p0,p1,p2,p3])
 

   (8)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 17

--S 18 of 185
point(space,p0)
 

   (9)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 18

--S 19 of 185
components(space)
 

   (10)
   [3-Space with 1 component,3-Space with 1 component,3-Space with 1 component]
                                            Type: List ThreeSpace DoubleFloat
--R 
--R
--R   (10)
--R   [3-Space with 1 component,3-Space with 1 component,3-Space with 1 component]
--R                                            Type: List ThreeSpace DoubleFloat
--E 19

--S 20 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (11)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 20

--S 21 of 185
curve(space1,[p0,p1,p2,p3])
 

   (12)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (12)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 21

--S 22 of 185
point(space1,p0)
 

   (13)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 22

--S 23 of 185
space2 := point(p0)$(ThreeSpace DoubleFloat)
 

   (14)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (14)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 23

--S 24 of 185
space3 := curve[p0,p1,p2]$(ThreeSpace DoubleFloat)
 

   (15)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 24

--S 25 of 185
composite [space1,space2,space3]
 

   (16)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 25

--S 26 of 185
curve(space,[p0,p1,p2,p3])
 

   (17)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (17)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 26

--S 27 of 185
point(space,p0)
 

   (18)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (18)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 27

--S 28 of 185
point(space,p1)
 

   (19)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (19)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 28

--S 29 of 185
closedCurve(space,[p0,p1,p2])
 

   (20)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (20)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 29

--S 30 of 185
composite [space1,space2,space3]
 

   (21)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (21)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 30

--S 31 of 185
composites(space)
 

   (22)  []
                                            Type: List ThreeSpace DoubleFloat
--R 
--R
--R   (22)  []
--R                                            Type: List ThreeSpace DoubleFloat
--E 31

--S 32 of 185
curve(space,[p0,p1,p2,p3])
 

   (23)  3-Space with 8 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (23)  3-Space with 8 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 32

--S 33 of 185
point(space,p0)
 

   (24)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (24)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 33

--S 34 of 185
space4 := copy space
 

   (25)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (25)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 34

--S 35 of 185
curve(space,[p0,p1,p2])
 

   (26)  3-Space with 10 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (26)  3-Space with 10 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 35

--S 36 of 185
point(space,p0)
 

   (27)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (27)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 36

--S 37 of 185
sub := subspace(space)
 

   (28)  3-Space with depth of 3 and 11 components
                                                Type: SubSpace(3,DoubleFloat)
--R 
--R
--R   (28)  3-Space with depth of 3 and 11 components
--R                                                Type: SubSpace(3,DoubleFloat)
--E 37

--S 38 of 185
spNew := create3Space(sub)$(ThreeSpace DoubleFloat)
 

   (29)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (29)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 38

--S 39 of 185
curve(space,[p0,p1,p2,p3])
 

   (30)  3-Space with 12 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (30)  3-Space with 12 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 39

--S 40 of 185
curve(space,[[1,1,1],[1,0,0],[0,0,0],[0,1,1]])
 

   (31)  3-Space with 13 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (31)  3-Space with 13 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 40

--S 41 of 185
cspace := curve([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (32)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (32)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 41

--S 42 of 185
curve cspace
 

   (33)  [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (33)  [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 42

)clear all
 

--S 43 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 43

--S 44 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 44

--S 45 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 45

--S 46 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 46

--S 47 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 47

--S 48 of 185
curve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 48

--S 49 of 185
curve? space
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 49

)clear all
 

--S 50 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 50

--S 51 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 51

--S 52 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 52

--S 53 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 53

--S 54 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 54

--S 55 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 55

--S 56 of 185
curve(space,[p0,p1,p2,p3])
 

   (7)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 56

--S 57 of 185
point(space,p0)
 

   (8)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 57

--S 58 of 185
point(space,p3)
 

   (9)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 58

--S 59 of 185
polygon(space,[p0,p1,p3])
 

   (10)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 59

--S 60 of 185
polygon(space,[p0,p2,p3])
 

   (11)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 60

--S 61 of 185
lllip(space)
 

   (12)  [[[1,2,3,4]],[[5,6,7,8]],[[9]],[[10]],[[11],[12,13]],[[14],[15,16]]]
                                      Type: List List List NonNegativeInteger
--R 
--R
--R   (12)  [[[1,2,3,4]],[[5,6,7,8]],[[9]],[[10]],[[11],[12,13]],[[14],[15,16]]]
--R                                      Type: List List List NonNegativeInteger
--E 61

--S 62 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (13)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 62

--S 63 of 185
curve(space,[p0,p1,p2,p3])
 

   (14)  3-Space with 8 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (14)  3-Space with 8 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 63

--S 64 of 185
point(space,p0)
 

   (15)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 64

--S 65 of 185
polygon(space,[p0,p1,p3])
 

   (16)  3-Space with 10 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 10 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 65

--S 66 of 185
llprop(space)
 

   (17)
   [[Component is closed, not solid], [Component is not closed, not solid],
    [Component is not closed, not solid], [Component is not closed, not solid],
    [Component is not closed, not solid,Component is not closed, not solid],
    [Component is not closed, not solid,Component is not closed, not solid],
    [Component is closed, not solid], [Component is not closed, not solid],
    [Component is not closed, not solid],
    [Component is not closed, not solid,Component is not closed, not solid]]
                                    Type: List List SubSpaceComponentProperty
--R 
--R
--R   (17)
--R   [[Component is closed, not solid], [Component is not closed, not solid],
--R    [Component is not closed, not solid], [Component is not closed, not solid],
--R    [Component is not closed, not solid,Component is not closed, not solid],
--R    [Component is not closed, not solid,Component is not closed, not solid],
--R    [Component is closed, not solid], [Component is not closed, not solid],
--R    [Component is not closed, not solid],
--R    [Component is not closed, not solid,Component is not closed, not solid]]
--R                                    Type: List List SubSpaceComponentProperty
--E 66

--S 67 of 185
lprop(space)
 

   (18)
   [Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid, Component is not closed, not solid]
                                         Type: List SubSpaceComponentProperty
--R 
--R
--R   (18)
--R   [Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid, Component is not closed, not solid]
--R                                         Type: List SubSpaceComponentProperty
--E 67

--S 68 of 185
closedCurve(space,[p0,p1,p2,p3])
 

   (19)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (19)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 68

--S 69 of 185
curve(space,[p0,p1,p2,p3])
 

   (20)  3-Space with 12 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (20)  3-Space with 12 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 69

--S 70 of 185
point(space,p0)
 

   (21)  3-Space with 13 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (21)  3-Space with 13 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 70

--S 71 of 185
polygon(space,[p0,p1,p3])
 

   (22)  3-Space with 14 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (22)  3-Space with 14 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 71

--S 72 of 185
lp(space)
 

   (23)
   [[1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
    [0.,1.,1.], [1.,1.,1.], [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.],
    [1.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.],
    [1.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,1.,1.]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (23)
--R   [[1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,1.,1.], [1.,1.,1.], [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.],
--R    [1.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.],
--R    [0.,0.,0.], [0.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,0.,0.], [0.,1.,1.],
--R    [1.,1.,1.], [1.,1.,1.], [1.,0.,0.], [0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 72

--S 73 of 185
enterPointData(space,[p0,p1,p2,p3])
 

   (24)  44
                                                        Type: PositiveInteger
--R 
--R
--R   (24)  44
--R                                                        Type: PositiveInteger
--E 73

)clear all
 

--S 74 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 74

--S 75 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 75

--S 76 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 76

--S 77 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 77

--S 78 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 78

--S 79 of 185
curve(space1,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 79

--S 80 of 185
space2 := copy space1
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 80

--S 81 of 185
point(space1,p3)
 

   (8)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 81

--S 82 of 185
space3 := copy space1
 

   (9)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 82

--S 83 of 185
curve(space3,[p0,p1,p2])
 

   (10)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 83

--S 84 of 185
newSpace1 := merge [space1,space2,space3]
 

   (11)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 84

--S 85 of 185
newSpace2 := merge(space2,space3)
 

   (12)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (12)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 85

--S 86 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (13)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 86

--S 87 of 185
prop := new()$SubSpaceComponentProperty()
 

   (14)  Component is not closed, not solid
                                              Type: SubSpaceComponentProperty
--R 
--R
--R   (14)  Component is not closed, not solid
--R                                              Type: SubSpaceComponentProperty
--E 87

--S 88 of 185
lprop := [prop, prop, prop]
 

   (15)
   [Component is not closed, not solid, Component is not closed, not solid,
    Component is not closed, not solid]
                                         Type: List SubSpaceComponentProperty
--R 
--R
--R   (15)
--R   [Component is not closed, not solid, Component is not closed, not solid,
--R    Component is not closed, not solid]
--R                                         Type: List SubSpaceComponentProperty
--E 88

--S 89 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],lprop,prop)
 

   (16)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 89

--S 90 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],lprop,prop)
 

   (17)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (17)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 90

--S 91 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],closed?(prop),closed?(prop))
 

   (18)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (18)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 91

--S 92 of 185
b := close(prop,true)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 92

--S 93 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],b,b)
 

   (20)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (20)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 93

--S 94 of 185
mesh(space,[[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],closed?(prop),closed?(prop))
 

   (21)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (21)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 94

--S 95 of 185
mesh(space,[[[1,1,1],[1,0,0],[0,0,0]],[[1,0,0],[0,0,0],[0,1,1]],[[1,1,1],[0,0,0],[0,1,1]]],closed?(prop),closed?(prop))
 

   (22)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (22)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 95

--S 96 of 185
mesh(space,[[[1,1,1],[1,0,0],[0,0,0]],[[1,0,0],[0,0,0],[0,1,1]],[[1,1,1],[0,0,0],[0,1,1]]],b,b)
 

   (23)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (23)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 96

)clear all
 

--S 97 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (1)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (1)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 97

--S 98 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (2)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 98

--S 99 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (3)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 99

--S 100 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (4)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 100

--S 101 of 185
space := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (5)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (5)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 101

--S 102 of 185
space1 := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]],false,false)$(ThreeSpace DoubleFloat)
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 102

)clear all
 

--S 103 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (1)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (1)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 103

--S 104 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (2)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 104

--S 105 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (3)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 105

--S 106 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (4)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 106

--S 107 of 185
space := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (5)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (5)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 107

--S 108 of 185
mesh(space)
 

   (6)
   [[[1.,1.,1.],[0.,0.,0.],[0.,1.,1.]], [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]],
    [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.]]]
                                            Type: List List Point DoubleFloat
--R 
--R
--R   (6)
--R   [[[1.,1.,1.],[0.,0.,0.],[0.,1.,1.]], [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]],
--R    [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.]]]
--R                                            Type: List List Point DoubleFloat
--E 108

--S 109 of 185
s := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 109

--S 110 of 185
mesh(s)
 

   (8)
   [[[1.,1.,1.],[0.,0.,0.],[0.,1.,1.]], [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]],
    [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.]]]
                                            Type: List List Point DoubleFloat
--R 
--R
--R   (8)
--R   [[[1.,1.,1.],[0.,0.,0.],[0.,1.,1.]], [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]],
--R    [[1.,1.,1.],[1.,0.,0.],[0.,0.,0.]]]
--R                                            Type: List List Point DoubleFloat
--E 110

--S 111 of 185
space2 := create3Space()$(ThreeSpace DoubleFloat)
 

   (9)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 111

--S 112 of 185
curve(space2,[p0,p1,p2,p3])
 

   (10)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 112

--S 113 of 185
mesh?(space2)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 113

--S 114 of 185
s1 := mesh([[p0,p1,p2],[p1,p2,p3],[p0,p2,p3]])$(ThreeSpace DoubleFloat)
 

   (12)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (12)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 114

--S 115 of 185
mesh?(s1)
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 115

--S 116 of 185
i := enterPointData(space2,[p0,p1,p2,p3])::NNI
 

   (14)  8
                                                     Type: NonNegativeInteger
--R 
--R
--R   (14)  8
--R                                                     Type: NonNegativeInteger
--E 116

--S 117 of 185
modifyPointData(space2,i,p2)
 

   (15)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 117

--S 118 of 185
point(space2,p0)
 

   (16)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 118

--S 119 of 185
curve(space2,[p0,p1,p2,p3])
 

   (17)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (17)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 119

--S 120 of 185
numberOfComponents(space2)
 

   (18)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  3
--R                                                        Type: PositiveInteger
--E 120

)clear all
 

--S 121 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 121

--S 122 of 185
numberOfComposites(space1)
 

   (2)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (2)  0
--R                                                     Type: NonNegativeInteger
--E 122

--S 123 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (3)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 123

--S 124 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (4)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 124

--S 125 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (5)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 125

--S 126 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (6)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (6)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 126

--S 127 of 185
curve(space1,[p0,p1,p2,p3])
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 127

--S 128 of 185
point(space1,p0)
 

   (8)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 128

--S 129 of 185
space2 := point(p0)$(ThreeSpace DoubleFloat)
 

   (9)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (9)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 129

--S 130 of 185
space3 := curve [p0,p1,p2]$(ThreeSpace DoubleFloat)
 

   (10)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 130

--S 131 of 185
s := composite [space1,space2,space3]
 

   (11)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (11)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 131

--S 132 of 185
numberOfComposites(s)
 

   (12)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  1
--R                                                        Type: PositiveInteger
--E 132

--S 133 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (13)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (13)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 133

--S 134 of 185
point(space,p0)
 

   (14)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (14)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 134

--S 135 of 185
curve(space,[p0,p1,p2,p3])
 

   (15)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (15)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 135

--S 136 of 185
closedCurve(space,[p0,p1,p2])
 

   (16)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (16)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 136

--S 137 of 185
objects space
 

   (17)  [points= 1,curves= 2,polygons= 0,constructs= 0]
Type: Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger)
--R 
--R
--R   (17)  [points= 1,curves= 2,polygons= 0,constructs= 0]
--RType: Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger)
--E 137

)clear all
 

--S 138 of 185
s := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 138

--S 139 of 185
p := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 139

--S 140 of 185
point(s,p)
 

   (3)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (3)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 140

--S 141 of 185
point(s,[1,1,1])
 

   (4)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (4)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 141

--S 142 of 185
p0 := point [1,0,0]$(Point DoubleFloat)
 

   (5)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 142

--S 143 of 185
point(s,p)
 

   (6)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 143

--S 144 of 185
i := enterPointData(s,[p0])::NNI
 

   (7)  4
                                                     Type: NonNegativeInteger
--R 
--R
--R   (7)  4
--R                                                     Type: NonNegativeInteger
--E 144

--S 145 of 185
point(s,i)
 

   (8)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 145

--S 146 of 185
p := point [1,1,1]$(Point DoubleFloat)
 

   (9)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (9)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 146

--S 147 of 185
space := point(p)$(ThreeSpace DoubleFloat)
 

   (10)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 147

)clear all
 

--S 148 of 185
s := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 148

--S 149 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 149

--S 150 of 185
curve(s,[p0,p0])
 

   (3)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (3)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 150

--S 151 of 185
space1 := point(p0)$(ThreeSpace DoubleFloat)
 

   (4)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (4)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 151

--S 152 of 185
point(space1)
 

   (5)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 152

)clear all
 

--S 153 of 185
s := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 153

--S 154 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 154

--S 155 of 185
curve(s,[p0,p0,p0])
 

   (3)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (3)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 155

--S 156 of 185
point? s
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 156

--S 157 of 185
space := point(p0)$(ThreeSpace DoubleFloat)
 

   (5)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (5)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 157

--S 158 of 185
point? space
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 158

)clear all
 

--S 159 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 159

--S 160 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 160

--S 161 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 161

--S 162 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 162

--S 163 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 163

--S 164 of 185
polygon(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 164

--S 165 of 185
polygon(space,[[1,1,1],[0,0,-1],[1,0,1]])
 

   (7)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 165

--S 166 of 185
s := polygon([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (8)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 166

)clear all
 

--S 167 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 167

--S 168 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 168

--S 169 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 169

--S 170 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 170

--S 171 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 171

--S 172 of 185
curve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 172

--S 173 of 185
s := polygon([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (7)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (7)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 173

--S 174 of 185
polygon s
 

   (8)  [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (8)  [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 174

)clear all
 

--S 175 of 185
space := create3Space()$(ThreeSpace DoubleFloat)
 

   (1)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (1)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 175

--S 176 of 185
p0 := point [1,1,1]$(Point DoubleFloat)
 

   (2)  [1.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (2)  [1.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 176

--S 177 of 185
p1 := point [1,0,0]$(Point DoubleFloat)
 

   (3)  [1.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (3)  [1.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 177

--S 178 of 185
p2 := point [0,0,0]$(Point DoubleFloat)
 

   (4)  [0.,0.,0.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (4)  [0.,0.,0.]
--R                                                      Type: Point DoubleFloat
--E 178

--S 179 of 185
p3 := point [0,1,1]$(Point DoubleFloat)
 

   (5)  [0.,1.,1.]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (5)  [0.,1.,1.]
--R                                                      Type: Point DoubleFloat
--E 179

--S 180 of 185
curve(space,[p0,p1,p2,p3])
 

   (6)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (6)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 180

--S 181 of 185
polygon? space
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 181

--S 182 of 185
s := polygon([p0,p1,p2,p3])$(ThreeSpace DoubleFloat)
 

   (8)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (8)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 182

--S 183 of 185
polygon s
 

   (9)  [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
                                                 Type: List Point DoubleFloat
--R 
--R
--R   (9)  [[1.,0.,0.],[0.,0.,0.],[0.,1.,1.]]
--R                                                 Type: List Point DoubleFloat
--E 183

--S 184 of 185
space1 := create3Space()$(ThreeSpace DoubleFloat)
 

   (10)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (10)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 184

--S 185 of 185
sub := subspace(space1)
 

   (11)  3-Space with depth of 3 and 0 components
                                                Type: SubSpace(3,DoubleFloat)
--R 
--R
--R   (11)  3-Space with depth of 3 and 0 components
--R                                                Type: SubSpace(3,DoubleFloat)
--E 185
)spool 
 
Starts dribbling to odpol.output (2010/3/27, 18:30:31).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 36
dpol:= ODPOL(FRAC INT)
 

   (1)  OrderlyDifferentialPolynomial Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  OrderlyDifferentialPolynomial Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
w := makeVariable('w)$dpol
 

   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 2

--S 3 of 36
z := makeVariable('z)$dpol
 

   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 3

--S 4 of 36
w.5
 

   (4)  w
         5
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (4)  w
--R         5
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 4

--S 5 of 36
w 0
 

   (5)  w
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (5)  w
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 5

--S 6 of 36
[z.i for i in 1..5]
 

   (6)  [z ,z ,z ,z ,z ]
          1  2  3  4  5
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (6)  [z ,z ,z ,z ,z ]
--R          1  2  3  4  5
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 6

--S 7 of 36
f:= w.4 - w.1 * w.1 * z.3
 

               2
   (7)  w  - w  z
         4    1  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R               2
--R   (7)  w  - w  z
--R         4    1  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 7

--S 8 of 36
g:=(z.1)**3 * (z.2)**2 - w.2
 

          3  2
   (8)  z  z   - w
         1  2     2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R          3  2
--R   (8)  z  z   - w
--R         1  2     2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 8

--S 9 of 36
D(f)
 

               2
   (9)  w  - w  z  - 2w w z
         5    1  4     1 2 3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R               2
--R   (9)  w  - w  z  - 2w w z
--R         5    1  4     1 2 3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 9

--S 10 of 36
D(f,4)
 

   (10)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (10)
--R            2                               2
--R     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
--R      8    1  7     1 2 6         1 3      2   5     1 3 5
--R   + 
--R                                         2
--R     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
--R          1 4      2 3  4     2 3 4     3  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 10

--S 11 of 36
df:=makeVariable(f)$dpol
 

   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 11

--S 12 of 36
df.4
 

   (12)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (12)
--R            2                               2
--R     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
--R      8    1  7     1 2 6         1 3      2   5     1 3 5
--R   + 
--R                                         2
--R     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
--R          1 4      2 3  4     2 3 4     3  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 12

--S 13 of 36
order(g)
 

   (13)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  2
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 36
order(g, 'w)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 36
differentialVariables(g)
 

   (15)  [z,w]
                                                            Type: List Symbol
--R 
--R
--R   (15)  [z,w]
--R                                                            Type: List Symbol
--E 15

--S 16 of 36
degree(g)
 

           2  3
   (16)  z  z
          2  1
                    Type: IndexedExponents OrderlyDifferentialVariable Symbol
--R 
--R
--R           2  3
--R   (16)  z  z
--R          2  1
--R                    Type: IndexedExponents OrderlyDifferentialVariable Symbol
--E 16

--S 17 of 36
degree(g, 'w)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 36
weights(g)
 

   (18)  [7,2]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (18)  [7,2]
--R                                                Type: List NonNegativeInteger
--E 18

--S 19 of 36
weights(g,'w)
 

   (19)  [2]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (19)  [2]
--R                                                Type: List NonNegativeInteger
--E 19

--S 20 of 36
weight(g)
 

   (20)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  7
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 36
isobaric?(g)
 

   (21)  false
                                                                Type: Boolean
--R 
--R
--R   (21)  false
--R                                                                Type: Boolean
--E 21

--S 22 of 36
eval(g,['w::Symbol],[f])
 

                  2                           2        3  2
   (22)  - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
            6    1  5     1 2 4      1 3     2   3    1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R                  2                           2        3  2
--R   (22)  - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
--R            6    1  5     1 2 4      1 3     2   3    1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 22

--S 23 of 36
eval(g,variables(w.0),[f])
 

           3  2
   (23)  z  z   - w
          1  2     2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R           3  2
--R   (23)  z  z   - w
--R          1  2     2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 23

--S 24 of 36
monomials(g)
 

            3  2
   (24)  [z  z  ,- w ]
           1  2     2
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3  2
--R   (24)  [z  z  ,- w ]
--R           1  2     2
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 24

--S 25 of 36
variables(g)
 

   (25)  [z ,w ,z ]
           2  2  1
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (25)  [z ,w ,z ]
--R           2  2  1
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 25

--S 26 of 36
gcd(f,g)
 

   (26)  1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (26)  1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 26

--S 27 of 36
groebner([f,g])
 

                 2     3  2
   (27)  [w  - w  z ,z  z   - w ]
           4    1  3  1  2     2
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R                 2     3  2
--R   (27)  [w  - w  z ,z  z   - w ]
--R           4    1  3  1  2     2
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 27

--S 28 of 36
lg:=leader(g)
 

   (28)  z
          2
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (28)  z
--R          2
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 28

--S 29 of 36
sg:=separant(g)
 

            3
   (29)  2z  z
           1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3
--R   (29)  2z  z
--R           1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 29

--S 30 of 36
ig:=initial(g)
 

           3
   (30)  z
          1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R           3
--R   (30)  z
--R          1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 30

--S 31 of 36
g1 := D g
 

            3               2  3
   (31)  2z  z z  - w  + 3z  z
           1  2 3    3     1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3               2  3
--R   (31)  2z  z z  - w  + 3z  z
--R           1  2 3    3     1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 31

--S 32 of 36
lg1:= leader g1
 

   (32)  z
          3
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (32)  z
--R          3
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 32

--S 33 of 36
pdf:=D(f, lg1)
 

             2
   (33)  - w
            1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R             2
--R   (33)  - w
--R            1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 33

--S 34 of 36
prf:=sg * f- pdf * g1
 

            3         2        2  2  3
   (34)  2z  z w  - w  w  + 3w  z  z
           1  2 4    1  3     1  1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3         2        2  2  3
--R   (34)  2z  z w  - w  w  + 3w  z  z
--R           1  2 4    1  3     1  1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 34

--S 35 of 36
lcf:=leadingCoefficient univariate(prf, lg)
 

            2  2
   (35)  3w  z
           1  1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            2  2
--R   (35)  3w  z
--R           1  1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 35

--S 36 of 36
ig * prf - lcf * g * lg
 

            6         2  3        2  2
   (36)  2z  z w  - w  z  w  + 3w  z  w z
           1  2 4    1  1  3     1  1  2 2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            6         2  3        2  2
--R   (36)  2z  z w  - w  z  w  + 3w  z  w z
--R           1  2 4    1  1  3     1  1  2 2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 36
)spool 
 
Starts dribbling to series2.output (2010/3/27, 18:38:54).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 38
f1 := taylor(1 - x**2,x = 0)
 

             2
   (1)  1 - x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R             2
--R   (1)  1 - x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 38
asin f1
 

   (2)
   %pi     1   2     1    4      1    6      5     8       7     10      11
   --- - ---- x  - ----- x  - ------ x  - ------- x  - -------- x   + O(x  )
    2     +-+        +-+         +-+          +-+           +-+
         \|2       8\|2       32\|2       512\|2       2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R   %pi     1   2     1    4      1    6      5     8       7     10      11
--R   --- - ---- x  - ----- x  - ------ x  - ------- x  - -------- x   + O(x  )
--R    2     +-+        +-+         +-+          +-+           +-+
--R         \|2       8\|2       32\|2       512\|2       2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 2

--S 3 of 38
sin %
 

            1  4    1  6    7   8     5   10      11
   (3)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
            4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  4    1  6    7   8     5   10      11
--R   (3)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
--R            4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 38
acos f1
 

          1   2     1    4      1    6      5     8       7     10      11
   (4)  ---- x  + ----- x  + ------ x  + ------- x  + -------- x   + O(x  )
         +-+        +-+         +-+          +-+           +-+
        \|2       8\|2       32\|2       512\|2       2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R          1   2     1    4      1    6      5     8       7     10      11
--R   (4)  ---- x  + ----- x  + ------ x  + ------- x  + -------- x   + O(x  )
--R         +-+        +-+         +-+          +-+           +-+
--R        \|2       8\|2       32\|2       512\|2       2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 38
cos %
 

            1  4    1  6    7   8     5   10      11
   (5)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
            4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  4    1  6    7   8     5   10      11
--R   (5)  1 - - x  - -- x  - --- x  - ---- x   + O(x  )
--R            4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 5

--S 6 of 38
f2 := taylor(1 + x**2,x = 0)
 

             2
   (6)  1 + x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R             2
--R   (6)  1 + x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 6

--S 7 of 38
acsc f2
 

   (7)
   %pi     1   2     5    4     43    6     177    8      2867    10      11
   --- - ---- x  + ----- x  - ------ x  + ------- x  - --------- x   + O(x  )
    2     +-+        +-+         +-+          +-+            +-+
         \|2       8\|2       96\|2       512\|2       10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (7)
--R   %pi     1   2     5    4     43    6     177    8      2867    10      11
--R   --- - ---- x  + ----- x  - ------ x  + ------- x  - --------- x   + O(x  )
--R    2     +-+        +-+         +-+          +-+            +-+
--R         \|2       8\|2       96\|2       512\|2       10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 7

--S 8 of 38
csc %
 

            1  4    5  6   287  8   1361  10      11
   (8)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
            4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  4    5  6   287  8   1361  10      11
--R   (8)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
--R            4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 8

--S 9 of 38
asec f2
 

          1   2     5    4     43    6     177    8      2867    10      11
   (9)  ---- x  - ----- x  + ------ x  - ------- x  + --------- x   + O(x  )
         +-+        +-+         +-+          +-+            +-+
        \|2       8\|2       96\|2       512\|2       10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R          1   2     5    4     43    6     177    8      2867    10      11
--R   (9)  ---- x  - ----- x  + ------ x  - ------- x  + --------- x   + O(x  )
--R         +-+        +-+         +-+          +-+            +-+
--R        \|2       8\|2       96\|2       512\|2       10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 9

--S 10 of 38
sec %
 

             1  4    5  6   287  8   1361  10      11
   (10)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
             4      16      768      3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R             1  4    5  6   287  8   1361  10      11
--R   (10)  1 + - x  - -- x  + --- x  - ---- x   + O(x  )
--R             4      16      768      3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 10

--S 11 of 38
f3 := taylor(1 - (x - a)**2,x = a)
 

                    2
   (11)  1 - (x - a)
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R                    2
--R   (11)  1 - (x - a)
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 11

--S 12 of 38
asin f3
 

   (12)
     %pi     1         2     1          4      1          6      5           8
     --- - ---- (x - a)  - ----- (x - a)  - ------ (x - a)  - ------- (x - a)
      2     +-+              +-+               +-+                +-+
           \|2             8\|2             32\|2             512\|2
   + 
           7           10            11
     - -------- (x - a)   + O((x - a)  )
            +-+
       2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (12)
--R     %pi     1         2     1          4      1          6      5           8
--R     --- - ---- (x - a)  - ----- (x - a)  - ------ (x - a)  - ------- (x - a)
--R      2     +-+              +-+               +-+                +-+
--R           \|2             8\|2             32\|2             512\|2
--R   + 
--R           7           10            11
--R     - -------- (x - a)   + O((x - a)  )
--R            +-+
--R       2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 12

--S 13 of 38
sin %
 

   (13)
       1        4    1        6    7         8     5         10            11
   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (13)
--R       1        4    1        6    7         8     5         10            11
--R   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 13

--S 14 of 38
acos f3
 

   (14)
       1         2     1          4      1          6      5           8
     ---- (x - a)  + ----- (x - a)  + ------ (x - a)  + ------- (x - a)
      +-+              +-+               +-+                +-+
     \|2             8\|2             32\|2             512\|2
   + 
         7           10            11
     -------- (x - a)   + O((x - a)  )
          +-+
     2048\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (14)
--R       1         2     1          4      1          6      5           8
--R     ---- (x - a)  + ----- (x - a)  + ------ (x - a)  + ------- (x - a)
--R      +-+              +-+               +-+                +-+
--R     \|2             8\|2             32\|2             512\|2
--R   + 
--R         7           10            11
--R     -------- (x - a)   + O((x - a)  )
--R          +-+
--R     2048\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 14

--S 15 of 38
cos %
 

   (15)
       1        4    1        6    7         8     5         10            11
   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (15)
--R       1        4    1        6    7         8     5         10            11
--R   1 - - (x - a)  - -- (x - a)  - --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 15

--S 16 of 38
f4 := taylor(1 + (x - a)**2,x = a)
 

                    2
   (16)  1 + (x - a)
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R                    2
--R   (16)  1 + (x - a)
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 16

--S 17 of 38
acsc f4
 

   (17)
     %pi     1         2     5          4     43          6     177          8
     --- - ---- (x - a)  + ----- (x - a)  - ------ (x - a)  + ------- (x - a)
      2     +-+              +-+               +-+                +-+
           \|2             8\|2             96\|2             512\|2
   + 
          2867          10            11
     - --------- (x - a)   + O((x - a)  )
             +-+
       10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (17)
--R     %pi     1         2     5          4     43          6     177          8
--R     --- - ---- (x - a)  + ----- (x - a)  - ------ (x - a)  + ------- (x - a)
--R      2     +-+              +-+               +-+                +-+
--R           \|2             8\|2             96\|2             512\|2
--R   + 
--R          2867          10            11
--R     - --------- (x - a)   + O((x - a)  )
--R             +-+
--R       10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 17

--S 18 of 38
csc %
 

   (18)
       1        4    5        6   287        8   1361        10            11
   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (18)
--R       1        4    5        6   287        8   1361        10            11
--R   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 18

--S 19 of 38
asec f4
 

   (19)
       1         2     5          4     43          6     177          8
     ---- (x - a)  - ----- (x - a)  + ------ (x - a)  - ------- (x - a)
      +-+              +-+               +-+                +-+
     \|2             8\|2             96\|2             512\|2
   + 
        2867          10            11
     --------- (x - a)   + O((x - a)  )
           +-+
     10240\|2
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (19)
--R       1         2     5          4     43          6     177          8
--R     ---- (x - a)  - ----- (x - a)  + ------ (x - a)  - ------- (x - a)
--R      +-+              +-+               +-+                +-+
--R     \|2             8\|2             96\|2             512\|2
--R   + 
--R        2867          10            11
--R     --------- (x - a)   + O((x - a)  )
--R           +-+
--R     10240\|2
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 19

--S 20 of 38
sec %
 

   (20)
       1        4    5        6   287        8   1361        10            11
   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
       4            16            768            3072
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (20)
--R       1        4    5        6   287        8   1361        10            11
--R   1 + - (x - a)  - -- (x - a)  + --- (x - a)  - ---- (x - a)   + O((x - a)  )
--R       4            16            768            3072
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 20

--S 21 of 38
f5 := taylor(%i + x**2,x = 0)
 

               2
   (21)  %i + x
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--R 
--R
--R               2
--R   (21)  %i + x
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--E 21

--S 22 of 38
asinh f5
 

   (22)
                             +---+             +---+
          +---+         - %i\|2%i  + 4  2    9\|2%i  + 4 + 16%i   4
     log(\|2%i  + %i) + -------------- x  + -------------------- x
                           +---+               +---+
                         4\|2%i  + 4%i      64\|2%i  + 64 + 32%i
   + 
                       +---+
       (- 239 + 106%i)\|2%i  - 312 - 96%i   6
     ------------------------------------- x
                     +---+
     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
   + 
                          +---+
       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i   8
     -------------------------------------------- x
                        +---+
     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
   + 
                                 +---+
         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i     10      11
     ------------------------------------------------------------ x   + O(x  )
                                +---+
     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--R 
--R
--R   (22)
--R                             +---+             +---+
--R          +---+         - %i\|2%i  + 4  2    9\|2%i  + 4 + 16%i   4
--R     log(\|2%i  + %i) + -------------- x  + -------------------- x
--R                           +---+               +---+
--R                         4\|2%i  + 4%i      64\|2%i  + 64 + 32%i
--R   + 
--R                       +---+
--R       (- 239 + 106%i)\|2%i  - 312 - 96%i   6
--R     ------------------------------------- x
--R                     +---+
--R     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
--R   + 
--R                          +---+
--R       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i   8
--R     -------------------------------------------- x
--R                        +---+
--R     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
--R   + 
--R                                 +---+
--R         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i     10      11
--R     ------------------------------------------------------------ x   + O(x  )
--R                                +---+
--R     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--E 22

--S 23 of 38
map(normalize,sinh %)
 

   (23)
        +---+                     +---+
     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6  2
     ----------------- + ------------------ x
         +---+              +---+
        \|2%i  + %i       8\|2%i  + 8 + 4%i
   + 
                   +---+
         (8 + 3%i)\|2%i  + 18%i      4
     ------------------------------ x
                 +---+
     (64 + 96%i)\|2%i  - 32 + 192%i
   + 
                      +---+
       (118 + 1355%i)\|2%i  - 1216 + 1456%i    6
     ---------------------------------------- x
                      +---+
     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
   + 
                                       +---+
       (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i   8
     ---------------------------------------------------------------------- x
                                     +---+
     (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
   + 
                                                                      +---+
           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
         + 
           17079087293650217758937952 + 6236244540731754948247086%i
      /
                                                                         +---+
           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
         + 
           - 367150215832379728071180288 + 1001034013523215543416922112%i
    *
        10
       x
   + 
        11
     O(x  )
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--R 
--R
--R   (23)
--R        +---+                     +---+
--R     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6  2
--R     ----------------- + ------------------ x
--R         +---+              +---+
--R        \|2%i  + %i       8\|2%i  + 8 + 4%i
--R   + 
--R                   +---+
--R         (8 + 3%i)\|2%i  + 18%i      4
--R     ------------------------------ x
--R                 +---+
--R     (64 + 96%i)\|2%i  - 32 + 192%i
--R   + 
--R                      +---+
--R       (118 + 1355%i)\|2%i  - 1216 + 1456%i    6
--R     ---------------------------------------- x
--R                      +---+
--R     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
--R   + 
--R                                       +---+
--R       (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i   8
--R     ---------------------------------------------------------------------- x
--R                                     +---+
--R     (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
--R   + 
--R                                                                      +---+
--R           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
--R         + 
--R           17079087293650217758937952 + 6236244540731754948247086%i
--R      /
--R                                                                         +---+
--R           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
--R         + 
--R           - 367150215832379728071180288 + 1001034013523215543416922112%i
--R    *
--R        10
--R       x
--R   + 
--R        11
--R     O(x  )
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,0)
--E 23

--S 24 of 38
acosh f1
 

   (24)
                          +---+              +---+
          +---+        - \|- 2  - 4  2   - 9\|- 2  - 12  4
     log(\|- 2  + 1) + ------------ x  + -------------- x
                          +---+              +---+
                        4\|- 2  + 4       64\|- 2  - 32
   + 
          +---+                    +---+
      133\|- 2  - 152   6     2237\|- 2  - 3760   8
     ----------------- x  + -------------------- x
          +---+                    +---+
     1536\|- 2  + 2688      114688\|- 2  + 34816
   + 
              +---+
       140517\|- 2  - 342216    10      11
     ------------------------- x   + O(x  )
              +---+
     18841600\|- 2  - 13475840
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (24)
--R                          +---+              +---+
--R          +---+        - \|- 2  - 4  2   - 9\|- 2  - 12  4
--R     log(\|- 2  + 1) + ------------ x  + -------------- x
--R                          +---+              +---+
--R                        4\|- 2  + 4       64\|- 2  - 32
--R   + 
--R          +---+                    +---+
--R      133\|- 2  - 152   6     2237\|- 2  - 3760   8
--R     ----------------- x  + -------------------- x
--R          +---+                    +---+
--R     1536\|- 2  + 2688      114688\|- 2  + 34816
--R   + 
--R              +---+
--R       140517\|- 2  - 342216    10      11
--R     ------------------------- x   + O(x  )
--R              +---+
--R     18841600\|- 2  - 13475840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 24

--S 25 of 38
map(normalize,cosh %)
 

   (25)
        +---+         +---+              +---+                 +---+
       \|- 2      - 3\|- 2  + 6  2    11\|- 2  + 14  4   - 453\|- 2  + 240  6
     ---------- + ------------- x  + -------------- x  + ----------------- x
      +---+          +---+              +---+                 +---+
     \|- 2  + 1    8\|- 2  - 4       32\|- 2  - 160      7168\|- 2  + 2176
   + 
                +---+
     - 22730863\|- 2  + 116622452  8
     ---------------------------- x
               +---+
     670183424\|- 2  - 3124590592
   + 
                        +---+
       2255055395845397\|- 2  - 186126275620338262    10      11
     ----------------------------------------------- x   + O(x  )
                         +---+
     2942149446728507392\|- 2  + 7713476525184163840
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (25)
--R        +---+         +---+              +---+                 +---+
--R       \|- 2      - 3\|- 2  + 6  2    11\|- 2  + 14  4   - 453\|- 2  + 240  6
--R     ---------- + ------------- x  + -------------- x  + ----------------- x
--R      +---+          +---+              +---+                 +---+
--R     \|- 2  + 1    8\|- 2  - 4       32\|- 2  - 160      7168\|- 2  + 2176
--R   + 
--R                +---+
--R     - 22730863\|- 2  + 116622452  8
--R     ---------------------------- x
--R               +---+
--R     670183424\|- 2  - 3124590592
--R   + 
--R                        +---+
--R       2255055395845397\|- 2  - 186126275620338262    10      11
--R     ----------------------------------------------- x   + O(x  )
--R                         +---+
--R     2942149446728507392\|- 2  + 7713476525184163840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 25

--S 26 of 38
asech f2
 

   (26)
                           +---+             +---+
          +---+        - 3\|- 2  - 4  2   31\|- 2  - 12  4
     log(\|- 2  + 1) + ------------- x  + ------------- x
                          +---+              +---+
                        4\|- 2  + 4       64\|- 2  - 32
   + 
           +---+                   +---+
     - 481\|- 2  - 904  6    28397\|- 2  + 9296   8
     ----------------- x  + -------------------- x
          +---+                    +---+
     1536\|- 2  + 2688      114688\|- 2  + 34816
   + 
                +---+
     - 15819247\|- 2  + 48750368  10      11
     --------------------------- x   + O(x  )
               +---+
      77987840\|- 2  - 245063680
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (26)
--R                           +---+             +---+
--R          +---+        - 3\|- 2  - 4  2   31\|- 2  - 12  4
--R     log(\|- 2  + 1) + ------------- x  + ------------- x
--R                          +---+              +---+
--R                        4\|- 2  + 4       64\|- 2  - 32
--R   + 
--R           +---+                   +---+
--R     - 481\|- 2  - 904  6    28397\|- 2  + 9296   8
--R     ----------------- x  + -------------------- x
--R          +---+                    +---+
--R     1536\|- 2  + 2688      114688\|- 2  + 34816
--R   + 
--R                +---+
--R     - 15819247\|- 2  + 48750368  10      11
--R     --------------------------- x   + O(x  )
--R               +---+
--R      77987840\|- 2  - 245063680
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 26

--S 27 of 38
sech %
 

   (27)
                                 +---+               +---+
               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))  2
     --------------------- + ----------------------------------- x
               +---+            +---+               +---+      2
     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
   + 
               +---+               +---+      2
           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
         + 
                 +---+                +---+                +---+
           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                 +---+               +---+      2
           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
      /
             +---+                +---+      3
         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
    *
        4
       x
   + 
                  +---+                   +---+      3
           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
         + 
                    +---+                    +---+                +---+      2
           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                    +---+                   +---+      2          +---+
           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                  +---+                   +---+      3
           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
      /
                +---+                    +---+      4
         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
    *
        6
       x
   + 
                            +---+                             +---+      4
           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
         + 
                                 +---+                             +---+
             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
          *
                       +---+      3
             sinh(log(\|- 2  + 1))
         + 
                              +---+                             +---+      2
             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
          *
                       +---+      2
             sinh(log(\|- 2  + 1))
         + 
                               +---+                             +---+      3
             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
          *
                       +---+
             sinh(log(\|- 2  + 1))
         + 
                              +---+                           +---+      4
           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
      /
                           +---+                            +---+      5
         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
    *
        8
       x
   + 
                                                              +---+
               - 12221152405486797005988545574943642796394656\|- 2
             + 
               37637519606679038130877931502289421788636480
          *
                       +---+      5
             sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               17253119387520025009474512785116571944492864\|- 2
             + 
               - 108013651440447643426633659223764934754997824
          *
                       +---+                +---+      4
             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               15685216146928883301596685922653051925359412\|- 2
             + 
               67214446812749454239537980137157117493694568
          *
                       +---+      2          +---+      3
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                              +---+
               - 26995359328188426534667967009323500335310964\|- 2
             + 
               55273964842367651019386962337683658570477492
          *
                       +---+      3          +---+      2
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               - 386525745609157558466191079238605101103613\|- 2
             + 
               - 65032045559085732400544188402961111578157364
          *
                       +---+      4          +---+
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                           +---+
               7027759893774203888781041210243035688470658\|- 2
             + 
               12868136868984040775294141040070021247885438
          *
                       +---+      5
             cosh(log(\|- 2  + 1))
      /
                                                          +---+
             18629821302375761537774756048822860358942720\|- 2
           + 
             94473907670457185816258586943170775874920448
        *
                     +---+      6
           cosh(log(\|- 2  + 1))
    *
        10
       x
   + 
        11
     O(x  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (27)
--R                                 +---+               +---+
--R               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))  2
--R     --------------------- + ----------------------------------- x
--R               +---+            +---+               +---+      2
--R     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
--R   + 
--R               +---+               +---+      2
--R           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+                +---+                +---+
--R           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+               +---+      2
--R           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
--R      /
--R             +---+                +---+      3
--R         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
--R    *
--R        4
--R       x
--R   + 
--R                  +---+                   +---+      3
--R           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                    +---+                +---+      2
--R           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                   +---+      2          +---+
--R           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                  +---+                   +---+      3
--R           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
--R      /
--R                +---+                    +---+      4
--R         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
--R    *
--R        6
--R       x
--R   + 
--R                            +---+                             +---+      4
--R           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
--R         + 
--R                                 +---+                             +---+
--R             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      3
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                             +---+      2
--R             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      2
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                               +---+                             +---+      3
--R             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                           +---+      4
--R           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
--R      /
--R                           +---+                            +---+      5
--R         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
--R    *
--R        8
--R       x
--R   + 
--R                                                              +---+
--R               - 12221152405486797005988545574943642796394656\|- 2
--R             + 
--R               37637519606679038130877931502289421788636480
--R          *
--R                       +---+      5
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               17253119387520025009474512785116571944492864\|- 2
--R             + 
--R               - 108013651440447643426633659223764934754997824
--R          *
--R                       +---+                +---+      4
--R             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               15685216146928883301596685922653051925359412\|- 2
--R             + 
--R               67214446812749454239537980137157117493694568
--R          *
--R                       +---+      2          +---+      3
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                              +---+
--R               - 26995359328188426534667967009323500335310964\|- 2
--R             + 
--R               55273964842367651019386962337683658570477492
--R          *
--R                       +---+      3          +---+      2
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               - 386525745609157558466191079238605101103613\|- 2
--R             + 
--R               - 65032045559085732400544188402961111578157364
--R          *
--R                       +---+      4          +---+
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                           +---+
--R               7027759893774203888781041210243035688470658\|- 2
--R             + 
--R               12868136868984040775294141040070021247885438
--R          *
--R                       +---+      5
--R             cosh(log(\|- 2  + 1))
--R      /
--R                                                          +---+
--R             18629821302375761537774756048822860358942720\|- 2
--R           + 
--R             94473907670457185816258586943170775874920448
--R        *
--R                     +---+      6
--R           cosh(log(\|- 2  + 1))
--R    *
--R        10
--R       x
--R   + 
--R        11
--R     O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 27

--S 28 of 38
acsch f1
 

   (28)
                       +-+             +-+               +-+
          +-+         \|2  + 2  2    9\|2  + 12  4   221\|2  + 312  6
     log(\|2  + 1) + --------- x  + ----------- x  + ------------- x
                       +-+             +-+               +-+
                     2\|2  + 2      16\|2  + 24      576\|2  + 816
   + 
           +-+                        +-+
     14425\|2  + 20400  8   124515259\|2  + 176091168  10      11
     ----------------- x  + ------------------------- x   + O(x  )
           +-+                        +-+
     52224\|2  + 73856      602664960\|2  + 852296960
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (28)
--R                       +-+             +-+               +-+
--R          +-+         \|2  + 2  2    9\|2  + 12  4   221\|2  + 312  6
--R     log(\|2  + 1) + --------- x  + ----------- x  + ------------- x
--R                       +-+             +-+               +-+
--R                     2\|2  + 2      16\|2  + 24      576\|2  + 816
--R   + 
--R           +-+                        +-+
--R     14425\|2  + 20400  8   124515259\|2  + 176091168  10      11
--R     ----------------- x  + ------------------------- x   + O(x  )
--R           +-+                        +-+
--R     52224\|2  + 73856      602664960\|2  + 852296960
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 28

--S 29 of 38
map(normalize,csch %)
 

              2      11
   (29)  1 - x  + O(x  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R              2      11
--R   (29)  1 - x  + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 29

--S 30 of 38
f6 := taylor(%i + (x - a)**2,x = a)
 

                     2
   (30)  %i + (x - a)
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--R 
--R
--R                     2
--R   (30)  %i + (x - a)
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--E 30

--S 31 of 38
asinh f6
 

   (31)
                             +---+                   +---+
          +---+         - %i\|2%i  + 4        2    9\|2%i  + 4 + 16%i         4
     log(\|2%i  + %i) + -------------- (x - a)  + -------------------- (x - a)
                           +---+                     +---+
                         4\|2%i  + 4%i            64\|2%i  + 64 + 32%i
   + 
                       +---+
       (- 239 + 106%i)\|2%i  - 312 - 96%i         6
     ------------------------------------- (x - a)
                     +---+
     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
   + 
                          +---+
       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i         8
     -------------------------------------------- (x - a)
                        +---+
     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
   + 
                                 +---+
         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i           10
     ------------------------------------------------------------ (x - a)
                                +---+
     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
   + 
              11
     O((x - a)  )
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--R 
--R
--R   (31)
--R                             +---+                   +---+
--R          +---+         - %i\|2%i  + 4        2    9\|2%i  + 4 + 16%i         4
--R     log(\|2%i  + %i) + -------------- (x - a)  + -------------------- (x - a)
--R                           +---+                     +---+
--R                         4\|2%i  + 4%i            64\|2%i  + 64 + 32%i
--R   + 
--R                       +---+
--R       (- 239 + 106%i)\|2%i  - 312 - 96%i         6
--R     ------------------------------------- (x - a)
--R                     +---+
--R     (3072 + 1536%i)\|2%i  + 1152 + 4608%i
--R   + 
--R                          +---+
--R       (- 8055 - 12814%i)\|2%i  + 4624 - 20800%i         8
--R     -------------------------------------------- (x - a)
--R                        +---+
--R     (442368 + 98304%i)\|2%i  + 344064 + 538624%i
--R   + 
--R                                 +---+
--R         (36259219 - 19680060%i)\|2%i  + 55940064 + 16579392%i           10
--R     ------------------------------------------------------------ (x - a)
--R                                +---+
--R     (2513436672 + 287440896%i)\|2%i  + 2225987584 + 2800893952%i
--R   + 
--R              11
--R     O((x - a)  )
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--E 31

--S 32 of 38
map(normalize,sinh %)
 

   (32)
        +---+                     +---+
     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6        2
     ----------------- + ------------------ (x - a)
         +---+              +---+
        \|2%i  + %i       8\|2%i  + 8 + 4%i
   + 
                   +---+
         (8 + 3%i)\|2%i  + 18%i            4
     ------------------------------ (x - a)
                 +---+
     (64 + 96%i)\|2%i  - 32 + 192%i
   + 
                      +---+
       (118 + 1355%i)\|2%i  - 1216 + 1456%i          6
     ---------------------------------------- (x - a)
                      +---+
     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
   + 
                                         +---+
         (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i
       ----------------------------------------------------------------------
                                       +---+
       (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
    *
              8
       (x - a)
   + 
                                                                      +---+
           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
         + 
           17079087293650217758937952 + 6236244540731754948247086%i
      /
                                                                         +---+
           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
         + 
           - 367150215832379728071180288 + 1001034013523215543416922112%i
    *
              10
       (x - a)
   + 
              11
     O((x - a)  )
                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--R 
--R
--R   (32)
--R        +---+                     +---+
--R     %i\|2%i  - 1 + %i   (4 - %i)\|2%i  + 6        2
--R     ----------------- + ------------------ (x - a)
--R         +---+              +---+
--R        \|2%i  + %i       8\|2%i  + 8 + 4%i
--R   + 
--R                   +---+
--R         (8 + 3%i)\|2%i  + 18%i            4
--R     ------------------------------ (x - a)
--R                 +---+
--R     (64 + 96%i)\|2%i  - 32 + 192%i
--R   + 
--R                      +---+
--R       (118 + 1355%i)\|2%i  - 1216 + 1456%i          6
--R     ---------------------------------------- (x - a)
--R                      +---+
--R     (27648 + 6144%i)\|2%i  + 21504 + 33664%i
--R   + 
--R                                         +---+
--R         (- 10723239267 - 22732932140%i)\|2%i  + 12009693172 - 33456171528%i
--R       ----------------------------------------------------------------------
--R                                       +---+
--R       (239050510336 + 850943508480%i)\|2%i  - 611892998144 + 1089994016768%i
--R    *
--R              8
--R       (x - a)
--R   + 
--R                                                                      +---+
--R           (11657665917190986353592000 - 5421421376459231405345859%i)\|2%i
--R         + 
--R           17079087293650217758937952 + 6236244540731754948247086%i
--R      /
--R                                                                         +---+
--R           (316941898845417907672866816 + 684092114677797635744055296%i)\|2%i
--R         + 
--R           - 367150215832379728071180288 + 1001034013523215543416922112%i
--R    *
--R              10
--R       (x - a)
--R   + 
--R              11
--R     O((x - a)  )
--R                 Type: UnivariateTaylorSeries(Expression Complex Integer,x,a)
--E 32

--S 33 of 38
acosh f3
 

   (33)
                          +---+                    +---+
          +---+        - \|- 2  - 4        2   - 9\|- 2  - 12        4
     log(\|- 2  + 1) + ------------ (x - a)  + -------------- (x - a)
                          +---+                    +---+
                        4\|- 2  + 4             64\|- 2  - 32
   + 
          +---+                          +---+
      133\|- 2  - 152         6     2237\|- 2  - 3760         8
     ----------------- (x - a)  + -------------------- (x - a)
          +---+                          +---+
     1536\|- 2  + 2688            114688\|- 2  + 34816
   + 
              +---+
       140517\|- 2  - 342216          10            11
     ------------------------- (x - a)   + O((x - a)  )
              +---+
     18841600\|- 2  - 13475840
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (33)
--R                          +---+                    +---+
--R          +---+        - \|- 2  - 4        2   - 9\|- 2  - 12        4
--R     log(\|- 2  + 1) + ------------ (x - a)  + -------------- (x - a)
--R                          +---+                    +---+
--R                        4\|- 2  + 4             64\|- 2  - 32
--R   + 
--R          +---+                          +---+
--R      133\|- 2  - 152         6     2237\|- 2  - 3760         8
--R     ----------------- (x - a)  + -------------------- (x - a)
--R          +---+                          +---+
--R     1536\|- 2  + 2688            114688\|- 2  + 34816
--R   + 
--R              +---+
--R       140517\|- 2  - 342216          10            11
--R     ------------------------- (x - a)   + O((x - a)  )
--R              +---+
--R     18841600\|- 2  - 13475840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 33

--S 34 of 38
map(normalize,cosh %)
 

   (34)
        +---+         +---+                    +---+
       \|- 2      - 3\|- 2  + 6        2    11\|- 2  + 14        4
     ---------- + ------------- (x - a)  + -------------- (x - a)
      +---+          +---+                    +---+
     \|- 2  + 1    8\|- 2  - 4             32\|- 2  - 160
   + 
           +---+                             +---+
     - 453\|- 2  + 240        6   - 22730863\|- 2  + 116622452        8
     ----------------- (x - a)  + ---------------------------- (x - a)
          +---+                             +---+
     7168\|- 2  + 2176            670183424\|- 2  - 3124590592
   + 
                        +---+
       2255055395845397\|- 2  - 186126275620338262          10            11
     ----------------------------------------------- (x - a)   + O((x - a)  )
                         +---+
     2942149446728507392\|- 2  + 7713476525184163840
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (34)
--R        +---+         +---+                    +---+
--R       \|- 2      - 3\|- 2  + 6        2    11\|- 2  + 14        4
--R     ---------- + ------------- (x - a)  + -------------- (x - a)
--R      +---+          +---+                    +---+
--R     \|- 2  + 1    8\|- 2  - 4             32\|- 2  - 160
--R   + 
--R           +---+                             +---+
--R     - 453\|- 2  + 240        6   - 22730863\|- 2  + 116622452        8
--R     ----------------- (x - a)  + ---------------------------- (x - a)
--R          +---+                             +---+
--R     7168\|- 2  + 2176            670183424\|- 2  - 3124590592
--R   + 
--R                        +---+
--R       2255055395845397\|- 2  - 186126275620338262          10            11
--R     ----------------------------------------------- (x - a)   + O((x - a)  )
--R                         +---+
--R     2942149446728507392\|- 2  + 7713476525184163840
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 34

--S 35 of 38
asech f4
 

   (35)
                           +---+                   +---+
          +---+        - 3\|- 2  - 4        2   31\|- 2  - 12        4
     log(\|- 2  + 1) + ------------- (x - a)  + ------------- (x - a)
                          +---+                    +---+
                        4\|- 2  + 4             64\|- 2  - 32
   + 
           +---+                         +---+
     - 481\|- 2  - 904        6    28397\|- 2  + 9296         8
     ----------------- (x - a)  + -------------------- (x - a)
          +---+                          +---+
     1536\|- 2  + 2688            114688\|- 2  + 34816
   + 
                +---+
     - 15819247\|- 2  + 48750368        10            11
     --------------------------- (x - a)   + O((x - a)  )
               +---+
      77987840\|- 2  - 245063680
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (35)
--R                           +---+                   +---+
--R          +---+        - 3\|- 2  - 4        2   31\|- 2  - 12        4
--R     log(\|- 2  + 1) + ------------- (x - a)  + ------------- (x - a)
--R                          +---+                    +---+
--R                        4\|- 2  + 4             64\|- 2  - 32
--R   + 
--R           +---+                         +---+
--R     - 481\|- 2  - 904        6    28397\|- 2  + 9296         8
--R     ----------------- (x - a)  + -------------------- (x - a)
--R          +---+                          +---+
--R     1536\|- 2  + 2688            114688\|- 2  + 34816
--R   + 
--R                +---+
--R     - 15819247\|- 2  + 48750368        10            11
--R     --------------------------- (x - a)   + O((x - a)  )
--R               +---+
--R      77987840\|- 2  - 245063680
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 35

--S 36 of 38
sech %
 

   (36)
                                 +---+               +---+
               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))        2
     --------------------- + ----------------------------------- (x - a)
               +---+            +---+               +---+      2
     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
   + 
               +---+               +---+      2
           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
         + 
                 +---+                +---+                +---+
           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                 +---+               +---+      2
           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
      /
             +---+                +---+      3
         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
    *
              4
       (x - a)
   + 
                  +---+                   +---+      3
           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
         + 
                    +---+                    +---+                +---+      2
           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                    +---+                   +---+      2          +---+
           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                  +---+                   +---+      3
           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
      /
                +---+                    +---+      4
         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
    *
              6
       (x - a)
   + 
                            +---+                             +---+      4
           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
         + 
                                 +---+                             +---+
             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
          *
                       +---+      3
             sinh(log(\|- 2  + 1))
         + 
                              +---+                             +---+      2
             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
          *
                       +---+      2
             sinh(log(\|- 2  + 1))
         + 
                               +---+                             +---+      3
             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
          *
                       +---+
             sinh(log(\|- 2  + 1))
         + 
                              +---+                           +---+      4
           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
      /
                           +---+                            +---+      5
         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
    *
              8
       (x - a)
   + 
                                                              +---+
               - 12221152405486797005988545574943642796394656\|- 2
             + 
               37637519606679038130877931502289421788636480
          *
                       +---+      5
             sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               17253119387520025009474512785116571944492864\|- 2
             + 
               - 108013651440447643426633659223764934754997824
          *
                       +---+                +---+      4
             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               15685216146928883301596685922653051925359412\|- 2
             + 
               67214446812749454239537980137157117493694568
          *
                       +---+      2          +---+      3
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                              +---+
               - 26995359328188426534667967009323500335310964\|- 2
             + 
               55273964842367651019386962337683658570477492
          *
                       +---+      3          +---+      2
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                            +---+
               - 386525745609157558466191079238605101103613\|- 2
             + 
               - 65032045559085732400544188402961111578157364
          *
                       +---+      4          +---+
             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
         + 
                                                           +---+
               7027759893774203888781041210243035688470658\|- 2
             + 
               12868136868984040775294141040070021247885438
          *
                       +---+      5
             cosh(log(\|- 2  + 1))
      /
                                                          +---+
             18629821302375761537774756048822860358942720\|- 2
           + 
             94473907670457185816258586943170775874920448
        *
                     +---+      6
           cosh(log(\|- 2  + 1))
    *
              10
       (x - a)
   + 
              11
     O((x - a)  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (36)
--R                                 +---+               +---+
--R               1              (3\|- 2  + 4)sinh(log(\|- 2  + 1))        2
--R     --------------------- + ----------------------------------- (x - a)
--R               +---+            +---+               +---+      2
--R     cosh(log(\|- 2  + 1))   (4\|- 2  + 4)cosh(log(\|- 2  + 1))
--R   + 
--R               +---+               +---+      2
--R           (48\|- 2  - 4)sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+                +---+                +---+
--R           (- 31\|- 2  + 12)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                 +---+               +---+      2
--R           (- 24\|- 2  + 2)cosh(log(\|- 2  + 1))
--R      /
--R             +---+                +---+      3
--R         (64\|- 2  - 32)cosh(log(\|- 2  + 1))
--R    *
--R              4
--R       (x - a)
--R   + 
--R                  +---+                   +---+      3
--R           (36692\|- 2  - 81184)sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                    +---+                +---+      2
--R           (- 32120\|- 2  + 120532)cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                    +---+                   +---+      2          +---+
--R           (- 23811\|- 2  + 15618)cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                  +---+                   +---+      3
--R           (16060\|- 2  - 60266)cosh(log(\|- 2  + 1))
--R      /
--R                +---+                    +---+      4
--R         (16768\|- 2  - 159872)cosh(log(\|- 2  + 1))
--R    *
--R              6
--R       (x - a)
--R   + 
--R                            +---+                             +---+      4
--R           (917040033820768\|- 2  + 769478330788000)sinh(log(\|- 2  + 1))
--R         + 
--R                                 +---+                             +---+
--R             (- 2024826947095704\|- 2  - 971819819460816)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      3
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                             +---+      2
--R             (561327386270964\|- 2  - 572600834130900)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+      2
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                               +---+                             +---+      3
--R             (1159287723524931\|- 2  + 817645948038654)cosh(log(\|- 2  + 1))
--R          *
--R                       +---+
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                              +---+                           +---+      4
--R           (- 624553705818270\|- 2  - 2253956980050)cosh(log(\|- 2  + 1))
--R      /
--R                           +---+                            +---+      5
--R         (2124490945165312\|- 2  - 79521392875520)cosh(log(\|- 2  + 1))
--R    *
--R              8
--R       (x - a)
--R   + 
--R                                                              +---+
--R               - 12221152405486797005988545574943642796394656\|- 2
--R             + 
--R               37637519606679038130877931502289421788636480
--R          *
--R                       +---+      5
--R             sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               17253119387520025009474512785116571944492864\|- 2
--R             + 
--R               - 108013651440447643426633659223764934754997824
--R          *
--R                       +---+                +---+      4
--R             cosh(log(\|- 2  + 1))sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               15685216146928883301596685922653051925359412\|- 2
--R             + 
--R               67214446812749454239537980137157117493694568
--R          *
--R                       +---+      2          +---+      3
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                              +---+
--R               - 26995359328188426534667967009323500335310964\|- 2
--R             + 
--R               55273964842367651019386962337683658570477492
--R          *
--R                       +---+      3          +---+      2
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                            +---+
--R               - 386525745609157558466191079238605101103613\|- 2
--R             + 
--R               - 65032045559085732400544188402961111578157364
--R          *
--R                       +---+      4          +---+
--R             cosh(log(\|- 2  + 1)) sinh(log(\|- 2  + 1))
--R         + 
--R                                                           +---+
--R               7027759893774203888781041210243035688470658\|- 2
--R             + 
--R               12868136868984040775294141040070021247885438
--R          *
--R                       +---+      5
--R             cosh(log(\|- 2  + 1))
--R      /
--R                                                          +---+
--R             18629821302375761537774756048822860358942720\|- 2
--R           + 
--R             94473907670457185816258586943170775874920448
--R        *
--R                     +---+      6
--R           cosh(log(\|- 2  + 1))
--R    *
--R              10
--R       (x - a)
--R   + 
--R              11
--R     O((x - a)  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 36

--S 37 of 38
acsch f3
 

   (37)
                       +-+                   +-+
          +-+         \|2  + 2        2    9\|2  + 12        4
     log(\|2  + 1) + --------- (x - a)  + ----------- (x - a)
                       +-+                   +-+
                     2\|2  + 2            16\|2  + 24
   + 
         +-+                        +-+
     221\|2  + 312        6   14425\|2  + 20400        8
     ------------- (x - a)  + ----------------- (x - a)
         +-+                        +-+
     576\|2  + 816            52224\|2  + 73856
   + 
               +-+
     124515259\|2  + 176091168        10            11
     ------------------------- (x - a)   + O((x - a)  )
               +-+
     602664960\|2  + 852296960
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R   (37)
--R                       +-+                   +-+
--R          +-+         \|2  + 2        2    9\|2  + 12        4
--R     log(\|2  + 1) + --------- (x - a)  + ----------- (x - a)
--R                       +-+                   +-+
--R                     2\|2  + 2            16\|2  + 24
--R   + 
--R         +-+                        +-+
--R     221\|2  + 312        6   14425\|2  + 20400        8
--R     ------------- (x - a)  + ----------------- (x - a)
--R         +-+                        +-+
--R     576\|2  + 816            52224\|2  + 73856
--R   + 
--R               +-+
--R     124515259\|2  + 176091168        10            11
--R     ------------------------- (x - a)   + O((x - a)  )
--R               +-+
--R     602664960\|2  + 852296960
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 37

--S 38 of 38
map(normalize,csch %)
 

                    2            11
   (38)  1 - (x - a)  + O((x - a)  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--R 
--R
--R                    2            11
--R   (38)  1 - (x - a)  + O((x - a)  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,a)
--E 38
)spool 
 
Starts dribbling to frac.output (2010/3/27, 18:26:22).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 12
a := 11/12
 

        11
   (1)  --
        12
                                                       Type: Fraction Integer
--R 
--R
--R        11
--R   (1)  --
--R        12
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 12
b := 23/24
 

        23
   (2)  --
        24
                                                       Type: Fraction Integer
--R 
--R
--R        23
--R   (2)  --
--R        24
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 12
3 - a*b**2 + a + b/a
 

        313271
   (3)  ------
         76032
                                                       Type: Fraction Integer
--R 
--R
--R        313271
--R   (3)  ------
--R         76032
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 12
numer(a)
 

   (4)  11
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  11
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 12
denom(b)
 

   (5)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  24
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 12
r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1)
 

         2
        x  + 2x + 1
   (6)  -----------
         2
        x  - 2x + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 2x + 1
--R   (6)  -----------
--R         2
--R        x  - 2x + 1
--R                                            Type: Fraction Polynomial Integer
--E 6

--S 7 of 12
factor(r)
 

         2
        x  + 2x + 1
   (7)  -----------
         2
        x  - 2x + 1
                                   Type: Factored Fraction Polynomial Integer
--R 
--R
--R         2
--R        x  + 2x + 1
--R   (7)  -----------
--R         2
--R        x  - 2x + 1
--R                                   Type: Factored Fraction Polynomial Integer
--E 7

--S 8 of 12
map(factor,r)
 

               2
        (x + 1)
   (8)  --------
               2
        (x - 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R               2
--R        (x + 1)
--R   (8)  --------
--R               2
--R        (x - 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 8

--S 9 of 12
continuedFraction(7/12)
 

          1 |     1 |     1 |     1 |
   (9)  +---+ + +---+ + +---+ + +---+
        | 1     | 1     | 2     | 2
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1 |     1 |
--R   (9)  +---+ + +---+ + +---+ + +---+
--R        | 1     | 1     | 2     | 2
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 12
partialFraction(7,12)
 

              3   1
   (10)  1 - -- + -
              2   3
             2
                                                Type: PartialFraction Integer
--R 
--R
--R              3   1
--R   (10)  1 - -- + -
--R              2   3
--R             2
--R                                                Type: PartialFraction Integer
--E 10

--S 11 of 12
g := 2/3 + 4/5*%i
 

         2   4
   (11)  - + - %i
         3   5
                                               Type: Complex Fraction Integer
--R 
--R
--R         2   4
--R   (11)  - + - %i
--R         3   5
--R                                               Type: Complex Fraction Integer
--E 11

--S 12 of 12
g :: FRAC COMPLEX INT
 

         10 + 12%i
   (12)  ---------
             15
                                               Type: Fraction Complex Integer
--R 
--R
--R         10 + 12%i
--R   (12)  ---------
--R             15
--R                                               Type: Fraction Complex Integer
--E 12
)spool 
 
Starts dribbling to sersolve.output (2010/3/27, 18:38:56).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 10
eq := D(y x,x) - x*cos(y x) - exp(x)
 

         ,                      x
   (2)  y (x) - x cos(y(x)) - %e

                                                     Type: Expression Integer
--R 
--R
--R         ,                      x
--R   (2)  y (x) - x cos(y(x)) - %e
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 10
seriesSolve(eq,y,x=0,y(0) = 0)
 
   Compiling function %A with type UnivariateTaylorSeries(Expression 
      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 

   (3)
          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
              6      12      120      360      5040      4032      362880
   + 
      161   10      11
     ----- x   + O(x  )
     10368
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function %A with type UnivariateTaylorSeries(Expression 
--R      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 
--R
--R   (3)
--R          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
--R     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
--R              6      12      120      360      5040      4032      362880
--R   + 
--R      161   10      11
--R     ----- x   + O(x  )
--R     10368
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

)set streams calculate 10
 

--S 4 of 10
R := EXPR INT
 

   (4)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (4)  Expression Integer
--R                                                                 Type: Domain
--E 4

--S 5 of 10
uts := UTS(R,'x,0)
 

   (5)  UnivariateTaylorSeries(Expression Integer,x,0)
                                                                 Type: Domain
--R 
--R
--R   (5)  UnivariateTaylorSeries(Expression Integer,x,0)
--R                                                                 Type: Domain
--E 5

--S 6 of 10
foo: uts -> uts
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
foo y ==
  xx := monomial(1,1)$uts
  xx * cos(y) + exp(xx)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 10
y := ode1(foo,0)$UTSODE(R,uts)
 
   Compiling function foo with type UnivariateTaylorSeries(Expression 
      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 

   (8)
          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
              6      12      120      360      5040      4032      362880
   + 
      161   10      11
     ----- x   + O(x  )
     10368
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function foo with type UnivariateTaylorSeries(Expression 
--R      Integer,x,0) -> UnivariateTaylorSeries(Expression Integer,x,0) 
--R
--R   (8)
--R          2   1  3    1  4    23  5    37  6    61   7    271  8    21617  9
--R     x + x  + - x  - -- x  - --- x  - --- x  + ---- x  + ---- x  + ------ x
--R              6      12      120      360      5040      4032      362880
--R   + 
--R      161   10      11
--R     ----- x   + O(x  )
--R     10368
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 8

--S 9 of 10
x : uts := x
 
   Compiled code for %A has been cleared.

   (9)  x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiled code for %A has been cleared.
--R
--R   (9)  x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 9

--S 10 of 10
x * cos(y) + exp(x)
 

   (10)
              1  2   1  3   23  4   37  5    61  6   271  7   21617  8    805  9
     1 + 2x + - x  - - x  - -- x  - -- x  + --- x  + --- x  + ----- x  + ---- x
              2      3      24      60      720      504      40320      5184
   + 
        841499  10      11
     - ------- x   + O(x  )
       3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (10)
--R              1  2   1  3   23  4   37  5    61  6   271  7   21617  8    805  9
--R     1 + 2x + - x  - - x  - -- x  - -- x  + --- x  + --- x  + ----- x  + ---- x
--R              2      3      24      60      720      504      40320      5184
--R   + 
--R        841499  10      11
--R     - ------- x   + O(x  )
--R       3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 10
)spool 
 
Starts dribbling to AssociationList.output (2010/3/27, 18:41:43).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
Data := Record(monthsOld : Integer, gender : String)
 

   (1)  Record(monthsOld: Integer,gender: String)
                                                                 Type: Domain
--R 
--R
--R   (1)  Record(monthsOld: Integer,gender: String)
--R                                                                 Type: Domain
--E 1

--S 2 of 10
al : AssociationList(String,Data)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 10
al := table()
 

   (3)  table()
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (3)  table()
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 3

--S 4 of 10
al."bob" := [407,"male"]$Data
 

   (4)  [monthsOld= 407,gender= "male"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (4)  [monthsOld= 407,gender= "male"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 4

--S 5 of 10
al."judith" := [366,"female"]$Data
 

   (5)  [monthsOld= 366,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (5)  [monthsOld= 366,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 5

--S 6 of 10
al."katie" := [24,"female"]$Data
 

   (6)  [monthsOld= 24,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (6)  [monthsOld= 24,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 6

--S 7 of 10
al."smokie" := [200,"female"]$Data
 

   (7)  [monthsOld= 200,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (7)  [monthsOld= 200,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 7

--S 8 of 10
al
 

   (8)
   table
      "smokie"= [monthsOld= 200,gender= "female"]
  ,
      "katie"= [monthsOld= 24,gender= "female"]
  ,
      "judith"= [monthsOld= 366,gender= "female"]
  ,
      "bob"= [monthsOld= 407,gender= "male"]
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (8)
--R   table
--R      "smokie"= [monthsOld= 200,gender= "female"]
--R  ,
--R      "katie"= [monthsOld= 24,gender= "female"]
--R  ,
--R      "judith"= [monthsOld= 366,gender= "female"]
--R  ,
--R      "bob"= [monthsOld= 407,gender= "male"]
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 8

--S 9 of 10
al."katie" := [23,"female"]$Data
 

   (9)  [monthsOld= 23,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (9)  [monthsOld= 23,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 9

--S 10 of 10
delete!(al,1)
 

   (10)
   table
      "katie"= [monthsOld= 23,gender= "female"]
  ,
      "judith"= [monthsOld= 366,gender= "female"]
  ,
      "bob"= [monthsOld= 407,gender= "male"]
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (10)
--R   table
--R      "katie"= [monthsOld= 23,gender= "female"]
--R  ,
--R      "judith"= [monthsOld= 366,gender= "female"]
--R  ,
--R      "bob"= [monthsOld= 407,gender= "male"]
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 10
)spool
 
Starts dribbling to intbypart.output (2010/3/27, 18:26:58).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
integrate(x*log(x),x)
 

          2          2
        2x log(x) - x
   (1)  --------------
               4
                                          Type: Union(Expression Integer,...)
--R
--R          2          2
--R        2x log(x) - x
--R   (1)  --------------
--R               4
--R                                          Type: Union(Expression Integer,...)
--E 1
--S 2 of 16
integrate(x*exp(x),x)
 

                 x
   (2)  (x - 1)%e
                                          Type: Union(Expression Integer,...)
--R
--R                 x
--R   (2)  (x - 1)%e
--R                                          Type: Union(Expression Integer,...)
--E 2
--S 3 of 16
integrate(exp(x)*sin(x),x)
 

          x                 x
        %e sin(x) - cos(x)%e
   (3)  ---------------------
                  2
                                          Type: Union(Expression Integer,...)
--R
--R          x                 x
--R        %e sin(x) - cos(x)%e
--R   (3)  ---------------------
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E 3
--S 4 of 16
integrate(x^3*exp(x^2),x)
 

                   2
          2       x
        (x  - 1)%e
   (4)  ------------
              2
                                          Type: Union(Expression Integer,...)
--R
--R                   2
--R          2       x
--R        (x  - 1)%e
--R   (4)  ------------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 16
integrate(log(x^2+2),x)
 

                                   +-+
               2          +-+     \|2
   (5)  x log(x  + 2) - 2\|2 atan(----) - 2x
                                    x
                                          Type: Union(Expression Integer,...)
--R
--R                                   +-+
--R               2          +-+     \|2
--R   (5)  x log(x  + 2) - 2\|2 atan(----) - 2x
--R                                    x
--R                                          Type: Union(Expression Integer,...)
--E 5
--S 6 of 16
integrate(x*sin(x),x)
 

   (6)  sin(x) - x cos(x)
                                          Type: Union(Expression Integer,...)
--R
--R   (6)  sin(x) - x cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 6
--S 7 of 16
integrate(x*cos(x),x)
 

   (7)  x sin(x) + cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (7)  x sin(x) + cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 7
--S 8 of 16
integrate(x^2*cos(x),x)
 

          2
   (8)  (x  - 2)sin(x) + 2x cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2
--R   (8)  (x  - 2)sin(x) + 2x cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 8
--S 9 of 16
integrate(sin(x)*cos(x),x)
 

                2
          cos(x)
   (9)  - -------
             2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R          cos(x)
--R   (9)  - -------
--R             2
--R                                          Type: Union(Expression Integer,...)
--E 9
--S 10 of 16
integrate(log(x),x)
 

   (10)  x log(x) - x
                                          Type: Union(Expression Integer,...)
--R
--R   (10)  x log(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 10
--S 11 of 16
integrate(x^2*log(x),x)
 

           3          3
         3x log(x) - x
   (11)  --------------
                9
                                          Type: Union(Expression Integer,...)
--R
--R           3          3
--R         3x log(x) - x
--R   (11)  --------------
--R                9
--R                                          Type: Union(Expression Integer,...)
--E 11
--S 12 of 16
integrate(x^2*exp(x),x)
 

           2            x
   (12)  (x  - 2x + 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2            x
--R   (12)  (x  - 2x + 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 12
--S 13 of 16
integrate(asin(x),x)
 

                     +--------+
                     |   2           +--------+
                  2x\|- x  + 1       |   2
         - x atan(-------------) + 2\|- x  + 1
                       2
                     2x  - 1
   (13)  --------------------------------------
                            2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +--------+
--R                     |   2           +--------+
--R                  2x\|- x  + 1       |   2
--R         - x atan(-------------) + 2\|- x  + 1
--R                       2
--R                     2x  - 1
--R   (13)  --------------------------------------
--R                            2
--R                                          Type: Union(Expression Integer,...)
--E 13
--S 14 of 16
integrate(atan(x),x)
 

                2                 2x
         - log(x  + 1) - x atan(------)
                                 2
                                x  - 1
   (14)  ------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2                 2x
--R         - log(x  + 1) - x atan(------)
--R                                 2
--R                                x  - 1
--R   (14)  ------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 14
--S 15 of 16
integrate(sec(x)^3,x)
 

   (15)
         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
                   cos(x) + 1                        cos(x) + 1
   --------------------------------------------------------------------------
                                           2
                                    2cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (15)
--R         2    sin(x) + cos(x) + 1          2    sin(x) - cos(x) - 1
--R   cos(x) log(-------------------) - cos(x) log(-------------------) + sin(x)
--R                   cos(x) + 1                        cos(x) + 1
--R   --------------------------------------------------------------------------
--R                                           2
--R                                    2cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 15
--S 16 of 16
integrate(x^3*exp(2*x),x)
 

            3     2            2x
         (4x  - 6x  + 6x - 3)%e
   (16)  ------------------------
                     8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            3     2            2x
--R         (4x  - 6x  + 6x - 3)%e
--R   (16)  ------------------------
--R                     8
--R                                          Type: Union(Expression Integer,...)
--E 16
)spool
 
Starts dribbling to exp.output (2010/3/27, 18:25:41).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.0,     1.000000000000000,  exp(0.0), exp(0.0)-     1.000000000000000],_
 [0.1,     1.105170918075648,  exp(0.1), exp(0.1)-     1.105170918075648],_
 [0.2,     1.221402758160170,  exp(0.2), exp(0.2)-     1.221402758160170],_
 [0.3,     1.349858807576003,  exp(0.3), exp(0.3)-     1.349858807576003],_
 [0.4,     1.491824697641270,  exp(0.4), exp(0.4)-     1.491824697641270],_
 [0.5,     1.648721270700128,  exp(0.5), exp(0.5)-     1.648721270700128],_
 [0.6,     1.822118800390509,  exp(0.6), exp(0.6)-     1.822118800390509],_
 [0.7,     2.013752707470477,  exp(0.7), exp(0.7)-     2.013752707470477],_
 [0.8,     2.225540928492468,  exp(0.8), exp(0.8)-     2.225540928492468],_
 [0.9,     2.459603111156950,  exp(0.9), exp(0.9)-     2.459603111156950],_
 [1.0,     2.718281828459045,  exp(1.0), exp(1.0)-     2.718281828459045],_
 [1.1,     3.004166023946433,  exp(1.1), exp(1.1)-     3.004166023946433],_
 [1.2,     3.320116922736547,  exp(1.2), exp(1.2)-     3.320116922736547],_
 [1.3,     3.669296667619244,  exp(1.3), exp(1.3)-     3.669296667619244],_
 [1.4,     4.055199966844675,  exp(1.4), exp(1.4)-     4.055199966844675],_
 [1.5,     4.481689070338065,  exp(1.5), exp(1.5)-     4.481689070338065],_
 [1.6,     4.953032424395115,  exp(1.6), exp(1.6)-     4.953032424395115],_
 [1.7,     5.473947391727200,  exp(1.7), exp(1.7)-     5.473947391727200],_
 [1.8,     6.049647464412946,  exp(1.8), exp(1.8)-     6.049647464412946],_
 [1.9,     6.685894442279269,  exp(1.9), exp(1.9)-     6.685894442279269],_
 [2.0,     7.389056098930650,  exp(2.0), exp(2.0)-     7.389056098930650],_
 [2.1,     8.166169912567650,  exp(2.1), exp(2.1)-     8.166169912567650],_
 [2.2,     9.025013499434121,  exp(2.2), exp(2.2)-     9.025013499434121],_
 [2.3,     9.974182454814721,  exp(2.3), exp(2.3)-     9.974182454814721],_
 [2.4,    11.023176380641602,  exp(2.4), exp(2.4)-    11.023176380641602],_
 [2.5,    12.182493960703473,  exp(2.5), exp(2.5)-    12.182493960703473],_
 [2.6,    13.463738035001690,  exp(2.6), exp(2.6)-    13.463738035001690],_
 [2.7,    14.879731724872834,  exp(2.7), exp(2.7)-    14.879731724872834],_
 [2.8,    16.444646771097050,  exp(2.8), exp(2.8)-    16.444646771097050],_
 [2.9,    18.174145369443061,  exp(2.9), exp(2.9)-    18.174145369443061],_
 [3.0,    20.085536923187668,  exp(3.0), exp(3.0)-    20.085536923187668],_
 [3.1,    22.197951281441633,  exp(3.1), exp(3.1)-    22.197951281441633],_
 [3.2,    24.532530197109349,  exp(3.2), exp(3.2)-    24.532530197109349],_
 [3.3,    27.112638920657887,  exp(3.3), exp(3.3)-    27.112638920657887],_
 [3.4,    29.964100047397013,  exp(3.4), exp(3.4)-    29.964100047397013],_
 [3.5,    33.115451958692314,  exp(3.5), exp(3.5)-    33.115451958692314],_
 [3.6,    36.598234443677988,  exp(3.6), exp(3.6)-    36.598234443677988],_
 [3.7,    40.447304360067391,  exp(3.7), exp(3.7)-    40.447304360067391],_
 [3.8,    44.701184493300823,  exp(3.8), exp(3.8)-    44.701184493300823],_
 [3.9,    49.402449105530174,  exp(3.9), exp(3.9)-    49.402449105530174],_
 [4.0,    54.598150033144239,  exp(4.0), exp(4.0)-    54.598150033144239],_
 [4.1,    60.340287597361969,  exp(4.1), exp(4.1)-    60.340287597361969],_
 [4.2,    66.686331040925142,  exp(4.2), exp(4.2)-    66.686331040925142],_
 [4.3,    73.699793699595797,  exp(4.3), exp(4.3)-    73.699793699595797],_
 [4.4,    81.450868664968117,  exp(4.4), exp(4.4)-    81.450868664968117],_
 [4.5,    90.017131300521814,  exp(4.5), exp(4.5)-    90.017131300521814],_
 [4.6,    99.484315641933809,  exp(4.6), exp(4.6)-    99.484315641933809],_
 [4.7,   109.947172452123499,  exp(4.7), exp(4.7)-   109.947172452123499],_
 [4.8,   121.510417518734881,  exp(4.8), exp(4.8)-   121.510417518734881],_
 [4.9,   134.289779684935485,  exp(4.9), exp(4.9)-   134.289779684935485],_
 [5.0,   148.413159102577,     exp(5.0), exp(5.0)-   148.413159102577],_
 [5.1,   164.021907299902,     exp(5.1), exp(5.1)-   164.021907299902],_
 [5.2,   181.272241875151,     exp(5.2), exp(5.2)-   181.272241875151],_
 [5.3,   200.336809974792,     exp(5.3), exp(5.3)-   200.336809974792],_
 [5.4,   221.406416204187,     exp(5.4), exp(5.4)-   221.406416204187],_
 [5.5,   244.691932264220,     exp(5.5), exp(5.5)-   244.691932264220],_
 [5.6,   270.426407426153,     exp(5.6), exp(5.6)-   270.426407426153],_
 [5.7,   298.867400967060,     exp(5.7), exp(5.7)-   298.867400967060],_
 [5.8,   330.299559909649,     exp(5.8), exp(5.8)-   330.299559909649],_
 [5.9,   365.037467865329,     exp(5.9), exp(5.9)-   365.037467865329],_
 [6.0,   403.428793492735,     exp(6.0), exp(6.0)-   403.428793492735],_
 [6.1,   445.857770082517,     exp(6.1), exp(6.1)-   445.857770082517],_
 [6.2,   492.749041093256,     exp(6.2), exp(6.2)-   492.749041093256],_
 [6.3,   544.571910125929,     exp(6.3), exp(6.3)-   544.571910125929],_
 [6.4,   601.845037872082,     exp(6.4), exp(6.4)-   601.845037872082],_
 [6.5,   665.141633044362,     exp(6.5), exp(6.5)-   665.141633044362],_
 [6.6,   735.095189241973,     exp(6.6), exp(6.6)-   735.095189241973],_
 [6.7,   812.405825167543,     exp(6.7), exp(6.7)-   812.405825167543],_
 [6.8,   897.847291650418,     exp(6.8), exp(6.8)-   897.847291650418],_
 [6.9,   992.274715605026,     exp(6.9), exp(6.9)-   992.274715605026],_
 [7.0,  1096.633158428459,     exp(7.0), exp(7.0)-  1096.633158428459],_
 [7.1,  1211.967074492577,     exp(7.1), exp(7.1)-  1211.967074492577],_
 [7.2,  1339.430764394418,     exp(7.2), exp(7.2)-  1339.430764394418],_
 [7.3,  1480.299927584545,     exp(7.3), exp(7.3)-  1480.299927584545],_
 [7.4,  1635.984429995927,     exp(7.4), exp(7.4)-  1635.984429995927],_
 [7.5,  1808.042414456063,     exp(7.5), exp(7.5)-  1808.042414456063],_
 [7.6,  1998.195895104118,     exp(7.6), exp(7.6)-  1998.195895104118],_
 [7.7,  2208.347991887209,     exp(7.7), exp(7.7)-  2208.347991887209],_
 [7.8,  2440.601977624499,     exp(7.8), exp(7.8)-  2440.601977624499],_
 [7.9,  2697.282328268509,     exp(7.9), exp(7.9)-  2697.282328268509],_
 [8.0,  2980.957987041728,     exp(8.0), exp(8.0)-  2980.957987041728],_
 [8.1,  3294.468075283841,     exp(8.1), exp(8.1)-  3294.468075283841],_
 [8.2,  3640.950307332355,     exp(8.2), exp(8.2)-  3640.950307332355],_
 [8.3,  4023.872393822310,     exp(8.3), exp(8.3)-  4023.872393822310],_
 [8.4,  4447.066747699856,     exp(8.4), exp(8.4)-  4447.066747699856],_
 [8.5,  4914.768840299134,     exp(8.5), exp(8.5)-  4914.768840299134],_
 [8.6,  5431.659591362980,     exp(8.6), exp(8.6)-  5431.659591362980],_
 [8.7,  6002.912217261022,     exp(8.7), exp(8.7)-  6002.912217261022],_
 [8.8,  6634.244006277885,     exp(8.8), exp(8.8)-  6634.244006277885],_
 [8.9,  7331.973539155993,     exp(8.9), exp(8.9)-  7331.973539155993],_
 [9.0,  8103.083927575384,     exp(9.0), exp(9.0)-  8103.083927575384],_
 [9.1,  8955.292703482512,     exp(9.1), exp(9.1)-  8955.292703482512],_
 [9.2,  9897.129058743916,     exp(9.2), exp(9.2)-  9897.129058743916],_
 [9.3, 10938.019208165184,     exp(9.3), exp(9.3)- 10938.019208165184],_
 [9.4, 12088.380730216984,     exp(9.4), exp(9.4)- 12088.380730216984],_
 [9.5, 13359.726829661872,     exp(9.5), exp(9.5)- 13359.726829661872],_
 [9.6, 14764.781565577273,     exp(9.6), exp(9.6)- 14764.781565577273],_
 [9.7, 16317.607198015432,     exp(9.7), exp(9.7)- 16317.607198015432],_
 [9.8, 18033.744927828511,     exp(9.8), exp(9.8)- 18033.744927828511],_
 [9.9, 19930.370438230289,     exp(9.9), exp(9.9)- 19930.370438230289],_
[10.0, 22026.465794806717,    exp(10.0), exp(10.0)-22026.465794806717]]
 

   (1)
   [[0.0,1.0,1.0,0.0],
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    [0.2,1.2214027581 6017,1.2214027581 601698339,- 0.1661 E -15],
    [0.3,1.3498588075 76003,1.3498588075 76003104,0.104 E -15],
    [0.4,1.4918246976 4127,1.4918246976 412703178,0.3178 E -15],
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    [0.8,2.2255409284 92468,2.2255409284 924676046,- 0.3954 E -15],
    [0.9,2.4596031111 5695,2.4596031111 569496638,- 0.3362 E -15],
    [1.0,2.7182818284 59045,2.7182818284 590452354,0.2354 E -15],
    [1.1,3.0041660239 46433,3.0041660239 464331121,0.112 E -15],
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    [1.4,4.0551999668 44675,4.0551999668 446745872,- 0.413 E -15],
    [1.5,4.4816890703 38065,4.4816890703 380648226,- 0.177 E -15],
    [1.6,4.9530324243 95115,4.9530324243 951148037,- 0.196 E -15],
    [1.7,5.4739473917 272,5.4739473917 271997608,- 0.239 E -15],
    [1.8,6.0496474644 12946,6.0496474644 129460837,0.837 E -16],
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    [3.0,20.0855369231 87668,20.0855369231 87667741,- 0.259 E -15],
    [3.1,22.1979512814 41633,22.1979512814 41633405,0.405 E -15],
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    [3.4,29.9641000473 97013,29.9641000473 97013348,0.348 E -15],
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    [3.9,49.4024491055 30174,49.4024491055 3017388,- 0.12 E -15],
    [4.0,54.5981500331 44239,54.5981500331 44239078,0.78 E -16],
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    [4.2,66.6863310409 25142,66.6863310409 25141644,- 0.36 E -15],
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    [4.4,81.4508686649 68117,81.4508686649 68117445,0.445 E -15],
    [4.5,90.0171313005 21814,90.0171313005 2181355,- 0.45 E -15],
    [4.6,99.4843156419 33809,99.4843156419 33808735,- 0.26 E -15],
    [4.7,109.9471724521 23499,109.9471724521 2349888,- 0.12 E -15],
    [4.8,121.5104175187 34881,121.5104175187 3488076,- 0.24 E -15],
    [4.9,134.2897796849 35485,134.2897796849 3548484,- 0.16 E -15],
    [5.0,148.4131591025 77,148.4131591025 7660342,- 0.39658 E -12],
    [5.1,164.0219072999 02,164.0219072999 0174394,- 0.25606 E -12],
    [5.2,181.2722418751 51,181.2722418751 5117937,0.17937 E -12],
    [5.3,200.3368099747 92,200.3368099747 9168484,- 0.31516 E -12],
    [5.4,221.4064162041 87,221.4064162041 8708703,0.8703 E -13],
    [5.5,244.6919322642 2,244.6919322642 2038792,0.38792 E -12],
    [5.6,270.4264074261 53,270.4264074261 5262815,- 0.37185 E -12],
    [5.7,298.8674009670 6,298.8674009670 6023267,0.23267 E -12],
    [5.8,330.2995599096 49,330.2995599096 4865412,- 0.34588 E -12],
    [5.9,365.0374678653 29,365.0374678653 2877732,- 0.2227 E -12],
    [6.0,403.4287934927 35,403.4287934927 3512261,0.1226 E -12],
    [6.1,445.8577700825 17,445.8577700825 1693179,- 0.6821 E -13],
    [6.2,492.7490410932 56,492.7490410932 5625456,0.25456 E -12],
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    [6.4,601.8450378720 82,601.8450378720 8205661,0.566 E -13],
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    [6.6,735.0951892419 73,735.0951892419 728949,- 0.1051 E -12],
    [6.7,812.4058251675 43,812.4058251675 4311346,0.1135 E -12],
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    [7.2,1339.4307643944 18,1339.4307643944 178297,- 0.1703 E -12],
    [7.3,1480.2999275845 45,1480.2999275845 452229,0.2228 E -12],
    [7.4,1635.9844299959 27,1635.9844299959 265401,- 0.4599 E -12],
    [7.5,1808.0424144560 63,1808.0424144560 632069,0.2069 E -12],
    [7.6,1998.1958951041 18,1998.1958951041 179592,- 0.408 E -13],
    [7.7,2208.3479918872 09,2208.3479918872 08524,- 0.476 E -12],
    [7.8,2440.6019776244 99,2440.6019776244 990773,0.773 E -13],
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                                                        Type: List List Float
--R 
--R
--R   (1)
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--R    [1.6,4.9530324243 95115,4.9530324243 951148037,- 0.196 E -15],
--R    [1.7,5.4739473917 272,5.4739473917 271997608,- 0.239 E -15],
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--R    [4.6,99.4843156419 33809,99.4843156419 33808735,- 0.26 E -15],
--R    [4.7,109.9471724521 23499,109.9471724521 2349888,- 0.12 E -15],
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--R    [8.8,6634.2440062778 85,6634.2440062778 851586,0.159 E -12],
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--R    [9.9,19930.3704382302 89,19930.3704382302 8949,0.49 E -12],
--R    [10.0,22026.4657948067 17,22026.4657948067 16517,- 0.483 E -12]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
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 [8.2,0.00027465356997214233,exp(-8.2),exp(-8.2)-0.00027465356997214233],_
 [8.3,0.00024851682710795202,exp(-8.3),exp(-8.3)-0.00024851682710795202],_
 [8.4,0.00022486732417884827,exp(-8.4),exp(-8.4)-0.00022486732417884827],_
 [8.5,0.00020346836901064417,exp(-8.5),exp(-8.5)-0.00020346836901064417],_
 [8.6,0.00018410579366757912,exp(-8.6),exp(-8.6)-0.00018410579366757912],_
 [8.7,0.00016658581098763341,exp(-8.7),exp(-8.7)-0.00016658581098763341],_
 [8.8,0.00015073307509547660,exp(-8.8),exp(-8.8)-0.00015073307509547660],_
 [8.9,0.00013638892648201145,exp(-8.9),exp(-8.9)-0.00013638892648201145],_
 [9.0,0.00012340980408667955,exp(-9.0),exp(-9.0)-0.00012340980408667955],_
 [9.1,0.00011166580849011474,exp(-9.1),exp(-9.1)-0.00011166580849011474],_
 [9.2,0.00010103940183709335,exp(-9.2),exp(-9.2)-0.00010103940183709335],_
 [9.3,0.00009142423147817334,exp(-9.3),exp(-9.3)-0.00009142423147817334],_
 [9.4,0.00008272406555663226,exp(-9.4),exp(-9.4)-0.00008272406555663226],_
 [9.5,0.00007485182988770059,exp(-9.5),exp(-9.5)-0.00007485182988770059],_
 [9.6,0.00006772873649085387,exp(-9.6),exp(-9.6)-0.00006772873649085387],_
 [9.7,0.00006128349505322210,exp(-9.7),exp(-9.7)-0.00006128349505322210],_
 [9.8,0.00005545159943217698,exp(-9.8),exp(-9.8)-0.00005545159943217698],_
 [9.9,0.00005017468205617530,exp(-9.9),exp(-9.9)-0.00005017468205617530],_
[10.0,0.00004539992976248485,exp(-10.0),exp(-10.0)-0.00004539992976248485]]
 

   (2)
   [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20],
    [0.2,0.8187307530 7798185867,0.8187307530 7798185867,0.0],
    [0.3,0.7408182206 8171786607,0.7408182206 8171786606,- 0.7 E -20],
    [0.4,0.6703200460 3563930074,0.6703200460 3563930075,0.3 E -20],
    [0.5,0.6065306597 126334236,0.6065306597 126334236,0.3 E -20],
    [0.6,0.5488116360 9402643263,0.5488116360 9402643263,- 0.3 E -20],
    [0.7,0.4965853037 914095147,0.4965853037 9140951471,0.5 E -20],
    [0.8,0.4493289641 1722159143,0.4493289641 1722159143,0.0],
    [0.9,0.4065696597 4059911188,0.4065696597 4059911188,0.3 E -20],
    [1.0,0.3678794411 714423216,0.3678794411 7144232159,- 0.5 E -20],
    [1.1,0.3328710836 9807955329,0.3328710836 9807955329,- 0.2 E -20],
    [1.2,0.3011942119 1220209664,0.3011942119 1220209664,0.3 E -20],
    [1.3,0.2725317930 3401260312,0.2725317930 3401260312,0.3 E -20],
    [1.4,0.2465969639 4160647694,0.2465969639 4160647694,0.0],
    [1.5,0.2231301601 4842982893,0.2231301601 4842982893,0.3 E -20],
    [1.6,0.2018965179 9465540849,0.2018965179 9465540848,- 0.5 E -20],
    [1.7,0.1826835240 5273465022,0.1826835240 5273465022,0.3 E -20],
    [1.8,0.1652988882 215865383,0.1652988882 215865383,- 0.3 E -20],
    [1.9,0.1495686192 2263505264,0.1495686192 2263505264,0.8 E -21],
    [2.0,0.1353352832 3661269189,0.1353352832 3661269189,0.4 E -20],
    [2.1,0.1224564282 5298191022,0.1224564282 5298191022,- 0.8 E -21],
    [2.2,0.1108031583 6233388333,0.1108031583 6233388333,0.4 E -20],
    [2.3,0.1002588437 2280373373,0.1002588437 2280373373,0.0],
    [2.4,0.0907179532 8941250338,0.0907179532 8941250337 5,- 0.6 E -20],
    [2.5,0.0820849986 2389879517,0.0820849986 2389879516 9,- 0.4 E -21],
    [2.6,0.0742735782 1433388043,0.0742735782 1433388042 9,- 0.1 E -20],
    [2.7,0.0672055127 3974976513,0.0672055127 3974976512 6,- 0.4 E -20],
    [2.8,0.0608100626 25217965,0.0608100626 2521796499 6,- 0.4 E -20],
    [2.9,0.0550232200 5640722903,0.0550232200 5640722903,- 0.4 E -21],
    [3.0,0.0497870683 6786394298,0.0497870683 6786394297 9,- 0.6 E -21],
    [3.1,0.0450492023 9355780607,0.0450492023 9355780606 9,- 0.1 E -20],
    [3.2,0.0407622039 7836621517,0.0407622039 7836621516 6,- 0.4 E -20],
    [3.3,0.0368831674 0124000545,0.0368831674 0124000544 6,- 0.4 E -20],
    [3.4,0.0333732699 6032607948,0.0333732699 6032607948 2,0.2 E -20],
    [3.5,0.0301973834 2231850074,0.0301973834 2231850074,- 0.2 E -21],
    [3.6,0.0273237224 472925608,0.0273237224 4729256080 2,0.2 E -20],
    [3.7,0.0247235264 703393912,0.0247235264 7033939120 3,0.3 E -20],
    [3.8,0.0223707718 5616559578,0.0223707718 5616559577 9,- 0.1 E -20],
    [3.9,0.0202419114 4580438847,0.0202419114 4580438847 2,0.2 E -20],
    [4.0,0.0183156388 8873418029,0.0183156388 8873418029 4,0.4 E -20],
    [4.1,0.0165726754 0176124754,0.0165726754 0176124754 2,0.2 E -20],
    [4.2,0.0149955768 2047770621,0.0149955768 2047770621 2,0.2 E -20],
    [4.3,0.0135685590 1220093176,0.0135685590 1220093175 7,- 0.3 E -20],
    [4.4,0.0122773399 0306844118,0.0122773399 0306844117 9,- 0.1 E -20],
    [4.5,0.0111089965 382423065,0.0111089965 3824230649 6,- 0.4 E -20],
    [4.6,0.0100518357 4463358164,0.0100518357 4463358164 2,0.2 E -20],
    [4.7,0.0090952771 0169581709,0.0090952771 0169581709 21,0.2 E -20],
    [4.8,0.0082297470 4902002884,0.0082297470 4902002884 13,0.1 E -20],
    [4.9,0.0074465830 7092434052,0.0074465830 7092434051 82,- 0.2 E -20],
    [5.0,0.0067379469 990854671,0.0067379469 9908546709 66,- 0.3 E -20],
    [5.1,0.0060967465 6551563611,0.0060967465 6551563610 72,- 0.3 E -20],
    [5.2,0.0055165644 2076077242,0.0055165644 2076077241 81,- 0.2 E -20],
    [5.3,0.0049915939 0691021621,0.0049915939 0691021621 22,0.2 E -20],
    [5.4,0.0045165809 4261266798,0.0045165809 4261266798 16,0.2 E -20],
    [5.5,0.0040867714 3846406699,0.0040867714 3846406699 35,0.35 E -20],
    [5.6,0.0036978637 1648293082,0.0036978637 1648293082 07,0.7 E -21],
    [5.7,0.0033459654 5747127277,0.0033459654 5747127276 58,- 0.42 E -20],
    [5.8,0.0030275547 4537581475,0.0030275547 4537581474 82,- 0.18 E -20],
    [5.9,0.0027394448 1876836923,0.0027394448 1876836923 28,0.28 E -20],
    [6.0,0.0024787521 7666635842,0.0024787521 7666635842 3,0.3 E -20],
    [6.1,0.0022428677 1948580247,0.0022428677 1948580247 32,0.32 E -20],
    [6.2,0.0020294306 3629573436,0.0020294306 3629573436 34,0.34 E -20],
    [6.3,0.0018363047 7702890683,0.0018363047 7702890682 52,- 0.48 E -20],
    [6.4,0.0016615572 731739345,0.0016615572 7317393449 91,- 0.93 E -21],
    [6.5,0.0015034391 9297757245,0.0015034391 9297757244 74,- 0.26 E -20],
    [6.6,0.0013603680 3754789342,0.0013603680 3754789341 69,- 0.31 E -20],
    [6.7,0.0012309119 0267348118,0.0012309119 0267348118 46,0.46 E -20],
    [6.8,0.0011137751 4784480308,0.0011137751 4784480307 88,- 0.12 E -20],
    [6.9,0.0010077854 2904851076,0.0010077854 2904851076 14,0.14 E -20],
    [7.0,0.0009118819 6555451621,0.0009118819 6555451620 8,- 0.2 E -20],
    [7.1,0.0008251049 2326590427,0.0008251049 2326590427 015,0.1 E -21],
    [7.2,0.0007465858 0837667937,0.0007465858 0837667936 81,- 0.19 E -20],
    [7.3,0.0006755387 7519384424,0.0006755387 7519384423 783,- 0.22 E -20],
    [7.4,0.0006112527 6112957256,0.0006112527 6112957255 567,- 0.433 E -20],
    [7.5,0.0005530843 7014783358,0.0005530843 7014783358 31,0.31 E -20],
    [7.6,0.0005004514 334406107,0.0005004514 3344061069 551,- 0.449 E -20],
    [7.7,0.0004528271 8288679706,0.0004528271 8288679705 8,- 0.2 E -20],
    [7.8,0.0004097349 7897978671,0.0004097349 7897978670 846,- 0.15 E -20],
    [7.9,0.0003707435 4045908837,0.0003707435 4045908837 443,0.443 E -20],
    [8.0,0.0003354626 2790251184,0.0003354626 2790251183 882,- 0.12 E -20],
    [8.1,0.0003035391 3807886666,0.0003035391 3807886666 086,0.86 E -21],
    [8.2,0.0002746535 6997214233,0.0002746535 6997214232 763,- 0.237 E -20],
    [8.3,0.0002485168 2710795202,0.0002485168 2710795202 08,0.8 E -21],
    [8.4,0.0002248673 2417884827,0.0002248673 2417884827 28,0.28 E -20],
    [8.5,0.0002034683 6901064417,0.0002034683 6901064417 437,0.437 E -20],
    [8.6,0.0001841057 9366757912,0.0001841057 9366757912 495,0.495 E -20],
    [8.7,0.0001665858 1098763341,0.0001665858 1098763341 149,0.149 E -20],
    [8.8,0.0001507330 750954766,0.0001507330 7509547660 064,0.64 E -21],
    [8.9,0.0001363889 2648201145,0.0001363889 2648201144 785,- 0.215 E -20],
    [9.0,0.0001234098 0408667955,0.0001234098 0408667954 95,- 0.5 E -21],
    [9.1,0.0001116658 0849011474,0.0001116658 0849011473 564,- 0.436 E -20],
    [9.2,0.0001010394 0183709335,0.0001010394 0183709335 073,0.732 E -21],
    [9.3,0.0000914242 3147817334,0.0000914242 3147817333 7862,- 0.214 E -20],
    [9.4,0.0000827240 6555663226,0.0000827240 6555663226 2731,0.273 E -20],
    [9.5,0.0000748518 2988770059,0.0000748518 2988770059 1471,0.147 E -20],
    [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20],
    [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20],
    [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20],
    [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20],
    [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20],
--R    [0.2,0.8187307530 7798185867,0.8187307530 7798185867,0.0],
--R    [0.3,0.7408182206 8171786607,0.7408182206 8171786606,- 0.7 E -20],
--R    [0.4,0.6703200460 3563930074,0.6703200460 3563930075,0.3 E -20],
--R    [0.5,0.6065306597 126334236,0.6065306597 126334236,0.3 E -20],
--R    [0.6,0.5488116360 9402643263,0.5488116360 9402643263,- 0.3 E -20],
--R    [0.7,0.4965853037 914095147,0.4965853037 9140951471,0.5 E -20],
--R    [0.8,0.4493289641 1722159143,0.4493289641 1722159143,0.0],
--R    [0.9,0.4065696597 4059911188,0.4065696597 4059911188,0.3 E -20],
--R    [1.0,0.3678794411 714423216,0.3678794411 7144232159,- 0.5 E -20],
--R    [1.1,0.3328710836 9807955329,0.3328710836 9807955329,- 0.2 E -20],
--R    [1.2,0.3011942119 1220209664,0.3011942119 1220209664,0.3 E -20],
--R    [1.3,0.2725317930 3401260312,0.2725317930 3401260312,0.3 E -20],
--R    [1.4,0.2465969639 4160647694,0.2465969639 4160647694,0.0],
--R    [1.5,0.2231301601 4842982893,0.2231301601 4842982893,0.3 E -20],
--R    [1.6,0.2018965179 9465540849,0.2018965179 9465540848,- 0.5 E -20],
--R    [1.7,0.1826835240 5273465022,0.1826835240 5273465022,0.3 E -20],
--R    [1.8,0.1652988882 215865383,0.1652988882 215865383,- 0.3 E -20],
--R    [1.9,0.1495686192 2263505264,0.1495686192 2263505264,0.8 E -21],
--R    [2.0,0.1353352832 3661269189,0.1353352832 3661269189,0.4 E -20],
--R    [2.1,0.1224564282 5298191022,0.1224564282 5298191022,- 0.8 E -21],
--R    [2.2,0.1108031583 6233388333,0.1108031583 6233388333,0.4 E -20],
--R    [2.3,0.1002588437 2280373373,0.1002588437 2280373373,0.0],
--R    [2.4,0.0907179532 8941250338,0.0907179532 8941250337 5,- 0.6 E -20],
--R    [2.5,0.0820849986 2389879517,0.0820849986 2389879516 9,- 0.4 E -21],
--R    [2.6,0.0742735782 1433388043,0.0742735782 1433388042 9,- 0.1 E -20],
--R    [2.7,0.0672055127 3974976513,0.0672055127 3974976512 6,- 0.4 E -20],
--R    [2.8,0.0608100626 25217965,0.0608100626 2521796499 6,- 0.4 E -20],
--R    [2.9,0.0550232200 5640722903,0.0550232200 5640722903,- 0.4 E -21],
--R    [3.0,0.0497870683 6786394298,0.0497870683 6786394297 9,- 0.6 E -21],
--R    [3.1,0.0450492023 9355780607,0.0450492023 9355780606 9,- 0.1 E -20],
--R    [3.2,0.0407622039 7836621517,0.0407622039 7836621516 6,- 0.4 E -20],
--R    [3.3,0.0368831674 0124000545,0.0368831674 0124000544 6,- 0.4 E -20],
--R    [3.4,0.0333732699 6032607948,0.0333732699 6032607948 2,0.2 E -20],
--R    [3.5,0.0301973834 2231850074,0.0301973834 2231850074,- 0.2 E -21],
--R    [3.6,0.0273237224 472925608,0.0273237224 4729256080 2,0.2 E -20],
--R    [3.7,0.0247235264 703393912,0.0247235264 7033939120 3,0.3 E -20],
--R    [3.8,0.0223707718 5616559578,0.0223707718 5616559577 9,- 0.1 E -20],
--R    [3.9,0.0202419114 4580438847,0.0202419114 4580438847 2,0.2 E -20],
--R    [4.0,0.0183156388 8873418029,0.0183156388 8873418029 4,0.4 E -20],
--R    [4.1,0.0165726754 0176124754,0.0165726754 0176124754 2,0.2 E -20],
--R    [4.2,0.0149955768 2047770621,0.0149955768 2047770621 2,0.2 E -20],
--R    [4.3,0.0135685590 1220093176,0.0135685590 1220093175 7,- 0.3 E -20],
--R    [4.4,0.0122773399 0306844118,0.0122773399 0306844117 9,- 0.1 E -20],
--R    [4.5,0.0111089965 382423065,0.0111089965 3824230649 6,- 0.4 E -20],
--R    [4.6,0.0100518357 4463358164,0.0100518357 4463358164 2,0.2 E -20],
--R    [4.7,0.0090952771 0169581709,0.0090952771 0169581709 21,0.2 E -20],
--R    [4.8,0.0082297470 4902002884,0.0082297470 4902002884 13,0.1 E -20],
--R    [4.9,0.0074465830 7092434052,0.0074465830 7092434051 82,- 0.2 E -20],
--R    [5.0,0.0067379469 990854671,0.0067379469 9908546709 66,- 0.3 E -20],
--R    [5.1,0.0060967465 6551563611,0.0060967465 6551563610 72,- 0.3 E -20],
--R    [5.2,0.0055165644 2076077242,0.0055165644 2076077241 81,- 0.2 E -20],
--R    [5.3,0.0049915939 0691021621,0.0049915939 0691021621 22,0.2 E -20],
--R    [5.4,0.0045165809 4261266798,0.0045165809 4261266798 16,0.2 E -20],
--R    [5.5,0.0040867714 3846406699,0.0040867714 3846406699 35,0.35 E -20],
--R    [5.6,0.0036978637 1648293082,0.0036978637 1648293082 07,0.7 E -21],
--R    [5.7,0.0033459654 5747127277,0.0033459654 5747127276 58,- 0.42 E -20],
--R    [5.8,0.0030275547 4537581475,0.0030275547 4537581474 82,- 0.18 E -20],
--R    [5.9,0.0027394448 1876836923,0.0027394448 1876836923 28,0.28 E -20],
--R    [6.0,0.0024787521 7666635842,0.0024787521 7666635842 3,0.3 E -20],
--R    [6.1,0.0022428677 1948580247,0.0022428677 1948580247 32,0.32 E -20],
--R    [6.2,0.0020294306 3629573436,0.0020294306 3629573436 34,0.34 E -20],
--R    [6.3,0.0018363047 7702890683,0.0018363047 7702890682 52,- 0.48 E -20],
--R    [6.4,0.0016615572 731739345,0.0016615572 7317393449 91,- 0.93 E -21],
--R    [6.5,0.0015034391 9297757245,0.0015034391 9297757244 74,- 0.26 E -20],
--R    [6.6,0.0013603680 3754789342,0.0013603680 3754789341 69,- 0.31 E -20],
--R    [6.7,0.0012309119 0267348118,0.0012309119 0267348118 46,0.46 E -20],
--R    [6.8,0.0011137751 4784480308,0.0011137751 4784480307 88,- 0.12 E -20],
--R    [6.9,0.0010077854 2904851076,0.0010077854 2904851076 14,0.14 E -20],
--R    [7.0,0.0009118819 6555451621,0.0009118819 6555451620 8,- 0.2 E -20],
--R    [7.1,0.0008251049 2326590427,0.0008251049 2326590427 015,0.1 E -21],
--R    [7.2,0.0007465858 0837667937,0.0007465858 0837667936 81,- 0.19 E -20],
--R    [7.3,0.0006755387 7519384424,0.0006755387 7519384423 783,- 0.22 E -20],
--R    [7.4,0.0006112527 6112957256,0.0006112527 6112957255 567,- 0.433 E -20],
--R    [7.5,0.0005530843 7014783358,0.0005530843 7014783358 31,0.31 E -20],
--R    [7.6,0.0005004514 334406107,0.0005004514 3344061069 551,- 0.449 E -20],
--R    [7.7,0.0004528271 8288679706,0.0004528271 8288679705 8,- 0.2 E -20],
--R    [7.8,0.0004097349 7897978671,0.0004097349 7897978670 846,- 0.15 E -20],
--R    [7.9,0.0003707435 4045908837,0.0003707435 4045908837 443,0.443 E -20],
--R    [8.0,0.0003354626 2790251184,0.0003354626 2790251183 882,- 0.12 E -20],
--R    [8.1,0.0003035391 3807886666,0.0003035391 3807886666 086,0.86 E -21],
--R    [8.2,0.0002746535 6997214233,0.0002746535 6997214232 763,- 0.237 E -20],
--R    [8.3,0.0002485168 2710795202,0.0002485168 2710795202 08,0.8 E -21],
--R    [8.4,0.0002248673 2417884827,0.0002248673 2417884827 28,0.28 E -20],
--R    [8.5,0.0002034683 6901064417,0.0002034683 6901064417 437,0.437 E -20],
--R    [8.6,0.0001841057 9366757912,0.0001841057 9366757912 495,0.495 E -20],
--R    [8.7,0.0001665858 1098763341,0.0001665858 1098763341 149,0.149 E -20],
--R    [8.8,0.0001507330 750954766,0.0001507330 7509547660 064,0.64 E -21],
--R    [8.9,0.0001363889 2648201145,0.0001363889 2648201144 785,- 0.215 E -20],
--R    [9.0,0.0001234098 0408667955,0.0001234098 0408667954 95,- 0.5 E -21],
--R    [9.1,0.0001116658 0849011474,0.0001116658 0849011473 564,- 0.436 E -20],
--R    [9.2,0.0001010394 0183709335,0.0001010394 0183709335 073,0.732 E -21],
--R    [9.3,0.0000914242 3147817334,0.0000914242 3147817333 7862,- 0.214 E -20],
--R    [9.4,0.0000827240 6555663226,0.0000827240 6555663226 2731,0.273 E -20],
--R    [9.5,0.0000748518 2988770059,0.0000748518 2988770059 1471,0.147 E -20],
--R    [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20],
--R    [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20],
--R    [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20],
--R    [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20],
--R    [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to ipftest.output (2010/3/27, 18:27:16).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 8
gf2 := PF 2
 

   (1)  PrimeField 2
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 2
--R                                                                 Type: Domain
--E 1

--S 2 of 8
a : gf2 := primitiveElement()$gf2
 

   (2)  1
                                                           Type: PrimeField 2
--R 
--R
--R   (2)  1
--R                                                           Type: PrimeField 2
--E 2

--S 3 of 8
order a                          
 

   (3)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 8
primitive? a
 

   (4)  true
                                                                Type: Boolean
--R 
--R
--R   (4)  true
--R                                                                Type: Boolean
--E 4

--S 5 of 8
createPrimitivePoly(2)$FFPOLY(gf2)
 

         2
   (5)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         2
--R   (5)  ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 5

--S 6 of 8
createPrimitivePoly(4)$FFPOLY(gf2)
 

         4
   (6)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         4
--R   (6)  ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 6

--S 7 of 8
createPrimitivePoly(12)$FFPOLY(gf2)
 

         12    6    4
   (7)  ?   + ?  + ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         12    6    4
--R   (7)  ?   + ?  + ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 7

--S 8 of 8
createPrimitivePoly(5)$FFPOLY(PF 3)
 

         5    3
   (8)  ?  + ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         5    3
--R   (8)  ?  + ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 8
)spool 
 
Starts dribbling to free.output (2010/3/27, 18:26:27).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 8
Z2:=FreeAbelianGroup Symbol
 

   (1)  FreeAbelianGroup Symbol
                                                                 Type: Domain
--R
--R   (1)  FreeAbelianGroup Symbol
--R                                                                 Type: Domain
--E 1

--S 2 of 8
a:=a::FreeAbelianGroup Symbol
 

   (2)  a
                                                Type: FreeAbelianGroup Symbol
--R
--R   (2)  a
--R                                                Type: FreeAbelianGroup Symbol
--E 2

--S 3 of 8
b:=b::FreeAbelianGroup Symbol
 

   (3)  b
                                                Type: FreeAbelianGroup Symbol
--R
--R   (3)  b
--R                                                Type: FreeAbelianGroup Symbol
--E 3

--S 4 of 8
z:=0::FreeAbelianGroup Symbol
 

   (4)  0
                                                Type: FreeAbelianGroup Symbol
--R
--R   (4)  0
--R                                                Type: FreeAbelianGroup Symbol
--E 4

--S 5 of 8
a < -b
 

   (5)  false
                                                                Type: Boolean
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 8
-b < z
 

   (6)  true
                                                                Type: Boolean
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 8
z < a
 

   (7)  true
                                                                Type: Boolean
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 8
a < b
 

   (8)  true
                                                                Type: Boolean
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

)spool 
 
Starts dribbling to unittest4.output (2010/3/27, 18:41:35).
)set mes auto off
 
)clear all
 


--S 1 of 4
gcdPolynomial((3*x^2+6)::SUP(FRAC(INT)),(9*x^3+12)::SUP(FRAC(INT)))$FRAC(POLY(INT))
 

   (1)  1
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 1

--S 2 of 4
)lisp (trace |FRAC;gcdPolynomial;3Sup;35!0|)
 
Value = (|FRAC;gcdPolynomial;3Sup;35!0|)
--R 
--RValue = (|FRAC;gcdPolynomial;3Sup;35!0|)
--E 2

--S 3 of 4
)lisp (trace |FRAC;gcdPolynomial;3Sup;35!1|)
 
Value = (|FRAC;gcdPolynomial;3Sup;35!1|)
--R 
--RValue = (|FRAC;gcdPolynomial;3Sup;35!1|)
--E 3

--S 4 of 4
gcdPolynomial((3*x^2+6)::SUP(FRAC(INT)),(9*x^3+12)::SUP(FRAC(INT)))$FRAC(POLY(INT))
 
  1> (|FRAC;gcdPolynomial;3Sup;35!0| ((0 . 3) 0 . 1) #<vector 09390ccc>)
  <1 (|FRAC;gcdPolynomial;3Sup;35!0| (0 . 3))
  1> (|FRAC;gcdPolynomial;3Sup;35!0| ((0 . 6) 0 . 1) #<vector 09390ccc>)
  <1 (|FRAC;gcdPolynomial;3Sup;35!0| (0 . 6))
  1> (|FRAC;gcdPolynomial;3Sup;35!1| ((0 . 9) 0 . 1) #<vector 09390cb0>)
  <1 (|FRAC;gcdPolynomial;3Sup;35!1| (0 . 9))
  1> (|FRAC;gcdPolynomial;3Sup;35!1| ((0 . 12) 0 . 1) #<vector 09390cb0>)
  <1 (|FRAC;gcdPolynomial;3Sup;35!1| (0 . 12))

   (2)  1
                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--R 
--I  1> (|FRAC;gcdPolynomial;3Sup;35!0| ((0 . 3) 0 . 1) #<vector 0918c524>)
--R  <1 (|FRAC;gcdPolynomial;3Sup;35!0| (0 . 3))
--I  1> (|FRAC;gcdPolynomial;3Sup;35!0| ((0 . 6) 0 . 1) #<vector 0918c524>)
--R  <1 (|FRAC;gcdPolynomial;3Sup;35!0| (0 . 6))
--I  1> (|FRAC;gcdPolynomial;3Sup;35!1| ((0 . 9) 0 . 1) #<vector 0918c508>)
--R  <1 (|FRAC;gcdPolynomial;3Sup;35!1| (0 . 9))
--I  1> (|FRAC;gcdPolynomial;3Sup;35!1| ((0 . 12) 0 . 1) #<vector 0918c508>)
--R  <1 (|FRAC;gcdPolynomial;3Sup;35!1| (0 . 12))
--R
--R   (2)  1
--R                 Type: SparseUnivariatePolynomial Fraction Polynomial Integer
--E 4

)spool
 
Starts dribbling to AlgebraicallyClosedField.output (2010/3/27, 18:41:41).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 14
pi:Polynomial(Integer):=-3*x^3+2*x+13
 

            3
   (1)  - 3x  + 2x + 13
                                                     Type: Polynomial Integer
--R 
--R
--R            3
--R   (1)  - 3x  + 2x + 13
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 14
rootOf(pi)
 

   (2)  x
                                                        Type: AlgebraicNumber
--R 
--R
--R   (2)  x
--R                                                        Type: AlgebraicNumber
--E 2

--S 3 of 14
rootsOf(pi)
 

   (3)  [%x0,%x1,- %x1 - %x0]
                                                   Type: List AlgebraicNumber
--R 
--R
--R   (3)  [%x0,%x1,- %x1 - %x0]
--R                                                   Type: List AlgebraicNumber
--E 3

--S 4 of 14
zeroOf(pi)
 

   (4)  x
                                                        Type: AlgebraicNumber
--R 
--R
--R   (4)  x
--R                                                        Type: AlgebraicNumber
--E 4

--S 5 of 14
zerosOf(pi)
 

                +-------------+         +-------------+
                |       2               |       2
             - \|- 27%x3  + 24  - 3%x3 \|- 27%x3  + 24  - 3%x3
   (5)  [%x3,-------------------------,-----------------------]
                         6                        6
                                                   Type: List AlgebraicNumber
--R 
--R
--R                +-------------+         +-------------+
--R                |       2               |       2
--R             - \|- 27%x3  + 24  - 3%x3 \|- 27%x3  + 24  - 3%x3
--R   (5)  [%x3,-------------------------,-----------------------]
--R                         6                        6
--R                                                   Type: List AlgebraicNumber
--E 5

--S 6 of 14
sup:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13
 

            3
   (6)  - 3?  + 2? + 13
                                     Type: SparseUnivariatePolynomial Integer
--R 
--R
--R            3
--R   (6)  - 3?  + 2? + 13
--R                                     Type: SparseUnivariatePolynomial Integer
--E 6

--S 7 of 14
rootOf(sup)
 

   (7)  %B
                                                        Type: AlgebraicNumber
--R 
--R
--R   (7)  %B
--R                                                        Type: AlgebraicNumber
--E 7

--S 8 of 14
rootOf(sup,x)
 

   (8)  x
                                                        Type: AlgebraicNumber
--R 
--R
--R   (8)  x
--R                                                        Type: AlgebraicNumber
--E 8

--S 9 of 14
rootsOf(sup)
 

   (9)  [%%C0,%%C1,- %%C1 - %%C0]
                                                   Type: List AlgebraicNumber
--R 
--R
--R   (9)  [%%C0,%%C1,- %%C1 - %%C0]
--R                                                   Type: List AlgebraicNumber
--E 9

--S 10 of 14
rootsOf(sup,x)
 

   (10)  [%x6,%x7,- %x7 - %x6]
                                                   Type: List AlgebraicNumber
--R 
--R
--R   (10)  [%x6,%x7,- %x7 - %x6]
--R                                                   Type: List AlgebraicNumber
--E 10

--S 11 of 14
zeroOf(sup)
 

   (11)  %D
                                                        Type: AlgebraicNumber
--R 
--R
--R   (11)  %D
--R                                                        Type: AlgebraicNumber
--E 11

--S 12 of 14
zeroOf(sup,x)
 

   (12)  x
                                                        Type: AlgebraicNumber
--R 
--R
--R   (12)  x
--R                                                        Type: AlgebraicNumber
--E 12

--S 13 of 14
zerosOf(sup)
 

                  +--------------+          +--------------+
                  |        2                |        2
               - \|- 27%%E0  + 24  - 3%%E0 \|- 27%%E0  + 24  - 3%%E0
   (13)  [%%E0,---------------------------,-------------------------]
                            6                          6
                                                   Type: List AlgebraicNumber
--R 
--R
--R                  +--------------+          +--------------+
--R                  |        2                |        2
--R               - \|- 27%%E0  + 24  - 3%%E0 \|- 27%%E0  + 24  - 3%%E0
--R   (13)  [%%E0,---------------------------,-------------------------]
--R                            6                          6
--R                                                   Type: List AlgebraicNumber
--E 13

--S 14 of 14
zerosOf(sup,x)
 

                 +-------------+         +-------------+
                 |       2               |       2
              - \|- 27%x9  + 24  - 3%x9 \|- 27%x9  + 24  - 3%x9
   (14)  [%x9,-------------------------,-----------------------]
                          6                        6
                                                   Type: List AlgebraicNumber
--R 
--R
--R                 +-------------+         +-------------+
--R                 |       2               |       2
--R              - \|- 27%x9  + 24  - 3%x9 \|- 27%x9  + 24  - 3%x9
--R   (14)  [%x9,-------------------------,-----------------------]
--R                          6                        6
--R                                                   Type: List AlgebraicNumber
--E 14

)spool
 
Starts dribbling to asinatan.output (2010/3/27, 18:23:8).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.01,0.010000166674,asin(0.01),asin(0.01)-0.010000166674],_
[0.02,0.020001333573,asin(0.02),asin(0.02)-0.020001333573],_
[0.03,0.030004501823,asin(0.03),asin(0.03)-0.030004501823],_
[0.04,0.040010674354,asin(0.04),asin(0.04)-0.040010674354],_
[0.05,0.050020856806,asin(0.05),asin(0.05)-0.050020856806],_
[0.06,0.060036058445,asin(0.06),asin(0.06)-0.060036058445],_
[0.07,0.070057293088,asin(0.07),asin(0.07)-0.070057293088],_
[0.08,0.080085580034,asin(0.08),asin(0.08)-0.080085580034],_
[0.09,0.090121945015,asin(0.09),asin(0.09)-0.090121945015],_
[0.10,0.100167421162,asin(0.10),asin(0.10)-0.100167421162],_
[0.11,0.110223049988,asin(0.11),asin(0.11)-0.110223049988],_
[0.12,0.120289882395,asin(0.12),asin(0.12)-0.120289882395],_
[0.13,0.130368979703,asin(0.13),asin(0.13)-0.130368979703],_
[0.14,0.140461414710,asin(0.14),asin(0.14)-0.140461414710],_
[0.15,0.150568272777,asin(0.15),asin(0.15)-0.150568272777],_
[0.16,0.160690652952,asin(0.16),asin(0.16)-0.160690652952],_
[0.17,0.170829669129,asin(0.17),asin(0.17)-0.170829669129],_
[0.18,0.180986451247,asin(0.18),asin(0.18)-0.180986451247],_
[0.19,0.191162146531,asin(0.19),asin(0.19)-0.191162146531],_
[0.20,0.201357920790,asin(0.20),asin(0.20)-0.201357920790],_
[0.21,0.211574959758,asin(0.21),asin(0.21)-0.211574959758],_
[0.22,0.221814470497,asin(0.22),asin(0.22)-0.221814470497],_
[0.23,0.232077682863,asin(0.23),asin(0.23)-0.232077682863],_
[0.24,0.242365851039,asin(0.24),asin(0.24)-0.242365851039],_
[0.25,0.252680255142,asin(0.25),asin(0.25)-0.252680255142],_
[0.26,0.263022202908,asin(0.26),asin(0.26)-0.263022202908],_
[0.27,0.273393031467,asin(0.27),asin(0.27)-0.273393031467],_
[0.28,0.283794109208,asin(0.28),asin(0.28)-0.283794109208],_
[0.29,0.294226837749,asin(0.29),asin(0.29)-0.294226837749],_
[0.30,0.304692654015,asin(0.30),asin(0.30)-0.304692654015],_
[0.31,0.315193032441,asin(0.31),asin(0.31)-0.315193032441],_
[0.32,0.325729487295,asin(0.32),asin(0.32)-0.325729487295],_
[0.33,0.336303575154,asin(0.33),asin(0.33)-0.336303575154],_
[0.34,0.346916897527,asin(0.34),asin(0.34)-0.346916897527],_
[0.35,0.357571103646,asin(0.35),asin(0.35)-0.357571103646],_
[0.36,0.368267893437,asin(0.36),asin(0.36)-0.368267893437],_
[0.37,0.379009020696,asin(0.37),asin(0.37)-0.379009020696],_
[0.38,0.389796296474,asin(0.38),asin(0.38)-0.389796296474],_
[0.39,0.400631592701,asin(0.39),asin(0.39)-0.400631592701],_
[0.40,0.411516846067,asin(0.40),asin(0.40)-0.411516846067],_
[0.41,0.422454062187,asin(0.41),asin(0.41)-0.422454062187],_
[0.42,0.433445320070,asin(0.42),asin(0.42)-0.433445320070],_
[0.43,0.444492776936,asin(0.43),asin(0.43)-0.444492776936],_
[0.44,0.455598673396,asin(0.44),asin(0.44)-0.455598673396],_
[0.45,0.466765339047,asin(0.45),asin(0.45)-0.466765339047],_
[0.46,0.477995198519,asin(0.46),asin(0.46)-0.477995198519],_
[0.47,0.489290778014,asin(0.47),asin(0.47)-0.489290778014],_
[0.48,0.500654712405,asin(0.48),asin(0.48)-0.500654712405],_
[0.49,0.512089752934,asin(0.49),asin(0.49)-0.512089752934],_
[0.50,0.523598775598,asin(0.50),asin(0.50)-0.523598775598],_
[0.51,0.535184790276,asin(0.51),asin(0.51)-0.535184790276],_
[0.52,0.546850950696,asin(0.52),asin(0.52)-0.546850950696],_
[0.53,0.558600565343,asin(0.53),asin(0.53)-0.558600565343],_
[0.54,0.570437109400,asin(0.54),asin(0.54)-0.570437109400],_
[0.55,0.582364237869,asin(0.55),asin(0.55)-0.582364237869],_
[0.56,0.594385800001,asin(0.56),asin(0.56)-0.594385800001],_
[0.57,0.606505855213,asin(0.57),asin(0.57)-0.606505855213],_
[0.58,0.618728690672,asin(0.58),asin(0.58)-0.618728690672],_
[0.59,0.631058840778,asin(0.59),asin(0.59)-0.631058840778],_
[0.60,0.643501108793,asin(0.60),asin(0.60)-0.643501108793],_
[0.61,0.656060590925,asin(0.61),asin(0.61)-0.656060590925],_
[0.62,0.668742703202,asin(0.62),asin(0.62)-0.668742703202],_
[0.63,0.681553211563,asin(0.63),asin(0.63)-0.681553211563],_
[0.64,0.694498265627,asin(0.64),asin(0.64)-0.694498265627],_
[0.65,0.707584436725,asin(0.65),asin(0.65)-0.707584436725],_
[0.66,0.720818760870,asin(0.66),asin(0.66)-0.720818760870],_
[0.67,0.734208787453,asin(0.67),asin(0.67)-0.734208787453],_
[0.68,0.747762634660,asin(0.68),asin(0.68)-0.747762634660],_
[0.69,0.761489052748,asin(0.69),asin(0.69)-0.761489052748],_
[0.70,0.775397496611,asin(0.70),asin(0.70)-0.775397496611],_
[0.71,0.789498209346,asin(0.71),asin(0.71)-0.789498209346],_
[0.72,0.803802318933,asin(0.72),asin(0.72)-0.803802318933],_
[0.73,0.818321950632,asin(0.73),asin(0.73)-0.818321950632],_
[0.74,0.833070358342,asin(0.74),asin(0.74)-0.833070358342],_
[0.75,0.848062078981,asin(0.75),asin(0.75)-0.848062078981],_
[0.76,0.863313115016,asin(0.76),asin(0.76)-0.863313115016],_
[0.77,0.878841151669,asin(0.77),asin(0.77)-0.878841151669],_
[0.78,0.894665817234,asin(0.78),asin(0.78)-0.894665817234],_
[0.79,0.910808997407,asin(0.79),asin(0.79)-0.910808997407],_
[0.80,0.927295218002,asin(0.80),asin(0.80)-0.927295218002],_
[0.81,0.944152115154,asin(0.81),asin(0.81)-0.944152115154],_
[0.82,0.961411018764,asin(0.82),asin(0.82)-0.961411018764],_
[0.83,0.979107684368,asin(0.83),asin(0.83)-0.979107684368],_
[0.84,0.997283222372,asin(0.84),asin(0.84)-0.997283222372],_
[0.85,1.015985293815,asin(0.85),asin(0.85)-1.015985293815],_
[0.86,1.035269672481,asin(0.86),asin(0.86)-1.035269672481],_
[0.87,1.055202320549,asin(0.87),asin(0.87)-1.055202320549],_
[0.88,1.075862200454,asin(0.88),asin(0.88)-1.075862200454],_
[0.89,1.097345169523,asin(0.89),asin(0.89)-1.097345169523],_
[0.90,1.119769514999,asin(0.90),asin(0.90)-1.119769514999],_
[0.91,1.143284061850,asin(0.91),asin(0.91)-1.143284061850],_
[0.92,1.168080485214,asin(0.92),asin(0.92)-1.168080485214],_
[0.93,1.194412844477,asin(0.93),asin(0.93)-1.194412844477],_
[0.94,1.222630305522,asin(0.94),asin(0.94)-1.222630305522],_
[0.95,1.253235897503,asin(0.95),asin(0.95)-1.253235897503],_
[0.96,1.287002217587,asin(0.96),asin(0.96)-1.287002217587],_
[0.97,1.325230809280,asin(0.97),asin(0.97)-1.325230809280],_
[0.98,1.370461484472,asin(0.98),asin(0.98)-1.370461484472],_
[0.99,1.429256853470,asin(0.99),asin(0.99)-1.429256853470],_
[1.00,1.570796326795,asin(1.00),asin(1.00)-1.570796326795]]
 

   (1)
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    [1.0,1.5707963267 95,1.5707963267 948966192,- 0.103381 E -12]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.01,0.0100001666 74,0.0100001666 7416711312 6,0.167113126 E -12],
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--R    [1.0,1.5707963267 95,1.5707963267 948966192,- 0.103381 E -12]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
[[0.01,0.009999666687,atan(0.01),atan(0.01)-0.009999666687],_
[0.02,0.019997333973,atan(0.02),atan(0.02)-0.019997333973],_
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[0.99,0.780373080067,atan(0.99),atan(0.99)-0.780373080067],_
[1.00,0.785398163397,atan(1.00),atan(1.00)-0.785398163397]]
 

   (2)
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    [1.0,0.7853981633 97,0.7853981633 9744830961,0.4483096 E -12]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,0.0099996666 87,0.0099996666 8666523820 63,- 0.334761794 E -12],
--R    [0.02,0.0199973339 73,0.0199973339 7315053306 1,0.150533061 E -12],
--R    [0.03,0.0299910048 57,0.0299910048 5687789967 7,- 0.122100323 E -12],
--R    [0.04,0.0399786871 23,0.0399786871 2329004141 4,0.290041414 E -12],
--R    [0.05,0.0499583957 22,0.0499583957 2194276141,- 0.5723859 E -13],
--R    [0.06,0.0599281551 21,0.0599281551 2120788443 2,0.20788443 E -12],
--R    [0.07,0.0698860016 35,0.0698860016 3464249929 5,- 0.35750071 E -12],
--R    [0.08,0.0798299857 12,0.0798299857 1223731589 3,0.23731589 E -12],
--R    [0.09,0.0897581741 9,0.0897581741 8995052315,- 0.4947685 E -13],
--R    [0.1,0.0996686524 91,0.0996686524 9116202737 9,0.16202738 E -12],
--R    [0.11,0.1095595267 74,0.1095595267 7394434487,- 0.5565513 E -13],
--R    [0.12,0.1194289260 18,0.1194289260 1833845181,0.33845181 E -12],
--R    [0.13,0.1292750040 48,0.1292750040 4814305472,0.14305472 E -12],
--R    [0.14,0.1390959414 82,0.1390959414 820713243,0.713243 E -13],
--R    [0.15,0.1488899476 09,0.1488899476 0949725059,0.49725059 E -12],
--R    [0.16,0.1586552621 86,0.1586552621 8640140386,0.40140386 E -12],
--R    [0.17,0.1683901571 48,0.1683901571 4752989727,- 0.47010272 E -12],
--R    [0.18,0.1780929382 31,0.1780929382 3119754967,0.19754967 E -12],
--R    [0.19,0.1877619465 14,0.1877619465 135934152,- 0.4065848 E -12],
--R    [0.2,0.1973955598 5,0.1973955598 4988075837,- 0.11924163 E -12],
--R    [0.21,0.2069921942 2,0.2069921942 198210249,- 0.1789751 E -12],
--R    [0.22,0.2165503049 76,0.2165503049 7608927648,0.8927648 E -13],
--R    [0.23,0.2260683879 94,0.2260683879 9388390584,- 0.11609416 E -12],
--R    [0.24,0.2355449807 21,0.2355449807 2086334143,- 0.13665857 E -12],
--R    [0.25,0.2449786631 27,0.2449786631 2686415417,- 0.13584583 E -12],
--R    [0.26,0.2543680585 53,0.2543680585 5326593143,0.26593143 E -12],
--R    [0.27,0.2637118344 62,0.2637118344 6226612016,0.26612016 E -12],
--R    [0.28,0.2730087030 87,0.2730087030 8671060295,- 0.28939705 E -12],
--R    [0.29,0.2822574219 81,0.2822574219 8149112127,0.49112127 E -12],
--R    [0.3,0.2914567944 78,0.2914567944 77867092,- 0.132908 E -12],
--R    [0.31,0.3006056700 42,0.3006056700 4239540423,0.39540423 E -12],
--R    [0.32,0.3097029445 42,0.3097029445 4245619992,0.45619992 E -12],
--R    [0.33,0.3187475604 21,0.3187475604 2064443712,- 0.35556288 E -12],
--R    [0.34,0.3277385067 81,0.3277385067 80555446,- 0.444554 E -12],
--R    [0.35,0.3366748193 87,0.3366748193 867271814,- 0.2728186 E -12],
--R    [0.36,0.3455555805 82,0.3455555805 8171213686,- 0.28786314 E -12],
--R    [0.37,0.3543799191 23,0.3543799191 2343780983,0.43780983 E -12],
--R    [0.38,0.3631470099 46,0.3631470099 4617628972,0.1762897 E -12],
--R    [0.39,0.3718560738 49,0.3718560738 485812575,- 0.4187425 E -12],
--R    [0.4,0.3805063771 12,0.3805063771 123648863,0.3648863 E -12],
--R    [0.41,0.3890972310 55,0.3890972310 5527841924,0.27841924 E -12],
--R    [0.42,0.3976279915 22,0.3976279915 22129314,0.129314 E -12],
--R    [0.43,0.4060980583 18,0.4060980583 1761564783,- 0.38435217 E -12],
--R    [0.44,0.4145068745 85,0.4145068745 8478593834,- 0.2140617 E -12],
--R    [0.45,0.4228539261 33,0.4228539261 3294071297,- 0.5928703 E -13],
--R    [0.46,0.4311387407 19,0.4311387407 1878218339,- 0.2178166 E -12],
--R    [0.47,0.4393608872 85,0.4393608872 8459143742,- 0.40856258 E -12],
--R    [0.48,0.4475199751 57,0.4475199751 5716987972,0.1698797 E -12],
--R    [0.49,0.4556156532 11,0.4556156532 1122449214,0.2244921 E -12],
--R    [0.5,0.4636476090 01,0.4636476090 0080611621,- 0.1938838 E -12],
--R    [0.51,0.4716155678 62,0.4716155678 6232766012,0.32766012 E -12],
--R    [0.52,0.4795192919 93,0.4795192919 9259616542,- 0.40383458 E -12],
--R    [0.53,0.4873585795 05,0.4873585795 0519028312,0.1902831 E -12],
--R    [0.54,0.4951332634 68,0.4951332634 6840412185,0.40412185 E -12],
--R    [0.55,0.5028432109 28,0.5028432109 2786082733,- 0.1391727 E -12],
--R    [0.56,0.5104883219 17,0.5104883219 1677576997,- 0.22423 E -12],
--R    [0.57,0.5180685284 57,0.5180685284 56720949,- 0.279051 E -12],
--R    [0.58,0.5255837935 52,0.5255837935 5161020277,- 0.3897972 E -12],
--R    [0.59,0.5330341101 77,0.5330341101 7749002604,0.49002604 E -12],
--R    [0.6,0.5404195002 71,0.5404195002 7058415544,- 0.4158446 E -12],
--R    [0.61,0.5477400137 16,0.5477400137 1590245052,- 0.9754948 E -13],
--R    [0.62,0.5549957273 39,0.5549957273 3858676242,- 0.4132376 E -12],
--R    [0.63,0.5621867439,0.5621867439 0002917485,0.291748 E -13],
--R    [0.64,0.5693131911 01,0.5693131911 0066188631,- 0.3381137 E -12],
--R    [0.65,0.5763752205 91,0.5763752205 9118368022,0.1836802 E -12],
--R    [0.66,0.5833730069 94,0.5833730069 9385593947,- 0.1440605 E -12],
--R    [0.67,0.5903067469 35,0.5903067469 3537198239,0.3719824 E -12],
--R    [0.68,0.5971766580 93,0.5971766580 9267754844,- 0.3224516 E -12],
--R    [0.69,0.6039829782 53,0.6039829782 5299790738,- 0.20926 E -14],
--R    [0.7,0.6107259643 89,0.6107259643 8920861654,0.2086165 E -12],
--R    [0.71,0.6174058917 52,0.6174058917 5157266652,- 0.4273335 E -12],
--R    [0.72,0.6240230529 77,0.6240230529 7675684759,- 0.2431524 E -12],
--R    [0.73,0.6305777572 15,0.6305777572 1493480666,- 0.6519333 E -13],
--R    [0.74,0.6370703292 76,0.6370703292 7568357172,- 0.3164283 E -12],
--R    [0.75,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12],
--R    [0.76,0.6498704494 12,0.6498704494 1194757749,- 0.524225 E -13],
--R    [0.77,0.6561787179 91,0.6561787179 9139487538,0.3948754 E -12],
--R    [0.78,0.6624262938 33,0.6624262938 3315116177,0.1511618 E -12],
--R    [0.79,0.6686135679 28,0.6686135679 2782091069,- 0.1790893 E -12],
--R    [0.8,0.6747409422 24,0.6747409422 2355266306,- 0.4473369 E -12],
--R    [0.81,0.6808088289 16,0.6808088289 1582756649,- 0.1724335 E -12],
--R    [0.82,0.6868176497 59,0.6868176497 5864527553,- 0.3547245 E -12],
--R    [0.83,0.6927678353 97,0.6927678353 9712221066,0.1222107 E -12],
--R    [0.84,0.6986598247 21,0.6986598247 214631978,0.4631978 E -12],
--R    [0.85,0.7044940642 42,0.7044940642 4221771666,0.2177167 E -12],
--R    [0.86,0.7102710074 87,0.7102710074 8668623033,- 0.3137697 E -12],
--R    [0.87,0.7159911144 16,0.7159911144 1630019894,0.3001989 E -12],
--R    [0.88,0.7216548508 65,0.7216548508 6476123707,- 0.2387629 E -12],
--R    [0.89,0.7272626879 97,0.7272626879 9669029805,- 0.309702 E -12],
--R    [0.9,0.7328151017 87,0.7328151017 8650659164,- 0.49340836 E -12],
--R    [0.91,0.7383125725 17,0.7383125725 1722800021,0.2280002 E -12],
--R    [0.92,0.7437555842 99,0.7437555842 9885988576,- 0.1401142 E -12],
--R    [0.93,0.7491446246 06,0.7491446246 0601721032,0.172103 E -13],
--R    [0.94,0.7544801838 34,0.7544801838 3440566231,0.4056623 E -12],
--R    [0.95,0.7597627548 76,0.7597627548 7577082892,- 0.2291711 E -12],
--R    [0.96,0.7649928327 11,0.7649928327 1091022317,- 0.8977683 E -13],
--R    [0.97,0.7701709140 2,0.7701709140 2033100726,0.3310073 E -12],
--R    [0.98,0.7752974968 12,0.7752974968 1212640304,0.126403 E -12],
--R    [0.99,0.7803730800 67,0.7803730800 666358989,- 0.3641011 E -12],
--R    [1.0,0.7853981633 97,0.7853981633 9744830961,0.4483096 E -12]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to Void.output (2010/3/27, 18:46:42).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 5
r := (a; b; if c then d else e; f) 
 
 
Daly Bug
   An expression following if/when must evaluate to a Boolean and you 
      have written one that does not.
--R 
--R 
--RDaly Bug
--R   An expression following if/when must evaluate to a Boolean and you 
--R      have written one that does not.
--E 1

--S 2 of 5
a : Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

)set message void on
 

--S 3 of 5
b : Fraction Integer
 

   (2)  "()"
                                                                   Type: Void
--R 
--R
--R   (2)  "()"
--R                                                                   Type: Void
--E 3

)set message void off
 
 
--S 4 of 5
3::Void
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
% :: PositiveInteger
 
 
Daly Bug
   Cannot convert from type Void to PositiveInteger for value
   "()"

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Void to PositiveInteger for value
--R   "()"
--R
--E 5
)spool
 
Starts dribbling to ApplicationProgramInterface.output (2010/3/27, 18:41:43).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 5
getDomains 'Collection
 

   (1)
   {AssociationList, Bits, CharacterClass, DataList, EqTable, FlexibleArray,
    GeneralPolynomialSet, GeneralSparseTable, GeneralTriangularSet, HashTable,
    IndexedBits, IndexedFlexibleArray, IndexedList, IndexedOneDimensionalArray,
    IndexedString, IndexedVector, InnerTable, KeyedAccessFile, Library, List,
    ListMultiDictionary, Multiset, OneDimensionalArray, Point, PrimitiveArray,
    RegularChain, RegularTriangularSet, Result, RoutinesTable, Set,
    SparseTable, SquareFreeRegularTriangularSet, Stream, String, StringTable,
    Table, Vector, WuWenTsunTriangularSet}
                                                             Type: Set Symbol
--R
--R   (1)
--R   {AssociationList, Bits, CharacterClass, DataList, EqTable, FlexibleArray,
--R    GeneralPolynomialSet, GeneralSparseTable, GeneralTriangularSet, HashTable,
--R    IndexedBits, IndexedFlexibleArray, IndexedList, IndexedOneDimensionalArray,
--R    IndexedString, IndexedVector, InnerTable, KeyedAccessFile, Library, List,
--R    ListMultiDictionary, Multiset, OneDimensionalArray, Point, PrimitiveArray,
--R    RegularChain, RegularTriangularSet, Result, RoutinesTable, Set,
--R    SparseTable, SquareFreeRegularTriangularSet, Stream, String, StringTable,
--R    Table, Vector, WuWenTsunTriangularSet}
--R                                                             Type: Set Symbol
--E 1

--S 2 of 5
difference(getDomains 'IndexedAggregate,getDomains 'Collection)
 

   (2)
   {DirectProduct, DirectProductMatrixModule, DirectProductModule,
    HomogeneousDirectProduct, OrderedDirectProduct,
    SplitHomogeneousDirectProduct}
                                                             Type: Set Symbol
--R
--R   (2)
--R   {DirectProduct, DirectProductMatrixModule, DirectProductModule,
--R    HomogeneousDirectProduct, OrderedDirectProduct,
--R    SplitHomogeneousDirectProduct}
--R                                                             Type: Set Symbol
--E 2

--S 3 of 5
credits()
 
An alphabetical listing of contributors to AXIOM:
Cyril Alberga          Roy Adler              Christian Aistleitner
Richard Anderson       George Andrews         S.J. Atkins
Henry Baker            Stephen Balzac         Yurij Baransky
David R. Barton        Gerald Baumgartner     Gilbert Baumslag
Michael Becker         Jay Belanger           David Bindel
Fred Blair             Vladimir Bondarenko    Mark Botch
Alexandre Bouyer       Peter A. Broadbery     Martin Brock
Manuel Bronstein       Stephen Buchwald       Florian Bundschuh
Luanne Burns           William Burge
Quentin Carpent        Robert Caviness        Bruce Char
Ondrej Certik          Cheekai Chin           David V. Chudnovsky
Gregory V. Chudnovsky  Josh Cohen             Christophe Conil
Don Coppersmith        George Corliss         Robert Corless
Gary Cornell           Meino Cramer           Claire Di Crescenzo
David Cyganski
Timothy Daly Sr.       Timothy Daly Jr.       James H. Davenport
Didier Deshommes       Michael Dewar
Jean Della Dora        Gabriel Dos Reis       Claire DiCrescendo
Sam Dooley             Lionel Ducos           Martin Dunstan
Brian Dupee            Dominique Duval
Robert Edwards         Heow Eide-Goodman      Lars Erickson
Richard Fateman        Bertfried Fauser       Stuart Feldman
Brian Ford             Albrecht Fortenbacher  George Frances
Constantine Frangos    Timothy Freeman        Korrinn Fu
Marc Gaetano           Rudiger Gebauer        Kathy Gerber
Patricia Gianni        Samantha Goldrich      Holger Gollan
Teresa Gomez-Diaz      Laureano Gonzalez-Vega Stephen Gortler
Johannes Grabmeier     Matt Grayson           Klaus Ebbe Grue
James Griesmer         Vladimir Grinberg      Oswald Gschnitzer
Jocelyn Guidry
Steve Hague            Satoshi Hamaguchi      Mike Hansen
Richard Harke          Vilya Harvey           Martin Hassner
Arthur S. Hathaway     Dan Hatton             Waldek Hebisch
Karl Hegbloom          Ralf Hemmecke          Henderson
Antoine Hersen         Gernot Hueber
Pietro Iglio
Alejandro Jakubi       Richard Jenks
Kai Kaminski           Grant Keady            Tony Kennedy
Paul Kosinski          Klaus Kusche           Bernhard Kutzler
Tim Lahey              Larry Lambe            Franz Lehner
Frederic Lehobey       Michel Levaud          Howard Levy
Liu Xiaojun            Rudiger Loos           Michael Lucks
Richard Luczak
Camm Maguire           Francois Maltey        Alasdair McAndrew
Bob McElrath           Michael McGettrick     Ian Meikle
David Mentre           Victor S. Miller       Gerard Milmeister
Mohammed Mobarak       H. Michael Moeller     Michael Monagan
Marc Moreno-Maza       Scott Morrison         Joel Moses
Mark Murray
William Naylor         C. Andrew Neff         John Nelder
Godfrey Nolan          Arthur Norman          Jinzhong Niu
Michael O'Connor       Summat Oemrawsingh     Kostas Oikonomou
Humberto Ortiz-Zuazaga
Julian A. Padget       Bill Page              Susan Pelzel
Michel Petitot         Didier Pinchon         Ayal Pinkus
Jose Alfredo Portes
Claude Quitte
Arthur C. Ralfs        Norman Ramsey          Anatoly Raportirenko
Michael Richardson     Renaud Rioboo          Jean Rivlin
Nicolas Robidoux       Simon Robinson         Raymond Rogers
Michael Rothstein      Martin Rubey
Philip Santas          Alfred Scheerhorn      William Schelter
Gerhard Schneider      Martin Schoenert       Marshall Schor
Frithjof Schulze       Fritz Schwarz          Steven Segletes
Nick Simicich          William Sit            Elena Smirnova
Jonathan Steinbach     Fabio Stumbo           Christine Sundaresan
Robert Sutor           Moss E. Sweedler       Eugene Surowitz
Max Tegmark            James Thatcher         Balbir Thomas
Mike Thomas            Dylan Thurston         Barry Trager
Themos T. Tsikas
Gregory Vanuxem
Bernhard Wall          Stephen Watt           Jaap Weel
Juergen Weiss          M. Weller              Mark Wegman
James Wen              Thorsten Werther       Michael Wester
John M. Wiley          Berhard Will           Clifton J. Williamson
Stephen Wilson         Shmuel Winograd        Robert Wisbauer
Sandra Wityak          Waldemar Wiwianka      Knut Wolf
Clifford Yapp          David Yun
Vadim Zhytnikov        Richard Zippel         Evelyn Zoernack
Bruno Zuercher         Dan Zwillinger
                                                                   Type: Void
--R 
--RAn alphabetical listing of contributors to AXIOM:
--RCyril Alberga          Roy Adler              Christian Aistleitner
--RRichard Anderson       George Andrews         S.J. Atkins
--RHenry Baker            Stephen Balzac         Yurij Baransky
--RDavid R. Barton        Gerald Baumgartner     Gilbert Baumslag
--RMichael Becker         Jay Belanger           David Bindel
--RFred Blair             Vladimir Bondarenko    Mark Botch
--RAlexandre Bouyer       Peter A. Broadbery     Martin Brock
--RManuel Bronstein       Stephen Buchwald       Florian Bundschuh
--RLuanne Burns           William Burge
--RQuentin Carpent        Robert Caviness        Bruce Char
--ROndrej Certik          Cheekai Chin           David V. Chudnovsky
--RGregory V. Chudnovsky  Josh Cohen             Christophe Conil
--RDon Coppersmith        George Corliss         Robert Corless
--RGary Cornell           Meino Cramer           Claire Di Crescenzo
--RDavid Cyganski
--RTimothy Daly Sr.       Timothy Daly Jr.       James H. Davenport
--RDidier Deshommes       Michael Dewar
--RJean Della Dora        Gabriel Dos Reis       Claire DiCrescendo
--RSam Dooley             Lionel Ducos           Martin Dunstan
--RBrian Dupee            Dominique Duval
--RRobert Edwards         Heow Eide-Goodman      Lars Erickson
--RRichard Fateman        Bertfried Fauser       Stuart Feldman
--RBrian Ford             Albrecht Fortenbacher  George Frances
--RConstantine Frangos    Timothy Freeman        Korrinn Fu
--RMarc Gaetano           Rudiger Gebauer        Kathy Gerber
--RPatricia Gianni        Samantha Goldrich      Holger Gollan
--RTeresa Gomez-Diaz      Laureano Gonzalez-Vega Stephen Gortler
--RJohannes Grabmeier     Matt Grayson           Klaus Ebbe Grue
--RJames Griesmer         Vladimir Grinberg      Oswald Gschnitzer
--RJocelyn Guidry
--RSteve Hague            Satoshi Hamaguchi      Mike Hansen
--RRichard Harke          Vilya Harvey           Martin Hassner
--RArthur S. Hathaway     Dan Hatton             Waldek Hebisch
--RKarl Hegbloom          Ralf Hemmecke          Henderson
--RAntoine Hersen         Gernot Hueber
--RPietro Iglio
--RAlejandro Jakubi       Richard Jenks
--RKai Kaminski           Grant Keady            Tony Kennedy
--RPaul Kosinski          Klaus Kusche           Bernhard Kutzler
--RTim Lahey              Larry Lambe            Franz Lehner
--RFrederic Lehobey       Michel Levaud          Howard Levy
--RLiu Xiaojun            Rudiger Loos           Michael Lucks
--RRichard Luczak
--RCamm Maguire           Francois Maltey        Alasdair McAndrew
--RBob McElrath           Michael McGettrick     Ian Meikle
--RDavid Mentre           Victor S. Miller       Gerard Milmeister
--RMohammed Mobarak       H. Michael Moeller     Michael Monagan
--RMarc Moreno-Maza       Scott Morrison         Joel Moses
--RMark Murray
--RWilliam Naylor         C. Andrew Neff         John Nelder
--RGodfrey Nolan          Arthur Norman          Jinzhong Niu
--RMichael O'Connor       Summat Oemrawsingh     Kostas Oikonomou
--RHumberto Ortiz-Zuazaga
--RJulian A. Padget       Bill Page              Susan Pelzel
--RMichel Petitot         Didier Pinchon         Ayal Pinkus
--RJose Alfredo Portes
--RClaude Quitte
--RArthur C. Ralfs        Norman Ramsey          Anatoly Raportirenko
--RMichael Richardson     Renaud Rioboo          Jean Rivlin
--RNicolas Robidoux       Simon Robinson         Raymond Rogers
--RMichael Rothstein      Martin Rubey
--RPhilip Santas          Alfred Scheerhorn      William Schelter
--RGerhard Schneider      Martin Schoenert       Marshall Schor
--RFrithjof Schulze       Fritz Schwarz          Steven Segletes
--RNick Simicich          William Sit            Elena Smirnova
--RJonathan Steinbach     Fabio Stumbo           Christine Sundaresan
--RRobert Sutor           Moss E. Sweedler       Eugene Surowitz
--RMax Tegmark            James Thatcher         Balbir Thomas
--RMike Thomas            Dylan Thurston         Barry Trager
--RThemos T. Tsikas
--RGregory Vanuxem
--RBernhard Wall          Stephen Watt           Jaap Weel
--RJuergen Weiss          M. Weller              Mark Wegman
--RJames Wen              Thorsten Werther       Michael Wester
--RJohn M. Wiley          Berhard Will           Clifton J. Williamson
--RStephen Wilson         Shmuel Winograd        Robert Wisbauer
--RSandra Wityak          Waldemar Wiwianka      Knut Wolf
--RClifford Yapp          David Yun
--RVadim Zhytnikov        Richard Zippel         Evelyn Zoernack
--RBruno Zuercher         Dan Zwillinger
--R                                                                   Type: Void
--E 3

--S 4 of 5
summary()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
)show API
 
 ApplicationProgramInterface  is a package constructor
 Abbreviation for ApplicationProgramInterface is API 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for API 

------------------------------- Operations --------------------------------
 credits : () -> Void                  getDomains : Symbol -> Set Symbol
 summary : () -> Void                 

--R ApplicationProgramInterface  is a package constructor
--R Abbreviation for ApplicationProgramInterface is API 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for API 
--R
--R------------------------------- Operations --------------------------------
--R credits : () -> Void                  getDomains : Symbol -> Set Symbol
--R summary : () -> Void                 
--R
--E 5

)spool
 
Starts dribbling to kamke4.output (2010/3/27, 18:28:25).
)set break resume
 
)set mes auto off
 
)clear all
 
--S 1 of 127
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 127
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 127
f0:=operator 'f0
 

   (3)  f0
                                                          Type: BasicOperator
--R 
--R
--R   (3)  f0
--R                                                          Type: BasicOperator
--E 3

--S 4 of 127
f1:=operator 'f1
 

   (4)  f1
                                                          Type: BasicOperator
--R 
--R
--R   (4)  f1
--R                                                          Type: BasicOperator
--E 4

--S 5 of 127
f2:=operator 'f2
 

   (5)  f2
                                                          Type: BasicOperator
--R 
--R
--R   (5)  f2
--R                                                          Type: BasicOperator
--E 5

--S 6 of 127
g:=operator 'g
 

   (6)  g
                                                          Type: BasicOperator
--R 
--R
--R   (6)  g
--R                                                          Type: BasicOperator
--E 6

--S 7 of 127
tg:=operator 'tg
 

   (7)  tg
                                                          Type: BasicOperator
--R 
--R
--R   (7)  tg
--R                                                          Type: BasicOperator
--E 7

--S 8 of 127
h:=operator 'h
 

   (8)  h
                                                          Type: BasicOperator
--R 
--R
--R   (8)  h
--R                                                          Type: BasicOperator
--E 8

--S 9 of 127
ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)**2-D(f(x),x)*y(x)-2*f(x)**2
 

              ,           ,               2        2
   (9)  2f(x)y (x) - y(x)f (x) + 2f(x)y(x)  - 2f(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,           ,               2        2
--R   (9)  2f(x)y (x) - y(x)f (x) + 2f(x)y(x)  - 2f(x)
--R
--R                                                     Type: Expression Integer
--E 9

--S 10 of 127
solve(ode201,y,x)
 

   (10)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (10)  "failed"
--R                                                    Type: Union("failed",...)
--E 10

--S 11 of 127
ode202 := f(x)*D(y(x),x)+g(x)*tg(y(x))+h(x)
 

              ,
   (11)  f(x)y (x) + g(x)tg(y(x)) + h(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,
--R   (11)  f(x)y (x) + g(x)tg(y(x)) + h(x)
--R
--R                                                     Type: Expression Integer
--E 11

--S 12 of 127
solve(ode202,y,x)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 127
ode203 := y(x)*D(y(x),x)+y(x)+x**3
 

              ,              3
   (13)  y(x)y (x) + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              ,              3
--R   (13)  y(x)y (x) + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 13

--S 14 of 127
solve(ode203,y,x)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 14

--S 15 of 127
ode204 := y(x)*D(y(x),x)+a*y(x)+x
 

              ,
   (15)  y(x)y (x) + a y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R              ,
--R   (15)  y(x)y (x) + a y(x) + x
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 127
solve(ode204,y,x)
 

   (16)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (16)  "failed"
--R                                                    Type: Union("failed",...)
--E 16

--S 17 of 127
ode205 := y(x)*D(y(x),x)+a*y(x)+(a**2-1)/(4)*x+b*x**n
 

               ,          n               2
         4y(x)y (x) + 4b x  + 4a y(x) + (a  - 1)x

   (17)  ----------------------------------------
                             4
                                                     Type: Expression Integer
--R 
--R
--R               ,          n               2
--R         4y(x)y (x) + 4b x  + 4a y(x) + (a  - 1)x
--R
--R   (17)  ----------------------------------------
--R                             4
--R                                                     Type: Expression Integer
--E 17

--S 18 of 127
solve(ode205,y,x)
 

   (18)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (18)  "failed"
--R                                                    Type: Union("failed",...)
--E 18

--S 19 of 127
ode206 := y(x)*D(y(x),x)+a*y(x)+b*exp(x)-2*a
 

              ,          x
   (19)  y(x)y (x) + b %e  + a y(x) - 2a

                                                     Type: Expression Integer
--R 
--R
--R              ,          x
--R   (19)  y(x)y (x) + b %e  + a y(x) - 2a
--R
--R                                                     Type: Expression Integer
--E 19

--S 20 of 127
solve(ode206,y,x)
 

   (20)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (20)  "failed"
--R                                                    Type: Union("failed",...)
--E 20

--S 21 of 127
ode207 := y(x)*D(y(x),x)+y(x)**2+4*x*(x+1)
 

              ,          2     2
   (21)  y(x)y (x) + y(x)  + 4x  + 4x

                                                     Type: Expression Integer
--R 
--R
--R              ,          2     2
--R   (21)  y(x)y (x) + y(x)  + 4x  + 4x
--R
--R                                                     Type: Expression Integer
--E 21

--S 22 of 127
yx:=solve(ode207,y,x)
 

              2     2   2x
         (y(x)  + 4x )%e
   (22)  -----------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2     2   2x
--R         (y(x)  + 4x )%e
--R   (22)  -----------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 22

--S 23 of 127
ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1)
 

   (23)
             3     2        2x 2 ,
       (2y(x)  + 8x y(x))(%e  ) y (x)

     + 
             4       2          2      4      3    2x 2      2
       (3y(x)  + (24x  + 8x)y(x)  + 48x  + 32x )(%e  )  + 16x  + 16x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (23)
--R             3     2        2x 2 ,
--R       (2y(x)  + 8x y(x))(%e  ) y (x)
--R
--R     + 
--R             4       2          2      4      3    2x 2      2
--R       (3y(x)  + (24x  + 8x)y(x)  + 48x  + 32x )(%e  )  + 16x  + 16x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 23

--S 24 of 127
ode208 := y(x)*D(y(x),x)+a*y(x)**2-b*cos(x+c)
 

              ,                           2
   (24)  y(x)y (x) - b cos(x + c) + a y(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,                           2
--R   (24)  y(x)y (x) - b cos(x + c) + a y(x)
--R
--R                                                     Type: Expression Integer
--E 24

--S 25 of 127
yx:=solve(ode208,y,x)
 

                2a x                                     2         2   2a x
         - 2b %e    sin(x + c) + (- 4a b cos(x + c) + (4a  + 1)y(x) )%e
   (25)  ------------------------------------------------------------------
                                         2
                                       8a  + 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2a x                                     2         2   2a x
--R         - 2b %e    sin(x + c) + (- 4a b cos(x + c) + (4a  + 1)y(x) )%e
--R   (25)  ------------------------------------------------------------------
--R                                         2
--R                                       8a  + 2
--R                                          Type: Union(Expression Integer,...)
--E 25

--S 26 of 127
ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c)
 

   (26)
                 2              2a x 2
           (- 16a  - 4)b y(x)(%e    ) sin(x + c)
         + 
                  3                             4      2         3    2a x 2
           ((- 32a  - 8a)b y(x)cos(x + c) + (32a  + 16a  + 2)y(x) )(%e    )
      *
          ,
         y (x)

     + 
           2   2a x 2          2
       4a b (%e    ) sin(x + c)
     + 
            2      2                   3            2    2a x 2
       ((32a  + 4)b cos(x + c) + (- 32a  - 8a)b y(x) )(%e    ) sin(x + c)
     + 
               3       2          2         4      2           2
           (48a  + 8a)b cos(x + c)  + (- 96a  - 32a  - 2)b y(x) cos(x + c)
         + 
               5      3          4
           (48a  + 24a  + 3a)y(x)
      *
            2a x 2
         (%e    )
     + 
             4      2
       (- 64a  - 32a  - 4)b cos(x + c)
  /
        4      2
     64a  + 32a  + 4
                                                     Type: Expression Integer
--R 
--R
--R   (26)
--R                 2              2a x 2
--R           (- 16a  - 4)b y(x)(%e    ) sin(x + c)
--R         + 
--R                  3                             4      2         3    2a x 2
--R           ((- 32a  - 8a)b y(x)cos(x + c) + (32a  + 16a  + 2)y(x) )(%e    )
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R           2   2a x 2          2
--R       4a b (%e    ) sin(x + c)
--R     + 
--R            2      2                   3            2    2a x 2
--R       ((32a  + 4)b cos(x + c) + (- 32a  - 8a)b y(x) )(%e    ) sin(x + c)
--R     + 
--R               3       2          2         4      2           2
--R           (48a  + 8a)b cos(x + c)  + (- 96a  - 32a  - 2)b y(x) cos(x + c)
--R         + 
--R               5      3          4
--R           (48a  + 24a  + 3a)y(x)
--R      *
--R            2a x 2
--R         (%e    )
--R     + 
--R             4      2
--R       (- 64a  - 32a  - 4)b cos(x + c)
--R  /
--R        4      2
--R     64a  + 32a  + 4
--R                                                     Type: Expression Integer
--E 26

--S 27 of 127
ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)**2+b)
 

                      +-----------+
              ,       |      2
   (27)  y(x)y (x) - \|a y(x)  + b

                                                     Type: Expression Integer
--R 
--R
--R                      +-----------+
--R              ,       |      2
--R   (27)  y(x)y (x) - \|a y(x)  + b
--R
--R                                                     Type: Expression Integer
--E 27

--S 28 of 127
yx:=solve(ode209,y,x)
 

                 +-----------+
             +-+ |      2            2 +-+
         - x\|b \|a y(x)  + b  + y(x) \|b  + b x
   (28)  ---------------------------------------
                       +-----------+
                   +-+ |      2
                  \|b \|a y(x)  + b  - b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-----------+
--R             +-+ |      2            2 +-+
--R         - x\|b \|a y(x)  + b  + y(x) \|b  + b x
--R   (28)  ---------------------------------------
--R                       +-----------+
--R                   +-+ |      2
--R                  \|b \|a y(x)  + b  - b
--R                                          Type: Union(Expression Integer,...)
--E 28

--S 29 of 127
ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b)
 

   (29)
                               +-----------+
                      2     2  |      2          2    4            2     2  +-+
         ((- 3a b y(x)  - 4b )\|a y(x)  + b  + (a y(x)  + 5a b y(x)  + 4b )\|b )
      *
         ROOT
                                                +-----------+
                      2       +-+            2  |      2                 2 +-+
                ((2a x  + 2b)\|b  + 2a x y(x) )\|a y(x)  + b  - 2a x y(x) \|b
              + 
                        4       2 2           2         2     2
                - a y(x)  + (- a x  - a b)y(x)  - 2a b x  - 2b
           /
                    +-----------+
                +-+ |      2              2
              2\|b \|a y(x)  + b  - a y(x)  - 2b
     + 
                                                    +-----------+
                     3              +-+          3  |      2
           ((a x y(x)  + 4b x y(x))\|b  + 2b y(x) )\|a y(x)  + b
         + 
                    5          3  +-+              3     2
           (- a y(x)  - 2b y(x) )\|b  - 3a b x y(x)  - 4b x y(x)
      *
          ,
         y (x)

     + 
                                                        +-----------+
               4          2  +-+              2     2   |      2
       ((a y(x)  + 2b y(x) )\|b  + 3a b x y(x)  + 4b x)\|a y(x)  + b
     + 
           2      4              2     2   +-+            4     2    2
       (- a x y(x)  - 5a b x y(x)  - 4b x)\|b  - 2a b y(x)  - 2b y(x)
  /
                        +-----------+
               2     2  |      2            2    4            2     2  +-+
     (3a b y(x)  + 4b )\|a y(x)  + b  + (- a y(x)  - 5a b y(x)  - 4b )\|b
                                                     Type: Expression Integer
--R 
--R
--R   (29)
--R                               +-----------+
--R                      2     2  |      2          2    4            2     2  +-+
--R         ((- 3a b y(x)  - 4b )\|a y(x)  + b  + (a y(x)  + 5a b y(x)  + 4b )\|b )
--R      *
--R         ROOT
--R                                                +-----------+
--R                      2       +-+            2  |      2                 2 +-+
--R                ((2a x  + 2b)\|b  + 2a x y(x) )\|a y(x)  + b  - 2a x y(x) \|b
--R              + 
--R                        4       2 2           2         2     2
--R                - a y(x)  + (- a x  - a b)y(x)  - 2a b x  - 2b
--R           /
--R                    +-----------+
--R                +-+ |      2              2
--R              2\|b \|a y(x)  + b  - a y(x)  - 2b
--R     + 
--R                                                    +-----------+
--R                     3              +-+          3  |      2
--R           ((a x y(x)  + 4b x y(x))\|b  + 2b y(x) )\|a y(x)  + b
--R         + 
--R                    5          3  +-+              3     2
--R           (- a y(x)  - 2b y(x) )\|b  - 3a b x y(x)  - 4b x y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                                                        +-----------+
--R               4          2  +-+              2     2   |      2
--R       ((a y(x)  + 2b y(x) )\|b  + 3a b x y(x)  + 4b x)\|a y(x)  + b
--R     + 
--R           2      4              2     2   +-+            4     2    2
--R       (- a x y(x)  - 5a b x y(x)  - 4b x)\|b  - 2a b y(x)  - 2b y(x)
--R  /
--R                        +-----------+
--R               2     2  |      2            2    4            2     2  +-+
--R     (3a b y(x)  + 4b )\|a y(x)  + b  + (- a y(x)  - 5a b y(x)  - 4b )\|b
--R                                                     Type: Expression Integer
--E 29

--S 30 of 127
ode210 := y(x)*D(y(x),x)+x*y(x)**2-4*x
 

              ,            2
   (30)  y(x)y (x) + x y(x)  - 4x

                                                     Type: Expression Integer
--R 
--R
--R              ,            2
--R   (30)  y(x)y (x) + x y(x)  - 4x
--R
--R                                                     Type: Expression Integer
--E 30

--S 31 of 127
yx:=solve(ode210,y,x)
 

                       2
              2       x
         (y(x)  - 4)%e
   (31)  ---------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       2
--R              2       x
--R         (y(x)  - 4)%e
--R   (31)  ---------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 31

--S 32 of 127
ode210expr := yx*D(yx,x)+x*yx**2-4*x
 

   (32)
                       2 2                                        2 2
         3            x    ,              4           2          x
   (2y(x)  - 8y(x))(%e  ) y (x) + (3x y(x)  - 24x y(x)  + 48x)(%e  )  - 16x

   ------------------------------------------------------------------------
                                       4
                                                     Type: Expression Integer
--R 
--R
--R   (32)
--R                       2 2                                        2 2
--R         3            x    ,              4           2          x
--R   (2y(x)  - 8y(x))(%e  ) y (x) + (3x y(x)  - 24x y(x)  + 48x)(%e  )  - 16x
--R
--R   ------------------------------------------------------------------------
--R                                       4
--R                                                     Type: Expression Integer
--E 32

--S 33 of 127
ode211 := y(x)*D(y(x),x)-x*exp(x/y(x))
 

                           x
                         ----
              ,          y(x)
   (33)  y(x)y (x) - x %e

                                                     Type: Expression Integer
--R 
--R
--R                           x
--R                         ----
--R              ,          y(x)
--R   (33)  y(x)y (x) - x %e
--R
--R                                                     Type: Expression Integer
--E 33

--S 34 of 127
solve(ode211,y,x)
 

   (34)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (34)  "failed"
--R                                                    Type: Union("failed",...)
--E 34

--S 35 of 127
ode212 := y(x)*D(y(x),x)+f(x**2+y(x)**2)*g(x)+x
 

              ,                2    2
   (35)  y(x)y (x) + g(x)f(y(x)  + x ) + x

                                                     Type: Expression Integer
--R 
--R
--R              ,                2    2
--R   (35)  y(x)y (x) + g(x)f(y(x)  + x ) + x
--R
--R                                                     Type: Expression Integer
--E 35

--S 36 of 127
solve(ode212,y,x)
 

   (36)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

--S 37 of 127
ode213 := (y(x)+1)*D(y(x),x)-y(x)-x
 

                    ,
   (37)  (y(x) + 1)y (x) - y(x) - x

                                                     Type: Expression Integer
--R 
--R
--R                    ,
--R   (37)  (y(x) + 1)y (x) - y(x) - x
--R
--R                                                     Type: Expression Integer
--E 37

--S 38 of 127
solve(ode213,y,x)
 

   (38)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (38)  "failed"
--R                                                    Type: Union("failed",...)
--E 38

--S 39 of 127
ode214 := (y(x)+x-1)*D(y(x),x)-y(x)+2*x+3
 

                        ,
   (39)  (y(x) + x - 1)y (x) - y(x) + 2x + 3

                                                     Type: Expression Integer
--R 
--R
--R                        ,
--R   (39)  (y(x) + x - 1)y (x) - y(x) + 2x + 3
--R
--R                                                     Type: Expression Integer
--E 39

--S 40 of 127
solve(ode214,y,x)
 

   (40)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (40)  "failed"
--R                                                    Type: Union("failed",...)
--E 40

--S 41 of 127
ode215 := (y(x)+2*x-2)*D(y(x),x)-y(x)+x+1
 

                         ,
   (41)  (y(x) + 2x - 2)y (x) - y(x) + x + 1

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (41)  (y(x) + 2x - 2)y (x) - y(x) + x + 1
--R
--R                                                     Type: Expression Integer
--E 41

--S 42 of 127
solve(ode215,y,x)
 

   (42)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (42)  "failed"
--R                                                    Type: Union("failed",...)
--E 42

--S 43 of 127
ode216 := (y(x)-2*x+1)*D(y(x),x)+y(x)+x
 

                         ,
   (43)  (y(x) - 2x + 1)y (x) + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (43)  (y(x) - 2x + 1)y (x) + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 43

--S 44 of 127
solve(ode216,y,x)
 

   (44)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (44)  "failed"
--R                                                    Type: Union("failed",...)
--E 44

--S 45 of 127
ode217 := (y(x)-x**2)*D(y(x),x)-x
 

                  2  ,
   (45)  (y(x) - x )y (x) - x

                                                     Type: Expression Integer
--R 
--R
--R                  2  ,
--R   (45)  (y(x) - x )y (x) - x
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 127
yx:=solve(ode217,y,x)
 

                    2       2y(x)
         (2y(x) - 2x  - 1)%e
   (46)  ------------------------
                     4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2       2y(x)
--R         (2y(x) - 2x  - 1)%e
--R   (46)  ------------------------
--R                     4
--R                                          Type: Union(Expression Integer,...)
--E 46

--S 47 of 127
ode217expr := (yx-x**2)*D(yx,x)-x
 

   (47)
                 2        2              4    2    2y(x) 2
           (2y(x)  + (- 4x  - 1)y(x) + 2x  + x )(%e     )
         + 
                2         4   2y(x)
           (- 4x y(x) + 4x )%e
      *
          ,
         y (x)

     + 
                      3        2y(x) 2     3  2y(x)
       (- 2x y(x) + 2x  + x)(%e     )  + 4x %e      - 4x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (47)
--R                 2        2              4    2    2y(x) 2
--R           (2y(x)  + (- 4x  - 1)y(x) + 2x  + x )(%e     )
--R         + 
--R                2         4   2y(x)
--R           (- 4x y(x) + 4x )%e
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                      3        2y(x) 2     3  2y(x)
--R       (- 2x y(x) + 2x  + x)(%e     )  + 4x %e      - 4x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 47

--S 48 of 127
ode218 := (y(x)-x**2)*D(y(x),x)+4*x*y(x)
 

                  2  ,
   (48)  (y(x) - x )y (x) + 4x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                  2  ,
--R   (48)  (y(x) - x )y (x) + 4x y(x)
--R
--R                                                     Type: Expression Integer
--E 48

--S 49 of 127
yx:=solve(ode218,y,x)
 

                   2
         2y(x) + 2x
   (49)  -----------
            +----+
           \|y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2
--R         2y(x) + 2x
--R   (49)  -----------
--R            +----+
--R           \|y(x)
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 127
ode218expr := (yx-x**2)*D(yx,x)+4*x*yx
 

   (50)
              2     4  +----+    2    2    4      ,
       ((2y(x)  - 2x )\|y(x)  - x y(x)  + x y(x))y (x)

     + 
               2     3      +----+          3     3    2
       (8x y(x)  + 8x y(x))\|y(x)  + 8x y(x)  + 4x y(x)
  /
         2 +----+
     y(x) \|y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (50)
--R              2     4  +----+    2    2    4      ,
--R       ((2y(x)  - 2x )\|y(x)  - x y(x)  + x y(x))y (x)
--R
--R     + 
--R               2     3      +----+          3     3    2
--R       (8x y(x)  + 8x y(x))\|y(x)  + 8x y(x)  + 4x y(x)
--R  /
--R         2 +----+
--R     y(x) \|y(x)
--R                                                     Type: Expression Integer
--E 50

--S 51 of 127
ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)**2-f1(x)*y(x)-f0(x)
 

                       ,               2
   (51)  (y(x) + g(x))y (x) - f2(x)y(x)  - f1(x)y(x) - f0(x)

                                                     Type: Expression Integer
--R 
--R
--R                       ,               2
--R   (51)  (y(x) + g(x))y (x) - f2(x)y(x)  - f1(x)y(x) - f0(x)
--R
--R                                                     Type: Expression Integer
--E 51

--S 52 of 127
solve(ode219,y,x)
 

   (52)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (52)  "failed"
--R                                                    Type: Union("failed",...)
--E 52

--S 53 of 127
ode220 := 2*y(x)*D(y(x),x)-x*y(x)**2-x**3
 

               ,            2    3
   (53)  2y(x)y (x) - x y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R               ,            2    3
--R   (53)  2y(x)y (x) - x y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 127
yx:=solve(ode220,y,x)
 

                              2
                             x
                           - --
              2    2          2
   (54)  (y(x)  + x  + 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              2
--R                             x
--R                           - --
--R              2    2          2
--R   (54)  (y(x)  + x  + 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 54

--S 55 of 127
ode220expr := 2*yx*D(yx,x)-x*yx**2-x**3
 

   (55)
                                   2 2
                                  x
                                - --
           3      2                2   ,
     (4y(x)  + (4x  + 8)y(x))(%e    ) y (x)

   + 
                                                            2 2
                                                           x
                                                         - --
               4        3          2     5     3            2      3
     (- 3x y(x)  + (- 6x  - 8x)y(x)  - 3x  - 8x  - 4x)(%e    )  - x
                                                     Type: Expression Integer
--R 
--R
--R   (55)
--R                                   2 2
--R                                  x
--R                                - --
--R           3      2                2   ,
--R     (4y(x)  + (4x  + 8)y(x))(%e    ) y (x)
--R
--R   + 
--R                                                            2 2
--R                                                           x
--R                                                         - --
--R               4        3          2     5     3            2      3
--R     (- 3x y(x)  + (- 6x  - 8x)y(x)  - 3x  - 8x  - 4x)(%e    )  - x
--R                                                     Type: Expression Integer
--E 55

--S 56 of 127
ode221 := (2*y(x)+x+1)*D(y(x),x)-(2*y(x)+x-1)
 

                         ,
   (56)  (2y(x) + x + 1)y (x) - 2y(x) - x + 1

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (56)  (2y(x) + x + 1)y (x) - 2y(x) - x + 1
--R
--R                                                     Type: Expression Integer
--E 56

--S 57 of 127
solve(ode221,y,x)
 

   (57)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (57)  "failed"
--R                                                    Type: Union("failed",...)
--E 57

--S 58 of 127
ode222 := (2*y(x)+x+7)*D(y(x),x)-y(x)+2*x+4
 

                         ,
   (58)  (2y(x) + x + 7)y (x) - y(x) + 2x + 4

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (58)  (2y(x) + x + 7)y (x) - y(x) + 2x + 4
--R
--R                                                     Type: Expression Integer
--E 58

--S 59 of 127
solve(ode222,y,x)
 

   (59)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (59)  "failed"
--R                                                    Type: Union("failed",...)
--E 59

--S 60 of 127
ode223 := (2*y(x)-x)*D(y(x),x)-y(x)-2*x
 

                     ,
   (60)  (2y(x) - x)y (x) - y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R                     ,
--R   (60)  (2y(x) - x)y (x) - y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 127
yx:=solve(ode223,y,x)
 

             2             2
   (61)  y(x)  - x y(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2             2
--R   (61)  y(x)  - x y(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 127
ode223expr := (2*yx-x)*D(yx,x)-yx-2*x
 

   (62)
           3          2        2               3    2  ,           3
     (4y(x)  - 6x y(x)  + (- 2x  - 2x)y(x) + 2x  + x )y (x) - 2y(x)

   + 
                   2      2               3     2
     (- 2x - 1)y(x)  + (6x  + 2x)y(x) + 4x  + 3x  - 2x
                                                     Type: Expression Integer
--R 
--R
--R   (62)
--R           3          2        2               3    2  ,           3
--R     (4y(x)  - 6x y(x)  + (- 2x  - 2x)y(x) + 2x  + x )y (x) - 2y(x)
--R
--R   + 
--R                   2      2               3     2
--R     (- 2x - 1)y(x)  + (6x  + 2x)y(x) + 4x  + 3x  - 2x
--R                                                     Type: Expression Integer
--E 62

--S 63 of 127
ode224 := (2*y(x)-6*x)*D(y(x),x)-y(x)+3*x+2
 

                      ,
   (63)  (2y(x) - 6x)y (x) - y(x) + 3x + 2

                                                     Type: Expression Integer
--R 
--R
--R                      ,
--R   (63)  (2y(x) - 6x)y (x) - y(x) + 3x + 2
--R
--R                                                     Type: Expression Integer
--E 63

--S 64 of 127
solve(ode224,y,x)
 

   (64)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (64)  "failed"
--R                                                    Type: Union("failed",...)
--E 64

--S 65 of 127
ode225 := (4*y(x)+2*x+3)*D(y(x),x)-2*y(x)-x-1
 

                          ,
   (65)  (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1

                                                     Type: Expression Integer
--R 
--R
--R                          ,
--R   (65)  (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1
--R
--R                                                     Type: Expression Integer
--E 65

--S 66 of 127
solve(ode225,y,x)
 

   (66)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (66)  "failed"
--R                                                    Type: Union("failed",...)
--E 66

--S 67 of 127
ode226 := (4*y(x)-2*x-3)*D(y(x),x)+2*y(x)-x-1
 

                          ,
   (67)  (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1

                                                     Type: Expression Integer
--R 
--R
--R                          ,
--R   (67)  (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1
--R
--R                                                     Type: Expression Integer
--E 67

--S 68 of 127
solve(ode226,y,x)
 

   (68)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (68)  "failed"
--R                                                    Type: Union("failed",...)
--E 68

--S 69 of 127
ode227 := (4*y(x)-3*x-5)*D(y(x),x)-3*y(x)+7*x+2
 

                          ,
   (69)  (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2

                                                     Type: Expression Integer
--R 
--R
--R                          ,
--R   (69)  (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2
--R
--R                                                     Type: Expression Integer
--E 69

--S 70 of 127
yx:=solve(ode227,y,x)
 

              2                       2
         4y(x)  + (- 6x - 10)y(x) + 7x  + 4x
   (70)  -----------------------------------
                          2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2                       2
--R         4y(x)  + (- 6x - 10)y(x) + 7x  + 4x
--R   (70)  -----------------------------------
--R                          2
--R                                          Type: Union(Expression Integer,...)
--E 70

--S 71 of 127
ode227expr := (4*yx-3*x-5)*D(yx,x)-3*yx+7*x+2
 

   (71)
                 3                     2        2                        3
           64y(x)  + (- 144x - 240)y(x)  + (184x  + 280x + 160)y(x) - 84x
         + 
                 2
           - 170x  - 20x + 50
      *
          ,
         y (x)

     + 
               3                   2          2                        3       2
       - 48y(x)  + (184x + 140)y(x)  + (- 252x  - 340x - 20)y(x) + 196x  + 105x
     + 
       - 48x - 16
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (71)
--R                 3                     2        2                        3
--R           64y(x)  + (- 144x - 240)y(x)  + (184x  + 280x + 160)y(x) - 84x
--R         + 
--R                 2
--R           - 170x  - 20x + 50
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R               3                   2          2                        3       2
--R       - 48y(x)  + (184x + 140)y(x)  + (- 252x  - 340x - 20)y(x) + 196x  + 105x
--R     + 
--R       - 48x - 16
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 71

--S 72 of 127
ode228 := (4*y(x)+11*x-11) *D(y(x),x)-25*y(x)-8*x+62
 

                            ,
   (72)  (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62

                                                     Type: Expression Integer
--R 
--R
--R                            ,
--R   (72)  (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 127
solve(ode228,y,x)
 

   (73)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (73)  "failed"
--R                                                    Type: Union("failed",...)
--E 73

--S 74 of 127
ode229 := (12*y(x)-5*x-8)*D(y(x),x)-5*y(x)+2*x+3
 

                           ,
   (74)  (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3

                                                     Type: Expression Integer
--R 
--R
--R                           ,
--R   (74)  (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 127
yx:=solve(ode229,y,x)
 

              2                     2
   (75)  6y(x)  + (- 5x - 8)y(x) + x  + 3x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2                     2
--R   (75)  6y(x)  + (- 5x - 8)y(x) + x  + 3x
--R                                          Type: Union(Expression Integer,...)
--E 75

--S 76 of 127
ode229expr := (12*yx-5*x-8)*D(yx,x)-5*yx+2*x+3
 

   (76)
                3                       2        2                         3
         864y(x)  + (- 1080x - 1728)y(x)  + (444x  + 1332x + 672)y(x) - 60x
       + 
               2
         - 251x  - 208x + 64
    *
        ,
       y (x)

   + 
              3                   2          2                        3      2
     - 360y(x)  + (444x + 666)y(x)  + (- 180x  - 502x - 208)y(x) + 24x  + 93x
   + 
     64x - 21
                                                     Type: Expression Integer
--R 
--R
--R   (76)
--R                3                       2        2                         3
--R         864y(x)  + (- 1080x - 1728)y(x)  + (444x  + 1332x + 672)y(x) - 60x
--R       + 
--R               2
--R         - 251x  - 208x + 64
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R              3                   2          2                        3      2
--R     - 360y(x)  + (444x + 666)y(x)  + (- 180x  - 502x - 208)y(x) + 24x  + 93x
--R   + 
--R     64x - 21
--R                                                     Type: Expression Integer
--E 76

--S 77 of 127
ode230 := a*y(x)*D(y(x),x)+b*y(x)**2+f(x)
 

                ,            2
   (77)  a y(x)y (x) + b y(x)  + f(x)

                                                     Type: Expression Integer
--R 
--R
--R                ,            2
--R   (77)  a y(x)y (x) + b y(x)  + f(x)
--R
--R                                                     Type: Expression Integer
--E 77

--S 78 of 127
solve(ode230,y,x)
 

                                 2%L b
            x                    -----
          ++         2             a
   (78)   |   (b y(x)  + f(%L))%e     d%L
         ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                                 2%I b
--R            x                    -----
--R          ++         2             a
--I   (78)   |   (b y(x)  + f(%I))%e     d%I
--R         ++
--R                                          Type: Union(Expression Integer,...)
--E 78

--S 79 of 127
ode231 := (a*y(x)+b*x+c)*D(y(x),x)+alpha*y(x)+beta*x+gamma
 

                            ,
   (79)  (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma

                                                     Type: Expression Integer
--R 
--R
--R                            ,
--R   (79)  (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma
--R
--R                                                     Type: Expression Integer
--E 79

--S 80 of 127
solve(ode231,y,x)
 

   (80)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (80)  "failed"
--R                                                    Type: Union("failed",...)
--E 80

--S 81 of 127
ode232 := x*y(x)*D(y(x),x)+y(x)**2+x**2
 

                ,          2    2
   (81)  x y(x)y (x) + y(x)  + x

                                                     Type: Expression Integer
--R 
--R
--R                ,          2    2
--R   (81)  x y(x)y (x) + y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 81

--S 82 of 127
yx:=solve(ode232,y,x)
 

           2    2    4
         2x y(x)  + x
   (82)  -------------
               4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2    2    4
--R         2x y(x)  + x
--R   (82)  -------------
--R               4
--R                                          Type: Union(Expression Integer,...)
--E 82

--S 83 of 127
ode232expr := x*yx*D(yx,x)+yx**2+x**2
 

            5    3     7      ,         4    4      6    2     8      2
         (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 16x y(x)  + 5x  + 16x

   (83)  --------------------------------------------------------------
                                       16
                                                     Type: Expression Integer
--R 
--R
--R            5    3     7      ,         4    4      6    2     8      2
--R         (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 16x y(x)  + 5x  + 16x
--R
--R   (83)  --------------------------------------------------------------
--R                                       16
--R                                                     Type: Expression Integer
--E 83

--S 84 of 127
ode233 := x*y(x)*D(y(x),x)-y(x)**2+a*x**3*cos(x)
 

                ,         3             2
   (84)  x y(x)y (x) + a x cos(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                ,         3             2
--R   (84)  x y(x)y (x) + a x cos(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 127
yx:=solve(ode233,y,x)
 

             2             2
         2a x sin(x) + y(x)
   (85)  -------------------
                   2
                 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2             2
--R         2a x sin(x) + y(x)
--R   (85)  -------------------
--R                   2
--R                 2x
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 127
ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x)
 

   (86)
            3                    3  ,        2 4      2
       (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x)

     + 
          2 5             2    2               3    2       7               4
       (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x)  + 4a x )cos(x) - 3y(x)
  /
       4
     4x
                                                     Type: Expression Integer
--R 
--R
--R   (86)
--R            3                    3  ,        2 4      2
--R       (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x)
--R
--R     + 
--R          2 5             2    2               3    2       7               4
--R       (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x)  + 4a x )cos(x) - 3y(x)
--R  /
--R       4
--R     4x
--R                                                     Type: Expression Integer
--E 86

--S 87 of 127
ode234 := x*y(x)*D(y(x),x)-y(x)**2+x*y(x)+x**3-2*x**2
 

                ,          2             3     2
   (87)  x y(x)y (x) - y(x)  + x y(x) + x  - 2x

                                                     Type: Expression Integer
--R 
--R
--R                ,          2             3     2
--R   (87)  x y(x)y (x) - y(x)  + x y(x) + x  - 2x
--R
--R                                                     Type: Expression Integer
--E 87

--S 88 of 127
solve(ode234,y,x)
 

   (88)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (88)  "failed"
--R                                                    Type: Union("failed",...)
--E 88

--S 89 of 127
ode235 := (x*y(x)+a)*D(y(x),x)+b*y(x)
 

                      ,
   (89)  (x y(x) + a)y (x) + b y(x)

                                                     Type: Expression Integer
--R 
--R
--R                      ,
--R   (89)  (x y(x) + a)y (x) + b y(x)
--R
--R                                                     Type: Expression Integer
--E 89

--S 90 of 127
yx:=solve(ode235,y,x)
 

               y(x)
               ----
                 b         y(x)
   (90)  b x %e     + a Ei(----)
                             b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               y(x)
--R               ----
--R                 b         y(x)
--R   (90)  b x %e     + a Ei(----)
--R                             b
--R                                          Type: Union(Expression Integer,...)
--E 90

--S 91 of 127
ode235expr := (x*yx+a)*D(yx,x)+b*yx
 

   (91)
                                 y(x) 2
                                 ----
               3            2      b
           (b x y(x) + a b x )(%e    )
         + 
                                                       y(x)
                                                       ----
                2        2     y(x)                2     b
           ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e
                                 b
      *
          ,
         y (x)

     + 
                  y(x) 2                                           y(x)
                  ----                                             ----
        2 2         b                    y(x)      2                 b
       b x y(x)(%e    )  + (a b x y(x)Ei(----) + (b x + a b)y(x))%e
                                           b
     + 
                  y(x)
       a b y(x)Ei(----)
                    b
  /
     y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (91)
--R                                 y(x) 2
--R                                 ----
--R               3            2      b
--R           (b x y(x) + a b x )(%e    )
--R         + 
--R                                                       y(x)
--R                                                       ----
--R                2        2     y(x)                2     b
--R           ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e
--R                                 b
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                  y(x) 2                                           y(x)
--R                  ----                                             ----
--R        2 2         b                    y(x)      2                 b
--R       b x y(x)(%e    )  + (a b x y(x)Ei(----) + (b x + a b)y(x))%e
--R                                           b
--R     + 
--R                  y(x)
--R       a b y(x)Ei(----)
--R                    b
--R  /
--R     y(x)
--R                                                     Type: Expression Integer
--E 91

--S 92 of 127
ode236 := x*(y(x)+4)*D(y(x),x)-y(x)**2-2*y(x)-2*x
 

                       ,          2
   (92)  (x y(x) + 4x)y (x) - y(x)  - 2y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R                       ,          2
--R   (92)  (x y(x) + 4x)y (x) - y(x)  - 2y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 92

--S 93 of 127
solve(ode236,y,x)
 

   (93)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (93)  "failed"
--R                                                    Type: Union("failed",...)
--E 93

--S 94 of 127
ode237 := x*(y(x)+a)*D(y(x),x)+b*y(x)+c*x
 

                        ,
   (94)  (x y(x) + a x)y (x) + b y(x) + c x

                                                     Type: Expression Integer
--R 
--R
--R                        ,
--R   (94)  (x y(x) + a x)y (x) + b y(x) + c x
--R
--R                                                     Type: Expression Integer
--E 94

--S 95 of 127
solve(ode237,y,x)
 

   (95)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (95)  "failed"
--R                                                    Type: Union("failed",...)
--E 95

--S 96 of 127
ode238 := (x*(y(x)+x)+a)*D(y(x),x)-y(x)*(y(x)+x)-b
 

                    2      ,          2
   (96)  (x y(x) + x  + a)y (x) - y(x)  - x y(x) - b

                                                     Type: Expression Integer
--R 
--R
--R                    2      ,          2
--R   (96)  (x y(x) + x  + a)y (x) - y(x)  - x y(x) - b
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 127
solve(ode238,y,x)
 

   (97)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (97)  "failed"
--R                                                    Type: Union("failed",...)
--E 97

--S 98 of 127
ode239 := (x*y(x)-x**2)*D(y(x),x)+y(x)**2-3*x*y(x)-2*x**2
 

                    2  ,          2               2
   (98)  (x y(x) - x )y (x) + y(x)  - 3x y(x) - 2x

                                                     Type: Expression Integer
--R 
--R
--R                    2  ,          2               2
--R   (98)  (x y(x) - x )y (x) + y(x)  - 3x y(x) - 2x
--R
--R                                                     Type: Expression Integer
--E 98

--S 99 of 127
yx:=solve(ode239,y,x)
 

          2    2     3        4
         x y(x)  - 2x y(x) - x
   (99)  ----------------------
                    2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2     3        4
--R         x y(x)  - 2x y(x) - x
--R   (99)  ----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 99

--S 100 of 127
ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2
 

   (100)
          5    3     6    2      7     4          8     5  ,        4    4
       (2x y(x)  - 6x y(x)  + (2x  - 4x )y(x) + 2x  + 4x )y (x) + 3x y(x)

     + 
            5    3      6      3     2       7      4          8      5     2
       - 14x y(x)  + (8x  - 10x )y(x)  + (18x  + 24x )y(x) + 5x  + 14x  - 8x
  /
     4
                                                     Type: Expression Integer
--R 
--R
--R   (100)
--R          5    3     6    2      7     4          8     5  ,        4    4
--R       (2x y(x)  - 6x y(x)  + (2x  - 4x )y(x) + 2x  + 4x )y (x) + 3x y(x)
--R
--R     + 
--R            5    3      6      3     2       7      4          8      5     2
--R       - 14x y(x)  + (8x  - 10x )y(x)  + (18x  + 24x )y(x) + 5x  + 14x  - 8x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 100

--S 101 of 127
ode240 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x
 

                  ,          2
   (101)  2x y(x)y (x) - y(x)  + a x

                                                     Type: Expression Integer
--R 
--R
--R                  ,          2
--R   (101)  2x y(x)y (x) - y(x)  + a x
--R
--R                                                     Type: Expression Integer
--E 101

--S 102 of 127
yx:=solve(ode240,y,x)
 

                           2
          a x log(x) + y(x)
   (102)  ------------------
                   x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           2
--R          a x log(x) + y(x)
--R   (102)  ------------------
--R                   x
--R                                          Type: Union(Expression Integer,...)
--E 102

--S 103 of 127
ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x
 

   (103)
            2                    3  ,       2 2      2
       (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x)

     + 
                   2     2 2               4            2      3
       (- 4a x y(x)  + 2a x )log(x) - 3y(x)  + 2a x y(x)  + a x
  /
      2
     x
                                                     Type: Expression Integer
--R 
--R
--R   (103)
--R            2                    3  ,       2 2      2
--R       (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x)
--R
--R     + 
--R                   2     2 2               4            2      3
--R       (- 4a x y(x)  + 2a x )log(x) - 3y(x)  + 2a x y(x)  + a x
--R  /
--R      2
--R     x
--R                                                     Type: Expression Integer
--E 103

--S 104 of 127
ode241 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x**2
 

                  ,          2      2
   (104)  2x y(x)y (x) - y(x)  + a x

                                                     Type: Expression Integer
--R 
--R
--R                  ,          2      2
--R   (104)  2x y(x)y (x) - y(x)  + a x
--R
--R                                                     Type: Expression Integer
--E 104

--S 105 of 127
yx:=solve(ode241,y,x)
 

              2      2
          y(x)  + a x
   (105)  ------------
                x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              2      2
--R          y(x)  + a x
--R   (105)  ------------
--R                x
--R                                          Type: Union(Expression Integer,...)
--E 105

--S 106 of 127
ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2
 

                  3       3      ,           4       2    2     2      4
          (4x y(x)  + 4a x y(x))y (x) - 3y(x)  - 2a x y(x)  + (a  + a)x

   (106)  --------------------------------------------------------------
                                         2
                                        x
                                                     Type: Expression Integer
--R 
--R
--R                  3       3      ,           4       2    2     2      4
--R          (4x y(x)  + 4a x y(x))y (x) - 3y(x)  - 2a x y(x)  + (a  + a)x
--R
--R   (106)  --------------------------------------------------------------
--R                                         2
--R                                        x
--R                                                     Type: Expression Integer
--E 106

--S 107 of 127
ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)**2+1
 

                  ,           2
   (107)  2x y(x)y (x) + 2y(x)  + 1

                                                     Type: Expression Integer
--R 
--R
--R                  ,           2
--R   (107)  2x y(x)y (x) + 2y(x)  + 1
--R
--R                                                     Type: Expression Integer
--E 107

--S 108 of 127
yx:=solve(ode242,y,x)
 

            2    2    2
          2x y(x)  + x
   (108)  -------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2    2
--R          2x y(x)  + x
--R   (108)  -------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 108

--S 109 of 127
ode242expr := 2*x*yx*D(yx,x)+2*yx**2+1
 

             5    3     5      ,         4    4      4    2     4
          (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 12x y(x)  + 3x  + 2

   (109)  -----------------------------------------------------------
                                       2
                                                     Type: Expression Integer
--R 
--R
--R             5    3     5      ,         4    4      4    2     4
--R          (8x y(x)  + 4x y(x))y (x) + 12x y(x)  + 12x y(x)  + 3x  + 2
--R
--R   (109)  -----------------------------------------------------------
--R                                       2
--R                                                     Type: Expression Integer
--E 109

--S 110 of 127
ode243 := x*(2*y(x)+x-1)*D(y(x),x)-y(x)*(y(x)+2*x+1)
 

                      2      ,          2
   (110)  (2x y(x) + x  - x)y (x) - y(x)  + (- 2x - 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R                      2      ,          2
--R   (110)  (2x y(x) + x  - x)y (x) - y(x)  + (- 2x - 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 110

--S 111 of 127
solve(ode243,y,x)
 

   (111)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (111)  "failed"
--R                                                    Type: Union("failed",...)
--E 111

--S 112 of 127
ode244 := x*(2*y(x)-x-1)*D(y(x),x)+y(x)*(2*x-y(x)-1)
 

                      2      ,          2
   (112)  (2x y(x) - x  - x)y (x) - y(x)  + (2x - 1)y(x)

                                                     Type: Expression Integer
--R 
--R
--R                      2      ,          2
--R   (112)  (2x y(x) - x  - x)y (x) - y(x)  + (2x - 1)y(x)
--R
--R                                                     Type: Expression Integer
--E 112

--S 113 of 127
solve(ode244,y,x)
 

   (113)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (113)  "failed"
--R                                                    Type: Union("failed",...)
--E 113

--S 114 of 127
ode245 := (2*x*y(x)+4*x**3)*D(y(x),x)+y(x)**2+112*x**2*y(x)
 

                       3  ,          2       2
   (114)  (2x y(x) + 4x )y (x) + y(x)  + 112x y(x)

                                                     Type: Expression Integer
--R 
--R
--R                       3  ,          2       2
--R   (114)  (2x y(x) + 4x )y (x) + y(x)  + 112x y(x)
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 127
solve(ode245,y,x)
 

   (115)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (115)  "failed"
--R                                                    Type: Union("failed",...)
--E 115

--S 116 of 127
ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)**2
 

                       2  ,           2               2
   (116)  (3x y(x) + 2x )y (x) + 3y(x)  + 6x y(x) + 3x

                                                     Type: Expression Integer
--R 
--R
--R                       2  ,           2               2
--R   (116)  (3x y(x) + 2x )y (x) + 3y(x)  + 6x y(x) + 3x
--R
--R                                                     Type: Expression Integer
--E 116

--S 117 of 127
yx:=solve(ode246,y,x)
 

            2    2     3         4
          6x y(x)  + 8x y(x) + 3x
   (117)  ------------------------
                      4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2     3         4
--R          6x y(x)  + 8x y(x) + 3x
--R   (117)  ------------------------
--R                      4
--R                                          Type: Union(Expression Integer,...)
--E 117

--S 118 of 127
ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2
 

   (118)
            5    3       6    2        7      4           8      5  ,
       (216x y(x)  + 432x y(x)  + (300x  + 96x )y(x) + 72x  + 64x )y (x)

     + 
           4    4        5    3         6       3     2        7       4
       324x y(x)  + 1008x y(x)  + (1200x  + 240x )y(x)  + (648x  + 384x )y(x)
     + 
           8       5      2
       135x  + 168x  + 48x
  /
     16
                                                     Type: Expression Integer
--R 
--R
--R   (118)
--R            5    3       6    2        7      4           8      5  ,
--R       (216x y(x)  + 432x y(x)  + (300x  + 96x )y(x) + 72x  + 64x )y (x)
--R
--R     + 
--R           4    4        5    3         6       3     2        7       4
--R       324x y(x)  + 1008x y(x)  + (1200x  + 240x )y(x)  + (648x  + 384x )y(x)
--R     + 
--R           8       5      2
--R       135x  + 168x  + 48x
--R  /
--R     16
--R                                                     Type: Expression Integer
--E 118

--S 119 of 127
ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)**2+x*y(x)-7*x**2-9*x-3
 

                            2           ,          2              2
   (119)  ((3x + 2)y(x) - 6x  - 7x - 2)y (x) - y(x)  + x y(x) - 7x  - 9x - 3

                                                     Type: Expression Integer
--R 
--R
--R                            2           ,          2              2
--R   (119)  ((3x + 2)y(x) - 6x  - 7x - 2)y (x) - y(x)  + x y(x) - 7x  - 9x - 3
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 127
solve(ode247,y,x)
 

   (120)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (120)  "failed"
--R                                                    Type: Union("failed",...)
--E 120

--S 121 of 127
ode248 := (6*x*y(x)+x**2+3)*D(y(x),x)+3*y(x)**2+2*x*y(x)+2*x
 

                      2      ,           2
   (121)  (6x y(x) + x  + 3)y (x) + 3y(x)  + 2x y(x) + 2x

                                                     Type: Expression Integer
--R 
--R
--R                      2      ,           2
--R   (121)  (6x y(x) + x  + 3)y (x) + 3y(x)  + 2x y(x) + 2x
--R
--R                                                     Type: Expression Integer
--E 121

--S 122 of 127
yx:=solve(ode248,y,x)
 

                 2     2             2
   (122)  3x y(x)  + (x  + 3)y(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2     2             2
--R   (122)  3x y(x)  + (x  + 3)y(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 122

--S 123 of 127
ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x
 

   (123)
             3    3       4       2     2      5      4      3                5
         108x y(x)  + (54x  + 162x )y(x)  + (6x  + 36x  + 42x  + 72x)y(x) + 6x
       + 
          4      3     2
         x  + 18x  + 6x  + 9
    *
        ,
       y (x)

   + 
        2    4       3            3       4      3      2          2
     81x y(x)  + (72x  + 108x)y(x)  + (15x  + 72x  + 63x  + 36)y(x)
   + 
         4     3      2                 4     3
     (30x  + 4x  + 54x  + 12x)y(x) + 15x  + 4x  + 8x
                                                     Type: Expression Integer
--R 
--R
--R   (123)
--R             3    3       4       2     2      5      4      3                5
--R         108x y(x)  + (54x  + 162x )y(x)  + (6x  + 36x  + 42x  + 72x)y(x) + 6x
--R       + 
--R          4      3     2
--R         x  + 18x  + 6x  + 9
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R        2    4       3            3       4      3      2          2
--R     81x y(x)  + (72x  + 108x)y(x)  + (15x  + 72x  + 63x  + 36)y(x)
--R   + 
--R         4     3      2                 4     3
--R     (30x  + 4x  + 54x  + 12x)y(x) + 15x  + 4x  + 8x
--R                                                     Type: Expression Integer
--E 123

--S 124 of 127
ode249 := (a*x*y(x)+b*x**n)*D(y(x),x)+alpha*y(x)**3+beta*y(x)**2
 

              n             ,                3            2
   (124)  (b x  + a x y(x))y (x) + alpha y(x)  + beta y(x)

                                                     Type: Expression Integer
--R 
--R
--R              n             ,                3            2
--R   (124)  (b x  + a x y(x))y (x) + alpha y(x)  + beta y(x)
--R
--R                                                     Type: Expression Integer
--E 124

--S 125 of 127
solve(ode249,y,x)
 

   (125)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (125)  "failed"
--R                                                    Type: Union("failed",...)
--E 125

--S 126 of 127
ode250 := (B*x*y(x)+A*x**2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)**2+_
             A*x*y(x)+alpha*x+beta*y(x)+gamma
 

   (126)
                         2            ,                               2
     ((B x + b)y(x) + A x  + a x + c)y (x) + (A x + beta)y(x) - B g(x)

   + 
     alpha x + gamma
                                                     Type: Expression Integer
--R 
--R
--R   (126)
--R                         2            ,                               2
--R     ((B x + b)y(x) + A x  + a x + c)y (x) + (A x + beta)y(x) - B g(x)
--R
--R   + 
--R     alpha x + gamma
--R                                                     Type: Expression Integer
--E 126

--S 127 of 127
solve(ode250,y,x)
 

   (127)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (127)  "failed"
--R                                                    Type: Union("failed",...)
--E 127

)spool
 
Starts dribbling to FullPartialFractionExpansion.output (2010/3/27, 18:42:4).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
Fx := FRAC UP(x, FRAC INT)
 

   (1)  Fraction UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 16
f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2) 
 

                     36
   (2)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (2)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 2

--S 3 of 16
g := fullPartialFraction f 
 

          4       4        --+      - 3%A - 6
   (3)  ----- - ----- +    >        ---------
        x - 2   x + 1      --+              2
                          2         (x - %A)
                        %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          4       4        --+      - 3%A - 6
--R   (3)  ----- - ----- +    >        ---------
--R        x - 2   x + 1      --+              2
--R                          2         (x - %A)
--R                        %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 16
g :: Fx
 

                     36
   (4)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (4)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 4

--S 5 of 16
g5 := D(g, 5)
 

             480        480        --+      2160%A + 4320
   (5)  - -------- + -------- +    >        -------------
                 6          6      --+                7
          (x - 2)    (x + 1)      2           (x - %A)
                                %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R             480        480        --+      2160%A + 4320
--R   (5)  - -------- + -------- +    >        -------------
--R                 6          6      --+                7
--R          (x - 2)    (x + 1)      2           (x - %A)
--R                                %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 16
f5 := D(f, 5)
 

   (6)
                10           9            8            7            6
       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
     + 
                5            4            3           2
       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
  /
        20      19      18      17       16       15       14        13
       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
     + 
            12        11        10        9        8        7        6        5
       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
     + 
           4        3       2
       276x  - 1184x  + 208x  + 192x - 64
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (6)
--R                10           9            8            7            6
--R       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
--R     + 
--R                5            4            3           2
--R       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
--R  /
--R        20      19      18      17       16       15       14        13
--R       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
--R     + 
--R            12        11        10        9        8        7        6        5
--R       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
--R     + 
--R           4        3       2
--R       276x  - 1184x  + 208x  + 192x - 64
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 16
g5::Fx - f5
 

   (7)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (7)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 16
f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)
 

                       6    5
                      x  - x
   (8)  -----------------------------------
         7     6     5     3     2
        x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                       6    5
--R                      x  - x
--R   (8)  -----------------------------------
--R         7     6     5     3     2
--R        x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 16
g := fullPartialFraction f 
 

   (9)
      1952       464        32                          179       135
      ----       ---        --                       - ---- %A + ----
      2401       343        49            --+          2401      2401
     ------ + -------- + -------- +       >          ----------------
      x - 2          2          3         --+             x - %A
              (x - 2)    (x - 2)      2
                                    %A  + %A + 1= 0
   + 
                       37        20
                      ---- %A + ----
           --+        1029      1029
           >          --------------
           --+                   2
       2                 (x - %A)
     %A  + %A + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (9)
--R      1952       464        32                          179       135
--R      ----       ---        --                       - ---- %A + ----
--R      2401       343        49            --+          2401      2401
--R     ------ + -------- + -------- +       >          ----------------
--R      x - 2          2          3         --+             x - %A
--R              (x - 2)    (x - 2)      2
--R                                    %A  + %A + 1= 0
--R   + 
--R                       37        20
--R                      ---- %A + ----
--R           --+        1029      1029
--R           >          --------------
--R           --+                   2
--R       2                 (x - %A)
--R     %A  + %A + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 16
g :: Fx - f
 

   (10)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (10)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 10

--S 11 of 16
f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8) 
 

             7     5      3
           2x  - 7x  + 26x  + 8x
   (11)  ------------------------
          8     6     4     2
         x  - 5x  + 6x  + 4x  - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             7     5      3
--R           2x  - 7x  + 26x  + 8x
--R   (11)  ------------------------
--R          8     6     4     2
--R         x  - 5x  + 6x  + 4x  - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 11

--S 12 of 16
g := fullPartialFraction f
 

                        1                                            1
                        -                                            -
            --+         2        --+          1          --+         2
   (12)     >        ------ +    >        --------- +    >        ------
            --+      x - %A      --+              3      --+      x - %A
           2                    2         (x - %A)      2
         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R                        1                                            1
--R                        -                                            -
--R            --+         2        --+          1          --+         2
--R   (12)     >        ------ +    >        --------- +    >        ------
--R            --+      x - %A      --+              3      --+      x - %A
--R           2                    2         (x - %A)      2
--R         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 12

--S 13 of 16
g :: Fx - f 
 

   (13)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (13)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 13

--S 14 of 16
f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x**15 + 30*x**14 + 36*x**13 + 40*x**12 + 47*x**11 + 46*x**10 + 49*x**9 + 43*x**8 + 38*x**7 + 32*x**6 + 23*x**5 + 19*x**4 + 10*x**3 + 7*x**2 + 2*x + 1)
 

   (14)
      3
     x
  /
        21     20     19     18      17      16      15      14      13      12
       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
     + 
          11      10      9      8      7      6      5      4      3     2
       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
     + 
       1
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (14)
--R      3
--R     x
--R  /
--R        21     20     19     18      17      16      15      14      13      12
--R       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
--R     + 
--R          11      10      9      8      7      6      5      4      3     2
--R       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
--R     + 
--R       1
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 14

--S 15 of 16
g := fullPartialFraction f 
 

   (15)
                  1                        1      19
                  - %A                     - %A - --
        --+       2             --+        9      27
        >        ------ +       >          ---------
        --+      x - %A         --+          x - %A
       2                    2
     %A  + 1= 0           %A  + %A + 1= 0
   + 
                       1       1
                      -- %A - --
           --+        27      27
           >          ----------
           --+                 2
       2               (x - %A)
     %A  + %A + 1= 0
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
               96556567040   4   420961732891   3    59101056149   2
            - ------------ %A  + ------------ %A  - ------------ %A
              912390759099       912390759099       912390759099
          + 
              373545875923      529673492498
            - ------------ %A + ------------
              912390759099      912390759099
       /
          x - %A
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
           5580868   4    2024443   3    4321919   2    84614        5070620
        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
          94070601       94070601       94070601       1542141      94070601
        --------------------------------------------------------------------
                                              2
                                      (x - %A)
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
         1610957   4    2763014   3    2016775   2    266953        4529359
        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
        94070601       94070601       94070601       94070601      94070601
        -------------------------------------------------------------------
                                             3
                                     (x - %A)
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (15)
--R                  1                        1      19
--R                  - %A                     - %A - --
--R        --+       2             --+        9      27
--R        >        ------ +       >          ---------
--R        --+      x - %A         --+          x - %A
--R       2                    2
--R     %A  + 1= 0           %A  + %A + 1= 0
--R   + 
--R                       1       1
--R                      -- %A - --
--R           --+        27      27
--R           >          ----------
--R           --+                 2
--R       2               (x - %A)
--R     %A  + %A + 1= 0
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R               96556567040   4   420961732891   3    59101056149   2
--R            - ------------ %A  + ------------ %A  - ------------ %A
--R              912390759099       912390759099       912390759099
--R          + 
--R              373545875923      529673492498
--R            - ------------ %A + ------------
--R              912390759099      912390759099
--R       /
--R          x - %A
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R           5580868   4    2024443   3    4321919   2    84614        5070620
--R        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
--R          94070601       94070601       94070601       1542141      94070601
--R        --------------------------------------------------------------------
--R                                              2
--R                                      (x - %A)
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R         1610957   4    2763014   3    2016775   2    266953        4529359
--R        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
--R        94070601       94070601       94070601       94070601      94070601
--R        -------------------------------------------------------------------
--R                                             3
--R                                     (x - %A)
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 15

--S 16 of 16
g :: Fx - f
 

   (16)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (16)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 16
)spool
 
Starts dribbling to eigen.output (2010/3/27, 18:25:20).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 36
m:=matrix([[1,2,1],[2,1,-2],[1,-2,4]])
 

        +1   2    1 +
        |           |
   (1)  |2   1   - 2|
        |           |
        +1  - 2   4 +
                                                         Type: Matrix Integer
--R 
--R
--R        +1   2    1 +
--R        |           |
--R   (1)  |2   1   - 2|
--R        |           |
--R        +1  - 2   4 +
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 36
characteristicPolynomial m
 

            3      2
   (2)  - %A  + 6%A  - 25
                                                     Type: Polynomial Integer
--R 
--R
--R            3      2
--R   (2)  - %A  + 6%A  - 25
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 36
characteristicPolynomial(m,x)
 

           3     2
   (3)  - x  + 6x  - 25
                                                     Type: Polynomial Integer
--R 
--R
--R           3     2
--R   (3)  - x  + 6x  - 25
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 36
p:=matrix([[x+1,2-x*y,x**2+1],[2-x,y+2*x,x**2-2],[y**2,x-2,4-x*y]])
 

        +                      2      +
        | x + 1   - x y + 2   x  + 1  |
        |                             |
   (4)  |                      2      |
        |- x + 2   y + 2x     x  - 2  |
        |                             |
        |   2                         |
        +  y        x - 2    - x y + 4+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +                      2      +
--R        | x + 1   - x y + 2   x  + 1  |
--R        |                             |
--R   (4)  |                      2      |
--R        |- x + 2   y + 2x     x  - 2  |
--R        |                             |
--R        |   2                         |
--R        +  y        x - 2    - x y + 4+
--R                                              Type: Matrix Polynomial Integer
--E 4

--S 5 of 36
characteristicPolynomial p
 

   (5)
         3    2           3       3            2                       2
     (- x  - x  + 2x - 1)y  + (- x  + (%B - 1)x  + (%B - 3)x + %B - 4)y
   + 
          3             2        2                  2                 4
     (- 2x  + (4%B - 8)x  + (- %B  - 2%B + 16)x + %B  - 5%B + 4)y - 2x
   + 
              3               2       2                   3      2
     (%B + 5)x  + (- 4%B + 7)x  + (3%B  - 18%B + 18)x - %B  + 5%B  + 4%B - 24
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)
--R         3    2           3       3            2                       2
--R     (- x  - x  + 2x - 1)y  + (- x  + (%B - 1)x  + (%B - 3)x + %B - 4)y
--R   + 
--R          3             2        2                  2                 4
--R     (- 2x  + (4%B - 8)x  + (- %B  - 2%B + 16)x + %B  - 5%B + 4)y - 2x
--R   + 
--R              3               2       2                   3      2
--R     (%B + 5)x  + (- 4%B + 7)x  + (3%B  - 18%B + 18)x - %B  + 5%B  + 4%B - 24
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 36
characteristicPolynomial(p,t)
 

   (6)
         3    2           3       3           2                     2
     (- x  - x  + 2x - 1)y  + (- x  + (t - 1)x  + (t - 3)x + t - 4)y
   + 
          3            2       2                2                4           3
     (- 2x  + (4t - 8)x  + (- t  - 2t + 16)x + t  - 5t + 4)y - 2x  + (t + 5)x
   + 
                2      2                 3     2
     (- 4t + 7)x  + (3t  - 18t + 18)x - t  + 5t  + 4t - 24
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)
--R         3    2           3       3           2                     2
--R     (- x  - x  + 2x - 1)y  + (- x  + (t - 1)x  + (t - 3)x + t - 4)y
--R   + 
--R          3            2       2                2                4           3
--R     (- 2x  + (4t - 8)x  + (- t  - 2t + 16)x + t  - 5t + 4)y - 2x  + (t + 5)x
--R   + 
--R                2      2                 3     2
--R     (- 4t + 7)x  + (3t  - 18t + 18)x - t  + 5t  + 4t - 24
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 36
n:=matrix([[a,b,c],[d,e,f],[g,h,k]])
 

        +a  b  c+
        |       |
   (7)  |d  e  f|
        |       |
        +g  h  k+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +a  b  c+
--R        |       |
--R   (7)  |d  e  f|
--R        |       |
--R        +g  h  k+
--R                                              Type: Matrix Polynomial Integer
--E 7

--S 8 of 36
characteristicPolynomial n
 

   (8)
                                 2
     ((a - %C)e - b d - %C a + %C )k + ((- a + %C)f + c d)h
   + 
                                       2                2      3
     (b f - c e + %C c)g + (- %C a + %C )e + %C b d + %C a - %C
                                                     Type: Polynomial Integer
--R 
--R
--R   (8)
--R                                 2
--R     ((a - %C)e - b d - %C a + %C )k + ((- a + %C)f + c d)h
--R   + 
--R                                       2                2      3
--R     (b f - c e + %C c)g + (- %C a + %C )e + %C b d + %C a - %C
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 36
leig := eigenvalues m
 

                  2
   (9)  [5,%D | %D  - %D - 5]
Type: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--R 
--R
--R                  2
--R   (9)  [5,%D | %D  - %D - 5]
--RType: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--E 9

--S 10 of 36
alpha:=leig.1
 

   (10)  5
                                 Type: Union(Fraction Polynomial Integer,...)
--R 
--R
--R   (10)  5
--R                                 Type: Union(Fraction Polynomial Integer,...)
--E 10

--S 11 of 36
eigenvector(alpha,m)
 

          + 0 +
          |   |
          |  1|
   (11)  [|- -|]
          |  2|
          |   |
          + 1 +
                       Type: List Matrix Fraction Polynomial Fraction Integer
--R 
--R
--R          + 0 +
--R          |   |
--R          |  1|
--R   (11)  [|- -|]
--R          |  2|
--R          |   |
--R          + 1 +
--R                       Type: List Matrix Fraction Polynomial Fraction Integer
--E 11

--S 12 of 36
beta:=leig.2
 

                2
   (12)  %D | %D  - %D - 5
                         Type: Union(SuchThat(Symbol,Polynomial Integer),...)
--R 
--R
--R                2
--R   (12)  %D | %D  - %D - 5
--R                         Type: Union(SuchThat(Symbol,Polynomial Integer),...)
--E 12

--S 13 of 36
eigenvector(beta,m)$EP(INT)
 

          +%D+
          |  |
   (13)  [|2 |]
          |  |
          +1 +
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +%D+
--R          |  |
--R   (13)  [|2 |]
--R          |  |
--R          +1 +
--R                                Type: List Matrix Fraction Polynomial Integer
--E 13

-- eigenvector(beta,m)  not accepted by the interpreter

--S 14 of 36
eigenvectors m
 

   (14)
                                   + 0 +
                                   |   |
                                   |  1|
   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
                                   |  2|
                                   |   |
                                   + 1 +
                                                     +%E+
                     2                               |  |
    [eigval= (%E | %E  - %E - 5),eigmult= 1,eigvec= [|2 |]]]
                                                     |  |
                                                     +1 +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (14)
--R                                   + 0 +
--R                                   |   |
--R                                   |  1|
--R   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
--R                                   |  2|
--R                                   |   |
--R                                   + 1 +
--R                                                     +%E+
--R                     2                               |  |
--R    [eigval= (%E | %E  - %E - 5),eigmult= 1,eigvec= [|2 |]]]
--R                                                     |  |
--R                                                     +1 +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 14

--S 15 of 36
q:=matrix [[x**2-y**2,(x-y)*(2*x+3*y)],[x+y,2*x+3*y]]
 

         +   2    2      2           2+
   (15)  |- y  + x   - 3y  + x y + 2x |
         |                            |
         +  y + x         3y + 2x     +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +   2    2      2           2+
--R   (15)  |- y  + x   - 3y  + x y + 2x |
--R         |                            |
--R         +  y + x         3y + 2x     +
--R                                              Type: Matrix Polynomial Integer
--E 15

--S 16 of 36
eigenvectors(q)
 

   (16)
                2         2                          +- y + x+
   [[eigval= - y  + 3y + x  + 2x,eigmult= 1,eigvec= [|       |]],
                                                     +   1   +
                                   +- 3y - 2x+
                                   |---------|
    [eigval= 0,eigmult= 1,eigvec= [|  y + x  |]]]
                                   |         |
                                   +    1    +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (16)
--R                2         2                          +- y + x+
--R   [[eigval= - y  + 3y + x  + 2x,eigmult= 1,eigvec= [|       |]],
--R                                                     +   1   +
--R                                   +- 3y - 2x+
--R                                   |---------|
--R    [eigval= 0,eigmult= 1,eigvec= [|  y + x  |]]]
--R                                   |         |
--R                                   +    1    +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 16

--S 17 of 36
p:=matrix([[76,-18,58,-10],[-4,78,2,-2],[-6,15,45,3],[22,-75,7,41]])
 

         +76   - 18  58  - 10+
         |                   |
         |- 4   78   2   - 2 |
   (17)  |                   |
         |- 6   15   45   3  |
         |                   |
         +22   - 75  7    41 +
                                                         Type: Matrix Integer
--R 
--R
--R         +76   - 18  58  - 10+
--R         |                   |
--R         |- 4   78   2   - 2 |
--R   (17)  |                   |
--R         |- 6   15   45   3  |
--R         |                   |
--R         +22   - 75  7    41 +
--R                                                         Type: Matrix Integer
--E 17

--S 18 of 36
ll := eigenvectors p
 

   (18)
                                    +10 +
                                    |-- |
                                    | 7 |
                                    |   |
                                    | 2 |
                                    | - |
   [[eigval= 48,eigmult= 2,eigvec= [| 7 |]],
                                    |   |
                                    |  3|
                                    |- -|
                                    |  7|
                                    |   |
                                    + 1 +
                                    +- 2+
                                    |   |
                                    |- 1|
    [eigval= 72,eigmult= 2,eigvec= [|   |]]]
                                    | 0 |
                                    |   |
                                    + 1 +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (18)
--R                                    +10 +
--R                                    |-- |
--R                                    | 7 |
--R                                    |   |
--R                                    | 2 |
--R                                    | - |
--R   [[eigval= 48,eigmult= 2,eigvec= [| 7 |]],
--R                                    |   |
--R                                    |  3|
--R                                    |- -|
--R                                    |  7|
--R                                    |   |
--R                                    + 1 +
--R                                    +- 2+
--R                                    |   |
--R                                    |- 1|
--R    [eigval= 72,eigmult= 2,eigvec= [|   |]]]
--R                                    | 0 |
--R                                    |   |
--R                                    + 1 +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 18


--S 19 of 36
generalizedEigenvectors p
 

   (19)
                            +  10+
                            |- --|
                            |   3| +0+                           +- 12+ +- 2+
                            |    | | |                           |    | |   |
                            |  2 | |0|                           |- 3 | |- 1|
   [[eigval= 48,geneigvec= [|- - |,| |]],[eigval= 72,geneigvec= [|    |,|   |]]]
                            |  3 | |0|                           | 1  | | 0 |
                            |    | | |                           |    | |   |
                            | 1  | +1+                           + 0  + + 1 +
                            |    |
                            + 0  +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),geneigvec: List Matrix Fraction Polynomial Integer)
--R 
--R
--R   (19)
--R                            +  10+
--R                            |- --|
--R                            |   3| +0+                           +- 12+ +- 2+
--R                            |    | | |                           |    | |   |
--R                            |  2 | |0|                           |- 3 | |- 1|
--R   [[eigval= 48,geneigvec= [|- - |,| |]],[eigval= 72,geneigvec= [|    |,|   |]]]
--R                            |  3 | |0|                           | 1  | | 0 |
--R                            |    | | |                           |    | |   |
--R                            | 1  | +1+                           + 0  + + 1 +
--R                            |    |
--R                            + 0  +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),geneigvec: List Matrix Fraction Polynomial Integer)
--E 19

--S 20 of 36
generalizedEigenvector(ll.1,p)$EP(INT)
 

          +  10+
          |- --|
          |   3| +0+
          |    | | |
          |  2 | |0|
   (20)  [|- - |,| |]
          |  3 | |0|
          |    | | |
          | 1  | +1+
          |    |
          + 0  +
                                Type: List Matrix Fraction Polynomial Integer
--R 
--R
--R          +  10+
--R          |- --|
--R          |   3| +0+
--R          |    | | |
--R          |  2 | |0|
--R   (20)  [|- - |,| |]
--R          |  3 | |0|
--R          |    | | |
--R          | 1  | +1+
--R          |    |
--R          + 0  +
--R                                Type: List Matrix Fraction Polynomial Integer
--E 20

-- generalizedEigenvector(ll.1,p) the interpreter can not handle this

--S 21 of 36
m
 

         +1   2    1 +
         |           |
   (21)  |2   1   - 2|
         |           |
         +1  - 2   4 +
                                                         Type: Matrix Integer
--R 
--R
--R         +1   2    1 +
--R         |           |
--R   (21)  |2   1   - 2|
--R         |           |
--R         +1  - 2   4 +
--R                                                         Type: Matrix Integer
--E 21

--S 22 of 36
mm:=matrix([[30,4,24],[-17,8,-7],[-31,-54,-5]])
 

         + 30    4    24 +
         |               |
   (22)  |- 17   8    - 7|
         |               |
         +- 31  - 54  - 5+
                                                         Type: Matrix Integer
--R 
--R
--R         + 30    4    24 +
--R         |               |
--R   (22)  |- 17   8    - 7|
--R         |               |
--R         +- 31  - 54  - 5+
--R                                                         Type: Matrix Integer
--E 22

--S 23 of 36
le1:=radicalEigenvalues m
 

             +--+      +--+
          - \|21  + 1 \|21  + 1
   (23)  [-----------,---------,5]
               2          2
                                                Type: List Expression Integer
--R 
--R
--R             +--+      +--+
--R          - \|21  + 1 \|21  + 1
--R   (23)  [-----------,---------,5]
--R               2          2
--R                                                Type: List Expression Integer
--E 23

--S 24 of 36
le2:=radicalEigenvalues mm
 

             +---+      +---+
   (24)  [22\|- 1 ,- 22\|- 1 ,33]
                                                Type: List Expression Integer
--R 
--R
--R             +---+      +---+
--R   (24)  [22\|- 1 ,- 22\|- 1 ,33]
--R                                                Type: List Expression Integer
--E 24

--S 25 of 36
radicalEigenvector(le1.2, m)
 

          +    10   +
          |---------|
          | +--+    |
   (25)  [|\|21  - 1|]
          |         |
          |    2    |
          |         |
          +    1    +
                                         Type: List Matrix Expression Integer
--R 
--R
--R          +    10   +
--R          |---------|
--R          | +--+    |
--R   (25)  [|\|21  - 1|]
--R          |         |
--R          |    2    |
--R          |         |
--R          +    1    +
--R                                         Type: List Matrix Expression Integer
--E 25

--S 26 of 36
radicalEigenvector(le2.2,mm)
 

          +       +---+       +
          |- 1449\|- 1  + 1720|
          |-------------------|
          |      +---+        |
          |  328\|- 1  - 3343 |
          |                   |
   (26)  [|      +---+        |]
          |    7\|- 1  - 9    |
          |   ------------    |
          |      +---+        |
          |   38\|- 1  - 8    |
          |                   |
          +         1         +
                                         Type: List Matrix Expression Integer
--R 
--R
--R          +       +---+       +
--R          |- 1449\|- 1  + 1720|
--R          |-------------------|
--R          |      +---+        |
--R          |  328\|- 1  - 3343 |
--R          |                   |
--R   (26)  [|      +---+        |]
--R          |    7\|- 1  - 9    |
--R          |   ------------    |
--R          |      +---+        |
--R          |   38\|- 1  - 8    |
--R          |                   |
--R          +         1         +
--R                                         Type: List Matrix Expression Integer
--E 26

--S 27 of 36
radicalEigenvectors m
 

   (27)
                                            + +--+    +
              +--+                          |\|21  + 1|
             \|21  + 1                      |---------|
   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
                 2                          |         |
                                            |    2    |
                                            |         |
                                            +    1    +
                                              +   +--+    +
                +--+                          |- \|21  + 1|
             - \|21  + 1                      |-----------|
    [radval= -----------,radmult= 1,radvect= [|     2     |]],
                  2                           |           |
                                              |     2     |
                                              |           |
                                              +     1     +
                                    + 0 +
                                    |   |
                                    |  1|
    [radval= 5,radmult= 1,radvect= [|- -|]]]
                                    |  2|
                                    |   |
                                    + 1 +
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R 
--R
--R   (27)
--R                                            + +--+    +
--R              +--+                          |\|21  + 1|
--R             \|21  + 1                      |---------|
--R   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
--R                 2                          |         |
--R                                            |    2    |
--R                                            |         |
--R                                            +    1    +
--R                                              +   +--+    +
--R                +--+                          |- \|21  + 1|
--R             - \|21  + 1                      |-----------|
--R    [radval= -----------,radmult= 1,radvect= [|     2     |]],
--R                  2                           |           |
--R                                              |     2     |
--R                                              |           |
--R                                              +     1     +
--R                                    + 0 +
--R                                    |   |
--R                                    |  1|
--R    [radval= 5,radmult= 1,radvect= [|- -|]]]
--R                                    |  2|
--R                                    |   |
--R                                    + 1 +
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E 27

--S 28 of 36
radicalEigenvectors mm
 

   (28)
                                             +   +---+     +
                                             |11\|- 1  - 16|
                                             |-------------|
                                             |      29     |
                  +---+                      |             |
   [[radval= - 22\|- 1 ,radmult= 1,radvect= [|   +---+     |]],
                                             |11\|- 1  + 13|
                                             |-------------|
                                             |      58     |
                                             |             |
                                             +      1      +
                                           +     +---+     +
                                           |- 11\|- 1  - 16|
                                           |---------------|
                                           |       29      |
                +---+                      |               |
    [radval= 22\|- 1 ,radmult= 1,radvect= [|     +---+     |]],
                                           |- 11\|- 1  + 13|
                                           |---------------|
                                           |       58      |
                                           |               |
                                           +       1       +
                                     + 4 +
                                     |   |
    [radval= 33,radmult= 1,radvect= [|- 3|]]]
                                     |   |
                                     + 1 +
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R 
--R
--R   (28)
--R                                             +   +---+     +
--R                                             |11\|- 1  - 16|
--R                                             |-------------|
--R                                             |      29     |
--R                  +---+                      |             |
--R   [[radval= - 22\|- 1 ,radmult= 1,radvect= [|   +---+     |]],
--R                                             |11\|- 1  + 13|
--R                                             |-------------|
--R                                             |      58     |
--R                                             |             |
--R                                             +      1      +
--R                                           +     +---+     +
--R                                           |- 11\|- 1  - 16|
--R                                           |---------------|
--R                                           |       29      |
--R                +---+                      |               |
--R    [radval= 22\|- 1 ,radmult= 1,radvect= [|     +---+     |]],
--R                                           |- 11\|- 1  + 13|
--R                                           |---------------|
--R                                           |       58      |
--R                                           |               |
--R                                           +       1       +
--R                                     + 4 +
--R                                     |   |
--R    [radval= 33,radmult= 1,radvect= [|- 3|]]]
--R                                     |   |
--R                                     + 1 +
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E 28

--S 29 of 36
realEigenvalues(m,1/1000000)
 

            3756603   5853755
   (29)  [- -------,5,-------]
            2097152   2097152
                                                  Type: List Fraction Integer
--R 
--R
--R            3756603   5853755
--R   (29)  [- -------,5,-------]
--R            2097152   2097152
--R                                                  Type: List Fraction Integer
--E 29

--S 30 of 36
complexEigenvalues(mm,1/1000000)
 

   (30)  [- 22%i,22%i,33]
                                          Type: List Complex Fraction Integer
--R 
--R
--R   (30)  [- 22%i,22%i,33]
--R                                          Type: List Complex Fraction Integer
--E 30

--S 31 of 36
realEigenvectors(m,1/1000000)
 

   (31)
                                    + 0 +
                                    |   |
                                    |  1|
   [[outval= 5,outmult= 1,outvect= [|- -|]],
                                    |  2|
                                    |   |
                                    + 1 +
                                          +5853755+
                                          |-------|
             5853755                      |2097152|
    [outval= -------,outmult= 1,outvect= [|       |]],
             2097152                      |   2   |
                                          |       |
                                          +   1   +
                                            +  3756603+
                                            |- -------|
               3756603                      |  2097152|
    [outval= - -------,outmult= 1,outvect= [|         |]]]
               2097152                      |    2    |
                                            |         |
                                            +    1    +
Type: List Record(outval: Fraction Integer,outmult: Integer,outvect: List Matrix Fraction Integer)
--R 
--R
--R   (31)
--R                                    + 0 +
--R                                    |   |
--R                                    |  1|
--R   [[outval= 5,outmult= 1,outvect= [|- -|]],
--R                                    |  2|
--R                                    |   |
--R                                    + 1 +
--R                                          +5853755+
--R                                          |-------|
--R             5853755                      |2097152|
--R    [outval= -------,outmult= 1,outvect= [|       |]],
--R             2097152                      |   2   |
--R                                          |       |
--R                                          +   1   +
--R                                            +  3756603+
--R                                            |- -------|
--R               3756603                      |  2097152|
--R    [outval= - -------,outmult= 1,outvect= [|         |]]]
--R               2097152                      |    2    |
--R                                            |         |
--R                                            +    1    +
--RType: List Record(outval: Fraction Integer,outmult: Integer,outvect: List Matrix Fraction Integer)
--E 31

--S 32 of 36
complexEigenvectors(mm,1/1000000)
 

   (32)
                                     + 4 +
                                     |   |
   [[outval= 33,outmult= 1,outvect= [|- 3|]],
                                     |   |
                                     + 1 +
                                       +  16   11   +
                                       |- -- - -- %i|
                                       |  29   29   |
                                       |            |
    [outval= 22%i,outmult= 1,outvect= [| 13   11    |]],
                                       | -- - -- %i |
                                       | 58   58    |
                                       |            |
                                       +     1      +
                                         +  16   11   +
                                         |- -- + -- %i|
                                         |  29   29   |
                                         |            |
    [outval= - 22%i,outmult= 1,outvect= [| 13   11    |]]]
                                         | -- + -- %i |
                                         | 58   58    |
                                         |            |
                                         +     1      +
Type: List Record(outval: Complex Fraction Integer,outmult: Integer,outvect: List Matrix Complex Fraction Integer)
--R 
--R
--R   (32)
--R                                     + 4 +
--R                                     |   |
--R   [[outval= 33,outmult= 1,outvect= [|- 3|]],
--R                                     |   |
--R                                     + 1 +
--R                                       +  16   11   +
--R                                       |- -- - -- %i|
--R                                       |  29   29   |
--R                                       |            |
--R    [outval= 22%i,outmult= 1,outvect= [| 13   11    |]],
--R                                       | -- - -- %i |
--R                                       | 58   58    |
--R                                       |            |
--R                                       +     1      +
--R                                         +  16   11   +
--R                                         |- -- + -- %i|
--R                                         |  29   29   |
--R                                         |            |
--R    [outval= - 22%i,outmult= 1,outvect= [| 13   11    |]]]
--R                                         | -- + -- %i |
--R                                         | 58   58    |
--R                                         |            |
--R                                         +     1      +
--RType: List Record(outval: Complex Fraction Integer,outmult: Integer,outvect: List Matrix Complex Fraction Integer)
--E 32

--S 33 of 36
realEigenvalues(m,.000001)
 

   (33)  [- 1.7912878990 173339844,5.0,2.7912878990 173339844]
                                                             Type: List Float
--R 
--R
--R   (33)  [- 1.7912878990 173339844,5.0,2.7912878990 173339844]
--R                                                             Type: List Float
--E 33

--S 34 of 36
realEigenvectors(m,.000001)
 

   (34)
                                      + 0.0 +
                                      |     |
   [[outval= 5.0,outmult= 1,outvect= [|- 0.5|]],
                                      |     |
                                      + 1.0 +

     [outval= 2.7912878990 173339844, outmult= 1,
                +2.7912878990 173339844+
                |                      |
      outvect= [|         2.0          |]]
                |                      |
                +         1.0          +
     ,

     [outval= - 1.7912878990 173339844, outmult= 1,
                +- 1.7912878990 173339844+
                |                        |
      outvect= [|          2.0           |]]
                |                        |
                +          1.0           +
     ]
 Type: List Record(outval: Float,outmult: Integer,outvect: List Matrix Float)
--R 
--R
--R   (34)
--R                                      + 0.0 +
--R                                      |     |
--R   [[outval= 5.0,outmult= 1,outvect= [|- 0.5|]],
--R                                      |     |
--R                                      + 1.0 +
--R
--R     [outval= 2.7912878990 173339844, outmult= 1,
--R                +2.7912878990 173339844+
--R                |                      |
--R      outvect= [|         2.0          |]]
--R                |                      |
--R                +         1.0          +
--R     ,
--R
--R     [outval= - 1.7912878990 173339844, outmult= 1,
--R                +- 1.7912878990 173339844+
--R                |                        |
--R      outvect= [|          2.0           |]]
--R                |                        |
--R                +          1.0           +
--R     ]
--R Type: List Record(outval: Float,outmult: Integer,outvect: List Matrix Float)
--E 34

--S 35 of 36
complexEigenvalues(mm,.000001)
 

   (35)  [- 22.0 %i,22.0 %i,33.0]
                                                     Type: List Complex Float
--R 
--R
--R   (35)  [- 22.0 %i,22.0 %i,33.0]
--R                                                     Type: List Complex Float
--E 35

--S 36 of 36
complexEigenvectors(mm,.000001)
 

   (36)
                                       + 4.0 +
                                       |     |
   [[outval= 33.0,outmult= 1,outvect= [|- 3.0|]],
                                       |     |
                                       + 1.0 +

     [outval= 22.0 %i, outmult= 1,
                +- 0.5517241379 3103448276 - 0.3793103448 275862069 %i+
                |                                                     |
      outvect= [|0.2241379310 3448275862 - 0.1896551724 1379310345 %i |]]
                |                                                     |
                +                         1.0                         +
     ,

     [outval= - 22.0 %i, outmult= 1,
                +- 0.5517241379 3103448276 + 0.3793103448 275862069 %i+
                |                                                     |
      outvect= [|0.2241379310 3448275862 + 0.1896551724 1379310345 %i |]]
                |                                                     |
                +                         1.0                         +
     ]
Type: List Record(outval: Complex Float,outmult: Integer,outvect: List Matrix Complex Float)
--R 
--R
--R   (36)
--R                                       + 4.0 +
--R                                       |     |
--R   [[outval= 33.0,outmult= 1,outvect= [|- 3.0|]],
--R                                       |     |
--R                                       + 1.0 +
--R
--R     [outval= 22.0 %i, outmult= 1,
--R                +- 0.5517241379 3103448276 - 0.3793103448 275862069 %i+
--R                |                                                     |
--R      outvect= [|0.2241379310 3448275862 - 0.1896551724 1379310345 %i |]]
--R                |                                                     |
--R                +                         1.0                         +
--R     ,
--R
--R     [outval= - 22.0 %i, outmult= 1,
--R                +- 0.5517241379 3103448276 + 0.3793103448 275862069 %i+
--R                |                                                     |
--R      outvect= [|0.2241379310 3448275862 + 0.1896551724 1379310345 %i |]]
--R                |                                                     |
--R                +                         1.0                         +
--R     ]
--RType: List Record(outval: Complex Float,outmult: Integer,outvect: List Matrix Complex Float)
--E 36
)spool
 
Starts dribbling to genups.output (2010/3/27, 18:26:40).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 40
taylor(n +-> 1/factorial(n),x = 0)      -- expansion of exp(x) at x = 0
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 40
taylor(n +-> (-1)**(n-1)/n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (2)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10            11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
     7            8            9            10
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (2)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10            11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
--R     7            8            9            10
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 2

--S 3 of 40
taylor(n +-> (-1)**(n-1)/n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (3)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (3)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 3

--S 4 of 40
laurent(m +-> m**2,x = 7,-2..)          -- infinite Laurent expansion
 

   (4)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (4)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 4

--S 5 of 40
laurent(m +-> m**2,x = 7,-2..5)         --   finite Laurent expansion
 

   (5)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (5)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 5

--S 6 of 40
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)  -- sin(x) at x = 0
 

            1  3    1   5     1   7      1    9       1     11      12
   (6)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
            6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      1    9       1     11      12
--R   (6)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R            6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 6

--S 7 of 40
puiseux(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2)      -- cos(x) at x = 0
 

            1  2    1  4    1   6     1    8      1     10      11
   (7)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
            2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  2    1  4    1   6     1    8      1     10      11
--R   (7)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R            2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 7

-- puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 8 of 40
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
 

            1  3    1   5     1   7      1    9
   (8)  x - - x  + --- x  - ---- x  + ------ x
            6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1   5     1   7      1    9
--R   (8)  x - - x  + --- x  - ---- x  + ------ x
--R            6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 8

--S 9 of 40
puiseux(j +-> j,x = 8,-4/3..,1/2)
 

   (9)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (9)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 9

--S 10 of 40
puiseux(j +-> j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (10)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (10)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 10

--S 11 of 40
taylor(1/factorial(n),n,x = 0)      -- expansion of exp(x) at x = 0
 

   (11)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (11)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 11

--S 12 of 40
taylor((-1)**(n-1)/n,n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (12)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10            11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
     7            8            9            10
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (12)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10            11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + O((x - 1)  )
--R     7            8            9            10
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 12

--S 13 of 40
taylor((-1)**(n-1)/n,n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (13)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R
--R   (13)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 13

--S 14 of 40
laurent(m**2,m,x = 7,-2..)          -- infinite Laurent expansion
 

   (14)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (14)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 14

--S 15 of 40
laurent(m**2,m,x = 7,-2..5)         --   finite Laurent expansion
 

   (15)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--R 
--R
--R   (15)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,7)
--E 15

--S 16 of 40
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2)  -- sin(x) at x = 0
 

             1  3    1   5     1   7      1    9       1     11      12
   (16)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
             6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9       1     11      12
--R   (16)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R             6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 16

--S 17 of 40
puiseux((-1)**(i/2)/factorial(i),i,x = 0,0..,2)      -- cos(x) at x = 0
 

             1  2    1  4    1   6     1    8      1     10      11
   (17)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
             2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  2    1  4    1   6     1    8      1     10      11
--R   (17)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R             2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 17

-- puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 18 of 40
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
 

             1  3    1   5     1   7      1    9
   (18)  x - - x  + --- x  - ---- x  + ------ x
             6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9
--R   (18)  x - - x  + --- x  - ---- x  + ------ x
--R             6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 18

--S 19 of 40
puiseux(j,j,x = 8,-4/3..,1/2)
 

   (19)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (19)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 19

--S 20 of 40
puiseux(j,j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (20)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (20)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 20

--S 21 of 40
series(n +-> 1/factorial(n),x = 0)      -- expansion of exp(x) at x = 0
 

   (21)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (21)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 21

--S 22 of 40
series(n +-> (-1)**(n-1)/n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (22)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10    1        11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
     7            8            9            10             11
   + 
              12
     O((x - 1)  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (22)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10    1        11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
--R     7            8            9            10             11
--R   + 
--R              12
--R     O((x - 1)  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 22

--S 23 of 40
series(n +-> (-1)**(n-1)/n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (23)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (23)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 23

--S 24 of 40
series(m +-> m**2,x = 7,-2..)          -- infinite Laurent expansion
 

   (24)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (24)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 24

--S 25 of 40
series(m +-> m**2,x = 7,-2..5)         --   finite Laurent expansion
 

   (25)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (25)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 25

--S 26 of 40
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)  -- sin(x) at x = 0
 

             1  3    1   5     1   7      1    9       1     11      12
   (26)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
             6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9       1     11      12
--R   (26)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R             6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 26

--S 27 of 40
series(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2)      -- cos(x) at x = 0
 

             1  2    1  4    1   6     1    8      1     10      11
   (27)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
             2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  2    1  4    1   6     1    8      1     10      11
--R   (27)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R             2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 27

-- series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 28 of 40
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
 

             1  3    1   5     1   7      1    9
   (28)  x - - x  + --- x  - ---- x  + ------ x
             6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9
--R   (28)  x - - x  + --- x  - ---- x  + ------ x
--R             6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 28

--S 29 of 40
series(j +-> j,x = 8,-4/3..,1/2)
 

   (29)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (29)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 29

--S 30 of 40
series(j +-> j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (30)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (30)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 30

--S 31 of 40
series(1/factorial(n),n,x = 0)      -- expansion of exp(x) at x = 0
 

   (31)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (31)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 31

--S 32 of 40
series((-1)**(n-1)/n,n,x = 1,1..)   -- expansion of log(x) at x = 1
 

   (32)
               1        2   1        3   1        4   1        5   1        6
     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
               2            3            4            5            6
   + 
     1        7   1        8   1        9    1        10    1        11
     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
     7            8            9            10             11
   + 
              12
     O((x - 1)  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (32)
--R               1        2   1        3   1        4   1        5   1        6
--R     (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R               2            3            4            5            6
--R   + 
--R     1        7   1        8   1        9    1        10    1        11
--R     - (x - 1)  - - (x - 1)  + - (x - 1)  - -- (x - 1)   + -- (x - 1)
--R     7            8            9            10             11
--R   + 
--R              12
--R     O((x - 1)  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 32

--S 33 of 40
series((-1)**(n-1)/n,n,x = 1,1..6)  -- truncated expansion of log(x)
 

   (33)
             1        2   1        3   1        4   1        5   1        6
   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
             2            3            4            5            6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--R 
--R
--R   (33)
--R             1        2   1        3   1        4   1        5   1        6
--R   (x - 1) - - (x - 1)  + - (x - 1)  - - (x - 1)  + - (x - 1)  - - (x - 1)
--R             2            3            4            5            6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,1)
--E 33

--S 34 of 40
series(m**2,m,x = 7,-2..)          -- infinite Laurent expansion
 

   (34)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5            6            7            8            9
     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (34)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5            6            7            8            9
--R     25(x - 7)  + 36(x - 7)  + 49(x - 7)  + 64(x - 7)  + O((x - 7) )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 34

--S 35 of 40
series(m**2,m,x = 7,-2..5)         --   finite Laurent expansion
 

   (35)
             - 2          - 1                     2           3            4
     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
   + 
              5
     25(x - 7)
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--R 
--R
--R   (35)
--R             - 2          - 1                     2           3            4
--R     4(x - 7)    + (x - 7)    + (x - 7) + 4(x - 7)  + 9(x - 7)  + 16(x - 7)
--R   + 
--R              5
--R     25(x - 7)
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,7)
--E 35

--S 36 of 40
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2)  -- sin(x) at x = 0
 

             1  3    1   5     1   7      1    9       1     11      12
   (36)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
             6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9       1     11      12
--R   (36)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R             6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 36

--S 37 of 40
series((-1)**(i/2)/factorial(i),i,x = 0,0..,2)      -- cos(x) at x = 0
 

             1  2    1  4    1   6     1    8      1     10      11
   (37)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
             2      24      720      40320      3628800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  2    1  4    1   6     1    8      1     10      11
--R   (37)  1 - - x  + -- x  - --- x  + ----- x  - ------- x   + O(x  )
--R             2      24      720      40320      3628800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 37

-- series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
--S 38 of 40
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
 

             1  3    1   5     1   7      1    9
   (38)  x - - x  + --- x  - ---- x  + ------ x
             6      120      5040      362880
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             1  3    1   5     1   7      1    9
--R   (38)  x - - x  + --- x  - ---- x  + ------ x
--R             6      120      5040      362880
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 38

--S 39 of 40
series(j,j,x = 8,-4/3..,1/2)
 

   (39)
                4              5              1            1            1
              - -            - -            - -            -            -
     4          3   5          6   1          3   1        6            2
   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
     3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R   (39)
--R                4              5              1            1            1
--R              - -            - -            - -            -            -
--R     4          3   5          6   1          3   1        6            2
--R   - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)  + O((x - 8) )
--R     3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 39

--S 40 of 40
series(j,j,x = 8,-4/3..1/6,1/2)
 

                      4              5              1            1
                    - -            - -            - -            -
           4          3   5          6   1          3   1        6
   (40)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
           3              6              3              6
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--R 
--R
--R                      4              5              1            1
--R                    - -            - -            - -            -
--R           4          3   5          6   1          3   1        6
--R   (40)  - - (x - 8)    - - (x - 8)    - - (x - 8)    + - (x - 8)
--R           3              6              3              6
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,8)
--E 40
)spool 
 
Starts dribbling to coercels.output (2010/3/27, 18:24:33).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 8
alternatingGroup 4
 

   (1)  <(1 2)(3 4),(1 2 3)>
                                               Type: PermutationGroup Integer
--R 
--R
--R   (1)  <(1 2)(3 4),(1 2 3)>
--R                                               Type: PermutationGroup Integer
--E 1

--S 2 of 8
% :: List Permutation Integer
 

   (2)  [(1 2)(3 4),(1 2 3)]
                                               Type: List Permutation Integer
--R 
--R
--R   (2)  [(1 2)(3 4),(1 2 3)]
--R                                               Type: List Permutation Integer
--E 2

--S 3 of 8
li := %
 

   (3)  [(1 2)(3 4),(1 2 3)]
                                               Type: List Permutation Integer
--R 
--R
--R   (3)  [(1 2)(3 4),(1 2 3)]
--R                                               Type: List Permutation Integer
--E 3

--S 4 of 8
pgr := MonoidRing(Polynomial PrimeField 5, Permutation Integer)
 

   (4)  MonoidRing(Polynomial PrimeField 5,Permutation Integer)
                                                                 Type: Domain
--R 
--R
--R   (4)  MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R                                                                 Type: Domain
--E 4

--S 5 of 8
p : pgr := first  li
 

   (5)  (1 2)(3 4)
                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (5)  (1 2)(3 4)
--R                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 5

--S 6 of 8
q : pgr := first  li
 

   (6)  (1 2)(3 4)
                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (6)  (1 2)(3 4)
--R                Type: MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 6

--S 7 of 8
basis  := [p,q,p*p,p*q, q*p,q*q, p*q*q, p*q*p, q*p*q,q*q*p,q*p*q*q,q*q*p*q]
 

   (7)
   [(1 2)(3 4), (1 2)(3 4), 1, 1, 1, 1, (1 2)(3 4), (1 2)(3 4), (1 2)(3 4),
    (1 2)(3 4), 1, 1]
           Type: List MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (7)
--R   [(1 2)(3 4), (1 2)(3 4), 1, 1, 1, 1, (1 2)(3 4), (1 2)(3 4), (1 2)(3 4),
--R    (1 2)(3 4), 1, 1]
--R           Type: List MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 7

--S 8 of 8
% :: Set          MonoidRing(Polynomial PrimeField 5,Permutation Integer)
 

   (8)  {(1 2)(3 4),1}
            Type: Set MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--R 
--R
--R   (8)  {(1 2)(3 4),1}
--R            Type: Set MonoidRing(Polynomial PrimeField 5,Permutation Integer)
--E 8
)spool
 
Starts dribbling to exit.output (2010/3/27, 18:25:39).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
n := 0
 

   (1)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (1)  0
--R                                                     Type: NonNegativeInteger
--E 1

--S 2 of 6
gasp(): Exit ==
    free n
    n := n + 1
    error "Oh no!"
 
   Function declaration gasp : () -> Exit has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration gasp : () -> Exit has been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 6
half(k) ==
  if odd? k then gasp()
  else k quo 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 6
half 4
 
   Compiling function gasp with type () -> Exit 
   Compiling function half with type PositiveInteger -> Integer 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling function gasp with type () -> Exit 
--R   Compiling function half with type PositiveInteger -> Integer 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 6
half 3
 
 
Daly Bug
   Error signalled from user code in function gasp: 
      Oh no!
--R 
--R 
--RDaly Bug
--R   Error signalled from user code in function gasp: 
--R      Oh no!
--E 5

--S 6 of 6
n
 

   (5)  1
                                                     Type: NonNegativeInteger
--R 
--R
--R   (5)  1
--R                                                     Type: NonNegativeInteger
--E 6
)spool 
 
Starts dribbling to liu.output (2010/3/27, 18:28:41).
)set message test on
 
)set message auto off
 
)set message type off
 
)clear all
 
 
--S 1 of 9
Dx: LODO(EXPR INT, f+->D(f,x)) := D()
 

   (1)  D
--R
--R   (1)  D
--E 1

--S 2 of 9
u := operator 'u
 

   (2)  u
--R
--R   (2)  u
--E 2

--S 3 of 9
L := Dx + u(x)
 

   (3)  D + u(x)
--R
--R   (3)  D + u(x)
--E 3

--S 4 of 9
L**2 = L*L
 

         2                2   2             ,          2
   (4)  D  + 2u(x)D + u(x) = D  + 2u(x)D + u (x) + u(x)

--R
--R         2                2   2             ,          2
--R   (4)  D  + 2u(x)D + u(x) = D  + 2u(x)D + u (x) + u(x)
--R
--E 4

)clear all
 

--S 5 of 9
f: INT->INT:=x+->x+1
 

   (1)  theMap(Closure)
--R
--R   (1)  theMap(Closure)
--E 5

--S 6 of 9
K := OREUP ( x, INT, 1, f);
 

--R
--E 6

--S 7 of 9
x:K
 
--E 7

--S 8 of 9
L:=x+1
 

   (4)  x + 1
--R
--R   (4)  x + 1
--E 8

--S 9 of 9
L^2=L*L
 

         2            2
   (5)  x  + 2x + 1= x  + 4x + 3
--R
--R         2            2
--R   (5)  x  + 2x + 1= x  + 4x + 3
--E 9

)spool 
 
Starts dribbling to OrderedFreeMonoid.output (2010/3/27, 18:46:11).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 24
m1:=(x*y*y*z)$OFMONOID(Symbol)
 

           2
   (1)  x y z
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R           2
--R   (1)  x y z
--R                                               Type: OrderedFreeMonoid Symbol
--E 1

--S 2 of 24
m2:=(x*y)$OFMONOID(Symbol)
 

   (2)  x y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R   (2)  x y
--R                                               Type: OrderedFreeMonoid Symbol
--E 2

--S 3 of 24
lquo(m1,m2)
 

   (3)  y z
                                    Type: Union(OrderedFreeMonoid Symbol,...)
--R 
--R
--R   (3)  y z
--R                                    Type: Union(OrderedFreeMonoid Symbol,...)
--E 3

--S 4 of 24
m3:=(y*y)$OFMONOID(Symbol)
 

         2
   (4)  y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R         2
--R   (4)  y
--R                                               Type: OrderedFreeMonoid Symbol
--E 4

--S 5 of 24
divide(m1,m2)
 

   (5)  [lm= y z,rm= "failed"]
Type: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...)
--R 
--R
--R   (5)  [lm= y z,rm= "failed"]
--RType: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...)
--E 5

--S 6 of 24
divide(m1,m3)
 

   (6)  [lm= "failed",rm= "failed"]
Type: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...)
--R 
--R
--R   (6)  [lm= "failed",rm= "failed"]
--RType: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...)
--E 6

--S 7 of 24
m4:=(y^3)$OFMONOID(Symbol)
 

         3
   (7)  y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R         3
--R   (7)  y
--R                                               Type: OrderedFreeMonoid Symbol
--E 7

--S 8 of 24
divide(m1,m4)
 

   (8)  [lm= "failed",rm= "failed"]
Type: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...)
--R 
--R
--R   (8)  [lm= "failed",rm= "failed"]
--RType: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...)
--E 8

)set function compile on
 
 

-- Build the non-commutative algebra h=k[x,y] and then make computations
-- in h using some predefined rules for x and y. For example, giving
--   x*y*x=y*x*y
--   x*x=a*x+b
--   y*y=a*y+b
-- where a dn b are generic elements of k.
-- Then reduce the polynomials in x and y according to the previous rules.
-- That is, given
--   (x+y)^2   ( = x^2+x*y+y*x+y^2)
-- should reduce to
--   a*(x+y)+2*b+x*y+y*x

-- Generic elements of k (OVAR is OrderedVariableList)

--S 9 of 24
C ==> OVAR [a,b]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

-- Commutative Field: k = Q[a,b]
-- Q = Fraction Integer
-- SMP = SparseMultivariatePolynomials

--S 10 of 24
K ==> SMP(FRAC INT,C)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

-- Non-commutative variables

--S 11 of 24
V ==> OVAR [x,y]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

-- Non-commuative algebra k=k[x,y]
-- XDPOLY XDistributedPolynomial

--S 12 of 24
H ==> XDPOLY(V,K)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

-- Free Monoid

--S 13 of 24
M ==> OFMONOID V
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

-- Substitution rules are applied to words from the monoid over the 
-- variables and retun polynomials

--S 14 of 24
subs(w:M):H ==
  -- x*y*x = y*x*y
  n1:=lquo(w,(x::V*y::V*x::V)$M)$M
  n1 case "failed" => monom(w,1)$H
      -- x*x = a*x+b
    n2:=lquo(w,(x::V^2)$M)$M
    n2 case "failed" => monom(w,1)$H
      -- y*y = a*y+b
      n3:lquo(w,(y::V^2)$M)$M
      n3 case "failed" => monom(w,1)$H
      monom(n3,1)$H * (a::K*y::V+b::K)$M * monom(n3,1)$H
    monom(n2,1)$H * (a::K*x::V+b::K)$H * monom(n2,1)$H
  monom(n1,1)$H * (y::V*x::V*y::V)$H * monom(n1,1)$H
 
   Function declaration subs : OrderedFreeMonoid OrderedVariableList [x
      ,y] -> XDistributedPolynomial(OrderedVariableList [x,y],
      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
      [a,b])) has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration subs : OrderedFreeMonoid OrderedVariableList [x
--R      ,y] -> XDistributedPolynomial(OrderedVariableList [x,y],
--R      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
--R      [a,b])) has been added to workspace.
--R                                                                   Type: Void
--E 14

-- Apply rules to a term. Keep coefficients
--S 15 of 24
newterm(x:Record(k:M,c:K)):H == x.c*subs(x,k)
 
   Function declaration newterm : Record(k: OrderedFreeMonoid 
      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
      Fraction Integer,OrderedVariableList [a,b])) -> 
      XDistributedPolynomial(OrderedVariableList [x,y],
      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
      [a,b])) has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration newterm : Record(k: OrderedFreeMonoid 
--R      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
--R      Fraction Integer,OrderedVariableList [a,b])) -> 
--R      XDistributedPolynomial(OrderedVariableList [x,y],
--R      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
--R      [a,b])) has been added to workspace.
--R                                                                   Type: Void
--E 15

-- Reconstruct the polynomial term by term

--S 16 of 24
newpoly(t:H):H == reduce(+,map(newterm,listOfTerms(t)))
 
   Function declaration newpoly : XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration newpoly : XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) has been added to workspace.
--R                                                                   Type: Void
--E 16

-- Example calcuations

--S 17 of 24
p1:(x::V+y::V)$H^2
 
 
Daly Bug
   Category, domain or package constructor ^ is not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor ^ is not available.
--E 17

--S 18 of 24
newpoly(p1)
 
   Compiling function newpoly with type XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function newterm with type Record(k: OrderedFreeMonoid 
      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
      Fraction Integer,OrderedVariableList [a,b])) -> 
      XDistributedPolynomial(OrderedVariableList [x,y],
      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
      [a,b])) 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   Compiling function newpoly with type XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function newterm with type Record(k: OrderedFreeMonoid 
--R      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
--R      Fraction Integer,OrderedVariableList [a,b])) -> 
--R      XDistributedPolynomial(OrderedVariableList [x,y],
--R      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
--R      [a,b])) 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18

--S 19 of 24
p2:=(x::V+y::V)$H^3
 

          3    2               2      2            2     3
   (17)  y  + y x + y x y + y x  + x y  + x y x + x y + x
Type: XDistributedPolynomial(OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R 
--R
--R          3    2               2      2            2     3
--R   (17)  y  + y x + y x y + y x  + x y  + x y x + x y + x
--RType: XDistributedPolynomial(OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--E 19

--S 20 of 24
pNew:=newpoly(p2)
 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function newterm with type Record(k: OrderedFreeMonoid 
      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
      Fraction Integer,OrderedVariableList [a,b])) -> 
      XDistributedPolynomial(OrderedVariableList [x,y],
      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
      [a,b])) 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function newterm with type Record(k: OrderedFreeMonoid 
--R      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
--R      Fraction Integer,OrderedVariableList [a,b])) -> 
--R      XDistributedPolynomial(OrderedVariableList [x,y],
--R      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
--R      [a,b])) 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20

-- But the rules should be applied more than once
--S 21 of 24
while pNew ~= p2 repeat
  p2 := pNew
  pNew := newpoly(p2)
 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function newterm with type Record(k: OrderedFreeMonoid 
      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
      Fraction Integer,OrderedVariableList [a,b])) -> 
      XDistributedPolynomial(OrderedVariableList [x,y],
      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
      [a,b])) 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function newterm with type Record(k: OrderedFreeMonoid 
--R      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
--R      Fraction Integer,OrderedVariableList [a,b])) -> 
--R      XDistributedPolynomial(OrderedVariableList [x,y],
--R      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
--R      [a,b])) 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21

--S 22 of 24
pNew
 

   (18)  pNew
                                                          Type: Variable pNew
--R 
--R
--R   (18)  pNew
--R                                                          Type: Variable pNew
--E 22

--S 23 of 24
reduce(p:H):H ==
  p2 := newpoly(p)
  p3 := newpoly(p2)
  while p3 ~= p2 repeat
    p2 := p3
    p3 := newpoly(p2)
  p3
 
   Function declaration reduce : XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) has been added to workspace.
   Compiled code for newpoly has been cleared.
                                                                   Type: Void
--R 
--R   Function declaration reduce : XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) has been added to workspace.
--R   Compiled code for newpoly has been cleared.
--R                                                                   Type: Void
--E 23

--S 24 of 24
reduce(p2)
 
   Compiling function newpoly with type XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) 
   Compiling function reduce with type XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
      Integer,OrderedVariableList [a,b])) 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function newterm with type Record(k: OrderedFreeMonoid 
      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
      Fraction Integer,OrderedVariableList [a,b])) -> 
      XDistributedPolynomial(OrderedVariableList [x,y],
      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
      [a,b])) 
   There are no library operations named subs 
      Use HyperDoc Browse or issue
                                )what op subs
      to learn if there is any operation containing " subs " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
Record(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
                                 Variable k
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   Compiling function newpoly with type XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) 
--R   Compiling function reduce with type XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial(
--R      OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction 
--R      Integer,OrderedVariableList [a,b])) 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function newterm with type Record(k: OrderedFreeMonoid 
--R      OrderedVariableList [x,y],c: SparseMultivariatePolynomial(
--R      Fraction Integer,OrderedVariableList [a,b])) -> 
--R      XDistributedPolynomial(OrderedVariableList [x,y],
--R      SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList
--R      [a,b])) 
--R   There are no library operations named subs 
--R      Use HyperDoc Browse or issue
--R                                )what op subs
--R      to learn if there is any operation containing " subs " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named subs 
--R      with argument type(s) 
--RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b]))
--R                                 Variable k
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24

)spool
 
Starts dribbling to spline.output (2010/3/27, 18:37:7).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 16
incoef:=[_
[0  ,  0, 1,   0,  0, 0,   0,  0, 0,   0,     0,   0,   0,     0,   0],_
[100, 10, 1,   0,  0, 0,   0,  0, 0,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0, 100, 10, 1,   0,  0, 0,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0, 225, 15, 1,   0,  0, 0,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0, 225, 15, 1,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0, 400, 20, 1,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0,   0,  0, 0, 400,    20,   1,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0,   0,  0, 0, 506.25, 22.5, 1,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0,   0,  0, 0,   0,     0,   0, 506.25, 22.5, 1],_
[  0,  0, 0,   0,  0, 0,   0,  0, 0,   0,     0,   0, 900,    30,   1],_
[ 20,  1, 0, -20, -1, 0,   0,  0, 0,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0,  30,  1, 0, -30, -1, 0,   0,     0,   0,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0,  40,  1, 0, -40,    -1,   0,   0,     0,   0],_
[  0,  0, 0,   0,  0, 0,   0,  0, 0,  45,     1,   0, -45,    -1,   0],_
[  1,  0, 0,   0,  0, 0,   0,  0, 0,   0,     0,   0,   0,     0,   0]]
 

   (1)
   [[0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [100.0,10.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,100.0,10.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,225.0,15.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,225.0,15.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,400.0,20.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,400.0,20.0,1.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,506.25,22.5,1.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,506.25,22.5,1.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,900.0,30.0,1.0],
    [20.0,1.0,0.0,- 20.0,- 1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,30.0,1.0,0.0,- 30.0,- 1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,40.0,1.0,0.0,- 40.0,- 1.0,0.0,0.0,0.0,0.0],
    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,45.0,1.0,0.0,- 45.0,- 1.0,0.0],
    [1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [100.0,10.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,100.0,10.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,225.0,15.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,225.0,15.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,400.0,20.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,400.0,20.0,1.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,506.25,22.5,1.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,506.25,22.5,1.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,900.0,30.0,1.0],
--R    [20.0,1.0,0.0,- 20.0,- 1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,30.0,1.0,0.0,- 30.0,- 1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,40.0,1.0,0.0,- 40.0,- 1.0,0.0,0.0,0.0,0.0],
--R    [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,45.0,1.0,0.0,- 45.0,- 1.0,0.0],
--R    [1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]]
--R                                                        Type: List List Float
--E 1

--S 2 of 16
vals:Vector(Float):=_
[0,227.04,227.04,362.78,362.78,517.35,517.35,602.97,602.97,901.67,0,0,0,0,0]
 

   (2)
   [0.0, 227.04, 227.04, 362.78, 362.78, 517.35, 517.35, 602.97, 602.97,
    901.67, 0.0, 0.0, 0.0, 0.0, 0.0]
                                                           Type: Vector Float
--R 
--R
--R   (2)
--R   [0.0, 227.04, 227.04, 362.78, 362.78, 517.35, 517.35, 602.97, 602.97,
--R    901.67, 0.0, 0.0, 0.0, 0.0, 0.0]
--R                                                           Type: Vector Float
--E 2

--S 3 of 16
digits(5)
 

   (3)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  20
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 16
outcoef:=solve(incoef,vals)
 

   (4)
   [
     particular =
       [0.0, 22.704, 0.0, 0.88882, 4.926, 88.888, - 0.1356, 35.66, - 141.6,
        1.6045, - 33.94, 554.41, 0.20905, 28.851, - 152.01]
     ,
    basis= [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]]]
Type: Record(particular: Union(Vector Float,"failed"),basis: List Vector Float)
--R 
--R
--R   (4)
--R   [
--R     particular =
--R       [0.0, 22.704, 0.0, 0.88882, 4.926, 88.888, - 0.1356, 35.66, - 141.6,
--R        1.6045, - 33.94, 554.41, 0.20905, 28.851, - 152.01]
--R     ,
--R    basis= [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]]]
--RType: Record(particular: Union(Vector Float,"failed"),basis: List Vector Float)
--E 4

--S 5 of 16
D:=outcoef.particular
 

   (5)
   [0.0, 22.704, 0.0, 0.88882, 4.926, 88.888, - 0.1356, 35.66, - 141.6, 1.6045,
    - 33.94, 554.41, 0.20905, 28.851, - 152.01]
                                                Type: Union(Vector Float,...)
--R 
--R
--R   (5)
--R   [0.0, 22.704, 0.0, 0.88882, 4.926, 88.888, - 0.1356, 35.66, - 141.6, 1.6045,
--R    - 33.94, 554.41, 0.20905, 28.851, - 152.01]
--R                                                Type: Union(Vector Float,...)
--E 5

--S 6 of 16
s1:=D.1*t^2+D.2*t+D.3
 

   (6)  22.704 t
                                                       Type: Polynomial Float
--R 
--R
--R   (6)  22.704 t
--R                                                       Type: Polynomial Float
--E 6

--S 7 of 16
s2:=D.4*t^2+D.5*t+D.6
 

                 2
   (7)  0.88882 t  + 4.926 t + 88.888
                                                       Type: Polynomial Float
--R 
--R
--R                 2
--R   (7)  0.88882 t  + 4.926 t + 88.888
--R                                                       Type: Polynomial Float
--E 7

--S 8 of 16
s3:=D.7*t^2+D.8*t+D.9
 

                  2
   (8)  - 0.1356 t  + 35.66 t - 141.6
                                                       Type: Polynomial Float
--R 
--R
--R                  2
--R   (8)  - 0.1356 t  + 35.66 t - 141.6
--R                                                       Type: Polynomial Float
--E 8

--S 9 of 16
s4:=D.10*t^2+D.11*t+D.12
 

                2
   (9)  1.6045 t  - 33.94 t + 554.41
                                                       Type: Polynomial Float
--R 
--R
--R                2
--R   (9)  1.6045 t  - 33.94 t + 554.41
--R                                                       Type: Polynomial Float
--E 9

--S 10 of 16
s5:=D.13*t^2+D.14*t+D.15
 

                  2
   (10)  0.20905 t  + 28.851 t - 152.01
                                                       Type: Polynomial Float
--R 
--R
--R                  2
--R   (10)  0.20905 t  + 28.851 t - 152.01
--R                                                       Type: Polynomial Float
--E 10

--S 11 of 16
s3(16)
 

   (11)  394.26
                                                                  Type: Float
--R 
--R
--R   (11)  394.26
--R                                                                  Type: Float
--E 11

--S 12 of 16
s3d:=differentiate(s3,t)
 

   (12)  - 0.27112 t + 35.66
                                                       Type: Polynomial Float
--R 
--R
--R   (12)  - 0.27112 t + 35.66
--R                                                       Type: Polynomial Float
--E 12

--S 13 of 16
s3d(16)
 

   (13)  31.323
                                                                  Type: Float
--R 
--R
--R   (13)  31.323
--R                                                                  Type: Float
--E 13

--S 14 of 16
s2i:=integrate(s2,t)
 

                  3          2
   (14)  0.29628 t  + 2.463 t  + 88.888 t
                                                       Type: Polynomial Float
--R 
--R
--R                  3          2
--R   (14)  0.29628 t  + 2.463 t  + 88.888 t
--R                                                       Type: Polynomial Float
--E 14

--S 15 of 16
s3i:=integrate(s3,t)
 

                     3          2
   (15)  - 0.045187 t  + 17.83 t  - 141.6 t
                                                       Type: Polynomial Float
--R 
--R
--R                     3          2
--R   (15)  - 0.045187 t  + 17.83 t  - 141.6 t
--R                                                       Type: Polynomial Float
--E 15

--S 16 of 16
(s2i(15)-s2i(11)) + (s3i(16)-s3i(15))
 

   (16)  1595.9
                                                                  Type: Float
--R 
--R
--R   (16)  1595.9
--R                                                                  Type: Float
--E 16

)spool 
 
Starts dribbling to schaum5.output (2010/3/27, 18:37:15).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 45
aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
 

   (1)
   [
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
    /
        +---+
       \|a p
     ,
                   +---------------------------+
           +-----+ |     2                          +-----+ +---+
          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
    2atan(-------------------------------------------------------)
                                   a p x
    --------------------------------------------------------------]
                                +-----+
                               \|- a p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R    /
--R        +---+
--R       \|a p
--R     ,
--R                   +---------------------------+
--R           +-----+ |     2                          +-----+ +---+
--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R    2atan(-------------------------------------------------------)
--R                                   a p x
--R    --------------------------------------------------------------]
--R                                +-----+
--R                               \|- a p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 2 of 45
aa1:=aa.1
 

   (2)
     log
                                     +---------------------------+
               +---+ +---+           |     2
            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
          + 
                   +---+            2                          +---+
            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
       /
                  +---------------------------+
            +---+ |     2
          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (2)
--R     log
--R                                     +---------------------------+
--R               +---+ +---+           |     2
--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R          + 
--R                   +---+            2                          +---+
--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R       /
--R                  +---------------------------+
--R            +---+ |     2
--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 3 of 45
aa2:=aa.2
 

                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
        2atan(-------------------------------------------------------)
                                       a p x
   (3)  --------------------------------------------------------------
                                    +-----+
                                   \|- a p
                                                     Type: Expression Integer
--R
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R        2atan(-------------------------------------------------------)
--R                                       a p x
--R   (3)  --------------------------------------------------------------
--R                                    +-----+
--R                                   \|- a p
--R                                                     Type: Expression Integer
--E

--S 4 of 45
bb1:=2/sqrt(a*p)*log(sqrt(a*(p*x+q))+sqrt(p*(a*x+b)))
 

              +-----------+    +-----------+
        2log(\|a p x + a q  + \|a p x + b p )
   (4)  -------------------------------------
                         +---+
                        \|a p
                                                     Type: Expression Integer
--R
--R              +-----------+    +-----------+
--R        2log(\|a p x + a q  + \|a p x + b p )
--R   (4)  -------------------------------------
--R                         +---+
--R                        \|a p
--R                                                     Type: Expression Integer
--E

--S 5 of 45
bb2:=2/sqrt(-a*p)*atan(sqrt((-p*(a*x+b))/(a*(p*x+q))))
 

               +-------------+
               |- a p x - b p
        2atan( |------------- )
              \| a p x + a q
   (5)  -----------------------
                 +-----+
                \|- a p
                                                     Type: Expression Integer
--R
--R               +-------------+
--R               |- a p x - b p
--R        2atan( |------------- )
--R              \| a p x + a q
--R   (5)  -----------------------
--R                 +-----+
--R                \|- a p
--R                                                     Type: Expression Integer
--E

--S 6 of 45
cc1:=aa1-bb1
 

   (6)
               +-----------+    +-----------+
       - 2log(\|a p x + a q  + \|a p x + b p )
     + 
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (6)
--R               +-----------+    +-----------+
--R       - 2log(\|a p x + a q  + \|a p x + b p )
--R     + 
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 7 of 45
cc2:=aa1-bb2
 

   (7)
          +-----+
         \|- a p
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                      +-------------+
           +---+      |- a p x - b p
       - 2\|a p atan( |------------- )
                     \| a p x + a q
  /
      +-----+ +---+
     \|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (7)
--R          +-----+
--R         \|- a p
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                      +-------------+
--R           +---+      |- a p x - b p
--R       - 2\|a p atan( |------------- )
--R                     \| a p x + a q
--R  /
--R      +-----+ +---+
--R     \|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 8 of 45
cc3:=aa2-bb1
 

   (8)
           +-----+     +-----------+    +-----------+
       - 2\|- a p log(\|a p x + a q  + \|a p x + b p )
     + 
                            +---------------------------+
                    +-----+ |     2                          +-----+ +---+
         +---+     \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
       2\|a p atan(-------------------------------------------------------)
                                            a p x
  /
      +-----+ +---+
     \|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (8)
--R           +-----+     +-----------+    +-----------+
--R       - 2\|- a p log(\|a p x + a q  + \|a p x + b p )
--R     + 
--R                            +---------------------------+
--R                    +-----+ |     2                          +-----+ +---+
--R         +---+     \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R       2\|a p atan(-------------------------------------------------------)
--R                                            a p x
--R  /
--R      +-----+ +---+
--R     \|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 9 of 45      14:120 Axiom cannot simplify these answers
cc4:=aa2-bb2
 

   (9)
                      +---------------------------+
              +-----+ |     2                          +-----+ +---+
             \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
       2atan(-------------------------------------------------------)
                                      a p x
     + 
                +-------------+
                |- a p x - b p
       - 2atan( |------------- )
               \| a p x + a q
  /
      +-----+
     \|- a p
                                                     Type: Expression Integer
--R
--R   (9)
--R                      +---------------------------+
--R              +-----+ |     2                          +-----+ +---+
--R             \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R       2atan(-------------------------------------------------------)
--R                                      a p x
--R     + 
--R                +-------------+
--R                |- a p x - b p
--R       - 2atan( |------------- )
--R               \| a p x + a q
--R  /
--R      +-----+
--R     \|- a p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 10 of 45
aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x)
 

   (1)
   [
                                 +---------------------------+
                           +---+ |     2
             (2a q + 2b p)\|b q \|a p x  + (a q + b p)x + b q
           + 
                 2 2               2 2           2     2
             (- a q  - 2a b p q - b p )x - 2a b q  - 2b p q
        *
           log
                                           +---------------------------+
                     +---+ +---+           |     2
                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
                + 
                           +---+            2                          +---+
                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
             /
                        +---------------------------+
                  +---+ |     2
                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
       + 
                                +---------------------------+
                          +---+ |     2
         (- 2a q - 2b p)x\|a p \|a p x  + (a q + b p)x + b q
       + 
                2                   +---+ +---+
         (4a p x  + (2a q + 2b p)x)\|a p \|b q
    /
                          +---------------------------+
              +---+ +---+ |     2
         4a p\|a p \|b q \|a p x  + (a q + b p)x + b q
       + 
               2            2               +---+
         ((- 2a p q - 2a b p )x - 4a b p q)\|a p
     ,

                                   +---------------------------+
                             +---+ |     2
             (- 2a q - 2b p)\|b q \|a p x  + (a q + b p)x + b q
           + 
               2 2               2 2           2     2
             (a q  + 2a b p q + b p )x + 2a b q  + 2b p q
        *
                         +---------------------------+
                 +-----+ |     2                          +-----+ +---+
                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
           atan(-------------------------------------------------------)
                                         a p x
       + 
                                +---------------------------+
                        +-----+ |     2
         (- a q - b p)x\|- a p \|a p x  + (a q + b p)x + b q
       + 
                2                 +-----+ +---+
         (2a p x  + (a q + b p)x)\|- a p \|b q
    /
                            +---------------------------+
              +-----+ +---+ |     2
         2a p\|- a p \|b q \|a p x  + (a q + b p)x + b q
       + 
              2           2               +-----+
         ((- a p q - a b p )x - 2a b p q)\|- a p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                                 +---------------------------+
--R                           +---+ |     2
--R             (2a q + 2b p)\|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R                 2 2               2 2           2     2
--R             (- a q  - 2a b p q - b p )x - 2a b q  - 2b p q
--R        *
--R           log
--R                                           +---------------------------+
--R                     +---+ +---+           |     2
--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R                + 
--R                           +---+            2                          +---+
--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R             /
--R                        +---------------------------+
--R                  +---+ |     2
--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R       + 
--R                                +---------------------------+
--R                          +---+ |     2
--R         (- 2a q - 2b p)x\|a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                2                   +---+ +---+
--R         (4a p x  + (2a q + 2b p)x)\|a p \|b q
--R    /
--R                          +---------------------------+
--R              +---+ +---+ |     2
--R         4a p\|a p \|b q \|a p x  + (a q + b p)x + b q
--R       + 
--R               2            2               +---+
--R         ((- 2a p q - 2a b p )x - 4a b p q)\|a p
--R     ,
--R
--R                                   +---------------------------+
--R                             +---+ |     2
--R             (- 2a q - 2b p)\|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R               2 2               2 2           2     2
--R             (a q  + 2a b p q + b p )x + 2a b q  + 2b p q
--R        *
--R                         +---------------------------+
--R                 +-----+ |     2                          +-----+ +---+
--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R           atan(-------------------------------------------------------)
--R                                         a p x
--R       + 
--R                                +---------------------------+
--R                        +-----+ |     2
--R         (- a q - b p)x\|- a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                2                 +-----+ +---+
--R         (2a p x  + (a q + b p)x)\|- a p \|b q
--R    /
--R                            +---------------------------+
--R              +-----+ +---+ |     2
--R         2a p\|- a p \|b q \|a p x  + (a q + b p)x + b q
--R       + 
--R              2           2               +-----+
--R         ((- a p q - a b p )x - 2a b p q)\|- a p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 11 of 45
bb1:=integrate(1/(sqrt(a*x+b)*(p*x+q)),x)
 

   (2)
                                                          +--------------+
                      2  +-------+                        |             2
        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
    log(------------------------------------------------------------------)
                                      p x + q
   [-----------------------------------------------------------------------,
                                +--------------+
                                |             2
                               \|- a p q + b p
           +------------+
           |           2  +-------+
          \|a p q - b p  \|a x + b
    2atan(-------------------------)
                  a q - b p
    --------------------------------]
              +------------+
              |           2
             \|a p q - b p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R                                                          +--------------+
--R                      2  +-------+                        |             2
--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R    log(------------------------------------------------------------------)
--R                                      p x + q
--R   [-----------------------------------------------------------------------,
--R                                +--------------+
--R                                |             2
--R                               \|- a p q + b p
--R           +------------+
--R           |           2  +-------+
--R          \|a p q - b p  \|a x + b
--R    2atan(-------------------------)
--R                  a q - b p
--R    --------------------------------]
--R              +------------+
--R              |           2
--R             \|a p q - b p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 12 of 45
bb2:=sqrt((a*x+b)*(p*x+q))/(a*p)-(b*p+a*q)/(2*a*p)
 

          +---------------------------+
          |     2
        2\|a p x  + (a q + b p)x + b q  - a q - b p
   (3)  -------------------------------------------
                            2a p
                                                     Type: Expression Integer
--R
--R          +---------------------------+
--R          |     2
--R        2\|a p x  + (a q + b p)x + b q  - a q - b p
--R   (3)  -------------------------------------------
--R                            2a p
--R                                                     Type: Expression Integer
--E

--S 13 of 45
bb:=bb2*bb1
 

   (4)
   [
            +---------------------------+
            |     2
         (2\|a p x  + (a q + b p)x + b q  - a q - b p)
      *
                                                             +--------------+
                         2  +-------+                        |             2
           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
       log(------------------------------------------------------------------)
                                         p x + q
    /
            +--------------+
            |             2
       2a p\|- a p q + b p
     ,
                                                       +------------+
       +---------------------------+                   |           2  +-------+
       |     2                                        \|a p q - b p  \|a x + b
    (2\|a p x  + (a q + b p)x + b q  - a q - b p)atan(-------------------------)
                                                              a q - b p
    ----------------------------------------------------------------------------
                                     +------------+
                                     |           2
                                 a p\|a p q - b p
     ]
                                              Type: Vector Expression Integer
--R
--R   (4)
--R   [
--R            +---------------------------+
--R            |     2
--R         (2\|a p x  + (a q + b p)x + b q  - a q - b p)
--R      *
--R                                                             +--------------+
--R                         2  +-------+                        |             2
--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R       log(------------------------------------------------------------------)
--R                                         p x + q
--R    /
--R            +--------------+
--R            |             2
--R       2a p\|- a p q + b p
--R     ,
--R                                                       +------------+
--R       +---------------------------+                   |           2  +-------+
--R       |     2                                        \|a p q - b p  \|a x + b
--R    (2\|a p x  + (a q + b p)x + b q  - a q - b p)atan(-------------------------)
--R                                                              a q - b p
--R    ----------------------------------------------------------------------------
--R                                     +------------+
--R                                     |           2
--R                                 a p\|a p q - b p
--R     ]
--R                                              Type: Vector Expression Integer
--E

--S 14 of 45     14:121 Axiom cannot simplify this answer
cc:=aa-bb
 

   (5)
   [
                              +---+ +---+                           +---+
               ((2a q + 2b p)\|a p \|b q  + ((2a q + 2b p)x + 4b q)\|a p )
            *
                +---------------------------+
                |     2
               \|a p x  + (a q + b p)x + b q
           + 
                      2                            +---+ +---+
             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|a p \|b q
           + 
                  2 2               2 2           2     2     +---+
             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|a p
        *
                                                               +--------------+
                           2  +-------+                        |             2
             (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
         log(------------------------------------------------------------------)
                                           p x + q
       + 
                           +--------------+       +---------------------------+
                           |             2  +---+ |     2
             (2a q + 2b p)\|- a p q + b p  \|b q \|a p x  + (a q + b p)x + b q
           + 
                                                              +--------------+
                  2 2               2 2           2     2     |             2
             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p q + b p
        *
           log
                                           +---------------------------+
                     +---+ +---+           |     2
                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
                + 
                           +---+            2                          +---+
                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
             /
                        +---------------------------+
                  +---+ |     2
                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
       + 
                          +--------------+       +---------------------------+
                          |             2  +---+ |     2
         (- 2a q - 2b p)x\|- a p q + b p  \|a p \|a p x  + (a q + b p)x + b q
       + 
                                    +--------------+
                2                   |             2  +---+ +---+
         (4a p x  + (2a q + 2b p)x)\|- a p q + b p  \|a p \|b q
    /
              +--------------+             +---------------------------+
              |             2  +---+ +---+ |     2
         4a p\|- a p q + b p  \|a p \|b q \|a p x  + (a q + b p)x + b q
       + 
                                            +--------------+
               2            2               |             2  +---+
         ((- 2a p q - 2a b p )x - 4a b p q)\|- a p q + b p  \|a p
     ,

                                   +------------+ +---------------------------+
                             +---+ |           2  |     2
             (- 2a q - 2b p)\|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
           + 
                                                            +------------+
                2 2               2 2           2     2     |           2
             ((a q  + 2a b p q + b p )x + 2a b q  + 2b p q)\|a p q - b p
        *
                         +---------------------------+
                 +-----+ |     2                          +-----+ +---+
                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
           atan(-------------------------------------------------------)
                                         a p x
       + 
                              +-----+ +---+                           +-----+
               ((2a q + 2b p)\|- a p \|b q  + ((2a q + 2b p)x + 4b q)\|- a p )
            *
                +---------------------------+
                |     2
               \|a p x  + (a q + b p)x + b q
           + 
                      2                            +-----+ +---+
             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|- a p \|b q
           + 
                  2 2               2 2           2     2     +-----+
             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p
        *
                 +------------+
                 |           2  +-------+
                \|a p q - b p  \|a x + b
           atan(-------------------------)
                        a q - b p
       + 
                                +------------+ +---------------------------+
                        +-----+ |           2  |     2
         (- a q - b p)x\|- a p \|a p q - b p  \|a p x  + (a q + b p)x + b q
       + 
                                                +------------+
                2                 +-----+ +---+ |           2
         (2a p x  + (a q + b p)x)\|- a p \|b q \|a p q - b p
    /
                            +------------+ +---------------------------+
              +-----+ +---+ |           2  |     2
         2a p\|- a p \|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
       + 
                                                  +------------+
              2           2               +-----+ |           2
         ((- a p q - a b p )x - 2a b p q)\|- a p \|a p q - b p
     ]
                                              Type: Vector Expression Integer
--R
--R   (5)
--R   [
--R                              +---+ +---+                           +---+
--R               ((2a q + 2b p)\|a p \|b q  + ((2a q + 2b p)x + 4b q)\|a p )
--R            *
--R                +---------------------------+
--R                |     2
--R               \|a p x  + (a q + b p)x + b q
--R           + 
--R                      2                            +---+ +---+
--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|a p \|b q
--R           + 
--R                  2 2               2 2           2     2     +---+
--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|a p
--R        *
--R                                                               +--------------+
--R                           2  +-------+                        |             2
--R             (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
--R         log(------------------------------------------------------------------)
--R                                           p x + q
--R       + 
--R                           +--------------+       +---------------------------+
--R                           |             2  +---+ |     2
--R             (2a q + 2b p)\|- a p q + b p  \|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R                                                              +--------------+
--R                  2 2               2 2           2     2     |             2
--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p q + b p
--R        *
--R           log
--R                                           +---------------------------+
--R                     +---+ +---+           |     2
--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R                + 
--R                           +---+            2                          +---+
--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R             /
--R                        +---------------------------+
--R                  +---+ |     2
--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R       + 
--R                          +--------------+       +---------------------------+
--R                          |             2  +---+ |     2
--R         (- 2a q - 2b p)x\|- a p q + b p  \|a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                                    +--------------+
--R                2                   |             2  +---+ +---+
--R         (4a p x  + (2a q + 2b p)x)\|- a p q + b p  \|a p \|b q
--R    /
--R              +--------------+             +---------------------------+
--R              |             2  +---+ +---+ |     2
--R         4a p\|- a p q + b p  \|a p \|b q \|a p x  + (a q + b p)x + b q
--R       + 
--R                                            +--------------+
--R               2            2               |             2  +---+
--R         ((- 2a p q - 2a b p )x - 4a b p q)\|- a p q + b p  \|a p
--R     ,
--R
--R                                   +------------+ +---------------------------+
--R                             +---+ |           2  |     2
--R             (- 2a q - 2b p)\|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
--R           + 
--R                                                            +------------+
--R                2 2               2 2           2     2     |           2
--R             ((a q  + 2a b p q + b p )x + 2a b q  + 2b p q)\|a p q - b p
--R        *
--R                         +---------------------------+
--R                 +-----+ |     2                          +-----+ +---+
--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R           atan(-------------------------------------------------------)
--R                                         a p x
--R       + 
--R                              +-----+ +---+                           +-----+
--R               ((2a q + 2b p)\|- a p \|b q  + ((2a q + 2b p)x + 4b q)\|- a p )
--R            *
--R                +---------------------------+
--R                |     2
--R               \|a p x  + (a q + b p)x + b q
--R           + 
--R                      2                            +-----+ +---+
--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|- a p \|b q
--R           + 
--R                  2 2               2 2           2     2     +-----+
--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p
--R        *
--R                 +------------+
--R                 |           2  +-------+
--R                \|a p q - b p  \|a x + b
--R           atan(-------------------------)
--R                        a q - b p
--R       + 
--R                                +------------+ +---------------------------+
--R                        +-----+ |           2  |     2
--R         (- a q - b p)x\|- a p \|a p q - b p  \|a p x  + (a q + b p)x + b q
--R       + 
--R                                                +------------+
--R                2                 +-----+ +---+ |           2
--R         (2a p x  + (a q + b p)x)\|- a p \|b q \|a p q - b p
--R    /
--R                            +------------+ +---------------------------+
--R              +-----+ +---+ |           2  |     2
--R         2a p\|- a p \|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
--R       + 
--R                                                  +------------+
--R              2           2               +-----+ |           2
--R         ((- a p q - a b p )x - 2a b p q)\|- a p \|a p q - b p
--R     ]
--R                                              Type: Vector Expression Integer
--E
)clear all
 

--S 15 of 45
aa:=integrate(sqrt((a*x+b)*(p*x+q)),x)
 

   (1)
   [
                    3 3     2     2       2 2      3 3       2   3        2   2
                 (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
               + 
                   3 2
                 8b p q
            *
                      +---------------------------+
                +---+ |     2
               \|b q \|a p x  + (a q + b p)x + b q
           + 
                 4 4     3     3      2 2 2 2       3 3     4 4  2
             (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
           + 
                  3   4     2 2   3       3 2 2     4 3        2 2 4
             (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
           + 
                  3   3     4 2 2
             16a b p q  - 8b p q
        *
           log
                                           +---------------------------+
                     +---+ +---+           |     2
                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
                + 
                           +---+            2                          +---+
                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
             /
                        +---------------------------+
                  +---+ |     2
                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
       + 
                  3   2      2   2        2 3  3
             (- 4a p q  - 24a b p q - 4a b p )x
           + 
                  3 3      2     2        2 2      3 3  2
             (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
           + 
                  2   3        2   2     3 2
             (- 8a b q  - 48a b p q  - 8b p q)x
        *
                  +---------------------------+
            +---+ |     2
           \|a p \|a p x  + (a q + b p)x + b q
       + 
                 3 2       2   3  4       3   2      2   2         2 3  3
             (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
           + 
                3 3      2     2        2 2      3 3  2
             (6a q  + 74a b p q  + 74a b p q + 6b p )x
           + 
                2   3        2   2     3 2
             (8a b q  + 48a b p q  + 8b p q)x
        *
            +---+ +---+
           \|a p \|b q
    /
                2             2                +---+ +---+
           ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
        *
            +---------------------------+
            |     2
           \|a p x  + (a q + b p)x + b q
       + 
                  3   2      2   2        2 3  2         2     2        2 2
             (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
           + 
                    2   2
             - 64a b p q
        *
            +---+
           \|a p
     ,

                      3 3     2     2       2 2      3 3       2   3
                 (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q
               + 
                      2   2     3 2
                 16a b p q  - 8b p q
            *
                      +---------------------------+
                +---+ |     2
               \|b q \|a p x  + (a q + b p)x + b q
           + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
             (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
           + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
             (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
           + 
               4 2 2
             8b p q
        *
                         +---------------------------+
                 +-----+ |     2                          +-----+ +---+
                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
           atan(-------------------------------------------------------)
                                         a p x
       + 
                  3   2      2   2        2 3  3
             (- 2a p q  - 12a b p q - 2a b p )x
           + 
                 3 3      2     2        2 2     3 3  2
             (- a q  - 23a b p q  - 23a b p q - b p )x
           + 
                  2   3        2   2     3 2
             (- 4a b q  - 24a b p q  - 4b p q)x
        *
                    +---------------------------+
            +-----+ |     2
           \|- a p \|a p x  + (a q + b p)x + b q
       + 
                3 2      2   3  4       3   2      2   2         2 3  3
             (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
           + 
                3 3      2     2        2 2      3 3  2
             (3a q  + 37a b p q  + 37a b p q + 3b p )x
           + 
                2   3        2   2     3 2
             (4a b q  + 24a b p q  + 4b p q)x
        *
            +-----+ +---+
           \|- a p \|b q
    /
                2             2                +-----+ +---+
           ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
        *
            +---------------------------+
            |     2
           \|a p x  + (a q + b p)x + b q
       + 
                  3   2      2   2        2 3  2         2     2        2 2
             (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
           + 
                    2   2
             - 32a b p q
        *
            +-----+
           \|- a p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                    3 3     2     2       2 2      3 3       2   3        2   2
--R                 (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R               + 
--R                   3 2
--R                 8b p q
--R            *
--R                      +---------------------------+
--R                +---+ |     2
--R               \|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R                 4 4     3     3      2 2 2 2       3 3     4 4  2
--R             (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R           + 
--R                  3   4     2 2   3       3 2 2     4 3        2 2 4
--R             (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
--R           + 
--R                  3   3     4 2 2
--R             16a b p q  - 8b p q
--R        *
--R           log
--R                                           +---------------------------+
--R                     +---+ +---+           |     2
--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R                + 
--R                           +---+            2                          +---+
--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R             /
--R                        +---------------------------+
--R                  +---+ |     2
--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R       + 
--R                  3   2      2   2        2 3  3
--R             (- 4a p q  - 24a b p q - 4a b p )x
--R           + 
--R                  3 3      2     2        2 2      3 3  2
--R             (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
--R           + 
--R                  2   3        2   2     3 2
--R             (- 8a b q  - 48a b p q  - 8b p q)x
--R        *
--R                  +---------------------------+
--R            +---+ |     2
--R           \|a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                 3 2       2   3  4       3   2      2   2         2 3  3
--R             (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
--R           + 
--R                3 3      2     2        2 2      3 3  2
--R             (6a q  + 74a b p q  + 74a b p q + 6b p )x
--R           + 
--R                2   3        2   2     3 2
--R             (8a b q  + 48a b p q  + 8b p q)x
--R        *
--R            +---+ +---+
--R           \|a p \|b q
--R    /
--R                2             2                +---+ +---+
--R           ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R        *
--R            +---------------------------+
--R            |     2
--R           \|a p x  + (a q + b p)x + b q
--R       + 
--R                  3   2      2   2        2 3  2         2     2        2 2
--R             (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R           + 
--R                    2   2
--R             - 64a b p q
--R        *
--R            +---+
--R           \|a p
--R     ,
--R
--R                      3 3     2     2       2 2      3 3       2   3
--R                 (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q
--R               + 
--R                      2   2     3 2
--R                 16a b p q  - 8b p q
--R            *
--R                      +---------------------------+
--R                +---+ |     2
--R               \|b q \|a p x  + (a q + b p)x + b q
--R           + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R             (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
--R           + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R             (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
--R           + 
--R               4 2 2
--R             8b p q
--R        *
--R                         +---------------------------+
--R                 +-----+ |     2                          +-----+ +---+
--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R           atan(-------------------------------------------------------)
--R                                         a p x
--R       + 
--R                  3   2      2   2        2 3  3
--R             (- 2a p q  - 12a b p q - 2a b p )x
--R           + 
--R                 3 3      2     2        2 2     3 3  2
--R             (- a q  - 23a b p q  - 23a b p q - b p )x
--R           + 
--R                  2   3        2   2     3 2
--R             (- 4a b q  - 24a b p q  - 4b p q)x
--R        *
--R                    +---------------------------+
--R            +-----+ |     2
--R           \|- a p \|a p x  + (a q + b p)x + b q
--R       + 
--R                3 2      2   3  4       3   2      2   2         2 3  3
--R             (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
--R           + 
--R                3 3      2     2        2 2      3 3  2
--R             (3a q  + 37a b p q  + 37a b p q + 3b p )x
--R           + 
--R                2   3        2   2     3 2
--R             (4a b q  + 24a b p q  + 4b p q)x
--R        *
--R            +-----+ +---+
--R           \|- a p \|b q
--R    /
--R                2             2                +-----+ +---+
--R           ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
--R        *
--R            +---------------------------+
--R            |     2
--R           \|a p x  + (a q + b p)x + b q
--R       + 
--R                  3   2      2   2        2 3  2         2     2        2 2
--R             (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
--R           + 
--R                    2   2
--R             - 32a b p q
--R        *
--R            +-----+
--R           \|- a p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E
--S 16 of 45
aa1:=aa.1
 

   (2)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                3   2      2   2        2 3  3
           (- 4a p q  - 24a b p q - 4a b p )x
         + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
         + 
                2   3        2   2     3 2
           (- 8a b q  - 48a b p q  - 8b p q)x
      *
                +---------------------------+
          +---+ |     2
         \|a p \|a p x  + (a q + b p)x + b q
     + 
               3 2       2   3  4       3   2      2   2         2 3  3
           (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
         + 
              3 3      2     2        2 2      3 3  2
           (6a q  + 74a b p q  + 74a b p q + 6b p )x
         + 
              2   3        2   2     3 2
           (8a b q  + 48a b p q  + 8b p q)x
      *
          +---+ +---+
         \|a p \|b q
  /
              2             2                +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +---+
         \|a p
                                                     Type: Expression Integer
--R
--R   (2)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                3   2      2   2        2 3  3
--R           (- 4a p q  - 24a b p q - 4a b p )x
--R         + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
--R         + 
--R                2   3        2   2     3 2
--R           (- 8a b q  - 48a b p q  - 8b p q)x
--R      *
--R                +---------------------------+
--R          +---+ |     2
--R         \|a p \|a p x  + (a q + b p)x + b q
--R     + 
--R               3 2       2   3  4       3   2      2   2         2 3  3
--R           (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
--R         + 
--R              3 3      2     2        2 2      3 3  2
--R           (6a q  + 74a b p q  + 74a b p q + 6b p )x
--R         + 
--R              2   3        2   2     3 2
--R           (8a b q  + 48a b p q  + 8b p q)x
--R      *
--R          +---+ +---+
--R         \|a p \|b q
--R  /
--R              2             2                +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +---+
--R         \|a p
--R                                                     Type: Expression Integer
--E

--S 17 of 45
aa2:=aa.2
 

   (3)
                    3 3     2     2       2 2      3 3       2   3        2   2
               (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q  + 16a b p q
             + 
                   3 2
               - 8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
             4 4     3     3      2 2 2 2       3 3     4 4  2
           (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
         + 
              3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
         + 
             4 2 2
           8b p q
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                3   2      2   2        2 3  3
           (- 2a p q  - 12a b p q - 2a b p )x
         + 
               3 3      2     2        2 2     3 3  2
           (- a q  - 23a b p q  - 23a b p q - b p )x
         + 
                2   3        2   2     3 2
           (- 4a b q  - 24a b p q  - 4b p q)x
      *
                  +---------------------------+
          +-----+ |     2
         \|- a p \|a p x  + (a q + b p)x + b q
     + 
              3 2      2   3  4       3   2      2   2         2 3  3
           (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
         + 
              3 3      2     2        2 2      3 3  2
           (3a q  + 37a b p q  + 37a b p q + 3b p )x
         + 
              2   3        2   2     3 2
           (4a b q  + 24a b p q  + 4b p q)x
      *
          +-----+ +---+
         \|- a p \|b q
  /
              2             2                +-----+ +---+
         ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
         + 
                  2   2
           - 32a b p q
      *
          +-----+
         \|- a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                    3 3     2     2       2 2      3 3       2   3        2   2
--R               (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q  + 16a b p q
--R             + 
--R                   3 2
--R               - 8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R             4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
--R         + 
--R              3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
--R         + 
--R             4 2 2
--R           8b p q
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                3   2      2   2        2 3  3
--R           (- 2a p q  - 12a b p q - 2a b p )x
--R         + 
--R               3 3      2     2        2 2     3 3  2
--R           (- a q  - 23a b p q  - 23a b p q - b p )x
--R         + 
--R                2   3        2   2     3 2
--R           (- 4a b q  - 24a b p q  - 4b p q)x
--R      *
--R                  +---------------------------+
--R          +-----+ |     2
--R         \|- a p \|a p x  + (a q + b p)x + b q
--R     + 
--R              3 2      2   3  4       3   2      2   2         2 3  3
--R           (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
--R         + 
--R              3 3      2     2        2 2      3 3  2
--R           (3a q  + 37a b p q  + 37a b p q + 3b p )x
--R         + 
--R              2   3        2   2     3 2
--R           (4a b q  + 24a b p q  + 4b p q)x
--R      *
--R          +-----+ +---+
--R         \|- a p \|b q
--R  /
--R              2             2                +-----+ +---+
--R         ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
--R         + 
--R                  2   2
--R           - 32a b p q
--R      *
--R          +-----+
--R         \|- a p
--R                                                     Type: Expression Integer
--E
--S 18 of 45
bba:=((2*a*p*x+b*p+a*q)/(4*a*p))*sqrt((a*x+b)*(p*x+q))
 

                             +---------------------------+
                             |     2
        (2a p x + a q + b p)\|a p x  + (a q + b p)x + b q
   (4)  --------------------------------------------------
                               4a p
                                                     Type: Expression Integer
--R
--R                             +---------------------------+
--R                             |     2
--R        (2a p x + a q + b p)\|a p x  + (a q + b p)x + b q
--R   (4)  --------------------------------------------------
--R                               4a p
--R                                                     Type: Expression Integer
--E

--S 19 of 45
bbb:=-(b*p-a*q)^2/(8*a*p)
 

           2 2               2 2
        - a q  + 2a b p q - b p
   (5)  ------------------------
                  8a p
                                            Type: Fraction Polynomial Integer
--R
--R           2 2               2 2
--R        - a q  + 2a b p q - b p
--R   (5)  ------------------------
--R                  8a p
--R                                            Type: Fraction Polynomial Integer
--E

--S 20 of 45
bbc:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
 

   (6)
   [
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
    /
        +---+
       \|a p
     ,
                   +---------------------------+
           +-----+ |     2                          +-----+ +---+
          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
    2atan(-------------------------------------------------------)
                                   a p x
    --------------------------------------------------------------]
                                +-----+
                               \|- a p
                                     Type: Union(List Expression Integer,...)
--R
--R   (6)
--R   [
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R    /
--R        +---+
--R       \|a p
--R     ,
--R                   +---------------------------+
--R           +-----+ |     2                          +-----+ +---+
--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R    2atan(-------------------------------------------------------)
--R                                   a p x
--R    --------------------------------------------------------------]
--R                                +-----+
--R                               \|- a p
--R                                     Type: Union(List Expression Integer,...)
--E
--S 21 of 45
bbc1:=bbc.1
 

   (7)
     log
                                     +---------------------------+
               +---+ +---+           |     2
            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
          + 
                   +---+            2                          +---+
            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
       /
                  +---------------------------+
            +---+ |     2
          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (7)
--R     log
--R                                     +---------------------------+
--R               +---+ +---+           |     2
--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R          + 
--R                   +---+            2                          +---+
--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R       /
--R                  +---------------------------+
--R            +---+ |     2
--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 22 of 45
bbc2:=bbc.2
 

                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
        2atan(-------------------------------------------------------)
                                       a p x
   (8)  --------------------------------------------------------------
                                    +-----+
                                   \|- a p
                                                     Type: Expression Integer
--R
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R        2atan(-------------------------------------------------------)
--R                                       a p x
--R   (8)  --------------------------------------------------------------
--R                                    +-----+
--R                                   \|- a p
--R                                                     Type: Expression Integer
--E
--S 23 of 45
bb1:=bba+bbb*bbc1
 

   (9)
             2 2               2 2
         (- a q  + 2a b p q - b p )
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                                    +---------------------------+
                              +---+ |     2
       (4a p x + 2a q + 2b p)\|a p \|a p x  + (a q + b p)x + b q
  /
          +---+
     8a p\|a p
                                                     Type: Expression Integer
--R
--R   (9)
--R             2 2               2 2
--R         (- a q  + 2a b p q - b p )
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                                    +---------------------------+
--R                              +---+ |     2
--R       (4a p x + 2a q + 2b p)\|a p \|a p x  + (a q + b p)x + b q
--R  /
--R          +---+
--R     8a p\|a p
--R                                                     Type: Expression Integer
--E

--S 24 of 45
bb2:=bba+bbb*bbc2
 

   (10)
             2 2               2 2
         (- a q  + 2a b p q - b p )
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                                    +---------------------------+
                            +-----+ |     2
       (2a p x + a q + b p)\|- a p \|a p x  + (a q + b p)x + b q
  /
          +-----+
     4a p\|- a p
                                                     Type: Expression Integer
--R
--R   (10)
--R             2 2               2 2
--R         (- a q  + 2a b p q - b p )
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                                    +---------------------------+
--R                            +-----+ |     2
--R       (2a p x + a q + b p)\|- a p \|a p x  + (a q + b p)x + b q
--R  /
--R          +-----+
--R     4a p\|- a p
--R                                                     Type: Expression Integer
--E
--S 25 of 45
cc1:=aa1-bb1
 

   (11)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
             2   3        2   2     3 2           2 3      3   2  +---+
         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
         + 
                 2   3        2   2      3 2           2 3      3   2
           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
      *
          +---+ +---+
         \|a p \|b q
  /
              2             2                +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +---+
         \|a p
                                                     Type: Expression Integer
--R
--R   (11)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R             2   3        2   2     3 2           2 3      3   2  +---+
--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
--R         + 
--R                 2   3        2   2      3 2           2 3      3   2
--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
--R      *
--R          +---+ +---+
--R         \|a p \|b q
--R  /
--R              2             2                +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +---+
--R         \|a p
--R                                                     Type: Expression Integer
--E

--S 26 of 45
cc2:=aa1-bb2
 

   (12)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                            +---------------------------+
              +-----+ +---+ |     2
             \|- a p \|b q \|a p x  + (a q + b p)x + b q
         + 
                   4 4     3     3      2 2 2 2       3 3     4 4  2
               (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
             + 
                    3   4     2 2   3       3 2 2     4 3        2 2 4
               (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
             + 
                    3   3     4 2 2
               16a b p q  - 8b p q
          *
              +-----+
             \|- a p
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                  3 3     2     2       2 2      3 3        2   3        2   2
               (8a q  - 8a b p q  - 8a b p q + 8b p )x + 16a b q  - 32a b p q
             + 
                  3 2
               16b p q
          *
                          +---------------------------+
              +---+ +---+ |     2
             \|a p \|b q \|a p x  + (a q + b p)x + b q
         + 
                    4 4     3     3      2 2 2 2       3 3      4 4  2
               (- 2a q  - 8a b p q  + 20a b p q  - 8a b p q - 2b p )x
             + 
                     3   4      2 2   3        3 2 2      4 3         2 2 4
               (- 16a b q  + 16a b p q  + 16a b p q  - 16b p q)x - 16a b q
             + 
                    3   3      4 2 2
               32a b p q  - 16b p q
          *
              +---+
             \|a p
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
             2   3        2   2     3 2           2 3      3   2  +-----+ +---+
         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|- a p \|a p
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
         + 
                 2   3        2   2      3 2           2 3      3   2
           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
      *
          +-----+ +---+ +---+
         \|- a p \|a p \|b q
  /
              2             2                +-----+ +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|- a p \|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +-----+ +---+
         \|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (12)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                            +---------------------------+
--R              +-----+ +---+ |     2
--R             \|- a p \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R                   4 4     3     3      2 2 2 2       3 3     4 4  2
--R               (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R             + 
--R                    3   4     2 2   3       3 2 2     4 3        2 2 4
--R               (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
--R             + 
--R                    3   3     4 2 2
--R               16a b p q  - 8b p q
--R          *
--R              +-----+
--R             \|- a p
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                  3 3     2     2       2 2      3 3        2   3        2   2
--R               (8a q  - 8a b p q  - 8a b p q + 8b p )x + 16a b q  - 32a b p q
--R             + 
--R                  3 2
--R               16b p q
--R          *
--R                          +---------------------------+
--R              +---+ +---+ |     2
--R             \|a p \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R                    4 4     3     3      2 2 2 2       3 3      4 4  2
--R               (- 2a q  - 8a b p q  + 20a b p q  - 8a b p q - 2b p )x
--R             + 
--R                     3   4      2 2   3        3 2 2      4 3         2 2 4
--R               (- 16a b q  + 16a b p q  + 16a b p q  - 16b p q)x - 16a b q
--R             + 
--R                    3   3      4 2 2
--R               32a b p q  - 16b p q
--R          *
--R              +---+
--R             \|a p
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R             2   3        2   2     3 2           2 3      3   2  +-----+ +---+
--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|- a p \|a p
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
--R         + 
--R                 2   3        2   2      3 2           2 3      3   2
--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
--R      *
--R          +-----+ +---+ +---+
--R         \|- a p \|a p \|b q
--R  /
--R              2             2                +-----+ +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|- a p \|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +-----+ +---+
--R         \|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 27 of 45
cc3:=aa1-bb1
 

   (13)
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                         +---+            2                          +---+
                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                  3 3     2     2       2 2      3 3       2   3        2   2
               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
             + 
                 3 2
               8b p q
          *
                    +---------------------------+
              +---+ |     2
             \|b q \|a p x  + (a q + b p)x + b q
         + 
               4 4     3     3      2 2 2 2       3 3     4 4  2
           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
         + 
                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
         + 
               4 2 2
           - 8b p q
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
             2   3        2   2     3 2           2 3      3   2  +---+
         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3 3      2     2        2 2      3 3  2
           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
         + 
                 2   3        2   2      3 2           2 3      3   2
           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
      *
          +---+ +---+
         \|a p \|b q
  /
              2             2                +---+ +---+
         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
                3   2      2   2        2 3  2         2     2        2 2
           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
         + 
                  2   2
           - 64a b p q
      *
          +---+
         \|a p
                                                     Type: Expression Integer
--R
--R   (13)
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                         +---+            2                          +---+
--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                  3 3     2     2       2 2      3 3       2   3        2   2
--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
--R             + 
--R                 3 2
--R               8b p q
--R          *
--R                    +---------------------------+
--R              +---+ |     2
--R             \|b q \|a p x  + (a q + b p)x + b q
--R         + 
--R               4 4     3     3      2 2 2 2       3 3     4 4  2
--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
--R         + 
--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
--R         + 
--R               4 2 2
--R           - 8b p q
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R             2   3        2   2     3 2           2 3      3   2  +---+
--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3 3      2     2        2 2      3 3  2
--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
--R         + 
--R                 2   3        2   2      3 2           2 3      3   2
--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
--R      *
--R          +---+ +---+
--R         \|a p \|b q
--R  /
--R              2             2                +---+ +---+
--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R                3   2      2   2        2 3  2         2     2        2 2
--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
--R         + 
--R                  2   2
--R           - 64a b p q
--R      *
--R          +---+
--R         \|a p
--R                                                     Type: Expression Integer
--E

--S 28 of 45     14:122 Axiom cannot simplify this answer
cc4:=aa2-bb2
 

   (14)
             2   3       2   2     3 2          2 3     3   2
         ((4a b q  + 8a b p q  + 4b p q)x + 8a b q  + 8b p q )
      *
          +---------------------------+
          |     2
         \|a p x  + (a q + b p)x + b q
     + 
               3 3     2     2       2 2     3 3  2
           (- a q  - 7a b p q  - 7a b p q - b p )x
         + 
                2   3        2   2     3 2          2 3     3   2
           (- 8a b q  - 16a b p q  - 8b p q)x - 8a b q  - 8b p q
      *
          +---+
         \|b q
  /
                                                 +---------------------------+
            2             2                +---+ |     2
       ((16a p q + 16a b p )x + 32a b p q)\|b q \|a p x  + (a q + b p)x + b q
     + 
            3   2      2   2        2 3  2         2     2        2 2
       (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
     + 
              2   2
       - 32a b p q
                                                     Type: Expression Integer
--R
--R   (14)
--R             2   3       2   2     3 2          2 3     3   2
--R         ((4a b q  + 8a b p q  + 4b p q)x + 8a b q  + 8b p q )
--R      *
--R          +---------------------------+
--R          |     2
--R         \|a p x  + (a q + b p)x + b q
--R     + 
--R               3 3     2     2       2 2     3 3  2
--R           (- a q  - 7a b p q  - 7a b p q - b p )x
--R         + 
--R                2   3        2   2     3 2          2 3     3   2
--R           (- 8a b q  - 16a b p q  - 8b p q)x - 8a b q  - 8b p q
--R      *
--R          +---+
--R         \|b q
--R  /
--R                                                 +---------------------------+
--R            2             2                +---+ |     2
--R       ((16a p q + 16a b p )x + 32a b p q)\|b q \|a p x  + (a q + b p)x + b q
--R     + 
--R            3   2      2   2        2 3  2         2     2        2 2
--R       (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
--R     + 
--R              2   2
--R       - 32a b p q
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 29 of 45
aa:=integrate(sqrt((p*x+q)/(a*x+b)),x)
 

   (1)
   [
           (a q - b p)
        *
                                                              +-------+
                                    +---+      2              |p x + q
           log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                             \|a x + b
       + 
                     +-------+
                     |p x + q  +---+
         (2a x + 2b) |------- \|a p
                    \|a x + b
    /
          +---+
       2a\|a p
     ,
                             +-------+
                     +-----+ |p x + q
                    \|- a p  |-------                       +-------+
                            \|a x + b               +-----+ |p x + q
    (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
                             p                             \|a x + b
    -----------------------------------------------------------------]
                                  +-----+
                                a\|- a p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           (a q - b p)
--R        *
--R                                                              +-------+
--R                                    +---+      2              |p x + q
--R           log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                             \|a x + b
--R       + 
--R                     +-------+
--R                     |p x + q  +---+
--R         (2a x + 2b) |------- \|a p
--R                    \|a x + b
--R    /
--R          +---+
--R       2a\|a p
--R     ,
--R                             +-------+
--R                     +-----+ |p x + q
--R                    \|- a p  |-------                       +-------+
--R                            \|a x + b               +-----+ |p x + q
--R    (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
--R                             p                             \|a x + b
--R    -----------------------------------------------------------------]
--R                                  +-----+
--R                                a\|- a p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 30 of 45
aa1:=aa.1
 

   (2)
                                                                     +-------+
                                           +---+      2              |p x + q
       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                                    \|a x + b
     + 
                   +-------+
                   |p x + q  +---+
       (2a x + 2b) |------- \|a p
                  \|a x + b
  /
        +---+
     2a\|a p
                                                     Type: Expression Integer
--R
--R   (2)
--R                                                                     +-------+
--R                                           +---+      2              |p x + q
--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                                    \|a x + b
--R     + 
--R                   +-------+
--R                   |p x + q  +---+
--R       (2a x + 2b) |------- \|a p
--R                  \|a x + b
--R  /
--R        +---+
--R     2a\|a p
--R                                                     Type: Expression Integer
--E

--S 31 of 45
aa2:=aa.2
 

                                 +-------+
                         +-----+ |p x + q
                        \|- a p  |-------                       +-------+
                                \|a x + b               +-----+ |p x + q
        (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
                                 p                             \|a x + b
   (3)  -----------------------------------------------------------------
                                      +-----+
                                    a\|- a p
                                                     Type: Expression Integer
--R
--R                                 +-------+
--R                         +-----+ |p x + q
--R                        \|- a p  |-------                       +-------+
--R                                \|a x + b               +-----+ |p x + q
--R        (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
--R                                 p                             \|a x + b
--R   (3)  -----------------------------------------------------------------
--R                                      +-----+
--R                                    a\|- a p
--R                                                     Type: Expression Integer
--E

--S 32 of 45
bba:=sqrt((a*x+b)*(p*x+q))/a
 

         +---------------------------+
         |     2
        \|a p x  + (a q + b p)x + b q
   (4)  ------------------------------
                       a
                                                     Type: Expression Integer
--R
--R         +---------------------------+
--R         |     2
--R        \|a p x  + (a q + b p)x + b q
--R   (4)  ------------------------------
--R                       a
--R                                                     Type: Expression Integer
--E

--S 33 of 45
bbb:=(a*q-b*p)/(2*a)
 

        a q - b p
   (5)  ---------
            2a
                                            Type: Fraction Polynomial Integer
--R
--R        a q - b p
--R   (5)  ---------
--R            2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 34 of 45
bbc:=integrate(1/(sqrt((a*x+b)*(p*x+q))),x)
 

   (6)
   [
       log
                                       +---------------------------+
                 +---+ +---+           |     2
              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
            + 
                     +---+            2                          +---+
              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
         /
                    +---------------------------+
              +---+ |     2
            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
    /
        +---+
       \|a p
     ,
                   +---------------------------+
           +-----+ |     2                          +-----+ +---+
          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
    2atan(-------------------------------------------------------)
                                   a p x
    --------------------------------------------------------------]
                                +-----+
                               \|- a p
                                     Type: Union(List Expression Integer,...)
--R
--R   (6)
--R   [
--R       log
--R                                       +---------------------------+
--R                 +---+ +---+           |     2
--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R            + 
--R                     +---+            2                          +---+
--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R         /
--R                    +---------------------------+
--R              +---+ |     2
--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R    /
--R        +---+
--R       \|a p
--R     ,
--R                   +---------------------------+
--R           +-----+ |     2                          +-----+ +---+
--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R    2atan(-------------------------------------------------------)
--R                                   a p x
--R    --------------------------------------------------------------]
--R                                +-----+
--R                               \|- a p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 35 of 45
bbc1:=bbc.1
 

   (7)
     log
                                     +---------------------------+
               +---+ +---+           |     2
            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
          + 
                   +---+            2                          +---+
            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
       /
                  +---------------------------+
            +---+ |     2
          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
  /
      +---+
     \|a p
                                                     Type: Expression Integer
--R
--R   (7)
--R     log
--R                                     +---------------------------+
--R               +---+ +---+           |     2
--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R          + 
--R                   +---+            2                          +---+
--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R       /
--R                  +---------------------------+
--R            +---+ |     2
--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R  /
--R      +---+
--R     \|a p
--R                                                     Type: Expression Integer
--E

--S 36 of 45
bbc2:=bbc.2
 

                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
        2atan(-------------------------------------------------------)
                                       a p x
   (8)  --------------------------------------------------------------
                                    +-----+
                                   \|- a p
                                                     Type: Expression Integer
--R
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R        2atan(-------------------------------------------------------)
--R                                       a p x
--R   (8)  --------------------------------------------------------------
--R                                    +-----+
--R                                   \|- a p
--R                                                     Type: Expression Integer
--E

--S 37 of 45
bb1:=bba+bbb*bbc1
 

   (9)
         (a q - b p)
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
               +---------------------------+
         +---+ |     2
       2\|a p \|a p x  + (a q + b p)x + b q
  /
        +---+
     2a\|a p
                                                     Type: Expression Integer
--R
--R   (9)
--R         (a q - b p)
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R               +---------------------------+
--R         +---+ |     2
--R       2\|a p \|a p x  + (a q + b p)x + b q
--R  /
--R        +---+
--R     2a\|a p
--R                                                     Type: Expression Integer
--E

--S 38 of 45
bb2:=bba+bbb*bbc2
 

   (10)
                                +---------------------------+
                        +-----+ |     2                          +-----+ +---+
                       \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
       (a q - b p)atan(-------------------------------------------------------)
                                                a p x
     + 
                +---------------------------+
        +-----+ |     2
       \|- a p \|a p x  + (a q + b p)x + b q
  /
       +-----+
     a\|- a p
                                                     Type: Expression Integer
--R
--R   (10)
--R                                +---------------------------+
--R                        +-----+ |     2                          +-----+ +---+
--R                       \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R       (a q - b p)atan(-------------------------------------------------------)
--R                                                a p x
--R     + 
--R                +---------------------------+
--R        +-----+ |     2
--R       \|- a p \|a p x  + (a q + b p)x + b q
--R  /
--R       +-----+
--R     a\|- a p
--R                                                     Type: Expression Integer
--E

--S 39 of 45
cc1:=aa1-bb1
 

   (11)
                                                                     +-------+
                                           +---+      2              |p x + q
       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                                    \|a x + b
     + 
         (- a q + b p)
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                 +---------------------------+               +-------+
           +---+ |     2                                     |p x + q  +---+
       - 2\|a p \|a p x  + (a q + b p)x + b q  + (2a x + 2b) |------- \|a p
                                                            \|a x + b
  /
        +---+
     2a\|a p
                                                     Type: Expression Integer
--R
--R   (11)
--R                                                                     +-------+
--R                                           +---+      2              |p x + q
--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                                    \|a x + b
--R     + 
--R         (- a q + b p)
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                 +---------------------------+               +-------+
--R           +---+ |     2                                     |p x + q  +---+
--R       - 2\|a p \|a p x  + (a q + b p)x + b q  + (2a x + 2b) |------- \|a p
--R                                                            \|a x + b
--R  /
--R        +---+
--R     2a\|a p
--R                                                     Type: Expression Integer
--E

--S 40 of 45
cc2:=aa1-bb2
 

   (12)
                     +-----+
         (a q - b p)\|- a p
      *
                                                            +-------+
                                  +---+      2              |p x + q
         log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
                                                           \|a x + b
     + 
                         +---+
         (- 2a q + 2b p)\|a p
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                         +---------------------------+
           +-----+ +---+ |     2
       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
     + 
                           +-------+
                   +-----+ |p x + q  +---+
       (2a x + 2b)\|- a p  |------- \|a p
                          \|a x + b
  /
        +-----+ +---+
     2a\|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (12)
--R                     +-----+
--R         (a q - b p)\|- a p
--R      *
--R                                                            +-------+
--R                                  +---+      2              |p x + q
--R         log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
--R                                                           \|a x + b
--R     + 
--R                         +---+
--R         (- 2a q + 2b p)\|a p
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                         +---------------------------+
--R           +-----+ +---+ |     2
--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
--R     + 
--R                           +-------+
--R                   +-----+ |p x + q  +---+
--R       (2a x + 2b)\|- a p  |------- \|a p
--R                          \|a x + b
--R  /
--R        +-----+ +---+
--R     2a\|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 41 of 45
cc3:=aa2-bb1
 

   (13)
                       +-----+
         (- a q + b p)\|- a p
      *
         log
                                         +---------------------------+
                   +---+ +---+           |     2
                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
              + 
                       +---+            2                          +---+
                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
           /
                      +---------------------------+
                +---+ |     2
              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
     + 
                                        +-------+
                                +-----+ |p x + q
                               \|- a p  |-------
                     +---+             \|a x + b
       (2a q - 2b p)\|a p atan(------------------)
                                        p
     + 
                         +---------------------------+
           +-----+ +---+ |     2
       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
     + 
                           +-------+
                   +-----+ |p x + q  +---+
       (2a x + 2b)\|- a p  |------- \|a p
                          \|a x + b
  /
        +-----+ +---+
     2a\|- a p \|a p
                                                     Type: Expression Integer
--R
--R   (13)
--R                       +-----+
--R         (- a q + b p)\|- a p
--R      *
--R         log
--R                                         +---------------------------+
--R                   +---+ +---+           |     2
--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
--R              + 
--R                       +---+            2                          +---+
--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
--R           /
--R                      +---------------------------+
--R                +---+ |     2
--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
--R     + 
--R                                        +-------+
--R                                +-----+ |p x + q
--R                               \|- a p  |-------
--R                     +---+             \|a x + b
--R       (2a q - 2b p)\|a p atan(------------------)
--R                                        p
--R     + 
--R                         +---------------------------+
--R           +-----+ +---+ |     2
--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
--R     + 
--R                           +-------+
--R                   +-----+ |p x + q  +---+
--R       (2a x + 2b)\|- a p  |------- \|a p
--R                          \|a x + b
--R  /
--R        +-----+ +---+
--R     2a\|- a p \|a p
--R                                                     Type: Expression Integer
--E

--S 42 of 45     14:123 Axiom cannot simplify these results
cc4:=aa2-bb2
 

   (14)
         (- a q + b p)
      *
                       +---------------------------+
               +-----+ |     2                          +-----+ +---+
              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
         atan(-------------------------------------------------------)
                                       a p x
     + 
                                +-------+
                        +-----+ |p x + q
                       \|- a p  |-------
                               \|a x + b
       (a q - b p)atan(------------------)
                                p
     + 
                  +---------------------------+                     +-------+
          +-----+ |     2                                   +-----+ |p x + q
       - \|- a p \|a p x  + (a q + b p)x + b q  + (a x + b)\|- a p  |-------
                                                                   \|a x + b
  /
       +-----+
     a\|- a p
                                                     Type: Expression Integer
--R
--R   (14)
--R         (- a q + b p)
--R      *
--R                       +---------------------------+
--R               +-----+ |     2                          +-----+ +---+
--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
--R         atan(-------------------------------------------------------)
--R                                       a p x
--R     + 
--R                                +-------+
--R                        +-----+ |p x + q
--R                       \|- a p  |-------
--R                               \|a x + b
--R       (a q - b p)atan(------------------)
--R                                p
--R     + 
--R                  +---------------------------+                     +-------+
--R          +-----+ |     2                                   +-----+ |p x + q
--R       - \|- a p \|a p x  + (a q + b p)x + b q  + (a x + b)\|- a p  |-------
--R                                                                   \|a x + b
--R  /
--R       +-----+
--R     a\|- a p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 43 of 45
aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x)
 

                                 2x
   (1)  ---------------------------------------------------
          +---------------------------+
          |     2                                     +---+
        q\|a p x  + (a q + b p)x + b q  + (- p x - q)\|b q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 2x
--R   (1)  ---------------------------------------------------
--R          +---------------------------+
--R          |     2                                     +---+
--R        q\|a p x  + (a q + b p)x + b q  + (- p x - q)\|b q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 44 of 45
bb:=(2*sqrt(a*x+b))/((a*q-b*p)*sqrt(p*x+q))
 

               +-------+
             2\|a x + b
   (2)  ---------------------
                    +-------+
        (a q - b p)\|p x + q
                                                     Type: Expression Integer
--R
--R               +-------+
--R             2\|a x + b
--R   (2)  ---------------------
--R                    +-------+
--R        (a q - b p)\|p x + q
--R                                                     Type: Expression Integer
--E

--S 45 of 45     14:124 Axiom cannot simplify this result
cc:=aa-bb
 

   (3)
                      +---------------------------+
            +-------+ |     2                                        +-------+
       - 2q\|a x + b \|a p x  + (a q + b p)x + b q  + (2a q - 2b p)x\|p x + q
     + 
                   +---+ +-------+
       (2p x + 2q)\|b q \|a x + b
  /
                                +---------------------------+
           2          +-------+ |     2
       (a q  - b p q)\|p x + q \|a p x  + (a q + b p)x + b q
     + 
                      2        2          +---+ +-------+
       ((- a p q + b p )x - a q  + b p q)\|b q \|p x + q
                                                     Type: Expression Integer
--R
--R   (3)
--R                      +---------------------------+
--R            +-------+ |     2                                        +-------+
--R       - 2q\|a x + b \|a p x  + (a q + b p)x + b q  + (2a q - 2b p)x\|p x + q
--R     + 
--R                   +---+ +-------+
--R       (2p x + 2q)\|b q \|a x + b
--R  /
--R                                +---------------------------+
--R           2          +-------+ |     2
--R       (a q  - b p q)\|p x + q \|a p x  + (a q + b p)x + b q
--R     + 
--R                      2        2          +---+ +-------+
--R       ((- a p q + b p )x - a q  + b p q)\|b q \|p x + q
--R                                                     Type: Expression Integer
--E


)spool
 
Starts dribbling to intmix.output (2010/3/27, 18:27:12).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
(x + 1) / (x * (x + log x)**(3/2)) - 1/(x * log(x)**2)
 

                       +----------+                2
        (- log(x) - x)\|log(x) + x  + (x + 1)log(x)
   (1)  --------------------------------------------
                     3    2      2  +----------+
            (x log(x)  + x log(x) )\|log(x) + x
                                                     Type: Expression Integer
--R 
--R
--R                       +----------+                2
--R        (- log(x) - x)\|log(x) + x  + (x + 1)log(x)
--R   (1)  --------------------------------------------
--R                     3    2      2  +----------+
--R            (x log(x)  + x log(x) )\|log(x) + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 6
integrate(%, x)
 

                  +----------+
        - 2log(x)\|log(x) + x  + log(x) + x
   (2)  -----------------------------------
                       2
                 log(x)  + x log(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +----------+
--R        - 2log(x)\|log(x) + x  + log(x) + x
--R   (2)  -----------------------------------
--R                       2
--R                 log(x)  + x log(x)
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 6
((5*x**4+2*x-2)/x**2 * (1+1/sqrt(x**3+1))+x/sqrt(x**3+1)) * exp(x*sqrt(x**3+1))
 

                                                         +------+
                        +------+                         | 3
            4           | 3          4    3            x\|x  + 1
        ((5x  + 2x - 2)\|x  + 1  + 5x  + x  + 2x - 2)%e
   (3)  ---------------------------------------------------------
                                  +------+
                                2 | 3
                               x \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                                                         +------+
--R                        +------+                         | 3
--R            4           | 3          4    3            x\|x  + 1
--R        ((5x  + 2x - 2)\|x  + 1  + 5x  + x  + 2x - 2)%e
--R   (3)  ---------------------------------------------------------
--R                                  +------+
--R                                2 | 3
--R                               x \|x  + 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 6
integrate(%, x)
 

                            +------+
           +------+         | 3
           | 3            x\|x  + 1
        (2\|x  + 1  + 2)%e
   (4)  ----------------------------
                      x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            +------+
--R           +------+         | 3
--R           | 3            x\|x  + 1
--R        (2\|x  + 1  + 2)%e
--R   (4)  ----------------------------
--R                      x
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 6
log(1 + exp x)**(1/3) / (1 + log(1 + exp x))
 

          +------------+
         3|      x
         \|log(%e  + 1)
   (5)  ----------------
              x
        log(%e  + 1) + 1
                                                     Type: Expression Integer
--R 
--R
--R          +------------+
--R         3|      x
--R         \|log(%e  + 1)
--R   (5)  ----------------
--R              x
--R        log(%e  + 1) + 1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 6
integrate(%, x)
 

               +-------------+
           x  3|      %T
         ++   \|log(%e   + 1)
   (6)   |   ----------------- d%T
        ++         %T
             log(%e   + 1) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------------+
--R           x  3|      %T
--R         ++   \|log(%e   + 1)
--R   (6)   |   ----------------- d%T
--R        ++         %T
--R             log(%e   + 1) + 1
--R                                          Type: Union(Expression Integer,...)
--E 6
)spool 
 
Starts dribbling to schaum11.output (2010/3/27, 18:37:30).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 170
aa:=integrate(1/(sqrt(a^2-x^2)),x)
 

                 +---------+
                 |   2    2
                \|- x  + a   - a
   (1)  - 2atan(----------------)
                        x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   - a
--R   (1)  - 2atan(----------------)
--R                        x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 170
bb:=asin(x/a)
 

             x
   (2)  asin(-)
             a
                                                     Type: Expression Integer
--R
--R             x
--R   (2)  asin(-)
--R             a
--R                                                     Type: Expression Integer
--E

--S 3 of 170
cc:=aa-bb
 

                 +---------+
                 |   2    2
                \|- x  + a   - a         x
   (3)  - 2atan(----------------) - asin(-)
                        x                a
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2
--R                \|- x  + a   - a         x
--R   (3)  - 2atan(----------------) - asin(-)
--R                        x                a
--R                                                     Type: Expression Integer
--E

--S 4 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 5 of 170
dd:=atanrule cc
 

                  +---------+
                  |   2    2
               - \|- x  + a   + %i x + a         x
   (5)  %i log(-------------------------) - asin(-)
                 +---------+                     a
                 |   2    2
                \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                  +---------+
--R                  |   2    2
--R               - \|- x  + a   + %i x + a         x
--R   (5)  %i log(-------------------------) - asin(-)
--R                 +---------+                     a
--R                 |   2    2
--R                \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 6 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 7 of 170
ee:=asinrule dd
 

                   +---------+
                   |   2    2
                   |- x  + a
                 a |---------  - %i x              +---------+
                   |     2                         |   2    2
                  \|    a                       - \|- x  + a   + %i x + a
   (7)  - %i log(--------------------) + %i log(-------------------------)
                           a                      +---------+
                                                  |   2    2
                                                 \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                   +---------+
--R                   |   2    2
--R                   |- x  + a
--R                 a |---------  - %i x              +---------+
--R                   |     2                         |   2    2
--R                  \|    a                       - \|- x  + a   + %i x + a
--R   (7)  - %i log(--------------------) + %i log(-------------------------)
--R                           a                      +---------+
--R                                                  |   2    2
--R                                                 \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 8 of 170
ff:=rootSimp ee
 

                    +-------+                     +-------+
                    | 2    2                      | 2    2
                 %i\|x  - a   - %i x           - \|x  - a   + x - %i a
   (8)  - %i log(-------------------) + %i log(-----------------------)
                          a                      +-------+
                                                 | 2    2
                                                \|x  - a   + x + %i a
                                             Type: Expression Complex Integer
--R
--R                    +-------+                     +-------+
--R                    | 2    2                      | 2    2
--R                 %i\|x  - a   - %i x           - \|x  - a   + x - %i a
--R   (8)  - %i log(-------------------) + %i log(-----------------------)
--R                          a                      +-------+
--R                                                 | 2    2
--R                                                \|x  - a   + x + %i a
--R                                             Type: Expression Complex Integer
--E

--S 9 of 170      14:238 Schaums and Axiom agree
gg:=complexNormalize ff
 

   (9)  0
                                             Type: Expression Complex Integer
--R
--R   (9)  0
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 10 of 170
aa:=integrate(x/(sqrt(a^2-x^2)),x)
 

                2
               x
   (1)  ----------------
         +---------+
         |   2    2
        \|- x  + a   - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2
--R               x
--R   (1)  ----------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a   - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 170
bb:=-sqrt(a^2-x^2)
 

           +---------+
           |   2    2
   (2)  - \|- x  + a
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2
--R   (2)  - \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 12 of 170     14:238 Schaums and Axiom differ by a constant
cc:=aa-bb
 

   (3)  - a
                                                     Type: Expression Integer
--R
--R   (3)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 170
aa:=integrate(x^2/sqrt(a^2-x^2),x)
 

   (1)
                                              +---------+
              +---------+                     |   2    2
            3 |   2    2      2 2     4      \|- x  + a   - a
       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
                                                     x
     + 
                     +---------+
           3     2   |   2    2        3     3
       (- x  + 2a x)\|- x  + a   + 2a x  - 2a x
  /
        +---------+
        |   2    2      2     2
     4a\|- x  + a   + 2x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                              +---------+
--R              +---------+                     |   2    2
--R            3 |   2    2      2 2     4      \|- x  + a   - a
--R       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
--R                                                     x
--R     + 
--R                     +---------+
--R           3     2   |   2    2        3     3
--R       (- x  + 2a x)\|- x  + a   + 2a x  - 2a x
--R  /
--R        +---------+
--R        |   2    2      2     2
--R     4a\|- x  + a   + 2x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 170
bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
 

            +---------+
            |   2    2     2     x
        - x\|- x  + a   + a asin(-)
                                 a
   (2)  ---------------------------
                     2
                                                     Type: Expression Integer
--R
--R            +---------+
--R            |   2    2     2     x
--R        - x\|- x  + a   + a asin(-)
--R                                 a
--R   (2)  ---------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 15 of 170
cc:=aa-bb
 

                   +---------+
                   |   2    2
            2     \|- x  + a   - a     2     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            2     \|- x  + a   - a     2     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 16 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 17 of 170
dd:=atanrule cc
 

                    +---------+
                    |   2    2
            2    - \|- x  + a   + %i x + a     2     x
        %i a log(-------------------------) - a asin(-)
                   +---------+                       a
                   |   2    2
                  \|- x  + a   + %i x - a
   (5)  -----------------------------------------------
                               2
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R            2    - \|- x  + a   + %i x + a     2     x
--R        %i a log(-------------------------) - a asin(-)
--R                   +---------+                       a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R   (5)  -----------------------------------------------
--R                               2
--R                                             Type: Expression Complex Integer
--E

--S 18 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 19 of 170
ee:=asinrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              2     \|    a                    2    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           2
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              2     \|    a                    2    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           2
--R                                             Type: Expression Complex Integer
--E

--S 20 of 170
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             2      |- x  + a                 2     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           2     |   2    2                    2             2
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             2      |- x  + a                 2     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           2     |   2    2                    2             2
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 21 of 170
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             2       | 2    2                    2       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           2       | 2    2                    2             2
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             2       | 2    2                    2       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           2       | 2    2                    2             2
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 22 of 170     14:239 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 23 of 170
aa:=integrate(x^3/sqrt(a^2-x^2),x)
 

                   +---------+
                 4 |   2    2     6     2 4
             3a x \|- x  + a   + x  - 3a x
   (1)  ---------------------------------------
                     +---------+
           2      2  |   2    2        2      3
        (3x  - 12a )\|- x  + a   - 9a x  + 12a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +---------+
--R                 4 |   2    2     6     2 4
--R             3a x \|- x  + a   + x  - 3a x
--R   (1)  ---------------------------------------
--R                     +---------+
--R           2      2  |   2    2        2      3
--R        (3x  - 12a )\|- x  + a   - 9a x  + 12a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 170
bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2)
 

                     +---------+
            2     2  |   2    2
        (- x  - 2a )\|- x  + a
   (2)  ------------------------
                    3
                                                     Type: Expression Integer
--R
--R                     +---------+
--R            2     2  |   2    2
--R        (- x  - 2a )\|- x  + a
--R   (2)  ------------------------
--R                    3
--R                                                     Type: Expression Integer
--E

--S 25 of 170     14:240 Schaums and Axiom differ by a constant
cc:=aa-bb
 

            3
          2a
   (3)  - ---
           3
                                                     Type: Expression Integer
--R
--R            3
--R          2a
--R   (3)  - ---
--R           3
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 26 of 170
aa:=integrate(1/(x*sqrt(a^2-x^2)),x)
 

             +---------+
             |   2    2
            \|- x  + a   - a
        log(----------------)
                    x
   (1)  ---------------------
                  a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             +---------+
--R             |   2    2
--R            \|- x  + a   - a
--R        log(----------------)
--R                    x
--R   (1)  ---------------------
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27 of 170
bb:=-1/a*log((a+sqrt(a^2-x^2))/x)
 

               +---------+
               |   2    2
              \|- x  + a   + a
          log(----------------)
                      x
   (2)  - ---------------------
                    a
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   + a
--R          log(----------------)
--R                      x
--R   (2)  - ---------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 28 of 170
cc:=aa-bb
 

             +---------+             +---------+
             |   2    2              |   2    2
            \|- x  + a   + a        \|- x  + a   - a
        log(----------------) + log(----------------)
                    x                       x
   (3)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R            \|- x  + a   + a        \|- x  + a   - a
--R        log(----------------) + log(----------------)
--R                    x                       x
--R   (3)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 29 of 170
dd:=expandLog cc
 

             +---------+             +---------+
             |   2    2              |   2    2
        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
   (4)  -------------------------------------------------------
                                   a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
--R   (4)  -------------------------------------------------------
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 30 of 170
ee:=complexNormalize dd
 

                  x
          2log(-------)
                +----+
                |   2
               \|- x
   (5)  - -------------
                a
                                                     Type: Expression Integer
--R
--R                  x
--R          2log(-------)
--R                +----+
--R                |   2
--R               \|- x
--R   (5)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 31 of 170     14:241 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

              +---+
        2log(\|- 1 )
   (6)  ------------
              a
                                                     Type: Expression Integer
--R
--R              +---+
--R        2log(\|- 1 )
--R   (6)  ------------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 32 of 170
aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x)
 

          +---------+
          |   2    2     2    2
        a\|- x  + a   + x  - a
   (1)  -----------------------
             +---------+
          2  |   2    2     3
         a x\|- x  + a   - a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +---------+
--R          |   2    2     2    2
--R        a\|- x  + a   + x  - a
--R   (1)  -----------------------
--R             +---------+
--R          2  |   2    2     3
--R         a x\|- x  + a   - a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33 of 170
bb:=-sqrt(a^2-x^2)/(a^2*x)
 

           +---------+
           |   2    2
          \|- x  + a
   (2)  - ------------
                2
               a x
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2
--R          \|- x  + a
--R   (2)  - ------------
--R                2
--R               a x
--R                                                     Type: Expression Integer
--E

--S 34 of 170     14:242 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 35 of 170
aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x)
 

   (1)
                                            +---------+
              +---------+                   |   2    2
            2 |   2    2     4     2 2     \|- x  + a   - a
       (2a x \|- x  + a   + x  - 2a x )log(----------------)
                                                   x
     + 
                      +---------+
             2     3  |   2    2      2 2     4
       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
  /
           +---------+
       4 2 |   2    2      3 4     5 2
     4a x \|- x  + a   + 2a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                            +---------+
--R              +---------+                   |   2    2
--R            2 |   2    2     4     2 2     \|- x  + a   - a
--R       (2a x \|- x  + a   + x  - 2a x )log(----------------)
--R                                                   x
--R     + 
--R                      +---------+
--R             2     3  |   2    2      2 2     4
--R       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
--R  /
--R           +---------+
--R       4 2 |   2    2      3 4     5 2
--R     4a x \|- x  + a   + 2a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36 of 170
bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x)
 

                 +---------+
                 |   2    2           +---------+
           2    \|- x  + a   + a      |   2    2
        - x log(----------------) - a\|- x  + a
                        x
   (2)  -----------------------------------------
                            3 2
                          2a x
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2           +---------+
--R           2    \|- x  + a   + a      |   2    2
--R        - x log(----------------) - a\|- x  + a
--R                        x
--R   (2)  -----------------------------------------
--R                            3 2
--R                          2a x
--R                                                     Type: Expression Integer
--E

--S 37 of 170
cc:=aa-bb
 

             +---------+             +---------+
             |   2    2              |   2    2
            \|- x  + a   + a        \|- x  + a   - a
        log(----------------) + log(----------------)
                    x                       x
   (3)  ---------------------------------------------
                               3
                             2a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R            \|- x  + a   + a        \|- x  + a   - a
--R        log(----------------) + log(----------------)
--R                    x                       x
--R   (3)  ---------------------------------------------
--R                               3
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 38 of 170
dd:=expandLog cc
 

             +---------+             +---------+
             |   2    2              |   2    2
        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
   (4)  -------------------------------------------------------
                                    3
                                  2a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
--R   (4)  -------------------------------------------------------
--R                                    3
--R                                  2a
--R                                                     Type: Expression Integer
--E

--S 39 of 170
ee:=complexNormalize dd
 

                 x
          log(-------)
               +----+
               |   2
              \|- x
   (5)  - ------------
                3
               a
                                                     Type: Expression Integer
--R
--R                 x
--R          log(-------)
--R               +----+
--R               |   2
--R              \|- x
--R   (5)  - ------------
--R                3
--R               a
--R                                                     Type: Expression Integer
--E 

--S 40 of 170     14:243 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

             +---+
        log(\|- 1 )
   (6)  -----------
              3
             a
                                                     Type: Expression Integer
--R
--R             +---+
--R        log(\|- 1 )
--R   (6)  -----------
--R              3
--R             a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 41 of 170
aa:=integrate(sqrt(a^2-x^2),x)
 

   (1)
                                              +---------+
              +---------+                     |   2    2
            3 |   2    2      2 2     4      \|- x  + a   - a
       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
                                                     x
     + 
                   +---------+
         3     2   |   2    2        3     3
       (x  - 2a x)\|- x  + a   - 2a x  + 2a x
  /
        +---------+
        |   2    2      2     2
     4a\|- x  + a   + 2x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                              +---------+
--R              +---------+                     |   2    2
--R            3 |   2    2      2 2     4      \|- x  + a   - a
--R       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
--R                                                     x
--R     + 
--R                   +---------+
--R         3     2   |   2    2        3     3
--R       (x  - 2a x)\|- x  + a   - 2a x  + 2a x
--R  /
--R        +---------+
--R        |   2    2      2     2
--R     4a\|- x  + a   + 2x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42 of 170
bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
 

          +---------+
          |   2    2     2     x
        x\|- x  + a   + a asin(-)
                               a
   (2)  -------------------------
                    2
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2     2     x
--R        x\|- x  + a   + a asin(-)
--R                               a
--R   (2)  -------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 43 of 170
cc:=aa-bb
 

                   +---------+
                   |   2    2
            2     \|- x  + a   - a     2     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            2     \|- x  + a   - a     2     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 44 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 45 of 170
dd:=asinrule cc
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x             +---------+
                     |     2                        |   2    2
              2     \|    a                  2     \|- x  + a   - a
        - %i a log(--------------------) - 2a atan(----------------)
                             a                             x
   (5)  ------------------------------------------------------------
                                      2
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x             +---------+
--R                     |     2                        |   2    2
--R              2     \|    a                  2     \|- x  + a   - a
--R        - %i a log(--------------------) - 2a atan(----------------)
--R                             a                             x
--R   (5)  ------------------------------------------------------------
--R                                      2
--R                                             Type: Expression Complex Integer
--E

--S 46 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 47 of 170
ee:=atanrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              2     \|    a                    2    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           2
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              2     \|    a                    2    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           2
--R                                             Type: Expression Complex Integer
--E

--S 48 of 170
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             2      |- x  + a                 2     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           2     |   2    2                    2             2
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             2      |- x  + a                 2     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           2     |   2    2                    2             2
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 49 of 170
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             2       | 2    2                    2       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           2       | 2    2                    2             2
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             2       | 2    2                    2       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           2       | 2    2                    2             2
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 50 of 170     14:244 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 51 of 170
aa:=integrate(x*sqrt(a^2-x^2),x)
 

                          +---------+
               4     3 2  |   2    2     6     2 4     4 2
        (- 3a x  + 6a x )\|- x  + a   - x  + 6a x  - 6a x
   (1)  --------------------------------------------------
                           +---------+
                 2      2  |   2    2        2      3
              (3x  - 12a )\|- x  + a   - 9a x  + 12a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +---------+
--R               4     3 2  |   2    2     6     2 4     4 2
--R        (- 3a x  + 6a x )\|- x  + a   - x  + 6a x  - 6a x
--R   (1)  --------------------------------------------------
--R                           +---------+
--R                 2      2  |   2    2        2      3
--R              (3x  - 12a )\|- x  + a   - 9a x  + 12a
--R                                          Type: Union(Expression Integer,...)
--E

--S 52 of 170
bb:=-(a^2-x^2)^(3/2)/3
 

                  +---------+
          2    2  |   2    2
        (x  - a )\|- x  + a
   (2)  ---------------------
                  3
                                                     Type: Expression Integer
--R
--R                  +---------+
--R          2    2  |   2    2
--R        (x  - a )\|- x  + a
--R   (2)  ---------------------
--R                  3
--R                                                     Type: Expression Integer
--E

--S 53 of 170     14:245 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           3
          a
   (3)  - --
           3
                                                     Type: Expression Integer
--R
--R           3
--R          a
--R   (3)  - --
--R           3
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 54 of 170
aa:=integrate(x^2*sqrt(a^2-x^2),x)
 

   (1)
                           +---------+
               5 2      7  |   2    2      4 4      6 2      8
         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                    +---------+
        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
  /
                     +---------+
           2      3  |   2    2      4      2 2      4
     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +---------+
--R               5 2      7  |   2    2      4 4      6 2      8
--R         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                    +---------+
--R        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
--R     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
--R  /
--R                     +---------+
--R           2      3  |   2    2      4      2 2      4
--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 55 of 170
bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a)
 

                    +---------+
           3    2   |   2    2     4     x
        (2x  - a x)\|- x  + a   + a asin(-)
                                         a
   (2)  -----------------------------------
                         8
                                                     Type: Expression Integer
--R
--R                    +---------+
--R           3    2   |   2    2     4     x
--R        (2x  - a x)\|- x  + a   + a asin(-)
--R                                         a
--R   (2)  -----------------------------------
--R                         8
--R                                                     Type: Expression Integer
--E

--S 56 of 170
cc:=aa-bb
 

                   +---------+
                   |   2    2
            4     \|- x  + a   - a     4     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           8
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            4     \|- x  + a   - a     4     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           8
--R                                                     Type: Expression Integer
--E

--S 57 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 58 of 170
dd:=atanrule cc
 

                    +---------+
                    |   2    2
            4    - \|- x  + a   + %i x + a     4     x
        %i a log(-------------------------) - a asin(-)
                   +---------+                       a
                   |   2    2
                  \|- x  + a   + %i x - a
   (5)  -----------------------------------------------
                               8
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R            4    - \|- x  + a   + %i x + a     4     x
--R        %i a log(-------------------------) - a asin(-)
--R                   +---------+                       a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R   (5)  -----------------------------------------------
--R                               8
--R                                             Type: Expression Complex Integer
--E

--S 59 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 60 of 170
ee:=asinrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              4     \|    a                    4    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           8
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              4     \|    a                    4    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           8
--R                                             Type: Expression Complex Integer
--E

--S 61 of 170
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             4      |- x  + a                 4     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           4     |   2    2                    4             4
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             4      |- x  + a                 4     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           4     |   2    2                    4             4
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 62 of 170
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             4       | 2    2                    4       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           4       | 2    2                    4             4
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             4       | 2    2                    4       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           4       | 2    2                    4             4
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 63 of 170     14:246 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 64 of 170
aa:=integrate(x^3*sqrt(a^2-x^2),x)
 

   (1)
                                +---------+
           8      3 6      5 4  |   2    2      10      2 8      4 6      6 4
   (- 15a x  + 65a x  - 60a x )\|- x  + a   - 3x   + 40a x  - 95a x  + 60a x
   --------------------------------------------------------------------------
                                  +---------+
             4       2 2       4  |   2    2         4       3 2       5
         (15x  - 180a x  + 240a )\|- x  + a   - 75a x  + 300a x  - 240a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                +---------+
--R           8      3 6      5 4  |   2    2      10      2 8      4 6      6 4
--R   (- 15a x  + 65a x  - 60a x )\|- x  + a   - 3x   + 40a x  - 95a x  + 60a x
--R   --------------------------------------------------------------------------
--R                                  +---------+
--R             4       2 2       4  |   2    2         4       3 2       5
--R         (15x  - 180a x  + 240a )\|- x  + a   - 75a x  + 300a x  - 240a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 65 of 170
bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3
 

                           +---------+
           4    2 2     4  |   2    2
        (3x  - a x  - 2a )\|- x  + a
   (2)  ------------------------------
                      15
                                                     Type: Expression Integer
--R
--R                           +---------+
--R           4    2 2     4  |   2    2
--R        (3x  - a x  - 2a )\|- x  + a
--R   (2)  ------------------------------
--R                      15
--R                                                     Type: Expression Integer
--E 

--S 66 of 170     14:247 Schaums and Axiom differ by a constant
cc:=aa-bb
 

            5
          2a
   (3)  - ---
           15
                                                     Type: Expression Integer
--R
--R            5
--R          2a
--R   (3)  - ---
--R           15
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 67 of 170
aa:=integrate(sqrt(a^2-x^2)/x,x)
 

                                 +---------+
           +---------+           |   2    2
           |   2    2     2     \|- x  + a   - a     2
        (a\|- x  + a   - a )log(----------------) - x
                                        x
   (1)  ----------------------------------------------
                        +---------+
                        |   2    2
                       \|- x  + a   - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 +---------+
--R           +---------+           |   2    2
--R           |   2    2     2     \|- x  + a   - a     2
--R        (a\|- x  + a   - a )log(----------------) - x
--R                                        x
--R   (1)  ----------------------------------------------
--R                        +---------+
--R                        |   2    2
--R                       \|- x  + a   - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68 of 170
bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x)
 

                 +---------+
                 |   2    2          +---------+
                \|- x  + a   + a     |   2    2
   (2)  - a log(----------------) + \|- x  + a
                        x
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2          +---------+
--R                \|- x  + a   + a     |   2    2
--R   (2)  - a log(----------------) + \|- x  + a
--R                        x
--R                                                     Type: Expression Integer
--E

--S 69 of 170
cc:=aa-bb
 

               +---------+               +---------+
               |   2    2                |   2    2
              \|- x  + a   + a          \|- x  + a   - a
   (3)  a log(----------------) + a log(----------------) + a
                      x                         x
                                                     Type: Expression Integer
--R
--R               +---------+               +---------+
--R               |   2    2                |   2    2
--R              \|- x  + a   + a          \|- x  + a   - a
--R   (3)  a log(----------------) + a log(----------------) + a
--R                      x                         x
--R                                                     Type: Expression Integer
--E

--S 70 of 170
dd:=expandLog cc
 

               +---------+               +---------+
               |   2    2                |   2    2
   (4)  a log(\|- x  + a   + a) + a log(\|- x  + a   - a) - 2a log(x) + a
                                                     Type: Expression Integer
--R
--R               +---------+               +---------+
--R               |   2    2                |   2    2
--R   (4)  a log(\|- x  + a   + a) + a log(\|- x  + a   - a) - 2a log(x) + a
--R                                                     Type: Expression Integer
--E

--S 71 of 170
ee:=complexNormalize dd
 

                    x
   (5)  - 2a log(-------) + a
                  +----+
                  |   2
                 \|- x
                                                     Type: Expression Integer
--R
--R                    x
--R   (5)  - 2a log(-------) + a
--R                  +----+
--R                  |   2
--R                 \|- x
--R                                                     Type: Expression Integer
--E

--S 72 of 170     14:248 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

                +---+
   (6)  2a log(\|- 1 ) + a
                                                     Type: Expression Integer
--R
--R                +---+
--R   (6)  2a log(\|- 1 ) + a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 73 of 170
aa:=integrate(sqrt(a^2-x^2)/x^2,x)
 

   (1)
                                +---------+
       +---------+              |   2    2           +---------+
       |   2    2              \|- x  + a   - a      |   2    2     2    2
   (2x\|- x  + a   - 2a x)atan(----------------) + a\|- x  + a   + x  - a
                                       x
   -----------------------------------------------------------------------
                               +---------+
                               |   2    2
                             x\|- x  + a   - a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                +---------+
--R       +---------+              |   2    2           +---------+
--R       |   2    2              \|- x  + a   - a      |   2    2     2    2
--R   (2x\|- x  + a   - 2a x)atan(----------------) + a\|- x  + a   + x  - a
--R                                       x
--R   -----------------------------------------------------------------------
--R                               +---------+
--R                               |   2    2
--R                             x\|- x  + a   - a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 74 of 170
bb:=-sqrt(a^2-x^2)/x-asin(x/a)
 

           +---------+
           |   2    2           x
        - \|- x  + a   - x asin(-)
                                a
   (2)  --------------------------
                     x
                                                     Type: Expression Integer
--R
--R           +---------+
--R           |   2    2           x
--R        - \|- x  + a   - x asin(-)
--R                                a
--R   (2)  --------------------------
--R                     x
--R                                                     Type: Expression Integer
--E

--S 75 of 170
cc:=aa-bb
 

               +---------+
               |   2    2
              \|- x  + a   - a         x
   (3)  2atan(----------------) + asin(-)
                      x                a
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a         x
--R   (3)  2atan(----------------) + asin(-)
--R                      x                a
--R                                                     Type: Expression Integer
--E

--S 76 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 77 of 170
dd:=asinrule cc
 

                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x           +---------+
                 |     2                      |   2    2
                \|    a                      \|- x  + a   - a
   (5)  %i log(--------------------) + 2atan(----------------)
                         a                           x
                                             Type: Expression Complex Integer
--R
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x           +---------+
--R                 |     2                      |   2    2
--R                \|    a                      \|- x  + a   - a
--R   (5)  %i log(--------------------) + 2atan(----------------)
--R                         a                           x
--R                                             Type: Expression Complex Integer
--E

--S 78 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 79 of 170
ee:=atanrule dd
 

                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x              +---------+
                 |     2                         |   2    2
                \|    a                       - \|- x  + a   + %i x + a
   (7)  %i log(--------------------) - %i log(-------------------------)
                         a                      +---------+
                                                |   2    2
                                               \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x              +---------+
--R                 |     2                         |   2    2
--R                \|    a                       - \|- x  + a   + %i x + a
--R   (7)  %i log(--------------------) - %i log(-------------------------)
--R                         a                      +---------+
--R                                                |   2    2
--R                                               \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 80 of 170
ff:=expandLog ee
 

   (8)
              +---------+
              |   2    2                    +---------+
              |- x  + a                     |   2    2
     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
              |     2
             \|    a
   + 
               +---------+
               |   2    2
     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (8)
--R              +---------+
--R              |   2    2                    +---------+
--R              |- x  + a                     |   2    2
--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
--R              |     2
--R             \|    a
--R   + 
--R               +---------+
--R               |   2    2
--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 81 of 170
gg:=rootSimp ff
 

   (9)
               +-------+                         +-------+
               | 2    2                          | 2    2
     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +-------+                         +-------+
--R               | 2    2                          | 2    2
--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 82 of 170     14:249 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 83 of 170
aa:=integrate(sqrt(a^2-x^2)/x^3,x)
 

   (1)
                                              +---------+
                +---------+                   |   2    2
              2 |   2    2     4     2 2     \|- x  + a   - a
       (- 2a x \|- x  + a   - x  + 2a x )log(----------------)
                                                     x
     + 
                      +---------+
             2     3  |   2    2      2 2     4
       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
  /
           +---------+
       2 2 |   2    2        4     3 2
     4a x \|- x  + a   + 2a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                              +---------+
--R                +---------+                   |   2    2
--R              2 |   2    2     4     2 2     \|- x  + a   - a
--R       (- 2a x \|- x  + a   - x  + 2a x )log(----------------)
--R                                                     x
--R     + 
--R                      +---------+
--R             2     3  |   2    2      2 2     4
--R       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
--R  /
--R           +---------+
--R       2 2 |   2    2        4     3 2
--R     4a x \|- x  + a   + 2a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84 of 170
bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x)
 

               +---------+
               |   2    2           +---------+
         2    \|- x  + a   + a      |   2    2
        x log(----------------) - a\|- x  + a
                      x
   (2)  ---------------------------------------
                             2
                         2a x
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2           +---------+
--R         2    \|- x  + a   + a      |   2    2
--R        x log(----------------) - a\|- x  + a
--R                      x
--R   (2)  ---------------------------------------
--R                             2
--R                         2a x
--R                                                     Type: Expression Integer
--E

--S 85 of 170
cc:=aa-bb
 

               +---------+             +---------+
               |   2    2              |   2    2
              \|- x  + a   + a        \|- x  + a   - a
        - log(----------------) - log(----------------)
                      x                       x
   (3)  -----------------------------------------------
                               2a
                                                     Type: Expression Integer
--R
--R               +---------+             +---------+
--R               |   2    2              |   2    2
--R              \|- x  + a   + a        \|- x  + a   - a
--R        - log(----------------) - log(----------------)
--R                      x                       x
--R   (3)  -----------------------------------------------
--R                               2a
--R                                                     Type: Expression Integer
--E

--S 86 of 170
dd:=expandLog cc
 

               +---------+             +---------+
               |   2    2              |   2    2
        - log(\|- x  + a   + a) - log(\|- x  + a   - a) + 2log(x)
   (4)  ---------------------------------------------------------
                                    2a
                                                     Type: Expression Integer
--R
--R               +---------+             +---------+
--R               |   2    2              |   2    2
--R        - log(\|- x  + a   + a) - log(\|- x  + a   - a) + 2log(x)
--R   (4)  ---------------------------------------------------------
--R                                    2a
--R                                                     Type: Expression Integer
--E

--S 87 of 170
ee:=complexNormalize dd
 

               x
        log(-------)
             +----+
             |   2
            \|- x
   (5)  ------------
              a
                                                     Type: Expression Integer
--R
--R               x
--R        log(-------)
--R             +----+
--R             |   2
--R            \|- x
--R   (5)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 88 of 170     14:250 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

               +---+
          log(\|- 1 )
   (6)  - -----------
               a
                                                     Type: Expression Integer
--R
--R               +---+
--R          log(\|- 1 )
--R   (6)  - -----------
--R               a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 89 of 170
aa:=integrate(1/(a^2-x^2)^(3/2),x)
 

               +---------+
               |   2    2
           - x\|- x  + a   + a x
   (1)  --------------------------
           +---------+
         3 |   2    2     2 2    4
        a \|- x  + a   + a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +---------+
--R               |   2    2
--R           - x\|- x  + a   + a x
--R   (1)  --------------------------
--R           +---------+
--R         3 |   2    2     2 2    4
--R        a \|- x  + a   + a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 90 of 170
bb:=x/(a^2*sqrt(a^2-x^2))
 

               x
   (2)  --------------
           +---------+
         2 |   2    2
        a \|- x  + a
                                                     Type: Expression Integer
--R
--R               x
--R   (2)  --------------
--R           +---------+
--R         2 |   2    2
--R        a \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 91 of 170     14:251 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 92 of 170
aa:=integrate(x/(a^2-x^2)^(3/2),x)
 

                     2
                    x
   (1)  --------------------------
           +---------+
         2 |   2    2       2    3
        a \|- x  + a   + a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R                    x
--R   (1)  --------------------------
--R           +---------+
--R         2 |   2    2       2    3
--R        a \|- x  + a   + a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 93 of 170
bb:=1/sqrt(a^2-x^2)
 

              1
   (2)  ------------
         +---------+
         |   2    2
        \|- x  + a
                                                     Type: Expression Integer
--R
--R              1
--R   (2)  ------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 94 of 170     14:252 Schaums and Axiom differ by a constant
cc:=aa-bb
 

        1
   (3)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (3)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 95 of 170
aa:=integrate(x^2/(a^2-x^2)^(3/2),x)
 

   (1)
                                     +---------+
       +---------+                   |   2    2           +---------+
       |   2    2      2     2      \|- x  + a   - a      |   2    2
   (2a\|- x  + a   + 2x  - 2a )atan(----------------) - x\|- x  + a   + a x
                                            x
   ------------------------------------------------------------------------
                              +---------+
                              |   2    2     2    2
                            a\|- x  + a   + x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                     +---------+
--R       +---------+                   |   2    2           +---------+
--R       |   2    2      2     2      \|- x  + a   - a      |   2    2
--R   (2a\|- x  + a   + 2x  - 2a )atan(----------------) - x\|- x  + a   + a x
--R                                            x
--R   ------------------------------------------------------------------------
--R                              +---------+
--R                              |   2    2     2    2
--R                            a\|- x  + a   + x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 96 of 170
bb:=x/sqrt(a^2-x^2)-asin(x/a)
 

                  +---------+
               x  |   2    2
        - asin(-)\|- x  + a   + x
               a
   (2)  -------------------------
                +---------+
                |   2    2
               \|- x  + a
                                                     Type: Expression Integer
--R
--R                  +---------+
--R               x  |   2    2
--R        - asin(-)\|- x  + a   + x
--R               a
--R   (2)  -------------------------
--R                +---------+
--R                |   2    2
--R               \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 97 of 170
cc:=aa-bb
 

               +---------+
               |   2    2
              \|- x  + a   - a         x
   (3)  2atan(----------------) + asin(-)
                      x                a
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a         x
--R   (3)  2atan(----------------) + asin(-)
--R                      x                a
--R                                                     Type: Expression Integer
--E

--S 98 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 99 of 170
dd:=atanrule cc
 

                    +---------+
                    |   2    2
                 - \|- x  + a   + %i x + a         x
   (5)  - %i log(-------------------------) + asin(-)
                   +---------+                     a
                   |   2    2
                  \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R                 - \|- x  + a   + %i x + a         x
--R   (5)  - %i log(-------------------------) + asin(-)
--R                   +---------+                     a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 100 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 101 of 170
ee:=asinrule dd
 

                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x              +---------+
                 |     2                         |   2    2
                \|    a                       - \|- x  + a   + %i x + a
   (7)  %i log(--------------------) - %i log(-------------------------)
                         a                      +---------+
                                                |   2    2
                                               \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x              +---------+
--R                 |     2                         |   2    2
--R                \|    a                       - \|- x  + a   + %i x + a
--R   (7)  %i log(--------------------) - %i log(-------------------------)
--R                         a                      +---------+
--R                                                |   2    2
--R                                               \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 102 of 170
ff:=expandLog ee
 

   (8)
              +---------+
              |   2    2                    +---------+
              |- x  + a                     |   2    2
     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
              |     2
             \|    a
   + 
               +---------+
               |   2    2
     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (8)
--R              +---------+
--R              |   2    2                    +---------+
--R              |- x  + a                     |   2    2
--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
--R              |     2
--R             \|    a
--R   + 
--R               +---------+
--R               |   2    2
--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 103 of 170
gg:=rootSimp ff
 

   (9)
               +-------+                         +-------+
               | 2    2                          | 2    2
     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +-------+                         +-------+
--R               | 2    2                          | 2    2
--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 104 of 170    14:253 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 105 of 170
aa:=integrate(x^3/(a^2-x^2)^(3/2),x)
 

                            4
                           x
   (1)  - ------------------------------------
                     +---------+
            2     2  |   2    2        2     3
          (x  - 2a )\|- x  + a   - 2a x  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            4
--R                           x
--R   (1)  - ------------------------------------
--R                     +---------+
--R            2     2  |   2    2        2     3
--R          (x  - 2a )\|- x  + a   - 2a x  + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 106 of 170
bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2)
 

            2     2
         - x  + 2a
   (2)  ------------
         +---------+
         |   2    2
        \|- x  + a
                                                     Type: Expression Integer
--R
--R            2     2
--R         - x  + 2a
--R   (2)  ------------
--R         +---------+
--R         |   2    2
--R        \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 107 of 170    14:254 Schaums and Axiom differ by a constant
cc:=aa-bb
 

   (3)  2a
                                                     Type: Expression Integer
--R
--R   (3)  2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 108 of 170
aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x)
 

                                      +---------+
           +---------+                |   2    2
           |   2    2     2    2     \|- x  + a   - a     2
        (a\|- x  + a   + x  - a )log(----------------) + x
                                             x
   (1)  ---------------------------------------------------
                        +---------+
                      4 |   2    2     3 2    5
                     a \|- x  + a   + a x  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                      +---------+
--R           +---------+                |   2    2
--R           |   2    2     2    2     \|- x  + a   - a     2
--R        (a\|- x  + a   + x  - a )log(----------------) + x
--R                                             x
--R   (1)  ---------------------------------------------------
--R                        +---------+
--R                      4 |   2    2     3 2    5
--R                     a \|- x  + a   + a x  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 109 of 170
bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x)
 

                           +---------+
           +---------+     |   2    2
           |   2    2     \|- x  + a   + a
        - \|- x  + a  log(----------------) + a
                                  x
   (2)  ---------------------------------------
                        +---------+
                      3 |   2    2
                     a \|- x  + a
                                                     Type: Expression Integer
--R
--R                           +---------+
--R           +---------+     |   2    2
--R           |   2    2     \|- x  + a   + a
--R        - \|- x  + a  log(----------------) + a
--R                                  x
--R   (2)  ---------------------------------------
--R                        +---------+
--R                      3 |   2    2
--R                     a \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 110 of 170
cc:=aa-bb
 

             +---------+             +---------+
             |   2    2              |   2    2
            \|- x  + a   + a        \|- x  + a   - a
        log(----------------) + log(----------------) + 1
                    x                       x
   (3)  -------------------------------------------------
                                 3
                                a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R            \|- x  + a   + a        \|- x  + a   - a
--R        log(----------------) + log(----------------) + 1
--R                    x                       x
--R   (3)  -------------------------------------------------
--R                                 3
--R                                a
--R                                                     Type: Expression Integer
--E

--S 111 of 170
dd:=expandLog cc
 

             +---------+             +---------+
             |   2    2              |   2    2
        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x) + 1
   (4)  -----------------------------------------------------------
                                      3
                                     a
                                                     Type: Expression Integer
--R
--R             +---------+             +---------+
--R             |   2    2              |   2    2
--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x) + 1
--R   (4)  -----------------------------------------------------------
--R                                      3
--R                                     a
--R                                                     Type: Expression Integer
--E

--S 112 of 170
ee:=complexNormalize dd
 

                  x
        - 2log(-------) + 1
                +----+
                |   2
               \|- x
   (5)  -------------------
                  3
                 a
                                                     Type: Expression Integer
--R
--R                  x
--R        - 2log(-------) + 1
--R                +----+
--R                |   2
--R               \|- x
--R   (5)  -------------------
--R                  3
--R                 a
--R                                                     Type: Expression Integer
--E

--S 113 of 170    14:255 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

              +---+
        2log(\|- 1 ) + 1
   (6)  ----------------
                3
               a
                                                     Type: Expression Integer
--R
--R              +---+
--R        2log(\|- 1 ) + 1
--R   (6)  ----------------
--R                3
--R               a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 114 of 170
aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x)
 

                      +---------+
             2     3  |   2    2      4     2 2     4
        (4a x  - 2a )\|- x  + a   + 2x  - 5a x  + 2a
   (1)  ---------------------------------------------
                         +---------+
             4 3     6   |   2    2      5 3     7
           (a x  - 2a x)\|- x  + a   - 2a x  + 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      +---------+
--R             2     3  |   2    2      4     2 2     4
--R        (4a x  - 2a )\|- x  + a   + 2x  - 5a x  + 2a
--R   (1)  ---------------------------------------------
--R                         +---------+
--R             4 3     6   |   2    2      5 3     7
--R           (a x  - 2a x)\|- x  + a   - 2a x  + 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 115 of 170
bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2))
 

              2    2
            2x  - a
   (2)  ---------------
            +---------+
         4  |   2    2
        a x\|- x  + a
                                                     Type: Expression Integer
--R
--R              2    2
--R            2x  - a
--R   (2)  ---------------
--R            +---------+
--R         4  |   2    2
--R        a x\|- x  + a
--R                                                     Type: Expression Integer
--E

--S 116 of 170    14:256 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 117 of 170
aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x)
 

   (1)
                           +---------+
               4      3 2  |   2    2      6      2 4      4 2
         ((9a x  - 12a x )\|- x  + a   + 3x  - 15a x  + 12a x )
      *
              +---------+
              |   2    2
             \|- x  + a   - a
         log(----------------)
                     x
     + 
                             +---------+
            4     3 2     5  |   2    2      6    2 4     4 2     6
       (3a x  + 5a x  - 4a )\|- x  + a   + 2x  - a x  - 7a x  + 4a
  /
                     +---------+
        6 4     8 2  |   2    2      5 6      7 4     9 2
     (6a x  - 8a x )\|- x  + a   + 2a x  - 10a x  + 8a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                           +---------+
--R               4      3 2  |   2    2      6      2 4      4 2
--R         ((9a x  - 12a x )\|- x  + a   + 3x  - 15a x  + 12a x )
--R      *
--R              +---------+
--R              |   2    2
--R             \|- x  + a   - a
--R         log(----------------)
--R                     x
--R     + 
--R                             +---------+
--R            4     3 2     5  |   2    2      6    2 4     4 2     6
--R       (3a x  + 5a x  - 4a )\|- x  + a   + 2x  - a x  - 7a x  + 4a
--R  /
--R                     +---------+
--R        6 4     8 2  |   2    2      5 6      7 4     9 2
--R     (6a x  - 8a x )\|- x  + a   + 2a x  - 10a x  + 8a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 118 of 170
bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a^2-x^2))/x)
 

                              +---------+
              +---------+     |   2    2
            2 |   2    2     \|- x  + a   + a        2    3
        - 3x \|- x  + a  log(----------------) + 3a x  - a
                                     x
   (2)  ---------------------------------------------------
                               +---------+
                           5 2 |   2    2
                         2a x \|- x  + a
                                                     Type: Expression Integer
--R
--R                              +---------+
--R              +---------+     |   2    2
--R            2 |   2    2     \|- x  + a   + a        2    3
--R        - 3x \|- x  + a  log(----------------) + 3a x  - a
--R                                     x
--R   (2)  ---------------------------------------------------
--R                               +---------+
--R                           5 2 |   2    2
--R                         2a x \|- x  + a
--R                                                     Type: Expression Integer
--E

--S 119 of 170
cc:=aa-bb
 

              +---------+              +---------+
              |   2    2               |   2    2
             \|- x  + a   + a         \|- x  + a   - a
        3log(----------------) + 3log(----------------) + 2
                     x                        x
   (3)  ---------------------------------------------------
                                  5
                                2a
                                                     Type: Expression Integer
--R
--R              +---------+              +---------+
--R              |   2    2               |   2    2
--R             \|- x  + a   + a         \|- x  + a   - a
--R        3log(----------------) + 3log(----------------) + 2
--R                     x                        x
--R   (3)  ---------------------------------------------------
--R                                  5
--R                                2a
--R                                                     Type: Expression Integer
--E

--S 120 of 170
dd:=expandLog cc
 

              +---------+              +---------+
              |   2    2               |   2    2
        3log(\|- x  + a   + a) + 3log(\|- x  + a   - a) - 6log(x) + 2
   (4)  -------------------------------------------------------------
                                       5
                                     2a
                                                     Type: Expression Integer
--R
--R              +---------+              +---------+
--R              |   2    2               |   2    2
--R        3log(\|- x  + a   + a) + 3log(\|- x  + a   - a) - 6log(x) + 2
--R   (4)  -------------------------------------------------------------
--R                                       5
--R                                     2a
--R                                                     Type: Expression Integer
--E

--S 121 of 170
ee:=complexNormalize dd
 

                  x
        - 3log(-------) + 1
                +----+
                |   2
               \|- x
   (5)  -------------------
                  5
                 a
                                                     Type: Expression Integer
--R
--R                  x
--R        - 3log(-------) + 1
--R                +----+
--R                |   2
--R               \|- x
--R   (5)  -------------------
--R                  5
--R                 a
--R                                                     Type: Expression Integer
--E

--S 122 of 170    14:257 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

              +---+
        3log(\|- 1 ) + 1
   (6)  ----------------
                5
               a
                                                     Type: Expression Integer
--R
--R              +---+
--R        3log(\|- 1 ) + 1
--R   (6)  ----------------
--R                5
--R               a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 123 of 170
aa:=integrate((a^2-x^2)^(3/2),x)
 

   (1)
                            +---------+
                5 2      7  |   2    2      4 4      6 2      8
         ((- 24a x  + 48a )\|- x  + a   - 6a x  + 48a x  - 48a )
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                         +---------+
            7      2 5      4 3      6   |   2    2        7      3 5      5 3
       (- 2x  + 21a x  - 56a x  + 40a x)\|- x  + a   + 8a x  - 44a x  + 76a x
     + 
            7
       - 40a x
  /
                     +---------+
           2      3  |   2    2      4      2 2      4
     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                            +---------+
--R                5 2      7  |   2    2      4 4      6 2      8
--R         ((- 24a x  + 48a )\|- x  + a   - 6a x  + 48a x  - 48a )
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                         +---------+
--R            7      2 5      4 3      6   |   2    2        7      3 5      5 3
--R       (- 2x  + 21a x  - 56a x  + 40a x)\|- x  + a   + 8a x  - 44a x  + 76a x
--R     + 
--R            7
--R       - 40a x
--R  /
--R                     +---------+
--R           2      3  |   2    2      4      2 2      4
--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 124 of 170
bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a)
 

                       +---------+
             3     2   |   2    2      4     x
        (- 2x  + 5a x)\|- x  + a   + 3a asin(-)
                                             a
   (2)  ---------------------------------------
                           8
                                                     Type: Expression Integer
--R
--R                       +---------+
--R             3     2   |   2    2      4     x
--R        (- 2x  + 5a x)\|- x  + a   + 3a asin(-)
--R                                             a
--R   (2)  ---------------------------------------
--R                           8
--R                                                     Type: Expression Integer
--E

--S 125 of 170
cc:=aa-bb
 

                   +---------+
                   |   2    2
            4     \|- x  + a   - a      4     x
        - 6a atan(----------------) - 3a asin(-)
                          x                   a
   (3)  ----------------------------------------
                            8
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            4     \|- x  + a   - a      4     x
--R        - 6a atan(----------------) - 3a asin(-)
--R                          x                   a
--R   (3)  ----------------------------------------
--R                            8
--R                                                     Type: Expression Integer
--E

--S 126 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 

--S 127 of 170
ee:=asinrule cc
 

                      +---------+
                      |   2    2
                      |- x  + a
                    a |---------  - %i x             +---------+
                      |     2                        |   2    2
               4     \|    a                  4     \|- x  + a   - a
        - 3%i a log(--------------------) - 6a atan(----------------)
                              a                             x
   (5)  -------------------------------------------------------------
                                      8
                                             Type: Expression Complex Integer
--R
--R                      +---------+
--R                      |   2    2
--R                      |- x  + a
--R                    a |---------  - %i x             +---------+
--R                      |     2                        |   2    2
--R               4     \|    a                  4     \|- x  + a   - a
--R        - 3%i a log(--------------------) - 6a atan(----------------)
--R                              a                             x
--R   (5)  -------------------------------------------------------------
--R                                      8
--R                                             Type: Expression Complex Integer
--E

--S 128 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 129 of 170
ff:=atanrule ee
 

   (7)
                 +---------+
                 |   2    2
                 |- x  + a
               a |---------  - %i x                 +---------+
                 |     2                            |   2    2
          4     \|    a                     4    - \|- x  + a   + %i x + a
   - 3%i a log(--------------------) + 3%i a log(-------------------------)
                         a                         +---------+
                                                   |   2    2
                                                  \|- x  + a   + %i x - a
   ------------------------------------------------------------------------
                                       8
                                             Type: Expression Complex Integer
--R
--R   (7)
--R                 +---------+
--R                 |   2    2
--R                 |- x  + a
--R               a |---------  - %i x                 +---------+
--R                 |     2                            |   2    2
--R          4     \|    a                     4    - \|- x  + a   + %i x + a
--R   - 3%i a log(--------------------) + 3%i a log(-------------------------)
--R                         a                         +---------+
--R                                                   |   2    2
--R                                                  \|- x  + a   + %i x - a
--R   ------------------------------------------------------------------------
--R                                       8
--R                                             Type: Expression Complex Integer
--E

--S 130 of 170
gg:=expandLog ff
 

   (8)
                     +---------+
                     |   2    2                       +---------+
              4      |- x  + a                  4     |   2    2
       - 3%i a log(a |---------  - %i x) - 3%i a log(\|- x  + a   + %i x - a)
                     |     2
                    \|    a
     + 
                  +---------+
            4     |   2    2                     4              4
       3%i a log(\|- x  + a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                     +---------+
--R                     |   2    2                       +---------+
--R              4      |- x  + a                  4     |   2    2
--R       - 3%i a log(a |---------  - %i x) - 3%i a log(\|- x  + a   + %i x - a)
--R                     |     2
--R                    \|    a
--R     + 
--R                  +---------+
--R            4     |   2    2                     4              4
--R       3%i a log(\|- x  + a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 131 of 170
hh:=rootSimp gg
 

   (9)
                      +-------+                            +-------+
              4       | 2    2                     4       | 2    2
       - 3%i a log(%i\|x  - a   + %i x - a) - 3%i a log(%i\|x  - a   - %i x)
     + 
                    +-------+
            4       | 2    2                     4              4
       3%i a log(%i\|x  - a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
  /
     8
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                      +-------+                            +-------+
--R              4       | 2    2                     4       | 2    2
--R       - 3%i a log(%i\|x  - a   + %i x - a) - 3%i a log(%i\|x  - a   - %i x)
--R     + 
--R                    +-------+
--R            4       | 2    2                     4              4
--R       3%i a log(%i\|x  - a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
--R  /
--R     8
--R                                             Type: Expression Complex Integer
--E

--S 132 of 170    14:258 Schaums and Axiom agree
ii:=complexNormalize hh
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 133 of 170
aa:=integrate(x*(a^2-x^2)^(3/2),x)
 

   (1)
                                          +---------+
            8      3 6      5 4      7 2  |   2    2     10      2 8      4 6
       (5a x  - 30a x  + 60a x  - 40a x )\|- x  + a   + x   - 15a x  + 55a x
     + 
            6 4      8 2
       - 80a x  + 40a x
  /
                           +---------+
        4      2 2      4  |   2    2         4       3 2      5
     (5x  - 60a x  + 80a )\|- x  + a   - 25a x  + 100a x  - 80a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                          +---------+
--R            8      3 6      5 4      7 2  |   2    2     10      2 8      4 6
--R       (5a x  - 30a x  + 60a x  - 40a x )\|- x  + a   + x   - 15a x  + 55a x
--R     + 
--R            6 4      8 2
--R       - 80a x  + 40a x
--R  /
--R                           +---------+
--R        4      2 2      4  |   2    2         4       3 2      5
--R     (5x  - 60a x  + 80a )\|- x  + a   - 25a x  + 100a x  - 80a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 134 of 170
bb:=-(a^2-x^2)^(5/2)/5
 

                            +---------+
            4     2 2    4  |   2    2
        (- x  + 2a x  - a )\|- x  + a
   (2)  -------------------------------
                       5
                                                     Type: Expression Integer
--R
--R                            +---------+
--R            4     2 2    4  |   2    2
--R        (- x  + 2a x  - a )\|- x  + a
--R   (2)  -------------------------------
--R                       5
--R                                                     Type: Expression Integer
--E

--S 135 of 170    14:259 Schaums and Axiom differ by a constant
cc:=aa-bb
 

           5
          a
   (3)  - --
           5
                                                     Type: Expression Integer
--R
--R           5
--R          a
--R   (3)  - --
--R           5
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 136 of 170
aa:=integrate(x^2*(a^2-x^2)^(3/2),x)
 

   (1)
                                         +---------+
                 7 4       9 2       11  |   2    2      6 6       8 4
           (- 36a x  + 192a x  - 192a  )\|- x  + a   - 6a x  + 108a x
         + 
                 10 2       12
           - 288a  x  + 192a
      *
               +---------+
               |   2    2
              \|- x  + a   - a
         atan(----------------)
                      x
     + 
                                                                 +---------+
            11       2 9       4 7       6 5       8 3      10   |   2    2
       (- 8x   + 158a x  - 639a x  + 982a x  - 592a x  + 96a  x)\|- x  + a
     + 
            11       3 9        5 7        7 5       9 3      11
       48a x   - 388a x  + 1062a x  - 1266a x  + 640a x  - 96a  x
  /
                                     +---------+
              4        3 2        5  |   2    2       6       2 4        4 2
       (288a x  - 1536a x  + 1536a )\|- x  + a   + 48x  - 864a x  + 2304a x
     + 
              6
       - 1536a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         +---------+
--R                 7 4       9 2       11  |   2    2      6 6       8 4
--R           (- 36a x  + 192a x  - 192a  )\|- x  + a   - 6a x  + 108a x
--R         + 
--R                 10 2       12
--R           - 288a  x  + 192a
--R      *
--R               +---------+
--R               |   2    2
--R              \|- x  + a   - a
--R         atan(----------------)
--R                      x
--R     + 
--R                                                                 +---------+
--R            11       2 9       4 7       6 5       8 3      10   |   2    2
--R       (- 8x   + 158a x  - 639a x  + 982a x  - 592a x  + 96a  x)\|- x  + a
--R     + 
--R            11       3 9        5 7        7 5       9 3      11
--R       48a x   - 388a x  + 1062a x  - 1266a x  + 640a x  - 96a  x
--R  /
--R                                     +---------+
--R              4        3 2        5  |   2    2       6       2 4        4 2
--R       (288a x  - 1536a x  + 1536a )\|- x  + a   + 48x  - 864a x  + 2304a x
--R     + 
--R              6
--R       - 1536a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 137 of 170
bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a^6/16*asin(x/a)
 

                                +---------+
             5      2 3     4   |   2    2      6     x
        (- 8x  + 14a x  - 3a x)\|- x  + a   + 3a asin(-)
                                                      a
   (2)  ------------------------------------------------
                               48
                                                     Type: Expression Integer
--R
--R                                +---------+
--R             5      2 3     4   |   2    2      6     x
--R        (- 8x  + 14a x  - 3a x)\|- x  + a   + 3a asin(-)
--R                                                      a
--R   (2)  ------------------------------------------------
--R                               48
--R                                                     Type: Expression Integer
--E

--S 138 of 170
cc:=aa-bb
 

                   +---------+
                   |   2    2
            6     \|- x  + a   - a     6     x
        - 2a atan(----------------) - a asin(-)
                          x                  a
   (3)  ---------------------------------------
                           16
                                                     Type: Expression Integer
--R
--R                   +---------+
--R                   |   2    2
--R            6     \|- x  + a   - a     6     x
--R        - 2a atan(----------------) - a asin(-)
--R                          x                  a
--R   (3)  ---------------------------------------
--R                           16
--R                                                     Type: Expression Integer
--E 

--S 139 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (4)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (4)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 140 of 170
dd:=atanrule cc
 

                    +---------+
                    |   2    2
            6    - \|- x  + a   + %i x + a     6     x
        %i a log(-------------------------) - a asin(-)
                   +---------+                       a
                   |   2    2
                  \|- x  + a   + %i x - a
   (5)  -----------------------------------------------
                               16
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R            6    - \|- x  + a   + %i x + a     6     x
--R        %i a log(-------------------------) - a asin(-)
--R                   +---------+                       a
--R                   |   2    2
--R                  \|- x  + a   + %i x - a
--R   (5)  -----------------------------------------------
--R                               16
--R                                             Type: Expression Complex Integer
--E

--S 141 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 142 of 170
ee:=asinrule dd
 

                     +---------+
                     |   2    2
                     |- x  + a
                   a |---------  - %i x                +---------+
                     |     2                           |   2    2
              6     \|    a                    6    - \|- x  + a   + %i x + a
        - %i a log(--------------------) + %i a log(-------------------------)
                             a                        +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                          16
                                             Type: Expression Complex Integer
--R
--R                     +---------+
--R                     |   2    2
--R                     |- x  + a
--R                   a |---------  - %i x                +---------+
--R                     |     2                           |   2    2
--R              6     \|    a                    6    - \|- x  + a   + %i x + a
--R        - %i a log(--------------------) + %i a log(-------------------------)
--R                             a                        +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                          16
--R                                             Type: Expression Complex Integer
--E

--S 143 of 170
ff:=expandLog ee
 

   (8)
                    +---------+
                    |   2    2                      +---------+
             6      |- x  + a                 6     |   2    2
       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
                    |     2
                   \|    a
     + 
                 +---------+
           6     |   2    2                    6             6
       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     16
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                    +---------+
--R                    |   2    2                      +---------+
--R             6      |- x  + a                 6     |   2    2
--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
--R                    |     2
--R                   \|    a
--R     + 
--R                 +---------+
--R           6     |   2    2                    6             6
--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     16
--R                                             Type: Expression Complex Integer
--E

--S 144 of 170
gg:=rootSimp ff
 

   (9)
                     +-------+                           +-------+
             6       | 2    2                    6       | 2    2
       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
     + 
                   +-------+
           6       | 2    2                    6             6
       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
  /
     16
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                     +-------+                           +-------+
--R             6       | 2    2                    6       | 2    2
--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R     + 
--R                   +-------+
--R           6       | 2    2                    6             6
--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R  /
--R     16
--R                                             Type: Expression Complex Integer
--E

--S 145 of 170    14:260 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 146 of 170
aa:=integrate(x^3*(a^2-x^2)^(3/2),x)
 

   (1)
                                                            +---------+
             12       3 10        5 8        7 6       9 4  |   2    2      14
       (35a x   - 336a x   + 1015a x  - 1260a x  + 560a x )\|- x  + a   + 5x
     + 
             2 12       4 10        6 8        8 6       10 4
       - 133a x   + 721a x   - 1575a x  + 1540a x  - 560a  x
  /
                                            +---------+
           6       2 4        4 2        6  |   2    2          6        3 4
       (35x  - 840a x  + 2800a x  - 2240a )\|- x  + a   - 245a x  + 1960a x
     + 
              5 2        7
       - 3920a x  + 2240a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                            +---------+
--R             12       3 10        5 8        7 6       9 4  |   2    2      14
--R       (35a x   - 336a x   + 1015a x  - 1260a x  + 560a x )\|- x  + a   + 5x
--R     + 
--R             2 12       4 10        6 8        8 6       10 4
--R       - 133a x   + 721a x   - 1575a x  + 1540a x  - 560a  x
--R  /
--R                                            +---------+
--R           6       2 4        4 2        6  |   2    2          6        3 4
--R       (35x  - 840a x  + 2800a x  - 2240a )\|- x  + a   - 245a x  + 1960a x
--R     + 
--R              5 2        7
--R       - 3920a x  + 2240a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 147 of 170
bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5
 

                                     +---------+
             6     2 4    4 2     6  |   2    2
        (- 5x  + 8a x  - a x  - 2a )\|- x  + a
   (2)  ----------------------------------------
                           35
                                                     Type: Expression Integer
--R
--R                                     +---------+
--R             6     2 4    4 2     6  |   2    2
--R        (- 5x  + 8a x  - a x  - 2a )\|- x  + a
--R   (2)  ----------------------------------------
--R                           35
--R                                                     Type: Expression Integer
--E

--S 148 of 170    14:261 Schaums and Axiom differ by a constant
cc:=aa-bb
 

            7
          2a
   (3)  - ---
           35
                                                     Type: Expression Integer
--R
--R            7
--R          2a
--R   (3)  - ---
--R           35
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 149 of 170
aa:=integrate((a^2-x^2)^(3/2)/x,x)
 

   (1)
                                                       +---------+
                       +---------+                     |   2    2
           3 2      5  |   2    2      4 2      6     \|- x  + a   - a
       ((3a x  - 12a )\|- x  + a   - 9a x  + 12a )log(----------------)
                                                              x
     + 
                        +---------+
            4      3 2  |   2    2     6     2 4      4 2
       (3a x  - 12a x )\|- x  + a   + x  - 9a x  + 12a x
  /
                  +---------+
        2      2  |   2    2        2      3
     (3x  - 12a )\|- x  + a   - 9a x  + 12a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                       +---------+
--R                       +---------+                     |   2    2
--R           3 2      5  |   2    2      4 2      6     \|- x  + a   - a
--R       ((3a x  - 12a )\|- x  + a   - 9a x  + 12a )log(----------------)
--R                                                              x
--R     + 
--R                        +---------+
--R            4      3 2  |   2    2     6     2 4      4 2
--R       (3a x  - 12a x )\|- x  + a   + x  - 9a x  + 12a x
--R  /
--R                  +---------+
--R        2      2  |   2    2        2      3
--R     (3x  - 12a )\|- x  + a   - 9a x  + 12a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 150 of 170
bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x)
 

                  +---------+
                  |   2    2                      +---------+
            3    \|- x  + a   + a        2     2  |   2    2
        - 3a log(----------------) + (- x  + 4a )\|- x  + a
                         x
   (2)  -----------------------------------------------------
                                  3
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2                      +---------+
--R            3    \|- x  + a   + a        2     2  |   2    2
--R        - 3a log(----------------) + (- x  + 4a )\|- x  + a
--R                         x
--R   (2)  -----------------------------------------------------
--R                                  3
--R                                                     Type: Expression Integer
--E

--S 151 of 170
cc:=aa-bb
 

                +---------+                +---------+
                |   2    2                 |   2    2
          3    \|- x  + a   + a      3    \|- x  + a   - a      3
        3a log(----------------) + 3a log(----------------) + 4a
                       x                          x
   (3)  ---------------------------------------------------------
                                    3
                                                     Type: Expression Integer
--R
--R                +---------+                +---------+
--R                |   2    2                 |   2    2
--R          3    \|- x  + a   + a      3    \|- x  + a   - a      3
--R        3a log(----------------) + 3a log(----------------) + 4a
--R                       x                          x
--R   (3)  ---------------------------------------------------------
--R                                    3
--R                                                     Type: Expression Integer
--E

--S 152 of 170
dd:=expandLog cc
 

                +---------+                +---------+
          3     |   2    2           3     |   2    2           3           3
        3a log(\|- x  + a   + a) + 3a log(\|- x  + a   - a) - 6a log(x) + 4a
   (4)  ---------------------------------------------------------------------
                                          3
                                                     Type: Expression Integer
--R
--R                +---------+                +---------+
--R          3     |   2    2           3     |   2    2           3           3
--R        3a log(\|- x  + a   + a) + 3a log(\|- x  + a   - a) - 6a log(x) + 4a
--R   (4)  ---------------------------------------------------------------------
--R                                          3
--R                                                     Type: Expression Integer
--E

--S 153 of 170
ee:=complexNormalize dd
 

            3       x         3
        - 6a log(-------) + 4a
                  +----+
                  |   2
                 \|- x
   (5)  -----------------------
                   3
                                                     Type: Expression Integer
--R
--R            3       x         3
--R        - 6a log(-------) + 4a
--R                  +----+
--R                  |   2
--R                 \|- x
--R   (5)  -----------------------
--R                   3
--R                                                     Type: Expression Integer
--E

--S 154 of 170    14:262 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

          3     +---+      3
        6a log(\|- 1 ) + 4a
   (6)  --------------------
                  3
                                                     Type: Expression Integer
--R
--R          3     +---+      3
--R        6a log(\|- 1 ) + 4a
--R   (6)  --------------------
--R                  3
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 155 of 170
aa:=integrate((a^2-x^2)^{3/2}/x^2,x)
 

   (1)
                                                           +---------+
                        +---------+                        |   2    2
           2 3      4   |   2    2       3 3      5       \|- x  + a   - a
       ((6a x  - 24a x)\|- x  + a   - 18a x  + 24a x)atan(----------------)
                                                                  x
     + 
                             +---------+
            4     3 2     5  |   2    2     6     2 4     4 2     6
       (3a x  + 2a x  - 8a )\|- x  + a   + x  - 3a x  - 6a x  + 8a
  /
                  +---------+
        3     2   |   2    2        3     3
     (2x  - 8a x)\|- x  + a   - 6a x  + 8a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                           +---------+
--R                        +---------+                        |   2    2
--R           2 3      4   |   2    2       3 3      5       \|- x  + a   - a
--R       ((6a x  - 24a x)\|- x  + a   - 18a x  + 24a x)atan(----------------)
--R                                                                  x
--R     + 
--R                             +---------+
--R            4     3 2     5  |   2    2     6     2 4     4 2     6
--R       (3a x  + 2a x  - 8a )\|- x  + a   + x  - 3a x  - 6a x  + 8a
--R  /
--R                  +---------+
--R        3     2   |   2    2        3     3
--R     (2x  - 8a x)\|- x  + a   - 6a x  + 8a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 156 of 170
bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a)
 

                     +---------+
            2     2  |   2    2      2       x
        (- x  - 2a )\|- x  + a   - 3a x asin(-)
                                             a
   (2)  ---------------------------------------
                           2x
                                                     Type: Expression Integer
--R
--R                     +---------+
--R            2     2  |   2    2      2       x
--R        (- x  - 2a )\|- x  + a   - 3a x asin(-)
--R                                             a
--R   (2)  ---------------------------------------
--R                           2x
--R                                                     Type: Expression Integer
--E

--S 157 of 170
cc:=aa-bb
 

                 +---------+
                 |   2    2
          2     \|- x  + a   - a      2     x
        6a atan(----------------) + 3a asin(-)
                        x                   a
   (3)  --------------------------------------
                           2
                                                     Type: Expression Integer
--R
--R                 +---------+
--R                 |   2    2
--R          2     \|- x  + a   - a      2     x
--R        6a atan(----------------) + 3a asin(-)
--R                        x                   a
--R   (3)  --------------------------------------
--R                           2
--R                                                     Type: Expression Integer
--E

--S 158 of 170
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 159 of 170
dd:=asinrule cc
 

                    +---------+
                    |   2    2
                    |- x  + a
                  a |---------  - %i x             +---------+
                    |     2                        |   2    2
             2     \|    a                  2     \|- x  + a   - a
        3%i a log(--------------------) + 6a atan(----------------)
                            a                             x
   (5)  -----------------------------------------------------------
                                     2
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R                    |- x  + a
--R                  a |---------  - %i x             +---------+
--R                    |     2                        |   2    2
--R             2     \|    a                  2     \|- x  + a   - a
--R        3%i a log(--------------------) + 6a atan(----------------)
--R                            a                             x
--R   (5)  -----------------------------------------------------------
--R                                     2
--R                                             Type: Expression Complex Integer
--E

--S 160 of 170
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (6)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (6)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 161 of 170
ee:=atanrule dd
 

                    +---------+
                    |   2    2
                    |- x  + a
                  a |---------  - %i x                 +---------+
                    |     2                            |   2    2
             2     \|    a                     2    - \|- x  + a   + %i x + a
        3%i a log(--------------------) - 3%i a log(-------------------------)
                            a                         +---------+
                                                      |   2    2
                                                     \|- x  + a   + %i x - a
   (7)  ----------------------------------------------------------------------
                                           2
                                             Type: Expression Complex Integer
--R
--R                    +---------+
--R                    |   2    2
--R                    |- x  + a
--R                  a |---------  - %i x                 +---------+
--R                    |     2                            |   2    2
--R             2     \|    a                     2    - \|- x  + a   + %i x + a
--R        3%i a log(--------------------) - 3%i a log(-------------------------)
--R                            a                         +---------+
--R                                                      |   2    2
--R                                                     \|- x  + a   + %i x - a
--R   (7)  ----------------------------------------------------------------------
--R                                           2
--R                                             Type: Expression Complex Integer
--E

--S 162 of 170
ff:=expandLog ee
 

   (8)
                   +---------+
                   |   2    2                       +---------+
            2      |- x  + a                  2     |   2    2
       3%i a log(a |---------  - %i x) + 3%i a log(\|- x  + a   + %i x - a)
                   |     2
                  \|    a
     + 
                    +---------+
              2     |   2    2                     2              2
       - 3%i a log(\|- x  + a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (8)
--R                   +---------+
--R                   |   2    2                       +---------+
--R            2      |- x  + a                  2     |   2    2
--R       3%i a log(a |---------  - %i x) + 3%i a log(\|- x  + a   + %i x - a)
--R                   |     2
--R                  \|    a
--R     + 
--R                    +---------+
--R              2     |   2    2                     2              2
--R       - 3%i a log(\|- x  + a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E 

--S 163 of 170
gg:=rootSimp ff
 

   (9)
                    +-------+                            +-------+
            2       | 2    2                     2       | 2    2
       3%i a log(%i\|x  - a   + %i x - a) + 3%i a log(%i\|x  - a   - %i x)
     + 
                      +-------+
              2       | 2    2                     2              2
       - 3%i a log(%i\|x  - a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
  /
     2
                                             Type: Expression Complex Integer
--R
--R   (9)
--R                    +-------+                            +-------+
--R            2       | 2    2                     2       | 2    2
--R       3%i a log(%i\|x  - a   + %i x - a) + 3%i a log(%i\|x  - a   - %i x)
--R     + 
--R                      +-------+
--R              2       | 2    2                     2              2
--R       - 3%i a log(%i\|x  - a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
--R  /
--R     2
--R                                             Type: Expression Complex Integer
--E

--S 164 of 170    14:263 Schaums and Axiom agree
hh:=complexNormalize gg
 

   (10)  0
                                             Type: Expression Complex Integer
--R
--R   (10)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 165 of 170
aa:=integrate((a^2-x^2)^(3/2)/x^3,x)
 

   (1)
                                                             +---------+
                           +---------+                       |   2    2
               4      3 2  |   2    2      2 4      4 2     \|- x  + a   - a
       ((- 3a x  + 12a x )\|- x  + a   + 9a x  - 12a x )log(----------------)
                                                                    x
     + 
                             +---------+
            4     3 2     5  |   2    2      6     2 4     4 2     6
       (4a x  + 3a x  - 4a )\|- x  + a   + 2x  - 3a x  - 5a x  + 4a
  /
                   +---------+
        4     2 2  |   2    2        4     3 2
     (2x  - 8a x )\|- x  + a   - 6a x  + 8a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                             +---------+
--R                           +---------+                       |   2    2
--R               4      3 2  |   2    2      2 4      4 2     \|- x  + a   - a
--R       ((- 3a x  + 12a x )\|- x  + a   + 9a x  - 12a x )log(----------------)
--R                                                                    x
--R     + 
--R                             +---------+
--R            4     3 2     5  |   2    2      6     2 4     4 2     6
--R       (4a x  + 3a x  - 4a )\|- x  + a   + 2x  - 3a x  - 5a x  + 4a
--R  /
--R                   +---------+
--R        4     2 2  |   2    2        4     3 2
--R     (2x  - 8a x )\|- x  + a   - 6a x  + 8a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 166 of 170
bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x)
 

                  +---------+
                  |   2    2                      +---------+
            2    \|- x  + a   + a         2    2  |   2    2
        3a x log(----------------) + (- 2x  - a )\|- x  + a
                         x
   (2)  -----------------------------------------------------
                                   2
                                 2x
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2                      +---------+
--R            2    \|- x  + a   + a         2    2  |   2    2
--R        3a x log(----------------) + (- 2x  - a )\|- x  + a
--R                         x
--R   (2)  -----------------------------------------------------
--R                                   2
--R                                 2x
--R                                                     Type: Expression Integer
--E

--S 167 of 170
cc:=aa-bb
 

                  +---------+                +---------+
                  |   2    2                 |   2    2
                 \|- x  + a   + a           \|- x  + a   - a
        - 3a log(----------------) - 3a log(----------------) - 2a
                         x                          x
   (3)  ----------------------------------------------------------
                                     2
                                                     Type: Expression Integer
--R
--R                  +---------+                +---------+
--R                  |   2    2                 |   2    2
--R                 \|- x  + a   + a           \|- x  + a   - a
--R        - 3a log(----------------) - 3a log(----------------) - 2a
--R                         x                          x
--R   (3)  ----------------------------------------------------------
--R                                     2
--R                                                     Type: Expression Integer
--E

--S 168 of 170
dd:=expandLog cc
 

                  +---------+                +---------+
                  |   2    2                 |   2    2
        - 3a log(\|- x  + a   + a) - 3a log(\|- x  + a   - a) + 6a log(x) - 2a
   (4)  ----------------------------------------------------------------------
                                           2
                                                     Type: Expression Integer
--R
--R                  +---------+                +---------+
--R                  |   2    2                 |   2    2
--R        - 3a log(\|- x  + a   + a) - 3a log(\|- x  + a   - a) + 6a log(x) - 2a
--R   (4)  ----------------------------------------------------------------------
--R                                           2
--R                                                     Type: Expression Integer
--E

--S 169 of 170
ee:=complexNormalize dd
 

                  x
   (5)  3a log(-------) - a
                +----+
                |   2
               \|- x
                                                     Type: Expression Integer
--R
--R                  x
--R   (5)  3a log(-------) - a
--R                +----+
--R                |   2
--R               \|- x
--R                                                     Type: Expression Integer
--E

--S 170 of 170    14:264 Schaums and Axiom differ by a constant
ff:=rootSimp ee
 

                  +---+
   (6)  - 3a log(\|- 1 ) - a
                                                     Type: Expression Integer
--R
--R                  +---+
--R   (6)  - 3a log(\|- 1 ) - a
--R                                                     Type: Expression Integer
--E

)spool
 
Starts dribbling to HexadecimalExpansion.output (2010/3/27, 18:42:9).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
r := hex(22/7)
 

          ___
   (1)  3.249
                                                   Type: HexadecimalExpansion
--R 
--R
--R          ___
--R   (1)  3.249
--R                                                   Type: HexadecimalExpansion
--E 1

--S 2 of 7
r + hex(6/7)
 

   (2)  4
                                                   Type: HexadecimalExpansion
--R 
--R
--R   (2)  4
--R                                                   Type: HexadecimalExpansion
--E 2

--S 3 of 7
[hex(1/i) for i in 350..354]
 

   (3)
       _______________    _________      _____    ______________________
   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
       _____________________________
    0.00B92143FA36F5E02E4850FE8DBD78]
                                              Type: List HexadecimalExpansion
--R 
--R
--R   (3)
--R       _______________    _________      _____    ______________________
--R   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
--R       _____________________________
--R    0.00B92143FA36F5E02E4850FE8DBD78]
--R                                              Type: List HexadecimalExpansion
--E 3

--S 4 of 7
hex(1/1007)
 

   (4)
   0.
     OVERBAR
        0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
          DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
                                                   Type: HexadecimalExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
--R          DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
--R                                                   Type: HexadecimalExpansion
--E 4

--S 5 of 7
p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)
 

            2     _      ___
   (5)  0.4x  + 0.Ax + 0.71C
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R            2     _      ___
--R   (5)  0.4x  + 0.Ax + 0.71C
--R                                        Type: Polynomial HexadecimalExpansion
--E 5

--S 6 of 7
q := D(p, x)
 

                 _
   (6)  0.8x + 0.A
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R                 _
--R   (6)  0.8x + 0.A
--R                                        Type: Polynomial HexadecimalExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              _
   (7)  x + 1.5
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R              _
--R   (7)  x + 1.5
--R                                        Type: Polynomial HexadecimalExpansion
--E 7
)spool
 
Starts dribbling to carten.output (2010/3/27, 18:24:24).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from CartesianTensorXmpPage

--S 1 of 48
CT := CARTEN(i0 := 1, 2, Integer)
 

   (1)  CartesianTensor(1,2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  CartesianTensor(1,2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 48
t0: CT := 8
 

   (2)  8
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (2)  8
--R                                           Type: CartesianTensor(1,2,Integer)
--E 2

--S 3 of 48
rank t0
 

   (3)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  0
--R                                                     Type: NonNegativeInteger
--E 3

--S 4 of 48
v: DirectProduct(2, Integer) := directProduct [3,4]
 

   (4)  [3,4]
                                               Type: DirectProduct(2,Integer)
--R 
--R
--R   (4)  [3,4]
--R                                               Type: DirectProduct(2,Integer)
--E 4

--S 5 of 48
Tv: CT := v
 

   (5)  [3,4]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (5)  [3,4]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 5

--S 6 of 48
m: SquareMatrix(2, Integer) := matrix [[1,2],[4,5]]
 

        +1  2+
   (6)  |    |
        +4  5+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (6)  |    |
--R        +4  5+
--R                                                Type: SquareMatrix(2,Integer)
--E 6

--S 7 of 48
Tm: CT := m
 

        +1  2+
   (7)  |    |
        +4  5+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +4  5+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 7

--S 8 of 48
n: SquareMatrix(2, Integer) := matrix [[2,3],[0,1]]
 

        +2  3+
   (8)  |    |
        +0  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +2  3+
--R   (8)  |    |
--R        +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 48
Tn: CT := n
 

        +2  3+
   (9)  |    |
        +0  1+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R        +2  3+
--R   (9)  |    |
--R        +0  1+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 9

--S 10 of 48
t1: CT := [2, 3]
 

   (10)  [2,3]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (10)  [2,3]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 10

--S 11 of 48
rank t1
 

   (11)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  1
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 48
t2: CT := [t1, t1]
 

         +2  3+
   (12)  |    |
         +2  3+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  3+
--R   (12)  |    |
--R         +2  3+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 12

--S 13 of 48
t3: CT := [t2, t2]
 

          +2  3+ +2  3+
   (13)  [|    |,|    |]
          +2  3+ +2  3+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R          +2  3+ +2  3+
--R   (13)  [|    |,|    |]
--R          +2  3+ +2  3+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 13

--S 14 of 48
tt: CT := [t3, t3]; tt := [tt, tt]
 

          ++2  3+  +2  3++ ++2  3+  +2  3++
          ||    |  |    || ||    |  |    ||
          |+2  3+  +2  3+| |+2  3+  +2  3+|
   (14)  [|              |,|              |]
          |+2  3+  +2  3+| |+2  3+  +2  3+|
          ||    |  |    || ||    |  |    ||
          ++2  3+  +2  3++ ++2  3+  +2  3++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R          ++2  3+  +2  3++ ++2  3+  +2  3++
--R          ||    |  |    || ||    |  |    ||
--R          |+2  3+  +2  3+| |+2  3+  +2  3+|
--R   (14)  [|              |,|              |]
--R          |+2  3+  +2  3+| |+2  3+  +2  3+|
--R          ||    |  |    || ||    |  |    ||
--R          ++2  3+  +2  3++ ++2  3+  +2  3++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 14

--S 15 of 48
rank tt
 

   (15)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  5
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 48
Tmn := product(Tm, Tn)
 

         ++2  3+    +4  6+ +
         ||    |    |    | |
         |+0  1+    +0  2+ |
   (16)  |                 |
         |+8  12+  +10  15+|
         ||     |  |      ||
         ++0  4 +  +0   5 ++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  3+    +4  6+ +
--R         ||    |    |    | |
--R         |+0  1+    +0  2+ |
--R   (16)  |                 |
--R         |+8  12+  +10  15+|
--R         ||     |  |      ||
--R         ++0  4 +  +0   5 ++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 16

--S 17 of 48
Tmv := contract(Tm,2,Tv,1)
 

   (17)  [11,32]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (17)  [11,32]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 17

--S 18 of 48
Tm*Tv
 

   (18)  [11,32]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (18)  [11,32]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 18

--S 19 of 48
Tmv = m * v
 

   (19)  [11,32]= [11,32]
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R   (19)  [11,32]= [11,32]
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 19

--S 20 of 48
t0()
 

   (20)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  8
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 48
t1(1+1)
 

   (21)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  3
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 48
t2(2,1)
 

   (22)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  2
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 48
t3(2,1,2)
 

   (23)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  3
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 48
Tmn(2,1,2,1)
 

   (24)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (24)  0
--R                                                     Type: NonNegativeInteger
--E 24

--S 25 of 48
t0[]
 

   (25)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  8
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 48
t1[2]
 

   (26)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  3
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 48
t2[2,1]
 

   (27)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  2
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 48
t3[2,1,2]
 

   (28)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (28)  3
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 48
Tmn[2,1,2,1]
 

   (29)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (29)  0
--R                                                     Type: NonNegativeInteger
--E 29

--S 30 of 48
cTmn := contract(Tmn,1,2)
 

         +12  18+
   (30)  |      |
         +0   6 +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +12  18+
--R   (30)  |      |
--R         +0   6 +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 30

--S 31 of 48
trace(m) * n
 

         +12  18+
   (31)  |      |
         +0   6 +
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +12  18+
--R   (31)  |      |
--R         +0   6 +
--R                                                Type: SquareMatrix(2,Integer)
--E 31

--S 32 of 48
contract(Tmn,1,2) = trace(m) * n
 

         +12  18+  +12  18+
   (32)  |      |= |      |
         +0   6 +  +0   6 +
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +12  18+  +12  18+
--R   (32)  |      |= |      |
--R         +0   6 +  +0   6 +
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 32

--S 33 of 48
contract(Tmn,1,3) = transpose(m) * n
 

         +2  7 +  +2  7 +
   (33)  |     |= |     |
         +4  11+  +4  11+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  7 +  +2  7 +
--R   (33)  |     |= |     |
--R         +4  11+  +4  11+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 33

--S 34 of 48
contract(Tmn,1,4) = transpose(m) * transpose(n)
 

         +14  4+  +14  4+
   (34)  |     |= |     |
         +19  5+  +19  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +14  4+  +14  4+
--R   (34)  |     |= |     |
--R         +19  5+  +19  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 34

--S 35 of 48
contract(Tmn,2,3) = m * n
 

         +2  5 +  +2  5 +
   (35)  |     |= |     |
         +8  17+  +8  17+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +2  5 +  +2  5 +
--R   (35)  |     |= |     |
--R         +8  17+  +8  17+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 35

--S 36 of 48
contract(Tmn,2,4) = m * transpose(n)
 

         +8   2+  +8   2+
   (36)  |     |= |     |
         +23  5+  +23  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +8   2+  +8   2+
--R   (36)  |     |= |     |
--R         +23  5+  +23  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 36

--S 37 of 48
contract(Tmn,3,4) = trace(n) * m
 

         +3   6 +  +3   6 +
   (37)  |      |= |      |
         +12  15+  +12  15+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +3   6 +  +3   6 +
--R   (37)  |      |= |      |
--R         +12  15+  +12  15+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 37

--S 38 of 48
tTmn := transpose(Tmn,1,3)
 

         ++2  3 +  +4   6 ++
         ||     |  |      ||
         |+8  12+  +10  15+|
   (38)  |                 |
         |+0  1+    +0  2+ |
         ||    |    |    | |
         ++0  4+    +0  5+ +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  3 +  +4   6 ++
--R         ||     |  |      ||
--R         |+8  12+  +10  15+|
--R   (38)  |                 |
--R         |+0  1+    +0  2+ |
--R         ||    |    |    | |
--R         ++0  4+    +0  5+ +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 38

--S 39 of 48
transpose Tmn
 

         ++2  8+   +4  10++
         ||    |   |     ||
         |+0  0+   +0  0 +|
   (39)  |                |
         |+3  12+  +6  15+|
         ||     |  |     ||
         ++1  4 +  +2  5 ++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  8+   +4  10++
--R         ||    |   |     ||
--R         |+0  0+   +0  0 +|
--R   (39)  |                |
--R         |+3  12+  +6  15+|
--R         ||     |  |     ||
--R         ++1  4 +  +2  5 ++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 39

--S 40 of 48
transpose Tm = transpose m
 

         +1  4+  +1  4+
   (40)  |    |= |    |
         +2  5+  +2  5+
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         +1  4+  +1  4+
--R   (40)  |    |= |    |
--R         +2  5+  +2  5+
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 40

--S 41 of 48
rTmn := reindex(Tmn, [1,4,2,3])
 

         ++2  0+   +3  1+ +
         ||    |   |    | |
         |+4  0+   +6  2+ |
   (41)  |                |
         |+8   0+  +12  4+|
         ||     |  |     ||
         ++10  0+  +15  5++
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++2  0+   +3  1+ +
--R         ||    |   |    | |
--R         |+4  0+   +6  2+ |
--R   (41)  |                |
--R         |+8   0+  +12  4+|
--R         ||     |  |     ||
--R         ++10  0+  +15  5++
--R                                           Type: CartesianTensor(1,2,Integer)
--E 41

--S 42 of 48
tt := transpose(Tm)*Tn - Tn*transpose(Tm)
 

         +- 6  - 16+
   (42)  |         |
         + 2    6  +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +- 6  - 16+
--R   (42)  |         |
--R         + 2    6  +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 42

--S 43 of 48
Tv*(tt+Tn)
 

   (43)  [- 4,- 11]
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R   (43)  [- 4,- 11]
--R                                           Type: CartesianTensor(1,2,Integer)
--E 43

--S 44 of 48
reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm)
 

         ++46   84 +  +57   114++
         ||        |  |        ||
         |+174  212+  +228  285+|
   (44)  |                      |
         | +18  24+    +17  30+ |
         | |      |    |      | |
         + +57  63+    +63  76+ +
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         ++46   84 +  +57   114++
--R         ||        |  |        ||
--R         |+174  212+  +228  285+|
--R   (44)  |                      |
--R         | +18  24+    +17  30+ |
--R         | |      |    |      | |
--R         + +57  63+    +63  76+ +
--R                                           Type: CartesianTensor(1,2,Integer)
--E 44

--S 45 of 48
delta:  CT := kroneckerDelta()
 

         +1  0+
   (45)  |    |
         +0  1+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         +1  0+
--R   (45)  |    |
--R         +0  1+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 45

--S 46 of 48
contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2])
 

         + +2  4+   +0  0++  + +2  4+   +0  0++
         | |    |   |    ||  | |    |   |    ||
         | +3  6+   +1  2+|  | +3  6+   +1  2+|
   (46)  |                |= |                |
         |+8   10+  +0  0+|  |+8   10+  +0  0+|
         ||      |  |    ||  ||      |  |    ||
         ++12  15+  +4  5++  ++12  15+  +4  5++
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R         + +2  4+   +0  0++  + +2  4+   +0  0++
--R         | |    |   |    ||  | |    |   |    ||
--R         | +3  6+   +1  2+|  | +3  6+   +1  2+|
--R   (46)  |                |= |                |
--R         |+8   10+  +0  0+|  |+8   10+  +0  0+|
--R         ||      |  |    ||  ||      |  |    ||
--R         ++12  15+  +4  5++  ++12  15+  +4  5++
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 46

--S 47 of 48
epsilon:CT := leviCivitaSymbol()
 

         + 0   1+
   (47)  |      |
         +- 1  0+
                                           Type: CartesianTensor(1,2,Integer)
--R 
--R
--R         + 0   1+
--R   (47)  |      |
--R         +- 1  0+
--R                                           Type: CartesianTensor(1,2,Integer)
--E 47

--S 48 of 48
contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m
 

   (48)  - 6= - 6
                                  Type: Equation CartesianTensor(1,2,Integer)
--R 
--R
--R   (48)  - 6= - 6
--R                                  Type: Equation CartesianTensor(1,2,Integer)
--E 48
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read tutchap3
 
--Copyright The Numerical Algorithms Group Limited 1996.
D(x^2,x)
 

   (1)  2x
                                                     Type: Polynomial Integer
D(sin x,x)
 

   (2)  cos(x)
                                                     Type: Expression Integer
D(sin(log(x/tan(x))),x)
 

                   2                         x
        (- x tan(x)  + tan(x) - x)cos(log(------))
                                          tan(x)
   (3)  ------------------------------------------
                         x tan(x)
                                                     Type: Expression Integer
D(tan x,x,2)
 

               3
   (4)  2tan(x)  + 2tan(x)
                                                     Type: Expression Integer
D(tan x,x,3)
 

               4          2
   (5)  6tan(x)  + 8tan(x)  + 2
                                                     Type: Expression Integer
D(sin(x*y),x)
 

   (6)  y cos(x y)
                                                     Type: Expression Integer
D(sin(x*y),[y,x,x])
 

                           2
   (7)  - 2y sin(x y) - x y cos(x y)
                                                     Type: Expression Integer
dalembert := operator _[_]
 

   (8)  []
                                                          Type: BasicOperator
dalembert u
 

   (9)  [](u)
                                                     Type: Expression Integer
J0 := operator script(J,[[0]]::List List OutputForm)
 

   (10)  J
          0
                                                          Type: BasicOperator
symbol[sub1,sub2]
 

   (11)  symbol
               sub1,sub2
                                                                 Type: Symbol
f := operator 'f; g := operator 'g;
 

                                                          Type: BasicOperator
D(f(x)*g(x),x)
 

              ,           ,
   (13)  f(x)g (x) + g(x)f (x)

                                                     Type: Expression Integer
D(f(x)/g(x),x)
 

                ,           ,
         - f(x)g (x) + g(x)f (x)

   (14)  -----------------------
                      2
                  g(x)
                                                     Type: Expression Integer
D(f(g(x)),x)
 

          ,       ,
   (15)  f (g(x))g (x)

                                                     Type: Expression Integer
r := operator 'r; theta := operator 'theta ;
 

                                                          Type: BasicOperator
x(t) == r(t)*cos theta t
 
                                                                   Type: Void
y(t) == r(t)*sin theta t
 
                                                                   Type: Void
D(x(t),t)
 
   Compiling function x with type Variable t -> Expression Integer 

                                 ,                    ,
   (19)  - r(t)sin(theta(t))theta (t) + cos(theta(t))r (t)

                                                     Type: Expression Integer
D(y(t),t)
 
   Compiling function y with type Variable t -> Expression Integer 

                               ,                    ,
   (20)  r(t)cos(theta(t))theta (t) + sin(theta(t))r (t)

                                                     Type: Expression Integer
)clear all
 
r := operator 'r; theta := operator 'theta;
 

                                                          Type: BasicOperator
r := r(t); theta := theta(t);
 

                                                     Type: Expression Integer
x == r*cos theta; y == r*sin theta;
 
                                                                   Type: Void
ax := D(x,t,2); ay := D(y,t,2);
 
   Compiling body of rule x to compute value of type Expression Integer
      
   Compiling body of rule y to compute value of type Expression Integer
      

                                                     Type: Expression Integer
eval(ax,theta=0)
 

         ,,               ,   2
   (5)  r  (t) - r(t)theta (t)

                                                     Type: Expression Integer
eval(ay,theta=0)
 

                 ,,        ,        ,
   (6)  r(t)theta  (t) + 2r (t)theta (t)

                                                     Type: Expression Integer
f := operator 'f
 

   (7)  f
                                                          Type: BasicOperator
D(f(r,theta),t)
 

             ,                         ,
   (8)  theta (t)f  (r(t),theta(t)) + r (t)f  (r(t),theta(t))
                  ,2                        ,1
                                                     Type: Expression Integer
D(f(r,theta),t,2)
 

   (9)
          ,   2                        ,   2
     theta (t) f    (r(t),theta(t)) + r (t) f    (r(t),theta(t))
                ,2,2                         ,1,1
   + 
                            ,,                         ,,
     f  (r(t),theta(t))theta  (t) + f  (r(t),theta(t))r  (t)
      ,2                             ,1
   + 
      ,        ,                           ,        ,
     r (t)theta (t)f    (r(t),theta(t)) + r (t)theta (t)f    (r(t),theta(t))
                    ,2,1                                 ,1,2
                                                     Type: Expression Integer
)clear p x -- since x has a value
 
   Compiled code for x has been cleared.
integrate(x^2,x)
 

         1  3
   (10)  - x
         3
                                            Type: Polynomial Fraction Integer
integrate(%e^x,x)
 

           x
   (11)  %e
                                          Type: Union(Expression Integer,...)
integrate(1/x,x)
 

   (12)  log(x)
                                          Type: Union(Expression Integer,...)
integrate(sin x,x)
 

   (13)  - cos(x)
                                          Type: Union(Expression Integer,...)
I ==> integrate  
 
                                                                   Type: Void
I(x^3,x)
 

         1  4
   (15)  - x
         4
                                            Type: Polynomial Fraction Integer
I(sin sin x,x)
 

            x
          ++
   (16)   |   sin(sin(%R))d%R
         ++
                                          Type: Union(Expression Integer,...)
I(x^n,x)
 

             n log(x)
         x %e
   (17)  ------------
             n + 1
                                          Type: Union(Expression Integer,...)
% - 1/(n + 1)
 

             n log(x)
         x %e         - 1
   (18)  ----------------
               n + 1
                                                     Type: Expression Integer
limit(%,n=-1)
 

   (19)  log(x)
                        Type: Union(OrderedCompletion Expression Integer,...)
In := %% 17 
 

             n log(x)
         x %e
   (20)  ------------
             n + 1
                                          Type: Union(Expression Integer,...)
limit(%,n=-1)
 

   (21)  [leftHandLimit= - infinity,rightHandLimit=  + infinity]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
)set stream calculate 5
 
series(In,n=-1)          --  expand In in powers of (n+1)
 

   (22)
                                                           2  - log(x)
         - log(x)       - 1             - log(x)   x log(x) %e
     x %e        (n + 1)    + x log(x)%e         + ------------------- (n + 1)
                                                            2
   + 
             3  - log(x)                    4  - log(x)
     x log(x) %e                2   x log(x) %e                3
     ------------------- (n + 1)  + ------------------- (n + 1)
              6                              24
   + 
             5  - log(x)
     x log(x) %e                4            5
     ------------------- (n + 1)  + O((n + 1) )
             120
                       Type: UnivariatePuiseuxSeries(Expression Integer,n,-1)
In2 := In - x*%e^(-log(x))*(n+1)^(-1)
 

             n log(x)       - log(x)
         x %e         - x %e
   (23)  ---------------------------
                    n + 1
                                                     Type: Expression Integer
limit(In2,n=-1)
 

                   - log(x)
   (24)  x log(x)%e
                        Type: Union(OrderedCompletion Expression Integer,...)
limit(x^(n+1)/(n+1),n=-1)
 

   (25)  [leftHandLimit= - infinity,rightHandLimit=  + infinity]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
limit(x^(n+1)/(n+1)-1/(n+1),n=-1)
 

   (26)  log(x)
                        Type: Union(OrderedCompletion Expression Integer,...)
I(1/(a+x^2),x)
 

                2      +---+
              (x  - a)\|- a  + 2a x         +-+
          log(---------------------)      x\|a
                       2             atan(-----)
                      x  + a                a
   (27)  [--------------------------,-----------]
                      +---+               +-+
                    2\|- a               \|a
                                     Type: Union(List Expression Integer,...)
series(second %, a=0)
 

                1                           5
              - -                           -
         %pi    2   1    1       1   2      2
   (28)  --- a    - - + --- a - --- a  + O(a )
          2         x     3       5
                        3x      5x
                        Type: UnivariatePuiseuxSeries(Expression Integer,a,0)
second %% 27
 

                +-+
              x\|a
         atan(-----)
                a
   (29)  -----------
              +-+
             \|a
                                                     Type: Expression Integer
(rule atan A == acot(1/A)) %
 

                a
         acot(-----)
                +-+
              x\|a
   (30)  -----------
              +-+
             \|a
                                                     Type: Expression Integer
I(atan x - acot(1/x),x)
 

   (31)  0
                                          Type: Union(Expression Integer,...)
atanRule := rule atan(A) == acot(1/A)
 

                         1
   (32)  atan(A) == acot(-)
                         A
                        Type: RewriteRule(Integer,Integer,Expression Integer)
atanRule atan x
 

              1
   (33)  acot(-)
              x
                                                     Type: Expression Integer
rSimp := rule(sqrt(x^(2*(n|even? n))) == x^n)
 

          +---+
          | 2n      n
   (34)  \|x    == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
rSimp(sqrt(x^4))
 

          2
   (35)  x
                                                     Type: Expression Integer
rSimp(sqrt(x^6))
 

          +--+
          | 6
   (36)  \|x
                                                     Type: Expression Integer
f := operator 'f; g := operator 'g; dprod := D(f(x)*g(x),x)
 

              ,           ,
   (37)  f(x)g (x) + g(x)f (x)

                                                     Type: Expression Integer
(rule f x == sin x)%
 

                ,
   (38)  sin(x)g (x) + g(x)cos(x)

                                                     Type: Expression Integer
(rule g x == exp x)%
 

           x                 x
   (39)  %e sin(x) + cos(x)%e
                                                     Type: Expression Integer
(rule (f x == sin x; g x == cos x))dprod
 

                 2         2
   (40)  - sin(x)  + cos(x)
                                                     Type: Expression Integer
substitutions := (rule (f x == sec x; g x == csc x))
 

   (41)  {f(x) == sec(x),g(x) == csc(x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
substitutions dprod
 

   (42)  csc(x)sec(x)tan(x) - cot(x)csc(x)sec(x)
                                                     Type: Expression Integer
I(cot x, x)
 

                sin(2x)               2
         2log(-----------) - log(-----------)
              cos(2x) + 1        cos(2x) + 1
   (43)  ------------------------------------
                           2
                                          Type: Union(Expression Integer,...)
normalize %
 

                     2
         - log(tan(x)  + 1) + 2log(tan(x))
   (44)  ---------------------------------
                         2
                                                     Type: Expression Integer
simplify %
 

              sin(x)           1
         2log(------) - log(-------)
              cos(x)              2
                            cos(x)
   (45)  ---------------------------
                      2
                                                     Type: Expression Integer
(rule N*log A + M*log B == log(A^N*B^M)) %
 

                   2
         log(sin(x) )
   (46)  ------------
               2
                                                     Type: Expression Integer
(rule log(A^N) == N*log A)%
 

   (47)  log(sin(x))
                                                     Type: Expression Integer
ii:=I(1/(x^3 + x + 1),x)
 

   (48)
           +---------------+
           |         2          +--+
         (\|- 93%%BC0  + 12  - \|31 %%BC0)
      *
         log
                                    +---------------+
                 +--+         +--+  |         2                2
              (2\|31 %%BC0 + \|31 )\|- 93%%BC0  + 12  + 62%%BC0  - 31%%BC0 + 18x
            + 
              - 4
     + 
             +---------------+
             |         2          +--+
         (- \|- 93%%BC0  + 12  - \|31 %%BC0)
      *
         log
                                      +---------------+
                   +--+         +--+  |         2                2
              (- 2\|31 %%BC0 - \|31 )\|- 93%%BC0  + 12  + 62%%BC0  - 31%%BC0
            + 
              18x - 4
     + 
         +--+                   2
       2\|31 %%BC0 log(- 62%%BC0  + 31%%BC0 + 9x + 4)
  /
       +--+
     2\|31
                                          Type: Union(Expression Integer,...)
T0:= (tower ii).2 ::EXPR INT 
 

          +--+
   (49)  \|31
                                                     Type: Expression Integer
f:=definingPolynomial  T0
 

              2
   (50)  %%var  - 31
                                                     Type: Expression Integer
outputGeneral 5                      
 
                                                                   Type: Void
solve((numerator f) :: POLY INT,0.00001)
 

   (52)  [%%var= - 5.5678,%%var= 5.5678]
                                         Type: List Equation Polynomial Float
eval(ii :: EXPR COMPLEX FLOAT,T0= rhs first %)
 
 
Daly Bug
   >> Error detected within library code:
   left hand side must be a single kernel

(53) -> 
Starts dribbling to cyfactor.output (2010/3/27, 18:24:47).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 10
factor(x**84 - 1)
 

   (1)
                     2           2       2           4    2
     (x - 1)(x + 1)(x  - x + 1)(x  + 1)(x  + x + 1)(x  - x  + 1)
  *
       6    5    4    3    2           6    5    4    3    2
     (x  - x  + x  - x  + x  - x + 1)(x  + x  + x  + x  + x  + x + 1)
  *
       12    11    9    8    6    4    3
     (x   - x   + x  - x  + x  - x  + x  - x + 1)
  *
       12    10    8    6    4    2
     (x   - x   + x  - x  + x  - x  + 1)
  *
       12    11    9    8    6    4    3
     (x   + x   - x  - x  + x  - x  - x  + x + 1)
  *
       24    22    18    16    12    8    6    2
     (x   + x   - x   - x   + x   - x  - x  + x  + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (1)
--R                     2           2       2           4    2
--R     (x - 1)(x + 1)(x  - x + 1)(x  + 1)(x  + x + 1)(x  - x  + 1)
--R  *
--R       6    5    4    3    2           6    5    4    3    2
--R     (x  - x  + x  - x  + x  - x + 1)(x  + x  + x  + x  + x  + x + 1)
--R  *
--R       12    11    9    8    6    4    3
--R     (x   - x   + x  - x  + x  - x  + x  - x + 1)
--R  *
--R       12    10    8    6    4    2
--R     (x   - x   + x  - x  + x  - x  + 1)
--R  *
--R       12    11    9    8    6    4    3
--R     (x   + x   - x  - x  + x  - x  - x  + x + 1)
--R  *
--R       24    22    18    16    12    8    6    2
--R     (x   + x   - x   - x   + x   - x  - x  + x  + 1)
--R                                            Type: Factored Polynomial Integer
--E 1

--S 2 of 10
factor(-(x**68 -1))
 

   (2)
   -
                        2
        (x - 1)(x + 1)(x  + 1)
     *
           16    15    14    13    12    11    10    9    8    7    6    5    4
          x   - x   + x   - x   + x   - x   + x   - x  + x  - x  + x  - x  + x
        + 
             3    2
          - x  + x  - x + 1
     *
           16    15    14    13    12    11    10    9    8    7    6    5    4
          x   + x   + x   + x   + x   + x   + x   + x  + x  + x  + x  + x  + x
        + 
           3    2
          x  + x  + x + 1
     *
           32    30    28    26    24    22    20    18    16    14    12    10
          x   - x   + x   - x   + x   - x   + x   - x   + x   - x   + x   - x
        + 
           8    6    4    2
          x  - x  + x  - x  + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (2)
--R   -
--R                        2
--R        (x - 1)(x + 1)(x  + 1)
--R     *
--R           16    15    14    13    12    11    10    9    8    7    6    5    4
--R          x   - x   + x   - x   + x   - x   + x   - x  + x  - x  + x  - x  + x
--R        + 
--R             3    2
--R          - x  + x  - x + 1
--R     *
--R           16    15    14    13    12    11    10    9    8    7    6    5    4
--R          x   + x   + x   + x   + x   + x   + x   + x  + x  + x  + x  + x  + x
--R        + 
--R           3    2
--R          x  + x  + x + 1
--R     *
--R           32    30    28    26    24    22    20    18    16    14    12    10
--R          x   - x   + x   - x   + x   - x   + x   - x   + x   - x   + x   - x
--R        + 
--R           8    6    4    2
--R          x  - x  + x  - x  + 1
--R                                            Type: Factored Polynomial Integer
--E 2

--S 3 of 10
factor(x**99 + 1)
 

   (3)
              2           6    3
     (x + 1)(x  - x + 1)(x  - x  + 1)
  *
       10    9    8    7    6    5    4    3    2
     (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
  *
        20    19    17    16    14    13    11    10    9    7    6    4    3
       x   + x   - x   - x   + x   + x   - x   - x   - x  + x  + x  - x  - x
     + 
       x + 1
  *
        60    57    51    48    42    39    33    30    27    21    18    12
       x   + x   - x   - x   + x   + x   - x   - x   - x   + x   + x   - x
     + 
          9    3
       - x  + x  + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (3)
--R              2           6    3
--R     (x + 1)(x  - x + 1)(x  - x  + 1)
--R  *
--R       10    9    8    7    6    5    4    3    2
--R     (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
--R  *
--R        20    19    17    16    14    13    11    10    9    7    6    4    3
--R       x   + x   - x   - x   + x   + x   - x   - x   - x  + x  + x  - x  - x
--R     + 
--R       x + 1
--R  *
--R        60    57    51    48    42    39    33    30    27    21    18    12
--R       x   + x   - x   - x   + x   + x   - x   - x   - x   + x   + x   - x
--R     + 
--R          9    3
--R       - x  + x  + 1
--R                                            Type: Factored Polynomial Integer
--E 3

--S 4 of 10
factor(-(x**77 +1))
 

   (4)
   -
                 6    5    4    3    2
        (x + 1)(x  - x  + x  - x  + x  - x + 1)
     *
          10    9    8    7    6    5    4    3    2
        (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
     *
           60    59    53    52    49    48    46    45    42    41    39    37
          x   + x   - x   - x   - x   - x   + x   + x   + x   + x   - x   + x
        + 
             35    34    32    30    28    26    25    23    21    19    18
          - x   - x   + x   - x   + x   - x   - x   + x   - x   + x   + x
        + 
           15    14    12    11    8    7
          x   + x   - x   - x   - x  - x  + x + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (4)
--R   -
--R                 6    5    4    3    2
--R        (x + 1)(x  - x  + x  - x  + x  - x + 1)
--R     *
--R          10    9    8    7    6    5    4    3    2
--R        (x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1)
--R     *
--R           60    59    53    52    49    48    46    45    42    41    39    37
--R          x   + x   - x   - x   - x   - x   + x   + x   + x   + x   - x   + x
--R        + 
--R             35    34    32    30    28    26    25    23    21    19    18
--R          - x   - x   + x   - x   + x   - x   - x   + x   - x   + x   + x
--R        + 
--R           15    14    12    11    8    7
--R          x   + x   - x   - x   - x  - x  + x + 1
--R                                            Type: Factored Polynomial Integer
--E 4

--S 5 of 10
ind := 2**6
 

   (5)  64
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  64
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
factor(x**ind + 1)
 

         64
   (6)  x   + 1
                                            Type: Factored Polynomial Integer
--R 
--R
--R         64
--R   (6)  x   + 1
--R                                            Type: Factored Polynomial Integer
--E 6

--S 7 of 10
ind := 2**7
 

   (7)  128
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  128
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 10
factor(-(x**ind + 1))
 

            128
   (8)  - (x    + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R            128
--R   (8)  - (x    + 1)
--R                                            Type: Factored Polynomial Integer
--E 8

--S 9 of 10
factor(x**84 + 1)
 

   (9)
       4       8    4       24    20    16    12    8    4
     (x  + 1)(x  - x  + 1)(x   - x   + x   - x   + x  - x  + 1)
  *
       48    44    36    32    24    16    12    4
     (x   + x   - x   - x   + x   - x   - x   + x  + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (9)
--R       4       8    4       24    20    16    12    8    4
--R     (x  + 1)(x  - x  + 1)(x   - x   + x   - x   + x  - x  + 1)
--R  *
--R       48    44    36    32    24    16    12    4
--R     (x   + x   - x   - x   + x   - x   - x   + x  + 1)
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10 of 10
D
 

   (10)  D
                                                             Type: Variable D
--R 
--R
--R   (10)  D
--R                                                             Type: Variable D
--E 10
)spool
 
Starts dribbling to rubey.output (2010/3/27, 18:36:58).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 10
mons arg == 
 if #arg = 1 
  then arg
   else concat(map(m+->m+first arg, mons rest arg),
               map(m+->m-first arg, mons rest arg))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 10
summ arg == reduce (+,[m^4 for m in mons arg])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 10
t2 n == reduce(+,[reduce(+, 
           [summ[x[i],x[j]] 
             for j in i+1..n]) 
               for i in 1..n-1])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 10
t3 n == reduce(+, [reduce(+, [reduce(+, 
           [summ[x[i],x[j],x[k]] 
             for k in j+1..n]) 
               for j in i+1..n-1])
                 for i in 1..n-2])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 10
t4 n == reduce(+, [reduce(+, [reduce(+, [reduce(+, 
           [summ[x[i],x[j],x[k],x[m]] 
             for m in k+1..n])
               for k in j+1..n-1]) 
                 for j in i+1..n-2])
                   for i in 1..n-3])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
t5 n == reduce(+, [reduce(+, [reduce(+, [reduce(+, [reduce(+, 
           [summ[x[i],x[j],x[k],x[m],x[p]] 
             for p in m+1..n])
               for m in k+1..n-1])
                 for k in j+1..n-2]) 
                   for j in i+1..n-3])
                     for i in 1..n-4])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
factor t2 4
 
   Compiling function mons with type List Symbol -> List Polynomial 
      Integer 
   Compiling function summ with type List Symbol -> Polynomial Integer 
   Compiling function t2 with type PositiveInteger -> Polynomial 
      Integer 

            2     2     2     2 2
   (7)  6(x   + x   + x   + x  )
           4     3     2     1
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function mons with type List Symbol -> List Polynomial 
--R      Integer 
--R   Compiling function summ with type List Symbol -> Polynomial Integer 
--R   Compiling function t2 with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R            2     2     2     2 2
--R   (7)  6(x   + x   + x   + x  )
--R           4     3     2     1
--R                                            Type: Factored Polynomial Integer
--E 7

--S 8 of 10
factor t3 7
 
   Compiling function t3 with type PositiveInteger -> Polynomial 
      Integer 

             2     2     2     2     2     2     2 2
   (8)  60(x   + x   + x   + x   + x   + x   + x  )
            7     6     5     4     3     2     1
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function t3 with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R             2     2     2     2     2     2     2 2
--R   (8)  60(x   + x   + x   + x   + x   + x   + x  )
--R            7     6     5     4     3     2     1
--R                                            Type: Factored Polynomial Integer
--E 8

--S 9 of 10
factor t4 10
 
   Compiling function t4 with type PositiveInteger -> Polynomial 
      Integer 

               2     2     2     2     2     2     2     2     2     2 2
   (9)  672(x    + x   + x   + x   + x   + x   + x   + x   + x   + x  )
             10     9     8     7     6     5     4     3     2     1
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function t4 with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R               2     2     2     2     2     2     2     2     2     2 2
--R   (9)  672(x    + x   + x   + x   + x   + x   + x   + x   + x   + x  )
--R             10     9     8     7     6     5     4     3     2     1
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10 of 10
factor t5 13
 
   Compiling function t5 with type PositiveInteger -> Polynomial 
      Integer 

   (10)
     7920
  *
            2      2      2      2     2     2     2     2     2     2     2
         x    + x    + x    + x    + x   + x   + x   + x   + x   + x   + x
          13     12     11     10     9     8     7     6     5     4     3
       + 
           2     2
         x   + x
          2     1
    **
       2
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function t5 with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R   (10)
--R     7920
--R  *
--R            2      2      2      2     2     2     2     2     2     2     2
--R         x    + x    + x    + x    + x   + x   + x   + x   + x   + x   + x
--R          13     12     11     10     9     8     7     6     5     4     3
--R       + 
--R           2     2
--R         x   + x
--R          2     1
--R    **
--R       2
--R                                            Type: Factored Polynomial Integer
--E 10

)spool 
 
Starts dribbling to schaum7.output (2010/3/27, 18:37:19).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 80
aa:=integrate(1/(x^2-a^2),x)
 

        - log(x + a) + log(x - a)
   (1)  -------------------------
                    2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(x + a) + log(x - a)
--R   (1)  -------------------------
--R                    2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 80
bb:=1/(2*a)*log((x-a)/(x+a))
 

            x - a
        log(-----)
            x + a
   (2)  ----------
            2a
                                                     Type: Expression Integer
--R
--R            x - a
--R        log(-----)
--R            x + a
--R   (2)  ----------
--R            2a
--R                                                     Type: Expression Integer
--E

--S 3 of 80
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 4 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 80      14:144 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 6 of 80
aa:=integrate(x/(x^2-a^2),x)
 

             2    2
        log(x  - a )
   (1)  ------------
              2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R        log(x  - a )
--R   (1)  ------------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7 of 80
bb:=1/2*log(x^2-a^2)
 

             2    2
        log(x  - a )
   (2)  ------------
              2
                                                     Type: Expression Integer
--R
--R             2    2
--R        log(x  - a )
--R   (2)  ------------
--R              2
--R                                                     Type: Expression Integer
--E

--S 8 of 80      14:145 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 9 of 80
aa:=integrate(x^2/(x^2-a^2),x)
 

        - a log(x + a) + a log(x - a) + 2x
   (1)  ----------------------------------
                         2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - a log(x + a) + a log(x - a) + 2x
--R   (1)  ----------------------------------
--R                         2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 10 of 80
bb:=x+a/2*log((x-a)/(x+a))
 

              x - a
        a log(-----) + 2x
              x + a
   (2)  -----------------
                2
                                                     Type: Expression Integer
--R
--R              x - a
--R        a log(-----) + 2x
--R              x + a
--R   (2)  -----------------
--R                2
--R                                                     Type: Expression Integer
--E

--S 11 of 80
cc:=aa-bb
 

                                              x - a
        - a log(x + a) + a log(x - a) - a log(-----)
                                              x + a
   (3)  --------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R                                              x - a
--R        - a log(x + a) + a log(x - a) - a log(-----)
--R                                              x + a
--R   (3)  --------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 12 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 13 of 80     14:146 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 14 of 80
aa:=integrate(x^3/(x^2-a^2),x)
 

         2     2    2     2
        a log(x  - a ) + x
   (1)  -------------------
                 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         2     2    2     2
--R        a log(x  - a ) + x
--R   (1)  -------------------
--R                 2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 15 of 80
bb:=x^2/2+a^2/2*log(x^2-a^2)
 

         2     2    2     2
        a log(x  - a ) + x
   (2)  -------------------
                 2
                                                     Type: Expression Integer
--R
--R         2     2    2     2
--R        a log(x  - a ) + x
--R   (2)  -------------------
--R                 2
--R                                                     Type: Expression Integer
--E

--S 16 of 80     14:147 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 17 of 80
aa:=integrate(1/(x*(x^2-a^2)),x)
 

             2    2
        log(x  - a ) - 2log(x)
   (1)  ----------------------
                    2
                  2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2    2
--R        log(x  - a ) - 2log(x)
--R   (1)  ----------------------
--R                    2
--R                  2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 18 of 80
bb:=1/(2*a^2)*log((x^2-a^2)/x^2)
 

             2    2
            x  - a
        log(-------)
                2
               x
   (2)  ------------
               2
             2a
                                                     Type: Expression Integer
--R
--R             2    2
--R            x  - a
--R        log(-------)
--R                2
--R               x
--R   (2)  ------------
--R               2
--R             2a
--R                                                     Type: Expression Integer
--E

--S 19 of 80
cc:=aa-bb
 

                                      2    2
             2    2                  x  - a
        log(x  - a ) - 2log(x) - log(-------)
                                         2
                                        x
   (3)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                                      2    2
--R             2    2                  x  - a
--R        log(x  - a ) - 2log(x) - log(-------)
--R                                         2
--R                                        x
--R   (3)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 20 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 21 of 80
dd:=divlog cc
 

             2
        log(x ) - 2log(x)
   (5)  -----------------
                 2
               2a
                                                     Type: Expression Integer
--R
--R             2
--R        log(x ) - 2log(x)
--R   (5)  -----------------
--R                 2
--R               2a
--R                                                     Type: Expression Integer
--E

--S 22 of 80
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 23 of 80     14:148 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 24 of 80
aa:=integrate(1/(x^2*(x^2-a^2)),x)
 

        - x log(x + a) + x log(x - a) + 2a
   (1)  ----------------------------------
                         3
                       2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - x log(x + a) + x log(x - a) + 2a
--R   (1)  ----------------------------------
--R                         3
--R                       2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25 of 80
bb:=1/(a^2*x)+1/(2*a^3)*log((x-a)/(x+a))
 

              x - a
        x log(-----) + 2a
              x + a
   (2)  -----------------
                 3
               2a x
                                                     Type: Expression Integer
--R
--R              x - a
--R        x log(-----) + 2a
--R              x + a
--R   (2)  -----------------
--R                 3
--R               2a x
--R                                                     Type: Expression Integer
--E

--S 26 of 80
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                            3
                          2a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                            3
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 27 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 28 of 80     14:149 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 29 of 80
aa:=integrate(1/(x^3*(x^2-a^2)),x)
 

         2     2    2      2          2
        x log(x  - a ) - 2x log(x) + a
   (1)  -------------------------------
                       4 2
                     2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         2     2    2      2          2
--R        x log(x  - a ) - 2x log(x) + a
--R   (1)  -------------------------------
--R                       4 2
--R                     2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 80
bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))
 

                    2
           2       x        2
        - x log(-------) + a
                 2    2
                x  - a
   (2)  ---------------------
                  4 2
                2a x
                                                     Type: Expression Integer
--R
--R                    2
--R           2       x        2
--R        - x log(-------) + a
--R                 2    2
--R                x  - a
--R   (2)  ---------------------
--R                  4 2
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 31 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 32 of 80
t1:=divlog bb
 

           2     2     2     2    2     2
        - x log(x ) + x log(x  - a ) + a
   (4)  ---------------------------------
                        4 2
                      2a x
                                                     Type: Expression Integer
--R
--R           2     2     2     2    2     2
--R        - x log(x ) + x log(x  - a ) + a
--R   (4)  ---------------------------------
--R                        4 2
--R                      2a x
--R                                                     Type: Expression Integer
--E

--S 33 of 80
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (5)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (5)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34 of 80
t2:=logpow t1
 

         2     2    2      2          2
        x log(x  - a ) - 2x log(x) + a
   (6)  -------------------------------
                       4 2
                     2a x
                                                     Type: Expression Integer
--R
--R         2     2    2      2          2
--R        x log(x  - a ) - 2x log(x) + a
--R   (6)  -------------------------------
--R                       4 2
--R                     2a x
--R                                                     Type: Expression Integer
--E

--S 35 of 80     14:150 Schaums and Axiom agree
cc:=aa-t2
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 36 of 80
aa:=integrate(1/((x^2-a^2)^2),x)
 

          2    2                  2    2
        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                              3 2     5
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2                  2    2
--R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                              3 2     5
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 37 of 80
bb:=-x/(2*a^2*(x^2-a^2))-1/(4*a^3)*log((x-a)/(x+a))
 

            2    2     x - a
        (- x  + a )log(-----) - 2a x
                       x + a
   (2)  ----------------------------
                   3 2     5
                 4a x  - 4a
                                                     Type: Expression Integer
--R
--R            2    2     x - a
--R        (- x  + a )log(-----) - 2a x
--R                       x + a
--R   (2)  ----------------------------
--R                   3 2     5
--R                 4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 38 of 80
cc:=aa-bb
 

                                      x - a
        log(x + a) - log(x - a) + log(-----)
                                      x + a
   (3)  ------------------------------------
                           3
                         4a
                                                     Type: Expression Integer
--R
--R                                      x - a
--R        log(x + a) - log(x - a) + log(-----)
--R                                      x + a
--R   (3)  ------------------------------------
--R                           3
--R                         4a
--R                                                     Type: Expression Integer
--E

--S 39 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 40 of 80     14:151 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 41 of 80
aa:=integrate(x/((x^2-a^2)^2),x)
 

              1
   (1)  - ---------
            2     2
          2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            2     2
--R          2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42 of 80
bb:=-1/(2*(x^2-a^2))
 

              1
   (2)  - ---------
            2     2
          2x  - 2a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            2     2
--R          2x  - 2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 43 of 80     14:152 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 44 of 80
aa:=integrate(x^2/((x^2-a^2)^2),x)
 

            2    2                2    2
        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                                2     3
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2                2    2
--R        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                                2     3
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 45 of 80
bb:=-x/(2*(x^2-a^2))+1/(4*a)*log((x-a)/(x+a))
 

          2    2     x - a
        (x  - a )log(-----) - 2a x
                     x + a
   (2)  --------------------------
                    2     3
                4a x  - 4a
                                                     Type: Expression Integer
--R
--R          2    2     x - a
--R        (x  - a )log(-----) - 2a x
--R                     x + a
--R   (2)  --------------------------
--R                    2     3
--R                4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 46 of 80
cc:=aa-bb
 

                                        x - a
        - log(x + a) + log(x - a) - log(-----)
                                        x + a
   (3)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R                                        x - a
--R        - log(x + a) + log(x - a) - log(-----)
--R                                        x + a
--R   (3)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 47 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 48 of 80     14:153 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 49 of 80
aa:=integrate(x^3/((x^2-a^2)^2),x)
 

          2    2      2    2     2
        (x  - a )log(x  - a ) - a
   (1)  --------------------------
                   2     2
                 2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      2    2     2
--R        (x  - a )log(x  - a ) - a
--R   (1)  --------------------------
--R                   2     2
--R                 2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50 of 80
bb:=-a^2/(2*(x^2-a^2))+1/2*log(x^2-a^2)
 

          2    2      2    2     2
        (x  - a )log(x  - a ) - a
   (2)  --------------------------
                   2     2
                 2x  - 2a
                                                     Type: Expression Integer
--R
--R          2    2      2    2     2
--R        (x  - a )log(x  - a ) - a
--R   (2)  --------------------------
--R                   2     2
--R                 2x  - 2a
--R                                                     Type: Expression Integer
--E

--S 51 of 80     14:154 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 52 of 80
aa:=integrate(1/(x*(x^2-a^2)^2),x)
 

            2    2      2    2       2     2           2
        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
   (1)  ------------------------------------------------
                             4 2     6
                           2a x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2      2    2       2     2           2
--R        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
--R   (1)  ------------------------------------------------
--R                             4 2     6
--R                           2a x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53 of 80
bb:=-1/(2*a^2*(x^2-a^2))+1/(2*a^4)*log(x^2/(x^2-a^2))
 

                         2
          2    2        x        2
        (x  - a )log(-------) - a
                      2    2
                     x  - a
   (2)  --------------------------
                  4 2     6
                2a x  - 2a
                                                     Type: Expression Integer
--R
--R                         2
--R          2    2        x        2
--R        (x  - a )log(-------) - a
--R                      2    2
--R                     x  - a
--R   (2)  --------------------------
--R                  4 2     6
--R                2a x  - 2a
--R                                                     Type: Expression Integer
--E

--S 54 of 80
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  - a ) + 2log(x) - log(-------)
                                        2    2
                                       x  - a
   (3)  ---------------------------------------
                            4
                          2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  - a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  - a
--R   (3)  ---------------------------------------
--R                            4
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 55 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 56 of 80
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 57 of 80
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 58 of 80     14:155 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 59 of 80
aa:=integrate(1/(x^2*(x^2-a^2)^2),x)
 

           3     2                    3     2                   2     3
        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
   (1)  ---------------------------------------------------------------
                                    5 3     7
                                  4a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R
--R           3     2                    3     2                   2     3
--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
--R   (1)  ---------------------------------------------------------------
--R                                    5 3     7
--R                                  4a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 60 of 80
bb:=-1/(a^4*x)-x/(2*a^4*(x^2-a^2))-3/(4*a^5)*log((x-a)/(x+a))
 

             3     2      x - a        2     3
        (- 3x  + 3a x)log(-----) - 6a x  + 4a
                          x + a
   (2)  --------------------------------------
                       5 3     7
                     4a x  - 4a x
                                                     Type: Expression Integer
--R
--R             3     2      x - a        2     3
--R        (- 3x  + 3a x)log(-----) - 6a x  + 4a
--R                          x + a
--R   (2)  --------------------------------------
--R                       5 3     7
--R                     4a x  - 4a x
--R                                                     Type: Expression Integer
--E

--S 61 of 80
cc:=aa-bb
 

                                         x - a
        3log(x + a) - 3log(x - a) + 3log(-----)
                                         x + a
   (3)  ---------------------------------------
                            5
                          4a
                                                     Type: Expression Integer
--R
--R                                         x - a
--R        3log(x + a) - 3log(x - a) + 3log(-----)
--R                                         x + a
--R   (3)  ---------------------------------------
--R                            5
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 62 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 63 of 80     14:156 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 64 of 80
aa:=integrate(1/(x^3*(x^2-a^2)^2),x)
 

             4     2 2      2    2       4     2 2            2 2    4
        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
   (1)  --------------------------------------------------------------
                                   6 4     8 2
                                 2a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4     2 2      2    2       4     2 2            2 2    4
--R        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
--R   (1)  --------------------------------------------------------------
--R                                   6 4     8 2
--R                                 2a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 65 of 80
bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2-a^2))+1/a^6*log(x^2/(x^2-a^2))
 

                             2
           4     2 2        x         2 2    4
        (2x  - 2a x )log(-------) - 2a x  + a
                          2    2
                         x  - a
   (2)  --------------------------------------
                       6 4     8 2
                     2a x  - 2a x
                                                     Type: Expression Integer
--R
--R                             2
--R           4     2 2        x         2 2    4
--R        (2x  - 2a x )log(-------) - 2a x  + a
--R                          2    2
--R                         x  - a
--R   (2)  --------------------------------------
--R                       6 4     8 2
--R                     2a x  - 2a x
--R                                                     Type: Expression Integer
--E

--S 66 of 80
cc:=aa-bb
 

                                           2
               2    2                     x
        - log(x  - a ) + 2log(x) - log(-------)
                                        2    2
                                       x  - a
   (3)  ---------------------------------------
                            6
                           a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  - a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  - a
--R   (3)  ---------------------------------------
--R                            6
--R                           a
--R                                                     Type: Expression Integer
--E

--S 67 of 80
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 68 of 80
dd:=divlog cc
 

               2
        - log(x ) + 2log(x)
   (5)  -------------------
                  6
                 a
                                                     Type: Expression Integer
--R
--R               2
--R        - log(x ) + 2log(x)
--R   (5)  -------------------
--R                  6
--R                 a
--R                                                     Type: Expression Integer
--E

--S 69 of 80
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (6)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (6)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 70 of 80     14:157 Schaums and Axiom agree
ee:=logpow dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 71 of 80     14:158 Axiom cannot do this integral
aa:=integrate(1/((x^2-a^2)^n),x)
 

           x
         ++        1
   (1)   |   ------------- d%L
        ++       2     2 n
             (- a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++        1
--I   (1)   |   ------------- d%L
--R        ++       2     2 n
--I             (- a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 72 of 80
aa:=integrate(x/((x^2-a^2)^n),x)
 

                   2    2
                - x  + a
   (1)  ------------------------
                         2    2
                  n log(x  - a )
        (2n - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2    2
--R                - x  + a
--R   (1)  ------------------------
--R                         2    2
--R                  n log(x  - a )
--R        (2n - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 73 of 80
bb:=-1/(2*(n-1)*(x^2-a^2)^(n-1))
 

                     1
   (2)  - ----------------------
                    2    2 n - 1
          (2n - 2)(x  - a )
                                                     Type: Expression Integer
--R
--R                     1
--R   (2)  - ----------------------
--R                    2    2 n - 1
--R          (2n - 2)(x  - a )
--R                                                     Type: Expression Integer
--E

--S 74 of 80
cc:=aa-bb
 

                 2    2
          n log(x  - a )       2    2   2    2 n - 1
        %e               + (- x  + a )(x  - a )
   (3)  --------------------------------------------
                                          2    2
                     2    2 n - 1  n log(x  - a )
           (2n - 2)(x  - a )     %e
                                                     Type: Expression Integer
--R
--R                 2    2
--R          n log(x  - a )       2    2   2    2 n - 1
--R        %e               + (- x  + a )(x  - a )
--R   (3)  --------------------------------------------
--R                                          2    2
--R                     2    2 n - 1  n log(x  - a )
--R           (2n - 2)(x  - a )     %e
--R                                                     Type: Expression Integer
--E

--S 75 of 80
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 76 of 80
dd:=explog cc
 

          2    2 n       2    2   2    2 n - 1
        (x  - a )  + (- x  + a )(x  - a )
   (5)  --------------------------------------
                     2    2 n - 1  2    2 n
           (2n - 2)(x  - a )     (x  - a )
                                                     Type: Expression Integer
--R
--R          2    2 n       2    2   2    2 n - 1
--R        (x  - a )  + (- x  + a )(x  - a )
--R   (5)  --------------------------------------
--R                     2    2 n - 1  2    2 n
--R           (2n - 2)(x  - a )     (x  - a )
--R                                                     Type: Expression Integer
--E

--S 77 of 80     14:159 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 78 of 80     14:160 Axiom cannot compute this integral
aa:=integrate(1/(x*(x^2-a^2)^n),x)
 

           x
         ++          1
   (1)   |   ---------------- d%L
        ++          2     2 n
             %L (- a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++          1
--I   (1)   |   ---------------- d%L
--R        ++          2     2 n
--I             %L (- a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 79 of 80     14:161 Axiom cannot compute this integral
aa:=integrate(x^m/((x^2-a^2)^n),x)
 

           x        m
         ++       %L
   (1)   |   ------------- d%L
        ++       2     2 n
             (- a  + %L )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x        m
--I         ++       %L
--I   (1)   |   ------------- d%L
--R        ++       2     2 n
--I             (- a  + %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 80 of 80     14:162 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(x^2-a^2)^n),x)
 

           x
         ++          1
   (1)   |   ---------------- d%L
        ++       2     2 n  m
             (- a  + %L ) %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++          1
--I   (1)   |   ---------------- d%L
--R        ++       2     2 n  m
--I             (- a  + %L ) %L
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to polycoer.output (2010/3/27, 18:30:49).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 41
u : UP(x,COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 41
u := (2+3*%i)*x**5 - 7*x**4 +x**2 + 89
 

                  5     4    2
   (2)  (2 + 3%i)x  - 7x  + x  + 89
                                Type: UnivariatePolynomial(x,Complex Integer)
--R 
--R
--R                  5     4    2
--R   (2)  (2 + 3%i)x  - 7x  + x  + 89
--R                                Type: UnivariatePolynomial(x,Complex Integer)
--E 2

--S 3 of 41
m : MPOLY([x,y,z],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 41
m := u
 

                  5     4    2
   (4)  (2 + 3%i)x  - 7x  + x  + 89
                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                  5     4    2
--R   (4)  (2 + 3%i)x  - 7x  + x  + 89
--R                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--E 4

--S 5 of 41
m := m*y - z**2
 

                    5       4      2          2
   (5)  (2 + 3%i)y x  - 7y x  + y x  + 89y - z
                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                    5       4      2          2
--R   (5)  (2 + 3%i)y x  - 7y x  + y x  + 89y - z
--R                        Type: MultivariatePolynomial([x,y,z],Complex Integer)
--E 5

--S 6 of 41
m1 : MPOLY([r,z,t,x,s,y],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 41
m1 := m
 

           2               5       4      2
   (7)  - z  + (2 + 3%i)y x  - 7y x  + y x  + 89y
                  Type: MultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--R 
--R
--R           2               5       4      2
--R   (7)  - z  + (2 + 3%i)y x  - 7y x  + y x  + 89y
--R                  Type: MultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--E 7

--S 8 of 41
v : DMP([x,y,z],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 41
v := u
 

                  5     4    2
   (9)  (2 + 3%i)x  - 7x  + x  + 89
             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                  5     4    2
--R   (9)  (2 + 3%i)x  - 7x  + x  + 89
--R             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--E 9

--S 10 of 41
u := v
 

                   5     4    2
   (10)  (2 + 3%i)x  - 7x  + x  + 89
                                Type: UnivariatePolynomial(x,Complex Integer)
--R 
--R
--R                   5     4    2
--R   (10)  (2 + 3%i)x  - 7x  + x  + 89
--R                                Type: UnivariatePolynomial(x,Complex Integer)
--E 11

--S 12 of 41
v1 : DMP([r,z,t,x,s,y],COMPLEX INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 41
v1 := v
 

                   5     4    2
   (12)  (2 + 3%i)x  - 7x  + x  + 89
       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--R 
--R
--R                   5     4    2
--R   (12)  (2 + 3%i)x  - 7x  + x  + 89
--R       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--E 13

--S 14 of 41
v := m
 

                   5      4     2           2
   (13)  (2 + 3%i)x y - 7x y + x y + 89y - z
             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--R 
--R
--R                   5      4     2           2
--R   (13)  (2 + 3%i)x y - 7x y + x y + 89y - z
--R             Type: DistributedMultivariatePolynomial([x,y,z],Complex Integer)
--E 14

--S 15 of 41
v1 := m1
 

            2             5      4     2
   (14)  - z  + (2 + 3%i)x y - 7x y + x y + 89y
       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--R 
--R
--R            2             5      4     2
--R   (14)  - z  + (2 + 3%i)x y - 7x y + x y + 89y
--R       Type: DistributedMultivariatePolynomial([r,z,t,x,s,y],Complex Integer)
--E 15

)clear all
 

--S 16 of 41
u : DMP([x,y],INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 16

--S 17 of 41
f : UP(x,UP(y,INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 41
u := x + y
 

   (3)  x + y
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R   (3)  x + y
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 18

--S 19 of 41
f := u
 

   (4)  x + y
                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--R 
--R
--R   (4)  x + y
--R                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--E 19

--S 20 of 41
u := x**2*y**9 - x**2*y**2
 

         2 9    2 2
   (5)  x y  - x y
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R         2 9    2 2
--R   (5)  x y  - x y
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 20

--S 21 of 41
f := u
 

          9    2  2
   (6)  (y  - y )x
                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--R 
--R
--R          9    2  2
--R   (6)  (y  - y )x
--R                Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
--E 21

)clear all
 

--S 22 of 41
u : DMP([z,x,y],INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 41
f : UP(x,DMP([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 41
u := x + y + z
 

   (3)  z + x + y
                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--R 
--R
--R   (3)  z + x + y
--R                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--E 24

--S 25 of 41
f := u
 

   (4)  x + y + z
Type: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R   (4)  x + y + z
--RType: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--E 25

--S 26 of 41
u := x**2*y - z*x**2 + y*z - x**3*y*z + 3
 

             3       2          2
   (5)  - z x y - z x  + z y + x y + 3
                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--R 
--R
--R             3       2          2
--R   (5)  - z x y - z x  + z y + x y + 3
--R                     Type: DistributedMultivariatePolynomial([z,x,y],Integer)
--E 26

--S 27 of 41
f := x**2*y - z*x**2 + y*z - x**3*y*z + 3
 

               3           2
   (6)  - y z x  + (y - z)x  + y z + 3
Type: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R               3           2
--R   (6)  - y z x  + (y - z)x  + y z + 3
--RType: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--E 27

--S 28 of 41
f := u
 

               3           2
   (7)  - y z x  + (y - z)x  + y z + 3
Type: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R               3           2
--R   (7)  - y z x  + (y - z)x  + y z + 3
--RType: UnivariatePolynomial(x,DistributedMultivariatePolynomial([y,z],Integer))
--E 28

)clear all
 

--S 29 of 41
u : DMP([x,y,z,w],INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 41
f : UP(w,DMP([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 41
u := y**2 - w**5*y**2 - z*w + 3
 

           2 5    2
   (3)  - y w  + y  - z w + 3
                   Type: DistributedMultivariatePolynomial([x,y,z,w],Integer)
--R 
--R
--R           2 5    2
--R   (3)  - y w  + y  - z w + 3
--R                   Type: DistributedMultivariatePolynomial([x,y,z,w],Integer)
--E 31

--S 32 of 41
f := y**2 - w**5*y**2 - z*w + 3
 

           2 5          2
   (4)  - y w  - z w + y  + 3
Type: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R           2 5          2
--R   (4)  - y w  - z w + y  + 3
--RType: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--E 32

--S 33 of 41
f := u
 

           2 5          2
   (5)  - y w  - z w + y  + 3
Type: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--R 
--R
--R           2 5          2
--R   (5)  - y w  - z w + y  + 3
--RType: UnivariatePolynomial(w,DistributedMultivariatePolynomial([y,z],Integer))
--E 33

)clear all
 

--S 34 of 41
(x1,x2,x3) : DMP([a,b,c,d,e,f],Fraction INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 41
x1 := 2*a + 3*b - c
 

   (2)  2a + 3b - c
      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (2)  2a + 3b - c
--R      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 35

--S 36 of 41
x2 := 3 - 3*e + f
 

   (3)  - 3e + f + 3
      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (3)  - 3e + f + 3
--R      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 36

--S 37 of 41
x3 := a + b + c + d + e + f
 

   (4)  a + b + c + d + e + f
      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (4)  a + b + c + d + e + f
--R      Type: DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 37

--S 38 of 41
l1 : List DMP([a,b,c,d,e,f],Fraction INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 38

--S 39 of 41
l2 : List UP(f,DMP([a,b,c,d,e],Fraction INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 39

--S 40 of 41
l1 := [x1,x2,x3]
 

   (7)  [2a + 3b - c,- 3e + f + 3,a + b + c + d + e + f]
 Type: List DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--R 
--R
--R   (7)  [2a + 3b - c,- 3e + f + 3,a + b + c + d + e + f]
--R Type: List DistributedMultivariatePolynomial([a,b,c,d,e,f],Fraction Integer)
--E 40

--S 41 of 41
l2 := l1
 

   (8)  [2a + 3b - c,f - 3e + 3,f + a + b + c + d + e]
Type: List UnivariatePolynomial(f,DistributedMultivariatePolynomial([a,b,c,d,e],Fraction Integer))
--R 
--R
--R   (8)  [2a + 3b - c,f - 3e + 3,f + a + b + c + d + e]
--RType: List UnivariatePolynomial(f,DistributedMultivariatePolynomial([a,b,c,d,e],Fraction Integer))
--E 41
)spool 
 
Starts dribbling to Permutation.output (2010/3/27, 18:46:15).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 8
p := coercePreimagesImages([[1,2,3],[1,2,3]])
 

   (1)  1
                                            Type: Permutation PositiveInteger
--R 
--R
--R   (1)  1
--R                                            Type: Permutation PositiveInteger
--E 1

--S 2 of 8
movedPoints p    -- should return {}
 

   (2)  {}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (2)  {}
--R                                                    Type: Set PositiveInteger
--E 2

--S 3 of 8
even? p          -- should return true
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 8
p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4
 

   (4)  (1 0 3)
                                               Type: Permutation IntegerMod 4
--R 
--R
--R   (4)  (1 0 3)
--R                                               Type: Permutation IntegerMod 4
--E 4

--S 5 of 8
fixedPoints p    -- should return {2}
 

   (5)  {2}
                                                       Type: Set IntegerMod 4
--R 
--R
--R   (5)  {2}
--R                                                       Type: Set IntegerMod 4
--E 5

--S 6 of 8
q := coercePreimagesImages([[0,1,2,3],[1,0]])$PERM ZMOD 4
 

   (6)  (1 0)
                                               Type: Permutation IntegerMod 4
--R 
--R
--R   (6)  (1 0)
--R                                               Type: Permutation IntegerMod 4
--E 6

--S 7 of 8
fixedPoints(p*q) -- should return {2,0}
 

   (7)  {2,0}
                                                       Type: Set IntegerMod 4
--R 
--R
--R   (7)  {2,0}
--R                                                       Type: Set IntegerMod 4
--E 7

--S 8 of 8
even?(p*q)       -- should return false
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8
)spool
 
Starts dribbling to classtalk.output (2010/3/27, 18:24:29).
)set message test on
 
)set message auto off
 
)set break resume
 
)clear all
 

--S 1 of 72
1
 

   (1)  1
                                                        Type: PositiveInteger
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 72
1/2
 

        1
   (2)  -
        2
                                                       Type: Fraction Integer
--R
--R        1
--R   (2)  -
--R        2
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 72
3+4*%i
 

   (3)  3 + 4%i
                                                        Type: Complex Integer
--R
--R   (3)  3 + 4%i
--R                                                        Type: Complex Integer
--E 3

--S 4 of 72
3.4
 

   (4)  3.4
                                                                  Type: Float
--R
--R   (4)  3.4
--R                                                                  Type: Float
--E 4

--S 5 of 72
X::ROMAN
 

   (5)  X
                                                           Type: RomanNumeral
--R
--R   (5)  X
--R                                                           Type: RomanNumeral
--E 5

--S 6 of 72
binary(5)
 

   (6)  101
                                                        Type: BinaryExpansion
--R
--R   (6)  101
--R                                                        Type: BinaryExpansion
--E 6

--S 7 of 72
factor(60)
 

         2
   (7)  2 3 5
                                                       Type: Factored Integer
--R
--R         2
--R   (7)  2 3 5
--R                                                       Type: Factored Integer
--E 7

--S 8 of 72
q:=(y-1)*x*(z+5)
 

   (8)  (x y - x)z + 5x y - 5x
                                                     Type: Polynomial Integer
--R
--R   (8)  (x y - x)z + 5x y - 5x
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 72
factor q
 

   (9)  x(y - 1)(z + 5)
                                            Type: Factored Polynomial Integer
--R
--R   (9)  x(y - 1)(z + 5)
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10 of 72
eval(q,[x=5,y=6,z=7])
 

   (10)  300
                                                     Type: Polynomial Integer
--R
--R   (10)  300
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 72
eval(q,[x=5,y=6])
 

   (11)  25z + 125
                                                     Type: Polynomial Integer
--R
--R   (11)  25z + 125
--R                                                     Type: Polynomial Integer
--E 11

--S 12 of 72
b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a]
 

                   a
   (12)  [log(a),%e ,asin(a),acos(a),atan(a),acot(a),sinh(a)]
                                                Type: List Expression Integer
--R
--R                   a
--R   (12)  [log(a),%e ,asin(a),acos(a),atan(a),acot(a),sinh(a)]
--R                                                Type: List Expression Integer
--E 12

--S 13 of 72
[exp b.1, log b.2, sin b.3, cos b.4, tan b.5, cot b.6, asinh b.7]
 

   (13)  [a,a,a,a,a,a,a]
                                                Type: List Expression Integer
--R
--R   (13)  [a,a,a,a,a,a,a]
--R                                                Type: List Expression Integer
--E 13

--S 14 of 72
a:=.7
 

   (14)  0.7
                                                                  Type: Float
--R
--R   (14)  0.7
--R                                                                  Type: Float
--E 14

--S 15 of 72
b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a]
 

   (15)
   [- 0.3566749439 3873237891, 2.0137527074 704765216, 0.7753974966 1075306374,
    0.7953988301 8414355549, 0.6107259643 8920861654, 0.9600703624 0568800269,
    0.7585837018 3953350346]
                                                             Type: List Float
--R
--R   (15)
--R   [- 0.3566749439 3873237891, 2.0137527074 704765216, 0.7753974966 1075306374,
--R    0.7953988301 8414355549, 0.6107259643 8920861654, 0.9600703624 0568800269,
--R    0.7585837018 3953350346]
--R                                                             Type: List Float
--E 15

--S 16 of 72
[exp b.1, log b.2, sin b.3, cos b.4, tan b.5, cot b.6, asinh b.7]
 

   (16)  [0.7,0.7,0.7,0.7,0.7,0.7,0.7]
                                                             Type: List Float
--R
--R   (16)  [0.7,0.7,0.7,0.7,0.7,0.7,0.7]
--R                                                             Type: List Float
--E 16

--S 17 of 72
simplify(sin(x)**2+cos(x)**2)
 

   (17)  1
                                                     Type: Expression Integer
--R
--R   (17)  1
--R                                                     Type: Expression Integer
--E 17

)clear all
 
--S 18 of 72
eq1:=A*x^2 + B*x*y + C*y^2 + D*x + E*y + F
 

           2                   2
   (1)  C y  + (B x + E)y + A x  + D x + F
                                                     Type: Polynomial Integer
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 72
rotatex:=x'*cos(t)-y'*sin(t)
 

   (2)  - y' sin(t) + x' cos(t)
                                                     Type: Expression Integer
--R
--R   (2)  - y' sin(t) + x' cos(t)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 72
rotatey:=x'*sin(t)+y'*cos(t)
 

   (3)  x' sin(t) + y' cos(t)
                                                     Type: Expression Integer
--R
--R   (3)  x' sin(t) + y' cos(t)
--R                                                     Type: Expression Integer
--E 20

--S 21 of 72
eval(eq1,[x=rotatex, y=rotatey])
 

   (4)
          2                 2       2
     (A y'  - B x' y' + C x' )sin(t)
   + 
             2                        2
     ((- B y'  + (2C - 2A)x' y' + B x' )cos(t) - D y' + E x')sin(t)
   + 
          2                 2       2
     (C y'  + B x' y' + A x' )cos(t)  + (E y' + D x')cos(t) + F
                                                     Type: Expression Integer
--R
--R   (4)
--R          2                 2       2
--R     (A y'  - B x' y' + C x' )sin(t)
--R   + 
--R             2                        2
--R     ((- B y'  + (2C - 2A)x' y' + B x' )cos(t) - D y' + E x')sin(t)
--R   + 
--R          2                 2       2
--R     (C y'  + B x' y' + A x' )cos(t)  + (E y' + D x')cos(t) + F
--R                                                     Type: Expression Integer
--E 21

)clear all
 
--S 22 of 72
a:=rootOf(a^2+a+1)
 

   (1)  a
                                                        Type: AlgebraicNumber
--R
--R   (1)  a
--R                                                        Type: AlgebraicNumber
--E 22

--S 23 of 72
factor(x^2+3)
 

         2
   (2)  x  + 3
                                            Type: Factored Polynomial Integer
--R
--R         2
--R   (2)  x  + 3
--R                                            Type: Factored Polynomial Integer
--E 23

--S 24 of 72
factor(x^2+3,[a])
 

   (3)  (x - 2a - 1)(x + 2a + 1)
                                    Type: Factored Polynomial AlgebraicNumber
--R
--R   (3)  (x - 2a - 1)(x + 2a + 1)
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 24

--S 25 of 72
definingPolynomial(a)
 

         2
   (4)  a  + a + 1
                                                        Type: AlgebraicNumber
--R
--R         2
--R   (4)  a  + a + 1
--R                                                        Type: AlgebraicNumber
--E 25

--S 26 of 72
zerosOf(b^2+b+1,b)
 

          +---+        +---+
         \|- 3  - 1 - \|- 3  - 1
   (5)  [----------,------------]
              2           2
                                                Type: List Expression Integer
--R
--R          +---+        +---+
--R         \|- 3  - 1 - \|- 3  - 1
--R   (5)  [----------,------------]
--R              2           2
--R                                                Type: List Expression Integer
--E 26

--S 27 of 72
differentiate(sin(x),x)
 

   (6)  cos(x)
                                                     Type: Expression Integer
--R
--R   (6)  cos(x)
--R                                                     Type: Expression Integer
--E 27

--S 28 of 72
differentiate(sin(x),x,2)
 

   (7)  - sin(x)
                                                     Type: Expression Integer
--R
--R   (7)  - sin(x)
--R                                                     Type: Expression Integer
--E 28

--S 29 of 72
differentiate(cos(z)/(x^2+y^3),[x,y,z],[1,2,3])
 

                    4      3
            (- 84x y  + 24x y)sin(z)
   (8)  --------------------------------
         12     2 9     4 6     6 3    8
        y   + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R
--R                    4      3
--R            (- 84x y  + 24x y)sin(z)
--R   (8)  --------------------------------
--R         12     2 9     4 6     6 3    8
--R        y   + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E 29

--S 30 of 72
y:=operator y
 

   (9)  y
                                                          Type: BasicOperator
--R
--R   (9)  y
--R                                                          Type: BasicOperator
--E 30

--S 31 of 72
deqx:=D(y(x),x,2)+D(y(x),x)+y(x)
 

          ,,       ,
   (10)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R          ,,       ,
--R   (10)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 31

--S 32 of 72
solve(deqx,y,x)
 

                                              x     x
                                      +-+   - -   - -      +-+
                                    x\|3      2     2    x\|3
   (11)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                                      2                    2
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R
--R                                              x     x
--R                                      +-+   - -   - -      +-+
--R                                    x\|3      2     2    x\|3
--R   (11)  [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
--R                                      2                    2
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 32

)clear all
 
--S 33 of 72
limit((x^2-3*x+2)/(x^2-1),x=1)
 

          1
   (1)  - -
          2
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R
--R          1
--R   (1)  - -
--R          2
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 33

--S 34 of 72
limit(x*log(x),x=0)
 

   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R
--R   (2)  [leftHandLimit= "failed",rightHandLimit= 0]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 34

--S 35 of 72
limit(sinh(a*x)/tan(b*x),x=0)
 

        a
   (3)  -
        b
                        Type: Union(OrderedCompletion Expression Integer,...)
--R
--R        a
--R   (3)  -
--R        b
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 35

--S 36 of 72
limit(sqrt(3*x^2+1)/(5*x),x=%plusInfinity)
 

         +-+
        \|3
   (4)  ----
          5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R
--R         +-+
--R        \|3
--R   (4)  ----
--R          5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 36

--S 37 of 72
complexLimit((2+z)/(1-z),z=%infinity)
 

   (5)  - 1
                         Type: OnePointCompletion Fraction Polynomial Integer
--R
--R   (5)  - 1
--R                         Type: OnePointCompletion Fraction Polynomial Integer
--E 37

)clear all
 
--S 38 of 72
integrate(1+sqrt(x)/x,x)
 

          +-+
   (1)  2\|x  + x
                                          Type: Union(Expression Integer,...)
--R
--R          +-+
--R   (1)  2\|x  + x
--R                                          Type: Union(Expression Integer,...)
--E 38

--S 39 of 72
integrate(sin(x)/x,x)
 

   (2)  Si(x)
                                          Type: Union(Expression Integer,...)
--R
--R   (2)  Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 39

--S 40 of 72
integrate(exp(-a*x^2),x)
 

           x       2
         ++    - %Q a
   (3)   |   %e      d%Q
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x       2
--R         ++    - %Q a
--R   (3)   |   %e      d%Q
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 40

--S 41 of 72
integrate(sin(x)/x^2,x)
 

           x
         ++  sin(%Q)
   (4)   |   ------- d%Q
        ++       2
               %Q
                                          Type: Union(Expression Integer,...)
--R
--R           x
--R         ++  sin(%Q)
--R   (4)   |   ------- d%Q
--R        ++       2
--R               %Q
--R                                          Type: Union(Expression Integer,...)
--E 41

)clear all
 
--S 42 of 72
integrate(exp(-x)/sqrt(x),x=0..%plusInfinity)
 

         _ 1
   (1)  | (-)
           2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R         _ 1
--R   (1)  | (-)
--R           2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 42

--S 43 of 72
integrate(1/x^2,x=-1..1)
 
 
Daly Bug
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 43

)clear all
 

--S 44 of 72
integrate(sin(x)^3/(sin(x)^3+cos(x)^3),x=0..%pi/2,"noPole")
 

        2log(16) - 4log(4) + 3%pi
   (1)  -------------------------
                    12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R        2log(16) - 4log(4) + 3%pi
--R   (1)  -------------------------
--R                    12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 44

--S 45 of 72
integrate(exp(-x^2)*log(x)^2,x=0..%plusInfinity)
 

         _ 1             1     _ 1         1 2
        | (-)polygamma(1,-) + | (-)digamma(-)
           2             2       2         2
   (2)  --------------------------------------
                           8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R
--R         _ 1             1     _ 1         1 2
--R        | (-)polygamma(1,-) + | (-)digamma(-)
--R           2             2       2         2
--R   (2)  --------------------------------------
--R                           8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 45

)clear all
 

--S 46 of 72
laplace(sin(a*t)*cosh(a*t)-cos(a*t)*sinh(a*t),t,s)
 

             3
           4a
   (1)  --------
         4     4
        s  + 4a
                                                     Type: Expression Integer
--R
--R             3
--R           4a
--R   (1)  --------
--R         4     4
--R        s  + 4a
--R                                                     Type: Expression Integer
--E 46

--S 47 of 72
laplace(2/t * (1-cos(a*t)),t,s)
 

             2    2
   (2)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R
--R             2    2
--R   (2)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 47

--S 48 of 72
laplace((exp(a*t)-exp(b*t))/t,t,s)
 

   (3)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R
--R   (3)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 48

--S 49 of 72
laplace(exp(a*t+b)*Ei(c*t),t,s)
 

          b    s + c - a
        %e log(---------)
                   c
   (4)  -----------------
              s - a
                                                     Type: Expression Integer
--R
--R          b    s + c - a
--R        %e log(---------)
--R                   c
--R   (4)  -----------------
--R              s - a
--R                                                     Type: Expression Integer
--E 49

)clear all
 
--S 50 of 72
K:=Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 50

--S 51 of 72
qf:QFORM(2,K):=quadraticForm matrix([[-1,0],[0,-1]])$(SQMATRIX(2,K))
 

        +- 1   0 +
   (2)  |        |
        + 0   - 1+
                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--R
--R        +- 1   0 +
--R   (2)  |        |
--R        + 0   - 1+
--R                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--E 51

--S 52 of 72
i:=e(1)$CLIF(2,K,qf)
 

   (3)  e
         1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (3)  e
--R         1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 52

--S 53 of 72
j:=e(2)$CLIF(2,K,qf)
 

   (4)  e
         2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (4)  e
--R         2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 53

--S 54 of 72
k:=i*j
 

   (5)  e e
         1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (5)  e e
--R         1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 54

--S 55 of 72
x:=a+b*i+c*j+d*k
 

   (6)  a + b e  + c e  + d e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (6)  a + b e  + c e  + d e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 55

--S 56 of 72
y:=m+f*i+g*j+h*k
 

   (7)  m + f e  + g e  + h e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (7)  m + f e  + g e  + h e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 56

--S 57 of 72
x+y
 

   (8)  m + a + (f + b)e  + (g + c)e  + (h + d)e e
                        1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (8)  m + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                        1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 57

--S 58 of 72
x*y
 

   (9)
     a m - d h - c g - b f + (b m + c h - d g + a f)e
                                                     1
   + 
     (c m - b h + a g + d f)e  + (d m + a h + b g - c f)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R
--R   (9)
--R     a m - d h - c g - b f + (b m + c h - d g + a f)e
--R                                                     1
--R   + 
--R     (c m - b h + a g + d f)e  + (d m + a h + b g - c f)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 58

)clear all
 
--S 59 of 72
taylor(sin(x),x=0)
 

            1  3    1   5     1   7      1    9      11
   (1)  x - - x  + --- x  - ---- x  + ------ x  + O(x  )
            6      120      5040      362880
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R
--R            1  3    1   5     1   7      1    9      11
--R   (1)  x - - x  + --- x  - ---- x  + ------ x  + O(x  )
--R            6      120      5040      362880
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 59

--S 60 of 72
laurent(x/log(x),x=1)
 

   (2)
            - 1   3    5            1        2    11        3    11         4
     (x - 1)    + - + -- (x - 1) - -- (x - 1)  + --- (x - 1)  - ---- (x - 1)
                  2   12           24            720            1440
   + 
      271         5    13         6     7297         7     425         8
     ----- (x - 1)  - ---- (x - 1)  + ------- (x - 1)  - ------ (x - 1)
     60480            4480            3628800            290304
   + 
       530113         9            10
     --------- (x - 1)  + O((x - 1)  )
     479001600
                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--R
--R   (2)
--R            - 1   3    5            1        2    11        3    11         4
--R     (x - 1)    + - + -- (x - 1) - -- (x - 1)  + --- (x - 1)  - ---- (x - 1)
--R                  2   12           24            720            1440
--R   + 
--R      271         5    13         6     7297         7     425         8
--R     ----- (x - 1)  - ---- (x - 1)  + ------- (x - 1)  - ------ (x - 1)
--R     60480            4480            3628800            290304
--R   + 
--R       530113         9            10
--R     --------- (x - 1)  + O((x - 1)  )
--R     479001600
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--E 60

--S 61 of 72
puiseux(sqrt(sec(x)),x=3*%pi/2)
 

                    1                3                 7
                  - -                -                 -
             3%pi   2    1      3%pi 2    1       3%pi 2          3%pi 5
   (3)  (x - ----)    + -- (x - ----)  + --- (x - ----)  + O((x - ----) )
               2        12        2      160        2               2
                 Type: UnivariatePuiseuxSeries(Expression Integer,x,(3*pi)/2)
--R 
--R
--R                    1                3                 7
--R                  - -                -                 -
--R             3%pi   2    1      3%pi 2    1       3%pi 2          3%pi 5
--R   (3)  (x - ----)    + -- (x - ----)  + --- (x - ----)  + O((x - ----) )
--R               2        12        2      160        2               2
--R                 Type: UnivariatePuiseuxSeries(Expression Integer,x,(3*pi)/2)
--E 61

--S 62 of 72
series(x^x,x=0)
 

   (4)
                         2            3            4            5
                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
                      2            6            24          120
   + 
           6            7            8            9            10
     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
       720          5040        40320        362880       3628800
                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--R
--R   (4)
--R                         2            3            4            5
--R                   log(x)   2   log(x)   3   log(x)   4   log(x)   5
--R     1 + log(x)x + ------- x  + ------- x  + ------- x  + ------- x
--R                      2            6            24          120
--R   + 
--R           6            7            8            9            10
--R     log(x)   6   log(x)   7   log(x)   8   log(x)   9   log(x)    10      11
--R     ------- x  + ------- x  + ------- x  + ------- x  + -------- x   + O(x  )
--R       720          5040        40320        362880       3628800
--R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--E 62

)clear all
 
--S 63 of 72
m:=matrix [[1,2],[3,4]]
 

        +1  2+
   (1)  |    |
        +3  4+
                                                         Type: Matrix Integer
--R
--R        +1  2+
--R   (1)  |    |
--R        +3  4+
--R                                                         Type: Matrix Integer
--E 63

--S 64 of 72
4*m*(-5)
 

        +- 20  - 40+
   (2)  |          |
        +- 60  - 80+
                                                         Type: Matrix Integer
--R
--R        +- 20  - 40+
--R   (2)  |          |
--R        +- 60  - 80+
--R                                                         Type: Matrix Integer
--E 64

--S 65 of 72
n:=matrix [[1,0,-2],[-3,5,1]]
 

        + 1   0  - 2+
   (3)  |           |
        +- 3  5   1 +
                                                         Type: Matrix Integer
--R
--R        + 1   0  - 2+
--R   (3)  |           |
--R        +- 3  5   1 +
--R                                                         Type: Matrix Integer
--E 65

--S 66 of 72
m*n
 

        +- 5  10   0 +
   (4)  |            |
        +- 9  20  - 2+
                                                         Type: Matrix Integer
--R
--R        +- 5  10   0 +
--R   (4)  |            |
--R        +- 9  20  - 2+
--R                                                         Type: Matrix Integer
--E 66

--S 67 of 72
hilb:=matrix([[1/(i+j) for i in 1..3] for j in 1..3])
 

        +1  1  1+
        |-  -  -|
        |2  3  4|
        |       |
        |1  1  1|
   (5)  |-  -  -|
        |3  4  5|
        |       |
        |1  1  1|
        |-  -  -|
        +4  5  6+
                                                Type: Matrix Fraction Integer
--R
--R        +1  1  1+
--R        |-  -  -|
--R        |2  3  4|
--R        |       |
--R        |1  1  1|
--R   (5)  |-  -  -|
--R        |3  4  5|
--R        |       |
--R        |1  1  1|
--R        |-  -  -|
--R        +4  5  6+
--R                                                Type: Matrix Fraction Integer
--E 67

--S 68 of 72
inverse(hilb)
 

        + 72    - 240   180 +
        |                   |
   (6)  |- 240   900   - 720|
        |                   |
        + 180   - 720   600 +
                                     Type: Union(Matrix Fraction Integer,...)
--R
--R        + 72    - 240   180 +
--R        |                   |
--R   (6)  |- 240   900   - 720|
--R        |                   |
--R        + 180   - 720   600 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 68

)clear all
 
--S 69 of 72
solve([x+y+z=8,3*x-2*y+z=0,x+2*y+2*z=17],[x,y,z])
 

   (1)  [[x= - 1,y= 2,z= 7]]
                         Type: List List Equation Fraction Polynomial Integer
--R
--R   (1)  [[x= - 1,y= 2,z= 7]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 69

--S 70 of 72
solve([x+2*y+3*z=2,2*x+3*y+4*z=2,3*x+4*y+5*z=2],[x,y,z])
 

   (2)  [[x= %BC - 2,y= - 2%BC + 2,z= %BC]]
                         Type: List List Equation Fraction Polynomial Integer
--R
--I   (2)  [[x= %W - 2,y= - 2%W + 2,z= %W]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 70

--S 71 of 72
solve([[1,1,1],[3,-2,1],[1,2,2]],[8,0,17])
 

   (3)  [particular= [- 1,2,7],basis= [[0,0,0]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R
--R   (3)  [particular= [- 1,2,7],basis= [[0,0,0]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 71

--S 72 of 72
solve([[1,2,3],[2,3,4],[3,4,5]],[2,2,2])
 

   (4)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
Type: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--R
--R   (4)  [particular= [- 2,2,0],basis= [[1,- 2,1]]]
--RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer)
--E 72
)spool 
 
Starts dribbling to stream2.output (2010/3/27, 18:41:4).
)set message test on
 
)set message auto off
 
)clear all
 
)set stream calculate 20
 
)set functions cache all
 
   In general, interpreter functions will cache all values.
)set functions compile on
 

--S 1 of 55
u==[i+j for i in (-4)..10 | i < 5 for j in 4.. | j < 10]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 55
u
 
   Compiling body of rule u to compute value of type Stream Integer 
   u will cache all previously computed values.

   (2)  [0,2,4,6,8,10]
                                                         Type: Stream Integer
--R 
--R   Compiling body of rule u to compute value of type Stream Integer 
--R   u will cache all previously computed values.
--R
--R   (2)  [0,2,4,6,8,10]
--R                                                         Type: Stream Integer
--E 2

--S 3 of 55
reduce(0::Integer,+,u)
 

   (3)  30
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  30
--R                                                        Type: PositiveInteger
--E 3

)clear all
 

--S 4 of 55
u(m,n)==[i for i in m..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 55
u(3,6)
 
   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
      List PositiveInteger 
   u will cache all previously computed values.

   (2)  [3,4,5,6]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
--R      List PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (2)  [3,4,5,6]
--R                                                   Type: List PositiveInteger
--E 5

--S 6 of 55
reduce(+,u(3,6))
 

   (3)  18
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  18
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 55
reduce(+,u(3,8))
 

   (4)  33
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  33
--R                                                        Type: PositiveInteger
--E 7

)clear all
 

--S 8 of 55
n==10
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 55
u:=[i for i in 0..n]
 
   Compiling body of rule n to compute value of type PositiveInteger 
   n will cache all previously computed values.

   (2)  [0,1,2,3,4,5,6,7,8,9,10]
                                                Type: List NonNegativeInteger
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   n will cache all previously computed values.
--R
--R   (2)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                Type: List NonNegativeInteger
--E 9

--S 10 of 55
v==[i for i in 0..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 55
v
 
   Compiling body of rule v to compute value of type List 
      NonNegativeInteger 
   v will cache all previously computed values.

   (4)  [0,1,2,3,4,5,6,7,8,9,10]
                                                Type: List NonNegativeInteger
--R 
--R   Compiling body of rule v to compute value of type List 
--R      NonNegativeInteger 
--R   v will cache all previously computed values.
--R
--R   (4)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                Type: List NonNegativeInteger
--E 11

--S 12 of 55
n==15
 
   Compiled code for n has been cleared.
   Compiled code for v has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for v has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 12

--S 13 of 55
u
 

   (6)  [0,1,2,3,4,5,6,7,8,9,10]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (6)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                Type: List NonNegativeInteger
--E 13

--S 14 of 55
v
 
   Compiling body of rule n to compute value of type PositiveInteger 
   n will cache all previously computed values.
   Compiling body of rule v to compute value of type List 
      NonNegativeInteger 
   v will cache all previously computed values.

   (7)  [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
                                                Type: List NonNegativeInteger
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   n will cache all previously computed values.
--R   Compiling body of rule v to compute value of type List 
--R      NonNegativeInteger 
--R   v will cache all previously computed values.
--R
--R   (7)  [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
--R                                                Type: List NonNegativeInteger
--E 14

)clear all
 

--S 15 of 55
n:=2
 

   (1)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 55
m:=3
 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 55
u:=[[i*j for j in 1..n] for i in 1..m]
 

   (3)  [[1,2],[2,4],[3,6]]
                                              Type: List List PositiveInteger
--R 
--R
--R   (3)  [[1,2],[2,4],[3,6]]
--R                                              Type: List List PositiveInteger
--E 17

--S 18 of 55
n:=10
 

   (4)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  10
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 55
u
 

   (5)  [[1,2],[2,4],[3,6]]
                                              Type: List List PositiveInteger
--R 
--R
--R   (5)  [[1,2],[2,4],[3,6]]
--R                                              Type: List List PositiveInteger
--E 19

)clear all
 

--S 20 of 55
u==[i for i in m..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

)set mes test off
 

--S 21 of 55
u
 
 
   The lower bound in a loop must be an integer.
--R 
--R 
--R   The lower bound in a loop must be an integer.
--E 21

)set mes test on
 

--S 22 of 55
n:=7
 

   (2)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  7
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 55
m:=3
 

   (3)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  3
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 55
u
 
   Compiling body of rule u to compute value of type List 
      PositiveInteger 
   u will cache all previously computed values.

   (4)  [3,4,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R   Compiling body of rule u to compute value of type List 
--R      PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (4)  [3,4,5,6,7]
--R                                                   Type: List PositiveInteger
--E 24

--S 25 of 55
reduce(+,u)
 

   (5)  25
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  25
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 55
n:=2
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 55
u
 

   (7)  [3,4,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (7)  [3,4,5,6,7]
--R                                                   Type: List PositiveInteger
--E 27

--S 28 of 55
reduce(+,u)
 

   (8)  25
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  25
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 55
m:=-3
 
   Compiled code for u has been cleared.

   (9)  - 3
                                                                Type: Integer
--R 
--R   Compiled code for u has been cleared.
--R
--R   (9)  - 3
--R                                                                Type: Integer
--E 29

--S 30 of 55
u
 
   Compiling body of rule u to compute value of type List Integer 
   u will cache all previously computed values.

   (10)  [- 3,- 2,- 1,0,1,2]
                                                           Type: List Integer
--R 
--R   Compiling body of rule u to compute value of type List Integer 
--R   u will cache all previously computed values.
--R
--R   (10)  [- 3,- 2,- 1,0,1,2]
--R                                                           Type: List Integer
--E 30

--S 31 of 55
reduce(+,u)
 

   (11)  - 3
                                                                Type: Integer
--R 
--R
--R   (11)  - 3
--R                                                                Type: Integer
--E 31

)clear all
 

--S 32 of 55
u==[[i+j for i in 0..j] for j in 0..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

)set mes test off
 

--S 33 of 55
u
 
 
   The upper bound in a loop must be an integer.
--R 
--R 
--R   The upper bound in a loop must be an integer.
--E 33

)set mes test on
 

--S 34 of 55
n:=5
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 55
u
 
   Compiling body of rule u to compute value of type List List 
      NonNegativeInteger 
   u will cache all previously computed values.

   (3)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
                                           Type: List List NonNegativeInteger
--R 
--R   Compiling body of rule u to compute value of type List List 
--R      NonNegativeInteger 
--R   u will cache all previously computed values.
--R
--R   (3)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
--R                                           Type: List List NonNegativeInteger
--E 35

--S 36 of 55
n:=10
 

   (4)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  10
--R                                                        Type: PositiveInteger
--E 36

--S 37 of 55
u
 

   (5)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
                                           Type: List List NonNegativeInteger
--R 
--R
--R   (5)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
--R                                           Type: List List NonNegativeInteger
--E 37

--S 38 of 55
n:=1
 

   (6)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  1
--R                                                        Type: PositiveInteger
--E 38

--S 39 of 55
u
 

   (7)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
                                           Type: List List NonNegativeInteger
--R 
--R
--R   (7)  [[0],[1,2],[2,3,4],[3,4,5,6],[4,5,6,7,8],[5,6,7,8,9,10]]
--R                                           Type: List List NonNegativeInteger
--E 39

--S 40 of 55
n:= 0
 
   Compiled code for u has been cleared.

   (8)  0
                                                     Type: NonNegativeInteger
--R 
--R   Compiled code for u has been cleared.
--R
--R   (8)  0
--R                                                     Type: NonNegativeInteger
--E 40

--S 41 of 55
u
 
   Compiling body of rule u to compute value of type List List 
      NonNegativeInteger 
   u will cache all previously computed values.

   (9)  [[0]]
                                           Type: List List NonNegativeInteger
--R 
--R   Compiling body of rule u to compute value of type List List 
--R      NonNegativeInteger 
--R   u will cache all previously computed values.
--R
--R   (9)  [[0]]
--R                                           Type: List List NonNegativeInteger
--E 41

--S 42 of 55
n:=-1
 
   Compiled code for u has been cleared.

   (10)  - 1
                                                                Type: Integer
--R 
--R   Compiled code for u has been cleared.
--R
--R   (10)  - 1
--R                                                                Type: Integer
--E 42

--S 43 of 55
u
 
   Compiling body of rule u to compute value of type List List Integer 
   u will cache all previously computed values.

   (11)  []
                                                      Type: List List Integer
--R 
--R   Compiling body of rule u to compute value of type List List Integer 
--R   u will cache all previously computed values.
--R
--R   (11)  []
--R                                                      Type: List List Integer
--E 43

)clear all
 

)set streams calculate 10
 

--S 44 of 55
u==[[i+j for i in 0..] for j in 0..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 44

--S 45 of 55
u
 
   Compiling body of rule u to compute value of type Stream Stream 
      Integer 
   u will cache all previously computed values.

   (2)
   [[0,1,2,3,4,5,6,7,8,9,...], [1,2,3,4,5,6,7,8,9,10,...],
    [2,3,4,5,6,7,8,9,10,11,...], [3,4,5,6,7,8,9,10,11,12,...],
    [4,5,6,7,8,9,10,11,12,13,...], [5,6,7,8,9,10,11,12,13,14,...],
    [6,7,8,9,10,11,12,13,14,15,...], [7,8,9,10,11,12,13,14,15,16,...],
    [8,9,10,11,12,13,14,15,16,17,...], [9,10,11,12,13,14,15,16,17,18,...], ...]
                                                  Type: Stream Stream Integer
--R 
--R   Compiling body of rule u to compute value of type Stream Stream 
--R      Integer 
--R   u will cache all previously computed values.
--R
--R   (2)
--R   [[0,1,2,3,4,5,6,7,8,9,...], [1,2,3,4,5,6,7,8,9,10,...],
--R    [2,3,4,5,6,7,8,9,10,11,...], [3,4,5,6,7,8,9,10,11,12,...],
--R    [4,5,6,7,8,9,10,11,12,13,...], [5,6,7,8,9,10,11,12,13,14,...],
--R    [6,7,8,9,10,11,12,13,14,15,...], [7,8,9,10,11,12,13,14,15,16,...],
--R    [8,9,10,11,12,13,14,15,16,17,...], [9,10,11,12,13,14,15,16,17,18,...], ...]
--R                                                  Type: Stream Stream Integer
--E 45

)clear all
 

--S 46 of 55
u(m,n)==[[i+j for j in 1..m] for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 46

--S 47 of 55
u(3,6)
 
   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
      List List PositiveInteger 
   u will cache all previously computed values.

   (2)  [[2,3,4],[3,4,5],[4,5,6],[5,6,7],[6,7,8],[7,8,9]]
                                              Type: List List PositiveInteger
--R 
--R   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
--R      List List PositiveInteger 
--R   u will cache all previously computed values.
--R
--R   (2)  [[2,3,4],[3,4,5],[4,5,6],[5,6,7],[6,7,8],[7,8,9]]
--R                                              Type: List List PositiveInteger
--E 47

--S 48 of 55
reduce(append,u(3,6))
 

   (3)  [2,3,4,3,4,5,4,5,6,5,6,7,6,7,8,7,8,9]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [2,3,4,3,4,5,4,5,6,5,6,7,6,7,8,7,8,9]
--R                                                   Type: List PositiveInteger
--E 48

)clear all
 

--S 49 of 55
u(m,n)==[[i*j for j in m..] for i in n..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 49

--S 50 of 55
u(3,6)
 
   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
      Stream Stream Integer 
   u will cache all previously computed values.

   (2)
   [[18,24,30,36,42,48,54,60,66,72,...], [21,28,35,42,49,56,63,70,77,84,...],
    [24,32,40,48,56,64,72,80,88,96,...], [27,36,45,54,63,72,81,90,99,108,...],
    [30,40,50,60,70,80,90,100,110,120,...],
    [33,44,55,66,77,88,99,110,121,132,...],
    [36,48,60,72,84,96,108,120,132,144,...],
    [39,52,65,78,91,104,117,130,143,156,...],
    [42,56,70,84,98,112,126,140,154,168,...],
    [45,60,75,90,105,120,135,150,165,180,...], ...]
                                                  Type: Stream Stream Integer
--R 
--R   Compiling function u with type (PositiveInteger,PositiveInteger) -> 
--R      Stream Stream Integer 
--R   u will cache all previously computed values.
--R
--R   (2)
--R   [[18,24,30,36,42,48,54,60,66,72,...], [21,28,35,42,49,56,63,70,77,84,...],
--R    [24,32,40,48,56,64,72,80,88,96,...], [27,36,45,54,63,72,81,90,99,108,...],
--R    [30,40,50,60,70,80,90,100,110,120,...],
--R    [33,44,55,66,77,88,99,110,121,132,...],
--R    [36,48,60,72,84,96,108,120,132,144,...],
--R    [39,52,65,78,91,104,117,130,143,156,...],
--R    [42,56,70,84,98,112,126,140,154,168,...],
--R    [45,60,75,90,105,120,135,150,165,180,...], ...]
--R                                                  Type: Stream Stream Integer
--E 50

)clear all
 

)set streams calculate 3
 

--S 51 of 55
[[[i+j+k for i in 0..] for j in 0..] for k in 0..]
 

   (1)
   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...], ...]
                                           Type: Stream Stream Stream Integer
--R 
--R
--R   (1)
--R   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
--R    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
--R    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...], ...]
--R                                           Type: Stream Stream Stream Integer
--E 51

--S 52 of 55
n:=5
 

   (2)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  5
--R                                                        Type: PositiveInteger
--E 52

--S 53 of 55
[[[i+j+k for i in 0..] for j in 0..] for k in 0..n]
 

   (3)
   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...],
    [[3,4,5,...],[4,5,6,...],[5,6,7,...],...],
    [[4,5,6,...],[5,6,7,...],[6,7,8,...],...],
    [[5,6,7,...],[6,7,8,...],[7,8,9,...],...]]
                                             Type: List Stream Stream Integer
--R 
--R
--R   (3)
--R   [[[0,1,2,...],[1,2,3,...],[2,3,4,...],...],
--R    [[1,2,3,...],[2,3,4,...],[3,4,5,...],...],
--R    [[2,3,4,...],[3,4,5,...],[4,5,6,...],...],
--R    [[3,4,5,...],[4,5,6,...],[5,6,7,...],...],
--R    [[4,5,6,...],[5,6,7,...],[6,7,8,...],...],
--R    [[5,6,7,...],[6,7,8,...],[7,8,9,...],...]]
--R                                             Type: List Stream Stream Integer
--E 53

--S 54 of 55
[[[i+j+k for i in 0..j] for j in 0..k] for k in 0..]
 

   (4)  [[[0]],[[1],[2,3]],[[2],[3,4],[4,5,6]],...]
                                    Type: Stream List List NonNegativeInteger
--R 
--R
--R   (4)  [[[0]],[[1],[2,3]],[[2],[3,4],[4,5,6]],...]
--R                                    Type: Stream List List NonNegativeInteger
--E 54

--S 55 of 55
[[[i+j+k for i in 0..j] for j in 0..k] for k in 0..n]
 

   (5)
   [[[0]], [[1],[2,3]], [[2],[3,4],[4,5,6]], [[3],[4,5],[5,6,7],[6,7,8,9]],
    [[4],[5,6],[6,7,8],[7,8,9,10],[8,9,10,11,12]],
    [[5],[6,7],[7,8,9],[8,9,10,11],[9,10,11,12,13],[10,11,12,13,14,15]]]
                                      Type: List List List NonNegativeInteger
--R 
--R
--R   (5)
--R   [[[0]], [[1],[2,3]], [[2],[3,4],[4,5,6]], [[3],[4,5],[5,6,7],[6,7,8,9]],
--R    [[4],[5,6],[6,7,8],[7,8,9,10],[8,9,10,11,12]],
--R    [[5],[6,7],[7,8,9],[8,9,10,11],[9,10,11,12,13],[10,11,12,13,14,15]]]
--R                                      Type: List List List NonNegativeInteger
--E 55
)spool 
 
Starts dribbling to equation.output (2010/3/27, 18:25:35).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 12
eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x)
 

            3      2         4
   (1)  - 6x  + 13x  + 4= - x  + 12x
                                            Type: Equation Polynomial Integer
--R 
--R
--R            3      2         4
--R   (1)  - 6x  + 13x  + 4= - x  + 12x
--R                                            Type: Equation Polynomial Integer
--E 1

--S 2 of 12
eq2 := x**4+13*x**2-12*x = 6*x**3-4
 

         4      2          3
   (2)  x  + 13x  - 12x= 6x  - 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R         4      2          3
--R   (2)  x  + 13x  - 12x= 6x  - 4
--R                                            Type: Equation Polynomial Integer
--E 2

--S 3 of 12
eq := eq1*y**2+eq2
 

             3      2      2    4      2            4        2     3
   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R             3      2      2    4      2            4        2     3
--R   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
--R                                            Type: Equation Polynomial Integer
--E 3

--S 4 of 12
swap %
 

            4        2     3           3      2      2    4      2
   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
                                            Type: Equation Polynomial Integer
--R 
--R
--R            4        2     3           3      2      2    4      2
--R   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
--R                                            Type: Equation Polynomial Integer
--E 4

--S 5 of 12
% + 4
 

            4        2     3       3      2      2    4      2
   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R            4        2     3       3      2      2    4      2
--R   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E 5

--S 6 of 12
%-6*x**3
 

            4        2       3      2      2    4     3      2
   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R            4        2       3      2      2    4     3      2
--R   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E 6

--S 7 of 12
leftZero %
 

             4     3      2            2    4     3      2
   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
                                            Type: Equation Polynomial Integer
--R 
--R
--R             4     3      2            2    4     3      2
--R   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
--R                                            Type: Equation Polynomial Integer
--E 7

--S 8 of 12
swap %
 

          4     3      2            2    4     3      2
   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R          4     3      2            2    4     3      2
--R   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
--R                                            Type: Equation Polynomial Integer
--E 8

--S 9 of 12
factor lhs %
 

               2       2  2
   (9)  (x - 2) (x - 1) (y  + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2       2  2
--R   (9)  (x - 2) (x - 1) (y  + 1)
--R                                            Type: Factored Polynomial Integer
--E 9

--S 10 of 12
factorAndSplit eq
 

                             2
   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
                                       Type: List Equation Polynomial Integer
--R 
--R
--R                             2
--R   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
--R                                       Type: List Equation Polynomial Integer
--E 10

--S 11 of 12
inv (eq :: EQ FRAC POLY INT)
 

                             1                                1
   (11)  - ------------------------------------= - ----------------------
              3      2      2    4      2            4        2     3
           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
                                   Type: Equation Fraction Polynomial Integer
--R 
--R
--R                             1                                1
--R   (11)  - ------------------------------------= - ----------------------
--R              3      2      2    4      2            4        2     3
--R           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
--R                                   Type: Equation Fraction Polynomial Integer
--E 11

--S 12 of 12
- %
 

                           1                              1
   (12)  ------------------------------------= ----------------------
            3      2      2    4      2          4        2     3
         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
                                   Type: Equation Fraction Polynomial Integer
--R 
--R
--R                           1                              1
--R   (12)  ------------------------------------= ----------------------
--R            3      2      2    4      2          4        2     3
--R         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
--R                                   Type: Equation Fraction Polynomial Integer
--E 12
)spool
 
Starts dribbling to SquareFreeRegularTriangularSet.output (2010/3/27, 18:46:35).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 23
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 23
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 23
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 23
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 23
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 23
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 23
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 23
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 23
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 23
ST := SREGSET(R,E,V,P)
 

   (10)
  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
  r,OrderedVariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
--R  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
--R  r,OrderedVariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 23
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 23
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 23
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 23
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 23
zeroSetSplit(lp)$ST
 

            5    4      2     3     8     5    3    2   4                2
   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R            5    4      2     3     8     5    3    2   4                2
--R   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 15

--S 16 of 23
zeroSetSplit(lp,false)$ST
 

   (16)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5            2    2
    {t  - 1,z  - t,t y + z ,z x  - t}, {t,z,y,x}]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5            2    2
--R    {t  - 1,z  - t,t y + z ,z x  - t}, {t,z,y,x}]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16

--S 17 of 23
T := REGSET(R,E,V,P)
 

   (17)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (17)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
--R  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
--R  ariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 17

--S 18 of 23
lts := zeroSetSplit(lp,false)$T
 

   (18)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5          2     3         2
    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (18)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5          2     3         2
--R    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 18

--S 19 of 23
ts := lts.2
 

           3      5          2     3         2
   (19)  {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}
Type: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R           3      5          2     3         2
--R   (19)  {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}
--RType: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 19

--S 20 of 23
pol := select(ts,'y)$T
 

              2     3
   (20)  t z y  + 2z y + 1
Type: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
--R 
--R
--R              2     3
--R   (20)  t z y  + 2z y + 1
--RType: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
--E 20

--S 21 of 23
tower := collectUnder(ts,'y)$T
 

           3      5
   (21)  {t  - 1,z  - t}
Type: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R           3      5
--R   (21)  {t  - 1,z  - t}
--RType: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 21

--S 22 of 23
pack := RegularTriangularSetGcdPackage(R,E,V,P,T)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R 
--R
--R   (22)
--R  RegularTriangularSetGcdPackage(Integer,IndexedExponents OrderedVariableList [
--R  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
--R  r,OrderedVariableList [x,y,z,t]),RegularTriangularSet(Integer,IndexedExponent
--R  s OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultiv
--R  ariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--R                                                                 Type: Domain
--E 22

--S 23 of 23
toseSquareFreePart(pol,tower)$pack
 

                       2          3      5
   (22)  [[val= t y + z ,tower= {t  - 1,z  - t}]]
Type: List Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),tower: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--R 
--R
--R                       2          3      5
--R   (23)  [[val= t y + z ,tower= {t  - 1,z  - t}]]
--RType: List Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),tower: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--E 23
)spool
 
Starts dribbling to numericgamma.output (2010/3/27, 18:30:11).
)set message test on
 
)set message auto off
 
)clear all
 
)sys cp $AXIOM/../../src/input/numericgamma.input.pamphlet .
 
)lisp (tangle "numericgamma.input.pamphlet" "sfx.spad" "sfx.spad")
 
Value = NIL
)co sfx.spad
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/sfx.spad using 
      old system compiler.
   SFX abbreviates package SpecialFunctionExtended 
   processing macro definition ITMAX ==> ::((elt (Float) float)(100,Zero,10),DoubleFloat) 
   processing macro definition FPMIN ==> ::((elt (Float) float)(One,-323,10),DoubleFloat) 
   processing macro definition Exports ==> -- the constructor category 
   processing macro definition Implementation ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing nrlib SFX for SpecialFunctionExtended 
   compiling into nrlib SFX 
   compiling exported NGamma : (DoubleFloat,DoubleFloat) -> DoubleFloat
Time: 0.06 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |SpecialFunctionExtended| REDEFINED

;;;     ***       |SpecialFunctionExtended| REDEFINED
Time: 0 SEC.

 
   Warnings: 
      [1] NGamma:  d has no value
      [2] NGamma:  c has no value
 

   Cumulative Statistics for Constructor SpecialFunctionExtended
      Time: 0.06 seconds
 
   finalizing nrlib SFX 
   Processing SpecialFunctionExtended for Browser database:
--->-->SpecialFunctionExtended((NGamma ((DoubleFloat) (DoubleFloat) (DoubleFloat)))): Not documented!!!!
--->-->SpecialFunctionExtended(constructor): Not documented!!!!
--->-->SpecialFunctionExtended(): Missing Description
------------------------------------------------------------------------
   SpecialFunctionExtended is now explicitly exposed in frame initial 
   SpecialFunctionExtended will be automatically loaded when needed 
      from 
      /home/camm/debian/axiom/axiom-20091101/int/input/SFX.nrlib/code


--S 1 of 36
Gam(a:Float,x:Float):Float ==
  if x < 0.0 or a < 0.0 then error "Invalid arguments"
  if x = 0.0 then return Gamma(a)

  ITMAX ==> 100        -- Maximum allowed number of iterations
  FPMIN ==> 1.0e-1000  -- near the smallest representable number
                       -- (there is no smallest representable float)

  EPS := (10.0^(-digits()$Float+1))$Float  -- Relative accuracy

  an: Float
  del: Float

  b:Float:=x+1.0-a     -- Set up for evaluating continued fractions
  c:Float:=1.0/FPMIN   -- by modified Lentz's method
  d:Float:=1.0/b       -- with b_0 = 0
  h:Float:=d
  i:=1
  repeat               -- iterate to convergence
    an:=-i*(i-a)
    b:=b+2.0
    d:=an*d+b
    if abs(d) < FPMIN then d:=FPMIN
    c:=b+an/c;
    if abs(c) < FPMIN then c:=FPMIN
    d:=1.0/d
    del:=d*c
    h:=h*del
    if i > ITMAX or abs(del-1.0) < EPS then break
    i:=i+1
  if i > ITMAX then error("a too large, ITMAX too small")
  exp(-x)*x^a*h        -- put factors in front
 
   Function declaration Gam : (Float,Float) -> Float has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration Gam : (Float,Float) -> Float has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 36
Gam(0,1)
 
   Compiling function Gam with type (Float,Float) -> Float 
 
Daly Bug
   Error signalled from user code in function Gam: 
      a too large, ITMAX too small
--R 
--R   Compiling function Gam with type (Float,Float) -> Float 
--R 
--RDaly Bug
--R   Error signalled from user code in function Gam: 
--R      a too large, ITMAX too small
--E 2

--S 3 of 36
Gam(1.1.1)
 
   There are 1 exposed and 1 unexposed library operations named elt 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op elt
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find application of object of type Float to argument(s) of 
      type(s) 
                                    Float
      
--R 
--R   There are 1 exposed and 1 unexposed library operations named elt 
--R      having 1 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op elt
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find application of object of type Float to argument(s) of 
--R      type(s) 
--R                                    Float
--R      
--E 3

--S 4 of 36
Gam(5,10)
 

   (2)  0.7020645138 4706574415
                                                                  Type: Float
--R 
--R
--R   (2)  0.7020645138 4706574415
--R                                                                  Type: Float
--E 4

--S 5 of 36
Gam(5,11)
 

   (3)  0.3625104156 5228203538
                                                                  Type: Float
--R 
--R
--R   (3)  0.3625104156 5228203538
--R                                                                  Type: Float
--E 5

--S 6 of 36
Gam(7,0)
 

   (4)  720.0000000000 0011369
                                                                  Type: Float
--R 
--R
--R   (4)  720.0000000000 0011369
--R                                                                  Type: Float
--E 6

--S 7 of 36
digits 100
 

   (5)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  20
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 36
Gam(0,1)
 
 
Daly Bug
   Error signalled from user code in function Gam: 
      a too large, ITMAX too small
--R 
--R 
--RDaly Bug
--R   Error signalled from user code in function Gam: 
--R      a too large, ITMAX too small
--E 8

--S 9 of 36
Gam(1,1.1)
 

   (6)
  0.3328710836 9807955328 8846906431 3155216124 7952156921 2491793331 386750747
  0 8541284431 1612617072 7005478519
                                                                  Type: Float
--R 
--R
--R   (6)
--R  0.3328710836 9807955328 8846906431 3155216124 7952156921 2491793331 386750747
--R  0 8541284431 1612617072 7005478519
--R                                                                  Type: Float
--E 9

--S 10 of 36
Gam(1,1)
 

   (7)
  0.3678794411 7144232159 5523770161 4608674458 1113103176 7834507836 801697461
  4 9574489980 3357147274 3459196437
                                                                  Type: Float
--R 
--R
--R   (7)
--R  0.3678794411 7144232159 5523770161 4608674458 1113103176 7834507836 801697461
--R  4 9574489980 3357147274 3459196437
--R                                                                  Type: Float
--E 10

--S 11 of 36
Gam(1,1.1)
 

   (8)
  0.3328710836 9807955328 8846906431 3155216124 7952156921 2491793331 386750747
  0 8541284431 1612617072 7005478519
                                                                  Type: Float
--R 
--R
--R   (8)
--R  0.3328710836 9807955328 8846906431 3155216124 7952156921 2491793331 386750747
--R  0 8541284431 1612617072 7005478519
--R                                                                  Type: Float
--E 11

--S 12 of 36
Gam(5,10)
 

   (9)
  0.7020645138 4706574414 6387196628 3546367191 6532623256 0684622278 670587055
  0 5584357048 3474646670 2985365058
                                                                  Type: Float
--R 
--R
--R   (9)
--R  0.7020645138 4706574414 6387196628 3546367191 6532623256 0684622278 670587055
--R  0 5584357048 3474646670 2985365058
--R                                                                  Type: Float
--E 12

--S 13 of 36
Gam(5,11)
 

   (10)
  0.3625104156 5228203538 0753904311 4079803866 4530925132 7036797697 419049037
  4 2658968752 0305953551 1648548436
                                                                  Type: Float
--R 
--R
--R   (10)
--R  0.3625104156 5228203538 0753904311 4079803866 4530925132 7036797697 419049037
--R  4 2658968752 0305953551 1648548436
--R                                                                  Type: Float
--E 13


--S 14 of 36
Gam(7,0)
 

   (11)  720.0000000000 0011368683 7721616029 7393798828 125
                                                                  Type: Float
--R 
--R
--R   (11)  720.0000000000 0011368683 7721616029 7393798828 125
--R                                                                  Type: Float
--E 14

--S 15 of 36
Gam(7,0.1)
 

   (12)
  719.9999999869 1035963050 9717349089 5137595484 2683243460 6577519316 5312727
  417 6619922456 9102294155 8764196
                                                                  Type: Float
--R 
--R
--R   (12)
--R  719.9999999869 1035963050 9717349089 5137595484 2683243460 6577519316 5312727
--R  417 6619922456 9102294155 8764196
--R                                                                  Type: Float
--E 15

--S 16 of 36
Gam(7,0.2)
 

   (13)
  719.9999984646 1597708521 8246915701 3222705579 4693807497 2229652513 6047137
  980 7138425860 0596921944 0451807
                                                                  Type: Float
--R 
--R
--R   (13)
--R  719.9999984646 1597708521 8246915701 3222705579 4693807497 2229652513 6047137
--R  980 7138425860 0596921944 0451807
--R                                                                  Type: Float
--E 16


--S 17 of 36
NGamma(a,x)
 
   There are 1 exposed and 0 unexposed library operations named NGamma 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op NGamma
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      NGamma with argument type(s) 
                                 Variable a
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 1 exposed and 0 unexposed library operations named NGamma 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                             )display op NGamma
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      NGamma with argument type(s) 
--R                                 Variable a
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17

--S 18 of 36
NGamma(0,1)
 

   (14)  0.21938393439551901
                                                            Type: DoubleFloat
--R 
--R
--R   (14)  0.21938393439551901
--R                                                            Type: DoubleFloat
--E 18

--S 19 of 36
NGamma(0,2)
 

   (15)  4.8900510708060993E-2
                                                            Type: DoubleFloat
--R 
--R
--R   (15)  4.8900510708060993E-2
--R                                                            Type: DoubleFloat
--E 19

--S 20 of 36
NGamma(1,1)
 

   (16)  0.36787944117144233
                                                            Type: DoubleFloat
--R 
--R
--R   (16)  0.36787944117144233
--R                                                            Type: DoubleFloat
--E 20

--S 21 of 36
NGamma(1,1.1)
 

   (17)  0.33287108369807955
                                                            Type: DoubleFloat
--R 
--R
--R   (17)  0.33287108369807966
--R                                                            Type: DoubleFloat
--E 21

--S 22 of 36
NGamma(5,10)
 

   (18)  0.70206451384706692
                                                            Type: DoubleFloat
--R 
--R
--R   (18)  0.70206451384706692
--R                                                            Type: DoubleFloat
--E 22

--S 23 of 36
NGamma(5,11)
 

   (19)  0.36251041565228215
                                                            Type: DoubleFloat
--R 
--R
--R   (19)  0.36251041565228215
--R                                                            Type: DoubleFloat
--E 23

--S 24 of 36
NGamma(7,0)
 

   (20)  720.00000000000011
                                                            Type: DoubleFloat
--R 
--R
--R   (20)  720.00000000000011
--R                                                            Type: DoubleFloat
--E 24

--S 25 of 36
NGamma(7,0.1)
 

   (21)  719.99620051670547
                                                            Type: DoubleFloat
--R 
--R
--R   (21)  719.99620051670286
--R                                                            Type: DoubleFloat
--E 25

--S 26 of 36
NGamma(7,0.2)
 

   (22)  719.99974844402982
                                                            Type: DoubleFloat
--R 
--R
--R   (22)  719.99974844402846
--R                                                            Type: DoubleFloat
--E 26

)set functions compile on
 

--S 27 of 36
j:=120
 

   (23)  120
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  120
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 36
nume(a) == cons(1::Float,[((a-i)*i)::Float for i in 1..])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 36
dene(a,x) == [(x+2*i+1-a)::Float for i in 0..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 36
cfe(a,x) == continuedFraction(0,nume(a),dene(a,x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 36
ccfe(a,x) == convergents cfe(a,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 36
gamcfe(a,x) == exp(-x)*x^a*(ccfe(a,x).j)::Float
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 36
gamcfe(2,3)
 
   Compiling function nume with type PositiveInteger -> Stream Float 
   Compiling function dene with type (PositiveInteger,PositiveInteger)
       -> Stream Float 
   Compiling function cfe with type (PositiveInteger,PositiveInteger)
       -> ContinuedFraction Float 
   Compiling function ccfe with type (PositiveInteger,PositiveInteger)
       -> Stream Fraction Float 
   Compiling function gamcfe with type (PositiveInteger,PositiveInteger
      ) -> Expression Float 

   (29)
  0.1991482734 7145577191 7369662600 2471065267 9836875369 2862270510 910424242
  6 7092079820 0616216976 9465333782
                                                       Type: Expression Float
--R 
--R   Compiling function nume with type PositiveInteger -> Stream Float 
--R   Compiling function dene with type (PositiveInteger,PositiveInteger)
--R       -> Stream Float 
--R   Compiling function cfe with type (PositiveInteger,PositiveInteger)
--R       -> ContinuedFraction Float 
--R   Compiling function ccfe with type (PositiveInteger,PositiveInteger)
--R       -> Stream Fraction Float 
--R   Compiling function gamcfe with type (PositiveInteger,PositiveInteger
--R      ) -> Expression Float 
--R
--R   (29)
--R  0.1991482734 7145577191 7369662600 2471065267 9836875369 2862270510 910424242
--R  6 7092079820 0616216976 9465333782
--R                                                       Type: Expression Float
--E 33

--S 34 of 36
E1fun(x) == gamcfe(0,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 36
E1fun(2.0)
 
   Compiling function nume with type NonNegativeInteger -> Stream Float
      
   Compiling function dene with type (NonNegativeInteger,Float) -> 
      Stream Float 
   Compiling function cfe with type (NonNegativeInteger,Float) -> 
      ContinuedFraction Float 
   Compiling function ccfe with type (NonNegativeInteger,Float) -> 
      Stream Fraction Float 
   Compiling function gamcfe with type (NonNegativeInteger,Float) -> 
      Float 
   Compiling function E1fun with type Float -> Float 

   (31)
  0.0489005107 0806111956 7239826914 3472898212 1544510421 3277251841 716377988
  0 9149832755 9949235928 1965882172 4
                                                                  Type: Float
--R 
--R   Compiling function nume with type NonNegativeInteger -> Stream Float
--R      
--R   Compiling function dene with type (NonNegativeInteger,Float) -> 
--R      Stream Float 
--R   Compiling function cfe with type (NonNegativeInteger,Float) -> 
--R      ContinuedFraction Float 
--R   Compiling function ccfe with type (NonNegativeInteger,Float) -> 
--R      Stream Fraction Float 
--R   Compiling function gamcfe with type (NonNegativeInteger,Float) -> 
--R      Float 
--R   Compiling function E1fun with type Float -> Float 
--R
--R   (31)
--R  0.0489005107 0806111956 7239826914 3472898212 1544510421 3277251841 716377988
--R  0 9149832755 9949235928 1965882172 4
--R                                                                  Type: Float
--E 35

--S 36 of 36
E1fun(2.0)-E1(2.0)
 

   (32)  1.1102230246251565E-16
                                         Type: OnePointCompletion DoubleFloat
--R 
--R
--R   (32)  1.1102230246251565E-16
--R                                         Type: OnePointCompletion DoubleFloat
--E 36

)spool 
 
Starts dribbling to Expression.output (2010/3/27, 18:41:59).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 23
sin(x) + 3*cos(x)**2
 

                        2
   (1)  sin(x) + 3cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (1)  sin(x) + 3cos(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 23
tan(x) - 3.45*x
 

   (2)  tan(x) - 3.45 x
                                                       Type: Expression Float
--R 
--R
--R   (2)  tan(x) - 3.45 x
--R                                                       Type: Expression Float
--E 2

--S 3 of 23
(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))
 

               +-+ 2         +--+      +-+         +--+ 2
        - tan(\|7 )  + 2sin(\|11 )tan(\|7 ) - sin(\|11 )
   (3)  -------------------------------------------------
                          cos(y - x) - 4
                                                     Type: Expression Integer
--R 
--R
--R               +-+ 2         +--+      +-+         +--+ 2
--R        - tan(\|7 )  + 2sin(\|11 )tan(\|7 ) - sin(\|11 )
--R   (3)  -------------------------------------------------
--R                          cos(y - x) - 4
--R                                                     Type: Expression Integer
--E 3

--S 4 of 23
log(exp  x)@Expression(Integer)
 

   (4)  x
                                                     Type: Expression Integer
--R 
--R
--R   (4)  x
--R                                                     Type: Expression Integer
--E 4

--S 5 of 23
log(exp  x)@Expression(Complex Integer)
 

              x
   (5)  log(%e )
                                             Type: Expression Complex Integer
--R 
--R
--R              x
--R   (5)  log(%e )
--R                                             Type: Expression Complex Integer
--E 5

--S 6 of 23
sqrt 3 + sqrt(2 + sqrt(-5))
 

         +----------+
         | +---+         +-+
   (6)  \|\|- 5  + 2  + \|3
                                                        Type: AlgebraicNumber
--R 
--R
--R         +----------+
--R         | +---+         +-+
--R   (6)  \|\|- 5  + 2  + \|3
--R                                                        Type: AlgebraicNumber
--E 6

--S 7 of 23
% :: Expression Integer
 

         +----------+
         | +---+         +-+
   (7)  \|\|- 5  + 2  + \|3
                                                     Type: Expression Integer
--R 
--R
--R         +----------+
--R         | +---+         +-+
--R   (7)  \|\|- 5  + 2  + \|3
--R                                                     Type: Expression Integer
--E 7

--S 8 of 23
height mainKernel sin(x + 4)
 

   (8)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  2
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 23
e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) ) 
 

                2
        - sin(x)  + 8sin(x) - 16
   (9)  ------------------------
                 +---+
              2y\|- y  - 1
                                                     Type: Expression Integer
--R 
--R
--R                2
--R        - sin(x)  + 8sin(x) - 16
--R   (9)  ------------------------
--R                 +---+
--R              2y\|- y  - 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 23
numer e 
 

                 2
   (10)  - sin(x)  + 8sin(x) - 16
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R
--R                 2
--R   (10)  - sin(x)  + 8sin(x) - 16
--R        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 10

--S 11 of 23
denom e
 

            +---+
   (11)  2y\|- y  - 1
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R
--R            +---+
--R   (11)  2y\|- y  - 1
--R        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 11

--S 12 of 23
D(e, x) 
 

                                        +---+
         (4y cos(x)sin(x) - 16y cos(x))\|- y  - 2cos(x)sin(x) + 8cos(x)
   (12)  --------------------------------------------------------------
                                  +---+     3
                               4y\|- y  + 4y  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                        +---+
--R         (4y cos(x)sin(x) - 16y cos(x))\|- y  - 2cos(x)sin(x) + 8cos(x)
--R   (12)  --------------------------------------------------------------
--R                                  +---+     3
--R                               4y\|- y  + 4y  - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 23
D(e, [x, y], [1, 2])
 

   (13)
                7       4                      7        4         +---+
       ((- 2304y  + 960y )cos(x)sin(x) + (9216y  - 3840y )cos(x))\|- y
     + 
              9        6       3
       (- 960y  + 2160y  - 180y  - 3)cos(x)sin(x)
     + 
             9        6       3
       (3840y  - 8640y  + 720y  + 12)cos(x)
  /
            12        9        6       3      +---+        11        8       5
       (256y   - 1792y  + 1120y  - 112y  + 1)\|- y  - 1024y   + 1792y  - 448y
     + 
          2
       16y
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R                7       4                      7        4         +---+
--R       ((- 2304y  + 960y )cos(x)sin(x) + (9216y  - 3840y )cos(x))\|- y
--R     + 
--R              9        6       3
--R       (- 960y  + 2160y  - 180y  - 3)cos(x)sin(x)
--R     + 
--R             9        6       3
--R       (3840y  - 8640y  + 720y  + 12)cos(x)
--R  /
--R            12        9        6       3      +---+        11        8       5
--R       (256y   - 1792y  + 1120y  - 112y  + 1)\|- y  - 1024y   + 1792y  - 448y
--R     + 
--R          2
--R       16y
--R                                                     Type: Expression Integer
--E 13

--S 14 of 23
complexNumeric(cos(2 - 3*%i))
 

   (14)  - 4.1896256909 688072301 + 9.1092278937 55336598 %i
                                                          Type: Complex Float
--R 
--R
--R   (14)  - 4.1896256909 688072301 + 9.1092278937 55336598 %i
--R                                                          Type: Complex Float
--E 14

--S 15 of 23
numeric(tan 3.8)
 

   (15)  0.7735560905 0312607286
                                                                  Type: Float
--R 
--R
--R   (15)  0.7735560905 0312607286
--R                                                                  Type: Float
--E 15

--S 16 of 23
e2 := cos(x**2 - y + 3) 
 

                  2
   (16)  cos(y - x  - 3)
                                                     Type: Expression Integer
--R 
--R
--R                  2
--R   (16)  cos(y - x  - 3)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 23
e3 := asin(e2) - %pi/2
 

                2
   (17)  - y + x  + 3
                                                     Type: Expression Integer
--R 
--R
--R                2
--R   (17)  - y + x  + 3
--R                                                     Type: Expression Integer
--E 17

--S 18 of 23
e3 :: Polynomial Integer
 

                2
   (18)  - y + x  + 3
                                                     Type: Polynomial Integer
--R 
--R
--R                2
--R   (18)  - y + x  + 3
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 23
e3 :: DMP([x, y], Integer) 
 

          2
   (19)  x  - y + 3
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R          2
--R   (19)  x  - y + 3
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 19

--S 20 of 23
sin %pi
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 20

--S 21 of 23
cos(%pi / 4)
 

          +-+
         \|2
   (21)  ----
           2
                                                     Type: Expression Integer
--R 
--R
--R          +-+
--R         \|2
--R   (21)  ----
--R           2
--R                                                     Type: Expression Integer
--E 21

--S 22 of 23
tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1 
 

               6          4          2
   (22)  tan(x)  + 3tan(x)  + 3tan(x)  + 1
                                                     Type: Expression Integer
--R 
--R
--R               6          4          2
--R   (22)  tan(x)  + 3tan(x)  + 3tan(x)  + 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 23
simplify % 
 

            1
   (23)  -------
               6
         cos(x)
                                                     Type: Expression Integer
--R 
--R
--R            1
--R   (23)  -------
--R               6
--R         cos(x)
--R                                                     Type: Expression Integer
--E 23
)spool
 
Starts dribbling to RegularTriangularSet.output (2010/3/27, 18:46:29).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 34
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 34
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 34
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 34
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 34
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 34
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 34
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 34
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 34
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 34
T := REGSET(R,E,V,P)
 

   (10)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
--R  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
--R  ariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 34
p1 := x ** 31 - x ** 6 - x - y 
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 34
p2 := x ** 8  - z 
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 34
p3 := x ** 10 - t 
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 34
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 34
zeroSetSplit(lp)$T
 

            5    4      2     3     8     5    3    2   4                2
   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R            5    4      2     3     8     5    3    2   4                2
--R   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 15

--S 16 of 34
lts := zeroSetSplit(lp,false)$T
 

   (16)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5          2     3         2
    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5          2     3         2
--R    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16

--S 17 of 34
[coHeight(ts) for ts in lts]
 

   (17)  [1,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (17)  [1,0,0]
--R                                                Type: List NonNegativeInteger
--E 17

--S 18 of 34
f1 := y**2*z+2*x*y*t-2*x-z
 

                          2
   (18)  (2t y - 2)x + z y  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                          2
--R   (18)  (2t y - 2)x + z y  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 18

--S 19 of 34
f2:=-x**3*z+ 4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2
 

              3              2        2              3      2
   (19)  - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R              3              2        2              3      2
--R   (19)  - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 19

--S 20 of 34
f3 :=  2*y*z*t+x*t**2-x-2*z 
 

           2
   (20)  (t  - 1)x + 2t z y - 2z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           2
--R   (20)  (t  - 1)x + 2t z y - 2z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 20

--S 21 of 34
f4:=-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t- 10*t**2+2
 

             3      2                2     3             2      2
   (21)  (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R             3      2                2     3             2      2
--R   (21)  (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 21

--S 22 of 34
lf := [f1, f2, f3, f4]
 

   (22)
                     2
   [(2t y - 2)x + z y  - z,
         3              2        2              3      2
    - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2,
      2
    (t  - 1)x + 2t z y - 2z,
        3      2                2     3             2      2
    (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (22)
--R                     2
--R   [(2t y - 2)x + z y  - z,
--R         3              2        2              3      2
--R    - z x  + (4t y + 4)x  + (4z y  + 4z)x + 2t y  - 10y  - 10t y + 2,
--R      2
--R    (t  - 1)x + 2t z y - 2z,
--R        3      2                2     3             2      2
--R    (- z  + (4t  + 4)z)x + (4t z  + 2t  - 10t)y + 4z  - 10t  + 2]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 22

--S 23 of 34
zeroSetSplit(lf)$T
 

   (23)
      2      8      6       2                 3            2
   [{t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
       2      2     2
    {3t  + 1,z  - 7t  - 1,y + t,x + z},
      8      6      2         3            2
    {t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
      2      2
    {t  + 3,z  - 4,y + t,x - z}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (23)
--R      2      8      6       2                 3            2
--R   [{t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
--R       2      2     2
--R    {3t  + 1,z  - 7t  - 1,y + t,x + z},
--R      8      6      2         3            2
--R    {t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
--R      2      2
--R    {t  + 3,z  - 4,y + t,x - z}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 23

--S 24 of 34
lts2 := zeroSetSplit(lf,false)$T
 

   (24)
      8      6      2         3            2
   [{t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
      2      8      6       2                 3            2
    {t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
       2      2     2                     2      2
    {3t  + 1,z  - 7t  - 1,y + t,x + z}, {t  + 3,z  - 4,y + t,x - z}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (24)
--R      8      6      2         3            2
--R   [{t  - 10t  + 10t  - 1,z,(t  - 5t)y - 5t  + 1,x},
--R      2      8      6       2                 3            2
--R    {t  - 1,z  - 16z  + 256z  - 256,t y - 1,(z  - 8z)x - 8z  + 16},
--R       2      2     2                     2      2
--R    {3t  + 1,z  - 7t  - 1,y + t,x + z}, {t  + 3,z  - 4,y + t,x - z}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 24

--S 25 of 34
[coHeight(ts) for ts in lts2]
 

   (25)  [0,0,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (25)  [0,0,0,0]
--R                                                Type: List NonNegativeInteger
--E 25

--S 26 of 34
degrees := [degree(ts) for ts in lts2]
 

   (26)  [8,16,4,4]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (26)  [8,16,4,4]
--R                                                Type: List NonNegativeInteger
--E 26

--S 27 of 34
reduce(+,degrees)
 

   (27)  32
                                                        Type: PositiveInteger
--R 
--R
--R   (27)  32
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 34
u : R := 2 
 

   (28)  2
                                                                Type: Integer
--R 
--R
--R   (28)  2
--R                                                                Type: Integer
--E 28

--S 29 of 34
q1 := 2*(u-1)**2+ 2*(x-z*x+z**2)+ y**2*(x-1)**2- 2*u*x+ 2*y*t*(1-x)*(x-z)+_
      2*u*z*t*(t-y)+ u**2*t**2*(1-2*z)+ 2*u*t**2*(z-x)+ 2*u*t*y*(z-1)+_
      2*u*z*x*(y+1)+ (u**2-2*u)*z**2*t**2+ 2*u**2*z**2+ 4*u*(1-u)*z+_
      t**2*(z-x)**2
 

   (29)
       2           2  2        2                            2           2
     (y  - 2t y + t )x  + (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x
   + 
      2                      2       2          2
     y  + (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (29)
--R       2           2  2        2                            2           2
--R     (y  - 2t y + t )x  + (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x
--R   + 
--R      2                      2       2          2
--R     y  + (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 29

--S 30 of 34
q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+_
      u*y*(x+u-z*x-1)+ u*(u+1)*z**2*t
 

                                               2
   (30)  (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                                               2
--R   (30)  (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 30

--S 31 of 34
q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1)
 

                         2
   (31)  (- 2z - 2)x - 2z  + 8z - 2
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R                         2
--R   (31)  (- 2z - 2)x - 2z  + 8z - 2
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 31

--S 32 of 34
q4 := u**2+4*(z-x**2)+3*y**2*(x-1)**2- 3*t**2*(z-x)**2+_
      3*u**2*t**2*(z-1)**2+u**2*z*(z-2)+6*u*t*y*(z+x+z*x-1)
 

   (32)
        2     2      2        2                      2        2
     (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y  + (12t z - 12t)y
   + 
        2      2         2            2
     (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (32)
--R        2     2      2        2                      2        2
--R     (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y  + (12t z - 12t)y
--R   + 
--R        2      2         2            2
--R     (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 32

--S 33 of 34
lq := [q1, q2, q3, q4]
 

   (33)
   [
         2           2  2
       (y  - 2t y + t )x
     + 
            2                            2           2          2
       (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x + y
     + 
                          2       2          2
       (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
     ,
                                          2                         2
    (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z, (- 2z - 2)x - 2z  + 8z - 2,

          2     2      2        2                      2        2
       (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y
     + 
                           2      2         2            2
       (12t z - 12t)y + (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
     ]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (33)
--R   [
--R         2           2  2
--R       (y  - 2t y + t )x
--R     + 
--R            2                            2           2          2
--R       (- 2y  + ((2t + 4)z + 2t)y + (- 2t  + 2)z - 4t  - 2)x + y
--R     + 
--R                          2       2          2
--R       (- 2t z - 4t)y + (t  + 10)z  - 8z + 4t  + 2
--R     ,
--R                                          2                         2
--R    (- 3z y + 2t z + t)x + (z + 4)y + 4t z  - 7t z, (- 2z - 2)x - 2z  + 8z - 2,
--R
--R          2     2      2        2                      2        2
--R       (3y  - 3t  - 4)x  + (- 6y  + (12t z + 12t)y + 6t z)x + 3y
--R     + 
--R                           2      2         2            2
--R       (12t z - 12t)y + (9t  + 4)z  + (- 24t  - 4)z + 12t  + 4
--R     ]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 33

--S 34 of 34
zeroSetSplit(lq,true,true)$T
 
[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; {0}][2 <4,1>,<3,1> -> |7|; {0}][1 <3,1> -> |3|; {0}]G[2 <4,1>,<4,1> -> |8|; {0}]W[3 <5,1>,<4,1>,<3,2> -> |12|; {0}]GI[3 <4,2>,<4,1>,<3,2> -> |11|; {0}]GWw[3 <4,1>,<3,2>,<5,2> -> |12|; {0}][3 <3,2>,<3,2>,<5,2> -> |11|; {0}]GIwWWWw[4 <3,2>,<4,2>,<5,2>,<2,3> -> |14|; {0}][4 <2,2>,<4,2>,<5,2>,<2,3> -> |13|; {0}]Gwww[5 <3,2>,<3,2>,<4,2>,<5,2>,<2,3> -> |17|; {0}]Gwwwwww[8 <3,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}]Gwwwwww[8 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |31|; {0}][8 <3,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}][8 <2,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |29|; {0}][8 <1,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |28|; {0}][7 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |27|; {0}][6 <4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |23|; {0}][5 <4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |19|; {0}]GIGIWwww[6 <5,2>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |23|; {0}][6 <4,3>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |22|; {0}]GIGI[6 <3,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |21|; {0}][6 <2,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |20|; {0}]GGG[5 <4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |18|; {0}]GIGIWwwwW[6 <5,2>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |22|; {0}][6 <4,3>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |21|; {0}]GIwwWwWWWWWWWwWWWWwwwww[8 <4,2>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][8 <3,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}][8 <2,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |25|; {0}]Gwwwwwwwwwwwwwwwwwwww[9 <5,2>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |29|; {0}]GI[9 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |28|; {0}][9 <3,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][9 <2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}]GGwwwwwwwwwwwwWWwwwwwwww[11 <3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {0}][11 <2,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {0}][11 <1,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |31|; {0}]GGGwwwwwwwwwwwww[12 <2,3>,<2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {0}]GGwwwwwwwwwwwww[13 <3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}]Gwwwwwwwwwwwww[13 <2,3>,<3,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]GGGwwwwwwwwwwwww[15 <3,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {0}][14 <4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {0}]GIGGGGIGGI[14 <3,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GGG[14 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}][14 <1,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}]GGG[13 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]Gwwwwwwwwwwwww[15 <3,3>,<3,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]Gwwwwwwwwwwwww[15 <4,3>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |49|; {0}]GIGI[15 <3,4>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]G[14 <4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {0}][13 <3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]Gwwwwwwwwwwwww[13 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GIGGGGIGGI[13 <3,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]GGGGGGGG[13 <2,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}][13 <1,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}][13 <0,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}][12 <4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][11 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {1}][10 <3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |30|; {1}][10 <2,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |29|; {1}]GGGwwwwwwwwwwwww[11 <3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {1}]GGGwwwwwwwwwwwww[12 <4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}]Gwwwwwwwwwwwww[12 <3,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]GGwwwwwwwwwwwww[13 <5,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}]GIGGGGIGGIW[13 <4,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GGW[13 <3,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {1}]GGG[12 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]Gwwwwwwwwwwwww[12 <4,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]Gwwwwwwwwwwwww[13 <5,3>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {1}]GIGIW[13 <4,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {1}][13 <3,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}][13 <2,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GG[12 <5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {1}]GIGGGGIGGIW[12 <4,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]GGGGGGW[12 <3,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}][12 <2,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][12 <1,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |37|; {1}]GGG[11 <4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |36|; {1}][10 <5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {1}][9 <3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |27|; {1}]W[9 <2,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |26|; {1}][9 <1,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |25|; {1}][8 <3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |24|; {1}]W[8 <2,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}][8 <1,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][7 <4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]w[7 <3,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}][7 <2,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}][7 <1,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}][6 <2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}]GGwwwwww[7 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]GIW[7 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}]GG[6 <3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]Gwwwwww[7 <4,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}]GIW[7 <3,4>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][6 <4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}]GIW[6 <3,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]GGW[6 <2,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}][6 <1,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |16|; {1}]GGG[5 <3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |15|; {1}]GIW[5 <2,4>,<3,3>,<3,3>,<3,4>,<3,4> -> |14|; {1}]GG[4 <3,3>,<3,3>,<3,4>,<3,4> -> |12|; {1}][3 <3,3>,<3,4>,<3,4> -> |9|; {1}]W[3 <2,4>,<3,4>,<3,4> -> |8|; {1}][3 <1,4>,<3,4>,<3,4> -> |7|; {1}]G[2 <3,4>,<3,4> -> |6|; {1}]G[1 <3,4> -> |3|; {1}][1 <2,4> -> |2|; {1}][1 <1,4> -> |1|; {1}]
   *** QCMPACK Statistics ***
      Table     size:  36
      Entries reused:  255

   *** REGSETGCD: Gcd Statistics ***
      Table     size:  125
      Entries reused:  0

   *** REGSETGCD: Inv Set Statistics ***
      Table     size:  30
      Entries reused:  0

   (34)
   [
     {
                         24                   23                    22
         960725655771966t   + 386820897948702t   + 8906817198608181t
       + 
                          21                     20                    19
         2704966893949428t   + 37304033340228264t   + 7924782817170207t
       + 
                           18                     17                      16
         93126799040354990t   + 13101273653130910t   + 156146250424711858t
       + 
                           15                      14                     13
         16626490957259119t   + 190699288479805763t   + 24339173367625275t
       + 
                            12                     11                      10
         180532313014960135t   + 35288089030975378t   + 135054975747656285t
       + 
                           9                     8                     7
         34733736952488540t  + 75947600354493972t  + 19772555692457088t
       + 
                           6                    5                    4
         28871558573755428t  + 5576152439081664t  + 6321711820352976t
       + 
                       3                   2
       438314209312320t  + 581105748367008t  - 60254467992576t + 1449115951104
       ,

                                                                         23
             26604210869491302385515265737052082361668474181372891857784t
           + 
                                                                          22
             443104378424686086067294899528296664238693556855017735265295t
           + 
                                                                          21
             279078393286701234679141342358988327155321305829547090310242t
           + 
                                                                           20
             3390276361413232465107617176615543054620626391823613392185226t
           + 
                                                                          19
             941478179503540575554198645220352803719793196473813837434129t
           + 
                                                                            18
             11547855194679475242211696749673949352585747674184320988144390t
           + 
                                                                           17
             1343609566765597789881701656699413216467215660333356417241432t
           + 
                                                                            16
             23233813868147873503933551617175640859899102987800663566699334t
           + 
                                                                          15
             869574020537672336950845440508790740850931336484983573386433t
           + 
                                                                            14
             31561554305876934875419461486969926554241750065103460820476969t
           + 
                                                                           13
             1271400990287717487442065952547731879554823889855386072264931t
           + 
                                                                            12
             31945089913863736044802526964079540198337049550503295825160523t
           + 
                                                                           11
             3738735704288144509871371560232845884439102270778010470931960t
           + 
                                                                            10
             25293997512391412026144601435771131587561905532992045692885927t
           + 
                                                                           9
             5210239009846067123469262799870052773410471135950175008046524t
           + 
                                                                            8
             15083887986930297166259870568608270427403187606238713491129188t
           + 
                                                                           7
             3522087234692930126383686270775779553481769125670839075109000t
           + 
                                                                           6
             6079945200395681013086533792568886491101244247440034969288588t
           + 
                                                                           5
             1090634852433900888199913756247986023196987723469934933603680t
           + 
                                                                           4
             1405819430871907102294432537538335402102838994019667487458352t
           + 
                                                                         3
             88071527950320450072536671265507748878347828884933605202432t
           + 
                                                                          2
             135882489433640933229781177155977768016065765482378657129440t
           + 
             - 13957283442882262230559894607400314082516690749975646520320t
           + 
             334637692973189299277258325709308472592117112855749713920
        *
           z
       + 
                                                                    23
         8567175484043952879756725964506833932149637101090521164936t
       + 
                                                                      22
         149792392864201791845708374032728942498797519251667250945721t
       + 
                                                                     21
         77258371783645822157410861582159764138123003074190374021550t
       + 
                                                                       20
         1108862254126854214498918940708612211184560556764334742191654t
       + 
                                                                      19
         213250494460678865219774480106826053783815789621501732672327t
       + 
                                                                       18
         3668929075160666195729177894178343514501987898410131431699882t
       + 
                                                                      17
         171388906471001872879490124368748236314765459039567820048872t
       + 
                                                                       16
         7192430746914602166660233477331022483144921771645523139658986t
       + 
                                                                        15
         - 128798674689690072812879965633090291959663143108437362453385t
       + 
                                                                       14
         9553010858341425909306423132921134040856028790803526430270671t
       + 
                                                                       13
         - 13296096245675492874538687646300437824658458709144441096603t
       + 
                                                                       12
         9475806805814145326383085518325333106881690568644274964864413t
       + 
                                                                      11
         803234687925133458861659855664084927606298794799856265539336t
       + 
                                                                       10
         7338202759292865165994622349207516400662174302614595173333825t
       + 
                                                                       9
         1308004628480367351164369613111971668880538855640917200187108t
       + 
                                                                       8
         4268059455741255498880229598973705747098216067697754352634748t
       + 
                                                                      7
         892893526858514095791318775904093300103045601514470613580600t
       + 
                                                                       6
         1679152575460683956631925852181341501981598137465328797013652t
       + 
                                                                      5
         269757415767922980378967154143357835544113158280591408043936t
       + 
                                                                      4
         380951527864657529033580829801282724081345372680202920198224t
       + 
                                                                     3
         19785545294228495032998826937601341132725035339452913286656t
       + 
                                                                     2
         36477412057384782942366635303396637763303928174935079178528t
       + 
         - 3722212879279038648713080422224976273210890229485838670848t
       + 
         89079724853114348361230634484013862024728599906874105856
       ,
         3      2                  3       2
      (3z  - 11z  + 8z + 4)y + 2t z  + 4t z  - 5t z - t,
                  2
      (z + 1)x + z  - 4z + 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; {0}][2 <4,1>,<3,1> -> |7|; {0}][1 <3,1> -> |3|; {0}]G[2 <4,1>,<4,1> -> |8|; {0}]W[3 <5,1>,<4,1>,<3,2> -> |12|; {0}]GI[3 <4,2>,<4,1>,<3,2> -> |11|; {0}]GWw[3 <4,1>,<3,2>,<5,2> -> |12|; {0}][3 <3,2>,<3,2>,<5,2> -> |11|; {0}]GIwWWWw[4 <3,2>,<4,2>,<5,2>,<2,3> -> |14|; {0}][4 <2,2>,<4,2>,<5,2>,<2,3> -> |13|; {0}]Gwww[5 <3,2>,<3,2>,<4,2>,<5,2>,<2,3> -> |17|; {0}]Gwwwwww[8 <3,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}]Gwwwwww[8 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |31|; {0}][8 <3,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |30|; {0}][8 <2,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |29|; {0}][8 <1,3>,<4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |28|; {0}][7 <4,2>,<4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |27|; {0}][6 <4,2>,<4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |23|; {0}][5 <4,2>,<4,2>,<4,2>,<5,2>,<2,3> -> |19|; {0}]GIGIWwww[6 <5,2>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |23|; {0}][6 <4,3>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |22|; {0}]GIGI[6 <3,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |21|; {0}][6 <2,4>,<4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |20|; {0}]GGG[5 <4,2>,<4,2>,<5,2>,<3,3>,<2,3> -> |18|; {0}]GIGIWwwwW[6 <5,2>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |22|; {0}][6 <4,3>,<4,2>,<5,2>,<3,3>,<3,3>,<2,3> -> |21|; {0}]GIwwWwWWWWWWWwWWWWwwwww[8 <4,2>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][8 <3,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}][8 <2,3>,<5,2>,<3,3>,<3,3>,<4,3>,<2,3>,<3,4>,<3,4> -> |25|; {0}]Gwwwwwwwwwwwwwwwwwwww[9 <5,2>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |29|; {0}]GI[9 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |28|; {0}][9 <3,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |27|; {0}][9 <2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,4>,<3,4> -> |26|; {0}]GGwwwwwwwwwwwwWWwwwwwwww[11 <3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {0}][11 <2,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {0}][11 <1,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |31|; {0}]GGGwwwwwwwwwwwww[12 <2,3>,<2,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {0}]GGwwwwwwwwwwwww[13 <3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}]Gwwwwwwwwwwwww[13 <2,3>,<3,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]GGGwwwwwwwwwwwww[15 <3,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {0}][14 <4,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {0}]GIGGGGIGGI[14 <3,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GGG[14 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}][14 <1,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}]GGG[13 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}]Gwwwwwwwwwwwww[15 <3,3>,<3,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]Gwwwwwwwwwwwww[15 <4,3>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |49|; {0}]GIGI[15 <3,4>,<4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |48|; {0}]G[14 <4,3>,<3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {0}][13 <3,3>,<4,3>,<4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]Gwwwwwwwwwwwww[13 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {0}]GIGGGGIGGI[13 <3,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {0}]GGGGGGGG[13 <2,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {0}][13 <1,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {0}][13 <0,4>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {0}][12 <4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][11 <4,3>,<3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |34|; {1}][10 <3,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |30|; {1}][10 <2,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |29|; {1}]GGGwwwwwwwwwwwww[11 <3,3>,<3,3>,<4,3>,<3,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |33|; {1}]GGGwwwwwwwwwwwww[12 <4,3>,<3,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}]Gwwwwwwwwwwwww[12 <3,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]GGwwwwwwwwwwwww[13 <5,3>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}]GIGGGGIGGIW[13 <4,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GGW[13 <3,4>,<4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |42|; {1}]GGG[12 <4,3>,<4,3>,<4,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}]Gwwwwwwwwwwwww[12 <4,3>,<4,3>,<5,3>,<3,3>,<4,3>,<3,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]Gwwwwwwwwwwwww[13 <5,3>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |46|; {1}]GIGIW[13 <4,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |45|; {1}][13 <3,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |44|; {1}][13 <2,4>,<5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |43|; {1}]GG[12 <5,3>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |41|; {1}]GIGGGGIGGIW[12 <4,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |40|; {1}]GGGGGGW[12 <3,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |39|; {1}][12 <2,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |38|; {1}][12 <1,4>,<4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |37|; {1}]GGG[11 <4,3>,<5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |36|; {1}][10 <5,3>,<3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |32|; {1}][9 <3,3>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |27|; {1}]W[9 <2,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |26|; {1}][9 <1,4>,<3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |25|; {1}][8 <3,3>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |24|; {1}]W[8 <2,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}][8 <1,4>,<4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][7 <4,3>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]w[7 <3,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}][7 <2,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}][7 <1,4>,<2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}][6 <2,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}]GGwwwwww[7 <3,3>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |21|; {1}]GIW[7 <2,4>,<3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |20|; {1}]GG[6 <3,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]Gwwwwww[7 <4,3>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |23|; {1}]GIW[7 <3,4>,<4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |22|; {1}][6 <4,3>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |19|; {1}]GIW[6 <3,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |18|; {1}]GGW[6 <2,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |17|; {1}][6 <1,4>,<3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |16|; {1}]GGG[5 <3,3>,<3,3>,<3,3>,<3,4>,<3,4> -> |15|; {1}]GIW[5 <2,4>,<3,3>,<3,3>,<3,4>,<3,4> -> |14|; {1}]GG[4 <3,3>,<3,3>,<3,4>,<3,4> -> |12|; {1}][3 <3,3>,<3,4>,<3,4> -> |9|; {1}]W[3 <2,4>,<3,4>,<3,4> -> |8|; {1}][3 <1,4>,<3,4>,<3,4> -> |7|; {1}]G[2 <3,4>,<3,4> -> |6|; {1}]G[1 <3,4> -> |3|; {1}][1 <2,4> -> |2|; {1}][1 <1,4> -> |1|; {1}]
--R   *** QCMPACK Statistics ***
--R      Table     size:  36
--R      Entries reused:  255
--R
--R   *** REGSETGCD: Gcd Statistics ***
--R      Table     size:  125
--R      Entries reused:  0
--R
--R   *** REGSETGCD: Inv Set Statistics ***
--R      Table     size:  30
--R      Entries reused:  0
--R
--R   (34)
--R   [
--R     {
--R                         24                   23                    22
--R         960725655771966t   + 386820897948702t   + 8906817198608181t
--R       + 
--R                          21                     20                    19
--R         2704966893949428t   + 37304033340228264t   + 7924782817170207t
--R       + 
--R                           18                     17                      16
--R         93126799040354990t   + 13101273653130910t   + 156146250424711858t
--R       + 
--R                           15                      14                     13
--R         16626490957259119t   + 190699288479805763t   + 24339173367625275t
--R       + 
--R                            12                     11                      10
--R         180532313014960135t   + 35288089030975378t   + 135054975747656285t
--R       + 
--R                           9                     8                     7
--R         34733736952488540t  + 75947600354493972t  + 19772555692457088t
--R       + 
--R                           6                    5                    4
--R         28871558573755428t  + 5576152439081664t  + 6321711820352976t
--R       + 
--R                       3                   2
--R       438314209312320t  + 581105748367008t  - 60254467992576t + 1449115951104
--R       ,
--R
--R                                                                         23
--R             26604210869491302385515265737052082361668474181372891857784t
--R           + 
--R                                                                          22
--R             443104378424686086067294899528296664238693556855017735265295t
--R           + 
--R                                                                          21
--R             279078393286701234679141342358988327155321305829547090310242t
--R           + 
--R                                                                           20
--R             3390276361413232465107617176615543054620626391823613392185226t
--R           + 
--R                                                                          19
--R             941478179503540575554198645220352803719793196473813837434129t
--R           + 
--R                                                                            18
--R             11547855194679475242211696749673949352585747674184320988144390t
--R           + 
--R                                                                           17
--R             1343609566765597789881701656699413216467215660333356417241432t
--R           + 
--R                                                                            16
--R             23233813868147873503933551617175640859899102987800663566699334t
--R           + 
--R                                                                          15
--R             869574020537672336950845440508790740850931336484983573386433t
--R           + 
--R                                                                            14
--R             31561554305876934875419461486969926554241750065103460820476969t
--R           + 
--R                                                                           13
--R             1271400990287717487442065952547731879554823889855386072264931t
--R           + 
--R                                                                            12
--R             31945089913863736044802526964079540198337049550503295825160523t
--R           + 
--R                                                                           11
--R             3738735704288144509871371560232845884439102270778010470931960t
--R           + 
--R                                                                            10
--R             25293997512391412026144601435771131587561905532992045692885927t
--R           + 
--R                                                                           9
--R             5210239009846067123469262799870052773410471135950175008046524t
--R           + 
--R                                                                            8
--R             15083887986930297166259870568608270427403187606238713491129188t
--R           + 
--R                                                                           7
--R             3522087234692930126383686270775779553481769125670839075109000t
--R           + 
--R                                                                           6
--R             6079945200395681013086533792568886491101244247440034969288588t
--R           + 
--R                                                                           5
--R             1090634852433900888199913756247986023196987723469934933603680t
--R           + 
--R                                                                           4
--R             1405819430871907102294432537538335402102838994019667487458352t
--R           + 
--R                                                                         3
--R             88071527950320450072536671265507748878347828884933605202432t
--R           + 
--R                                                                          2
--R             135882489433640933229781177155977768016065765482378657129440t
--R           + 
--R             - 13957283442882262230559894607400314082516690749975646520320t
--R           + 
--R             334637692973189299277258325709308472592117112855749713920
--R        *
--R           z
--R       + 
--R                                                                    23
--R         8567175484043952879756725964506833932149637101090521164936t
--R       + 
--R                                                                      22
--R         149792392864201791845708374032728942498797519251667250945721t
--R       + 
--R                                                                     21
--R         77258371783645822157410861582159764138123003074190374021550t
--R       + 
--R                                                                       20
--R         1108862254126854214498918940708612211184560556764334742191654t
--R       + 
--R                                                                      19
--R         213250494460678865219774480106826053783815789621501732672327t
--R       + 
--R                                                                       18
--R         3668929075160666195729177894178343514501987898410131431699882t
--R       + 
--R                                                                      17
--R         171388906471001872879490124368748236314765459039567820048872t
--R       + 
--R                                                                       16
--R         7192430746914602166660233477331022483144921771645523139658986t
--R       + 
--R                                                                        15
--R         - 128798674689690072812879965633090291959663143108437362453385t
--R       + 
--R                                                                       14
--R         9553010858341425909306423132921134040856028790803526430270671t
--R       + 
--R                                                                       13
--R         - 13296096245675492874538687646300437824658458709144441096603t
--R       + 
--R                                                                       12
--R         9475806805814145326383085518325333106881690568644274964864413t
--R       + 
--R                                                                      11
--R         803234687925133458861659855664084927606298794799856265539336t
--R       + 
--R                                                                       10
--R         7338202759292865165994622349207516400662174302614595173333825t
--R       + 
--R                                                                       9
--R         1308004628480367351164369613111971668880538855640917200187108t
--R       + 
--R                                                                       8
--R         4268059455741255498880229598973705747098216067697754352634748t
--R       + 
--R                                                                      7
--R         892893526858514095791318775904093300103045601514470613580600t
--R       + 
--R                                                                       6
--R         1679152575460683956631925852181341501981598137465328797013652t
--R       + 
--R                                                                      5
--R         269757415767922980378967154143357835544113158280591408043936t
--R       + 
--R                                                                      4
--R         380951527864657529033580829801282724081345372680202920198224t
--R       + 
--R                                                                     3
--R         19785545294228495032998826937601341132725035339452913286656t
--R       + 
--R                                                                     2
--R         36477412057384782942366635303396637763303928174935079178528t
--R       + 
--R         - 3722212879279038648713080422224976273210890229485838670848t
--R       + 
--R         89079724853114348361230634484013862024728599906874105856
--R       ,
--R         3      2                  3       2
--R      (3z  - 11z  + 8z + 4)y + 2t z  + 4t z  - 5t z - t,
--R                  2
--R      (z + 1)x + z  - 4z + 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 34
)spool
 
Starts dribbling to CombinatorialFunction.output (2010/3/27, 18:41:49).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 1

--S 2 of 6
D(product(f(i,x),i=1..m),x)
 

          m           m    f  (i,x)
        ++-++        --+    ,2
   (2)   | |   f(i,x)>     --------
         | |         --+    f(i,x)
        i= 1         i= 1
                                                     Type: Expression Integer
--R 
--R
--R          m           m    f  (i,x)
--R        ++-++        --+    ,2
--R   (2)   | |   f(i,x)>     --------
--R         | |         --+    f(i,x)
--R        i= 1         i= 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
)set expose add constructor OutputForm
 
   OutputForm is now explicitly exposed in frame initial 
--R 
--I   OutputForm is already explicitly exposed in frame frame0 
--E 3

--S 4 of 6
pascalRow(n) == [right(binomial(n,i),4) for i in 0..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 6
displayRow(n)==output center blankSeparate pascalRow(n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 6
for i in 0..7 repeat displayRow i
 
   Compiling function pascalRow with type NonNegativeInteger -> List 
      OutputForm 
   Compiling function displayRow with type NonNegativeInteger -> Void 
                                     1
                                  1    1
                                1    2    1
                             1    3    3    1
                           1    4    6    4    1
                        1    5   10   10    5    1
                      1    6   15   20   15    6    1
                   1    7   21   35   35   21    7    1
                                                                   Type: Void
--R 
--R   Compiling function pascalRow with type NonNegativeInteger -> List 
--R      OutputForm 
--R   Compiling function displayRow with type NonNegativeInteger -> Void 
--R                                     1
--R                                  1    1
--R                                1    2    1
--R                             1    3    3    1
--R                           1    4    6    4    1
--R                        1    5   10   10    5    1
--R                      1    6   15   20   15    6    1
--R                   1    7   21   35   35   21    7    1
--R                                                                   Type: Void
--E 6


)spool
 
Starts dribbling to unittest1.output (2010/3/27, 18:41:34).
)set mes auto off
 
)clear all
 

--S 1 of 97
)with API
 
   )library cannot find the file API.
--R   )library cannot find the file API.
--E 1

--S 2 of 97 this command generates random output
--)apropos matrix
--E 2

--S 3 of 97
)what categories set
 
------------------------------- Categories --------------------------------

Categories with names matching patterns:
     set 

 CACHSET  CachableSet                  FSAGG    FiniteSetAggregate
 MSETAGG  MultisetAggregate
 NTSCAT   NormalizedTriangularSetCategory
 OMSAGG   OrderedMultisetAggregate     ORDSET   OrderedSet
 PSETCAT  PolynomialSetCategory        RSETCAT  RegularTriangularSetCategory
 SETAGG   SetAggregate                 SETCAT   SetCategory
 SFRTCAT  SquareFreeRegularTriangularSetCategory
 SNTSCAT  SquareFreeNormalizedTriangularSetCategory
 TSETCAT  TriangularSetCategory
--R 
--R------------------------------- Categories --------------------------------
--R
--RCategories with names matching patterns:
--R     set 
--R
--R CACHSET  CachableSet                  FSAGG    FiniteSetAggregate
--R MSETAGG  MultisetAggregate
--R NTSCAT   NormalizedTriangularSetCategory
--R OMSAGG   OrderedMultisetAggregate     ORDSET   OrderedSet
--R PSETCAT  PolynomialSetCategory        RSETCAT  RegularTriangularSetCategory
--R SETAGG   SetAggregate                 SETCAT   SetCategory
--R SFRTCAT  SquareFreeRegularTriangularSetCategory
--R SNTSCAT  SquareFreeNormalizedTriangularSetCategory
--R TSETCAT  TriangularSetCategory
--E 3

--S 4 of 97
)what commands set
 
--------------- System Commands for User Level: development ---------------

System commands at this level matching patterns:
     set 

set    
 
--R 
--R--------------- System Commands for User Level: development ---------------
--R
--RSystem commands at this level matching patterns:
--R     set 
--R
--Rset    
--R 
--E 4

--S 5 of 97 this command generates random output
--)what domains set
--E 5

--S 6 of 97 this command generates random output
--)what operations set
--E 6

--S 7 of 97
)what packages set
 
-------------------------------- Packages ---------------------------------

Packages with names matching patterns:
     set 

 FSAGG2   FiniteSetAggregateFunctions2 LAZM3PK  LazardSetSolvingPackage
 PSETPK   PolynomialSetUtilitiesPackage
 QALGSET2 QuasiAlgebraicSet2
 RSDCMPK  RegularSetDecompositionPackage
 RSETGCD  RegularTriangularSetGcdPackage
 SFRGCD   SquareFreeRegularTriangularSetGcdPackage
 SRDCMPK  SquareFreeRegularSetDecompositionPackage
--R 
--R-------------------------------- Packages ---------------------------------
--R
--RPackages with names matching patterns:
--R     set 
--R
--R FSAGG2   FiniteSetAggregateFunctions2 LAZM3PK  LazardSetSolvingPackage
--R PSETPK   PolynomialSetUtilitiesPackage
--R QALGSET2 QuasiAlgebraicSet2
--R RSDCMPK  RegularSetDecompositionPackage
--R RSETGCD  RegularTriangularSetGcdPackage
--R SFRGCD   SquareFreeRegularTriangularSetGcdPackage
--R SRDCMPK  SquareFreeRegularSetDecompositionPackage
--E 7

--S 8 of 97
)what synonym set
 
------------------------- System Command Synonyms -------------------------

   No user-defined synonyms satisfying patterns:
       set 

--R 
--R------------------------- System Command Synonyms -------------------------
--R
--R   No user-defined synonyms satisfying patterns:
--R       set 
--R
--E 8

--S 9 of 97 this command generates random output
--)what things set
--E 9

--S 10 of 97 this command generates random output
--)apropos set
--E 10

--S 11 of 97
)prompt
 
---------------------------- The prompt Option ----------------------------

 Description: set type of input prompt to display

 The prompt option may be followed by any one of the following:

    none
    frame
    plain
 -> step 
    verbose

 The current setting is indicated.

--R---------------------------- The prompt Option ----------------------------
--R
--R Description: set type of input prompt to display
--R
--R The prompt option may be followed by any one of the following:
--R
--R    none
--R    frame
--R    plain
--R -> step 
--R    verbose
--R
--R The current setting is indicated.
--R
--E 11

--S 12 of 97
)version
 
Value = "Saturday March 27, 2010 at 17:32:44 "
--R 
--IValue = "Saturday February 21, 2009 at 17:59:27 "
--E 12

--S 13 of 97
)zsys )from )c
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 13

--S 14 of 97
)zsys )from )d
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 14

--S 15 of 97
)zsys )from )dt
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 15

--S 16 of 97
)zsys )from )ct
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 16

--S 17 of 97
)zsys )from )ctl
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 17

--S 18 of 97
)zsys )from )ec
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 18

--S 19 of 97
)zsys )from )ect
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 19

--S 20 of 97
)zsys )from )e
 
 
   >> System error:
   Cannot open the file /home/camm/debian/axiom/axiom-20091101/mnt/linux/../../src/interp/TAGS.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--I   Cannot open the file /research/test/mnt/fedora10/../../src/interp/TAGS.
--R
--R   Continuing to read the file...
--R
--E 20

--S 21 of 97
)zsys )from )version
 
--R 
--E 21

--S 22 of 97
)zsys )from )update
 
 
   >> System error:
   /UPDATE-1 [or a callee] requires more than one argument.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   /UPDATE-1 [or a callee] requires more than one argument.
--R
--R   Continuing to read the file...
--R
--E 22

--S 23 of 97
)zsys )from )patch
 
 
   >> System error:
   The function /UPDATE-LIB-1 is undefined.

   Continuing to read the file...

--R 
--R 
--R   >> System error:
--R   The function /UPDATE-LIB-1 is undefined.
--R
--R   Continuing to read the file...
--R
--E 23

--S 24 of 97
)zsys )from )there 1
 

   Unknown option: there 
   Available options are c ct e ec ect cls pause update patch compare record 

--R 
--R
--R   Unknown option: there 
--R   Available options are c ct e ec ect cls pause update patch compare record 
--R
--E 24

--S 25 of 97
)zsys )from )compare
 
   An argument is required for compare 
--R 
--R   An argument is required for compare 
--E 25

--S 26 of 97
)zsys )from )record
 
   An argument is required for record 
--R 
--R   An argument is required for record 
--E 26

--S 27 of 97
)summary
 
--R 
--E 27

--S 28 of 97
--R)credits
--RAn alphabetical listing of contributors to AXIOM:
--RCyril Alberga          Roy Adler              Christian Aistleitner
--RRichard Anderson       George Andrews         S.J. Atkins
--RHenry Baker            Stephen Balzac         Yurij Baransky
--RDavid R. Barton        Gerald Baumgartner     Gilbert Baumslag
--RJay Belanger           David Bindel           Fred Blair
--RVladimir Bondarenko    Mark Botch
--RAlexandre Bouyer       Peter A. Broadbery     Martin Brock
--RManuel Bronstein       Stephen Buchwald       Florian Bundschuh
--RLuanne Burns           William Burge
--RQuentin Carpent        Robert Caviness        Bruce Char
--ROndrej Certik          Cheekai Chin           David V. Chudnovsky
--RGregory V. Chudnovsky  Josh Cohen             Christophe Conil
--RDon Coppersmith        George Corliss         Robert Corless
--RGary Cornell           Meino Cramer           Claire Di Crescenzo
--RDavid Cyganski
--RTimothy Daly Sr.       Timothy Daly Jr.       James H. Davenport
--RDidier Deshommes       Michael Dewar
--RJean Della Dora        Gabriel Dos Reis       Claire DiCrescendo
--RSam Dooley             Lionel Ducos           Martin Dunstan
--RBrian Dupee            Dominique Duval
--RRobert Edwards         Heow Eide-Goodman      Lars Erickson
--RRichard Fateman        Bertfried Fauser       Stuart Feldman
--RBrian Ford             Albrecht Fortenbacher  George Frances
--RConstantine Frangos    Timothy Freeman        Korrinn Fu
--RMarc Gaetano           Rudiger Gebauer        Kathy Gerber
--RPatricia Gianni        Samantha Goldrich      Holger Gollan
--RTeresa Gomez-Diaz      Laureano Gonzalez-Vega Stephen Gortler
--RJohannes Grabmeier     Matt Grayson           Klaus Ebbe Grue
--RJames Griesmer         Vladimir Grinberg      Oswald Gschnitzer
--RJocelyn Guidry
--RSteve Hague            Satoshi Hamaguchi      Mike Hansen
--RRichard Harke          Vilya Harvey           Martin Hassner
--RArthur S. Hathaway     Dan Hatton             Waldek Hebisch
--RKarl Hegbloom          Ralf Hemmecke          Henderson
--RAntoine Hersen         Gernot Hueber
--RPietro Iglio
--RAlejandro Jakubi       Richard Jenks
--RKai Kaminski           Grant Keady            Tony Kennedy
--RPaul Kosinski          Klaus Kusche           Bernhard Kutzler
--RTim Lahey              Larry Lambe            Franz Lehner
--RFrederic Lehobey       Michel Levaud          Howard Levy
--RLiu Xiaojun            Rudiger Loos           Michael Lucks
--RRichard Luczak
--RCamm Maguire           Francois Maltey        Alasdair McAndrew
--RBob McElrath           Michael McGettrick     Ian Meikle
--RDavid Mentre           Victor S. Miller       Gerard Milmeister
--RMohammed Mobarak       H. Michael Moeller     Michael Monagan
--RMarc Moreno-Maza       Scott Morrison         Joel Moses
--RMark Murray
--RWilliam Naylor         C. Andrew Neff         John Nelder
--RGodfrey Nolan          Arthur Norman          Jinzhong Niu
--RMichael O'Connor       Summat Oemrawsingh     Kostas Oikonomou
--RHumberto Ortiz-Zuazaga
--RJulian A. Padget       Bill Page              Susan Pelzel
--RMichel Petitot         Didier Pinchon         Ayal Pinkus
--RJose Alfredo Portes
--RClaude Quitte
--RArthur C. Ralfs        Norman Ramsey          Anatoly Raportirenko
--RMichael Richardson     Renaud Rioboo          Jean Rivlin
--RNicolas Robidoux       Simon Robinson         Raymond Rogers
--RMichael Rothstein      Martin Rubey
--RPhilip Santas          Alfred Scheerhorn      William Schelter
--RGerhard Schneider      Martin Schoenert       Marshall Schor
--RFrithjof Schulze       Fritz Schwarz          Nick Simicich
--RWilliam Sit            Elena Smirnova         Jonathan Steinbach
--RFabio Stumbo           Christine Sundaresan   Robert Sutor
--RMoss E. Sweedler       Eugene Surowitz
--RMax Tegmark            James Thatcher         Balbir Thomas
--RMike Thomas            Dylan Thurston         Barry Trager
--RThemos T. Tsikas
--RGregory Vanuxem
--RBernhard Wall          Stephen Watt           Jaap Weel
--RJuergen Weiss          M. Weller              Mark Wegman
--RJames Wen              Thorsten Werther       Michael Wester
--RJohn M. Wiley          Berhard Will           Clifton J. Williamson
--RStephen Wilson         Shmuel Winograd        Robert Wisbauer
--RSandra Wityak          Waldemar Wiwianka      Knut Wolf
--RClifford Yapp          David Yun
--RVadim Zhytnikov        Richard Zippel         Evelyn Zoernack
--RBruno Zuercher         Dan Zwillinger
--E 28

--S 29 of 97
)set expose
 
---------------------------- The expose Option ----------------------------

 Description: control interpreter constructor exposure

   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   The following constructors are explicitly hidden in the current 
      frame:
                there are no explicitly hidden constructors                
 
   When )set expose is followed by no arguments, the information you 
      now see is displayed. When followed by the initialize argument, 
      the exposure group data in the file interp.exposed is read and is
      then available. The arguments add and drop are used to add or 
      drop exposure groups or explicit constructors from the local 
      frame exposure data. Issue
                  )set expose add    or    )set expose drop 
      for more information.
--R---------------------------- The expose Option ----------------------------
--R
--R Description: control interpreter constructor exposure
--R
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                there are no explicitly hidden constructors                
--R 
--R   When )set expose is followed by no arguments, the information you 
--R      now see is displayed. When followed by the initialize argument, 
--R      the exposure group data in the file interp.exposed is read and is
--R      then available. The arguments add and drop are used to add or 
--R      drop exposure groups or explicit constructors from the local 
--R      frame exposure data. Issue
--R                  )set expose add    or    )set expose drop 
--R      for more information.
--E 29

--S 30 of 97
)set expose add
 
----------------------------- The add Option ------------------------------
   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   When )set expose add is followed by no arguments, the information 
      you now see is displayed. The arguments group and constructor are
      used to specify exposure groups or an explicit constructor to be 
      added to the local frame exposure data. Issue
                            )set expose add group 
      or
                         )set expose add constructor 
      for more information.
--R----------------------------- The add Option ------------------------------
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   When )set expose add is followed by no arguments, the information 
--R      you now see is displayed. The arguments group and constructor are
--R      used to specify exposure groups or an explicit constructor to be 
--R      added to the local frame exposure data. Issue
--R                            )set expose add group 
--R      or
--R                         )set expose add constructor 
--R      for more information.
--E 30

--S 31 of 97
)set expose drop
 
----------------------------- The drop Option -----------------------------
   The following constructors are explicitly hidden in the current 
      frame:
                there are no explicitly hidden constructors                
 
   When )set expose drop is followed by no arguments, the information 
      you now see is displayed. The arguments group and constructor are
      used to specify exposure groups or an explicit constructor to be 
      dropped from the local frame exposure data. Issue
                           )set expose drop group 
      or
                        )set expose drop constructor 
      for more information.
--R----------------------------- The drop Option -----------------------------
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                there are no explicitly hidden constructors                
--R 
--R   When )set expose drop is followed by no arguments, the information 
--R      you now see is displayed. The arguments group and constructor are
--R      used to specify exposure groups or an explicit constructor to be 
--R      dropped from the local frame exposure data. Issue
--R                           )set expose drop group 
--R      or
--R                        )set expose drop constructor 
--R      for more information.
--E 31

--S 32 of 97
)set expose add group
 
---------------------------- The group Option -----------------------------
   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
 
   When )set expose add group is followed by no arguments, the 
      information you now see is displayed. Otherwise, the words 
      following group must be valid names of exposure groups defined in
      interp.exposed . The group all is special: using this group name 
      causes all known constructors to be exposed. The known exposure 
      group names are:
 
basic         naglink       anna          categories    Hidden        
defaults      
--R---------------------------- The group Option -----------------------------
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--R 
--R   When )set expose add group is followed by no arguments, the 
--R      information you now see is displayed. Otherwise, the words 
--R      following group must be valid names of exposure groups defined in
--R      interp.exposed . The group all is special: using this group name 
--R      causes all known constructors to be exposed. The known exposure 
--R      group names are:
--R 
--Rbasic         naglink       anna          categories    Hidden        
--Rdefaults      
--E 32

--S 33 of 97
)set expose add constructor
 
------------------------- The constructor Option --------------------------
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
--R------------------------- The constructor Option --------------------------
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--E 33

--S 34 of 97
)set expose drop group
 
---------------------------- The group Option -----------------------------
   When followed by one or more exposure group names, this option 
      allows you to remove those groups from the local frame exposure 
      data.
 
   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
--R---------------------------- The group Option -----------------------------
--R   When followed by one or more exposure group names, this option 
--R      allows you to remove those groups from the local frame exposure 
--R      data.
--R 
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--E 34

--S 35 of 97
)set expose drop constructor
 
------------------------- The constructor Option --------------------------
   When followed by one or more constructor names, this option allows 
      you to explicitly hide constructors in this frame.
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   The following constructors are explicitly hidden in the current 
      frame:
                there are no explicitly hidden constructors                
--R------------------------- The constructor Option --------------------------
--R   When followed by one or more constructor names, this option allows 
--R      you to explicitly hide constructors in this frame.
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                there are no explicitly hidden constructors                
--E 35

--S 36 of 97
)show SQMATRIX
 
 SquareMatrix(ndim: NonNegativeInteger,R: Ring)  is a domain constructor
 Abbreviation for SquareMatrix is SQMATRIX 
 This constructor is not exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for SQMATRIX 

------------------------------- Operations --------------------------------
 ?*? : (R,%) -> %                      ?*? : (%,R) -> %
 ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
 ?+? : (%,%) -> %                      ?-? : (%,%) -> %
 -? : % -> %                           ?=? : (%,%) -> Boolean
 D : % -> % if R has DIFRING           D : (%,(R -> R)) -> %
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        antisymmetric? : % -> Boolean
 coerce : % -> Matrix R                coerce : R -> %
 coerce : Integer -> %                 coerce : % -> OutputForm
 copy : % -> %                         diagonal? : % -> Boolean
 diagonalMatrix : List R -> %          diagonalProduct : % -> R
 elt : (%,Integer,Integer) -> R        elt : (%,Integer,Integer,R) -> R
 empty : () -> %                       empty? : % -> Boolean
 eq? : (%,%) -> Boolean                hash : % -> SingleInteger
 latex : % -> String                   listOfLists : % -> List List R
 map : ((R -> R),%) -> %               map : (((R,R) -> R),%,%) -> %
 matrix : List List R -> %             maxColIndex : % -> Integer
 maxRowIndex : % -> Integer            minColIndex : % -> Integer
 minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
 nrows : % -> NonNegativeInteger       one? : % -> Boolean
 qelt : (%,Integer,Integer) -> R       recip : % -> Union(%,"failed")
 retract : % -> R                      sample : () -> %
 scalarMatrix : R -> %                 square? : % -> Boolean
 squareMatrix : Matrix R -> %          symmetric? : % -> Boolean
 trace : % -> R                        transpose : % -> %
 zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R)
 ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R)
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,Integer) -> % if R has FIELD
 ?**? : (%,NonNegativeInteger) -> %
 ?/? : (%,R) -> % if R has FIELD
 D : (%,NonNegativeInteger) -> % if R has DIFRING
 D : (%,Symbol) -> % if R has PDRING SYMBOL
 D : (%,List Symbol) -> % if R has PDRING SYMBOL
 D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
 D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
 D : (%,(R -> R),NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %
 any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 characteristic : () -> NonNegativeInteger
 coerce : Fraction Integer -> % if R has RETRACT FRAC INT
 column : (%,Integer) -> DirectProduct(ndim,R)
 convert : % -> InputForm if R has KONVERT INFORM
 count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT
 count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 determinant : % -> R if R has commutative *
 diagonal : % -> DirectProduct(ndim,R)
 differentiate : % -> % if R has DIFRING
 differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
 differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
 differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
 differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
 differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
 differentiate : (%,(R -> R),NonNegativeInteger) -> %
 differentiate : (%,(R -> R)) -> %
 eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
 every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 exquo : (%,R) -> Union(%,"failed") if R has INTDOM
 inverse : % -> Union(%,"failed") if R has FIELD
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((R -> R),%) -> % if $ has shallowlyMutable
 member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
 members : % -> List R if $ has finiteAggregate
 minordet : % -> R if R has commutative *
 more? : (%,NonNegativeInteger) -> Boolean
 nullSpace : % -> List DirectProduct(ndim,R) if R has INTDOM
 nullity : % -> NonNegativeInteger if R has INTDOM
 parts : % -> List R if $ has finiteAggregate
 rank : % -> NonNegativeInteger if R has INTDOM
 reducedSystem : Matrix % -> Matrix R
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
 reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
 retract : % -> Fraction Integer if R has RETRACT FRAC INT
 retract : % -> Integer if R has RETRACT INT
 retractIfCan : % -> Union(R,"failed")
 retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
 retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
 row : (%,Integer) -> DirectProduct(ndim,R)
 rowEchelon : % -> % if R has EUCDOM
 size? : (%,NonNegativeInteger) -> Boolean
 subtractIfCan : (%,%) -> Union(%,"failed")

--R SquareMatrix(ndim: NonNegativeInteger,R: Ring)  is a domain constructor
--R Abbreviation for SquareMatrix is SQMATRIX 
--R This constructor is not exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for SQMATRIX 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (R,%) -> %                      ?*? : (%,R) -> %
--R ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> %                      ?-? : (%,%) -> %
--R -? : % -> %                           ?=? : (%,%) -> Boolean
--R D : % -> % if R has DIFRING           D : (%,(R -> R)) -> %
--R 1 : () -> %                           0 : () -> %
--R ?^? : (%,PositiveInteger) -> %        antisymmetric? : % -> Boolean
--R coerce : % -> Matrix R                coerce : R -> %
--R coerce : Integer -> %                 coerce : % -> OutputForm
--R copy : % -> %                         diagonal? : % -> Boolean
--R diagonalMatrix : List R -> %          diagonalProduct : % -> R
--R elt : (%,Integer,Integer) -> R        elt : (%,Integer,Integer,R) -> R
--R empty : () -> %                       empty? : % -> Boolean
--R eq? : (%,%) -> Boolean                hash : % -> SingleInteger
--R latex : % -> String                   listOfLists : % -> List List R
--R map : ((R -> R),%) -> %               map : (((R,R) -> R),%,%) -> %
--R matrix : List List R -> %             maxColIndex : % -> Integer
--R maxRowIndex : % -> Integer            minColIndex : % -> Integer
--R minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
--R nrows : % -> NonNegativeInteger       one? : % -> Boolean
--R qelt : (%,Integer,Integer) -> R       recip : % -> Union(%,"failed")
--R retract : % -> R                      sample : () -> %
--R scalarMatrix : R -> %                 square? : % -> Boolean
--R squareMatrix : Matrix R -> %          symmetric? : % -> Boolean
--R trace : % -> R                        transpose : % -> %
--R zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R)
--R ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R)
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
--R D : (%,Symbol) -> % if R has PDRING SYMBOL
--R D : (%,List Symbol) -> % if R has PDRING SYMBOL
--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
--R D : (%,(R -> R),NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R characteristic : () -> NonNegativeInteger
--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
--R column : (%,Integer) -> DirectProduct(ndim,R)
--R convert : % -> InputForm if R has KONVERT INFORM
--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R determinant : % -> R if R has commutative *
--R diagonal : % -> DirectProduct(ndim,R)
--R differentiate : % -> % if R has DIFRING
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
--R differentiate : (%,(R -> R)) -> %
--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R inverse : % -> Union(%,"failed") if R has FIELD
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((R -> R),%) -> % if $ has shallowlyMutable
--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
--R members : % -> List R if $ has finiteAggregate
--R minordet : % -> R if R has commutative *
--R more? : (%,NonNegativeInteger) -> Boolean
--R nullSpace : % -> List DirectProduct(ndim,R) if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
--R parts : % -> List R if $ has finiteAggregate
--R rank : % -> NonNegativeInteger if R has INTDOM
--R reducedSystem : Matrix % -> Matrix R
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
--R retract : % -> Fraction Integer if R has RETRACT FRAC INT
--R retract : % -> Integer if R has RETRACT INT
--R retractIfCan : % -> Union(R,"failed")
--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
--R row : (%,Integer) -> DirectProduct(ndim,R)
--R rowEchelon : % -> % if R has EUCDOM
--R size? : (%,NonNegativeInteger) -> Boolean
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 36

--S 37 of 97
)set expose add constructor SQMATRIX
 
   SquareMatrix is now explicitly exposed in frame initial 
--I   SquareMatrix is now explicitly exposed in frame frame0 
--E 37

--S 38 of 97
)show SQMATRIX
 
 SquareMatrix(ndim: NonNegativeInteger,R: Ring)  is a domain constructor
 Abbreviation for SquareMatrix is SQMATRIX 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for SQMATRIX 

------------------------------- Operations --------------------------------
 ?*? : (R,%) -> %                      ?*? : (%,R) -> %
 ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
 ?+? : (%,%) -> %                      ?-? : (%,%) -> %
 -? : % -> %                           ?=? : (%,%) -> Boolean
 D : % -> % if R has DIFRING           D : (%,(R -> R)) -> %
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        antisymmetric? : % -> Boolean
 coerce : % -> Matrix R                coerce : R -> %
 coerce : Integer -> %                 coerce : % -> OutputForm
 copy : % -> %                         diagonal? : % -> Boolean
 diagonalMatrix : List R -> %          diagonalProduct : % -> R
 elt : (%,Integer,Integer) -> R        elt : (%,Integer,Integer,R) -> R
 empty : () -> %                       empty? : % -> Boolean
 eq? : (%,%) -> Boolean                hash : % -> SingleInteger
 latex : % -> String                   listOfLists : % -> List List R
 map : ((R -> R),%) -> %               map : (((R,R) -> R),%,%) -> %
 matrix : List List R -> %             maxColIndex : % -> Integer
 maxRowIndex : % -> Integer            minColIndex : % -> Integer
 minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
 nrows : % -> NonNegativeInteger       one? : % -> Boolean
 qelt : (%,Integer,Integer) -> R       recip : % -> Union(%,"failed")
 retract : % -> R                      sample : () -> %
 scalarMatrix : R -> %                 square? : % -> Boolean
 squareMatrix : Matrix R -> %          symmetric? : % -> Boolean
 trace : % -> R                        transpose : % -> %
 zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R)
 ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R)
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,Integer) -> % if R has FIELD
 ?**? : (%,NonNegativeInteger) -> %
 ?/? : (%,R) -> % if R has FIELD
 D : (%,NonNegativeInteger) -> % if R has DIFRING
 D : (%,Symbol) -> % if R has PDRING SYMBOL
 D : (%,List Symbol) -> % if R has PDRING SYMBOL
 D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
 D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
 D : (%,(R -> R),NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %
 any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 characteristic : () -> NonNegativeInteger
 coerce : Fraction Integer -> % if R has RETRACT FRAC INT
 column : (%,Integer) -> DirectProduct(ndim,R)
 convert : % -> InputForm if R has KONVERT INFORM
 count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT
 count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 determinant : % -> R if R has commutative *
 diagonal : % -> DirectProduct(ndim,R)
 differentiate : % -> % if R has DIFRING
 differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
 differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
 differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
 differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
 differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
 differentiate : (%,(R -> R),NonNegativeInteger) -> %
 differentiate : (%,(R -> R)) -> %
 eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
 every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 exquo : (%,R) -> Union(%,"failed") if R has INTDOM
 inverse : % -> Union(%,"failed") if R has FIELD
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((R -> R),%) -> % if $ has shallowlyMutable
 member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
 members : % -> List R if $ has finiteAggregate
 minordet : % -> R if R has commutative *
 more? : (%,NonNegativeInteger) -> Boolean
 nullSpace : % -> List DirectProduct(ndim,R) if R has INTDOM
 nullity : % -> NonNegativeInteger if R has INTDOM
 parts : % -> List R if $ has finiteAggregate
 rank : % -> NonNegativeInteger if R has INTDOM
 reducedSystem : Matrix % -> Matrix R
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
 reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
 retract : % -> Fraction Integer if R has RETRACT FRAC INT
 retract : % -> Integer if R has RETRACT INT
 retractIfCan : % -> Union(R,"failed")
 retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
 retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
 row : (%,Integer) -> DirectProduct(ndim,R)
 rowEchelon : % -> % if R has EUCDOM
 size? : (%,NonNegativeInteger) -> Boolean
 subtractIfCan : (%,%) -> Union(%,"failed")

--R SquareMatrix(ndim: NonNegativeInteger,R: Ring)  is a domain constructor
--R Abbreviation for SquareMatrix is SQMATRIX 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for SQMATRIX 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (R,%) -> %                      ?*? : (%,R) -> %
--R ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> %                      ?-? : (%,%) -> %
--R -? : % -> %                           ?=? : (%,%) -> Boolean
--R D : % -> % if R has DIFRING           D : (%,(R -> R)) -> %
--R 1 : () -> %                           0 : () -> %
--R ?^? : (%,PositiveInteger) -> %        antisymmetric? : % -> Boolean
--R coerce : % -> Matrix R                coerce : R -> %
--R coerce : Integer -> %                 coerce : % -> OutputForm
--R copy : % -> %                         diagonal? : % -> Boolean
--R diagonalMatrix : List R -> %          diagonalProduct : % -> R
--R elt : (%,Integer,Integer) -> R        elt : (%,Integer,Integer,R) -> R
--R empty : () -> %                       empty? : % -> Boolean
--R eq? : (%,%) -> Boolean                hash : % -> SingleInteger
--R latex : % -> String                   listOfLists : % -> List List R
--R map : ((R -> R),%) -> %               map : (((R,R) -> R),%,%) -> %
--R matrix : List List R -> %             maxColIndex : % -> Integer
--R maxRowIndex : % -> Integer            minColIndex : % -> Integer
--R minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
--R nrows : % -> NonNegativeInteger       one? : % -> Boolean
--R qelt : (%,Integer,Integer) -> R       recip : % -> Union(%,"failed")
--R retract : % -> R                      sample : () -> %
--R scalarMatrix : R -> %                 square? : % -> Boolean
--R squareMatrix : Matrix R -> %          symmetric? : % -> Boolean
--R trace : % -> R                        transpose : % -> %
--R zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R)
--R ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R)
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
--R D : (%,Symbol) -> % if R has PDRING SYMBOL
--R D : (%,List Symbol) -> % if R has PDRING SYMBOL
--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
--R D : (%,(R -> R),NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R characteristic : () -> NonNegativeInteger
--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
--R column : (%,Integer) -> DirectProduct(ndim,R)
--R convert : % -> InputForm if R has KONVERT INFORM
--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R determinant : % -> R if R has commutative *
--R diagonal : % -> DirectProduct(ndim,R)
--R differentiate : % -> % if R has DIFRING
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
--R differentiate : (%,(R -> R)) -> %
--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R inverse : % -> Union(%,"failed") if R has FIELD
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((R -> R),%) -> % if $ has shallowlyMutable
--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
--R members : % -> List R if $ has finiteAggregate
--R minordet : % -> R if R has commutative *
--R more? : (%,NonNegativeInteger) -> Boolean
--R nullSpace : % -> List DirectProduct(ndim,R) if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
--R parts : % -> List R if $ has finiteAggregate
--R rank : % -> NonNegativeInteger if R has INTDOM
--R reducedSystem : Matrix % -> Matrix R
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
--R retract : % -> Fraction Integer if R has RETRACT FRAC INT
--R retract : % -> Integer if R has RETRACT INT
--R retractIfCan : % -> Union(R,"failed")
--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
--R row : (%,Integer) -> DirectProduct(ndim,R)
--R rowEchelon : % -> % if R has EUCDOM
--R size? : (%,NonNegativeInteger) -> Boolean
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 38

--S 39 of 97
)set expose add
 
----------------------------- The add Option ------------------------------
   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
 
   The following constructors are explicitly exposed in the current 
      frame:
                               SquareMatrix                                
 
   When )set expose add is followed by no arguments, the information 
      you now see is displayed. The arguments group and constructor are
      used to specify exposure groups or an explicit constructor to be 
      added to the local frame exposure data. Issue
                            )set expose add group 
      or
                         )set expose add constructor 
      for more information.
--R----------------------------- The add Option ------------------------------
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R                               SquareMatrix                                
--R 
--R   When )set expose add is followed by no arguments, the information 
--R      you now see is displayed. The arguments group and constructor are
--R      used to specify exposure groups or an explicit constructor to be 
--R      added to the local frame exposure data. Issue
--R                            )set expose add group 
--R      or
--R                         )set expose add constructor 
--R      for more information.
--E 39

--S 40 of 97
)set expose drop constructor SQMATRIX
 
   SquareMatrix is now explicitly hidden in frame initial 
--I   SquareMatrix is now explicitly hidden in frame frame0 
--E 40

--S 41 of 97
)show SQMATRIX
 
 SquareMatrix(ndim: NonNegativeInteger,R: Ring)  is a domain constructor
 Abbreviation for SquareMatrix is SQMATRIX 
 This constructor is not exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for SQMATRIX 

------------------------------- Operations --------------------------------
 ?*? : (R,%) -> %                      ?*? : (%,R) -> %
 ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
 ?+? : (%,%) -> %                      ?-? : (%,%) -> %
 -? : % -> %                           ?=? : (%,%) -> Boolean
 D : % -> % if R has DIFRING           D : (%,(R -> R)) -> %
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        antisymmetric? : % -> Boolean
 coerce : % -> Matrix R                coerce : R -> %
 coerce : Integer -> %                 coerce : % -> OutputForm
 copy : % -> %                         diagonal? : % -> Boolean
 diagonalMatrix : List R -> %          diagonalProduct : % -> R
 elt : (%,Integer,Integer) -> R        elt : (%,Integer,Integer,R) -> R
 empty : () -> %                       empty? : % -> Boolean
 eq? : (%,%) -> Boolean                hash : % -> SingleInteger
 latex : % -> String                   listOfLists : % -> List List R
 map : ((R -> R),%) -> %               map : (((R,R) -> R),%,%) -> %
 matrix : List List R -> %             maxColIndex : % -> Integer
 maxRowIndex : % -> Integer            minColIndex : % -> Integer
 minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
 nrows : % -> NonNegativeInteger       one? : % -> Boolean
 qelt : (%,Integer,Integer) -> R       recip : % -> Union(%,"failed")
 retract : % -> R                      sample : () -> %
 scalarMatrix : R -> %                 square? : % -> Boolean
 squareMatrix : Matrix R -> %          symmetric? : % -> Boolean
 trace : % -> R                        transpose : % -> %
 zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R)
 ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R)
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,Integer) -> % if R has FIELD
 ?**? : (%,NonNegativeInteger) -> %
 ?/? : (%,R) -> % if R has FIELD
 D : (%,NonNegativeInteger) -> % if R has DIFRING
 D : (%,Symbol) -> % if R has PDRING SYMBOL
 D : (%,List Symbol) -> % if R has PDRING SYMBOL
 D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
 D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
 D : (%,(R -> R),NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %
 any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 characteristic : () -> NonNegativeInteger
 coerce : Fraction Integer -> % if R has RETRACT FRAC INT
 column : (%,Integer) -> DirectProduct(ndim,R)
 convert : % -> InputForm if R has KONVERT INFORM
 count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT
 count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 determinant : % -> R if R has commutative *
 diagonal : % -> DirectProduct(ndim,R)
 differentiate : % -> % if R has DIFRING
 differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
 differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
 differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
 differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
 differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
 differentiate : (%,(R -> R),NonNegativeInteger) -> %
 differentiate : (%,(R -> R)) -> %
 eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
 eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
 every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
 exquo : (%,R) -> Union(%,"failed") if R has INTDOM
 inverse : % -> Union(%,"failed") if R has FIELD
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((R -> R),%) -> % if $ has shallowlyMutable
 member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
 members : % -> List R if $ has finiteAggregate
 minordet : % -> R if R has commutative *
 more? : (%,NonNegativeInteger) -> Boolean
 nullSpace : % -> List DirectProduct(ndim,R) if R has INTDOM
 nullity : % -> NonNegativeInteger if R has INTDOM
 parts : % -> List R if $ has finiteAggregate
 rank : % -> NonNegativeInteger if R has INTDOM
 reducedSystem : Matrix % -> Matrix R
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
 reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
 retract : % -> Fraction Integer if R has RETRACT FRAC INT
 retract : % -> Integer if R has RETRACT INT
 retractIfCan : % -> Union(R,"failed")
 retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
 retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
 row : (%,Integer) -> DirectProduct(ndim,R)
 rowEchelon : % -> % if R has EUCDOM
 size? : (%,NonNegativeInteger) -> Boolean
 subtractIfCan : (%,%) -> Union(%,"failed")

--R SquareMatrix(ndim: NonNegativeInteger,R: Ring)  is a domain constructor
--R Abbreviation for SquareMatrix is SQMATRIX 
--R This constructor is not exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for SQMATRIX 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (R,%) -> %                      ?*? : (%,R) -> %
--R ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> %                      ?-? : (%,%) -> %
--R -? : % -> %                           ?=? : (%,%) -> Boolean
--R D : % -> % if R has DIFRING           D : (%,(R -> R)) -> %
--R 1 : () -> %                           0 : () -> %
--R ?^? : (%,PositiveInteger) -> %        antisymmetric? : % -> Boolean
--R coerce : % -> Matrix R                coerce : R -> %
--R coerce : Integer -> %                 coerce : % -> OutputForm
--R copy : % -> %                         diagonal? : % -> Boolean
--R diagonalMatrix : List R -> %          diagonalProduct : % -> R
--R elt : (%,Integer,Integer) -> R        elt : (%,Integer,Integer,R) -> R
--R empty : () -> %                       empty? : % -> Boolean
--R eq? : (%,%) -> Boolean                hash : % -> SingleInteger
--R latex : % -> String                   listOfLists : % -> List List R
--R map : ((R -> R),%) -> %               map : (((R,R) -> R),%,%) -> %
--R matrix : List List R -> %             maxColIndex : % -> Integer
--R maxRowIndex : % -> Integer            minColIndex : % -> Integer
--R minRowIndex : % -> Integer            ncols : % -> NonNegativeInteger
--R nrows : % -> NonNegativeInteger       one? : % -> Boolean
--R qelt : (%,Integer,Integer) -> R       recip : % -> Union(%,"failed")
--R retract : % -> R                      sample : () -> %
--R scalarMatrix : R -> %                 square? : % -> Boolean
--R squareMatrix : Matrix R -> %          symmetric? : % -> Boolean
--R trace : % -> R                        transpose : % -> %
--R zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R)
--R ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R)
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
--R D : (%,Symbol) -> % if R has PDRING SYMBOL
--R D : (%,List Symbol) -> % if R has PDRING SYMBOL
--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
--R D : (%,(R -> R),NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R characteristic : () -> NonNegativeInteger
--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
--R column : (%,Integer) -> DirectProduct(ndim,R)
--R convert : % -> InputForm if R has KONVERT INFORM
--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R determinant : % -> R if R has commutative *
--R diagonal : % -> DirectProduct(ndim,R)
--R differentiate : % -> % if R has DIFRING
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
--R differentiate : (%,(R -> R)) -> %
--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R inverse : % -> Union(%,"failed") if R has FIELD
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((R -> R),%) -> % if $ has shallowlyMutable
--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
--R members : % -> List R if $ has finiteAggregate
--R minordet : % -> R if R has commutative *
--R more? : (%,NonNegativeInteger) -> Boolean
--R nullSpace : % -> List DirectProduct(ndim,R) if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
--R parts : % -> List R if $ has finiteAggregate
--R rank : % -> NonNegativeInteger if R has INTDOM
--R reducedSystem : Matrix % -> Matrix R
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
--R retract : % -> Fraction Integer if R has RETRACT FRAC INT
--R retract : % -> Integer if R has RETRACT INT
--R retractIfCan : % -> Union(R,"failed")
--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
--R row : (%,Integer) -> DirectProduct(ndim,R)
--R rowEchelon : % -> % if R has EUCDOM
--R size? : (%,NonNegativeInteger) -> Boolean
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 41

--S 42 of 97
)set expose
 
---------------------------- The expose Option ----------------------------

 Description: control interpreter constructor exposure

   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   The following constructors are explicitly hidden in the current 
      frame:
                               SquareMatrix                                
 
   When )set expose is followed by no arguments, the information you 
      now see is displayed. When followed by the initialize argument, 
      the exposure group data in the file interp.exposed is read and is
      then available. The arguments add and drop are used to add or 
      drop exposure groups or explicit constructors from the local 
      frame exposure data. Issue
                  )set expose add    or    )set expose drop 
      for more information.
--R---------------------------- The expose Option ----------------------------
--R
--R Description: control interpreter constructor exposure
--R
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                               SquareMatrix                                
--R 
--R   When )set expose is followed by no arguments, the information you 
--R      now see is displayed. When followed by the initialize argument, 
--R      the exposure group data in the file interp.exposed is read and is
--R      then available. The arguments add and drop are used to add or 
--R      drop exposure groups or explicit constructors from the local 
--R      frame exposure data. Issue
--R                  )set expose add    or    )set expose drop 
--R      for more information.
--E 42

--S 43 of 97
)set expose drop group anna
 
   anna is no longer an exposure group for frame initial 
--I   anna is no longer an exposure group for frame frame0 
--E 43

--S 44 of 97
)set expose
 
---------------------------- The expose Option ----------------------------

 Description: control interpreter constructor exposure

   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   The following constructors are explicitly hidden in the current 
      frame:
                               SquareMatrix                                
 
   When )set expose is followed by no arguments, the information you 
      now see is displayed. When followed by the initialize argument, 
      the exposure group data in the file interp.exposed is read and is
      then available. The arguments add and drop are used to add or 
      drop exposure groups or explicit constructors from the local 
      frame exposure data. Issue
                  )set expose add    or    )set expose drop 
      for more information.
--R---------------------------- The expose Option ----------------------------
--R
--R Description: control interpreter constructor exposure
--R
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                               SquareMatrix                                
--R 
--R   When )set expose is followed by no arguments, the information you 
--R      now see is displayed. When followed by the initialize argument, 
--R      the exposure group data in the file interp.exposed is read and is
--R      then available. The arguments add and drop are used to add or 
--R      drop exposure groups or explicit constructors from the local 
--R      frame exposure data. Issue
--R                  )set expose add    or    )set expose drop 
--R      for more information.
--E 44

--S 45 of 97
)set expose add group
 
---------------------------- The group Option -----------------------------
   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
 
   When )set expose add group is followed by no arguments, the 
      information you now see is displayed. Otherwise, the words 
      following group must be valid names of exposure groups defined in
      interp.exposed . The group all is special: using this group name 
      causes all known constructors to be exposed. The known exposure 
      group names are:
 
basic         naglink       anna          categories    Hidden        
defaults      
--R---------------------------- The group Option -----------------------------
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R 
--R   When )set expose add group is followed by no arguments, the 
--R      information you now see is displayed. Otherwise, the words 
--R      following group must be valid names of exposure groups defined in
--R      interp.exposed . The group all is special: using this group name 
--R      causes all known constructors to be exposed. The known exposure 
--R      group names are:
--R 
--Rbasic         naglink       anna          categories    Hidden        
--Rdefaults      
--E 45

--S 46 of 97
)set expose add group anna
 
   anna is now an exposure group for frame initial 
--I   anna is now an exposure group for frame frame0 
--E 46

--S 47 of 97
)set expose
 
---------------------------- The expose Option ----------------------------

 Description: control interpreter constructor exposure

   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   anna                                    
                                   basic                                   
                                categories                                 
                                  naglink                                  
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   The following constructors are explicitly hidden in the current 
      frame:
                               SquareMatrix                                
 
   When )set expose is followed by no arguments, the information you 
      now see is displayed. When followed by the initialize argument, 
      the exposure group data in the file interp.exposed is read and is
      then available. The arguments add and drop are used to add or 
      drop exposure groups or explicit constructors from the local 
      frame exposure data. Issue
                  )set expose add    or    )set expose drop 
      for more information.
--R---------------------------- The expose Option ----------------------------
--R
--R Description: control interpreter constructor exposure
--R
--R   The following groups are explicitly exposed in the current frame 
--I      (called frame0 ):
--R                                   anna                                    
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                               SquareMatrix                                
--R 
--R   When )set expose is followed by no arguments, the information you 
--R      now see is displayed. When followed by the initialize argument, 
--R      the exposure group data in the file interp.exposed is read and is
--R      then available. The arguments add and drop are used to add or 
--R      drop exposure groups or explicit constructors from the local 
--R      frame exposure data. Issue
--R                  )set expose add    or    )set expose drop 
--R      for more information.
--E 47

--S 48 of 97
)display
 

  )display keyword arguments are
     abbreviations
     all
     macros
     modes
     names
     operations
     properties
     types
     values
  or abbreviations thereof

--R
--R  )display keyword arguments are
--R     abbreviations
--R     all
--R     macros
--R     modes
--R     names
--R     operations
--R     properties
--R     types
--R     values
--R  or abbreviations thereof
--R
--E 48

--S 49 of 97
)display abb
 
   You have requested that all abbreviations be displayed. As there are
      several hundred abbreviations, please confirm your request by 
      typing y or yes and then pressing Enter :
 
   >> System error:
   %.EOF is not of type SEQUENCE.

   Continuing to read the file...

--R 
--R   You have requested that all abbreviations be displayed. As there are
--R      several hundred abbreviations, please confirm your request by 
--R      typing y or yes and then pressing Enter :
--R 
--R   >> System error:
--R   %.EOF is not of type SEQUENCE.
--R
--R   Continuing to read the file...
--R
--E 49

--S 50 of 97
)display all
 
Properties of %e :
   This is a system-defined macro.
   macro %e () == exp(1)
Properties of %i :
   This is a system-defined macro.
   macro %i () == complex(0,1)
Properties of %infinity :
   This is a system-defined macro.
   macro %infinity () == infinity()
Properties of %minusInfinity :
   This is a system-defined macro.
   macro %minusInfinity () == minusInfinity()
Properties of %pi :
   This is a system-defined macro.
   macro %pi () == pi()
Properties of %plusInfinity :
   This is a system-defined macro.
   macro %plusInfinity () == plusInfinity()
Properties of SF :
   This is a system-defined macro.
   macro SF () == DoubleFloat()
--RProperties of %e :
--R   This is a system-defined macro.
--R   macro %e () == exp(1)
--RProperties of %i :
--R   This is a system-defined macro.
--R   macro %i () == complex(0,1)
--RProperties of %infinity :
--R   This is a system-defined macro.
--R   macro %infinity () == infinity()
--RProperties of %minusInfinity :
--R   This is a system-defined macro.
--R   macro %minusInfinity () == minusInfinity()
--RProperties of %pi :
--R   This is a system-defined macro.
--R   macro %pi () == pi()
--RProperties of %plusInfinity :
--R   This is a system-defined macro.
--R   macro %plusInfinity () == plusInfinity()
--RProperties of SF :
--R   This is a system-defined macro.
--R   macro SF () == DoubleFloat()
--E 50

--S 51 of 97
)display macros
 

System-defined macros:
   macro %e () == exp(1)
   macro %i () == complex(0,1)
   macro %infinity () == infinity()
   macro %minusInfinity () == minusInfinity()
   macro %pi () == pi()
   macro %plusInfinity () == plusInfinity()
   macro SF () == DoubleFloat()
--R
--RSystem-defined macros:
--R   macro %e () == exp(1)
--R   macro %i () == complex(0,1)
--R   macro %infinity () == infinity()
--R   macro %minusInfinity () == minusInfinity()
--R   macro %pi () == pi()
--R   macro %plusInfinity () == plusInfinity()
--R   macro SF () == DoubleFloat()
--E 51

--S 52 of 97
)display modes
 
   Type of value of %e:  (none)
   Type of value of %i:  (none)
   Type of value of %infinity:  (none)
   Type of value of %minusInfinity:  (none)
   Type of value of %pi:  (none)
   Type of value of %plusInfinity:  (none)
   Type of value of SF:  (none)
--R   Type of value of %e:  (none)
--R   Type of value of %i:  (none)
--R   Type of value of %infinity:  (none)
--R   Type of value of %minusInfinity:  (none)
--R   Type of value of %pi:  (none)
--R   Type of value of %plusInfinity:  (none)
--R   Type of value of SF:  (none)
--E 52

--S 53 of 97
)display names
 

Names of User-Defined Objects in the Workspace:

   * None *

Names of System-Defined Objects in the Workspace:

%e                %i                %infinity         %minusInfinity    
%pi               %plusInfinity     SF                
--R
--RNames of User-Defined Objects in the Workspace:
--R
--R   * None *
--R
--RNames of System-Defined Objects in the Workspace:
--R
--R%e                %i                %infinity         %minusInfinity    
--R%pi               %plusInfinity     SF                
--E 53

--S 54 of 97
)display operations
 
   You have requested that all information about all AXIOM operations 
      (functions) be displayed. As there are several hundred 
      operations, please confirm your request by typing y or yes and 
      then pressing Enter :
 
   >> System error:
   %.EOF is not of type SEQUENCE.

   Continuing to read the file...

--R 
--R   You have requested that all information about all AXIOM operations 
--R      (functions) be displayed. As there are several hundred 
--R      operations, please confirm your request by typing y or yes and 
--R      then pressing Enter :
--R 
--R   >> System error:
--R   %.EOF is not of type SEQUENCE.
--R
--R   Continuing to read the file...
--R
--E 54

--S 55 of 97
)display properties
 
Properties of %e :
   This is a system-defined macro.
   macro %e () == exp(1)
Properties of %i :
   This is a system-defined macro.
   macro %i () == complex(0,1)
Properties of %infinity :
   This is a system-defined macro.
   macro %infinity () == infinity()
Properties of %minusInfinity :
   This is a system-defined macro.
   macro %minusInfinity () == minusInfinity()
Properties of %pi :
   This is a system-defined macro.
   macro %pi () == pi()
Properties of %plusInfinity :
   This is a system-defined macro.
   macro %plusInfinity () == plusInfinity()
Properties of SF :
   This is a system-defined macro.
   macro SF () == DoubleFloat()
--RProperties of %e :
--R   This is a system-defined macro.
--R   macro %e () == exp(1)
--RProperties of %i :
--R   This is a system-defined macro.
--R   macro %i () == complex(0,1)
--RProperties of %infinity :
--R   This is a system-defined macro.
--R   macro %infinity () == infinity()
--RProperties of %minusInfinity :
--R   This is a system-defined macro.
--R   macro %minusInfinity () == minusInfinity()
--RProperties of %pi :
--R   This is a system-defined macro.
--R   macro %pi () == pi()
--RProperties of %plusInfinity :
--R   This is a system-defined macro.
--R   macro %plusInfinity () == plusInfinity()
--RProperties of SF :
--R   This is a system-defined macro.
--R   macro SF () == DoubleFloat()
--E 55

--S 56 of 97
)display types
 
   Type of value of %e:  (none)
   Type of value of %i:  (none)
   Type of value of %infinity:  (none)
   Type of value of %minusInfinity:  (none)
   Type of value of %pi:  (none)
   Type of value of %plusInfinity:  (none)
   Type of value of SF:  (none)
--R   Type of value of %e:  (none)
--R   Type of value of %i:  (none)
--R   Type of value of %infinity:  (none)
--R   Type of value of %minusInfinity:  (none)
--R   Type of value of %pi:  (none)
--R   Type of value of %plusInfinity:  (none)
--R   Type of value of SF:  (none)
--E 56

--S 57 of 97
)display values
 
   Value of %e:  (none)
   Value of %i:  (none)
   Value of %infinity:  (none)
   Value of %minusInfinity:  (none)
   Value of %pi:  (none)
   Value of %plusInfinity:  (none)
   Value of SF:  (none)
--R   Value of %e:  (none)
--R   Value of %i:  (none)
--R   Value of %infinity:  (none)
--R   Value of %minusInfinity:  (none)
--R   Value of %pi:  (none)
--R   Value of %plusInfinity:  (none)
--R   Value of SF:  (none)
--E 57

--S 58 of 97
)display abb DHMATRIX
 
   DHMATRIX abbreviates domain DenavitHartenbergMatrix 
--R   DHMATRIX abbreviates domain DenavitHartenbergMatrix 
--E 58

--S 59 of 97
)display abb DenavitHartenbergMatrix
 
   DHMATRIX abbreviates domain DenavitHartenbergMatrix 
--R   DHMATRIX abbreviates domain DenavitHartenbergMatrix 
--E 59

--S 60 of 97
)display operations rotatex
 

There is one exposed function called rotatex :
   [1] D1 -> DenavitHartenbergMatrix D1 from DenavitHartenbergMatrix D1
            if D1 has Join(Field,TranscendentalFunctionCategory)

Examples of rotatex from DenavitHartenbergMatrix

--R
--RThere is one exposed function called rotatex :
--R   [1] D1 -> DenavitHartenbergMatrix D1 from DenavitHartenbergMatrix D1
--R            if D1 has Join(Field,TranscendentalFunctionCategory)
--R
--RExamples of rotatex from DenavitHartenbergMatrix
--R
--E 60

--S 61 of 97
)set fortran calling
 
                   Current Values of  calling  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
tempfile     set location of temporary data files       /tmp/ 
directory    set location of generated FORTRAN files    ./ 
linker       linker arguments (e.g. libraries to search) -lxlf 

--R                   Current Values of  calling  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rtempfile     set location of temporary data files       /tmp/ 
--Rdirectory    set location of generated FORTRAN files    ./ 
--Rlinker       linker arguments (e.g. libraries to search) -lxlf 
--R
--E 61

--S 62 of 97
)set fortran calling tempfile
 
--------------------------- The tempfile Option ---------------------------

 Description: set location of temporary data files

 )set fortran calling tempfile  is used to tell AXIOM where
 to place intermediate FORTRAN data files . This must be the 
 name of a valid existing directory to which you have permission 
 to write (including the final slash).

 Syntax:
   )set fortran calling tempfile DIRECTORYNAME

 The current setting is /tmp/ 
--R--------------------------- The tempfile Option ---------------------------
--R
--R Description: set location of temporary data files
--R
--R )set fortran calling tempfile  is used to tell AXIOM where
--R to place intermediate FORTRAN data files . This must be the 
--R name of a valid existing directory to which you have permission 
--R to write (including the final slash).
--R
--R Syntax:
--R   )set fortran calling tempfile DIRECTORYNAME
--R
--R The current setting is /tmp/ 
--E 62

--S 63 of 97
)set fortran calling tempfile /home/daly
 
--E 63

--S 64 of 97
)set fortran calling tempfile
 
--------------------------- The tempfile Option ---------------------------

 Description: set location of temporary data files

 )set fortran calling tempfile  is used to tell AXIOM where
 to place intermediate FORTRAN data files . This must be the 
 name of a valid existing directory to which you have permission 
 to write (including the final slash).

 Syntax:
   )set fortran calling tempfile DIRECTORYNAME

 The current setting is /home/daly 
--R--------------------------- The tempfile Option ---------------------------
--R
--R Description: set location of temporary data files
--R
--R )set fortran calling tempfile  is used to tell AXIOM where
--R to place intermediate FORTRAN data files . This must be the 
--R name of a valid existing directory to which you have permission 
--R to write (including the final slash).
--R
--R Syntax:
--R   )set fortran calling tempfile DIRECTORYNAME
--R
--R The current setting is /home/daly 
--E 64

--S 65 of 97
)set fortran calling directory
 
-------------------------- The directory Option ---------------------------

 Description: set location of generated FORTRAN files

 )set fortran calling directory  is used to tell AXIOM where
 to place generated FORTRAN files. This must be the name 
 of a valid existing directory to which you have permission 
 to write (including the final slash).

 Syntax:
   )set fortran calling directory DIRECTORYNAME

 The current setting is ./ 
--R-------------------------- The directory Option ---------------------------
--R
--R Description: set location of generated FORTRAN files
--R
--R )set fortran calling directory  is used to tell AXIOM where
--R to place generated FORTRAN files. This must be the name 
--R of a valid existing directory to which you have permission 
--R to write (including the final slash).
--R
--R Syntax:
--R   )set fortran calling directory DIRECTORYNAME
--R
--R The current setting is ./ 
--E 65

--S 66 of 97
)set fortran calling directory /home/daly/
 
--E 66

--S 67 of 97
)set fortran calling directory
 
-------------------------- The directory Option ---------------------------

 Description: set location of generated FORTRAN files

 )set fortran calling directory  is used to tell AXIOM where
 to place generated FORTRAN files. This must be the name 
 of a valid existing directory to which you have permission 
 to write (including the final slash).

 Syntax:
   )set fortran calling directory DIRECTORYNAME

 The current setting is /home/daly/ 
--R-------------------------- The directory Option ---------------------------
--R
--R Description: set location of generated FORTRAN files
--R
--R )set fortran calling directory  is used to tell AXIOM where
--R to place generated FORTRAN files. This must be the name 
--R of a valid existing directory to which you have permission 
--R to write (including the final slash).
--R
--R Syntax:
--R   )set fortran calling directory DIRECTORYNAME
--R
--R The current setting is /home/daly/ 
--E 67

--S 68 of 97
)set fortran calling linker
 
---------------------------- The linker Option ----------------------------

 Description: linker arguments (e.g. libraries to search)

 )set fortran calling linkerargs  is used to pass arguments to the linker
 when using  mkFort  to create functions which call Fortran code.
 For example, it might give a list of libraries to be searched,
 and their locations.
 The string is passed verbatim, so must be the correct syntax for
 the particular linker being used.

 Example: )set fortran calling linker "-lxlf"

 The current setting is -lxlf 
--R---------------------------- The linker Option ----------------------------
--R
--R Description: linker arguments (e.g. libraries to search)
--R
--R )set fortran calling linkerargs  is used to pass arguments to the linker
--R when using  mkFort  to create functions which call Fortran code.
--R For example, it might give a list of libraries to be searched,
--R and their locations.
--R The string is passed verbatim, so must be the correct syntax for
--R the particular linker being used.
--R
--R Example: )set fortran calling linker "-lxlf"
--R
--R The current setting is -lxlf 
--E 68

--S 69 of 97
)set fortran calling linker "-TPD"
 
--E 69

--S 70 of 97
)set fortran calling linker
 
---------------------------- The linker Option ----------------------------

 Description: linker arguments (e.g. libraries to search)

 )set fortran calling linkerargs  is used to pass arguments to the linker
 when using  mkFort  to create functions which call Fortran code.
 For example, it might give a list of libraries to be searched,
 and their locations.
 The string is passed verbatim, so must be the correct syntax for
 the particular linker being used.

 Example: )set fortran calling linker "-lxlf"

 The current setting is -TPD 
--R---------------------------- The linker Option ----------------------------
--R
--R Description: linker arguments (e.g. libraries to search)
--R
--R )set fortran calling linkerargs  is used to pass arguments to the linker
--R when using  mkFort  to create functions which call Fortran code.
--R For example, it might give a list of libraries to be searched,
--R and their locations.
--R The string is passed verbatim, so must be the correct syntax for
--R the particular linker being used.
--R
--R Example: )set fortran calling linker "-lxlf"
--R
--R The current setting is -TPD 
--E 70


--S 71 of 97
)set kernel
 
                   Current Values of  kernel  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
warn         warn when re-definition is attempted       off 
protect      prevent re-definition of kernel functions  off 

--R                   Current Values of  kernel  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rwarn         warn when re-definition is attempted       off 
--Rprotect      prevent re-definition of kernel functions  off 
--R
--E 71

--S 72 of 97
)set kernel warn
 
----------------------------- The warn Option -----------------------------

 Description: warn when re-definition is attempted

Some AXIOM library functions are compiled into the kernel for efficiency
reasons.  To prevent them being re-defined when loaded from a library
they are specially protected.  If a user wishes to know when an attempt
is made to re-define such a function, he or she should issue the command:
        )set kernel warn on
To restore the default behaviour, he or she should issue the command:
        )set kernel warn off
--R----------------------------- The warn Option -----------------------------
--R
--R Description: warn when re-definition is attempted
--R
--RSome AXIOM library functions are compiled into the kernel for efficiency
--Rreasons.  To prevent them being re-defined when loaded from a library
--Rthey are specially protected.  If a user wishes to know when an attempt
--Ris made to re-define such a function, he or she should issue the command:
--R        )set kernel warn on
--RTo restore the default behaviour, he or she should issue the command:
--R        )set kernel warn off
--E 72

--S 73 of 97
)set kernel warn on
 
--E 73

--S 74 of 97
)set kernel
 
                   Current Values of  kernel  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
warn         warn when re-definition is attempted       off 
protect      prevent re-definition of kernel functions  off 

--R                   Current Values of  kernel  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rwarn         warn when re-definition is attempted       off 
--Rprotect      prevent re-definition of kernel functions  off 
--R
--E 74

--S 75 of 97
)set kernel protect
 
--------------------------- The protect Option ----------------------------

 Description: prevent re-definition of kernel functions

Some AXIOM library functions are compiled into the kernel for efficiency
reasons.  To prevent them being re-defined when loaded from a library
they are specially protected.  If a user wishes to re-define these
functions, he or she should issue the command:
        )set kernel protect off
To restore the default behaviour, he or she should issue the command:
        )set kernel protect on
--R--------------------------- The protect Option ----------------------------
--R
--R Description: prevent re-definition of kernel functions
--R
--RSome AXIOM library functions are compiled into the kernel for efficiency
--Rreasons.  To prevent them being re-defined when loaded from a library
--Rthey are specially protected.  If a user wishes to re-define these
--Rfunctions, he or she should issue the command:
--R        )set kernel protect off
--RTo restore the default behaviour, he or she should issue the command:
--R        )set kernel protect on
--E 75

--S 76 of 97
)set kernel protect on
 
--E 76

--S 77 of 97
)set kernel
 
                   Current Values of  kernel  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
warn         warn when re-definition is attempted       off 
protect      prevent re-definition of kernel functions  off 

--R                   Current Values of  kernel  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rwarn         warn when re-definition is attempted       off 
--Rprotect      prevent re-definition of kernel functions  off 
--R
--E 77

--S 78 of 97
)set mes auto
 
--------------------------- The autoload Option ---------------------------

 Description: print file auto-load messages

 The autoload option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R 
--R--------------------------- The autoload Option ---------------------------
--R
--R Description: print file auto-load messages
--R
--R The autoload option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 78

--S 79 of 97
)set mes auto off
 
--E 79

--S 80 of 97
)set mes auto
 
--------------------------- The autoload Option ---------------------------

 Description: print file auto-load messages

 The autoload option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R 
--R--------------------------- The autoload Option ---------------------------
--R
--R Description: print file auto-load messages
--R
--R The autoload option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 80

--S 81 of 97
)set mes auto on
 
--E 81

--S 82 of 97
)set mes auto
 
--------------------------- The autoload Option ---------------------------

 Description: print file auto-load messages

 The autoload option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R 
--R--------------------------- The autoload Option ---------------------------
--R
--R Description: print file auto-load messages
--R
--R The autoload option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 82

--S 83 of 97
)lisp |$printLoadMsgs|
 
Value = T
--R 
--RValue = T
--E 83

--S 84 of 97
)set naglink
 
                   Current Values of  naglink  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
host         internet address of host for NAGLink       localhost 
persistence  number of (fortran) functions to remember  1 
messages     show NAGLink messages                      on 
double       enforce DOUBLE PRECISION ASPs              on 

--R                   Current Values of  naglink  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rhost         internet address of host for NAGLink       localhost 
--Rpersistence  number of (fortran) functions to remember  1 
--Rmessages     show NAGLink messages                      on 
--Rdouble       enforce DOUBLE PRECISION ASPs              on 
--R
--E 84

--S 85 of 97
)set naglink host
 
----------------------------- The host Option -----------------------------

 Description: internet address of host for NAGLink

 )set naglink host is used to tell  AXIOM which  host to contact for
 a NAGLink request. An Internet address should be supplied. The host
 specified must be running the NAGLink daemon.

 The current setting is localhost 
--R----------------------------- The host Option -----------------------------
--R
--R Description: internet address of host for NAGLink
--R
--R )set naglink host is used to tell  AXIOM which  host to contact for
--R a NAGLink request. An Internet address should be supplied. The host
--R specified must be running the NAGLink daemon.
--R
--R The current setting is localhost 
--E 85

--S 86 of 97
)set naglink persistence
 
------------------------- The persistence Option --------------------------

 Description: number of (fortran) functions to remember

 )set naglink persistence is used to tell  the  nagd  daemon how  many ASP
 source and object files to keep around in case you reuse them. This helps
 to avoid needless recompilations. The number specified should be a 
 non-negative integer.

 The current setting is 1 
--R------------------------- The persistence Option --------------------------
--R
--R Description: number of (fortran) functions to remember
--R
--R )set naglink persistence is used to tell  the  nagd  daemon how  many ASP
--R source and object files to keep around in case you reuse them. This helps
--R to avoid needless recompilations. The number specified should be a 
--R non-negative integer.
--R
--R The current setting is 1 
--E 86

--S 87 of 97
)set naglink messages
 
--------------------------- The messages Option ---------------------------

 Description: show NAGLink messages

 The messages option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The messages Option ---------------------------
--R
--R Description: show NAGLink messages
--R
--R The messages option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 87

--S 88 of 97
)set naglink double
 
---------------------------- The double Option ----------------------------

 Description: enforce DOUBLE PRECISION ASPs

 The double option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R---------------------------- The double Option ----------------------------
--R
--R Description: enforce DOUBLE PRECISION ASPs
--R
--R The double option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 88

--S 89 of 97
)set naglink host axiom-developer.org
 
--E 89

--S 90 of 97
)set naglink host
 
----------------------------- The host Option -----------------------------

 Description: internet address of host for NAGLink

 )set naglink host is used to tell  AXIOM which  host to contact for
 a NAGLink request. An Internet address should be supplied. The host
 specified must be running the NAGLink daemon.

 The current setting is axiom-developer.org 
--R----------------------------- The host Option -----------------------------
--R
--R Description: internet address of host for NAGLink
--R
--R )set naglink host is used to tell  AXIOM which  host to contact for
--R a NAGLink request. An Internet address should be supplied. The host
--R specified must be running the NAGLink daemon.
--R
--R The current setting is axiom-developer.org 
--E 90

--S 91 of 97
)set naglink persistence 10
 
--E 91

--S 92 of 97
)set naglink persistence
 
------------------------- The persistence Option --------------------------

 Description: number of (fortran) functions to remember

 )set naglink persistence is used to tell  the  nagd  daemon how  many ASP
 source and object files to keep around in case you reuse them. This helps
 to avoid needless recompilations. The number specified should be a 
 non-negative integer.

 The current setting is 10 
--R------------------------- The persistence Option --------------------------
--R
--R Description: number of (fortran) functions to remember
--R
--R )set naglink persistence is used to tell  the  nagd  daemon how  many ASP
--R source and object files to keep around in case you reuse them. This helps
--R to avoid needless recompilations. The number specified should be a 
--R non-negative integer.
--R
--R The current setting is 10 
--E 92

--S 93 of 97
)set naglink messages off
 
--E 93

--S 94 of 97
)set naglink messages
 
--------------------------- The messages Option ---------------------------

 Description: show NAGLink messages

 The messages option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The messages Option ---------------------------
--R
--R Description: show NAGLink messages
--R
--R The messages option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 94

--S 95 of 97
)set naglink double off
 
--E 95

--S 96 of 97
)set naglink double
 
---------------------------- The double Option ----------------------------

 Description: enforce DOUBLE PRECISION ASPs

 The double option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R---------------------------- The double Option ----------------------------
--R
--R Description: enforce DOUBLE PRECISION ASPs
--R
--R The double option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 96

--S 97 of 97
)set naglink
 
                   Current Values of  naglink  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
host         internet address of host for NAGLink       axiom-developer.org 
persistence  number of (fortran) functions to remember  10 
messages     show NAGLink messages                      off 
double       enforce DOUBLE PRECISION ASPs              off 

--R                   Current Values of  naglink  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rhost         internet address of host for NAGLink       axiom-developer.org 
--Rpersistence  number of (fortran) functions to remember  10 
--Rmessages     show NAGLink messages                      off 
--Rdouble       enforce DOUBLE PRECISION ASPs              off 
--R
--E 97

)spool
 
Starts dribbling to OrderlyDifferentialPolynomial.output (2010/3/27, 18:46:13).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 36
dpol:= ODPOL(FRAC INT)
 

   (1)  OrderlyDifferentialPolynomial Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  OrderlyDifferentialPolynomial Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
w := makeVariable('w)$dpol
 

   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 2

--S 3 of 36
z := makeVariable('z)$dpol
 

   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 3

--S 4 of 36
w.5
 

   (4)  w
         5
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (4)  w
--R         5
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 4

--S 5 of 36
w 0
 

   (5)  w
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (5)  w
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 5

--S 6 of 36
[z.i for i in 1..5]
 

   (6)  [z ,z ,z ,z ,z ]
          1  2  3  4  5
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (6)  [z ,z ,z ,z ,z ]
--R          1  2  3  4  5
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 6

--S 7 of 36
f:= w.4 - w.1 * w.1 * z.3 
 

               2
   (7)  w  - w  z
         4    1  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R               2
--R   (7)  w  - w  z
--R         4    1  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 7

--S 8 of 36
g:=(z.1)**3 * (z.2)**2 - w.2
 

          3  2
   (8)  z  z   - w
         1  2     2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R          3  2
--R   (8)  z  z   - w
--R         1  2     2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 8

--S 9 of 36
D(f)
 

               2
   (9)  w  - w  z  - 2w w z
         5    1  4     1 2 3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R               2
--R   (9)  w  - w  z  - 2w w z
--R         5    1  4     1 2 3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 9

--S 10 of 36
D(f,4)
 

   (10)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (10)
--R            2                               2
--R     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
--R      8    1  7     1 2 6         1 3      2   5     1 3 5
--R   + 
--R                                         2
--R     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
--R          1 4      2 3  4     2 3 4     3  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 10

--S 11 of 36
df:=makeVariable(f)$dpol
 

   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
 Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--R 
--R
--R   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,0)
--R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)
--E 11

--S 12 of 36
df.4
 

   (12)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (12)
--R            2                               2
--R     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
--R      8    1  7     1 2 6         1 3      2   5     1 3 5
--R   + 
--R                                         2
--R     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
--R          1 4      2 3  4     2 3 4     3  3
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 12

--S 13 of 36
order(g)
 

   (13)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  2
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 36
order(g, 'w)
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 36
differentialVariables(g)
 

   (15)  [z,w]
                                                            Type: List Symbol
--R 
--R
--R   (15)  [z,w]
--R                                                            Type: List Symbol
--E 15

--S 16 of 36
degree(g)
 

           2  3
   (16)  z  z
          2  1
                    Type: IndexedExponents OrderlyDifferentialVariable Symbol
--R 
--R
--R           2  3
--R   (16)  z  z
--R          2  1
--R                    Type: IndexedExponents OrderlyDifferentialVariable Symbol
--E 16

--S 17 of 36
degree(g, 'w) 
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 36
weights(g)
 

   (18)  [7,2]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (18)  [7,2]
--R                                                Type: List NonNegativeInteger
--E 18

--S 19 of 36
weights(g,'w)
 

   (19)  [2]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (19)  [2]
--R                                                Type: List NonNegativeInteger
--E 19

--S 20 of 36
weight(g)
 

   (20)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  7
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 36
isobaric?(g)
 

   (21)  false
                                                                Type: Boolean
--R 
--R
--R   (21)  false
--R                                                                Type: Boolean
--E 21

--S 22 of 36
eval(g,['w::Symbol],[f])
 

                  2                           2        3  2
   (22)  - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
            6    1  5     1 2 4      1 3     2   3    1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R                  2                           2        3  2
--R   (22)  - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
--R            6    1  5     1 2 4      1 3     2   3    1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 22

--S 23 of 36
eval(g,variables(w.0),[f])
 

           3  2
   (23)  z  z   - w
          1  2     2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R           3  2
--R   (23)  z  z   - w
--R          1  2     2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 23

--S 24 of 36
monomials(g)
 

            3  2
   (24)  [z  z  ,- w ]
           1  2     2
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3  2
--R   (24)  [z  z  ,- w ]
--R           1  2     2
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 24

--S 25 of 36
variables(g)
 

   (25)  [z ,w ,z ]
           2  2  1
                                Type: List OrderlyDifferentialVariable Symbol
--R 
--R
--R   (25)  [z ,w ,z ]
--R           2  2  1
--R                                Type: List OrderlyDifferentialVariable Symbol
--E 25

--S 26 of 36
gcd(f,g)
 

   (26)  1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R   (26)  1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 26

--S 27 of 36
groebner([f,g])
 

                 2     3  2
   (27)  [w  - w  z ,z  z   - w ]
           4    1  3  1  2     2
                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R                 2     3  2
--R   (27)  [w  - w  z ,z  z   - w ]
--R           4    1  3  1  2     2
--R                    Type: List OrderlyDifferentialPolynomial Fraction Integer
--E 27

--S 28 of 36
lg:=leader(g)
 

   (28)  z
          2
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (28)  z
--R          2
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 28

--S 29 of 36
sg:=separant(g)
 

            3
   (29)  2z  z
           1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3
--R   (29)  2z  z
--R           1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 29

--S 30 of 36
ig:=initial(g)
 

           3
   (30)  z
          1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R           3
--R   (30)  z
--R          1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 30

--S 31 of 36
g1 := D g
 

            3               2  3
   (31)  2z  z z  - w  + 3z  z
           1  2 3    3     1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3               2  3
--R   (31)  2z  z z  - w  + 3z  z
--R           1  2 3    3     1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 31

--S 32 of 36
lg1:= leader g1
 

   (32)  z
          3
                                     Type: OrderlyDifferentialVariable Symbol
--R 
--R
--R   (32)  z
--R          3
--R                                     Type: OrderlyDifferentialVariable Symbol
--E 32

--S 33 of 36
pdf:=D(f, lg1)
 

             2
   (33)  - w
            1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R             2
--R   (33)  - w
--R            1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 33

--S 34 of 36
prf:=sg * f- pdf * g1
 

            3         2        2  2  3
   (34)  2z  z w  - w  w  + 3w  z  z
           1  2 4    1  3     1  1  2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            3         2        2  2  3
--R   (34)  2z  z w  - w  w  + 3w  z  z
--R           1  2 4    1  3     1  1  2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 34

--S 35 of 36
lcf:=leadingCoefficient univariate(prf, lg)
 

            2  2
   (35)  3w  z
           1  1
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            2  2
--R   (35)  3w  z
--R           1  1
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 35

--S 36 of 36
ig * prf - lcf * g * lg
 

            6         2  3        2  2
   (36)  2z  z w  - w  z  w  + 3w  z  w z
           1  2 4    1  1  3     1  1  2 2
                         Type: OrderlyDifferentialPolynomial Fraction Integer
--R 
--R
--R            6         2  3        2  2
--R   (36)  2z  z w  - w  z  w  + 3w  z  w z
--R           1  2 4    1  1  3     1  1  2 2
--R                         Type: OrderlyDifferentialPolynomial Fraction Integer
--E 36
)spool
 
Starts dribbling to log.output (2010/3/27, 18:28:54).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 1
[[0.01, -4.6051701859880914, log(0.01), log(0.01)-(-4.6051701859880914)], _
[0.02, -3.9120230054281461, log(0.02), log(0.02)-(-3.9120230054281461)], _
[0.03, -3.5065578973199817, log(0.03), log(0.03)-(-3.5065578973199817)], _
[0.04, -3.2188758248682007, log(0.04), log(0.04)-(-3.2188758248682007)], _
[0.05, -2.9957322735539910, log(0.05), log(0.05)-(-2.9957322735539910)], _
[0.06, -2.8134107167600364, log(0.06), log(0.06)-(-2.8134107167600364)], _
[0.07, -2.6592600369327781, log(0.07), log(0.07)-(-2.6592600369327781)], _
[0.08, -2.5257286443082554, log(0.08), log(0.08)-(-2.5257286443082554)], _
[0.09, -2.4079456086518720, log(0.09), log(0.09)-(-2.4079456086518720)], _
[0.10, -2.3025850929940457, log(0.10), log(0.10)-(-2.3025850929940457)], _
[0.11, -2.2072749131897208, log(0.11), log(0.11)-(-2.2072749131897208)], _
[0.12, -2.1202635362000911, log(0.12), log(0.12)-(-2.1202635362000911)], _
[0.13, -2.0402208285265546, log(0.13), log(0.13)-(-2.0402208285265546)], _
[0.14, -1.9661128563728328, log(0.14), log(0.14)-(-1.9661128563728328)], _
[0.15, -1.8971199848858813, log(0.15), log(0.15)-(-1.8971199848858813)], _
[0.16, -1.8325814637483101, log(0.16), log(0.16)-(-1.8325814637483101)], _
[0.17, -1.7719568419318753, log(0.17), log(0.17)-(-1.7719568419318753)], _
[0.18, -1.7147984280919267, log(0.18), log(0.18)-(-1.7147984280919267)], _
[0.19, -1.6607312068216509, log(0.19), log(0.19)-(-1.6607312068216509)], _
[0.20, -1.6094379124341004, log(0.20), log(0.20)-(-1.6094379124341004)], _
[0.21, -1.5606477482646684, log(0.21), log(0.21)-(-1.5606477482646684)], _
[0.22, -1.5141277326297755, log(0.22), log(0.22)-(-1.5141277326297755)], _
[0.23, -1.4696759700589417, log(0.23), log(0.23)-(-1.4696759700589417)], _
[0.24, -1.4271163556401457, log(0.24), log(0.24)-(-1.4271163556401457)], _
[0.25, -1.3862943611198906, log(0.25), log(0.25)-(-1.3862943611198906)], _
[0.26, -1.3470736479666093, log(0.26), log(0.26)-(-1.3470736479666093)], _
[0.27, -1.3093333199837623, log(0.27), log(0.27)-(-1.3093333199837623)], _
[0.28, -1.2729656758128874, log(0.28), log(0.28)-(-1.2729656758128874)], _
[0.29, -1.2378743560016173, log(0.29), log(0.29)-(-1.2378743560016173)], _
[0.30, -1.2039728043259360, log(0.30), log(0.30)-(-1.2039728043259360)], _
[0.31, -1.1711829815029451, log(0.31), log(0.31)-(-1.1711829815029451)], _
[0.32, -1.1394342831883648, log(0.32), log(0.32)-(-1.1394342831883648)], _
[0.33, -1.1086626245216111, log(0.33), log(0.33)-(-1.1086626245216111)], _
[0.34, -1.0788096613719300, log(0.34), log(0.34)-(-1.0788096613719300)], _
[0.35, -1.0498221244986777, log(0.35), log(0.35)-(-1.0498221244986777)], _
[0.36, -1.0216512475319814, log(0.36), log(0.36)-(-1.0216512475319814)], _
[0.37, -0.9942522733438669, log(0.37), log(0.37)-(-0.9942522733438669)], _
[0.38, -0.9675840262617056, log(0.38), log(0.38)-(-0.9675840262617056)], _
[0.39, -0.9416085398584449, log(0.39), log(0.39)-(-0.9416085398584449)], _
[0.40, -0.9162907318741551, log(0.40), log(0.40)-(-0.9162907318741551)], _
[0.41, -0.8915981192837836, log(0.41), log(0.41)-(-0.8915981192837836)], _
[0.42, -0.8675005677047231, log(0.42), log(0.42)-(-0.8675005677047231)], _
[0.43, -0.8439700702945289, log(0.43), log(0.43)-(-0.8439700702945289)], _
[0.44, -0.8209805520698302, log(0.44), log(0.44)-(-0.8209805520698302)], _
[0.45, -0.7985076962177716, log(0.45), log(0.45)-(-0.7985076962177716)], _
[0.46, -0.7765287894989964, log(0.46), log(0.46)-(-0.7765287894989964)], _
[0.47, -0.7550225842780328, log(0.47), log(0.47)-(-0.7550225842780328)], _
[0.48, -0.7339691750802004, log(0.48), log(0.48)-(-0.7339691750802004)], _
[0.49, -0.7133498878774648, log(0.49), log(0.49)-(-0.7133498878774648)], _
[0.50, -0.6931471805599453, log(0.50), log(0.50)-(-0.6931471805599453)], _
[0.51, -0.6733445532637656, log(0.51), log(0.51)-(-0.6733445532637656)], _
[0.52, -0.6539264674066640, log(0.52), log(0.52)-(-0.6539264674066640)], _
[0.53, -0.6348782724359695, log(0.53), log(0.53)-(-0.6348782724359695)], _
[0.54, -0.6161861394238170, log(0.54), log(0.54)-(-0.6161861394238170)], _
[0.55, -0.5978370007556204, log(0.55), log(0.55)-(-0.5978370007556204)], _
[0.56, -0.5798184952529421, log(0.56), log(0.56)-(-0.5798184952529421)], _
[0.57, -0.5621189181535412, log(0.57), log(0.57)-(-0.5621189181535412)], _
[0.58, -0.5447271754416720, log(0.58), log(0.58)-(-0.5447271754416720)], _
[0.59, -0.5276327420823719, log(0.59), log(0.59)-(-0.5276327420823719)], _
[0.60, -0.5108256237659907, log(0.60), log(0.60)-(-0.5108256237659907)], _
[0.61, -0.4942963218147801, log(0.61), log(0.61)-(-0.4942963218147801)], _
[0.62, -0.4780358009429998, log(0.62), log(0.62)-(-0.4780358009429998)], _
[0.63, -0.4620354595965587, log(0.63), log(0.63)-(-0.4620354595965587)], _
[0.64, -0.4462871026284195, log(0.64), log(0.64)-(-0.4462871026284195)], _
[0.65, -0.4307829160924543, log(0.65), log(0.65)-(-0.4307829160924543)], _
[0.66, -0.4155154439616658, log(0.66), log(0.66)-(-0.4155154439616658)], _
[0.67, -0.4004775665971253, log(0.67), log(0.67)-(-0.4004775665971253)], _
[0.68, -0.3856624808119847, log(0.68), log(0.68)-(-0.3856624808119847)], _
[0.69, -0.3710636813908320, log(0.69), log(0.69)-(-0.3710636813908320)], _
[0.70, -0.3566749439387324, log(0.70), log(0.70)-(-0.3566749439387324)], _
[0.71, -0.3424903089467759, log(0.71), log(0.71)-(-0.3424903089467759)], _
[0.72, -0.3285040669720361, log(0.72), log(0.72)-(-0.3285040669720361)], _
[0.73, -0.3147107448397002, log(0.73), log(0.73)-(-0.3147107448397002)], _
[0.74, -0.3011050927839216, log(0.74), log(0.74)-(-0.3011050927839216)], _
[0.75, -0.2876820724517809, log(0.75), log(0.75)-(-0.2876820724517809)], _
[0.76, -0.2744368457017603, log(0.76), log(0.76)-(-0.2744368457017603)], _
[0.77, -0.2613647641344075, log(0.77), log(0.77)-(-0.2613647641344075)], _
[0.78, -0.2484613592984996, log(0.78), log(0.78)-(-0.2484613592984996)], _
[0.79, -0.2357223335210699, log(0.79), log(0.79)-(-0.2357223335210699)], _
[0.80, -0.2231435513142098, log(0.80), log(0.80)-(-0.2231435513142098)], _
[0.81, -0.2107210313156526, log(0.81), log(0.81)-(-0.2107210313156526)], _
[0.82, -0.1984509387238383, log(0.82), log(0.82)-(-0.1984509387238383)], _
[0.83, -0.1863295781914934, log(0.83), log(0.83)-(-0.1863295781914934)], _
[0.84, -0.1743533871447778, log(0.84), log(0.84)-(-0.1743533871447778)], _
[0.85, -0.1625189294977749, log(0.85), log(0.85)-(-0.1625189294977749)], _
[0.86, -0.1508228897345836, log(0.86), log(0.86)-(-0.1508228897345836)], _
[0.87, -0.1392620673335076, log(0.87), log(0.87)-(-0.1392620673335076)], _
[0.88, -0.1278333715098849, log(0.88), log(0.88)-(-0.1278333715098849)], _
[0.89, -0.1165338162559515, log(0.89), log(0.89)-(-0.1165338162559515)], _
[0.90, -0.1053605156578263, log(0.90), log(0.90)-(-0.1053605156578263)], _
[0.91, -0.0943106794712413, log(0.91), log(0.91)-(-0.0943106794712413)], _
[0.92, -0.0833816089390511, log(0.92), log(0.92)-(-0.0833816089390511)], _
[0.93, -0.0725706928348354, log(0.93), log(0.93)-(-0.0725706928348354)], _
[0.94, -0.0618754037180875, log(0.94), log(0.94)-(-0.0618754037180875)], _
[0.95, -0.0512932943875505, log(0.95), log(0.95)-(-0.0512932943875505)], _
[0.96, -0.0408219945202551, log(0.96), log(0.96)-(-0.0408219945202551)], _
[0.97, -0.0304592074847085, log(0.97), log(0.97)-(-0.0304592074847085)], _
[0.98, -0.0202027073175194, log(0.98), log(0.98)-(-0.0202027073175194)], _
[0.99, -0.0100503358535014, log(0.99), log(0.99)-(-0.0100503358535014)], _
[1.00, 0.0000000000000000, log(1.00), log(1.00)-(0.0000000000000000)], _
[1.01, 0.0099503308531681, log(1.01), log(1.01)-(0.0099503308531681)], _
[1.02, 0.0198026272961797, log(1.02), log(1.02)-(0.0198026272961797)], _
[1.03, 0.0295588022415444, log(1.03), log(1.03)-(0.0295588022415444)], _
[1.04, 0.0392207131532813, log(1.04), log(1.04)-(0.0392207131532813)], _
[1.05, 0.0487901641694320, log(1.05), log(1.05)-(0.0487901641694320)], _
[1.06, 0.0582689081239758, log(1.06), log(1.06)-(0.0582689081239758)], _
[1.07, 0.0676586484738148, log(1.07), log(1.07)-(0.0676586484738148)], _
[1.08, 0.0769610411361283, log(1.08), log(1.08)-(0.0769610411361283)], _
[1.09, 0.0861776962410523, log(1.09), log(1.09)-(0.0861776962410523)], _
[1.10, 0.0953101798043249, log(1.10), log(1.10)-(0.0953101798043249)], _
[1.11, 0.1043600153242428, log(1.11), log(1.11)-(0.1043600153242428)], _
[1.12, 0.1133286853070032, log(1.12), log(1.12)-(0.1133286853070032)], _
[1.13, 0.1222176327242492, log(1.13), log(1.13)-(0.1222176327242492)], _
[1.14, 0.1310282624064041, log(1.14), log(1.14)-(0.1310282624064041)], _
[1.15, 0.1397619423751587, log(1.15), log(1.15)-(0.1397619423751587)], _
[1.16, 0.1484200051182733, log(1.16), log(1.16)-(0.1484200051182733)], _
[1.17, 0.1570037488096648, log(1.17), log(1.17)-(0.1570037488096648)], _
[1.18, 0.1655144384775734, log(1.18), log(1.18)-(0.1655144384775734)], _
[1.19, 0.1739533071234380, log(1.19), log(1.19)-(0.1739533071234380)], _
[1.20, 0.1823215567939546, log(1.20), log(1.20)-(0.1823215567939546)], _
[1.21, 0.1906203596086497, log(1.21), log(1.21)-(0.1906203596086497)], _
[1.22, 0.1988508587451652, log(1.22), log(1.22)-(0.1988508587451652)], _
[1.23, 0.2070141693843261, log(1.23), log(1.23)-(0.2070141693843261)], _
[1.24, 0.2151113796169455, log(1.24), log(1.24)-(0.2151113796169455)], _
[1.25, 0.2231435513142098, log(1.25), log(1.25)-(0.2231435513142098)], _
[1.26, 0.2311117209633866, log(1.26), log(1.26)-(0.2311117209633866)], _
[1.27, 0.2390169004704999, log(1.27), log(1.27)-(0.2390169004704999)], _
[1.28, 0.2468600779315258, log(1.28), log(1.28)-(0.2468600779315258)], _
[1.29, 0.2546422183735807, log(1.29), log(1.29)-(0.2546422183735807)], _
[1.30, 0.2623642644674911, log(1.30), log(1.30)-(0.2623642644674911)], _
[1.31, 0.2700271372130602, log(1.31), log(1.31)-(0.2700271372130602)], _
[1.32, 0.2776317365982795, log(1.32), log(1.32)-(0.2776317365982795)], _
[1.33, 0.2851789422336624, log(1.33), log(1.33)-(0.2851789422336624)], _
[1.34, 0.2926696139628200, log(1.34), log(1.34)-(0.2926696139628200)], _
[1.35, 0.3001045924503381, log(1.35), log(1.35)-(0.3001045924503381)], _
[1.36, 0.3074846997479606, log(1.36), log(1.36)-(0.3074846997479606)], _
[1.37, 0.3148107398400335, log(1.37), log(1.37)-(0.3148107398400335)], _
[1.38, 0.3220834991691133, log(1.38), log(1.38)-(0.3220834991691133)], _
[1.39, 0.3293037471426004, log(1.39), log(1.39)-(0.3293037471426004)], _
[1.40, 0.3364722366212129, log(1.40), log(1.40)-(0.3364722366212129)], _
[1.41, 0.3435897043900769, log(1.41), log(1.41)-(0.3435897043900769)], _
[1.42, 0.3506568716131694, log(1.42), log(1.42)-(0.3506568716131694)], _
[1.43, 0.3576744442718159, log(1.43), log(1.43)-(0.3576744442718159)], _
[1.44, 0.3646431135879093, log(1.44), log(1.44)-(0.3646431135879093)], _
[1.45, 0.3715635564324830, log(1.45), log(1.45)-(0.3715635564324830)], _
[1.46, 0.3784364357202451, log(1.46), log(1.46)-(0.3784364357202451)], _
[1.47, 0.3852624007906449, log(1.47), log(1.47)-(0.3852624007906449)], _
[1.48, 0.3920420877760237, log(1.48), log(1.48)-(0.3920420877760237)], _
[1.49, 0.3987761199573678, log(1.49), log(1.49)-(0.3987761199573678)], _
[1.50, 0.4054651081081644, log(1.50), log(1.50)-(0.4054651081081644)], _
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[1.52, 0.4187103348581850, log(1.52), log(1.52)-(0.4187103348581850)], _
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   (1)
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                                                        Type: List List Float
--R 
--R
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--R    [1.77,0.5709795465 857378,0.5709795465 8573777398,- 0.26 E -16],
--R    [1.78,0.5766133643 039938,0.5766133643 039937797,- 0.203 E -16],
--R    [1.79,0.5822156198 526636,0.5822156198 5266362814,0.281 E -16],
--R    [1.8,0.5877866649 02119,0.5877866649 0211900819,0.819 E -17],
--R    [1.81,0.5933268452 777344,0.5933268452 777343788,- 0.212 E -16],
--R    [1.82,0.5988365010 88704,0.5988365010 8870398254,- 0.175 E -16],
--R    [1.83,0.6043159668 533296,0.6043159668 5332957211,- 0.279 E -16],
--R    [1.84,0.6097655716 208943,0.6097655716 2089425102,- 0.49 E -16],
--R    [1.85,0.6151856390 902335,0.6151856390 9023345093,- 0.491 E -16],
--R    [1.86,0.6205764877 251099,0.6205764877 2510987871,- 0.213 E -16],
--R    [1.87,0.6259384308 664953,0.6259384308 6649525628,- 0.437 E -16],
--R    [1.88,0.6312717768 418578,0.6312717768 4185783762,0.376 E -16],
--R    [1.89,0.6365768290 71551,0.6365768290 7155101126,0.113 E -16],
--R    [1.9,0.6418538861 723948,0.6418538861 7239477599,- 0.24 E -16],
--R    [1.91,0.6471032420 585385,0.6471032420 5853850481,0.481 E -17],
--R    [1.92,0.6523251860 396902,0.6523251860 3969017986,- 0.201 E -16],
--R    [1.93,0.6575200029 167942,0.6575200029 1679418382,- 0.162 E -16],
--R    [1.94,0.6626879730 752368,0.6626879730 752367635,- 0.365 E -16],
--R    [1.95,0.6678293725 756554,0.6678293725 7565543401,0.34 E -16],
--R    [1.96,0.6729444732 424259,0.6729444732 4242586101,- 0.39 E -16],
--R    [1.97,0.6780335427 498971,0.6780335427 4989713874,0.387 E -16],
--R    [1.98,0.6830968447 064439,0.6830968447 0644386823,- 0.318 E -16],
--R    [1.99,0.6881346387 36401,0.6881346387 3640102737,0.274 E -16],
--R    [2.0,0.6931471805 599453,0.6931471805 5994530942,0.942 E -17]]
--R                                                        Type: List List Float
--E 1
)spool 
 
Starts dribbling to clifford.output (2010/3/27, 18:24:31).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 39
K := FRAC POLY INT
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--% The complex numbers as a Clifford Algebra
)clear p qf
 

--S 2  of 39
qf: QFORM(1, K) := quadraticForm(matrix([[-1]])$(SQMATRIX(1,K)))
 

   (2)  [- 1]
                           Type: QuadraticForm(1,Fraction Polynomial Integer)
--R 
--R
--R   (2)  [- 1]
--R                           Type: QuadraticForm(1,Fraction Polynomial Integer)
--E 2

--S 3 of 39
C := CLIF(1, K, qf)
 

   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 3

--S 4 of 39
i := e(1)$C
 

   (4)  e
         1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 4

--S 5 of 39
x := a + b * i
 

   (5)  a + b e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  a + b e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 5

--S 6 of 39
y := c + d * i
 

   (6)  c + d e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  c + d e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 6

--S 7 of 39
x * y
 

   (7)  - b d + a c + (a d + b c)e
                                  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  - b d + a c + (a d + b c)e
--R                                  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 7

--S 8 of 39
recip %
 

               - b d + a c                 - a d - b c
   (8)  ------------------------- + ------------------------- e
          2    2  2     2    2  2     2    2  2     2    2  2  1
        (b  + a )d  + (b  + a )c    (b  + a )d  + (b  + a )c
       Type: Union(CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX),...)
--R 
--R
--R               - b d + a c                 - a d - b c
--R   (8)  ------------------------- + ------------------------- e
--R          2    2  2     2    2  2     2    2  2     2    2  2  1
--R        (b  + a )d  + (b  + a )c    (b  + a )d  + (b  + a )c
--R       Type: Union(CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX),...)
--E 8

--S 9 of 39
x*%
 

           c         d
   (9)  ------- - ------- e
         2    2    2    2  1
        d  + c    d  + c
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R           c         d
--R   (9)  ------- - ------- e
--R         2    2    2    2  1
--R        d  + c    d  + c
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 9

--S 10 of 39
%*y
 

   (10)  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (10)  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 10
 
--% The quaternions as a Clifford Algebra
)clear p qf
 

--S 11 of 39
qf:QFORM(2, K) :=quadraticForm matrix([[-1, 0], [0, -1]])$(SQMATRIX(2,K))
 

         +- 1   0 +
   (11)  |        |
         + 0   - 1+
                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--R 
--R
--R         +- 1   0 +
--R   (11)  |        |
--R         + 0   - 1+
--R                           Type: QuadraticForm(2,Fraction Polynomial Integer)
--E 11

--S 12 of 39
H  := CLIF(2, K, qf)
 

   (12)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (12)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 12

--S 13 of 39
i  := e(1)$H
 

   (13)  e
          1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (13)  e
--R          1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 13

--S 14 of 39
j  := e(2)$H
 

   (14)  e
          2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (14)  e
--R          2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 14

--S 15 of 39
k  := i * j
 

   (15)  e e
          1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (15)  e e
--R          1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 15

--S 16 of 39
x := a + b * i + c * j + d * k
 

   (16)  a + b e  + c e  + d e e
                1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (16)  a + b e  + c e  + d e e
--R                1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 16

--S 17 of 39
y := e + f * i + g * j + h * k
 

   (17)  e + f e  + g e  + h e e
                1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (17)  e + f e  + g e  + h e e
--R                1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 17

--S 18 of 39
x + y
 

   (18)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
                         1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (18)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                         1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 18

--S 19 of 39
x * y
 

   (19)
     - d h - c g - b f + a e + (c h - d g + a f + b e)e
                                                       1
   + 
     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
                               2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (19)
--R     - d h - c g - b f + a e + (c h - d g + a f + b e)e
--R                                                       1
--R   + 
--R     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
--R                               2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 19

--S 20 of 39
y * x
 

   (20)
     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
                                                         1
   + 
     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (20)
--R     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
--R                                                         1
--R   + 
--R     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 20
 
--% The exterior algebra on a 3 space.
)clear p qf
 
 
--S 21 of 39
qf: QFORM(3, K) := quadraticForm(0::SQMATRIX(3,K))
 

         +0  0  0+
         |       |
   (21)  |0  0  0|
         |       |
         +0  0  0+
                           Type: QuadraticForm(3,Fraction Polynomial Integer)
--R 
--R
--R         +0  0  0+
--R         |       |
--R   (21)  |0  0  0|
--R         |       |
--R         +0  0  0+
--R                           Type: QuadraticForm(3,Fraction Polynomial Integer)
--E 21

--S 22 of 39
Ext := CLIF(3,K,qf)
 

   (22)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (22)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 22

--S 23 of 39
i := e(1)$Ext
 

   (23)  e
          1
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (23)  e
--R          1
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 23

--S 24 of 39
j := e(2)$Ext
 

   (24)  e
          2
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (24)  e
--R          2
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 24

--S 25 of 39
k := e(3)$Ext
 

   (25)  e
          3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (25)  e
--R          3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 25

--S 26 of 39
x := x1*i + x2*j + x3*k
 

   (26)  x1 e  + x2 e  + x3 e
             1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (26)  x1 e  + x2 e  + x3 e
--R             1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 26

--S 27 of 39
y := y1*i + y2*j + y3*k
 

   (27)  y1 e  + y2 e  + y3 e
             1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (27)  y1 e  + y2 e  + y3 e
--R             1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 27

--S 28 of 39
x + y
 

   (28)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
                   1             2             3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (28)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
--R                   1             2             3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 28

--S 29 of 39
x * y + y * x
 

   (29)  0
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (29)  0
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 29

--S 30 of 39
dual2 a ==
    coefficient(a,[2,3])$Ext * i + _
    coefficient(a,[3,1])$Ext * j + _
    coefficient(a,[1,2])$Ext * k 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 39
dual2(x*y)
 
   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) 

   (31)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
                         1                     2                   3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) 
--R
--R   (31)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
--R                         1                     2                   3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 31

)clear p qf
 
 
--S 32 of 39
K := FRAC INT
 

   (32)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (32)  Fraction Integer
--R                                                                 Type: Domain
--E 32

--S 33 of 39
g: SQMATRIX(4, K) := [[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]]
 

         +1   0    0    0 +
         |                |
         |0  - 1   0    0 |
   (33)  |                |
         |0   0   - 1   0 |
         |                |
         +0   0    0   - 1+
                                       Type: SquareMatrix(4,Fraction Integer)
--R 
--R
--R         +1   0    0    0 +
--R         |                |
--R         |0  - 1   0    0 |
--R   (33)  |                |
--R         |0   0   - 1   0 |
--R         |                |
--R         +0   0    0   - 1+
--R                                       Type: SquareMatrix(4,Fraction Integer)
--E 33

--S 34 of 39
qf: QFORM(4, K) := quadraticForm g
 

         +1   0    0    0 +
         |                |
         |0  - 1   0    0 |
   (34)  |                |
         |0   0   - 1   0 |
         |                |
         +0   0    0   - 1+
                                      Type: QuadraticForm(4,Fraction Integer)
--R 
--R
--R         +1   0    0    0 +
--R         |                |
--R         |0  - 1   0    0 |
--R   (34)  |                |
--R         |0   0   - 1   0 |
--R         |                |
--R         +0   0    0   - 1+
--R                                      Type: QuadraticForm(4,Fraction Integer)
--E 34

--S 35 of 39
D := CLIF(4,K,qf)
 

   (35)  CliffordAlgebra(4,Fraction Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (35)  CliffordAlgebra(4,Fraction Integer,MATRIX)
--R                                                                 Type: Domain
--E 35

--S 36 of 39
gam := [e(i)$D for i in 1..4]
 

   (36)  [e ,e ,e ,e ]
           1  2  3  4
                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (36)  [e ,e ,e ,e ]
--R           1  2  3  4
--R                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 36
 

-- Verify this identity for m=1,n=2,r=3,s=4
--S 37 of 39
m := 1; n:= 2; r := 3; s := 4;
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 37

--S 38 of 39
lhs := reduce(+,[reduce(+,[g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t)
             for l in 1..4]) for t in 1..4])
 

   (38)  - 4e e e e
             1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (38)  - 4e e e e
--R             1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 38

--S 39 of 39
rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)
 

   (39)  - 4e e e e
             1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (39)  - 4e e e e
--R             1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 39
)spool
 
Starts dribbling to quat1.output (2010/3/27, 18:30:52).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 11
q := quatern(2/11,-8,3/4,1)
 

         2        3
   (1)  -- - 8i + - j + k
        11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         2        3
--R   (1)  -- - 8i + - j + k
--R        11        4
--R                                            Type: Quaternion Fraction Integer
--E 1

--S 2 of 11
[real q, imagI q, imagJ q, imagK q]
 

          2     3
   (2)  [--,- 8,-,1]
         11     4
                                                  Type: List Fraction Integer
--R 
--R
--R          2     3
--R   (2)  [--,- 8,-,1]
--R         11     4
--R                                                  Type: List Fraction Integer
--E 2

--S 3 of 11
inv q
 

          352     15488      484       1936
   (3)  ------ + ------ i - ----- j - ------ k
        126993   126993     42331     126993
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          352     15488      484       1936
--R   (3)  ------ + ------ i - ----- j - ------ k
--R        126993   126993     42331     126993
--R                                            Type: Quaternion Fraction Integer
--E 3

--S 4 of 11
q**6
 

          2029490709319345   48251690851     144755072553     48251690851
   (4)  - ---------------- - ----------- i + ------------ j + ----------- k
             7256313856        1288408         41229056         10307264
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2029490709319345   48251690851     144755072553     48251690851
--R   (4)  - ---------------- - ----------- i + ------------ j + ----------- k
--R             7256313856        1288408         41229056         10307264
--R                                            Type: Quaternion Fraction Integer
--E 4

--S 5 of 11
r := quatern(-2,3,23/9,-89); q + r
 

          20        119
   (5)  - -- - 5i + --- j - 88k
          11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          20        119
--R   (5)  - -- - 5i + --- j - 88k
--R          11         36
--R                                            Type: Quaternion Fraction Integer
--E 5

--S 6 of 11
q * r - r * q
 

          2495             817
   (6)  - ---- i - 1418j - --- k
           18               18
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2495             817
--R   (6)  - ---- i - 1418j - --- k
--R           18               18
--R                                            Type: Quaternion Fraction Integer
--E 6

--S 7 of 11
i:=quatern(0,1,0,0); j:=quatern(0,0,1,0); k:=quatern(0,0,0,1)
 

   (7)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (7)  k
--R                                                     Type: Quaternion Integer
--E 7

--S 8 of 11
[i*i, j*j, k*k, i*j, j*k, k*i, q*i]
 

                                2         3
   (8)  [- 1,- 1,- 1,k,i,j,8 + -- i + j - - k]
                               11         4
                                       Type: List Quaternion Fraction Integer
--R 
--R
--R                                2         3
--R   (8)  [- 1,- 1,- 1,k,i,j,8 + -- i + j - - k]
--R                               11         4
--R                                       Type: List Quaternion Fraction Integer
--E 8

--S 9 of 11
norm q
 

        126993
   (9)  ------
         1936
                                                       Type: Fraction Integer
--R 
--R
--R        126993
--R   (9)  ------
--R         1936
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 11
conjugate q
 

          2        3
   (10)  -- + 8i - - j - k
         11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2        3
--R   (10)  -- + 8i - - j - k
--R         11        4
--R                                            Type: Quaternion Fraction Integer
--E 10

--S 11 of 11
q * %
 

         126993
   (11)  ------
          1936
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         126993
--R   (11)  ------
--R          1936
--R                                            Type: Quaternion Fraction Integer
--E 11
)spool 
 
Starts dribbling to collect.output (2010/3/27, 18:24:33).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 55
a := [i**3 for i in 0..10]
 

   (1)  [0,1,8,27,64,125,216,343,512,729,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (1)  [0,1,8,27,64,125,216,343,512,729,1000]
--R                                                Type: List NonNegativeInteger
--E 1

--S 2 of 55
b := expand [0..10]
 

   (2)  [0,1,2,3,4,5,6,7,8,9,10]
                                                           Type: List Integer
--R 
--R
--R   (2)  [0,1,2,3,4,5,6,7,8,9,10]
--R                                                           Type: List Integer
--E 2

--S 3 of 55
c := [x**3 for x in b]
 

   (3)  [0,1,8,27,64,125,216,343,512,729,1000]
                                                           Type: List Integer
--R 
--R
--R   (3)  [0,1,8,27,64,125,216,343,512,729,1000]
--R                                                           Type: List Integer
--E 3

--S 4 of 55
d := [i**3 for i in 0..10 | even? i]
 

   (4)  [0,8,64,216,512,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (4)  [0,8,64,216,512,1000]
--R                                                Type: List NonNegativeInteger
--E 4

--S 5 of 55
d := [x**3 for x in b | even? x]
 

   (5)  [0,8,64,216,512,1000]
                                                           Type: List Integer
--R 
--R
--R   (5)  [0,8,64,216,512,1000]
--R                                                           Type: List Integer
--E 5

--S 6 of 55
d := [x for x in c | even? x]
 

   (6)  [0,8,64,216,512,1000]
                                                           Type: List Integer
--R 
--R
--R   (6)  [0,8,64,216,512,1000]
--R                                                           Type: List Integer
--E 6

--S 7 of 55
d := [i**3 for i in 0..10 by 2 | even? i]
 

   (7)  [0,8,64,216,512,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (7)  [0,8,64,216,512,1000]
--R                                                Type: List NonNegativeInteger
--E 7

--S 8 of 55
e := reverse [i**3 for i in 10..0 by -2 | even? i]
 

   (8)  [0,8,64,216,512,1000]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (8)  [0,8,64,216,512,1000]
--R                                                Type: List NonNegativeInteger
--E 8

--S 9 of 55
[x - y for x in d for y in e]
 

   (9)  [0,0,0,0,0,0]
                                                           Type: List Integer
--R 
--R
--R   (9)  [0,0,0,0,0,0]
--R                                                           Type: List Integer
--E 9

--S 10 of 55
[x**3 - y for x in b | even? x for y in e]
 

   (10)  [0,- 56,- 448]
                                                           Type: List Integer
--R
--R   (10)  [0,- 56,- 448]
--R                                                           Type: List Integer
--E 10

--S 11 of 55
f := [i**3 for i in 0..]
 

   (11)  [0,1,8,27,64,125,216,343,512,729,...]
                                              Type: Stream NonNegativeInteger
--R
--R   (11)  [0,1,8,27,64,125,216,343,512,729,...]
--R                                              Type: Stream NonNegativeInteger
--E 11

--S 12 of 55
[i**3 for i in 0..10]
 

   (12)  [0,1,8,27,64,125,216,343,512,729,1000]
                                                Type: List NonNegativeInteger
--R
--R   (12)  [0,1,8,27,64,125,216,343,512,729,1000]
--R                                                Type: List NonNegativeInteger
--E 12

--S 13 of 55
[i**3 for i in 0.. while i < 11]
 

   (13)  [0,1,8,27,64,125,216,343,512,729,...]
                                              Type: Stream NonNegativeInteger
--R
--R   (13)  [0,1,8,27,64,125,216,343,512,729,...]
--R                                              Type: Stream NonNegativeInteger
--E 13

--S 14 of 55
[i**3 for i in 0.. for x in 0..10]
 

   (14)  [0,1,8,27,64,125,216,343,512,729,...]
                                              Type: Stream NonNegativeInteger
--R
--R   (14)  [0,1,8,27,64,125,216,343,512,729,...]
--R                                              Type: Stream NonNegativeInteger
--E 14

--S 15 of 55
[ [i**j for j in 0..3] for i in 0..]
 

   (15)
   [[1,0,0,0], [1,1,1,1], [1,2,4,8], [1,3,9,27], [1,4,16,64], [1,5,25,125],
    [1,6,36,216], [1,7,49,343], [1,8,64,512], [1,9,81,729], ...]
                                         Type: Stream List NonNegativeInteger
--R
--R   (15)
--R   [[1,0,0,0], [1,1,1,1], [1,2,4,8], [1,3,9,27], [1,4,16,64], [1,5,25,125],
--R    [1,6,36,216], [1,7,49,343], [1,8,64,512], [1,9,81,729], ...]
--R                                         Type: Stream List NonNegativeInteger
--E 15

--S 16 of 55
[ [i**j for j in 0..] for i in 0..3]
 

   (16)
   [[1,0,0,0,0,0,0,0,0,0,...], [1,1,1,1,1,1,1,1,1,1,...],
    [1,2,4,8,16,32,64,128,256,512,...],
    [1,3,9,27,81,243,729,2187,6561,19683,...]]
                                           Type: List Stream Fraction Integer
--R
--R   (16)
--R   [[1,0,0,0,0,0,0,0,0,0,...], [1,1,1,1,1,1,1,1,1,1,...],
--R    [1,2,4,8,16,32,64,128,256,512,...],
--R    [1,3,9,27,81,243,729,2187,6561,19683,...]]
--R                                           Type: List Stream Fraction Integer
--E 16

--S 17 of 55
brace [i**3 for i in 10..0 by -2]
 

   (17)  {0,8,64,216,512,1000}
                                                 Type: Set NonNegativeInteger
--R
--R   (17)  {0,8,64,216,512,1000}
--R                                                 Type: Set NonNegativeInteger
--E 17

-- Input generated from ContinuedFractionXmpPage
)clear all
 

--S 18 of 55
c := continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 18

--S 19 of 55
partialQuotients c
 

   (2)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (2)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 19

--S 20 of 55
convergents c
 

           22 333 355 9208 9563 76149 314159
   (3)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R           22 333 355 9208 9563 76149 314159
--R   (3)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 20

--S 21 of 55
approximants c
 

                                      ______
           22 333 355 9208 9563 76149 314159
   (4)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R                                      ______
--R           22 333 355 9208 9563 76149 314159
--R   (4)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 21

--S 22 of 55
pq := partialQuotients(1/c)
 

   (5)  [0,3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 22

--S 23 of 55
continuedFraction(first pq,repeating [1],rest pq)
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 23

--S 24 of 55
z:=continuedFraction(3,repeating [1],repeating [3,6])
 

   (7)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
   + 
       1 |
     +---+ + ...
     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
--R         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 6
--R                                              Type: ContinuedFraction Integer
--E 24

--S 25 of 55
dens:Stream Integer := cons(1,generate((x+->x+4),6))
 

   (8)  [1,6,10,14,18,22,26,30,34,38,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [1,6,10,14,18,22,26,30,34,38,...]
--R                                                         Type: Stream Integer
--E 25

--S 26 of 55
cf := continuedFraction(0,repeating [1],dens)
 

   (9)
       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
   + 
       1  |     1  |
     +----+ + +----+ + ...
     | 34     | 38
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (9)
--R       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
--R     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
--R     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
--R   + 
--R       1  |     1  |
--R     +----+ + +----+ + ...
--R     | 34     | 38
--R                                              Type: ContinuedFraction Integer
--E 26

--S 27 of 55
ccf := convergents cf
 

              6 61  860 15541 342762  8927353 268163352  9126481321
   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
              7 71 1001 18089 398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              6 61  860 15541 342762  8927353 268163352  9126481321
--R   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
--R              7 71 1001 18089 398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 27

--S 28 of 55
eConvergents := [2*e + 1 for e in ccf]
 

              19 193 2721 49171 1084483 28245729 848456353 28875761731
   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
               7  71 1001 18089  398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              19 193 2721 49171 1084483 28245729 848456353 28875761731
--R   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
--R               7  71 1001 18089  398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 28

--S 29 of 55
eConvergents :: Stream Float
 

   (12)
   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (12)
--R   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
--R    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
--R    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
--R    ...]
--R                                                           Type: Stream Float
--E 29

--S 30 of 55
exp 1.0
 

   (13)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (13)  2.7182818284 590452354
--R                                                                  Type: Float
--E 30

--S 31 of 55
cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])
 

   (14)
           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
   + 
       289 |     361 |
     +-----+ + +-----+ + ...
     |  2      |  2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (14)
--R           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
--R     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
--R         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
--R   + 
--R       289 |     361 |
--R     +-----+ + +-----+ + ...
--R     |  2      |  2
--R                                              Type: ContinuedFraction Integer
--E 31

--S 32 of 55
ccf := convergents cf
 

            3 15 105 315 3465 45045 45045 765765 14549535
   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
            2 13  76 263 2578 36979 33976 622637 11064338
                                                Type: Stream Fraction Integer
--R 
--R
--R            3 15 105 315 3465 45045 45045 765765 14549535
--R   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
--R            2 13  76 263 2578 36979 33976 622637 11064338
--R                                                Type: Stream Fraction Integer
--E 32

--S 33 of 55
piConvergents := [4/p for p in ccf]
 

            8 52 304 1052 10312 147916 135904 2490548 44257352
   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
            3 15 105  315  3465  45045  45045  765765 14549535
                                                Type: Stream Fraction Integer
--R 
--R
--R            8 52 304 1052 10312 147916 135904 2490548 44257352
--R   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
--R            3 15 105  315  3465  45045  45045  765765 14549535
--R                                                Type: Stream Fraction Integer
--E 33

--S 34 of 55
piConvergents :: Stream Float
 

   (17)
   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
    3.0418396189 294022111, ...]
                                                           Type: Stream Float
--R 
--R
--R   (17)
--R   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
--R    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
--R    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
--R    3.0418396189 294022111, ...]
--R                                                           Type: Stream Float
--E 34

--S 35 of 55
continuedFraction((- 122 + 597*%i)/(4 - 4*%i))
 

                            1    |         1     |
   (18)  - 90 + 59%i + +---------+ + +-----------+
                       | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1    |         1     |
--R   (18)  - 90 + 59%i + +---------+ + +-----------+
--R                       | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 35

--S 36 of 55
r : Fraction UnivariatePolynomial(x,Fraction Integer)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 55
r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))
 

           2
          x  - 3x + 2
   (20)  ------------
          2
         x  - 7x + 12
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2
--R          x  - 3x + 2
--R   (20)  ------------
--R          2
--R         x  - 7x + 12
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 37

--S 38 of 55
continuedFraction r
 

                  1    |         1     |
   (21)  1 + +---------+ + +-----------+
             | 1     9     | 16     40
             | - x - -     | -- x - --
             | 4     8     |  3      3
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                  1    |         1     |
--R   (21)  1 + +---------+ + +-----------+
--R             | 1     9     | 16     40
--R             | - x - -     | -- x - --
--R             | 4     8     |  3      3
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 38

--S 39 of 55
[i*i for i in convergents(z) :: Stream Float]
 

   (22)
   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (22)
--R   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
--R    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
--R    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
--R    ...]
--R                                                           Type: Stream Float
--E 39

-- Input for page ForCollectionDetailPage
)clear all
 

--S 40 of 55
u := [i**3 for i in 1..10]
 

   (1)  [1,8,27,64,125,216,343,512,729,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,8,27,64,125,216,343,512,729,1000]
--R                                                   Type: List PositiveInteger
--E 40

--S 41 of 55
u(4)
 

   (2)  64
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  64
--R                                                        Type: PositiveInteger
--E 41

--S 42 of 55
[8*i**3 for n in 1..5]
 

           3   3   3   3   3
   (3)  [8i ,8i ,8i ,8i ,8i ]
                                                Type: List Polynomial Integer
--R 
--R
--R           3   3   3   3   3
--R   (3)  [8i ,8i ,8i ,8i ,8i ]
--R                                                Type: List Polynomial Integer
--E 42

--S 43 of 55
[u(2*n) for n in 1..5]
 

   (4)  [8,64,216,512,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [8,64,216,512,1000]
--R                                                   Type: List PositiveInteger
--E 43

--S 44 of 55
[u(i) for i in 1..10 | even? i]
 

   (5)  [8,64,216,512,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [8,64,216,512,1000]
--R                                                   Type: List PositiveInteger
--E 44

--S 45 of 55
[x for x in u | even? x]
 

   (6)  [8,64,216,512,1000]
                                                   Type: List PositiveInteger
--R 
--R
--R   (6)  [8,64,216,512,1000]
--R                                                   Type: List PositiveInteger
--E 45

-- Input for page ForStreamDetailPage
)clear all
 

--S 46 of 55
u := [i**3 for i in 1..]
 

   (1)  [1,8,27,64,125,216,343,512,729,1000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (1)  [1,8,27,64,125,216,343,512,729,1000,...]
--R                                                 Type: Stream PositiveInteger
--E 46

--S 47 of 55
u(4)
 

   (2)  64
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  64
--R                                                        Type: PositiveInteger
--E 47

--S 48 of 55
u
 

   (3)  [1,8,27,64,125,216,343,512,729,1000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (3)  [1,8,27,64,125,216,343,512,729,1000,...]
--R                                                 Type: Stream PositiveInteger
--E 48

--S 49 of 55
u(16)
 

   (4)  4096
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  4096
--R                                                        Type: PositiveInteger
--E 49

--S 50 of 55
[i**3 for i in 0.. | even? i]
 

   (5)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (5)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
--R                                              Type: Stream NonNegativeInteger
--E 50

--S 51 of 55
[8*i**3 for i in 0..]
 

   (6)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (6)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
--R                                              Type: Stream NonNegativeInteger
--E 51

--S 52 of 55
[i**3 for i in 0.. by 2]
 

   (7)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (7)  [0,8,64,216,512,1000,1728,2744,4096,5832,...]
--R                                              Type: Stream NonNegativeInteger
--E 52

--S 53 of 55
[u(i) for i in 1.. | even? i]
 

   (8)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (8)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
--R                                                 Type: Stream PositiveInteger
--E 53

--S 54 of 55
[u(2*i) for i in 1..]
 

   (9)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (9)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
--R                                                 Type: Stream PositiveInteger
--E 54

--S 55 of 55
[x for x in u | even? x]
 

   (10)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (10)  [8,64,216,512,1000,1728,2744,4096,5832,8000,...]
--R                                                 Type: Stream PositiveInteger
--E 55
)spool
 
Starts dribbling to hyperbolicrules.output (2010/3/27, 18:26:51).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 298
sinhdef:=rule(sinh(x) == (e^x-e^(-x))/2)
 

                    x    - x
                   e  - e
   (1)  sinh(x) == ---------
                       2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    x    - x
--R                   e  - e
--R   (1)  sinh(x) == ---------
--R                       2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 1

--S 2 of 298
t1:=sinh(x) - (e^x-e^(-x))/2
 

           x    - x
        - e  + e    + 2sinh(x)
   (2)  ----------------------
                   2
                                                     Type: Expression Integer
--R
--R           x    - x
--R        - e  + e    + 2sinh(x)
--R   (2)  ----------------------
--R                   2
--R                                                     Type: Expression Integer
--E 2

--S 3 of 298
t2:=sinhdef t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 3

)clear all
 

--S 4 of 298
coshdef:=rule(cosh(x) == (e^x+e^(-x))/2)
 

                    x    - x
                   e  + e
   (1)  cosh(x) == ---------
                       2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    x    - x
--R                   e  + e
--R   (1)  cosh(x) == ---------
--R                       2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 4

--S 5 of 298
t1:=cosh(x) - (e^x+e^(-x))/2
 

           x    - x
        - e  - e    + 2cosh(x)
   (2)  ----------------------
                   2
                                                     Type: Expression Integer
--R
--R           x    - x
--R        - e  - e    + 2cosh(x)
--R   (2)  ----------------------
--R                   2
--R                                                     Type: Expression Integer
--E 5

--S 6 of 298
t2:=coshdef t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 6

)clear all
 

--S 7 of 298
tanhdef:=rule(tanh(x) == (e^x-e*(-x))/(e^x+e*(-x)))
 

                    x
                   e  + e x
   (1)  tanh(x) == --------
                    x
                   e  - e x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    x
--R                   e  + e x
--R   (1)  tanh(x) == --------
--R                    x
--R                   e  - e x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 7

--S 8 of 298
t1:=tanh(x) - (e^x-e*(-x))/(e^x+e*(-x))
 

                      x
        (tanh(x) - 1)e  - e x tanh(x) - e x
   (2)  -----------------------------------
                       x
                      e  - e x
                                                     Type: Expression Integer
--R
--R                      x
--R        (tanh(x) - 1)e  - e x tanh(x) - e x
--R   (2)  -----------------------------------
--R                       x
--R                      e  - e x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 298
t2:=tanhdef t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 9

)clear all
 

--S 10 of 298
cothdef:=rule(coth(x) == (e^x+e*(-x))/(e^x-e*(-x)))
 

                    x
                   e  - e x
   (1)  coth(x) == --------
                    x
                   e  + e x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    x
--R                   e  - e x
--R   (1)  coth(x) == --------
--R                    x
--R                   e  + e x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 10

--S 11 of 298
t1:=coth(x) - (e^x+e*(-x))/(e^x-e*(-x))
 

                      x
        (coth(x) - 1)e  + e x coth(x) + e x
   (2)  -----------------------------------
                       x
                      e  + e x
                                                     Type: Expression Integer
--R
--R                      x
--R        (coth(x) - 1)e  + e x coth(x) + e x
--R   (2)  -----------------------------------
--R                       x
--R                      e  + e x
--R                                                     Type: Expression Integer
--E 11

--S 12 of 298
t2:=cothdef t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 12

)clear all
 

--S 13 of 298
sechdef:=rule(sech(x) == 2/(e^x+e*(-x)))
 

                       2
   (1)  sech(x) == --------
                    x
                   e  - e x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                       2
--R   (1)  sech(x) == --------
--R                    x
--R                   e  - e x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 13

--S 14 of 298
t1:=sech(x) - 2/(e^x+e*(-x))
 

                x
        sech(x)e  - e x sech(x) - 2
   (2)  ---------------------------
                   x
                  e  - e x
                                                     Type: Expression Integer
--R
--R                x
--R        sech(x)e  - e x sech(x) - 2
--R   (2)  ---------------------------
--R                   x
--R                  e  - e x
--R                                                     Type: Expression Integer
--E 14

--S 15 of 298
t2:=sechdef t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 15

)clear all
 

--S 16 of 298
cschdef:=rule(csch(x) == 2/(e^x-e*(-x)))
 

                       2
   (1)  csch(x) == --------
                    x
                   e  + e x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                       2
--R   (1)  csch(x) == --------
--R                    x
--R                   e  + e x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 16

--S 17 of 298
t1:=csch(x) - 2/(e^x-e*(-x))
 

                x
        csch(x)e  + e x csch(x) - 2
   (2)  ---------------------------
                   x
                  e  + e x
                                                     Type: Expression Integer
--R
--R                x
--R        csch(x)e  + e x csch(x) - 2
--R   (2)  ---------------------------
--R                   x
--R                  e  + e x
--R                                                     Type: Expression Integer
--E 17

--S 18 of 298
t2:=cschdef t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 18

)clear all
 

--S 19 of 298
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (1)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (1)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 19

--S 20 of 298
t1:=tanh(x) - sinh(x)/cosh(x)
 

        cosh(x)tanh(x) - sinh(x)
   (2)  ------------------------
                 cosh(x)
                                                     Type: Expression Integer
--R
--R        cosh(x)tanh(x) - sinh(x)
--R   (2)  ------------------------
--R                 cosh(x)
--R                                                     Type: Expression Integer
--E 20

--S 21 of 298
t2:=tanhrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 21

)clear all
 

--S 22 of 298
cothrule:=rule(coth(x) == 1/tanh(x))
 

                      1
   (1)  coth(x) == -------
                   tanh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (1)  coth(x) == -------
--R                   tanh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 22

--S 23 of 298
t1:=coth(x) - 1/tanh(x)
 

        coth(x)tanh(x) - 1
   (2)  ------------------
              tanh(x)
                                                     Type: Expression Integer
--R
--R        coth(x)tanh(x) - 1
--R   (2)  ------------------
--R              tanh(x)
--R                                                     Type: Expression Integer
--E 23

--S 24 of 298
t2:=cothrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 24

--S 25 of 298
cothrule2:=rule(coth(x) == cosh(x)/sinh(x))
 

                   cosh(x)
   (4)  coth(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   cosh(x)
--R   (4)  coth(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 25

--S 26 of 298
t3:=coth(x) - cosh(x)/sinh(x)
 

        coth(x)sinh(x) - cosh(x)
   (5)  ------------------------
                 sinh(x)
                                                     Type: Expression Integer
--R
--R        coth(x)sinh(x) - cosh(x)
--R   (5)  ------------------------
--R                 sinh(x)
--R                                                     Type: Expression Integer
--E 26

--S 27 of 298
t4:=cothrule2 t3
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E 27

)clear all
 

--S 28 of 298
sechrule:=rule(sech(x) == 1/cosh(x))
 

                      1
   (1)  sech(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (1)  sech(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 28

--S 29 of 298
t1:=sech(x) - 1/cosh(x)
 

        cosh(x)sech(x) - 1
   (2)  ------------------
              cosh(x)
                                                     Type: Expression Integer
--R
--R        cosh(x)sech(x) - 1
--R   (2)  ------------------
--R              cosh(x)
--R                                                     Type: Expression Integer
--E 29

--S 30 of 298
t2:=sechrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 30

)clear all
 

--S 31 of 298
cschrule:=rule(csch(x) == 1/sinh(x))
 

                      1
   (1)  csch(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (1)  csch(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 31

--S 32 of 298
t1:=csch(x) - 1/sinh(x)
 

        csch(x)sinh(x) - 1
   (2)  ------------------
              sinh(x)
                                                     Type: Expression Integer
--R
--R        csch(x)sinh(x) - 1
--R   (2)  ------------------
--R              sinh(x)
--R                                                     Type: Expression Integer
--E 32

--S 33 of 298
t2:=cschrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 33

)clear all
 

--S 34 of 298
coshsinh:=rule(cosh(x)^2-sinh(x)^2 == 1)
 

                 2          2
   (1)  - sinh(x)  + cosh(x)  + %B == %B + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                 2          2
--I   (1)  - sinh(x)  + cosh(x)  + %Y == %Y + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 34

--S 35 of 298
t1:=cosh(x)^2-sinh(x)^2 - 1
 

                 2          2
   (2)  - sinh(x)  + cosh(x)  - 1
                                                     Type: Expression Integer
--R
--R                 2          2
--R   (2)  - sinh(x)  + cosh(x)  - 1
--R                                                     Type: Expression Integer
--E 35

--S 36 of 298
t2:=coshsinh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 36

)clear all
 

--S 37 of 298
sechtanh:=rule(sech(x)^2+tanh(x)^2 == 1)
 

               2          2
   (1)  tanh(x)  + sech(x)  + %C == %C + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2          2
--I   (1)  tanh(x)  + sech(x)  + %Z == %Z + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 37

--S 38 of 298
t1:=sech(x)^2+tanh(x)^2 - 1
 

               2          2
   (2)  tanh(x)  + sech(x)  - 1
                                                     Type: Expression Integer
--R
--R               2          2
--R   (2)  tanh(x)  + sech(x)  - 1
--R                                                     Type: Expression Integer
--E 38

--S 39 of 298
t2:=sechtanh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 39

)clear all
 

--S 40 of 298
cothcsch:=rule(coth(x)^2-csch(x)^2 == 1)
 

                 2          2
   (1)  - csch(x)  + coth(x)  + %D == %D + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                 2          2
--I   (1)  - csch(x)  + coth(x)  + %BA == %BA + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 40

--S 41 of 298
t1:=coth(x)^2-csch(x)^2 - 1
 

                 2          2
   (2)  - csch(x)  + coth(x)  - 1
                                                     Type: Expression Integer
--R
--R                 2          2
--R   (2)  - csch(x)  + coth(x)  - 1
--R                                                     Type: Expression Integer
--E 41

--S 42 of 298
t2:=cothcsch t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 42

)clear all
 

--S 43 of 298
sinh(-x)
 

   (1)  - sinh(x)
                                                     Type: Expression Integer
--R
--R   (1)  - sinh(x)
--R                                                     Type: Expression Integer
--E 43


)clear all
 

--S 44 of 298
cosh(-x)
 

   (1)  cosh(x)
                                                     Type: Expression Integer
--R
--R   (1)  cosh(x)
--R                                                     Type: Expression Integer
--E 44

)clear all
 

--S 45 of 298
tanh(-x)
 

   (1)  - tanh(x)
                                                     Type: Expression Integer
--R
--R   (1)  - tanh(x)
--R                                                     Type: Expression Integer
--E 45

)clear all
 

--S 46 of 298
csch(-x)
 

   (1)  - csch(x)
                                                     Type: Expression Integer
--R
--R   (1)  - csch(x)
--R                                                     Type: Expression Integer
--E 46

)clear all
 

--S 47 of 298
sech(-x)
 

   (1)  sech(x)
                                                     Type: Expression Integer
--R
--R   (1)  sech(x)
--R                                                     Type: Expression Integer
--E 47

)clear all
 

--S 48 of 298
coth(-x)
 

   (1)  - coth(x)
                                                     Type: Expression Integer
--R
--R   (1)  - coth(x)
--R                                                     Type: Expression Integer
--E 48

)clear all
 

--S 49 of 298
sinhadd:=rule(sinh(x+y) == sinh(x)*cosh(y)+cosh(x)*sinh(y))
 

   (1)  sinh(y + x) == cosh(x)sinh(y) + cosh(y)sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (1)  sinh(y + x) == cosh(x)sinh(y) + cosh(y)sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 49

--S 50 of 298
t1:=sinh(x+y) - (sinh(x)*cosh(y)+cosh(x)*sinh(y))
 

   (2)  sinh(y + x) - cosh(x)sinh(y) - cosh(y)sinh(x)
                                                     Type: Expression Integer
--R
--R   (2)  sinh(y + x) - cosh(x)sinh(y) - cosh(y)sinh(x)
--R                                                     Type: Expression Integer
--E 50

--S 51 of 298
t2:=sinhadd t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 51

--S 52 of 298
sinhsub:=rule(sinh(x-y) == sinh(x)*cosh(y)-cosh(x)*sinh(y))
 

   (4)  - %E sinh(y - x) == - %E cosh(x)sinh(y) + %E cosh(y)sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (4)  - %T sinh(y - x) == - %T cosh(x)sinh(y) + %T cosh(y)sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 52

--S 53 of 298
t3:=sinh(x-y) - (sinh(x)*cosh(y)-cosh(x)*sinh(y))
 

   (5)  cosh(x)sinh(y) - sinh(y - x) - cosh(y)sinh(x)
                                                     Type: Expression Integer
--R
--R   (5)  cosh(x)sinh(y) - sinh(y - x) - cosh(y)sinh(x)
--R                                                     Type: Expression Integer
--E 53

--S 54 of 298
t4:=sinhsub t3
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E 54 

)clear all
 

--S 55 of 298
coshadd:=rule(cosh(x+y) == cosh(x)*cosh(y)+sinh(x)*sinh(y))
 

   (1)  cosh(y + x) == sinh(x)sinh(y) + cosh(x)cosh(y)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (1)  cosh(y + x) == sinh(x)sinh(y) + cosh(x)cosh(y)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 55

--S 56 of 298
t1:=cosh(x+y) - (cosh(x)*cosh(y)+sinh(x)*sinh(y))
 

   (2)  - sinh(x)sinh(y) + cosh(y + x) - cosh(x)cosh(y)
                                                     Type: Expression Integer
--R
--R   (2)  - sinh(x)sinh(y) + cosh(y + x) - cosh(x)cosh(y)
--R                                                     Type: Expression Integer
--E 56

--S 57 of 298
t2:=coshadd t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 57

--S 58 of 298
coshsub:=rule(cosh(x-y) == cosh(x)*cosh(y)-sinh(x)*sinh(y))
 

   (4)  cosh(y - x) == - sinh(x)sinh(y) + cosh(x)cosh(y)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (4)  cosh(y - x) == - sinh(x)sinh(y) + cosh(x)cosh(y)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 58

--S 59 of 298
t3:=cosh(x-y) - (cosh(x)*cosh(y)-sinh(x)*sinh(y))
 

   (5)  sinh(x)sinh(y) - cosh(x)cosh(y) + cosh(y - x)
                                                     Type: Expression Integer
--R
--R   (5)  sinh(x)sinh(y) - cosh(x)cosh(y) + cosh(y - x)
--R                                                     Type: Expression Integer
--E 59

--S 60 of 298
t4:=coshsub t3
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E 60

)clear all
 

--S 61 of 298
tanhadd:=rule(tanh(x+y) == (tanh(x)+tanh(y))/(1+tanh(x)*tanh(y)))
 

                        tanh(y) + tanh(x)
   (1)  tanh(y + x) == ------------------
                       tanh(x)tanh(y) + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        tanh(y) + tanh(x)
--R   (1)  tanh(y + x) == ------------------
--R                       tanh(x)tanh(y) + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 61

--S 62 of 298
t1:=tanh(x+y) - (tanh(x)+tanh(y))/(1+tanh(x)*tanh(y))
 

        (tanh(x)tanh(y) + 1)tanh(y + x) - tanh(y) - tanh(x)
   (2)  ---------------------------------------------------
                         tanh(x)tanh(y) + 1
                                                     Type: Expression Integer
--R
--R        (tanh(x)tanh(y) + 1)tanh(y + x) - tanh(y) - tanh(x)
--R   (2)  ---------------------------------------------------
--R                         tanh(x)tanh(y) + 1
--R                                                     Type: Expression Integer
--E 62

--S 63 of 298
t2:=tanhadd t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 63

--S 64 of 298
tanhneg:=rule(tanh(x-y) == (tanh(x)-tanh(y))/(1-tanh(x)*tanh(y)))
 

                            %F tanh(y) - %F tanh(x)
   (4)  - %F tanh(y - x) == -----------------------
                               tanh(x)tanh(y) - 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                            %V tanh(y) - %V tanh(x)
--I   (4)  - %V tanh(y - x) == -----------------------
--R                               tanh(x)tanh(y) - 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 64

--S 65 of 298
t3:=tanh(x-y) - (tanh(x)-tanh(y))/(1-tanh(x)*tanh(y))
 

        (- tanh(x)tanh(y - x) - 1)tanh(y) + tanh(y - x) + tanh(x)
   (5)  ---------------------------------------------------------
                            tanh(x)tanh(y) - 1
                                                     Type: Expression Integer
--R
--R        (- tanh(x)tanh(y - x) - 1)tanh(y) + tanh(y - x) + tanh(x)
--R   (5)  ---------------------------------------------------------
--R                            tanh(x)tanh(y) - 1
--R                                                     Type: Expression Integer
--E 65

--S 66 of 298
-- t4:=tanhneg t3
--E 66

)clear all
 

--S 67 of 298
cothadd:=rule(coth(x+y) == (coth(x)*coth(y)+1)/(coth(y)+coth(x)))
 

                       coth(x)coth(y) + 1
   (1)  coth(y + x) == ------------------
                        coth(y) + coth(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                       coth(x)coth(y) + 1
--R   (1)  coth(y + x) == ------------------
--R                        coth(y) + coth(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 67

--S 68 of 298
t1:=coth(x+y) - (coth(x)*coth(y)+1)/(coth(y)+coth(x))
 

        (coth(y) + coth(x))coth(y + x) - coth(x)coth(y) - 1
   (2)  ---------------------------------------------------
                         coth(y) + coth(x)
                                                     Type: Expression Integer
--R
--R        (coth(y) + coth(x))coth(y + x) - coth(x)coth(y) - 1
--R   (2)  ---------------------------------------------------
--R                         coth(y) + coth(x)
--R                                                     Type: Expression Integer
--E 68

--S 69 of 298
t2:=cothadd t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 69

--S 70 of 298
cothneg:=rule(coth(x-y) == (coth(x)*coth(y)-1)/(coth(y)-coth(x)))
 

                            %G coth(x)coth(y) - %G
   (4)  - %G coth(y - x) == ----------------------
                               coth(y) - coth(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                            %W coth(x)coth(y) - %W
--I   (4)  - %W coth(y - x) == ----------------------
--R                               coth(y) - coth(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 70

--S 71 of 298
t3:=coth(x-y) - (coth(x)*coth(y)-1)/(coth(y)-coth(x))
 

        (- coth(y - x) - coth(x))coth(y) + coth(x)coth(y - x) + 1
   (5)  ---------------------------------------------------------
                            coth(y) - coth(x)
                                                     Type: Expression Integer
--R
--R        (- coth(y - x) - coth(x))coth(y) + coth(x)coth(y - x) + 1
--R   (5)  ---------------------------------------------------------
--R                            coth(y) - coth(x)
--R                                                     Type: Expression Integer
--E 71

--S 72 of 298
--t4:=cothneg t3
--E 72

)clear all
 

--S 73 of 298
sinh2x:=rule(sinh(2*x) == 2*sinh(x)*cosh(x))
 

   (1)  sinh(2x) == 2cosh(x)sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (1)  sinh(2x) == 2cosh(x)sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 73

--S 74 of 298
t1:=sinh(2*x) - 2*sinh(x)*cosh(x)
 

   (2)  sinh(2x) - 2cosh(x)sinh(x)
                                                     Type: Expression Integer
--R
--R   (2)  sinh(2x) - 2cosh(x)sinh(x)
--R                                                     Type: Expression Integer
--E 74

--S 75 of 298
t2:=sinh2x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 75

)clear all
 

--S 76 of 298
cosh2x:=rule(cosh(2*x) == cosh(x)^2+sinh(x)^2)
 

                           2          2
   (1)  cosh(2x) == sinh(x)  + cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                           2          2
--R   (1)  cosh(2x) == sinh(x)  + cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 76

--S 77 of 298
t1:=cosh(2*x) - (cosh(x)^2+sinh(x)^2)
 

                 2                     2
   (2)  - sinh(x)  + cosh(2x) - cosh(x)
                                                     Type: Expression Integer
--R
--R                 2                     2
--R   (2)  - sinh(x)  + cosh(2x) - cosh(x)
--R                                                     Type: Expression Integer
--E 77

--S 78 of 298
t2:=cosh2x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 78

--S 79 of 298
cosh2x2:=rule(cosh(2*x) == 2*cosh(x)^2-1)
 

                            2
   (4)  cosh(2x) == 2cosh(x)  - 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                            2
--R   (4)  cosh(2x) == 2cosh(x)  - 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 79

--S 80 of 298
t3:=cosh(2*x) - (2*cosh(x)^2-1)
 

                           2
   (5)  cosh(2x) - 2cosh(x)  + 1
                                                     Type: Expression Integer
--R
--R                           2
--R   (5)  cosh(2x) - 2cosh(x)  + 1
--R                                                     Type: Expression Integer
--E 80

--S 81 of 298
t4:=cosh2x2 t3
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E 81

--S 82 of 298
cosh2x3:=rule(cosh(2*x) == 1+2*sinh(x)^2)
 

                            2
   (7)  cosh(2x) == 2sinh(x)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                            2
--R   (7)  cosh(2x) == 2sinh(x)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 82

--S 83 of 298
t5:=cosh(2*x) - (1+2*sinh(x)^2)
 

                  2
   (8)  - 2sinh(x)  + cosh(2x) - 1
                                                     Type: Expression Integer
--R
--R                  2
--R   (8)  - 2sinh(x)  + cosh(2x) - 1
--R                                                     Type: Expression Integer
--E 83

--S 84 of 298
t6:=cosh2x3 t5
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E 84

)clear all
 

--S 85 of 298
tanh2x:=rule(tanh(2*x) == (2*tanh(x))/(1+tanh(x)^2))
 

                      2tanh(x)
   (1)  tanh(2x) == ------------
                           2
                    tanh(x)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      2tanh(x)
--R   (1)  tanh(2x) == ------------
--R                           2
--R                    tanh(x)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 85

--S 86 of 298
t1:=tanh(2*x) - (2*tanh(x))/(1+tanh(x)^2)
 

                2
        (tanh(x)  + 1)tanh(2x) - 2tanh(x)
   (2)  ---------------------------------
                          2
                   tanh(x)  + 1
                                                     Type: Expression Integer
--R
--R                2
--R        (tanh(x)  + 1)tanh(2x) - 2tanh(x)
--R   (2)  ---------------------------------
--R                          2
--R                   tanh(x)  + 1
--R                                                     Type: Expression Integer
--E 86

--S 87 of 298
t2:=tanh2x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 87

)clear all
 

--S 88 of 298
sinhhalf:=rule(sinh(x/2) == sqrt((cosh(x)-1)/2))
 

                    +-----------+
             x     \|cosh(x) - 1
   (1)  sinh(-) == --------------
             2           +-+
                        \|2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    +-----------+
--R             x     \|cosh(x) - 1
--R   (1)  sinh(-) == --------------
--R             2           +-+
--R                        \|2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 88

--S 89 of 298
t1:=sinh(x/2) - sqrt((cosh(x)-1)/2)
 

           +-----------+    +-+     x
        - \|cosh(x) - 1  + \|2 sinh(-)
                                    2
   (2)  ------------------------------
                      +-+
                     \|2
                                                     Type: Expression Integer
--R
--R           +-----------+    +-+     x
--R        - \|cosh(x) - 1  + \|2 sinh(-)
--R                                    2
--R   (2)  ------------------------------
--R                      +-+
--R                     \|2
--R                                                     Type: Expression Integer
--E 89

--S 90 of 298
t2:=sinhhalf t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 90

)clear all
 

--S 91 of 298
sinhhalfneg:=rule(sinh(x/2) == -sqrt((cosh(x)-1)/2))
 

                      +-----------+
             x       \|cosh(x) - 1
   (1)  sinh(-) == - --------------
             2             +-+
                          \|2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      +-----------+
--R             x       \|cosh(x) - 1
--R   (1)  sinh(-) == - --------------
--R             2             +-+
--R                          \|2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 91

--S 92 of 298
t1:=sinh(x/2) - -sqrt((cosh(x)-1)/2)
 

         +-----------+    +-+     x
        \|cosh(x) - 1  + \|2 sinh(-)
                                  2
   (2)  ----------------------------
                     +-+
                    \|2
                                                     Type: Expression Integer
--R
--R         +-----------+    +-+     x
--R        \|cosh(x) - 1  + \|2 sinh(-)
--R                                  2
--R   (2)  ----------------------------
--R                     +-+
--R                    \|2
--R                                                     Type: Expression Integer
--E 92

--S 93 of 298
t2:=sinhhalfneg t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 93

)clear all
 

--S 94 of 298
coshhalf:=rule(cosh(x/2) == sqrt((cosh(x)+1)/2))
 

                    +-----------+
             x     \|cosh(x) + 1
   (1)  cosh(-) == --------------
             2           +-+
                        \|2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    +-----------+
--R             x     \|cosh(x) + 1
--R   (1)  cosh(-) == --------------
--R             2           +-+
--R                        \|2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 94

--S 95 of 298
t1:=cosh(x/2) - sqrt((cosh(x)+1)/2)
 

           +-----------+    +-+     x
        - \|cosh(x) + 1  + \|2 cosh(-)
                                    2
   (2)  ------------------------------
                      +-+
                     \|2
                                                     Type: Expression Integer
--R
--R           +-----------+    +-+     x
--R        - \|cosh(x) + 1  + \|2 cosh(-)
--R                                    2
--R   (2)  ------------------------------
--R                      +-+
--R                     \|2
--R                                                     Type: Expression Integer
--E 95

--S 96 of 298
t2:=coshhalf t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 96

)clear all
 

--S 97 of 298
tanhhalf:=rule(tanh(x/2) == sqrt((cosh(x)-1)/(cosh(x)+1)))
 

                    +-----------+
             x      |cosh(x) - 1
   (1)  tanh(-) ==  |-----------
             2     \|cosh(x) + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    +-----------+
--R             x      |cosh(x) - 1
--R   (1)  tanh(-) ==  |-----------
--R             2     \|cosh(x) + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 97

--S 98 of 298
t1:=tanh(x/2) -sqrt((cosh(x)-1)/(cosh(x)+1))
 

           +-----------+
           |cosh(x) - 1         x
   (2)  -  |-----------  + tanh(-)
          \|cosh(x) + 1         2
                                                     Type: Expression Integer
--R
--R           +-----------+
--R           |cosh(x) - 1         x
--R   (2)  -  |-----------  + tanh(-)
--R          \|cosh(x) + 1         2
--R                                                     Type: Expression Integer
--E 98

--S 99 of 298
t2:=tanhhalf t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 99

)clear all
 

--S 100 of 298
tanhhalfneg:=rule(tanh(x/2) == -sqrt((cosh(x)-1)/(cosh(x)+1)))
 

                      +-----------+
             x        |cosh(x) - 1
   (1)  tanh(-) == -  |-----------
             2       \|cosh(x) + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      +-----------+
--R             x        |cosh(x) - 1
--R   (1)  tanh(-) == -  |-----------
--R             2       \|cosh(x) + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 100

--S 101 of 298
t1:=tanh(x/2) - -sqrt((cosh(x)-1)/(cosh(x)+1))
 

         +-----------+
         |cosh(x) - 1         x
   (2)   |-----------  + tanh(-)
        \|cosh(x) + 1         2
                                                     Type: Expression Integer
--R
--R         +-----------+
--R         |cosh(x) - 1         x
--R   (2)   |-----------  + tanh(-)
--R        \|cosh(x) + 1         2
--R                                                     Type: Expression Integer
--E 101

--S 102 of 298
t2:=tanhhalfneg t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 102

)clear all
 

--S 103 of 298
tanhhalf2:=rule(tanh(x/2) == sinh(x)/(cosh(x)+1))
 

             x       sinh(x)
   (1)  tanh(-) == -----------
             2     cosh(x) + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             x       sinh(x)
--R   (1)  tanh(-) == -----------
--R             2     cosh(x) + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 103

--S 104 of 298
t1:=tanh(x/2) - sinh(x)/(cosh(x)+1)
 

                          x
        (cosh(x) + 1)tanh(-) - sinh(x)
                          2
   (2)  ------------------------------
                  cosh(x) + 1
                                                     Type: Expression Integer
--R
--R                          x
--R        (cosh(x) + 1)tanh(-) - sinh(x)
--R                          2
--R   (2)  ------------------------------
--R                  cosh(x) + 1
--R                                                     Type: Expression Integer
--E 104

--S 105 of 298
t2:=tanhhalf2 t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 105

)clear all
 

--S 106 of 298
tanhhalf3:=rule(tanh(x/2) == (cosh(x)-1)/sinh(x))
 

             x     cosh(x) - 1
   (1)  tanh(-) == -----------
             2       sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             x     cosh(x) - 1
--R   (1)  tanh(-) == -----------
--R             2       sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 106

--S 107 of 298
t1:=tanh(x/2) - (cosh(x)-1)/sinh(x)
 

                    x
        sinh(x)tanh(-) - cosh(x) + 1
                    2
   (2)  ----------------------------
                   sinh(x)
                                                     Type: Expression Integer
--R
--R                    x
--R        sinh(x)tanh(-) - cosh(x) + 1
--R                    2
--R   (2)  ----------------------------
--R                   sinh(x)
--R                                                     Type: Expression Integer
--E 107

--S 108 of 298
t2:=tanhhalf3 t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 108

)clear all
 

--S 109 of 298
sinh3x:=rule(sinh(3*x) == 3*sinh(x)+4*sinh(x)^3)
 

                            3
   (1)  sinh(3x) == 4sinh(x)  + 3sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                            3
--R   (1)  sinh(3x) == 4sinh(x)  + 3sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 109

--S 110 of 298
t1:=sinh(3*x) - (3*sinh(x)+4*sinh(x)^3)
 

                           3
   (2)  sinh(3x) - 4sinh(x)  - 3sinh(x)
                                                     Type: Expression Integer
--R
--R                           3
--R   (2)  sinh(3x) - 4sinh(x)  - 3sinh(x)
--R                                                     Type: Expression Integer
--E 110

--S 111 of 298
t2:=sinh3x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 111

)clear all
 

--S 112 of 298
cosh3x:=rule(cosh(3*x) == 4*cosh(x)^3-3*cosh(x))
 

                            3
   (1)  cosh(3x) == 4cosh(x)  - 3cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                            3
--R   (1)  cosh(3x) == 4cosh(x)  - 3cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 112

--S 113 of 298
t1:=cosh(3*x) - (4*cosh(x)^3-3*cosh(x))
 

                           3
   (2)  cosh(3x) - 4cosh(x)  + 3cosh(x)
                                                     Type: Expression Integer
--R
--R                           3
--R   (2)  cosh(3x) - 4cosh(x)  + 3cosh(x)
--R                                                     Type: Expression Integer
--E 113

--S 114 of 298
t2:=cosh3x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 114

)clear all
 

--S 115 of 298
tanh3x:=rule(tanh(3*x) == (3*tanh(x)+tanh(x)^3)/(1+3*tanh(x)^2))
 

                           3
                    tanh(x)  + 3tanh(x)
   (1)  tanh(3x) == -------------------
                               2
                       3tanh(x)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                           3
--R                    tanh(x)  + 3tanh(x)
--R   (1)  tanh(3x) == -------------------
--R                               2
--R                       3tanh(x)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 115

--S 116 of 298
t1:=tanh(3*x) - (3*tanh(x)+tanh(x)^3)/(1+3*tanh(x)^2)
 

                 2                       3
        (3tanh(x)  + 1)tanh(3x) - tanh(x)  - 3tanh(x)
   (2)  ---------------------------------------------
                                2
                        3tanh(x)  + 1
                                                     Type: Expression Integer
--R
--R                 2                       3
--R        (3tanh(x)  + 1)tanh(3x) - tanh(x)  - 3tanh(x)
--R   (2)  ---------------------------------------------
--R                                2
--R                        3tanh(x)  + 1
--R                                                     Type: Expression Integer
--E 116

--S 117 of 298
t2:=tanh3x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 117

)clear all
 

--S 118 of 298
sinh4x:=rule(sinh(4*x) == 8*sinh(x)^3*cosh(x)+4*sinh(x)*cosh(x))
 

                                   3
   (1)  sinh(4x) == 8cosh(x)sinh(x)  + 4cosh(x)sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                   3
--R   (1)  sinh(4x) == 8cosh(x)sinh(x)  + 4cosh(x)sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 118

--S 119 of 298
t1:=sinh(4*x) - (8*sinh(x)^3*cosh(x)+4*sinh(x)*cosh(x))
 

                                  3
   (2)  sinh(4x) - 8cosh(x)sinh(x)  - 4cosh(x)sinh(x)
                                                     Type: Expression Integer
--R
--R                                  3
--R   (2)  sinh(4x) - 8cosh(x)sinh(x)  - 4cosh(x)sinh(x)
--R                                                     Type: Expression Integer
--E 119

--S 120 of 298
t2:=sinh4x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 120

)clear all
 

--S 121 of 298
cosh4x:=rule(cosh(4*x) == 8*cosh(x)^4-8*cosh(x)^2+1)
 

                            4           2
   (1)  cosh(4x) == 8cosh(x)  - 8cosh(x)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                            4           2
--R   (1)  cosh(4x) == 8cosh(x)  - 8cosh(x)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 121

--S 122 of 298
t1:=cosh(4*x) - (8*cosh(x)^4-8*cosh(x)^2+1)
 

                           4           2
   (2)  cosh(4x) - 8cosh(x)  + 8cosh(x)  - 1
                                                     Type: Expression Integer
--R
--R                           4           2
--R   (2)  cosh(4x) - 8cosh(x)  + 8cosh(x)  - 1
--R                                                     Type: Expression Integer
--E 122

--S 123 of 298
t2:=cosh4x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 123

)clear all
 

--S 124 of 298
tanh4x:=rule(tanh(4*x) == (4*tanh(x)+4*tanh(x)^3)/(1+6*tanh(x)^2+tanh(x)^4))
 

                              3
                      4tanh(x)  + 4tanh(x)
   (1)  tanh(4x) == ------------------------
                           4           2
                    tanh(x)  + 6tanh(x)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                              3
--R                      4tanh(x)  + 4tanh(x)
--R   (1)  tanh(4x) == ------------------------
--R                           4           2
--R                    tanh(x)  + 6tanh(x)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 124

--S 125 of 298
t1:=tanh(4*x) - (4*tanh(x)+4*tanh(x)^3)/(1+6*tanh(x)^2+tanh(x)^4)
 

                4           2                        3
        (tanh(x)  + 6tanh(x)  + 1)tanh(4x) - 4tanh(x)  - 4tanh(x)
   (2)  ---------------------------------------------------------
                                4           2
                         tanh(x)  + 6tanh(x)  + 1
                                                     Type: Expression Integer
--R
--R                4           2                        3
--R        (tanh(x)  + 6tanh(x)  + 1)tanh(4x) - 4tanh(x)  - 4tanh(x)
--R   (2)  ---------------------------------------------------------
--R                                4           2
--R                         tanh(x)  + 6tanh(x)  + 1
--R                                                     Type: Expression Integer
--E 125

--S 126 of 298
t2:=tanh4x t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 126

)clear all
 

--S 127 of 298
sinhsquared:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (1)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (1)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 127

--S 128 of 298
t1:=sinh(x)^2 - (1/2*cosh(2*x)-1/2)
 

                2
        2sinh(x)  - cosh(2x) + 1
   (2)  ------------------------
                    2
                                                     Type: Expression Integer
--R
--R                2
--R        2sinh(x)  - cosh(2x) + 1
--R   (2)  ------------------------
--R                    2
--R                                                     Type: Expression Integer
--E 128

--S 129 of 298
t2:=sinhsquared t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 129

)clear all
 

--S 130 of 298
coshsquared:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (1)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 130

--S 131 of 298
t1:=cosh(x)^2 - (1/2*cosh(2*x)+1/2)
 

                             2
        - cosh(2x) + 2cosh(x)  - 1
   (2)  --------------------------
                     2
                                                     Type: Expression Integer
--E 131

--S 132 of 298
t2:=coshsquared t1
 

   (3)  0
                                                     Type: Expression Integer
--E 132

)clear all
 

--S 133 of 298
sinhcubed:=rule(sinh(x)^3 == 1/4*sinh(3*x)-3/4*sinh(x))
 

               3    sinh(3x) - 3sinh(x)
   (1)  sinh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    sinh(3x) - 3sinh(x)
--R   (1)  sinh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 133

--S 134 of 298
t1:=sinh(x)^3 - (1/4*sinh(3*x)-3/4*sinh(x))
 

                             3
        - sinh(3x) + 4sinh(x)  + 3sinh(x)
   (2)  ---------------------------------
                        4
                                                     Type: Expression Integer
--R
--R                             3
--R        - sinh(3x) + 4sinh(x)  + 3sinh(x)
--R   (2)  ---------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E 134

--S 135 of 298
t2:=sinhcubed t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 135

)clear all
 

--S 136 of 298
coshcubed:=rule(cosh(x)^3 == 1/4*cosh(3*x)+3/4*cosh(x))
 

               3    cosh(3x) + 3cosh(x)
   (1)  cosh(x)  == -------------------
                             4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               3    cosh(3x) + 3cosh(x)
--R   (1)  cosh(x)  == -------------------
--R                             4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 136

--S 137 of 298
t1:=cosh(x)^3 - (1/4*cosh(3*x)+3/4*cosh(x))
 

                             3
        - cosh(3x) + 4cosh(x)  - 3cosh(x)
   (2)  ---------------------------------
                        4
                                                     Type: Expression Integer
--R
--R                             3
--R        - cosh(3x) + 4cosh(x)  - 3cosh(x)
--R   (2)  ---------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E 137

--S 138 of 298
t2:=coshcubed t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 138

)clear all
 

--S 139 of 298
sinhfourth:=rule(sinh(x)^4 == 3/8-1/2*cosh(2*x)+1/8*cosh(4*x))
 

               4    cosh(4x) - 4cosh(2x) + 3
   (1)  sinh(x)  == ------------------------
                                8
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               4    cosh(4x) - 4cosh(2x) + 3
--R   (1)  sinh(x)  == ------------------------
--R                                8
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 139

--S 140 of 298
t1:=sinh(x)^4 - (3/8-1/2*cosh(2*x)+1/8*cosh(4*x))
 

                4
        8sinh(x)  - cosh(4x) + 4cosh(2x) - 3
   (2)  ------------------------------------
                          8
                                                     Type: Expression Integer
--R
--R                4
--R        8sinh(x)  - cosh(4x) + 4cosh(2x) - 3
--R   (2)  ------------------------------------
--R                          8
--R                                                     Type: Expression Integer
--E 140

--S 141 of 298
t2:=sinhfourth t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 141

)clear all
 

--S 142 of 298
coshfourth:=rule(cosh(x)^4 == 3/8+1/2*cosh(2*x)+1/8*cosh(4*x))
 

               4    cosh(4x) + 4cosh(2x) + 3
   (1)  cosh(x)  == ------------------------
                                8
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               4    cosh(4x) + 4cosh(2x) + 3
--R   (1)  cosh(x)  == ------------------------
--R                                8
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 142

--S 143 of 298
t1:=cosh(x)^4 - (3/8+1/2*cosh(2*x)+1/8*cosh(4*x))
 

                                         4
        - cosh(4x) - 4cosh(2x) + 8cosh(x)  - 3
   (2)  --------------------------------------
                           8
                                                     Type: Expression Integer
--R
--R                                         4
--R        - cosh(4x) - 4cosh(2x) + 8cosh(x)  - 3
--R   (2)  --------------------------------------
--R                           8
--R                                                     Type: Expression Integer
--E 143

--S 144 of 298
t2:=coshfourth t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 144

)clear all
 

--S 145 of 298
sinhplussinh:=rule(sinh(x)+sinh(y) == 2*sinh(1/2*(x+y))*cosh(1/2*(x-y)))
 

                                        y - x      y + x
   (1)  sinh(y) + sinh(x) + %H == 2cosh(-----)sinh(-----) + %H
                                          2          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                        y - x      y + x
--I   (1)  sinh(y) + sinh(x) + %M == 2cosh(-----)sinh(-----) + %M
--R                                          2          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 145

--S 146 of 298
t1:=sinh(x)+sinh(y) - 2*sinh(1/2*(x+y))*cosh(1/2*(x-y))
 

                        y - x      y + x
   (2)  sinh(y) - 2cosh(-----)sinh(-----) + sinh(x)
                          2          2
                                                     Type: Expression Integer
--R
--R                        y - x      y + x
--R   (2)  sinh(y) - 2cosh(-----)sinh(-----) + sinh(x)
--R                          2          2
--R                                                     Type: Expression Integer
--E 146

--S 147 of 298
t2:=sinhplussinh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 147

)clear all
 

--S 148 of 298
sinhminussinh:=rule(sinh(x)-sinh(y) == 2*cosh(1/2*(x+y))*sinh(1/2*(x-y)))
 

                                            y + x      y - x
   (1)  - sinh(y) + sinh(x) + %I == - 2cosh(-----)sinh(-----) + %I
                                              2          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                            y + x      y - x
--I   (1)  - sinh(y) + sinh(x) + %N == - 2cosh(-----)sinh(-----) + %N
--R                                              2          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 148

--S 149 of 298
t1:=sinh(x)-sinh(y) - 2*cosh(1/2*(x+y))*sinh(1/2*(x-y))
 

                          y + x      y - x
   (2)  - sinh(y) + 2cosh(-----)sinh(-----) + sinh(x)
                            2          2
                                                     Type: Expression Integer
--R
--R                          y + x      y - x
--R   (2)  - sinh(y) + 2cosh(-----)sinh(-----) + sinh(x)
--R                            2          2
--R                                                     Type: Expression Integer
--E 149

--S 150 of 298
t2:=sinhminussinh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 150

)clear all
 

--S 151 of 298
coshpluscosh:=rule(cosh(x)+cosh(y) == 2*cosh(1/2*(x+y))*cosh(1/2*(x-y)))
 

                                        y - x      y + x
   (1)  cosh(y) + cosh(x) + %J == 2cosh(-----)cosh(-----) + %J
                                          2          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                        y - x      y + x
--I   (1)  cosh(y) + cosh(x) + %O == 2cosh(-----)cosh(-----) + %O
--R                                          2          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 151

--S 152 of 298
t1:=cosh(x)+cosh(y) - 2*cosh(1/2*(x+y))*cosh(1/2*(x-y))
 

                        y - x      y + x
   (2)  cosh(y) - 2cosh(-----)cosh(-----) + cosh(x)
                          2          2
                                                     Type: Expression Integer
--R
--R                        y - x      y + x
--R   (2)  cosh(y) - 2cosh(-----)cosh(-----) + cosh(x)
--R                          2          2
--R                                                     Type: Expression Integer
--E 152

--S 153 of 298
t2:=coshpluscosh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 153

)clear all
 

--S 154 of 298
coshminuscosh:=rule(cosh(x)-cosh(y) == 2*sinh(1/2*(x+y))*sinh(1/2*(x-y)))
 

                                            y - x      y + x
   (1)  - cosh(y) + cosh(x) + %K == - 2sinh(-----)sinh(-----) + %K
                                              2          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                            y - x      y + x
--I   (1)  - cosh(y) + cosh(x) + %P == - 2sinh(-----)sinh(-----) + %P
--R                                              2          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 154

--S 155 of 298
t1:=cosh(x)-cosh(y) - 2*sinh(1/2*(x+y))*sinh(1/2*(x-y))
 

              y - x      y + x
   (2)  2sinh(-----)sinh(-----) - cosh(y) + cosh(x)
                2          2
                                                     Type: Expression Integer
--R
--R              y - x      y + x
--R   (2)  2sinh(-----)sinh(-----) - cosh(y) + cosh(x)
--R                2          2
--R                                                     Type: Expression Integer
--E 155

--S 156 of 298
t2:=coshminuscosh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 156

)clear all
 

--S 157 of 298
sinhtimessinh:=rule(sinh(x)*sinh(y) == 1/2*(cosh(x+y)-cosh(x-y)))
 

                             %L cosh(y + x) - %L cosh(y - x)
   (1)  %L sinh(x)sinh(y) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %Q cosh(y + x) - %Q cosh(y - x)
--I   (1)  %Q sinh(x)sinh(y) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 157

--S 158 of 298
t1:=sinh(x)*sinh(y) - (1/2*(cosh(x+y)-cosh(x-y)))
 

        2sinh(x)sinh(y) - cosh(y + x) + cosh(y - x)
   (2)  -------------------------------------------
                             2
                                                     Type: Expression Integer
--R
--R        2sinh(x)sinh(y) - cosh(y + x) + cosh(y - x)
--R   (2)  -------------------------------------------
--R                             2
--R                                                     Type: Expression Integer
--E 158

--S 159 of 298
t2:=sinhtimessinh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 159

)clear all
 

--S 160 of 298
coshtimescosh:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                             %M cosh(y + x) + %M cosh(y - x)
   (1)  %M cosh(x)cosh(y) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %R cosh(y + x) + %R cosh(y - x)
--I   (1)  %R cosh(x)cosh(y) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 160

--S 161 of 298
t1:=cosh(x)*cosh(y) - 1/2*(cosh(x+y)+cosh(x-y))
 

        - cosh(y + x) + 2cosh(x)cosh(y) - cosh(y - x)
   (2)  ---------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R        - cosh(y + x) + 2cosh(x)cosh(y) - cosh(y - x)
--R   (2)  ---------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E 161

--S 162 of 298
t2:=coshtimescosh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 162

)clear all
 

--S 163 of 298
sinhtimescosh:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %N sinh(y + x) - %N sinh(y - x)
   (1)  %N cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %S sinh(y + x) - %S sinh(y - x)
--I   (1)  %S cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 163

--S 164 of 298
t1:=sinh(x)*cosh(y) - 1/2*(sinh(x+y)+sinh(x-y))
 

        - sinh(y + x) + sinh(y - x) + 2cosh(y)sinh(x)
   (2)  ---------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R        - sinh(y + x) + sinh(y - x) + 2cosh(y)sinh(x)
--R   (2)  ---------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E 164

--S 165 of 298
t2:=sinhtimescosh t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 165

)clear all
 

--S 166 of 298
asinhrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (1)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (1)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 166

--S 167 of 298
t1:=asinh(x) - log(x+sqrt(x^2+1))
 

               +------+
               | 2
   (2)  - log(\|x  + 1  + x) + asinh(x)
                                                     Type: Expression Integer
--R
--R               +------+
--R               | 2
--R   (2)  - log(\|x  + 1  + x) + asinh(x)
--R                                                     Type: Expression Integer
--E 167

--S 168 of 298
t2:=asinhrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 168

)clear all
 

--S 169 of 298
acoshrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (1)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (1)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 169

--S 170 of 298
t1:=acosh(x) - log(x+sqrt(x^2-1))
 

               +------+
               | 2
   (2)  - log(\|x  - 1  + x) + acosh(x)
                                                     Type: Expression Integer
--R
--R               +------+
--R               | 2
--R   (2)  - log(\|x  - 1  + x) + acosh(x)
--R                                                     Type: Expression Integer
--E 170

--S 171 of 298
t2:=acoshrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 171

)clear all
 

--S 172 of 298
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (1)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (1)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 172

--S 173 of 298
t1:=atanh(x) - 1/2*log((1+x)/(1-x))
 

              - x - 1
        - log(-------) + 2atanh(x)
               x - 1
   (2)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R              - x - 1
--R        - log(-------) + 2atanh(x)
--R               x - 1
--R   (2)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E 173

--S 174 of 298
t2:=atanhrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 174

)clear all
 

--S 175 of 298
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (1)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (1)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 175

--S 176 of 298
t1:=acoth(x) - 1/2*log((x+1)/(x-1))
 

              x + 1
        - log(-----) + 2acoth(x)
              x - 1
   (2)  ------------------------
                    2
                                                     Type: Expression Integer
--R
--R              x + 1
--R        - log(-----) + 2acoth(x)
--R              x - 1
--R   (2)  ------------------------
--R                    2
--R                                                     Type: Expression Integer
--E 176

--S 177 of 298
t2:=acothrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 177

)clear all
 

--S 178 of 298
asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
 

                          +--------+
                          |   2
                          |- x  + 1
                        x |--------  + 1
                          |    2
                         \|   x
   (1)  asech(x) == log(----------------)
                                x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          +--------+
--R                          |   2
--R                          |- x  + 1
--R                        x |--------  + 1
--R                          |    2
--R                         \|   x
--R   (1)  asech(x) == log(----------------)
--R                                x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 178

--S 179 of 298
t1:=asech(x) - log(1/x+sqrt(1/x^2-1))
 

                +--------+
                |   2
                |- x  + 1
              x |--------  + 1
                |    2
               \|   x
   (2)  - log(----------------) + asech(x)
                      x
                                                     Type: Expression Integer
--R
--R                +--------+
--R                |   2
--R                |- x  + 1
--R              x |--------  + 1
--R                |    2
--R               \|   x
--R   (2)  - log(----------------) + asech(x)
--R                      x
--R                                                     Type: Expression Integer
--E 179

--S 180 of 298
t2:=asechrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 180

)clear all
 

--S 181 of 298
acschrule:=rule(acsch(x) == log(1/x+sqrt(1/x^2+1)))
 

                          +------+
                          | 2
                          |x  + 1
                        x |------  + 1
                          |   2
                         \|  x
   (1)  acsch(x) == log(--------------)
                               x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          +------+
--R                          | 2
--R                          |x  + 1
--R                        x |------  + 1
--R                          |   2
--R                         \|  x
--R   (1)  acsch(x) == log(--------------)
--R                               x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 181

--S 182 of 298
t1:=acsch(x) - log(1/x+sqrt(1/x^2+1))
 

                +------+
                | 2
                |x  + 1
              x |------  + 1
                |   2
               \|  x
   (2)  - log(--------------) + acsch(x)
                     x
                                                     Type: Expression Integer
--R
--R                +------+
--R                | 2
--R                |x  + 1
--R              x |------  + 1
--R                |   2
--R               \|  x
--R   (2)  - log(--------------) + acsch(x)
--R                     x
--R                                                     Type: Expression Integer
--E 182

--S 183 of 298
t2:=acschrule t1
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E 183

)clear all
 

--S 184 of 298
cschinv:=rule(csch(x)^(-1) == sinh(1/x)^(-1))
 

           1          1
   (1)  ------- == -------
        csch(x)         1
                   sinh(-)
                        x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           1          1
--R   (1)  ------- == -------
--R        csch(x)         1
--R                   sinh(-)
--R                        x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 184

--S 185 of 298
t1:=csch(x)^(-1) - sinh(1/x)^(-1)
 

             1
        sinh(-) - csch(x)
             x
   (2)  -----------------
                      1
          csch(x)sinh(-)
                      x
                                                     Type: Expression Integer
--R
--R             1
--R        sinh(-) - csch(x)
--R             x
--R   (2)  -----------------
--R                      1
--R          csch(x)sinh(-)
--R                      x
--R                                                     Type: Expression Integer
--E 185

--S 186 of 298
t2:=cschinv t1
 

             1
        sinh(-) - csch(x)
             x
   (3)  -----------------
                      1
          csch(x)sinh(-)
                      x
                                                     Type: Expression Integer
--R
--R             1
--R        sinh(-) - csch(x)
--R             x
--R   (3)  -----------------
--R                      1
--R          csch(x)sinh(-)
--R                      x
--R                                                     Type: Expression Integer
--E 186

)clear all
 

--S 187 of 298
sechinv:=rule(sech(x)^(-1) == cosh(1/x)^(-1))
 

           1          1
   (1)  ------- == -------
        sech(x)         1
                   cosh(-)
                        x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           1          1
--R   (1)  ------- == -------
--R        sech(x)         1
--R                   cosh(-)
--R                        x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 187

--S 188 of 298
t1:=sech(x)^(-1) - cosh(1/x)^(-1)
 

                         1
        - sech(x) + cosh(-)
                         x
   (2)  -------------------
                1
           cosh(-)sech(x)
                x
                                                     Type: Expression Integer
--R
--R                         1
--R        - sech(x) + cosh(-)
--R                         x
--R   (2)  -------------------
--R                1
--R           cosh(-)sech(x)
--R                x
--R                                                     Type: Expression Integer
--E 188

--S 189 of 298
t2:=sechinv t1
 

                         1
        - sech(x) + cosh(-)
                         x
   (3)  -------------------
                1
           cosh(-)sech(x)
                x
                                                     Type: Expression Integer
--R
--R                         1
--R        - sech(x) + cosh(-)
--R                         x
--R   (3)  -------------------
--R                1
--R           cosh(-)sech(x)
--R                x
--R                                                     Type: Expression Integer
--E 189

)clear all
 

--S 190 of 298
cothinv:=rule(coth(x)^(-1) == tanh(1/x)^(-1))
 

           1          1
   (1)  ------- == -------
        coth(x)         1
                   tanh(-)
                        x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           1          1
--R   (1)  ------- == -------
--R        coth(x)         1
--R                   tanh(-)
--R                        x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 190

--S 191 of 298
t1:=coth(x)^(-1) - tanh(1/x)^(-1)
 

             1
        tanh(-) - coth(x)
             x
   (2)  -----------------
                      1
          coth(x)tanh(-)
                      x
                                                     Type: Expression Integer
--R
--R             1
--R        tanh(-) - coth(x)
--R             x
--R   (2)  -----------------
--R                      1
--R          coth(x)tanh(-)
--R                      x
--R                                                     Type: Expression Integer
--E 191

--S 192 of 298
t2:=cothinv t1
 

             1
        tanh(-) - coth(x)
             x
   (3)  -----------------
                      1
          coth(x)tanh(-)
                      x
                                                     Type: Expression Integer
--R
--R             1
--R        tanh(-) - coth(x)
--R             x
--R   (3)  -----------------
--R                      1
--R          coth(x)tanh(-)
--R                      x
--R                                                     Type: Expression Integer
--E 192

)clear all
 

--S 193 of 298
t1:=sinh(-x)^(-1) - -sinh(x)^(-1)
 

   (1)  0
                                                     Type: Expression Integer
--R
--R   (1)  0
--R                                                     Type: Expression Integer
--E 193

)clear all
 

--S 194 of 298
t1:=tanh(-x)^(-1) - -tanh(x)^(-1)
 

   (1)  0
                                                     Type: Expression Integer
--R
--R   (1)  0
--R                                                     Type: Expression Integer
--E 194

)clear all
 

--S 195 of 298
t1:=coth(-x)^(-1) - -coth(x)^(-1)
 

   (1)  0
                                                     Type: Expression Integer
--R
--R   (1)  0
--R                                                     Type: Expression Integer
--E 195

)clear all
 

--S 196 of 298
t1:=csch(-x)^(-1) - -csch(x)^(-1)
 

   (1)  0
                                                     Type: Expression Integer
--R
--R   (1)  0
--R                                                     Type: Expression Integer
--E 196

)clear all
 

--S 197 of 298
sininv:=rule(sin(%i*x) == %i*sinh(x))
 

   (1)  sin(%i x) == %i sinh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  sin(%i x) == %i sinh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 197

--S 198 of 298
t1:=sin(x*%i) - %i*sinh(x)
 

   (2)  - %i sinh(x) + sin(%i x)
                                             Type: Expression Complex Integer
--R
--R   (2)  - %i sinh(x) + sin(%i x)
--R                                             Type: Expression Complex Integer
--E 198

--S 199 of 298
t2:=sininv t1
 

   (3)  - %i sinh(x) + sin(%i x)
                                             Type: Expression Complex Integer
--R
--R   (3)  - %i sinh(x) + sin(%i x)
--R                                             Type: Expression Complex Integer
--E 199

)clear all
 

--S 200 of 298
cosinv:=rule(cos(x*%i) == cosh(x))
 

   (1)  cos(%i x) == cosh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  cos(%i x) == cosh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 200

--S 201 of 298
t1:=cos(x*%i) - cosh(x)
 

   (2)  - cosh(x) + cos(%i x)
                                             Type: Expression Complex Integer
--R
--R   (2)  - cosh(x) + cos(%i x)
--R                                             Type: Expression Complex Integer
--E 201

--S 202 of 298
t2:=cosinv t1
 

   (3)  - cosh(x) + cos(%i x)
                                             Type: Expression Complex Integer
--R
--R   (3)  - cosh(x) + cos(%i x)
--R                                             Type: Expression Complex Integer
--E 202

)clear all
 

--S 203 of 298
taninv:=rule(tan(x*%i) == %i*tanh(x))
 

   (1)  tan(%i x) == %i tanh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  tan(%i x) == %i tanh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 203

--S 204 of 298
t1:=tan(x*%i) - %i*tanh(x)
 

   (2)  - %i tanh(x) + tan(%i x)
                                             Type: Expression Complex Integer
--R
--R   (2)  - %i tanh(x) + tan(%i x)
--R                                             Type: Expression Complex Integer
--E 204

--S 205 of 298
t2:=taninv t1
 

   (3)  - %i tanh(x) + tan(%i x)
                                             Type: Expression Complex Integer
--R
--R   (3)  - %i tanh(x) + tan(%i x)
--R                                             Type: Expression Complex Integer
--E 205

)clear all
 

--S 206 of 298
cscinv:=rule(csc(x*%i) == -%i*csch(x))
 

   (1)  csc(%i x) == - %i csch(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  csc(%i x) == - %i csch(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 206

--S 207 of 298
t1:=csc(x*%i) - -%i*csch(x)
 

   (2)  %i csch(x) + csc(%i x)
                                             Type: Expression Complex Integer
--R
--R   (2)  %i csch(x) + csc(%i x)
--R                                             Type: Expression Complex Integer
--E 207

--S 208 of 298
t2:=cscinv t1
 

   (3)  %i csch(x) + csc(%i x)
                                             Type: Expression Complex Integer
--R
--R   (3)  %i csch(x) + csc(%i x)
--R                                             Type: Expression Complex Integer
--E 208

)clear all
 

--S 209 of 298
secinv:=rule(sec(x*%i) == sech(x))
 

   (1)  sec(%i x) == sech(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  sec(%i x) == sech(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 209

--S 210 of 298
t1:=sec(x*%i) - sech(x)
 

   (2)  - sech(x) + sec(%i x)
                                             Type: Expression Complex Integer
--R
--R   (2)  - sech(x) + sec(%i x)
--R                                             Type: Expression Complex Integer
--E 210

--S 211 of 298
t2:=secinv t1
 

   (3)  - sech(x) + sec(%i x)
                                             Type: Expression Complex Integer
--R
--R   (3)  - sech(x) + sec(%i x)
--R                                             Type: Expression Complex Integer
--E 211

)clear all
 

--S 212 of 298
cotinv:=rule(cot(x*%i) == -%i*coth(x))
 

   (1)  cot(%i x) == - %i coth(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  cot(%i x) == - %i coth(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 212

--S 213 of 298
t1:=cot(x*%i) - -%i*coth(x)
 

   (2)  %i coth(x) + cot(%i x)
                                             Type: Expression Complex Integer
--R
--R   (2)  %i coth(x) + cot(%i x)
--R                                             Type: Expression Complex Integer
--E 213

--S 214 of 298
t2:=cotinv t1
 

   (3)  %i coth(x) + cot(%i x)
                                             Type: Expression Complex Integer
--R
--R   (3)  %i coth(x) + cot(%i x)
--R                                             Type: Expression Complex Integer
--E 214 

)clear all
 

--S 215 of 298
sinhinv:=rule(sinh(x*%i) == %i*sin(x))
 

   (1)  sinh(%i x) == %i sin(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  sinh(%i x) == %i sin(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 215

--S 216 of 298
t1:=sinh(x*%i) - %i*sin(x)
 

   (2)  sinh(%i x) - %i sin(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  sinh(%i x) - %i sin(x)
--R                                             Type: Expression Complex Integer
--E 216

--S 217 of 298
t2:=sinhinv t1
 

   (3)  sinh(%i x) - %i sin(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  sinh(%i x) - %i sin(x)
--R                                             Type: Expression Complex Integer
--E 217

)clear all
 

--S 218 of 298
coshinv:=rule(cosh(x*%i) == cos(x))
 

   (1)  cosh(%i x) == cos(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  cosh(%i x) == cos(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 218

--S 219 of 298
t1:=cosh(x*%i) - cos(x)
 

   (2)  cosh(%i x) - cos(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  cosh(%i x) - cos(x)
--R                                             Type: Expression Complex Integer
--E 219

--S 220 of 298
t2:=coshinv t1
 

   (3)  cosh(%i x) - cos(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  cosh(%i x) - cos(x)
--R                                             Type: Expression Complex Integer
--E 220

)clear all
 

--S 221 of 298
tanhinv:=rule(tanh(x*%i) == %i*tan(x))
 

   (1)  tanh(%i x) == %i tan(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  tanh(%i x) == %i tan(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 221

--S 222 of 298
t1:=tanh(x*%i) - %i*tan(x)
 

   (2)  tanh(%i x) - %i tan(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  tanh(%i x) - %i tan(x)
--R                                             Type: Expression Complex Integer
--E 222

--S 223 of 298
t2:=tanhinv t1
 

   (3)  tanh(%i x) - %i tan(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  tanh(%i x) - %i tan(x)
--R                                             Type: Expression Complex Integer
--E 223

)clear all
 

--S 224 of 298
cschinv:=rule(x*%i == -%i*csc(x))
 

   (1)  %i x == - %i csc(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  %i x == - %i csc(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 224

--S 225 of 298
t1:=x*%i - -%i*csc(x)
 

   (2)  %i csc(x) + %i x
                                             Type: Expression Complex Integer
--R
--R   (2)  %i csc(x) + %i x
--R                                             Type: Expression Complex Integer
--E 225

--S 226 of 298
t2:=cschinv t1
 

   (3)  %i csc(x) + %i x
                                             Type: Expression Complex Integer
--R
--R   (3)  %i csc(x) + %i x
--R                                             Type: Expression Complex Integer
--E 226

)clear all
 

--S 227 of 298
sechinv:=rule(sech(x*%i) == sec(x))
 

   (1)  sech(%i x) == sec(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  sech(%i x) == sec(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 227

--S 228 of 298
t1:=sech(x*%i) - sec(x)
 

   (2)  sech(%i x) - sec(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  sech(%i x) - sec(x)
--R                                             Type: Expression Complex Integer
--E 228

--S 229 of 298
t2:=sechinv t1
 

   (3)  sech(%i x) - sec(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  sech(%i x) - sec(x)
--R                                             Type: Expression Complex Integer
--E 229

)clear all
 

--S 230 of 298
cothinv:=rule(coth(x*%i) == -%i*cot(x))
 

   (1)  coth(%i x) == - %i cot(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  coth(%i x) == - %i cot(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 230

--S 231 of 298
t1:=coth(x*%i) - -%i*cot(x)
 

   (2)  coth(%i x) + %i cot(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  coth(%i x) + %i cot(x)
--R                                             Type: Expression Complex Integer
--E 231

--S 232 of 298
t2:=cothinv t1
 

   (3)  coth(%i x) + %i cot(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  coth(%i x) + %i cot(x)
--R                                             Type: Expression Complex Integer
--E 232

)clear all
 

--S 233 of 298
sinhperiod:=rule(sinh(x+2*k*%pi*%i) == sinh(x))
 

   (1)  sinh(x + 2%i k %pi) == sinh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  sinh(x + 2%i k %pi) == sinh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 233

--S 234 of 298
t1:=sinh(x+2*k*%pi*%i) - sinh(x)
 

   (2)  sinh(x + 2%i k %pi) - sinh(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  sinh(x + 2%i k %pi) - sinh(x)
--R                                             Type: Expression Complex Integer
--E 234

--S 235 of 298
t2:=sinhperiod t1
 

   (3)  sinh(x + 2%i k %pi) - sinh(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  sinh(x + 2%i k %pi) - sinh(x)
--R                                             Type: Expression Complex Integer
--E 235

)clear all
 

--S 236 of 298
coshperiod:=rule(cosh(x+2*k*%pi*%i) == cosh(x))
 

   (1)  cosh(x + 2%i k %pi) == cosh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  cosh(x + 2%i k %pi) == cosh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 236

--S 237 of 298
t1:=cosh(x+2*k*%pi*%i) - cosh(x)
 

   (2)  cosh(x + 2%i k %pi) - cosh(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  cosh(x + 2%i k %pi) - cosh(x)
--R                                             Type: Expression Complex Integer
--E 237

--S 238 of 298
t2:=coshperiod t1
 

   (3)  cosh(x + 2%i k %pi) - cosh(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  cosh(x + 2%i k %pi) - cosh(x)
--R                                             Type: Expression Complex Integer
--E 238

)clear all
 

--S 239 of 298
tanhperiod:=rule(tanh(x+k*%pi*%i) == tanh(x))
 

   (1)  tanh(x + %i k %pi) == tanh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  tanh(x + %i k %pi) == tanh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 239

--S 240 of 298
t1:=tanh(x+k*%pi*%i) - tanh(x)
 

   (2)  tanh(x + %i k %pi) - tanh(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  tanh(x + %i k %pi) - tanh(x)
--R                                             Type: Expression Complex Integer
--E 240

--S 241 of 298
t2:=tanhperiod t1
 

   (3)  tanh(x + %i k %pi) - tanh(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  tanh(x + %i k %pi) - tanh(x)
--R                                             Type: Expression Complex Integer
--E 241

)clear all
 

--S 242 of 298
cschperiod:=rule(csch(x+2*k*%pi*%i) == csch(x))
 

   (1)  csch(x + 2%i k %pi) == csch(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  csch(x + 2%i k %pi) == csch(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 242

--S 243 of 298
t1:=csch(x+2*k*%pi*%i) - csch(x)
 

   (2)  csch(x + 2%i k %pi) - csch(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  csch(x + 2%i k %pi) - csch(x)
--R                                             Type: Expression Complex Integer
--E 243

--S 244 of 298
t2:=cschperiod t1
 

   (3)  csch(x + 2%i k %pi) - csch(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  csch(x + 2%i k %pi) - csch(x)
--R                                             Type: Expression Complex Integer
--E 244

)clear all
 

--S 245 of 298
sechperiod:=rule(sech(x+2*k*%pi*%i) == sech(x))
 

   (1)  sech(x + 2%i k %pi) == sech(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  sech(x + 2%i k %pi) == sech(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 245

--S 246 of 298
t1:=sech(x+2*k*%pi*%i) - sech(x)
 

   (2)  sech(x + 2%i k %pi) - sech(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  sech(x + 2%i k %pi) - sech(x)
--R                                             Type: Expression Complex Integer
--E 246

--S 247 of 298
t2:=sechperiod t1
 

   (3)  sech(x + 2%i k %pi) - sech(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  sech(x + 2%i k %pi) - sech(x)
--R                                             Type: Expression Complex Integer
--E 247

)clear all
 

--S 248 of 298
cothperiod:=rule(coth(x+k*%pi*%i) == coth(x))
 

   (1)  coth(x + %i k %pi) == coth(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R   (1)  coth(x + %i k %pi) == coth(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 248

--S 249 of 298
t1:=coth(x+k*%pi*%i) - coth(x)
 

   (2)  coth(x + %i k %pi) - coth(x)
                                             Type: Expression Complex Integer
--R
--R   (2)  coth(x + %i k %pi) - coth(x)
--R                                             Type: Expression Complex Integer
--E 249

--S 250 of 298
t2:=cothperiod t1
 

   (3)  coth(x + %i k %pi) - coth(x)
                                             Type: Expression Complex Integer
--R
--R   (3)  coth(x + %i k %pi) - coth(x)
--R                                             Type: Expression Complex Integer
--E 250

)clear all
 

--S 251 of 298
sinsinh:=rule(sin(%i*x)^(-1) == %i*sinh(x)^(-1))
 

            1           %i
   (1)  --------- == -------
        sin(%i x)    sinh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R            1           %i
--R   (1)  --------- == -------
--R        sin(%i x)    sinh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 251

--S 252 of 298
t1:=sin(%i*x)^(-1) - %i*sinh(x)^(-1)
 

        sinh(x) - %i sin(%i x)
   (2)  ----------------------
           sin(%i x)sinh(x)
                                             Type: Expression Complex Integer
--R
--R        sinh(x) - %i sin(%i x)
--R   (2)  ----------------------
--R           sin(%i x)sinh(x)
--R                                             Type: Expression Complex Integer
--E 252

--S 253 of 298
t2:=sinsinh t1
 

        sinh(x) - %i sin(%i x)
   (3)  ----------------------
           sin(%i x)sinh(x)
                                             Type: Expression Complex Integer
--R
--R        sinh(x) - %i sin(%i x)
--R   (3)  ----------------------
--R           sin(%i x)sinh(x)
--R                                             Type: Expression Complex Integer
--E 253

)clear all
 

--S 254 of 298
sinhsin:=rule(sinh(%i*x)^(-1) == %i*sin(x)^(-1))
 

             1          %i
   (1)  ---------- == ------
        sinh(%i x)    sin(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R             1          %i
--R   (1)  ---------- == ------
--R        sinh(%i x)    sin(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 254

--S 255 of 298
t1:=sinh(%i*x)^(-1) - %i*sin(x)^(-1)
 

        - %i sinh(%i x) + sin(x)
   (2)  ------------------------
            sin(x)sinh(%i x)
                                             Type: Expression Complex Integer
--R
--R        - %i sinh(%i x) + sin(x)
--R   (2)  ------------------------
--R            sin(x)sinh(%i x)
--R                                             Type: Expression Complex Integer
--E 255

--S 256 of 298
t2:=sinhsin t1
 

        - %i sinh(%i x) + sin(x)
   (3)  ------------------------
            sin(x)sinh(%i x)
                                             Type: Expression Complex Integer
--R
--R        - %i sinh(%i x) + sin(x)
--R   (3)  ------------------------
--R            sin(x)sinh(%i x)
--R                                             Type: Expression Complex Integer
--E 256

)clear all
 

--S 257 of 298
coscosh:=rule(cos(x)^(-1) == %i*cosh(x)^(-1))
 

           1         %i
   (1)  ------ == -------
        cos(x)    cosh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1         %i
--R   (1)  ------ == -------
--R        cos(x)    cosh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 257

--S 258 of 298
t1:=cos(x)^(-1) - %i*cosh(x)^(-1)
 

        cosh(x) - %i cos(x)
   (2)  -------------------
           cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        cosh(x) - %i cos(x)
--R   (2)  -------------------
--R           cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 258

--S 259 of 298
t2:=coscosh t1
 

        cosh(x) - %i cos(x)
   (3)  -------------------
           cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        cosh(x) - %i cos(x)
--R   (3)  -------------------
--R           cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 259

)clear all
 

--S 260 of 298
coscosh2:=rule(cos(x)^(-1) == -%i*cosh(x)^(-1))
 

           1           %i
   (1)  ------ == - -------
        cos(x)      cosh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1           %i
--R   (1)  ------ == - -------
--R        cos(x)      cosh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 260

--S 261 of 298
t1:=cos(x)^(-1) - -%i*cosh(x)^(-1)
 

        cosh(x) + %i cos(x)
   (2)  -------------------
           cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        cosh(x) + %i cos(x)
--R   (2)  -------------------
--R           cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 261

--S 262 of 298
t2:=coscosh2 t1
 

        cosh(x) + %i cos(x)
   (3)  -------------------
           cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        cosh(x) + %i cos(x)
--R   (3)  -------------------
--R           cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 262

)clear all
 

--S 263 of 298
coshcos:=rule(cosh(x)^(-1) == %i*cos(x)^(-1))
 

           1         %i
   (1)  ------- == ------
        cosh(x)    cos(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1         %i
--R   (1)  ------- == ------
--R        cosh(x)    cos(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 263

--S 264 of 298
t1:=cosh(x)^(-1) - %i*cos(x)^(-1)
 

        - %i cosh(x) + cos(x)
   (2)  ---------------------
            cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        - %i cosh(x) + cos(x)
--R   (2)  ---------------------
--R            cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 264

--S 265 of 298
t2:=coshcos t1
 

        - %i cosh(x) + cos(x)
   (3)  ---------------------
            cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        - %i cosh(x) + cos(x)
--R   (3)  ---------------------
--R            cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 265

)clear all
 

--S 266 of 298
coshcos2:=rule(cosh(x)^(-1) == -%i*cos(x)^(-1))
 

           1           %i
   (1)  ------- == - ------
        cosh(x)      cos(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1           %i
--R   (1)  ------- == - ------
--R        cosh(x)      cos(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 266

--S 267 of 298
t1:=cosh(x)^(-1) - -%i*cos(x)^(-1)
 

        %i cosh(x) + cos(x)
   (2)  -------------------
           cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        %i cosh(x) + cos(x)
--R   (2)  -------------------
--R           cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 267

--S 268 of 298
t2:=coshcos2 t1
 

        %i cosh(x) + cos(x)
   (3)  -------------------
           cos(x)cosh(x)
                                             Type: Expression Complex Integer
--R
--R        %i cosh(x) + cos(x)
--R   (3)  -------------------
--R           cos(x)cosh(x)
--R                                             Type: Expression Complex Integer
--E 268

)clear all
 

--S 269 of 298
tantanh:=rule(tan(%i*x)^(-1) == %i*tanh(x)^(-1))
 

            1           %i
   (1)  --------- == -------
        tan(%i x)    tanh(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R            1           %i
--R   (1)  --------- == -------
--R        tan(%i x)    tanh(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 269

--S 270 of 298
t1:=tan(%i*x)^(-1) - %i*tanh(x)^(-1)
 

        tanh(x) - %i tan(%i x)
   (2)  ----------------------
           tan(%i x)tanh(x)
                                             Type: Expression Complex Integer
--R
--R        tanh(x) - %i tan(%i x)
--R   (2)  ----------------------
--R           tan(%i x)tanh(x)
--R                                             Type: Expression Complex Integer
--E 270

--S 271 of 298
t2:=tantanh t1
 

        tanh(x) - %i tan(%i x)
   (3)  ----------------------
           tan(%i x)tanh(x)
                                             Type: Expression Complex Integer
--R
--R        tanh(x) - %i tan(%i x)
--R   (3)  ----------------------
--R           tan(%i x)tanh(x)
--R                                             Type: Expression Complex Integer
--E 271

)clear all
 

--S 272 of 298
tanhtan:=rule(tanh(%i*x)^(-1) == %i*tan(x)^(-1))
 

             1          %i
   (1)  ---------- == ------
        tanh(%i x)    tan(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R             1          %i
--R   (1)  ---------- == ------
--R        tanh(%i x)    tan(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 272

--S 273 of 298
t1:=tanh(%i*x)^(-1) - %i*tan(x)^(-1)
 

        - %i tanh(%i x) + tan(x)
   (2)  ------------------------
            tan(x)tanh(%i x)
                                             Type: Expression Complex Integer
--R
--R        - %i tanh(%i x) + tan(x)
--R   (2)  ------------------------
--R            tan(x)tanh(%i x)
--R                                             Type: Expression Complex Integer
--E 273

--S 274 of 298
t2:=tanhtan t1
 

        - %i tanh(%i x) + tan(x)
   (3)  ------------------------
            tan(x)tanh(%i x)
                                             Type: Expression Complex Integer
--R
--R        - %i tanh(%i x) + tan(x)
--R   (3)  ------------------------
--R            tan(x)tanh(%i x)
--R                                             Type: Expression Complex Integer
--E 274

)clear all
 

--S 275 of 298
cotcoth:=rule(cot(%i*x)^(-1) == -%i*coth(x)^(-1))
 

            1             %i
   (1)  --------- == - -------
        cot(%i x)      coth(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R            1             %i
--R   (1)  --------- == - -------
--R        cot(%i x)      coth(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 275

--S 276 of 298
t1:=cot(%i*x)^(-1) - -%i*coth(x)^(-1)
 

        coth(x) + %i cot(%i x)
   (2)  ----------------------
           cot(%i x)coth(x)
                                             Type: Expression Complex Integer
--R
--R        coth(x) + %i cot(%i x)
--R   (2)  ----------------------
--R           cot(%i x)coth(x)
--R                                             Type: Expression Complex Integer
--E 276

--S 277 of 298
t2:=cotcoth t1
 

        coth(x) + %i cot(%i x)
   (3)  ----------------------
           cot(%i x)coth(x)
                                             Type: Expression Complex Integer
--R
--R        coth(x) + %i cot(%i x)
--R   (3)  ----------------------
--R           cot(%i x)coth(x)
--R                                             Type: Expression Complex Integer
--E 277

)clear all
 

--S 278 of 298
cothcot:=rule(coth(%i*x)^(-1) == -%i*cot(x)^(-1))
 

             1            %i
   (1)  ---------- == - ------
        coth(%i x)      cot(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R             1            %i
--R   (1)  ---------- == - ------
--R        coth(%i x)      cot(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 278

--S 279 of 298
t1:=coth(%i*x)^(-1) - -%i*cot(x)^(-1)
 

        %i coth(%i x) + cot(x)
   (2)  ----------------------
           cot(x)coth(%i x)
                                             Type: Expression Complex Integer
--R
--R        %i coth(%i x) + cot(x)
--R   (2)  ----------------------
--R           cot(x)coth(%i x)
--R                                             Type: Expression Complex Integer
--E 279

--S 280 of 298
t2:=cothcot t1
 

        %i coth(%i x) + cot(x)
   (3)  ----------------------
           cot(x)coth(%i x)
                                             Type: Expression Complex Integer
--R
--R        %i coth(%i x) + cot(x)
--R   (3)  ----------------------
--R           cot(x)coth(%i x)
--R                                             Type: Expression Complex Integer
--E 280

)clear all
 

--S 281 of 298
secsech:=rule(sec(x)^(-1) == %i*sech(x)^(-1))
 

           1         %i
   (1)  ------ == -------
        sec(x)    sech(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1         %i
--R   (1)  ------ == -------
--R        sec(x)    sech(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 281

--S 282 of 298
t1:=sec(x)^(-1) - %i*sech(x)^(-1)
 

        sech(x) - %i sec(x)
   (2)  -------------------
           sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        sech(x) - %i sec(x)
--R   (2)  -------------------
--R           sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 282

--S 283 of 298
t2:=secsech t1
 

        sech(x) - %i sec(x)
   (3)  -------------------
           sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        sech(x) - %i sec(x)
--R   (3)  -------------------
--R           sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 283

)clear all
 

--S 284 of 298
secsech2:=rule(sec(x)^(-1) == -%i*sech(x)^(-1))
 

           1           %i
   (1)  ------ == - -------
        sec(x)      sech(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1           %i
--R   (1)  ------ == - -------
--R        sec(x)      sech(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 284

--S 285 of 298
t1:=sec(x)^(-1) - -%i*sech(x)^(-1)
 

        sech(x) + %i sec(x)
   (2)  -------------------
           sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        sech(x) + %i sec(x)
--R   (2)  -------------------
--R           sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 285

--S 286 of 298
t2:=secsech2 t1
 

        sech(x) + %i sec(x)
   (3)  -------------------
           sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        sech(x) + %i sec(x)
--R   (3)  -------------------
--R           sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 286

)clear all
 

--S 287 of 298
sechsec:=rule(sech(x)^(-1) == %i*sec(x)^(-1))
 

           1         %i
   (1)  ------- == ------
        sech(x)    sec(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1         %i
--R   (1)  ------- == ------
--R        sech(x)    sec(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 287

--S 288 of 298
t1:=sech(x)^(-1) - %i*sec(x)^(-1)
 

        - %i sech(x) + sec(x)
   (2)  ---------------------
            sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        - %i sech(x) + sec(x)
--R   (2)  ---------------------
--R            sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 288

--S 289 of 298
t2:=sechsec t1
 

        - %i sech(x) + sec(x)
   (3)  ---------------------
            sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        - %i sech(x) + sec(x)
--R   (3)  ---------------------
--R            sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 289

)clear all
 

--S 290 of 298
sechsec:=rule(sech(x)^(-1) == -%i*sec(x)^(-1))
 

           1           %i
   (1)  ------- == - ------
        sech(x)      sec(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R           1           %i
--R   (1)  ------- == - ------
--R        sech(x)      sec(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 290

--S 291 of 298
t1:=sech(x)^(-1) - -%i*sec(x)^(-1)
 

        %i sech(x) + sec(x)
   (2)  -------------------
           sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        %i sech(x) + sec(x)
--R   (2)  -------------------
--R           sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 291

--S 292 of 298
t2:=sechsec t1
 

        %i sech(x) + sec(x)
   (3)  -------------------
           sec(x)sech(x)
                                             Type: Expression Complex Integer
--R
--R        %i sech(x) + sec(x)
--R   (3)  -------------------
--R           sec(x)sech(x)
--R                                             Type: Expression Complex Integer
--E 292

)clear all
 

--S 293 of 298
csccsch:=rule(csc(%i*x)^(-1) == -%i*csch(x)^(-1))
 

            1             %i
   (1)  --------- == - -------
        csc(%i x)      csch(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R            1             %i
--R   (1)  --------- == - -------
--R        csc(%i x)      csch(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 293

--S 294 of 298
t1:=csc(%i*x)^(-1) - -%i*csch(x)^(-1)
 

        csch(x) + %i csc(%i x)
   (2)  ----------------------
           csc(%i x)csch(x)
                                             Type: Expression Complex Integer
--R
--R        csch(x) + %i csc(%i x)
--R   (2)  ----------------------
--R           csc(%i x)csch(x)
--R                                             Type: Expression Complex Integer
--E 294

--S 295 of 298
t2:=csccsch t1
 

        csch(x) + %i csc(%i x)
   (3)  ----------------------
           csc(%i x)csch(x)
                                             Type: Expression Complex Integer
--R
--R        csch(x) + %i csc(%i x)
--R   (3)  ----------------------
--R           csc(%i x)csch(x)
--R                                             Type: Expression Complex Integer
--E 295

)clear all
 

--S 296 of 298
cschcsc:=rule(csch(%i*x)^(-1) == -%i*csc(x)^(-1))
 

             1            %i
   (1)  ---------- == - ------
        csch(%i x)      csc(x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R             1            %i
--R   (1)  ---------- == - ------
--R        csch(%i x)      csc(x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E 296

--S 297 of 298
t1:=csch(%i*x)^(-1) - -%i*csc(x)^(-1)
 

        %i csch(%i x) + csc(x)
   (2)  ----------------------
           csc(x)csch(%i x)
                                             Type: Expression Complex Integer
--R
--R        %i csch(%i x) + csc(x)
--R   (2)  ----------------------
--R           csc(x)csch(%i x)
--R                                             Type: Expression Complex Integer
--E 297

--S 298 of 298
t2:=cschcsc t1
 

        %i csch(%i x) + csc(x)
   (3)  ----------------------
           csc(x)csch(%i x)
                                             Type: Expression Complex Integer
--R
--R        %i csch(%i x) + csc(x)
--R   (3)  ----------------------
--R           csc(x)csch(%i x)
--R                                             Type: Expression Complex Integer
--E 298

)spool 
 
Starts dribbling to intmix2.output (2010/3/27, 18:27:11).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 4
(x + 1) / (x * (x + log x)**(3/2))
 

                    x + 1
   (1)  ----------------------------
                     2  +----------+
        (x log(x) + x )\|log(x) + x
                                                     Type: Expression Integer
--R 
--R
--R                    x + 1
--R   (1)  ----------------------------
--R                     2  +----------+
--R        (x log(x) + x )\|log(x) + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 4
integrate(%, x)
 

            +----------+
          2\|log(x) + x
   (2)  - --------------
            log(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +----------+
--R          2\|log(x) + x
--R   (2)  - --------------
--R            log(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 4
log(1 + exp x)**(1/3) / (1 + log(1 + exp x))
 

          +------------+
         3|      x
         \|log(%e  + 1)
   (3)  ----------------
              x
        log(%e  + 1) + 1
                                                     Type: Expression Integer
--R 
--R
--R          +------------+
--R         3|      x
--R         \|log(%e  + 1)
--R   (3)  ----------------
--R              x
--R        log(%e  + 1) + 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 4
integrate(%, x)
 

               +-------------+
           x  3|      %P
         ++   \|log(%e   + 1)
   (4)   |   ----------------- d%P
        ++         %P
             log(%e   + 1) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-------------+
--R           x  3|      %P
--R         ++   \|log(%e   + 1)
--R   (4)   |   ----------------- d%P
--R        ++         %P
--R             log(%e   + 1) + 1
--R                                          Type: Union(Expression Integer,...)
--E 4
)spool 
 
Starts dribbling to unittest3.output (2010/3/27, 18:41:35).
)set mes auto off
 
)clear all
 

--S 1 of 75
)lisp (identity |$inputPromptType|)
 
Value = |step|
--R 
--RValue = |step|
--E 1

--S 2 of 75
)lisp (setq |$inputPromptType| '|none|)
 
Value = |none|
--R 
--RValue = |none|
--E 2

--S 3 of 75
1
 

   (1)  1
                                                        Type: PositiveInteger
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 75
)lisp (setq |$inputPromptType| '|plain|)
 
Value = |plain|
--RValue = |plain|
--E 4

--S 5 of 75
2
 

   (2)  2
                                                        Type: PositiveInteger
--R
--R   (2)  2
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 75
)lisp (setq |$inputPromptType| '|step|)
 
Value = |step|
--R 
--RValue = |step|
--E 6

--S 7 of 75
2
 

   (3)  2
                                                        Type: PositiveInteger
--R
--R   (3)  2
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 75
)lisp (setq |$inputPromptType| '|frame|)
 
Value = |frame|
--R 
--RValue = |frame|
--E 8

--S 9 of 75
2
 

   (4)  2
                                                        Type: PositiveInteger
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 75
)lisp (setq |$inputPromptType| t)
 
Value = T
--R 
--RValue = T
--E 10

--S 11 of 75
2
 

   (5)  2
                                                        Type: PositiveInteger
--R
--R   (5)  2
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 75
)set debug
 
                    Current Values of  debug  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
lambdatype   show type information for #1 syntax        off 
dalymode     Interpret leading open paren as lisp       off 

--R                    Current Values of  debug  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rlambdatype   show type information for #1 syntax        off 
--Rdalymode     Interpret leading open paren as lisp       off 
--R
--E 12

--S 13 of 75
)set debug lambdatype 
 
-------------------------- The lambdatype Option --------------------------

 Description: show type information for #1 syntax

 The lambdatype option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The lambdatype Option --------------------------
--R
--R Description: show type information for #1 syntax
--R
--R The lambdatype option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 13

--S 14 of 75
)set debug lambdatype on
 
--E 14

--S 15 of 75
)set debug lambdatype
 
-------------------------- The lambdatype Option --------------------------

 Description: show type information for #1 syntax

 The lambdatype option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R-------------------------- The lambdatype Option --------------------------
--R
--R Description: show type information for #1 syntax
--R
--R The lambdatype option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 15

--S 16 of 75
)set debug dalymode
 
--------------------------- The dalymode Option ---------------------------

 Description: Interpret leading open paren as lisp

 The dalymode option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The dalymode Option ---------------------------
--R
--R Description: Interpret leading open paren as lisp
--R
--R The dalymode option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 16

--S 17 of 75
)set debug dalymode on
 
--E 17

--S 18 of 75
)set debug dalymode
 
--------------------------- The dalymode Option ---------------------------

 Description: Interpret leading open paren as lisp

 The dalymode option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The dalymode Option ---------------------------
--R
--R Description: Interpret leading open paren as lisp
--R
--R The dalymode option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 18

--S 19 of 75
)set debug
 
                    Current Values of  debug  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
lambdatype   show type information for #1 syntax        on 
dalymode     Interpret leading open paren as lisp       on 

--R                    Current Values of  debug  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rlambdatype   show type information for #1 syntax        on 
--Rdalymode     Interpret leading open paren as lisp       on 
--R
--E 19

--S 20 of 75
)lisp |$frameAlist|
 
Value = NIL
--R 
--RValue = NIL
--E 20

--S 21 of 75
)lisp |$frameNumber|
 
Value = 0
--R 
--RValue = 0
--E 21

--S 22 of 75
)lisp |$currentFrameNum|
 
Value = 0
--R 
--RValue = 0
--E 22

--S 23 of 75
)lisp |$EndServerSession|
 
Value = NIL
--R 
--RValue = NIL
--E 23

--S 24 of 75
)lisp |$NeedToSignalSessionManager|
 
Value = T
--R 
--RValue = T
--E 24

--S 25 of 75
)lisp |$sockBufferLength|
 
Value = 9217
--R 
--RValue = 9217
--E 25

--S 26 of 75
)lisp SessionManager
 
Value = 1
--R 
--RValue = 1
--E 26

--S 27 of 75
)lisp |$SessionManager|
 
Value = 1
--R 
--RValue = 1
--E 27

--S 28 of 75
)lisp ViewportServer
 
Value = 2
--R 
--RValue = 2
--E 28

--S 29 of 75
)lisp |$ViewportServer|
 
Value = 2
--R 
--RValue = 2
--E 29

--S 30 of 75
)lisp MenuServer
 
Value = 3
--R 
--RValue = 3
--E 30

--S 31 of 75
)lisp |$MenuServer|
 
Value = 3
--R 
--RValue = 3
--E 31

--S 32 of 75
)lisp SessionIO
 
Value = 4
--R 
--RValue = 4
--E 32

--S 33 of 75
)lisp |$SessionIO|
 
Value = 4
--R 
--RValue = 4
--E 33

--S 34 of 75
)lisp MessageServer
 
Value = 5
--R 
--RValue = 5
--E 34

--S 35 of 75
)lisp |$MessageServer|
 
Value = 5
--R 
--RValue = 5
--E 35

--S 36 of 75
)lisp InterpWindow
 
Value = 6
--R 
--RValue = 6
--E 36

--S 37 of 75
)lisp |$InterpWindow|
 
Value = 6
--R 
--RValue = 6
--E 37

--S 38 of 75
)lisp KillSpad
 
Value = 7
--R 
--RValue = 7
--E 38

--S 39 of 75
)lisp |$KillSpad|
 
Value = 7
--R 
--RValue = 7
--E 39

--S 40 of 75
)lisp DebugWindow
 
Value = 8
--R 
--RValue = 8
--E 40

--S 41 of 75
)lisp |$DebugWindow|
 
Value = 8
--R 
--RValue = 8
--E 41

--S 42 of 75
)lisp NAGLinkServer
 
Value = 8
--R 
--RValue = 8
--E 42

--S 43 of 75
)lisp |$NAGLinkServer|
 
Value = 8
--R 
--RValue = 8
--E 43

--S 44 of 75
)lisp Forker
 
Value = 9
--R 
--RValue = 9
--E 44

--S 45 of 75
)lisp |$Forker|
 
Value = 9
--R 
--RValue = 9
--E 45

--S 46 of 75
)lisp CreateFrame
 
Value = 1
--R 
--RValue = 1
--E 46

--S 47 of 75
)lisp |$CreateFrame|
 
Value = 1
--R 
--RValue = 1
--E 47

--S 48 of 75
)lisp SwitchFrames
 
Value = 2
--R 
--RValue = 2
--E 48

--S 49 of 75
)lisp |$SwitchFrames|
 
Value = 2
--R 
--RValue = 2
--E 49

--S 50 of 75
)lisp EndOfOutput
 
Value = 3
--R 
--RValue = 3
--E 50

--S 51 of 75
)lisp |$EndOfOutput|
 
Value = 3
--R 
--RValue = 3
--E 51

--S 52 of 75
)lisp CallInterp
 
Value = 4
--R 
--RValue = 4
--E 52

--S 53 of 75
)lisp |$CallInterp|
 
Value = 4
--R 
--RValue = 4
--E 53

--S 54 of 75
)lisp EndSession
 
Value = 5
--R 
--RValue = 5
--E 54

--S 55 of 75
)lisp |$EndSession|
 
Value = 5
--R 
--RValue = 5
--E 55

--S 56 of 75
)lisp LispCommand
 
Value = 6
--R 
--RValue = 6
--E 56

--S 57 of 75
)lisp |$LispCommand|
 
Value = 6
--R 
--RValue = 6
--E 57

--S 58 of 75
)lisp SpadCommand
 
Value = 7
--R 
--RValue = 7
--E 58

--S 59 of 75
)lisp |$SpadCommand|
 
Value = 7
--R 
--RValue = 7
--E 59

--S 60 of 75
)lisp SendXEventToHyperTeX
 
Value = 8
--R 
--RValue = 8
--E 60

--S 61 of 75
)lisp |$SendXEventToHyperTeX|
 
Value = 8
--R 
--RValue = 8
--E 61

--S 62 of 75
)lisp QuietSpadCommand
 
Value = 9
--R 
--RValue = 9
--E 62

--S 63 of 75
)lisp |$QuietSpadCommand|
 
Value = 9
--R 
--RValue = 9
--E 63

--S 64 of 75
)lisp CloseClient
 
Value = 10
--R 
--RValue = 10
--E 64

--S 65 of 75
)lisp |$CloseClient|
 
Value = 10
--R 
--RValue = 10
--E 65

--S 66 of 75
)lisp QueryClients
 
Value = 11
--R 
--RValue = 11
--E 66

--S 67 of 75
)lisp |$QueryClients|
 
Value = 11
--R 
--RValue = 11
--E 67

--S 68 of 75
)lisp QuerySpad
 
Value = 12
--R 
--RValue = 12
--E 68

--S 69 of 75
)lisp |$QuerySpad|
 
Value = 12
--R 
--RValue = 12
--E 69

--S 70 of 75
)lisp NonSmanSession
 
Value = 13
--R 
--RValue = 13
--E 70

--S 71 of 75
)lisp |$NonSmanSession|
 
Value = 13
--R 
--RValue = 13
--E 71

--S 72 of 75
)lisp KillLispSystem
 
Value = 14
--R 
--RValue = 14
--E 72

--S 73 of 75
)lisp |$KillLispSystem|
 
Value = 14
--R 
--RValue = 14
--E 73

--S 74 of 75
)lisp CreateFrameAnswer
 
Value = 50
--R 
--RValue = 50
--E 74

--S 75 of 75
)lisp |$CreateFrameAnswer|
 
Value = 50
--R 
--RValue = 50
--E 75

)spool
 
Starts dribbling to kamke3.output (2010/3/27, 18:27:50).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 139
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 139
ode151 := (x**2+1)*D(y(x),x) + (y(x)**2+1)*(2*x*y(x) - 1)
 

          2      ,             3       2
   (2)  (x  + 1)y (x) + 2x y(x)  - y(x)  + 2x y(x) - 1

                                                     Type: Expression Integer
--R 
--R
--R          2      ,             3       2
--R   (2)  (x  + 1)y (x) + 2x y(x)  - y(x)  + 2x y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 139
ode151a:=solve(ode151,y,x)
 

   (3)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (3)  "failed"
--R                                                    Type: Union("failed",...)
--E 3

--S 4 of 139
ode152 := (x**2+1)*D(y(x),x) + x*sin(y(x))*cos(y(x)) - x*(x**2+1)*cos(y(x))**2
 

          2      ,                                 3              2
   (4)  (x  + 1)y (x) + x cos(y(x))sin(y(x)) + (- x  - x)cos(y(x))

                                                     Type: Expression Integer
--R 
--R
--R          2      ,                                 3              2
--R   (4)  (x  + 1)y (x) + x cos(y(x))sin(y(x)) + (- x  - x)cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 139
ode152a:=solve(ode152,y,x)
 

   (5)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (5)  "failed"
--R                                                    Type: Union("failed",...)
--E 5

--S 6 of 139
ode153 := (x**2-1)*D(y(x),x) - x*y(x) + a
 

          2      ,
   (6)  (x  - 1)y (x) - x y(x) + a

                                                     Type: Expression Integer
--R 
--R
--R          2      ,
--R   (6)  (x  - 1)y (x) - x y(x) + a
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 139
ode153a:=solve(ode153,y,x)
 

                                  +------+
                                  | 2
   (7)  [particular= a x,basis= [\|x  - 1 ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                  +------+
--R                                  | 2
--R   (7)  [particular= a x,basis= [\|x  - 1 ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 7

--S 8 of 139
yx:=ode153a.particular
 

   (8)  a x
                                                     Type: Expression Integer
--R 
--R
--R   (8)  a x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 139
ode153expr := (x**2-1)*D(yx,x) - x*yx + a
 

   (9)  0
                                                     Type: Expression Integer
--R 
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E 9

--S 10 of 139
ode154 := (x**2-1)*D(y(x),x) + 2*x*y(x) - cos(x)
 

           2      ,
   (10)  (x  - 1)y (x) - cos(x) + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,
--R   (10)  (x  - 1)y (x) - cos(x) + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 139
ode154a:=solve(ode154,y,x)
 

                      sin(x)            1
   (11)  [particular= ------,basis= [------]]
                       2              2
                      x  - 1         x  - 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                      sin(x)            1
--R   (11)  [particular= ------,basis= [------]]
--R                       2              2
--R                      x  - 1         x  - 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 11

--S 12 of 139
yx:=ode154a.particular
 

         sin(x)
   (12)  ------
          2
         x  - 1
                                                     Type: Expression Integer
--R 
--R
--R         sin(x)
--R   (12)  ------
--R          2
--R         x  - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 139
ode154expr := (x**2-1)*D(yx,x) + 2*x*yx - cos(x)
 

   (13)  0
                                                     Type: Expression Integer
--R 
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 139
ode155 := (x**2-1)*D(y(x),x) + y(x)**2 - 2*x*y(x) + 1
 

           2      ,          2
   (14)  (x  - 1)y (x) + y(x)  - 2x y(x) + 1

                                                     Type: Expression Integer
--R 
--R
--R           2      ,          2
--R   (14)  (x  - 1)y (x) + y(x)  - 2x y(x) + 1
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 139
yx:=solve(ode155,y,x)
 

         (y(x) - x)log(x + 1) + (- y(x) + x)log(x - 1) + 2
   (15)  -------------------------------------------------
                             2y(x) - 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         (y(x) - x)log(x + 1) + (- y(x) + x)log(x - 1) + 2
--R   (15)  -------------------------------------------------
--R                             2y(x) - 2x
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 139
ode155expr := (x**2-1)*D(yx,x) + yx**2 - 2*x*yx + 1
 

   (16)
            2      ,           2              2           2
       (- 4x  + 4)y (x) + (y(x)  - 2x y(x) + x )log(x + 1)

     + 
                   2               2                     2      2              3
           (- 2y(x)  + 4x y(x) - 2x )log(x - 1) - 4x y(x)  + (8x  + 4)y(x) - 4x
         + 
           - 4x
      *
         log(x + 1)
     + 
            2              2           2
       (y(x)  - 2x y(x) + x )log(x - 1)
     + 
               2        2              3                                2
       (4x y(x)  + (- 8x  - 4)y(x) + 4x  + 4x)log(x - 1) - 8x y(x) + 12x
  /
          2               2
     4y(x)  - 8x y(x) + 4x
                                                     Type: Expression Integer
--R 
--R
--R   (16)
--R            2      ,           2              2           2
--R       (- 4x  + 4)y (x) + (y(x)  - 2x y(x) + x )log(x + 1)
--R
--R     + 
--R                   2               2                     2      2              3
--R           (- 2y(x)  + 4x y(x) - 2x )log(x - 1) - 4x y(x)  + (8x  + 4)y(x) - 4x
--R         + 
--R           - 4x
--R      *
--R         log(x + 1)
--R     + 
--R            2              2           2
--R       (y(x)  - 2x y(x) + x )log(x - 1)
--R     + 
--R               2        2              3                                2
--R       (4x y(x)  + (- 8x  - 4)y(x) + 4x  + 4x)log(x - 1) - 8x y(x) + 12x
--R  /
--R          2               2
--R     4y(x)  - 8x y(x) + 4x
--R                                                     Type: Expression Integer
--E 16

--S 17 of 139
ode156 := (x**2-1)*D(y(x),x) - y(x)*(y(x)-x)
 

           2      ,          2
   (17)  (x  - 1)y (x) - y(x)  + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,          2
--R   (17)  (x  - 1)y (x) - y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 17

--S 18 of 139
yx:=solve(ode156,y,x)
 

          - x y(x) + 1
   (18)  -------------
              +------+
              | 2
         y(x)\|x  - 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          - x y(x) + 1
--R   (18)  -------------
--R              +------+
--R              | 2
--R         y(x)\|x  - 1
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 139
ode156expr := (x**2-1)*D(yx,x) - yx*(yx-x)
 

   (19)
                                                         +------+
           4     2      ,          2    2                | 2
       (- x  + 2x  - 1)y (x) + (- x y(x)  + 2x y(x) - 1)\|x  - 1

     + 
           4     2         2
       (- x  + 2x  - 1)y(x)
  /
                   +------+
       2         2 | 2
     (x  - 1)y(x) \|x  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (19)
--R                                                         +------+
--R           4     2      ,          2    2                | 2
--R       (- x  + 2x  - 1)y (x) + (- x y(x)  + 2x y(x) - 1)\|x  - 1
--R
--R     + 
--R           4     2         2
--R       (- x  + 2x  - 1)y(x)
--R  /
--R                   +------+
--R       2         2 | 2
--R     (x  - 1)y(x) \|x  - 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 139
ode157 := (x**2-1)*D(y(x),x) + a*(y(x)**2-2*x*y(x)+1)
 

           2      ,            2
   (20)  (x  - 1)y (x) + a y(x)  - 2a x y(x) + a

                                                     Type: Expression Integer
--R 
--R
--R           2      ,            2
--R   (20)  (x  - 1)y (x) + a y(x)  - 2a x y(x) + a
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 139
ode157a:=solve(ode157,y,x)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--S 22 of 139
ode158 := (x**2-1)*D(y(x),x) + a*x*y(x)**2 + x*y(x)
 

           2      ,              2
   (22)  (x  - 1)y (x) + a x y(x)  + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,              2
--R   (22)  (x  - 1)y (x) + a x y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 22

--S 23 of 139
yx:=solve(ode158,y,x)
 

           2 2    2
          a x y(x)  + 2a y(x) + 1
   (23)  ------------------------
           4    2     3         2
         2a y(x)  + 4a y(x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2    2
--R          a x y(x)  + 2a y(x) + 1
--R   (23)  ------------------------
--R           4    2     3         2
--R         2a y(x)  + 4a y(x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 23

--S 24 of 139
ode158expr := (x**2-1)*D(yx,x) + a*x*yx**2 + x*yx
 

   (24)
           4 4     4 2     4     2      3 4     3 2     3       ,
       ((4a x  - 8a x  + 4a )y(x)  + (4a x  - 8a x  + 4a )y(x))y (x)

     + 
         4 5     5 3     5      4        4     3  3     4      3
       (a x  + 6a x  - 4a x)y(x)  + ((12a  + 4a )x  - 4a x)y(x)
     + 
           3     2  3      3     2       2      2
       ((6a  + 2a )x  + (6a  + 4a )x)y(x)  + (8a  + 4a)x y(x) + (2a + 1)x
  /
       7    4      6    3      5    2      4         3
     4a y(x)  + 16a y(x)  + 24a y(x)  + 16a y(x) + 4a
                                                     Type: Expression Integer
--R 
--R
--R   (24)
--R           4 4     4 2     4     2      3 4     3 2     3       ,
--R       ((4a x  - 8a x  + 4a )y(x)  + (4a x  - 8a x  + 4a )y(x))y (x)
--R
--R     + 
--R         4 5     5 3     5      4        4     3  3     4      3
--R       (a x  + 6a x  - 4a x)y(x)  + ((12a  + 4a )x  - 4a x)y(x)
--R     + 
--R           3     2  3      3     2       2      2
--R       ((6a  + 2a )x  + (6a  + 4a )x)y(x)  + (8a  + 4a)x y(x) + (2a + 1)x
--R  /
--R       7    4      6    3      5    2      4         3
--R     4a y(x)  + 16a y(x)  + 24a y(x)  + 16a y(x) + 4a
--R                                                     Type: Expression Integer
--E 24

--S 25 of 139
ode159 := (x**2-1)*D(y(x),x) - 2*x*y(x)*log(y(x))
 

           2      ,
   (25)  (x  - 1)y (x) - 2x y(x)log(y(x))

                                                     Type: Expression Integer
--R 
--R
--R           2      ,
--R   (25)  (x  - 1)y (x) - 2x y(x)log(y(x))
--R
--R                                                     Type: Expression Integer
--E 25

--S 26 of 139
yx:=solve(ode159,y,x)
 

             2
          - x  + 1
   (26)  ---------
         log(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             2
--R          - x  + 1
--R   (26)  ---------
--R         log(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 26

--S 27 of 139
ode159expr := (x**2-1)*D(yx,x) - 2*x*yx*log(yx)
 

   (27)
                                      2
          3                        - x  + 1      4     2      ,
       (2x  - 2x)y(x)log(y(x))log(---------) + (x  - 2x  + 1)y (x)
                                  log(y(x))
     + 
            3
       (- 2x  + 2x)y(x)log(y(x))
  /
                  2
     y(x)log(y(x))
                                                     Type: Expression Integer
--R 
--R
--R   (27)
--R                                      2
--R          3                        - x  + 1      4     2      ,
--R       (2x  - 2x)y(x)log(y(x))log(---------) + (x  - 2x  + 1)y (x)
--R                                  log(y(x))
--R     + 
--R            3
--R       (- 2x  + 2x)y(x)log(y(x))
--R  /
--R                  2
--R     y(x)log(y(x))
--R                                                     Type: Expression Integer
--E 27

--S 28 of 139
ode160 := (x**2-4)*D(y(x),x) + (x+2)*y(x)**2 - 4*y(x)
 

           2      ,                 2
   (28)  (x  - 4)y (x) + (x + 2)y(x)  - 4y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2      ,                 2
--R   (28)  (x  - 4)y (x) + (x + 2)y(x)  - 4y(x)
--R
--R                                                     Type: Expression Integer
--E 28

--S 29 of 139
yx:=solve(ode160,y,x)
 

         (- x - 2)y(x)log(x + 2) + x - 2
   (29)  -------------------------------
                   (x + 2)y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         (- x - 2)y(x)log(x + 2) + x - 2
--R   (29)  -------------------------------
--R                   (x + 2)y(x)
--R                                          Type: Union(Expression Integer,...)
--E 29

--S 30 of 139
ode160expr := (x**2-4)*D(yx,x) + (x+2)*yx**2 - 4*yx
 

   (30)
           3     2           ,        2              2          2
       (- x  + 2x  + 4x - 8)y (x) + (x  + 4x + 4)y(x) log(x + 2)

     + 
                  2        2                           2         2    2
     ((4x + 8)y(x)  + (- 2x  + 8)y(x))log(x + 2) + (- x  + 4)y(x)  + x  - 4x + 4
  /
                2
     (x + 2)y(x)
                                                     Type: Expression Integer
--R 
--R
--R   (30)
--R           3     2           ,        2              2          2
--R       (- x  + 2x  + 4x - 8)y (x) + (x  + 4x + 4)y(x) log(x + 2)
--R
--R     + 
--R                  2        2                           2         2    2
--R     ((4x + 8)y(x)  + (- 2x  + 8)y(x))log(x + 2) + (- x  + 4)y(x)  + x  - 4x + 4
--R  /
--R                2
--R     (x + 2)y(x)
--R                                                     Type: Expression Integer
--E 30

--S 31 of 139
ode161 := (x**2-5*x+6)*D(y(x),x) + 3*x*y(x) - 8*y(x) + x**2
 

           2           ,                      2
   (31)  (x  - 5x + 6)y (x) + (3x - 8)y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R           2           ,                      2
--R   (31)  (x  - 5x + 6)y (x) + (3x - 8)y(x) + x
--R
--R                                                     Type: Expression Integer
--E 31

--S 32 of 139
ode161a:=solve(ode161,y,x)
 

                              4     3
                          - 3x  + 8x  - 144                     1
   (32)  [particular= ------------------------,basis= [-------------------]]
                         3      2                       3     2
                      12x  - 84x  + 192x - 144         x  - 7x  + 16x - 12
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                              4     3
--R                          - 3x  + 8x  - 144                     1
--R   (32)  [particular= ------------------------,basis= [-------------------]]
--R                         3      2                       3     2
--R                      12x  - 84x  + 192x - 144         x  - 7x  + 16x - 12
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 32

--S 33 of 139
yx:=ode161a.particular
 

                 4     3
             - 3x  + 8x  - 144
   (33)  ------------------------
            3      2
         12x  - 84x  + 192x - 144
                                                     Type: Expression Integer
--R 
--R
--R                 4     3
--R             - 3x  + 8x  - 144
--R   (33)  ------------------------
--R            3      2
--R         12x  - 84x  + 192x - 144
--R                                                     Type: Expression Integer
--E 33

--S 34 of 139
ode161expr := (x**2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x**2
 

   (34)  0
                                                     Type: Expression Integer
--R 
--R
--R   (34)  0
--R                                                     Type: Expression Integer
--E 34

--S 35 of 139
ode162 := (x-a)*(x-b)*D(y(x),x) + y(x)**2 + k*(y(x)+x-a)*(y(x)+x-b)
 

   (35)
       2                     ,                 2
     (x  + (- b - a)x + a b)y (x) + (k + 1)y(x)  + (2k x + (- b - a)k)y(x)

   + 
        2
     k x  + (- b - a)k x + a b k
                                                     Type: Expression Integer
--R 
--R
--R   (35)
--R       2                     ,                 2
--R     (x  + (- b - a)x + a b)y (x) + (k + 1)y(x)  + (2k x + (- b - a)k)y(x)
--R
--R   + 
--R        2
--R     k x  + (- b - a)k x + a b k
--R                                                     Type: Expression Integer
--E 35
--S 36 of 139
ode163 := 2*x**2*D(y(x),x) - 2*y(x)**2 - x*y(x) + 2*a**2*x
 

           2 ,           2              2
   (36)  2x y (x) - 2y(x)  - x y(x) + 2a x

                                                     Type: Expression Integer
--R 
--R
--R           2 ,           2              2
--R   (36)  2x y (x) - 2y(x)  - x y(x) + 2a x
--R
--R                                                     Type: Expression Integer
--E 36

--S 37 of 139
yx:=solve(ode163,y,x)
 

                   +-+
                 a\|x  - y(x)
   (37)  ---------------------------
                                 4a
                              - ----
                                 +-+
            2 +-+               \|x
         (2a \|x  + 2a y(x))%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +-+
--R                 a\|x  - y(x)
--R   (37)  ---------------------------
--R                                 4a
--R                              - ----
--R                                 +-+
--R            2 +-+               \|x
--R         (2a \|x  + 2a y(x))%e
--R                                          Type: Union(Expression Integer,...)
--E 37

--S 38 of 139
ode163expr := 2*x**2*D(yx,x) - 2*yx**2 - x*yx + 2*a**2*x
 

   (38)
                                                                   4a
                                                                - ----
                                                                   +-+
              3 3    2     5 4  +-+     2 3    3      4 4         \|x  ,
       ((- 12a x y(x)  - 4a x )\|x  - 4a x y(x)  - 12a x y(x))%e      y (x)

     + 
              4      5      6 2    3      8 3      +-+      5 2    4
           (4a x y(x)  + 40a x y(x)  + 20a x y(x))\|x  + 20a x y(x)
         + 
              7 3    2     9 4
           40a x y(x)  + 4a x
      *
               4a  2
            - ----
               +-+
              \|x
         (%e      )
     + 
                       5      3      4     3 2    3     5 2    2    5 3
               a x y(x)  + 12a x y(x)  + 8a x y(x)  - 8a x y(x)  - a x y(x)
             + 
                   7 3
               - 4a x
          *
              +-+
             \|x
         + 
           2      5     2 2    4     4 2    3     4 3    2      6 3        6 4
         4a x y(x)  + 5a x y(x)  + 8a x y(x)  + 4a x y(x)  - 12a x y(x) - a x
      *
              4a
           - ----
              +-+
             \|x
         %e
     + 
              5     2      3    4 2      +-+           4     3 2    2    5 3
       (- y(x)  + 2a x y(x)  - a x y(x))\|x  - a x y(x)  + 2a x y(x)  - a x
  /
            2    5      4      3      6 2      +-+      3      4      5 2    2
         (2a y(x)  + 20a x y(x)  + 10a x y(x))\|x  + 10a x y(x)  + 20a x y(x)
       + 
           7 3
         2a x
    *
             4a  2
          - ----
             +-+
            \|x
       (%e      )
                                                     Type: Expression Integer
--R 
--R
--R   (38)
--R                                                                   4a
--R                                                                - ----
--R                                                                   +-+
--R              3 3    2     5 4  +-+     2 3    3      4 4         \|x  ,
--R       ((- 12a x y(x)  - 4a x )\|x  - 4a x y(x)  - 12a x y(x))%e      y (x)
--R
--R     + 
--R              4      5      6 2    3      8 3      +-+      5 2    4
--R           (4a x y(x)  + 40a x y(x)  + 20a x y(x))\|x  + 20a x y(x)
--R         + 
--R              7 3    2     9 4
--R           40a x y(x)  + 4a x
--R      *
--R               4a  2
--R            - ----
--R               +-+
--R              \|x
--R         (%e      )
--R     + 
--R                       5      3      4     3 2    3     5 2    2    5 3
--R               a x y(x)  + 12a x y(x)  + 8a x y(x)  - 8a x y(x)  - a x y(x)
--R             + 
--R                   7 3
--R               - 4a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R           2      5     2 2    4     4 2    3     4 3    2      6 3        6 4
--R         4a x y(x)  + 5a x y(x)  + 8a x y(x)  + 4a x y(x)  - 12a x y(x) - a x
--R      *
--R              4a
--R           - ----
--R              +-+
--R             \|x
--R         %e
--R     + 
--R              5     2      3    4 2      +-+           4     3 2    2    5 3
--R       (- y(x)  + 2a x y(x)  - a x y(x))\|x  - a x y(x)  + 2a x y(x)  - a x
--R  /
--R            2    5      4      3      6 2      +-+      3      4      5 2    2
--R         (2a y(x)  + 20a x y(x)  + 10a x y(x))\|x  + 10a x y(x)  + 20a x y(x)
--R       + 
--R           7 3
--R         2a x
--R    *
--R             4a  2
--R          - ----
--R             +-+
--R            \|x
--R       (%e      )
--R                                                     Type: Expression Integer
--E 38

--S 39 of 139
ode164 := 2*x**2*D(y(x),x) - 2*y(x)**2 - 3*x*y(x) + 2*a**2*x
 

           2 ,           2               2
   (39)  2x y (x) - 2y(x)  - 3x y(x) + 2a x

                                                     Type: Expression Integer
--R 
--R
--R           2 ,           2               2
--R   (39)  2x y (x) - 2y(x)  - 3x y(x) + 2a x
--R
--R                                                     Type: Expression Integer
--E 39

--S 40 of 139
yx:=solve(ode164,y,x)
 

                              +-+
                (- 2y(x) - x)\|x  + 2a x
   (40)  -------------------------------------
                                           4a
                                        - ----
                                           +-+
                           +-+     2      \|x
         ((4a y(x) + 2a x)\|x  + 4a x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              +-+
--R                (- 2y(x) - x)\|x  + 2a x
--R   (40)  -------------------------------------
--R                                           4a
--R                                        - ----
--R                                           +-+
--R                           +-+     2      \|x
--R         ((4a y(x) + 2a x)\|x  + 4a x)%e
--R                                          Type: Union(Expression Integer,...)
--E 40

--S 41 of 139
ode164expr := 2*x**2*D(yx,x) - 2*yx**2 - 3*x*yx + 2*a**2*x
 

   (41)
                     2 2    3       2 3    2         2 4       4 3           2 5
               - 128a x y(x)  - 192a x y(x)  + (- 96a x  - 384a x )y(x) - 16a x
             + 
                     4 4
               - 192a x
          *
              +-+
             \|x
         + 
                 3 3    2       3 4          3 5       5 4
           - 384a x y(x)  - 384a x y(x) - 96a x  - 128a x
      *
              4a
           - ----
              +-+
             \|x  ,
         %e      y (x)

     + 
                   5      4        5 2    3        5 3        7 2     2
               640a x y(x)  + 1280a x y(x)  + (960a x  + 1280a x )y(x)
             + 
                    5 4        7 3           5 5       7 4       9 3
               (320a x  + 1280a x )y(x) + 40a x  + 320a x  + 128a x
          *
              +-+
             \|x
         + 
               4      5       4 2    4        4 3        6 2     3
           128a x y(x)  + 320a x y(x)  + (320a x  + 1280a x )y(x)
         + 
                4 4        6 3     2       4 5       6 4       8 3          4 6
           (160a x  + 1920a x )y(x)  + (40a x  + 960a x  + 640a x )y(x) + 4a x
         + 
               6 5       8 4
           160a x  + 320a x
      *
               4a  2
            - ----
               +-+
              \|x
         (%e      )
     + 
                   2    5       2      4        2 2       4      3
               128a y(x)  + 672a x y(x)  + (960a x  + 256a x)y(x)
             + 
                    2 3       4 2     2        2 4       6 2           2 5
               (592a x  + 384a x )y(x)  + (168a x  - 384a x )y(x) + 18a x
             + 
                    4 4       6 3
               - 64a x  - 288a x
          *
              +-+
             \|x
         + 
                     5          2       3      4          3        3 2     3
           96a x y(x)  + (240a x  + 384a x)y(x)  + (240a x  + 1152a x )y(x)
         + 
                  4       3 3       5 2     2         5       3 4       5 3
           (120a x  + 960a x  - 256a x )y(x)  + (30a x  + 288a x  - 480a x )y(x)
         + 
               6      3 5       5 4       7 3
           3a x  + 24a x  - 240a x  - 128a x
      *
              4a
           - ----
              +-+
             \|x
         %e
     + 
                     4             3           2      3      2
           - 32a y(x)  - 64a x y(x)  + (- 48a x  + 64a x)y(x)
         + 
                   3      3 2            4      3 3      5 2
           (- 16a x  + 64a x )y(x) - 2a x  + 16a x  - 32a x
      *
          +-+
         \|x
     + 
               5           4         2      2      3         3      2 2     2
       - 32y(x)  - 80x y(x)  + (- 80x  + 64a x)y(x)  + (- 40x  + 96a x )y(x)
     + 
             4      2 3      4 2         5     2 4      4 3
       (- 10x  + 48a x  - 32a x )y(x) - x  + 8a x  - 16a x
  /
                 3    4       3      3        3 2       5      2
             320a y(x)  + 640a x y(x)  + (480a x  + 640a x)y(x)
           + 
                  3 3       5 2           3 4       5 3      7 2
             (160a x  + 640a x )y(x) + 20a x  + 160a x  + 64a x
        *
            +-+
           \|x
       + 
            2    5       2      4        2 2       4      3
         64a y(x)  + 160a x y(x)  + (160a x  + 640a x)y(x)
       + 
             2 3       4 2     2       2 4       4 3       6 2          2 5
         (80a x  + 960a x )y(x)  + (20a x  + 480a x  + 320a x )y(x) + 2a x
       + 
            4 4       6 3
         80a x  + 160a x
    *
             4a  2
          - ----
             +-+
            \|x
       (%e      )
                                                     Type: Expression Integer
--R 
--R
--R   (41)
--R                     2 2    3       2 3    2         2 4       4 3           2 5
--R               - 128a x y(x)  - 192a x y(x)  + (- 96a x  - 384a x )y(x) - 16a x
--R             + 
--R                     4 4
--R               - 192a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R                 3 3    2       3 4          3 5       5 4
--R           - 384a x y(x)  - 384a x y(x) - 96a x  - 128a x
--R      *
--R              4a
--R           - ----
--R              +-+
--R             \|x  ,
--R         %e      y (x)
--R
--R     + 
--R                   5      4        5 2    3        5 3        7 2     2
--R               640a x y(x)  + 1280a x y(x)  + (960a x  + 1280a x )y(x)
--R             + 
--R                    5 4        7 3           5 5       7 4       9 3
--R               (320a x  + 1280a x )y(x) + 40a x  + 320a x  + 128a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R               4      5       4 2    4        4 3        6 2     3
--R           128a x y(x)  + 320a x y(x)  + (320a x  + 1280a x )y(x)
--R         + 
--R                4 4        6 3     2       4 5       6 4       8 3          4 6
--R           (160a x  + 1920a x )y(x)  + (40a x  + 960a x  + 640a x )y(x) + 4a x
--R         + 
--R               6 5       8 4
--R           160a x  + 320a x
--R      *
--R               4a  2
--R            - ----
--R               +-+
--R              \|x
--R         (%e      )
--R     + 
--R                   2    5       2      4        2 2       4      3
--R               128a y(x)  + 672a x y(x)  + (960a x  + 256a x)y(x)
--R             + 
--R                    2 3       4 2     2        2 4       6 2           2 5
--R               (592a x  + 384a x )y(x)  + (168a x  - 384a x )y(x) + 18a x
--R             + 
--R                    4 4       6 3
--R               - 64a x  - 288a x
--R          *
--R              +-+
--R             \|x
--R         + 
--R                     5          2       3      4          3        3 2     3
--R           96a x y(x)  + (240a x  + 384a x)y(x)  + (240a x  + 1152a x )y(x)
--R         + 
--R                  4       3 3       5 2     2         5       3 4       5 3
--R           (120a x  + 960a x  - 256a x )y(x)  + (30a x  + 288a x  - 480a x )y(x)
--R         + 
--R               6      3 5       5 4       7 3
--R           3a x  + 24a x  - 240a x  - 128a x
--R      *
--R              4a
--R           - ----
--R              +-+
--R             \|x
--R         %e
--R     + 
--R                     4             3           2      3      2
--R           - 32a y(x)  - 64a x y(x)  + (- 48a x  + 64a x)y(x)
--R         + 
--R                   3      3 2            4      3 3      5 2
--R           (- 16a x  + 64a x )y(x) - 2a x  + 16a x  - 32a x
--R      *
--R          +-+
--R         \|x
--R     + 
--R               5           4         2      2      3         3      2 2     2
--R       - 32y(x)  - 80x y(x)  + (- 80x  + 64a x)y(x)  + (- 40x  + 96a x )y(x)
--R     + 
--R             4      2 3      4 2         5     2 4      4 3
--R       (- 10x  + 48a x  - 32a x )y(x) - x  + 8a x  - 16a x
--R  /
--R                 3    4       3      3        3 2       5      2
--R             320a y(x)  + 640a x y(x)  + (480a x  + 640a x)y(x)
--R           + 
--R                  3 3       5 2           3 4       5 3      7 2
--R             (160a x  + 640a x )y(x) + 20a x  + 160a x  + 64a x
--R        *
--R            +-+
--R           \|x
--R       + 
--R            2    5       2      4        2 2       4      3
--R         64a y(x)  + 160a x y(x)  + (160a x  + 640a x)y(x)
--R       + 
--R             2 3       4 2     2       2 4       4 3       6 2          2 5
--R         (80a x  + 960a x )y(x)  + (20a x  + 480a x  + 320a x )y(x) + 2a x
--R       + 
--R            4 4       6 3
--R         80a x  + 160a x
--R    *
--R             4a  2
--R          - ----
--R             +-+
--R            \|x
--R       (%e      )
--R                                                     Type: Expression Integer
--E 41

--S 42 of 139
ode165 := x*(2*x-1)*D(y(x),x) + y(x)**2 - (4*x+1)*y(x) + 4*x
 

            2      ,          2
   (42)  (2x  - x)y (x) + y(x)  + (- 4x - 1)y(x) + 4x

                                                     Type: Expression Integer
--R 
--R
--R            2      ,          2
--R   (42)  (2x  - x)y (x) + y(x)  + (- 4x - 1)y(x) + 4x
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 139
yx:=solve(ode165,y,x)
 

                    2
         x y(x) - 2x
   (43)  ------------
           y(x) - 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2
--R         x y(x) - 2x
--R   (43)  ------------
--R           y(x) - 1
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 139
ode165expr := x*(2*x-1)*D(yx,x) + yx**2 - (4*x+1)*yx + 4*x
 

   (44)
          4     3    2  ,          2          2        3     2               4
       (4x  - 4x  + x )y (x) + (- x  + 2x)y(x)  + (- 4x  + 8x  - 6x)y(x) + 4x

     + 
           2
       - 6x  + 4x
  /
         2
     y(x)  - 2y(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R   (44)
--R          4     3    2  ,          2          2        3     2               4
--R       (4x  - 4x  + x )y (x) + (- x  + 2x)y(x)  + (- 4x  + 8x  - 6x)y(x) + 4x
--R
--R     + 
--R           2
--R       - 6x  + 4x
--R  /
--R         2
--R     y(x)  - 2y(x) + 1
--R                                                     Type: Expression Integer
--E 44

--S 45 of 139
ode166 := 2*x*(x-1)*D(y(x),x) + (x-1)*y(x)**2 - x
 

            2       ,                 2
   (45)  (2x  - 2x)y (x) + (x - 1)y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R            2       ,                 2
--R   (45)  (2x  - 2x)y (x) + (x - 1)y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 139
ode166a:=solve(ode166,y,x)
 

   (46)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (46)  "failed"
--R                                                    Type: Union("failed",...)
--E 46

--S 47 of 139
ode167 := 3*x**2*D(y(x),x) - 7*y(x)**2 - 3*x*y(x) - x**2
 

           2 ,           2              2
   (47)  3x y (x) - 7y(x)  - 3x y(x) - x

                                                     Type: Expression Integer
--R 
--R
--R           2 ,           2              2
--R   (47)  3x y (x) - 7y(x)  - 3x y(x) - x
--R
--R                                                     Type: Expression Integer
--E 47

--S 48 of 139
yx:=solve(ode167,y,x)
 

                        +---+                    +---+
                 (- 497\|- 7  + 1197)y(x) + 171x\|- 7  + 497x
   (48)  ------------------------------------------------------------
                                                          +---+
                                                        2\|- 7 log(x)
                                                      - -------------
               +---+                   +---+                  3
         ((342\|- 7  + 994)y(x) - 142x\|- 7  + 342x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        +---+                    +---+
--R                 (- 497\|- 7  + 1197)y(x) + 171x\|- 7  + 497x
--R   (48)  ------------------------------------------------------------
--R                                                          +---+
--R                                                        2\|- 7 log(x)
--R                                                      - -------------
--R               +---+                   +---+                  3
--R         ((342\|- 7  + 994)y(x) - 142x\|- 7  + 342x)%e
--R                                          Type: Union(Expression Integer,...)
--E 48

--S 49 of 139
ode167expr := 3*x**2*D(yx,x) - 7*yx**2 - 3*x*yx - x**2
 

   (49)
                        3 +---+             3                 4 +---+
           (- 275142420x \|- 7  + 547274532x )y(x) - 78182076x \|- 7
         + 
                       4
           - 275142420x
      *
               +---+
             2\|- 7 log(x)
           - -------------
                   3       ,
         %e               y (x)

     + 
                       2 +---+             2     3
           (- 91714140x \|- 7  + 182424844x )y(x)
         + 
                       3 +---+             3     2
           (- 78182076x \|- 7  - 275142420x )y(x)
         + 
                     4 +---+            4                5 +---+            5
           (39306060x \|- 7  - 78182076x )y(x) + 3722956x \|- 7  + 13102020x
      *
                +---+       2
              2\|- 7 log(x)
            - -------------
                    3
         (%e               )
     + 
                       +---+                   3
           (368361714x\|- 7  - 2239972378x)y(x)
         + 
                      2 +---+             2     2
           (595138474x \|- 7  - 178912818x )y(x)
         + 
                      3 +---+            3                 4 +---+            4
           (130805178x \|- 7  - 44853634x )y(x) + 45713722x \|- 7  + 52623102x
      *
               +---+
             2\|- 7 log(x)
           - -------------
                   3
         %e
     + 
                   +---+                  3
       (1123498215\|- 7  - 2234704339)y(x)
     + 
                     +---+                   2
       (- 319243477x\|- 7  - 1123498215x)y(x)
     + 
                  2 +---+             2                 3 +---+             3
       (160499745x \|- 7  - 319243477x )y(x) - 45606211x \|- 7  - 160499745x
  /
                   +---+                 3              +---+                  2
         (91714140\|- 7  - 182424844)y(x)  + (78182076x\|- 7  + 275142420x)y(x)
       + 
                     2 +---+            2                3 +---+            3
         (- 39306060x \|- 7  + 78182076x )y(x) - 3722956x \|- 7  - 13102020x
    *
              +---+       2
            2\|- 7 log(x)
          - -------------
                  3
       (%e               )
                                                     Type: Expression Integer
--R 
--R
--R   (49)
--R                        3 +---+             3                 4 +---+
--R           (- 275142420x \|- 7  + 547274532x )y(x) - 78182076x \|- 7
--R         + 
--R                       4
--R           - 275142420x
--R      *
--R               +---+
--R             2\|- 7 log(x)
--R           - -------------
--R                   3       ,
--R         %e               y (x)
--R
--R     + 
--R                       2 +---+             2     3
--R           (- 91714140x \|- 7  + 182424844x )y(x)
--R         + 
--R                       3 +---+             3     2
--R           (- 78182076x \|- 7  - 275142420x )y(x)
--R         + 
--R                     4 +---+            4                5 +---+            5
--R           (39306060x \|- 7  - 78182076x )y(x) + 3722956x \|- 7  + 13102020x
--R      *
--R                +---+       2
--R              2\|- 7 log(x)
--R            - -------------
--R                    3
--R         (%e               )
--R     + 
--R                       +---+                   3
--R           (368361714x\|- 7  - 2239972378x)y(x)
--R         + 
--R                      2 +---+             2     2
--R           (595138474x \|- 7  - 178912818x )y(x)
--R         + 
--R                      3 +---+            3                 4 +---+            4
--R           (130805178x \|- 7  - 44853634x )y(x) + 45713722x \|- 7  + 52623102x
--R      *
--R               +---+
--R             2\|- 7 log(x)
--R           - -------------
--R                   3
--R         %e
--R     + 
--R                   +---+                  3
--R       (1123498215\|- 7  - 2234704339)y(x)
--R     + 
--R                     +---+                   2
--R       (- 319243477x\|- 7  - 1123498215x)y(x)
--R     + 
--R                  2 +---+             2                 3 +---+             3
--R       (160499745x \|- 7  - 319243477x )y(x) - 45606211x \|- 7  - 160499745x
--R  /
--R                   +---+                 3              +---+                  2
--R         (91714140\|- 7  - 182424844)y(x)  + (78182076x\|- 7  + 275142420x)y(x)
--R       + 
--R                     2 +---+            2                3 +---+            3
--R         (- 39306060x \|- 7  + 78182076x )y(x) - 3722956x \|- 7  - 13102020x
--R    *
--R              +---+       2
--R            2\|- 7 log(x)
--R          - -------------
--R                  3
--R       (%e               )
--R                                                     Type: Expression Integer
--E 49

--S 50 of 139
ode168 := 3*(x**2-4)*D(y(x),x) + y(x)**2 - x*y(x) - 3
 

            2       ,          2
   (50)  (3x  - 12)y (x) + y(x)  - x y(x) - 3

                                                     Type: Expression Integer
--R 
--R
--R            2       ,          2
--R   (50)  (3x  - 12)y (x) + y(x)  - x y(x) - 3
--R
--R                                                     Type: Expression Integer
--E 50

--S 51 of 139
ode168a:=solve(ode168,y,x)
 

   (51)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (51)  "failed"
--R                                                    Type: Union("failed",...)
--E 51

--S 52 of 139
ode169 := (a*x+b)**2*D(y(x),x) + (a*x+b)*y(x)**3 + c*y(x)**2
 

           2 2             2  ,                   3         2
   (52)  (a x  + 2a b x + b )y (x) + (a x + b)y(x)  + c y(x)

                                                     Type: Expression Integer
--R 
--R
--R           2 2             2  ,                   3         2
--R   (52)  (a x  + 2a b x + b )y (x) + (a x + b)y(x)  + c y(x)
--R
--R                                                     Type: Expression Integer
--E 52

--S 53 of 139
ode169a:=solve(ode169,y,x)
 

   (53)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (53)  "failed"
--R                                                    Type: Union("failed",...)
--E 53

--S 54 of 139
ode170 := x**3*D(y(x),x) - y(x)**2 - x**4
 

          3 ,          2    4
   (54)  x y (x) - y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R          3 ,          2    4
--R   (54)  x y (x) - y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 54

--S 55 of 139
yx:=solve(ode170,y,x)
 

                  2           2
         (y(x) - x )log(x) + x
   (55)  ----------------------
                        2
                y(x) - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2           2
--R         (y(x) - x )log(x) + x
--R   (55)  ----------------------
--R                        2
--R                y(x) - x
--R                                          Type: Union(Expression Integer,...)
--E 55

--S 56 of 139
ode170expr := x**3*D(yx,x) - yx**2 - x**4
 

   (56)
          5 ,             2     2        4       2        2         4
       - x y (x) + (- y(x)  + 2x y(x) - x )log(x)  + (- 2x y(x) + 2x )log(x)

     + 
           4    2     2     6        8    6    4
       (- x  + x )y(x)  + 2x y(x) - x  + x  - x
  /
         2     2        4
     y(x)  - 2x y(x) + x
                                                     Type: Expression Integer
--R 
--R
--R   (56)
--R          5 ,             2     2        4       2        2         4
--R       - x y (x) + (- y(x)  + 2x y(x) - x )log(x)  + (- 2x y(x) + 2x )log(x)
--R
--R     + 
--R           4    2     2     6        8    6    4
--R       (- x  + x )y(x)  + 2x y(x) - x  + x  - x
--R  /
--R         2     2        4
--R     y(x)  - 2x y(x) + x
--R                                                     Type: Expression Integer
--E 56

--S 57 of 139
ode171 := x**3*D(y(x),x) - y(x)**2 - x**2*y(x)
 

          3 ,          2    2
   (57)  x y (x) - y(x)  - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          3 ,          2    2
--R   (57)  x y (x) - y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 139
yx:=solve(ode171,y,x)
 

                   2
         - y(x) + x
   (58)  -----------
            x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2
--R         - y(x) + x
--R   (58)  -----------
--R            x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 139
ode171expr := x**3*D(yx,x) - yx**2 - x**2*yx
 

            6 ,         3         2     2        4
         - x y (x) + (2x  - 1)y(x)  + 2x y(x) - x

   (59)  -----------------------------------------
                           2    2
                          x y(x)
                                                     Type: Expression Integer
--R 
--R
--R            6 ,         3         2     2        4
--R         - x y (x) + (2x  - 1)y(x)  + 2x y(x) - x
--R
--R   (59)  -----------------------------------------
--R                           2    2
--R                          x y(x)
--R                                                     Type: Expression Integer
--E 59

--S 60 of 139
ode172 := x**3*D(y(x),x) - x**4*y(x)**2 + x**2*y(x) + 20
 

          3 ,       4    2    2
   (60)  x y (x) - x y(x)  + x y(x) + 20

                                                     Type: Expression Integer
--R 
--R
--R          3 ,       4    2    2
--R   (60)  x y (x) - x y(x)  + x y(x) + 20
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 139
yx:=solve(ode172,y,x)
 

              11      2           9
           (7x   - 11x )y(x) + 35x  + 44
   (61)  --------------------------------
             11      2            9
         (36x   - 36x )y(x) + 180x  + 144
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              11      2           9
--R           (7x   - 11x )y(x) + 35x  + 44
--R   (61)  --------------------------------
--R             11      2            9
--R         (36x   - 36x )y(x) + 180x  + 144
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 139
ode172expr := x**3*D(yx,x) - x**4*yx**2 + x**2*yx + 20
 

   (62)
              14 ,
       - 1296x  y (x)

     + 
                26       24         22       17       15         13       8
           - 49x   + 252x   + 25920x   + 154x   + 648x   - 51840x   - 121x
         + 
               6         4
           396x  + 25920x
      *
             2
         y(x)
     + 
                 24        22          20       15        13         11       6
           - 490x   + 2520x   + 259200x   + 154x   - 1944x   - 51840x   + 968x
         + 
                  4          2
           - 3168x  - 207360x
      *
         y(x)
     + 
              22        20          18        13         11           9        4
       - 1225x   + 6300x   + 648000x   - 3080x   - 12960x   + 1036800x  - 1936x
     + 
            2
       6336x  + 414720
  /
             22        13        4     2          20        11         2
       (1296x   - 2592x   + 1296x )y(x)  + (12960x   - 2592x   - 10368x )y(x)
     + 
             18         9
       32400x   + 51840x  + 20736
                                                     Type: Expression Integer
--R 
--R
--R   (62)
--R              14 ,
--R       - 1296x  y (x)
--R
--R     + 
--R                26       24         22       17       15         13       8
--R           - 49x   + 252x   + 25920x   + 154x   + 648x   - 51840x   - 121x
--R         + 
--R               6         4
--R           396x  + 25920x
--R      *
--R             2
--R         y(x)
--R     + 
--R                 24        22          20       15        13         11       6
--R           - 490x   + 2520x   + 259200x   + 154x   - 1944x   - 51840x   + 968x
--R         + 
--R                  4          2
--R           - 3168x  - 207360x
--R      *
--R         y(x)
--R     + 
--R              22        20          18        13         11           9        4
--R       - 1225x   + 6300x   + 648000x   - 3080x   - 12960x   + 1036800x  - 1936x
--R     + 
--R            2
--R       6336x  + 414720
--R  /
--R             22        13        4     2          20        11         2
--R       (1296x   - 2592x   + 1296x )y(x)  + (12960x   - 2592x   - 10368x )y(x)
--R     + 
--R             18         9
--R       32400x   + 51840x  + 20736
--R                                                     Type: Expression Integer
--E 62

--S 63 of 139
ode173 := x**3*D(y(x),x) - x**6*y(x)**2 - (2*x-3)*x**2*y(x) + 3
 

          3 ,       6    2        3     2
   (63)  x y (x) - x y(x)  + (- 2x  + 3x )y(x) + 3

                                                     Type: Expression Integer
--R 
--R
--R          3 ,       6    2        3     2
--R   (63)  x y (x) - x y(x)  + (- 2x  + 3x )y(x) + 3
--R
--R                                                     Type: Expression Integer
--E 63

--S 64 of 139
yx:=solve(ode173,y,x)
 

               3
            - x y(x) + 1
   (64)  ------------------
            3            4x
         (4x y(x) + 12)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3
--R            - x y(x) + 1
--R   (64)  ------------------
--R            3            4x
--R         (4x y(x) + 12)%e
--R                                          Type: Union(Expression Integer,...)
--E 64

--S 65 of 139
ode173expr := x**3*D(yx,x) - x**6*yx**2 - (2*x-3)*x**2*yx + 3
 

   (65)
            6  4x ,          6    2       3              4x 2
       - 16x %e  y (x) + (48x y(x)  + 288x y(x) + 432)(%e  )

     + 
            9      8     2       6      5           3      2   4x    12    2
       ((24x  - 12x )y(x)  + (48x  - 72x )y(x) - 72x  + 36x )%e   - x  y(x)
     + 
         9        6
       2x y(x) - x
  /
         6    2      3              4x 2
     (16x y(x)  + 96x y(x) + 144)(%e  )
                                                     Type: Expression Integer
--R 
--R
--R   (65)
--R            6  4x ,          6    2       3              4x 2
--R       - 16x %e  y (x) + (48x y(x)  + 288x y(x) + 432)(%e  )
--R
--R     + 
--R            9      8     2       6      5           3      2   4x    12    2
--R       ((24x  - 12x )y(x)  + (48x  - 72x )y(x) - 72x  + 36x )%e   - x  y(x)
--R     + 
--R         9        6
--R       2x y(x) - x
--R  /
--R         6    2      3              4x 2
--R     (16x y(x)  + 96x y(x) + 144)(%e  )
--R                                                     Type: Expression Integer
--E 65

--S 66 of 139
ode174 := x*(x**2+1)*D(y(x),x) + x**2*y(x)
 

           3      ,       2
   (66)  (x  + x)y (x) + x y(x)

                                                     Type: Expression Integer
--R 
--R
--R           3      ,       2
--R   (66)  (x  + x)y (x) + x y(x)
--R
--R                                                     Type: Expression Integer
--E 66

--S 67 of 139
ode174a:=solve(ode174,y,x)
 

                                    1
   (67)  [particular= 0,basis= [---------]]
                                 +------+
                                 | 2
                                \|x  + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                    1
--R   (67)  [particular= 0,basis= [---------]]
--R                                 +------+
--R                                 | 2
--R                                \|x  + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 67

--S 68 of 139
yx:=ode174a.particular
 

   (68)  0
                                                     Type: Expression Integer
--R 
--R
--R   (68)  0
--R                                                     Type: Expression Integer
--E 68

--S 69 of 139
ode174expr := x*(x**2+1)*D(yx,x) + x**2*yx
 

   (69)  0
                                                     Type: Expression Integer
--R 
--R
--R   (69)  0
--R                                                     Type: Expression Integer
--E 69

--S 70 of 139
ode175 := x*(x**2-1)*D(y(x),x) - (2*x**2-1)*y(x) + a*x**3
 

           3      ,           2               3
   (70)  (x  - x)y (x) + (- 2x  + 1)y(x) + a x

                                                     Type: Expression Integer
--R 
--R
--R           3      ,           2               3
--R   (70)  (x  - x)y (x) + (- 2x  + 1)y(x) + a x
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 139
ode175a:=solve(ode175,y,x)
 

                                    +------+
                                    | 2
   (71)  [particular= a x,basis= [x\|x  - 1 ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                    +------+
--R                                    | 2
--R   (71)  [particular= a x,basis= [x\|x  - 1 ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 71

--S 72 of 139
yx:=ode175a.particular
 

   (72)  a x
                                                     Type: Expression Integer
--R 
--R
--R   (72)  a x
--R                                                     Type: Expression Integer
--E 72

--S 73 of 139
ode175expr := x*(x**2-1)*D(yx,x) - (2*x**2-1)*yx + a*x**3
 

   (73)  0
                                                     Type: Expression Integer
--R 
--R
--R   (73)  0
--R                                                     Type: Expression Integer
--E 73

--S 74 of 139
ode176 := x*(x**2-1)*D(y(x),x) + (x**2-1)*y(x)**2 - x**2
 

           3      ,        2         2    2
   (74)  (x  - x)y (x) + (x  - 1)y(x)  - x

                                                     Type: Expression Integer
--R 
--R
--R           3      ,        2         2    2
--R   (74)  (x  - x)y (x) + (x  - 1)y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 139
ode176a:=solve(ode176,y,x)
 

   (75)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (75)  "failed"
--R                                                    Type: Union("failed",...)
--E 75

--S 76 of 139
ode177 := x**2*(x-1)*D(y(x),x) - y(x)**2 - x*(x-2)*y(x)
 

           3    2  ,          2       2
   (76)  (x  - x )y (x) - y(x)  + (- x  + 2x)y(x)

                                                     Type: Expression Integer
--R 
--R
--R           3    2  ,          2       2
--R   (76)  (x  - x )y (x) - y(x)  + (- x  + 2x)y(x)
--R
--R                                                     Type: Expression Integer
--E 76

--S 77 of 139
yx:=solve(ode177,y,x)
 

                   2
         - y(x) + x
   (77)  -----------
         (x - 1)y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2
--R         - y(x) + x
--R   (77)  -----------
--R         (x - 1)y(x)
--R                                          Type: Union(Expression Integer,...)
--E 77

--S 78 of 139
ode177expr := x**2*(x-1)*D(yx,x) - yx**2 - x*(x-2)*yx
 

             6     5    4  ,         3     2              2     2        4
         (- x  + 2x  - x )y (x) + (2x  - 4x  + 2x - 1)y(x)  + 2x y(x) - x

   (78)  -----------------------------------------------------------------
                                   2              2
                                 (x  - 2x + 1)y(x)
                                                     Type: Expression Integer
--R 
--R
--R             6     5    4  ,         3     2              2     2        4
--R         (- x  + 2x  - x )y (x) + (2x  - 4x  + 2x - 1)y(x)  + 2x y(x) - x
--R
--R   (78)  -----------------------------------------------------------------
--R                                   2              2
--R                                 (x  - 2x + 1)y(x)
--R                                                     Type: Expression Integer
--E 78

--S 79 of 139
ode178 := 2*x*(x**2-1)*D(y(x),x) + 2*(x**2-1)*y(x)**2 _
           - (3*x**2-5)*y(x) + x**2 - 3
 

            3       ,         2         2        2             2
   (79)  (2x  - 2x)y (x) + (2x  - 2)y(x)  + (- 3x  + 5)y(x) + x  - 3

                                                     Type: Expression Integer
--R 
--R
--R            3       ,         2         2        2             2
--R   (79)  (2x  - 2x)y (x) + (2x  - 2)y(x)  + (- 3x  + 5)y(x) + x  - 3
--R
--R                                                     Type: Expression Integer
--E 79

--S 80 of 139
yx:=solve(ode178,y,x)
 

                      +------+   x      +---+
                      | 2      ++      \|%CL               +-+
         (- y(x) + 1)\|x  - 1  |   -------------- d%CL  + \|x
                              ++       +--------+
                                       |   2
                                   %CL\|%CL  - 1
   (80)  -----------------------------------------------------
                                     +------+
                                     | 2
                          (y(x) - 1)\|x  - 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      +------+   x      +---+
--I                      | 2      ++      \|%CL               +-+
--I         (- y(x) + 1)\|x  - 1  |   -------------- d%CL  + \|x
--R                              ++       +--------+
--R                                       |   2
--I                                   %CL\|%CL  - 1
--R   (80)  -----------------------------------------------------
--R                                     +------+
--R                                     | 2
--R                          (y(x) - 1)\|x  - 1
--R                                          Type: Union(Expression Integer,...)
--E 80

--S 81 of 139
ode178expr := 2*x*(x**2-1)*D(yx,x) + 2*(x**2-1)*yx**2 _
               - (3*x**2-5)*yx + x**2 - 3
 

   (81)
                                                          +------+
             2         2        2              2      +-+ | 2
         ((2x  - 2)y(x)  + (- 4x  + 4)y(x) + 2x  - 2)\|x \|x  - 1
      *
            x      +---+          2
          ++      \|%CL
          |   -------------- d%CL
         ++       +--------+
                  |   2
              %CL\|%CL  - 1
     + 
                                                             +------+
               2         2        2               2      +-+ | 2
           ((3x  - 5)y(x)  + (- 6x  + 10)y(x) + 3x  - 5)\|x \|x  - 1
         + 
                3               3
           (- 4x  + 4x)y(x) + 4x  - 4x
      *
            x      +---+
          ++      \|%CL
          |   -------------- d%CL
         ++       +--------+
                  |   2
              %CL\|%CL  - 1
     + 
            4     2  ,
       (- 2x  + 2x )y (x)

     + 
                                                           +------+
          2         2        2             2           +-+ | 2
       ((x  - 3)y(x)  + (- 2x  + 6)y(x) + x  + 2x - 3)\|x \|x  - 1
     + 
            3          2     3
       (- 2x  + 2x)y(x)  + 2x  - 2x
  /
                             +------+
          2              +-+ | 2
     (y(x)  - 2y(x) + 1)\|x \|x  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (81)
--R                                                          +------+
--R             2         2        2              2      +-+ | 2
--R         ((2x  - 2)y(x)  + (- 4x  + 4)y(x) + 2x  - 2)\|x \|x  - 1
--R      *
--R            x      +---+          2
--I          ++      \|%CL
--I          |   -------------- d%CL
--R         ++       +--------+
--R                  |   2
--I              %CL\|%CL  - 1
--R     + 
--R                                                             +------+
--R               2         2        2               2      +-+ | 2
--R           ((3x  - 5)y(x)  + (- 6x  + 10)y(x) + 3x  - 5)\|x \|x  - 1
--R         + 
--R                3               3
--R           (- 4x  + 4x)y(x) + 4x  - 4x
--R      *
--R            x      +---+
--I          ++      \|%CL
--I          |   -------------- d%CL
--R         ++       +--------+
--R                  |   2
--I              %CL\|%CL  - 1
--R     + 
--R            4     2  ,
--R       (- 2x  + 2x )y (x)
--R
--R     + 
--R                                                           +------+
--R          2         2        2             2           +-+ | 2
--R       ((x  - 3)y(x)  + (- 2x  + 6)y(x) + x  + 2x - 3)\|x \|x  - 1
--R     + 
--R            3          2     3
--R       (- 2x  + 2x)y(x)  + 2x  - 2x
--R  /
--R                             +------+
--R          2              +-+ | 2
--R     (y(x)  - 2y(x) + 1)\|x \|x  - 1
--R                                                     Type: Expression Integer
--E 81

--S 82 of 139
ode179 := 3*x*(x**2-1)*D(y(x),x) + x*y(x)**2 - (x**2+1)*y(x) - 3*x
 

            3       ,            2       2
   (82)  (3x  - 3x)y (x) + x y(x)  + (- x  - 1)y(x) - 3x

                                                     Type: Expression Integer
--R 
--R
--R            3       ,            2       2
--R   (82)  (3x  - 3x)y (x) + x y(x)  + (- x  - 1)y(x) - 3x
--R
--R                                                     Type: Expression Integer
--E 82

--S 83 of 139
ode179a:=solve(ode179,y,x)
 

   (83)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (83)  "failed"
--R                                                    Type: Union("failed",...)
--E 83

--S 84 of 139
ode180 := (a*x**2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)**2 + x**2
 

             3      2        ,          2         2                   2
   (84)  (a x  + b x  + c x)y (x) - y(x)  + (- a x  - b x - c)y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R             3      2        ,          2         2                   2
--R   (84)  (a x  + b x  + c x)y (x) - y(x)  + (- a x  - b x - c)y(x) + x
--R
--R                                                     Type: Expression Integer
--E 84

--S 85 of 139  random generation, FAILURE OK.
yx:=solve(ode180,y,x)
 
   WARNING (genufact): No known algorithm to factor
                     2            2
      4   - 4a c + 2b   2        b
     ?  + ------------ ?  - -----------, trying square-free.
             3     2 2        5     4 2
           4a c - a b       4a c - a b
   WARNING (genufact): No known algorithm to factor
                     2            2         2            2
      4   - 4a c + 2b  - 4a b + 4a   2   - b  + 4a b - 4a
     ?  + ------------------------- ?  + -----------------, trying square-free.
                   3     2 2                  5     4 2
                 4a c - a b                 4a c - a b
   WARNING (genufact): No known algorithm to factor
                           2              4      2
        9   9b  8   (144a b  - 24a)c - 36b  + 12b   7
       ?  - -- ?  + ------------------------------ ?
             a                  3     2 2
                              4a c - a b
     + 
                3                 5      3
       (- 336a b  + 168a b)c + 84b  - 84b   6
       ----------------------------------- ?
                     4     3 2
                   4a c - a b
     + 
                   2 4        2 2       2  2
             (2016a b  - 2016a b  + 144a )c
           + 
                       6          4         2         8       6      4
             (- 1008a b  + 1512a b  - 192a b )c + 126b  - 252b  + 48b
        /
              6 2     5 2     4 4
           16a c  - 8a b c + a b
      *
          5
         ?
     + 
                     2 5        2 3       2   2
             (- 2016a b  + 3360a b  - 720a b)c
           + 
                     7          5         3         9       7       5
             (1008a b  - 2520a b  + 960a b )c - 126b  + 420b  - 240b
        /
              7 2     6 2     5 4
           16a c  - 8a b c + a b
      *
          4
         ?
     + 
                   3 6         3 4        3 2       3  3
             (5376a b  - 13440a b  + 5760a b  - 256a )c
           + 
                     2 8         2 6        2 4       2 2  2
             (- 4032a b  + 13440a b  - 9120a b  + 640a b )c
           + 
                     10          8          6         4        12       10
             (1008a b   - 4200a b  + 3840a b  - 384a b )c - 84b   + 420b
           + 
                   8      6
             - 480b  + 64b
        /
              9 3      8 2 2      7 4     6 6
           64a c  - 48a b c  + 12a b c - a b
      *
          3
         ?
     + 
                     3 7        3 5        3 3       3   3
             (- 2304a b  + 8064a b  - 5760a b  + 768a b)c
           + 
                   2 9        2 7        2 5        2 3  2
             (1728a b  - 8064a b  + 9120a b  - 1920a b )c
           + 
                      11          9          7          5        13       11
             (- 432a b   + 2520a b  - 3840a b  + 1152a b )c + 36b   - 252b
           + 
                 9       7
             480b  - 192b
        /
              10 3      9 2 2      8 4     7 6
           64a  c  - 48a b c  + 12a b c - a b
      *
          2
         ?
     + 
                  3 8        3 6        3 4       3 2  3
             (576a b  - 2688a b  + 2880a b  - 768a b )c
           + 
                    2 10        2 8        2 6        2 4       2 2  2
             (- 432a b   + 2688a b  - 4560a b  + 1920a b  - 256a b )c
           + 
                    12         10          8          6       14      12
             (108a b   - 840a b   + 1920a b  - 1152a b )c - 9b   + 84b
           + 
                   10       8
             - 240b   + 192b
        /
              11 3      10 2 2      9 4     8 6
           64a  c  - 48a  b c  + 12a b c - a b
      *
         ?
     + 
                 3 9       3 7       3 5       3 3  3
           (- 64a b  + 384a b  - 576a b  + 256a b )c
         + 
               2 11       2 9       2 7       2 5       2 3  2
           (48a b   - 384a b  + 912a b  - 640a b  + 256a b )c
         + 
                   13         11         9         7      15      13      11
           (- 12a b   + 120a b   - 384a b  + 384a b )c + b   - 12b   + 48b
         + 
                9
           - 64b
      /
            12 3      11 2 2      10 4     9 6
         64a  c  - 48a  b c  + 12a  b c - a b
     , trying square-free.
   WARNING (genufact): No known algorithm to factor
        9   18b - 18a  8
       ?  + --------- ?
                a
     + 
                    2        2        3               4         3
             (576a b  - 1152a b + 576a  - 96a)c - 144b  + 288a b
           + 
                    2       2              2
             (- 144a  + 48)b  - 48a b + 24a
        /
             3     2 2
           4a c - a b
      *
          7
         ?
     + 
                     3        2 2         3                  4        2
             (2688a b  - 8064a b  + (8064a  - 1344a)b - 2688a  + 1344a )c
           + 
                   5          4           2        3        3          2
             - 672b  + 2016a b  + (- 2016a  + 672)b  + (672a  - 1344a)b
           + 
                  2        3
             1008a b - 336a
        /
             4     3 2
           4a c - a b
      *
          6
         ?
     + 
                       2 4          3 3           4         2  2
                 32256a b  - 129024a b  + (193536a  - 32256a )b
               + 
                           5         3           6         4        2
                 (- 129024a  + 64512a )b + 32256a  - 32256a  + 2304a
            *
                2
               c
           + 
                           6         2 5            3           4
                 - 16128a b  + 64512a b  + (- 96768a  + 24192a)b
               + 
                        4         2  3            5         3          2
                 (64512a  - 64512a )b  + (- 16128a  + 64512a  - 3072a)b
               + 
                          4        2          5        3
                 (- 32256a  + 3840a )b + 8064a  - 1920a
            *
               c
           + 
                  8          7          2         6           3           5
             2016b  - 8064a b  + (12096a  - 4032)b  + (- 8064a  + 12096a)b
           + 
                   4         2        4         3          3
             (2016a  - 14112a  + 768)b  + (8064a  - 1536a)b
           + 
                     4        2  2       3        4
             (- 2016a  + 1344a )b  - 576a b + 144a
        /
              6 2     5 2     4 4
           16a c  - 8a b c + a b
      *
          5
         ?
     + 
                       2 5          3 4           4          2  3
                 64512a b  - 322560a b  + (645120a  - 107520a )b
               + 
                           5          3  2           6          4         2
                 (- 645120a  + 322560a )b  + (322560a  - 322560a  + 23040a )b
               + 
                         7          5         3
                 - 64512a  + 107520a  - 23040a
            *
                2
               c
           + 
                           7          2 6             3           5
                 - 32256a b  + 161280a b  + (- 322560a  + 80640a)b
               + 
                         4          2  4             5          3           3
                 (322560a  - 295680a )b  + (- 161280a  + 430080a  - 30720a)b
               + 
                        6          4         2  2           5         3
                 (32256a  - 322560a  + 69120a )b  + (134400a  - 57600a )b
               + 
                         6         4
                 - 26880a  + 19200a
            *
               c
           + 
                  9           8          2          7            3           6
             4032b  - 20160a b  + (40320a  - 13440)b  + (- 40320a  + 53760a)b
           + 
                    4         2         5           5         3           4
             (20160a  - 87360a  + 7680)b  + (- 4032a  + 73920a  - 23040a)b
           + 
                      4         2  3         5         3  2        4         5
             (- 33600a  + 28800a )b  + (6720a  - 19200a )b  + 7200a b - 1440a
        /
              7 2     6 2     5 4
           16a c  - 8a b c + a b
      *
          4
         ?
     + 
                        3 6           4 5            5          3  4
                 344064a b  - 2064384a b  + (5160960a  - 860160a )b
               + 
                            6           4  3
                 (- 6881280a  + 3440640a )b
               + 
                          7           5          3  2
                 (5160960a  - 5160960a  + 368640a )b
               + 
                            8           6          4            9          7
                 (- 2064384a  + 3440640a  - 737280a )b + 344064a  - 860160a
               + 
                        5         3
                 368640a  - 16384a
            *
                3
               c
           + 
                          2 8           3 7              4          2  6
                 - 258048a b  + 1548288a b  + (- 3870720a  + 860160a )b
               + 
                          5           3  5
                 (5160960a  - 3870720a )b
               + 
                            6           4          2  4
                 (- 3870720a  + 7096320a  - 583680a )b
               + 
                          7           5           3  3
                 (1548288a  - 6881280a  + 1781760a )b
               + 
                           8           6           4         2  2
                 (- 258048a  + 3870720a  - 2119680a  + 40960a )b
               + 
                            7           5         3            8          6
                 (- 1290240a  + 1228800a  - 57344a )b + 215040a  - 307200a
               + 
                       4
                 28672a
            *
                2
               c
           + 
                         10          2 9           3            8
                 64512a b   - 387072a b  + (967680a  - 268800a)b
               + 
                            4           2  7
                 (- 1290240a  + 1290240a )b
               + 
                         5           3            6
                 (967680a  - 2580480a  + 245760a)b
               + 
                           6           4          2  5
                 (- 387072a  + 2795520a  - 890880a )b
               + 
                        7           5           3           4
                 (64512a  - 1774080a  + 1336320a  - 24576a)b
               + 
                         6           4         2  3
                 (645120a  - 1075200a  + 57344a )b
               + 
                           7          5         3  2             6         4
                 (- 107520a  + 499200a  - 57344a )b  + (- 138240a  + 28672a )b
               + 
                       7        5
                 23040a  - 7168a
            *
               c
           + 
                    12           11            2          10
             - 5376b   + 32256a b   + (- 80640a  + 26880)b
           + 
                     3            9            4          2          8
             (107520a  - 134400a)b  + (- 80640a  + 282240a  - 30720)b
           + 
                    5          3            7
             (32256a  - 322560a  + 122880a)b
           + 
                     6          4          2         6
             (- 5376a  + 215040a  - 207360a  + 4096)b
           + 
                      5          3           5
             (- 80640a  + 192000a  - 12288a)b
           + 
                    6          4         2  4          5         3  3
             (13440a  - 105600a  + 16384a )b  + (34560a  - 12288a )b
           + 
                     6        4  2        5        6
             (- 5760a  + 5632a )b  - 1536a b + 256a
        /
              9 3      8 2 2      7 4     6 6
           64a c  - 48a b c  + 12a b c - a b
      *
          3
         ?
     + 
                        3 7           4 6            5           3  5
                 294912a b  - 2064384a b  + (6193152a  - 1032192a )b
               + 
                             6           4  4
                 (- 10321920a  + 5160960a )b
               + 
                           7            5          3  3
                 (10321920a  - 10321920a  + 737280a )b
               + 
                            8            6           4  2
                 (- 6193152a  + 10321920a  - 2211840a )b
               + 
                          9           7           5         3            10
                 (2064384a  - 5160960a  + 2211840a  - 98304a )b - 294912a
               + 
                         8          6         4
                 1032192a  - 737280a  + 98304a
            *
                3
               c
           + 
                          2 9           3 8              4           2  7
                 - 221184a b  + 1548288a b  + (- 4644864a  + 1032192a )b
               + 
                          5           3  6
                 (7741440a  - 5677056a )b
               + 
                            6            4           2  5
                 (- 7741440a  + 13160448a  - 1167360a )b
               + 
                          7            5           3  4
                 (4644864a  - 16773120a  + 4730880a )b
               + 
                            8            6           4          2  3
                 (- 1548288a  + 12902400a  - 7802880a  + 245760a )b
               + 
                         9           7           5          3  2
                 (221184a  - 6193152a  + 6696960a  - 589824a )b
               + 
                          8           6          4            9          7
                 (1806336a  - 3072000a  + 516096a )b - 258048a  + 614400a
               + 
                          5
                 - 172032a
            *
                2
               c
           + 
                         11          2 10            3            9
                 55296a b   - 387072a b   + (1161216a  - 322560a)b
               + 
                            4           2  8
                 (- 1935360a  + 1870848a )b
               + 
                          5           3            7
                 (1935360a  - 4644864a  + 491520a)b
               + 
                            6           4           2  6
                 (- 1161216a  + 6451200a  - 2273280a )b
               + 
                         7           5           3            5
                 (387072a  - 5483520a  + 4454400a  - 147456a)b
               + 
                          8           6           4          2  4
                 (- 55296a  + 2903040a  - 4823040a  + 491520a )b
               + 
                           7           5          3  3
                 (- 903168a  + 3148800a  - 688128a )b
               + 
                         8           6          4  2           7          5
                 (129024a  - 1274880a  + 516096a )b  + (322560a  - 215040a )b
               + 
                         8         6
                 - 46080a  + 43008a
            *
               c
           + 
                    13           12            2          11
             - 4608b   + 32256a b   + (- 96768a  + 32256)b
           + 
                     3            10             4          2          9
             (161280a  - 193536a)b   + (- 161280a  + 499968a  - 61440)b
           + 
                    5          3            8
             (96768a  - 725760a  + 307200a)b
           + 
                      6          4          2          7
             (- 32256a  + 645120a  - 660480a  + 24576)b
           + 
                   7          5          3           6
             (4608a  - 354816a  + 798720a  - 98304a)b
           + 
                     6          4          2  5
             (112896a  - 595200a  + 172032a )b
           + 
                      7          5          3  4            6          4  3
             (- 16128a  + 280320a  - 172032a )b  + (- 80640a  + 107520a )b
           + 
                    7         5  2         6         7
             (11520a  - 43008a )b  + 10752a b - 1536a
        /
              10 3      9 2 2      8 4     7 6
           64a  c  - 48a b c  + 12a b c - a b
      *
          2
         ?
     + 
                        3 8           4 7            5          3  6
                 147456a b  - 1179648a b  + (4128768a  - 688128a )b
               + 
                            6           4  5
                 (- 8257536a  + 4128768a )b
               + 
                           7            5          3  4
                 (10321920a  - 10321920a  + 737280a )b
               + 
                            8            6           4  3
                 (- 8257536a  + 13762560a  - 2949120a )b
               + 
                          9            7           5          3  2
                 (4128768a  - 10321920a  + 4423680a  - 196608a )b
               + 
                            10           8           6          4            11
                 (- 1179648a   + 4128768a  - 2949120a  + 393216a )b + 147456a
               + 
                          9          7          5
                 - 688128a  + 737280a  - 196608a
            *
                3
               c
           + 
                          2 10          3 9              4          2  8
                 - 110592a b   + 884736a b  + (- 3096576a  + 688128a )b
               + 
                          5           3  7
                 (6193152a  - 4472832a )b
               + 
                            6            4           2  6
                 (- 7741440a  + 12558336a  - 1167360a )b
               + 
                          7            5           3  5
                 (6193152a  - 19955712a  + 5898240a )b
               + 
                            8            6            4          2  4
                 (- 3096576a  + 19783680a  - 12533760a  + 491520a )b
               + 
                         9            7            5           3  3
                 (884736a  - 12730368a  + 14499840a  - 1671168a )b
               + 
                           10           8           6           4         2  2
                 (- 110592a   + 5332992a  - 9768960a  + 2211840a  - 65536a )b
               + 
                            9           7           5          3            10
                 (- 1376256a  + 3686400a  - 1376256a  + 131072a )b + 172032a
               + 
                          8          6         4
                 - 614400a  + 344064a  - 65536a
            *
                2
               c
           + 
                         12          2 11           3            10
                 27648a b   - 221184a b   + (774144a  - 215040a)b
               + 
                            4           2  9
                 (- 1548288a  + 1462272a )b
               + 
                          5           3            8
                 (1935360a  - 4343808a  + 491520a)b
               + 
                            6           4           2  7
                 (- 1548288a  + 7397376a  - 2764800a )b
               + 
                         7           5           3            6
                 (774144a  - 7956480a  + 6727680a  - 294912a)b
               + 
                           8           6           4           2  5
                 (- 221184a  + 5591040a  - 9277440a  + 1277952a )b
               + 
                        9           7           5           3  4
                 (27648a  - 2537472a  + 7971840a  - 2359296a )b
               + 
                         8           6           4         2  3
                 (688128a  - 4423680a  + 2408448a  + 65536a )b
               + 
                          9           7           5          3  2
                 (- 86016a  + 1597440a  - 1462272a  - 163840a )b
               + 
                         8          6          4           9         7         5
               (- 368640a  + 516096a  + 131072a )b + 46080a  - 86016a  - 32768a
            *
               c
           + 
                    14           13            2          12
             - 2304b   + 18432a b   + (- 64512a  + 21504)b
           + 
                     3            11             4          2          10
             (129024a  - 150528a)b   + (- 161280a  + 462336a  - 61440)b
           + 
                     5          3            9
             (129024a  - 817152a  + 368640a)b
           + 
                      6          4          2          8
             (- 64512a  + 913920a  - 967680a  + 49152)b
           + 
                    7          5           3            7
             (18432a  - 666624a  + 1459200a  - 245760a)b
           + 
                     8          6           4          2  6
             (- 2304a  + 311808a  - 1393920a  + 540672a )b
           + 
                      7          5          3  5
             (- 86016a  + 875520a  - 688128a )b
           + 
                    8          6          4         2  4
             (10752a  - 360960a  + 559104a  - 16384a )b
           + 
                    7          5         3  3
             (92160a  - 301056a  + 49152a )b
           + 
                      8          6         4  2            7         5
             (- 11520a  + 107520a  - 53248a )b  + (- 24576a  + 24576a )b
           + 
                  8        6
             3072a  - 4096a
        /
              11 3      10 2 2      9 4     8 6
           64a  c  - 48a  b c  + 12a b c - a b
      *
         ?
     + 
                     3 9          4 8            5          3  7
               32768a b  - 294912a b  + (1179648a  - 196608a )b
             + 
                          6           4  6
               (- 2752512a  + 1376256a )b
             + 
                        7           5          3  5
               (4128768a  - 4128768a  + 294912a )b
             + 
                          8           6           4  4
               (- 4128768a  + 6881280a  - 1474560a )b
             + 
                        9           7           5          3  3
               (2752512a  - 6881280a  + 2949120a  - 131072a )b
             + 
                          10           8           6          4  2
               (- 1179648a   + 4128768a  - 2949120a  + 393216a )b
             + 
                       11           9           7          5           12
               (294912a   - 1376256a  + 1474560a  - 393216a )b - 32768a
             + 
                      10          8          6
               196608a   - 294912a  + 131072a
          *
              3
             c
         + 
                       2 11          3 10             4          2  9
               - 24576a b   + 221184a b   + (- 884736a  + 196608a )b
             + 
                        5           3  8
               (2064384a  - 1474560a )b
             + 
                          6           4          2  7
               (- 3096576a  + 4866048a  - 466944a )b
             + 
                        7           5           3  6
               (3096576a  - 9289728a  + 2826240a )b
             + 
                          8            6           4          2  5
               (- 2064384a  + 11354112a  - 7372800a  + 327680a )b
             + 
                       9           7            5           3  4
               (884736a  - 9289728a  + 10813440a  - 1441792a )b
             + 
                         10           8           6           4          2  3
               (- 221184a   + 5160960a  - 9707520a  + 2588672a  - 131072a )b
             + 
                      11           9           7           5          3  2
               (24576a   - 1916928a  + 5382144a  - 2392064a  + 393216a )b
             + 
                       10           8           6          4           11
               (442368a   - 1720320a  + 1146880a  - 393216a )b - 49152a
             + 
                      9          7          5
               245760a  - 229376a  + 131072a
          *
              2
             c
         + 
                      13         2 12           3           11
               6144a b   - 55296a b   + (221184a  - 61440a)b
             + 
                         4          2  10           5           3            9
               (- 516096a  + 479232a )b   + (774144a  - 1658880a  + 196608a)b
             + 
                         6           4           2  8
               (- 774144a  + 3354624a  - 1302528a )b
             + 
                       7           5           3            7
               (516096a  - 4386816a  + 3796992a  - 196608a)b
             + 
                         8           6           4           2  6
               (- 221184a  + 3870720a  - 6402048a  + 1048576a )b
             + 
                      9           7           5           3  5
               (55296a  - 2322432a  + 6899712a  - 2424832a )b
             + 
                       10          8           6           4          2  4
               (- 6144a   + 921600a  - 4958208a  + 3178496a  + 131072a )b
             + 
                         9           7           5          3  3
               (- 221184a  + 2408448a  - 2580480a  - 458752a )b
             + 
                      10          8           6          4  2
               (24576a   - 786432a  + 1318912a  + 589824a )b
             + 
                       9          7          5           10         8         6
               (165888a  - 401408a  - 327680a )b - 18432a   + 57344a  + 65536a
          *
             c
         + 
                 15          14            2         13          3           12
           - 512b   + 4608a b   + (- 18432a  + 6144)b   + (43008a  - 49152a)b
         + 
                    4          2          11          5          3            10
           (- 64512a  + 175104a  - 24576)b   + (64512a  - 365568a  + 172032a)b
         + 
                    6          4          2          9
           (- 43008a  + 494592a  - 534528a  + 32768)b
         + 
                  7          5          3            8
           (18432a  - 451584a  + 970752a  - 196608a)b
         + 
                   8          6           4          2  7
           (- 4608a  + 279552a  - 1141248a  + 524288a )b
         + 
                9          7          5          3  6
           (512a  - 113664a  + 907776a  - 819200a )b
         + 
                  8          6          4         2  5
           (27648a  - 494592a  + 831488a  - 32768a )b
         + 
                   9          7          5          3  4
           (- 3072a  + 181248a  - 573440a  + 131072a )b
         + 
                    8          6          4  3         9         7          5  2
           (- 41472a  + 272384a  - 204800a )b  + (4608a  - 88064a  + 155648a )b
         + 
                  8         6          9        7
           (18432a  - 57344a )b - 2048a  + 8192a
      /
            12 3      11 2 2      10 4     9 6
         64a  c  - 48a  b c  + 12a  b c - a b
     , trying square-free.

   (85)
     - y(x) + x
  /
       (2y(x) + 2x)
    *
         %e
      **
             2
          *
             log
                                                 +-----------+
                       2 2                    2  |          2       2        2
                    (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                  + 
                              3
                    4a b c - b
               /
                     2
                  a x  + b x + c
        /
            +-----------+
            |          2
           \|- 4a c + b
                                          Type: Union(Expression Integer,...)
--R 
--R   WARNING (genufact): No known algorithm to factor
--R                     2            2
--R      4   - 4a c + 2b   2        b
--R     ?  + ------------ ?  - -----------, trying square-free.
--R             3     2 2        5     4 2
--R           4a c - a b       4a c - a b
--R   WARNING (genufact): No known algorithm to factor
--R                     2            2         2            2
--R      4   - 4a c + 2b  - 4a b + 4a   2   - b  + 4a b - 4a
--R     ?  + ------------------------- ?  + -----------------, trying square-free.
--R                   3     2 2                  5     4 2
--R                 4a c - a b                 4a c - a b
--R   WARNING (genufact): No known algorithm to factor
--R                           2              4      2
--R        9   9b  8   (144a b  - 24a)c - 36b  + 12b   7
--R       ?  - -- ?  + ------------------------------ ?
--R             a                  3     2 2
--R                              4a c - a b
--R     + 
--R                3                 5      3
--R       (- 336a b  + 168a b)c + 84b  - 84b   6
--R       ----------------------------------- ?
--R                     4     3 2
--R                   4a c - a b
--R     + 
--R                   2 4        2 2       2  2
--R             (2016a b  - 2016a b  + 144a )c
--R           + 
--R                       6          4         2         8       6      4
--R             (- 1008a b  + 1512a b  - 192a b )c + 126b  - 252b  + 48b
--R        /
--R              6 2     5 2     4 4
--R           16a c  - 8a b c + a b
--R      *
--R          5
--R         ?
--R     + 
--R                     2 5        2 3       2   2
--R             (- 2016a b  + 3360a b  - 720a b)c
--R           + 
--R                     7          5         3         9       7       5
--R             (1008a b  - 2520a b  + 960a b )c - 126b  + 420b  - 240b
--R        /
--R              7 2     6 2     5 4
--R           16a c  - 8a b c + a b
--R      *
--R          4
--R         ?
--R     + 
--R                   3 6         3 4        3 2       3  3
--R             (5376a b  - 13440a b  + 5760a b  - 256a )c
--R           + 
--R                     2 8         2 6        2 4       2 2  2
--R             (- 4032a b  + 13440a b  - 9120a b  + 640a b )c
--R           + 
--R                     10          8          6         4        12       10
--R             (1008a b   - 4200a b  + 3840a b  - 384a b )c - 84b   + 420b
--R           + 
--R                   8      6
--R             - 480b  + 64b
--R        /
--R              9 3      8 2 2      7 4     6 6
--R           64a c  - 48a b c  + 12a b c - a b
--R      *
--R          3
--R         ?
--R     + 
--R                     3 7        3 5        3 3       3   3
--R             (- 2304a b  + 8064a b  - 5760a b  + 768a b)c
--R           + 
--R                   2 9        2 7        2 5        2 3  2
--R             (1728a b  - 8064a b  + 9120a b  - 1920a b )c
--R           + 
--R                      11          9          7          5        13       11
--R             (- 432a b   + 2520a b  - 3840a b  + 1152a b )c + 36b   - 252b
--R           + 
--R                 9       7
--R             480b  - 192b
--R        /
--R              10 3      9 2 2      8 4     7 6
--R           64a  c  - 48a b c  + 12a b c - a b
--R      *
--R          2
--R         ?
--R     + 
--R                  3 8        3 6        3 4       3 2  3
--R             (576a b  - 2688a b  + 2880a b  - 768a b )c
--R           + 
--R                    2 10        2 8        2 6        2 4       2 2  2
--R             (- 432a b   + 2688a b  - 4560a b  + 1920a b  - 256a b )c
--R           + 
--R                    12         10          8          6       14      12
--R             (108a b   - 840a b   + 1920a b  - 1152a b )c - 9b   + 84b
--R           + 
--R                   10       8
--R             - 240b   + 192b
--R        /
--R              11 3      10 2 2      9 4     8 6
--R           64a  c  - 48a  b c  + 12a b c - a b
--R      *
--R         ?
--R     + 
--R                 3 9       3 7       3 5       3 3  3
--R           (- 64a b  + 384a b  - 576a b  + 256a b )c
--R         + 
--R               2 11       2 9       2 7       2 5       2 3  2
--R           (48a b   - 384a b  + 912a b  - 640a b  + 256a b )c
--R         + 
--R                   13         11         9         7      15      13      11
--R           (- 12a b   + 120a b   - 384a b  + 384a b )c + b   - 12b   + 48b
--R         + 
--R                9
--R           - 64b
--R      /
--R            12 3      11 2 2      10 4     9 6
--R         64a  c  - 48a  b c  + 12a  b c - a b
--R     , trying square-free.
--R   WARNING (genufact): No known algorithm to factor
--R        9   9b - 18a  8
--R       ?  + -------- ?
--R                a
--R     + 
--R                    2       2        3              4         3
--R             (144a b  - 576a b + 576a  - 24a)c - 36b  + 144a b
--R           + 
--R                    2       2              2
--R             (- 144a  + 12)b  - 24a b + 24a
--R        /
--R             3     2 2
--R           4a c - a b
--R      *
--R          7
--R         ?
--R     + 
--R                    3        2 2         3                 4       2        5
--R             (336a b  - 2016a b  + (4032a  - 168a)b - 2688a  + 336a )c - 84b
--R           + 
--R                   4           2       3        3         2       2        3
--R             504a b  + (- 1008a  + 84)b  + (672a  - 336a)b  + 504a b - 336a
--R        /
--R             4     3 2
--R           4a c - a b
--R      *
--R          6
--R         ?
--R     + 
--R                      2 4         3 3          4        2  2
--R                 2016a b  - 16128a b  + (48384a  - 2016a )b
--R               + 
--R                          5        3           6        4       2
--R                 (- 64512a  + 8064a )b + 32256a  - 8064a  + 144a
--R            *
--R                2
--R               c
--R           + 
--R                          6        2 5            3          4
--R                 - 1008a b  + 8064a b  + (- 24192a  + 1512a)b
--R               + 
--R                        4        2  3            5         3         2
--R                 (32256a  - 8064a )b  + (- 16128a  + 16128a  - 192a)b
--R               + 
--R                          4       2          5       3
--R                 (- 16128a  + 480a )b + 8064a  - 480a
--R            *
--R               c
--R           + 
--R                 8          7         2        6           3          5
--R             126b  - 1008a b  + (3024a  - 252)b  + (- 4032a  + 1512a)b
--R           + 
--R                   4        2       4         3         3           4       2  2
--R             (2016a  - 3528a  + 48)b  + (4032a  - 192a)b  + (- 2016a  + 336a )b
--R           + 
--R                   3        4
--R             - 288a b + 144a
--R        /
--R              6 2     5 2     4 4
--R           16a c  - 8a b c + a b
--R      *
--R          5
--R         ?
--R     + 
--R                      2 5         3 4          4        2  3
--R                 2016a b  - 20160a b  + (80640a  - 3360a )b
--R               + 
--R                           5         3  2           6         4       2
--R                 (- 161280a  + 20160a )b  + (161280a  - 40320a  + 720a )b
--R               + 
--R                         7         5        3
--R                 - 64512a  + 26880a  - 1440a
--R            *
--R                2
--R               c
--R           + 
--R                          7         2 6            3          5
--R                 - 1008a b  + 10080a b  + (- 40320a  + 2520a)b
--R               + 
--R                        4         2  4            5         3         3
--R                 (80640a  - 18480a )b  + (- 80640a  + 53760a  - 960a)b
--R               + 
--R                        6         4        2  2          5        3           6
--R                 (32256a  - 80640a  + 4320a )b  + (67200a  - 7200a )b - 26880a
--R               + 
--R                      4
--R                 4800a
--R            *
--R               c
--R           + 
--R                 9          8         2        7            3          6
--R             126b  - 1260a b  + (5040a  - 420)b  + (- 10080a  + 3360a)b
--R           + 
--R                    4         2        5           5         3          4
--R             (10080a  - 10920a  + 240)b  + (- 4032a  + 18480a  - 1440a)b
--R           + 
--R                      4        2  3         5        3  2        4         5
--R             (- 16800a  + 3600a )b  + (6720a  - 4800a )b  + 3600a b - 1440a
--R        /
--R              7 2     6 2     5 4
--R           16a c  - 8a b c + a b
--R      *
--R          4
--R         ?
--R     + 
--R                      3 6         4 5           5         3  4
--R                 5376a b  - 64512a b  + (322560a  - 13440a )b
--R               + 
--R                           6          4  3            7          5        3  2
--R                 (- 860160a  + 107520a )b  + (1290240a  - 322560a  + 5760a )b
--R               + 
--R                            8          6         4            9          7
--R                 (- 1032192a  + 430080a  - 23040a )b + 344064a  - 215040a
--R               + 
--R                       5       3
--R                 23040a  - 256a
--R            *
--R                3
--R               c
--R           + 
--R                        2 8         3 7             4         2  6
--R                 - 4032a b  + 48384a b  + (- 241920a  + 13440a )b
--R               + 
--R                         5          3  5             6          4        2  4
--R                 (645120a  - 120960a )b  + (- 967680a  + 443520a  - 9120a )b
--R               + 
--R                         7          5         3  3
--R                 (774144a  - 860160a  + 55680a )b
--R               + 
--R                           8          6          4       2  2
--R                 (- 258048a  + 967680a  - 132480a  + 640a )b
--R               + 
--R                         7          5        3            8         6        4
--R               (- 645120a  + 153600a  - 1792a )b + 215040a  - 76800a  + 1792a
--R            *
--R                2
--R               c
--R           + 
--R                        10         2 9          3          8
--R                 1008a b   - 12096a b  + (60480a  - 4200a)b
--R               + 
--R                           4         2  7           5          3          6
--R                 (- 161280a  + 40320a )b  + (241920a  - 161280a  + 3840a)b
--R               + 
--R                           6          4         2  5
--R                 (- 193536a  + 349440a  - 27840a )b
--R               + 
--R                        7          5         3         4
--R                 (64512a  - 443520a  + 83520a  - 384a)b
--R               + 
--R                         6          4        2  3
--R                 (322560a  - 134400a  + 1792a )b
--R               + 
--R                           7          5        3  2            6        4
--R                 (- 107520a  + 124800a  - 3584a )b  + (- 69120a  + 3584a )b
--R               + 
--R                       7        5
--R                 23040a  - 1792a
--R            *
--R               c
--R           + 
--R                  12          11           2        10          3          9
--R             - 84b   + 1008a b   + (- 5040a  + 420)b   + (13440a  - 4200a)b
--R           + 
--R                      4         2        8          5         3          7
--R             (- 20160a  + 17640a  - 480)b  + (16128a  - 40320a  + 3840a)b
--R           + 
--R                     6         4         2       6
--R             (- 5376a  + 53760a  - 12960a  + 64)b
--R           + 
--R                      5         3         5          6         4        2  4
--R             (- 40320a  + 24000a  - 384a)b  + (13440a  - 26400a  + 1024a )b
--R           + 
--R                    5        3  3           6        4  2       5        6
--R             (17280a  - 1536a )b  + (- 5760a  + 1408a )b  - 768a b + 256a
--R        /
--R              9 3      8 2 2      7 4     6 6
--R           64a c  - 48a b c  + 12a b c - a b
--R      *
--R          3
--R         ?
--R     + 
--R                      3 7         4 6           5        3  5
--R                 2304a b  - 32256a b  + (193536a  - 8064a )b
--R               + 
--R                           6         4  4            7          5        3  3
--R                 (- 645120a  + 80640a )b  + (1290240a  - 322560a  + 5760a )b
--R               + 
--R                            8          6         4  2
--R                 (- 1548288a  + 645120a  - 34560a )b
--R               + 
--R                          9          7         5       3            10
--R                 (1032192a  - 645120a  + 69120a  - 768a )b - 294912a
--R               + 
--R                        8         6        4
--R                 258048a  - 46080a  + 1536a
--R            *
--R                3
--R               c
--R           + 
--R                        2 9         3 8             4        2  7
--R                 - 1728a b  + 24192a b  + (- 145152a  + 8064a )b
--R               + 
--R                         5         3  6             6          4        2  5
--R                 (483840a  - 88704a )b  + (- 967680a  + 411264a  - 9120a )b
--R               + 
--R                          7           5         3  4
--R                 (1161216a  - 1048320a  + 73920a )b
--R               + 
--R                           8           6          4        2  3
--R                 (- 774144a  + 1612800a  - 243840a  + 1920a )b
--R               + 
--R                         9           7          5        3  2
--R                 (221184a  - 1548288a  + 418560a  - 9216a )b
--R               + 
--R                       8          6         4            9          7         5
--R               (903168a  - 384000a  + 16128a )b - 258048a  + 153600a  - 10752a
--R            *
--R                2
--R               c
--R           + 
--R                       11        2 10          3          9
--R                 432a b   - 6048a b   + (36288a  - 2520a)b
--R               + 
--R                           4         2  8           5          3          7
--R                 (- 120960a  + 29232a )b  + (241920a  - 145152a  + 3840a)b
--R               + 
--R                           6          4         2  6
--R                 (- 290304a  + 403200a  - 35520a )b
--R               + 
--R                         7          5          3          5
--R                 (193536a  - 685440a  + 139200a  - 1152a)b
--R               + 
--R                          8          6          4        2  4
--R                 (- 55296a  + 725760a  - 301440a  + 7680a )b
--R               + 
--R                           7          5         3  3
--R                 (- 451584a  + 393600a  - 21504a )b
--R               + 
--R                         8          6         4  2           7         5
--R                 (129024a  - 318720a  + 32256a )b  + (161280a  - 26880a )b
--R               + 
--R                         8         6
--R                 - 46080a  + 10752a
--R            *
--R               c
--R           + 
--R                  13         12           2        11          3          10
--R             - 36b   + 504a b   + (- 3024a  + 252)b   + (10080a  - 3024a)b
--R           + 
--R                      4         2        9          5         3          8
--R             (- 20160a  + 15624a  - 480)b  + (24192a  - 45360a  + 4800a)b
--R           + 
--R                      6         4         2        7
--R             (- 16128a  + 80640a  - 20640a  + 192)b
--R           + 
--R                   7         5         3          6
--R             (4608a  - 88704a  + 49920a  - 1536a)b
--R           + 
--R                    6         4        2  5            7         5         3  4
--R             (56448a  - 74400a  + 5376a )b  + (- 16128a  + 70080a  - 10752a )b
--R           + 
--R                      6         4  3          7         5  2        6         7
--R             (- 40320a  + 13440a )b  + (11520a  - 10752a )b  + 5376a b - 1536a
--R        /
--R              10 3      9 2 2      8 4     7 6
--R           64a  c  - 48a b c  + 12a b c - a b
--R      *
--R          2
--R         ?
--R     + 
--R                     3 8        4 7          5        3  6
--R                 576a b  - 9216a b  + (64512a  - 2688a )b
--R               + 
--R                           6         4  5           7          5        3  4
--R                 (- 258048a  + 32256a )b  + (645120a  - 161280a  + 2880a )b
--R               + 
--R                            8          6         4  3
--R                 (- 1032192a  + 430080a  - 23040a )b
--R               + 
--R                          9          7         5       3  2
--R                 (1032192a  - 645120a  + 69120a  - 768a )b
--R               + 
--R                           10          8         6        4            11
--R                 (- 589824a   + 516096a  - 92160a  + 3072a )b + 147456a
--R               + 
--R                          9         7        5
--R                 - 172032a  + 46080a  - 3072a
--R            *
--R                3
--R               c
--R           + 
--R                       2 10        3 9            4        2  8
--R                 - 432a b   + 6912a b  + (- 48384a  + 2688a )b
--R               + 
--R                         5         3  7             6          4        2  6
--R                 (193536a  - 34944a )b  + (- 483840a  + 196224a  - 4560a )b
--R               + 
--R                         7          5         3  5
--R                 (774144a  - 623616a  + 46080a )b
--R               + 
--R                           8           6          4        2  4
--R                 (- 774144a  + 1236480a  - 195840a  + 1920a )b
--R               + 
--R                         9           7          5         3  3
--R                 (442368a  - 1591296a  + 453120a  - 13056a )b
--R               + 
--R                           10           8          6         4       2  2
--R                 (- 110592a   + 1333248a  - 610560a  + 34560a  - 256a )b
--R               + 
--R                           9          7         5        3            10
--R                 (- 688128a  + 460800a  - 43008a  + 1024a )b + 172032a
--R               + 
--R                          8         6        4
--R                 - 153600a  + 21504a  - 1024a
--R            *
--R                2
--R               c
--R           + 
--R                       12        2 11          3         10
--R                 108a b   - 1728a b   + (12096a  - 840a)b
--R               + 
--R                          4         2  9           5         3          8
--R                 (- 48384a  + 11424a )b  + (120960a  - 67872a  + 1920a)b
--R               + 
--R                           6          4         2  7
--R                 (- 193536a  + 231168a  - 21600a )b
--R               + 
--R                         7          5          3          6
--R                 (193536a  - 497280a  + 105120a  - 1152a)b
--R               + 
--R                           8          6          4        2  5
--R                 (- 110592a  + 698880a  - 289920a  + 9984a )b
--R               + 
--R                        9          7          5         3  4
--R                 (27648a  - 634368a  + 498240a  - 36864a )b
--R               + 
--R                         8          6         4       2  3
--R                 (344064a  - 552960a  + 75264a  + 512a )b
--R               + 
--R                          9          7         5        3  2
--R                 (- 86016a  + 399360a  - 91392a  - 2560a )b
--R               + 
--R                           8         6        4           9         7        5
--R                 (- 184320a  + 64512a  + 4096a )b + 46080a  - 21504a  - 2048a
--R            *
--R               c
--R           + 
--R                 14         13           2       12         3          11
--R             - 9b   + 144a b   + (- 1008a  + 84)b   + (4032a  - 1176a)b
--R           + 
--R                      4        2        10          5         3          9
--R             (- 10080a  + 7224a  - 240)b   + (16128a  - 25536a  + 2880a)b
--R           + 
--R                      6         4         2        8
--R             (- 16128a  + 57120a  - 15120a  + 192)b
--R           + 
--R                   7         5         3          7
--R             (9216a  - 83328a  + 45600a  - 1920a)b
--R           + 
--R                     8         6         4        2  6
--R             (- 2304a  + 77952a  - 87120a  + 8448a )b
--R           + 
--R                      7          5         3  5
--R             (- 43008a  + 109440a  - 21504a )b
--R           + 
--R                    8         6         4       2  4
--R             (10752a  - 90240a  + 34944a  - 256a )b
--R           + 
--R                    7         5        3  3            8         6        4  2
--R             (46080a  - 37632a  + 1536a )b  + (- 11520a  + 26880a  - 3328a )b
--R           + 
--R                      7        5          8        6
--R             (- 12288a  + 3072a )b + 3072a  - 1024a
--R        /
--R              11 3      10 2 2      9 4     8 6
--R           64a  c  - 48a  b c  + 12a b c - a b
--R      *
--R         ?
--R     + 
--R                  3 9        4 8         5       3  7            6        4  6
--R               64a b  - 1152a b  + (9216a  - 384a )b  + (- 43008a  + 5376a )b
--R             + 
--R                       7         5       3  5
--R               (129024a  - 32256a  + 576a )b
--R             + 
--R                         8          6        4  4
--R               (- 258048a  + 107520a  - 5760a )b
--R             + 
--R                       9          7         5       3  3
--R               (344064a  - 215040a  + 23040a  - 256a )b
--R             + 
--R                         10          8         6        4  2
--R               (- 294912a   + 258048a  - 46080a  + 1536a )b
--R             + 
--R                       11          9         7        5           12         10
--R               (147456a   - 172032a  + 46080a  - 3072a )b - 32768a   + 49152a
--R             + 
--R                       8        6
--R               - 18432a  + 2048a
--R          *
--R              3
--R             c
--R         + 
--R                    2 11       3 10           4       2  9
--R               - 48a b   + 864a b   + (- 6912a  + 384a )b
--R             + 
--R                      5        3  8            6         4       2  7
--R               (32256a  - 5760a )b  + (- 96768a  + 38016a  - 912a )b
--R             + 
--R                       7          5         3  6
--R               (193536a  - 145152a  + 11040a )b
--R             + 
--R                         8          6         4       2  5
--R               (- 258048a  + 354816a  - 57600a  + 640a )b
--R             + 
--R                       9          7          5        3  4
--R               (221184a  - 580608a  + 168960a  - 5632a )b
--R             + 
--R                         10          8          6         4       2  3
--R               (- 110592a   + 645120a  - 303360a  + 20224a  - 256a )b
--R             + 
--R                      11          9          7         5        3  2
--R               (24576a   - 479232a  + 336384a  - 37376a  + 1536a )b
--R             + 
--R                       10          8         6        4           11         9
--R               (221184a   - 215040a  + 35840a  - 3072a )b - 49152a   + 61440a
--R             + 
--R                       7        5
--R               - 14336a  + 2048a
--R          *
--R              2
--R             c
--R         + 
--R                    13       2 12         3         11           4        2  10
--R               12a b   - 216a b   + (1728a  - 120a)b   + (- 8064a  + 1872a )b
--R             + 
--R                      5         3         9            6         4        2  8
--R               (24192a  - 12960a  + 384a)b  + (- 48384a  + 52416a  - 5088a )b
--R             + 
--R                      7          5         3         7
--R               (64512a  - 137088a  + 29664a  - 384a)b
--R             + 
--R                        8          6          4        2  6
--R               (- 55296a  + 241920a  - 100032a  + 4096a )b
--R             + 
--R                      9          7          5         3  5
--R               (27648a  - 290304a  + 215616a  - 18944a )b
--R             + 
--R                       10          8          6         4       2  4
--R               (- 6144a   + 230400a  - 309888a  + 49664a  + 512a )b
--R             + 
--R                         9          7         5        3  3
--R               (- 110592a  + 301056a  - 80640a  - 3584a )b
--R             + 
--R                      10          8         6        4  2
--R               (24576a   - 196608a  + 82432a  + 9216a )b
--R             + 
--R                      9         7         5           10         8        6
--R               (82944a  - 50176a  - 10240a )b - 18432a   + 14336a  + 4096a
--R          *
--R             c
--R         + 
--R              15        14          2       13        3         12
--R           - b   + 18a b   + (- 144a  + 12)b   + (672a  - 192a)b
--R         + 
--R                   4        2       11         5        3         10
--R           (- 2016a  + 1368a  - 48)b   + (4032a  - 5712a  + 672a)b
--R         + 
--R                   6         4        2       9
--R           (- 5376a  + 15456a  - 4176a  + 64)b
--R         + 
--R                 7         5         3         8
--R           (4608a  - 28224a  + 15168a  - 768a)b
--R         + 
--R                   8         6         4        2  7
--R           (- 2304a  + 34944a  - 35664a  + 4096a )b
--R         + 
--R                9         7         5         3  6
--R           (512a  - 28416a  + 56736a  - 12800a )b
--R         + 
--R                  8         6         4       2  5
--R           (13824a  - 61824a  + 25984a  - 256a )b
--R         + 
--R                   9         7         5        3  4
--R           (- 3072a  + 45312a  - 35840a  + 2048a )b
--R         + 
--R                    8         6        4  3         9         7        5  2
--R           (- 20736a  + 34048a  - 6400a )b  + (4608a  - 22016a  + 9728a )b
--R         + 
--R                 8        6          9        7
--R           (9216a  - 7168a )b - 2048a  + 2048a
--R      /
--R            12 3      11 2 2      10 4     9 6
--R         64a  c  - 48a  b c  + 12a  b c - a b
--R     , trying square-free.
--R
--R   (85)
--R     - y(x) + x
--R  /
--R       (2y(x) + 2x)
--R    *
--R         %e
--R      **
--R             2
--R          *
--R             log
--R                                                 +-----------+
--R                       2 2                    2  |          2       2        2
--R                    (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                  + 
--R                              3
--R                    4a b c - b
--R               /
--R                     2
--R                  a x  + b x + c
--R        /
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 139
ode180expr := (a*x**2+b*x+c)*(x*D(yx,x)-yx) - yx**2 + x**2
 

   (86)
            2    2     3         4
         (4x y(x)  + 8x y(x) + 4x )
      *
             %e
          **
                 2
              *
                 log
                                                     +-----------+
                           2 2                    2  |          2
                        (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                      + 
                           2        2               3
                        (8a c - 2a b )x + 4a b c - b
                   /
                         2
                      a x  + b x + c
            /
                +-----------+
                |          2
               \|- 4a c + b
        **
           2
     + 
                  4       3       2  ,           2                      2
           (- 4a x  - 4b x  - 4c x )y (x) + (2a x  + (2b + 4)x + 2c)y(x)

         + 
                3       2                   4              3       2
           (4a x  + 4b x  + 4c x)y(x) - 2a x  + (- 2b - 4)x  - 2c x
      *
           %e
        **
               2
            *
               log
                                                   +-----------+
                         2 2                    2  |          2
                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                    + 
                         2        2               3
                      (8a c - 2a b )x + 4a b c - b
                 /
                       2
                    a x  + b x + c
          /
              +-----------+
              |          2
             \|- 4a c + b
     + 
             2              2
       - y(x)  + 2x y(x) - x
  /
             2               2
       (4y(x)  + 8x y(x) + 4x )
    *
           %e
        **
               2
            *
               log
                                                   +-----------+
                         2 2                    2  |          2
                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                    + 
                         2        2               3
                      (8a c - 2a b )x + 4a b c - b
                 /
                       2
                    a x  + b x + c
          /
              +-----------+
              |          2
             \|- 4a c + b
      **
         2
                                                     Type: Expression Integer
--R 
--R
--R   (86)
--R            2    2     3         4
--R         (4x y(x)  + 8x y(x) + 4x )
--R      *
--R             %e
--R          **
--R                 2
--R              *
--R                 log
--R                                                     +-----------+
--R                           2 2                    2  |          2
--R                        (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                      + 
--R                           2        2               3
--R                        (8a c - 2a b )x + 4a b c - b
--R                   /
--R                         2
--R                      a x  + b x + c
--R            /
--R                +-----------+
--R                |          2
--R               \|- 4a c + b
--R        **
--R           2
--R     + 
--R                  4       3       2  ,           2                      2
--R           (- 4a x  - 4b x  - 4c x )y (x) + (2a x  + (2b + 4)x + 2c)y(x)
--R
--R         + 
--R                3       2                   4              3       2
--R           (4a x  + 4b x  + 4c x)y(x) - 2a x  + (- 2b - 4)x  - 2c x
--R      *
--R           %e
--R        **
--R               2
--R            *
--R               log
--R                                                   +-----------+
--R                         2 2                    2  |          2
--R                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                    + 
--R                         2        2               3
--R                      (8a c - 2a b )x + 4a b c - b
--R                 /
--R                       2
--R                    a x  + b x + c
--R          /
--R              +-----------+
--R              |          2
--R             \|- 4a c + b
--R     + 
--R             2              2
--R       - y(x)  + 2x y(x) - x
--R  /
--R             2               2
--R       (4y(x)  + 8x y(x) + 4x )
--R    *
--R           %e
--R        **
--R               2
--R            *
--R               log
--R                                                   +-----------+
--R                         2 2                    2  |          2
--R                      (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                    + 
--R                         2        2               3
--R                      (8a c - 2a b )x + 4a b c - b
--R                 /
--R                       2
--R                    a x  + b x + c
--R          /
--R              +-----------+
--R              |          2
--R             \|- 4a c + b
--R      **
--R         2
--R                                                     Type: Expression Integer
--E 86

--S 87 of 139
ode181 := x**4*(D(y(x),x)+y(x)**2) + a
 

          4 ,       4    2
   (87)  x y (x) + x y(x)  + a

                                                     Type: Expression Integer
--R 
--R
--R          4 ,       4    2
--R   (87)  x y (x) + x y(x)  + a
--R
--R                                                     Type: Expression Integer
--E 87

--S 88 of 139
yx:=solve(ode181,y,x)
 
                                                     2
   WARNING (genufact): No known algorithm to factor ?  + a, trying square-free.

                   +---+    2
                  \|- a  - x y(x) + x
   (88)  ------------------------------------
                                        +---+
                                      2\|- a
                                      -------
             2           +---+           x
         ((2x y(x) - 2x)\|- a  - 2a)%e
                                          Type: Union(Expression Integer,...)
--R 
--R                                                     2
--R   WARNING (genufact): No known algorithm to factor ?  + a, trying square-free.
--R
--R                   +---+    2
--R                  \|- a  - x y(x) + x
--R   (88)  ------------------------------------
--R                                        +---+
--R                                      2\|- a
--R                                      -------
--R             2           +---+           x
--R         ((2x y(x) - 2x)\|- a  - 2a)%e
--R                                          Type: Union(Expression Integer,...)
--E 88

--S 89 of 139
ode181expr := x**4*(D(yx,x)+yx**2) + a
 

   (89)
                  +---+
                2\|- a
                -------
             6     x    ,
       - 4a x %e       y (x)

     + 
             2 2         2   +---+     2 4    2     2 3         2 2     3
         ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
      *
              +---+ 2
            2\|- a
            -------
               x
         (%e       )
     + 
                                 +---+
                               2\|- a
                               -------
              6    2     2 2      x         6         5  +---+    8    2
       (- 4a x y(x)  - 4a x )%e        + (2x y(x) - 2x )\|- a  - x y(x)
     + 
         7        6      4
       2x y(x) - x  + a x
  /
             2             +---+       4    2       3           2     2
       ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
    *
            +---+ 2
          2\|- a
          -------
             x
       (%e       )
                                                     Type: Expression Integer
--R 
--R
--R   (89)
--R                  +---+
--R                2\|- a
--R                -------
--R             6     x    ,
--R       - 4a x %e       y (x)
--R
--R     + 
--R             2 2         2   +---+     2 4    2     2 3         2 2     3
--R         ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
--R      *
--R              +---+ 2
--R            2\|- a
--R            -------
--R               x
--R         (%e       )
--R     + 
--R                                 +---+
--R                               2\|- a
--R                               -------
--R              6    2     2 2      x         6         5  +---+    8    2
--R       (- 4a x y(x)  - 4a x )%e        + (2x y(x) - 2x )\|- a  - x y(x)
--R     + 
--R         7        6      4
--R       2x y(x) - x  + a x
--R  /
--R             2             +---+       4    2       3           2     2
--R       ((8a x y(x) - 8a x)\|- a  + 4a x y(x)  - 8a x y(x) + 4a x  - 4a )
--R    *
--R            +---+ 2
--R          2\|- a
--R          -------
--R             x
--R       (%e       )
--R                                                     Type: Expression Integer
--E 89

--S 90 of 139
ode182 := x*(x**3-1)*D(y(x),x) - 2*x*y(x)**2 + y(x) + x**2
 

           4      ,             2           2
   (90)  (x  - x)y (x) - 2x y(x)  + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R           4      ,             2           2
--R   (90)  (x  - x)y (x) - 2x y(x)  + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 90

--S 91 of 139
ode183 := (2*x**4-x)*D(y(x),x) - 2*(x**3-1)*y(x)
 

            4      ,           3
   (91)  (2x  - x)y (x) + (- 2x  + 2)y(x)

                                                     Type: Expression Integer
--R 
--R
--R            4      ,           3
--R   (91)  (2x  - x)y (x) + (- 2x  + 2)y(x)
--R
--R                                                     Type: Expression Integer
--E 91

--S 92 of 139
ode183a:=solve(ode183,y,x)
 

                                     2
                                    x
   (92)  [particular= 0,basis= [----------]]
                                 +-------+
                                3|  3
                                \|2x  - 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                     2
--R                                    x
--R   (92)  [particular= 0,basis= [----------]]
--R                                 +-------+
--R                                3|  3
--R                                \|2x  - 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 92

--S 93 of 139
yx:=ode183a.particular
 

   (93)  0
                                                     Type: Expression Integer
--R 
--R
--R   (93)  0
--R                                                     Type: Expression Integer
--E 93

--S 94 of 139
ode183expr := (2*x**4-x)*D(yx,x) - 2*(x**3-1)*yx
 

   (94)  0
                                                     Type: Expression Integer
--R 
--R
--R   (94)  0
--R                                                     Type: Expression Integer
--E 94

--S 95 of 139
ode184 := (a*x**2+b*x+c)**2*(D(y(x),x)+y(x)**2) + A
 

   (95)
       2 4         3            2  2             2  ,
     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y (x)

   + 
       2 4         3            2  2             2     2
     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y(x)  + A
                                                     Type: Expression Integer
--R 
--R
--R   (95)
--R       2 4         3            2  2             2  ,
--R     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y (x)
--R
--R   + 
--R       2 4         3            2  2             2     2
--R     (a x  + 2a b x  + (2a c + b )x  + 2b c x + c )y(x)  + A
--R                                                     Type: Expression Integer
--E 95


--S 96 of 139
ode185 := x**7*D(y(x),x) + 2*(x**2+1)*y(x)**3 + 5*x**3*y(x)**2
 

          7 ,         2         3     3    2
   (96)  x y (x) + (2x  + 2)y(x)  + 5x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          7 ,         2         3     3    2
--R   (96)  x y (x) + (2x  + 2)y(x)  + 5x y(x)
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 139
ode185a:=solve(ode185,y,x)
 

   (97)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (97)  "failed"
--R                                                    Type: Union("failed",...)
--E 97

--S 98 of 139
ode186 := x**n*D(y(x),x) + y(x)**2 -(n-1)*x**(n-1)*y(x) + x**(2*n-2)
 

          n ,       2n - 2                 n - 1       2
   (98)  x y (x) + x       + (- n + 1)y(x)x      + y(x)

                                                     Type: Expression Integer
--R 
--R
--R          n ,       2n - 2                 n - 1       2
--R   (98)  x y (x) + x       + (- n + 1)y(x)x      + y(x)
--R
--R                                                     Type: Expression Integer
--E 98

--S 99 of 139
ode186a:=solve(ode186,y,x)
 

   (99)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (99)  "failed"
--R                                                    Type: Union("failed",...)
--E 99

--S 100 of 139
ode187 := x**n*D(y(x),x) - a*y(x)**2 - b*x**(2*n-2)
 

           n ,         2n - 2         2
   (100)  x y (x) - b x       - a y(x)

                                                     Type: Expression Integer
--R 
--R
--R           n ,         2n - 2         2
--R   (100)  x y (x) - b x       - a y(x)
--R
--R                                                     Type: Expression Integer
--E 100

--S 101 of 139
ode187a:=solve(ode187,y,x)
 

   (101)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (101)  "failed"
--R                                                    Type: Union("failed",...)
--E 101

--S 102 of 139
ode188 := x**(2*n+1)*D(y(x),x) - a*y(x)**3 - b*x**3*n
 

           2n + 1 ,            3        3
   (102)  x      y (x) - a y(x)  - b n x

                                                     Type: Expression Integer
--R 
--R
--R           2n + 1 ,            3        3
--R   (102)  x      y (x) - a y(x)  - b n x
--R
--R                                                     Type: Expression Integer
--E 102

--S 103 of 139
ode188a:=solve(ode188,y,x)
 

   (103)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (103)  "failed"
--R                                                    Type: Union("failed",...)
--E 103

--S 104 of 139
ode189 := x**(m*(n-1)+n)*D(y(x),x) - a*y(x)**n - b*x**(n*(m+1))
 

           (m + 1)n - m ,            n      (m + 1)n
   (104)  x            y (x) - a y(x)  - b x

                                                     Type: Expression Integer
--R 
--R
--R           (m + 1)n - m ,            n      (m + 1)n
--R   (104)  x            y (x) - a y(x)  - b x
--R
--R                                                     Type: Expression Integer
--E 104

--S 105 of 139
ode189a:=solve(ode189,y,x)
 

   (105)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (105)  "failed"
--R                                                    Type: Union("failed",...)
--E 105

--S 106 of 139
ode190 := sqrt(x**2-1)*D(y(x),x) - sqrt(y(x)**2-1)
 

           +------+         +---------+
           | 2      ,       |    2
   (106)  \|x  - 1 y (x) - \|y(x)  - 1

                                                     Type: Expression Integer
--R 
--R
--R           +------+         +---------+
--R           | 2      ,       |    2
--R   (106)  \|x  - 1 y (x) - \|y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 106

--S 107 of 139
ode190a:=solve(ode190,y,x)
 

   (107)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (107)  "failed"
--R                                                    Type: Union("failed",...)
--E 107

--S 108 of 139
ode191 := sqrt(1-x**2)*D(y(x),x) - y(x)*sqrt(y(x)**2-1)
 

           +--------+             +---------+
           |   2      ,           |    2
   (108)  \|- x  + 1 y (x) - y(x)\|y(x)  - 1

                                                     Type: Expression Integer
--R 
--R
--R           +--------+             +---------+
--R           |   2      ,           |    2
--R   (108)  \|- x  + 1 y (x) - y(x)\|y(x)  - 1
--R
--R                                                     Type: Expression Integer
--E 108

--S 109 of 139
ode191a:=solve(ode191,y,x)
 

   (109)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (109)  "failed"
--R                                                    Type: Union("failed",...)
--E 109

--S 110 of 139
ode192 := sqrt(x**2+a**2)*D(y(x),x) + y(x) - sqrt(x**2+a**2) + x
 

           +-------+         +-------+
           | 2    2  ,       | 2    2
   (110)  \|x  + a  y (x) - \|x  + a   + y(x) + x

                                                     Type: Expression Integer
--R 
--R
--R           +-------+         +-------+
--R           | 2    2  ,       | 2    2
--R   (110)  \|x  + a  y (x) - \|x  + a   + y(x) + x
--R
--R                                                     Type: Expression Integer
--E 110

--S 111 of 139
ode192a:=solve(ode192,y,x)
 

   (111)
                    +-------+          +-------+               +-------+
                    | 2    2           | 2    2                | 2    2
   [particular= (- \|x  + a   + x)log(\|x  + a   - x),basis= [\|x  + a   - x]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (111)
--R                    +-------+          +-------+               +-------+
--R                    | 2    2           | 2    2                | 2    2
--R   [particular= (- \|x  + a   + x)log(\|x  + a   - x),basis= [\|x  + a   - x]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 111

--S 112 of 139
yx:=ode192a.particular
 

              +-------+          +-------+
              | 2    2           | 2    2
   (112)  (- \|x  + a   + x)log(\|x  + a   - x)
                                                     Type: Expression Integer
--R 
--R
--R              +-------+          +-------+
--R              | 2    2           | 2    2
--R   (112)  (- \|x  + a   + x)log(\|x  + a   - x)
--R                                                     Type: Expression Integer
--E 112

--S 113 of 139
ode192expr := sqrt(x**2+a**2)*D(yx,x) + yx - sqrt(x**2+a**2) + x
 

   (113)  0
                                                     Type: Expression Integer
--R 
--R
--R   (113)  0
--R                                                     Type: Expression Integer
--E 113

--S 114 of 139
ode193 := x*D(y(x),x)*log(x) + y(x) - a*x*(log(x)+1)
 

                   ,
   (114)  x log(x)y (x) - a x log(x) + y(x) - a x

                                                     Type: Expression Integer
--R 
--R
--R                   ,
--R   (114)  x log(x)y (x) - a x log(x) + y(x) - a x
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 139
ode193a:=solve(ode193,y,x)
 

                                      1
   (115)  [particular= a x,basis= [------]]
                                   log(x)
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                      1
--R   (115)  [particular= a x,basis= [------]]
--R                                   log(x)
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 115

--S 116 of 139
yx:=ode193a.particular
 

   (116)  a x
                                                     Type: Expression Integer
--R
--R   (116)  a x
--R                                                     Type: Expression Integer
--E 116

--S 117 of 139
ode193expr := x*D(yx,x)*log(x) + yx - a*x*(log(x)+1)
 

   (117)  0
                                                     Type: Expression Integer
--R
--R   (117)  0
--R                                                     Type: Expression Integer
--E 117

--S 118 of 139
ode194 := x*D(y(x),x)*log(x) - y(x)**2*log(x) - _
            (2*log(x)**2+1)*y(x) - log(x)**3
 

                   ,            3              2       2
   (118)  x log(x)y (x) - log(x)  - 2y(x)log(x)  - y(x) log(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                   ,            3              2       2
--R   (118)  x log(x)y (x) - log(x)  - 2y(x)log(x)  - y(x) log(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 118

--S 119 of 139
ode194a:=solve(ode194,y,x)
 

   (119)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (119)  "failed"
--R                                                    Type: Union("failed",...)
--E 119

--S 120 of 139
ode195 := sin(x)*D(y(x),x) - y(x)**2*sin(x)**2 + (cos(x) - 3*sin(x))*y(x) + 4
 

                 ,          2      2
   (120)  sin(x)y (x) - y(x) sin(x)  - 3y(x)sin(x) + y(x)cos(x) + 4

                                                     Type: Expression Integer
--R 
--R
--R                 ,          2      2
--R   (120)  sin(x)y (x) - y(x) sin(x)  - 3y(x)sin(x) + y(x)cos(x) + 4
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 139
yx:=solve(ode195,y,x)
 

              - y(x)sin(x) + 1
   (121)  ------------------------
                 5x             5x
          5y(x)%e  sin(x) + 20%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - y(x)sin(x) + 1
--R   (121)  ------------------------
--R                 5x             5x
--R          5y(x)%e  sin(x) + 20%e
--R                                          Type: Union(Expression Integer,...)
--E 121

--S 122 of 139
ode195expr:=sin(x)*D(yx,x) - yx**2*sin(x)**2 + (cos(x) - 3*sin(x))*yx + 4
 

   (122)
             5x      2 ,          2      4          2  5x               3
       - 25%e  sin(x) y (x) - y(x) sin(x)  + (40y(x) %e   + 2y(x))sin(x)

     + 
               2   5x 2           2                   5x           2
       (100y(x) (%e  )  + (- 5y(x) cos(x) + 120y(x))%e   - 1)sin(x)
     + 
                  5x 2                           5x                 5x 2
       (800y(x)(%e  )  + (- 40y(x)cos(x) - 160)%e  )sin(x) + 1600(%e  )
     + 
                 5x
       20cos(x)%e
  /
           2   5x 2      2             5x 2               5x 2
     25y(x) (%e  ) sin(x)  + 200y(x)(%e  ) sin(x) + 400(%e  )
                                                     Type: Expression Integer
--R 
--R
--R   (122)
--R             5x      2 ,          2      4          2  5x               3
--R       - 25%e  sin(x) y (x) - y(x) sin(x)  + (40y(x) %e   + 2y(x))sin(x)
--R
--R     + 
--R               2   5x 2           2                   5x           2
--R       (100y(x) (%e  )  + (- 5y(x) cos(x) + 120y(x))%e   - 1)sin(x)
--R     + 
--R                  5x 2                           5x                 5x 2
--R       (800y(x)(%e  )  + (- 40y(x)cos(x) - 160)%e  )sin(x) + 1600(%e  )
--R     + 
--R                 5x
--R       20cos(x)%e
--R  /
--R           2   5x 2      2             5x 2               5x 2
--R     25y(x) (%e  ) sin(x)  + 200y(x)(%e  ) sin(x) + 400(%e  )
--R                                                     Type: Expression Integer
--E 122

--S 123 of 139
ode196 := cos(x)*D(y(x),x) + y(x) + (1 + sin(x))*cos(x)
 

                 ,
   (123)  cos(x)y (x) + cos(x)sin(x) + cos(x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 ,
--R   (123)  cos(x)y (x) + cos(x)sin(x) + cos(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 123

--S 124 of 139
ode196a:=solve(ode196,y,x)
 

   (124)
   [
     particular =
                                        sin(x) - cos(x) - 1
           (- 4sin(x) + 4cos(x) + 4)log(-------------------)
                                             cos(x) + 1
         + 
                                         2              2
         (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
                                    cos(x) + 1
      /
         sin(x) + cos(x) + 1
     ,
            sin(x) - cos(x) - 1
    basis= [-------------------]]
            sin(x) + cos(x) + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (124)
--R   [
--R     particular =
--R                                        sin(x) - cos(x) - 1
--R           (- 4sin(x) + 4cos(x) + 4)log(-------------------)
--R                                             cos(x) + 1
--R         + 
--R                                         2              2
--R         (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
--R                                    cos(x) + 1
--R      /
--R         sin(x) + cos(x) + 1
--R     ,
--R            sin(x) - cos(x) - 1
--R    basis= [-------------------]]
--R            sin(x) + cos(x) + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 124

--S 125 of 139
yx:=ode196a.particular
 

   (125)
                                    sin(x) - cos(x) - 1
       (- 4sin(x) + 4cos(x) + 4)log(-------------------)
                                         cos(x) + 1
     + 
                                       2              2
       (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
                                  cos(x) + 1
  /
     sin(x) + cos(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R   (125)
--R                                    sin(x) - cos(x) - 1
--R       (- 4sin(x) + 4cos(x) + 4)log(-------------------)
--R                                         cos(x) + 1
--R     + 
--R                                       2              2
--R       (2sin(x) - 2cos(x) - 2)log(----------) - sin(x)  + (cos(x) + 1)sin(x)
--R                                  cos(x) + 1
--R  /
--R     sin(x) + cos(x) + 1
--R                                                     Type: Expression Integer
--E 125

--S 126 of 139
ode196expr := cos(x)*D(yx,x) + yx + (1 + sin(x))*cos(x)
 

   (126)
                     2                      2          4           3          2
           (- 8cos(x)  - 12cos(x) - 4)sin(x)  - 8cos(x)  - 12cos(x)  + 4cos(x)
         + 
           12cos(x) + 4
      *
             sin(x) - cos(x) - 1
         log(-------------------)
                  cos(x) + 1
     + 
                   2                     2          4          3          2
           (4cos(x)  + 6cos(x) + 2)sin(x)  + 4cos(x)  + 6cos(x)  - 2cos(x)
         + 
           - 6cos(x) - 2
      *
                  2
         log(----------)
             cos(x) + 1
     + 
                2                     3          3                2
       (- cos(x)  - 4cos(x) - 1)sin(x)  + (cos(x)  - cos(x))sin(x)
     + 
                4          3                              5          3
       (- cos(x)  - 4cos(x)  + 4cos(x) + 1)sin(x) + cos(x)  - 2cos(x)  + cos(x)
  /
                         2           2                              3          2
       (cos(x) + 1)sin(x)  + (2cos(x)  + 4cos(x) + 2)sin(x) + cos(x)  + 3cos(x)
     + 
       3cos(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R   (126)
--R                     2                      2          4           3          2
--R           (- 8cos(x)  - 12cos(x) - 4)sin(x)  - 8cos(x)  - 12cos(x)  + 4cos(x)
--R         + 
--R           12cos(x) + 4
--R      *
--R             sin(x) - cos(x) - 1
--R         log(-------------------)
--R                  cos(x) + 1
--R     + 
--R                   2                     2          4          3          2
--R           (4cos(x)  + 6cos(x) + 2)sin(x)  + 4cos(x)  + 6cos(x)  - 2cos(x)
--R         + 
--R           - 6cos(x) - 2
--R      *
--R                  2
--R         log(----------)
--R             cos(x) + 1
--R     + 
--R                2                     3          3                2
--R       (- cos(x)  - 4cos(x) - 1)sin(x)  + (cos(x)  - cos(x))sin(x)
--R     + 
--R                4          3                              5          3
--R       (- cos(x)  - 4cos(x)  + 4cos(x) + 1)sin(x) + cos(x)  - 2cos(x)  + cos(x)
--R  /
--R                         2           2                              3          2
--R       (cos(x) + 1)sin(x)  + (2cos(x)  + 4cos(x) + 2)sin(x) + cos(x)  + 3cos(x)
--R     + 
--R       3cos(x) + 1
--R                                                     Type: Expression Integer
--E 126

--S 127 of 139
ode197 := cos(x)*D(y(x),x) - y(x)**4 - y(x)*sin(x)
 

                 ,                       4
   (127)  cos(x)y (x) - y(x)sin(x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                 ,                       4
--R   (127)  cos(x)y (x) - y(x)sin(x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 127

--S 128 of 139
yx:=solve(ode197,y,x)
 

                3      2       3
          (2y(x) cos(x)  + y(x) )sin(x) + 1
   (128)  ---------------------------------
                         3      3
                     y(x) cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3      2       3
--R          (2y(x) cos(x)  + y(x) )sin(x) + 1
--R   (128)  ---------------------------------
--R                         3      3
--R                     y(x) cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 128

--S 129 of 139
ode197expr := cos(x)*D(yx,x) - yx**4 - yx*sin(x)
 

   (129)
              8      10 ,
       - 3y(x) cos(x)  y (x)

     + 
                   12      8         12      6         12      4
           - 16y(x)  cos(x)  - 32y(x)  cos(x)  - 24y(x)  cos(x)
         + 
                  12      2       12
           - 8y(x)  cos(x)  - y(x)
      *
               4
         sin(x)
     + 
                9      6         9      4         9      2        9       3
       (- 32y(x) cos(x)  - 48y(x) cos(x)  - 24y(x) cos(x)  - 4y(x) )sin(x)
     + 
             12      9         6      4         6      2        6       2
       (2y(x)  cos(x)  - 24y(x) cos(x)  - 24y(x) cos(x)  - 6y(x) )sin(x)
     + 
             9      9        3      2        3               12      13
       (2y(x) cos(x)  - 8y(x) cos(x)  - 4y(x) )sin(x) + 2y(x)  cos(x)
     + 
           12      11
       y(x)  cos(x)   - 1
  /
         12      12
     y(x)  cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (129)
--R              8      10 ,
--R       - 3y(x) cos(x)  y (x)
--R
--R     + 
--R                   12      8         12      6         12      4
--R           - 16y(x)  cos(x)  - 32y(x)  cos(x)  - 24y(x)  cos(x)
--R         + 
--R                  12      2       12
--R           - 8y(x)  cos(x)  - y(x)
--R      *
--R               4
--R         sin(x)
--R     + 
--R                9      6         9      4         9      2        9       3
--R       (- 32y(x) cos(x)  - 48y(x) cos(x)  - 24y(x) cos(x)  - 4y(x) )sin(x)
--R     + 
--R             12      9         6      4         6      2        6       2
--R       (2y(x)  cos(x)  - 24y(x) cos(x)  - 24y(x) cos(x)  - 6y(x) )sin(x)
--R     + 
--R             9      9        3      2        3               12      13
--R       (2y(x) cos(x)  - 8y(x) cos(x)  - 4y(x) )sin(x) + 2y(x)  cos(x)
--R     + 
--R           12      11
--R       y(x)  cos(x)   - 1
--R  /
--R         12      12
--R     y(x)  cos(x)
--R                                                     Type: Expression Integer
--E 129

--S 130 of 139
ode198 := sin(x)*cos(x)*D(y(x),x) - y(x) - sin(x)**3
 

                       ,            3
   (130)  cos(x)sin(x)y (x) - sin(x)  - y(x)

                                                     Type: Expression Integer
--R 
--R
--R                       ,            3
--R   (130)  cos(x)sin(x)y (x) - sin(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 130

--S 131 of 139
ode198a:=solve(ode198,y,x)
 

                                        sin(x)
   (131)  [particular= - sin(x),basis= [------]]
                                        cos(x)
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                        sin(x)
--R   (131)  [particular= - sin(x),basis= [------]]
--R                                        cos(x)
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 131

--S 132 of 139
yx:=ode198a.particular
 

   (132)  - sin(x)
                                                     Type: Expression Integer
--R 
--R
--R   (132)  - sin(x)
--R                                                     Type: Expression Integer
--E 132

--S 133 of 139
ode198expr := sin(x)*cos(x)*D(yx,x) - yx - sin(x)**3
 

                  3            2
   (133)  - sin(x)  + (- cos(x)  + 1)sin(x)
                                                     Type: Expression Integer
--R 
--R
--R                  3            2
--R   (133)  - sin(x)  + (- cos(x)  + 1)sin(x)
--R                                                     Type: Expression Integer
--E 133

--S 134 of 139
ode199 := sin(2*x)*D(y(x),x) + sin(2*y(x))
 

                  ,
   (134)  sin(2x)y (x) + sin(2y(x))

                                                     Type: Expression Integer
--R 
--R
--R                  ,
--R   (134)  sin(2x)y (x) + sin(2y(x))
--R
--R                                                     Type: Expression Integer
--E 134

--S 135 of 139
ode199a:=solve(ode199,y,x)
 

   (135)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (135)  "failed"
--R                                                    Type: Union("failed",...)
--E 135

--S 136 of 139
ode200 := (a*sin(x)**2+b)*D(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)**2+c)
 

                   2      ,                                  2
   (136)  (a sin(x)  + b)y (x) + a y(x)sin(2x) + A a x sin(x)  + A c x

                                                     Type: Expression Integer
--R 
--R
--R                   2      ,                                  2
--R   (136)  (a sin(x)  + b)y (x) + a y(x)sin(2x) + A a x sin(x)  + A c x
--R
--R                                                     Type: Expression Integer
--E 136

--S 137 of 139
ode200a:=solve(ode200,y,x)
 

   (137)
                                                  2                2
                - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
   [particular= ----------------------------------------------------,
                                         2
                                4a cos(x)  - 4b - 4a
                    1
    basis= [-----------------]]
                    2
            a cos(x)  - b - a
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (137)
--R                                                  2                2
--R                - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
--R   [particular= ----------------------------------------------------,
--R                                         2
--R                                4a cos(x)  - 4b - 4a
--R                    1
--R    basis= [-----------------]]
--R                    2
--R            a cos(x)  - b - a
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 137

--S 138 of 139
yx:=ode200a.particular
 

                                            2                2
          - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
   (138)  ----------------------------------------------------
                                   2
                          4a cos(x)  - 4b - 4a
                                                     Type: Expression Integer
--R 
--R
--R                                            2                2
--R          - 2A a x cos(x)sin(x) - A a cos(x)  + (2A c + A a)x
--R   (138)  ----------------------------------------------------
--R                                   2
--R                          4a cos(x)  - 4b - 4a
--R                                                     Type: Expression Integer
--E 138

--S 139 of 139
ode200expr := (a*sin(x)**2+b)*D(yx,x) + a*yx*sin(2*x) + A*x*(a*sin(x)**2+c)
 

   (139)
                  3        3        2        3                      3      4
           (- 2A a x cos(x)  + (2A a b + 2A a )x cos(x))sin(x) - A a cos(x)
         + 
                 2       3  2      2       3       2
           ((2A a c + A a )x  + A a b + A a )cos(x)
         + 
                            2        2       3  2
           ((- 2A a b - 2A a )c - A a b - A a )x
      *
         sin(2x)
     + 
              3        2          2        3         4
       (- 2A a x cos(x)  + (- 2A a b - 2A a )x)sin(x)
     + 
              3      3        2        3  2             3
       (- 2A a cos(x)  + (4A a c + 2A a )x cos(x))sin(x)
     + 
               3        4        2        2        3         2
           2A a x cos(x)  + (4A a c - 8A a b - 4A a )x cos(x)
         + 
                            2           2       2        3
           ((- 4A a b - 4A a )c + 2A a b  + 4A a b + 2A a )x
      *
               2
         sin(x)
     + 
              2        3                   2   2
       (- 2A a b cos(x)  + (4A a b c + 2A a b)x cos(x))sin(x)
     + 
            2        2          4
       (4A a c - 2A a b)x cos(x)
     + 
                        2           2       2          2
       ((- 4A a b - 8A a )c + 2A a b  + 4A a b)x cos(x)
     + 
                      2           2       2
       ((4A a b + 4A a )c - 2A a b  - 2A a b)x
  /
       2      4               2       2     2            2
     4a cos(x)  + (- 8a b - 8a )cos(x)  + 4b  + 8a b + 4a
                                                     Type: Expression Integer
--R 
--R
--R   (139)
--R                  3        3        2        3                      3      4
--R           (- 2A a x cos(x)  + (2A a b + 2A a )x cos(x))sin(x) - A a cos(x)
--R         + 
--R                 2       3  2      2       3       2
--R           ((2A a c + A a )x  + A a b + A a )cos(x)
--R         + 
--R                            2        2       3  2
--R           ((- 2A a b - 2A a )c - A a b - A a )x
--R      *
--R         sin(2x)
--R     + 
--R              3        2          2        3         4
--R       (- 2A a x cos(x)  + (- 2A a b - 2A a )x)sin(x)
--R     + 
--R              3      3        2        3  2             3
--R       (- 2A a cos(x)  + (4A a c + 2A a )x cos(x))sin(x)
--R     + 
--R               3        4        2        2        3         2
--R           2A a x cos(x)  + (4A a c - 8A a b - 4A a )x cos(x)
--R         + 
--R                            2           2       2        3
--R           ((- 4A a b - 4A a )c + 2A a b  + 4A a b + 2A a )x
--R      *
--R               2
--R         sin(x)
--R     + 
--R              2        3                   2   2
--R       (- 2A a b cos(x)  + (4A a b c + 2A a b)x cos(x))sin(x)
--R     + 
--R            2        2          4
--R       (4A a c - 2A a b)x cos(x)
--R     + 
--R                        2           2       2          2
--R       ((- 4A a b - 8A a )c + 2A a b  + 4A a b)x cos(x)
--R     + 
--R                      2           2       2
--R       ((4A a b + 4A a )c - 2A a b  - 2A a b)x
--R  /
--R       2      4               2       2     2            2
--R     4a cos(x)  + (- 8a b - 8a )cos(x)  + 4b  + 8a b + 4a
--R                                                     Type: Expression Integer
--E 139

)spool
 
Starts dribbling to r20abugs.output (2010/3/27, 18:30:52).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 34
m : Matrix Expression Integer := matrix [[i*x^j for i in 1..3] for j in 1..3]
 

        +x   2x   3x +
        |            |
        | 2    2    2|
   (1)  |x   2x   3x |
        |            |
        | 3    3    3|
        +x   2x   3x +
                                              Type: Matrix Expression Integer
--R 
--R
--R        +x   2x   3x +
--R        |            |
--R        | 2    2    2|
--R   (1)  |x   2x   3x |
--R        |            |
--R        | 3    3    3|
--R        +x   2x   3x +
--R                                              Type: Matrix Expression Integer
--E 1

--S 2 of 34
eval(m,x=0)
 

        +0  0  0+
        |       |
   (2)  |0  0  0|
        |       |
        +0  0  0+
                                              Type: Matrix Expression Integer
--R 
--R
--R        +0  0  0+
--R        |       |
--R   (2)  |0  0  0|
--R        |       |
--R        +0  0  0+
--R                                              Type: Matrix Expression Integer
--E 2


)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
--S 3 of 34
s:= seed();
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 34
r1 := randnum();
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 34
for i in 1..10 repeat randnum();
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 34
reseed s;
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 34
r2 := randnum();
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 34
r1 - r2
 

   (6)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (6)  0
--R                                                     Type: NonNegativeInteger
--E 8


)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 9 of 34
r3:=rule(3==%pi) -- biblical approximation
 

   (1)  3 == %pi
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)  3 == %pi
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 9

--S 10 of 34
numeric(%pi)
 

   (2)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 897932385
--R                                                                  Type: Float
--E 10

--S 11 of 34
numeric(r3(3))
 

   (3)  3.1415926535 897932385
                                                                  Type: Float
--R 
--R
--R   (3)  3.1415926535 897932385
--R                                                                  Type: Float
--E 11

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.


--S 12 of 34
sin(atan(sqrt 3)/2)
 

        1
   (1)  -
        2
                                                     Type: Expression Integer
--R 
--R
--R        1
--R   (1)  -
--R        2
--R                                                     Type: Expression Integer
--E 12

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 13 of 34
R := IntegerMod(4)
 

   (1)  IntegerMod 4
                                                                 Type: Domain
--R 
--R
--R   (1)  IntegerMod 4
--R                                                                 Type: Domain
--E 13

--S 14 of 34
PolR := UP('X, R)
 

   (2)  UnivariatePolynomial(X,IntegerMod 4)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(X,IntegerMod 4)
--R                                                                 Type: Domain
--E 14

--S 15 of 34
X : PolR := monomial(1, 1)
 

   (3)  X
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R   (3)  X
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 15

--S 16 of 34
a : PolR := 2 * X**2
 

          2
   (4)  2X
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R          2
--R   (4)  2X
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 16

--S 17 of 34
b : PolR := X**2 + 2*X + 1
 

         2
   (5)  X  + 2X + 1
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R         2
--R   (5)  X  + 2X + 1
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 17

--S 18 of 34
qr := monicDivide(a, b)
 

   (6)  [quotient= 2,remainder= 2]
Type: Record(quotient: UnivariatePolynomial(X,IntegerMod 4),remainder: UnivariatePolynomial(X,IntegerMod 4))
--R 
--R
--R   (6)  [quotient= 2,remainder= 2]
--RType: Record(quotient: UnivariatePolynomial(X,IntegerMod 4),remainder: UnivariatePolynomial(X,IntegerMod 4))
--E 18

--S 19 of 34
a - (qr.quotient * b + qr.remainder)
 

   (7)  0
                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--R 
--R
--R   (7)  0
--R                                   Type: UnivariatePolynomial(X,IntegerMod 4)
--E 19

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 20 of 34
limit(%e^(1/x^2)/(%e^(1/x^2) + %e^(1/x^4)), x=0)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 20
)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 21 of 34
integrate((sin(t))*sin((%pi-t)/6),t)
 

   (1)
             t - %pi 6           t - %pi 4          t - %pi 2          t - %pi
   (- 960cos(-------)  + 1536cos(-------)  - 612cos(-------)  + 36)sin(-------)
                6                   6                  6                  6
   ----------------------------------------------------------------------------
                                        35
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R             t - %pi 6           t - %pi 4          t - %pi 2          t - %pi
--R   (- 960cos(-------)  + 1536cos(-------)  - 612cos(-------)  + 36)sin(-------)
--R                6                   6                  6                  6
--R   ----------------------------------------------------------------------------
--R                                        35
--R                                          Type: Union(Expression Integer,...)
--E 21

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 22 of 34
(x+1.0)/(x+1.0)
 

   (1)  1.0
                                              Type: Fraction Polynomial Float
--R 
--R
--R   (1)  1.0
--R                                              Type: Fraction Polynomial Float
--E 22

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 23 of 34
b := D(Ci(x),x)
 

        cos(x)
   (1)  ------
           x
                                                     Type: Expression Integer
--R 
--R
--R        cos(x)
--R   (1)  ------
--R           x
--R                                                     Type: Expression Integer
--E 23

--S 24 of 34
integrate(b,x)
 

   (2)  Ci(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)  Ci(x)
--R                                          Type: Union(Expression Integer,...)
--E 24

--S 25 of 34
integrate((1 - sin x)/x,x)
 

   (3)  log(x) - Si(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (3)  log(x) - Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 25

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 26 of 34
limit(erf(x),x=c)
 

   (1)  erf(c)
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  erf(c)
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 26

--S 27 of 34
(sqrt(2)*sqrt(3)=sqrt(6))@Boolean
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 34
integrate((a + b*x)*exp(-x^2),x)
 

                                2
                 +---+       - x
        a erf(x)\|%pi  - b %e
   (3)  -------------------------
                    2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                2
--R                 +---+       - x
--R        a erf(x)\|%pi  - b %e
--R   (3)  -------------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 28

--S 29 of 34
laplace(sin(t)^2/t^(3/2),t,s)
 

                       +---+ 4         +---+ 2
                     t\|- 1          t\|- 1
                - (%e       )  + 2(%e       )  - 1
   (4)  laplace(----------------------------------,t,s)
                                +---+ 2
                              t\|- 1    +-+
                        4t (%e       ) \|t
                                                     Type: Expression Integer
--R 
--R
--R                       +---+ 4         +---+ 2
--R                     t\|- 1          t\|- 1
--R                - (%e       )  + 2(%e       )  - 1
--R   (4)  laplace(----------------------------------,t,s)
--R                                +---+ 2
--R                              t\|- 1    +-+
--R                        4t (%e       ) \|t
--R                                                     Type: Expression Integer
--E 29

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 30 of 34
P:=x^4+x^3+x^2+x+1
 

         4    3    2
   (1)  x  + x  + x  + x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         4    3    2
--R   (1)  x  + x  + x  + x + 1
--R                                                     Type: Polynomial Integer
--E 30

--S 31 of 34
Q:=x^5+x^4+2*x^3+2*x^2+2*x-2+4*sqrt(-1+sqrt(3))
 

                                     +--------+
         5    4     3     2          | +-+
   (2)  x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R                                     +--------+
--R         5    4     3     2          | +-+
--R   (2)  x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
--R                                             Type: Polynomial AlgebraicNumber
--E 31

--S 32 of 34
int := P/Q
 

                     4    3    2
                    x  + x  + x  + x + 1
   (3)  -------------------------------------------
                                     +--------+
         5    4     3     2          | +-+
        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
                                    Type: Fraction Polynomial AlgebraicNumber
--R 
--R
--R                     4    3    2
--R                    x  + x  + x  + x + 1
--R   (3)  -------------------------------------------
--R                                     +--------+
--R         5    4     3     2          | +-+
--R        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
--R                                    Type: Fraction Polynomial AlgebraicNumber
--E 32

--S 33 of 34
int2 := int pretend FRAC POLY IAN
 

                     4    3    2
                    x  + x  + x  + x + 1
   (4)  -------------------------------------------
                                     +--------+
         5    4     3     2          | +-+
        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
                               Type: Fraction Polynomial InnerAlgebraicNumber
--R 
--R
--R                     4    3    2
--R                    x  + x  + x  + x + 1
--R   (4)  -------------------------------------------
--R                                     +--------+
--R         5    4     3     2          | +-+
--R        x  + x  + 2x  + 2x  + 2x + 4\|\|3  - 1  - 2
--R                               Type: Fraction Polynomial InnerAlgebraicNumber
--E 33

--S 34 of 34
ans:=integrate(int2,x)
 

   (5)
           ROOT
                                2
                - 7810694562%%F2
              + 
                (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
              + 
                                2
                - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
              + 
                                2
                - 7810694562%%F0  + 5207129708%%F0
              + 
                                             +--------+
                            +-+              | +-+                 +-+
                (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
              + 
                - 1685296141
         + 
              +----------+        +----------+        +----------+
           - \|2603564854 %%F2 - \|2603564854 %%F1 - \|2603564854 %%F0
         + 
            +----------+
           \|2603564854
      /
           +----------+
         2\|2603564854
    *
       log
            x
          + 
                                                +-+                 +----------+
                                  (791590596224\|3  + 598661610816)\|2603564854
                               *
                                   +--------+
                                   | +-+
                                  \|\|3  - 1
                              + 
                                               +-+                  +----------+
                              (- 2397286715776\|3  + 2403741928832)\|2603564854
                           *
                              %%F0
                          + 
                                              +-+                 +----------+
                              (- 148579737216\|3  - 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                          +-+                 +----------+
                            (507356852544\|3  - 475624619408)\|2603564854
                       *
                          %%F1
                      + 
                                              +-+                 +----------+
                              (- 148579737216\|3  - 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                          +-+                 +----------+
                            (507356852544\|3  - 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                                                     +--------+
                                     +-+                +----------+ | +-+
                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
                      + 
                                        +-+                +----------+
                        (- 105798682864\|3  + 94208190216)\|2603564854
                   *
                      %%F2
                  + 
                                              +-+                 +----------+
                              (- 148579737216\|3  - 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                          +-+                 +----------+
                            (507356852544\|3  - 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                                                     +--------+
                                     +-+                +----------+ | +-+
                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
                      + 
                                        +-+                +----------+
                        (- 105798682864\|3  + 94208190216)\|2603564854
                   *
                      %%F1
                  + 
                                                                     +--------+
                                     +-+                +----------+ | +-+
                        (27739806288\|3  + 54861033808)\|2603564854 \|\|3  - 1
                      + 
                                        +-+                +----------+
                        (- 105798682864\|3  + 94208190216)\|2603564854
                   *
                      %%F0
                  + 
                                                                  +--------+
                                  +-+                +----------+ | +-+
                    (- 5137573312\|3  - 12986675368)\|2603564854 \|\|3  - 1
                  + 
                                 +-+                +----------+
                    (21754940736\|3  - 18755586294)\|2603564854
               *
                  ROOT
                                       2
                       - 7810694562%%F2
                     + 
                       (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
                     + 
                                       2
                       - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
                     + 
                                       2
                       - 7810694562%%F0  + 5207129708%%F0
                     + 
                                                    +--------+
                                   +-+              | +-+                 +-+
                       (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
                     + 
                       - 1685296141
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F2
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F1
                  + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                              2
                          %%F0
                      + 
                                                         +-+
                                - 2447794436917844917760\|3
                              + 
                                - 2090231849158026910336
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                            7562427907875099825280\|3  - 7496617546780959556960
                       *
                          %%F0
                      + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F2
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F1
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F1
              + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F0
              + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F0
              + 
                                                                 +--------+
                                     +-+                         | +-+
                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
              + 
                                       +-+
                - 33670351123600429986\|3  + 29207247737687098805
           /
              99053573869819283
   + 
       %%F1
    *
       log
            x
          + 
                                                            +--------+
                                       +-+                  | +-+
                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
                      + 
                                        +-+
                        - 9589146863104\|3  + 9614967715328
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
                  + 
                                  +-+
                    2029427410176\|3  - 1902498477632
               *
                      3
                  %%F1
              + 
                                                            +--------+
                                       +-+                  | +-+
                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
                      + 
                                        +-+
                        - 9589146863104\|3  + 9614967715328
                   *
                          2
                      %%F0
                  + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                      %%F0
                  + 
                                                      +--------+
                                  +-+                 | +-+
                    (483359723712\|3  + 597247669440)\|\|3  - 1
                  + 
                                    +-+
                    - 1606232678720\|3  + 1525665716768
               *
                      2
                  %%F1
              + 
                                                            +--------+
                                       +-+                  | +-+
                        (3166362384896\|3  + 2394646443264)\|\|3  - 1
                      + 
                                        +-+
                        - 9589146863104\|3  + 9614967715328
                   *
                          3
                      %%F0
                  + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                          2
                      %%F0
                  + 
                                                           +--------+
                                       +-+                 | +-+
                        (1266224220576\|3  + 930590163424)\|\|3  - 1
                      + 
                                        +-+
                        - 3826137578368\|3  + 3840459797248
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 147325640064\|3  - 153462964896)\|\|3  - 1
                  + 
                                 +-+
                    473720495592\|3  - 459140624672
               *
                  %%F1
              + 
                                                        +--------+
                                   +-+                  | +-+
                    (3166362384896\|3  + 2394646443264)\|\|3  - 1
                  + 
                                    +-+
                    - 9589146863104\|3  + 9614967715328
               *
                      4
                  %%F0
              + 
                                                          +--------+
                                     +-+                  | +-+
                    (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                  + 
                                  +-+
                    9589146863104\|3  - 9614967715328
               *
                      3
                  %%F0
              + 
                                                       +--------+
                                   +-+                 | +-+
                    (1266224220576\|3  + 930590163424)\|\|3  - 1
                  + 
                                    +-+
                    - 3826137578368\|3  + 3840459797248
               *
                      2
                  %%F0
              + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 253275272864\|3  - 176488982240)\|\|3  - 1
                  + 
                                 +-+
                    762298416608\|3  - 767050528864
               *
                  %%F0
              + 
                                                +--------+
                             +-+                | +-+                    +-+
                (19959069548\|3  + 16362854321)\|\|3  - 1  - 61872513890\|3
              + 
                61405017927
           /
              76090729
   + 
       %%F0
    *
       log
            x
          + 
                                                          +--------+
                                     +-+                  | +-+
                    (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                  + 
                                  +-+
                    9589146863104\|3  - 9614967715328
               *
                      4
                  %%F0
              + 
                                                        +--------+
                                   +-+                  | +-+
                    (2572043436032\|3  + 1577954638592)\|\|3  - 1
                  + 
                                    +-+
                    - 7559719452928\|3  + 7712469237696
               *
                      3
                  %%F0
              + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 782864496864\|3  - 333342493984)\|\|3  - 1
                  + 
                                  +-+
                    2219904899648\|3  - 2314794080480
               *
                      2
                  %%F0
              + 
                                                     +--------+
                                  +-+                | +-+
                    (105949632800\|3  + 23026017344)\|\|3  - 1
                  + 
                                   +-+
                    - 288577921016\|3  + 307909904192
               *
                  %%F0
              + 
                                               +--------+
                              +-+              | +-+                    +-+
                (- 5377952768\|3  - 147961292)\|\|3  - 1  + 14063435544\|3
              + 
                - 15251710219
           /
              76090729
   + 
       %%F2
    *
       log
            x
          + 
                                                                  +--------+
                                             +-+                  | +-+
                            (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                          + 
                                          +-+
                            9589146863104\|3  - 9614967715328
                       *
                          %%F0
                      + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                      %%F1
                  + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 110959225152\|3  - 219444135232)\|\|3  - 1
                  + 
                                 +-+
                    423194731456\|3  - 376832760864
               *
                      2
                  %%F2
              + 
                                                                  +--------+
                                             +-+                  | +-+
                            (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                          + 
                                          +-+
                            9589146863104\|3  - 9614967715328
                       *
                          %%F0
                      + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                          2
                      %%F1
                  + 
                                                                  +--------+
                                             +-+                  | +-+
                            (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                          + 
                                          +-+
                            9589146863104\|3  - 9614967715328
                       *
                              2
                          %%F0
                      + 
                                                                +--------+
                                           +-+                  | +-+
                            (3760681333760\|3  + 3211338247936)\|\|3  - 1
                          + 
                                             +-+
                            - 11618574273280\|3  + 11517466192960
                       *
                          %%F0
                      + 
                                                            +--------+
                                        +-+                 | +-+
                        (- 594318948864\|3  - 816691804672)\|\|3  - 1
                      + 
                                      +-+
                        2029427410176\|3  - 1902498477632
                   *
                      %%F1
                  + 
                                                          +--------+
                                      +-+                 | +-+
                        (594318948864\|3  + 816691804672)\|\|3  - 1
                      + 
                                        +-+
                        - 2029427410176\|3  + 1902498477632
                   *
                          2
                      %%F0
                  + 
                                                            +--------+
                                        +-+                 | +-+
                        (- 594318948864\|3  - 816691804672)\|\|3  - 1
                      + 
                                      +-+
                        2029427410176\|3  - 1902498477632
                   *
                      %%F0
                  + 
                                                     +--------+
                                 +-+                 | +-+
                    (90408931904\|3  + 167497433760)\|\|3  - 1
                  + 
                                   +-+
                    - 336174968512\|3  + 301810415688
               *
                  %%F2
              + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                      %%F0
                  + 
                                                      +--------+
                                  +-+                 | +-+
                    (594318948864\|3  + 816691804672)\|\|3  - 1
                  + 
                                    +-+
                    - 2029427410176\|3  + 1902498477632
               *
                      3
                  %%F1
              + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                          2
                      %%F0
                  + 
                                                            +--------+
                                       +-+                  | +-+
                        (3760681333760\|3  + 3211338247936)\|\|3  - 1
                      + 
                                         +-+
                        - 11618574273280\|3  + 11517466192960
                   *
                      %%F0
                  + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
                  + 
                                  +-+
                    2029427410176\|3  - 1902498477632
               *
                      2
                  %%F1
              + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 3166362384896\|3  - 2394646443264)\|\|3  - 1
                      + 
                                      +-+
                        9589146863104\|3  - 9614967715328
                   *
                          3
                      %%F0
                  + 
                                                            +--------+
                                       +-+                  | +-+
                        (3760681333760\|3  + 3211338247936)\|\|3  - 1
                      + 
                                         +-+
                        - 11618574273280\|3  + 11517466192960
                   *
                          2
                      %%F0
                  + 
                                                              +--------+
                                         +-+                  | +-+
                        (- 1860543169440\|3  - 1747281968096)\|\|3  - 1
                      + 
                                      +-+
                        5855564988544\|3  - 5742958274880
                   *
                      %%F0
                  + 
                                                      +--------+
                                  +-+                 | +-+
                    (237734571968\|3  + 320960398656)\|\|3  - 1
                  + 
                                   +-+
                    - 809895464104\|3  + 760951040360
               *
                  %%F1
              + 
                                                      +--------+
                                  +-+                 | +-+
                    (594318948864\|3  + 816691804672)\|\|3  - 1
                  + 
                                    +-+
                    - 2029427410176\|3  + 1902498477632
               *
                      3
                  %%F0
              + 
                                                        +--------+
                                    +-+                 | +-+
                    (- 594318948864\|3  - 816691804672)\|\|3  - 1
                  + 
                                  +-+
                    2029427410176\|3  - 1902498477632
               *
                      2
                  %%F0
              + 
                                                      +--------+
                                  +-+                 | +-+
                    (237734571968\|3  + 320960398656)\|\|3  - 1
                  + 
                                   +-+
                    - 809895464104\|3  + 760951040360
               *
                  %%F0
              + 
                                                  +--------+
                               +-+                | +-+                    +-+
                (- 27607601380\|3  - 45816414455)\|\|3  - 1  + 99538692182\|3
              + 
                - 90949919409
           /
              76090729
   + 
           -
              ROOT
                                   2
                   - 7810694562%%F2
                 + 
                   (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
                 + 
                                   2
                   - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
                 + 
                                   2
                   - 7810694562%%F0  + 5207129708%%F0
                 + 
                                                +--------+
                               +-+              | +-+                 +-+
                   (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
                 + 
                   - 1685296141
         + 
              +----------+        +----------+        +----------+
           - \|2603564854 %%F2 - \|2603564854 %%F1 - \|2603564854 %%F0
         + 
            +----------+
           \|2603564854
      /
           +----------+
         2\|2603564854
    *
       log
            x
          + 
                                                  +-+
                                  (- 791590596224\|3  - 598661610816)
                               *
                                                +--------+
                                   +----------+ | +-+
                                  \|2603564854 \|\|3  - 1
                              + 
                                             +-+                  +----------+
                              (2397286715776\|3  - 2403741928832)\|2603564854
                           *
                              %%F0
                          + 
                                            +-+                 +----------+
                              (148579737216\|3  + 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                            +-+                 +----------+
                            (- 507356852544\|3  + 475624619408)\|2603564854
                       *
                          %%F1
                      + 
                                            +-+                 +----------+
                              (148579737216\|3  + 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                            +-+                 +----------+
                            (- 507356852544\|3  + 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                         +-+                +----------+
                          (- 27739806288\|3  - 54861033808)\|2603564854
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                      +-+                +----------+
                        (105798682864\|3  - 94208190216)\|2603564854
                   *
                      %%F2
                  + 
                                            +-+                 +----------+
                              (148579737216\|3  + 204172951168)\|2603564854
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                            +-+                 +----------+
                            (- 507356852544\|3  + 475624619408)\|2603564854
                       *
                          %%F0
                      + 
                                         +-+                +----------+
                          (- 27739806288\|3  - 54861033808)\|2603564854
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                      +-+                +----------+
                        (105798682864\|3  - 94208190216)\|2603564854
                   *
                      %%F1
                  + 
                                         +-+                +----------+
                          (- 27739806288\|3  - 54861033808)\|2603564854
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                      +-+                +----------+
                        (105798682864\|3  - 94208190216)\|2603564854
                   *
                      %%F0
                  + 
                                                                +--------+
                                +-+                +----------+ | +-+
                    (5137573312\|3  + 12986675368)\|2603564854 \|\|3  - 1
                  + 
                                   +-+                +----------+
                    (- 21754940736\|3  + 18755586294)\|2603564854
               *
                  ROOT
                                       2
                       - 7810694562%%F2
                     + 
                       (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
                     + 
                                       2
                       - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
                     + 
                                       2
                       - 7810694562%%F0  + 5207129708%%F0
                     + 
                                                    +--------+
                                   +-+              | +-+                 +-+
                       (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
                     + 
                       - 1685296141
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F2
              + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                          %%F0
                      + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F1
                  + 
                                                       +-+
                                2060957455085711511296\|3
                              + 
                                1558654329359563860864
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                          - 6241491438155480936704\|3  + 6258298003993164470528
                       *
                              2
                          %%F0
                      + 
                                                         +-+
                                - 2447794436917844917760\|3
                              + 
                                - 2090231849158026910336
                           *
                               +--------+
                               | +-+
                              \|\|3  - 1
                          + 
                                                   +-+
                            7562427907875099825280\|3  - 7496617546780959556960
                       *
                          %%F0
                      + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F1
                  + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F2
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                      %%F0
                  + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F1
              + 
                                                   +-+
                          (- 386836981832133406464\|3  - 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                               +-+
                        1320936469719618888576\|3  - 1238319542787795086432
                   *
                          2
                      %%F0
                  + 
                                                 +-+
                          (386836981832133406464\|3  + 531577519798463049472)
                       *
                           +--------+
                           | +-+
                          \|\|3  - 1
                      + 
                                                 +-+
                        - 1320936469719618888576\|3  + 1238319542787795086432
                   *
                      %%F0
                  + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F1
              + 
                                            +-+
                      (72222384708205001952\|3  + 142834259476614584032)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                            +-+
                    - 275453732304202461856\|3  + 245277133005324268464
               *
                      2
                  %%F0
              + 
                                              +-+
                      (- 58846379398233425504\|3  - 109022607918182267760)
                   *
                       +--------+
                       | +-+
                      \|\|3  - 1
                  + 
                                          +-+
                    218813333203099969312\|3  - 196445747714101757388
               *
                  %%F0
              + 
                                                                 +--------+
                                     +-+                         | +-+
                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
              + 
                                       +-+
                - 33670351123600429986\|3  + 29207247737687098805
           /
              99053573869819283
                             Type: Union(Expression InnerAlgebraicNumber,...)
--R 
--R
--R   (5)
--R           ROOT
--R                                2
--R                - 7810694562%%F2
--R              + 
--R                (- 5207129708%%F1 - 5207129708%%F0 + 5207129708)%%F2
--R              + 
--R                                2
--R                - 7810694562%%F1  + (- 5207129708%%F0 + 5207129708)%%F1
--R              + 
--R                                2
--R                - 7810694562%%F0  + 5207129708%%F0
--R              + 
--R                                             +--------+
--R                            +-+              | +-+                 +-+
--R                (- 96969608\|3  - 156742856)\|\|3  - 1  - 74069389\|3
--R              + 
--R                - 1685296141
--R         + 
--R              +----------+        +----------+        +----------+
--R           - \|2603564854 %%F2 - \|2603564854 %%F1 - \|2603564854 %%F0
--R         + 
--R            +----------+
--R           \|2603564854
--R      /
--R           +----------+
--R         2\|2603564854
--R    *
--R       log
--R            x
--R          + 
--R                                                +-+                 +----------+
--R                                  (791590596224\|3  + 598661610816)\|2603564854
--R                               *
--R                                   +--------+
--R                                   | +-+
--R                                  \|\|3  - 1
--R                              + 
--R                                               +-+                  +----------+
--R                              (- 2397286715776\|3  + 2403741928832)\|2603564854
--R                           *
--R                              %%F0
--R                          + 
--R                                              +-+                 +----------+
--R                              (- 148579737216\|3  - 204172951168)\|2603564854
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                          +-+                 +----------+
--R                            (507356852544\|3  - 475624619408)\|2603564854
--R                       *
--R                          %%F1
--R                      + 
--R                                              +-+                 +----------+
--R                              (- 148579737216\|3  - 204172951168)\|2603564854
--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
--R                          + 
--R                                          +-+                 +----------+
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--R                                                        +--------+
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--R                                                      +--------+
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--R                                                  +--------+
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--R              + 
--R                - 90949919409
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--R                                                +--------+
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--R                              \|\|3  - 1
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--R                              \|\|3  - 1
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--R                   *
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--R                               +--------+
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--R                              \|\|3  - 1
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--R                                            +-+                 +----------+
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--R                                      +-+                +----------+
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--R                                                                +--------+
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--R                               +--------+
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--R                           +--------+
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--R                           +--------+
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--R                        1320936469719618888576\|3  - 1238319542787795086432
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--R                                                       +-+
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--R                               +--------+
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--R                              \|\|3  - 1
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--R                       *
--R                          %%F0
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--R                       *
--R                           +--------+
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--R                          \|\|3  - 1
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--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
--R                          2
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--R                                                       +-+
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--R                               +--------+
--R                               | +-+
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--R                                                   +-+
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--R                      + 
--R                                                         +-+
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--R                           *
--R                               +--------+
--R                               | +-+
--R                              \|\|3  - 1
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--R                                                   +-+
--R                            7562427907875099825280\|3  - 7496617546780959556960
--R                       *
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--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
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--R                                                 +-+
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--R                   *
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--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
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--R                                               +-+
--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
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--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
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--R                                                 +-+
--R                        - 1320936469719618888576\|3  + 1238319542787795086432
--R                   *
--R                      %%F0
--R                  + 
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--R                      (- 58846379398233425504\|3  - 109022607918182267760)
--R                   *
--R                       +--------+
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--R               *
--R                  %%F2
--R              + 
--R                                                   +-+
--R                          (- 386836981832133406464\|3  - 531577519798463049472)
--R                       *
--R                           +--------+
--R                           | +-+
--R                          \|\|3  - 1
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--R                        1320936469719618888576\|3  - 1238319542787795086432
--R                   *
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--R                       +--------+
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--R               *
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--R                           +--------+
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--R                           +--------+
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--R                   *
--R                       +--------+
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--R               *
--R                      2
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--R                                              +-+
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--R                   *
--R                       +--------+
--R                       | +-+
--R                      \|\|3  - 1
--R                  + 
--R                                          +-+
--R                    218813333203099969312\|3  - 196445747714101757388
--R               *
--R                  %%F0
--R              + 
--R                                                                 +--------+
--R                                     +-+                         | +-+
--R                (8478824368933062100\|3  + 19267370202415390451)\|\|3  - 1
--R              + 
--R                                       +-+
--R                - 33670351123600429986\|3  + 29207247737687098805
--R           /
--R              99053573869819283
--R                             Type: Union(Expression InnerAlgebraicNumber,...)
--E 34
)spool 
 
Starts dribbling to schaum2.output (2010/3/27, 18:37:10).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 98
aa:=integrate(1/sqrt(a*x+b),x)
 

          +-------+
        2\|a x + b
   (1)  -----------
             a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +-------+
--R        2\|a x + b
--R   (1)  -----------
--R             a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 98
bb:=(2*sqrt(a*x+b))/a
 

          +-------+
        2\|a x + b
   (2)  -----------
             a
                                                     Type: Expression Integer
--R 
--R
--R          +-------+
--R        2\|a x + b
--R   (2)  -----------
--R             a
--R                                                     Type: Expression Integer
--E

--S 3 of 98      14:84 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 98
aa:=integrate(x/sqrt(a*x+b),x)
 

                    +-------+
        (2a x - 4b)\|a x + b
   (1)  ---------------------
                   2
                 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-------+
--R        (2a x - 4b)\|a x + b
--R   (1)  ---------------------
--R                   2
--R                 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 98
bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b)
 

                    +-------+
        (2a x - 4b)\|a x + b
   (2)  ---------------------
                   2
                 3a
                                                     Type: Expression Integer
--R 
--R
--R                    +-------+
--R        (2a x - 4b)\|a x + b
--R   (2)  ---------------------
--R                   2
--R                 3a
--R                                                     Type: Expression Integer
--E

--S 6 of 98      14:85 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 98
aa:=integrate(x^2/sqrt(a*x+b),x)
 

           2 2               2  +-------+
        (6a x  - 8a b x + 16b )\|a x + b
   (1)  ---------------------------------
                          3
                       15a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2               2  +-------+
--R        (6a x  - 8a b x + 16b )\|a x + b
--R   (1)  ---------------------------------
--R                          3
--R                       15a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 98
bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b)
 

           2 2               2  +-------+
        (6a x  - 8a b x + 16b )\|a x + b
   (2)  ---------------------------------
                          3
                       15a
                                                     Type: Expression Integer
--R 
--R
--R           2 2               2  +-------+
--R        (6a x  - 8a b x + 16b )\|a x + b
--R   (2)  ---------------------------------
--R                          3
--R                       15a
--R                                                     Type: Expression Integer
--E

--S 9 of 98      14:86 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 98
aa:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (1)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (1)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E 
--S 11 of 98
bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b)))
 

             +-------+    +-+
            \|a x + b  - \|b
        log(-----------------)
             +-------+    +-+
            \|a x + b  + \|b
   (2)  ----------------------
                  +-+
                 \|b
                                                     Type: Expression Integer
--R 
--R
--R             +-------+    +-+
--R            \|a x + b  - \|b
--R        log(-----------------)
--R             +-------+    +-+
--R            \|a x + b  + \|b
--R   (2)  ----------------------
--R                  +-+
--R                 \|b
--R                                                     Type: Expression Integer
--E
--S 12 of 98
cc11:=aa.1-bb1
 

               +-------+    +-+             +-------+              +-+
              \|a x + b  - \|b         - 2b\|a x + b  + (a x + 2b)\|b
        - log(-----------------) + log(-------------------------------)
               +-------+    +-+                       x
              \|a x + b  + \|b
   (3)  ---------------------------------------------------------------
                                       +-+
                                      \|b
                                                     Type: Expression Integer
--R
--R               +-------+    +-+             +-------+              +-+
--R              \|a x + b  - \|b         - 2b\|a x + b  + (a x + 2b)\|b
--R        - log(-----------------) + log(-------------------------------)
--R               +-------+    +-+                       x
--R              \|a x + b  + \|b
--R   (3)  ---------------------------------------------------------------
--R                                       +-+
--R                                      \|b
--R                                                     Type: Expression Integer
--E
--S 13 of 98
ff:=exp(aa.1*sqrt(b))
 

             +-------+              +-+
        - 2b\|a x + b  + (a x + 2b)\|b
   (4)  -------------------------------
                       x
                                                     Type: Expression Integer
--R
--R             +-------+              +-+
--R        - 2b\|a x + b  + (a x + 2b)\|b
--R   (4)  -------------------------------
--R                       x
--R                                                     Type: Expression Integer
--E
--S 14 of 98
gg:=exp(bb1*sqrt(b))
 

         +-------+    +-+
        \|a x + b  - \|b
   (5)  -----------------
         +-------+    +-+
        \|a x + b  + \|b
                                                     Type: Expression Integer
--R
--R         +-------+    +-+
--R        \|a x + b  - \|b
--R   (5)  -----------------
--R         +-------+    +-+
--R        \|a x + b  + \|b
--R                                                     Type: Expression Integer
--E
--S 15 of 98
gg1:=gg*(sqrt(a*x+b) - sqrt(b))
 

            +-+ +-------+
        - 2\|b \|a x + b  + a x + 2b
   (6)  ----------------------------
               +-------+    +-+
              \|a x + b  + \|b
                                                     Type: Expression Integer
--R
--R            +-+ +-------+
--R        - 2\|b \|a x + b  + a x + 2b
--R   (6)  ----------------------------
--R               +-------+    +-+
--R              \|a x + b  + \|b
--R                                                     Type: Expression Integer
--E
--S 16 of 98
gg2:=gg1/(sqrt(a*x+b) - sqrt(b))
 

            +-+ +-------+
        - 2\|b \|a x + b  + a x + 2b
   (7)  ----------------------------
                     a x
                                                     Type: Expression Integer
--R
--R            +-+ +-------+
--R        - 2\|b \|a x + b  + a x + 2b
--R   (7)  ----------------------------
--R                     a x
--R                                                     Type: Expression Integer
--E
--S 17 of 98
gg3:=gg2*(a*sqrt(b))
 

             +-------+              +-+
        - 2b\|a x + b  + (a x + 2b)\|b
   (8)  -------------------------------
                       x
                                                     Type: Expression Integer
--R
--R             +-------+              +-+
--R        - 2b\|a x + b  + (a x + 2b)\|b
--R   (8)  -------------------------------
--R                       x
--R                                                     Type: Expression Integer
--E
--S 18 of 98     14:87a Schaums and Axiom differ by a constant
ff-gg3
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
--S 19 of 98
t1:=aa.2-bb1
 

                      +-------+    +-+               +---+ +-------+
            +---+    \|a x + b  - \|b       +-+     \|- b \|a x + b
         - \|- b log(-----------------) - 2\|b atan(----------------)
                      +-------+    +-+                      b
                     \|a x + b  + \|b
   (10)  ------------------------------------------------------------
                                   +---+ +-+
                                  \|- b \|b
                                                     Type: Expression Integer
--R
--R                      +-------+    +-+               +---+ +-------+
--R            +---+    \|a x + b  - \|b       +-+     \|- b \|a x + b
--R         - \|- b log(-----------------) - 2\|b atan(----------------)
--R                      +-------+    +-+                      b
--R                     \|a x + b  + \|b
--R   (10)  ------------------------------------------------------------
--R                                   +---+ +-+
--R                                  \|- b \|b
--R                                                     Type: Expression Integer
--E
--S 20 of 98
D(t1,x)
 

   (11)  0
                                                     Type: Expression Integer
--R
--R   (11)  0
--R                                                     Type: Expression Integer
--E
--S 21 of 98
target:=1/(x*sqrt(a*x+b))
 

              1
   (12)  -----------
           +-------+
         x\|a x + b
                                                     Type: Expression Integer
--R
--R              1
--R   (12)  -----------
--R           +-------+
--R         x\|a x + b
--R                                                     Type: Expression Integer
--E
--S 22 of 98
aa2:=aa.2
 

                  +---+ +-------+
                 \|- b \|a x + b
           2atan(----------------)
                         b
   (13)  - -----------------------
                     +---+
                    \|- b
                                                     Type: Expression Integer
--R
--R                  +---+ +-------+
--R                 \|- b \|a x + b
--R           2atan(----------------)
--R                         b
--R   (13)  - -----------------------
--R                     +---+
--R                    \|- b
--R                                                     Type: Expression Integer
--E
--S 23 of 98
ad2:=D(aa2,x)
 

              1
   (14)  -----------
           +-------+
         x\|a x + b
                                                     Type: Expression Integer
--R
--R              1
--R   (14)  -----------
--R           +-------+
--R         x\|a x + b
--R                                                     Type: Expression Integer
--E
--S 24 of 98
ad2-target
 

   (15)  0
                                                     Type: Expression Integer
--R
--R   (15)  0
--R                                                     Type: Expression Integer
--E
--S 25 of 98
ab1:=D(bb1,x)
 

                +-------+    +-+
               \|a x + b  + \|b
   (16)  ----------------------------
           +-+ +-------+      2
         x\|b \|a x + b  + a x  + b x
                                                     Type: Expression Integer
--R
--R                +-------+    +-+
--R               \|a x + b  + \|b
--R   (16)  ----------------------------
--R           +-+ +-------+      2
--R         x\|b \|a x + b  + a x  + b x
--R                                                     Type: Expression Integer
--E
--S 26 of 98     14:87b Schaums and Axiom differ by a constant
ab1-target
 

   (17)  0
                                                     Type: Expression Integer
--R
--R   (17)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 98
aa:=integrate(1/(x^2*sqrt(a*x+b)),x)
 

   (1)
               +-------+              +-+
            2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
    a x log(-----------------------------) - 2\|b \|a x + b
                          x
   [--------------------------------------------------------,
                                 +-+
                            2b x\|b
              +---+ +-------+
             \|- b \|a x + b      +---+ +-------+
    a x atan(----------------) - \|- b \|a x + b
                     b
    ---------------------------------------------]
                          +---+
                      b x\|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R               +-------+              +-+
--R            2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R    a x log(-----------------------------) - 2\|b \|a x + b
--R                          x
--R   [--------------------------------------------------------,
--R                                 +-+
--R                            2b x\|b
--R              +---+ +-------+
--R             \|- b \|a x + b      +---+ +-------+
--R    a x atan(----------------) - \|- b \|a x + b
--R                     b
--R    ---------------------------------------------]
--R                          +---+
--R                      b x\|- b
--R                                     Type: Union(List Expression Integer,...)
--E 
--S 28 of 98
dd:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (2)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (2)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E
--S 29 of 98
bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1
 

                       +-------+              +-+
                  - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
        - a x log(-------------------------------) - 2\|b \|a x + b
                                 x
   (3)  ------------------------------------------------------------
                                       +-+
                                  2b x\|b
                                                     Type: Expression Integer
--R 
--R
--R                       +-------+              +-+
--R                  - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R        - a x log(-------------------------------) - 2\|b \|a x + b
--R                                 x
--R   (3)  ------------------------------------------------------------
--R                                       +-+
--R                                  2b x\|b
--R                                                     Type: Expression Integer
--E
--S 30 of 98
bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2
 

                  +---+ +-------+
                 \|- b \|a x + b      +---+ +-------+
        a x atan(----------------) - \|- b \|a x + b
                         b
   (4)  ---------------------------------------------
                              +---+
                          b x\|- b
                                                     Type: Expression Integer
--R 
--R
--R                  +---+ +-------+
--R                 \|- b \|a x + b      +---+ +-------+
--R        a x atan(----------------) - \|- b \|a x + b
--R                         b
--R   (4)  ---------------------------------------------
--R                              +---+
--R                          b x\|- b
--R                                                     Type: Expression Integer
--E
--S 31 of 98
cc11:=bb1-aa.1
 

   (5)
                  +-------+              +-+
               2b\|a x + b  + (a x + 2b)\|b
       - a log(-----------------------------)
                             x
     + 
                    +-------+              +-+
               - 2b\|a x + b  + (a x + 2b)\|b
       - a log(-------------------------------)
                              x
  /
        +-+
     2b\|b
                                                     Type: Expression Integer
--R
--R   (5)
--R                  +-------+              +-+
--R               2b\|a x + b  + (a x + 2b)\|b
--R       - a log(-----------------------------)
--R                             x
--R     + 
--R                    +-------+              +-+
--R               - 2b\|a x + b  + (a x + 2b)\|b
--R       - a log(-------------------------------)
--R                              x
--R  /
--R        +-+
--R     2b\|b
--R                                                     Type: Expression Integer
--E
--S 32 of 98
D(cc11,x)
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
--S 33 of 98
target:=1/(x^2*sqrt(a*x+b))
 

              1
   (7)  ------------
         2 +-------+
        x \|a x + b
                                                     Type: Expression Integer
--R
--R              1
--R   (7)  ------------
--R         2 +-------+
--R        x \|a x + b
--R                                                     Type: Expression Integer
--E
--S 34 of 98
ad1:=D(aa.1,x)
 

                             +-+ +-------+              2
                  (a x + 2b)\|b \|a x + b  + 2a b x + 2b
   (8)  ----------------------------------------------------------
               3     2 2  +-------+     2 4         3     2 2  +-+
        (2a b x  + 2b x )\|a x + b  + (a x  + 3a b x  + 2b x )\|b
                                                     Type: Expression Integer
--R
--R                             +-+ +-------+              2
--R                  (a x + 2b)\|b \|a x + b  + 2a b x + 2b
--R   (8)  ----------------------------------------------------------
--R               3     2 2  +-------+     2 4         3     2 2  +-+
--R        (2a b x  + 2b x )\|a x + b  + (a x  + 3a b x  + 2b x )\|b
--R                                                     Type: Expression Integer
--E
--S 35 of 98
ad1-target
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
--S 36 of 98
bd1:=D(bb1,x)
 

                                +-+ +-------+              2
                   (- a x - 2b)\|b \|a x + b  + 2a b x + 2b
   (10)  ------------------------------------------------------------
                3     2 2  +-------+       2 4         3     2 2  +-+
         (2a b x  + 2b x )\|a x + b  + (- a x  - 3a b x  - 2b x )\|b
                                                     Type: Expression Integer
--R
--R                                +-+ +-------+              2
--R                   (- a x - 2b)\|b \|a x + b  + 2a b x + 2b
--R   (10)  ------------------------------------------------------------
--R                3     2 2  +-------+       2 4         3     2 2  +-+
--R         (2a b x  + 2b x )\|a x + b  + (- a x  - 3a b x  - 2b x )\|b
--R                                                     Type: Expression Integer
--E
--S 37 of 98
bd1-target
 

   (11)  0
                                                     Type: Expression Integer
--R
--R   (11)  0
--R                                                     Type: Expression Integer
--E
--S 38 of 98     14:88 Schaums and Axiom differ by a constant
cc22:=bb2-aa.2
 

   (12)  0
                                                     Type: Expression Integer
--R 
--R
--R   (12)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 98
aa:=integrate(sqrt(a*x+b),x)
 

                    +-------+
        (2a x + 2b)\|a x + b
   (1)  ---------------------
                  3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-------+
--R        (2a x + 2b)\|a x + b
--R   (1)  ---------------------
--R                  3a
--R                                          Type: Union(Expression Integer,...)
--E 
--S 40 of 98
bb:=(2*sqrt((a*x+b)^3))/(3*a)
 

          +----------------------------+
          | 3 3     2   2       2     3
        2\|a x  + 3a b x  + 3a b x + b
   (2)  --------------------------------
                       3a
                                                     Type: Expression Integer
--R 
--R
--R          +----------------------------+
--R          | 3 3     2   2       2     3
--R        2\|a x  + 3a b x  + 3a b x + b
--R   (2)  --------------------------------
--R                       3a
--R                                                     Type: Expression Integer
--E
--S 41 of 98
cc:=aa-bb
 

            +----------------------------+
            | 3 3     2   2       2     3                +-------+
        - 2\|a x  + 3a b x  + 3a b x + b   + (2a x + 2b)\|a x + b
   (3)  ----------------------------------------------------------
                                    3a
                                                     Type: Expression Integer
--R
--R            +----------------------------+
--R            | 3 3     2   2       2     3                +-------+
--R        - 2\|a x  + 3a b x  + 3a b x + b   + (2a x + 2b)\|a x + b
--R   (3)  ----------------------------------------------------------
--R                                    3a
--R                                                     Type: Expression Integer
--E
--S 42 of 98
target:=sqrt(a*x+b)
 

         +-------+
   (4)  \|a x + b
                                                     Type: Expression Integer
--R
--R         +-------+
--R   (4)  \|a x + b
--R                                                     Type: Expression Integer
--E
--S 43 of 98
t1:=D(aa,x)
 

          a x + b
   (5)  ----------
         +-------+
        \|a x + b
                                                     Type: Expression Integer
--R
--R          a x + b
--R   (5)  ----------
--R         +-------+
--R        \|a x + b
--R                                                     Type: Expression Integer
--E
--S 44 of 98
t1-target
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
--S 45 of 98
t2:=D(bb,x)
 

                2 2             2
               a x  + 2a b x + b
   (7)  -------------------------------
         +----------------------------+
         | 3 3     2   2       2     3
        \|a x  + 3a b x  + 3a b x + b
                                                     Type: Expression Integer
--R
--R                2 2             2
--R               a x  + 2a b x + b
--R   (7)  -------------------------------
--R         +----------------------------+
--R         | 3 3     2   2       2     3
--R        \|a x  + 3a b x  + 3a b x + b
--R                                                     Type: Expression Integer
--E
--S 46 of 98
nn:=(a*x+b)^2
 

         2 2             2
   (8)  a x  + 2a b x + b
                                                     Type: Polynomial Integer
--R
--R         2 2             2
--R   (8)  a x  + 2a b x + b
--R                                                     Type: Polynomial Integer
--E
--S 47 of 98
mm:=(a*x+b)^3
 

         3 3     2   2       2     3
   (9)  a x  + 3a b x  + 3a b x + b
                                                     Type: Polynomial Integer
--R
--R         3 3     2   2       2     3
--R   (9)  a x  + 3a b x  + 3a b x + b
--R                                                     Type: Polynomial Integer
--E
--S 48 of 98     14:89 Schaums and Axiom differ by a constant
result=nn/sqrt(mm)
 

                         2 2             2
                        a x  + 2a b x + b
   (10)  result= -------------------------------
                  +----------------------------+
                  | 3 3     2   2       2     3
                 \|a x  + 3a b x  + 3a b x + b
                                            Type: Equation Expression Integer
--R
--R                         2 2             2
--R                        a x  + 2a b x + b
--R   (10)  result= -------------------------------
--R                  +----------------------------+
--R                  | 3 3     2   2       2     3
--R                 \|a x  + 3a b x  + 3a b x + b
--R                                            Type: Equation Expression Integer
--E
)clear all
 

--S 49 of 98
aa:=integrate(x*sqrt(a*x+b),x)
 

           2 2              2  +-------+
        (6a x  + 2a b x - 4b )\|a x + b
   (1)  --------------------------------
                         2
                      15a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2              2  +-------+
--R        (6a x  + 2a b x - 4b )\|a x + b
--R   (1)  --------------------------------
--R                         2
--R                      15a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50 of 98
bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3)
 

                    +----------------------------+
                    | 3 3     2   2       2     3
        (6a x - 4b)\|a x  + 3a b x  + 3a b x + b
   (2)  ------------------------------------------
                              2
                           15a
                                                     Type: Expression Integer
--R 
--R
--R                    +----------------------------+
--R                    | 3 3     2   2       2     3
--R        (6a x - 4b)\|a x  + 3a b x  + 3a b x + b
--R   (2)  ------------------------------------------
--R                              2
--R                           15a
--R                                                     Type: Expression Integer
--E

--S 51 of 98
cc:=aa-bb
 

   (3)
                     +----------------------------+
                     | 3 3     2   2       2     3
       (- 6a x + 4b)\|a x  + 3a b x  + 3a b x + b
     + 
          2 2              2  +-------+
       (6a x  + 2a b x - 4b )\|a x + b
  /
        2
     15a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     +----------------------------+
--R                     | 3 3     2   2       2     3
--R       (- 6a x + 4b)\|a x  + 3a b x  + 3a b x + b
--R     + 
--R          2 2              2  +-------+
--R       (6a x  + 2a b x - 4b )\|a x + b
--R  /
--R        2
--R     15a
--R                                                     Type: Expression Integer
--E

--S 52 of 98     14:90 Schaums and Axiom agree
dd:=rootSimp cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 53 of 98
aa:=integrate(x^2*sqrt(a*x+b),x)
 

            3 3     2   2       2       3  +-------+
        (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
   (1)  --------------------------------------------
                                3
                            105a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            3 3     2   2       2       3  +-------+
--R        (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
--R   (1)  --------------------------------------------
--R                                3
--R                            105a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54 of 98
bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^3)*sqrt((a+b*x)^3)
 

                                  +----------------------------+
            2 2                2  | 3 3       2 2     2       3
        (30a x  - 24a b x + 16b )\|b x  + 3a b x  + 3a b x + a
   (2)  --------------------------------------------------------
                                      3
                                  105a
                                                     Type: Expression Integer
--R 
--R
--R                                  +----------------------------+
--R            2 2                2  | 3 3       2 2     2       3
--R        (30a x  - 24a b x + 16b )\|b x  + 3a b x  + 3a b x + a
--R   (2)  --------------------------------------------------------
--R                                      3
--R                                  105a
--R                                                     Type: Expression Integer
--E

--S 55 of 98     14:91 Axiom cannot simplify this expression. Schaums typo?
cc:=aa-bb
 

   (3)
                                   +----------------------------+
             2 2                2  | 3 3       2 2     2       3
       (- 30a x  + 24a b x - 16b )\|b x  + 3a b x  + 3a b x + a
     + 
           3 3     2   2       2       3  +-------+
       (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
  /
         3
     105a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                   +----------------------------+
--R             2 2                2  | 3 3       2 2     2       3
--R       (- 30a x  + 24a b x - 16b )\|b x  + 3a b x  + 3a b x + a
--R     + 
--R           3 3     2   2       2       3  +-------+
--R       (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
--R  /
--R         3
--R     105a
--R                                                     Type: Expression Integer
--E

--S 56 of 98
factor numer aa
 

                      2 2               2  +-------+
   (4)  2(a x + b)(15a x  - 12a b x + 8b )\|a x + b
Type: Factored SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R
--R                      2 2               2  +-------+
--R   (4)  2(a x + b)(15a x  - 12a b x + 8b )\|a x + b
--RType: Factored SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E
)clear all
 

--S 57 of 98
aa:=integrate(sqrt(a*x+b)/x,x)
 

   (1)
                +-+ +-------+
     +-+    - 2\|b \|a x + b  + a x + 2b      +-------+
   [\|b log(----------------------------) + 2\|a x + b ,
                          x
                   +-------+
        +---+     \|a x + b       +-------+
    - 2\|- b atan(----------) + 2\|a x + b ]
                     +---+
                    \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                +-+ +-------+
--R     +-+    - 2\|b \|a x + b  + a x + 2b      +-------+
--R   [\|b log(----------------------------) + 2\|a x + b ,
--R                          x
--R                   +-------+
--R        +---+     \|a x + b       +-------+
--R    - 2\|- b atan(----------) + 2\|a x + b ]
--R                     +---+
--R                    \|- b
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 58 of 98
dd:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (2)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (2)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 59 of 98
bb1:=2*sqrt(a*x+b)+b*dd.1
 

                   +-------+              +-+
              - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
        b log(-------------------------------) + 2\|b \|a x + b
                             x
   (3)  --------------------------------------------------------
                                   +-+
                                  \|b
                                                     Type: Expression Integer
--R 
--R
--R                   +-------+              +-+
--R              - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R        b log(-------------------------------) + 2\|b \|a x + b
--R                             x
--R   (3)  --------------------------------------------------------
--R                                   +-+
--R                                  \|b
--R                                                     Type: Expression Integer
--E

--S 60 of 98
bb2:=2*sqrt(a*x+b)+b*dd.2
 

                   +---+ +-------+
                  \|- b \|a x + b       +---+ +-------+
        - 2b atan(----------------) + 2\|- b \|a x + b
                          b
   (4)  -----------------------------------------------
                              +---+
                             \|- b
                                                     Type: Expression Integer
--R 
--R
--R                   +---+ +-------+
--R                  \|- b \|a x + b       +---+ +-------+
--R        - 2b atan(----------------) + 2\|- b \|a x + b
--R                          b
--R   (4)  -----------------------------------------------
--R                              +---+
--R                             \|- b
--R                                                     Type: Expression Integer
--E

--S 61 of 98
cc11:=bb1-aa.1
 

   (5)
              +-------+              +-+              +-+ +-------+
         - 2b\|a x + b  + (a x + 2b)\|b           - 2\|b \|a x + b  + a x + 2b
   b log(-------------------------------) - b log(----------------------------)
                        x                                       x
   ----------------------------------------------------------------------------
                                        +-+
                                       \|b
                                                     Type: Expression Integer
--R 
--R
--R   (5)
--R              +-------+              +-+              +-+ +-------+
--R         - 2b\|a x + b  + (a x + 2b)\|b           - 2\|b \|a x + b  + a x + 2b
--R   b log(-------------------------------) - b log(----------------------------)
--R                        x                                       x
--R   ----------------------------------------------------------------------------
--R                                        +-+
--R                                       \|b
--R                                                     Type: Expression Integer
--E

--S 62 of 98
cc12:=bb1-aa.2
 

                   +-------+              +-+                     +-------+
              - 2b\|a x + b  + (a x + 2b)\|b       +---+ +-+     \|a x + b
        b log(-------------------------------) + 2\|- b \|b atan(----------)
                             x                                      +---+
                                                                   \|- b
   (6)  --------------------------------------------------------------------
                                         +-+
                                        \|b
                                                     Type: Expression Integer
--R 
--R
--R                   +-------+              +-+                     +-------+
--R              - 2b\|a x + b  + (a x + 2b)\|b       +---+ +-+     \|a x + b
--R        b log(-------------------------------) + 2\|- b \|b atan(----------)
--R                             x                                      +---+
--R                                                                   \|- b
--R   (6)  --------------------------------------------------------------------
--R                                         +-+
--R                                        \|b
--R                                                     Type: Expression Integer
--E

--S 63 of 98
cc21:=bb2-aa.1
 

   (7)
                       +-+ +-------+                        +---+ +-------+
      +---+ +-+    - 2\|b \|a x + b  + a x + 2b            \|- b \|a x + b
   - \|- b \|b log(----------------------------) - 2b atan(----------------)
                                 x                                 b
   -------------------------------------------------------------------------
                                      +---+
                                     \|- b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                       +-+ +-------+                        +---+ +-------+
--R      +---+ +-+    - 2\|b \|a x + b  + a x + 2b            \|- b \|a x + b
--R   - \|- b \|b log(----------------------------) - 2b atan(----------------)
--R                                 x                                 b
--R   -------------------------------------------------------------------------
--R                                      +---+
--R                                     \|- b
--R                                                     Type: Expression Integer
--E

--S 64 of 98
cc22:=bb2-aa.2
 

                   +---+ +-------+             +-------+
                  \|- b \|a x + b             \|a x + b
        - 2b atan(----------------) - 2b atan(----------)
                          b                      +---+
                                                \|- b
   (8)  -------------------------------------------------
                               +---+
                              \|- b
                                                     Type: Expression Integer
--R 
--R
--R                   +---+ +-------+             +-------+
--R                  \|- b \|a x + b             \|a x + b
--R        - 2b atan(----------------) - 2b atan(----------)
--R                          b                      +---+
--R                                                \|- b
--R   (8)  -------------------------------------------------
--R                               +---+
--R                              \|- b
--R                                                     Type: Expression Integer
--E

--S 65 of 98     14:92 Schaums and Axiom agree
dd22:=ratDenom cc22
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 65 of 98
aa:=integrate(sqrt(a*x+b)/x^2,x)
 

   (1)
                 +-------+              +-+
            - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
    a x log(-------------------------------) - 2\|b \|a x + b
                           x
   [----------------------------------------------------------,
                                 +-+
                              2x\|b
                +---+ +-------+
               \|- b \|a x + b      +---+ +-------+
    - a x atan(----------------) - \|- b \|a x + b
                       b
    -----------------------------------------------]
                          +---+
                        x\|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                 +-------+              +-+
--R            - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R    a x log(-------------------------------) - 2\|b \|a x + b
--R                           x
--R   [----------------------------------------------------------,
--R                                 +-+
--R                              2x\|b
--R                +---+ +-------+
--R               \|- b \|a x + b      +---+ +-------+
--R    - a x atan(----------------) - \|- b \|a x + b
--R                       b
--R    -----------------------------------------------]
--R                          +---+
--R                        x\|- b
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 66 of 98
dd:=integrate(1/(x*sqrt(a*x+b)),x)
 

                  +-------+              +-+           +---+ +-------+
             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
         log(-------------------------------)   2atan(----------------)
                            x                                 b
   (2)  [------------------------------------,- -----------------------]
                          +-+                             +---+
                         \|b                             \|- b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                  +-------+              +-+           +---+ +-------+
--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
--R         log(-------------------------------)   2atan(----------------)
--R                            x                                 b
--R   (2)  [------------------------------------,- -----------------------]
--R                          +-+                             +---+
--R                         \|b                             \|- b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 67 of 98
bb1:=-sqrt(a*x+b)/x+a/2*dd.1
 

                     +-------+              +-+
                - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
        a x log(-------------------------------) - 2\|b \|a x + b
                               x
   (3)  ----------------------------------------------------------
                                     +-+
                                  2x\|b
                                                     Type: Expression Integer
--R 
--R
--R                     +-------+              +-+
--R                - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
--R        a x log(-------------------------------) - 2\|b \|a x + b
--R                               x
--R   (3)  ----------------------------------------------------------
--R                                     +-+
--R                                  2x\|b
--R                                                     Type: Expression Integer
--E

--S 68 of 98
bb2:=-sqrt(a*x+b)/x+a/2*dd.2
 

                    +---+ +-------+
                   \|- b \|a x + b      +---+ +-------+
        - a x atan(----------------) - \|- b \|a x + b
                           b
   (4)  -----------------------------------------------
                              +---+
                            x\|- b
                                                     Type: Expression Integer
--R 
--R
--R                    +---+ +-------+
--R                   \|- b \|a x + b      +---+ +-------+
--R        - a x atan(----------------) - \|- b \|a x + b
--R                           b
--R   (4)  -----------------------------------------------
--R                              +---+
--R                            x\|- b
--R                                                     Type: Expression Integer
--E

--S 69 of 98
cc11:=bb1-aa.1
 

   (5)  0
                                                     Type: Expression Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

--S 70 of 98
cc21:=bb-aa.1
 

   (6)
                  +-------+              +-+
             - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+         +-+
   - a x log(-------------------------------) + 2\|b \|a x + b  + 2bb x\|b
                            x
   ------------------------------------------------------------------------
                                       +-+
                                    2x\|b
                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                  +-------+              +-+
--R             - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+         +-+
--R   - a x log(-------------------------------) + 2\|b \|a x + b  + 2bb x\|b
--R                            x
--R   ------------------------------------------------------------------------
--R                                       +-+
--R                                    2x\|b
--R                                                     Type: Expression Integer
--E

--S 71 of 98
cc12:=bb1-aa.2
 

   (7)
                   +-------+              +-+                +---+ +-------+
     +---+    - 2b\|a x + b  + (a x + 2b)\|b        +-+     \|- b \|a x + b
   a\|- b log(-------------------------------) + 2a\|b atan(----------------)
                             x                                      b
   --------------------------------------------------------------------------
                                     +---+ +-+
                                   2\|- b \|b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                   +-------+              +-+                +---+ +-------+
--R     +---+    - 2b\|a x + b  + (a x + 2b)\|b        +-+     \|- b \|a x + b
--R   a\|- b log(-------------------------------) + 2a\|b atan(----------------)
--R                             x                                      b
--R   --------------------------------------------------------------------------
--R                                     +---+ +-+
--R                                   2\|- b \|b
--R                                                     Type: Expression Integer
--E

--S 72 of 98     14:93 Schaums and Axiom agree
cc22:=bb2-aa.2
 

   (8)  0
                                                     Type: Expression Integer
--R 
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 73 of 98     14:94 Axiom cannot do this integral
aa:=integrate(x^m/sqrt(a*x+b),x)
 

           x       m
         ++      %L
   (1)   |   ----------- d%L
        ++    +--------+
             \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %L
--I   (1)   |   ----------- d%L
--R        ++    +--------+
--I             \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 74 of 98     14:95 Axiom cannot do this integral
aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++     m +--------+
             %L \|b + %L a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++     m +--------+
--I             %L \|b + %L a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 75 of 98     14:96 Axiom cannot do this integral
aa:=integrate(x^m*sqrt(a*x+b),x)
 

           x
         ++    m +--------+
   (1)   |   %L \|b + %L a d%L
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    m +--------+
--I   (1)   |   %L \|b + %L a d%L
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 76 of 98     14:97 Axiom cannot do this integral
aa:=integrate(sqrt(a*x+b)/x^m,x)
 

           x  +--------+
         ++  \|b + %L a
   (1)   |   ----------- d%L
        ++         m
                 %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +--------+
--I         ++  \|b + %L a
--I   (1)   |   ----------- d%L
--R        ++         m
--I                 %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 77 of 98     14:98 Axiom cannot do this integral
aa:=integrate(sqrt(a*x+b)/x^m,x)
 

           x  +--------+
         ++  \|b + %L a
   (1)   |   ----------- d%L
        ++         m
                 %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +--------+
--I         ++  \|b + %L a
--I   (1)   |   ----------- d%L
--R        ++         m
--I                 %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 78 of 98
aa:=integrate((a*x+b)^(m/2),x)
 

                     m log(a x + b)
                     --------------
                            2
        (2a x + 2b)%e
   (1)  ---------------------------
                  a m + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     m log(a x + b)
--R                     --------------
--R                            2
--R        (2a x + 2b)%e
--R   (1)  ---------------------------
--R                  a m + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 79 of 98
bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
 

                  m + 2
                  -----
                    2
        2(a x + b)
   (2)  ---------------
            a m + 2a
                                                     Type: Expression Integer
--R 
--R
--R                  m + 2
--R                  -----
--R                    2
--R        2(a x + b)
--R   (2)  ---------------
--R            a m + 2a
--R                                                     Type: Expression Integer
--E

--S 80 of 98
cc:=aa-bb
 

                     m log(a x + b)             m + 2
                     --------------             -----
                            2                     2
        (2a x + 2b)%e               - 2(a x + b)
   (3)  ---------------------------------------------
                           a m + 2a
                                                     Type: Expression Integer
--R 
--R
--R                     m log(a x + b)             m + 2
--R                     --------------             -----
--R                            2                     2
--R        (2a x + 2b)%e               - 2(a x + b)
--R   (3)  ---------------------------------------------
--R                           a m + 2a
--R                                                     Type: Expression Integer
--E

--S 81 of 98
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 82 of 98
dd:=explog cc
 

                    m + 2                       m
                    -----                       -
                      2                         2
        - 2(a x + b)      + (2a x + 2b)(a x + b)
   (5)  -----------------------------------------
                         a m + 2a
                                                     Type: Expression Integer
--R
--R                    m + 2                       m
--R                    -----                       -
--R                      2                         2
--R        - 2(a x + b)      + (2a x + 2b)(a x + b)
--R   (5)  -----------------------------------------
--R                         a m + 2a
--R                                                     Type: Expression Integer
--E

--S 83 of 98     14:99 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 84 of 98
aa:=integrate(x*(a*x+b)^(m/2),x)
 

                                           m log(a x + b)
                                           --------------
            2      2  2                2          2
        ((2a m + 4a )x  + 2a b m x - 4b )%e
   (1)  -------------------------------------------------
                         2 2     2      2
                        a m  + 6a m + 8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                           m log(a x + b)
--R                                           --------------
--R            2      2  2                2          2
--R        ((2a m + 4a )x  + 2a b m x - 4b )%e
--R   (1)  -------------------------------------------------
--R                         2 2     2      2
--R                        a m  + 6a m + 8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 85 of 98
bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2))
 

                         m + 4                         m + 2
                         -----                         -----
                           2                             2
        (2m + 4)(a x + b)      + (- 2b m - 8b)(a x + b)
   (2)  ----------------------------------------------------
                           2 2     2      2
                          a m  + 6a m + 8a
                                                     Type: Expression Integer
--R 
--R
--R                         m + 4                         m + 2
--R                         -----                         -----
--R                           2                             2
--R        (2m + 4)(a x + b)      + (- 2b m - 8b)(a x + b)
--R   (2)  ----------------------------------------------------
--R                           2 2     2      2
--R                          a m  + 6a m + 8a
--R                                                     Type: Expression Integer
--E

--S 86 of 98
cc:=aa-bb
 

   (3)
                                          m log(a x + b)
                                          --------------
           2      2  2                2          2
       ((2a m + 4a )x  + 2a b m x - 4b )%e
     + 
                          m + 4                       m + 2
                          -----                       -----
                            2                           2
       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
  /
      2 2     2      2
     a m  + 6a m + 8a
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                                          m log(a x + b)
--R                                          --------------
--R           2      2  2                2          2
--R       ((2a m + 4a )x  + 2a b m x - 4b )%e
--R     + 
--R                          m + 4                       m + 2
--R                          -----                       -----
--R                            2                           2
--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
--R  /
--R      2 2     2      2
--R     a m  + 6a m + 8a
--R                                                     Type: Expression Integer
--E

--S 87 of 98
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 88 of 98
dd:=explog cc
 

   (5)
                          m + 4                       m + 2
                          -----                       -----
                            2                           2
       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
     + 
                                                 m
                                                 -
           2      2  2                2          2
       ((2a m + 4a )x  + 2a b m x - 4b )(a x + b)
  /
      2 2     2      2
     a m  + 6a m + 8a
                                                     Type: Expression Integer
--R
--R   (5)
--R                          m + 4                       m + 2
--R                          -----                       -----
--R                            2                           2
--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
--R     + 
--R                                                 m
--R                                                 -
--R           2      2  2                2          2
--R       ((2a m + 4a )x  + 2a b m x - 4b )(a x + b)
--R  /
--R      2 2     2      2
--R     a m  + 6a m + 8a
--R                                                     Type: Expression Integer
--E

--S 89 of 98     14:100 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 90 of 98
aa:=integrate(x^2*(a*x+b)^(m/2),x)
 

   (1)
           3 2      3       3  3      2   2     2     2       2         3
       ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
    *
         m log(a x + b)
         --------------
                2
       %e
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R           3 2      3       3  3      2   2     2     2       2         3
--R       ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
--R    *
--R         m log(a x + b)
--R         --------------
--R                2
--R       %e
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91 of 98
bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
      (4*b*(a*x+b)^((m+4)/2))/(a^3*(m+4))+_
        (2*b^2*(a*x+b)^((m+2)/2))/(a^3*(m+2))
 

   (2)
                                m + 6                                   m + 4
                                -----                                   -----
          2                       2            2                          2
       (2m  + 12m + 16)(a x + b)      + (- 4b m  - 32b m - 48b)(a x + b)
     + 
                                      m + 2
                                      -----
          2 2      2       2            2
       (2b m  + 20b m + 48b )(a x + b)
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                                     Type: Expression Integer
--R 
--R
--R   (2)
--R                                m + 6                                   m + 4
--R                                -----                                   -----
--R          2                       2            2                          2
--R       (2m  + 12m + 16)(a x + b)      + (- 4b m  - 32b m - 48b)(a x + b)
--R     + 
--R                                      m + 2
--R                                      -----
--R          2 2      2       2            2
--R       (2b m  + 20b m + 48b )(a x + b)
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                                     Type: Expression Integer
--E

--S 92 of 98
cc:=aa-bb
 

   (3)
             3 2      3       3  3      2   2     2     2       2         3
         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
      *
           m log(a x + b)
           --------------
                  2
         %e
     + 
                                  m + 6                                 m + 4
                                  -----                                 -----
            2                       2          2                          2
       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
     + 
                                        m + 2
                                        -----
            2 2      2       2            2
       (- 2b m  - 20b m - 48b )(a x + b)
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R             3 2      3       3  3      2   2     2     2       2         3
--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
--R      *
--R           m log(a x + b)
--R           --------------
--R                  2
--R         %e
--R     + 
--R                                  m + 6                                 m + 4
--R                                  -----                                 -----
--R            2                       2          2                          2
--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
--R     + 
--R                                        m + 2
--R                                        -----
--R            2 2      2       2            2
--R       (- 2b m  - 20b m - 48b )(a x + b)
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                                     Type: Expression Integer
--E

--S 93 of 98
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 94 of 98
dd:=explog cc
 

   (5)
                                  m + 6                                 m + 4
                                  -----                                 -----
            2                       2          2                          2
       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
     + 
                                        m + 2
                                        -----
            2 2      2       2            2
       (- 2b m  - 20b m - 48b )(a x + b)
     + 
             3 2      3       3  3      2   2     2     2       2         3
         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
      *
                  m
                  -
                  2
         (a x + b)
  /
      3 3      3 2      3       3
     a m  + 12a m  + 44a m + 48a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                  m + 6                                 m + 4
--R                                  -----                                 -----
--R            2                       2          2                          2
--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
--R     + 
--R                                        m + 2
--R                                        -----
--R            2 2      2       2            2
--R       (- 2b m  - 20b m - 48b )(a x + b)
--R     + 
--R             3 2      3       3  3      2   2     2     2       2         3
--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
--R      *
--R                  m
--R                  -
--R                  2
--R         (a x + b)
--R  /
--R      3 3      3 2      3       3
--R     a m  + 12a m  + 44a m + 48a
--R                                                     Type: Expression Integer
--E

--S 95 of 98     14:101 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 96 of 98     14:102 Axiom cannot do this integral
aa:=integrate((a*x+b)^(m/2)/x,x)
 

                       m
                       -
           x           2
         ++  (b + %L a)
   (1)   |   ----------- d%L
        ++        %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       m
--R                       -
--R           x           2
--I         ++  (b + %L a)
--I   (1)   |   ----------- d%L
--I        ++        %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 97 of 98     14:103 Axiom cannot do this integral
aa:=integrate((a*x+b)^(m/2)/x^2,x)
 

                       m
                       -
           x           2
         ++  (b + %L a)
   (1)   |   ----------- d%L
        ++         2
                 %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                       m
--R                       -
--R           x           2
--I         ++  (b + %L a)
--I   (1)   |   ----------- d%L
--R        ++         2
--I                 %L
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 98 of 98     14:104 Axiom cannot do this integral
aa:=integrate(1/(x*(a*x+b)^(m/2)),x)
 

           x
         ++         1
   (1)   |   -------------- d%L
        ++                m
                          -
                          2
             %L (b + %L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++                m
--R                          -
--R                          2
--I             %L (b + %L a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to exprpoly.output (2010/3/27, 18:25:48).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 20
a := sin(i)*x**2 - y*x*sin(j)
 

                        2
   (1)  - x y sin(j) + x sin(i)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (1)  - x y sin(j) + x sin(i)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 20
a :: DMP([x,y], EXPR INT)
 

               2
   (2)  sin(i)x  - sin(j)x y
            Type: DistributedMultivariatePolynomial([x,y],Expression Integer)
--R 
--R
--R               2
--R   (2)  sin(i)x  - sin(j)x y
--R            Type: DistributedMultivariatePolynomial([x,y],Expression Integer)
--E 2

--S 3 of 20
leadingCoefficient %
 

   (3)  sin(i)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(i)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 20
a :: HDMP([x,y], EXPR INT)
 

               2
   (4)  sin(i)x  - sin(j)x y
 Type: HomogeneousDistributedMultivariatePolynomial([x,y],Expression Integer)
--R 
--R
--R               2
--R   (4)  sin(i)x  - sin(j)x y
--R Type: HomogeneousDistributedMultivariatePolynomial([x,y],Expression Integer)
--E 4

--S 5 of 20
a :: MPOLY([x,y], EXPR INT)
 

               2
   (5)  sin(i)x  - sin(j)y x
                       Type: MultivariatePolynomial([x,y],Expression Integer)
--R 
--R
--R               2
--R   (5)  sin(i)x  - sin(j)y x
--R                       Type: MultivariatePolynomial([x,y],Expression Integer)
--E 5

--S 6 of 20
a :: MPOLY([y,x], EXPR INT)
 

                             2
   (6)  - sin(j)x y + sin(i)x
                       Type: MultivariatePolynomial([y,x],Expression Integer)
--R 
--R
--R                             2
--R   (6)  - sin(j)x y + sin(i)x
--R                       Type: MultivariatePolynomial([y,x],Expression Integer)
--E 6

--S 7 of 20
% :: EXPR INT
 

                        2
   (7)  - x y sin(j) + x sin(i)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (7)  - x y sin(j) + x sin(i)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 20
a - %
 

   (8)  0
                                                     Type: Expression Integer
--R 
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E 8

--S 9 of 20
a :: UP(x, EXPR INT)
 

               2
   (9)  sin(i)x  - y sin(j)x
                             Type: UnivariatePolynomial(x,Expression Integer)
--R 
--R
--R               2
--R   (9)  sin(i)x  - y sin(j)x
--R                             Type: UnivariatePolynomial(x,Expression Integer)
--E 9

--S 10 of 20
a :: UP(y, EXPR INT)
 

                        2
   (10)  - x sin(j)y + x sin(i)
                             Type: UnivariatePolynomial(y,Expression Integer)
--R 
--R
--R                        2
--R   (10)  - x sin(j)y + x sin(i)
--R                             Type: UnivariatePolynomial(y,Expression Integer)
--E 10

--S 11 of 20
a :: UP(y, UP(x, EXPR INT))
 

                              2
   (11)  - sin(j)x y + sin(i)x
     Type: UnivariatePolynomial(y,UnivariatePolynomial(x,Expression Integer))
--R 
--R
--R                              2
--R   (11)  - sin(j)x y + sin(i)x
--R     Type: UnivariatePolynomial(y,UnivariatePolynomial(x,Expression Integer))
--E 11

--S 12 of 20
% :: EXPR INT
 

                         2
   (12)  - x y sin(j) + x sin(i)
                                                     Type: Expression Integer
--R 
--R
--R                         2
--R   (12)  - x y sin(j) + x sin(i)
--R                                                     Type: Expression Integer
--E 12

--S 13 of 20
a - %
 

   (13)  0
                                                     Type: Expression Integer
--R 
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 20
b : EXPR INT := (x - 2*y + 3*z)**3
 

   (14)
      3                 2       2             2       3        2     2     3
   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
                                                     Type: Expression Integer
--R 
--R
--R   (14)
--R      3                 2       2             2       3        2     2     3
--R   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
--R                                                     Type: Expression Integer
--E 14

--S 15 of 20
b :: DMP([x,y,z], Integer)
 

   (15)
    3     2      2         2                  2     3      2         2      3
   x  - 6x y + 9x z + 12x y  - 36x y z + 27x z  - 8y  + 36y z - 54y z  + 27z
                     Type: DistributedMultivariatePolynomial([x,y,z],Integer)
--R 
--R
--R   (15)
--R    3     2      2         2                  2     3      2         2      3
--R   x  - 6x y + 9x z + 12x y  - 36x y z + 27x z  - 8y  + 36y z - 54y z  + 27z
--R                     Type: DistributedMultivariatePolynomial([x,y,z],Integer)
--E 15

--S 16 of 20
b :: HDMP([y,x,z], Integer)
 

   (16)
       3      2        2    3      2                2         2        2      3
   - 8y  + 12y x - 6y x  + x  + 36y z - 36y x z + 9x z - 54y z  + 27x z  + 27z
          Type: HomogeneousDistributedMultivariatePolynomial([y,x,z],Integer)
--R 
--R
--R   (16)
--R       3      2        2    3      2                2         2        2      3
--R   - 8y  + 12y x - 6y x  + x  + 36y z - 36y x z + 9x z - 54y z  + 27x z  + 27z
--R          Type: HomogeneousDistributedMultivariatePolynomial([y,x,z],Integer)
--E 16

--S 17 of 20
b - (% :: EXPR INT)
 

   (17)  0
                                                     Type: Expression Integer
--R 
--R
--R   (17)  0
--R                                                     Type: Expression Integer
--E 17

--S 18 of 20
b :: MPOLY([z,y,x], Integer)
 

   (18)
      3                 2       2             2       3        2     2     3
   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
                                Type: MultivariatePolynomial([z,y,x],Integer)
--R 
--R
--R   (18)
--R      3                 2       2             2       3        2     2     3
--R   27z  + (- 54y + 27x)z  + (36y  - 36x y + 9x )z - 8y  + 12x y  - 6x y + x
--R                                Type: MultivariatePolynomial([z,y,x],Integer)
--E 18

--S 19 of 20
b :: UP(y, HDMP([x,z], Integer))
 

   (19)
       3               2        2              2      3     2         2      3
   - 8y  + (12x + 36z)y  + (- 6x  - 36x z - 54z )y + x  + 9x z + 27x z  + 27z
Type: UnivariatePolynomial(y,HomogeneousDistributedMultivariatePolynomial([x,z],Integer))
--R 
--R
--R   (19)
--R       3               2        2              2      3     2         2      3
--R   - 8y  + (12x + 36z)y  + (- 6x  - 36x z - 54z )y + x  + 9x z + 27x z  + 27z
--RType: UnivariatePolynomial(y,HomogeneousDistributedMultivariatePolynomial([x,z],Integer))
--E 19

--S 20 of 20
b - (% :: EXPR INT)
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 20
)spool 
 
Starts dribbling to gstbl.output (2010/3/27, 18:26:47).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 1
patrons: GeneralSparseTable(String, Integer, KeyedAccessFile(Integer), 0) := table() ;
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "kaf1680.sdata"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   File is not readable
--I   "kaf1414.sdata"
--R
--R   Continuing to read the file...
--R
--E 1
)spool 
 
Starts dribbling to LinearOrdinaryDifferentialOperator1.output (2010/3/27, 18:46:0).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
RFZ := Fraction UnivariatePolynomial('x, Integer)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 20
x : RFZ := 'x
 

   (2)  x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (2)  x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 2

--S 3 of 20
Dx : LODO1 RFZ := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 3

--S 4 of 20
b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 4

--S 5 of 20
a : LODO1 RFZ := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 5

--S 6 of 20
p := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 6

--S 7 of 20
(a*b - b*a) p
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 20
ld := leftDivide(a,b)
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 8

--S 9 of 20
a = b * ld.quotient + ld.remainder
 

           3 3       2        2         7     3 3       2        2         7
   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
                                        x                                  x
Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7     3 3       2        2         7
--R   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                        x                                  x
--RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 9

--S 10 of 20
rd := rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 10

--S 11 of 20
a = rd.quotient * b + rd.remainder
 

            3 3       2        2         7     3 3       2        2         7
   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
                                         x                                  x
Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7     3 3       2        2         7
--R   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                         x                                  x
--RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 11

--S 12 of 20
rightQuotient(a,b)
 

   (12)  5x D + 7
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (12)  5x D + 7
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 12

--S 13 of 20
rightRemainder(a,b)
 

               5
   (13)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (13)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 20
leftExactQuotient(a,b)
 

   (14)  5x D + 7
Type: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...)
--R 
--R
--R   (14)  5x D + 7
--RType: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...)
--E 14

--S 15 of 20
e := leftGcd(a,b)
 

           2 2        1
   (15)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (15)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 20
leftRemainder(a, e)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 20
rightRemainder(a, e)
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18 of 20
f := rightLcm(a,b)
 

            3 3       2        2         7
   (18)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (18)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 18

--S 19 of 20
rightRemainder(f, b)
 

               5
   (19)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (19)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 20
leftRemainder(f, b)
 

   (20)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (20)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 20
)spool
 
Starts dribbling to sae.output (2010/3/27, 18:37:6).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
pol1:=x^2+1
 

         2
   (1)  x  + 1
                                                     Type: Polynomial Integer
--R
--R         2
--R   (1)  x  + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 6
pol2:=z^3-2
 

         3
   (2)  z  - 2
                                                     Type: Polynomial Integer
--R
--R         3
--R   (2)  z  - 2
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 6
primrec:=primitiveElement([pol1,pol2],[x,z])$PrimitiveElement(FRAC(INT))
 

   (3)
   [coef= [- 1,- 1],

     poly =
         6  5    9  4   20  3   39  2   39     91
       [-- ?  + -- ?  + -- ?  + -- ?  + -- ? - --,
        11      22      11      11      11     22
           6  5    9  4   20  3   39  2   50     91
        - -- ?  - -- ?  - -- ?  - -- ?  - -- ? + --]
          11      22      11      11      11     22
     ,
           6     4     3     2
    prim= ?  + 3?  + 4?  + 3?  - 12? + 5]
Type: Record(coef: List Integer,poly: List SparseUnivariatePolynomial Fraction Integer,prim: SparseUnivariatePolynomial Fraction Integer)
--I
--I   (3)
--I   [coef= [- 3,- 1],
--I
--I     poly =
--I            2   5     1   4    20  3    13   2   2431      91
--I       [- ---- ?  - ---- ?  - --- ?  - ---- ?  - ---- ? + ---,
--I          1293      7758      431      1293      3879     862
--I         2   5     1   4    60  3    13  2   1138     273
--I        --- ?  + ---- ?  + --- ?  + --- ?  + ---- ? - ---]
--I        431      2586      431      431      1293     862
--I     ,
--I           6      4     3       2
--I    prim= ?  + 27?  + 4?  + 243?  - 108? + 733]
--IType: Record(coef: List Integer,poly: List SparseUnivariatePolynomial Fraction Integer,prim: SparseUnivariatePolynomial Fraction Integer)
--E 3

--S 4 of 6
Ae:=SAE(FRAC(INT),SparseUnivariatePolynomial(FRAC(INT)),primrec.prim)
 

   (4)
  SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction
   Integer,?**6+3*?**4+4*?**3+3*?*?+(-12*?)+5)
                                                                 Type: Domain
--I
--I   (4)
--I  SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction
--I   Integer,?**6+27*?**4+4*?**3+243*?*?+(-108*?)+733)
--I                                                                 Type: Domain
--E 4

--S 5 of 6
(primrec.poly.1::Ae)^2
 

   (5)  - 1
Type: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+3*?**4+4*?**3+3*?*?+(-12*?)+5)
--R
--R   (5)  - 1
--IType: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+27*?**4+4*?**3+243*?*?+(-108*?)+733)
--E 5

--S 6 of 6
(primrec.poly.2::Ae)^3
 

   (6)  2
Type: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+3*?**4+4*?**3+3*?*?+(-12*?)+5)
--R
--R   (6)  2
--IType: SimpleAlgebraicExtension(Fraction Integer,SparseUnivariatePolynomial Fraction Integer,?**6+27*?**4+4*?**3+243*?*?+(-108*?)+733)
--E 6

)spool 
 
Starts dribbling to Table.output (2010/3/27, 18:46:37).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 18
t: Table(Polynomial Integer, String) := table()
 

   (1)  table()
                                       Type: Table(Polynomial Integer,String)
--R 
--R
--R   (1)  table()
--R                                       Type: Table(Polynomial Integer,String)
--E 1

--S 2 of 18
setelt(t, x**2 - 1, "Easy to factor")
 

   (2)  "Easy to factor"
                                                                 Type: String
--R 
--R
--R   (2)  "Easy to factor"
--R                                                                 Type: String
--E 2

--S 3 of 18
t(x**3 + 1) := "Harder to factor"
 

   (3)  "Harder to factor"
                                                                 Type: String
--R 
--R
--R   (3)  "Harder to factor"
--R                                                                 Type: String
--E 3

--S 4 of 18
t(x) := "The easiest to factor"
 

   (4)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (4)  "The easiest to factor"
--R                                                                 Type: String
--E 4

--S 5 of 18
elt(t, x)
 

   (5)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (5)  "The easiest to factor"
--R                                                                 Type: String
--E 5

--S 6 of 18
t.x
 

   (6)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (6)  "The easiest to factor"
--R                                                                 Type: String
--E 6

--S 7 of 18
t x
 

   (7)  "The easiest to factor"
                                                                 Type: String
--R 
--R
--R   (7)  "The easiest to factor"
--R                                                                 Type: String
--E 7

--S 8 of 18
t.(x**2 - 1)
 

   (8)  "Easy to factor"
                                                                 Type: String
--R 
--R
--R   (8)  "Easy to factor"
--R                                                                 Type: String
--E 8

--S 9 of 18
t (x**3 + 1)
 

   (9)  "Harder to factor"
                                                                 Type: String
--R 
--R
--R   (9)  "Harder to factor"
--R                                                                 Type: String
--E 9

--S 10 of 18
keys t
 

             3      2
   (10)  [x,x  + 1,x  - 1]
                                                Type: List Polynomial Integer
--R 
--R
--R             3      2
--R   (10)  [x,x  + 1,x  - 1]
--R                                                Type: List Polynomial Integer
--E 10

--S 11 of 18
search(x, t)
 

   (11)  "The easiest to factor"
                                                      Type: Union(String,...)
--R 
--R
--R   (11)  "The easiest to factor"
--R                                                      Type: Union(String,...)
--E 11

--S 12 of 18
search(x**2, t)
 

   (12)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (12)  "failed"
--R                                                    Type: Union("failed",...)
--E 12

--S 13 of 18
search(x**2, t) case "failed"
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 18
remove!(x**2-1, t)
 

   (14)  "Easy to factor"
                                                      Type: Union(String,...)
--R 
--R
--R   (14)  "Easy to factor"
--R                                                      Type: Union(String,...)
--E 14

--S 15 of 18
remove!(x-1, t)
 

   (15)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (15)  "failed"
--R                                                    Type: Union("failed",...)
--E 15

--S 16 of 18
#t
 

   (16)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 18
members t
 

   (17)  ["The easiest to factor","Harder to factor"]
                                                            Type: List String
--R 
--R
--R   (17)  ["The easiest to factor","Harder to factor"]
--R                                                            Type: List String
--E 17

--S 18 of 18
count(s: String +-> prefix?("Hard", s), t)
 

   (18)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  1
--R                                                        Type: PositiveInteger
--E 18
)spool
 
Starts dribbling to ElementaryFunction.output (2010/3/27, 18:41:57).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 32
)trace EF
 
 
   Parameterized constructors traced:
      EF
--R 
--R 
--R   Parameterized constructors traced:
--R      EF
--E 1

--S 2 of 32
D(cos(3*x+6*y),x)
 
1<enter ElementaryFunction.cos,64 : ((1 #<vector 0936471c> (1 0 . 6) (0 1 #<vector 0936d55c> (1 0 . 3))) 0 . 1)
 1<enter ElementaryFunction.iicos,154 : ((1 #<vector 0936471c> (1 0 . 6) (0 1 #<vector 0936d55c> (1 0 . 3))) 0 . 1)
  1<enter ElementaryFunction.iisqrt2,58 : 
  1>exit  ElementaryFunction.iisqrt2,58 : ((1 #<vector 094064d0> (1 0 . 1)) 0 . 1)
  1<enter ElementaryFunction.iisqrt3,59 : 
  1>exit  ElementaryFunction.iisqrt3,59 : ((1 #<vector 0940cc40> (1 0 . 1)) 0 . 1)
  1<enter ElementaryFunction.specialTrigs,116 : ((1 #<vector 0936471c> (1 0 . 6) (0 1 #<vector 0936d55c> (1 0 . 3))) 0 . 1)\((((0 . 1) 0 . 1)) (((0 . -1) 0 . 1)) (((0 . 0) 0 . 1)) (((0 . 0) 0 . 1)) (((0 . 1) 0 . 2)) (((0 . -1) 0 . 2)) (((0 . -1) 0 . 2)) (((0 . 1) 0 . 2)) (((1 #<vector 094064d0> (1 0 . 1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . -1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . -1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . 1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . 1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . -1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . -1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . 1)) 0 . 2)))
   1<enter ElementaryFunction.pi,46 : 
   1>exit  ElementaryFunction.pi,46 : ((1 #<vector 09377914> (1 0 . 1)) 0 . 1)
  1>exit  ElementaryFunction.specialTrigs,116 : (1 . "failed")
 1>exit  ElementaryFunction.iicos,154 : ((1 #<vector 09403e8c> (1 0 . 1)) 0 . 1)
1>exit  ElementaryFunction.cos,64 : ((1 #<vector 09403e8c> (1 0 . 1)) 0 . 1)
1<enter ElementaryFunction.sin,63 : ((1 #<vector 0936471c> (1 0 . 6) (0 1 #<vector 0936d55c> (1 0 . 3))) 0 . 1)
 1<enter ElementaryFunction.iisin,152 : ((1 #<vector 0936471c> (1 0 . 6) (0 1 #<vector 0936d55c> (1 0 . 3))) 0 . 1)
  1<enter ElementaryFunction.iisqrt2,58 : 
  1>exit  ElementaryFunction.iisqrt2,58 : ((1 #<vector 094064d0> (1 0 . 1)) 0 . 1)
  1<enter ElementaryFunction.iisqrt3,59 : 
  1>exit  ElementaryFunction.iisqrt3,59 : ((1 #<vector 0940cc40> (1 0 . 1)) 0 . 1)
  1<enter ElementaryFunction.specialTrigs,116 : ((1 #<vector 0936471c> (1 0 . 6) (0 1 #<vector 0936d55c> (1 0 . 3))) 0 . 1)\((((0 . 0) 0 . 1)) (((0 . 0) 0 . 1)) (((0 . 1) 0 . 1)) (((0 . -1) 0 . 1)) (((1 #<vector 0940cc40> (1 0 . 1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . 1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . -1)) 0 . 2)) (((1 #<vector 0940cc40> (1 0 . -1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . 1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . 1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . -1)) 0 . 2)) (((1 #<vector 094064d0> (1 0 . -1)) 0 . 2)) (((0 . 1) 0 . 2)) (((0 . 1) 0 . 2)) (((0 . -1) 0 . 2)) (((0 . -1) 0 . 2)))
   1<enter ElementaryFunction.pi,46 : 
   1>exit  ElementaryFunction.pi,46 : ((1 #<vector 09377914> (1 0 . 1)) 0 . 1)
  1>exit  ElementaryFunction.specialTrigs,116 : (1 . "failed")
 1>exit  ElementaryFunction.iisin,152 : ((1 #<vector 09403498> (1 0 . 1)) 0 . 1)
1>exit  ElementaryFunction.sin,63 : ((1 #<vector 09403498> (1 0 . 1)) 0 . 1)

   (1)  - 3sin(6y + 3x)
                                                     Type: Expression Integer
--I 
--I1<enter ElementaryFunction.cos,64 : ((1 #<vector 0941ef18> (1 0 . 6) (0 1 #<vector 0941eee0> (1 0 . 3))) 0 . 1)
--I 1<enter ElementaryFunction.iicos,154 : ((1 #<vector 0941ef18> (1 0 . 6) (0 1 #<vector 0941eee0> (1 0 . 3))) 0 . 1)
--I  1<enter ElementaryFunction.iisqrt2,58 : 
--I  1>exit  ElementaryFunction.iisqrt2,58 : ((1 #<vector 0917aab8> (1 0 . 1)) 0 . 1)
--I  1<enter ElementaryFunction.iisqrt3,59 : 
--I  1>exit  ElementaryFunction.iisqrt3,59 : ((1 #<vector 0917a1dc> (1 0 . 1)) 0 . 1)
--I  1<enter ElementaryFunction.specialTrigs,116 : ((1 #<vector 0941ef18> (1 0 . 6) (0 1 #<vector 0941eee0> (1 0 . 3))) 0 . 1)\((((0 . 1) 0 . 1)) (((0 . -1) 0 . 1)) (((0 . 0) 0 . 1)) (((0 . 0) 0 . 1)) (((0 . 1) 0 . 2)) (((0 . -1) 0 . 2)) (((0 . -1) 0 . 2)) (((0 . 1) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . 1)) 0 . 2)))
--I   1<enter ElementaryFunction.pi,46 : 
--I   1>exit  ElementaryFunction.pi,46 : ((1 #<vector 090c3a64> (1 0 . 1)) 0 . 1)
--I  1>exit  ElementaryFunction.specialTrigs,116 : (1 . "failed")
--I 1>exit  ElementaryFunction.iicos,154 : ((1 #<vector 0941ed74> (1 0 . 1)) 0 . 1)
--I1>exit  ElementaryFunction.cos,64 : ((1 #<vector 0941ed74> (1 0 . 1)) 0 . 1)
--I1<enter ElementaryFunction.sin,63 : ((1 #<vector 0941ef18> (1 0 . 6) (0 1 #<vector 0941eee0> (1 0 . 3))) 0 . 1)
--I 1<enter ElementaryFunction.iisin,152 : ((1 #<vector 0941ef18> (1 0 . 6) (0 1 #<vector 0941eee0> (1 0 . 3))) 0 . 1)
--I  1<enter ElementaryFunction.iisqrt2,58 : 
--I  1>exit  ElementaryFunction.iisqrt2,58 : ((1 #<vector 0917aab8> (1 0 . 1)) 0 . 1)
--I  1<enter ElementaryFunction.iisqrt3,59 : 
--I  1>exit  ElementaryFunction.iisqrt3,59 : ((1 #<vector 0917a1dc> (1 0 . 1)) 0 . 1)
--I  1<enter ElementaryFunction.specialTrigs,116 : ((1 #<vector 0941ef18> (1 0 . 6) (0 1 #<vector 0941eee0> (1 0 . 3))) 0 . 1)\((((0 . 0) 0 . 1)) (((0 . 0) 0 . 1)) (((0 . 1) 0 . 1)) (((0 . -1) 0 . 1)) (((1 #<vector 0917a1dc> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917a1dc> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . 1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . -1)) 0 . 2)) (((1 #<vector 0917aab8> (1 0 . -1)) 0 . 2)) (((0 . 1) 0 . 2)) (((0 . 1) 0 . 2)) (((0 . -1) 0 . 2)) (((0 . -1) 0 . 2)))
--I   1<enter ElementaryFunction.pi,46 : 
--I   1>exit  ElementaryFunction.pi,46 : ((1 #<vector 090c3a64> (1 0 . 1)) 0 . 1)
--I  1>exit  ElementaryFunction.specialTrigs,116 : (1 . "failed")
--I 1>exit  ElementaryFunction.iisin,152 : ((1 #<vector 0941eb60> (1 0 . 1)) 0 . 1)
--I1>exit  ElementaryFunction.sin,63 : ((1 #<vector 0941eb60> (1 0 . 1)) 0 . 1)
--R
--R   (1)  - 3sin(6y + 3x)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 32
)trace )off
 

   Nothing is traced now.

--R 
--R
--R   Nothing is traced now.
--R
--E 3


--S 4 of 32
D(sin(3*x+6*y),x)
 

   (2)  3cos(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  3cos(6y + 3x)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 32
D(cos(3*x+6*y),x)
 

   (3)  - 3sin(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - 3sin(6y + 3x)
--R                                                     Type: Expression Integer
--E 5


--S 6 of 32
D(tan(3*x+6*y),x)
 

                     2
   (4)  3tan(6y + 3x)  + 3
                                                     Type: Expression Integer
--R 
--R
--R                     2
--R   (4)  3tan(6y + 3x)  + 3
--R                                                     Type: Expression Integer
--E 6

--S 7 of 32
simplify ((3*tan(6*y+3*x)^2+3) - (3*sec(3*x+6*y)^2))
 

   (5)  0
                                                     Type: Expression Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E 7


--S 8 of 32
D(cot(3*x+6*y),x)
 

                       2
   (6)  - 3cot(6y + 3x)  - 3
                                                     Type: Expression Integer
--R 
--R
--R                       2
--R   (6)  - 3cot(6y + 3x)  - 3
--R                                                     Type: Expression Integer
--E 8

--S 9 of 32
simplify ((-3*cot(6*y+3*x)^2-3) -(-3*csc(3*x+6*y)^2))
 

   (7)  0
                                                     Type: Expression Integer
--R 
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E 9

--S 10 of 32
D(sec(3*x+6*y),x)
 

   (8)  3sec(6y + 3x)tan(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (8)  3sec(6y + 3x)tan(6y + 3x)
--R                                                     Type: Expression Integer
--E 10

--S 11 of 32
D(csc(3*x+6*y),x)
 

   (9)  - 3cot(6y + 3x)csc(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (9)  - 3cot(6y + 3x)csc(6y + 3x)
--R                                                     Type: Expression Integer
--E 11

--S 12 of 32
D(asin(3*x+6*y),x)
 

                      3
   (10)  ---------------------------
          +------------------------+
          |     2             2
         \|- 36y  - 36x y - 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                      3
--R   (10)  ---------------------------
--R          +------------------------+
--R          |     2             2
--R         \|- 36y  - 36x y - 9x  + 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 32
D(acos(3*x+6*y),x)
 

                        3
   (11)  - ---------------------------
            +------------------------+
            |     2             2
           \|- 36y  - 36x y - 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                        3
--R   (11)  - ---------------------------
--R            +------------------------+
--R            |     2             2
--R           \|- 36y  - 36x y - 9x  + 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 32
D(atan(3*x+6*y),x)
 

                    3
   (12)  ----------------------
            2             2
         36y  + 36x y + 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                    3
--R   (12)  ----------------------
--R            2             2
--R         36y  + 36x y + 9x  + 1
--R                                                     Type: Expression Integer
--E 14

--S 15 of 32
D(acot(3*x+6*y),x)
 

                      3
   (13)  - ----------------------
              2             2
           36y  + 36x y + 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                      3
--R   (13)  - ----------------------
--R              2             2
--R           36y  + 36x y + 9x  + 1
--R                                                     Type: Expression Integer
--E 15


--S 16 of 32
D(asec(3*x+6*y),x)
 

                         1
   (14)  ---------------------------------
                  +----------------------+
                  |   2             2
         (2y + x)\|36y  + 36x y + 9x  - 1
                                                     Type: Expression Integer
--R 
--R
--R                         1
--R   (14)  ---------------------------------
--R                  +----------------------+
--R                  |   2             2
--R         (2y + x)\|36y  + 36x y + 9x  - 1
--R                                                     Type: Expression Integer
--E 16


--S 17 of 32
3/((3*x+6*y)*sqrt((3*x+6*y)^2-1))
 

                         1
   (15)  ---------------------------------
                  +----------------------+
                  |   2             2
         (2y + x)\|36y  + 36x y + 9x  - 1
                                                     Type: Expression Integer
--R 
--R
--R                         1
--R   (15)  ---------------------------------
--R                  +----------------------+
--R                  |   2             2
--R         (2y + x)\|36y  + 36x y + 9x  - 1
--R                                                     Type: Expression Integer
--E 17


--S 18 of 32
D(acsc(3*x+6*y),x)
 

                           1
   (16)  - ---------------------------------
                    +----------------------+
                    |   2             2
           (2y + x)\|36y  + 36x y + 9x  - 1
                                                     Type: Expression Integer
--R 
--R
--R                           1
--R   (16)  - ---------------------------------
--R                    +----------------------+
--R                    |   2             2
--R           (2y + x)\|36y  + 36x y + 9x  - 1
--R                                                     Type: Expression Integer
--E 18

--S 19 of 32
D(sinh(3*x+6*y),x)
 

   (17)  3cosh(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (17)  3cosh(6y + 3x)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 32
D(cosh(3*x+6*y),x)
 

   (18)  3sinh(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (18)  3sinh(6y + 3x)
--R                                                     Type: Expression Integer
--E 20


--S 21 of 32
D(tanh(3*x+6*y),x)
 

                         2
   (19)  - 3tanh(6y + 3x)  + 3
                                                     Type: Expression Integer
--R 
--R
--R                         2
--R   (19)  - 3tanh(6y + 3x)  + 3
--R                                                     Type: Expression Integer
--E 21

--S 22 of 32
simplify ((-3*tanh(6*y+3*x)^2+3)-(3*sech(3*x+6*y)^2))
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 22

Mathematica and Maxima return
 
  Line 238: --R 
  Line 239: --R
  Line 240: --R   (20)  0
  Line 241: --R                                                     Type: Expression Integer
  Line 242: --E 22
  Line 243: 
  Line 244: Mathematica and Maxima return
           .......................A
  Error  A: Improper syntax.
   1 error(s) parsing 
\[-3 csch(3*x+6*y)^2\]
 
 
Daly Bug
   Cannot find a definition or applicable library operation named 3 
      with argument type(s) 
                             Expression Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
Maple returns Axiom's answer. Both are equivalent.
 
  Line 246: Maple returns Axiom's answer. Both are equivalent.
           .................................................A
  Error  A: syntax error at top level
  Error  A: Improper syntax.
   2 error(s) parsing 

--S 23 of 32
D(coth(3*x+6*y),x)
 

                         2
   (21)  - 3coth(6y + 3x)  + 3
                                                     Type: Expression Integer
--R 
--R
--R                         2
--R   (21)  - 3coth(6y + 3x)  + 3
--R                                                     Type: Expression Integer
--E 23

--S 24 of 32
simplify ((-3*coth(6*y+3*x)^2+3) - (-3*csch(3*x+6*y)^2))
 

   (22)  0
                                                     Type: Expression Integer
--R 
--R
--R   (22)  0
--R                                                     Type: Expression Integer
--E 24

--S 25 of 32
D(sech(3*x+6*y),x)
 

   (23)  - 3sech(6y + 3x)tanh(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (23)  - 3sech(6y + 3x)tanh(6y + 3x)
--R                                                     Type: Expression Integer
--E 25

--S 26 of 32
D(csch(3*x+6*y),x)
 

   (24)  - 3coth(6y + 3x)csch(6y + 3x)
                                                     Type: Expression Integer
--R 
--R
--R   (24)  - 3coth(6y + 3x)csch(6y + 3x)
--R                                                     Type: Expression Integer
--E 26

--S 27 of 32
D(asinh(3*x+6*y),x)
 

                     3
   (25)  -------------------------
          +----------------------+
          |   2             2
         \|36y  + 36x y + 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                     3
--R   (25)  -------------------------
--R          +----------------------+
--R          |   2             2
--R         \|36y  + 36x y + 9x  + 1
--R                                                     Type: Expression Integer
--E 27


--S 28 of 32
D(acosh(3*x+6*y),x)
 

                     3
   (26)  -------------------------
          +----------------------+
          |   2             2
         \|36y  + 36x y + 9x  - 1
                                                     Type: Expression Integer
--R 
--R
--R                     3
--R   (26)  -------------------------
--R          +----------------------+
--R          |   2             2
--R         \|36y  + 36x y + 9x  - 1
--R                                                     Type: Expression Integer
--E 28

--S 29 of 32
D(atanh(3*x+6*y),x)
 

                      3
   (27)  - ----------------------
              2             2
           36y  + 36x y + 9x  - 1
                                                     Type: Expression Integer
--R 
--R
--R                      3
--R   (27)  - ----------------------
--R              2             2
--R           36y  + 36x y + 9x  - 1
--R                                                     Type: Expression Integer
--E 29

--S 30 of 32
D(acoth(3*x+6*y),x)
 

                      3
   (28)  - ----------------------
              2             2
           36y  + 36x y + 9x  - 1
                                                     Type: Expression Integer
--R 
--R
--R                      3
--R   (28)  - ----------------------
--R              2             2
--R           36y  + 36x y + 9x  - 1
--R                                                     Type: Expression Integer
--E 30


--S 31 of 32
D(asech(3*x+6*y),x)
 

                            1
   (29)  - -----------------------------------
                    +------------------------+
                    |     2             2
           (2y + x)\|- 36y  - 36x y - 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                            1
--R   (29)  - -----------------------------------
--R                    +------------------------+
--R                    |     2             2
--R           (2y + x)\|- 36y  - 36x y - 9x  + 1
--R                                                     Type: Expression Integer
--E 31


--S 32 of 32
D(acsch(3*x+6*y),x)
 

                           1
   (30)  - ---------------------------------
                    +----------------------+
                    |   2             2
           (2y + x)\|36y  + 36x y + 9x  + 1
                                                     Type: Expression Integer
--R 
--R
--R                           1
--R   (30)  - ---------------------------------
--R                    +----------------------+
--R                    |   2             2
--R           (2y + x)\|36y  + 36x y + 9x  + 1
--R                                                     Type: Expression Integer
--E 32

)spool
 
Starts dribbling to XPolynomial.output (2010/3/27, 18:46:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 14
poly := XPolynomial(Integer)
 

   (1)  XPolynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  XPolynomial Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 14
pr: poly := 2*x + 3*y-5 
 

   (2)  - 5 + x 2 + y 3
                                                    Type: XPolynomial Integer
--R 
--R
--R   (2)  - 5 + x 2 + y 3
--R                                                    Type: XPolynomial Integer
--E 2

--S 3 of 14
pr2: poly := pr*pr
 

   (3)  25 + x(- 20 + x 4 + y 6) + y(- 30 + x 6 + y 9)
                                                    Type: XPolynomial Integer
--R 
--R
--R   (3)  25 + x(- 20 + x 4 + y 6) + y(- 30 + x 6 + y 9)
--R                                                    Type: XPolynomial Integer
--E 3

--S 4 of 14
pd  := expand pr
 

   (4)  - 5 + 2x + 3y
                                 Type: XDistributedPolynomial(Symbol,Integer)
--R 
--R
--R   (4)  - 5 + 2x + 3y
--R                                 Type: XDistributedPolynomial(Symbol,Integer)
--E 4

--S 5 of 14
pd2 := pd*pd
 

                           2                   2
   (5)  25 - 20x - 30y + 4x  + 6x y + 6y x + 9y
                                 Type: XDistributedPolynomial(Symbol,Integer)
--R 
--R
--R                           2                   2
--R   (5)  25 - 20x - 30y + 4x  + 6x y + 6y x + 9y
--R                                 Type: XDistributedPolynomial(Symbol,Integer)
--E 5

--S 6 of 14
expand(pr2) - pd2
 

   (6)  0
                                 Type: XDistributedPolynomial(Symbol,Integer)
--R 
--R
--R   (6)  0
--R                                 Type: XDistributedPolynomial(Symbol,Integer)
--E 6

--S 7 of 14
qr :=  pr**3
 

   (7)
     - 125 + x(150 + x(- 60 + x 8 + y 12) + y(- 90 + x 12 + y 18))
   + 
     y(225 + x(- 90 + x 12 + y 18) + y(- 135 + x 18 + y 27))
                                                    Type: XPolynomial Integer
--R 
--R
--R   (7)
--R     - 125 + x(150 + x(- 60 + x 8 + y 12) + y(- 90 + x 12 + y 18))
--R   + 
--R     y(225 + x(- 90 + x 12 + y 18) + y(- 135 + x 18 + y 27))
--R                                                    Type: XPolynomial Integer
--E 7

--S 8 of 14
qd :=  pd**3
 

   (8)
                              2                       2     3      2
     - 125 + 150x + 225y - 60x  - 90x y - 90y x - 135y  + 8x  + 12x y + 12x y x
   + 
          2        2                2       3
     18x y  + 12y x  + 18y x y + 18y x + 27y
                                 Type: XDistributedPolynomial(Symbol,Integer)
--R 
--R
--R   (8)
--R                              2                       2     3      2
--R     - 125 + 150x + 225y - 60x  - 90x y - 90y x - 135y  + 8x  + 12x y + 12x y x
--R   + 
--R          2        2                2       3
--R     18x y  + 12y x  + 18y x y + 18y x + 27y
--R                                 Type: XDistributedPolynomial(Symbol,Integer)
--E 8

--S 9 of 14
trunc(qd,2)
 

                                 2                       2
   (9)  - 125 + 150x + 225y - 60x  - 90x y - 90y x - 135y
                                 Type: XDistributedPolynomial(Symbol,Integer)
--R 
--R
--R                                 2                       2
--R   (9)  - 125 + 150x + 225y - 60x  - 90x y - 90y x - 135y
--R                                 Type: XDistributedPolynomial(Symbol,Integer)
--E 9

--S 10 of 14
trunc(qr,2)
 

   (10)  - 125 + x(150 + x(- 60) + y(- 90)) + y(225 + x(- 90) + y(- 135))
                                                    Type: XPolynomial Integer
--R 
--R
--R   (10)  - 125 + x(150 + x(- 60) + y(- 90)) + y(225 + x(- 90) + y(- 135))
--R                                                    Type: XPolynomial Integer
--E 10

--S 11 of 14
Word := OrderedFreeMonoid Symbol
 

   (11)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (11)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 11

--S 12 of 14
w: Word := x*y**2
 

            2
   (12)  x y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R            2
--R   (12)  x y
--R                                               Type: OrderedFreeMonoid Symbol
--E 12

--S 13 of 14
rquo(qr,w)
 

   (13)  18
                                                    Type: XPolynomial Integer
--R 
--R
--R   (13)  18
--R                                                    Type: XPolynomial Integer
--E 13

--S 14 of 14
sh(pr,w::poly)
 

   (14)  x(x y y 4 + y(x y 2 + y(- 5 + x 2 + y 9))) + y x y y 3
                                                    Type: XPolynomial Integer
--R 
--R
--R   (14)  x(x y y 4 + y(x y 2 + y(- 5 + x 2 + y 9))) + y x y y 3
--R                                                    Type: XPolynomial Integer
--E 14
)spool
 
Starts dribbling to hexadec.output (2010/3/27, 18:26:50).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
r := hex(22/7)
 

          ___
   (1)  3.249
                                                   Type: HexadecimalExpansion
--R 
--R
--R          ___
--R   (1)  3.249
--R                                                   Type: HexadecimalExpansion
--E 1

--S 2 of 7
r + hex(6/7)
 

   (2)  4
                                                   Type: HexadecimalExpansion
--R 
--R
--R   (2)  4
--R                                                   Type: HexadecimalExpansion
--E 2

--S 3 of 7
[hex(1/i) for i in 350..354] 
 

   (3)
       _______________    _________      _____    ______________________
   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
       _____________________________
    0.00B92143FA36F5E02E4850FE8DBD78]
                                              Type: List HexadecimalExpansion
--R 
--R
--R   (3)
--R       _______________    _________      _____    ______________________
--R   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
--R       _____________________________
--R    0.00B92143FA36F5E02E4850FE8DBD78]
--R                                              Type: List HexadecimalExpansion
--E 3

--S 4 of 7
hex(1/1007) 
 

   (4)
   0.
     OVERBAR
        0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
          DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
                                                   Type: HexadecimalExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
--R          DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
--R                                                   Type: HexadecimalExpansion
--E 4

--S 5 of 7
p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)
 

            2     _      ___
   (5)  0.4x  + 0.Ax + 0.71C
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R            2     _      ___
--R   (5)  0.4x  + 0.Ax + 0.71C
--R                                        Type: Polynomial HexadecimalExpansion
--E 5

--S 6 of 7
q := D(p, x)
 

                 _
   (6)  0.8x + 0.A
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R                 _
--R   (6)  0.8x + 0.A
--R                                        Type: Polynomial HexadecimalExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              _
   (7)  x + 1.5
                                        Type: Polynomial HexadecimalExpansion
--R 
--R
--R              _
--R   (7)  x + 1.5
--R                                        Type: Polynomial HexadecimalExpansion
--E 7
)spool 
 
Starts dribbling to nsfip.output (2010/3/27, 18:30:22).
)set message test on
 
)set message auto off
 
)clear all
 


--S 1 of 141
outputGeneral 4
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1


--S 2 of 141 used to work?
nagExpInt(2) :: Float
 
   There are no library operations named nagExpInt 
      Use HyperDoc Browse or issue
                             )what op nagExpInt
      to learn if there is any operation containing " nagExpInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagExpInt with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagExpInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagExpInt
--R      to learn if there is any operation containing " nagExpInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagExpInt with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 2
--       0.0489

--S 3 of 141
nagExpInt(-1) :: Float
 
   There are no library operations named nagExpInt 
      Use HyperDoc Browse or issue
                             )what op nagExpInt
      to learn if there is any operation containing " nagExpInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagExpInt with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagExpInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagExpInt
--R      to learn if there is any operation containing " nagExpInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagExpInt with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 3
--
-- ** ABNORMAL EXIT from NAG Library routine S13AAF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S13AAF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 4 of 141 used to work?
nagSinInt(0) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4
--       0.0

--S 5 of 141 used to work?
nagSinInt(0.2) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5
--       0.1996

--S 6 of 141 used to work?
nagSinInt(0.4) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6
--       0.3965

--S 7 of 141 used to work?
nagSinInt(0.6) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 7
--       0.5881

--S 8 of 141 used to work?
nagSinInt(0.8) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 8
--       0.7721

--S 9 of 141 used to work?
nagSinInt(1) :: Float
 
   There are no library operations named nagSinInt 
      Use HyperDoc Browse or issue
                             )what op nagSinInt
      to learn if there is any operation containing " nagSinInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagSinInt with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagSinInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagSinInt
--R      to learn if there is any operation containing " nagSinInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagSinInt with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9
--       0.9461


--S 10 of 141 used to work?
nagCosInt(0.2) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 10
--       - 1.042

--S 11 of 141 used to work?
nagCosInt(0.4) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11
--       - 0.3788

--S 12 of 141
nagCosInt(0.6) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12
--       - 0.02227

--S 13 of 141
nagCosInt(0.8) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 13
--       0.1983

--S 14 of 141
nagCosInt(1) :: Float
 
   There are no library operations named nagCosInt 
      Use HyperDoc Browse or issue
                             )what op nagCosInt
      to learn if there is any operation containing " nagCosInt " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagCosInt with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagCosInt 
--R      Use HyperDoc Browse or issue
--R                             )what op nagCosInt
--R      to learn if there is any operation containing " nagCosInt " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagCosInt with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 14
--       0.3374


--S 15 of 141
nagIncompleteGammaP(2,3) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15
--       0.8009

--S 16 of 141
nagIncompleteGammaP(7,1) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16
--       0.00008324

--S 17 of 141
nagIncompleteGammaP(0.5,99) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       1.0

--S 18 of 141
nagIncompleteGammaP(20,21) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18
--       0.6157

--S 19 of 141
nagIncompleteGammaP(21,20) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 19
--       0.4409


--S 20 of 141
nagIncompleteGammaP(7,1,0.1) :: Float
 
   There are no library operations named nagIncompleteGammaP 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaP
      to learn if there is any operation containing " 
      nagIncompleteGammaP " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaP with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaP 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaP
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaP " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaP with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
--       0.00008313


--S 21 of 141
nagIncompleteGammaQ(2,3) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21
--       0.1991

--S 22 of 141
nagIncompleteGammaQ(7,1) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 22
--       0.9999

--S 23 of 141
nagIncompleteGammaQ(0.5,99) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23
--       0.5705 E -44

--S 24 of 141
nagIncompleteGammaQ(20,21) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24
--       0.3843

--S 25 of 141
nagIncompleteGammaQ(21,20) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25
--       0.5591

--S 26 of 141
nagIncompleteGammaQ(25,14) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 26
--       0.995


--S 27 of 141
nagIncompleteGammaQ(25,14,0.1) :: Float
 
   There are no library operations named nagIncompleteGammaQ 
      Use HyperDoc Browse or issue
                        )what op nagIncompleteGammaQ
      to learn if there is any operation containing " 
      nagIncompleteGammaQ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagIncompleteGammaQ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagIncompleteGammaQ 
--R      Use HyperDoc Browse or issue
--R                        )what op nagIncompleteGammaQ
--R      to learn if there is any operation containing " 
--R      nagIncompleteGammaQ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagIncompleteGammaQ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 27
--       0.9953


--S 28 of 141
nagErf(-6) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 28
--       - 1.0

--S 29 of 141
nagErf(-4.5) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 29
--       - 1.0

--S 30 of 141
nagErf(-1) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 30
--       - 0.8427

--S 31 of 141
nagErf(1) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 31
--       0.8427

--S 32 of 141
nagErf(4.5) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 32
--       1.0

--S 33 of 141
nagErf(6) :: Float
 
   There are no library operations named nagErf 
      Use HyperDoc Browse or issue
                               )what op nagErf
      to learn if there is any operation containing " nagErf " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErf with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErf 
--R      Use HyperDoc Browse or issue
--R                               )what op nagErf
--R      to learn if there is any operation containing " nagErf " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErf with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 33
--       1.0


--S 34 of 141
nagErfC(-10) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 34
--       2.0

--S 35 of 141
nagErfC(-1) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 35
--       1.843

--S 36 of 141
nagErfC(0) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 36
--       1.0

--S 37 of 141
nagErfC(1) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 37
--       0.1573

--S 38 of 141
nagErfC(15) :: Float
 
   There are no library operations named nagErfC 
      Use HyperDoc Browse or issue
                              )what op nagErfC
      to learn if there is any operation containing " nagErfC " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagErfC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagErfC 
--R      Use HyperDoc Browse or issue
--R                              )what op nagErfC
--R      to learn if there is any operation containing " nagErfC " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagErfC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 38
--       0.7213 E -99

--S 39 of 141
nagDAiryAi(-10) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 39
--       0.9963

--S 40 of 141
nagDAiryAi(-1) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 40
--       - 0.01016

--S 41 of 141
nagDAiryAi(0) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 41
--       - 0.2588

--S 42 of 141
nagDAiryAi(1) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 42
--       - 0.1591

--S 43 of 141
nagDAiryAi(5) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 43
--       - 0.0002474

--S 44 of 141
nagDAiryAi(10) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 44
--       - 0.3521 E -9

--S 45 of 141
nagDAiryAi(20) :: Float
 
   There are no library operations named nagDAiryAi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryAi
      to learn if there is any operation containing " nagDAiryAi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryAi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 45
--       - 0.7586 E -26

--S 46 of 141
--RnagDAiryAi(0.3+0.4*%i) :: Complex Float
--R 
--R   There are no library operations named nagDAiryAi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryAi
--R      to learn if there is any operation containing " nagDAiryAi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryAi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 46
--       - 0.2612 + 0.03848 %i

--S 47 of 141
nagDAiryBi(-10) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 47
--       0.1194

--S 48 of 141
nagDAiryBi(-1) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 48
--       0.5924

--S 49 of 141
nagDAiryBi(0) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 49
--       0.4483

--S 50 of 141
nagDAiryBi(1) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 50
--       0.9324

--S 51 of 141
nagDAiryBi(5) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 51
--       1436.0

--S 52 of 141
nagDAiryBi(10) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 52
--       0.1429 E 10

--S 53 of 141
nagDAiryBi(20) :: Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 53
--       0.9382 E 26


--S 54 of 141
nagDAiryBi(0.3+0.4*%i) :: Complex Float
 
   There are no library operations named nagDAiryBi 
      Use HyperDoc Browse or issue
                             )what op nagDAiryBi
      to learn if there is any operation containing " nagDAiryBi " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDAiryBi with argument type(s) 
                                Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDAiryBi 
--R      Use HyperDoc Browse or issue
--R                             )what op nagDAiryBi
--R      to learn if there is any operation containing " nagDAiryBi " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDAiryBi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 54
--       0.4093 + 0.07966 %i

--S 55 of 141
nagScaledDAiryAi(0.3+0.4*%i) :: Complex Float
 
   There are no library operations named nagScaledDAiryAi 
      Use HyperDoc Browse or issue
                          )what op nagScaledDAiryAi
      to learn if there is any operation containing " nagScaledDAiryAi 
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledDAiryAi with argument type(s) 
                                Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledDAiryAi 
--R      Use HyperDoc Browse or issue
--R                          )what op nagScaledDAiryAi
--R      to learn if there is any operation containing " nagScaledDAiryAi 
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledDAiryAi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 55
--       - 0.2744 - 0.02356 %i

--S 56 of 141
nagScaledDAiryBi(0.3+0.4*%i) :: Complex Float
 
   There are no library operations named nagScaledDAiryBi 
      Use HyperDoc Browse or issue
                          )what op nagScaledDAiryBi
      to learn if there is any operation containing " nagScaledDAiryBi 
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledDAiryBi with argument type(s) 
                                Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledDAiryBi 
--R      Use HyperDoc Browse or issue
--R                          )what op nagScaledDAiryBi
--R      to learn if there is any operation containing " nagScaledDAiryBi 
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledDAiryBi with argument type(s) 
--R                                Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 56
--       0.3924 + 0.07638 %i

--S 57 of 141
nagHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH1 
      Use HyperDoc Browse or issue
                            )what op nagHankelH1
      to learn if there is any operation containing " nagHankelH1 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH1 with argument type(s) 
                             NonNegativeInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH1 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH1
--R      to learn if there is any operation containing " nagHankelH1 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH1 with argument type(s) 
--R                             NonNegativeInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 57
--       [0.3466 - 0.5588 %i  - 0.7912 - 0.8178 %i]

--S 58 of 141
nagHankelH1(2.3,2,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH1 
      Use HyperDoc Browse or issue
                            )what op nagHankelH1
      to learn if there is any operation containing " nagHankelH1 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH1 with argument type(s) 
                                    Float
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH1 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH1
--R      to learn if there is any operation containing " nagHankelH1 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH1 with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 58
--       [0.2721 - 0.7398 %i  0.08902 - 1.412 %i]

--S 59 of 141
nagHankelH1(2.12,-1,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH1 
      Use HyperDoc Browse or issue
                            )what op nagHankelH1
      to learn if there is any operation containing " nagHankelH1 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH1 with argument type(s) 
                                    Float
                                   Integer
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH1 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH1
--R      to learn if there is any operation containing " nagHankelH1 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH1 with argument type(s) 
--R                                    Float
--R                                   Integer
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 59
--       [- 0.7722 - 1.693 %i  2.601 + 6.527 %i]


--S 60 of 141
nagHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagHankelH2 
      Use HyperDoc Browse or issue
                            )what op nagHankelH2
      to learn if there is any operation containing " nagHankelH2 " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHankelH2 with argument type(s) 
                               PositiveInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHankelH2 
--R      Use HyperDoc Browse or issue
--R                            )what op nagHankelH2
--R      to learn if there is any operation containing " nagHankelH2 " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHankelH2 with argument type(s) 
--R                               PositiveInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 60
--       [- 1.371 - 1.28 %i  - 1.491 - 5.993 %i]

--S 61 of 141
nagScaledHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagScaledHankelH1 
      Use HyperDoc Browse or issue
                         )what op nagScaledHankelH1
      to learn if there is any operation containing " nagScaledHankelH1
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledHankelH1 with argument type(s) 
                             NonNegativeInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledHankelH1 
--R      Use HyperDoc Browse or issue
--R                         )what op nagScaledHankelH1
--R      to learn if there is any operation containing " nagScaledHankelH1
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledHankelH1 with argument type(s) 
--R                             NonNegativeInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 61
--       [0.2477 - 0.9492 %i  - 1.488 - 0.8166 %i]


--S 62 of 141
nagScaledHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float
 
   There are no library operations named nagScaledHankelH2 
      Use HyperDoc Browse or issue
                         )what op nagScaledHankelH2
      to learn if there is any operation containing " nagScaledHankelH2
      " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagScaledHankelH2 with argument type(s) 
                               PositiveInteger
                                Complex Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagScaledHankelH2 
--R      Use HyperDoc Browse or issue
--R                         )what op nagScaledHankelH2
--R      to learn if there is any operation containing " nagScaledHankelH2
--R      " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagScaledHankelH2 with argument type(s) 
--R                               PositiveInteger
--R                                Complex Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 62
--       [7.05 + 6.052 %i  8.614 + 29.35 %i]


--S 63 of 141
nagKelvinBer(0.1) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 63
--       1.0

--S 64 of 141
nagKelvinBer(1) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 64
--       0.9844

--S 65 of 141
nagKelvinBer(2.5) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 65
--       0.4

--S 66 of 141
nagKelvinBer(5) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 66
--       - 6.23

--S 67 of 141
nagKelvinBer(10) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 67
--       138.8

--S 68 of 141
nagKelvinBer(15) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 68
--       - 2967.0

--S 69 of 141
nagKelvinBer(60) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 69
--
-- ** ABNORMAL EXIT from NAG Library routine S19AAF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19AAF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 70 of 141
nagKelvinBer(-1) :: Float
 
   There are no library operations named nagKelvinBer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBer
      to learn if there is any operation containing " nagKelvinBer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBer with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBer
--R      to learn if there is any operation containing " nagKelvinBer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBer with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 70
--       0.9844

--S 71 of 141
nagKelvinBei(0.1) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 71
--       0.0025

--S 72 of 141
nagKelvinBei(1) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 72
--       0.2496

--S 73 of 141
nagKelvinBei(2.5) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 73
--       1.457

--S 74 of 141
nagKelvinBei(5) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 74
--       0.116

--S 75 of 141
nagKelvinBei(10) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 75
--       56.37

--S 76 of 141
nagKelvinBei(15) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 76
--       - 2953.0

--S 77 of 141
nagKelvinBei(60) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 77
--
-- ** ABNORMAL EXIT from NAG Library routine S19ABF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ABF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 77a of 141
nagKelvinBei(-1) :: Float
 
   There are no library operations named nagKelvinBei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinBei
      to learn if there is any operation containing " nagKelvinBei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinBei with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinBei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinBei
--R      to learn if there is any operation containing " nagKelvinBei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinBei with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 77a
--       0.2496


--S 78 of 141
nagKelvinKer(0) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 78
--
-- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL =     2
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ACF. The error number (IFAIL value) is 2, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 79 of 141
nagKelvinKer(0.1) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 79
--       2.42

--S 80 of 141
nagKelvinKer(1) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 80
--       0.2867

--S 81 of 141
nagKelvinKer(2.5) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 81
--       - 0.06969

--S 82 of 141
nagKelvinKer(5) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 82
--       - 0.01151

--S 83 of 141
nagKelvinKer(10) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 83
--       0.0001295

--S 84 of 141
nagKelvinKer(15) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 84
--       - 0.1514 E -7

--S 85 of 141
nagKelvinKer(1100) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 85
--
-- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ACF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 86 of 141
nagKelvinKer(-1) :: Float
 
   There are no library operations named nagKelvinKer 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKer
      to learn if there is any operation containing " nagKelvinKer " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKer with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKer 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKer
--R      to learn if there is any operation containing " nagKelvinKer " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKer with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 86
--
-- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL =     2
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ACF. The error number (IFAIL value) is 2, please consult the 
--      NAG manual via the Browser for diagnostic information.


--S 87 of 141
nagKelvinKei(0) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 87
--       - 0.7854

--S 88 of 141
nagKelvinKei(0.1) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 88
--       - 0.7769

--S 89 of 141
nagKelvinKei(1) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 89
--       - 0.495

--S 90 of 141
nagKelvinKei(2.5) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 90
--       - 0.1107

--S 91 of 141
nagKelvinKei(5) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 91
--       0.01119

--S 92 of 141
nagKelvinKei(10) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 92
--       - 0.0003075

--S 93 of 141
nagKelvinKei(15) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 93
--       0.000007963

--S 94 of 141
nagKelvinKei(1100) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 94
--
-- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL =     1
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ADF. The error number (IFAIL value) is 1, please consult the 
--      NAG manual via the Browser for diagnostic information.

--S 95 of 141
nagKelvinKei(-1) :: Float
 
   There are no library operations named nagKelvinKei 
      Use HyperDoc Browse or issue
                            )what op nagKelvinKei
      to learn if there is any operation containing " nagKelvinKei " in
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagKelvinKei with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagKelvinKei 
--R      Use HyperDoc Browse or issue
--R                            )what op nagKelvinKei
--R      to learn if there is any operation containing " nagKelvinKei " in
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagKelvinKei with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 95
--
-- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL =     2
-- ** NAG soft failure - control returned
-- 
--   Error signalled from user code:
--      An error was detected when calling the NAG Library routine 
--      S19ADF. The error number (IFAIL value) is 2, please consult the 
--      NAG manual via the Browser for diagnostic information.


--S 96 of 141
nagFresnelS(0) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 96
--       0.0

--S 97 of 141
nagFresnelS(0.5) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 97
--       0.06473

--S 98 of 141
nagFresnelS(1) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 98
--       0.4383

--S 99 of 141
nagFresnelS(2) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 99
--       0.3434

--S 100 of 141
nagFresnelS(4) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 100
--       0.4205

--S 101 of 141
nagFresnelS(5) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 101
--       0.4992

--S 102 of 141
nagFresnelS(6) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 102
--       0.447

--S 103 of 141
nagFresnelS(8) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 103
--       0.4602

--S 104 of 141
nagFresnelS(10) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 104
--       0.4682

--S 105 of 141
nagFresnelS(-1) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 105
--       - 0.4383

--S 106 of 141
nagFresnelS(1000) :: Float
 
   There are no library operations named nagFresnelS 
      Use HyperDoc Browse or issue
                            )what op nagFresnelS
      to learn if there is any operation containing " nagFresnelS " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelS with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelS 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelS
--R      to learn if there is any operation containing " nagFresnelS " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelS with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 106
--       0.4997


--S 107 of 141
nagFresnelC(0) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                             NonNegativeInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                             NonNegativeInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 107
--       0.0

--S 108 of 141
nagFresnelC(0.5) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 108
--       0.4923

--S 109 of 141
nagFresnelC(1) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 109
--       0.7799

--S 110 of 141
nagFresnelC(2) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 110
--       0.4883

--S 111 of 141
nagFresnelC(4) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 111
--       0.4984

--S 112 of 141
nagFresnelC(5) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 112
--       0.5636

--S 113 of 141
nagFresnelC(6) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 113
--       0.4995

--S 114 of 141
nagFresnelC(8) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 114
--       0.4998

--S 115 of 141
nagFresnelC(10) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 115
--       0.4999

--S 116 of 141
nagFresnelC(-1) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                                   Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                                   Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 116
--       - 0.7799

--S 117 of 141
nagFresnelC(1000) :: Float
 
   There are no library operations named nagFresnelC 
      Use HyperDoc Browse or issue
                            )what op nagFresnelC
      to learn if there is any operation containing " nagFresnelC " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagFresnelC with argument type(s) 
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagFresnelC 
--R      Use HyperDoc Browse or issue
--R                            )what op nagFresnelC
--R      to learn if there is any operation containing " nagFresnelC " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagFresnelC with argument type(s) 
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 117
--       0.5


--S 118 of 141
nagEllipticIntegralRC(0.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRC 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRC
      to learn if there is any operation containing " 
      nagEllipticIntegralRC " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRC with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRC 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRC
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRC " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRC with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 118
--       1.111

--S 119 of 141
nagEllipticIntegralRC(1,1) :: Float
 
   There are no library operations named nagEllipticIntegralRC 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRC
      to learn if there is any operation containing " 
      nagEllipticIntegralRC " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRC with argument type(s) 
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRC 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRC
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRC " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRC with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 119
--       1.0

--S 120 of 141
nagEllipticIntegralRC(1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRC 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRC
      to learn if there is any operation containing " 
      nagEllipticIntegralRC " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRC with argument type(s) 
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRC 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRC
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRC " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRC with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 120
--       0.9312

--S 121 of 141
nagEllipticIntegralRD(0.5,0.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 121
--       1.479

--S 122 of 141
nagEllipticIntegralRD(0.5,1,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 122
--       1.211

--S 123 of 141
nagEllipticIntegralRD(0.5,1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 123
--       1.061

--S 124 of 141
nagEllipticIntegralRD(1,1,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 124
--       1.0

--S 125 of 141
nagEllipticIntegralRD(1,1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 125
--       0.8805

--S 126 of 141
nagEllipticIntegralRD(1.5,1.5,1) :: Float
 
   There are no library operations named nagEllipticIntegralRD 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRD
      to learn if there is any operation containing " 
      nagEllipticIntegralRD " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRD with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRD 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRD
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRD " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRD with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 126
--       0.7775

--S 127 of 141
nagEllipticIntegralRF(0.5,1,1.5) :: Float
 
   There are no library operations named nagEllipticIntegralRF 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRF
      to learn if there is any operation containing " 
      nagEllipticIntegralRF " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRF with argument type(s) 
                                    Float
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRF 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRF
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRF " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRF with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 127
--       1.028

--S 128 of 141
nagEllipticIntegralRF(1,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRF 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRF
      to learn if there is any operation containing " 
      nagEllipticIntegralRF " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRF with argument type(s) 
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRF 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRF
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRF " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRF with argument type(s) 
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 128
--       0.826

--S 129 of 141
nagEllipticIntegralRF(1.5,2,2.5) :: Float
 
   There are no library operations named nagEllipticIntegralRF 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRF
      to learn if there is any operation containing " 
      nagEllipticIntegralRF " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRF with argument type(s) 
                                    Float
                               PositiveInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRF 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRF
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRF " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRF with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                                    Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 129
--       0.7116

--S 130 of 141
nagEllipticIntegralRJ(0.5,0.5,0.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 130
--       1.118

--S 131 of 141
nagEllipticIntegralRJ(0.5,0.5,1,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 131
--       0.9221

--S 132 of 141
nagEllipticIntegralRJ(0.5,0.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 132
--       0.8115

--S 133 of 141
nagEllipticIntegralRJ(0.5,1,1,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 133
--       0.7671

--S 134 of 141
nagEllipticIntegralRJ(0.5,1,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 134
--       0.6784

--S 135 of 141
nagEllipticIntegralRJ(0.5,1.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 135
--       0.6017

--S 136 of 141
nagEllipticIntegralRJ(1,1,1,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 136
--       0.6438

--S 137 of 141
nagEllipticIntegralRJ(1,1,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                               PositiveInteger
                               PositiveInteger
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                               PositiveInteger
--R                               PositiveInteger
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 137
--       0.5722

--S 138 of 141
nagEllipticIntegralRJ(1,1.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                               PositiveInteger
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                               PositiveInteger
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 138
--       0.5101

--S 139 of 141
nagEllipticIntegralRJ(1.5,1.5,1.5,2) :: Float
 
   There are no library operations named nagEllipticIntegralRJ 
      Use HyperDoc Browse or issue
                       )what op nagEllipticIntegralRJ
      to learn if there is any operation containing " 
      nagEllipticIntegralRJ " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagEllipticIntegralRJ with argument type(s) 
                                    Float
                                    Float
                                    Float
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagEllipticIntegralRJ 
--R      Use HyperDoc Browse or issue
--R                       )what op nagEllipticIntegralRJ
--R      to learn if there is any operation containing " 
--R      nagEllipticIntegralRJ " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagEllipticIntegralRJ with argument type(s) 
--R                                    Float
--R                                    Float
--R                                    Float
--R                               PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 139
--       0.4561

--S 140 of 141
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 140

--S 141 of 141
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 141
)spool 
 
Starts dribbling to zimmbron.output (2010/3/27, 18:41:39).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 143
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1 

--S 2 of 143
y' := D(y x, x)
 

         ,
   (2)  y (x)

                                                     Type: Expression Integer
--R 
--R
--R         ,
--R   (2)  y (x)
--R
--R                                                     Type: Expression Integer
--E 2 

--S 3 of 143
y'' := D(y', x)
 

         ,,
   (3)  y  (x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (3)  y  (x)
--R
--R                                                     Type: Expression Integer
--E 3 

--S 4 of146
y1 := operator y1
 

   (4)  y1
                                                          Type: BasicOperator
--R 
--R
--R   (4)  y1
--R                                                          Type: BasicOperator
--E 4

--S 5 of 143
y2 := operator y2
 

   (5)  y2
                                                          Type: BasicOperator
--R 
--R
--R   (5)  y2
--R                                                          Type: BasicOperator
--E 5

--S 6 of 143
y1' := D(y1 t, t)
 

          ,
   (6)  y1 (t)

                                                     Type: Expression Integer
--R 
--R
--R          ,
--R   (6)  y1 (t)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 143
y2' := D(y2 t, t)
 

          ,
   (7)  y2 (t)

                                                     Type: Expression Integer
--R 
--R
--R          ,
--R   (7)  y2 (t)
--R
--R                                                     Type: Expression Integer
--E 7

--S 8 of 143
eq := (x^4 - x^3) * y' + 2 * x^4 * y x = x^3/3 + C
 

                                   3
          4    3  ,        4      x  + 3C
   (8)  (x  - x )y (x) + 2x y(x)= -------
                                     3
                                            Type: Equation Expression Integer
--R 
--R
--R                                   3
--R          4    3  ,        4      x  + 3C
--R   (8)  (x  - x )y (x) + 2x y(x)= -------
--R                                     3
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 143
solve(eq,y,x)
 

                         3     2                     - 2x
                       2x  - 3x  + 6C              %e
   (9)  [particular= ------------------,basis= [-----------]]
                        4      3      2          2
                     12x  - 24x  + 12x          x  - 2x + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                         3     2                     - 2x
--R                       2x  - 3x  + 6C              %e
--R   (9)  [particular= ------------------,basis= [-----------]]
--R                        4      3      2          2
--R                     12x  - 24x  + 12x          x  - 2x + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 9

--S 10 of 143
eq := - y' / 2 + y x = sin x
 

            ,
         - y (x) + 2y(x)

   (10)  ---------------= sin(x)
                2
                                            Type: Equation Expression Integer
--R 
--R
--R            ,
--R         - y (x) + 2y(x)
--R
--R   (10)  ---------------= sin(x)
--R                2
--R                                            Type: Equation Expression Integer
--E 10

--S 11 of 143
solve(eq,y,x)
 

                      4sin(x) + 2cos(x)           2x
   (11)  [particular= -----------------,basis= [%e  ]]
                              5
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                      4sin(x) + 2cos(x)           2x
--R   (11)  [particular= -----------------,basis= [%e  ]]
--R                              5
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 11

--S 12 of 143
eq := y' = y x / (y x * log y x + x)
 

          ,            y(x)
   (12)  y (x)= -----------------
                y(x)log(y(x)) + x
                                            Type: Equation Expression Integer
--R 
--R
--R          ,            y(x)
--R   (12)  y (x)= -----------------
--R                y(x)log(y(x)) + x
--R                                            Type: Equation Expression Integer
--E 12

--S 13 of 143
solve(eq,y,x)
 

                      2
         y(x)log(y(x))  - 2x
   (13)  -------------------
                2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2
--R         y(x)log(y(x))  - 2x
--R   (13)  -------------------
--R                2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 143
eq := 2*(y x)*y'**2-2*x*y'-y x=0
 

               ,   2      ,
   (14)  2y(x)y (x)  - 2xy (x) - y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R               ,   2      ,
--R   (14)  2y(x)y (x)  - 2xy (x) - y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 14

--S 15 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 15

--S 16 of 143
eq := y' + y x = y(x)^3 * sin x
 

          ,                3
   (15)  y (x) + y(x)= y(x) sin(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,                3
--R   (15)  y (x) + y(x)= y(x) sin(x)
--R
--R                                            Type: Equation Expression Integer
--E 16

--S 17 of 143
solve(eq,y,x)
 

                2              2
         - 4y(x) sin(x) - 2y(x) cos(x) + 5
   (16)  ---------------------------------
                          2  2x
                     5y(x) %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2              2
--R         - 4y(x) sin(x) - 2y(x) cos(x) + 5
--R   (16)  ---------------------------------
--R                          2  2x
--R                     5y(x) %e
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 143
P := operator P
 

   (17)  P
                                                          Type: BasicOperator
--R 
--R
--R   (17)  P
--R                                                          Type: BasicOperator
--E 18

--S 19 of 143
Q := operator Q
 

   (18)  Q
                                                          Type: BasicOperator
--R 
--R
--R   (18)  Q
--R                                                          Type: BasicOperator
--E 19

--S 20 of 143
eq := y' + P x * y x = Q x * y(x)^n
 

          ,                        n
   (19)  y (x) + P(x)y(x)= Q(x)y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,                        n
--R   (19)  y (x) + P(x)y(x)= Q(x)y(x)
--R
--R                                            Type: Equation Expression Integer
--E 20

--S 21 of 143
solve(eq,y,x)
 

   (20)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (20)  "failed"
--R                                                    Type: Union("failed",...)
--E 21

--S 22 of 143
eq := y' + P x * y x = Q x * y(x)^2
 

          ,                        2
   (21)  y (x) + P(x)y(x)= Q(x)y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,                        2
--R   (21)  y (x) + P(x)y(x)= Q(x)y(x)
--R
--R                                            Type: Equation Expression Integer
--E 22

--S 23 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 23

--S 24 of 143
eq := y' + P x * y x = Q x * y(x)^(2/3)
 

          ,                    3+----+2
   (22)  y (x) + P(x)y(x)= Q(x)\|y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,                    3+----+2
--R   (22)  y (x) + P(x)y(x)= Q(x)\|y(x)
--R
--R                                            Type: Equation Expression Integer
--E 24

--S 25 of 143
solve(eq,y,x)
 

   (23)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (23)  "failed"
--R                                                    Type: Union("failed",...)
--E 25

--S 26 of 143
eq := y' + P x * y x = Q x * y(x)^3
 

          ,                        3
   (24)  y (x) + P(x)y(x)= Q(x)y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,                        3
--R   (24)  y (x) + P(x)y(x)= Q(x)y(x)
--R
--R                                            Type: Equation Expression Integer
--E 26

--S 27 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   Function not supported by Risch d.e.
--R
--R   Continuing to read the file...
--R
--E 27

--S 28 of 143
eq := (x^2-1)*y'^2-2*x*y(x)*y'+y(x)^2-1=0
 

           2      ,   2           ,          2
   (25)  (x  - 1)y (x)  - 2x y(x)y (x) + y(x)  - 1= 0

                                            Type: Equation Expression Integer
--R 
--R
--R           2      ,   2           ,          2
--R   (25)  (x  - 1)y (x)  - 2x y(x)y (x) + y(x)  - 1= 0
--R
--R                                            Type: Equation Expression Integer
--E 28

--S 29 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 29

--S 30 of 143
f := operator f
 

   (26)  f
                                                          Type: BasicOperator
--R 
--R
--R   (26)  f
--R                                                          Type: BasicOperator
--E 30

--S 31 of 143
g := operator g
 

   (27)  g
                                                          Type: BasicOperator
--R 
--R
--R   (27)  g
--R                                                          Type: BasicOperator
--E 31

--S 32 of 143
eq := f(x*y'-y(x))=g(y')
 

             ,                ,
   (28)  f(xy (x) - y(x))= g(y (x))

                                            Type: Equation Expression Integer
--R 
--R
--R             ,                ,
--R   (28)  f(xy (x) - y(x))= g(y (x))
--R
--R                                            Type: Equation Expression Integer
--E 32

--S 33 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseODE: equation has order 0
--R
--R   Continuing to read the file...
--R
--E 33

--S 34 of 143
eq := y' = (3 * x^2 - y(x)^2 - 7) / (exp y x + 2 * x * y x + 1)
 

                        2     2
          ,       - y(x)  + 3x  - 7
   (29)  y (x)= --------------------
                  y(x)
                %e     + 2x y(x) + 1
                                            Type: Equation Expression Integer
--R 
--R
--R                        2     2
--R          ,       - y(x)  + 3x  - 7
--R   (29)  y (x)= --------------------
--R                  y(x)
--R                %e     + 2x y(x) + 1
--R                                            Type: Equation Expression Integer
--E 34

--S 35 of 143
solve(eq,y,x)
 

           y(x)         2           3
   (30)  %e     + x y(x)  + y(x) - x  + 7x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           y(x)         2           3
--R   (30)  %e     + x y(x)  + y(x) - x  + 7x
--R                                          Type: Union(Expression Integer,...)
--E 35

--S 36 of 143
eq := y' = (2 * x^3 * y x - y(x)^4) / (x^4 - 2 * x * y(x)^3)
 

                    4     3
          ,     y(x)  - 2x y(x)
   (31)  y (x)= ---------------
                        3    4
                 2x y(x)  - x
                                            Type: Equation Expression Integer
--R 
--R
--R                    4     3
--R          ,     y(x)  - 2x y(x)
--R   (31)  y (x)= ---------------
--R                        3    4
--R                 2x y(x)  - x
--R                                            Type: Equation Expression Integer
--E 36

--S 37 of 143
solve(eq,y,x)
 

   (32)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (32)  "failed"
--R                                                    Type: Union("failed",...)
--E 37

--S 38 of 143
eq := y'*(y'+y(x))=x*(x+y(x))
 

          ,   2        ,               2
   (33)  y (x)  + y(x)y (x)= x y(x) + x

                                            Type: Equation Expression Integer
--R 
--R
--R          ,   2        ,               2
--R   (33)  y (x)  + y(x)y (x)= x y(x) + x
--R
--R                                            Type: Equation Expression Integer
--E 38

--S 39 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 39

--S 40 of 143
eq := y' = x / (x^2 * y(x)^2 + y(x)^5)
 

          ,            x
   (34)  y (x)= ---------------
                    5    2    2
                y(x)  + x y(x)
                                            Type: Equation Expression Integer
--R 
--R
--R          ,            x
--R   (34)  y (x)= ---------------
--R                    5    2    2
--R                y(x)  + x y(x)
--R                                            Type: Equation Expression Integer
--E 40

--S 41 of 143
solve(eq,y,x)
 

                                      3
                                 2y(x)
                               - ------
                 3     2            3
         (- 2y(x)  - 2x  - 3)%e
   (35)  ------------------------------
                        4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                      3
--R                                 2y(x)
--R                               - ------
--R                 3     2            3
--R         (- 2y(x)  - 2x  - 3)%e
--R   (35)  ------------------------------
--R                        4
--R                                          Type: Union(Expression Integer,...)
--E 41

--S 42 of 143
eq := y(x)=2*x*y'-a*y'^3
 

                    ,   3      ,
   (36)  y(x)= - a y (x)  + 2xy (x)

                                            Type: Equation Expression Integer
--R 
--R
--R                    ,   3      ,
--R   (36)  y(x)= - a y (x)  + 2xy (x)
--R
--R                                            Type: Equation Expression Integer
--E 42

--S 43 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 43

--S 44 of 143
eq := y(x)=2*x*y'-y'^2
 

                  ,   2      ,
   (37)  y(x)= - y (x)  + 2xy (x)

                                            Type: Equation Expression Integer
--R 
--R
--R                  ,   2      ,
--R   (37)  y(x)= - y (x)  + 2xy (x)
--R
--R                                            Type: Equation Expression Integer
--E 44

--S 45 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 45

--S 46 of 143
eq := y' = exp x * y(x)^2 - y x + exp(-x)
 

          ,         2  x     - x
   (38)  y (x)= y(x) %e  + %e    - y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,         2  x     - x
--R   (38)  y (x)= y(x) %e  + %e    - y(x)
--R
--R                                            Type: Equation Expression Integer
--E 46

--S 47 of 143
solve(eq,y,x)
 

   (39)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (39)  "failed"
--R                                                    Type: Union("failed",...)
--E 47

--S 48 of 143
eq := y' = y(x)^2 - x * y x + 1
 

          ,         2
   (40)  y (x)= y(x)  - x y(x) + 1

                                            Type: Equation Expression Integer
--R 
--R
--R          ,         2
--R   (40)  y (x)= y(x)  - x y(x) + 1
--R
--R                                            Type: Equation Expression Integer
--E 48

--S 49 of 143
solve(eq,y,x)
 

                          2
                         x
                       - --   x
                          2 ++       1
         (- y(x) + x)%e     |   - ------- d%M  + 1
                           ++           2
                                      %M
                                    - ---
                                       2
                                  %e
   (41)  -----------------------------------------
                                     2
                                    x
                                  - --
                                     2
                      (y(x) - x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          2
--R                         x
--R                       - --   x
--R                          2 ++       1
--R         (- y(x) + x)%e     |   - ------- d%M  + 1
--R                           ++           2
--R                                      %M
--R                                    - ---
--R                                       2
--R                                  %e
--R   (41)  -----------------------------------------
--R                                     2
--R                                    x
--R                                  - --
--R                                     2
--R                      (y(x) - x)%e
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 143
eq := y' = (9 * x^8 + 1) / (y(x)^2 + 1)
 

                   8
          ,      9x  + 1
   (42)  y (x)= ---------
                    2
                y(x)  + 1
                                            Type: Equation Expression Integer
--R 
--R
--R                   8
--R          ,      9x  + 1
--R   (42)  y (x)= ---------
--R                    2
--R                y(x)  + 1
--R                                            Type: Equation Expression Integer
--E 50

--S 51 of 143
solve(eq,y,x)
 

             3             9
         y(x)  + 3y(x) - 3x  - 3x
   (43)  ------------------------
                     3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3             9
--R         y(x)  + 3y(x) - 3x  - 3x
--R   (43)  ------------------------
--R                     3
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 143
eq := y(x) = 2*x*y'+y(x)*y'^2
 

                    ,   2      ,
   (44)  y(x)= y(x)y (x)  + 2xy (x)

                                            Type: Equation Expression Integer
--R 
--R
--R                    ,   2      ,
--R   (44)  y(x)= y(x)y (x)  + 2xy (x)
--R
--R                                            Type: Equation Expression Integer
--E 52

--S 53 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 53

--S 54 of 143
eq := x = y(x)*y'-x*y'^2
 

                 ,   2        ,
   (45)  x= - x y (x)  + y(x)y (x)

                                            Type: Equation Expression Integer
--R 
--R
--R                 ,   2        ,
--R   (45)  x= - x y (x)  + y(x)y (x)
--R
--R                                            Type: Equation Expression Integer
--E 54

--S 55 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 55

--S 56 of 143
eq := y''*(a*x+b)^2+4*y'*(a*x+b)*a+2*y(x)*a^2 = 0
 

           2 2             2  ,,         2          ,        2
   (46)  (a x  + 2a b x + b )y  (x) + (4a x + 4a b)y (x) + 2a y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R           2 2             2  ,,         2          ,        2
--R   (46)  (a x  + 2a b x + b )y  (x) + (4a x + 4a b)y (x) + 2a y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 56

--S 57 of 143
solve(eq,y,x)
 

                                         x              2a x + b
   (47)  [particular= 0,basis= [------------------,------------------]]
                                 2 2             2  2 2             2
                                a x  + 2a b x + b  a x  + 2a b x + b
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                         x              2a x + b
--R   (47)  [particular= 0,basis= [------------------,------------------]]
--R                                 2 2             2  2 2             2
--R                                a x  + 2a b x + b  a x  + 2a b x + b
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 57

--S 58 of 143
eq := (x^2-x)*y'' + (2*x^2+4*x-3)*y' + 8*x*y(x) = 1
 

           2      ,,         2           ,
   (48)  (x  - x)y  (x) + (2x  + 4x - 3)y (x) + 8x y(x)= 1

                                            Type: Equation Expression Integer
--R 
--R
--R           2      ,,         2           ,
--R   (48)  (x  - x)y  (x) + (2x  + 4x - 3)y (x) + 8x y(x)= 1
--R
--R                                            Type: Equation Expression Integer
--E 58

--S 59 of 143
solve(eq,y,x)
 

                          3     2                                   - 2x
                        2x  - 3x  + 53                 1          %e
   (49)  [particular= ------------------,basis= [-------------,-----------]]
                         4      3      2          4     3    2  2
                      12x  - 24x  + 12x          x  - 2x  + x  x  - 2x + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                          3     2                                   - 2x
--R                        2x  - 3x  + 53                 1          %e
--R   (49)  [particular= ------------------,basis= [-------------,-----------]]
--R                         4      3      2          4     3    2  2
--R                      12x  - 24x  + 12x          x  - 2x  + x  x  - 2x + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 59

--S 60 of 143
eq := (x^2-x)*y'' + (1-2*x^2)*y' + (4*x-2)*y(x) = 0
 

           2      ,,           2      ,
   (50)  (x  - x)y  (x) + (- 2x  + 1)y (x) + (4x - 2)y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R           2      ,,           2      ,
--R   (50)  (x  - x)y  (x) + (- 2x  + 1)y (x) + (4x - 2)y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 60

--S 61 of 143
solve(eq,y,x)
 

                                 2   2x
   (51)  [particular= 0,basis= [x ,%e  ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                 2   2x
--R   (51)  [particular= 0,basis= [x ,%e  ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 61

--S 62 of 143
eq := y''-y' = 2*y(x)*y'
 

          ,,       ,           ,
   (52)  y  (x) - y (x)= 2y(x)y (x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,       ,           ,
--R   (52)  y  (x) - y (x)= 2y(x)y (x)
--R
--R                                            Type: Equation Expression Integer
--E 62

--S 63 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getfreelincoeff: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getfreelincoeff: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 63

--S 64 of 143
eq := y''/y(x)-y'^2/y(x)^2-1+1/y(x)^3 = 0
 

             2 ,,           ,   2       3
         y(x) y  (x) - y(x)y (x)  - y(x)  + 1

   (53)  ------------------------------------= 0
                             3
                         y(x)
                                            Type: Equation Expression Integer
--R 
--R
--R             2 ,,           ,   2       3
--R         y(x) y  (x) - y(x)y (x)  - y(x)  + 1
--R
--R   (53)  ------------------------------------= 0
--R                             3
--R                         y(x)
--R                                            Type: Equation Expression Integer
--E 64

--S 65 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseLODE: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 65

--S 66 of 143
eq := y'' + 2 * x * y' = 2 * x
 

          ,,         ,
   (54)  y  (x) + 2xy (x)= 2x

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,         ,
--R   (54)  y  (x) + 2xy (x)= 2x
--R
--R                                            Type: Equation Expression Integer
--E 66

--S 67 of 143
solve(eq,y,x)
 

   (55)  [particular= x,basis= [1,erf(x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (55)  [particular= x,basis= [1,erf(x)]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 67

--S 68 of 143
eq := 2*y(x)*y''-y'^2 = (y'-x*y'')^2/3
 

                                2 ,,   2      ,    ,,       ,   2
                               x y  (x)  - 2xy (x)y  (x) + y (x)
               ,,       ,   2
   (56)  2y(x)y  (x) - y (x) = ----------------------------------
                                                3
                                            Type: Equation Expression Integer
--R 
--R
--R                                2 ,,   2      ,    ,,       ,   2
--R                               x y  (x)  - 2xy (x)y  (x) + y (x)
--R               ,,       ,   2
--R   (56)  2y(x)y  (x) - y (x) = ----------------------------------
--R                                                3
--R                                            Type: Equation Expression Integer
--E 68

--S 69 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 69

--S 70 of 143
eq := x*y'' = 2*y(x)*y'
 

           ,,           ,
   (57)  xy  (x)= 2y(x)y (x)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,           ,
--R   (57)  xy  (x)= 2y(x)y (x)
--R
--R                                            Type: Equation Expression Integer
--E 70

--S 71 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getfreelincoeff: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getfreelincoeff: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 71

--S 72 of 143
eq := (1-x)*(y(x)*y''-y'^2)+x^2*y(x)^2 = 0
 

                       ,,              ,   2    2    2
   (58)  (- x + 1)y(x)y  (x) + (x - 1)y (x)  + x y(x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R                       ,,              ,   2    2    2
--R   (58)  (- x + 1)y(x)y  (x) + (x - 1)y (x)  + x y(x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 72

--S 73 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseLODE: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 73

--S 74 of 143
eq := x*y(x)*y''+x*y'^2+y(x)*y'=0
 

                ,,         ,   2        ,
   (59)  x y(x)y  (x) + x y (x)  + y(x)y (x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R                ,,         ,   2        ,
--R   (59)  x y(x)y  (x) + x y (x)  + y(x)y (x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 74

--S 75 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseLODE: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 75

--S 76 of 143
eq := y''^2-2*y'*y''+2*y(x)*y'-y(x)^2=0
 

          ,,   2     ,    ,,            ,          2
   (60)  y  (x)  - 2y (x)y  (x) + 2y(x)y (x) - y(x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,   2     ,    ,,            ,          2
--R   (60)  y  (x)  - 2y (x)y  (x) + 2y(x)y (x) - y(x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 76

--S 77 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 77

--S 78 of 143
eq := (x^3/2-x^2)*y'' + (2*x^2-3*x+1)*y' + (x-1)*y(x) = 0
 

           3     2  ,,         2           ,
         (x  - 2x )y  (x) + (4x  - 6x + 2)y (x) + (2x - 2)y(x)

   (61)  -----------------------------------------------------= 0
                                   2
                                            Type: Equation Expression Integer
--R 
--R
--R           3     2  ,,         2           ,
--R         (x  - 2x )y  (x) + (4x  - 6x + 2)y (x) + (2x - 2)y(x)
--R
--R   (61)  -----------------------------------------------------= 0
--R                                   2
--R                                            Type: Equation Expression Integer
--E 78

--S 79 of 143
solve(eq,y,x)
 

   (62)
   [particular= 0,
                1               1                  1
              - - +-------+   - - +-------+   x   -- +----------+
                x |   1         x |   1     ++    %M |     1
    basis= [%e    |------- ,%e    |-------  |   %e   |---------- d%M ]]
                  | 2             | 2      ++        |  4      3
                 \|x  - 2x       \|x  - 2x          \|%M  - 2%M
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (62)
--R   [particular= 0,
--R                1               1                  1
--R              - - +-------+   - - +-------+   x   -- +----------+
--R                x |   1         x |   1     ++    %M |     1
--R    basis= [%e    |------- ,%e    |-------  |   %e   |---------- d%M ]]
--R                  | 2             | 2      ++        |  4      3
--R                 \|x  - 2x       \|x  - 2x          \|%M  - 2%M
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 79

--S 80 of 143
eq := y'' - 2 * x * y' + 2 * y x = 3
 

          ,,         ,
   (63)  y  (x) - 2xy (x) + 2y(x)= 3

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,         ,
--R   (63)  y  (x) - 2xy (x) + 2y(x)= 3
--R
--R                                            Type: Equation Expression Integer
--E 80

--S 81 of 143
solve(eq,y,x)
 

                                            2
                                      x   %M
                      3             ++  %e
   (64)  [particular= -,basis= [x,x |   ----- d%M ]]
                      2            ++      2
                                         %M
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                            2
--R                                      x   %M
--R                      3             ++  %e
--R   (64)  [particular= -,basis= [x,x |   ----- d%M ]]
--R                      2            ++      2
--R                                         %M
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 81

--S 82 of 143
eq := sqrt(x) * y'' + 2 * x * y' + 3 * y x = 0
 

          +-+ ,,         ,
   (65)  \|x y  (x) + 2xy (x) + 3y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R          +-+ ,,         ,
--R   (65)  \|x y  (x) + 2xy (x) + 3y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 82

--S 83 of 143
solve(eq,y,x)
 

   (66)  [particular= 0,basis= []]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (66)  [particular= 0,basis= []]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 83

--S 84 of 143
eq := x^2*y''+3*x*y'+2*y(x)=1/y(x)^3/x^4
 

          2 ,,         ,                1
   (67)  x y  (x) + 3xy (x) + 2y(x)= -------
                                      4    3
                                     x y(x)
                                            Type: Equation Expression Integer
--R 
--R
--R          2 ,,         ,                1
--R   (67)  x y  (x) + 3xy (x) + 2y(x)= -------
--R                                      4    3
--R                                     x y(x)
--R                                            Type: Equation Expression Integer
--E 84

--S 85 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 85

--S 86 of 143
eq := y'' - 2 / x^2 * y x = 7 * x^4 + 3 * x^3
 

          2 ,,
         x y  (x) - 2y(x)
                             4     3
   (68)  ----------------= 7x  + 3x
                 2
                x
                                            Type: Equation Expression Integer
--R 
--R
--R          2 ,,
--R         x y  (x) - 2y(x)
--R                             4     3
--R   (68)  ----------------= 7x  + 3x
--R                 2
--R                x
--R                                            Type: Equation Expression Integer
--E 86

--S 97 of 143
solve(eq,y,x)
 

                        7     6     3               3      3
                      3x  + 2x  - 7x  + 14         x  - 1 x  + 2
   (69)  [particular= --------------------,basis= [------,------]]
                               12x                    x      x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                        7     6     3               3      3
--R                      3x  + 2x  - 7x  + 14         x  - 1 x  + 2
--R   (69)  [particular= --------------------,basis= [------,------]]
--R                               12x                    x      x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 97

--S 88 of 143
eq := y'' + y x = csc x
 

          ,,
   (70)  y  (x) + y(x)= csc(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (70)  y  (x) + y(x)= csc(x)
--R
--R                                            Type: Equation Expression Integer
--E 88

--S 89 of 143
solve(eq,y,x)
 

   (71)
                            sin(x)                     2
   [particular= sin(x)log(----------) - sin(x)log(----------) - x cos(x),
                          cos(x) + 1              cos(x) + 1
    basis= [cos(x),sin(x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (71)
--R                            sin(x)                     2
--R   [particular= sin(x)log(----------) - sin(x)log(----------) - x cos(x),
--R                          cos(x) + 1              cos(x) + 1
--R    basis= [cos(x),sin(x)]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 89

--S 90 of 143
eq := D(y x,x,7) - 14 * D(y x,x,6) + 80 * D(y x,x,5) - _
       242 * D(y x,x,4) + 419 * D(y x,x,3) - 416 * y'' + _
        220 * y' - 48 * y x = 0
 

   (72)
      (vii)         (vi)         (v)          (iv)          ,,,          ,,
     y     (x) - 14y    (x) + 80y   (x) - 242y    (x) + 419y   (x) - 416y  (x)

   + 
         ,
     220y (x) - 48y(x)

     =
     0
                                            Type: Equation Expression Integer
--R 
--R
--R   (72)
--R      (vii)         (vi)         (v)          (iv)          ,,,          ,,
--R     y     (x) - 14y    (x) + 80y   (x) - 242y    (x) + 419y   (x) - 416y  (x)
--R
--R   + 
--R         ,
--R     220y (x) - 48y(x)
--R
--R     =
--R     0
--R                                            Type: Equation Expression Integer
--E 90

--S 91 of 143
solve(eq,y,x)
 

                                  4x   3x   2x     2x   x     x  2  x
   (73)  [particular= 0,basis= [%e  ,%e  ,%e  ,x %e  ,%e ,x %e ,x %e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                  4x   3x   2x     2x   x     x  2  x
--R   (73)  [particular= 0,basis= [%e  ,%e  ,%e  ,x %e  ,%e ,x %e ,x %e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 91

--S 92 of 143
eq := D(y x,x,4) - 4/x^2 * y'' + 8/x^3 * y' -8/x^4 * y x = 0
 

          4 (iv)        2 ,,         ,
         x y    (x) - 4x y  (x) + 8xy (x) - 8y(x)

   (74)  ----------------------------------------= 0
                             4
                            x
                                            Type: Equation Expression Integer
--R 
--R
--R          4 (iv)        2 ,,         ,
--R         x y    (x) - 4x y  (x) + 8xy (x) - 8y(x)
--R
--R   (74)  ----------------------------------------= 0
--R                             4
--R                            x
--R                                            Type: Equation Expression Integer
--E 92

--S 93 of 143
solve(eq,y,x)
 

   (75)
   [particular= 0,

     basis =
         5     3     2       5     3      2       5      3     2
        x  - 5x  + 5x  - 1  x  + 5x  - 10x  + 4  x  - 10x  + 5x  + 4
       [------------------, -------------------, -------------------,
                 x                   x                    x
         5      3      2
        x  - 10x  + 20x  + 4
        --------------------]
                  x
     ]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (75)
--R   [particular= 0,
--R
--R     basis =
--R         5     3     2       5     3      2       5      3     2
--R        x  - 5x  + 5x  - 1  x  + 5x  - 10x  + 4  x  - 10x  + 5x  + 4
--R       [------------------, -------------------, -------------------,
--R                 x                   x                    x
--R         5      3      2
--R        x  - 10x  + 20x  + 4
--R        --------------------]
--R                  x
--R     ]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 93

--S 94 of 143
eq := (1+x+x^2)*D(y x,x,3) + (3+6*x)*y'' + 6*y' = 6*x
 

           2          ,,,               ,,        ,
   (76)  (x  + x + 1)y   (x) + (6x + 3)y  (x) + 6y (x)= 6x

                                            Type: Equation Expression Integer
--R 
--R
--R           2          ,,,               ,,        ,
--R   (76)  (x  + x + 1)y   (x) + (6x + 3)y  (x) + 6y (x)= 6x
--R
--R                                            Type: Equation Expression Integer
--E 94

--S 95 of 143
solve(eq,y,x)
 

                          4
                         x  - 4                 1        x + 1
   (77)  [particular= ------------,basis= [----------,----------,1]]
                        2                   2          2
                      4x  + 4x + 4         x  + x + 1 x  + x + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                          4
--R                         x  - 4                 1        x + 1
--R   (77)  [particular= ------------,basis= [----------,----------,1]]
--R                        2                   2          2
--R                      4x  + 4x + 4         x  + x + 1 x  + x + 1
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 95

--S 96 of 143
eq := (y'^2+1)*D(y(x),x,3)-3*y'*y''^2 = 0
 

           ,   2      ,,,        ,    ,,   2
   (78)  (y (x)  + 1)y   (x) - 3y (x)y  (x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R           ,   2      ,,,        ,    ,,   2
--R   (78)  (y (x)  + 1)y   (x) - 3y (x)y  (x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 96

--S 97 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseLODE: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 97

--S 98 of 143
eq := 3*y''*D(y(x),x,4)-5*D(y(x),x,3)^2 = 0
 

           ,,    (iv)        ,,,   2
   (79)  3y  (x)y    (x) - 5y   (x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,    (iv)        ,,,   2
--R   (79)  3y  (x)y    (x) - 5y   (x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 98

--S 99 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseLODE: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 99

--S 100 of 143
eq := y'+a*y(x-1) = 0
 

          ,
   (80)  y (x) + a y(x - 1)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (80)  y (x) + a y(x - 1)= 0
--R
--R                                            Type: Equation Expression Integer
--E 100

--S 101 of 143
solve(eq,y,x)
 

            x
          ++
   (81)   |   a y(%M - 1)d%M  + y(x)
         ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            x
--R          ++
--R   (81)   |   a y(%M - 1)d%M  + y(x)
--R         ++
--R                                          Type: Union(Expression Integer,...)
--E 101

--S 102 of 143
eq := D(y(x,a),x,1) = a*y(x,a)
 

   (82)  y  (x,a)= a y(x,a)
          ,1
                                            Type: Equation Expression Integer
--R 
--R
--R   (82)  y  (x,a)= a y(x,a)
--R          ,1
--R                                            Type: Equation Expression Integer
--E 102

--S 103 of 143
solve(eq,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseODE: equation has order 0
--R
--R   Continuing to read the file...
--R
--E 103

--S 104 of 143
eq := D(y x,x,4) = sin x
 

          (iv)
   (83)  y    (x)= sin(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          (iv)
--R   (83)  y    (x)= sin(x)
--R
--R                                            Type: Equation Expression Integer
--E 104

--S 105 of 143
ini := [0, 0, 0, 0]
 

   (84)  [0,0,0,0]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (84)  [0,0,0,0]
--R                                                Type: List NonNegativeInteger
--E 105

--S 106 of 143
solve(eq,y,x=0,ini)
 

                    3
         6sin(x) + x  - 6x
   (85)  -----------------
                 6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    3
--R         6sin(x) + x  - 6x
--R   (85)  -----------------
--R                 6
--R                                          Type: Union(Expression Integer,...)
--E 106

--S 107 of 143
eq := x * y'' + y' + 2 * x * y x = 0
 

           ,,       ,
   (86)  xy  (x) + y (x) + 2x y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,       ,
--R   (86)  xy  (x) + y (x) + 2x y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 107

--S 108 of 143
solve(eq,y,x=0,[1,0])
 

   (87)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (87)  "failed"
--R                                                    Type: Union("failed",...)
--E 108

--S 109 of 143
eq := x*y'^2-y(x)^2+1=0
 

            ,   2       2
   (88)  x y (x)  - y(x)  + 1= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            ,   2       2
--R   (88)  x y (x)  - y(x)  + 1= 0
--R
--R                                            Type: Equation Expression Integer
--E 109

--S 110 of 143
solve(eq,y,x=0,[1])
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 110

--S 111 of 143
eq := y' = sqrt((y(x)^2-1)/x)
 

                 +---------+
                 |    2
          ,      |y(x)  - 1
   (89)  y (x)=  |---------
                \|    x
                                            Type: Equation Expression Integer
--R 
--R
--R                 +---------+
--R                 |    2
--R          ,      |y(x)  - 1
--R   (89)  y (x)=  |---------
--R                \|    x
--R                                            Type: Equation Expression Integer
--E 111

--S 112 of 143
solve(eq,y,x=0,[1])
 
 
Daly Bug
   >> Error detected within library code:
   catdef: division by zero

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   catdef: division by zero
--R
--R   Continuing to read the file...
--R
--E 112

--S 113 of 143
eq := y''+y(x)*y'^3 = 0
 

          ,,           ,   3
   (90)  y  (x) + y(x)y (x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,           ,   3
--R   (90)  y  (x) + y(x)y (x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 113

--S 114 of 143
solve(eq,y,x=0,[0,2])
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 114

)clear all
 
 

--S 115 of 143
x := operator x
 

   (1)  x
                                                          Type: BasicOperator
--R 
--R
--R   (1)  x
--R                                                          Type: BasicOperator
--E 115

--S 116 of 143
y := operator y
 

   (2)  y
                                                          Type: BasicOperator
--R 
--R
--R   (2)  y
--R                                                          Type: BasicOperator
--E 116

--S 117 of 143
z := operator z
 

   (3)  z
                                                          Type: BasicOperator
--R 
--R
--R   (3)  z
--R                                                          Type: BasicOperator
--E 117

--S 118 of 143
x' := D(x(t),t)
 

         ,
   (4)  x (t)

                                                     Type: Expression Integer
--R 
--R
--R         ,
--R   (4)  x (t)
--R
--R                                                     Type: Expression Integer
--E 118

--S 119 of 143
y' := D(y(t),t)
 

         ,
   (5)  y (t)

                                                     Type: Expression Integer
--R 
--R
--R         ,
--R   (5)  y (t)
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 143
z' := D(z(t),t)
 

         ,
   (6)  z (t)

                                                     Type: Expression Integer
--R 
--R
--R         ,
--R   (6)  z (t)
--R
--R                                                     Type: Expression Integer
--E 120

--S 121 of 143
sys:=[x'=-3*y(t)*z(t),y'=3*x(t)*z(t),z'=-x(t)*y(t)]
 

          ,                  ,                ,
   (7)  [x (t)= - 3y(t)z(t),y (t)= 3x(t)z(t),z (t)= - x(t)y(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R          ,                  ,                ,
--R   (7)  [x (t)= - 3y(t)z(t),y (t)= 3x(t)z(t),z (t)= - x(t)y(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 121

--S 122 of 143
solve(sys,[x,y,z],t)
 
 
Daly Bug
   >> Error detected within library code:
   getfreelincoeff: not a linear ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getfreelincoeff: not a linear ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 122

--S 123 of 143
a := operator a
 

   (8)  a
                                                          Type: BasicOperator
--R 
--R
--R   (8)  a
--R                                                          Type: BasicOperator
--E 123

--S 124 of 143
b := operator b
 

   (9)  b
                                                          Type: BasicOperator
--R 
--R
--R   (9)  b
--R                                                          Type: BasicOperator
--E 124

--S 125 of 143
eq1 := x'=a(t)*(y(t)^2-x(t)^2)+2*b(t)*x(t)*y(t)+2*c*x(t)
 

          ,             2                           2
   (10)  x (t)= a(t)y(t)  + 2b(t)x(t)y(t) - a(t)x(t)  + 2c x(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,             2                           2
--R   (10)  x (t)= a(t)y(t)  + 2b(t)x(t)y(t) - a(t)x(t)  + 2c x(t)
--R
--R                                            Type: Equation Expression Integer
--E 125

--S 126 of 143
eq2 := y'=b(t)*(y(t)^2-x(t)^2)-2*a(t)*x(t)*y(t)+2*c*y(t)
 

          ,             2                                    2
   (11)  y (t)= b(t)y(t)  + (- 2a(t)x(t) + 2c)y(t) - b(t)x(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,             2                                    2
--R   (11)  y (t)= b(t)y(t)  + (- 2a(t)x(t) + 2c)y(t) - b(t)x(t)
--R
--R                                            Type: Equation Expression Integer
--E 126

--S 127 of 143
solve([eq1,eq2],[x,y],t)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 127

--S 128 of 143
eq1 := x'=x(t)*(1+cos(t)/(2+sin(t)))
 

          ,     x(t)sin(t) + x(t)cos(t) + 2x(t)
   (12)  x (t)= -------------------------------
                           sin(t) + 2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,     x(t)sin(t) + x(t)cos(t) + 2x(t)
--R   (12)  x (t)= -------------------------------
--R                           sin(t) + 2
--R                                            Type: Equation Expression Integer
--E 128

--S 129 of 143
eq2 := y'=x(t)-y(t)
 

          ,
   (13)  y (t)= - y(t) + x(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (13)  y (t)= - y(t) + x(t)
--R
--R                                            Type: Equation Expression Integer
--E 129

--S 130 of 143
solve([eq1,eq2],[x,y],t)
 

   (14)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (14)  "failed"
--R                                                    Type: Union("failed",...)
--E 130

--S 131 of 143
eq1 := x' = 9*x(t)+2*y(t)
 

          ,
   (15)  x (t)= 2y(t) + 9x(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (15)  x (t)= 2y(t) + 9x(t)
--R
--R                                            Type: Equation Expression Integer
--E 131

--S 132 of 143
eq2 := y' = x(t)+8*y(t)
 

          ,
   (16)  y (t)= 8y(t) + x(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (16)  y (t)= 8y(t) + x(t)
--R
--R                                            Type: Equation Expression Integer
--E 132

--S 133 of 143
solve([eq1,eq2],[x,y],t)
 

                                             10t
                                       10t %e        7t     7t
   (17)  [particular= [0,0],basis= [[%e   ,-----],[%e  ,- %e  ]]]
                                             2
Type: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...)
--R 
--R
--R                                             10t
--R                                       10t %e        7t     7t
--R   (17)  [particular= [0,0],basis= [[%e   ,-----],[%e  ,- %e  ]]]
--R                                             2
--RType: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...)
--E 133

--S 134 of 143
eq1 := x'-x(t)+2*y(t)=0
 

          ,
   (18)  x (t) + 2y(t) - x(t)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (18)  x (t) + 2y(t) - x(t)= 0
--R
--R                                            Type: Equation Expression Integer
--E 134

--S 135 of 143
eq2 := D(x(t),t,2)-2*y'=2*t-cot(2*t)
 

          ,,        ,
   (19)  x  (t) - 2y (t)= - cot(2t) + 2t

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,        ,
--R   (19)  x  (t) - 2y (t)= - cot(2t) + 2t
--R
--R                                            Type: Equation Expression Integer
--E 135

--S 136 of 143
solve([eq1,eq2],[x,y],t)
 
 
Daly Bug
   >> Error detected within library code:
   solve: not a first order linear system

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   solve: not a first order linear system
--R
--R   Continuing to read the file...
--R
--E 136

--S 137 of 143
eq1 := x' = -x(t)/t/(t^2+1)+y(t)/t^2/(t^2+1)+1/t
 

                                 3
          ,     y(t) - t x(t) + t  + t
   (20)  x (t)= ----------------------
                         4    2
                        t  + t
                                            Type: Equation Expression Integer
--R 
--R
--R                                 3
--R          ,     y(t) - t x(t) + t  + t
--R   (20)  x (t)= ----------------------
--R                         4    2
--R                        t  + t
--R                                            Type: Equation Expression Integer
--E 137

--S 138 of 143
eq2 := y' = -t^2*x(t)/(t^2+1)+(2*t^2+1)*y(t)/t/(t^2+1)+1
 

                   2             3        3
          ,     (2t  + 1)y(t) - t x(t) + t  + t
   (21)  y (t)= -------------------------------
                              3
                             t  + t
                                            Type: Equation Expression Integer
--R 
--R
--R                   2             3        3
--R          ,     (2t  + 1)y(t) - t x(t) + t  + t
--R   (21)  y (t)= -------------------------------
--R                              3
--R                             t  + t
--R                                            Type: Equation Expression Integer
--E 138

--S 139 of 143
solve([eq1,eq2],[x,y],t)
 

                                                         1    2
   (22)  [particular= [log(t) - 1,t log(t) - t],basis= [[-,- t ],[1,t]]]
                                                         t
Type: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...)
--R 
--R
--R                                                         1    2
--R   (22)  [particular= [log(t) - 1,t log(t) - t],basis= [[-,- t ],[1,t]]]
--R                                                         t
--RType: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...)
--E 139

)clear all
 

--S 140 of 143
s := sqrt(-222)
 

         +-----+
   (1)  \|- 222
                                                        Type: AlgebraicNumber
--R 
--R
--R         +-----+
--R   (1)  \|- 222
--R                                                        Type: AlgebraicNumber
--E 140

--S 141 of 143
a0 := 104/25*x^10+(274/25-22/15*s)*x^8+(7754/75-68/15*s)*x^6
 

                        +-----+                  +-----+
        104  10   - 110\|- 222  + 822  8   - 340\|- 222  + 7754  6
   (2)  --- x   + ------------------- x  + -------------------- x
         25                75                       75
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R                        +-----+                  +-----+
--R        104  10   - 110\|- 222  + 822  8   - 340\|- 222  + 7754  6
--R   (2)  --- x   + ------------------- x  + -------------------- x
--R         25                75                       75
--R                                             Type: Polynomial AlgebraicNumber
--E 141

--S 142 of 143
a0 := a0+(11248/75-194/15*s)*x^4+(29452/75-296/5*s)*x^2-10952/5-148/3*s
 

   (3)
                     +-----+                  +-----+
     104  10   - 110\|- 222  + 822  8   - 340\|- 222  + 7754  6
     --- x   + ------------------- x  + -------------------- x
      25                75                       75
   + 
         +-----+                     +-----+                    +-----+
   - 970\|- 222  + 11248  4   - 4440\|- 222  + 29452  2   - 740\|- 222  - 32856
   --------------------- x  + ---------------------- x  + ---------------------
             75                         75                          15
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R   (3)
--R                     +-----+                  +-----+
--R     104  10   - 110\|- 222  + 822  8   - 340\|- 222  + 7754  6
--R     --- x   + ------------------- x  + -------------------- x
--R      25                75                       75
--R   + 
--R         +-----+                     +-----+                    +-----+
--R   - 970\|- 222  + 11248  4   - 4440\|- 222  + 29452  2   - 740\|- 222  - 32856
--R   --------------------- x  + ---------------------- x  + ---------------------
--R             75                         75                          15
--R                                             Type: Polynomial AlgebraicNumber
--E 142

--S 143 of 143
a2 := x^12+2*x^10+151/3*x^8+296/3*x^6+5920/9*x^4+10952/9*x^2+5476/9
 

         12     10   151  8   296  6   5920  4   10952  2   5476
   (4)  x   + 2x   + --- x  + --- x  + ---- x  + ----- x  + ----
                      3        3         9         9          9
                                            Type: Polynomial Fraction Integer
--R 
--R
--R         12     10   151  8   296  6   5920  4   10952  2   5476
--R   (4)  x   + 2x   + --- x  + --- x  + ---- x  + ----- x  + ----
--R                      3        3         9         9          9
--R                                            Type: Polynomial Fraction Integer
--E 143

--y := operator y
--y' := D(y x, x)
--y'' := D(y', x)
--eq := a2*y'' - a0*y(x)
--solve(eq,y,x)
--R 
--R   WARNING (genufact): No known algorithm to factor
--R      8     43808    6   827062184  4   44060595526144  2   27067141014651136
--R     ?  + --------- ?  - --------- ?  - -------------- ?  - -----------------
--R            +-----+         5625               +-----+           31640625
--R          5\|- 222                      253125\|- 222
--R     , trying square-free.
--R   WARNING (genufact): No known algorithm to factor
--R      8   4292  6   16006348  4   58334426144  2   94037902336
--R     ?  + ---- ?  + -------- ?  + ----------- ?  + -----------
--R           25         1875           421875           140625
--R     , trying square-free.
--R   WARNING (genufact): No known algorithm to factor
--R      8      1776    6   151034  4     108731456   2   902641936
--R     ?  - --------- ?  - ------ ?  + ------------ ?  - ---------
--R            +-----+        625            +-----+        390625
--R          5\|- 222                   9375\|- 222
--R     , trying square-free.
--R   WARNING (genufact): No known algorithm to factor
--R        8      7   3426  6   14364  5   903369  4   277938  3   31725044  2
--R       ?  - 18?  + ---- ?  - ----- ?  + ------ ?  - ------ ?  + -------- ?
--R                    25         25         625         125         15625
--R     + 
--R         15594264     3118752
--R       - -------- ? + -------
--R           15625       15625
--R     , trying square-free.
--R

--solve(15*D(y(x),x)+24*y(x)^2=7*x^(-8/3),y,x)

)spool 
 
Starts dribbling to Bezier.output (2010/3/27, 18:41:45).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
n:=linearBezier([2.0,2.0],[4.0,4.0])
 

   (1)  theMap(BEZIER;linearBezier;2LM;1!0,0)
                                                  Type: (Float -> List Float)
--R
--I   (1)  theMap(BEZIER;linearBezier;2LM;1!0,707)
--R                                                  Type: (Float -> List Float)
--E 1

--S 2 of 9
[n(t/10.0) for t in 0..10 by 1]
 

   (2)
   [[2.0,2.0], [2.2,2.2], [2.4,2.4], [2.6,2.6], [2.8,2.8], [3.0,3.0],
    [3.2,3.2], [3.4,3.4], [3.6,3.6], [3.8,3.8], [4.0,4.0]]
                                                        Type: List List Float
--R
--R   (2)
--R   [[2.0,2.0], [2.2,2.2], [2.4,2.4], [2.6,2.6], [2.8,2.8], [3.0,3.0],
--R    [3.2,3.2], [3.4,3.4], [3.6,3.6], [3.8,3.8], [4.0,4.0]]
--R                                                        Type: List List Float
--E 2

--S 3 of 9
n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0])
 

   (3)  theMap(BEZIER;quadraticBezier;3LM;2!0,0)
                                                  Type: (Float -> List Float)
--R
--I   (3)  theMap(BEZIER;quadraticBezier;3LM;2!0,291)
--R                                                  Type: (Float -> List Float)
--E 3

--S 4 of 9
[n(t/10.0) for t in 0..10 by 1]
 

   (4)
   [[2.0,2.0], [2.4,2.36], [2.8,2.64], [3.2,2.84], [3.6,2.96], [4.0,3.0],
    [4.4,2.96], [4.8,2.84], [5.2,2.64], [5.6,2.36], [6.0,2.0]]
                                                        Type: List List Float
--R
--R   (4)
--R   [[2.0,2.0], [2.4,2.36], [2.8,2.64], [3.2,2.84], [3.6,2.96], [4.0,3.0],
--R    [4.4,2.96], [4.8,2.84], [5.2,2.64], [5.6,2.36], [6.0,2.0]]
--R                                                        Type: List List Float
--E 4

--S 5 of 9
n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0])
 

   (5)  theMap(BEZIER;cubicBezier;4LM;3!0,0)
                                                  Type: (Float -> List Float)
--R
--I   (5)  theMap(BEZIER;cubicBezier;4LM;3!0,915)
--R                                                  Type: (Float -> List Float)
--E 5

--S 6 of 9
[n(t/10.0) for t in 0..10 by 1]
 

   (6)
   [[2.0,2.0], [2.112,2.54], [2.416,2.96], [2.864,3.26], [3.408,3.44],
    [4.0,3.5], [4.592,3.44], [5.136,3.26], [5.584,2.96], [5.888,2.54],
    [6.0,2.0]]
                                                        Type: List List Float
--R
--R   (6)
--R   [[2.0,2.0], [2.112,2.54], [2.416,2.96], [2.864,3.26], [3.408,3.44],
--R    [4.0,3.5], [4.592,3.44], [5.136,3.26], [5.584,2.96], [5.888,2.54],
--R    [6.0,2.0]]
--R                                                        Type: List List Float
--E 6

--S 7 of 9
line:=[[i::Float,4.0] for i in -4..4 by 1]
 

   (7)
   [[- 4.0,4.0], [- 3.0,4.0], [- 2.0,4.0], [- 1.0,4.0], [0.0,4.0], [1.0,4.0],
    [2.0,4.0], [3.0,4.0], [4.0,4.0]]
                                                        Type: List List Float
--E 7

--S 8 of 9
functions:=[quadraticBezier([2.0,2.0],m,[6.0,2.0]) for m in line]
 

   (8)
   [theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0),
    theMap(BEZIER;quadraticBezier;3LM;2!0,0)]
                                             Type: List (Float -> List Float)
--E 8

--S 9 of 9
graphs:=[[point(((functions.i)(j/100.0))::LIST(DFLOAT)) for j in 0..100] for i in 1..9]
 

   (9)
   [
     [[2.,2.], [1.8815999999999999,2.0396000000000001],
      [1.7664,2.0783999999999998], [1.6543999999999999,2.1163999999999996],
      [1.5455999999999999,2.1536], [1.4399999999999999,2.1899999999999999],
      [1.3375999999999999,2.2256], [1.2383999999999999,2.2603999999999997],
      [1.1423999999999999,2.2944], [1.0495999999999999,2.3275999999999999],
      [0.95999999999999996,2.3599999999999999],
      [0.87359999999999993,2.3915999999999999],
      [0.79039999999999999,2.4223999999999997],
      [0.71039999999999992,2.4523999999999999],
      [0.63359999999999994,2.4815999999999998],
      [0.56000000000000005,2.5099999999999998],
      [0.48959999999999998,2.5375999999999999], [0.4224,2.5644],
      [0.3584,2.5903999999999998], [0.29759999999999998,2.6155999999999997],
      [0.23999999999999999,2.6399999999999997],
      [0.18559999999999999,2.6635999999999997],
      [0.13439999999999999,2.6863999999999999],
      [8.6400000000000005E-2,2.7084000000000001],
      [4.1599999999999998E-2,2.7295999999999996], [0.,2.75],
      [- 3.8400000000000004E-2,2.7695999999999996],
      [- 7.3599999999999999E-2,2.7884000000000002], [- 0.1056,2.8064],
      [- 0.13440000000000002,2.8235999999999999],
      [- 0.15999999999999998,2.8399999999999999],
      [- 0.18239999999999998,2.8555999999999999],
      [- 0.20159999999999997,2.8704000000000001],
      [- 0.21760000000000002,2.8843999999999999],
      [- 0.23039999999999999,2.8975999999999997],
      [- 0.23999999999999999,2.9100000000000001],
      [- 0.24639999999999998,2.9215999999999998],
      [- 0.24959999999999999,2.9323999999999999],
      [- 0.24959999999999999,2.9424000000000001],
      [- 0.24639999999999998,2.9516], [- 0.23999999999999999,2.96],
      [- 0.23039999999999999,2.9676],
      [- 0.21760000000000002,2.9744000000000002],
      [- 0.20159999999999997,2.9803999999999999],
      [- 0.18239999999999998,2.9855999999999998],
      [- 0.15999999999999998,2.9900000000000002],
      [- 0.13440000000000002,2.9935999999999998], [- 0.1056,2.9964],
      [- 7.3599999999999999E-2,2.9984000000000002],
      [- 3.8400000000000004E-2,2.9996], [0.,3.],
      [4.1599999999999998E-2,2.9996],
      [8.6400000000000005E-2,2.9984000000000002], [0.13439999999999999,2.9964],
      [0.18559999999999999,2.9935999999999998],
      [0.23999999999999999,2.9900000000000002],
      [0.29759999999999998,2.9855999999999998], [0.3584,2.9803999999999999],
      [0.4224,2.9744000000000002], [0.48959999999999998,2.9676],
      [0.56000000000000005,2.96], [0.63359999999999994,2.9516],
      [0.71039999999999992,2.9424000000000001],
      [0.79039999999999999,2.9323999999999999],
      [0.87359999999999993,2.9215999999999998],
      [0.95999999999999996,2.9100000000000001],
      [1.0495999999999999,2.8975999999999997],
      [1.1423999999999999,2.8843999999999999],
      [1.2383999999999999,2.8704000000000001],
      [1.3375999999999999,2.8555999999999999],
      [1.4399999999999999,2.8399999999999999],
      [1.5455999999999999,2.8235999999999999], [1.6543999999999999,2.8064],
      [1.7664,2.7884000000000002], [1.8815999999999999,2.7695999999999996],
      [2.,2.75], [2.1215999999999999,2.7295999999999996],
      [2.2464,2.7084000000000001], [2.3743999999999996,2.6863999999999999],
      [2.5055999999999998,2.6635999999999997],
      [2.6399999999999997,2.6399999999999997],
      [2.7775999999999996,2.6155999999999997],
      [2.9184000000000001,2.5903999999999998], [3.0623999999999998,2.5644],
      [3.2096,2.5375999999999999], [3.3599999999999999,2.5099999999999998],
      [3.5135999999999998,2.4815999999999998],
      [3.6703999999999999,2.4523999999999999], [3.8304,2.4223999999999997],
      [3.9935999999999998,2.3915999999999999],
      [4.1600000000000001,2.3599999999999999],
      [4.3295999999999992,2.3275999999999999], [4.5023999999999997,2.2944],
      [4.6783999999999999,2.2603999999999997], [4.8575999999999997,2.2256],
      [5.0399999999999991,2.1899999999999999], [5.2256,2.1536],
      [5.4143999999999997,2.1163999999999996],
      [5.6063999999999998,2.0783999999999998],
      [5.8015999999999996,2.0396000000000001], [6.,2.]]
     ,

     [[2.,2.], [1.9014,2.0396000000000001],
      [1.8056000000000001,2.0783999999999998],
      [1.7125999999999999,2.1163999999999996], [1.6223999999999998,2.1536],
      [1.5349999999999999,2.1899999999999999], [1.4503999999999999,2.2256],
      [1.3685999999999998,2.2603999999999997], [1.2896000000000001,2.2944],
      [1.2134,2.3275999999999999], [1.1399999999999999,2.3599999999999999],
      [1.0693999999999999,2.3915999999999999],
      [1.0015999999999998,2.4223999999999997],
      [0.93659999999999999,2.4523999999999999],
      [0.87439999999999996,2.4815999999999998],
      [0.81499999999999995,2.5099999999999998],
      [0.75839999999999996,2.5375999999999999], [0.70459999999999989,2.5644],
      [0.65359999999999996,2.5903999999999998],
      [0.60539999999999994,2.6155999999999997],
      [0.56000000000000005,2.6399999999999997],
      [0.51739999999999997,2.6635999999999997],
      [0.47760000000000002,2.6863999999999999],
      [0.44059999999999999,2.7084000000000001],
      [0.40639999999999998,2.7295999999999996], [0.375,2.75],
      [0.34639999999999999,2.7695999999999996], [0.3206,2.7884000000000002],
      [0.29759999999999998,2.8064], [0.27739999999999998,2.8235999999999999],
      [0.26000000000000001,2.8399999999999999],
      [0.24540000000000001,2.8555999999999999],
      [0.23359999999999997,2.8704000000000001],
      [0.22459999999999999,2.8843999999999999],
      [0.21839999999999998,2.8975999999999997], [0.215,2.9100000000000001],
      [0.21439999999999998,2.9215999999999998],
      [0.21659999999999999,2.9323999999999999],
      [0.22159999999999999,2.9424000000000001], [0.22939999999999999,2.9516],
      [0.23999999999999999,2.96], [0.25339999999999996,2.9676],
      [0.26959999999999995,2.9744000000000002],
      [0.28859999999999997,2.9803999999999999],
      [0.31040000000000001,2.9855999999999998],
      [0.33499999999999996,2.9900000000000002], [0.3624,2.9935999999999998],
      [0.39259999999999995,2.9964], [0.42559999999999998,2.9984000000000002],
      [0.46139999999999998,2.9996], [0.5,3.], [0.54139999999999999,2.9996],
      [0.5855999999999999,2.9984000000000002], [0.63260000000000005,2.9964],
      [0.6823999999999999,2.9935999999999998],
      [0.73499999999999999,2.9900000000000002],
      [0.79039999999999999,2.9855999999999998],
      [0.84860000000000002,2.9803999999999999],
      [0.90959999999999996,2.9744000000000002], [0.97340000000000004,2.9676],
      [1.04,2.96], [1.1093999999999999,2.9516], [1.1816,2.9424000000000001],
      [1.2565999999999999,2.9323999999999999], [1.3344,2.9215999999999998],
      [1.415,2.9100000000000001], [1.4984,2.8975999999999997],
      [1.5846,2.8843999999999999], [1.6736,2.8704000000000001],
      [1.7654000000000001,2.8555999999999999],
      [1.8599999999999999,2.8399999999999999],
      [1.9573999999999998,2.8235999999999999], [2.0575999999999999,2.8064],
      [2.1605999999999996,2.7884000000000002], [2.2664,2.7695999999999996],
      [2.375,2.75], [2.4863999999999997,2.7295999999999996],
      [2.6006,2.7084000000000001], [2.7176,2.6863999999999999],
      [2.8373999999999997,2.6635999999999997], [2.96,2.6399999999999997],
      [3.0853999999999999,2.6155999999999997],
      [3.2135999999999996,2.5903999999999998], [3.3445999999999998,2.5644],
      [3.4783999999999997,2.5375999999999999],
      [3.6150000000000002,2.5099999999999998], [3.7544,2.4815999999999998],
      [3.8965999999999998,2.4523999999999999],
      [4.0415999999999999,2.4223999999999997],
      [4.1893999999999991,2.3915999999999999],
      [4.3399999999999999,2.3599999999999999],
      [4.4933999999999994,2.3275999999999999], [4.6495999999999995,2.2944],
      [4.8086000000000002,2.2603999999999997], [4.9703999999999997,2.2256],
      [5.1349999999999998,2.1899999999999999], [5.3023999999999996,2.1536],
      [5.4725999999999999,2.1163999999999996], [5.6456,2.0783999999999998],
      [5.8213999999999997,2.0396000000000001], [6.,2.]]
     ,

     [[2.,2.], [1.9211999999999998,2.0396000000000001],
      [1.8448,2.0783999999999998], [1.7707999999999999,2.1163999999999996],
      [1.6991999999999998,2.1536], [1.6299999999999999,2.1899999999999999],
      [1.5631999999999999,2.2256], [1.4987999999999999,2.2603999999999997],
      [1.4367999999999999,2.2944], [1.3772,2.3275999999999999],
      [1.3199999999999998,2.3599999999999999],
      [1.2652000000000001,2.3915999999999999],
      [1.2128000000000001,2.4223999999999997],
      [1.1627999999999998,2.4523999999999999], [1.1152,2.4815999999999998],
      [1.0699999999999998,2.5099999999999998],
      [1.0271999999999999,2.5375999999999999], [0.9867999999999999,2.5644],
      [0.94879999999999998,2.5903999999999998],
      [0.91320000000000001,2.6155999999999997],
      [0.87999999999999989,2.6399999999999997],
      [0.84919999999999995,2.6635999999999997],
      [0.82079999999999997,2.6863999999999999],
      [0.79479999999999995,2.7084000000000001], [0.7712,2.7295999999999996],
      [0.75,2.75], [0.73119999999999996,2.7695999999999996],
      [0.71479999999999999,2.7884000000000002], [0.70079999999999998,2.8064],
      [0.68920000000000003,2.8235999999999999],
      [0.67999999999999994,2.8399999999999999],
      [0.67320000000000002,2.8555999999999999],
      [0.66879999999999995,2.8704000000000001],
      [0.66679999999999995,2.8843999999999999],
      [0.66720000000000002,2.8975999999999997],
      [0.66999999999999993,2.9100000000000001],
      [0.67520000000000002,2.9215999999999998],
      [0.68279999999999996,2.9323999999999999],
      [0.69279999999999997,2.9424000000000001], [0.70520000000000005,2.9516],
      [0.71999999999999997,2.96], [0.73719999999999997,2.9676],
      [0.75679999999999992,2.9744000000000002],
      [0.77879999999999994,2.9803999999999999],
      [0.80319999999999991,2.9855999999999998],
      [0.82999999999999996,2.9900000000000002],
      [0.85919999999999996,2.9935999999999998], [0.89080000000000004,2.9964],
      [0.92479999999999996,2.9984000000000002], [0.96120000000000005,2.9996],
      [1.,3.], [1.0411999999999999,2.9996], [1.0848,2.9984000000000002],
      [1.1307999999999998,2.9964], [1.1791999999999998,2.9935999999999998],
      [1.23,2.9900000000000002], [1.2831999999999999,2.9855999999999998],
      [1.3388,2.9803999999999999], [1.3967999999999998,2.9744000000000002],
      [1.4571999999999998,2.9676], [1.52,2.96], [1.5851999999999999,2.9516],
      [1.6528,2.9424000000000001], [1.7227999999999999,2.9323999999999999],
      [1.7951999999999999,2.9215999999999998],
      [1.8700000000000001,2.9100000000000001], [1.9472,2.8975999999999997],
      [2.0267999999999997,2.8843999999999999],
      [2.1087999999999996,2.8704000000000001], [2.1932,2.8555999999999999],
      [2.2799999999999998,2.8399999999999999],
      [2.3692000000000002,2.8235999999999999], [2.4607999999999999,2.8064],
      [2.5548000000000002,2.7884000000000002],
      [2.6511999999999998,2.7695999999999996], [2.75,2.75],
      [2.8512,2.7295999999999996], [2.9547999999999996,2.7084000000000001],
      [3.0608,2.6863999999999999], [3.1692,2.6635999999999997],
      [3.2799999999999998,2.6399999999999997],
      [3.3932000000000002,2.6155999999999997],
      [3.5087999999999999,2.5903999999999998], [3.6267999999999998,2.5644],
      [3.7471999999999999,2.5375999999999999],
      [3.8700000000000001,2.5099999999999998],
      [3.9951999999999996,2.4815999999999998],
      [4.1227999999999998,2.4523999999999999],
      [4.2527999999999997,2.4223999999999997],
      [4.3851999999999993,2.3915999999999999],
      [4.5199999999999996,2.3599999999999999],
      [4.6571999999999996,2.3275999999999999], [4.7967999999999993,2.2944],
      [4.9387999999999996,2.2603999999999997], [5.0831999999999997,2.2256],
      [5.2300000000000004,2.1899999999999999], [5.3792,2.1536],
      [5.5307999999999993,2.1163999999999996],
      [5.6847999999999992,2.0783999999999998],
      [5.8411999999999997,2.0396000000000001], [6.,2.]]
     ,

     [[2.,2.], [1.9409999999999998,2.0396000000000001],
      [1.8839999999999999,2.0783999999999998], [1.829,2.1163999999999996],
      [1.7759999999999998,2.1536], [1.7250000000000001,2.1899999999999999],
      [1.6759999999999999,2.2256], [1.629,2.2603999999999997],
      [1.5840000000000001,2.2944], [1.5409999999999999,2.3275999999999999],
      [1.5,2.3599999999999999], [1.4609999999999999,2.3915999999999999],
      [1.4239999999999999,2.4223999999999997],
      [1.3889999999999998,2.4523999999999999],
      [1.3559999999999999,2.4815999999999998], [1.325,2.5099999999999998],
      [1.2959999999999998,2.5375999999999999], [1.2689999999999999,2.5644],
      [1.244,2.5903999999999998], [1.2210000000000001,2.6155999999999997],
      [1.2,2.6399999999999997], [1.181,2.6635999999999997],
      [1.1639999999999999,2.6863999999999999], [1.149,2.7084000000000001],
      [1.1359999999999999,2.7295999999999996], [1.125,2.75],
      [1.1160000000000001,2.7695999999999996], [1.109,2.7884000000000002],
      [1.1040000000000001,2.8064], [1.101,2.8235999999999999],
      [1.1000000000000001,2.8399999999999999], [1.101,2.8555999999999999],
      [1.1040000000000001,2.8704000000000001], [1.109,2.8843999999999999],
      [1.1160000000000001,2.8975999999999997], [1.125,2.9100000000000001],
      [1.1359999999999999,2.9215999999999998], [1.149,2.9323999999999999],
      [1.1639999999999999,2.9424000000000001], [1.181,2.9516], [1.2,2.96],
      [1.2210000000000001,2.9676], [1.244,2.9744000000000002],
      [1.2689999999999999,2.9803999999999999],
      [1.2959999999999998,2.9855999999999998], [1.325,2.9900000000000002],
      [1.3559999999999999,2.9935999999999998], [1.3889999999999998,2.9964],
      [1.4239999999999999,2.9984000000000002], [1.4609999999999999,2.9996],
      [1.5,3.], [1.5409999999999999,2.9996],
      [1.5840000000000001,2.9984000000000002], [1.629,2.9964],
      [1.6759999999999999,2.9935999999999998],
      [1.7250000000000001,2.9900000000000002],
      [1.7759999999999998,2.9855999999999998], [1.829,2.9803999999999999],
      [1.8839999999999999,2.9744000000000002], [1.9409999999999998,2.9676],
      [2.,2.96], [2.0609999999999999,2.9516],
      [2.1239999999999997,2.9424000000000001],
      [2.1890000000000001,2.9323999999999999],
      [2.2559999999999998,2.9215999999999998],
      [2.3250000000000002,2.9100000000000001],
      [2.3959999999999999,2.8975999999999997],
      [2.4689999999999999,2.8843999999999999],
      [2.5439999999999996,2.8704000000000001], [2.621,2.8555999999999999],
      [2.7000000000000002,2.8399999999999999],
      [2.7809999999999997,2.8235999999999999], [2.8639999999999999,2.8064],
      [2.9489999999999998,2.7884000000000002],
      [3.0359999999999996,2.7695999999999996], [3.125,2.75],
      [3.2160000000000002,2.7295999999999996],
      [3.3090000000000002,2.7084000000000001],
      [3.4039999999999999,2.6863999999999999],
      [3.5009999999999999,2.6635999999999997],
      [3.5999999999999996,2.6399999999999997],
      [3.7009999999999996,2.6155999999999997],
      [3.8039999999999998,2.5903999999999998], [3.9089999999999998,2.5644],
      [4.016,2.5375999999999999], [4.125,2.5099999999999998],
      [4.2359999999999998,2.4815999999999998],
      [4.3490000000000002,2.4523999999999999],
      [4.4640000000000004,2.4223999999999997],
      [4.5809999999999995,2.3915999999999999],
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      [5.1999999999999993,2.6399999999999997],
      [5.2400000000000002,2.6155999999999997],
      [5.2799999999999994,2.5903999999999998], [5.3200000000000003,2.5644],
      [5.3599999999999994,2.5375999999999999],
      [5.4000000000000004,2.5099999999999998],
      [5.4399999999999995,2.4815999999999998],
      [5.4800000000000004,2.4523999999999999],
      [5.5199999999999996,2.4223999999999997],
      [5.5599999999999996,2.3915999999999999],
      [5.5999999999999996,2.3599999999999999],
      [5.6399999999999997,2.3275999999999999], [5.6799999999999997,2.2944],
      [5.7199999999999998,2.2603999999999997], [5.7599999999999998,2.2256],
      [5.7999999999999998,2.1899999999999999], [5.8399999999999999,2.1536],
      [5.8799999999999999,2.1163999999999996],
      [5.9199999999999999,2.0783999999999998], [5.96,2.0396000000000001],
      [6.,2.]]
     ]
                                            Type: List List Point DoubleFloat
(10) -> Starts dribbling to noonburg.output (2010/3/27, 18:30:17).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
RN := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 6
dmp0 := DMP([x,y,z,c],RN)
 

   (2)  DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 6
px : dmp0 := 1-c*x +x*(y**2 + z**2)
 

           2      2
   (3)  x y  + x z  - x c + 1
          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R           2      2
--R   (3)  x y  + x z  - x c + 1
--R          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 3

--S 4 of 6
py : dmp0 := 1-c*y +y*(z**2 + x**2)
 

         2       2
   (4)  x y + y z  - y c + 1
          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R         2       2
--R   (4)  x y + y z  - y c + 1
--R          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 4

--S 5 of 6
pz : dmp0 := 1-c*z +z*(x**2 + y**2)
 

         2     2
   (5)  x z + y z - z c + 1
          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R         2     2
--R   (5)  x z + y z - z c + 1
--R          Type: DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 5

--S 6 of 6
gb0 := groebnerFactorize [px,py,pz]
 

   (6)
   [
           3 2     2    1    3       1  2       3 2     2    1    3       1  2
     [x - z c  + 2z c + - z c  - z + - c , y - z c  + 2z c + - z c  - z + - c ,
                        2            2                       2            2
       4     3   1  2 2         1
      z c - z  - - z c  - z c - -]
                 2              2
     ,

     [
              1    3   1      1  3 5   4  3 2    2  2 4   8  2    4    3
         x - -- y c  - - y + -- z c  - - z c  - -- z c  + - z c - - z c  + z
             15        5     15        5        15        5       3
       + 
            1  5   2  2
         - -- c  + - c
           30      5
       ,

          2    1    5    7    2    2  3 4   8  3     4  2 3   11  2    1    5
         y  + -- y c  - -- y c  - -- z c  + - z c + -- z c  - -- z  + -- z c
              90        15        15        5       15         5      18
       + 
           1    2    1  4   9
         - - z c  + -- c  - - c
           3        15      5
       ,

                1    5    7    2    2  3 4   2  3     4  2 3   1  2    1    5
         y z - -- y c  + -- y c  + -- z c  + - z c - -- z c  + - z  - -- z c
               90        15        15        5       15        5      18
       + 
           2    2    1  4   1
         - - z c  - -- c  - - c
           3        15      5
       ,
       4    1  3 5    3 2   1  2         1   5   1  2   6      3
      z  + -- z c  - z c  - - z c - z + --- c  - - c , c  - 54c  + 54]
           54               2           108      2
     ,
                  2             3             4   3  2    1     1  2
    [x - z,y z - z  + c,y c - 2z  + 2z c - 1,z  - - z c + - z + - c ],
                                                  2       2     2

           1    3   1      1   3 5    8  3 2    2    3   7      1   5    4  2
     [x - -- y c  - - y - --- z c  + -- z c  - -- z c  - - z - --- c  + -- c ,
          15        5     135        15        15        5     270      15

          2    1    5    7    2    2   3 4   16  3     2    1    5   31    2
         y  + -- y c  - -- y c  + --- z c  - -- z c + z  - -- z c  + -- z c
              90        15        135        15            30        15
       + 
          1   4   23
         --- c  - -- c
         135      15
       ,

                1    5    7    2    1  3 4   14  3     2    1    5   14    2
         y z - -- y c  + -- y c  + -- z c  - -- z c - z  - -- z c  + -- z c
               90        15        45        15            45        15
       + 
          1  4    8
         -- c  + -- c
         90      15
       ,
       4   3  2    1     1  2   6      3
      z  - - z c + - z + - c , c  - 54c  + 54]
           2       2     2
     ,
                2          2      3
    [x + y + z,y  + y z + z  - c,z  - z c - 1], [1],
            2             3                   4   3  2    1     1  2
    [x z - z  + c,x c - 2z  + 2z c - 1,y - z,z  - - z c + - z + - c ],
                                                  2       2     2
                  3   1       1
    [x - z,y - z,z  - - z c + -]]
                      2       2
Type: List List DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--R 
--R
--R   (6)
--R   [
--R           3 2     2    1    3       1  2       3 2     2    1    3       1  2
--R     [x - z c  + 2z c + - z c  - z + - c , y - z c  + 2z c + - z c  - z + - c ,
--R                        2            2                       2            2
--R       4     3   1  2 2         1
--R      z c - z  - - z c  - z c - -]
--R                 2              2
--R     ,
--R
--R     [
--R              1    3   1      1  3 5   4  3 2    2  2 4   8  2    4    3
--R         x - -- y c  - - y + -- z c  - - z c  - -- z c  + - z c - - z c  + z
--R             15        5     15        5        15        5       3
--R       + 
--R            1  5   2  2
--R         - -- c  + - c
--R           30      5
--R       ,
--R
--R          2    1    5    7    2    2  3 4   8  3     4  2 3   11  2    1    5
--R         y  + -- y c  - -- y c  - -- z c  + - z c + -- z c  - -- z  + -- z c
--R              90        15        15        5       15         5      18
--R       + 
--R           1    2    1  4   9
--R         - - z c  + -- c  - - c
--R           3        15      5
--R       ,
--R
--R                1    5    7    2    2  3 4   2  3     4  2 3   1  2    1    5
--R         y z - -- y c  + -- y c  + -- z c  + - z c - -- z c  + - z  - -- z c
--R               90        15        15        5       15        5      18
--R       + 
--R           2    2    1  4   1
--R         - - z c  - -- c  - - c
--R           3        15      5
--R       ,
--R       4    1  3 5    3 2   1  2         1   5   1  2   6      3
--R      z  + -- z c  - z c  - - z c - z + --- c  - - c , c  - 54c  + 54]
--R           54               2           108      2
--R     ,
--R                  2             3             4   3  2    1     1  2
--R    [x - z,y z - z  + c,y c - 2z  + 2z c - 1,z  - - z c + - z + - c ],
--R                                                  2       2     2
--R
--R           1    3   1      1   3 5    8  3 2    2    3   7      1   5    4  2
--R     [x - -- y c  - - y - --- z c  + -- z c  - -- z c  - - z - --- c  + -- c ,
--R          15        5     135        15        15        5     270      15
--R
--R          2    1    5    7    2    2   3 4   16  3     2    1    5   31    2
--R         y  + -- y c  - -- y c  + --- z c  - -- z c + z  - -- z c  + -- z c
--R              90        15        135        15            30        15
--R       + 
--R          1   4   23
--R         --- c  - -- c
--R         135      15
--R       ,
--R
--R                1    5    7    2    1  3 4   14  3     2    1    5   14    2
--R         y z - -- y c  + -- y c  + -- z c  - -- z c - z  - -- z c  + -- z c
--R               90        15        45        15            45        15
--R       + 
--R          1  4    8
--R         -- c  + -- c
--R         90      15
--R       ,
--R       4   3  2    1     1  2   6      3
--R      z  - - z c + - z + - c , c  - 54c  + 54]
--R           2       2     2
--R     ,
--R                2          2      3
--R    [x + y + z,y  + y z + z  - c,z  - z c - 1], [1],
--R            2             3                   4   3  2    1     1  2
--R    [x z - z  + c,x c - 2z  + 2z c - 1,y - z,z  - - z c + - z + - c ],
--R                                                  2       2     2
--R                  3   1       1
--R    [x - z,y - z,z  - - z c + -]]
--R                      2       2
--RType: List List DistributedMultivariatePolynomial([x,y,z,c],Fraction Integer)
--E 6
)spool 
 
Starts dribbling to oct.output (2010/3/27, 18:30:29).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 15
oci1 := octon(1,2,3,4,5,6,7,8)
 

   (1)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
                                                       Type: Octonion Integer
--R 
--R
--R   (1)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
--R                                                       Type: Octonion Integer
--E 1

--S 2 of 15
oci2 := octon(7,2,3,-4,5,6,-7,0)
 

   (2)  7 + 2i + 3j - 4k + 5E + 6I - 7J
                                                       Type: Octonion Integer
--R 
--R
--R   (2)  7 + 2i + 3j - 4k + 5E + 6I - 7J
--R                                                       Type: Octonion Integer
--E 2

--S 3 of 15
oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0))
 

   (3)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
                                                       Type: Octonion Integer
--R 
--R
--R   (3)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
--R                                                       Type: Octonion Integer
--E 3

--S 4 of 15
(oci1 * oci2) * oci3 - oci1 * (oci2 * oci3)
 

   (4)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
                                                       Type: Octonion Integer
--R 
--R
--R   (4)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
--R                                                       Type: Octonion Integer
--E 4

--S 5 of 15
[real oci1, imagi oci1, imagj oci1, imagk oci1, imagE oci1, imagI oci1, imagJ oci1, imagK oci1]
 

   (5)  [1,2,3,4,5,6,7,8]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [1,2,3,4,5,6,7,8]
--R                                                   Type: List PositiveInteger
--E 5

--S 6 of 15
q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk)
 

   (6)  q1 + qi i + qj j + qk k
                                          Type: Quaternion Polynomial Integer
--R 
--R
--R   (6)  q1 + qi i + qj j + qk k
--R                                          Type: Quaternion Polynomial Integer
--E 6

--S 7 of 15
E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0)
 

   (7)  E
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (7)  E
--R                                            Type: Octonion Polynomial Integer
--E 7

--S 8 of 15
q * E
 

   (8)  q1 E + qi I + qj J + qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (8)  q1 E + qi I + qj J + qk K
--R                                            Type: Octonion Polynomial Integer
--E 8

--S 9 of 15
E * q
 

   (9)  q1 E - qi I - qj J - qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (9)  q1 E - qi I - qj J - qk K
--R                                            Type: Octonion Polynomial Integer
--E 9

--S 10 of 15
q * 1$(Octonion Polynomial Integer)
 

   (10)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (10)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 10

--S 11 of 15
1$(Octonion Polynomial Integer) * q
 

   (11)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (11)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 11

--S 12 of 15
o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK)
 

   (12)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (12)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
--R                                            Type: Octonion Polynomial Integer
--E 12

--S 13 of 15
norm o
 

           2     2     2     2     2     2     2     2
   (13)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
                                                     Type: Polynomial Integer
--R 
--R
--R           2     2     2     2     2     2     2     2
--R   (13)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
--R                                                     Type: Polynomial Integer
--E 13

--S 14 of 15
p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK)
 

   (14)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (14)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
--R                                            Type: Octonion Polynomial Integer
--E 14

--S 15 of 15
norm(o*p)-norm(p)*norm(p)
 

   (15)
         4
     - pk
   + 
              2      2      2      2      2      2      2     2     2     2
         - 2pj  - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi
       + 
           2     2     2     2     2
         oK  + oJ  + oI  + oE  + o1
    *
         2
       pk
   + 
         4
     - pj
   + 
              2      2      2      2      2      2     2     2     2     2     2
         - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ
       + 
           2     2     2
         oI  + oE  + o1
    *
         2
       pj
   + 
         4
     - pi
   + 
              2      2      2      2      2     2     2     2     2     2     2
         - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI
       + 
           2     2
         oE  + o1
    *
         2
       pi
   + 
         4
     - pK
   + 
              2      2      2      2     2     2     2     2     2     2     2
         - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE
       + 
           2
         o1
    *
         2
       pK
   + 
         4
     - pJ
   + 
           2      2      2     2     2     2     2     2     2     2     2   2
     (- 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pJ
   + 
         4         2      2     2     2     2     2     2     2     2     2   2
     - pI  + (- 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pI
   + 
         4         2     2     2     2     2     2     2     2     2   2     4
     - pE  + (- 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pE  - p1
   + 
        2     2     2     2     2     2     2     2   2
     (ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )p1
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)
--R         4
--R     - pk
--R   + 
--R              2      2      2      2      2      2      2     2     2     2
--R         - 2pj  - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi
--R       + 
--R           2     2     2     2     2
--R         oK  + oJ  + oI  + oE  + o1
--R    *
--R         2
--R       pk
--R   + 
--R         4
--R     - pj
--R   + 
--R              2      2      2      2      2      2     2     2     2     2     2
--R         - 2pi  - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ
--R       + 
--R           2     2     2
--R         oI  + oE  + o1
--R    *
--R         2
--R       pj
--R   + 
--R         4
--R     - pi
--R   + 
--R              2      2      2      2      2     2     2     2     2     2     2
--R         - 2pK  - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI
--R       + 
--R           2     2
--R         oE  + o1
--R    *
--R         2
--R       pi
--R   + 
--R         4
--R     - pK
--R   + 
--R              2      2      2      2     2     2     2     2     2     2     2
--R         - 2pJ  - 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE
--R       + 
--R           2
--R         o1
--R    *
--R         2
--R       pK
--R   + 
--R         4
--R     - pJ
--R   + 
--R           2      2      2     2     2     2     2     2     2     2     2   2
--R     (- 2pI  - 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pJ
--R   + 
--R         4         2      2     2     2     2     2     2     2     2     2   2
--R     - pI  + (- 2pE  - 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pI
--R   + 
--R         4         2     2     2     2     2     2     2     2     2   2     4
--R     - pE  + (- 2p1  + ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )pE  - p1
--R   + 
--R        2     2     2     2     2     2     2     2   2
--R     (ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1 )p1
--R                                                     Type: Polynomial Integer
--E 15
)spool 
 
Starts dribbling to cclass.output (2010/3/27, 18:24:25).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from CharacterClassXmpPage

--S 1 of 16
cl1 := charClass [char "a", char "e", char "i", char "o", char "u", char "y"]
 

   (1)  "aeiouy"
                                                         Type: CharacterClass
--R 
--R
--R   (1)  "aeiouy"
--R                                                         Type: CharacterClass
--E 1

--S 2 of 16
cl2 := charClass "bcdfghjklmnpqrstvwxyz"
 

   (2)  "bcdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (2)  "bcdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 2

--S 3 of 16
digit()
 

   (3)  "0123456789"
                                                         Type: CharacterClass
--R 
--R
--R   (3)  "0123456789"
--R                                                         Type: CharacterClass
--E 3

--S 4 of 16
hexDigit()
 

   (4)  "0123456789ABCDEFabcdef"
                                                         Type: CharacterClass
--R 
--R
--R   (4)  "0123456789ABCDEFabcdef"
--R                                                         Type: CharacterClass
--E 4

--S 5 of 16
upperCase()
 

   (5)  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
                                                         Type: CharacterClass
--R 
--R
--R   (5)  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
--R                                                         Type: CharacterClass
--E 5

--S 6 of 16
lowerCase()
 

   (6)  "abcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (6)  "abcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 6

--S 7 of 16
alphabetic()
 

   (7)  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (7)  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 7

--S 8 of 16
alphanumeric()
 

   (8)  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (8)  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 8

--S 9 of 16
member?(char "a", cl1)
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 16
member?(char "a", cl2)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 16
intersect(cl1, cl2)
 

   (11)  "y"
                                                         Type: CharacterClass
--R 
--R
--R   (11)  "y"
--R                                                         Type: CharacterClass
--E 11

--S 12 of 16
union(cl1,cl2)
 

   (12)  "abcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (12)  "abcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 12

--S 13 of 16
difference(cl1,cl2)
 

   (13)  "aeiou"
                                                         Type: CharacterClass
--R 
--R
--R   (13)  "aeiou"
--R                                                         Type: CharacterClass
--E 13

--S 14 of 16
intersect(complement(cl1),cl2)
 

   (14)  "bcdfghjklmnpqrstvwxz"
                                                         Type: CharacterClass
--R 
--R
--R   (14)  "bcdfghjklmnpqrstvwxz"
--R                                                         Type: CharacterClass
--E 14

--S 15 of 16
insert!(char "a", cl2)
 

   (15)  "abcdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (15)  "abcdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 15

--S 16 of 16
remove!(char "b", cl2)
 

   (16)  "acdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (16)  "acdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 16
)spool
 
Starts dribbling to fferr.output (2010/3/27, 18:25:55).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 7
pf := PF 3
 

   (1)  PrimeField 3
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 3
--R                                                                 Type: Domain
--E 1

--S 2 of 7
createIrreduciblePoly(6)$FFPOLY(pf)
 

         6
   (2)  ?  + ? + 2
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         6
--R   (2)  ?  + ? + 2
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 2

--S 3 of 7
createNormalPoly(6)$FFPOLY(pf)
 

         6     5    3
   (3)  ?  + 2?  + ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         6     5    3
--R   (3)  ?  + 2?  + ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 3

--S 4 of 7
createPrimitivePoly(3)$FFPOLY(pf)
 

         3
   (4)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3
--R   (4)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 4

--S 5 of 7
createIrreduciblePoly(3)$FFPOLY(pf)
 

         3
   (5)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3
--R   (5)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 5

--S 6 of 7
createNormalPoly(3)$FFPOLY(pf)
 

         3     2
   (6)  ?  + 2?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3     2
--R   (6)  ?  + 2?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 6

--S 7 of 7
createPrimitivePoly(3)$FFPOLY(pf)
 

         3
   (7)  ?  + 2? + 1
                                Type: SparseUnivariatePolynomial PrimeField 3
--R 
--R
--R         3
--R   (7)  ?  + 2? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 3
--E 7
)spool 
 
Starts dribbling to SingleInteger.output (2010/3/27, 18:46:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 11
min()$SingleInteger
 

   (1)  - 2147483648
                                                          Type: SingleInteger
--R 
--R
--R   (1)  - 2147483648
--R                                                          Type: SingleInteger
--E 1

--S 2 of 11
max()$SingleInteger
 

   (2)  2147483647
                                                          Type: SingleInteger
--R 
--R
--R   (2)  2147483647
--R                                                          Type: SingleInteger
--E 2

--S 3 of 11
a := 1234 :: SingleInteger
 

   (3)  1234
                                                          Type: SingleInteger
--R 
--R
--R   (3)  1234
--R                                                          Type: SingleInteger
--E 3

--S 4 of 11
b := 124$SingleInteger
 

   (4)  124
                                                          Type: SingleInteger
--R 
--R
--R   (4)  124
--R                                                          Type: SingleInteger
--E 4

--S 5 of 11
gcd(a,b)
 

   (5)  2
                                                          Type: SingleInteger
--R 
--R
--R   (5)  2
--R                                                          Type: SingleInteger
--E 5

--S 6 of 11
lcm(a,b)
 

   (6)  76508
                                                          Type: SingleInteger
--R 
--R
--R   (6)  76508
--R                                                          Type: SingleInteger
--E 6

--S 7 of 11
mulmod(5,6,13)$SingleInteger
 

   (7)  4
                                                          Type: SingleInteger
--R 
--R
--R   (7)  4
--R                                                          Type: SingleInteger
--E 7

--S 8 of 11
positiveRemainder(37,13)$SingleInteger
 

   (8)  11
                                                          Type: SingleInteger
--R 
--R
--R   (8)  11
--R                                                          Type: SingleInteger
--E 8

--S 9 of 11
And(3,4)$SingleInteger
 

   (9)  0
                                                          Type: SingleInteger
--R 
--R
--R   (9)  0
--R                                                          Type: SingleInteger
--E 9

--S 10 of 11
shift(1,4)$SingleInteger
 

   (10)  16
                                                          Type: SingleInteger
--R 
--R
--R   (10)  16
--R                                                          Type: SingleInteger
--E 10

--S 11 of 11
shift(31,-1)$SingleInteger
 

   (11)  15
                                                          Type: SingleInteger
--R 
--R
--R   (11)  15
--R                                                          Type: SingleInteger
--E 11
)spool
 
Starts dribbling to sregset.output (2010/3/27, 18:41:3).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 23
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 23
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 23
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 23
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 23
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 23
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 23
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 23
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 23
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 23
ST := SREGSET(R,E,V,P)
 

   (10)
  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
  r,OrderedVariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
--R  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
--R  r,OrderedVariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 23
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 23
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 23
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 23
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 23
zeroSetSplit(lp)$ST
 

            5    4      2     3     8     5    3    2   4                2
   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R            5    4      2     3     8     5    3    2   4                2
--R   (15)  [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z }]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 15

--S 16 of 23
zeroSetSplit(lp,false)$ST
 

   (16)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5            2    2
    {t  - 1,z  - t,t y + z ,z x  - t}, {t,z,y,x}]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5            2    2
--R    {t  - 1,z  - t,t y + z ,z x  - t}, {t,z,y,x}]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16

--S 17 of 23
T := REGSET(R,E,V,P)
 

   (17)
  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (17)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],O
--R  rderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedV
--R  ariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 17

--S 18 of 23
lts := zeroSetSplit(lp,false)$T
 

   (18)
      5    4      2     3     8     5    3    2   4                2
   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
      3      5          2     3         2
    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (18)
--R      5    4      2     3     8     5    3    2   4                2
--R   [{z  - t ,t z y  + 2z y - t  + 2t  + t  - t ,(t  - t)x - t y - z },
--R      3      5          2     3         2
--R    {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}, {t,z,y,x}]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 18

--S 19 of 23
ts := lts.2
 

           3      5          2     3         2
   (19)  {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}
Type: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R           3      5          2     3         2
--R   (19)  {t  - 1,z  - t,t z y  + 2z y + 1,z x  - t}
--RType: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 19

--S 20 of 23
pol := select(ts,'y)$T
 

              2     3
   (20)  t z y  + 2z y + 1
Type: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
--R 
--R
--R              2     3
--R   (20)  t z y  + 2z y + 1
--RType: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
--E 20

--S 21 of 23
tower := collectUnder(ts,'y)$T
 

           3      5
   (21)  {t  - 1,z  - t}
Type: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R           3      5
--R   (21)  {t  - 1,z  - t}
--RType: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 21

--S 22 of 23
pack := RegularTriangularSetGcdPackage(R,E,V,P,T)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R 
--R
--R   (22)
--R  RegularTriangularSetGcdPackage(Integer,IndexedExponents OrderedVariableList [
--R  x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Intege
--R  r,OrderedVariableList [x,y,z,t]),RegularTriangularSet(Integer,IndexedExponent
--R  s OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultiv
--R  ariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--R                                                                 Type: Domain
--E 22

--S 23 of 23
toseSquareFreePart(pol,tower)$pack
 

                       2          3      5
   (22)  [[val= t y + z ,tower= {t  - 1,z  - t}]]
Type: List Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),tower: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--R 
--R
--R                       2          3      5
--R   (23)  [[val= t y + z ,tower= {t  - 1,z  - t}]]
--RType: List Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),tower: RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])))
--E 23
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read zdsolve
 

R := Integer
 

   (1)  Integer
                                                                 Type: Domain
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
ls2 : List Symbol := [x,y,z,t,new()$Symbol]
 

   (3)  [x,y,z,t,%A]
                                                            Type: List Symbol
pack := ZDSOLVE(R,ls,ls2)
 

   (4)  ZeroDimensionalSolvePackage(Integer,[x,y,z,t],[x,y,z,t,%A])
                                                                 Type: Domain
p1 := x**2*y*z + x*y**2*z + x*y*z**2 + x*y*z + x*y + x*z + y*z
 

             2       2     2
   (5)  x y z  + (x y  + (x  + x + 1)y + x)z + x y
                                                     Type: Polynomial Integer
p2 := x**2*y**2*z + x*y**2*z**2 + x**2*y*z + x*y*z + y*z + x + z
 

           2 2     2 2     2
   (6)  x y z  + (x y  + (x  + x + 1)y + 1)z + x
                                                     Type: Polynomial Integer
p3 := x**2*y**2*z**2 + x**2*y**2*z + x*y**2*z + x*y*z + x*z + z + 1
 

         2 2 2      2      2
   (7)  x y z  + ((x  + x)y  + x y + x + 1)z + 1
                                                     Type: Polynomial Integer
lp := [p1, p2, p3]
 

   (8)
         2       2     2
   [x y z  + (x y  + (x  + x + 1)y + x)z + x y,
       2 2     2 2     2
    x y z  + (x y  + (x  + x + 1)y + 1)z + x,
     2 2 2      2      2
    x y z  + ((x  + x)y  + x y + x + 1)z + 1]
                                                Type: List Polynomial Integer
triangSolve(lp)$pack
 

   (9)
   [
     {
          20     19      18      17       16      15       14       13       12
         z   - 6z   - 41z   + 71z   + 106z   + 92z   + 197z   + 145z   + 257z
       + 
             11       10       9       8       7       6      5       4      3
         278z   + 201z   + 278z  + 257z  + 145z  + 197z  + 92z  + 106z  + 71z
       + 
              2
         - 41z  - 6z + 1
       ,

                      19            18             17             16
             14745844z   + 50357474z   - 130948857z   - 185261586z
           + 
                         15             14             13             12
             - 180077775z   - 338007307z   - 275379623z   - 453190404z
           + 
                         11             10             9             8
             - 474597456z   - 366147695z   - 481433567z  - 430613166z
           + 
                         7             6             5             4
             - 261878358z  - 326073537z  - 163008796z  - 177213227z
           + 
                         3            2
             - 104356755z  + 65241699z  + 9237732z - 1567348
        *
           y
       + 
                 19           18            17            16            15
         1917314z   + 6508991z   - 16973165z   - 24000259z   - 23349192z
       + 
                    14            13            12            11            10
         - 43786426z   - 35696474z   - 58724172z   - 61480792z   - 47452440z
       + 
                    9            8            7            6            5
         - 62378085z  - 55776527z  - 33940618z  - 42233406z  - 21122875z
       + 
                    4            3           2
         - 22958177z  - 13504569z  + 8448317z  + 1195888z - 202934
       ,
         3       2       3    2               2              2
      ((z  - 2z)y  + (- z  - z  - 2z - 1)y - z  - z + 1)x + z  - 1}
     ]
                                   Type: List RegularChain(Integer,[x,y,z,t])
univariateSolve(lp)$pack
 

   (10)
   [
     [
       complexRoots =
            12      11      10     9     8      7      6      5     4     3
           ?   - 12?   + 24?   + 4?  - 9?  + 27?  - 21?  + 27?  - 9?  + 4?
         + 
              2
           24?  - 12? + 1
       ,

       coordinates =
         [
                       11        10         9        8        7         6
             63x + 62%A   - 721%A   + 1220%A  + 705%A  - 285%A  + 1512%A
           + 
                    5         4       3        2
             - 735%A  + 1401%A  - 21%A  + 215%A  + 1577%A - 142
           ,

                       11        10         9        8        7         6
             63y - 75%A   + 890%A   - 1682%A  - 516%A  + 588%A  - 1953%A
           + 
                   5         4        3        2
             1323%A  - 1815%A  + 426%A  - 243%A  - 1801%A + 679
           ,
          z - %A]
       ]
     ,

                     6    5    4    3    2
     [complexRoots= ?  + ?  + ?  + ?  + ?  + ? + 1,
                          5       3
      coordinates= [x - %A ,y - %A ,z - %A]]
     ,
                    2
    [complexRoots= ?  + 5? + 1,coordinates= [x - 1,y - 1,z - %A]]]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
lr := realSolve(lp)$pack
 

   (11)
   [
     [%B1,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B1   - ------- %B1   - ------- %B1   + -------- %B1
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B1   + -------- %B1   + ------ %B1   + --------- %B1
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B1   + --------- %B1   + --------- %B1  + --------- %B1
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B1  + ------- %B1  + ------ %B1  + ------- %B1
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B1  + -------- %B1  - ---- %B1 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B1   + ------ %B1   + ------- %B1   - ------- %B1
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B1   - -------- %B1   - -------- %B1   - ------ %B1
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B1   - -------- %B1   - -------- %B1  - ------- %B1
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B1  - -------- %B1  - -------- %B1  - -------- %B1
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B1  - -------- %B1  - ------- %B1 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B2,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B2   - ------- %B2   - ------- %B2   + -------- %B2
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B2   + -------- %B2   + ------ %B2   + --------- %B2
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B2   + --------- %B2   + --------- %B2  + --------- %B2
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B2  + ------- %B2  + ------ %B2  + ------- %B2
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B2  + -------- %B2  - ---- %B2 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B2   + ------ %B2   + ------- %B2   - ------- %B2
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B2   - -------- %B2   - -------- %B2   - ------ %B2
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B2   - -------- %B2   - -------- %B2  - ------- %B2
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B2  - -------- %B2  - -------- %B2  - -------- %B2
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B2  - -------- %B2  - ------- %B2 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B3,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B3   - ------- %B3   - ------- %B3   + -------- %B3
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B3   + -------- %B3   + ------ %B3   + --------- %B3
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B3   + --------- %B3   + --------- %B3  + --------- %B3
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B3  + ------- %B3  + ------ %B3  + ------- %B3
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B3  + -------- %B3  - ---- %B3 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B3   + ------ %B3   + ------- %B3   - ------- %B3
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B3   - -------- %B3   - -------- %B3   - ------ %B3
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B3   - -------- %B3   - -------- %B3  - ------- %B3
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B3  - -------- %B3  - -------- %B3  - -------- %B3
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B3  - -------- %B3  - ------- %B3 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B4,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B4   - ------- %B4   - ------- %B4   + -------- %B4
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B4   + -------- %B4   + ------ %B4   + --------- %B4
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B4   + --------- %B4   + --------- %B4  + --------- %B4
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B4  + ------- %B4  + ------ %B4  + ------- %B4
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B4  + -------- %B4  - ---- %B4 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B4   + ------ %B4   + ------- %B4   - ------- %B4
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B4   - -------- %B4   - -------- %B4   - ------ %B4
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B4   - -------- %B4   - -------- %B4  - ------- %B4
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B4  - -------- %B4  - -------- %B4  - -------- %B4
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B4  - -------- %B4  - ------- %B4 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B5,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B5   - ------- %B5   - ------- %B5   + -------- %B5
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B5   + -------- %B5   + ------ %B5   + --------- %B5
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B5   + --------- %B5   + --------- %B5  + --------- %B5
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B5  + ------- %B5  + ------ %B5  + ------- %B5
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B5  + -------- %B5  - ---- %B5 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B5   + ------ %B5   + ------- %B5   - ------- %B5
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B5   - -------- %B5   - -------- %B5   - ------ %B5
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B5   - -------- %B5   - -------- %B5  - ------- %B5
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B5  - -------- %B5  - -------- %B5  - -------- %B5
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B5  - -------- %B5  - ------- %B5 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B6,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B6   - ------- %B6   - ------- %B6   + -------- %B6
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B6   + -------- %B6   + ------ %B6   + --------- %B6
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B6   + --------- %B6   + --------- %B6  + --------- %B6
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B6  + ------- %B6  + ------ %B6  + ------- %B6
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B6  + -------- %B6  - ---- %B6 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B6   + ------ %B6   + ------- %B6   - ------- %B6
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B6   - -------- %B6   - -------- %B6   - ------ %B6
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B6   - -------- %B6   - -------- %B6  - ------- %B6
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B6  - -------- %B6  - -------- %B6  - -------- %B6
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B6  - -------- %B6  - ------- %B6 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B7,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B7   - ------- %B7   - ------- %B7   + -------- %B7
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B7   + -------- %B7   + ------ %B7   + --------- %B7
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B7   + --------- %B7   + --------- %B7  + --------- %B7
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B7  + ------- %B7  + ------ %B7  + ------- %B7
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B7  + -------- %B7  - ---- %B7 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B7   + ------ %B7   + ------- %B7   - ------- %B7
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B7   - -------- %B7   - -------- %B7   - ------ %B7
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B7   - -------- %B7   - -------- %B7  - ------- %B7
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B7  - -------- %B7  - -------- %B7  - -------- %B7
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B7  - -------- %B7  - ------- %B7 + ------
            26117         705159          705159       705159
       ]
     ,

     [%B8,

         1184459    19   2335702    18   5460230    17   79900378    16
         ------- %B8   - ------- %B8   - ------- %B8   + -------- %B8
         1645371          548457          182819          1645371
       + 
         43953929    15   13420192    14   553986    13   193381378    12
         -------- %B8   + -------- %B8   + ------ %B8   + --------- %B8
          548457           182819           3731           1645371
       + 
         35978916    11   358660781    10   271667666    9   118784873    8
         -------- %B8   + --------- %B8   + --------- %B8  + --------- %B8
          182819           1645371           1645371           548457
       + 
         337505020    7   1389370    6   688291    5   3378002    4
         --------- %B8  + ------- %B8  + ------ %B8  + ------- %B8
          1645371          11193          4459          42189
       + 
         140671876    3   32325724    2   8270       9741532
         --------- %B8  + -------- %B8  - ---- %B8 - -------
          1645371          548457          343       1645371
       ,

            91729    19   487915    18   4114333    17   1276987    16
         - ------ %B8   + ------ %B8   + ------- %B8   - ------- %B8
           705159         705159          705159          235053
       + 
           13243117    15   16292173    14   26536060    13   722714    12
         - -------- %B8   - -------- %B8   - -------- %B8   - ------ %B8
            705159           705159           705159           18081
       + 
           5382578    11   15449995    10   14279770    9   6603890    8
         - ------- %B8   - -------- %B8   - -------- %B8  - ------- %B8
            100737          235053           235053          100737
       + 
           409930    7   37340389    6   34893715    5   26686318    4
         - ------ %B8  - -------- %B8  - -------- %B8  - -------- %B8
            6027          705159          705159          705159
       + 
           801511    3   17206178    2   4406102       377534
         - ------ %B8  - -------- %B8  - ------- %B8 + ------
            26117         705159          705159       705159
       ]
     ]
                                 Type: List List RealClosure Fraction Integer
# lr
 

   (12)  8
                                                        Type: PositiveInteger
[ [approximate(r,1/1000000) for r in point] for point in lr]
 

   (13)
   [
        10048059
     [- --------,
         2097152

        4503057316985387943524397913838966414596731976211768219335881208385516_
         314058924567176091423629695777403099833360761048898228916578137094309_
         838597331137202584846939132376157019506760357601165917454986815382098_
         789094851523420392811293126141329856546977145464661495487825919941188_
         447041722440491921567263542158028061437758844364634410045253024786561_
         923163288214175
      /
        4503057283025245488516511806985826635083100693757320465280554706865644_
         949577509916867201889438090408354817931718593862797624551518983570793_
         048774424291488708829840324189200301436123314860200821443733790755311_
         243632919864895421704228949571290016119498807957023663865443069392027_
         148979688266712323356043491523434068924275280417338574817381189277066_
         143312396681216
       ,

        2106260768823475073894798680486016596249607148690685538763683715020639_
         680858649650790055889505646893309447097099937802187329095325898785247_
         249020717504983660482075156618738724514685333060011202964635166381351_
         543255982200250305283981086837110614842307026091211297929876896285681_
         830479054760056380762664905618462055306047816191782011588703789138988_
         1895
      /
        2106260609498464192472113804816474175341962953296434102413903142368757_
         967685273888585590975965211778862189872881953943640246297357061959812_
         326103659799025126863258676567202342106877031710184247484181423288921_
         837681237062708470295706218485928867400771937828499200923760593314168_
         901000666373896347598118228556731037072026474496776228383762993923280_
         0768
       ]
     ,

        2563013
     [- -------,
        2097152

       -
           2611346176791927789698617693237757719238259963063541781922752330440_
            189899668072928338490768623593207442125925986733815932243504809294_
            837523030237337236806668167446173001727271353311571242897
         /
           1165225400505222530583981916004589143757226610276858990008790134819_
            914940922413753983971394019523433320408139928153188829495755455163_
            963417619308395977544797140231469234269034921938055593984
       ,

        3572594550275917221096588729615788272998517054675603239578198141006034_
         091735282826590621902304466963941971038923304526273329316373757450061_
         9789892286110976997087250466235373
      /
        1039548269345598936877071244834026055800814551120170592200522366591759_
         409659486442339141029452950265179989960104811875822530205346505131581_
         2439017247289173865014702966308864
       ]
     ,

        1715967
     [- -------,
        2097152

       -
           4213093533784303521084839517977082390377261503969586224828998436606_
            030656076359374564813773498376603121267822565801436206939519951465_
            18222580524697287410022543952491
         /
           9441814144185374458649692034349224052436597470966253663930641960795_
            805882585493199840191699917659443264824641135187383583888147867340_
            19307857605820364195856822304768
       ,

        7635833347112644222515625424410831225347475669008589338834162172501904_
         994376346730876809042845208919919925302105720971453918982731389072591_
         4035
      /
        2624188764086097199784297610478066633934230467895851602278580978503784_
         549205788499019640602266966026891580103543567625039018629887141284916_
         75648
       ]
     ,

         437701
     [- -------,
        2097152

        1683106908638349588322172332654225913562986313181951031452750161441497_
         473455328150721364868355579646781603507777199075077835213366484533654_
         91383623741304759
      /
        1683106868095213389001709982705913638963077668731226111167785188004907_
         425226298680325887810962614140298597366984264887998908377068799998454_
         23381649008099328
       ,

        4961550109835010186422681013422108735958714801003760639707968096646912_
         82670847283444311723917219104249213450966312411133
      /
        4961549872757738315509192078210209029852897118611097126236384040829376_
         59261914313170254867464792718363492160482442215424
       ]
     ,

       222801
     [-------,
      2097152

       -
           8994884880402428265107595121970691427136045692541978275573001865213_
            759921588137716696126349101655220195142994932299137183241705867672_
            383477
         /
           1167889998665026372177765100691888582708969960229934769690835752457_
            077779416435209473767866507769405888942764587718542434255625992456_
            372224
       ,

       -
           2389704888133156878320801544373808395612771509208491019847452991885_
            509546519525467839016613593999693886640036283570552321155037871291_
            458703265
         /
           5355487273645096326090403286689931905988225444685411433221593833681_
            192957562833671468654290340746993656285925599117602120446183443145_
            479421952
       ]
     ,

       765693
     [-------,
      2097152

        8558969219816716267873244761178198088724698958616670140213765754322002_
         303251685786118678330840203328837654339523418704917749518340772512899_
         000391009630373148561
      /
        2941442445533010790976428411376393499815580215945856917906452535495723_
         013856818941702330228779890141296236721138154231997238917322156711965_
         2444639331719460159488
       ,

       -
           2057618230582572101247650324860242561111302581543588808843923662767_
            549382241659362712290777612800192921420574408948085193743688582762_
            2246433251878894899015
         /
           2671598203325735538097952353501450220576313759890835097091722520642_
            710198771902667183948906289863714759678360292483949204616471537777_
            775324180661095366656
       ]
     ,

      5743879
     [-------,
      2097152

        1076288816968906847955546394773570208171456724942618614023663123574768_
         960850434263971398072546592772662158833449797698617455397887562900072_
         984768000608343553189801693408727205047612559889232757563830528688953_
         535421809482771058917542602890060941949620874083007858366669453501766_
         24841488732463225
      /
        3131768957080317946648461940023552044190376613458584986228549631916196_
         601616219781765615532532294746529648276430583810894079374566460757823_
         146888581195556029208515218838883200318658407469399426063260589828612_
         309231596669129707986481319851571942927230340622934023923486703042068_
         1530440845099008
       ,

       -
           2113286699185750918364120475565458437870172489865485994389828135335_
            264444665284557526492734931691731407872701432935503473348172076098_
            720545849008780077564160534317894688366119529739980502944162668550_
            098127961950496210221942878089359674925850594427768502251789758706_
            752831632503615
         /
           1627615584937987580242906624347104580889144466168459718043153839408_
            372525533309808070363699585502216011211087103263609551026027769414_
            087391148126221168139781682587438075322591466131939975457200522349_
            838568964285634448018562038272378787354460106106141518010935617205_
            1706396253618176
       ]
     ,

      19739877
     [--------,
       2097152

       -
           2997249936832703303799015804861520949215040387500707177701285766720_
            192530579422478953566024359860143101547801638082771611160372212874_
            847778035809872843149225484238365858013629341705321702582333350918_
            009601789937023985935304900460493389873837030853410347089908880814_
            853981132018464582458800615394770741699487295875960210750215891948_
            814476854871031530931295467332190133702671098200902282300510751860_
            7185928457030277807397796525813862762239286996106809728023675
         /
           2308433274852278590728910081191811023906504141321432646123936794873_
            933319270608960702138193417647898360620229519176632937631786851455_
            014766027206259022252505551741823688896883806636602574431760472240_
            292093196729475160247268834121141893318848728661844434927287285112_
            897080767552864895056585864033178565910387065006112801516403522741_
            037360990556054476949527059227070809593049491257519554708879259595_
            52929920110858560812556635485429471554031675979542656381353984
       ,

       -
           5128189263548228489096276397868940080600938410663080459407966335845_
            009264109490520459825316250084723010047035024497436523038925818959_
            289312931584701353927621435434398674263047293909122850133851990696_
            490231566094371994333795070782624011727587749989296611277318372294_
            624207116537910436554574146082884701305543912620419354885410735940_
            157775896602822364575864611831512943973974715166920465061850603762_
            87516256195847052412587282839139194642913955
         /
           2288281939778439330531208793181290471183631092455368990386390824243_
            509463644236249773080647438987739144921607794682653851741189091711_
            741868145114978337284191822497675868358729486644730856622552687209_
            203724411800481405702837198310642291275676195774614443815996713502_
            629391749783590041470860127752372996488627742672487622480063268808_
            889324891850842494934347337603075939980268208482904859678177751444_
            65749979827872616963053217673201717237252096
       ]
     ]
                                             Type: List List Fraction Integer
lpr := positiveSolve(lp)$pack
 

   (14)  []
                                 Type: List List RealClosure Fraction Integer
f0 := x**3 + y + z + t- 1
 

                  3
   (15)  z + y + x  + t - 1
                                                     Type: Polynomial Integer
f1 := x + y**3 + z + t -1
 

              3
   (16)  z + y  + x + t - 1
                                                     Type: Polynomial Integer
f2 := x + y + z**3 + t-1
 

          3
   (17)  z  + y + x + t - 1
                                                     Type: Polynomial Integer
f3 := x + y + z + t**3 -1
 

                      3
   (18)  z + y + x + t  - 1
                                                     Type: Polynomial Integer
lf := [f0, f1, f2, f3]
 

   (19)
             3              3              3                              3
   [z + y + x  + t - 1,z + y  + x + t - 1,z  + y + x + t - 1,z + y + x + t  - 1]
                                                Type: List Polynomial Integer
lts := triangSolve(lf)$pack
 

   (20)
   [
       2           3        3
     {t  + t + 1, z  - z - t  + t,

                 3      2      2      3           6     3            3      2
         (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
       + 
            6     3          9     6     3
         (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
       ,
      x + y + z}
     ,

       16     13     10     7      4      2
     {t   - 6t   + 9t   + 4t  + 15t  - 54t  + 27,

                     15            14             13            12            11
             4907232t   + 40893984t   - 115013088t   + 22805712t   + 36330336t
           + 
                       10             9             8             7
             162959040t   - 159859440t  - 156802608t  + 117168768t
           + 
                       6             5             4             3
             126282384t  - 129351600t  + 306646992t  + 475302816t
           + 
                          2
             - 1006837776t  - 237269088t + 480716208
        *
           z
       + 
            54       51        48      46         45        43          42
         48t   - 912t   + 8232t   - 72t   - 46848t   + 1152t   + 186324t
       + 
                40          39        38         37           36         35
         - 3780t   - 543144t   - 3168t   - 21384t   + 1175251t   + 41184t
       + 
                34           33          32           31           30
         278003t   - 1843242t   - 301815t   - 1440726t   + 1912012t
       + 
                 29           28          27           26            25
         1442826t   + 4696262t   - 922481t   - 4816188t   - 10583524t
       + 
                  24            23            22          21            20
         - 208751t   + 11472138t   + 16762859t   - 857663t   - 19328175t
       + 
                    19           18            17            16           15
         - 18270421t   + 4914903t   + 22483044t   + 12926517t   - 8605511t
       + 
                    14           13           12           11          10
         - 17455518t   - 5014597t   + 8108814t   + 8465535t   + 190542t
       + 
                   9           8          7           6          5          4
         - 4305624t  - 2226123t  + 661905t  + 1169775t  + 226260t  - 209952t
       + 
                  3
         - 141183t  + 27216t
       ,

                 3      2      2      3           6     3            3      2
         (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
       + 
            6     3          9     6     3
         (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
       ,
                   3
      x + y + z + t  - 1}
     ,
              2                       2                     2
    {t,z - 1,y  - 1,x + y}, {t - 1,z,y  - 1,x + y}, {t - 1,z  - 1,z y + 1,x},

       16     13     10     7      4      2
     {t   - 6t   + 9t   + 4t  + 15t  - 54t  + 27,

                     29            28             27           26             25
             4907232t   + 40893984t   - 115013088t   - 1730448t   - 168139584t
           + 
                       24             23             22              21
             738024480t   - 195372288t   + 315849456t   - 2567279232t
           + 
                       20              19              18              17
             937147968t   + 1026357696t   + 4780488240t   - 2893767696t
           + 
                          16              15              14              13
             - 5617160352t   - 3427651728t   + 5001100848t   + 8720098416t
           + 
                        12             11               10              9
             2331732960t   - 499046544t   - 16243306272t   - 9748123200t
           + 
                        8               7               6               5
             3927244320t  + 25257280896t  + 10348032096t  - 17128672128t
           + 
                           4             3               2
             - 14755488768t  + 544086720t  + 10848188736t  + 1423614528t
           + 
             - 2884297248
        *
           z
       + 
              68        65         62       60          59        57          56
         - 48t   + 1152t   - 13560t   + 360t   + 103656t   - 7560t   - 572820t
       + 
               54           53        52          51           50         49
         71316t   + 2414556t   + 2736t   - 402876t   - 7985131t   - 49248t
       + 
                 48            47          46           45            44
         1431133t   + 20977409t   + 521487t   - 2697635t   - 43763654t
       + 
                   43           42            41            40            39
         - 3756573t   - 2093410t   + 71546495t   + 19699032t   + 35025028t
       + 
                    38            37             36            35             34
         - 89623786t   - 77798760t   - 138654191t   + 87596128t   + 235642497t
       + 
                   33            32             31             30             29
         349607642t   - 93299834t   - 551563167t   - 630995176t   + 186818962t
       + 
                   28             27             26              25
         995427468t   + 828416204t   - 393919231t   - 1076617485t
       + 
                      24             23              22              21
         - 1609479791t   + 595738126t   + 1198787136t   + 4342832069t
       + 
                      20              19              18              17
         - 2075938757t   - 4390835799t   - 4822843033t   + 6932747678t
       + 
                    16              15              14              13
         6172196808t   + 1141517740t   - 4981677585t   - 9819815280t
       + 
                      12             11               10               9
         - 7404299976t   - 157295760t   + 29124027630t   + 14856038208t
       + 
                       8               7              6               5
         - 16184101410t  - 26935440354t  - 3574164258t  + 10271338974t
       + 
                     4              3              2
         11191425264t  + 6869861262t  - 9780477840t  - 3586674168t + 2884297248
       ,

            3      3      2      6      3           9     6    3
         (3z  + (6t  - 6)z  + (6t  - 12t  + 3)z + 2t  - 6t  + t  + 3t)y
       + 
            3      3      6      3      2      9      6      3          12     9
         (3t  - 3)z  + (6t  - 12t  + 6)z  + (4t  - 12t  + 11t  - 3)z + t   - 4t
       + 
           6     3
         5t  - 2t
       ,
                   3
      x + y + z + t  - 1}
     ,
            2
    {t - 1,z  - 1,y,x + z},

       8    7    6     5     4     3      2
     {t  + t  + t  - 2t  - 2t  - 2t  + 19t  + 19t - 8,

                     7           6           5            4           3
             2395770t  + 3934440t  - 3902067t  - 10084164t  - 1010448t
           + 
                      2
             32386932t  + 22413225t - 10432368
        *
           z
       + 
                  7           6           5           4            3
         - 463519t  + 3586833t  + 9494955t  - 8539305t  - 33283098t
       + 
                  2
         35479377t  + 46263256t - 17419896
       ,

               4      3      3       6      3      2          3
             3z  + (9t  - 9)z  + (12t  - 24t  + 9)z  + (- 152t  + 219t - 67)z
           + 
                  6      4      3
             - 41t  + 57t  + 25t  - 57t + 16
        *
           y
       + 
            3      4      6      3      3          3              2
         (3t  - 3)z  + (9t  - 18t  + 9)z  + (- 181t  + 270t - 89)z
       + 
               6       4      3                    7      6      4       3
         (- 92t  + 135t  + 49t  - 135t + 43)z + 27t  - 27t  - 54t  + 396t
       + 
         - 486t + 144
       ,
                   3
      x + y + z + t  - 1}
     ,
            3
    {t,z - t  + 1,y - 1,x - 1}, {t - 1,z,y,x}, {t,z - 1,y,x}, {t,z,y - 1,x},
    {t,z,y,x - 1}]
                                   Type: List RegularChain(Integer,[x,y,z,t])
univariateSolve(lf)$pack
 

   (21)
   [[complexRoots= ?,coordinates= [x - 1,y - 1,z + 1,t - %A]],
    [complexRoots= ?,coordinates= [x,y - 1,z,t - %A]],
    [complexRoots= ? - 1,coordinates= [x,y,z,t - %A]],
    [complexRoots= ?,coordinates= [x - 1,y,z,t - %A]],
    [complexRoots= ?,coordinates= [x,y,z - 1,t - %A]],
    [complexRoots= ? - 2,coordinates= [x - 1,y + 1,z,t - 1]],
    [complexRoots= ?,coordinates= [x + 1,y - 1,z,t - 1]],
    [complexRoots= ? - 1,coordinates= [x - 1,y + 1,z - 1,t]],
    [complexRoots= ? + 1,coordinates= [x + 1,y - 1,z - 1,t]],

                     6     3     2
     [complexRoots= ?  - 2?  + 3?  - 3,
                           3                 3
      coordinates= [2x + %A  + %A - 1,2y + %A  + %A - 1,z - %A,t - %A]]
     ,

                     5     3     2
     [complexRoots= ?  + 3?  - 2?  + 3? - 3,
                                        3
      coordinates= [x - %A,y - %A,z + %A  + 2%A - 1,t - %A]]
     ,

                     4    3     2
     [complexRoots= ?  - ?  - 2?  + 3,
                          3                3                3
      coordinates= [x + %A  - %A - 1,y + %A  - %A - 1,z - %A  + 2%A + 1,t - %A]]
     ,
    [complexRoots= ? + 1,coordinates= [x - 1,y - 1,z,t - %A]],

                     6     3     2
     [complexRoots= ?  + 2?  + 3?  - 3,
                           3                        3
      coordinates= [2x - %A  - %A - 1,y + %A,2z - %A  - %A - 1,t + %A]]
     ,

                     6      4      3      2
     [complexRoots= ?  + 12?  + 20?  - 45?  - 42? - 953,

       coordinates =
                       5       4       3        2
         [12609x + 23%A  + 49%A  - 46%A  + 362%A  - 5015%A - 8239,
                       5       4       3        2
          25218y + 23%A  + 49%A  - 46%A  + 362%A  + 7594%A - 8239,
                       5       4       3        2
          25218z + 23%A  + 49%A  - 46%A  + 362%A  + 7594%A - 8239,
                       5       4       3        2
          12609t + 23%A  + 49%A  - 46%A  + 362%A  - 5015%A - 8239]
       ]
     ,

                     5      3      2
     [complexRoots= ?  + 12?  - 16?  + 48? - 96,
                           3
      coordinates= [8x + %A  + 8%A - 8,2y - %A,2z - %A,2t - %A]]
     ,

                     5    4     3     2
     [complexRoots= ?  + ?  - 5?  - 3?  + 9? + 3,

       coordinates =
                 3                   3                   3
         [2x - %A  + 2%A - 1, 2y + %A  - 4%A + 1, 2z - %A  + 2%A - 1,
                 3
          2t - %A  + 2%A - 1]
       ]
     ,

                     4     3     2
     [complexRoots= ?  - 3?  + 4?  - 6? + 13,

       coordinates =
                  3      2                  3      2
         [9x - 2%A  + 4%A  - %A + 2, 9y + %A  - 2%A  + 5%A - 1,
                 3      2                   3      2
          9z + %A  - 2%A  + 5%A - 1, 9t + %A  - 2%A  - 4%A - 1]
       ]
     ,

                     4      2
     [complexRoots= ?  - 11?  + 37,

       coordinates =
                 2            2                  2            2
         [3x - %A  + 7,6y + %A  + 3%A - 7,3z - %A  + 7,6t + %A  - 3%A - 7]
       ]
     ,
    [complexRoots= ? + 1,coordinates= [x - 1,y,z - 1,t + 1]],
    [complexRoots= ? + 2,coordinates= [x,y - 1,z - 1,t + 1]],
    [complexRoots= ? - 2,coordinates= [x,y - 1,z + 1,t - 1]],
    [complexRoots= ?,coordinates= [x,y + 1,z - 1,t - 1]],
    [complexRoots= ? - 2,coordinates= [x - 1,y,z + 1,t - 1]],
    [complexRoots= ?,coordinates= [x + 1,y,z - 1,t - 1]],

                     4     3      2
     [complexRoots= ?  + 5?  + 16?  + 30? + 57,

       coordinates =
                     3       2                          3       2
         [151x + 15%A  + 54%A  + 104%A + 93, 151y - 10%A  - 36%A  - 19%A - 62,
                    3       2                        3       2
          151z - 5%A  - 18%A  - 85%A - 31, 151t - 5%A  - 18%A  - 85%A - 31]
       ]
     ,

                     4    3     2
     [complexRoots= ?  - ?  - 2?  + 3,
                          3                 3                       3
      coordinates= [x - %A  + 2%A + 1,y + %A  - %A - 1,z - %A,t + %A  - %A - 1]]
     ,

                     4     3     2
     [complexRoots= ?  + 2?  - 8?  + 48,

       coordinates =
                 3                          3                  3
         [8x - %A  + 4%A - 8,2y + %A,8z + %A  - 8%A + 8,8t - %A  + 4%A - 8]
       ]
     ,

                     5    4     3     2
     [complexRoots= ?  + ?  - 2?  - 4?  + 5? + 8,
                           3            3            3
      coordinates= [3x + %A  - 1,3y + %A  - 1,3z + %A  - 1,t - %A]]
     ,
                    3
    [complexRoots= ?  + 3? - 1,coordinates= [x - %A,y - %A,z - %A,t - %A]]]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
ts := lts.1
 

   (22)
     2           3        3
   {t  + t + 1, z  - z - t  + t,

               3      2      2      3           6     3            3      2
       (3z + 3t  - 3)y  + (3z  + (6t  - 6)z + 3t  - 6t  + 3)y + (3t  - 3)z
     + 
          6     3          9     6     3
       (3t  - 6t  + 3)z + t  - 3t  + 5t  - 3t
     ,
    x + y + z}
                                        Type: RegularChain(Integer,[x,y,z,t])
univariateSolve(ts)$pack
 

   (23)
   [
                     4     3      2
     [complexRoots= ?  + 5?  + 16?  + 30? + 57,

       coordinates =
                     3       2                          3       2
         [151x + 15%A  + 54%A  + 104%A + 93, 151y - 10%A  - 36%A  - 19%A - 62,
                    3       2                        3       2
          151z - 5%A  - 18%A  - 85%A - 31, 151t - 5%A  - 18%A  - 85%A - 31]
       ]
     ,

                     4    3     2
     [complexRoots= ?  - ?  - 2?  + 3,
                          3                 3                       3
      coordinates= [x - %A  + 2%A + 1,y + %A  - %A - 1,z - %A,t + %A  - %A - 1]]
     ,

                     4     3     2
     [complexRoots= ?  + 2?  - 8?  + 48,

       coordinates =
                 3                          3                  3
         [8x - %A  + 4%A - 8,2y + %A,8z + %A  - 8%A + 8,8t - %A  + 4%A - 8]
       ]
     ]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
realSolve(ts)$pack
 

   (24)  []
                                 Type: List List RealClosure Fraction Integer
lr2 := realSolve(lf)$pack
 

   (25)
   [[0,- 1,1,1], [0,0,1,0], [1,0,0,0], [0,0,0,1], [0,1,0,0], [1,0,%B37,- %B37],
    [1,0,%B38,- %B38], [0,1,%B35,- %B35], [0,1,%B36,- %B36], [- 1,0,1,1],

     [%B32,

          1     15    2     14    1     13    4     12   11     11    4     10
         -- %B32   + -- %B32   + -- %B32   - -- %B32   - -- %B32   - -- %B32
         27          27          27          27          27          27
       + 
          1     9   14     8    1     7   2     6   1     5   2     4       3
         -- %B32  + -- %B32  + -- %B32  + - %B32  + - %B32  + - %B32  + %B32
         27         27         27         9         3         9
       + 
         4     2
         - %B32  - %B32 - 2
         3
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B32   - -- %B32   - -- %B32   + -- %B32   + -- %B32   + -- %B32
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B32  - -- %B32  - -- %B32  - - %B32  - - %B32  - - %B32  - %B32
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B32  + - %B32 + -
           3         2        2
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B32   - -- %B32   - -- %B32   + -- %B32   + -- %B32   + -- %B32
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B32  - -- %B32  - -- %B32  - - %B32  - - %B32  - - %B32  - %B32
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B32  + - %B32 + -
           3         2        2
       ]
     ,

     [%B33,

          1     15    2     14    1     13    4     12   11     11    4     10
         -- %B33   + -- %B33   + -- %B33   - -- %B33   - -- %B33   - -- %B33
         27          27          27          27          27          27
       + 
          1     9   14     8    1     7   2     6   1     5   2     4       3
         -- %B33  + -- %B33  + -- %B33  + - %B33  + - %B33  + - %B33  + %B33
         27         27         27         9         3         9
       + 
         4     2
         - %B33  - %B33 - 2
         3
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B33   - -- %B33   - -- %B33   + -- %B33   + -- %B33   + -- %B33
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B33  - -- %B33  - -- %B33  - - %B33  - - %B33  - - %B33  - %B33
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B33  + - %B33 + -
           3         2        2
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B33   - -- %B33   - -- %B33   + -- %B33   + -- %B33   + -- %B33
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B33  - -- %B33  - -- %B33  - - %B33  - - %B33  - - %B33  - %B33
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B33  + - %B33 + -
           3         2        2
       ]
     ,

     [%B34,

          1     15    2     14    1     13    4     12   11     11    4     10
         -- %B34   + -- %B34   + -- %B34   - -- %B34   - -- %B34   - -- %B34
         27          27          27          27          27          27
       + 
          1     9   14     8    1     7   2     6   1     5   2     4       3
         -- %B34  + -- %B34  + -- %B34  + - %B34  + - %B34  + - %B34  + %B34
         27         27         27         9         3         9
       + 
         4     2
         - %B34  - %B34 - 2
         3
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B34   - -- %B34   - -- %B34   + -- %B34   + -- %B34   + -- %B34
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B34  - -- %B34  - -- %B34  - - %B34  - - %B34  - - %B34  - %B34
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B34  + - %B34 + -
           3         2        2
       ,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B34   - -- %B34   - -- %B34   + -- %B34   + -- %B34   + -- %B34
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B34  - -- %B34  - -- %B34  - - %B34  - - %B34  - - %B34  - %B34
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B34  + - %B34 + -
           3         2        2
       ]
     ,
    [- 1,1,0,1], [- 1,1,1,0],

     [%B23,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B23   - -- %B23   - -- %B23   + -- %B23   + -- %B23   + -- %B23
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B23  - -- %B23  - -- %B23  - - %B23  - - %B23  - - %B23  - %B23
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B23  + - %B23 + -
           3         2        2
       ,
      %B30,

                   1     15    1     14    1     13    2     12   11     11
         - %B30 + -- %B23   + -- %B23   + -- %B23   - -- %B23   - -- %B23
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B23   + -- %B23  + -- %B23  + -- %B23  + - %B23  + - %B23
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B23  + - %B23  - - %B23 - -
         9         3         2        2
       ]
     ,

     [%B23,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B23   - -- %B23   - -- %B23   + -- %B23   + -- %B23   + -- %B23
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B23  - -- %B23  - -- %B23  - - %B23  - - %B23  - - %B23  - %B23
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B23  + - %B23 + -
           3         2        2
       ,
      %B31,

                   1     15    1     14    1     13    2     12   11     11
         - %B31 + -- %B23   + -- %B23   + -- %B23   - -- %B23   - -- %B23
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B23   + -- %B23  + -- %B23  + -- %B23  + - %B23  + - %B23
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B23  + - %B23  - - %B23 - -
         9         3         2        2
       ]
     ,

     [%B24,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B24   - -- %B24   - -- %B24   + -- %B24   + -- %B24   + -- %B24
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B24  - -- %B24  - -- %B24  - - %B24  - - %B24  - - %B24  - %B24
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B24  + - %B24 + -
           3         2        2
       ,
      %B28,

                   1     15    1     14    1     13    2     12   11     11
         - %B28 + -- %B24   + -- %B24   + -- %B24   - -- %B24   - -- %B24
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B24   + -- %B24  + -- %B24  + -- %B24  + - %B24  + - %B24
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B24  + - %B24  - - %B24 - -
         9         3         2        2
       ]
     ,

     [%B24,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B24   - -- %B24   - -- %B24   + -- %B24   + -- %B24   + -- %B24
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B24  - -- %B24  - -- %B24  - - %B24  - - %B24  - - %B24  - %B24
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B24  + - %B24 + -
           3         2        2
       ,
      %B29,

                   1     15    1     14    1     13    2     12   11     11
         - %B29 + -- %B24   + -- %B24   + -- %B24   - -- %B24   - -- %B24
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B24   + -- %B24  + -- %B24  + -- %B24  + - %B24  + - %B24
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B24  + - %B24  - - %B24 - -
         9         3         2        2
       ]
     ,

     [%B25,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B25   - -- %B25   - -- %B25   + -- %B25   + -- %B25   + -- %B25
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B25  - -- %B25  - -- %B25  - - %B25  - - %B25  - - %B25  - %B25
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B25  + - %B25 + -
           3         2        2
       ,
      %B26,

                   1     15    1     14    1     13    2     12   11     11
         - %B26 + -- %B25   + -- %B25   + -- %B25   - -- %B25   - -- %B25
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B25   + -- %B25  + -- %B25  + -- %B25  + - %B25  + - %B25
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B25  + - %B25  - - %B25 - -
         9         3         2        2
       ]
     ,

     [%B25,

            1     15    1     14    1     13    2     12   11     11    2     10
         - -- %B25   - -- %B25   - -- %B25   + -- %B25   + -- %B25   + -- %B25
           54          27          54          27          54          27
       + 
            1     9    7     8    1     7   1     6   1     5   1     4       3
         - -- %B25  - -- %B25  - -- %B25  - - %B25  - - %B25  - - %B25  - %B25
           54         27         54         9         6         9
       + 
           2     2   1        3
         - - %B25  + - %B25 + -
           3         2        2
       ,
      %B27,

                   1     15    1     14    1     13    2     12   11     11
         - %B27 + -- %B25   + -- %B25   + -- %B25   - -- %B25   - -- %B25
                  54          27          54          27          54
       + 
            2     10    1     9    7     8    1     7   1     6   1     5
         - -- %B25   + -- %B25  + -- %B25  + -- %B25  + - %B25  + - %B25
           27          54         27         54         9         6
       + 
         1     4   2     2   1        1
         - %B25  + - %B25  - - %B25 - -
         9         3         2        2
       ]
     ,
    [1,%B21,- %B21,0], [1,%B22,- %B22,0], [1,%B19,0,- %B19], [1,%B20,0,- %B20],
            1     3   1   1     3   1   1     3   1
    [%B17,- - %B17  + -,- - %B17  + -,- - %B17  + -],
            3         3   3         3   3         3
            1     3   1   1     3   1   1     3   1
    [%B18,- - %B18  + -,- - %B18  + -,- - %B18  + -]]
            3         3   3         3   3         3
                                 Type: List List RealClosure Fraction Integer
#lr2
 

   (26)  27
                                                        Type: PositiveInteger
lpr2 := positiveSolve(lf)$pack
 

                  1     3   1   1     3   1   1     3   1
   (27)  [[%B40,- - %B40  + -,- - %B40  + -,- - %B40  + -]]
                  3         3   3         3   3         3
                                 Type: List List RealClosure Fraction Integer
[approximate(r,1/10**21)::Float for r in lpr2.1]
 

   (28)
   [0.3221853546 2608559291, 0.3221853546 2608559291, 0.3221853546 2608559291,
    0.3221853546 2608559291]
                                                             Type: List Float
)lisp (bye)
 
Starts dribbling to schaum14.output (2010/3/27, 18:37:51).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 39
aa:=integrate(1/(x^3+a^3),x)
 

                                                                    +-+
           +-+     2          2      +-+                   (2x - a)\|3
        - \|3 log(x  - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
                                                                3a
   (1)  ----------------------------------------------------------------
                                       2 +-+
                                     6a \|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                    +-+
--R           +-+     2          2      +-+                   (2x - a)\|3
--R        - \|3 log(x  - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
--R                                                                3a
--R   (1)  ----------------------------------------------------------------
--R                                       2 +-+
--R                                     6a \|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 39
bb:=1/(6*a^2)*log((x+a)^2/(x^2-a*x+a^2))+1/(a^2*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

             2           2                       +-+
            x  + 2a x + a       +-+     (2x - a)\|3
        log(--------------) + 2\|3 atan(------------)
              2          2                   3a
             x  - a x + a
   (2)  ---------------------------------------------
                               2
                             6a
                                                     Type: Expression Integer
--R
--R             2           2                       +-+
--R            x  + 2a x + a       +-+     (2x - a)\|3
--R        log(--------------) + 2\|3 atan(------------)
--R              2          2                   3a
--R             x  - a x + a
--R   (2)  ---------------------------------------------
--R                               2
--R                             6a
--R                                                     Type: Expression Integer
--E

--S 3 of 39
cc:=aa-bb
 

                                                  2           2
               2          2                      x  + 2a x + a
        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
                                                   2          2
                                                  x  - a x + a
   (3)  --------------------------------------------------------
                                     2
                                   6a
                                                     Type: Expression Integer
--R
--R                                                  2           2
--R               2          2                      x  + 2a x + a
--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
--R                                                   2          2
--R                                                  x  - a x + a
--R   (3)  --------------------------------------------------------
--R                                     2
--R                                   6a
--R                                                     Type: Expression Integer
--E

--S 4 of 39      14:299 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 5 of 39
aa:=integrate(x/(x^3+a^3),x)
 

                                                                  +-+
         +-+     2          2      +-+                   (2x - a)\|3
        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
                                                              3a
   (1)  --------------------------------------------------------------
                                       +-+
                                    6a\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                  +-+
--R         +-+     2          2      +-+                   (2x - a)\|3
--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
--R                                                              3a
--R   (1)  --------------------------------------------------------------
--R                                       +-+
--R                                    6a\|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 6 of 39
bb:=1/(6*a)*log((x^2-a*x+a^2)/(x+a)^2)+1/(a*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

              2          2                       +-+
             x  - a x + a       +-+     (2x - a)\|3
        log(--------------) + 2\|3 atan(------------)
             2           2                   3a
            x  + 2a x + a
   (2)  ---------------------------------------------
                              6a
                                                     Type: Expression Integer
--R
--R              2          2                       +-+
--R             x  - a x + a       +-+     (2x - a)\|3
--R        log(--------------) + 2\|3 atan(------------)
--R             2           2                   3a
--R            x  + 2a x + a
--R   (2)  ---------------------------------------------
--R                              6a
--R                                                     Type: Expression Integer
--E

--S 7 of 39
cc:=aa-bb
 

                                                 2          2
             2          2                       x  - a x + a
        log(x  - a x + a ) - 2log(x + a) - log(--------------)
                                                2           2
                                               x  + 2a x + a
   (3)  ------------------------------------------------------
                                  6a
                                                     Type: Expression Integer
--R
--R                                                 2          2
--R             2          2                       x  - a x + a
--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
--R                                                2           2
--R                                               x  + 2a x + a
--R   (3)  ------------------------------------------------------
--R                                  6a
--R                                                     Type: Expression Integer
--E

--S 8 of 39      14:300 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 9 of 39
aa:=integrate(x^2/(x^3+a^3),x)
 

             3    3
        log(x  + a )
   (1)  ------------
              3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3    3
--R        log(x  + a )
--R   (1)  ------------
--R              3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 10 of 39
bb:=1/3*log(x^3+a^3)
 

             3    3
        log(x  + a )
   (2)  ------------
              3
                                                     Type: Expression Integer
--R
--R             3    3
--R        log(x  + a )
--R   (2)  ------------
--R              3
--R                                                     Type: Expression Integer
--E

--S 11 of 39     14:301 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 12 of 39
aa:=integrate(1/(x*(x^3+a^3)),x)
 

               3    3
        - log(x  + a ) + 3log(x)
   (1)  ------------------------
                     3
                   3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3    3
--R        - log(x  + a ) + 3log(x)
--R   (1)  ------------------------
--R                     3
--R                   3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13 of 39
bb:=1/(3*a^3)*log(x^3/(x^3+a^3))
 

                3
               x
        log(-------)
             3    3
            x  + a
   (2)  ------------
               3
             3a
                                                     Type: Expression Integer
--R
--R                3
--R               x
--R        log(-------)
--R             3    3
--R            x  + a
--R   (2)  ------------
--R               3
--R             3a
--R                                                     Type: Expression Integer
--E

--S 14 of 39
cc:=aa-bb
 

                                           3
               3    3                     x
        - log(x  + a ) + 3log(x) - log(-------)
                                        3    3
                                       x  + a
   (3)  ---------------------------------------
                            3
                          3a
                                                     Type: Expression Integer
--R
--R                                           3
--R               3    3                     x
--R        - log(x  + a ) + 3log(x) - log(-------)
--R                                        3    3
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            3
--R                          3a
--R                                                     Type: Expression Integer
--E

--S 15 of 39     14:302 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 15 of 39
aa:=integrate(1/(x^2*(x^3+a^3)),x)
 

   (1)
                                                                   +-+
       +-+     2          2       +-+                     (2x - a)\|3        +-+
   - x\|3 log(x  - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) - 6a\|3
                                                               3a
   -----------------------------------------------------------------------------
                                        4  +-+
                                      6a x\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                   +-+
--R       +-+     2          2       +-+                     (2x - a)\|3        +-+
--R   - x\|3 log(x  - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) - 6a\|3
--R                                                               3a
--R   -----------------------------------------------------------------------------
--R                                        4  +-+
--R                                      6a x\|3
--R                                          Type: Union(Expression Integer,...)
--E

--S 16 of 39
bb:=-1/(a^3*x)-1/(6*a^4)*log((x^2-a*x+a^2)/(x+a)^2)-1/(a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

                  2          2                        +-+
                 x  - a x + a        +-+     (2x - a)\|3
        - x log(--------------) - 2x\|3 atan(------------) - 6a
                 2           2                    3a
                x  + 2a x + a
   (2)  -------------------------------------------------------
                                    4
                                  6a x
                                                     Type: Expression Integer
--R
--R                  2          2                        +-+
--R                 x  - a x + a        +-+     (2x - a)\|3
--R        - x log(--------------) - 2x\|3 atan(------------) - 6a
--R                 2           2                    3a
--R                x  + 2a x + a
--R   (2)  -------------------------------------------------------
--R                                    4
--R                                  6a x
--R                                                     Type: Expression Integer
--E 

--S 17 of 39
cc:=aa-bb
 

                                                   2          2
               2          2                       x  - a x + a
        - log(x  - a x + a ) + 2log(x + a) + log(--------------)
                                                  2           2
                                                 x  + 2a x + a
   (3)  --------------------------------------------------------
                                     4
                                   6a
                                                     Type: Expression Integer
--R
--R                                                   2          2
--R               2          2                       x  - a x + a
--R        - log(x  - a x + a ) + 2log(x + a) + log(--------------)
--R                                                  2           2
--R                                                 x  + 2a x + a
--R   (3)  --------------------------------------------------------
--R                                     4
--R                                   6a
--R                                                     Type: Expression Integer
--E

--S 18 of 39     14:303 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 39
aa:=integrate(1/(x^3+a^3)^2,x)
 

   (1)
           3    3  +-+     2          2       3     3  +-+
       (- x  - a )\|3 log(x  - a x + a ) + (2x  + 2a )\|3 log(x + a)
     + 
                                +-+
          3     3      (2x - a)\|3       2  +-+
       (6x  + 6a )atan(------------) + 3a x\|3
                            3a
  /
        5 3     8  +-+
     (9a x  + 9a )\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R           3    3  +-+     2          2       3     3  +-+
--R       (- x  - a )\|3 log(x  - a x + a ) + (2x  + 2a )\|3 log(x + a)
--R     + 
--R                                +-+
--R          3     3      (2x - a)\|3       2  +-+
--R       (6x  + 6a )atan(------------) + 3a x\|3
--R                            3a
--R  /
--R        5 3     8  +-+
--R     (9a x  + 9a )\|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 20 of 39
bb:=x/(3*a^3*(x^3+a^3))+1/(9*a^5)*log((x+a)^2/(x^2-a*x+a^2))+2/(3*a^5*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

   (2)
                 2           2                                 +-+
     3    3     x  + 2a x + a        3     3  +-+     (2x - a)\|3       2
   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 3a x
                  2          2                             3a
                 x  - a x + a
   -----------------------------------------------------------------------
                                   5 3     8
                                 9a x  + 9a
                                                     Type: Expression Integer
--R
--R   (2)
--R                 2           2                                 +-+
--R     3    3     x  + 2a x + a        3     3  +-+     (2x - a)\|3       2
--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 3a x
--R                  2          2                             3a
--R                 x  - a x + a
--R   -----------------------------------------------------------------------
--R                                   5 3     8
--R                                 9a x  + 9a
--R                                                     Type: Expression Integer
--E

--S 21 of 39
cc:=aa-bb
 

                                                  2           2
               2          2                      x  + 2a x + a
        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
                                                   2          2
                                                  x  - a x + a
   (3)  --------------------------------------------------------
                                     5
                                   9a
                                                     Type: Expression Integer
--R
--R                                                  2           2
--R               2          2                      x  + 2a x + a
--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
--R                                                   2          2
--R                                                  x  - a x + a
--R   (3)  --------------------------------------------------------
--R                                     5
--R                                   9a
--R                                                     Type: Expression Integer
--E

--S 22 of 39     14:304 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 23 of 39
aa:=integrate(x/(x^3+a^3)^2,x)
 

   (1)
         3    3  +-+     2          2         3     3  +-+
       (x  + a )\|3 log(x  - a x + a ) + (- 2x  - 2a )\|3 log(x + a)
     + 
                                +-+
          3     3      (2x - a)\|3         2 +-+
       (6x  + 6a )atan(------------) + 6a x \|3
                            3a
  /
         4 3      7  +-+
     (18a x  + 18a )\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R         3    3  +-+     2          2         3     3  +-+
--R       (x  + a )\|3 log(x  - a x + a ) + (- 2x  - 2a )\|3 log(x + a)
--R     + 
--R                                +-+
--R          3     3      (2x - a)\|3         2 +-+
--R       (6x  + 6a )atan(------------) + 6a x \|3
--R                            3a
--R  /
--R         4 3      7  +-+
--R     (18a x  + 18a )\|3
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 39
bb:=x^2/(3*a^3*(x^3+a^3))+1/(18*a^4)*log((x^2-a*x+a^2)/(x+a)^2)+1/(3*a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
 

   (2)
                  2          2                                 +-+
     3    3      x  - a x + a        3     3  +-+     (2x - a)\|3         2
   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 6a x
                 2           2                             3a
                x  + 2a x + a
   ------------------------------------------------------------------------
                                    4 3      7
                                 18a x  + 18a
                                                     Type: Expression Integer
--R
--R   (2)
--R                  2          2                                 +-+
--R     3    3      x  - a x + a        3     3  +-+     (2x - a)\|3         2
--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 6a x
--R                 2           2                             3a
--R                x  + 2a x + a
--R   ------------------------------------------------------------------------
--R                                    4 3      7
--R                                 18a x  + 18a
--R                                                     Type: Expression Integer
--E

--S 25 of 39
cc:=aa-bb
 

                                                 2          2
             2          2                       x  - a x + a
        log(x  - a x + a ) - 2log(x + a) - log(--------------)
                                                2           2
                                               x  + 2a x + a
   (3)  ------------------------------------------------------
                                    4
                                 18a
                                                     Type: Expression Integer
--R
--R                                                 2          2
--R             2          2                       x  - a x + a
--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
--R                                                2           2
--R                                               x  + 2a x + a
--R   (3)  ------------------------------------------------------
--R                                    4
--R                                 18a
--R                                                     Type: Expression Integer
--E

--S 26 of 39     14:305 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 39
aa:=integrate(x^2/(x^3+a^3)^2,x)
 

              1
   (1)  - ---------
            3     3
          3x  + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            3     3
--R          3x  + 3a
--R                                          Type: Union(Expression Integer,...)
--E

--S 28 of 39
bb:=-1/(3*(x^3+a^3))
 

              1
   (2)  - ---------
            3     3
          3x  + 3a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            3     3
--R          3x  + 3a
--R                                            Type: Fraction Polynomial Integer
--E 

--S 29 of 39     14:306 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 30 of 39
aa:=integrate(1/(x*(x^3+a^3)^2),x)
 

            3    3      3    3       3     3           3
        (- x  - a )log(x  + a ) + (3x  + 3a )log(x) + a
   (1)  ------------------------------------------------
                             6 3     9
                           3a x  + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            3    3      3    3       3     3           3
--R        (- x  - a )log(x  + a ) + (3x  + 3a )log(x) + a
--R   (1)  ------------------------------------------------
--R                             6 3     9
--R                           3a x  + 3a
--R                                          Type: Union(Expression Integer,...)
--E

--S 31 of 39
bb:=1/(3*a^3*(x^3+a^3))+1/(3*a^6)*log(x^3/(x^3+a^3))
 

                         3
          3    3        x        3
        (x  + a )log(-------) + a
                      3    3
                     x  + a
   (2)  --------------------------
                  6 3     9
                3a x  + 3a
                                                     Type: Expression Integer
--R
--R                         3
--R          3    3        x        3
--R        (x  + a )log(-------) + a
--R                      3    3
--R                     x  + a
--R   (2)  --------------------------
--R                  6 3     9
--R                3a x  + 3a
--R                                                     Type: Expression Integer
--E

--S 32 of 39
cc:=aa-bb
 

                                           3
               3    3                     x
        - log(x  + a ) + 3log(x) - log(-------)
                                        3    3
                                       x  + a
   (3)  ---------------------------------------
                            6
                          3a
                                                     Type: Expression Integer
--R
--R                                           3
--R               3    3                     x
--R        - log(x  + a ) + 3log(x) - log(-------)
--R                                        3    3
--R                                       x  + a
--R   (3)  ---------------------------------------
--R                            6
--R                          3a
--R                                                     Type: Expression Integer
--E

--S 33 of 39     14:307 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 34 of 39
aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
 

   (1)
            4     3   +-+     2          2       4     3   +-+
       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
     + 
                                     +-+
             4      3       (2x - a)\|3             3     4  +-+
       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
                                 3a
  /
        7 4     10   +-+
     (9a x  + 9a  x)\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            4     3   +-+     2          2       4     3   +-+
--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
--R     + 
--R                                     +-+
--R             4      3       (2x - a)\|3             3     4  +-+
--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
--R                                 3a
--R  /
--R        7 4     10   +-+
--R     (9a x  + 9a  x)\|3
--R                                          Type: Union(Expression Integer,...)
--E

--S 35 of 39
t1:=integrate(x/(x^3+a^3),x)
 

                                                                  +-+
         +-+     2          2      +-+                   (2x - a)\|3
        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
                                                              3a
   (2)  --------------------------------------------------------------
                                       +-+
                                    6a\|3
                                          Type: Union(Expression Integer,...)
--R
--R                                                                  +-+
--R         +-+     2          2      +-+                   (2x - a)\|3
--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
--R                                                              3a
--R   (2)  --------------------------------------------------------------
--R                                       +-+
--R                                    6a\|3
--R                                          Type: Union(Expression Integer,...)
--E

--S 36 of 39
bb:=-1/(a^6*x)-x^2/(3*a^6*(x^3+a^3))-4/(3*a^6)*t1
 

   (3)
            4     3   +-+     2          2       4     3   +-+
       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
     + 
                                     +-+
             4      3       (2x - a)\|3             3     4  +-+
       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
                                 3a
  /
        7 4     10   +-+
     (9a x  + 9a  x)\|3
                                                     Type: Expression Integer
--R
--R   (3)
--R            4     3   +-+     2          2       4     3   +-+
--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
--R     + 
--R                                     +-+
--R             4      3       (2x - a)\|3             3     4  +-+
--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
--R                                 3a
--R  /
--R        7 4     10   +-+
--R     (9a x  + 9a  x)\|3
--R                                                     Type: Expression Integer
--E 

--S 37 of 39     14:308 Schaums and Axiom agree
cc:=aa-bb
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 38 of 39     14:309 Axiom cannot compute this integral
aa:=integrate(x^m/(x^3+a^3),x)
 

           x      m
         ++     %Q
   (1)   |   -------- d%Q
        ++    3     3
             a  + %Q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x      m
--I         ++     %L
--I   (1)   |   -------- d%L
--R        ++    3     3
--I             a  + %L
--R                                          Type: Union(Expression Integer,...)
--E
)clear all
 

--S 39 of 39     14:310 Axiom cannot compute this integral
aa:=integrate(1/(x^n*(x^3+a^3)),x)
 

           x
         ++        1
   (1)   |   ------------- d%Q
        ++     3     3   n
             (a  + %Q )%Q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++        1
--I   (1)   |   ------------- d%L
--R        ++     3     3   n
--I             (a  + %L )%L
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to noptip.output (2010/3/27, 18:30:21).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
outputGeneral 5
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
f := %e^x*(4*x^2 + 2*y^2 + 4*x*y + 2*y + 1);
 

                                                     Type: Expression Integer
--R 
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
start := [x=-1.0, y=1.0];
 

                                         Type: List Equation Polynomial Float
--R 
--R
--R                                         Type: List Equation Polynomial Float
--E 3

--S 4 of 6 used to work?
nagMin(f,start) :: List Equation Polynomial Float
 
   There are no library operations named nagMin 
      Use HyperDoc Browse or issue
                               )what op nagMin
      to learn if there is any operation containing " nagMin " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagMin with argument type(s) 
                             Expression Integer
                       List Equation Polynomial Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagMin 
--R      Use HyperDoc Browse or issue
--R                               )what op nagMin
--R      to learn if there is any operation containing " nagMin " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagMin with argument type(s) 
--R                             Expression Integer
--R                       List Equation Polynomial Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4
--       [x= 0.5,y= - 1.0]

--S 5 of 6
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 6
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 6
)spool 
 
Starts dribbling to exseries.output (2010/3/27, 18:25:46).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 9
f := taylor(exp(x))
 

   (1)
             1  2   1  3    1  4    1   5    1   6     1   7     1    8
     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
             2      6      24      120      720      5040      40320
   + 
        1    9      1     10      11
     ------ x  + ------- x   + O(x  )
     362880      3628800
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 9
eval(f,1.0)
 

   (2)
   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
    2.7182787698 412698413, 2.7182815255 731922399, ...]
                                                Type: Stream Expression Float
--R 
--R
--R   (2)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                Type: Stream Expression Float
--E 2

)clear all
 

--S 3 of 9
series(sin(a*x),x = 0)
 

               3        5        7          9            11
              a   3    a   5    a    7     a     9      a      11      12
   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
               6      120      5040      362880      39916800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               3        5        7          9            11
--R              a   3    a   5    a    7     a     9      a      11      12
--R   (1)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
--R               6      120      5040      362880      39916800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 3

--S 4 of 9
series(sin(a*x),a = %pi/4)
 

   (2)
                                           2    %pi x
                                          x sin(-----)
         %pi x          %pi x      %pi            4         %pi 2
     sin(-----) + x cos(-----)(a - ---) - ------------ (a - ---)
           4              4         4           2            4
   + 
        3    %pi x                4    %pi x
       x cos(-----)              x sin(-----)
               4         %pi 3           4         %pi 4
     - ------------ (a - ---)  + ------------ (a - ---)
             6            4           24            4
   + 
      5    %pi x                6    %pi x                7    %pi x
     x cos(-----)              x sin(-----)              x cos(-----)
             4         %pi 5           4         %pi 6           4         %pi 7
     ------------ (a - ---)  - ------------ (a - ---)  - ------------ (a - ---)
          120           4           720           4          5040           4
   + 
      8    %pi x                9    %pi x
     x sin(-----)              x cos(-----)
             4         %pi 8           4         %pi 9
     ------------ (a - ---)  + ------------ (a - ---)
         40320          4         362880          4
   + 
        10    %pi x
       x  sin(-----)
                4         %pi 10          %pi 11
     - ------------- (a - ---)   + O((a - ---)  )
          3628800          4               4
                     Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4)
--R 
--R
--R   (2)
--R                                           2    %pi x
--R                                          x sin(-----)
--R         %pi x          %pi x      %pi            4         %pi 2
--R     sin(-----) + x cos(-----)(a - ---) - ------------ (a - ---)
--R           4              4         4           2            4
--R   + 
--R        3    %pi x                4    %pi x
--R       x cos(-----)              x sin(-----)
--R               4         %pi 3           4         %pi 4
--R     - ------------ (a - ---)  + ------------ (a - ---)
--R             6            4           24            4
--R   + 
--R      5    %pi x                6    %pi x                7    %pi x
--R     x cos(-----)              x sin(-----)              x cos(-----)
--R             4         %pi 5           4         %pi 6           4         %pi 7
--R     ------------ (a - ---)  - ------------ (a - ---)  - ------------ (a - ---)
--R          120           4           720           4          5040           4
--R   + 
--R      8    %pi x                9    %pi x
--R     x sin(-----)              x cos(-----)
--R             4         %pi 8           4         %pi 9
--R     ------------ (a - ---)  + ------------ (a - ---)
--R         40320          4         362880          4
--R   + 
--R        10    %pi x
--R       x  sin(-----)
--R                4         %pi 10          %pi 11
--R     - ------------- (a - ---)   + O((a - ---)  )
--R          3628800          4               4
--R                     Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4)
--E 4

)clear all
 

--S 5 of 9
f := series(1/(1-x),x = 0)
 

                 2    3    4    5    6    7    8    9    10      11
   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 5

--S 6 of 9
g := log(f)
 

   (2)
         1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9    1  10    1  11
     x + - x  + - x  + - x  + - x  + - x  + - x  + - x  + - x  + -- x   + -- x
         2      3      4      5      6      7      8      9      10       11
   + 
        12
     O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R         1  2   1  3   1  4   1  5   1  6   1  7   1  8   1  9    1  10    1  11
--R     x + - x  + - x  + - x  + - x  + - x  + - x  + - x  + - x  + -- x   + -- x
--R         2      3      4      5      6      7      8      9      10       11
--R   + 
--R        12
--R     O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 6

--S 7 of 9
exp(g)
 

                 2    3    4    5    6    7    8    9    10      11
   (3)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (3)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 7

)clear all
 

--S 8 of 9
f := series(1/(1-x),x = 0)
 

                 2    3    4    5    6    7    8    9    10      11
   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (1)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 8

--S 9 of 9
f ** 2
 

   (2)
              2     3     4     5     6     7     8      9      10      11
   1 + 2x + 3x  + 4x  + 5x  + 6x  + 7x  + 8x  + 9x  + 10x  + 11x   + O(x  )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (2)
--R              2     3     4     5     6     7     8      9      10      11
--R   1 + 2x + 3x  + 4x  + 5x  + 6x  + 7x  + 8x  + 9x  + 10x  + 11x   + O(x  )
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 9
)spool 
 
Starts dribbling to schaum19.output (2010/3/27, 18:38:14).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 185
aa:=integrate(sin(a*x)*cos(a*x),x)
 

                  2
          cos(a x)
   (1)  - ---------
              2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R          cos(a x)
--R   (1)  - ---------
--R              2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 185
bb:=sin(a*x)^2/(2*a)
 

                2
        sin(a x)
   (2)  ---------
            2a
                                                     Type: Expression Integer
--R
--R                2
--R        sin(a x)
--R   (2)  ---------
--R            2a
--R                                                     Type: Expression Integer
--E

--S 3 of 185
cc:=aa-bb
 

                  2           2
        - sin(a x)  - cos(a x)
   (3)  -----------------------
                   2a
                                                     Type: Expression Integer
--R
--R                  2           2
--R        - sin(a x)  - cos(a x)
--R   (3)  -----------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 4 of 185
cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
 

              2            2
   (4)  cos(a)  == - sin(a)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2            2
--R   (4)  cos(a)  == - sin(a)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 185      14:399 Schaums and Axiom differ by a constant
dd:=cossqrrule cc
 

           1
   (5)  - --
          2a
                                                     Type: Expression Integer
--R
--R           1
--R   (5)  - --
--R          2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 6 of 185
aa:=integrate(sin(p*x)*cos(q*x),x)
 

        q sin(p x)sin(q x) + p cos(p x)cos(q x)
   (1)  ---------------------------------------
                         2    2
                        q  - p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        q sin(p x)sin(q x) + p cos(p x)cos(q x)
--R   (1)  ---------------------------------------
--R                         2    2
--R                        q  - p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7 of 185
bb:=-cos((p-q)*x)/(2*(p-q))-cos((p+q)*x)/(2*(p+q))
 

        (- q + p)cos((q + p)x) + (q + p)cos((q - p)x)
   (2)  ---------------------------------------------
                            2     2
                          2q  - 2p
                                                     Type: Expression Integer
--R
--R        (- q + p)cos((q + p)x) + (q + p)cos((q - p)x)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 8 of 185
cc:=aa-bb
 

   (3)
       2q sin(p x)sin(q x) + (q - p)cos((q + p)x) + 2p cos(p x)cos(q x)
     + 
       (- q - p)cos((q - p)x)
  /
       2     2
     2q  - 2p
                                                     Type: Expression Integer
--R
--R   (3)
--R       2q sin(p x)sin(q x) + (q - p)cos((q + p)x) + 2p cos(p x)cos(q x)
--R     + 
--R       (- q - p)cos((q - p)x)
--R  /
--R       2     2
--R     2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 9 of 185      14:400 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 185
aa:=integrate(sin(a*x)^n*cos(a*x),x)
 

                  n log(sin(a x))
        sin(a x)%e
   (1)  -------------------------
                 a n + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  n log(sin(a x))
--R        sin(a x)%e
--R   (1)  -------------------------
--R                 a n + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 185
bb:=sin(a*x)^(n+1)/((n+1)*a)
 

                n + 1
        sin(a x)
   (2)  -------------
           a n + a
                                                     Type: Expression Integer
--R
--R                n + 1
--R        sin(a x)
--R   (2)  -------------
--R           a n + a
--R                                                     Type: Expression Integer
--E

--S 12 of 185
cc:=aa-bb
 

                  n log(sin(a x))           n + 1
        sin(a x)%e                - sin(a x)
   (3)  -----------------------------------------
                         a n + a
                                                     Type: Expression Integer
--R
--R                  n log(sin(a x))           n + 1
--R        sin(a x)%e                - sin(a x)
--R   (3)  -----------------------------------------
--R                         a n + a
--R                                                     Type: Expression Integer
--E

--S 13 of 185
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 14 of 185
dd:=explog cc
 

                  n + 1                   n
        - sin(a x)      + sin(a x)sin(a x)
   (5)  -----------------------------------
                      a n + a
                                                     Type: Expression Integer
--R
--R                  n + 1                   n
--R        - sin(a x)      + sin(a x)sin(a x)
--R   (5)  -----------------------------------
--R                      a n + a
--R                                                     Type: Expression Integer
--E

--S 15 of 185     14:401 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 185
aa:=integrate(cos(a*x)^n*sin(a*x),x)
 

                    n log(cos(a x))
          cos(a x)%e
   (1)  - -------------------------
                   a n + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    n log(cos(a x))
--R          cos(a x)%e
--R   (1)  - -------------------------
--R                   a n + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 17 of 185
bb:=-cos(a*x)^(n+1)/((n+1)*a)
 

                  n + 1
          cos(a x)
   (2)  - -------------
             a n + a
                                                     Type: Expression Integer
--R
--R                  n + 1
--R          cos(a x)
--R   (2)  - -------------
--R             a n + a
--R                                                     Type: Expression Integer
--E 

--S 18 of 185
cc:=aa-bb
 

                    n log(cos(a x))           n + 1
        - cos(a x)%e                + cos(a x)
   (3)  -------------------------------------------
                          a n + a
                                                     Type: Expression Integer
--R
--R                    n log(cos(a x))           n + 1
--R        - cos(a x)%e                + cos(a x)
--R   (3)  -------------------------------------------
--R                          a n + a
--R                                                     Type: Expression Integer
--E

--S 19 of 185
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20 of 185
dd:=explog cc
 

                n + 1                   n
        cos(a x)      - cos(a x)cos(a x)
   (5)  ---------------------------------
                     a n + a
                                                     Type: Expression Integer
--R
--R                n + 1                   n
--R        cos(a x)      - cos(a x)cos(a x)
--R   (5)  ---------------------------------
--R                     a n + a
--R                                                     Type: Expression Integer
--E

--S 21 of 185     14:402 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 22 of 185
aa:=integrate(sin(a*x)^2*cos(a*x)^2,x)
 

                    3
        (- 2cos(a x)  + cos(a x))sin(a x) + a x
   (1)  ---------------------------------------
                           8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    3
--R        (- 2cos(a x)  + cos(a x))sin(a x) + a x
--R   (1)  ---------------------------------------
--R                           8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 23 of 185
bb:=x/8-sin(4*a*x)/(32*a)
 

        - sin(4a x) + 4a x
   (2)  ------------------
                32a
                                                     Type: Expression Integer
--R
--R        - sin(4a x) + 4a x
--R   (2)  ------------------
--R                32a
--R                                                     Type: Expression Integer
--E

--S 24 of 185
cc:=aa-bb
 

                                3
        sin(4a x) + (- 8cos(a x)  + 4cos(a x))sin(a x)
   (3)  ----------------------------------------------
                              32a
                                                     Type: Expression Integer
--R
--R                                3
--R        sin(4a x) + (- 8cos(a x)  + 4cos(a x))sin(a x)
--R   (3)  ----------------------------------------------
--R                              32a
--R                                                     Type: Expression Integer
--E

--S 25 of 185     14:403 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 26 of 185
aa:=integrate(1/(sin(a*x)*cos(a*x)),x)
 

              sin(a x)              2cos(a x)
        log(------------) - log(- ------------)
            cos(a x) + 1          cos(a x) + 1
   (1)  ---------------------------------------
                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)              2cos(a x)
--R        log(------------) - log(- ------------)
--R            cos(a x) + 1          cos(a x) + 1
--R   (1)  ---------------------------------------
--R                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 27 of 185
bb:=1/a*log(tan(a*x))
 

        log(tan(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(tan(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 28 of 185
cc:=aa-bb
 

                                sin(a x)              2cos(a x)
        - log(tan(a x)) + log(------------) - log(- ------------)
                              cos(a x) + 1          cos(a x) + 1
   (3)  ---------------------------------------------------------
                                    a
                                                     Type: Expression Integer
--R
--R                                sin(a x)              2cos(a x)
--R        - log(tan(a x)) + log(------------) - log(- ------------)
--R                              cos(a x) + 1          cos(a x) + 1
--R   (3)  ---------------------------------------------------------
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 29 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 30 of 185
dd:=tanrule cc
 

              sin(a x)          sin(a x)              2cos(a x)
        - log(--------) + log(------------) - log(- ------------)
              cos(a x)        cos(a x) + 1          cos(a x) + 1
   (5)  ---------------------------------------------------------
                                    a
                                                     Type: Expression Integer
--R
--R              sin(a x)          sin(a x)              2cos(a x)
--R        - log(--------) + log(------------) - log(- ------------)
--R              cos(a x)        cos(a x) + 1          cos(a x) + 1
--R   (5)  ---------------------------------------------------------
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 31 of 185     14:404 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

          log(- 2)
   (6)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 2)
--R   (6)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 32 of 185
aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x)
 

   (1)
                   sin(a x) + cos(a x) + 1
       sin(a x)log(-----------------------)
                         cos(a x) + 1
     + 
                     sin(a x) - cos(a x) - 1
       - sin(a x)log(-----------------------) - 1
                           cos(a x) + 1
  /
     a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   sin(a x) + cos(a x) + 1
--R       sin(a x)log(-----------------------)
--R                         cos(a x) + 1
--R     + 
--R                     sin(a x) - cos(a x) - 1
--R       - sin(a x)log(-----------------------) - 1
--R                           cos(a x) + 1
--R  /
--R     a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33 of 185
bb:=1/a*log(tan(%pi/4+(a*x)/2))-1/(a*sin(a*x))
 

                        2a x + %pi
        sin(a x)log(tan(----------)) - 1
                             4
   (2)  --------------------------------
                   a sin(a x)
                                                     Type: Expression Integer
--R
--R                        2a x + %pi
--R        sin(a x)log(tan(----------)) - 1
--R                             4
--R   (2)  --------------------------------
--R                   a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 34 of 185
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 35 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36 of 185
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------)
                 2a x + %pi
             cos(----------)
                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------)
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 37 of 185
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------))
                      4                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------))
--R                      4                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 38 of 185     14:405 Schaums and Axiom differ by a constant
ff:=complexNormalize %
 

        log(- 1)
   (7)  --------
            a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 185
aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x)
 

                      sin(a x)
        cos(a x)log(------------) + cos(a x) + 1
                    cos(a x) + 1
   (1)  ----------------------------------------
                       a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      sin(a x)
--R        cos(a x)log(------------) + cos(a x) + 1
--R                    cos(a x) + 1
--R   (1)  ----------------------------------------
--R                       a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40 of 185
bb:=1/a*log(tan((a*x)/2))+1/(a*cos(a*x))
 

                        a x
        cos(a x)log(tan(---)) + 1
                         2
   (2)  -------------------------
                a cos(a x)
                                                     Type: Expression Integer
--R
--R                        a x
--R        cos(a x)log(tan(---)) + 1
--R                         2
--R   (2)  -------------------------
--R                a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 41 of 185
cc:=aa-bb
 

                  a x           sin(a x)
        - log(tan(---)) + log(------------) + 1
                   2          cos(a x) + 1
   (3)  ---------------------------------------
                           a
                                                     Type: Expression Integer
--R
--R                  a x           sin(a x)
--R        - log(tan(---)) + log(------------) + 1
--R                   2          cos(a x) + 1
--R   (3)  ---------------------------------------
--R                           a
--R                                                     Type: Expression Integer
--E

--S 42 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 43 of 185
dd:=tanrule cc
 

                                    a x
                                sin(---)
              sin(a x)               2
        log(------------) - log(--------) + 1
            cos(a x) + 1            a x
                                cos(---)
                                     2
   (5)  -------------------------------------
                          a
                                                     Type: Expression Integer
--R
--R                                    a x
--R                                sin(---)
--R              sin(a x)               2
--R        log(------------) - log(--------) + 1
--R            cos(a x) + 1            a x
--R                                cos(---)
--R                                     2
--R   (5)  -------------------------------------
--R                          a
--R                                                     Type: Expression Integer
--E

--S 44 of 185
ee:=expandLog dd
 

                                a x                                 a x
        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---)) + 1
                                 2                                   2
   (6)  ---------------------------------------------------------------------
                                          a
                                                     Type: Expression Integer
--R
--R                                a x                                 a x
--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---)) + 1
--R                                 2                                   2
--R   (6)  ---------------------------------------------------------------------
--R                                          a
--R                                                     Type: Expression Integer
--E

--S 45 of 185     14:406 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        1
   (7)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (7)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 46 of 185
aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x)
 

                    2
         - 2cos(a x)  + 1
   (1)  ------------------
        a cos(a x)sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2
--R         - 2cos(a x)  + 1
--R   (1)  ------------------
--R        a cos(a x)sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 47 of 185
bb:=-(2*cot(2*a*x))/a
 

          2cot(2a x)
   (2)  - ----------
               a
                                                     Type: Expression Integer
--R
--R          2cot(2a x)
--R   (2)  - ----------
--R               a
--R                                                     Type: Expression Integer
--E

--S 48 of 185
cc:=aa-bb
 

                                              2
        2cos(a x)cot(2a x)sin(a x) - 2cos(a x)  + 1
   (3)  -------------------------------------------
                     a cos(a x)sin(a x)
                                                     Type: Expression Integer
--R
--R                                              2
--R        2cos(a x)cot(2a x)sin(a x) - 2cos(a x)  + 1
--R   (3)  -------------------------------------------
--R                     a cos(a x)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 49 of 185
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 50 of 185
dd:=cotrule cc
 

                    2
        (- 2cos(a x)  + 1)sin(2a x) + 2cos(a x)cos(2a x)sin(a x)
   (5)  --------------------------------------------------------
                       a cos(a x)sin(a x)sin(2a x)
                                                     Type: Expression Integer
--R
--R                    2
--R        (- 2cos(a x)  + 1)sin(2a x) + 2cos(a x)cos(2a x)sin(a x)
--R   (5)  --------------------------------------------------------
--R                       a cos(a x)sin(a x)sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 51 of 185     14:407 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 52 of 185
aa:=integrate(sin(a*x)^2/cos(a*x),x)
 

            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
        log(-----------------------) - log(-----------------------) - sin(a x)
                  cos(a x) + 1                   cos(a x) + 1
   (1)  ----------------------------------------------------------------------
                                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R        log(-----------------------) - log(-----------------------) - sin(a x)
--R                  cos(a x) + 1                   cos(a x) + 1
--R   (1)  ----------------------------------------------------------------------
--R                                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53 of 185
bb:=-sin(a*x)/a+1/a*log(tan((a*x)/2+%pi/4))
 

                2a x + %pi
        log(tan(----------)) - sin(a x)
                     4
   (2)  -------------------------------
                       a
                                                     Type: Expression Integer
--R
--R                2a x + %pi
--R        log(tan(----------)) - sin(a x)
--R                     4
--R   (2)  -------------------------------
--R                       a
--R                                                     Type: Expression Integer
--E

--S 54 of 185
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 55 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 56 of 185
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------)
                 2a x + %pi
             cos(----------)
                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------)
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 57 of 185
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------))
                      4                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------))
--R                      4                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 58 of 185     14:408 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        log(- 1)
   (7)  --------
            a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 59 of 185
aa:=integrate(cos(a*x)^2/sin(a*x),x)
 

              sin(a x)
        log(------------) + cos(a x)
            cos(a x) + 1
   (1)  ----------------------------
                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)
--R        log(------------) + cos(a x)
--R            cos(a x) + 1
--R   (1)  ----------------------------
--R                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 60 of 185
bb:=cos(a*x)/a+1/a*log(tan((a*x)/2))
 

                a x
        log(tan(---)) + cos(a x)
                 2
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---)) + cos(a x)
--R                 2
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 61 of 185
cc:=aa-bb
 

                  a x           sin(a x)
        - log(tan(---)) + log(------------)
                   2          cos(a x) + 1
   (3)  -----------------------------------
                         a
                                                     Type: Expression Integer
--R
--R                  a x           sin(a x)
--R        - log(tan(---)) + log(------------)
--R                   2          cos(a x) + 1
--R   (3)  -----------------------------------
--R                         a
--R                                                     Type: Expression Integer
--E

--S 62 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 63 of 185
dd:=tanrule cc
 

                                    a x
                                sin(---)
              sin(a x)               2
        log(------------) - log(--------)
            cos(a x) + 1            a x
                                cos(---)
                                     2
   (5)  ---------------------------------
                        a
                                                     Type: Expression Integer
--R
--R                                    a x
--R                                sin(---)
--R              sin(a x)               2
--R        log(------------) - log(--------)
--R            cos(a x) + 1            a x
--R                                cos(---)
--R                                     2
--R   (5)  ---------------------------------
--R                        a
--R                                                     Type: Expression Integer
--E

--S 64 of 185
ee:=expandLog dd
 

                                a x                                 a x
        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
                                 2                                   2
   (6)  -----------------------------------------------------------------
                                        a
                                                     Type: Expression Integer
--R
--R                                a x                                 a x
--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
--R                                 2                                   2
--R   (6)  -----------------------------------------------------------------
--R                                        a
--R                                                     Type: Expression Integer
--E

--S 65 of 185     14:409 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 66 of 185
aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x)
 

   (1)
                         sin(a x) + cos(a x) + 1
       (sin(a x) + 1)log(-----------------------)
                               cos(a x) + 1
     + 
                           sin(a x) - cos(a x) - 1
       (- sin(a x) - 1)log(-----------------------) + sin(a x)
                                 cos(a x) + 1
  /
     2a sin(a x) + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                         sin(a x) + cos(a x) + 1
--R       (sin(a x) + 1)log(-----------------------)
--R                               cos(a x) + 1
--R     + 
--R                           sin(a x) - cos(a x) - 1
--R       (- sin(a x) - 1)log(-----------------------) + sin(a x)
--R                                 cos(a x) + 1
--R  /
--R     2a sin(a x) + 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 67 of 185
bb:=-1/(2*a*(1+sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
 

                              2a x + %pi
        (sin(a x) + 1)log(tan(----------)) - 1
                                   4
   (2)  --------------------------------------
                   2a sin(a x) + 2a
                                                     Type: Expression Integer
--R
--R                              2a x + %pi
--R        (sin(a x) + 1)log(tan(----------)) - 1
--R                                   4
--R   (2)  --------------------------------------
--R                   2a sin(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 68 of 185
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------) + 1
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------) + 1
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 69 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 70 of 185
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------) + 1
                 2a x + %pi
             cos(----------)
                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------) + 1
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 71 of 185
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------)) + 1
                      4                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------)) + 1
--R                      4                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 72 of 185
ff:=complexNormalize ee
 

        log(- 1) + 1
   (7)  ------------
             2a
                                                     Type: Expression Integer
--R
--R        log(- 1) + 1
--R   (7)  ------------
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all 
 

--S 73 of 185
aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x)
 

   (1)
                         sin(a x) + cos(a x) + 1
       (sin(a x) - 1)log(-----------------------)
                               cos(a x) + 1
     + 
                           sin(a x) - cos(a x) - 1
       (- sin(a x) + 1)log(-----------------------) - sin(a x)
                                 cos(a x) + 1
  /
     2a sin(a x) - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                         sin(a x) + cos(a x) + 1
--R       (sin(a x) - 1)log(-----------------------)
--R                               cos(a x) + 1
--R     + 
--R                           sin(a x) - cos(a x) - 1
--R       (- sin(a x) + 1)log(-----------------------) - sin(a x)
--R                                 cos(a x) + 1
--R  /
--R     2a sin(a x) - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 74 of 185
bb:=1/(2*a*(1-sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
 

                              2a x + %pi
        (sin(a x) - 1)log(tan(----------)) - 1
                                   4
   (2)  --------------------------------------
                   2a sin(a x) - 2a
                                                     Type: Expression Integer
--R
--R                              2a x + %pi
--R        (sin(a x) - 1)log(tan(----------)) - 1
--R                                   4
--R   (2)  --------------------------------------
--R                   2a sin(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 75 of 185
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------) - 1
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------) - 1
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 76 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 77 of 185
dd:=tanrule cc
 

   (5)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------) - 1
                 2a x + %pi
             cos(----------)
                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (5)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------) - 1
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 78 of 185
ee:=expandLog dd
 

   (6)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------)) - 1
                      4                      4
  /
     2a
                                                     Type: Expression Integer
--R
--R   (6)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------)) - 1
--R                      4                      4
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 79 of 185     14:410 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        log(- 1) - 1
   (7)  ------------
             2a
                                                     Type: Expression Integer
--R
--R        log(- 1) - 1
--R   (7)  ------------
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 80 of 185
aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x)
 

                             sin(a x)
        (2cos(a x) + 2)log(------------) - cos(a x) + 1
                           cos(a x) + 1
   (1)  -----------------------------------------------
                        4a cos(a x) + 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             sin(a x)
--R        (2cos(a x) + 2)log(------------) - cos(a x) + 1
--R                           cos(a x) + 1
--R   (1)  -----------------------------------------------
--R                        4a cos(a x) + 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 81 of 185
bb:=1/(2*a*(1+cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
 

                              a x
        (cos(a x) + 1)log(tan(---)) + 1
                               2
   (2)  -------------------------------
                2a cos(a x) + 2a
                                                     Type: Expression Integer
--R
--R                              a x
--R        (cos(a x) + 1)log(tan(---)) + 1
--R                               2
--R   (2)  -------------------------------
--R                2a cos(a x) + 2a
--R                                                     Type: Expression Integer
--E

--S 82 of 185
cc:=aa-bb
 

                   a x            sin(a x)
        - 2log(tan(---)) + 2log(------------) - 1
                    2           cos(a x) + 1
   (3)  -----------------------------------------
                            4a
                                                     Type: Expression Integer
--R
--R                   a x            sin(a x)
--R        - 2log(tan(---)) + 2log(------------) - 1
--R                    2           cos(a x) + 1
--R   (3)  -----------------------------------------
--R                            4a
--R                                                     Type: Expression Integer
--E

--S 83 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 84 of 185
dd:=tanrule cc
 

                                      a x
                                  sin(---)
               sin(a x)                2
        2log(------------) - 2log(--------) - 1
             cos(a x) + 1             a x
                                  cos(---)
                                       2
   (5)  ---------------------------------------
                           4a
                                                     Type: Expression Integer
--R
--R                                      a x
--R                                  sin(---)
--R               sin(a x)                2
--R        2log(------------) - 2log(--------) - 1
--R             cos(a x) + 1             a x
--R                                  cos(---)
--R                                       2
--R   (5)  ---------------------------------------
--R                           4a
--R                                                     Type: Expression Integer
--E

--S 85 of 185
ee:=expandLog dd
 

   (6)
                             a x                                   a x
   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) - 1
                              2                                     2
   -------------------------------------------------------------------------
                                       4a
                                                     Type: Expression Integer
--R
--R   (6)
--R                             a x                                   a x
--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) - 1
--R                              2                                     2
--R   -------------------------------------------------------------------------
--R                                       4a
--R                                                     Type: Expression Integer
--E

--S 86 of 185
ff:=complexNormalize ee
 

           1
   (7)  - --
          4a
                                                     Type: Expression Integer
--R
--R           1
--R   (7)  - --
--R          4a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 87 of 185
aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x)
 

                             sin(a x)
        (2cos(a x) - 2)log(------------) + cos(a x) + 1
                           cos(a x) + 1
   (1)  -----------------------------------------------
                        4a cos(a x) - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             sin(a x)
--R        (2cos(a x) - 2)log(------------) + cos(a x) + 1
--R                           cos(a x) + 1
--R   (1)  -----------------------------------------------
--R                        4a cos(a x) - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 88 of 185
bb:=-1/(2*a*(1-cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
 

                              a x
        (cos(a x) - 1)log(tan(---)) + 1
                               2
   (2)  -------------------------------
                2a cos(a x) - 2a
                                                     Type: Expression Integer
--R
--R                              a x
--R        (cos(a x) - 1)log(tan(---)) + 1
--R                               2
--R   (2)  -------------------------------
--R                2a cos(a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 89 of 185
cc:=aa-bb
 

                   a x            sin(a x)
        - 2log(tan(---)) + 2log(------------) + 1
                    2           cos(a x) + 1
   (3)  -----------------------------------------
                            4a
                                                     Type: Expression Integer
--R
--R                   a x            sin(a x)
--R        - 2log(tan(---)) + 2log(------------) + 1
--R                    2           cos(a x) + 1
--R   (3)  -----------------------------------------
--R                            4a
--R                                                     Type: Expression Integer
--E

--S 90 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 91 of 185
dd:=tanrule cc
 

                                      a x
                                  sin(---)
               sin(a x)                2
        2log(------------) - 2log(--------) + 1
             cos(a x) + 1             a x
                                  cos(---)
                                       2
   (5)  ---------------------------------------
                           4a
                                                     Type: Expression Integer
--R
--R                                      a x
--R                                  sin(---)
--R               sin(a x)                2
--R        2log(------------) - 2log(--------) + 1
--R             cos(a x) + 1             a x
--R                                  cos(---)
--R                                       2
--R   (5)  ---------------------------------------
--R                           4a
--R                                                     Type: Expression Integer
--E

--S 92 of 185
ee:=expandLog dd
 

   (6)
                             a x                                   a x
   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) + 1
                              2                                     2
   -------------------------------------------------------------------------
                                       4a
                                                     Type: Expression Integer
--R
--R   (6)
--R                             a x                                   a x
--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) + 1
--R                              2                                     2
--R   -------------------------------------------------------------------------
--R                                       4a
--R                                                     Type: Expression Integer
--E

--S 93 of 185     14:411 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

         1
   (7)  --
        4a
                                                     Type: Expression Integer
--R
--R         1
--R   (7)  --
--R        4a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 94 of 185
aa:=integrate(1/(sin(a*x)+cos(a*x)),x)
 

                    +-+                  +-+                 +-+
         +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
        \|2 log(----------------------------------------------------)
                                 sin(a x) + cos(a x)
   (1)  -------------------------------------------------------------
                                      2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-+                  +-+                 +-+
--R         +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
--R        \|2 log(----------------------------------------------------)
--R                                 sin(a x) + cos(a x)
--R   (1)  -------------------------------------------------------------
--R                                      2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 95 of 185
bb:=1/(a*sqrt(2))*log(tan((a*x)/2+%pi/8))
 

         +-+        4a x + %pi
        \|2 log(tan(----------))
                         8
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R         +-+        4a x + %pi
--R        \|2 log(tan(----------))
--R                         8
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 96 of 185
cc:=aa-bb
 

   (3)
          +-+        4a x + %pi
       - \|2 log(tan(----------))
                          8
     + 
                   +-+                  +-+                 +-+
        +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
       \|2 log(----------------------------------------------------)
                                sin(a x) + cos(a x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R          +-+        4a x + %pi
--R       - \|2 log(tan(----------))
--R                          8
--R     + 
--R                   +-+                  +-+                 +-+
--R        +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
--R       \|2 log(----------------------------------------------------)
--R                                sin(a x) + cos(a x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 97 of 185
complexNormalize cc
 

                 +-+
         +-+    \|2  - 2
        \|2 log(--------)
                   +-+
                  \|2
   (4)  -----------------
                2a
                                                     Type: Expression Integer
--R
--R                 +-+
--R         +-+    \|2  - 2
--R        \|2 log(--------)
--R                   +-+
--R                  \|2
--R   (4)  -----------------
--R                2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 98 of 185
aa:=integrate(1/(sin(a*x)-cos(a*x)),x)
 

                    +-+                    +-+                 +-+
         +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
        \|2 log(------------------------------------------------------)
                                  sin(a x) - cos(a x)
   (1)  ---------------------------------------------------------------
                                       2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    +-+                    +-+                 +-+
--R         +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
--R        \|2 log(------------------------------------------------------)
--R                                  sin(a x) - cos(a x)
--R   (1)  ---------------------------------------------------------------
--R                                       2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 99 of 185
bb:=1/(a*sqrt(2))*log(tan((a*x)/2-%pi/8))
 

         +-+        4a x - %pi
        \|2 log(tan(----------))
                         8
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R         +-+        4a x - %pi
--R        \|2 log(tan(----------))
--R                         8
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 100 of 185
cc:=aa-bb
 

   (3)
          +-+        4a x - %pi
       - \|2 log(tan(----------))
                          8
     + 
                   +-+                    +-+                 +-+
        +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
       \|2 log(------------------------------------------------------)
                                 sin(a x) - cos(a x)
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R          +-+        4a x - %pi
--R       - \|2 log(tan(----------))
--R                          8
--R     + 
--R                   +-+                    +-+                 +-+
--R        +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
--R       \|2 log(------------------------------------------------------)
--R                                 sin(a x) - cos(a x)
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 101 of 185    14:412 Schaums and Axiom differ by a constant
complexNormalize cc
 

         +-+     +-+
        \|2 log(\|2  - 1)
   (4)  -----------------
                2a
                                                     Type: Expression Integer
--R
--R         +-+     +-+
--R        \|2 log(\|2  - 1)
--R   (4)  -----------------
--R                2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 102 of 185
aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x)
 

                  2             - 2sin(a x) - 2cos(a x)
        log(------------) - log(-----------------------) + a x
            cos(a x) + 1              cos(a x) + 1
   (1)  ------------------------------------------------------
                                  2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2             - 2sin(a x) - 2cos(a x)
--R        log(------------) - log(-----------------------) + a x
--R            cos(a x) + 1              cos(a x) + 1
--R   (1)  ------------------------------------------------------
--R                                  2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103 of 185
bb:=x/2-1/(2*a)*log(sin(a*x)+cos(a*x))
 

        - log(sin(a x) + cos(a x)) + a x
   (2)  --------------------------------
                       2a
                                                     Type: Expression Integer
--R
--R        - log(sin(a x) + cos(a x)) + a x
--R   (2)  --------------------------------
--R                       2a
--R                                                     Type: Expression Integer
--E

--S 104 of 185
cc:=aa-bb
 

   (3)
                                        2             - 2sin(a x) - 2cos(a x)
   log(sin(a x) + cos(a x)) + log(------------) - log(-----------------------)
                                  cos(a x) + 1              cos(a x) + 1
   ---------------------------------------------------------------------------
                                        2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                        2             - 2sin(a x) - 2cos(a x)
--R   log(sin(a x) + cos(a x)) + log(------------) - log(-----------------------)
--R                                  cos(a x) + 1              cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                        2a
--R                                                     Type: Expression Integer
--E

--S 105 of 185
dd:=expandLog cc
 

        log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x))
   (4)  -----------------------------------------------------
                                  2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x))
--R   (4)  -----------------------------------------------------
--R                                  2a
--R                                                     Type: Expression Integer
--E

--S 106 of 185
ee:=complexNormalize dd
 

        log(- 1)
   (5)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all 
 

--S 107 of 185
aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x)
 

            2sin(a x) - 2cos(a x)              2
        log(---------------------) - log(------------) + a x
                 cos(a x) + 1            cos(a x) + 1
   (1)  ----------------------------------------------------
                                 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2sin(a x) - 2cos(a x)              2
--R        log(---------------------) - log(------------) + a x
--R                 cos(a x) + 1            cos(a x) + 1
--R   (1)  ----------------------------------------------------
--R                                 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 108 of 185
bb:=x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
 

        log(sin(a x) - cos(a x)) + a x
   (2)  ------------------------------
                      2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) - cos(a x)) + a x
--R   (2)  ------------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 109 of 185
cc:=aa-bb
 

   (3)
                                    2sin(a x) - 2cos(a x)              2
   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
                                         cos(a x) + 1            cos(a x) + 1
   ---------------------------------------------------------------------------
                                        2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2sin(a x) - 2cos(a x)              2
--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
--R                                         cos(a x) + 1            cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                        2a
--R                                                     Type: Expression Integer
--E

--S 110 of 185    14:413 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 111 of 185
aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x)
 

                    2             - 2sin(a x) - 2cos(a x)
        - log(------------) + log(-----------------------) + a x
              cos(a x) + 1              cos(a x) + 1
   (1)  --------------------------------------------------------
                                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2             - 2sin(a x) - 2cos(a x)
--R        - log(------------) + log(-----------------------) + a x
--R              cos(a x) + 1              cos(a x) + 1
--R   (1)  --------------------------------------------------------
--R                                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 112 of 185
bb:=x/2+1/(2*a)*log(sin(a*x)+cos(a*x))
 

        log(sin(a x) + cos(a x)) + a x
   (2)  ------------------------------
                      2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) + cos(a x)) + a x
--R   (2)  ------------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 113 of 185
cc:=aa-bb
 

   (3)
                                          2             - 2sin(a x) - 2cos(a x)
   - log(sin(a x) + cos(a x)) - log(------------) + log(-----------------------)
                                    cos(a x) + 1              cos(a x) + 1
   -----------------------------------------------------------------------------
                                         2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                          2             - 2sin(a x) - 2cos(a x)
--R   - log(sin(a x) + cos(a x)) - log(------------) + log(-----------------------)
--R                                    cos(a x) + 1              cos(a x) + 1
--R   -----------------------------------------------------------------------------
--R                                         2a
--R                                                     Type: Expression Integer
--E

--S 114 of 185
dd:=expandLog cc
 

        - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x))
   (4)  -------------------------------------------------------
                                   2a
                                                     Type: Expression Integer
--R
--R        - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x))
--R   (4)  -------------------------------------------------------
--R                                   2a
--R                                                     Type: Expression Integer
--E

--S 115 of 185
ee:=complexNormalize dd
 

          log(- 1)
   (5)  - --------
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (5)  - --------
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 116 of 185
aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x)
 

            2sin(a x) - 2cos(a x)              2
        log(---------------------) - log(------------) - a x
                 cos(a x) + 1            cos(a x) + 1
   (1)  ----------------------------------------------------
                                 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2sin(a x) - 2cos(a x)              2
--R        log(---------------------) - log(------------) - a x
--R                 cos(a x) + 1            cos(a x) + 1
--R   (1)  ----------------------------------------------------
--R                                 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 117 of 185
bb:=-x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
 

        log(sin(a x) - cos(a x)) - a x
   (2)  ------------------------------
                      2a
                                                     Type: Expression Integer
--R
--R        log(sin(a x) - cos(a x)) - a x
--R   (2)  ------------------------------
--R                      2a
--R                                                     Type: Expression Integer
--E

--S 118 of 185
cc:=aa-bb
 

   (3)
                                    2sin(a x) - 2cos(a x)              2
   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
                                         cos(a x) + 1            cos(a x) + 1
   ---------------------------------------------------------------------------
                                        2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2sin(a x) - 2cos(a x)              2
--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
--R                                         cos(a x) + 1            cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                        2a
--R                                                     Type: Expression Integer
--E

--S 119 of 185    14:414 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 120 of 185
aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x)
 

                  2             - 2q cos(a x) - 2p
        log(------------) - log(------------------)
            cos(a x) + 1           cos(a x) + 1
   (1)  -------------------------------------------
                            a q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2             - 2q cos(a x) - 2p
--R        log(------------) - log(------------------)
--R            cos(a x) + 1           cos(a x) + 1
--R   (1)  -------------------------------------------
--R                            a q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 121 of 185
bb:=-1/(a*q)*log(p+q*cos(a*x))
 

          log(q cos(a x) + p)
   (2)  - -------------------
                  a q
                                                     Type: Expression Integer
--R
--R          log(q cos(a x) + p)
--R   (2)  - -------------------
--R                  a q
--R                                                     Type: Expression Integer
--E

--S 122 of 185
cc:=aa-bb
 

                                        2             - 2q cos(a x) - 2p
        log(q cos(a x) + p) + log(------------) - log(------------------)
                                  cos(a x) + 1           cos(a x) + 1
   (3)  -----------------------------------------------------------------
                                       a q
                                                     Type: Expression Integer
--R
--R                                        2             - 2q cos(a x) - 2p
--R        log(q cos(a x) + p) + log(------------) - log(------------------)
--R                                  cos(a x) + 1           cos(a x) + 1
--R   (3)  -----------------------------------------------------------------
--R                                       a q
--R                                                     Type: Expression Integer
--E

--S 123 of 185
dd:=expandLog cc
 

        log(q cos(a x) + p) - log(- q cos(a x) - p)
   (4)  -------------------------------------------
                            a q
                                                     Type: Expression Integer
--R
--R        log(q cos(a x) + p) - log(- q cos(a x) - p)
--R   (4)  -------------------------------------------
--R                            a q
--R                                                     Type: Expression Integer
--E

--S 124 of 185    14:415 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        log(- 1)
   (5)  --------
           a q
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R           a q
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 125 of 185
aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x)
 

            2q sin(a x) + 2p              2
        log(----------------) - log(------------)
              cos(a x) + 1          cos(a x) + 1
   (1)  -----------------------------------------
                           a q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2q sin(a x) + 2p              2
--R        log(----------------) - log(------------)
--R              cos(a x) + 1          cos(a x) + 1
--R   (1)  -----------------------------------------
--R                           a q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 126 of 185
bb:=1/(a*q)*log(p+q*sin(a*x))
 

        log(q sin(a x) + p)
   (2)  -------------------
                a q
                                                     Type: Expression Integer
--R
--R        log(q sin(a x) + p)
--R   (2)  -------------------
--R                a q
--R                                                     Type: Expression Integer
--E

--S 127 of 185
cc:=aa-bb
 

                                    2q sin(a x) + 2p              2
        - log(q sin(a x) + p) + log(----------------) - log(------------)
                                      cos(a x) + 1          cos(a x) + 1
   (3)  -----------------------------------------------------------------
                                       a q
                                                     Type: Expression Integer
--R
--R                                    2q sin(a x) + 2p              2
--R        - log(q sin(a x) + p) + log(----------------) - log(------------)
--R                                      cos(a x) + 1          cos(a x) + 1
--R   (3)  -----------------------------------------------------------------
--R                                       a q
--R                                                     Type: Expression Integer
--E

--S 128 of 185    14:416 Schaums and Axiom agree
dd:=expandLog cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 129 of 185
aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x)
 

                  q cos(a x) + p
   (1)  ----------------------------------
                     n log(q cos(a x) + p)
        (a n - a)q %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  q cos(a x) + p
--R   (1)  ----------------------------------
--R                     n log(q cos(a x) + p)
--R        (a n - a)q %e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 130 of 185
bb:=1/(a*q*(n-1)*(p+q*cos(a*x))^(n-1))
 

                        1
   (2)  --------------------------------
                                   n - 1
        (a n - a)q (q cos(a x) + p)
                                                     Type: Expression Integer
--R
--R                        1
--R   (2)  --------------------------------
--R                                   n - 1
--R        (a n - a)q (q cos(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 131 of 185
cc:=aa-bb
 

            n log(q cos(a x) + p)                                   n - 1
        - %e                      + (q cos(a x) + p)(q cos(a x) + p)
   (3)  -----------------------------------------------------------------
                                        n - 1  n log(q cos(a x) + p)
             (a n - a)q (q cos(a x) + p)     %e
                                                     Type: Expression Integer
--R
--R            n log(q cos(a x) + p)                                   n - 1
--R        - %e                      + (q cos(a x) + p)(q cos(a x) + p)
--R   (3)  -----------------------------------------------------------------
--R                                        n - 1  n log(q cos(a x) + p)
--R             (a n - a)q (q cos(a x) + p)     %e
--R                                                     Type: Expression Integer
--E

--S 132 of 185
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 133 of 185
dd:=explog cc
 

                          n                                   n - 1
        - (q cos(a x) + p)  + (q cos(a x) + p)(q cos(a x) + p)
   (5)  -----------------------------------------------------------
                                        n - 1                n
             (a n - a)q (q cos(a x) + p)     (q cos(a x) + p)
                                                     Type: Expression Integer
--R
--R                          n                                   n - 1
--R        - (q cos(a x) + p)  + (q cos(a x) + p)(q cos(a x) + p)
--R   (5)  -----------------------------------------------------------
--R                                        n - 1                n
--R             (a n - a)q (q cos(a x) + p)     (q cos(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 134 of 185    14:417 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 135 of 185
aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x)
 

                 - q sin(a x) - p
   (1)  ----------------------------------
                     n log(q sin(a x) + p)
        (a n - a)q %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 - q sin(a x) - p
--R   (1)  ----------------------------------
--R                     n log(q sin(a x) + p)
--R        (a n - a)q %e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 136 of 185
bb:=-1/(a*q*(n-1)*(p+q*sin(a*x))^(n-1))
 

                          1
   (2)  - --------------------------------
                                     n - 1
          (a n - a)q (q sin(a x) + p)
                                                     Type: Expression Integer
--R
--R                          1
--R   (2)  - --------------------------------
--R                                     n - 1
--R          (a n - a)q (q sin(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 137 of 185
cc:=aa-bb
 

          n log(q sin(a x) + p)                                     n - 1
        %e                      + (- q sin(a x) - p)(q sin(a x) + p)
   (3)  -----------------------------------------------------------------
                                        n - 1  n log(q sin(a x) + p)
             (a n - a)q (q sin(a x) + p)     %e
                                                     Type: Expression Integer
--R
--R          n log(q sin(a x) + p)                                     n - 1
--R        %e                      + (- q sin(a x) - p)(q sin(a x) + p)
--R   (3)  -----------------------------------------------------------------
--R                                        n - 1  n log(q sin(a x) + p)
--R             (a n - a)q (q sin(a x) + p)     %e
--R                                                     Type: Expression Integer
--E

--S 138 of 185
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 139 of 185
dd:=explog cc
 

                        n                                     n - 1
        (q sin(a x) + p)  + (- q sin(a x) - p)(q sin(a x) + p)
   (5)  -----------------------------------------------------------
                                        n - 1                n
             (a n - a)q (q sin(a x) + p)     (q sin(a x) + p)
                                                     Type: Expression Integer
--R
--R                        n                                     n - 1
--R        (q sin(a x) + p)  + (- q sin(a x) - p)(q sin(a x) + p)
--R   (5)  -----------------------------------------------------------
--R                                        n - 1                n
--R             (a n - a)q (q sin(a x) + p)     (q sin(a x) + p)
--R                                                     Type: Expression Integer
--E

--S 140 of 185    14:418 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 141 of 185
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x)
 

   (1)
     log
                                                  +-------+
                             2            2    2  | 2    2
            (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
          + 
                3    2                 2    3               2    3
            (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
       /
          p sin(a x) + q cos(a x)
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     log
--R                                                  +-------+
--R                             2            2    2  | 2    2
--R            (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
--R          + 
--R                3    2                 2    3               2    3
--R            (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
--R       /
--R          p sin(a x) + q cos(a x)
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 142 of 185
bb:=1/(a*sqrt(p^2+q^2))*log(tan((a*x+atan(q/p))/2))
 

                     q
                atan(-) + a x
                     p
        log(tan(-------------))
                      2
   (2)  -----------------------
                +-------+
                | 2    2
              a\|q  + p
                                                     Type: Expression Integer
--R
--R                     q
--R                atan(-) + a x
--R                     p
--R        log(tan(-------------))
--R                      2
--R   (2)  -----------------------
--R                +-------+
--R                | 2    2
--R              a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 143 of 185
cc:=aa-bb
 

   (3)
                      q
                 atan(-) + a x
                      p
       - log(tan(-------------))
                       2
     + 
       log
                                                    +-------+
                               2            2    2  | 2    2
              (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
            + 
                  3    2                 2    3               2    3
              (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
         /
            p sin(a x) + q cos(a x)
  /
       +-------+
       | 2    2
     a\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                      q
--R                 atan(-) + a x
--R                      p
--R       - log(tan(-------------))
--R                       2
--R     + 
--R       log
--R                                                    +-------+
--R                               2            2    2  | 2    2
--R              (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
--R            + 
--R                  3    2                 2    3               2    3
--R              (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
--R         /
--R            p sin(a x) + q cos(a x)
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 144 of 185
dd:=normalize cc
 

                            +-------+
                            | 2    2     2     2
                       - 2p\|q  + p   + q  + 2p
          log(------------------------------------------)
                            +-------+
                   2     3  | 2    2     4     2 2     4
              (3p q  + 4p )\|q  + p   - q  - 5p q  - 4p
   (4)  - -----------------------------------------------
                              +-------+
                              | 2    2
                            a\|q  + p
                                                     Type: Expression Integer
--R
--R                            +-------+
--R                            | 2    2     2     2
--R                       - 2p\|q  + p   + q  + 2p
--R          log(------------------------------------------)
--R                            +-------+
--R                   2     3  | 2    2     4     2 2     4
--R              (3p q  + 4p )\|q  + p   - q  - 5p q  - 4p
--R   (4)  - -----------------------------------------------
--R                              +-------+
--R                              | 2    2
--R                            a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 145 of 185    14:419 Schaums and Axiom differ by a constant
ee:=ratDenom dd
 

                            +-------+
           +-------+        | 2    2     2    2
           | 2    2     - p\|q  + p   - q  - p
          \|q  + p  log(-----------------------)
                                4    2 2
                               q  + p q
   (5)  - --------------------------------------
                           2      2
                        a q  + a p
                                                     Type: Expression Integer
--R
--R                            +-------+
--R           +-------+        | 2    2     2    2
--R           | 2    2     - p\|q  + p   - q  - p
--R          \|q  + p  log(-----------------------)
--R                                4    2 2
--R                               q  + p q
--R   (5)  - --------------------------------------
--R                           2      2
--R                        a q  + a p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 146 of 185
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x)
 

   (1)
   [
       log
                                              2          2                   2
                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
                  + 
                     2
                    p
             *
                 +--------------+
                 |   2    2    2
                \|- r  + q  + p
            + 
                3      2       2    2      3    2
              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
            + 
                  2      2    3               2      2    3
              (p r  - p q  - p )cos(a x) + p r  - p q  - p
         /
            p sin(a x) + q cos(a x) + r
    /
         +--------------+
         |   2    2    2
       a\|- r  + q  + p
     ,
                                             +------------+
                                             | 2    2    2
          ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
    2atan(-------------------------------------------------)
                  2    2    2             2    2    2
                (r  - q  - p )cos(a x) + r  - q  - p
    --------------------------------------------------------]
                          +------------+
                          | 2    2    2
                        a\|r  - q  - p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                                              2          2                   2
--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
--R                  + 
--R                     2
--R                    p
--R             *
--R                 +--------------+
--R                 |   2    2    2
--R                \|- r  + q  + p
--R            + 
--R                3      2       2    2      3    2
--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
--R            + 
--R                  2      2    3               2      2    3
--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
--R         /
--R            p sin(a x) + q cos(a x) + r
--R    /
--R         +--------------+
--R         |   2    2    2
--R       a\|- r  + q  + p
--R     ,
--R                                             +------------+
--R                                             | 2    2    2
--R          ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
--R    2atan(-------------------------------------------------)
--R                  2    2    2             2    2    2
--R                (r  - q  - p )cos(a x) + r  - q  - p
--R    --------------------------------------------------------]
--R                          +------------+
--R                          | 2    2    2
--R                        a\|r  - q  - p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 147 of 185
bb1:=2/(a*sqrt(r^2-p^2-q^2))*atan((p+(r-q)*tan((a*x)/2))/sqrt(r^2-p^2-q^2))
 

                         a x
              (r - q)tan(---) + p
                          2
        2atan(-------------------)
                 +------------+
                 | 2    2    2
                \|r  - q  - p
   (2)  --------------------------
               +------------+
               | 2    2    2
             a\|r  - q  - p
                                                     Type: Expression Integer
--R
--R                         a x
--R              (r - q)tan(---) + p
--R                          2
--R        2atan(-------------------)
--R                 +------------+
--R                 | 2    2    2
--R                \|r  - q  - p
--R   (2)  --------------------------
--R               +------------+
--R               | 2    2    2
--R             a\|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 148 of 185
bb2:=1/(a*sqrt(p^2+q^2-r^2))*log((p-sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))/(p+sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2)))
 

               +--------------+
               |   2    2    2               a x
            - \|- r  + q  + p   + (r - q)tan(---) + p
                                              2
        log(-----------------------------------------)
              +--------------+
              |   2    2    2               a x
             \|- r  + q  + p   + (r - q)tan(---) + p
                                             2
   (3)  ----------------------------------------------
                        +--------------+
                        |   2    2    2
                      a\|- r  + q  + p
                                                     Type: Expression Integer
--R
--R               +--------------+
--R               |   2    2    2               a x
--R            - \|- r  + q  + p   + (r - q)tan(---) + p
--R                                              2
--R        log(-----------------------------------------)
--R              +--------------+
--R              |   2    2    2               a x
--R             \|- r  + q  + p   + (r - q)tan(---) + p
--R                                             2
--R   (3)  ----------------------------------------------
--R                        +--------------+
--R                        |   2    2    2
--R                      a\|- r  + q  + p
--R                                                     Type: Expression Integer
--E

--S 149 of 185
cc1:=aa.1-bb1
 

   (4)
          +------------+
          | 2    2    2
         \|r  - q  - p
      *
         log
                                              2          2                   2
                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
                  + 
                     2
                    p
               *
                   +--------------+
                   |   2    2    2
                  \|- r  + q  + p
              + 
                  3      2       2    2      3    2
                (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
              + 
                    2      2    3               2      2    3
                (p r  - p q  - p )cos(a x) + p r  - p q  - p
           /
              p sin(a x) + q cos(a x) + r
     + 
                                           a x
           +--------------+     (r - q)tan(---) + p
           |   2    2    2                  2
       - 2\|- r  + q  + p  atan(-------------------)
                                   +------------+
                                   | 2    2    2
                                  \|r  - q  - p
  /
       +--------------+ +------------+
       |   2    2    2  | 2    2    2
     a\|- r  + q  + p  \|r  - q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +------------+
--R          | 2    2    2
--R         \|r  - q  - p
--R      *
--R         log
--R                                              2          2                   2
--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
--R                  + 
--R                     2
--R                    p
--R               *
--R                   +--------------+
--R                   |   2    2    2
--R                  \|- r  + q  + p
--R              + 
--R                  3      2       2    2      3    2
--R                (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
--R              + 
--R                    2      2    3               2      2    3
--R                (p r  - p q  - p )cos(a x) + p r  - p q  - p
--R           /
--R              p sin(a x) + q cos(a x) + r
--R     + 
--R                                           a x
--R           +--------------+     (r - q)tan(---) + p
--R           |   2    2    2                  2
--R       - 2\|- r  + q  + p  atan(-------------------)
--R                                   +------------+
--R                                   | 2    2    2
--R                                  \|r  - q  - p
--R  /
--R       +--------------+ +------------+
--R       |   2    2    2  | 2    2    2
--R     a\|- r  + q  + p  \|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 150 of 185
cc2:=aa.2-bb1
 

   (5)
                                                +------------+
                                                | 2    2    2
             ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
       2atan(-------------------------------------------------)
                     2    2    2             2    2    2
                   (r  - q  - p )cos(a x) + r  - q  - p
     + 
                          a x
               (r - q)tan(---) + p
                           2
       - 2atan(-------------------)
                  +------------+
                  | 2    2    2
                 \|r  - q  - p
  /
       +------------+
       | 2    2    2
     a\|r  - q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                +------------+
--R                                                | 2    2    2
--R             ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
--R       2atan(-------------------------------------------------)
--R                     2    2    2             2    2    2
--R                   (r  - q  - p )cos(a x) + r  - q  - p
--R     + 
--R                          a x
--R               (r - q)tan(---) + p
--R                           2
--R       - 2atan(-------------------)
--R                  +------------+
--R                  | 2    2    2
--R                 \|r  - q  - p
--R  /
--R       +------------+
--R       | 2    2    2
--R     a\|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 151 of 185
cc3:=aa.1-bb2
 

   (6)
       log
                                              2          2                   2
                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
                  + 
                     2
                    p
             *
                 +--------------+
                 |   2    2    2
                \|- r  + q  + p
            + 
                3      2       2    2      3    2
              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
            + 
                  2      2    3               2      2    3
              (p r  - p q  - p )cos(a x) + p r  - p q  - p
         /
            p sin(a x) + q cos(a x) + r
     + 
                +--------------+
                |   2    2    2               a x
             - \|- r  + q  + p   + (r - q)tan(---) + p
                                               2
       - log(-----------------------------------------)
               +--------------+
               |   2    2    2               a x
              \|- r  + q  + p   + (r - q)tan(---) + p
                                              2
  /
       +--------------+
       |   2    2    2
     a\|- r  + q  + p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                                              2          2                   2
--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
--R                  + 
--R                     2
--R                    p
--R             *
--R                 +--------------+
--R                 |   2    2    2
--R                \|- r  + q  + p
--R            + 
--R                3      2       2    2      3    2
--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
--R            + 
--R                  2      2    3               2      2    3
--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
--R         /
--R            p sin(a x) + q cos(a x) + r
--R     + 
--R                +--------------+
--R                |   2    2    2               a x
--R             - \|- r  + q  + p   + (r - q)tan(---) + p
--R                                               2
--R       - log(-----------------------------------------)
--R               +--------------+
--R               |   2    2    2               a x
--R              \|- r  + q  + p   + (r - q)tan(---) + p
--R                                              2
--R  /
--R       +--------------+
--R       |   2    2    2
--R     a\|- r  + q  + p
--R                                                     Type: Expression Integer
--E

--S 152 of 185
cc4:=aa.2-bb2
 

   (7)
                               +--------------+
                               |   2    2    2               a x
          +------------+    - \|- r  + q  + p   + (r - q)tan(---) + p
          | 2    2    2                                       2
       - \|r  - q  - p  log(-----------------------------------------)
                              +--------------+
                              |   2    2    2               a x
                             \|- r  + q  + p   + (r - q)tan(---) + p
                                                             2
     + 
                                                               +------------+
       +--------------+                                        | 2    2    2
       |   2    2    2      ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
     2\|- r  + q  + p  atan(-------------------------------------------------)
                                    2    2    2             2    2    2
                                  (r  - q  - p )cos(a x) + r  - q  - p
  /
       +--------------+ +------------+
       |   2    2    2  | 2    2    2
     a\|- r  + q  + p  \|r  - q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                               +--------------+
--R                               |   2    2    2               a x
--R          +------------+    - \|- r  + q  + p   + (r - q)tan(---) + p
--R          | 2    2    2                                       2
--R       - \|r  - q  - p  log(-----------------------------------------)
--R                              +--------------+
--R                              |   2    2    2               a x
--R                             \|- r  + q  + p   + (r - q)tan(---) + p
--R                                                             2
--R     + 
--R                                                               +------------+
--R       +--------------+                                        | 2    2    2
--R       |   2    2    2      ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
--R     2\|- r  + q  + p  atan(-------------------------------------------------)
--R                                    2    2    2             2    2    2
--R                                  (r  - q  - p )cos(a x) + r  - q  - p
--R  /
--R       +--------------+ +------------+
--R       |   2    2    2  | 2    2    2
--R     a\|- r  + q  + p  \|r  - q  - p
--R                                                     Type: Expression Integer
--E

--S 153 of 185    14:420 Schaums and Axiom agree
dd2:=normalize cc2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 154 of 185
aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x)
 

            p sin(a x) + q cos(a x) + q
        log(---------------------------)
                    cos(a x) + 1
   (1)  --------------------------------
                       a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            p sin(a x) + q cos(a x) + q
--R        log(---------------------------)
--R                    cos(a x) + 1
--R   (1)  --------------------------------
--R                       a p
--R                                          Type: Union(Expression Integer,...)
--E

--S 155 of 185
bb:=1/(a*p)*log(q+p*tan((a*x)/2))
 

                  a x
        log(p tan(---) + q)
                   2
   (2)  -------------------
                a p
                                                     Type: Expression Integer
--R
--R                  a x
--R        log(p tan(---) + q)
--R                   2
--R   (2)  -------------------
--R                a p
--R                                                     Type: Expression Integer
--E 

--S 156 of 185
cc:=aa-bb
 

                    a x             p sin(a x) + q cos(a x) + q
        - log(p tan(---) + q) + log(---------------------------)
                     2                      cos(a x) + 1
   (3)  --------------------------------------------------------
                                   a p
                                                     Type: Expression Integer
--R
--R                    a x             p sin(a x) + q cos(a x) + q
--R        - log(p tan(---) + q) + log(---------------------------)
--R                     2                      cos(a x) + 1
--R   (3)  --------------------------------------------------------
--R                                   a p
--R                                                     Type: Expression Integer
--E

--S 157 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 158 of 185
dd:=tanrule cc
 

                                                     a x          a x
                                               p sin(---) + q cos(---)
            p sin(a x) + q cos(a x) + q               2            2
        log(---------------------------) - log(-----------------------)
                    cos(a x) + 1                           a x
                                                       cos(---)
                                                            2
   (5)  ---------------------------------------------------------------
                                      a p
                                                     Type: Expression Integer
--R
--R                                                     a x          a x
--R                                               p sin(---) + q cos(---)
--R            p sin(a x) + q cos(a x) + q               2            2
--R        log(---------------------------) - log(-----------------------)
--R                    cos(a x) + 1                           a x
--R                                                       cos(---)
--R                                                            2
--R   (5)  ---------------------------------------------------------------
--R                                      a p
--R                                                     Type: Expression Integer
--E

--S 159 of 185
ee:=expandLog dd
 

   (6)
                                                    a x          a x
       log(p sin(a x) + q cos(a x) + q) - log(p sin(---) + q cos(---))
                                                     2            2
     + 
                                     a x
       - log(cos(a x) + 1) + log(cos(---))
                                      2
  /
     a p
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                    a x          a x
--R       log(p sin(a x) + q cos(a x) + q) - log(p sin(---) + q cos(---))
--R                                                     2            2
--R     + 
--R                                     a x
--R       - log(cos(a x) + 1) + log(cos(---))
--R                                      2
--R  /
--R     a p
--R                                                     Type: Expression Integer
--E

--S 160 of 185    14:421 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 161 of 185
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x)
 

   (1)
                                                                 +-------+
            5      2 3      4                5      2 3      4   | 2    2
       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
     + 
             6      2 4      4 2     6               6      2 4      4 2     6
       (- 64q  - 96p q  - 36p q  - 2p )cos(a x) - 64q  - 96p q  - 36p q  - 2p
  /
                 6        2 4        4 2      6
           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
         + 
                   5        3 3       5                    5        3 3       5
         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
      *
          +-------+
          | 2    2
         \|q  + p
     + 
               7         2 5        4 3       6
       (- 64a q  - 112a p q  - 56a p q  - 7a p q)sin(a x)
     + 
               6        3 4        5 2      7                   6        3 4
       (32a p q  + 48a p q  + 18a p q  + a p )cos(a x) + 32a p q  + 48a p q
     + 
            5 2      7
       18a p q  + a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                 +-------+
--R            5      2 3      4                5      2 3      4   | 2    2
--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
--R     + 
--R             6      2 4      4 2     6               6      2 4      4 2     6
--R       (- 64q  - 96p q  - 36p q  - 2p )cos(a x) - 64q  - 96p q  - 36p q  - 2p
--R  /
--R                 6        2 4        4 2      6
--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
--R         + 
--R                   5        3 3       5                    5        3 3       5
--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R               7         2 5        4 3       6
--R       (- 64a q  - 112a p q  - 56a p q  - 7a p q)sin(a x)
--R     + 
--R               6        3 4        5 2      7                   6        3 4
--R       (32a p q  + 48a p q  + 18a p q  + a p )cos(a x) + 32a p q  + 48a p q
--R     + 
--R            5 2      7
--R       18a p q  + a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 162 of 185
bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4-(a*x+atan(q/p))/2)
 

                  q
            2atan(-) + 2a x - %pi
                  p
        tan(---------------------)
                      4
   (2)  --------------------------
                  +-------+
                  | 2    2
                a\|q  + p
                                                     Type: Expression Integer
--R
--R                  q
--R            2atan(-) + 2a x - %pi
--R                  p
--R        tan(---------------------)
--R                      4
--R   (2)  --------------------------
--R                  +-------+
--R                  | 2    2
--R                a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 163 of 185
cc:=aa-bb
 

   (3)
                   6      2 4      4 2    6
               (64q  + 80p q  + 24p q  + p )sin(a x)
             + 
                       5      3 3     5                  5      3 3     5
               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
          *
              +-------+
              | 2    2
             \|q  + p
         + 
                 7       2 5      4 3     6
           (- 64q  - 112p q  - 56p q  - 7p q)sin(a x)
         + 
               6      3 4      5 2    7                 6      3 4      5 2    7
         (32p q  + 48p q  + 18p q  + p )cos(a x) + 32p q  + 48p q  + 18p q  + p
      *
                   q
             2atan(-) + 2a x - %pi
                   p
         tan(---------------------)
                       4
     + 
              6      2 4      4 2     6               6      2 4      4 2     6
         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
      *
          +-------+
          | 2    2
         \|q  + p
     + 
             7       2 5      4 3      6                7       2 5      4 3
       (- 64q  - 128p q  - 76p q  - 12p q)cos(a x) - 64q  - 128p q  - 76p q
     + 
            6
       - 12p q
  /
                 7         2 5        4 3       6
           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
         + 
                     6        3 4        5 2      7                   6
           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
         + 
                  3 4        5 2      7
           - 48a p q  - 18a p q  - a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
               8         2 6         4 4        6 2      8
       (- 64a q  - 144a p q  - 104a p q  - 25a p q  - a p )sin(a x)
     + 
               7        3 5        5 3       7                    7        3 5
       (32a p q  + 64a p q  + 38a p q  + 6a p q)cos(a x) + 32a p q  + 64a p q
     + 
            5 3       7
       38a p q  + 6a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R                   6      2 4      4 2    6
--R               (64q  + 80p q  + 24p q  + p )sin(a x)
--R             + 
--R                       5      3 3     5                  5      3 3     5
--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
--R          *
--R              +-------+
--R              | 2    2
--R             \|q  + p
--R         + 
--R                 7       2 5      4 3     6
--R           (- 64q  - 112p q  - 56p q  - 7p q)sin(a x)
--R         + 
--R               6      3 4      5 2    7                 6      3 4      5 2    7
--R         (32p q  + 48p q  + 18p q  + p )cos(a x) + 32p q  + 48p q  + 18p q  + p
--R      *
--R                   q
--R             2atan(-) + 2a x - %pi
--R                   p
--R         tan(---------------------)
--R                       4
--R     + 
--R              6      2 4      4 2     6               6      2 4      4 2     6
--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R             7       2 5      4 3      6                7       2 5      4 3
--R       (- 64q  - 128p q  - 76p q  - 12p q)cos(a x) - 64q  - 128p q  - 76p q
--R     + 
--R            6
--R       - 12p q
--R  /
--R                 7         2 5        4 3       6
--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
--R         + 
--R                     6        3 4        5 2      7                   6
--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
--R         + 
--R                  3 4        5 2      7
--R           - 48a p q  - 18a p q  - a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R               8         2 6         4 4        6 2      8
--R       (- 64a q  - 144a p q  - 104a p q  - 25a p q  - a p )sin(a x)
--R     + 
--R               7        3 5        5 3       7                    7        3 5
--R       (32a p q  + 64a p q  + 38a p q  + 6a p q)cos(a x) + 32a p q  + 64a p q
--R     + 
--R            5 3       7
--R       38a p q  + 6a p q
--R                                                     Type: Expression Integer
--E

--S 164 of 185
dd:=normalize cc
 

   (4)
                                                                  +-------+
               6      2 5      3 4      4 3      5 2     6     7  | 2    2
       (- 32p q  - 16p q  - 48p q  - 20p q  - 18p q  - 5p q - p )\|q  + p
     + 
            7      2 6      3 5      4 4      5 3      6 2     7     8
       32p q  + 16p q  + 64p q  + 28p q  + 38p q  + 13p q  + 6p q + p
  /
                8          7         2 6        3 5         4 4        5 3
           64a q  + 32a p q  + 144a p q  + 64a p q  + 104a p q  + 38a p q
         + 
                6 2       7       8
           25a p q  + 6a p q + a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
              9          8         2 7        3 6         4 5        5 4
       - 64a q  - 32a p q  - 176a p q  - 80a p q  - 168a p q  - 66a p q
     + 
              6 3        7 2       8       9
       - 63a p q  - 19a p q  - 7a p q - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                  +-------+
--R               6      2 5      3 4      4 3      5 2     6     7  | 2    2
--R       (- 32p q  - 16p q  - 48p q  - 20p q  - 18p q  - 5p q - p )\|q  + p
--R     + 
--R            7      2 6      3 5      4 4      5 3      6 2     7     8
--R       32p q  + 16p q  + 64p q  + 28p q  + 38p q  + 13p q  + 6p q + p
--R  /
--R                8          7         2 6        3 5         4 4        5 3
--R           64a q  + 32a p q  + 144a p q  + 64a p q  + 104a p q  + 38a p q
--R         + 
--R                6 2       7       8
--R           25a p q  + 6a p q + a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R              9          8         2 7        3 6         4 5        5 4
--R       - 64a q  - 32a p q  - 176a p q  - 80a p q  - 168a p q  - 66a p q
--R     + 
--R              6 3        7 2       8       9
--R       - 63a p q  - 19a p q  - 7a p q - a p
--R                                                     Type: Expression Integer
--E

--S 165 of 185
ee:=ratDenom dd
 

            +-------+
            | 2    2     2    2
        - q\|q  + p   - q  - p
   (5)  -----------------------
                  2      3
             a p q  + a p
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2    2
--R        - q\|q  + p   - q  - p
--R   (5)  -----------------------
--R                  2      3
--R             a p q  + a p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 166 of 185
aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x)
 

   (1)
                                                                 +-------+
            5      2 3      4                5      2 3      4   | 2    2
       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
     + 
           6      2 4      4 2     6               6      2 4      4 2     6
       (64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p
  /
                 6        2 4        4 2      6
           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
         + 
                   5        3 3       5                    5        3 3       5
         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
      *
          +-------+
          | 2    2
         \|q  + p
     + 
             7         2 5        4 3       6
       (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
     + 
                 6        3 4        5 2      7                   6        3 4
       (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q  - 48a p q
     + 
              5 2      7
       - 18a p q  - a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                                 +-------+
--R            5      2 3      4                5      2 3      4   | 2    2
--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
--R     + 
--R           6      2 4      4 2     6               6      2 4      4 2     6
--R       (64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p
--R  /
--R                 6        2 4        4 2      6
--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
--R         + 
--R                   5        3 3       5                    5        3 3       5
--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R             7         2 5        4 3       6
--R       (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
--R     + 
--R                 6        3 4        5 2      7                   6        3 4
--R       (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q  - 48a p q
--R     + 
--R              5 2      7
--R       - 18a p q  - a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 167 of 185
bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4+(a*x+atan(q/p))/2)
 

                    q
              2atan(-) + 2a x + %pi
                    p
          tan(---------------------)
                        4
   (2)  - --------------------------
                    +-------+
                    | 2    2
                  a\|q  + p
                                                     Type: Expression Integer
--R
--R                    q
--R              2atan(-) + 2a x + %pi
--R                    p
--R          tan(---------------------)
--R                        4
--R   (2)  - --------------------------
--R                    +-------+
--R                    | 2    2
--R                  a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 168 of 185
cc:=aa-bb
 

   (3)
                   6      2 4      4 2    6
               (64q  + 80p q  + 24p q  + p )sin(a x)
             + 
                       5      3 3     5                  5      3 3     5
               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
          *
              +-------+
              | 2    2
             \|q  + p
         + 
               7       2 5      4 3     6
           (64q  + 112p q  + 56p q  + 7p q)sin(a x)
         + 
                   6      3 4      5 2    7                 6      3 4      5 2
           (- 32p q  - 48p q  - 18p q  - p )cos(a x) - 32p q  - 48p q  - 18p q
         + 
              7
           - p
      *
                   q
             2atan(-) + 2a x + %pi
                   p
         tan(---------------------)
                       4
     + 
              6      2 4      4 2     6               6      2 4      4 2     6
         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
      *
          +-------+
          | 2    2
         \|q  + p
     + 
         7       2 5      4 3      6                7       2 5      4 3      6
     (64q  + 128p q  + 76p q  + 12p q)cos(a x) + 64q  + 128p q  + 76p q  + 12p q
  /
                 7         2 5        4 3       6
           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
         + 
                     6        3 4        5 2      7                   6
           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
         + 
                  3 4        5 2      7
           - 48a p q  - 18a p q  - a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
             8         2 6         4 4        6 2      8
       (64a q  + 144a p q  + 104a p q  + 25a p q  + a p )sin(a x)
     + 
                 7        3 5        5 3       7                    7        3 5
       (- 32a p q  - 64a p q  - 38a p q  - 6a p q)cos(a x) - 32a p q  - 64a p q
     + 
              5 3       7
       - 38a p q  - 6a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R                   6      2 4      4 2    6
--R               (64q  + 80p q  + 24p q  + p )sin(a x)
--R             + 
--R                       5      3 3     5                  5      3 3     5
--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
--R          *
--R              +-------+
--R              | 2    2
--R             \|q  + p
--R         + 
--R               7       2 5      4 3     6
--R           (64q  + 112p q  + 56p q  + 7p q)sin(a x)
--R         + 
--R                   6      3 4      5 2    7                 6      3 4      5 2
--R           (- 32p q  - 48p q  - 18p q  - p )cos(a x) - 32p q  - 48p q  - 18p q
--R         + 
--R              7
--R           - p
--R      *
--R                   q
--R             2atan(-) + 2a x + %pi
--R                   p
--R         tan(---------------------)
--R                       4
--R     + 
--R              6      2 4      4 2     6               6      2 4      4 2     6
--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R         7       2 5      4 3      6                7       2 5      4 3      6
--R     (64q  + 128p q  + 76p q  + 12p q)cos(a x) + 64q  + 128p q  + 76p q  + 12p q
--R  /
--R                 7         2 5        4 3       6
--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
--R         + 
--R                     6        3 4        5 2      7                   6
--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
--R         + 
--R                  3 4        5 2      7
--R           - 48a p q  - 18a p q  - a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R             8         2 6         4 4        6 2      8
--R       (64a q  + 144a p q  + 104a p q  + 25a p q  + a p )sin(a x)
--R     + 
--R                 7        3 5        5 3       7                    7        3 5
--R       (- 32a p q  - 64a p q  - 38a p q  - 6a p q)cos(a x) - 32a p q  - 64a p q
--R     + 
--R              5 3       7
--R       - 38a p q  - 6a p q
--R                                                     Type: Expression Integer
--E

--S 169 of 185
dd:=normalize cc
 

   (4)
                                                                  +-------+
               6      2 5      3 4      4 3      5 2     6     7  | 2    2
       (- 32p q  + 16p q  - 48p q  + 20p q  - 18p q  + 5p q - p )\|q  + p
     + 
              7      2 6      3 5      4 4      5 3      6 2     7     8
       - 32p q  + 16p q  - 64p q  + 28p q  - 38p q  + 13p q  - 6p q + p
  /
                8          7         2 6        3 5         4 4        5 3
           64a q  - 32a p q  + 144a p q  - 64a p q  + 104a p q  - 38a p q
         + 
                6 2       7       8
           25a p q  - 6a p q + a p
      *
          +-------+
          | 2    2
         \|q  + p
     + 
            9          8         2 7        3 6         4 5        5 4
       64a q  - 32a p q  + 176a p q  - 80a p q  + 168a p q  - 66a p q
     + 
            6 3        7 2       8       9
       63a p q  - 19a p q  + 7a p q - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                  +-------+
--R               6      2 5      3 4      4 3      5 2     6     7  | 2    2
--R       (- 32p q  + 16p q  - 48p q  + 20p q  - 18p q  + 5p q - p )\|q  + p
--R     + 
--R              7      2 6      3 5      4 4      5 3      6 2     7     8
--R       - 32p q  + 16p q  - 64p q  + 28p q  - 38p q  + 13p q  - 6p q + p
--R  /
--R                8          7         2 6        3 5         4 4        5 3
--R           64a q  - 32a p q  + 144a p q  - 64a p q  + 104a p q  - 38a p q
--R         + 
--R                6 2       7       8
--R           25a p q  - 6a p q + a p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R     + 
--R            9          8         2 7        3 6         4 5        5 4
--R       64a q  - 32a p q  + 176a p q  - 80a p q  + 168a p q  - 66a p q
--R     + 
--R            6 3        7 2       8       9
--R       63a p q  - 19a p q  + 7a p q - a p
--R                                                     Type: Expression Integer
--E

--S 170 of 185    14:422 Schaums and Axiom differ by a constant
ee:=ratDenom dd
 

          +-------+
          | 2    2     2    2
        q\|q  + p   - q  - p
   (5)  ---------------------
                 2      3
            a p q  + a p
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2    2
--R        q\|q  + p   - q  - p
--R   (5)  ---------------------
--R                 2      3
--R            a p q  + a p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 171 of 185
aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x)
 

                   2     2              2
                ((q  - 2p )cos(a x) - 2p )sin(a x)            q sin(a x)
        - atan(-----------------------------------) + atan(----------------)
                           2                               2p cos(a x) + 2p
               p q cos(a x)  + 2p q cos(a x) + p q
   (1)  --------------------------------------------------------------------
                                        a p q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2     2              2
--R                ((q  - 2p )cos(a x) - 2p )sin(a x)            q sin(a x)
--R        - atan(-----------------------------------) + atan(----------------)
--R                           2                               2p cos(a x) + 2p
--R               p q cos(a x)  + 2p q cos(a x) + p q
--R   (1)  --------------------------------------------------------------------
--R                                        a p q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 172 of 185
bb:=1/(a*p*q)*atan((p*tan(a*x))/q)
 

             p tan(a x)
        atan(----------)
                  q
   (2)  ----------------
              a p q
                                                     Type: Expression Integer
--R
--R             p tan(a x)
--R        atan(----------)
--R                  q
--R   (2)  ----------------
--R              a p q
--R                                                     Type: Expression Integer
--E

--S 173 of 185
cc:=aa-bb
 

   (3)
                                     2     2              2
              p tan(a x)          ((q  - 2p )cos(a x) - 2p )sin(a x)
       - atan(----------) - atan(-----------------------------------)
                   q                         2
                                 p q cos(a x)  + 2p q cos(a x) + p q
     + 
               q sin(a x)
       atan(----------------)
            2p cos(a x) + 2p
  /
     a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R                                     2     2              2
--R              p tan(a x)          ((q  - 2p )cos(a x) - 2p )sin(a x)
--R       - atan(----------) - atan(-----------------------------------)
--R                   q                         2
--R                                 p q cos(a x)  + 2p q cos(a x) + p q
--R     + 
--R               q sin(a x)
--R       atan(----------------)
--R            2p cos(a x) + 2p
--R  /
--R     a p q
--R                                                     Type: Expression Integer
--E

--S 174 of 185    14:423 Schaums and Axiom agree
dd:=normalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E


)clear all
 

--S 175 of 185
aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x)
 

            2p sin(a x) - 2q cos(a x)        - 2p sin(a x) - 2q cos(a x)
        log(-------------------------) - log(---------------------------)
                   cos(a x) + 1                      cos(a x) + 1
   (1)  -----------------------------------------------------------------
                                      2a p q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2p sin(a x) - 2q cos(a x)        - 2p sin(a x) - 2q cos(a x)
--R        log(-------------------------) - log(---------------------------)
--R                   cos(a x) + 1                      cos(a x) + 1
--R   (1)  -----------------------------------------------------------------
--R                                      2a p q
--R                                          Type: Union(Expression Integer,...)
--E

--S 176 of 185
bb:=1/(2*a*p*q)*log((p*tan(a*x)-q)/(p*tan(a*x)+q))
 

            p tan(a x) - q
        log(--------------)
            p tan(a x) + q
   (2)  -------------------
               2a p q
                                                     Type: Expression Integer
--R
--R            p tan(a x) - q
--R        log(--------------)
--R            p tan(a x) + q
--R   (2)  -------------------
--R               2a p q
--R                                                     Type: Expression Integer
--E 

--S 177 of 185
cc:=aa-bb
 

   (3)
           2p sin(a x) - 2q cos(a x)        p tan(a x) - q
       log(-------------------------) - log(--------------)
                  cos(a x) + 1              p tan(a x) + q
     + 
             - 2p sin(a x) - 2q cos(a x)
       - log(---------------------------)
                     cos(a x) + 1
  /
     2a p q
                                                     Type: Expression Integer
--R
--R   (3)
--R           2p sin(a x) - 2q cos(a x)        p tan(a x) - q
--R       log(-------------------------) - log(--------------)
--R                  cos(a x) + 1              p tan(a x) + q
--R     + 
--R             - 2p sin(a x) - 2q cos(a x)
--R       - log(---------------------------)
--R                     cos(a x) + 1
--R  /
--R     2a p q
--R                                                     Type: Expression Integer
--E

--S 178 of 185
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 179 of 185
dd:=tanrule cc
 

   (5)
           2p sin(a x) - 2q cos(a x)        p sin(a x) - q cos(a x)
       log(-------------------------) - log(-----------------------)
                  cos(a x) + 1              p sin(a x) + q cos(a x)
     + 
             - 2p sin(a x) - 2q cos(a x)
       - log(---------------------------)
                     cos(a x) + 1
  /
     2a p q
                                                     Type: Expression Integer
--R
--R   (5)
--R           2p sin(a x) - 2q cos(a x)        p sin(a x) - q cos(a x)
--R       log(-------------------------) - log(-----------------------)
--R                  cos(a x) + 1              p sin(a x) + q cos(a x)
--R     + 
--R             - 2p sin(a x) - 2q cos(a x)
--R       - log(---------------------------)
--R                     cos(a x) + 1
--R  /
--R     2a p q
--R                                                     Type: Expression Integer
--E

--S 180 of 185
ee:=expandLog dd
 

        log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x))
   (6)  -------------------------------------------------------------
                                    2a p q
                                                     Type: Expression Integer
--R
--R        log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x))
--R   (6)  -------------------------------------------------------------
--R                                    2a p q
--R                                                     Type: Expression Integer
--E

--S 181 of 185    14:424 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

        log(- 1)
   (7)  --------
         2a p q
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R         2a p q
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 182 of 185    14:425 Axiom cannot compute this integral
aa:=integrate(sin(a*x)^m*cos(a*x)^n,x)
 

           x
         ++           n         m
   (1)   |   cos(%L a) sin(%L a) d%L
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n         m
--I   (1)   |   cos(%H a) sin(%H a) d%H
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 183 of 185    14:426 Axiom cannot compute this integral
aa:=integrate(sin(a*x)^m/cos(a*x)^n,x)
 

           x          m
         ++  sin(%L a)
   (1)   |   ---------- d%L
        ++            n
             cos(%L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x          m
--I         ++  sin(%H a)
--I   (1)   |   ---------- d%H
--R        ++            n
--I             cos(%H a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 184 of 185    14:427 Axiom cannot compute this integral
aa:=integrate(cos(a*x)^m/sin(a*x)^n,x)
 

           x          m
         ++  cos(%L a)
   (1)   |   ---------- d%L
        ++            n
             sin(%L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x          m
--I         ++  cos(%H a)
--I   (1)   |   ---------- d%H
--R        ++            n
--I             sin(%H a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 185 of 185    14:428 Axiom cannot compute this integral
aa:=integrate(1/(sin(a*x)^m*cos(a*x)^n),x)
 

           x
         ++            1
   (1)   |   -------------------- d%L
        ++            n         m
             cos(%L a) sin(%L a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            1
--I   (1)   |   -------------------- d%H
--R        ++            n         m
--I             cos(%H a) sin(%H a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to nqip.output (2010/3/27, 18:30:21).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 14
outputGeneral 5
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 14
xvals := [0.00,0.04,0.08,0.12,0.22,0.26,0.30,0.38,0.39,0.42,0.45, 
               0.46,0.60,0.68,0.72,0.73,0.83,0.85,0.88,0.90,1.00];
 

                                                             Type: List Float
--R 
--R
--R                                                             Type: List Float
--E 2

--S 3 of 14
yvals := [4.0000,3.9936,3.9746,3.9432,3.8135,3.7467,3.6697,3.4943,
                 3.4719,3.4002,3.3264,3.3017,2.9412,2.7352,2.6344,
                        2.6094,2.3684,2.3222,2.2543,2.2099,2.0000];
 

                                                             Type: List Float
--R 
--R
--R                                                             Type: List Float
--E 3

--S 4 of 14
result := nagPolygonIntegrate(xvals,yvals);
 
   There are no library operations named nagPolygonIntegrate 
      Use HyperDoc Browse or issue
                        )what op nagPolygonIntegrate
      to learn if there is any operation containing " 
      nagPolygonIntegrate " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagPolygonIntegrate with argument type(s) 
                                 List Float
                                 List Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagPolygonIntegrate 
--R      Use HyperDoc Browse or issue
--R                        )what op nagPolygonIntegrate
--R      to learn if there is any operation containing " 
--R      nagPolygonIntegrate " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagPolygonIntegrate with argument type(s) 
--R                                 List Float
--R                                 List Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4

--S 5 of 14 used to work?
result.integral :: Float             
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                              Variable integral
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                              Variable integral
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 5
--       3.1414

--S 6 of 14 used to work?
result.errorEstimate :: Float        
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                           Variable errorEstimate
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                           Variable errorEstimate
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 6
--       - 0.000025627

--S 7 of 14
coords := transpose matrix [xvals, yvals];
 

                                                           Type: Matrix Float
--R 
--R
--R                                                           Type: Matrix Float
--E 7

--S 8 of 14
result := nagPolygonIntegrate coords;
 
   There are no library operations named nagPolygonIntegrate 
      Use HyperDoc Browse or issue
                        )what op nagPolygonIntegrate
      to learn if there is any operation containing " 
      nagPolygonIntegrate " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagPolygonIntegrate with argument type(s) 
                                Matrix Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagPolygonIntegrate 
--R      Use HyperDoc Browse or issue
--R                        )what op nagPolygonIntegrate
--R      to learn if there is any operation containing " 
--R      nagPolygonIntegrate " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagPolygonIntegrate with argument type(s) 
--R                                Matrix Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 8

--S 9 of 14 used to work?
result.integral :: Float             
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                              Variable integral
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                              Variable integral
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 9
--       3.1414

--S 10 of 14 used to work?
result.errorEstimate :: Float        
 
   There are no exposed library operations named result but there is 
      one unexposed operation with that name. Use HyperDoc Browse or 
      issue
                             )display op result
      to learn more about the available operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      result with argument type(s) 
                           Variable errorEstimate
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no exposed library operations named result but there is 
--R      one unexposed operation with that name. Use HyperDoc Browse or 
--R      issue
--R                             )display op result
--R      to learn more about the available operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      result with argument type(s) 
--R                           Variable errorEstimate
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 10
--       - 0.000025627

--S 11 of 14 broken
nagPolygonIntegrate([1,2,3],[1,2,3,4])
 
   There are no library operations named nagPolygonIntegrate 
      Use HyperDoc Browse or issue
                        )what op nagPolygonIntegrate
      to learn if there is any operation containing " 
      nagPolygonIntegrate " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagPolygonIntegrate with argument type(s) 
                            List PositiveInteger
                            List PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagPolygonIntegrate 
--R      Use HyperDoc Browse or issue
--R                        )what op nagPolygonIntegrate
--R      to learn if there is any operation containing " 
--R      nagPolygonIntegrate " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagPolygonIntegrate with argument type(s) 
--R                            List PositiveInteger
--R                            List PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 11
-- 
--   Error signalled from user code:
--      The lists supplied to nagPolygonIntegrate are of different 
--      lengths: 3 and 4.

--S 12 of 14 broken
nagPolygonIntegrate([[1,2,3],[4,5,6]])
 

   (5)  nagPolygonIntegrate
                           [1,2,3],[4,5,6]
                                                                 Type: Symbol
--R 
--R
--R   (5)  nagPolygonIntegrate
--R                           [1,2,3],[4,5,6]
--R                                                                 Type: Symbol
--E 12
--
--   Error signalled from user code:
--      Please supply the coordinate matrix in nagPolygonIntegrate with
--      each row consisting of single a x-y pair.

--S 13 of 14
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 14
output "End of tests"
 
   End of tests
                                                                   Type: Void
--R 
--R   End of tests
--R                                                                   Type: Void
--E 14
)spool 
 
Starts dribbling to patch51.output (2010/3/27, 18:30:39).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 1 bug #355 fix
D(besselK(a,x),x)
 

        - besselK(a + 1,x) - besselK(a - 1,x)
   (1)  -------------------------------------
                          2
                                                     Type: Expression Integer
--R 
--R
--R        - besselK(a + 1,x) - besselK(a - 1,x)
--R   (1)  -------------------------------------
--R                          2
--R                                                     Type: Expression Integer
--E 1
)spool 
 
Starts dribbling to int.output (2010/3/27, 18:27:13).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 47
2**(5678 - 4856 + 2 * 17)
 

   (1)
  4804810770435008147181540925125924391239526139871682263473855610088084200076_
   308293086342527091412083743074572278211496076276922026433435687527334980249_
   539302425425230458177649495442143929053063884787051467457680738771416988598_
   15495632935288783334250628775936
                                                        Type: PositiveInteger
--R 
--R
--R   (1)
--R  4804810770435008147181540925125924391239526139871682263473855610088084200076_
--R   308293086342527091412083743074572278211496076276922026433435687527334980249_
--R   539302425425230458177649495442143929053063884787051467457680738771416988598_
--R   15495632935288783334250628775936
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 47
x := -101
 

   (2)  - 101
                                                                Type: Integer
--R 
--R
--R   (2)  - 101
--R                                                                Type: Integer
--E 2

--S 3 of 47
abs(x)
 

   (3)  101
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  101
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 47
sign(x)
 

   (4)  - 1
                                                                Type: Integer
--R 
--R
--R   (4)  - 1
--R                                                                Type: Integer
--E 4

--S 5 of 47
x < 0
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5

--S 6 of 47
x <= -1
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 47
negative?(x)
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 47
x > 0
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 47
x >= 1
 

   (9)  false
                                                                Type: Boolean
--R 
--R
--R   (9)  false
--R                                                                Type: Boolean
--E 9

--S 10 of 47
positive?(x)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 47
zero?(x)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 47
one?(x)
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 47
(x = -101)@Boolean
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 47
odd?(x)
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 47
even?(x)
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 47
gcd(56788,43688)
 

   (16)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  4
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 47
lcm(56788,43688)
 

   (17)  620238536
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  620238536
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 47
max(678,567)
 

   (18)  678
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  678
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 47
min(678,567)
 

   (19)  567
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  567
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 47
reduce(max,[2,45,-89,78,100,-45])
 

   (20)  100
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  100
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 47
reduce(min,[2,45,-89,78,100,-45])
 

   (21)  - 89
                                                                Type: Integer
--R 
--R
--R   (21)  - 89
--R                                                                Type: Integer
--E 21

--S 22 of 47
reduce(gcd,[2,45,-89,78,100,-45])
 

   (22)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  1
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 47
reduce(lcm,[2,45,-89,78,100,-45])
 

   (23)  1041300
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1041300
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 47
13 / 4
 

         13
   (24)  --
          4
                                                       Type: Fraction Integer
--R 
--R
--R         13
--R   (24)  --
--R          4
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 47
13 quo 4
 

   (25)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  3
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 47
13 rem 4
 

   (26)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  1
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 47
zero?(167604736446952 rem 2003644)
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 47
d := divide(13,4)
 

   (28)  [quotient= 3,remainder= 1]
                           Type: Record(quotient: Integer,remainder: Integer)
--R 
--R
--R   (28)  [quotient= 3,remainder= 1]
--R                           Type: Record(quotient: Integer,remainder: Integer)
--E 28

--S 29 of 47
d.quotient
 

   (29)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (29)  3
--R                                                        Type: PositiveInteger
--E 29

--S 30 of 47
d.remainder
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

)clear all
 

--S 31 of 47
factor 102400
 

         12 2
   (1)  2  5
                                                       Type: Factored Integer
--R 
--R
--R         12 2
--R   (1)  2  5
--R                                                       Type: Factored Integer
--E 31

--S 32 of 47
prime? 7
 

   (2)  true
                                                                Type: Boolean
--R 
--R
--R   (2)  true
--R                                                                Type: Boolean
--E 32

--S 33 of 47
prime? 8
 

   (3)  false
                                                                Type: Boolean
--R 
--R
--R   (3)  false
--R                                                                Type: Boolean
--E 33

--S 34 of 47
nextPrime 100
 

   (4)  101
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  101
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 47
prevPrime 100
 

   (5)  97
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  97
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 47
primes(100,175)
 

   (6)  [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101]
                                                           Type: List Integer
--R 
--R
--R   (6)  [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101]
--R                                                           Type: List Integer
--E 36

--S 37 of 47
factor(2 :: Complex Integer)
 

                     2
   (7)  - %i (1 + %i)
                                               Type: Factored Complex Integer
--R 
--R
--R                     2
--R   (7)  - %i (1 + %i)
--R                                               Type: Factored Complex Integer
--E 37

)clear all
 

--S 38 of 47
[fibonacci(k) for k in 0..]
 

   (1)  [0,1,1,2,3,5,8,13,21,34,...]
                                                         Type: Stream Integer
--R 
--R
--R   (1)  [0,1,1,2,3,5,8,13,21,34,...]
--R                                                         Type: Stream Integer
--E 38

--S 39 of 47
[legendre(i,11) for i in 0..10]
 

   (2)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
                                                           Type: List Integer
--R 
--R
--R   (2)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
--R                                                           Type: List Integer
--E 39

--S 40 of 47
[jacobi(i,15) for i in 0..9]
 

   (3)  [0,1,1,0,1,0,0,- 1,1,0]
                                                           Type: List Integer
--R 
--R
--R   (3)  [0,1,1,0,1,0,0,- 1,1,0]
--R                                                           Type: List Integer
--E 40

--S 41 of 47
[eulerPhi i for i in 1..]
 

   (4)  [1,1,2,2,4,2,6,4,6,4,...]
                                                         Type: Stream Integer
--R 
--R
--R   (4)  [1,1,2,2,4,2,6,4,6,4,...]
--R                                                         Type: Stream Integer
--E 41

--S 42 of 47
[moebiusMu i for i in 1..]
 

   (5)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
--R                                                         Type: Stream Integer
--E 42

--S 43 of 47
a := roman(78)
 

   (6)  LXXVIII
                                                           Type: RomanNumeral
--R 
--R
--R   (6)  LXXVIII
--R                                                           Type: RomanNumeral
--E 43

--S 44 of 47
b := roman(87)
 

   (7)  LXXXVII
                                                           Type: RomanNumeral
--R 
--R
--R   (7)  LXXXVII
--R                                                           Type: RomanNumeral
--E 44

--S 45 of 47
a + b
 

   (8)  CLXV
                                                           Type: RomanNumeral
--R 
--R
--R   (8)  CLXV
--R                                                           Type: RomanNumeral
--E 45

--S 46 of 47
a * b
 

   (9)  MMMMMMDCCLXXXVI
                                                           Type: RomanNumeral
--R 
--R
--R   (9)  MMMMMMDCCLXXXVI
--R                                                           Type: RomanNumeral
--E 46

--S 47 of 47
b rem a
 

   (10)  IX
                                                           Type: RomanNumeral
--R 
--R
--R   (10)  IX
--R                                                           Type: RomanNumeral
--E 47
)spool 
 
Starts dribbling to e1.output (2010/3/27, 18:25:4).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 7
G:DFLOAT:=0.577215664901532860606512::DFLOAT
 

   (1)  0.57721566490153275
                                                            Type: DoubleFloat
--R
--R   (1)  0.57721566490153287
--R                                                            Type: DoubleFloat
--E 1
--S 2 of 7
f(x)==x^-1 * (E1(x)::DFLOAT + log(x) + G)
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 2
--S 3 of 7
[[0.01,0.9975055452, f(0.01), f(0.01)-0.9975055452],_
[0.02,0.9950221392, f(0.02), f(0.02)-0.9950221392],_
[0.03,0.9925497201, f(0.03), f(0.03)-0.9925497201],_
[0.04,0.9900882265, f(0.04), f(0.04)-0.9900882265],_
[0.05,0.9876375971, f(0.05), f(0.05)-0.9876375971],_
[0.06,0.9851977714, f(0.06), f(0.06)-0.9851977714],_
[0.07,0.9827686889, f(0.07), f(0.07)-0.9827686889],_
[0.08,0.9803502898, f(0.08), f(0.08)-0.9803502898],_
[0.09,0.9779425142, f(0.09), f(0.09)-0.9779425142],_
[0.10,0.9755453033, f(0.10), f(0.10)-0.9755453033],_
[0.11,0.9731585980, f(0.11), f(0.11)-0.9731585980],_
[0.12,0.9707823399, f(0.12), f(0.12)-0.9707823399],_
[0.13,0.9684164710, f(0.13), f(0.13)-0.9684164710],_
[0.14,0.9660609336, f(0.14), f(0.14)-0.9660609336],_
[0.15,0.9637156702, f(0.15), f(0.15)-0.9637156702],_
[0.16,0.9613806240, f(0.16), f(0.16)-0.9613806240],_
[0.17,0.9590557383, f(0.17), f(0.17)-0.9590557383],_
[0.18,0.9567409569, f(0.18), f(0.18)-0.9567409569],_
[0.19,0.9544362237, f(0.19), f(0.19)-0.9544362237],_
[0.20,0.9521414833, f(0.20), f(0.20)-0.9521414833],_
[0.21,0.9498566804, f(0.21), f(0.21)-0.9498566804],_
[0.22,0.9475817603, f(0.22), f(0.22)-0.9475817603],_
[0.23,0.9453166684, f(0.23), f(0.23)-0.9453166684],_
[0.24,0.9430613506, f(0.24), f(0.24)-0.9430613506],_
[0.25,0.9408157528, f(0.25), f(0.25)-0.9408157528],_
[0.26,0.9385798221, f(0.26), f(0.26)-0.9385798221],_
[0.27,0.9363535046, f(0.27), f(0.27)-0.9363535046],_
[0.28,0.9341367481, f(0.28), f(0.28)-0.9341367481],_
[0.29,0.9319294997, f(0.29), f(0.29)-0.9319294997],_
[0.30,0.9297317075, f(0.30), f(0.30)-0.9297317075],_
[0.31,0.9275433196, f(0.31), f(0.31)-0.9275433196],_
[0.32,0.9253642845, f(0.32), f(0.32)-0.9253642845],_
[0.33,0.9231945510, f(0.33), f(0.33)-0.9231945510],_
[0.34,0.9210340684, f(0.34), f(0.34)-0.9210340684],_
[0.35,0.9188827858, f(0.35), f(0.35)-0.9188827858],_
[0.36,0.9167406533, f(0.36), f(0.36)-0.9167406533],_
[0.37,0.9146076209, f(0.37), f(0.37)-0.9146076209],_
[0.38,0.9124836388, f(0.38), f(0.38)-0.9124836388],_
[0.39,0.9103686582, f(0.39), f(0.39)-0.9103686582],_
[0.40,0.9082626297, f(0.40), f(0.40)-0.9082626297],_
[0.41,0.9061655048, f(0.41), f(0.41)-0.9061655048],_
[0.42,0.9040772350, f(0.42), f(0.42)-0.9040772350],_
[0.43,0.9019977725, f(0.43), f(0.43)-0.9019977725],_
[0.44,0.8999270693, f(0.44), f(0.44)-0.8999270693],_
[0.45,0.8978650778, f(0.45), f(0.45)-0.8978650778],_
[0.46,0.8958117511, f(0.46), f(0.46)-0.8958117511],_
[0.47,0.8937670423, f(0.47), f(0.47)-0.8937670423],_
[0.48,0.8917309048, f(0.48), f(0.48)-0.8917309048],_
[0.49,0.8897032920, f(0.49), f(0.49)-0.8897032920],_
[0.50,0.8876841584, f(0.50), f(0.50)-0.8876841584]]::LIST(LIST(DFLOAT))
 
   Compiling function f with type Float -> DoubleFloat 

   (3)
   [
     [9.9999999999999985E-3, 0.9975055451999999, 0.99750554515560808,
      - 4.4391823550427034E-11]
     ,

     [1.9999999999999997E-2, 0.99502213920000004, 0.99502213915481086,
      - 4.5189185726712822E-11]
     ,

     [2.9999999999999999E-2, 0.99254972009999998, 0.99254972009440801,
      - 5.5919713304319885E-12]
     ,

     [3.9999999999999994E-2, 0.99008822649999995, 0.99008822646530215,
      - 3.4697800188610017E-11]
     ,

     [5.0000000000000003E-2, 0.98763759709999999, 0.98763759715032151,
      5.0321524724949995E-11]
     ,

     [5.9999999999999998E-2, 0.98519777139999998, 0.98519777142131992,
      2.1319945808784269E-11]
     ,

     [7.0000000000000007E-2, 0.98276868890000002, 0.98276868893647817,
      3.6478153830898918E-11]
     ,

     [7.9999999999999988E-2, 0.98035028980000005, 0.98035028973774141,
      - 6.2258642685719678E-11]
     ,

     [8.9999999999999997E-2, 0.9779425142, 0.97794251424804612,
      4.8046122635980737E-11]
     ,

     [0.10000000000000001, 0.9755453033, 0.97554530326877886,
      - 3.122113678699634E-11]
     ,

     [0.10999999999999999, 0.97315859799999993, 0.97315859797713866,
      - 2.2861268433871373E-11]
     ,
    [0.12,0.97078233989999996,0.9707823399235388,2.3538837545800106E-11],
    [0.13,0.96841647099999995,0.96841647102903716,2.9037217075256194E-11],

     [0.14000000000000001, 0.96606093359999989, 0.96606093358278911,
      - 1.7210788350041639E-11]
     ,

     [0.14999999999999999, 0.96371567020000004, 0.96371567023951921,
      3.9519165717649685E-11]
     ,

     [0.15999999999999998, 0.96138062400000002, 0.9613806240169831,
      1.698308160769102E-11]
     ,

     [0.16999999999999998, 0.95905573830000002, 0.95905573829349067,
      - 6.5093486156797553E-12]
     ,

     [0.17999999999999999, 0.95674095690000005, 0.95674095680541671,
      - 9.4583341159193424E-11]
     ,
    [0.19,0.95443622369999992,0.95443622364474789,- 5.5252025177310315E-11],

     [0.20000000000000001, 0.95214148329999992, 0.95214148325662773,
      - 4.337219472461129E-11]
     ,

     [0.20999999999999999, 0.94985668039999993, 0.94985668043693716,
      3.6937231051581421E-11]
     ,

     [0.21999999999999997, 0.94758176029999996, 0.94758176032988517,
      2.9885205421464889E-11]
     ,

     [0.22999999999999998, 0.94531666839999995, 0.94531666842562345,
      2.5623503319138763E-11]
     ,

     [0.23999999999999999, 0.94306135059999996, 0.943061350557861,
      - 4.2138958988857667E-11]
     ,
    [0.25,0.94081575279999996,0.94081575290152131,1.0152134688468095E-10],

     [0.26000000000000001, 0.93857982209999991, 0.93857982197039858,
      - 1.2960132966810534E-10]
     ,
    [0.27000000000000002,0.9363535046,0.9363535046148318,1.4831802452874854E-11]
     ,

     [0.28000000000000003, 0.93413674810000003, 0.9341367480194056,
      - 8.0594420026613989E-11]
     ,

     [0.28999999999999998, 0.93192949970000005, 0.93192949970065853,
      6.5847327590518034E-13]
     ,

     [0.29999999999999999, 0.9297317075, 0.92973170750481271,
      4.8127057894475911E-12]
     ,
    [0.31,0.92754331960000003,0.92754331960551928,5.5192517223190407E-12],

     [0.31999999999999995, 0.92536428449999997, 0.92536428450162023,
      1.6202594821379535E-12]
     ,

     [0.32999999999999996, 0.92319455099999992, 0.92319455101492243,
      1.4922507673986729E-11]
     ,

     [0.33999999999999997, 0.92103406840000002, 0.92103406828799461,
      - 1.1200540495082123E-10]
     ,

     [0.34999999999999998, 0.91888278579999993, 0.91888278578197424,
      - 1.8025692050116504E-11]
     ,

     [0.35999999999999999, 0.91674065329999999, 0.91674065327439824,
      - 2.560174294785611E-11]
     ,
    [0.37,0.91460762090000003,0.91460762085703518,- 4.2964853896876321E-11],
    [0.38,0.91248363879999994,0.91248363893375173,1.3375178742336402E-10],

     [0.39000000000000001, 0.9103686581999999, 0.91036865821837931,
      1.8379409105762079E-11]
     ,

     [0.40000000000000002, 0.90826262970000005, 0.90826262973260075,
      3.2600699917395559E-11]
     ,

     [0.40999999999999998, 0.90616550479999991, 0.9061655048038586,
      3.8586911443871941E-12]
     ,

     [0.41999999999999998, 0.90407723499999992, 0.90407723506326854,
      6.3268612571221183E-11]
     ,

     [0.42999999999999999, 0.90199777249999991, 0.90199777244355617,
      - 5.6443738571942959E-11]
     ,

     [0.43999999999999995, 0.89992706929999999, 0.89992706917700027,
      - 1.2299972151907923E-10]
     ,

     [0.44999999999999996, 0.89786507779999991, 0.89786507779340152,
      - 6.5983885022546929E-12]
     ,

     [0.45999999999999996, 0.8958117511, 0.89581175111805533,
      1.8055335004873996E-11]
     ,

     [0.46999999999999997, 0.89376704229999993, 0.89376704226974857,
      - 3.0251356974986265E-11]
     ,

     [0.47999999999999998, 0.89173090479999995, 0.89173090465876192,
      - 1.4123802127841145E-10]
     ,

     [0.48999999999999999, 0.88970329199999998, 0.88970329198489451,
      - 1.5105472428444955E-11]
     ,
    [0.5,0.88768415839999992,0.8876841582354964,- 1.6450352191554884E-10]]
                                                  Type: List List DoubleFloat
--R 
--R   Compiling function f with type Float -> DoubleFloat 
--R
--R   (3)
--R   [[1.0E-2,0.99750554520000001,0.99750554515544154,- 4.455846802642327E-11],
--R    [2.0E-2,0.99502213920000004,0.99502213915481641,- 4.5183634611589696E-11],
--R
--R     [2.9999999999999999E-2, 0.99254972009999998, 0.99254972009439713,
--R      - 5.602851516073315E-12]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.99008822649999995, 0.99008822646530492,
--R      - 3.4695024631048454E-11]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.98763759709999999, 0.98763759715033261,
--R      5.0332626955196247E-11]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.98519777139999998, 0.98519777142131459,
--R      2.1314616738266068E-11]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.98276868890000002, 0.98276868893648617,
--R      3.648614743667622E-11]
--R     ,
--R
--R     [8.0000000000000002E-2, 0.98035028980000005, 0.98035028973773719,
--R      - 6.2262861533213254E-11]
--R     ,
--R
--R     [8.9999999999999997E-2, 0.9779425142, 0.97794251424804735,
--R      4.8047343881307825E-11]
--R     ,
--R
--R     [0.10000000000000001, 0.9755453033, 0.97554530326877553,
--R      - 3.1224467456070215E-11]
--R     ,
--R    [0.11,0.97315859800000004,0.97315859797713988,- 2.2860158210846748E-11],
--R    [0.12,0.97078233989999996,0.97078233992354002,2.3540058791127194E-11],
--R    [0.13,0.96841647099999995,0.96841647102903816,2.9038216275978357E-11],
--R
--R     [0.14000000000000001, 0.9660609336, 0.96606093358279166,
--R      - 1.7208345859387464E-11]
--R     ,
--R
--R     [0.14999999999999999, 0.96371567020000004, 0.96371567023951998,
--R      3.9519942873766922E-11]
--R     ,
--R    [0.16,0.96138062400000002,0.96138062401698243,1.6982415473876245E-11],
--R
--R     [0.17000000000000001, 0.95905573830000002, 0.95905573829349,
--R      - 6.5100147494945304E-12]
--R     ,
--R
--R     [0.17999999999999999, 0.95674095690000005, 0.9567409568054186,
--R      - 9.4581453780051561E-11]
--R     ,
--R    [0.19,0.95443622370000003,0.95443622364474956,- 5.525047086507584E-11],
--R
--R     [0.20000000000000001, 0.95214148330000004, 0.9521414832566294,
--R      - 4.3370640412376815E-11]
--R     ,
--R
--R     [0.20999999999999999, 0.94985668040000004, 0.94985668043693772,
--R      3.6937675140791271E-11]
--R     ,
--R    [0.22,0.94758176029999996,0.94758176032988584,2.9885871555279664E-11],
--R
--R     [0.23000000000000001, 0.94531666839999995, 0.9453166684256229,
--R      2.562294820762645E-11]
--R     ,
--R
--R     [0.23999999999999999, 0.94306135059999996, 0.94306135055786067,
--R      - 4.2139292055765054E-11]
--R     ,
--R    [0.25,0.94081575279999996,0.94081575290152264,1.015226791523105E-10],
--R
--R     [0.26000000000000001, 0.93857982210000002, 0.93857982197039913,
--R      - 1.2960088557889549E-10]
--R     ,
--R
--R     [0.27000000000000002, 0.9363535046, 0.93635350461483224,
--R      1.4832246542084704E-11]
--R     ,
--R
--R     [0.28000000000000003, 0.93413674810000003, 0.93413674801940527,
--R      - 8.0594753093521376E-11]
--R     ,
--R
--R     [0.28999999999999998, 0.93192949970000005, 0.93192949970065808,
--R      6.5802918669533028E-13]
--R     ,
--R
--R     [0.29999999999999999, 0.9297317075, 0.92973170750481327,
--R      4.8132609009599037E-12]
--R     ,
--R    [0.31,0.92754331960000003,0.92754331960551961,5.5195847892264283E-12],
--R
--R     [0.32000000000000001, 0.92536428449999997, 0.92536428450162023,
--R      1.6202594821379535E-12]
--R     ,
--R
--R     [0.33000000000000002, 0.92319455100000003, 0.92319455101492243,
--R      1.4922396651684267E-11]
--R     ,
--R
--R     [0.34000000000000002, 0.92103406840000002, 0.92103406828799361,
--R      - 1.1200640415154339E-10]
--R     ,
--R
--R     [0.34999999999999998, 0.91888278580000005, 0.91888278578197524,
--R      - 1.8024803871696804E-11]
--R     ,
--R
--R     [0.35999999999999999, 0.91674065329999999, 0.91674065327439791,
--R      - 2.5602076014763497E-11]
--R     ,
--R    [0.37,0.91460762090000003,0.91460762085703573,- 4.2964298785364008E-11],
--R    [0.38,0.91248363880000005,0.91248363893375239,1.3375234253487633E-10],
--R
--R     [0.39000000000000001, 0.91036865820000001, 0.91036865821837942,
--R      1.8379409105762079E-11]
--R     ,
--R
--R     [0.40000000000000002, 0.90826262970000005, 0.90826262973260075,
--R      3.2600699917395559E-11]
--R     ,
--R
--R     [0.40999999999999998, 0.90616550480000002, 0.90616550480385905,
--R      3.8590242112945816E-12]
--R     ,
--R
--R     [0.41999999999999998, 0.90407723500000003, 0.90407723506326909,
--R      6.3269056660431033E-11]
--R     ,
--R
--R     [0.42999999999999999, 0.90199777250000002, 0.90199777244355628,
--R      - 5.6443738571942959E-11]
--R     ,
--R    [0.44,0.89992706929999999,0.89992706917700038,- 1.2299961049677677E-10],
--R
--R     [0.45000000000000001, 0.89786507780000002, 0.8978650777934013,
--R      - 6.5987215691620804E-12]
--R     ,
--R
--R     [0.46000000000000002, 0.8958117511, 0.89581175111805511,
--R      1.8055112960269071E-11]
--R     ,
--R
--R     [0.46999999999999997, 0.89376704230000004, 0.89376704226974857,
--R      - 3.0251467997288728E-11]
--R     ,
--R
--R     [0.47999999999999998, 0.89173090479999995, 0.89173090465876237,
--R      - 1.412375771892016E-10]
--R     ,
--R
--R     [0.48999999999999999, 0.88970329199999998, 0.88970329198489473,
--R      - 1.510525038384003E-11]
--R     ,
--R    [0.5,0.88768415840000003,0.88768415823549685,- 1.6450318884864146E-10]]
--R                                                  Type: List List DoubleFloat
--E 3
--S 4 of 7
[[0.50, 0.559773595, E1(0.50), E1(0.50)-0.559773595],_
[0.51, 0.547822352, E1(0.51), E1(0.51)-0.547822352],_
[0.52, 0.536219798, E1(0.52), E1(0.52)-0.536219798],_
[0.53, 0.524951510, E1(0.53), E1(0.53)-0.524951510],_
[0.54, 0.514003886, E1(0.54), E1(0.54)-0.514003886],_
[0.55, 0.503364081, E1(0.55), E1(0.55)-0.503364081],_
[0.56, 0.493019959, E1(0.56), E1(0.56)-0.493019959],_
[0.57, 0.482960034, E1(0.57), E1(0.57)-0.482960034],_
[0.58, 0.473173433, E1(0.58), E1(0.58)-0.473173433],_
[0.59, 0.463649849, E1(0.59), E1(0.59)-0.463649849],_
[0.60, 0.454379503, E1(0.60), E1(0.60)-0.454379503],_
[0.61, 0.445353112, E1(0.61), E1(0.61)-0.445353112],_
[0.62, 0.436561854, E1(0.62), E1(0.62)-0.436561854],_
[0.63, 0.427997338, E1(0.63), E1(0.63)-0.427997338],_
[0.64, 0.419651581, E1(0.64), E1(0.64)-0.419651581],_
[0.65, 0.411516976, E1(0.65), E1(0.65)-0.411516976],_
[0.66, 0.403586275, E1(0.66), E1(0.66)-0.403586275],_
[0.67, 0.395852563, E1(0.67), E1(0.67)-0.395852563],_
[0.68, 0.388309243, E1(0.68), E1(0.68)-0.388309243],_
[0.69, 0.380950010, E1(0.69), E1(0.69)-0.380950010],_
[0.70, 0.373768843, E1(0.70), E1(0.70)-0.373768843],_
[0.71, 0.366759981, E1(0.71), E1(0.71)-0.366759981],_
[0.72, 0.359917914, E1(0.72), E1(0.72)-0.359917914],_
[0.73, 0.353237364, E1(0.73), E1(0.73)-0.353237364],_
[0.74, 0.346713279, E1(0.74), E1(0.74)-0.346713279],_
[0.75, 0.340340813, E1(0.75), E1(0.75)-0.340340813],_
[0.76, 0.334115321, E1(0.76), E1(0.76)-0.334115321],_
[0.77, 0.328032346, E1(0.77), E1(0.77)-0.328032346],_
[0.78, 0.322087610, E1(0.78), E1(0.78)-0.322087610],_
[0.79, 0.316277004, E1(0.79), E1(0.79)-0.316277004],_
[0.80, 0.310596579, E1(0.80), E1(0.80)-0.310596579],_
[0.81, 0.305042539, E1(0.81), E1(0.81)-0.305042539],_
[0.82, 0.299611236, E1(0.82), E1(0.82)-0.299611236],_
[0.83, 0.294299155, E1(0.83), E1(0.83)-0.294299155],_
[0.84, 0.289102918, E1(0.84), E1(0.84)-0.289102918],_
[0.85, 0.284019269, E1(0.85), E1(0.85)-0.284019269],_
[0.86, 0.279045070, E1(0.86), E1(0.86)-0.279045070],_
[0.87, 0.274177301, E1(0.87), E1(0.87)-0.274177301],_
[0.88, 0.269413046, E1(0.88), E1(0.88)-0.269413046],_
[0.89, 0.264749496, E1(0.89), E1(0.89)-0.264749496],_
[0.90, 0.260183939, E1(0.90), E1(0.90)-0.260183939],_
[0.91, 0.255713758, E1(0.91), E1(0.91)-0.255713758],_
[0.92, 0.251336425, E1(0.92), E1(0.92)-0.251336425],_
[0.93, 0.247049501, E1(0.93), E1(0.93)-0.247049501],_
[0.94, 0.242850627, E1(0.94), E1(0.94)-0.242850627],_
[0.95, 0.238737524, E1(0.95), E1(0.95)-0.238737524],_
[0.96, 0.234707988, E1(0.96), E1(0.96)-0.234707988],_
[0.97, 0.230759890, E1(0.97), E1(0.97)-0.230759890],_
[0.98, 0.226891167, E1(0.98), E1(0.98)-0.226891167],_
[0.99, 0.223099826, E1(0.99), E1(0.99)-0.223099826],_
[1.00, 0.219383934, E1(1.00), E1(1.00)-0.219383934],_
[1.01, 0.215741624, E1(1.01), E1(1.01)-0.215741624],_
[1.02, 0.212171083, E1(1.02), E1(1.02)-0.212171083],_
[1.03, 0.208670559, E1(1.03), E1(1.03)-0.208670559],_
[1.04, 0.205238352, E1(1.04), E1(1.04)-0.205238352],_
[1.05, 0.201872813, E1(1.05), E1(1.05)-0.201872813],_
[1.06, 0.198572347, E1(1.06), E1(1.06)-0.198572347],_
[1.07, 0.195335403, E1(1.07), E1(1.07)-0.195335403],_
[1.08, 0.192160479, E1(1.08), E1(1.08)-0.192160479],_
[1.09, 0.189046118, E1(1.09), E1(1.09)-0.189046118],_
[1.10, 0.185990905, E1(1.10), E1(1.10)-0.185990905],_
[1.11, 0.182993465, E1(1.11), E1(1.11)-0.182993465],_
[1.12, 0.180052467, E1(1.12), E1(1.12)-0.180052467],_
[1.13, 0.177166615, E1(1.13), E1(1.13)-0.177166615],_
[1.14, 0.174334651, E1(1.14), E1(1.14)-0.174334651],_
[1.15, 0.171555354, E1(1.15), E1(1.15)-0.171555354],_
[1.16, 0.168827535, E1(1.16), E1(1.16)-0.168827535],_
[1.17, 0.166150040, E1(1.17), E1(1.17)-0.166150040],_
[1.18, 0.163521748, E1(1.18), E1(1.18)-0.163521748],_
[1.19, 0.160941567, E1(1.19), E1(1.19)-0.160941567],_
[1.20, 0.158408437, E1(1.20), E1(1.20)-0.158408437],_
[1.21, 0.155921324, E1(1.21), E1(1.21)-0.155921324],_
[1.22, 0.153479226, E1(1.22), E1(1.22)-0.153479226],_
[1.23, 0.151081164, E1(1.23), E1(1.23)-0.151081164],_
[1.24, 0.148726188, E1(1.24), E1(1.24)-0.148726188],_
[1.25, 0.146413373, E1(1.25), E1(1.25)-0.146413373],_
[1.26, 0.144141815, E1(1.26), E1(1.26)-0.144141815],_
[1.27, 0.141910639, E1(1.27), E1(1.27)-0.141910639],_
[1.28, 0.139718989, E1(1.28), E1(1.28)-0.139718989],_
[1.29, 0.137566032, E1(1.29), E1(1.29)-0.137566032],_
[1.30, 0.135450958, E1(1.30), E1(1.30)-0.135450958],_
[1.31, 0.133372975, E1(1.31), E1(1.31)-0.133372975],_
[1.32, 0.131331314, E1(1.32), E1(1.32)-0.131331314],_
[1.33, 0.129325224, E1(1.33), E1(1.33)-0.129325224],_
[1.34, 0.127353972, E1(1.34), E1(1.34)-0.127353972],_
[1.35, 0.125416844, E1(1.35), E1(1.35)-0.125416844],_
[1.36, 0.123513146, E1(1.36), E1(1.36)-0.123513146],_
[1.37, 0.121642198, E1(1.37), E1(1.37)-0.121642198],_
[1.38, 0.119803337, E1(1.38), E1(1.38)-0.119803337],_
[1.39, 0.117995919, E1(1.39), E1(1.39)-0.117995919],_
[1.40, 0.116219313, E1(1.40), E1(1.40)-0.116219313],_
[1.41, 0.114472903, E1(1.41), E1(1.41)-0.114472903],_
[1.42, 0.112756090, E1(1.42), E1(1.42)-0.112756090],_
[1.43, 0.111068287, E1(1.43), E1(1.43)-0.111068287],_
[1.44, 0.109408923, E1(1.44), E1(1.44)-0.109408923],_
[1.45, 0.107777440, E1(1.45), E1(1.45)-0.107777440],_
[1.46, 0.106173291, E1(1.46), E1(1.46)-0.106173291],_
[1.47, 0.104595946, E1(1.47), E1(1.47)-0.104595946],_
[1.48, 0.103044882, E1(1.48), E1(1.48)-0.103044882],_
[1.49, 0.101519593, E1(1.49), E1(1.49)-0.101519593],_
[1.50, 0.100019582, E1(1.50), E1(1.50)-0.100019582],_
[1.51, 0.098544365, E1(1.51), E1(1.51)-0.098544365],_
[1.52, 0.097093466, E1(1.52), E1(1.52)-0.097093466],_
[1.53, 0.095666424, E1(1.53), E1(1.53)-0.095666424],_
[1.54, 0.094262786, E1(1.54), E1(1.54)-0.094262786],_
[1.55, 0.092882108, E1(1.55), E1(1.55)-0.092882108],_
[1.56, 0.091523960, E1(1.56), E1(1.56)-0.091523960],_
[1.57, 0.090187917, E1(1.57), E1(1.57)-0.090187917],_
[1.58, 0.088873566, E1(1.58), E1(1.58)-0.088873566],_
[1.59, 0.087580504, E1(1.59), E1(1.59)-0.087580504],_
[1.60, 0.086308334, E1(1.60), E1(1.60)-0.086308334],_
[1.61, 0.085056670, E1(1.61), E1(1.61)-0.085056670],_
[1.62, 0.083825133, E1(1.62), E1(1.62)-0.083825133],_
[1.63, 0.082613354, E1(1.63), E1(1.63)-0.082613354],_
[1.64, 0.081420970, E1(1.64), E1(1.64)-0.081420970],_
[1.65, 0.080247627, E1(1.65), E1(1.65)-0.080247627],_
[1.66, 0.079092978, E1(1.66), E1(1.66)-0.079092978],_
[1.67, 0.077956684, E1(1.67), E1(1.67)-0.077956684],_
[1.68, 0.076838412, E1(1.68), E1(1.68)-0.076838412],_
[1.69, 0.075737839, E1(1.69), E1(1.69)-0.075737839],_
[1.70, 0.074654644, E1(1.70), E1(1.70)-0.074654644],_
[1.71, 0.073588518, E1(1.71), E1(1.71)-0.073588518],_
[1.72, 0.072539154, E1(1.72), E1(1.72)-0.072539154],_
[1.73, 0.071506255, E1(1.73), E1(1.73)-0.071506255],_
[1.74, 0.070489527, E1(1.74), E1(1.74)-0.070489527],_
[1.75, 0.069488685, E1(1.75), E1(1.75)-0.069488685],_
[1.76, 0.068503447, E1(1.76), E1(1.76)-0.068503447],_
[1.77, 0.067533539, E1(1.77), E1(1.77)-0.067533539],_
[1.78, 0.066578691, E1(1.78), E1(1.78)-0.066578691],_
[1.79, 0.065638641, E1(1.79), E1(1.79)-0.065638641],_
[1.80, 0.064713129, E1(1.80), E1(1.80)-0.064713129],_
[1.81, 0.063801903, E1(1.81), E1(1.81)-0.063801903],_
[1.82, 0.062904715, E1(1.82), E1(1.82)-0.062904715],_
[1.83, 0.062021320, E1(1.83), E1(1.83)-0.062021320],_
[1.84, 0.061151482, E1(1.84), E1(1.84)-0.061151482],_
[1.85, 0.060294967, E1(1.85), E1(1.85)-0.060294967],_
[1.86, 0.059451545, E1(1.86), E1(1.86)-0.059451545],_
[1.87, 0.058620994, E1(1.87), E1(1.87)-0.058620994],_
[1.88, 0.057803091, E1(1.88), E1(1.88)-0.057803091],_
[1.89, 0.056997623, E1(1.89), E1(1.89)-0.056997623],_
[1.90, 0.056204378, E1(1.90), E1(1.90)-0.056204378],_
[1.91, 0.055423149, E1(1.91), E1(1.91)-0.055423149],_
[1.92, 0.054653731, E1(1.92), E1(1.92)-0.054653731],_
[1.93, 0.053895927, E1(1.93), E1(1.93)-0.053895927],_
[1.94, 0.053149540, E1(1.94), E1(1.94)-0.053149540],_
[1.95, 0.052414380, E1(1.95), E1(1.95)-0.052414380],_
[1.96, 0.051690257, E1(1.96), E1(1.96)-0.051690257],_
[1.97, 0.050976988, E1(1.97), E1(1.97)-0.050976988],_
[1.98, 0.050274392, E1(1.98), E1(1.98)-0.050274392],_
[1.99, 0.049582291, E1(1.99), E1(1.99)-0.049582291],_
[2.00, 0.048900511, E1(2.00), E1(2.00)-0.048900511]]::LIST(LIST(DFLOAT))
 

   (4)
   [[0.5,0.55977359500000001,0.55977359477616084,- 2.2383916942203541E-10],

     [0.51000000000000001, 0.54782235199999996, 0.54782235178082872,
      - 2.1917123671499894E-10]
     ,

     [0.52000000000000002, 0.53621979799999997, 0.53621979784563623,
      - 1.5436374400934483E-10]
     ,

     [0.53000000000000003, 0.52495150999999995, 0.52495151011486541,
      1.148654504845581E-10]
     ,

     [0.54000000000000004, 0.51400388600000002, 0.51400388570224909,
      - 2.9775093501882566E-10]
     ,

     [0.55000000000000004, 0.50336408099999996, 0.50336408139239386,
      3.9239389515444145E-10]
     ,

     [0.56000000000000005, 0.49301995899999995, 0.49301995877649291,
      - 2.235070462042188E-10]
     ,

     [0.56999999999999995, 0.48296003399999998, 0.48296003424511297,
      2.451129854641465E-10]
     ,

     [0.57999999999999996, 0.47317343299999998, 0.47317343333112627,
      3.3112629305165342E-10]
     ,

     [0.58999999999999997, 0.46364984899999995, 0.46364984895652972,
      - 4.3470227417685692E-11]
     ,

     [0.59999999999999998, 0.45437950299999996, 0.45437950318940223,
      1.8940227164421231E-10]
     ,
    [0.60999999999999999,0.445353112,0.44535311216282059,1.628205903436708E-10],
    [0.62,0.43656185400000003,0.43656185384719159,- 1.5280843257414745E-10],

     [0.62999999999999989, 0.42799733799999995, 0.42799733840201865,
      4.0201869611067309E-10]
     ,

     [0.6399999999999999, 0.419651581, 0.41965158086333343,
      - 1.3666656695221491E-10]
     ,

     [0.64999999999999991, 0.41151697599999998, 0.41151697594947972,
      - 5.0520254646357898E-11]
     ,

     [0.65999999999999992, 0.40358627499999999, 0.40358627479116593,
      - 2.0883406115501657E-10]
     ,

     [0.66999999999999993, 0.39585256299999999, 0.39585256341213704,
      4.1213704671250184E-10]
     ,

     [0.67999999999999994, 0.38830924300000003, 0.38830924280482576,
      - 1.9517426563808726E-10]
     ,

     [0.68999999999999995, 0.38095000999999995, 0.38095001046125104,
      4.6125109287586952E-10]
     ,

     [0.69999999999999996, 0.37376884300000002, 0.37376884323350923,
      2.3350921196652052E-10]
     ,

     [0.70999999999999996, 0.36675998099999996, 0.36675998141067723,
      4.1067726996857346E-10]
     ,

     [0.71999999999999997, 0.35991791399999995, 0.35991791391003464,
      - 8.9965312977113854E-11]
     ,
    [0.72999999999999998,0.353237364,0.35323736449036641,4.9036641414090809E-10]
     ,

     [0.73999999999999999, 0.34671327899999999, 0.34671327890389447,
      - 9.6105512437105745E-11]
     ,
    [0.75,0.34034081299999996,0.34034081291123008,- 8.8769880335348716E-11],

     [0.76000000000000001, 0.33411532099999997, 0.33411532109074837,
      9.0748408787533208E-11]
     ,

     [0.77000000000000002, 0.32803234599999997, 0.3280323463800649,
      3.8006492397713032E-10]
     ,

     [0.78000000000000003, 0.32208760999999997, 0.32208761029292271,
      2.9292274161818455E-10]
     ,

     [0.79000000000000004, 0.31627700399999997, 0.31627700375985612,
      - 2.4014384925052923E-10]
     ,

     [0.80000000000000004, 0.31059657899999998, 0.31059657854554301,
      - 4.5445697205437341E-10]
     ,
    [0.81000000000000005,0.305042539,0.30504253919985258,1.9985257893040398E-10]
     ,

     [0.81999999999999995, 0.29961123599999995, 0.29961123550328905,
      - 4.9671089463743101E-10]
     ,

     [0.82999999999999996, 0.29429915499999998, 0.29429915537086676,
      3.7086678172926213E-10]
     ,

     [0.83999999999999997, 0.28910291799999999, 0.28910291818146794,
      1.8146795177642616E-10]
     ,

     [0.84999999999999998, 0.28401926899999996, 0.28401926850246151,
      - 4.975384548799866E-10]
     ,

     [0.85999999999999999, 0.27904507000000001, 0.27904507018183955,
      1.818395434227682E-10]
     ,
    [0.87,0.27417730099999998,0.27417730078237235,- 2.1762763813271135E-10],

     [0.87999999999999989, 0.26941304599999999, 0.26941304633432028,
      3.3432029367119753E-10]
     ,

     [0.8899999999999999, 0.26474949599999997, 0.26474949638510148,
      3.8510150623949357E-10]
     ,

     [0.89999999999999991, 0.26018393899999998, 0.26018393932599976,
      3.2599978272429553E-10]
     ,

     [0.90999999999999992, 0.25571375799999996, 0.25571375797753937,
      - 2.2460588944284154E-11]
     ,

     [0.91999999999999993, 0.25133642499999997, 0.25133642541656154,
      4.1656156302138925E-10]
     ,
    [0.92999999999999994,0.247049501,0.24704950102931619,2.931618836576888E-11],

     [0.93999999999999995, 0.24285062699999999, 0.24285062677606084,
      - 2.2393914500540291E-10]
     ,

     [0.94999999999999996, 0.23873752399999998, 0.23873752365373468,
      - 3.4626529421544205E-10]
     ,

     [0.95999999999999996, 0.23470798799999998, 0.23470798834425502,
      3.442550411403289E-10]
     ,
    [0.96999999999999997,0.23075989,0.23075989003689171,3.6891711907571789E-11],
    [0.97999999999999998,0.226891167,0.22689116741400336,4.1400335937247235E-10]
     ,

     [0.98999999999999999, 0.223099826, 0.22309982579017729,
      - 2.0982271475844527E-10]
     ,
    [1.,0.219383934,0.21938393439552029,3.9552028319178589E-10],

     [1.0099999999999998, 0.21574162399999999, 0.21574162379449013,
      - 2.0550985913025954E-10]
     ,
    [1.02,0.21217108299999998,0.21217108343224891,4.3224893109261586E-10],

     [1.0299999999999998, 0.20867055899999998, 0.20867055930107375,
      3.0107377702037752E-10]
     ,
    [1.04,0.20523835200000001,0.20523835171985608,- 2.8014393582687092E-10],

     [1.0499999999999998, 0.20187281299999998, 0.20187281322019668,
      2.2019669421169397E-10]
     ,

     [1.0600000000000001, 0.19857234699999998, 0.19857234653302808,
      - 4.6697190558830926E-10]
     ,

     [1.0699999999999998, 0.19533540299999999, 0.19533540267009875,
      - 3.2990124521070641E-10]
     ,
    [1.0800000000000001,0.192160479,0.19216047909501838,9.5018382051392791E-11],

     [1.0899999999999999, 0.18904611799999999, 0.18904611797891235,
      - 2.1087631640881455E-11]
     ,

     [1.1000000000000001, 0.18599090499999998, 0.18599090453604011,
      - 4.6395987052250121E-10]
     ,

     [1.1099999999999999, 0.18299346499999999, 0.18299346543503958,
      4.3503958768731366E-10]
     ,

     [1.1200000000000001, 0.18005246699999999, 0.18005246728171573,
      2.8171573407398398E-10]
     ,
    [1.1299999999999999,0.177166615,0.17716661516956433,1.6956433479542454E-10],

     [1.1399999999999999, 0.17433465100000001, 0.17433465129443834,
      2.9443833482467596E-10]
     ,

     [1.1499999999999999, 0.17155535399999999, 0.1715553536299986,
      - 3.7000139063714244E-10]
     ,

     [1.1599999999999999, 0.16882753499999997, 0.16882753466078662,
      - 3.3921335185205237E-10]
     ,
    [1.1699999999999999,0.16615004,0.16615004016994619,1.6994619600474437E-10],

     [1.1799999999999999, 0.16352174799999999, 0.16352174807880468,
      7.8804684999767005E-11]
     ,

     [1.1899999999999999, 0.16094156700000001, 0.1609415673356836,
      3.3568359203428599E-10]
     ,
    [1.2,0.15840843700000001,0.15840843685146253,- 1.4853748786514132E-10],
    [1.21,0.15592132399999997,0.15592132447956802,4.7956805193649643E-10],
    [1.22,0.153479226,0.15347922603818953,3.8189534867782982E-11],
    [1.23,0.15108116399999999,0.15108116437265298,3.7265299179800593E-10],
    [1.24,0.14872618799999998,0.1487261884559975,4.5599751752334328E-10],
    [1.25,0.14641337300000001,0.1464133725259103,- 4.7408971193263483E-10],

     [1.2599999999999998, 0.14414181500000001, 0.14414181525628317,
      2.5628316135950513E-10]
     ,
    [1.27,0.14191063900000001,0.14191063896174175,- 3.8258257673007279E-11],

     [1.2799999999999998, 0.13971898899999999, 0.13971898883359635,
      - 1.6640364086661918E-10]
     ,
    [1.29,0.137566032,0.13756603220574354,2.0574353332136752E-10],

     [1.2999999999999998, 0.13545095800000001, 0.13545095784912925,
      - 1.5087076032926916E-10]
     ,
    [1.3100000000000001,0.133372975,0.13337297529345732,2.9345731400454156E-10],

     [1.3199999999999998, 0.13133131399999998, 0.1313313141748999,
      1.7489992787389497E-10]
     ,

     [1.3300000000000001, 0.12932522399999999, 0.12932522360862764,
      - 3.9137235119390823E-10]
     ,

     [1.3399999999999999, 0.12735397199999998, 0.12735397158504436,
      - 4.1495562541626896E-10]
     ,
    [1.3500000000000001,0.125416844,0.12541684438866441,3.8866440621454501E-10],

     [1.3599999999999999, 0.12351314599999999, 0.12351314603863228,
      3.8632291810003494E-11]
     ,

     [1.3700000000000001, 0.12164219800000001, 0.1216421977499248,
      - 2.5007521053943549E-10]
     ,
    [1.3799999999999999,0.119803337,0.11980333741433752,4.1433752262509671E-10],
    [1.3899999999999999,0.117995919,0.11799591910039348,1.0039347131396426E-10],

     [1.3999999999999999, 0.11621931299999999, 0.11621931257135804,
      - 4.2864195526348681E-10]
     ,

     [1.4099999999999999, 0.11447290299999999, 0.11447290282058731,
      - 1.7941267915766446E-10]
     ,
    [1.4199999999999999,0.11275609,0.11275608962347,- 3.7653000162229944E-10],

     [1.4299999999999999, 0.11106828699999999, 0.11106828710526567,
      1.0526568505753175E-10]
     ,

     [1.4399999999999999, 0.10940892299999999, 0.10940892332417029,
      3.2417030171316696E-10]
     ,
    [1.45,0.10777744,0.10777743986897664,- 1.3102335882919647E-10],
    [1.46,0.106173291,0.10617329147072602,4.7072601372377676E-10],
    [1.47,0.104595946,0.10459594562777541,- 3.722245844883787E-10],
    [1.48,0.103044882,0.10304488224373409,2.4373408846756206E-10],
    [1.49,0.10151959299999999,0.10151959327774779,2.7774779698397367E-10],
    [1.5,0.100019582,0.10001958240663278,4.0663278300101524E-10],

     [1.5099999999999998, 9.8544364999999995E-2, 9.8544364698385567E-2,
      - 3.0161442787779436E-10]
     ,
    [1.52,9.7093465999999989E-2,9.7093466296618358E-2,2.9661836875582992E-10],

     [1.5299999999999998, 9.5666424E-2, 9.5666424115486925E-2,
      1.1548692557816764E-10]
     ,
    [1.54,9.4262785999999987E-2,9.4262785544698358E-2,- 4.5530162973150823E-10],

     [1.5499999999999998, 9.2882107999999991E-2, 9.2882108164209332E-2,
      1.6420934056959879E-10]
     ,

     [1.5600000000000001, 9.1523959999999988E-2, 9.1523959468236882E-2,
      - 5.3176310577107699E-10]
     ,

     [1.5699999999999998, 9.0187917000000006E-2, 9.0187916598222895E-2,
      - 4.0177711158051466E-10]
     ,

     [1.5800000000000001, 8.8873565999999987E-2, 8.887356608441227E-2,
      8.4412282719270593E-11]
     ,

     [1.5899999999999999, 8.7580504000000003E-2, 8.7580503595715009E-2,
      - 4.0428499437084042E-10]
     ,

     [1.6000000000000001, 8.6308333999999987E-2, 8.6308333697539708E-2,
      - 3.0246027904468065E-10]
     ,

     [1.6099999999999999, 8.5056670000000001E-2, 8.505666961730296E-2,
      - 3.8269704072391164E-10]
     ,

     [1.6200000000000001, 8.3825132999999996E-2, 8.3825133017319142E-2,
      1.7319146117245054E-11]
     ,

     [1.6299999999999999, 8.2613354E-2, 8.2613353774808662E-2,
      - 2.25191337799302E-10]
     ,

     [1.6399999999999999, 8.1420969999999995E-2, 8.1420969768751739E-2,
      - 2.312482566546592E-10]
     ,

     [1.6499999999999999, 8.0247626999999988E-2, 8.0247626673343175E-2,
      - 3.266568127102687E-10]
     ,

     [1.6599999999999999, 7.9092977999999994E-2, 7.9092977757806437E-2,
      - 2.4219355687638E-10]
     ,

     [1.6699999999999999, 7.7956683999999998E-2, 7.7956683692333661E-2,
      - 3.0766633685175293E-10]
     ,

     [1.6799999999999999, 7.6838411999999995E-2, 7.6838412359934938E-2,
      3.5993494296171491E-10]
     ,

     [1.6899999999999999, 7.5737839000000001E-2, 7.5737838673983315E-2,
      - 3.2601668586984545E-10]
     ,
    [1.7,7.4654643999999992E-2,7.4654644401253134E-2,4.0125314182404281E-10],
    [1.71,7.3588517999999992E-2,7.3588517990256452E-2,- 9.7435393087152988E-12],
    [1.72,7.2539153999999995E-2,7.2539154404693273E-2,4.0469327888814632E-10],
    [1.73,7.1506254999999991E-2,7.150625496183538E-2,- 3.8164610360880147E-11],
    [1.74,7.0489526999999996E-2,7.0489527175668809E-2,1.7566881282959912E-10],
    [1.75,6.9488684999999994E-2,6.9488684604638973E-2,- 3.9536102169890341E-10],

     [1.7599999999999998, 6.8503446999999995E-2, 6.8503446703828685E-2,
      - 2.9617130969938898E-10]
     ,
    [1.77,6.7533539000000004E-2,6.7533538681429417E-2,- 3.1857058657713822E-10],

     [1.7799999999999998, 6.6578690999999995E-2, 6.6578691359347131E-2,
      3.5934713538132712E-10]
     ,
    [1.79,6.5638640999999998E-2,6.5638641037815249E-2,3.7815250930606226E-11],

     [1.7999999999999998, 6.4713128999999994E-2, 6.4713129363868638E-2,
      3.6386864354920334E-10]
     ,

     [1.8100000000000001, 6.3801902999999993E-2, 6.3801903203559385E-2,
      2.0355939156502245E-10]
     ,

     [1.8199999999999998, 6.2904715E-2, 6.2904714517779348E-2,
      - 4.8222065229808209E-10]
     ,

     [1.8300000000000001, 6.2021319999999998E-2, 6.2021320241580691E-2,
      2.415806929501052E-10]
     ,

     [1.8399999999999999, 6.1151481999999993E-2, 6.1151482166870497E-2,
      1.6687050352626187E-10]
     ,

     [1.8500000000000001, 6.0294966999999998E-2, 6.0294966828373431E-2,
      - 1.7162656712477187E-10]
     ,

     [1.8599999999999999, 5.9451544999999995E-2, 5.9451545392755878E-2,
      3.9275588337162048E-10]
     ,

     [1.8700000000000001, 5.8620993999999996E-2, 5.8620993550804079E-2,
      - 4.4919591657421876E-10]
     ,

     [1.8799999999999999, 5.7803091000000001E-2, 5.7803091412567897E-2,
      4.1256789651278325E-10]
     ,

     [1.8899999999999999, 5.6997622999999997E-2, 5.6997623405359743E-2,
      4.0535974576982881E-10]
     ,

     [1.8999999999999999, 5.6204377999999999E-2, 5.620437817453483E-2,
      1.7453483103224698E-10]
     ,

     [1.9099999999999999, 5.5423148999999998E-2, 5.5423148486950624E-2,
      - 5.1304937381813076E-10]
     ,

     [1.9199999999999999, 5.4653730999999997E-2, 5.4653731137026984E-2,
      1.3702698697937166E-10]
     ,

     [1.9299999999999999, 5.3895926999999996E-2, 5.3895926855325071E-2,
      - 1.4467492481795574E-10]
     ,

     [1.9399999999999999, 5.3149539999999995E-2, 5.3149540219563529E-2,
      2.1956353402075024E-10]
     ,
    [1.95,5.2414379999999997E-2,5.241437956799877E-2,- 4.3200122645803418E-10],
    [1.96,5.1690257000000003E-2,5.1690256915094213E-2,- 8.4905790731504283E-11],
    [1.97,5.0976988000000001E-2,5.0976987869409518E-2,- 1.3059048287189512E-10],
    [1.98,5.0274392000000001E-2,5.0274391553639219E-2,- 4.4636078166959692E-10],
    [1.99,4.9582291000000001E-2,4.958229052673635E-2,- 4.7326365049116248E-10],
    [2.,4.8900510999999994E-2,4.8900510708061007E-2,- 2.91938986873852E-10]]
                                                  Type: List List DoubleFloat
--R 
--R
--R   (4)
--R   [[0.5,0.55977359500000001,0.55977359477616084,- 2.2383916942203541E-10],
--R
--R     [0.51000000000000001, 0.54782235199999996, 0.54782235178082872,
--R      - 2.1917123671499894E-10]
--R     ,
--R
--R     [0.52000000000000002, 0.53621979799999997, 0.53621979784563623,
--R      - 1.5436374400934483E-10]
--R     ,
--R
--R     [0.53000000000000003, 0.52495150999999995, 0.52495151011486541,
--R      1.148654504845581E-10]
--R     ,
--R
--R     [0.54000000000000004, 0.51400388600000002, 0.51400388570224909,
--R      - 2.9775093501882566E-10]
--R     ,
--R
--R     [0.55000000000000004, 0.50336408099999996, 0.50336408139239386,
--R      3.9239389515444145E-10]
--R     ,
--R
--R     [0.56000000000000005, 0.49301995900000001, 0.49301995877649291,
--R      - 2.2350710171537003E-10]
--R     ,
--R
--R     [0.56999999999999995, 0.48296003399999998, 0.48296003424511297,
--R      2.451129854641465E-10]
--R     ,
--R
--R     [0.57999999999999996, 0.47317343299999998, 0.47317343333112627,
--R      3.3112629305165342E-10]
--R     ,
--R
--R     [0.58999999999999997, 0.463649849, 0.46364984895652972,
--R      - 4.3470282928836923E-11]
--R     ,
--R
--R     [0.59999999999999998, 0.45437950300000002, 0.45437950318940223,
--R      1.8940221613306107E-10]
--R     ,
--R    [0.60999999999999999,0.445353112,0.44535311216282059,1.628205903436708E-10],
--R    [0.62,0.43656185400000003,0.43656185384719148,- 1.5280854359644991E-10],
--R    [0.63,0.427997338,0.42799733840201848,4.0201847406606817E-10],
--R
--R     [0.64000000000000001, 0.419651581, 0.41965158086333326,
--R      - 1.366667334856686E-10]
--R     ,
--R
--R     [0.65000000000000002, 0.41151697599999998, 0.41151697594947956,
--R      - 5.0520421179811592E-11]
--R     ,
--R
--R     [0.66000000000000003, 0.40358627499999999, 0.40358627479116588,
--R      - 2.088341166661678E-10]
--R     ,
--R
--R     [0.67000000000000004, 0.39585256299999999, 0.39585256341213687,
--R      4.1213688017904815E-10]
--R     ,
--R
--R     [0.68000000000000005, 0.38830924300000003, 0.38830924280482559,
--R      - 1.9517443217154096E-10]
--R     ,
--R
--R     [0.68999999999999995, 0.38095001000000001, 0.38095001046125104,
--R      4.6125103736471829E-10]
--R     ,
--R
--R     [0.69999999999999996, 0.37376884300000002, 0.37376884323350923,
--R      2.3350921196652052E-10]
--R     ,
--R
--R     [0.70999999999999996, 0.36675998100000001, 0.36675998141067723,
--R      4.1067721445742222E-10]
--R     ,
--R
--R     [0.71999999999999997, 0.35991791400000001, 0.35991791391003464,
--R      - 8.9965368488265085E-11]
--R     ,
--R    [0.72999999999999998,0.353237364,0.35323736449036641,4.9036641414090809E-10]
--R     ,
--R
--R     [0.73999999999999999, 0.34671327899999999, 0.34671327890389447,
--R      - 9.6105512437105745E-11]
--R     ,
--R    [0.75,0.34034081300000002,0.34034081291123008,- 8.8769935846499948E-11],
--R
--R     [0.76000000000000001, 0.33411532100000002, 0.33411532109074837,
--R      9.0748353276381977E-11]
--R     ,
--R
--R     [0.77000000000000002, 0.32803234599999997, 0.3280323463800649,
--R      3.8006492397713032E-10]
--R     ,
--R
--R     [0.78000000000000003, 0.32208761000000002, 0.32208761029292271,
--R      2.9292268610703331E-10]
--R     ,
--R
--R     [0.79000000000000004, 0.31627700399999997, 0.31627700375985612,
--R      - 2.4014384925052923E-10]
--R     ,
--R
--R     [0.80000000000000004, 0.31059657899999998, 0.31059657854554301,
--R      - 4.5445697205437341E-10]
--R     ,
--R    [0.81000000000000005,0.305042539,0.30504253919985258,1.9985257893040398E-10]
--R     ,
--R
--R     [0.81999999999999995, 0.299611236, 0.29961123550328894,
--R      - 4.967110611708847E-10]
--R     ,
--R
--R     [0.82999999999999996, 0.29429915499999998, 0.29429915537086676,
--R      3.7086678172926213E-10]
--R     ,
--R
--R     [0.83999999999999997, 0.28910291799999999, 0.28910291818146794,
--R      1.8146795177642616E-10]
--R     ,
--R
--R     [0.84999999999999998, 0.28401926900000002, 0.2840192685024614,
--R      - 4.975386214134403E-10]
--R     ,
--R
--R     [0.85999999999999999, 0.27904507000000001, 0.27904507018183955,
--R      1.818395434227682E-10]
--R     ,
--R    [0.87,0.27417730099999998,0.27417730078237224,- 2.1762774915501382E-10],
--R    [0.88,0.26941304599999999,0.26941304633432023,3.343202381600463E-10],
--R
--R     [0.89000000000000001, 0.26474949599999997, 0.26474949638510148,
--R      3.8510150623949357E-10]
--R     ,
--R
--R     [0.90000000000000002, 0.26018393899999998, 0.26018393932599954,
--R      3.259995606796906E-10]
--R     ,
--R
--R     [0.91000000000000003, 0.25571375800000001, 0.25571375797753926,
--R      - 2.2460755477737848E-11]
--R     ,
--R
--R     [0.92000000000000004, 0.25133642499999997, 0.25133642541656154,
--R      4.1656156302138925E-10]
--R     ,
--R    [0.93000000000000005,0.247049501,0.24704950102931605,2.9316049587890802E-11]
--R     ,
--R
--R     [0.93999999999999995, 0.24285062700000001, 0.24285062677606084,
--R      - 2.2393917276097852E-10]
--R     ,
--R
--R     [0.94999999999999996, 0.23873752400000001, 0.23873752365373468,
--R      - 3.4626532197101767E-10]
--R     ,
--R
--R     [0.95999999999999996, 0.23470798800000001, 0.23470798834425491,
--R      3.4425490236245082E-10]
--R     ,
--R    [0.96999999999999997,0.23075989,0.23075989003689171,3.6891711907571789E-11],
--R    [0.97999999999999998,0.226891167,0.22689116741400336,4.1400335937247235E-10]
--R     ,
--R
--R     [0.98999999999999999, 0.223099826, 0.22309982579017718,
--R      - 2.0982282578074773E-10]
--R     ,
--R    [1.,0.219383934,0.21938393439552029,3.9552028319178589E-10],
--R    [1.01,0.21574162399999999,0.21574162379448991,- 2.0551008117486447E-10],
--R    [1.02,0.21217108300000001,0.2121710834322488,4.3224879231473778E-10],
--R    [1.03,0.20867055900000001,0.20867055930107367,3.0107366599807506E-10],
--R    [1.04,0.20523835200000001,0.20523835171985597,- 2.8014404684917338E-10],
--R    [1.05,0.20187281300000001,0.20187281322019657,2.2019655543381589E-10],
--R
--R     [1.0600000000000001, 0.19857234700000001, 0.19857234653302808,
--R      - 4.6697193334388487E-10]
--R     ,
--R
--R     [1.0700000000000001, 0.19533540299999999, 0.19533540267009863,
--R      - 3.2990135623300887E-10]
--R     ,
--R    [1.0800000000000001,0.192160479,0.19216047909501838,9.5018382051392791E-11],
--R
--R     [1.0900000000000001, 0.18904611800000001, 0.18904611797891213,
--R      - 2.1087881441061995E-11]
--R     ,
--R
--R     [1.1000000000000001, 0.18599090500000001, 0.18599090453604011,
--R      - 4.6395989827807682E-10]
--R     ,
--R
--R     [1.1100000000000001, 0.18299346499999999, 0.1829934654350395,
--R      4.3503950442058681E-10]
--R     ,
--R
--R     [1.1200000000000001, 0.18005246699999999, 0.18005246728171573,
--R      2.8171573407398398E-10]
--R     ,
--R    [1.1299999999999999,0.177166615,0.17716661516956422,1.6956422377312208E-10],
--R
--R     [1.1399999999999999, 0.17433465100000001, 0.17433465129443812,
--R      2.9443811278007104E-10]
--R     ,
--R
--R     [1.1499999999999999, 0.17155535399999999, 0.1715553536299986,
--R      - 3.7000139063714244E-10]
--R     ,
--R
--R     [1.1599999999999999, 0.168827535, 0.16882753466078662,
--R      - 3.3921337960762799E-10]
--R     ,
--R    [1.1699999999999999,0.16615004,0.16615004016994619,1.6994619600474437E-10],
--R
--R     [1.1799999999999999, 0.16352174799999999, 0.16352174807880468,
--R      7.8804684999767005E-11]
--R     ,
--R
--R     [1.1899999999999999, 0.16094156700000001, 0.1609415673356836,
--R      3.3568359203428599E-10]
--R     ,
--R    [1.2,0.15840843700000001,0.15840843685146253,- 1.4853748786514132E-10],
--R    [1.21,0.155921324,0.15592132447956802,4.7956802418092082E-10],
--R    [1.22,0.153479226,0.15347922603818942,3.8189423845480519E-11],
--R    [1.23,0.15108116399999999,0.15108116437265298,3.7265299179800593E-10],
--R    [1.24,0.14872618800000001,0.14872618845599739,4.559973787454652E-10],
--R    [1.25,0.14641337300000001,0.14641337252591019,- 4.7408982295493729E-10],
--R    [1.26,0.14414181500000001,0.14414181525628297,2.5628296707047582E-10],
--R    [1.27,0.14191063900000001,0.14191063896174164,- 3.8258368695309741E-11],
--R    [1.28,0.13971898899999999,0.1397189888335964,- 1.6640358535546795E-10],
--R    [1.29,0.137566032,0.13756603220574354,2.0574353332136752E-10],
--R    [1.3,0.13545095800000001,0.13545095784912908,- 1.5087092686272285E-10],
--R    [1.3100000000000001,0.133372975,0.13337297529345732,2.9345731400454156E-10],
--R    [1.3200000000000001,0.131331314,0.13133131417489974,1.7489973358486566E-10],
--R
--R     [1.3300000000000001, 0.12932522399999999, 0.12932522360862764,
--R      - 3.9137235119390823E-10]
--R     ,
--R
--R     [1.3400000000000001, 0.12735397200000001, 0.12735397158504419,
--R      - 4.1495581970529827E-10]
--R     ,
--R    [1.3500000000000001,0.125416844,0.12541684438866441,3.8866440621454501E-10],
--R    [1.3600000000000001,0.123513146,0.12351314603863212,3.8632111398761992E-11],
--R
--R     [1.3700000000000001, 0.12164219800000001, 0.1216421977499248,
--R      - 2.5007521053943549E-10]
--R     ,
--R    [1.3799999999999999,0.119803337,0.11980333741433752,4.1433752262509671E-10],
--R    [1.3899999999999999,0.117995919,0.11799591910039325,1.0039324926935933E-10],
--R
--R     [1.3999999999999999, 0.116219313, 0.11621931257135804,
--R      - 4.2864196914127461E-10]
--R     ,
--R
--R     [1.4099999999999999, 0.114472903, 0.11447290282058709,
--R      - 1.7941291508005719E-10]
--R     ,
--R    [1.4199999999999999,0.11275609,0.11275608962347,- 3.7653000162229944E-10],
--R    [1.4299999999999999,0.111068287,0.11106828710526567,1.0526567117974395E-10],
--R
--R     [1.4399999999999999, 0.10940892300000001, 0.10940892332417007,
--R      3.2417006579077423E-10]
--R     ,
--R    [1.45,0.10777744,0.10777743986897642,- 1.3102358087380139E-10],
--R    [1.46,0.106173291,0.10617329147072579,4.7072579167917183E-10],
--R    [1.47,0.104595946,0.10459594562777519,- 3.7222480653298362E-10],
--R    [1.48,0.103044882,0.10304488224373387,2.4373386642295714E-10],
--R    [1.49,0.10151959300000001,0.10151959327774779,2.7774778310618586E-10],
--R    [1.5,0.100019582,0.10001958240663256,4.0663256095641032E-10],
--R    [1.51,9.8544364999999995E-2,9.85443646983854E-2,- 3.0161459441124805E-10],
--R    [1.52,9.7093466000000003E-2,9.7093466296618358E-2,2.9661835487804211E-10],
--R    [1.53,9.5666424E-2,9.5666424115486592E-2,1.1548659251126026E-10],
--R    [1.54,9.4262786000000001E-2,9.4262785544698136E-2,- 4.5530186565390096E-10],
--R    [1.55,9.2882108000000005E-2,9.2882108164209165E-2,1.6420916015835729E-10],
--R
--R     [1.5600000000000001, 9.1523960000000001E-2, 9.152395946823666E-2,
--R      - 5.3176334169346973E-10]
--R     ,
--R
--R     [1.5700000000000001, 9.0187917000000006E-2, 9.0187916598222728E-2,
--R      - 4.0177727811396835E-10]
--R     ,
--R
--R     [1.5800000000000001, 8.8873566000000001E-2, 8.8873566084412048E-2,
--R      8.441204679687786E-11]
--R     ,
--R
--R     [1.5900000000000001, 8.7580504000000003E-2, 8.7580503595714843E-2,
--R      - 4.0428516090429412E-10]
--R     ,
--R
--R     [1.6000000000000001, 8.6308334E-2, 8.6308333697539708E-2,
--R      - 3.0246029292246845E-10]
--R     ,
--R
--R     [1.6100000000000001, 8.5056670000000001E-2, 8.5056669617302794E-2,
--R      - 3.8269720725736533E-10]
--R     ,
--R
--R     [1.6200000000000001, 8.3825132999999996E-2, 8.3825133017319142E-2,
--R      1.7319146117245054E-11]
--R     ,
--R
--R     [1.6299999999999999, 8.2613354E-2, 8.2613353774808662E-2,
--R      - 2.25191337799302E-10]
--R     ,
--R
--R     [1.6399999999999999, 8.1420969999999995E-2, 8.1420969768751517E-2,
--R      - 2.3124847869926413E-10]
--R     ,
--R
--R     [1.6499999999999999, 8.0247627000000002E-2, 8.0247626673343175E-2,
--R      - 3.266568265880565E-10]
--R     ,
--R
--R     [1.6599999999999999, 7.9092977999999994E-2, 7.9092977757806437E-2,
--R      - 2.4219355687638E-10]
--R     ,
--R
--R     [1.6699999999999999, 7.7956683999999998E-2, 7.7956683692333661E-2,
--R      - 3.0766633685175293E-10]
--R     ,
--R
--R     [1.6799999999999999, 7.6838411999999995E-2, 7.6838412359934938E-2,
--R      3.5993494296171491E-10]
--R     ,
--R
--R     [1.6899999999999999, 7.5737839000000001E-2, 7.5737838673983093E-2,
--R      - 3.2601690791445037E-10]
--R     ,
--R    [1.7,7.4654644000000006E-2,7.4654644401252912E-2,4.0125290590165008E-10],
--R    [1.71,7.3588518000000006E-2,7.358851799025623E-2,- 9.7437752311080317E-12],
--R    [1.72,7.2539153999999995E-2,7.2539154404693273E-2,4.0469327888814632E-10],
--R    [1.73,7.1506255000000005E-2,7.150625496183538E-2,- 3.8164624238667955E-11],
--R    [1.74,7.0489526999999996E-2,7.0489527175668809E-2,1.7566881282959912E-10],
--R    [1.75,6.9488684999999994E-2,6.9488684604638751E-2,- 3.9536124374350834E-10],
--R    [1.76,6.8503446999999995E-2,6.8503446703828352E-2,- 2.9617164276629637E-10],
--R    [1.77,6.7533539000000004E-2,6.7533538681429195E-2,- 3.1857080862174314E-10],
--R    [1.78,6.6578690999999995E-2,6.657869135934702E-2,3.5934702435902466E-10],
--R    [1.79,6.5638640999999998E-2,6.5638641037815026E-2,3.7815028886001301E-11],
--R    [1.8,6.4713128999999994E-2,6.4713129363868749E-2,3.638687545715058E-10],
--R
--R     [1.8100000000000001, 6.3801902999999993E-2, 6.3801903203559385E-2,
--R      2.0355939156502245E-10]
--R     ,
--R
--R     [1.8200000000000001, 6.2904715E-2, 6.2904714517779237E-2,
--R      - 4.8222076332038455E-10]
--R     ,
--R
--R     [1.8300000000000001, 6.2021319999999998E-2, 6.2021320241580469E-2,
--R      2.4158047090550028E-10]
--R     ,
--R
--R     [1.8400000000000001, 6.1151482E-2, 6.1151482166870164E-2,
--R      1.6687016352046058E-10]
--R     ,
--R
--R     [1.8500000000000001, 6.0294966999999998E-2, 6.0294966828373431E-2,
--R      - 1.7162656712477187E-10]
--R     ,
--R
--R     [1.8600000000000001, 5.9451545000000001E-2, 5.9451545392755656E-2,
--R      3.9275565438812166E-10]
--R     ,
--R
--R     [1.8700000000000001, 5.8620994000000003E-2, 5.8620993550804079E-2,
--R      - 4.4919592351311266E-10]
--R     ,
--R
--R     [1.8799999999999999, 5.7803091000000001E-2, 5.7803091412567897E-2,
--R      4.1256789651278325E-10]
--R     ,
--R
--R     [1.8899999999999999, 5.6997622999999997E-2, 5.6997623405359299E-2,
--R      4.0535930168061896E-10]
--R     ,
--R
--R     [1.8999999999999999, 5.6204377999999999E-2, 5.6204378174534608E-2,
--R      1.7453460898764206E-10]
--R     ,
--R
--R     [1.9099999999999999, 5.5423148999999998E-2, 5.5423148486950402E-2,
--R      - 5.1304959586273569E-10]
--R     ,
--R
--R     [1.9199999999999999, 5.4653730999999997E-2, 5.4653731137026984E-2,
--R      1.3702698697937166E-10]
--R     ,
--R
--R     [1.9299999999999999, 5.3895927000000003E-2, 5.3895926855324849E-2,
--R      - 1.4467515380145457E-10]
--R     ,
--R
--R     [1.9399999999999999, 5.3149540000000002E-2, 5.3149540219563307E-2,
--R      2.1956330503725141E-10]
--R     ,
--R    [1.95,5.2414380000000003E-2,5.2414379567998548E-2,- 4.3200145544153301E-10],
--R    [1.96,5.1690257000000003E-2,5.1690256915094213E-2,- 8.4905790731504283E-11],
--R    [1.97,5.0976988000000001E-2,5.0976987869409074E-2,- 1.3059092696110497E-10],
--R    [1.98,5.0274392000000001E-2,5.0274391553638775E-2,- 4.4636122575880677E-10],
--R    [1.99,4.9582291000000001E-2,4.9582290526736128E-2,- 4.732638725357674E-10],
--R    [2.,4.8900511000000001E-2,4.8900510708061007E-2,- 2.9193899381274591E-10]]
--R                                                  Type: List List DoubleFloat
--E 4
--S 5 of 7
g(x)==x * %e^x * E1(x)::DFLOAT
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 5
--S 6 of 7
[[2.0,0.722657234,g(2.0),g(2.0)-0.722657234],_
[2.1,0.730791502,g(2.1),g(2.1)-0.730791502],_
[2.2,0.738431132,g(2.2),g(2.2)-0.738431132],_
[2.3,0.745622149,g(2.3),g(2.3)-0.745622149],_
[2.4,0.752404829,g(2.4),g(2.4)-0.752404829],_
[2.5,0.758814592,g(2.5),g(2.5)-0.758814592],_
[2.6,0.764882722,g(2.6),g(2.6)-0.764882722],_
[2.7,0.770636987,g(2.7),g(2.7)-0.770636987],_
[2.8,0.776102123,g(2.8),g(2.8)-0.776102123],_
[2.9,0.781300252,g(2.9),g(2.9)-0.781300252],_
[3.0,0.786251221,g(3.0),g(3.0)-0.786251221],_
[3.1,0.790972800,g(3.1),g(3.1)-0.790972800],_
[3.2,0.795481422,g(3.2),g(3.2)-0.795481422],_
[3.3,0.799791408,g(3.3),g(3.3)-0.799791408],_
[3.4,0.803916127,g(3.4),g(3.4)-0.803916127],_
[3.5,0.807867661,g(3.5),g(3.5)-0.807867661],_
[3.6,0.811657037,g(3.6),g(3.6)-0.811657037],_
[3.7,0.815294342,g(3.7),g(3.7)-0.815294342],_
[3.8,0.818788821,g(3.8),g(3.8)-0.818788821],_
[3.9,0.822148967,g(3.9),g(3.9)-0.822148967],_
[4.0,0.825382500,g(4.0),g(4.0)-0.825382500],_
[4.1,0.828496926,g(4.1),g(4.1)-0.828496926],_
[4.2,0.831498602,g(4.2),g(4.2)-0.831498602],_
[4.3,0.834393794,g(4.3),g(4.3)-0.834393794],_
[4.4,0.837188207,g(4.4),g(4.4)-0.837188207],_
[4.5,0.839887144,g(4.5),g(4.5)-0.839887144],_
[4.6,0.842495539,g(4.6),g(4.6)-0.842495539],_
[4.7,0.845017971,g(4.7),g(4.7)-0.845017971],_
[4.8,0.847458721,g(4.8),g(4.8)-0.847458721],_
[4.9,0.849821778,g(4.9),g(4.9)-0.849821778],_
[5.0,0.852110880,g(5.0),g(5.0)-0.852110880],_
[5.1,0.854329519,g(5.1),g(5.1)-0.854329519],_
[5.2,0.856480958,g(5.2),g(5.2)-0.856480958],_
[5.3,0.858568275,g(5.3),g(5.3)-0.858568275],_
[5.4,0.860594348,g(5.4),g(5.4)-0.860594348],_
[5.5,0.862561885,g(5.5),g(5.5)-0.862561885],_
[5.6,0.864473436,g(5.6),g(5.6)-0.864473436],_
[5.7,0.866331399,g(5.7),g(5.7)-0.866331399],_
[5.8,0.868138040,g(5.8),g(5.8)-0.868138040],_
[5.9,0.869895494,g(5.9),g(5.9)-0.869895494],_
[6.0,0.871605775,g(6.0),g(6.0)-0.871605775],_
[6.1,0.873270793,g(6.1),g(6.1)-0.873270793],_
[6.2,0.874892347,g(6.2),g(6.2)-0.874892347],_
[6.3,0.876472150,g(6.3),g(6.3)-0.876472150],_
[6.4,0.878011816,g(6.4),g(6.4)-0.878011816],_
[6.5,0.879512881,g(6.5),g(6.5)-0.879512881],_
[6.6,0.880976797,g(6.6),g(6.6)-0.880976797],_
[6.7,0.882404955,g(6.7),g(6.7)-0.882404955],_
[6.8,0.883798662,g(6.8),g(6.8)-0.883798662],_
[6.9,0.885159176,g(6.9),g(6.9)-0.885159176],_
[7.0,0.886487675,g(7.0),g(7.0)-0.886487675],_
[7.1,0.887785294,g(7.1),g(7.1)-0.887785294],_
[7.2,0.889053119,g(7.2),g(7.2)-0.889053119],_
[7.3,0.890292173,g(7.3),g(7.3)-0.890292173],_
[7.4,0.891503440,g(7.4),g(7.4)-0.891503440],_
[7.5,0.892687854,g(7.5),g(7.5)-0.892687854],_
[7.6,0.893846312,g(7.6),g(7.6)-0.893846312],_
[7.7,0.894979666,g(7.7),g(7.7)-0.894979666],_
[7.8,0.896088737,g(7.8),g(7.8)-0.896088737],_
[7.9,0.897174302,g(7.9),g(7.9)-0.897174302],_
[8.0,0.898237113,g(8.0),g(8.0)-0.898237113],_
[8.1,0.899277888,g(8.1),g(8.1)-0.899277888],_
[8.2,0.900297306,g(8.2),g(8.2)-0.900297306],_
[8.3,0.901296033,g(8.3),g(8.3)-0.901296033],_
[8.4,0.902274695,g(8.4),g(8.4)-0.902274695],_
[8.5,0.903233900,g(8.5),g(8.5)-0.903233900],_
[8.6,0.904174228,g(8.6),g(8.6)-0.904174228],_
[8.7,0.905096235,g(8.7),g(8.7)-0.905096235],_
[8.8,0.906000459,g(8.8),g(8.8)-0.906000459],_
[8.9,0.906887414,g(8.9),g(8.9)-0.906887414],_
[9.0,0.907757602,g(9.0),g(9.0)-0.907757602],_
[9.1,0.908611483,g(9.1),g(9.1)-0.908611483],_
[9.2,0.909449530,g(9.2),g(9.2)-0.909449530],_
[9.3,0.910272177,g(9.3),g(9.3)-0.910272177],_
[9.4,0.911079850,g(9.4),g(9.4)-0.911079850],_
[9.5,0.911872958,g(9.5),g(9.5)-0.911872958],_
[9.6,0.912651897,g(9.6),g(9.6)-0.912651897],_
[9.7,0.913417043,g(9.7),g(9.7)-0.913417043],_
[9.8,0.914168766,g(9.8),g(9.8)-0.914168766],_
[9.9,0.914907418,g(9.9),g(9.9)-0.914907418],_
[10.0,0.915633339,g(10.0),g(10.0)-0.915633339]]
 
   Compiling function g with type Float -> Expression DoubleFloat 

   (6)
   [[2.,0.72265723399999993,0.72265723377644353,- 2.2355639561766338E-10],

     [2.0999999999999996, 0.73079150199999998, 0.73079150228850687,
      2.8850688504888922E-10]
     ,

     [2.2000000000000002, 0.73843113199999999, 0.73843113069659072,
      - 1.3034092694041988E-9]
     ,

     [2.2999999999999998, 0.7456221489999999, 0.74562214881923949,
      - 1.8076040664283255E-10]
     ,

     [2.3999999999999999, 0.75240482900000005, 0.75240483025619209,
      1.2561920392784032E-9]
     ,
    [2.5,0.75881459200000001,0.75881459121495154,- 7.8504847067506489E-10],

     [2.5999999999999996, 0.76488272199999996, 0.7648827221797786,
      1.7977863642215652E-10]
     ,

     [2.7000000000000002, 0.77063698700000005, 0.77063698825334548,
      1.2533454274432643E-9]
     ,

     [2.7999999999999998, 0.77610212300000003, 0.77610212535833478,
      2.3583347497080354E-9]
     ,

     [2.8999999999999999, 0.78130025199999997, 0.781300253147442,
      1.1474420302803878E-9]
     ,
    [3.,0.78625122099999989,0.786251220765942,- 2.3405788418529028E-10],

     [3.0999999999999996, 0.79097280000000003, 0.79097289808240079,
      9.8082400756815957E-8]
     ,

     [3.2000000000000002, 0.79548142199999994, 0.79548142232757213,
      3.2757219159407214E-10]
     ,

     [3.2999999999999998, 0.79979140799999993, 0.79979140803710758,
      3.7107650285861382E-11]
     ,

     [3.3999999999999999, 0.80391612699999992, 0.80391612661328316,
      - 3.8671676971802071E-10]
     ,
    [3.5,0.80786766099999996,0.80786766059303128,- 4.0696868097711558E-10],

     [3.5999999999999996, 0.81165703700000003, 0.81165703674708656,
      - 2.5291346794631409E-10]
     ,

     [3.7000000000000002, 0.81529434199999995, 0.81529434137295376,
      - 6.2704619274711604E-10]
     ,

     [3.7999999999999998, 0.81878882100000006, 0.81878882054065494,
      - 4.5934511749834428E-10]
     ,

     [3.8999999999999999, 0.82214896699999995, 0.8221489675671817,
      5.6718174601400051E-10]
     ,
    [4.,0.82538249999999991,0.82538259960420768,9.9604207770553899E-8],

     [4.0999999999999996, 0.82849692599999991, 0.82849692490969951,
      - 1.0903004055151655E-9]
     ,

     [4.1999999999999993, 0.83149860199999992, 0.83149860211639404,
      1.1639411656716447E-10]
     ,

     [4.2999999999999998, 0.83439379399999991, 0.83439379260257418,
      - 1.3974257306870186E-9]
     ,

     [4.4000000000000004, 0.83718820699999996, 0.83718820689462148,
      - 1.0537848371683367E-10]
     ,
    [4.5,0.83988714399999997,0.83988714589085944,1.8908594690003611E-9],

     [4.5999999999999996, 0.84249553899999996, 0.84249553757701467,
      - 1.4229852851599389E-9]
     ,

     [4.6999999999999993, 0.84501797099999998, 0.84501796980531507,
      - 1.1946849065580523E-9]
     ,

     [4.7999999999999998, 0.84745872099999997, 0.84745871962692321,
      - 1.3730767634001495E-9]
     ,

     [4.9000000000000004, 0.84982177799999992, 0.84982177959827732,
      1.5982773993172827E-9]
     ,
    [5.,0.8521108799999999,0.85211088142366143,1.4236615220042381E-9],

     [5.0999999999999996, 0.85432951899999998, 0.85432951724709605,
      - 1.7529039331165563E-9]
     ,

     [5.1999999999999993, 0.8564809579999999, 0.8564809588648743,
      8.6487439432403335E-10]
     ,

     [5.2999999999999998, 0.85856827499999999, 0.85856827509448064,
      9.4480645529415597E-11]
     ,

     [5.4000000000000004, 0.86059434800000001, 0.86059434750532948,
      - 4.946705267627749E-10]
     ,
    [5.5,0.86256188499999997,0.86256188469070161,- 3.0929836469795191E-10],

     [5.5999999999999996, 0.86447343599999993, 0.86447343523800857,
      - 7.6199135889964964E-10]
     ,

     [5.6999999999999993, 0.86633139899999989, 0.8663313995352464,
      5.3524651377756527E-10]
     ,

     [5.7999999999999998, 0.86813804000000006, 0.86813804053493893,
      5.3493887097744164E-10]
     ,

     [5.9000000000000004, 0.86989549399999999, 0.86989549358247464,
      - 4.1752534762906635E-10]
     ,
    [6.,0.87160577499999992,0.87160577540332174,4.0332182038582687E-10],

     [6.0999999999999996, 0.87327079299999999, 0.8732707923327413,
      - 6.6725869274364413E-10]
     ,

     [6.1999999999999993, 0.87489234699999996, 0.87489234786216596,
      8.6216600525546028E-10]
     ,

     [6.2999999999999998, 0.87647214999999989, 0.87647214956817143,
      - 4.318284618776147E-10]
     ,

     [6.4000000000000004, 0.87801181599999989, 0.87801181548273144,
      - 5.1726845029520518E-10]
     ,
    [6.5,0.87951288099999991,0.87951287995710281,- 1.0428971020104427E-9],

     [6.5999999999999996, 0.88097679699999998, 0.88097679906610149,
      2.0661015120992943E-9]
     ,

     [6.6999999999999993, 0.88240495499999994, 0.8824049555946607,
      5.946607650741953E-10]
     ,

     [6.7999999999999998, 0.88379866200000001, 0.88379866364416337,
      1.6441633610142503E-9]
     ,

     [6.9000000000000004, 0.88515917599999994, 0.88515917289225332,
      - 3.1077466156048672E-9]
     ,
    [7.,0.88648767499999992,0.88648767253642946,- 2.4635704587439022E-9],

     [7.0999999999999996, 0.88778529399999995, 0.8877852949486843,
      9.4868435329686918E-10]
     ,

     [7.1999999999999993, 0.88905311899999995, 0.88905311906582607,
      6.5826122330747694E-11]
     ,

     [7.2999999999999998, 0.89029217299999996, 0.89029217353766832,
      5.3766835428348259E-10]
     ,

     [7.4000000000000004, 0.89150343999999992, 0.89150343965322676,
      - 3.4677316573805683E-10]
     ,
    [7.5,0.89268785399999995,0.89268785406308437,6.308442657143587E-11],

     [7.5999999999999996, 0.89384631199999998, 0.89384631131444836,
      - 6.8555161547578791E-10]
     ,

     [7.6999999999999993, 0.89497966600000001, 0.89497966621388259,
      2.1388257831489454E-10]
     ,

     [7.7999999999999998, 0.89608873699999991, 0.89608873603132189,
      - 9.6867802668043623E-10]
     ,

     [7.9000000000000004, 0.89717430200000003, 0.8971743025577732,
      5.5777316099181462E-10]
     ,
    [8.,0.89823711299999998,0.89823711402799578,1.0279957995962263E-9],

     [8.0999999999999996, 0.89927788799999997, 0.89927788691844668,
      - 1.0815532913710513E-9]
     ,

     [8.1999999999999993, 0.90029730599999991, 0.90029730762992677,
      1.6299268601471795E-9]
     ,

     [8.3000000000000007, 0.90129603299999994, 0.90129603406349024,
      1.0634902958273074E-9]
     ,

     [8.3999999999999986, 0.90227469500000002, 0.90227469709753483,
      2.0975348125062965E-9]
     ,
    [8.5,0.90323390000000003,0.90323390197320852,1.9732084854950926E-9],

     [8.5999999999999996, 0.90417422800000002, 0.90417422959485139,
      1.594851362085592E-9]
     ,

     [8.6999999999999993, 0.90509623500000003, 0.90509623775141723,
      2.7514172051823493E-9]
     ,

     [8.8000000000000007, 0.90600045899999992, 0.90600046226454201,
      3.2645420811050485E-9]
     ,

     [8.8999999999999986, 0.90688741399999995, 0.90688741806836426,
      4.0683643121042223E-9]
     ,
    [9.,0.907757602,0.9077576002257679,- 1.7742320945757228E-9],

     [9.0999999999999996, 0.90861148300000005, 0.9086114848854826,
      1.885482547869799E-9]
     ,

     [9.1999999999999993, 0.90944952999999995, 0.90944953018395813,
      1.8395818202066039E-10]
     ,

     [9.3000000000000007, 0.91027217699999996, 0.91027217709579156,
      9.5791596876892982E-11]
     ,

     [9.3999999999999986, 0.91107984999999991, 0.91107985023607507,
      2.3607515942103419E-10]
     ,
    [9.5,0.91187295800000001,0.91187295861782758,6.1782756688444351E-10],

     [9.5999999999999996, 0.91265189699999993, 0.91265189636747834,
      - 6.3252159065996238E-10]
     ,

     [9.6999999999999993, 0.91341704299999993, 0.91341704340103613,
      4.0103620424503106E-10]
     ,

     [9.8000000000000007, 0.91416876599999997, 0.91416876606351216,
      6.3512195502823943E-11]
     ,

     [9.8999999999999986, 0.91490741799999997, 0.9149074177339076,
      - 2.6609237036012701E-10]
     ,
    [10.,0.91563333899999999,0.91563333939788116,3.9788117245365129E-10]]
                                       Type: List List Expression DoubleFloat
--R 
--R   Compiling function g with type Float -> Expression DoubleFloat 
--R
--R   (6)
--R   [[2.,0.72265723400000004,0.72265723377644353,- 2.2355650663996585E-10],
--R
--R     [2.1000000000000001, 0.73079150199999998, 0.73079150228850298,
--R      2.8850299926830303E-10]
--R     ,
--R
--R     [2.2000000000000002, 0.73843113199999999, 0.73843113069659072,
--R      - 1.3034092694041988E-9]
--R     ,
--R
--R     [2.2999999999999998, 0.74562214900000001, 0.74562214881923961,
--R      - 1.8076040664283255E-10]
--R     ,
--R
--R     [2.3999999999999999, 0.75240482900000005, 0.75240483025618621,
--R      1.2561861550963727E-9]
--R     ,
--R    [2.5,0.75881459200000001,0.75881459121494477,- 7.850552430355151E-10],
--R
--R     [2.6000000000000001, 0.76488272199999996, 0.76488272217978248,
--R      1.7978252220274271E-10]
--R     ,
--R
--R     [2.7000000000000002, 0.77063698700000005, 0.77063698825333671,
--R      1.2533366566813697E-9]
--R     ,
--R
--R     [2.7999999999999998, 0.77610212300000003, 0.77610212535832457,
--R      2.3583245356562088E-9]
--R     ,
--R
--R     [2.8999999999999999, 0.78130025199999997, 0.78130025314743023,
--R      1.1474302619163268E-9]
--R     ,
--R    [3.,0.786251221,0.78625122076592868,- 2.3407131788388824E-10],
--R
--R     [3.1000000000000001, 0.79097280000000003, 0.79097289808240101,
--R      9.8082400978860562E-8]
--R     ,
--R
--R     [3.2000000000000002, 0.79548142200000005, 0.7954814223275547,
--R      3.2755465007028306E-10]
--R     ,
--R
--R     [3.2999999999999998, 0.79979140800000004, 0.79979140803702831,
--R      3.7028269339600683E-11]
--R     ,
--R
--R     [3.3999999999999999, 0.80391612700000004, 0.80391612661323797,
--R      - 3.8676206681742542E-10]
--R     ,
--R    [3.5,0.80786766099999996,0.80786766059300552,- 4.0699443815128689E-10],
--R
--R     [3.6000000000000001, 0.81165703700000003, 0.81165703674711587,
--R      - 2.5288415805846398E-10]
--R     ,
--R
--R     [3.7000000000000002, 0.81529434199999995, 0.81529434137285406,
--R      - 6.2714589077472738E-10]
--R     ,
--R
--R     [3.7999999999999998, 0.81878882100000006, 0.81878882054050406,
--R      - 4.5949599680739084E-10]
--R     ,
--R
--R     [3.8999999999999999, 0.82214896699999995, 0.8221489675670105,
--R      5.6701054962360331E-10]
--R     ,
--R    [4.,0.82538250000000002,0.82538259960411076,9.9604110737061546E-8],
--R
--R     [4.0999999999999996, 0.82849692600000002, 0.82849692490970006,
--R      - 1.0902999614259556E-9]
--R     ,
--R
--R     [4.2000000000000002, 0.83149860200000003, 0.83149860211639337,
--R      1.1639333941104724E-10]
--R     ,
--R
--R     [4.2999999999999998, 0.83439379400000002, 0.83439379260257418,
--R      - 1.397425841709321E-9]
--R     ,
--R
--R     [4.4000000000000004, 0.83718820699999996, 0.83718820689462137,
--R      - 1.0537859473913613E-10]
--R     ,
--R    [4.5,0.83988714399999997,0.83988714589085944,1.8908594690003611E-9],
--R
--R     [4.5999999999999996, 0.84249553899999996, 0.84249553757701434,
--R      - 1.4229856182268463E-9]
--R     ,
--R
--R     [4.7000000000000002, 0.84501797099999998, 0.84501796980531307,
--R      - 1.1946869049594966E-9]
--R     ,
--R
--R     [4.7999999999999998, 0.84745872099999997, 0.84745871962692243,
--R      - 1.3730775405562667E-9]
--R     ,
--R
--R     [4.9000000000000004, 0.84982177800000003, 0.84982177959827732,
--R      1.5982772882949803E-9]
--R     ,
--R    [5.,0.85211088000000001,0.85211088142366165,1.4236616330265406E-9],
--R
--R     [5.0999999999999996, 0.85432951899999998, 0.85432951724709605,
--R      - 1.7529039331165563E-9]
--R     ,
--R
--R     [5.2000000000000002, 0.85648095800000001, 0.85648095886487274,
--R      8.6487272898949641E-10]
--R     ,
--R
--R     [5.2999999999999998, 0.85856827499999999, 0.85856827509448064,
--R      9.4480645529415597E-11]
--R     ,
--R
--R     [5.4000000000000004, 0.86059434800000001, 0.86059434750532948,
--R      - 4.946705267627749E-10]
--R     ,
--R    [5.5,0.86256188499999997,0.86256188469070161,- 3.0929836469795191E-10],
--R
--R     [5.5999999999999996, 0.86447343600000004, 0.86447343523800879,
--R      - 7.6199124787734718E-10]
--R     ,
--R    [5.7000000000000002,0.866331399,0.8663313995352464,5.3524640275526281E-10],
--R
--R     [5.7999999999999998, 0.86813804000000006, 0.86813804053493893,
--R      5.3493887097744164E-10]
--R     ,
--R
--R     [5.9000000000000004, 0.86989549399999999, 0.86989549358247464,
--R      - 4.1752534762906635E-10]
--R     ,
--R    [6.,0.87160577500000003,0.87160577540332174,4.0332170936352441E-10],
--R
--R     [6.0999999999999996, 0.87327079299999999, 0.8732707923327413,
--R      - 6.6725869274364413E-10]
--R     ,
--R
--R     [6.2000000000000002, 0.87489234699999996, 0.8748923478621643,
--R      8.6216433992092334E-10]
--R     ,
--R
--R     [6.2999999999999998, 0.87647215000000001, 0.87647214956817143,
--R      - 4.3182857289991716E-10]
--R     ,
--R
--R     [6.4000000000000004, 0.878011816, 0.87801181548273155,
--R      - 5.1726845029520518E-10]
--R     ,
--R    [6.5,0.87951288100000002,0.87951287995710281,- 1.0428972130327452E-9],
--R
--R     [6.5999999999999996, 0.88097679699999998, 0.88097679906610149,
--R      2.0661015120992943E-9]
--R     ,
--R
--R     [6.7000000000000002, 0.88240495500000005, 0.8824049555946607,
--R      5.9466065405189283E-10]
--R     ,
--R
--R     [6.7999999999999998, 0.88379866200000001, 0.88379866364416337,
--R      1.6441633610142503E-9]
--R     ,
--R
--R     [6.9000000000000004, 0.88515917600000005, 0.88515917289225332,
--R      - 3.1077467266271697E-9]
--R     ,
--R    [7.,0.88648767500000003,0.88648767253642946,- 2.4635705697662047E-9],
--R
--R     [7.0999999999999996, 0.88778529399999995, 0.8877852949486843,
--R      9.4868435329686918E-10]
--R     ,
--R
--R     [7.2000000000000002, 0.88905311899999995, 0.88905311906582485,
--R      6.5824901085420606E-11]
--R     ,
--R
--R     [7.2999999999999998, 0.89029217299999996, 0.89029217353766843,
--R      5.3766846530578505E-10]
--R     ,
--R
--R     [7.4000000000000004, 0.89150344000000004, 0.89150343965322676,
--R      - 3.4677327676035929E-10]
--R     ,
--R    [7.5,0.89268785399999995,0.89268785406308437,6.308442657143587E-11],
--R
--R     [7.5999999999999996, 0.89384631199999998, 0.89384631131444836,
--R      - 6.8555161547578791E-10]
--R     ,
--R
--R     [7.7000000000000002, 0.89497966600000001, 0.89497966621388148,
--R      2.1388146809186992E-10]
--R     ,
--R
--R     [7.7999999999999998, 0.89608873700000002, 0.89608873603132189,
--R      - 9.686781377027387E-10]
--R     ,
--R
--R     [7.9000000000000004, 0.89717430200000003, 0.8971743025577732,
--R      5.5777316099181462E-10]
--R     ,
--R    [8.,0.89823711299999998,0.89823711402799578,1.0279957995962263E-9],
--R
--R     [8.0999999999999996, 0.89927788799999997, 0.89927788691844668,
--R      - 1.0815532913710513E-9]
--R     ,
--R
--R     [8.1999999999999993, 0.90029730600000002, 0.90029730762992677,
--R      1.629926749124877E-9]
--R     ,
--R
--R     [8.3000000000000007, 0.90129603300000005, 0.90129603406349046,
--R      1.0634904068496098E-9]
--R     ,
--R
--R     [8.4000000000000004, 0.90227469500000002, 0.90227469709753316,
--R      2.0975331471717595E-9]
--R     ,
--R    [8.5,0.90323390000000003,0.90323390197320852,1.9732084854950926E-9],
--R
--R     [8.5999999999999996, 0.90417422800000002, 0.9041742295948515,
--R      1.5948514731078944E-9]
--R     ,
--R
--R     [8.6999999999999993, 0.90509623500000003, 0.90509623775141723,
--R      2.7514172051823493E-9]
--R     ,
--R
--R     [8.8000000000000007, 0.90600045900000004, 0.90600046226454201,
--R      3.264541970082746E-9]
--R     ,
--R
--R     [8.9000000000000004, 0.90688741399999995, 0.90688741806836271,
--R      4.0683627577919879E-9]
--R     ,
--R    [9.,0.907757602,0.90775760022576812,- 1.7742318725311179E-9],
--R
--R     [9.0999999999999996, 0.90861148300000005, 0.90861148488548271,
--R      1.8854826588921014E-9]
--R     ,
--R
--R     [9.1999999999999993, 0.90944952999999995, 0.90944953018395813,
--R      1.8395818202066039E-10]
--R     ,
--R
--R     [9.3000000000000007, 0.91027217699999996, 0.91027217709579178,
--R      9.5791818921497907E-11]
--R     ,
--R
--R     [9.4000000000000004, 0.91107985000000002, 0.91107985023607185,
--R      2.3607182875196031E-10]
--R     ,
--R    [9.5,0.91187295800000001,0.91187295861782769,6.1782767790674598E-10],
--R
--R     [9.5999999999999996, 0.91265189700000005, 0.91265189636747834,
--R      - 6.3252170168226485E-10]
--R     ,
--R
--R     [9.6999999999999993, 0.91341704300000004, 0.91341704340103613,
--R      4.010360932227286E-10]
--R     ,
--R
--R     [9.8000000000000007, 0.91416876599999997, 0.91416876606351216,
--R      6.3512195502823943E-11]
--R     ,
--R
--R     [9.9000000000000004, 0.91490741799999997, 0.9149074177339066,
--R      - 2.6609336956084917E-10]
--R     ,
--R    [10.,0.91563333899999999,0.91563333939788116,3.9788117245365129E-10]]
--R                                       Type: List List Expression DoubleFloat
--E 6

--S 7 of 7
E1(0.0)
 

   (7)  infinity
                                         Type: OnePointCompletion DoubleFloat
--R
--R   (7)  infinity
--R                                         Type: OnePointCompletion DoubleFloat
--E 7
)spool 
 
Starts dribbling to LexTriangularPackage.output (2010/3/27, 18:42:29).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 22
ls : List Symbol := [a,b,c,d,e,f]
 

   (2)  [a,b,c,d,e,f]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [a,b,c,d,e,f]
--R                                                            Type: List Symbol
--E 2

--S 3 of 22
V := OVAR(ls)
 

   (3)  OrderedVariableList [a,b,c,d,e,f]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [a,b,c,d,e,f]
--R                                                                 Type: Domain
--E 3

--S 4 of 22
P := NSMP(R, V)
 

   (4)
   NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
                                                                 Type: Domain
--R 
--R
--R   (4)
--R   NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R                                                                 Type: Domain
--E 4

--S 5 of 22
p1: P :=  a*b*c*d*e*f - 1
 

   (5)  f e d c b a - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (5)  f e d c b a - 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 5

--S 6 of 22
p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f 
 

   (6)  ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (6)  ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 6

--S 7 of 22
p3: P :=  a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f 
 

   (7)  (((d + f)c + f e)b + f e d)a + e d c b + f e d c
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (7)  (((d + f)c + f e)b + f e d)a + e d c b + f e d c
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 7

--S 8 of 22
p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f 
 

   (8)  ((c + f)b + f e)a + d c b + e d c + f e d
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (8)  ((c + f)b + f e)a + d c b + e d c + f e d
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 8

--S 9 of 22
p5: P := a*b + a*f + b*c + c*d + d*e + e*f 
 

   (9)  (b + f)a + c b + d c + e d + f e
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (9)  (b + f)a + c b + d c + e d + f e
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 9

--S 10 of 22
p6: P := a + b + c + d + e + f 
 

   (10)  a + b + c + d + e + f
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (10)  a + b + c + d + e + f
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 10

--S 11 of 22
lp := [p1, p2, p3, p4, p5, p6]
 

   (11)
   [f e d c b a - 1, ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b,
    (((d + f)c + f e)b + f e d)a + e d c b + f e d c,
    ((c + f)b + f e)a + d c b + e d c + f e d,
    (b + f)a + c b + d c + e d + f e, a + b + c + d + e + f]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (11)
--R   [f e d c b a - 1, ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b,
--R    (((d + f)c + f e)b + f e d)a + e d c b + f e d c,
--R    ((c + f)b + f e)a + d c b + e d c + f e d,
--R    (b + f)a + c b + d c + e d + f e, a + b + c + d + e + f]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 11

--S 12 of 22
lextripack :=  LEXTRIPK(R,ls)
 

   (12)  LexTriangularPackage(Integer,[a,b,c,d,e,f])
                                                                 Type: Domain
--R 
--R
--R   (12)  LexTriangularPackage(Integer,[a,b,c,d,e,f])
--R                                                                 Type: Domain
--E 12

--S 13 of 22
lg := groebner(lp)$lextripack
 

   (13)
   [a + b + c + d + e + f,

                        2                                           2
       3968379498283200b  + 15873517993132800f b + 3968379498283200d
     + 
                                               3 5                     4 4
       15873517993132800f d + 3968379498283200f e  - 15873517993132800f e
     + 
                         5 3                       6                       2
       23810276989699200f e  + (206355733910726400f  + 230166010900425600)e
     + 
                             43                       37
           - 729705987316687f   + 1863667496867205421f
         + 
                                 31                         25
           291674853771731104461f   + 365285994691106921745f
         + 
                              19                         13
           549961185828911895f   - 365048404038768439269f
         + 
                                   7
           - 292382820431504027669f  - 2271898467631865497f
      *
         e
     + 
                          44                        38
       - 3988812642545399f   + 10187423878429609997f
     + 
                              32                          26
       1594377523424314053637f   + 1994739308439916238065f
     + 
                           20                          14
       1596840088052642815f   - 1993494118301162145413f
     + 
                                8                        2
       - 1596049742289689815053f  - 11488171330159667449f
     ,

                                                                      2
       (23810276989699200c - 23810276989699200f)b + 23810276989699200c
     + 
                                                2
       71430830969097600f c - 23810276989699200d  - 95241107958796800f d
     + 
                           3 5                      4 4                      5 3
       - 55557312975964800f e  + 174608697924460800f e  - 174608697924460800f e
     + 
                              6                        2
       (- 2428648252949318400f  - 2611193709870345600)e
     + 
                            43                        37
           8305444561289527f   - 21212087151945459641f
         + 
                                    31                          25
           - 3319815883093451385381f   - 4157691646261657136445f
         + 
                                 19                          13
           - 6072721607510764095f   + 4154986709036460221649f
         + 
                                  7
           3327761311138587096749f  + 25885340608290841637f
      *
         e
     + 
                         44                         38
       45815897629010329f   - 117013765582151891207f
     + 
                                 32                           26
       - 18313166848970865074187f   - 22909971239649297438915f
     + 
                              20                           14
       - 16133250761305157265f   + 22897305857636178256623f
     + 
                               8                         2
       18329944781867242497923f  + 130258531002020420699f
     ,

       (7936758996566400d - 7936758996566400f)b - 7936758996566400f d
     + 
                          3 5                     4 4                     5 3
       - 7936758996566400f e  + 23810276989699200f e  - 23810276989699200f e
     + 
                             6                       2
       (- 337312257354072000f  - 369059293340337600)e
     + 
                            43                       37
           1176345388640471f   - 3004383582891473073f
         + 
                                   31                         25
           - 470203502707246105653f   - 588858183402644348085f
         + 
                                19                         13
           - 856939308623513535f   + 588472674242340526377f
         + 
                                 7
           471313241958371103517f  + 3659742549078552381f
      *
         e
     + 
                        44                        38                          32
       6423170513956901f   - 16404772137036480803f   - 2567419165227528774463f
     + 
                                26                       20
       - 3211938090825682172335f   - 2330490332697587485f
     + 
                              14                          8
       3210100109444754864587f   + 2569858315395162617847f
     + 
                            2
       18326089487427735751f
     ,

                                                                     3 5
       (11905138494849600e - 11905138494849600f)b - 3968379498283200f e
     + 
                         4 4                     5 3
       15873517993132800f e  - 27778656487982400f e
     + 
                             6                       2
       (- 208339923659868000f  - 240086959646133600)e
     + 
                           43                       37
           786029984751110f   - 2007519008182245250f
         + 
                                   31                         25
           - 314188062908073807090f   - 393423667537929575250f
         + 
                                19                         13
           - 550329120654394950f   + 393196408728889612770f
         + 
                                 7
           314892372799176495730f  + 2409386515146668530f
      *
         e
     + 
                        44                        38                          32
       4177638546747827f   - 10669685294602576381f   - 1669852980419949524601f
     + 
                                26                       20
       - 2089077057287904170745f   - 1569899763580278795f
     + 
                              14                          8
       2087864026859015573349f   + 1671496085945199577969f
     + 
                            2
       11940257226216280177f
     ,

                          6                                           2 5
       (11905138494849600f  - 11905138494849600)b - 15873517993132800f e
     + 
                         3 4                     4 3
       39683794982832000f e  - 39683794982832000f e
     + 
                             11                      5  2
       (- 686529653202993600f   - 607162063237329600f )e
     + 
                          42                      36                        30
           65144531306704f   - 166381280901088652f   - 26033434502470283472f
         + 
                                  24                      18
           - 31696259583860650140f   + 971492093167581360f
         + 
                              12                        6
         32220085033691389548f   + 25526177666070529808f  + 138603268355749244
      *
         e
     + 
                       43                      37                        31
       167620036074811f   - 428102417974791473f   - 66997243801231679313f
     + 
                              25                      19
       - 83426716722148750485f   + 203673895369980765f
     + 
                            13                        7
       83523056326010432457f   + 66995789640238066937f  + 478592855549587901f
     ,

                    3                   2                 2                45
       801692827936c  + 2405078483808f c  - 2405078483808f c - 13752945467f
     + 
                      39                    33                    27
       35125117815561f   + 5496946957826433f   + 6834659447749117f
     + 
                        21                    15                    9
       - 44484880462461f   - 6873406230093057f   - 5450844938762633f
     + 
                     3
       1216586044571f
     ,

                                                                      2
       (23810276989699200d - 23810276989699200f)c + 23810276989699200d
     + 
                                               3 5                     4 4
       71430830969097600f d + 7936758996566400f e  - 31747035986265600f e
     + 
                         5 3                       6                       2
       31747035986265600f e  + (404774708824886400f  + 396837949828320000)e
     + 
                              43                       37
           - 1247372229446701f   + 3185785654596621203f
         + 
                                 31                         25
           498594866849974751463f   + 624542545845791047935f
         + 
                              19                         13
           931085755769682885f   - 624150663582417063387f
         + 
                                   7
           - 499881859388360475647f  - 3926885313819527351f
      *
         e
     + 
                          44                        38
       - 7026011547118141f   + 17944427051950691243f
     + 
                              32                          26
       2808383522593986603543f   + 3513624142354807530135f
     + 
                           20                          14
       2860757006705537685f   - 3511356735642190737267f
     + 
                                8                        2
       - 2811332494697103819887f  - 20315011631522847311f
     ,

       (7936758996566400e - 7936758996566400f)c
     + 
                           43                     37                       31
           - 4418748183673f   + 11285568707456559f   + 1765998617294451019f
         + 
                               25                     19
           2173749283622606155f   - 55788292195402895f
         + 
                               13                       7
         - 2215291421788292951f   - 1718142665347430851f  + 30256569458230237f
      *
         e
     + 
                     44                     38                       32
       4418748183673f   - 11285568707456559f   - 1765998617294451019f
     + 
                             26                     20                       14
       - 2173749283622606155f   + 55788292195402895f   + 2215291421788292951f
     + 
                           8                     2
       1718142665347430851f  - 30256569458230237f
     ,

                       6                                  43
       (72152354514240f  - 72152354514240)c + 40950859449f
     + 
                         37                     31                     25
       - 104588980990367f   - 16367227395575307f   - 20268523416527355f
     + 
                       19                     13                     7
       442205002259535f   + 20576059935789063f   + 15997133796970563f
     + 
       - 275099892785581f
     ,

                        3                      2                    2
       1984189749141600d  + 5952569247424800f d  - 5952569247424800f d
     + 
                          4 5                     5 4                     3
       - 3968379498283200f e  + 15873517993132800f e  + 17857707742274400e
     + 
                             7                        2
       (- 148814231185620000f  - 162703559429611200f)e
     + 
                             44                      38
           - 390000914678878f   + 996062704593756434f
         + 
                                 32                         26
           155886323972034823914f   + 194745956143985421330f
         + 
                            20                         14
           6205077595574430f   - 194596512653299068786f
         + 
                                   8                       2
           - 155796897940756922666f  - 1036375759077320978f
      *
         e
     + 
                         45                      39                         33
       - 374998630035991f   + 957747106595453993f   + 149889155566764891693f
     + 
                             27                      21
       187154171443494641685f   - 127129015426348065f
     + 
                             15                         9                      3
     - 187241533243115040417f   - 149719983567976534037f  - 836654081239648061f
     ,

                                                                   3 5
       (5952569247424800e - 5952569247424800f)d - 3968379498283200f e
     + 
                        4 4                    5 3
       9920948745708000f e  - 3968379498283200f e
     + 
                             6                       2
       (- 148814231185620000f  - 150798420934761600)e
     + 
                           43                       37
           492558110242553f   - 1257992359608074599f
         + 
                                   31                         25
           - 196883094539368513959f   - 246562115745735428055f
         + 
                                19                         13
           - 325698701993885505f   + 246417769883651808111f
         + 
                                 7
           197327352068200652911f  + 1523373796389332143f
      *
         e
     + 
                        44                       38                          32
       2679481081803026f   - 6843392695421906608f   - 1071020459642646913578f
     + 
                                26                      20
       - 1339789169692041240060f   - 852746750910750210f
     + 
                              14                          8
       1339105101971878401312f   + 1071900289758712984762f
     + 
                           2
       7555239072072727756f
     ,

                          6                                          2 5
       (11905138494849600f  - 11905138494849600)d - 7936758996566400f e
     + 
                         3 4                     4 3
       31747035986265600f e  - 31747035986265600f e
     + 
                             11                      5  2
       (- 420648226818019200f   - 404774708824886400f )e
     + 
                          42                     36                       30
           15336187600889f   - 39169739565161107f   - 6127176127489690827f
         + 
                                 24                      18
           - 7217708742310509615f   + 538628483890722735f
         + 
                               12                       6
           7506804353843507643f   + 5886160769782607203f  + 63576108396535879
      *
         e
     + 
                      43                      37                        31
       71737781777066f   - 183218856207557938f   - 28672874271132276078f
     + 
                              25                      19
       - 35625223686939812010f   + 164831339634084390f
     + 
                            13                        7
       35724160423073052642f   + 28627022578664910622f  + 187459987029680506f
     ,

                        6                      5                    2 4
       1322793166094400e  - 3968379498283200f e  + 3968379498283200f e
     + 
                          3 3
       - 5291172664377600f e
     + 
                             10                      4  2
       (- 230166010900425600f   - 226197631402142400f )e
     + 
                                47                         41
           - 152375364610443885f   + 389166626064854890415f
         + 
                                   35                           29
           60906097841360558987335f   + 76167367934608798697275f
         + 
                                23                           17
           27855066785995181125f   - 76144952817052723145495f
         + 
                                     11                         5
           - 60933629892463517546975f   - 411415071682002547795f
      *
         e
     + 
                         42                      36                        30
       - 209493533143822f   + 535045979490560586f   + 83737947964973553146f
     + 
                             24                      18
       104889507084213371570f   + 167117997269207870f
     + 
                               12                        6
       - 104793725781390615514f   - 83842685189903180394f  - 569978796672974242
     ,

                       6                   3
       (25438330117200f  + 25438330117200)e
     + 
                       7                    2
       (76314990351600f  + 76314990351600f)e
     + 
                           44                    38                      32
           - 1594966552735f   + 4073543370415745f   + 637527159231148925f
         + 
                              26                   20                      14
           797521176113606525f   + 530440941097175f   - 797160527306433145f
         + 
                                8                    2
           - 638132320196044965f  - 4510507167940725f
      *
         e
     + 
                       45                     39                       33
       - 6036376800443f   + 15416903421476909f   + 2412807646192304449f
     + 
                           27                    21                       15
       3017679923028013705f   + 1422320037411955f   - 3016560402417843941f
     + 
                             9                     3
       - 2414249368183033161f  - 16561862361763873f
     ,

                      12                  2
       (1387545279120f   - 1387545279120)e
     + 
                      43                  37                    31
           4321823003f   - 11037922310209f   - 1727510711947989f
         + 
                              25                 19                    13
           - 2165150991154425f   - 5114342560755f   + 2162682824948601f
         + 
                            7
           1732620732685741f  + 13506088516033f
      *
         e
     + 
                   44                  38                    32
       24177661775f   - 61749727185325f   - 9664106795754225f
     + 
                           26                 20                     14
       - 12090487758628245f   - 8787672733575f   + 12083693383005045f
     + 
                        8                  2
       9672870290826025f  + 68544102808525f
     ,
     48        42          36          30          18          12        6
    f   - 2554f   - 399710f   - 499722f   + 499722f   + 399710f   + 2554f  - 1]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (13)
--R   [a + b + c + d + e + f,
--R
--R                        2                                           2
--R       3968379498283200b  + 15873517993132800f b + 3968379498283200d
--R     + 
--R                                               3 5                     4 4
--R       15873517993132800f d + 3968379498283200f e  - 15873517993132800f e
--R     + 
--R                         5 3                       6                       2
--R       23810276989699200f e  + (206355733910726400f  + 230166010900425600)e
--R     + 
--R                             43                       37
--R           - 729705987316687f   + 1863667496867205421f
--R         + 
--R                                 31                         25
--R           291674853771731104461f   + 365285994691106921745f
--R         + 
--R                              19                         13
--R           549961185828911895f   - 365048404038768439269f
--R         + 
--R                                   7
--R           - 292382820431504027669f  - 2271898467631865497f
--R      *
--R         e
--R     + 
--R                          44                        38
--R       - 3988812642545399f   + 10187423878429609997f
--R     + 
--R                              32                          26
--R       1594377523424314053637f   + 1994739308439916238065f
--R     + 
--R                           20                          14
--R       1596840088052642815f   - 1993494118301162145413f
--R     + 
--R                                8                        2
--R       - 1596049742289689815053f  - 11488171330159667449f
--R     ,
--R
--R                                                                      2
--R       (23810276989699200c - 23810276989699200f)b + 23810276989699200c
--R     + 
--R                                                2
--R       71430830969097600f c - 23810276989699200d  - 95241107958796800f d
--R     + 
--R                           3 5                      4 4                      5 3
--R       - 55557312975964800f e  + 174608697924460800f e  - 174608697924460800f e
--R     + 
--R                              6                        2
--R       (- 2428648252949318400f  - 2611193709870345600)e
--R     + 
--R                            43                        37
--R           8305444561289527f   - 21212087151945459641f
--R         + 
--R                                    31                          25
--R           - 3319815883093451385381f   - 4157691646261657136445f
--R         + 
--R                                 19                          13
--R           - 6072721607510764095f   + 4154986709036460221649f
--R         + 
--R                                  7
--R           3327761311138587096749f  + 25885340608290841637f
--R      *
--R         e
--R     + 
--R                         44                         38
--R       45815897629010329f   - 117013765582151891207f
--R     + 
--R                                 32                           26
--R       - 18313166848970865074187f   - 22909971239649297438915f
--R     + 
--R                              20                           14
--R       - 16133250761305157265f   + 22897305857636178256623f
--R     + 
--R                               8                         2
--R       18329944781867242497923f  + 130258531002020420699f
--R     ,
--R
--R       (7936758996566400d - 7936758996566400f)b - 7936758996566400f d
--R     + 
--R                          3 5                     4 4                     5 3
--R       - 7936758996566400f e  + 23810276989699200f e  - 23810276989699200f e
--R     + 
--R                             6                       2
--R       (- 337312257354072000f  - 369059293340337600)e
--R     + 
--R                            43                       37
--R           1176345388640471f   - 3004383582891473073f
--R         + 
--R                                   31                         25
--R           - 470203502707246105653f   - 588858183402644348085f
--R         + 
--R                                19                         13
--R           - 856939308623513535f   + 588472674242340526377f
--R         + 
--R                                 7
--R           471313241958371103517f  + 3659742549078552381f
--R      *
--R         e
--R     + 
--R                        44                        38                          32
--R       6423170513956901f   - 16404772137036480803f   - 2567419165227528774463f
--R     + 
--R                                26                       20
--R       - 3211938090825682172335f   - 2330490332697587485f
--R     + 
--R                              14                          8
--R       3210100109444754864587f   + 2569858315395162617847f
--R     + 
--R                            2
--R       18326089487427735751f
--R     ,
--R
--R                                                                     3 5
--R       (11905138494849600e - 11905138494849600f)b - 3968379498283200f e
--R     + 
--R                         4 4                     5 3
--R       15873517993132800f e  - 27778656487982400f e
--R     + 
--R                             6                       2
--R       (- 208339923659868000f  - 240086959646133600)e
--R     + 
--R                           43                       37
--R           786029984751110f   - 2007519008182245250f
--R         + 
--R                                   31                         25
--R           - 314188062908073807090f   - 393423667537929575250f
--R         + 
--R                                19                         13
--R           - 550329120654394950f   + 393196408728889612770f
--R         + 
--R                                 7
--R           314892372799176495730f  + 2409386515146668530f
--R      *
--R         e
--R     + 
--R                        44                        38                          32
--R       4177638546747827f   - 10669685294602576381f   - 1669852980419949524601f
--R     + 
--R                                26                       20
--R       - 2089077057287904170745f   - 1569899763580278795f
--R     + 
--R                              14                          8
--R       2087864026859015573349f   + 1671496085945199577969f
--R     + 
--R                            2
--R       11940257226216280177f
--R     ,
--R
--R                          6                                           2 5
--R       (11905138494849600f  - 11905138494849600)b - 15873517993132800f e
--R     + 
--R                         3 4                     4 3
--R       39683794982832000f e  - 39683794982832000f e
--R     + 
--R                             11                      5  2
--R       (- 686529653202993600f   - 607162063237329600f )e
--R     + 
--R                          42                      36                        30
--R           65144531306704f   - 166381280901088652f   - 26033434502470283472f
--R         + 
--R                                  24                      18
--R           - 31696259583860650140f   + 971492093167581360f
--R         + 
--R                              12                        6
--R         32220085033691389548f   + 25526177666070529808f  + 138603268355749244
--R      *
--R         e
--R     + 
--R                       43                      37                        31
--R       167620036074811f   - 428102417974791473f   - 66997243801231679313f
--R     + 
--R                              25                      19
--R       - 83426716722148750485f   + 203673895369980765f
--R     + 
--R                            13                        7
--R       83523056326010432457f   + 66995789640238066937f  + 478592855549587901f
--R     ,
--R
--R                    3                   2                 2                45
--R       801692827936c  + 2405078483808f c  - 2405078483808f c - 13752945467f
--R     + 
--R                      39                    33                    27
--R       35125117815561f   + 5496946957826433f   + 6834659447749117f
--R     + 
--R                        21                    15                    9
--R       - 44484880462461f   - 6873406230093057f   - 5450844938762633f
--R     + 
--R                     3
--R       1216586044571f
--R     ,
--R
--R                                                                      2
--R       (23810276989699200d - 23810276989699200f)c + 23810276989699200d
--R     + 
--R                                               3 5                     4 4
--R       71430830969097600f d + 7936758996566400f e  - 31747035986265600f e
--R     + 
--R                         5 3                       6                       2
--R       31747035986265600f e  + (404774708824886400f  + 396837949828320000)e
--R     + 
--R                              43                       37
--R           - 1247372229446701f   + 3185785654596621203f
--R         + 
--R                                 31                         25
--R           498594866849974751463f   + 624542545845791047935f
--R         + 
--R                              19                         13
--R           931085755769682885f   - 624150663582417063387f
--R         + 
--R                                   7
--R           - 499881859388360475647f  - 3926885313819527351f
--R      *
--R         e
--R     + 
--R                          44                        38
--R       - 7026011547118141f   + 17944427051950691243f
--R     + 
--R                              32                          26
--R       2808383522593986603543f   + 3513624142354807530135f
--R     + 
--R                           20                          14
--R       2860757006705537685f   - 3511356735642190737267f
--R     + 
--R                                8                        2
--R       - 2811332494697103819887f  - 20315011631522847311f
--R     ,
--R
--R       (7936758996566400e - 7936758996566400f)c
--R     + 
--R                           43                     37                       31
--R           - 4418748183673f   + 11285568707456559f   + 1765998617294451019f
--R         + 
--R                               25                     19
--R           2173749283622606155f   - 55788292195402895f
--R         + 
--R                               13                       7
--R         - 2215291421788292951f   - 1718142665347430851f  + 30256569458230237f
--R      *
--R         e
--R     + 
--R                     44                     38                       32
--R       4418748183673f   - 11285568707456559f   - 1765998617294451019f
--R     + 
--R                             26                     20                       14
--R       - 2173749283622606155f   + 55788292195402895f   + 2215291421788292951f
--R     + 
--R                           8                     2
--R       1718142665347430851f  - 30256569458230237f
--R     ,
--R
--R                       6                                  43
--R       (72152354514240f  - 72152354514240)c + 40950859449f
--R     + 
--R                         37                     31                     25
--R       - 104588980990367f   - 16367227395575307f   - 20268523416527355f
--R     + 
--R                       19                     13                     7
--R       442205002259535f   + 20576059935789063f   + 15997133796970563f
--R     + 
--R       - 275099892785581f
--R     ,
--R
--R                        3                      2                    2
--R       1984189749141600d  + 5952569247424800f d  - 5952569247424800f d
--R     + 
--R                          4 5                     5 4                     3
--R       - 3968379498283200f e  + 15873517993132800f e  + 17857707742274400e
--R     + 
--R                             7                        2
--R       (- 148814231185620000f  - 162703559429611200f)e
--R     + 
--R                             44                      38
--R           - 390000914678878f   + 996062704593756434f
--R         + 
--R                                 32                         26
--R           155886323972034823914f   + 194745956143985421330f
--R         + 
--R                            20                         14
--R           6205077595574430f   - 194596512653299068786f
--R         + 
--R                                   8                       2
--R           - 155796897940756922666f  - 1036375759077320978f
--R      *
--R         e
--R     + 
--R                         45                      39                         33
--R       - 374998630035991f   + 957747106595453993f   + 149889155566764891693f
--R     + 
--R                             27                      21
--R       187154171443494641685f   - 127129015426348065f
--R     + 
--R                             15                         9                      3
--R     - 187241533243115040417f   - 149719983567976534037f  - 836654081239648061f
--R     ,
--R
--R                                                                   3 5
--R       (5952569247424800e - 5952569247424800f)d - 3968379498283200f e
--R     + 
--R                        4 4                    5 3
--R       9920948745708000f e  - 3968379498283200f e
--R     + 
--R                             6                       2
--R       (- 148814231185620000f  - 150798420934761600)e
--R     + 
--R                           43                       37
--R           492558110242553f   - 1257992359608074599f
--R         + 
--R                                   31                         25
--R           - 196883094539368513959f   - 246562115745735428055f
--R         + 
--R                                19                         13
--R           - 325698701993885505f   + 246417769883651808111f
--R         + 
--R                                 7
--R           197327352068200652911f  + 1523373796389332143f
--R      *
--R         e
--R     + 
--R                        44                       38                          32
--R       2679481081803026f   - 6843392695421906608f   - 1071020459642646913578f
--R     + 
--R                                26                      20
--R       - 1339789169692041240060f   - 852746750910750210f
--R     + 
--R                              14                          8
--R       1339105101971878401312f   + 1071900289758712984762f
--R     + 
--R                           2
--R       7555239072072727756f
--R     ,
--R
--R                          6                                          2 5
--R       (11905138494849600f  - 11905138494849600)d - 7936758996566400f e
--R     + 
--R                         3 4                     4 3
--R       31747035986265600f e  - 31747035986265600f e
--R     + 
--R                             11                      5  2
--R       (- 420648226818019200f   - 404774708824886400f )e
--R     + 
--R                          42                     36                       30
--R           15336187600889f   - 39169739565161107f   - 6127176127489690827f
--R         + 
--R                                 24                      18
--R           - 7217708742310509615f   + 538628483890722735f
--R         + 
--R                               12                       6
--R           7506804353843507643f   + 5886160769782607203f  + 63576108396535879
--R      *
--R         e
--R     + 
--R                      43                      37                        31
--R       71737781777066f   - 183218856207557938f   - 28672874271132276078f
--R     + 
--R                              25                      19
--R       - 35625223686939812010f   + 164831339634084390f
--R     + 
--R                            13                        7
--R       35724160423073052642f   + 28627022578664910622f  + 187459987029680506f
--R     ,
--R
--R                        6                      5                    2 4
--R       1322793166094400e  - 3968379498283200f e  + 3968379498283200f e
--R     + 
--R                          3 3
--R       - 5291172664377600f e
--R     + 
--R                             10                      4  2
--R       (- 230166010900425600f   - 226197631402142400f )e
--R     + 
--R                                47                         41
--R           - 152375364610443885f   + 389166626064854890415f
--R         + 
--R                                   35                           29
--R           60906097841360558987335f   + 76167367934608798697275f
--R         + 
--R                                23                           17
--R           27855066785995181125f   - 76144952817052723145495f
--R         + 
--R                                     11                         5
--R           - 60933629892463517546975f   - 411415071682002547795f
--R      *
--R         e
--R     + 
--R                         42                      36                        30
--R       - 209493533143822f   + 535045979490560586f   + 83737947964973553146f
--R     + 
--R                             24                      18
--R       104889507084213371570f   + 167117997269207870f
--R     + 
--R                               12                        6
--R       - 104793725781390615514f   - 83842685189903180394f  - 569978796672974242
--R     ,
--R
--R                       6                   3
--R       (25438330117200f  + 25438330117200)e
--R     + 
--R                       7                    2
--R       (76314990351600f  + 76314990351600f)e
--R     + 
--R                           44                    38                      32
--R           - 1594966552735f   + 4073543370415745f   + 637527159231148925f
--R         + 
--R                              26                   20                      14
--R           797521176113606525f   + 530440941097175f   - 797160527306433145f
--R         + 
--R                                8                    2
--R           - 638132320196044965f  - 4510507167940725f
--R      *
--R         e
--R     + 
--R                       45                     39                       33
--R       - 6036376800443f   + 15416903421476909f   + 2412807646192304449f
--R     + 
--R                           27                    21                       15
--R       3017679923028013705f   + 1422320037411955f   - 3016560402417843941f
--R     + 
--R                             9                     3
--R       - 2414249368183033161f  - 16561862361763873f
--R     ,
--R
--R                      12                  2
--R       (1387545279120f   - 1387545279120)e
--R     + 
--R                      43                  37                    31
--R           4321823003f   - 11037922310209f   - 1727510711947989f
--R         + 
--R                              25                 19                    13
--R           - 2165150991154425f   - 5114342560755f   + 2162682824948601f
--R         + 
--R                            7
--R           1732620732685741f  + 13506088516033f
--R      *
--R         e
--R     + 
--R                   44                  38                    32
--R       24177661775f   - 61749727185325f   - 9664106795754225f
--R     + 
--R                           26                 20                     14
--R       - 12090487758628245f   - 8787672733575f   + 12083693383005045f
--R     + 
--R                        8                  2
--R       9672870290826025f  + 68544102808525f
--R     ,
--R     48        42          36          30          18          12        6
--R    f   - 2554f   - 399710f   - 499722f   + 499722f   + 399710f   + 2554f  - 1]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 13

--S 14 of 22
lexTriangular(lg,false)$lextripack
 

   (14)
   [
       6       6       5     2 4     3 3     4 2     5
     {f  + 1, e  - 3f e  + 3f e  - 4f e  + 3f e  - 3f e - 1,
            2 5     3 4     4 3     5 2
      3d + f e  - 4f e  + 4f e  - 2f e  - 2e + 2f, c + f,
             2 5     3 4     4 3      5 2
      3b + 2f e  - 5f e  + 5f e  - 10f e  - 4e + 7f,
           2 5     3 4     4 3     5 2
      a - f e  + 3f e  - 3f e  + 4f e  + 3e - 3f}
     ,
      6                  2           2                    2
    {f  - 1,e - f,d - f,c  + 4f c + f ,(c - f)b - f c - 5f ,a + b + c + 3f},
      6                        2           2
    {f  - 1,e - f,d - f,c - f,b  + 4f b + f ,a + b + 4f},
      6            2           2                    2
    {f  - 1,e - f,d  + 4f d + f ,(d - f)c - f d - 5f ,b - f,a + c + d + 3f},

       36        30          24          18          12        6
     {f   - 2554f   - 399709f   - 502276f   - 399709f   - 2554f  + 1,

                    12              2
         (161718564f   - 161718564)e
       + 
                      31              25                19                13
             - 504205f   + 1287737951f   + 201539391380f   + 253982817368f
           + 
                          7
             201940704665f  + 1574134601f
        *
           e
       + 
                   32              26                 20                 14
         - 2818405f   + 7198203911f   + 1126548149060f   + 1416530563364f
       + 
                       8              2
         1127377589345f  + 7988820725f
       ,

                       6                                 2 5                 3 4
         (693772639560f  - 693772639560)d - 462515093040f e  + 1850060372160f e
       + 
                         4 3                     11                  5  2
         - 1850060372160f e  + (- 24513299931120f   - 23588269745040f )e
       + 
                         30                 24                   18
             - 890810428f   + 2275181044754f   + 355937263869776f
           + 
                             12                   6
             413736880104344f   + 342849304487996f  + 3704966481878
        *
           e
       + 
                      31                  25                    19
         - 4163798003f   + 10634395752169f   + 1664161760192806f
       + 
                          13                    7
         2079424391370694f   + 1668153650635921f  + 10924274392693f
       ,

                      6                           31               25
         (12614047992f  - 12614047992)c - 7246825f   + 18508536599f
       + 
                       19                 13                 7
         2896249516034f   + 3581539649666f   + 2796477571739f  - 48094301893f
       ,

                       6                                 2 5                 3 4
         (693772639560f  - 693772639560)b - 925030186080f e  + 2312575465200f e
       + 
                         4 3                     11                  5  2
         - 2312575465200f e  + (- 40007555547960f   - 35382404617560f )e
       + 
                          30                 24                    18
             - 3781280823f   + 9657492291789f   + 1511158913397906f
           + 
                              12                    6
             1837290892286154f   + 1487216006594361f  + 8077238712093
        *
           e
       + 
                      31                  25                    19
         - 9736390478f   + 24866827916734f   + 3891495681905296f
       + 
                          13                    7
         4872556418871424f   + 3904047887269606f  + 27890075838538f
       ,
      a + b + c + d + e + f}
     ,
      6      2           2                    2
    {f  - 1,e  + 4f e + f ,(e - f)d - f e - 5f ,c - f,b - f,a + d + e + 3f}]
                               Type: List RegularChain(Integer,[a,b,c,d,e,f])
--R 
--R
--R   (14)
--R   [
--R       6       6       5     2 4     3 3     4 2     5
--R     {f  + 1, e  - 3f e  + 3f e  - 4f e  + 3f e  - 3f e - 1,
--R            2 5     3 4     4 3     5 2
--R      3d + f e  - 4f e  + 4f e  - 2f e  - 2e + 2f, c + f,
--R             2 5     3 4     4 3      5 2
--R      3b + 2f e  - 5f e  + 5f e  - 10f e  - 4e + 7f,
--R           2 5     3 4     4 3     5 2
--R      a - f e  + 3f e  - 3f e  + 4f e  + 3e - 3f}
--R     ,
--R      6                  2           2                    2
--R    {f  - 1,e - f,d - f,c  + 4f c + f ,(c - f)b - f c - 5f ,a + b + c + 3f},
--R      6                        2           2
--R    {f  - 1,e - f,d - f,c - f,b  + 4f b + f ,a + b + 4f},
--R      6            2           2                    2
--R    {f  - 1,e - f,d  + 4f d + f ,(d - f)c - f d - 5f ,b - f,a + c + d + 3f},
--R
--R       36        30          24          18          12        6
--R     {f   - 2554f   - 399709f   - 502276f   - 399709f   - 2554f  + 1,
--R
--R                    12              2
--R         (161718564f   - 161718564)e
--R       + 
--R                      31              25                19                13
--R             - 504205f   + 1287737951f   + 201539391380f   + 253982817368f
--R           + 
--R                          7
--R             201940704665f  + 1574134601f
--R        *
--R           e
--R       + 
--R                   32              26                 20                 14
--R         - 2818405f   + 7198203911f   + 1126548149060f   + 1416530563364f
--R       + 
--R                       8              2
--R         1127377589345f  + 7988820725f
--R       ,
--R
--R                       6                                 2 5                 3 4
--R         (693772639560f  - 693772639560)d - 462515093040f e  + 1850060372160f e
--R       + 
--R                         4 3                     11                  5  2
--R         - 1850060372160f e  + (- 24513299931120f   - 23588269745040f )e
--R       + 
--R                         30                 24                   18
--R             - 890810428f   + 2275181044754f   + 355937263869776f
--R           + 
--R                             12                   6
--R             413736880104344f   + 342849304487996f  + 3704966481878
--R        *
--R           e
--R       + 
--R                      31                  25                    19
--R         - 4163798003f   + 10634395752169f   + 1664161760192806f
--R       + 
--R                          13                    7
--R         2079424391370694f   + 1668153650635921f  + 10924274392693f
--R       ,
--R
--R                      6                           31               25
--R         (12614047992f  - 12614047992)c - 7246825f   + 18508536599f
--R       + 
--R                       19                 13                 7
--R         2896249516034f   + 3581539649666f   + 2796477571739f  - 48094301893f
--R       ,
--R
--R                       6                                 2 5                 3 4
--R         (693772639560f  - 693772639560)b - 925030186080f e  + 2312575465200f e
--R       + 
--R                         4 3                     11                  5  2
--R         - 2312575465200f e  + (- 40007555547960f   - 35382404617560f )e
--R       + 
--R                          30                 24                    18
--R             - 3781280823f   + 9657492291789f   + 1511158913397906f
--R           + 
--R                              12                    6
--R             1837290892286154f   + 1487216006594361f  + 8077238712093
--R        *
--R           e
--R       + 
--R                      31                  25                    19
--R         - 9736390478f   + 24866827916734f   + 3891495681905296f
--R       + 
--R                          13                    7
--R         4872556418871424f   + 3904047887269606f  + 27890075838538f
--R       ,
--R      a + b + c + d + e + f}
--R     ,
--R      6      2           2                    2
--R    {f  - 1,e  + 4f e + f ,(e - f)d - f e - 5f ,c - f,b - f,a + d + e + 3f}]
--R                               Type: List RegularChain(Integer,[a,b,c,d,e,f])
--E 14

--S 15 of 22
lts := lexTriangular(lg,true)$lextripack
 

   (15)
   [
       6       6       5     2 4     3 3     4 2     5
     {f  + 1, e  - 3f e  + 3f e  - 4f e  + 3f e  - 3f e - 1,
            2 5     3 4     4 3     5 2
      3d + f e  - 4f e  + 4f e  - 2f e  - 2e + 2f, c + f,
             2 5     3 4     4 3      5 2
      3b + 2f e  - 5f e  + 5f e  - 10f e  - 4e + 7f,
           2 5     3 4     4 3     5 2
      a - f e  + 3f e  - 3f e  + 4f e  + 3e - 3f}
     ,
      6                  2           2
    {f  - 1,e - f,d - f,c  + 4f c + f ,b + c + 4f,a - f},
      6                        2           2
    {f  - 1,e - f,d - f,c - f,b  + 4f b + f ,a + b + 4f},
      6            2           2
    {f  - 1,e - f,d  + 4f d + f ,c + d + 4f,b - f,a - f},

       36        30          24          18          12        6
     {f   - 2554f   - 399709f   - 502276f   - 399709f   - 2554f  + 1,

                       2
         1387545279120e
       + 
                        31                  25                    19
             4321823003f   - 11037922310209f   - 1727506390124986f
           + 
                                13                    7
             - 2176188913464634f   - 1732620732685741f  - 13506088516033f
        *
           e
       + 
                     32                  26                    20
         24177661775f   - 61749727185325f   - 9664082618092450f
       + 
                             14                    8                  2
         - 12152237485813570f   - 9672870290826025f  - 68544102808525f
       ,

         1387545279120d
       + 
                          30                 24                   18
             - 1128983050f   + 2883434331830f   + 451234998755840f
           + 
                             12                   6
             562426491685760f   + 447129055314890f  - 165557857270
        *
           e
       + 
                      31                 25                   19
         - 1816935351f   + 4640452214013f   + 726247129626942f
       + 
                         13                   7
         912871801716798f   + 726583262666877f  + 4909358645961f
       ,

                                    31                 25                   19
         1387545279120c + 778171189f   - 1987468196267f   - 310993556954378f
       + 
                           13                   7
         - 383262822316802f   - 300335488637543f  + 5289595037041f
       ,

         1387545279120b
       + 
                        30                 24                   18
             1128983050f   - 2883434331830f   - 451234998755840f
           + 
                               12                   6
             - 562426491685760f   - 447129055314890f  + 165557857270
        *
           e
       + 
                      31                 25                    19
         - 3283058841f   + 8384938292463f   + 1312252817452422f
       + 
                          13                    7
         1646579934064638f   + 1306372958656407f  + 4694680112151f
       ,

                                                      31                  25
         1387545279120a + 1387545279120e + 4321823003f   - 11037922310209f
       + 
                            19                    13                    7
         - 1727506390124986f   - 2176188913464634f   - 1732620732685741f
       + 
         - 13506088516033f
       }
     ,
      6      2           2
    {f  - 1,e  + 4f e + f ,d + e + 4f,c - f,b - f,a - f}]
                               Type: List RegularChain(Integer,[a,b,c,d,e,f])
--R 
--R
--R   (15)
--R   [
--R       6       6       5     2 4     3 3     4 2     5
--R     {f  + 1, e  - 3f e  + 3f e  - 4f e  + 3f e  - 3f e - 1,
--R            2 5     3 4     4 3     5 2
--R      3d + f e  - 4f e  + 4f e  - 2f e  - 2e + 2f, c + f,
--R             2 5     3 4     4 3      5 2
--R      3b + 2f e  - 5f e  + 5f e  - 10f e  - 4e + 7f,
--R           2 5     3 4     4 3     5 2
--R      a - f e  + 3f e  - 3f e  + 4f e  + 3e - 3f}
--R     ,
--R      6                  2           2
--R    {f  - 1,e - f,d - f,c  + 4f c + f ,b + c + 4f,a - f},
--R      6                        2           2
--R    {f  - 1,e - f,d - f,c - f,b  + 4f b + f ,a + b + 4f},
--R      6            2           2
--R    {f  - 1,e - f,d  + 4f d + f ,c + d + 4f,b - f,a - f},
--R
--R       36        30          24          18          12        6
--R     {f   - 2554f   - 399709f   - 502276f   - 399709f   - 2554f  + 1,
--R
--R                       2
--R         1387545279120e
--R       + 
--R                        31                  25                    19
--R             4321823003f   - 11037922310209f   - 1727506390124986f
--R           + 
--R                                13                    7
--R             - 2176188913464634f   - 1732620732685741f  - 13506088516033f
--R        *
--R           e
--R       + 
--R                     32                  26                    20
--R         24177661775f   - 61749727185325f   - 9664082618092450f
--R       + 
--R                             14                    8                  2
--R         - 12152237485813570f   - 9672870290826025f  - 68544102808525f
--R       ,
--R
--R         1387545279120d
--R       + 
--R                          30                 24                   18
--R             - 1128983050f   + 2883434331830f   + 451234998755840f
--R           + 
--R                             12                   6
--R             562426491685760f   + 447129055314890f  - 165557857270
--R        *
--R           e
--R       + 
--R                      31                 25                   19
--R         - 1816935351f   + 4640452214013f   + 726247129626942f
--R       + 
--R                         13                   7
--R         912871801716798f   + 726583262666877f  + 4909358645961f
--R       ,
--R
--R                                    31                 25                   19
--R         1387545279120c + 778171189f   - 1987468196267f   - 310993556954378f
--R       + 
--R                           13                   7
--R         - 383262822316802f   - 300335488637543f  + 5289595037041f
--R       ,
--R
--R         1387545279120b
--R       + 
--R                        30                 24                   18
--R             1128983050f   - 2883434331830f   - 451234998755840f
--R           + 
--R                               12                   6
--R             - 562426491685760f   - 447129055314890f  + 165557857270
--R        *
--R           e
--R       + 
--R                      31                 25                    19
--R         - 3283058841f   + 8384938292463f   + 1312252817452422f
--R       + 
--R                          13                    7
--R         1646579934064638f   + 1306372958656407f  + 4694680112151f
--R       ,
--R
--R                                                      31                  25
--R         1387545279120a + 1387545279120e + 4321823003f   - 11037922310209f
--R       + 
--R                            19                    13                    7
--R         - 1727506390124986f   - 2176188913464634f   - 1732620732685741f
--R       + 
--R         - 13506088516033f
--R       }
--R     ,
--R      6      2           2
--R    {f  - 1,e  + 4f e + f ,d + e + 4f,c - f,b - f,a - f}]
--R                               Type: List RegularChain(Integer,[a,b,c,d,e,f])
--E 15

--S 16 of 22
[ [init(p) for p in (ts :: List(P))] for ts in lts]
 

   (16)
   [[1,3,1,3,1,1], [1,1,1,1,1,1], [1,1,1,1,1,1], [1,1,1,1,1,1],
    [1387545279120,1387545279120,1387545279120,1387545279120,1387545279120,1],
    [1,1,1,1,1,1]]
Type: List List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--R 
--R
--R   (16)
--R   [[1,3,1,3,1,1], [1,1,1,1,1,1], [1,1,1,1,1,1], [1,1,1,1,1,1],
--R    [1387545279120,1387545279120,1387545279120,1387545279120,1387545279120,1],
--R    [1,1,1,1,1,1]]
--RType: List List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
--E 16

--S 17 of 22
squareFreeLexTriangular(lg,true)$lextripack
 

   (17)
   [
       6       6       5     2 4     3 3     4 2     5
     {f  + 1, e  - 3f e  + 3f e  - 4f e  + 3f e  - 3f e - 1,
            2 5     3 4     4 3     5 2
      3d + f e  - 4f e  + 4f e  - 2f e  - 2e + 2f, c + f,
             2 5     3 4     4 3      5 2
      3b + 2f e  - 5f e  + 5f e  - 10f e  - 4e + 7f,
           2 5     3 4     4 3     5 2
      a - f e  + 3f e  - 3f e  + 4f e  + 3e - 3f}
     ,
      6                  2           2
    {f  - 1,e - f,d - f,c  + 4f c + f ,b + c + 4f,a - f},
      6                        2           2
    {f  - 1,e - f,d - f,c - f,b  + 4f b + f ,a + b + 4f},
      6            2           2
    {f  - 1,e - f,d  + 4f d + f ,c + d + 4f,b - f,a - f},

       36        30          24          18          12        6
     {f   - 2554f   - 399709f   - 502276f   - 399709f   - 2554f  + 1,

                       2
         1387545279120e
       + 
                        31                  25                    19
             4321823003f   - 11037922310209f   - 1727506390124986f
           + 
                                13                    7
             - 2176188913464634f   - 1732620732685741f  - 13506088516033f
        *
           e
       + 
                     32                  26                    20
         24177661775f   - 61749727185325f   - 9664082618092450f
       + 
                             14                    8                  2
         - 12152237485813570f   - 9672870290826025f  - 68544102808525f
       ,

         1387545279120d
       + 
                          30                 24                   18
             - 1128983050f   + 2883434331830f   + 451234998755840f
           + 
                             12                   6
             562426491685760f   + 447129055314890f  - 165557857270
        *
           e
       + 
                      31                 25                   19
         - 1816935351f   + 4640452214013f   + 726247129626942f
       + 
                         13                   7
         912871801716798f   + 726583262666877f  + 4909358645961f
       ,

                                    31                 25                   19
         1387545279120c + 778171189f   - 1987468196267f   - 310993556954378f
       + 
                           13                   7
         - 383262822316802f   - 300335488637543f  + 5289595037041f
       ,

         1387545279120b
       + 
                        30                 24                   18
             1128983050f   - 2883434331830f   - 451234998755840f
           + 
                               12                   6
             - 562426491685760f   - 447129055314890f  + 165557857270
        *
           e
       + 
                      31                 25                    19
         - 3283058841f   + 8384938292463f   + 1312252817452422f
       + 
                          13                    7
         1646579934064638f   + 1306372958656407f  + 4694680112151f
       ,

                                                      31                  25
         1387545279120a + 1387545279120e + 4321823003f   - 11037922310209f
       + 
                            19                    13                    7
         - 1727506390124986f   - 2176188913464634f   - 1732620732685741f
       + 
         - 13506088516033f
       }
     ,
      6      2           2
    {f  - 1,e  + 4f e + f ,d + e + 4f,c - f,b - f,a - f}]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [a,b,c,d,e,f],OrderedVariableList [a,b,c,d,e,f],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]))
--R 
--R
--R   (17)
--R   [
--R       6       6       5     2 4     3 3     4 2     5
--R     {f  + 1, e  - 3f e  + 3f e  - 4f e  + 3f e  - 3f e - 1,
--R            2 5     3 4     4 3     5 2
--R      3d + f e  - 4f e  + 4f e  - 2f e  - 2e + 2f, c + f,
--R             2 5     3 4     4 3      5 2
--R      3b + 2f e  - 5f e  + 5f e  - 10f e  - 4e + 7f,
--R           2 5     3 4     4 3     5 2
--R      a - f e  + 3f e  - 3f e  + 4f e  + 3e - 3f}
--R     ,
--R      6                  2           2
--R    {f  - 1,e - f,d - f,c  + 4f c + f ,b + c + 4f,a - f},
--R      6                        2           2
--R    {f  - 1,e - f,d - f,c - f,b  + 4f b + f ,a + b + 4f},
--R      6            2           2
--R    {f  - 1,e - f,d  + 4f d + f ,c + d + 4f,b - f,a - f},
--R
--R       36        30          24          18          12        6
--R     {f   - 2554f   - 399709f   - 502276f   - 399709f   - 2554f  + 1,
--R
--R                       2
--R         1387545279120e
--R       + 
--R                        31                  25                    19
--R             4321823003f   - 11037922310209f   - 1727506390124986f
--R           + 
--R                                13                    7
--R             - 2176188913464634f   - 1732620732685741f  - 13506088516033f
--R        *
--R           e
--R       + 
--R                     32                  26                    20
--R         24177661775f   - 61749727185325f   - 9664082618092450f
--R       + 
--R                             14                    8                  2
--R         - 12152237485813570f   - 9672870290826025f  - 68544102808525f
--R       ,
--R
--R         1387545279120d
--R       + 
--R                          30                 24                   18
--R             - 1128983050f   + 2883434331830f   + 451234998755840f
--R           + 
--R                             12                   6
--R             562426491685760f   + 447129055314890f  - 165557857270
--R        *
--R           e
--R       + 
--R                      31                 25                   19
--R         - 1816935351f   + 4640452214013f   + 726247129626942f
--R       + 
--R                         13                   7
--R         912871801716798f   + 726583262666877f  + 4909358645961f
--R       ,
--R
--R                                    31                 25                   19
--R         1387545279120c + 778171189f   - 1987468196267f   - 310993556954378f
--R       + 
--R                           13                   7
--R         - 383262822316802f   - 300335488637543f  + 5289595037041f
--R       ,
--R
--R         1387545279120b
--R       + 
--R                        30                 24                   18
--R             1128983050f   - 2883434331830f   - 451234998755840f
--R           + 
--R                               12                   6
--R             - 562426491685760f   - 447129055314890f  + 165557857270
--R        *
--R           e
--R       + 
--R                      31                 25                    19
--R         - 3283058841f   + 8384938292463f   + 1312252817452422f
--R       + 
--R                          13                    7
--R         1646579934064638f   + 1306372958656407f  + 4694680112151f
--R       ,
--R
--R                                                      31                  25
--R         1387545279120a + 1387545279120e + 4321823003f   - 11037922310209f
--R       + 
--R                            19                    13                    7
--R         - 1727506390124986f   - 2176188913464634f   - 1732620732685741f
--R       + 
--R         - 13506088516033f
--R       }
--R     ,
--R      6      2           2
--R    {f  - 1,e  + 4f e + f ,d + e + 4f,c - f,b - f,a - f}]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [a,b,c,d,e,f],OrderedVariableList [a,b,c,d,e,f],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]))
--E 17

--S 18 of 22
reduce(+,[degree(ts) for ts in lts])
 

   (18)  156
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  156
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 22
ls2 : List Symbol := concat(ls,new()$Symbol)
 

   (19)  [a,b,c,d,e,f,%A]
                                                            Type: List Symbol
--R 
--R
--R   (19)  [a,b,c,d,e,f,%A]
--R                                                            Type: List Symbol
--E 19

--S 20 of 22
zdpack := ZDSOLVE(R,ls,ls2)
 

   (20)  ZeroDimensionalSolvePackage(Integer,[a,b,c,d,e,f],[a,b,c,d,e,f,%A])
                                                                 Type: Domain
--R 
--R
--R   (20)  ZeroDimensionalSolvePackage(Integer,[a,b,c,d,e,f],[a,b,c,d,e,f,%A])
--R                                                                 Type: Domain
--E 20

--S 21 of 22
concat [univariateSolve(ts)$zdpack for ts in lts]
 

   (21)
   [
                     4      2
     [complexRoots= ?  - 13?  + 49,

       coordinates =
                 3                3                3                3
         [7a + %A  - 6%A, 21b + %A  + %A, 21c - 2%A  + 19%A, 7d - %A  + 6%A,
                  3                3
          21e - %A  - %A, 21f + 2%A  - 19%A]
       ]
     ,

                     4      2
     [complexRoots= ?  + 11?  + 49,

       coordinates =
                   3                 3                  3
         [35a + 3%A  + 19%A, 35b + %A  + 18%A, 35c - 2%A  - %A,
                   3                 3                  3
          35d - 3%A  - 19%A, 35e - %A  - 18%A, 35f + 2%A  + %A]
       ]
     ,

     [
       complexRoots =
          8      7      6       5       4       3       2
         ?  - 12?  + 58?  - 120?  + 207?  - 360?  + 802?  - 1332? + 1369
       ,

       coordinates =
         [
                                7           6            5            4
             43054532a + 33782%A  - 546673%A  + 3127348%A  - 6927123%A
           + 
                      3             2
             4365212%A  - 25086957%A  + 39582814%A - 107313172
           ,

                                7           6            5            4
             43054532b - 33782%A  + 546673%A  - 3127348%A  + 6927123%A
           + 
                        3             2
             - 4365212%A  + 25086957%A  - 39582814%A + 107313172
           ,

                                7           6            5            4
             21527266c - 22306%A  + 263139%A  - 1166076%A  + 1821805%A
           + 
                        3             2
             - 2892788%A  + 10322663%A  - 9026596%A + 12950740
           ,

                                7           6            5            4
             43054532d + 22306%A  - 263139%A  + 1166076%A  - 1821805%A
           + 
                      3             2
             2892788%A  - 10322663%A  + 30553862%A - 12950740
           ,

                                7           6            5            4
             43054532e - 22306%A  + 263139%A  - 1166076%A  + 1821805%A
           + 
                        3             2
             - 2892788%A  + 10322663%A  - 30553862%A + 12950740
           ,

                                7           6            5            4
             21527266f + 22306%A  - 263139%A  + 1166076%A  - 1821805%A
           + 
                      3             2
             2892788%A  - 10322663%A  + 9026596%A - 12950740
           ]
       ]
     ,

     [
       complexRoots =
          8      7      6       5       4       3       2
         ?  + 12?  + 58?  + 120?  + 207?  + 360?  + 802?  + 1332? + 1369
       ,

       coordinates =
         [
                                7           6            5            4
             43054532a + 33782%A  + 546673%A  + 3127348%A  + 6927123%A
           + 
                      3             2
             4365212%A  + 25086957%A  + 39582814%A + 107313172
           ,

                                7           6            5            4
             43054532b - 33782%A  - 546673%A  - 3127348%A  - 6927123%A
           + 
                        3             2
             - 4365212%A  - 25086957%A  - 39582814%A - 107313172
           ,

                                7           6            5            4
             21527266c - 22306%A  - 263139%A  - 1166076%A  - 1821805%A
           + 
                        3             2
             - 2892788%A  - 10322663%A  - 9026596%A - 12950740
           ,

                                7           6            5            4
             43054532d + 22306%A  + 263139%A  + 1166076%A  + 1821805%A
           + 
                      3             2
             2892788%A  + 10322663%A  + 30553862%A + 12950740
           ,

                                7           6            5            4
             43054532e - 22306%A  - 263139%A  - 1166076%A  - 1821805%A
           + 
                        3             2
             - 2892788%A  - 10322663%A  - 30553862%A - 12950740
           ,

                                7           6            5            4
             21527266f + 22306%A  + 263139%A  + 1166076%A  + 1821805%A
           + 
                      3             2
             2892788%A  + 10322663%A  + 9026596%A + 12950740
           ]
       ]
     ,

                     4    2
     [complexRoots= ?  - ?  + 1,
                                 3            3              3            3
      coordinates= [a - %A,b + %A  - %A,c + %A ,d + %A,e - %A  + %A,f - %A ]]
     ,

                     8     6      4      2
     [complexRoots= ?  + 4?  + 12?  + 16?  + 4,

       coordinates =
                  7      5       3                 7      5       3
         [4a - 2%A  - 7%A  - 20%A  - 22%A, 4b + 2%A  + 7%A  + 20%A  + 22%A,
                 7      5       3                7      5       3
          4c + %A  + 3%A  + 10%A  + 10%A, 4d + %A  + 3%A  + 10%A  + 6%A,
                 7      5       3               7      5       3
          4e - %A  - 3%A  - 10%A  - 6%A, 4f - %A  - 3%A  - 10%A  - 10%A]
       ]
     ,

                     4     3      2
     [complexRoots= ?  + 6?  + 30?  + 36? + 36,

       coordinates =
                  3      2                    3      2
         [30a - %A  - 5%A  - 30%A - 6, 6b + %A  + 5%A  + 24%A + 6,
                  3      2              3      2
          30c - %A  - 5%A  - 6, 30d - %A  - 5%A  - 30%A - 6,
                  3      2                     3      2
          30e - %A  - 5%A  - 30%A - 6, 30f - %A  - 5%A  - 30%A - 6]
       ]
     ,

                     4     3      2
     [complexRoots= ?  - 6?  + 30?  - 36? + 36,

       coordinates =
                  3      2                    3      2
         [30a - %A  + 5%A  - 30%A + 6, 6b + %A  - 5%A  + 24%A - 6,
                  3      2              3      2
          30c - %A  + 5%A  + 6, 30d - %A  + 5%A  - 30%A + 6,
                  3      2                     3      2
          30e - %A  + 5%A  - 30%A + 6, 30f - %A  + 5%A  - 30%A + 6]
       ]
     ,

                     2
     [complexRoots= ?  + 6? + 6,
      coordinates= [a + 1,b - %A - 5,c + %A + 1,d + 1,e + 1,f + 1]]
     ,

                     2
     [complexRoots= ?  - 6? + 6,
      coordinates= [a - 1,b - %A + 5,c + %A - 1,d - 1,e - 1,f - 1]]
     ,

                     4     3      2
     [complexRoots= ?  + 6?  + 30?  + 36? + 36,

       coordinates =
                 3      2                     3      2
         [6a + %A  + 5%A  + 24%A + 6, 30b - %A  - 5%A  - 6,
                  3      2                     3      2
          30c - %A  - 5%A  - 30%A - 6, 30d - %A  - 5%A  - 30%A - 6,
                  3      2                     3      2
          30e - %A  - 5%A  - 30%A - 6, 30f - %A  - 5%A  - 30%A - 6]
       ]
     ,

                     4     3      2
     [complexRoots= ?  - 6?  + 30?  - 36? + 36,

       coordinates =
                 3      2                     3      2
         [6a + %A  - 5%A  + 24%A - 6, 30b - %A  + 5%A  + 6,
                  3      2                     3      2
          30c - %A  + 5%A  - 30%A + 6, 30d - %A  + 5%A  - 30%A + 6,
                  3      2                     3      2
          30e - %A  + 5%A  - 30%A + 6, 30f - %A  + 5%A  - 30%A + 6]
       ]
     ,

                     2
     [complexRoots= ?  + 6? + 6,
      coordinates= [a - %A - 5,b + %A + 1,c + 1,d + 1,e + 1,f + 1]]
     ,

                     2
     [complexRoots= ?  - 6? + 6,
      coordinates= [a - %A + 5,b + %A - 1,c - 1,d - 1,e - 1,f - 1]]
     ,

                     4     3      2
     [complexRoots= ?  + 6?  + 30?  + 36? + 36,

       coordinates =
                  3      2                     3      2
         [30a - %A  - 5%A  - 30%A - 6, 30b - %A  - 5%A  - 30%A - 6,
                 3      2                     3      2
          6c + %A  + 5%A  + 24%A + 6, 30d - %A  - 5%A  - 6,
                  3      2                     3      2
          30e - %A  - 5%A  - 30%A - 6, 30f - %A  - 5%A  - 30%A - 6]
       ]
     ,

                     4     3      2
     [complexRoots= ?  - 6?  + 30?  - 36? + 36,

       coordinates =
                  3      2                     3      2
         [30a - %A  + 5%A  - 30%A + 6, 30b - %A  + 5%A  - 30%A + 6,
                 3      2                     3      2
          6c + %A  - 5%A  + 24%A - 6, 30d - %A  + 5%A  + 6,
                  3      2                     3      2
          30e - %A  + 5%A  - 30%A + 6, 30f - %A  + 5%A  - 30%A + 6]
       ]
     ,

                     2
     [complexRoots= ?  + 6? + 6,
      coordinates= [a + 1,b + 1,c - %A - 5,d + %A + 1,e + 1,f + 1]]
     ,

                     2
     [complexRoots= ?  - 6? + 6,
      coordinates= [a - 1,b - 1,c - %A + 5,d + %A - 1,e - 1,f - 1]]
     ,

                     8     7      6      5      4     2
     [complexRoots= ?  + 6?  + 16?  + 24?  + 18?  - 8?  + 4,

       coordinates =
                  7      6       5       4      3       2
         [2a + 2%A  + 9%A  + 18%A  + 19%A  + 4%A  - 10%A  - 2%A + 4,
                  7      6       5       4      3       2
          2b + 2%A  + 9%A  + 18%A  + 19%A  + 4%A  - 10%A  - 4%A + 4,
                 7      6      5      4      3
          2c - %A  - 4%A  - 8%A  - 9%A  - 4%A  - 2%A - 4,
                 7      6      5      4      3
          2d + %A  + 4%A  + 8%A  + 9%A  + 4%A  + 2%A + 4,
                  7      6       5       4      3       2
          2e - 2%A  - 9%A  - 18%A  - 19%A  - 4%A  + 10%A  + 4%A - 4,
                  7      6       5       4      3       2
          2f - 2%A  - 9%A  - 18%A  - 19%A  - 4%A  + 10%A  + 2%A - 4]
       ]
     ,

     [
       complexRoots =
          8      7      6       5       4       3        2
         ?  + 12?  + 64?  + 192?  + 432?  + 768?  + 1024?  + 768? + 256
       ,

       coordinates =
         [
                         7        6        5         4         3         2
             1408a - 19%A  - 200%A  - 912%A  - 2216%A  - 4544%A  - 6784%A
           + 
             - 6976%A - 1792
           ,

                         7        6         5         4          3          2
             1408b - 37%A  - 408%A  - 1952%A  - 5024%A  - 10368%A  - 16768%A
           + 
             - 17920%A - 5120
           ,

                         7        6         5         4          3          2
             1408c + 37%A  + 408%A  + 1952%A  + 5024%A  + 10368%A  + 16768%A
           + 
             17920%A + 5120
           ,

                         7        6        5         4         3         2
             1408d + 19%A  + 200%A  + 912%A  + 2216%A  + 4544%A  + 6784%A
           + 
             6976%A + 1792
           ,
          2e + %A, 2f - %A]
       ]
     ,

                     8     6      4      2
     [complexRoots= ?  + 4?  + 12?  + 16?  + 4,

       coordinates =
                 7      5       3               7      5       3
         [4a - %A  - 3%A  - 10%A  - 6%A, 4b - %A  - 3%A  - 10%A  - 10%A,
                  7      5       3                 7      5       3
          4c - 2%A  - 7%A  - 20%A  - 22%A, 4d + 2%A  + 7%A  + 20%A  + 22%A,
                 7      5       3                7      5       3
          4e + %A  + 3%A  + 10%A  + 10%A, 4f + %A  + 3%A  + 10%A  + 6%A]
       ]
     ,

                     8      6      4       2
     [complexRoots= ?  + 16?  - 96?  + 256?  + 256,

       coordinates =
                   7       5        3
         [512a - %A  - 12%A  + 176%A  - 448%A,
                   7       5       3
          128b - %A  - 16%A  + 96%A  - 256%A,
                   7       5       3
          128c + %A  + 16%A  - 96%A  + 256%A,
                   7       5        3
          512d + %A  + 12%A  - 176%A  + 448%A, 2e + %A, 2f - %A]
       ]
     ,

     [
       complexRoots =
          8      7      6       5       4       3        2
         ?  - 12?  + 64?  - 192?  + 432?  - 768?  + 1024?  - 768? + 256
       ,

       coordinates =
         [
                         7        6        5         4         3         2
             1408a - 19%A  + 200%A  - 912%A  + 2216%A  - 4544%A  + 6784%A
           + 
             - 6976%A + 1792
           ,

                         7        6         5         4          3          2
             1408b - 37%A  + 408%A  - 1952%A  + 5024%A  - 10368%A  + 16768%A
           + 
             - 17920%A + 5120
           ,

                         7        6         5         4          3          2
             1408c + 37%A  - 408%A  + 1952%A  - 5024%A  + 10368%A  - 16768%A
           + 
             17920%A - 5120
           ,

                         7        6        5         4         3         2
             1408d + 19%A  - 200%A  + 912%A  - 2216%A  + 4544%A  - 6784%A
           + 
             6976%A - 1792
           ,
          2e + %A, 2f - %A]
       ]
     ,

                     8     7      6      5      4     2
     [complexRoots= ?  - 6?  + 16?  - 24?  + 18?  - 8?  + 4,

       coordinates =
                  7      6       5       4      3       2
         [2a + 2%A  - 9%A  + 18%A  - 19%A  + 4%A  + 10%A  - 2%A - 4,
                  7      6       5       4      3       2
          2b + 2%A  - 9%A  + 18%A  - 19%A  + 4%A  + 10%A  - 4%A - 4,
                 7      6      5      4      3
          2c - %A  + 4%A  - 8%A  + 9%A  - 4%A  - 2%A + 4,
                 7      6      5      4      3
          2d + %A  - 4%A  + 8%A  - 9%A  + 4%A  + 2%A - 4,
                  7      6       5       4      3       2
          2e - 2%A  + 9%A  - 18%A  + 19%A  - 4%A  - 10%A  + 4%A + 4,
                  7      6       5       4      3       2
          2f - 2%A  + 9%A  - 18%A  + 19%A  - 4%A  - 10%A  + 2%A + 4]
       ]
     ,

                     4      2
     [complexRoots= ?  + 12?  + 144,

       coordinates =
                  2               2               2               2
         [12a - %A  - 12, 12b - %A  - 12, 12c - %A  - 12, 12d - %A  - 12,
                 2                    2
          6e + %A  + 3%A + 12, 6f + %A  - 3%A + 12]
       ]
     ,

                     4     3      2
     [complexRoots= ?  + 6?  + 30?  + 36? + 36,

       coordinates =
                 3      2                     3      2
         [6a - %A  - 5%A  - 24%A - 6, 30b + %A  + 5%A  + 30%A + 6,
                  3      2                     3      2
          30c + %A  + 5%A  + 30%A + 6, 30d + %A  + 5%A  + 30%A + 6,
                  3      2                     3      2
          30e + %A  + 5%A  + 30%A + 6, 30f + %A  + 5%A  + 6]
       ]
     ,

                     4     3      2
     [complexRoots= ?  - 6?  + 30?  - 36? + 36,

       coordinates =
                 3      2                     3      2
         [6a - %A  + 5%A  - 24%A + 6, 30b + %A  - 5%A  + 30%A - 6,
                  3      2                     3      2
          30c + %A  - 5%A  + 30%A - 6, 30d + %A  - 5%A  + 30%A - 6,
                  3      2                     3      2
          30e + %A  - 5%A  + 30%A - 6, 30f + %A  - 5%A  - 6]
       ]
     ,

                     4      2
     [complexRoots= ?  + 12?  + 144,

       coordinates =
                  2               2               2               2
         [12a + %A  + 12, 12b + %A  + 12, 12c + %A  + 12, 12d + %A  + 12,
                 2                    2
          6e - %A  + 3%A - 12, 6f - %A  - 3%A - 12]
       ]
     ,

                     2
     [complexRoots= ?  - 12,
      coordinates= [a - 1,b - 1,c - 1,d - 1,2e + %A + 4,2f - %A + 4]]
     ,

                     2
     [complexRoots= ?  + 6? + 6,
      coordinates= [a + %A + 5,b - 1,c - 1,d - 1,e - 1,f - %A - 1]]
     ,

                     2
     [complexRoots= ?  - 6? + 6,
      coordinates= [a + %A - 5,b + 1,c + 1,d + 1,e + 1,f - %A + 1]]
     ,

                     2
     [complexRoots= ?  - 12,
      coordinates= [a + 1,b + 1,c + 1,d + 1,2e + %A - 4,2f - %A - 4]]
     ,

                     4     3      2
     [complexRoots= ?  + 6?  + 30?  + 36? + 36,

       coordinates =
                  3      2                     3      2
         [30a - %A  - 5%A  - 30%A - 6, 30b - %A  - 5%A  - 30%A - 6,
                  3      2                    3      2
          30c - %A  - 5%A  - 30%A - 6, 6d + %A  + 5%A  + 24%A + 6,
                  3      2              3      2
          30e - %A  - 5%A  - 6, 30f - %A  - 5%A  - 30%A - 6]
       ]
     ,

                     4     3      2
     [complexRoots= ?  - 6?  + 30?  - 36? + 36,

       coordinates =
                  3      2                     3      2
         [30a - %A  + 5%A  - 30%A + 6, 30b - %A  + 5%A  - 30%A + 6,
                  3      2                    3      2
          30c - %A  + 5%A  - 30%A + 6, 6d + %A  - 5%A  + 24%A - 6,
                  3      2              3      2
          30e - %A  + 5%A  + 6, 30f - %A  + 5%A  - 30%A + 6]
       ]
     ,

                     2
     [complexRoots= ?  + 6? + 6,
      coordinates= [a + 1,b + 1,c + 1,d - %A - 5,e + %A + 1,f + 1]]
     ,

                     2
     [complexRoots= ?  - 6? + 6,
      coordinates= [a - 1,b - 1,c - 1,d - %A + 5,e + %A - 1,f - 1]]
     ]
Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--R 
--R
--R   (21)
--R   [
--R                     4      2
--R     [complexRoots= ?  - 13?  + 49,
--R
--R       coordinates =
--R                 3                3                3                3
--R         [7a + %A  - 6%A, 21b + %A  + %A, 21c - 2%A  + 19%A, 7d - %A  + 6%A,
--R                  3                3
--R          21e - %A  - %A, 21f + 2%A  - 19%A]
--R       ]
--R     ,
--R
--R                     4      2
--R     [complexRoots= ?  + 11?  + 49,
--R
--R       coordinates =
--R                   3                 3                  3
--R         [35a + 3%A  + 19%A, 35b + %A  + 18%A, 35c - 2%A  - %A,
--R                   3                 3                  3
--R          35d - 3%A  - 19%A, 35e - %A  - 18%A, 35f + 2%A  + %A]
--R       ]
--R     ,
--R
--R     [
--R       complexRoots =
--R          8      7      6       5       4       3       2
--R         ?  - 12?  + 58?  - 120?  + 207?  - 360?  + 802?  - 1332? + 1369
--R       ,
--R
--R       coordinates =
--R         [
--R                                7           6            5            4
--R             43054532a + 33782%A  - 546673%A  + 3127348%A  - 6927123%A
--R           + 
--R                      3             2
--R             4365212%A  - 25086957%A  + 39582814%A - 107313172
--R           ,
--R
--R                                7           6            5            4
--R             43054532b - 33782%A  + 546673%A  - 3127348%A  + 6927123%A
--R           + 
--R                        3             2
--R             - 4365212%A  + 25086957%A  - 39582814%A + 107313172
--R           ,
--R
--R                                7           6            5            4
--R             21527266c - 22306%A  + 263139%A  - 1166076%A  + 1821805%A
--R           + 
--R                        3             2
--R             - 2892788%A  + 10322663%A  - 9026596%A + 12950740
--R           ,
--R
--R                                7           6            5            4
--R             43054532d + 22306%A  - 263139%A  + 1166076%A  - 1821805%A
--R           + 
--R                      3             2
--R             2892788%A  - 10322663%A  + 30553862%A - 12950740
--R           ,
--R
--R                                7           6            5            4
--R             43054532e - 22306%A  + 263139%A  - 1166076%A  + 1821805%A
--R           + 
--R                        3             2
--R             - 2892788%A  + 10322663%A  - 30553862%A + 12950740
--R           ,
--R
--R                                7           6            5            4
--R             21527266f + 22306%A  - 263139%A  + 1166076%A  - 1821805%A
--R           + 
--R                      3             2
--R             2892788%A  - 10322663%A  + 9026596%A - 12950740
--R           ]
--R       ]
--R     ,
--R
--R     [
--R       complexRoots =
--R          8      7      6       5       4       3       2
--R         ?  + 12?  + 58?  + 120?  + 207?  + 360?  + 802?  + 1332? + 1369
--R       ,
--R
--R       coordinates =
--R         [
--R                                7           6            5            4
--R             43054532a + 33782%A  + 546673%A  + 3127348%A  + 6927123%A
--R           + 
--R                      3             2
--R             4365212%A  + 25086957%A  + 39582814%A + 107313172
--R           ,
--R
--R                                7           6            5            4
--R             43054532b - 33782%A  - 546673%A  - 3127348%A  - 6927123%A
--R           + 
--R                        3             2
--R             - 4365212%A  - 25086957%A  - 39582814%A - 107313172
--R           ,
--R
--R                                7           6            5            4
--R             21527266c - 22306%A  - 263139%A  - 1166076%A  - 1821805%A
--R           + 
--R                        3             2
--R             - 2892788%A  - 10322663%A  - 9026596%A - 12950740
--R           ,
--R
--R                                7           6            5            4
--R             43054532d + 22306%A  + 263139%A  + 1166076%A  + 1821805%A
--R           + 
--R                      3             2
--R             2892788%A  + 10322663%A  + 30553862%A + 12950740
--R           ,
--R
--R                                7           6            5            4
--R             43054532e - 22306%A  - 263139%A  - 1166076%A  - 1821805%A
--R           + 
--R                        3             2
--R             - 2892788%A  - 10322663%A  - 30553862%A - 12950740
--R           ,
--R
--R                                7           6            5            4
--R             21527266f + 22306%A  + 263139%A  + 1166076%A  + 1821805%A
--R           + 
--R                      3             2
--R             2892788%A  + 10322663%A  + 9026596%A + 12950740
--R           ]
--R       ]
--R     ,
--R
--R                     4    2
--R     [complexRoots= ?  - ?  + 1,
--R                                 3            3              3            3
--R      coordinates= [a - %A,b + %A  - %A,c + %A ,d + %A,e - %A  + %A,f - %A ]]
--R     ,
--R
--R                     8     6      4      2
--R     [complexRoots= ?  + 4?  + 12?  + 16?  + 4,
--R
--R       coordinates =
--R                  7      5       3                 7      5       3
--R         [4a - 2%A  - 7%A  - 20%A  - 22%A, 4b + 2%A  + 7%A  + 20%A  + 22%A,
--R                 7      5       3                7      5       3
--R          4c + %A  + 3%A  + 10%A  + 10%A, 4d + %A  + 3%A  + 10%A  + 6%A,
--R                 7      5       3               7      5       3
--R          4e - %A  - 3%A  - 10%A  - 6%A, 4f - %A  - 3%A  - 10%A  - 10%A]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  + 6?  + 30?  + 36? + 36,
--R
--R       coordinates =
--R                  3      2                    3      2
--R         [30a - %A  - 5%A  - 30%A - 6, 6b + %A  + 5%A  + 24%A + 6,
--R                  3      2              3      2
--R          30c - %A  - 5%A  - 6, 30d - %A  - 5%A  - 30%A - 6,
--R                  3      2                     3      2
--R          30e - %A  - 5%A  - 30%A - 6, 30f - %A  - 5%A  - 30%A - 6]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  - 6?  + 30?  - 36? + 36,
--R
--R       coordinates =
--R                  3      2                    3      2
--R         [30a - %A  + 5%A  - 30%A + 6, 6b + %A  - 5%A  + 24%A - 6,
--R                  3      2              3      2
--R          30c - %A  + 5%A  + 6, 30d - %A  + 5%A  - 30%A + 6,
--R                  3      2                     3      2
--R          30e - %A  + 5%A  - 30%A + 6, 30f - %A  + 5%A  - 30%A + 6]
--R       ]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  + 6? + 6,
--R      coordinates= [a + 1,b - %A - 5,c + %A + 1,d + 1,e + 1,f + 1]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 6? + 6,
--R      coordinates= [a - 1,b - %A + 5,c + %A - 1,d - 1,e - 1,f - 1]]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  + 6?  + 30?  + 36? + 36,
--R
--R       coordinates =
--R                 3      2                     3      2
--R         [6a + %A  + 5%A  + 24%A + 6, 30b - %A  - 5%A  - 6,
--R                  3      2                     3      2
--R          30c - %A  - 5%A  - 30%A - 6, 30d - %A  - 5%A  - 30%A - 6,
--R                  3      2                     3      2
--R          30e - %A  - 5%A  - 30%A - 6, 30f - %A  - 5%A  - 30%A - 6]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  - 6?  + 30?  - 36? + 36,
--R
--R       coordinates =
--R                 3      2                     3      2
--R         [6a + %A  - 5%A  + 24%A - 6, 30b - %A  + 5%A  + 6,
--R                  3      2                     3      2
--R          30c - %A  + 5%A  - 30%A + 6, 30d - %A  + 5%A  - 30%A + 6,
--R                  3      2                     3      2
--R          30e - %A  + 5%A  - 30%A + 6, 30f - %A  + 5%A  - 30%A + 6]
--R       ]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  + 6? + 6,
--R      coordinates= [a - %A - 5,b + %A + 1,c + 1,d + 1,e + 1,f + 1]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 6? + 6,
--R      coordinates= [a - %A + 5,b + %A - 1,c - 1,d - 1,e - 1,f - 1]]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  + 6?  + 30?  + 36? + 36,
--R
--R       coordinates =
--R                  3      2                     3      2
--R         [30a - %A  - 5%A  - 30%A - 6, 30b - %A  - 5%A  - 30%A - 6,
--R                 3      2                     3      2
--R          6c + %A  + 5%A  + 24%A + 6, 30d - %A  - 5%A  - 6,
--R                  3      2                     3      2
--R          30e - %A  - 5%A  - 30%A - 6, 30f - %A  - 5%A  - 30%A - 6]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  - 6?  + 30?  - 36? + 36,
--R
--R       coordinates =
--R                  3      2                     3      2
--R         [30a - %A  + 5%A  - 30%A + 6, 30b - %A  + 5%A  - 30%A + 6,
--R                 3      2                     3      2
--R          6c + %A  - 5%A  + 24%A - 6, 30d - %A  + 5%A  + 6,
--R                  3      2                     3      2
--R          30e - %A  + 5%A  - 30%A + 6, 30f - %A  + 5%A  - 30%A + 6]
--R       ]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  + 6? + 6,
--R      coordinates= [a + 1,b + 1,c - %A - 5,d + %A + 1,e + 1,f + 1]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 6? + 6,
--R      coordinates= [a - 1,b - 1,c - %A + 5,d + %A - 1,e - 1,f - 1]]
--R     ,
--R
--R                     8     7      6      5      4     2
--R     [complexRoots= ?  + 6?  + 16?  + 24?  + 18?  - 8?  + 4,
--R
--R       coordinates =
--R                  7      6       5       4      3       2
--R         [2a + 2%A  + 9%A  + 18%A  + 19%A  + 4%A  - 10%A  - 2%A + 4,
--R                  7      6       5       4      3       2
--R          2b + 2%A  + 9%A  + 18%A  + 19%A  + 4%A  - 10%A  - 4%A + 4,
--R                 7      6      5      4      3
--R          2c - %A  - 4%A  - 8%A  - 9%A  - 4%A  - 2%A - 4,
--R                 7      6      5      4      3
--R          2d + %A  + 4%A  + 8%A  + 9%A  + 4%A  + 2%A + 4,
--R                  7      6       5       4      3       2
--R          2e - 2%A  - 9%A  - 18%A  - 19%A  - 4%A  + 10%A  + 4%A - 4,
--R                  7      6       5       4      3       2
--R          2f - 2%A  - 9%A  - 18%A  - 19%A  - 4%A  + 10%A  + 2%A - 4]
--R       ]
--R     ,
--R
--R     [
--R       complexRoots =
--R          8      7      6       5       4       3        2
--R         ?  + 12?  + 64?  + 192?  + 432?  + 768?  + 1024?  + 768? + 256
--R       ,
--R
--R       coordinates =
--R         [
--R                         7        6        5         4         3         2
--R             1408a - 19%A  - 200%A  - 912%A  - 2216%A  - 4544%A  - 6784%A
--R           + 
--R             - 6976%A - 1792
--R           ,
--R
--R                         7        6         5         4          3          2
--R             1408b - 37%A  - 408%A  - 1952%A  - 5024%A  - 10368%A  - 16768%A
--R           + 
--R             - 17920%A - 5120
--R           ,
--R
--R                         7        6         5         4          3          2
--R             1408c + 37%A  + 408%A  + 1952%A  + 5024%A  + 10368%A  + 16768%A
--R           + 
--R             17920%A + 5120
--R           ,
--R
--R                         7        6        5         4         3         2
--R             1408d + 19%A  + 200%A  + 912%A  + 2216%A  + 4544%A  + 6784%A
--R           + 
--R             6976%A + 1792
--R           ,
--R          2e + %A, 2f - %A]
--R       ]
--R     ,
--R
--R                     8     6      4      2
--R     [complexRoots= ?  + 4?  + 12?  + 16?  + 4,
--R
--R       coordinates =
--R                 7      5       3               7      5       3
--R         [4a - %A  - 3%A  - 10%A  - 6%A, 4b - %A  - 3%A  - 10%A  - 10%A,
--R                  7      5       3                 7      5       3
--R          4c - 2%A  - 7%A  - 20%A  - 22%A, 4d + 2%A  + 7%A  + 20%A  + 22%A,
--R                 7      5       3                7      5       3
--R          4e + %A  + 3%A  + 10%A  + 10%A, 4f + %A  + 3%A  + 10%A  + 6%A]
--R       ]
--R     ,
--R
--R                     8      6      4       2
--R     [complexRoots= ?  + 16?  - 96?  + 256?  + 256,
--R
--R       coordinates =
--R                   7       5        3
--R         [512a - %A  - 12%A  + 176%A  - 448%A,
--R                   7       5       3
--R          128b - %A  - 16%A  + 96%A  - 256%A,
--R                   7       5       3
--R          128c + %A  + 16%A  - 96%A  + 256%A,
--R                   7       5        3
--R          512d + %A  + 12%A  - 176%A  + 448%A, 2e + %A, 2f - %A]
--R       ]
--R     ,
--R
--R     [
--R       complexRoots =
--R          8      7      6       5       4       3        2
--R         ?  - 12?  + 64?  - 192?  + 432?  - 768?  + 1024?  - 768? + 256
--R       ,
--R
--R       coordinates =
--R         [
--R                         7        6        5         4         3         2
--R             1408a - 19%A  + 200%A  - 912%A  + 2216%A  - 4544%A  + 6784%A
--R           + 
--R             - 6976%A + 1792
--R           ,
--R
--R                         7        6         5         4          3          2
--R             1408b - 37%A  + 408%A  - 1952%A  + 5024%A  - 10368%A  + 16768%A
--R           + 
--R             - 17920%A + 5120
--R           ,
--R
--R                         7        6         5         4          3          2
--R             1408c + 37%A  - 408%A  + 1952%A  - 5024%A  + 10368%A  - 16768%A
--R           + 
--R             17920%A - 5120
--R           ,
--R
--R                         7        6        5         4         3         2
--R             1408d + 19%A  - 200%A  + 912%A  - 2216%A  + 4544%A  - 6784%A
--R           + 
--R             6976%A - 1792
--R           ,
--R          2e + %A, 2f - %A]
--R       ]
--R     ,
--R
--R                     8     7      6      5      4     2
--R     [complexRoots= ?  - 6?  + 16?  - 24?  + 18?  - 8?  + 4,
--R
--R       coordinates =
--R                  7      6       5       4      3       2
--R         [2a + 2%A  - 9%A  + 18%A  - 19%A  + 4%A  + 10%A  - 2%A - 4,
--R                  7      6       5       4      3       2
--R          2b + 2%A  - 9%A  + 18%A  - 19%A  + 4%A  + 10%A  - 4%A - 4,
--R                 7      6      5      4      3
--R          2c - %A  + 4%A  - 8%A  + 9%A  - 4%A  - 2%A + 4,
--R                 7      6      5      4      3
--R          2d + %A  - 4%A  + 8%A  - 9%A  + 4%A  + 2%A - 4,
--R                  7      6       5       4      3       2
--R          2e - 2%A  + 9%A  - 18%A  + 19%A  - 4%A  - 10%A  + 4%A + 4,
--R                  7      6       5       4      3       2
--R          2f - 2%A  + 9%A  - 18%A  + 19%A  - 4%A  - 10%A  + 2%A + 4]
--R       ]
--R     ,
--R
--R                     4      2
--R     [complexRoots= ?  + 12?  + 144,
--R
--R       coordinates =
--R                  2               2               2               2
--R         [12a - %A  - 12, 12b - %A  - 12, 12c - %A  - 12, 12d - %A  - 12,
--R                 2                    2
--R          6e + %A  + 3%A + 12, 6f + %A  - 3%A + 12]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  + 6?  + 30?  + 36? + 36,
--R
--R       coordinates =
--R                 3      2                     3      2
--R         [6a - %A  - 5%A  - 24%A - 6, 30b + %A  + 5%A  + 30%A + 6,
--R                  3      2                     3      2
--R          30c + %A  + 5%A  + 30%A + 6, 30d + %A  + 5%A  + 30%A + 6,
--R                  3      2                     3      2
--R          30e + %A  + 5%A  + 30%A + 6, 30f + %A  + 5%A  + 6]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  - 6?  + 30?  - 36? + 36,
--R
--R       coordinates =
--R                 3      2                     3      2
--R         [6a - %A  + 5%A  - 24%A + 6, 30b + %A  - 5%A  + 30%A - 6,
--R                  3      2                     3      2
--R          30c + %A  - 5%A  + 30%A - 6, 30d + %A  - 5%A  + 30%A - 6,
--R                  3      2                     3      2
--R          30e + %A  - 5%A  + 30%A - 6, 30f + %A  - 5%A  - 6]
--R       ]
--R     ,
--R
--R                     4      2
--R     [complexRoots= ?  + 12?  + 144,
--R
--R       coordinates =
--R                  2               2               2               2
--R         [12a + %A  + 12, 12b + %A  + 12, 12c + %A  + 12, 12d + %A  + 12,
--R                 2                    2
--R          6e - %A  + 3%A - 12, 6f - %A  - 3%A - 12]
--R       ]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 12,
--R      coordinates= [a - 1,b - 1,c - 1,d - 1,2e + %A + 4,2f - %A + 4]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  + 6? + 6,
--R      coordinates= [a + %A + 5,b - 1,c - 1,d - 1,e - 1,f - %A - 1]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 6? + 6,
--R      coordinates= [a + %A - 5,b + 1,c + 1,d + 1,e + 1,f - %A + 1]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 12,
--R      coordinates= [a + 1,b + 1,c + 1,d + 1,2e + %A - 4,2f - %A - 4]]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  + 6?  + 30?  + 36? + 36,
--R
--R       coordinates =
--R                  3      2                     3      2
--R         [30a - %A  - 5%A  - 30%A - 6, 30b - %A  - 5%A  - 30%A - 6,
--R                  3      2                    3      2
--R          30c - %A  - 5%A  - 30%A - 6, 6d + %A  + 5%A  + 24%A + 6,
--R                  3      2              3      2
--R          30e - %A  - 5%A  - 6, 30f - %A  - 5%A  - 30%A - 6]
--R       ]
--R     ,
--R
--R                     4     3      2
--R     [complexRoots= ?  - 6?  + 30?  - 36? + 36,
--R
--R       coordinates =
--R                  3      2                     3      2
--R         [30a - %A  + 5%A  - 30%A + 6, 30b - %A  + 5%A  - 30%A + 6,
--R                  3      2                    3      2
--R          30c - %A  + 5%A  - 30%A + 6, 6d + %A  - 5%A  + 24%A - 6,
--R                  3      2              3      2
--R          30e - %A  + 5%A  + 6, 30f - %A  + 5%A  - 30%A + 6]
--R       ]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  + 6? + 6,
--R      coordinates= [a + 1,b + 1,c + 1,d - %A - 5,e + %A + 1,f + 1]]
--R     ,
--R
--R                     2
--R     [complexRoots= ?  - 6? + 6,
--R      coordinates= [a - 1,b - 1,c - 1,d - %A + 5,e + %A - 1,f - 1]]
--R     ]
--RType: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
--E 21

--S 22 of 22
concat [realSolve(ts)$zdpack for ts in lts] 
 

   (22)
   [[%B1,%B1,%B1,%B5,- %B5 - 4%B1,%B1], [%B1,%B1,%B1,%B6,- %B6 - 4%B1,%B1],
    [%B2,%B2,%B2,%B3,- %B3 - 4%B2,%B2], [%B2,%B2,%B2,%B4,- %B4 - 4%B2,%B2],
    [%B7,%B7,%B7,%B7,%B11,- %B11 - 4%B7], [%B7,%B7,%B7,%B7,%B12,- %B12 - 4%B7],
    [%B8,%B8,%B8,%B8,%B9,- %B9 - 4%B8], [%B8,%B8,%B8,%B8,%B10,- %B10 - 4%B8],
    [%B13,%B13,%B17,- %B17 - 4%B13,%B13,%B13],
    [%B13,%B13,%B18,- %B18 - 4%B13,%B13,%B13],
    [%B14,%B14,%B15,- %B15 - 4%B14,%B14,%B14],
    [%B14,%B14,%B16,- %B16 - 4%B14,%B14,%B14],

     [%B19, %B29,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B19   - ---------- %B19   - ----------- %B19
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B19   - ------------- %B19  - ----------- %B19
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B19   + ------------- %B19   + --------------- %B19
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B19   + --------------- %B19  - ------------ %B19
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B19   - ------------- %B19   - --------------- %B19
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B19   - --------------- %B19  - ------------- %B19
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B29 - ------------- %B19   + ------------ %B19
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B19   + ---------------- %B19
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B19  + -------------- %B19
           1387545279120           1387545279120
       ]
     ,

     [%B19, %B30,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B19   - ---------- %B19   - ----------- %B19
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B19   - ------------- %B19  - ----------- %B19
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B19   + ------------- %B19   + --------------- %B19
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B19   + --------------- %B19  - ------------ %B19
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B19   - ------------- %B19   - --------------- %B19
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B19   - --------------- %B19  - ------------- %B19
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B30 - ------------- %B19   + ------------ %B19
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B19   + ---------------- %B19
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B19  + -------------- %B19
           1387545279120           1387545279120
       ]
     ,

     [%B20, %B27,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B20   - ---------- %B20   - ----------- %B20
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B20   - ------------- %B20  - ----------- %B20
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B20   + ------------- %B20   + --------------- %B20
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B20   + --------------- %B20  - ------------ %B20
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B20   - ------------- %B20   - --------------- %B20
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B20   - --------------- %B20  - ------------- %B20
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B27 - ------------- %B20   + ------------ %B20
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B20   + ---------------- %B20
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B20  + -------------- %B20
           1387545279120           1387545279120
       ]
     ,

     [%B20, %B28,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B20   - ---------- %B20   - ----------- %B20
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B20   - ------------- %B20  - ----------- %B20
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B20   + ------------- %B20   + --------------- %B20
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B20   + --------------- %B20  - ------------ %B20
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B20   - ------------- %B20   - --------------- %B20
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B20   - --------------- %B20  - ------------- %B20
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B28 - ------------- %B20   + ------------ %B20
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B20   + ---------------- %B20
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B20  + -------------- %B20
           1387545279120           1387545279120
       ]
     ,

     [%B21, %B25,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B21   - ---------- %B21   - ----------- %B21
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B21   - ------------- %B21  - ----------- %B21
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B21   + ------------- %B21   + --------------- %B21
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B21   + --------------- %B21  - ------------ %B21
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B21   - ------------- %B21   - --------------- %B21
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B21   - --------------- %B21  - ------------- %B21
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B25 - ------------- %B21   + ------------ %B21
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B21   + ---------------- %B21
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B21  + -------------- %B21
           1387545279120           1387545279120
       ]
     ,

     [%B21, %B26,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B21   - ---------- %B21   - ----------- %B21
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B21   - ------------- %B21  - ----------- %B21
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B21   + ------------- %B21   + --------------- %B21
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B21   + --------------- %B21  - ------------ %B21
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B21   - ------------- %B21   - --------------- %B21
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B21   - --------------- %B21  - ------------- %B21
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B26 - ------------- %B21   + ------------ %B21
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B21   + ---------------- %B21
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B21  + -------------- %B21
           1387545279120           1387545279120
       ]
     ,

     [%B22, %B23,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B22   - ---------- %B22   - ----------- %B22
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B22   - ------------- %B22  - ----------- %B22
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B22   + ------------- %B22   + --------------- %B22
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B22   + --------------- %B22  - ------------ %B22
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B22   - ------------- %B22   - --------------- %B22
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B22   - --------------- %B22  - ------------- %B22
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B23 - ------------- %B22   + ------------ %B22
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B22   + ---------------- %B22
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B22  + -------------- %B22
           1387545279120           1387545279120
       ]
     ,

     [%B22, %B24,

           7865521      31   6696179241     25   25769893181     19
         ---------- %B22   - ---------- %B22   - ----------- %B22
         6006689520          2002229840            49235160
       + 
           1975912990729     13   1048460696489     7   21252634831
         - ------------- %B22   - ------------- %B22  - ----------- %B22
             3003344760             2002229840           6006689520
       ,

             778171189       31   1987468196267     25   155496778477189     19
         - ------------- %B22   + ------------- %B22   + --------------- %B22
           1387545279120          1387545279120            693772639560
       + 
         191631411158401     13   300335488637543     7   755656433863
         --------------- %B22   + --------------- %B22  - ------------ %B22
           693772639560            1387545279120          198220754160
       ,

          1094352947      31   2794979430821     25   218708802908737     19
         ------------ %B22   - ------------- %B22   - --------------- %B22
         462515093040           462515093040            231257546520
       + 
           91476663003591     13   145152550961823     7   1564893370717
         - -------------- %B22   - --------------- %B22  - ------------- %B22
             77085848840             154171697680           462515093040
       ,

                    4321823003      31   180949546069     25
         - %B24 - ------------- %B22   + ------------ %B22
                  1387545279120           22746643920
       + 
         863753195062493     19   1088094456732317     13
         --------------- %B22   + ---------------- %B22
           693772639560             693772639560
       + 
         1732620732685741     7   13506088516033
         ---------------- %B22  + -------------- %B22
           1387545279120           1387545279120
       ]
     ,
    [%B31,%B35,- %B35 - 4%B31,%B31,%B31,%B31],
    [%B31,%B36,- %B36 - 4%B31,%B31,%B31,%B31],
    [%B32,%B33,- %B33 - 4%B32,%B32,%B32,%B32],
    [%B32,%B34,- %B34 - 4%B32,%B32,%B32,%B32]]
                                 Type: List List RealClosure Fraction Integer
--R 
--R
--R   (22)
--R   [[%B1,%B1,%B1,%B5,- %B5 - 4%B1,%B1], [%B1,%B1,%B1,%B6,- %B6 - 4%B1,%B1],
--R    [%B2,%B2,%B2,%B3,- %B3 - 4%B2,%B2], [%B2,%B2,%B2,%B4,- %B4 - 4%B2,%B2],
--R    [%B7,%B7,%B7,%B7,%B11,- %B11 - 4%B7], [%B7,%B7,%B7,%B7,%B12,- %B12 - 4%B7],
--R    [%B8,%B8,%B8,%B8,%B9,- %B9 - 4%B8], [%B8,%B8,%B8,%B8,%B10,- %B10 - 4%B8],
--R    [%B13,%B13,%B17,- %B17 - 4%B13,%B13,%B13],
--R    [%B13,%B13,%B18,- %B18 - 4%B13,%B13,%B13],
--R    [%B14,%B14,%B15,- %B15 - 4%B14,%B14,%B14],
--R    [%B14,%B14,%B16,- %B16 - 4%B14,%B14,%B14],
--R
--R     [%B19, %B29,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B19   - ---------- %B19   - ----------- %B19
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B19   - ------------- %B19  - ----------- %B19
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B19   + ------------- %B19   + --------------- %B19
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B19   + --------------- %B19  - ------------ %B19
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B19   - ------------- %B19   - --------------- %B19
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B19   - --------------- %B19  - ------------- %B19
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B29 - ------------- %B19   + ------------ %B19
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B19   + ---------------- %B19
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B19  + -------------- %B19
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B19, %B30,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B19   - ---------- %B19   - ----------- %B19
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B19   - ------------- %B19  - ----------- %B19
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B19   + ------------- %B19   + --------------- %B19
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B19   + --------------- %B19  - ------------ %B19
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B19   - ------------- %B19   - --------------- %B19
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B19   - --------------- %B19  - ------------- %B19
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B30 - ------------- %B19   + ------------ %B19
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B19   + ---------------- %B19
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B19  + -------------- %B19
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B20, %B27,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B20   - ---------- %B20   - ----------- %B20
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B20   - ------------- %B20  - ----------- %B20
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B20   + ------------- %B20   + --------------- %B20
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B20   + --------------- %B20  - ------------ %B20
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B20   - ------------- %B20   - --------------- %B20
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B20   - --------------- %B20  - ------------- %B20
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B27 - ------------- %B20   + ------------ %B20
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B20   + ---------------- %B20
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B20  + -------------- %B20
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B20, %B28,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B20   - ---------- %B20   - ----------- %B20
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B20   - ------------- %B20  - ----------- %B20
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B20   + ------------- %B20   + --------------- %B20
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B20   + --------------- %B20  - ------------ %B20
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B20   - ------------- %B20   - --------------- %B20
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B20   - --------------- %B20  - ------------- %B20
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B28 - ------------- %B20   + ------------ %B20
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B20   + ---------------- %B20
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B20  + -------------- %B20
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B21, %B25,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B21   - ---------- %B21   - ----------- %B21
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B21   - ------------- %B21  - ----------- %B21
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B21   + ------------- %B21   + --------------- %B21
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B21   + --------------- %B21  - ------------ %B21
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B21   - ------------- %B21   - --------------- %B21
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B21   - --------------- %B21  - ------------- %B21
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B25 - ------------- %B21   + ------------ %B21
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B21   + ---------------- %B21
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B21  + -------------- %B21
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B21, %B26,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B21   - ---------- %B21   - ----------- %B21
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B21   - ------------- %B21  - ----------- %B21
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B21   + ------------- %B21   + --------------- %B21
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B21   + --------------- %B21  - ------------ %B21
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B21   - ------------- %B21   - --------------- %B21
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B21   - --------------- %B21  - ------------- %B21
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B26 - ------------- %B21   + ------------ %B21
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B21   + ---------------- %B21
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B21  + -------------- %B21
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B22, %B23,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B22   - ---------- %B22   - ----------- %B22
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B22   - ------------- %B22  - ----------- %B22
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B22   + ------------- %B22   + --------------- %B22
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B22   + --------------- %B22  - ------------ %B22
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B22   - ------------- %B22   - --------------- %B22
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B22   - --------------- %B22  - ------------- %B22
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B23 - ------------- %B22   + ------------ %B22
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B22   + ---------------- %B22
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B22  + -------------- %B22
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R
--R     [%B22, %B24,
--R
--R           7865521      31   6696179241     25   25769893181     19
--R         ---------- %B22   - ---------- %B22   - ----------- %B22
--R         6006689520          2002229840            49235160
--R       + 
--R           1975912990729     13   1048460696489     7   21252634831
--R         - ------------- %B22   - ------------- %B22  - ----------- %B22
--R             3003344760             2002229840           6006689520
--R       ,
--R
--R             778171189       31   1987468196267     25   155496778477189     19
--R         - ------------- %B22   + ------------- %B22   + --------------- %B22
--R           1387545279120          1387545279120            693772639560
--R       + 
--R         191631411158401     13   300335488637543     7   755656433863
--R         --------------- %B22   + --------------- %B22  - ------------ %B22
--R           693772639560            1387545279120          198220754160
--R       ,
--R
--R          1094352947      31   2794979430821     25   218708802908737     19
--R         ------------ %B22   - ------------- %B22   - --------------- %B22
--R         462515093040           462515093040            231257546520
--R       + 
--R           91476663003591     13   145152550961823     7   1564893370717
--R         - -------------- %B22   - --------------- %B22  - ------------- %B22
--R             77085848840             154171697680           462515093040
--R       ,
--R
--R                    4321823003      31   180949546069     25
--R         - %B24 - ------------- %B22   + ------------ %B22
--R                  1387545279120           22746643920
--R       + 
--R         863753195062493     19   1088094456732317     13
--R         --------------- %B22   + ---------------- %B22
--R           693772639560             693772639560
--R       + 
--R         1732620732685741     7   13506088516033
--R         ---------------- %B22  + -------------- %B22
--R           1387545279120           1387545279120
--R       ]
--R     ,
--R    [%B31,%B35,- %B35 - 4%B31,%B31,%B31,%B31],
--R    [%B31,%B36,- %B36 - 4%B31,%B31,%B31,%B31],
--R    [%B32,%B33,- %B33 - 4%B32,%B32,%B32,%B32],
--R    [%B32,%B34,- %B34 - 4%B32,%B32,%B32,%B32]]
--R                                 Type: List List RealClosure Fraction Integer
--E 22
)spool
 
Starts dribbling to TwoDimensionalArray.output (2010/3/27, 18:46:40).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
arr : ARRAY2 INT := new(5,4,0)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
        |          |
   (1)  |0  0  0  0|
        |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R        |          |
--R   (1)  |0  0  0  0|
--R        |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 1

--S 2 of 20
setelt(arr,1,1,17)
 

   (2)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  17
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 20
arr
 

        +17  0  0  0+
        |           |
        |0   0  0  0|
        |           |
   (3)  |0   0  0  0|
        |           |
        |0   0  0  0|
        |           |
        +0   0  0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R        +17  0  0  0+
--R        |           |
--R        |0   0  0  0|
--R        |           |
--R   (3)  |0   0  0  0|
--R        |           |
--R        |0   0  0  0|
--R        |           |
--R        +0   0  0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 3

--S 4 of 20
elt(arr,1,1)
 

   (4)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  17
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 20
arr(3,2) := 15
 

   (5)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  15
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 20
arr(3,2)
 

   (6)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  15
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 20
row(arr,1)
 

   (7)  [17,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (7)  [17,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 7

--S 8 of 20
column(arr,1)
 

   (8)  [17,0,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (8)  [17,0,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 8

--S 9 of 20
nrows(arr)
 

   (9)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  5
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 20
ncols(arr)
 

   (10)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  4
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 20
map(-,arr)
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (11)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (11)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 11

--S 12 of 20
map((x +-> x + x),arr)
 

         +34  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (12)  |0   30  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +34  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (12)  |0   30  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 12

--S 13 of 20
arrc := copy(arr)
 

         +17  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (13)  |0   15  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +17  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (13)  |0   15  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 13

--S 14 of 20
map!(-,arrc)
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (14)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (14)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 14

--S 15 of 20
arrc
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (15)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (15)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 15

--S 16 of 20
arr
 

         +17  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (16)  |0   15  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +17  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (16)  |0   15  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 16

--S 17 of 20
member?(17,arr)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 20
member?(10317,arr)
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 20
count(17,arr)
 

   (19)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  1
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 20
count(0,arr)
 

   (20)  18
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  18
--R                                                        Type: PositiveInteger
--E 20
)spool
 
Starts dribbling to mkfunc.output (2010/3/27, 18:29:59).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
expr := (x - exp x + 1)**2 * (sin(x**2) * x + 1)**3
 

   (1)
       3   x 2        4     3   x    5     4    3      2 3
     (x (%e )  + (- 2x  - 2x )%e  + x  + 2x  + x )sin(x )
   + 
        2   x 2        3     2   x     4     3     2      2 2
     (3x (%e )  + (- 6x  - 6x )%e  + 3x  + 6x  + 3x )sin(x )
   + 
            x 2        2        x     3     2           2       x 2
     (3x (%e )  + (- 6x  - 6x)%e  + 3x  + 6x  + 3x)sin(x ) + (%e )
   + 
                 x    2
     (- 2x - 2)%e  + x  + 2x + 1
                                                     Type: Expression Integer
--R 
--R
--R   (1)
--R       3   x 2        4     3   x    5     4    3      2 3
--R     (x (%e )  + (- 2x  - 2x )%e  + x  + 2x  + x )sin(x )
--R   + 
--R        2   x 2        3     2   x     4     3     2      2 2
--R     (3x (%e )  + (- 6x  - 6x )%e  + 3x  + 6x  + 3x )sin(x )
--R   + 
--R            x 2        2        x     3     2           2       x 2
--R     (3x (%e )  + (- 6x  - 6x)%e  + 3x  + 6x  + 3x)sin(x ) + (%e )
--R   + 
--R                 x    2
--R     (- 2x - 2)%e  + x  + 2x + 1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 9
function(expr, f, x)
 

   (2)  f
                                                                 Type: Symbol
--R 
--R
--R   (2)  f
--R                                                                 Type: Symbol
--E 2

--S 3 of 9
tbl := [f(0.1 * i - 1) for i in 0..20];
 
   Compiling function f with type Float -> Float 

                                                             Type: List Float
--R 
--R   Compiling function f with type Float -> Float 
--R
--R                                                             Type: List Float
--E 3

--S 4 of 9
e := (x - y + 1)**2 * (x**2 * y + 1)**2
 

   (4)
      4 4        5     4     2  3     6     5    4     3     2      2
     x y  + (- 2x  - 2x  + 2x )y  + (x  + 2x  + x  - 4x  - 4x  + 1)y
   + 
        4     3     2               2
     (2x  + 4x  + 2x  - 2x - 2)y + x  + 2x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)
--R      4 4        5     4     2  3     6     5    4     3     2      2
--R     x y  + (- 2x  - 2x  + 2x )y  + (x  + 2x  + x  - 4x  - 4x  + 1)y
--R   + 
--R        4     3     2               2
--R     (2x  + 4x  + 2x  - 2x - 2)y + x  + 2x + 1
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 9
function(e, g, [x, y])
 

   (5)  g
                                                                 Type: Symbol
--R 
--R
--R   (5)  g
--R                                                                 Type: Symbol
--E 5

--S 6 of 9
function(e, h, x, y)
 

   (6)  h
                                                                 Type: Symbol
--R 
--R
--R   (6)  h
--R                                                                 Type: Symbol
--E 6

--S 7 of 9
m1 := squareMatrix [[1, 2], [3, 4]]
 

        +1  2+
   (7)  |    |
        +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 7

--S 8 of 9
m2 := squareMatrix [[1, 0], [-1, 1]]
 

        + 1   0+
   (8)  |      |
        +- 1  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        + 1   0+
--R   (8)  |      |
--R        +- 1  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 9
h(m1, m2)
 
   Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix
      (2,Integer)) -> SquareMatrix(2,Integer) 

        +- 7836   8960 +
   (9)  |              |
        +- 17132  19588+
                                                Type: SquareMatrix(2,Integer)
--R 
--R   Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix
--R      (2,Integer)) -> SquareMatrix(2,Integer) 
--R
--R        +- 7836   8960 +
--R   (9)  |              |
--R        +- 17132  19588+
--R                                                Type: SquareMatrix(2,Integer)
--E 9
)spool 
 
Starts dribbling to schaum8.output (2010/3/27, 18:37:21).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 99
aa:=integrate(1/(a^2-x^2),x)
 

        log(x + a) - log(x - a)
   (1)  -----------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        log(x + a) - log(x - a)
--R   (1)  -----------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 99
bb:=1/(2*a)*log((a+x)/(a-x))
 

            - x - a
        log(-------)
             x - a
   (2)  ------------
             2a
                                                     Type: Expression Integer
--R
--R            - x - a
--R        log(-------)
--R             x - a
--R   (2)  ------------
--R             2a
--R                                                     Type: Expression Integer
--E

--S 3 of 99
cc:=aa-bb
 

                                      - x - a
        log(x + a) - log(x - a) - log(-------)
                                       x - a
   (3)  --------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                                      - x - a
--R        log(x + a) - log(x - a) - log(-------)
--R                                       x - a
--R   (3)  --------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 4 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 99
dd:=divlog cc
 

        log(x + a) - log(- x - a)
   (5)  -------------------------
                    2a
                                                     Type: Expression Integer
--R
--R        log(x + a) - log(- x - a)
--R   (5)  -------------------------
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 6 of 99
logminus:=rule(log(x + a) - log(- x - a) == log(-1))
 

   (6)  log(x + a) - log(- x - a) + %G == log(- 1) + %G
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(x + a) - log(- x - a) + %I == log(- 1) + %I
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 7 of 99      14:163 Schaums and Axiom differ by a constant
ee:=logminus dd
 

        log(- 1)
   (7)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 8 of 99
aa:=integrate(x/(a^2-x^2),x)
 

               2    2
          log(x  - a )
   (1)  - ------------
                2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R          log(x  - a )
--R   (1)  - ------------
--R                2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 99
bb:=-1/2*log(a^2-x^2)
 

                 2    2
          log(- x  + a )
   (2)  - --------------
                 2
                                                     Type: Expression Integer
--R
--R                 2    2
--R          log(- x  + a )
--R   (2)  - --------------
--R                 2
--R                                                     Type: Expression Integer
--E

--S 10 of 99
cc:=aa-bb
 

               2    2           2    2
        - log(x  - a ) + log(- x  + a )
   (3)  -------------------------------
                       2
                                                     Type: Expression Integer
--R
--R               2    2           2    2
--R        - log(x  - a ) + log(- x  + a )
--R   (3)  -------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E

--S 11 of 99
logminus1:=rule(-log(x^2-a^2)+log(-x^2+a^2) == log(-1))
 

               2    2           2    2
   (4)  - log(x  - a ) + log(- x  + a ) + %H == log(- 1) + %H
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    2           2    2
--I   (4)  - log(x  - a ) + log(- x  + a ) + %H == log(- 1) + %H
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12 of 99     14:164 Schaums and Axiom differ by a constant
dd:=logminus1 cc
 

        log(- 1)
   (5)  --------
            2
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R            2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 99
aa:=integrate(x^2/(a^2-x^2),x)
 

        a log(x + a) - a log(x - a) - 2x
   (1)  --------------------------------
                        2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a log(x + a) - a log(x - a) - 2x
--R   (1)  --------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 99
bb:=-x+a/2*log((a+x)/(a-x))
 

              - x - a
        a log(-------) - 2x
               x - a
   (2)  -------------------
                 2
                                                     Type: Expression Integer
--R
--R              - x - a
--R        a log(-------) - 2x
--R               x - a
--R   (2)  -------------------
--R                 2
--R                                                     Type: Expression Integer
--E

--S 15 of 99
cc:=aa-bb
 

                                            - x - a
        a log(x + a) - a log(x - a) - a log(-------)
                                             x - a
   (3)  --------------------------------------------
                              2
                                                     Type: Expression Integer
--R
--R                                            - x - a
--R        a log(x + a) - a log(x - a) - a log(-------)
--R                                             x - a
--R   (3)  --------------------------------------------
--R                              2
--R                                                     Type: Expression Integer
--E

--S 16 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 17 of 99
dd:=divlog cc
 

        a log(x + a) - a log(- x - a)
   (5)  -----------------------------
                      2
                                                     Type: Expression Integer
--R
--R        a log(x + a) - a log(- x - a)
--R   (5)  -----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 18 of 99
logminusa:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
 

   (6)  b log(x + a) - b log(- x - a) + %I == b log(- 1) + %I
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  b log(x + a) - b log(- x - a) + %M == b log(- 1) + %M
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19 of 99     14:165 Schaums and Axiom differ by a constant
ee:=logminusa dd
 

        a log(- 1)
   (7)  ----------
             2
                                                     Type: Expression Integer
--R
--R        a log(- 1)
--R   (7)  ----------
--R             2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 20 of 99
aa:=integrate(x^3/(a^2-x^2),x)
 

           2     2    2     2
        - a log(x  - a ) - x
   (1)  ---------------------
                  2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2     2
--R        - a log(x  - a ) - x
--R   (1)  ---------------------
--R                  2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21 of 99
bb:=-x^2/2-a^2/2*log(a^2-x^2)
 

           2       2    2     2
        - a log(- x  + a ) - x
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R           2       2    2     2
--R        - a log(- x  + a ) - x
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 22 of 99
cc:=aa-bb
 

           2     2    2     2       2    2
        - a log(x  - a ) + a log(- x  + a )
   (3)  -----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R           2     2    2     2       2    2
--R        - a log(x  - a ) + a log(- x  + a )
--R   (3)  -----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 23 of 99
logminus1b:=rule(-b*log(x^2-a^2)+b*log(-x^2+a^2) == b*log(-1))
 

                 2    2             2    2
   (4)  - b log(x  - a ) + b log(- x  + a ) + %J == b log(- 1) + %J
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                 2    2             2    2
--I   (4)  - b log(x  - a ) + b log(- x  + a ) + %N == b log(- 1) + %N
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 24 of 99     14:166 Schaums and Axiom differ by a constant
dd:=logminus1b cc
 

         2
        a log(- 1)
   (5)  ----------
             2
                                                     Type: Expression Integer
--R
--R         2
--R        a log(- 1)
--R   (5)  ----------
--R             2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 25 of 99
aa:=integrate(1/(x*(a^2-x^2)),x)
 

               2    2
        - log(x  - a ) + 2log(x)
   (1)  ------------------------
                     2
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2
--R        - log(x  - a ) + 2log(x)
--R   (1)  ------------------------
--R                     2
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 26 of 99
bb:=1/(2*a^2)*log(x^2/(a^2-x^2))
 

                  2
                 x
        log(- -------)
               2    2
              x  - a
   (2)  --------------
                2
              2a
                                                     Type: Expression Integer
--R
--R                  2
--R                 x
--R        log(- -------)
--R               2    2
--R              x  - a
--R   (2)  --------------
--R                2
--R              2a
--R                                                     Type: Expression Integer
--E

--S 27 of 99
cc:=aa-bb
 

                                             2
               2    2                       x
        - log(x  - a ) + 2log(x) - log(- -------)
                                          2    2
                                         x  - a
   (3)  -----------------------------------------
                             2
                           2a
                                                     Type: Expression Integer
--R
--R                                             2
--R               2    2                       x
--R        - log(x  - a ) + 2log(x) - log(- -------)
--R                                          2    2
--R                                         x  - a
--R   (3)  -----------------------------------------
--R                             2
--R                           2a
--R                                                     Type: Expression Integer
--E

--S 28 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29 of 99
dd:=divlog cc
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  2
                2a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  2
--R                2a
--R                                                     Type: Expression Integer
--E

--S 30 of 99
logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
 

               n
   (6)  log(- a ) == n log(a) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- a ) == n log(a) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 31 of 99     14:167 Schaums and Axiom differ by a constant
ee:=logpowminus dd
 

          log(- 1)
   (7)  - --------
               2
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R               2
--R             2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 32 of 99
aa:=integrate(1/(x^2*(a^2-x^2)),x)
 

        x log(x + a) - x log(x - a) - 2a
   (1)  --------------------------------
                        3
                      2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        x log(x + a) - x log(x - a) - 2a
--R   (1)  --------------------------------
--R                        3
--R                      2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 33 of 99
bb:=-1/(a^2*x)+1/(2*a^3)*log((a+x)/(a-x))
 

              - x - a
        x log(-------) - 2a
               x - a
   (2)  -------------------
                  3
                2a x
                                                     Type: Expression Integer
--R
--R              - x - a
--R        x log(-------) - 2a
--R               x - a
--R   (2)  -------------------
--R                  3
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 34 of 99
cc:=aa-bb
 

                                      - x - a
        log(x + a) - log(x - a) - log(-------)
                                       x - a
   (3)  --------------------------------------
                            3
                          2a
                                                     Type: Expression Integer
--R
--R                                      - x - a
--R        log(x + a) - log(x - a) - log(-------)
--R                                       x - a
--R   (3)  --------------------------------------
--R                            3
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 35 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36 of 99
dd:=divlog cc
 

        log(x + a) - log(- x - a)
   (5)  -------------------------
                     3
                   2a
                                                     Type: Expression Integer
--R
--R        log(x + a) - log(- x - a)
--R   (5)  -------------------------
--R                     3
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 37 of 99
logminus:=rule(log(x + a) - log(- x - a) == log(-1))
 

   (6)  log(x + a) - log(- x - a) + %K == log(- 1) + %K
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(x + a) - log(- x - a) + %O == log(- 1) + %O
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38 of 99     14:168 Schaums and Axiom differ by a constant
ee:=logminus dd
 

        log(- 1)
   (7)  --------
             3
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R             3
--R           2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 39 of 99
aa:=integrate(1/(x^3*(a^2-x^2)),x)
 

           2     2    2      2          2
        - x log(x  - a ) + 2x log(x) - a
   (1)  ---------------------------------
                        4 2
                      2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2     2    2      2          2
--R        - x log(x  - a ) + 2x log(x) - a
--R   (1)  ---------------------------------
--R                        4 2
--R                      2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40 of 99
bb:=-1/(2*a^2*x^2)+1/(2*a^4)*log(x^2/(a^2-x^2))
 

                    2
         2         x        2
        x log(- -------) - a
                 2    2
                x  - a
   (2)  ---------------------
                  4 2
                2a x
                                                     Type: Expression Integer
--R
--R                    2
--R         2         x        2
--R        x log(- -------) - a
--R                 2    2
--R                x  - a
--R   (2)  ---------------------
--R                  4 2
--R                2a x
--R                                                     Type: Expression Integer
--E

--S 41 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 42 of 99
bb1:=divlog bb
 

           2     2    2     2       2     2
        - x log(x  - a ) + x log(- x ) - a
   (4)  -----------------------------------
                         4 2
                       2a x
                                                     Type: Expression Integer
--R
--R           2     2    2     2       2     2
--R        - x log(x  - a ) + x log(- x ) - a
--R   (4)  -----------------------------------
--R                         4 2
--R                       2a x
--R                                                     Type: Expression Integer
--E

--S 43 of 99
cc:=aa-bb1
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 44 of 99
logminuspow:=rule(log(-x^n) == n*log(x)+log(-1))
 

               n
   (6)  log(- x ) == n log(x) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- x ) == n log(x) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 45 of 99     14:169 Schaums and Axiom differ by a constant
dd:=logminuspow cc
 

          log(- 1)
   (7)  - --------
               4
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R               4
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 46 of 99
aa:=integrate(1/((a^2-x^2)^2),x)
 

          2    2                  2    2
        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                              3 2     5
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2                  2    2
--R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                              3 2     5
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 47 of 99
bb:=x/(2*a^2*(a^2-x^2))+1/(4*a^3)*log((a+x)/(a-x))
 

          2    2     - x - a
        (x  - a )log(-------) - 2a x
                      x - a
   (2)  ----------------------------
                   3 2     5
                 4a x  - 4a
                                                     Type: Expression Integer
--R
--R          2    2     - x - a
--R        (x  - a )log(-------) - 2a x
--R                      x - a
--R   (2)  ----------------------------
--R                   3 2     5
--R                 4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 48 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 49 of 99
bb1:=divlog bb
 

            2    2                2    2
        (- x  + a )log(x - a) + (x  - a )log(- x - a) - 2a x
   (4)  ----------------------------------------------------
                               3 2     5
                             4a x  - 4a
                                                     Type: Expression Integer
--R
--R            2    2                2    2
--R        (- x  + a )log(x - a) + (x  - a )log(- x - a) - 2a x
--R   (4)  ----------------------------------------------------
--R                               3 2     5
--R                             4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 50 of 99
cc:=aa-bb1
 

        log(x + a) - log(- x - a)
   (5)  -------------------------
                     3
                   4a
                                                     Type: Expression Integer
--R
--R        log(x + a) - log(- x - a)
--R   (5)  -------------------------
--R                     3
--R                   4a
--R                                                     Type: Expression Integer
--E

--S 51 of 99
logminus:=rule(log(x + a) - log(- x - a) == log(-1))
 

   (6)  log(x + a) - log(- x - a) + %L == log(- 1) + %L
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  log(x + a) - log(- x - a) + %P == log(- 1) + %P
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 52 of 99     14:170 Schaums and Axiom differ by a constant
dd:=logminus cc
 

        log(- 1)
   (7)  --------
             3
           4a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R             3
--R           4a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 53 of 99
aa:=integrate(x/((a^2-x^2)^2),x)
 

              1
   (1)  - ---------
            2     2
          2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              1
--R   (1)  - ---------
--R            2     2
--R          2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 54 of 99
bb:=1/(2*(a^2-x^2))
 

              1
   (2)  - ---------
            2     2
          2x  - 2a
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R            2     2
--R          2x  - 2a
--R                                            Type: Fraction Polynomial Integer
--E

--S 55 of 99     14:171 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 56 of 99
aa:=integrate(x^2/((a^2-x^2)^2),x)
 

            2    2                2    2
        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
   (1)  --------------------------------------------------
                                2     3
                            4a x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2                2    2
--R        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
--R   (1)  --------------------------------------------------
--R                                2     3
--R                            4a x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 57 of 99
bb:=x/(2*(a^2-x^2))-1/(4*a)*log((a+x)/(a-x))
 

            2    2     - x - a
        (- x  + a )log(-------) - 2a x
                        x - a
   (2)  ------------------------------
                      2     3
                  4a x  - 4a
                                                     Type: Expression Integer
--R
--R            2    2     - x - a
--R        (- x  + a )log(-------) - 2a x
--R                        x - a
--R   (2)  ------------------------------
--R                      2     3
--R                  4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 58 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 59 of 99
bb1:=divlog bb
 

          2    2                  2    2
        (x  - a )log(x - a) + (- x  + a )log(- x - a) - 2a x
   (4)  ----------------------------------------------------
                                 2     3
                             4a x  - 4a
                                                     Type: Expression Integer
--R
--R          2    2                  2    2
--R        (x  - a )log(x - a) + (- x  + a )log(- x - a) - 2a x
--R   (4)  ----------------------------------------------------
--R                                 2     3
--R                             4a x  - 4a
--R                                                     Type: Expression Integer
--E

--S 60 of 99
cc:=aa-bb1
 

        - log(x + a) + log(- x - a)
   (5)  ---------------------------
                     4a
                                                     Type: Expression Integer
--R
--R        - log(x + a) + log(- x - a)
--R   (5)  ---------------------------
--R                     4a
--R                                                     Type: Expression Integer
--E

--S 61 of 99
logminus2:=rule(-log(x + a) + log(- x - a) == log(-1))
 

   (6)  - log(x + a) + log(- x - a) + %M == log(- 1) + %M
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (6)  - log(x + a) + log(- x - a) + %S == log(- 1) + %S
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 62 of 99     14:172 Schaums and Axiom differ by a constant
dd:=logminus2 cc
 

        log(- 1)
   (7)  --------
           4a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (7)  --------
--R           4a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 63 of 99
aa:=integrate(x^3/((a^2-x^2)^2),x)
 

          2    2      2    2     2
        (x  - a )log(x  - a ) - a
   (1)  --------------------------
                   2     2
                 2x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2      2    2     2
--R        (x  - a )log(x  - a ) - a
--R   (1)  --------------------------
--R                   2     2
--R                 2x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 64 of 99
bb:=a^2/(2*(a^2-x^2))+1/2*log(a^2-x^2)
 

          2    2        2    2     2
        (x  - a )log(- x  + a ) - a
   (2)  ----------------------------
                    2     2
                  2x  - 2a
                                                     Type: Expression Integer
--R
--R          2    2        2    2     2
--R        (x  - a )log(- x  + a ) - a
--R   (2)  ----------------------------
--R                    2     2
--R                  2x  - 2a
--R                                                     Type: Expression Integer
--E

--S 65 of 99
cc:=aa-bb
 

             2    2           2    2
        log(x  - a ) - log(- x  + a )
   (3)  -----------------------------
                      2
                                                     Type: Expression Integer
--R
--R             2    2           2    2
--R        log(x  - a ) - log(- x  + a )
--R   (3)  -----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 66 of 99
logminus3:=rule(log(x^2-a^2)-log(-x^2+a^2) == log(-1))
 

             2    2           2    2
   (4)  log(x  - a ) - log(- x  + a ) + %N == log(- 1) + %N
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             2    2           2    2
--I   (4)  log(x  - a ) - log(- x  + a ) + %T == log(- 1) + %T
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 67 of 99     14:173 Schaums and Axiom differ by a constant
dd:=logminus3 cc
 

        log(- 1)
   (5)  --------
            2
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (5)  --------
--R            2
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 68 of 99
aa:=integrate(1/(x*(a^2-x^2)^2),x)
 

            2    2      2    2       2     2           2
        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
   (1)  ------------------------------------------------
                             4 2     6
                           2a x  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2    2      2    2       2     2           2
--R        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
--R   (1)  ------------------------------------------------
--R                             4 2     6
--R                           2a x  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 69 of 99
bb:=1/(2*a^2*(a^2-x^2))+1/(2*a^4)*log(x^2/(a^2-x^2))
 

                           2
          2    2          x        2
        (x  - a )log(- -------) - a
                        2    2
                       x  - a
   (2)  ----------------------------
                   4 2     6
                 2a x  - 2a
                                                     Type: Expression Integer
--R
--R                           2
--R          2    2          x        2
--R        (x  - a )log(- -------) - a
--R                        2    2
--R                       x  - a
--R   (2)  ----------------------------
--R                   4 2     6
--R                 2a x  - 2a
--R                                                     Type: Expression Integer
--E

--S 70 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 71 of 99
bb1:=divlog bb
 

            2    2      2    2      2    2        2     2
        (- x  + a )log(x  - a ) + (x  - a )log(- x ) - a
   (4)  -------------------------------------------------
                             4 2     6
                           2a x  - 2a
                                                     Type: Expression Integer
--R
--R            2    2      2    2      2    2        2     2
--R        (- x  + a )log(x  - a ) + (x  - a )log(- x ) - a
--R   (4)  -------------------------------------------------
--R                             4 2     6
--R                           2a x  - 2a
--R                                                     Type: Expression Integer
--E

--S 72 of 99
cc:=aa-bb1
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  4
                2a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  4
--R                2a
--R                                                     Type: Expression Integer
--E

--S 73 of 99
logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
 

               n
   (6)  log(- a ) == n log(a) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- a ) == n log(a) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 74 of 99     14:174 Schaums and Axiom differ by a constant
dd:=logpowminus cc
 

          log(- 1)
   (7)  - --------
               4
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R               4
--R             2a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 75 of 99
aa:=integrate(1/(x^2*(a^2-x^2)^2),x)
 

           3     2                    3     2                   2     3
        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
   (1)  ---------------------------------------------------------------
                                    5 3     7
                                  4a x  - 4a x
                                          Type: Union(Expression Integer,...)
--R
--R           3     2                    3     2                   2     3
--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
--R   (1)  ---------------------------------------------------------------
--R                                    5 3     7
--R                                  4a x  - 4a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 76 of 99
bb:=-1/(a^4*x)+x/(2*a^4*(a^2-x^2))+3/(4*a^5)*log((a+x)/(a-x))
 

           3     2      - x - a        2     3
        (3x  - 3a x)log(-------) - 6a x  + 4a
                         x - a
   (2)  --------------------------------------
                       5 3     7
                     4a x  - 4a x
                                                     Type: Expression Integer
--R
--R           3     2      - x - a        2     3
--R        (3x  - 3a x)log(-------) - 6a x  + 4a
--R                         x - a
--R   (2)  --------------------------------------
--R                       5 3     7
--R                     4a x  - 4a x
--R                                                     Type: Expression Integer
--E

--S 77 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 78 of 99
bb1:=divlog bb
 

             3     2                  3     2                     2     3
        (- 3x  + 3a x)log(x - a) + (3x  - 3a x)log(- x - a) - 6a x  + 4a
   (4)  -----------------------------------------------------------------
                                     5 3     7
                                   4a x  - 4a x
                                                     Type: Expression Integer
--R
--R             3     2                  3     2                     2     3
--R        (- 3x  + 3a x)log(x - a) + (3x  - 3a x)log(- x - a) - 6a x  + 4a
--R   (4)  -----------------------------------------------------------------
--R                                     5 3     7
--R                                   4a x  - 4a x
--R                                                     Type: Expression Integer
--E

--S 79 of 99
cc:=aa-bb
 

                                         - x - a
        3log(x + a) - 3log(x - a) - 3log(-------)
                                          x - a
   (5)  -----------------------------------------
                             5
                           4a
                                                     Type: Expression Integer
--R
--R                                         - x - a
--R        3log(x + a) - 3log(x - a) - 3log(-------)
--R                                          x - a
--R   (5)  -----------------------------------------
--R                             5
--R                           4a
--R                                                     Type: Expression Integer
--E

--S 80 of 99
dd:=divlog cc
 

        3log(x + a) - 3log(- x - a)
   (6)  ---------------------------
                      5
                    4a
                                                     Type: Expression Integer
--R
--R        3log(x + a) - 3log(- x - a)
--R   (6)  ---------------------------
--R                      5
--R                    4a
--R                                                     Type: Expression Integer
--E

--S 81 of 99
logminusb:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
 

   (7)  b log(x + a) - b log(- x - a) + %O == b log(- 1) + %O
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I   (7)  b log(x + a) - b log(- x - a) + %U == b log(- 1) + %U
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 82 of 99     14:175 Schaums and Axiom differ by a constant
ee:=logminusb dd
 

        3log(- 1)
   (8)  ---------
             5
           4a
                                                     Type: Expression Integer
--R
--R        3log(- 1)
--R   (8)  ---------
--R             5
--R           4a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 83 of 99
aa:=integrate(1/(x^3*(a^2-x^2)^2),x)
 

             4     2 2      2    2       4     2 2            2 2    4
        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
   (1)  --------------------------------------------------------------
                                   6 4     8 2
                                 2a x  - 2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             4     2 2      2    2       4     2 2            2 2    4
--R        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
--R   (1)  --------------------------------------------------------------
--R                                   6 4     8 2
--R                                 2a x  - 2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 84 of 99
bb:=-1/(2*a^4*x^2)+1/(2*a^4*(a^2-x^2))+1/a^6*log(x^2/(a^2-x^2))
 

                               2
           4     2 2          x         2 2    4
        (2x  - 2a x )log(- -------) - 2a x  + a
                            2    2
                           x  - a
   (2)  ----------------------------------------
                        6 4     8 2
                      2a x  - 2a x
                                                     Type: Expression Integer
--R
--R                               2
--R           4     2 2          x         2 2    4
--R        (2x  - 2a x )log(- -------) - 2a x  + a
--R                            2    2
--R                           x  - a
--R   (2)  ----------------------------------------
--R                        6 4     8 2
--R                      2a x  - 2a x
--R                                                     Type: Expression Integer
--E

--S 85 of 99
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (3)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (3)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 86 of 99
bb1:=divlog bb
 

             4     2 2      2    2       4     2 2        2      2 2    4
        (- 2x  + 2a x )log(x  - a ) + (2x  - 2a x )log(- x ) - 2a x  + a
   (4)  -----------------------------------------------------------------
                                    6 4     8 2
                                  2a x  - 2a x
                                                     Type: Expression Integer
--R
--R             4     2 2      2    2       4     2 2        2      2 2    4
--R        (- 2x  + 2a x )log(x  - a ) + (2x  - 2a x )log(- x ) - 2a x  + a
--R   (4)  -----------------------------------------------------------------
--R                                    6 4     8 2
--R                                  2a x  - 2a x
--R                                                     Type: Expression Integer
--E

--S 87 of 99
cc:=aa-bb1
 

                         2
        2log(x) - log(- x )
   (5)  -------------------
                  6
                 a
                                                     Type: Expression Integer
--R
--R                         2
--R        2log(x) - log(- x )
--R   (5)  -------------------
--R                  6
--R                 a
--R                                                     Type: Expression Integer
--E

--S 88 of 99
logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
 

               n
   (6)  log(- a ) == n log(a) + log(- 1)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               n
--R   (6)  log(- a ) == n log(a) + log(- 1)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 89 of 99     14:176 Schaums and Axiom differ by a constant
dd:=logpowminus cc
 

          log(- 1)
   (7)  - --------
              6
             a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (7)  - --------
--R              6
--R             a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 90 of 99     14:177 Axiom cannot do this integration
aa:=integrate(1/((a^2-x^2)^n),x)
 

           x
         ++       1
   (1)   |   ----------- d%U
        ++     2     2 n
             (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 91 of 99
aa:=integrate(x/((a^2-x^2)^n),x)
 

                    2    2
                 - x  + a
   (1)  --------------------------
                           2    2
                  n log(- x  + a )
        (2n - 2)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2    2
--R                 - x  + a
--R   (1)  --------------------------
--R                           2    2
--R                  n log(- x  + a )
--R        (2n - 2)%e
--R                                          Type: Union(Expression Integer,...)
--E 

--S 92 of 99
bb:=1/(2*(n-1)*(a^2-x^2)^(n-1))
 

                    1
   (2)  ------------------------
                    2    2 n - 1
        (2n - 2)(- x  + a )
                                                     Type: Expression Integer
--R
--R                    1
--R   (2)  ------------------------
--R                    2    2 n - 1
--R        (2n - 2)(- x  + a )
--R                                                     Type: Expression Integer
--E

--S 93 of 99
cc:=aa-bb
 

                     2    2
            n log(- x  + a )       2    2     2    2 n - 1
        - %e                 + (- x  + a )(- x  + a )
   (3)  --------------------------------------------------
                                               2    2
                        2    2 n - 1  n log(- x  + a )
            (2n - 2)(- x  + a )     %e
                                                     Type: Expression Integer
--R
--R                     2    2
--R            n log(- x  + a )       2    2     2    2 n - 1
--R        - %e                 + (- x  + a )(- x  + a )
--R   (3)  --------------------------------------------------
--R                                               2    2
--R                        2    2 n - 1  n log(- x  + a )
--R            (2n - 2)(- x  + a )     %e
--R                                                     Type: Expression Integer
--E

--S 94 of 99
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 95 of 99
dd:=explog cc
 

              2    2 n       2    2     2    2 n - 1
        - (- x  + a )  + (- x  + a )(- x  + a )
   (5)  --------------------------------------------
                        2    2 n - 1    2    2 n
            (2n - 2)(- x  + a )     (- x  + a )
                                                     Type: Expression Integer
--R
--R              2    2 n       2    2     2    2 n - 1
--R        - (- x  + a )  + (- x  + a )(- x  + a )
--R   (5)  --------------------------------------------
--R                        2    2 n - 1    2    2 n
--R            (2n - 2)(- x  + a )     (- x  + a )
--R                                                     Type: Expression Integer
--E

--S 96 of 99     14:178 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 97 of 99     14:179 Axiom cannot integrate this expression
aa:=integrate(1/(x*(a^2-x^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%U
        ++        2     2 n
             %U (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++        2     2 n
--I             %L (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 98 of 99     14:180 Axiom cannot integrate this expression
aa:=integrate(x^m/((a^2-x^2)^n),x)
 

           x       m
         ++      %U
   (1)   |   ----------- d%U
        ++     2     2 n
             (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %L
--I   (1)   |   ----------- d%L
--R        ++     2     2 n
--I             (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 99 of 99     14:181 Axiom cannot integrate this expression
aa:=integrate(1/(x^m*(a^2-x^2)^n),x)
 

           x
         ++         1
   (1)   |   -------------- d%U
        ++     m  2     2 n
             %U (a  - %U )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%L
--R        ++     m  2     2 n
--I             %L (a  - %L )
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to bug101.output (2010/3/27, 18:23:21).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
laplace(log(z),z,w)
 

   (1)  laplace(log(z),z,w)
                                                     Type: Expression Integer
--R
--R   (1)  laplace(log(z),z,w)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 2
laplace(log(z),w,z)
 

        log(z)
   (2)  ------
           z
                                                     Type: Expression Integer
--R
--R        log(z)
--R   (2)  ------
--R           z
--R                                                     Type: Expression Integer
--E 2
)spool 
 
Starts dribbling to r20bugs.output (2010/3/27, 18:30:56).
)set message test on
 
)set message auto off
 
)clear all
 
 

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 1 of 27
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
--R 
--R
--R   (1)  x
--R                                                          Type: BasicOperator
--E 1

--S 2 of 27
sum( (x i - mu)**2, i=1..N )
 

         N
        --+       2                2
   (2)  >     x(i)  - 2mu x(i) + mu
        --+
        i= 1
                                                     Type: Expression Integer
--R 
--R
--R         N
--R        --+       2                2
--R   (2)  >     x(i)  - 2mu x(i) + mu
--R        --+
--R        i= 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 27
D(%,mu)
 

         N
        --+
   (3)  >     - 2x(i) + 2mu
        --+
        i= 1
                                                     Type: Expression Integer
--R 
--R
--R         N
--R        --+
--R   (3)  >     - 2x(i) + 2mu
--R        --+
--R        i= 1
--R                                                     Type: Expression Integer
--E 3

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 4 of 27
z := log(x+.3*%i)
 

   (1)  log(x + 0.3 %i)
                                               Type: Expression Complex Float
--R 
--R
--R   (1)  log(x + 0.3 %i)
--R                                               Type: Expression Complex Float
--E 4

--S 5 of 27
z1 : EXPR Complex Float := z
 

   (2)  log(x + 0.3 %i)
                                               Type: Expression Complex Float
--R 
--R
--R   (2)  log(x + 0.3 %i)
--R                                               Type: Expression Complex Float
--E 5

--S 6 of 27
complexForm(z1)$CTRIGMNP(Float, EXPR Complex Float)
 

                 2                0.3
   (3)  0.5 log(x  + 0.09) + atan(---)%i
                                   x
                                               Type: Complex Expression Float
--R 
--R
--R                 2                0.3
--R   (3)  0.5 log(x  + 0.09) + atan(---)%i
--R                                   x
--R                                               Type: Complex Expression Float
--E 6

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 7 of 27
acot(-1)
 

        3%pi
   (1)  ----
          4
                                                     Type: Expression Integer
--R 
--R
--R        3%pi
--R   (1)  ----
--R          4
--R                                                     Type: Expression Integer
--E 7

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 8 of 27
sqrt(-1.0::COMPLEX FLOAT)
 

   (1)  %i
                                                          Type: Complex Float
--R 
--R
--R   (1)  %i
--R                                                          Type: Complex Float
--E 8

--S 9 of 27
log(x+%i)::EXPR COMPLEX FLOAT
 

   (2)  log(x + %i)
                                               Type: Expression Complex Float
--R 
--R
--R   (2)  log(x + %i)
--R                                               Type: Expression Complex Float
--E 9

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 10 of 27
positiveRemainder(-1,-5)
 

   (1)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  4
--R                                                        Type: PositiveInteger
--E 10

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 11 of 27
f:POLY FRAC COMPLEX INT := x^2+y^2
 

         2    2
   (1)  y  + x
                                    Type: Polynomial Fraction Complex Integer
--R 
--R
--R         2    2
--R   (1)  y  + x
--R                                    Type: Polynomial Fraction Complex Integer
--E 11

--S 12 of 27
factor f
 

   (2)  (y - %i x)(y + %i x)
                           Type: Factored Polynomial Fraction Complex Integer
--R 
--R
--R   (2)  (y - %i x)(y + %i x)
--R                           Type: Factored Polynomial Fraction Complex Integer
--E 12

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 13 of 27
acot(-y)
 

   (1)  acot(- y)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  acot(- y)
--R                                                     Type: Expression Integer
--E 13

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 14 of 27
a:=matrix [[1,2],[2,-1]]
 

        +1   2 +
   (1)  |      |
        +2  - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +1   2 +
--R   (1)  |      |
--R        +2  - 1+
--R                                                         Type: Matrix Integer
--E 14

--S 15 of 27
eigenMatrix a
 

        +   +-+       +-+    +
        |- \|5  + 1  \|5  + 1|
   (2)  |----------  --------|
        |     2          2   |
        |                    |
        +    1          1    +
                                   Type: Union(Matrix Expression Integer,...)
--R 
--R
--R        +   +-+       +-+    +
--R        |- \|5  + 1  \|5  + 1|
--R   (2)  |----------  --------|
--R        |     2          2   |
--R        |                    |
--R        +    1          1    +
--R                                   Type: Union(Matrix Expression Integer,...)
--E 15

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 16 of 27
positiveRemainder(-1::SINT,-5::SINT)
 

   (1)  4
                                                          Type: SingleInteger
--R 
--R
--R   (1)  4
--R                                                          Type: SingleInteger
--E 16

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 17 of 27
complexRoots([u**2-v+1,v**2-4],[u,v],0.01)
 

   (1)
   [[1.732421875 %i,- 2.0],[- 1.732421875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]]
                                                Type: List List Complex Float
--R 
--R
--R   (1)
--R   [[1.732421875 %i,- 2.0],[- 1.732421875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]]
--R                                                Type: List List Complex Float
--E 17

--S 18 of 27
complexRoots([u**2-v+1,v**2-4],[v,u],0.01)
 

   (2)  [[- 2.0,- 1.73046875 %i],[- 2.0,1.73046875 %i],[2.0,- 1.0],[2.0,1.0]]
                                                Type: List List Complex Float
--R 
--R
--R   (2)  [[- 2.0,- 1.73046875 %i],[- 2.0,1.73046875 %i],[2.0,- 1.0],[2.0,1.0]]
--R                                                Type: List List Complex Float
--E 18

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 19 of 27
R := Record(key:Symbol,entry:Integer)
 

   (1)  Record(key: Symbol,entry: Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Record(key: Symbol,entry: Integer)
--R                                                                 Type: Domain
--E 19

--S 20 of 27
tab := table([[a,1]$R,[b,2]$R,[c,3]$R])$Table(Symbol,Integer)
 

   (2)  table(c= 3,b= 2,a= 1)
                                                  Type: Table(Symbol,Integer)
--R 
--R
--R   (2)  table(c= 3,b= 2,a= 1)
--R                                                  Type: Table(Symbol,Integer)
--E 20

--S 21 of 27
remove!(b::Symbol,tab)
 

   (3)  2
                                                     Type: Union(Integer,...)
--R 
--R
--R   (3)  2
--R                                                     Type: Union(Integer,...)
--E 21

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 22 of 27
limit((x^a-a^x)/(x^x-a^a),x=a)
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 22

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 23 of 27
(4*x^6+16*x^4+16*x^2)*y^2+(-4*x^6+16*x^2)*y-8*x^6-16*x^4
 

           6      4      2  2        6      2       6      4
   (1)  (4x  + 16x  + 16x )y  + (- 4x  + 16x )y - 8x  - 16x
                                                     Type: Polynomial Integer
--R 
--R
--R           6      4      2  2        6      2       6      4
--R   (1)  (4x  + 16x  + 16x )y  + (- 4x  + 16x )y - 8x  - 16x
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 27
eval(%,x,z)
 

           2           6       2       4       2        2
   (2)  (4y  - 4y - 8)z  + (16y  - 16)z  + (16y  + 16y)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2           6       2       4       2        2
--R   (2)  (4y  - 4y - 8)z  + (16y  - 16)z  + (16y  + 16y)z
--R                                                     Type: Polynomial Integer
--E 24

--S 25 of 27
exquo(%,expand factor %)
 

   (3)  1
                                          Type: Union(Polynomial Integer,...)
--R 
--R
--R   (3)  1
--R                                          Type: Union(Polynomial Integer,...)
--E 25

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 26 of 27
log exp z
 

   (1)  z
                                                     Type: Expression Integer
--R 
--R
--R   (1)  z
--R                                                     Type: Expression Integer
--E 26

--S 27 of 27
normalize %
 

   (2)  z
                                                     Type: Expression Integer
--R 
--R
--R   (2)  z
--R                                                     Type: Expression Integer
--E 27
)spool 
 
Starts dribbling to lodesys.output (2010/3/27, 18:28:43).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 13
M := matrix [[ 1+4*t,  -5*t,   7*t,  -8*t,   8*t,  -6*t],_
             [ -10*t, 1+9*t, -14*t,  16*t, -16*t,  12*t],_
             [  -5*t,   5*t, 1-8*t,   8*t,  -8*t,   6*t],_
             [  10*t, -10*t,  14*t,1-17*t,  16*t, -12*t],_
             [   5*t,  -5*t,   7*t,  -8*t, 1+7*t,  -6*t],_
             [  -5*t,   5*t,  -7*t,   8*t,  -8*t, 1+5*t]]
 

        +4t + 1   - 5t      7t       - 8t       8t     - 6t +
        |                                                   |
        |- 10t   9t + 1   - 14t       16t     - 16t    12t  |
        |                                                   |
        | - 5t     5t    - 8t + 1     8t       - 8t     6t  |
   (1)  |                                                   |
        | 10t    - 10t     14t     - 17t + 1   16t    - 12t |
        |                                                   |
        |  5t     - 5t      7t       - 8t     7t + 1   - 6t |
        |                                                   |
        + - 5t     5t      - 7t       8t       - 8t   5t + 1+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R        +4t + 1   - 5t      7t       - 8t       8t     - 6t +
--R        |                                                   |
--R        |- 10t   9t + 1   - 14t       16t     - 16t    12t  |
--R        |                                                   |
--R        | - 5t     5t    - 8t + 1     8t       - 8t     6t  |
--R   (1)  |                                                   |
--R        | 10t    - 10t     14t     - 17t + 1   16t    - 12t |
--R        |                                                   |
--R        |  5t     - 5t      7t       - 8t     7t + 1   - 6t |
--R        |                                                   |
--R        + - 5t     5t      - 7t       8t       - 8t   5t + 1+
--R                                              Type: Matrix Polynomial Integer
--E 1

--S 2 of 13
sol := solve(inv(t**2) * M, t)
 

   (2)
           1          1         1        1       1         1
         - -        - -       - -      - -     - -       - -
      5    t     5    t    5    t   5    t  5    t    5    t
   [[t %e   ,- 2t %e   ,- t %e   ,2t %e   ,t %e   ,- t %e   ],
         1        1       1      1     1       1           1     1
       - -      - -     - -    - -   - -     - -         - -   - -
         t        t       t      t     t       t           t     t
     %e      4%e      %e    2%e    %e      %e         7%e    %e
    [-----,- ------,- -----,------,-----,- -----], [0,------,-----,0,0,0],
       t       5t       t      t     t       t          5t     t
              1       1               1         1               1           1
            - -     - -             - -       - -             - -         - -
              t       t               t         t               t           t
         8%e      %e             8%e        %e             6%e          %e
    [0,- ------,0,-----,0,0], [0,------,0,0,-----,0], [0,- ------,0,0,0,-----]]
           5t       t              5t         t              5t           t
                              Type: Union(List Vector Expression Integer,...)
--R 
--R
--R   (2)
--R           1          1         1        1       1         1
--R         - -        - -       - -      - -     - -       - -
--R      5    t     5    t    5    t   5    t  5    t    5    t
--R   [[t %e   ,- 2t %e   ,- t %e   ,2t %e   ,t %e   ,- t %e   ],
--R         1        1       1      1     1       1           1     1
--R       - -      - -     - -    - -   - -     - -         - -   - -
--R         t        t       t      t     t       t           t     t
--R     %e      4%e      %e    2%e    %e      %e         7%e    %e
--R    [-----,- ------,- -----,------,-----,- -----], [0,------,-----,0,0,0],
--R       t       5t       t      t     t       t          5t     t
--R              1       1               1         1               1           1
--R            - -     - -             - -       - -             - -         - -
--R              t       t               t         t               t           t
--R         8%e      %e             8%e        %e             6%e          %e
--R    [0,- ------,0,-----,0,0], [0,------,0,0,-----,0], [0,- ------,0,0,0,-----]]
--R           5t       t              5t         t              5t           t
--R                              Type: Union(List Vector Expression Integer,...)
--E 2

--S 3 of 13
[t**2 * map(h +-> D(h, t), v) - M * v for v in sol]
 

   (3)
   [[0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0],
    [0,0,0,0,0,0]]
                                         Type: List Vector Expression Integer
--R 
--R
--R   (3)
--R   [[0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0], [0,0,0,0,0,0],
--R    [0,0,0,0,0,0]]
--R                                         Type: List Vector Expression Integer
--E 3

--S 4 of 13
x := operator x
 

   (4)  x
                                                          Type: BasicOperator
--R 
--R
--R   (4)  x
--R                                                          Type: BasicOperator
--E 4

--S 5 of 13
y := operator y
 

   (5)  y
                                                          Type: BasicOperator
--R 
--R
--R   (5)  y
--R                                                          Type: BasicOperator
--E 5

--S 6 of 13
sys := [D(x t, t) = x t + sqrt 3 * y t, D(y t, t) = sqrt 3 * x t - y t]
 

          ,      +-+             ,               +-+
   (6)  [x (t)= \|3 y(t) + x(t),y (t)= - y(t) + \|3 x(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R          ,      +-+             ,               +-+
--R   (6)  [x (t)= \|3 y(t) + x(t),y (t)= - y(t) + \|3 x(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 6

--S 7 of 13
solve(sys, [x, y], t).basis
 

                 2t               - 2t
            2t %e       - 2t   3%e
   (7)  [[%e  ,----],[%e    ,- -------]]
                +-+               +-+
               \|3               \|3
                                         Type: List Vector Expression Integer
--R 
--R
--R                 2t               - 2t
--R            2t %e       - 2t   3%e
--R   (7)  [[%e  ,----],[%e    ,- -------]]
--R                +-+               +-+
--R               \|3               \|3
--R                                         Type: List Vector Expression Integer
--E 7

--S 8 of 13
v := vector [1, (-29*t + 19)/5, -1, t + 1, - 2*t + 3, -1]
 

             29     19
   (8)  [1,- -- t + --,- 1,t + 1,- 2t + 3,- 1]
              5      5
                                     Type: Vector Polynomial Fraction Integer
--R 
--R
--R             29     19
--R   (8)  [1,- -- t + --,- 1,t + 1,- 2t + 3,- 1]
--R              5      5
--R                                     Type: Vector Polynomial Fraction Integer
--E 8

--S 9 of 13
solp := solve(inv(t**2) * M, inv(t**2) * v, t).particular
 

               19
   (9)  [- 1,- --,1,- 1,- 3,1]
                5
                                              Type: Vector Expression Integer
--R 
--R
--R               19
--R   (9)  [- 1,- --,1,- 1,- 3,1]
--R                5
--R                                              Type: Vector Expression Integer
--E 9

--S 10 of 13
t**2 * map(h +-> D(h, t), solp) - M * solp - v
 

   (10)  [0,0,0,0,0,0]
                                              Type: Vector Expression Integer
--R 
--R
--R   (10)  [0,0,0,0,0,0]
--R                                              Type: Vector Expression Integer
--E 10

--S 11 of 13
z := operator z
 

   (11)  z
                                                          Type: BasicOperator
--R 
--R
--R   (11)  z
--R                                                          Type: BasicOperator
--E 11

--S 12 of 13
sys := [D(x t, t) = y t + z t + t, D(y t, t) = x t + z t, D(z t, t) = x t + y t]
 

           ,                      ,                  ,
   (12)  [x (t)= z(t) + y(t) + t,y (t)= z(t) + x(t),z (t)= y(t) + x(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R           ,                      ,                  ,
--R   (12)  [x (t)= z(t) + y(t) + t,y (t)= z(t) + x(t),z (t)= y(t) + x(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 12

--S 13 of 13
solve(sys, [x, y, z], t).particular
 

          2t - 3 - 2t + 1 - 2t + 1
   (13)  [------,--------,--------]
             4       4        4
                                              Type: Vector Expression Integer
--R 
--R
--R          2t - 3 - 2t + 1 - 2t + 1
--R   (13)  [------,--------,--------]
--R             4       4        4
--R                                              Type: Vector Expression Integer
--E 13
)spool 
 
Starts dribbling to rules.output (2010/3/27, 18:36:58).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 21
logrule := rule log(x) + log(y) == log(x * y)
 

   (1)  log(y) + log(x) + %B == log(x y) + %B
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)  log(y) + log(x) + %B == log(x y) + %B
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 1

--S 2 of 21
f := log sin x + log x
 

   (2)  log(sin(x)) + log(x)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  log(sin(x)) + log(x)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 21
logrule f
 

   (3)  log(x sin(x))
                                                     Type: Expression Integer
--R 
--R
--R   (3)  log(x sin(x))
--R                                                     Type: Expression Integer
--E 3

--S 4 of 21
logrules := rule
  log(x) + log(y) == log(x * y)
  y * log x       == log(x ** y)
 

                                                                y
   (4)  {log(y) + log(x) + %C == log(x y) + %C,y log(x) == log(x )}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R                                                                y
--R   (4)  {log(y) + log(x) + %C == log(x y) + %C,y log(x) == log(x )}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 4

--S 5 of 21
f := a * log(sin x) - 2 * log x
 

   (5)  a log(sin(x)) - 2log(x)
                                                     Type: Expression Integer
--R 
--R
--R   (5)  a log(sin(x)) - 2log(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 21
logrules f
 

                  a
            sin(x)
   (6)  log(-------)
                2
               x
                                                     Type: Expression Integer
--R 
--R
--R                  a
--R            sin(x)
--R   (6)  log(-------)
--R                2
--R               x
--R                                                     Type: Expression Integer
--E 6

--S 7 of 21
logrules2 := rule
  log(x) + log(y)          == log(x * y)
  (y | integer? y) * log x == log(x ** y)
 

                                                                y
   (7)  {log(y) + log(x) + %D == log(x y) + %D,y log(x) == log(x )}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R                                                                y
--R   (7)  {log(y) + log(x) + %D == log(x y) + %D,y log(x) == log(x )}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 7

--S 8 of 21
logrules2 f
 

                             1
   (8)  a log(sin(x)) + log(--)
                             2
                            x
                                                     Type: Expression Integer
--R 
--R
--R                             1
--R   (8)  a log(sin(x)) + log(--)
--R                             2
--R                            x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 21
trigLinearize := rule
  sin(x) * sin(y)                      == cos(x-y)/2 - cos(x+y)/2
  cos(x) * cos(y)                      == cos(x+y)/2 + cos(x-y)/2
  sin(x) * cos(y)                      == sin(x+y)/2 + sin(x-y)/2
  sin(x) ** (n | integer? n and n > 1) == (1-cos(2*x))/2 * sin(x)**(n-2)
  cos(x) ** (n | integer? n and n > 1) == (1+cos(2*x))/2 * cos(x)**(n-2)
 

   (9)
                       - %F cos(y + x) + %F cos(y - x)
   {%F sin(x)sin(y) == -------------------------------,
                                      2
                       %G cos(y + x) + %G cos(y - x)
    %G cos(x)cos(y) == -----------------------------,
                                     2
                       %H sin(y + x) - %H sin(y - x)
    %H cos(y)sin(x) == -----------------------------,
                                     2
                                    n - 2                                n - 2
          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
    sin(x)  == --------------------------, cos(x)  == ------------------------}
                            2                                     2
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (9)
--R                       - %F cos(y + x) + %F cos(y - x)
--R   {%F sin(x)sin(y) == -------------------------------,
--R                                      2
--R                       %G cos(y + x) + %G cos(y - x)
--R    %G cos(x)cos(y) == -----------------------------,
--R                                     2
--R                       %H sin(y + x) - %H sin(y - x)
--R    %H cos(y)sin(x) == -----------------------------,
--R                                     2
--R                                    n - 2                                n - 2
--R          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
--R    sin(x)  == --------------------------, cos(x)  == ------------------------}
--R                            2                                     2
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 9

--S 10 of 21
g := sin(a)*cos(b) + sin(a)*cos(a) + cos(2*a)*cos(3*a)
 

   (10)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
                                                     Type: Expression Integer
--R 
--R
--R   (10)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
--R                                                     Type: Expression Integer
--E 10

--S 11 of 21
trigLinearize g
 

         sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
   (11)  ----------------------------------------------------
                                   2
                                                     Type: Expression Integer
--R 
--R
--R         sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
--R   (11)  ----------------------------------------------------
--R                                   2
--R                                                     Type: Expression Integer
--E 11

--S 12 of 21
eirule := rule integral((?y + exp x)/x,x) == integral(y/x,x) + Ei x
 

            x   %K
          ++  %e   + y                   y
   (12)   |   -------- d%K  == 'integral(-,x) + 'Ei(x)
         ++      %K                      x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R            x   %K
--R          ++  %e   + y                   y
--R   (12)   |   -------- d%K  == 'integral(-,x) + 'Ei(x)
--R         ++      %K                      x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 12

--S 13 of 21
eirule integral(exp u/u, u)
 

   (13)  Ei(u)
                                                     Type: Expression Integer
--R 
--R
--R   (13)  Ei(u)
--R                                                     Type: Expression Integer
--E 13

--S 14 of 21
eirule integral(sin u + exp u/u, u)
 

            u
          ++
   (14)   |   sin(%K)d%K  + Ei(u)
         ++
                                                     Type: Expression Integer
--R 
--R
--R            u
--R          ++
--R   (14)   |   sin(%K)d%K  + Ei(u)
--R         ++
--R                                                     Type: Expression Integer
--E 14

--S 15 of 21
u := operator u
 

   (15)  u
                                                          Type: BasicOperator
--R 
--R
--R   (15)  u
--R                                                          Type: BasicOperator
--E 15

--S 16 of 21
v := operator v
 

   (16)  v
                                                          Type: BasicOperator
--R 
--R
--R   (16)  v
--R                                                          Type: BasicOperator
--E 16

--S 17 of 21
myrule := rule u(x + y) == u x + v y
 

   (17)  u(y + x) == 'v(y) + 'u(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (17)  u(y + x) == 'v(y) + 'u(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 17

--S 18 of 21
h := u(a + b + c + d)
 

   (18)  u(d + c + b + a)
                                                     Type: Expression Integer
--R 
--R
--R   (18)  u(d + c + b + a)
--R                                                     Type: Expression Integer
--E 18

--S 19 of 21
myrule h
 

   (19)  v(d + c + b) + u(a)
                                                     Type: Expression Integer
--R 
--R
--R   (19)  v(d + c + b) + u(a)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 21
myrule2 := rule u(:x + y) == u x + v y
 

   (20)  u(y + x) == 'v(y) + 'u(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R   (20)  u(y + x) == 'v(y) + 'u(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 20

--S 21 of 21
myrule2 h
 

   (21)  v(c) + v(b) + v(a) + u(d)
                                                     Type: Expression Integer
--R 
--R
--R   (21)  v(c) + v(b) + v(a) + u(d)
--R                                                     Type: Expression Integer
--E 21
)spool 
 
Starts dribbling to cachedf.output (2010/3/27, 18:23:27).
)set message test on
 
)set message auto off
 
)clear all
 
)sys cp $AXIOM/../../src/input/cachedf.input.pamphlet .
 
)lisp (tangle "cachedf.input.pamphlet" "cachedf.spad" "cachedf.spad")
 
Value = NIL
)set message time on
 

--S 1 of 8
)co cachedf
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/cachedf.spad 
      using old system compiler.
   CACHEDF abbreviates domain CachedFunction 
   processing macro definition Exports ==> -- the constructor category 
   processing macro definition Implementation ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing nrlib CACHEDF for CachedFunction 
   compiling into nrlib CACHEDF 
   compiling exported function : $ -> A -> B
      CACHEDF;function;$M;1 is replaced by QCDR 
Time: 0.02 SEC.

   compiling exported cachedFunction : A -> B -> $
Time: 0.01 SEC.

   compiling exported apply : ($,A) -> B
Time: 0 SEC.

   compiling exported recursiveDefine : ($,A -> B) -> $
Time: 0 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |CachedFunction| REDEFINED

;;;     ***       |CachedFunction| REDEFINED
Time: 0 SEC.


   Cumulative Statistics for Constructor CachedFunction
      Time: 0.03 seconds
 
   finalizing nrlib CACHEDF 
   Processing CachedFunction for Browser database:
--->-->CachedFunction((function ((Mapping B A) %))): Not documented!!!!
--->-->CachedFunction((cachedFunction (% (Mapping B A)))): Not documented!!!!
--->-->CachedFunction((apply (B % A))): Not documented!!!!
--->-->CachedFunction((recursiveDefine (% % (Mapping B A)))): Not documented!!!!
--------constructor---------
------------------------------------------------------------------------
   CachedFunction is now explicitly exposed in frame initial 
   CachedFunction will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/CACHEDF.nrlib/code

--R 
--R   Compiling AXIOM source code from file 
--I      /research/test/int/input/cachedf.spad using old system compiler.
--R   CACHEDF abbreviates domain CachedFunction 
--R   processing macro definition Exports ==> -- the constructor category 
--R   processing macro definition Implementation ==> -- the constructor capsule 
--R------------------------------------------------------------------------
--R   initializing nrlib CACHEDF for CachedFunction 
--R   compiling into nrlib CACHEDF 
--R   compiling exported function : $ -> A -> B
--R      CACHEDF;function;$M;1 is replaced by QCDR 
--ITime: 0.01 SEC.
--R
--R   compiling exported cachedFunction : A -> B -> $
--ITime: 0.01 SEC.
--R
--R   compiling exported apply : ($,A) -> B
--ITime: 0 SEC.
--R
--R   compiling exported recursiveDefine : ($,A -> B) -> $
--ITime: 0 SEC.
--R
--R(time taken in buildFunctor:  0 . NIL)
--R
--R;;;     ***       |CachedFunction| REDEFINED
--R
--R;;;     ***       |CachedFunction| REDEFINED
--ITime: 0 SEC.
--R
--R
--R   Cumulative Statistics for Constructor CachedFunction
--I      Time: 0.02 seconds
--R 
--R   finalizing nrlib CACHEDF 
--R   Processing CachedFunction for Browser database:
--R--->-->CachedFunction((function ((Mapping B A) %))): Not documented!!!!
--R--->-->CachedFunction((cachedFunction (% (Mapping B A)))): Not documented!!!!
--R--->-->CachedFunction((apply (B % A))): Not documented!!!!
--R--->-->CachedFunction((recursiveDefine (% % (Mapping B A)))): Not documented!!!!
--R--------constructor---------
--R------------------------------------------------------------------------
--I   CachedFunction is now explicitly exposed in frame frame0 
--R   CachedFunction will be automatically loaded when needed from 
--I      /research/test/int/input/CACHEDF.nrlib/code
--R
--E 1

--S 2 of 8
I := Integer
 

   (1)  Integer
                                                                 Type: Domain
                                                                  Time: 0 sec
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--I                                                                  Time: 0 sec
--E 2

--S 3 of 8
f(n:I):I == 1
 
   Function declaration f : Integer -> Integer has been added to 
      workspace.
                                                                   Type: Void
                                                                  Time: 0 sec
--R 
--R   Function declaration f : Integer -> Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--I                                                                  Time: 0 sec
--E 3

--S 4 of 8
fib: CachedFunction(I,I) := cachedFunction(f)
 
   Compiling function f with type Integer -> Integer 

 LISP output:
(#<hash-table 0943208c> *1;f;1;initial)
                                        Type: CachedFunction(Integer,Integer)
                                                   Time: 0.01 (OT) = 0.01 sec
--R 
--R   Compiling function f with type Integer -> Integer 
--R
--R LISP output:
--I(#<hash-table 092ec78c> *1;f;1;frame0)
--R                                        Type: CachedFunction(Integer,Integer)
--I                                                                  Time: 0 sec
--E 4

--S 5 of 8
recursiveDefine(fib,(n:I):I +-> if n<2 then 1 else fib(n-1)+fib(n-2))
 

 LISP output:
(#<hash-table 0943208c> (LAMBDA-CLOSURE    (G1725 envArg) (COND ((SPADCALL G1725 2 (ELT *1;anonymousFunction;0;initial;internal;MV 0)) 1) ((QUOTE T) (SPADCALL (SPADCALL (getValueFromEnvironment (QUOTE fib) (QUOTE (CachedFunction (Integer) (Integer)))) (SPADCALL G1725 1 (ELT *1;anonymousFunction;0;initial;internal;MV 1)) (ELT *1;anonymousFunction;0;initial;internal;MV 2)) (SPADCALL (getValueFromEnvironment (QUOTE fib) (QUOTE (CachedFunction (Integer) (Integer)))) (SPADCALL G1725 2 (ELT *1;anonymousFunction;0;initial;internal;MV 1)) (ELT *1;anonymousFunction;0;initial;internal;MV 2)) (ELT *1;anonymousFunction;0;initial;internal;MV 3))))))
                                        Type: CachedFunction(Integer,Integer)
                           Time: 0.02 (IN) + 0.01 (OT) + 0.01 (GC) = 0.04 sec
--R 
--R
--R LISP output:
--I(#<hash-table 092ec78c> (LAMBDA-CLOSURE    (G2554 envArg) (COND ((SPADCALL G2554 2 (ELT *1;anonymousFunction;0;frame0;internal;MV 0)) 1) ((QUOTE T) (SPADCALL (SPADCALL (getValueFromEnvironment (QUOTE fib) (QUOTE (CachedFunction (Integer) (Integer)))) (SPADCALL G2554 1 (ELT *1;anonymousFunction;0;frame0;internal;MV 1)) (ELT *1;anonymousFunction;0;frame0;internal;MV 2)) (SPADCALL (getValueFromEnvironment (QUOTE fib) (QUOTE (CachedFunction (Integer) (Integer)))) (SPADCALL G2554 2 (ELT *1;anonymousFunction;0;frame0;internal;MV 1)) (ELT *1;anonymousFunction;0;frame0;internal;MV 2)) (ELT *1;anonymousFunction;0;frame0;internal;MV 3))))))
--R                                        Type: CachedFunction(Integer,Integer)
--I                                       Time: 0.02 (IN) + 0.01 (GC) = 0.03 sec
--E 5

--S 6 of 8
fib 40
 

   (5)  165580141
                                                        Type: PositiveInteger
                                                   Time: 0.01 (IN) = 0.01 sec
--R 
--R
--R   (5)  165580141
--R                                                        Type: PositiveInteger
--I                                                   Time: 0.01 (IN) = 0.01 sec
--E 6

--S 7 of 8
g(n:I):I == if n<2 then 1 else g(n-1)+g(n-2)
 
   Function declaration g : Integer -> Integer has been added to 
      workspace.
                                                                   Type: Void
                                                                  Time: 0 sec
--R 
--R   Function declaration g : Integer -> Integer has been added to 
--R      workspace.
--R                                                                   Type: Void
--I                                                                  Time: 0 sec
--E 7

--S 8 of 8
g 40
 
   Compiling function g with type Integer -> Integer 

   (7)  165580141
                                                        Type: PositiveInteger
                                     Time: 51.23 (EV) + 0.04 (GC) = 51.27 sec
--R 
--R   Compiling function g with type Integer -> Integer 
--R
--R   (7)  165580141
--R                                                        Type: PositiveInteger
--I                                     Time: 36.42 (EV) + 0.02 (GC) = 36.44 sec
--E 8
)spool
 
Starts dribbling to schaum22.output (2010/3/27, 18:38:23).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 52
aa:=integrate(sec(a*x),x)
 

            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
        log(-----------------------) - log(-----------------------)
                  cos(a x) + 1                   cos(a x) + 1
   (1)  -----------------------------------------------------------
                                     a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R        log(-----------------------) - log(-----------------------)
--R                  cos(a x) + 1                   cos(a x) + 1
--R   (1)  -----------------------------------------------------------
--R                                     a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 52
bb1:=1/a*log(sec(a*x)+tan(a*x))
 

        log(tan(a x) + sec(a x))
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R        log(tan(a x) + sec(a x))
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 3 of 52
bb2:=1/a*log(tan((a*x)/2+%pi/4))
 

                2a x + %pi
        log(tan(----------))
                     4
   (3)  --------------------
                  a
                                                     Type: Expression Integer
--R
--R                2a x + %pi
--R        log(tan(----------))
--R                     4
--R   (3)  --------------------
--R                  a
--R                                                     Type: Expression Integer
--E

--S 4 of 52
cc1:=aa-bb1
 

   (4)
                                        sin(a x) + cos(a x) + 1
       - log(tan(a x) + sec(a x)) + log(-----------------------)
                                              cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                        sin(a x) + cos(a x) + 1
--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
--R                                              cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 5 of 52
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (5)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (5)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 6 of 52
dd1:=tanrule cc1
 

   (6)
             sin(a x) + cos(a x)sec(a x)        sin(a x) + cos(a x) + 1
       - log(---------------------------) + log(-----------------------)
                       cos(a x)                       cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (6)
--R             sin(a x) + cos(a x)sec(a x)        sin(a x) + cos(a x) + 1
--R       - log(---------------------------) + log(-----------------------)
--R                       cos(a x)                       cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 7 of 52
secrule:=rule(sec(a) == 1/cos(a))
 

                     1
   (7)  sec(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (7)  sec(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 8 of 52
ee1:=secrule dd1
 

   (8)
             sin(a x) + 1        sin(a x) + cos(a x) + 1
       - log(------------) + log(-----------------------)
               cos(a x)                cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (8)
--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
--R       - log(------------) + log(-----------------------)
--R               cos(a x)                cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 9 of 52
ff1:=expandLog ee1
 

   (9)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
     + 
       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
  /
     a
                                                     Type: Expression Integer
--R
--R   (9)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
--R     + 
--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 10 of 52
gg1:=complexNormalize ff1
 

         log(- 1)
   (10)  --------
             a
                                                     Type: Expression Integer
--R
--R         log(- 1)
--R   (10)  --------
--R             a
--R                                                     Type: Expression Integer
--E

--S 11 of 52
cc2:=aa-bb2
 

   (11)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (11)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 12 of 52
dd2:=tanrule cc2
 

   (12)
           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
       log(-----------------------) - log(-----------------------)
                 cos(a x) + 1                   cos(a x) + 1
     + 
                 2a x + %pi
             sin(----------)
                      4
       - log(---------------)
                 2a x + %pi
             cos(----------)
                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (12)
--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R       log(-----------------------) - log(-----------------------)
--R                 cos(a x) + 1                   cos(a x) + 1
--R     + 
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R       - log(---------------)
--R                 2a x + %pi
--R             cos(----------)
--R                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 13 of 52
ee2:=expandLog dd2
 

   (13)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
     + 
                 2a x + %pi             2a x + %pi
       - log(sin(----------)) + log(cos(----------))
                      4                      4
  /
     a
                                                     Type: Expression Integer
--R
--R   (13)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
--R     + 
--R                 2a x + %pi             2a x + %pi
--R       - log(sin(----------)) + log(cos(----------))
--R                      4                      4
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 14 of 52     14:451 Schaums and Axiom differ by a constant
ff2:=complexNormalize ee2
 

         log(- 1)
   (14)  --------
             a
                                                     Type: Expression Integer
--R
--R         log(- 1)
--R   (14)  --------
--R             a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 15 of 52
aa:=integrate(sec(a*x)^2,x)
 

         sin(a x)
   (1)  ----------
        a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         sin(a x)
--R   (1)  ----------
--R        a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16 of 52
bb:=tan(a*x)/a
 

        tan(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        tan(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E

--S 17 of 52
cc:=aa-bb
 

        - cos(a x)tan(a x) + sin(a x)
   (3)  -----------------------------
                  a cos(a x)
                                                     Type: Expression Integer
--R
--R        - cos(a x)tan(a x) + sin(a x)
--R   (3)  -----------------------------
--R                  a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 18 of 52
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19 of 52     14:452 Schaums and Axiom agree
dd:=tanrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 20 of 52
aa:=integrate(sec(a*x)^3,x)
 

   (1)
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
                 2    sin(a x) - cos(a x) - 1
       - cos(a x) log(-----------------------) + sin(a x)
                            cos(a x) + 1
  /
                2
     2a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R                 2    sin(a x) - cos(a x) - 1
--R       - cos(a x) log(-----------------------) + sin(a x)
--R                            cos(a x) + 1
--R  /
--R                2
--R     2a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21 of 52
bb:=(sec(a*x)*tan(a*x))/(2*a)+1/(2*a)*log(sec(a*x)+tan(a*x))
 

        log(tan(a x) + sec(a x)) + sec(a x)tan(a x)
   (2)  -------------------------------------------
                             2a
                                                     Type: Expression Integer
--R
--R        log(tan(a x) + sec(a x)) + sec(a x)tan(a x)
--R   (2)  -------------------------------------------
--R                             2a
--R                                                     Type: Expression Integer
--E

--S 22 of 52
cc:=aa-bb
 

   (3)
                 2
       - cos(a x) log(tan(a x) + sec(a x))
     + 
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
                 2    sin(a x) - cos(a x) - 1            2
       - cos(a x) log(-----------------------) - cos(a x) sec(a x)tan(a x)
                            cos(a x) + 1
     + 
       sin(a x)
  /
                2
     2a cos(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2
--R       - cos(a x) log(tan(a x) + sec(a x))
--R     + 
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R                 2    sin(a x) - cos(a x) - 1            2
--R       - cos(a x) log(-----------------------) - cos(a x) sec(a x)tan(a x)
--R                            cos(a x) + 1
--R     + 
--R       sin(a x)
--R  /
--R                2
--R     2a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 23 of 52
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 24 of 52
dd:=tanrule cc
 

   (5)
                 2    sin(a x) + cos(a x)sec(a x)
       - cos(a x) log(---------------------------)
                                cos(a x)
     + 
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
               2    sin(a x) - cos(a x) - 1
     - cos(a x) log(-----------------------) + (- cos(a x)sec(a x) + 1)sin(a x)
                          cos(a x) + 1
  /
                2
     2a cos(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                 2    sin(a x) + cos(a x)sec(a x)
--R       - cos(a x) log(---------------------------)
--R                                cos(a x)
--R     + 
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R               2    sin(a x) - cos(a x) - 1
--R     - cos(a x) log(-----------------------) + (- cos(a x)sec(a x) + 1)sin(a x)
--R                          cos(a x) + 1
--R  /
--R                2
--R     2a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 25 of 52
secrule:=rule(sec(a) == 1/cos(a))
 

                     1
   (6)  sec(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                     1
--R   (6)  sec(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26 of 52
ee:=secrule dd
 

   (7)
             sin(a x) + 1        sin(a x) + cos(a x) + 1
       - log(------------) + log(-----------------------)
               cos(a x)                cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (7)
--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
--R       - log(------------) + log(-----------------------)
--R               cos(a x)                cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 27 of 52
ff:=expandLog ee
 

   (8)
       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
     + 
       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
  /
     2a
                                                     Type: Expression Integer
--R
--R   (8)
--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
--R     + 
--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 28 of 52     14:453 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

        log(- 1)
   (9)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (9)  --------
--R           2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 29 of 52
aa:=integrate(sec(a*x)^n*tan(a*x),x)
 

                    1
          n log(---------)
                        2
                cos(a x)
          ----------------
                  2
        %e
   (1)  ------------------
                a n
                                          Type: Union(Expression Integer,...)
--R
--R                    1
--R          n log(---------)
--R                        2
--R                cos(a x)
--R          ----------------
--R                  2
--R        %e
--R   (1)  ------------------
--R                a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 52
bb:=sec(a*x)^n/(n*a)
 

                n
        sec(a x)
   (2)  ---------
           a n
                                                     Type: Expression Integer
--R
--R                n
--R        sec(a x)
--R   (2)  ---------
--R           a n
--R                                                     Type: Expression Integer
--E

--S 31 of 52
cc:=aa-bb
 

                    1
          n log(---------)
                        2
                cos(a x)
          ----------------
                  2                  n
        %e                 - sec(a x)
   (3)  ------------------------------
                      a n
                                                     Type: Expression Integer
--R
--R                    1
--R          n log(---------)
--R                        2
--R                cos(a x)
--R          ----------------
--R                  2                  n
--R        %e                 - sec(a x)
--R   (3)  ------------------------------
--R                      a n
--R                                                     Type: Expression Integer
--E

--S 32 of 52     14:454 Schaums and Axiom agree
normalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 33 of 52
aa:=integrate(1/sec(a*x),x)
 

        sin(a x)
   (1)  --------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sin(a x)
--R   (1)  --------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E

--S 34 of 52
bb:=sin(a*x)/a
 

        sin(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        sin(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E 

--S 35 of 52     14:455 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 36 of 52     14:456 Axiom cannot compute this integral
aa:=integrate(x*sec(a*x),x)
 

           x
         ++
   (1)   |   %P sec(%P a)d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %N sec(%N a)d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 37 of 52     14:457 Axiom cannot compute this integral
aa:=integrate(sec(a*x)/x,x)
 

           x
         ++  sec(%P a)
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sec(%N a)
--I   (1)   |   --------- d%N
--I        ++       %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 38 of 52
aa:=integrate(x*sec(a*x)^2,x)
 

   (1)
                       2                         2cos(a x)
   - cos(a x)log(------------) + cos(a x)log(- ------------) + a x sin(a x)
                 cos(a x) + 1                  cos(a x) + 1
   ------------------------------------------------------------------------
                                   2
                                  a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       2                         2cos(a x)
--R   - cos(a x)log(------------) + cos(a x)log(- ------------) + a x sin(a x)
--R                 cos(a x) + 1                  cos(a x) + 1
--R   ------------------------------------------------------------------------
--R                                   2
--R                                  a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 39 of 52
bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x))
 

        log(cos(a x)) + a x tan(a x)
   (2)  ----------------------------
                      2
                     a
                                                     Type: Expression Integer
--R
--R        log(cos(a x)) + a x tan(a x)
--R   (2)  ----------------------------
--R                      2
--R                     a
--R                                                     Type: Expression Integer
--E

--S 40 of 52
cc:=aa-bb
 

   (3)
                                                   2
       - cos(a x)log(cos(a x)) - cos(a x)log(------------)
                                             cos(a x) + 1
     + 
                       2cos(a x)
       cos(a x)log(- ------------) - a x cos(a x)tan(a x) + a x sin(a x)
                     cos(a x) + 1
  /
      2
     a cos(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                   2
--R       - cos(a x)log(cos(a x)) - cos(a x)log(------------)
--R                                             cos(a x) + 1
--R     + 
--R                       2cos(a x)
--R       cos(a x)log(- ------------) - a x cos(a x)tan(a x) + a x sin(a x)
--R                     cos(a x) + 1
--R  /
--R      2
--R     a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 41 of 52
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 42 of 52
dd:=tanrule cc
 

                                    2                 2cos(a x)
        - log(cos(a x)) - log(------------) + log(- ------------)
                              cos(a x) + 1          cos(a x) + 1
   (5)  ---------------------------------------------------------
                                     2
                                    a
                                                     Type: Expression Integer
--R
--R                                    2                 2cos(a x)
--R        - log(cos(a x)) - log(------------) + log(- ------------)
--R                              cos(a x) + 1          cos(a x) + 1
--R   (5)  ---------------------------------------------------------
--R                                     2
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 43 of 52     14:458 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

        - log(2) + log(- 2)
   (6)  -------------------
                  2
                 a
                                                     Type: Expression Integer
--R
--R        - log(2) + log(- 2)
--R   (6)  -------------------
--R                  2
--R                 a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 44 of 52
aa:=integrate(1/(q+p*sec(a*x)),x)
 

   (1)
                             +-------+
                             | 2    2      2    2                 +-------+
          (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)        | 2    2
    p log(------------------------------------------------) + a x\|q  - p
                           q cos(a x) + p
   [-----------------------------------------------------------------------,
                                     +-------+
                                     | 2    2
                                 a q\|q  - p
                         +---------+
                         |   2    2          +---------+
                sin(a x)\|- q  + p           |   2    2
    - 2p atan(-----------------------) + a x\|- q  + p
              (q + p)cos(a x) + q + p
    ----------------------------------------------------]
                           +---------+
                           |   2    2
                       a q\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                             +-------+
--R                             | 2    2      2    2                 +-------+
--R          (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)        | 2    2
--R    p log(------------------------------------------------) + a x\|q  - p
--R                           q cos(a x) + p
--R   [-----------------------------------------------------------------------,
--R                                     +-------+
--R                                     | 2    2
--R                                 a q\|q  - p
--R                         +---------+
--R                         |   2    2          +---------+
--R                sin(a x)\|- q  + p           |   2    2
--R    - 2p atan(-----------------------) + a x\|- q  + p
--R              (q + p)cos(a x) + q + p
--R    ----------------------------------------------------]
--R                           +---------+
--R                           |   2    2
--R                       a q\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 45 of 52
t1:=integrate(1/(p+q*cos(a*x)),x)
 

   (2)
                           +-------+
                           | 2    2        2    2
        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
    log(--------------------------------------------------)
                          q cos(a x) + p
   [-------------------------------------------------------,
                            +-------+
                            | 2    2
                          a\|q  - p
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p
    2atan(-----------------------)
          (q + p)cos(a x) + q + p
    ------------------------------]
               +---------+
               |   2    2
             a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R                           +-------+
--R                           | 2    2        2    2
--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R    log(--------------------------------------------------)
--R                          q cos(a x) + p
--R   [-------------------------------------------------------,
--R                            +-------+
--R                            | 2    2
--R                          a\|q  - p
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p
--R    2atan(-----------------------)
--R          (q + p)cos(a x) + q + p
--R    ------------------------------]
--R               +---------+
--R               |   2    2
--R             a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 46 of 52
bb1:=x/q-p/q*t1.1
 

   (3)
                              +-------+
                              | 2    2        2    2                 +-------+
           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)        | 2    2
   - p log(--------------------------------------------------) + a x\|q  - p
                             q cos(a x) + p
   ---------------------------------------------------------------------------
                                      +-------+
                                      | 2    2
                                  a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R                              +-------+
--R                              | 2    2        2    2                 +-------+
--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)        | 2    2
--R   - p log(--------------------------------------------------) + a x\|q  - p
--R                             q cos(a x) + p
--R   ---------------------------------------------------------------------------
--R                                      +-------+
--R                                      | 2    2
--R                                  a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 47 of 52
bb2:=x/q-p/q*t1.2
 

                             +---------+
                             |   2    2          +---------+
                    sin(a x)\|- q  + p           |   2    2
        - 2p atan(-----------------------) + a x\|- q  + p
                  (q + p)cos(a x) + q + p
   (4)  ----------------------------------------------------
                               +---------+
                               |   2    2
                           a q\|- q  + p
                                                     Type: Expression Integer
--R
--R                             +---------+
--R                             |   2    2          +---------+
--R                    sin(a x)\|- q  + p           |   2    2
--R        - 2p atan(-----------------------) + a x\|- q  + p
--R                  (q + p)cos(a x) + q + p
--R   (4)  ----------------------------------------------------
--R                               +---------+
--R                               |   2    2
--R                           a q\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 48 of 52
cc1:=aa.1-bb1
 

   (5)
                                +-------+
                                | 2    2      2    2
             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p log(------------------------------------------------)
                              q cos(a x) + p
     + 
                                +-------+
                                | 2    2        2    2
             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p log(--------------------------------------------------)
                               q cos(a x) + p
  /
         +-------+
         | 2    2
     a q\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                +-------+
--R                                | 2    2      2    2
--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p log(------------------------------------------------)
--R                              q cos(a x) + p
--R     + 
--R                                +-------+
--R                                | 2    2        2    2
--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p log(--------------------------------------------------)
--R                               q cos(a x) + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  - p
--R                                                     Type: Expression Integer
--E

--S 49 of 52
cc2:=aa.1-bb2
 

   (6)
                                           +-------+
         +---------+                       | 2    2      2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p\|- q  + p  log(------------------------------------------------)
                                         q cos(a x) + p
     + 
                                   +---------+
          +-------+                |   2    2
          | 2    2        sin(a x)\|- q  + p
       2p\|q  - p  atan(-----------------------)
                        (q + p)cos(a x) + q + p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                                           +-------+
--R         +---------+                       | 2    2      2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p\|- q  + p  log(------------------------------------------------)
--R                                         q cos(a x) + p
--R     + 
--R                                   +---------+
--R          +-------+                |   2    2
--R          | 2    2        sin(a x)\|- q  + p
--R       2p\|q  - p  atan(-----------------------)
--R                        (q + p)cos(a x) + q + p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 50 of 52
cc3:=aa.2-bb1
 

   (7)
                                           +-------+
         +---------+                       | 2    2        2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p\|- q  + p  log(--------------------------------------------------)
                                          q cos(a x) + p
     + 
                                     +---------+
            +-------+                |   2    2
            | 2    2        sin(a x)\|- q  + p
       - 2p\|q  - p  atan(-----------------------)
                          (q + p)cos(a x) + q + p
  /
         +---------+ +-------+
         |   2    2  | 2    2
     a q\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                           +-------+
--R         +---------+                       | 2    2        2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p\|- q  + p  log(--------------------------------------------------)
--R                                          q cos(a x) + p
--R     + 
--R                                     +---------+
--R            +-------+                |   2    2
--R            | 2    2        sin(a x)\|- q  + p
--R       - 2p\|q  - p  atan(-----------------------)
--R                          (q + p)cos(a x) + q + p
--R  /
--R         +---------+ +-------+
--R         |   2    2  | 2    2
--R     a q\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 51 of 52     14:459 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 52 of 52     14:460 Axiom cannot compute this integral
aa:=integrate(sec(a*x)^n,x)
 

           x
         ++           n
   (1)   |   sec(%P a) d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   sec(%N a) d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to Plot.output (2010/3/27, 18:46:16).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 2
fp:=(t:DFLOAT):DFLOAT +-> sin(t)
 

   (1)  theMap(Closure)
                                           Type: (DoubleFloat -> DoubleFloat)
--R
--R   (1)  theMap(Closure)
--R                                           Type: (DoubleFloat -> DoubleFloat)
--E 1

--S 2 of 2
plot(fp,-1.0..1.0)$PLOT
 

   (2)  PLOT(x = (- 1.)..1.   y = (- 0.8414709848078965)..0.8414709848078965)
                               [- 1.,- 0.8414709848078965]
                      [- 0.95833333333333337,- 0.81823456433427133]
                      [- 0.91666666666666674,- 0.79357780324894212]
                      [- 0.87500000000000011,- 0.76754350223602708]
                      [- 0.83333333333333348,- 0.74017685319603721]
                      [- 0.79166666666666685,- 0.7115253607990657]
                      [- 0.75000000000000022,- 0.68163876002333434]
                      [- 0.70833333333333359,- 0.65056892982223602]
                      [- 0.66666666666666696,- 0.61836980306973721]
                      [- 0.62500000000000033,- 0.58509727294046243]
                      [- 0.5833333333333337,- 0.55080909588697013]
                      [- 0.54166666666666707,- 0.51556479138264011]
                      [- 0.50000000000000044,- 0.47942553860420339]
                      [- 0.45833333333333376,- 0.44245407023325911]
                      [- 0.41666666666666707,- 0.40471456356112506]
                      [- 0.37500000000000039,- 0.3662725290860479]
                       [- 0.3333333333333337,- 0.3271946967961526]
                      [- 0.29166666666666702,- 0.28754890033552849]
                      [- 0.25000000000000033,- 0.24740395925452324]
                      [- 0.20833333333333368,- 0.20682955954864138]
                      [- 0.16666666666666702,- 0.16589613269341538]
                      [- 0.12500000000000036,- 0.12467473338522805]
                    [- 8.3333333333333703E-2,- 8.3236916200310623E-2]
                    [- 4.1666666666667039E-2,- 4.1654611386019461E-2]
                   [- 3.7470027081099033E-16,- 3.7470027081099033E-16]
                      [4.166666666666629E-2,4.1654611386018711E-2]
                      [8.3333333333332954E-2,8.3236916200309874E-2]
                        [0.12499999999999961,0.1246747333852273]
                        [0.16666666666666627,0.16589613269341463]
                        [0.20833333333333293,0.20682955954864066]
                        [0.24999999999999958,0.24740395925452252]
                        [0.29166666666666624,0.28754890033552777]
                        [0.33333333333333293,0.32719469679615187]
                        [0.37499999999999961,0.36627252908604718]
                         [0.4166666666666663,0.4047145635611244]
                        [0.45833333333333298,0.44245407023325839]
                        [0.49999999999999967,0.47942553860420273]
                        [0.5416666666666663,0.51556479138263944]
                        [0.58333333333333293,0.55080909588696947]
                        [0.62499999999999956,0.58509727294046177]
                        [0.66666666666666619,0.61836980306973666]
                        [0.70833333333333282,0.65056892982223535]
                        [0.74999999999999944,0.68163876002333379]
                        [0.79166666666666607,0.71152536079906514]
                        [0.8333333333333327,0.74017685319603665]
                        [0.87499999999999933,0.76754350223602663]
                        [0.91666666666666596,0.79357780324894167]
                        [0.95833333333333259,0.81823456433427078]
                                 [1.,0.8414709848078965]
                                                                   Type: Plot
--R 
--R
--R   (2)  PLOT(x = (- 1.)..1.   y = (- 0.8414709848078965)..0.8414709848078965)
--R                               [- 1.,- 0.8414709848078965]
--R                      [- 0.95833333333333337,- 0.81823456433427133]
--R                      [- 0.91666666666666674,- 0.79357780324894212]
--R                      [- 0.87500000000000011,- 0.76754350223602708]
--R                      [- 0.83333333333333348,- 0.74017685319603721]
--R                      [- 0.79166666666666685,- 0.7115253607990657]
--R                      [- 0.75000000000000022,- 0.68163876002333434]
--R                      [- 0.70833333333333359,- 0.65056892982223602]
--R                      [- 0.66666666666666696,- 0.61836980306973721]
--R                      [- 0.62500000000000033,- 0.58509727294046243]
--R                      [- 0.5833333333333337,- 0.55080909588697013]
--R                      [- 0.54166666666666707,- 0.51556479138264011]
--R                      [- 0.50000000000000044,- 0.47942553860420339]
--R                      [- 0.45833333333333376,- 0.44245407023325911]
--R                      [- 0.41666666666666707,- 0.40471456356112506]
--R                      [- 0.37500000000000039,- 0.3662725290860479]
--R                       [- 0.3333333333333337,- 0.3271946967961526]
--R                      [- 0.29166666666666702,- 0.28754890033552849]
--R                      [- 0.25000000000000033,- 0.24740395925452324]
--R                      [- 0.20833333333333368,- 0.20682955954864138]
--R                      [- 0.16666666666666702,- 0.16589613269341538]
--R                      [- 0.12500000000000036,- 0.12467473338522805]
--R                    [- 8.3333333333333703E-2,- 8.3236916200310623E-2]
--R                    [- 4.1666666666667039E-2,- 4.1654611386019461E-2]
--R                   [- 3.7470027081099033E-16,- 3.7470027081099033E-16]
--R                      [4.166666666666629E-2,4.1654611386018711E-2]
--R                      [8.3333333333332954E-2,8.3236916200309874E-2]
--R                        [0.12499999999999961,0.1246747333852273]
--R                        [0.16666666666666627,0.16589613269341463]
--R                        [0.20833333333333293,0.20682955954864066]
--R                        [0.24999999999999958,0.24740395925452252]
--R                        [0.29166666666666624,0.28754890033552777]
--R                        [0.33333333333333293,0.32719469679615187]
--R                        [0.37499999999999961,0.36627252908604718]
--R                         [0.4166666666666663,0.4047145635611244]
--R                        [0.45833333333333298,0.44245407023325839]
--R                        [0.49999999999999967,0.47942553860420273]
--R                        [0.5416666666666663,0.51556479138263944]
--R                        [0.58333333333333293,0.55080909588696947]
--R                        [0.62499999999999956,0.58509727294046177]
--R                        [0.66666666666666619,0.61836980306973666]
--R                        [0.70833333333333282,0.65056892982223535]
--R                        [0.74999999999999944,0.68163876002333379]
--R                        [0.79166666666666607,0.71152536079906514]
--R                        [0.8333333333333327,0.74017685319603665]
--R                        [0.87499999999999933,0.76754350223602663]
--R                        [0.91666666666666596,0.79357780324894167]
--R                        [0.95833333333333259,0.81823456433427078]
--R                                 [1.,0.8414709848078965]
--R                                                                   Type: Plot
--E 2
)spool
 
Starts dribbling to t111293.output (2010/3/27, 18:41:10).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 13
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 13
deq := differentiate(y x, x, 2) + differentiate(y x, x) + y x
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 13
solve(deq, y, x).basis
 

                       x     x
               +-+   - -   - -      +-+
             x\|3      2     2    x\|3
   (3)  [cos(-----)%e   ,%e   sin(-----)]
               2                    2
                                                Type: List Expression Integer
--R 
--R
--R                       x     x
--R               +-+   - -   - -      +-+
--R             x\|3      2     2    x\|3
--R   (3)  [cos(-----)%e   ,%e   sin(-----)]
--R               2                    2
--R                                                Type: List Expression Integer
--E 3

)clear all
 

--S 4 of 13
f := sin
 

   (1)  sin
                                                           Type: Variable sin
--R 
--R
--R   (1)  sin
--R                                                           Type: Variable sin
--E 4

--S 5 of 13
f 5
 

   (2)  sin(5)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  sin(5)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 13
f 5.6
 

   (3)  - 0.6312666378 7232131147
                                                                  Type: Float
--R 
--R
--R   (3)  - 0.6312666378 7232131147
--R                                                                  Type: Float
--E 6

--S 7 of 13
g(f,x) == f x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 13
g(cos, x)
 
   Compiling function g with type (Variable cos,Variable x) -> 
      Expression Integer 

   (5)  cos(x)
                                                     Type: Expression Integer
--R 
--R   Compiling function g with type (Variable cos,Variable x) -> 
--R      Expression Integer 
--R
--R   (5)  cos(x)
--R                                                     Type: Expression Integer
--E 8

--S 9 of 13
g(f, x)
 
   Compiling function g with type (Variable sin,Variable x) -> 
      Expression Integer 

   (6)  sin(x)
                                                     Type: Expression Integer
--R 
--R   Compiling function g with type (Variable sin,Variable x) -> 
--R      Expression Integer 
--R
--R   (6)  sin(x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 13
g(log, 8.38)
 
   Compiling function g with type (Variable log,Float) -> Float 

   (7)  2.1258479144 939916724
                                                                  Type: Float
--R 
--R   Compiling function g with type (Variable log,Float) -> Float 
--R
--R   (7)  2.1258479144 939916724
--R                                                                  Type: Float
--E 10

)clear all
 

--S 11 of 13
sin := [1,2,3,4,5,6,7]
 

   (1)  [1,2,3,4,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,6,7]
--R                                                   Type: List PositiveInteger
--E 11

--S 12 of 13
sin 4
 

   (2)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 13
sin(4)$Expression(Integer)
 

   (3)  sin(4)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(4)
--R                                                     Type: Expression Integer
--E 13
)spool 
 
Starts dribbling to RealClosure.output (2010/3/27, 18:46:22).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 67
Ran := RECLOS(FRAC INT)
 

   (1)  RealClosure Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  RealClosure Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 67
fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran==sqrt(a)+sqrt(b)-sqrt(c)-sqrt(d)
 
   Function declaration fourSquares : (RealClosure Fraction Integer,
      RealClosure Fraction Integer,RealClosure Fraction Integer,
      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration fourSquares : (RealClosure Fraction Integer,
--R      RealClosure Fraction Integer,RealClosure Fraction Integer,
--R      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 67
squareDiff1 := fourSquares(73,548,60,586)
 
   Compiling function fourSquares with type (RealClosure Fraction 
      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 

           +---+    +--+    +---+    +--+
   (3)  - \|586  - \|60  + \|548  + \|73
                                           Type: RealClosure Fraction Integer
--R 
--R   Compiling function fourSquares with type (RealClosure Fraction 
--R      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
--R      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 
--R
--R           +---+    +--+    +---+    +--+
--R   (3)  - \|586  - \|60  + \|548  + \|73
--R                                           Type: RealClosure Fraction Integer
--E 3

--S 4 of 67
recip(squareDiff1)
 

   (4)
             +---+          +--+  +--+         +--+ +---+            +---+
     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
   + 
             +--+ +---+             +--+            +---+            +--+
     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (4)
--R             +---+          +--+  +--+         +--+ +---+            +---+
--R     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
--R   + 
--R             +--+ +---+             +--+            +---+            +--+
--R     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 4

--S 5 of 67
sign(squareDiff1)
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 67
squareDiff2 := fourSquares(165,778,86,990)
 

           +---+    +--+    +---+    +---+
   (6)  - \|990  - \|86  + \|778  + \|165
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +--+    +---+    +---+
--R   (6)  - \|990  - \|86  + \|778  + \|165
--R                                           Type: RealClosure Fraction Integer
--E 6

--S 7 of 67
recip(squareDiff2)
 

   (7)
                +---+           +---+  +--+          +---+ +---+
       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
    *
        +---+
       \|990
   + 
              +---+ +---+              +--+             +---+             +---+
     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (7)
--R                +---+           +---+  +--+          +---+ +---+
--R       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
--R    *
--R        +---+
--R       \|990
--R   + 
--R              +---+ +---+              +--+             +---+             +---+
--R     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 7

--S 8 of 67
sign(squareDiff2)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 67
squareDiff3 := fourSquares(217,708,226,692)
 

           +---+    +---+    +---+    +---+
   (9)  - \|692  - \|226  + \|708  + \|217
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +---+    +---+    +---+
--R   (9)  - \|692  - \|226  + \|708  + \|217
--R                                           Type: RealClosure Fraction Integer
--E 9

--S 10 of 67
recip(squareDiff3)
 

   (10)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (10)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 10

--S 11 of 67
sign(squareDiff3)
 

   (11)  - 1
                                                                Type: Integer
--R 
--R
--R   (11)  - 1
--R                                                                Type: Integer
--E 11

--S 12 of 67
squareDiff4 := fourSquares(155,836,162,820)
 

            +---+    +---+    +---+    +---+
   (12)  - \|820  - \|162  + \|836  + \|155
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (12)  - \|820  - \|162  + \|836  + \|155
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 67
recip(squareDiff4)
 

   (13)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (13)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 13

--S 14 of 67
sign(squareDiff4)
 

   (14)  - 1
                                                                Type: Integer
--R 
--R
--R   (14)  - 1
--R                                                                Type: Integer
--E 14

--S 15 of 67
squareDiff5 := fourSquares(591,772,552,818)
 

            +---+    +---+    +---+    +---+
   (15)  - \|818  - \|552  + \|772  + \|591
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (15)  - \|818  - \|552  + \|772  + \|591
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 67
recip(squareDiff5)
 

   (16)
             +---+         +---+  +---+         +---+ +---+             +---+
     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
   + 
            +---+ +---+             +---+            +---+            +---+
     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (16)
--R             +---+         +---+  +---+         +---+ +---+             +---+
--R     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
--R   + 
--R            +---+ +---+             +---+            +---+            +---+
--R     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 16

--S 17 of 67
sign(squareDiff5)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 67
squareDiff6 := fourSquares(434,1053,412,1088)
 

            +----+    +---+    +----+    +---+
   (18)  - \|1088  - \|412  + \|1053  + \|434
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (18)  - \|1088  - \|412  + \|1053  + \|434
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 67
recip(squareDiff6)
 

   (19)
                +----+          +---+  +---+          +---+ +----+
       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
    *
        +----+
       \|1088
   + 
           +---+ +----+              +---+            +----+             +---+
   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (19)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
--R    *
--R        +----+
--R       \|1088
--R   + 
--R           +---+ +----+              +---+            +----+             +---+
--R   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 19

--S 20 of 67
sign(squareDiff6)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 67
squareDiff7 := fourSquares(514,1049,446,1152)
 

            +----+    +---+    +----+    +---+
   (21)  - \|1152  - \|446  + \|1049  + \|514
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (21)  - \|1152  - \|446  + \|1049  + \|514
--R                                           Type: RealClosure Fraction Integer
--E 21

--S 22 of 67
recip(squareDiff7)
 

   (22)
                +----+          +---+  +---+          +---+ +----+
       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
    *
        +----+
       \|1152
   + 
           +---+ +----+              +---+             +----+             +---+
   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (22)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
--R    *
--R        +----+
--R       \|1152
--R   + 
--R           +---+ +----+              +---+             +----+             +---+
--R   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 22

--S 23 of 67
sign(squareDiff7)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 67
squareDiff8 := fourSquares(190,1751,208,1698)
 

            +----+    +---+    +----+    +---+
   (24)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (24)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 24

--S 25 of 67
recip(squareDiff8)
 

   (25)
                     +----+          +---+  +---+          +---+ +----+
           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
         + 
           - 129571901
    *
        +----+
       \|1698
   + 
               +---+ +----+              +---+             +----+
     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
   + 
                 +---+
     - 387349387\|190
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (25)
--R                     +----+          +---+  +---+          +---+ +----+
--R           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
--R         + 
--R           - 129571901
--R    *
--R        +----+
--R       \|1698
--R   + 
--R               +---+ +----+              +---+             +----+
--R     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
--R   + 
--R                 +---+
--R     - 387349387\|190
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 25

--S 26 of 67
sign(squareDiff8)
 

   (26)  - 1
                                                                Type: Integer
--R 
--R
--R   (26)  - 1
--R                                                                Type: Integer
--E 26

--S 27 of 67
relativeApprox(squareDiff8,10**(-3))::Float
 

   (27)  - 0.2340527771 5937700123 E -10
                                                                  Type: Float
--R 
--R
--R   (27)  - 0.2340527771 5937700123 E -10
--R                                                                  Type: Float
--E 27

--S 28 of 67
l := allRootsOf((x**2-2)**2-2)$Ran
 

   (28)  [%A33,%A34,%A35,%A36]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (28)  [%A33,%A34,%A35,%A36]
--R                                      Type: List RealClosure Fraction Integer
--E 28

--S 29 of 67
removeDuplicates map(mainDefiningPolynomial,l)
 

           4     2
   (29)  [?  - 4?  + 2]
Type: List Union(SparseUnivariatePolynomial RealClosure Fraction Integer,"failed")
--R 
--R
--R           4     2
--R   (29)  [?  - 4?  + 2]
--RType: List Union(SparseUnivariatePolynomial RealClosure Fraction Integer,"failed")
--E 29

--S 30 of 67
map(mainCharacterization,l)
 

   (30)  [[- 2,- 1[,[- 1,0[,[0,1[,[1,2[]
Type: List Union(RightOpenIntervalRootCharacterization(RealClosure Fraction Integer,SparseUnivariatePolynomial RealClosure Fraction Integer),"failed")
--R 
--R
--R   (30)  [[- 2,- 1[,[- 1,0[,[0,1[,[1,2[]
--RType: List Union(RightOpenIntervalRootCharacterization(RealClosure Fraction Integer,SparseUnivariatePolynomial RealClosure Fraction Integer),"failed")
--E 30

--S 31 of 67
[reduce(+,l),reduce(*,l)-2]
 

   (31)  [0,0]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (31)  [0,0]
--R                                      Type: List RealClosure Fraction Integer
--E 31

--S 32 of 67
(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran)
 

          +--+
   (32)  \|10
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R   (32)  \|10
--R                                           Type: RealClosure Fraction Integer
--E 32

--S 33 of 67
eq1:=sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
 

            +---------+ +--------+    +---------+ +--------+   +-----------+
            | +--+      | +-+         | +--+      | +-+        |   +-+
   (33)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +---------+ +--------+    +---------+ +--------+   +-----------+
--R            | +--+      | +-+         | +--+      | +-+        |   +-+
--R   (33)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
--R                                  Type: Equation RealClosure Fraction Integer
--E 33

--S 34 of 67
eq1::Boolean
 

   (34)  true
                                                                Type: Boolean
--R 
--R
--R   (34)  true
--R                                                                Type: Boolean
--E 34

--S 35 of 67
eq2:=sqrt(s5+2)*sqrt(s2+1) - sqrt(s5-2)*sqrt(s2-1) = sqrt(2*s10+2)
 

            +--------+ +--------+    +--------+ +--------+   +----------+
            | +-+      | +-+         | +-+      | +-+        |  +--+
   (35)  - \|\|5  - 2 \|\|2  - 1  + \|\|5  + 2 \|\|2  + 1 = \|2\|10  + 2
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +--------+ +--------+    +--------+ +--------+   +----------+
--R            | +-+      | +-+         | +-+      | +-+        |  +--+
--R   (35)  - \|\|5  - 2 \|\|2  - 1  + \|\|5  + 2 \|\|2  + 1 = \|2\|10  + 2
--R                                  Type: Equation RealClosure Fraction Integer
--E 35

--S 36 of 67
eq2::Boolean
 

   (36)  true
                                                                Type: Boolean
--R 
--R
--R   (36)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 67
s3 := sqrt(3)$Ran
 

          +-+
   (37)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (37)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 37

--S 38 of 67
s7:= sqrt(7)$Ran
 

          +-+
   (38)  \|7
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (38)  \|7
--R                                           Type: RealClosure Fraction Integer
--E 38

--S 39 of 67
e1 := sqrt(2*s7-3*s3,3)
 

          +-------------+
         3|  +-+     +-+
   (39)  \|2\|7  - 3\|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-------------+
--R         3|  +-+     +-+
--R   (39)  \|2\|7  - 3\|3
--R                                           Type: RealClosure Fraction Integer
--E 39

--S 40 of 67
e2 := sqrt(2*s7+3*s3,3)
 

          +-------------+
         3|  +-+     +-+
   (40)  \|2\|7  + 3\|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-------------+
--R         3|  +-+     +-+
--R   (40)  \|2\|7  + 3\|3
--R                                           Type: RealClosure Fraction Integer
--E 40

--S 41 of 67
e2-e1-s3
 

   (41)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (41)  0
--R                                           Type: RealClosure Fraction Integer
--E 41

--S 42 of 67
pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3)
 

          4   7  2         100
   (42)  x  + - x  + 30x - ---
              3             3
                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--R 
--R
--R          4   7  2         100
--R   (42)  x  + - x  + 30x - ---
--R              3             3
--R                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--E 42

--S 43 of 67
r1 := sqrt(7633)$Ran
 

          +----+
   (43)  \|7633
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +----+
--R   (43)  \|7633
--R                                           Type: RealClosure Fraction Integer
--E 43

--S 44 of 67
alpha := sqrt(5*r1-436,3)/3
 

            +--------------+
         1 3|  +----+
   (44)  - \|5\|7633  - 436
         3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +--------------+
--R         1 3|  +----+
--R   (44)  - \|5\|7633  - 436
--R         3
--R                                           Type: RealClosure Fraction Integer
--E 44

--S 45 of 67
beta := -sqrt(5*r1+436,3)/3 
 

              +--------------+
           1 3|  +----+
   (45)  - - \|5\|7633  + 436
           3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R              +--------------+
--R           1 3|  +----+
--R   (45)  - - \|5\|7633  + 436
--R           3
--R                                           Type: RealClosure Fraction Integer
--E 45

--S 46 of 67
pol.(alpha+beta-1/3)
 

   (46)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (46)  0
--R                                           Type: RealClosure Fraction Integer
--E 46

--S 47 of 67
qol : UP(x,Ran) := x**5+10*x**3+20*x+22
 

          5      3
   (47)  x  + 10x  + 20x + 22
                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--R 
--R
--R          5      3
--R   (47)  x  + 10x  + 20x + 22
--R                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--E 47

--S 48 of 67
r2 := sqrt(153)$Ran
 

          +---+
   (48)  \|153
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +---+
--R   (48)  \|153
--R                                           Type: RealClosure Fraction Integer
--E 48

--S 49 of 67
alpha2 := sqrt(r2-11,5)
 

          +-----------+
         5| +---+
   (49)  \|\|153  - 11
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-----------+
--R         5| +---+
--R   (49)  \|\|153  - 11
--R                                           Type: RealClosure Fraction Integer
--E 49

--S 50 of 67
beta2 := -sqrt(r2+11,5)
 

            +-----------+
           5| +---+
   (50)  - \|\|153  + 11
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +-----------+
--R           5| +---+
--R   (50)  - \|\|153  + 11
--R                                           Type: RealClosure Fraction Integer
--E 50

--S 51 of 67
qol(alpha2+beta2)
 

   (51)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (51)  0
--R                                           Type: RealClosure Fraction Integer
--E 51

--S 52 of 67
dst1:=sqrt(9+4*s2)=1+2*s2
 

          +---------+
          |  +-+         +-+
   (52)  \|4\|2  + 9 = 2\|2  + 1
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +---------+
--R          |  +-+         +-+
--R   (52)  \|4\|2  + 9 = 2\|2  + 1
--R                                  Type: Equation RealClosure Fraction Integer
--E 52

--S 53 of 67
dst1::Boolean
 

   (53)  true
                                                                Type: Boolean
--R 
--R
--R   (53)  true
--R                                                                Type: Boolean
--E 53

--S 54 of 67
s6:Ran:=sqrt 6
 

          +-+
   (54)  \|6
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (54)  \|6
--R                                           Type: RealClosure Fraction Integer
--E 54

--S 55 of 67
dst2:=sqrt(5+2*s6)+sqrt(5-2*s6) = 2*s3
 

          +-----------+    +---------+
          |    +-+         |  +-+         +-+
   (55)  \|- 2\|6  + 5  + \|2\|6  + 5 = 2\|3
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +-----------+    +---------+
--R          |    +-+         |  +-+         +-+
--R   (55)  \|- 2\|6  + 5  + \|2\|6  + 5 = 2\|3
--R                                  Type: Equation RealClosure Fraction Integer
--E 55

--S 56 of 67
dst2::Boolean
 

   (56)  true
                                                                Type: Boolean
--R 
--R
--R   (56)  true
--R                                                                Type: Boolean
--E 56

--S 57 of 67
s29:Ran:=sqrt 29
 

          +--+
   (57)  \|29
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R   (57)  \|29
--R                                           Type: RealClosure Fraction Integer
--E 57

--S 58 of 67
dst4:=sqrt(16-2*s29+2*sqrt(55-10*s29)) = sqrt(22+2*s5)-sqrt(11+2*s29)+s5
 

   (58)
    +--------------------------------+
    |  +--------------+                    +-----------+    +----------+
    |  |     +--+           +--+           |  +--+          |  +-+          +-+
   \|2\|- 10\|29  + 55  - 2\|29  + 16 = - \|2\|29  + 11  + \|2\|5  + 22  + \|5
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R   (58)
--R    +--------------------------------+
--R    |  +--------------+                    +-----------+    +----------+
--R    |  |     +--+           +--+           |  +--+          |  +-+          +-+
--R   \|2\|- 10\|29  + 55  - 2\|29  + 16 = - \|2\|29  + 11  + \|2\|5  + 22  + \|5
--R                                  Type: Equation RealClosure Fraction Integer
--E 58

--S 59 of 67
dst4::Boolean
 

   (59)  true
                                                                Type: Boolean
--R 
--R
--R   (59)  true
--R                                                                Type: Boolean
--E 59

--S 60 of 67
dst6:=sqrt((112+70*s2)+(46+34*s2)*s5) = (5+4*s2)+(3+s2)*s5 
 

          +--------------------------------+
          |    +-+       +-+      +-+           +-+      +-+     +-+
   (60)  \|(34\|2  + 46)\|5  + 70\|2  + 112 = (\|2  + 3)\|5  + 4\|2  + 5
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +--------------------------------+
--R          |    +-+       +-+      +-+           +-+      +-+     +-+
--R   (60)  \|(34\|2  + 46)\|5  + 70\|2  + 112 = (\|2  + 3)\|5  + 4\|2  + 5
--R                                  Type: Equation RealClosure Fraction Integer
--E 60

--S 61 of 67
dst6::Boolean
 

   (61)  true
                                                                Type: Boolean
--R 
--R
--R   (61)  true
--R                                                                Type: Boolean
--E 61

--S 62 of 67
f3:Ran:=sqrt(3,5)
 

         5+-+
   (62)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         5+-+
--R   (62)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 62

--S 63 of 67
f25:Ran:=sqrt(1/25,5)
 

          +--+
          | 1
   (63)  5|--
         \|25
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          | 1
--R   (63)  5|--
--R         \|25
--R                                           Type: RealClosure Fraction Integer
--E 63

--S 64 of 67
f32:Ran:=sqrt(32/5,5)
 

          +--+
          |32
   (64)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |32
--R   (64)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 64

--S 65 of 67
f27:Ran:=sqrt(27/5,5)
 

          +--+
          |27
   (65)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |27
--R   (65)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 65

--S 66 of 67
dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3**2)
 

          +---------------+
          |   +--+    +--+                         +--+
          |   |27     |32       5+-+2   5+-+       | 1
   (66)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
         \|  \| 5    \| 5                         \|25
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +---------------+
--R          |   +--+    +--+                         +--+
--R          |   |27     |32       5+-+2   5+-+       | 1
--R   (66)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
--R         \|  \| 5    \| 5                         \|25
--R                                  Type: Equation RealClosure Fraction Integer
--E 66

--S 67 of 67
dst5::Boolean
 

   (67)  true
                                                                Type: Boolean
--R 
--R
--R   (67)  true
--R                                                                Type: Boolean
--E 67
)spool
 
Starts dribbling to exprode.output (2010/3/27, 18:25:44).
)set message test on
 
)set message auto off
 
)clear all
 
)set streams calculate 7
 

--S 1 of 13
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 13
eq := differentiate(y x, x, 3) - sin differentiate(y x, x, 2) * exp y x
           = cos x
 

         ,,,        y(x)     ,,
   (2)  y   (x) - %e    sin(y  (x))= cos(x)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,,        y(x)     ,,
--R   (2)  y   (x) - %e    sin(y  (x))= cos(x)
--R
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 13
seriesSolve(eq, y, x = 0, [1, 0, 0])
 
   Compiling function %B with type List UnivariateTaylorSeries(
      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
      Integer,x,0) 

   (3)
                          2            3              4      2
         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
         6      24        120           720                 5040
   + 
        8
     O(x )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function %B with type List UnivariateTaylorSeries(
--R      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,0) 
--R
--R   (3)
--R                          2            3              4      2
--R         1  3   %e  4   %e  - 1  5   %e  - 2%e  6   %e  - 8%e  + 4%e + 1  7
--R     1 + - x  + -- x  + ------- x  + --------- x  + -------------------- x
--R         6      24        120           720                 5040
--R   + 
--R        8
--R     O(x )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3
 
--S 4 of 13
airy := differentiate(y x, x, 2) - x * y x
 

         ,,
   (4)  y  (x) - x y(x)

                                                     Type: Expression Integer
--R 
--R
--R         ,,
--R   (4)  y  (x) - x y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 13
seriesSolve(airy, y, x = 0, [a0, a1])
 
   Compiling function %D with type List UnivariateTaylorSeries(
      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
      Integer,x,0) 

                    a0  3   a1  4    a0  6    a1  7      8
   (5)  a0 + a1 x + -- x  + -- x  + --- x  + --- x  + O(x )
                     6      12      180      504
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R   Compiling function %D with type List UnivariateTaylorSeries(
--R      Expression Integer,x,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,0) 
--R
--R                    a0  3   a1  4    a0  6    a1  7      8
--R   (5)  a0 + a1 x + -- x  + -- x  + --- x  + --- x  + O(x )
--R                     6      12      180      504
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 5

--S 6 of 13
seriesSolve(airy, y, x = 1, [a0, a1])
 
   Compiling function %F with type List UnivariateTaylorSeries(
      Expression Integer,x,1) -> UnivariateTaylorSeries(Expression 
      Integer,x,1) 

   (6)
                      a0        2   a1 + a0        3   2a1 + a0        4
     a0 + a1(x - 1) + -- (x - 1)  + ------- (x - 1)  + -------- (x - 1)
                       2               6                  24
   + 
     a1 + 4a0        5   6a1 + 5a0        6   11a1 + 9a0        7            8
     -------- (x - 1)  + --------- (x - 1)  + ---------- (x - 1)  + O((x - 1) )
        120                 720                  5040
                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--R 
--R   Compiling function %F with type List UnivariateTaylorSeries(
--R      Expression Integer,x,1) -> UnivariateTaylorSeries(Expression 
--R      Integer,x,1) 
--R
--R   (6)
--R                      a0        2   a1 + a0        3   2a1 + a0        4
--R     a0 + a1(x - 1) + -- (x - 1)  + ------- (x - 1)  + -------- (x - 1)
--R                       2               6                  24
--R   + 
--R     a1 + 4a0        5   6a1 + 5a0        6   11a1 + 9a0        7            8
--R     -------- (x - 1)  + --------- (x - 1)  + ---------- (x - 1)  + O((x - 1) )
--R        120                 720                  5040
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,1)
--E 6

--S 7 of 13
x := operator 'x
 
   Compiled code for %F has been cleared.
   Compiled code for %D has been cleared.
   Compiled code for %B has been cleared.

   (7)  x
                                                          Type: BasicOperator
--R 
--R   Compiled code for %F has been cleared.
--R   Compiled code for %D has been cleared.
--R   Compiled code for %B has been cleared.
--R
--R   (7)  x
--R                                                          Type: BasicOperator
--E 7

--S 8 of 13
eq1 := differentiate(x t, t) = 1 + x(t)**2
 

         ,         2
   (8)  x (t)= x(t)  + 1

                                            Type: Equation Expression Integer
--R 
--R
--R         ,         2
--R   (8)  x (t)= x(t)  + 1
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 13
eq2 := differentiate(y t, t) = x(t) * y(t)
 

         ,
   (9)  y (t)= x(t)y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R         ,
--R   (9)  y (t)= x(t)y(t)
--R
--R                                            Type: Equation Expression Integer
--E 9

--S 10 of 13
seriesSolve([eq2, eq1], [x, y], t = 0, [y 0 = 1, x 0 = 0])
 
   Compiling function %H with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 
   Compiling function %I with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 

              1  3    2  5    17  7      8      1  2    5  4    61  6      8
   (10)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
              3      15      315                2      24      720
                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function %H with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R   Compiling function %I with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R
--R              1  3    2  5    17  7      8      1  2    5  4    61  6      8
--R   (10)  [t + - t  + -- t  + --- t  + O(t ),1 + - t  + -- t  + --- t  + O(t )]
--R              3      15      315                2      24      720
--R                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--E 10

--S 11 of 13
eq1 := differentiate(x t, t) = y t
 

          ,
   (11)  x (t)= y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (11)  x (t)= y(t)
--R
--R                                            Type: Equation Expression Integer
--E 11

--S 12 of 13
eq2 := differentiate(y t, t) = - g * sin(x t) - c * y t
 

          ,
   (12)  y (t)= - g sin(x(t)) - c y(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,
--R   (12)  y (t)= - g sin(x(t)) - c y(t)
--R
--R                                            Type: Equation Expression Integer
--E 12

--S 13 of 13
seriesSolve([eq1, eq2], [x, y], t = 0, [y 0 = a, x 0 = b])
 
   Compiling function %K with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 
   Compiling function %L with type List UnivariateTaylorSeries(
      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
      Integer,t,0) 

   (13)
   [
                                                                    2
                 - g sin(b) - a c  2   c g sin(b) - a g cos(b) + a c   3
       b + a t + ---------------- t  + ------------------------------ t
                         2                            6
     + 
         2             2    2                               3
       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   4
       ------------------------------------------------------ t
                                 24
     + 
                   2      2          2           3     2                2      2
             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
           + 
                    2    3               4
             (- 3a c  + a )g cos(b) + a c
        /
           120
      *
          5
         t
     + 
               3      3          2      2
             3g sin(b)  + 13a c g sin(b)
           + 
                 3      2      2      2  2             4      2 2    4
             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
           + 
                     2      2        3     3                5
             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
        /
           720
      *
          6
         t
     + 
                    3      3         3                 2      3  2       2
             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
           + 
                    3      2        3      2   2           5      2 3      4
               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
            *
               sin(b)
           + 
                  3      3        2      3  2      2
             - a g cos(b)  + (6a c  - 11a )g cos(b)
           + 
                    4      3 2    5               6
             (- 5a c  + 32a c  - a )g cos(b) + a c
        /
           5040
      *
          7
         t
     + 
          8
       O(t )
     ,

                                                              2
                                 c g sin(b) - a g cos(b) + a c   2
       a + (- g sin(b) - a c)t + ------------------------------ t
                                                2
     + 
         2             2    2                               3
       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   3
       ------------------------------------------------------ t
                                  6
     + 
                   2      2          2           3     2                2      2
             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
           + 
                    2    3               4
             (- 3a c  + a )g cos(b) + a c
        /
           24
      *
          4
         t
     + 
               3      3          2      2
             3g sin(b)  + 13a c g sin(b)
           + 
                 3      2      2      2  2             4      2 2    4
             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
           + 
                     2      2        3     3                5
             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
        /
           120
      *
          5
         t
     + 
                    3      3         3                 2      3  2       2
             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
           + 
                    3      2        3      2   2           5      2 3      4
               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
            *
               sin(b)
           + 
                  3      3        2      3  2      2
             - a g cos(b)  + (6a c  - 11a )g cos(b)
           + 
                    4      3 2    5               6
             (- 5a c  + 32a c  - a )g cos(b) + a c
        /
           720
      *
          6
         t
     + 
                   4             2      2  3       3
             (- 33g cos(b) + (38c  - 78a )g )sin(b)
           + 
                        3               3       3   2       2
             (- 228a c g cos(b) + (94a c  - 164a c)g )sin(b)
           + 
                  4      3        2       2  3      2
                 g cos(b)  + (- 6c  + 102a )g cos(b)
               + 
                  4       2 2      4  2             6      2 4      4 2    6
               (5c  - 334a c  + 57a )g cos(b) + (- c  + 57a c  - 76a c  + a )g
            *
               sin(b)
           + 
                   3      3           3       3   2      2
             4a c g cos(b)  + (- 10a c  + 108a c)g cos(b)
           + 
                  5       3 3      5                7
             (6a c  - 122a c  + 16a c)g cos(b) - a c
        /
           5040
      *
          7
         t
     + 
          8
       O(t )
     ]
                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function %K with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R   Compiling function %L with type List UnivariateTaylorSeries(
--R      Expression Integer,t,0) -> UnivariateTaylorSeries(Expression 
--R      Integer,t,0) 
--R
--R   (13)
--R   [
--R                                                                    2
--R                 - g sin(b) - a c  2   c g sin(b) - a g cos(b) + a c   3
--R       b + a t + ---------------- t  + ------------------------------ t
--R                         2                            6
--R     + 
--R         2             2    2                               3
--R       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   4
--R       ------------------------------------------------------ t
--R                                 24
--R     + 
--R                   2      2          2           3     2                2      2
--R             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
--R           + 
--R                    2    3               4
--R             (- 3a c  + a )g cos(b) + a c
--R        /
--R           120
--R      *
--R          5
--R         t
--R     + 
--R               3      3          2      2
--R             3g sin(b)  + 13a c g sin(b)
--R           + 
--R                 3      2      2      2  2             4      2 2    4
--R             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
--R           + 
--R                     2      2        3     3                5
--R             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
--R        /
--R           720
--R      *
--R          6
--R         t
--R     + 
--R                    3      3         3                 2      3  2       2
--R             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
--R           + 
--R                    3      2        3      2   2           5      2 3      4
--R               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
--R            *
--R               sin(b)
--R           + 
--R                  3      3        2      3  2      2
--R             - a g cos(b)  + (6a c  - 11a )g cos(b)
--R           + 
--R                    4      3 2    5               6
--R             (- 5a c  + 32a c  - a )g cos(b) + a c
--R        /
--R           5040
--R      *
--R          7
--R         t
--R     + 
--R          8
--R       O(t )
--R     ,
--R
--R                                                              2
--R                                 c g sin(b) - a g cos(b) + a c   2
--R       a + (- g sin(b) - a c)t + ------------------------------ t
--R                                                2
--R     + 
--R         2             2    2                               3
--R       (g cos(b) + (- c  + a )g)sin(b) + 2a c g cos(b) - a c   3
--R       ------------------------------------------------------ t
--R                                  6
--R     + 
--R                   2      2          2           3     2                2      2
--R             - 3a g sin(b)  + (- 2c g cos(b) + (c  - 4a c)g)sin(b) + a g cos(b)
--R           + 
--R                    2    3               4
--R             (- 3a c  + a )g cos(b) + a c
--R        /
--R           24
--R      *
--R          4
--R         t
--R     + 
--R               3      3          2      2
--R             3g sin(b)  + 13a c g sin(b)
--R           + 
--R                 3      2      2      2  2             4      2 2    4
--R             (- g cos(b)  + (3c  - 11a )g cos(b) + (- c  + 11a c  - a )g)sin(b)
--R           + 
--R                     2      2        3     3                5
--R             - 3a c g cos(b)  + (4a c  - 7a c)g cos(b) - a c
--R        /
--R           120
--R      *
--R          5
--R         t
--R     + 
--R                    3      3         3                 2      3  2       2
--R             - 13c g sin(b)  + (33a g cos(b) + (- 38a c  + 15a )g )sin(b)
--R           + 
--R                    3      2        3      2   2           5      2 3      4
--R               (3c g cos(b)  + (- 4c  + 75a c)g cos(b) + (c  - 26a c  + 11a c)g)
--R            *
--R               sin(b)
--R           + 
--R                  3      3        2      3  2      2
--R             - a g cos(b)  + (6a c  - 11a )g cos(b)
--R           + 
--R                    4      3 2    5               6
--R             (- 5a c  + 32a c  - a )g cos(b) + a c
--R        /
--R           720
--R      *
--R          6
--R         t
--R     + 
--R                   4             2      2  3       3
--R             (- 33g cos(b) + (38c  - 78a )g )sin(b)
--R           + 
--R                        3               3       3   2       2
--R             (- 228a c g cos(b) + (94a c  - 164a c)g )sin(b)
--R           + 
--R                  4      3        2       2  3      2
--R                 g cos(b)  + (- 6c  + 102a )g cos(b)
--R               + 
--R                  4       2 2      4  2             6      2 4      4 2    6
--R               (5c  - 334a c  + 57a )g cos(b) + (- c  + 57a c  - 76a c  + a )g
--R            *
--R               sin(b)
--R           + 
--R                   3      3           3       3   2      2
--R             4a c g cos(b)  + (- 10a c  + 108a c)g cos(b)
--R           + 
--R                  5       3 3      5                7
--R             (6a c  - 122a c  + 16a c)g cos(b) - a c
--R        /
--R           5040
--R      *
--R          7
--R         t
--R     + 
--R          8
--R       O(t )
--R     ]
--R                    Type: List UnivariateTaylorSeries(Expression Integer,t,0)
--E 13
)spool 
 
Starts dribbling to RationalFunctionSum.output (2010/3/27, 18:46:22).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 13
sum(i::Polynomial(Integer),variable(i=1..n))
 

          2
        6i  - 6i + 1
   (1)  ------------
             12
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          2
--R        6i  - 6i + 1
--R   (1)  ------------
--R             12
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 13
sum(i::Fraction(Polynomial(Integer)),i::Symbol)
 

          2
        6i  - 6i + 1
   (2)  ------------
             12
                                 Type: Union(Fraction Polynomial Integer,...)
--R 
--R
--R          2
--R        6i  - 6i + 1
--R   (2)  ------------
--R             12
--R                                 Type: Union(Fraction Polynomial Integer,...)
--E 2

--S 3 of 13
sum(i,i=1..n)
 

         2
        n  + n
   (3)  ------
           2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         2
--R        n  + n
--R   (3)  ------
--R           2
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 13
sum(i::Fraction(Polynomial(Integer)),i=1..n)
 

         2
        n  + n
   (4)  ------
           2
                                 Type: Union(Fraction Polynomial Integer,...)
--R 
--R
--R         2
--R        n  + n
--R   (4)  ------
--R           2
--R                                 Type: Union(Fraction Polynomial Integer,...)
--E 4

--S 5 of 13
s:=i=1..n
 

   (5)  i= 1..n
                                      Type: SegmentBinding Polynomial Integer
--R 
--R
--R   (5)  i= 1..n
--R                                      Type: SegmentBinding Polynomial Integer
--E 5

--S 6 of 13
hiseg:=high(segment(s))
 

   (6)  n
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  n
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 13
loseg:=low(segment(s))
 

   (7)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  1
--R                                                     Type: Polynomial Integer
--E 7

--S 8 of 13
v:=variable s
 

   (8)  i
                                                                 Type: Symbol
--R 
--R
--R   (8)  i
--R                                                                 Type: Symbol
--E 8

--S 9 of 13
p:=i::Polynomial(Integer)
 

   (9)  i
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)  i
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 13
f:=sum(p,v)
 

           2
         6i  - 6i + 1
   (10)  ------------
              12
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2
--R         6i  - 6i + 1
--R   (10)  ------------
--R              12
--R                                            Type: Fraction Polynomial Integer
--E 10

--S 11 of 13
t1:=eval(f,v,(1+hiseg))
 

           2
         6n  + 6n + 1
   (11)  ------------
              12
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2
--R         6n  + 6n + 1
--R   (11)  ------------
--R              12
--R                                            Type: Fraction Polynomial Integer
--E 11

--S 12 of 13
t2:=eval(f,v,loseg)
 

          1
   (12)  --
         12
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          1
--R   (12)  --
--R         12
--R                                            Type: Fraction Polynomial Integer
--E 12

--S 13 of 13
t1-t2
 

          2
         n  + n
   (13)  ------
            2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          2
--R         n  + n
--R   (13)  ------
--R            2
--R                                            Type: Fraction Polynomial Integer
--E 13

)spool
 
Starts dribbling to setcmd.output (2010/3/27, 18:38:58).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 143
)set breakmode
 
-------------------------- The breakmode Option ---------------------------

 Description: execute break processing on error

 The breakmode option may be followed by any one of the following:

    nobreak
    break
    query
 -> resume 
    fastlinks

 The current setting is indicated.

--R-------------------------- The breakmode Option ---------------------------
--R
--R Description: execute break processing on error
--R
--R The breakmode option may be followed by any one of the following:
--R
--R    nobreak
--R    break
--R    query
--R -> resume 
--R    fastlinks
--R
--R The current setting is indicated.
--R
--E 1

--S 2 of 143
)set compiler
 
                  Current Values of  compiler  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
output       library in which to place compiled code    user.lib 
input        controls libraries from which to load compiled code  
args         arguments for compiling AXIOM code         -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra 

--R                  Current Values of  compiler  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Routput       library in which to place compiled code    user.lib 
--Rinput        controls libraries from which to load compiled code  
--Rargs         arguments for compiling AXIOM code         -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra 
--R
--E 2

--S 3 of 143
)set compiler
 
                  Current Values of  compiler  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
output       library in which to place compiled code    user.lib 
input        controls libraries from which to load compiled code  
args         arguments for compiling AXIOM code         -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra 

--R                  Current Values of  compiler  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Routput       library in which to place compiled code    user.lib 
--Rinput        controls libraries from which to load compiled code  
--Rargs         arguments for compiling AXIOM code         -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra 
--R
--E 3

--S 4 of 143
)set compiler input
 
---------------------------- The input Option -----------------------------

 Description: controls libraries from which to load compiled code

 )set compiler input add library is used to tell AXIOM to add library to
the front of the path used to find compile code.
 )set compiler input drop library is used to tell AXIOM to remove library 
from this path.
--R---------------------------- The input Option -----------------------------
--R
--R Description: controls libraries from which to load compiled code
--R
--R )set compiler input add library is used to tell AXIOM to add library to
--Rthe front of the path used to find compile code.
--R )set compiler input drop library is used to tell AXIOM to remove library 
--Rfrom this path.
--E 4

--S 5 of 143
)set compiler output
 
---------------------------- The output Option ----------------------------

 Description: library in which to place compiled code

 )set compiler output library is used to tell the compiler where to place
compiled code generated by the library compiler.  By default it goes
in a file called user.lib in the current directory.
--R 
--R---------------------------- The output Option ----------------------------
--R
--R Description: library in which to place compiled code
--R
--R )set compiler output library is used to tell the compiler where to place
--Rcompiled code generated by the library compiler.  By default it goes
--Rin a file called user.lib in the current directory.
--E 5

--S 6 of 143
)set compiler args
 
----------------------------- The args Option -----------------------------

 Description: arguments for compiling AXIOM code

 )set compiler args  is used to tell AXIOM how to invoke the library compiler 
 when compiling code for AXIOM.
 The args option is followed by a string enclosed in double quotes.

 The current setting is
 "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra" 
--R----------------------------- The args Option -----------------------------
--R
--R Description: arguments for compiling AXIOM code
--R
--R )set compiler args  is used to tell AXIOM how to invoke the library compiler 
--R when compiling code for AXIOM.
--R The args option is followed by a string enclosed in double quotes.
--R
--R The current setting is
--R "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra" 
--E 6

--S 7 of 143
)set expose
 
---------------------------- The expose Option ----------------------------

 Description: control interpreter constructor exposure

   The following groups are explicitly exposed in the current frame 
      (called initial ):
                                   basic                                   
                                categories                                 
                                  naglink                                  
                                   anna                                    
 
   The following constructors are explicitly exposed in the current 
      frame:
               there are no explicitly exposed constructors                
 
   The following constructors are explicitly hidden in the current 
      frame:
                there are no explicitly hidden constructors                
 
   When )set expose is followed by no arguments, the information you 
      now see is displayed. When followed by the initialize argument, 
      the exposure group data in the file interp.exposed is read and is
      then available. The arguments add and drop are used to add or 
      drop exposure groups or explicit constructors from the local 
      frame exposure data. Issue
                  )set expose add    or    )set expose drop 
      for more information.
--R---------------------------- The expose Option ----------------------------
--R
--R Description: control interpreter constructor exposure
--R
--R   The following groups are explicitly exposed in the current frame 
--I      (called initial ):
--R                                   basic                                   
--R                                categories                                 
--R                                  naglink                                  
--R                                   anna                                    
--R 
--R   The following constructors are explicitly exposed in the current 
--R      frame:
--R               there are no explicitly exposed constructors                
--R 
--R   The following constructors are explicitly hidden in the current 
--R      frame:
--R                there are no explicitly hidden constructors                
--R 
--R   When )set expose is followed by no arguments, the information you 
--R      now see is displayed. When followed by the initialize argument, 
--R      the exposure group data in the file interp.exposed is read and is
--R      then available. The arguments add and drop are used to add or 
--R      drop exposure groups or explicit constructors from the local 
--R      frame exposure data. Issue
--R                  )set expose add    or    )set expose drop 
--R      for more information.
--E 7

--S 8 of 143
)set functions
 
                  Current Values of  functions  Variables                  

Variable     Description                                Current Value
-----------------------------------------------------------------------------
cache        number of function results to cache        0 
compile      compile, don't just define function bodies on 
recurrence   specially compile recurrence relations     on 

--R                  Current Values of  functions  Variables                  
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rcache        number of function results to cache        0 
--Rcompile      compile, don't just define function bodies on 
--Rrecurrence   specially compile recurrence relations     on 
--R
--E 8

--S 9 of 143
)set functions cache
 
---------------------------- The cache Option -----------------------------

 Description: number of function results to cache

 )set functions cache is used to tell AXIOM how many
 values computed by interpreter functions should be saved.  This
 can save quite a bit of time in recursive functions, though one
 must consider that the cached values will take up (perhaps
 valuable) room in the workspace.

 The value given after cache must either be the word all or a positive integer.
 This may be followed by any number of function names whose cache
 sizes you wish to so set.  If no functions are given, the default
 cache size is set.

 Examples:
   )set fun cache all         )set fun cache 10 f g Legendre

 In general, functions will cache no returned values.
--R 
--R---------------------------- The cache Option -----------------------------
--R
--R Description: number of function results to cache
--R
--R )set functions cache is used to tell AXIOM how many
--R values computed by interpreter functions should be saved.  This
--R can save quite a bit of time in recursive functions, though one
--R must consider that the cached values will take up (perhaps
--R valuable) room in the workspace.
--R
--R The value given after cache must either be the word all or a positive integer.
--R This may be followed by any number of function names whose cache
--R sizes you wish to so set.  If no functions are given, the default
--R cache size is set.
--R
--R Examples:
--R   )set fun cache all         )set fun cache 10 f g Legendre
--R
--R In general, functions will cache no returned values.
--E 9

--S 10 of 143
)set functions compile
 
--------------------------- The compile Option ----------------------------

 Description: compile, don't just define function bodies

 The compile option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The compile Option ----------------------------
--R
--R Description: compile, don't just define function bodies
--R
--R The compile option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 10

--S 11 of 143
)set functions recurrence
 
-------------------------- The recurrence Option --------------------------

 Description: specially compile recurrence relations

 The recurrence option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R-------------------------- The recurrence Option --------------------------
--R
--R Description: specially compile recurrence relations
--R
--R The recurrence option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 11

--S 12 of 143
)set fortran
 
                   Current Values of  fortran  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
ints2floats  where sensible, coerce integers to reals   on 
fortindent   the number of characters indented          6 
fortlength   the number of characters on a line         72 
typedecs     print type and dimension lines             on 
defaulttype  default generic type for FORTRAN object    REAL 
precision    precision of generated FORTRAN objects     double 
intrinsic    whether to use INTRINSIC FORTRAN functions off 
explength    character limit for FORTRAN expressions    1320 
segment      split long FORTRAN expressions             on 
optlevel     FORTRAN optimisation level                 0 
startindex   starting index for FORTRAN arrays          1 
calling      options for external FORTRAN calls         ... 

Variables with current values of ... have further sub-options. For example,
issue )set  calling to see what the options are for calling .
For more information, issue )help set .
--R                   Current Values of  fortran  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rints2floats  where sensible, coerce integers to reals   on 
--Rfortindent   the number of characters indented          6 
--Rfortlength   the number of characters on a line         72 
--Rtypedecs     print type and dimension lines             on 
--Rdefaulttype  default generic type for FORTRAN object    REAL 
--Rprecision    precision of generated FORTRAN objects     double 
--Rintrinsic    whether to use INTRINSIC FORTRAN functions off 
--Rexplength    character limit for FORTRAN expressions    1320 
--Rsegment      split long FORTRAN expressions             on 
--Roptlevel     FORTRAN optimisation level                 0 
--Rstartindex   starting index for FORTRAN arrays          1 
--Rcalling      options for external FORTRAN calls         ... 
--R
--RVariables with current values of ... have further sub-options. For example,
--Rissue )set  calling to see what the options are for calling .
--RFor more information, issue )help set .
--E 12

--S 13 of 143
)set fortran ints2floats
 
------------------------- The ints2floats Option --------------------------

 Description: where sensible, coerce integers to reals

 The ints2floats option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R------------------------- The ints2floats Option --------------------------
--R
--R Description: where sensible, coerce integers to reals
--R
--R The ints2floats option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 13

--S 14 of 143
)set fortran fortindent
 
-------------------------- The fortindent Option --------------------------

 Description: the number of characters indented

 The fortindent option may be followed by an integer in the range 0 to
  inclusive. The current setting is 6 

--R-------------------------- The fortindent Option --------------------------
--R
--R Description: the number of characters indented
--R
--R The fortindent option may be followed by an integer in the range 0 to
--R  inclusive. The current setting is 6 
--R
--E 14

--S 15 of 143
)set fortran fortlength
 
-------------------------- The fortlength Option --------------------------

 Description: the number of characters on a line

 The fortlength option may be followed by an integer in the range 1 to
  inclusive. The current setting is 72 

--R-------------------------- The fortlength Option --------------------------
--R
--R Description: the number of characters on a line
--R
--R The fortlength option may be followed by an integer in the range 1 to
--R  inclusive. The current setting is 72 
--R
--E 15

--S 16 of 143
)set fortran typedecs
 
--------------------------- The typedecs Option ---------------------------

 Description: print type and dimension lines

 The typedecs option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The typedecs Option ---------------------------
--R
--R Description: print type and dimension lines
--R
--R The typedecs option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 16

--S 17 of 143
)set fortran defaulttype
 
------------------------- The defaulttype Option --------------------------

 Description: default generic type for FORTRAN object

 The defaulttype option may be followed by any one of the following:

 -> REAL 
    INTEGER
    COMPLEX
    LOGICAL
    CHARACTER

 The current setting is indicated.

--R------------------------- The defaulttype Option --------------------------
--R
--R Description: default generic type for FORTRAN object
--R
--R The defaulttype option may be followed by any one of the following:
--R
--R -> REAL 
--R    INTEGER
--R    COMPLEX
--R    LOGICAL
--R    CHARACTER
--R
--R The current setting is indicated.
--R
--E 17

--S 18 of 143
)set fortran precision
 
-------------------------- The precision Option ---------------------------

 Description: precision of generated FORTRAN objects

 The precision option may be followed by any one of the following:

    single
 -> double 

 The current setting is indicated.

--R-------------------------- The precision Option ---------------------------
--R
--R Description: precision of generated FORTRAN objects
--R
--R The precision option may be followed by any one of the following:
--R
--R    single
--R -> double 
--R
--R The current setting is indicated.
--R
--E 18

--S 19 of 143
)set fortran intrinsic
 
-------------------------- The intrinsic Option ---------------------------

 Description: whether to use INTRINSIC FORTRAN functions

 The intrinsic option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The intrinsic Option ---------------------------
--R
--R Description: whether to use INTRINSIC FORTRAN functions
--R
--R The intrinsic option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 19

--S 20 of 143
)set fortran explength
 
-------------------------- The explength Option ---------------------------

 Description: character limit for FORTRAN expressions

 The explength option may be followed by an integer in the range 0 to
  inclusive. The current setting is 1320 

--R-------------------------- The explength Option ---------------------------
--R
--R Description: character limit for FORTRAN expressions
--R
--R The explength option may be followed by an integer in the range 0 to
--R  inclusive. The current setting is 1320 
--R
--E 20

--S 21 of 143
)set fortran segment
 
--------------------------- The segment Option ----------------------------

 Description: split long FORTRAN expressions

 The segment option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The segment Option ----------------------------
--R
--R Description: split long FORTRAN expressions
--R
--R The segment option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 21

--S 22 of 143
)set fortran optlevel
 
--------------------------- The optlevel Option ---------------------------

 Description: FORTRAN optimisation level

 The optlevel option may be followed by an integer in the range 0 to
 2 inclusive. The current setting is 0 

--R--------------------------- The optlevel Option ---------------------------
--R
--R Description: FORTRAN optimisation level
--R
--R The optlevel option may be followed by an integer in the range 0 to
--R 2 inclusive. The current setting is 0 
--R
--E 22

--S 23 of 143
)set fortran startindex
 
-------------------------- The startindex Option --------------------------

 Description: starting index for FORTRAN arrays

 The startindex option may be followed by an integer in the range 0 to
 1 inclusive. The current setting is 1 

--R-------------------------- The startindex Option --------------------------
--R
--R Description: starting index for FORTRAN arrays
--R
--R The startindex option may be followed by an integer in the range 0 to
--R 1 inclusive. The current setting is 1 
--R
--E 23

--S 24 of 143
)set fortran calling
 
                   Current Values of  calling  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
tempfile     set location of temporary data files       /tmp/ 
directory    set location of generated FORTRAN files    ./ 
linker       linker arguments (e.g. libraries to search) -lxlf 

--R                   Current Values of  calling  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rtempfile     set location of temporary data files       /tmp/ 
--Rdirectory    set location of generated FORTRAN files    ./ 
--Rlinker       linker arguments (e.g. libraries to search) -lxlf 
--R
--E 24

--S 25 of 143
)set fortran calling tempfile
 
--------------------------- The tempfile Option ---------------------------

 Description: set location of temporary data files

 )set fortran calling tempfile  is used to tell AXIOM where
 to place intermediate FORTRAN data files . This must be the 
 name of a valid existing directory to which you have permission 
 to write (including the final slash).

 Syntax:
   )set fortran calling tempfile DIRECTORYNAME

 The current setting is /tmp/ 
--R--------------------------- The tempfile Option ---------------------------
--R
--R Description: set location of temporary data files
--R
--R )set fortran calling tempfile  is used to tell AXIOM where
--R to place intermediate FORTRAN data files . This must be the 
--R name of a valid existing directory to which you have permission 
--R to write (including the final slash).
--R
--R Syntax:
--R   )set fortran calling tempfile DIRECTORYNAME
--R
--R The current setting is /tmp/ 
--E 25

--S 26 of 143
)set fortran calling directory
 
-------------------------- The directory Option ---------------------------

 Description: set location of generated FORTRAN files

 )set fortran calling directory  is used to tell AXIOM where
 to place generated FORTRAN files. This must be the name 
 of a valid existing directory to which you have permission 
 to write (including the final slash).

 Syntax:
   )set fortran calling directory DIRECTORYNAME

 The current setting is ./ 
--R-------------------------- The directory Option ---------------------------
--R
--R Description: set location of generated FORTRAN files
--R
--R )set fortran calling directory  is used to tell AXIOM where
--R to place generated FORTRAN files. This must be the name 
--R of a valid existing directory to which you have permission 
--R to write (including the final slash).
--R
--R Syntax:
--R   )set fortran calling directory DIRECTORYNAME
--R
--R The current setting is ./ 
--E 26

--S 27 of 143
)set fortran calling linker
 
---------------------------- The linker Option ----------------------------

 Description: linker arguments (e.g. libraries to search)

 )set fortran calling linkerargs  is used to pass arguments to the linker
 when using  mkFort  to create functions which call Fortran code.
 For example, it might give a list of libraries to be searched,
 and their locations.
 The string is passed verbatim, so must be the correct syntax for
 the particular linker being used.

 Example: )set fortran calling linker "-lxlf"

 The current setting is -lxlf 
--R---------------------------- The linker Option ----------------------------
--R
--R Description: linker arguments (e.g. libraries to search)
--R
--R )set fortran calling linkerargs  is used to pass arguments to the linker
--R when using  mkFort  to create functions which call Fortran code.
--R For example, it might give a list of libraries to be searched,
--R and their locations.
--R The string is passed verbatim, so must be the correct syntax for
--R the particular linker being used.
--R
--R Example: )set fortran calling linker "-lxlf"
--R
--R The current setting is -lxlf 
--E 27

--S 28 of 143
)set kernel
 
                   Current Values of  kernel  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
warn         warn when re-definition is attempted       off 
protect      prevent re-definition of kernel functions  off 

--R                   Current Values of  kernel  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rwarn         warn when re-definition is attempted       off 
--Rprotect      prevent re-definition of kernel functions  off 
--R
--E 28

--S 29 of 143
)set kernel warn
 
----------------------------- The warn Option -----------------------------

 Description: warn when re-definition is attempted

Some AXIOM library functions are compiled into the kernel for efficiency
reasons.  To prevent them being re-defined when loaded from a library
they are specially protected.  If a user wishes to know when an attempt
is made to re-define such a function, he or she should issue the command:
        )set kernel warn on
To restore the default behaviour, he or she should issue the command:
        )set kernel warn off
--R----------------------------- The warn Option -----------------------------
--R
--R Description: warn when re-definition is attempted
--R
--RSome AXIOM library functions are compiled into the kernel for efficiency
--Rreasons.  To prevent them being re-defined when loaded from a library
--Rthey are specially protected.  If a user wishes to know when an attempt
--Ris made to re-define such a function, he or she should issue the command:
--R        )set kernel warn on
--RTo restore the default behaviour, he or she should issue the command:
--R        )set kernel warn off
--E 29

--S 30 of 143
)set kernel protect
 
--------------------------- The protect Option ----------------------------

 Description: prevent re-definition of kernel functions

Some AXIOM library functions are compiled into the kernel for efficiency
reasons.  To prevent them being re-defined when loaded from a library
they are specially protected.  If a user wishes to re-define these
functions, he or she should issue the command:
        )set kernel protect off
To restore the default behaviour, he or she should issue the command:
        )set kernel protect on
--R--------------------------- The protect Option ----------------------------
--R
--R Description: prevent re-definition of kernel functions
--R
--RSome AXIOM library functions are compiled into the kernel for efficiency
--Rreasons.  To prevent them being re-defined when loaded from a library
--Rthey are specially protected.  If a user wishes to re-define these
--Rfunctions, he or she should issue the command:
--R        )set kernel protect off
--RTo restore the default behaviour, he or she should issue the command:
--R        )set kernel protect on
--E 30

--S 31 of 143
)set hyperdoc
 
                  Current Values of  hyperdoc  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
fullscreen   use full screen for this facility          off 
mathwidth    screen width for history output            120 

--R                  Current Values of  hyperdoc  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rfullscreen   use full screen for this facility          off 
--Rmathwidth    screen width for history output            120 
--R
--E 31

--S 32 of 143
)set hyperdoc fullscreen
 
-------------------------- The fullscreen Option --------------------------

 Description: use full screen for this facility

 The fullscreen option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The fullscreen Option --------------------------
--R
--R Description: use full screen for this facility
--R
--R The fullscreen option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 32

--S 33 of 143
)set hyperdoc mathwidth
 
-------------------------- The mathwidth Option ---------------------------

 Description: screen width for history output

 The mathwidth option may be followed by an integer in the range 0 to
  inclusive. The current setting is 120 

--R-------------------------- The mathwidth Option ---------------------------
--R
--R Description: screen width for history output
--R
--R The mathwidth option may be followed by an integer in the range 0 to
--R  inclusive. The current setting is 120 
--R
--E 33

--S 34 of 143
)set help
 
                    Current Values of  help  Variables                     

Variable     Description                                Current Value
-----------------------------------------------------------------------------
fullscreen   use fullscreen facility, if possible       off 

--R                    Current Values of  help  Variables                     
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rfullscreen   use fullscreen facility, if possible       off 
--R
--E 34

--S 35 of 143
)set help fullscreen
 
-------------------------- The fullscreen Option --------------------------

 Description: use fullscreen facility, if possible

 The fullscreen option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The fullscreen Option --------------------------
--R
--R Description: use fullscreen facility, if possible
--R
--R The fullscreen option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 35

--S 36 of 143
)set history
 
--------------------------- The history Option ----------------------------

 Description: save workspace values in a history file

 The history option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The history Option ----------------------------
--R
--R Description: save workspace values in a history file
--R
--R The history option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 36

--S 37 of 143
)set messages
 
                  Current Values of  messages  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
any          print the internal type of objects of domain Any on 
autoload     print file auto-load messages              off 
bottomup     display bottom up modemap selection        off 
coercion     display datatype coercion messages         off 
dropmap      display old map defn when replaced         off 
expose       warning for unexposed functions            off 
file         print msgs also to SPADMSG LISTING         off 
frame        display messages about frames              off 
highlighting use highlighting in system messages        off 
instant      present instantiation summary              off 
insteach     present instantiation info                 off 
interponly   say when function code is interpreted      on 
naglink      show NAGLink messages                      on 
number       display message number with message        off 
prompt       set type of input prompt to display        step 
selection    display function selection msgs            off 
set          show )set setting after assignment         off 
startup      display messages on start-up               on 
summary      print statistics after computation         off 
testing      print system testing header                on 
time         print timings after computation            off 
type         print type after computation               on 
void         print Void value when it occurs            off 

--R                  Current Values of  messages  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rany          print the internal type of objects of domain Any on 
--Rautoload     print file auto-load messages              off 
--Rbottomup     display bottom up modemap selection        off 
--Rcoercion     display datatype coercion messages         off 
--Rdropmap      display old map defn when replaced         off 
--Rexpose       warning for unexposed functions            off 
--Rfile         print msgs also to SPADMSG LISTING         off 
--Rframe        display messages about frames              off 
--Rhighlighting use highlighting in system messages        off 
--Rinstant      present instantiation summary              off 
--Rinsteach     present instantiation info                 off 
--Rinterponly   say when function code is interpreted      on 
--Rnaglink      show NAGLink messages                      on 
--Rnumber       display message number with message        off 
--Rprompt       set type of input prompt to display        step 
--Rselection    display function selection msgs            off 
--Rset          show )set setting after assignment         off 
--Rstartup      display messages on start-up               on 
--Rsummary      print statistics after computation         off 
--Rtesting      print system testing header                on 
--Rtime         print timings after computation            off 
--Rtype         print type after computation               on 
--Rvoid         print Void value when it occurs            off 
--R
--E 37

--S 38 of 143
)set messages autoload
 
--------------------------- The autoload Option ---------------------------

 Description: print file auto-load messages

 The autoload option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R 
--R--------------------------- The autoload Option ---------------------------
--R
--R Description: print file auto-load messages
--R
--R The autoload option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 38

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)set messages bottomup
 
--------------------------- The bottomup Option ---------------------------

 Description: display bottom up modemap selection

 The bottomup option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The bottomup Option ---------------------------
--R
--R Description: display bottom up modemap selection
--R
--R The bottomup option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 39

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)set messages coercion
 
--------------------------- The coercion Option ---------------------------

 Description: display datatype coercion messages

 The coercion option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The coercion Option ---------------------------
--R
--R Description: display datatype coercion messages
--R
--R The coercion option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 40

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)set messages dropmap
 
--------------------------- The dropmap Option ----------------------------

 Description: display old map defn when replaced

 The dropmap option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The dropmap Option ----------------------------
--R
--R Description: display old map defn when replaced
--R
--R The dropmap option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 41

--S 42 of 143
)set messages expose
 
---------------------------- The expose Option ----------------------------

 Description: warning for unexposed functions

 The expose option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R---------------------------- The expose Option ----------------------------
--R
--R Description: warning for unexposed functions
--R
--R The expose option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 42

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)set messages file
 
----------------------------- The file Option -----------------------------

 Description: print msgs also to SPADMSG LISTING

 The file option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R----------------------------- The file Option -----------------------------
--R
--R Description: print msgs also to SPADMSG LISTING
--R
--R The file option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 43

--S 44 of 143
)set messages frame
 
---------------------------- The frame Option -----------------------------

 Description: display messages about frames

 The frame option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R---------------------------- The frame Option -----------------------------
--R
--R Description: display messages about frames
--R
--R The frame option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 44

--S 45 of 143
)set messages highlighting
 
------------------------- The highlighting Option -------------------------

 Description: use highlighting in system messages

 The highlighting option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R------------------------- The highlighting Option -------------------------
--R
--R Description: use highlighting in system messages
--R
--R The highlighting option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 45

--S 46 of 143
)set messages instant
 
--------------------------- The instant Option ----------------------------

 Description: present instantiation summary

 The instant option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The instant Option ----------------------------
--R
--R Description: present instantiation summary
--R
--R The instant option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 46

--S 47 of 143
)set messages insteach
 
--------------------------- The insteach Option ---------------------------

 Description: present instantiation info

 The insteach option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The insteach Option ---------------------------
--R
--R Description: present instantiation info
--R
--R The insteach option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 47

--S 48 of 143
)set messages interponly
 
-------------------------- The interponly Option --------------------------

 Description: say when function code is interpreted

 The interponly option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R-------------------------- The interponly Option --------------------------
--R
--R Description: say when function code is interpreted
--R
--R The interponly option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 48

--S 49 of 143
)set messages number
 
---------------------------- The number Option ----------------------------

 Description: display message number with message

 The number option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R---------------------------- The number Option ----------------------------
--R
--R Description: display message number with message
--R
--R The number option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 49

--S 50 of 143
)set messages prompt
 
---------------------------- The prompt Option ----------------------------

 Description: set type of input prompt to display

 The prompt option may be followed by any one of the following:

    none
    frame
    plain
 -> step 
    verbose

 The current setting is indicated.

--R---------------------------- The prompt Option ----------------------------
--R
--R Description: set type of input prompt to display
--R
--R The prompt option may be followed by any one of the following:
--R
--R    none
--R    frame
--R    plain
--R -> step 
--R    verbose
--R
--R The current setting is indicated.
--R
--E 50

--S 51 of 143
)set messages selection
 
-------------------------- The selection Option ---------------------------

 Description: display function selection msgs

 The selection option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The selection Option ---------------------------
--R
--R Description: display function selection msgs
--R
--R The selection option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 51

--S 52 of 143
)set messages set
 
----------------------------- The set Option ------------------------------

 Description: show )set setting after assignment

 The set option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R----------------------------- The set Option ------------------------------
--R
--R Description: show )set setting after assignment
--R
--R The set option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 52

--S 53 of 143
)set messages startup
 
--------------------------- The startup Option ----------------------------

 Description: display messages on start-up

 The startup option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The startup Option ----------------------------
--R
--R Description: display messages on start-up
--R
--R The startup option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 53

--S 54 of 143
)set messages summary
 
--------------------------- The summary Option ----------------------------

 Description: print statistics after computation

 The summary option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The summary Option ----------------------------
--R
--R Description: print statistics after computation
--R
--R The summary option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 54

--S 55 of 143
)set messages testing
 
--------------------------- The testing Option ----------------------------

 Description: print system testing header

 The testing option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The testing Option ----------------------------
--R
--R Description: print system testing header
--R
--R The testing option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 55

--S 56 of 143
)set messages time
 
----------------------------- The time Option -----------------------------

 Description: print timings after computation

 The time option may be followed by any one of the following:

    on
 -> off 
    long

 The current setting is indicated.

--R----------------------------- The time Option -----------------------------
--R
--R Description: print timings after computation
--R
--R The time option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R    long
--R
--R The current setting is indicated.
--R
--E 56

--S 57 of 143
)set messages type
 
----------------------------- The type Option -----------------------------

 Description: print type after computation

 The type option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R----------------------------- The type Option -----------------------------
--R
--R Description: print type after computation
--R
--R The type option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 57

--S 58 of 143
)set messages void
 
----------------------------- The void Option -----------------------------

 Description: print Void value when it occurs

 The void option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R----------------------------- The void Option -----------------------------
--R
--R Description: print Void value when it occurs
--R
--R The void option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 58

--S 59 of 143
)set messages any
 
----------------------------- The any Option ------------------------------

 Description: print the internal type of objects of domain Any

 The any option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R----------------------------- The any Option ------------------------------
--R
--R Description: print the internal type of objects of domain Any
--R
--R The any option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 59

--S 60 of 143
)set messages naglink
 
--------------------------- The naglink Option ----------------------------

 Description: show NAGLink messages

 The naglink option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The naglink Option ----------------------------
--R
--R Description: show NAGLink messages
--R
--R The naglink option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 60

--S 61 of 143
)set naglink host
 
----------------------------- The host Option -----------------------------

 Description: internet address of host for NAGLink

 )set naglink host is used to tell  AXIOM which  host to contact for
 a NAGLink request. An Internet address should be supplied. The host
 specified must be running the NAGLink daemon.

 The current setting is localhost 
--R----------------------------- The host Option -----------------------------
--R
--R Description: internet address of host for NAGLink
--R
--R )set naglink host is used to tell  AXIOM which  host to contact for
--R a NAGLink request. An Internet address should be supplied. The host
--R specified must be running the NAGLink daemon.
--R
--R The current setting is localhost 
--E 61

--S 62 of 143
)set naglink persistence
 
------------------------- The persistence Option --------------------------

 Description: number of (fortran) functions to remember

 )set naglink persistence is used to tell  the  nagd  daemon how  many ASP
 source and object files to keep around in case you reuse them. This helps
 to avoid needless recompilations. The number specified should be a 
 non-negative integer.

 The current setting is 1 
--R------------------------- The persistence Option --------------------------
--R
--R Description: number of (fortran) functions to remember
--R
--R )set naglink persistence is used to tell  the  nagd  daemon how  many ASP
--R source and object files to keep around in case you reuse them. This helps
--R to avoid needless recompilations. The number specified should be a 
--R non-negative integer.
--R
--R The current setting is 1 
--E 62

--S 63 of 143
)set naglink messages
 
--------------------------- The messages Option ---------------------------

 Description: show NAGLink messages

 The messages option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R--------------------------- The messages Option ---------------------------
--R
--R Description: show NAGLink messages
--R
--R The messages option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 63

--S 64 of 143
)set naglink double
 
---------------------------- The double Option ----------------------------

 Description: enforce DOUBLE PRECISION ASPs

 The double option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R---------------------------- The double Option ----------------------------
--R
--R Description: enforce DOUBLE PRECISION ASPs
--R
--R The double option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 64

--S 65 of 143
)set output 
 
                   Current Values of  output  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
abbreviate   abbreviate type names                      off 
algebra      display output in algebraic form           On:CONSOLE 
characters   choose special output character set        plain 
fortran      create output in FORTRAN format            Off:CONSOLE 
fraction     how fractions are formatted                vertical 
length       line length of output displays             77 
mathml       create output in MathML style              Off:CONSOLE 
openmath     create output in OpenMath style            Off:CONSOLE 
script       display output in SCRIPT formula format    Off:CONSOLE 
scripts      show subscripts,... linearly               off 
showeditor   view output of )show in editor             off 
tex          create output in TeX style                 Off:CONSOLE 

--R                   Current Values of  output  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rabbreviate   abbreviate type names                      off 
--Ralgebra      display output in algebraic form           On:CONSOLE 
--Rcharacters   choose special output character set        plain 
--Rfortran      create output in FORTRAN format            Off:CONSOLE 
--Rfraction     how fractions are formatted                vertical 
--Rlength       line length of output displays             77 
--Rmathml       create output in MathML style              Off:CONSOLE 
--Ropenmath     create output in OpenMath style            Off:CONSOLE 
--Rscript       display output in SCRIPT formula format    Off:CONSOLE 
--Rscripts      show subscripts,... linearly               off 
--Rshoweditor   view output of )show in editor             off 
--Rtex          create output in TeX style                 Off:CONSOLE 
--R
--E 65

--S 66 of 143
)set output abbreviate
 
-------------------------- The abbreviate Option --------------------------

 Description: abbreviate type names

 The abbreviate option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The abbreviate Option --------------------------
--R
--R Description: abbreviate type names
--R
--R The abbreviate option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 66

--S 67 of 143
)set output algebra
 
--------------------------- The algebra Option ----------------------------

 Description: display output in algebraic form

 )set output algebra is used to tell AXIOM to turn algebra-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output algebra <arg>
    where arg can be one of
  on          turn algebra printing on (default state)
  off         turn algebra printing off
  console     send algebra output to screen (default state)
  fp<.fe>     send algebra output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .spout.

If you wish to send the output to a file, you may need to issue this command
twice: once with on and once with the file name. For example, to send
algebra output to the file polymer.spout, issue the two commands

  )set output algebra on
  )set output algebra polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R--------------------------- The algebra Option ----------------------------
--R
--R Description: display output in algebraic form
--R
--R )set output algebra is used to tell AXIOM to turn algebra-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output algebra <arg>
--R    where arg can be one of
--R  on          turn algebra printing on (default state)
--R  off         turn algebra printing off
--R  console     send algebra output to screen (default state)
--R  fp<.fe>     send algebra output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .spout.
--R
--RIf you wish to send the output to a file, you may need to issue this command
--Rtwice: once with on and once with the file name. For example, to send
--Ralgebra output to the file polymer.spout, issue the two commands
--R
--R  )set output algebra on
--R  )set output algebra polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 67

--S 68 of 143
)set output characters
 
-------------------------- The characters Option --------------------------

 Description: choose special output character set


 The characters option may be followed by any one of the following:

    default
 -> plain 

 The current setting is indicated within the list.  This option determines 
 the special characters used for algebraic output.  This is what the
 current choice of special characters looks like:
   ulc is shown as +          urc is shown as +       
   llc is shown as +          lrc is shown as +       
   vbar is shown as |         hbar is shown as -      
   quad is shown as ?         lbrk is shown as [      
   rbrk is shown as ]         lbrc is shown as {      
   rbrc is shown as }         ttee is shown as +      
   btee is shown as +         rtee is shown as +      
   ltee is shown as +         ctee is shown as +      
   bslash is shown as \    
--R-------------------------- The characters Option --------------------------
--R
--R Description: choose special output character set
--R
--R
--R The characters option may be followed by any one of the following:
--R
--R    default
--R -> plain 
--R
--R The current setting is indicated within the list.  This option determines 
--R the special characters used for algebraic output.  This is what the
--R current choice of special characters looks like:
--R   ulc is shown as +          urc is shown as +       
--R   llc is shown as +          lrc is shown as +       
--R   vbar is shown as |         hbar is shown as -      
--R   quad is shown as ?         lbrk is shown as [      
--R   rbrk is shown as ]         lbrc is shown as {      
--R   rbrc is shown as }         ttee is shown as +      
--R   btee is shown as +         rtee is shown as +      
--R   ltee is shown as +         ctee is shown as +      
--R   bslash is shown as \    
--E 68

--S 69 of 143
)set output fortran
 
--------------------------- The fortran Option ----------------------------

 Description: create output in FORTRAN format

 )set output fortran is used to tell AXIOM to turn FORTRAN-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Also See: )set fortran

Syntax:   )set output fortran <arg>
    where arg can be one of
  on          turn FORTRAN printing on
  off         turn FORTRAN printing off (default state)
  console     send FORTRAN output to screen (default state)
  fp<.fe>     send FORTRAN output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .sfort.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands

  )set output fortran on
  )set output fortran polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R--------------------------- The fortran Option ----------------------------
--R
--R Description: create output in FORTRAN format
--R
--R )set output fortran is used to tell AXIOM to turn FORTRAN-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RAlso See: )set fortran
--R
--RSyntax:   )set output fortran <arg>
--R    where arg can be one of
--R  on          turn FORTRAN printing on
--R  off         turn FORTRAN printing off (default state)
--R  console     send FORTRAN output to screen (default state)
--R  fp<.fe>     send FORTRAN output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .sfort.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RFORTRAN output to the file polymer.sfort, issue the two commands
--R
--R  )set output fortran on
--R  )set output fortran polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 69

--S 70 of 143
)set output fraction
 
--------------------------- The fraction Option ---------------------------

 Description: how fractions are formatted

 The fraction option may be followed by any one of the following:

 -> vertical 
    horizontal

 The current setting is indicated.

--R--------------------------- The fraction Option ---------------------------
--R
--R Description: how fractions are formatted
--R
--R The fraction option may be followed by any one of the following:
--R
--R -> vertical 
--R    horizontal
--R
--R The current setting is indicated.
--R
--E 70

--S 71 of 143
)set output length
 
---------------------------- The length Option ----------------------------

 Description: line length of output displays

 The length option may be followed by an integer in the range 10 to
 245 inclusive. The current setting is 77 

--R---------------------------- The length Option ----------------------------
--R
--R Description: line length of output displays
--R
--R The length option may be followed by an integer in the range 10 to
--R 245 inclusive. The current setting is 77 
--R
--E 71

--S 72 of 143
)set output mathml
 
---------------------------- The mathml Option ----------------------------

 Description: create output in MathML style

 )set output mathml is used to tell AXIOM to turn MathML-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output mathml <arg>
    where arg can be one of
  on          turn MathML printing on
  off         turn MathML printing off (default state)
  console     send MathML output to screen (default state)
  fp<.fe>     send MathML output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
MathML output to the file polymer.smml, issue the two commands

  )set output mathml on
  )set output mathml polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R---------------------------- The mathml Option ----------------------------
--R
--R Description: create output in MathML style
--R
--R )set output mathml is used to tell AXIOM to turn MathML-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output mathml <arg>
--R    where arg can be one of
--R  on          turn MathML printing on
--R  off         turn MathML printing off (default state)
--R  console     send MathML output to screen (default state)
--R  fp<.fe>     send MathML output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RMathML output to the file polymer.smml, issue the two commands
--R
--R  )set output mathml on
--R  )set output mathml polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 72

--S 73 of 143
)set output openmath
 
--------------------------- The openmath Option ---------------------------

 Description: create output in OpenMath style

 )set output openmath is used to tell AXIOM to turn OpenMath output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output openmath <arg>
    where arg can be one of
  on          turn OpenMath printing on
  off         turn OpenMath printing off (default state)
  console     send OpenMath output to screen (default state)
  fp<.fe>     send OpenMath output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .som.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
OpenMath output to the file polymer.som, issue the two commands

  )set output openmath on
  )set output openmath polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R--------------------------- The openmath Option ---------------------------
--R
--R Description: create output in OpenMath style
--R
--R )set output openmath is used to tell AXIOM to turn OpenMath output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output openmath <arg>
--R    where arg can be one of
--R  on          turn OpenMath printing on
--R  off         turn OpenMath printing off (default state)
--R  console     send OpenMath output to screen (default state)
--R  fp<.fe>     send OpenMath output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .som.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--ROpenMath output to the file polymer.som, issue the two commands
--R
--R  )set output openmath on
--R  )set output openmath polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 73

--S 74 of 143
)set output script
 
---------------------------- The script Option ----------------------------

 Description: display output in SCRIPT formula format

 )set output script is used to tell AXIOM to turn IBM Script formula-style
output printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output script <arg>
    where arg can be one of
  on          turn IBM Script formula printing on
  off         turn IBM Script formula printing off (default state)
  console     send IBM Script formula output to screen (default state)
  fp<.fe>     send IBM Script formula output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .sform.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands

  )set output script on
  )set output script polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R---------------------------- The script Option ----------------------------
--R
--R Description: display output in SCRIPT formula format
--R
--R )set output script is used to tell AXIOM to turn IBM Script formula-style
--Routput printing on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output script <arg>
--R    where arg can be one of
--R  on          turn IBM Script formula printing on
--R  off         turn IBM Script formula printing off (default state)
--R  console     send IBM Script formula output to screen (default state)
--R  fp<.fe>     send IBM Script formula output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .sform.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RIBM Script formula output to the file polymer.sform, issue the two commands
--R
--R  )set output script on
--R  )set output script polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 74

--S 75 of 143
)set output scripts
 
--------------------------- The scripts Option ----------------------------

 Description: show subscripts,... linearly

 The scripts option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The scripts Option ----------------------------
--R
--R Description: show subscripts,... linearly
--R
--R The scripts option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 75

--S 76 of 143
)set output showeditor
 
-------------------------- The showeditor Option --------------------------

 Description: view output of )show in editor

 The showeditor option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R-------------------------- The showeditor Option --------------------------
--R
--R Description: view output of )show in editor
--R
--R The showeditor option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 76

--S 77 of 143
)set output tex
 
----------------------------- The tex Option ------------------------------

 Description: create output in TeX style

 )set output tex is used to tell AXIOM to turn TeX-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output tex <arg>
    where arg can be one of
  on          turn TeX printing on
  off         turn TeX printing off (default state)
  console     send TeX output to screen (default state)
  fp<.fe>     send TeX output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands

  )set output tex on
  )set output tex polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R----------------------------- The tex Option ------------------------------
--R
--R Description: create output in TeX style
--R
--R )set output tex is used to tell AXIOM to turn TeX-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output tex <arg>
--R    where arg can be one of
--R  on          turn TeX printing on
--R  off         turn TeX printing off (default state)
--R  console     send TeX output to screen (default state)
--R  fp<.fe>     send TeX output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RTeX output to the file polymer.stex, issue the two commands
--R
--R  )set output tex on
--R  )set output tex polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 77

--S 78 of 143
)set quit
 
----------------------------- The quit Option -----------------------------

 Description: protected or unprotected quit

 The quit option may be followed by any one of the following:

 -> protected 
    unprotected

 The current setting is indicated.

--R----------------------------- The quit Option -----------------------------
--R
--R Description: protected or unprotected quit
--R
--R The quit option may be followed by any one of the following:
--R
--R -> protected 
--R    unprotected
--R
--R The current setting is indicated.
--R
--E 78

--S 79 of 143
)set streams
 
                   Current Values of  streams  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
calculate    specify number of elements to calculate    10 
showall      display all stream elements computed       off 

--R                   Current Values of  streams  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rcalculate    specify number of elements to calculate    10 
--Rshowall      display all stream elements computed       off 
--R
--E 79

--S 80 of 143
)set streams calculate
 
-------------------------- The calculate Option ---------------------------

 Description: specify number of elements to calculate

   )set streams calculate is used to tell AXIOM how many elements of a 
      stream to calculate when a computation uses the stream. The value
      given after calculate must either be the word all or a positive 
      integer.

      The current setting is 10 .
--R-------------------------- The calculate Option ---------------------------
--R
--R Description: specify number of elements to calculate
--R
--R   )set streams calculate is used to tell AXIOM how many elements of a 
--R      stream to calculate when a computation uses the stream. The value
--R      given after calculate must either be the word all or a positive 
--R      integer.
--R
--R      The current setting is 10 .
--E 80

--S 81 of 143
)set streams showall
 
--------------------------- The showall Option ----------------------------

 Description: display all stream elements computed

 The showall option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R--------------------------- The showall Option ----------------------------
--R
--R Description: display all stream elements computed
--R
--R The showall option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 81

--S 82 of 143
)set system
 
                   Current Values of  system  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
functioncode show gen. LISP for functions when compiled off 
optimization show optimized LISP code                   off 
prettyprint  prettyprint BOOT func's as they compile    on 

--R                   Current Values of  system  Variables                    
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Rfunctioncode show gen. LISP for functions when compiled off 
--Roptimization show optimized LISP code                   off 
--Rprettyprint  prettyprint BOOT func's as they compile    on 
--R
--E 82

--S 83 of 143
)set system functioncode
 
------------------------- The functioncode Option -------------------------

 Description: show gen. LISP for functions when compiled

 The functioncode option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R------------------------- The functioncode Option -------------------------
--R
--R Description: show gen. LISP for functions when compiled
--R
--R The functioncode option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 83

--S 84 of 143
)set system optimization
 
------------------------- The optimization Option -------------------------

 Description: show optimized LISP code

 The optimization option may be followed by any one of the following:

    on
 -> off 

 The current setting is indicated.

--R------------------------- The optimization Option -------------------------
--R
--R Description: show optimized LISP code
--R
--R The optimization option may be followed by any one of the following:
--R
--R    on
--R -> off 
--R
--R The current setting is indicated.
--R
--E 84

--S 85 of 143
)set system prettyprint
 
------------------------- The prettyprint Option --------------------------

 Description: prettyprint BOOT func's as they compile

 The prettyprint option may be followed by any one of the following:

 -> on 
    off

 The current setting is indicated.

--R------------------------- The prettyprint Option --------------------------
--R
--R Description: prettyprint BOOT func's as they compile
--R
--R The prettyprint option may be followed by any one of the following:
--R
--R -> on 
--R    off
--R
--R The current setting is indicated.
--R
--E 85

--S 86 of 143
)set userlevel
 
-------------------------- The userlevel Option ---------------------------

 Description: operation access level of system user

 The userlevel option may be followed by any one of the following:

    interpreter
    compiler
 -> development 

 The current setting is indicated.

--R-------------------------- The userlevel Option ---------------------------
--R
--R Description: operation access level of system user
--R
--R The userlevel option may be followed by any one of the following:
--R
--R    interpreter
--R    compiler
--R -> development 
--R
--R The current setting is indicated.
--R
--E 86

--S 87 of 143
)set output char
 
-------------------------- The characters Option --------------------------

 Description: choose special output character set


 The characters option may be followed by any one of the following:

    default
 -> plain 

 The current setting is indicated within the list.  This option determines 
 the special characters used for algebraic output.  This is what the
 current choice of special characters looks like:
   ulc is shown as +          urc is shown as +       
   llc is shown as +          lrc is shown as +       
   vbar is shown as |         hbar is shown as -      
   quad is shown as ?         lbrk is shown as [      
   rbrk is shown as ]         lbrc is shown as {      
   rbrc is shown as }         ttee is shown as +      
   btee is shown as +         rtee is shown as +      
   ltee is shown as +         ctee is shown as +      
   bslash is shown as \    
--R-------------------------- The characters Option --------------------------
--R
--R Description: choose special output character set
--R
--R
--R The characters option may be followed by any one of the following:
--R
--R    default
--R -> plain 
--R
--R The current setting is indicated within the list.  This option determines 
--R the special characters used for algebraic output.  This is what the
--R current choice of special characters looks like:
--R   ulc is shown as +          urc is shown as +       
--R   llc is shown as +          lrc is shown as +       
--R   vbar is shown as |         hbar is shown as -      
--R   quad is shown as ?         lbrk is shown as [      
--R   rbrk is shown as ]         lbrc is shown as {      
--R   rbrc is shown as }         ttee is shown as +      
--R   btee is shown as +         rtee is shown as +      
--R   ltee is shown as +         ctee is shown as +      
--R   bslash is shown as \    
--E 87

--S 88 of 143
)set output char default
 
--E 88

--S 89 of 143
)set output char
 
 The characters Option 

 Description: choose special output character set


 The characters option may be followed by any one of the following:

 -> default 
    plain

 The current setting is indicated within the list.  This option determines 
 the special characters used for algebraic output.  This is what the
 current choice of special characters looks like:
   ulc is shown as           urc is shown as        
   llc is shown as           lrc is shown as        
   vbar is shown as          hbar is shown as       
   quad is shown as NIL       lbrk is shown as [      
   rbrk is shown as ]         lbrc is shown as {      
   rbrc is shown as }         ttee is shown as       
   btee is shown as          rtee is shown as       
   ltee is shown as          ctee is shown as       
   bslash is shown as \    
--R The characters Option 
--R
--R Description: choose special output character set
--R
--R
--R The characters option may be followed by any one of the following:
--R
--R -> default 
--R    plain
--R
--R The current setting is indicated within the list.  This option determines 
--R the special characters used for algebraic output.  This is what the
--R current choice of special characters looks like:
--R   ulc is shown as           urc is shown as        
--R   llc is shown as           lrc is shown as        
--R   vbar is shown as          hbar is shown as       
--R   quad is shown as NIL       lbrk is shown as [      
--R   rbrk is shown as ]         lbrc is shown as {      
--R   rbrc is shown as }         ttee is shown as       
--R   btee is shown as          rtee is shown as       
--R   ltee is shown as          ctee is shown as       
--R   bslash is shown as \    
--E 89

--S 90 of 143
)set output char plain
 
--E 90

--S 91 of 143
)set output char
 
-------------------------- The characters Option --------------------------

 Description: choose special output character set


 The characters option may be followed by any one of the following:

    default
 -> plain 

 The current setting is indicated within the list.  This option determines 
 the special characters used for algebraic output.  This is what the
 current choice of special characters looks like:
   ulc is shown as +          urc is shown as +       
   llc is shown as +          lrc is shown as +       
   vbar is shown as |         hbar is shown as -      
   quad is shown as ?         lbrk is shown as [      
   rbrk is shown as ]         lbrc is shown as {      
   rbrc is shown as }         ttee is shown as +      
   btee is shown as +         rtee is shown as +      
   ltee is shown as +         ctee is shown as +      
   bslash is shown as \    
--R-------------------------- The characters Option --------------------------
--R
--R Description: choose special output character set
--R
--R
--R The characters option may be followed by any one of the following:
--R
--R    default
--R -> plain 
--R
--R The current setting is indicated within the list.  This option determines 
--R the special characters used for algebraic output.  This is what the
--R current choice of special characters looks like:
--R   ulc is shown as +          urc is shown as +       
--R   llc is shown as +          lrc is shown as +       
--R   vbar is shown as |         hbar is shown as -      
--R   quad is shown as ?         lbrk is shown as [      
--R   rbrk is shown as ]         lbrc is shown as {      
--R   rbrc is shown as }         ttee is shown as +      
--R   btee is shown as +         rtee is shown as +      
--R   ltee is shown as +         ctee is shown as +      
--R   bslash is shown as \    
--E 91

--S 92 of 143
)set output fortran
 
--------------------------- The fortran Option ----------------------------

 Description: create output in FORTRAN format

 )set output fortran is used to tell AXIOM to turn FORTRAN-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Also See: )set fortran

Syntax:   )set output fortran <arg>
    where arg can be one of
  on          turn FORTRAN printing on
  off         turn FORTRAN printing off (default state)
  console     send FORTRAN output to screen (default state)
  fp<.fe>     send FORTRAN output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .sfort.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands

  )set output fortran on
  )set output fortran polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R--------------------------- The fortran Option ----------------------------
--R
--R Description: create output in FORTRAN format
--R
--R )set output fortran is used to tell AXIOM to turn FORTRAN-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RAlso See: )set fortran
--R
--RSyntax:   )set output fortran <arg>
--R    where arg can be one of
--R  on          turn FORTRAN printing on
--R  off         turn FORTRAN printing off (default state)
--R  console     send FORTRAN output to screen (default state)
--R  fp<.fe>     send FORTRAN output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .sfort.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RFORTRAN output to the file polymer.sfort, issue the two commands
--R
--R  )set output fortran on
--R  )set output fortran polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 92

--S 93 of 143
)set output fortran foo
 
   FORTRAN output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/foo.sfort .
--I   FORTRAN output will be written to file /research/test/foo.sfort .
--E 93

--S 94 of 143
)set output fortran
 
--------------------------- The fortran Option ----------------------------

 Description: create output in FORTRAN format

 )set output fortran is used to tell AXIOM to turn FORTRAN-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Also See: )set fortran

Syntax:   )set output fortran <arg>
    where arg can be one of
  on          turn FORTRAN printing on
  off         turn FORTRAN printing off (default state)
  console     send FORTRAN output to screen (default state)
  fp<.fe>     send FORTRAN output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .sfort.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands

  )set output fortran on
  )set output fortran polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:/home/camm/debian/axiom/axiom-20091101/int/input/foo.sfort 
--R--------------------------- The fortran Option ----------------------------
--R
--R Description: create output in FORTRAN format
--R
--R )set output fortran is used to tell AXIOM to turn FORTRAN-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RAlso See: )set fortran
--R
--RSyntax:   )set output fortran <arg>
--R    where arg can be one of
--R  on          turn FORTRAN printing on
--R  off         turn FORTRAN printing off (default state)
--R  console     send FORTRAN output to screen (default state)
--R  fp<.fe>     send FORTRAN output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .sfort.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RFORTRAN output to the file polymer.sfort, issue the two commands
--R
--R  )set output fortran on
--R  )set output fortran polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  Off:/research/test/foo.sfort 
--E 94

--S 95 of 143
)set output fortran on
 
--E 95

--S 96 of 143
)set output fortran
 
--------------------------- The fortran Option ----------------------------

 Description: create output in FORTRAN format

 )set output fortran is used to tell AXIOM to turn FORTRAN-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Also See: )set fortran

Syntax:   )set output fortran <arg>
    where arg can be one of
  on          turn FORTRAN printing on
  off         turn FORTRAN printing off (default state)
  console     send FORTRAN output to screen (default state)
  fp<.fe>     send FORTRAN output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .sfort.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands

  )set output fortran on
  )set output fortran polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo.sfort 
--R--------------------------- The fortran Option ----------------------------
--R
--R Description: create output in FORTRAN format
--R
--R )set output fortran is used to tell AXIOM to turn FORTRAN-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RAlso See: )set fortran
--R
--RSyntax:   )set output fortran <arg>
--R    where arg can be one of
--R  on          turn FORTRAN printing on
--R  off         turn FORTRAN printing off (default state)
--R  console     send FORTRAN output to screen (default state)
--R  fp<.fe>     send FORTRAN output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .sfort.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RFORTRAN output to the file polymer.sfort, issue the two commands
--R
--R  )set output fortran on
--R  )set output fortran polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/foo.sfort 
--E 96

--S 97 of 143
)set output fortran append
 
   FORTRAN output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/NIL.sfort .
--I   FORTRAN output will be written to file /research/test/NIL.sfort .
--E 97

--S 98 of 143
)set output fortran
 
--------------------------- The fortran Option ----------------------------

 Description: create output in FORTRAN format

 )set output fortran is used to tell AXIOM to turn FORTRAN-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Also See: )set fortran

Syntax:   )set output fortran <arg>
    where arg can be one of
  on          turn FORTRAN printing on
  off         turn FORTRAN printing off (default state)
  console     send FORTRAN output to screen (default state)
  fp<.fe>     send FORTRAN output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .sfort.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands

  )set output fortran on
  )set output fortran polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/NIL.sfort 
--R--------------------------- The fortran Option ----------------------------
--R
--R Description: create output in FORTRAN format
--R
--R )set output fortran is used to tell AXIOM to turn FORTRAN-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RAlso See: )set fortran
--R
--RSyntax:   )set output fortran <arg>
--R    where arg can be one of
--R  on          turn FORTRAN printing on
--R  off         turn FORTRAN printing off (default state)
--R  console     send FORTRAN output to screen (default state)
--R  fp<.fe>     send FORTRAN output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .sfort.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RFORTRAN output to the file polymer.sfort, issue the two commands
--R
--R  )set output fortran on
--R  )set output fortran polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/NIL.sfort 
--E 98

--S 99 of 143
)set output fortran foo
 
   FORTRAN output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/foo.sfort .
--I   FORTRAN output will be written to file /research/test/foo.sfort .
--E 99

--S 100 of 143
)set output fortran
 
--------------------------- The fortran Option ----------------------------

 Description: create output in FORTRAN format

 )set output fortran is used to tell AXIOM to turn FORTRAN-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Also See: )set fortran

Syntax:   )set output fortran <arg>
    where arg can be one of
  on          turn FORTRAN printing on
  off         turn FORTRAN printing off (default state)
  console     send FORTRAN output to screen (default state)
  fp<.fe>     send FORTRAN output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .sfort.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands

  )set output fortran on
  )set output fortran polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo.sfort 
--R--------------------------- The fortran Option ----------------------------
--R
--R Description: create output in FORTRAN format
--R
--R )set output fortran is used to tell AXIOM to turn FORTRAN-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RAlso See: )set fortran
--R
--RSyntax:   )set output fortran <arg>
--R    where arg can be one of
--R  on          turn FORTRAN printing on
--R  off         turn FORTRAN printing off (default state)
--R  console     send FORTRAN output to screen (default state)
--R  fp<.fe>     send FORTRAN output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .sfort.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RFORTRAN output to the file polymer.sfort, issue the two commands
--R
--R  )set output fortran on
--R  )set output fortran polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/foo.sfort 
--E 100

--S 101 of 143
)set output algebra
 
--------------------------- The algebra Option ----------------------------

 Description: display output in algebraic form

 )set output algebra is used to tell AXIOM to turn algebra-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output algebra <arg>
    where arg can be one of
  on          turn algebra printing on (default state)
  off         turn algebra printing off
  console     send algebra output to screen (default state)
  fp<.fe>     send algebra output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .spout.

If you wish to send the output to a file, you may need to issue this command
twice: once with on and once with the file name. For example, to send
algebra output to the file polymer.spout, issue the two commands

  )set output algebra on
  )set output algebra polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R--------------------------- The algebra Option ----------------------------
--R
--R Description: display output in algebraic form
--R
--R )set output algebra is used to tell AXIOM to turn algebra-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output algebra <arg>
--R    where arg can be one of
--R  on          turn algebra printing on (default state)
--R  off         turn algebra printing off
--R  console     send algebra output to screen (default state)
--R  fp<.fe>     send algebra output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .spout.
--R
--RIf you wish to send the output to a file, you may need to issue this command
--Rtwice: once with on and once with the file name. For example, to send
--Ralgebra output to the file polymer.spout, issue the two commands
--R
--R  )set output algebra on
--R  )set output algebra polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 101

--S 102 of 143
)set output algebra foo
 
--E 102

--S 103 of 143
)set output algebra
 
--------------------------- The algebra Option ----------------------------

 Description: display output in algebraic form

 )set output algebra is used to tell AXIOM to turn algebra-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output algebra <arg>
    where arg can be one of
  on          turn algebra printing on (default state)
  off         turn algebra printing off
  console     send algebra output to screen (default state)
  fp<.fe>     send algebra output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .spout.

If you wish to send the output to a file, you may need to issue this command
twice: once with on and once with the file name. For example, to send
algebra output to the file polymer.spout, issue the two commands

  )set output algebra on
  )set output algebra polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo.spout 
--R--------------------------- The algebra Option ----------------------------
--R
--R Description: display output in algebraic form
--R
--R )set output algebra is used to tell AXIOM to turn algebra-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output algebra <arg>
--R    where arg can be one of
--R  on          turn algebra printing on (default state)
--R  off         turn algebra printing off
--R  console     send algebra output to screen (default state)
--R  fp<.fe>     send algebra output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .spout.
--R
--RIf you wish to send the output to a file, you may need to issue this command
--Rtwice: once with on and once with the file name. For example, to send
--Ralgebra output to the file polymer.spout, issue the two commands
--R
--R  )set output algebra on
--R  )set output algebra polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/tmp/foo.spout 
--E 103

--S 104 of 143
)set output algebra off
 
--E 104

--S 105 of 143
)set output algebra
 
--------------------------- The algebra Option ----------------------------

 Description: display output in algebraic form

 )set output algebra is used to tell AXIOM to turn algebra-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output algebra <arg>
    where arg can be one of
  on          turn algebra printing on (default state)
  off         turn algebra printing off
  console     send algebra output to screen (default state)
  fp<.fe>     send algebra output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .spout.

If you wish to send the output to a file, you may need to issue this command
twice: once with on and once with the file name. For example, to send
algebra output to the file polymer.spout, issue the two commands

  )set output algebra on
  )set output algebra polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:/home/camm/debian/axiom/axiom-20091101/int/input/foo.spout 
--R--------------------------- The algebra Option ----------------------------
--R
--R Description: display output in algebraic form
--R
--R )set output algebra is used to tell AXIOM to turn algebra-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output algebra <arg>
--R    where arg can be one of
--R  on          turn algebra printing on (default state)
--R  off         turn algebra printing off
--R  console     send algebra output to screen (default state)
--R  fp<.fe>     send algebra output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .spout.
--R
--RIf you wish to send the output to a file, you may need to issue this command
--Rtwice: once with on and once with the file name. For example, to send
--Ralgebra output to the file polymer.spout, issue the two commands
--R
--R  )set output algebra on
--R  )set output algebra polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  Off:/tmp/foo.spout 
--E 105

--S 106 of 143
)set output algebra console
 
--E 106

--S 107 of 143
)set output algebra
 
--------------------------- The algebra Option ----------------------------

 Description: display output in algebraic form

 )set output algebra is used to tell AXIOM to turn algebra-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output algebra <arg>
    where arg can be one of
  on          turn algebra printing on (default state)
  off         turn algebra printing off
  console     send algebra output to screen (default state)
  fp<.fe>     send algebra output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .spout.

If you wish to send the output to a file, you may need to issue this command
twice: once with on and once with the file name. For example, to send
algebra output to the file polymer.spout, issue the two commands

  )set output algebra on
  )set output algebra polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R--------------------------- The algebra Option ----------------------------
--R
--R Description: display output in algebraic form
--R
--R )set output algebra is used to tell AXIOM to turn algebra-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output algebra <arg>
--R    where arg can be one of
--R  on          turn algebra printing on (default state)
--R  off         turn algebra printing off
--R  console     send algebra output to screen (default state)
--R  fp<.fe>     send algebra output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .spout.
--R
--RIf you wish to send the output to a file, you may need to issue this command
--Rtwice: once with on and once with the file name. For example, to send
--Ralgebra output to the file polymer.spout, issue the two commands
--R
--R  )set output algebra on
--R  )set output algebra polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 107

--S 108 of 143
)set output algebra on
 
--E 108

--S 109 of 143
)set output algebra
 
--------------------------- The algebra Option ----------------------------

 Description: display output in algebraic form

 )set output algebra is used to tell AXIOM to turn algebra-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output algebra <arg>
    where arg can be one of
  on          turn algebra printing on (default state)
  off         turn algebra printing off
  console     send algebra output to screen (default state)
  fp<.fe>     send algebra output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .spout.

If you wish to send the output to a file, you may need to issue this command
twice: once with on and once with the file name. For example, to send
algebra output to the file polymer.spout, issue the two commands

  )set output algebra on
  )set output algebra polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R--------------------------- The algebra Option ----------------------------
--R
--R Description: display output in algebraic form
--R
--R )set output algebra is used to tell AXIOM to turn algebra-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output algebra <arg>
--R    where arg can be one of
--R  on          turn algebra printing on (default state)
--R  off         turn algebra printing off
--R  console     send algebra output to screen (default state)
--R  fp<.fe>     send algebra output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .spout.
--R
--RIf you wish to send the output to a file, you may need to issue this command
--Rtwice: once with on and once with the file name. For example, to send
--Ralgebra output to the file polymer.spout, issue the two commands
--R
--R  )set output algebra on
--R  )set output algebra polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 109

--S 110 of 143
)set output mathml
 
---------------------------- The mathml Option ----------------------------

 Description: create output in MathML style

 )set output mathml is used to tell AXIOM to turn MathML-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output mathml <arg>
    where arg can be one of
  on          turn MathML printing on
  off         turn MathML printing off (default state)
  console     send MathML output to screen (default state)
  fp<.fe>     send MathML output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
MathML output to the file polymer.smml, issue the two commands

  )set output mathml on
  )set output mathml polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R---------------------------- The mathml Option ----------------------------
--R
--R Description: create output in MathML style
--R
--R )set output mathml is used to tell AXIOM to turn MathML-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output mathml <arg>
--R    where arg can be one of
--R  on          turn MathML printing on
--R  off         turn MathML printing off (default state)
--R  console     send MathML output to screen (default state)
--R  fp<.fe>     send MathML output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RMathML output to the file polymer.smml, issue the two commands
--R
--R  )set output mathml on
--R  )set output mathml polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 110

--S 111 of 143
)set output mathml foo
 
   MathML output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/foo.smml .
--I   MathML output will be written to file /research/test/foo.smml .
--E 111

--S 112 of 143
)set output mathml
 
---------------------------- The mathml Option ----------------------------

 Description: create output in MathML style

 )set output mathml is used to tell AXIOM to turn MathML-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output mathml <arg>
    where arg can be one of
  on          turn MathML printing on
  off         turn MathML printing off (default state)
  console     send MathML output to screen (default state)
  fp<.fe>     send MathML output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
MathML output to the file polymer.smml, issue the two commands

  )set output mathml on
  )set output mathml polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:/home/camm/debian/axiom/axiom-20091101/int/input/foo.smml 
--R---------------------------- The mathml Option ----------------------------
--R
--R Description: create output in MathML style
--R
--R )set output mathml is used to tell AXIOM to turn MathML-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output mathml <arg>
--R    where arg can be one of
--R  on          turn MathML printing on
--R  off         turn MathML printing off (default state)
--R  console     send MathML output to screen (default state)
--R  fp<.fe>     send MathML output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RMathML output to the file polymer.smml, issue the two commands
--R
--R  )set output mathml on
--R  )set output mathml polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  Off:/research/test/foo.smml 
--E 112

--S 113 of 143
)set output mathml on
 
--E 113

--S 114 of 143
)set output mathml
 
---------------------------- The mathml Option ----------------------------

 Description: create output in MathML style

 )set output mathml is used to tell AXIOM to turn MathML-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output mathml <arg>
    where arg can be one of
  on          turn MathML printing on
  off         turn MathML printing off (default state)
  console     send MathML output to screen (default state)
  fp<.fe>     send MathML output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
MathML output to the file polymer.smml, issue the two commands

  )set output mathml on
  )set output mathml polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo.smml 
--R---------------------------- The mathml Option ----------------------------
--R
--R Description: create output in MathML style
--R
--R )set output mathml is used to tell AXIOM to turn MathML-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output mathml <arg>
--R    where arg can be one of
--R  on          turn MathML printing on
--R  off         turn MathML printing off (default state)
--R  console     send MathML output to screen (default state)
--R  fp<.fe>     send MathML output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RMathML output to the file polymer.smml, issue the two commands
--R
--R  )set output mathml on
--R  )set output mathml polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/foo.smml 
--E 114

--S 115 of 143
)set output mathml console
 
--E 115

--S 116 of 143
)set output mathml
 
---------------------------- The mathml Option ----------------------------

 Description: create output in MathML style

 )set output mathml is used to tell AXIOM to turn MathML-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output mathml <arg>
    where arg can be one of
  on          turn MathML printing on
  off         turn MathML printing off (default state)
  console     send MathML output to screen (default state)
  fp<.fe>     send MathML output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
MathML output to the file polymer.smml, issue the two commands

  )set output mathml on
  )set output mathml polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R---------------------------- The mathml Option ----------------------------
--R
--R Description: create output in MathML style
--R
--R )set output mathml is used to tell AXIOM to turn MathML-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output mathml <arg>
--R    where arg can be one of
--R  on          turn MathML printing on
--R  off         turn MathML printing off (default state)
--R  console     send MathML output to screen (default state)
--R  fp<.fe>     send MathML output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RMathML output to the file polymer.smml, issue the two commands
--R
--R  )set output mathml on
--R  )set output mathml polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 116

--S 117 of 143
)set output openmath
 
--------------------------- The openmath Option ---------------------------

 Description: create output in OpenMath style

 )set output openmath is used to tell AXIOM to turn OpenMath output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output openmath <arg>
    where arg can be one of
  on          turn OpenMath printing on
  off         turn OpenMath printing off (default state)
  console     send OpenMath output to screen (default state)
  fp<.fe>     send OpenMath output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .som.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
OpenMath output to the file polymer.som, issue the two commands

  )set output openmath on
  )set output openmath polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R--------------------------- The openmath Option ---------------------------
--R
--R Description: create output in OpenMath style
--R
--R )set output openmath is used to tell AXIOM to turn OpenMath output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output openmath <arg>
--R    where arg can be one of
--R  on          turn OpenMath printing on
--R  off         turn OpenMath printing off (default state)
--R  console     send OpenMath output to screen (default state)
--R  fp<.fe>     send OpenMath output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .som.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--ROpenMath output to the file polymer.som, issue the two commands
--R
--R  )set output openmath on
--R  )set output openmath polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 117

--S 118 of 143
)set output openmath on
 
--E 118

--S 119 of 143
)set output openmath
 
--------------------------- The openmath Option ---------------------------

 Description: create output in OpenMath style

 )set output openmath is used to tell AXIOM to turn OpenMath output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output openmath <arg>
    where arg can be one of
  on          turn OpenMath printing on
  off         turn OpenMath printing off (default state)
  console     send OpenMath output to screen (default state)
  fp<.fe>     send OpenMath output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .som.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
OpenMath output to the file polymer.som, issue the two commands

  )set output openmath on
  )set output openmath polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R--------------------------- The openmath Option ---------------------------
--R
--R Description: create output in OpenMath style
--R
--R )set output openmath is used to tell AXIOM to turn OpenMath output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output openmath <arg>
--R    where arg can be one of
--R  on          turn OpenMath printing on
--R  off         turn OpenMath printing off (default state)
--R  console     send OpenMath output to screen (default state)
--R  fp<.fe>     send OpenMath output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .som.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--ROpenMath output to the file polymer.som, issue the two commands
--R
--R  )set output openmath on
--R  )set output openmath polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 119

--S 120 of 143
)set output openmath foo
 
   OpenMath output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/foo.som .
--I   OpenMath output will be written to file /research/test/foo.som .
--E 120

--S 121 of 143
)set output openmath
 
--------------------------- The openmath Option ---------------------------

 Description: create output in OpenMath style

 )set output openmath is used to tell AXIOM to turn OpenMath output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output openmath <arg>
    where arg can be one of
  on          turn OpenMath printing on
  off         turn OpenMath printing off (default state)
  console     send OpenMath output to screen (default state)
  fp<.fe>     send OpenMath output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .som.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
OpenMath output to the file polymer.som, issue the two commands

  )set output openmath on
  )set output openmath polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo.som 
--R--------------------------- The openmath Option ---------------------------
--R
--R Description: create output in OpenMath style
--R
--R )set output openmath is used to tell AXIOM to turn OpenMath output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output openmath <arg>
--R    where arg can be one of
--R  on          turn OpenMath printing on
--R  off         turn OpenMath printing off (default state)
--R  console     send OpenMath output to screen (default state)
--R  fp<.fe>     send OpenMath output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .som.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--ROpenMath output to the file polymer.som, issue the two commands
--R
--R  )set output openmath on
--R  )set output openmath polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/foo.som 
--E 121

--S 122 of 143
)set output openmath off
 
--E 122

--S 123 of 143
)set output openmath
 
--------------------------- The openmath Option ---------------------------

 Description: create output in OpenMath style

 )set output openmath is used to tell AXIOM to turn OpenMath output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output openmath <arg>
    where arg can be one of
  on          turn OpenMath printing on
  off         turn OpenMath printing off (default state)
  console     send OpenMath output to screen (default state)
  fp<.fe>     send OpenMath output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .som.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
OpenMath output to the file polymer.som, issue the two commands

  )set output openmath on
  )set output openmath polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:/home/camm/debian/axiom/axiom-20091101/int/input/foo.som 
--R--------------------------- The openmath Option ---------------------------
--R
--R Description: create output in OpenMath style
--R
--R )set output openmath is used to tell AXIOM to turn OpenMath output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output openmath <arg>
--R    where arg can be one of
--R  on          turn OpenMath printing on
--R  off         turn OpenMath printing off (default state)
--R  console     send OpenMath output to screen (default state)
--R  fp<.fe>     send OpenMath output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .som.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--ROpenMath output to the file polymer.som, issue the two commands
--R
--R  )set output openmath on
--R  )set output openmath polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  Off:/research/test/foo.som 
--E 123

--S 124 of 143
)set output openmath console
 
--E 124

--S 125 of 143
)set output openmath
 
--------------------------- The openmath Option ---------------------------

 Description: create output in OpenMath style

 )set output openmath is used to tell AXIOM to turn OpenMath output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output openmath <arg>
    where arg can be one of
  on          turn OpenMath printing on
  off         turn OpenMath printing off (default state)
  console     send OpenMath output to screen (default state)
  fp<.fe>     send OpenMath output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .som.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
OpenMath output to the file polymer.som, issue the two commands

  )set output openmath on
  )set output openmath polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R--------------------------- The openmath Option ---------------------------
--R
--R Description: create output in OpenMath style
--R
--R )set output openmath is used to tell AXIOM to turn OpenMath output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output openmath <arg>
--R    where arg can be one of
--R  on          turn OpenMath printing on
--R  off         turn OpenMath printing off (default state)
--R  console     send OpenMath output to screen (default state)
--R  fp<.fe>     send OpenMath output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .som.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--ROpenMath output to the file polymer.som, issue the two commands
--R
--R  )set output openmath on
--R  )set output openmath polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 125

--S 126 of 143
)set output script
 
---------------------------- The script Option ----------------------------

 Description: display output in SCRIPT formula format

 )set output script is used to tell AXIOM to turn IBM Script formula-style
output printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output script <arg>
    where arg can be one of
  on          turn IBM Script formula printing on
  off         turn IBM Script formula printing off (default state)
  console     send IBM Script formula output to screen (default state)
  fp<.fe>     send IBM Script formula output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .sform.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands

  )set output script on
  )set output script polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R---------------------------- The script Option ----------------------------
--R
--R Description: display output in SCRIPT formula format
--R
--R )set output script is used to tell AXIOM to turn IBM Script formula-style
--Routput printing on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output script <arg>
--R    where arg can be one of
--R  on          turn IBM Script formula printing on
--R  off         turn IBM Script formula printing off (default state)
--R  console     send IBM Script formula output to screen (default state)
--R  fp<.fe>     send IBM Script formula output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .sform.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RIBM Script formula output to the file polymer.sform, issue the two commands
--R
--R  )set output script on
--R  )set output script polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 126

--S 127 of 143
)set output script on
 
--E 127

--S 128 of 143
)set output script
 
---------------------------- The script Option ----------------------------

 Description: display output in SCRIPT formula format

 )set output script is used to tell AXIOM to turn IBM Script formula-style
output printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output script <arg>
    where arg can be one of
  on          turn IBM Script formula printing on
  off         turn IBM Script formula printing off (default state)
  console     send IBM Script formula output to screen (default state)
  fp<.fe>     send IBM Script formula output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .sform.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands

  )set output script on
  )set output script polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R---------------------------- The script Option ----------------------------
--R
--R Description: display output in SCRIPT formula format
--R
--R )set output script is used to tell AXIOM to turn IBM Script formula-style
--Routput printing on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output script <arg>
--R    where arg can be one of
--R  on          turn IBM Script formula printing on
--R  off         turn IBM Script formula printing off (default state)
--R  console     send IBM Script formula output to screen (default state)
--R  fp<.fe>     send IBM Script formula output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .sform.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RIBM Script formula output to the file polymer.sform, issue the two commands
--R
--R  )set output script on
--R  )set output script polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 128

--S 129 of 143
)set output script foo
 
   IBM Script formula output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/foo .
--I   IBM Script formula output will be written to file 
--I      /research/test/foo.sform .
--E 129

--S 130 of 143
)set output script
 
---------------------------- The script Option ----------------------------

 Description: display output in SCRIPT formula format

 )set output script is used to tell AXIOM to turn IBM Script formula-style
output printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output script <arg>
    where arg can be one of
  on          turn IBM Script formula printing on
  off         turn IBM Script formula printing off (default state)
  console     send IBM Script formula output to screen (default state)
  fp<.fe>     send IBM Script formula output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .sform.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands

  )set output script on
  )set output script polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo 
--R---------------------------- The script Option ----------------------------
--R
--R Description: display output in SCRIPT formula format
--R
--R )set output script is used to tell AXIOM to turn IBM Script formula-style
--Routput printing on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output script <arg>
--R    where arg can be one of
--R  on          turn IBM Script formula printing on
--R  off         turn IBM Script formula printing off (default state)
--R  console     send IBM Script formula output to screen (default state)
--R  fp<.fe>     send IBM Script formula output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .sform.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RIBM Script formula output to the file polymer.sform, issue the two commands
--R
--R  )set output script on
--R  )set output script polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/foo.sform 
--E 130

--S 131 of 143
)set output script console
 
--E 131

--S 132 of 143
)set output script
 
---------------------------- The script Option ----------------------------

 Description: display output in SCRIPT formula format

 )set output script is used to tell AXIOM to turn IBM Script formula-style
output printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output script <arg>
    where arg can be one of
  on          turn IBM Script formula printing on
  off         turn IBM Script formula printing off (default state)
  console     send IBM Script formula output to screen (default state)
  fp<.fe>     send IBM Script formula output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .sform.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands

  )set output script on
  )set output script polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R---------------------------- The script Option ----------------------------
--R
--R Description: display output in SCRIPT formula format
--R
--R )set output script is used to tell AXIOM to turn IBM Script formula-style
--Routput printing on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output script <arg>
--R    where arg can be one of
--R  on          turn IBM Script formula printing on
--R  off         turn IBM Script formula printing off (default state)
--R  console     send IBM Script formula output to screen (default state)
--R  fp<.fe>     send IBM Script formula output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .sform.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RIBM Script formula output to the file polymer.sform, issue the two commands
--R
--R  )set output script on
--R  )set output script polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 132

--S 133 of 143
)set output script off
 
--E 133

--S 134 of 143
)set output script
 
---------------------------- The script Option ----------------------------

 Description: display output in SCRIPT formula format

 )set output script is used to tell AXIOM to turn IBM Script formula-style
output printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output script <arg>
    where arg can be one of
  on          turn IBM Script formula printing on
  off         turn IBM Script formula printing off (default state)
  console     send IBM Script formula output to screen (default state)
  fp<.fe>     send IBM Script formula output to file with file prefix fp
              and file extension .fe. If not given, .fe defaults to .sform.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands

  )set output script on
  )set output script polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R---------------------------- The script Option ----------------------------
--R
--R Description: display output in SCRIPT formula format
--R
--R )set output script is used to tell AXIOM to turn IBM Script formula-style
--Routput printing on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output script <arg>
--R    where arg can be one of
--R  on          turn IBM Script formula printing on
--R  off         turn IBM Script formula printing off (default state)
--R  console     send IBM Script formula output to screen (default state)
--R  fp<.fe>     send IBM Script formula output to file with file prefix fp
--R              and file extension .fe. If not given, .fe defaults to .sform.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RIBM Script formula output to the file polymer.sform, issue the two commands
--R
--R  )set output script on
--R  )set output script polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 134

--S 135 of 143
)set output tex
 
----------------------------- The tex Option ------------------------------

 Description: create output in TeX style

 )set output tex is used to tell AXIOM to turn TeX-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output tex <arg>
    where arg can be one of
  on          turn TeX printing on
  off         turn TeX printing off (default state)
  console     send TeX output to screen (default state)
  fp<.fe>     send TeX output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands

  )set output tex on
  )set output tex polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R----------------------------- The tex Option ------------------------------
--R
--R Description: create output in TeX style
--R
--R )set output tex is used to tell AXIOM to turn TeX-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output tex <arg>
--R    where arg can be one of
--R  on          turn TeX printing on
--R  off         turn TeX printing off (default state)
--R  console     send TeX output to screen (default state)
--R  fp<.fe>     send TeX output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RTeX output to the file polymer.stex, issue the two commands
--R
--R  )set output tex on
--R  )set output tex polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 135

--S 136 of 143
)set output tex on
 
--E 136

--S 137 of 143
)set output tex
 
----------------------------- The tex Option ------------------------------

 Description: create output in TeX style

 )set output tex is used to tell AXIOM to turn TeX-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output tex <arg>
    where arg can be one of
  on          turn TeX printing on
  off         turn TeX printing off (default state)
  console     send TeX output to screen (default state)
  fp<.fe>     send TeX output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands

  )set output tex on
  )set output tex polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:CONSOLE 
--R----------------------------- The tex Option ------------------------------
--R
--R Description: create output in TeX style
--R
--R )set output tex is used to tell AXIOM to turn TeX-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output tex <arg>
--R    where arg can be one of
--R  on          turn TeX printing on
--R  off         turn TeX printing off (default state)
--R  console     send TeX output to screen (default state)
--R  fp<.fe>     send TeX output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RTeX output to the file polymer.stex, issue the two commands
--R
--R  )set output tex on
--R  )set output tex polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  On:CONSOLE 
--E 137

--S 138 of 143
)set output tex foo
 
   TeX output will be written to file 
      /home/camm/debian/axiom/axiom-20091101/int/input/foo.stex .
--I   TeX output will be written to file /research/test/foo.stex .
--E 138

--S 139 of 143
)set output tex
 
----------------------------- The tex Option ------------------------------

 Description: create output in TeX style

 )set output tex is used to tell AXIOM to turn TeX-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output tex <arg>
    where arg can be one of
  on          turn TeX printing on
  off         turn TeX printing off (default state)
  console     send TeX output to screen (default state)
  fp<.fe>     send TeX output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands

  )set output tex on
  )set output tex polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  On:/home/camm/debian/axiom/axiom-20091101/int/input/foo.stex 
--R----------------------------- The tex Option ------------------------------
--R
--R Description: create output in TeX style
--R
--R )set output tex is used to tell AXIOM to turn TeX-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output tex <arg>
--R    where arg can be one of
--R  on          turn TeX printing on
--R  off         turn TeX printing off (default state)
--R  console     send TeX output to screen (default state)
--R  fp<.fe>     send TeX output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RTeX output to the file polymer.stex, issue the two commands
--R
--R  )set output tex on
--R  )set output tex polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  On:/research/test/foo.stex 
--E 139

--S 140 of 143
)set output tex off
 
--E 140

--S 141 of 143
)set output tex
 
----------------------------- The tex Option ------------------------------

 Description: create output in TeX style

 )set output tex is used to tell AXIOM to turn TeX-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output tex <arg>
    where arg can be one of
  on          turn TeX printing on
  off         turn TeX printing off (default state)
  console     send TeX output to screen (default state)
  fp<.fe>     send TeX output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands

  )set output tex on
  )set output tex polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:/home/camm/debian/axiom/axiom-20091101/int/input/foo.stex 
--R----------------------------- The tex Option ------------------------------
--R
--R Description: create output in TeX style
--R
--R )set output tex is used to tell AXIOM to turn TeX-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output tex <arg>
--R    where arg can be one of
--R  on          turn TeX printing on
--R  off         turn TeX printing off (default state)
--R  console     send TeX output to screen (default state)
--R  fp<.fe>     send TeX output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RTeX output to the file polymer.stex, issue the two commands
--R
--R  )set output tex on
--R  )set output tex polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--IThe current setting is:  Off:/research/test/foo.stex 
--E 141

--S 142 of 143
)set output tex console
 
--E 142

--S 143 of 143
)set output tex
 
----------------------------- The tex Option ------------------------------

 Description: create output in TeX style

 )set output tex is used to tell AXIOM to turn TeX-style output
printing on and off, and where to place the output.  By default, the
destination for the output is the screen but printing is turned off.

Syntax:   )set output tex <arg>
    where arg can be one of
  on          turn TeX printing on
  off         turn TeX printing off (default state)
  console     send TeX output to screen (default state)
  fp<.fe>     send TeX output to file with file prefix fp and file
              extension .fe. If not given, .fe defaults to .stex.

If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands

  )set output tex on
  )set output tex polymer

The output is placed in the directory from which you invoked AXIOM or
the one you set with the )cd system command.
The current setting is:  Off:CONSOLE 
--R----------------------------- The tex Option ------------------------------
--R
--R Description: create output in TeX style
--R
--R )set output tex is used to tell AXIOM to turn TeX-style output
--Rprinting on and off, and where to place the output.  By default, the
--Rdestination for the output is the screen but printing is turned off.
--R
--RSyntax:   )set output tex <arg>
--R    where arg can be one of
--R  on          turn TeX printing on
--R  off         turn TeX printing off (default state)
--R  console     send TeX output to screen (default state)
--R  fp<.fe>     send TeX output to file with file prefix fp and file
--R              extension .fe. If not given, .fe defaults to .stex.
--R
--RIf you wish to send the output to a file, you must issue this command
--Rtwice: once with on and once with the file name. For example, to send
--RTeX output to the file polymer.stex, issue the two commands
--R
--R  )set output tex on
--R  )set output tex polymer
--R
--RThe output is placed in the directory from which you invoked AXIOM or
--Rthe one you set with the )cd system command.
--RThe current setting is:  Off:CONSOLE 
--E 143

)spool 
 
Starts dribbling to distexpr.output (2010/3/27, 18:24:57).
)set message test on
 
)set message auto off
 
)clear all
 
)sys cp $AXIOM/../../src/input/distexpr.input.pamphlet .
 
)lisp (tangle "distexpr.input.pamphlet" "distexpr.spad" "distexpr.spad")
 
Value = NIL
)co distexpr
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/distexpr.spad 
      using old system compiler.
   DEXPR abbreviates domain DistributedExpression 
   processing macro definition EXPRR ==> Expression R 
   processing macro definition AN ==> AlgebraicNumber 
   processing macro definition SUP ==> SparseUnivariatePolynomial 
------------------------------------------------------------------------
   initializing nrlib DEXPR for DistributedExpression 
   compiling into nrlib DEXPR 
****** Domain: R already in scope
   compiling local out : (Polynomial R,List $,List $) -> OutputForm
Time: 0.12 SEC.

   compiling exported coerce : $ -> OutputForm
****** Domain: R already in scope
augmenting R: (IntegralDomain . NIL)
augmenting $: (SIGNATURE $ reduce ($ $ . NIL) . NIL)
augmenting $: (SIGNATURE $ number? ((Boolean . NIL) $ . NIL) . NIL)
augmenting $: (SIGNATURE $ simplifyPower ($ $ (Integer . NIL) . NIL) . NIL)
Time: 0.20 SEC.

   compiling exported coerce : Expression R -> $
      DEXPR;coerce;E$;3 is replaced by p 
Time: 0 SEC.

****** Domain: R already in scope
augmenting R: (GcdDomain . NIL)
****** Domain: R already in scope
augmenting R: (IntegralDomain . NIL)
augmenting $: (SIGNATURE $ reduce ($ $ . NIL) . NIL)
augmenting $: (SIGNATURE $ number? ((Boolean . NIL) $ . NIL) . NIL)
augmenting $: (SIGNATURE $ simplifyPower ($ $ (Integer . NIL) . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (RetractableTo (Integer . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (LinearlyExplicitRingOver (Integer . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (IntegralDomain . NIL)
augmenting $: (SIGNATURE $ reduce ($ $ . NIL) . NIL)
augmenting $: (SIGNATURE $ number? ((Boolean . NIL) $ . NIL) . NIL)
augmenting $: (SIGNATURE $ simplifyPower ($ $ (Integer . NIL) . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (RetractableTo (Integer . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (LinearlyExplicitRingOver (Integer . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (Group . NIL)
****** Domain: R already in scope
augmenting R: (IntegralDomain . NIL)
augmenting $: (SIGNATURE $ reduce ($ $ . NIL) . NIL)
augmenting $: (SIGNATURE $ number? ((Boolean . NIL) $ . NIL) . NIL)
augmenting $: (SIGNATURE $ simplifyPower ($ $ (Integer . NIL) . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (RetractableTo (Integer . NIL) . NIL)
****** Domain: $ already in scope
augmenting $: (RetractableTo (Integer . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (CharacteristicNonZero . NIL)
****** Domain: R already in scope
augmenting R: (CommutativeRing . NIL)
****** Domain: R already in scope
augmenting R: (ConvertibleTo (InputForm . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (ConvertibleTo (Pattern (Float . NIL) . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (ConvertibleTo (Pattern (Integer . NIL) . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (Group . NIL)
****** Domain: R already in scope
augmenting R: (IntegralDomain . NIL)
augmenting $: (SIGNATURE $ reduce ($ $ . NIL) . NIL)
augmenting $: (SIGNATURE $ number? ((Boolean . NIL) $ . NIL) . NIL)
augmenting $: (SIGNATURE $ simplifyPower ($ $ (Integer . NIL) . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (PatternMatchable (Float . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (PatternMatchable (Integer . NIL) . NIL)
****** Domain: R already in scope
augmenting R: (RetractableTo (Integer . NIL) . NIL)
(time taken in buildFunctor:  89 . NIL)

;;;     ***       |DistributedExpression| REDEFINED

;;;     ***       |DistributedExpression| REDEFINED
Time: 1.47 SEC.

 
   Warnings: 
      [1] not known that (Ring) is of mode (CATEGORY domain (SIGNATURE simplifyPower ($ $ (Integer))))
      [2] not known that (OrderedSet) is of mode (CATEGORY domain (SIGNATURE simplifyPower ($ $ (Integer))))
      [3] not known that (IntegralDomain) is of mode (CATEGORY domain (SIGNATURE simplifyPower ($ $ (Integer))))
 

   Cumulative Statistics for Constructor DistributedExpression
      Time: 1.79 seconds
 
   finalizing nrlib DEXPR 
   Processing DistributedExpression for Browser database:
--------(reduce (% %))---------
--------(number? ((Boolean) %))---------
--------(simplifyPower (% % (Integer)))---------
--------(factorPolynomial ((Factored (SUP %)) (SUP %)))---------
--------(squareFreePolynomial ((Factored (SUP %)) (SUP %)))---------
--->-->DistributedExpression((coerce (% EXPRR))): Not documented!!!!
--->-->DistributedExpression(constructor): Not documented!!!!
--->-->DistributedExpression(): Missing Description
------------------------------------------------------------------------
   DistributedExpression is now explicitly exposed in frame initial 
   DistributedExpression will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/DEXPR.nrlib/code

 
--S 1 of 6
ex1:=(2*log(x)+3*exp(y))*(4*sin(z)+2*log(x))
 

                       y                 2      y
   (1)  (8log(x) + 12%e )sin(z) + 4log(x)  + 6%e log(x)
                                                     Type: Expression Integer
--R 
--R
--R                       y                 2      y
--R   (1)  (8log(x) + 12%e )sin(z) + 4log(x)  + 6%e log(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 6
ex2:=8*log(x)*sin(z)+4*log(x)^2+12*exp(y)*sin(z)+6*exp(y)*log(x)
 

                       y                 2      y
   (2)  (8log(x) + 12%e )sin(z) + 4log(x)  + 6%e log(x)
                                                     Type: Expression Integer
--R 
--R
--R                       y                 2      y
--R   (2)  (8log(x) + 12%e )sin(z) + 4log(x)  + 6%e log(x)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 6
subst(ex1, kernels ex1, [x1,x2,x3])::DMP([x1,x2,x3],INT)
 

                              2
   (3)  8x1 x2 + 12x1 x3 + 4x2  + 6x2 x3
                  Type: DistributedMultivariatePolynomial([x1,x2,x3],Integer)
--R 
--R
--R                              2
--R   (3)  8x1 x2 + 12x1 x3 + 4x2  + 6x2 x3
--R                  Type: DistributedMultivariatePolynomial([x1,x2,x3],Integer)
--E 3

--S 4 of 6
ex1::DistributedExpression(Integer)
 

           y             y                2
   (4)  6%e log(x) + 12%e sin(z) + 4log(x)  + 8log(x)sin(z)
                                          Type: DistributedExpression Integer
--R 
--R
--R           y             y                2
--R   (4)  6%e log(x) + 12%e sin(z) + 4log(x)  + 8log(x)sin(z)
--R                                          Type: DistributedExpression Integer
--E 4

--S 5 of 6
((1+2*a+3*b)*(4*c+5*d))::DEXPR INT
 

   (5)  8a c + 10a d + 12b c + 15b d + 4c + 5d
                                          Type: DistributedExpression Integer
--R 
--R
--R   (5)  8a c + 10a d + 12b c + 15b d + 4c + 5d
--R                                          Type: DistributedExpression Integer
--E 5

--S 6 of 6
((1+2*a+3*b)*(4*c+5*d))::POLY INT
 

   (6)  (15b + 10a + 5)d + (12b + 8a + 4)c
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  (15b + 10a + 5)d + (12b + 8a + 4)c
--R                                                     Type: Polynomial Integer
--E 6

)spool 
 
Starts dribbling to heap.output (2010/3/27, 18:26:47).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 8
h := heap [-4,9,11,2,7,-7]
 

   (1)  [11,7,9,- 4,2,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (1)  [11,7,9,- 4,2,- 7]
--R                                                           Type: Heap Integer
--E 1

--S 2 of 8
insert!(3,h)
 

   (2)  [11,7,9,- 4,2,- 7,3]
                                                           Type: Heap Integer
--R 
--R
--R   (2)  [11,7,9,- 4,2,- 7,3]
--R                                                           Type: Heap Integer
--E 2

--S 3 of 8
extract! h
 

   (3)  11
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  11
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 8
h
 

   (4)  [9,7,3,- 4,2,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (4)  [9,7,3,- 4,2,- 7]
--R                                                           Type: Heap Integer
--E 4

--S 5 of 8
[extract!(h) while not empty?(h)]
 

   (5)  [9,7,3,2,- 4,- 7]
                                                           Type: List Integer
--R 
--R
--R   (5)  [9,7,3,2,- 4,- 7]
--R                                                           Type: List Integer
--E 5

--S 6 of 8
heapsort(x) == (empty? x => []; cons(extract!(x),heapsort x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 8
h1 := heap [17,-4,9,-11,2,7,-7]
 

   (7)  [17,2,9,- 11,- 4,7,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (7)  [17,2,9,- 11,- 4,7,- 7]
--R                                                           Type: Heap Integer
--E 7

--S 8 of 8
heapsort h1
 
   Compiling function heapsort with type Heap Integer -> List Integer 

   (8)  [17,9,7,2,- 4,- 7,- 11]
                                                           Type: List Integer
--R 
--R   Compiling function heapsort with type Heap Integer -> List Integer 
--R
--R   (8)  [17,9,7,2,- 4,- 7,- 11]
--R                                                           Type: List Integer
--E 8
)spool 
 
Starts dribbling to GroebnerPackage.output (2010/3/27, 18:42:8).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 24
s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
 

   (1)  45p + 35s - 165b - 36
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (1)  45p + 35s - 165b - 36
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 1

--S 2 of 24
s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
 

   (2)  35p + 40z + 25t - 27s
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (2)  35p + 40z + 25t - 27s
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 2

--S 3 of 24
s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
 

                                      2
   (3)  15w + 25p s + 30z - 18t - 165b
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R                                      2
--R   (3)  15w + 25p s + 30z - 18t - 165b
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 3

--S 4 of 24
s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
 

   (4)  - 9w + 15p t + 20z s
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (4)  - 9w + 15p t + 20z s
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 4

--S 5 of 24
s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
 

                        3
   (5)  w p + 2z t - 11b
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R                        3
--R   (5)  w p + 2z t - 11b
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 5

--S 6 of 24
s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
 

                        2
   (6)  99w - 11s b + 3b
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R                        2
--R   (6)  99w - 11s b + 3b
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 6

--S 7 of 24
s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
 

         2   33      2673
   (7)  b  + -- b + -----
             50     10000
      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R         2   33      2673
--R   (7)  b  + -- b + -----
--R             50     10000
--R      Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 7

--S 8 of 24
sn7:=[s1,s2,s3,s4,s5,s6,s7]
 

   (8)
   [45p + 35s - 165b - 36, 35p + 40z + 25t - 27s,
                                  2                                        3
    15w + 25p s + 30z - 18t - 165b , - 9w + 15p t + 20z s, w p + 2z t - 11b ,
                    2   2   33      2673
    99w - 11s b + 3b , b  + -- b + -----]
                            50     10000
 Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (8)
--R   [45p + 35s - 165b - 36, 35p + 40z + 25t - 27s,
--R                                  2                                        3
--R    15w + 25p s + 30z - 18t - 165b , - 9w + 15p t + 20z s, w p + 2z t - 11b ,
--R                    2   2   33      2673
--R    99w - 11s b + 3b , b  + -- b + -----]
--R                            50     10000
--R Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 8

--S 9 of 24
groebner(sn7)
 

   (9)
         19      1323      31     153      49     1143      37      27
   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
        120     20000      18     200      36     2000      15     250
        5      9    2   33      2673
    s - - b - ---, b  + -- b + -----]
        2     200       50     10000
 Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (9)
--R         19      1323      31     153      49     1143      37      27
--R   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
--R        120     20000      18     200      36     2000      15     250
--R        5      9    2   33      2673
--R    s - - b - ---, b  + -- b + -----]
--R        2     200       50     10000
--R Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 9

--S 10 of 24
groebner(sn7,"redcrit")
 


    reduced Critpair - Polynom :


       5     61     77      7
   z + - t - -- s + -- b + --
       8     45     24     10




    reduced Critpair - Polynom :


         66        603     278  2   11       672     2277     415881
   t s - -- t b + ---- t - --- s  + -- s b - --- s - ---- b - ------
         29       1450     435      29       725     7250     725000




    reduced Critpair - Polynom :


       100  2   160       104      37      79
   t + --- s  - --- s b - --- s - --- b - ---
       189       63        63     105     125




    reduced Critpair - Polynom :


    3   1026  2    5424  2   2529       1326807     12717      660717
   s  - ---- s b - ---- s  - ---- s b - ------- s + ----- b + -------
         145       3625       725        362500      6250     3625000




    reduced Critpair - Polynom :


      2     91248294  2   6550614        7087292937     20020838931
     s b + --------- s  - ------- s b + ----------- s - ----------- b
           128176525      5127061       12817652500     12817652500
   + 
       37595502243
     - -----------
       51270610000




    reduced Critpair - Polynom :


      2   4746183626079988       1015195815329760     30723564870033201
     s  - ---------------- s b - ---------------- s - ----------------- b
           987357073521193        987357073521193     24683926838029825
   + 
       3696123458901625353
     - -------------------
       2468392683802982500




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


           16827373608076633182513471     1262793163581645698534964
     s b + -------------------------- s - ------------------------- b
           23063714246644859914108300     5765928561661214978527075
   + 
      91594345205981119652436033
     ---------------------------
     144148214041530374463176875




    reduced Critpair - Polynom :


       5      9
   s - - b - ---
       2     200




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0


       THE GROEBNER BASIS POLYNOMIALS

   (10)
         19      1323      31     153      49     1143      37      27
   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
        120     20000      18     200      36     2000      15     250
        5      9    2   33      2673
    s - - b - ---, b  + -- b + -----]
        2     200       50     10000
 Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5     61     77      7
--R   z + - t - -- s + -- b + --
--R       8     45     24     10
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         66        603     278  2   11       672     2277     415881
--R   t s - -- t b + ---- t - --- s  + -- s b - --- s - ---- b - ------
--R         29       1450     435      29       725     7250     725000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       100  2   160       104      37      79
--R   t + --- s  - --- s b - --- s - --- b - ---
--R       189       63        63     105     125
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R    3   1026  2    5424  2   2529       1326807     12717      660717
--R   s  - ---- s b - ---- s  - ---- s b - ------- s + ----- b + -------
--R         145       3625       725        362500      6250     3625000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R      2     91248294  2   6550614        7087292937     20020838931
--R     s b + --------- s  - ------- s b + ----------- s - ----------- b
--R           128176525      5127061       12817652500     12817652500
--R   + 
--R       37595502243
--R     - -----------
--R       51270610000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R      2   4746183626079988       1015195815329760     30723564870033201
--R     s  - ---------------- s b - ---------------- s - ----------------- b
--R           987357073521193        987357073521193     24683926838029825
--R   + 
--R       3696123458901625353
--R     - -------------------
--R       2468392683802982500
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R           16827373608076633182513471     1262793163581645698534964
--R     s b + -------------------------- s - ------------------------- b
--R           23063714246644859914108300     5765928561661214978527075
--R   + 
--R      91594345205981119652436033
--R     ---------------------------
--R     144148214041530374463176875
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5      9
--R   s - - b - ---
--R       2     200
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R       THE GROEBNER BASIS POLYNOMIALS
--R
--R   (10)
--R         19      1323      31     153      49     1143      37      27
--R   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
--R        120     20000      18     200      36     2000      15     250
--R        5      9    2   33      2673
--R    s - - b - ---, b  + -- b + -----]
--R        2     200       50     10000
--R Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 10

--S 11 of 24
groebner(sn7,"info")
 

   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 3]]


   [[ci= w,tci= 3,cj= w,tcj= 5,c= p t,tc= 6,rc= t s,trc= 8,tF= 5,tD= 2]]


   [[ci= w,tci= 3,cj= w,tcj= 3,c= p t,tc= 4,rc= t,trc= 6,tF= 5,tD= 2]]


                                                   3
   [[ci= t s,tci= 8,cj= t,tcj= 6,c= t b,tc= 9,rc= s ,trc= 7,tF= 6,tD= 1]]


                                                     2
   [[ci= w p,tci= 3,cj= w,tcj= 3,c= p s b,tc= 4,rc= s b,trc= 6,tF= 7,tD= 2]]


          2             2             2             2
   [[ci= b ,tci= 3,cj= s b,tcj= 6,c= s b,tc= 6,rc= s ,trc= 5,tF= 6,tD= 2]]


          2              2            2
   [[ci= s b,tci= 6,cj= s ,tcj= 5,c= s ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 1]]


          3             2            2
   [[ci= s ,tci= 7,cj= s ,tcj= 5,c= s b,tc= 6,rc= s b,trc= 4,tF= 7,tD= 2]]


          2
   [[ci= b ,tci= 3,cj= s b,tcj= 4,c= s b,tc= 4,rc= s,trc= 3,tF= 6,tD= 2]]


   [[ci= s b,tci= 4,cj= s,tcj= 3,c= s,tc= 4,rc= 0,trc= 0,tF= 6,tD= 1]]


          2
   [[ci= s ,tci= 5,cj= s,tcj= 3,c= s b,tc= 4,rc= 0,trc= 0,tF= 6,tD= 0]]


     There are

   6

     Groebner Basis Polynomials.


       THE GROEBNER BASIS POLYNOMIALS

   (11)
         19      1323      31     153      49     1143      37      27
   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
        120     20000      18     200      36     2000      15     250
        5      9    2   33      2673
    s - - b - ---, b  + -- b + -----]
        2     200       50     10000
 Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 3]]
--R
--R
--R   [[ci= w,tci= 3,cj= w,tcj= 5,c= p t,tc= 6,rc= t s,trc= 8,tF= 5,tD= 2]]
--R
--R
--R   [[ci= w,tci= 3,cj= w,tcj= 3,c= p t,tc= 4,rc= t,trc= 6,tF= 5,tD= 2]]
--R
--R
--R                                                   3
--R   [[ci= t s,tci= 8,cj= t,tcj= 6,c= t b,tc= 9,rc= s ,trc= 7,tF= 6,tD= 1]]
--R
--R
--R                                                     2
--R   [[ci= w p,tci= 3,cj= w,tcj= 3,c= p s b,tc= 4,rc= s b,trc= 6,tF= 7,tD= 2]]
--R
--R
--R          2             2             2             2
--R   [[ci= b ,tci= 3,cj= s b,tcj= 6,c= s b,tc= 6,rc= s ,trc= 5,tF= 6,tD= 2]]
--R
--R
--R          2              2            2
--R   [[ci= s b,tci= 6,cj= s ,tcj= 5,c= s ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 1]]
--R
--R
--R          3             2            2
--R   [[ci= s ,tci= 7,cj= s ,tcj= 5,c= s b,tc= 6,rc= s b,trc= 4,tF= 7,tD= 2]]
--R
--R
--R          2
--R   [[ci= b ,tci= 3,cj= s b,tcj= 4,c= s b,tc= 4,rc= s,trc= 3,tF= 6,tD= 2]]
--R
--R
--R   [[ci= s b,tci= 4,cj= s,tcj= 3,c= s,tc= 4,rc= 0,trc= 0,tF= 6,tD= 1]]
--R
--R
--R          2
--R   [[ci= s ,tci= 5,cj= s,tcj= 3,c= s b,tc= 4,rc= 0,trc= 0,tF= 6,tD= 0]]
--R
--R
--R     There are
--R
--R   6
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS POLYNOMIALS
--R
--R   (11)
--R         19      1323      31     153      49     1143      37      27
--R   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
--R        120     20000      18     200      36     2000      15     250
--R        5      9    2   33      2673
--R    s - - b - ---, b  + -- b + -----]
--R        2     200       50     10000
--R Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 11

--S 12 of 24
groebner(sn7,"redcrit","info")
 


    reduced Critpair - Polynom :


       5     61     77      7
   z + - t - -- s + -- b + --
       8     45     24     10



   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 3]]



    reduced Critpair - Polynom :


         66        603     278  2   11       672     2277     415881
   t s - -- t b + ---- t - --- s  + -- s b - --- s - ---- b - ------
         29       1450     435      29       725     7250     725000



   [[ci= w,tci= 3,cj= w,tcj= 5,c= p t,tc= 6,rc= t s,trc= 8,tF= 5,tD= 2]]



    reduced Critpair - Polynom :


       100  2   160       104      37      79
   t + --- s  - --- s b - --- s - --- b - ---
       189       63        63     105     125



   [[ci= w,tci= 3,cj= w,tcj= 3,c= p t,tc= 4,rc= t,trc= 6,tF= 5,tD= 2]]



    reduced Critpair - Polynom :


    3   1026  2    5424  2   2529       1326807     12717      660717
   s  - ---- s b - ---- s  - ---- s b - ------- s + ----- b + -------
         145       3625       725        362500      6250     3625000



                                                   3
   [[ci= t s,tci= 8,cj= t,tcj= 6,c= t b,tc= 9,rc= s ,trc= 7,tF= 6,tD= 1]]



    reduced Critpair - Polynom :


      2     91248294  2   6550614        7087292937     20020838931
     s b + --------- s  - ------- s b + ----------- s - ----------- b
           128176525      5127061       12817652500     12817652500
   + 
       37595502243
     - -----------
       51270610000



                                                     2
   [[ci= w p,tci= 3,cj= w,tcj= 3,c= p s b,tc= 4,rc= s b,trc= 6,tF= 7,tD= 2]]



    reduced Critpair - Polynom :


      2   4746183626079988       1015195815329760     30723564870033201
     s  - ---------------- s b - ---------------- s - ----------------- b
           987357073521193        987357073521193     24683926838029825
   + 
       3696123458901625353
     - -------------------
       2468392683802982500



          2             2             2             2
   [[ci= b ,tci= 3,cj= s b,tcj= 6,c= s b,tc= 6,rc= s ,trc= 5,tF= 6,tD= 2]]



    reduced Critpair - Polynom :


   0



          2              2            2
   [[ci= s b,tci= 6,cj= s ,tcj= 5,c= s ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 1]]



    reduced Critpair - Polynom :


           16827373608076633182513471     1262793163581645698534964
     s b + -------------------------- s - ------------------------- b
           23063714246644859914108300     5765928561661214978527075
   + 
      91594345205981119652436033
     ---------------------------
     144148214041530374463176875



          3             2            2
   [[ci= s ,tci= 7,cj= s ,tcj= 5,c= s b,tc= 6,rc= s b,trc= 4,tF= 7,tD= 2]]



    reduced Critpair - Polynom :


       5      9
   s - - b - ---
       2     200



          2
   [[ci= b ,tci= 3,cj= s b,tcj= 4,c= s b,tc= 4,rc= s,trc= 3,tF= 6,tD= 2]]



    reduced Critpair - Polynom :


   0



   [[ci= s b,tci= 4,cj= s,tcj= 3,c= s,tc= 4,rc= 0,trc= 0,tF= 6,tD= 1]]



    reduced Critpair - Polynom :


   0



          2
   [[ci= s ,tci= 5,cj= s,tcj= 3,c= s b,tc= 4,rc= 0,trc= 0,tF= 6,tD= 0]]


     There are

   6

     Groebner Basis Polynomials.


       THE GROEBNER BASIS POLYNOMIALS

   (12)
         19      1323      31     153      49     1143      37      27
   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
        120     20000      18     200      36     2000      15     250
        5      9    2   33      2673
    s - - b - ---, b  + -- b + -----]
        2     200       50     10000
 Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5     61     77      7
--R   z + - t - -- s + -- b + --
--R       8     45     24     10
--R
--R
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         66        603     278  2   11       672     2277     415881
--R   t s - -- t b + ---- t - --- s  + -- s b - --- s - ---- b - ------
--R         29       1450     435      29       725     7250     725000
--R
--R
--R
--R   [[ci= w,tci= 3,cj= w,tcj= 5,c= p t,tc= 6,rc= t s,trc= 8,tF= 5,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       100  2   160       104      37      79
--R   t + --- s  - --- s b - --- s - --- b - ---
--R       189       63        63     105     125
--R
--R
--R
--R   [[ci= w,tci= 3,cj= w,tcj= 3,c= p t,tc= 4,rc= t,trc= 6,tF= 5,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R    3   1026  2    5424  2   2529       1326807     12717      660717
--R   s  - ---- s b - ---- s  - ---- s b - ------- s + ----- b + -------
--R         145       3625       725        362500      6250     3625000
--R
--R
--R
--R                                                   3
--R   [[ci= t s,tci= 8,cj= t,tcj= 6,c= t b,tc= 9,rc= s ,trc= 7,tF= 6,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R      2     91248294  2   6550614        7087292937     20020838931
--R     s b + --------- s  - ------- s b + ----------- s - ----------- b
--R           128176525      5127061       12817652500     12817652500
--R   + 
--R       37595502243
--R     - -----------
--R       51270610000
--R
--R
--R
--R                                                     2
--R   [[ci= w p,tci= 3,cj= w,tcj= 3,c= p s b,tc= 4,rc= s b,trc= 6,tF= 7,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R      2   4746183626079988       1015195815329760     30723564870033201
--R     s  - ---------------- s b - ---------------- s - ----------------- b
--R           987357073521193        987357073521193     24683926838029825
--R   + 
--R       3696123458901625353
--R     - -------------------
--R       2468392683802982500
--R
--R
--R
--R          2             2             2             2
--R   [[ci= b ,tci= 3,cj= s b,tcj= 6,c= s b,tc= 6,rc= s ,trc= 5,tF= 6,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          2              2            2
--R   [[ci= s b,tci= 6,cj= s ,tcj= 5,c= s ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R           16827373608076633182513471     1262793163581645698534964
--R     s b + -------------------------- s - ------------------------- b
--R           23063714246644859914108300     5765928561661214978527075
--R   + 
--R      91594345205981119652436033
--R     ---------------------------
--R     144148214041530374463176875
--R
--R
--R
--R          3             2            2
--R   [[ci= s ,tci= 7,cj= s ,tcj= 5,c= s b,tc= 6,rc= s b,trc= 4,tF= 7,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5      9
--R   s - - b - ---
--R       2     200
--R
--R
--R
--R          2
--R   [[ci= b ,tci= 3,cj= s b,tcj= 4,c= s b,tc= 4,rc= s,trc= 3,tF= 6,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R   [[ci= s b,tci= 4,cj= s,tcj= 3,c= s,tc= 4,rc= 0,trc= 0,tF= 6,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          2
--R   [[ci= s ,tci= 5,cj= s,tcj= 3,c= s b,tc= 4,rc= 0,trc= 0,tF= 6,tD= 0]]
--R
--R
--R     There are
--R
--R   6
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS POLYNOMIALS
--R
--R   (12)
--R         19      1323      31     153      49     1143      37      27
--R   [w + --- b + -----, p - -- b - ---, z + -- b + ----, t - -- b + ---,
--R        120     20000      18     200      36     2000      15     250
--R        5      9    2   33      2673
--R    s - - b - ---, b  + -- b + -----]
--R        2     200       50     10000
--R Type: List DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 12

--S 13 of 24
hs1:HDMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
 

   (13)  45p + 35s - 165b - 36
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (13)  45p + 35s - 165b - 36
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 13

--S 14 of 24
hs2:HDMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
 

   (14)  35p + 40z + 25t - 27s
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (14)  35p + 40z + 25t - 27s
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 14

--S 15 of 24
hs3:HDMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
 

                     2
   (15)  25p s - 165b  + 15w + 30z - 18t
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R                     2
--R   (15)  25p s - 165b  + 15w + 30z - 18t
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 15

--S 16 of 24
hs4:HDMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
 

   (16)  15p t + 20z s - 9w
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (16)  15p t + 20z s - 9w
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 16

--S 17 of 24
hs5:HDMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
 

              3
   (17)  - 11b  + w p + 2z t
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R              3
--R   (17)  - 11b  + w p + 2z t
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 17

--S 18 of 24
hs6:HDMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
 

                     2
   (18)  - 11s b + 3b  + 99w
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R                     2
--R   (18)  - 11s b + 3b  + 99w
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 18

--S 19 of 24
hs7:HDMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
 

          2   33      2673
   (19)  b  + -- b + -----
              50     10000
Type: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R          2   33      2673
--R   (19)  b  + -- b + -----
--R              50     10000
--RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 19

--S 20 of 24
hsn7:=[hs1,hs2,hs3,hs4,hs5,hs6,hs7]
 

   (20)
   [45p + 35s - 165b - 36, 35p + 40z + 25t - 27s,
                2                                             3
    25p s - 165b  + 15w + 30z - 18t, 15p t + 20z s - 9w, - 11b  + w p + 2z t,
                2         2   33      2673
    - 11s b + 3b  + 99w, b  + -- b + -----]
                              50     10000
Type: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (20)
--R   [45p + 35s - 165b - 36, 35p + 40z + 25t - 27s,
--R                2                                             3
--R    25p s - 165b  + 15w + 30z - 18t, 15p t + 20z s - 9w, - 11b  + w p + 2z t,
--R                2         2   33      2673
--R    - 11s b + 3b  + 99w, b  + -- b + -----]
--R                              50     10000
--RType: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 20

--S 21 of 24
groebner(hsn7)
 

   (21)
     2   33      2673       19      1323      31     153      49     1143
   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
         50     10000      120     20000      18     200      36     2000
        37      27      5      9
    t - -- b + ---, s - - b - ---]
        15     250      2     200
Type: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   (21)
--R     2   33      2673       19      1323      31     153      49     1143
--R   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
--R         50     10000      120     20000      18     200      36     2000
--R        37      27      5      9
--R    t - -- b + ---, s - - b - ---]
--R        15     250      2     200
--RType: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 21

--S 22 of 24
groebner(hsn7,"redcrit")
 


    reduced Critpair - Polynom :


       5     61     77      7
   z + - t - -- s + -- b + --
       8     45     24     10




    reduced Critpair - Polynom :


    2   216     189     78      99     10557
   s  - --- w + --- t - -- s + --- b - -----
         5      100     25     500     12500




    reduced Critpair - Polynom :


         66       17541     5886     10588      9273     8272413
   t s - -- t b - ----- w + ---- t - ----- s - ----- b - -------
         29        725      3625      3625     36250     7250000




    reduced Critpair - Polynom :


      2   28       44       143       962712     420652     5166944
     t  + -- w s - -- w b + --- t b - ------ w + ------ t - ------- s
          45       15       725        18125      90625      815625
   + 
     5036339     83580953
     ------- b - --------
     5437500     90625000




    reduced Critpair - Polynom :


         33      297        81
   w b + -- w + ----- s - ----- b
         50     10000     10000




    reduced Critpair - Polynom :


          21        33      6723      2031      104247
   w s + --- t b - --- w + ----- s - ----- b + -------
         100       250     50000     25000     5000000




    reduced Critpair - Polynom :


         2373       41563      17253      578853      258751      11330361
   w t + ---- t b - ----- w + ------ t + ------- s - ------- b + ---------
         7250       36250     290000     7250000     3625000     362500000




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


         51061712      91248294     1516761889      481096937      5789482077
   t b - -------- w + --------- t - ---------- s + ---------- b + -----------
          5127061     128176525     1922647875     1281765250     51270610000




    reduced Critpair - Polynom :


         2962071220563579     1229379913128787     4524811449715289
     w + ---------------- t - ---------------- s + ---------------- b
          98138188260880       36801820597830       490690941304400
   + 
     59240140318722273
     -----------------
     12267273532610000




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


       172832706542351932      47302810289036749      2736061156820726
   t - ------------------ s + ------------------ b + -----------------
       155991468675747195     155991468675747195     17332385408416355




    reduced Critpair - Polynom :


       5      9
   s - - b - ---
       2     200




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0




    reduced Critpair - Polynom :


   0


       THE GROEBNER BASIS POLYNOMIALS

   (22)
     2   33      2673       19      1323      31     153      49     1143
   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
         50     10000      120     20000      18     200      36     2000
        37      27      5      9
    t - -- b + ---, s - - b - ---]
        15     250      2     200
Type: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5     61     77      7
--R   z + - t - -- s + -- b + --
--R       8     45     24     10
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R    2   216     189     78      99     10557
--R   s  - --- w + --- t - -- s + --- b - -----
--R         5      100     25     500     12500
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         66       17541     5886     10588      9273     8272413
--R   t s - -- t b - ----- w + ---- t - ----- s - ----- b - -------
--R         29        725      3625      3625     36250     7250000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R      2   28       44       143       962712     420652     5166944
--R     t  + -- w s - -- w b + --- t b - ------ w + ------ t - ------- s
--R          45       15       725        18125      90625      815625
--R   + 
--R     5036339     83580953
--R     ------- b - --------
--R     5437500     90625000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         33      297        81
--R   w b + -- w + ----- s - ----- b
--R         50     10000     10000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          21        33      6723      2031      104247
--R   w s + --- t b - --- w + ----- s - ----- b + -------
--R         100       250     50000     25000     5000000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2373       41563      17253      578853      258751      11330361
--R   w t + ---- t b - ----- w + ------ t + ------- s - ------- b + ---------
--R         7250       36250     290000     7250000     3625000     362500000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         51061712      91248294     1516761889      481096937      5789482077
--R   t b - -------- w + --------- t - ---------- s + ---------- b + -----------
--R          5127061     128176525     1922647875     1281765250     51270610000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2962071220563579     1229379913128787     4524811449715289
--R     w + ---------------- t - ---------------- s + ---------------- b
--R          98138188260880       36801820597830       490690941304400
--R   + 
--R     59240140318722273
--R     -----------------
--R     12267273532610000
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       172832706542351932      47302810289036749      2736061156820726
--R   t - ------------------ s + ------------------ b + -----------------
--R       155991468675747195     155991468675747195     17332385408416355
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5      9
--R   s - - b - ---
--R       2     200
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R       THE GROEBNER BASIS POLYNOMIALS
--R
--R   (22)
--R     2   33      2673       19      1323      31     153      49     1143
--R   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
--R         50     10000      120     20000      18     200      36     2000
--R        37      27      5      9
--R    t - -- b + ---, s - - b - ---]
--R        15     250      2     200
--RType: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 22

--S 23 of 24
groebner(hsn7,"info")
 

   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 5]]


                                                   2
   [[ci= p s,tci= 5,cj= p,tcj= 4,c= z s,tc= 7,rc= s ,trc= 6,tF= 5,tD= 5]]


   [[ci= p t,tci= 3,cj= p,tcj= 4,c= z t,tc= 5,rc= t s,trc= 7,tF= 6,tD= 6]]


          3             2                          2
   [[ci= b ,tci= 3,cj= b ,tcj= 3,c= w p,tc= 4,rc= t ,trc= 9,tF= 7,tD= 6]]


                         2            3
   [[ci= s b,tci= 3,cj= b ,tcj= 3,c= b ,tc= 4,rc= w b,trc= 4,tF= 8,tD= 7]]


                         2              2
   [[ci= s b,tci= 3,cj= s ,tcj= 6,c= s b ,tc= 7,rc= w s,trc= 6,tF= 9,tD= 9]]


                                         2
   [[ci= s b,tci= 3,cj= t s,tcj= 7,c= t b ,tc= 7,rc= w t,trc= 7,tF= 10,tD= 11]]


                                         2
   [[ci= p s,tci= 5,cj= s b,tcj= 3,c= p b ,tc= 6,rc= 0,trc= 0,tF= 10,tD= 10]]


          2
   [[ci= s ,tci= 6,cj= t s,tcj= 7,c= t s b,tc= 10,rc= t b,trc= 6,tF= 11,tD= 13]]


          2
   [[ci= b ,tci= 3,cj= t b,tcj= 6,c= w b,tc= 6,rc= w,trc= 5,tF= 9,tD= 14]]


          2
   [[ci= b ,tci= 3,cj= w b,tcj= 4,c= s b,tc= 3,rc= 0,trc= 0,tF= 9,tD= 13]]


                                         2
   [[ci= s b,tci= 3,cj= t b,tcj= 6,c= t b ,tc= 7,rc= t,trc= 4,tF= 7,tD= 11]]


                                         2
   [[ci= s b,tci= 3,cj= w b,tcj= 4,c= w b ,tc= 5,rc= s,trc= 3,tF= 6,tD= 9]]


                                       2
   [[ci= w b,tci= 4,cj= t b,tcj= 6,c= w ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 8]]


                                     2
   [[ci= s b,tci= 3,cj= s,tcj= 3,c= b ,tc= 3,rc= 0,trc= 0,tF= 6,tD= 7]]


   [[ci= t b,tci= 6,cj= t,tcj= 4,c= s b,tc= 7,rc= 0,trc= 0,tF= 6,tD= 6]]


   [[ci= w b,tci= 4,cj= w,tcj= 5,c= t b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 5]]


          2
   [[ci= s ,tci= 6,cj= s,tcj= 3,c= s b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 4]]


                                     2
   [[ci= t s,tci= 7,cj= t,tcj= 4,c= s ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 3]]


   [[ci= w s,tci= 6,cj= w,tcj= 5,c= t s,tc= 8,rc= 0,trc= 0,tF= 6,tD= 2]]


          2
   [[ci= t ,tci= 9,cj= t,tcj= 4,c= w s,tc= 9,rc= 0,trc= 0,tF= 6,tD= 1]]


                                     2
   [[ci= w t,tci= 7,cj= w,tcj= 5,c= t ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 0]]


     There are

   6

     Groebner Basis Polynomials.


       THE GROEBNER BASIS POLYNOMIALS

   (23)
     2   33      2673       19      1323      31     153      49     1143
   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
         50     10000      120     20000      18     200      36     2000
        37      27      5      9
    t - -- b + ---, s - - b - ---]
        15     250      2     200
Type: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 5]]
--R
--R
--R                                                   2
--R   [[ci= p s,tci= 5,cj= p,tcj= 4,c= z s,tc= 7,rc= s ,trc= 6,tF= 5,tD= 5]]
--R
--R
--R   [[ci= p t,tci= 3,cj= p,tcj= 4,c= z t,tc= 5,rc= t s,trc= 7,tF= 6,tD= 6]]
--R
--R
--R          3             2                          2
--R   [[ci= b ,tci= 3,cj= b ,tcj= 3,c= w p,tc= 4,rc= t ,trc= 9,tF= 7,tD= 6]]
--R
--R
--R                         2            3
--R   [[ci= s b,tci= 3,cj= b ,tcj= 3,c= b ,tc= 4,rc= w b,trc= 4,tF= 8,tD= 7]]
--R
--R
--R                         2              2
--R   [[ci= s b,tci= 3,cj= s ,tcj= 6,c= s b ,tc= 7,rc= w s,trc= 6,tF= 9,tD= 9]]
--R
--R
--R                                         2
--R   [[ci= s b,tci= 3,cj= t s,tcj= 7,c= t b ,tc= 7,rc= w t,trc= 7,tF= 10,tD= 11]]
--R
--R
--R                                         2
--R   [[ci= p s,tci= 5,cj= s b,tcj= 3,c= p b ,tc= 6,rc= 0,trc= 0,tF= 10,tD= 10]]
--R
--R
--R          2
--R   [[ci= s ,tci= 6,cj= t s,tcj= 7,c= t s b,tc= 10,rc= t b,trc= 6,tF= 11,tD= 13]]
--R
--R
--R          2
--R   [[ci= b ,tci= 3,cj= t b,tcj= 6,c= w b,tc= 6,rc= w,trc= 5,tF= 9,tD= 14]]
--R
--R
--R          2
--R   [[ci= b ,tci= 3,cj= w b,tcj= 4,c= s b,tc= 3,rc= 0,trc= 0,tF= 9,tD= 13]]
--R
--R
--R                                         2
--R   [[ci= s b,tci= 3,cj= t b,tcj= 6,c= t b ,tc= 7,rc= t,trc= 4,tF= 7,tD= 11]]
--R
--R
--R                                         2
--R   [[ci= s b,tci= 3,cj= w b,tcj= 4,c= w b ,tc= 5,rc= s,trc= 3,tF= 6,tD= 9]]
--R
--R
--R                                       2
--R   [[ci= w b,tci= 4,cj= t b,tcj= 6,c= w ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 8]]
--R
--R
--R                                     2
--R   [[ci= s b,tci= 3,cj= s,tcj= 3,c= b ,tc= 3,rc= 0,trc= 0,tF= 6,tD= 7]]
--R
--R
--R   [[ci= t b,tci= 6,cj= t,tcj= 4,c= s b,tc= 7,rc= 0,trc= 0,tF= 6,tD= 6]]
--R
--R
--R   [[ci= w b,tci= 4,cj= w,tcj= 5,c= t b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 5]]
--R
--R
--R          2
--R   [[ci= s ,tci= 6,cj= s,tcj= 3,c= s b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 4]]
--R
--R
--R                                     2
--R   [[ci= t s,tci= 7,cj= t,tcj= 4,c= s ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 3]]
--R
--R
--R   [[ci= w s,tci= 6,cj= w,tcj= 5,c= t s,tc= 8,rc= 0,trc= 0,tF= 6,tD= 2]]
--R
--R
--R          2
--R   [[ci= t ,tci= 9,cj= t,tcj= 4,c= w s,tc= 9,rc= 0,trc= 0,tF= 6,tD= 1]]
--R
--R
--R                                     2
--R   [[ci= w t,tci= 7,cj= w,tcj= 5,c= t ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 0]]
--R
--R
--R     There are
--R
--R   6
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS POLYNOMIALS
--R
--R   (23)
--R     2   33      2673       19      1323      31     153      49     1143
--R   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
--R         50     10000      120     20000      18     200      36     2000
--R        37      27      5      9
--R    t - -- b + ---, s - - b - ---]
--R        15     250      2     200
--RType: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 23

--S 24 of 24
groebner(hsn7,"redcrit","info")
 


    reduced Critpair - Polynom :


       5     61     77      7
   z + - t - -- s + -- b + --
       8     45     24     10



   you choose option  -info-
   abbrev. for the following information strings are
     ci  =>  Leading monomial  for critpair calculation
     tci =>  Number of terms of polynomial i
     cj  =>  Leading monomial  for critpair calculation
     tcj =>  Number of terms of polynomial j
     c   =>  Leading monomial of critpair polynomial
     tc  =>  Number of terms of critpair polynomial
     rc  =>  Leading monomial of redcritpair polynomial
     trc =>  Number of terms of redcritpair polynomial
     tF  =>  Number of polynomials in reduction list F
     tD  =>  Number of critpairs still to do





   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 5]]



    reduced Critpair - Polynom :


    2   216     189     78      99     10557
   s  - --- w + --- t - -- s + --- b - -----
         5      100     25     500     12500



                                                   2
   [[ci= p s,tci= 5,cj= p,tcj= 4,c= z s,tc= 7,rc= s ,trc= 6,tF= 5,tD= 5]]



    reduced Critpair - Polynom :


         66       17541     5886     10588      9273     8272413
   t s - -- t b - ----- w + ---- t - ----- s - ----- b - -------
         29        725      3625      3625     36250     7250000



   [[ci= p t,tci= 3,cj= p,tcj= 4,c= z t,tc= 5,rc= t s,trc= 7,tF= 6,tD= 6]]



    reduced Critpair - Polynom :


      2   28       44       143       962712     420652     5166944
     t  + -- w s - -- w b + --- t b - ------ w + ------ t - ------- s
          45       15       725        18125      90625      815625
   + 
     5036339     83580953
     ------- b - --------
     5437500     90625000



          3             2                          2
   [[ci= b ,tci= 3,cj= b ,tcj= 3,c= w p,tc= 4,rc= t ,trc= 9,tF= 7,tD= 6]]



    reduced Critpair - Polynom :


         33      297        81
   w b + -- w + ----- s - ----- b
         50     10000     10000



                         2            3
   [[ci= s b,tci= 3,cj= b ,tcj= 3,c= b ,tc= 4,rc= w b,trc= 4,tF= 8,tD= 7]]



    reduced Critpair - Polynom :


          21        33      6723      2031      104247
   w s + --- t b - --- w + ----- s - ----- b + -------
         100       250     50000     25000     5000000



                         2              2
   [[ci= s b,tci= 3,cj= s ,tcj= 6,c= s b ,tc= 7,rc= w s,trc= 6,tF= 9,tD= 9]]



    reduced Critpair - Polynom :


         2373       41563      17253      578853      258751      11330361
   w t + ---- t b - ----- w + ------ t + ------- s - ------- b + ---------
         7250       36250     290000     7250000     3625000     362500000



                                         2
   [[ci= s b,tci= 3,cj= t s,tcj= 7,c= t b ,tc= 7,rc= w t,trc= 7,tF= 10,tD= 11]]



    reduced Critpair - Polynom :


   0



                                         2
   [[ci= p s,tci= 5,cj= s b,tcj= 3,c= p b ,tc= 6,rc= 0,trc= 0,tF= 10,tD= 10]]



    reduced Critpair - Polynom :


         51061712      91248294     1516761889      481096937      5789482077
   t b - -------- w + --------- t - ---------- s + ---------- b + -----------
          5127061     128176525     1922647875     1281765250     51270610000



          2
   [[ci= s ,tci= 6,cj= t s,tcj= 7,c= t s b,tc= 10,rc= t b,trc= 6,tF= 11,tD= 13]]



    reduced Critpair - Polynom :


         2962071220563579     1229379913128787     4524811449715289
     w + ---------------- t - ---------------- s + ---------------- b
          98138188260880       36801820597830       490690941304400
   + 
     59240140318722273
     -----------------
     12267273532610000



          2
   [[ci= b ,tci= 3,cj= t b,tcj= 6,c= w b,tc= 6,rc= w,trc= 5,tF= 9,tD= 14]]



    reduced Critpair - Polynom :


   0



          2
   [[ci= b ,tci= 3,cj= w b,tcj= 4,c= s b,tc= 3,rc= 0,trc= 0,tF= 9,tD= 13]]



    reduced Critpair - Polynom :


       172832706542351932      47302810289036749      2736061156820726
   t - ------------------ s + ------------------ b + -----------------
       155991468675747195     155991468675747195     17332385408416355



                                         2
   [[ci= s b,tci= 3,cj= t b,tcj= 6,c= t b ,tc= 7,rc= t,trc= 4,tF= 7,tD= 11]]



    reduced Critpair - Polynom :


       5      9
   s - - b - ---
       2     200



                                         2
   [[ci= s b,tci= 3,cj= w b,tcj= 4,c= w b ,tc= 5,rc= s,trc= 3,tF= 6,tD= 9]]



    reduced Critpair - Polynom :


   0



                                       2
   [[ci= w b,tci= 4,cj= t b,tcj= 6,c= w ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 8]]



    reduced Critpair - Polynom :


   0



                                     2
   [[ci= s b,tci= 3,cj= s,tcj= 3,c= b ,tc= 3,rc= 0,trc= 0,tF= 6,tD= 7]]



    reduced Critpair - Polynom :


   0



   [[ci= t b,tci= 6,cj= t,tcj= 4,c= s b,tc= 7,rc= 0,trc= 0,tF= 6,tD= 6]]



    reduced Critpair - Polynom :


   0



   [[ci= w b,tci= 4,cj= w,tcj= 5,c= t b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 5]]



    reduced Critpair - Polynom :


   0



          2
   [[ci= s ,tci= 6,cj= s,tcj= 3,c= s b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 4]]



    reduced Critpair - Polynom :


   0



                                     2
   [[ci= t s,tci= 7,cj= t,tcj= 4,c= s ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 3]]



    reduced Critpair - Polynom :


   0



   [[ci= w s,tci= 6,cj= w,tcj= 5,c= t s,tc= 8,rc= 0,trc= 0,tF= 6,tD= 2]]



    reduced Critpair - Polynom :


   0



          2
   [[ci= t ,tci= 9,cj= t,tcj= 4,c= w s,tc= 9,rc= 0,trc= 0,tF= 6,tD= 1]]



    reduced Critpair - Polynom :


   0



                                     2
   [[ci= w t,tci= 7,cj= w,tcj= 5,c= t ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 0]]


     There are

   6

     Groebner Basis Polynomials.


       THE GROEBNER BASIS POLYNOMIALS

   (24)
     2   33      2673       19      1323      31     153      49     1143
   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
         50     10000      120     20000      18     200      36     2000
        37      27      5      9
    t - -- b + ---, s - - b - ---]
        15     250      2     200
Type: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5     61     77      7
--R   z + - t - -- s + -- b + --
--R       8     45     24     10
--R
--R
--R
--R   you choose option  -info-
--R   abbrev. for the following information strings are
--R     ci  =>  Leading monomial  for critpair calculation
--R     tci =>  Number of terms of polynomial i
--R     cj  =>  Leading monomial  for critpair calculation
--R     tcj =>  Number of terms of polynomial j
--R     c   =>  Leading monomial of critpair polynomial
--R     tc  =>  Number of terms of critpair polynomial
--R     rc  =>  Leading monomial of redcritpair polynomial
--R     trc =>  Number of terms of redcritpair polynomial
--R     tF  =>  Number of polynomials in reduction list F
--R     tD  =>  Number of critpairs still to do
--R
--R
--R
--R
--R
--R   [[ci= p,tci= 4,cj= p,tcj= 4,c= z,tc= 5,rc= z,trc= 5,tF= 4,tD= 5]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R    2   216     189     78      99     10557
--R   s  - --- w + --- t - -- s + --- b - -----
--R         5      100     25     500     12500
--R
--R
--R
--R                                                   2
--R   [[ci= p s,tci= 5,cj= p,tcj= 4,c= z s,tc= 7,rc= s ,trc= 6,tF= 5,tD= 5]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         66       17541     5886     10588      9273     8272413
--R   t s - -- t b - ----- w + ---- t - ----- s - ----- b - -------
--R         29        725      3625      3625     36250     7250000
--R
--R
--R
--R   [[ci= p t,tci= 3,cj= p,tcj= 4,c= z t,tc= 5,rc= t s,trc= 7,tF= 6,tD= 6]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R      2   28       44       143       962712     420652     5166944
--R     t  + -- w s - -- w b + --- t b - ------ w + ------ t - ------- s
--R          45       15       725        18125      90625      815625
--R   + 
--R     5036339     83580953
--R     ------- b - --------
--R     5437500     90625000
--R
--R
--R
--R          3             2                          2
--R   [[ci= b ,tci= 3,cj= b ,tcj= 3,c= w p,tc= 4,rc= t ,trc= 9,tF= 7,tD= 6]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         33      297        81
--R   w b + -- w + ----- s - ----- b
--R         50     10000     10000
--R
--R
--R
--R                         2            3
--R   [[ci= s b,tci= 3,cj= b ,tcj= 3,c= b ,tc= 4,rc= w b,trc= 4,tF= 8,tD= 7]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R          21        33      6723      2031      104247
--R   w s + --- t b - --- w + ----- s - ----- b + -------
--R         100       250     50000     25000     5000000
--R
--R
--R
--R                         2              2
--R   [[ci= s b,tci= 3,cj= s ,tcj= 6,c= s b ,tc= 7,rc= w s,trc= 6,tF= 9,tD= 9]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2373       41563      17253      578853      258751      11330361
--R   w t + ---- t b - ----- w + ------ t + ------- s - ------- b + ---------
--R         7250       36250     290000     7250000     3625000     362500000
--R
--R
--R
--R                                         2
--R   [[ci= s b,tci= 3,cj= t s,tcj= 7,c= t b ,tc= 7,rc= w t,trc= 7,tF= 10,tD= 11]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                                         2
--R   [[ci= p s,tci= 5,cj= s b,tcj= 3,c= p b ,tc= 6,rc= 0,trc= 0,tF= 10,tD= 10]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         51061712      91248294     1516761889      481096937      5789482077
--R   t b - -------- w + --------- t - ---------- s + ---------- b + -----------
--R          5127061     128176525     1922647875     1281765250     51270610000
--R
--R
--R
--R          2
--R   [[ci= s ,tci= 6,cj= t s,tcj= 7,c= t s b,tc= 10,rc= t b,trc= 6,tF= 11,tD= 13]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R         2962071220563579     1229379913128787     4524811449715289
--R     w + ---------------- t - ---------------- s + ---------------- b
--R          98138188260880       36801820597830       490690941304400
--R   + 
--R     59240140318722273
--R     -----------------
--R     12267273532610000
--R
--R
--R
--R          2
--R   [[ci= b ,tci= 3,cj= t b,tcj= 6,c= w b,tc= 6,rc= w,trc= 5,tF= 9,tD= 14]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          2
--R   [[ci= b ,tci= 3,cj= w b,tcj= 4,c= s b,tc= 3,rc= 0,trc= 0,tF= 9,tD= 13]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       172832706542351932      47302810289036749      2736061156820726
--R   t - ------------------ s + ------------------ b + -----------------
--R       155991468675747195     155991468675747195     17332385408416355
--R
--R
--R
--R                                         2
--R   [[ci= s b,tci= 3,cj= t b,tcj= 6,c= t b ,tc= 7,rc= t,trc= 4,tF= 7,tD= 11]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R       5      9
--R   s - - b - ---
--R       2     200
--R
--R
--R
--R                                         2
--R   [[ci= s b,tci= 3,cj= w b,tcj= 4,c= w b ,tc= 5,rc= s,trc= 3,tF= 6,tD= 9]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                                       2
--R   [[ci= w b,tci= 4,cj= t b,tcj= 6,c= w ,tc= 7,rc= 0,trc= 0,tF= 6,tD= 8]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                                     2
--R   [[ci= s b,tci= 3,cj= s,tcj= 3,c= b ,tc= 3,rc= 0,trc= 0,tF= 6,tD= 7]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R   [[ci= t b,tci= 6,cj= t,tcj= 4,c= s b,tc= 7,rc= 0,trc= 0,tF= 6,tD= 6]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R   [[ci= w b,tci= 4,cj= w,tcj= 5,c= t b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 5]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          2
--R   [[ci= s ,tci= 6,cj= s,tcj= 3,c= s b,tc= 6,rc= 0,trc= 0,tF= 6,tD= 4]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                                     2
--R   [[ci= t s,tci= 7,cj= t,tcj= 4,c= s ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 3]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R   [[ci= w s,tci= 6,cj= w,tcj= 5,c= t s,tc= 8,rc= 0,trc= 0,tF= 6,tD= 2]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R          2
--R   [[ci= t ,tci= 9,cj= t,tcj= 4,c= w s,tc= 9,rc= 0,trc= 0,tF= 6,tD= 1]]
--R
--R
--R
--R    reduced Critpair - Polynom :
--R
--R
--R   0
--R
--R
--R
--R                                     2
--R   [[ci= w t,tci= 7,cj= w,tcj= 5,c= t ,tc= 8,rc= 0,trc= 0,tF= 6,tD= 0]]
--R
--R
--R     There are
--R
--R   6
--R
--R     Groebner Basis Polynomials.
--R
--R
--R       THE GROEBNER BASIS POLYNOMIALS
--R
--R   (24)
--R     2   33      2673       19      1323      31     153      49     1143
--R   [b  + -- b + -----, w + --- b + -----, p - -- b - ---, z + -- b + ----,
--R         50     10000      120     20000      18     200      36     2000
--R        37      27      5      9
--R    t - -- b + ---, s - - b - ---]
--R        15     250      2     200
--RType: List HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction Integer)
--E 24

)spool
 
Starts dribbling to psgenfcn.output (2010/3/27, 18:30:51).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 19
ORD := 20
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 19
approximateEquality(series1,series2) ==
  -- tests that 2 series are equal to order ORD
  uts1 := series1 :: UTS(EXPR INT,'t,0)
  uts2 := series2 :: UTS(EXPR INT,'t,0)
  flag := (order(uts1 - uts2,ORD) = ORD) :: Boolean
  flag => true
  error "series do not agree to specified order"
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 19
bernoulliPolynomial(n) ==
  -- returns the nth Bernoulli polynomial as an EXPR INT
  sup := bernoulli(n)$(PNTHEORY)
  p : POLY FRAC INT := multivariate(sup,'x)
  p :: (EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 19
eulerPolynomial(n) ==
  -- returns the nth Euler polynomial as an EXPR INT
  sup := euler(n)$(PNTHEORY)
  p : POLY FRAC INT := multivariate(sup,'x)
  p :: (EXPR INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 19
f1 := taylor(t/(1 - t - t**2))
 

             2     3     4     5     6      7      8      9      10      11
   (5)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             2     3     4     5     6      7      8      9      10      11
--R   (5)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 5

--S 6 of 19
f2 := taylor(n +-> fibonacci(n),t = 0)
 

             2     3     4     5     6      7      8      9      10      11
   (6)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             2     3     4     5     6      7      8      9      10      11
--R   (6)  t + t  + 2t  + 3t  + 5t  + 8t  + 13t  + 21t  + 34t  + 55t   + O(t  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 6

--S 7 of 19
approximateEquality(f1,f2)
 
   Compiling function approximateEquality with type (Any,Any) -> 
      Boolean 

   (7)  true
                                                                Type: Boolean
--R 
--R   Compiling function approximateEquality with type (Any,Any) -> 
--R      Boolean 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 19
g1 := taylor(t/(exp(t) - 1))
 

   (8)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (8)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 8

--S 9 of 19
g2 := taylor(n +-> bernoulli(n)/factorial(n),t = 0)
 

   (9)
       1      1  2    1   4     1    6      1     8       1     10      11
   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
       2     12      720      30240      1209600      47900160
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (9)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 9

--S 10 of 19
approximateEquality(g1,g2)
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 19
gg1 := taylor(t*exp(t*x)/(exp(t) - 1),t = 0)
 

   (11)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
     ---------------------- t  + --------------------- t
               720                        720
   + 
        6       5       4      2            7      6      5     3
     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
     ------------------------------- t  + --------------------------- t
                  30240                              30240
   + 
        8       7       6      4      2
     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
     -------------------------------------- t
                     1209600
   + 
        9      8      7      5      3
     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
     ------------------------------------- t
                    3628800
   + 
        10       9       8       6       4      2
     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
     ------------------------------------------------ t   + O(t  )
                         239500800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (11)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
--R     ---------------------- t  + --------------------- t
--R               720                        720
--R   + 
--R        6       5       4      2            7      6      5     3
--R     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
--R     ------------------------------- t  + --------------------------- t
--R                  30240                              30240
--R   + 
--R        8       7       6      4      2
--R     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
--R     -------------------------------------- t
--R                     1209600
--R   + 
--R        9      8      7      5      3
--R     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
--R     ------------------------------------- t
--R                    3628800
--R   + 
--R        10       9       8       6       4      2
--R     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
--R     ------------------------------------------------ t   + O(t  )
--R                         239500800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 11

--S 12 of 19
gg2 := taylor(n +-> bernoulliPolynomial(n)/factorial(n),t = 0)
 
   Compiling function bernoulliPolynomial with type Integer -> 
      Expression Integer 

   (12)
                      2                 3     2
         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
     1 + ------ t + ------------ t  + ------------- t
            2            12                 12
   + 
        4      3      2            5      4      3
     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
     ---------------------- t  + --------------------- t
               720                        720
   + 
        6       5       4      2            7      6      5     3
     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
     ------------------------------- t  + --------------------------- t
                  30240                              30240
   + 
        8       7       6      4      2
     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
     -------------------------------------- t
                     1209600
   + 
        9      8      7      5      3
     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
     ------------------------------------- t
                    3628800
   + 
        10       9       8       6       4      2
     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
     ------------------------------------------------ t   + O(t  )
                         239500800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function bernoulliPolynomial with type Integer -> 
--R      Expression Integer 
--R
--R   (12)
--R                      2                 3     2
--R         2x - 1     6x  - 6x + 1  2   2x  - 3x  + x  3
--R     1 + ------ t + ------------ t  + ------------- t
--R            2            12                 12
--R   + 
--R        4      3      2            5      4      3
--R     30x  - 60x  + 30x  - 1  4   6x  - 15x  + 10x  - x  5
--R     ---------------------- t  + --------------------- t
--R               720                        720
--R   + 
--R        6       5       4      2            7      6      5     3
--R     42x  - 126x  + 105x  - 21x  + 1  6   6x  - 21x  + 21x  - 7x  + x  7
--R     ------------------------------- t  + --------------------------- t
--R                  30240                              30240
--R   + 
--R        8       7       6      4      2
--R     30x  - 120x  + 140x  - 70x  + 20x  - 1  8
--R     -------------------------------------- t
--R                     1209600
--R   + 
--R        9      8      7      5      3
--R     10x  - 45x  + 60x  - 42x  + 20x  - 3x  9
--R     ------------------------------------- t
--R                    3628800
--R   + 
--R        10       9       8       6       4      2
--R     66x   - 330x  + 495x  - 462x  + 330x  - 99x  + 5  10      11
--R     ------------------------------------------------ t   + O(t  )
--R                         239500800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 12

--S 13 of 19
approximateEquality(gg1,gg2)
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 19
h1 := taylor(2*exp(t/2)/(exp(t) + 1))
 

             1  2    5   4     61   6     277    8      50521    10      11
   (14)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
             8      384      46080      2064384      3715891200
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             1  2    5   4     61   6     277    8      50521    10      11
--R   (14)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
--R             8      384      46080      2064384      3715891200
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 14

--S 15 of 19
h2 := taylor(n +-> euler(n)/(2**n * factorial(n)),t = 0)
 

             1  2    5   4     61   6     277    8      50521    10      11
   (15)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
             8      384      46080      2064384      3715891200
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R             1  2    5   4     61   6     277    8      50521    10      11
--R   (15)  1 - - t  + --- t  - ----- t  + ------- t  - ---------- t   + O(t  )
--R             8      384      46080      2064384      3715891200
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 15

--S 16 of 19
approximateEquality(h1,h2)
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 19
hh1 := taylor(2*exp(t*x)/(exp(t) + 1),t = 0)
 

   (17)
                     2            3     2           4     3
         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
     1 + ------ t + ------ t  + ------------- t  + ------------ t
            2          2              24                24
   + 
       5     4     2           6     5     3
     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
     ------------------- t  + ------------------- t
             240                      720
   + 
       7      6      4      2            8     7      5      3
     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
     ----------------------------- t  + ---------------------------- t
                 40320                              40320
   + 
       9     8      6       4       2
     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
     ------------------------------------- t
                     725760
   + 
      10     9      7       5       3
     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
     --------------------------------------- t   + O(t  )
                     3628800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R
--R   (17)
--R                     2            3     2           4     3
--R         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
--R     1 + ------ t + ------ t  + ------------- t  + ------------ t
--R            2          2              24                24
--R   + 
--R       5     4     2           6     5     3
--R     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
--R     ------------------- t  + ------------------- t
--R             240                      720
--R   + 
--R       7      6      4      2            8     7      5      3
--R     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
--R     ----------------------------- t  + ---------------------------- t
--R                 40320                              40320
--R   + 
--R       9     8      6       4       2
--R     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
--R     ------------------------------------- t
--R                     725760
--R   + 
--R      10     9      7       5       3
--R     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
--R     --------------------------------------- t   + O(t  )
--R                     3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 17

--S 18 of 19
hh2 := taylor(n +-> eulerPolynomial(n)/factorial(n),t = 0)
 
   Compiling function eulerPolynomial with type Integer -> Expression 
      Integer 

   (18)
                     2            3     2           4     3
         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
     1 + ------ t + ------ t  + ------------- t  + ------------ t
            2          2              24                24
   + 
       5     4     2           6     5     3
     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
     ------------------- t  + ------------------- t
             240                      720
   + 
       7      6      4      2            8     7      5      3
     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
     ----------------------------- t  + ---------------------------- t
                 40320                              40320
   + 
       9     8      6       4       2
     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
     ------------------------------------- t
                     725760
   + 
      10     9      7       5       3
     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
     --------------------------------------- t   + O(t  )
                     3628800
                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--R 
--R   Compiling function eulerPolynomial with type Integer -> Expression 
--R      Integer 
--R
--R   (18)
--R                     2            3     2           4     3
--R         2x - 1     x  - x  2   4x  - 6x  + 1  3   x  - 2x  + x  4
--R     1 + ------ t + ------ t  + ------------- t  + ------------ t
--R            2          2              24                24
--R   + 
--R       5     4     2           6     5     3
--R     2x  - 5x  + 5x  - 1  5   x  - 3x  + 5x  - 3x  6
--R     ------------------- t  + ------------------- t
--R             240                      720
--R   + 
--R       7      6      4      2            8     7      5      3
--R     8x  - 28x  + 70x  - 84x  + 17  7   x  - 4x  + 14x  - 28x  + 17x  8
--R     ----------------------------- t  + ---------------------------- t
--R                 40320                              40320
--R   + 
--R       9     8      6       4       2
--R     2x  - 9x  + 42x  - 126x  + 153x  - 31  9
--R     ------------------------------------- t
--R                     725760
--R   + 
--R      10     9      7       5       3
--R     x   - 5x  + 30x  - 126x  + 255x  - 155x  10      11
--R     --------------------------------------- t   + O(t  )
--R                     3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,t,0)
--E 18

--S 19 of 19
approximateEquality(hh1,hh2)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19
)spool 
 
Starts dribbling to laplace.output (2010/3/27, 18:28:36).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 27
f n == t**(n-1)*exp(-a*t)/factorial(n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 27
f 2
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

            - a t
   (2)  t %e
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R            - a t
--R   (2)  t %e
--R                                                     Type: Expression Integer
--E 2

--S 3 of 27
laplace(%, t, s)
 

               1
   (3)  --------------
         2           2
        s  + 2a s + a
                                                     Type: Expression Integer
--R 
--R
--R               1
--R   (3)  --------------
--R         2           2
--R        s  + 2a s + a
--R                                                     Type: Expression Integer
--E 3

--S 4 of 27
f 5
 

         4  - a t
        t %e
   (4)  ---------
            24
                                                     Type: Expression Integer
--R 
--R
--R         4  - a t
--R        t %e
--R   (4)  ---------
--R            24
--R                                                     Type: Expression Integer
--E 4

--S 5 of 27
laplace(%, t, s)
 

                            1
   (5)  ----------------------------------------
         5       4      2 3      3 2     4     5
        s  + 5a s  + 10a s  + 10a s  + 5a s + a
                                                     Type: Expression Integer
--R 
--R
--R                            1
--R   (5)  ----------------------------------------
--R         5       4      2 3      3 2     4     5
--R        s  + 5a s  + 10a s  + 10a s  + 5a s + a
--R                                                     Type: Expression Integer
--E 5

--S 6 of 27
sin(a*t) - a*t*cos(a*t)
 

   (6)  sin(a t) - a t cos(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (6)  sin(a t) - a t cos(a t)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 27
laplace(%, t, s)
 

                3
              2a
   (7)  ---------------
         4     2 2    4
        s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                3
--R              2a
--R   (7)  ---------------
--R         4     2 2    4
--R        s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 7

--S 8 of 27
(cosh(a*t) - cos(a*t))/(2*a**2)
 

        cosh(a t) - cos(a t)
   (8)  --------------------
                   2
                 2a
                                                     Type: Expression Integer
--R 
--R
--R        cosh(a t) - cos(a t)
--R   (8)  --------------------
--R                   2
--R                 2a
--R                                                     Type: Expression Integer
--E 8

--S 9 of 27
laplace(%, t, s)
 

           s
   (9)  -------
         4    4
        s  - a
                                                     Type: Expression Integer
--R 
--R
--R           s
--R   (9)  -------
--R         4    4
--R        s  - a
--R                                                     Type: Expression Integer
--E 9

--S 10 of 27
exp(-a*t) * sin(b*t) / b**2
 

           - a t
         %e     sin(b t)
   (10)  ---------------
                 2
                b
                                                     Type: Expression Integer
--R 
--R
--R           - a t
--R         %e     sin(b t)
--R   (10)  ---------------
--R                 2
--R                b
--R                                                     Type: Expression Integer
--E 10

--S 11 of 27
laplace(%, t, s)
 

                     1
   (11)  ------------------------
            2             3    2
         b s  + 2a b s + b  + a b
                                                     Type: Expression Integer
--R 
--R
--R                     1
--R   (11)  ------------------------
--R            2             3    2
--R         b s  + 2a b s + b  + a b
--R                                                     Type: Expression Integer
--E 11

--S 12 of 27
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
 

   (12)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
                                                     Type: Expression Integer
--R 
--R
--R   (12)  - cos(a t)sinh(a t) + cosh(a t)sin(a t)
--R                                                     Type: Expression Integer
--E 12

--S 13 of 27
laplace(%, t, s)
 

              3
            4a
   (13)  --------
          4     4
         s  + 4a
                                                     Type: Expression Integer
--R 
--R
--R              3
--R            4a
--R   (13)  --------
--R          4     4
--R         s  + 4a
--R                                                     Type: Expression Integer
--E 13

--S 14 of 27
(exp(a*t) - exp(b*t))/t
 

             b t     a t
         - %e    + %e
   (14)  ---------------
                t
                                                     Type: Expression Integer
--R 
--R
--R             b t     a t
--R         - %e    + %e
--R   (14)  ---------------
--R                t
--R                                                     Type: Expression Integer
--E 14

--S 15 of 27
laplace(%, t, s)
 

   (15)  - log(s - a) + log(s - b)
                                                     Type: Expression Integer
--R 
--R
--R   (15)  - log(s - a) + log(s - b)
--R                                                     Type: Expression Integer
--E 15

--S 16 of 27
2/t * (1 - cosh(a*t))
 

         - 2cosh(a t) + 2
   (16)  ----------------
                 t
                                                     Type: Expression Integer
--R 
--R
--R         - 2cosh(a t) + 2
--R   (16)  ----------------
--R                 t
--R                                                     Type: Expression Integer
--E 16

--S 17 of 27
laplace(%, t, s)
 

              2    2
   (17)  log(s  - a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R              2    2
--R   (17)  log(s  - a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 17

--S 18 of 27
2/t * (1 - cos(a*t))
 

         - 2cos(a t) + 2
   (18)  ---------------
                t
                                                     Type: Expression Integer
--R 
--R
--R         - 2cos(a t) + 2
--R   (18)  ---------------
--R                t
--R                                                     Type: Expression Integer
--E 18

--S 19 of 27
laplace(%, t, s)
 

              2    2
   (19)  log(s  + a ) - 2log(s)
                                                     Type: Expression Integer
--R 
--R
--R              2    2
--R   (19)  log(s  + a ) - 2log(s)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 27
(cos(a*t) - cos(b*t))/t
 

         - cos(b t) + cos(a t)
   (20)  ---------------------
                   t
                                                     Type: Expression Integer
--R 
--R
--R         - cos(b t) + cos(a t)
--R   (20)  ---------------------
--R                   t
--R                                                     Type: Expression Integer
--E 20

--S 21 of 27
laplace(%, t, s)
 

              2    2         2    2
         log(s  + b ) - log(s  + a )
   (21)  ---------------------------
                      2
                                                     Type: Expression Integer
--R 
--R
--R              2    2         2    2
--R         log(s  + b ) - log(s  + a )
--R   (21)  ---------------------------
--R                      2
--R                                                     Type: Expression Integer
--E 21

--S 22 of 27
a*Ci(b*t) + c*Si(d*t)
 

   (22)  c Si(d t) + a Ci(b t)
                                                     Type: Expression Integer
--R 
--R
--R   (22)  c Si(d t) + a Ci(b t)
--R                                                     Type: Expression Integer
--E 22

--S 23 of 27
laplace(%, t, s)
 

                2    2
               s  + b             d
         a log(-------) + 2c atan(-)
                   2              s
                  b
   (23)  ---------------------------
                      2s
                                                     Type: Expression Integer
--R 
--R
--R                2    2
--R               s  + b             d
--R         a log(-------) + 2c atan(-)
--R                   2              s
--R                  b
--R   (23)  ---------------------------
--R                      2s
--R                                                     Type: Expression Integer
--E 23

--S 24 of 27
exp(a*t+b)*Ei(c*t)
 

                  a t + b
   (24)  Ei(c t)%e
                                                     Type: Expression Integer
--R 
--R
--R                  a t + b
--R   (24)  Ei(c t)%e
--R                                                     Type: Expression Integer
--E 24

--S 25 of 27
laplace(%, t, s)
 

           b    s + c - a
         %e log(---------)
                    c
   (25)  -----------------
               s - a
                                                     Type: Expression Integer
--R 
--R
--R           b    s + c - a
--R         %e log(---------)
--R                    c
--R   (25)  -----------------
--R               s - a
--R                                                     Type: Expression Integer
--E 25

--S 26 of 27
sin(a*t) - a*t*cos(a*t) + exp(t**2)
 

                       2
                      t
   (26)  sin(a t) + %e   - a t cos(a t)
                                                     Type: Expression Integer
--R 
--R
--R                       2
--R                      t
--R   (26)  sin(a t) + %e   - a t cos(a t)
--R                                                     Type: Expression Integer
--E 26

--S 27 of 27
laplace(%, t, s)
 

                                     2
           4     2 2    4           t           3
         (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
   (27)  ----------------------------------------
                       4     2 2    4
                      s  + 2a s  + a
                                                     Type: Expression Integer
--R 
--R
--R                                     2
--R           4     2 2    4           t           3
--R         (s  + 2a s  + a )laplace(%e  ,t,s) + 2a
--R   (27)  ----------------------------------------
--R                       4     2 2    4
--R                      s  + 2a s  + a
--R                                                     Type: Expression Integer
--E 27
)spool 
 
Starts dribbling to fparfrac.output (2010/3/27, 18:26:18).
)set message test on
 
)set message auto off
 
)clear all
 
 

--S 1 of 18
Q := FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 18
Px := UP(x, Q)
 

   (2)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 18
Fx := FRAC Px
 

   (3)  Fraction UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (3)  Fraction UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 3

--S 4 of 18
f:Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2)
 

                     36
   (4)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (4)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 4

--S 5 of 18
g := fullPartialFraction f
 

          4       4        --+      - 3%A - 6
   (5)  ----- - ----- +    >        ---------
        x - 2   x + 1      --+              2
                          2         (x - %A)
                        %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          4       4        --+      - 3%A - 6
--R   (5)  ----- - ----- +    >        ---------
--R        x - 2   x + 1      --+              2
--R                          2         (x - %A)
--R                        %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 18
g::Fx
 

                     36
   (6)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (6)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 18
g5 := D(g, 5)
 

             480        480        --+      2160%A + 4320
   (7)  - -------- + -------- +    >        -------------
                 6          6      --+                7
          (x - 2)    (x + 1)      2           (x - %A)
                                %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R             480        480        --+      2160%A + 4320
--R   (7)  - -------- + -------- +    >        -------------
--R                 6          6      --+                7
--R          (x - 2)    (x + 1)      2           (x - %A)
--R                                %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 7

--S 8 of 18
f5 := D(f, 5)
 

   (8)
                10           9            8            7            6
       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
     + 
                5            4            3           2
       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
  /
        20      19      18      17       16       15       14        13
       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
     + 
            12        11        10        9        8        7        6        5
       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
     + 
           4        3       2
       276x  - 1184x  + 208x  + 192x - 64
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (8)
--R                10           9            8            7            6
--R       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
--R     + 
--R                5            4            3           2
--R       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
--R  /
--R        20      19      18      17       16       15       14        13
--R       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
--R     + 
--R            12        11        10        9        8        7        6        5
--R       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
--R     + 
--R           4        3       2
--R       276x  - 1184x  + 208x  + 192x - 64
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 18
g5::Fx - f5
 

   (9)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (9)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 18
f:Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)
 

                        6    5
                       x  - x
   (10)  -----------------------------------
          7     6     5     3     2
         x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                        6    5
--R                       x  - x
--R   (10)  -----------------------------------
--R          7     6     5     3     2
--R         x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 10

--S 11 of 18
g := fullPartialFraction f
 

   (11)
      1952       464        32                          179       135
      ----       ---        --                       - ---- %A + ----
      2401       343        49            --+          2401      2401
     ------ + -------- + -------- +       >          ----------------
      x - 2          2          3         --+             x - %A
              (x - 2)    (x - 2)      2
                                    %A  + %A + 1= 0
   + 
                       37        20
                      ---- %A + ----
           --+        1029      1029
           >          --------------
           --+                   2
       2                 (x - %A)
     %A  + %A + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (11)
--R      1952       464        32                          179       135
--R      ----       ---        --                       - ---- %A + ----
--R      2401       343        49            --+          2401      2401
--R     ------ + -------- + -------- +       >          ----------------
--R      x - 2          2          3         --+             x - %A
--R              (x - 2)    (x - 2)      2
--R                                    %A  + %A + 1= 0
--R   + 
--R                       37        20
--R                      ---- %A + ----
--R           --+        1029      1029
--R           >          --------------
--R           --+                   2
--R       2                 (x - %A)
--R     %A  + %A + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 11

--S 12 of 18
g::Fx - f
 

   (12)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (12)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 12

--S 13 of 18
f:Fx := (2*x**7-7*x**5+26*x**3+8*x)/(x**8-5*x**6+6*x**4+4*x**2-8)
 

             7     5      3
           2x  - 7x  + 26x  + 8x
   (13)  ------------------------
          8     6     4     2
         x  - 5x  + 6x  + 4x  - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             7     5      3
--R           2x  - 7x  + 26x  + 8x
--R   (13)  ------------------------
--R          8     6     4     2
--R         x  - 5x  + 6x  + 4x  - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 13

--S 14 of 18
g := fullPartialFraction f
 

                        1                                            1
                        -                                            -
            --+         2        --+          1          --+         2
   (14)     >        ------ +    >        --------- +    >        ------
            --+      x - %A      --+              3      --+      x - %A
           2                    2         (x - %A)      2
         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R                        1                                            1
--R                        -                                            -
--R            --+         2        --+          1          --+         2
--R   (14)     >        ------ +    >        --------- +    >        ------
--R            --+      x - %A      --+              3      --+      x - %A
--R           2                    2         (x - %A)      2
--R         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 14

--S 15 of 18
g::Fx - f
 

   (15)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (15)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 15

--S 16 of 18
f:Fx := x**3/(x**21+2*x**20+4*x**19+7*x**18+10*x**17+17*x**16+22*x**15+30*x**14
                +36*x**13+40*x**12+47*x**11+46*x**10+49*x**9+43*x**8+38*x**7
                  +32*x**6+23*x**5+19*x**4+10*x**3+7*x**2+2*x+1)
 

   (16)
      3
     x
  /
        21     20     19     18      17      16      15      14      13      12
       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
     + 
          11      10      9      8      7      6      5      4      3     2
       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
     + 
       1
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (16)
--R      3
--R     x
--R  /
--R        21     20     19     18      17      16      15      14      13      12
--R       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
--R     + 
--R          11      10      9      8      7      6      5      4      3     2
--R       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
--R     + 
--R       1
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 16

--S 17 of 18
g := fullPartialFraction f
 

   (17)
                  1                        1      19
                  - %A                     - %A - --
        --+       2             --+        9      27
        >        ------ +       >          ---------
        --+      x - %A         --+          x - %A
       2                    2
     %A  + 1= 0           %A  + %A + 1= 0
   + 
                       1       1
                      -- %A - --
           --+        27      27
           >          ----------
           --+                 2
       2               (x - %A)
     %A  + %A + 1= 0
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
               96556567040   4   420961732891   3    59101056149   2
            - ------------ %A  + ------------ %A  - ------------ %A
              912390759099       912390759099       912390759099
          + 
              373545875923      529673492498
            - ------------ %A + ------------
              912390759099      912390759099
       /
          x - %A
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
           5580868   4    2024443   3    4321919   2    84614        5070620
        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
          94070601       94070601       94070601       1542141      94070601
        --------------------------------------------------------------------
                                              2
                                      (x - %A)
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
         1610957   4    2763014   3    2016775   2    266953        4529359
        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
        94070601       94070601       94070601       94070601      94070601
        -------------------------------------------------------------------
                                             3
                                     (x - %A)
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (17)
--R                  1                        1      19
--R                  - %A                     - %A - --
--R        --+       2             --+        9      27
--R        >        ------ +       >          ---------
--R        --+      x - %A         --+          x - %A
--R       2                    2
--R     %A  + 1= 0           %A  + %A + 1= 0
--R   + 
--R                       1       1
--R                      -- %A - --
--R           --+        27      27
--R           >          ----------
--R           --+                 2
--R       2               (x - %A)
--R     %A  + %A + 1= 0
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R               96556567040   4   420961732891   3    59101056149   2
--R            - ------------ %A  + ------------ %A  - ------------ %A
--R              912390759099       912390759099       912390759099
--R          + 
--R              373545875923      529673492498
--R            - ------------ %A + ------------
--R              912390759099      912390759099
--R       /
--R          x - %A
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R           5580868   4    2024443   3    4321919   2    84614        5070620
--R        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
--R          94070601       94070601       94070601       1542141      94070601
--R        --------------------------------------------------------------------
--R                                              2
--R                                      (x - %A)
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R         1610957   4    2763014   3    2016775   2    266953        4529359
--R        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
--R        94070601       94070601       94070601       94070601      94070601
--R        -------------------------------------------------------------------
--R                                             3
--R                                     (x - %A)
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 17

--S 18 of 18
g::Fx - f
 

   (18)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (18)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 18
)spool 
 
Starts dribbling to expr.output (2010/3/27, 18:25:45).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 29
foo := operator 'foo
 

   (1)  foo
                                                          Type: BasicOperator
--R 
--R
--R   (1)  foo
--R                                                          Type: BasicOperator
--E 1

--S 2 of 29
bar := operator 'bar
 

   (2)  bar
                                                          Type: BasicOperator
--R 
--R
--R   (2)  bar
--R                                                          Type: BasicOperator
--E 2

--S 3 of 29
g := foo x
 

   (3)  foo(x)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  foo(x)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 29
eval(g, x = x**2 + 1)
 

             2
   (4)  foo(x  + 1)
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (4)  foo(x  + 1)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 29
differentiate(%, x)
 

             ,  2
   (5)  2xfoo (x  + 1)

                                                     Type: Expression Integer
--R 
--R
--R             ,  2
--R   (5)  2xfoo (x  + 1)
--R
--R                                                     Type: Expression Integer
--E 5

--S 6 of 29
f := bar(x, y)
 

   (6)  bar(x,y)
                                                     Type: Expression Integer
--R 
--R
--R   (6)  bar(x,y)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 29
eval(f, [x = y, y = x])
 

   (7)  bar(y,x)
                                                     Type: Expression Integer
--R 
--R
--R   (7)  bar(y,x)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 29
[differentiate(f, x), differentiate(f, y)]
 

   (8)  [bar  (x,y),bar  (x,y)]
            ,1         ,2
                                                Type: List Expression Integer
--R 
--R
--R   (8)  [bar  (x,y),bar  (x,y)]
--R            ,1         ,2
--R                                                Type: List Expression Integer
--E 8

--S 9 of 29
ff := eval(f, [x = x**2 * foo y, y = x + y])
 

             2
   (9)  bar(x foo(y),y + x)
                                                     Type: Expression Integer
--R 
--R
--R             2
--R   (9)  bar(x foo(y),y + x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 29
differentiate(ff, x)
 

                2                                2
   (10)  bar  (x foo(y),y + x) + 2x foo(y)bar  (x foo(y),y + x)
            ,2                               ,1
                                                     Type: Expression Integer
--R 
--R
--R                2                                2
--R   (10)  bar  (x foo(y),y + x) + 2x foo(y)bar  (x foo(y),y + x)
--R            ,2                               ,1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 29
differentiate(ff, y)
 

                2                 2       2                ,
   (11)  bar  (x foo(y),y + x) + x bar  (x foo(y),y + x)foo (y)
            ,2                        ,1
                                                     Type: Expression Integer
--R 
--R
--R                2                 2       2                ,
--R   (11)  bar  (x foo(y),y + x) + x bar  (x foo(y),y + x)foo (y)
--R            ,2                        ,1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 29
pbar(l:List OUTFORM):OUTFORM == infix(" @ "::SYMBOL::OUTFORM, l)
 
   Function declaration pbar : List OutputForm -> OutputForm has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration pbar : List OutputForm -> OutputForm has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 12

--S 13 of 29
display(bar, pbar)
 
   Compiling function pbar with type List OutputForm -> OutputForm 

   (13)  bar
                                                          Type: BasicOperator
--R 
--R   Compiling function pbar with type List OutputForm -> OutputForm 
--R
--R   (13)  bar
--R                                                          Type: BasicOperator
--E 13

--S 14 of 29
f
 

   (14)  x @ y
                                                     Type: Expression Integer
--R 
--R
--R   (14)  x @ y
--R                                                     Type: Expression Integer
--E 14

--S 15 of 29
ff
 

          2
   (15)  x foo(y) @ y + x
                                                     Type: Expression Integer
--R 
--R
--R          2
--R   (15)  x foo(y) @ y + x
--R                                                     Type: Expression Integer
--E 15

--S 16 of 29
deleteProperty(bar, "%display")
 
   There are no library operations named deleteProperty 
      Use HyperDoc Browse or issue
                           )what op deleteProperty
      to learn if there is any operation containing " deleteProperty " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      deleteProperty with argument type(s) 
                                BasicOperator
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named deleteProperty 
--R      Use HyperDoc Browse or issue
--R                           )what op deleteProperty
--R      to learn if there is any operation containing " deleteProperty " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      deleteProperty with argument type(s) 
--R                                BasicOperator
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 16

--S 17 of 29
f
 

   (16)  x @ y
                                                     Type: Expression Integer
--R 
--R
--R   (16)  x @ y
--R                                                     Type: Expression Integer
--E 17

--S 18 of 29
bar1 l == last l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 29
bar2 l == first l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 29
derivative(bar, [bar1, bar2]$(LIST(LIST(EXPR INT) -> EXPR INT)))
 
   Compiling function bar1 with type List Expression Integer -> 
      Expression Integer 
   Compiling function bar2 with type List Expression Integer -> 
      Expression Integer 

   (19)  bar
                                                          Type: BasicOperator
--R 
--R   Compiling function bar1 with type List Expression Integer -> 
--R      Expression Integer 
--R   Compiling function bar2 with type List Expression Integer -> 
--R      Expression Integer 
--R
--R   (19)  bar
--R                                                          Type: BasicOperator
--E 20

--S 21 of 29
[differentiate(f, x), differentiate(f, y)]
 

   (20)  [y,x]
                                                Type: List Expression Integer
--R 
--R
--R   (20)  [y,x]
--R                                                Type: List Expression Integer
--E 21

--S 22 of 29
[differentiate(ff, x), differentiate(ff, y)]
 

                    2          2     3    ,       2
   (21)  [(2x y + 3x )foo(y),(x y + x )foo (y) + x foo(y)]

                                                Type: List Expression Integer
--R 
--R
--R                    2          2     3    ,       2
--R   (21)  [(2x y + 3x )foo(y),(x y + x )foo (y) + x foo(y)]
--R
--R                                                Type: List Expression Integer
--E 22

--S 23 of 29
h := inv(x + f + g**2)
 

                  1
   (22)  -------------------
               2
         foo(x)  + x @ y + x
                                                     Type: Expression Integer
--R 
--R
--R                  1
--R   (22)  -------------------
--R               2
--R         foo(x)  + x @ y + x
--R                                                     Type: Expression Integer
--E 23

--S 24 of 29
isPower h
 

                     2
   (23)  [val= foo(x)  + x @ y + x,exponent= - 1]
           Type: Union(Record(val: Expression Integer,exponent: Integer),...)
--R 
--R
--R                     2
--R   (23)  [val= foo(x)  + x @ y + x,exponent= - 1]
--R           Type: Union(Record(val: Expression Integer,exponent: Integer),...)
--E 24

--S 25 of 29
y * g**2 * h
 

                      2
              y foo(x)
   (24)  -------------------
               2
         foo(x)  + x @ y + x
                                                     Type: Expression Integer
--R 
--R
--R                      2
--R              y foo(x)
--R   (24)  -------------------
--R               2
--R         foo(x)  + x @ y + x
--R                                                     Type: Expression Integer
--E 25

--S 26 of 29
isTimes %
 

                2            1
   (25)  [foo(x) ,y,-------------------]
                          2
                    foo(x)  + x @ y + x
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                2            1
--R   (25)  [foo(x) ,y,-------------------]
--R                          2
--R                    foo(x)  + x @ y + x
--R                                     Type: Union(List Expression Integer,...)
--E 26

--S 27 of 29
isPlus(denom(h)::EXPR(INT))
 

                2
   (26)  [foo(x) ,x @ y,x]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R                2
--R   (26)  [foo(x) ,x @ y,x]
--R                                     Type: Union(List Expression Integer,...)
--E 27

--S 28 of 29
isExpt(inv(g**2), "foo")
 

   (27)  [var= foo(x),exponent= - 2]
    Type: Union(Record(var: Kernel Expression Integer,exponent: Integer),...)
--R 
--R
--R   (27)  [var= foo(x),exponent= - 2]
--R    Type: Union(Record(var: Kernel Expression Integer,exponent: Integer),...)
--E 28

--S 29 of 29
isExpt(inv(g**2), "bar")
 

   (28)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (28)  "failed"
--R                                                    Type: Union("failed",...)
--E 29
)spool 
 
Starts dribbling to multiple.output (2010/3/27, 18:30:2).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 8
draw(sin(x),x=0..2*%pi)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (1)  TwoDimensionalViewport: "sin x"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (1)  TwoDimensionalViewport: "sin x"
--R                                                 Type: TwoDimensionalViewport
--E 1

--S 2 of 8
v1 := %
 

   (2)  TwoDimensionalViewport: "sin x"
                                                 Type: TwoDimensionalViewport
--R 
--R
--R   (2)  TwoDimensionalViewport: "sin x"
--R                                                 Type: TwoDimensionalViewport
--E 2

--S 3 of 8
draw(cos(x),x=0..2*%pi,curveColor==light red())
 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (3)  TwoDimensionalViewport: "cos x"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %D with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (3)  TwoDimensionalViewport: "cos x"
--R                                                 Type: TwoDimensionalViewport
--E 3

--S 4 of 8
v2 := %
 

   (4)  TwoDimensionalViewport: "cos x"
                                                 Type: TwoDimensionalViewport
--R 
--R
--R   (4)  TwoDimensionalViewport: "cos x"
--R                                                 Type: TwoDimensionalViewport
--E 4

--S 5 of 8
graphs v1
 

   (5)
   [Graph with 1 point list, undefined, undefined, undefined, undefined,
    undefined, undefined, undefined, undefined]
                                     Type: Vector Union(GraphImage,undefined)
--R 
--R
--R   (5)
--R   [Graph with 1 point list, undefined, undefined, undefined, undefined,
--R    undefined, undefined, undefined, undefined]
--R                                     Type: Vector Union(GraphImage,undefined)
--E 5

--g1 := elt(graphs v1,1)::GraphImage
--S 6 of 8
g1 := getGraph(v1,1)
 

   (6)  Graph with 1 point list
                                                             Type: GraphImage
--R 
--R
--R   (6)  Graph with 1 point list
--R                                                             Type: GraphImage
--E 6

--S 7 of 8
putGraph(v2,g1,2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 8
makeViewport2D(v2)
 
   AXIOM2D data being transmitted to the viewport manager...

   (8)  TwoDimensionalViewport: "cos x"
                                                 Type: TwoDimensionalViewport
--R 
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (8)  TwoDimensionalViewport: "cos x"
--R                                                 Type: TwoDimensionalViewport
--E 8
)spool 
 
Starts dribbling to Equation.output (2010/3/27, 18:41:58).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
eq1 := 3*x + 4*y = 5 
 

   (1)  4y + 3x= 5
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (1)  4y + 3x= 5
--R                                            Type: Equation Polynomial Integer
--E 1

--S 2 of 12
eq2 := 2*x + 2*y = 3 
 

   (2)  2y + 2x= 3
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (2)  2y + 2x= 3
--R                                            Type: Equation Polynomial Integer
--E 2

--S 3 of 12
lhs eq1
 

   (3)  4y + 3x
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)  4y + 3x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 12
rhs eq1
 

   (4)  5
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  5
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 12
eq1 + eq2 
 

   (5)  6y + 5x= 8
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (5)  6y + 5x= 8
--R                                            Type: Equation Polynomial Integer
--E 5

--S 6 of 12
eq1 * eq2 
 

          2             2
   (6)  8y  + 14x y + 6x = 15
                                            Type: Equation Polynomial Integer
--R 
--R
--R          2             2
--R   (6)  8y  + 14x y + 6x = 15
--R                                            Type: Equation Polynomial Integer
--E 6

--S 7 of 12
2*eq2 - eq1
 

   (7)  x= 1
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (7)  x= 1
--R                                            Type: Equation Polynomial Integer
--E 7

--S 8 of 12
eq1**2
 

           2             2
   (8)  16y  + 24x y + 9x = 25
                                            Type: Equation Polynomial Integer
--R 
--R
--R           2             2
--R   (8)  16y  + 24x y + 9x = 25
--R                                            Type: Equation Polynomial Integer
--E 8

--S 9 of 12
if x+1 = y then "equal" else "unequal"
 

   (9)  "unequal"
                                                                 Type: String
--R 
--R
--R   (9)  "unequal"
--R                                                                 Type: String
--E 9

--S 10 of 12
eqpol := x+1 = y 
 

   (10)  x + 1= y
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (10)  x + 1= y
--R                                            Type: Equation Polynomial Integer
--E 10

--S 11 of 12
if eqpol then "equal" else "unequal"
 

   (11)  "unequal"
                                                                 Type: String
--R 
--R
--R   (11)  "unequal"
--R                                                                 Type: String
--E 11

--S 12 of 12
eqpol::Boolean
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12
)spool
 
Starts dribbling to bug100.output (2010/3/27, 18:23:20).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 1
integrate((z^a+1)^b,z)
 

           z
         ++     a     b
   (1)   |   (%I  + 1) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           z
--R         ++     a     b
--R   (1)   |   (%I  + 1) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 1
)spool 
 
Starts dribbling to MultivariatePolynomial.output (2010/3/27, 18:46:7).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
m : MPOLY([x,y],INT) := (x^2 - x*y^3 +3*y)^2
 

         4     3 3     6       2     4      2
   (1)  x  - 2y x  + (y  + 6y)x  - 6y x + 9y
                                  Type: MultivariatePolynomial([x,y],Integer)
--R 
--R
--R         4     3 3     6       2     4      2
--R   (1)  x  - 2y x  + (y  + 6y)x  - 6y x + 9y
--R                                  Type: MultivariatePolynomial([x,y],Integer)
--E 1

--S 2 of 9
m :: MPOLY([y,x],INT)
 

         2 6       4     3 3     2     2     4
   (2)  x y  - 6x y  - 2x y  + 9y  + 6x y + x
                                  Type: MultivariatePolynomial([y,x],Integer)
--R 
--R
--R         2 6       4     3 3     2     2     4
--R   (2)  x y  - 6x y  - 2x y  + 9y  + 6x y + x
--R                                  Type: MultivariatePolynomial([y,x],Integer)
--E 2

--S 3 of 9
p : MPOLY([x,y],POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 9
p :: POLY INT
 

   (4)  p
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  p
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 9
% :: MPOLY([a,b],POLY INT)
 

   (5)  p
                       Type: MultivariatePolynomial([a,b],Polynomial Integer)
--R 
--R
--R   (5)  p
--R                       Type: MultivariatePolynomial([a,b],Polynomial Integer)
--E 5

--S 6 of 9
q : UP(x, FRAC MPOLY([y,z],INT))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 9
q := (x^2 - x*(z+1)/y +2)^2 
 

                             2    2
         4   - 2z - 2  3   4y  + z  + 2z + 1  2   - 4z - 4
   (7)  x  + -------- x  + ----------------- x  + -------- x + 4
                 y                  2                 y
                                   y
 Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer))
--R 
--R
--R                             2    2
--R         4   - 2z - 2  3   4y  + z  + 2z + 1  2   - 4z - 4
--R   (7)  x  + -------- x  + ----------------- x  + -------- x + 4
--R                 y                  2                 y
--R                                   y
--R Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer))
--E 7

--S 8 of 9
q :: UP(z, FRAC MPOLY([x,y],INT))
 

   (8)
    2            3     2             2 4       3      2      2            2
   x   2   - 2y x  + 2x  - 4y x     y x  - 2y x  + (4y  + 1)x  - 4y x + 4y
   -- z  + -------------------- z + ---------------------------------------
    2                2                                  2
   y                y                                  y
 Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer))
--R 
--R
--R   (8)
--R    2            3     2             2 4       3      2      2            2
--R   x   2   - 2y x  + 2x  - 4y x     y x  - 2y x  + (4y  + 1)x  - 4y x + 4y
--R   -- z  + -------------------- z + ---------------------------------------
--R    2                2                                  2
--R   y                y                                  y
--R Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer))
--E 8

--S 9 of 9
q :: MPOLY([x,z], FRAC UP(y,INT))
 

                                               2
         4      2     2  3     1  2    2     4y  + 1  2      4     4
   (9)  x  + (- - z - -)x  + (-- z  + -- z + -------)x  + (- - z - -)x + 4
                y     y        2       2         2           y     y
                              y       y         y
 Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer))
--R 
--R
--R                                               2
--R         4      2     2  3     1  2    2     4y  + 1  2      4     4
--R   (9)  x  + (- - z - -)x  + (-- z  + -- z + -------)x  + (- - z - -)x + 4
--R                y     y        2       2         2           y     y
--R                              y       y         y
--R Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer))
--E 9
)spool
 
Starts dribbling to bini.output (2010/3/27, 18:23:13).
)set message test on
 
)set message type off
 
)set message auto off
 
)clear all
 

)clear all
 

--S 1 of 276
t1:=2*y^2*(y^2+x^2)+(b^2-3*a^2)*y^2-2*b*y^2*(x+y)+2*a^2*b*(y+x)_
    -a^2*x^2+a^2*(a^2-b^2)
 

   (1)
     4       3      2           2     2  2     2       2 2     2       2 2    4
   2y  - 2b y  + (2x  - 2b x + b  - 3a )y  + 2a b y - a x  + 2a b x - a b  + a
--R 
--R
--R   (1)
--R     4       3      2           2     2  2     2       2 2     2       2 2    4
--R   2y  - 2b y  + (2x  - 2b x + b  - 3a )y  + 2a b y - a x  + 2a b x - a b  + a
--E 1

--S 2 of 276
t2:=4*y^3+4*y*(y^2+x^2)-2*b*y^2-4*b*y*(y+x)+2*(b^2-3*a^2)*y+2*a^2*b
 

          3       2      2            2     2       2
   (2)  8y  - 6b y  + (4x  - 4b x + 2b  - 6a )y + 2a b
--R 
--R
--R          3       2      2            2     2       2
--R   (2)  8y  - 6b y  + (4x  - 4b x + 2b  - 6a )y + 2a b
--E 2

--S 3 of 276
t3:=4*x*y^2-2*b*y^2-2*a^2*x+2*a^2*b
 

                  2     2      2
   (3)  (4x - 2b)y  - 2a x + 2a b
--R 
--R
--R                  2     2      2
--R   (3)  (4x - 2b)y  - 2a x + 2a b
--E 3

)clear all
 

--S 4 of 276
t1:=8*x^2-2*x*y-6*x*z+3*x+3*y^2-7*y*z+10*y+10*z^2-8*z-4
 

           2                        2                    2
   (1)  10z  + (- 7y - 6x - 8)z + 3y  + (- 2x + 10)y + 8x  + 3x - 4
--R 
--R
--R           2                        2                    2
--R   (1)  10z  + (- 7y - 6x - 8)z + 3y  + (- 2x + 10)y + 8x  + 3x - 4
--E 4

--S 5 of 276
t2:=10*x^2-2*x*y+6*x*z-6*x+9*y^2-y*z-4*y-2*z^2+5*z-9
 

            2                       2                    2
   (2)  - 2z  + (- y + 6x + 5)z + 9y  + (- 2x - 4)y + 10x  - 6x - 9
--R 
--R
--R            2                       2                    2
--R   (2)  - 2z  + (- y + 6x + 5)z + 9y  + (- 2x - 4)y + 10x  - 6x - 9
--E 5

--S 6 of 276
t3:=5*x^2+8*x*y+4*x*z+8*x+9*y^2-6*y*z+2*y-z^2-7*x+5
 

           2                    2                 2
   (3)  - z  + (- 6y + 4x)z + 9y  + (8x + 2)y + 5x  + x + 5
--R 
--R
--R           2                    2                 2
--R   (3)  - z  + (- 6y + 4x)z + 9y  + (8x + 2)y + 5x  + x + 5
--E 6


)clear all
 
--S 7 of 276
t1:=2*(b-1)^2 + 2*(q-p*q+p^2) + c^2*(q-1)^2 -2*b*q + 2*c*d*(1-q)*(q-p)_
    +2*b*p*q*d*(d-c) + b^2*d^2*(1-2*p) + 2*b*d^2*(p-q) + 2*b*d*c*(p-1)_
    +2*b*p*q*(c+1) + (b^2 - 2*b)*p^2*d^2 + 2*b^2*p^2 + 4*b*(1-b)*p_
    + d^2*(p-1)^2
 

   (1)
                2  2
     (- 2c d + c )q
   + 
           2                                         2            2
     ((2b d  + (- 2b + 2)c d + 2b c + 2b - 2)p - 2b d  + 2c d - 2c  - 2b + 2)q
   + 
        2           2     2      2
     ((b  - 2b + 1)d  + 2b  + 2)p
   + 
           2           2                   2            2      2             2
     ((- 2b  + 2b - 2)d  + (2b - 2)c d - 4b  + 4b)p + (b  + 1)d  - 2b c d + c
   + 
       2
     2b  - 4b + 2
--R 
--R
--R   (1)
--R                2  2
--R     (- 2c d + c )q
--R   + 
--R           2                                         2            2
--R     ((2b d  + (- 2b + 2)c d + 2b c + 2b - 2)p - 2b d  + 2c d - 2c  - 2b + 2)q
--R   + 
--R        2           2     2      2
--R     ((b  - 2b + 1)d  + 2b  + 2)p
--R   + 
--R           2           2                   2            2      2             2
--R     ((- 2b  + 2b - 2)d  + (2b - 2)c d - 4b  + 4b)p + (b  + 1)d  - 2b c d + c
--R   + 
--R       2
--R     2b  - 4b + 2
--E 7

--S 8 of 276
t2:=d*(2*p+1)*(q-p) + c*(p+2)*(1-q) + b*(b-2)*d + b*(1-2*b)*p*d_
    +b*c*(q+p-p*q-1) + b*(b+1)*p^2*d
 

   (2)
                                              2            2
     ((2d + (- b - 1)c)p + d + (b - 2)c)q + (b  + b - 2)d p
   + 
           2                            2
     ((- 2b  + b - 1)d + (b + 1)c)p + (b  - 2b)d + (- b + 2)c
--R 
--R
--R   (2)
--R                                              2            2
--R     ((2d + (- b - 1)c)p + d + (b - 2)c)q + (b  + b - 2)d p
--R   + 
--R           2                            2
--R     ((- 2b  + b - 1)d + (b + 1)c)p + (b  - 2b)d + (- b + 2)c
--E 8

--S 9 of 276
t3:=-b^2*(p-1)^2 + 2*p*(p-q) - 2*(q-1)
 

                          2      2     2     2
   (3)  (- 2p - 2)q + (- b  + 2)p  + 2b p - b  + 2
--R 
--R
--R                          2      2     2     2
--R   (3)  (- 2p - 2)q + (- b  + 2)p  + 2b p - b  + 2
--E 9

--S 10 of 276
t4:=b^2 + 4*(p-q^2) + 3*c^2*(q-1)^2 - 3*d^2*(p-q)^2 + 3*b^2*d^2*(p-1)^2_
    +b^2*p*(p-2) + 6*b*d*c*(p+q+q*p-1)
 

   (4)
          2     2      2       2                         2
     (- 3d  + 3c  - 4)q  + ((6d  + 6b c d)p + 6b c d - 6c )q
   + 
         2      2    2  2        2 2              2           2 2              2
     ((3b  - 3)d  + b )p  + (- 6b d  + 6b c d - 2b  + 4)p + 3b d  - 6b c d + 3c
   + 
      2
     b
--R 
--R
--R   (4)
--R          2     2      2       2                         2
--R     (- 3d  + 3c  - 4)q  + ((6d  + 6b c d)p + 6b c d - 6c )q
--R   + 
--R         2      2    2  2        2 2              2           2 2              2
--R     ((3b  - 3)d  + b )p  + (- 6b d  + 6b c d - 2b  + 4)p + 3b d  - 6b c d + 3c
--R   + 
--R      2
--R     b
--E 10


)clear all
 

--S 11 of 276
t1:=a*x^2+b*x*y+c*x+d*y^2+e*y+f
 

           2                   2
   (1)  d y  + (b x + e)y + a x  + c x + f
--R 
--R
--R           2                   2
--R   (1)  d y  + (b x + e)y + a x  + c x + f
--E 11

--S 12 of 276
t2:=b*x^2+4*d*x*y+2*e*x+g*y^2+h*y+k
 

           2                    2
   (2)  g y  + (4d x + h)y + b x  + 2e x + k
--R 
--R
--R           2                    2
--R   (2)  g y  + (4d x + h)y + b x  + 2e x + k
--E 12

)clear all
 

--S 13 of 276
t1:=x^2+a*y*z+d*x+g
 

                 2
   (1)  a y z + x  + d x + g
--R 
--R
--R                 2
--R   (1)  a y z + x  + d x + g
--E 13

--S 14 of 276
t2:=y^2+b*z*x+e*y+h
 

                 2
   (2)  b x z + y  + e y + h
--R 
--R
--R                 2
--R   (2)  b x z + y  + e y + h
--E 14

--S 15 of 276
t3:=z^2+c*x*y+f*z+k
 

         2
   (3)  z  + f z + c x y + k
--R 
--R
--R         2
--R   (3)  z  + f z + c x y + k
--E 15

)clear all
 

--S 16 of 276
t1:=(x^2-A)^2 + (x^3+b*x-B)*(x^3+b*x-B-a)^2
 

   (1)
      9       7               6     2 5                      4
     x  + 3b x  + (- 2a - 3B)x  + 3b x  + ((- 4a - 6B)b + 1)x
   + 
       3    2            2  3                2       2     2            2
     (b  + a  + 4B a + 3B )x  + ((- 2a - 3B)b  - 2A)x  + (a  + 4B a + 3B )b x
   + 
          2     2     3    2
     - B a  - 2B a - B  + A
--R 
--R
--R   (1)
--R      9       7               6     2 5                      4
--R     x  + 3b x  + (- 2a - 3B)x  + 3b x  + ((- 4a - 6B)b + 1)x
--R   + 
--R       3    2            2  3                2       2     2            2
--R     (b  + a  + 4B a + 3B )x  + ((- 2a - 3B)b  - 2A)x  + (a  + 4B a + 3B )b x
--R   + 
--R          2     2     3    2
--R     - B a  - 2B a - B  + A
--E 16

--S 17 of 276
t2:=4*x*(x^2-A)+(3*x^2+b)*(x^3+b*x-B-a)*(3*(x^3+b*x-B)-a)
 

   (2)
       8        6                 5      2 4                        3
     9x  + 21b x  + (- 12a - 18B)x  + 15b x  + ((- 16a - 24B)b + 4)x
   + 
        3     2             2  2                2            2            2
     (3b  + 3a  + 12B a + 9B )x  + ((- 4a - 6B)b  - 4A)x + (a  + 4B a + 3B )b
--R 
--R
--R   (2)
--R       8        6                 5      2 4                        3
--R     9x  + 21b x  + (- 12a - 18B)x  + 15b x  + ((- 16a - 24B)b + 4)x
--R   + 
--R        3     2             2  2                2            2            2
--R     (3b  + 3a  + 12B a + 9B )x  + ((- 4a - 6B)b  - 4A)x + (a  + 4B a + 3B )b
--E 17

--S 18 of 276
t3:=12*x^2-4*A+6*x*(x^3+b*x-B-a)^2+4*(3*x^2+b)^2*(x^3+b*x-B-a)_
    +2*(x^3+b*x-B)*(3*x^2+b)^2+12*x*(x^3+b*x-B)*(x^3+b*x-B-a)
 

   (3)
        7         5                 4      2 3                         2
     72x  + 126b x  + (- 60a - 90B)x  + 60b x  + ((- 48a - 72B)b + 12)x
   + 
        3     2              2                 2
     (6b  + 6a  + 24B a + 18B )x + (- 4a - 6B)b  - 4A
--R 
--R
--R   (3)
--R        7         5                 4      2 3                         2
--R     72x  + 126b x  + (- 60a - 90B)x  + 60b x  + ((- 48a - 72B)b + 12)x
--R   + 
--R        3     2              2                 2
--R     (6b  + 6a  + 24B a + 18B )x + (- 4a - 6B)b  - 4A
--E 18

--S 19 of 276
t4:=24*x+6*(x^3+b*x-B-a)^2+72*x*(x^3+b*x-B-a)*(3*x^2+b)+6*(3*x^2+b)^3_
    +36*x*(x^3+b*x-B)*(3*x^2+b)+12*(x^3+b*x-B)*(x^3+b*x-B-a)
 

   (4)
         6         4                   3       2 2
     504x  + 630b x  + (- 240a - 360B)x  + 180b x  + ((- 96a - 144B)b + 24)x
   + 
       3     2              2
     6b  + 6a  + 24B a + 18B
--R 
--R
--R   (4)
--R         6         4                   3       2 2
--R     504x  + 630b x  + (- 240a - 360B)x  + 180b x  + ((- 96a - 144B)b + 24)x
--R   + 
--R       3     2              2
--R     6b  + 6a  + 24B a + 18B
--E 19

)clear all
 

--S 20 of 276
t1:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1
 

                    4        2
   (1)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--R 
--R
--R                    4        2
--R   (1)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--E 20

--S 21 of 276
t2:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2
 

                    4        2
   (2)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--R 
--R
--R                    4        2
--R   (2)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--E 21

--S 22 of 276
t3:=2*z2+6*a*y2+20*y2^3+2*c
 

                  3
   (3)  2z2 + 20y2  + 6a y2 + 2c
--R 
--R
--R                  3
--R   (3)  2z2 + 20y2  + 6a y2 + 2c
--E 22

--S 23 of 276
t4:=3*z1^2+y1^2+b
 

           2     2
   (4)  3z1  + y1  + b
--R 
--R
--R           2     2
--R   (4)  3z1  + y1  + b
--E 23

--S 24 of 276
t5:=3*z2^2+y2^2+b
 

           2     2
   (5)  3z2  + y2  + b
--R 
--R
--R           2     2
--R   (5)  3z2  + y2  + b
--E 24

)clear all
 

--S 25 of 276
t1:=3*z1^2+y1^2+b
 

           2     2
   (1)  3z1  + y1  + b
--R 
--R
--R           2     2
--R   (1)  3z1  + y1  + b
--E 25

--S 26 of 276
t2:=3*z1^2+y2^2+b
 

           2     2
   (2)  3z1  + y2  + b
--R 
--R
--R           2     2
--R   (2)  3z1  + y2  + b
--E 26

--S 27 of 276
t3:=3*z3^2+y3^2+b
 

           2     2
   (3)  3z3  + y3  + b
--R 
--R
--R           2     2
--R   (3)  3z3  + y3  + b
--E 27

--S 28 of 276
t4:=y1^2*z1+2*a*y1^3+4*y1^5+c*y1^2-z1^3-b*z1-y2^2*z2-2*a*y2^3_
    -4*y2^5-c*y2^2+z2^3+b*z2
 

   (4)
       3        2            3      2             5        3       2      5
     z2  + (- y2  + b)z2 - z1  + (y1  - b)z1 - 4y2  - 2a y2  - c y2  + 4y1
   + 
          3       2
     2a y1  + c y1
--R 
--R
--R   (4)
--R       3        2            3      2             5        3       2      5
--R     z2  + (- y2  + b)z2 - z1  + (y1  - b)z1 - 4y2  - 2a y2  - c y2  + 4y1
--R   + 
--R          3       2
--R     2a y1  + c y1
--E 28

--S 29 of 276
t5:=y2^2*z2+2*a*y2^3+4*y2^5+c*y2^2-z2^3-b*z2-y3^2*z3-2*a*y3^3_
    -4*y3^5-c*y3^2+z3^3+b*z3
 

   (5)
       3        2            3      2             5        3       2      5
     z3  + (- y3  + b)z3 - z2  + (y2  - b)z2 - 4y3  - 2a y3  - c y3  + 4y2
   + 
          3       2
     2a y2  + c y2
--R 
--R
--R   (5)
--R       3        2            3      2             5        3       2      5
--R     z3  + (- y3  + b)z3 - z2  + (y2  - b)z2 - 4y3  - 2a y3  - c y3  + 4y2
--R   + 
--R          3       2
--R     2a y2  + c y2
--E 29

--S 30 of 276
t6:=y3^2*z3+2*a*y3^3+4*y3^5+c*y3^2-z3^3-b*z3-y1^2*z1-2*a*y1^3_
    -4*y1^5-c*y1^2+z1^3+b*z1
 

   (6)
         3      2            3        2             5        3       2      5
     - z3  + (y3  - b)z3 + z1  + (- y1  + b)z1 + 4y3  + 2a y3  + c y3  - 4y1
   + 
            3       2
     - 2a y1  - c y1
--R 
--R
--R   (6)
--R         3      2            3        2             5        3       2      5
--R     - z3  + (y3  - b)z3 + z1  + (- y1  + b)z1 + 4y3  + 2a y3  + c y3  - 4y1
--R   + 
--R            3       2
--R     - 2a y1  - c y1
--E 30

)clear all
 

--S 31 of 276
t1:=3*z1^2+y1^2+b
 

           2     2
   (1)  3z1  + y1  + b
--R 
--R
--R           2     2
--R   (1)  3z1  + y1  + b
--E 31

--S 32 of 276
t2:=3*z2^2+y2^2+b
 

           2     2
   (2)  3z2  + y2  + b
--R 
--R
--R           2     2
--R   (2)  3z2  + y2  + b
--E 32

--S 33 of 276
t3:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1
 

                    4        2
   (3)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--R 
--R
--R                    4        2
--R   (3)  2y1 z1 + 5y1  + 3a y1  + 2c y1 + x
--E 33

--S 34 of 276
t4:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2
 

                    4        2
   (4)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--R 
--R
--R                    4        2
--R   (4)  2y2 z2 + 5y2  + 3a y2  + 2c y2 + x
--E 34

--S 35 of 276
t5:=x*y1+z1^3+y1^2*z1+a*y1^3+y1^5+b*z1+c*y1^2-x*y2-z2^3-y2^2*z2_
    -a*y2^3-y2^5-b*z2-c*y2^2
 

   (5)
         3        2            3      2            5       3       2
     - z2  + (- y2  - b)z2 + z1  + (y1  + b)z1 - y2  - a y2  - c y2  - x y2
   + 
       5       3       2
     y1  + a y1  + c y1  + x y1
--R 
--R
--R   (5)
--R         3        2            3      2            5       3       2
--R     - z2  + (- y2  - b)z2 + z1  + (y1  + b)z1 - y2  - a y2  - c y2  - x y2
--R   + 
--R       5       3       2
--R     y1  + a y1  + c y1  + x y1
--E 35

--S 36 of 276
t6:=(6*z1^2+18*a*z1*y1+6*y1-y1^3*z1+6*c*y1^2*z1-2*y1^2)_
    *(3*z2^2*y2+9*a*y2^2*z2+45*y2^4*z2-y2^3-3*x*z2+b*y2)_
    -(6*z2^2+18*a*z2*y2+60*y2^3*z2+6*c*y2^2*z2-2*y2^2)_
    *(3*z1^2*y1+9*a*y1^2*z1+45*y1^4*z1-y1^3-3*x*z1+b*y1)
 

   (6)
                        2
         (18y2 - 18y1)z1
       + 
                3         2                    4         2
         ((- 3y1  + 18c y1  + 54a y1)y2 - 270y1  - 54a y1  + 18x)z1
       + 
               2                3
         (- 6y1  + 18y1)y2 + 6y1  - 6b y1
    *
         2
       z2
   + 
               4           3                     2                     2
         (270y2  - 180y1 y2  + (- 18c y1 + 54a)y2  - 54a y1 y2 - 18x)z1
       + 
                    3          2             4
             (- 45y1  + 270c y1  + 810a y1)y2
           + 
                      4          2          3
             (- 2700y1  - 540a y1  + 180x)y2
           + 
                       4        3       2             2
             (- 270c y1  - 9a y1  + 162a y1 + 18c x)y2
           + 
                       4       2  2                   3           2
             (- 810a y1  - 162a y1  + 54a x)y2 + 3x y1  - 18c x y1  - 54a x y1
        *
           z1
       + 
                2           4        3            3
         (- 90y1  + 270y1)y2  + (60y1  - 60b y1)y2
       + 
               3         2                      2          3
         (6c y1  - 18a y1  + (- 6b c + 54a)y1)y2  + (18a y1  - 18a b y1)y2
       + 
              2
         6x y1  - 18x y1
    *
       z2
   + 
           3         2           2
     (- 6y2  + 6y1 y2  + 6b y2)z1
   + 
            3        2            3        4         2        2
         (y1  - 6c y1  - 18a y1)y2  + (90y1  + 18a y1  - 6x)y2
       + 
                3          2
         (- b y1  + 6b c y1  + 18a b y1)y2
    *
       z1
   + 
         2         3         3           2           2
     (2y1  - 6y1)y2  + (- 2y1  + 2b y1)y2  + (- 2b y1  + 6b y1)y2
--R 
--R
--R   (6)
--R                        2
--R         (18y2 - 18y1)z1
--R       + 
--R                3         2                    4         2
--R         ((- 3y1  + 18c y1  + 54a y1)y2 - 270y1  - 54a y1  + 18x)z1
--R       + 
--R               2                3
--R         (- 6y1  + 18y1)y2 + 6y1  - 6b y1
--R    *
--R         2
--R       z2
--R   + 
--R               4           3                     2                     2
--R         (270y2  - 180y1 y2  + (- 18c y1 + 54a)y2  - 54a y1 y2 - 18x)z1
--R       + 
--R                    3          2             4
--R             (- 45y1  + 270c y1  + 810a y1)y2
--R           + 
--R                      4          2          3
--R             (- 2700y1  - 540a y1  + 180x)y2
--R           + 
--R                       4        3       2             2
--R             (- 270c y1  - 9a y1  + 162a y1 + 18c x)y2
--R           + 
--R                       4       2  2                   3           2
--R             (- 810a y1  - 162a y1  + 54a x)y2 + 3x y1  - 18c x y1  - 54a x y1
--R        *
--R           z1
--R       + 
--R                2           4        3            3
--R         (- 90y1  + 270y1)y2  + (60y1  - 60b y1)y2
--R       + 
--R               3         2                      2          3
--R         (6c y1  - 18a y1  + (- 6b c + 54a)y1)y2  + (18a y1  - 18a b y1)y2
--R       + 
--R              2
--R         6x y1  - 18x y1
--R    *
--R       z2
--R   + 
--R           3         2           2
--R     (- 6y2  + 6y1 y2  + 6b y2)z1
--R   + 
--R            3        2            3        4         2        2
--R         (y1  - 6c y1  - 18a y1)y2  + (90y1  + 18a y1  - 6x)y2
--R       + 
--R                3          2
--R         (- b y1  + 6b c y1  + 18a b y1)y2
--R    *
--R       z1
--R   + 
--R         2         3         3           2           2
--R     (2y1  - 6y1)y2  + (- 2y1  + 2b y1)y2  + (- 2b y1  + 6b y1)y2
--E 36

)clear all
 

--S 37 of 276
t1:=x4*x13 + x5*x14 + x6*(1-x13-x14)
 

   (1)  (- x14 - x13 + 1)x6 + x14 x5 + x13 x4
--R 
--R
--R   (1)  (- x14 - x13 + 1)x6 + x14 x5 + x13 x4
--E 37

--S 38 of 276
t2:=x4*x15 + x5*x16 - x6*(x15+x16)
 

   (2)  (- x16 - x15)x6 + x16 x5 + x15 x4
--R 
--R
--R   (2)  (- x16 - x15)x6 + x16 x5 + x15 x4
--E 38

--S 39 of 276
t3:=x7*x13 + x8*x14 + x9*(1-x13-x14)
 

   (3)  (- x14 - x13 + 1)x9 + x14 x8 + x13 x7
--R 
--R
--R   (3)  (- x14 - x13 + 1)x9 + x14 x8 + x13 x7
--E 39

--S 40 of 276
t4:=x7*x15 + x8*x16 - x9*(x15+x16)-1
 

   (4)  (- x16 - x15)x9 + x16 x8 + x15 x7 - 1
--R 
--R
--R   (4)  (- x16 - x15)x9 + x16 x8 + x15 x7 - 1
--E 40

--S 41 of 276
t5:=x10*x13 + x11*x14 + x12*(1-x13-x14)
 

   (5)  (- x12 + x11)x14 + (- x12 + x10)x13 + x12
--R 
--R
--R   (5)  (- x12 + x11)x14 + (- x12 + x10)x13 + x12
--E 41

--S 42 of 276
t6:=x10*x15 + x11*x16 - x12*(x15+x16)
 

   (6)  (- x12 + x11)x16 + (- x12 + x10)x15
--R 
--R
--R   (6)  (- x12 + x11)x16 + (- x12 + x10)x15
--E 42

--S 43 of 276
t7:=x1*x13 + x2*x14 + x3*(1-x13-x14)
 

   (7)  (- x14 - x13 + 1)x3 + x14 x2 + x1 x13
--R 
--R
--R   (7)  (- x14 - x13 + 1)x3 + x14 x2 + x1 x13
--E 43

--S 44 of 276
t8:=x1*x15 + x2*x16 - x3*(x15+x16)
 

   (8)  (- x16 - x15)x3 + x16 x2 + x1 x15
--R 
--R
--R   (8)  (- x16 - x15)x3 + x16 x2 + x1 x15
--E 44

--S 45 of 276
t9:=x1*x4*x13 + x2*x5*x14 + x3*x6*(1-x13-x14)-1
 

   (9)  (- x14 - x13 + 1)x3 x6 + x14 x2 x5 + x1 x13 x4 - 1
--R 
--R
--R   (9)  (- x14 - x13 + 1)x3 x6 + x14 x2 x5 + x1 x13 x4 - 1
--E 45

--S 46 of 276
t10:=x1*x4*x15 + x2*x5*x16 - x3*x6*(x15+x16)
 

   (10)  (- x16 - x15)x3 x6 + x16 x2 x5 + x1 x15 x4
--R 
--R
--R   (10)  (- x16 - x15)x3 x6 + x16 x2 x5 + x1 x15 x4
--E 46

--S 47 of 276
t11:=x1*x7*x13 + x2*x8*x14 + x3*x9*(1-x13-x14)
 

   (11)  (- x14 - x13 + 1)x3 x9 + x14 x2 x8 + x1 x13 x7
--R 
--R
--R   (11)  (- x14 - x13 + 1)x3 x9 + x14 x2 x8 + x1 x13 x7
--E 47

--S 48 of 276
t12:=x1*x7*x15 + x2*x8*x16 - x3*x9*(x15+x16)
 

   (12)  (- x16 - x15)x3 x9 + x16 x2 x8 + x1 x15 x7
--R 
--R
--R   (12)  (- x16 - x15)x3 x9 + x16 x2 x8 + x1 x15 x7
--E 48

--S 49 of 276
t13:=x1*x10*x13 + x2*x11*x14 + x3*x12*(1-x13-x14)
 

   (13)  (- x12 x14 - x12 x13 + x12)x3 + x11 x14 x2 + x1 x10 x13
--R 
--R
--R   (13)  (- x12 x14 - x12 x13 + x12)x3 + x11 x14 x2 + x1 x10 x13
--E 49

--S 50 of 276
t14:=x1*x10*x15 + x2*x11*x16 - x3*x12*(x15+x16)-1
 

   (14)  (- x12 x16 - x12 x15)x3 + x11 x16 x2 + x1 x10 x15 - 1
--R 
--R
--R   (14)  (- x12 x16 - x12 x15)x3 + x11 x16 x2 + x1 x10 x15 - 1
--E 50

)clear all
 

--S 51 of 276
t1:=2*x^2-2*y^2+2*z^2-2*t^2-1
 

          2     2     2     2
   (1)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          2     2     2     2
--R   (1)  2z  - 2y  + 2x  - 2t  - 1
--E 51

--S 52 of 276
t2:=2*x^3-2*y^3+2*z^3-2*t^3-1
 

          3     3     3     3
   (2)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          3     3     3     3
--R   (2)  2z  - 2y  + 2x  - 2t  - 1
--E 52

--S 53 of 276
t3:=2*x^4-2*y^4+2*z^4-2*t^4-1
 

          4     4     4     4
   (3)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          4     4     4     4
--R   (3)  2z  - 2y  + 2x  - 2t  - 1
--E 53

--S 54 of 276
t4:=2*x^5-2*y^5+2*z^5-2*t^5-1
 

          5     5     5     5
   (4)  2z  - 2y  + 2x  - 2t  - 1
--R 
--R
--R          5     5     5     5
--R   (4)  2z  - 2y  + 2x  - 2t  - 1
--E 54

)clear all
 

--S 55 of 276
t1:=2*x^2-2*y^2+2*z^2-2*t^2+2*u^2-1
 

          2     2     2     2     2
   (1)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          2     2     2     2     2
--R   (1)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 55

--S 56 of 276
t2:=2*x^3-2*y^3+2*z^3-2*t^3+2*u^3-1
 

          3     3     3     3     3
   (2)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          3     3     3     3     3
--R   (2)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 56

--S 57 of 276
t3:=2*x^4-2*y^4+2*z^4-2*t^4+2*u^4-1
 

          4     4     4     4     4
   (3)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          4     4     4     4     4
--R   (3)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 57

--S 58 of 276
t4:=2*x^5-2*y^5+2*z^5-2*t^5+2*u^5-1
 

          5     5     5     5     5
   (4)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          5     5     5     5     5
--R   (4)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 58

--S 59 of 276
t5:=2*x^6-2*y^6+2*z^6-2*t^6+2*u^6-1
 

          6     6     6     6     6
   (5)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--R 
--R
--R          6     6     6     6     6
--R   (5)  2z  - 2y  + 2x  + 2u  - 2t  - 1
--E 59

)clear all
 

--S 60 of 276
t1:=y*w-1/2*z*w+t*w
 

          1
   (1)  - - w z + w y + t w
          2
--R 
--R
--R          1
--R   (1)  - - w z + w y + t w
--R          2
--E 60

--S 61 of 276
t2:=-2/7*u*w^2+10/7*v*w^2-20/7*w^3+t*u-5*t*v+10*t*w
 

          20  3    10     2    2
   (2)  - -- w  + (-- v - - u)w  + 10t w - 5t v + t u
           7        7     7
--R 
--R
--R          20  3    10     2    2
--R   (2)  - -- w  + (-- v - - u)w  + 10t w - 5t v + t u
--R           7        7     7
--E 61

--S 62 of 276
t3:=2/7*y*w^2-2/7*z*w^2+6/7*t*w^2-y*t+z*t-3*t^2
 

           2  2          2  2         6    2     2
   (3)  (- - w  + t)z + (- w  - t)y + - t w  - 3t
           7             7            7
--R 
--R
--R           2  2          2  2         6    2     2
--R   (3)  (- - w  + t)z + (- w  - t)y + - t w  - 3t
--R           7             7            7
--E 62

--S 63 of 276
t4:=-2*v^3+4*u*v*w+5*v^2*w-6*u*w^2-7*v*w^2+15*w^3+42*y*v_
    -14*z*v-63*y*w+21*z*w-42*t*w+147*x
 

   (4)
                                               3               2
     (21w - 14v)z + (- 63w + 42v)y + 147x + 15w  + (- 7v - 6u)w
   + 
        2                    3
     (5v  + 4u v - 42t)w - 2v
--R 
--R
--R   (4)
--R                                               3               2
--R     (21w - 14v)z + (- 63w + 42v)y + 147x + 15w  + (- 7v - 6u)w
--R   + 
--R        2                    3
--R     (5v  + 4u v - 42t)w - 2v
--E 63

--S 64 of 276
t5:=-9/7*u*w^3+45/7*v*w^3-135/7*w^4+2*z*v^2-2*t*v^2-4*z*u*w+10*t*u*w_
    -2*z*v*w-28*t*v*w+4*z*w^2+86*t*w^2-42*y*z+14*z^2+42*y*t_
    -14*z*t-21*x*u+105*x*v-315*x*w
 

   (5)
        2              2                    2
     14z  + (- 42y + 4w  + (- 2v - 4u)w + 2v  - 14t)z + 42t y
   + 
                              135  4    45     9    3        2
     (- 315w + 105v - 21u)x - --- w  + (-- v - - u)w  + 86t w
                               7         7     7
   + 
                              2
     (- 28t v + 10t u)w - 2t v
--R 
--R
--R   (5)
--R        2              2                    2
--R     14z  + (- 42y + 4w  + (- 2v - 4u)w + 2v  - 14t)z + 42t y
--R   + 
--R                              135  4    45     9    3        2
--R     (- 315w + 105v - 21u)x - --- w  + (-- v - - u)w  + 86t w
--R                               7         7     7
--R   + 
--R                              2
--R     (- 28t v + 10t u)w - 2t v
--E 64

--S 65 of 276
t6:=6/7*y*w^3-9/7*z*w^3+36/7*t*w^3-2*x*v^2-4*y*t*w+6*z*t*w_
    -24*t^2*w+4*x*u*w+2*x*v*w-4*x*w^2+56*x*y-35*x*z+84*x*t
 

   (6)
              9  3                   6  3
     (- 35x - - w  + 6t w)z + (56x + - w  - 4t w)y
              7                      7
   + 
          2                  2           36    3      2
     (- 4w  + (2v + 4u)w - 2v  + 84t)x + -- t w  - 24t w
                                          7
--R 
--R
--R   (6)
--R              9  3                   6  3
--R     (- 35x - - w  + 6t w)z + (56x + - w  - 4t w)y
--R              7                      7
--R   + 
--R          2                  2           36    3      2
--R     (- 4w  + (2v + 4u)w - 2v  + 84t)x + -- t w  - 24t w
--R                                          7
--E 65

--S 66 of 276
t7:=2*u*v*w-6*v^2*w-u*w^2+13*v*w^2-5*w^3+14*y*w-28*t*w
 

                  3             2        2
   (7)  14w y - 5w  + (13v - u)w  + (- 6v  + 2u v - 28t)w
--R 
--R
--R                  3             2        2
--R   (7)  14w y - 5w  + (13v - u)w  + (- 6v  + 2u v - 28t)w
--E 66

--S 67 of 276
t8:=u^2*w-3*u*v*w+5*u*w^2+14*y*w-28*t*w
 

                    2              2
   (8)  14w y + 5u w  + (- 3u v + u  - 28t)w
--R 
--R
--R                    2              2
--R   (8)  14w y + 5u w  + (- 3u v + u  - 28t)w
--E 67

--S 68 of 276
t9:=-2*z*u*w-2*t*u*w+4*y*v*w+6*z*v*w-2*t*v*w-16*y*w^2_
    -10*z*w^2+22*t*w^2+42*x*w
 

   (9)
         2                        2                         2
   (- 10w  + (6v - 2u)w)z + (- 16w  + 4v w)y + 42w x + 22t w  + (- 2t v - 2t u)w
--R 
--R
--R   (9)
--R         2                        2                         2
--R   (- 10w  + (6v - 2u)w)z + (- 16w  + 4v w)y + 42w x + 22t w  + (- 2t v - 2t u)w
--E 68

--S 69 of 276
t10:=28/3*y*u*w+8/3*z*u*w-20/3*t*u*w-88/3*y*v*w-8*z*v*w_
    +68/3*t*v*w+52*y*w^2+40/3*z*w^2-44*t*w^2-84*x*w
 

   (10)
      40  2           8             2      88     28                      2
     (-- w  + (- 8v + - u)w)z + (52w  + (- -- v + -- u)w)y - 84w x - 44t w
       3              3                     3      3
   + 
      68       20
     (-- t v - -- t u)w
       3        3
--R 
--R
--R   (10)
--R      40  2           8             2      88     28                      2
--R     (-- w  + (- 8v + - u)w)z + (52w  + (- -- v + -- u)w)y - 84w x - 44t w
--R       3              3                     3      3
--R   + 
--R      68       20
--R     (-- t v - -- t u)w
--R       3        3
--E 69

--S 70 of 276
t11:=-4*y*z*w+10*y*t*w+8*z*t*w-20*t^2*w+12*x*u*w-30*x*v*w+15*x*w^2
 

                                          2                         2
   (11)  (- 4w y + 8t w)z + 10t w y + (15w  + (- 30v + 12u)w)x - 20t w
--R 
--R
--R                                          2                         2
--R   (11)  (- 4w y + 8t w)z + 10t w y + (15w  + (- 30v + 12u)w)x - 20t w
--E 70

--S 71 of 276
t12:=-y^2*w+1/2*y*z*w+y*t*w-z*t*w+2*t^2*w-3*x*u*w+6*x*v*w-3*x*w^2
 

          1                  2                2                    2
   (12)  (- w y - t w)z - w y  + t w y + (- 3w  + (6v - 3u)w)x + 2t w
          2
--R 
--R
--R          1                  2                2                    2
--R   (12)  (- w y - t w)z - w y  + t w y + (- 3w  + (6v - 3u)w)x + 2t w
--R          2
--E 71

--S 72 of 276
t13:=8*x*y*w-4*x*z*w+8*x*t*w
 

   (13)  - 4w x z + 8w x y + 8t w x
--R 
--R
--R   (13)  - 4w x z + 8w x y + 8t w x
--E 72

)clear all
 

--S 73 of 276
t1:=35*y^4-30*x*y^2-210*y^2*z+3*x^2+30*x*z-105*z^2+140*y*t-21*u
 

              2          2              4        2              2
   (1)  - 105z  + (- 210y  + 30x)z + 35y  - 30x y  + 140t y + 3x  - 21u
--R 
--R
--R              2          2              4        2              2
--R   (1)  - 105z  + (- 210y  + 30x)z + 35y  - 30x y  + 140t y + 3x  - 21u
--E 73

--S 74 of 276
t2:=5*x*y^3-140*y^3*z-3*x^2*y+45*x*y*z-420*y*z^2+210*y^2*t_
    -25*x*t+70*z*t+126*y*u
 

   (2)
             2          3                       3         2        2
     - 420y z  + (- 140y  + 45x y + 70t)z + 5x y  + 210t y  + (- 3x  + 126u)y
   + 
     - 25t x
--R 
--R
--R   (2)
--R             2          3                       3         2        2
--R     - 420y z  + (- 140y  + 45x y + 70t)z + 5x y  + 210t y  + (- 3x  + 126u)y
--R   + 
--R     - 25t x
--E 74

)clear all
 

--S 75 of 276
t1:=6*x*y^2*t-x^2*z*t-6*x*y*z*t+3*x*z^2*t-2*z^3*t-6*x*y^2+6*x*y*z-2*x*z^2
 

              3              2                       2                2
   (1)  - 2t z  + (3t - 2)x z  + ((- 6t + 6)x y - t x )z + (6t - 6)x y
--R 
--R
--R              3              2                       2                2
--R   (1)  - 2t z  + (3t - 2)x z  + ((- 6t + 6)x y - t x )z + (6t - 6)x y
--E 75

--S 76 of 276
t2:=-63*x*y^2*t^2+9*x^2*z*t^2+63*x*y*z*t^2+18*y^2*z*t^2-27*x*z^2*t^2_
    -18*y*z^2*t^2+18*z^3*t^2+78*x*y^2*t-78*x*y*z*t-18*y^2*z*t_
    +24*x*z^2*t+18*y*z^2*t-9*z^3*t-15*x*y^2+15*x*y*z-5*x*z^2
 

   (2)
         2       3          2                 2              2
     (18t  - 9t)z  + ((- 18t  + 18t)y + (- 27t  + 24t - 5)x)z
   + 
          2        2       2                    2 2           2               2
     ((18t  - 18t)y  + (63t  - 78t + 15)x y + 9t x )z + (- 63t  + 78t - 15)x y
--R 
--R
--R   (2)
--R         2       3          2                 2              2
--R     (18t  - 9t)z  + ((- 18t  + 18t)y + (- 27t  + 24t - 5)x)z
--R   + 
--R          2        2       2                    2 2           2               2
--R     ((18t  - 18t)y  + (63t  - 78t + 15)x y + 9t x )z + (- 63t  + 78t - 15)x y
--E 76

--S 77 of 276
t3:=18*x^2*y^2*t-3*x^3*z*t-18*x^2*y*z*t+12*x*y^2*z*t+5*x^2*z^2*t_
    -12*x*y*z^2*t+6*x*z^3*t-8*z^4*t-18*x^2*y^2+18*x^2*y*z-12*x*y^2*z_
    -4*x^2*z^2+12*x*y*z^2-6*x*z^3
 

   (3)
           4              3                               2  2
     - 8t z  + (6t - 6)x z  + ((- 12t + 12)x y + (5t - 4)x )z
   + 
                   2                2        3                2 2
     ((12t - 12)x y  + (- 18t + 18)x y - 3t x )z + (18t - 18)x y
--R 
--R
--R   (3)
--R           4              3                               2  2
--R     - 8t z  + (6t - 6)x z  + ((- 12t + 12)x y + (5t - 4)x )z
--R   + 
--R                   2                2        3                2 2
--R     ((12t - 12)x y  + (- 18t + 18)x y - 3t x )z + (18t - 18)x y
--E 77

--S 78 of 276
t4:=-x^2*y*t+3*x*y^2*t+10*y^3*t-15*y^2*z*t+3*y*z^2*t-3*x*y^2-10*y^3+x*y*z_
    +15*y^2*z-5*y*z^2
 

   (4)
              2                 2                      3              2      2
   (3t - 5)y z  + ((- 15t + 15)y  + x y)z + (10t - 10)y  + (3t - 3)x y  - t x y
--R 
--R
--R   (4)
--R              2                 2                      3              2      2
--R   (3t - 5)y z  + ((- 15t + 15)y  + x y)z + (10t - 10)y  + (3t - 3)x y  - t x y
--E 78

)clear all
 

--S 79 of 276
t1:=y*t-y*u-u*b+u*c
 

   (1)  (- u + t)y + (c - b)u
--R 
--R
--R   (1)  (- u + t)y + (c - b)u
--E 79

--S 80 of 276
t2:=2*x*y^2*t-x*y^2*u-2*y^2*t*v+y^2*u*v-x*y*z*a+12*x*t^2*a-4*x*t*u*a_
    -x*u^2*a+y*z*v*a-2*t*u*v*a+u^2*v*a-x*u*w*a+u*v*w*a-6*x*z*a*b
 

   (2)
                                                            2
     ((- a x + a v)y - 6a b x)z + ((- u + 2t)x + (u - 2t)v)y
   + 
                   2                 2                   2
     (- a u w - a u  - 4a t u + 12a t )x + a u v w + (a u  - 2a t u)v
--R 
--R
--R   (2)
--R                                                            2
--R     ((- a x + a v)y - 6a b x)z + ((- u + 2t)x + (u - 2t)v)y
--R   + 
--R                   2                 2                   2
--R     (- a u w - a u  - 4a t u + 12a t )x + a u v w + (a u  - 2a t u)v
--E 80

--S 81 of 276
t3:=x*y^2*z-y^2*z*v+6*x*z*t*a+x*z*u*a-z*u*v*a-2*x*y*z*b+2*y*z*v*b_
    -2*x*u*w*b+2*u*v*w*b-12*x*z*b^2+x*y*z*c-y*z*v*c+x*u*w*c_
    -u*v*w*c+6*x*z*b*c
 

   (3)
                 2                                                        2
         (x - v)y  + ((c - 2b)x + (- c + 2b)v)y + (a u + 6a t + 6b c - 12b )x
       + 
         - a u v
    *
       z
   + 
     (c - 2b)u w x + (- c + 2b)u v w
--R 
--R
--R   (3)
--R                 2                                                        2
--R         (x - v)y  + ((c - 2b)x + (- c + 2b)v)y + (a u + 6a t + 6b c - 12b )x
--R       + 
--R         - a u v
--R    *
--R       z
--R   + 
--R     (c - 2b)u w x + (- c + 2b)u v w
--E 81

--S 82 of 276
t4:=x*y*u-y*u*v+3*x*z*a+3*x*t*b+x*u*b-u*v*b
 

   (4)  3a x z + (u x - u v)y + (b u + 3b t)x - b u v
--R 
--R
--R   (4)  3a x z + (u x - u v)y + (b u + 3b t)x - b u v
--E 82

--S 83 of 276
t5:=5*x^2*y*t-5*x^2*y*u-10*x*y*t*v+10*x*y*u*v+5*y*t*v^2-5*y*u*v^2_
    -6*x^2*z*a-12*x*z*v*a+4*x^2*t*b-7*x^2*u*b+16*x*t*v*b+8*x*u*v*b_
    -2*t*v^2*b-u*v^2*b+8*x^2*t*c+x^2*u*c-10*x*t*v*c-2*x*u*v*c_
    +2*t*v^2*c+u*v^2*c
 

   (5)
            2                            2                                2
     (- 6a x  - 12a v x)z + ((- 5u + 5t)x  + (10u - 10t)v x + (- 5u + 5t)v )y
   + 
                              2
     ((c - 7b)u + (8c + 4b)t)x  + ((- 2c + 8b)u + (- 10c + 16b)t)v x
   + 
                             2
     ((c - b)u + (2c - 2b)t)v
--R 
--R
--R   (5)
--R            2                            2                                2
--R     (- 6a x  - 12a v x)z + ((- 5u + 5t)x  + (10u - 10t)v x + (- 5u + 5t)v )y
--R   + 
--R                              2
--R     ((c - 7b)u + (8c + 4b)t)x  + ((- 2c + 8b)u + (- 10c + 16b)t)v x
--R   + 
--R                             2
--R     ((c - b)u + (2c - 2b)t)v
--E 83

--S 84 of 276
t6:=-9*x^4*t*v*c+9*x^4*u*v*c-18*x^3*t*v^2*c-9*x^3*u*v^2*c+3*x^4*y*t_
    -4*x^4*y*u-9*x^3*y*t*v+10*x^3*y*u*v+9*x^2*y*t*v^2-6*x^2*y*u*v^2_
    -3*x*y*t*v^3-2*x*y*u*v^3+2*y*u*v^4-6*x^4*z*a-45*x^3*z*v*a_
    -27*x^2*z*v^2*a-3*x*z*v^3*a-6*x^4*t*b-2*x^4*u*b-45*x^3*t*v*b_
    +32*x^3*u*v*b-27*x^2*t*v^2*b-30*x^2*u*v^2*b-3*x*t*v^3*b-x*u*v^3*b+u*v^4*b
 

   (6)
            4          3        2 2       3
     (- 6a x  - 45a v x  - 27a v x  - 3a v x)z
   + 
                       4                3               2 2               3
           (- 4u + 3t)x  + (10u - 9t)v x  + (- 6u + 9t)v x  + (- 2u - 3t)v x
         + 
               4
           2u v
    *
       y
   + 
                                    4
     ((9c u - 9c t)v - 2b u - 6b t)x
   + 
                       2                     3                     2 2
     ((- 9c u - 18c t)v  + (32b u - 45b t)v)x  + (- 30b u - 27b t)v x
   + 
                    3         4
     (- b u - 3b t)v x + b u v
--R 
--R
--R   (6)
--R            4          3        2 2       3
--R     (- 6a x  - 45a v x  - 27a v x  - 3a v x)z
--R   + 
--R                       4                3               2 2               3
--R           (- 4u + 3t)x  + (10u - 9t)v x  + (- 6u + 9t)v x  + (- 2u - 3t)v x
--R         + 
--R               4
--R           2u v
--R    *
--R       y
--R   + 
--R                                    4
--R     ((9c u - 9c t)v - 2b u - 6b t)x
--R   + 
--R                       2                     3                     2 2
--R     ((- 9c u - 18c t)v  + (32b u - 45b t)v)x  + (- 30b u - 27b t)v x
--R   + 
--R                    3         4
--R     (- b u - 3b t)v x + b u v
--E 84

--S 85 of 276
t7:=w*b-t*c+u*c-w*c
 

   (7)  (- c + b)w + c u - c t
--R 
--R
--R   (7)  (- c + b)w + c u - c t
--E 85

--S 86 of 276
t8:=-6*z*t*v*a+x*z*w*a-z*v*w*a-2*x*w^2*b+2*v*w^2*b+12*z*v*b^2_
    +x*y*z*c-y*z*v*c+x*w^2*c-v*w^2*c-2*x*z*b*c-4*z*v*b*c+x*z*c^2-z*v*c^2
 

   (8)
                             2                               2             2
     ((c x - c v)y + (a w + c  - 2b c)x - a v w + (- 6a t - c  - 4b c + 12b )v)z
   + 
              2                 2
     (c - 2b)w x + (- c + 2b)v w
--R 
--R
--R   (8)
--R                             2                               2             2
--R     ((c x - c v)y + (a w + c  - 2b c)x - a v w + (- 6a t - c  - 4b c + 12b )v)z
--R   + 
--R              2                 2
--R     (c - 2b)w x + (- c + 2b)v w
--E 86

--S 87 of 276
t9:=-12*t^2*v*a+6*t*u*v*a+2*x*t*w*a-x*u*w*a-2*t*v*w*a+u*v*w*a_
    -x*w^2*a+v*w^2*a+6*z*v*a*b+2*x*y*t*c-x*y*u*c-2*y*t*v*c+y*u*v*c_
    -x*z*a*c+z*v*a*c
 

   (9)
     (- a c x + (a c + 6a b)v)z + ((- c u + 2c t)x + (c u - 2c t)v)y
   + 
         2                            2                                    2
   (- a w  + (- a u + 2a t)w)x + a v w  + (a u - 2a t)v w + (6a t u - 12a t )v
--R 
--R
--R   (9)
--R     (- a c x + (a c + 6a b)v)z + ((- c u + 2c t)x + (c u - 2c t)v)y
--R   + 
--R         2                            2                                    2
--R   (- a w  + (- a u + 2a t)w)x + a v w  + (a u - 2a t)v w + (6a t u - 12a t )v
--E 87

--S 88 of 276
t10:=3*z*v*a+3*t*v*b-x*t*c+t*v*c-x*w*c+v*w*c
 

   (10)  3a v z + (- c w - c t)x + c v w + (c + 3b)t v
--R 
--R
--R   (10)  3a v z + (- c w - c t)x + c v w + (c + 3b)t v
--E 88

--S 89 of 276
t11:=-12*x*z*v*a-6*z*v^2*a-2*x^2*t*b+2*x^2*u*b+16*x*t*v*b-10*x*u*v*b_
    +4*t*v^2*b+8*u*v^2*b+5*x^2*w*b-10*x*v*w*b+5*v^2*w*b-x^2*t*c_
    +x^2*u*c+8*x*t*v*c-2*x*u*v*c-7*t*v^2*c+u*v^2*c-5*x^2*w*c_
    +10*x*v*w*c-5*v^2*w*c
 

   (11)
                      2                                              2
     (- 12a v x - 6a v )z + ((- 5c + 5b)w + (c + 2b)u + (- c - 2b)t)x
   + 
                                                                      2
     ((10c - 10b)v w + ((- 2c - 10b)u + (8c + 16b)t)v)x + (- 5c + 5b)v w
   + 
                                2
     ((c + 8b)u + (- 7c + 4b)t)v
--R 
--R
--R   (11)
--R                      2                                              2
--R     (- 12a v x - 6a v )z + ((- 5c + 5b)w + (c + 2b)u + (- c - 2b)t)x
--R   + 
--R                                                                      2
--R     ((10c - 10b)v w + ((- 2c - 10b)u + (8c + 16b)t)v)x + (- 5c + 5b)v w
--R   + 
--R                                2
--R     ((c + 8b)u + (- 7c + 4b)t)v
--E 89

--S 90 of 276
t12:=-18*x^2*u*v^3*b-9*x*u*v^4*b-9*x^2*u*v^3*c+9*x*u*v^4*c-3*x^3*z*v*a_
    -27*x^2*z*v^2*a-45*x*z*v^3*a-6*z*v^4*a-3*x^3*t*v*b_
    -27*x^2*t*v^2*b-45*x*t*v^3*b-6*t*v^4*b-3*x^3*v*w*b_
    +9*x^2*v^2*w*b-9*x*v^3*w*b+3*v^4*w*b+x^4*t*c-x^3*t*v*c_
    -30*x^2*t*v^2*c+32*x*t*v^3*c-2*t*v^4*c+2*x^4*w*c-2*x^3*v*w*c_
    -6*x^2*v^2*w*c+10*x*v^3*w*c-4*v^4*w*c
 

   (12)
              3        2 2        3        4                  4
     (- 3a v x  - 27a v x  - 45a v x - 6a v )z + (2c w + c t)x
   + 
                                      3
     ((- 2c - 3b)v w + (- c - 3b)t v)x
   + 
                  2                   3                   2  2
     ((- 6c + 9b)v w + (- 9c - 18b)u v  + (- 30c - 27b)t v )x
   + 
                 3                4                 3                 4
     ((10c - 9b)v w + (9c - 9b)u v  + (32c - 45b)t v )x + (- 4c + 3b)v w
   + 
                   4
     (- 2c - 6b)t v
--R 
--R
--R   (12)
--R              3        2 2        3        4                  4
--R     (- 3a v x  - 27a v x  - 45a v x - 6a v )z + (2c w + c t)x
--R   + 
--R                                      3
--R     ((- 2c - 3b)v w + (- c - 3b)t v)x
--R   + 
--R                  2                   3                   2  2
--R     ((- 6c + 9b)v w + (- 9c - 18b)u v  + (- 30c - 27b)t v )x
--R   + 
--R                 3                4                 3                 4
--R     ((10c - 9b)v w + (9c - 9b)u v  + (32c - 45b)t v )x + (- 4c + 3b)v w
--R   + 
--R                   4
--R     (- 2c - 6b)t v
--E 90

)clear all
 

--S 91 of 276
t1:=v*A
 

   (1)  A v
--R 
--R
--R   (1)  A v
--E 91

--S 92 of 276
t2:=u*A+14*B
 

   (2)  A u + 14B
--R 
--R
--R   (2)  A u + 14B
--E 92

--S 93 of 276
t3:=z*A
 

   (3)  A z
--R 
--R
--R   (3)  A z
--E 93

--S 94 of 276
t4:=u*a*A+3*z*A+2*t*A+168*B
 

   (4)  3A z + A a u + 2A t + 168B
--R 
--R
--R   (4)  3A z + A a u + 2A t + 168B
--E 94

--S 95 of 276
t5:=y*A+5*u*B
 

   (5)  A y + 5B u
--R 
--R
--R   (5)  A y + 5B u
--E 95

--S 96 of 276
t6:=5*v*C+21*D
 

   (6)  5C v + 21D
--R 
--R
--R   (6)  5C v + 21D
--E 96

--S 97 of 276
t7:=10*u*C+14*E
 

   (7)  10C u + 14E
--R 
--R
--R   (7)  10C u + 14E
--E 97

--S 98 of 276
t8:=-5*y*C-u*E+105*F
 

   (8)  - 5C y - E u + 105F
--R 
--R
--R   (8)  - 5C y - E u + 105F
--E 98

--S 99 of 276
t9:=5*z*C+2*u*D
 

   (9)  5C z + 2D u
--R 
--R
--R   (9)  5C z + 2D u
--E 99

--S 100 of 276
t10:=-2/7*v^2+t-4*u-A
 

           2  2
   (10)  - - v  - 4u + t - A
           7
--R 
--R
--R           2  2
--R   (10)  - - v  - 4u + t - A
--R           7
--E 100

--S 101 of 276
t11:=-2/7*u^2+y-B
 

             2  2
   (11)  y - - u  - B
             7
--R 
--R
--R             2  2
--R   (11)  y - - u  - B
--R             7
--E 101

--S 102 of 276
t12:=7*u-C
 

   (12)  7u - C
--R 
--R
--R   (12)  7u - C
--E 102

--S 103 of 276
t13:=3/7*v^3-2*t*v+6*u*v-7*z-D
 

                3  3
   (13)  - 7z + - v  + (6u - 2t)v - D
                7
--R 
--R
--R                3  3
--R   (13)  - 7z + - v  + (6u - 2t)v - D
--R                7
--E 103

--S 104 of 276
t14:=9/7*u*v^2-2*t*u+16*u^2-6*z*v-42*y-E
 

                        9    2      2
   (14)  - 6v z - 42y + - u v  + 16u  - 2t u - E
                        7
--R 
--R
--R                        9    2      2
--R   (14)  - 6v z - 42y + - u v  + 16u  - 2t u - E
--R                        7
--E 104

--S 105 of 276
t15:=3/7*u^3-2*y*u+7*x-F
 

                       3  3
   (15)  - 2u y + 7x + - u  - F
                       7
--R 
--R
--R                       3  3
--R   (15)  - 2u y + 7x + - u  - F
--R                       7
--E 105

)clear all
 

--S 106 of 276
t1:=-2*y^3*z+6*x^2*z*t-6*x*y*z*t+3*y^2*z*t-y*z*t^2-6*x^2*t+6*x*y*t-2*y^2*t
 

             3       2              2         2         2                2
   (1)  (- 2y  + 3t y  + (- 6t x - t )y + 6t x )z - 2t y  + 6t x y - 6t x
--R 
--R
--R             3       2              2         2         2                2
--R   (1)  (- 2y  + 3t y  + (- 6t x - t )y + 6t x )z - 2t y  + 6t x y - 6t x
--E 106

--S 107 of 276
t1:=18*x^2*y*z^2-18*x*y^2*z^2+18*y^2*z^2-63*x^2*z^2*t+63*x*y*z^2*t_
    -27*y^2*z^2*t+9*y*z^2*t^2-18*x^2*y*z+18*x*y^2*z-9*y^3*z_
    +78*x^2*z*t-78*x*y*z*t+24*y^2*z*t-15*x^2*t+15*x*y*t-5*y^2*t
 

   (2)
                         2       2             2          2  2
     ((- 18x - 27t + 18)y  + (18x  + 63t x + 9t )y - 63t x )z
   + 
          3               2         2                  2         2
     (- 9y  + (18x + 24t)y  + (- 18x  - 78t x)y + 78t x )z - 5t y  + 15t x y
   + 
            2
     - 15t x
--R 
--R
--R   (2)
--R                         2       2             2          2  2
--R     ((- 18x - 27t + 18)y  + (18x  + 63t x + 9t )y - 63t x )z
--R   + 
--R          3               2         2                  2         2
--R     (- 9y  + (18x + 24t)y  + (- 18x  - 78t x)y + 78t x )z - 5t y  + 15t x y
--R   + 
--R            2
--R     - 15t x
--E 107

--S 108 of 276
t1:=-8*y^4*z+12*x^2*y*z*t-12*x*y^2*z*t+6*y^3*z*t+18*x^2*z*t^2_
    -18*x*y*z*t^2+5*y^2*z*t^2-3*y*z*t^3-12*x^2*y*t+12*x*y^2*t_
    -6*y^3*t-18*x^2*t^2+18*x*y*t^2-4*y^2*t^2
 

   (3)
          4       3                2  2         2      2      3        2 2
     (- 8y  + 6t y  + (- 12t x + 5t )y  + (12t x  - 18t x - 3t )y + 18t x )z
   + 
           3              2  2           2      2         2 2
     - 6t y  + (12t x - 4t )y  + (- 12t x  + 18t x)y - 18t x
--R 
--R
--R   (3)
--R          4       3                2  2         2      2      3        2 2
--R     (- 8y  + 6t y  + (- 12t x + 5t )y  + (12t x  - 18t x - 3t )y + 18t x )z
--R   + 
--R           3              2  2           2      2         2 2
--R     - 6t y  + (12t x - 4t )y  + (- 12t x  + 18t x)y - 18t x
--E 108

--S 109 of 276
t1:=10*x^3*z-15*x^2*y*z+3*x*y^3*z+3*x^2*z*t-x*z*t^2-10*x^3+15*x^2*y_
    -5*x*y^2-3*x^2*t+x*y*t
 

   (4)
        3      2       3       2    2          2       2              3       2
   (3x y  - 15x y + 10x  + 3t x  - t x)z - 5x y  + (15x  + t x)y - 10x  - 3t x
--R 
--R
--R   (4)
--R        3      2       3       2    2          2       2              3       2
--R   (3x y  - 15x y + 10x  + 3t x  - t x)z - 5x y  + (15x  + t x)y - 10x  - 3t x
--E 109

)clear all
 

--S 110 of 276
t1:=a-f
 

   (1)  - f + a
--R 
--R
--R   (1)  - f + a
--E 110

--S 111 of 276
t2:=b-g-h
 

   (2)  - h - g + b
--R 
--R
--R   (2)  - h - g + b
--E 111

--S 112 of 276
t3:=c+d+e-1
 

   (3)  e + d + c - 1
--R 
--R
--R   (3)  e + d + c - 1
--E 112

--S 113 of 276
t4:=b*c+a*d-1/2
 

                    1
   (4)  a d + b c - -
                    2
--R 
--R
--R                    1
--R   (4)  a d + b c - -
--R                    2
--E 113

--S 114 of 276
t5:=b^2*c+a^2*d-1/3
 

         2     2    1
   (5)  a d + b c - -
                    3
--R 
--R
--R         2     2    1
--R   (5)  a d + b c - -
--R                    3
--E 114

--S 115 of 276
t6:=a*c*g-1/6
 

                1
   (6)  a c g - -
                6
--R 
--R
--R                1
--R   (6)  a c g - -
--R                6
--E 115

)clear all
 

--S 116 of 276
t1:=d+e+f+g-1
 

   (1)  g + f + e + d - 1
--R 
--R
--R   (1)  g + f + e + d - 1
--E 116

--S 117 of 276
t2:=c*d+b*e+a*f-1/2
 

                          1
   (2)  a f + b e + c d - -
                          2
--R 
--R
--R                          1
--R   (2)  a f + b e + c d - -
--R                          2
--E 117

--S 118 of 276
t3:=c^2*d+b^2*e+a^2*f-1/3
 

         2     2     2    1
   (3)  a f + b e + c d - -
                          3
--R 
--R
--R         2     2     2    1
--R   (3)  a f + b e + c d - -
--R                          3
--E 118

--S 119 of 276
t4:=a*e*i+a*d*l+b*d*m-1/6
 

                                1
   (4)  b d m + a d l + a e i - -
                                6
--R 
--R
--R                                1
--R   (4)  b d m + a d l + a e i - -
--R                                6
--E 119

--S 120 of 276
t5:=c^3*d+b^3*e+a^3*f-1/4
 

         3     3     3    1
   (5)  a f + b e + c d - -
                          4
--R 
--R
--R         3     3     3    1
--R   (5)  a f + b e + c d - -
--R                          4
--E 120

--S 121 of 276
t6:=a*b*e*i+a*c*d*l+b*c*d*m-1/8
 

                                      1
   (6)  b c d m + a c d l + a b e i - -
                                      8
--R 
--R
--R                                      1
--R   (6)  b c d m + a c d l + a b e i - -
--R                                      8
--E 121

--S 122 of 276
t7:=a^2*e*i+a^2*d*l+b^2*d*m-1/2
 

         2       2       2      1
   (7)  b d m + a d l + a e i - -
                                2
--R 
--R
--R         2       2       2      1
--R   (7)  b d m + a d l + a e i - -
--R                                2
--E 122

--S 123 of 276
t8:=a*d*i*m-1/24
 

                   1
   (8)  a d i m - --
                  24
--R 
--R
--R                   1
--R   (8)  a d i m - --
--R                  24
--E 123

--S 124 of 276
t9:=a-h
 

   (9)  - h + a
--R 
--R
--R   (9)  - h + a
--E 124

--S 125 of 276
t10:=b-i-j
 

   (10)  - j - i + b
--R 
--R
--R   (10)  - j - i + b
--E 125

--S 126 of 276
t11:=c-k-l-m
 

   (11)  - m - l - k + c
--R 
--R
--R   (11)  - m - l - k + c
--E 126

)clear all
 

--S 127 of 276
t1:=a*e+b*f+c*g+d*h-1/2
 

                                1
   (1)  d h + c g + b f + a e - -
                                2
--R 
--R
--R                                1
--R   (1)  d h + c g + b f + a e - -
--R                                2
--E 127

--S 128 of 276
t2:=a^2*e+b^2*f+c^2*g+d^2*h-1/3
 

         2     2     2     2    1
   (2)  d h + c g + b f + a e - -
                                3
--R 
--R
--R         2     2     2     2    1
--R   (2)  d h + c g + b f + a e - -
--R                                3
--E 128

--S 129 of 276
t3:=a*f*i+a*g*j+b*g*k+a*h*l+b*h*m+c*h*n-1/6
 

                                                        1
   (3)  c h n + b h m + a h l + b g k + a g j + a f i - -
                                                        6
--R 
--R
--R                                                        1
--R   (3)  c h n + b h m + a h l + b g k + a g j + a f i - -
--R                                                        6
--E 129

--S 130 of 276
t4:=a^3*e+b^3*f+c^3*g+d^3*h-1/4
 

         3     3     3     3    1
   (4)  d h + c g + b f + a e - -
                                4
--R 
--R
--R         3     3     3     3    1
--R   (4)  d h + c g + b f + a e - -
--R                                4
--E 130

--S 131 of 276
t5:=a*b*f*i+a*c*g*j+b*c*g*k+a*d*h*l+b*d*h*m+c*d*h*n-1/8
 

                                                                    1
   (5)  c d h n + b d h m + a d h l + b c g k + a c g j + a b f i - -
                                                                    8
--R 
--R
--R                                                                    1
--R   (5)  c d h n + b d h m + a d h l + b c g k + a c g j + a b f i - -
--R                                                                    8
--E 131

--S 132 of 276
t6:=a^2*f*i+a^2*g*j+b^2*g*k+a^2*h*l+b^2*h*m+c^2*h*n-1/12
 

         2       2       2       2       2       2       1
   (6)  c h n + b h m + a h l + b g k + a g j + a f i - --
                                                        12
--R 
--R
--R         2       2       2       2       2       2       1
--R   (6)  c h n + b h m + a h l + b g k + a g j + a f i - --
--R                                                        12
--E 132

--S 133 of 276
t7:=a*g*i*k+a*h*i*m+a*h*j*n+b*h*k*n-1/24
 

                                                1
   (7)  (b h k + a h j)n + a h i m + a g i k - --
                                               24
--R 
--R
--R                                                1
--R   (7)  (b h k + a h j)n + a h i m + a g i k - --
--R                                               24
--E 133

--S 134 of 276
t8:=a^4*e+b^4*f+c^4*g+d^4*h-1/5
 

         4     4     4     4    1
   (8)  d h + c g + b f + a e - -
                                5
--R 
--R
--R         4     4     4     4    1
--R   (8)  d h + c g + b f + a e - -
--R                                5
--E 134

--S 135 of 276
t9:=a*b^2*f*i+a*c^2*g*j+b*c^2*g*k+ad^2*h*l+b*d^2*h*m+c*d^2*h*n-1/10
 

           2         2        2         2         2         2       1
   (9)  c d h n + b d h m + ad h l + b c g k + a c g j + a b f i - --
                                                                   10
--R 
--R
--R           2         2        2         2         2         2       1
--R   (9)  c d h n + b d h m + ad h l + b c g k + a c g j + a b f i - --
--R                                                                   10
--E 135

--S 136 of 276
t10:=a^2*b*f*i+a^2*c*g*j+b^2*c*g*k+a^3*h*l+b^2*d*h*m+c^2*d*h*n-1/15
 

          2         2         3       2         2         2         1
   (10)  c d h n + b d h m + a h l + b c g k + a c g j + a b f i - --
                                                                   15
--R 
--R
--R          2         2         3       2         2         2         1
--R   (10)  c d h n + b d h m + a h l + b c g k + a c g j + a b f i - --
--R                                                                   15
--E 136

--S 137 of 276
t11:=a*c*g*i*k+a*d*h*i*m+a*d*h*j*n+b*d*h*k*n-1/30
 

                                                         1
   (11)  (b d h k + a d h j)n + a d h i m + a c g i k - --
                                                        30
--R 
--R
--R                                                         1
--R   (11)  (b d h k + a d h j)n + a d h i m + a c g i k - --
--R                                                        30
--E 137

--S 138 of 276
t12:=a^2*f*i^2+a^2*g*j^2+2*a*b*g*j*k+b^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m
    +b^2*h*m^2+2*a*c*h*l*n+2*b*c*h*m*n+c^2*h*n^2-1/20
 

   (12)
      2   2                             2   2                 2   2    2   2
     c h n  + (2b c h m + 2a c h l)n + b h m  + 2a b h l m + a h l  + b g k
   + 
                   2   2    2   2    1
     2a b g j k + a g j  + a f i  - --
                                    20
--R 
--R
--R   (12)
--R      2   2                             2   2                 2   2    2   2
--R     c h n  + (2b c h m + 2a c h l)n + b h m  + 2a b h l m + a h l  + b g k
--R   + 
--R                   2   2    2   2    1
--R     2a b g j k + a g j  + a f i  - --
--R                                    20
--E 138

--S 139 of 276
t13:=a^2*f*i+a^3*g*j+b^3*g*k+a^3*h*l+b^3*h*m+c^3*h*n-1/20
 

          3       3       3       3       3       2       1
   (13)  c h n + b h m + a h l + b g k + a g j + a f i - --
                                                         20
--R 
--R
--R          3       3       3       3       3       2       1
--R   (13)  c h n + b h m + a h l + b g k + a g j + a f i - --
--R                                                         20
--E 139

--S 140 of 276
t14:=a*b*g*i*k+a*b*h*i*m+a*c*h*j*n+b*c*h*k*n-1/40
 

                                                         1
   (14)  (b c h k + a c h j)n + a b h i m + a b g i k - --
                                                        40
--R 
--R
--R                                                         1
--R   (14)  (b c h k + a c h j)n + a b h i m + a b g i k - --
--R                                                        40
--E 140

--S 141 of 276
t15:=a^2*g*i*k+a^2*h*i*m+a^2*h*j*n+b^2*h*k*n-1/60
 

           2       2         2         2         1
   (15)  (b h k + a h j)n + a h i m + a g i k - --
                                                60
--R 
--R
--R           2       2         2         2         1
--R   (15)  (b h k + a h j)n + a h i m + a g i k - --
--R                                                60
--E 141

--S 142 of 276
t16:=a*h*i*k*n-1/120
 

                      1
   (16)  a h i k n - ---
                     120
--R 
--R
--R                      1
--R   (16)  a h i k n - ---
--R                     120
--E 142

)clear all
 

--S 143 of 276
t1:=a*f+b*g+c*h+d*i+e*j-1/2
 

                                      1
   (1)  e j + d i + c h + b g + a f - -
                                      2
--R 
--R
--R                                      1
--R   (1)  e j + d i + c h + b g + a f - -
--R                                      2
--E 143

--S 144 of 276
t2:=a^2*f+b^2*g+c^2*h+d^2*i+e^2*j-1/3
 

         2     2     2     2     2    1
   (2)  e j + d i + c h + b g + a f - -
                                      3
--R 
--R
--R         2     2     2     2     2    1
--R   (2)  e j + d i + c h + b g + a f - -
--R                                      3
--E 144

--S 145 of 276
t3:=t*d*j+a*g*k+a*h*l+b*h*m+a*i*n+b*i*o+c*i*p+a*j*q+b*j*r+c*j*s-1/6
 

   (3)
     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
   + 
             1
     a g k - -
             6
--R 
--R
--R   (3)
--R     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
--R   + 
--R             1
--R     a g k - -
--R             6
--E 145

--S 146 of 276
t4:=a^3*f+b^3*g+c^3*h+d^3*i+e^3*j-1/4
 

         3     3     3     3     3    1
   (4)  e j + d i + c h + b g + a f - -
                                      4
--R 
--R
--R         3     3     3     3     3    1
--R   (4)  e j + d i + c h + b g + a f - -
--R                                      4
--E 146

--S 147 of 276
t5:=t*d*e*j+a*b*g*k+a*c*h*l+b*c*h*m+a*d*i*n+b*d*i*o+c*d*i*p+a*e*j*q_
    +b*e*j*r+c*e*j*s-1/8
 

   (5)
     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
   + 
                                   1
     b c h m + a c h l + a b g k - -
                                   8
--R 
--R
--R   (5)
--R     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
--R   + 
--R                                   1
--R     b c h m + a c h l + a b g k - -
--R                                   8
--E 147

--S 148 of 276
t6:=t*d^2*j+a^2*g*k+a^2*h*l+b^2*h*m+a^2*i*n+b^2*i*o+c^2*i*p+a^2*j*g_
    +b^2*j*r+c^2*j*s-1/12
 

   (6)
      2       2       2       2       2       2       2       2       2
     d j t + c j s + b j r + c i p + b i o + a i n + b h m + a h l + a g k
   + 
      2       1
     a g j - --
             12
--R 
--R
--R   (6)
--R      2       2       2       2       2       2       2       2       2
--R     d j t + c j s + b j r + c i p + b i o + a i n + b h m + a h l + a g k
--R   + 
--R      2       1
--R     a g j - --
--R             12
--E 148

--S 149 of 276
t7:=a*h*k*m+t*a*j*n+t*b*j*o+a*i*k*o+t*c*j*p+a*i*l*p+b*i*m*p+a*j*k*r_
    +a*j*l*s+b*j*m*s-1/24
 

   (7)
     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
   + 
                          1
     a i k o + a h k m - --
                         24
--R 
--R
--R   (7)
--R     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
--R   + 
--R                          1
--R     a i k o + a h k m - --
--R                         24
--E 149

--S 150 of 276
t8:=a^4*f+b^4*g+c^4*h+d^4*i+e^4*j-1/5
 

         4     4     4     4     4    1
   (8)  e j + d i + c h + b g + a f - -
                                      5
--R 
--R
--R         4     4     4     4     4    1
--R   (8)  e j + d i + c h + b g + a f - -
--R                                      5
--E 150

--S 151 of 276
t9:=t*d*e^2*j+a*b^2*g*k+a*c^2*h*l+b*c^2*h*m+a*d^2*i*n+b*d^2*i*o_
    +c*d^2*i*p+a*e^2*j*g+b*e^2*j*r+c*e^2*j*s-1/10
 

   (9)
        2         2         2         2         2         2         2
     d e j t + c e j s + b e j r + c d i p + b d i o + a d i n + b c h m
   + 
        2         2         2       1
     a c h l + a b g k + a e g j - --
                                   10
--R 
--R
--R   (9)
--R        2         2         2         2         2         2         2
--R     d e j t + c e j s + b e j r + c d i p + b d i o + a d i n + b c h m
--R   + 
--R        2         2         2       1
--R     a c h l + a b g k + a e g j - --
--R                                   10
--E 151

--S 152 of 276
t10:=t*d^2*e*j+a^2*b*g*k+a^2*c*h*l+b^2*c*h*m+a^2*d*i*n+b^2*d*i*o_
    +c^2*d*i*p+a^2*e*j*q+b^2*e*j*r+c^2*e*j*s-1/15
 

   (10)
      2         2         2         2         2         2         2
     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
   + 
      2         2         2         1
     b c h m + a c h l + a b g k - --
                                   15
--R 
--R
--R   (10)
--R      2         2         2         2         2         2         2
--R     d e j t + c e j s + b e j r + a e j q + c d i p + b d i o + a d i n
--R   + 
--R      2         2         2         1
--R     b c h m + a c h l + a b g k - --
--R                                   15
--E 152

--S 153 of 276
t11:=a*c*h*k*m+t*a*e*j*n+t*b*e*j*o+a*d*i*k*o+t*c*e*j*p+a*d*i*l*p_
    +b*d*i*m*p+a*e*j*k*r+a*e*j*l*s+b*e*j*m*s-1/30
 

   (11)
     (c e j p + b e j o + a e j n)t + (b e j m + a e j l)s + a e j k r
   + 
                                                     1
     (b d i m + a d i l)p + a d i k o + a c h k m - --
                                                    30
--R 
--R
--R   (11)
--R     (c e j p + b e j o + a e j n)t + (b e j m + a e j l)s + a e j k r
--R   + 
--R                                                     1
--R     (b d i m + a d i l)p + a d i k o + a c h k m - --
--R                                                    30
--E 153

--S 154 of 276
t12:=t^2*d^2*j+a^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m+b^2*h*m^2+a^2*i*n^2_
    +2*a*b*i*n*o+b^2*i*o^2+2*a*c*i*n*p+2*b*c*i*o*p+c^2*i*p^2_
    +2*t*a*d*j*q+a^2*j*q^2+2*t*b*d*j*r+2*a*b*j*q*r+b^2*j*r^2_
    +2*t*c*d*j*s+2*a*c*j*q*s+2*b*c*j*r*s+c^2*j*s^2-1/20
 

   (12)
      2   2                                        2   2
     d j t  + (2c d j s + 2b d j r + 2a d j q)t + c j s
   + 
                               2   2                 2   2    2   2
     (2b c j r + 2a c j q)s + b j r  + 2a b j q r + a j q  + c i p
   + 
                               2   2                 2   2    2   2
     (2b c i o + 2a c i n)p + b i o  + 2a b i n o + a i n  + b h m  + 2a b h l m
   + 
      2   2    2   2    1
     a h l  + a g k  - --
                       20
--R 
--R
--R   (12)
--R      2   2                                        2   2
--R     d j t  + (2c d j s + 2b d j r + 2a d j q)t + c j s
--R   + 
--R                               2   2                 2   2    2   2
--R     (2b c j r + 2a c j q)s + b j r  + 2a b j q r + a j q  + c i p
--R   + 
--R                               2   2                 2   2    2   2
--R     (2b c i o + 2a c i n)p + b i o  + 2a b i n o + a i n  + b h m  + 2a b h l m
--R   + 
--R      2   2    2   2    1
--R     a h l  + a g k  - --
--R                       20
--E 154

--S 155 of 276
t13:=t*d^3*j+a^3*g*k+a^3*h*l+b^3*h*m+a^3*i*n+b^3*i*o+c^3*i*p_
    +a^3*j*q+b^3*j*r+c^3*j*s-1/20
 

   (13)
      3       3       3       3       3       3       3       3       3
     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
   + 
      3       1
     a g k - --
             20
--R 
--R
--R   (13)
--R      3       3       3       3       3       3       3       3       3
--R     d j t + c j s + b j r + a j q + c i p + b i o + a i n + b h m + a h l
--R   + 
--R      3       1
--R     a g k - --
--R             20
--E 155

--S 156 of 276
t14:=a*b*h*k*m+t*a*d*j*n+t*b*d*j*o+a*b*i*k*o+t*c*d*j*p+a*c*i*l*p_
    +b*c*i*m*p+a*b*j*k*r+a*c*j*l*s+b*c*j*m*s-1/40
 

   (14)
     (c d j p + b d j o + a d j n)t + (b c j m + a c j l)s + a b j k r
   + 
                                                     1
     (b c i m + a c i l)p + a b i k o + a b h k m - --
                                                    40
--R 
--R
--R   (14)
--R     (c d j p + b d j o + a d j n)t + (b c j m + a c j l)s + a b j k r
--R   + 
--R                                                     1
--R     (b c i m + a c i l)p + a b i k o + a b h k m - --
--R                                                    40
--E 156

--S 157 of 276
t15:=a^2*h*k*m+t*a^2*j*n+t*b^2*j*o+a^2*i*k*o+t*c^2*j*p+a^2*i*l*p_
    +b^2*i*m*p+a^2*j*k*r+a^2*j*l*s+b^2*j*m*s-1/60
 

   (15)
       2       2       2          2       2         2          2       2
     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
   + 
      2         2         1
     a i k o + a h k m - --
                         60
--R 
--R
--R   (15)
--R       2       2       2          2       2         2          2       2
--R     (c j p + b j o + a j n)t + (b j m + a j l)s + a j k r + (b i m + a i l)p
--R   + 
--R      2         2         1
--R     a i k o + a h k m - --
--R                         60
--E 157

--S 158 of 276
t16:=t*a*j*k*o+t*a*j*l*p+t*b*j*m*p+a*i*k*m*p+a*j*k*m*s-1/20
 

                                                                  1
   (16)  ((b j m + a j l)p + a j k o)t + a j k m s + a i k m p - --
                                                                 20
--R 
--R
--R                                                                  1
--R   (16)  ((b j m + a j l)p + a j k o)t + a j k m s + a i k m p - --
--R                                                                 20
--E 158

)clear all
 

--S 159 of 276
t1:=c^2*p-a*c+c*l+a-p-h
 

          2
   (1)  (c  - 1)p + c l - h - a c + a
--R 
--R
--R          2
--R   (1)  (c  - 1)p + c l - h - a c + a
--E 159

--S 160 of 276
t2:=a*c*h+c^2+c*n+m*h
 

                             2
   (2)  c n + h m + a c h + c
--R 
--R
--R                             2
--R   (2)  c n + h m + a c h + c
--E 160

--S 161 of 276
t3:=-a^2*c+a*c*l+a*c*g-c*l*h+a^2+2*c^2-a*m-a*h+l*h-2
 

                                                      2    2     2
   (3)  - a m + ((- c + 1)h + a c)l - a h + a c g + 2c  - a c + a  - 2
--R 
--R
--R                                                      2    2     2
--R   (3)  - a m + ((- c + 1)h + a c)l - a h + a c g + 2c  - a c + a  - 2
--E 161

--S 162 of 276
t4:=-a*c^2+a*c*j-c^2*m+a*c*n+c^2*v-c*n*h-c*m+n*h
 

         2                              2                    2
   (4)  c v + ((- c + 1)h + a c)n + (- c  - c)m + a c j - a c
--R 
--R
--R         2                              2                    2
--R   (4)  c v + ((- c + 1)h + a c)n + (- c  - c)m + a c j - a c
--E 162

--S 163 of 276
t5:=-c*l*g-a*l-j-1
 

   (5)  (- c g - a)l - j - 1
--R 
--R
--R   (5)  (- c g - a)l - j - 1
--E 163

--S 164 of 276
t6:=-c*n*g-c*l-c*m+j*m+c*g+c*h
 

   (6)  - c g n + (j - c)m - c l + c h + c g
--R 
--R
--R   (6)  - c g n + (j - c)m - c l + c h + c g
--E 164

--S 165 of 276
t7:=-c*j*l-a*j+j*l-a*n+c*g+a-v+g
 

   (7)  - v - a n + (- c + 1)j l - a j + (c + 1)g + a
--R 
--R
--R   (7)  - v - a n + (- c + 1)j l - a j + (c + 1)g + a
--E 165

--S 166 of 276
t8:=-c*j*n+c*j-c*n+j*n
 

   (8)  ((- c + 1)j - c)n + c j
--R 
--R
--R   (8)  ((- c + 1)j - c)n + c j
--E 166

--S 167 of 276
t9:=c*m*p-l*n*p+a*l+l*m+a*p-l*p+c-n-2
 

   (9)  (- l n + c m - l + a)p - n + l m + a l + c - 2
--R 
--R
--R   (9)  (- l n + c m - l + a)p - n + l m + a l + c - 2
--E 167

--S 168 of 276
t10:=-n^2*p+c*l+c*m+2*m*n+c*p-c*h+m
 

             2
   (10)  (- n  + c)p + 2m n + (c + 1)m + c l - c h
--R 
--R
--R             2
--R   (10)  (- n  + c)p + 2m n + (c + 1)m + c l - c h
--E 168

--S 169 of 276
t11:=-l*m*h+a*c+2*c*m-l*n+m*n-c*g-a+p+h
 

   (11)  p + (m - l)n + (- h l + 2c)m + h - c g + a c - a
--R 
--R
--R   (11)  p + (m - l)n + (- h l + 2c)m + h - c g + a c - a
--E 169

--S 170 of 276
t12:=-c*l*m-c*m^2+a*m*n-m^2*n+c*m*v-m*n*h+c^2-c*j-n^2+n
 

                  2       2                         2                  2
   (12)  c m v - n  + (- m  + (- h + a)m + 1)n - c m  - c l m - c j + c
--R 
--R
--R                  2       2                         2                  2
--R   (12)  c m v - n  + (- m  + (- h + a)m + 1)n - c m  - c l m - c j + c
--E 170

--S 171 of 276
t13:=a^2*l-a*l^2+c*n*p-l*m*g-c*l-a*n+2*a-l+m-v+g
 

                                               2           2
   (13)  - v + c n p - a n + (- g l + 1)m - a l  + (- c + a  - 1)l + g + 2a
--R 
--R
--R                                               2           2
--R   (13)  - v + c n p - a n + (- g l + 1)m - a l  + (- c + a  - 1)l + g + 2a
--E 171

--S 172 of 276
t14:=a*c*l-c*l^2+a*m*n-l*m*n-m*n*g+c*l*h-m^2+c*n-n^2+m*v+2*c
 

                2                            2      2
   (14)  m v - n  + ((- l - g + a)m + c)n - m  - c l  + (c h + a c)l + 2c
--R 
--R
--R                2                            2      2
--R   (14)  m v - n  + ((- l - g + a)m + c)n - m  - c l  + (c h + a c)l + 2c
--E 172

--S 173 of 276
t15:=-j*l*m-l*n*v+c*l*g+a*l+c*n+n^2+j+1
 

                    2
   (15)  - l n v + n  + c n - j l m + (c g + a)l + j + 1
--R 
--R
--R                    2
--R   (15)  - l n v + n  + c n - j l m + (c g + a)l + j + 1
--E 173

--S 174 of 276
t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+c*n*v-n^2*v+n*v
 

             2                          2
   (16)  (- n  + (c + 1)n)v + (- m + a)n  + (- j m - c l)n + c j l
--R 
--R
--R             2                          2
--R   (16)  (- n  + (c + 1)n)v + (- m + a)n  + (- j m - c l)n + c j l
--E 174

--S 175 of 276
t17:=-j*l*p+c*m*p+n*p*h-a*l-a*m+a*g-p*g+a*h+c-j+n-1
 

   (17)  (h n + c m - j l - g)p + n - a m - a l - j + a h + a g + c - 1
--R 
--R
--R   (17)  (h n + c m - j l - g)p + n - a m - a l - j + a h + a g + c - 1
--E 175

--S 176 of 276
t18:=-j*n*p+l*m*h-c*l+j*m+c*g+n*h
 

   (18)  - j n p + h n + (h l + j)m - c l + c g
--R 
--R
--R   (18)  - j n p + h n + (h l + j)m - c l + c g
--E 176

--S 177 of 276
t19:=l^2*h-l*h^2+a*c-c*l-j*l+c*m+j*m-n*g+c*h+n*h-a-l-g+h
 

   (19)
                            2           2
   (h - g)n + (j + c)m + h l  + (- j - h  - c - 1)l + (c + 1)h - g + a c - a
--R 
--R
--R   (19)
--R                            2           2
--R   (h - g)n + (j + c)m + h l  + (- j - h  - c - 1)l + (c + 1)h - g + a c - a
--E 177

--S 178 of 276
t20:=a*j*m-j*m^2+c*m*v-c*m*g-c*m*h+l*n*h+n*v*h-n*h^2+c^2-c*n-2*j*n
 

                                     2            2                         2
   (20)  (h n + c m)v + (h l - 2j - h  - c)n - j m  + (a j - c h - c g)m + c
--R 
--R
--R                                     2            2                         2
--R   (20)  (h n + c m)v + (h l - 2j - h  - c)n - j m  + (a j - c h - c g)m + c
--E 178

--S 179 of 276
t21:=j*n*p-l*g*h-j*l-n*g-m+h
 

   (21)  j n p - g n - m + (- j - g h)l + h
--R 
--R
--R   (21)  j n p - g n - m + (- j - g h)l + h
--E 179

--S 180 of 276
t22:=j*l^2-j*l*v-a*n*g+n*g^2-j*l*h+2*j*n+l*g+m*g-v*g+j-1
 

                               2                    2
   (22)  (- j l - g)v + (2j + g  - a g)n + g m + j l  + (- h j + g)l + j - 1
--R 
--R
--R                               2                    2
--R   (22)  (- j l - g)v + (2j + g  - a g)n + g m + j l  + (- h j + g)l + j - 1
--E 180

--S 181 of 276
t23:=j*l*n-j*m*n-c*n*g+j*n*g-j*n*h+j*m
 

   (23)  (- j m + j l + (- h + g)j - c g)n + j m
--R 
--R
--R   (23)  (- j m + j l + (- h + g)j - c g)n + j m
--E 181

--S 182 of 276
t24:=-a^2*p+a*l*p+m^2*p-l*p*v+3*a+2*m-v
 

                          2          2
   (24)  (- l p - 1)v + (m  + a l - a )p + 2m + 3a
--R 
--R
--R                          2          2
--R   (24)  (- l p - 1)v + (m  + a l - a )p + 2m + 3a
--E 182

--S 183 of 276
t25:=-a*c*p+c*l*p-n*p*v+n*p*h-a*m+l*m+m*v-m*h+2*c+2*n
 

   (25)  (- n p + m)v + (h n + c l - a c)p + 2n + (l - h - a)m + 2c
--R 
--R
--R   (25)  (- n p + m)v + (h n + c l - a c)p + 2n + (l - h - a)m + 2c
--E 183

--S 184 of 276
t26:=-a*c*p+n*p*g+l^2-a*m-l*m+m^2+l*p-l*v+m*v-m*g-l*h-p*h+c+n
 

   (26)
                                          2                     2
   (m - l)v + (g n + l - h - a c)p + n + m  + (- l - g - a)m + l  - h l + c
--R 
--R
--R   (26)
--R                                          2                     2
--R   (m - l)v + (g n + l - h - a c)p + n + m  + (- l - g - a)m + l  - h l + c
--E 184

--S 185 of 276
t27:=-c^2*p+j*n*p-2*c*m-j*m+l*n-m*n-n*h
 

                 2
   (27)  (j n - c )p + (- m + l - h)n + (- j - 2c)m
--R 
--R
--R                 2
--R   (27)  (j n - c )p + (- m + l - h)n + (- j - 2c)m
--E 185

--S 186 of 276
t28:=m*n*p+n*p*v-a*l-l*m-a*p-l*v-l*g-p*g
 

   (28)  (n p - l)v + (m n - g - a)p - l m + (- g - a)l
--R 
--R
--R   (28)  (n p - l)v + (m n - g - a)p - l m + (- g - a)l
--E 186

--S 187 of 276
t29:=l*m*h-c*l-c*p-n*g+n*h-m
 

   (29)  - c p + (h - g)n + (h l - 1)m - c l
--R 
--R
--R   (29)  - c p + (h - g)n + (h l - 1)m - c l
--E 187

--S 188 of 276
t30:=l^2*v-l*v^2+l*m*g-j*l-a*n-l*n+m*n-j*p+2*n*v+n*g-v
 

              2          2
   (30)  - l v  + (2n + l  - 1)v - j p + (m - l + g - a)n + g l m - j l
--R 
--R
--R              2          2
--R   (30)  - l v  + (2n + l  - 1)v - j p + (m - l + g - a)n + g l m - j l
--E 188

--S 189 of 276
t31:=j*l*m+l*n*v-c*n-n^2
 

                  2
   (31)  l n v - n  - c n + j l m
--R 
--R
--R                  2
--R   (31)  l n v - n  - c n + j l m
--E 189

)clear all
 
 
--S 190 of 276
t1:=-a*b*k+a*c*k+b*k*l-c*k*l-b^2*p+c^2*p+b*k
 

          2    2
   (1)  (c  - b )p + (- c + b)k l + (a c + (- a + 1)b)k
--R 
--R
--R          2    2
--R   (1)  (c  - b )p + (- c + b)k l + (a c + (- a + 1)b)k
--E 190

--S 191 of 276
t2:=-c^2*k+a*c*l+b*l*m-c*k*n+a*c+c^2+b*m
 

                                        2     2
   (2)  - c k n + (b l + b)m + a c l - c k + c  + a c
--R 
--R
--R                                        2     2
--R   (2)  - c k n + (b l + b)m + a c l - c k + c  + a c
--E 191

--S 192 of 276
t3:=a^2*b-a^2*c+2*b^2*k-2*c^2*k-a*b*l+a*c*l+b*l^2-c*l^2-a*b*m+a*c*m_
-a*b-b^2+c^2+b*l-c*l
 

   (3)
                              2                                   2     2      2
     (a c - a b)m + (- c + b)l  + ((a - 1)c + (- a + 1)b)l + (- 2c  + 2b )k + c
   + 
        2     2     2
     - a c - b  + (a  - a)b
--R 
--R
--R   (3)
--R                              2                                   2     2      2
--R     (a c - a b)m + (- c + b)l  + ((a - 1)c + (- a + 1)b)l + (- 2c  + 2b )k + c
--R   + 
--R        2     2     2
--R     - a c - b  + (a  - a)b
--E 192

--S 193 of 276
t4:=-a*c^2+a*c*j-b*c*m-c^2*m+a*c*n+b*l*n-c*l*n+c^2*v+b*n-c*n
 

         2                                       2                      2
   (4)  c v + ((- c + b)l + (a - 1)c + b)n + (- c  - b c)m + a c j - a c
--R 
--R
--R         2                                       2                      2
--R   (4)  c v + ((- c + b)l + (a - 1)c + b)n + (- c  - b c)m + a c j - a c
--E 193

--S 194 of 276
t5:=b^2*k+b*j*k-a*b*l-c*l*m-b^2
 

                                  2      2
   (5)  - c l m - a b l + (b j + b )k - b
--R 
--R
--R                                  2      2
--R   (5)  - c l m - a b l + (b j + b )k - b
--E 194

--S 195 of 276
t6:=b*j*m-c*m*n+b*c
 

   (6)  - c m n + b j m + b c
--R 
--R
--R   (6)  - c m n + b j m + b c
--E 195

--S 196 of 276
t7:=a*b^2-a*b*j+b*j*l-c*j*l+b^2*m+b*c*m-a*b*n-b^2*v
 

           2                    2                               2
   (7)  - b v - a b n + (b c + b )m + (- c + b)j l - a b j + a b
--R 
--R
--R           2                    2                               2
--R   (7)  - b v - a b n + (b c + b )m + (- c + b)j l - a b j + a b
--E 196

--S 197 of 276
t8:=b*c*j-b*c*n+b*j*n-c*j*n
 

   (8)  ((- c + b)j - b c)n + b c j
--R 
--R
--R   (8)  ((- c + b)j - b c)n + b c j
--E 197

--S 198 of 276
t9:=-2*b*k^2+c*k^2-a*k*l-k*l*m-k^2*n+a*b*p-b*l*p+c*m*p-l*n*p+b*k
 

                                      2                             2
   (9)  (- l n + c m - b l + a b)p - k n - k l m - a k l + (c - 2b)k  + b k
--R 
--R
--R                                      2                             2
--R   (9)  (- l n + c m - b l + a b)p - k n - k l m - a k l + (c - 2b)k  + b k
--E 198

--S 199 of 276
t10:=-b*k*m-c*k*m-2*k*m*n+b*c*p-n^2*p+c*k+b*m+c*m
 

             2
   (10)  (- n  + b c)p - 2k m n + ((- c - b)k + c + b)m + c k
--R 
--R
--R             2
--R   (10)  (- n  + b c)p - 2k m n + ((- c - b)k + c + b)m + c k
--E 199

--S 200 of 276
t11:=a*b*k-a*c*k-b*k*l-c*k*m-l^2*m+k*l*n-k*m*n+b^2*p-b*k+c*m-l*m-l*n
 

   (11)
      2                              2
     b p + (- k m + (k - 1)l)n + (- l  - l - c k + c)m - b k l
   + 
     (- a c + (a - 1)b)k
--R 
--R
--R   (11)
--R      2                              2
--R     b p + (- k m + (k - 1)l)n + (- l  - l - c k + c)m - b k l
--R   + 
--R     (- a c + (a - 1)b)k
--E 200

--S 201 of 276
t12:=-c^2*k+c*j*k-c*l*m-c*m^2-b*k*n+a*m*n-l*m*n-m^2*n+k*n^2+c*m*v+b*n-m*n-n^2
 

   (12)
                     2       2                                   2
     c m v + (k - 1)n  + (- m  + (- l + a - 1)m - b k + b)n - c m  - c l m
   + 
             2
     (c j - c )k
--R 
--R
--R   (12)
--R                     2       2                                   2
--R     c m v + (k - 1)n  + (- m  + (- l + a - 1)m - b k + b)n - c m  - c l m
--R   + 
--R             2
--R     (c j - c )k
--E 201

--S 202 of 276
t13:=-2*a*b*k+a^2*l+b*k*l+c*k*l-a*l^2-2*b*k*m-l*m^2+a*k*n+c*n*p_
    +b*k*v+a*b-b*l-l*n
 

   (13)
                                       2               2                    2
     b k v + c n p + (- l + a k)n - l m  - 2b k m - a l  + ((c + b)k - b + a )l
   + 
     - 2a b k + a b
--R 
--R
--R   (13)
--R                                       2               2                    2
--R     b k v + c n p + (- l + a k)n - l m  - 2b k m - a l  + ((c + b)k - b + a )l
--R   + 
--R     - 2a b k + a b
--E 202

--S 203 of 276
t14:=-2*b*c*k+a*c*l-b*m^2-c*k*n+a*m*n-l*m*n-m^2*n+k*n^2+b*m*v_
    +b*c+c*l+c*n-n^2
 

   (14)
                     2       2                               2
     b m v + (k - 1)n  + (- m  + (- l + a)m - c k + c)n - b m  + (a + 1)c l
   + 
     - 2b c k + b c
--R 
--R
--R   (14)
--R                     2       2                               2
--R     b m v + (k - 1)n  + (- m  + (- l + a)m - c k + c)n - b m  + (a + 1)c l
--R   + 
--R     - 2b c k + b c
--E 203

--S 204 of 276
t15:=-b^2*k-b*j*k+a*b*l+c*l*m-j*l*m-c*k*n-k*n^2-l*n*v+b^2+c*n
 

   (15)
                2                                                   2      2
   - l n v - k n  + (- c k + c)n + (- j + c)l m + a b l + (- b j - b )k + b
--R 
--R
--R   (15)
--R                2                                                   2      2
--R   - l n v - k n  + (- c k + c)n + (- j + c)l m + a b l + (- b j - b )k + b
--E 204

--S 205 of 276
t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+b*n*v+c*n*v-n^2*v
 

             2                          2
   (16)  (- n  + (c + b)n)v + (- m + a)n  + (- j m - c l)n + c j l
--R 
--R
--R             2                          2
--R   (16)  (- n  + (c + b)n)v + (- m + a)n  + (- j m - c l)n + c j l
--E 205

--S 206 of 276
t17:=-b*k^2+c*k^2-j*k^2+k^2*n-j*l*p-b*m*p+c*m*p+l*n*p-a*k+n*p
 

                                         2                  2
   (17)  ((l + 1)n + (c - b)m - j l)p + k n + (- j + c - b)k  - a k
--R 
--R
--R                                         2                  2
--R   (17)  ((l + 1)n + (c - b)m - j l)p + k n + (- j + c - b)k  - a k
--E 206

--S 207 of 276
t18:=c*l*k-c*k*m-j*k*m+l^2*m-k*l*n-j*n*p+c*m+l*m-k*n+l*n+n
 

                                             2
   (18)  - j n p + ((- k + 1)l - k + 1)n + (l  + l + (- j - c)k + c)m + c k l
--R 
--R
--R                                             2
--R   (18)  - j n p + ((- k + 1)l - k + 1)n + (l  + l + (- j - c)k + c)m + c k l
--E 207

--S 208 of 276
t19:=a*b*k-a*c*k+j*k*l+b*k*m-c*k*m-j*k*m-k*l*n+k*m*n_
    -b*k-c*k-j*l-l^2-b*m+c*m-k*n+l*n-l+n
 

   (19)
                                                                2
     (k m + (- k + 1)l - k + 1)n + ((- j - c + b)k + c - b)m - l
   + 
     (j k - j - 1)l + ((- a - 1)c + (a - 1)b)k
--R 
--R
--R   (19)
--R                                                                2
--R     (k m + (- k + 1)l - k + 1)n + ((- j - c + b)k + c - b)m - l
--R   + 
--R     (j k - j - 1)l + ((- a - 1)c + (a - 1)b)k
--E 208

--S 209 of 276
t20:=-c^2*k+a*j*m-c*l*m-c*m^2-j*m^2+c*k*n+2*j*k*n+c*m*v+l*n*v_
    -c*m-j*n-l*n+n*v-n
 

   (20)
                                                                2
     ((l + 1)n + c m)v + (- l + (2j + c)k - j - 1)n + (- j - c)m
   + 
                           2
     (- c l + a j - c)m - c k
--R 
--R
--R   (20)
--R                                                                2
--R     ((l + 1)n + c m)v + (- l + (2j + c)k - j - 1)n + (- j - c)m
--R   + 
--R                           2
--R     (- c l + a j - c)m - c k
--E 209

--S 210 of 276
t21:=-b*k*l+j*k*l+b*k*m-l^2*m+k*m*n+j*n*p-b*k-j*l-b*m-l*m
 

                             2
   (21)  j n p + k m n + (- l  - l + b k - b)m + ((j - b)k - j)l - b k
--R 
--R
--R                             2
--R   (21)  j n p + k m n + (- l  - l + b k - b)m + ((j - b)k - j)l - b k
--E 210

--S 211 of 276
t22:=b^2*k-b*j*k+b*l*m+b*m^2-2*j*k*n-a*m*n+m^2*n-j*l*v-b*m*v-j*l+j*n
 

   (22)
                      2                         2                           2
   (- b m - j l)v + (m  - a m - 2j k + j)n + b m  + b l m - j l + (- b j + b )k
--R 
--R
--R   (22)
--R                      2                         2                           2
--R   (- b m - j l)v + (m  - a m - 2j k + j)n + b m  + b l m - j l + (- b j + b )k
--E 211

--S 212 of 276
t23:=b*j*m-c*m*n-j*n
 

   (23)  (- c m - j)n + b j m
--R 
--R
--R   (23)  (- c m - j)n + b j m
--E 212

--S 213 of 276
t24:=3*a*k^2+2*k^2*m-a^2*p+a*l*p+m^2*p-k^2*v-l*p*v-2*a*k-b*p+n*p
 

                   2           2              2       2        2
   (24)  (- l p - k )v + (n + m  + a l - b - a )p + 2k m + 3a k  - 2a k
--R 
--R
--R                   2           2              2       2        2
--R   (24)  (- l p - k )v + (n + m  + a l - b - a )p + 2k m + 3a k  - 2a k
--E 213

--S 214 of 276
t25:=2*c*k^2+a*k*m+2*k^2*n-a*c*p+c*l*p+l*n*p-k*m*v-n*p*v-c*k-a*m_
    +k*m+l*m+m^2-3*k*n+n*p+n
 

   (25)
                                                   2               2
     (- n p - k m)v + ((l + 1)n + c l - a c)p + (2k  - 3k + 1)n + m
   + 
                               2
     (l + (a + 1)k - a)m + 2c k  - c k
--R 
--R
--R   (25)
--R                                                   2               2
--R     (- n p - k m)v + ((l + 1)n + c l - a c)p + (2k  - 3k + 1)n + m
--R   + 
--R                               2
--R     (l + (a + 1)k - a)m + 2c k  - c k
--E 214

--S 215 of 276
t26:=c*k^2+a*k*m+k*l*m+k^2*n-a*c*p+m*n*p+k*l*v-k*m*v_
    +2*b*k-c*k+k*l-a*m+m^2-2*k*n-b*p-l*v-b-l+n
 

   (26)
                                                2               2
     (- k m + (k - 1)l)v + (m n - a c - b)p + (k  - 2k + 1)n + m
   + 
                                      2
     (k l + a k - a)m + (k - 1)l + c k  + (- c + 2b)k - b
--R 
--R
--R   (26)
--R                                                2               2
--R     (- k m + (k - 1)l)v + (m n - a c - b)p + (k  - 2k + 1)n + m
--R   + 
--R                                      2
--R     (k l + a k - a)m + (k - 1)l + c k  + (- c + 2b)k - b
--E 215

--S 216 of 276
t27:=2*c*k*m+j*k*m+k*m*n-c^2*p+j*n*p-2*c*m+k*n-n
 

                 2
   (27)  (j n - c )p + (k m + k - 1)n + ((j + 2c)k - 2c)m
--R 
--R
--R                 2
--R   (27)  (j n - c )p + (k m + k - 1)n + ((j + 2c)k - 2c)m
--E 216

--S 217 of 276
t28:=a*k*l+2*k*l*m-a*b*p-b*m*p+m*n*p+k*l*v+n*p*v+b*k-l*m+k*n-l*v-b
 

   (28)
   (n p + (k - 1)l)v + (m n - b m - a b)p + k n + (2k - 1)l m + a k l + b k - b
--R 
--R
--R   (28)
--R   (n p + (k - 1)l)v + (m n - b m - a b)p + k n + (2k - 1)l m + a k l + b k - b
--E 217

)clear all
 

--S 218 of 276
t1:=-x^2+y^2
 

         2    2
   (1)  y  - x
--R 
--R
--R         2    2
--R   (1)  y  - x
--E 218

--S 219 of 276
t2:=x*u*v+y*u*a-x-w
 

   (2)  a u y + (u v - 1)x - w
--R 
--R
--R   (2)  a u y + (u v - 1)x - w
--E 219

--S 220 of 276
t3:=x*u^2-y*u^2+y*z*a-x*u*a+y*u*a-x*v*a+x*a^2-y*a^2
 

                    2          2               2          2
   (3)  a y z + (- u  + a u - a )y + (- a v + u  - a u + a )x
--R 
--R
--R                    2          2               2          2
--R   (3)  a y z + (- u  + a u - a )y + (- a v + u  - a u + a )x
--E 220

--S 221 of 276
t4:=-x*y*v-y^2*v+x*u*w-y*u*w+y*t*a+y*w*a-v^2+a^2
 

             2                                          2    2
   (4)  - v y  + (- v x + (- u + a)w + a t)y + u w x - v  + a
--R 
--R
--R             2                                          2    2
--R   (4)  - v y  + (- v x + (- u + a)w + a t)y + u w x - v  + a
--E 221

--S 222 of 276
t5:=-y*z*u-x*u*a+y+t
 

   (5)  - u y z + y - a u x + t
--R 
--R
--R   (5)  - u y z + y - a u x + t
--E 222

--S 223 of 276
t6:=x*y*z-x*y*v+x*t*v-y*z*w+z*u-u*v-z*a-v*a
 

   (6)  ((x - w)y + u - a)z - v x y + t v x + (- u - a)v
--R 
--R
--R   (6)  ((x - w)y + u - a)z - v x y + t v x + (- u - a)v
--E 223

--S 224 of 276
t7:=x^2*z+x*y*z+x*t*u-y*t*u-x*t*a-x*w*a+z^2-a^2
 

         2           2                                     2
   (7)  z  + (x y + x )z - t u y + (- a w + t u - a t)x - a
--R 
--R
--R         2           2                                     2
--R   (7)  z  + (x y + x )z - t u y + (- a w + t u - a t)x - a
--E 224

--S 225 of 276
t8:=x*y*t-x*y*w+x*t*w-y*t*w+x*z+z*t-y*v-v*w
 

   (8)  (x + t)z + ((- w + t)x - t w - v)y + t w x - v w
--R 
--R
--R   (8)  (x + t)z + ((- w + t)x - t w - v)y + t w x - v w
--E 225

--S 226 of 276
t9:=-x*u+y*v-u*w+x*a
 

   (9)  v y + (- u + a)x - u w
--R 
--R
--R   (9)  v y + (- u + a)x - u w
--E 226

--S 227 of 276
t10:=x*y-w^2
 

                2
   (10)  x y - w
--R 
--R
--R                2
--R   (10)  x y - w
--E 227

--S 228 of 276
t11:=-u^2*v+x^2+z
 

              2    2
   (11)  z + x  - u v
--R 
--R
--R              2    2
--R   (11)  z + x  - u v
--E 228

--S 229 of 276
t12:=-y*u*v-y*v^2-u*v*w-v^2*w+y*v*a+u*w*a+x+t
 

             2                          2
   (12)  (- v  + (- u + a)v)y + x + (- v  - u v + a u)w + t
--R 
--R
--R             2                          2
--R   (12)  (- v  + (- u + a)v)y + x + (- v  - u v + a u)w + t
--E 229

--S 230 of 276
t13:=-z*u*v-u^2*a+u*a^2+y*w+a
 

                            2    2
   (13)  - u v z + w y - a u  + a u + a
--R 
--R
--R                            2    2
--R   (13)  - u v z + w y - a u  + a u + a
--E 230

--S 231 of 276
t14:=-x*v^2-z*v*w-u*v*w+y*u*a+x*v*a+v*w*a
 

                               2
   (14)  - v w z + a u y + (- v  + a v)x + (- u + a)v w
--R 
--R
--R                               2
--R   (14)  - v w z + a u y + (- v  + a v)x + (- u + a)v w
--E 231

--S 232 of 276
t15:=y*z*u-t*u*v+x*u*a-u*w*a
 

   (15)  u y z + a u x - a u w - t u v
--R 
--R
--R   (15)  u y z + a u x - a u w - t u v
--E 232

--S 233 of 276
t16:=y*t*u-y*u*w-t*v*w-v*w^2+x*w*a+y*w*a-v^2+a^2
 

                                          2            2    2
   (16)  ((- u + a)w + t u)y + a w x - v w  - t v w - v  + a
--R 
--R
--R                                          2            2    2
--R   (16)  ((- u + a)w + t u)y + a w x - v w  - t v w - v  + a
--E 233

--S 234 of 276
t17:=-x*z-t*u+y*v+u*w
 

   (17)  - x z + v y + u w - t u
--R 
--R
--R   (17)  - x z + v y + u w - t u
--E 234

--S 235 of 276
t18:=u^2*v-t*w-z
 

                      2
   (18)  - z - t w + u v
--R 
--R
--R                      2
--R   (18)  - z - t w + u v
--E 235

--S 236 of 276
t19:=-y*z*v-y*u*v-t*v^2+y*v*a+t*v*a+u*w*a
 

                                             2
   (19)  - v y z + (- u + a)v y + a u w - t v  + a t v
--R 
--R
--R                                             2
--R   (19)  - v y z + (- u + a)v y + a u w - t v  + a t v
--E 236

--S 237 of 276
t20:=-z*u^2+t*w+v
 

            2
   (20)  - u z + t w + v
--R 
--R
--R            2
--R   (20)  - u z + t w + v
--E 237

--S 238 of 276
t21:=x*z*u+x*z*v+z^2*w-x*z*a-t*u*a-z*w*a
 

            2
   (21)  w z  + ((v + u - a)x - a w)z - a t u
--R 
--R
--R            2
--R   (21)  w z  + ((v + u - a)x - a w)z - a t u
--E 238

--S 239 of 276
t22:=x*t*v-y*z*w+z*t*w-t*v*w+z*u-u*v-z*a+v*a
 

   (22)  (- w y + t w + u - a)z + t v x - t v w + (- u + a)v
--R 
--R
--R   (22)  (- w y + t w + u - a)z + t v x - t v w + (- u + a)v
--E 239

--S 240 of 276
t23:=v^2-a^2
 

          2    2
   (23)  v  - a
--R 
--R
--R          2    2
--R   (23)  v  - a
--E 240

--S 241 of 276
t24:=y*u+u*w-y*a-w*a
 

   (24)  (u - a)y + (u - a)w
--R 
--R
--R   (24)  (u - a)y + (u - a)w
--E 241

--S 242 of 276
t25:=z*w-y*a
 

   (25)  w z - a y
--R 
--R
--R   (25)  w z - a y
--E 242

--S 243 of 276
t26:=-y^2+t*w
 

            2
   (26)  - y  + t w
--R 
--R
--R            2
--R   (26)  - y  + t w
--E 243

--S 244 of 276
t27:=-x*z+v*w-x*a+w*a
 

   (27)  - x z - a x + (v + a)w
--R 
--R
--R   (27)  - x z - a x + (v + a)w
--E 244

--S 245 of 276
t28:=u^2*v-x*y-z
 

                      2
   (28)  - z - x y + u v
--R 
--R
--R                      2
--R   (28)  - z - x y + u v
--E 245

--S 246 of 276
t29:=z*u*v+u^2*a-u*a^2-x*t-a
 

                          2    2
   (29)  u v z - t x + a u  - a u - a
--R 
--R
--R                          2    2
--R   (29)  u v z - t x + a u  - a u - a
--E 246

--S 247 of 276
t30:=t*u*v+u*w*a-y-t
 

   (30)  - y + a u w + t u v - t
--R 
--R
--R   (30)  - y + a u w + t u v - t
--E 247

--S 248 of 276
t31:=-x*z+y*u+t*u-y*a
 

   (31)  - x z + (u - a)y + t u
--R 
--R
--R   (31)  - x z + (u - a)y + t u
--E 248

)clear all
 

--S 249 of 276
t1:=-x^5-y^5-z^5+5*x*y*z*t*u-u^5
 

           5                 5    5    5
   (1)  - z  + 5t u x y z - y  - x  - u
--R 
--R
--R           5                 5    5    5
--R   (1)  - z  + 5t u x y z - y  - x  - u
--E 249

--S 250 of 276
t2:=x*y^3*z+y*z^3*t+x^3*y*u+z*t^3*u+z*t*u^3
 

             3       3      3    3         3
   (2)  t y z  + (x y  + t u  + t u)z + u x y
--R 
--R
--R             3       3      3    3         3
--R   (2)  t y z  + (x y  + t u  + t u)z + u x y
--E 250

--S 251 of 276
t3:=x^2*y*z^2+y^2*z*t^2+x^2*t^2*u+x*y^2*u^2+z^2*t*u^2
 

          2       2  2    2 2     2   2    2   2
   (3)  (x y + t u )z  + t y z + u x y  + t u x
--R 
--R
--R          2       2  2    2 2     2   2    2   2
--R   (3)  (x y + t u )z  + t y z + u x y  + t u x
--E 251

--S 252 of 276
t4:=x*y*z^5-y^4*z^2*t-2*x^2*y^2*z*t*u+x*z^3*t^2*u-x^4*t*u^2_
    +y*z*t^2*u^3+x*y*u^5
 

             5    2     3      4 2            2 2    2 3       5         2 4
   (4)  x y z  + t u x z  - t y z  + (- 2t u x y  + t u y)z + u x y - t u x
--R 
--R
--R             5    2     3      4 2            2 2    2 3       5         2 4
--R   (4)  x y z  + t u x z  - t y z  + (- 2t u x y  + t u y)z + u x y - t u x
--E 252

--S 253 of 276
t5:=x*y^2*z^4-y^5*z*t-x^2*y^3*t*u+2*x*y*z^2*t^2*u+x*t^4*u^2_
    -x^2*y*z*u^3-z*t*u^5
 

           2 4     2       2         5    3 2       5          2 3    4 2
   (5)  x y z  + 2t u x y z  + (- t y  - u x y - t u )z - t u x y  + t u x
--R 
--R
--R           2 4     2       2         5    3 2       5          2 3    4 2
--R   (5)  x y z  + 2t u x y z  + (- t y  - u x y - t u )z - t u x y  + t u x
--E 253

--S 254 of 276
t6:=x^3*y^2*t-y*z^2*t^4+x*y^2*z^3*u-y^5*t*u-t^6*u+3*x*y*z*t^2*u^2_
    -x^2*y*u^4-t*u^6
 

             2 3    4   2     2 2             5      3 2    4 2       6    6
   (6)  u x y z  - t y z  + 3t u x y z - t u y  + t x y  - u x y - t u  - t u
--R 
--R
--R             2 3    4   2     2 2             5      3 2    4 2       6    6
--R   (6)  u x y z  - t y z  + 3t u x y z - t u y  + t x y  - u x y - t u  - t u
--E 254

--S 255 of 276
t7:=x^4*y^2*z-x*y*z^2*t^3-x*y^5*u-y^3*z^2*t*u-x*t^5*u_
    +2*x^2*y*z*t*u^2+z*t^2*u^4
 

                3    3     2     4 2       2 2     2 4          5    5
   (7)  (- t u y  - t x y)z  + (x y  + 2t u x y + t u )z - u x y  - t u x
--R 
--R
--R                3    3     2     4 2       2 2     2 4          5    5
--R   (7)  (- t u y  - t x y)z  + (x y  + 2t u x y + t u )z - u x y  - t u x
--E 255

--S 256 of 276
t8:=y^6*z+y*z^6+x^2*y^4*u-3*x*y^2*z^2*t*u+z^4*t^2*u-x^3*z*t*u^2_
-x*y*t^3*u^3+y*z*u^5
 

           6    2   4           2 2     6    5       2 3        2 4    3 3
   (8)  y z  + t u z  - 3t u x y z  + (y  + u y - t u x )z + u x y  - t u x y
--R 
--R
--R           6    2   4           2 2     6    5       2 3        2 4    3 3
--R   (8)  y z  + t u z  - 3t u x y z  + (y  + u y - t u x )z + u x y  - t u x y
--E 256

)clear all
 

--S 257 of 276
t1:=a+b+c+d+e+f+g+h-1
 

   (1)  h + g + f + e + d + c + b + a - 1
--R 
--R
--R   (1)  h + g + f + e + d + c + b + a - 1
--E 257

--S 258 of 276
t2:=-a^2*k-2*a*b*k-b^2*k-a*c*k-b*c*k-a*d*k-b*d*k-a*e*k_
    -b*e*k-c*e*k-d*e*k-a*f*k-b*f*k-c*f*k-d*f*k+a+b
 

   (2)
                                                                              2
         (- d - c - b - a)f + (- d - c - b - a)e + (- b - a)d + (- b - a)c - b
       + 
                   2
         - 2a b - a
    *
       k
   + 
     b + a
--R 
--R
--R   (2)
--R                                                                              2
--R         (- d - c - b - a)f + (- d - c - b - a)e + (- b - a)d + (- b - a)c - b
--R       + 
--R                   2
--R         - 2a b - a
--R    *
--R       k
--R   + 
--R     b + a
--E 258

--S 259 of 276
t3:=-a^2*l-a*b*l-a*c*l-a*d*l-a*e*l-b*e*l-c*e*l-d*e*l_
    +a^2+2*a*b+b^2+a*e+b*e+a*f+b*f
 

   (3)
                                              2                            2
     ((- d - c - b - a)e - a d - a c - a b - a )l + (b + a)f + (b + a)e + b
   + 
             2
     2a b + a
--R 
--R
--R   (3)
--R                                              2                            2
--R     ((- d - c - b - a)e - a d - a c - a b - a )l + (b + a)f + (b + a)e + b
--R   + 
--R             2
--R     2a b + a
--E 259

--S 260 of 276
t4:=a+c+e+g-m
 

   (4)  - m + g + e + c + a
--R 
--R
--R   (4)  - m + g + e + c + a
--E 260

)clear all
 

--S 261 of 276
t1:=-y*z+x*t
 

   (1)  - y z + t x
--R 
--R
--R   (1)  - y z + t x
--E 261

--S 262 of 276
t2:=-y*u+x*v+y-v
 

   (2)  (- u + 1)y + v x - v
--R 
--R
--R   (2)  (- u + 1)y + v x - v
--E 262

--S 263 of 276
t3:=z^2+t^2-w^2
 

         2    2    2
   (3)  z  - w  + t
--R 
--R
--R         2    2    2
--R   (3)  z  - w  + t
--E 263

--S 264 of 276
t4:=u^2+v^2-a^2-2*u+1
 

         2    2         2
   (4)  v  + u  - 2u - a  + 1
--R 
--R
--R         2    2         2
--R   (4)  v  + u  - 2u - a  + 1
--E 264

--S 265 of 276
t5:=z^2+t^2-2*z*u+u^2-2*t*v+v^2-b^2
 

         2           2           2    2    2
   (5)  z  - 2u z + v  - 2t v + u  + t  - b
--R 
--R
--R         2           2           2    2    2
--R   (5)  z  - 2u z + v  - 2t v + u  + t  - b
--E 265

)clear all
 

--S 266 of 276
t1:=x*y+x*z+x*t-u^2
 

                           2
   (1)  x z + x y + t x - u
--R 
--R
--R                           2
--R   (1)  x z + x y + t x - u
--E 266

--S 267 of 276
t2:=x*y+y*z+y*t-v^2
 

                          2
   (2)  y z + (x + t)y - v
--R 
--R
--R                          2
--R   (2)  y z + (x + t)y - v
--E 267

--S 268 of 276
t3:=x*z+y*z+z*t-w^2
 

                        2
   (3)  (y + x + t)z - w
--R 
--R
--R                        2
--R   (3)  (y + x + t)z - w
--E 268

--S 269 of 276
t4:=x*t+y*t+z*t-a^2
 

                           2
   (4)  t z + t y + t x - a
--R 
--R
--R                           2
--R   (4)  t z + t y + t x - a
--E 269

)clear all
 

--S 270 of 276
t1:=t+v-a
 

   (1)  v + t - a
--R 
--R
--R   (1)  v + t - a
--E 270

--S 271 of 276
t2:=x+y+z+t-u-w-a
 

   (2)  z + y + x - w - u + t - a
--R 
--R
--R   (2)  z + y + x - w - u + t - a
--E 271

--S 272 of 276
t3:=x*z+y*z+x*t+z*t-u*w-u*a-w*a
 

   (3)  (y + x + t)z + t x + (- u - a)w - a u
--R 
--R
--R   (3)  (y + x + t)z + t x + (- u - a)w - a u
--E 272

--S 273 of 276
t4:=x*z*t-u*w*a
 

   (4)  t x z - a u w
--R 
--R
--R   (4)  t x z - a u w
--E 273


--S 274 of 276
t1:=y^4-20/7*x^2
 

         4   20  2
   (5)  y  - -- x
              7
--R 
--R
--R         4   20  2
--R   (5)  y  - -- x
--R              7
--E 274

--S 275 of 276
t2:=x^2*z^4 + 7/10*x*z^4 + 7/48*z^4 - 50/27*x^2 - 35/27*x - 49/216
 

          2    7      7  4   50  2   35      49
   (6)  (x  + -- x + --)z  - -- x  - -- x - ---
              10     48      27      27     216
--R 
--R
--R          2    7      7  4   50  2   35      49
--R   (6)  (x  + -- x + --)z  - -- x  - -- x - ---
--R              10     48      27      27     216
--E 275

--S 276 of 276
t3:=3/5*x^6*y^2*z + x^5*y^3 + 3/7*x^5*y^2*z + 7/5*x^4*y^3_
   - 7/20*x^4*y*z^2 - 3/20*x^4*z^3 + 609/1000*x^3*y^3_
   + 63/200*x^3*y^2*z - 77/125*x^3*y*z^2 - 21/50*x^3*z^3_
   + 49/1250*x^2*y^3 + 147/2000*x^2*y^2*z - 23863/60000*x^2*y*z^2_
   - 91/400*x^2*z^3 - 27391/800000*x*y^3 + 4137/800000*x*y^2*z_
   - 1078/9375*x*y*z^2 - 5887/200000*x*z^3 - 1029/160000*y^3_
   - 24353/1920000*y*z^2 - 343/128000*z^3
 

   (7)
         3  4   21  3    91  2    5887        343   3
     (- -- x  - -- x  - --- x  - ------ x - ------)z
        20      50      400      200000     128000
   + 
         7  4    77  3   23863  2   1078      24353     2
     (- -- x  - --- x  - ----- x  - ---- x - -------)y z
        20      125      60000      9375     1920000
   + 
      3  6   3  5    63  3    147  2    4137     2
     (- x  + - x  + --- x  + ---- x  + ------ x)y z
      5      7      200      2000      800000
   + 
       5   7  4    609  3    49   2    27391      1029   3
     (x  + - x  + ---- x  + ---- x  - ------ x - ------)y
           5      1000      1250      800000     160000
--R 
--R
--R   (7)
--R         3  4   21  3    91  2    5887        343   3
--R     (- -- x  - -- x  - --- x  - ------ x - ------)z
--R        20      50      400      200000     128000
--R   + 
--R         7  4    77  3   23863  2   1078      24353     2
--R     (- -- x  - --- x  - ----- x  - ---- x - -------)y z
--R        20      125      60000      9375     1920000
--R   + 
--R      3  6   3  5    63  3    147  2    4137     2
--R     (- x  + - x  + --- x  + ---- x  + ------ x)y z
--R      5      7      200      2000      800000
--R   + 
--R       5   7  4    609  3    49   2    27391      1029   3
--R     (x  + - x  + ---- x  + ---- x  - ------ x - ------)y
--R           5      1000      1250      800000     160000
--E 276

)spool 
 
Starts dribbling to expr1.output (2010/3/27, 18:25:43).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 23
sin(x) + 3*cos(x)**2
 

                        2
   (1)  sin(x) + 3cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                        2
--R   (1)  sin(x) + 3cos(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 23
tan(x) - 3.45*x
 

   (2)  tan(x) - 3.45 x
                                                       Type: Expression Float
--R 
--R
--R   (2)  tan(x) - 3.45 x
--R                                                       Type: Expression Float
--E 2

--S 3 of 23
(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))
 

               +-+ 2         +--+      +-+         +--+ 2
        - tan(\|7 )  + 2sin(\|11 )tan(\|7 ) - sin(\|11 )
   (3)  -------------------------------------------------
                          cos(y - x) - 4
                                                     Type: Expression Integer
--R 
--R
--R               +-+ 2         +--+      +-+         +--+ 2
--R        - tan(\|7 )  + 2sin(\|11 )tan(\|7 ) - sin(\|11 )
--R   (3)  -------------------------------------------------
--R                          cos(y - x) - 4
--R                                                     Type: Expression Integer
--E 3

--S 4 of 23
log(exp  x)@Expression(Integer)
 

   (4)  x
                                                     Type: Expression Integer
--R 
--R
--R   (4)  x
--R                                                     Type: Expression Integer
--E 4

--S 5 of 23
log(exp  x)@Expression(Complex Integer)
 

              x
   (5)  log(%e )
                                             Type: Expression Complex Integer
--R 
--R
--R              x
--R   (5)  log(%e )
--R                                             Type: Expression Complex Integer
--E 5

--S 6 of 23
sqrt 3 + sqrt(2 + sqrt(-5))
 

         +----------+
         | +---+         +-+
   (6)  \|\|- 5  + 2  + \|3
                                                        Type: AlgebraicNumber
--R 
--R
--R         +----------+
--R         | +---+         +-+
--R   (6)  \|\|- 5  + 2  + \|3
--R                                                        Type: AlgebraicNumber
--E 6

--S 7 of 23
% :: Expression Integer
 

         +----------+
         | +---+         +-+
   (7)  \|\|- 5  + 2  + \|3
                                                     Type: Expression Integer
--R 
--R
--R         +----------+
--R         | +---+         +-+
--R   (7)  \|\|- 5  + 2  + \|3
--R                                                     Type: Expression Integer
--E 7

--S 8 of 23
height mainKernel sin(x + 4)
 

   (8)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  2
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 23
e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) )
 

                2
        - sin(x)  + 8sin(x) - 16
   (9)  ------------------------
                 +---+
              2y\|- y  - 1
                                                     Type: Expression Integer
--R 
--R
--R                2
--R        - sin(x)  + 8sin(x) - 16
--R   (9)  ------------------------
--R                 +---+
--R              2y\|- y  - 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 23
numer e
 

                 2
   (10)  - sin(x)  + 8sin(x) - 16
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R
--R                 2
--R   (10)  - sin(x)  + 8sin(x) - 16
--R        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 10

--S 11 of 23
denom e
 

            +---+
   (11)  2y\|- y  - 1
        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--R 
--R
--R            +---+
--R   (11)  2y\|- y  - 1
--R        Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
--E 11

--S 12 of 23
D(e, x)
 

                                        +---+
         (4y cos(x)sin(x) - 16y cos(x))\|- y  - 2cos(x)sin(x) + 8cos(x)
   (12)  --------------------------------------------------------------
                                  +---+     3
                               4y\|- y  + 4y  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                        +---+
--R         (4y cos(x)sin(x) - 16y cos(x))\|- y  - 2cos(x)sin(x) + 8cos(x)
--R   (12)  --------------------------------------------------------------
--R                                  +---+     3
--R                               4y\|- y  + 4y  - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 23
D(e, [x, y], [1, 2])
 

   (13)
                7       4                      7        4         +---+
       ((- 2304y  + 960y )cos(x)sin(x) + (9216y  - 3840y )cos(x))\|- y
     + 
              9        6       3
       (- 960y  + 2160y  - 180y  - 3)cos(x)sin(x)
     + 
             9        6       3
       (3840y  - 8640y  + 720y  + 12)cos(x)
  /
            12        9        6       3      +---+        11        8       5
       (256y   - 1792y  + 1120y  - 112y  + 1)\|- y  - 1024y   + 1792y  - 448y
     + 
          2
       16y
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R                7       4                      7        4         +---+
--R       ((- 2304y  + 960y )cos(x)sin(x) + (9216y  - 3840y )cos(x))\|- y
--R     + 
--R              9        6       3
--R       (- 960y  + 2160y  - 180y  - 3)cos(x)sin(x)
--R     + 
--R             9        6       3
--R       (3840y  - 8640y  + 720y  + 12)cos(x)
--R  /
--R            12        9        6       3      +---+        11        8       5
--R       (256y   - 1792y  + 1120y  - 112y  + 1)\|- y  - 1024y   + 1792y  - 448y
--R     + 
--R          2
--R       16y
--R                                                     Type: Expression Integer
--E 13

--S 14 of 23
complexNumeric(cos(2 - 3*%i))
 

   (14)  - 4.1896256909 688072301 + 9.1092278937 55336598 %i
                                                          Type: Complex Float
--R 
--R
--R   (14)  - 4.1896256909 688072301 + 9.1092278937 55336598 %i
--R                                                          Type: Complex Float
--E 14

--S 15 of 23
numeric(tan 3.8)
 

   (15)  0.7735560905 0312607286
                                                                  Type: Float
--R 
--R
--R   (15)  0.7735560905 0312607286
--R                                                                  Type: Float
--E 15

--S 16 of 23
e2 := cos(x**2 - y + 3)
 

                  2
   (16)  cos(y - x  - 3)
                                                     Type: Expression Integer
--R 
--R
--R                  2
--R   (16)  cos(y - x  - 3)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 23
e3 := asin(e2) - %pi/2
 

                2
   (17)  - y + x  + 3
                                                     Type: Expression Integer
--R 
--R
--R                2
--R   (17)  - y + x  + 3
--R                                                     Type: Expression Integer
--E 17

--S 18 of 23
e3 :: Polynomial Integer
 

                2
   (18)  - y + x  + 3
                                                     Type: Polynomial Integer
--R 
--R
--R                2
--R   (18)  - y + x  + 3
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 23
e3 :: DMP([x, y], Integer)
 

          2
   (19)  x  - y + 3
                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--R 
--R
--R          2
--R   (19)  x  - y + 3
--R                       Type: DistributedMultivariatePolynomial([x,y],Integer)
--E 19

--S 20 of 23
sin %pi
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 20

--S 21 of 23
cos(%pi / 4)
 

          +-+
         \|2
   (21)  ----
           2
                                                     Type: Expression Integer
--R 
--R
--R          +-+
--R         \|2
--R   (21)  ----
--R           2
--R                                                     Type: Expression Integer
--E 21

--S 22 of 23
tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1
 

               6          4          2
   (22)  tan(x)  + 3tan(x)  + 3tan(x)  + 1
                                                     Type: Expression Integer
--R 
--R
--R               6          4          2
--R   (22)  tan(x)  + 3tan(x)  + 3tan(x)  + 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 23
simplify %
 

            1
   (23)  -------
               6
         cos(x)
                                                     Type: Expression Integer
--R 
--R
--R            1
--R   (23)  -------
--R               6
--R         cos(x)
--R                                                     Type: Expression Integer
--E 23
)spool 
 
Starts dribbling to schaum27.output (2010/3/27, 18:38:34).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 84
aa:=integrate(sinh(a*x),x)
 

        cosh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R
--R        cosh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 84
bb:=cosh(a*x)/a
 

        cosh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        cosh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 3 of 84      14:540 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 84
aa:=integrate(x*sinh(a*x),x)
 

        - sinh(a x) + a x cosh(a x)
   (1)  ---------------------------
                      2
                     a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - sinh(a x) + a x cosh(a x)
--R   (1)  ---------------------------
--R                      2
--R                     a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 84
bb:=(x*cosh(a*x))/a-sinh(a*x)/a^2
 

        - sinh(a x) + a x cosh(a x)
   (2)  ---------------------------
                      2
                     a
                                                     Type: Expression Integer
--R
--R        - sinh(a x) + a x cosh(a x)
--R   (2)  ---------------------------
--R                      2
--R                     a
--R                                                     Type: Expression Integer
--E

--S 6 of 84      14:541 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 84
aa:=integrate(x^2*sinh(a*x),x)
 

                             2 2
        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
   (1)  --------------------------------------
                           3
                          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             2 2
--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
--R   (1)  --------------------------------------
--R                           3
--R                          a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 84
bb:=(x^2/a+2/a^3)*cosh(a*x)-(2*x)/a^2*sinh(a*x)
 

                             2 2
        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
   (2)  --------------------------------------
                           3
                          a
                                                     Type: Expression Integer
--R
--R                             2 2
--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
--R   (2)  --------------------------------------
--R                           3
--R                          a
--R                                                     Type: Expression Integer
--E

--S 9 of 84      14:542 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 84     14:543 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)/x,x)
 

           x
         ++  sinh(%N a)
   (1)   |   ---------- d%N
        ++       %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sinh(%N a)
--I   (1)   |   ---------- d%N
--I        ++       %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 11 of 84     14:544 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)/x^2,x)
 

           x
         ++  sinh(%N a)
   (1)   |   ---------- d%N
        ++         2
                 %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sinh(%N a)
--I   (1)   |   ---------- d%N
--R        ++         2
--I                 %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 12 of 84
aa:=integrate(1/sinh(a*x),x)
 

        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
   (1)  -----------------------------------------------------------------
                                        a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R   (1)  -----------------------------------------------------------------
--R                                        a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13 of 84
bb:=1/a*log(tanh(a*x)/2)
 

            tanh(a x)
        log(---------)
                2
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R            tanh(a x)
--R        log(---------)
--R                2
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 14 of 84     14:545 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
             tanh(a x)
       - log(---------) - log(sinh(a x) + cosh(a x) + 1)
                 2
     + 
       log(sinh(a x) + cosh(a x) - 1)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R             tanh(a x)
--R       - log(---------) - log(sinh(a x) + cosh(a x) + 1)
--R                 2
--R     + 
--R       log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 15 of 84     14:546 Axiom cannot compute this integral
aa:=integrate(x/sinh(a*x),x)
 

           x
         ++      %N
   (1)   |   ---------- d%N
        ++   sinh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %N
--I   (1)   |   ---------- d%N
--I        ++   sinh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 16 of 84
aa:=integrate(sinh(a*x)^2,x)
 

        cosh(a x)sinh(a x) - a x
   (1)  ------------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cosh(a x)sinh(a x) - a x
--R   (1)  ------------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 17 of 84
bb:=(sinh(a*x)*cosh(a*x))/(2*a)-x/2
 

        cosh(a x)sinh(a x) - a x
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R        cosh(a x)sinh(a x) - a x
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 18 of 84     14:547 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 84
aa:=integrate(x*sinh(a*x)^2,x)
 

                   2                                      2     2 2
        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  - 2a x
   (1)  -----------------------------------------------------------
                                      2
                                    8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2                                      2     2 2
--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  - 2a x
--R   (1)  -----------------------------------------------------------
--R                                      2
--R                                    8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 20 of 84
bb:=(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)-x^2/4
 

                                         2 2
        2a x sinh(2a x) - cosh(2a x) - 2a x
   (2)  ------------------------------------
                           2
                         8a
                                                     Type: Expression Integer
--R
--R                                         2 2
--R        2a x sinh(2a x) - cosh(2a x) - 2a x
--R   (2)  ------------------------------------
--R                           2
--R                         8a
--R                                                     Type: Expression Integer
--E

--S 21 of 84
cc:=aa-bb
 

   (3)
                                    2
       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
     + 
                  2
       - cosh(a x)
  /
       2
     8a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2
--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
--R     + 
--R                  2
--R       - cosh(a x)
--R  /
--R       2
--R     8a
--R                                                     Type: Expression Integer
--E

--S 22 of 84
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 23 of 84
dd:=sinhsqrrule cc
 

   (5)
                                                                        2
   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
   --------------------------------------------------------------------------
                                         2
                                      16a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                                        2
--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
--R   --------------------------------------------------------------------------
--R                                         2
--R                                      16a
--R                                                     Type: Expression Integer
--E

--S 24 of 84
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25 of 84
ee:=coshsqrrule dd
 

        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
   (7)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
--R   (7)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 26 of 84
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (8)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %K sinh(y + x) - %K sinh(y - x)
--I   (8)  %K cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27 of 84     14:548 Schaums and Axiom agree
ff:=sinhcoshrule ee
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 84
aa:=integrate(1/sinh(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29 of 84
bb:=-coth(a*x)/a
 

          coth(a x)
   (2)  - ---------
              a
                                                     Type: Expression Integer
--R
--R          coth(a x)
--R   (2)  - ---------
--R              a
--R                                                     Type: Expression Integer
--E

--S 30 of 84
cc:=aa-bb
 

   (3)
                         2
       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
     + 
                 2
       (cosh(a x)  - 1)coth(a x) - 2
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                         2
--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
--R     + 
--R                 2
--R       (cosh(a x)  - 1)coth(a x) - 2
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 31 of 84
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 32 of 84
dd:=sinhsqrrule cc
 

   (5)
                                                          2
   4cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) + 2cosh(a x)  - 3)coth(a x) - 4
   --------------------------------------------------------------------------
                                                               2
            4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                          2
--R   4cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) + 2cosh(a x)  - 3)coth(a x) - 4
--R   --------------------------------------------------------------------------
--R                                                               2
--R            4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
--R                                                     Type: Expression Integer
--E

--S 33 of 84
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34 of 84
ee:=coshsqrrule dd
 

        2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2
   (7)  ------------------------------------------------------------
                  2a cosh(a x)sinh(a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R        2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2
--R   (7)  ------------------------------------------------------------
--R                  2a cosh(a x)sinh(a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 35 of 84
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %Q sinh(y + x) - %Q sinh(y - x)
   (8)  %Q cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--I                             %B sinh(y + x) - %B sinh(y - x)
--I   (8)  %B cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36 of 84
ff:=sinhcoshrule ee
 

        coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2
   (9)  ---------------------------------------------------
                  a sinh(2a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R        coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2
--R   (9)  ---------------------------------------------------
--R                  a sinh(2a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 37 of 84
cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 

                    cosh(x)
   (10)  coth(x) == -------
                    sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                    cosh(x)
--R   (10)  coth(x) == -------
--R                    sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38 of 84
gg:=cothrule ff
 

         cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x)
   (11)  ------------------------------------------------------------------
                 a sinh(a x)sinh(2a x) + (a cosh(2a x) - a)sinh(a x)
                                                     Type: Expression Integer
--R
--R         cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x)
--R   (11)  ------------------------------------------------------------------
--R                 a sinh(a x)sinh(2a x) + (a cosh(2a x) - a)sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 39 of 84
hh:=sinhcoshrule gg
 

         sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
   (12)  -----------------------------------------------------------
             a sinh(3a x) + 2a sinh(a x)sinh(2a x) - 3a sinh(a x)
                                                     Type: Expression Integer
--R
--R         sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
--R   (12)  -----------------------------------------------------------
--R             a sinh(3a x) + 2a sinh(a x)sinh(2a x) - 3a sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 40 of 84
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %R cosh(y + x) - %R cosh(y - x)
   (13)  %R sinh(x)sinh(y) == -------------------------------
                                             2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %M cosh(y + x) - %M cosh(y - x)
--I   (13)  %M sinh(x)sinh(y) == -------------------------------
--R                                             2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 41 of 84
ii:=sinhsinhrule gg
 

         2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
   (14)  ---------------------------------------------------------------------
               (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
                                                     Type: Expression Integer
--R
--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
--R   (14)  ---------------------------------------------------------------------
--R               (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 42 of 84
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                              %S cosh(y + x) + %S cosh(y - x)
   (15)  %S cosh(x)cosh(y) == -------------------------------
                                             2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %N cosh(y + x) + %N cosh(y - x)
--I   (15)  %N cosh(x)cosh(y) == -------------------------------
--R                                             2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 43 of 84
jj:=coshcoshrule ii
 

         2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x)
   (16)  ----------------------------------------------------------
         (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
                                                     Type: Expression Integer
--R
--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x)
--R   (16)  ----------------------------------------------------------
--R         (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 44 of 84     14:549 Schaums and Axiom differ by a constant
kk:=sinhcoshrule jj
 

         1
   (17)  -
         a
                                                     Type: Expression Integer
--R
--R         1
--R   (17)  -
--R         a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 45 of 84
aa:=integrate(sinh(a*x)*sinh(p*x),x)
 

        a cosh(a x)sinh(p x) - p cosh(p x)sinh(a x)
   (1)  -------------------------------------------
          2    2          2       2    2          2
        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a cosh(a x)sinh(p x) - p cosh(p x)sinh(a x)
--R   (1)  -------------------------------------------
--R          2    2          2       2    2          2
--R        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 46 of 84
bb:=(sinh(a+p)*x)/(2*(a+p))-(sinh(a-p)*x)/(2*(a-p))
 

        (p - a)x sinh(p + a) + (- p - a)x sinh(p - a)
   (2)  ---------------------------------------------
                            2     2
                          2p  - 2a
                                                     Type: Expression Integer
--R
--R        (p - a)x sinh(p + a) + (- p - a)x sinh(p - a)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 47 of 84     14:550 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       2a cosh(a x)sinh(p x)
     + 
                                                               2
       ((- p + a)x sinh(p + a) + (p + a)x sinh(p - a))sinh(a x)
     + 
                                                   2
       - 2p cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
     + 
                           2
       (- p - a)x cosh(a x) sinh(p - a)
  /
        2     2          2        2     2          2
     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       2a cosh(a x)sinh(p x)
--R     + 
--R                                                               2
--R       ((- p + a)x sinh(p + a) + (p + a)x sinh(p - a))sinh(a x)
--R     + 
--R                                                   2
--R       - 2p cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
--R     + 
--R                           2
--R       (- p - a)x cosh(a x) sinh(p - a)
--R  /
--R        2     2          2        2     2          2
--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 48 of 84
aa:=integrate(sinh(a*x)*sin(p*x),x)
 

   (1)
                                         2
       (a sin(p x) - p cos(p x))sinh(a x)
     + 
       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (a cosh(a x)  + a)sin(p x) - p cos(p x)cosh(a x)  + p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (a sin(p x) - p cos(p x))sinh(a x)
--R     + 
--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (a cosh(a x)  + a)sin(p x) - p cos(p x)cosh(a x)  + p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 49 of 84
bb:=(a*cosh(a*x)*sin(p*x)-p*sinh(a*x)*cos(p*x))/(a^2+p^2)
 

        - p cos(p x)sinh(a x) + a cosh(a x)sin(p x)
   (2)  -------------------------------------------
                           2    2
                          p  + a
                                                     Type: Expression Integer
--R
--R        - p cos(p x)sinh(a x) + a cosh(a x)sin(p x)
--R   (2)  -------------------------------------------
--R                           2    2
--R                          p  + a
--R                                                     Type: Expression Integer
--E

--S 50 of 84
cc:=aa-bb
 

   (3)
                                         2                 2
       (a sin(p x) + p cos(p x))sinh(a x)  + (- a cosh(a x)  + a)sin(p x)
     + 
                            2
       - p cos(p x)cosh(a x)  + p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                         2                 2
--R       (a sin(p x) + p cos(p x))sinh(a x)  + (- a cosh(a x)  + a)sin(p x)
--R     + 
--R                            2
--R       - p cos(p x)cosh(a x)  + p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 51 of 84
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 52 of 84
dd:=sinhsqrrule cc
 

   (5)
                                   2
       (a cosh(2a x) - 2a cosh(a x)  + a)sin(p x) + p cos(p x)cosh(2a x)
     + 
                             2
       - 2p cos(p x)cosh(a x)  + p cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                   2
--R       (a cosh(2a x) - 2a cosh(a x)  + a)sin(p x) + p cos(p x)cosh(2a x)
--R     + 
--R                             2
--R       - 2p cos(p x)cosh(a x)  + p cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 53 of 84
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 54 of 84     14:551 Schaums and Axiom agree
ee:=coshsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 55 of 84
aa:=integrate(sinh(a*x)*cos(p*x),x)
 

   (1)
                                         2
       (p sin(p x) + a cos(p x))sinh(a x)
     + 
       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(a x)  + a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (p sin(p x) + a cos(p x))sinh(a x)
--R     + 
--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(a x)  + a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 56 of 84
bb:=(a*cosh(a*x)*cos(p*x)+p*sinh(a*x)*sin(p*x))/(a^2+p^2)
 

        p sin(p x)sinh(a x) + a cos(p x)cosh(a x)
   (2)  -----------------------------------------
                          2    2
                         p  + a
                                                     Type: Expression Integer
--R
--R        p sin(p x)sinh(a x) + a cos(p x)cosh(a x)
--R   (2)  -----------------------------------------
--R                          2    2
--R                         p  + a
--R                                                     Type: Expression Integer
--E

--S 57 of 84
cc:=aa-bb
 

   (3)
                                           2               2
       (- p sin(p x) + a cos(p x))sinh(a x)  + (p cosh(a x)  - p)sin(p x)
     + 
                            2
       - a cos(p x)cosh(a x)  + a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2               2
--R       (- p sin(p x) + a cos(p x))sinh(a x)  + (p cosh(a x)  - p)sin(p x)
--R     + 
--R                            2
--R       - a cos(p x)cosh(a x)  + a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 58 of 84
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 59 of 84
dd:=sinhsqrrule cc
 

   (5)
                                     2
       (- p cosh(2a x) + 2p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(2a x)
     + 
                             2
       - 2a cos(p x)cosh(a x)  + a cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                     2
--R       (- p cosh(2a x) + 2p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(2a x)
--R     + 
--R                             2
--R       - 2a cos(p x)cosh(a x)  + a cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 60 of 84
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 61 of 84     14:552 Schaums and Axiom agree
ee:=coshsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 62 of 84
aa:=integrate(1/(p+q*sinh(a*x)),x)
 

   (1)
     log
                 2         2      2                              2         2
                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
              + 
                                  2     2
                2p q cosh(a x) + q  + 2p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                 3     2                   3     2                  2     3
            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
       /
                       2                                             2
            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
          + 
            2p cosh(a x) - q
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     log
--R                 2         2      2                              2         2
--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R              + 
--R                                  2     2
--R                2p q cosh(a x) + q  + 2p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                 3     2                   3     2                  2     3
--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R       /
--R                       2                                             2
--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R          + 
--R            2p cosh(a x) - q
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63 of 84
bb:=1/(a*sqrt(p^2+q^2))*log((q*%e^(a*x)+p-sqrt(p^2+q^2))/(q*%e^(a*x)+p+sqrt(p^2+q^2)))
 

               +-------+
               | 2    2        a x
            - \|q  + p   + q %e    + p
        log(--------------------------)
              +-------+
              | 2    2        a x
             \|q  + p   + q %e    + p
   (2)  -------------------------------
                    +-------+
                    | 2    2
                  a\|q  + p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2        a x
--R            - \|q  + p   + q %e    + p
--R        log(--------------------------)
--R              +-------+
--R              | 2    2        a x
--R             \|q  + p   + q %e    + p
--R   (2)  -------------------------------
--R                    +-------+
--R                    | 2    2
--R                  a\|q  + p
--R                                                     Type: Expression Integer
--E

--S 64 of 84     14:553 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) + q  + 2p
             *
                 +-------+
                 | 2    2
                \|q  + p
            + 
                   3     2                   3     2                  2     3
              (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) - q
     + 
                +-------+
                | 2    2        a x
             - \|q  + p   + q %e    + p
       - log(--------------------------)
               +-------+
               | 2    2        a x
              \|q  + p   + q %e    + p
  /
       +-------+
       | 2    2
     a\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) + q  + 2p
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R            + 
--R                   3     2                   3     2                  2     3
--R              (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) - q
--R     + 
--R                +-------+
--R                | 2    2        a x
--R             - \|q  + p   + q %e    + p
--R       - log(--------------------------)
--R               +-------+
--R               | 2    2        a x
--R              \|q  + p   + q %e    + p
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 65 of 84
aa:=integrate(1/(p*q*sinh(a*x))^2,x)
 

   (1)
                                         2
   - ------------------------------------------------------------------------
        2 2         2       2 2                        2 2         2      2 2
     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R   - ------------------------------------------------------------------------
--R        2 2         2       2 2                        2 2         2      2 2
--R     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
--R                                          Type: Union(Expression Integer,...)
--E 

--S 66 of 84
t1:=integrate(1/(p+q*sinh(a*x)),x)
 

   (2)
     log
                 2         2      2                              2         2
                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
              + 
                                  2     2
                2p q cosh(a x) + q  + 2p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                 3     2                   3     2                  2     3
            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
       /
                       2                                             2
            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
          + 
            2p cosh(a x) - q
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R
--R   (2)
--R     log
--R                 2         2      2                              2         2
--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R              + 
--R                                  2     2
--R                2p q cosh(a x) + q  + 2p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                 3     2                   3     2                  2     3
--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R       /
--R                       2                                             2
--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R          + 
--R            2p cosh(a x) - q
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E

--S 67 of 84
bb:=(-q*cosh(a*x))/(a*(p^2+q^2)*(p+q*sinh(a*x)))+p/(p^2+q^2)*t1
 

   (3)
                           2
         (p q sinh(a x) + p )
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
                     +-------+
                     | 2    2
       - q cosh(a x)\|q  + p
  /
                                               +-------+
          3      2                   2      3  | 2    2
     ((a q  + a p q)sinh(a x) + a p q  + a p )\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                           2
--R         (p q sinh(a x) + p )
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R                     +-------+
--R                     | 2    2
--R       - q cosh(a x)\|q  + p
--R  /
--R                                               +-------+
--R          3      2                   2      3  | 2    2
--R     ((a q  + a p q)sinh(a x) + a p q  + a p )\|q  + p
--R                                                     Type: Expression Integer
--E

--S 68 of 84     14:554 Axiom cannot simplify this expression
cc:=aa-bb
 

   (4)
              3 3         3        3 3             4 2          2
           - p q sinh(a x)  + (- 2p q cosh(a x) - p q )sinh(a x)
         + 
               3 3         2     4 2             3 3              4 2         2
           (- p q cosh(a x)  - 2p q cosh(a x) + p q )sinh(a x) - p q cosh(a x)
         + 
            4 2
           p q
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
            2 3                  2      2 3         2     3     2
           p q cosh(a x)sinh(a x)  + (2p q cosh(a x)  - 2q  - 2p q)sinh(a x)
         + 
            2 3         3    2 3                2     3
           p q cosh(a x)  - p q cosh(a x) - 2p q  - 2p
      *
          +-------+
          | 2    2
         \|q  + p
  /
             2 5      4 3          3
         (a p q  + a p q )sinh(a x)
       + 
               2 5       4 3                3 4      5 2          2
         ((2a p q  + 2a p q )cosh(a x) + a p q  + a p q )sinh(a x)
       + 
                 2 5      4 3          2        3 4       5 2                2 5
             (a p q  + a p q )cosh(a x)  + (2a p q  + 2a p q )cosh(a x) - a p q
           + 
                  4 3
             - a p q
        *
           sinh(a x)
       + 
             3 4      5 2          2      3 4      5 2
         (a p q  + a p q )cosh(a x)  - a p q  - a p q
    *
        +-------+
        | 2    2
       \|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R              3 3         3        3 3             4 2          2
--R           - p q sinh(a x)  + (- 2p q cosh(a x) - p q )sinh(a x)
--R         + 
--R               3 3         2     4 2             3 3              4 2         2
--R           (- p q cosh(a x)  - 2p q cosh(a x) + p q )sinh(a x) - p q cosh(a x)
--R         + 
--R            4 2
--R           p q
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R            2 3                  2      2 3         2     3     2
--R           p q cosh(a x)sinh(a x)  + (2p q cosh(a x)  - 2q  - 2p q)sinh(a x)
--R         + 
--R            2 3         3    2 3                2     3
--R           p q cosh(a x)  - p q cosh(a x) - 2p q  - 2p
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R  /
--R             2 5      4 3          3
--R         (a p q  + a p q )sinh(a x)
--R       + 
--R               2 5       4 3                3 4      5 2          2
--R         ((2a p q  + 2a p q )cosh(a x) + a p q  + a p q )sinh(a x)
--R       + 
--R                 2 5      4 3          2        3 4       5 2                2 5
--R             (a p q  + a p q )cosh(a x)  + (2a p q  + 2a p q )cosh(a x) - a p q
--R           + 
--R                  4 3
--R             - a p q
--R        *
--R           sinh(a x)
--R       + 
--R             3 4      5 2          2      3 4      5 2
--R         (a p q  + a p q )cosh(a x)  - a p q  - a p q
--R    *
--R        +-------+
--R        | 2    2
--R       \|q  + p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 69 of 84
aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 

   (1)
   [
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                + 
                     4         3        4     2 2
                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4        4     2 2          2    4     2 2     4
                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                   4     3 2          2        4     3 2
              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                   4     3 2          2       4      3 2     5
              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
            + 
                 2         3        2     2                        2         4
              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                   2     2          2    2
              (- 2q  + 4p )cosh(a x)  + q
    /
            +---------+
            |   2    2
       2a p\|- q  + p
     ,

       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
    /
           +-------+
           | 2    2
       a p\|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3        4     2 2
--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4        4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                   4     3 2          2        4     3 2
--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                   4     3 2          2       4      3 2     5
--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3        2     2                        2         4
--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                   2     2          2    2
--R              (- 2q  + 4p )cosh(a x)  + q
--R    /
--R            +---------+
--R            |   2    2
--R       2a p\|- q  + p
--R     ,
--R
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R    /
--R           +-------+
--R           | 2    2
--R       a p\|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 70 of 84
bb1:=1/(a*p*sqrt(q^2-p^2))*atan((sqrt(q^2-p^2)*tanh(a*x))/p)
 

                       +-------+
                       | 2    2
             tanh(a x)\|q  - p
        atan(-------------------)
                      p
   (2)  -------------------------
                  +-------+
                  | 2    2
              a p\|q  - p
                                                     Type: Expression Integer
--R
--R                       +-------+
--R                       | 2    2
--R             tanh(a x)\|q  - p
--R        atan(-------------------)
--R                      p
--R   (2)  -------------------------
--R                  +-------+
--R                  | 2    2
--R              a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 71 of 84
bb2:=1/(2*a*p*sqrt(p^2-q^2))*log((p+sqrt(p^2-q^2)*tanh(a*x))/(p-sqrt(p^2-q^2)*tanh(a*x)))
 

                        +---------+
                        |   2    2
            - tanh(a x)\|- q  + p   - p
        log(---------------------------)
                       +---------+
                       |   2    2
             tanh(a x)\|- q  + p   - p
   (3)  --------------------------------
                     +---------+
                     |   2    2
                2a p\|- q  + p
                                                     Type: Expression Integer
--R
--R                        +---------+
--R                        |   2    2
--R            - tanh(a x)\|- q  + p   - p
--R        log(---------------------------)
--R                       +---------+
--R                       |   2    2
--R             tanh(a x)\|- q  + p   - p
--R   (3)  --------------------------------
--R                     +---------+
--R                     |   2    2
--R                2a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 72 of 84
cc1:=aa.1-bb1
 

   (4)
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     4         4     4                  3
                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
                  + 
                       4         2     4     2 2          2
                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                  + 
                       4         3        4     2 2
                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                  + 
                     4         4        4     2 2          2    4     2 2     4
                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     4     3 2          2        4     3 2
                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
              + 
                     4     3 2          2       4      3 2     5
                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
           /
                 2         4     2                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   2         2     2     2          2
                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
              + 
                   2         3        2     2                        2         4
                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                     2     2          2    2
                (- 2q  + 4p )cosh(a x)  + q
     + 
                                     +-------+
           +---------+               | 2    2
           |   2    2      tanh(a x)\|q  - p
       - 2\|- q  + p  atan(-------------------)
                                    p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     4         4     4                  3
--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                  + 
--R                       4         2     4     2 2          2
--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                  + 
--R                       4         3        4     2 2
--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                  + 
--R                     4         4        4     2 2          2    4     2 2     4
--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     4     3 2          2        4     3 2
--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R              + 
--R                     4     3 2          2       4      3 2     5
--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R           /
--R                 2         4     2                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   2         2     2     2          2
--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R              + 
--R                   2         3        2     2                        2         4
--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                     2     2          2    2
--R                (- 2q  + 4p )cosh(a x)  + q
--R     + 
--R                                     +-------+
--R           +---------+               | 2    2
--R           |   2    2      tanh(a x)\|q  - p
--R       - 2\|- q  + p  atan(-------------------)
--R                                    p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 73 of 84
cc2:=aa.2-bb1
 

   (5)
                        +-------+
                        | 2    2
              tanh(a x)\|q  - p
       - atan(-------------------)
                       p
     + 
       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
  /
         +-------+
         | 2    2
     a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                        +-------+
--R                        | 2    2
--R              tanh(a x)\|q  - p
--R       - atan(-------------------)
--R                       p
--R     + 
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 74 of 84
cc3:=aa.2-bb1
 

   (6)
                        +-------+
                        | 2    2
              tanh(a x)\|q  - p
       - atan(-------------------)
                       p
     + 
       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
  /
         +-------+
         | 2    2
     a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                        +-------+
--R                        | 2    2
--R              tanh(a x)\|q  - p
--R       - atan(-------------------)
--R                       p
--R     + 
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 75 of 84     14:555 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (7)
                                   +---------+
          +-------+                |   2    2
          | 2    2     - tanh(a x)\|- q  + p   - p
       - \|q  - p  log(---------------------------)
                                  +---------+
                                  |   2    2
                        tanh(a x)\|- q  + p   - p
     + 
           +---------+
           |   2    2
         2\|- q  + p
      *
         atan
                  2         2     2                      2         2    2     2
                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
             *
                 +-------+
                 | 2    2
                \|q  - p
           /
                  2     3
              2p q  - 2p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                   +---------+
--R          +-------+                |   2    2
--R          | 2    2     - tanh(a x)\|- q  + p   - p
--R       - \|q  - p  log(---------------------------)
--R                                  +---------+
--R                                  |   2    2
--R                        tanh(a x)\|- q  + p   - p
--R     + 
--R           +---------+
--R           |   2    2
--R         2\|- q  + p
--R      *
--R         atan
--R                  2         2     2                      2         2    2     2
--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  - p
--R           /
--R                  2     3
--R              2p q  - 2p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 76 of 84
aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 

   (1)
   [
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                + 
                     4         3        4     2 2
                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4        4     2 2          2    4     2 2     4
                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                   4     3 2          2        4     3 2
              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                   4     3 2          2       4      3 2     5
              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
            + 
                 2         3        2     2                        2         4
              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                   2     2          2    2
              (- 2q  + 4p )cosh(a x)  + q
    /
            +---------+
            |   2    2
       2a p\|- q  + p
     ,

       atan
                2         2     2                      2         2    2     2
              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
           *
               +-------+
               | 2    2
              \|q  - p
         /
                2     3
            2p q  - 2p
    /
           +-------+
           | 2    2
       a p\|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3        4     2 2
--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4        4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                   4     3 2          2        4     3 2
--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                   4     3 2          2       4      3 2     5
--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3        2     2                        2         4
--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                   2     2          2    2
--R              (- 2q  + 4p )cosh(a x)  + q
--R    /
--R            +---------+
--R            |   2    2
--R       2a p\|- q  + p
--R     ,
--R
--R       atan
--R                2         2     2                      2         2    2     2
--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  - p
--R         /
--R                2     3
--R            2p q  - 2p
--R    /
--R           +-------+
--R           | 2    2
--R       a p\|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 77 of 84
bb:=1/(2*a*p*sqrt(p^2+q^2))*log((p+sqrt(p^2+q^2)*tanh(a*x))/(p-sqrt(p^2+q^2)*tanh(a*x)))
 

                        +-------+
                        | 2    2
            - tanh(a x)\|q  + p   - p
        log(-------------------------)
                       +-------+
                       | 2    2
             tanh(a x)\|q  + p   - p
   (2)  ------------------------------
                     +-------+
                     | 2    2
                2a p\|q  + p
                                                     Type: Expression Integer
--R
--R                        +-------+
--R                        | 2    2
--R            - tanh(a x)\|q  + p   - p
--R        log(-------------------------)
--R                       +-------+
--R                       | 2    2
--R             tanh(a x)\|q  + p   - p
--R   (2)  ------------------------------
--R                     +-------+
--R                     | 2    2
--R                2a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 78 of 84
cc1:=aa.1-bb
 

   (3)
          +-------+
          | 2    2
         \|q  + p
      *
         log
                     4         4     4                  3
                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
                  + 
                       4         2     4     2 2          2
                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
                  + 
                       4         3        4     2 2
                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
                  + 
                     4         4        4     2 2          2    4     2 2     4
                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     4     3 2          2        4     3 2
                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
              + 
                     4     3 2          2       4      3 2     5
                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
           /
                 2         4     2                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   2         2     2     2          2
                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
              + 
                   2         3        2     2                        2         4
                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                     2     2          2    2
                (- 2q  + 4p )cosh(a x)  + q
     + 
                                     +-------+
          +---------+                | 2    2
          |   2    2     - tanh(a x)\|q  + p   - p
       - \|- q  + p  log(-------------------------)
                                    +-------+
                                    | 2    2
                          tanh(a x)\|q  + p   - p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R          +-------+
--R          | 2    2
--R         \|q  + p
--R      *
--R         log
--R                     4         4     4                  3
--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                  + 
--R                       4         2     4     2 2          2
--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
--R                  + 
--R                       4         3        4     2 2
--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
--R                  + 
--R                     4         4        4     2 2          2    4     2 2     4
--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     4     3 2          2        4     3 2
--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
--R              + 
--R                     4     3 2          2       4      3 2     5
--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R           /
--R                 2         4     2                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   2         2     2     2          2
--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
--R              + 
--R                   2         3        2     2                        2         4
--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                     2     2          2    2
--R                (- 2q  + 4p )cosh(a x)  + q
--R     + 
--R                                     +-------+
--R          +---------+                | 2    2
--R          |   2    2     - tanh(a x)\|q  + p   - p
--R       - \|- q  + p  log(-------------------------)
--R                                    +-------+
--R                                    | 2    2
--R                          tanh(a x)\|q  + p   - p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  + p
--R                                                     Type: Expression Integer
--E

--S 79 of 84     14:556 Axiom cannot simplify this expression
cc2:=aa.2-bb
 

   (4)
                                   +-------+
          +-------+                | 2    2
          | 2    2     - tanh(a x)\|q  + p   - p
       - \|q  - p  log(-------------------------)
                                  +-------+
                                  | 2    2
                        tanh(a x)\|q  + p   - p
     + 
           +-------+
           | 2    2
         2\|q  + p
      *
         atan
                  2         2     2                      2         2    2     2
                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
             *
                 +-------+
                 | 2    2
                \|q  - p
           /
                  2     3
              2p q  - 2p
  /
          +-------+ +-------+
          | 2    2  | 2    2
     2a p\|q  - p  \|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                   +-------+
--R          +-------+                | 2    2
--R          | 2    2     - tanh(a x)\|q  + p   - p
--R       - \|q  - p  log(-------------------------)
--R                                  +-------+
--R                                  | 2    2
--R                        tanh(a x)\|q  + p   - p
--R     + 
--R           +-------+
--R           | 2    2
--R         2\|q  + p
--R      *
--R         atan
--R                  2         2     2                      2         2    2     2
--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  - p
--R           /
--R                  2     3
--R              2p q  - 2p
--R  /
--R          +-------+ +-------+
--R          | 2    2  | 2    2
--R     2a p\|q  - p  \|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 80 of 84     14:557 Axiom cannot compute this integral
aa:=integrate(x^m*sinh(a*x),x)
 

           x
         ++              m
   (1)   |   sinh(%N a)%N d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++              m
--I   (1)   |   sinh(%N a)%N d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 81 of 84     14:558 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)^n,x)
 

           x
         ++            n
   (1)   |   sinh(%N a) d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   sinh(%N a) d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 82 of 84     14:559 Axiom cannot compute this integral
aa:=integrate(sinh(a*x)/x^n,x)
 

           x
         ++  sinh(%N a)
   (1)   |   ---------- d%N
        ++         n
                 %N
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++  sinh(%T a)
--I   (3)   |   ---------- d%T
--R        ++         n
--I                 %T
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 83 of 84     14:560 Axiom cannot compute this integral
aa:=integrate(1/sinh(a*x)^n,x)
 

           x
         ++       1
   (1)   |   ----------- d%N
        ++             n
             sinh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%N
--R        ++             n
--I             sinh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 84 of 84     14:561 Axiom cannot compute this integral
aa:=integrate(x/sinh(a*x)^n,x)
 

           x
         ++       %N
   (1)   |   ----------- d%N
        ++             n
             sinh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++       %N
--I   (1)   |   ----------- d%N
--R        ++             n
--I             sinh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to perman.output (2010/3/27, 18:30:41).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
kn n ==
  r : MATRIX INT := new(n,n,1)
  for i in 1..n repeat
    r.i.i := 0
  r
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 3
permanent(kn(5) :: SQMATRIX(5,INT))
 
   Compiling function kn with type PositiveInteger -> Matrix Integer 

   (2)  44
                                                        Type: PositiveInteger
--R 
--R   Compiling function kn with type PositiveInteger -> Matrix Integer 
--R
--R   (2)  44
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 3
[permanent(kn(n) :: SQMATRIX(n,INT)) for n in 1..13]
 
   Cannot compile conversion for types involving local variables. In 
      particular, could not compile the expression involving :: 
      SQMATRIX(n,INT) 
   AXIOM will attempt to step through and interpret the code.

   (3)
   [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932]
                                                Type: List NonNegativeInteger
--R 
--R   Cannot compile conversion for types involving local variables. In 
--R      particular, could not compile the expression involving :: 
--R      SQMATRIX(n,INT) 
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (3)
--R   [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932]
--R                                                Type: List NonNegativeInteger
--E 3
)spool 
 
Starts dribbling to r21bugsbig.output (2010/3/27, 18:30:59).
)set message test on
 
)set message auto off
 
)clear all
 
 
)set expose add constructor CyclotomicPolynomialPackage
 
   CyclotomicPolynomialPackage is now explicitly exposed in frame 
      initial 
)set message type off
 
)set message time off
 

--S 1 of 22
n : PositiveInteger := 5
 

   (1)  5
--R 
--R
--R   (1)  5
--E 1

--S 2 of 22
UZn : List(PositiveInteger) := [i for i in 1 .. n-1 | gcd(i,n) = 1]
 

   (2)  [1,2,3,4]
--R 
--R
--R   (2)  [1,2,3,4]
--E 2

--S 3 of 22
vars : List(Symbol) := [concat("t", i::String)::Symbol for i in 0 ..#UZn-1] 
 

   (3)  [t0,t1,t2,t3]
--R 
--R
--R   (3)  [t0,t1,t2,t3]
--E 3

--S 4 of 22
Zt := DistributedMultivariatePolynomial(vars, Integer) ;   K :=Fraction(Zt) 
 

   (4)  Fraction DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)
--R 
--R
--R   (4)  Fraction DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)
--E 4 

--S 5 of 22
t : List(K) := [v::K for v in vars]
 

   (5)  [t0,t1,t2,t3]
--R 
--R
--R   (5)  [t0,t1,t2,t3]
--E 5

--S 6 of 22
t(#t) := 0 ; t
 

   (6)  [t0,t1,t2,0]
--R 
--R
--R   (6)  [t0,t1,t2,0]
--E 6

--S 7 of 22
Zn := IntegerMod(n) 
 

   (7)  IntegerMod 5
--R 
--R
--R   (7)  IntegerMod 5
--E 7 

--S 8 of 22
rapport(i : Integer, j : Integer) : Integer ==   -- returns <i/j> modulo n
   k : Zn := i * recip(j::Zn)::Zn
   return convert(k)
 
   Function declaration rapport : (Integer,Integer) -> Integer has been
      added to workspace.
--R 
--R   Function declaration rapport : (Integer,Integer) -> Integer has been
--R      added to workspace.
--E 8

--S 9 of 22
Phi : UP('xi, K) := map(coerce, cyclotomic(n))
 

          4     3     2
   (9)  xi  + xi  + xi  + xi + 1
--R 
--R
--R          4     3     2
--R   (9)  xi  + xi  + xi  + xi + 1
--E 9

--S 10 of 22
E := SimpleAlgebraicExtension(K, UP('xi, K), Phi) 
 

   (10)
  SimpleAlgebraicExtension(Fraction DistributedMultivariatePolynomial([t0,t1,t2
  ,t3],Integer),UnivariatePolynomial(xi,Fraction DistributedMultivariatePolynom
  ial([t0,t1,t2,t3],Integer)),xi**4+xi**3+xi*xi+xi+1)
--R 
--R
--R   (10)
--R  SimpleAlgebraicExtension(Fraction DistributedMultivariatePolynomial([t0,t1,t2
--R  ,t3],Integer),UnivariatePolynomial(xi,Fraction DistributedMultivariatePolynom
--R  ial([t0,t1,t2,t3],Integer)),xi**4+xi**3+xi*xi+xi+1)
--E 10 

--S 11 of 22
xi : E := generator()$E 
 

   (11)  xi
--R 
--R
--R   (11)  xi
--E 11 

--S 12 of 22
bList : List(E) := [reduce(+, [t(i+1) * xi**(i*j) for i in 0 .. #UZn-1]) for j in UZn]
 

   (12)
         2                      3              2
   [t2 xi  + t1 xi + t0, - t2 xi  + (t1 - t2)xi  - t2 xi + t0 - t2,
         3                            3        2
    t1 xi  + t2 xi + t0, (- t1 + t2)xi  - t1 xi  - t1 xi + t0 - t1]
--R 
--R
--R   (12)
--R         2                      3              2
--R   [t2 xi  + t1 xi + t0, - t2 xi  + (t1 - t2)xi  - t2 xi + t0 - t2,
--R         3                            3        2
--R    t1 xi  + t2 xi + t0, (- t1 + t2)xi  - t1 xi  - t1 xi + t0 - t1]
--E 12

--S 13 of 22
delta : List(E) :=
  [reduce(*, [b**((j*rapport(1,k)) quo n) for b in bList for k in UZn]) for j in UZn] 
 
   Compiling function rapport with type (Integer,Integer) -> Integer 

   (13)
   [1,

                          3                2   2                        2
       (- t0 t1 + t1 t2)xi  + (- t0 t2 + t2 )xi  + (- t0 t1 - t0 t2 + t1 )xi
     + 
         2
       t0  - t0 t1 - t0 t2 + t1 t2
     ,

               3       3       2  2      2           2  2         3        2
           - t0 t1 + t0 t2 + t0 t1  + 3t0 t1 t2 - 2t0 t2  - 2t0 t1  - t0 t1 t2
         + 
                 3     4     2  2
           2t0 t2  + t1  - t1 t2
      *
           3
         xi
     + 
               3       3        2  2      2              3            2        3
           - t0 t1 - t0 t2 + 2t0 t1  + 3t0 t1 t2 - 2t0 t1  - 3t0 t1 t2  + t0 t2
         + 
              3        2  2        3
           2t1 t2 - 2t1 t2  + t1 t2
      *
           2
         xi
     + 
                3        2  2      2          2  2        3        2
           - 2t0 t1 + 2t0 t1  + 2t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
         + 
                   2     3       2  2        3     4
           t0 t1 t2  + t1 t2 - t1 t2  - t1 t2  + t2
      *
         xi
     + 
         4      3       3       2  2      2          2  2        3        2
       t0  - 2t0 t1 - t0 t2 + t0 t1  + 4t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
     + 
                 2        3     3          3
       - t0 t1 t2  + t0 t2  + t1 t2 - t1 t2
     ,

                5       5        4  2      4           4  2      3  3
           - 2t0 t1 + t0 t2 + 2t0 t1  + 8t0 t1 t2 - 2t0 t2  - 3t0 t1
         + 
                 3  2        3     2      3  3      2  4     2  3
           - 11t0 t1 t2 - 3t0 t1 t2  + 4t0 t2  + 4t0 t1  + t0 t1 t2
         + 
               2  2  2      2     3     2  4         4           3  2
           12t0 t1 t2  - 6t0 t1 t2  - t0 t2  - 3t0 t1 t2 - 3t0 t1 t2
         + 
                   2  3            4         5     6      5       4  2     2  4
           - 4t0 t1 t2  + 9t0 t1 t2  - 2t0 t2  - t1  + 3t1 t2 - t1 t2  + t1 t2
         + 
                   5     6
           - 3t1 t2  + t2
      *
           3
         xi
     + 
               5        5        4  2      4           4  2      3  3
           - t0 t1 - 2t0 t2 + 2t0 t1  + 8t0 t1 t2 + 3t0 t2  - 4t0 t1
         + 
                3  2         3     2     3  3     2  4      2  2  2      2     3
           - 2t0 t1 t2 - 10t0 t1 t2  + t0 t2  + t0 t1  + 3t0 t1 t2  + 4t0 t1 t2
         + 
                 5         4           3  2         2  3            4        5
           2t0 t1  - 2t0 t1 t2 + 2t0 t1 t2  - 8t0 t1 t2  + 5t0 t1 t2  - t0 t2
         + 
               6     5       4  2      3  3      2  4         5
           - t1  + t1 t2 + t1 t2  - 3t1 t2  + 5t1 t2  - 3t1 t2
      *
           2
         xi
     + 
                5       5        4  2      4           3  3      3  2
           - 3t0 t1 - t0 t2 + 5t0 t1  + 5t0 t1 t2 - 3t0 t1  - 8t0 t1 t2
         + 
              3     2     3  3     2  4      2  3        2  2  2       2     3
           4t0 t1 t2  + t0 t2  + t0 t1  + 2t0 t1 t2 + 3t0 t1 t2  - 10t0 t1 t2
         + 
              2  4        5         4           2  3            4         5
           3t0 t2  + t0 t1  - 2t0 t1 t2 - 2t0 t1 t2  + 8t0 t1 t2  - 2t0 t2
         + 
               6      5       4  2      3  3      2  4        5
           - t1  + 2t1 t2 + t1 t2  - 4t1 t2  + 2t1 t2  - t1 t2
      *
         xi
     + 
         6      5        5       4  2      4          4  2      3  2
       t0  - 3t0 t1 - 2t0 t2 + t0 t1  + 9t0 t1 t2 - t0 t2  - 4t0 t1 t2
     + 
            3     2      3  3     2  4      2  3         2  2  2      2     3
       - 6t0 t1 t2  + 4t0 t2  - t0 t1  - 3t0 t1 t2 + 12t0 t1 t2  - 3t0 t1 t2
     + 
            2  4         5         4          3  2          2  3            4
       - 2t0 t2  + 3t0 t1  - 3t0 t1 t2 + t0 t1 t2  - 11t0 t1 t2  + 8t0 t1 t2
     + 
            5     6      4  2      3  3      2  4         5
       t0 t2  - t1  + 4t1 t2  - 3t1 t2  + 2t1 t2  - 2t1 t2
     ]
--R 
--R   Compiling function rapport with type (Integer,Integer) -> Integer 
--R
--R   (13)
--R   [1,
--R
--R                          3                2   2                        2
--R       (- t0 t1 + t1 t2)xi  + (- t0 t2 + t2 )xi  + (- t0 t1 - t0 t2 + t1 )xi
--R     + 
--R         2
--R       t0  - t0 t1 - t0 t2 + t1 t2
--R     ,
--R
--R               3       3       2  2      2           2  2         3        2
--R           - t0 t1 + t0 t2 + t0 t1  + 3t0 t1 t2 - 2t0 t2  - 2t0 t1  - t0 t1 t2
--R         + 
--R                 3     4     2  2
--R           2t0 t2  + t1  - t1 t2
--R      *
--R           3
--R         xi
--R     + 
--R               3       3        2  2      2              3            2        3
--R           - t0 t1 - t0 t2 + 2t0 t1  + 3t0 t1 t2 - 2t0 t1  - 3t0 t1 t2  + t0 t2
--R         + 
--R              3        2  2        3
--R           2t1 t2 - 2t1 t2  + t1 t2
--R      *
--R           2
--R         xi
--R     + 
--R                3        2  2      2          2  2        3        2
--R           - 2t0 t1 + 2t0 t1  + 2t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
--R         + 
--R                   2     3       2  2        3     4
--R           t0 t1 t2  + t1 t2 - t1 t2  - t1 t2  + t2
--R      *
--R         xi
--R     + 
--R         4      3       3       2  2      2          2  2        3        2
--R       t0  - 2t0 t1 - t0 t2 + t0 t1  + 4t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
--R     + 
--R                 2        3     3          3
--R       - t0 t1 t2  + t0 t2  + t1 t2 - t1 t2
--R     ,
--R
--R                5       5        4  2      4           4  2      3  3
--R           - 2t0 t1 + t0 t2 + 2t0 t1  + 8t0 t1 t2 - 2t0 t2  - 3t0 t1
--R         + 
--R                 3  2        3     2      3  3      2  4     2  3
--R           - 11t0 t1 t2 - 3t0 t1 t2  + 4t0 t2  + 4t0 t1  + t0 t1 t2
--R         + 
--R               2  2  2      2     3     2  4         4           3  2
--R           12t0 t1 t2  - 6t0 t1 t2  - t0 t2  - 3t0 t1 t2 - 3t0 t1 t2
--R         + 
--R                   2  3            4         5     6      5       4  2     2  4
--R           - 4t0 t1 t2  + 9t0 t1 t2  - 2t0 t2  - t1  + 3t1 t2 - t1 t2  + t1 t2
--R         + 
--R                   5     6
--R           - 3t1 t2  + t2
--R      *
--R           3
--R         xi
--R     + 
--R               5        5        4  2      4           4  2      3  3
--R           - t0 t1 - 2t0 t2 + 2t0 t1  + 8t0 t1 t2 + 3t0 t2  - 4t0 t1
--R         + 
--R                3  2         3     2     3  3     2  4      2  2  2      2     3
--R           - 2t0 t1 t2 - 10t0 t1 t2  + t0 t2  + t0 t1  + 3t0 t1 t2  + 4t0 t1 t2
--R         + 
--R                 5         4           3  2         2  3            4        5
--R           2t0 t1  - 2t0 t1 t2 + 2t0 t1 t2  - 8t0 t1 t2  + 5t0 t1 t2  - t0 t2
--R         + 
--R               6     5       4  2      3  3      2  4         5
--R           - t1  + t1 t2 + t1 t2  - 3t1 t2  + 5t1 t2  - 3t1 t2
--R      *
--R           2
--R         xi
--R     + 
--R                5       5        4  2      4           3  3      3  2
--R           - 3t0 t1 - t0 t2 + 5t0 t1  + 5t0 t1 t2 - 3t0 t1  - 8t0 t1 t2
--R         + 
--R              3     2     3  3     2  4      2  3        2  2  2       2     3
--R           4t0 t1 t2  + t0 t2  + t0 t1  + 2t0 t1 t2 + 3t0 t1 t2  - 10t0 t1 t2
--R         + 
--R              2  4        5         4           2  3            4         5
--R           3t0 t2  + t0 t1  - 2t0 t1 t2 - 2t0 t1 t2  + 8t0 t1 t2  - 2t0 t2
--R         + 
--R               6      5       4  2      3  3      2  4        5
--R           - t1  + 2t1 t2 + t1 t2  - 4t1 t2  + 2t1 t2  - t1 t2
--R      *
--R         xi
--R     + 
--R         6      5        5       4  2      4          4  2      3  2
--R       t0  - 3t0 t1 - 2t0 t2 + t0 t1  + 9t0 t1 t2 - t0 t2  - 4t0 t1 t2
--R     + 
--R            3     2      3  3     2  4      2  3         2  2  2      2     3
--R       - 6t0 t1 t2  + 4t0 t2  - t0 t1  - 3t0 t1 t2 + 12t0 t1 t2  - 3t0 t1 t2
--R     + 
--R            2  4         5         4          3  2          2  3            4
--R       - 2t0 t2  + 3t0 t1  - 3t0 t1 t2 + t0 t1 t2  - 11t0 t1 t2  + 8t0 t1 t2
--R     + 
--R            5     6      4  2      3  3      2  4         5
--R       t0 t2  - t1  + 4t1 t2  - 3t1 t2  + 2t1 t2  - 2t1 t2
--R     ]
--E 13

--S 14 of 22
B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) for j in UZn] 
 

   (14)
   [
                9       9        8  2      8           8  2      7  3
           - 2t0 t1 + t0 t2 + 4t0 t1  + 9t0 t1 t2 - 3t0 t2  - 7t0 t1
         + 
                 7  2        7     2      7  3       6  4       6  3
           - 24t0 t1 t2 - 9t0 t1 t2  + 7t0 t2  + 11t0 t1  + 32t0 t1 t2
         + 
               6  2  2     6     3      6  4       5  5       5  4
           35t0 t1 t2  + t0 t1 t2  - 8t0 t2  - 11t0 t1  - 36t0 t1 t2
         + 
                 5  3  2      5     4      5  5      4  6       4  5
           - 65t0 t1 t2  + 6t0 t1 t2  + 6t0 t2  + 8t0 t1  + 41t0 t1 t2
         + 
               4  4  2       4  3  3       4  2  4      4     5      4  6
           45t0 t1 t2  + 20t0 t1 t2  - 20t0 t1 t2  + 3t0 t1 t2  - 4t0 t2
         + 
                3  7       3  6         3  5  2       3  4  3       3  3  4
           - 6t0 t1  - 26t0 t1 t2 - 13t0 t1 t2  - 45t0 t1 t2  + 40t0 t1 t2
         + 
                 3  2  5      3     6      3  7      2  8     2  7
           - 11t0 t1 t2  + 4t0 t1 t2  + 2t0 t2  + 3t0 t1  + t0 t1 t2
         + 
               2  6  2       2  5  3       2  4  4       2  3  5       2  2  6
           31t0 t1 t2  - 13t0 t1 t2  + 20t0 t1 t2  - 47t0 t1 t2  + 41t0 t1 t2
         + 
                 2     7      2  8        9         8            7  2
           - 19t0 t1 t2  + 2t0 t2  + t0 t1  - 3t0 t1 t2 - 10t0 t1 t2
         + 
                 6  3         5  4          4  5          3  6          2  7
           6t0 t1 t2  + 7t0 t1 t2  - 14t0 t1 t2  + 22t0 t1 t2  - 25t0 t1 t2
         + 
                     8         9     10      9        8  2      7  3      6  4
           16t0 t1 t2  - 3t0 t2  - t1   + 4t1 t2 - 5t1 t2  + 5t1 t2  - 4t1 t2
         + 
              4  6      3  7      2  8         9     10
           4t1 t2  - 5t1 t2  + 5t1 t2  - 4t1 t2  + t2
      *
           3
         xi
     + 
               9        9        8  2       8           8  2      7  3
           - t0 t1 - 2t0 t2 + 3t0 t1  + 11t0 t1 t2 + 5t0 t2  - 7t0 t1
         + 
                 7  2         7     2      7  3      6  4       6  3
           - 16t0 t1 t2 - 26t0 t1 t2  - 4t0 t2  + 8t0 t1  + 23t0 t1 t2
         + 
               6  2  2       6     3      6  4      5  5       5  4
           40t0 t1 t2  + 24t0 t1 t2  + 4t0 t2  - 6t0 t1  - 28t0 t1 t2
         + 
                 5  3  2       5  2  3      5     4      5  5      4  6
           - 41t0 t1 t2  - 32t0 t1 t2  - 8t0 t1 t2  - 5t0 t2  + 4t0 t1
         + 
               4  5         4  4  2       4  3  3      4  2  4       4     5
           23t0 t1 t2 + 10t0 t1 t2  + 45t0 t1 t2  - 5t0 t1 t2  + 14t0 t1 t2
         + 
              4  6      3  7     3  6         3  5  2      3  4  3       3  3  4
           3t0 t2  - 2t0 t1  + t0 t1 t2 - 15t0 t1 t2  - 5t0 t1 t2  - 30t0 t1 t2
         + 
               3  2  5      3     6      2  8      2  7         2  6  2
           13t0 t1 t2  - 9t0 t1 t2  - 2t0 t1  - 6t0 t1 t2 + 14t0 t1 t2
         + 
                2  5  3       2  4  4       2  3  5       2  2  6      2     7
           - 4t0 t1 t2  + 25t0 t1 t2  - 27t0 t1 t2  + 19t0 t1 t2  - 6t0 t1 t2
         + 
             2  8         9         8            6  3          5  4
           t0 t2  + 3t0 t1  - 2t0 t1 t2 - 11t0 t1 t2  + 24t0 t1 t2
         + 
                    4  5          3  6          2  7            8        9
           - 37t0 t1 t2  + 38t0 t1 t2  - 25t0 t1 t2  + 9t0 t1 t2  - t0 t2
         + 
               10      9       8  2      7  3      6  4       5  5       4  6
           - t1   + 2t1 t2 - t1 t2  - 2t1 t2  + 7t1 t2  - 11t1 t2  + 12t1 t2
         + 
                 3  7      2  8         9
           - 11t1 t2  + 8t1 t2  - 3t1 t2
      *
           2
         xi
     + 
                9       9        8  2      8          8  2       7  3
           - 3t0 t1 - t0 t2 + 8t0 t1  + 9t0 t1 t2 + t0 t2  - 11t0 t1
         + 
                 7  2        7     2       6  4       6  3         6  2  2
           - 25t0 t1 t2 - 6t0 t1 t2  + 12t0 t1  + 38t0 t1 t2 + 19t0 t1 t2
         + 
                6     3      6  4       5  5       5  4         5  3  2
           - 9t0 t1 t2  + 3t0 t2  - 11t0 t1  - 37t0 t1 t2 - 27t0 t1 t2
         + 
               5  2  3       5     4      5  5      4  6       4  5
           13t0 t1 t2  + 14t0 t1 t2  - 5t0 t2  + 7t0 t1  + 24t0 t1 t2
         + 
               4  4  2       4  3  3      4  2  4      4     5      4  6
           25t0 t1 t2  - 30t0 t1 t2  - 5t0 t1 t2  - 8t0 t1 t2  + 4t0 t2
         + 
                3  7       3  6        3  5  2      3  4  3       3  3  4
           - 2t0 t1  - 11t0 t1 t2 - 4t0 t1 t2  - 5t0 t1 t2  + 45t0 t1 t2
         + 
                 3  2  5       3     6      3  7     2  8       2  6  2
           - 32t0 t1 t2  + 24t0 t1 t2  - 4t0 t2  - t0 t1  + 14t0 t1 t2
         + 
                 2  5  3       2  4  4       2  3  5       2  2  6       2     7
           - 15t0 t1 t2  + 10t0 t1 t2  - 41t0 t1 t2  + 40t0 t1 t2  - 26t0 t1 t2
         + 
              2  8         9         8           7  2        6  3          5  4
           5t0 t2  + 2t0 t1  - 2t0 t1 t2 - 6t0 t1 t2  + t0 t1 t2  + 23t0 t1 t2
         + 
                    4  5          3  6          2  7             8         9
           - 28t0 t1 t2  + 23t0 t1 t2  - 16t0 t1 t2  + 11t0 t1 t2  - 2t0 t2
         + 
               10      9        8  2      7  3      6  4      5  5      4  6
           - t1   + 3t1 t2 - 2t1 t2  - 2t1 t2  + 4t1 t2  - 6t1 t2  + 8t1 t2
         + 
                3  7      2  8        9
           - 7t1 t2  + 3t1 t2  - t1 t2
      *
         xi
     + 
         10      9        9        8  2       8           8  2      7  3
       t0   - 4t0 t1 - 3t0 t2 + 5t0 t1  + 16t0 t1 t2 + 2t0 t2  - 5t0 t1
     + 
             7  2         7     2      7  3      6  4       6  3         6  2  2
       - 25t0 t1 t2 - 19t0 t1 t2  + 2t0 t2  + 4t0 t1  + 22t0 t1 t2 + 41t0 t1 t2
     + 
          6     3      6  4       5  4         5  3  2       5  2  3
       4t0 t1 t2  - 4t0 t2  - 14t0 t1 t2 - 47t0 t1 t2  - 11t0 t1 t2
     + 
          5     4      5  5      4  6      4  5         4  4  2       4  3  3
       3t0 t1 t2  + 6t0 t2  - 4t0 t1  + 7t0 t1 t2 + 20t0 t1 t2  + 40t0 t1 t2
     + 
             4  2  4      4     5      4  6      3  7      3  6         3  5  2
       - 20t0 t1 t2  + 6t0 t1 t2  - 8t0 t2  + 5t0 t1  + 6t0 t1 t2 - 13t0 t1 t2
     + 
             3  4  3       3  3  4     3     6      3  7      2  8       2  7
       - 45t0 t1 t2  + 20t0 t1 t2  + t0 t1 t2  + 7t0 t2  - 5t0 t1  - 10t0 t1 t2
     + 
           2  6  2       2  5  3       2  4  4       2  3  5       2  2  6
       31t0 t1 t2  - 13t0 t1 t2  + 45t0 t1 t2  - 65t0 t1 t2  + 35t0 t1 t2
     + 
            2     7      2  8         9         8          7  2          6  3
       - 9t0 t1 t2  - 3t0 t2  + 4t0 t1  - 3t0 t1 t2 + t0 t1 t2  - 26t0 t1 t2
     + 
              5  4          4  5          3  6          2  7            8
       41t0 t1 t2  - 36t0 t1 t2  + 32t0 t1 t2  - 24t0 t1 t2  + 9t0 t1 t2
     + 
            9     10     9        8  2      7  3      6  4       5  5       4  6
       t0 t2  - t1   + t1 t2 + 3t1 t2  - 6t1 t2  + 8t1 t2  - 11t1 t2  + 11t1 t2
     + 
            3  7      2  8         9
       - 7t1 t2  + 4t1 t2  - 2t1 t2
     ,

             9        9        8  2       8           8  2      7  3
           t0 t1 + 2t0 t2 - 3t0 t1  - 11t0 t1 t2 - 5t0 t2  + 7t0 t1
         + 
               7  2         7     2      7  3      6  4       6  3
           16t0 t1 t2 + 26t0 t1 t2  + 4t0 t2  - 8t0 t1  - 23t0 t1 t2
         + 
                 6  2  2       6     3      6  4      5  5       5  4
           - 40t0 t1 t2  - 24t0 t1 t2  - 4t0 t2  + 6t0 t1  + 28t0 t1 t2
         + 
               5  3  2       5  2  3      5     4      5  5      4  6
           41t0 t1 t2  + 32t0 t1 t2  + 8t0 t1 t2  + 5t0 t2  - 4t0 t1
         + 
                 4  5         4  4  2       4  3  3      4  2  4       4     5
           - 23t0 t1 t2 - 10t0 t1 t2  - 45t0 t1 t2  + 5t0 t1 t2  - 14t0 t1 t2
         + 
                4  6      3  7     3  6         3  5  2      3  4  3
           - 3t0 t2  + 2t0 t1  - t0 t1 t2 + 15t0 t1 t2  + 5t0 t1 t2
         + 
               3  3  4       3  2  5      3     6      2  8      2  7
           30t0 t1 t2  - 13t0 t1 t2  + 9t0 t1 t2  + 2t0 t1  + 6t0 t1 t2
         + 
                 2  6  2      2  5  3       2  4  4       2  3  5       2  2  6
           - 14t0 t1 t2  + 4t0 t1 t2  - 25t0 t1 t2  + 27t0 t1 t2  - 19t0 t1 t2
         + 
              2     7     2  8         9         8            6  3          5  4
           6t0 t1 t2  - t0 t2  - 3t0 t1  + 2t0 t1 t2 + 11t0 t1 t2  - 24t0 t1 t2
         + 
                  4  5          3  6          2  7            8        9     10
           37t0 t1 t2  - 38t0 t1 t2  + 25t0 t1 t2  - 9t0 t1 t2  + t0 t2  + t1
         + 
                9       8  2      7  3      6  4       5  5       4  6
           - 2t1 t2 + t1 t2  + 2t1 t2  - 7t1 t2  + 11t1 t2  - 12t1 t2
         + 
               3  7      2  8         9
           11t1 t2  - 8t1 t2  + 3t1 t2
      *
           3
         xi
     + 
                9       9        8  2      8           8  2      7  3
           - 2t0 t1 + t0 t2 + 5t0 t1  - 2t0 t1 t2 - 4t0 t2  - 4t0 t1
         + 
                7  2         7     2      7  3      6  4       6  3
           - 9t0 t1 t2 + 20t0 t1 t2  + 4t0 t2  + 4t0 t1  + 15t0 t1 t2
         + 
                 6  2  2       6     3     6  4      5  5      5  4
           - 21t0 t1 t2  - 33t0 t1 t2  - t0 t2  - 5t0 t1  - 9t0 t1 t2
         + 
               5  3  2       5  2  3       5     4      4  6     4  5
           14t0 t1 t2  + 45t0 t1 t2  + 22t0 t1 t2  + 3t0 t1  + t0 t1 t2
         + 
               4  4  2       4  3  3       4     5     4  6       3  6
           15t0 t1 t2  - 75t0 t1 t2  - 22t0 t1 t2  + t0 t2  - 12t0 t1 t2
         + 
               3  5  2       3  3  4       3  2  5       3     6      3  7
           11t0 t1 t2  + 75t0 t1 t2  - 45t0 t1 t2  + 33t0 t1 t2  - 4t0 t2
         + 
             2  8      2  7         2  5  3       2  4  4       2  3  5
           t0 t1  + 6t0 t1 t2 - 11t0 t1 t2  - 15t0 t1 t2  - 14t0 t1 t2
         + 
               2  2  6       2     7      2  8        9         7  2
           21t0 t1 t2  - 20t0 t1 t2  + 4t0 t2  - t0 t1  - 6t0 t1 t2
         + 
                  6  3        5  4         4  5          3  6         2  7
           12t0 t1 t2  - t0 t1 t2  + 9t0 t1 t2  - 15t0 t1 t2  + 9t0 t1 t2
         + 
                    8        9     9       8  2      6  4      5  5      4  6
           2t0 t1 t2  - t0 t2  + t1 t2 - t1 t2  - 3t1 t2  + 5t1 t2  - 4t1 t2
         + 
              3  7      2  8         9
           4t1 t2  - 5t1 t2  + 2t1 t2
      *
           2
         xi
     + 
               9        9       8  2      8           8  2      7  2
           - t0 t1 + 3t0 t2 + t0 t1  - 2t0 t1 t2 - 8t0 t2  - 8t0 t1 t2
         + 
               7     2       7  3      6  4      6  3        6  2  2
           17t0 t1 t2  + 11t0 t2  + 3t0 t1  + 9t0 t1 t2 - 5t0 t1 t2
         + 
                 6     3       6  4      5  5      5  4         5  3  2
           - 23t0 t1 t2  - 12t0 t2  - 5t0 t1  - 8t0 t1 t2 - 24t0 t1 t2
         + 
               5  2  3       5     4       5  5      4  6       4  5
           32t0 t1 t2  + 14t0 t1 t2  + 11t0 t2  + 4t0 t1  + 18t0 t1 t2
         + 
               4  4  2       4  3  3       4  2  4       4     5      4  6
           35t0 t1 t2  - 25t0 t1 t2  - 15t0 t1 t2  - 11t0 t1 t2  - 7t0 t2
         + 
                3  7       3  6        3  5  2       3  4  3       3  3  4
           - 4t0 t1  - 27t0 t1 t2 + 2t0 t1 t2  - 40t0 t1 t2  + 70t0 t1 t2
         + 
                 3  2  5       3     6      3  7      2  8      2  7
           - 24t0 t1 t2  + 13t0 t1 t2  + 2t0 t2  + 5t0 t1  + 7t0 t1 t2
         + 
               2  6  2      2  5  3      2  4  4       2  3  5       2  2  6
           17t0 t1 t2  - 9t0 t1 t2  - 5t0 t1 t2  - 20t0 t1 t2  + 22t0 t1 t2
         + 
                 2     7     2  8         9        8            7  2
           - 13t0 t1 t2  + t0 t2  - 2t0 t1  - t0 t1 t2 - 10t0 t1 t2
         + 
                  6  3          5  4          4  5          3  6            8
           17t0 t1 t2  - 17t0 t1 t2  + 23t0 t1 t2  - 16t0 t1 t2  + 7t0 t1 t2
         + 
                   9      9        8  2      7  3       6  4       5  5
           - 2t0 t2  + 2t1 t2 - 4t1 t2  + 7t1 t2  - 11t1 t2  + 11t1 t2
         + 
                4  6      3  7      2  8        9     10
           - 8t1 t2  + 6t1 t2  - 3t1 t2  - t1 t2  + t2
      *
         xi
     + 
         10      9       9        8  2      8           8  2      7  3
       t0   - 3t0 t1 - t0 t2 + 2t0 t1  + 5t0 t1 t2 - 3t0 t2  + 2t0 t1
     + 
            7  2        7     2      7  3      6  4     6  3       6  2  2
       - 9t0 t1 t2 + 7t0 t1 t2  + 6t0 t2  - 4t0 t1  - t0 t1 t2 + t0 t1 t2
     + 
             6     3      6  4      5  5       5  4        5  3  2       5  2  3
       - 20t0 t1 t2  - 8t0 t2  + 6t0 t1  + 14t0 t1 t2 - 6t0 t1 t2  + 21t0 t1 t2
     + 
           5     4       5  5      4  6       4  5         4  4  2      4  3  3
       11t0 t1 t2  + 11t0 t2  - 8t0 t1  - 16t0 t1 t2 + 10t0 t1 t2  - 5t0 t1 t2
     + 
             4  2  4      4     5       4  6      3  7      3  6        3  5  2
       - 15t0 t1 t2  - 8t0 t1 t2  - 11t0 t2  + 7t0 t1  + 5t0 t1 t2 + 2t0 t1 t2
     + 
             3  4  3       3  3  4       3  2  5       3     6      3  7
       - 40t0 t1 t2  + 50t0 t1 t2  - 13t0 t1 t2  + 10t0 t1 t2  + 7t0 t2
     + 
            2  8      2  7         2  6  2      2  5  3       2  4  4
       - 3t0 t1  - 4t0 t1 t2 + 17t0 t1 t2  - 9t0 t1 t2  + 20t0 t1 t2
     + 
             2  3  5       2  2  6      2     7      2  8        9        8
       - 38t0 t1 t2  + 16t0 t1 t2  - 3t0 t1 t2  - 4t0 t2  + t0 t1  - t0 t1 t2
     + 
            7  2          6  3          5  4        4  5         3  6
       t0 t1 t2  - 15t0 t1 t2  + 17t0 t1 t2  + t0 t1 t2  - 6t0 t1 t2
     + 
            2  7         9     9        8  2      7  3     6  4     4  6
       t0 t1 t2  + 2t0 t2  - t1 t2 + 4t1 t2  - 4t1 t2  + t1 t2  - t1 t2
     + 
          3  7      2  8        9
       4t1 t2  - 4t1 t2  + t1 t2
     ,

               9        9        8  2      8  2      7  3     7  2
           - t0 t1 - 2t0 t2 + 4t0 t1  + 4t0 t2  - 4t0 t1  - t0 t1 t2
         + 
              7     2      7  3     6  4      6  3         6  2  2       6     3
           3t0 t1 t2  - 7t0 t2  + t0 t1  + 6t0 t1 t2 - 16t0 t1 t2  - 10t0 t1 t2
         + 
               6  4     5  4         5  3  2       5  2  3      5     4
           11t0 t2  - t0 t1 t2 + 38t0 t1 t2  + 13t0 t1 t2  + 8t0 t1 t2
         + 
                 5  5     4  6       4  5         4  4  2       4  3  3
           - 11t0 t2  - t0 t1  - 17t0 t1 t2 - 20t0 t1 t2  - 50t0 t1 t2
         + 
               4  2  4       4     5      4  6      3  7       3  6
           15t0 t1 t2  - 11t0 t1 t2  + 8t0 t2  + 4t0 t1  + 15t0 t1 t2
         + 
              3  5  2       3  4  3      3  3  4       3  2  5       3     6
           9t0 t1 t2  + 40t0 t1 t2  + 5t0 t1 t2  - 21t0 t1 t2  + 20t0 t1 t2
         + 
                3  7      2  8     2  7         2  6  2      2  5  3
           - 6t0 t2  - 4t0 t1  - t0 t1 t2 - 17t0 t1 t2  - 2t0 t1 t2
         + 
                 2  4  4      2  3  5     2  2  6      2     7      2  8
           - 10t0 t1 t2  + 6t0 t1 t2  - t0 t1 t2  - 7t0 t1 t2  + 3t0 t2
         + 
                9        8           7  2         6  3          5  4
           t0 t1  + t0 t1 t2 + 4t0 t1 t2  - 5t0 t1 t2  + 16t0 t1 t2
         + 
                    4  5        3  6         2  7            8        9     9
           - 14t0 t1 t2  + t0 t1 t2  + 9t0 t1 t2  - 5t0 t1 t2  + t0 t2  - t1 t2
         + 
              8  2      7  3      6  4      5  5      4  6      3  7      2  8
           3t1 t2  - 7t1 t2  + 8t1 t2  - 6t1 t2  + 4t1 t2  - 2t1 t2  - 2t1 t2
         + 
                 9     10
           3t1 t2  - t2
      *
           3
         xi
     + 
              9       9        8  2      8           8  2      7  3       7  2
           2t0 t1 - t0 t2 - 4t0 t1  - 9t0 t1 t2 + 3t0 t2  + 7t0 t1  + 24t0 t1 t2
         + 
              7     2      7  3       6  4       6  3         6  2  2
           9t0 t1 t2  - 7t0 t2  - 11t0 t1  - 32t0 t1 t2 - 35t0 t1 t2
         + 
               6     3      6  4       5  5       5  4         5  3  2
           - t0 t1 t2  + 8t0 t2  + 11t0 t1  + 36t0 t1 t2 + 65t0 t1 t2
         + 
                5     4      5  5      4  6       4  5         4  4  2
           - 6t0 t1 t2  - 6t0 t2  - 8t0 t1  - 41t0 t1 t2 - 45t0 t1 t2
         + 
                 4  3  3       4  2  4      4     5      4  6      3  7
           - 20t0 t1 t2  + 20t0 t1 t2  - 3t0 t1 t2  + 4t0 t2  + 6t0 t1
         + 
               3  6         3  5  2       3  4  3       3  3  4       3  2  5
           26t0 t1 t2 + 13t0 t1 t2  + 45t0 t1 t2  - 40t0 t1 t2  + 11t0 t1 t2
         + 
                3     6      3  7      2  8     2  7         2  6  2
           - 4t0 t1 t2  - 2t0 t2  - 3t0 t1  - t0 t1 t2 - 31t0 t1 t2
         + 
               2  5  3       2  4  4       2  3  5       2  2  6       2     7
           13t0 t1 t2  - 20t0 t1 t2  + 47t0 t1 t2  - 41t0 t1 t2  + 19t0 t1 t2
         + 
                2  8        9         8            7  2         6  3
           - 2t0 t2  - t0 t1  + 3t0 t1 t2 + 10t0 t1 t2  - 6t0 t1 t2
         + 
                   5  4          4  5          3  6          2  7             8
           - 7t0 t1 t2  + 14t0 t1 t2  - 22t0 t1 t2  + 25t0 t1 t2  - 16t0 t1 t2
         + 
                 9     10      9        8  2      7  3      6  4      4  6
           3t0 t2  + t1   - 4t1 t2 + 5t1 t2  - 5t1 t2  + 4t1 t2  - 4t1 t2
         + 
              3  7      2  8         9     10
           5t1 t2  - 5t1 t2  + 4t1 t2  - t2
      *
           2
         xi
     + 
             9        9       8  2      8           8  2      7  2
           t0 t1 - 3t0 t2 - t0 t1  + 2t0 t1 t2 + 8t0 t2  + 8t0 t1 t2
         + 
                 7     2       7  3      6  4      6  3        6  2  2
           - 17t0 t1 t2  - 11t0 t2  - 3t0 t1  - 9t0 t1 t2 + 5t0 t1 t2
         + 
               6     3       6  4      5  5      5  4         5  3  2
           23t0 t1 t2  + 12t0 t2  + 5t0 t1  + 8t0 t1 t2 + 24t0 t1 t2
         + 
                 5  2  3       5     4       5  5      4  6       4  5
           - 32t0 t1 t2  - 14t0 t1 t2  - 11t0 t2  - 4t0 t1  - 18t0 t1 t2
         + 
                 4  4  2       4  3  3       4  2  4       4     5      4  6
           - 35t0 t1 t2  + 25t0 t1 t2  + 15t0 t1 t2  + 11t0 t1 t2  + 7t0 t2
         + 
              3  7       3  6        3  5  2       3  4  3       3  3  4
           4t0 t1  + 27t0 t1 t2 - 2t0 t1 t2  + 40t0 t1 t2  - 70t0 t1 t2
         + 
               3  2  5       3     6      3  7      2  8      2  7
           24t0 t1 t2  - 13t0 t1 t2  - 2t0 t2  - 5t0 t1  - 7t0 t1 t2
         + 
                 2  6  2      2  5  3      2  4  4       2  3  5       2  2  6
           - 17t0 t1 t2  + 9t0 t1 t2  + 5t0 t1 t2  + 20t0 t1 t2  - 22t0 t1 t2
         + 
               2     7     2  8         9        8            7  2          6  3
           13t0 t1 t2  - t0 t2  + 2t0 t1  + t0 t1 t2 + 10t0 t1 t2  - 17t0 t1 t2
         + 
                  5  4          4  5          3  6            8         9
           17t0 t1 t2  - 23t0 t1 t2  + 16t0 t1 t2  - 7t0 t1 t2  + 2t0 t2
         + 
                9        8  2      7  3       6  4       5  5      4  6
           - 2t1 t2 + 4t1 t2  - 7t1 t2  + 11t1 t2  - 11t1 t2  + 8t1 t2
         + 
                3  7      2  8        9     10
           - 6t1 t2  + 3t1 t2  + t1 t2  - t2
      *
         xi
     + 
         10      9        9       8  2      8           8  2      7  3
       t0   - 2t0 t1 - 4t0 t2 + t0 t1  + 7t0 t1 t2 + 5t0 t2  + 2t0 t1
     + 
           7  2         7     2      7  3      6  4       6  3        6  2  2
       - t0 t1 t2 - 10t0 t1 t2  - 5t0 t2  - 7t0 t1  - 10t0 t1 t2 + 6t0 t1 t2
     + 
          6     3      6  4       5  5       5  4         5  3  2       5  2  3
       3t0 t1 t2  + 4t0 t2  + 11t0 t1  + 22t0 t1 t2 + 18t0 t1 t2  - 11t0 t1 t2
     + 
            5     4       4  6       4  5         4  4  2       4  3  3
       - 3t0 t1 t2  - 12t0 t1  - 34t0 t1 t2 - 25t0 t1 t2  + 20t0 t1 t2
     + 
          4     5      4  6       3  7       3  6         3  3  4       3  2  5
       3t0 t1 t2  - 4t0 t2  + 11t0 t1  + 32t0 t1 t2 - 20t0 t1 t2  + 11t0 t1 t2
     + 
            3     6      3  7      2  8       2  7         2  4  4       2  3  5
       - 3t0 t1 t2  + 5t0 t2  - 8t0 t1  - 11t0 t1 t2 + 25t0 t1 t2  - 18t0 t1 t2
     + 
            2  2  6       2     7      2  8         9          7  2
       - 6t0 t1 t2  + 10t0 t1 t2  - 5t0 t2  + 3t0 t1  + 11t0 t1 t2
     + 
                6  3          5  4          4  5          3  6        2  7
       - 32t0 t1 t2  + 34t0 t1 t2  - 22t0 t1 t2  + 10t0 t1 t2  + t0 t1 t2
     + 
                  8         9      9        8  2       7  3       6  4
       - 7t0 t1 t2  + 4t0 t2  - 3t1 t2 + 8t1 t2  - 11t1 t2  + 12t1 t2
     + 
             5  5      4  6      3  7     2  8         9     10
       - 11t1 t2  + 7t1 t2  - 2t1 t2  - t1 t2  + 2t1 t2  - t2
     ,

              9       9        8  2      8           8  2      7  3      7  2
           2t0 t1 - t0 t2 - 5t0 t1  + 2t0 t1 t2 + 4t0 t2  + 4t0 t1  + 9t0 t1 t2
         + 
                 7     2      7  3      6  4       6  3         6  2  2
           - 20t0 t1 t2  - 4t0 t2  - 4t0 t1  - 15t0 t1 t2 + 21t0 t1 t2
         + 
               6     3     6  4      5  5      5  4         5  3  2
           33t0 t1 t2  + t0 t2  + 5t0 t1  + 9t0 t1 t2 - 14t0 t1 t2
         + 
                 5  2  3       5     4      4  6     4  5         4  4  2
           - 45t0 t1 t2  - 22t0 t1 t2  - 3t0 t1  - t0 t1 t2 - 15t0 t1 t2
         + 
               4  3  3       4     5     4  6       3  6         3  5  2
           75t0 t1 t2  + 22t0 t1 t2  - t0 t2  + 12t0 t1 t2 - 11t0 t1 t2
         + 
                 3  3  4       3  2  5       3     6      3  7     2  8
           - 75t0 t1 t2  + 45t0 t1 t2  - 33t0 t1 t2  + 4t0 t2  - t0 t1
         + 
                2  7         2  5  3       2  4  4       2  3  5       2  2  6
           - 6t0 t1 t2 + 11t0 t1 t2  + 15t0 t1 t2  + 14t0 t1 t2  - 21t0 t1 t2
         + 
               2     7      2  8        9         7  2          6  3        5  4
           20t0 t1 t2  - 4t0 t2  + t0 t1  + 6t0 t1 t2  - 12t0 t1 t2  + t0 t1 t2
         + 
                   4  5          3  6         2  7            8        9     9
           - 9t0 t1 t2  + 15t0 t1 t2  - 9t0 t1 t2  - 2t0 t1 t2  + t0 t2  - t1 t2
         + 
             8  2      6  4      5  5      4  6      3  7      2  8         9
           t1 t2  + 3t1 t2  - 5t1 t2  + 4t1 t2  - 4t1 t2  + 5t1 t2  - 2t1 t2
      *
           3
         xi
     + 
             9        9        8  2      8  2      7  3     7  2        7     2
           t0 t1 + 2t0 t2 - 4t0 t1  - 4t0 t2  + 4t0 t1  + t0 t1 t2 - 3t0 t1 t2
         + 
              7  3     6  4      6  3         6  2  2       6     3       6  4
           7t0 t2  - t0 t1  - 6t0 t1 t2 + 16t0 t1 t2  + 10t0 t1 t2  - 11t0 t2
         + 
             5  4         5  3  2       5  2  3      5     4       5  5     4  6
           t0 t1 t2 - 38t0 t1 t2  - 13t0 t1 t2  - 8t0 t1 t2  + 11t0 t2  + t0 t1
         + 
               4  5         4  4  2       4  3  3       4  2  4       4     5
           17t0 t1 t2 + 20t0 t1 t2  + 50t0 t1 t2  - 15t0 t1 t2  + 11t0 t1 t2
         + 
                4  6      3  7       3  6        3  5  2       3  4  3
           - 8t0 t2  - 4t0 t1  - 15t0 t1 t2 - 9t0 t1 t2  - 40t0 t1 t2
         + 
                3  3  4       3  2  5       3     6      3  7      2  8
           - 5t0 t1 t2  + 21t0 t1 t2  - 20t0 t1 t2  + 6t0 t2  + 4t0 t1
         + 
             2  7         2  6  2      2  5  3       2  4  4      2  3  5
           t0 t1 t2 + 17t0 t1 t2  + 2t0 t1 t2  + 10t0 t1 t2  - 6t0 t1 t2
         + 
             2  2  6      2     7      2  8        9        8           7  2
           t0 t1 t2  + 7t0 t1 t2  - 3t0 t2  - t0 t1  - t0 t1 t2 - 4t0 t1 t2
         + 
                 6  3          5  4          4  5        3  6         2  7
           5t0 t1 t2  - 16t0 t1 t2  + 14t0 t1 t2  - t0 t1 t2  - 9t0 t1 t2
         + 
                    8        9     9        8  2      7  3      6  4      5  5
           5t0 t1 t2  - t0 t2  + t1 t2 - 3t1 t2  + 7t1 t2  - 8t1 t2  + 6t1 t2
         + 
                4  6      3  7      2  8         9     10
           - 4t1 t2  + 2t1 t2  + 2t1 t2  - 3t1 t2  + t2
      *
           2
         xi
     + 
              9       9        8  2      8          8  2       7  3       7  2
           3t0 t1 + t0 t2 - 8t0 t1  - 9t0 t1 t2 - t0 t2  + 11t0 t1  + 25t0 t1 t2
         + 
              7     2       6  4       6  3         6  2  2      6     3
           6t0 t1 t2  - 12t0 t1  - 38t0 t1 t2 - 19t0 t1 t2  + 9t0 t1 t2
         + 
                6  4       5  5       5  4         5  3  2       5  2  3
           - 3t0 t2  + 11t0 t1  + 37t0 t1 t2 + 27t0 t1 t2  - 13t0 t1 t2
         + 
                 5     4      5  5      4  6       4  5         4  4  2
           - 14t0 t1 t2  + 5t0 t2  - 7t0 t1  - 24t0 t1 t2 - 25t0 t1 t2
         + 
               4  3  3      4  2  4      4     5      4  6      3  7
           30t0 t1 t2  + 5t0 t1 t2  + 8t0 t1 t2  - 4t0 t2  + 2t0 t1
         + 
               3  6        3  5  2      3  4  3       3  3  4       3  2  5
           11t0 t1 t2 + 4t0 t1 t2  + 5t0 t1 t2  - 45t0 t1 t2  + 32t0 t1 t2
         + 
                 3     6      3  7     2  8       2  6  2       2  5  3
           - 24t0 t1 t2  + 4t0 t2  + t0 t1  - 14t0 t1 t2  + 15t0 t1 t2
         + 
                 2  4  4       2  3  5       2  2  6       2     7      2  8
           - 10t0 t1 t2  + 41t0 t1 t2  - 40t0 t1 t2  + 26t0 t1 t2  - 5t0 t2
         + 
                   9         8           7  2        6  3          5  4
           - 2t0 t1  + 2t0 t1 t2 + 6t0 t1 t2  - t0 t1 t2  - 23t0 t1 t2
         + 
                  4  5          3  6          2  7             8         9
           28t0 t1 t2  - 23t0 t1 t2  + 16t0 t1 t2  - 11t0 t1 t2  + 2t0 t2
         + 
             10      9        8  2      7  3      6  4      5  5      4  6
           t1   - 3t1 t2 + 2t1 t2  + 2t1 t2  - 4t1 t2  + 6t1 t2  - 8t1 t2
         + 
              3  7      2  8        9
           7t1 t2  - 3t1 t2  + t1 t2
      *
         xi
     + 
         10     9        9        8  2      8          8  2      7  3
       t0   - t0 t1 - 2t0 t2 - 3t0 t1  + 7t0 t1 t2 + t0 t2  + 6t0 t1
     + 
             7     2      7  3      6  4       6  3         6  2  2
       - 13t0 t1 t2  + 2t0 t2  - 8t0 t1  - 16t0 t1 t2 + 22t0 t1 t2
     + 
           6     3      6  4       5  5       5  4         5  3  2       5  2  3
       13t0 t1 t2  - 7t0 t2  + 11t0 t1  + 23t0 t1 t2 - 20t0 t1 t2  - 24t0 t1 t2
     + 
             5     4       5  5       4  6       4  5        4  4  2
       - 11t0 t1 t2  + 11t0 t2  - 11t0 t1  - 17t0 t1 t2 - 5t0 t1 t2
     + 
           4  3  3       4  2  4       4     5       4  6      3  7       3  6
       70t0 t1 t2  - 15t0 t1 t2  + 14t0 t1 t2  - 12t0 t2  + 7t0 t1  + 17t0 t1 t2
     + 
            3  5  2       3  4  3       3  3  4       3  2  5       3     6
       - 9t0 t1 t2  - 40t0 t1 t2  - 25t0 t1 t2  + 32t0 t1 t2  - 23t0 t1 t2
     + 
           3  7      2  8       2  7         2  6  2      2  5  3       2  4  4
       11t0 t2  - 4t0 t1  - 10t0 t1 t2 + 17t0 t1 t2  + 2t0 t1 t2  + 35t0 t1 t2
     + 
             2  3  5      2  2  6       2     7      2  8         9        8
       - 24t0 t1 t2  - 5t0 t1 t2  + 17t0 t1 t2  - 8t0 t2  + 2t0 t1  - t0 t1 t2
     + 
             7  2          6  3          5  4         4  5         3  6
       7t0 t1 t2  - 27t0 t1 t2  + 18t0 t1 t2  - 8t0 t1 t2  + 9t0 t1 t2
     + 
               2  7            8         9      9        8  2      7  3
       - 8t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t1 t2 + 5t1 t2  - 4t1 t2
     + 
          6  4      5  5      4  6     2  8        9
       4t1 t2  - 5t1 t2  + 3t1 t2  + t1 t2  - t1 t2
     ]
--R 
--R
--R   (14)
--R   [
--R                9       9        8  2      8           8  2      7  3
--R           - 2t0 t1 + t0 t2 + 4t0 t1  + 9t0 t1 t2 - 3t0 t2  - 7t0 t1
--R         + 
--R                 7  2        7     2      7  3       6  4       6  3
--R           - 24t0 t1 t2 - 9t0 t1 t2  + 7t0 t2  + 11t0 t1  + 32t0 t1 t2
--R         + 
--R               6  2  2     6     3      6  4       5  5       5  4
--R           35t0 t1 t2  + t0 t1 t2  - 8t0 t2  - 11t0 t1  - 36t0 t1 t2
--R         + 
--R                 5  3  2      5     4      5  5      4  6       4  5
--R           - 65t0 t1 t2  + 6t0 t1 t2  + 6t0 t2  + 8t0 t1  + 41t0 t1 t2
--R         + 
--R               4  4  2       4  3  3       4  2  4      4     5      4  6
--R           45t0 t1 t2  + 20t0 t1 t2  - 20t0 t1 t2  + 3t0 t1 t2  - 4t0 t2
--R         + 
--R                3  7       3  6         3  5  2       3  4  3       3  3  4
--R           - 6t0 t1  - 26t0 t1 t2 - 13t0 t1 t2  - 45t0 t1 t2  + 40t0 t1 t2
--R         + 
--R                 3  2  5      3     6      3  7      2  8     2  7
--R           - 11t0 t1 t2  + 4t0 t1 t2  + 2t0 t2  + 3t0 t1  + t0 t1 t2
--R         + 
--R               2  6  2       2  5  3       2  4  4       2  3  5       2  2  6
--R           31t0 t1 t2  - 13t0 t1 t2  + 20t0 t1 t2  - 47t0 t1 t2  + 41t0 t1 t2
--R         + 
--R                 2     7      2  8        9         8            7  2
--R           - 19t0 t1 t2  + 2t0 t2  + t0 t1  - 3t0 t1 t2 - 10t0 t1 t2
--R         + 
--R                 6  3         5  4          4  5          3  6          2  7
--R           6t0 t1 t2  + 7t0 t1 t2  - 14t0 t1 t2  + 22t0 t1 t2  - 25t0 t1 t2
--R         + 
--R                     8         9     10      9        8  2      7  3      6  4
--R           16t0 t1 t2  - 3t0 t2  - t1   + 4t1 t2 - 5t1 t2  + 5t1 t2  - 4t1 t2
--R         + 
--R              4  6      3  7      2  8         9     10
--R           4t1 t2  - 5t1 t2  + 5t1 t2  - 4t1 t2  + t2
--R      *
--R           3
--R         xi
--R     + 
--R               9        9        8  2       8           8  2      7  3
--R           - t0 t1 - 2t0 t2 + 3t0 t1  + 11t0 t1 t2 + 5t0 t2  - 7t0 t1
--R         + 
--R                 7  2         7     2      7  3      6  4       6  3
--R           - 16t0 t1 t2 - 26t0 t1 t2  - 4t0 t2  + 8t0 t1  + 23t0 t1 t2
--R         + 
--R               6  2  2       6     3      6  4      5  5       5  4
--R           40t0 t1 t2  + 24t0 t1 t2  + 4t0 t2  - 6t0 t1  - 28t0 t1 t2
--R         + 
--R                 5  3  2       5  2  3      5     4      5  5      4  6
--R           - 41t0 t1 t2  - 32t0 t1 t2  - 8t0 t1 t2  - 5t0 t2  + 4t0 t1
--R         + 
--R               4  5         4  4  2       4  3  3      4  2  4       4     5
--R           23t0 t1 t2 + 10t0 t1 t2  + 45t0 t1 t2  - 5t0 t1 t2  + 14t0 t1 t2
--R         + 
--R              4  6      3  7     3  6         3  5  2      3  4  3       3  3  4
--R           3t0 t2  - 2t0 t1  + t0 t1 t2 - 15t0 t1 t2  - 5t0 t1 t2  - 30t0 t1 t2
--R         + 
--R               3  2  5      3     6      2  8      2  7         2  6  2
--R           13t0 t1 t2  - 9t0 t1 t2  - 2t0 t1  - 6t0 t1 t2 + 14t0 t1 t2
--R         + 
--R                2  5  3       2  4  4       2  3  5       2  2  6      2     7
--R           - 4t0 t1 t2  + 25t0 t1 t2  - 27t0 t1 t2  + 19t0 t1 t2  - 6t0 t1 t2
--R         + 
--R             2  8         9         8            6  3          5  4
--R           t0 t2  + 3t0 t1  - 2t0 t1 t2 - 11t0 t1 t2  + 24t0 t1 t2
--R         + 
--R                    4  5          3  6          2  7            8        9
--R           - 37t0 t1 t2  + 38t0 t1 t2  - 25t0 t1 t2  + 9t0 t1 t2  - t0 t2
--R         + 
--R               10      9       8  2      7  3      6  4       5  5       4  6
--R           - t1   + 2t1 t2 - t1 t2  - 2t1 t2  + 7t1 t2  - 11t1 t2  + 12t1 t2
--R         + 
--R                 3  7      2  8         9
--R           - 11t1 t2  + 8t1 t2  - 3t1 t2
--R      *
--R           2
--R         xi
--R     + 
--R                9       9        8  2      8          8  2       7  3
--R           - 3t0 t1 - t0 t2 + 8t0 t1  + 9t0 t1 t2 + t0 t2  - 11t0 t1
--R         + 
--R                 7  2        7     2       6  4       6  3         6  2  2
--R           - 25t0 t1 t2 - 6t0 t1 t2  + 12t0 t1  + 38t0 t1 t2 + 19t0 t1 t2
--R         + 
--R                6     3      6  4       5  5       5  4         5  3  2
--R           - 9t0 t1 t2  + 3t0 t2  - 11t0 t1  - 37t0 t1 t2 - 27t0 t1 t2
--R         + 
--R               5  2  3       5     4      5  5      4  6       4  5
--R           13t0 t1 t2  + 14t0 t1 t2  - 5t0 t2  + 7t0 t1  + 24t0 t1 t2
--R         + 
--R               4  4  2       4  3  3      4  2  4      4     5      4  6
--R           25t0 t1 t2  - 30t0 t1 t2  - 5t0 t1 t2  - 8t0 t1 t2  + 4t0 t2
--R         + 
--R                3  7       3  6        3  5  2      3  4  3       3  3  4
--R           - 2t0 t1  - 11t0 t1 t2 - 4t0 t1 t2  - 5t0 t1 t2  + 45t0 t1 t2
--R         + 
--R                 3  2  5       3     6      3  7     2  8       2  6  2
--R           - 32t0 t1 t2  + 24t0 t1 t2  - 4t0 t2  - t0 t1  + 14t0 t1 t2
--R         + 
--R                 2  5  3       2  4  4       2  3  5       2  2  6       2     7
--R           - 15t0 t1 t2  + 10t0 t1 t2  - 41t0 t1 t2  + 40t0 t1 t2  - 26t0 t1 t2
--R         + 
--R              2  8         9         8           7  2        6  3          5  4
--R           5t0 t2  + 2t0 t1  - 2t0 t1 t2 - 6t0 t1 t2  + t0 t1 t2  + 23t0 t1 t2
--R         + 
--R                    4  5          3  6          2  7             8         9
--R           - 28t0 t1 t2  + 23t0 t1 t2  - 16t0 t1 t2  + 11t0 t1 t2  - 2t0 t2
--R         + 
--R               10      9        8  2      7  3      6  4      5  5      4  6
--R           - t1   + 3t1 t2 - 2t1 t2  - 2t1 t2  + 4t1 t2  - 6t1 t2  + 8t1 t2
--R         + 
--R                3  7      2  8        9
--R           - 7t1 t2  + 3t1 t2  - t1 t2
--R      *
--R         xi
--R     + 
--R         10      9        9        8  2       8           8  2      7  3
--R       t0   - 4t0 t1 - 3t0 t2 + 5t0 t1  + 16t0 t1 t2 + 2t0 t2  - 5t0 t1
--R     + 
--R             7  2         7     2      7  3      6  4       6  3         6  2  2
--R       - 25t0 t1 t2 - 19t0 t1 t2  + 2t0 t2  + 4t0 t1  + 22t0 t1 t2 + 41t0 t1 t2
--R     + 
--R          6     3      6  4       5  4         5  3  2       5  2  3
--R       4t0 t1 t2  - 4t0 t2  - 14t0 t1 t2 - 47t0 t1 t2  - 11t0 t1 t2
--R     + 
--R          5     4      5  5      4  6      4  5         4  4  2       4  3  3
--R       3t0 t1 t2  + 6t0 t2  - 4t0 t1  + 7t0 t1 t2 + 20t0 t1 t2  + 40t0 t1 t2
--R     + 
--R             4  2  4      4     5      4  6      3  7      3  6         3  5  2
--R       - 20t0 t1 t2  + 6t0 t1 t2  - 8t0 t2  + 5t0 t1  + 6t0 t1 t2 - 13t0 t1 t2
--R     + 
--R             3  4  3       3  3  4     3     6      3  7      2  8       2  7
--R       - 45t0 t1 t2  + 20t0 t1 t2  + t0 t1 t2  + 7t0 t2  - 5t0 t1  - 10t0 t1 t2
--R     + 
--R           2  6  2       2  5  3       2  4  4       2  3  5       2  2  6
--R       31t0 t1 t2  - 13t0 t1 t2  + 45t0 t1 t2  - 65t0 t1 t2  + 35t0 t1 t2
--R     + 
--R            2     7      2  8         9         8          7  2          6  3
--R       - 9t0 t1 t2  - 3t0 t2  + 4t0 t1  - 3t0 t1 t2 + t0 t1 t2  - 26t0 t1 t2
--R     + 
--R              5  4          4  5          3  6          2  7            8
--R       41t0 t1 t2  - 36t0 t1 t2  + 32t0 t1 t2  - 24t0 t1 t2  + 9t0 t1 t2
--R     + 
--R            9     10     9        8  2      7  3      6  4       5  5       4  6
--R       t0 t2  - t1   + t1 t2 + 3t1 t2  - 6t1 t2  + 8t1 t2  - 11t1 t2  + 11t1 t2
--R     + 
--R            3  7      2  8         9
--R       - 7t1 t2  + 4t1 t2  - 2t1 t2
--R     ,
--R
--R             9        9        8  2       8           8  2      7  3
--R           t0 t1 + 2t0 t2 - 3t0 t1  - 11t0 t1 t2 - 5t0 t2  + 7t0 t1
--R         + 
--R               7  2         7     2      7  3      6  4       6  3
--R           16t0 t1 t2 + 26t0 t1 t2  + 4t0 t2  - 8t0 t1  - 23t0 t1 t2
--R         + 
--R                 6  2  2       6     3      6  4      5  5       5  4
--R           - 40t0 t1 t2  - 24t0 t1 t2  - 4t0 t2  + 6t0 t1  + 28t0 t1 t2
--R         + 
--R               5  3  2       5  2  3      5     4      5  5      4  6
--R           41t0 t1 t2  + 32t0 t1 t2  + 8t0 t1 t2  + 5t0 t2  - 4t0 t1
--R         + 
--R                 4  5         4  4  2       4  3  3      4  2  4       4     5
--R           - 23t0 t1 t2 - 10t0 t1 t2  - 45t0 t1 t2  + 5t0 t1 t2  - 14t0 t1 t2
--R         + 
--R                4  6      3  7     3  6         3  5  2      3  4  3
--R           - 3t0 t2  + 2t0 t1  - t0 t1 t2 + 15t0 t1 t2  + 5t0 t1 t2
--R         + 
--R               3  3  4       3  2  5      3     6      2  8      2  7
--R           30t0 t1 t2  - 13t0 t1 t2  + 9t0 t1 t2  + 2t0 t1  + 6t0 t1 t2
--R         + 
--R                 2  6  2      2  5  3       2  4  4       2  3  5       2  2  6
--R           - 14t0 t1 t2  + 4t0 t1 t2  - 25t0 t1 t2  + 27t0 t1 t2  - 19t0 t1 t2
--R         + 
--R              2     7     2  8         9         8            6  3          5  4
--R           6t0 t1 t2  - t0 t2  - 3t0 t1  + 2t0 t1 t2 + 11t0 t1 t2  - 24t0 t1 t2
--R         + 
--R                  4  5          3  6          2  7            8        9     10
--R           37t0 t1 t2  - 38t0 t1 t2  + 25t0 t1 t2  - 9t0 t1 t2  + t0 t2  + t1
--R         + 
--R                9       8  2      7  3      6  4       5  5       4  6
--R           - 2t1 t2 + t1 t2  + 2t1 t2  - 7t1 t2  + 11t1 t2  - 12t1 t2
--R         + 
--R               3  7      2  8         9
--R           11t1 t2  - 8t1 t2  + 3t1 t2
--R      *
--R           3
--R         xi
--R     + 
--R                9       9        8  2      8           8  2      7  3
--R           - 2t0 t1 + t0 t2 + 5t0 t1  - 2t0 t1 t2 - 4t0 t2  - 4t0 t1
--R         + 
--R                7  2         7     2      7  3      6  4       6  3
--R           - 9t0 t1 t2 + 20t0 t1 t2  + 4t0 t2  + 4t0 t1  + 15t0 t1 t2
--R         + 
--R                 6  2  2       6     3     6  4      5  5      5  4
--R           - 21t0 t1 t2  - 33t0 t1 t2  - t0 t2  - 5t0 t1  - 9t0 t1 t2
--R         + 
--R               5  3  2       5  2  3       5     4      4  6     4  5
--R           14t0 t1 t2  + 45t0 t1 t2  + 22t0 t1 t2  + 3t0 t1  + t0 t1 t2
--R         + 
--R               4  4  2       4  3  3       4     5     4  6       3  6
--R           15t0 t1 t2  - 75t0 t1 t2  - 22t0 t1 t2  + t0 t2  - 12t0 t1 t2
--R         + 
--R               3  5  2       3  3  4       3  2  5       3     6      3  7
--R           11t0 t1 t2  + 75t0 t1 t2  - 45t0 t1 t2  + 33t0 t1 t2  - 4t0 t2
--R         + 
--R             2  8      2  7         2  5  3       2  4  4       2  3  5
--R           t0 t1  + 6t0 t1 t2 - 11t0 t1 t2  - 15t0 t1 t2  - 14t0 t1 t2
--R         + 
--R               2  2  6       2     7      2  8        9         7  2
--R           21t0 t1 t2  - 20t0 t1 t2  + 4t0 t2  - t0 t1  - 6t0 t1 t2
--R         + 
--R                  6  3        5  4         4  5          3  6         2  7
--R           12t0 t1 t2  - t0 t1 t2  + 9t0 t1 t2  - 15t0 t1 t2  + 9t0 t1 t2
--R         + 
--R                    8        9     9       8  2      6  4      5  5      4  6
--R           2t0 t1 t2  - t0 t2  + t1 t2 - t1 t2  - 3t1 t2  + 5t1 t2  - 4t1 t2
--R         + 
--R              3  7      2  8         9
--R           4t1 t2  - 5t1 t2  + 2t1 t2
--R      *
--R           2
--R         xi
--R     + 
--R               9        9       8  2      8           8  2      7  2
--R           - t0 t1 + 3t0 t2 + t0 t1  - 2t0 t1 t2 - 8t0 t2  - 8t0 t1 t2
--R         + 
--R               7     2       7  3      6  4      6  3        6  2  2
--R           17t0 t1 t2  + 11t0 t2  + 3t0 t1  + 9t0 t1 t2 - 5t0 t1 t2
--R         + 
--R                 6     3       6  4      5  5      5  4         5  3  2
--R           - 23t0 t1 t2  - 12t0 t2  - 5t0 t1  - 8t0 t1 t2 - 24t0 t1 t2
--R         + 
--R               5  2  3       5     4       5  5      4  6       4  5
--R           32t0 t1 t2  + 14t0 t1 t2  + 11t0 t2  + 4t0 t1  + 18t0 t1 t2
--R         + 
--R               4  4  2       4  3  3       4  2  4       4     5      4  6
--R           35t0 t1 t2  - 25t0 t1 t2  - 15t0 t1 t2  - 11t0 t1 t2  - 7t0 t2
--R         + 
--R                3  7       3  6        3  5  2       3  4  3       3  3  4
--R           - 4t0 t1  - 27t0 t1 t2 + 2t0 t1 t2  - 40t0 t1 t2  + 70t0 t1 t2
--R         + 
--R                 3  2  5       3     6      3  7      2  8      2  7
--R           - 24t0 t1 t2  + 13t0 t1 t2  + 2t0 t2  + 5t0 t1  + 7t0 t1 t2
--R         + 
--R               2  6  2      2  5  3      2  4  4       2  3  5       2  2  6
--R           17t0 t1 t2  - 9t0 t1 t2  - 5t0 t1 t2  - 20t0 t1 t2  + 22t0 t1 t2
--R         + 
--R                 2     7     2  8         9        8            7  2
--R           - 13t0 t1 t2  + t0 t2  - 2t0 t1  - t0 t1 t2 - 10t0 t1 t2
--R         + 
--R                  6  3          5  4          4  5          3  6            8
--R           17t0 t1 t2  - 17t0 t1 t2  + 23t0 t1 t2  - 16t0 t1 t2  + 7t0 t1 t2
--R         + 
--R                   9      9        8  2      7  3       6  4       5  5
--R           - 2t0 t2  + 2t1 t2 - 4t1 t2  + 7t1 t2  - 11t1 t2  + 11t1 t2
--R         + 
--R                4  6      3  7      2  8        9     10
--R           - 8t1 t2  + 6t1 t2  - 3t1 t2  - t1 t2  + t2
--R      *
--R         xi
--R     + 
--R         10      9       9        8  2      8           8  2      7  3
--R       t0   - 3t0 t1 - t0 t2 + 2t0 t1  + 5t0 t1 t2 - 3t0 t2  + 2t0 t1
--R     + 
--R            7  2        7     2      7  3      6  4     6  3       6  2  2
--R       - 9t0 t1 t2 + 7t0 t1 t2  + 6t0 t2  - 4t0 t1  - t0 t1 t2 + t0 t1 t2
--R     + 
--R             6     3      6  4      5  5       5  4        5  3  2       5  2  3
--R       - 20t0 t1 t2  - 8t0 t2  + 6t0 t1  + 14t0 t1 t2 - 6t0 t1 t2  + 21t0 t1 t2
--R     + 
--R           5     4       5  5      4  6       4  5         4  4  2      4  3  3
--R       11t0 t1 t2  + 11t0 t2  - 8t0 t1  - 16t0 t1 t2 + 10t0 t1 t2  - 5t0 t1 t2
--R     + 
--R             4  2  4      4     5       4  6      3  7      3  6        3  5  2
--R       - 15t0 t1 t2  - 8t0 t1 t2  - 11t0 t2  + 7t0 t1  + 5t0 t1 t2 + 2t0 t1 t2
--R     + 
--R             3  4  3       3  3  4       3  2  5       3     6      3  7
--R       - 40t0 t1 t2  + 50t0 t1 t2  - 13t0 t1 t2  + 10t0 t1 t2  + 7t0 t2
--R     + 
--R            2  8      2  7         2  6  2      2  5  3       2  4  4
--R       - 3t0 t1  - 4t0 t1 t2 + 17t0 t1 t2  - 9t0 t1 t2  + 20t0 t1 t2
--R     + 
--R             2  3  5       2  2  6      2     7      2  8        9        8
--R       - 38t0 t1 t2  + 16t0 t1 t2  - 3t0 t1 t2  - 4t0 t2  + t0 t1  - t0 t1 t2
--R     + 
--R            7  2          6  3          5  4        4  5         3  6
--R       t0 t1 t2  - 15t0 t1 t2  + 17t0 t1 t2  + t0 t1 t2  - 6t0 t1 t2
--R     + 
--R            2  7         9     9        8  2      7  3     6  4     4  6
--R       t0 t1 t2  + 2t0 t2  - t1 t2 + 4t1 t2  - 4t1 t2  + t1 t2  - t1 t2
--R     + 
--R          3  7      2  8        9
--R       4t1 t2  - 4t1 t2  + t1 t2
--R     ,
--R
--R               9        9        8  2      8  2      7  3     7  2
--R           - t0 t1 - 2t0 t2 + 4t0 t1  + 4t0 t2  - 4t0 t1  - t0 t1 t2
--R         + 
--R              7     2      7  3     6  4      6  3         6  2  2       6     3
--R           3t0 t1 t2  - 7t0 t2  + t0 t1  + 6t0 t1 t2 - 16t0 t1 t2  - 10t0 t1 t2
--R         + 
--R               6  4     5  4         5  3  2       5  2  3      5     4
--R           11t0 t2  - t0 t1 t2 + 38t0 t1 t2  + 13t0 t1 t2  + 8t0 t1 t2
--R         + 
--R                 5  5     4  6       4  5         4  4  2       4  3  3
--R           - 11t0 t2  - t0 t1  - 17t0 t1 t2 - 20t0 t1 t2  - 50t0 t1 t2
--R         + 
--R               4  2  4       4     5      4  6      3  7       3  6
--R           15t0 t1 t2  - 11t0 t1 t2  + 8t0 t2  + 4t0 t1  + 15t0 t1 t2
--R         + 
--R              3  5  2       3  4  3      3  3  4       3  2  5       3     6
--R           9t0 t1 t2  + 40t0 t1 t2  + 5t0 t1 t2  - 21t0 t1 t2  + 20t0 t1 t2
--R         + 
--R                3  7      2  8     2  7         2  6  2      2  5  3
--R           - 6t0 t2  - 4t0 t1  - t0 t1 t2 - 17t0 t1 t2  - 2t0 t1 t2
--R         + 
--R                 2  4  4      2  3  5     2  2  6      2     7      2  8
--R           - 10t0 t1 t2  + 6t0 t1 t2  - t0 t1 t2  - 7t0 t1 t2  + 3t0 t2
--R         + 
--R                9        8           7  2         6  3          5  4
--R           t0 t1  + t0 t1 t2 + 4t0 t1 t2  - 5t0 t1 t2  + 16t0 t1 t2
--R         + 
--R                    4  5        3  6         2  7            8        9     9
--R           - 14t0 t1 t2  + t0 t1 t2  + 9t0 t1 t2  - 5t0 t1 t2  + t0 t2  - t1 t2
--R         + 
--R              8  2      7  3      6  4      5  5      4  6      3  7      2  8
--R           3t1 t2  - 7t1 t2  + 8t1 t2  - 6t1 t2  + 4t1 t2  - 2t1 t2  - 2t1 t2
--R         + 
--R                 9     10
--R           3t1 t2  - t2
--R      *
--R           3
--R         xi
--R     + 
--R              9       9        8  2      8           8  2      7  3       7  2
--R           2t0 t1 - t0 t2 - 4t0 t1  - 9t0 t1 t2 + 3t0 t2  + 7t0 t1  + 24t0 t1 t2
--R         + 
--R              7     2      7  3       6  4       6  3         6  2  2
--R           9t0 t1 t2  - 7t0 t2  - 11t0 t1  - 32t0 t1 t2 - 35t0 t1 t2
--R         + 
--R               6     3      6  4       5  5       5  4         5  3  2
--R           - t0 t1 t2  + 8t0 t2  + 11t0 t1  + 36t0 t1 t2 + 65t0 t1 t2
--R         + 
--R                5     4      5  5      4  6       4  5         4  4  2
--R           - 6t0 t1 t2  - 6t0 t2  - 8t0 t1  - 41t0 t1 t2 - 45t0 t1 t2
--R         + 
--R                 4  3  3       4  2  4      4     5      4  6      3  7
--R           - 20t0 t1 t2  + 20t0 t1 t2  - 3t0 t1 t2  + 4t0 t2  + 6t0 t1
--R         + 
--R               3  6         3  5  2       3  4  3       3  3  4       3  2  5
--R           26t0 t1 t2 + 13t0 t1 t2  + 45t0 t1 t2  - 40t0 t1 t2  + 11t0 t1 t2
--R         + 
--R                3     6      3  7      2  8     2  7         2  6  2
--R           - 4t0 t1 t2  - 2t0 t2  - 3t0 t1  - t0 t1 t2 - 31t0 t1 t2
--R         + 
--R               2  5  3       2  4  4       2  3  5       2  2  6       2     7
--R           13t0 t1 t2  - 20t0 t1 t2  + 47t0 t1 t2  - 41t0 t1 t2  + 19t0 t1 t2
--R         + 
--R                2  8        9         8            7  2         6  3
--R           - 2t0 t2  - t0 t1  + 3t0 t1 t2 + 10t0 t1 t2  - 6t0 t1 t2
--R         + 
--R                   5  4          4  5          3  6          2  7             8
--R           - 7t0 t1 t2  + 14t0 t1 t2  - 22t0 t1 t2  + 25t0 t1 t2  - 16t0 t1 t2
--R         + 
--R                 9     10      9        8  2      7  3      6  4      4  6
--R           3t0 t2  + t1   - 4t1 t2 + 5t1 t2  - 5t1 t2  + 4t1 t2  - 4t1 t2
--R         + 
--R              3  7      2  8         9     10
--R           5t1 t2  - 5t1 t2  + 4t1 t2  - t2
--R      *
--R           2
--R         xi
--R     + 
--R             9        9       8  2      8           8  2      7  2
--R           t0 t1 - 3t0 t2 - t0 t1  + 2t0 t1 t2 + 8t0 t2  + 8t0 t1 t2
--R         + 
--R                 7     2       7  3      6  4      6  3        6  2  2
--R           - 17t0 t1 t2  - 11t0 t2  - 3t0 t1  - 9t0 t1 t2 + 5t0 t1 t2
--R         + 
--R               6     3       6  4      5  5      5  4         5  3  2
--R           23t0 t1 t2  + 12t0 t2  + 5t0 t1  + 8t0 t1 t2 + 24t0 t1 t2
--R         + 
--R                 5  2  3       5     4       5  5      4  6       4  5
--R           - 32t0 t1 t2  - 14t0 t1 t2  - 11t0 t2  - 4t0 t1  - 18t0 t1 t2
--R         + 
--R                 4  4  2       4  3  3       4  2  4       4     5      4  6
--R           - 35t0 t1 t2  + 25t0 t1 t2  + 15t0 t1 t2  + 11t0 t1 t2  + 7t0 t2
--R         + 
--R              3  7       3  6        3  5  2       3  4  3       3  3  4
--R           4t0 t1  + 27t0 t1 t2 - 2t0 t1 t2  + 40t0 t1 t2  - 70t0 t1 t2
--R         + 
--R               3  2  5       3     6      3  7      2  8      2  7
--R           24t0 t1 t2  - 13t0 t1 t2  - 2t0 t2  - 5t0 t1  - 7t0 t1 t2
--R         + 
--R                 2  6  2      2  5  3      2  4  4       2  3  5       2  2  6
--R           - 17t0 t1 t2  + 9t0 t1 t2  + 5t0 t1 t2  + 20t0 t1 t2  - 22t0 t1 t2
--R         + 
--R               2     7     2  8         9        8            7  2          6  3
--R           13t0 t1 t2  - t0 t2  + 2t0 t1  + t0 t1 t2 + 10t0 t1 t2  - 17t0 t1 t2
--R         + 
--R                  5  4          4  5          3  6            8         9
--R           17t0 t1 t2  - 23t0 t1 t2  + 16t0 t1 t2  - 7t0 t1 t2  + 2t0 t2
--R         + 
--R                9        8  2      7  3       6  4       5  5      4  6
--R           - 2t1 t2 + 4t1 t2  - 7t1 t2  + 11t1 t2  - 11t1 t2  + 8t1 t2
--R         + 
--R                3  7      2  8        9     10
--R           - 6t1 t2  + 3t1 t2  + t1 t2  - t2
--R      *
--R         xi
--R     + 
--R         10      9        9       8  2      8           8  2      7  3
--R       t0   - 2t0 t1 - 4t0 t2 + t0 t1  + 7t0 t1 t2 + 5t0 t2  + 2t0 t1
--R     + 
--R           7  2         7     2      7  3      6  4       6  3        6  2  2
--R       - t0 t1 t2 - 10t0 t1 t2  - 5t0 t2  - 7t0 t1  - 10t0 t1 t2 + 6t0 t1 t2
--R     + 
--R          6     3      6  4       5  5       5  4         5  3  2       5  2  3
--R       3t0 t1 t2  + 4t0 t2  + 11t0 t1  + 22t0 t1 t2 + 18t0 t1 t2  - 11t0 t1 t2
--R     + 
--R            5     4       4  6       4  5         4  4  2       4  3  3
--R       - 3t0 t1 t2  - 12t0 t1  - 34t0 t1 t2 - 25t0 t1 t2  + 20t0 t1 t2
--R     + 
--R          4     5      4  6       3  7       3  6         3  3  4       3  2  5
--R       3t0 t1 t2  - 4t0 t2  + 11t0 t1  + 32t0 t1 t2 - 20t0 t1 t2  + 11t0 t1 t2
--R     + 
--R            3     6      3  7      2  8       2  7         2  4  4       2  3  5
--R       - 3t0 t1 t2  + 5t0 t2  - 8t0 t1  - 11t0 t1 t2 + 25t0 t1 t2  - 18t0 t1 t2
--R     + 
--R            2  2  6       2     7      2  8         9          7  2
--R       - 6t0 t1 t2  + 10t0 t1 t2  - 5t0 t2  + 3t0 t1  + 11t0 t1 t2
--R     + 
--R                6  3          5  4          4  5          3  6        2  7
--R       - 32t0 t1 t2  + 34t0 t1 t2  - 22t0 t1 t2  + 10t0 t1 t2  + t0 t1 t2
--R     + 
--R                  8         9      9        8  2       7  3       6  4
--R       - 7t0 t1 t2  + 4t0 t2  - 3t1 t2 + 8t1 t2  - 11t1 t2  + 12t1 t2
--R     + 
--R             5  5      4  6      3  7     2  8         9     10
--R       - 11t1 t2  + 7t1 t2  - 2t1 t2  - t1 t2  + 2t1 t2  - t2
--R     ,
--R
--R              9       9        8  2      8           8  2      7  3      7  2
--R           2t0 t1 - t0 t2 - 5t0 t1  + 2t0 t1 t2 + 4t0 t2  + 4t0 t1  + 9t0 t1 t2
--R         + 
--R                 7     2      7  3      6  4       6  3         6  2  2
--R           - 20t0 t1 t2  - 4t0 t2  - 4t0 t1  - 15t0 t1 t2 + 21t0 t1 t2
--R         + 
--R               6     3     6  4      5  5      5  4         5  3  2
--R           33t0 t1 t2  + t0 t2  + 5t0 t1  + 9t0 t1 t2 - 14t0 t1 t2
--R         + 
--R                 5  2  3       5     4      4  6     4  5         4  4  2
--R           - 45t0 t1 t2  - 22t0 t1 t2  - 3t0 t1  - t0 t1 t2 - 15t0 t1 t2
--R         + 
--R               4  3  3       4     5     4  6       3  6         3  5  2
--R           75t0 t1 t2  + 22t0 t1 t2  - t0 t2  + 12t0 t1 t2 - 11t0 t1 t2
--R         + 
--R                 3  3  4       3  2  5       3     6      3  7     2  8
--R           - 75t0 t1 t2  + 45t0 t1 t2  - 33t0 t1 t2  + 4t0 t2  - t0 t1
--R         + 
--R                2  7         2  5  3       2  4  4       2  3  5       2  2  6
--R           - 6t0 t1 t2 + 11t0 t1 t2  + 15t0 t1 t2  + 14t0 t1 t2  - 21t0 t1 t2
--R         + 
--R               2     7      2  8        9         7  2          6  3        5  4
--R           20t0 t1 t2  - 4t0 t2  + t0 t1  + 6t0 t1 t2  - 12t0 t1 t2  + t0 t1 t2
--R         + 
--R                   4  5          3  6         2  7            8        9     9
--R           - 9t0 t1 t2  + 15t0 t1 t2  - 9t0 t1 t2  - 2t0 t1 t2  + t0 t2  - t1 t2
--R         + 
--R             8  2      6  4      5  5      4  6      3  7      2  8         9
--R           t1 t2  + 3t1 t2  - 5t1 t2  + 4t1 t2  - 4t1 t2  + 5t1 t2  - 2t1 t2
--R      *
--R           3
--R         xi
--R     + 
--R             9        9        8  2      8  2      7  3     7  2        7     2
--R           t0 t1 + 2t0 t2 - 4t0 t1  - 4t0 t2  + 4t0 t1  + t0 t1 t2 - 3t0 t1 t2
--R         + 
--R              7  3     6  4      6  3         6  2  2       6     3       6  4
--R           7t0 t2  - t0 t1  - 6t0 t1 t2 + 16t0 t1 t2  + 10t0 t1 t2  - 11t0 t2
--R         + 
--R             5  4         5  3  2       5  2  3      5     4       5  5     4  6
--R           t0 t1 t2 - 38t0 t1 t2  - 13t0 t1 t2  - 8t0 t1 t2  + 11t0 t2  + t0 t1
--R         + 
--R               4  5         4  4  2       4  3  3       4  2  4       4     5
--R           17t0 t1 t2 + 20t0 t1 t2  + 50t0 t1 t2  - 15t0 t1 t2  + 11t0 t1 t2
--R         + 
--R                4  6      3  7       3  6        3  5  2       3  4  3
--R           - 8t0 t2  - 4t0 t1  - 15t0 t1 t2 - 9t0 t1 t2  - 40t0 t1 t2
--R         + 
--R                3  3  4       3  2  5       3     6      3  7      2  8
--R           - 5t0 t1 t2  + 21t0 t1 t2  - 20t0 t1 t2  + 6t0 t2  + 4t0 t1
--R         + 
--R             2  7         2  6  2      2  5  3       2  4  4      2  3  5
--R           t0 t1 t2 + 17t0 t1 t2  + 2t0 t1 t2  + 10t0 t1 t2  - 6t0 t1 t2
--R         + 
--R             2  2  6      2     7      2  8        9        8           7  2
--R           t0 t1 t2  + 7t0 t1 t2  - 3t0 t2  - t0 t1  - t0 t1 t2 - 4t0 t1 t2
--R         + 
--R                 6  3          5  4          4  5        3  6         2  7
--R           5t0 t1 t2  - 16t0 t1 t2  + 14t0 t1 t2  - t0 t1 t2  - 9t0 t1 t2
--R         + 
--R                    8        9     9        8  2      7  3      6  4      5  5
--R           5t0 t1 t2  - t0 t2  + t1 t2 - 3t1 t2  + 7t1 t2  - 8t1 t2  + 6t1 t2
--R         + 
--R                4  6      3  7      2  8         9     10
--R           - 4t1 t2  + 2t1 t2  + 2t1 t2  - 3t1 t2  + t2
--R      *
--R           2
--R         xi
--R     + 
--R              9       9        8  2      8          8  2       7  3       7  2
--R           3t0 t1 + t0 t2 - 8t0 t1  - 9t0 t1 t2 - t0 t2  + 11t0 t1  + 25t0 t1 t2
--R         + 
--R              7     2       6  4       6  3         6  2  2      6     3
--R           6t0 t1 t2  - 12t0 t1  - 38t0 t1 t2 - 19t0 t1 t2  + 9t0 t1 t2
--R         + 
--R                6  4       5  5       5  4         5  3  2       5  2  3
--R           - 3t0 t2  + 11t0 t1  + 37t0 t1 t2 + 27t0 t1 t2  - 13t0 t1 t2
--R         + 
--R                 5     4      5  5      4  6       4  5         4  4  2
--R           - 14t0 t1 t2  + 5t0 t2  - 7t0 t1  - 24t0 t1 t2 - 25t0 t1 t2
--R         + 
--R               4  3  3      4  2  4      4     5      4  6      3  7
--R           30t0 t1 t2  + 5t0 t1 t2  + 8t0 t1 t2  - 4t0 t2  + 2t0 t1
--R         + 
--R               3  6        3  5  2      3  4  3       3  3  4       3  2  5
--R           11t0 t1 t2 + 4t0 t1 t2  + 5t0 t1 t2  - 45t0 t1 t2  + 32t0 t1 t2
--R         + 
--R                 3     6      3  7     2  8       2  6  2       2  5  3
--R           - 24t0 t1 t2  + 4t0 t2  + t0 t1  - 14t0 t1 t2  + 15t0 t1 t2
--R         + 
--R                 2  4  4       2  3  5       2  2  6       2     7      2  8
--R           - 10t0 t1 t2  + 41t0 t1 t2  - 40t0 t1 t2  + 26t0 t1 t2  - 5t0 t2
--R         + 
--R                   9         8           7  2        6  3          5  4
--R           - 2t0 t1  + 2t0 t1 t2 + 6t0 t1 t2  - t0 t1 t2  - 23t0 t1 t2
--R         + 
--R                  4  5          3  6          2  7             8         9
--R           28t0 t1 t2  - 23t0 t1 t2  + 16t0 t1 t2  - 11t0 t1 t2  + 2t0 t2
--R         + 
--R             10      9        8  2      7  3      6  4      5  5      4  6
--R           t1   - 3t1 t2 + 2t1 t2  + 2t1 t2  - 4t1 t2  + 6t1 t2  - 8t1 t2
--R         + 
--R              3  7      2  8        9
--R           7t1 t2  - 3t1 t2  + t1 t2
--R      *
--R         xi
--R     + 
--R         10     9        9        8  2      8          8  2      7  3
--R       t0   - t0 t1 - 2t0 t2 - 3t0 t1  + 7t0 t1 t2 + t0 t2  + 6t0 t1
--R     + 
--R             7     2      7  3      6  4       6  3         6  2  2
--R       - 13t0 t1 t2  + 2t0 t2  - 8t0 t1  - 16t0 t1 t2 + 22t0 t1 t2
--R     + 
--R           6     3      6  4       5  5       5  4         5  3  2       5  2  3
--R       13t0 t1 t2  - 7t0 t2  + 11t0 t1  + 23t0 t1 t2 - 20t0 t1 t2  - 24t0 t1 t2
--R     + 
--R             5     4       5  5       4  6       4  5        4  4  2
--R       - 11t0 t1 t2  + 11t0 t2  - 11t0 t1  - 17t0 t1 t2 - 5t0 t1 t2
--R     + 
--R           4  3  3       4  2  4       4     5       4  6      3  7       3  6
--R       70t0 t1 t2  - 15t0 t1 t2  + 14t0 t1 t2  - 12t0 t2  + 7t0 t1  + 17t0 t1 t2
--R     + 
--R            3  5  2       3  4  3       3  3  4       3  2  5       3     6
--R       - 9t0 t1 t2  - 40t0 t1 t2  - 25t0 t1 t2  + 32t0 t1 t2  - 23t0 t1 t2
--R     + 
--R           3  7      2  8       2  7         2  6  2      2  5  3       2  4  4
--R       11t0 t2  - 4t0 t1  - 10t0 t1 t2 + 17t0 t1 t2  + 2t0 t1 t2  + 35t0 t1 t2
--R     + 
--R             2  3  5      2  2  6       2     7      2  8         9        8
--R       - 24t0 t1 t2  - 5t0 t1 t2  + 17t0 t1 t2  - 8t0 t2  + 2t0 t1  - t0 t1 t2
--R     + 
--R             7  2          6  3          5  4         4  5         3  6
--R       7t0 t1 t2  - 27t0 t1 t2  + 18t0 t1 t2  - 8t0 t1 t2  + 9t0 t1 t2
--R     + 
--R               2  7            8         9      9        8  2      7  3
--R       - 8t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t1 t2 + 5t1 t2  - 4t1 t2
--R     + 
--R          6  4      5  5      4  6     2  8        9
--R       4t1 t2  - 5t1 t2  + 3t1 t2  + t1 t2  - t1 t2
--R     ]
--E 14

--S 15 of 22
[B(1)**j - b * d**n for b in B for d in delta for j in UZn]
 

   (15)  [0,0,0,0]
--R
--R   (15)  [0,0,0,0]
--E 15 

--S 16 of 22
L := SimpleAlgebraicExtension(E, UP('C1, E), C1**n - B(1)) ;  C1 : L := generator()$L 
 

   (16)  C1
--R 
--R
--R   (16)  C1
--E 16 

--S 17 of 22
retraction(z : L) : Zt ==
   zE : E := retract(z)
   zK : K := retract(zE)
   zt : Zt := retract(zK)
   return zt
 
   Function declaration retraction : SimpleAlgebraicExtension(
      SimpleAlgebraicExtension(Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
      UnivariatePolynomial(xi,Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
      xi**3+xi*xi+xi+1),UnivariatePolynomial(C1,
      SimpleAlgebraicExtension(Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
      UnivariatePolynomial(xi,Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
      xi**3+xi*xi+xi+1)),C1**5+(2*t0**9*t1+(-t0**9*t2)+(-4*t0**8*t1*t1)
      +(-9*t0**8*t1*t2)+3*t0**8*t2*t2+7*t0**7*t1**3+24*t0**7*t1*t1*t2+9
      *t0**7*t1*t2*t2+(-7*t0**7*t2**3)+(-11*t0**6*t1**4)+(-32*t0**6*t1
      **3*t2)+(-35*t0**6*t1*t1*t2*t2)+(-t0**6*t1*t2**3)+8*t0**6*t2**4+
      11*t0**5*t1**5+36*t0**5*t1**4*t2+65*t0**5*t1**3*t2*t2+(-6*t0**5*
      t1*t2**4)+(-6*t0**5*t2**5)+(-8*t0**4*t1**6)+(-41*t0**4*t1**5*t2)+
      (-45*t0**4*t1**4*t2*t2)+(-20*t0**4*t1**3*t2**3)+20*t0**4*t1*t1*t2
      **4+(-3*t0**4*t1*t2**5)+4*t0**4*t2**6+6*t0**3*t1**7+26*t0**3*t1**
      6*t2+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**3+(-40*t0**3*t1**3*
      t2**4)+11*t0**3*t1*t1*t2**5+(-4*t0**3*t1*t2**6)+(-2*t0**3*t2**7)+
      (-3*t0*t0*t1**8)+(-t0*t0*t1**7*t2)+(-31*t0*t0*t1**6*t2*t2)+13*t0*
      t0*t1**5*t2**3+(-20*t0*t0*t1**4*t2**4)+47*t0*t0*t1**3*t2**5+(-41*
      t0*t0*t1*t1*t2**6)+19*t0*t0*t1*t2**7+(-2*t0*t0*t2**8)+(-t0*t1**9)
      +3*t0*t1**8*t2+10*t0*t1**7*t2*t2+(-6*t0*t1**6*t2**3)+(-7*t0*t1**5
      *t2**4)+14*t0*t1**4*t2**5+(-22*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+
      (-16*t0*t1*t2**8)+3*t0*t2**9+t1**10+(-4*t1**9*t2)+5*t1**8*t2*t2+(
      -5*t1**7*t2**3)+4*t1**6*t2**4+(-4*t1**4*t2**6)+5*t1**3*t2**7+(-5*
      t1*t1*t2**8)+4*t1*t2**9+(-t2**10))*xi**3+(t0**9*t1+2*t0**9*t2+(-3
      *t0**8*t1*t1)+(-11*t0**8*t1*t2)+(-5*t0**8*t2*t2)+7*t0**7*t1**3+16
      *t0**7*t1*t1*t2+26*t0**7*t1*t2*t2+4*t0**7*t2**3+(-8*t0**6*t1**4)+
      (-23*t0**6*t1**3*t2)+(-40*t0**6*t1*t1*t2*t2)+(-24*t0**6*t1*t2**3)
      +(-4*t0**6*t2**4)+6*t0**5*t1**5+28*t0**5*t1**4*t2+41*t0**5*t1**3*
      t2*t2+32*t0**5*t1*t1*t2**3+8*t0**5*t1*t2**4+5*t0**5*t2**5+(-4*t0
      **4*t1**6)+(-23*t0**4*t1**5*t2)+(-10*t0**4*t1**4*t2*t2)+(-45*t0**
      4*t1**3*t2**3)+5*t0**4*t1*t1*t2**4+(-14*t0**4*t1*t2**5)+(-3*t0**4
      *t2**6)+2*t0**3*t1**7+(-t0**3*t1**6*t2)+15*t0**3*t1**5*t2*t2+5*t0
      **3*t1**4*t2**3+30*t0**3*t1**3*t2**4+(-13*t0**3*t1*t1*t2**5)+9*t0
      **3*t1*t2**6+2*t0*t0*t1**8+6*t0*t0*t1**7*t2+(-14*t0*t0*t1**6*t2*
      t2)+4*t0*t0*t1**5*t2**3+(-25*t0*t0*t1**4*t2**4)+27*t0*t0*t1**3*t2
      **5+(-19*t0*t0*t1*t1*t2**6)+6*t0*t0*t1*t2**7+(-t0*t0*t2**8)+(-3*
      t0*t1**9)+2*t0*t1**8*t2+11*t0*t1**6*t2**3+(-24*t0*t1**5*t2**4)+37
      *t0*t1**4*t2**5+(-38*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+(-9*t0*t1*
      t2**8)+t0*t2**9+t1**10+(-2*t1**9*t2)+t1**8*t2*t2+2*t1**7*t2**3+(-
      7*t1**6*t2**4)+11*t1**5*t2**5+(-12*t1**4*t2**6)+11*t1**3*t2**7+(-
      8*t1*t1*t2**8)+3*t1*t2**9)*xi*xi+(3*t0**9*t1+t0**9*t2+(-8*t0**8*
      t1*t1)+(-9*t0**8*t1*t2)+(-t0**8*t2*t2)+11*t0**7*t1**3+25*t0**7*t1
      *t1*t2+6*t0**7*t1*t2*t2+(-12*t0**6*t1**4)+(-38*t0**6*t1**3*t2)+(-
      19*t0**6*t1*t1*t2*t2)+9*t0**6*t1*t2**3+(-3*t0**6*t2**4)+11*t0**5*
      t1**5+37*t0**5*t1**4*t2+27*t0**5*t1**3*t2*t2+(-13*t0**5*t1*t1*t2
      **3)+(-14*t0**5*t1*t2**4)+5*t0**5*t2**5+(-7*t0**4*t1**6)+(-24*t0
      **4*t1**5*t2)+(-25*t0**4*t1**4*t2*t2)+30*t0**4*t1**3*t2**3+5*t0**
      4*t1*t1*t2**4+8*t0**4*t1*t2**5+(-4*t0**4*t2**6)+2*t0**3*t1**7+11*
      t0**3*t1**6*t2+4*t0**3*t1**5*t2*t2+5*t0**3*t1**4*t2**3+(-45*t0**3
      *t1**3*t2**4)+32*t0**3*t1*t1*t2**5+(-24*t0**3*t1*t2**6)+4*t0**3*
      t2**7+t0*t0*t1**8+(-14*t0*t0*t1**6*t2*t2)+15*t0*t0*t1**5*t2**3+(-
      10*t0*t0*t1**4*t2**4)+41*t0*t0*t1**3*t2**5+(-40*t0*t0*t1*t1*t2**6
      )+26*t0*t0*t1*t2**7+(-5*t0*t0*t2**8)+(-2*t0*t1**9)+2*t0*t1**8*t2+
      6*t0*t1**7*t2*t2+(-t0*t1**6*t2**3)+(-23*t0*t1**5*t2**4)+28*t0*t1
      **4*t2**5+(-23*t0*t1**3*t2**6)+16*t0*t1*t1*t2**7+(-11*t0*t1*t2**8
      )+2*t0*t2**9+t1**10+(-3*t1**9*t2)+2*t1**8*t2*t2+2*t1**7*t2**3+(-4
      *t1**6*t2**4)+6*t1**5*t2**5+(-8*t1**4*t2**6)+7*t1**3*t2**7+(-3*t1
      *t1*t2**8)+t1*t2**9)*xi+(-t0**10)+4*t0**9*t1+3*t0**9*t2+(-5*t0**8
      *t1*t1)+(-16*t0**8*t1*t2)+(-2*t0**8*t2*t2)+5*t0**7*t1**3+25*t0**7
      *t1*t1*t2+19*t0**7*t1*t2*t2+(-2*t0**7*t2**3)+(-4*t0**6*t1**4)+(-
      22*t0**6*t1**3*t2)+(-41*t0**6*t1*t1*t2*t2)+(-4*t0**6*t1*t2**3)+4*
      t0**6*t2**4+14*t0**5*t1**4*t2+47*t0**5*t1**3*t2*t2+11*t0**5*t1*t1
      *t2**3+(-3*t0**5*t1*t2**4)+(-6*t0**5*t2**5)+4*t0**4*t1**6+(-7*t0
      **4*t1**5*t2)+(-20*t0**4*t1**4*t2*t2)+(-40*t0**4*t1**3*t2**3)+20*
      t0**4*t1*t1*t2**4+(-6*t0**4*t1*t2**5)+8*t0**4*t2**6+(-5*t0**3*t1
      **7)+(-6*t0**3*t1**6*t2)+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**
      3+(-20*t0**3*t1**3*t2**4)+(-t0**3*t1*t2**6)+(-7*t0**3*t2**7)+5*t0
      *t0*t1**8+10*t0*t0*t1**7*t2+(-31*t0*t0*t1**6*t2*t2)+13*t0*t0*t1**
      5*t2**3+(-45*t0*t0*t1**4*t2**4)+65*t0*t0*t1**3*t2**5+(-35*t0*t0*
      t1*t1*t2**6)+9*t0*t0*t1*t2**7+3*t0*t0*t2**8+(-4*t0*t1**9)+3*t0*t1
      **8*t2+(-t0*t1**7*t2*t2)+26*t0*t1**6*t2**3+(-41*t0*t1**5*t2**4)+
      36*t0*t1**4*t2**5+(-32*t0*t1**3*t2**6)+24*t0*t1*t1*t2**7+(-9*t0*
      t1*t2**8)+(-t0*t2**9)+t1**10+(-t1**9*t2)+(-3*t1**8*t2*t2)+6*t1**7
      *t2**3+(-8*t1**6*t2**4)+11*t1**5*t2**5+(-11*t1**4*t2**6)+7*t1**3*
      t2**7+(-4*t1*t1*t2**8)+2*t1*t2**9) -> 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) has been
      added to workspace.
--R 
--R   Function declaration retraction : SimpleAlgebraicExtension(
--R      SimpleAlgebraicExtension(Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
--R      UnivariatePolynomial(xi,Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
--R      xi**3+xi*xi+xi+1),UnivariatePolynomial(C1,
--R      SimpleAlgebraicExtension(Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
--R      UnivariatePolynomial(xi,Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
--R      xi**3+xi*xi+xi+1)),C1**5+(2*t0**9*t1+(-t0**9*t2)+(-4*t0**8*t1*t1)
--R      +(-9*t0**8*t1*t2)+3*t0**8*t2*t2+7*t0**7*t1**3+24*t0**7*t1*t1*t2+9
--R      *t0**7*t1*t2*t2+(-7*t0**7*t2**3)+(-11*t0**6*t1**4)+(-32*t0**6*t1
--R      **3*t2)+(-35*t0**6*t1*t1*t2*t2)+(-t0**6*t1*t2**3)+8*t0**6*t2**4+
--R      11*t0**5*t1**5+36*t0**5*t1**4*t2+65*t0**5*t1**3*t2*t2+(-6*t0**5*
--R      t1*t2**4)+(-6*t0**5*t2**5)+(-8*t0**4*t1**6)+(-41*t0**4*t1**5*t2)+
--R      (-45*t0**4*t1**4*t2*t2)+(-20*t0**4*t1**3*t2**3)+20*t0**4*t1*t1*t2
--R      **4+(-3*t0**4*t1*t2**5)+4*t0**4*t2**6+6*t0**3*t1**7+26*t0**3*t1**
--R      6*t2+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**3+(-40*t0**3*t1**3*
--R      t2**4)+11*t0**3*t1*t1*t2**5+(-4*t0**3*t1*t2**6)+(-2*t0**3*t2**7)+
--R      (-3*t0*t0*t1**8)+(-t0*t0*t1**7*t2)+(-31*t0*t0*t1**6*t2*t2)+13*t0*
--R      t0*t1**5*t2**3+(-20*t0*t0*t1**4*t2**4)+47*t0*t0*t1**3*t2**5+(-41*
--R      t0*t0*t1*t1*t2**6)+19*t0*t0*t1*t2**7+(-2*t0*t0*t2**8)+(-t0*t1**9)
--R      +3*t0*t1**8*t2+10*t0*t1**7*t2*t2+(-6*t0*t1**6*t2**3)+(-7*t0*t1**5
--R      *t2**4)+14*t0*t1**4*t2**5+(-22*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+
--R      (-16*t0*t1*t2**8)+3*t0*t2**9+t1**10+(-4*t1**9*t2)+5*t1**8*t2*t2+(
--R      -5*t1**7*t2**3)+4*t1**6*t2**4+(-4*t1**4*t2**6)+5*t1**3*t2**7+(-5*
--R      t1*t1*t2**8)+4*t1*t2**9+(-t2**10))*xi**3+(t0**9*t1+2*t0**9*t2+(-3
--R      *t0**8*t1*t1)+(-11*t0**8*t1*t2)+(-5*t0**8*t2*t2)+7*t0**7*t1**3+16
--R      *t0**7*t1*t1*t2+26*t0**7*t1*t2*t2+4*t0**7*t2**3+(-8*t0**6*t1**4)+
--R      (-23*t0**6*t1**3*t2)+(-40*t0**6*t1*t1*t2*t2)+(-24*t0**6*t1*t2**3)
--R      +(-4*t0**6*t2**4)+6*t0**5*t1**5+28*t0**5*t1**4*t2+41*t0**5*t1**3*
--R      t2*t2+32*t0**5*t1*t1*t2**3+8*t0**5*t1*t2**4+5*t0**5*t2**5+(-4*t0
--R      **4*t1**6)+(-23*t0**4*t1**5*t2)+(-10*t0**4*t1**4*t2*t2)+(-45*t0**
--R      4*t1**3*t2**3)+5*t0**4*t1*t1*t2**4+(-14*t0**4*t1*t2**5)+(-3*t0**4
--R      *t2**6)+2*t0**3*t1**7+(-t0**3*t1**6*t2)+15*t0**3*t1**5*t2*t2+5*t0
--R      **3*t1**4*t2**3+30*t0**3*t1**3*t2**4+(-13*t0**3*t1*t1*t2**5)+9*t0
--R      **3*t1*t2**6+2*t0*t0*t1**8+6*t0*t0*t1**7*t2+(-14*t0*t0*t1**6*t2*
--R      t2)+4*t0*t0*t1**5*t2**3+(-25*t0*t0*t1**4*t2**4)+27*t0*t0*t1**3*t2
--R      **5+(-19*t0*t0*t1*t1*t2**6)+6*t0*t0*t1*t2**7+(-t0*t0*t2**8)+(-3*
--R      t0*t1**9)+2*t0*t1**8*t2+11*t0*t1**6*t2**3+(-24*t0*t1**5*t2**4)+37
--R      *t0*t1**4*t2**5+(-38*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+(-9*t0*t1*
--R      t2**8)+t0*t2**9+t1**10+(-2*t1**9*t2)+t1**8*t2*t2+2*t1**7*t2**3+(-
--R      7*t1**6*t2**4)+11*t1**5*t2**5+(-12*t1**4*t2**6)+11*t1**3*t2**7+(-
--R      8*t1*t1*t2**8)+3*t1*t2**9)*xi*xi+(3*t0**9*t1+t0**9*t2+(-8*t0**8*
--R      t1*t1)+(-9*t0**8*t1*t2)+(-t0**8*t2*t2)+11*t0**7*t1**3+25*t0**7*t1
--R      *t1*t2+6*t0**7*t1*t2*t2+(-12*t0**6*t1**4)+(-38*t0**6*t1**3*t2)+(-
--R      19*t0**6*t1*t1*t2*t2)+9*t0**6*t1*t2**3+(-3*t0**6*t2**4)+11*t0**5*
--R      t1**5+37*t0**5*t1**4*t2+27*t0**5*t1**3*t2*t2+(-13*t0**5*t1*t1*t2
--R      **3)+(-14*t0**5*t1*t2**4)+5*t0**5*t2**5+(-7*t0**4*t1**6)+(-24*t0
--R      **4*t1**5*t2)+(-25*t0**4*t1**4*t2*t2)+30*t0**4*t1**3*t2**3+5*t0**
--R      4*t1*t1*t2**4+8*t0**4*t1*t2**5+(-4*t0**4*t2**6)+2*t0**3*t1**7+11*
--R      t0**3*t1**6*t2+4*t0**3*t1**5*t2*t2+5*t0**3*t1**4*t2**3+(-45*t0**3
--R      *t1**3*t2**4)+32*t0**3*t1*t1*t2**5+(-24*t0**3*t1*t2**6)+4*t0**3*
--R      t2**7+t0*t0*t1**8+(-14*t0*t0*t1**6*t2*t2)+15*t0*t0*t1**5*t2**3+(-
--R      10*t0*t0*t1**4*t2**4)+41*t0*t0*t1**3*t2**5+(-40*t0*t0*t1*t1*t2**6
--R      )+26*t0*t0*t1*t2**7+(-5*t0*t0*t2**8)+(-2*t0*t1**9)+2*t0*t1**8*t2+
--R      6*t0*t1**7*t2*t2+(-t0*t1**6*t2**3)+(-23*t0*t1**5*t2**4)+28*t0*t1
--R      **4*t2**5+(-23*t0*t1**3*t2**6)+16*t0*t1*t1*t2**7+(-11*t0*t1*t2**8
--R      )+2*t0*t2**9+t1**10+(-3*t1**9*t2)+2*t1**8*t2*t2+2*t1**7*t2**3+(-4
--R      *t1**6*t2**4)+6*t1**5*t2**5+(-8*t1**4*t2**6)+7*t1**3*t2**7+(-3*t1
--R      *t1*t2**8)+t1*t2**9)*xi+(-t0**10)+4*t0**9*t1+3*t0**9*t2+(-5*t0**8
--R      *t1*t1)+(-16*t0**8*t1*t2)+(-2*t0**8*t2*t2)+5*t0**7*t1**3+25*t0**7
--R      *t1*t1*t2+19*t0**7*t1*t2*t2+(-2*t0**7*t2**3)+(-4*t0**6*t1**4)+(-
--R      22*t0**6*t1**3*t2)+(-41*t0**6*t1*t1*t2*t2)+(-4*t0**6*t1*t2**3)+4*
--R      t0**6*t2**4+14*t0**5*t1**4*t2+47*t0**5*t1**3*t2*t2+11*t0**5*t1*t1
--R      *t2**3+(-3*t0**5*t1*t2**4)+(-6*t0**5*t2**5)+4*t0**4*t1**6+(-7*t0
--R      **4*t1**5*t2)+(-20*t0**4*t1**4*t2*t2)+(-40*t0**4*t1**3*t2**3)+20*
--R      t0**4*t1*t1*t2**4+(-6*t0**4*t1*t2**5)+8*t0**4*t2**6+(-5*t0**3*t1
--R      **7)+(-6*t0**3*t1**6*t2)+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**
--R      3+(-20*t0**3*t1**3*t2**4)+(-t0**3*t1*t2**6)+(-7*t0**3*t2**7)+5*t0
--R      *t0*t1**8+10*t0*t0*t1**7*t2+(-31*t0*t0*t1**6*t2*t2)+13*t0*t0*t1**
--R      5*t2**3+(-45*t0*t0*t1**4*t2**4)+65*t0*t0*t1**3*t2**5+(-35*t0*t0*
--R      t1*t1*t2**6)+9*t0*t0*t1*t2**7+3*t0*t0*t2**8+(-4*t0*t1**9)+3*t0*t1
--R      **8*t2+(-t0*t1**7*t2*t2)+26*t0*t1**6*t2**3+(-41*t0*t1**5*t2**4)+
--R      36*t0*t1**4*t2**5+(-32*t0*t1**3*t2**6)+24*t0*t1*t1*t2**7+(-9*t0*
--R      t1*t2**8)+(-t0*t2**9)+t1**10+(-t1**9*t2)+(-3*t1**8*t2*t2)+6*t1**7
--R      *t2**3+(-8*t1**6*t2**4)+11*t1**5*t2**5+(-11*t1**4*t2**6)+7*t1**3*
--R      t2**7+(-4*t1*t1*t2**8)+2*t1*t2**9) -> 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) has been
--R      added to workspace.
--E 17

--S 18 of 22
C : List(L) := [C1**j / d for j in UZn for d in delta] 
 

   (18)
   [C1,

                       2     2
             t0 t1 - t1  + t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
        *
             3
           xi
       + 
                       2
             t0 t2 - t1  + t1 t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
        *
             2
           xi
       + 
                               2
             t0 t1 + t0 t2 - t1
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
        *
           xi
       + 
             2     2
           t0  - t1  + t1 t2
        /
               4     3       3       2  2      2          2  2        3
             t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
           + 
                     2              2        3     4     3       2  2        3
             - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
           + 
               4
             t2
    *
         2
       C1
     ,

                 3       3       2          2  2        3        2
               t0 t1 - t0 t2 + t0 t1 t2 + t0 t2  - t0 t1  + t0 t1 t2
             + 
                          2        3     3       2  2         3     4
               - 4t0 t1 t2  + t0 t2  + t1 t2 - t1 t2  + 2t1 t2  - t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
        *
             3
           xi
       + 
                 3       3       2  2     2          2  2        3           2
               t0 t1 + t0 t2 - t0 t1  + t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
             + 
                     3     4     3          3     4
               2t0 t2  + t1  - t1 t2 + t1 t2  - t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
        *
             2
           xi
       + 
                  3        2  2      2          2  2        3        2
               2t0 t1 - 2t0 t1  - 2t0 t1 t2 + t0 t2  + t0 t1  + t0 t1 t2
             + 
                         2     3       2  2        3     4
               - t0 t1 t2  - t1 t2 + t1 t2  + t1 t2  - t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
        *
           xi
       + 
             4     3       2  2      2                 2        3     2  2     4
           t0  - t0 t2 - t0 t1  + 2t0 t1 t2 - 2t0 t1 t2  + t0 t2  + t1 t2  - t2
        /
               8      7        7        6  2      6           6  2      5  3
             t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
           + 
                   5  2        5     2      5  3      4  4       4  3
             - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
           + 
                 4  2  2      4  4      3  5       3  4         3  3  2
             10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
           + 
                  3  5      2  6      2  5        2  4  2       2  3  3
             - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
           + 
                 2  2  4      2     5      2  6         7         6
             10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
           + 
                   5  2          4  3          3  4          2  5            6
             8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
           + 
                     7     8      7        6  2      5  3      4  4      3  5
             - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
           + 
                2  6         7     8
             3t1 t2  - 2t1 t2  + t2
    *
         3
       C1
     ,

                  5       5        4  2      4           4  2     3  3
               2t0 t1 - t0 t2 - 3t0 t1  + 3t0 t1 t2 + 3t0 t2  - t0 t1
             + 
                  3  2         3     2      2  3         2     3      2  4
               6t0 t1 t2 - 14t0 t1 t2  - 2t0 t1 t2 + 14t0 t1 t2  - 3t0 t2
             + 
                    5         3  2         2  3            4        5     5
               t0 t1  + 2t0 t1 t2  - 6t0 t1 t2  - 3t0 t1 t2  + t0 t2  - t1 t2
             + 
                 3  3      2  4         5
               t1 t2  + 3t1 t2  - 2t1 t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
        *
             3
           xi
       + 
                 5        5        4  2      4           4  2      3  2
               t0 t1 + 2t0 t2 - 3t0 t1  + 3t0 t1 t2 - 2t0 t2  - 3t0 t1 t2
             + 
                    3     2      3  3      2  4     2  3        2  2  2
               - 7t0 t1 t2  + 3t0 t2  + 3t0 t1  - t0 t1 t2 + 9t0 t1 t2
             + 
                  2     3      2  4        5        4           3  2
               4t0 t1 t2  - 4t0 t2  - t0 t1  - t0 t1 t2 - 3t0 t1 t2
             + 
                       2  3           4     5        4  2      3  3     2  4
               - 2t0 t1 t2  + t0 t1 t2  + t1 t2 - 2t1 t2  + 4t1 t2  - t1 t2
             + 
                       5     6
               - 2t1 t2  + t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
        *
             2
           xi
       + 
                  5       5        4  2      4           3  3      3  2
               3t0 t1 + t0 t2 - 5t0 t1  - 5t0 t1 t2 + 3t0 t1  + 8t0 t1 t2
             + 
                    3     2     3  3     2  4      2  3        2  2  2
               - 4t0 t1 t2  - t0 t2  - t0 t1  - 2t0 t1 t2 - 3t0 t1 t2
             + 
                   2     3      2  4        5         4           2  3
               10t0 t1 t2  - 3t0 t2  - t0 t1  + 2t0 t1 t2 + 2t0 t1 t2
             + 
                          4         5     6      5       4  2      3  3
               - 8t0 t1 t2  + 2t0 t2  + t1  - 2t1 t2 - t1 t2  + 4t1 t2
             + 
                    2  4        5
               - 2t1 t2  + t1 t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
        *
           xi
       + 
               6     5        4  2      4          4  2      3  3      3  2
             t0  - t0 t2 - 4t0 t1  + 4t0 t1 t2 - t0 t2  + 3t0 t1  + 4t0 t1 t2
           + 
                   3     2      3  3      2  4      2  3        2  2  2
             - 10t0 t1 t2  + 3t0 t2  - 2t0 t1  - 5t0 t1 t2 + 9t0 t1 t2
           + 
                2     3      2  4         5        4          3  2         2  3
             7t0 t1 t2  - 5t0 t2  + 2t0 t1  - t0 t1 t2 + t0 t1 t2  - 9t0 t1 t2
           + 
                   5      5        4  2     3  3        5
             3t0 t2  - 2t1 t2 + 3t1 t2  + t1 t2  - t1 t2
        /
               12      11        11        10  2       10           10  2
             t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
           + 
                   9  3       9  2         9     2       9  3       8  4
             - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
           + 
                 8  3         8  2  2       8     3       8  4       7  5
             45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
           + 
                   7  4         7  3  2       7  2  3       7     4       7  5
             - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
           + 
                 6  6       6  5         6  4  2       6  3  3       6  2  4
             19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
           + 
                6     5       6  6       5  7       5  6         5  5  2
             9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
           + 
                   5  4  3       5  3  4       5  2  5      5     6       5  7
             - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
           + 
                 4  8       4  7         4  6  2       4  5  3       4  3  5
             15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
           + 
                 4  2  6       4     7       4  8       3  9       3  8
             45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
           + 
                   3  7  2       3  6  3       3  5  4       3  4  5
             - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
           + 
                 3  3  6       3  2  7       3     8       3  9      2  10
             20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
           + 
                 2  9         2  7  3       2  6  4       2  5  5       2  4  6
             15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2
           + 
                   2  3  7       2  2  8       2     9      2  10         11
             - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1
           + 
                     10            9  2          8  3          7  4
             - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
           + 
                      6  5          5  6          4  7          3  8
             - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
           + 
                      2  9             10         11     12      11        10  2
             - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2
           + 
                   9  3       8  4       7  5       6  6       5  7       4  8
             - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2
           + 
                   3  9      2  10         11     12
             - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
    *
         4
       C1
     ]
--R 
--R
--R   (18)
--R   [C1,
--R
--R                       2     2
--R             t0 t1 - t1  + t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R        *
--R             3
--R           xi
--R       + 
--R                       2
--R             t0 t2 - t1  + t1 t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R        *
--R             2
--R           xi
--R       + 
--R                               2
--R             t0 t1 + t0 t2 - t1
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R        *
--R           xi
--R       + 
--R             2     2
--R           t0  - t1  + t1 t2
--R        /
--R               4     3       3       2  2      2          2  2        3
--R             t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R           + 
--R                     2              2        3     4     3       2  2        3
--R             - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R           + 
--R               4
--R             t2
--R    *
--R         2
--R       C1
--R     ,
--R
--R                 3       3       2          2  2        3        2
--R               t0 t1 - t0 t2 + t0 t1 t2 + t0 t2  - t0 t1  + t0 t1 t2
--R             + 
--R                          2        3     3       2  2         3     4
--R               - 4t0 t1 t2  + t0 t2  + t1 t2 - t1 t2  + 2t1 t2  - t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R        *
--R             3
--R           xi
--R       + 
--R                 3       3       2  2     2          2  2        3           2
--R               t0 t1 + t0 t2 - t0 t1  + t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
--R             + 
--R                     3     4     3          3     4
--R               2t0 t2  + t1  - t1 t2 + t1 t2  - t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R        *
--R             2
--R           xi
--R       + 
--R                  3        2  2      2          2  2        3        2
--R               2t0 t1 - 2t0 t1  - 2t0 t1 t2 + t0 t2  + t0 t1  + t0 t1 t2
--R             + 
--R                         2     3       2  2        3     4
--R               - t0 t1 t2  - t1 t2 + t1 t2  + t1 t2  - t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R        *
--R           xi
--R       + 
--R             4     3       2  2      2                 2        3     2  2     4
--R           t0  - t0 t2 - t0 t1  + 2t0 t1 t2 - 2t0 t1 t2  + t0 t2  + t1 t2  - t2
--R        /
--R               8      7        7        6  2      6           6  2      5  3
--R             t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R           + 
--R                   5  2        5     2      5  3      4  4       4  3
--R             - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R           + 
--R                 4  2  2      4  4      3  5       3  4         3  3  2
--R             10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R           + 
--R                  3  5      2  6      2  5        2  4  2       2  3  3
--R             - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R           + 
--R                 2  2  4      2     5      2  6         7         6
--R             10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R           + 
--R                   5  2          4  3          3  4          2  5            6
--R             8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R           + 
--R                     7     8      7        6  2      5  3      4  4      3  5
--R             - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R           + 
--R                2  6         7     8
--R             3t1 t2  - 2t1 t2  + t2
--R    *
--R         3
--R       C1
--R     ,
--R
--R                  5       5        4  2      4           4  2     3  3
--R               2t0 t1 - t0 t2 - 3t0 t1  + 3t0 t1 t2 + 3t0 t2  - t0 t1
--R             + 
--R                  3  2         3     2      2  3         2     3      2  4
--R               6t0 t1 t2 - 14t0 t1 t2  - 2t0 t1 t2 + 14t0 t1 t2  - 3t0 t2
--R             + 
--R                    5         3  2         2  3            4        5     5
--R               t0 t1  + 2t0 t1 t2  - 6t0 t1 t2  - 3t0 t1 t2  + t0 t2  - t1 t2
--R             + 
--R                 3  3      2  4         5
--R               t1 t2  + 3t1 t2  - 2t1 t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R        *
--R             3
--R           xi
--R       + 
--R                 5        5        4  2      4           4  2      3  2
--R               t0 t1 + 2t0 t2 - 3t0 t1  + 3t0 t1 t2 - 2t0 t2  - 3t0 t1 t2
--R             + 
--R                    3     2      3  3      2  4     2  3        2  2  2
--R               - 7t0 t1 t2  + 3t0 t2  + 3t0 t1  - t0 t1 t2 + 9t0 t1 t2
--R             + 
--R                  2     3      2  4        5        4           3  2
--R               4t0 t1 t2  - 4t0 t2  - t0 t1  - t0 t1 t2 - 3t0 t1 t2
--R             + 
--R                       2  3           4     5        4  2      3  3     2  4
--R               - 2t0 t1 t2  + t0 t1 t2  + t1 t2 - 2t1 t2  + 4t1 t2  - t1 t2
--R             + 
--R                       5     6
--R               - 2t1 t2  + t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R        *
--R             2
--R           xi
--R       + 
--R                  5       5        4  2      4           3  3      3  2
--R               3t0 t1 + t0 t2 - 5t0 t1  - 5t0 t1 t2 + 3t0 t1  + 8t0 t1 t2
--R             + 
--R                    3     2     3  3     2  4      2  3        2  2  2
--R               - 4t0 t1 t2  - t0 t2  - t0 t1  - 2t0 t1 t2 - 3t0 t1 t2
--R             + 
--R                   2     3      2  4        5         4           2  3
--R               10t0 t1 t2  - 3t0 t2  - t0 t1  + 2t0 t1 t2 + 2t0 t1 t2
--R             + 
--R                          4         5     6      5       4  2      3  3
--R               - 8t0 t1 t2  + 2t0 t2  + t1  - 2t1 t2 - t1 t2  + 4t1 t2
--R             + 
--R                    2  4        5
--R               - 2t1 t2  + t1 t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R        *
--R           xi
--R       + 
--R               6     5        4  2      4          4  2      3  3      3  2
--R             t0  - t0 t2 - 4t0 t1  + 4t0 t1 t2 - t0 t2  + 3t0 t1  + 4t0 t1 t2
--R           + 
--R                   3     2      3  3      2  4      2  3        2  2  2
--R             - 10t0 t1 t2  + 3t0 t2  - 2t0 t1  - 5t0 t1 t2 + 9t0 t1 t2
--R           + 
--R                2     3      2  4         5        4          3  2         2  3
--R             7t0 t1 t2  - 5t0 t2  + 2t0 t1  - t0 t1 t2 + t0 t1 t2  - 9t0 t1 t2
--R           + 
--R                   5      5        4  2     3  3        5
--R             3t0 t2  - 2t1 t2 + 3t1 t2  + t1 t2  - t1 t2
--R        /
--R               12      11        11        10  2       10           10  2
--R             t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R           + 
--R                   9  3       9  2         9     2       9  3       8  4
--R             - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R           + 
--R                 8  3         8  2  2       8     3       8  4       7  5
--R             45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R           + 
--R                   7  4         7  3  2       7  2  3       7     4       7  5
--R             - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R           + 
--R                 6  6       6  5         6  4  2       6  3  3       6  2  4
--R             19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R           + 
--R                6     5       6  6       5  7       5  6         5  5  2
--R             9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R           + 
--R                   5  4  3       5  3  4       5  2  5      5     6       5  7
--R             - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R           + 
--R                 4  8       4  7         4  6  2       4  5  3       4  3  5
--R             15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R           + 
--R                 4  2  6       4     7       4  8       3  9       3  8
--R             45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R           + 
--R                   3  7  2       3  6  3       3  5  4       3  4  5
--R             - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R           + 
--R                 3  3  6       3  2  7       3     8       3  9      2  10
--R             20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R           + 
--R                 2  9         2  7  3       2  6  4       2  5  5       2  4  6
--R             15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2
--R           + 
--R                   2  3  7       2  2  8       2     9      2  10         11
--R             - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1
--R           + 
--R                     10            9  2          8  3          7  4
--R             - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R           + 
--R                      6  5          5  6          4  7          3  8
--R             - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R           + 
--R                      2  9             10         11     12      11        10  2
--R             - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2
--R           + 
--R                   9  3       8  4       7  5       6  6       5  7       4  8
--R             - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2
--R           + 
--R                   3  9      2  10         11     12
--R             - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R    *
--R         4
--R       C1
--R     ]
--E 18 

--S 19 of 22
r : List(L) := [reduce(+, [c * xi**(k*j) for j in UZn for c in C]) for k in 0 .. n-1] 
 

   (19)
   [
                    5       5        4  2      4           4  2     3  3
                 2t0 t1 - t0 t2 - 3t0 t1  + 3t0 t1 t2 + 3t0 t2  - t0 t1
               + 
                    3  2         3     2      2  3         2     3      2  4
                 6t0 t1 t2 - 14t0 t1 t2  - 2t0 t1 t2 + 14t0 t1 t2  - 3t0 t2
               + 
                      5         3  2         2  3            4        5     5
                 t0 t1  + 2t0 t1 t2  - 6t0 t1 t2  - 3t0 t1 t2  + t0 t2  - t1 t2
               + 
                   3  3      2  4         5
                 t1 t2  + 3t1 t2  - 2t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               3
             xi
         + 
                   5        5        4  2      4           4  2      3  2
                 t0 t1 + 2t0 t2 - 3t0 t1  + 3t0 t1 t2 - 2t0 t2  - 3t0 t1 t2
               + 
                      3     2      3  3      2  4     2  3        2  2  2
                 - 7t0 t1 t2  + 3t0 t2  + 3t0 t1  - t0 t1 t2 + 9t0 t1 t2
               + 
                    2     3      2  4        5        4           3  2
                 4t0 t1 t2  - 4t0 t2  - t0 t1  - t0 t1 t2 - 3t0 t1 t2
               + 
                         2  3           4     5        4  2      3  3     2  4
                 - 2t0 t1 t2  + t0 t1 t2  + t1 t2 - 2t1 t2  + 4t1 t2  - t1 t2
               + 
                         5     6
                 - 2t1 t2  + t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               2
             xi
         + 
                    5       5        4  2      4           3  3      3  2
                 3t0 t1 + t0 t2 - 5t0 t1  - 5t0 t1 t2 + 3t0 t1  + 8t0 t1 t2
               + 
                      3     2     3  3     2  4      2  3        2  2  2
                 - 4t0 t1 t2  - t0 t2  - t0 t1  - 2t0 t1 t2 - 3t0 t1 t2
               + 
                     2     3      2  4        5         4           2  3
                 10t0 t1 t2  - 3t0 t2  - t0 t1  + 2t0 t1 t2 + 2t0 t1 t2
               + 
                            4         5     6      5       4  2      3  3
                 - 8t0 t1 t2  + 2t0 t2  + t1  - 2t1 t2 - t1 t2  + 4t1 t2
               + 
                      2  4        5
                 - 2t1 t2  + t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
             xi
         + 
                 6     5        4  2      4          4  2      3  3      3  2
               t0  - t0 t2 - 4t0 t1  + 4t0 t1 t2 - t0 t2  + 3t0 t1  + 4t0 t1 t2
             + 
                     3     2      3  3      2  4      2  3        2  2  2
               - 10t0 t1 t2  + 3t0 t2  - 2t0 t1  - 5t0 t1 t2 + 9t0 t1 t2
             + 
                  2     3      2  4         5        4          3  2
               7t0 t1 t2  - 5t0 t2  + 2t0 t1  - t0 t1 t2 + t0 t1 t2
             + 
                       2  3         5      5        4  2     3  3        5
               - 9t0 t1 t2  + 3t0 t2  - 2t1 t2 + 3t1 t2  + t1 t2  - t1 t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
      *
           4
         C1
     + 
                   3       3       2          2  2        3        2
                 t0 t1 - t0 t2 + t0 t1 t2 + t0 t2  - t0 t1  + t0 t1 t2
               + 
                            2        3     3       2  2         3     4
                 - 4t0 t1 t2  + t0 t2  + t1 t2 - t1 t2  + 2t1 t2  - t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               3
             xi
         + 
                   3       3       2  2     2          2  2        3           2
                 t0 t1 + t0 t2 - t0 t1  + t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
               + 
                       3     4     3          3     4
                 2t0 t2  + t1  - t1 t2 + t1 t2  - t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               2
             xi
         + 
                    3        2  2      2          2  2        3        2
                 2t0 t1 - 2t0 t1  - 2t0 t1 t2 + t0 t2  + t0 t1  + t0 t1 t2
               + 
                           2     3       2  2        3     4
                 - t0 t1 t2  - t1 t2 + t1 t2  + t1 t2  - t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
             xi
         + 
                 4     3       2  2      2                 2        3     2  2
               t0  - t0 t2 - t0 t1  + 2t0 t1 t2 - 2t0 t1 t2  + t0 t2  + t1 t2
             + 
                   4
               - t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
      *
           3
         C1
     + 
                         2     2
               t0 t1 - t1  + t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               3
             xi
         + 
                         2
               t0 t2 - t1  + t1 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               2
             xi
         + 
                                 2
               t0 t1 + t0 t2 - t1
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
             xi
         + 
               2     2
             t0  - t1  + t1 t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
      *
           2
         C1
     + 
       C1
     ,

                     6     5        4  2      4          4  2      3  3
                 - t0  + t0 t2 + 4t0 t1  - 4t0 t1 t2 + t0 t2  - 3t0 t1
               + 
                      3  2         3     2      3  3      2  4      2  3
                 - 4t0 t1 t2 + 10t0 t1 t2  - 3t0 t2  + 2t0 t1  + 5t0 t1 t2
               + 
                      2  2  2      2     3      2  4         5        4
                 - 9t0 t1 t2  - 7t0 t1 t2  + 5t0 t2  - 2t0 t1  + t0 t1 t2
               + 
                        3  2         2  3         5      5        4  2     3  3
                 - t0 t1 t2  + 9t0 t1 t2  - 3t0 t2  + 2t1 t2 - 3t1 t2  - t1 t2
               + 
                      5
                 t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               3
             xi
         + 
                     6      5       4  2     4           4  2      3  3
                 - t0  + 2t0 t1 + t0 t1  - t0 t1 t2 + 4t0 t2  - 4t0 t1
               + 
                    3  2        3     2      3  3      2  4      2  3
                 2t0 t1 t2 - 4t0 t1 t2  - 3t0 t2  + 2t0 t1  + 3t0 t1 t2
               + 
                      2  2  2      2     3      2  4        5        4
                 - 9t0 t1 t2  + 7t0 t1 t2  + 2t0 t2  - t0 t1  + t0 t1 t2
               + 
                      3  2         2  3            4         5     5        4  2
                 t0 t1 t2  + 3t0 t1 t2  - 3t0 t1 t2  - 2t0 t2  + t1 t2 - 3t1 t2
               + 
                    2  4        5
                 3t1 t2  - t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               2
             xi
         + 
                     6     5        5       4  2     4          4  2      3  3
                 - t0  + t0 t1 + 3t0 t2 + t0 t1  - t0 t1 t2 - t0 t2  - 3t0 t1
               + 
                      3  2        3     2      2  4      2  3        2     3
                 - 7t0 t1 t2 + 3t0 t1 t2  + 5t0 t1  + 4t0 t1 t2 - 3t0 t1 t2
               + 
                   2  4         5         3  2         2  3           4
                 t0 t2  - 3t0 t1  - 4t0 t1 t2  + 7t0 t1 t2  + t0 t1 t2
               + 
                         5      5        4  2      3  3     2  4        5     6
                 - 3t0 t2  + 3t1 t2 - 5t1 t2  + 3t1 t2  - t1 t2  - t1 t2  + t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
             xi
         + 
                   6      5        5       4  2      4          4  2      3  2
               - t0  + 3t0 t1 + 2t0 t2 - t0 t1  - 9t0 t1 t2 + t0 t2  + 4t0 t1 t2
             + 
                  3     2      3  3     2  4      2  3         2  2  2
               6t0 t1 t2  - 4t0 t2  + t0 t1  + 3t0 t1 t2 - 12t0 t1 t2
             + 
                  2     3      2  4         5         4          3  2
               3t0 t1 t2  + 2t0 t2  - 3t0 t1  + 3t0 t1 t2 - t0 t1 t2
             + 
                      2  3            4        5     6      4  2      3  3
               11t0 t1 t2  - 8t0 t1 t2  - t0 t2  + t1  - 4t1 t2  + 3t1 t2
             + 
                    2  4         5
               - 2t1 t2  + 2t1 t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
      *
           4
         C1
     + 
                   4      3       3       2  2      2          2  2        3
                 t0  - 2t0 t1 - t0 t2 + t0 t1  + 4t0 t1 t2 - t0 t2  - t0 t1
               + 
                        2             2        3     3          3
                 - t0 t1 t2 - t0 t1 t2  + t0 t2  + t1 t2 - t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               3
             xi
         + 
                      3        2  2      2          2  2        3        2
                 - 2t0 t1 + 2t0 t1  + 2t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
               + 
                         2     3       2  2        3     4
                 t0 t1 t2  + t1 t2 - t1 t2  - t1 t2  + t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               2
             xi
         + 
                     3       3        2  2      2              3            2
                 - t0 t1 - t0 t2 + 2t0 t1  + 3t0 t1 t2 - 2t0 t1  - 3t0 t1 t2
               + 
                      3      3        2  2        3
                 t0 t2  + 2t1 t2 - 2t1 t2  + t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
             xi
         + 
                   3       3       2  2      2           2  2         3
               - t0 t1 + t0 t2 + t0 t1  + 3t0 t1 t2 - 2t0 t2  - 2t0 t1
             + 
                      2           3     4     2  2
               - t0 t1 t2 + 2t0 t2  + t1  - t1 t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
      *
           3
         C1
     + 
               t0 t1 - t1 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               3
             xi
         + 
                 2
               t0  - t0 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               2
             xi
         + 
                           2
               - t0 t2 + t1  - t1 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
             xi
         + 
                                       2
             t0 t1 - t0 t2 - t1 t2 + t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
      *
           2
         C1
     + 
       xi C1
     ,

                   6      5        5       4  2      4          4  2      3  2
                 t0  - 3t0 t1 - 2t0 t2 + t0 t1  + 9t0 t1 t2 - t0 t2  - 4t0 t1 t2
               + 
                      3     2      3  3     2  4      2  3         2  2  2
                 - 6t0 t1 t2  + 4t0 t2  - t0 t1  - 3t0 t1 t2 + 12t0 t1 t2
               + 
                      2     3      2  4         5         4          3  2
                 - 3t0 t1 t2  - 2t0 t2  + 3t0 t1  - 3t0 t1 t2 + t0 t1 t2
               + 
                          2  3            4        5     6      4  2      3  3
                 - 11t0 t1 t2  + 8t0 t1 t2  + t0 t2  - t1  + 4t1 t2  - 3t1 t2
               + 
                    2  4         5
                 2t1 t2  - 2t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               3
             xi
         + 
                      5       5        4  2      4           3  3      3  2
                 - 3t0 t1 - t0 t2 + 5t0 t1  + 5t0 t1 t2 - 3t0 t1  - 8t0 t1 t2
               + 
                    3     2     3  3     2  4      2  3        2  2  2
                 4t0 t1 t2  + t0 t2  + t0 t1  + 2t0 t1 t2 + 3t0 t1 t2
               + 
                       2     3      2  4        5         4           2  3
                 - 10t0 t1 t2  + 3t0 t2  + t0 t1  - 2t0 t1 t2 - 2t0 t1 t2
               + 
                          4         5     6      5       4  2      3  3
                 8t0 t1 t2  - 2t0 t2  - t1  + 2t1 t2 + t1 t2  - 4t1 t2
               + 
                    2  4        5
                 2t1 t2  - t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               2
             xi
         + 
                     5        5        4  2      4           4  2      3  3
                 - t0 t1 - 2t0 t2 + 2t0 t1  + 8t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                      3  2         3     2     3  3     2  4      2  2  2
                 - 2t0 t1 t2 - 10t0 t1 t2  + t0 t2  + t0 t1  + 3t0 t1 t2
               + 
                    2     3         5         4           3  2         2  3
                 4t0 t1 t2  + 2t0 t1  - 2t0 t1 t2 + 2t0 t1 t2  - 8t0 t1 t2
               + 
                          4        5     6     5       4  2      3  3      2  4
                 5t0 t1 t2  - t0 t2  - t1  + t1 t2 + t1 t2  - 3t1 t2  + 5t1 t2
               + 
                         5
                 - 3t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
             xi
         + 
                    5       5        4  2      4           4  2      3  3
               - 2t0 t1 + t0 t2 + 2t0 t1  + 8t0 t1 t2 - 2t0 t2  - 3t0 t1
             + 
                     3  2        3     2      3  3      2  4     2  3
               - 11t0 t1 t2 - 3t0 t1 t2  + 4t0 t2  + 4t0 t1  + t0 t1 t2
             + 
                   2  2  2      2     3     2  4         4           3  2
               12t0 t1 t2  - 6t0 t1 t2  - t0 t2  - 3t0 t1 t2 - 3t0 t1 t2
             + 
                       2  3            4         5     6      5       4  2
               - 4t0 t1 t2  + 9t0 t1 t2  - 2t0 t2  - t1  + 3t1 t2 - t1 t2
             + 
                 2  4         5     6
               t1 t2  - 3t1 t2  + t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
      *
           4
         C1
     + 
                    3       2  2      2  2        2              2        3
                 2t0 t2 - t0 t1  - 2t0 t2  - t0 t1 t2 + 3t0 t1 t2  + t0 t2
               + 
                   4      3       2  2        3
                 t1  - 2t1 t2 + t1 t2  - t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               3
             xi
         + 
                   3       3        2  2      2              3            2
                 t0 t1 + t0 t2 - 2t0 t1  - 3t0 t1 t2 + 2t0 t1  + 3t0 t1 t2
               + 
                        3      3        2  2        3
                 - t0 t2  - 2t1 t2 + 2t1 t2  - t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               2
             xi
         + 
                   4     3       2  2     2          2  2        3        2
                 t0  - t0 t1 - t0 t1  + t0 t1 t2 - t0 t2  + t0 t1  - t0 t1 t2
               + 
                          2     3        2  2         3
                 2t0 t1 t2  - t1 t2 + 2t1 t2  - 2t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
             xi
         + 
                   3       3       2          2  2        3        2
               - t0 t1 + t0 t2 - t0 t1 t2 - t0 t2  + t0 t1  - t0 t1 t2
             + 
                        2        3     3       2  2         3     4
               4t0 t1 t2  - t0 t2  - t1 t2 + t1 t2  - 2t1 t2  + t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
      *
           3
         C1
     + 
                   2     2
               - t0  + t1  - t1 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               3
             xi
         + 
                   2                     2
               - t0  + t0 t1 - t1 t2 + t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               2
             xi
         + 
                   2
               - t0  + t0 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
             xi
         + 
                 2
             - t0  + t0 t1 + t0 t2 - t1 t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
      *
           2
         C1
     + 
         2
       xi C1
     ,

                    5       5        4  2      4           4  2      3  3
                 2t0 t1 - t0 t2 - 2t0 t1  - 8t0 t1 t2 + 2t0 t2  + 3t0 t1
               + 
                     3  2        3     2      3  3      2  4     2  3
                 11t0 t1 t2 + 3t0 t1 t2  - 4t0 t2  - 4t0 t1  - t0 t1 t2
               + 
                       2  2  2      2     3     2  4         4           3  2
                 - 12t0 t1 t2  + 6t0 t1 t2  + t0 t2  + 3t0 t1 t2 + 3t0 t1 t2
               + 
                       2  3            4         5     6      5       4  2
                 4t0 t1 t2  - 9t0 t1 t2  + 2t0 t2  + t1  - 3t1 t2 + t1 t2
               + 
                     2  4         5     6
                 - t1 t2  + 3t1 t2  - t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               3
             xi
         + 
                   6     5        5       4  2     4          4  2      3  3
                 t0  - t0 t1 - 3t0 t2 - t0 t1  + t0 t1 t2 + t0 t2  + 3t0 t1
               + 
                    3  2        3     2      2  4      2  3        2     3
                 7t0 t1 t2 - 3t0 t1 t2  - 5t0 t1  - 4t0 t1 t2 + 3t0 t1 t2
               + 
                     2  4         5         3  2         2  3           4
                 - t0 t2  + 3t0 t1  + 4t0 t1 t2  - 7t0 t1 t2  - t0 t1 t2
               + 
                       5      5        4  2      3  3     2  4        5     6
                 3t0 t2  - 3t1 t2 + 5t1 t2  - 3t1 t2  + t1 t2  + t1 t2  - t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               2
             xi
         + 
                     5        5        4  2      4           4  2      3  2
                 - t0 t1 - 2t0 t2 + 3t0 t1  - 3t0 t1 t2 + 2t0 t2  + 3t0 t1 t2
               + 
                    3     2      3  3      2  4     2  3        2  2  2
                 7t0 t1 t2  - 3t0 t2  - 3t0 t1  + t0 t1 t2 - 9t0 t1 t2
               + 
                      2     3      2  4        5        4           3  2
                 - 4t0 t1 t2  + 4t0 t2  + t0 t1  + t0 t1 t2 + 3t0 t1 t2
               + 
                       2  3           4     5        4  2      3  3     2  4
                 2t0 t1 t2  - t0 t1 t2  - t1 t2 + 2t1 t2  - 4t1 t2  + t1 t2
               + 
                       5     6
                 2t1 t2  - t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
             xi
         + 
                 5        5        4  2     3  3      3  2        3     2
               t0 t1 - 3t0 t2 + 5t0 t2  - t0 t1  + 9t0 t1 t2 - 7t0 t1 t2
             + 
                    3  3      2  4     2  3        2  2  2       2     3
               - 3t0 t2  - 3t0 t1  - t0 t1 t2 - 9t0 t1 t2  + 10t0 t1 t2
             + 
                 2  4         5        4           3  2         2  3
               t0 t2  + 2t0 t1  + t0 t1 t2 + 5t0 t1 t2  - 4t0 t1 t2
             + 
                        4        5      5        4  2      3  3      2  4     6
             - 4t0 t1 t2  + t0 t2  - 2t1 t2 + 2t1 t2  - 3t1 t2  + 4t1 t2  - t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
      *
           4
         C1
     + 
                     4     3       2  2      2                 2        3
                 - t0  + t0 t2 + t0 t1  - 2t0 t1 t2 + 2t0 t1 t2  - t0 t2
               + 
                     2  2     4
                 - t1 t2  + t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               3
             xi
         + 
                     4     3       2  2     2          2  2        3        2
                 - t0  + t0 t1 + t0 t1  - t0 t1 t2 + t0 t2  - t0 t1  + t0 t1 t2
               + 
                            2     3        2  2         3
                 - 2t0 t1 t2  + t1 t2 - 2t1 t2  + 2t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               2
             xi
         + 
                     4     3        3       2          2  2        3           2
                 - t0  + t0 t1 + 2t0 t2 - t0 t1 t2 - t0 t2  - t0 t1  + t0 t1 t2
               + 
                      3     4     3       2  2        3
                 t0 t2  + t1  - t1 t2 - t1 t2  + t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
             xi
         + 
                   4      3       3       2  2      2          2  2        3
               - t0  + 2t0 t1 + t0 t2 - t0 t1  - 4t0 t1 t2 + t0 t2  + t0 t1
             + 
                    2             2        3     3          3
               t0 t1 t2 + t0 t1 t2  - t0 t2  - t1 t2 + t1 t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
      *
           3
         C1
     + 
                                           2
               - t0 t1 + t0 t2 + t1 t2 - t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               3
             xi
         + 
                         2
               t0 t2 - t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               2
             xi
         + 
                 2                     2
               t0  - t0 t1 + t1 t2 - t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
             xi
         + 
                         2     2
             - t0 t1 + t1  - t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
      *
           2
         C1
     + 
         3
       xi C1
     ,

                     5        5        4  2     3  3      3  2        3     2
                 - t0 t1 + 3t0 t2 - 5t0 t2  + t0 t1  - 9t0 t1 t2 + 7t0 t1 t2
               + 
                    3  3      2  4     2  3        2  2  2       2     3
                 3t0 t2  + 3t0 t1  + t0 t1 t2 + 9t0 t1 t2  - 10t0 t1 t2
               + 
                     2  4         5        4           3  2         2  3
                 - t0 t2  - 2t0 t1  - t0 t1 t2 - 5t0 t1 t2  + 4t0 t1 t2
               + 
                        4        5      5        4  2      3  3      2  4     6
               4t0 t1 t2  - t0 t2  + 2t1 t2 - 2t1 t2  + 3t1 t2  - 4t1 t2  + t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               3
             xi
         + 
                   5        5        4  2      4           4  2      3  3
                 t0 t1 + 2t0 t2 - 2t0 t1  - 8t0 t1 t2 - 3t0 t2  + 4t0 t1
               + 
                    3  2         3     2     3  3     2  4      2  2  2
                 2t0 t1 t2 + 10t0 t1 t2  - t0 t2  - t0 t1  - 3t0 t1 t2
               + 
                      2     3         5         4           3  2         2  3
                 - 4t0 t1 t2  - 2t0 t1  + 2t0 t1 t2 - 2t0 t1 t2  + 8t0 t1 t2
               + 
                            4        5     6     5       4  2      3  3
                 - 5t0 t1 t2  + t0 t2  + t1  - t1 t2 - t1 t2  + 3t1 t2
               + 
                      2  4         5
                 - 5t1 t2  + 3t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
               2
             xi
         + 
                   6      5       4  2     4           4  2      3  3
                 t0  - 2t0 t1 - t0 t1  + t0 t1 t2 - 4t0 t2  + 4t0 t1
               + 
                      3  2        3     2      3  3      2  4      2  3
                 - 2t0 t1 t2 + 4t0 t1 t2  + 3t0 t2  - 2t0 t1  - 3t0 t1 t2
               + 
                    2  2  2      2     3      2  4        5        4
                 9t0 t1 t2  - 7t0 t1 t2  - 2t0 t2  + t0 t1  - t0 t1 t2
               + 
                        3  2         2  3            4         5     5
                 - t0 t1 t2  - 3t0 t1 t2  + 3t0 t1 t2  + 2t0 t2  - t1 t2
               + 
                    4  2      2  4        5
                 3t1 t2  - 3t1 t2  + t1 t2
            /
                   12      11        11        10  2       10           10  2
                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
               + 
                       9  3       9  2         9     2       9  3       8  4
                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
               + 
                     8  3         8  2  2       8     3       8  4       7  5
                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
               + 
                       7  4         7  3  2       7  2  3       7     4
                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
               + 
                       7  5       6  6       6  5         6  4  2       6  3  3
                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
               + 
                     6  2  4      6     5       6  6       5  7       5  6
                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
               + 
                       5  5  2       5  4  3       5  3  4       5  2  5
                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
               + 
                    5     6       5  7       4  8       4  7         4  6  2
                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
               + 
                     4  5  3       4  3  5       4  2  6       4     7
                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
               + 
                     4  8       3  9       3  8         3  7  2       3  6  3
                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
               + 
                     3  5  4       3  4  5       3  3  6       3  2  7
                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
               + 
                     3     8       3  9      2  10       2  9         2  7  3
                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
               + 
                     2  6  4       2  5  5       2  4  6       2  3  7
                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
               + 
                     2  2  8       2     9      2  10         11         10
                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
               + 
                        9  2          8  3          7  4          6  5
                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
               + 
                        5  6          4  7          3  8          2  9
                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
               + 
                           10         11     12      11        10  2       9  3
                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
               + 
                     8  4       7  5       6  6       5  7       4  8       3  9
                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
               + 
                    2  10         11     12
                 6t1 t2   - 3t1 t2   + t2
          *
             xi
         + 
                    5       5        4  2      4           4  2     3  3
               - 2t0 t1 + t0 t2 + 3t0 t1  - 3t0 t1 t2 - 3t0 t2  + t0 t1
             + 
                    3  2         3     2      2  3         2     3      2  4
               - 6t0 t1 t2 + 14t0 t1 t2  + 2t0 t1 t2 - 14t0 t1 t2  + 3t0 t2
             + 
                      5         3  2         2  3            4        5     5
               - t0 t1  - 2t0 t1 t2  + 6t0 t1 t2  + 3t0 t1 t2  - t0 t2  + t1 t2
             + 
                   3  3      2  4         5
               - t1 t2  - 3t1 t2  + 2t1 t2
          /
                 12      11        11        10  2       10           10  2
               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
             + 
                     9  3       9  2         9     2       9  3       8  4
               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
             + 
                   8  3         8  2  2       8     3       8  4       7  5
               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
             + 
                     7  4         7  3  2       7  2  3       7     4       7  5
               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
             + 
                   6  6       6  5         6  4  2       6  3  3       6  2  4
               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
             + 
                  6     5       6  6       5  7       5  6         5  5  2
               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
             + 
                     5  4  3       5  3  4       5  2  5      5     6       5  7
               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
             + 
                   4  8       4  7         4  6  2       4  5  3       4  3  5
               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
             + 
                   4  2  6       4     7       4  8       3  9       3  8
               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
             + 
                     3  7  2       3  6  3       3  5  4       3  4  5
               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
             + 
                   3  3  6       3  2  7       3     8       3  9      2  10
               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
             + 
                   2  9         2  7  3       2  6  4       2  5  5
               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
             + 
                   2  4  6       2  3  7       2  2  8       2     9      2  10
               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
             + 
                       11         10            9  2          8  3          7  4
               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
             + 
                        6  5          5  6          4  7          3  8
               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
             + 
                        2  9             10         11     12      11
               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
             + 
                  10  2       9  3       8  4       7  5       6  6       5  7
               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
             + 
                   4  8       3  9      2  10         11     12
               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
      *
           4
         C1
     + 
                   3       3       2  2      2           2  2         3
                 t0 t1 - t0 t2 - t0 t1  - 3t0 t1 t2 + 2t0 t2  + 2t0 t1
               + 
                      2           3     4     2  2
                 t0 t1 t2 - 2t0 t2  - t1  + t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               3
             xi
         + 
                   4     3        3       2          2  2        3           2
                 t0  - t0 t1 - 2t0 t2 + t0 t1 t2 + t0 t2  + t0 t1  - t0 t1 t2
               + 
                        3     4     3       2  2        3
                 - t0 t2  - t1  + t1 t2 + t1 t2  - t1 t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
               2
             xi
         + 
                     3       3       2  2     2          2  2        3
                 - t0 t1 - t0 t2 + t0 t1  - t0 t1 t2 + t0 t2  + t0 t1
               + 
                         2         3     4     3          3     4
                 t0 t1 t2  - 2t0 t2  - t1  + t1 t2 - t1 t2  + t2
            /
                   8      7        7        6  2      6           6  2      5  3
                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
               + 
                       5  2        5     2      5  3      4  4       4  3
                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
               + 
                     4  2  2      4  4      3  5       3  4         3  3  2
                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
               + 
                      3  5      2  6      2  5        2  4  2       2  3  3
                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
               + 
                     2  2  4      2     5      2  6         7         6
                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
               + 
                       5  2          4  3          3  4          2  5
                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
               + 
                          6         7     8      7        6  2      5  3
                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
               + 
                    4  4      3  5      2  6         7     8
                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
          *
             xi
         + 
                    3       2  2      2  2        2              2        3
               - 2t0 t2 + t0 t1  + 2t0 t2  + t0 t1 t2 - 3t0 t1 t2  - t0 t2
             + 
                   4      3       2  2        3
               - t1  + 2t1 t2 - t1 t2  + t1 t2
          /
                 8      7        7        6  2      6           6  2      5  3
               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
             + 
                     5  2        5     2      5  3      4  4       4  3
               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
             + 
                   4  2  2      4  4      3  5       3  4         3  3  2
               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
             + 
                    3  5      2  6      2  5        2  4  2       2  3  3
               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
             + 
                   2  2  4      2     5      2  6         7         6
               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
             + 
                     5  2          4  3          3  4          2  5            6
               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
             + 
                       7     8      7        6  2      5  3      4  4      3  5
               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
             + 
                  2  6         7     8
               3t1 t2  - 2t1 t2  + t2
      *
           3
         C1
     + 
                 2
               t0  - t0 t1 - t0 t2 + t1 t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               3
             xi
         + 
                                   2
               - t0 t1 - t0 t2 + t1
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
               2
             xi
         + 
                           2
               - t0 t2 + t2
            /
                   4     3       3       2  2      2          2  2        3
                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
               + 
                         2              2        3     4     3       2  2
                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
               + 
                        3     4
                 - t1 t2  + t2
          *
             xi
         + 
             - t0 t1 + t1 t2
          /
                 4     3       3       2  2      2          2  2        3
               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
             + 
                       2              2        3     4     3       2  2        3
               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
             + 
                 4
               t2
      *
           2
         C1
     + 
            3     2
       (- xi  - xi  - xi - 1)C1
     ]
--R 
--R
--R   (19)
--R   [
--R                    5       5        4  2      4           4  2     3  3
--R                 2t0 t1 - t0 t2 - 3t0 t1  + 3t0 t1 t2 + 3t0 t2  - t0 t1
--R               + 
--R                    3  2         3     2      2  3         2     3      2  4
--R                 6t0 t1 t2 - 14t0 t1 t2  - 2t0 t1 t2 + 14t0 t1 t2  - 3t0 t2
--R               + 
--R                      5         3  2         2  3            4        5     5
--R                 t0 t1  + 2t0 t1 t2  - 6t0 t1 t2  - 3t0 t1 t2  + t0 t2  - t1 t2
--R               + 
--R                   3  3      2  4         5
--R                 t1 t2  + 3t1 t2  - 2t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   5        5        4  2      4           4  2      3  2
--R                 t0 t1 + 2t0 t2 - 3t0 t1  + 3t0 t1 t2 - 2t0 t2  - 3t0 t1 t2
--R               + 
--R                      3     2      3  3      2  4     2  3        2  2  2
--R                 - 7t0 t1 t2  + 3t0 t2  + 3t0 t1  - t0 t1 t2 + 9t0 t1 t2
--R               + 
--R                    2     3      2  4        5        4           3  2
--R                 4t0 t1 t2  - 4t0 t2  - t0 t1  - t0 t1 t2 - 3t0 t1 t2
--R               + 
--R                         2  3           4     5        4  2      3  3     2  4
--R                 - 2t0 t1 t2  + t0 t1 t2  + t1 t2 - 2t1 t2  + 4t1 t2  - t1 t2
--R               + 
--R                         5     6
--R                 - 2t1 t2  + t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               2
--R             xi
--R         + 
--R                    5       5        4  2      4           3  3      3  2
--R                 3t0 t1 + t0 t2 - 5t0 t1  - 5t0 t1 t2 + 3t0 t1  + 8t0 t1 t2
--R               + 
--R                      3     2     3  3     2  4      2  3        2  2  2
--R                 - 4t0 t1 t2  - t0 t2  - t0 t1  - 2t0 t1 t2 - 3t0 t1 t2
--R               + 
--R                     2     3      2  4        5         4           2  3
--R                 10t0 t1 t2  - 3t0 t2  - t0 t1  + 2t0 t1 t2 + 2t0 t1 t2
--R               + 
--R                            4         5     6      5       4  2      3  3
--R                 - 8t0 t1 t2  + 2t0 t2  + t1  - 2t1 t2 - t1 t2  + 4t1 t2
--R               + 
--R                      2  4        5
--R                 - 2t1 t2  + t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R             xi
--R         + 
--R                 6     5        4  2      4          4  2      3  3      3  2
--R               t0  - t0 t2 - 4t0 t1  + 4t0 t1 t2 - t0 t2  + 3t0 t1  + 4t0 t1 t2
--R             + 
--R                     3     2      3  3      2  4      2  3        2  2  2
--R               - 10t0 t1 t2  + 3t0 t2  - 2t0 t1  - 5t0 t1 t2 + 9t0 t1 t2
--R             + 
--R                  2     3      2  4         5        4          3  2
--R               7t0 t1 t2  - 5t0 t2  + 2t0 t1  - t0 t1 t2 + t0 t1 t2
--R             + 
--R                       2  3         5      5        4  2     3  3        5
--R               - 9t0 t1 t2  + 3t0 t2  - 2t1 t2 + 3t1 t2  + t1 t2  - t1 t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R      *
--R           4
--R         C1
--R     + 
--R                   3       3       2          2  2        3        2
--R                 t0 t1 - t0 t2 + t0 t1 t2 + t0 t2  - t0 t1  + t0 t1 t2
--R               + 
--R                            2        3     3       2  2         3     4
--R                 - 4t0 t1 t2  + t0 t2  + t1 t2 - t1 t2  + 2t1 t2  - t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   3       3       2  2     2          2  2        3           2
--R                 t0 t1 + t0 t2 - t0 t1  + t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
--R               + 
--R                       3     4     3          3     4
--R                 2t0 t2  + t1  - t1 t2 + t1 t2  - t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                    3        2  2      2          2  2        3        2
--R                 2t0 t1 - 2t0 t1  - 2t0 t1 t2 + t0 t2  + t0 t1  + t0 t1 t2
--R               + 
--R                           2     3       2  2        3     4
--R                 - t0 t1 t2  - t1 t2 + t1 t2  + t1 t2  - t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                 4     3       2  2      2                 2        3     2  2
--R               t0  - t0 t2 - t0 t1  + 2t0 t1 t2 - 2t0 t1 t2  + t0 t2  + t1 t2
--R             + 
--R                   4
--R               - t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R      *
--R           3
--R         C1
--R     + 
--R                         2     2
--R               t0 t1 - t1  + t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                         2
--R               t0 t2 - t1  + t1 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                                 2
--R               t0 t1 + t0 t2 - t1
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R             xi
--R         + 
--R               2     2
--R             t0  - t1  + t1 t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R      *
--R           2
--R         C1
--R     + 
--R       C1
--R     ,
--R
--R                     6     5        4  2      4          4  2      3  3
--R                 - t0  + t0 t2 + 4t0 t1  - 4t0 t1 t2 + t0 t2  - 3t0 t1
--R               + 
--R                      3  2         3     2      3  3      2  4      2  3
--R                 - 4t0 t1 t2 + 10t0 t1 t2  - 3t0 t2  + 2t0 t1  + 5t0 t1 t2
--R               + 
--R                      2  2  2      2     3      2  4         5        4
--R                 - 9t0 t1 t2  - 7t0 t1 t2  + 5t0 t2  - 2t0 t1  + t0 t1 t2
--R               + 
--R                        3  2         2  3         5      5        4  2     3  3
--R                 - t0 t1 t2  + 9t0 t1 t2  - 3t0 t2  + 2t1 t2 - 3t1 t2  - t1 t2
--R               + 
--R                      5
--R                 t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               3
--R             xi
--R         + 
--R                     6      5       4  2     4           4  2      3  3
--R                 - t0  + 2t0 t1 + t0 t1  - t0 t1 t2 + 4t0 t2  - 4t0 t1
--R               + 
--R                    3  2        3     2      3  3      2  4      2  3
--R                 2t0 t1 t2 - 4t0 t1 t2  - 3t0 t2  + 2t0 t1  + 3t0 t1 t2
--R               + 
--R                      2  2  2      2     3      2  4        5        4
--R                 - 9t0 t1 t2  + 7t0 t1 t2  + 2t0 t2  - t0 t1  + t0 t1 t2
--R               + 
--R                      3  2         2  3            4         5     5        4  2
--R                 t0 t1 t2  + 3t0 t1 t2  - 3t0 t1 t2  - 2t0 t2  + t1 t2 - 3t1 t2
--R               + 
--R                    2  4        5
--R                 3t1 t2  - t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               2
--R             xi
--R         + 
--R                     6     5        5       4  2     4          4  2      3  3
--R                 - t0  + t0 t1 + 3t0 t2 + t0 t1  - t0 t1 t2 - t0 t2  - 3t0 t1
--R               + 
--R                      3  2        3     2      2  4      2  3        2     3
--R                 - 7t0 t1 t2 + 3t0 t1 t2  + 5t0 t1  + 4t0 t1 t2 - 3t0 t1 t2
--R               + 
--R                   2  4         5         3  2         2  3           4
--R                 t0 t2  - 3t0 t1  - 4t0 t1 t2  + 7t0 t1 t2  + t0 t1 t2
--R               + 
--R                         5      5        4  2      3  3     2  4        5     6
--R                 - 3t0 t2  + 3t1 t2 - 5t1 t2  + 3t1 t2  - t1 t2  - t1 t2  + t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R             xi
--R         + 
--R                   6      5        5       4  2      4          4  2      3  2
--R               - t0  + 3t0 t1 + 2t0 t2 - t0 t1  - 9t0 t1 t2 + t0 t2  + 4t0 t1 t2
--R             + 
--R                  3     2      3  3     2  4      2  3         2  2  2
--R               6t0 t1 t2  - 4t0 t2  + t0 t1  + 3t0 t1 t2 - 12t0 t1 t2
--R             + 
--R                  2     3      2  4         5         4          3  2
--R               3t0 t1 t2  + 2t0 t2  - 3t0 t1  + 3t0 t1 t2 - t0 t1 t2
--R             + 
--R                      2  3            4        5     6      4  2      3  3
--R               11t0 t1 t2  - 8t0 t1 t2  - t0 t2  + t1  - 4t1 t2  + 3t1 t2
--R             + 
--R                    2  4         5
--R               - 2t1 t2  + 2t1 t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R      *
--R           4
--R         C1
--R     + 
--R                   4      3       3       2  2      2          2  2        3
--R                 t0  - 2t0 t1 - t0 t2 + t0 t1  + 4t0 t1 t2 - t0 t2  - t0 t1
--R               + 
--R                        2             2        3     3          3
--R                 - t0 t1 t2 - t0 t1 t2  + t0 t2  + t1 t2 - t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                      3        2  2      2          2  2        3        2
--R                 - 2t0 t1 + 2t0 t1  + 2t0 t1 t2 - t0 t2  - t0 t1  - t0 t1 t2
--R               + 
--R                         2     3       2  2        3     4
--R                 t0 t1 t2  + t1 t2 - t1 t2  - t1 t2  + t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                     3       3        2  2      2              3            2
--R                 - t0 t1 - t0 t2 + 2t0 t1  + 3t0 t1 t2 - 2t0 t1  - 3t0 t1 t2
--R               + 
--R                      3      3        2  2        3
--R                 t0 t2  + 2t1 t2 - 2t1 t2  + t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                   3       3       2  2      2           2  2         3
--R               - t0 t1 + t0 t2 + t0 t1  + 3t0 t1 t2 - 2t0 t2  - 2t0 t1
--R             + 
--R                      2           3     4     2  2
--R               - t0 t1 t2 + 2t0 t2  + t1  - t1 t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R      *
--R           3
--R         C1
--R     + 
--R               t0 t1 - t1 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                 2
--R               t0  - t0 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                           2
--R               - t0 t2 + t1  - t1 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                                       2
--R             t0 t1 - t0 t2 - t1 t2 + t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R      *
--R           2
--R         C1
--R     + 
--R       xi C1
--R     ,
--R
--R                   6      5        5       4  2      4          4  2      3  2
--R                 t0  - 3t0 t1 - 2t0 t2 + t0 t1  + 9t0 t1 t2 - t0 t2  - 4t0 t1 t2
--R               + 
--R                      3     2      3  3     2  4      2  3         2  2  2
--R                 - 6t0 t1 t2  + 4t0 t2  - t0 t1  - 3t0 t1 t2 + 12t0 t1 t2
--R               + 
--R                      2     3      2  4         5         4          3  2
--R                 - 3t0 t1 t2  - 2t0 t2  + 3t0 t1  - 3t0 t1 t2 + t0 t1 t2
--R               + 
--R                          2  3            4        5     6      4  2      3  3
--R                 - 11t0 t1 t2  + 8t0 t1 t2  + t0 t2  - t1  + 4t1 t2  - 3t1 t2
--R               + 
--R                    2  4         5
--R                 2t1 t2  - 2t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               3
--R             xi
--R         + 
--R                      5       5        4  2      4           3  3      3  2
--R                 - 3t0 t1 - t0 t2 + 5t0 t1  + 5t0 t1 t2 - 3t0 t1  - 8t0 t1 t2
--R               + 
--R                    3     2     3  3     2  4      2  3        2  2  2
--R                 4t0 t1 t2  + t0 t2  + t0 t1  + 2t0 t1 t2 + 3t0 t1 t2
--R               + 
--R                       2     3      2  4        5         4           2  3
--R                 - 10t0 t1 t2  + 3t0 t2  + t0 t1  - 2t0 t1 t2 - 2t0 t1 t2
--R               + 
--R                          4         5     6      5       4  2      3  3
--R                 8t0 t1 t2  - 2t0 t2  - t1  + 2t1 t2 + t1 t2  - 4t1 t2
--R               + 
--R                    2  4        5
--R                 2t1 t2  - t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               2
--R             xi
--R         + 
--R                     5        5        4  2      4           4  2      3  3
--R                 - t0 t1 - 2t0 t2 + 2t0 t1  + 8t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                      3  2         3     2     3  3     2  4      2  2  2
--R                 - 2t0 t1 t2 - 10t0 t1 t2  + t0 t2  + t0 t1  + 3t0 t1 t2
--R               + 
--R                    2     3         5         4           3  2         2  3
--R                 4t0 t1 t2  + 2t0 t1  - 2t0 t1 t2 + 2t0 t1 t2  - 8t0 t1 t2
--R               + 
--R                          4        5     6     5       4  2      3  3      2  4
--R                 5t0 t1 t2  - t0 t2  - t1  + t1 t2 + t1 t2  - 3t1 t2  + 5t1 t2
--R               + 
--R                         5
--R                 - 3t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R             xi
--R         + 
--R                    5       5        4  2      4           4  2      3  3
--R               - 2t0 t1 + t0 t2 + 2t0 t1  + 8t0 t1 t2 - 2t0 t2  - 3t0 t1
--R             + 
--R                     3  2        3     2      3  3      2  4     2  3
--R               - 11t0 t1 t2 - 3t0 t1 t2  + 4t0 t2  + 4t0 t1  + t0 t1 t2
--R             + 
--R                   2  2  2      2     3     2  4         4           3  2
--R               12t0 t1 t2  - 6t0 t1 t2  - t0 t2  - 3t0 t1 t2 - 3t0 t1 t2
--R             + 
--R                       2  3            4         5     6      5       4  2
--R               - 4t0 t1 t2  + 9t0 t1 t2  - 2t0 t2  - t1  + 3t1 t2 - t1 t2
--R             + 
--R                 2  4         5     6
--R               t1 t2  - 3t1 t2  + t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R      *
--R           4
--R         C1
--R     + 
--R                    3       2  2      2  2        2              2        3
--R                 2t0 t2 - t0 t1  - 2t0 t2  - t0 t1 t2 + 3t0 t1 t2  + t0 t2
--R               + 
--R                   4      3       2  2        3
--R                 t1  - 2t1 t2 + t1 t2  - t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   3       3        2  2      2              3            2
--R                 t0 t1 + t0 t2 - 2t0 t1  - 3t0 t1 t2 + 2t0 t1  + 3t0 t1 t2
--R               + 
--R                        3      3        2  2        3
--R                 - t0 t2  - 2t1 t2 + 2t1 t2  - t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                   4     3       2  2     2          2  2        3        2
--R                 t0  - t0 t1 - t0 t1  + t0 t1 t2 - t0 t2  + t0 t1  - t0 t1 t2
--R               + 
--R                          2     3        2  2         3
--R                 2t0 t1 t2  - t1 t2 + 2t1 t2  - 2t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                   3       3       2          2  2        3        2
--R               - t0 t1 + t0 t2 - t0 t1 t2 - t0 t2  + t0 t1  - t0 t1 t2
--R             + 
--R                        2        3     3       2  2         3     4
--R               4t0 t1 t2  - t0 t2  - t1 t2 + t1 t2  - 2t1 t2  + t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R      *
--R           3
--R         C1
--R     + 
--R                   2     2
--R               - t0  + t1  - t1 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   2                     2
--R               - t0  + t0 t1 - t1 t2 + t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                   2
--R               - t0  + t0 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                 2
--R             - t0  + t0 t1 + t0 t2 - t1 t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R      *
--R           2
--R         C1
--R     + 
--R         2
--R       xi C1
--R     ,
--R
--R                    5       5        4  2      4           4  2      3  3
--R                 2t0 t1 - t0 t2 - 2t0 t1  - 8t0 t1 t2 + 2t0 t2  + 3t0 t1
--R               + 
--R                     3  2        3     2      3  3      2  4     2  3
--R                 11t0 t1 t2 + 3t0 t1 t2  - 4t0 t2  - 4t0 t1  - t0 t1 t2
--R               + 
--R                       2  2  2      2     3     2  4         4           3  2
--R                 - 12t0 t1 t2  + 6t0 t1 t2  + t0 t2  + 3t0 t1 t2 + 3t0 t1 t2
--R               + 
--R                       2  3            4         5     6      5       4  2
--R                 4t0 t1 t2  - 9t0 t1 t2  + 2t0 t2  + t1  - 3t1 t2 + t1 t2
--R               + 
--R                     2  4         5     6
--R                 - t1 t2  + 3t1 t2  - t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   6     5        5       4  2     4          4  2      3  3
--R                 t0  - t0 t1 - 3t0 t2 - t0 t1  + t0 t1 t2 + t0 t2  + 3t0 t1
--R               + 
--R                    3  2        3     2      2  4      2  3        2     3
--R                 7t0 t1 t2 - 3t0 t1 t2  - 5t0 t1  - 4t0 t1 t2 + 3t0 t1 t2
--R               + 
--R                     2  4         5         3  2         2  3           4
--R                 - t0 t2  + 3t0 t1  + 4t0 t1 t2  - 7t0 t1 t2  - t0 t1 t2
--R               + 
--R                       5      5        4  2      3  3     2  4        5     6
--R                 3t0 t2  - 3t1 t2 + 5t1 t2  - 3t1 t2  + t1 t2  + t1 t2  - t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               2
--R             xi
--R         + 
--R                     5        5        4  2      4           4  2      3  2
--R                 - t0 t1 - 2t0 t2 + 3t0 t1  - 3t0 t1 t2 + 2t0 t2  + 3t0 t1 t2
--R               + 
--R                    3     2      3  3      2  4     2  3        2  2  2
--R                 7t0 t1 t2  - 3t0 t2  - 3t0 t1  + t0 t1 t2 - 9t0 t1 t2
--R               + 
--R                      2     3      2  4        5        4           3  2
--R                 - 4t0 t1 t2  + 4t0 t2  + t0 t1  + t0 t1 t2 + 3t0 t1 t2
--R               + 
--R                       2  3           4     5        4  2      3  3     2  4
--R                 2t0 t1 t2  - t0 t1 t2  - t1 t2 + 2t1 t2  - 4t1 t2  + t1 t2
--R               + 
--R                       5     6
--R                 2t1 t2  - t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R             xi
--R         + 
--R                 5        5        4  2     3  3      3  2        3     2
--R               t0 t1 - 3t0 t2 + 5t0 t2  - t0 t1  + 9t0 t1 t2 - 7t0 t1 t2
--R             + 
--R                    3  3      2  4     2  3        2  2  2       2     3
--R               - 3t0 t2  - 3t0 t1  - t0 t1 t2 - 9t0 t1 t2  + 10t0 t1 t2
--R             + 
--R                 2  4         5        4           3  2         2  3
--R               t0 t2  + 2t0 t1  + t0 t1 t2 + 5t0 t1 t2  - 4t0 t1 t2
--R             + 
--R                        4        5      5        4  2      3  3      2  4     6
--R             - 4t0 t1 t2  + t0 t2  - 2t1 t2 + 2t1 t2  - 3t1 t2  + 4t1 t2  - t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R      *
--R           4
--R         C1
--R     + 
--R                     4     3       2  2      2                 2        3
--R                 - t0  + t0 t2 + t0 t1  - 2t0 t1 t2 + 2t0 t1 t2  - t0 t2
--R               + 
--R                     2  2     4
--R                 - t1 t2  + t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                     4     3       2  2     2          2  2        3        2
--R                 - t0  + t0 t1 + t0 t1  - t0 t1 t2 + t0 t2  - t0 t1  + t0 t1 t2
--R               + 
--R                            2     3        2  2         3
--R                 - 2t0 t1 t2  + t1 t2 - 2t1 t2  + 2t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                     4     3        3       2          2  2        3           2
--R                 - t0  + t0 t1 + 2t0 t2 - t0 t1 t2 - t0 t2  - t0 t1  + t0 t1 t2
--R               + 
--R                      3     4     3       2  2        3
--R                 t0 t2  + t1  - t1 t2 - t1 t2  + t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                   4      3       3       2  2      2          2  2        3
--R               - t0  + 2t0 t1 + t0 t2 - t0 t1  - 4t0 t1 t2 + t0 t2  + t0 t1
--R             + 
--R                    2             2        3     3          3
--R               t0 t1 t2 + t0 t1 t2  - t0 t2  - t1 t2 + t1 t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R      *
--R           3
--R         C1
--R     + 
--R                                           2
--R               - t0 t1 + t0 t2 + t1 t2 - t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                         2
--R               t0 t2 - t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                 2                     2
--R               t0  - t0 t1 + t1 t2 - t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                         2     2
--R             - t0 t1 + t1  - t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R      *
--R           2
--R         C1
--R     + 
--R         3
--R       xi C1
--R     ,
--R
--R                     5        5        4  2     3  3      3  2        3     2
--R                 - t0 t1 + 3t0 t2 - 5t0 t2  + t0 t1  - 9t0 t1 t2 + 7t0 t1 t2
--R               + 
--R                    3  3      2  4     2  3        2  2  2       2     3
--R                 3t0 t2  + 3t0 t1  + t0 t1 t2 + 9t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  4         5        4           3  2         2  3
--R                 - t0 t2  - 2t0 t1  - t0 t1 t2 - 5t0 t1 t2  + 4t0 t1 t2
--R               + 
--R                        4        5      5        4  2      3  3      2  4     6
--R               4t0 t1 t2  - t0 t2  + 2t1 t2 - 2t1 t2  + 3t1 t2  - 4t1 t2  + t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   5        5        4  2      4           4  2      3  3
--R                 t0 t1 + 2t0 t2 - 2t0 t1  - 8t0 t1 t2 - 3t0 t2  + 4t0 t1
--R               + 
--R                    3  2         3     2     3  3     2  4      2  2  2
--R                 2t0 t1 t2 + 10t0 t1 t2  - t0 t2  - t0 t1  - 3t0 t1 t2
--R               + 
--R                      2     3         5         4           3  2         2  3
--R                 - 4t0 t1 t2  - 2t0 t1  + 2t0 t1 t2 - 2t0 t1 t2  + 8t0 t1 t2
--R               + 
--R                            4        5     6     5       4  2      3  3
--R                 - 5t0 t1 t2  + t0 t2  + t1  - t1 t2 - t1 t2  + 3t1 t2
--R               + 
--R                      2  4         5
--R                 - 5t1 t2  + 3t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R               2
--R             xi
--R         + 
--R                   6      5       4  2     4           4  2      3  3
--R                 t0  - 2t0 t1 - t0 t1  + t0 t1 t2 - 4t0 t2  + 4t0 t1
--R               + 
--R                      3  2        3     2      3  3      2  4      2  3
--R                 - 2t0 t1 t2 + 4t0 t1 t2  + 3t0 t2  - 2t0 t1  - 3t0 t1 t2
--R               + 
--R                    2  2  2      2     3      2  4        5        4
--R                 9t0 t1 t2  - 7t0 t1 t2  - 2t0 t2  + t0 t1  - t0 t1 t2
--R               + 
--R                        3  2         2  3            4         5     5
--R                 - t0 t1 t2  - 3t0 t1 t2  + 3t0 t1 t2  + 2t0 t2  - t1 t2
--R               + 
--R                    4  2      2  4        5
--R                 3t1 t2  - 3t1 t2  + t1 t2
--R            /
--R                   12      11        11        10  2       10           10  2
--R                 t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R               + 
--R                       9  3       9  2         9     2       9  3       8  4
--R                 - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R               + 
--R                     8  3         8  2  2       8     3       8  4       7  5
--R                 45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R               + 
--R                       7  4         7  3  2       7  2  3       7     4
--R                 - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                       7  5       6  6       6  5         6  4  2       6  3  3
--R                 - 18t0 t2  + 19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2
--R               + 
--R                     6  2  4      6     5       6  6       5  7       5  6
--R                 45t0 t1 t2  + 9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2
--R               + 
--R                       5  5  2       5  4  3       5  3  4       5  2  5
--R                 - 63t0 t1 t2  - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2
--R               + 
--R                    5     6       5  7       4  8       4  7         4  6  2
--R                 9t0 t1 t2  - 18t0 t2  + 15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2
--R               + 
--R                     4  5  3       4  3  5       4  2  6       4     7
--R                 15t0 t1 t2  + 15t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2
--R               + 
--R                     4  8       3  9       3  8         3  7  2       3  6  3
--R                 15t0 t2  - 10t0 t1  - 30t0 t1 t2 - 30t0 t1 t2  + 15t0 t1 t2
--R               + 
--R                     3  5  4       3  4  5       3  3  6       3  2  7
--R                 15t0 t1 t2  - 60t0 t1 t2  + 20t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                     3     8       3  9      2  10       2  9         2  7  3
--R                 15t0 t1 t2  - 10t0 t2  + 6t0 t1   + 15t0 t1 t2 - 30t0 t1 t2
--R               + 
--R                     2  6  4       2  5  5       2  4  6       2  3  7
--R                 60t0 t1 t2  - 63t0 t1 t2  + 90t0 t1 t2  - 75t0 t1 t2
--R               + 
--R                     2  2  8       2     9      2  10         11         10
--R                 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2   - 3t0 t1   - 3t0 t1  t2
--R               + 
--R                        9  2          8  3          7  4          6  5
--R                 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2  - 66t0 t1 t2
--R               + 
--R                        5  6          4  7          3  8          2  9
--R                 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2  - 30t0 t1 t2
--R               + 
--R                           10         11     12      11        10  2       9  3
--R                 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2 + 6t1  t2  - 10t1 t2
--R               + 
--R                     8  4       7  5       6  6       5  7       4  8       3  9
--R                 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2  + 15t1 t2  - 10t1 t2
--R               + 
--R                    2  10         11     12
--R                 6t1 t2   - 3t1 t2   + t2
--R          *
--R             xi
--R         + 
--R                    5       5        4  2      4           4  2     3  3
--R               - 2t0 t1 + t0 t2 + 3t0 t1  - 3t0 t1 t2 - 3t0 t2  + t0 t1
--R             + 
--R                    3  2         3     2      2  3         2     3      2  4
--R               - 6t0 t1 t2 + 14t0 t1 t2  + 2t0 t1 t2 - 14t0 t1 t2  + 3t0 t2
--R             + 
--R                      5         3  2         2  3            4        5     5
--R               - t0 t1  - 2t0 t1 t2  + 6t0 t1 t2  + 3t0 t1 t2  - t0 t2  + t1 t2
--R             + 
--R                   3  3      2  4         5
--R               - t1 t2  - 3t1 t2  + 2t1 t2
--R          /
--R                 12      11        11        10  2       10           10  2
--R               t0   - 3t0  t1 - 3t0  t2 + 6t0  t1  + 12t0  t1 t2 + 6t0  t2
--R             + 
--R                     9  3       9  2         9     2       9  3       8  4
--R               - 10t0 t1  - 30t0 t1 t2 - 15t0 t1 t2  - 10t0 t2  + 15t0 t1
--R             + 
--R                   8  3         8  2  2       8     3       8  4       7  5
--R               45t0 t1 t2 + 45t0 t1 t2  + 15t0 t1 t2  + 15t0 t2  - 18t0 t1
--R             + 
--R                     7  4         7  3  2       7  2  3       7     4       7  5
--R               - 60t0 t1 t2 - 75t0 t1 t2  - 30t0 t1 t2  - 15t0 t1 t2  - 18t0 t2
--R             + 
--R                   6  6       6  5         6  4  2       6  3  3       6  2  4
--R               19t0 t1  + 69t0 t1 t2 + 90t0 t1 t2  + 20t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                  6     5       6  6       5  7       5  6         5  5  2
--R               9t0 t1 t2  + 19t0 t2  - 18t0 t1  - 66t0 t1 t2 - 63t0 t1 t2
--R             + 
--R                     5  4  3       5  3  4       5  2  5      5     6       5  7
--R               - 60t0 t1 t2  + 15t0 t1 t2  - 63t0 t1 t2  + 9t0 t1 t2  - 18t0 t2
--R             + 
--R                   4  8       4  7         4  6  2       4  5  3       4  3  5
--R               15t0 t1  + 45t0 t1 t2 + 60t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2
--R             + 
--R                   4  2  6       4     7       4  8       3  9       3  8
--R               45t0 t1 t2  - 15t0 t1 t2  + 15t0 t2  - 10t0 t1  - 30t0 t1 t2
--R             + 
--R                     3  7  2       3  6  3       3  5  4       3  4  5
--R               - 30t0 t1 t2  + 15t0 t1 t2  + 15t0 t1 t2  - 60t0 t1 t2
--R             + 
--R                   3  3  6       3  2  7       3     8       3  9      2  10
--R               20t0 t1 t2  - 30t0 t1 t2  + 15t0 t1 t2  - 10t0 t2  + 6t0 t1
--R             + 
--R                   2  9         2  7  3       2  6  4       2  5  5
--R               15t0 t1 t2 - 30t0 t1 t2  + 60t0 t1 t2  - 63t0 t1 t2
--R             + 
--R                   2  4  6       2  3  7       2  2  8       2     9      2  10
--R               90t0 t1 t2  - 75t0 t1 t2  + 45t0 t1 t2  - 15t0 t1 t2  + 6t0 t2
--R             + 
--R                       11         10            9  2          8  3          7  4
--R               - 3t0 t1   - 3t0 t1  t2 + 15t0 t1 t2  - 30t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        6  5          5  6          4  7          3  8
--R               - 66t0 t1 t2  + 69t0 t1 t2  - 60t0 t1 t2  + 45t0 t1 t2
--R             + 
--R                        2  9             10         11     12      11
--R               - 30t0 t1 t2  + 12t0 t1 t2   - 3t0 t2   + t1   - 3t1  t2
--R             + 
--R                  10  2       9  3       8  4       7  5       6  6       5  7
--R               6t1  t2  - 10t1 t2  + 15t1 t2  - 18t1 t2  + 19t1 t2  - 18t1 t2
--R             + 
--R                   4  8       3  9      2  10         11     12
--R               15t1 t2  - 10t1 t2  + 6t1 t2   - 3t1 t2   + t2
--R      *
--R           4
--R         C1
--R     + 
--R                   3       3       2  2      2           2  2         3
--R                 t0 t1 - t0 t2 - t0 t1  - 3t0 t1 t2 + 2t0 t2  + 2t0 t1
--R               + 
--R                      2           3     4     2  2
--R                 t0 t1 t2 - 2t0 t2  - t1  + t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                   4     3        3       2          2  2        3           2
--R                 t0  - t0 t1 - 2t0 t2 + t0 t1 t2 + t0 t2  + t0 t1  - t0 t1 t2
--R               + 
--R                        3     4     3       2  2        3
--R                 - t0 t2  - t1  + t1 t2 + t1 t2  - t1 t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                     3       3       2  2     2          2  2        3
--R                 - t0 t1 - t0 t2 + t0 t1  - t0 t1 t2 + t0 t2  + t0 t1
--R               + 
--R                         2         3     4     3          3     4
--R                 t0 t1 t2  - 2t0 t2  - t1  + t1 t2 - t1 t2  + t2
--R            /
--R                   8      7        7        6  2      6           6  2      5  3
--R                 t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R               + 
--R                       5  2        5     2      5  3      4  4       4  3
--R                 - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R               + 
--R                     4  2  2      4  4      3  5       3  4         3  3  2
--R                 10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R               + 
--R                      3  5      2  6      2  5        2  4  2       2  3  3
--R                 - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R               + 
--R                     2  2  4      2     5      2  6         7         6
--R                 10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R               + 
--R                       5  2          4  3          3  4          2  5
--R                 8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2
--R               + 
--R                          6         7     8      7        6  2      5  3
--R                 6t0 t1 t2  - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2
--R               + 
--R                    4  4      3  5      2  6         7     8
--R                 5t1 t2  - 4t1 t2  + 3t1 t2  - 2t1 t2  + t2
--R          *
--R             xi
--R         + 
--R                    3       2  2      2  2        2              2        3
--R               - 2t0 t2 + t0 t1  + 2t0 t2  + t0 t1 t2 - 3t0 t1 t2  - t0 t2
--R             + 
--R                   4      3       2  2        3
--R               - t1  + 2t1 t2 - t1 t2  + t1 t2
--R          /
--R                 8      7        7        6  2      6           6  2      5  3
--R               t0  - 2t0 t1 - 2t0 t2 + 3t0 t1  + 6t0 t1 t2 + 3t0 t2  - 4t0 t1
--R             + 
--R                     5  2        5     2      5  3      4  4       4  3
--R               - 12t0 t1 t2 - 2t0 t1 t2  - 4t0 t2  + 5t0 t1  + 10t0 t1 t2
--R             + 
--R                   4  2  2      4  4      3  5       3  4         3  3  2
--R               10t0 t1 t2  + 5t0 t2  - 4t0 t1  - 10t0 t1 t2 - 10t0 t1 t2
--R             + 
--R                    3  5      2  6      2  5        2  4  2       2  3  3
--R               - 4t0 t2  + 3t0 t1  + 8t0 t1 t2 + 5t0 t1 t2  - 10t0 t1 t2
--R             + 
--R                   2  2  4      2     5      2  6         7         6
--R               10t0 t1 t2  - 2t0 t1 t2  + 3t0 t2  - 2t0 t1  - 4t0 t1 t2
--R             + 
--R                     5  2          4  3          3  4          2  5            6
--R               8t0 t1 t2  - 10t0 t1 t2  + 10t0 t1 t2  - 12t0 t1 t2  + 6t0 t1 t2
--R             + 
--R                       7     8      7        6  2      5  3      4  4      3  5
--R               - 2t0 t2  + t1  - 2t1 t2 + 3t1 t2  - 4t1 t2  + 5t1 t2  - 4t1 t2
--R             + 
--R                  2  6         7     8
--R               3t1 t2  - 2t1 t2  + t2
--R      *
--R           3
--R         C1
--R     + 
--R                 2
--R               t0  - t0 t1 - t0 t2 + t1 t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               3
--R             xi
--R         + 
--R                                   2
--R               - t0 t1 - t0 t2 + t1
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R               2
--R             xi
--R         + 
--R                           2
--R               - t0 t2 + t2
--R            /
--R                   4     3       3       2  2      2          2  2        3
--R                 t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R               + 
--R                         2              2        3     4     3       2  2
--R                 - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2
--R               + 
--R                        3     4
--R                 - t1 t2  + t2
--R          *
--R             xi
--R         + 
--R             - t0 t1 + t1 t2
--R          /
--R                 4     3       3       2  2      2          2  2        3
--R               t0  - t0 t1 - t0 t2 + t0 t1  + 2t0 t1 t2 + t0 t2  - t0 t1
--R             + 
--R                       2              2        3     4     3       2  2        3
--R               - 3t0 t1 t2 + 2t0 t1 t2  - t0 t2  + t1  - t1 t2 + t1 t2  - t1 t2
--R             + 
--R                 4
--R               t2
--R      *
--R           2
--R         C1
--R     + 
--R            3     2
--R       (- xi  - xi  - xi - 1)C1
--R     ]
--E 19 

--S 20 of 22
LX := UP('X, L) ;  X : LX := monomial(1, 1) 
 

   (20)  X
--R 
--R
--R   (20)  X
--E 20 

--S 21 of 22
g : LX := reduce(*, [X - rho for rho in r]) 
 

   (21)
      5
     X
   + 
               4       3         3         2  2       2            2  2
         - 10t0  + 10t0 t1 + 10t0 t2 - 10t0 t1  - 20t0 t1 t2 - 10t0 t2
       + 
                3          2               2          3       4       3
         10t0 t1  + 30t0 t1 t2 - 20t0 t1 t2  + 10t0 t2  - 10t1  + 10t1 t2
       + 
               2  2          3       4
         - 10t1 t2  + 10t1 t2  - 10t2
    *
        3
       X
   + 
               6       5         5         4  2       4            4  2
         - 20t0  + 30t0 t1 + 30t0 t2 - 25t0 t1  - 75t0 t1 t2 - 25t0 t2
       + 
             3  3        3  2         3  3       2  4       2  3         2  2  2
         25t0 t1  + 100t0 t1 t2 + 25t0 t2  - 25t0 t1  - 25t0 t1 t2 - 50t0 t1 t2
       + 
             2     3       2  4         5          3  2          2  3
         25t0 t1 t2  - 25t0 t2  + 5t0 t1  + 50t0 t1 t2  - 50t0 t1 t2
       + 
                   4         5      6       5         4  2       3  3       2  4
         25t0 t1 t2  + 5t0 t2  + 5t1  - 20t1 t2 + 25t1 t2  - 25t1 t2  + 25t1 t2
       + 
                  5      6
         - 20t1 t2  + 5t2
    *
        2
       X
   + 
               8       7         7         6  2       6            6  2
         - 15t0  + 30t0 t1 + 30t0 t2 - 20t0 t1  - 90t0 t1 t2 - 20t0 t2
       + 
             5  3        5  2         5     2       5  3       4  3
         10t0 t1  + 105t0 t1 t2 + 55t0 t1 t2  + 10t0 t2  - 50t0 t1 t2
       + 
                4  2  2       4     3       3  5       3  4          3  3  2
         - 100t0 t1 t2  + 25t0 t1 t2  - 15t0 t1  - 25t0 t1 t2 + 125t0 t1 t2
       + 
               3  2  3       3     4       3  5       2  6      2  5
         - 75t0 t1 t2  + 25t0 t1 t2  - 15t0 t2  + 30t0 t1  + 5t0 t1 t2
       + 
                2  3  3        2  2  4       2     5       2  6          7
         - 125t0 t1 t2  + 150t0 t1 t2  - 45t0 t1 t2  + 30t0 t2  - 20t0 t1
       + 
                  6            5  2          4  3          3  4          2  5
         - 15t0 t1 t2 + 80t0 t1 t2  - 25t0 t1 t2  - 50t0 t1 t2  - 20t0 t1 t2
       + 
                   6          7       8       7        6  2       5  3
         35t0 t1 t2  - 20t0 t2  + 10t1  - 20t1 t2 + 5t1 t2  + 10t1 t2
       + 
             3  5       2  6         7       8
         10t1 t2  - 20t1 t2  + 5t1 t2  + 10t2
    *
       X
   + 
          10       9         9        8  2       8           8  2      7  3
     - 4t0   + 10t0 t1 + 10t0 t2 - 5t0 t1  - 35t0 t1 t2 - 5t0 t2  - 5t0 t1
   + 
         7  2         7     2      7  3       6  4      6  3         6  2  2
     35t0 t1 t2 + 35t0 t1 t2  - 5t0 t2  + 15t0 t1  + 5t0 t1 t2 - 70t0 t1 t2
   + 
         6  4       5  5       5  4         5  3  2       5  2  3       5  5
     15t0 t2  - 28t0 t1  - 45t0 t1 t2 + 55t0 t1 t2  + 25t0 t1 t2  - 28t0 t2
   + 
         4  6       4  5          4  3  3       4  2  4       4     5       4  6
     35t0 t1  + 60t0 t1 t2 - 125t0 t1 t2  + 50t0 t1 t2  - 15t0 t1 t2  + 35t0 t2
   + 
           3  7       3  6         3  5  2        3  4  3       3  3  4
     - 30t0 t1  - 60t0 t1 t2 + 20t0 t1 t2  + 125t0 t1 t2  - 25t0 t1 t2
   + 
           3  2  5       3     6       3  7       2  8       2  7
     - 30t0 t1 t2  + 15t0 t1 t2  - 30t0 t2  + 20t0 t1  + 35t0 t1 t2
   + 
           2  6  2       2  5  3        2  4  4        2  3  5       2  2  6
     - 65t0 t1 t2  + 20t0 t1 t2  - 125t0 t1 t2  + 145t0 t1 t2  - 40t0 t1 t2
   + 
           2     7       2  8          9         8            7  2
     - 15t0 t1 t2  + 20t0 t2  - 10t0 t1  + 5t0 t1 t2 - 20t0 t1 t2
   + 
             6  3           5  4          4  5          3  6          2  7
     100t0 t1 t2  - 110t0 t1 t2  + 65t0 t1 t2  - 45t0 t1 t2  + 30t0 t1 t2
   + 
              9     10      9         8  2       7  3       6  4       5  5
     - 10t0 t2  + t1   + 5t1 t2 - 20t1 t2  + 25t1 t2  - 25t1 t2  + 27t1 t2
   + 
           4  6      3  7     10
     - 20t1 t2  + 5t1 t2  + t2
--R 
--R
--R   (21)
--R      5
--R     X
--R   + 
--R               4       3         3         2  2       2            2  2
--R         - 10t0  + 10t0 t1 + 10t0 t2 - 10t0 t1  - 20t0 t1 t2 - 10t0 t2
--R       + 
--R                3          2               2          3       4       3
--R         10t0 t1  + 30t0 t1 t2 - 20t0 t1 t2  + 10t0 t2  - 10t1  + 10t1 t2
--R       + 
--R               2  2          3       4
--R         - 10t1 t2  + 10t1 t2  - 10t2
--R    *
--R        3
--R       X
--R   + 
--R               6       5         5         4  2       4            4  2
--R         - 20t0  + 30t0 t1 + 30t0 t2 - 25t0 t1  - 75t0 t1 t2 - 25t0 t2
--R       + 
--R             3  3        3  2         3  3       2  4       2  3         2  2  2
--R         25t0 t1  + 100t0 t1 t2 + 25t0 t2  - 25t0 t1  - 25t0 t1 t2 - 50t0 t1 t2
--R       + 
--R             2     3       2  4         5          3  2          2  3
--R         25t0 t1 t2  - 25t0 t2  + 5t0 t1  + 50t0 t1 t2  - 50t0 t1 t2
--R       + 
--R                   4         5      6       5         4  2       3  3       2  4
--R         25t0 t1 t2  + 5t0 t2  + 5t1  - 20t1 t2 + 25t1 t2  - 25t1 t2  + 25t1 t2
--R       + 
--R                  5      6
--R         - 20t1 t2  + 5t2
--R    *
--R        2
--R       X
--R   + 
--R               8       7         7         6  2       6            6  2
--R         - 15t0  + 30t0 t1 + 30t0 t2 - 20t0 t1  - 90t0 t1 t2 - 20t0 t2
--R       + 
--R             5  3        5  2         5     2       5  3       4  3
--R         10t0 t1  + 105t0 t1 t2 + 55t0 t1 t2  + 10t0 t2  - 50t0 t1 t2
--R       + 
--R                4  2  2       4     3       3  5       3  4          3  3  2
--R         - 100t0 t1 t2  + 25t0 t1 t2  - 15t0 t1  - 25t0 t1 t2 + 125t0 t1 t2
--R       + 
--R               3  2  3       3     4       3  5       2  6      2  5
--R         - 75t0 t1 t2  + 25t0 t1 t2  - 15t0 t2  + 30t0 t1  + 5t0 t1 t2
--R       + 
--R                2  3  3        2  2  4       2     5       2  6          7
--R         - 125t0 t1 t2  + 150t0 t1 t2  - 45t0 t1 t2  + 30t0 t2  - 20t0 t1
--R       + 
--R                  6            5  2          4  3          3  4          2  5
--R         - 15t0 t1 t2 + 80t0 t1 t2  - 25t0 t1 t2  - 50t0 t1 t2  - 20t0 t1 t2
--R       + 
--R                   6          7       8       7        6  2       5  3
--R         35t0 t1 t2  - 20t0 t2  + 10t1  - 20t1 t2 + 5t1 t2  + 10t1 t2
--R       + 
--R             3  5       2  6         7       8
--R         10t1 t2  - 20t1 t2  + 5t1 t2  + 10t2
--R    *
--R       X
--R   + 
--R          10       9         9        8  2       8           8  2      7  3
--R     - 4t0   + 10t0 t1 + 10t0 t2 - 5t0 t1  - 35t0 t1 t2 - 5t0 t2  - 5t0 t1
--R   + 
--R         7  2         7     2      7  3       6  4      6  3         6  2  2
--R     35t0 t1 t2 + 35t0 t1 t2  - 5t0 t2  + 15t0 t1  + 5t0 t1 t2 - 70t0 t1 t2
--R   + 
--R         6  4       5  5       5  4         5  3  2       5  2  3       5  5
--R     15t0 t2  - 28t0 t1  - 45t0 t1 t2 + 55t0 t1 t2  + 25t0 t1 t2  - 28t0 t2
--R   + 
--R         4  6       4  5          4  3  3       4  2  4       4     5       4  6
--R     35t0 t1  + 60t0 t1 t2 - 125t0 t1 t2  + 50t0 t1 t2  - 15t0 t1 t2  + 35t0 t2
--R   + 
--R           3  7       3  6         3  5  2        3  4  3       3  3  4
--R     - 30t0 t1  - 60t0 t1 t2 + 20t0 t1 t2  + 125t0 t1 t2  - 25t0 t1 t2
--R   + 
--R           3  2  5       3     6       3  7       2  8       2  7
--R     - 30t0 t1 t2  + 15t0 t1 t2  - 30t0 t2  + 20t0 t1  + 35t0 t1 t2
--R   + 
--R           2  6  2       2  5  3        2  4  4        2  3  5       2  2  6
--R     - 65t0 t1 t2  + 20t0 t1 t2  - 125t0 t1 t2  + 145t0 t1 t2  - 40t0 t1 t2
--R   + 
--R           2     7       2  8          9         8            7  2
--R     - 15t0 t1 t2  + 20t0 t2  - 10t0 t1  + 5t0 t1 t2 - 20t0 t1 t2
--R   + 
--R             6  3           5  4          4  5          3  6          2  7
--R     100t0 t1 t2  - 110t0 t1 t2  + 65t0 t1 t2  - 45t0 t1 t2  + 30t0 t1 t2
--R   + 
--R              9     10      9         8  2       7  3       6  4       5  5
--R     - 10t0 t2  + t1   + 5t1 t2 - 20t1 t2  + 25t1 t2  - 25t1 t2  + 27t1 t2
--R   + 
--R           4  6      3  7     10
--R     - 20t1 t2  + 5t1 t2  + t2
--E 21

--S 22 of 22
f : UP('X, Zt) := map(retraction, g)
 
   Compiling function retraction with type SimpleAlgebraicExtension(
      SimpleAlgebraicExtension(Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
      UnivariatePolynomial(xi,Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
      xi**3+xi*xi+xi+1),UnivariatePolynomial(C1,
      SimpleAlgebraicExtension(Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
      UnivariatePolynomial(xi,Fraction 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
      xi**3+xi*xi+xi+1)),C1**5+(2*t0**9*t1+(-t0**9*t2)+(-4*t0**8*t1*t1)
      +(-9*t0**8*t1*t2)+3*t0**8*t2*t2+7*t0**7*t1**3+24*t0**7*t1*t1*t2+9
      *t0**7*t1*t2*t2+(-7*t0**7*t2**3)+(-11*t0**6*t1**4)+(-32*t0**6*t1
      **3*t2)+(-35*t0**6*t1*t1*t2*t2)+(-t0**6*t1*t2**3)+8*t0**6*t2**4+
      11*t0**5*t1**5+36*t0**5*t1**4*t2+65*t0**5*t1**3*t2*t2+(-6*t0**5*
      t1*t2**4)+(-6*t0**5*t2**5)+(-8*t0**4*t1**6)+(-41*t0**4*t1**5*t2)+
      (-45*t0**4*t1**4*t2*t2)+(-20*t0**4*t1**3*t2**3)+20*t0**4*t1*t1*t2
      **4+(-3*t0**4*t1*t2**5)+4*t0**4*t2**6+6*t0**3*t1**7+26*t0**3*t1**
      6*t2+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**3+(-40*t0**3*t1**3*
      t2**4)+11*t0**3*t1*t1*t2**5+(-4*t0**3*t1*t2**6)+(-2*t0**3*t2**7)+
      (-3*t0*t0*t1**8)+(-t0*t0*t1**7*t2)+(-31*t0*t0*t1**6*t2*t2)+13*t0*
      t0*t1**5*t2**3+(-20*t0*t0*t1**4*t2**4)+47*t0*t0*t1**3*t2**5+(-41*
      t0*t0*t1*t1*t2**6)+19*t0*t0*t1*t2**7+(-2*t0*t0*t2**8)+(-t0*t1**9)
      +3*t0*t1**8*t2+10*t0*t1**7*t2*t2+(-6*t0*t1**6*t2**3)+(-7*t0*t1**5
      *t2**4)+14*t0*t1**4*t2**5+(-22*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+
      (-16*t0*t1*t2**8)+3*t0*t2**9+t1**10+(-4*t1**9*t2)+5*t1**8*t2*t2+(
      -5*t1**7*t2**3)+4*t1**6*t2**4+(-4*t1**4*t2**6)+5*t1**3*t2**7+(-5*
      t1*t1*t2**8)+4*t1*t2**9+(-t2**10))*xi**3+(t0**9*t1+2*t0**9*t2+(-3
      *t0**8*t1*t1)+(-11*t0**8*t1*t2)+(-5*t0**8*t2*t2)+7*t0**7*t1**3+16
      *t0**7*t1*t1*t2+26*t0**7*t1*t2*t2+4*t0**7*t2**3+(-8*t0**6*t1**4)+
      (-23*t0**6*t1**3*t2)+(-40*t0**6*t1*t1*t2*t2)+(-24*t0**6*t1*t2**3)
      +(-4*t0**6*t2**4)+6*t0**5*t1**5+28*t0**5*t1**4*t2+41*t0**5*t1**3*
      t2*t2+32*t0**5*t1*t1*t2**3+8*t0**5*t1*t2**4+5*t0**5*t2**5+(-4*t0
      **4*t1**6)+(-23*t0**4*t1**5*t2)+(-10*t0**4*t1**4*t2*t2)+(-45*t0**
      4*t1**3*t2**3)+5*t0**4*t1*t1*t2**4+(-14*t0**4*t1*t2**5)+(-3*t0**4
      *t2**6)+2*t0**3*t1**7+(-t0**3*t1**6*t2)+15*t0**3*t1**5*t2*t2+5*t0
      **3*t1**4*t2**3+30*t0**3*t1**3*t2**4+(-13*t0**3*t1*t1*t2**5)+9*t0
      **3*t1*t2**6+2*t0*t0*t1**8+6*t0*t0*t1**7*t2+(-14*t0*t0*t1**6*t2*
      t2)+4*t0*t0*t1**5*t2**3+(-25*t0*t0*t1**4*t2**4)+27*t0*t0*t1**3*t2
      **5+(-19*t0*t0*t1*t1*t2**6)+6*t0*t0*t1*t2**7+(-t0*t0*t2**8)+(-3*
      t0*t1**9)+2*t0*t1**8*t2+11*t0*t1**6*t2**3+(-24*t0*t1**5*t2**4)+37
      *t0*t1**4*t2**5+(-38*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+(-9*t0*t1*
      t2**8)+t0*t2**9+t1**10+(-2*t1**9*t2)+t1**8*t2*t2+2*t1**7*t2**3+(-
      7*t1**6*t2**4)+11*t1**5*t2**5+(-12*t1**4*t2**6)+11*t1**3*t2**7+(-
      8*t1*t1*t2**8)+3*t1*t2**9)*xi*xi+(3*t0**9*t1+t0**9*t2+(-8*t0**8*
      t1*t1)+(-9*t0**8*t1*t2)+(-t0**8*t2*t2)+11*t0**7*t1**3+25*t0**7*t1
      *t1*t2+6*t0**7*t1*t2*t2+(-12*t0**6*t1**4)+(-38*t0**6*t1**3*t2)+(-
      19*t0**6*t1*t1*t2*t2)+9*t0**6*t1*t2**3+(-3*t0**6*t2**4)+11*t0**5*
      t1**5+37*t0**5*t1**4*t2+27*t0**5*t1**3*t2*t2+(-13*t0**5*t1*t1*t2
      **3)+(-14*t0**5*t1*t2**4)+5*t0**5*t2**5+(-7*t0**4*t1**6)+(-24*t0
      **4*t1**5*t2)+(-25*t0**4*t1**4*t2*t2)+30*t0**4*t1**3*t2**3+5*t0**
      4*t1*t1*t2**4+8*t0**4*t1*t2**5+(-4*t0**4*t2**6)+2*t0**3*t1**7+11*
      t0**3*t1**6*t2+4*t0**3*t1**5*t2*t2+5*t0**3*t1**4*t2**3+(-45*t0**3
      *t1**3*t2**4)+32*t0**3*t1*t1*t2**5+(-24*t0**3*t1*t2**6)+4*t0**3*
      t2**7+t0*t0*t1**8+(-14*t0*t0*t1**6*t2*t2)+15*t0*t0*t1**5*t2**3+(-
      10*t0*t0*t1**4*t2**4)+41*t0*t0*t1**3*t2**5+(-40*t0*t0*t1*t1*t2**6
      )+26*t0*t0*t1*t2**7+(-5*t0*t0*t2**8)+(-2*t0*t1**9)+2*t0*t1**8*t2+
      6*t0*t1**7*t2*t2+(-t0*t1**6*t2**3)+(-23*t0*t1**5*t2**4)+28*t0*t1
      **4*t2**5+(-23*t0*t1**3*t2**6)+16*t0*t1*t1*t2**7+(-11*t0*t1*t2**8
      )+2*t0*t2**9+t1**10+(-3*t1**9*t2)+2*t1**8*t2*t2+2*t1**7*t2**3+(-4
      *t1**6*t2**4)+6*t1**5*t2**5+(-8*t1**4*t2**6)+7*t1**3*t2**7+(-3*t1
      *t1*t2**8)+t1*t2**9)*xi+(-t0**10)+4*t0**9*t1+3*t0**9*t2+(-5*t0**8
      *t1*t1)+(-16*t0**8*t1*t2)+(-2*t0**8*t2*t2)+5*t0**7*t1**3+25*t0**7
      *t1*t1*t2+19*t0**7*t1*t2*t2+(-2*t0**7*t2**3)+(-4*t0**6*t1**4)+(-
      22*t0**6*t1**3*t2)+(-41*t0**6*t1*t1*t2*t2)+(-4*t0**6*t1*t2**3)+4*
      t0**6*t2**4+14*t0**5*t1**4*t2+47*t0**5*t1**3*t2*t2+11*t0**5*t1*t1
      *t2**3+(-3*t0**5*t1*t2**4)+(-6*t0**5*t2**5)+4*t0**4*t1**6+(-7*t0
      **4*t1**5*t2)+(-20*t0**4*t1**4*t2*t2)+(-40*t0**4*t1**3*t2**3)+20*
      t0**4*t1*t1*t2**4+(-6*t0**4*t1*t2**5)+8*t0**4*t2**6+(-5*t0**3*t1
      **7)+(-6*t0**3*t1**6*t2)+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**
      3+(-20*t0**3*t1**3*t2**4)+(-t0**3*t1*t2**6)+(-7*t0**3*t2**7)+5*t0
      *t0*t1**8+10*t0*t0*t1**7*t2+(-31*t0*t0*t1**6*t2*t2)+13*t0*t0*t1**
      5*t2**3+(-45*t0*t0*t1**4*t2**4)+65*t0*t0*t1**3*t2**5+(-35*t0*t0*
      t1*t1*t2**6)+9*t0*t0*t1*t2**7+3*t0*t0*t2**8+(-4*t0*t1**9)+3*t0*t1
      **8*t2+(-t0*t1**7*t2*t2)+26*t0*t1**6*t2**3+(-41*t0*t1**5*t2**4)+
      36*t0*t1**4*t2**5+(-32*t0*t1**3*t2**6)+24*t0*t1*t1*t2**7+(-9*t0*
      t1*t2**8)+(-t0*t2**9)+t1**10+(-t1**9*t2)+(-3*t1**8*t2*t2)+6*t1**7
      *t2**3+(-8*t1**6*t2**4)+11*t1**5*t2**5+(-11*t1**4*t2**6)+7*t1**3*
      t2**7+(-4*t1*t1*t2**8)+2*t1*t2**9) -> 
      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) 

   (22)
      5
     X
   + 
               4       3         3         2  2       2            2  2
         - 10t0  + 10t0 t1 + 10t0 t2 - 10t0 t1  - 20t0 t1 t2 - 10t0 t2
       + 
                3          2               2          3       4       3
         10t0 t1  + 30t0 t1 t2 - 20t0 t1 t2  + 10t0 t2  - 10t1  + 10t1 t2
       + 
               2  2          3       4
         - 10t1 t2  + 10t1 t2  - 10t2
    *
        3
       X
   + 
               6       5         5         4  2       4            4  2
         - 20t0  + 30t0 t1 + 30t0 t2 - 25t0 t1  - 75t0 t1 t2 - 25t0 t2
       + 
             3  3        3  2         3  3       2  4       2  3         2  2  2
         25t0 t1  + 100t0 t1 t2 + 25t0 t2  - 25t0 t1  - 25t0 t1 t2 - 50t0 t1 t2
       + 
             2     3       2  4         5          3  2          2  3
         25t0 t1 t2  - 25t0 t2  + 5t0 t1  + 50t0 t1 t2  - 50t0 t1 t2
       + 
                   4         5      6       5         4  2       3  3       2  4
         25t0 t1 t2  + 5t0 t2  + 5t1  - 20t1 t2 + 25t1 t2  - 25t1 t2  + 25t1 t2
       + 
                  5      6
         - 20t1 t2  + 5t2
    *
        2
       X
   + 
               8       7         7         6  2       6            6  2
         - 15t0  + 30t0 t1 + 30t0 t2 - 20t0 t1  - 90t0 t1 t2 - 20t0 t2
       + 
             5  3        5  2         5     2       5  3       4  3
         10t0 t1  + 105t0 t1 t2 + 55t0 t1 t2  + 10t0 t2  - 50t0 t1 t2
       + 
                4  2  2       4     3       3  5       3  4          3  3  2
         - 100t0 t1 t2  + 25t0 t1 t2  - 15t0 t1  - 25t0 t1 t2 + 125t0 t1 t2
       + 
               3  2  3       3     4       3  5       2  6      2  5
         - 75t0 t1 t2  + 25t0 t1 t2  - 15t0 t2  + 30t0 t1  + 5t0 t1 t2
       + 
                2  3  3        2  2  4       2     5       2  6          7
         - 125t0 t1 t2  + 150t0 t1 t2  - 45t0 t1 t2  + 30t0 t2  - 20t0 t1
       + 
                  6            5  2          4  3          3  4          2  5
         - 15t0 t1 t2 + 80t0 t1 t2  - 25t0 t1 t2  - 50t0 t1 t2  - 20t0 t1 t2
       + 
                   6          7       8       7        6  2       5  3
         35t0 t1 t2  - 20t0 t2  + 10t1  - 20t1 t2 + 5t1 t2  + 10t1 t2
       + 
             3  5       2  6         7       8
         10t1 t2  - 20t1 t2  + 5t1 t2  + 10t2
    *
       X
   + 
          10       9         9        8  2       8           8  2      7  3
     - 4t0   + 10t0 t1 + 10t0 t2 - 5t0 t1  - 35t0 t1 t2 - 5t0 t2  - 5t0 t1
   + 
         7  2         7     2      7  3       6  4      6  3         6  2  2
     35t0 t1 t2 + 35t0 t1 t2  - 5t0 t2  + 15t0 t1  + 5t0 t1 t2 - 70t0 t1 t2
   + 
         6  4       5  5       5  4         5  3  2       5  2  3       5  5
     15t0 t2  - 28t0 t1  - 45t0 t1 t2 + 55t0 t1 t2  + 25t0 t1 t2  - 28t0 t2
   + 
         4  6       4  5          4  3  3       4  2  4       4     5       4  6
     35t0 t1  + 60t0 t1 t2 - 125t0 t1 t2  + 50t0 t1 t2  - 15t0 t1 t2  + 35t0 t2
   + 
           3  7       3  6         3  5  2        3  4  3       3  3  4
     - 30t0 t1  - 60t0 t1 t2 + 20t0 t1 t2  + 125t0 t1 t2  - 25t0 t1 t2
   + 
           3  2  5       3     6       3  7       2  8       2  7
     - 30t0 t1 t2  + 15t0 t1 t2  - 30t0 t2  + 20t0 t1  + 35t0 t1 t2
   + 
           2  6  2       2  5  3        2  4  4        2  3  5       2  2  6
     - 65t0 t1 t2  + 20t0 t1 t2  - 125t0 t1 t2  + 145t0 t1 t2  - 40t0 t1 t2
   + 
           2     7       2  8          9         8            7  2
     - 15t0 t1 t2  + 20t0 t2  - 10t0 t1  + 5t0 t1 t2 - 20t0 t1 t2
   + 
             6  3           5  4          4  5          3  6          2  7
     100t0 t1 t2  - 110t0 t1 t2  + 65t0 t1 t2  - 45t0 t1 t2  + 30t0 t1 t2
   + 
              9     10      9         8  2       7  3       6  4       5  5
     - 10t0 t2  + t1   + 5t1 t2 - 20t1 t2  + 25t1 t2  - 25t1 t2  + 27t1 t2
   + 
           4  6      3  7     10
     - 20t1 t2  + 5t1 t2  + t2
--R 
--R   Compiling function retraction with type SimpleAlgebraicExtension(
--R      SimpleAlgebraicExtension(Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
--R      UnivariatePolynomial(xi,Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
--R      xi**3+xi*xi+xi+1),UnivariatePolynomial(C1,
--R      SimpleAlgebraicExtension(Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer),
--R      UnivariatePolynomial(xi,Fraction 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer)),xi**4+
--R      xi**3+xi*xi+xi+1)),C1**5+(2*t0**9*t1+(-t0**9*t2)+(-4*t0**8*t1*t1)
--R      +(-9*t0**8*t1*t2)+3*t0**8*t2*t2+7*t0**7*t1**3+24*t0**7*t1*t1*t2+9
--R      *t0**7*t1*t2*t2+(-7*t0**7*t2**3)+(-11*t0**6*t1**4)+(-32*t0**6*t1
--R      **3*t2)+(-35*t0**6*t1*t1*t2*t2)+(-t0**6*t1*t2**3)+8*t0**6*t2**4+
--R      11*t0**5*t1**5+36*t0**5*t1**4*t2+65*t0**5*t1**3*t2*t2+(-6*t0**5*
--R      t1*t2**4)+(-6*t0**5*t2**5)+(-8*t0**4*t1**6)+(-41*t0**4*t1**5*t2)+
--R      (-45*t0**4*t1**4*t2*t2)+(-20*t0**4*t1**3*t2**3)+20*t0**4*t1*t1*t2
--R      **4+(-3*t0**4*t1*t2**5)+4*t0**4*t2**6+6*t0**3*t1**7+26*t0**3*t1**
--R      6*t2+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**3+(-40*t0**3*t1**3*
--R      t2**4)+11*t0**3*t1*t1*t2**5+(-4*t0**3*t1*t2**6)+(-2*t0**3*t2**7)+
--R      (-3*t0*t0*t1**8)+(-t0*t0*t1**7*t2)+(-31*t0*t0*t1**6*t2*t2)+13*t0*
--R      t0*t1**5*t2**3+(-20*t0*t0*t1**4*t2**4)+47*t0*t0*t1**3*t2**5+(-41*
--R      t0*t0*t1*t1*t2**6)+19*t0*t0*t1*t2**7+(-2*t0*t0*t2**8)+(-t0*t1**9)
--R      +3*t0*t1**8*t2+10*t0*t1**7*t2*t2+(-6*t0*t1**6*t2**3)+(-7*t0*t1**5
--R      *t2**4)+14*t0*t1**4*t2**5+(-22*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+
--R      (-16*t0*t1*t2**8)+3*t0*t2**9+t1**10+(-4*t1**9*t2)+5*t1**8*t2*t2+(
--R      -5*t1**7*t2**3)+4*t1**6*t2**4+(-4*t1**4*t2**6)+5*t1**3*t2**7+(-5*
--R      t1*t1*t2**8)+4*t1*t2**9+(-t2**10))*xi**3+(t0**9*t1+2*t0**9*t2+(-3
--R      *t0**8*t1*t1)+(-11*t0**8*t1*t2)+(-5*t0**8*t2*t2)+7*t0**7*t1**3+16
--R      *t0**7*t1*t1*t2+26*t0**7*t1*t2*t2+4*t0**7*t2**3+(-8*t0**6*t1**4)+
--R      (-23*t0**6*t1**3*t2)+(-40*t0**6*t1*t1*t2*t2)+(-24*t0**6*t1*t2**3)
--R      +(-4*t0**6*t2**4)+6*t0**5*t1**5+28*t0**5*t1**4*t2+41*t0**5*t1**3*
--R      t2*t2+32*t0**5*t1*t1*t2**3+8*t0**5*t1*t2**4+5*t0**5*t2**5+(-4*t0
--R      **4*t1**6)+(-23*t0**4*t1**5*t2)+(-10*t0**4*t1**4*t2*t2)+(-45*t0**
--R      4*t1**3*t2**3)+5*t0**4*t1*t1*t2**4+(-14*t0**4*t1*t2**5)+(-3*t0**4
--R      *t2**6)+2*t0**3*t1**7+(-t0**3*t1**6*t2)+15*t0**3*t1**5*t2*t2+5*t0
--R      **3*t1**4*t2**3+30*t0**3*t1**3*t2**4+(-13*t0**3*t1*t1*t2**5)+9*t0
--R      **3*t1*t2**6+2*t0*t0*t1**8+6*t0*t0*t1**7*t2+(-14*t0*t0*t1**6*t2*
--R      t2)+4*t0*t0*t1**5*t2**3+(-25*t0*t0*t1**4*t2**4)+27*t0*t0*t1**3*t2
--R      **5+(-19*t0*t0*t1*t1*t2**6)+6*t0*t0*t1*t2**7+(-t0*t0*t2**8)+(-3*
--R      t0*t1**9)+2*t0*t1**8*t2+11*t0*t1**6*t2**3+(-24*t0*t1**5*t2**4)+37
--R      *t0*t1**4*t2**5+(-38*t0*t1**3*t2**6)+25*t0*t1*t1*t2**7+(-9*t0*t1*
--R      t2**8)+t0*t2**9+t1**10+(-2*t1**9*t2)+t1**8*t2*t2+2*t1**7*t2**3+(-
--R      7*t1**6*t2**4)+11*t1**5*t2**5+(-12*t1**4*t2**6)+11*t1**3*t2**7+(-
--R      8*t1*t1*t2**8)+3*t1*t2**9)*xi*xi+(3*t0**9*t1+t0**9*t2+(-8*t0**8*
--R      t1*t1)+(-9*t0**8*t1*t2)+(-t0**8*t2*t2)+11*t0**7*t1**3+25*t0**7*t1
--R      *t1*t2+6*t0**7*t1*t2*t2+(-12*t0**6*t1**4)+(-38*t0**6*t1**3*t2)+(-
--R      19*t0**6*t1*t1*t2*t2)+9*t0**6*t1*t2**3+(-3*t0**6*t2**4)+11*t0**5*
--R      t1**5+37*t0**5*t1**4*t2+27*t0**5*t1**3*t2*t2+(-13*t0**5*t1*t1*t2
--R      **3)+(-14*t0**5*t1*t2**4)+5*t0**5*t2**5+(-7*t0**4*t1**6)+(-24*t0
--R      **4*t1**5*t2)+(-25*t0**4*t1**4*t2*t2)+30*t0**4*t1**3*t2**3+5*t0**
--R      4*t1*t1*t2**4+8*t0**4*t1*t2**5+(-4*t0**4*t2**6)+2*t0**3*t1**7+11*
--R      t0**3*t1**6*t2+4*t0**3*t1**5*t2*t2+5*t0**3*t1**4*t2**3+(-45*t0**3
--R      *t1**3*t2**4)+32*t0**3*t1*t1*t2**5+(-24*t0**3*t1*t2**6)+4*t0**3*
--R      t2**7+t0*t0*t1**8+(-14*t0*t0*t1**6*t2*t2)+15*t0*t0*t1**5*t2**3+(-
--R      10*t0*t0*t1**4*t2**4)+41*t0*t0*t1**3*t2**5+(-40*t0*t0*t1*t1*t2**6
--R      )+26*t0*t0*t1*t2**7+(-5*t0*t0*t2**8)+(-2*t0*t1**9)+2*t0*t1**8*t2+
--R      6*t0*t1**7*t2*t2+(-t0*t1**6*t2**3)+(-23*t0*t1**5*t2**4)+28*t0*t1
--R      **4*t2**5+(-23*t0*t1**3*t2**6)+16*t0*t1*t1*t2**7+(-11*t0*t1*t2**8
--R      )+2*t0*t2**9+t1**10+(-3*t1**9*t2)+2*t1**8*t2*t2+2*t1**7*t2**3+(-4
--R      *t1**6*t2**4)+6*t1**5*t2**5+(-8*t1**4*t2**6)+7*t1**3*t2**7+(-3*t1
--R      *t1*t2**8)+t1*t2**9)*xi+(-t0**10)+4*t0**9*t1+3*t0**9*t2+(-5*t0**8
--R      *t1*t1)+(-16*t0**8*t1*t2)+(-2*t0**8*t2*t2)+5*t0**7*t1**3+25*t0**7
--R      *t1*t1*t2+19*t0**7*t1*t2*t2+(-2*t0**7*t2**3)+(-4*t0**6*t1**4)+(-
--R      22*t0**6*t1**3*t2)+(-41*t0**6*t1*t1*t2*t2)+(-4*t0**6*t1*t2**3)+4*
--R      t0**6*t2**4+14*t0**5*t1**4*t2+47*t0**5*t1**3*t2*t2+11*t0**5*t1*t1
--R      *t2**3+(-3*t0**5*t1*t2**4)+(-6*t0**5*t2**5)+4*t0**4*t1**6+(-7*t0
--R      **4*t1**5*t2)+(-20*t0**4*t1**4*t2*t2)+(-40*t0**4*t1**3*t2**3)+20*
--R      t0**4*t1*t1*t2**4+(-6*t0**4*t1*t2**5)+8*t0**4*t2**6+(-5*t0**3*t1
--R      **7)+(-6*t0**3*t1**6*t2)+13*t0**3*t1**5*t2*t2+45*t0**3*t1**4*t2**
--R      3+(-20*t0**3*t1**3*t2**4)+(-t0**3*t1*t2**6)+(-7*t0**3*t2**7)+5*t0
--R      *t0*t1**8+10*t0*t0*t1**7*t2+(-31*t0*t0*t1**6*t2*t2)+13*t0*t0*t1**
--R      5*t2**3+(-45*t0*t0*t1**4*t2**4)+65*t0*t0*t1**3*t2**5+(-35*t0*t0*
--R      t1*t1*t2**6)+9*t0*t0*t1*t2**7+3*t0*t0*t2**8+(-4*t0*t1**9)+3*t0*t1
--R      **8*t2+(-t0*t1**7*t2*t2)+26*t0*t1**6*t2**3+(-41*t0*t1**5*t2**4)+
--R      36*t0*t1**4*t2**5+(-32*t0*t1**3*t2**6)+24*t0*t1*t1*t2**7+(-9*t0*
--R      t1*t2**8)+(-t0*t2**9)+t1**10+(-t1**9*t2)+(-3*t1**8*t2*t2)+6*t1**7
--R      *t2**3+(-8*t1**6*t2**4)+11*t1**5*t2**5+(-11*t1**4*t2**6)+7*t1**3*
--R      t2**7+(-4*t1*t1*t2**8)+2*t1*t2**9) -> 
--R      DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) 
--R
--R   (22)
--R      5
--R     X
--R   + 
--R               4       3         3         2  2       2            2  2
--R         - 10t0  + 10t0 t1 + 10t0 t2 - 10t0 t1  - 20t0 t1 t2 - 10t0 t2
--R       + 
--R                3          2               2          3       4       3
--R         10t0 t1  + 30t0 t1 t2 - 20t0 t1 t2  + 10t0 t2  - 10t1  + 10t1 t2
--R       + 
--R               2  2          3       4
--R         - 10t1 t2  + 10t1 t2  - 10t2
--R    *
--R        3
--R       X
--R   + 
--R               6       5         5         4  2       4            4  2
--R         - 20t0  + 30t0 t1 + 30t0 t2 - 25t0 t1  - 75t0 t1 t2 - 25t0 t2
--R       + 
--R             3  3        3  2         3  3       2  4       2  3         2  2  2
--R         25t0 t1  + 100t0 t1 t2 + 25t0 t2  - 25t0 t1  - 25t0 t1 t2 - 50t0 t1 t2
--R       + 
--R             2     3       2  4         5          3  2          2  3
--R         25t0 t1 t2  - 25t0 t2  + 5t0 t1  + 50t0 t1 t2  - 50t0 t1 t2
--R       + 
--R                   4         5      6       5         4  2       3  3       2  4
--R         25t0 t1 t2  + 5t0 t2  + 5t1  - 20t1 t2 + 25t1 t2  - 25t1 t2  + 25t1 t2
--R       + 
--R                  5      6
--R         - 20t1 t2  + 5t2
--R    *
--R        2
--R       X
--R   + 
--R               8       7         7         6  2       6            6  2
--R         - 15t0  + 30t0 t1 + 30t0 t2 - 20t0 t1  - 90t0 t1 t2 - 20t0 t2
--R       + 
--R             5  3        5  2         5     2       5  3       4  3
--R         10t0 t1  + 105t0 t1 t2 + 55t0 t1 t2  + 10t0 t2  - 50t0 t1 t2
--R       + 
--R                4  2  2       4     3       3  5       3  4          3  3  2
--R         - 100t0 t1 t2  + 25t0 t1 t2  - 15t0 t1  - 25t0 t1 t2 + 125t0 t1 t2
--R       + 
--R               3  2  3       3     4       3  5       2  6      2  5
--R         - 75t0 t1 t2  + 25t0 t1 t2  - 15t0 t2  + 30t0 t1  + 5t0 t1 t2
--R       + 
--R                2  3  3        2  2  4       2     5       2  6          7
--R         - 125t0 t1 t2  + 150t0 t1 t2  - 45t0 t1 t2  + 30t0 t2  - 20t0 t1
--R       + 
--R                  6            5  2          4  3          3  4          2  5
--R         - 15t0 t1 t2 + 80t0 t1 t2  - 25t0 t1 t2  - 50t0 t1 t2  - 20t0 t1 t2
--R       + 
--R                   6          7       8       7        6  2       5  3
--R         35t0 t1 t2  - 20t0 t2  + 10t1  - 20t1 t2 + 5t1 t2  + 10t1 t2
--R       + 
--R             3  5       2  6         7       8
--R         10t1 t2  - 20t1 t2  + 5t1 t2  + 10t2
--R    *
--R       X
--R   + 
--R          10       9         9        8  2       8           8  2      7  3
--R     - 4t0   + 10t0 t1 + 10t0 t2 - 5t0 t1  - 35t0 t1 t2 - 5t0 t2  - 5t0 t1
--R   + 
--R         7  2         7     2      7  3       6  4      6  3         6  2  2
--R     35t0 t1 t2 + 35t0 t1 t2  - 5t0 t2  + 15t0 t1  + 5t0 t1 t2 - 70t0 t1 t2
--R   + 
--R         6  4       5  5       5  4         5  3  2       5  2  3       5  5
--R     15t0 t2  - 28t0 t1  - 45t0 t1 t2 + 55t0 t1 t2  + 25t0 t1 t2  - 28t0 t2
--R   + 
--R         4  6       4  5          4  3  3       4  2  4       4     5       4  6
--R     35t0 t1  + 60t0 t1 t2 - 125t0 t1 t2  + 50t0 t1 t2  - 15t0 t1 t2  + 35t0 t2
--R   + 
--R           3  7       3  6         3  5  2        3  4  3       3  3  4
--R     - 30t0 t1  - 60t0 t1 t2 + 20t0 t1 t2  + 125t0 t1 t2  - 25t0 t1 t2
--R   + 
--R           3  2  5       3     6       3  7       2  8       2  7
--R     - 30t0 t1 t2  + 15t0 t1 t2  - 30t0 t2  + 20t0 t1  + 35t0 t1 t2
--R   + 
--R           2  6  2       2  5  3        2  4  4        2  3  5       2  2  6
--R     - 65t0 t1 t2  + 20t0 t1 t2  - 125t0 t1 t2  + 145t0 t1 t2  - 40t0 t1 t2
--R   + 
--R           2     7       2  8          9         8            7  2
--R     - 15t0 t1 t2  + 20t0 t2  - 10t0 t1  + 5t0 t1 t2 - 20t0 t1 t2
--R   + 
--R             6  3           5  4          4  5          3  6          2  7
--R     100t0 t1 t2  - 110t0 t1 t2  + 65t0 t1 t2  - 45t0 t1 t2  + 30t0 t1 t2
--R   + 
--R              9     10      9         8  2       7  3       6  4       5  5
--R     - 10t0 t2  + t1   + 5t1 t2 - 20t1 t2  + 25t1 t2  - 25t1 t2  + 27t1 t2
--R   + 
--R           4  6      3  7     10
--R     - 20t1 t2  + 5t1 t2  + t2
--E 22
)spool 
 
Starts dribbling to MappingPackage2.output (2010/3/27, 18:46:4).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 26
power(q: FRAC INT, n: INT): FRAC INT == q**n
 
   Function declaration power : (Fraction Integer,Integer) -> Fraction 
      Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration power : (Fraction Integer,Integer) -> Fraction 
--R      Integer has been added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 26
power(2,3)
 
   Compiling function power with type (Fraction Integer,Integer) -> 
      Fraction Integer 

   (2)  8
                                                       Type: Fraction Integer
--R 
--R   Compiling function power with type (Fraction Integer,Integer) -> 
--R      Fraction Integer 
--R
--R   (2)  8
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 26
rewop := twist power
 

   (3)  theMap(MAPPKG3;twist;MM;5!0)
                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--I   (3)  theMap(MAPPKG3;twist;MM;5!0)
--R                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--E 3

--S 4 of 26
rewop(3, 2)
 

   (4)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (4)  8
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 26
square: FRAC INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 26
square:= curryRight(power, 2)
 

   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--I   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 6

--S 7 of 26
square 4
 

   (7)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (7)  16
--R                                                       Type: Fraction Integer
--E 7

--S 8 of 26
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
 

   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--I   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
--R              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--E 8

--S 9 of 26
squirrel(1/2, 1/3)
 

        1
   (9)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (9)  -
--R        4
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 26
sixteen := curry(square, 4/1)
 

   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                               Type: (() -> Fraction Integer)
--R 
--R
--I   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                               Type: (() -> Fraction Integer)
--E 10

--S 11 of 26
sixteen()
 

   (11)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  16
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 26
square2:=square*square
 

   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--I   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 12

--S 13 of 26
square2 3
 

   (13)  81
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  81
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 26
sc(x: FRAC INT): FRAC INT == x + 1
 
   Function declaration sc : Fraction Integer -> Fraction Integer has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration sc : Fraction Integer -> Fraction Integer has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 14

--S 15 of 26
incfns := [sc**i for i in 0..10]
 
   Compiling function sc with type Fraction Integer -> Fraction Integer
      

   (15)
   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0)]
                            Type: List (Fraction Integer -> Fraction Integer)
--R 
--R   Compiling function sc with type Fraction Integer -> Fraction Integer
--R      
--R
--R   (15)
--I   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0)]
--R                            Type: List (Fraction Integer -> Fraction Integer)
--E 15

--S 16 of 26
[f 4 for f in incfns]
 

   (16)  [4,5,6,7,8,9,10,11,12,13,14]
                                                  Type: List Fraction Integer
--R 
--R
--R   (16)  [4,5,6,7,8,9,10,11,12,13,14]
--R                                                  Type: List Fraction Integer
--E 16

--S 17 of 26
times(n:NNI, i:INT):INT == n*i
 
   Function declaration times : (NonNegativeInteger,Integer) -> Integer
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration times : (NonNegativeInteger,Integer) -> Integer
--R      has been added to workspace.
--R                                                                   Type: Void
--E 17

--S 18 of 26
r := recur(times)
 
   Compiling function times with type (NonNegativeInteger,Integer) -> 
      Integer 

   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
                              Type: ((NonNegativeInteger,Integer) -> Integer)
--R 
--R   Compiling function times with type (NonNegativeInteger,Integer) -> 
--R      Integer 
--R
--I   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
--R                              Type: ((NonNegativeInteger,Integer) -> Integer)
--E 18

--S 19 of 26
fact := curryRight(r, 1)
 

   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                        Type: (NonNegativeInteger -> Integer)
--R 
--R
--I   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                        Type: (NonNegativeInteger -> Integer)
--E 19

--S 20 of 26
fact 4
 

   (20)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  24
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 26
mto2ton(m, n) ==
  raiser := square^n
  raiser m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 26
mto2ton(3, 3)
 
   Compiling function mto2ton with type (PositiveInteger,
      PositiveInteger) -> Fraction Integer 

   (22)  6561
                                                       Type: Fraction Integer
--R 
--R   Compiling function mto2ton with type (PositiveInteger,
--R      PositiveInteger) -> Fraction Integer 
--R
--R   (22)  6561
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 26
shiftfib(r: List INT) : INT ==
  t := r.1
  r.1 := r.2
  r.2 := r.2 + t
  t
 
   Function declaration shiftfib : List Integer -> Integer has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration shiftfib : List Integer -> Integer has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 23

--S 24 of 26
fibinit: List INT := [0, 1]
 

   (24)  [0,1]
                                                           Type: List Integer
--R 
--R
--R   (24)  [0,1]
--R                                                           Type: List Integer
--E 24

--S 25 of 26
fibs := curry(shiftfib, fibinit)
 
   Compiling function shiftfib with type List Integer -> Integer 

   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                                        Type: (() -> Integer)
--R 
--R   Compiling function shiftfib with type List Integer -> Integer 
--R
--I   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                                        Type: (() -> Integer)
--E 25

--S 26 of 26
[fibs() for i in 0..30]
 

   (26)
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
    317811, 514229, 832040]
                                                           Type: List Integer
--R 
--R
--R   (26)
--R   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
--R    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
--R    317811, 514229, 832040]
--R                                                           Type: List Integer
--E 26
)spool
 
Starts dribbling to roots.output (2010/3/27, 18:36:57).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 7
lr:=rootsOf(x**4+1,x)
 

   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
                                                Type: List Expression Integer
--R 
--R
--R   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
--R                                                Type: List Expression Integer
--E 1

--S 2 of 7
definingPolynomial %x0
 

           4
   (2)  %x0  + 1
                                                     Type: Expression Integer
--R 
--R
--R           4
--R   (2)  %x0  + 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 7
definingPolynomial %x1
 

           2
   (3)  %x1  + 1
                                                     Type: Expression Integer
--R 
--R
--R           2
--R   (3)  %x1  + 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 7
lr.1 * lr.2 * lr.3
 

             3
   (4)  - %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R             3
--R   (4)  - %x0 %x1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 7
%**4
 

   (5)  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (5)  - 1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 7
lr.1 + lr.2 + lr.3
 

   (6)  %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R   (6)  %x0 %x1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 7
%**4
 

   (7)  - 1
                                                     Type: Expression Integer
--R 
--R
--R   (7)  - 1
--R                                                     Type: Expression Integer
--E 7
)spool 
 
Starts dribbling to StringTable.output (2010/3/27, 18:46:36).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
t: StringTable(Integer) := table()
 

   (1)  table()
                                                    Type: StringTable Integer
--R 
--R
--R   (1)  table()
--R                                                    Type: StringTable Integer
--E 1

--S 2 of 3
for s in split("My name is Ian Watt.",char " ")
  repeat
    t.s := #s
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 3
for key in keys t repeat output [key, t.key]
 
   ["Watt.",5]
   ["Ian",3]
   ["is",2]
   ["name",4]
   ["My",2]
                                                                   Type: Void
--R 
--R   ["Watt.",5]
--R   ["Ian",3]
--R   ["is",2]
--R   ["name",4]
--R   ["My",2]
--R                                                                   Type: Void
--E 3
)spool
 
Starts dribbling to complexfactor.output (2010/3/27, 18:24:35).
)set message test on
 
)set message auto off
 
)clear all
 
)set message bottomup on
 
 
--S 1 of 4
t1:=-7*x^6 + 10*x^4 + 24*x^3 - 14*x^2 - 27*x - 42 + _
     %i*(3*x^6 - 9*x^5 + 30*x^4 + 15*x^3 + 17*x*2 - 33*x -7)
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
   -> no appropriate ** found in Variable x 
   -> no appropriate ** found in PositiveInteger 
   -> no appropriate ** found in Symbol 
   -> no appropriate ** found in Integer 
   -> no appropriate ** found in Polynomial Integer 
   -> no appropriate ** found in Variable x 
   -> no appropriate ** found in PositiveInteger 
   -> no appropriate ** found in Symbol 
   -> no appropriate ** found in Integer 
cost=50000 for **: (Polynomial Integer,NonNegativeInteger) -> Polynomial Integer
cost=50000 for **: (Polynomial Integer,PositiveInteger) -> Polynomial Integer
   -> no appropriate ^ found in Variable x 
   -> no appropriate ^ found in PositiveInteger 
   -> no appropriate ^ found in Symbol 
   -> no appropriate ^ found in Integer 
   -> no appropriate ^ found in Polynomial Integer 
   -> no appropriate ^ found in Variable x 
   -> no appropriate ^ found in PositiveInteger 
   -> no appropriate ^ found in Symbol 
   -> no appropriate ^ found in Integer 
cost=50000 for ^: (Polynomial Integer,NonNegativeInteger) -> Polynomial Integer
cost=50000 for ^: (Polynomial Integer,PositiveInteger) -> Polynomial Integer
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: POLY INT 
 
 [1]  signature:   POLY INT -> POLY INT
      implemented: slot $$ from POLY INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for +
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for +
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for *
      Arguments: (PI,VARIABLE x) 
   -> no appropriate * found in PositiveInteger 
   -> no appropriate * found in Variable x 
   -> no appropriate * found in Integer 
   -> no appropriate * found in Symbol 
   -> no appropriate * found in Polynomial Integer 
   -> no appropriate * found in PositiveInteger 
   -> no appropriate * found in Variable x 
   -> no appropriate * found in Integer 
   -> no appropriate * found in Symbol 
cost=52300 for *: (Integer,Polynomial Integer) -> Polynomial Integer
cost=52300 for *: (Integer,Polynomial Integer) -> Polynomial Integer
cost=52300 for *: (NonNegativeInteger,Polynomial Integer) -> Polynomial Integer
cost=92300 for *: (Polynomial Integer,Polynomial Integer) -> Polynomial Integer
cost=52300 for *: (PositiveInteger,Polynomial Integer) -> Polynomial Integer
 
 [1]  signature:   (INT,POLY INT) -> POLY INT
      implemented: slot $(Integer)$ from POLY INT
 [2]  signature:   (INT,POLY INT) -> POLY INT
      implemented: slot $(Integer)$ from POLY INT
 [3]  signature:   (NNI,POLY INT) -> POLY INT
      implemented: slot $(NonNegativeInteger)$ from POLY INT
 [4]  signature:   (PI,POLY INT) -> POLY INT
      implemented: slot $(PositiveInteger)$ from POLY INT
 [5]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: (POLY INT,PI) 
   -> no appropriate - found in Polynomial Integer 
   -> no appropriate - found in PositiveInteger 
   -> no appropriate - found in Integer 
   -> no appropriate - found in PositiveInteger 
   -> no appropriate - found in Integer 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for complex
      Arguments: (NNI,PI) 
   -> no appropriate complex found in NonNegativeInteger 
   -> no appropriate complex found in PositiveInteger 
   -> no appropriate complex found in Integer 
   -> no appropriate complex found in NonNegativeInteger 
   -> no appropriate complex found in PositiveInteger 
   -> no appropriate complex found in Integer 

 Modemaps from Associated Packages 
   no modemaps

 Remaining General Modemaps 
   [1] (D1,D1) -> D from D if D has COMPCAT D1 and D1 has COMRING
 
 [1]  signature:   (INT,INT) -> COMPLEX INT
      implemented: slot $(Integer)(Integer) from COMPLEX INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for +
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for ^
      Arguments: (VARIABLE x,PI) 
      Default target type: Polynomial Integer 
 
 [1]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [2]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 [3]  signature:   (POLY INT,NNI) -> POLY INT
      implemented: slot $$(NonNegativeInteger) from POLY INT
 [4]  signature:   (POLY INT,PI) -> POLY INT
      implemented: slot $$(PositiveInteger) from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for +
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for *
      Arguments: (PI,VARIABLE x) 
 
 [1]  signature:   (INT,POLY INT) -> POLY INT
      implemented: slot $(Integer)$ from POLY INT
 [2]  signature:   (INT,POLY INT) -> POLY INT
      implemented: slot $(Integer)$ from POLY INT
 [3]  signature:   (NNI,POLY INT) -> POLY INT
      implemented: slot $(NonNegativeInteger)$ from POLY INT
 [4]  signature:   (PI,POLY INT) -> POLY INT
      implemented: slot $(PositiveInteger)$ from POLY INT
 [5]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for *
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for +
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for *
      Arguments: (PI,VARIABLE x) 
 
 [1]  signature:   (INT,POLY INT) -> POLY INT
      implemented: slot $(Integer)$ from POLY INT
 [2]  signature:   (INT,POLY INT) -> POLY INT
      implemented: slot $(Integer)$ from POLY INT
 [3]  signature:   (NNI,POLY INT) -> POLY INT
      implemented: slot $(NonNegativeInteger)$ from POLY INT
 [4]  signature:   (PI,POLY INT) -> POLY INT
      implemented: slot $(PositiveInteger)$ from POLY INT
 [5]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: (POLY INT,POLY INT) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for -
      Arguments: (POLY INT,PI) 
 
 [1]  signature:   (POLY INT,POLY INT) -> POLY INT
      implemented: slot $$$ from POLY INT
 

 Function Selection for *
      Arguments: (COMPLEX INT,POLY INT) 
   -> no appropriate * found in Complex Integer 
   -> no appropriate * found in Polynomial Integer 
   -> no appropriate * found in Polynomial Complex Integer 
   -> no appropriate * found in Complex Integer 
   -> no appropriate * found in Polynomial Integer 
cost=43300 for *: (Complex Integer,Polynomial Complex Integer) -> Polynomial Complex Integer
cost=83300 for *: (Polynomial Complex Integer,Polynomial Complex Integer) -> Polynomial Complex Integer
 
 [1]  signature:   (COMPLEX INT,POLY COMPLEX INT) -> POLY COMPLEX INT
      implemented: slot $(Complex (Integer))$ from POLY COMPLEX INT
 [2]  signature:   (POLY COMPLEX INT,POLY COMPLEX INT) -> POLY COMPLEX INT
      implemented: slot $$$ from POLY COMPLEX INT
 

 Function Selection for map by coercion facility (map) 
      Arguments: ((INT -> COMPLEX INT),POLY INT) 
      Target type: POLY COMPLEX INT 
   -> no appropriate map found in Polynomial Integer 
   -> no appropriate map found in Polynomial Complex Integer 
   -> no appropriate map found in Complex Integer 
   -> no appropriate map found in Integer 
   -> no appropriate map found in Complex Integer 

 Modemaps from Associated Packages 
   [1] ((D4 -> D5),D3) -> D1
            from UnivariatePolynomialCategoryFunctions2(D4,D3,D5,D1)
            if D4 has RING and D5 has RING and D1 has UPOLYC D5 and D3 
            has UPOLYC D4
   [2] ((D5 -> D7),UnivariatePolynomial(D4,D5)) -> UnivariatePolynomial
            (D6,D7)
            from UnivariatePolynomialFunctions2(D4,D5,D6,D7)
            if D4: SYMBOL and D5 has RING and D7 has RING and D6: 
            SYMBOL
   [3] ((D4 -> D5),SparseUnivariatePolynomial D4) -> 
            SparseUnivariatePolynomial D5
            from SparseUnivariatePolynomialFunctions2(D4,D5)
            if D4 has RING and D5 has RING
   [4] ((D4 -> D5),Polynomial D4) -> Polynomial D5
            from PolynomialFunctions2(D4,D5)
            if D4 has RING and D5 has RING
 
 [1]  signature:   ((INT -> COMPLEX INT),POLY INT) -> POLY COMPLEX INT
      implemented: slot (Polynomial (Complex (Integer)))(Mapping (Complex (Integer)) (Integer))(Polynomial (Integer)) from POLY2(INT,COMPLEX INT)
 

 Function Selection for +
      Arguments: (POLY INT,POLY COMPLEX INT) 
   -> no appropriate + found in Polynomial Integer 
   -> no appropriate + found in Polynomial Complex Integer 
   -> no appropriate + found in Polynomial Integer 
 
 [1]  signature:   (POLY COMPLEX INT,POLY COMPLEX INT) -> POLY COMPLEX INT
      implemented: slot $$$ from POLY COMPLEX INT
 

 Function Selection for map by coercion facility (map) 
      Arguments: ((INT -> COMPLEX INT),POLY INT) 
      Target type: POLY COMPLEX INT 
 
 [1]  signature:   ((INT -> COMPLEX INT),POLY INT) -> POLY COMPLEX INT
      implemented: slot (Polynomial (Complex (Integer)))(Mapping (Complex (Integer)) (Integer))(Polynomial (Integer)) from POLY2(INT,COMPLEX INT)
 

   (1)
                 6        5               4               3      2
     (- 7 + 3%i)x  - 9%i x  + (10 + 30%i)x  + (24 + 15%i)x  - 14x
   + 
     (- 27 + %i)x - 42 - 7%i
                                             Type: Polynomial Complex Integer
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R   -> no appropriate ** found in Variable x 
--R   -> no appropriate ** found in PositiveInteger 
--R   -> no appropriate ** found in Symbol 
--R   -> no appropriate ** found in Integer 
--R   -> no appropriate ** found in Polynomial Integer 
--R   -> no appropriate ** found in Variable x 
--R   -> no appropriate ** found in PositiveInteger 
--R   -> no appropriate ** found in Symbol 
--R   -> no appropriate ** found in Integer 
--Rcost=50000 for **: (Polynomial Integer,NonNegativeInteger) -> Polynomial Integer
--Rcost=50000 for **: (Polynomial Integer,PositiveInteger) -> Polynomial Integer
--R   -> no appropriate ^ found in Variable x 
--R   -> no appropriate ^ found in PositiveInteger 
--R   -> no appropriate ^ found in Symbol 
--R   -> no appropriate ^ found in Integer 
--R   -> no appropriate ^ found in Polynomial Integer 
--R   -> no appropriate ^ found in Variable x 
--R   -> no appropriate ^ found in PositiveInteger 
--R   -> no appropriate ^ found in Symbol 
--R   -> no appropriate ^ found in Integer 
--Rcost=50000 for ^: (Polynomial Integer,NonNegativeInteger) -> Polynomial Integer
--Rcost=50000 for ^: (Polynomial Integer,PositiveInteger) -> Polynomial Integer
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: POLY INT 
--R 
--R [1]  signature:   POLY INT -> POLY INT
--R      implemented: slot $$ from POLY INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for +
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for +
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (PI,VARIABLE x) 
--R   -> no appropriate * found in PositiveInteger 
--R   -> no appropriate * found in Variable x 
--R   -> no appropriate * found in Integer 
--R   -> no appropriate * found in Symbol 
--R   -> no appropriate * found in Polynomial Integer 
--R   -> no appropriate * found in PositiveInteger 
--R   -> no appropriate * found in Variable x 
--R   -> no appropriate * found in Integer 
--R   -> no appropriate * found in Symbol 
--Rcost=52300 for *: (Integer,Polynomial Integer) -> Polynomial Integer
--Rcost=52300 for *: (Integer,Polynomial Integer) -> Polynomial Integer
--Rcost=52300 for *: (NonNegativeInteger,Polynomial Integer) -> Polynomial Integer
--Rcost=92300 for *: (Polynomial Integer,Polynomial Integer) -> Polynomial Integer
--Rcost=52300 for *: (PositiveInteger,Polynomial Integer) -> Polynomial Integer
--R 
--R [1]  signature:   (INT,POLY INT) -> POLY INT
--R      implemented: slot $(Integer)$ from POLY INT
--R [2]  signature:   (INT,POLY INT) -> POLY INT
--R      implemented: slot $(Integer)$ from POLY INT
--R [3]  signature:   (NNI,POLY INT) -> POLY INT
--R      implemented: slot $(NonNegativeInteger)$ from POLY INT
--R [4]  signature:   (PI,POLY INT) -> POLY INT
--R      implemented: slot $(PositiveInteger)$ from POLY INT
--R [5]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: (POLY INT,PI) 
--R   -> no appropriate - found in Polynomial Integer 
--R   -> no appropriate - found in PositiveInteger 
--R   -> no appropriate - found in Integer 
--R   -> no appropriate - found in PositiveInteger 
--R   -> no appropriate - found in Integer 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for complex
--R      Arguments: (NNI,PI) 
--R   -> no appropriate complex found in NonNegativeInteger 
--R   -> no appropriate complex found in PositiveInteger 
--R   -> no appropriate complex found in Integer 
--R   -> no appropriate complex found in NonNegativeInteger 
--R   -> no appropriate complex found in PositiveInteger 
--R   -> no appropriate complex found in Integer 
--R
--R Modemaps from Associated Packages 
--R   no modemaps
--R
--R Remaining General Modemaps 
--R   [1] (D1,D1) -> D from D if D has COMPCAT D1 and D1 has COMRING
--R 
--R [1]  signature:   (INT,INT) -> COMPLEX INT
--R      implemented: slot $(Integer)(Integer) from COMPLEX INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for +
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for ^
--R      Arguments: (VARIABLE x,PI) 
--R      Default target type: Polynomial Integer 
--R 
--R [1]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [2]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R [3]  signature:   (POLY INT,NNI) -> POLY INT
--R      implemented: slot $$(NonNegativeInteger) from POLY INT
--R [4]  signature:   (POLY INT,PI) -> POLY INT
--R      implemented: slot $$(PositiveInteger) from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for +
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (PI,VARIABLE x) 
--R 
--R [1]  signature:   (INT,POLY INT) -> POLY INT
--R      implemented: slot $(Integer)$ from POLY INT
--R [2]  signature:   (INT,POLY INT) -> POLY INT
--R      implemented: slot $(Integer)$ from POLY INT
--R [3]  signature:   (NNI,POLY INT) -> POLY INT
--R      implemented: slot $(NonNegativeInteger)$ from POLY INT
--R [4]  signature:   (PI,POLY INT) -> POLY INT
--R      implemented: slot $(PositiveInteger)$ from POLY INT
--R [5]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for +
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (PI,VARIABLE x) 
--R 
--R [1]  signature:   (INT,POLY INT) -> POLY INT
--R      implemented: slot $(Integer)$ from POLY INT
--R [2]  signature:   (INT,POLY INT) -> POLY INT
--R      implemented: slot $(Integer)$ from POLY INT
--R [3]  signature:   (NNI,POLY INT) -> POLY INT
--R      implemented: slot $(NonNegativeInteger)$ from POLY INT
--R [4]  signature:   (PI,POLY INT) -> POLY INT
--R      implemented: slot $(PositiveInteger)$ from POLY INT
--R [5]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: (POLY INT,POLY INT) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for -
--R      Arguments: (POLY INT,PI) 
--R 
--R [1]  signature:   (POLY INT,POLY INT) -> POLY INT
--R      implemented: slot $$$ from POLY INT
--R 
--R
--R Function Selection for *
--R      Arguments: (COMPLEX INT,POLY INT) 
--R   -> no appropriate * found in Complex Integer 
--R   -> no appropriate * found in Polynomial Integer 
--R   -> no appropriate * found in Polynomial Complex Integer 
--R   -> no appropriate * found in Complex Integer 
--R   -> no appropriate * found in Polynomial Integer 
--Rcost=43300 for *: (Complex Integer,Polynomial Complex Integer) -> Polynomial Complex Integer
--Rcost=83300 for *: (Polynomial Complex Integer,Polynomial Complex Integer) -> Polynomial Complex Integer
--R 
--R [1]  signature:   (COMPLEX INT,POLY COMPLEX INT) -> POLY COMPLEX INT
--R      implemented: slot $(Complex (Integer))$ from POLY COMPLEX INT
--R [2]  signature:   (POLY COMPLEX INT,POLY COMPLEX INT) -> POLY COMPLEX INT
--R      implemented: slot $$$ from POLY COMPLEX INT
--R 
--R
--R Function Selection for map by coercion facility (map) 
--R      Arguments: ((INT -> COMPLEX INT),POLY INT) 
--R      Target type: POLY COMPLEX INT 
--R   -> no appropriate map found in Polynomial Integer 
--R   -> no appropriate map found in Polynomial Complex Integer 
--R   -> no appropriate map found in Complex Integer 
--R   -> no appropriate map found in Integer 
--R   -> no appropriate map found in Complex Integer 
--R
--R Modemaps from Associated Packages 
--R   [1] ((D4 -> D5),D3) -> D1
--R            from UnivariatePolynomialCategoryFunctions2(D4,D3,D5,D1)
--R            if D4 has RING and D5 has RING and D1 has UPOLYC D5 and D3 
--R            has UPOLYC D4
--R   [2] ((D5 -> D7),UnivariatePolynomial(D4,D5)) -> UnivariatePolynomial
--R            (D6,D7)
--R            from UnivariatePolynomialFunctions2(D4,D5,D6,D7)
--R            if D4: SYMBOL and D5 has RING and D7 has RING and D6: 
--R            SYMBOL
--R   [3] ((D4 -> D5),SparseUnivariatePolynomial D4) -> 
--R            SparseUnivariatePolynomial D5
--R            from SparseUnivariatePolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [4] ((D4 -> D5),Polynomial D4) -> Polynomial D5
--R            from PolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R 
--R [1]  signature:   ((INT -> COMPLEX INT),POLY INT) -> POLY COMPLEX INT
--R      implemented: slot (Polynomial (Complex (Integer)))(Mapping (Complex (Integer)) (Integer))(Polynomial (Integer)) from POLY2(INT,COMPLEX INT)
--R 
--R
--R Function Selection for +
--R      Arguments: (POLY INT,POLY COMPLEX INT) 
--R   -> no appropriate + found in Polynomial Integer 
--R   -> no appropriate + found in Polynomial Complex Integer 
--R   -> no appropriate + found in Polynomial Integer 
--R 
--R [1]  signature:   (POLY COMPLEX INT,POLY COMPLEX INT) -> POLY COMPLEX INT
--R      implemented: slot $$$ from POLY COMPLEX INT
--R 
--R
--R Function Selection for map by coercion facility (map) 
--R      Arguments: ((INT -> COMPLEX INT),POLY INT) 
--R      Target type: POLY COMPLEX INT 
--R 
--R [1]  signature:   ((INT -> COMPLEX INT),POLY INT) -> POLY COMPLEX INT
--R      implemented: slot (Polynomial (Complex (Integer)))(Mapping (Complex (Integer)) (Integer))(Polynomial (Integer)) from POLY2(INT,COMPLEX INT)
--R 
--R
--R   (1)
--R                 6        5               4               3      2
--R     (- 7 + 3%i)x  - 9%i x  + (10 + 30%i)x  + (24 + 15%i)x  - 14x
--R   + 
--R     (- 27 + %i)x - 42 - 7%i
--R                                             Type: Polynomial Complex Integer
--E 1

--S 2 of 4
t2:=factor t1
 

 Function Selection for factor
      Arguments: POLY COMPLEX INT 
   -> no appropriate factor found in Polynomial Complex Integer 
   -> no appropriate factor found in Polynomial Complex Integer 

 Modemaps from Associated Packages 
   no modemaps

 Remaining General Modemaps 
   [1] D -> Factored D from D if D has UFD
   [2] D2 -> Factored D2 from SAERationalFunctionAlgFactor(D3,D4,D2)
            if D3 has UPOLYC FRAC POLY INT and D4 has Join(Field,
            CharacteristicZero,MonogenicAlgebra(Fraction Polynomial 
            Integer,D3)) and D2 has UPOLYC D4
   [3] D2 -> Factored D2 from SimpleAlgebraicExtensionAlgFactor(D3,D4,
            D2)
            if D3 has UPOLYC FRAC INT and D4 has Join(Field,
            CharacteristicZero,MonogenicAlgebra(Fraction Integer,D3)) 
            and D2 has UPOLYC D4
   [4] D2 -> Factored D2 from RationalFunctionFactor D2
            if D2 has UPOLYC FRAC POLY INT
   [5] SparseUnivariatePolynomial D6 -> Factored 
            SparseUnivariatePolynomial D6
            from MultivariateFactorize(D3,D4,D5,D6)
            if D3 has ORDSET and D4 has OAMONS and D5 has Join(
            EuclideanDomain,CharacteristicZero) and D6 has POLYCAT(D5,
            D4,D3)
   [6] D2 -> Factored D2 from MultivariateFactorize(D3,D4,D5,D2)
            if D3 has ORDSET and D4 has OAMONS and D5 has Join(
            EuclideanDomain,CharacteristicZero) and D2 has POLYCAT(D5,
            D4,D3)
   [7] D2 -> Factored D2 from MPolyCatRationalFunctionFactorizer(D3,D4,
            D5,D2)
            if D3 has OAMONS and D4 has OrderedSet with 
               convert : % -> Symbol and D5 has INTDOM and D2 has 
            POLYCAT(FRAC POLY D5,D3,D4)
   [8] SparseUnivariatePolynomial D6 -> Factored 
            SparseUnivariatePolynomial D6
            from MultFiniteFactorize(D3,D4,D5,D6)
            if D3 has ORDSET and D4 has OAMONS and D5 has FFIELDC and 
            D6 has POLYCAT(D5,D4,D3)
   [9] D2 -> Factored D2 from MultFiniteFactorize(D3,D4,D5,D2)
            if D3 has ORDSET and D4 has OAMONS and D5 has FFIELDC and 
            D2 has POLYCAT(D5,D4,D3)
   [10] Complex Integer -> Factored Complex Integer
            from GaussianFactorizationPackage
   [11] D2 -> Factored D2 from DistinctDegreeFactorize(D3,D2)
            if D3 has FFIELDC and D2 has UPOLYC D3
   [12] D2 -> Factored D2 from ComplexFactorization(D3,D2)
            if D3 has EUCDOM and D2 has UPOLYC COMPLEX D3
   [13] D2 -> Factored D2 from AlgFactor D2 if D2 has UPOLYC AN
   -> no appropriate map found in Complex Integer 
   -> no appropriate map found in Integer 
   -> no appropriate map found in Complex Polynomial Integer 
   -> no appropriate map found in Polynomial Integer 
   -> no appropriate map found in Integer 
   -> no appropriate map found in Polynomial Integer 

 Modemaps from Associated Packages 
   [1] ((D4 -> D5),Complex D4) -> Complex D5 from ComplexFunctions2(D4,
            D5)
            if D4 has COMRING and D5 has COMRING
cost=54500 for factor: Expression Complex Integer -> Factored Expression Complex Integer
cost=14500 for factor: Polynomial Complex Integer -> Factored Polynomial Complex Integer
cost=55500 for factor: SparseUnivariatePolynomial Polynomial Complex Integer -> Factored SparseUnivariatePolynomial Polynomial Complex Integer
 
 [1]  signature:   POLY COMPLEX INT -> FR POLY COMPLEX INT
      implemented: slot (Factored (Polynomial (Complex (Integer))))(Polynomial (Complex (Integer))) from MULTFACT(SYMBOL,INDE SYMBOL,COMPLEX INT,POLY COMPLEX INT)
 [2]  signature:   EXPR COMPLEX INT -> FR EXPR COMPLEX INT
      implemented: slot (Factored $)$ from EXPR COMPLEX INT
 [3]  signature:   SUP POLY COMPLEX INT -> FR SUP POLY COMPLEX INT
      implemented: slot (Factored (SparseUnivariatePolynomial (Polynomial (Complex (Integer)))))(SparseUnivariatePolynomial (Polynomial (Complex (Integer)))) from MULTFACT(SYMBOL,INDE SYMBOL,COMPLEX INT,POLY COMPLEX INT)
 

   (2)
     %i
  *
                 6     5               4               3         2
       (3 + 7%i)x  - 9x  + (30 - 10%i)x  + (15 - 24%i)x  + 14%i x  + (1 + 27%i)x
     + 
       - 7 + 42%i
                                    Type: Factored Polynomial Complex Integer
--R 
--R
--R Function Selection for factor
--R      Arguments: POLY COMPLEX INT 
--R   -> no appropriate factor found in Polynomial Complex Integer 
--R   -> no appropriate factor found in Polynomial Complex Integer 
--R
--R Modemaps from Associated Packages 
--R   no modemaps
--R
--R Remaining General Modemaps 
--R   [1] D -> Factored D from D if D has UFD
--R   [2] D2 -> Factored D2 from SAERationalFunctionAlgFactor(D3,D4,D2)
--R            if D3 has UPOLYC FRAC POLY INT and D4 has Join(Field,
--R            CharacteristicZero,MonogenicAlgebra(Fraction Polynomial 
--R            Integer,D3)) and D2 has UPOLYC D4
--R   [3] D2 -> Factored D2 from SimpleAlgebraicExtensionAlgFactor(D3,D4,
--R            D2)
--R            if D3 has UPOLYC FRAC INT and D4 has Join(Field,
--R            CharacteristicZero,MonogenicAlgebra(Fraction Integer,D3)) 
--R            and D2 has UPOLYC D4
--R   [4] D2 -> Factored D2 from RationalFunctionFactor D2
--R            if D2 has UPOLYC FRAC POLY INT
--R   [5] SparseUnivariatePolynomial D6 -> Factored 
--R            SparseUnivariatePolynomial D6
--R            from MultivariateFactorize(D3,D4,D5,D6)
--R            if D3 has ORDSET and D4 has OAMONS and D5 has Join(
--R            EuclideanDomain,CharacteristicZero) and D6 has POLYCAT(D5,
--R            D4,D3)
--R   [6] D2 -> Factored D2 from MultivariateFactorize(D3,D4,D5,D2)
--R            if D3 has ORDSET and D4 has OAMONS and D5 has Join(
--R            EuclideanDomain,CharacteristicZero) and D2 has POLYCAT(D5,
--R            D4,D3)
--R   [7] D2 -> Factored D2 from MPolyCatRationalFunctionFactorizer(D3,D4,
--R            D5,D2)
--R            if D3 has OAMONS and D4 has OrderedSet with 
--R               convert : % -> Symbol and D5 has INTDOM and D2 has 
--R            POLYCAT(FRAC POLY D5,D3,D4)
--R   [8] SparseUnivariatePolynomial D6 -> Factored 
--R            SparseUnivariatePolynomial D6
--R            from MultFiniteFactorize(D3,D4,D5,D6)
--R            if D3 has ORDSET and D4 has OAMONS and D5 has FFIELDC and 
--R            D6 has POLYCAT(D5,D4,D3)
--R   [9] D2 -> Factored D2 from MultFiniteFactorize(D3,D4,D5,D2)
--R            if D3 has ORDSET and D4 has OAMONS and D5 has FFIELDC and 
--R            D2 has POLYCAT(D5,D4,D3)
--R   [10] Complex Integer -> Factored Complex Integer
--R            from GaussianFactorizationPackage
--R   [11] D2 -> Factored D2 from DistinctDegreeFactorize(D3,D2)
--R            if D3 has FFIELDC and D2 has UPOLYC D3
--R   [12] D2 -> Factored D2 from ComplexFactorization(D3,D2)
--R            if D3 has EUCDOM and D2 has UPOLYC COMPLEX D3
--R   [13] D2 -> Factored D2 from AlgFactor D2 if D2 has UPOLYC AN
--R   -> no appropriate map found in Complex Integer 
--R   -> no appropriate map found in Integer 
--R   -> no appropriate map found in Complex Polynomial Integer 
--R   -> no appropriate map found in Polynomial Integer 
--R   -> no appropriate map found in Integer 
--R   -> no appropriate map found in Polynomial Integer 
--R
--R Modemaps from Associated Packages 
--R   [1] ((D4 -> D5),Complex D4) -> Complex D5 from ComplexFunctions2(D4,
--R            D5)
--R            if D4 has COMRING and D5 has COMRING
--Rcost=54500 for factor: Expression Complex Integer -> Factored Expression Complex Integer
--Rcost=14500 for factor: Polynomial Complex Integer -> Factored Polynomial Complex Integer
--Rcost=55500 for factor: SparseUnivariatePolynomial Polynomial Complex Integer -> Factored SparseUnivariatePolynomial Polynomial Complex Integer
--R 
--R [1]  signature:   POLY COMPLEX INT -> FR POLY COMPLEX INT
--R      implemented: slot (Factored (Polynomial (Complex (Integer))))(Polynomial (Complex (Integer))) from MULTFACT(SYMBOL,INDE SYMBOL,COMPLEX INT,POLY COMPLEX INT)
--R [2]  signature:   EXPR COMPLEX INT -> FR EXPR COMPLEX INT
--R      implemented: slot (Factored $)$ from EXPR COMPLEX INT
--R [3]  signature:   SUP POLY COMPLEX INT -> FR SUP POLY COMPLEX INT
--R      implemented: slot (Factored (SparseUnivariatePolynomial (Polynomial (Complex (Integer)))))(SparseUnivariatePolynomial (Polynomial (Complex (Integer)))) from MULTFACT(SYMBOL,INDE SYMBOL,COMPLEX INT,POLY COMPLEX INT)
--R 
--R
--R   (2)
--R     %i
--R  *
--R                 6     5               4               3         2
--R       (3 + 7%i)x  - 9x  + (30 - 10%i)x  + (15 - 24%i)x  + 14%i x  + (1 + 27%i)x
--R     + 
--R       - 7 + 42%i
--R                                    Type: Factored Polynomial Complex Integer
--E 2

--S 3 of 4
t3:=factors t2
 

 Function Selection for factors
      Arguments: FR POLY COMPLEX INT 
 
 [1]  signature:   FR POLY COMPLEX INT -> LIST Record(factor: POLY COMPLEX INT,exponent: INT)
      implemented: slot (List (Record (: factor (Polynomial (Complex (Integer)))) (: exponent (Integer))))$ from FR POLY COMPLEX INT
 

   (3)
   [
     [
       factor =
                     6     5               4               3         2
           (3 + 7%i)x  - 9x  + (30 - 10%i)x  + (15 - 24%i)x  + 14%i x
         + 
           (1 + 27%i)x - 7 + 42%i
       ,
      exponent= 1]
     ]
      Type: List Record(factor: Polynomial Complex Integer,exponent: Integer)
--R 
--R
--R Function Selection for factors
--R      Arguments: FR POLY COMPLEX INT 
--R 
--R [1]  signature:   FR POLY COMPLEX INT -> LIST Record(factor: POLY COMPLEX INT,exponent: INT)
--R      implemented: slot (List (Record (: factor (Polynomial (Complex (Integer)))) (: exponent (Integer))))$ from FR POLY COMPLEX INT
--R 
--R
--R   (3)
--R   [
--R     [
--R       factor =
--R                     6     5               4               3         2
--R           (3 + 7%i)x  - 9x  + (30 - 10%i)x  + (15 - 24%i)x  + 14%i x
--R         + 
--R           (1 + 27%i)x - 7 + 42%i
--R       ,
--R      exponent= 1]
--R     ]
--R      Type: List Record(factor: Polynomial Complex Integer,exponent: Integer)
--E 3

--S 4 of 4
t4:=unit t2
 

 Function Selection for unit
      Arguments: FR POLY COMPLEX INT 
 
 [1]  signature:   FR POLY COMPLEX INT -> POLY COMPLEX INT
      implemented: slot (Polynomial (Complex (Integer)))$ from FR POLY COMPLEX INT
 

   (4)  %i
                                             Type: Polynomial Complex Integer
--R 
--R
--R Function Selection for unit
--R      Arguments: FR POLY COMPLEX INT 
--R 
--R [1]  signature:   FR POLY COMPLEX INT -> POLY COMPLEX INT
--R      implemented: slot (Polynomial (Complex (Integer)))$ from FR POLY COMPLEX INT
--R 
--R
--R   (4)  %i
--R                                             Type: Polynomial Complex Integer
--E 4

)spool
 
Starts dribbling to PartialFractionPackage.output (2010/3/27, 18:46:14).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 4
a:=x+1/(y+1)
 

        x y + x + 1
   (1)  -----------
           y + 1
                                            Type: Fraction Polynomial Integer
--R
--R        x y + x + 1
--R   (1)  -----------
--R           y + 1
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 4
partialFraction(a,y)$PFRPAC(INT)
 

              1
   (2)  x + -----
            y + 1
    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--R
--R              1
--R   (2)  x + -----
--R            y + 1
--R    Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer)
--E 2

--S 3 of 4
b:=y+1/(x+1)
 

        (x + 1)y + 1
   (3)  ------------
            x + 1
                                            Type: Fraction Polynomial Integer
--R
--R        (x + 1)y + 1
--R   (3)  ------------
--R            x + 1
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 4
partialFraction(b,x)$PFRPAC(INT)
 

              1
   (4)  y + -----
            x + 1
    Type: PartialFraction UnivariatePolynomial(x,Fraction Polynomial Integer)
--R
--R              1
--R   (4)  y + -----
--R            x + 1
--R    Type: PartialFraction UnivariatePolynomial(x,Fraction Polynomial Integer)
--E 4

)spool 
 
Starts dribbling to schaum21.output (2010/3/27, 18:38:22).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 53
aa:=integrate(cot(a*x),x)
 

               sin(2a x)                2
        2log(-------------) - log(-------------)
             cos(2a x) + 1        cos(2a x) + 1
   (1)  ----------------------------------------
                           2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               sin(2a x)                2
--R        2log(-------------) - log(-------------)
--R             cos(2a x) + 1        cos(2a x) + 1
--R   (1)  ----------------------------------------
--R                           2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 53
bb:=1/a*log(sin(a*x))
 

        log(sin(a x))
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R        log(sin(a x))
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3 of 53
cc:=aa-bb
 

               sin(2a x)                                 2
        2log(-------------) - 2log(sin(a x)) - log(-------------)
             cos(2a x) + 1                         cos(2a x) + 1
   (3)  ---------------------------------------------------------
                                    2a
                                                     Type: Expression Integer
--R
--R               sin(2a x)                                 2
--R        2log(-------------) - 2log(sin(a x)) - log(-------------)
--R             cos(2a x) + 1                         cos(2a x) + 1
--R   (3)  ---------------------------------------------------------
--R                                    2a
--R                                                     Type: Expression Integer
--E

--S 4 of 53
dd:=expandLog cc
 

        2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2)
   (4)  --------------------------------------------------------------
                                      2a
                                                     Type: Expression Integer
--R
--R        2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2)
--R   (4)  --------------------------------------------------------------
--R                                      2a
--R                                                     Type: Expression Integer
--E

--S 5 of 53      14:440 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 6 of 53
aa:=integrate(cot(a*x)^2,x)
 

        - a x sin(2a x) - cos(2a x) - 1
   (1)  -------------------------------
                  a sin(2a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - a x sin(2a x) - cos(2a x) - 1
--R   (1)  -------------------------------
--R                  a sin(2a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7 of 53
bb:=-cot(a*x)/a-x
 

        - cot(a x) - a x
   (2)  ----------------
                a
                                                     Type: Expression Integer
--R
--R        - cot(a x) - a x
--R   (2)  ----------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 8 of 53
cc:=aa-bb
 

        cot(a x)sin(2a x) - cos(2a x) - 1
   (3)  ---------------------------------
                   a sin(2a x)
                                                     Type: Expression Integer
--R
--R        cot(a x)sin(2a x) - cos(2a x) - 1
--R   (3)  ---------------------------------
--R                   a sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 9 of 53
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 10 of 53
dd:=cotrule cc
 

        cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x)
   (5)  ---------------------------------------------
                     a sin(a x)sin(2a x)
                                                     Type: Expression Integer
--R
--R        cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x)
--R   (5)  ---------------------------------------------
--R                     a sin(a x)sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 11 of 53     14:441 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 12 of 53
aa:=integrate(cot(a*x)^3,x)
 

   (1)
                               sin(2a x)                               2
       (- 2cos(2a x) + 2)log(-------------) + (cos(2a x) - 1)log(-------------)
                             cos(2a x) + 1                       cos(2a x) + 1
     + 
       cos(2a x) + 1
  /
     2a cos(2a x) - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                               sin(2a x)                               2
--R       (- 2cos(2a x) + 2)log(-------------) + (cos(2a x) - 1)log(-------------)
--R                             cos(2a x) + 1                       cos(2a x) + 1
--R     + 
--R       cos(2a x) + 1
--R  /
--R     2a cos(2a x) - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13 of 53
bb:=-cot(a*x)^2/(2*a)-1/a*log(sin(a*x))
 

                                   2
        - 2log(sin(a x)) - cot(a x)
   (2)  ----------------------------
                     2a
                                                     Type: Expression Integer
--R
--R                                   2
--R        - 2log(sin(a x)) - cot(a x)
--R   (2)  ----------------------------
--R                     2a
--R                                                     Type: Expression Integer
--E

--S 14 of 53
cc:=aa-bb
 

   (3)
                               sin(2a x)
       (- 2cos(2a x) + 2)log(-------------) + (2cos(2a x) - 2)log(sin(a x))
                             cos(2a x) + 1
     + 
                                2                                 2
       (cos(2a x) - 1)log(-------------) + (cos(2a x) - 1)cot(a x)  + cos(2a x)
                          cos(2a x) + 1
     + 
       1
  /
     2a cos(2a x) - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                               sin(2a x)
--R       (- 2cos(2a x) + 2)log(-------------) + (2cos(2a x) - 2)log(sin(a x))
--R                             cos(2a x) + 1
--R     + 
--R                                2                                 2
--R       (cos(2a x) - 1)log(-------------) + (cos(2a x) - 1)cot(a x)  + cos(2a x)
--R                          cos(2a x) + 1
--R     + 
--R       1
--R  /
--R     2a cos(2a x) - 2a
--R                                                     Type: Expression Integer
--E

--S 15 of 53
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 16 of 53
dd:=cotrule cc
 

   (5)
                                 2      sin(2a x)
       (- 2cos(2a x) + 2)sin(a x) log(-------------)
                                      cos(2a x) + 1
     + 
                               2
       (2cos(2a x) - 2)sin(a x) log(sin(a x))
     + 
                              2          2                                 2
       (cos(2a x) - 1)sin(a x) log(-------------) + (cos(2a x) + 1)sin(a x)
                                   cos(2a x) + 1
     + 
               2                    2
       cos(a x) cos(2a x) - cos(a x)
  /
                                2
     (2a cos(2a x) - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                 2      sin(2a x)
--R       (- 2cos(2a x) + 2)sin(a x) log(-------------)
--R                                      cos(2a x) + 1
--R     + 
--R                               2
--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
--R     + 
--R                              2          2                                 2
--R       (cos(2a x) - 1)sin(a x) log(-------------) + (cos(2a x) + 1)sin(a x)
--R                                   cos(2a x) + 1
--R     + 
--R               2                    2
--R       cos(a x) cos(2a x) - cos(a x)
--R  /
--R                                2
--R     (2a cos(2a x) - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 17 of 53
ee:=expandLog dd
 

   (6)
                                 2
       (- 2cos(2a x) + 2)sin(a x) log(sin(2a x))
     + 
                               2
       (2cos(2a x) - 2)sin(a x) log(sin(a x))
     + 
                              2
       (cos(2a x) - 1)sin(a x) log(cos(2a x) + 1)
     + 
                                                   2           2
       ((log(2) + 1)cos(2a x) - log(2) + 1)sin(a x)  + cos(a x) cos(2a x)
     + 
                 2
       - cos(a x)
  /
                                2
     (2a cos(2a x) - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (6)
--R                                 2
--R       (- 2cos(2a x) + 2)sin(a x) log(sin(2a x))
--R     + 
--R                               2
--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
--R     + 
--R                              2
--R       (cos(2a x) - 1)sin(a x) log(cos(2a x) + 1)
--R     + 
--R                                                   2           2
--R       ((log(2) + 1)cos(2a x) - log(2) + 1)sin(a x)  + cos(a x) cos(2a x)
--R     + 
--R                 2
--R       - cos(a x)
--R  /
--R                                2
--R     (2a cos(2a x) - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 18 of 53     14:442 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 53
aa:=integrate(cot(a*x)^n*csc(a*x)^2,x)
 

                          cos(a x)
                    n log(--------)
                          sin(a x)
          cos(a x)%e
   (1)  - -------------------------
              (a n + a)sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          cos(a x)
--R                    n log(--------)
--R                          sin(a x)
--R          cos(a x)%e
--R   (1)  - -------------------------
--R              (a n + a)sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 20 of 53
bb:=-cot(a*x)^(n+1)/((n+1)*a)
 

                  n + 1
          cot(a x)
   (2)  - -------------
             a n + a
                                                     Type: Expression Integer
--R
--R                  n + 1
--R          cot(a x)
--R   (2)  - -------------
--R             a n + a
--R                                                     Type: Expression Integer
--E

--S 21 of 53
cc:=aa-bb
 

                          cos(a x)
                    n log(--------)
                          sin(a x)                    n + 1
        - cos(a x)%e                + sin(a x)cot(a x)
   (3)  ---------------------------------------------------
                         (a n + a)sin(a x)
                                                     Type: Expression Integer
--R
--R                          cos(a x)
--R                    n log(--------)
--R                          sin(a x)                    n + 1
--R        - cos(a x)%e                + sin(a x)cot(a x)
--R   (3)  ---------------------------------------------------
--R                         (a n + a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 22 of 53
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 23 of 53
dd:=explog cc
 

                        n + 1            cos(a x) n
        sin(a x)cot(a x)      - cos(a x)(--------)
                                         sin(a x)
   (5)  -------------------------------------------
                     (a n + a)sin(a x)
                                                     Type: Expression Integer
--R
--R                        n + 1            cos(a x) n
--R        sin(a x)cot(a x)      - cos(a x)(--------)
--R                                         sin(a x)
--R   (5)  -------------------------------------------
--R                     (a n + a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 24 of 53
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (6)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (6)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 25 of 53
ee:=cotrule dd
 

                 cos(a x) n + 1            cos(a x) n
        sin(a x)(--------)      - cos(a x)(--------)
                 sin(a x)                  sin(a x)
   (7)  ---------------------------------------------
                      (a n + a)sin(a x)
                                                     Type: Expression Integer
--R
--R                 cos(a x) n + 1            cos(a x) n
--R        sin(a x)(--------)      - cos(a x)(--------)
--R                 sin(a x)                  sin(a x)
--R   (7)  ---------------------------------------------
--R                      (a n + a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 26 of 53     14:443 Schaums and Axiom agree
ff:=complexNormalize ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 53
aa:=integrate(csc(a*x)^2/cot(a*x),x)
 

              sin(a x)              2cos(a x)
        log(------------) - log(- ------------)
            cos(a x) + 1          cos(a x) + 1
   (1)  ---------------------------------------
                           a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)              2cos(a x)
--R        log(------------) - log(- ------------)
--R            cos(a x) + 1          cos(a x) + 1
--R   (1)  ---------------------------------------
--R                           a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28 of 53
bb:=-1/a*log(cot(a*x))
 

          log(cot(a x))
   (2)  - -------------
                a
                                                     Type: Expression Integer
--R
--R          log(cot(a x))
--R   (2)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 29 of 53
cc:=aa-bb
 

              sin(a x)                              2cos(a x)
        log(------------) + log(cot(a x)) - log(- ------------)
            cos(a x) + 1                          cos(a x) + 1
   (3)  -------------------------------------------------------
                                   a
                                                     Type: Expression Integer
--R
--R              sin(a x)                              2cos(a x)
--R        log(------------) + log(cot(a x)) - log(- ------------)
--R            cos(a x) + 1                          cos(a x) + 1
--R   (3)  -------------------------------------------------------
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 30 of 53
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 31 of 53
dd:=cotrule cc
 

              sin(a x)          cos(a x)            2cos(a x)
        log(------------) + log(--------) - log(- ------------)
            cos(a x) + 1        sin(a x)          cos(a x) + 1
   (5)  -------------------------------------------------------
                                   a
                                                     Type: Expression Integer
--R
--R              sin(a x)          cos(a x)            2cos(a x)
--R        log(------------) + log(--------) - log(- ------------)
--R            cos(a x) + 1        sin(a x)          cos(a x) + 1
--R   (5)  -------------------------------------------------------
--R                                   a
--R                                                     Type: Expression Integer
--E

--S 32 of 53     14:444 Schaums and Axiom differ by a constant
ee:=expandLog dd
 

          log(- 2)
   (6)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 2)
--R   (6)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 33 of 53
aa:=integrate(1/cot(a*x),x)
 

                  2
        log(-------------)
            cos(2a x) + 1
   (1)  ------------------
                2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R        log(-------------)
--R            cos(2a x) + 1
--R   (1)  ------------------
--R                2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34 of 53
bb:=-1/a*log(cos(a*x))
 

          log(cos(a x))
   (2)  - -------------
                a
                                                     Type: Expression Integer
--R
--R          log(cos(a x))
--R   (2)  - -------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 35 of 53
cc:=aa-bb
 

                                   2
        2log(cos(a x)) + log(-------------)
                             cos(2a x) + 1
   (3)  -----------------------------------
                         2a
                                                     Type: Expression Integer
--R
--R                                   2
--R        2log(cos(a x)) + log(-------------)
--R                             cos(2a x) + 1
--R   (3)  -----------------------------------
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 36 of 53
dd:=expandLog cc
 

        - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2)
   (4)  ----------------------------------------------
                              2a
                                                     Type: Expression Integer
--R
--R        - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2)
--R   (4)  ----------------------------------------------
--R                              2a
--R                                                     Type: Expression Integer
--E

--S 37 of 53     14:445 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 38 of 53     14:446 Axiom cannot compute this integral
aa:=integrate(x*cot(a*x),x)
 

           x
         ++
   (1)   |   %R cot(%R a)d%R
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %I cot(%I a)d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 39 of 53     14:447 Axiom cannot compute this integral
aa:=integrate(cot(a*x)/x,x)
 

           x
         ++  cot(%R a)
   (1)   |   --------- d%R
        ++       %R
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cot(%I a)
--I   (1)   |   --------- d%I
--I        ++       %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 40 of 53
aa:=integrate(x*cot(a*x)^2,x)
 

   (1)
                       sin(2a x)                         2
       2sin(2a x)log(-------------) - sin(2a x)log(-------------)
                     cos(2a x) + 1                 cos(2a x) + 1
     + 
          2 2
       - a x sin(2a x) - 2a x cos(2a x) - 2a x
  /
       2
     2a sin(2a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                       sin(2a x)                         2
--R       2sin(2a x)log(-------------) - sin(2a x)log(-------------)
--R                     cos(2a x) + 1                 cos(2a x) + 1
--R     + 
--R          2 2
--R       - a x sin(2a x) - 2a x cos(2a x) - 2a x
--R  /
--R       2
--R     2a sin(2a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 41 of 53
bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))-x^2/2
 

                                          2 2
        2log(sin(a x)) - 2a x cot(a x) - a x
   (2)  -------------------------------------
                           2
                         2a
                                                     Type: Expression Integer
--R
--R                                          2 2
--R        2log(sin(a x)) - 2a x cot(a x) - a x
--R   (2)  -------------------------------------
--R                           2
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 42 of 53
cc:=aa-bb
 

   (3)
                       sin(2a x)
       2sin(2a x)log(-------------) - 2sin(2a x)log(sin(a x))
                     cos(2a x) + 1
     + 
                            2
       - sin(2a x)log(-------------) + 2a x cot(a x)sin(2a x) - 2a x cos(2a x)
                      cos(2a x) + 1
     + 
       - 2a x
  /
       2
     2a sin(2a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                       sin(2a x)
--R       2sin(2a x)log(-------------) - 2sin(2a x)log(sin(a x))
--R                     cos(2a x) + 1
--R     + 
--R                            2
--R       - sin(2a x)log(-------------) + 2a x cot(a x)sin(2a x) - 2a x cos(2a x)
--R                      cos(2a x) + 1
--R     + 
--R       - 2a x
--R  /
--R       2
--R     2a sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 43 of 53
dd:=expandLog cc
 

   (4)
       2sin(2a x)log(sin(2a x)) - 2sin(2a x)log(sin(a x))
     + 
       - sin(2a x)log(cos(2a x) + 1) + (2a x cot(a x) - log(2))sin(2a x)
     + 
       - 2a x cos(2a x) - 2a x
  /
       2
     2a sin(2a x)
                                                     Type: Expression Integer
--R
--R   (4)
--R       2sin(2a x)log(sin(2a x)) - 2sin(2a x)log(sin(a x))
--R     + 
--R       - sin(2a x)log(cos(2a x) + 1) + (2a x cot(a x) - log(2))sin(2a x)
--R     + 
--R       - 2a x cos(2a x) - 2a x
--R  /
--R       2
--R     2a sin(2a x)
--R                                                     Type: Expression Integer
--E

--S 44 of 53     14:448 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 45 of 53
aa:=integrate(1/(p+q*cot(a*x)),x)
 

   (1)
            p sin(2a x) + q cos(2a x) + q                2
   - 2q log(-----------------------------) + q log(-------------) + 2a p x
                    cos(2a x) + 1                  cos(2a x) + 1
   -----------------------------------------------------------------------
                                    2       2
                                2a q  + 2a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R            p sin(2a x) + q cos(2a x) + q                2
--R   - 2q log(-----------------------------) + q log(-------------) + 2a p x
--R                    cos(2a x) + 1                  cos(2a x) + 1
--R   -----------------------------------------------------------------------
--R                                    2       2
--R                                2a q  + 2a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 46 of 53
bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x))
 

        - q log(p sin(a x) + q cos(a x)) + a p x
   (2)  ----------------------------------------
                          2      2
                       a q  + a p
                                                     Type: Expression Integer
--R
--R        - q log(p sin(a x) + q cos(a x)) + a p x
--R   (2)  ----------------------------------------
--R                          2      2
--R                       a q  + a p
--R                                                     Type: Expression Integer
--E

--S 47 of 53
cc:=aa-bb
 

   (3)
                p sin(2a x) + q cos(2a x) + q
       - 2q log(-----------------------------) + 2q log(p sin(a x) + q cos(a x))
                        cos(2a x) + 1
     + 
                   2
       q log(-------------)
             cos(2a x) + 1
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                p sin(2a x) + q cos(2a x) + q
--R       - 2q log(-----------------------------) + 2q log(p sin(a x) + q cos(a x))
--R                        cos(2a x) + 1
--R     + 
--R                   2
--R       q log(-------------)
--R             cos(2a x) + 1
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 48 of 53
sindblrule:=rule(sin(2*a) == 2*sin(a)*cos(a))
 

   (4)  sin(2a) == 2cos(a)sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R   (4)  sin(2a) == 2cos(a)sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 49 of 53
dd:=sindblrule cc
 

   (5)
       2q log(p sin(a x) + q cos(a x))
     + 
                2p cos(a x)sin(a x) + q cos(2a x) + q                2
       - 2q log(-------------------------------------) + q log(-------------)
                            cos(2a x) + 1                      cos(2a x) + 1
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (5)
--R       2q log(p sin(a x) + q cos(a x))
--R     + 
--R                2p cos(a x)sin(a x) + q cos(2a x) + q                2
--R       - 2q log(-------------------------------------) + q log(-------------)
--R                            cos(2a x) + 1                      cos(2a x) + 1
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 50 of 53
cosdblrule:=rule(cos(2*a) == 2*cos(a)^2-1)
 

                          2
   (6)  cos(2a) == 2cos(a)  - 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          2
--R   (6)  cos(2a) == 2cos(a)  - 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 51 of 53
ee:=cosdblrule dd
 

   (7)
                                                p sin(a x) + q cos(a x)
       2q log(p sin(a x) + q cos(a x)) - 2q log(-----------------------)
                                                        cos(a x)
     + 
                 1
       q log(---------)
                     2
             cos(a x)
  /
         2       2
     2a q  + 2a p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                                p sin(a x) + q cos(a x)
--R       2q log(p sin(a x) + q cos(a x)) - 2q log(-----------------------)
--R                                                        cos(a x)
--R     + 
--R                 1
--R       q log(---------)
--R                     2
--R             cos(a x)
--R  /
--R         2       2
--R     2a q  + 2a p
--R                                                     Type: Expression Integer
--E

--S 52 of 53     14:449 Schaums and Axiom agree
ff:=expandLog %
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 53 of 53     14:450 Axiom cannot compute this integral
aa:=integrate(cot(a*x)^n,x)
 

           x
         ++           n
   (1)   |   cot(%R a) d%R
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   cot(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to linalg.output (2010/3/27, 18:28:38).
)set message test on
 
)set message auto off
 
)set break resume
 
)clear all
 

-- Input for page MatrixMoreFunctionsPage
)clear all
 

--S 1 of 82
m1 := matrix([[1,-2,1],[4,2,-4]])
 

        +1  - 2   1 +
   (1)  |           |
        +4   2   - 4+
                                                         Type: Matrix Integer
--R
--R        +1  - 2   1 +
--R   (1)  |           |
--R        +4   2   - 4+
--R                                                         Type: Matrix Integer
--E 1

--S 2 of 82
m2 := matrix([[0,1,2],[2,3,4],[3,4,5]])
 

        +0  1  2+
        |       |
   (2)  |2  3  4|
        |       |
        +3  4  5+
                                                         Type: Matrix Integer
--R
--R        +0  1  2+
--R        |       |
--R   (2)  |2  3  4|
--R        |       |
--R        +3  4  5+
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 82
m3 := matrix([[1,2,3],[2,4,6]])
 

        +1  2  3+
   (3)  |       |
        +2  4  6+
                                                         Type: Matrix Integer
--R
--R        +1  2  3+
--R   (3)  |       |
--R        +2  4  6+
--R                                                         Type: Matrix Integer
--E 3

--S 4 of 82
m1 + m3
 

        +2  0  4+
   (4)  |       |
        +6  6  2+
                                                         Type: Matrix Integer
--R
--R        +2  0  4+
--R   (4)  |       |
--R        +6  6  2+
--R                                                         Type: Matrix Integer
--E 4

--S 5 of 82
100 * m1
 

        +100  - 200   100 +
   (5)  |                 |
        +400   200   - 400+
                                                         Type: Matrix Integer
--R
--R        +100  - 200   100 +
--R   (5)  |                 |
--R        +400   200   - 400+
--R                                                         Type: Matrix Integer
--E 5

--S 6 of 82
m1 * m2
 

        +- 1  - 1  - 1+
   (6)  |             |
        +- 8  - 6  - 4+
                                                         Type: Matrix Integer
--R
--R        +- 1  - 1  - 1+
--R   (6)  |             |
--R        +- 8  - 6  - 4+
--R                                                         Type: Matrix Integer
--E 6

--S 7 of 82
-m1 + m3 * m2
 

        +12  21  24+
   (7)  |          |
        +22  36  54+
                                                         Type: Matrix Integer
--R
--R        +12  21  24+
--R   (7)  |          |
--R        +22  36  54+
--R                                                         Type: Matrix Integer
--E 7

--S 8 of 82
m2 * m1
 
 
Daly Bug
   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   can't multiply matrices of incompatible dimensions
--R
--R   Continuing to read the file...
--R
--E 8

--S 9 of 82
v := vector([1,0,1])
 

   (8)  [1,0,1]
                                              Type: Vector NonNegativeInteger
--R
--R   (8)  [1,0,1]
--R                                              Type: Vector NonNegativeInteger
--E 9

--S 10 of 82
m3 * v
 

   (9)  [4,8]
                                                         Type: Vector Integer
--R
--R   (9)  [4,8]
--R                                                         Type: Vector Integer
--E 10

--S 11 of 82
m5 : MATRIX POLY INT := new(4,4,1)
 

         +1  1  1  1+
         |          |
         |1  1  1  1|
   (10)  |          |
         |1  1  1  1|
         |          |
         +1  1  1  1+
                                              Type: Matrix Polynomial Integer
--R
--R         +1  1  1  1+
--R         |          |
--R         |1  1  1  1|
--R   (10)  |          |
--R         |1  1  1  1|
--R         |          |
--R         +1  1  1  1+
--R                                              Type: Matrix Polynomial Integer
--E 11

--S 12 of 82
vars : LIST POLY INT := [x,y,z,u]
 

   (11)  [x,y,z,u]
                                                Type: List Polynomial Integer
--R
--R   (11)  [x,y,z,u]
--R                                                Type: List Polynomial Integer
--E 12

--S 13 of 82
for i in 1..4 repeat for j in 1..3 repeat m5(i,j + 1) := (vars.i)**j
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 13

--S 14 of 82
m5
 

         +       2   3+
         |1  x  x   x |
         |            |
         |       2   3|
         |1  y  y   y |
   (13)  |            |
         |       2   3|
         |1  z  z   z |
         |            |
         |       2   3|
         +1  u  u   u +
                                              Type: Matrix Polynomial Integer
--R
--R         +       2   3+
--R         |1  x  x   x |
--R         |            |
--R         |       2   3|
--R         |1  y  y   y |
--R   (13)  |            |
--R         |       2   3|
--R         |1  z  z   z |
--R         |            |
--R         |       2   3|
--R         +1  u  u   u +
--R                                              Type: Matrix Polynomial Integer
--E 14

--S 15 of 82
trace(m5)
 

          2        3
   (14)  z  + y + u  + 1
                                                     Type: Polynomial Integer
--R
--R          2        3
--R   (14)  z  + y + u  + 1
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 82
det := determinant(m5)
 

   (15)
                2     2    2        2    2   3
     ((- x + u)y  + (x  - u )y - u x  + u x)z
   + 
              3       3    3        3    3   2
     ((x - u)y  + (- x  + u )y + u x  - u x)z
   + 
          2    2  3     3    3  2    2 3    3 2         2    2   3
     ((- x  + u )y  + (x  - u )y  - u x  + u x )z + (u x  - u x)y
   + 
           3    3   2     2 3    3 2
     (- u x  + u x)y  + (u x  - u x )y
                                                     Type: Polynomial Integer
--R
--R   (15)
--R                2     2    2        2    2   3
--R     ((- x + u)y  + (x  - u )y - u x  + u x)z
--R   + 
--R              3       3    3        3    3   2
--R     ((x - u)y  + (- x  + u )y + u x  - u x)z
--R   + 
--R          2    2  3     3    3  2    2 3    3 2         2    2   3
--R     ((- x  + u )y  + (x  - u )y  - u x  + u x )z + (u x  - u x)y
--R   + 
--R           3    3   2     2 3    3 2
--R     (- u x  + u x)y  + (u x  - u x )y
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 82
factor(det)
 

   (16)  - (x - u)(y - x)(y - u)(z - y)(z - x)(z - u)
                                            Type: Factored Polynomial Integer
--R
--R   (16)  - (x - u)(y - x)(y - u)(z - y)(z - x)(z - u)
--R                                            Type: Factored Polynomial Integer
--E 17

--S 18 of 82
m6 := matrix([[1,2,1],[-2,3,4],[-1,5,6]])
 

         + 1   2  1+
         |         |
   (17)  |- 2  3  4|
         |         |
         +- 1  5  6+
                                                         Type: Matrix Integer
--R
--R         + 1   2  1+
--R         |         |
--R   (17)  |- 2  3  4|
--R         |         |
--R         +- 1  5  6+
--R                                                         Type: Matrix Integer
--E 18

--S 19 of 82
m6inv := inverse(m6)
 

         +  2        5 +
         |- -  - 1   - |
         |  7        7 |
         |             |
   (18)  | 8          6|
         | -    1   - -|
         | 7          7|
         |             |
         +- 1  - 1   1 +
                                     Type: Union(Matrix Fraction Integer,...)
--R
--R         +  2        5 +
--R         |- -  - 1   - |
--R         |  7        7 |
--R         |             |
--R   (18)  | 8          6|
--R         | -    1   - -|
--R         | 7          7|
--R         |             |
--R         +- 1  - 1   1 +
--R                                     Type: Union(Matrix Fraction Integer,...)
--E 19

--S 20 of 82
m6 * m6inv
 

         +1  0  0+
         |       |
   (19)  |0  1  0|
         |       |
         +0  0  1+
                                                Type: Matrix Fraction Integer
--R
--R         +1  0  0+
--R         |       |
--R   (19)  |0  1  0|
--R         |       |
--R         +0  0  1+
--R                                                Type: Matrix Fraction Integer
--E 20

--S 21 of 82
m7 := matrix([[1,2,1],[-2,3,4],[-1,5,5]])
 

         + 1   2  1+
         |         |
   (20)  |- 2  3  4|
         |         |
         +- 1  5  5+
                                                         Type: Matrix Integer
--R
--R         + 1   2  1+
--R         |         |
--R   (20)  |- 2  3  4|
--R         |         |
--R         +- 1  5  5+
--R                                                         Type: Matrix Integer
--E 21

--S 22 of 82
inverse(m7)
 

   (21)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (21)  "failed"
--R                                                    Type: Union("failed",...)
--E 22

--S 23 of 82
determinant(m7)
 

   (22)  0
                                                     Type: NonNegativeInteger
--R
--R   (22)  0
--R                                                     Type: NonNegativeInteger
--E 23

--S 24 of 82
m8 : SQMATRIX(2,INT) := matrix([[1,2],[2,3]])
 

         +1  2+
   (23)  |    |
         +2  3+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +1  2+
--R   (23)  |    |
--R         +2  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 24

--S 25 of 82
m9 : SQMATRIX(2,INT) := matrix([[1,1],[0,1]])
 

         +1  1+
   (24)  |    |
         +0  1+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +1  1+
--R   (24)  |    |
--R         +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 25

--S 26 of 82
m8 ** 2
 

         +5  8 +
   (25)  |     |
         +8  13+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +5  8 +
--R   (25)  |     |
--R         +8  13+
--R                                                Type: SquareMatrix(2,Integer)
--E 26

--S 27 of 82
m9 ** 3
 

         +1  3+
   (26)  |    |
         +0  1+
                                                Type: SquareMatrix(2,Integer)
--R
--R         +1  3+
--R   (26)  |    |
--R         +0  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 27

--S 28 of 82
mm : SQMATRIX(2,SQMATRIX(2,INT)) := matrix([[1,m8],[m9,0]])
 

         ++1  0+  +1  2++
         ||    |  |    ||
         |+0  1+  +2  3+|
   (27)  |              |
         |+1  1+  +0  0+|
         ||    |  |    ||
         ++0  1+  +0  0++
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++1  0+  +1  2++
--R         ||    |  |    ||
--R         |+0  1+  +2  3+|
--R   (27)  |              |
--R         |+1  1+  +0  0+|
--R         ||    |  |    ||
--R         ++0  1+  +0  0++
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 28

--S 29 of 82
100 * mm
 

         ++100   0 +  +100  200++
         ||        |  |        ||
         |+ 0   100+  +200  300+|
   (28)  |                      |
         |+100  100+    +0  0+  |
         ||        |    |    |  |
         ++ 0   100+    +0  0+  +
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++100   0 +  +100  200++
--R         ||        |  |        ||
--R         |+ 0   100+  +200  300+|
--R   (28)  |                      |
--R         |+100  100+    +0  0+  |
--R         ||        |    |    |  |
--R         ++ 0   100+    +0  0+  +
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 29

--S 30 of 82
m8 * mm
 

         ++1  2+  +5  8 ++
         ||    |  |     ||
         |+2  3+  +8  13+|
   (29)  |               |
         |+1  3+  +0  0+ |
         ||    |  |    | |
         ++2  5+  +0  0+ +
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++1  2+  +5  8 ++
--R         ||    |  |     ||
--R         |+2  3+  +8  13+|
--R   (29)  |               |
--R         |+1  3+  +0  0+ |
--R         ||    |  |    | |
--R         ++2  5+  +0  0+ +
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 30

--S 31 of 82
mm * mm
 

         ++2  3+  +1  2++
         ||    |  |    ||
         |+2  6+  +2  3+|
   (30)  |              |
         |+1  1+  +3  5+|
         ||    |  |    ||
         ++0  1+  +2  3++
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R
--R         ++2  3+  +1  2++
--R         ||    |  |    ||
--R         |+2  6+  +2  3+|
--R   (30)  |              |
--R         |+1  1+  +3  5+|
--R         ||    |  |    ||
--R         ++0  1+  +2  3++
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 31

--S 32 of 82
p : POLY SQMATRIX(2,INT) := m8 * x**2 + m9 * x + m8 * m9
 

         +1  2+ 2   +1  1+    +1  3+
   (31)  |    |x  + |    |x + |    |
         +2  3+     +0  1+    +2  5+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +1  2+ 2   +1  1+    +1  3+
--R   (31)  |    |x  + |    |x + |    |
--R         +2  3+     +0  1+    +2  5+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 32

--S 33 of 82
100 * p
 

         +100  200+ 2   +100  100+    +100  300+
   (32)  |        |x  + |        |x + |        |
         +200  300+     + 0   100+    +200  500+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +100  200+ 2   +100  100+    +100  300+
--R   (32)  |        |x  + |        |x + |        |
--R         +200  300+     + 0   100+    +200  500+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 33

--S 34 of 82
m8 * p
 

         +5  8 + 2   +1  3+    +5  13+
   (33)  |     |x  + |    |x + |     |
         +8  13+     +2  5+    +8  21+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +5  8 + 2   +1  3+    +5  13+
--R   (33)  |     |x  + |    |x + |     |
--R         +8  13+     +2  5+    +8  21+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 34

--S 35 of 82
p * p
 

         +5  8 + 4   +4  8+ 3   +13  26+ 2   +4  12+    +7   18+
   (34)  |     |x  + |    |x  + |      |x  + |     |x + |      |
         +8  13+     +4  8+     +20  41+     +4  12+    +12  31+
                                     Type: Polynomial SquareMatrix(2,Integer)
--R
--R         +5  8 + 4   +4  8+ 3   +13  26+ 2   +4  12+    +7   18+
--R   (34)  |     |x  + |    |x  + |      |x  + |     |x + |      |
--R         +8  13+     +4  8+     +20  41+     +4  12+    +12  31+
--R                                     Type: Polynomial SquareMatrix(2,Integer)
--E 35

-- Input for page MatrixCanonicalFormsPage
)clear all
 

--S 36 of 82
m1 := matrix([[0,4,1],[5,3,-7],[-5,5,9]])
 

        + 0   4   1 +
        |           |
   (1)  | 5   3  - 7|
        |           |
        +- 5  5   9 +
                                                         Type: Matrix Integer
--R
--R        + 0   4   1 +
--R        |           |
--R   (1)  | 5   3  - 7|
--R        |           |
--R        +- 5  5   9 +
--R                                                         Type: Matrix Integer
--E 36

--S 37 of 82
rank(m1)
 

   (2)  2
                                                        Type: PositiveInteger
--R
--R   (2)  2
--R                                                        Type: PositiveInteger
--E 37

--S 38 of 82
rowEchelon(m1)
 

        +5  3  - 7+
        |         |
   (3)  |0  4   1 |
        |         |
        +0  0   0 +
                                                         Type: Matrix Integer
--R
--R        +5  3  - 7+
--R        |         |
--R   (3)  |0  4   1 |
--R        |         |
--R        +0  0   0 +
--R                                                         Type: Matrix Integer
--E 38

--S 39 of 82
nullSpace(m1)
 

   (4)  [[31,- 5,20]]
                                                    Type: List Vector Integer
--R
--R   (4)  [[31,- 5,20]]
--R                                                    Type: List Vector Integer
--E 39

--S 40 of 82
t := eigenMatrix(m1)
 

        + +----+          +----+          +
        |\|- 11  + 2   - \|- 11  + 2   31 |
        |-----------   -------------   -- |
        |     5              5         20 |
        |                                 |
   (5)  |  +----+          +----+         |
        |2\|- 11  - 1  - 2\|- 11  - 1    1|
        |------------  --------------  - -|
        |      5              5          4|
        |                                 |
        +     1              1          1 +
                                   Type: Union(Matrix Expression Integer,...)
--R
--R        + +----+          +----+          +
--R        |\|- 11  + 2   - \|- 11  + 2   31 |
--R        |-----------   -------------   -- |
--R        |     5              5         20 |
--R        |                                 |
--R   (5)  |  +----+          +----+         |
--R        |2\|- 11  - 1  - 2\|- 11  - 1    1|
--R        |------------  --------------  - -|
--R        |      5              5          4|
--R        |                                 |
--R        +     1              1          1 +
--R                                   Type: Union(Matrix Expression Integer,...)
--E 40

--S 41 of 82
inverse(t) * m1 * t
 

        +           +----+                                +
        |5581634906\|- 11  - 55255461173                  |
        |-------------------------------        0        0|
        |            +----+                               |
        | 1888197247\|- 11  - 5747548576                  |
        |                                                 |
   (6)  |                                   +----+        |
        |                                 6\|- 11  + 11   |
        |               0                 -------------  0|
        |                                     +----+      |
        |                                    \|- 11       |
        |                                                 |
        +               0                       0        0+
                                              Type: Matrix Expression Integer
--R
--R        +           +----+                                +
--R        |5581634906\|- 11  - 55255461173                  |
--R        |-------------------------------        0        0|
--R        |            +----+                               |
--R        | 1888197247\|- 11  - 5747548576                  |
--R        |                                                 |
--R   (6)  |                                   +----+        |
--R        |                                 6\|- 11  + 11   |
--R        |               0                 -------------  0|
--R        |                                     +----+      |
--R        |                                    \|- 11       |
--R        |                                                 |
--R        +               0                       0        0+
--R                                              Type: Matrix Expression Integer
--E 41

-- Input for page MatrixBasicFunctionsPage
)clear all
 

--S 42 of 82
m1 := matrix([[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,7]])
 

        +1  2  3  4+
        |          |
        |2  3  4  5|
   (1)  |          |
        |3  4  5  6|
        |          |
        +4  5  6  7+
                                                         Type: Matrix Integer
--R
--R        +1  2  3  4+
--R        |          |
--R        |2  3  4  5|
--R   (1)  |          |
--R        |3  4  5  6|
--R        |          |
--R        +4  5  6  7+
--R                                                         Type: Matrix Integer
--E 42

--S 43 of 82
m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])
 

        +1    0    2 +
        |            |
   (2)  |20  30   10 |
        |            |
        +0   200  100+
                                                         Type: Matrix Integer
--R
--R        +1    0    2 +
--R        |            |
--R   (2)  |20  30   10 |
--R        |            |
--R        +0   200  100+
--R                                                         Type: Matrix Integer
--E 43

--S 44 of 82
(m3,m4) : MATRIX PF 7
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 44

--S 45 of 82
m3 := matrix([[1,0,1],[5,0,1]])
 

        +1  0  1+
   (4)  |       |
        +5  0  1+
                                                    Type: Matrix PrimeField 7
--R
--R        +1  0  1+
--R   (4)  |       |
--R        +5  0  1+
--R                                                    Type: Matrix PrimeField 7
--E 45

--S 46 of 82
m4 := matrix([[1],[2],[5],[6]])
 

        +1+
        | |
        |2|
   (5)  | |
        |5|
        | |
        +6+
                                                    Type: Matrix PrimeField 7
--R
--R        +1+
--R        | |
--R        |2|
--R   (5)  | |
--R        |5|
--R        | |
--R        +6+
--R                                                    Type: Matrix PrimeField 7
--E 46

--S 47 of 82
m2(1,1)
 

   (6)  1
                                                        Type: PositiveInteger
--R
--R   (6)  1
--R                                                        Type: PositiveInteger
--E 47

--S 48 of 82
m2(1,1) := 99
 

   (7)  99
                                                        Type: PositiveInteger
--R
--R   (7)  99
--R                                                        Type: PositiveInteger
--E 48

--S 49 of 82
m2
 

        +99   0    2 +
        |            |
   (8)  |20  30   10 |
        |            |
        +0   200  100+
                                                         Type: Matrix Integer
--R
--R        +99   0    2 +
--R        |            |
--R   (8)  |20  30   10 |
--R        |            |
--R        +0   200  100+
--R                                                         Type: Matrix Integer
--E 49

--S 50 of 82
row(m2,2)
 

   (9)  [20,30,10]
                                                         Type: Vector Integer
--R
--R   (9)  [20,30,10]
--R                                                         Type: Vector Integer
--E 50

--S 51 of 82
setRow!(m2,2,vector [66,77,88])
 

         +99   0    2 +
         |            |
   (10)  |66  77   88 |
         |            |
         +0   200  100+
                                                         Type: Matrix Integer
--R
--R         +99   0    2 +
--R         |            |
--R   (10)  |66  77   88 |
--R         |            |
--R         +0   200  100+
--R                                                         Type: Matrix Integer
--E 51

--S 52 of 82
r := column(m2,1)
 

   (11)  [99,66,0]
                                                         Type: Vector Integer
--R
--R   (11)  [99,66,0]
--R                                                         Type: Vector Integer
--E 52

--S 53 of 82
setColumn!(m2,2,r)
 

         +99  99   2 +
         |           |
   (12)  |66  66  88 |
         |           |
         +0   0   100+
                                                         Type: Matrix Integer
--R
--R         +99  99   2 +
--R         |           |
--R   (12)  |66  66  88 |
--R         |           |
--R         +0   0   100+
--R                                                         Type: Matrix Integer
--E 53

--S 54 of 82
nrows(m1)
 

   (13)  4
                                                        Type: PositiveInteger
--R
--R   (13)  4
--R                                                        Type: PositiveInteger
--E 54

--S 55 of 82
m5 : MATRIX INT := new(12,12,0)
 

         +0  0  0  0  0  0  0  0  0  0  0  0+
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
   (14)  |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  0|
         |                                  |
         +0  0  0  0  0  0  0  0  0  0  0  0+
                                                         Type: Matrix Integer
--R
--R         +0  0  0  0  0  0  0  0  0  0  0  0+
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R   (14)  |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         +0  0  0  0  0  0  0  0  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 55

--S 56 of 82
for i in 2..nrows(m5) repeat m5(i-1,i):= 1
 
                                                                   Type: Void
--R                                                                   Type: Void
--E 56

--S 57 of 82
m5
 

         +0  1  0  0  0  0  0  0  0  0  0  0+
         |                                  |
         |0  0  1  0  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  1  0  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  1  0  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  1  0  0  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  1  0  0  0  0  0|
   (16)  |                                  |
         |0  0  0  0  0  0  0  1  0  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  1  0  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  1  0  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  1  0|
         |                                  |
         |0  0  0  0  0  0  0  0  0  0  0  1|
         |                                  |
         +0  0  0  0  0  0  0  0  0  0  0  0+
                                                         Type: Matrix Integer
--R
--R         +0  1  0  0  0  0  0  0  0  0  0  0+
--R         |                                  |
--R         |0  0  1  0  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  1  0  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  1  0  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  1  0  0  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  1  0  0  0  0  0|
--R   (16)  |                                  |
--R         |0  0  0  0  0  0  0  1  0  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  1  0  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  1  0  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  1  0|
--R         |                                  |
--R         |0  0  0  0  0  0  0  0  0  0  0  1|
--R         |                                  |
--R         +0  0  0  0  0  0  0  0  0  0  0  0+
--R                                                         Type: Matrix Integer
--E 57

--S 58 of 82
d : MATRIX INT := diagonalMatrix([1,2,3,2,1])
 

         +1  0  0  0  0+
         |             |
         |0  2  0  0  0|
         |             |
   (17)  |0  0  3  0  0|
         |             |
         |0  0  0  2  0|
         |             |
         +0  0  0  0  1+
                                                         Type: Matrix Integer
--R
--R         +1  0  0  0  0+
--R         |             |
--R         |0  2  0  0  0|
--R         |             |
--R   (17)  |0  0  3  0  0|
--R         |             |
--R         |0  0  0  2  0|
--R         |             |
--R         +0  0  0  0  1+
--R                                                         Type: Matrix Integer
--E 58

--S 59 of 82
m6 := matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])
 

         +0   1   2   3   4 +
         |                  |
   (18)  |5   6   7   8   9 |
         |                  |
         +10  11  12  13  14+
                                                         Type: Matrix Integer
--R
--R         +0   1   2   3   4 +
--R         |                  |
--R   (18)  |5   6   7   8   9 |
--R         |                  |
--R         +10  11  12  13  14+
--R                                                         Type: Matrix Integer
--E 59

--S 60 of 82
m7 := subMatrix(m6,1,3,2,4)
 

         +1   2   3 +
         |          |
   (19)  |6   7   8 |
         |          |
         +11  12  13+
                                                         Type: Matrix Integer
--R
--R         +1   2   3 +
--R         |          |
--R   (19)  |6   7   8 |
--R         |          |
--R         +11  12  13+
--R                                                         Type: Matrix Integer
--E 60

--S 61 of 82
horizConcat(m6,m7)
 

         +0   1   2   3   4   1   2   3 +
         |                              |
   (20)  |5   6   7   8   9   6   7   8 |
         |                              |
         +10  11  12  13  14  11  12  13+
                                                         Type: Matrix Integer
--R
--R         +0   1   2   3   4   1   2   3 +
--R         |                              |
--R   (20)  |5   6   7   8   9   6   7   8 |
--R         |                              |
--R         +10  11  12  13  14  11  12  13+
--R                                                         Type: Matrix Integer
--E 61

--S 62 of 82
vertConcat(m6,subMatrix(m6,1,1,1,5))
 

         +0   1   2   3   4 +
         |                  |
         |5   6   7   8   9 |
   (21)  |                  |
         |10  11  12  13  14|
         |                  |
         +0   1   2   3   4 +
                                                         Type: Matrix Integer
--R
--R         +0   1   2   3   4 +
--R         |                  |
--R         |5   6   7   8   9 |
--R   (21)  |                  |
--R         |10  11  12  13  14|
--R         |                  |
--R         +0   1   2   3   4 +
--R                                                         Type: Matrix Integer
--E 62

--S 63 of 82
transpose(m6)
 

         +0  5  10+
         |        |
         |1  6  11|
         |        |
   (22)  |2  7  12|
         |        |
         |3  8  13|
         |        |
         +4  9  14+
                                                         Type: Matrix Integer
--R
--R         +0  5  10+
--R         |        |
--R         |1  6  11|
--R         |        |
--R   (22)  |2  7  12|
--R         |        |
--R         |3  8  13|
--R         |        |
--R         +4  9  14+
--R                                                         Type: Matrix Integer
--E 63

--S 64 of 82
setsubMatrix!(m6,1,3,transpose(subMatrix(m6,1,3,1,3)))
 

         +0   1   0  5  10+
         |                |
   (23)  |5   6   1  6  11|
         |                |
         +10  11  2  7  12+
                                                         Type: Matrix Integer
--R
--R         +0   1   0  5  10+
--R         |                |
--R   (23)  |5   6   1  6  11|
--R         |                |
--R         +10  11  2  7  12+
--R                                                         Type: Matrix Integer
--E 64

--S 65 of 82
m6
 

         +0   1   0  5  10+
         |                |
   (24)  |5   6   1  6  11|
         |                |
         +10  11  2  7  12+
                                                         Type: Matrix Integer
--R
--R         +0   1   0  5  10+
--R         |                |
--R   (24)  |5   6   1  6  11|
--R         |                |
--R         +10  11  2  7  12+
--R                                                         Type: Matrix Integer
--E 65

--S 66 of 82
m8 := matrix([[1,2],[3,4]])
 

         +1  2+
   (25)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (25)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 66

--S 67 of 82
m9 := m8
 

         +1  2+
   (26)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (26)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 67

--S 68 of 82
m10 := copy(m8)
 

         +1  2+
   (27)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (27)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 68

--S 69 of 82
m8(1,1) := 1000000
 

   (28)  1000000
                                                        Type: PositiveInteger
--R
--R   (28)  1000000
--R                                                        Type: PositiveInteger
--E 69

--S 70 of 82
m8
 

         +1000000  2+
   (29)  |          |
         +   3     4+
                                                         Type: Matrix Integer
--R
--R         +1000000  2+
--R   (29)  |          |
--R         +   3     4+
--R                                                         Type: Matrix Integer
--E 70

--S 71 of 82
m9
 

         +1000000  2+
   (30)  |          |
         +   3     4+
                                                         Type: Matrix Integer
--R
--R         +1000000  2+
--R   (30)  |          |
--R         +   3     4+
--R                                                         Type: Matrix Integer
--E 71

--S 72 of 82
m10
 

         +1  2+
   (31)  |    |
         +3  4+
                                                         Type: Matrix Integer
--R
--R         +1  2+
--R   (31)  |    |
--R         +3  4+
--R                                                         Type: Matrix Integer
--E 72

-- Input for page EigenPage
)clear all
 

--S 73 of 82
m1 : MATRIX FRAC INT := [[1,2,1],[2,1,-2],[1,-2,4]]
 

        +1   2    1 +
        |           |
   (1)  |2   1   - 2|
        |           |
        +1  - 2   4 +
                                                Type: Matrix Fraction Integer
--R
--R        +1   2    1 +
--R        |           |
--R   (1)  |2   1   - 2|
--R        |           |
--R        +1  - 2   4 +
--R                                                Type: Matrix Fraction Integer
--E 73

--S 74 of 82
leig := eigenvalues(m1)
 

                  2
   (2)  [5,%B | %B  - %B - 5]
Type: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--R
--R                  2
--I   (2)  [5,%A | %A  - %A - 5]
--RType: List Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer))
--E 74

--S 75 of 82
eigenvector(first(leig),m1)
 

         + 0 +
         |   |
         |  1|
   (3)  [|- -|]
         |  2|
         |   |
         + 1 +
                       Type: List Matrix Fraction Polynomial Fraction Integer
--R
--R         + 0 +
--R         |   |
--R         |  1|
--R   (3)  [|- -|]
--R         |  2|
--R         |   |
--R         + 1 +
--R                       Type: List Matrix Fraction Polynomial Fraction Integer
--E 75

--S 76 of 82
eigenvectors(m1)
 

   (4)
                                   + 0 +
                                   |   |
                                   |  1|
   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
                                   |  2|
                                   |   |
                                   + 1 +
                                                     +%C+
                     2                               |  |
    [eigval= (%C | %C  - %C - 5),eigmult= 1,eigvec= [|2 |]]]
                                                     |  |
                                                     +1 +
Type: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--R
--R   (4)
--R                                   + 0 +
--R                                   |   |
--R                                   |  1|
--R   [[eigval= 5,eigmult= 1,eigvec= [|- -|]],
--R                                   |  2|
--R                                   |   |
--R                                   + 1 +
--R                                                     +%C+
--R                     2                               |  |
--R    [eigval= (%C | %C  - %C - 5),eigmult= 1,eigvec= [|2 |]]]
--R                                                     |  |
--R                                                     +1 +
--RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer)
--E 76

--S 77 of 82
radicalEigenvectors(m1)
 

   (5)
                                            + +--+    +
              +--+                          |\|21  + 1|
             \|21  + 1                      |---------|
   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
                 2                          |         |
                                            |    2    |
                                            |         |
                                            +    1    +
                                              +   +--+    +
                +--+                          |- \|21  + 1|
             - \|21  + 1                      |-----------|
    [radval= -----------,radmult= 1,radvect= [|     2     |]],
                  2                           |           |
                                              |     2     |
                                              |           |
                                              +     1     +
                                    + 0 +
                                    |   |
                                    |  1|
    [radval= 5,radmult= 1,radvect= [|- -|]]]
                                    |  2|
                                    |   |
                                    + 1 +
Type: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--R
--R   (5)
--R                                            + +--+    +
--R              +--+                          |\|21  + 1|
--R             \|21  + 1                      |---------|
--R   [[radval= ---------,radmult= 1,radvect= [|    2    |]],
--R                 2                          |         |
--R                                            |    2    |
--R                                            |         |
--R                                            +    1    +
--R                                              +   +--+    +
--R                +--+                          |- \|21  + 1|
--R             - \|21  + 1                      |-----------|
--R    [radval= -----------,radmult= 1,radvect= [|     2     |]],
--R                  2                           |           |
--R                                              |     2     |
--R                                              |           |
--R                                              +     1     +
--R                                    + 0 +
--R                                    |   |
--R                                    |  1|
--R    [radval= 5,radmult= 1,radvect= [|- -|]]]
--R                                    |  2|
--R                                    |   |
--R                                    + 1 +
--RType: List Record(radval: Expression Integer,radmult: Integer,radvect: List Matrix Expression Integer)
--E 77

--S 78 of 82
eigenMatrix(m1)
 

        + +--+         +--+         +
        |\|21  + 1  - \|21  + 1     |
        |---------  -----------   0 |
        |    2           2          |
   (6)  |                           |
        |                          1|
        |    2           2       - -|
        |                          2|
        |                           |
        +    1           1        1 +
                                   Type: Union(Matrix Expression Integer,...)
--R
--R        + +--+         +--+         +
--R        |\|21  + 1  - \|21  + 1     |
--R        |---------  -----------   0 |
--R        |    2           2          |
--R   (6)  |                           |
--R        |                          1|
--R        |    2           2       - -|
--R        |                          2|
--R        |                           |
--R        +    1           1        1 +
--R                                   Type: Union(Matrix Expression Integer,...)
--E 78

--S 79 of 82
m2 : MATRIX FRAC INT := [[-5,-2],[18,7]]
 

        +- 5  - 2+
   (7)  |        |
        +18    7 +
                                                Type: Matrix Fraction Integer
--R
--R        +- 5  - 2+
--R   (7)  |        |
--R        +18    7 +
--R                                                Type: Matrix Fraction Integer
--E 79

--S 80 of 82
eigenMatrix(m2)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 80

--S 81 of 82
m3 : MATRIX FRAC INT := [[1,2],[2,1]]
 

        +1  2+
   (9)  |    |
        +2  1+
                                                Type: Matrix Fraction Integer
--R
--R        +1  2+
--R   (9)  |    |
--R        +2  1+
--R                                                Type: Matrix Fraction Integer
--E 81

--S 82 of 82
orthonormalBasis(m3)
 

          +    1 + +  1 +
          |- ----| |----|
          |   +-+| | +-+|
          |  \|2 | |\|2 |
   (10)  [|      |,|    |]
          |   1  | |  1 |
          | ---- | |----|
          |  +-+ | | +-+|
          + \|2  + +\|2 +
                                         Type: List Matrix Expression Integer
--R
--R          +    1 + +  1 +
--R          |- ----| |----|
--R          |   +-+| | +-+|
--R          |  \|2 | |\|2 |
--R   (10)  [|      |,|    |]
--R          |   1  | |  1 |
--R          | ---- | |----|
--R          |  +-+ | | +-+|
--R          + \|2  + +\|2 +
--R                                         Type: List Matrix Expression Integer
--E 82

)spool 
 
Starts dribbling to ifthenelse.output (2010/3/27, 18:26:56).
)set message test on
 
)set message auto off
 
)clear all
 

 
--S 1 of 20
i:=2
 

   (1)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2
--R                                                        Type: PositiveInteger
--E 1


--S 2 of 20
for i in 2..2 repeat
  if i>0 then output("positive") else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 2

--S 3 of 20
for i in 2..2 repeat
  if i>0 then output("positive") 
    else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 3

--S 4 of 20
for i in 2..2 repeat
  if i>0 then output("positive") 
  else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 4

--S 5 of 20
for i in 2..2 repeat
  if i>0 
  then output("positive") 
  else output("nonpositive")
 
   positive
                                                                   Type: Void
--R 
--R   positive
--R                                                                   Type: Void
--E 5

--S 6 of 20
for i in 2..2 repeat
  if i>0 
    then output("positive") 
    else output("nonpositive")
 
  Line  48: --R 
  Line  49: --R   positive
  Line  50: --R                                                                   Type: Void
  Line  51: --E 5
  Line  52: 
  Line  53: --S 6 of 20
  Line  54: for i in 2..2 repeat
  Line  55:   if i>0 
           ..A
  Error  A: (from #\A and on) Ignored from here
  Line  56:     then output("positive") 
           ....A
  Error  A: Improper syntax.
  Error  A: (from #\A up to ) Ignored.
  Line  57:     else output("nonpositive")
           ....A........................B
  Error  A: Improper syntax.
  Error  A: (from #\A up to #\B) Ignored.
  Error  B: Possibly missing a then 
  Error  B: (up to #\B) to here.
   7 error(s) parsing 
--R 
--R  Line  48: --R 
--R  Line  49: --R   positive
--R  Line  50: --R                                                                   Type: Void
--R  Line  51: --E 5
--R  Line  52: 
--R  Line  53: --S 6 of 20
--R  Line  54: for i in 2..2 repeat
--R  Line  55:   if i>0 
--R           ..A
--R  Error  A: (from #\A and on) Ignored from here
--R  Line  56:     then output("positive") 
--R           ....A
--R  Error  A: Improper syntax.
--R  Error  A: (from #\A up to ) Ignored.
--R  Line  57:     else output("nonpositive")
--R           ....A........................B
--R  Error  A: Improper syntax.
--R  Error  A: (from #\A up to #\B) Ignored.
--R  Error  B: Possibly missing a then 
--R  Error  B: (up to #\B) to here.
--R   7 error(s) parsing 
--E 6

--S 7 of 20
i:=2
 

   (6)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  2
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 20
for i in 2..2 repeat
  if i>0 then
    output(i)
    output("positive") 
  else
    output(i)
    else output("nonpositive")
 
  Line  84: --R 
  Line  85: --R
  Line  86: --R   (6)  2
  Line  87: --R                                                        Type: PositiveInteger
  Line  88: --E 7
  Line  89: 
  Line  90: --S 8 of 20
  Line  91: for i in 2..2 repeat
  Line  92:   if i>0 then
  Line  93:     output(i)
  Line  94:     output("positive") 
  Line  95:   else
  Line  96:     output(i)
  Line  97:     else output("nonpositive")
           ....A
  Error  A: (from #\A up to ) Ignored.
  Error  A: Improper syntax.
   2 error(s) parsing 
--R 
--R  Line  84: --R 
--R  Line  85: --R
--R  Line  86: --R   (6)  2
--R  Line  87: --R                                                        Type: PositiveInteger
--R  Line  88: --E 7
--R  Line  89: 
--R  Line  90: --S 8 of 20
--R  Line  91: for i in 2..2 repeat
--R  Line  92:   if i>0 then
--R  Line  93:     output(i)
--R  Line  94:     output("positive") 
--R  Line  95:   else
--R  Line  96:     output(i)
--R  Line  97:     else output("nonpositive")
--R           ....A
--R  Error  A: (from #\A up to ) Ignored.
--R  Error  A: Improper syntax.
--R   2 error(s) parsing 
--E 8

--S 9 of 20
i:=1.5
 

   (7)  1.5
                                                                  Type: Float
--R 
--R
--R   (7)  1.5
--R                                                                  Type: Float
--E 9

--S 10 of 20
a:=
  if i > 0 then
    j:=sin(i*pi())
    exp(j+1/j)
  else
    j:=cos(i*0.5*pi())
    log(abs(j)**5+1)
 

   (8)  0.1353352832 3661269189
                                                                  Type: Float
--R 
--R
--R   (8)  0.1353352832 3661269189
--R                                                                  Type: Float
--E 10


--S 11 of 20
test: (INT,INT) -> List(INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 20
test(a,b) ==
  x:=0; y:=0
  if (a rem b = 0) and b < 0 then
    x := 1
    y := 1
  [x,y]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 20
4 rem -2
 

   (11)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (11)  0
--R                                                     Type: NonNegativeInteger
--E 13

--S 14 of 20
test(4,-2)
 
   Compiling function test with type (Integer,Integer) -> List Integer 

   (12)  [1,1]
                                                           Type: List Integer
--R 
--R   Compiling function test with type (Integer,Integer) -> List Integer 
--R
--R   (12)  [1,1]
--R                                                           Type: List Integer
--E 14


--S 15 of 20
4 rem -3
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 20
test(4,-3)
 

   (14)  [0,0]
                                                           Type: List Integer
--R 
--R
--R   (14)  [0,0]
--R                                                           Type: List Integer
--E 16


--S 17 of 20
4 rem 2
 

   (15)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (15)  0
--R                                                     Type: NonNegativeInteger
--E 17

--S 18 of 20
test(4,2)
 

   (16)  [0,0]
                                                           Type: List Integer
--R 
--R
--R   (16)  [0,0]
--R                                                           Type: List Integer
--E 18


--S 19 of 20
test1: (INT,INT) -> List(INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 20
test1(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then x := 1 ; y := 1
  [x,y]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

)spool 
 
Starts dribbling to schaum16.output (2010/3/27, 18:37:59).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 45
aa:=integrate(1/(x*(x^n+a^n)),x)
 

                n log(x)    n
        - log(%e         + a ) + n log(x)
   (1)  ---------------------------------
                          n
                       n a
                                          Type: Union(Expression Integer,...)
--R
--R                n log(x)    n
--R        - log(%e         + a ) + n log(x)
--R   (1)  ---------------------------------
--R                          n
--R                       n a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 45
bb:=1/(n*a^n)*log(x^n/(x^n+a^n))
 

                n
               x
        log(-------)
             n    n
            x  + a
   (2)  ------------
               n
            n a
                                                     Type: Expression Integer
--R
--R                n
--R               x
--R        log(-------)
--R             n    n
--R            x  + a
--R   (2)  ------------
--R               n
--R            n a
--R                                                     Type: Expression Integer
--E

--S 3 of 45
cc:=aa-bb
 

                                         n
                n log(x)    n           x
        - log(%e         + a ) - log(-------) + n log(x)
                                      n    n
                                     x  + a
   (3)  ------------------------------------------------
                                 n
                              n a
                                                     Type: Expression Integer
--R
--R                                         n
--R                n log(x)    n           x
--R        - log(%e         + a ) - log(-------) + n log(x)
--R                                      n    n
--R                                     x  + a
--R   (3)  ------------------------------------------------
--R                                 n
--R                              n a
--R                                                     Type: Expression Integer
--E

--S 4 of 45
dd:=expandLog cc
 

                n log(x)    n         n    n         n
        - log(%e         + a ) + log(x  + a ) - log(x ) + n log(x)
   (4)  ----------------------------------------------------------
                                      n
                                   n a
                                                     Type: Expression Integer
--R
--R                n log(x)    n         n    n         n
--R        - log(%e         + a ) + log(x  + a ) - log(x ) + n log(x)
--R   (4)  ----------------------------------------------------------
--R                                      n
--R                                   n a
--R                                                     Type: Expression Integer
--E

--S 5 of 45      14:325 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 8 of 45
aa:=integrate(x^(n-1)/(x^n+a^n),x)
 

              n log(x)    n
        log(%e         + a )
   (1)  --------------------
                  n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              n log(x)    n
--R        log(%e         + a )
--R   (1)  --------------------
--R                  n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 45
bb:=1/n*log(x^n+a^n)
 

             n    n
        log(x  + a )
   (2)  ------------
              n
                                                     Type: Expression Integer
--R
--R             n    n
--R        log(x  + a )
--R   (2)  ------------
--R              n
--R                                                     Type: Expression Integer
--E

--S 10 of 45
cc:=aa-bb
 

              n log(x)    n         n    n
        log(%e         + a ) - log(x  + a )
   (3)  -----------------------------------
                         n
                                                     Type: Expression Integer
--R
--R              n log(x)    n         n    n
--R        log(%e         + a ) - log(x  + a )
--R   (3)  -----------------------------------
--R                         n
--R                                                     Type: Expression Integer
--E

--S 11 of 45
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12 of 45     14:326 Schaums and Axiom agree
dd:=explog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 45     14:327 Axiom cannot compute this integral
aa:=integrate(x^m/(x^n+a^n)^r,x)
 

           x       m
         ++      %O
   (1)   |   ----------- d%O
        ++     n     n r
             (a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       m
--I         ++      %J
--I   (1)   |   ----------- d%J
--R        ++     n     n r
--I             (a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 14 of 45     14:328 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(x^n+a^n)^r),x)
 

           x
         ++         1
   (1)   |   -------------- d%O
        ++     m  n     n r
             %O (a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++         1
--I   (1)   |   -------------- d%J
--R        ++     m  n     n r
--I             %J (a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 15 of 45
aa:=integrate(1/(x*sqrt(x^n+a^n)),x)
 

   (1)
              +---------------+                      +--+
            n |  n log(x)    n       n log(x)     n  | n
        - 2a \|%e         + a   + (%e         + 2a )\|a
    log(-------------------------------------------------)
                              n log(x)
                            %e
   [------------------------------------------------------,
                              +--+
                              | n
                            n\|a
             +----+ +---------------+
             |   n  |  n log(x)    n
            \|- a  \|%e         + a
      2atan(-------------------------)
                         n
                        a
    - --------------------------------]
                    +----+
                    |   n
                  n\|- a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R              +---------------+                      +--+
--R            n |  n log(x)    n       n log(x)     n  | n
--R        - 2a \|%e         + a   + (%e         + 2a )\|a
--R    log(-------------------------------------------------)
--R                              n log(x)
--R                            %e
--R   [------------------------------------------------------,
--R                              +--+
--R                              | n
--R                            n\|a
--R             +----+ +---------------+
--R             |   n  |  n log(x)    n
--R            \|- a  \|%e         + a
--R      2atan(-------------------------)
--R                         n
--R                        a
--R    - --------------------------------]
--R                    +----+
--R                    |   n
--R                  n\|- a
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 16 of 45
bb:=1/(n*sqrt(a^n))*log((sqrt(x^n+a^n)-sqrt(a^n))/(sqrt(x^n+a^n)+sqrt(a^n)))
 

             +-------+    +--+
             | n    n     | n
            \|x  + a   - \|a
        log(------------------)
             +-------+    +--+
             | n    n     | n
            \|x  + a   + \|a
   (2)  -----------------------
                   +--+
                   | n
                 n\|a
                                                     Type: Expression Integer
--R
--R             +-------+    +--+
--R             | n    n     | n
--R            \|x  + a   - \|a
--R        log(------------------)
--R             +-------+    +--+
--R             | n    n     | n
--R            \|x  + a   + \|a
--R   (2)  -----------------------
--R                   +--+
--R                   | n
--R                 n\|a
--R                                                     Type: Expression Integer
--E

--S 17 of 45
cc1:=aa.1-bb
 

   (3)
                 +---------------+                      +--+
               n |  n log(x)    n       n log(x)     n  | n
           - 2a \|%e         + a   + (%e         + 2a )\|a
       log(-------------------------------------------------)
                                 n log(x)
                               %e
     + 
              +-------+    +--+
              | n    n     | n
             \|x  + a   - \|a
       - log(------------------)
              +-------+    +--+
              | n    n     | n
             \|x  + a   + \|a
  /
       +--+
       | n
     n\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 +---------------+                      +--+
--R               n |  n log(x)    n       n log(x)     n  | n
--R           - 2a \|%e         + a   + (%e         + 2a )\|a
--R       log(-------------------------------------------------)
--R                                 n log(x)
--R                               %e
--R     + 
--R              +-------+    +--+
--R              | n    n     | n
--R             \|x  + a   - \|a
--R       - log(------------------)
--R              +-------+    +--+
--R              | n    n     | n
--R             \|x  + a   + \|a
--R  /
--R       +--+
--R       | n
--R     n\|a
--R                                                     Type: Expression Integer
--E

--S 18 of 45
dd1:=expandLog cc1
 

   (4)
               +---------------+                        +--+
             n |  n log(x)    n         n log(x)     n  | n
       log(2a \|%e         + a   + (- %e         - 2a )\|a  )
     + 
            +-------+    +--+         +-------+    +--+
            | n    n     | n          | n    n     | n
       log(\|x  + a   + \|a  ) - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
  /
       +--+
       | n
     n\|a
                                                     Type: Expression Integer
--R
--R   (4)
--R               +---------------+                        +--+
--R             n |  n log(x)    n         n log(x)     n  | n
--R       log(2a \|%e         + a   + (- %e         - 2a )\|a  )
--R     + 
--R            +-------+    +--+         +-------+    +--+
--R            | n    n     | n          | n    n     | n
--R       log(\|x  + a   + \|a  ) - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
--R  /
--R       +--+
--R       | n
--R     n\|a
--R                                                     Type: Expression Integer
--E

--S 19 of 45
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (5)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (5)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20 of 45
ee1:=explog dd1
 

   (6)
               +-------+                +--+         +-------+    +--+
             n | n    n        n     n  | n          | n    n     | n
       log(2a \|x  + a   + (- x  - 2a )\|a  ) + log(\|x  + a   + \|a  )
     + 
              +-------+    +--+
              | n    n     | n
       - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
  /
       +--+
       | n
     n\|a
                                                     Type: Expression Integer
--R
--R   (6)
--R               +-------+                +--+         +-------+    +--+
--R             n | n    n        n     n  | n          | n    n     | n
--R       log(2a \|x  + a   + (- x  - 2a )\|a  ) + log(\|x  + a   + \|a  )
--R     + 
--R              +-------+    +--+
--R              | n    n     | n
--R       - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
--R  /
--R       +--+
--R       | n
--R     n\|a
--R                                                     Type: Expression Integer
--E

--S 21 of 45
ff1:=complexNormalize ee1
 

        n log(a) + 4log(- 1)
   (7)  --------------------
              +----------+
              |  n log(a)
           2n\|%e
                                                     Type: Expression Integer
--R
--R        n log(a) + 4log(- 1)
--R   (7)  --------------------
--R              +----------+
--R              |  n log(a)
--R           2n\|%e
--R                                                     Type: Expression Integer
--E

--S 22 of 45     14:329 Schaums and Axiom differ by a constant
gg1:=explog ff1
 

        n log(a) + 4log(- 1)
   (8)  --------------------
                  +--+
                  | n
               2n\|a
                                                     Type: Expression Integer
--R
--R        n log(a) + 4log(- 1)
--R   (8)  --------------------
--R                  +--+
--R                  | n
--R               2n\|a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 23 of 45
aa:=integrate(1/(x*(x^n-a^n)),x)
 

              n log(x)    n
        log(%e         - a ) - n log(x)
   (1)  -------------------------------
                         n
                      n a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              n log(x)    n
--R        log(%e         - a ) - n log(x)
--R   (1)  -------------------------------
--R                         n
--R                      n a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 45
bb:=1/(n*a^n)*log((x^n-a^n)/x^n)
 

             n    n
            x  - a
        log(-------)
                n
               x
   (2)  ------------
               n
            n a
                                                     Type: Expression Integer
--R
--R             n    n
--R            x  - a
--R        log(-------)
--R                n
--R               x
--R   (2)  ------------
--R               n
--R            n a
--R                                                     Type: Expression Integer
--E

--S 25 of 45
cc:=aa-bb
 

                                    n    n
              n log(x)    n        x  - a
        log(%e         - a ) - log(-------) - n log(x)
                                       n
                                      x
   (3)  ----------------------------------------------
                                n
                             n a
                                                     Type: Expression Integer
--R
--R                                    n    n
--R              n log(x)    n        x  - a
--R        log(%e         - a ) - log(-------) - n log(x)
--R                                       n
--R                                      x
--R   (3)  ----------------------------------------------
--R                                n
--R                             n a
--R                                                     Type: Expression Integer
--E

--S 26 of 45
dd:=expandLog cc
 

              n log(x)    n         n         n    n
        log(%e         - a ) + log(x ) - log(x  - a ) - n log(x)
   (4)  --------------------------------------------------------
                                     n
                                  n a
                                                     Type: Expression Integer
--R
--R              n log(x)    n         n         n    n
--R        log(%e         - a ) + log(x ) - log(x  - a ) - n log(x)
--R   (4)  --------------------------------------------------------
--R                                     n
--R                                  n a
--R                                                     Type: Expression Integer
--E

--S 27 of 45
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (5)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (5)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 28 of 45
ee:=explog dd
 

             n
        log(x ) - n log(x)
   (6)  ------------------
                  n
               n a
                                                     Type: Expression Integer
--R
--R             n
--R        log(x ) - n log(x)
--R   (6)  ------------------
--R                  n
--R               n a
--R                                                     Type: Expression Integer
--E

--S 29 of 45
logpow:=rule(log(a^n) == n*log(a))
 

             n
   (7)  log(a ) == n log(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R             n
--R   (7)  log(a ) == n log(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 30 of 45     14:330 Schaums and Axiom agree
ff:=logpow ee
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 31 of 45
aa:=integrate(x^(n-1)/(x^n-a^n),x)
 

              n log(x)    n
        log(%e         - a )
   (1)  --------------------
                  n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              n log(x)    n
--R        log(%e         - a )
--R   (1)  --------------------
--R                  n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 32 of 45
bb:=1/n*log(x^n-a^n)
 

             n    n
        log(x  - a )
   (2)  ------------
              n
                                                     Type: Expression Integer
--R
--R             n    n
--R        log(x  - a )
--R   (2)  ------------
--R              n
--R                                                     Type: Expression Integer
--E

--S 33 of 45
cc:=aa-bb
 

              n log(x)    n         n    n
        log(%e         - a ) - log(x  - a )
   (3)  -----------------------------------
                         n
                                                     Type: Expression Integer
--R
--R              n log(x)    n         n    n
--R        log(%e         - a ) - log(x  - a )
--R   (3)  -----------------------------------
--R                         n
--R                                                     Type: Expression Integer
--E

--S 34 of 45
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35 of 45     14:331 Schaums and Axiom agree
dd:=explog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 36 of 45     14:332 Axiom cannot compute this integral
aa:=integrate(x^m/(x^n-a^n)^r,x)
 

           x        m
         ++       %O
   (1)   |   ------------- d%O
        ++       n     n r
             (- a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x        m
--I         ++       %J
--I   (1)   |   ------------- d%J
--R        ++       n     n r
--I             (- a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 37 of 45     14:333 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(x^n-a^n)^r),x)
 

           x
         ++          1
   (1)   |   ---------------- d%O
        ++     m    n     n r
             %O (- a  + %O )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++          1
--I   (1)   |   ---------------- d%J
--R        ++     m    n     n r
--I             %J (- a  + %J )
--R                                          Type: Union(Expression Integer,...)
--E
)clear all
 

--S 38 of 45
aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
 

   (1)
            +---------------+                      +----+
          n |  n log(x)    n       n log(x)     n  |   n
        2a \|%e         - a   + (%e         - 2a )\|- a
    log(-------------------------------------------------)
                              n log(x)
                            %e
   [------------------------------------------------------,
                             +----+
                             |   n
                           n\|- a
           +--+ +---------------+
           | n  |  n log(x)    n
          \|a  \|%e         - a
    2atan(-----------------------)
                      n
                     a
    ------------------------------]
                  +--+
                  | n
                n\|a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R            +---------------+                      +----+
--R          n |  n log(x)    n       n log(x)     n  |   n
--R        2a \|%e         - a   + (%e         - 2a )\|- a
--R    log(-------------------------------------------------)
--R                              n log(x)
--R                            %e
--R   [------------------------------------------------------,
--R                             +----+
--R                             |   n
--R                           n\|- a
--R           +--+ +---------------+
--R           | n  |  n log(x)    n
--R          \|a  \|%e         - a
--R    2atan(-----------------------)
--R                      n
--R                     a
--R    ------------------------------]
--R                  +--+
--R                  | n
--R                n\|a
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 39 of 45
bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n))
 

               +--+
               | n
               |a
        2acos( |-- )
               | n
              \|x
   (2)  ------------
             +--+
             | n
           n\|a
                                                     Type: Expression Integer
--R
--R               +--+
--R               | n
--R               |a
--R        2acos( |-- )
--R               | n
--R              \|x
--R   (2)  ------------
--R             +--+
--R             | n
--R           n\|a
--R                                                     Type: Expression Integer
--E

--S 40 of 45
cc1:=aa.1-bb
 

   (3)
                    +---------------+                      +----+
        +--+      n |  n log(x)    n       n log(x)     n  |   n
        | n     2a \|%e         - a   + (%e         - 2a )\|- a
       \|a  log(-------------------------------------------------)
                                      n log(x)
                                    %e
     + 
                       +--+
           +----+      | n
           |   n       |a
       - 2\|- a  acos( |-- )
                       | n
                      \|x
  /
       +----+ +--+
       |   n  | n
     n\|- a  \|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                    +---------------+                      +----+
--R        +--+      n |  n log(x)    n       n log(x)     n  |   n
--R        | n     2a \|%e         - a   + (%e         - 2a )\|- a
--R       \|a  log(-------------------------------------------------)
--R                                      n log(x)
--R                                    %e
--R     + 
--R                       +--+
--R           +----+      | n
--R           |   n       |a
--R       - 2\|- a  acos( |-- )
--R                       | n
--R                      \|x
--R  /
--R       +----+ +--+
--R       |   n  | n
--R     n\|- a  \|a
--R                                                     Type: Expression Integer
--E

--S 41 of 45     14:334 Axiom cannot simplify this expression
cc2:=aa.2-bb
 

               +--+ +---------------+           +--+
               | n  |  n log(x)    n            | n
              \|a  \|%e         - a             |a
        2atan(-----------------------) - 2acos( |-- )
                          n                     | n
                         a                     \|x
   (4)  ---------------------------------------------
                              +--+
                              | n
                            n\|a
                                                     Type: Expression Integer
--R
--R               +--+ +---------------+           +--+
--R               | n  |  n log(x)    n            | n
--R              \|a  \|%e         - a             |a
--R        2atan(-----------------------) - 2acos( |-- )
--R                          n                     | n
--R                         a                     \|x
--R   (4)  ---------------------------------------------
--R                              +--+
--R                              | n
--R                            n\|a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 42 of 45     14:335 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x)
 

           x     p - 1
         ++    %O
   (1)   |   ---------- d%O
        ++    2m     2m
             a   + %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x     p - 1
--I         ++    %J
--I   (1)   |   ---------- d%J
--R        ++    2m     2m
--I             a   + %J
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 43 of 45     14:336 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x)
 

           x       p - 1
         ++      %O
   (1)   |   - ---------- d%O
        ++      2m     2m
               a   - %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       p - 1
--I         ++      %J
--I   (1)   |   - ---------- d%J
--R        ++      2m     2m
--I               a   - %J
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 44 of 45     14:337 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x)
 

           x         p - 1
         ++        %O
   (1)   |   ------------------ d%O
        ++    2m + 1     2m + 1
             a       + %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x         p - 1
--I         ++        %J
--I   (1)   |   ------------------ d%J
--R        ++    2m + 1     2m + 1
--I             a       + %J
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 45 of 45     14:338 Axiom cannot compute this integral
aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x)
 

           x           p - 1
         ++          %O
   (1)   |   - ------------------ d%O
        ++      2m + 1     2m + 1
               a       - %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           p - 1
--I         ++          %J
--I   (1)   |   - ------------------ d%J
--R        ++      2m + 1     2m + 1
--I               a       - %J
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to exdiff.output (2010/3/27, 18:25:37).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 10
differentiate(sin(x) * exp(x**2),x)
 

              2                  2
             x                  x
   (1)  2x %e  sin(x) + cos(x)%e
                                                     Type: Expression Integer
--R 
--R
--R              2                  2
--R             x                  x
--R   (1)  2x %e  sin(x) + cos(x)%e
--R                                                     Type: Expression Integer
--E 1

-- Input for page ExDiffSeveralVariables
)clear all
 

--S 2 of 10
differentiate(sin(x) * tan(y)/(x**2 + y**2),x)
 

                         2    2
        (- 2x sin(x) + (y  + x )cos(x))tan(y)
   (1)  -------------------------------------
                    4     2 2    4
                   y  + 2x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                         2    2
--R        (- 2x sin(x) + (y  + x )cos(x))tan(y)
--R   (1)  -------------------------------------
--R                    4     2 2    4
--R                   y  + 2x y  + x
--R                                                     Type: Expression Integer
--E 2

--S 3 of 10
differentiate(sin(x) * tan(y)/(x**2 + y**2),y)
 

          2    2             2                       2    2
        (y  + x )sin(x)tan(y)  - 2y sin(x)tan(y) + (y  + x )sin(x)
   (2)  ----------------------------------------------------------
                               4     2 2    4
                              y  + 2x y  + x
                                                     Type: Expression Integer
--R 
--R
--R          2    2             2                       2    2
--R        (y  + x )sin(x)tan(y)  - 2y sin(x)tan(y) + (y  + x )sin(x)
--R   (2)  ----------------------------------------------------------
--R                               4     2 2    4
--R                              y  + 2x y  + x
--R                                                     Type: Expression Integer
--E 3

-- Input for page ExDiffMultipleI
)clear all
 

--S 4 of 10
differentiate(sin(x)/(x**2 + y**2),[x,y])
 

                           3     2
        8x y sin(x) + (- 2y  - 2x y)cos(x)
   (1)  ----------------------------------
               6     2 4     4 2    6
              y  + 3x y  + 3x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                           3     2
--R        8x y sin(x) + (- 2y  - 2x y)cos(x)
--R   (1)  ----------------------------------
--R               6     2 4     4 2    6
--R              y  + 3x y  + 3x y  + x
--R                                                     Type: Expression Integer
--E 4

--S 5 of 10
differentiate(sin(x)/(x**2 + y**2),[x,y,y])
 

                2     3             4     2 2     4
        (- 40x y  + 8x )sin(x) + (6y  + 4x y  - 2x )cos(x)
   (2)  --------------------------------------------------
                   8     2 6     4 4     6 2    8
                  y  + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                2     3             4     2 2     4
--R        (- 40x y  + 8x )sin(x) + (6y  + 4x y  - 2x )cos(x)
--R   (2)  --------------------------------------------------
--R                   8     2 6     4 4     6 2    8
--R                  y  + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E 5


-- Input for page ExDiffMultipleII
)clear all
 

--S 6 of 10
differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])
 

                    4      3
            (- 84x y  + 24x y)sin(z)
   (1)  --------------------------------
         12     2 9     4 6     6 3    8
        y   + 4x y  + 6x y  + 4x y  + x
                                                     Type: Expression Integer
--R 
--R
--R                    4      3
--R            (- 84x y  + 24x y)sin(z)
--R   (1)  --------------------------------
--R         12     2 9     4 6     6 3    8
--R        y   + 4x y  + 6x y  + 4x y  + x
--R                                                     Type: Expression Integer
--E 6

-- Input for page ExDiffHigherOrder
)clear all
 

--S 7 of 10
differentiate(exp(x**2),x,4)
 

                             2
            4      2        x
   (1)  (16x  + 48x  + 12)%e
                                                     Type: Expression Integer
--R 
--R
--R                             2
--R            4      2        x
--R   (1)  (16x  + 48x  + 12)%e
--R                                                     Type: Expression Integer
--E 7

-- Input for page ExDiffFormalIntegral
)clear all
 
 
--S 8 of 10
f := integrate(sqrt(1 + t**3),t)
 

           t  +-------+
         ++   |  3
   (1)   |   \|%M  + 1 d%M
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           t  +-------+
--R         ++   |  3
--R   (1)   |   \|%M  + 1 d%M
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 10
differentiate(f,t)
 

         +------+
         | 3
   (2)  \|t  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +------+
--R         | 3
--R   (2)  \|t  + 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 10
differentiate(f * t**2,t)
 

             t  +-------+          +------+
           ++   |  3             2 | 3
   (3)  2t |   \|%M  + 1 d%M  + t \|t  + 1
          ++
                                                     Type: Expression Integer
--R 
--R
--R             t  +-------+          +------+
--R           ++   |  3             2 | 3
--R   (3)  2t |   \|%M  + 1 d%M  + t \|t  + 1
--R          ++
--R                                                     Type: Expression Integer
--E 10
)spool
 
Starts dribbling to danzwill.output (2010/3/27, 18:24:49).
)set message test on
 
)set message auto off
 
)clear all
 
)set break resume
 

--S 1 of 17
i1 := integrate( sin(x), x)
 

   (1)  - cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  - cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 1

--i2 := integrate( sqrt(tan(x)), x)

--S 2 of 17
i3 := integrate( x/(x**3-1),x)
 

                                                                 +-+
           +-+     2              +-+                   (2x + 1)\|3
        - \|3 log(x  + x + 1) + 2\|3 log(x - 1) + 6atan(------------)
                                                              3
   (2)  -------------------------------------------------------------
                                      +-+
                                    6\|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                                 +-+
--R           +-+     2              +-+                   (2x + 1)\|3
--R        - \|3 log(x  + x + 1) + 2\|3 log(x - 1) + 6atan(------------)
--R                                                              3
--R   (2)  -------------------------------------------------------------
--R                                      +-+
--R                                    6\|3
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 17
i4 := integrate( x/sin(x)**2, x)
 

                    sin(x)                     2
        sin(x)log(----------) - sin(x)log(----------) - x cos(x)
                  cos(x) + 1              cos(x) + 1
   (3)  --------------------------------------------------------
                                 sin(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    sin(x)                     2
--R        sin(x)log(----------) - sin(x)log(----------) - x cos(x)
--R                  cos(x) + 1              cos(x) + 1
--R   (3)  --------------------------------------------------------
--R                                 sin(x)
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 17
i5 := integrate( log(x)/sqrt(x+1), x)
 

              +-----+              +-----+                      +-----+
   (4)  2log(\|x + 1  + 1) - 2log(\|x + 1  - 1) + (2log(x) - 4)\|x + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              +-----+              +-----+                      +-----+
--R   (4)  2log(\|x + 1  + 1) - 2log(\|x + 1  - 1) + (2log(x) - 4)\|x + 1
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 17
i6 := integrate( exp(-a*x**2), x)
 

           x       2
         ++    - %N a
   (5)   |   %e      d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x       2
--R         ++    - %N a
--R   (5)   |   %e      d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 17
i7 := integrate( x/(log(x))**3, x)
 

               2                2          2
        4log(x) Ei(2log(x)) - 2x log(x) - x
   (6)  ------------------------------------
                             2
                      2log(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2                2          2
--R        4log(x) Ei(2log(x)) - 2x log(x) - x
--R   (6)  ------------------------------------
--R                             2
--R                      2log(x)
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 17
i8 := integrate( x/(sqrt(1+x)+sqrt(1-x)),x)
 

                +-----+             +-------+
        (x + 1)\|x + 1  + (- x + 1)\|- x + 1
   (7)  -------------------------------------
                          3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +-----+             +-------+
--R        (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (7)  -------------------------------------
--R                          3
--R                                          Type: Union(Expression Integer,...)
--E 7

--S 8 of 17
i9 := integrate( 1/(2+cos(x)),x)
 

                +-+
               \|3 sin(x)
        2atan(-----------)
              3cos(x) + 3
   (8)  ------------------
                +-+
               \|3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +-+
--R               \|3 sin(x)
--R        2atan(-----------)
--R              3cos(x) + 3
--R   (8)  ------------------
--R                +-+
--R               \|3
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 17
i10:= integrate( sin(x)/x**2, x)
 

           x
         ++  sin(%N)
   (9)   |   ------- d%N
        ++       2
               %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++  sin(%N)
--R   (9)   |   ------- d%N
--R        ++       2
--R               %N
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 17
d1:= integrate( 1/(2+cos(x)),x=0..4*%pi)
 

   (10)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (10)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 10

)set mes test off
 
 
--S 11 of 17
d2:= integrate( sin(x)/x,x=%minusInfinity..%plusInfinity)
 
 
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 11

)set mes test on
 
 
--S 12 of 17
d3:= integrate( x**2/(1+x**3),x=0..%plusInfinity)
 

   (11)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (11)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 12

--S 13 of 17
d4:= integrate( exp(-x)/sqrt(x),x=0..%plusInfinity)
 

          _ 1
   (12)  | (-)
            2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          _ 1
--R   (12)  | (-)
--R            2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 13

--S 14 of 17
d5:= integrate( exp(-x**2)*log(x)**2,x=0..%plusInfinity)
 

          _ 1             1     _ 1         1 2
         | (-)polygamma(1,-) + | (-)digamma(-)
            2             2       2         2
   (13)  --------------------------------------
                            8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          _ 1             1     _ 1         1 2
--R         | (-)polygamma(1,-) + | (-)digamma(-)
--R            2             2       2         2
--R   (13)  --------------------------------------
--R                            8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 14

--S 15 of 17
d6:= integrate( exp(-x)*log(x)**2*x**3,x=1..%plusInfinity)
 

   (14)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (14)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 15

--S 16 of 17
d7:= integrate( exp(-x)*x**(1/3),x=1..%plusInfinity)
 

   (15)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (15)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 16

--S 17 of 17
d8:= integrate( exp(-x)*x**2/(1-exp(-2*x)),x=0..%plusInfinity)
 

   (16)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (16)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 17
)spool
 
Starts dribbling to mset2.output (2010/3/27, 18:30:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10]
 

   (1)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (1)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 1

--S 2 of 12
insert!(3,s)
 

   (2)  {1,2: 2,4: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (2)  {1,2: 2,4: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 2

--S 3 of 12
remove!(3,s,1); s
 

   (3)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (3)  {1,2: 2,3: 3,4: 4,2: 5,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 3

--S 4 of 12
remove!(5,s); s
 

   (4)  {1,2: 2,3: 3,4: 4,6,7,10}
                                               Type: Multiset PositiveInteger
--R 
--R
--R   (4)  {1,2: 2,3: 3,4: 4,6,7,10}
--R                                               Type: Multiset PositiveInteger
--E 4

--S 5 of 12
count(5,s)
 

   (5)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (5)  0
--R                                                     Type: NonNegativeInteger
--E 5

--S 6 of 12
t := multiset [2,2,2,-9]
 

   (6)  {3: 2,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (6)  {3: 2,- 9}
--R                                                       Type: Multiset Integer
--E 6

--S 7 of 12
U := union(s,t)
 

   (7)  {1,5: 2,3: 3,4: 4,6,7,10,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (7)  {1,5: 2,3: 3,4: 4,6,7,10,- 9}
--R                                                       Type: Multiset Integer
--E 7

--S 8 of 12
I := intersect(s,t)
 

   (8)  {5: 2}
                                                       Type: Multiset Integer
--R 
--R
--R   (8)  {5: 2}
--R                                                       Type: Multiset Integer
--E 8

--S 9 of 12
difference(s,t)
 

   (9)  {1,3: 3,4: 4,6,7,10}
                                                       Type: Multiset Integer
--R 
--R
--R   (9)  {1,3: 3,4: 4,6,7,10}
--R                                                       Type: Multiset Integer
--E 9

--S 10 of 12
S := symmetricDifference(s,t)
 

   (10)  {1,3: 3,4: 4,6,7,10,- 9}
                                                       Type: Multiset Integer
--R 
--R
--R   (10)  {1,3: 3,4: 4,6,7,10,- 9}
--R                                                       Type: Multiset Integer
--E 10

--S 11 of 12
(U = union(S,I))@Boolean
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 12
t1 := multiset [1,2,2,3]; [t1 < t, t1 < s, t < s, t1 <= s]
 

   (12)  [false,true,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (12)  [false,true,false,true]
--R                                                           Type: List Boolean
--E 12
)spool 
 
Starts dribbling to schaum13.output (2010/3/27, 18:37:42).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 131
aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 2 of 131
bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)+2*a*x+b)
 

                  +--------------+
              +-+ |   2
        log(2\|a \|a x  + b x + c  + 2a x + b)
   (2)  --------------------------------------
                          +-+
                         \|a
                                                     Type: Expression Integer
--R
--R                  +--------------+
--R              +-+ |   2
--R        log(2\|a \|a x  + b x + c  + 2a x + b)
--R   (2)  --------------------------------------
--R                          +-+
--R                         \|a
--R                                                     Type: Expression Integer
--E

--S 3 of 131
bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c))
 

                  2a x + b
          asin(--------------)
                +-----------+
                |          2
               \|- 4a c + b
   (3)  - --------------------
                  +---+
                 \|- a
                                                     Type: Expression Integer
--R
--R                  2a x + b
--R          asin(--------------)
--R                +-----------+
--R                |          2
--R               \|- 4a c + b
--R   (3)  - --------------------
--R                  +---+
--R                 \|- a
--R                                                     Type: Expression Integer
--E

--S 4 of 131
bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2))
 

                2a x + b
        asinh(------------)
               +---------+
               |        2
              \|4a c - b
   (4)  -------------------
                 +-+
                \|a
                                                     Type: Expression Integer
--R
--R                2a x + b
--R        asinh(------------)
--R               +---------+
--R               |        2
--R              \|4a c - b
--R   (4)  -------------------
--R                 +-+
--R                \|a
--R                                                     Type: Expression Integer
--E

--S 5 of 131
cc1:=bb1-aa.1
 

   (5)
                 +--------------+
             +-+ |   2
       log(2\|a \|a x  + b x + c  + 2a x + b)
     + 
       -
          log
                                    +--------------+
                    +-+ +-+         |   2                   +-+
                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
               + 
                        2             +-+
                 (- 2a x  - b x - 2c)\|a
            /
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
  /
      +-+
     \|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                 +--------------+
--R             +-+ |   2
--R       log(2\|a \|a x  + b x + c  + 2a x + b)
--R     + 
--R       -
--R          log
--R                                    +--------------+
--R                    +-+ +-+         |   2                   +-+
--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R               + 
--R                        2             +-+
--R                 (- 2a x  - b x - 2c)\|a
--R            /
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R  /
--R      +-+
--R     \|a
--R                                                     Type: Expression Integer
--E

--S 6 of 131
cc2:=bb1-aa.2
 

   (6)
                       +--------------+
        +---+      +-+ |   2
       \|- a log(2\|a \|a x  + b x + c  + 2a x + b)
     + 
                          +--------------+
                    +---+ |   2               +---+ +-+
           +-+     \|- a \|a x  + b x + c  - \|- a \|c
       - 2\|a atan(------------------------------------)
                                    a x
  /
      +---+ +-+
     \|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R        +---+      +-+ |   2
--R       \|- a log(2\|a \|a x  + b x + c  + 2a x + b)
--R     + 
--R                          +--------------+
--R                    +---+ |   2               +---+ +-+
--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c
--R       - 2\|a atan(------------------------------------)
--R                                    a x
--R  /
--R      +---+ +-+
--R     \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 7 of 131
cc3:=bb2-aa.1
 

   (7)
       -
             +---+
            \|- a
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
          +-+        2a x + b
       - \|a asin(--------------)
                   +-----------+
                   |          2
                  \|- 4a c + b
  /
      +---+ +-+
     \|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R       -
--R             +---+
--R            \|- a
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R          +-+        2a x + b
--R       - \|a asin(--------------)
--R                   +-----------+
--R                   |          2
--R                  \|- 4a c + b
--R  /
--R      +---+ +-+
--R     \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 8 of 131
cc4:=bb2-aa.2
 

                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c             2a x + b
        - 2atan(------------------------------------) - asin(--------------)
                                 a x                          +-----------+
                                                              |          2
                                                             \|- 4a c + b
   (8)  --------------------------------------------------------------------
                                        +---+
                                       \|- a
                                                     Type: Expression Integer
--R
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c             2a x + b
--R        - 2atan(------------------------------------) - asin(--------------)
--R                                 a x                          +-----------+
--R                                                              |          2
--R                                                             \|- 4a c + b
--R   (8)  --------------------------------------------------------------------
--R                                        +---+
--R                                       \|- a
--R                                                     Type: Expression Integer
--E

--S 9 of 131
cc5:=bb3-aa.1
 

   (9)
       -
          log
                                    +--------------+
                    +-+ +-+         |   2                   +-+
                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
               + 
                        2             +-+
                 (- 2a x  - b x - 2c)\|a
            /
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
     + 
               2a x + b
       asinh(------------)
              +---------+
              |        2
             \|4a c - b
  /
      +-+
     \|a
                                                     Type: Expression Integer
--R
--R   (9)
--R       -
--R          log
--R                                    +--------------+
--R                    +-+ +-+         |   2                   +-+
--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R               + 
--R                        2             +-+
--R                 (- 2a x  - b x - 2c)\|a
--R            /
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R               2a x + b
--R       asinh(------------)
--R              +---------+
--R              |        2
--R             \|4a c - b
--R  /
--R      +-+
--R     \|a
--R                                                     Type: Expression Integer
--E

--S 10 of 131
cc6:=bb3-aa.2
 

   (10)
                      +--------------+
                +---+ |   2               +---+ +-+
       +-+     \|- a \|a x  + b x + c  - \|- a \|c      +---+        2a x + b
   - 2\|a atan(------------------------------------) + \|- a asinh(------------)
                                a x                                 +---------+
                                                                    |        2
                                                                   \|4a c - b
   -----------------------------------------------------------------------------
                                      +---+ +-+
                                     \|- a \|a
                                                     Type: Expression Integer
--R
--R   (10)
--R                      +--------------+
--R                +---+ |   2               +---+ +-+
--R       +-+     \|- a \|a x  + b x + c  - \|- a \|c      +---+        2a x + b
--R   - 2\|a atan(------------------------------------) + \|- a asinh(------------)
--R                                a x                                 +---------+
--R                                                                    |        2
--R                                                                   \|4a c - b
--R   -----------------------------------------------------------------------------
--R                                      +---+ +-+
--R                                     \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 11 of 131
dd1:=simplifyLog cc1
 

   (11)
     log
                                                  +--------------+
                         +-+                 +-+  |   2
            ((4a x + 2b)\|c  + (- 2b x - 4c)\|a )\|a x  + b x + c
          + 
                 2              +-+ +-+         2              2
            (4a x  + 4b x + 4c)\|a \|c  - 2a b x  + (- 4a c - b )x - 2b c
       /
                               +--------------+
               +-+ +-+         |   2                   +-+
            (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
          + 
                   2             +-+
            (- 2a x  - b x - 2c)\|a
  /
      +-+
     \|a
                                                     Type: Expression Integer
--R
--R   (11)
--R     log
--R                                                  +--------------+
--R                         +-+                 +-+  |   2
--R            ((4a x + 2b)\|c  + (- 2b x - 4c)\|a )\|a x  + b x + c
--R          + 
--R                 2              +-+ +-+         2              2
--R            (4a x  + 4b x + 4c)\|a \|c  - 2a b x  + (- 4a c - b )x - 2b c
--R       /
--R                               +--------------+
--R               +-+ +-+         |   2                   +-+
--R            (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R          + 
--R                   2             +-+
--R            (- 2a x  - b x - 2c)\|a
--R  /
--R      +-+
--R     \|a
--R                                                     Type: Expression Integer
--E

--S 12 of 131     14:280 Schaums and Axiom differ by a constant
ee1:=ratDenom dd1
 

                      +-+     +-+
          +-+    - 2a\|c  + b\|a
         \|a log(----------------)
                         a
   (12)  -------------------------
                     a
                                                     Type: Expression Integer
--R
--R                      +-+     +-+
--R          +-+    - 2a\|c  + b\|a
--R         \|a log(----------------)
--R                         a
--R   (12)  -------------------------
--R                     a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 11 of 131
aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                   +--------------+
               +-+ |   2               2
           (2b\|c \|a x  + b x + c  - b x - 2b c)
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                    +--------------+
                +-+ |   2                   2         +-+ +-+
         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
    /
                  +--------------+
          +-+ +-+ |   2                                +-+
       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
     ,

                     +--------------+
                 +-+ |   2               2
           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                     +--------------+
               +---+ |   2                   2        +---+ +-+
         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
    /
                    +--------------+
          +---+ +-+ |   2                               +---+
       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                   +--------------+
--R               +-+ |   2               2
--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                    +--------------+
--R                +-+ |   2                   2         +-+ +-+
--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
--R    /
--R                  +--------------+
--R          +-+ +-+ |   2                                +-+
--R       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
--R     ,
--R
--R                     +--------------+
--R                 +-+ |   2               2
--R           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                     +--------------+
--R               +---+ |   2                   2        +---+ +-+
--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
--R    /
--R                    +--------------+
--R          +---+ +-+ |   2                               +---+
--R       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 12 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 13 of 131
bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1
 

   (3)
       -
            b
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
             +--------------+
         +-+ |   2
       2\|a \|a x  + b x + c
  /
        +-+
     2a\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            b
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R             +--------------+
--R         +-+ |   2
--R       2\|a \|a x  + b x + c
--R  /
--R        +-+
--R     2a\|a
--R                                                     Type: Expression Integer
--E

--S 14 of 131
bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2
 

   (4)
                   +--------------+
             +---+ |   2               +---+ +-+           +--------------+
            \|- a \|a x  + b x + c  - \|- a \|c      +---+ |   2
   - b atan(------------------------------------) + \|- a \|a x  + b x + c
                             a x
   ------------------------------------------------------------------------
                                      +---+
                                    a\|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                   +--------------+
--R             +---+ |   2               +---+ +-+           +--------------+
--R            \|- a \|a x  + b x + c  - \|- a \|c      +---+ |   2
--R   - b atan(------------------------------------) + \|- a \|a x  + b x + c
--R                             a x
--R   ------------------------------------------------------------------------
--R                                      +---+
--R                                    a\|- a
--R                                                     Type: Expression Integer
--E

--S 15 of 131
cc1:=bb1-aa.1
 

   (5)
                   +--------------+
               +-+ |   2               2
         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   +--------------+
               +-+ |   2               2
         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                +--------------+
            +-+ |   2                          +-+ +-+
       - 4c\|a \|a x  + b x + c  + (2b x + 4c)\|a \|c
  /
                +--------------+
        +-+ +-+ |   2                                +-+
     4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                   +--------------+
--R               +-+ |   2               2
--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   +--------------+
--R               +-+ |   2               2
--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                +--------------+
--R            +-+ |   2                          +-+ +-+
--R       - 4c\|a \|a x  + b x + c  + (2b x + 4c)\|a \|c
--R  /
--R                +--------------+
--R        +-+ +-+ |   2                                +-+
--R     4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
--R                                                     Type: Expression Integer
--E

--S 16 of 131
cc2:=bb1-aa.2
 

   (6)
                         +--------------+
               +---+ +-+ |   2                2          +---+
         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                     +--------------+
             +-+ +-+ |   2                   2          +-+
         (4b\|a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|a )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                      +--------------+
            +---+ +-+ |   2                          +---+ +-+ +-+
       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
  /
                      +--------------+
        +---+ +-+ +-+ |   2                                +---+ +-+
     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                         +--------------+
--R               +---+ +-+ |   2                2          +---+
--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                     +--------------+
--R             +-+ +-+ |   2                   2          +-+
--R         (4b\|a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|a )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                      +--------------+
--R            +---+ +-+ |   2                          +---+ +-+ +-+
--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
--R  /
--R                      +--------------+
--R        +---+ +-+ +-+ |   2                                +---+ +-+
--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 17 of 131
cc3:=bb2-aa.1
 

   (7)
                         +--------------+
               +---+ +-+ |   2                2          +---+
         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                       +--------------+
               +-+ +-+ |   2                 2          +-+
         (- 4b\|a \|c \|a x  + b x + c  + (2b x + 4b c)\|a )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                      +--------------+
            +---+ +-+ |   2                          +---+ +-+ +-+
       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
  /
                      +--------------+
        +---+ +-+ +-+ |   2                                +---+ +-+
     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                         +--------------+
--R               +---+ +-+ |   2                2          +---+
--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                       +--------------+
--R               +-+ +-+ |   2                 2          +-+
--R         (- 4b\|a \|c \|a x  + b x + c  + (2b x + 4b c)\|a )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                      +--------------+
--R            +---+ +-+ |   2                          +---+ +-+ +-+
--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
--R  /
--R                      +--------------+
--R        +---+ +-+ +-+ |   2                                +---+ +-+
--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 18 of 131
cc4:=bb2-aa.2
 

             +--------------+
             |   2                         +-+
        - 2c\|a x  + b x + c  + (b x + 2c)\|c
   (8)  --------------------------------------
               +--------------+
           +-+ |   2
        2a\|c \|a x  + b x + c  - a b x - 2a c
                                                     Type: Expression Integer
--R
--R             +--------------+
--R             |   2                         +-+
--R        - 2c\|a x  + b x + c  + (b x + 2c)\|c
--R   (8)  --------------------------------------
--R               +--------------+
--R           +-+ |   2
--R        2a\|c \|a x  + b x + c  - a b x - 2a c
--R                                                     Type: Expression Integer
--E

--S 19 of 131     14:281 Schaums and Axiom differ by a constant
dd1:=ratDenom cc4
 

           +-+
          \|c
   (9)  - ----
            a
                                                     Type: Expression Integer
--R
--R           +-+
--R          \|c
--R   (9)  - ----
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 131
aa:=integrate(x^2/sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                                                      +--------------+
                            3          2      2   +-+ |   2
             ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
           + 
                 2 2       2      4  2             2      3           3      2 2
           (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  2        2  3                 3  2           2      2     +-+
           ((- 16a c - 4a b )x  + (- 8a b c + 6b )x  + (- 32a c  + 24b c)x)\|a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                  2   4       2        2  3                 3  2
               16a b x  + (32a c - 8a b )x  + (24a b c - 18b )x
             + 
                     2      2
               (32a c  - 24b c)x
        *
            +-+ +-+
           \|a \|c
    /
                                   +--------------+
             2         2   +-+ +-+ |   2
         (32a b x + 64a c)\|a \|c \|a x  + b x + c
       + 
                3      2 2  2      2           2 2  +-+
         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
     ,

                                                        +--------------+
                              3          2      2   +-+ |   2
             ((- 16a b c + 12b )x - 32a c  + 24b c)\|c \|a x  + b x + c
           + 
                 2 2       2      4  2           2      3           3      2 2
             (16a c  - 8a b c - 3b )x  + (32a b c  - 24b c)x + 32a c  - 24b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                 2        2  3                 3  2           2      2     +---+
           ((- 8a c - 2a b )x  + (- 4a b c + 3b )x  + (- 16a c  + 12b c)x)\|- a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
              2   4       2        2  3                3  2         2      2
           (8a b x  + (16a c - 4a b )x  + (12a b c - 9b )x  + (16a c  - 12b c)x)
        *
            +---+ +-+
           \|- a \|c
    /
                                     +--------------+
             2         2   +---+ +-+ |   2
         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
       + 
                3      2 2  2      2           2 2  +---+
         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R                                                      +--------------+
--R                            3          2      2   +-+ |   2
--R             ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
--R           + 
--R                 2 2       2      4  2             2      3           3      2 2
--R           (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  2        2  3                 3  2           2      2     +-+
--R           ((- 16a c - 4a b )x  + (- 8a b c + 6b )x  + (- 32a c  + 24b c)x)\|a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                  2   4       2        2  3                 3  2
--R               16a b x  + (32a c - 8a b )x  + (24a b c - 18b )x
--R             + 
--R                     2      2
--R               (32a c  - 24b c)x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                                   +--------------+
--R             2         2   +-+ +-+ |   2
--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R       + 
--R                3      2 2  2      2           2 2  +-+
--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R     ,
--R
--R                                                        +--------------+
--R                              3          2      2   +-+ |   2
--R             ((- 16a b c + 12b )x - 32a c  + 24b c)\|c \|a x  + b x + c
--R           + 
--R                 2 2       2      4  2           2      3           3      2 2
--R             (16a c  - 8a b c - 3b )x  + (32a b c  - 24b c)x + 32a c  - 24b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                 2        2  3                 3  2           2      2     +---+
--R           ((- 8a c - 2a b )x  + (- 4a b c + 3b )x  + (- 16a c  + 12b c)x)\|- a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R              2   4       2        2  3                3  2         2      2
--R           (8a b x  + (16a c - 4a b )x  + (12a b c - 9b )x  + (16a c  - 12b c)x)
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                                     +--------------+
--R             2         2   +---+ +-+ |   2
--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
--R       + 
--R                3      2 2  2      2           2 2  +---+
--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 20 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 21 of 131
bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1
 

   (3)
                     2
         (- 4a c + 3b )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                       +--------------+
                   +-+ |   2
       (4a x - 6b)\|a \|a x  + b x + c
  /
       2 +-+
     8a \|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     2
--R         (- 4a c + 3b )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                       +--------------+
--R                   +-+ |   2
--R       (4a x - 6b)\|a \|a x  + b x + c
--R  /
--R       2 +-+
--R     8a \|a
--R                                                     Type: Expression Integer
--E

--S 22 of 131
bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2
 

   (4)
                                 +--------------+
                           +---+ |   2               +---+ +-+
                   2      \|- a \|a x  + b x + c  - \|- a \|c
       (- 4a c + 3b )atan(------------------------------------)
                                           a x
     + 
                         +--------------+
                   +---+ |   2
       (2a x - 3b)\|- a \|a x  + b x + c
  /
       2 +---+
     4a \|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                 +--------------+
--R                           +---+ |   2               +---+ +-+
--R                   2      \|- a \|a x  + b x + c  - \|- a \|c
--R       (- 4a c + 3b )atan(------------------------------------)
--R                                           a x
--R     + 
--R                         +--------------+
--R                   +---+ |   2
--R       (2a x - 3b)\|- a \|a x  + b x + c
--R  /
--R       2 +---+
--R     4a \|- a
--R                                                     Type: Expression Integer
--E

--S 23 of 131
cc1:=aa.1-bb1
 

   (5)
                                                    +--------------+
                          3          2      2   +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
         + 
               2 2       2      4  2             2      3           3      2 2
         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                    +--------------+
                          3          2      2   +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
         + 
               2 2       2      4  2             2      3           3      2 2
         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                +--------------+
             2           2  +-+ |   2
       (- 24b c x - 48b c )\|a \|a x  + b x + c
     + 
                     3  2      2           2  +-+ +-+
       ((24a b c + 6b )x  + 48b c x + 48b c )\|a \|c
  /
                                 +--------------+
           2         2   +-+ +-+ |   2
       (32a b x + 64a c)\|a \|c \|a x  + b x + c
     + 
              3      2 2  2      2           2 2  +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                    +--------------+
--R                          3          2      2   +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
--R         + 
--R               2 2       2      4  2             2      3           3      2 2
--R         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                    +--------------+
--R                          3          2      2   +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
--R         + 
--R               2 2       2      4  2             2      3           3      2 2
--R         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                +--------------+
--R             2           2  +-+ |   2
--R       (- 24b c x - 48b c )\|a \|a x  + b x + c
--R     + 
--R                     3  2      2           2  +-+ +-+
--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|a \|c
--R  /
--R                                 +--------------+
--R           2         2   +-+ +-+ |   2
--R       (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R     + 
--R              3      2 2  2      2           2 2  +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R                                                     Type: Expression Integer
--E

--S 24 of 131
cc2:=aa.2-bb1
 

   (6)
                                                          +--------------+
                          3          2      2   +---+ +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
         + 
                     2 2       2      4  2             2      3           3
               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
             + 
                  2 2
               24b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                          +--------------+
                            3          2      2   +-+ +-+ |   2
           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
         + 
                     2 2        2      4  2           2      3           3
                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
               + 
                      2 2
                 - 48b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                      +--------------+
             2           2  +---+ +-+ |   2
       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
     + 
                     3  2      2           2  +---+ +-+ +-+
       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
  /
                                       +--------------+
           2         2   +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              3      2 2  2      2           2 2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                          +--------------+
--R                          3          2      2   +---+ +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                     2 2       2      4  2             2      3           3
--R               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
--R             + 
--R                  2 2
--R               24b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                          +--------------+
--R                            3          2      2   +-+ +-+ |   2
--R           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
--R         + 
--R                     2 2        2      4  2           2      3           3
--R                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
--R               + 
--R                      2 2
--R                 - 48b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                      +--------------+
--R             2           2  +---+ +-+ |   2
--R       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                     3  2      2           2  +---+ +-+ +-+
--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R           2         2   +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              3      2 2  2      2           2 2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 25 of 131
cc3:=aa.2-bb1
 

   (7)
                                                          +--------------+
                          3          2      2   +---+ +-+ |   2
           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
         + 
                     2 2       2      4  2             2      3           3
               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
             + 
                  2 2
               24b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                          +--------------+
                            3          2      2   +-+ +-+ |   2
           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
         + 
                     2 2        2      4  2           2      3           3
                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
               + 
                      2 2
                 - 48b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                      +--------------+
             2           2  +---+ +-+ |   2
       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
     + 
                     3  2      2           2  +---+ +-+ +-+
       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
  /
                                       +--------------+
           2         2   +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              3      2 2  2      2           2 2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                                                          +--------------+
--R                          3          2      2   +---+ +-+ |   2
--R           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                     2 2       2      4  2             2      3           3
--R               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
--R             + 
--R                  2 2
--R               24b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                          +--------------+
--R                            3          2      2   +-+ +-+ |   2
--R           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
--R         + 
--R                     2 2        2      4  2           2      3           3
--R                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
--R               + 
--R                      2 2
--R                 - 48b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                      +--------------+
--R             2           2  +---+ +-+ |   2
--R       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                     3  2      2           2  +---+ +-+ +-+
--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R           2         2   +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              3      2 2  2      2           2 2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 26 of 131
cc4:=aa.2-bb2
 

   (8)
                            +--------------+
             2           2  |   2
       (- 12b c x - 24b c )\|a x  + b x + c
     + 
                     3  2      2           2  +-+
       ((12a b c + 3b )x  + 24b c x + 24b c )\|c
  /
                             +--------------+
           2         2   +-+ |   2                    3      2 2  2      2
       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
     + 
            2 2
       - 32a c
                                                     Type: Expression Integer
--R
--R   (8)
--R                            +--------------+
--R             2           2  |   2
--R       (- 12b c x - 24b c )\|a x  + b x + c
--R     + 
--R                     3  2      2           2  +-+
--R       ((12a b c + 3b )x  + 24b c x + 24b c )\|c
--R  /
--R                             +--------------+
--R           2         2   +-+ |   2                    3      2 2  2      2
--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
--R     + 
--R            2 2
--R       - 32a c
--R                                                     Type: Expression Integer
--E

--S 27 of 131     14:282 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

             +-+
          3b\|c
   (9)  - ------
              2
            4a
                                                     Type: Expression Integer
--R
--R             +-+
--R          3b\|c
--R   (9)  - ------
--R              2
--R            4a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 131
aa:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (1)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (1)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28 of 131
bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x)
 

                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  + b x + 2c
          log(---------------------------------)
                              x
   (2)  - --------------------------------------
                            +-+
                           \|c
                                                     Type: Expression Integer
--R
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  + b x + 2c
--R          log(---------------------------------)
--R                              x
--R   (2)  - --------------------------------------
--R                            +-+
--R                           \|c
--R                                                     Type: Expression Integer
--E

--S 29 of 131
bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c)))
 

                 b x + 2c
        asin(---------------)
               +-----------+
               |          2
             x\|- 4a c + b
   (3)  ---------------------
                 +---+
                \|- c
                                                     Type: Expression Integer
--R
--R                 b x + 2c
--R        asin(---------------)
--R               +-----------+
--R               |          2
--R             x\|- 4a c + b
--R   (3)  ---------------------
--R                 +---+
--R                \|- c
--R                                                     Type: Expression Integer
--E

--S 30 of 131
bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(4*a*c-b^2)))
 

                   b x + 2c
          asinh(-------------)
                  +---------+
                  |        2
                x\|4a c - b
   (4)  - --------------------
                   +-+
                  \|c
                                                     Type: Expression Integer
--R
--R                   b x + 2c
--R          asinh(-------------)
--R                  +---------+
--R                  |        2
--R                x\|4a c - b
--R   (4)  - --------------------
--R                   +-+
--R                  \|c
--R                                                     Type: Expression Integer
--E

--S 31 of 131
cc1:=aa-bb1
 

   (5)
                 +--------------+
             +-+ |   2
           2\|c \|a x  + b x + c  + b x + 2c
       log(---------------------------------)
                           x
     + 
                 +--------------+
             +-+ |   2
           2\|c \|a x  + b x + c  - b x - 2c
       log(---------------------------------)
                           x
  /
      +-+
     \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                 +--------------+
--R             +-+ |   2
--R           2\|c \|a x  + b x + c  + b x + 2c
--R       log(---------------------------------)
--R                           x
--R     + 
--R                 +--------------+
--R             +-+ |   2
--R           2\|c \|a x  + b x + c  - b x - 2c
--R       log(---------------------------------)
--R                           x
--R  /
--R      +-+
--R     \|c
--R                                                     Type: Expression Integer
--E

--S 32 of 131
cc2:=aa-bb2
 

   (6)
                   +--------------+
               +-+ |   2
    +---+    2\|c \|a x  + b x + c  - b x - 2c     +-+         b x + 2c
   \|- c log(---------------------------------) - \|c asin(---------------)
                             x                               +-----------+
                                                             |          2
                                                           x\|- 4a c + b
   ------------------------------------------------------------------------
                                   +---+ +-+
                                  \|- c \|c
                                                     Type: Expression Integer
--R
--R   (6)
--R                   +--------------+
--R               +-+ |   2
--R    +---+    2\|c \|a x  + b x + c  - b x - 2c     +-+         b x + 2c
--R   \|- c log(---------------------------------) - \|c asin(---------------)
--R                             x                               +-----------+
--R                                                             |          2
--R                                                           x\|- 4a c + b
--R   ------------------------------------------------------------------------
--R                                   +---+ +-+
--R                                  \|- c \|c
--R                                                     Type: Expression Integer
--E

--S 33 of 131
cc3:=aa-bb3
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c             b x + 2c
        log(---------------------------------) + asinh(-------------)
                            x                            +---------+
                                                         |        2
                                                       x\|4a c - b
   (7)  -------------------------------------------------------------
                                      +-+
                                     \|c
                                                     Type: Expression Integer
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c             b x + 2c
--R        log(---------------------------------) + asinh(-------------)
--R                            x                            +---------+
--R                                                         |        2
--R                                                       x\|4a c - b
--R   (7)  -------------------------------------------------------------
--R                                      +-+
--R                                     \|c
--R                                                     Type: Expression Integer
--E

--S 34 of 131
dd1:=expandLog cc1
 

   (8)
                 +--------------+
             +-+ |   2
       log(2\|c \|a x  + b x + c  + b x + 2c)
     + 
                 +--------------+
             +-+ |   2
       log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)
  /
      +-+
     \|c
                                                     Type: Expression Integer
--R
--R   (8)
--R                 +--------------+
--R             +-+ |   2
--R       log(2\|c \|a x  + b x + c  + b x + 2c)
--R     + 
--R                 +--------------+
--R             +-+ |   2
--R       log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)
--R  /
--R      +-+
--R     \|c
--R                                                     Type: Expression Integer
--E

--S 35 of 131
ee1:=ratDenom dd1
 

   (9)
                     +--------------+
        +-+      +-+ |   2
       \|c log(2\|c \|a x  + b x + c  + b x + 2c)
     + 
                     +--------------+
        +-+      +-+ |   2                                  +-+
       \|c log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)\|c
  /
     c
                                                     Type: Expression Integer
--R
--R   (9)
--R                     +--------------+
--R        +-+      +-+ |   2
--R       \|c log(2\|c \|a x  + b x + c  + b x + 2c)
--R     + 
--R                     +--------------+
--R        +-+      +-+ |   2                                  +-+
--R       \|c log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)\|c
--R  /
--R     c
--R                                                     Type: Expression Integer
--E

--S 36 of 131     14:283 Schaums and Axiom differ by a constant
ff1:=complexNormalize ee1
 

                     2  +-+
         log(4a c - b )\|c
   (10)  ------------------
                  c
                                                     Type: Expression Integer
--R
--R                     2  +-+
--R         log(4a c - b )\|c
--R   (10)  ------------------
--R                  c
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 37 of 131
aa:=integrate(1/(x^2*sqrt(a*x^2+b*x+c)),x)
 

   (1)
                     +--------------+
                 +-+ |   2                2 2
         (- 4b x\|c \|a x  + b x + c  + 2b x  + 4b c x)
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                       +--------------+
                   +-+ |   2                         2  2              2
       (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
  /
          +--------------+
       2  |   2                       2     2   +-+
     8c x\|a x  + b x + c  + (- 4b c x  - 8c x)\|c
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                     +--------------+
--R                 +-+ |   2                2 2
--R         (- 4b x\|c \|a x  + b x + c  + 2b x  + 4b c x)
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                       +--------------+
--R                   +-+ |   2                         2  2              2
--R       (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
--R  /
--R          +--------------+
--R       2  |   2                       2     2   +-+
--R     8c x\|a x  + b x + c  + (- 4b c x  - 8c x)\|c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 38 of 131
t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (2)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (2)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 39 of 131
bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*c)*t1
 

                        +--------------+
                    +-+ |   2                                +--------------+
                  2\|c \|a x  + b x + c  - b x - 2c      +-+ |   2
        - b x log(---------------------------------) - 2\|c \|a x  + b x + c
                                  x
   (3)  ---------------------------------------------------------------------
                                            +-+
                                       2c x\|c
                                                     Type: Expression Integer
--R
--R                        +--------------+
--R                    +-+ |   2                                +--------------+
--R                  2\|c \|a x  + b x + c  - b x - 2c      +-+ |   2
--R        - b x log(---------------------------------) - 2\|c \|a x  + b x + c
--R                                  x
--R   (3)  ---------------------------------------------------------------------
--R                                            +-+
--R                                       2c x\|c
--R                                                     Type: Expression Integer
--E

--S 40 of 131
cc:=aa-bb
 

   (4)
               +--------------+
               |   2                   2          +-+
         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                 +--------------+
                 |   2                 2          +-+
         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
              +--------------+
              |   2                2          +-+
       - 2b c\|a x  + b x + c  + (b x + 2b c)\|c
  /
             +--------------+
       2 +-+ |   2                  2      3
     8c \|c \|a x  + b x + c  - 4b c x - 8c
                                                     Type: Expression Integer
--R
--R   (4)
--R               +--------------+
--R               |   2                   2          +-+
--R         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                 +--------------+
--R                 |   2                 2          +-+
--R         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R              +--------------+
--R              |   2                2          +-+
--R       - 2b c\|a x  + b x + c  + (b x + 2b c)\|c
--R  /
--R             +--------------+
--R       2 +-+ |   2                  2      3
--R     8c \|c \|a x  + b x + c  - 4b c x - 8c
--R                                                     Type: Expression Integer
--E

--S 41 of 131
dd:=expandLog cc
 

   (5)
               +--------------+
               |   2                   2          +-+
         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
      *
                   +--------------+
               +-+ |   2
         log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                 +--------------+
                 |   2                 2          +-+
         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
      *
                +--------------+
                |   2                           +-+
         log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                          +--------------+
                                          |   2
       (4b c log(c) + 4b c log(2) - 2b c)\|a x  + b x + c
     + 
             2                       2                   2          +-+
       ((- 2b x - 4b c)log(c) + (- 2b x - 4b c)log(2) + b x + 2b c)\|c
  /
             +--------------+
       2 +-+ |   2                  2      3
     8c \|c \|a x  + b x + c  - 4b c x - 8c
                                                     Type: Expression Integer
--R
--R   (5)
--R               +--------------+
--R               |   2                   2          +-+
--R         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R         log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                 +--------------+
--R                 |   2                 2          +-+
--R         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R         log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                          +--------------+
--R                                          |   2
--R       (4b c log(c) + 4b c log(2) - 2b c)\|a x  + b x + c
--R     + 
--R             2                       2                   2          +-+
--R       ((- 2b x - 4b c)log(c) + (- 2b x - 4b c)log(2) + b x + 2b c)\|c
--R  /
--R             +--------------+
--R       2 +-+ |   2                  2      3
--R     8c \|c \|a x  + b x + c  - 4b c x - 8c
--R                                                     Type: Expression Integer
--E

--S 42 of 131
ee:=ratDenom dd
 

   (6)
                       +--------------+
          +-+      +-+ |   2
       2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                      +--------------+
            +-+       |   2                           +-+
       - 2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                   +-+
       (2b log(c) + 2b log(2) - b)\|c
  /
       2
     4c
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R          +-+      +-+ |   2
--R       2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                      +--------------+
--R            +-+       |   2                           +-+
--R       - 2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                   +-+
--R       (2b log(c) + 2b log(2) - b)\|c
--R  /
--R       2
--R     4c
--R                                                     Type: Expression Integer
--E

--S 43 of 131     14:284 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

                                   +-+
        (b log(c) + 2b log(2) - b)\|c
   (7)  ------------------------------
                        2
                      4c
                                                     Type: Expression Integer
--R
--R                                   +-+
--R        (b log(c) + 2b log(2) - b)\|c
--R   (7)  ------------------------------
--R                        2
--R                      4c
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 44 of 131
aa:=integrate(sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  2        2  3                  3  2           2     2     +-+
           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                  2   4       2         2  3                3  2
               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
             + 
                     2     2
               (32a c  + 8b c)x
        *
            +-+ +-+
           \|a \|c
    /
                                   +--------------+
                           +-+ +-+ |   2
         (32a b x + 64a c)\|a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +-+
         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
     ,

                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                 2        2  3                 3  2           2     2     +---+
           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
              2   4       2         2  3                3  2         2     2
           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
        *
            +---+ +-+
           \|- a \|c
    /
                                     +--------------+
                           +---+ +-+ |   2
         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +---+
         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  2        2  3                  3  2           2     2     +-+
--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                  2   4       2         2  3                3  2
--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
--R             + 
--R                     2     2
--R               (32a c  + 8b c)x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                                   +--------------+
--R                           +-+ +-+ |   2
--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +-+
--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R     ,
--R
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                 2        2  3                 3  2           2     2     +---+
--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R              2   4       2         2  3                3  2         2     2
--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                                     +--------------+
--R                           +---+ +-+ |   2
--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +---+
--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 45 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 46 of 131
bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1
 

   (3)
                  2
         (4a c - b )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                       +--------------+
                   +-+ |   2
       (4a x + 2b)\|a \|a x  + b x + c
  /
        +-+
     8a\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2
--R         (4a c - b )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                       +--------------+
--R                   +-+ |   2
--R       (4a x + 2b)\|a \|a x  + b x + c
--R  /
--R        +-+
--R     8a\|a
--R                                                     Type: Expression Integer
--E

--S 47 of 131
bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2
 

   (4)
                              +--------------+
                        +---+ |   2               +---+ +-+
                2      \|- a \|a x  + b x + c  - \|- a \|c
       (4a c - b )atan(------------------------------------)
                                        a x
     + 
                        +--------------+
                  +---+ |   2
       (2a x + b)\|- a \|a x  + b x + c
  /
        +---+
     4a\|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                              +--------------+
--R                        +---+ |   2               +---+ +-+
--R                2      \|- a \|a x  + b x + c  - \|- a \|c
--R       (4a c - b )atan(------------------------------------)
--R                                        a x
--R     + 
--R                        +--------------+
--R                  +---+ |   2
--R       (2a x + b)\|- a \|a x  + b x + c
--R  /
--R        +---+
--R     4a\|- a
--R                                                     Type: Expression Integer
--E

--S 48 of 131
cc1:=aa.1-bb1
 

   (5)
                        +--------------+
          2          2  |   2
       (4b c x + 8b c )\|a x  + b x + c
     + 
                     3  2     2          2  +-+
       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
  /
                             +--------------+
                         +-+ |   2                    2        2  2
       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
     + 
              2
       - 32a c
                                                     Type: Expression Integer
--R
--R   (5)
--R                        +--------------+
--R          2          2  |   2
--R       (4b c x + 8b c )\|a x  + b x + c
--R     + 
--R                     3  2     2          2  +-+
--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
--R  /
--R                             +--------------+
--R                         +-+ |   2                    2        2  2
--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
--R     + 
--R              2
--R       - 32a c
--R                                                     Type: Expression Integer
--E

--S 49 of 131
cc2:=aa.2-bb1
 

   (6)
                                                          +--------------+
                           3          2     2   +---+ +-+ |   2
           ((- 16a b c + 4b )x - 32a c  + 8b c)\|- a \|c \|a x  + b x + c
         + 
                2 2    4  2           2     3           3     2 2  +---+
           ((16a c  - b )x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                       +--------------+
                         3          2      2   +-+ +-+ |   2
           ((32a b c - 8b )x + 64a c  - 16b c)\|a \|c \|a x  + b x + c
         + 
                  2 2     4  2             2      3           3      2 2  +-+
           ((- 32a c  + 2b )x  + (- 64a b c  + 16b c)x - 64a c  + 16b c )\|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                   +--------------+
          2           2  +---+ +-+ |   2
       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
     + 
                      3  2      2           2  +---+ +-+ +-+
       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
  /
                                       +--------------+
                         +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              2        2  2                    2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                          +--------------+
--R                           3          2     2   +---+ +-+ |   2
--R           ((- 16a b c + 4b )x - 32a c  + 8b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                2 2    4  2           2     3           3     2 2  +---+
--R           ((16a c  - b )x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                       +--------------+
--R                         3          2      2   +-+ +-+ |   2
--R           ((32a b c - 8b )x + 64a c  - 16b c)\|a \|c \|a x  + b x + c
--R         + 
--R                  2 2     4  2             2      3           3      2 2  +-+
--R           ((- 32a c  + 2b )x  + (- 64a b c  + 16b c)x - 64a c  + 16b c )\|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                   +--------------+
--R          2           2  +---+ +-+ |   2
--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                      3  2      2           2  +---+ +-+ +-+
--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R                         +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              2        2  2                    2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 50 of 131
cc3:=aa.1-bb2
 

   (7)
                                                        +--------------+
                         3          2     2   +---+ +-+ |   2
           ((16a b c - 4b )x + 32a c  - 8b c)\|- a \|c \|a x  + b x + c
         + 
                  2 2    4  2             2     3           3     2 2  +---+
           ((- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                                         +--------------+
                           3          2      2   +-+ +-+ |   2
           ((- 32a b c + 8b )x - 64a c  + 16b c)\|a \|c \|a x  + b x + c
         + 
                2 2     4  2           2      3           3      2 2  +-+
           ((32a c  - 2b )x  + (64a b c  - 16b c)x + 64a c  - 16b c )\|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                                   +--------------+
          2           2  +---+ +-+ |   2
       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
     + 
                      3  2      2           2  +---+ +-+ +-+
       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
  /
                                       +--------------+
                         +---+ +-+ +-+ |   2
       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
     + 
              2        2  2                    2  +---+ +-+
       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                                                        +--------------+
--R                         3          2     2   +---+ +-+ |   2
--R           ((16a b c - 4b )x + 32a c  - 8b c)\|- a \|c \|a x  + b x + c
--R         + 
--R                  2 2    4  2             2     3           3     2 2  +---+
--R           ((- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                                         +--------------+
--R                           3          2      2   +-+ +-+ |   2
--R           ((- 32a b c + 8b )x - 64a c  + 16b c)\|a \|c \|a x  + b x + c
--R         + 
--R                2 2     4  2           2      3           3      2 2  +-+
--R           ((32a c  - 2b )x  + (64a b c  - 16b c)x + 64a c  - 16b c )\|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                                   +--------------+
--R          2           2  +---+ +-+ |   2
--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
--R     + 
--R                      3  2      2           2  +---+ +-+ +-+
--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
--R  /
--R                                       +--------------+
--R                         +---+ +-+ +-+ |   2
--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
--R     + 
--R              2        2  2                    2  +---+ +-+
--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
--R                                                     Type: Expression Integer
--E

--S 51 of 131
cc4:=aa.2-bb2
 

   (8)
                        +--------------+
          2          2  |   2
       (4b c x + 8b c )\|a x  + b x + c
     + 
                     3  2     2          2  +-+
       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
  /
                             +--------------+
                         +-+ |   2                    2        2  2
       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
     + 
              2
       - 32a c
                                                     Type: Expression Integer
--R
--R   (8)
--R                        +--------------+
--R          2          2  |   2
--R       (4b c x + 8b c )\|a x  + b x + c
--R     + 
--R                     3  2     2          2  +-+
--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
--R  /
--R                             +--------------+
--R                         +-+ |   2                    2        2  2
--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
--R     + 
--R              2
--R       - 32a c
--R                                                     Type: Expression Integer
--E

--S 52 of 131     14:285 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

          +-+
        b\|c
   (9)  -----
          4a
                                                     Type: Expression Integer
--R
--R          +-+
--R        b\|c
--R   (9)  -----
--R          4a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 53 of 131
aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                     2   2        3       5  2          2 2      4
                 (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x
               + 
                         3      3 2
                 384a b c  - 96b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                    2 2 2        4      6  3
             (- 144a b c  + 24a b c + 3b )x
           + 
                    2   3         3 2      5   2            2 3       4 2
             (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
           + 
                       4      3 3
             - 384a b c  + 96b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                    3         2 3  5          3 2       2 2        4  4
             (- 192a b c - 16a b )x  + (- 384a c  - 336a b c - 4a b )x
           + 
                     2   2        3      5  3
             (- 1056a b c  - 16a b c + 6b )x
           + 
                    2 3         2 2      4   2              3      3 2
             (- 768a c  - 288a b c  + 72b c)x  + (- 384a b c  + 96b c )x
        *
                +--------------+
            +-+ |   2
           \|a \|a x  + b x + c
       + 
                  4       3 2  6        3          2 3  5
             (128a c + 96a b )x  + (672a b c + 120a b )x
           + 
                  3 2       2 2         4  4         2   2        3       5  3
             (768a c  + 816a b c - 12a b )x  + (1632a b c  + 64a b c - 30b )x
           + 
                  2 3         2 2       4   2            3      3 2
             (768a c  + 480a b c  - 120b c)x  + (384a b c  - 96b c )x
        *
            +-+ +-+
           \|a \|c
    /
                 3        2 2  2        2             2 2  +-+ +-+
           ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                    3         2 3  3           3 2       2 2   2        2   2
             (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
           + 
                    2 3
             - 1536a c
        *
            +-+
           \|a
     ,

                       2   2        3       5  2            2 2      4
                 (- 96a b c  - 48a b c + 18b )x  + (- 384a b c  + 96b c)x
               + 
                           3      3 2
                 - 384a b c  + 96b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                  2 2 2        4      6  3        2   3         3 2      5   2
             (144a b c  - 24a b c - 3b )x  + (288a b c  + 144a b c  - 54b c)x
           + 
                    2 3       4 2             4      3 3
             (576a b c  - 144b c )x + 384a b c  - 96b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                   3        2 3  5          3 2       2 2        4  4
             (- 96a b c - 8a b )x  + (- 192a c  - 168a b c - 2a b )x
           + 
                    2   2       3      5  3          2 3         2 2      4   2
             (- 528a b c  - 8a b c + 3b )x  + (- 384a c  - 144a b c  + 36b c)x
           + 
                        3      3 2
             (- 192a b c  + 48b c )x
        *
                  +--------------+
            +---+ |   2
           \|- a \|a x  + b x + c
       + 
                 4       3 2  6        3         2 3  5
             (64a c + 48a b )x  + (336a b c + 60a b )x
           + 
                  3 2       2 2        4  4        2   2        3       5  3
             (384a c  + 408a b c - 6a b )x  + (816a b c  + 32a b c - 15b )x
           + 
                  2 3         2 2      4   2            3      3 2
             (384a c  + 240a b c  - 60b c)x  + (192a b c  - 48b c )x
        *
            +---+ +-+
           \|- a \|c
    /
                 3        2 2  2       2            2 2  +---+ +-+
           ((192a c + 144a b )x  + 768a b c x + 768a c )\|- a \|c
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                    3         2 3  3          3 2       2 2   2        2   2
             (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x
           + 
                   2 3
             - 768a c
        *
            +---+
           \|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                     2   2        3       5  2          2 2      4
--R                 (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x
--R               + 
--R                         3      3 2
--R                 384a b c  - 96b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                    2 2 2        4      6  3
--R             (- 144a b c  + 24a b c + 3b )x
--R           + 
--R                    2   3         3 2      5   2            2 3       4 2
--R             (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
--R           + 
--R                       4      3 3
--R             - 384a b c  + 96b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                    3         2 3  5          3 2       2 2        4  4
--R             (- 192a b c - 16a b )x  + (- 384a c  - 336a b c - 4a b )x
--R           + 
--R                     2   2        3      5  3
--R             (- 1056a b c  - 16a b c + 6b )x
--R           + 
--R                    2 3         2 2      4   2              3      3 2
--R             (- 768a c  - 288a b c  + 72b c)x  + (- 384a b c  + 96b c )x
--R        *
--R                +--------------+
--R            +-+ |   2
--R           \|a \|a x  + b x + c
--R       + 
--R                  4       3 2  6        3          2 3  5
--R             (128a c + 96a b )x  + (672a b c + 120a b )x
--R           + 
--R                  3 2       2 2         4  4         2   2        3       5  3
--R             (768a c  + 816a b c - 12a b )x  + (1632a b c  + 64a b c - 30b )x
--R           + 
--R                  2 3         2 2       4   2            3      3 2
--R             (768a c  + 480a b c  - 120b c)x  + (384a b c  - 96b c )x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                 3        2 2  2        2             2 2  +-+ +-+
--R           ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                    3         2 3  3           3 2       2 2   2        2   2
--R             (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R           + 
--R                    2 3
--R             - 1536a c
--R        *
--R            +-+
--R           \|a
--R     ,
--R
--R                       2   2        3       5  2            2 2      4
--R                 (- 96a b c  - 48a b c + 18b )x  + (- 384a b c  + 96b c)x
--R               + 
--R                           3      3 2
--R                 - 384a b c  + 96b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                  2 2 2        4      6  3        2   3         3 2      5   2
--R             (144a b c  - 24a b c - 3b )x  + (288a b c  + 144a b c  - 54b c)x
--R           + 
--R                    2 3       4 2             4      3 3
--R             (576a b c  - 144b c )x + 384a b c  - 96b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                   3        2 3  5          3 2       2 2        4  4
--R             (- 96a b c - 8a b )x  + (- 192a c  - 168a b c - 2a b )x
--R           + 
--R                    2   2       3      5  3          2 3         2 2      4   2
--R             (- 528a b c  - 8a b c + 3b )x  + (- 384a c  - 144a b c  + 36b c)x
--R           + 
--R                        3      3 2
--R             (- 192a b c  + 48b c )x
--R        *
--R                  +--------------+
--R            +---+ |   2
--R           \|- a \|a x  + b x + c
--R       + 
--R                 4       3 2  6        3         2 3  5
--R             (64a c + 48a b )x  + (336a b c + 60a b )x
--R           + 
--R                  3 2       2 2        4  4        2   2        3       5  3
--R             (384a c  + 408a b c - 6a b )x  + (816a b c  + 32a b c - 15b )x
--R           + 
--R                  2 3         2 2      4   2            3      3 2
--R             (384a c  + 240a b c  - 60b c)x  + (192a b c  - 48b c )x
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                 3        2 2  2       2            2 2  +---+ +-+
--R           ((192a c + 144a b )x  + 768a b c x + 768a c )\|- a \|c
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                    3         2 3  3          3 2       2 2   2        2   2
--R             (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x
--R           + 
--R                   2 3
--R             - 768a c
--R        *
--R            +---+
--R           \|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 54 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 55 of 131
bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.1
 

   (3)
                        3
         (- 12a b c + 3b )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                           +--------------+
           2 2                      2  +-+ |   2
       (16a x  + 4a b x + 16a c - 6b )\|a \|a x  + b x + c
  /
        2 +-+
     48a \|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                        3
--R         (- 12a b c + 3b )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                           +--------------+
--R           2 2                      2  +-+ |   2
--R       (16a x  + 4a b x + 16a c - 6b )\|a \|a x  + b x + c
--R  /
--R        2 +-+
--R     48a \|a
--R                                                     Type: Expression Integer
--E

--S 56 of 131
bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.2
 

   (4)
                                    +--------------+
                              +---+ |   2               +---+ +-+
                      3      \|- a \|a x  + b x + c  - \|- a \|c
       (- 12a b c + 3b )atan(------------------------------------)
                                              a x
     + 
                                           +--------------+
          2 2                     2  +---+ |   2
       (8a x  + 2a b x + 8a c - 3b )\|- a \|a x  + b x + c
  /
        2 +---+
     24a \|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                    +--------------+
--R                              +---+ |   2               +---+ +-+
--R                      3      \|- a \|a x  + b x + c  - \|- a \|c
--R       (- 12a b c + 3b )atan(------------------------------------)
--R                                              a x
--R     + 
--R                                           +--------------+
--R          2 2                     2  +---+ |   2
--R       (8a x  + 2a b x + 8a c - 3b )\|- a \|a x  + b x + c
--R  /
--R        2 +---+
--R     24a \|- a
--R                                                     Type: Expression Integer
--E

--S 57 of 131
cc1:=aa.1-bb1
 

   (5)
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                  2 2 2        4      6  3          2   3         3 2      5   2
           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
         + 
                    2 3       4 2             4      3 3
           (- 576a b c  + 144b c )x - 384a b c  + 96b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                  2 2 2        4      6  3          2   3         3 2      5   2
           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
         + 
                    2 3       4 2             4      3 3
           (- 576a b c  + 144b c )x - 384a b c  + 96b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                2 3        2 2      4   2            3       3 2           4
           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
         + 
                 2 3
           - 192b c
      *
              +--------------+
          +-+ |   2
         \|a \|a x  + b x + c
     + 
                  2   2        3      5  3          2 3         2 2       4   2
           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
         + 
                      3       3 2           4       2 3
           (- 768a b c  + 288b c )x - 512a c  + 192b c
      *
          +-+ +-+
         \|a \|c
  /
                                                               +--------------+
             3        2 2  2        2             2 2  +-+ +-+ |   2
       ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c \|a x  + b x + c
     + 
                  3         2 3  3           3 2       2 2   2        2   2
           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
         + 
                  2 3
           - 1536a c
      *
          +-+
         \|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                  2 2 2        4      6  3          2   3         3 2      5   2
--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
--R         + 
--R                    2 3       4 2             4      3 3
--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                  2 2 2        4      6  3          2   3         3 2      5   2
--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
--R         + 
--R                    2 3       4 2             4      3 3
--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                2 3        2 2      4   2            3       3 2           4
--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
--R         + 
--R                 2 3
--R           - 192b c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|a \|a x  + b x + c
--R     + 
--R                  2   2        3      5  3          2 3         2 2       4   2
--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
--R         + 
--R                      3       3 2           4       2 3
--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
--R      *
--R          +-+ +-+
--R         \|a \|c
--R  /
--R                                                               +--------------+
--R             3        2 2  2        2             2 2  +-+ +-+ |   2
--R       ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c \|a x  + b x + c
--R     + 
--R                  3         2 3  3           3 2       2 2   2        2   2
--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R         + 
--R                  2 3
--R           - 1536a c
--R      *
--R          +-+
--R         \|a
--R                                                     Type: Expression Integer
--E

--S 58 of 131
cc2:=aa.2-bb1
 

   (6)
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                      2 2 2        4      6  3
               (- 144a b c  + 24a b c + 3b )x
             + 
                      2   3         3 2      5   2            2 3       4 2
               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
             + 
                         4      3 3
               - 384a b c  + 96b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                      2   2        3       5  2            2 2       4
               (- 192a b c  - 96a b c + 36b )x  + (- 768a b c  + 192b c)x
             + 
                         3       3 2
               - 768a b c  + 192b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                    2 2 2        4      6  3
               (288a b c  - 48a b c - 6b )x
             + 
                    2   3         3 2       5   2           2 3       4 2
               (576a b c  + 288a b c  - 108b c)x  + (1152a b c  - 288b c )x
             + 
                       4       3 3
               768a b c  - 192b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                2 3        2 2      4   2            3       3 2           4
           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
         + 
                 2 3
           - 192b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                  2   2        3      5  3          2 3         2 2       4   2
           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
         + 
                      3       3 2           4       2 3
           (- 768a b c  + 288b c )x - 512a c  + 192b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
               3        2 2  2        2             2 2  +---+ +-+ +-+
         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                  3         2 3  3           3 2       2 2   2        2   2
           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
         + 
                  2 3
           - 1536a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                      2 2 2        4      6  3
--R               (- 144a b c  + 24a b c + 3b )x
--R             + 
--R                      2   3         3 2      5   2            2 3       4 2
--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
--R             + 
--R                         4      3 3
--R               - 384a b c  + 96b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                      2   2        3       5  2            2 2       4
--R               (- 192a b c  - 96a b c + 36b )x  + (- 768a b c  + 192b c)x
--R             + 
--R                         3       3 2
--R               - 768a b c  + 192b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                    2 2 2        4      6  3
--R               (288a b c  - 48a b c - 6b )x
--R             + 
--R                    2   3         3 2       5   2           2 3       4 2
--R               (576a b c  + 288a b c  - 108b c)x  + (1152a b c  - 288b c )x
--R             + 
--R                       4       3 3
--R               768a b c  - 192b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                2 3        2 2      4   2            3       3 2           4
--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
--R         + 
--R                 2 3
--R           - 192b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                  2   2        3      5  3          2 3         2 2       4   2
--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
--R         + 
--R                      3       3 2           4       2 3
--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R               3        2 2  2        2             2 2  +---+ +-+ +-+
--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                  3         2 3  3           3 2       2 2   2        2   2
--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R         + 
--R                  2 3
--R           - 1536a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 59 of 131
cc3:=aa.1-bb2
 

   (7)
                   2   2        3       5  2          2 2      4              3
               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
             + 
                    3 2
               - 96b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                      2 2 2        4      6  3
               (- 144a b c  + 24a b c + 3b )x
             + 
                      2   3         3 2      5   2            2 3       4 2
               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
             + 
                         4      3 3
               - 384a b c  + 96b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                    2   2        3       5  2          2 2       4
               (192a b c  + 96a b c - 36b )x  + (768a b c  - 192b c)x
             + 
                       3       3 2
               768a b c  - 192b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                      2 2 2        4      6  3
               (- 288a b c  + 48a b c + 6b )x
             + 
                      2   3         3 2       5   2             2 3       4 2
               (- 576a b c  - 288a b c  + 108b c)x  + (- 1152a b c  + 288b c )x
             + 
                         4       3 3
               - 768a b c  + 192b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                2 3        2 2      4   2            3       3 2           4
           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
         + 
                 2 3
           - 192b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                  2   2        3      5  3          2 3         2 2       4   2
           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
         + 
                      3       3 2           4       2 3
           (- 768a b c  + 288b c )x - 512a c  + 192b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
               3        2 2  2        2             2 2  +---+ +-+ +-+
         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                  3         2 3  3           3 2       2 2   2        2   2
           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
         + 
                  2 3
           - 1536a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                   2   2        3       5  2          2 2      4              3
--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
--R             + 
--R                    3 2
--R               - 96b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                      2 2 2        4      6  3
--R               (- 144a b c  + 24a b c + 3b )x
--R             + 
--R                      2   3         3 2      5   2            2 3       4 2
--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
--R             + 
--R                         4      3 3
--R               - 384a b c  + 96b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                    2   2        3       5  2          2 2       4
--R               (192a b c  + 96a b c - 36b )x  + (768a b c  - 192b c)x
--R             + 
--R                       3       3 2
--R               768a b c  - 192b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                      2 2 2        4      6  3
--R               (- 288a b c  + 48a b c + 6b )x
--R             + 
--R                      2   3         3 2       5   2             2 3       4 2
--R               (- 576a b c  - 288a b c  + 108b c)x  + (- 1152a b c  + 288b c )x
--R             + 
--R                         4       3 3
--R               - 768a b c  + 192b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                2 3        2 2      4   2            3       3 2           4
--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
--R         + 
--R                 2 3
--R           - 192b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                  2   2        3      5  3          2 3         2 2       4   2
--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
--R         + 
--R                      3       3 2           4       2 3
--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R               3        2 2  2        2             2 2  +---+ +-+ +-+
--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                  3         2 3  3           3 2       2 2   2        2   2
--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
--R         + 
--R                  2 3
--R           - 1536a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 60 of 131
cc4:=aa.2-bb2
 

   (8)
               2 3        2 2      4   2            3      3 2           4
           (64a c  + 24a b c  - 18b c)x  + (256a b c  - 96b c )x + 256a c
         + 
                2 3
           - 96b c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                 2   2        3      5  3          2 3        2 2      4   2
           (- 96a b c  + 28a b c + 3b )x  + (- 192a c  - 72a b c  + 54b c)x
         + 
                      3       3 2           4      2 3
           (- 384a b c  + 144b c )x - 256a c  + 96b c
      *
          +-+
         \|c
  /
                                                         +--------------+
             3        2 2  2       2            2 2  +-+ |   2
       ((192a c + 144a b )x  + 768a b c x + 768a c )\|c \|a x  + b x + c
     + 
            3         2 3  3          3 2       2 2   2        2   2        2 3
     (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x - 768a c
                                                     Type: Expression Integer
--R
--R   (8)
--R               2 3        2 2      4   2            3      3 2           4
--R           (64a c  + 24a b c  - 18b c)x  + (256a b c  - 96b c )x + 256a c
--R         + 
--R                2 3
--R           - 96b c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                 2   2        3      5  3          2 3        2 2      4   2
--R           (- 96a b c  + 28a b c + 3b )x  + (- 192a c  - 72a b c  + 54b c)x
--R         + 
--R                      3       3 2           4      2 3
--R           (- 384a b c  + 144b c )x - 256a c  + 96b c
--R      *
--R          +-+
--R         \|c
--R  /
--R                                                         +--------------+
--R             3        2 2  2       2            2 2  +-+ |   2
--R       ((192a c + 144a b )x  + 768a b c x + 768a c )\|c \|a x  + b x + c
--R     + 
--R            3         2 3  3          3 2       2 2   2        2   2        2 3
--R     (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x - 768a c
--R                                                     Type: Expression Integer
--E

--S 61 of 131     14:286 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

                  2  +-+
        (8a c - 3b )\|c
   (9)  ----------------
                 2
              24a
                                                     Type: Expression Integer
--R
--R                  2  +-+
--R        (8a c - 3b )\|c
--R   (9)  ----------------
--R                 2
--R              24a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 62 of 131
aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
 

   (1)
   [
                       3   3        2 3 2        5        7  3
                 (1536a b c  - 1920a b c  - 96a b c + 120b )x
               + 
                       3 4       2 2 3          4 2        6   2
                 (3072a c  - 768a b c  - 4800a b c  + 1200b c)x
               + 
                       2   4           3 3        5 2          2 5          2 4
                 (9216a b c  - 13824a b c  + 2880b c )x + 6144a c  - 9216a b c
               + 
                      4 3
                 1920b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                    4 4        2 4 2         6       8  4
             (- 768a c  + 1440a b c  - 288a b c - 15b )x
           + 
                     3   4        2 3 3         5 2       7   3
             (- 6144a b c  + 7680a b c  + 384a b c  - 480b c)x
           + 
                     3 5        2 2 4          4 3        6 2  2
             (- 6144a c  + 1536a b c  + 9600a b c  - 2400b c )x
           + 
                      2   5           3 4        5 3          2 6          2 5
             (- 12288a b c  + 18432a b c  - 3840b c )x - 6144a c  + 9216a b c
           + 
                    4 4
             - 1920b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                     5 2        4 2       3 4  7
             (- 1536a c  - 2304a b c - 96a b )x
           + 
                      4   2        3 3       2 5  6
             (- 12544a b c  - 3456a b c - 16a b )x
           + 
                      4 3         3 2 2      2 4         6  5
             (- 13056a c  - 18240a b c  - 80a b c + 20a b )x
           + 
                      3   3       2 3 2        5       7  4
             (- 31104a b c  + 480a b c  + 24a b c - 30b )x
           + 
                      3 4       2 2 3          4 2       6   3
             (- 18432a c  + 768a b c  + 2816a b c  - 720b c)x
           + 
                     2   4           3 3        5 2  2
             (- 7680a b c  + 11520a b c  - 2400b c )x
           + 
                     2 5          2 4        4 3
             (- 6144a c  + 9216a b c  - 1920b c )x
        *
                +--------------+
            +-+ |   2
           \|a \|a x  + b x + c
       + 
                   5          4 3  8         5 2         4 2        3 4  7
             (3072a b c + 768a b )x  + (6144a c  + 11264a b c + 896a b )x
           + 
                    4   2        3 3       2 5  6
             (30208a b c  + 9984a b c - 32a b )x
           + 
                    4 3         3 2 2       2 4         6  5
             (21504a c  + 31488a b c  - 320a b c + 80a b )x
           + 
                    3   3        2 3 2         5        7  4
             (42624a b c  - 4896a b c  + 152a b c + 210b )x
           + 
                    3 4        2 2 3          4 2        6   3
             (21504a c  - 2304a b c  - 6464a b c  + 1680b c)x
           + 
                    2   4           3 3        5 2  2
             (10752a b c  - 16128a b c  + 3360b c )x
           + 
                   2 5          2 4        4 3
             (6144a c  - 9216a b c  + 1920b c )x
        *
            +-+ +-+
           \|a \|c
    /
                    4           3 3  3          4 2         3 2   2
             (12288a b c + 3072a b )x  + (24576a c  + 30720a b c)x
           + 
                   3   2          3 3
             73728a b c x + 49152a c
        *
                    +--------------+
            +-+ +-+ |   2
           \|a \|c \|a x  + b x + c
       + 
                     5 2        4 2        3 4  4
             (- 6144a c  - 9216a b c - 384a b )x
           + 
                      4   2         3 3   3            4 3         3 2 2  2
             (- 49152a b c  - 12288a b c)x  + (- 49152a c  - 61440a b c )x
           + 
                     3   3          3 4
             - 98304a b c x - 49152a c
        *
            +-+
           \|a
     ,

                         3   3        2 3 2        5        7  3
                 (- 1536a b c  + 1920a b c  + 96a b c - 120b )x
               + 
                         3 4       2 2 3          4 2        6   2
                 (- 3072a c  + 768a b c  + 4800a b c  - 1200b c)x
               + 
                         2   4           3 3        5 2          2 5
                 (- 9216a b c  + 13824a b c  - 2880b c )x - 6144a c
               + 
                        2 4        4 3
                 9216a b c  - 1920b c
            *
                    +--------------+
                +-+ |   2
               \|c \|a x  + b x + c
           + 
                  4 4        2 4 2         6       8  4
             (768a c  - 1440a b c  + 288a b c + 15b )x
           + 
                   3   4        2 3 3         5 2       7   3
             (6144a b c  - 7680a b c  - 384a b c  + 480b c)x
           + 
                   3 5        2 2 4          4 3        6 2  2
             (6144a c  - 1536a b c  - 9600a b c  + 2400b c )x
           + 
                    2   5           3 4        5 3          2 6          2 5
             (12288a b c  - 18432a b c  + 3840b c )x + 6144a c  - 9216a b c
           + 
                  4 4
             1920b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                    5 2        4 2       3 4  7
             (- 768a c  - 1152a b c - 48a b )x
           + 
                     4   2        3 3      2 5  6
             (- 6272a b c  - 1728a b c - 8a b )x
           + 
                     4 3        3 2 2      2 4         6  5
             (- 6528a c  - 9120a b c  - 40a b c + 10a b )x
           + 
                      3   3       2 3 2        5       7  4
             (- 15552a b c  + 240a b c  + 12a b c - 15b )x
           + 
                     3 4       2 2 3          4 2       6   3
             (- 9216a c  + 384a b c  + 1408a b c  - 360b c)x
           + 
                     2   4          3 3        5 2  2
             (- 3840a b c  + 5760a b c  - 1200b c )x
           + 
                     2 5          2 4       4 3
             (- 3072a c  + 4608a b c  - 960b c )x
        *
                  +--------------+
            +---+ |   2
           \|- a \|a x  + b x + c
       + 
                   5          4 3  8         5 2        4 2        3 4  7
             (1536a b c + 384a b )x  + (3072a c  + 5632a b c + 448a b )x
           + 
                    4   2        3 3       2 5  6
             (15104a b c  + 4992a b c - 16a b )x
           + 
                    4 3         3 2 2       2 4         6  5
             (10752a c  + 15744a b c  - 160a b c + 40a b )x
           + 
                    3   3        2 3 2        5        7  4
             (21312a b c  - 2448a b c  + 76a b c + 105b )x
           + 
                    3 4        2 2 3          4 2       6   3
             (10752a c  - 1152a b c  - 3232a b c  + 840b c)x
           + 
                   2   4          3 3        5 2  2
             (5376a b c  - 8064a b c  + 1680b c )x
           + 
                   2 5          2 4       4 3
             (3072a c  - 4608a b c  + 960b c )x
        *
            +---+ +-+
           \|- a \|c
    /
                   4           3 3  3          4 2         3 2   2
             (6144a b c + 1536a b )x  + (12288a c  + 15360a b c)x
           + 
                   3   2          3 3
             36864a b c x + 24576a c
        *
                      +--------------+
            +---+ +-+ |   2
           \|- a \|c \|a x  + b x + c
       + 
                     5 2        4 2        3 4  4
             (- 3072a c  - 4608a b c - 192a b )x
           + 
                      4   2        3 3   3            4 3         3 2 2  2
             (- 24576a b c  - 6144a b c)x  + (- 24576a c  - 30720a b c )x
           + 
                     3   3          3 4
             - 49152a b c x - 24576a c
        *
            +---+
           \|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                       3   3        2 3 2        5        7  3
--R                 (1536a b c  - 1920a b c  - 96a b c + 120b )x
--R               + 
--R                       3 4       2 2 3          4 2        6   2
--R                 (3072a c  - 768a b c  - 4800a b c  + 1200b c)x
--R               + 
--R                       2   4           3 3        5 2          2 5          2 4
--R                 (9216a b c  - 13824a b c  + 2880b c )x + 6144a c  - 9216a b c
--R               + 
--R                      4 3
--R                 1920b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                    4 4        2 4 2         6       8  4
--R             (- 768a c  + 1440a b c  - 288a b c - 15b )x
--R           + 
--R                     3   4        2 3 3         5 2       7   3
--R             (- 6144a b c  + 7680a b c  + 384a b c  - 480b c)x
--R           + 
--R                     3 5        2 2 4          4 3        6 2  2
--R             (- 6144a c  + 1536a b c  + 9600a b c  - 2400b c )x
--R           + 
--R                      2   5           3 4        5 3          2 6          2 5
--R             (- 12288a b c  + 18432a b c  - 3840b c )x - 6144a c  + 9216a b c
--R           + 
--R                    4 4
--R             - 1920b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                     5 2        4 2       3 4  7
--R             (- 1536a c  - 2304a b c - 96a b )x
--R           + 
--R                      4   2        3 3       2 5  6
--R             (- 12544a b c  - 3456a b c - 16a b )x
--R           + 
--R                      4 3         3 2 2      2 4         6  5
--R             (- 13056a c  - 18240a b c  - 80a b c + 20a b )x
--R           + 
--R                      3   3       2 3 2        5       7  4
--R             (- 31104a b c  + 480a b c  + 24a b c - 30b )x
--R           + 
--R                      3 4       2 2 3          4 2       6   3
--R             (- 18432a c  + 768a b c  + 2816a b c  - 720b c)x
--R           + 
--R                     2   4           3 3        5 2  2
--R             (- 7680a b c  + 11520a b c  - 2400b c )x
--R           + 
--R                     2 5          2 4        4 3
--R             (- 6144a c  + 9216a b c  - 1920b c )x
--R        *
--R                +--------------+
--R            +-+ |   2
--R           \|a \|a x  + b x + c
--R       + 
--R                   5          4 3  8         5 2         4 2        3 4  7
--R             (3072a b c + 768a b )x  + (6144a c  + 11264a b c + 896a b )x
--R           + 
--R                    4   2        3 3       2 5  6
--R             (30208a b c  + 9984a b c - 32a b )x
--R           + 
--R                    4 3         3 2 2       2 4         6  5
--R             (21504a c  + 31488a b c  - 320a b c + 80a b )x
--R           + 
--R                    3   3        2 3 2         5        7  4
--R             (42624a b c  - 4896a b c  + 152a b c + 210b )x
--R           + 
--R                    3 4        2 2 3          4 2        6   3
--R             (21504a c  - 2304a b c  - 6464a b c  + 1680b c)x
--R           + 
--R                    2   4           3 3        5 2  2
--R             (10752a b c  - 16128a b c  + 3360b c )x
--R           + 
--R                   2 5          2 4        4 3
--R             (6144a c  - 9216a b c  + 1920b c )x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                    4           3 3  3          4 2         3 2   2
--R             (12288a b c + 3072a b )x  + (24576a c  + 30720a b c)x
--R           + 
--R                   3   2          3 3
--R             73728a b c x + 49152a c
--R        *
--R                    +--------------+
--R            +-+ +-+ |   2
--R           \|a \|c \|a x  + b x + c
--R       + 
--R                     5 2        4 2        3 4  4
--R             (- 6144a c  - 9216a b c - 384a b )x
--R           + 
--R                      4   2         3 3   3            4 3         3 2 2  2
--R             (- 49152a b c  - 12288a b c)x  + (- 49152a c  - 61440a b c )x
--R           + 
--R                     3   3          3 4
--R             - 98304a b c x - 49152a c
--R        *
--R            +-+
--R           \|a
--R     ,
--R
--R                         3   3        2 3 2        5        7  3
--R                 (- 1536a b c  + 1920a b c  + 96a b c - 120b )x
--R               + 
--R                         3 4       2 2 3          4 2        6   2
--R                 (- 3072a c  + 768a b c  + 4800a b c  - 1200b c)x
--R               + 
--R                         2   4           3 3        5 2          2 5
--R                 (- 9216a b c  + 13824a b c  - 2880b c )x - 6144a c
--R               + 
--R                        2 4        4 3
--R                 9216a b c  - 1920b c
--R            *
--R                    +--------------+
--R                +-+ |   2
--R               \|c \|a x  + b x + c
--R           + 
--R                  4 4        2 4 2         6       8  4
--R             (768a c  - 1440a b c  + 288a b c + 15b )x
--R           + 
--R                   3   4        2 3 3         5 2       7   3
--R             (6144a b c  - 7680a b c  - 384a b c  + 480b c)x
--R           + 
--R                   3 5        2 2 4          4 3        6 2  2
--R             (6144a c  - 1536a b c  - 9600a b c  + 2400b c )x
--R           + 
--R                    2   5           3 4        5 3          2 6          2 5
--R             (12288a b c  - 18432a b c  + 3840b c )x + 6144a c  - 9216a b c
--R           + 
--R                  4 4
--R             1920b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                    5 2        4 2       3 4  7
--R             (- 768a c  - 1152a b c - 48a b )x
--R           + 
--R                     4   2        3 3      2 5  6
--R             (- 6272a b c  - 1728a b c - 8a b )x
--R           + 
--R                     4 3        3 2 2      2 4         6  5
--R             (- 6528a c  - 9120a b c  - 40a b c + 10a b )x
--R           + 
--R                      3   3       2 3 2        5       7  4
--R             (- 15552a b c  + 240a b c  + 12a b c - 15b )x
--R           + 
--R                     3 4       2 2 3          4 2       6   3
--R             (- 9216a c  + 384a b c  + 1408a b c  - 360b c)x
--R           + 
--R                     2   4          3 3        5 2  2
--R             (- 3840a b c  + 5760a b c  - 1200b c )x
--R           + 
--R                     2 5          2 4       4 3
--R             (- 3072a c  + 4608a b c  - 960b c )x
--R        *
--R                  +--------------+
--R            +---+ |   2
--R           \|- a \|a x  + b x + c
--R       + 
--R                   5          4 3  8         5 2        4 2        3 4  7
--R             (1536a b c + 384a b )x  + (3072a c  + 5632a b c + 448a b )x
--R           + 
--R                    4   2        3 3       2 5  6
--R             (15104a b c  + 4992a b c - 16a b )x
--R           + 
--R                    4 3         3 2 2       2 4         6  5
--R             (10752a c  + 15744a b c  - 160a b c + 40a b )x
--R           + 
--R                    3   3        2 3 2        5        7  4
--R             (21312a b c  - 2448a b c  + 76a b c + 105b )x
--R           + 
--R                    3 4        2 2 3          4 2       6   3
--R             (10752a c  - 1152a b c  - 3232a b c  + 840b c)x
--R           + 
--R                   2   4          3 3        5 2  2
--R             (5376a b c  - 8064a b c  + 1680b c )x
--R           + 
--R                   2 5          2 4       4 3
--R             (3072a c  - 4608a b c  + 960b c )x
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                   4           3 3  3          4 2         3 2   2
--R             (6144a b c + 1536a b )x  + (12288a c  + 15360a b c)x
--R           + 
--R                   3   2          3 3
--R             36864a b c x + 24576a c
--R        *
--R                      +--------------+
--R            +---+ +-+ |   2
--R           \|- a \|c \|a x  + b x + c
--R       + 
--R                     5 2        4 2        3 4  4
--R             (- 3072a c  - 4608a b c - 192a b )x
--R           + 
--R                      4   2        3 3   3            4 3         3 2 2  2
--R             (- 24576a b c  - 6144a b c)x  + (- 24576a c  - 30720a b c )x
--R           + 
--R                     3   3          3 4
--R             - 49152a b c x - 24576a c
--R        *
--R            +---+
--R           \|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 63 of 131
t1:=integrate(sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  2        2  3                  3  2           2     2     +-+
           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
                  2   4       2         2  3                3  2
               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
             + 
                     2     2
               (32a c  + 8b c)x
        *
            +-+ +-+
           \|a \|c
    /
                                   +--------------+
                           +-+ +-+ |   2
         (32a b x + 64a c)\|a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +-+
         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
     ,

                                                    +--------------+
                           3          2     2   +-+ |   2
             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
           + 
                   2 2    4  2             2     3           3     2 2
             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                 2        2  3                 3  2           2     2     +---+
           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
        *
            +--------------+
            |   2
           \|a x  + b x + c
       + 
              2   4       2         2  3                3  2         2     2
           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
        *
            +---+ +-+
           \|- a \|c
    /
                                     +--------------+
                           +---+ +-+ |   2
         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
       + 
                2        2  2                    2  +---+
         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  2        2  3                  3  2           2     2     +-+
--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R                  2   4       2         2  3                3  2
--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
--R             + 
--R                     2     2
--R               (32a c  + 8b c)x
--R        *
--R            +-+ +-+
--R           \|a \|c
--R    /
--R                                   +--------------+
--R                           +-+ +-+ |   2
--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +-+
--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
--R     ,
--R
--R                                                    +--------------+
--R                           3          2     2   +-+ |   2
--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
--R           + 
--R                   2 2    4  2             2     3           3     2 2
--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                 2        2  3                 3  2           2     2     +---+
--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
--R        *
--R            +--------------+
--R            |   2
--R           \|a x  + b x + c
--R       + 
--R              2   4       2         2  3                3  2         2     2
--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
--R        *
--R            +---+ +-+
--R           \|- a \|c
--R    /
--R                                     +--------------+
--R                           +---+ +-+ |   2
--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
--R       + 
--R                2        2  2                    2  +---+
--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 64 of 131
bb1:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.1
 

   (3)
                     2   2         3       5         2 3         2 2       4
             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                3 3       2 2 2        4       6  2
           (192a c  - 240a b c  - 12a b c + 15b )x
         + 
                2   3         3 2       5          2 4         2 3       4 2
           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                  4       3 2  5          3         2 3  4
           (- 384a c - 96a b )x  + (- 832a b c - 16a b )x
         + 
                  3 2      2 2         4  3         2   2         3       5  2
           (- 960a c  - 96a b c + 20a b )x  + (- 96a b c  + 144a b c - 30b )x
         + 
                  2 3         2 2       4              3
           (- 384a c  + 896a b c  - 120b c)x + 640a b c
      *
              +--------------+
          +-+ |   2
         \|a \|a x  + b x + c
     + 
               4   6        4        3 2  5         3         2 3  4
           384a b x  + (768a c + 448a b )x  + (1472a b c - 16a b )x
         + 
                 3 2       2 2         4  3         2   2         3       5  2
           (1152a c  - 192a b c + 40a b )x  + (- 32a b c  - 512a b c + 90b )x
         + 
                2 3          2 2       4              3
           (384a c  - 1216a b c  + 120b c)x - 640a b c
      *
          +-+ +-+
         \|a \|c
  /
                                     +--------------+
             3           3   +-+ +-+ |   2
       (1536a b x + 3072a c)\|a \|c \|a x  + b x + c
     + 
                4        3 2  2        3             3 2  +-+
       ((- 1536a c - 384a b )x  - 3072a b c x - 3072a c )\|a
                                                     Type: Expression Integer
--R
--R   (3)
--R                     2   2         3       5         2 3         2 2       4
--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                3 3       2 2 2        4       6  2
--R           (192a c  - 240a b c  - 12a b c + 15b )x
--R         + 
--R                2   3         3 2       5          2 4         2 3       4 2
--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                  4       3 2  5          3         2 3  4
--R           (- 384a c - 96a b )x  + (- 832a b c - 16a b )x
--R         + 
--R                  3 2      2 2         4  3         2   2         3       5  2
--R           (- 960a c  - 96a b c + 20a b )x  + (- 96a b c  + 144a b c - 30b )x
--R         + 
--R                  2 3         2 2       4              3
--R           (- 384a c  + 896a b c  - 120b c)x + 640a b c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|a \|a x  + b x + c
--R     + 
--R               4   6        4        3 2  5         3         2 3  4
--R           384a b x  + (768a c + 448a b )x  + (1472a b c - 16a b )x
--R         + 
--R                 3 2       2 2         4  3         2   2         3       5  2
--R           (1152a c  - 192a b c + 40a b )x  + (- 32a b c  - 512a b c + 90b )x
--R         + 
--R                2 3          2 2       4              3
--R           (384a c  - 1216a b c  + 120b c)x - 640a b c
--R      *
--R          +-+ +-+
--R         \|a \|c
--R  /
--R                                     +--------------+
--R             3           3   +-+ +-+ |   2
--R       (1536a b x + 3072a c)\|a \|c \|a x  + b x + c
--R     + 
--R                4        3 2  2        3             3 2  +-+
--R       ((- 1536a c - 384a b )x  - 3072a b c x - 3072a c )\|a
--R                                                     Type: Expression Integer
--E

--S 65 of 131
bb2:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.2
 

   (4)
                     2   2         3       5         2 3         2 2       4
             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                3 3       2 2 2        4       6  2
           (192a c  - 240a b c  - 12a b c + 15b )x
         + 
                2   3         3 2       5          2 4         2 3       4 2
           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                  4       3 2  5          3        2 3  4
           (- 192a c - 48a b )x  + (- 416a b c - 8a b )x
         + 
                  3 2      2 2         4  3         2   2        3       5  2
           (- 480a c  - 48a b c + 10a b )x  + (- 48a b c  + 72a b c - 15b )x
         + 
                  2 3         2 2      4              3
           (- 192a c  + 448a b c  - 60b c)x + 320a b c
      *
                +--------------+
          +---+ |   2
         \|- a \|a x  + b x + c
     + 
               4   6        4        3 2  5        3        2 3  4
           192a b x  + (384a c + 224a b )x  + (736a b c - 8a b )x
         + 
                3 2      2 2         4  3         2   2         3       5  2
           (576a c  - 96a b c + 20a b )x  + (- 16a b c  - 256a b c + 45b )x
         + 
                2 3         2 2      4              3
           (192a c  - 608a b c  + 60b c)x - 320a b c
      *
          +---+ +-+
         \|- a \|c
  /
                                      +--------------+
            3           3   +---+ +-+ |   2
       (768a b x + 1536a c)\|- a \|c \|a x  + b x + c
     + 
               4        3 2  2        3             3 2  +---+
       ((- 768a c - 192a b )x  - 1536a b c x - 1536a c )\|- a
                                                     Type: Expression Integer
--R
--R   (4)
--R                     2   2         3       5         2 3         2 2       4
--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                3 3       2 2 2        4       6  2
--R           (192a c  - 240a b c  - 12a b c + 15b )x
--R         + 
--R                2   3         3 2       5          2 4         2 3       4 2
--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                  4       3 2  5          3        2 3  4
--R           (- 192a c - 48a b )x  + (- 416a b c - 8a b )x
--R         + 
--R                  3 2      2 2         4  3         2   2        3       5  2
--R           (- 480a c  - 48a b c + 10a b )x  + (- 48a b c  + 72a b c - 15b )x
--R         + 
--R                  2 3         2 2      4              3
--R           (- 192a c  + 448a b c  - 60b c)x + 320a b c
--R      *
--R                +--------------+
--R          +---+ |   2
--R         \|- a \|a x  + b x + c
--R     + 
--R               4   6        4        3 2  5        3        2 3  4
--R           192a b x  + (384a c + 224a b )x  + (736a b c - 8a b )x
--R         + 
--R                3 2      2 2         4  3         2   2         3       5  2
--R           (576a c  - 96a b c + 20a b )x  + (- 16a b c  - 256a b c + 45b )x
--R         + 
--R                2 3         2 2      4              3
--R           (192a c  - 608a b c  + 60b c)x - 320a b c
--R      *
--R          +---+ +-+
--R         \|- a \|c
--R  /
--R                                      +--------------+
--R            3           3   +---+ +-+ |   2
--R       (768a b x + 1536a c)\|- a \|c \|a x  + b x + c
--R     + 
--R               4        3 2  2        3             3 2  +---+
--R       ((- 768a c - 192a b )x  - 1536a b c x - 1536a c )\|- a
--R                                                     Type: Expression Integer
--E

--S 66 of 131
cc1:=aa.1-bb1
 

   (5)
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                      5 5        4 2 4         3 4 3       2 6 2         8
               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
             + 
                    10
               - 15b
          *
              6
             x
         + 
                    4   5         3 3 4         2 5 3          7 2        9   5
           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
         + 
                    4 6          3 2 5          2 4 4         8 2  4
           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
         + 
                     3   6          2 3 5            5 4         7 3  3
           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
         + 
                     3 7          2 2 6            4 5          6 4  2
           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
         + 
                     2   7            3 6         5 5           2 8
           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
         + 
                    2 7         4 6
           147456a b c  - 30720b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                      5 5        4 2 4         3 4 3       2 6 2         8
               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
             + 
                    10
               - 15b
          *
              6
             x
         + 
                    4   5         3 3 4         2 5 3          7 2        9   5
           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
         + 
                    4 6          3 2 5          2 4 4         8 2  4
           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
         + 
                     3   6          2 3 5            5 4         7 3  3
           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
         + 
                     3 7          2 2 6            4 5          6 4  2
           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
         + 
                     2   7            3 6         5 5           2 8
           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
         + 
                    2 7         4 6
           147456a b c  - 30720b c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                    3 2 4         2 4 3         6 2  5
           (- 15360a b c  - 12800a b c  - 960a b c )x
         + 
                    3   5          2 3 4           5 3  4
           (- 30720a b c  - 107520a b c  - 22400a b c )x
         + 
                     2 2 5            4 4  3             2   6            3 5  2
           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
         + 
                      2 6               7
           - 409600a b c x - 163840a b c
      *
              +--------------+
          +-+ |   2
         \|a \|a x  + b x + c
     + 
                 4   4         3 3 3        2 5 2        7   6
           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
         + 
                  3 2 4         2 4 3          6 2  5
           (92160a b c  + 76800a b c  + 5760a b c )x
         + 
                  3   5          2 3 4           5 3  4
           (92160a b c  + 322560a b c  + 67200a b c )x
         + 
                   2 2 5            4 4  3           2   6            3 5  2
           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
         + 
                    2 6               7
           491520a b c x + 163840a b c
      *
          +-+ +-+
         \|a \|c
  /
                  5   2         4 3         3 5  5
           (73728a b c  + 61440a b c + 4608a b )x
         + 
                   5 3          4 2 2          3 4   4
           (147456a c  + 516096a b c  + 107520a b c)x
         + 
                    4   3          3 3 2  3           4 4           3 2 3  2
           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
         + 
                   3   4           3 5
           1966080a b c x + 786432a c
      *
                  +--------------+
          +-+ +-+ |   2
         \|a \|c \|a x  + b x + c
     + 
                    6 3         5 2 2         4 4        3 6  6
           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
         + 
                     5   3          4 3 2         3 5   5
           (- 442368a b c  - 368640a b c  - 27648a b c)x
         + 
                     5 4           4 2 3          3 4 2  4
           (- 442368a c  - 1548288a b c  - 322560a b c )x
         + 
                      4   4           3 3 3  3
           (- 2359296a b c  - 1376256a b c )x
         + 
                      4 5           3 2 4  2           3   5           3 6
           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
      *
          +-+
         \|a
                                                     Type: Expression Integer
--R
--R   (5)
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                      5 5        4 2 4         3 4 3       2 6 2         8
--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R             + 
--R                    10
--R               - 15b
--R          *
--R              6
--R             x
--R         + 
--R                    4   5         3 3 4         2 5 3          7 2        9   5
--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
--R         + 
--R                    4 6          3 2 5          2 4 4         8 2  4
--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R         + 
--R                     3   6          2 3 5            5 4         7 3  3
--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R         + 
--R                     3 7          2 2 6            4 5          6 4  2
--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R         + 
--R                     2   7            3 6         5 5           2 8
--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R         + 
--R                    2 7         4 6
--R           147456a b c  - 30720b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                      5 5        4 2 4         3 4 3       2 6 2         8
--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R             + 
--R                    10
--R               - 15b
--R          *
--R              6
--R             x
--R         + 
--R                    4   5         3 3 4         2 5 3          7 2        9   5
--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
--R         + 
--R                    4 6          3 2 5          2 4 4         8 2  4
--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R         + 
--R                     3   6          2 3 5            5 4         7 3  3
--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R         + 
--R                     3 7          2 2 6            4 5          6 4  2
--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R         + 
--R                     2   7            3 6         5 5           2 8
--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R         + 
--R                    2 7         4 6
--R           147456a b c  - 30720b c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                    3 2 4         2 4 3         6 2  5
--R           (- 15360a b c  - 12800a b c  - 960a b c )x
--R         + 
--R                    3   5          2 3 4           5 3  4
--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
--R         + 
--R                     2 2 5            4 4  3             2   6            3 5  2
--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
--R         + 
--R                      2 6               7
--R           - 409600a b c x - 163840a b c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|a \|a x  + b x + c
--R     + 
--R                 4   4         3 3 3        2 5 2        7   6
--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
--R         + 
--R                  3 2 4         2 4 3          6 2  5
--R           (92160a b c  + 76800a b c  + 5760a b c )x
--R         + 
--R                  3   5          2 3 4           5 3  4
--R           (92160a b c  + 322560a b c  + 67200a b c )x
--R         + 
--R                   2 2 5            4 4  3           2   6            3 5  2
--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
--R         + 
--R                    2 6               7
--R           491520a b c x + 163840a b c
--R      *
--R          +-+ +-+
--R         \|a \|c
--R  /
--R                  5   2         4 3         3 5  5
--R           (73728a b c  + 61440a b c + 4608a b )x
--R         + 
--R                   5 3          4 2 2          3 4   4
--R           (147456a c  + 516096a b c  + 107520a b c)x
--R         + 
--R                    4   3          3 3 2  3           4 4           3 2 3  2
--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
--R         + 
--R                   3   4           3 5
--R           1966080a b c x + 786432a c
--R      *
--R                  +--------------+
--R          +-+ +-+ |   2
--R         \|a \|c \|a x  + b x + c
--R     + 
--R                    6 3         5 2 2         4 4        3 6  6
--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
--R         + 
--R                     5   3          4 3 2         3 5   5
--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
--R         + 
--R                     5 4           4 2 3          3 4 2  4
--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
--R         + 
--R                      4   4           3 3 3  3
--R           (- 2359296a b c  - 1376256a b c )x
--R         + 
--R                      4 5           3 2 4  2           3   5           3 6
--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
--R      *
--R          +-+
--R         \|a
--R                                                     Type: Expression Integer
--E

--S 67 of 131
cc2:=aa.2-bb1
 

   (6)
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                          5 5        4 2 4         3 4 3       2 6 2         8
                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
                 + 
                        10
                   - 15b
              *
                  6
                 x
             + 
                           4   5         3 3 4         2 5 3          7 2
                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
                 + 
                          9
                   - 1080b c
              *
                  5
                 x
             + 
                        4 6          3 2 5          2 4 4         8 2  4
               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
             + 
                         3   6          2 3 5            5 4         7 3  3
               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
             + 
                         3 7          2 2 6            4 5          6 4  2
               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
             + 
                         2   7            3 6         5 5           2 8
               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
             + 
                        2 7         4 6
               147456a b c  - 30720b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                        4   4         3 3 3         2 5 2          7        9  5
               (- 18432a b c  + 12288a b c  + 16128a b c  - 3072a b c - 360b )x
             + 
                        4 5         3 2 4          2 4 3        8   4
               (- 36864a c  - 73728a b c  + 155136a b c  - 8400b c)x
             + 
                         3   5          2 3 4            5 3         7 2  3
               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
             + 
                         3 6          2 2 5            4 4          6 3  2
               (- 196608a c  - 147456a b c  + 602112a b c  - 138240b c )x
             + 
                         2   6            3 5          5 4            2 7
               (- 491520a b c  + 737280a b c  - 153600b c )x - 196608a c
             + 
                        2 6         4 5
               294912a b c  - 61440b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                        5 5         4 2 4         3 4 3        2 6 2          8
                   6144a c  + 13824a b c  - 26880a b c  - 1344a b c  + 1656a b c
                 + 
                      10
                   30b
              *
                  6
                 x
             + 
                          4   5         3 3 4         2 5 3           7 2
                   110592a b c  - 73728a b c  - 96768a b c  + 18432a b c
                 + 
                        9
                   2160b c
              *
                  5
                 x
             + 
                       4 6          3 2 5          2 4 4         8 2  4
               (110592a c  + 221184a b c  - 465408a b c  + 25200b c )x
             + 
                       3   6          2 3 5            5 4          7 3  3
               (589824a b c  - 540672a b c  - 331776a b c  + 107520b c )x
             + 
                       3 7          2 2 6            4 5          6 4  2
               (294912a c  + 221184a b c  - 903168a b c  + 207360b c )x
             + 
                       2   7            3 6          5 5            2 8
               (589824a b c  - 884736a b c  + 184320b c )x + 196608a c
             + 
                          2 7         4 6
               - 294912a b c  + 61440b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                    3 2 4         2 4 3         6 2  5
           (- 15360a b c  - 12800a b c  - 960a b c )x
         + 
                    3   5          2 3 4           5 3  4
           (- 30720a b c  - 107520a b c  - 22400a b c )x
         + 
                     2 2 5            4 4  3             2   6            3 5  2
           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
         + 
                      2 6               7
           - 409600a b c x - 163840a b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                 4   4         3 3 3        2 5 2        7   6
           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
         + 
                  3 2 4         2 4 3          6 2  5
           (92160a b c  + 76800a b c  + 5760a b c )x
         + 
                  3   5          2 3 4           5 3  4
           (92160a b c  + 322560a b c  + 67200a b c )x
         + 
                   2 2 5            4 4  3           2   6            3 5  2
           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
         + 
                    2 6               7
           491520a b c x + 163840a b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
                  5   2         4 3         3 5  5
           (73728a b c  + 61440a b c + 4608a b )x
         + 
                   5 3          4 2 2          3 4   4
           (147456a c  + 516096a b c  + 107520a b c)x
         + 
                    4   3          3 3 2  3           4 4           3 2 3  2
           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
         + 
                   3   4           3 5
           1966080a b c x + 786432a c
      *
                        +--------------+
          +---+ +-+ +-+ |   2
         \|- a \|a \|c \|a x  + b x + c
     + 
                    6 3         5 2 2         4 4        3 6  6
           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
         + 
                     5   3          4 3 2         3 5   5
           (- 442368a b c  - 368640a b c  - 27648a b c)x
         + 
                     5 4           4 2 3          3 4 2  4
           (- 442368a c  - 1548288a b c  - 322560a b c )x
         + 
                      4   4           3 3 3  3
           (- 2359296a b c  - 1376256a b c )x
         + 
                      4 5           3 2 4  2           3   5           3 6
           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                          5 5        4 2 4         3 4 3       2 6 2         8
--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R                 + 
--R                        10
--R                   - 15b
--R              *
--R                  6
--R                 x
--R             + 
--R                           4   5         3 3 4         2 5 3          7 2
--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
--R                 + 
--R                          9
--R                   - 1080b c
--R              *
--R                  5
--R                 x
--R             + 
--R                        4 6          3 2 5          2 4 4         8 2  4
--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R             + 
--R                         3   6          2 3 5            5 4         7 3  3
--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R             + 
--R                         3 7          2 2 6            4 5          6 4  2
--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R             + 
--R                         2   7            3 6         5 5           2 8
--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R             + 
--R                        2 7         4 6
--R               147456a b c  - 30720b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                        4   4         3 3 3         2 5 2          7        9  5
--R               (- 18432a b c  + 12288a b c  + 16128a b c  - 3072a b c - 360b )x
--R             + 
--R                        4 5         3 2 4          2 4 3        8   4
--R               (- 36864a c  - 73728a b c  + 155136a b c  - 8400b c)x
--R             + 
--R                         3   5          2 3 4            5 3         7 2  3
--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R             + 
--R                         3 6          2 2 5            4 4          6 3  2
--R               (- 196608a c  - 147456a b c  + 602112a b c  - 138240b c )x
--R             + 
--R                         2   6            3 5          5 4            2 7
--R               (- 491520a b c  + 737280a b c  - 153600b c )x - 196608a c
--R             + 
--R                        2 6         4 5
--R               294912a b c  - 61440b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                        5 5         4 2 4         3 4 3        2 6 2          8
--R                   6144a c  + 13824a b c  - 26880a b c  - 1344a b c  + 1656a b c
--R                 + 
--R                      10
--R                   30b
--R              *
--R                  6
--R                 x
--R             + 
--R                          4   5         3 3 4         2 5 3           7 2
--R                   110592a b c  - 73728a b c  - 96768a b c  + 18432a b c
--R                 + 
--R                        9
--R                   2160b c
--R              *
--R                  5
--R                 x
--R             + 
--R                       4 6          3 2 5          2 4 4         8 2  4
--R               (110592a c  + 221184a b c  - 465408a b c  + 25200b c )x
--R             + 
--R                       3   6          2 3 5            5 4          7 3  3
--R               (589824a b c  - 540672a b c  - 331776a b c  + 107520b c )x
--R             + 
--R                       3 7          2 2 6            4 5          6 4  2
--R               (294912a c  + 221184a b c  - 903168a b c  + 207360b c )x
--R             + 
--R                       2   7            3 6          5 5            2 8
--R               (589824a b c  - 884736a b c  + 184320b c )x + 196608a c
--R             + 
--R                          2 7         4 6
--R               - 294912a b c  + 61440b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                    3 2 4         2 4 3         6 2  5
--R           (- 15360a b c  - 12800a b c  - 960a b c )x
--R         + 
--R                    3   5          2 3 4           5 3  4
--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
--R         + 
--R                     2 2 5            4 4  3             2   6            3 5  2
--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
--R         + 
--R                      2 6               7
--R           - 409600a b c x - 163840a b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                 4   4         3 3 3        2 5 2        7   6
--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
--R         + 
--R                  3 2 4         2 4 3          6 2  5
--R           (92160a b c  + 76800a b c  + 5760a b c )x
--R         + 
--R                  3   5          2 3 4           5 3  4
--R           (92160a b c  + 322560a b c  + 67200a b c )x
--R         + 
--R                   2 2 5            4 4  3           2   6            3 5  2
--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
--R         + 
--R                    2 6               7
--R           491520a b c x + 163840a b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R                  5   2         4 3         3 5  5
--R           (73728a b c  + 61440a b c + 4608a b )x
--R         + 
--R                   5 3          4 2 2          3 4   4
--R           (147456a c  + 516096a b c  + 107520a b c)x
--R         + 
--R                    4   3          3 3 2  3           4 4           3 2 3  2
--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
--R         + 
--R                   3   4           3 5
--R           1966080a b c x + 786432a c
--R      *
--R                        +--------------+
--R          +---+ +-+ +-+ |   2
--R         \|- a \|a \|c \|a x  + b x + c
--R     + 
--R                    6 3         5 2 2         4 4        3 6  6
--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
--R         + 
--R                     5   3          4 3 2         3 5   5
--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
--R         + 
--R                     5 4           4 2 3          3 4 2  4
--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
--R         + 
--R                      4   4           3 3 3  3
--R           (- 2359296a b c  - 1376256a b c )x
--R         + 
--R                      4 5           3 2 4  2           3   5           3 6
--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 68 of 131
cc3:=aa.1-bb2
 

   (7)
                     4   4        3 3 3        2 5 2          7        9  5
               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
             + 
                      4 5         3 2 4         2 4 3        8   4
               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
             + 
                       3   5          2 3 4           5 3         7 2  3
               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
             + 
                      3 6         2 2 5            4 4         6 3  2
               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
             + 
                       2   6            3 5         5 4           2 7
               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
             + 
                          2 6         4 5
               - 147456a b c  + 30720b c
          *
                        +--------------+
              +---+ +-+ |   2
             \|- a \|c \|a x  + b x + c
         + 
                          5 5        4 2 4         3 4 3       2 6 2         8
                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
                 + 
                        10
                   - 15b
              *
                  6
                 x
             + 
                           4   5         3 3 4         2 5 3          7 2
                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
                 + 
                          9
                   - 1080b c
              *
                  5
                 x
             + 
                        4 6          3 2 5          2 4 4         8 2  4
               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
             + 
                         3   6          2 3 5            5 4         7 3  3
               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
             + 
                         3 7          2 2 6            4 5          6 4  2
               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
             + 
                         2   7            3 6         5 5           2 8
               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
             + 
                        2 7         4 6
               147456a b c  - 30720b c
          *
              +---+
             \|- a
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                      4   4         3 3 3         2 5 2          7        9  5
               (18432a b c  - 12288a b c  - 16128a b c  + 3072a b c + 360b )x
             + 
                      4 5         3 2 4          2 4 3        8   4
               (36864a c  + 73728a b c  - 155136a b c  + 8400b c)x
             + 
                       3   5          2 3 4            5 3         7 2  3
               (294912a b c  - 270336a b c  - 165888a b c  + 53760b c )x
             + 
                       3 6          2 2 5            4 4          6 3  2
               (196608a c  + 147456a b c  - 602112a b c  + 138240b c )x
             + 
                       2   6            3 5          5 4            2 7
               (491520a b c  - 737280a b c  + 153600b c )x + 196608a c
             + 
                          2 6         4 5
               - 294912a b c  + 61440b c
          *
                      +--------------+
              +-+ +-+ |   2
             \|a \|c \|a x  + b x + c
         + 
                          5 5         4 2 4         3 4 3        2 6 2
                   - 6144a c  - 13824a b c  + 26880a b c  + 1344a b c
                 + 
                            8       10
                   - 1656a b c - 30b
              *
                  6
                 x
             + 
                            4   5         3 3 4         2 5 3           7 2
                   - 110592a b c  + 73728a b c  + 96768a b c  - 18432a b c
                 + 
                          9
                   - 2160b c
              *
                  5
                 x
             + 
                         4 6          3 2 5          2 4 4         8 2  4
               (- 110592a c  - 221184a b c  + 465408a b c  - 25200b c )x
             + 
                         3   6          2 3 5            5 4          7 3  3
               (- 589824a b c  + 540672a b c  + 331776a b c  - 107520b c )x
             + 
                         3 7          2 2 6            4 5          6 4  2
               (- 294912a c  - 221184a b c  + 903168a b c  - 207360b c )x
             + 
                         2   7            3 6          5 5            2 8
               (- 589824a b c  + 884736a b c  - 184320b c )x - 196608a c
             + 
                        2 7         4 6
               294912a b c  - 61440b c
          *
              +-+
             \|a
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                    3 2 4         2 4 3         6 2  5
           (- 15360a b c  - 12800a b c  - 960a b c )x
         + 
                    3   5          2 3 4           5 3  4
           (- 30720a b c  - 107520a b c  - 22400a b c )x
         + 
                     2 2 5            4 4  3             2   6            3 5  2
           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
         + 
                      2 6               7
           - 409600a b c x - 163840a b c
      *
                    +--------------+
          +---+ +-+ |   2
         \|- a \|a \|a x  + b x + c
     + 
                 4   4         3 3 3        2 5 2        7   6
           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
         + 
                  3 2 4         2 4 3          6 2  5
           (92160a b c  + 76800a b c  + 5760a b c )x
         + 
                  3   5          2 3 4           5 3  4
           (92160a b c  + 322560a b c  + 67200a b c )x
         + 
                   2 2 5            4 4  3           2   6            3 5  2
           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
         + 
                    2 6               7
           491520a b c x + 163840a b c
      *
          +---+ +-+ +-+
         \|- a \|a \|c
  /
                  5   2         4 3         3 5  5
           (73728a b c  + 61440a b c + 4608a b )x
         + 
                   5 3          4 2 2          3 4   4
           (147456a c  + 516096a b c  + 107520a b c)x
         + 
                    4   3          3 3 2  3           4 4           3 2 3  2
           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
         + 
                   3   4           3 5
           1966080a b c x + 786432a c
      *
                        +--------------+
          +---+ +-+ +-+ |   2
         \|- a \|a \|c \|a x  + b x + c
     + 
                    6 3         5 2 2         4 4        3 6  6
           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
         + 
                     5   3          4 3 2         3 5   5
           (- 442368a b c  - 368640a b c  - 27648a b c)x
         + 
                     5 4           4 2 3          3 4 2  4
           (- 442368a c  - 1548288a b c  - 322560a b c )x
         + 
                      4   4           3 3 3  3
           (- 2359296a b c  - 1376256a b c )x
         + 
                      4 5           3 2 4  2           3   5           3 6
           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
      *
          +---+ +-+
         \|- a \|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                     4   4        3 3 3        2 5 2          7        9  5
--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
--R             + 
--R                      4 5         3 2 4         2 4 3        8   4
--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
--R             + 
--R                       3   5          2 3 4           5 3         7 2  3
--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
--R             + 
--R                      3 6         2 2 5            4 4         6 3  2
--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
--R             + 
--R                       2   6            3 5         5 4           2 7
--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
--R             + 
--R                          2 6         4 5
--R               - 147456a b c  + 30720b c
--R          *
--R                        +--------------+
--R              +---+ +-+ |   2
--R             \|- a \|c \|a x  + b x + c
--R         + 
--R                          5 5        4 2 4         3 4 3       2 6 2         8
--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
--R                 + 
--R                        10
--R                   - 15b
--R              *
--R                  6
--R                 x
--R             + 
--R                           4   5         3 3 4         2 5 3          7 2
--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
--R                 + 
--R                          9
--R                   - 1080b c
--R              *
--R                  5
--R                 x
--R             + 
--R                        4 6          3 2 5          2 4 4         8 2  4
--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
--R             + 
--R                         3   6          2 3 5            5 4         7 3  3
--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
--R             + 
--R                         3 7          2 2 6            4 5          6 4  2
--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
--R             + 
--R                         2   7            3 6         5 5           2 8
--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
--R             + 
--R                        2 7         4 6
--R               147456a b c  - 30720b c
--R          *
--R              +---+
--R             \|- a
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                      4   4         3 3 3         2 5 2          7        9  5
--R               (18432a b c  - 12288a b c  - 16128a b c  + 3072a b c + 360b )x
--R             + 
--R                      4 5         3 2 4          2 4 3        8   4
--R               (36864a c  + 73728a b c  - 155136a b c  + 8400b c)x
--R             + 
--R                       3   5          2 3 4            5 3         7 2  3
--R               (294912a b c  - 270336a b c  - 165888a b c  + 53760b c )x
--R             + 
--R                       3 6          2 2 5            4 4          6 3  2
--R               (196608a c  + 147456a b c  - 602112a b c  + 138240b c )x
--R             + 
--R                       2   6            3 5          5 4            2 7
--R               (491520a b c  - 737280a b c  + 153600b c )x + 196608a c
--R             + 
--R                          2 6         4 5
--R               - 294912a b c  + 61440b c
--R          *
--R                      +--------------+
--R              +-+ +-+ |   2
--R             \|a \|c \|a x  + b x + c
--R         + 
--R                          5 5         4 2 4         3 4 3        2 6 2
--R                   - 6144a c  - 13824a b c  + 26880a b c  + 1344a b c
--R                 + 
--R                            8       10
--R                   - 1656a b c - 30b
--R              *
--R                  6
--R                 x
--R             + 
--R                            4   5         3 3 4         2 5 3           7 2
--R                   - 110592a b c  + 73728a b c  + 96768a b c  - 18432a b c
--R                 + 
--R                          9
--R                   - 2160b c
--R              *
--R                  5
--R                 x
--R             + 
--R                         4 6          3 2 5          2 4 4         8 2  4
--R               (- 110592a c  - 221184a b c  + 465408a b c  - 25200b c )x
--R             + 
--R                         3   6          2 3 5            5 4          7 3  3
--R               (- 589824a b c  + 540672a b c  + 331776a b c  - 107520b c )x
--R             + 
--R                         3 7          2 2 6            4 5          6 4  2
--R               (- 294912a c  - 221184a b c  + 903168a b c  - 207360b c )x
--R             + 
--R                         2   7            3 6          5 5            2 8
--R               (- 589824a b c  + 884736a b c  - 184320b c )x - 196608a c
--R             + 
--R                        2 7         4 6
--R               294912a b c  - 61440b c
--R          *
--R              +-+
--R             \|a
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                    3 2 4         2 4 3         6 2  5
--R           (- 15360a b c  - 12800a b c  - 960a b c )x
--R         + 
--R                    3   5          2 3 4           5 3  4
--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
--R         + 
--R                     2 2 5            4 4  3             2   6            3 5  2
--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
--R         + 
--R                      2 6               7
--R           - 409600a b c x - 163840a b c
--R      *
--R                    +--------------+
--R          +---+ +-+ |   2
--R         \|- a \|a \|a x  + b x + c
--R     + 
--R                 4   4         3 3 3        2 5 2        7   6
--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
--R         + 
--R                  3 2 4         2 4 3          6 2  5
--R           (92160a b c  + 76800a b c  + 5760a b c )x
--R         + 
--R                  3   5          2 3 4           5 3  4
--R           (92160a b c  + 322560a b c  + 67200a b c )x
--R         + 
--R                   2 2 5            4 4  3           2   6            3 5  2
--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
--R         + 
--R                    2 6               7
--R           491520a b c x + 163840a b c
--R      *
--R          +---+ +-+ +-+
--R         \|- a \|a \|c
--R  /
--R                  5   2         4 3         3 5  5
--R           (73728a b c  + 61440a b c + 4608a b )x
--R         + 
--R                   5 3          4 2 2          3 4   4
--R           (147456a c  + 516096a b c  + 107520a b c)x
--R         + 
--R                    4   3          3 3 2  3           4 4           3 2 3  2
--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
--R         + 
--R                   3   4           3 5
--R           1966080a b c x + 786432a c
--R      *
--R                        +--------------+
--R          +---+ +-+ +-+ |   2
--R         \|- a \|a \|c \|a x  + b x + c
--R     + 
--R                    6 3         5 2 2         4 4        3 6  6
--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
--R         + 
--R                     5   3          4 3 2         3 5   5
--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
--R         + 
--R                     5 4           4 2 3          3 4 2  4
--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
--R         + 
--R                      4   4           3 3 3  3
--R           (- 2359296a b c  - 1376256a b c )x
--R         + 
--R                      4 5           3 2 4  2           3   5           3 6
--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
--R      *
--R          +---+ +-+
--R         \|- a \|a
--R                                                     Type: Expression Integer
--E

--S 69 of 131
cc4:=aa.2-bb2
 

   (8)
                  2 2 4         4 3      6 2  5
           (- 960a b c  - 800a b c  - 60b c )x
         + 
                   2   5          3 4        5 3  4
           (- 1920a b c  - 6720a b c  - 1400b c )x
         + 
                      2 5        4 4  3                6         3 5  2
           (- 15360a b c  - 8960b c )x  + (- 10240a b c  - 23040b c )x
         + 
                   2 6            7
           - 25600b c x - 10240b c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                3   4        2 3 3         5 2     7   6
           (320a b c  + 1200a b c  + 300a b c  + 5b c)x
         + 
                 2 2 4          4 3       6 2  5
           (5760a b c  + 4800a b c  + 360b c )x
         + 
                 2   5           3 4        5 3  4            2 5         4 4  3
           (5760a b c  + 20160a b c  + 4200b c )x  + (30720a b c  + 17920b c )x
         + 
                      6         3 5  2         2 6            7
           (15360a b c  + 34560b c )x  + 30720b c x + 10240b c
      *
          +-+
         \|c
  /
                 4   2        3 3        2 5  5
           (4608a b c  + 3840a b c + 288a b )x
         + 
                 4 3         3 2 2        2 4   4
           (9216a c  + 32256a b c  + 6720a b c)x
         + 
                  3   3         2 3 2  3          3 4          2 2 3  2
           (73728a b c  + 43008a b c )x  + (49152a c  + 110592a b c )x
         + 
                  2   4          2 5
           122880a b c x + 49152a c
      *
              +--------------+
          +-+ |   2
         \|c \|a x  + b x + c
     + 
               5 3        4 2 2        3 4       2 6  6
       (- 1536a c  - 5760a b c  - 1440a b c - 24a b )x
     + 
                4   3         3 3 2        2 5   5
       (- 27648a b c  - 23040a b c  - 1728a b c)x
     + 
                4 4         3 2 3         2 4 2  4
       (- 27648a c  - 96768a b c  - 20160a b c )x
     + 
                 3   4         2 3 3  3            3 5          2 2 4  2
       (- 147456a b c  - 86016a b c )x  + (- 73728a c  - 165888a b c )x
     + 
                2   5          2 6
       - 147456a b c x - 49152a c
                                                     Type: Expression Integer
--R
--R   (8)
--R                  2 2 4         4 3      6 2  5
--R           (- 960a b c  - 800a b c  - 60b c )x
--R         + 
--R                   2   5          3 4        5 3  4
--R           (- 1920a b c  - 6720a b c  - 1400b c )x
--R         + 
--R                      2 5        4 4  3                6         3 5  2
--R           (- 15360a b c  - 8960b c )x  + (- 10240a b c  - 23040b c )x
--R         + 
--R                   2 6            7
--R           - 25600b c x - 10240b c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                3   4        2 3 3         5 2     7   6
--R           (320a b c  + 1200a b c  + 300a b c  + 5b c)x
--R         + 
--R                 2 2 4          4 3       6 2  5
--R           (5760a b c  + 4800a b c  + 360b c )x
--R         + 
--R                 2   5           3 4        5 3  4            2 5         4 4  3
--R           (5760a b c  + 20160a b c  + 4200b c )x  + (30720a b c  + 17920b c )x
--R         + 
--R                      6         3 5  2         2 6            7
--R           (15360a b c  + 34560b c )x  + 30720b c x + 10240b c
--R      *
--R          +-+
--R         \|c
--R  /
--R                 4   2        3 3        2 5  5
--R           (4608a b c  + 3840a b c + 288a b )x
--R         + 
--R                 4 3         3 2 2        2 4   4
--R           (9216a c  + 32256a b c  + 6720a b c)x
--R         + 
--R                  3   3         2 3 2  3          3 4          2 2 3  2
--R           (73728a b c  + 43008a b c )x  + (49152a c  + 110592a b c )x
--R         + 
--R                  2   4          2 5
--R           122880a b c x + 49152a c
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|c \|a x  + b x + c
--R     + 
--R               5 3        4 2 2        3 4       2 6  6
--R       (- 1536a c  - 5760a b c  - 1440a b c - 24a b )x
--R     + 
--R                4   3         3 3 2        2 5   5
--R       (- 27648a b c  - 23040a b c  - 1728a b c)x
--R     + 
--R                4 4         3 2 3         2 4 2  4
--R       (- 27648a c  - 96768a b c  - 20160a b c )x
--R     + 
--R                 3   4         2 3 3  3            3 5          2 2 4  2
--R       (- 147456a b c  - 86016a b c )x  + (- 73728a c  - 165888a b c )x
--R     + 
--R                2   5          2 6
--R       - 147456a b c x - 49152a c
--R                                                     Type: Expression Integer
--E

--S 70 of 131     14:287 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

               +-+
          5b c\|c
   (9)  - --------
               2
            24a
                                                     Type: Expression Integer
--R
--R               +-+
--R          5b c\|c
--R   (9)  - --------
--R               2
--R            24a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 71 of 131
aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
 

   (1)
   [
                   +--------------+
               +-+ |   2                            +-+ +-+
           (4c\|a \|a x  + b x + c  + (- 2b x - 4c)\|a \|c )
        *
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
           log(---------------------------------)
                                +-+
                             2x\|c
       + 
                   +--------------+
               +-+ |   2               2
           (2b\|c \|a x  + b x + c  - b x - 2b c)
        *
           log
                              2           +-+          2              2  +-+
                    ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
                 *
                     +--------------+
                     |   2
                    \|a x  + b x + c
                + 
                           3              2  2              2  +-+ +-+     2   3
                  (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
                + 
                          2       2
                  6a b c x  + 8a c x
             /
                                 +--------------+
                              2  |   2
                  (4b c x + 8c )\|a x  + b x + c
                + 
                              2  2              2  +-+
                  ((- 4a c - b )x  - 8b c x - 8c )\|c
       + 
                    +--------------+
                +-+ |   2                   2         +-+ +-+
         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
    /
                 +--------------+
         +-+ +-+ |   2                            +-+
       4\|a \|c \|a x  + b x + c  + (- 2b x - 4c)\|a
     ,

                     +--------------+
               +---+ |   2                           +---+ +-+
           (2c\|- a \|a x  + b x + c  + (- b x - 2c)\|- a \|c )
        *
                     +--------------+
                 +-+ |   2
               2\|c \|a x  + b x + c  - b x - 2c
           log(---------------------------------)
                                +-+
                             2x\|c
       + 
                   +--------------+
               +-+ |   2               2
           (2b\|c \|a x  + b x + c  - b x - 2b c)
        *
                           +--------------+
                 +---+ +-+ |   2                +---+
                \|- a \|c \|a x  + b x + c  - c\|- a
           atan(-------------------------------------)
                                   +-+
                               a x\|c
       + 
                     +--------------+
               +---+ |   2                   2        +---+ +-+
         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
    /
                   +--------------+
         +---+ +-+ |   2                           +---+
       2\|- a \|c \|a x  + b x + c  + (- b x - 2c)\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                   +--------------+
--R               +-+ |   2                            +-+ +-+
--R           (4c\|a \|a x  + b x + c  + (- 2b x - 4c)\|a \|c )
--R        *
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R           log(---------------------------------)
--R                                +-+
--R                             2x\|c
--R       + 
--R                   +--------------+
--R               +-+ |   2               2
--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
--R        *
--R           log
--R                              2           +-+          2              2  +-+
--R                    ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
--R                 *
--R                     +--------------+
--R                     |   2
--R                    \|a x  + b x + c
--R                + 
--R                           3              2  2              2  +-+ +-+     2   3
--R                  (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
--R                + 
--R                          2       2
--R                  6a b c x  + 8a c x
--R             /
--R                                 +--------------+
--R                              2  |   2
--R                  (4b c x + 8c )\|a x  + b x + c
--R                + 
--R                              2  2              2  +-+
--R                  ((- 4a c - b )x  - 8b c x - 8c )\|c
--R       + 
--R                    +--------------+
--R                +-+ |   2                   2         +-+ +-+
--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
--R    /
--R                 +--------------+
--R         +-+ +-+ |   2                            +-+
--R       4\|a \|c \|a x  + b x + c  + (- 2b x - 4c)\|a
--R     ,
--R
--R                     +--------------+
--R               +---+ |   2                           +---+ +-+
--R           (2c\|- a \|a x  + b x + c  + (- b x - 2c)\|- a \|c )
--R        *
--R                     +--------------+
--R                 +-+ |   2
--R               2\|c \|a x  + b x + c  - b x - 2c
--R           log(---------------------------------)
--R                                +-+
--R                             2x\|c
--R       + 
--R                   +--------------+
--R               +-+ |   2               2
--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
--R        *
--R                           +--------------+
--R                 +---+ +-+ |   2                +---+
--R                \|- a \|c \|a x  + b x + c  - c\|- a
--R           atan(-------------------------------------)
--R                                   +-+
--R                               a x\|c
--R       + 
--R                     +--------------+
--R               +---+ |   2                   2        +---+ +-+
--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
--R    /
--R                   +--------------+
--R         +---+ +-+ |   2                           +---+
--R       2\|- a \|c \|a x  + b x + c  + (- b x - 2c)\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 72 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 73 of 131
t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (3)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (3)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 74 of 131
bb1:=sqrt(a*x^2+b*x+c)+b/2*t1.1+c*t2
 

   (4)
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|a log(---------------------------------)
                                 x
     + 
           +-+
         b\|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                 +--------------+
         +-+ +-+ |   2
       2\|a \|c \|a x  + b x + c
  /
       +-+ +-+
     2\|a \|c
                                                     Type: Expression Integer
--R
--R   (4)
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|a log(---------------------------------)
--R                                 x
--R     + 
--R           +-+
--R         b\|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                 +--------------+
--R         +-+ +-+ |   2
--R       2\|a \|c \|a x  + b x + c
--R  /
--R       +-+ +-+
--R     2\|a \|c
--R                                                     Type: Expression Integer
--E

--S 75 of 131
bb2:=sqrt(a*x^2+b*x+c)+b/2*t1.2+c*t2
 

   (5)
                        +--------------+
                    +-+ |   2
         +---+    2\|c \|a x  + b x + c  - b x - 2c
       c\|- a log(---------------------------------)
                                  x
     + 
                        +--------------+
                  +---+ |   2               +---+ +-+
         +-+     \|- a \|a x  + b x + c  - \|- a \|c
       b\|c atan(------------------------------------)
                                  a x
     + 
                  +--------------+
        +---+ +-+ |   2
       \|- a \|c \|a x  + b x + c
  /
      +---+ +-+
     \|- a \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                        +--------------+
--R                    +-+ |   2
--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       c\|- a log(---------------------------------)
--R                                  x
--R     + 
--R                        +--------------+
--R                  +---+ |   2               +---+ +-+
--R         +-+     \|- a \|a x  + b x + c  - \|- a \|c
--R       b\|c atan(------------------------------------)
--R                                  a x
--R     + 
--R                  +--------------+
--R        +---+ +-+ |   2
--R       \|- a \|c \|a x  + b x + c
--R  /
--R      +---+ +-+
--R     \|- a \|c
--R                                                     Type: Expression Integer
--E

--S 76 of 131
cc1:=aa.1-bb1
 

   (6)
                         +--------------+
                     +-+ |   2
            +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2c\|a log(---------------------------------)
                                   x
     + 
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|a log(---------------------------------)
                                  +-+
                               2x\|c
     + 
       -
              +-+
            b\|c
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
           +-+
         b\|c
      *
         log
                            2           +-+          2              2  +-+
                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
               *
                   +--------------+
                   |   2
                  \|a x  + b x + c
              + 
                         3              2  2              2  +-+ +-+     2   3
                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
              + 
                        2       2
                6a b c x  + 8a c x
           /
                               +--------------+
                            2  |   2
                (4b c x + 8c )\|a x  + b x + c
              + 
                            2  2              2  +-+
                ((- 4a c - b )x  - 8b c x - 8c )\|c
     + 
          +-+
       2c\|a
  /
       +-+ +-+
     2\|a \|c
                                                     Type: Expression Integer
--R
--R   (6)
--R                         +--------------+
--R                     +-+ |   2
--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2c\|a log(---------------------------------)
--R                                   x
--R     + 
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|a log(---------------------------------)
--R                                  +-+
--R                               2x\|c
--R     + 
--R       -
--R              +-+
--R            b\|c
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R           +-+
--R         b\|c
--R      *
--R         log
--R                            2           +-+          2              2  +-+
--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
--R               *
--R                   +--------------+
--R                   |   2
--R                  \|a x  + b x + c
--R              + 
--R                         3              2  2              2  +-+ +-+     2   3
--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
--R              + 
--R                        2       2
--R                6a b c x  + 8a c x
--R           /
--R                               +--------------+
--R                            2  |   2
--R                (4b c x + 8c )\|a x  + b x + c
--R              + 
--R                            2  2              2  +-+
--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
--R     + 
--R          +-+
--R       2c\|a
--R  /
--R       +-+ +-+
--R     2\|a \|c
--R                                                     Type: Expression Integer
--E

--S 77 of 131
cc2:=aa.2-bb1
 

   (7)
                               +--------------+
                           +-+ |   2
            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2c\|- a \|a log(---------------------------------)
                                         x
     + 
                             +--------------+
                         +-+ |   2
          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|- a \|a log(---------------------------------)
                                        +-+
                                     2x\|c
     + 
       -
              +---+ +-+
            b\|- a \|c
         *
            log
                                      +--------------+
                      +-+ +-+         |   2                   +-+
                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                 + 
                          2             +-+
                   (- 2a x  - b x - 2c)\|a
              /
                       +--------------+
                   +-+ |   2
                 2\|c \|a x  + b x + c  - b x - 2c
     + 
                                 +--------------+
                       +---+ +-+ |   2                +---+
          +-+ +-+     \|- a \|c \|a x  + b x + c  - c\|- a        +---+ +-+
       2b\|a \|c atan(-------------------------------------) + 2c\|- a \|a
                                         +-+
                                     a x\|c
  /
       +---+ +-+ +-+
     2\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (7)
--R                               +--------------+
--R                           +-+ |   2
--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2c\|- a \|a log(---------------------------------)
--R                                         x
--R     + 
--R                             +--------------+
--R                         +-+ |   2
--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|- a \|a log(---------------------------------)
--R                                        +-+
--R                                     2x\|c
--R     + 
--R       -
--R              +---+ +-+
--R            b\|- a \|c
--R         *
--R            log
--R                                      +--------------+
--R                      +-+ +-+         |   2                   +-+
--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                 + 
--R                          2             +-+
--R                   (- 2a x  - b x - 2c)\|a
--R              /
--R                       +--------------+
--R                   +-+ |   2
--R                 2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                 +--------------+
--R                       +---+ +-+ |   2                +---+
--R          +-+ +-+     \|- a \|c \|a x  + b x + c  - c\|- a        +---+ +-+
--R       2b\|a \|c atan(-------------------------------------) + 2c\|- a \|a
--R                                         +-+
--R                                     a x\|c
--R  /
--R       +---+ +-+ +-+
--R     2\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 78 of 131
cc3:=aa.1-bb2
 

   (8)
                               +--------------+
                           +-+ |   2
            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2c\|- a \|a log(---------------------------------)
                                         x
     + 
                             +--------------+
                         +-+ |   2
          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
       2c\|- a \|a log(---------------------------------)
                                        +-+
                                     2x\|c
     + 
           +---+ +-+
         b\|- a \|c
      *
         log
                            2           +-+          2              2  +-+
                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
               *
                   +--------------+
                   |   2
                  \|a x  + b x + c
              + 
                         3              2  2              2  +-+ +-+     2   3
                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
              + 
                        2       2
                6a b c x  + 8a c x
           /
                               +--------------+
                            2  |   2
                (4b c x + 8c )\|a x  + b x + c
              + 
                            2  2              2  +-+
                ((- 4a c - b )x  - 8b c x - 8c )\|c
     + 
                               +--------------+
                         +---+ |   2               +---+ +-+
            +-+ +-+     \|- a \|a x  + b x + c  - \|- a \|c        +---+ +-+
       - 2b\|a \|c atan(------------------------------------) + 2c\|- a \|a
                                         a x
  /
       +---+ +-+ +-+
     2\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (8)
--R                               +--------------+
--R                           +-+ |   2
--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2c\|- a \|a log(---------------------------------)
--R                                         x
--R     + 
--R                             +--------------+
--R                         +-+ |   2
--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       2c\|- a \|a log(---------------------------------)
--R                                        +-+
--R                                     2x\|c
--R     + 
--R           +---+ +-+
--R         b\|- a \|c
--R      *
--R         log
--R                            2           +-+          2              2  +-+
--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
--R               *
--R                   +--------------+
--R                   |   2
--R                  \|a x  + b x + c
--R              + 
--R                         3              2  2              2  +-+ +-+     2   3
--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
--R              + 
--R                        2       2
--R                6a b c x  + 8a c x
--R           /
--R                               +--------------+
--R                            2  |   2
--R                (4b c x + 8c )\|a x  + b x + c
--R              + 
--R                            2  2              2  +-+
--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
--R     + 
--R                               +--------------+
--R                         +---+ |   2               +---+ +-+
--R            +-+ +-+     \|- a \|a x  + b x + c  - \|- a \|c        +---+ +-+
--R       - 2b\|a \|c atan(------------------------------------) + 2c\|- a \|a
--R                                         a x
--R  /
--R       +---+ +-+ +-+
--R     2\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 79 of 131
cc4:=aa.2-bb2
 

   (9)
                          +--------------+
                      +-+ |   2
           +---+    2\|c \|a x  + b x + c  - b x - 2c
       - c\|- a log(---------------------------------)
                                    x
     + 
                        +--------------+
                    +-+ |   2
         +---+    2\|c \|a x  + b x + c  - b x - 2c
       c\|- a log(---------------------------------)
                                   +-+
                                2x\|c
     + 
                            +--------------+
                  +---+ +-+ |   2                +---+
         +-+     \|- a \|c \|a x  + b x + c  - c\|- a
       b\|c atan(-------------------------------------)
                                    +-+
                                a x\|c
     + 
                          +--------------+
                    +---+ |   2               +---+ +-+
           +-+     \|- a \|a x  + b x + c  - \|- a \|c       +---+
       - b\|c atan(------------------------------------) + c\|- a
                                    a x
  /
      +---+ +-+
     \|- a \|c
                                                     Type: Expression Integer
--R
--R   (9)
--R                          +--------------+
--R                      +-+ |   2
--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       - c\|- a log(---------------------------------)
--R                                    x
--R     + 
--R                        +--------------+
--R                    +-+ |   2
--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       c\|- a log(---------------------------------)
--R                                   +-+
--R                                2x\|c
--R     + 
--R                            +--------------+
--R                  +---+ +-+ |   2                +---+
--R         +-+     \|- a \|c \|a x  + b x + c  - c\|- a
--R       b\|c atan(-------------------------------------)
--R                                    +-+
--R                                a x\|c
--R     + 
--R                          +--------------+
--R                    +---+ |   2               +---+ +-+
--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c       +---+
--R       - b\|c atan(------------------------------------) + c\|- a
--R                                    a x
--R  /
--R      +---+ +-+
--R     \|- a \|c
--R                                                     Type: Expression Integer
--E

--S 80 of 131
dd4:=ratDenom cc4
 

   (10)
                     +--------------+
                 +-+ |   2
        +-+    2\|c \|a x  + b x + c  - b x - 2c
     - \|c log(---------------------------------)
                               x
   + 
                +--------------+
                |   2                           +-+
      +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
     \|c log(--------------------------------------) + \|c
                              2c x
                                                     Type: Expression Integer
--R
--R   (10)
--R                     +--------------+
--R                 +-+ |   2
--R        +-+    2\|c \|a x  + b x + c  - b x - 2c
--R     - \|c log(---------------------------------)
--R                               x
--R   + 
--R                +--------------+
--R                |   2                           +-+
--R      +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
--R     \|c log(--------------------------------------) + \|c
--R                              2c x
--R                                                     Type: Expression Integer
--E

--S 81 of 131
ee4:=expandLog dd4
 

   (11)
                     +--------------+
        +-+      +-+ |   2
     - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
   + 
              +--------------+
    +-+       |   2                           +-+                            +-+
   \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c ) + (- log(c) - log(2) + 1)\|c
                                                     Type: Expression Integer
--R
--R   (11)
--R                     +--------------+
--R        +-+      +-+ |   2
--R     - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R   + 
--R              +--------------+
--R    +-+       |   2                           +-+                            +-+
--R   \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c ) + (- log(c) - log(2) + 1)\|c
--R                                                     Type: Expression Integer
--E

--S 82 of 131     14:288 Schaums and Axiom differ by a constant
ff4:=complexNormalize ee4
 

                                  +-+
         (- log(c) - 2log(2) + 2)\|c
   (12)  ----------------------------
                       2
                                                     Type: Expression Integer
--R
--R                                  +-+
--R         (- log(c) - 2log(2) + 2)\|c
--R   (12)  ----------------------------
--R                       2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 83 of 131
aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
 

   (1)
   [
                     +--------------+
                 +-+ |   2                2 2
           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
        *
                  +--------------+
                  |   2                           +-+
               2c\|a x  + b x + c  + (- b x - 2c)\|c
           log(--------------------------------------)
                                2c x
       + 
                     +--------------+
                 +-+ |   2                     2         +-+ +-+
           (8c x\|a \|a x  + b x + c  + (- 4b x  - 8c x)\|a \|c )
        *
                              +--------------+
                +-+      +-+  |   2                 +-+ +-+       2
             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
         log(-----------------------------------------------------------------)
                                   +--------------+
                               +-+ |   2
                             2\|c \|a x  + b x + c  - b x - 2c
       + 
                         +--------------+
                     +-+ |   2                         2  2              2
         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
    /
            +--------------+
            |   2                     2         +-+
       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
     ,

                     +--------------+
                 +-+ |   2                2 2
           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
        *
                  +--------------+
                  |   2                           +-+
               2c\|a x  + b x + c  + (- b x - 2c)\|c
           log(--------------------------------------)
                                2c x
       + 
                        +--------------+
                  +---+ |   2                     2          +---+ +-+
           (16c x\|- a \|a x  + b x + c  + (- 8b x  - 16c x)\|- a \|c )
        *
                 +--------------+
                 |   2               +-+
                \|a x  + b x + c  - \|c
           atan(------------------------)
                           +---+
                         x\|- a
       + 
                         +--------------+
                     +-+ |   2                         2  2              2
         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
    /
            +--------------+
            |   2                     2         +-+
       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                     +--------------+
--R                 +-+ |   2                2 2
--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
--R        *
--R                  +--------------+
--R                  |   2                           +-+
--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
--R           log(--------------------------------------)
--R                                2c x
--R       + 
--R                     +--------------+
--R                 +-+ |   2                     2         +-+ +-+
--R           (8c x\|a \|a x  + b x + c  + (- 4b x  - 8c x)\|a \|c )
--R        *
--R                              +--------------+
--R                +-+      +-+  |   2                 +-+ +-+       2
--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
--R         log(-----------------------------------------------------------------)
--R                                   +--------------+
--R                               +-+ |   2
--R                             2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                         +--------------+
--R                     +-+ |   2                         2  2              2
--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
--R    /
--R            +--------------+
--R            |   2                     2         +-+
--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
--R     ,
--R
--R                     +--------------+
--R                 +-+ |   2                2 2
--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
--R        *
--R                  +--------------+
--R                  |   2                           +-+
--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
--R           log(--------------------------------------)
--R                                2c x
--R       + 
--R                        +--------------+
--R                  +---+ |   2                     2          +---+ +-+
--R           (16c x\|- a \|a x  + b x + c  + (- 8b x  - 16c x)\|- a \|c )
--R        *
--R                 +--------------+
--R                 |   2               +-+
--R                \|a x  + b x + c  - \|c
--R           atan(------------------------)
--R                           +---+
--R                         x\|- a
--R       + 
--R                         +--------------+
--R                     +-+ |   2                         2  2              2
--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
--R    /
--R            +--------------+
--R            |   2                     2         +-+
--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 84 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 85 of 131
t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (3)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (3)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 86 of 131
bb1:=-sqrt(a*x^2+b*x+c)/x+a*t1.1+b/2*t2
 

   (4)
                        +--------------+
                    +-+ |   2
           +-+    2\|c \|a x  + b x + c  - b x - 2c
       b x\|a log(---------------------------------)
                                  x
     + 
              +-+
         2a x\|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   +--------------+
           +-+ +-+ |   2
       - 2\|a \|c \|a x  + b x + c
  /
        +-+ +-+
     2x\|a \|c
                                                     Type: Expression Integer
--R
--R   (4)
--R                        +--------------+
--R                    +-+ |   2
--R           +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       b x\|a log(---------------------------------)
--R                                  x
--R     + 
--R              +-+
--R         2a x\|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   +--------------+
--R           +-+ +-+ |   2
--R       - 2\|a \|c \|a x  + b x + c
--R  /
--R        +-+ +-+
--R     2x\|a \|c
--R                                                     Type: Expression Integer
--E

--S 87 of 131
bb2:=-sqrt(a*x^2+b*x+c)/x+a*t1.2+b/2*t2
 

   (5)
                          +--------------+
                      +-+ |   2
           +---+    2\|c \|a x  + b x + c  - b x - 2c
       b x\|- a log(---------------------------------)
                                    x
     + 
                           +--------------+
                     +---+ |   2               +---+ +-+
            +-+     \|- a \|a x  + b x + c  - \|- a \|c
       4a x\|c atan(------------------------------------)
                                     a x
     + 
                     +--------------+
           +---+ +-+ |   2
       - 2\|- a \|c \|a x  + b x + c
  /
        +---+ +-+
     2x\|- a \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                          +--------------+
--R                      +-+ |   2
--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
--R       b x\|- a log(---------------------------------)
--R                                    x
--R     + 
--R                           +--------------+
--R                     +---+ |   2               +---+ +-+
--R            +-+     \|- a \|a x  + b x + c  - \|- a \|c
--R       4a x\|c atan(------------------------------------)
--R                                     a x
--R     + 
--R                     +--------------+
--R           +---+ +-+ |   2
--R       - 2\|- a \|c \|a x  + b x + c
--R  /
--R        +---+ +-+
--R     2x\|- a \|c
--R                                                     Type: Expression Integer
--E

--S 88 of 131
cc1:=aa.1-bb1
 

   (6)
                     +--------------+
                 +-+ |   2                 2          +-+ +-+
         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                   +--------------+
               +-+ |   2                   2          +-+ +-+
         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                     +--------------+
                 +-+ |   2                             2
         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                   +--------------+
               +-+ |   2                             2
         (8a c\|c \|a x  + b x + c  - 4a b c x - 8a c )
      *
                              +--------------+
                +-+      +-+  |   2                 +-+ +-+       2
             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
         log(-----------------------------------------------------------------)
                                   +--------------+
                               +-+ |   2
                             2\|c \|a x  + b x + c  - b x - 2c
     + 
                  +--------------+
              +-+ |   2                2          +-+ +-+
       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
  /
                +--------------+
        +-+ +-+ |   2                            2  +-+
     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
                                                     Type: Expression Integer
--R
--R   (6)
--R                     +--------------+
--R                 +-+ |   2                 2          +-+ +-+
--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                   +--------------+
--R               +-+ |   2                   2          +-+ +-+
--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                     +--------------+
--R                 +-+ |   2                             2
--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                   +--------------+
--R               +-+ |   2                             2
--R         (8a c\|c \|a x  + b x + c  - 4a b c x - 8a c )
--R      *
--R                              +--------------+
--R                +-+      +-+  |   2                 +-+ +-+       2
--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
--R         log(-----------------------------------------------------------------)
--R                                   +--------------+
--R                               +-+ |   2
--R                             2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                  +--------------+
--R              +-+ |   2                2          +-+ +-+
--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
--R  /
--R                +--------------+
--R        +-+ +-+ |   2                            2  +-+
--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
--R                                                     Type: Expression Integer
--E

--S 89 of 131
cc2:=aa.2-bb1
 

   (7)
                     +--------------+
                 +-+ |   2                 2          +-+ +-+
         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                   +--------------+
               +-+ |   2                   2          +-+ +-+
         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                     +--------------+
                 +-+ |   2                             2
         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                            +--------------+
              +---+ +-+ +-+ |   2                             2  +---+ +-+
         (16c\|- a \|a \|c \|a x  + b x + c  + (- 8b c x - 16c )\|- a \|a )
      *
               +--------------+
               |   2               +-+
              \|a x  + b x + c  - \|c
         atan(------------------------)
                         +---+
                       x\|- a
     + 
                  +--------------+
              +-+ |   2                2          +-+ +-+
       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
  /
                +--------------+
        +-+ +-+ |   2                            2  +-+
     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
                                                     Type: Expression Integer
--R
--R   (7)
--R                     +--------------+
--R                 +-+ |   2                 2          +-+ +-+
--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                   +--------------+
--R               +-+ |   2                   2          +-+ +-+
--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                     +--------------+
--R                 +-+ |   2                             2
--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                            +--------------+
--R              +---+ +-+ +-+ |   2                             2  +---+ +-+
--R         (16c\|- a \|a \|c \|a x  + b x + c  + (- 8b c x - 16c )\|- a \|a )
--R      *
--R               +--------------+
--R               |   2               +-+
--R              \|a x  + b x + c  - \|c
--R         atan(------------------------)
--R                         +---+
--R                       x\|- a
--R     + 
--R                  +--------------+
--R              +-+ |   2                2          +-+ +-+
--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
--R  /
--R                +--------------+
--R        +-+ +-+ |   2                            2  +-+
--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
--R                                                     Type: Expression Integer
--E

--S 90 of 131
cc3:=aa.1-bb2
 

   (8)
                       +--------------+
                 +---+ |   2                 2          +---+ +-+
         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                     +--------------+
               +---+ |   2                   2          +---+ +-+
         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                           +--------------+
             +---+ +-+ +-+ |   2                            2  +---+ +-+
         (8c\|- a \|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a \|a )
      *
                              +--------------+
                +-+      +-+  |   2                 +-+ +-+       2
             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
         log(-----------------------------------------------------------------)
                                   +--------------+
                               +-+ |   2
                             2\|c \|a x  + b x + c  - b x - 2c
     + 
                      +--------------+
                  +-+ |   2                              2
         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                    +--------------+
              +---+ |   2                2          +---+ +-+
       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
  /
                  +--------------+
        +---+ +-+ |   2                            2  +---+
     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
                                                     Type: Expression Integer
--R
--R   (8)
--R                       +--------------+
--R                 +---+ |   2                 2          +---+ +-+
--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                     +--------------+
--R               +---+ |   2                   2          +---+ +-+
--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                           +--------------+
--R             +---+ +-+ +-+ |   2                            2  +---+ +-+
--R         (8c\|- a \|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a \|a )
--R      *
--R                              +--------------+
--R                +-+      +-+  |   2                 +-+ +-+       2
--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
--R         log(-----------------------------------------------------------------)
--R                                   +--------------+
--R                               +-+ |   2
--R                             2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                      +--------------+
--R                  +-+ |   2                              2
--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                    +--------------+
--R              +---+ |   2                2          +---+ +-+
--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
--R  /
--R                  +--------------+
--R        +---+ +-+ |   2                            2  +---+
--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
--R                                                     Type: Expression Integer
--E

--S 91 of 131
cc4:=aa.2-bb2
 

   (9)
                       +--------------+
                 +---+ |   2                 2          +---+ +-+
         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                     +--------------+
               +---+ |   2                   2          +---+ +-+
         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
      *
                +--------------+
                |   2                           +-+
             2c\|a x  + b x + c  + (- b x - 2c)\|c
         log(--------------------------------------)
                              2c x
     + 
                      +--------------+
                  +-+ |   2                              2
         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                      +--------------+
                  +-+ |   2                              2
         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
      *
               +--------------+
               |   2               +-+
              \|a x  + b x + c  - \|c
         atan(------------------------)
                         +---+
                       x\|- a
     + 
                    +--------------+
              +---+ |   2                2          +---+ +-+
       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
  /
                  +--------------+
        +---+ +-+ |   2                            2  +---+
     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
                                                     Type: Expression Integer
--R
--R   (9)
--R                       +--------------+
--R                 +---+ |   2                 2          +---+ +-+
--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                     +--------------+
--R               +---+ |   2                   2          +---+ +-+
--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
--R      *
--R                +--------------+
--R                |   2                           +-+
--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
--R         log(--------------------------------------)
--R                              2c x
--R     + 
--R                      +--------------+
--R                  +-+ |   2                              2
--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                      +--------------+
--R                  +-+ |   2                              2
--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
--R      *
--R               +--------------+
--R               |   2               +-+
--R              \|a x  + b x + c  - \|c
--R         atan(------------------------)
--R                         +---+
--R                       x\|- a
--R     + 
--R                    +--------------+
--R              +---+ |   2                2          +---+ +-+
--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
--R  /
--R                  +--------------+
--R        +---+ +-+ |   2                            2  +---+
--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
--R                                                     Type: Expression Integer
--E

--S 92 of 131
dd4:=ratDenom cc4
 

   (10)
                         +--------------+
                     +-+ |   2
            +-+    2\|c \|a x  + b x + c  - b x - 2c
       - 2b\|c log(---------------------------------)
                                   x
     + 
                    +--------------+
                    |   2                           +-+
          +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c       +-+
       2b\|c log(--------------------------------------) - b\|c
                                  2c x
  /
     4c
                                                     Type: Expression Integer
--R
--R   (10)
--R                         +--------------+
--R                     +-+ |   2
--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - 2b\|c log(---------------------------------)
--R                                   x
--R     + 
--R                    +--------------+
--R                    |   2                           +-+
--R          +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c       +-+
--R       2b\|c log(--------------------------------------) - b\|c
--R                                  2c x
--R  /
--R     4c
--R                                                     Type: Expression Integer
--E

--S 93 of 131
ee4:=expandLog dd4
 

   (11)
                         +--------------+
            +-+      +-+ |   2
       - 2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                    +--------------+
          +-+       |   2                           +-+
       2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                     +-+
       (- 2b log(c) - 2b log(2) - b)\|c
  /
     4c
                                                     Type: Expression Integer
--R
--R   (11)
--R                         +--------------+
--R            +-+      +-+ |   2
--R       - 2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                    +--------------+
--R          +-+       |   2                           +-+
--R       2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                     +-+
--R       (- 2b log(c) - 2b log(2) - b)\|c
--R  /
--R     4c
--R                                                     Type: Expression Integer
--E

--S 94 of 131     14:289 Schaums and Axiom differ by a constant
ff4:=complexNormalize ee4
 

                                      +-+
         (- b log(c) - 2b log(2) - b)\|c
   (12)  --------------------------------
                        4c
                                                     Type: Expression Integer
--R
--R                                      +-+
--R         (- b log(c) - 2b log(2) - b)\|c
--R   (12)  --------------------------------
--R                        4c
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 95 of 131
aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 

                          +--------------+
                          |   2                 +-+
                     - 2x\|a x  + b x + c  + 2x\|c
   (1)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                          +--------------+
--R                          |   2                 +-+
--R                     - 2x\|a x  + b x + c  + 2x\|c
--R   (1)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 96 of 131
bb:=(2*(2*a*x+b))/((4*a*c-b^2)*sqrt(a*x^2+b*x+c))
 

                  4a x + 2b
   (2)  ----------------------------
                    +--------------+
                 2  |   2
        (4a c - b )\|a x  + b x + c
                                                     Type: Expression Integer
--R
--R                  4a x + 2b
--R   (2)  ----------------------------
--R                    +--------------+
--R                 2  |   2
--R        (4a c - b )\|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 97 of 131
cc:=aa-bb
 

   (3)
                           +--------------+
                       +-+ |   2                2
                    4b\|c \|a x  + b x + c  - 2b x - 4b c
   -----------------------------------------------------------------------
                  +--------------+
        2     2   |   2                            3         2     2   +-+
   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
                                                     Type: Expression Integer
--R
--R   (3)
--R                           +--------------+
--R                       +-+ |   2                2
--R                    4b\|c \|a x  + b x + c  - 2b x - 4b c
--R   -----------------------------------------------------------------------
--R                  +--------------+
--R        2     2   |   2                            3         2     2   +-+
--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
--R                                                     Type: Expression Integer
--E

--S 98 of 131     14:290 Schaums and Axiom differ by a constant
dd:=ratDenom cc
 

              +-+
           2b\|c
   (4)  -----------
            2    2
        4a c  - b c
                                                     Type: Expression Integer
--R
--R              +-+
--R           2b\|c
--R   (4)  -----------
--R            2    2
--R        4a c  - b c
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 99 of 131
aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
 

                                   2 +-+
                                 2x \|c
   (1)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                   2 +-+
--R                                 2x \|c
--R   (1)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 100 of 131
bb:=(2*(b*x+2*c))/((b^2-4*a*c)*sqrt(a*x^2+b*x+c))
 

                 - 2b x - 4c
   (2)  ----------------------------
                    +--------------+
                 2  |   2
        (4a c - b )\|a x  + b x + c
                                                     Type: Expression Integer
--R
--R                 - 2b x - 4c
--R   (2)  ----------------------------
--R                    +--------------+
--R                 2  |   2
--R        (4a c - b )\|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 101 of 131
cc:=aa-bb
 

   (3)
                            +--------------+
                        +-+ |   2                         2
                   - 8c\|c \|a x  + b x + c  + 4b c x + 8c
   -----------------------------------------------------------------------
                  +--------------+
        2     2   |   2                            3         2     2   +-+
   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
                                                     Type: Expression Integer
--R
--R   (3)
--R                            +--------------+
--R                        +-+ |   2                         2
--R                   - 8c\|c \|a x  + b x + c  + 4b c x + 8c
--R   -----------------------------------------------------------------------
--R                  +--------------+
--R        2     2   |   2                            3         2     2   +-+
--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
--R                                                     Type: Expression Integer
--E

--S 102 of 131    14:291 Schaums and Axiom differ by a constant
dd:=ratDenom cc
 

              +-+
            4\|c
   (4)  - ---------
                  2
          4a c - b
                                                     Type: Expression Integer
--R
--R              +-+
--R            4\|c
--R   (4)  - ---------
--R                  2
--R          4a c - b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 103 of 131
aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
 

   (1)
   [
                           +--------------+
                       +-+ |   2                    2              2
           ((b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c )
        *
           log
                                     +--------------+
                     +-+ +-+         |   2                   +-+
                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
                + 
                         2             +-+
                  (- 2a x  - b x - 2c)\|a
             /
                      +--------------+
                  +-+ |   2
                2\|c \|a x  + b x + c  - b x - 2c
       + 
                  +--------------+
              +-+ |   2                     2         +-+ +-+
         2c x\|a \|a x  + b x + c  + (- 2b x  - 2c x)\|a \|c
    /
                                +--------------+
                        +-+ +-+ |   2
         (a b x + 2a c)\|a \|c \|a x  + b x + c
       + 
              2   2                  2  +-+
         (- 2a c x  - 2a b c x - 2a c )\|a
     ,

                            +--------------+
                        +-+ |   2                    2              2
           ((2b x + 4c)\|c \|a x  + b x + c  - 4a c x  - 4b c x - 4c )
        *
                       +--------------+
                 +---+ |   2               +---+ +-+
                \|- a \|a x  + b x + c  - \|- a \|c
           atan(------------------------------------)
                                 a x
       + 
                    +--------------+
              +---+ |   2                     2         +---+ +-+
         2c x\|- a \|a x  + b x + c  + (- 2b x  - 2c x)\|- a \|c
    /
                                  +--------------+
                        +---+ +-+ |   2
         (a b x + 2a c)\|- a \|c \|a x  + b x + c
       + 
              2   2                  2  +---+
         (- 2a c x  - 2a b c x - 2a c )\|- a
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                           +--------------+
--R                       +-+ |   2                    2              2
--R           ((b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c )
--R        *
--R           log
--R                                     +--------------+
--R                     +-+ +-+         |   2                   +-+
--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R                + 
--R                         2             +-+
--R                  (- 2a x  - b x - 2c)\|a
--R             /
--R                      +--------------+
--R                  +-+ |   2
--R                2\|c \|a x  + b x + c  - b x - 2c
--R       + 
--R                  +--------------+
--R              +-+ |   2                     2         +-+ +-+
--R         2c x\|a \|a x  + b x + c  + (- 2b x  - 2c x)\|a \|c
--R    /
--R                                +--------------+
--R                        +-+ +-+ |   2
--R         (a b x + 2a c)\|a \|c \|a x  + b x + c
--R       + 
--R              2   2                  2  +-+
--R         (- 2a c x  - 2a b c x - 2a c )\|a
--R     ,
--R
--R                            +--------------+
--R                        +-+ |   2                    2              2
--R           ((2b x + 4c)\|c \|a x  + b x + c  - 4a c x  - 4b c x - 4c )
--R        *
--R                       +--------------+
--R                 +---+ |   2               +---+ +-+
--R                \|- a \|a x  + b x + c  - \|- a \|c
--R           atan(------------------------------------)
--R                                 a x
--R       + 
--R                    +--------------+
--R              +---+ |   2                     2         +---+ +-+
--R         2c x\|- a \|a x  + b x + c  + (- 2b x  - 2c x)\|- a \|c
--R    /
--R                                  +--------------+
--R                        +---+ +-+ |   2
--R         (a b x + 2a c)\|- a \|c \|a x  + b x + c
--R       + 
--R              2   2                  2  +---+
--R         (- 2a c x  - 2a b c x - 2a c )\|- a
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 104 of 131
t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                 +--------------+
                 +-+ +-+         |   2                   +-+
              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
            + 
                     2             +-+
              (- 2a x  - b x - 2c)\|a
         /
                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
    /
        +-+
       \|a
     ,
                 +--------------+
           +---+ |   2               +---+ +-+
          \|- a \|a x  + b x + c  - \|- a \|c
    2atan(------------------------------------)
                           a x
    -------------------------------------------]
                        +---+
                       \|- a
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                 +--------------+
--R                 +-+ +-+         |   2                   +-+
--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R            + 
--R                     2             +-+
--R              (- 2a x  - b x - 2c)\|a
--R         /
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R    /
--R        +-+
--R       \|a
--R     ,
--R                 +--------------+
--R           +---+ |   2               +---+ +-+
--R          \|- a \|a x  + b x + c  - \|- a \|c
--R    2atan(------------------------------------)
--R                           a x
--R    -------------------------------------------]
--R                        +---+
--R                       \|- a
--R                                     Type: Union(List Expression Integer,...)
--E

--S 105 of 131
bb1:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.1
 

   (3)
                     +--------------+
                  2  |   2
         (4a c - b )\|a x  + b x + c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                    2           +-+
       ((- 4a c + 2b )x + 2b c)\|a
  /
                       +--------------+
        2       2  +-+ |   2
     (4a c - a b )\|a \|a x  + b x + c
                                                     Type: Expression Integer
--R
--R   (3)
--R                     +--------------+
--R                  2  |   2
--R         (4a c - b )\|a x  + b x + c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                    2           +-+
--R       ((- 4a c + 2b )x + 2b c)\|a
--R  /
--R                       +--------------+
--R        2       2  +-+ |   2
--R     (4a c - a b )\|a \|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 106 of 131
bb2:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.2
 

   (4)
                                                +--------------+
                    +--------------+      +---+ |   2               +---+ +-+
                 2  |   2                \|- a \|a x  + b x + c  - \|- a \|c
       (8a c - 2b )\|a x  + b x + c atan(------------------------------------)
                                                          a x
     + 
                    2           +---+
       ((- 4a c + 2b )x + 2b c)\|- a
  /
                         +--------------+
        2       2  +---+ |   2
     (4a c - a b )\|- a \|a x  + b x + c
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                +--------------+
--R                    +--------------+      +---+ |   2               +---+ +-+
--R                 2  |   2                \|- a \|a x  + b x + c  - \|- a \|c
--R       (8a c - 2b )\|a x  + b x + c atan(------------------------------------)
--R                                                          a x
--R     + 
--R                    2           +---+
--R       ((- 4a c + 2b )x + 2b c)\|- a
--R  /
--R                         +--------------+
--R        2       2  +---+ |   2
--R     (4a c - a b )\|- a \|a x  + b x + c
--R                                                     Type: Expression Integer
--E

--S 107 of 131
cc1:=aa.1-bb1
 

   (5)
                              +--------------+
                          +-+ |   2                2          2
                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
   -----------------------------------------------------------------------------
                    +--------------+
      2 2       2   |   2                    2         3       2 2       2   +-+
   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                              +--------------+
--R                          +-+ |   2                2          2
--R                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
--R   -----------------------------------------------------------------------------
--R                    +--------------+
--R      2 2       2   |   2                    2         3       2 2       2   +-+
--R   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
--R                                                     Type: Expression Integer
--E

--S 108 of 131
cc2:=aa.2-bb1
 

   (6)
                                  +--------------+
                  2     2   +---+ |   2
           (- 8a c  + 2b c)\|- a \|a x  + b x + c
         + 
                       3         2     2   +---+ +-+
           ((4a b c - b )x + 8a c  - 2b c)\|- a \|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                               +--------------+
                 2     2   +-+ |   2
           (16a c  - 4b c)\|a \|a x  + b x + c
         + 
                          3          2     2   +-+ +-+
           ((- 8a b c + 2b )x - 16a c  + 4b c)\|a \|c
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                          +--------------+
            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
  /
                                  +--------------+
          2 2       2   +---+ +-+ |   2
       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
     + 
             2         3       2 2       2   +---+ +-+ +-+
       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (6)
--R                                  +--------------+
--R                  2     2   +---+ |   2
--R           (- 8a c  + 2b c)\|- a \|a x  + b x + c
--R         + 
--R                       3         2     2   +---+ +-+
--R           ((4a b c - b )x + 8a c  - 2b c)\|- a \|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                               +--------------+
--R                 2     2   +-+ |   2
--R           (16a c  - 4b c)\|a \|a x  + b x + c
--R         + 
--R                          3          2     2   +-+ +-+
--R           ((- 8a b c + 2b )x - 16a c  + 4b c)\|a \|c
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                          +--------------+
--R            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
--R       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
--R  /
--R                                  +--------------+
--R          2 2       2   +---+ +-+ |   2
--R       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
--R     + 
--R             2         3       2 2       2   +---+ +-+ +-+
--R       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 109 of 131
cc3:=aa.1-bb2
 

   (7)
                                +--------------+
                2     2   +---+ |   2
           (8a c  - 2b c)\|- a \|a x  + b x + c
         + 
                         3         2     2   +---+ +-+
           ((- 4a b c + b )x - 8a c  + 2b c)\|- a \|c
      *
         log
                                   +--------------+
                   +-+ +-+         |   2                   +-+
                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
              + 
                       2             +-+
                (- 2a x  - b x - 2c)\|a
           /
                    +--------------+
                +-+ |   2
              2\|c \|a x  + b x + c  - b x - 2c
     + 
                                 +--------------+
                   2     2   +-+ |   2
           (- 16a c  + 4b c)\|a \|a x  + b x + c
         + 
                        3          2     2   +-+ +-+
           ((8a b c - 2b )x + 16a c  - 4b c)\|a \|c
      *
                     +--------------+
               +---+ |   2               +---+ +-+
              \|- a \|a x  + b x + c  - \|- a \|c
         atan(------------------------------------)
                               a x
     + 
                          +--------------+
            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
  /
                                  +--------------+
          2 2       2   +---+ +-+ |   2
       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
     + 
             2         3       2 2       2   +---+ +-+ +-+
       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
                                                     Type: Expression Integer
--R
--R   (7)
--R                                +--------------+
--R                2     2   +---+ |   2
--R           (8a c  - 2b c)\|- a \|a x  + b x + c
--R         + 
--R                         3         2     2   +---+ +-+
--R           ((- 4a b c + b )x - 8a c  + 2b c)\|- a \|c
--R      *
--R         log
--R                                   +--------------+
--R                   +-+ +-+         |   2                   +-+
--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
--R              + 
--R                       2             +-+
--R                (- 2a x  - b x - 2c)\|a
--R           /
--R                    +--------------+
--R                +-+ |   2
--R              2\|c \|a x  + b x + c  - b x - 2c
--R     + 
--R                                 +--------------+
--R                   2     2   +-+ |   2
--R           (- 16a c  + 4b c)\|a \|a x  + b x + c
--R         + 
--R                        3          2     2   +-+ +-+
--R           ((8a b c - 2b )x + 16a c  - 4b c)\|a \|c
--R      *
--R                     +--------------+
--R               +---+ |   2               +---+ +-+
--R              \|- a \|a x  + b x + c  - \|- a \|c
--R         atan(------------------------------------)
--R                               a x
--R     + 
--R                          +--------------+
--R            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
--R       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
--R  /
--R                                  +--------------+
--R          2 2       2   +---+ +-+ |   2
--R       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
--R     + 
--R             2         3       2 2       2   +---+ +-+ +-+
--R       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
--R                                                     Type: Expression Integer
--E

--S 110 of 131
cc4:=aa.2-bb2
 

   (8)
                              +--------------+
                          +-+ |   2                2          2
                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
   -----------------------------------------------------------------------------
                    +--------------+
      2 2       2   |   2                    2         3       2 2       2   +-+
   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
                                                     Type: Expression Integer
--R
--R   (8)
--R                              +--------------+
--R                          +-+ |   2                2          2
--R                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
--R   -----------------------------------------------------------------------------
--R                    +--------------+
--R      2 2       2   |   2                    2         3       2 2       2   +-+
--R   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
--R                                                     Type: Expression Integer
--E

--S 111 of 131    14:292 Schaums and Axiom differ by a constant
dd4:=ratDenom cc4
 

              +-+
           2b\|c
   (9)  -----------
          2       2
        4a c - a b
                                                     Type: Expression Integer
--R
--R              +-+
--R           2b\|c
--R   (9)  -----------
--R          2       2
--R        4a c - a b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 112 of 131
aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
 

   (1)
                     +--------------+
                     |   2                     2              +-+
         ((b x + 2c)\|a x  + b x + c  + (- 2a x  - 2b x - 2c)\|c )
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
            +--------------+
            |   2                     2         +-+
       2b x\|a x  + b x + c  + (- 2a x  - 2b x)\|c
  /
                       +--------------+
                2  +-+ |   2                  2 2       2      3
     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                     +--------------+
--R                     |   2                     2              +-+
--R         ((b x + 2c)\|a x  + b x + c  + (- 2a x  - 2b x - 2c)\|c )
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R            +--------------+
--R            |   2                     2         +-+
--R       2b x\|a x  + b x + c  + (- 2a x  - 2b x)\|c
--R  /
--R                       +--------------+
--R                2  +-+ |   2                  2 2       2      3
--R     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 113 of 131
t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (2)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (2)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 114 of 131
t2:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 

                          +--------------+
                          |   2                 +-+
                     - 2x\|a x  + b x + c  + 2x\|c
   (3)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R
--R                          +--------------+
--R                          |   2                 +-+
--R                     - 2x\|a x  + b x + c  + 2x\|c
--R   (3)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E

--S 115 of 131
bb:=1/(c*sqrt(a*x^2+b*x+c))+1/c*t1-b/(2*c)*t2
 

   (4)
                                    +--------------+
                  2              2  |   2
           (2a c x  + 2b c x + 2c )\|a x  + b x + c
         + 
                   3              2  2              2  +-+
           (- a b x  + (- 2a c - b )x  - 3b c x - 2c )\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
             +--------------+
           2 |   2                      3            2  2             2  +-+
       - 2c \|a x  + b x + c  + (- a b x  + (2a c - b )x  + b c x + 2c )\|c
  /
                                    +--------------+
            2 2       2      3  +-+ |   2                   2 3
       (2a c x  + 2b c x + 2c )\|c \|a x  + b x + c  - a b c x
     + 
              3    2 2  2       3      4
       (- 2a c  - b c )x  - 3b c x - 2c
                                                     Type: Expression Integer
--R
--R   (4)
--R                                    +--------------+
--R                  2              2  |   2
--R           (2a c x  + 2b c x + 2c )\|a x  + b x + c
--R         + 
--R                   3              2  2              2  +-+
--R           (- a b x  + (- 2a c - b )x  - 3b c x - 2c )\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R             +--------------+
--R           2 |   2                      3            2  2             2  +-+
--R       - 2c \|a x  + b x + c  + (- a b x  + (2a c - b )x  + b c x + 2c )\|c
--R  /
--R                                    +--------------+
--R            2 2       2      3  +-+ |   2                   2 3
--R       (2a c x  + 2b c x + 2c )\|c \|a x  + b x + c  - a b c x
--R     + 
--R              3    2 2  2       3      4
--R       (- 2a c  - b c )x  - 3b c x - 2c
--R                                                     Type: Expression Integer
--E

--S 116 of 131
cc:=aa-bb
 

   (5)
                                            +--------------+
                       2  2              2  |   2
           ((- 4a c - b )x  - 8b c x - 8c )\|a x  + b x + c
         + 
                  3             2  2               2  +-+
           (4a b x  + (8a c + 4b )x  + 12b c x + 8c )\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                                          +--------------+
                     2  2              2  |   2
           ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
         + 
                    3               2  2               2  +-+
           (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
                                      +--------------+
                 2  2              2  |   2
       ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
     + 
                3               2  2               2  +-+
       (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
  /
                                            +--------------+
             2    2   2       2      3  +-+ |   2                    2 3
       ((4a c  + b c)x  + 8b c x + 8c )\|c \|a x  + b x + c  - 4a b c x
     + 
              3     2 2  2        3      4
       (- 8a c  - 4b c )x  - 12b c x - 8c
                                                     Type: Expression Integer
--R
--R   (5)
--R                                            +--------------+
--R                       2  2              2  |   2
--R           ((- 4a c - b )x  - 8b c x - 8c )\|a x  + b x + c
--R         + 
--R                  3             2  2               2  +-+
--R           (4a b x  + (8a c + 4b )x  + 12b c x + 8c )\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                                          +--------------+
--R                     2  2              2  |   2
--R           ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
--R         + 
--R                    3               2  2               2  +-+
--R           (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R                                      +--------------+
--R                 2  2              2  |   2
--R       ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
--R     + 
--R                3               2  2               2  +-+
--R       (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
--R  /
--R                                            +--------------+
--R             2    2   2       2      3  +-+ |   2                    2 3
--R       ((4a c  + b c)x  + 8b c x + 8c )\|c \|a x  + b x + c  - 4a b c x
--R     + 
--R              3     2 2  2        3      4
--R       (- 8a c  - 4b c )x  - 12b c x - 8c
--R                                                     Type: Expression Integer
--E

--S 117 of 131
dd:=ratDenom cc
 

   (6)
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       - \|c log(---------------------------------)
                                 x
     + 
                  +--------------+
                  |   2                           +-+
        +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
       \|c log(--------------------------------------) + \|c
                                2c x
  /
      2
     c
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       - \|c log(---------------------------------)
--R                                 x
--R     + 
--R                  +--------------+
--R                  |   2                           +-+
--R        +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
--R       \|c log(--------------------------------------) + \|c
--R                                2c x
--R  /
--R      2
--R     c
--R                                                     Type: Expression Integer
--E

--S 118 of 131
ee:=expandLog dd
 

   (7)
                       +--------------+
          +-+      +-+ |   2
       - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                  +--------------+
        +-+       |   2                           +-+
       \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                               +-+
       (- log(c) - log(2) + 1)\|c
  /
      2
     c
                                                     Type: Expression Integer
--R
--R   (7)
--R                       +--------------+
--R          +-+      +-+ |   2
--R       - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                  +--------------+
--R        +-+       |   2                           +-+
--R       \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                               +-+
--R       (- log(c) - log(2) + 1)\|c
--R  /
--R      2
--R     c
--R                                                     Type: Expression Integer
--E

--S 119 of 131    14:293 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

                                 +-+
        (- log(c) - 2log(2) + 2)\|c
   (8)  ----------------------------
                       2
                     2c
                                                     Type: Expression Integer
--R
--R                                 +-+
--R        (- log(c) - 2log(2) + 2)\|c
--R   (8)  ----------------------------
--R                       2
--R                     2c
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 120 of 131
aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
 

   (1)
                                                          +--------------+
                           3  3      2   2        2   +-+ |   2
           ((- 24a b c - 6b )x  - 48b c x  - 48b c x)\|c \|a x  + b x + c
         + 
                2   4           2      3   3      2 2 2        3
           24a b c x  + (48a b c  + 24b c)x  + 72b c x  + 48b c x
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
                      3  3         2      2   2        2       3  +-+
         ((4a b c - 9b )x  + (64a c  - 24b c)x  + 40b c x + 32c )\|c
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
             2 2        2   4             2      3   3           3     2 2  2
       (- 32a c  + 24a b c)x  + (- 48a b c  + 24b c)x  + (- 80a c  + 8b c )x
     + 
              3       4
       - 56b c x - 32c
  /
                                               +--------------+
              4     2 3  3        4 2      5   |   2
       ((16a c  + 4b c )x  + 32b c x  + 32c x)\|a x  + b x + c
     + 
                 3 4           4      2 3  3        4 2      5   +-+
       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                          +--------------+
--R                           3  3      2   2        2   +-+ |   2
--R           ((- 24a b c - 6b )x  - 48b c x  - 48b c x)\|c \|a x  + b x + c
--R         + 
--R                2   4           2      3   3      2 2 2        3
--R           24a b c x  + (48a b c  + 24b c)x  + 72b c x  + 48b c x
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R                      3  3         2      2   2        2       3  +-+
--R         ((4a b c - 9b )x  + (64a c  - 24b c)x  + 40b c x + 32c )\|c
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R             2 2        2   4             2      3   3           3     2 2  2
--R       (- 32a c  + 24a b c)x  + (- 48a b c  + 24b c)x  + (- 80a c  + 8b c )x
--R     + 
--R              3       4
--R       - 56b c x - 32c
--R  /
--R                                               +--------------+
--R              4     2 3  3        4 2      5   |   2
--R       ((16a c  + 4b c )x  + 32b c x  + 32c x)\|a x  + b x + c
--R     + 
--R                 3 4           4      2 3  3        4 2      5   +-+
--R       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
--R                                          Type: Union(Expression Integer,...)
--E 

--S 121 of 131
t1:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 

                          +--------------+
                          |   2                 +-+
                     - 2x\|a x  + b x + c  + 2x\|c
   (2)  --------------------------------------------------------
                       +--------------+
                   +-+ |   2                    2              2
        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
                                          Type: Union(Expression Integer,...)
--R
--R                          +--------------+
--R                          |   2                 +-+
--R                     - 2x\|a x  + b x + c  + 2x\|c
--R   (2)  --------------------------------------------------------
--R                       +--------------+
--R                   +-+ |   2                    2              2
--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
--R                                          Type: Union(Expression Integer,...)
--E

--S 122 of 131
t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
 

                  +--------------+
              +-+ |   2
            2\|c \|a x  + b x + c  - b x - 2c
        log(---------------------------------)
                            x
   (3)  --------------------------------------
                          +-+
                         \|c
                                          Type: Union(Expression Integer,...)
--R
--R                  +--------------+
--R              +-+ |   2
--R            2\|c \|a x  + b x + c  - b x - 2c
--R        log(---------------------------------)
--R                            x
--R   (3)  --------------------------------------
--R                          +-+
--R                         \|c
--R                                          Type: Union(Expression Integer,...)
--E

--S 123 of 131
bb:=-(a*x^2+2*b*x+c)/(c^2*x*sqrt(a*x^2+b*x+c))+(b^2-2*a*c)/(2*c^2)*t1-(3*b)/(2*c^2)*t2
 

   (4)
                                            +--------------+
                      3     2   2       2   |   2
           (- 6a b c x  - 6b c x  - 6b c x)\|a x  + b x + c
         + 
                2 4               3  3     2   2       2   +-+
           (3a b x  + (6a b c + 3b )x  + 9b c x  + 6b c x)\|c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                                                      +--------------+
                3        2     2   2        2      3  |   2
       (2a b c x  + (8a c  + 2b c)x  + 10b c x + 4c )\|a x  + b x + c
     + 
                2        2  4                  3  3           2     2   2
           (- 8a c + 2a b )x  + (- 16a b c + 2b )x  + (- 12a c  - 6b c)x
         + 
                  2      3
           - 12b c x - 4c
      *
          +-+
         \|c
  /
                                      +--------------+
            3 3       3 2     4   +-+ |   2                    3 4
       (4a c x  + 4b c x  + 4c x)\|c \|a x  + b x + c  - 2a b c x
     + 
              4     2 3  3       4 2     5
       (- 4a c  - 2b c )x  - 6b c x  - 4c x
                                                     Type: Expression Integer
--R
--R   (4)
--R                                            +--------------+
--R                      3     2   2       2   |   2
--R           (- 6a b c x  - 6b c x  - 6b c x)\|a x  + b x + c
--R         + 
--R                2 4               3  3     2   2       2   +-+
--R           (3a b x  + (6a b c + 3b )x  + 9b c x  + 6b c x)\|c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                                                      +--------------+
--R                3        2     2   2        2      3  |   2
--R       (2a b c x  + (8a c  + 2b c)x  + 10b c x + 4c )\|a x  + b x + c
--R     + 
--R                2        2  4                  3  3           2     2   2
--R           (- 8a c + 2a b )x  + (- 16a b c + 2b )x  + (- 12a c  - 6b c)x
--R         + 
--R                  2      3
--R           - 12b c x - 4c
--R      *
--R          +-+
--R         \|c
--R  /
--R                                      +--------------+
--R            3 3       3 2     4   +-+ |   2                    3 4
--R       (4a c x  + 4b c x  + 4c x)\|c \|a x  + b x + c  - 2a b c x
--R     + 
--R              4     2 3  3       4 2     5
--R       (- 4a c  - 2b c )x  - 6b c x  - 4c x
--R                                                     Type: Expression Integer
--E

--S 124 of 131
cc:=aa-bb
 

   (5)
                    2      4  3            2       3   2       2 2          3
             ((72a b c + 6b )x  + (144a b c  + 108b c)x  + 288b c x + 192b c )
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
                 2   2        3   4            2 2      4   3
           (- 48a b c  - 36a b c)x  + (- 240a b c  - 36b c)x
         + 
                      3       3 2  2       2 3          4
           (- 240a b c  - 228b c )x  - 384b c x - 192b c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                             x
     + 
                         2      4  3              2       3   2       2 2
                 (- 72a b c - 6b )x  + (- 144a b c  - 108b c)x  - 288b c x
               + 
                         3
                 - 192b c
          *
                  +--------------+
              +-+ |   2
             \|c \|a x  + b x + c
         + 
               2   2        3   4          2 2      4   3
           (48a b c  + 36a b c)x  + (240a b c  + 36b c)x
         + 
                    3       3 2  2       2 3          4
           (240a b c  + 228b c )x  + 384b c x + 192b c
      *
                   +--------------+
               +-+ |   2
             2\|c \|a x  + b x + c  - b x - 2c
         log(---------------------------------)
                              +-+
                           2x\|c
     + 
                  2      4  3              2      3   2       2 2          3
         ((- 60a b c - 5b )x  + (- 120a b c  - 90b c)x  - 240b c x - 160b c )
      *
              +--------------+
          +-+ |   2
         \|c \|a x  + b x + c
     + 
           2   2        3   4          2 2      4   3            3       3 2  2
       (40a b c  + 30a b c)x  + (200a b c  + 30b c)x  + (200a b c  + 190b c )x
     + 
           2 3          4
       320b c x + 160b c
  /
                  4     3 3  3         5      2 4  2         5        6
         ((48a b c  + 4b c )x  + (96a c  + 72b c )x  + 192b c x + 128c )
      *
          +--------------+
          |   2
         \|a x  + b x + c
     + 
                 2 4        2 3  4              4      3 3  3
           (- 32a c  - 24a b c )x  + (- 160a b c  - 24b c )x
         + 
                    5       2 4  2         5        6
           (- 160a c  - 152b c )x  - 256b c x - 128c
      *
          +-+
         \|c
                                                     Type: Expression Integer
--R
--R   (5)
--R                    2      4  3            2       3   2       2 2          3
--R             ((72a b c + 6b )x  + (144a b c  + 108b c)x  + 288b c x + 192b c )
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R                 2   2        3   4            2 2      4   3
--R           (- 48a b c  - 36a b c)x  + (- 240a b c  - 36b c)x
--R         + 
--R                      3       3 2  2       2 3          4
--R           (- 240a b c  - 228b c )x  - 384b c x - 192b c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                             x
--R     + 
--R                         2      4  3              2       3   2       2 2
--R                 (- 72a b c - 6b )x  + (- 144a b c  - 108b c)x  - 288b c x
--R               + 
--R                         3
--R                 - 192b c
--R          *
--R                  +--------------+
--R              +-+ |   2
--R             \|c \|a x  + b x + c
--R         + 
--R               2   2        3   4          2 2      4   3
--R           (48a b c  + 36a b c)x  + (240a b c  + 36b c)x
--R         + 
--R                    3       3 2  2       2 3          4
--R           (240a b c  + 228b c )x  + 384b c x + 192b c
--R      *
--R                   +--------------+
--R               +-+ |   2
--R             2\|c \|a x  + b x + c  - b x - 2c
--R         log(---------------------------------)
--R                              +-+
--R                           2x\|c
--R     + 
--R                  2      4  3              2      3   2       2 2          3
--R         ((- 60a b c - 5b )x  + (- 120a b c  - 90b c)x  - 240b c x - 160b c )
--R      *
--R              +--------------+
--R          +-+ |   2
--R         \|c \|a x  + b x + c
--R     + 
--R           2   2        3   4          2 2      4   3            3       3 2  2
--R       (40a b c  + 30a b c)x  + (200a b c  + 30b c)x  + (200a b c  + 190b c )x
--R     + 
--R           2 3          4
--R       320b c x + 160b c
--R  /
--R                  4     3 3  3         5      2 4  2         5        6
--R         ((48a b c  + 4b c )x  + (96a c  + 72b c )x  + 192b c x + 128c )
--R      *
--R          +--------------+
--R          |   2
--R         \|a x  + b x + c
--R     + 
--R                 2 4        2 3  4              4      3 3  3
--R           (- 32a c  - 24a b c )x  + (- 160a b c  - 24b c )x
--R         + 
--R                    5       2 4  2         5        6
--R           (- 160a c  - 152b c )x  - 256b c x - 128c
--R      *
--R          +-+
--R         \|c
--R                                                     Type: Expression Integer
--E

--S 125 of 131
dd:=ratDenom cc
 

   (6)
                       +--------------+
                   +-+ |   2
          +-+    2\|c \|a x  + b x + c  - b x - 2c
       6b\|c log(---------------------------------)
                                 x
     + 
                      +--------------+
                      |   2                           +-+
            +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c        +-+
       - 6b\|c log(--------------------------------------) - 5b\|c
                                    2c x
  /
       3
     4c
                                                     Type: Expression Integer
--R
--R   (6)
--R                       +--------------+
--R                   +-+ |   2
--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
--R       6b\|c log(---------------------------------)
--R                                 x
--R     + 
--R                      +--------------+
--R                      |   2                           +-+
--R            +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c        +-+
--R       - 6b\|c log(--------------------------------------) - 5b\|c
--R                                    2c x
--R  /
--R       3
--R     4c
--R                                                     Type: Expression Integer
--E

--S 126 of 131
ee:=expandLog dd
 

   (7)
                       +--------------+
          +-+      +-+ |   2
       6b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
     + 
                      +--------------+
            +-+       |   2                           +-+
       - 6b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
     + 
                                    +-+
       (6b log(c) + 6b log(2) - 5b)\|c
  /
       3
     4c
                                                     Type: Expression Integer
--R
--R   (7)
--R                       +--------------+
--R          +-+      +-+ |   2
--R       6b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
--R     + 
--R                      +--------------+
--R            +-+       |   2                           +-+
--R       - 6b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
--R     + 
--R                                    +-+
--R       (6b log(c) + 6b log(2) - 5b)\|c
--R  /
--R       3
--R     4c
--R                                                     Type: Expression Integer
--E

--S 127 of 131    14:294 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

                                     +-+
        (3b log(c) + 6b log(2) - 5b)\|c
   (8)  --------------------------------
                         3
                       4c
                                                     Type: Expression Integer
--R
--R                                     +-+
--R        (3b log(c) + 6b log(2) - 5b)\|c
--R   (8)  --------------------------------
--R                         3
--R                       4c
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 128 of 131    14:295 Axiom cannot compute this integral
aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
 

                              2n + 1
           x                  ------
         ++                2     2
   (1)   |   (c + %Q b + %Q a)      d%Q
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              2n + 1
--R           x                  ------
--R         ++                2     2
--I   (1)   |   (c + %N b + %N a)      d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 129 of 131    14:296 Axiom cannot compute this integral
aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
 

                                 2n + 1
           x                     ------
         ++                   2     2
   (1)   |   %Q (c + %Q b + %Q a)      d%Q
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                 2n + 1
--R           x                     ------
--R         ++                   2     2
--I   (1)   |   %N (c + %N b + %N a)      d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 130 of 131    14:297 Axiom cannot compute this integral
aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
 

           x
         ++             1
   (1)   |   ----------------------- d%Q
        ++                    2n + 1
                              ------
                           2     2
             (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             1
--I   (1)   |   ----------------------- d%N
--R        ++                    2n + 1
--R                              ------
--R                           2     2
--I             (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 131 of 131    14:298 Axiom cannot compute this integral
aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
 

           x
         ++               1
   (1)   |   -------------------------- d%Q
        ++                       2n + 1
                                 ------
                              2     2
             %Q (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++               1
--I   (1)   |   -------------------------- d%N
--R        ++                       2n + 1
--R                                 ------
--R                              2     2
--I             %N (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to solvetra.output (2010/3/27, 18:40:48).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 37
solve(sin(x)-8=0)
 

   (1)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (1)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 1

--S 2 of 37
solve(sin(x)-8=0,x)
 

   (2)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (2)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 2

--S 3 of 37
solve(sin(x)-8)    
 

   (3)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (3)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 3

--S 4 of 37
solve(sin(x)-8,x)
 

   (4)  [x= asin(8)]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (4)  [x= asin(8)]
--R                                       Type: List Equation Expression Integer
--E 4

--S 5 of 37
solve(sin(x**2)-2,x)       
 

               +-------+     +-------+
   (5)  [x= - \|asin(2) ,x= \|asin(2) ]
                                       Type: List Equation Expression Integer
--R 
--R
--R               +-------+     +-------+
--R   (5)  [x= - \|asin(2) ,x= \|asin(2) ]
--R                                       Type: List Equation Expression Integer
--E 5

--S 6 of 37
solve(sin(x**2)-3,x)
 

               +-------+     +-------+
   (6)  [x= - \|asin(3) ,x= \|asin(3) ]
                                       Type: List Equation Expression Integer
--R 
--R
--R               +-------+     +-------+
--R   (6)  [x= - \|asin(3) ,x= \|asin(3) ]
--R                                       Type: List Equation Expression Integer
--E 6

--S 7 of 37
solve(sin(x**2)**2-3,x)
 

   (7)
          +----------+     +----------+       +------------+     +------------+
          |      +-+       |      +-+         |        +-+       |        +-+
   [x= - \|asin(\|3 ) ,x= \|asin(\|3 ) ,x= - \|- asin(\|3 ) ,x= \|- asin(\|3 ) ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (7)
--R          +----------+     +----------+       +------------+     +------------+
--R          |      +-+       |      +-+         |        +-+       |        +-+
--R   [x= - \|asin(\|3 ) ,x= \|asin(\|3 ) ,x= - \|- asin(\|3 ) ,x= \|- asin(\|3 ) ]
--R                                       Type: List Equation Expression Integer
--E 7

--S 8 of 37
solve(sin(x+2)-2,x)
 

   (8)  [x= asin(2) - 2]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (8)  [x= asin(2) - 2]
--R                                       Type: List Equation Expression Integer
--E 8

--S 9 of 37
solve(sin(x**2+2)-2,x)
 

               +-----------+     +-----------+
   (9)  [x= - \|asin(2) - 2 ,x= \|asin(2) - 2 ]
                                       Type: List Equation Expression Integer
--R 
--R
--R               +-----------+     +-----------+
--R   (9)  [x= - \|asin(2) - 2 ,x= \|asin(2) - 2 ]
--R                                       Type: List Equation Expression Integer
--E 9

--S 10 of 37
solve(sin(x)*cos(8)*tan(88)*567-y*3+3,x)
 

                        y - 1
   (10)  [x= asin(----------------)]
                  189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R                        y - 1
--R   (10)  [x= asin(----------------)]
--R                  189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 10

--S 11 of 37
solve(sin(x-77)*cos(8)*tan(88)*567-y*3+3,x)
 

                        y - 1
   (11)  [x= asin(----------------) + 77]
                  189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R                        y - 1
--R   (11)  [x= asin(----------------) + 77]
--R                  189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 11

--S 12 of 37
solve(sin(x**2-77)*cos(8)*tan(88)*567-y*3+3,x)
 

   (12)
          +---------------------------+     +---------------------------+
          |           y - 1                 |           y - 1
   [x= -  |asin(----------------) + 77 ,x=  |asin(----------------) + 77 ]
         \|     189cos(8)tan(88)           \|     189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R   (12)
--R          +---------------------------+     +---------------------------+
--R          |           y - 1                 |           y - 1
--R   [x= -  |asin(----------------) + 77 ,x=  |asin(----------------) + 77 ]
--R         \|     189cos(8)tan(88)           \|     189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 12

--S 13 of 37
solve(sin(x)*cos(x)-2,x)                      
 

                   +----+                 +----+
                  \|- 15  + 1            \|- 15  - 1
   (13)  [x= atan(-----------),x= - atan(-----------)]
                       4                      4
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +----+                 +----+
--R                  \|- 15  + 1            \|- 15  - 1
--R   (13)  [x= atan(-----------),x= - atan(-----------)]
--R                       4                      4
--R                                       Type: List Equation Expression Integer
--E 13

--S 14 of 37
solve(sin(x**3-77)*cos(8)*tan(88)*567-y*3+3,x)
 

   (14)
                       +---------------------------+
           +---+       |           y - 1
       (- \|- 3  - 1) 3|asin(----------------) + 77
                      \|     189cos(8)tan(88)
   [x= --------------------------------------------,
                             2
                     +---------------------------+
         +---+       |           y - 1
       (\|- 3  - 1) 3|asin(----------------) + 77
                    \|     189cos(8)tan(88)
    x= ------------------------------------------,
                            2
        +---------------------------+
        |           y - 1
    x= 3|asin(----------------) + 77 ]
       \|     189cos(8)tan(88)
                                       Type: List Equation Expression Integer
--R 
--R
--R   (14)
--R                       +---------------------------+
--R           +---+       |           y - 1
--R       (- \|- 3  - 1) 3|asin(----------------) + 77
--R                      \|     189cos(8)tan(88)
--R   [x= --------------------------------------------,
--R                             2
--R                     +---------------------------+
--R         +---+       |           y - 1
--R       (\|- 3  - 1) 3|asin(----------------) + 77
--R                    \|     189cos(8)tan(88)
--R    x= ------------------------------------------,
--R                            2
--R        +---------------------------+
--R        |           y - 1
--R    x= 3|asin(----------------) + 77 ]
--R       \|     189cos(8)tan(88)
--R                                       Type: List Equation Expression Integer
--E 14

--S 15 of 37
solve(cos(x)+cos(3*x)+cos(5*x) ,x)
 

             %pi      %pi    %pi      %pi
   (15)  [x= ---,x= - ---,x= ---,x= - ---]
              3        3      6        6
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi      %pi    %pi      %pi
--R   (15)  [x= ---,x= - ---,x= ---,x= - ---]
--R              3        3      6        6
--R                                       Type: List Equation Expression Integer
--E 15

--S 16 of 37
solve(3*tan(3*x)-tan(x)+2,x)
 

                   +-+                 +-+
                  \|7  + 2            \|7  - 2
   (16)  [x= atan(--------),x= - atan(--------)]
                      3                   3
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +-+                 +-+
--R                  \|7  + 2            \|7  - 2
--R   (16)  [x= atan(--------),x= - atan(--------)]
--R                      3                   3
--R                                       Type: List Equation Expression Integer
--E 16

--S 17 of 37
solve(3*sech(x)**2+4*tanh(x)+1,x)
 

                  +---+            +---+            +-+              +-+
   (17)  [x= log(\|- 3 ),x= log(- \|- 3 ),x= - log(\|5 ),x= - log(- \|5 )]
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +---+            +---+            +-+              +-+
--R   (17)  [x= log(\|- 3 ),x= log(- \|- 3 ),x= - log(\|5 ),x= - log(- \|5 )]
--R                                       Type: List Equation Expression Integer
--E 17

--S 18 of 37
solve(cosh(x)-3*sinh(x),x)
 

                  +-+            +-+
   (18)  [x= log(\|2 ),x= log(- \|2 )]
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +-+            +-+
--R   (18)  [x= log(\|2 ),x= log(- \|2 )]
--R                                       Type: List Equation Expression Integer
--E 18

--S 19 of 37
solve(2*sinh(x)+6*cosh(x)-5,x)
 

                  +---+                +---+
                 \|- 7  + 5         - \|- 7  + 5
   (19)  [x= log(----------),x= log(------------)]
                      8                   8
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +---+                +---+
--R                 \|- 7  + 5         - \|- 7  + 5
--R   (19)  [x= log(----------),x= log(------------)]
--R                      8                   8
--R                                       Type: List Equation Expression Integer
--E 19

--S 20 of 37
solve(exp(3*x)-4*exp(x)+3*exp(-x),x)
 

                                   +-+            +-+
   (20)  [x= 0,x= log(- 1),x= log(\|3 ),x= log(- \|3 )]
                                       Type: List Equation Expression Integer
--R 
--R
--R                                   +-+            +-+
--R   (20)  [x= 0,x= log(- 1),x= log(\|3 ),x= log(- \|3 )]
--R                                       Type: List Equation Expression Integer
--E 20

--S 21 of 37
solve(log(x+1)+log(x-1)-3,x)
 

                +-------+     +-------+
                |  3          |  3
   (21)  [x= - \|%e  + 1 ,x= \|%e  + 1 ]
                                       Type: List Equation Expression Integer
--R 
--R
--R                +-------+     +-------+
--R                |  3          |  3
--R   (21)  [x= - \|%e  + 1 ,x= \|%e  + 1 ]
--R                                       Type: List Equation Expression Integer
--E 21

--S 22 of 37
solve(sin(x)*cos(x)-2,x)
 

                   +----+                 +----+
                  \|- 15  + 1            \|- 15  - 1
   (22)  [x= atan(-----------),x= - atan(-----------)]
                       4                      4
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +----+                 +----+
--R                  \|- 15  + 1            \|- 15  - 1
--R   (22)  [x= atan(-----------),x= - atan(-----------)]
--R                       4                      4
--R                                       Type: List Equation Expression Integer
--E 22

--S 23 of 37
solve(- cos(- x + a)*sin(x) + 2*cos(x)*sin(- x + a),x)
 

   (23)
             +------------------------+
             |     a 4         a 2             a 2
             |9tan(-)  + 14tan(-)  + 9  + 3tan(-)  - 3
            \|     2           2               2
   [x= atan(------------------------------------------),
                                   a
                              4tan(-)
                                   2
               +------------------------+
               |     a 4         a 2             a 2
               |9tan(-)  + 14tan(-)  + 9  - 3tan(-)  + 3
              \|     2           2               2
    x= - atan(------------------------------------------)]
                                     a
                                4tan(-)
                                     2
                                       Type: List Equation Expression Integer
--R 
--R
--R   (23)
--R             +------------------------+
--R             |     a 4         a 2             a 2
--R             |9tan(-)  + 14tan(-)  + 9  + 3tan(-)  - 3
--R            \|     2           2               2
--R   [x= atan(------------------------------------------),
--R                                   a
--R                              4tan(-)
--R                                   2
--R               +------------------------+
--R               |     a 4         a 2             a 2
--R               |9tan(-)  + 14tan(-)  + 9  - 3tan(-)  + 3
--R              \|     2           2               2
--R    x= - atan(------------------------------------------)]
--R                                     a
--R                                4tan(-)
--R                                     2
--R                                       Type: List Equation Expression Integer
--E 23

--S 24 of 37
solve(sin(x)+cos(x)=2,x)
 

                    +---+                  +---+
                   \|- 2  + 1             \|- 2  - 1
   (24)  [x= 2atan(----------),x= - 2atan(----------)]
                        3                      3
                                       Type: List Equation Expression Integer
--R 
--R
--R                    +---+                  +---+
--R                   \|- 2  + 1             \|- 2  - 1
--R   (24)  [x= 2atan(----------),x= - 2atan(----------)]
--R                        3                      3
--R                                       Type: List Equation Expression Integer
--E 24

--S 25 of 37
solve(- cos(- x )*sin(x),x)
 

             %pi           %pi
   (25)  [x= ---,x= 0,x= - ---]
              2             2
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi           %pi
--R   (25)  [x= ---,x= 0,x= - ---]
--R              2             2
--R                                       Type: List Equation Expression Integer
--E 25

--S 26 of 37
solve(- cos(- x + a)*sin(x),x)
 

                              a                    a
                          tan(-) + 1           tan(-) - 1
                              2                    2
   (26)  [x= 0,x= - 2atan(----------),x= 2atan(----------)]
                              a                    a
                          tan(-) - 1           tan(-) + 1
                              2                    2
                                       Type: List Equation Expression Integer
--R 
--R
--R                              a                    a
--R                          tan(-) + 1           tan(-) - 1
--R                              2                    2
--R   (26)  [x= 0,x= - 2atan(----------),x= 2atan(----------)]
--R                              a                    a
--R                          tan(-) - 1           tan(-) + 1
--R                              2                    2
--R                                       Type: List Equation Expression Integer
--E 26

--S 27 of 37
solve(log(sqrt(sqrt(sqrt(x+1)+4)+7))+5,x)
 

                    5 8          5 6         5 4        5 2
             2024(%e )  - 1260(%e )  + 286(%e )  - 28(%e )  + 1
   (27)  [x= --------------------------------------------------]
                                      5 8
                                   (%e )
                                       Type: List Equation Expression Integer
--R 
--R
--R                    5 8          5 6         5 4        5 2
--R             2024(%e )  - 1260(%e )  + 286(%e )  - 28(%e )  + 1
--R   (27)  [x= --------------------------------------------------]
--R                                      5 8
--R                                   (%e )
--R                                       Type: List Equation Expression Integer
--E 27

--S 28 of 37
solve(2**x-6,x)
 

             log(6)
   (28)  [x= ------]
             log(2)
                                       Type: List Equation Expression Integer
--R 
--R
--R             log(6)
--R   (28)  [x= ------]
--R             log(2)
--R                                       Type: List Equation Expression Integer
--E 28

--S 29 of 37
solve(sqrt(x+1)+sqrt(x+7)+1,x)
 

   (29)  []
                                       Type: List Equation Expression Integer
--R 
--R
--R   (29)  []
--R                                       Type: List Equation Expression Integer
--E 29

--S 30 of 37
solve(sqrt(sin(x))+1,x)
 

             %pi
   (30)  [x= ---]
              2
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi
--R   (30)  [x= ---]
--R              2
--R                                       Type: List Equation Expression Integer
--E 30

--S 31 of 37
solve(sqrt(sin(x))+sqrt(cos(x))+1,x)
 

                           +---+                  +---+
             %pi          \|- 7  - 1             \|- 7  + 1
   (31)  [x= ---,x= 2atan(----------),x= - 2atan(----------)]
              2                2                      2
                                       Type: List Equation Expression Integer
--R 
--R
--R                           +---+                  +---+
--R             %pi          \|- 7  - 1             \|- 7  + 1
--R   (31)  [x= ---,x= 2atan(----------),x= - 2atan(----------)]
--R              2                2                      2
--R                                       Type: List Equation Expression Integer
--E 31

--S 32 of 37
solve(sqrt(sin(x)+1)+(sin(x)+1)**(1/3)+7,x)
 

   (32)
                             +----------------------------+
                             |        2
                            \|- 3%x111  + 374%x111 + 10409  - %x111 + 187
   [x= asin(%x111), x= asin(---------------------------------------------),
                                                  2
               +----------------------------+
               |        2
              \|- 3%x111  + 374%x111 + 10409  + %x111 - 187
    x= - asin(---------------------------------------------)]
                                    2
                                       Type: List Equation Expression Integer
--R 
--R
--R   (32)
--R                             +----------------------------+
--R                             |        2
--R                            \|- 3%x111  + 374%x111 + 10409  - %x111 + 187
--R   [x= asin(%x111), x= asin(---------------------------------------------),
--R                                                  2
--R               +----------------------------+
--R               |        2
--R              \|- 3%x111  + 374%x111 + 10409  + %x111 - 187
--R    x= - asin(---------------------------------------------)]
--R                                    2
--R                                       Type: List Equation Expression Integer
--E 32

--S 33 of 37
solve(sqrt(sqrt(sqrt(1+x)+7)+1)+8-2,x)
 

   (33)  []
                                       Type: List Equation Expression Integer
--R 
--R
--R   (33)  []
--R                                       Type: List Equation Expression Integer
--E 33

--S 34 of 37
solve(sqrt(sin(x)+1)+(sin(x)+5)**(1/3)+7,x)
 

   (34)
                             +----------------------------+
                             |        2
                            \|- 3%x119  + 374%x119 + 11113  - %x119 + 187
   [x= asin(%x119), x= asin(---------------------------------------------),
                                                  2
               +----------------------------+
               |        2
              \|- 3%x119  + 374%x119 + 11113  + %x119 - 187
    x= - asin(---------------------------------------------)]
                                    2
                                       Type: List Equation Expression Integer
--R 
--R
--R   (34)
--R                             +----------------------------+
--R                             |        2
--R                            \|- 3%x119  + 374%x119 + 11113  - %x119 + 187
--R   [x= asin(%x119), x= asin(---------------------------------------------),
--R                                                  2
--R               +----------------------------+
--R               |        2
--R              \|- 3%x119  + 374%x119 + 11113  + %x119 - 187
--R    x= - asin(---------------------------------------------)]
--R                                    2
--R                                       Type: List Equation Expression Integer
--E 34

--S 35 of 37
solve(sqrt(sin(x+1))+sqrt(sin(x+7))+1,x)
 

   (35)
   [x= 2atan(%x125) - 7, x= 2atan(%x126) - 7,

     x =
           2
        *
           atan
                  ROOT
                                    8           7           6            5
                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                         + 
                                      4            3           2
                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                      *
                              2
                         %x126
                     + 
                                        8           7           6            5
                               - 2tan(3)  + 16tan(3)  - 56tan(3)  + 112tan(3)
                             + 
                                          4            3           2
                               - 140tan(3)  + 112tan(3)  - 56tan(3)  + 16tan(3)
                             + 
                               - 2
                          *
                             %x125
                         + 
                                   7            6            5           4
                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                         + 
                                     3            2
                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                      *
                         %x126
                     + 
                                    8           7           6            5
                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                         + 
                                      4            3           2
                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                      *
                              2
                         %x125
                     + 
                                   7            6            5           4
                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                         + 
                                     3            2
                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                      *
                         %x125
                     + 
                                 8            7            6            5
                       - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
                     + 
                               4            3           2
                       80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
                + 
                           4          3          2
                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x126
                + 
                           4          3          2
                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x125
                + 
                          3          2
                  16tan(3)  + 8tan(3)  + 8
             /
                       4          3           2
                2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
       + 
         - 7
     ,

     x =
         -
              2
           *
              atan
                     ROOT
                                       8           7           6            5
                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                            + 
                                       4            3           2
                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                         *
                                 2
                            %x126
                        + 
                                           8           7           6
                                  - 2tan(3)  + 16tan(3)  - 56tan(3)
                                + 
                                           5            4            3
                                  112tan(3)  - 140tan(3)  + 112tan(3)
                                + 
                                            2
                                  - 56tan(3)  + 16tan(3) - 2
                             *
                                %x125
                            + 
                                      7            6            5           4
                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                            + 
                                        3            2
                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                         *
                            %x126
                        + 
                                       8           7           6            5
                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
                            + 
                                       4            3           2
                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
                         *
                                 2
                            %x125
                        + 
                                      7            6            5           4
                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
                            + 
                                        3            2
                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
                         *
                            %x125
                        + 
                                    8            7            6            5
                          - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
                        + 
                                  4            3           2
                          80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
                   + 
                            4          3          2
                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x126
                   + 
                            4          3          2
                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x125
                   + 
                               3          2
                     - 16tan(3)  - 8tan(3)  - 8
                /
                          4          3           2
                   2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
       + 
         - 7
     ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (35)
--R   [x= 2atan(%x125) - 7, x= 2atan(%x126) - 7,
--R
--R     x =
--R           2
--R        *
--R           atan
--R                  ROOT
--R                                    8           7           6            5
--R                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                         + 
--R                                      4            3           2
--R                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                      *
--R                              2
--R                         %x126
--R                     + 
--R                                        8           7           6            5
--R                               - 2tan(3)  + 16tan(3)  - 56tan(3)  + 112tan(3)
--R                             + 
--R                                          4            3           2
--R                               - 140tan(3)  + 112tan(3)  - 56tan(3)  + 16tan(3)
--R                             + 
--R                               - 2
--R                          *
--R                             %x125
--R                         + 
--R                                   7            6            5           4
--R                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                         + 
--R                                     3            2
--R                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                      *
--R                         %x126
--R                     + 
--R                                    8           7           6            5
--R                           - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                         + 
--R                                      4            3           2
--R                           - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                      *
--R                              2
--R                         %x125
--R                     + 
--R                                   7            6            5           4
--R                           32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                         + 
--R                                     3            2
--R                           - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                      *
--R                         %x125
--R                     + 
--R                                 8            7            6            5
--R                       - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
--R                     + 
--R                               4            3           2
--R                       80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
--R                + 
--R                           4          3          2
--R                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x126
--R                + 
--R                           4          3          2
--R                  (- tan(3)  + 4tan(3)  - 6tan(3)  + 4tan(3) - 1)%x125
--R                + 
--R                          3          2
--R                  16tan(3)  + 8tan(3)  + 8
--R             /
--R                       4          3           2
--R                2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
--R       + 
--R         - 7
--R     ,
--R
--R     x =
--R         -
--R              2
--R           *
--R              atan
--R                     ROOT
--R                                       8           7           6            5
--R                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                            + 
--R                                       4            3           2
--R                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                         *
--R                                 2
--R                            %x126
--R                        + 
--R                                           8           7           6
--R                                  - 2tan(3)  + 16tan(3)  - 56tan(3)
--R                                + 
--R                                           5            4            3
--R                                  112tan(3)  - 140tan(3)  + 112tan(3)
--R                                + 
--R                                            2
--R                                  - 56tan(3)  + 16tan(3) - 2
--R                             *
--R                                %x125
--R                            + 
--R                                      7            6            5           4
--R                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                            + 
--R                                        3            2
--R                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                         *
--R                            %x126
--R                        + 
--R                                       8           7           6            5
--R                              - 3tan(3)  + 24tan(3)  - 84tan(3)  + 168tan(3)
--R                            + 
--R                                       4            3           2
--R                            - 210tan(3)  + 168tan(3)  - 84tan(3)  + 24tan(3) - 3
--R                         *
--R                                 2
--R                            %x125
--R                        + 
--R                                      7            6            5           4
--R                              32tan(3)  - 112tan(3)  + 128tan(3)  - 16tan(3)
--R                            + 
--R                                        3            2
--R                              - 96tan(3)  + 112tan(3)  - 64tan(3) + 16
--R                         *
--R                            %x125
--R                        + 
--R                                    8            7            6            5
--R                          - 72tan(3)  + 288tan(3)  - 160tan(3)  + 480tan(3)
--R                        + 
--R                                  4            3           2
--R                          80tan(3)  + 224tan(3)  + 96tan(3)  + 32tan(3) + 56
--R                   + 
--R                            4          3          2
--R                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x126
--R                   + 
--R                            4          3          2
--R                     (tan(3)  - 4tan(3)  + 6tan(3)  - 4tan(3) + 1)%x125
--R                   + 
--R                               3          2
--R                     - 16tan(3)  - 8tan(3)  - 8
--R                /
--R                          4          3           2
--R                   2tan(3)  - 8tan(3)  + 12tan(3)  - 8tan(3) + 2
--R       + 
--R         - 7
--R     ]
--R                                       Type: List Equation Expression Integer
--E 35

--S 36 of 37
solve(asin(x)+acot(x)-2,x)
 

   (36)
   [
     x =
           -
              ROOT
                             4                 4                      4
                          ------            ------                 ------
                           +---+             +---+                  +---+
                          \|- 1      2      \|- 1                  \|- 1      2
                     - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
                   + 
                             4   2         4
                          ------        ------
                           +---+         +---+
                          \|- 1         \|- 1
                     - (%e      )  - 2%e       - 1
                /
                        4
                     ------
                      +---+
                     \|- 1
                   %e
         + 
           - %x135 - %x134
      /
         2
     ,

     x =
           ROOT
                          4                 4                      4
                       ------            ------                 ------
                        +---+             +---+                  +---+
                       \|- 1      2      \|- 1                  \|- 1      2
                  - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
                + 
                          4   2         4
                       ------        ------
                        +---+         +---+
                       \|- 1         \|- 1
                  - (%e      )  - 2%e       - 1
             /
                     4
                  ------
                   +---+
                  \|- 1
                %e
         + 
           - %x135 - %x134
      /
         2
     ,
    x= %x135, x= %x134]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (36)
--R   [
--R     x =
--R           -
--R              ROOT
--R                             4                 4                      4
--R                          ------            ------                 ------
--R                           +---+             +---+                  +---+
--R                          \|- 1      2      \|- 1                  \|- 1      2
--R                     - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
--R                   + 
--R                             4   2         4
--R                          ------        ------
--R                           +---+         +---+
--R                          \|- 1         \|- 1
--R                     - (%e      )  - 2%e       - 1
--R                /
--R                        4
--R                     ------
--R                      +---+
--R                     \|- 1
--R                   %e
--R         + 
--R           - %x135 - %x134
--R      /
--R         2
--R     ,
--R
--R     x =
--R           ROOT
--R                          4                 4                      4
--R                       ------            ------                 ------
--R                        +---+             +---+                  +---+
--R                       \|- 1      2      \|- 1                  \|- 1      2
--R                  - 3%e      %x135  - 2%e      %x134 %x135 - 3%e      %x134
--R                + 
--R                          4   2         4
--R                       ------        ------
--R                        +---+         +---+
--R                       \|- 1         \|- 1
--R                  - (%e      )  - 2%e       - 1
--R             /
--R                     4
--R                  ------
--R                   +---+
--R                  \|- 1
--R                %e
--R         + 
--R           - %x135 - %x134
--R      /
--R         2
--R     ,
--R    x= %x135, x= %x134]
--R                                       Type: List Equation Expression Integer
--E 26

--S 37 of 37
solve(asinh(x)+acoth(x)-2,x)
 

   (37)
   [
     x =
              +---------------------------------------------------------------+
              |     4     2      4                 4     2      4 2      4
              |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
           -  |---------------------------------------------------------------
              |                                4
             \|                              %e
         + 
           - %x140 - %x139
      /
         2
     ,

     x =
            +---------------------------------------------------------------+
            |     4     2      4                 4     2      4 2      4
            |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
            |---------------------------------------------------------------
            |                                4
           \|                              %e
         + 
           - %x140 - %x139
      /
         2
     ,
    x= %x140, x= %x139]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (37)
--R   [
--R     x =
--R              +---------------------------------------------------------------+
--R              |     4     2      4                 4     2      4 2      4
--R              |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
--R           -  |---------------------------------------------------------------
--R              |                                4
--R             \|                              %e
--R         + 
--R           - %x140 - %x139
--R      /
--R         2
--R     ,
--R
--R     x =
--R            +---------------------------------------------------------------+
--R            |     4     2      4                 4     2      4 2      4
--R            |- 3%e %x140  - 2%e %x139 %x140 - 3%e %x139  + (%e )  + 2%e  + 1
--R            |---------------------------------------------------------------
--R            |                                4
--R           \|                              %e
--R         + 
--R           - %x140 - %x139
--R      /
--R         2
--R     ,
--R    x= %x140, x= %x139]
--R                                       Type: List Equation Expression Integer
--E 37
)spool 
 
Starts dribbling to textfile.output (2010/3/27, 18:41:24).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
f1: TextFile := open("/etc/group", "input")
 

   (1)  "/etc/group"
                                                               Type: TextFile
--R 
--R
--R   (1)  "/etc/group"
--R                                                               Type: TextFile
--E 1

--S 2 of 10
f2: TextFile := open("/tmp/MOTD", "output")
 

   (2)  "/tmp/MOTD"
                                                               Type: TextFile
--R 
--R
--R   (2)  "/tmp/MOTD"
--R                                                               Type: TextFile
--E 2

--S 3 of 10
l := readLine! f1
 

   (3)  "root:x:0:"
                                                                 Type: String
--R 
--R
--R   (3)  "root:x:0:root"
--R                                                                 Type: String
--E 3

--S 4 of 10
writeLine!(f2, upperCase l)
 

   (4)  "ROOT:X:0:"
                                                                 Type: String
--R 
--R
--R   (4)  "ROOT:X:0:ROOT"
--R                                                                 Type: String
--E 4

--S 5 of 10
while not endOfFile? f1 repeat
    s := readLine! f1
    writeLine!(f2, upperCase s)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
close! f1
 

   (6)  "/etc/group"
                                                               Type: TextFile
--R 
--R
--R   (6)  "/etc/group"
--R                                                               Type: TextFile
--E 6

--S 7 of 10
write!(f2, "-The-")
 

   (7)  "-The-"
                                                                 Type: String
--R 
--R
--R   (7)  "-The-"
--R                                                                 Type: String
--E 7

--S 8 of 10
write!(f2, "-End-")
 

   (8)  "-End-"
                                                                 Type: String
--R 
--R
--R   (8)  "-End-"
--R                                                                 Type: String
--E 8

--S 9 of 10
writeLine! f2
 

   (9)  ""
                                                                 Type: String
--R 
--R
--R   (9)  ""
--R                                                                 Type: String
--E 9

--S 10 of 10
close! f2
 

   (10)  "/tmp/MOTD"
                                                               Type: TextFile
--R 
--R
--R   (10)  "/tmp/MOTD"
--R                                                               Type: TextFile
--E 10

)system rm /tmp/MOTD
 
)spool 
 
Starts dribbling to stbl.output (2010/3/27, 18:41:3).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
t: SparseTable(Integer, String, "Try again!") := table()
 

   (1)  table()
                                 Type: SparseTable(Integer,String,Try again!)
--R 
--R
--R   (1)  table()
--R                                 Type: SparseTable(Integer,String,Try again!)
--E 1

--S 2 of 7
t.3 := "Number three"
 

   (2)  "Number three"
                                                                 Type: String
--R 
--R
--R   (2)  "Number three"
--R                                                                 Type: String
--E 2

--S 3 of 7
t.4 := "Number four"
 

   (3)  "Number four"
                                                                 Type: String
--R 
--R
--R   (3)  "Number four"
--R                                                                 Type: String
--E 3

--S 4 of 7
t.3
 

   (4)  "Number three"
                                                                 Type: String
--R 
--R
--R   (4)  "Number three"
--R                                                                 Type: String
--E 4

--S 5 of 7
t.2
 

   (5)  "Try again!"
                                                                 Type: String
--R 
--R
--R   (5)  "Try again!"
--R                                                                 Type: String
--E 5

--S 6 of 7
keys t
 

   (6)  [4,3]
                                                           Type: List Integer
--R 
--R
--R   (6)  [4,3]
--R                                                           Type: List Integer
--E 6

--S 7 of 7
entries t
 

   (7)  ["Number four","Number three"]
                                                            Type: List String
--R 
--R
--R   (7)  ["Number four","Number three"]
--R                                                            Type: List String
--E 7
)spool 
 
Starts dribbling to efi.output (2010/3/27, 18:25:19).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 15
EFI:=Expression Integer
 

   (1)  Expression Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Expression Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 15
ber:=operator 'ber
 

   (2)  ber
                                                          Type: BasicOperator
--R 
--R
--R   (2)  ber
--R                                                          Type: BasicOperator
--E 2

--S 3 of 15
s:=operator 's
 

   (3)  s
                                                          Type: BasicOperator
--R 
--R
--R   (3)  s
--R                                                          Type: BasicOperator
--E 3

-- s:OP EFI:=operator 's

--S 4 of 15
br:LIST EFI->EFI
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4


--S 5 of 15
br(x) == 
 (x.1) = 0 => limit(br([y]),y=0) 
 (x.1)/(exp((x.1))-1) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 15
br([1])
 
   Compiling function br with type List Expression Integer -> 
      Expression Integer 

           1
   (6)  ------
        %e - 1
                                                     Type: Expression Integer
--R 
--R   Compiling function br with type List Expression Integer -> 
--R      Expression Integer 
--R
--R           1
--R   (6)  ------
--R        %e - 1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 15
br([0])
 

   (7)  1
                                                     Type: Expression Integer
--R 
--R
--R   (7)  1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 15
fJ:List FRAC INT -> EFI
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 15
J(i:PI,j:PI):EFI==ber(s(i)-s(j))
 
   Function declaration J : (PositiveInteger,PositiveInteger) -> 
      Expression Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration J : (PositiveInteger,PositiveInteger) -> 
--R      Expression Integer has been added to workspace.
--R                                                                   Type: Void
--E 9

--S 10 of 15
function(J(1,2),'fJ,['s])
 
   Compiling function J with type (PositiveInteger,PositiveInteger) -> 
      Expression Integer 

   (10)  fJ
                                                                 Type: Symbol
--R 
--R   Compiling function J with type (PositiveInteger,PositiveInteger) -> 
--R      Expression Integer 
--R
--R   (10)  fJ
--R                                                                 Type: Symbol
--E 10

--S 11 of 15
evaluate(ber,br)$BOP1(EFI);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 11

--S 12 of 15
ss:=[1,2]
 

   (12)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (12)  [1,2]
--R                                                   Type: List PositiveInteger
--E 12

--S 13 of 15
fJ(ss)
 
   Compiling function fJ with type List Fraction Integer -> Expression 
      Integer 

           %e
   (13)  ------
         %e - 1
                                                     Type: Expression Integer
--R 
--R   Compiling function fJ with type List Fraction Integer -> Expression 
--R      Integer 
--R
--R           %e
--R   (13)  ------
--R         %e - 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 15
ss:=[1,1]
 

   (14)  [1,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (14)  [1,1]
--R                                                   Type: List PositiveInteger
--E 14

-- fJ doesn't know about the special definition at the origin
--S 15 of 15
fJ(ss)
 

   (15)  1
                                                     Type: Expression Integer
--R 
--R
--R   (15)  1
--R                                                     Type: Expression Integer
--E 15
)spool
 
Starts dribbling to fname.output (2010/3/27, 18:26:17).
)set message test on
 
)set message auto off
 
)clear all
 
 
)system touch /tmp/reado
 
)system chmod +r,-w /tmp/reado
 
)system touch /tmp/writo
 
)system chmod +w,-r /tmp/writo
 
 
--S 1 of 9
nullo: FNAME := new("", "nullo", "x")
 

   (1)  "nullo1680.x"
                                                               Type: FileName
--R 
--R
--I   (1)  "nullo1406.x"
--R                                                               Type: FileName
--E 1

--S 2 of 9
reado: FNAME := filename("/tmp", "reado", "")
 

   (2)  "/tmp/reado"
                                                               Type: FileName
--R 
--R
--R   (2)  "/tmp/reado"
--R                                                               Type: FileName
--E 2

--S 3 of 9
writo: FNAME := "/tmp/writo"
 

   (3)  "/tmp/writo"
                                                               Type: FileName
--R 
--R
--R   (3)  "/tmp/writo"
--R                                                               Type: FileName
--E 3

--S 4 of 9
[directory reado, name reado, extension reado]
 

   (4)  ["/tmp","reado",""]
                                                            Type: List String
--R 
--R
--R   (4)  ["/tmp","reado",""]
--R                                                            Type: List String
--E 4

--S 5 of 9
[directory writo, name writo, extension writo]
 

   (5)  ["/tmp","writo",""]
                                                            Type: List String
--R 
--R
--R   (5)  ["/tmp","writo",""]
--R                                                            Type: List String
--E 5

--S 6 of 9
[directory nullo, name nullo, extension nullo]
 

   (6)  ["","nullo1680","x"]
                                                            Type: List String
--R 
--R
--I   (6)  ["","nullo1406","x"]
--R                                                            Type: List String
--E 6

--S 7 of 9
[exists? reado, readable? reado, writable? reado]
 

   (7)  [true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (7)  [true,true,false]
--R                                                           Type: List Boolean
--E 7

--S 8 of 9
[exists? writo, readable? writo, writable? writo]
 

   (8)  [true,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,true,true]
--R                                                           Type: List Boolean
--E 8

--S 9 of 9
[exists? nullo, readable? nullo, writable? nullo]
 

   (9)  [false,false,true]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [false,false,true]
--R                                                           Type: List Boolean
--E 9
)system rm -f /tmp/reado
 
)system rm -f /tmp/writo
 
)spool 
 
Starts dribbling to multfact.output (2010/3/27, 18:30:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 5
a := rootOf(a**2+a+1)
 

   (1)  a
                                                        Type: AlgebraicNumber
--R 
--R
--R   (1)  a
--R                                                        Type: AlgebraicNumber
--E 1

--S 2 of 5
p := y*z**2 + a*z*x**2 + a*a*x*y**2
 

           2      2                2
   (2)  y z  + a x z + (- a - 1)x y
                                             Type: Polynomial AlgebraicNumber
--R 
--R
--R           2      2                2
--R   (2)  y z  + a x z + (- a - 1)x y
--R                                             Type: Polynomial AlgebraicNumber
--E 2

--S 3 of 5
factor(p,[a])
 

           2      2                2
   (3)  y z  + a x z + (- a - 1)x y
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R           2      2                2
--R   (3)  y z  + a x z + (- a - 1)x y
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 3

--S 4 of 5
b:=rootOf(b**2+1)
 

   (4)  b
                                                        Type: AlgebraicNumber
--R 
--R
--R   (4)  b
--R                                                        Type: AlgebraicNumber
--E 4

--S 5 of 5
factor(x**2*y**2+u**2*v**2,[b])
 

   (5)  (x y - b u v)(x y + b u v)
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R   (5)  (x y - b u v)(x y + b u v)
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 5
)spool 
 
Starts dribbling to kamke7.output (2010/3/27, 18:28:29).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 97
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 97
f:=operator 'f
 

   (2)  f
                                                          Type: BasicOperator
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 97
g:=operator 'g
 

   (3)  g
                                                          Type: BasicOperator
--R 
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--E 3

--S 4 of 97
h:=operator 'h
 

   (4)  h
                                                          Type: BasicOperator
--R 
--R
--R   (4)  h
--R                                                          Type: BasicOperator
--E 4

--S 5 of 97
fa:=operator 'fa
 

   (5)  fa
                                                          Type: BasicOperator
--R 
--R
--R   (5)  fa
--R                                                          Type: BasicOperator
--E 5

--S 6 of 97
fb:=operator 'fb
 

   (6)  fb
                                                          Type: BasicOperator
--R 
--R
--R   (6)  fb
--R                                                          Type: BasicOperator
--E 6

--S 7 of 97
fc:=operator 'fc
 

   (7)  fc
                                                          Type: BasicOperator
--R 
--R
--R   (7)  fc
--R                                                          Type: BasicOperator
--E 7

--S 8 of 97
fd:=operator 'fd
 

   (8)  fd
                                                          Type: BasicOperator
--R 
--R
--R   (8)  fd
--R                                                          Type: BasicOperator
--E 8

--S 9 of 97
fe:=operator 'fe
 

   (9)  fe
                                                          Type: BasicOperator
--R 
--R
--R   (9)  fe
--R                                                          Type: BasicOperator
--E 9

--S 10 of 97
ff:=operator 'ff
 

   (10)  ff
                                                          Type: BasicOperator
--R 
--R
--R   (10)  ff
--R                                                          Type: BasicOperator
--E 10

--S 11 of 97
ode352 := D(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-_
            sin(alpha)*sin(y(x)))*cos(x)
 

   (11)
               2                              ,
     (cos(y(x))  - sin(alpha)sin(x)cos(y(x)))y (x) - cos(x)sin(alpha)sin(y(x))

   + 
           2
     cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (11)
--R               2                              ,
--R     (cos(y(x))  - sin(alpha)sin(x)cos(y(x)))y (x) - cos(x)sin(alpha)sin(y(x))
--R
--R   + 
--R           2
--R     cos(x)
--R                                                     Type: Expression Integer
--E 11

--S 12 of 97
yx:=solve(ode352,y,x)
 

         (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
   (12)  ------------------------------------------------------------------
                                          2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
--R   (12)  ------------------------------------------------------------------
--R                                          2
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 97
ode352expr := D(yx,x)*(cos(yx)-sin(alpha)*sin(x))*cos(yx)+(cos(x)-_
                sin(alpha)*sin(yx))*cos(x)
 

   (13)
       -
            2cos(x)sin(alpha)
         *
            sin
                   (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x)
                 + 
                   y(x) + x
              /
                 2
     + 
                       2            2                                   ,
           (- sin(y(x))  + cos(y(x))  - 2sin(alpha)sin(x)cos(y(x)) + 1)y (x)

         + 
                                                2         2
           - 2cos(x)sin(alpha)sin(y(x)) - sin(x)  + cos(x)  + 1
      *
           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x 2
       cos(------------------------------------------------------------------)
                                            2
     + 
                                        2                            2
               sin(alpha)sin(x)sin(y(x))  - sin(alpha)sin(x)cos(y(x))
             + 
                          2      2
               2sin(alpha) sin(x) cos(y(x)) - sin(alpha)sin(x)
          *
              ,
             y (x)

         + 
                            2                                  3
           2cos(x)sin(alpha) sin(x)sin(y(x)) + sin(alpha)sin(x)
         + 
                    2
           (- cos(x)  - 1)sin(alpha)sin(x)
      *
           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
       cos(------------------------------------------------------------------)
                                            2
     + 
              2
       2cos(x)
  /
     2
                                                     Type: Expression Integer
--R 
--R
--R   (13)
--R       -
--R            2cos(x)sin(alpha)
--R         *
--R            sin
--R                   (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x)
--R                 + 
--R                   y(x) + x
--R              /
--R                 2
--R     + 
--R                       2            2                                   ,
--R           (- sin(y(x))  + cos(y(x))  - 2sin(alpha)sin(x)cos(y(x)) + 1)y (x)
--R
--R         + 
--R                                                2         2
--R           - 2cos(x)sin(alpha)sin(y(x)) - sin(x)  + cos(x)  + 1
--R      *
--R           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x 2
--R       cos(------------------------------------------------------------------)
--R                                            2
--R     + 
--R                                        2                            2
--R               sin(alpha)sin(x)sin(y(x))  - sin(alpha)sin(x)cos(y(x))
--R             + 
--R                          2      2
--R               2sin(alpha) sin(x) cos(y(x)) - sin(alpha)sin(x)
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                            2                                  3
--R           2cos(x)sin(alpha) sin(x)sin(y(x)) + sin(alpha)sin(x)
--R         + 
--R                    2
--R           (- cos(x)  - 1)sin(alpha)sin(x)
--R      *
--R           (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x
--R       cos(------------------------------------------------------------------)
--R                                            2
--R     + 
--R              2
--R       2cos(x)
--R  /
--R     2
--R                                                     Type: Expression Integer
--E 13

--S 14 of 97
ode353 := x*D(y(x),x)*cos(y(x))+sin(y(x))
 

                     ,
   (14)  x cos(y(x))y (x) + sin(y(x))

                                                     Type: Expression Integer
--R 
--R
--R                     ,
--R   (14)  x cos(y(x))y (x) + sin(y(x))
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 97
yx:=solve(ode353,y,x)
 

   (15)  x sin(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (15)  x sin(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 15

--S 16 of 97
ode353expr := x*D(yx,x)*cos(yx)+sin(yx)
 

                              2          ,
   (16)  sin(x sin(y(x))) + (x cos(y(x))y (x) + x sin(y(x)))cos(x sin(y(x)))

                                                     Type: Expression Integer
--R 
--R
--R                              2          ,
--R   (16)  sin(x sin(y(x))) + (x cos(y(x))y (x) + x sin(y(x)))cos(x sin(y(x)))
--R
--R                                                     Type: Expression Integer
--E 16

--S 17 of 97
ode354 := (x*sin(y(x))-1)*D(y(x),x)+cos(y(x))
 

                           ,
   (17)  (x sin(y(x)) - 1)y (x) + cos(y(x))

                                                     Type: Expression Integer
--R 
--R
--R                           ,
--R   (17)  (x sin(y(x)) - 1)y (x) + cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 17

--S 18 of 97
yx:=solve(ode354,y,x)
 

         - sin(y(x)) + x
   (18)  ---------------
            cos(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         - sin(y(x)) + x
--R   (18)  ---------------
--R            cos(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 97
ode354expr := (x*sin(yx)-1)*D(yx,x)+cos(yx)
 

   (19)
                      2    2                       2  ,
         ((x sin(y(x))  - x sin(y(x)) + x cos(y(x)) )y (x) - x cos(y(x)))

      *
             sin(y(x)) - x
         sin(-------------)
               cos(y(x))
     + 
                2    sin(y(x)) - x
       cos(y(x)) cos(-------------)
                       cos(y(x))
     + 
                 2                          2  ,
       (sin(y(x))  - x sin(y(x)) + cos(y(x)) )y (x) - cos(y(x))

  /
              2
     cos(y(x))
                                                     Type: Expression Integer
--R 
--R
--R   (19)
--R                      2    2                       2  ,
--R         ((x sin(y(x))  - x sin(y(x)) + x cos(y(x)) )y (x) - x cos(y(x)))
--R
--R      *
--R             sin(y(x)) - x
--R         sin(-------------)
--R               cos(y(x))
--R     + 
--R                2    sin(y(x)) - x
--R       cos(y(x)) cos(-------------)
--R                       cos(y(x))
--R     + 
--R                 2                          2  ,
--R       (sin(y(x))  - x sin(y(x)) + cos(y(x)) )y (x) - cos(y(x))
--R
--R  /
--R              2
--R     cos(y(x))
--R                                                     Type: Expression Integer
--E 19

--S 20 of 97
ode355 := (x*cos(y(x))+cos(x))*D(y(x),x)-y(x)*sin(x)+sin(y(x))
 

                                ,
   (20)  (x cos(y(x)) + cos(x))y (x) + sin(y(x)) - y(x)sin(x)

                                                     Type: Expression Integer
--R 
--R
--R                                ,
--R   (20)  (x cos(y(x)) + cos(x))y (x) + sin(y(x)) - y(x)sin(x)
--R
--R                                                     Type: Expression Integer
--E 20

--S 21 of 97
yx:=solve(ode355,y,x)
 

   (21)  x sin(y(x)) + y(x)cos(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (21)  x sin(y(x)) + y(x)cos(x)
--R                                          Type: Union(Expression Integer,...)
--E 21

--S 22 of 97
ode355expr := (x*cos(yx)+cos(x))*D(yx,x)-yx*sin(x)+sin(yx)
 

   (22)
     sin(x sin(y(x)) + y(x)cos(x))
   + 
          2                      ,
       ((x cos(y(x)) + x cos(x))y (x) + x sin(y(x)) - x y(x)sin(x))

    *
       cos(x sin(y(x)) + y(x)cos(x))
   + 
                                2  ,
     (x cos(x)cos(y(x)) + cos(x) )y (x) + (- x sin(x) + cos(x))sin(y(x))

   + 
     - 2y(x)cos(x)sin(x)
                                                     Type: Expression Integer
--R 
--R
--R   (22)
--R     sin(x sin(y(x)) + y(x)cos(x))
--R   + 
--R          2                      ,
--R       ((x cos(y(x)) + x cos(x))y (x) + x sin(y(x)) - x y(x)sin(x))
--R
--R    *
--R       cos(x sin(y(x)) + y(x)cos(x))
--R   + 
--R                                2  ,
--R     (x cos(x)cos(y(x)) + cos(x) )y (x) + (- x sin(x) + cos(x))sin(y(x))
--R
--R   + 
--R     - 2y(x)cos(x)sin(x)
--R                                                     Type: Expression Integer
--E 22

--S 23 of 97
ode356 := (x**2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)**2*cos(x)
 

           2                         ,                         2
   (23)  (x cos(y(x)) + 2y(x)sin(x))y (x) + 2x sin(y(x)) + y(x) cos(x)

                                                     Type: Expression Integer
--R 
--R
--R           2                         ,                         2
--R   (23)  (x cos(y(x)) + 2y(x)sin(x))y (x) + 2x sin(y(x)) + y(x) cos(x)
--R
--R                                                     Type: Expression Integer
--E 23

--S 24 of 97
yx:=solve(ode356,y,x)
 

          2                2
   (24)  x sin(y(x)) + y(x) sin(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2                2
--R   (24)  x sin(y(x)) + y(x) sin(x)
--R                                          Type: Union(Expression Integer,...)
--E 24

--S 25 of 97
ode356expr:=(x**2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx**2*cos(x)
 

   (25)
             2                2
     2x sin(x sin(y(x)) + y(x) sin(x))
   + 
          4              2            ,        3             2    2
       ((x cos(y(x)) + 2x y(x)sin(x))y (x) + 2x sin(y(x)) + x y(x) cos(x))

    *
            2                2
       cos(x sin(y(x)) + y(x) sin(x))
   + 
            4                    2          2
         (2x sin(x)cos(y(x)) + 4x y(x)sin(x) )sin(y(x))
       + 
           2    2      2                 3      3
         2x y(x) sin(x) cos(y(x)) + 4y(x) sin(x)
    *
        ,
       y (x)

   + 
        3          4                2
     (4x sin(x) + x cos(x))sin(y(x))
   + 
             2      2     2    2                              4            2
     (4x y(x) sin(x)  + 4x y(x) cos(x)sin(x))sin(y(x)) + 3y(x) cos(x)sin(x)
                                                     Type: Expression Integer
--R 
--R
--R   (25)
--R             2                2
--R     2x sin(x sin(y(x)) + y(x) sin(x))
--R   + 
--R          4              2            ,        3             2    2
--R       ((x cos(y(x)) + 2x y(x)sin(x))y (x) + 2x sin(y(x)) + x y(x) cos(x))
--R
--R    *
--R            2                2
--R       cos(x sin(y(x)) + y(x) sin(x))
--R   + 
--R            4                    2          2
--R         (2x sin(x)cos(y(x)) + 4x y(x)sin(x) )sin(y(x))
--R       + 
--R           2    2      2                 3      3
--R         2x y(x) sin(x) cos(y(x)) + 4y(x) sin(x)
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R        3          4                2
--R     (4x sin(x) + x cos(x))sin(y(x))
--R   + 
--R             2      2     2    2                              4            2
--R     (4x y(x) sin(x)  + 4x y(x) cos(x)sin(x))sin(y(x)) + 3y(x) cos(x)sin(x)
--R                                                     Type: Expression Integer
--E 25

--S 26 of 97
ode358 := D(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x)
 

                         ,
   (26)  cos(x)sin(y(x))y (x) + sin(x)cos(y(x))

                                                     Type: Expression Integer
--R 
--R
--R                         ,
--R   (26)  cos(x)sin(y(x))y (x) + sin(x)cos(y(x))
--R
--R                                                     Type: Expression Integer
--E 26

--S 27 of 97
yx:=solve(ode358,y,x)
 

   (27)  - cos(x)cos(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (27)  - cos(x)cos(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 27

--S 28 of 97
ode358expr := D(yx,x)*sin(yx)*cos(x)+cos(yx)*sin(x)
 

   (28)
              2          ,
     (- cos(x) sin(y(x))y (x) - cos(x)sin(x)cos(y(x)))sin(cos(x)cos(y(x)))

   + 
     sin(x)cos(cos(x)cos(y(x)))
                                                     Type: Expression Integer
--R 
--R
--R   (28)
--R              2          ,
--R     (- cos(x) sin(y(x))y (x) - cos(x)sin(x)cos(y(x)))sin(cos(x)cos(y(x)))
--R
--R   + 
--R     sin(x)cos(cos(x)cos(y(x)))
--R                                                     Type: Expression Integer
--E 28

--S 29 of 97
ode361 := (x*sin(x*y(x))+cos(x+y(x))-sin(y(x)))*D(y(x),x)+_
              y(x)*sin(x*y(x))+cos(x+y(x))+cos(x)
 

   (29)
                                                 ,
     (x sin(x y(x)) - sin(y(x)) + cos(y(x) + x))y (x) + y(x)sin(x y(x))

   + 
     cos(y(x) + x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (29)
--R                                                 ,
--R     (x sin(x y(x)) - sin(y(x)) + cos(y(x) + x))y (x) + y(x)sin(x y(x))
--R
--R   + 
--R     cos(y(x) + x) + cos(x)
--R                                                     Type: Expression Integer
--E 29

--S 30 of 97
yx:=solve(ode361,y,x)
 

   (30)
          y(x) 2                     y(x)                  y(x)
     2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
            2                          2                     2
   + 
     cos(y(x))
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (30)
--R          y(x) 2                     y(x)                  y(x)
--R     2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
--R            2                          2                     2
--R   + 
--R     cos(y(x))
--R                                          Type: Union(Expression Integer,...)
--E 30

--S 31 of 97
ode361expr:=(x*sin(x*yx)+cos(x+yx)-sin(yx))*D(yx,x)+_
              yx*sin(x*yx)+cos(x+yx)+cos(x)
 

   (31)
              2                                               y(x) 2
             x sin(x y(x)) - x sin(y(x)) + x cos(y(x) + x)sin(----)
                                                                2
           + 
                   y(x) 2
             x cos(----) cos(y(x) + x)
                     2
        *
            ,
           y (x)

       + 
                                     y(x)     y(x)         y(x) 2
         x y(x)sin(x y(x)) + (2x cos(----)sin(----) + 2cos(----) )sin(y(x) + x)
                                       2        2            2
       + 
                y(x)                  y(x)
         - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
                  2                     2
       + 
                y(x) 2
         2x cos(----) cos(y(x) + x) + cos(y(x))
                  2
    *
       sin
                   y(x) 2                       y(x)                  y(x)
            2x cos(----) sin(y(x) + x) - 2x cos(----)cos(y(x) + x)sin(----)
                     2                            2                     2
          + 
            - x cos(x y(x)) + x cos(y(x))
   + 
                                                            y(x) 2
             - x sin(x y(x)) + sin(y(x)) - cos(y(x) + x)sin(----)
                                                              2
           + 
                   y(x) 2
             - cos(----) cos(y(x) + x)
                     2
        *
            ,
           y (x)

       + 
                                  y(x)     y(x)
         - y(x)sin(x y(x)) - 2cos(----)sin(----)sin(y(x) + x)
                                    2        2
       + 
                y(x) 2
         - 2cos(----) cos(y(x) + x)
                  2
    *
       sin
                 y(x) 2                     y(x)                  y(x)
            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
                   2                          2                     2
          + 
            - cos(x y(x)) + cos(y(x))
   + 
                                                          y(x) 2
             x sin(x y(x)) - sin(y(x)) + cos(y(x) + x)sin(----)
                                                            2
           + 
                 y(x) 2
             cos(----) cos(y(x) + x)
                   2
        *
            ,
           y (x)

       + 
                                y(x)     y(x)
         y(x)sin(x y(x)) + 2cos(----)sin(----)sin(y(x) + x)
                                  2        2
       + 
              y(x) 2
         2cos(----) cos(y(x) + x) + 1
                2
    *
       cos
                 y(x) 2                     y(x)                  y(x)
            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
                   2                          2                     2
          + 
            - cos(x y(x)) + cos(y(x)) + x
   + 
     cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (31)
--R              2                                               y(x) 2
--R             x sin(x y(x)) - x sin(y(x)) + x cos(y(x) + x)sin(----)
--R                                                                2
--R           + 
--R                   y(x) 2
--R             x cos(----) cos(y(x) + x)
--R                     2
--R        *
--R            ,
--R           y (x)
--R
--R       + 
--R                                     y(x)     y(x)         y(x) 2
--R         x y(x)sin(x y(x)) + (2x cos(----)sin(----) + 2cos(----) )sin(y(x) + x)
--R                                       2        2            2
--R       + 
--R                y(x)                  y(x)
--R         - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x))
--R                  2                     2
--R       + 
--R                y(x) 2
--R         2x cos(----) cos(y(x) + x) + cos(y(x))
--R                  2
--R    *
--R       sin
--R                   y(x) 2                       y(x)                  y(x)
--R            2x cos(----) sin(y(x) + x) - 2x cos(----)cos(y(x) + x)sin(----)
--R                     2                            2                     2
--R          + 
--R            - x cos(x y(x)) + x cos(y(x))
--R   + 
--R                                                            y(x) 2
--R             - x sin(x y(x)) + sin(y(x)) - cos(y(x) + x)sin(----)
--R                                                              2
--R           + 
--R                   y(x) 2
--R             - cos(----) cos(y(x) + x)
--R                     2
--R        *
--R            ,
--R           y (x)
--R
--R       + 
--R                                  y(x)     y(x)
--R         - y(x)sin(x y(x)) - 2cos(----)sin(----)sin(y(x) + x)
--R                                    2        2
--R       + 
--R                y(x) 2
--R         - 2cos(----) cos(y(x) + x)
--R                  2
--R    *
--R       sin
--R                 y(x) 2                     y(x)                  y(x)
--R            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
--R                   2                          2                     2
--R          + 
--R            - cos(x y(x)) + cos(y(x))
--R   + 
--R                                                          y(x) 2
--R             x sin(x y(x)) - sin(y(x)) + cos(y(x) + x)sin(----)
--R                                                            2
--R           + 
--R                 y(x) 2
--R             cos(----) cos(y(x) + x)
--R                   2
--R        *
--R            ,
--R           y (x)
--R
--R       + 
--R                                y(x)     y(x)
--R         y(x)sin(x y(x)) + 2cos(----)sin(----)sin(y(x) + x)
--R                                  2        2
--R       + 
--R              y(x) 2
--R         2cos(----) cos(y(x) + x) + 1
--R                2
--R    *
--R       cos
--R                 y(x) 2                     y(x)                  y(x)
--R            2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----)
--R                   2                          2                     2
--R          + 
--R            - cos(x y(x)) + cos(y(x)) + x
--R   + 
--R     cos(x)
--R                                                     Type: Expression Integer
--E 31

--S 32 of 97
ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)**2+x
 

               y(x) 2 ,              y(x) 2
   (32)  x cos(----) y (x) - y(x)cos(----)  + x
                 x                     x
                                                     Type: Expression Integer
--R 
--R
--R               y(x) 2 ,              y(x) 2
--R   (32)  x cos(----) y (x) - y(x)cos(----)  + x
--R                 x                     x
--R                                                     Type: Expression Integer
--E 32

--S 33 of 97
yx:=solve(ode363,y,x)
 

               y(x)     y(x)
         x cos(----)sin(----) + 2x log(x) + y(x)
                 x        x
   (33)  ---------------------------------------
                            2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               y(x)     y(x)
--R         x cos(----)sin(----) + 2x log(x) + y(x)
--R                 x        x
--R   (33)  ---------------------------------------
--R                            2x
--R                                          Type: Union(Expression Integer,...)
--E 33

--S 34 of 97
ode363expr := (x*D(yx,x)-yx)*cos(yx/x)**2+x
 

   (34)
                    y(x) 2         y(x) 2      ,              y(x) 2
           (- x sin(----)  + x cos(----)  + x)y (x) + y(x)sin(----)
                      x              x                          x
         + 
                   y(x)     y(x)            y(x) 2
           - x cos(----)sin(----) - y(x)cos(----)  - 2x log(x) - 2y(x) + 2x
                     x        x               x
      *
                   y(x)     y(x)                     2
             x cos(----)sin(----) + 2x log(x) + y(x)
                     x        x
         cos(---------------------------------------)
                                 2
                               2x
     + 
         2
       2x
  /
     2x
                                                     Type: Expression Integer
--R 
--R
--R   (34)
--R                    y(x) 2         y(x) 2      ,              y(x) 2
--R           (- x sin(----)  + x cos(----)  + x)y (x) + y(x)sin(----)
--R                      x              x                          x
--R         + 
--R                   y(x)     y(x)            y(x) 2
--R           - x cos(----)sin(----) - y(x)cos(----)  - 2x log(x) - 2y(x) + 2x
--R                     x        x               x
--R      *
--R                   y(x)     y(x)                     2
--R             x cos(----)sin(----) + 2x log(x) + y(x)
--R                     x        x
--R         cos(---------------------------------------)
--R                                 2
--R                               2x
--R     + 
--R         2
--R       2x
--R  /
--R     2x
--R                                                     Type: Expression Integer
--E 34

--S 35 of 97
ode364 := (y(x)*sin(y(x)/x)-x*cos(y(x)/x))*x*D(y(x),x)-_
            (x*cos(y(x)/x)+y(x)*sin(y(x)/x))*y(x)
 

   (35)
              y(x)     2    y(x)   ,          2    y(x)              y(x)
   (x y(x)sin(----) - x cos(----))y (x) - y(x) sin(----) - x y(x)cos(----)
                x             x                      x                 x
                                                     Type: Expression Integer
--R 
--R
--R   (35)
--R              y(x)     2    y(x)   ,          2    y(x)              y(x)
--R   (x y(x)sin(----) - x cos(----))y (x) - y(x) sin(----) - x y(x)cos(----)
--R                x             x                      x                 x
--R                                                     Type: Expression Integer
--E 35

--S 36 of 97
yx:=solve(ode364,y,x)
 

                     y(x)
   (36)  - x y(x)cos(----)
                       x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     y(x)
--R   (36)  - x y(x)cos(----)
--R                       x
--R                                          Type: Union(Expression Integer,...)
--E 36

--S 37 of 97
ode364expr := (yx*sin(yx/x)-x*cos(yx/x))*x*D(yx,x)-_
                (x*cos(yx/x)+yx*sin(yx/x))*yx
 

   (37)
           2    2    y(x)     y(x)     3        y(x) 2  ,
         (x y(x) cos(----)sin(----) - x y(x)cos(----) )y (x)
                       x        x                 x
       + 
                 3    y(x)     y(x)
         - x y(x) cos(----)sin(----)
                        x        x
    *
                   y(x)
       sin(y(x)cos(----))
                     x
   + 
             2        y(x)     3    y(x)   ,            2    y(x)
         (- x y(x)sin(----) + x cos(----))y (x) + x y(x) sin(----)
                        x             x                        x
       + 
           2        y(x)
         2x y(x)cos(----)
                      x
    *
                   y(x)
       cos(y(x)cos(----))
                     x
                                                     Type: Expression Integer
--R 
--R
--R   (37)
--R           2    2    y(x)     y(x)     3        y(x) 2  ,
--R         (x y(x) cos(----)sin(----) - x y(x)cos(----) )y (x)
--R                       x        x                 x
--R       + 
--R                 3    y(x)     y(x)
--R         - x y(x) cos(----)sin(----)
--R                        x        x
--R    *
--R                   y(x)
--R       sin(y(x)cos(----))
--R                     x
--R   + 
--R             2        y(x)     3    y(x)   ,            2    y(x)
--R         (- x y(x)sin(----) + x cos(----))y (x) + x y(x) sin(----)
--R                        x             x                        x
--R       + 
--R           2        y(x)
--R         2x y(x)cos(----)
--R                      x
--R    *
--R                   y(x)
--R       cos(y(x)cos(----))
--R                     x
--R                                                     Type: Expression Integer
--E 37

--S 38 of 97
ode434 := D(y(x),x)-1
 

          ,
   (38)  y (x) - 1

                                                     Type: Expression Integer
--R 
--R
--R          ,
--R   (38)  y (x) - 1
--R
--R                                                     Type: Expression Integer
--E 38

--S 39 of 97
ode434a:=solve(ode434,y,x)
 

   (39)  [particular= x,basis= [1]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (39)  [particular= x,basis= [1]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 39

--S 40 of 97
yx:=ode434a.particular
 

   (40)  x
                                                     Type: Expression Integer
--R 
--R
--R   (40)  x
--R                                                     Type: Expression Integer
--E 40

--S 41 of 97
ode434expr := D(yx,x)-1
 

   (41)  0
                                                     Type: Expression Integer
--R 
--R
--R   (41)  0
--R                                                     Type: Expression Integer
--E 41

--S 42 of 97
ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x)
 

                  4    2    3          2
          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
   (42)  y (x)= ------------------------------------
                                  x
                                            Type: Equation Expression Integer
--R 
--R
--R                  4    2    3          2
--R          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
--R   (42)  y (x)= ------------------------------------
--R                                  x
--R                                            Type: Equation Expression Integer
--E 42

--S 43 of 97
solve(ode683,y,x)
 

                           - x y(x) + 1
   (43)  -----------------------------------------------
                           3     2          3     2
                         6x log(x  + x) - 4x  + 3x  - 6x
                         -------------------------------
               3+-----+                 18
         x y(x)\|x + 1 %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           - x y(x) + 1
--R   (43)  -----------------------------------------------
--R                           3     2          3     2
--R                         6x log(x  + x) - 4x  + 3x  - 6x
--R                         -------------------------------
--R               3+-----+                 18
--R         x y(x)\|x + 1 %e
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 97
ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_
            (x-1)/x)
 

                  2    2                    3    2       2
          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
   (44)  y (x)= -------------------------------------------------------
                                          2
                                         x  - x
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                    3    2       2
--R          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
--R   (44)  y (x)= -------------------------------------------------------
--R                                          2
--R                                         x  - x
--R                                            Type: Equation Expression Integer
--E 44

--S 45 of 97
solve(ode703,y,x)
 

                 - x y(x) + 1
   (45)  ----------------------------
           2           - dilog(x) + x
         (x  - x)y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 - x y(x) + 1
--R   (45)  ----------------------------
--R           2           - dilog(x) + x
--R         (x  - x)y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 45

--S 46 of 97
ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_
            y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x)
 

   (46)
            2    2                           1          x    3    2    2
          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
    ,                                        x
   y (x)= ------------------------------------------------------------------
                                         1        x
                                   x log(-) - x %e
                                         x
                                            Type: Equation Expression Integer
--R 
--R
--R   (46)
--R            2    2                           1          x    3    2    2
--R          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
--R    ,                                        x
--R   y (x)= ------------------------------------------------------------------
--R                                         1        x
--R                                   x log(-) - x %e
--R                                         x
--R                                            Type: Equation Expression Integer
--E 46

--S 47 of 97
solve(ode714,y,x)
 

   (47)
       -
                                         1      %L     2
                     x %L log(%L) + log(--) - %e   + %L
                   ++                   %L
                   |   --------------------------------- d%L
                  ++                  1         %L
                              %L log(--) - %L %e
                                     %L
            y(x)%e
         *
            INTSIGN
           ,
               x
           ,
                                                        2
                                       - %L log(%L) - %L
                 --------------------------------------------------------------
                                                           1      %L     2
                                      %L %L log(%L) + log(--) - %e   + %L
                                    ++                    %L
                                    |    --------------------------------- d%L
                                   ++                   1         %L
                                                %L log(--) - %L %e
                       1      %L                       %L
                 (log(--) - %e  )%e
                      %L
              *
                 d%L
     + 
       1
  /
                                  1      %L     2
              x %L log(%L) + log(--) - %e   + %L
            ++                   %L
            |   --------------------------------- d%L
           ++                  1         %L
                       %L log(--) - %L %e
                              %L
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (47)
--R       -
--I                                         1      %I     2
--I                     x %I log(%I) + log(--) - %e   + %I
--I                   ++                   %I
--I                   |   --------------------------------- d%I
--I                  ++                  1         %I
--I                              %I log(--) - %I %e
--I                                     %I
--R            y(x)%e
--R         *
--R            INTSIGN
--R           ,
--R               x
--R           ,
--R                                                        2
--I                                       - %I log(%I) - %I
--R                 --------------------------------------------------------------
--I                                                           1      %I     2
--I                                      %I %I log(%I) + log(--) - %e   + %I
--I                                    ++                    %I
--I                                    |    --------------------------------- d%I
--I                                   ++                   1         %I
--I                                                %I log(--) - %I %e
--I                       1      %I                       %I
--R                 (log(--) - %e  )%e
--I                      %I
--R              *
--I                 d%I
--R     + 
--R       1
--R  /
--I                                  1      %I     2
--I              x %I log(%I) + log(--) - %e   + %I
--I            ++                   %I
--I            |   --------------------------------- d%I
--I           ++                  1         %I
--I                       %I log(--) - %I %e
--I                              %I
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 47

--S 48 of 97
ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x))
 

                  2    2                          x
          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
   (48)  y (x)= -----------------------------------
                                   x
                               x %e
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                          x
--R          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
--R   (48)  y (x)= -----------------------------------
--R                                   x
--R                               x %e
--R                                            Type: Equation Expression Integer
--E 48

--S 49 of 97
solve(ode719,y,x)
 

                    - x y(x) + 1
   (49)  ----------------------------------
                  x                 %L
                ++  %L log(2%L) + %e
                |   ------------------ d%L
               ++              %L
                          %L %e
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    - x y(x) + 1
--R   (49)  ----------------------------------
--I                  x                 %I
--I                ++  %I log(2%I) + %e
--I                |   ------------------ d%I
--I               ++              %I
--I                          %I %e
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 49

--S 50 of 97
ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1))
 

                    2     2        4     2
          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
   (50)  y (x)= -----------------------------------
                               x + 1
                                            Type: Equation Expression Integer
--R 
--R
--R                    2     2        4     2
--R          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
--R   (50)  y (x)= -----------------------------------
--R                               x + 1
--R                                            Type: Equation Expression Integer
--E 50

--S 51 of 97
solve(ode736,y,x)
 

           2                  4     3     2
         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
   (51)  -------------------------------------------
                                 2
                       2y(x) - 2x  - 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2                  4     3     2
--R         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
--R   (51)  -------------------------------------------
--R                                 2
--R                       2y(x) - 2x  - 2
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 97
ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_
            log((x-1)*(1+x)/x)*x*y(x))/x)
 

                                     2
                       2            x  - 1
                (x y(x)  - y(x))log(------) - y(x)
          ,                            x
   (52)  y (x)= ----------------------------------
                                 x
                                            Type: Equation Expression Integer
--R 
--R
--R                                     2
--R                       2            x  - 1
--R                (x y(x)  - y(x))log(------) - y(x)
--R          ,                            x
--R   (52)  y (x)= ----------------------------------
--R                                 x
--R                                            Type: Equation Expression Integer
--E 52

--S 53 of 97
solve(ode765,y,x)
 

                   - x y(x) + 1
   (53)  --------------------------------
                          2
                        %L  - 1
                  x log(-------) + 1
                ++         %L
                |   ---------------- d%L
               ++          %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   - x y(x) + 1
--R   (53)  --------------------------------
--R                          2
--I                        %I  - 1
--R                  x log(-------) + 1
--I                ++         %I
--I                |   ---------------- d%I
--I               ++          %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 53

--S 54 of 97
ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_
            log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x))
 

                                                      2
                                 2    2              x  - 1
                - y(x)log(x) + (x y(x)  - x y(x))log(------)
          ,                                             x
   (54)  y (x)= --------------------------------------------
                                  x log(x)
                                            Type: Equation Expression Integer
--R 
--R
--R                                                      2
--R                                 2    2              x  - 1
--R                - y(x)log(x) + (x y(x)  - x y(x))log(------)
--R          ,                                             x
--R   (54)  y (x)= --------------------------------------------
--R                                  x log(x)
--R                                            Type: Equation Expression Integer
--E 54

--S 55 of 97
solve(ode766,y,x)
 

   (55)
       -
                                          2
                                        %L  - 1
                     x log(%L) + %L log(-------)
                   ++                      %L
                   |   ------------------------- d%L
                  ++           %L log(%L)
            y(x)%e
         *
                                           2
                                         %L  - 1
               x                  %L log(-------)
             ++                             %L
             |   - --------------------------------------------- d%L
            ++                                       2
                                                   %L  - 1
                               %L log(%L) + %L log(-------)
                             ++                       %L
                             |    ------------------------- d%L
                            ++            %L log(%L)
                   log(%L)%e
     + 
       1
  /
                                   2
                                 %L  - 1
              x log(%L) + %L log(-------)
            ++                      %L
            |   ------------------------- d%L
           ++           %L log(%L)
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (55)
--R       -
--R                                          2
--I                                        %I  - 1
--I                     x log(%I) + %I log(-------)
--I                   ++                      %I
--I                   |   ------------------------- d%I
--I                  ++           %I log(%I)
--R            y(x)%e
--R         *
--R                                           2
--I                                         %I  - 1
--I               x                  %I log(-------)
--I             ++                             %I
--I             |   - --------------------------------------------- d%I
--R            ++                                       2
--I                                                   %I  - 1
--I                               %I log(%I) + %I log(-------)
--I                             ++                       %I
--I                             |    ------------------------- d%I
--I                            ++            %I log(%I)
--I                   log(%I)%e
--R     + 
--R       1
--R  /
--R                                   2
--I                                 %I  - 1
--I              x log(%I) + %I log(-------)
--I            ++                      %I
--I            |   ------------------------- d%I
--I           ++           %I log(%I)
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 55

--S 56 of 97
ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_
              log((x**2+1)/x)*x**2*y(x))/x/log(1/x))
 

                                       2
                  2    2              x  + 1            1
                (x y(x)  - x y(x))log(------) - y(x)log(-)
          ,                              x              x
   (56)  y (x)= ------------------------------------------
                                       1
                                 x log(-)
                                       x
                                            Type: Equation Expression Integer
--R 
--R
--R                                       2
--R                  2    2              x  + 1            1
--R                (x y(x)  - x y(x))log(------) - y(x)log(-)
--R          ,                              x              x
--R   (56)  y (x)= ------------------------------------------
--R                                       1
--R                                 x log(-)
--R                                       x
--R                                            Type: Equation Expression Integer
--E 56

--S 57 of 97
solve(ode776,y,x)
 

                        - x y(x) + 1
   (57)  -----------------------------------------
                             2
                           %L  + 1         1
                  x %L log(-------) + log(--)
                ++            %L          %L
                |   ------------------------- d%L
               ++                   1
                            %L log(--)
                                   %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        - x y(x) + 1
--R   (57)  -----------------------------------------
--R                             2
--I                           %I  + 1         1
--I                  x %I log(-------) + log(--)
--I                ++            %I          %I
--I                |   ------------------------- d%I
--R               ++                   1
--I                            %I log(--)
--I                                   %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 57

--S 58 of 97
ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_
            25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/_
            (-5*y(x)+2*x**3+10*x**(1/2)-5)/x)
 

                               3       +-+      3          6      3
          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
   (58)  y (x)= --------------------------------------------------------------
                                    +-+                 4
                                50x\|x  - 25x y(x) + 10x  - 25x
                                            Type: Equation Expression Integer
--R 
--R
--R                               3       +-+      3          6      3
--R          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
--R   (58)  y (x)= --------------------------------------------------------------
--R                                    +-+                 4
--R                                50x\|x  - 25x y(x) + 10x  - 25x
--R                                            Type: Equation Expression Integer
--E 58

--S 59 of 97
solve(ode872,y,x)
 

   (59)
               +-+                  3        +-+         2       3
       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
     + 
           6      3
       - 4x  + 20x  - 100x
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (59)
--R               +-+                  3        +-+         2       3
--R       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
--R     + 
--R           6      3
--R       - 4x  + 20x  - 100x
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 59

--S 60 of 97
ode555 := sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x)
 

          +----------+
          | ,   2          ,
   (60)   |y (x)  + 1  + xy (x) - y(x)
         \|
                                                     Type: Expression Integer
--R 
--R
--R          +----------+
--R          | ,   2          ,
--R   (60)   |y (x)  + 1  + xy (x) - y(x)
--R         \|
--R                                                     Type: Expression Integer
--E 60

--S 61 of 97
solve(ode555,y,x)
 

               +-----------+
               | ,    2
            x  |y (%L)  + 1  - y(x)
          ++  \|
   (61)   |   --------------------- d%L
         ++              2
                       %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +-----------+
--R               | ,    2
--I            x  |y (%I)  + 1  - y(x)
--R          ++  \|
--I   (61)   |   --------------------- d%I
--R         ++              2
--I                       %I
--R                                          Type: Union(Expression Integer,...)
--E 61

--S 62 of 97
ode557 := x*(sqrt(D(y(x),x)**2+1)+D(y(x),x))-y(x)
 

           +----------+
           | ,   2          ,
   (62)  x |y (x)  + 1  + xy (x) - y(x)
          \|
                                                     Type: Expression Integer
--R 
--R
--R           +----------+
--R           | ,   2          ,
--R   (62)  x |y (x)  + 1  + xy (x) - y(x)
--R          \|
--R                                                     Type: Expression Integer
--E 62

--S 63 of 97
solve(ode557,y,x)
 

                 +-----------+
                 | ,    2
            x %L |y (%L)  + 1  - y(x)
          ++    \|
   (63)   |   ----------------------- d%L
         ++               2
                        %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-----------+
--R                 | ,    2
--I            x %I |y (%I)  + 1  - y(x)
--R          ++    \|
--I   (63)   |   ----------------------- d%I
--R         ++               2
--I                        %I
--R                                          Type: Union(Expression Integer,...)
--E 63

--S 64 of 97
ode558 := a*x*sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x)
 

             +----------+
             | ,   2          ,
   (64)  a x |y (x)  + 1  + xy (x) - y(x)
            \|
                                                     Type: Expression Integer
--R 
--R
--R             +----------+
--R             | ,   2          ,
--R   (64)  a x |y (x)  + 1  + xy (x) - y(x)
--R            \|
--R                                                     Type: Expression Integer
--E 64

--S 65 of 97
solve(ode558,y,x)
 

                   +-----------+
                   | ,    2
            x %L a |y (%L)  + 1  - y(x)
          ++      \|
   (65)   |   ------------------------- d%L
         ++                2
                         %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +-----------+
--R                   | ,    2
--I            x %I a |y (%I)  + 1  - y(x)
--R          ++      \|
--I   (65)   |   ------------------------- d%I
--R         ++                2
--I                         %I
--R                                          Type: Union(Expression Integer,...)
--E 65

--S 66 of 97
ode562 := a*(D(y(x),x)**3+1)**(1/3)+b*x*D(y(x),x)-y(x)
 

            +----------+
            | ,   3           ,
   (66)  a 3|y (x)  + 1 + b xy (x) - y(x)
           \|
                                                     Type: Expression Integer
--R 
--R
--R            +----------+
--R            | ,   3           ,
--R   (66)  a 3|y (x)  + 1 + b xy (x) - y(x)
--R           \|
--R                                                     Type: Expression Integer
--E 66

--S 67 of 97
solve(ode562,y,x)
 

                    log(%L)                         log(%L)
                  - -------  +-----------+        - -------
                       b     | ,    3                  b
            x a %e          3|y (%L)  + 1 - y(x)%e
          ++                \|
   (67)   |   --------------------------------------------- d%L
         ++                         %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                    log(%I)                         log(%I)
--R                  - -------  +-----------+        - -------
--R                       b     | ,    3                  b
--I            x a %e          3|y (%I)  + 1 - y(x)%e
--R          ++                \|
--I   (67)   |   --------------------------------------------- d%I
--I         ++                         %I
--R                                          Type: Union(Expression Integer,...)
--E 67

--S 68 of 97
ode563 := log(D(y(x),x))+x*D(y(x),x)+a*y(x)+b
 

              ,         ,
   (68)  log(y (x)) + xy (x) + a y(x) + b

                                                     Type: Expression Integer
--R 
--R
--R              ,         ,
--R   (68)  log(y (x)) + xy (x) + a y(x) + b
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 97
solve(ode563,y,x)
 

                a log(%L)     ,                      a log(%L)
            x %e         log(y (%L)) + (a y(x) + b)%e
          ++
   (69)   |   ------------------------------------------------ d%L
         ++                          %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                a log(%I)     ,                      a log(%I)
--I            x %e         log(y (%I)) + (a y(x) + b)%e
--R          ++
--I   (69)   |   ------------------------------------------------ d%I
--I         ++                          %I
--R                                          Type: Union(Expression Integer,...)
--E 69

--S 70 of 97
ode564 := log(D(y(x),x))+a*(x*D(y(x),x)-y(x))
 

              ,           ,
   (70)  log(y (x)) + a xy (x) - a y(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,           ,
--R   (70)  log(y (x)) + a xy (x) - a y(x)
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 97
solve(ode564,y,x)
 

                   ,
            x log(y (%L)) - a y(x)
          ++
   (71)   |   -------------------- d%L
         ++              2
                       %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   ,
--I            x log(y (%I)) - a y(x)
--R          ++
--I   (71)   |   -------------------- d%I
--R         ++              2
--I                       %I
--R                                          Type: Union(Expression Integer,...)
--E 71

--S 72 of 97
ode571 := a*x**n*f(D(y(x),x))+x*D(y(x),x)-y(x)
 

            n   ,         ,
   (72)  a x f(y (x)) + xy (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R            n   ,         ,
--R   (72)  a x f(y (x)) + xy (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 97
solve(ode571,y,x)
 

                  n   ,
            x a %L f(y (%L)) - y(x)
          ++
   (73)   |   --------------------- d%L
         ++              2
                       %L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  n   ,
--I            x a %I f(y (%I)) - y(x)
--R          ++
--I   (73)   |   --------------------- d%I
--R         ++              2
--I                       %I
--R                                          Type: Union(Expression Integer,...)
--E 73

--S 74 of 97
ode573 := f(x*D(y(x),x)**2)+2*x*D(y(x),x)-y(x)
 

              ,   2       ,
   (74)  f(x y (x) ) + 2xy (x) - y(x)

                                                     Type: Expression Integer
--R 
--R
--R              ,   2       ,
--R   (74)  f(x y (x) ) + 2xy (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 97
solve(ode573,y,x)
 

                    ,    2
            x f(%L y (%L) ) - y(x)
          ++
   (75)   |   -------------------- d%L
         ++             +--+
                     %L\|%L
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    ,    2
--I            x f(%I y (%I) ) - y(x)
--R          ++
--I   (75)   |   -------------------- d%I
--R         ++             +--+
--I                     %I\|%I
--R                                          Type: Union(Expression Integer,...)
--E 75

--S 76 of 97
ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x)
 

                  4    2    3          2
          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
   (76)  y (x)= ------------------------------------
                                  x
                                            Type: Equation Expression Integer
--R 
--R
--R                  4    2    3          2
--R          ,     (x y(x)  - x y(x))log(x  + x) - y(x)
--R   (76)  y (x)= ------------------------------------
--R                                  x
--R                                            Type: Equation Expression Integer
--E 76

--S 77 of 97
solve(ode683,y,x)
 

                           - x y(x) + 1
   (77)  -----------------------------------------------
                           3     2          3     2
                         6x log(x  + x) - 4x  + 3x  - 6x
                         -------------------------------
               3+-----+                 18
         x y(x)\|x + 1 %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           - x y(x) + 1
--R   (77)  -----------------------------------------------
--R                           3     2          3     2
--R                         6x log(x  + x) - 4x  + 3x  - 6x
--R                         -------------------------------
--R               3+-----+                 18
--R         x y(x)\|x + 1 %e
--R                                          Type: Union(Expression Integer,...)
--E 77

--S 78 of 97
ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_
            (x-1)/x)
 

                  2    2                    3    2       2
          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
   (78)  y (x)= -------------------------------------------------------
                                          2
                                         x  - x
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                    3    2       2
--R          ,     (x y(x)  - x y(x))log(x) + x y(x)  + (- x  - x + 1)y(x)
--R   (78)  y (x)= -------------------------------------------------------
--R                                          2
--R                                         x  - x
--R                                            Type: Equation Expression Integer
--E 78

--S 79 of 97
solve(ode703,y,x)
 

                 - x y(x) + 1
   (79)  ----------------------------
           2           - dilog(x) + x
         (x  - x)y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 - x y(x) + 1
--R   (79)  ----------------------------
--R           2           - dilog(x) + x
--R         (x  - x)y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 79

--S 80 of 97
ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_
           y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x)
 

   (80)
            2    2                           1          x    3    2    2
          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
    ,                                        x
   y (x)= ------------------------------------------------------------------
                                         1        x
                                   x log(-) - x %e
                                         x
                                            Type: Equation Expression Integer
--R 
--R
--R   (80)
--R            2    2                           1          x    3    2    2
--R          (x y(x)  - x y(x))log(x) - y(x)log(-) + y(x)%e  + x y(x)  - x y(x)
--R    ,                                        x
--R   y (x)= ------------------------------------------------------------------
--R                                         1        x
--R                                   x log(-) - x %e
--R                                         x
--R                                            Type: Equation Expression Integer
--E 80

--S 81 of 97
solve(ode714,y,x)
 

   (81)
       -
                                         1      %L     2
                     x %L log(%L) + log(--) - %e   + %L
                   ++                   %L
                   |   --------------------------------- d%L
                  ++                  1         %L
                              %L log(--) - %L %e
                                     %L
            y(x)%e
         *
            INTSIGN
           ,
               x
           ,
                                                        2
                                       - %L log(%L) - %L
                 --------------------------------------------------------------
                                                           1      %L     2
                                      %L %L log(%L) + log(--) - %e   + %L
                                    ++                    %L
                                    |    --------------------------------- d%L
                                   ++                   1         %L
                                                %L log(--) - %L %e
                       1      %L                       %L
                 (log(--) - %e  )%e
                      %L
              *
                 d%L
     + 
       1
  /
                                  1      %L     2
              x %L log(%L) + log(--) - %e   + %L
            ++                   %L
            |   --------------------------------- d%L
           ++                  1         %L
                       %L log(--) - %L %e
                              %L
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (81)
--R       -
--I                                         1      %I     2
--I                     x %I log(%I) + log(--) - %e   + %I
--I                   ++                   %I
--I                   |   --------------------------------- d%I
--I                  ++                  1         %I
--I                              %I log(--) - %I %e
--I                                     %I
--R            y(x)%e
--R         *
--R            INTSIGN
--R           ,
--R               x
--R           ,
--R                                                        2
--I                                       - %I log(%I) - %I
--R                 --------------------------------------------------------------
--I                                                           1      %I     2
--I                                      %I %I log(%I) + log(--) - %e   + %I
--I                                    ++                    %I
--I                                    |    --------------------------------- d%I
--I                                   ++                   1         %I
--I                                                %I log(--) - %I %e
--I                       1      %I                       %I
--R                 (log(--) - %e  )%e
--I                      %I
--R              *
--I                 d%I
--R     + 
--R       1
--R  /
--I                                  1      %I     2
--I              x %I log(%I) + log(--) - %e   + %I
--I            ++                   %I
--I            |   --------------------------------- d%I
--I           ++                  1         %I
--I                       %I log(--) - %I %e
--I                              %I
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 81

--S 82 of 97
ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x))
 

                  2    2                          x
          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
   (82)  y (x)= -----------------------------------
                                   x
                               x %e
                                            Type: Equation Expression Integer
--R 
--R
--R                  2    2                          x
--R          ,     (x y(x)  - x y(x))log(2x) - y(x)%e
--R   (82)  y (x)= -----------------------------------
--R                                   x
--R                               x %e
--R                                            Type: Equation Expression Integer
--E 82

--S 83 of 97
solve(ode719,y,x)
 

                    - x y(x) + 1
   (83)  ----------------------------------
                  x                 %L
                ++  %L log(2%L) + %e
                |   ------------------ d%L
               ++              %L
                          %L %e
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    - x y(x) + 1
--R   (83)  ----------------------------------
--I                  x                 %I
--I                ++  %I log(2%I) + %e
--I                |   ------------------ d%I
--I               ++              %I
--I                          %I %e
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 83

--S 84 of 97
ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1))
 

                    2     2        4     2
          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
   (84)  y (x)= -----------------------------------
                               x + 1
                                            Type: Equation Expression Integer
--R 
--R
--R                    2     2        4     2
--R          ,     y(x)  - 2x y(x) + x  + 2x  + 2x - 1
--R   (84)  y (x)= -----------------------------------
--R                               x + 1
--R                                            Type: Equation Expression Integer
--E 84

--S 85 of 97
solve(ode736,y,x)
 

           2                  4     3     2
         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
   (85)  -------------------------------------------
                                 2
                       2y(x) - 2x  - 2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2                  4     3     2
--R         (x  + 2x - 2)y(x) - x  - 2x  + 3x  + 2x + 4
--R   (85)  -------------------------------------------
--R                                 2
--R                       2y(x) - 2x  - 2
--R                                          Type: Union(Expression Integer,...)
--E 85

--S 86 of 97
ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_
            log((x-1)*(1+x)/x)*x*y(x))/x)
 

                                     2
                       2            x  - 1
                (x y(x)  - y(x))log(------) - y(x)
          ,                            x
   (86)  y (x)= ----------------------------------
                                 x
                                            Type: Equation Expression Integer
--R 
--R
--R                                     2
--R                       2            x  - 1
--R                (x y(x)  - y(x))log(------) - y(x)
--R          ,                            x
--R   (86)  y (x)= ----------------------------------
--R                                 x
--R                                            Type: Equation Expression Integer
--E 86

--S 87 of 97
solve(ode765,y,x)
 

                   - x y(x) + 1
   (87)  --------------------------------
                          2
                        %L  - 1
                  x log(-------) + 1
                ++         %L
                |   ---------------- d%L
               ++          %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   - x y(x) + 1
--R   (87)  --------------------------------
--R                          2
--I                        %I  - 1
--R                  x log(-------) + 1
--I                ++         %I
--I                |   ---------------- d%I
--I               ++          %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 87

--S 88 of 97
ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_
           log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x))
 

                                                      2
                                 2    2              x  - 1
                - y(x)log(x) + (x y(x)  - x y(x))log(------)
          ,                                             x
   (88)  y (x)= --------------------------------------------
                                  x log(x)
                                            Type: Equation Expression Integer
--R 
--R
--R                                                      2
--R                                 2    2              x  - 1
--R                - y(x)log(x) + (x y(x)  - x y(x))log(------)
--R          ,                                             x
--R   (88)  y (x)= --------------------------------------------
--R                                  x log(x)
--R                                            Type: Equation Expression Integer
--E 88

--S 89 of 97
solve(ode766,y,x)
 

   (89)
       -
                                          2
                                        %L  - 1
                     x log(%L) + %L log(-------)
                   ++                      %L
                   |   ------------------------- d%L
                  ++           %L log(%L)
            y(x)%e
         *
                                           2
                                         %L  - 1
               x                  %L log(-------)
             ++                             %L
             |   - --------------------------------------------- d%L
            ++                                       2
                                                   %L  - 1
                               %L log(%L) + %L log(-------)
                             ++                       %L
                             |    ------------------------- d%L
                            ++            %L log(%L)
                   log(%L)%e
     + 
       1
  /
                                   2
                                 %L  - 1
              x log(%L) + %L log(-------)
            ++                      %L
            |   ------------------------- d%L
           ++           %L log(%L)
     y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (89)
--R       -
--R                                          2
--I                                        %I  - 1
--I                     x log(%I) + %I log(-------)
--I                   ++                      %I
--I                   |   ------------------------- d%I
--I                  ++           %I log(%I)
--R            y(x)%e
--R         *
--R                                           2
--I                                         %I  - 1
--I               x                  %I log(-------)
--I             ++                             %I
--I             |   - --------------------------------------------- d%I
--R            ++                                       2
--I                                                   %I  - 1
--I                               %I log(%I) + %I log(-------)
--I                             ++                       %I
--I                             |    ------------------------- d%I
--I                            ++            %I log(%I)
--I                   log(%I)%e
--R     + 
--R       1
--R  /
--R                                   2
--I                                 %I  - 1
--I              x log(%I) + %I log(-------)
--I            ++                      %I
--I            |   ------------------------- d%I
--I           ++           %I log(%I)
--R     y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 89

--S 90 of 97
ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_
            log((x**2+1)/x)*x**2*y(x))/x/log(1/x))
 

                                       2
                  2    2              x  + 1            1
                (x y(x)  - x y(x))log(------) - y(x)log(-)
          ,                              x              x
   (90)  y (x)= ------------------------------------------
                                       1
                                 x log(-)
                                       x
                                            Type: Equation Expression Integer
--R 
--R
--R                                       2
--R                  2    2              x  + 1            1
--R                (x y(x)  - x y(x))log(------) - y(x)log(-)
--R          ,                              x              x
--R   (90)  y (x)= ------------------------------------------
--R                                       1
--R                                 x log(-)
--R                                       x
--R                                            Type: Equation Expression Integer
--E 90

--S 91 of 97
solve(ode776,y,x)
 

                        - x y(x) + 1
   (91)  -----------------------------------------
                             2
                           %L  + 1         1
                  x %L log(-------) + log(--)
                ++            %L          %L
                |   ------------------------- d%L
               ++                   1
                            %L log(--)
                                   %L
         y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        - x y(x) + 1
--R   (91)  -----------------------------------------
--R                             2
--I                           %I  + 1         1
--I                  x %I log(-------) + log(--)
--I                ++            %I          %I
--I                |   ------------------------- d%I
--R               ++                   1
--I                            %I log(--)
--I                                   %I
--R         y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 91

--S 92 of 97
ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_
            25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/(-5*y(x)+2*x**3+_
            10*x**(1/2)-5)/x)
 

                               3       +-+      3          6      3
          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
   (92)  y (x)= --------------------------------------------------------------
                                    +-+                 4
                                50x\|x  - 25x y(x) + 10x  - 25x
                                            Type: Equation Expression Integer
--R 
--R
--R                               3       +-+      3          6      3
--R          ,     (- 25y(x) + 70x  - 25)\|x  - 30x y(x) + 12x  - 30x  + 50x - 25
--R   (92)  y (x)= --------------------------------------------------------------
--R                                    +-+                 4
--R                                50x\|x  - 25x y(x) + 10x  - 25x
--R                                            Type: Equation Expression Integer
--E 92

--S 93 of 97
solve(ode872,y,x)
 

   (93)
               +-+                  3        +-+         2       3
       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
     + 
           6      3
       - 4x  + 20x  - 100x
  /
     2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (93)
--R               +-+                  3        +-+         2       3
--R       100log(\|x ) + (100y(x) - 40x  + 100)\|x  - 25y(x)  + (20x  - 50)y(x)
--R     + 
--R           6      3
--R       - 4x  + 20x  - 100x
--R  /
--R     2
--R                                          Type: Union(Expression Integer,...)
--E 93

--S 94 of 97
ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2-x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*log(x)+x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*y(x)+2*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)+x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)**2)/x)
 

   (94)
    ,
   y (x) =

             2    2      2      2    2    2               2    2    2
           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
        *
                     2
              2log(x)        2
             ---------- ----------
             log(x) + 1 log(x) + 1
           %e          x
       + 
         - y(x)
    /
       x log(x) + x
                                            Type: Equation Expression Integer
--R 
--R
--R   (94)
--R    ,
--R   y (x) =
--R
--R             2    2      2      2    2    2               2    2    2
--R           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
--R        *
--R                     2
--R              2log(x)        2
--R             ---------- ----------
--R             log(x) + 1 log(x) + 1
--R           %e          x
--R       + 
--R         - y(x)
--R    /
--R       x log(x) + x
--R                                            Type: Equation Expression Integer
--E 94

--S 95 of 97
solve(ode956,y,x)
 

          - y(x)log(x) - y(x) + 1
   (95)  -------------------------
                4                4
               x                x
               --               --
                4                4
         y(x)%e  log(x) + y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          - y(x)log(x) - y(x) + 1
--R   (95)  -------------------------
--R                4                4
--R               x                x
--R               --               --
--R                4                4
--R         y(x)%e  log(x) + y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 95

--S 96 of 97
ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)-x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*log(x)+x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*y(x)+2*x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)+x**3*x**(2/(1+log(x)))*_
            exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)**2)/x)
 

   (96)
    ,
   y (x) =

             3    2      2      3    2    3               3    2    3
           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
        *
                     2
              2log(x)        2
             ---------- ----------
             log(x) + 1 log(x) + 1
           %e          x
       + 
         - y(x)
    /
       x log(x) + x
                                            Type: Equation Expression Integer
--R 
--R
--R   (96)
--R    ,
--R   y (x) =
--R
--R             3    2      2      3    2    3               3    2    3
--R           (x y(x) log(x)  + (2x y(x)  - x y(x))log(x) + x y(x)  - x y(x))
--R        *
--R                     2
--R              2log(x)        2
--R             ---------- ----------
--R             log(x) + 1 log(x) + 1
--R           %e          x
--R       + 
--R         - y(x)
--R    /
--R       x log(x) + x
--R                                            Type: Equation Expression Integer
--E 96

--S 97 of 97
solve(ode957,y,x)
 

          - y(x)log(x) - y(x) + 1
   (97)  -------------------------
                5                5
               x                x
               --               --
                5                5
         y(x)%e  log(x) + y(x)%e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          - y(x)log(x) - y(x) + 1
--R   (97)  -------------------------
--R                5                5
--R               x                x
--R               --               --
--R                5                5
--R         y(x)%e  log(x) + y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 97
)spool
 
Starts dribbling to Magma.output (2010/3/27, 18:46:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
x:Symbol :='x
 

   (1)  x
                                                                 Type: Symbol
--R 
--R
--R   (1)  x
--R                                                                 Type: Symbol
--E 1

--S 2 of 22
y:Symbol :='y
 

   (2)  y
                                                                 Type: Symbol
--R 
--R
--R   (2)  y
--R                                                                 Type: Symbol
--E 2

--S 3 of 22
z:Symbol :='z
 

   (3)  z
                                                                 Type: Symbol
--R 
--R
--R   (3)  z
--R                                                                 Type: Symbol
--E 3

--S 4 of 22
word := OrderedFreeMonoid(Symbol)
 

   (4)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 22
tree := Magma(Symbol)
 

   (5)  Magma Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  Magma Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 22
a:tree := x*x 
 

   (6)  [x,x]
                                                           Type: Magma Symbol
--R 
--R
--R   (6)  [x,x]
--R                                                           Type: Magma Symbol
--E 6

--S 7 of 22
b:tree := y*y
 

   (7)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (7)  [y,y]
--R                                                           Type: Magma Symbol
--E 7

--S 8 of 22
c:tree := a*b
 

   (8)  [[x,x],[y,y]]
                                                           Type: Magma Symbol
--R 
--R
--R   (8)  [[x,x],[y,y]]
--R                                                           Type: Magma Symbol
--E 8

--S 9 of 22
left c
 

   (9)  [x,x]
                                                           Type: Magma Symbol
--R 
--R
--R   (9)  [x,x]
--R                                                           Type: Magma Symbol
--E 9

--S 10 of 22
right c
 

   (10)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (10)  [y,y]
--R                                                           Type: Magma Symbol
--E 10

--S 11 of 22
length c
 

   (11)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 22
c::word
 

          2 2
   (12)  x y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R          2 2
--R   (12)  x y
--R                                               Type: OrderedFreeMonoid Symbol
--E 12

--S 13 of 22
a < b
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 22
a < c
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 22
b < c
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 22
first c
 

   (16)  x
                                                                 Type: Symbol
--R 
--R
--R   (16)  x
--R                                                                 Type: Symbol
--E 16

--S 17 of 22
rest c
 

   (17)  [x,[y,y]]
                                                           Type: Magma Symbol
--R 
--R
--R   (17)  [x,[y,y]]
--R                                                           Type: Magma Symbol
--E 17

--S 18 of 22
rest rest c
 

   (18)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (18)  [y,y]
--R                                                           Type: Magma Symbol
--E 18

--S 19 of 22
ax:tree := a*x
 

   (19)  [[x,x],x]
                                                           Type: Magma Symbol
--R 
--R
--R   (19)  [[x,x],x]
--R                                                           Type: Magma Symbol
--E 19

--S 20 of 22
xa:tree := x*a
 

   (20)  [x,[x,x]]
                                                           Type: Magma Symbol
--R 
--R
--R   (20)  [x,[x,x]]
--R                                                           Type: Magma Symbol
--E 20

--S 21 of 22
xa < ax
 

   (21)  true
                                                                Type: Boolean
--R 
--R
--R   (21)  true
--R                                                                Type: Boolean
--E 21

--S 22 of 22
lexico(xa,ax)
 

   (22)  false
                                                                Type: Boolean
--R 
--R
--R   (22)  false
--R                                                                Type: Boolean
--E 22
)spool
 
Starts dribbling to cmds.output (2010/3/27, 18:24:32).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 23
)abbreviation domain TIM TimDaly )quiet
 
--R 
--E 1

--S 2 of 23
)abbreviation domain TIMD TimDalyDomain
 
   TIMD abbreviates domain TimDalyDomain 
--R 
--R   TIMD abbreviates domain TimDalyDomain 
--E 2

--S 3 of 23
)abbreviation category TIMC TimDalyCategory
 
   TIMC abbreviates category TimDalyCategory 
--R 
--R   TIMC abbreviates category TimDalyCategory 
--E 3

--S 4 of 23
)abbreviation package TIMP TimDalyPackage
 
   TIMP abbreviates package TimDalyPackage 
--R 
--R   TIMP abbreviates package TimDalyPackage 
--E 4

--S 5 of 23
)abbreviation query LIST
 
   LIST abbreviates domain List 
--R 
--R   LIST abbreviates domain List 
--E 5

--S 6 of 23
)abbreviation query List
 
   LIST abbreviates domain List 
--R 
--R   LIST abbreviates domain List 
--E 6

--S 7 of 23
)abbreviation query TIMD
 
   TIMD abbreviates domain TimDalyDomain 
--R 
--R   TIMD abbreviates domain TimDalyDomain 
--E 7

--S 8 of 23
)abbreviation remove TIMD
 
--R 
--E 8

--S 9 of 23
)abbreviation query TIMD
 
   TIMD is neither a constructor name nor a constructor abbreviation.
--R 
--R   TIMD is neither a constructor name nor a constructor abbreviation.
--E 9

--S 10 of 23
)abbreviation query TimDalyPackage
 
   TIMP abbreviates package TimDalyPackage 
--R 
--R   TIMP abbreviates package TimDalyPackage 
--E 10

--S 11 of 23
)abbreviation remove TimDalyPackage
 
--R 
--E 11

--S 12 of 23
)abbreviation query TimDalyPackage
 
   TIMP abbreviates package TimDalyPackage 
--R 
--R   TIMP abbreviates package TimDalyPackage 
--E 12

--S 13 of 23
)what categories
 
------------------------------- Categories --------------------------------
 A1AGG    OneDimensionalArrayAggregate ABELGRP  AbelianGroup
 ABELMON  AbelianMonoid                ABELSG   AbelianSemiGroup
 ACF      AlgebraicallyClosedField
 ACFS     AlgebraicallyClosedFunctionSpace
 AGG      Aggregate
 AHYP     ArcHyperbolicFunctionCategory
 ALAGG    AssociationListAggregate     ALGEBRA  Algebra
 AMR      AbelianMonoidRing            ARR2CAT  TwoDimensionalArrayCategory
 ATRIG    ArcTrigonometricFunctionCategory
 ATTREG   AttributeRegistry            BASTYPE  BasicType
 BGAGG    BagAggregate                 BMODULE  BiModule
 BRAGG    BinaryRecursiveAggregate     BTAGG    BitAggregate
 BTCAT    BinaryTreeCategory           CABMON   CancellationAbelianMonoid
 CACHSET  CachableSet
 CFCAT    CombinatorialFunctionCategory
 CHARNZ   CharacteristicNonZero        CHARZ    CharacteristicZero
 CLAGG    Collection                   COMBOPC  CombinatorialOpsCategory
 COMPCAT  ComplexCategory              COMRING  CommutativeRing
 DIAGG    Dictionary                   DIFEXT   DifferentialExtension
 DIFRING  DifferentialRing             DIOPS    DictionaryOperations
 DIRPCAT  DirectProductCategory        DIVRING  DivisionRing
 DLAGG    DoublyLinkedAggregate
 DPOLCAT  DifferentialPolynomialCategory
 DQAGG    DequeueAggregate             DVARCAT  DifferentialVariableCategory
 ELAGG    ExtensibleLinearAggregate    ELEMFUN  ElementaryFunctionCategory
 ELTAB    Eltable                      ELTAGG   EltableAggregate
 ENTIRER  EntireRing                   ES       ExpressionSpace
 EUCDOM   EuclideanDomain              EVALAB   Evalable
 FAMONC   FreeAbelianMonoidCategory    FAMR     FiniteAbelianMonoidRing
 FAXF     FiniteAlgebraicExtensionField
 FDIVCAT  FiniteDivisorCategory        FEVALAB  FullyEvalableOver
 FFCAT    FunctionFieldCategory        FFIELDC  FiniteFieldCategory
 FIELD    Field                        FILECAT  FileCategory
 FINAALG  FiniteRankNonAssociativeAlgebra
 FINITE   Finite                       FINRALG  FiniteRankAlgebra
 FLAGG    FiniteLinearAggregate        FLALG    FreeLieAlgebra
 FLINEXP  FullyLinearlyExplicitRingOver
 FMC      FortranMatrixCategory        FMCAT    FreeModuleCat
 FMFUN    FortranMatrixFunctionCategory
 FMTC     FortranMachineTypeCategory   FNCAT    FileNameCategory
 FORTCAT  FortranProgramCategory       FORTFN   FortranFunctionCategory
 FPATMAB  FullyPatternMatchable        FPC      FieldOfPrimeCharacteristic
 FPS      FloatingPointSystem          FRAMALG  FramedAlgebra
 FRETRCT  FullyRetractableTo           FRNAALG  FramedNonAssociativeAlgebra
 FS       FunctionSpace                FSAGG    FiniteSetAggregate
 FVC      FortranVectorCategory
 FVFUN    FortranVectorFunctionCategory
 GCDDOM   GcdDomain                    GRALG    GradedAlgebra
 GRMOD    GradedModule                 GROUP    Group
 HOAGG    HomogeneousAggregate         HYPCAT   HyperbolicFunctionCategory
 IDPC     IndexedDirectProductCategory IEVALAB  InnerEvalable
 INS      IntegerNumberSystem          INTCAT   IntervalCategory
 INTDOM   IntegralDomain               IXAGG    IndexedAggregate
 KDAGG    KeyedDictionary              KOERCE   CoercibleTo
 KONVERT  ConvertibleTo                LALG     LeftAlgebra
 LFCAT    LiouvillianFunctionCategory  LIECAT   LieAlgebra
 LINEXP   LinearlyExplicitRingOver     LMODULE  LeftModule
 LNAGG    LinearAggregate
 LODOCAT  LinearOrdinaryDifferentialOperatorCategory
 LOGIC    Logic                        LSAGG    ListAggregate
 LZSTAGG  LazyStreamAggregate          MATCAT   MatrixCategory
 MDAGG    MultiDictionary              MLO      MonogenicLinearOperator
 MODULE   Module                       MONAD    Monad
 MONADWU  MonadWithUnit                MONOGEN  MonogenicAlgebra
 MONOID   Monoid                       MSETAGG  MultisetAggregate
 MTSCAT   MultivariateTaylorSeriesCategory
 NAALG    NonAssociativeAlgebra        NARNG    NonAssociativeRng
 NASRING  NonAssociativeRing
 NTSCAT   NormalizedTriangularSetCategory
 NUMINT   NumericalIntegrationCategory OAGROUP  OrderedAbelianGroup
 OAMON    OrderedAbelianMonoid         OAMONS   OrderedAbelianMonoidSup
 OASGP    OrderedAbelianSemiGroup      OC       OctonionCategory
 OCAMON   OrderedCancellationAbelianMonoid
 ODECAT   OrdinaryDifferentialEquationsSolverCategory
 OINTDOM  OrderedIntegralDomain        OM       OpenMath
 OMSAGG   OrderedMultisetAggregate
 OPTCAT   NumericalOptimizationCategory
 ORDFIN   OrderedFinite                ORDMON   OrderedMonoid
 ORDRING  OrderedRing                  ORDSET   OrderedSet
 OREPCAT  UnivariateSkewPolynomialCategory
 PADICCT  PAdicIntegerCategory         PATAB    Patternable
 PATMAB   PatternMatchable
 PDECAT   PartialDifferentialEquationsSolverCategory
 PDRING   PartialDifferentialRing      PERMCAT  PermutationCategory
 PFECAT   PolynomialFactorizationExplicit
 PID      PrincipalIdealDomain         POLYCAT  PolynomialCategory
 PPCURVE  PlottablePlaneCurveCategory  PRIMCAT  PrimitiveFunctionCategory
 PRQAGG   PriorityQueueAggregate       PSCAT    PowerSeriesCategory
 PSCURVE  PlottableSpaceCurveCategory  PSETCAT  PolynomialSetCategory
 PTCAT    PointCategory
 PTRANFN  PartialTranscendentalFunctions
 QFCAT    QuotientFieldCategory        QUAGG    QueueAggregate
 QUATCAT  QuaternionCategory           RADCAT   RadicalCategory
 RCAGG    RecursiveAggregate           RCFIELD  RealClosedField
 REAL     RealConstant                 RETRACT  RetractableTo
 RING     Ring                         RMATCAT  RectangularMatrixCategory
 RMODULE  RightModule                  RNG      Rng
 RNS      RealNumberSystem             RPOLCAT  RecursivePolynomialCategory
 RRCC     RealRootCharacterizationCategory
 RSETCAT  RegularTriangularSetCategory SEGCAT   SegmentCategory
 SEGXCAT  SegmentExpansionCategory     SETAGG   SetAggregate
 SETCAT   SetCategory                  SEXCAT   SExpressionCategory
 SFRTCAT  SquareFreeRegularTriangularSetCategory
 SGROUP   SemiGroup                    SKAGG    StackAggregate
 SMATCAT  SquareMatrixCategory
 SNTSCAT  SquareFreeNormalizedTriangularSetCategory
 SPACEC   ThreeSpaceCategory           SPFCAT   SpecialFunctionCategory
 SRAGG    StringAggregate              STAGG    StreamAggregate
 STEP     StepThrough                  STRICAT  StringCategory
 TBAGG    TableAggregate
 TRANFUN  TranscendentalFunctionCategory
 TRIGCAT  TrigonometricFunctionCategory
 TSETCAT  TriangularSetCategory        TYPE     Type
 UFD      UniqueFactorizationDomain
 ULSCAT   UnivariateLaurentSeriesCategory
 ULSCCAT  UnivariateLaurentSeriesConstructorCategory
 UPOLYC   UnivariatePolynomialCategory
 UPSCAT   UnivariatePowerSeriesCategory
 UPXSCAT  UnivariatePuiseuxSeriesCategory
 UPXSCCA  UnivariatePuiseuxSeriesConstructorCategory
 URAGG    UnaryRecursiveAggregate
 UTSCAT   UnivariateTaylorSeriesCategory
 VECTCAT  VectorCategory               VSPACE   VectorSpace
 XALG     XAlgebra                     XF       ExtensionField
 XFALG    XFreeAlgebra                 XPOLYC   XPolynomialsCat
--R 
--R------------------------------- Categories --------------------------------
--R A1AGG    OneDimensionalArrayAggregate ABELGRP  AbelianGroup
--R ABELMON  AbelianMonoid                ABELSG   AbelianSemiGroup
--R ACF      AlgebraicallyClosedField
--R ACFS     AlgebraicallyClosedFunctionSpace
--R AGG      Aggregate
--R AHYP     ArcHyperbolicFunctionCategory
--R ALAGG    AssociationListAggregate     ALGEBRA  Algebra
--R AMR      AbelianMonoidRing            ARR2CAT  TwoDimensionalArrayCategory
--R ATRIG    ArcTrigonometricFunctionCategory
--R ATTREG   AttributeRegistry            BASTYPE  BasicType
--R BGAGG    BagAggregate                 BMODULE  BiModule
--R BRAGG    BinaryRecursiveAggregate     BTAGG    BitAggregate
--R BTCAT    BinaryTreeCategory           CABMON   CancellationAbelianMonoid
--R CACHSET  CachableSet
--R CFCAT    CombinatorialFunctionCategory
--R CHARNZ   CharacteristicNonZero        CHARZ    CharacteristicZero
--R CLAGG    Collection                   COMBOPC  CombinatorialOpsCategory
--R COMPCAT  ComplexCategory              COMRING  CommutativeRing
--R DIAGG    Dictionary                   DIFEXT   DifferentialExtension
--R DIFRING  DifferentialRing             DIOPS    DictionaryOperations
--R DIRPCAT  DirectProductCategory        DIVRING  DivisionRing
--R DLAGG    DoublyLinkedAggregate
--R DPOLCAT  DifferentialPolynomialCategory
--R DQAGG    DequeueAggregate             DVARCAT  DifferentialVariableCategory
--R ELAGG    ExtensibleLinearAggregate    ELEMFUN  ElementaryFunctionCategory
--R ELTAB    Eltable                      ELTAGG   EltableAggregate
--R ENTIRER  EntireRing                   ES       ExpressionSpace
--R EUCDOM   EuclideanDomain              EVALAB   Evalable
--R FAMONC   FreeAbelianMonoidCategory    FAMR     FiniteAbelianMonoidRing
--R FAXF     FiniteAlgebraicExtensionField
--R FDIVCAT  FiniteDivisorCategory        FEVALAB  FullyEvalableOver
--R FFCAT    FunctionFieldCategory        FFIELDC  FiniteFieldCategory
--R FIELD    Field                        FILECAT  FileCategory
--R FINAALG  FiniteRankNonAssociativeAlgebra
--R FINITE   Finite                       FINRALG  FiniteRankAlgebra
--R FLAGG    FiniteLinearAggregate        FLALG    FreeLieAlgebra
--R FLINEXP  FullyLinearlyExplicitRingOver
--R FMC      FortranMatrixCategory        FMCAT    FreeModuleCat
--R FMFUN    FortranMatrixFunctionCategory
--R FMTC     FortranMachineTypeCategory   FNCAT    FileNameCategory
--R FORTCAT  FortranProgramCategory       FORTFN   FortranFunctionCategory
--R FPATMAB  FullyPatternMatchable        FPC      FieldOfPrimeCharacteristic
--R FPS      FloatingPointSystem          FRAMALG  FramedAlgebra
--R FRETRCT  FullyRetractableTo           FRNAALG  FramedNonAssociativeAlgebra
--R FS       FunctionSpace                FSAGG    FiniteSetAggregate
--R FVC      FortranVectorCategory
--R FVFUN    FortranVectorFunctionCategory
--R GCDDOM   GcdDomain                    GRALG    GradedAlgebra
--R GRMOD    GradedModule                 GROUP    Group
--R HOAGG    HomogeneousAggregate         HYPCAT   HyperbolicFunctionCategory
--R IDPC     IndexedDirectProductCategory IEVALAB  InnerEvalable
--R INS      IntegerNumberSystem          INTCAT   IntervalCategory
--R INTDOM   IntegralDomain               IXAGG    IndexedAggregate
--R KDAGG    KeyedDictionary              KOERCE   CoercibleTo
--R KONVERT  ConvertibleTo                LALG     LeftAlgebra
--R LFCAT    LiouvillianFunctionCategory  LIECAT   LieAlgebra
--R LINEXP   LinearlyExplicitRingOver     LMODULE  LeftModule
--R LNAGG    LinearAggregate
--R LODOCAT  LinearOrdinaryDifferentialOperatorCategory
--R LOGIC    Logic                        LSAGG    ListAggregate
--R LZSTAGG  LazyStreamAggregate          MATCAT   MatrixCategory
--R MDAGG    MultiDictionary              MLO      MonogenicLinearOperator
--R MODULE   Module                       MONAD    Monad
--R MONADWU  MonadWithUnit                MONOGEN  MonogenicAlgebra
--R MONOID   Monoid                       MSETAGG  MultisetAggregate
--R MTSCAT   MultivariateTaylorSeriesCategory
--R NAALG    NonAssociativeAlgebra        NARNG    NonAssociativeRng
--R NASRING  NonAssociativeRing
--R NTSCAT   NormalizedTriangularSetCategory
--R NUMINT   NumericalIntegrationCategory OAGROUP  OrderedAbelianGroup
--R OAMON    OrderedAbelianMonoid         OAMONS   OrderedAbelianMonoidSup
--R OASGP    OrderedAbelianSemiGroup      OC       OctonionCategory
--R OCAMON   OrderedCancellationAbelianMonoid
--R ODECAT   OrdinaryDifferentialEquationsSolverCategory
--R OINTDOM  OrderedIntegralDomain        OM       OpenMath
--R OMSAGG   OrderedMultisetAggregate
--R OPTCAT   NumericalOptimizationCategory
--R ORDFIN   OrderedFinite                ORDMON   OrderedMonoid
--R ORDRING  OrderedRing                  ORDSET   OrderedSet
--R OREPCAT  UnivariateSkewPolynomialCategory
--R PADICCT  PAdicIntegerCategory         PATAB    Patternable
--R PATMAB   PatternMatchable
--R PDECAT   PartialDifferentialEquationsSolverCategory
--R PDRING   PartialDifferentialRing      PERMCAT  PermutationCategory
--R PFECAT   PolynomialFactorizationExplicit
--R PID      PrincipalIdealDomain         POLYCAT  PolynomialCategory
--R PPCURVE  PlottablePlaneCurveCategory  PRIMCAT  PrimitiveFunctionCategory
--R PRQAGG   PriorityQueueAggregate       PSCAT    PowerSeriesCategory
--R PSCURVE  PlottableSpaceCurveCategory  PSETCAT  PolynomialSetCategory
--R PTCAT    PointCategory
--R PTRANFN  PartialTranscendentalFunctions
--R QFCAT    QuotientFieldCategory        QUAGG    QueueAggregate
--R QUATCAT  QuaternionCategory           RADCAT   RadicalCategory
--R RCAGG    RecursiveAggregate           RCFIELD  RealClosedField
--R REAL     RealConstant                 RETRACT  RetractableTo
--R RING     Ring                         RMATCAT  RectangularMatrixCategory
--R RMODULE  RightModule                  RNG      Rng
--R RNS      RealNumberSystem             RPOLCAT  RecursivePolynomialCategory
--R RRCC     RealRootCharacterizationCategory
--R RSETCAT  RegularTriangularSetCategory SEGCAT   SegmentCategory
--R SEGXCAT  SegmentExpansionCategory     SETAGG   SetAggregate
--R SETCAT   SetCategory                  SEXCAT   SExpressionCategory
--R SFRTCAT  SquareFreeRegularTriangularSetCategory
--R SGROUP   SemiGroup                    SKAGG    StackAggregate
--R SMATCAT  SquareMatrixCategory
--R SNTSCAT  SquareFreeNormalizedTriangularSetCategory
--R SPACEC   ThreeSpaceCategory           SPFCAT   SpecialFunctionCategory
--R SRAGG    StringAggregate              STAGG    StreamAggregate
--R STEP     StepThrough                  STRICAT  StringCategory
--R TBAGG    TableAggregate
--R TRANFUN  TranscendentalFunctionCategory
--R TRIGCAT  TrigonometricFunctionCategory
--R TSETCAT  TriangularSetCategory        TYPE     Type
--R UFD      UniqueFactorizationDomain
--R ULSCAT   UnivariateLaurentSeriesCategory
--R ULSCCAT  UnivariateLaurentSeriesConstructorCategory
--R UPOLYC   UnivariatePolynomialCategory
--R UPSCAT   UnivariatePowerSeriesCategory
--R UPXSCAT  UnivariatePuiseuxSeriesCategory
--R UPXSCCA  UnivariatePuiseuxSeriesConstructorCategory
--R URAGG    UnaryRecursiveAggregate
--R UTSCAT   UnivariateTaylorSeriesCategory
--R VECTCAT  VectorCategory               VSPACE   VectorSpace
--R XALG     XAlgebra                     XF       ExtensionField
--R XFALG    XFreeAlgebra                 XPOLYC   XPolynomialsCat
--E 13

--S 14 of 23
)what domains
 
--------------------------------- Domains ---------------------------------
 A1AGG-   OneDimensionalArrayAggregate&
 ABELGRP- AbelianGroup&                ABELMON- AbelianMonoid&
 ABELSG-  AbelianSemiGroup&            ACF-     AlgebraicallyClosedField&
 ACFS-    AlgebraicallyClosedFunctionSpace&
 ACPLOT   PlaneAlgebraicCurvePlot      AGG-     Aggregate&
 ALGEBRA- Algebra&                     ALGFF    AlgebraicFunctionField
 ALGSC    AlgebraGivenByStructuralConstants
 ALIST    AssociationList              AMR-     AbelianMonoidRing&
 AN       AlgebraicNumber              ANON     AnonymousFunction
 ANTISYM  AntiSymm                     ANY      Any
 ARR2CAT- TwoDimensionalArrayCategory& ARRAY1   OneDimensionalArray
 ARRAY2   TwoDimensionalArray          ASP1     Asp1
 ASP10    Asp10                        ASP12    Asp12
 ASP19    Asp19                        ASP20    Asp20
 ASP24    Asp24                        ASP27    Asp27
 ASP28    Asp28                        ASP29    Asp29
 ASP30    Asp30                        ASP31    Asp31
 ASP33    Asp33                        ASP34    Asp34
 ASP35    Asp35                        ASP4     Asp4
 ASP41    Asp41                        ASP42    Asp42
 ASP49    Asp49                        ASP50    Asp50
 ASP55    Asp55                        ASP6     Asp6
 ASP7     Asp7                         ASP73    Asp73
 ASP74    Asp74                        ASP77    Asp77
 ASP78    Asp78                        ASP8     Asp8
 ASP80    Asp80                        ASP9     Asp9
 ASTACK   ArrayStack
 ATRIG-   ArcTrigonometricFunctionCategory&
 ATTRBUT  AttributeButtons             AUTOMOR  Automorphism
 BASTYPE- BasicType&                   BBTREE   BalancedBinaryTree
 BFUNCT   BasicFunctions               BGAGG-   BagAggregate&
 BINARY   BinaryExpansion              BINFILE  BinaryFile
 BITS     Bits                         BOOLEAN  Boolean
 BOP      BasicOperator                BPADIC   BalancedPAdicInteger
 BPADICRT BalancedPAdicRational        BRAGG-   BinaryRecursiveAggregate&
 BSTREE   BinarySearchTree             BTAGG-   BitAggregate&
 BTCAT-   BinaryTreeCategory&          BTOURN   BinaryTournament
 BTREE    BinaryTree                   CARD     CardinalNumber
 CARTEN   CartesianTensor              CCLASS   CharacterClass
 CHAR     Character                    CLAGG-   Collection&
 CLIF     CliffordAlgebra              COLOR    Color
 COMM     Commutator                   COMPCAT- ComplexCategory&
 COMPLEX  Complex                      COMPPROP SubSpaceComponentProperty
 CONTFRAC ContinuedFraction            D01AJFA  d01ajfAnnaType
 D01AKFA  d01akfAnnaType               D01ALFA  d01alfAnnaType
 D01AMFA  d01amfAnnaType               D01ANFA  d01anfAnnaType
 D01APFA  d01apfAnnaType               D01AQFA  d01aqfAnnaType
 D01ASFA  d01asfAnnaType               D01FCFA  d01fcfAnnaType
 D01GBFA  d01gbfAnnaType               D01TRNS  d01TransformFunctionType
 D02BBFA  d02bbfAnnaType               D02BHFA  d02bhfAnnaType
 D02CJFA  d02cjfAnnaType               D02EJFA  d02ejfAnnaType
 D03EEFA  d03eefAnnaType               D03FAFA  d03fafAnnaType
 DBASE    Database                     DECIMAL  DecimalExpansion
 DEQUEUE  Dequeue                      DERHAM   DeRhamComplex
 DFLOAT   DoubleFloat                  DHMATRIX DenavitHartenbergMatrix
 DIAGG-   Dictionary&                  DIFEXT-  DifferentialExtension&
 DIFRING- DifferentialRing&            DIOPS-   DictionaryOperations&
 DIRPCAT- DirectProductCategory&       DIRPROD  DirectProduct
 DIVRING- DivisionRing&                DLIST    DataList
 DMP      DistributedMultivariatePolynomial
 DPMM     DirectProductMatrixModule    DPMO     DirectProductModule
 DPOLCAT- DifferentialPolynomialCategory&
 DROPT    DrawOption
 DSMP     DifferentialSparseMultivariatePolynomial
 DVARCAT- DifferentialVariableCategory&
 E04DGFA  e04dgfAnnaType               E04FDFA  e04fdfAnnaType
 E04GCFA  e04gcfAnnaType               E04JAFA  e04jafAnnaType
 E04MBFA  e04mbfAnnaType               E04NAFA  e04nafAnnaType
 E04UCFA  e04ucfAnnaType               EAB      ExtAlgBasis
 EFULS    ElementaryFunctionsUnivariateLaurentSeries
 EFUPXS   ElementaryFunctionsUnivariatePuiseuxSeries
 ELAGG-   ExtensibleLinearAggregate&   ELEMFUN- ElementaryFunctionCategory&
 ELTAGG-  EltableAggregate&            EMR      EuclideanModularRing
 EQ       Equation                     EQTBL    EqTable
 ES-      ExpressionSpace&             EUCDOM-  EuclideanDomain&
 EVALAB-  Evalable&                    EXIT     Exit
 EXPEXPAN ExponentialExpansion         EXPR     Expression
 EXPUPXS  ExponentialOfUnivariatePuiseuxSeries
 FAGROUP  FreeAbelianGroup             FAMONOID FreeAbelianMonoid
 FAMR-    FiniteAbelianMonoidRing&     FARRAY   FlexibleArray
 FAXF-    FiniteAlgebraicExtensionField&
 FC       FortranCode                  FCOMP    FourierComponent
 FDIV     FiniteDivisor                FDIVCAT- FiniteDivisorCategory&
 FEVALAB- FullyEvalableOver&           FEXPR    FortranExpression
 FF       FiniteField                  FFCAT-   FunctionFieldCategory&
 FFCG     FiniteFieldCyclicGroup
 FFCGP    FiniteFieldCyclicGroupExtensionByPolynomial
 FFCGX    FiniteFieldCyclicGroupExtension
 FFIELDC- FiniteFieldCategory&         FFNB     FiniteFieldNormalBasis
 FFNBP    FiniteFieldNormalBasisExtensionByPolynomial
 FFNBX    FiniteFieldNormalBasisExtension
 FFP      FiniteFieldExtensionByPolynomial
 FFX      FiniteFieldExtension         FGROUP   FreeGroup
 FIELD-   Field&                       FILE     File
 FINAALG- FiniteRankNonAssociativeAlgebra&
 FINRALG- FiniteRankAlgebra&           FLAGG-   FiniteLinearAggregate&
 FLINEXP- FullyLinearlyExplicitRingOver&
 FLOAT    Float                        FM       FreeModule
 FM1      FreeModule1                  FMONOID  FreeMonoid
 FNAME    FileName                     FNLA     FreeNilpotentLie
 FORMULA  ScriptFormulaFormat          FORTRAN  FortranProgram
 FPARFRAC FullPartialFractionExpansion FPC-     FieldOfPrimeCharacteristic&
 FPS-     FloatingPointSystem&         FR       Factored
 FRAC     Fraction                     FRAMALG- FramedAlgebra&
 FRETRCT- FullyRetractableTo&          FRIDEAL  FractionalIdeal
 FRMOD    FramedModule                 FRNAALG- FramedNonAssociativeAlgebra&
 FS-      FunctionSpace&               FSAGG-   FiniteSetAggregate&
 FSERIES  FourierSeries                FST      FortranScalarType
 FT       FortranType                  FTEM     FortranTemplate
 FUNCTION FunctionCalled               GCDDOM-  GcdDomain&
 GCNAALG  GenericNonAssociativeAlgebra
 GDMP     GeneralDistributedMultivariatePolynomial
 GMODPOL  GeneralModulePolynomial      GOPT     GuessOption
 GOPT0    GuessOptionFunctions0        GPOLSET  GeneralPolynomialSet
 GRALG-   GradedAlgebra&               GRIMAGE  GraphImage
 GRMOD-   GradedModule&                GROUP-   Group&
 GSERIES  GeneralUnivariatePowerSeries GSTBL    GeneralSparseTable
 GTSET    GeneralTriangularSet         HACKPI   Pi
 HASHTBL  HashTable
 HDMP     HomogeneousDistributedMultivariatePolynomial
 HDP      HomogeneousDirectProduct     HEAP     Heap
 HELLFDIV HyperellipticFiniteDivisor   HEXADEC  HexadecimalExpansion
 HOAGG-   HomogeneousAggregate&        HYPCAT-  HyperbolicFunctionCategory&
 IAN      InnerAlgebraicNumber         IARRAY1  IndexedOneDimensionalArray
 IARRAY2  IndexedTwoDimensionalArray   IBITS    IndexedBits
 ICARD    IndexCard                    IDEAL    PolynomialIdeals
 IDPAG    IndexedDirectProductAbelianGroup
 IDPAM    IndexedDirectProductAbelianMonoid
 IDPO     IndexedDirectProductObject
 IDPOAM   IndexedDirectProductOrderedAbelianMonoid
 IDPOAMS  IndexedDirectProductOrderedAbelianMonoidSup
 IEVALAB- InnerEvalable&               IFAMON   InnerFreeAbelianMonoid
 IFARRAY  IndexedFlexibleArray         IFF      InnerFiniteField
 IIARRAY2 InnerIndexedTwoDimensionalArray
 ILIST    IndexedList                  IMATRIX  IndexedMatrix
 INDE     IndexedExponents             INFORM   InputForm
 INS-     IntegerNumberSystem&         INT      Integer
 INTABL   InnerTable                   INTDOM-  IntegralDomain&
 INTFTBL  IntegrationFunctionsTable    INTRVL   Interval
 IPADIC   InnerPAdicInteger            IPF      InnerPrimeField
 IR       IntegrationResult            ISTRING  IndexedString
 ISUPS    InnerSparseUnivariatePowerSeries
 ITAYLOR  InnerTaylorSeries            ITUPLE   InfiniteTuple
 IVECTOR  IndexedVector                IXAGG-   IndexedAggregate&
 JORDAN   AssociatedJordanAlgebra      KAFILE   KeyedAccessFile
 KDAGG-   KeyedDictionary&             KERNEL   Kernel
 LA       LocalAlgebra                 LALG-    LeftAlgebra&
 LAUPOL   LaurentPolynomial            LEXP     LieExponentials
 LIB      Library                      LIE      AssociatedLieAlgebra
 LIECAT-  LieAlgebra&                  LIST     List
 LMDICT   ListMultiDictionary          LMOPS    ListMonoidOps
 LNAGG-   LinearAggregate&             LO       Localize
 LODO     LinearOrdinaryDifferentialOperator
 LODO1    LinearOrdinaryDifferentialOperator1
 LODO2    LinearOrdinaryDifferentialOperator2
 LODOCAT- LinearOrdinaryDifferentialOperatorCategory&
 LOGIC-   Logic&                       LPOLY    LiePolynomial
 LSAGG-   ListAggregate&               LSQM     LieSquareMatrix
 LWORD    LyndonWord                   LZSTAGG- LazyStreamAggregate&
 M3D      ThreeDimensionalMatrix       MAGMA    Magma
 MATCAT-  MatrixCategory&              MATRIX   Matrix
 MCMPLX   MachineComplex               MFLOAT   MachineFloat
 MINT     MachineInteger               MKCHSET  MakeCachableSet
 MMLFORM  MathMLFormat                 MODFIELD ModularField
 MODMON   ModMonic                     MODMONOM ModuleMonomial
 MODOP    ModuleOperator               MODRING  ModularRing
 MODULE-  Module&                      MOEBIUS  MoebiusTransform
 MONAD-   Monad&                       MONADWU- MonadWithUnit&
 MONOGEN- MonogenicAlgebra&            MONOID-  Monoid&
 MPOLY    MultivariatePolynomial       MRING    MonoidRing
 MSET     Multiset                     MYEXPR   MyExpression
 MYUP     MyUnivariatePolynomial       NAALG-   NonAssociativeAlgebra&
 NARNG-   NonAssociativeRng&           NASRING- NonAssociativeRing&
       Enumeration                           Mapping
       Record                                Union
 NIPROB   NumericalIntegrationProblem  NNI      NonNegativeInteger
 NONE     None                         NOTTING  NottinghamGroup
 NSMP     NewSparseMultivariatePolynomial
 NSUP     NewSparseUnivariatePolynomial
 OC-      OctonionCategory&            OCT      Octonion
 ODEIFTBL ODEIntensityFunctionsTable   ODEPROB  NumericalODEProblem
 ODP      OrderedDirectProduct
 ODPOL    OrderlyDifferentialPolynomial
 ODR      OrdinaryDifferentialRing     ODVAR    OrderlyDifferentialVariable
 OFMONOID OrderedFreeMonoid            OMCONN   OpenMathConnection
 OMDEV    OpenMathDevice               OMENC    OpenMathEncoding
 OMERR    OpenMathError                OMERRK   OpenMathErrorKind
 OMLO     OppositeMonogenicLinearOperator
 ONECOMP  OnePointCompletion           OP       Operator
 OPTPROB  NumericalOptimizationProblem ORDCOMP  OrderedCompletion
 ORDRING- OrderedRing&                 ORDSET-  OrderedSet&
 OREPCAT- UnivariateSkewPolynomialCategory&
 ORESUP   SparseUnivariateSkewPolynomial
 OREUP    UnivariateSkewPolynomial     OSI      OrdSetInts
 OUTFORM  OutputForm                   OVAR     OrderedVariableList
 OWP      OrdinaryWeightedPolynomials  PADIC    PAdicInteger
 PADICRAT PAdicRational                PADICRC  PAdicRationalConstructor
 PALETTE  Palette                      PARPCURV ParametricPlaneCurve
 PARSCURV ParametricSpaceCurve         PARSURF  ParametricSurface
 PATLRES  PatternMatchListResult       PATRES   PatternMatchResult
 PATTERN  Pattern
 PBWLB    PoincareBirkhoffWittLyndonBasis
 PDEPROB  NumericalPDEProblem          PDRING-  PartialDifferentialRing&
 PENDTREE PendantTree                  PERM     Permutation
 PERMGRP  PermutationGroup             PF       PrimeField
 PFECAT-  PolynomialFactorizationExplicit&
 PFR      PartialFraction              PI       PositiveInteger
 PLOT     Plot                         PLOT3D   Plot3D
 POINT    Point                        POLY     Polynomial
 POLYCAT- PolynomialCategory&          PR       PolynomialRing
 PRIMARR  PrimitiveArray               PRODUCT  Product
 PRTITION Partition                    PSCAT-   PowerSeriesCategory&
 PSETCAT- PolynomialSetCategory&       QALGSET  QuasiAlgebraicSet
 QEQUAT   QueryEquation                QFCAT-   QuotientFieldCategory&
 QFORM    QuadraticForm                QUAT     Quaternion
 QUATCAT- QuaternionCategory&          QUEUE    Queue
 RADCAT-  RadicalCategory&             RADFF    RadicalFunctionField
 RADIX    RadixExpansion               RCAGG-   RecursiveAggregate&
 RCFIELD- RealClosedField&             RECLOS   RealClosure
 REF      Reference                    REGSET   RegularTriangularSet
 RESRING  ResidueRing                  RESULT   Result
 RETRACT- RetractableTo&               RGCHAIN  RegularChain
 RING-    Ring&                        RMATCAT- RectangularMatrixCategory&
 RMATRIX  RectangularMatrix            RNS-     RealNumberSystem&
 ROIRC    RightOpenIntervalRootCharacterization
 ROMAN    RomanNumeral                 ROUTINE  RoutinesTable
 RPOLCAT- RecursivePolynomialCategory&
 RRCC-    RealRootCharacterizationCategory&
 RSETCAT- RegularTriangularSetCategory&
 RULE     RewriteRule                  RULECOLD RuleCalled
 RULESET  Ruleset                      SAE      SimpleAlgebraicExtension
 SAOS     SingletonAsOrderedSet
 SDPOL    SequentialDifferentialPolynomial
 SDVAR    SequentialDifferentialVariable
 SEG      Segment                      SEGBIND  SegmentBinding
 SET      Set                          SETAGG-  SetAggregate&
 SETCAT-  SetCategory&                 SETMN    SetOfMIntegersInOneToN
 SEX      SExpression                  SEXOF    SExpressionOf
 SFORT    SimpleFortranProgram         SGROUP-  SemiGroup&
 SHDP     SplitHomogeneousDirectProduct
 SINT     SingleInteger                SMATCAT- SquareMatrixCategory&
 SMP      SparseMultivariatePolynomial
 SMTS     SparseMultivariateTaylorSeries
 SPACE3   ThreeSpace                   SPLNODE  SplittingNode
 SPLTREE  SplittingTree                SQMATRIX SquareMatrix
 SRAGG-   StringAggregate&
 SREGSET  SquareFreeRegularTriangularSet
 STACK    Stack                        STAGG-   StreamAggregate&
 STBL     SparseTable                  STREAM   Stream
 STRING   String                       STRTBL   StringTable
 SUBSPACE SubSpace                     SUCH     SuchThat
 SULS     SparseUnivariateLaurentSeries
 SUP      SparseUnivariatePolynomial
 SUPEXPR  SparseUnivariatePolynomialExpressions
 SUPXS    SparseUnivariatePuiseuxSeries
 SUTS     SparseUnivariateTaylorSeries SWITCH   Switch
 SYMBOL   Symbol                       SYMPOLY  SymmetricPolynomial
 SYMS     TheSymbolTable               SYMTAB   SymbolTable
 TABLE    Table                        TABLEAU  Tableau
 TBAGG-   TableAggregate&              TEX      TexFormat
 TEXTFILE TextFile
 TRANFUN- TranscendentalFunctionCategory&
 TREE     Tree
 TRIGCAT- TrigonometricFunctionCategory&
 TS       TaylorSeries                 TSETCAT- TriangularSetCategory&
 TUBE     TubePlot                     TUPLE    Tuple
 UFD-     UniqueFactorizationDomain&   UFPS     UnivariateFormalPowerSeries
 ULS      UnivariateLaurentSeries
 ULSCCAT- UnivariateLaurentSeriesConstructorCategory&
 ULSCONS  UnivariateLaurentSeriesConstructor
 UNISEG   UniversalSegment             UP       UnivariatePolynomial
 UPOLYC-  UnivariatePolynomialCategory&
 UPSCAT-  UnivariatePowerSeriesCategory&
 UPXS     UnivariatePuiseuxSeries
 UPXSCCA- UnivariatePuiseuxSeriesConstructorCategory&
 UPXSCONS UnivariatePuiseuxSeriesConstructor
 UPXSSING UnivariatePuiseuxSeriesWithExponentialSingularity
 URAGG-   UnaryRecursiveAggregate&     UTS      UnivariateTaylorSeries
 UTSCAT-  UnivariateTaylorSeriesCategory&
 VARIABLE Variable                     VECTCAT- VectorCategory&
 VECTOR   Vector                       VIEW2D   TwoDimensionalViewport
 VIEW3D   ThreeDimensionalViewport     VOID     Void
 VSPACE-  VectorSpace&                 WP       WeightedPolynomials
 WUTSET   WuWenTsunTriangularSet       XDPOLY   XDistributedPolynomial
 XF-      ExtensionField&              XPBWPOLY XPBWPolynomial
 XPOLY    XPolynomial                  XPR      XPolynomialRing
 XRPOLY   XRecursivePolynomial         ZMOD     IntegerMod
--R--------------------------------- Domains ---------------------------------
--R A1AGG-   OneDimensionalArrayAggregate&
--R ABELGRP- AbelianGroup&                ABELMON- AbelianMonoid&
--R ABELSG-  AbelianSemiGroup&            ACF-     AlgebraicallyClosedField&
--R ACFS-    AlgebraicallyClosedFunctionSpace&
--R ACPLOT   PlaneAlgebraicCurvePlot      AGG-     Aggregate&
--R ALGEBRA- Algebra&                     ALGFF    AlgebraicFunctionField
--R ALGSC    AlgebraGivenByStructuralConstants
--R ALIST    AssociationList              AMR-     AbelianMonoidRing&
--R AN       AlgebraicNumber              ANON     AnonymousFunction
--R ANTISYM  AntiSymm                     ANY      Any
--R ARR2CAT- TwoDimensionalArrayCategory& ARRAY1   OneDimensionalArray
--R ARRAY2   TwoDimensionalArray          ASP1     Asp1
--R ASP10    Asp10                        ASP12    Asp12
--R ASP19    Asp19                        ASP20    Asp20
--R ASP24    Asp24                        ASP27    Asp27
--R ASP28    Asp28                        ASP29    Asp29
--R ASP30    Asp30                        ASP31    Asp31
--R ASP33    Asp33                        ASP34    Asp34
--R ASP35    Asp35                        ASP4     Asp4
--R ASP41    Asp41                        ASP42    Asp42
--R ASP49    Asp49                        ASP50    Asp50
--R ASP55    Asp55                        ASP6     Asp6
--R ASP7     Asp7                         ASP73    Asp73
--R ASP74    Asp74                        ASP77    Asp77
--R ASP78    Asp78                        ASP8     Asp8
--R ASP80    Asp80                        ASP9     Asp9
--R ASTACK   ArrayStack
--R ATRIG-   ArcTrigonometricFunctionCategory&
--R ATTRBUT  AttributeButtons             AUTOMOR  Automorphism
--R BASTYPE- BasicType&                   BBTREE   BalancedBinaryTree
--R BFUNCT   BasicFunctions               BGAGG-   BagAggregate&
--R BINARY   BinaryExpansion              BINFILE  BinaryFile
--R BITS     Bits                         BOOLEAN  Boolean
--R BOP      BasicOperator                BPADIC   BalancedPAdicInteger
--R BPADICRT BalancedPAdicRational        BRAGG-   BinaryRecursiveAggregate&
--R BSTREE   BinarySearchTree             BTAGG-   BitAggregate&
--R BTCAT-   BinaryTreeCategory&          BTOURN   BinaryTournament
--R BTREE    BinaryTree                   CARD     CardinalNumber
--R CARTEN   CartesianTensor              CCLASS   CharacterClass
--R CHAR     Character                    CLAGG-   Collection&
--R CLIF     CliffordAlgebra              COLOR    Color
--R COMM     Commutator                   COMPCAT- ComplexCategory&
--R COMPLEX  Complex                      COMPPROP SubSpaceComponentProperty
--R CONTFRAC ContinuedFraction            D01AJFA  d01ajfAnnaType
--R D01AKFA  d01akfAnnaType               D01ALFA  d01alfAnnaType
--R D01AMFA  d01amfAnnaType               D01ANFA  d01anfAnnaType
--R D01APFA  d01apfAnnaType               D01AQFA  d01aqfAnnaType
--R D01ASFA  d01asfAnnaType               D01FCFA  d01fcfAnnaType
--R D01GBFA  d01gbfAnnaType               D01TRNS  d01TransformFunctionType
--R D02BBFA  d02bbfAnnaType               D02BHFA  d02bhfAnnaType
--R D02CJFA  d02cjfAnnaType               D02EJFA  d02ejfAnnaType
--R D03EEFA  d03eefAnnaType               D03FAFA  d03fafAnnaType
--R DBASE    Database                     DECIMAL  DecimalExpansion
--R DEQUEUE  Dequeue                      DERHAM   DeRhamComplex
--R DFLOAT   DoubleFloat                  DHMATRIX DenavitHartenbergMatrix
--R DIAGG-   Dictionary&                  DIFEXT-  DifferentialExtension&
--R DIFRING- DifferentialRing&            DIOPS-   DictionaryOperations&
--R DIRPCAT- DirectProductCategory&       DIRPROD  DirectProduct
--R DIVRING- DivisionRing&                DLIST    DataList
--R DMP      DistributedMultivariatePolynomial
--R DPMM     DirectProductMatrixModule    DPMO     DirectProductModule
--R DPOLCAT- DifferentialPolynomialCategory&
--R DROPT    DrawOption
--R DSMP     DifferentialSparseMultivariatePolynomial
--R DVARCAT- DifferentialVariableCategory&
--R E04DGFA  e04dgfAnnaType               E04FDFA  e04fdfAnnaType
--R E04GCFA  e04gcfAnnaType               E04JAFA  e04jafAnnaType
--R E04MBFA  e04mbfAnnaType               E04NAFA  e04nafAnnaType
--R E04UCFA  e04ucfAnnaType               EAB      ExtAlgBasis
--R EFULS    ElementaryFunctionsUnivariateLaurentSeries
--R EFUPXS   ElementaryFunctionsUnivariatePuiseuxSeries
--R ELAGG-   ExtensibleLinearAggregate&   ELEMFUN- ElementaryFunctionCategory&
--R ELTAGG-  EltableAggregate&            EMR      EuclideanModularRing
--R EQ       Equation                     EQTBL    EqTable
--R ES-      ExpressionSpace&             EUCDOM-  EuclideanDomain&
--R EVALAB-  Evalable&                    EXIT     Exit
--R EXPEXPAN ExponentialExpansion         EXPR     Expression
--R EXPUPXS  ExponentialOfUnivariatePuiseuxSeries
--R FAGROUP  FreeAbelianGroup             FAMONOID FreeAbelianMonoid
--R FAMR-    FiniteAbelianMonoidRing&     FARRAY   FlexibleArray
--R FAXF-    FiniteAlgebraicExtensionField&
--R FC       FortranCode                  FCOMP    FourierComponent
--R FDIV     FiniteDivisor                FDIVCAT- FiniteDivisorCategory&
--R FEVALAB- FullyEvalableOver&           FEXPR    FortranExpression
--R FF       FiniteField                  FFCAT-   FunctionFieldCategory&
--R FFCG     FiniteFieldCyclicGroup
--R FFCGP    FiniteFieldCyclicGroupExtensionByPolynomial
--R FFCGX    FiniteFieldCyclicGroupExtension
--R FFIELDC- FiniteFieldCategory&         FFNB     FiniteFieldNormalBasis
--R FFNBP    FiniteFieldNormalBasisExtensionByPolynomial
--R FFNBX    FiniteFieldNormalBasisExtension
--R FFP      FiniteFieldExtensionByPolynomial
--R FFX      FiniteFieldExtension         FGROUP   FreeGroup
--R FIELD-   Field&                       FILE     File
--R FINAALG- FiniteRankNonAssociativeAlgebra&
--R FINRALG- FiniteRankAlgebra&           FLAGG-   FiniteLinearAggregate&
--R FLINEXP- FullyLinearlyExplicitRingOver&
--R FLOAT    Float                        FM       FreeModule
--R FM1      FreeModule1                  FMONOID  FreeMonoid
--R FNAME    FileName                     FNLA     FreeNilpotentLie
--R FORMULA  ScriptFormulaFormat          FORTRAN  FortranProgram
--R FPARFRAC FullPartialFractionExpansion FPC-     FieldOfPrimeCharacteristic&
--R FPS-     FloatingPointSystem&         FR       Factored
--R FRAC     Fraction                     FRAMALG- FramedAlgebra&
--R FRETRCT- FullyRetractableTo&          FRIDEAL  FractionalIdeal
--R FRMOD    FramedModule                 FRNAALG- FramedNonAssociativeAlgebra&
--R FS-      FunctionSpace&               FSAGG-   FiniteSetAggregate&
--R FSERIES  FourierSeries                FST      FortranScalarType
--R FT       FortranType                  FTEM     FortranTemplate
--R FUNCTION FunctionCalled               GCDDOM-  GcdDomain&
--R GCNAALG  GenericNonAssociativeAlgebra
--R GDMP     GeneralDistributedMultivariatePolynomial
--R GMODPOL  GeneralModulePolynomial      GOPT     GuessOption
--R GOPT0    GuessOptionFunctions0        GPOLSET  GeneralPolynomialSet
--R GRALG-   GradedAlgebra&               GRIMAGE  GraphImage
--R GRMOD-   GradedModule&                GROUP-   Group&
--R GSERIES  GeneralUnivariatePowerSeries GSTBL    GeneralSparseTable
--R GTSET    GeneralTriangularSet         HACKPI   Pi
--R HASHTBL  HashTable
--R HDMP     HomogeneousDistributedMultivariatePolynomial
--R HDP      HomogeneousDirectProduct     HEAP     Heap
--R HELLFDIV HyperellipticFiniteDivisor   HEXADEC  HexadecimalExpansion
--R HOAGG-   HomogeneousAggregate&        HYPCAT-  HyperbolicFunctionCategory&
--R IAN      InnerAlgebraicNumber         IARRAY1  IndexedOneDimensionalArray
--R IARRAY2  IndexedTwoDimensionalArray   IBITS    IndexedBits
--R ICARD    IndexCard                    IDEAL    PolynomialIdeals
--R IDPAG    IndexedDirectProductAbelianGroup
--R IDPAM    IndexedDirectProductAbelianMonoid
--R IDPO     IndexedDirectProductObject
--R IDPOAM   IndexedDirectProductOrderedAbelianMonoid
--R IDPOAMS  IndexedDirectProductOrderedAbelianMonoidSup
--R IEVALAB- InnerEvalable&               IFAMON   InnerFreeAbelianMonoid
--R IFARRAY  IndexedFlexibleArray         IFF      InnerFiniteField
--R IIARRAY2 InnerIndexedTwoDimensionalArray
--R ILIST    IndexedList                  IMATRIX  IndexedMatrix
--R INDE     IndexedExponents             INFORM   InputForm
--R INS-     IntegerNumberSystem&         INT      Integer
--R INTABL   InnerTable                   INTDOM-  IntegralDomain&
--R INTFTBL  IntegrationFunctionsTable    INTRVL   Interval
--R IPADIC   InnerPAdicInteger            IPF      InnerPrimeField
--R IR       IntegrationResult            ISTRING  IndexedString
--R ISUPS    InnerSparseUnivariatePowerSeries
--R ITAYLOR  InnerTaylorSeries            ITUPLE   InfiniteTuple
--R IVECTOR  IndexedVector                IXAGG-   IndexedAggregate&
--R JORDAN   AssociatedJordanAlgebra      KAFILE   KeyedAccessFile
--R KDAGG-   KeyedDictionary&             KERNEL   Kernel
--R LA       LocalAlgebra                 LALG-    LeftAlgebra&
--R LAUPOL   LaurentPolynomial            LEXP     LieExponentials
--R LIB      Library                      LIE      AssociatedLieAlgebra
--R LIECAT-  LieAlgebra&                  LIST     List
--R LMDICT   ListMultiDictionary          LMOPS    ListMonoidOps
--R LNAGG-   LinearAggregate&             LO       Localize
--R LODO     LinearOrdinaryDifferentialOperator
--R LODO1    LinearOrdinaryDifferentialOperator1
--R LODO2    LinearOrdinaryDifferentialOperator2
--R LODOCAT- LinearOrdinaryDifferentialOperatorCategory&
--R LOGIC-   Logic&                       LPOLY    LiePolynomial
--R LSAGG-   ListAggregate&               LSQM     LieSquareMatrix
--R LWORD    LyndonWord                   LZSTAGG- LazyStreamAggregate&
--R M3D      ThreeDimensionalMatrix       MAGMA    Magma
--R MATCAT-  MatrixCategory&              MATRIX   Matrix
--R MCMPLX   MachineComplex               MFLOAT   MachineFloat
--R MINT     MachineInteger               MKCHSET  MakeCachableSet
--R MMLFORM  MathMLFormat                 MODFIELD ModularField
--R MODMON   ModMonic                     MODMONOM ModuleMonomial
--R MODOP    ModuleOperator               MODRING  ModularRing
--R MODULE-  Module&                      MOEBIUS  MoebiusTransform
--R MONAD-   Monad&                       MONADWU- MonadWithUnit&
--R MONOGEN- MonogenicAlgebra&            MONOID-  Monoid&
--R MPOLY    MultivariatePolynomial       MRING    MonoidRing
--R MSET     Multiset                     MYEXPR   MyExpression
--R MYUP     MyUnivariatePolynomial       NAALG-   NonAssociativeAlgebra&
--R NARNG-   NonAssociativeRng&           NASRING- NonAssociativeRing&
--R       Enumeration                           Mapping
--R       Record                                Union
--R NIPROB   NumericalIntegrationProblem  NNI      NonNegativeInteger
--R NONE     None                         NOTTING  NottinghamGroup
--R NSMP     NewSparseMultivariatePolynomial
--R NSUP     NewSparseUnivariatePolynomial
--R OC-      OctonionCategory&            OCT      Octonion
--R ODEIFTBL ODEIntensityFunctionsTable   ODEPROB  NumericalODEProblem
--R ODP      OrderedDirectProduct
--R ODPOL    OrderlyDifferentialPolynomial
--R ODR      OrdinaryDifferentialRing     ODVAR    OrderlyDifferentialVariable
--R OFMONOID OrderedFreeMonoid            OMCONN   OpenMathConnection
--R OMDEV    OpenMathDevice               OMENC    OpenMathEncoding
--R OMERR    OpenMathError                OMERRK   OpenMathErrorKind
--R OMLO     OppositeMonogenicLinearOperator
--R ONECOMP  OnePointCompletion           OP       Operator
--R OPTPROB  NumericalOptimizationProblem ORDCOMP  OrderedCompletion
--R ORDRING- OrderedRing&                 ORDSET-  OrderedSet&
--R OREPCAT- UnivariateSkewPolynomialCategory&
--R ORESUP   SparseUnivariateSkewPolynomial
--R OREUP    UnivariateSkewPolynomial     OSI      OrdSetInts
--R OUTFORM  OutputForm                   OVAR     OrderedVariableList
--R OWP      OrdinaryWeightedPolynomials  PADIC    PAdicInteger
--R PADICRAT PAdicRational                PADICRC  PAdicRationalConstructor
--R PALETTE  Palette                      PARPCURV ParametricPlaneCurve
--R PARSCURV ParametricSpaceCurve         PARSURF  ParametricSurface
--R PATLRES  PatternMatchListResult       PATRES   PatternMatchResult
--R PATTERN  Pattern
--R PBWLB    PoincareBirkhoffWittLyndonBasis
--R PDEPROB  NumericalPDEProblem          PDRING-  PartialDifferentialRing&
--R PENDTREE PendantTree                  PERM     Permutation
--R PERMGRP  PermutationGroup             PF       PrimeField
--R PFECAT-  PolynomialFactorizationExplicit&
--R PFR      PartialFraction              PI       PositiveInteger
--R PLOT     Plot                         PLOT3D   Plot3D
--R POINT    Point                        POLY     Polynomial
--R POLYCAT- PolynomialCategory&          PR       PolynomialRing
--R PRIMARR  PrimitiveArray               PRODUCT  Product
--R PRTITION Partition                    PSCAT-   PowerSeriesCategory&
--R PSETCAT- PolynomialSetCategory&       QALGSET  QuasiAlgebraicSet
--R QEQUAT   QueryEquation                QFCAT-   QuotientFieldCategory&
--R QFORM    QuadraticForm                QUAT     Quaternion
--R QUATCAT- QuaternionCategory&          QUEUE    Queue
--R RADCAT-  RadicalCategory&             RADFF    RadicalFunctionField
--R RADIX    RadixExpansion               RCAGG-   RecursiveAggregate&
--R RCFIELD- RealClosedField&             RECLOS   RealClosure
--R REF      Reference                    REGSET   RegularTriangularSet
--R RESRING  ResidueRing                  RESULT   Result
--R RETRACT- RetractableTo&               RGCHAIN  RegularChain
--R RING-    Ring&                        RMATCAT- RectangularMatrixCategory&
--R RMATRIX  RectangularMatrix            RNS-     RealNumberSystem&
--R ROIRC    RightOpenIntervalRootCharacterization
--R ROMAN    RomanNumeral                 ROUTINE  RoutinesTable
--R RPOLCAT- RecursivePolynomialCategory&
--R RRCC-    RealRootCharacterizationCategory&
--R RSETCAT- RegularTriangularSetCategory&
--R RULE     RewriteRule                  RULECOLD RuleCalled
--R RULESET  Ruleset                      SAE      SimpleAlgebraicExtension
--R SAOS     SingletonAsOrderedSet
--R SDPOL    SequentialDifferentialPolynomial
--R SDVAR    SequentialDifferentialVariable
--R SEG      Segment                      SEGBIND  SegmentBinding
--R SET      Set                          SETAGG-  SetAggregate&
--R SETCAT-  SetCategory&                 SETMN    SetOfMIntegersInOneToN
--R SEX      SExpression                  SEXOF    SExpressionOf
--R SFORT    SimpleFortranProgram         SGROUP-  SemiGroup&
--R SHDP     SplitHomogeneousDirectProduct
--R SINT     SingleInteger                SMATCAT- SquareMatrixCategory&
--R SMP      SparseMultivariatePolynomial
--R SMTS     SparseMultivariateTaylorSeries
--R SPACE3   ThreeSpace                   SPLNODE  SplittingNode
--R SPLTREE  SplittingTree                SQMATRIX SquareMatrix
--R SRAGG-   StringAggregate&
--R SREGSET  SquareFreeRegularTriangularSet
--R STACK    Stack                        STAGG-   StreamAggregate&
--R STBL     SparseTable                  STREAM   Stream
--R STRING   String                       STRTBL   StringTable
--R SUBSPACE SubSpace                     SUCH     SuchThat
--R SULS     SparseUnivariateLaurentSeries
--R SUP      SparseUnivariatePolynomial
--R SUPEXPR  SparseUnivariatePolynomialExpressions
--R SUPXS    SparseUnivariatePuiseuxSeries
--R SUTS     SparseUnivariateTaylorSeries SWITCH   Switch
--R SYMBOL   Symbol                       SYMPOLY  SymmetricPolynomial
--R SYMS     TheSymbolTable               SYMTAB   SymbolTable
--R TABLE    Table                        TABLEAU  Tableau
--R TBAGG-   TableAggregate&              TEX      TexFormat
--R TEXTFILE TextFile
--R TRANFUN- TranscendentalFunctionCategory&
--R TREE     Tree
--R TRIGCAT- TrigonometricFunctionCategory&
--R TS       TaylorSeries                 TSETCAT- TriangularSetCategory&
--R TUBE     TubePlot                     TUPLE    Tuple
--R UFD-     UniqueFactorizationDomain&   UFPS     UnivariateFormalPowerSeries
--R ULS      UnivariateLaurentSeries
--R ULSCCAT- UnivariateLaurentSeriesConstructorCategory&
--R ULSCONS  UnivariateLaurentSeriesConstructor
--R UNISEG   UniversalSegment             UP       UnivariatePolynomial
--R UPOLYC-  UnivariatePolynomialCategory&
--R UPSCAT-  UnivariatePowerSeriesCategory&
--R UPXS     UnivariatePuiseuxSeries
--R UPXSCCA- UnivariatePuiseuxSeriesConstructorCategory&
--R UPXSCONS UnivariatePuiseuxSeriesConstructor
--R UPXSSING UnivariatePuiseuxSeriesWithExponentialSingularity
--R URAGG-   UnaryRecursiveAggregate&     UTS      UnivariateTaylorSeries
--R UTSCAT-  UnivariateTaylorSeriesCategory&
--R VARIABLE Variable                     VECTCAT- VectorCategory&
--R VECTOR   Vector                       VIEW2D   TwoDimensionalViewport
--R VIEW3D   ThreeDimensionalViewport     VOID     Void
--R VSPACE-  VectorSpace&                 WP       WeightedPolynomials
--R WUTSET   WuWenTsunTriangularSet       XDPOLY   XDistributedPolynomial
--R XF-      ExtensionField&              XPBWPOLY XPBWPolynomial
--R XPOLY    XPolynomial                  XPR      XPolynomialRing
--R XRPOLY   XRecursivePolynomial         ZMOD     IntegerMod
--E 14

--S 15 of 23
)what packages
 
-------------------------------- Packages ---------------------------------
 AF       AlgebraicFunction            ALGFACT  AlgFactor
 ALGMANIP AlgebraicManipulations       ALGMFACT AlgebraicMultFact
 ALGPKG   AlgebraPackage               ANY1     AnyFunctions1
 API      ApplicationProgramInterface
 APPLYORE ApplyUnivariateSkewPolynomial
 APPRULE  ApplyRules
 ARRAY12  OneDimensionalArrayFunctions2
 ASSOCEQ  AssociatedEquations          AXSERV   AxiomServer
 BALFACT  BalancedFactorisation        BEZIER   Bezier
 BEZOUT   BezoutMatrix                 BOP1     BasicOperatorFunctions1
 BOUNDZRO BoundIntegerRoots            BRILL    BrillhartTests
 CARTEN2  CartesianTensorFunctions2    CDEN     CommonDenominator
 CHARPOL  CharacteristicPolynomialPackage
 CHVAR    ChangeOfVariable
 CINTSLPE ComplexIntegerSolveLinearPolynomialEquation
 CLIP     TwoDimensionalPlotClipping   CMPLXRT  ComplexRootPackage
 COMBF    CombinatorialFunction        COMBINAT IntegerCombinatoricFunctions
 COMMONOP CommonOperators
 COMMUPC  CommuteUnivariatePolynomialCategory
 COMPFACT ComplexFactorization         COMPLEX2 ComplexFunctions2
 COMPLPAT ComplexPattern               COORDSYS CoordinateSystems
 CPIMA    CharacteristicPolynomialInMonogenicalAlgebra
 CPMATCH  ComplexPatternMatch          CRAPACK  CRApackage
 CRFP     ComplexRootFindingPackage    CSTTOOLS CyclicStreamTools
 CTRIGMNP ComplexTrigonometricManipulations
 CVMP     CoerceVectorMatrixPackage    CYCLES   CycleIndicators
 CYCLOTOM CyclotomicPolynomialPackage  D01AGNT  d01AgentsPackage
 D01WGTS  d01WeightsPackage            D02AGNT  d02AgentsPackage
 D03AGNT  d03AgentsPackage             DBLRESP  DoubleResultantPackage
 DDFACT   DistinctDegreeFactorize
 DEFINTEF ElementaryFunctionDefiniteIntegration
 DEFINTRF RationalFunctionDefiniteIntegration
 DEGRED   DegreeReductionPackage       DFINTTLS DefiniteIntegrationTools
 DFSFUN   DoubleFloatSpecialFunctions  DIOSP    DiophantineSolutionPackage
 DIRPROD2 DirectProductFunctions2      DISPLAY  DisplayPackage
 DLP      DiscreteLogarithmPackage     DRAW     TopLevelDrawFunctions
 DRAWCFUN TopLevelDrawFunctionsForCompiledFunctions
 DRAWCURV TopLevelDrawFunctionsForAlgebraicCurves
 DRAWCX   DrawComplex                  DRAWHACK DrawNumericHack
 DRAWPT   TopLevelDrawFunctionsForPoints
 DROPT0   DrawOptionFunctions0         DROPT1   DrawOptionFunctions1
 E04AGNT  e04AgentsPackage             EF       ElementaryFunction
 EFSTRUC  ElementaryFunctionStructurePackage
 ELFUTS   EllipticFunctionsUnivariateTaylorSeries
 EP       EigenPackage                 EQ2      EquationFunctions2
 ERROR    ErrorFunctions               ES1      ExpressionSpaceFunctions1
 ES2      ExpressionSpaceFunctions2
 ESCONT   ExpertSystemContinuityPackage
 ESCONT1  ExpertSystemContinuityPackage1
 ESTOOLS  ExpertSystemToolsPackage     ESTOOLS1 ExpertSystemToolsPackage1
 ESTOOLS2 ExpertSystemToolsPackage2    EVALCYC  EvaluateCycleIndicators
 EXPR2    ExpressionFunctions2
 EXPR2UPS ExpressionToUnivariatePowerSeries
 EXPRODE  ExpressionSpaceODESolver     EXPRSOL  ExpressionSolve
 EXPRTUBE ExpressionTubePlot           FACTFUNC FactoredFunctions
 FACUTIL  FactoringUtilities
 FAMR2    FiniteAbelianMonoidRingFunctions2
 FCPAK1   FortranCodePackage1          FDIV2    FiniteDivisorFunctions2
 FFCAT2   FunctionFieldCategoryFunctions2
 FFF      FiniteFieldFunctions         FFFG     FractionFreeFastGaussian
 FFFGF    FractionFreeFastGaussianFractions
 FFHOM    FiniteFieldHomomorphisms     FFINTBAS FunctionFieldIntegralBasis
 FFPOLY   FiniteFieldPolynomialPackage
 FFPOLY2  FiniteFieldPolynomialPackage2
 FFSLPE   FiniteFieldSolveLinearPolynomialEquation
 FGLMICPK FGLMIfCanPackage
 FLAGG2   FiniteLinearAggregateFunctions2
 FLASORT  FiniteLinearAggregateSort    FLOATCP  FloatingComplexPackage
 FLOATRP  FloatingRealPackage          FOP      FortranOutputStackPackage
 FORDER   FindOrderFinite              FORMULA1 ScriptFormulaFormat1
 FORT     FortranPackage               FR2      FactoredFunctions2
 FRAC2    FractionFunctions2           FRIDEAL2 FractionalIdealFunctions2
 FRNAAF2  FramedNonAssociativeAlgebraFunctions2
 FRUTIL   FactoredFunctionUtilities    FS2      FunctionSpaceFunctions2
 FS2EXPXP FunctionSpaceToExponentialExpansion
 FS2UPS   FunctionSpaceToUnivariatePowerSeries
 FSAGG2   FiniteSetAggregateFunctions2
 FSCINT   FunctionSpaceComplexIntegration
 FSINT    FunctionSpaceIntegration     FSPECF   FunctionalSpecialFunction
 FSPRMELT FunctionSpacePrimitiveElement
 FSRED    FunctionSpaceReduce
 FSUPFACT FunctionSpaceUnivariatePolynomialFactor
 GALFACT  GaloisGroupFactorizer
 GALFACTU GaloisGroupFactorizationUtilities
 GALPOLYU GaloisGroupPolynomialUtilities
 GALUTIL  GaloisGroupUtilities         GAUSSFAC GaussianFactorizationPackage
 GB       GroebnerPackage
 GBEUCLID EuclideanGroebnerBasisPackage
 GBF      GroebnerFactorizationPackage GBINTERN GroebnerInternalPackage
 GENEEZ   GenExEuclid
 GENMFACT GeneralizedMultivariateFactorize
 GENPGCD  GeneralPolynomialGcdPackage  GENUFACT GenUFactorize
 GENUPS   GenerateUnivariatePowerSeries
 GHENSEL  GeneralHenselPackage         GOSPER   GosperSummationMethod
 GRAY     GrayCode                     GRDEF    GraphicsDefaults
 GROEBSOL GroebnerSolve                GUESS    Guess
 GUESSAN  GuessAlgebraicNumber         GUESSF   GuessFinite
 GUESSF1  GuessFiniteFunctions         GUESSINT GuessInteger
 GUESSP   GuessPolynomial              GUESSUP  GuessUnivariatePolynomial
 HB       HallBasis                    HEUGCD   HeuGcd
 IALGFACT InnerAlgFactor
 IBACHIN  ChineseRemainderToolsForIntegralBases
 IBATOOL  IntegralBasisTools           IBPTOOLS IntegralBasisPolynomialTools
 ICDEN    InnerCommonDenominator       IDECOMP  IdealDecompositionPackage
 IMATLIN  InnerMatrixLinearAlgebraFunctions
 IMATQF   InnerMatrixQuotientFieldFunctions
 INBFF    InnerNormalBasisFieldFunctions
 INCRMAPS IncrementingMaps             INEP     InnerNumericEigenPackage
 INFINITY Infinity                     INFORM1  InputFormFunctions1
 INFPROD0 InfiniteProductCharacteristicZero
 INFSP    InnerNumericFloatSolvePackage
 INMODGCD InnerModularGcd              INNMFACT InnerMultFact
 INPRODFF InfiniteProductFiniteField   INPRODPF InfiniteProductPrimeField
 INPSIGN  InnerPolySign                INTAF    AlgebraicIntegration
 INTALG   AlgebraicIntegrate           INTBIT   IntegerBits
 INTEF    ElementaryIntegration        INTFACT  IntegerFactorizationPackage
 INTG0    GenusZeroIntegration         INTHEORY IntegerNumberTheoryFunctions
 INTHERAL AlgebraicHermiteIntegration
 INTHERTR TranscendentalHermiteIntegration
 INTPACK  AnnaNumericalIntegrationPackage
 INTPAF   PureAlgebraicIntegration     INTPM    PatternMatchIntegration
 INTRAT   RationalIntegration          INTRET   IntegerRetractions
 INTRF    RationalFunctionIntegration
 INTSLPE  IntegerSolveLinearPolynomialEquation
 INTTOOLS IntegrationTools             INTTR    TranscendentalIntegration
 INVLAPLA InverseLaplaceTransform      IPRNTPK  InternalPrintPackage
 IR2      IntegrationResultFunctions2  IR2F     IntegrationResultToFunction
 IROOT    IntegerRoots                 IRREDFFX IrredPolyOverFiniteField
 IRRF2F   IntegrationResultRFToFunction
 IRSN     IrrRepSymNatPackage
 IRURPK   InternalRationalUnivariateRepresentationPackage
 ISUMP    InnerPolySum                 ITFUN2   InfiniteTupleFunctions2
 ITFUN3   InfiniteTupleFunctions3
 ITRIGMNP InnerTrigonometricManipulations
 KERNEL2  KernelFunctions2             KOVACIC  Kovacic
 LAPLACE  LaplaceTransform             LAZM3PK  LazardSetSolvingPackage
 LEADCDET LeadingCoefDetermination     LEXTRIPK LexTriangularPackage
 LF       LiouvillianFunction          LGROBP   LinGroebnerPackage
 LIMITPS  PowerSeriesLimitPackage      LIMITRF  RationalFunctionLimitPackage
 LINDEP   LinearDependence             LIST2    ListFunctions2
 LIST2MAP ListToMap                    LIST3    ListFunctions3
 LODEEF   ElementaryFunctionLODESolver
 LODOF    LinearOrdinaryDifferentialOperatorFactorizer
 LODOOPS  LinearOrdinaryDifferentialOperatorsOps
 LPEFRAC  LinearPolynomialEquationByFractions
 LSMP     LinearSystemMatrixPackage    LSMP1    LinearSystemMatrixPackage1
 LSPP     LinearSystemPolynomialPackage
 MAPHACK1 MappingPackageInternalHacks1 MAPHACK2 MappingPackageInternalHacks2
 MAPHACK3 MappingPackageInternalHacks3 MAPPKG1  MappingPackage1
 MAPPKG2  MappingPackage2              MAPPKG3  MappingPackage3
 MAPPKG4  MappingPackage4              MATCAT2  MatrixCategoryFunctions2
 MATLIN   MatrixLinearAlgebraFunctions
 MATSTOR  StorageEfficientMatrixOperations
 MCALCFN  MultiVariableCalculusFunctions
 MCDEN    MatrixCommonDenominator
 MDDFACT  ModularDistinctDegreeFactorizer
 MESH     MeshCreationRoutinesForThreeDimensions
 MFINFACT MultFiniteFactorize          MHROWRED ModularHermitianRowReduction
 MKBCFUNC MakeBinaryCompiledFunction   MKFLCFN  MakeFloatCompiledFunction
 MKFUNC   MakeFunction                 MKRECORD MakeRecord
 MKUCFUNC MakeUnaryCompiledFunction    MLIFT    MultivariateLifting
 MMAP     MultipleMap                  MONOTOOL MonomialExtensionTools
 MPC2     MPolyCatFunctions2           MPC3     MPolyCatFunctions3
 MPCPF    MPolyCatPolyFactorizer
 MPRFF    MPolyCatRationalFunctionFactorizer
 MRATFAC  MRationalFactorize           MRF2     MonoidRingFunctions2
 MSYSCMD  MoreSystemCommands           MTHING   MergeThing
 MULTFACT MultivariateFactorize        MULTSQFR MultivariateSquareFree
 NAGC02   NagPolynomialRootsPackage    NAGC05   NagRootFindingPackage
 NAGC06   NagSeriesSummationPackage    NAGD01   NagIntegrationPackage
 NAGD02   NagOrdinaryDifferentialEquationsPackage
 NAGD03   NagPartialDifferentialEquationsPackage
 NAGE01   NagInterpolationPackage      NAGE02   NagFittingPackage
 NAGE04   NagOptimisationPackage       NAGF01   NagMatrixOperationsPackage
 NAGF02   NagEigenPackage
 NAGF04   NagLinearEquationSolvingPackage
 NAGF07   NagLapack                    NAGS     NagSpecialFunctionsPackage
 NAGSP    NAGLinkSupportPackage        NCEP     NumericComplexEigenPackage
 NCNTFRAC NumericContinuedFraction
 NCODIV   NonCommutativeOperatorDivision
 NEWTON   NewtonInterpolation          NFINTBAS NumberFieldIntegralBasis
 NLINSOL  NonLinearSolvePackage        NODE1    NonLinearFirstOrderODESolver
 NONE1    NoneFunctions1               NORMMA   NormInMonogenicAlgebra
 NORMPK   NormalizationPackage         NORMRETR NormRetractPackage
 NPCOEF   NPCoef                       NREP     NumericRealEigenPackage
 NSUP2    NewSparseUnivariatePolynomialFunctions2
 NTPOLFN  NumberTheoreticPolynomialFunctions
 NUMERIC  Numeric                      NUMFMT   NumberFormats
 NUMODE   NumericalOrdinaryDifferentialEquations
 NUMQUAD  NumericalQuadrature          NUMTUBE  NumericTubePlot
 OCTCT2   OctonionCategoryFunctions2   ODECONST ConstantLODE
 ODEEF    ElementaryFunctionODESolver  ODEINT   ODEIntegration
 ODEPACK  AnnaOrdinaryDifferentialEquationPackage
 ODEPAL   PureAlgebraicLODE            ODEPRIM  PrimitiveRatDE
 ODEPRRIC PrimitiveRatRicDE            ODERAT   RationalLODE
 ODERED   ReduceLODE                   ODERTRIC RationalRicDE
 ODESYS   SystemODESolver              ODETOOLS ODETools
 OMEXPR   ExpressionToOpenMath         OMPKG    OpenMathPackage
 OMSERVER OpenMathServerPackage        ONECOMP2 OnePointCompletionFunctions2
 OPQUERY  OperationsQuery
 OPTPACK  AnnaNumericalOptimizationPackage
 ORDCOMP2 OrderedCompletionFunctions2  ORDFUNS  OrderingFunctions
 OREPCTO  UnivariateSkewPolynomialCategoryOps
 ORTHPOL  OrthogonalPolynomialFunctions
 OUT      OutputPackage                PADE     PadeApproximants
 PADEPAC  PadeApproximantPackage       PAN2EXPR PolynomialAN2Expression
 PARPC2   ParametricPlaneCurveFunctions2
 PARSC2   ParametricSpaceCurveFunctions2
 PARSU2   ParametricSurfaceFunctions2  PARTPERM PartitionsAndPermutations
 PATMATCH PatternMatch                 PATRES2  PatternMatchResultFunctions2
 PATTERN1 PatternFunctions1            PATTERN2 PatternFunctions2
 PCOMP    PolynomialComposition        PDECOMP  PolynomialDecomposition
 PDEPACK  AnnaPartialDifferentialEquationPackage
 PERMAN   Permanent
 PFBR     PolynomialFactorizationByRecursion
 PFBRU    PolynomialFactorizationByRecursionUnivariate
 PFO      PointsOfFiniteOrder          PFOQ     PointsOfFiniteOrderRational
 PFOTOOLS PointsOfFiniteOrderTools     PFRPAC   PartialFractionPackage
 PGCD     PolynomialGcdPackage         PGE      PermutationGroupExamples
 PGROEB   PolyGroebner                 PICOERCE PiCoercions
 PINTERP  PolynomialInterpolation
 PINTERPA PolynomialInterpolationAlgorithms
 PLEQN    ParametricLinearEquations    PLOT1    PlotFunctions1
 PLOTTOOL PlotTools                    PMASS    PatternMatchAssertions
 PMASSFS  FunctionSpaceAssertions      PMDOWN   PatternMatchPushDown
 PMFS     PatternMatchFunctionSpace
 PMINS    PatternMatchIntegerNumberSystem
 PMKERNEL PatternMatchKernel           PMLSAGG  PatternMatchListAggregate
 PMPLCAT  PatternMatchPolynomialCategory
 PMPRED   AttachPredicates
 PMPREDFS FunctionSpaceAttachPredicates
 PMQFCAT  PatternMatchQuotientFieldCategory
 PMSYM    PatternMatchSymbol           PMTOOLS  PatternMatchTools
 PNTHEORY PolynomialNumberTheoryFunctions
 POLTOPOL PolToPol
 POLUTIL  RealPolynomialUtilitiesPackage
 POLY2    PolynomialFunctions2
 POLY2UP  PolynomialToUnivariatePolynomial
 POLYCATQ PolynomialCategoryQuotientFunctions
 POLYLIFT PolynomialCategoryLifting    POLYROOT PolynomialRoots
 PREASSOC PrecomputedAssociatedEquations
 PRIMARR2 PrimitiveArrayFunctions2     PRIMELT  PrimitiveElement
 PRIMES   IntegerPrimesPackage         PRINT    PrintPackage
 PRS      PseudoRemainderSequence
 PSETPK   PolynomialSetUtilitiesPackage
 PSEUDLIN PseudoLinearNormalForm       PSQFR    PolynomialSquareFree
 PTFUNC2  PointFunctions2              PTPACK   PointPackage
 PUSHVAR  PushVariables
 PWFFINTB PAdicWildFunctionFieldIntegralBasis
 QALGSET2 QuasiAlgebraicSet2           QCMPACK  QuasiComponentPackage
 QFCAT2   QuotientFieldCategoryFunctions2
 QUATCT2  QuaternionCategoryFunctions2 RADUTIL  RadixUtilities
 RANDSRC  RandomNumberSource           RATFACT  RationalFactorize
 RATRET   RationalRetractions          RDEEF    ElementaryRischDE
 RDEEFS   ElementaryRischDESystem      RDETR    TranscendentalRischDE
 RDETRS   TranscendentalRischDESystem  RDIST    RandomDistributions
 RDIV     ReducedDivisor               REAL0    RealZeroPackage
 REAL0Q   RealZeroPackageQ             REALSOLV RealSolvePackage
 RECOP    RecurrenceOperator           REDORDER ReductionOfOrder
 REP      RadicalEigenPackage          REP1     RepresentationPackage1
 REP2     RepresentationPackage2       REPDB    RepeatedDoubling
 REPSQ    RepeatedSquaring             RESLATC  ResolveLatticeCompletion
 RETSOL   RetractSolvePackage          RF       RationalFunction
 RFDIST   RandomFloatDistributions     RFFACT   RationalFunctionFactor
 RFFACTOR RationalFunctionFactorizer   RIDIST   RandomIntegerDistributions
 RINTERP  RationalInterpolation
 RMCAT2   RectangularMatrixCategoryFunctions2
 RSDCMPK  RegularSetDecompositionPackage
 RSETGCD  RegularTriangularSetGcdPackage
 RURPK    RationalUnivariateRepresentationPackage
 SAEFACT  SimpleAlgebraicExtensionAlgFactor
 SAERFFC  SAERationalFunctionAlgFactor SCACHE   SortedCache
 SCPKG    StructuralConstantsPackage   SEG2     SegmentFunctions2
 SEGBIND2 SegmentBindingFunctions2
 SFQCMPK  SquareFreeQuasiComponentPackage
 SFRGCD   SquareFreeRegularTriangularSetGcdPackage
 SGCF     SymmetricGroupCombinatoricFunctions
 SHP      SturmHabichtPackage          SIGNEF   ElementaryFunctionSign
 SIGNRF   RationalFunctionSign
 SIMPAN   SimplifyAlgebraicNumberConvertPackage
 SMITH    SmithNormalForm              SOLVEFOR PolynomialSolveByFormulas
 SOLVERAD RadicalSolvePackage          SOLVESER TransSolvePackageService
 SOLVETRA TransSolvePackage            SORTPAK  SortPackage
 SPECOUT  SpecialOutputPackage
 SRDCMPK  SquareFreeRegularSetDecompositionPackage
 STINPROD StreamInfiniteProduct        STREAM1  StreamFunctions1
 STREAM2  StreamFunctions2             STREAM3  StreamFunctions3
 STTAYLOR StreamTaylorSeriesOperations
 STTF     StreamTranscendentalFunctions
 STTFNC   StreamTranscendentalFunctionsNonCommutative
 SUBRESP  SubResultantPackage          SUMFS    FunctionSpaceSum
 SUMRF    RationalFunctionSum
 SUP2     SparseUnivariatePolynomialFunctions2
 SUPFRACF SupFractionFactorizer        SYMFUNC  SymmetricFunctions
 SYSSOLP  SystemSolvePackage           TABLBUMP TableauxBumpers
 TANEXP   TangentExpansions            TBCMPPK  TabulatedComputationPackage
 TEMUTL   TemplateUtilities            TEX1     TexFormat1
 TOOLSIGN ToolsForSign                 TOPSP    TopLevelThreeSpace
 TRIGMNIP TrigonometricManipulations   TRIMAT   TriangularMatrixOperations
 TRMANIP  TranscendentalManipulations  TUBETOOL TubePlotTools
 TWOFACT  TwoFactorize                 UDPO     UserDefinedPartialOrdering
 UDVO     UserDefinedVariableOrdering
 UFPS1    UnivariateFormalPowerSeriesFunctions
 ULS2     UnivariateLaurentSeriesFunctions2
 UNIFACT  UnivariateFactorize          UNISEG2  UniversalSegmentFunctions2
 UP2      UnivariatePolynomialFunctions2
 UPCDEN   UnivariatePolynomialCommonDenominator
 UPDECOMP UnivariatePolynomialDecompositionPackage
 UPDIVP   UnivariatePolynomialDivisionPackage
 UPMP     UnivariatePolynomialMultiplicationPackage
 UPOLYC2  UnivariatePolynomialCategoryFunctions2
 UPSQFREE UnivariatePolynomialSquareFree
 UPXS2    UnivariatePuiseuxSeriesFunctions2
 UTS2     UnivariateTaylorSeriesFunctions2
 UTSODE   UnivariateTaylorSeriesODESolver
 UTSODETL UTSodetools                  UTSSOL   TaylorSolve
 VECTOR2  VectorFunctions2             VIEW     ViewportPackage
 VIEWDEF  ViewDefaultsPackage          WEIER    WeierstrassPreparation
 WFFINTBS WildFunctionFieldIntegralBasis
 XEXPPKG  XExponentialPackage
 YSTREAM  ParadoxicalCombinatorsForStreams
 ZDSOLVE  ZeroDimensionalSolvePackage  ZLINDEP  IntegerLinearDependence
--R 
--R-------------------------------- Packages ---------------------------------
--R AF       AlgebraicFunction            ALGFACT  AlgFactor
--R ALGMANIP AlgebraicManipulations       ALGMFACT AlgebraicMultFact
--R ALGPKG   AlgebraPackage               ANY1     AnyFunctions1
--R API      ApplicationProgramInterface
--R APPLYORE ApplyUnivariateSkewPolynomial
--R APPRULE  ApplyRules
--R ARRAY12  OneDimensionalArrayFunctions2
--R ASSOCEQ  AssociatedEquations          AXSERV   AxiomServer
--R BALFACT  BalancedFactorisation        BEZIER   Bezier
--R BEZOUT   BezoutMatrix                 BOP1     BasicOperatorFunctions1
--R BOUNDZRO BoundIntegerRoots            BRILL    BrillhartTests
--R CARTEN2  CartesianTensorFunctions2    CDEN     CommonDenominator
--R CHARPOL  CharacteristicPolynomialPackage
--R CHVAR    ChangeOfVariable
--R CINTSLPE ComplexIntegerSolveLinearPolynomialEquation
--R CLIP     TwoDimensionalPlotClipping   CMPLXRT  ComplexRootPackage
--R COMBF    CombinatorialFunction        COMBINAT IntegerCombinatoricFunctions
--R COMMONOP CommonOperators
--R COMMUPC  CommuteUnivariatePolynomialCategory
--R COMPFACT ComplexFactorization         COMPLEX2 ComplexFunctions2
--R COMPLPAT ComplexPattern               COORDSYS CoordinateSystems
--R CPIMA    CharacteristicPolynomialInMonogenicalAlgebra
--R CPMATCH  ComplexPatternMatch          CRAPACK  CRApackage
--R CRFP     ComplexRootFindingPackage    CSTTOOLS CyclicStreamTools
--R CTRIGMNP ComplexTrigonometricManipulations
--R CVMP     CoerceVectorMatrixPackage    CYCLES   CycleIndicators
--R CYCLOTOM CyclotomicPolynomialPackage  D01AGNT  d01AgentsPackage
--R D01WGTS  d01WeightsPackage            D02AGNT  d02AgentsPackage
--R D03AGNT  d03AgentsPackage             DBLRESP  DoubleResultantPackage
--R DDFACT   DistinctDegreeFactorize
--R DEFINTEF ElementaryFunctionDefiniteIntegration
--R DEFINTRF RationalFunctionDefiniteIntegration
--R DEGRED   DegreeReductionPackage       DFINTTLS DefiniteIntegrationTools
--R DFSFUN   DoubleFloatSpecialFunctions  DIOSP    DiophantineSolutionPackage
--R DIRPROD2 DirectProductFunctions2      DISPLAY  DisplayPackage
--R DLP      DiscreteLogarithmPackage     DRAW     TopLevelDrawFunctions
--R DRAWCFUN TopLevelDrawFunctionsForCompiledFunctions
--R DRAWCURV TopLevelDrawFunctionsForAlgebraicCurves
--R DRAWCX   DrawComplex                  DRAWHACK DrawNumericHack
--R DRAWPT   TopLevelDrawFunctionsForPoints
--R DROPT0   DrawOptionFunctions0         DROPT1   DrawOptionFunctions1
--R E04AGNT  e04AgentsPackage             EF       ElementaryFunction
--R EFSTRUC  ElementaryFunctionStructurePackage
--R ELFUTS   EllipticFunctionsUnivariateTaylorSeries
--R EP       EigenPackage                 EQ2      EquationFunctions2
--R ERROR    ErrorFunctions               ES1      ExpressionSpaceFunctions1
--R ES2      ExpressionSpaceFunctions2
--R ESCONT   ExpertSystemContinuityPackage
--R ESCONT1  ExpertSystemContinuityPackage1
--R ESTOOLS  ExpertSystemToolsPackage     ESTOOLS1 ExpertSystemToolsPackage1
--R ESTOOLS2 ExpertSystemToolsPackage2    EVALCYC  EvaluateCycleIndicators
--R EXPR2    ExpressionFunctions2
--R EXPR2UPS ExpressionToUnivariatePowerSeries
--R EXPRODE  ExpressionSpaceODESolver     EXPRSOL  ExpressionSolve
--R EXPRTUBE ExpressionTubePlot           FACTFUNC FactoredFunctions
--R FACUTIL  FactoringUtilities
--R FAMR2    FiniteAbelianMonoidRingFunctions2
--R FCPAK1   FortranCodePackage1          FDIV2    FiniteDivisorFunctions2
--R FFCAT2   FunctionFieldCategoryFunctions2
--R FFF      FiniteFieldFunctions         FFFG     FractionFreeFastGaussian
--R FFFGF    FractionFreeFastGaussianFractions
--R FFHOM    FiniteFieldHomomorphisms     FFINTBAS FunctionFieldIntegralBasis
--R FFPOLY   FiniteFieldPolynomialPackage
--R FFPOLY2  FiniteFieldPolynomialPackage2
--R FFSLPE   FiniteFieldSolveLinearPolynomialEquation
--R FGLMICPK FGLMIfCanPackage
--R FLAGG2   FiniteLinearAggregateFunctions2
--R FLASORT  FiniteLinearAggregateSort    FLOATCP  FloatingComplexPackage
--R FLOATRP  FloatingRealPackage          FOP      FortranOutputStackPackage
--R FORDER   FindOrderFinite              FORMULA1 ScriptFormulaFormat1
--R FORT     FortranPackage               FR2      FactoredFunctions2
--R FRAC2    FractionFunctions2           FRIDEAL2 FractionalIdealFunctions2
--R FRNAAF2  FramedNonAssociativeAlgebraFunctions2
--R FRUTIL   FactoredFunctionUtilities    FS2      FunctionSpaceFunctions2
--R FS2EXPXP FunctionSpaceToExponentialExpansion
--R FS2UPS   FunctionSpaceToUnivariatePowerSeries
--R FSAGG2   FiniteSetAggregateFunctions2
--R FSCINT   FunctionSpaceComplexIntegration
--R FSINT    FunctionSpaceIntegration     FSPECF   FunctionalSpecialFunction
--R FSPRMELT FunctionSpacePrimitiveElement
--R FSRED    FunctionSpaceReduce
--R FSUPFACT FunctionSpaceUnivariatePolynomialFactor
--R GALFACT  GaloisGroupFactorizer
--R GALFACTU GaloisGroupFactorizationUtilities
--R GALPOLYU GaloisGroupPolynomialUtilities
--R GALUTIL  GaloisGroupUtilities         GAUSSFAC GaussianFactorizationPackage
--R GB       GroebnerPackage
--R GBEUCLID EuclideanGroebnerBasisPackage
--R GBF      GroebnerFactorizationPackage GBINTERN GroebnerInternalPackage
--R GENEEZ   GenExEuclid
--R GENMFACT GeneralizedMultivariateFactorize
--R GENPGCD  GeneralPolynomialGcdPackage  GENUFACT GenUFactorize
--R GENUPS   GenerateUnivariatePowerSeries
--R GHENSEL  GeneralHenselPackage         GOSPER   GosperSummationMethod
--R GRAY     GrayCode                     GRDEF    GraphicsDefaults
--R GROEBSOL GroebnerSolve                GUESS    Guess
--R GUESSAN  GuessAlgebraicNumber         GUESSF   GuessFinite
--R GUESSF1  GuessFiniteFunctions         GUESSINT GuessInteger
--R GUESSP   GuessPolynomial              GUESSUP  GuessUnivariatePolynomial
--R HB       HallBasis                    HEUGCD   HeuGcd
--R IALGFACT InnerAlgFactor
--R IBACHIN  ChineseRemainderToolsForIntegralBases
--R IBATOOL  IntegralBasisTools           IBPTOOLS IntegralBasisPolynomialTools
--R ICDEN    InnerCommonDenominator       IDECOMP  IdealDecompositionPackage
--R IMATLIN  InnerMatrixLinearAlgebraFunctions
--R IMATQF   InnerMatrixQuotientFieldFunctions
--R INBFF    InnerNormalBasisFieldFunctions
--R INCRMAPS IncrementingMaps             INEP     InnerNumericEigenPackage
--R INFINITY Infinity                     INFORM1  InputFormFunctions1
--R INFPROD0 InfiniteProductCharacteristicZero
--R INFSP    InnerNumericFloatSolvePackage
--R INMODGCD InnerModularGcd              INNMFACT InnerMultFact
--R INPRODFF InfiniteProductFiniteField   INPRODPF InfiniteProductPrimeField
--R INPSIGN  InnerPolySign                INTAF    AlgebraicIntegration
--R INTALG   AlgebraicIntegrate           INTBIT   IntegerBits
--R INTEF    ElementaryIntegration        INTFACT  IntegerFactorizationPackage
--R INTG0    GenusZeroIntegration         INTHEORY IntegerNumberTheoryFunctions
--R INTHERAL AlgebraicHermiteIntegration
--R INTHERTR TranscendentalHermiteIntegration
--R INTPACK  AnnaNumericalIntegrationPackage
--R INTPAF   PureAlgebraicIntegration     INTPM    PatternMatchIntegration
--R INTRAT   RationalIntegration          INTRET   IntegerRetractions
--R INTRF    RationalFunctionIntegration
--R INTSLPE  IntegerSolveLinearPolynomialEquation
--R INTTOOLS IntegrationTools             INTTR    TranscendentalIntegration
--R INVLAPLA InverseLaplaceTransform      IPRNTPK  InternalPrintPackage
--R IR2      IntegrationResultFunctions2  IR2F     IntegrationResultToFunction
--R IROOT    IntegerRoots                 IRREDFFX IrredPolyOverFiniteField
--R IRRF2F   IntegrationResultRFToFunction
--R IRSN     IrrRepSymNatPackage
--R IRURPK   InternalRationalUnivariateRepresentationPackage
--R ISUMP    InnerPolySum                 ITFUN2   InfiniteTupleFunctions2
--R ITFUN3   InfiniteTupleFunctions3
--R ITRIGMNP InnerTrigonometricManipulations
--R KERNEL2  KernelFunctions2             KOVACIC  Kovacic
--R LAPLACE  LaplaceTransform             LAZM3PK  LazardSetSolvingPackage
--R LEADCDET LeadingCoefDetermination     LEXTRIPK LexTriangularPackage
--R LF       LiouvillianFunction          LGROBP   LinGroebnerPackage
--R LIMITPS  PowerSeriesLimitPackage      LIMITRF  RationalFunctionLimitPackage
--R LINDEP   LinearDependence             LIST2    ListFunctions2
--R LIST2MAP ListToMap                    LIST3    ListFunctions3
--R LODEEF   ElementaryFunctionLODESolver
--R LODOF    LinearOrdinaryDifferentialOperatorFactorizer
--R LODOOPS  LinearOrdinaryDifferentialOperatorsOps
--R LPEFRAC  LinearPolynomialEquationByFractions
--R LSMP     LinearSystemMatrixPackage    LSMP1    LinearSystemMatrixPackage1
--R LSPP     LinearSystemPolynomialPackage
--R MAPHACK1 MappingPackageInternalHacks1 MAPHACK2 MappingPackageInternalHacks2
--R MAPHACK3 MappingPackageInternalHacks3 MAPPKG1  MappingPackage1
--R MAPPKG2  MappingPackage2              MAPPKG3  MappingPackage3
--R MAPPKG4  MappingPackage4              MATCAT2  MatrixCategoryFunctions2
--R MATLIN   MatrixLinearAlgebraFunctions
--R MATSTOR  StorageEfficientMatrixOperations
--R MCALCFN  MultiVariableCalculusFunctions
--R MCDEN    MatrixCommonDenominator
--R MDDFACT  ModularDistinctDegreeFactorizer
--R MESH     MeshCreationRoutinesForThreeDimensions
--R MFINFACT MultFiniteFactorize          MHROWRED ModularHermitianRowReduction
--R MKBCFUNC MakeBinaryCompiledFunction   MKFLCFN  MakeFloatCompiledFunction
--R MKFUNC   MakeFunction                 MKRECORD MakeRecord
--R MKUCFUNC MakeUnaryCompiledFunction    MLIFT    MultivariateLifting
--R MMAP     MultipleMap                  MONOTOOL MonomialExtensionTools
--R MPC2     MPolyCatFunctions2           MPC3     MPolyCatFunctions3
--R MPCPF    MPolyCatPolyFactorizer
--R MPRFF    MPolyCatRationalFunctionFactorizer
--R MRATFAC  MRationalFactorize           MRF2     MonoidRingFunctions2
--R MSYSCMD  MoreSystemCommands           MTHING   MergeThing
--R MULTFACT MultivariateFactorize        MULTSQFR MultivariateSquareFree
--R NAGC02   NagPolynomialRootsPackage    NAGC05   NagRootFindingPackage
--R NAGC06   NagSeriesSummationPackage    NAGD01   NagIntegrationPackage
--R NAGD02   NagOrdinaryDifferentialEquationsPackage
--R NAGD03   NagPartialDifferentialEquationsPackage
--R NAGE01   NagInterpolationPackage      NAGE02   NagFittingPackage
--R NAGE04   NagOptimisationPackage       NAGF01   NagMatrixOperationsPackage
--R NAGF02   NagEigenPackage
--R NAGF04   NagLinearEquationSolvingPackage
--R NAGF07   NagLapack                    NAGS     NagSpecialFunctionsPackage
--R NAGSP    NAGLinkSupportPackage        NCEP     NumericComplexEigenPackage
--R NCNTFRAC NumericContinuedFraction
--R NCODIV   NonCommutativeOperatorDivision
--R NEWTON   NewtonInterpolation          NFINTBAS NumberFieldIntegralBasis
--R NLINSOL  NonLinearSolvePackage        NODE1    NonLinearFirstOrderODESolver
--R NONE1    NoneFunctions1               NORMMA   NormInMonogenicAlgebra
--R NORMPK   NormalizationPackage         NORMRETR NormRetractPackage
--R NPCOEF   NPCoef                       NREP     NumericRealEigenPackage
--R NSUP2    NewSparseUnivariatePolynomialFunctions2
--R NTPOLFN  NumberTheoreticPolynomialFunctions
--R NUMERIC  Numeric                      NUMFMT   NumberFormats
--R NUMODE   NumericalOrdinaryDifferentialEquations
--R NUMQUAD  NumericalQuadrature          NUMTUBE  NumericTubePlot
--R OCTCT2   OctonionCategoryFunctions2   ODECONST ConstantLODE
--R ODEEF    ElementaryFunctionODESolver  ODEINT   ODEIntegration
--R ODEPACK  AnnaOrdinaryDifferentialEquationPackage
--R ODEPAL   PureAlgebraicLODE            ODEPRIM  PrimitiveRatDE
--R ODEPRRIC PrimitiveRatRicDE            ODERAT   RationalLODE
--R ODERED   ReduceLODE                   ODERTRIC RationalRicDE
--R ODESYS   SystemODESolver              ODETOOLS ODETools
--R OMEXPR   ExpressionToOpenMath         OMPKG    OpenMathPackage
--R OMSERVER OpenMathServerPackage        ONECOMP2 OnePointCompletionFunctions2
--R OPQUERY  OperationsQuery
--R OPTPACK  AnnaNumericalOptimizationPackage
--R ORDCOMP2 OrderedCompletionFunctions2  ORDFUNS  OrderingFunctions
--R OREPCTO  UnivariateSkewPolynomialCategoryOps
--R ORTHPOL  OrthogonalPolynomialFunctions
--R OUT      OutputPackage                PADE     PadeApproximants
--R PADEPAC  PadeApproximantPackage       PAN2EXPR PolynomialAN2Expression
--R PARPC2   ParametricPlaneCurveFunctions2
--R PARSC2   ParametricSpaceCurveFunctions2
--R PARSU2   ParametricSurfaceFunctions2  PARTPERM PartitionsAndPermutations
--R PATMATCH PatternMatch                 PATRES2  PatternMatchResultFunctions2
--R PATTERN1 PatternFunctions1            PATTERN2 PatternFunctions2
--R PCOMP    PolynomialComposition        PDECOMP  PolynomialDecomposition
--R PDEPACK  AnnaPartialDifferentialEquationPackage
--R PERMAN   Permanent
--R PFBR     PolynomialFactorizationByRecursion
--R PFBRU    PolynomialFactorizationByRecursionUnivariate
--R PFO      PointsOfFiniteOrder          PFOQ     PointsOfFiniteOrderRational
--R PFOTOOLS PointsOfFiniteOrderTools     PFRPAC   PartialFractionPackage
--R PGCD     PolynomialGcdPackage         PGE      PermutationGroupExamples
--R PGROEB   PolyGroebner                 PICOERCE PiCoercions
--R PINTERP  PolynomialInterpolation
--R PINTERPA PolynomialInterpolationAlgorithms
--R PLEQN    ParametricLinearEquations    PLOT1    PlotFunctions1
--R PLOTTOOL PlotTools                    PMASS    PatternMatchAssertions
--R PMASSFS  FunctionSpaceAssertions      PMDOWN   PatternMatchPushDown
--R PMFS     PatternMatchFunctionSpace
--R PMINS    PatternMatchIntegerNumberSystem
--R PMKERNEL PatternMatchKernel           PMLSAGG  PatternMatchListAggregate
--R PMPLCAT  PatternMatchPolynomialCategory
--R PMPRED   AttachPredicates
--R PMPREDFS FunctionSpaceAttachPredicates
--R PMQFCAT  PatternMatchQuotientFieldCategory
--R PMSYM    PatternMatchSymbol           PMTOOLS  PatternMatchTools
--R PNTHEORY PolynomialNumberTheoryFunctions
--R POLTOPOL PolToPol
--R POLUTIL  RealPolynomialUtilitiesPackage
--R POLY2    PolynomialFunctions2
--R POLY2UP  PolynomialToUnivariatePolynomial
--R POLYCATQ PolynomialCategoryQuotientFunctions
--R POLYLIFT PolynomialCategoryLifting    POLYROOT PolynomialRoots
--R PREASSOC PrecomputedAssociatedEquations
--R PRIMARR2 PrimitiveArrayFunctions2     PRIMELT  PrimitiveElement
--R PRIMES   IntegerPrimesPackage         PRINT    PrintPackage
--R PRS      PseudoRemainderSequence
--R PSETPK   PolynomialSetUtilitiesPackage
--R PSEUDLIN PseudoLinearNormalForm       PSQFR    PolynomialSquareFree
--R PTFUNC2  PointFunctions2              PTPACK   PointPackage
--R PUSHVAR  PushVariables
--R PWFFINTB PAdicWildFunctionFieldIntegralBasis
--R QALGSET2 QuasiAlgebraicSet2           QCMPACK  QuasiComponentPackage
--R QFCAT2   QuotientFieldCategoryFunctions2
--R QUATCT2  QuaternionCategoryFunctions2 RADUTIL  RadixUtilities
--R RANDSRC  RandomNumberSource           RATFACT  RationalFactorize
--R RATRET   RationalRetractions          RDEEF    ElementaryRischDE
--R RDEEFS   ElementaryRischDESystem      RDETR    TranscendentalRischDE
--R RDETRS   TranscendentalRischDESystem  RDIST    RandomDistributions
--R RDIV     ReducedDivisor               REAL0    RealZeroPackage
--R REAL0Q   RealZeroPackageQ             REALSOLV RealSolvePackage
--R RECOP    RecurrenceOperator           REDORDER ReductionOfOrder
--R REP      RadicalEigenPackage          REP1     RepresentationPackage1
--R REP2     RepresentationPackage2       REPDB    RepeatedDoubling
--R REPSQ    RepeatedSquaring             RESLATC  ResolveLatticeCompletion
--R RETSOL   RetractSolvePackage          RF       RationalFunction
--R RFDIST   RandomFloatDistributions     RFFACT   RationalFunctionFactor
--R RFFACTOR RationalFunctionFactorizer   RIDIST   RandomIntegerDistributions
--R RINTERP  RationalInterpolation
--R RMCAT2   RectangularMatrixCategoryFunctions2
--R RSDCMPK  RegularSetDecompositionPackage
--R RSETGCD  RegularTriangularSetGcdPackage
--R RURPK    RationalUnivariateRepresentationPackage
--R SAEFACT  SimpleAlgebraicExtensionAlgFactor
--R SAERFFC  SAERationalFunctionAlgFactor SCACHE   SortedCache
--R SCPKG    StructuralConstantsPackage   SEG2     SegmentFunctions2
--R SEGBIND2 SegmentBindingFunctions2
--R SFQCMPK  SquareFreeQuasiComponentPackage
--R SFRGCD   SquareFreeRegularTriangularSetGcdPackage
--R SGCF     SymmetricGroupCombinatoricFunctions
--R SHP      SturmHabichtPackage          SIGNEF   ElementaryFunctionSign
--R SIGNRF   RationalFunctionSign
--R SIMPAN   SimplifyAlgebraicNumberConvertPackage
--R SMITH    SmithNormalForm              SOLVEFOR PolynomialSolveByFormulas
--R SOLVERAD RadicalSolvePackage          SOLVESER TransSolvePackageService
--R SOLVETRA TransSolvePackage            SORTPAK  SortPackage
--R SPECOUT  SpecialOutputPackage
--R SRDCMPK  SquareFreeRegularSetDecompositionPackage
--R STINPROD StreamInfiniteProduct        STREAM1  StreamFunctions1
--R STREAM2  StreamFunctions2             STREAM3  StreamFunctions3
--R STTAYLOR StreamTaylorSeriesOperations
--R STTF     StreamTranscendentalFunctions
--R STTFNC   StreamTranscendentalFunctionsNonCommutative
--R SUBRESP  SubResultantPackage          SUMFS    FunctionSpaceSum
--R SUMRF    RationalFunctionSum
--R SUP2     SparseUnivariatePolynomialFunctions2
--R SUPFRACF SupFractionFactorizer        SYMFUNC  SymmetricFunctions
--R SYSSOLP  SystemSolvePackage           TABLBUMP TableauxBumpers
--R TANEXP   TangentExpansions            TBCMPPK  TabulatedComputationPackage
--R TEMUTL   TemplateUtilities            TEX1     TexFormat1
--R TOOLSIGN ToolsForSign                 TOPSP    TopLevelThreeSpace
--R TRIGMNIP TrigonometricManipulations   TRIMAT   TriangularMatrixOperations
--R TRMANIP  TranscendentalManipulations  TUBETOOL TubePlotTools
--R TWOFACT  TwoFactorize                 UDPO     UserDefinedPartialOrdering
--R UDVO     UserDefinedVariableOrdering
--R UFPS1    UnivariateFormalPowerSeriesFunctions
--R ULS2     UnivariateLaurentSeriesFunctions2
--R UNIFACT  UnivariateFactorize          UNISEG2  UniversalSegmentFunctions2
--R UP2      UnivariatePolynomialFunctions2
--R UPCDEN   UnivariatePolynomialCommonDenominator
--R UPDECOMP UnivariatePolynomialDecompositionPackage
--R UPDIVP   UnivariatePolynomialDivisionPackage
--R UPMP     UnivariatePolynomialMultiplicationPackage
--R UPOLYC2  UnivariatePolynomialCategoryFunctions2
--R UPSQFREE UnivariatePolynomialSquareFree
--R UPXS2    UnivariatePuiseuxSeriesFunctions2
--R UTS2     UnivariateTaylorSeriesFunctions2
--R UTSODE   UnivariateTaylorSeriesODESolver
--R UTSODETL UTSodetools                  UTSSOL   TaylorSolve
--R VECTOR2  VectorFunctions2             VIEW     ViewportPackage
--R VIEWDEF  ViewDefaultsPackage          WEIER    WeierstrassPreparation
--R WFFINTBS WildFunctionFieldIntegralBasis
--R XEXPPKG  XExponentialPackage
--R YSTREAM  ParadoxicalCombinatorsForStreams
--R ZDSOLVE  ZeroDimensionalSolvePackage  ZLINDEP  IntegerLinearDependence
--E 15

--S 16 of 23
)set compiler
 
                  Current Values of  compiler  Variables                   

Variable     Description                                Current Value
-----------------------------------------------------------------------------
output       library in which to place compiled code    user.lib 
input        controls libraries from which to load compiled code  
args         arguments for compiling AXIOM code         -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra 

--R 
--R                  Current Values of  compiler  Variables                   
--R
--RVariable     Description                                Current Value
--R-----------------------------------------------------------------------------
--Routput       library in which to place compiled code    user.lib 
--Rinput        controls libraries from which to load compiled code  
--Rargs         arguments for compiling AXIOM code         -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra 
--R
--E 16

--S 17 of 23
)set compiler input
 
---------------------------- The input Option -----------------------------

 Description: controls libraries from which to load compiled code

 )set compiler input add library is used to tell AXIOM to add library to
the front of the path used to find compile code.
 )set compiler input drop library is used to tell AXIOM to remove library 
from this path.
--R 
--R---------------------------- The input Option -----------------------------
--R
--R Description: controls libraries from which to load compiled code
--R
--R )set compiler input add library is used to tell AXIOM to add library to
--Rthe front of the path used to find compile code.
--R )set compiler input drop library is used to tell AXIOM to remove library 
--Rfrom this path.
--E 17

--S 18 of 23
)set compiler input add
 
 )set compiler input add library is used to tell AXIOM to add library to
the front of the path used to find compile code.
 )set compiler input drop library is used to tell AXIOM to remove library 
from this path.
--R 
--R )set compiler input add library is used to tell AXIOM to add library to
--Rthe front of the path used to find compile code.
--R )set compiler input drop library is used to tell AXIOM to remove library 
--Rfrom this path.
--E 18

--S 19 of 23
)set compiler input add foo
 
--E 19

--S 20 of 23
)set compiler output
 
---------------------------- The output Option ----------------------------

 Description: library in which to place compiled code

 )set compiler output library is used to tell the compiler where to place
compiled code generated by the library compiler.  By default it goes
in a file called user.lib in the current directory.
--R---------------------------- The output Option ----------------------------
--R
--R Description: library in which to place compiled code
--R
--R )set compiler output library is used to tell the compiler where to place
--Rcompiled code generated by the library compiler.  By default it goes
--Rin a file called user.lib in the current directory.
--E 20

--S 21 of 23
)set compiler args
 
----------------------------- The args Option -----------------------------

 Description: arguments for compiling AXIOM code

 )set compiler args  is used to tell AXIOM how to invoke the library compiler 
 when compiling code for AXIOM.
 The args option is followed by a string enclosed in double quotes.

 The current setting is
 "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra" 
--R----------------------------- The args Option -----------------------------
--R
--R Description: arguments for compiling AXIOM code
--R
--R )set compiler args  is used to tell AXIOM how to invoke the library compiler 
--R when compiling code for AXIOM.
--R The args option is followed by a string enclosed in double quotes.
--R
--R The current setting is
--R "-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra" 
--E 21

--S 22 of 23
)set compiler args "-TPD"
 
--E 22

--S 23 of 23
)set compiler args
 
----------------------------- The args Option -----------------------------

 Description: arguments for compiling AXIOM code

 )set compiler args  is used to tell AXIOM how to invoke the library compiler 
 when compiling code for AXIOM.
 The args option is followed by a string enclosed in double quotes.

 The current setting is
 "-TPD" 
--R----------------------------- The args Option -----------------------------
--R
--R Description: arguments for compiling AXIOM code
--R
--R )set compiler args  is used to tell AXIOM how to invoke the library compiler 
--R when compiling code for AXIOM.
--R The args option is followed by a string enclosed in double quotes.
--R
--R The current setting is
--R "-TPD" 
--E 23

)spool 
 
Starts dribbling to ruleset.output (2010/3/27, 18:36:57).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 9
TrigLinearRules := rule
   sin(x) * sin(y) == cos(x-y)/2 - cos(x+y)/2
   cos(x) * cos(y) == cos(x+y)/2 + cos(x-y)/2
   sin(x) * cos(y) == sin(x+y)/2 + sin(x-y)/2
   sin(x)**(n | integer? n and n > 0) == (1-cos(2*x))/2 * sin(x)**(n-2)
   cos(x)**(n | integer? n and n > 0) == (1+cos(2*x))/2 * cos(x)**(n-2)
 

   (1)
                       - %B cos(y + x) + %B cos(y - x)
   {%B sin(x)sin(y) == -------------------------------,
                                      2
                       %C cos(y + x) + %C cos(y - x)
    %C cos(x)cos(y) == -----------------------------,
                                     2
                       %D sin(y + x) - %D sin(y - x)
    %D cos(y)sin(x) == -----------------------------,
                                     2
                                    n - 2                                n - 2
          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
    sin(x)  == --------------------------, cos(x)  == ------------------------}
                            2                                     2
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)
--R                       - %B cos(y + x) + %B cos(y - x)
--R   {%B sin(x)sin(y) == -------------------------------,
--R                                      2
--R                       %C cos(y + x) + %C cos(y - x)
--R    %C cos(x)cos(y) == -----------------------------,
--R                                     2
--R                       %D sin(y + x) - %D sin(y - x)
--R    %D cos(y)sin(x) == -----------------------------,
--R                                     2
--R                                    n - 2                                n - 2
--R          n    (- cos(2x) + 1)sin(x)             n    (cos(2x) + 1)cos(x)
--R    sin(x)  == --------------------------, cos(x)  == ------------------------}
--R                            2                                     2
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 1

--S 2 of 9
sin(a)*cos(b) + sin(a)*cos(a) + cos(2*a)*cos(3*a)
 

   (2)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
                                                     Type: Expression Integer
--R 
--R
--R   (2)  (cos(b) + cos(a))sin(a) + cos(2a)cos(3a)
--R                                                     Type: Expression Integer
--E 2

--S 3 of 9
TrigLinearRules %
 

        sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
   (3)  ----------------------------------------------------
                                  2
                                                     Type: Expression Integer
--R 
--R
--R        sin(b + a) - sin(b - a) + sin(2a) + cos(5a) + cos(a)
--R   (3)  ----------------------------------------------------
--R                                  2
--R                                                     Type: Expression Integer
--E 3

--S 4 of 9
sin(a) * sin(2*a) * sin(3*a) * sin(4*a)
 

   (4)  sin(a)sin(2a)sin(3a)sin(4a)
                                                     Type: Expression Integer
--R 
--R
--R   (4)  sin(a)sin(2a)sin(3a)sin(4a)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 9
TrigLinearRules %
 

        cos(10a) - cos(8a) - cos(6a) + 1
   (5)  --------------------------------
                        8
                                                     Type: Expression Integer
--R 
--R
--R        cos(10a) - cos(8a) - cos(6a) + 1
--R   (5)  --------------------------------
--R                        8
--R                                                     Type: Expression Integer
--E 5

--S 6 of 9
f := operator 'f
 

   (6)  f
                                                          Type: BasicOperator
--R 
--R
--R   (6)  f
--R                                                          Type: BasicOperator
--E 6

--S 7 of 9
FLinearRules := rule
  f(a + b, x) == f(a, x) + f(b, x)
  f(c * a, x | freeOf?(c, x)) == c * f(a, x)
 

   (7)  {f(b + a,x) == 'f(b,x) + 'f(a,x),f(a c,x) == c'f(a,x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (7)  {f(b + a,x) == 'f(b,x) + 'f(a,x),f(a c,x) == c'f(a,x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 7

--S 8 of 9
f(2*x + a * log(x) + x * log(x), x)
 

   (8)  f((x + a)log(x) + 2x,x)
                                                     Type: Expression Integer
--R 
--R
--R   (8)  f((x + a)log(x) + 2x,x)
--R                                                     Type: Expression Integer
--E 8

--S 9 of 9
FLinearRules %
 

   (9)  (f(x,x) + f(a,x))log(x) + 2f(x,x)
                                                     Type: Expression Integer
--R 
--R
--R   (9)  (f(x,x) + f(a,x))log(x) + 2f(x,x)
--R                                                     Type: Expression Integer
--E 9
)spool 
 
Starts dribbling to LazardSetSolvingPackage.output (2010/3/27, 18:42:23).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 36
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
ls : List Symbol := [b1,x,y,z,t,v,u,w] 
 

   (2)  [b1,x,y,z,t,v,u,w]
                                                            Type: List Symbol
--R
--R   (2)  [b1,x,y,z,t,v,u,w]
--R                                                            Type: List Symbol
--E 2

--S 3 of 36
V := OVAR(ls)
 

   (3)  OrderedVariableList [b1,x,y,z,t,v,u,w]
                                                                 Type: Domain
--R
--R   (3)  OrderedVariableList [b1,x,y,z,t,v,u,w]
--R                                                                 Type: Domain
--E 3

--S 4 of 36
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w]
                                                                 Type: Domain
--R
--R   (4)  IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w]
--R                                                                 Type: Domain
--E 4

--S 5 of 36
P := NSMP(R, V)
 

   (5)
  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w
  ])
                                                                 Type: Domain
--R
--R   (5)
--R  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w
--R  ])
--R                                                                 Type: Domain
--E 5

--S 6 of 36
b1: P := 'b1
 

   (6)  b1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (6)  b1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 6

--S 7 of 36
x: P := 'x
 

   (7)  x
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (7)  x
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 7

--S 8 of 36
y: P := 'y
 

   (8)  y
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (8)  y
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 8

--S 9 of 36
z: P := 'z
 

   (9)  z
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (9)  z
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 9

--S 10 of 36
t: P := 't
 

   (10)  t
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (10)  t
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 10

--S 11 of 36
u: P := 'u
 

   (11)  u
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (11)  u
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 11

--S 12 of 36
v: P := 'v
 

   (12)  v
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (12)  v
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 12

--S 13 of 36
w: P := 'w
 

   (13)  w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (13)  w
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 13

--S 14 of 36
T := REGSET(R,E,V,P)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R
--R   (14)
--R  RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t
--R  ,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomia
--R  l(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R                                                                 Type: Domain
--E 14

--S 15 of 36
p0 := b1 + y + z - t - w
 

   (14)  b1 + y + z - t - w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (15)  b1 + y + z - t - w
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 15

--S 16 of 36
p1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1
 

                                2
   (15)  2v y + 2u z + 2w t - 2w  - w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R                                2
--R   (16)  2v y + 2u z + 2w t - 2w  - w - 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 16

--S 17 of 36
p2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w
 

           2      2         2           3     2
   (16)  3v y + 3u z + (- 3w  - 1)t + 3w  + 3w  + 4w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R           2      2         2           3     2
--R   (17)  3v y + 3u z + (- 3w  - 1)t + 3w  + 3w  + 4w
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 17

--S 18 of 36
p3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w
 

                       2                3     2
   (17)  6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R                       2                3     2
--R   (18)  6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 18

--S 19 of 36
p4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1
 

           3      3       3            4     3      2
   (18)  4v y + 4u z + (4w  + 4w)t - 4w  - 6w  - 10w  - w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R           3      3       3            4     3      2
--R   (19)  4v y + 4u z + (4w  + 4w)t - 4w  - 6w  - 10w  - w - 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 19

--S 20 of 36
p5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1
 

                       3     2            4      3      2
   (19)  8u v z x + (8w  + 4w  + 4w)t - 8w  - 12w  - 14w  - 3w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R                       3     2            4      3      2
--R   (20)  8u v z x + (8w  + 4w  + 4w)t - 8w  - 12w  - 14w  - 3w - 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 20

--S 21 of 36
p6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1
 

            2          3      2             4      3      2
   (20)  12v z x + (12w  + 12w  + 8w)t - 12w  - 18w  - 14w  - w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R            2          3      2             4      3      2
--R   (21)  12v z x + (12w  + 12w  + 8w)t - 12w  - 18w  - 14w  - w - 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 21

--S 22 of 36
p7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1
 

               3      2             4      3      2
   (21)  (- 24w  - 24w  - 8w)t + 24w  + 36w  + 26w  + 7w + 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R               3      2             4      3      2
--R   (22)  (- 24w  - 24w  - 8w)t + 24w  + 36w  + 26w  + 7w + 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 22

--S 23 of 36
lp := [p0, p1, p2, p3, p4, p5, p6, p7]
 

   (22)
                                               2
   [b1 + y + z - t - w, 2v y + 2u z + 2w t - 2w  - w - 1,
      2      2         2           3     2
    3v y + 3u z + (- 3w  - 1)t + 3w  + 3w  + 4w,
                  2                3     2
    6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w,
      3      3       3            4     3      2
    4v y + 4u z + (4w  + 4w)t - 4w  - 6w  - 10w  - w - 1,
                  3     2            4      3      2
    8u v z x + (8w  + 4w  + 4w)t - 8w  - 12w  - 14w  - 3w - 1,
       2          3      2             4      3      2
    12v z x + (12w  + 12w  + 8w)t - 12w  - 18w  - 14w  - w - 1,
          3      2             4      3      2
    (- 24w  - 24w  - 8w)t + 24w  + 36w  + 26w  + 7w + 1]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (23)
--R                                               2
--R   [b1 + y + z - t - w, 2v y + 2u z + 2w t - 2w  - w - 1,
--R      2      2         2           3     2
--R    3v y + 3u z + (- 3w  - 1)t + 3w  + 3w  + 4w,
--R                  2                3     2
--R    6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w,
--R      3      3       3            4     3      2
--R    4v y + 4u z + (4w  + 4w)t - 4w  - 6w  - 10w  - w - 1,
--R                  3     2            4      3      2
--R    8u v z x + (8w  + 4w  + 4w)t - 8w  - 12w  - 14w  - 3w - 1,
--R       2          3      2             4      3      2
--R    12v z x + (12w  + 12w  + 8w)t - 12w  - 18w  - 14w  - w - 1,
--R          3      2             4      3      2
--R    (- 24w  - 24w  - 8w)t + 24w  + 36w  + 26w  + 7w + 1]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 23

--S 24 of 36
lts := zeroSetSplit(lp,false)$T
 

   (23)
   [{w + 1,u,v,t + 1,b1 + y + z + 2}, {w + 1,v,t + 1,z,b1 + y + 2},
    {w + 1,t + 1,z,y,b1 + 2}, {w + 1,v - u,t + 1,y + z,x,b1 + 2},
    {w + 1,u,t + 1,y,x,b1 + z + 2},

          5       4      3     2
     {144w  + 216w  + 96w  + 6w  - 11w - 1,
          2                 5       4      3     2
      (12w  + 9w + 1)u - 72w  - 108w  - 42w  - 9w  - 3w,
          2                 4      3      2
      (12w  + 9w + 1)v + 36w  + 54w  + 18w ,
          3      2             4      3      2
      (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,

                     2                 2                        4      3     2
         (12u v - 12u )z + (12w v + 12w  + 4)t + (3w - 5)v + 36w  + 42w  + 6w
       + 
         - 16w
       ,
                             2
      2v y + 2u z + 2w t - 2w  - w - 1,
                    2                3     2
      6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w, b1 + y + z - t - w}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R
--R   (24)
--R   [{w + 1,u,v,t + 1,b1 + y + z + 2}, {w + 1,v,t + 1,z,b1 + y + 2},
--R    {w + 1,t + 1,z,y,b1 + 2}, {w + 1,v - u,t + 1,y + z,x,b1 + 2},
--R    {w + 1,u,t + 1,y,x,b1 + z + 2},
--R
--R          5       4      3     2
--R     {144w  + 216w  + 96w  + 6w  - 11w - 1,
--R          2                 5       4      3     2
--R      (12w  + 9w + 1)u - 72w  - 108w  - 42w  - 9w  - 3w,
--R          2                 4      3      2
--R      (12w  + 9w + 1)v + 36w  + 54w  + 18w ,
--R          3      2             4      3      2
--R      (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,
--R
--R                     2                 2                        4      3     2
--R         (12u v - 12u )z + (12w v + 12w  + 4)t + (3w - 5)v + 36w  + 42w  + 6w
--R       + 
--R         - 16w
--R       ,
--R                             2
--R      2v y + 2u z + 2w t - 2w  - w - 1,
--R                    2                3     2
--R      6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w, b1 + y + z - t - w}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--E 24

--S 25 of 36
[coHeight(ts) for ts in lts]
 

   (24)  [3,3,3,2,2,0]
                                                Type: List NonNegativeInteger
--R
--R   (25)  [3,3,3,2,2,0]
--R                                                Type: List NonNegativeInteger
--E 25

--S 26 of 36
ST := SREGSET(R,E,V,P)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R
--R   (26)
--R  SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [
--R  b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariat
--R  ePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R                                                                 Type: Domain
--E 26

--S 27 of 36
pack := LAZM3PK(R,E,V,P,T,ST)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R
--R   (27)
--R  LazardSetSolvingPackage(Integer,IndexedExponents OrderedVariableList [b1,x,y,
--R  z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolyno
--R  mial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]),RegularTriangularSet(Int
--R  eger,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableL
--R  ist [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariabl
--R  eList [b1,x,y,z,t,v,u,w])),SquareFreeRegularTriangularSet(Integer,IndexedExpo
--R  nents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,
--R  v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,
--R  t,v,u,w])))
--R                                                                 Type: Domain
--E 27

--S 28 of 36
zeroSetSplit(lp,false)$pack
 

   (25)
   [{w + 1,t + 1,z,y,b1 + 2}, {w + 1,v,t + 1,z,b1 + y + 2},
    {w + 1,u,v,t + 1,b1 + y + z + 2}, {w + 1,v - u,t + 1,y + z,x,b1 + 2},
    {w + 1,u,t + 1,y,x,b1 + z + 2},

          5       4      3     2                   4      3      2
     {144w  + 216w  + 96w  + 6w  - 11w - 1, u - 24w  - 36w  - 14w  + w + 1,
              4      3      2                  4      3      2
      3v - 48w  - 60w  - 10w  + 8w + 2, t - 24w  - 36w  - 14w  - w + 1,
                  4        3        2
      486z - 2772w  - 4662w  - 2055w  + 30w + 127,
                    4         3        2
      2916y - 22752w  - 30312w  - 8220w  + 2064w + 1561,
                  4        3       2
      356x - 3696w  - 4536w  - 968w  + 822w + 371,
                     4         3         2
      2916b1 - 30600w  - 46692w  - 20274w  - 8076w + 593}
     ]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R
--R   (28)
--R   [{w + 1,t + 1,z,y,b1 + 2}, {w + 1,v,t + 1,z,b1 + y + 2},
--R    {w + 1,u,v,t + 1,b1 + y + z + 2}, {w + 1,v - u,t + 1,y + z,x,b1 + 2},
--R    {w + 1,u,t + 1,y,x,b1 + z + 2},
--R
--R          5       4      3     2                   4      3      2
--R     {144w  + 216w  + 96w  + 6w  - 11w - 1, u - 24w  - 36w  - 14w  + w + 1,
--R              4      3      2                  4      3      2
--R      3v - 48w  - 60w  - 10w  + 8w + 2, t - 24w  - 36w  - 14w  - w + 1,
--R                  4        3        2
--R      486z - 2772w  - 4662w  - 2055w  + 30w + 127,
--R                    4         3        2
--R      2916y - 22752w  - 30312w  - 8220w  + 2064w + 1561,
--R                  4        3       2
--R      356x - 3696w  - 4536w  - 968w  + 822w + 371,
--R                     4         3         2
--R      2916b1 - 30600w  - 46692w  - 20274w  - 8076w + 593}
--R     ]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--E 28

--S 29 of 36
f0 := (w - v) ** 2 + (u - t) ** 2 - 1
 

          2           2           2    2
   (26)  t  - 2u t + v  - 2w v + u  + w  - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R          2           2           2    2
--R   (29)  t  - 2u t + v  - 2w v + u  + w  - 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 29

--S 30 of 36
f1 := t ** 2 - v ** 3
 

          2    3
   (27)  t  - v
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R          2    3
--R   (30)  t  - v
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 30

--S 31 of 36
f2 := 2 * t * (w - v) + 3 * v ** 2 * (u - t)
 

              2                   2
   (28)  (- 3v  - 2v + 2w)t + 3u v
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R              2                   2
--R   (31)  (- 3v  - 2v + 2w)t + 3u v
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 31

--S 32 of 36
f3 := (3 * z * v ** 2 - 1) * (2 * z * t - 1)
 

           2   2             2
   (29)  6v t z  + (- 2t - 3v )z + 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R           2   2             2
--R   (32)  6v t z  + (- 2t - 3v )z + 1
--RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 32

--S 33 of 36
lf := [f0, f1, f2, f3]
 

   (30)
     2           2           2    2       2    3       2                   2
   [t  - 2u t + v  - 2w v + u  + w  - 1, t  - v , (- 3v  - 2v + 2w)t + 3u v ,
      2   2             2
    6v t z  + (- 2t - 3v )z + 1]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--R
--R   (33)
--R     2           2           2    2       2    3       2                   2
--R   [t  - 2u t + v  - 2w v + u  + w  - 1, t  - v , (- 3v  - 2v + 2w)t + 3u v ,
--R      2   2             2
--R    6v t z  + (- 2t - 3v )z + 1]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])
--E 33

--S 34 of 36
zeroSetSplit(lf,true)$T
 

   (31)
   [
     {
             6           3       2                 4
         729u  + (- 1458w  + 729w  - 4158w - 1685)u
       + 
              6        5        4        3       2                2       8
         (729w  - 1458w  - 2619w  - 4892w  - 297w  + 5814w + 427)u  + 729w
       + 
             7        6        5        4        3        2
         216w  - 2900w  - 2376w  + 3870w  + 4072w  - 1188w  - 1656w + 529
       ,

                  4           3       2                  2        6        5
             2187u  + (- 4374w  - 972w  - 12474w - 2868)u  + 2187w  - 1944w
           + 
                     4        3        2
             - 10125w  - 4800w  + 2501w  + 4968w - 1587
        *
           v
       + 
               3       2  2       6        5        4       3        2
         (1944w  - 108w )u  + 972w  + 3024w  - 1080w  + 496w  + 1116w
       ,
         2                   2                    2  2           2
      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R
--R   (34)
--R   [
--R     {
--R             6           3       2                 4
--R         729u  + (- 1458w  + 729w  - 4158w - 1685)u
--R       + 
--R              6        5        4        3       2                2       8
--R         (729w  - 1458w  - 2619w  - 4892w  - 297w  + 5814w + 427)u  + 729w
--R       + 
--R             7        6        5        4        3        2
--R         216w  - 2900w  - 2376w  + 3870w  + 4072w  - 1188w  - 1656w + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187u  + (- 4374w  - 972w  - 12474w - 2868)u  + 2187w  - 1944w
--R           + 
--R                     4        3        2
--R             - 10125w  - 4800w  + 2501w  + 4968w - 1587
--R        *
--R           v
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944w  - 108w )u  + 972w  + 3024w  - 1080w  + 496w  + 1116w
--R       ,
--R         2                   2                    2  2           2
--R      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--E 34

--S 35 of 36
zeroSetSplit(lf,false)$T
 

   (32)
   [
     {
             6           3       2                 4
         729u  + (- 1458w  + 729w  - 4158w - 1685)u
       + 
              6        5        4        3       2                2       8
         (729w  - 1458w  - 2619w  - 4892w  - 297w  + 5814w + 427)u  + 729w
       + 
             7        6        5        4        3        2
         216w  - 2900w  - 2376w  + 3870w  + 4072w  - 1188w  - 1656w + 529
       ,

                  4           3       2                  2        6        5
             2187u  + (- 4374w  - 972w  - 12474w - 2868)u  + 2187w  - 1944w
           + 
                     4        3        2
             - 10125w  - 4800w  + 2501w  + 4968w - 1587
        *
           v
       + 
               3       2  2       6        5        4       3        2
         (1944w  - 108w )u  + 972w  + 3024w  - 1080w  + 496w  + 1116w
       ,
         2                   2                    2  2           2
      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
     ,

         4     3      2                               2
     {27w  + 4w  - 54w  - 36w + 23, u, (12w + 2)v - 9w  - 2w + 9,
        2          2
      6t  - 2v - 3w  + 2w + 3, 2t z - 1}
     ,

            6         5         4          3         2
     {59049w  + 91854w  - 45198w  + 145152w  + 63549w  + 60922w + 21420,

                            5                  4                  3
             31484448266904w  - 18316865522574w  + 23676995746098w
           + 
                           2
             6657857188965w  + 8904703998546w + 3890631403260
        *
            2
           u
       + 
                        5                  4                  3
         94262810316408w  - 82887296576616w  + 89801831438784w
       + 
                        2
         28141734167208w  + 38070359425432w + 16003865949120
       ,
           2             2         2       3      2                    3     2
      (243w  + 36w + 85)v  + (- 81u  - 162w  + 36w  + 154w + 72)v - 72w  + 4w ,
         2                   2                    2  2           2
      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
     ,

         4     3      2                               2
     {27w  + 4w  - 54w  - 36w + 23, u, (12w + 2)v - 9w  - 2w + 9,
        2          2             2
      6t  - 2v - 3w  + 2w + 3, 3v z - 1}
     ]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R
--R   (35)
--R   [
--R     {
--R             6           3       2                 4
--R         729u  + (- 1458w  + 729w  - 4158w - 1685)u
--R       + 
--R              6        5        4        3       2                2       8
--R         (729w  - 1458w  - 2619w  - 4892w  - 297w  + 5814w + 427)u  + 729w
--R       + 
--R             7        6        5        4        3        2
--R         216w  - 2900w  - 2376w  + 3870w  + 4072w  - 1188w  - 1656w + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187u  + (- 4374w  - 972w  - 12474w - 2868)u  + 2187w  - 1944w
--R           + 
--R                     4        3        2
--R             - 10125w  - 4800w  + 2501w  + 4968w - 1587
--R        *
--R           v
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944w  - 108w )u  + 972w  + 3024w  - 1080w  + 496w  + 1116w
--R       ,
--R         2                   2                    2  2           2
--R      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
--R     ,
--R
--R         4     3      2                               2
--R     {27w  + 4w  - 54w  - 36w + 23, u, (12w + 2)v - 9w  - 2w + 9,
--R        2          2
--R      6t  - 2v - 3w  + 2w + 3, 2t z - 1}
--R     ,
--R
--R            6         5         4          3         2
--R     {59049w  + 91854w  - 45198w  + 145152w  + 63549w  + 60922w + 21420,
--R
--R                            5                  4                  3
--R             31484448266904w  - 18316865522574w  + 23676995746098w
--R           + 
--R                           2
--R             6657857188965w  + 8904703998546w + 3890631403260
--R        *
--R            2
--R           u
--R       + 
--R                        5                  4                  3
--R         94262810316408w  - 82887296576616w  + 89801831438784w
--R       + 
--R                        2
--R         28141734167208w  + 38070359425432w + 16003865949120
--R       ,
--R           2             2         2       3      2                    3     2
--R      (243w  + 36w + 85)v  + (- 81u  - 162w  + 36w  + 154w + 72)v - 72w  + 4w ,
--R         2                   2                    2  2           2
--R      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
--R     ,
--R
--R         4     3      2                               2
--R     {27w  + 4w  - 54w  - 36w + 23, u, (12w + 2)v - 9w  - 2w + 9,
--R        2          2             2
--R      6t  - 2v - 3w  + 2w + 3, 3v z - 1}
--R     ]
--RType: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--E 35

--S 36 of 36
zeroSetSplit(lf,false)$pack
 

   (33)
   [
     {
             6           3       2                 4
         729u  + (- 1458w  + 729w  - 4158w - 1685)u
       + 
              6        5        4        3       2                2       8
         (729w  - 1458w  - 2619w  - 4892w  - 297w  + 5814w + 427)u  + 729w
       + 
             7        6        5        4        3        2
         216w  - 2900w  - 2376w  + 3870w  + 4072w  - 1188w  - 1656w + 529
       ,

                  4           3       2                  2        6        5
             2187u  + (- 4374w  - 972w  - 12474w - 2868)u  + 2187w  - 1944w
           + 
                     4        3        2
             - 10125w  - 4800w  + 2501w  + 4968w - 1587
        *
           v
       + 
               3       2  2       6        5        4       3        2
         (1944w  - 108w )u  + 972w  + 3024w  - 1080w  + 496w  + 1116w
       ,
         2                   2                    2  2           2
      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
     ,

         2                 2                   2
     {81w  + 18w + 28, 729u  - 1890w - 533, 81v  + (- 162w + 27)v - 72w - 112,
      11881t + (972w + 2997)u v + (- 11448w - 11536)u,

                         2
         641237934604288z
       + 
                 (78614584763904w + 26785578742272)u + 236143618655616w
               + 
                 70221988585728
            *
               v
           + 
             (358520253138432w + 101922133759488)u + 142598803536000w
           + 
             54166419595008
        *
           z
       + 
         (32655103844499w - 44224572465882)u v
       + 
         (43213900115457w - 32432039102070)u
       }
     ,

         4     3      2                           3     2
     {27w  + 4w  - 54w  - 36w + 23, u, 218v - 162w  + 3w  + 160w + 153,
          2      3      2                             3      2
      109t  - 27w  - 54w  + 63w + 80, 1744z + (- 1458w  + 27w  + 1440w + 505)t}
     ,

         4     3      2                           3     2
     {27w  + 4w  - 54w  - 36w + 23, u, 218v - 162w  + 3w  + 160w + 153,
          2      3      2                         3     2
      109t  - 27w  - 54w  + 63w + 80, 1308z + 162w  - 3w  - 814w - 153}
     ,

          4       3        2                   2      2
     {729w  + 972w  - 1026w  + 1684w + 765, 81u  + 72w  + 16w - 72,
                 3       2
      702v - 162w  - 225w  + 40w - 99,
                    3       2
      11336t + (324w  - 603w  - 1718w - 1557)u,

                   2
         595003968z
       + 
                          3             2
             (- 963325386w  - 898607682w  + 1516286466w - 3239166186)u
           + 
                          3              2
             - 1579048992w  - 1796454288w  + 2428328160w - 4368495024
        *
           z
       + 
                     3              2
         (9713133306w  + 9678670317w  - 16726834476w + 28144233593)u
       }
     ]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--R
--R   (36)
--R   [
--R     {
--R             6           3       2                 4
--R         729u  + (- 1458w  + 729w  - 4158w - 1685)u
--R       + 
--R              6        5        4        3       2                2       8
--R         (729w  - 1458w  - 2619w  - 4892w  - 297w  + 5814w + 427)u  + 729w
--R       + 
--R             7        6        5        4        3        2
--R         216w  - 2900w  - 2376w  + 3870w  + 4072w  - 1188w  - 1656w + 529
--R       ,
--R
--R                  4           3       2                  2        6        5
--R             2187u  + (- 4374w  - 972w  - 12474w - 2868)u  + 2187w  - 1944w
--R           + 
--R                     4        3        2
--R             - 10125w  - 4800w  + 2501w  + 4968w - 1587
--R        *
--R           v
--R       + 
--R               3       2  2       6        5        4       3        2
--R         (1944w  - 108w )u  + 972w  + 3024w  - 1080w  + 496w  + 1116w
--R       ,
--R         2                   2                    2  2           2
--R      (3v  + 2v - 2w)t - 3u v , ((4v - 4w)t - 6u v )z  + (2t + 3v )z - 1}
--R     ,
--R
--R         2                 2                   2
--R     {81w  + 18w + 28, 729u  - 1890w - 533, 81v  + (- 162w + 27)v - 72w - 112,
--R      11881t + (972w + 2997)u v + (- 11448w - 11536)u,
--R
--R                         2
--R         641237934604288z
--R       + 
--R                 (78614584763904w + 26785578742272)u + 236143618655616w
--R               + 
--R                 70221988585728
--R            *
--R               v
--R           + 
--R             (358520253138432w + 101922133759488)u + 142598803536000w
--R           + 
--R             54166419595008
--R        *
--R           z
--R       + 
--R         (32655103844499w - 44224572465882)u v
--R       + 
--R         (43213900115457w - 32432039102070)u
--R       }
--R     ,
--R
--R         4     3      2                           3     2
--R     {27w  + 4w  - 54w  - 36w + 23, u, 218v - 162w  + 3w  + 160w + 153,
--R          2      3      2                             3      2
--R      109t  - 27w  - 54w  + 63w + 80, 1744z + (- 1458w  + 27w  + 1440w + 505)t}
--R     ,
--R
--R         4     3      2                           3     2
--R     {27w  + 4w  - 54w  - 36w + 23, u, 218v - 162w  + 3w  + 160w + 153,
--R          2      3      2                         3     2
--R      109t  - 27w  - 54w  + 63w + 80, 1308z + 162w  - 3w  - 814w - 153}
--R     ,
--R
--R          4       3        2                   2      2
--R     {729w  + 972w  - 1026w  + 1684w + 765, 81u  + 72w  + 16w - 72,
--R                 3       2
--R      702v - 162w  - 225w  + 40w - 99,
--R                    3       2
--R      11336t + (324w  - 603w  - 1718w - 1557)u,
--R
--R                   2
--R         595003968z
--R       + 
--R                          3             2
--R             (- 963325386w  - 898607682w  + 1516286466w - 3239166186)u
--R           + 
--R                          3              2
--R             - 1579048992w  - 1796454288w  + 2428328160w - 4368495024
--R        *
--R           z
--R       + 
--R                     3              2
--R         (9713133306w  + 9678670317w  - 16726834476w + 28144233593)u
--R       }
--R     ]
--RType: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
--E 36

)spool
 
Starts dribbling to schaum17.output (2010/3/27, 18:38:1).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 136
aa:=integrate(sin(a*x),x)
 

          cos(a x)
   (1)  - --------
              a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          cos(a x)
--R   (1)  - --------
--R              a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 136
bb:=-cos(a*x)/a
 

          cos(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cos(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3 of 136      14:339 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 136
aa:=integrate(x*sin(a*x),x)
 

        sin(a x) - a x cos(a x)
   (1)  -----------------------
                    2
                   a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sin(a x) - a x cos(a x)
--R   (1)  -----------------------
--R                    2
--R                   a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 136
bb:=sin(a*x)/a^2-(x*cos(a*x))/a
 

        sin(a x) - a x cos(a x)
   (2)  -----------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R        sin(a x) - a x cos(a x)
--R   (2)  -----------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E

--S 6 of 136      14:340 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 136
aa:=integrate(x^2*sin(a*x),x)
 

                            2 2
        2a x sin(a x) + (- a x  + 2)cos(a x)
   (1)  ------------------------------------
                          3
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            2 2
--R        2a x sin(a x) + (- a x  + 2)cos(a x)
--R   (1)  ------------------------------------
--R                          3
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 136
bb:=(2*x)/a^2*sin(a*x)+(2/a^3-x^2/a)*cos(a*x)
 

                            2 2
        2a x sin(a x) + (- a x  + 2)cos(a x)
   (2)  ------------------------------------
                          3
                         a
                                                     Type: Expression Integer
--R
--R                            2 2
--R        2a x sin(a x) + (- a x  + 2)cos(a x)
--R   (2)  ------------------------------------
--R                          3
--R                         a
--R                                                     Type: Expression Integer
--E

--S 9 of 136      14:341 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 136
aa:=integrate(x^3*sin(a*x),x)
 

           2 2                    3 3
        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
   (1)  ---------------------------------------------
                               4
                              a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           2 2                    3 3
--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
--R   (1)  ---------------------------------------------
--R                               4
--R                              a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 136
bb:=((3*x^2)/a^2-6/a^4)*sin(a*x)+(6*x/a^3-x^3/a)*cos(a*x)
 

           2 2                    3 3
        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
   (2)  ---------------------------------------------
                               4
                              a
                                                     Type: Expression Integer
--R
--R           2 2                    3 3
--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
--R   (2)  ---------------------------------------------
--R                               4
--R                              a
--R                                                     Type: Expression Integer
--E

--S 12 of 136     14:342 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 136     14:343 Schaums and Axiom agree by definition
aa:=integrate(sin(x)/x,x)
 

   (1)  Si(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  Si(x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 14 of 136     14:344 Axiom cannot compute this integral
aa:=integrate(sin(a*x)/x^2,x)
 

           x
         ++  sin(%I a)
   (1)   |   --------- d%I
        ++        2
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sin(%I a)
--I   (1)   |   --------- d%I
--R        ++        2
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 15 of 136
aa:=integrate(1/sin(a*x),x)
 

              sin(a x)
        log(------------)
            cos(a x) + 1
   (1)  -----------------
                a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              sin(a x)
--R        log(------------)
--R            cos(a x) + 1
--R   (1)  -----------------
--R                a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16 of 136
bb:=1/a*log(tan((a*x)/2))
 

                a x
        log(tan(---))
                 2
   (2)  -------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        log(tan(---))
--R                 2
--R   (2)  -------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 17 of 136
cc:=aa-bb
 

                  a x           sin(a x)
        - log(tan(---)) + log(------------)
                   2          cos(a x) + 1
   (3)  -----------------------------------
                         a
                                                     Type: Expression Integer
--R
--R                  a x           sin(a x)
--R        - log(tan(---)) + log(------------)
--R                   2          cos(a x) + 1
--R   (3)  -----------------------------------
--R                         a
--R                                                     Type: Expression Integer
--E

--S 18 of 136     14:345 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 19 of 136     14:346 Axiom cannot compute this integral
aa:=integrate(x/sin(a*x),x)
 

           x
         ++      %I
   (1)   |   --------- d%I
        ++   sin(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   --------- d%I
--I        ++   sin(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 20 of 136
aa:=integrate(sin(a*x)^2,x)
 

        - cos(a x)sin(a x) + a x
   (1)  ------------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - cos(a x)sin(a x) + a x
--R   (1)  ------------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 21 of 136
bb:=x/2-sin(2*a*x)/(4*a)
 

        - sin(2a x) + 2a x
   (2)  ------------------
                4a
                                                     Type: Expression Integer
--R
--R        - sin(2a x) + 2a x
--R   (2)  ------------------
--R                4a
--R                                                     Type: Expression Integer
--E

--S 22 of 136
cc:=aa-bb
 

        sin(2a x) - 2cos(a x)sin(a x)
   (3)  -----------------------------
                      4a
                                                     Type: Expression Integer
--R
--R        sin(2a x) - 2cos(a x)sin(a x)
--R   (3)  -----------------------------
--R                      4a
--R                                                     Type: Expression Integer
--E

--S 23 of 136     14:347 Schaums and Axiom agreee
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 24 of 136
aa:=integrate(x*sin(a*x)^2,x)
 

                                          2    2 2
        - 2a x cos(a x)sin(a x) - cos(a x)  + a x
   (1)  ------------------------------------------
                              2
                            4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                          2    2 2
--R        - 2a x cos(a x)sin(a x) - cos(a x)  + a x
--R   (1)  ------------------------------------------
--R                              2
--R                            4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25 of 136
bb:=x^2/4-(x*sin(2*a*x))/(4*a)-cos(2*a*x)/(8*a^2)
 

                                         2 2
        - 2a x sin(2a x) - cos(2a x) + 2a x
   (2)  ------------------------------------
                           2
                         8a
                                                     Type: Expression Integer
--R
--R                                         2 2
--R        - 2a x sin(2a x) - cos(2a x) + 2a x
--R   (2)  ------------------------------------
--R                           2
--R                         8a
--R                                                     Type: Expression Integer
--E

--S 26 of 136
cc:=aa-bb
 

                                                                      2
        2a x sin(2a x) - 4a x cos(a x)sin(a x) + cos(2a x) - 2cos(a x)
   (3)  ---------------------------------------------------------------
                                        2
                                      8a
                                                     Type: Expression Integer
--R
--R                                                                      2
--R        2a x sin(2a x) - 4a x cos(a x)sin(a x) + cos(2a x) - 2cos(a x)
--R   (3)  ---------------------------------------------------------------
--R                                        2
--R                                      8a
--R                                                     Type: Expression Integer
--E

--S 27 of 136     14:348 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

           1
   (4)  - ---
            2
          8a
                                                     Type: Expression Integer
--R
--R           1
--R   (4)  - ---
--R            2
--R          8a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 136
aa:=integrate(sin(a*x)^3,x)
 

                3
        cos(a x)  - 3cos(a x)
   (1)  ---------------------
                  3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                3
--R        cos(a x)  - 3cos(a x)
--R   (1)  ---------------------
--R                  3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 29 of 136
bb:=-cos(a*x)/a+cos(a*x)^3/(3*a)
 

                3
        cos(a x)  - 3cos(a x)
   (2)  ---------------------
                  3a
                                                     Type: Expression Integer
--R
--R                3
--R        cos(a x)  - 3cos(a x)
--R   (2)  ---------------------
--R                  3a
--R                                                     Type: Expression Integer
--E

--S 30 of 136     14:349 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 31 of 136
aa:=integrate(sin(a*x)^4,x)
 

                  3
        (2cos(a x)  - 5cos(a x))sin(a x) + 3a x
   (1)  ---------------------------------------
                           8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  3
--R        (2cos(a x)  - 5cos(a x))sin(a x) + 3a x
--R   (1)  ---------------------------------------
--R                           8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 32 of 136
bb:=(3*x)/8-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
 

        sin(4a x) - 8sin(2a x) + 12a x
   (2)  ------------------------------
                      32a
                                                     Type: Expression Integer
--R
--R        sin(4a x) - 8sin(2a x) + 12a x
--R   (2)  ------------------------------
--R                      32a
--R                                                     Type: Expression Integer
--E

--S 33 of 136
cc:=aa-bb
 

                                             3
        - sin(4a x) + 8sin(2a x) + (8cos(a x)  - 20cos(a x))sin(a x)
   (3)  ------------------------------------------------------------
                                     32a
                                                     Type: Expression Integer
--R
--R                                             3
--R        - sin(4a x) + 8sin(2a x) + (8cos(a x)  - 20cos(a x))sin(a x)
--R   (3)  ------------------------------------------------------------
--R                                     32a
--R                                                     Type: Expression Integer
--E

--S 34 of 136     14:350 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 35 of 136
aa:=integrate(1/sin(a*x)^2,x)
 

           cos(a x)
   (1)  - ----------
          a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           cos(a x)
--R   (1)  - ----------
--R          a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 36 of 136
bb:=-1/a*cot(a*x)
 

          cot(a x)
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R          cot(a x)
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 37 of 136
cc:=aa-bb
 

        cot(a x)sin(a x) - cos(a x)
   (3)  ---------------------------
                 a sin(a x)
                                                     Type: Expression Integer
--R
--R        cot(a x)sin(a x) - cos(a x)
--R   (3)  ---------------------------
--R                 a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 38 of 136     14:351 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 136
aa:=integrate(1/sin(a*x)^3,x)
 

                 2           sin(a x)
        (cos(a x)  - 1)log(------------) + cos(a x)
                           cos(a x) + 1
   (1)  -------------------------------------------
                                2
                     2a cos(a x)  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2           sin(a x)
--R        (cos(a x)  - 1)log(------------) + cos(a x)
--R                           cos(a x) + 1
--R   (1)  -------------------------------------------
--R                                2
--R                     2a cos(a x)  - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 40 of 136
bb:=-cos(a*x)/(2*a*sin(a*x)^2)+1/(2*a)*log(tan((a*x)/2))
 

                2        a x
        sin(a x) log(tan(---)) - cos(a x)
                          2
   (2)  ---------------------------------
                              2
                   2a sin(a x)
                                                     Type: Expression Integer
--R
--R                2        a x
--R        sin(a x) log(tan(---)) - cos(a x)
--R                          2
--R   (2)  ---------------------------------
--R                              2
--R                   2a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 41 of 136
cc:=aa-bb
 

   (3)
                  2             2        a x
       (- cos(a x)  + 1)sin(a x) log(tan(---))
                                          2
     + 
                2             2      sin(a x)                      2           3
       (cos(a x)  - 1)sin(a x) log(------------) + cos(a x)sin(a x)  + cos(a x)
                                   cos(a x) + 1
     + 
       - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2             2        a x
--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
--R                                          2
--R     + 
--R                2             2      sin(a x)                      2           3
--R       (cos(a x)  - 1)sin(a x) log(------------) + cos(a x)sin(a x)  + cos(a x)
--R                                   cos(a x) + 1
--R     + 
--R       - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 42 of 136
dd:=expandLog cc
 

   (4)
                  2             2        a x
       (- cos(a x)  + 1)sin(a x) log(tan(---))
                                          2
     + 
                2             2
       (cos(a x)  - 1)sin(a x) log(sin(a x))
     + 
                  2             2                                    2
       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1) + cos(a x)sin(a x)
     + 
               3
       cos(a x)  - cos(a x)
  /
                 2              2
     (2a cos(a x)  - 2a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (4)
--R                  2             2        a x
--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
--R                                          2
--R     + 
--R                2             2
--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
--R     + 
--R                  2             2                                    2
--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1) + cos(a x)sin(a x)
--R     + 
--R               3
--R       cos(a x)  - cos(a x)
--R  /
--R                 2              2
--R     (2a cos(a x)  - 2a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 43 of 136     14:352 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 44 of 136
aa:=integrate(sin(p*x)*sin(q*x),x)
 

        p cos(p x)sin(q x) - q cos(q x)sin(p x)
   (1)  ---------------------------------------
                         2    2
                        q  - p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        p cos(p x)sin(q x) - q cos(q x)sin(p x)
--R   (1)  ---------------------------------------
--R                         2    2
--R                        q  - p
--R                                          Type: Union(Expression Integer,...)
--E

--S 45 of 136
bb:=sin((p-q)*x)/(2*(p-q))-sin((p+q)*x)/(2*(p+q))
 

        (- q + p)sin((q + p)x) + (q + p)sin((q - p)x)
   (2)  ---------------------------------------------
                            2     2
                          2q  - 2p
                                                     Type: Expression Integer
--R
--R        (- q + p)sin((q + p)x) + (q + p)sin((q - p)x)
--R   (2)  ---------------------------------------------
--R                            2     2
--R                          2q  - 2p
--R                                                     Type: Expression Integer
--E 

--S 46 of 136
cc:=aa-bb
 

   (3)
       (q - p)sin((q + p)x) + 2p cos(p x)sin(q x) + (- q - p)sin((q - p)x)
     + 
       - 2q cos(q x)sin(p x)
  /
       2     2
     2q  - 2p
                                                     Type: Expression Integer
--R
--R   (3)
--R       (q - p)sin((q + p)x) + 2p cos(p x)sin(q x) + (- q - p)sin((q - p)x)
--R     + 
--R       - 2q cos(q x)sin(p x)
--R  /
--R       2     2
--R     2q  - 2p
--R                                                     Type: Expression Integer
--E

--S 47 of 136     14:353 Schams and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 48 of 136
aa:=integrate(1/(1-sin(a*x)),x)
 

              - 2cos(a x) - 2
   (1)  ---------------------------
        a sin(a x) - a cos(a x) - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - 2cos(a x) - 2
--R   (1)  ---------------------------
--R        a sin(a x) - a cos(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E

--S 49 of 136
bb:=1/a*tan(%pi/4+(a*x)/2)
 

            2a x + %pi
        tan(----------)
                 4
   (2)  ---------------
               a
                                                     Type: Expression Integer
--R
--R            2a x + %pi
--R        tan(----------)
--R                 4
--R   (2)  ---------------
--R               a
--R                                                     Type: Expression Integer
--E 

--S 50 of 136
cc:=aa-bb
 

                                       2a x + %pi
        (- sin(a x) + cos(a x) + 1)tan(----------) - 2cos(a x) - 2
                                            4
   (3)  ----------------------------------------------------------
                        a sin(a x) - a cos(a x) - a
                                                     Type: Expression Integer
--R
--R                                       2a x + %pi
--R        (- sin(a x) + cos(a x) + 1)tan(----------) - 2cos(a x) - 2
--R                                            4
--R   (3)  ----------------------------------------------------------
--R                        a sin(a x) - a cos(a x) - a
--R                                                     Type: Expression Integer
--E

--S 51 of 136     14:354 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

        1
   (4)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (4)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 52 of 136
aa:=integrate(x/(1-sin(a*x)),x)
 

   (1)
                                      sin(a x) - cos(a x) - 1
       (2sin(a x) - 2cos(a x) - 2)log(-----------------------)
                                            cos(a x) + 1
     + 
                                            2
       (- sin(a x) + cos(a x) + 1)log(------------) - a x sin(a x)
                                      cos(a x) + 1
     + 
       - a x cos(a x) - a x
  /
      2            2            2
     a sin(a x) - a cos(a x) - a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                                      sin(a x) - cos(a x) - 1
--R       (2sin(a x) - 2cos(a x) - 2)log(-----------------------)
--R                                            cos(a x) + 1
--R     + 
--R                                            2
--R       (- sin(a x) + cos(a x) + 1)log(------------) - a x sin(a x)
--R                                      cos(a x) + 1
--R     + 
--R       - a x cos(a x) - a x
--R  /
--R      2            2            2
--R     a sin(a x) - a cos(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 53 of 136
bb:=x/a*tan(%pi/4+(a*x)/2)+2/a^2*log(sin(%pi/4-(a*x)/2))
 

                   2a x - %pi             2a x + %pi
        2log(- sin(----------)) + a x tan(----------)
                        4                      4
   (2)  ---------------------------------------------
                               2
                              a
                                                     Type: Expression Integer
--R
--R                   2a x - %pi             2a x + %pi
--R        2log(- sin(----------)) + a x tan(----------)
--R                        4                      4
--R   (2)  ---------------------------------------------
--R                               2
--R                              a
--R                                                     Type: Expression Integer
--E

--S 54 of 136     14:355 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                                      sin(a x) - cos(a x) - 1
       (2sin(a x) - 2cos(a x) - 2)log(-----------------------)
                                            cos(a x) + 1
     + 
                                            2
       (- sin(a x) + cos(a x) + 1)log(------------)
                                      cos(a x) + 1
     + 
                                              2a x - %pi
       (- 2sin(a x) + 2cos(a x) + 2)log(- sin(----------))
                                                   4
     + 
                                                2a x + %pi
       (- a x sin(a x) + a x cos(a x) + a x)tan(----------) - a x sin(a x)
                                                     4
     + 
       - a x cos(a x) - a x
  /
      2            2            2
     a sin(a x) - a cos(a x) - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      sin(a x) - cos(a x) - 1
--R       (2sin(a x) - 2cos(a x) - 2)log(-----------------------)
--R                                            cos(a x) + 1
--R     + 
--R                                            2
--R       (- sin(a x) + cos(a x) + 1)log(------------)
--R                                      cos(a x) + 1
--R     + 
--R                                              2a x - %pi
--R       (- 2sin(a x) + 2cos(a x) + 2)log(- sin(----------))
--R                                                   4
--R     + 
--R                                                2a x + %pi
--R       (- a x sin(a x) + a x cos(a x) + a x)tan(----------) - a x sin(a x)
--R                                                     4
--R     + 
--R       - a x cos(a x) - a x
--R  /
--R      2            2            2
--R     a sin(a x) - a cos(a x) - a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 55 of 136
aa:=integrate(1/(1+sin(a*x)),x)
 

              - 2cos(a x) - 2
   (1)  ---------------------------
        a sin(a x) + a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R
--R              - 2cos(a x) - 2
--R   (1)  ---------------------------
--R        a sin(a x) + a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 56 of 136
bb:=-1/a*tan(%pi/4-(a*x)/2)
 

            2a x - %pi
        tan(----------)
                 4
   (2)  ---------------
               a
                                                     Type: Expression Integer
--R
--R            2a x - %pi
--R        tan(----------)
--R                 4
--R   (2)  ---------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 57 of 136
cc:=aa-bb
 

                                       2a x - %pi
        (- sin(a x) - cos(a x) - 1)tan(----------) - 2cos(a x) - 2
                                            4
   (3)  ----------------------------------------------------------
                        a sin(a x) + a cos(a x) + a
                                                     Type: Expression Integer
--R 
--R
--R                                       2a x - %pi
--R        (- sin(a x) - cos(a x) - 1)tan(----------) - 2cos(a x) - 2
--R                                            4
--R   (3)  ----------------------------------------------------------
--R                        a sin(a x) + a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 58 of 136
tanrule:=rule(tan(a/b) == sin(a)/cos(b))
 

            a     sin(a)
   (4)  tan(-) == ------
            b     cos(b)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a     sin(a)
--R   (4)  tan(-) == ------
--R            b     cos(b)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 59 of 136     14:356 Axiom cannot simplify this expression
dd:=tanrule cc
 

        (- sin(a x) - cos(a x) - 1)sin(2a x - %pi) - 2cos(4)cos(a x) - 2cos(4)
   (5)  ----------------------------------------------------------------------
                    a cos(4)sin(a x) + a cos(4)cos(a x) + a cos(4)
                                                     Type: Expression Integer
--R
--R        (- sin(a x) - cos(a x) - 1)sin(2a x - %pi) - 2cos(4)cos(a x) - 2cos(4)
--R   (5)  ----------------------------------------------------------------------
--R                    a cos(4)sin(a x) + a cos(4)cos(a x) + a cos(4)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 60 of 136
aa:=integrate(x/(1+sin(a*x)),x)
 

   (1)
                                      sin(a x) + cos(a x) + 1
       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
                                            cos(a x) + 1
     + 
                                            2
       (- sin(a x) - cos(a x) - 1)log(------------) + a x sin(a x)
                                      cos(a x) + 1
     + 
       - a x cos(a x) - a x
  /
      2            2            2
     a sin(a x) + a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                      sin(a x) + cos(a x) + 1
--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
--R                                            cos(a x) + 1
--R     + 
--R                                            2
--R       (- sin(a x) - cos(a x) - 1)log(------------) + a x sin(a x)
--R                                      cos(a x) + 1
--R     + 
--R       - a x cos(a x) - a x
--R  /
--R      2            2            2
--R     a sin(a x) + a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 61 of 136
bb:=-x/a*tan(%pi/4-(a*x)/2)+2/a^2*log(sin(%pi/4+(a*x)/2))
 

                 2a x + %pi             2a x - %pi
        2log(sin(----------)) + a x tan(----------)
                      4                      4
   (2)  -------------------------------------------
                              2
                             a
                                                     Type: Expression Integer
--R
--R                 2a x + %pi             2a x - %pi
--R        2log(sin(----------)) + a x tan(----------)
--R                      4                      4
--R   (2)  -------------------------------------------
--R                              2
--R                             a
--R                                                     Type: Expression Integer
--E

--S 62 of 136     14:257 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                                      sin(a x) + cos(a x) + 1
       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
                                            cos(a x) + 1
     + 
                                            2a x + %pi
       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
                                                 4
     + 
                                            2
       (- sin(a x) - cos(a x) - 1)log(------------)
                                      cos(a x) + 1
     + 
                                                2a x - %pi
       (- a x sin(a x) - a x cos(a x) - a x)tan(----------) + a x sin(a x)
                                                     4
     + 
       - a x cos(a x) - a x
  /
      2            2            2
     a sin(a x) + a cos(a x) + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      sin(a x) + cos(a x) + 1
--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
--R                                            cos(a x) + 1
--R     + 
--R                                            2a x + %pi
--R       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
--R                                                 4
--R     + 
--R                                            2
--R       (- sin(a x) - cos(a x) - 1)log(------------)
--R                                      cos(a x) + 1
--R     + 
--R                                                2a x - %pi
--R       (- a x sin(a x) - a x cos(a x) - a x)tan(----------) + a x sin(a x)
--R                                                     4
--R     + 
--R       - a x cos(a x) - a x
--R  /
--R      2            2            2
--R     a sin(a x) + a cos(a x) + a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 63 of 136
aa:=integrate(1/(1-sin(a*x))^2,x)
 

                                               2
             (3cos(a x) + 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
   (1)  ------------------------------------------------------------
                                                2
        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
                                          Type: Union(Expression Integer,...)
--R
--R                                               2
--R             (3cos(a x) + 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
--R   (1)  ------------------------------------------------------------
--R                                                2
--R        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
--R                                          Type: Union(Expression Integer,...)
--E

--S 64 of 136
bb:=1/(2*a)*tan(%pi/4+(a*x)/2)+1/(6*a)*tan(%pi/4+(a*x)/2)^3
 

            2a x + %pi 3        2a x + %pi
        tan(----------)  + 3tan(----------)
                 4                   4
   (2)  -----------------------------------
                         6a
                                                     Type: Expression Integer
--R
--R            2a x + %pi 3        2a x + %pi
--R        tan(----------)  + 3tan(----------)
--R                 4                   4
--R   (2)  -----------------------------------
--R                         6a
--R                                                     Type: Expression Integer
--E 

--S 65 of 136
cc:=aa-bb
 

   (3)
                                           2                    2a x + %pi 3
       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)tan(----------)
                                                                     4
     + 
                                             2                     2a x + %pi
       ((- 3cos(a x) - 6)sin(a x) - 3cos(a x)  + 3cos(a x) + 6)tan(----------)
                                                                        4
     + 
                                          2
       (6cos(a x) + 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
  /
                                              2
     (6a cos(a x) + 12a)sin(a x) + 6a cos(a x)  - 6a cos(a x) - 12a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2                    2a x + %pi 3
--R       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)tan(----------)
--R                                                                     4
--R     + 
--R                                             2                     2a x + %pi
--R       ((- 3cos(a x) - 6)sin(a x) - 3cos(a x)  + 3cos(a x) + 6)tan(----------)
--R                                                                        4
--R     + 
--R                                          2
--R       (6cos(a x) + 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
--R  /
--R                                              2
--R     (6a cos(a x) + 12a)sin(a x) + 6a cos(a x)  - 6a cos(a x) - 12a
--R                                                     Type: Expression Integer
--E

--S 66 of 136
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 67 of 136
dd:=tanrule cc
 

   (5)
                               2a x + %pi 3
           (- cos(a x) - 2)sin(----------)
                                    4
         + 
                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
                        4                           4                4
         + 
                2a x + %pi 3                2a x + %pi 3
           6cos(----------) cos(a x) + 6cos(----------)
                     4                           4
      *
         sin(a x)
     + 
                  2                    2a x + %pi 3
       (- cos(a x)  + cos(a x) + 2)sin(----------)
                                            4
     + 
                  2a x + %pi 2        2        2a x + %pi 2
           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
                       4                            4
         + 
                2a x + %pi 2
           6cos(----------)
                     4
      *
             2a x + %pi
         sin(----------)
                  4
     + 
          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
               4                            4                            4
  /
               2a x + %pi 3                   2a x + %pi 3
       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
                    4                              4
     + 
              2a x + %pi 3        2          2a x + %pi 3
       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
                   4                              4
     + 
                 2a x + %pi 3
       - 12a cos(----------)
                      4
                                                     Type: Expression Integer
--R
--R   (5)
--R                               2a x + %pi 3
--R           (- cos(a x) - 2)sin(----------)
--R                                    4
--R         + 
--R                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
--R                        4                           4                4
--R         + 
--R                2a x + %pi 3                2a x + %pi 3
--R           6cos(----------) cos(a x) + 6cos(----------)
--R                     4                           4
--R      *
--R         sin(a x)
--R     + 
--R                  2                    2a x + %pi 3
--R       (- cos(a x)  + cos(a x) + 2)sin(----------)
--R                                            4
--R     + 
--R                  2a x + %pi 2        2        2a x + %pi 2
--R           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
--R                       4                            4
--R         + 
--R                2a x + %pi 2
--R           6cos(----------)
--R                     4
--R      *
--R             2a x + %pi
--R         sin(----------)
--R                  4
--R     + 
--R          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
--R               4                            4                            4
--R  /
--R               2a x + %pi 3                   2a x + %pi 3
--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
--R                    4                              4
--R     + 
--R              2a x + %pi 3        2          2a x + %pi 3
--R       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
--R                   4                              4
--R     + 
--R                 2a x + %pi 3
--R       - 12a cos(----------)
--R                      4
--R                                                     Type: Expression Integer
--E

--S 68 of 136
sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4))
 

                 b - a              a     b           b     a
   (6)  - %Z sin(-----) == - %Z cos(-)sin(-) + %Z cos(-)sin(-)
                   4                4     4           4     4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                 b - a              a     b           b     a
--I   (6)  - %K sin(-----) == - %K cos(-)sin(-) + %K cos(-)sin(-)
--R                   4                4     4           4     4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 69 of 136
ee:=sindiffrule2 dd
 

   (7)
                               2a x + %pi 3
           (- cos(a x) - 2)sin(----------)
                                    4
         + 
                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
                        4                           4                4
         + 
                2a x + %pi 3                2a x + %pi 3
           6cos(----------) cos(a x) + 6cos(----------)
                     4                           4
      *
         sin(a x)
     + 
                  2                    2a x + %pi 3
       (- cos(a x)  + cos(a x) + 2)sin(----------)
                                            4
     + 
                  2a x + %pi 2        2        2a x + %pi 2
           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
                       4                            4
         + 
                2a x + %pi 2
           6cos(----------)
                     4
      *
             2a x + %pi
         sin(----------)
                  4
     + 
          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
               4                            4                            4
  /
               2a x + %pi 3                   2a x + %pi 3
       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
                    4                              4
     + 
              2a x + %pi 3        2          2a x + %pi 3
       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
                   4                              4
     + 
                 2a x + %pi 3
       - 12a cos(----------)
                      4
                                                     Type: Expression Integer
--R
--R   (7)
--R                               2a x + %pi 3
--R           (- cos(a x) - 2)sin(----------)
--R                                    4
--R         + 
--R                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
--R                        4                           4                4
--R         + 
--R                2a x + %pi 3                2a x + %pi 3
--R           6cos(----------) cos(a x) + 6cos(----------)
--R                     4                           4
--R      *
--R         sin(a x)
--R     + 
--R                  2                    2a x + %pi 3
--R       (- cos(a x)  + cos(a x) + 2)sin(----------)
--R                                            4
--R     + 
--R                  2a x + %pi 2        2        2a x + %pi 2
--R           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
--R                       4                            4
--R         + 
--R                2a x + %pi 2
--R           6cos(----------)
--R                     4
--R      *
--R             2a x + %pi
--R         sin(----------)
--R                  4
--R     + 
--R          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
--R               4                            4                            4
--R  /
--R               2a x + %pi 3                   2a x + %pi 3
--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
--R                    4                              4
--R     + 
--R              2a x + %pi 3        2          2a x + %pi 3
--R       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
--R                   4                              4
--R     + 
--R                 2a x + %pi 3
--R       - 12a cos(----------)
--R                      4
--R                                                     Type: Expression Integer
--E

--S 70 of 136
sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a))
 

              3    - sin(3a) + 3sin(a)
   (8)  sin(a)  == -------------------
                            4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              3    - sin(3a) + 3sin(a)
--R   (8)  sin(a)  == -------------------
--R                            4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 71 of 136
ff:=sincuberule ee
 

   (9)
                                         2                    6a x + 3%pi
       ((cos(a x) + 2)sin(a x) + cos(a x)  - cos(a x) - 2)sin(-----------)
                                                                   4
     + 
                       2a x + %pi 2                      2a x + %pi 2
             ((- 12cos(----------)  - 3)cos(a x) - 24cos(----------)  - 6)
                            4                                 4
          *
                 2a x + %pi
             sin(----------)
                      4
         + 
                 2a x + %pi 3                 2a x + %pi 3
           24cos(----------) cos(a x) + 24cos(----------)
                      4                            4
      *
         sin(a x)
     + 
                    2a x + %pi 2             2
           (- 12cos(----------)  - 3)cos(a x)
                         4
         + 
                  2a x + %pi 2                      2a x + %pi 2
           (12cos(----------)  + 3)cos(a x) + 24cos(----------)  + 6
                       4                                 4
      *
             2a x + %pi
         sin(----------)
                  4
     + 
            2a x + %pi 3        2         2a x + %pi 3
       8cos(----------) cos(a x)  - 32cos(----------) cos(a x)
                 4                             4
     + 
               2a x + %pi 3
       - 40cos(----------)
                    4
  /
                2a x + %pi 3                   2a x + %pi 3
       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
                     4                              4
     + 
               2a x + %pi 3        2           2a x + %pi 3
       24a cos(----------) cos(a x)  - 24a cos(----------) cos(a x)
                    4                               4
     + 
                 2a x + %pi 3
       - 48a cos(----------)
                      4
                                                     Type: Expression Integer
--R
--R   (9)
--R                                         2                    6a x + 3%pi
--R       ((cos(a x) + 2)sin(a x) + cos(a x)  - cos(a x) - 2)sin(-----------)
--R                                                                   4
--R     + 
--R                       2a x + %pi 2                      2a x + %pi 2
--R             ((- 12cos(----------)  - 3)cos(a x) - 24cos(----------)  - 6)
--R                            4                                 4
--R          *
--R                 2a x + %pi
--R             sin(----------)
--R                      4
--R         + 
--R                 2a x + %pi 3                 2a x + %pi 3
--R           24cos(----------) cos(a x) + 24cos(----------)
--R                      4                            4
--R      *
--R         sin(a x)
--R     + 
--R                    2a x + %pi 2             2
--R           (- 12cos(----------)  - 3)cos(a x)
--R                         4
--R         + 
--R                  2a x + %pi 2                      2a x + %pi 2
--R           (12cos(----------)  + 3)cos(a x) + 24cos(----------)  + 6
--R                       4                                 4
--R      *
--R             2a x + %pi
--R         sin(----------)
--R                  4
--R     + 
--R            2a x + %pi 3        2         2a x + %pi 3
--R       8cos(----------) cos(a x)  - 32cos(----------) cos(a x)
--R                 4                             4
--R     + 
--R               2a x + %pi 3
--R       - 40cos(----------)
--R                    4
--R  /
--R                2a x + %pi 3                   2a x + %pi 3
--R       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
--R                     4                              4
--R     + 
--R               2a x + %pi 3        2           2a x + %pi 3
--R       24a cos(----------) cos(a x)  - 24a cos(----------) cos(a x)
--R                    4                               4
--R     + 
--R                 2a x + %pi 3
--R       - 48a cos(----------)
--R                      4
--R                                                     Type: Expression Integer
--E

--S 72 of 136     14:358 Schaums and Axiom differ by a constant
complexNormalize %
 

          2
   (10)  --
         3a
                                                     Type: Expression Integer
--R
--R          2
--R   (10)  --
--R         3a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 73 of 136
aa:=integrate(1/(1+sin(a*x))^2,x)
 

                                                2
            (- 3cos(a x) - 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
   (1)  ------------------------------------------------------------
                                                2
        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
                                          Type: Union(Expression Integer,...)
--R
--R                                                2
--R            (- 3cos(a x) - 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
--R   (1)  ------------------------------------------------------------
--R                                                2
--R        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
--R                                          Type: Union(Expression Integer,...)
--E

--S 74 of 136
bb:=-1/(2*a)*tan(%pi/4-(a*x)/2)-1/(6*a)*tan(%pi/4-(a*x)/2)^3
 

            2a x - %pi 3        2a x - %pi
        tan(----------)  + 3tan(----------)
                 4                   4
   (2)  -----------------------------------
                         6a
                                                     Type: Expression Integer
--R
--R            2a x - %pi 3        2a x - %pi
--R        tan(----------)  + 3tan(----------)
--R                 4                   4
--R   (2)  -----------------------------------
--R                         6a
--R                                                     Type: Expression Integer
--E 

--S 75 of 136
cc:=aa-bb
 

   (3)
                                           2                    2a x - %pi 3
       ((- cos(a x) - 2)sin(a x) + cos(a x)  - cos(a x) - 2)tan(----------)
                                                                     4
     + 
                                             2                     2a x - %pi
       ((- 3cos(a x) - 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
                                                                        4
     + 
                                            2
       (- 6cos(a x) - 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
  /
                                              2
     (6a cos(a x) + 12a)sin(a x) - 6a cos(a x)  + 6a cos(a x) + 12a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2                    2a x - %pi 3
--R       ((- cos(a x) - 2)sin(a x) + cos(a x)  - cos(a x) - 2)tan(----------)
--R                                                                     4
--R     + 
--R                                             2                     2a x - %pi
--R       ((- 3cos(a x) - 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
--R                                                                        4
--R     + 
--R                                            2
--R       (- 6cos(a x) - 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
--R  /
--R                                              2
--R     (6a cos(a x) + 12a)sin(a x) - 6a cos(a x)  + 6a cos(a x) + 12a
--R                                                     Type: Expression Integer
--E

--S 76 of 136
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 77 of 136
dd:=tanrule cc
 

   (5)
                               2a x - %pi 3
           (- cos(a x) - 2)sin(----------)
                                    4
         + 
                   2a x - %pi 2                2a x - %pi 2     2a x - %pi
           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
                        4                           4                4
         + 
                  2a x - %pi 3                2a x - %pi 3
           - 6cos(----------) cos(a x) - 6cos(----------)
                       4                           4
      *
         sin(a x)
     + 
                2                    2a x - %pi 3
       (cos(a x)  - cos(a x) - 2)sin(----------)
                                          4
     + 
                2a x - %pi 2        2        2a x - %pi 2
           3cos(----------) cos(a x)  - 3cos(----------) cos(a x)
                     4                            4
         + 
                  2a x - %pi 2
           - 6cos(----------)
                       4
      *
             2a x - %pi
         sin(----------)
                  4
     + 
          2a x - %pi 3        2        2a x - %pi 3                 2a x - %pi 3
     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
               4                            4                            4
  /
               2a x - %pi 3                   2a x - %pi 3
       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
                    4                              4
     + 
                2a x - %pi 3        2          2a x - %pi 3
       - 6a cos(----------) cos(a x)  + 6a cos(----------) cos(a x)
                     4                              4
     + 
               2a x - %pi 3
       12a cos(----------)
                    4
                                                     Type: Expression Integer
--R
--R   (5)
--R                               2a x - %pi 3
--R           (- cos(a x) - 2)sin(----------)
--R                                    4
--R         + 
--R                   2a x - %pi 2                2a x - %pi 2     2a x - %pi
--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
--R                        4                           4                4
--R         + 
--R                  2a x - %pi 3                2a x - %pi 3
--R           - 6cos(----------) cos(a x) - 6cos(----------)
--R                       4                           4
--R      *
--R         sin(a x)
--R     + 
--R                2                    2a x - %pi 3
--R       (cos(a x)  - cos(a x) - 2)sin(----------)
--R                                          4
--R     + 
--R                2a x - %pi 2        2        2a x - %pi 2
--R           3cos(----------) cos(a x)  - 3cos(----------) cos(a x)
--R                     4                            4
--R         + 
--R                  2a x - %pi 2
--R           - 6cos(----------)
--R                       4
--R      *
--R             2a x - %pi
--R         sin(----------)
--R                  4
--R     + 
--R          2a x - %pi 3        2        2a x - %pi 3                 2a x - %pi 3
--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
--R               4                            4                            4
--R  /
--R               2a x - %pi 3                   2a x - %pi 3
--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
--R                    4                              4
--R     + 
--R                2a x - %pi 3        2          2a x - %pi 3
--R       - 6a cos(----------) cos(a x)  + 6a cos(----------) cos(a x)
--R                     4                              4
--R     + 
--R               2a x - %pi 3
--R       12a cos(----------)
--R                    4
--R                                                     Type: Expression Integer
--E

--S 78 of 136
sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4))
 

                  b - a               a     b            b     a
   (6)  - %BA sin(-----) == - %BA cos(-)sin(-) + %BA cos(-)sin(-)
                    4                 4     4            4     4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                 b - a              a     b           b     a
--I   (6)  - %U sin(-----) == - %U cos(-)sin(-) + %U cos(-)sin(-)
--I                   4                4     4           4     4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 79 of 136
ee:=sindiffrule2 dd
 

   (7)
                +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
           (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
                            4                               4            2
         + 
                                2a x - %pi 3
           (- 2cos(a x) - 4)sin(----------)
                                     4
         + 
              +-+    2a x - %pi 2    a x          2a x - %pi 3
           (3\|2 cos(----------) cos(---) - 12cos(----------) )cos(a x)
                          4           2                4
         + 
             +-+    2a x - %pi 2    a x          2a x - %pi 3
           6\|2 cos(----------) cos(---) - 12cos(----------)
                         4           2                4
      *
         sin(a x)
     + 
            +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
       (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
                        4                               4            2
     + 
                 2                     2a x - %pi 3
       (2cos(a x)  - 2cos(a x) - 4)sin(----------)
                                            4
     + 
            2a x - %pi 2        2    2a x - %pi         2a x - %pi 3        2
       6cos(----------) cos(a x) sin(----------) + 4cos(----------) cos(a x)
                 4                        4                  4
     + 
          +-+    2a x - %pi 2    a x          2a x - %pi 3
       (3\|2 cos(----------) cos(---) - 16cos(----------) )cos(a x)
                      4           2                4
     + 
         +-+    2a x - %pi 2    a x          2a x - %pi 3
       6\|2 cos(----------) cos(---) - 20cos(----------)
                     4           2                4
  /
                2a x - %pi 3                   2a x - %pi 3
       (12a cos(----------) cos(a x) + 24a cos(----------) )sin(a x)
                     4                              4
     + 
                 2a x - %pi 3        2           2a x - %pi 3
       - 12a cos(----------) cos(a x)  + 12a cos(----------) cos(a x)
                      4                               4
     + 
               2a x - %pi 3
       24a cos(----------)
                    4
                                                     Type: Expression Integer
--R
--R   (7)
--R                +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
--R           (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
--R                            4                               4            2
--R         + 
--R                                2a x - %pi 3
--R           (- 2cos(a x) - 4)sin(----------)
--R                                     4
--R         + 
--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           (3\|2 cos(----------) cos(---) - 12cos(----------) )cos(a x)
--R                          4           2                4
--R         + 
--R             +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           6\|2 cos(----------) cos(---) - 12cos(----------)
--R                         4           2                4
--R      *
--R         sin(a x)
--R     + 
--R            +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
--R       (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
--R                        4                               4            2
--R     + 
--R                 2                     2a x - %pi 3
--R       (2cos(a x)  - 2cos(a x) - 4)sin(----------)
--R                                            4
--R     + 
--R            2a x - %pi 2        2    2a x - %pi         2a x - %pi 3        2
--R       6cos(----------) cos(a x) sin(----------) + 4cos(----------) cos(a x)
--R                 4                        4                  4
--R     + 
--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       (3\|2 cos(----------) cos(---) - 16cos(----------) )cos(a x)
--R                      4           2                4
--R     + 
--R         +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       6\|2 cos(----------) cos(---) - 20cos(----------)
--R                     4           2                4
--R  /
--R                2a x - %pi 3                   2a x - %pi 3
--R       (12a cos(----------) cos(a x) + 24a cos(----------) )sin(a x)
--R                     4                              4
--R     + 
--R                 2a x - %pi 3        2           2a x - %pi 3
--R       - 12a cos(----------) cos(a x)  + 12a cos(----------) cos(a x)
--R                      4                               4
--R     + 
--R               2a x - %pi 3
--R       24a cos(----------)
--R                    4
--R                                                     Type: Expression Integer
--E

--S 80 of 136
sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a))
 

              3    - sin(3a) + 3sin(a)
   (8)  sin(a)  == -------------------
                            4
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              3    - sin(3a) + 3sin(a)
--R   (8)  sin(a)  == -------------------
--R                            4
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 81 of 136
ff:=sincuberule ee
 

   (9)
                                         2                    6a x - 3%pi
       ((cos(a x) + 2)sin(a x) - cos(a x)  + cos(a x) + 2)sin(-----------)
                                                                   4
     + 
                +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
           (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
                            4                                4            2
         + 
                                2a x - %pi
           (- 3cos(a x) - 6)sin(----------)
                                     4
         + 
              +-+    2a x - %pi 2    a x          2a x - %pi 3
           (6\|2 cos(----------) cos(---) - 24cos(----------) )cos(a x)
                          4           2                4
         + 
              +-+    2a x - %pi 2    a x          2a x - %pi 3
           12\|2 cos(----------) cos(---) - 24cos(----------)
                          4           2                4
      *
         sin(a x)
     + 
            +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
       (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
                        4                                4            2
     + 
               2a x - %pi 2             2                     2a x - %pi
       ((12cos(----------)  + 3)cos(a x)  - 3cos(a x) - 6)sin(----------)
                    4                                              4
     + 
            2a x - %pi 3        2
       8cos(----------) cos(a x)
                 4
     + 
          +-+    2a x - %pi 2    a x          2a x - %pi 3
       (6\|2 cos(----------) cos(---) - 32cos(----------) )cos(a x)
                      4           2                4
     + 
          +-+    2a x - %pi 2    a x          2a x - %pi 3
       12\|2 cos(----------) cos(---) - 40cos(----------)
                      4           2                4
  /
                2a x - %pi 3                   2a x - %pi 3
       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
                     4                              4
     + 
                 2a x - %pi 3        2           2a x - %pi 3
       - 24a cos(----------) cos(a x)  + 24a cos(----------) cos(a x)
                      4                               4
     + 
               2a x - %pi 3
       48a cos(----------)
                    4
                                                     Type: Expression Integer
--R
--R   (9)
--R                                         2                    6a x - 3%pi
--R       ((cos(a x) + 2)sin(a x) - cos(a x)  + cos(a x) + 2)sin(-----------)
--R                                                                   4
--R     + 
--R                +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
--R           (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
--R                            4                                4            2
--R         + 
--R                                2a x - %pi
--R           (- 3cos(a x) - 6)sin(----------)
--R                                     4
--R         + 
--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           (6\|2 cos(----------) cos(---) - 24cos(----------) )cos(a x)
--R                          4           2                4
--R         + 
--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
--R           12\|2 cos(----------) cos(---) - 24cos(----------)
--R                          4           2                4
--R      *
--R         sin(a x)
--R     + 
--R            +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
--R       (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
--R                        4                                4            2
--R     + 
--R               2a x - %pi 2             2                     2a x - %pi
--R       ((12cos(----------)  + 3)cos(a x)  - 3cos(a x) - 6)sin(----------)
--R                    4                                              4
--R     + 
--R            2a x - %pi 3        2
--R       8cos(----------) cos(a x)
--R                 4
--R     + 
--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       (6\|2 cos(----------) cos(---) - 32cos(----------) )cos(a x)
--R                      4           2                4
--R     + 
--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
--R       12\|2 cos(----------) cos(---) - 40cos(----------)
--R                      4           2                4
--R  /
--R                2a x - %pi 3                   2a x - %pi 3
--R       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
--R                     4                              4
--R     + 
--R                 2a x - %pi 3        2           2a x - %pi 3
--R       - 24a cos(----------) cos(a x)  + 24a cos(----------) cos(a x)
--R                      4                               4
--R     + 
--R               2a x - %pi 3
--R       48a cos(----------)
--R                    4
--R                                                     Type: Expression Integer
--E

--S 82 of 136     14:359 Schaums and Axiom differ by a constant
complexNormalize %
 

            2
   (10)  - --
           3a
                                                     Type: Expression Integer
--R
--R            2
--R   (10)  - --
--R           3a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 83 of 136
aa:=integrate(1/(p+q*sin(a*x)),x)
 

   (1)
   [
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
    /
         +-------+
         | 2    2
       a\|q  - p
     ,
                                          +---------+
                                          |   2    2
            (p sin(a x) + q cos(a x) + q)\|- q  + p
      2atan(-----------------------------------------)
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    - ------------------------------------------------]
                          +---------+
                          |   2    2
                        a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R    /
--R         +-------+
--R         | 2    2
--R       a\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
--R      2atan(-----------------------------------------)
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    - ------------------------------------------------]
--R                          +---------+
--R                          |   2    2
--R                        a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 84 of 136
bb1:=2/(a*sqrt(p^2-q^2))*atan((p*tan(a*x/2)+q)/sqrt(p^2-q^2))
 

                    a x
              p tan(---) + q
                     2
        2atan(--------------)
                +---------+
                |   2    2
               \|- q  + p
   (2)  ---------------------
              +---------+
              |   2    2
            a\|- q  + p
                                                     Type: Expression Integer
--R
--R                    a x
--R              p tan(---) + q
--R                     2
--R        2atan(--------------)
--R                +---------+
--R                |   2    2
--R               \|- q  + p
--R   (2)  ---------------------
--R              +---------+
--R              |   2    2
--R            a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 85 of 136
bb2:=1/(a*sqrt(q^2-p^2))*log((p*tan((a*x)/2)+q-sqrt(q^2-p^2))/(p*tan((a*x)/2)+q+sqrt(q^2-p^2)))
 

               +-------+
               | 2    2          a x
            - \|q  - p   + p tan(---) + q
                                  2
        log(-----------------------------)
              +-------+
              | 2    2          a x
             \|q  - p   + p tan(---) + q
                                 2
   (3)  ----------------------------------
                      +-------+
                      | 2    2
                    a\|q  - p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2          a x
--R            - \|q  - p   + p tan(---) + q
--R                                  2
--R        log(-----------------------------)
--R              +-------+
--R              | 2    2          a x
--R             \|q  - p   + p tan(---) + q
--R                                 2
--R   (3)  ----------------------------------
--R                      +-------+
--R                      | 2    2
--R                    a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 86 of 136
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |   2    2
         \|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                               a x
           +-------+     p tan(---) + q
           | 2    2             2
       - 2\|q  - p  atan(--------------)
                           +---------+
                           |   2    2
                          \|- q  + p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                               a x
--R           +-------+     p tan(---) + q
--R           | 2    2             2
--R       - 2\|q  - p  atan(--------------)
--R                           +---------+
--R                           |   2    2
--R                          \|- q  + p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 87 of 136
cc2:=aa.2-bb1
 

   (5)
                                         +---------+                a x
                                         |   2    2           p tan(---) + q
           (p sin(a x) + q cos(a x) + q)\|- q  + p                   2
   - 2atan(-----------------------------------------) - 2atan(--------------)
                    2    2             2    2                   +---------+
                  (q  - p )cos(a x) + q  - p                    |   2    2
                                                               \|- q  + p
   --------------------------------------------------------------------------
                                    +---------+
                                    |   2    2
                                  a\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                         +---------+                a x
--R                                         |   2    2           p tan(---) + q
--R           (p sin(a x) + q cos(a x) + q)\|- q  + p                   2
--R   - 2atan(-----------------------------------------) - 2atan(--------------)
--R                    2    2             2    2                   +---------+
--R                  (q  - p )cos(a x) + q  - p                    |   2    2
--R                                                               \|- q  + p
--R   --------------------------------------------------------------------------
--R                                    +---------+
--R                                    |   2    2
--R                                  a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 88 of 136
cc3:=aa.1-bb2
 

   (6)
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
     + 
                +-------+
                | 2    2          a x
             - \|q  - p   + p tan(---) + q
                                   2
       - log(-----------------------------)
               +-------+
               | 2    2          a x
              \|q  - p   + p tan(---) + q
                                  2
  /
       +-------+
       | 2    2
     a\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R     + 
--R                +-------+
--R                | 2    2          a x
--R             - \|q  - p   + p tan(---) + q
--R                                   2
--R       - log(-----------------------------)
--R               +-------+
--R               | 2    2          a x
--R              \|q  - p   + p tan(---) + q
--R                                  2
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 89 of 136
cc4:=aa.2-bb2
 

   (7)
                            +-------+
                            | 2    2          a x
          +---------+    - \|q  - p   + p tan(---) + q
          |   2    2                           2
       - \|- q  + p  log(-----------------------------)
                           +-------+
                           | 2    2          a x
                          \|q  - p   + p tan(---) + q
                                              2
     + 
                                                       +---------+
           +-------+                                   |   2    2
           | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       - 2\|q  - p  atan(-----------------------------------------)
                                  2    2             2    2
                                (q  - p )cos(a x) + q  - p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-------+
--R                            | 2    2          a x
--R          +---------+    - \|q  - p   + p tan(---) + q
--R          |   2    2                           2
--R       - \|- q  + p  log(-----------------------------)
--R                           +-------+
--R                           | 2    2          a x
--R                          \|q  - p   + p tan(---) + q
--R                                              2
--R     + 
--R                                                       +---------+
--R           +-------+                                   |   2    2
--R           | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       - 2\|q  - p  atan(-----------------------------------------)
--R                                  2    2             2    2
--R                                (q  - p )cos(a x) + q  - p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 90 of 136
dd2:=ratDenom cc2
 

   (8)
                                            +---------+
                                  a x       |   2    2
           +---------+     (p tan(---) + q)\|- q  + p
           |   2    2              2
       - 2\|- q  + p  atan(----------------------------)
                                       2    2
                                      q  - p
     + 
                                                       +---------+
         +---------+                                   |   2    2
         |   2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       2\|- q  + p  atan(-----------------------------------------)
                                  2    2             2    2
                                (q  - p )cos(a x) + q  - p
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (8)
--R                                            +---------+
--R                                  a x       |   2    2
--R           +---------+     (p tan(---) + q)\|- q  + p
--R           |   2    2              2
--R       - 2\|- q  + p  atan(----------------------------)
--R                                       2    2
--R                                      q  - p
--R     + 
--R                                                       +---------+
--R         +---------+                                   |   2    2
--R         |   2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       2\|- q  + p  atan(-----------------------------------------)
--R                                  2    2             2    2
--R                                (q  - p )cos(a x) + q  - p
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 91 of 136
atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
 

                     1                    1
   (9)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
                     2                    2
Type: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--R
--R                     1                    1
--R   (9)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
--R                     2                    2
--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--E

--S 92 of 136
ee2:=atanrule2 dd2
 

   (10)
                                                  +---------+
                                   1              |   2    2     2    2
          +---------+    (%i p tan(- a x) + %i q)\|- q  + p   + q  - p
          |   2    2               2
       %i\|- q  + p  log(----------------------------------------------)
                                              2    2
                                             q  - p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                                          +---------+
                                                          |   2    2
                   (%i p sin(a x) + %i q cos(a x) + %i q)\|- q  + p
                 + 
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
              /
                   2    2             2    2
                 (q  - p )cos(a x) + q  - p
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                                         +---------+
                                                         |   2    2
                (- %i p sin(a x) - %i q cos(a x) - %i q)\|- q  + p
              + 
                  2    2             2    2
                (q  - p )cos(a x) + q  - p
           /
                2    2             2    2
              (q  - p )cos(a x) + q  - p
     + 
                                                      +---------+
                                       1              |   2    2     2    2
            +---------+    (- %i p tan(- a x) - %i q)\|- q  + p   + q  - p
            |   2    2                 2
       - %i\|- q  + p  log(------------------------------------------------)
                                                 2    2
                                                q  - p
  /
        2      2
     a q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (10)
--R                                                  +---------+
--R                                   1              |   2    2     2    2
--R          +---------+    (%i p tan(- a x) + %i q)\|- q  + p   + q  - p
--R          |   2    2               2
--R       %i\|- q  + p  log(----------------------------------------------)
--R                                              2    2
--R                                             q  - p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                                          +---------+
--R                                                          |   2    2
--R                   (%i p sin(a x) + %i q cos(a x) + %i q)\|- q  + p
--R                 + 
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R              /
--R                   2    2             2    2
--R                 (q  - p )cos(a x) + q  - p
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                                         +---------+
--R                                                         |   2    2
--R                (- %i p sin(a x) - %i q cos(a x) - %i q)\|- q  + p
--R              + 
--R                  2    2             2    2
--R                (q  - p )cos(a x) + q  - p
--R           /
--R                2    2             2    2
--R              (q  - p )cos(a x) + q  - p
--R     + 
--R                                                      +---------+
--R                                       1              |   2    2     2    2
--R            +---------+    (- %i p tan(- a x) - %i q)\|- q  + p   + q  - p
--R            |   2    2                 2
--R       - %i\|- q  + p  log(------------------------------------------------)
--R                                                 2    2
--R                                                q  - p
--R  /
--R        2      2
--R     a q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 93 of 136
ff2:=expandLog ee2
 

   (11)
            +---------+                       +---------+
            |   2    2            1           |   2    2        2       2
       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
                                  2
     + 
          +---------+                       +---------+
          |   2    2            1           |   2    2        2       2
       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
                                2
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                            +---------+
                                            |   2    2
              (p sin(a x) + q cos(a x) + q)\|- q  + p
            + 
                   2       2                2       2
              (%i q  - %i p )cos(a x) + %i q  - %i p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                               +---------+
                                               |   2    2
                 (p sin(a x) + q cos(a x) + q)\|- q  + p
               + 
                        2       2                2       2
                 (- %i q  + %i p )cos(a x) - %i q  + %i p
  /
        2      2
     a q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (11)
--R            +---------+                       +---------+
--R            |   2    2            1           |   2    2        2       2
--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
--R                                  2
--R     + 
--R          +---------+                       +---------+
--R          |   2    2            1           |   2    2        2       2
--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
--R                                2
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                            +---------+
--R                                            |   2    2
--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
--R            + 
--R                   2       2                2       2
--R              (%i q  - %i p )cos(a x) + %i q  - %i p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                               +---------+
--R                                               |   2    2
--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
--R               + 
--R                        2       2                2       2
--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
--R  /
--R        2      2
--R     a q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 94 of 136
gg2:=numer(ff2)/denom(ff2)
 

   (12)
            +---------+                       +---------+
            |   2    2            1           |   2    2        2       2
       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
                                  2
     + 
          +---------+                       +---------+
          |   2    2            1           |   2    2        2       2
       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
                                2
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                            +---------+
                                            |   2    2
              (p sin(a x) + q cos(a x) + q)\|- q  + p
            + 
                   2       2                2       2
              (%i q  - %i p )cos(a x) + %i q  - %i p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                               +---------+
                                               |   2    2
                 (p sin(a x) + q cos(a x) + q)\|- q  + p
               + 
                        2       2                2       2
                 (- %i q  + %i p )cos(a x) - %i q  + %i p
  /
        2      2
     a q  - a p
Type: Fraction SparseMultivariatePolynomial(Complex Fraction Integer,Kernel Expression Complex Fraction Integer)
--R
--R   (12)
--R            +---------+                       +---------+
--R            |   2    2            1           |   2    2        2       2
--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
--R                                  2
--R     + 
--R          +---------+                       +---------+
--R          |   2    2            1           |   2    2        2       2
--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
--R                                2
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                            +---------+
--R                                            |   2    2
--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
--R            + 
--R                   2       2                2       2
--R              (%i q  - %i p )cos(a x) + %i q  - %i p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                               +---------+
--R                                               |   2    2
--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
--R               + 
--R                        2       2                2       2
--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
--R  /
--R        2      2
--R     a q  - a p
--RType: Fraction SparseMultivariatePolynomial(Complex Fraction Integer,Kernel Expression Complex Fraction Integer)
--E

--S 95 of 136
hh2:=gg2::Expression Complex Fraction Integer
 

   (13)
            +---------+                       +---------+
            |   2    2            1           |   2    2        2       2
       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
                                  2
     + 
          +---------+                       +---------+
          |   2    2            1           |   2    2        2       2
       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
                                2
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                            +---------+
                                            |   2    2
              (p sin(a x) + q cos(a x) + q)\|- q  + p
            + 
                   2       2                2       2
              (%i q  - %i p )cos(a x) + %i q  - %i p
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                               +---------+
                                               |   2    2
                 (p sin(a x) + q cos(a x) + q)\|- q  + p
               + 
                        2       2                2       2
                 (- %i q  + %i p )cos(a x) - %i q  + %i p
  /
        2      2
     a q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (13)
--R            +---------+                       +---------+
--R            |   2    2            1           |   2    2        2       2
--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
--R                                  2
--R     + 
--R          +---------+                       +---------+
--R          |   2    2            1           |   2    2        2       2
--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
--R                                2
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                            +---------+
--R                                            |   2    2
--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
--R            + 
--R                   2       2                2       2
--R              (%i q  - %i p )cos(a x) + %i q  - %i p
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                               +---------+
--R                                               |   2    2
--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
--R               + 
--R                        2       2                2       2
--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
--R  /
--R        2      2
--R     a q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 96 of 136     14:360 Schaums and Axiom agree
complexNormalize hh2
 

   (14)  0
                                    Type: Expression Complex Fraction Integer
--R
--R   (14)  0
--R                                    Type: Expression Complex Fraction Integer
--E
)clear all
 

--S 97 of 136
aa:=integrate(1/(p+q*sin(a*x))^2,x)
 

   (1)
   [
             2              3
           (p q sin(a x) + p )
        *
           log
                                                          +-------+
                                    2    2             2  | 2    2
                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
                + 
                      2    3              3    2              3    2
                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
             /
                q sin(a x) + p
       + 
                                             +-------+
             2                               | 2    2
         (- q sin(a x) - p q cos(a x) - p q)\|q  - p
    /
                                                  +-------+
              3      3                2 2      4  | 2    2
       ((a p q  - a p q)sin(a x) + a p q  - a p )\|q  - p
     ,

                                                                 +---------+
                                                                 |   2    2
            2               3      (p sin(a x) + q cos(a x) + q)\|- q  + p
         (2p q sin(a x) + 2p )atan(-----------------------------------------)
                                            2    2             2    2
                                          (q  - p )cos(a x) + q  - p
       + 
                                             +---------+
             2                               |   2    2
         (- q sin(a x) - p q cos(a x) - p q)\|- q  + p
    /
                                                  +---------+
              3      3                2 2      4  |   2    2
       ((a p q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R             2              3
--R           (p q sin(a x) + p )
--R        *
--R           log
--R                                                          +-------+
--R                                    2    2             2  | 2    2
--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R                + 
--R                      2    3              3    2              3    2
--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R             /
--R                q sin(a x) + p
--R       + 
--R                                             +-------+
--R             2                               | 2    2
--R         (- q sin(a x) - p q cos(a x) - p q)\|q  - p
--R    /
--R                                                  +-------+
--R              3      3                2 2      4  | 2    2
--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|q  - p
--R     ,
--R
--R                                                                 +---------+
--R                                                                 |   2    2
--R            2               3      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R         (2p q sin(a x) + 2p )atan(-----------------------------------------)
--R                                            2    2             2    2
--R                                          (q  - p )cos(a x) + q  - p
--R       + 
--R                                             +---------+
--R             2                               |   2    2
--R         (- q sin(a x) - p q cos(a x) - p q)\|- q  + p
--R    /
--R                                                  +---------+
--R              3      3                2 2      4  |   2    2
--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 98 of 136
t1:=integrate(1/(p+q*sin(a*x)),x)
 

   (2)
   [
       log
                                                      +-------+
                                2    2             2  | 2    2
              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
            + 
                    2    3                3    2              3    2
              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
         /
            q sin(a x) + p
    /
         +-------+
         | 2    2
       a\|q  - p
     ,
                                          +---------+
                                          |   2    2
            (p sin(a x) + q cos(a x) + q)\|- q  + p
      2atan(-----------------------------------------)
                     2    2             2    2
                   (q  - p )cos(a x) + q  - p
    - ------------------------------------------------]
                          +---------+
                          |   2    2
                        a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                                                      +-------+
--R                                2    2             2  | 2    2
--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R            + 
--R                    2    3                3    2              3    2
--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R         /
--R            q sin(a x) + p
--R    /
--R         +-------+
--R         | 2    2
--R       a\|q  - p
--R     ,
--R                                          +---------+
--R                                          |   2    2
--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
--R      2atan(-----------------------------------------)
--R                     2    2             2    2
--R                   (q  - p )cos(a x) + q  - p
--R    - ------------------------------------------------]
--R                          +---------+
--R                          |   2    2
--R                        a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 99 of 136
bb1:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.1
 

   (3)
                            2
         (- p q sin(a x) - p )
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                    +-------+
                    | 2    2
       - q cos(a x)\|q  - p
  /
                                              +-------+
          3      2                  2      3  | 2    2
     ((a q  - a p q)sin(a x) + a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R                            2
--R         (- p q sin(a x) - p )
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                    +-------+
--R                    | 2    2
--R       - q cos(a x)\|q  - p
--R  /
--R                                              +-------+
--R          3      2                  2      3  | 2    2
--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 100 of 136
bb2:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.2
 

   (4)
                                                               +---------+
                                                               |   2    2
                          2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       (2p q sin(a x) + 2p )atan(-----------------------------------------)
                                          2    2             2    2
                                        (q  - p )cos(a x) + q  - p
     + 
                    +---------+
                    |   2    2
       - q cos(a x)\|- q  + p
  /
                                              +---------+
          3      2                  2      3  |   2    2
     ((a q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                               +---------+
--R                                                               |   2    2
--R                          2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       (2p q sin(a x) + 2p )atan(-----------------------------------------)
--R                                          2    2             2    2
--R                                        (q  - p )cos(a x) + q  - p
--R     + 
--R                    +---------+
--R                    |   2    2
--R       - q cos(a x)\|- q  + p
--R  /
--R                                              +---------+
--R          3      2                  2      3  |   2    2
--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 101 of 136
cc1:=aa.1-bb1
 

   (5)
          2
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
          2
         p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
           +-------+
           | 2    2
       - q\|q  - p
  /
                     +-------+
           2      3  | 2    2
     (a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R          2
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R          2
--R         p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R           +-------+
--R           | 2    2
--R       - q\|q  - p
--R  /
--R                     +-------+
--R           2      3  | 2    2
--R     (a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 102 of 136
cc2:=aa.2-bb1
 

   (6)
            +---------+
          2 |   2    2
         p \|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                      2    3                3    2              3    2
                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
           /
              q sin(a x) + p
     + 
                                                       +---------+
           +-------+                                   |   2    2
         2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       2p \|q  - p  atan(-----------------------------------------)
                                  2    2             2    2
                                (q  - p )cos(a x) + q  - p
     + 
           +---------+ +-------+
           |   2    2  | 2    2
       - q\|- q  + p  \|q  - p
  /
                     +---------+ +-------+
           2      3  |   2    2  | 2    2
     (a p q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R            +---------+
--R          2 |   2    2
--R         p \|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                      2    3                3    2              3    2
--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                       +---------+
--R           +-------+                                   |   2    2
--R         2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       2p \|q  - p  atan(-----------------------------------------)
--R                                  2    2             2    2
--R                                (q  - p )cos(a x) + q  - p
--R     + 
--R           +---------+ +-------+
--R           |   2    2  | 2    2
--R       - q\|- q  + p  \|q  - p
--R  /
--R                     +---------+ +-------+
--R           2      3  |   2    2  | 2    2
--R     (a p q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 103 of 136
cc3:=aa.1-bb2
 

   (7)
            +---------+
          2 |   2    2
         p \|- q  + p
      *
         log
                                                        +-------+
                                  2    2             2  | 2    2
                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
              + 
                    2    3              3    2              3    2
                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
           /
              q sin(a x) + p
     + 
                                                         +---------+
             +-------+                                   |   2    2
           2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
       - 2p \|q  - p  atan(-----------------------------------------)
                                    2    2             2    2
                                  (q  - p )cos(a x) + q  - p
     + 
           +---------+ +-------+
           |   2    2  | 2    2
       - q\|- q  + p  \|q  - p
  /
                     +---------+ +-------+
           2      3  |   2    2  | 2    2
     (a p q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R            +---------+
--R          2 |   2    2
--R         p \|- q  + p
--R      *
--R         log
--R                                                        +-------+
--R                                  2    2             2  | 2    2
--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
--R              + 
--R                    2    3              3    2              3    2
--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
--R           /
--R              q sin(a x) + p
--R     + 
--R                                                         +---------+
--R             +-------+                                   |   2    2
--R           2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
--R       - 2p \|q  - p  atan(-----------------------------------------)
--R                                    2    2             2    2
--R                                  (q  - p )cos(a x) + q  - p
--R     + 
--R           +---------+ +-------+
--R           |   2    2  | 2    2
--R       - q\|- q  + p  \|q  - p
--R  /
--R                     +---------+ +-------+
--R           2      3  |   2    2  | 2    2
--R     (a p q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 104 of 136    14:361 Schaums and Axiom differ by a constant
cc4:=aa.2-bb2
 

                q
   (8)  - -------------
               2      3
          a p q  - a p
                                                     Type: Expression Integer
--R
--R                q
--R   (8)  - -------------
--R               2      3
--R          a p q  - a p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 105 of 136
aa:=integrate(1/(p^2+q^2*sin(a*x)^2),x)
 

   (1)
                             +-------+
                             | 2    2
                  p sin(a x)\|q  + p
       atan(-------------------------------)
               2     2              2     2
            (2q  + 2p )cos(a x) + 2q  + 2p
     + 
                 2    2              2     2
             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
       atan(-----------------------------------------)
                                            +-------+
                       2                    | 2    2
            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
  /
         +-------+
         | 2    2
     a p\|q  + p
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                             +-------+
--R                             | 2    2
--R                  p sin(a x)\|q  + p
--R       atan(-------------------------------)
--R               2     2              2     2
--R            (2q  + 2p )cos(a x) + 2q  + 2p
--R     + 
--R                 2    2              2     2
--R             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
--R       atan(-----------------------------------------)
--R                                            +-------+
--R                       2                    | 2    2
--R            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 106 of 136
bb:=1/(a*p*sqrt(p^2+q^2))*atan((sqrt(p^2+q^2)*tan(a*x))/p)
 

                      +-------+
                      | 2    2
             tan(a x)\|q  + p
        atan(------------------)
                      p
   (2)  ------------------------
                  +-------+
                  | 2    2
              a p\|q  + p
                                                     Type: Expression Integer
--R
--R                      +-------+
--R                      | 2    2
--R             tan(a x)\|q  + p
--R        atan(------------------)
--R                      p
--R   (2)  ------------------------
--R                  +-------+
--R                  | 2    2
--R              a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 107 of 136
cc:=aa-bb
 

   (3)
                       +-------+                          +-------+
                       | 2    2                           | 2    2
              tan(a x)\|q  + p                 p sin(a x)\|q  + p
       - atan(------------------) + atan(-------------------------------)
                       p                    2     2              2     2
                                         (2q  + 2p )cos(a x) + 2q  + 2p
     + 
                 2    2              2     2
             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
       atan(-----------------------------------------)
                                            +-------+
                       2                    | 2    2
            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
  /
         +-------+
         | 2    2
     a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                       +-------+                          +-------+
--R                       | 2    2                           | 2    2
--R              tan(a x)\|q  + p                 p sin(a x)\|q  + p
--R       - atan(------------------) + atan(-------------------------------)
--R                       p                    2     2              2     2
--R                                         (2q  + 2p )cos(a x) + 2q  + 2p
--R     + 
--R                 2    2              2     2
--R             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
--R       atan(-----------------------------------------)
--R                                            +-------+
--R                       2                    | 2    2
--R            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 108 of 136
dd:=ratDenom cc
 

   (4)
                                 +-------+
          +-------+              | 2    2
          | 2    2      tan(a x)\|q  + p
       - \|q  + p  atan(------------------)
                                 p
     + 
                                                                  +-------+
        +-------+            2    2              2     2          | 2    2
        | 2    2         ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
       \|q  + p  atan(--------------------------------------------------------)
                          2    3         2        2     3               2    3
                      (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                                       +-------+
        +-------+                      | 2    2
        | 2    2            p sin(a x)\|q  + p
       \|q  + p  atan(-------------------------------)
                         2     2              2     2
                      (2q  + 2p )cos(a x) + 2q  + 2p
  /
          2      3
     a p q  + a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                 +-------+
--R          +-------+              | 2    2
--R          | 2    2      tan(a x)\|q  + p
--R       - \|q  + p  atan(------------------)
--R                                 p
--R     + 
--R                                                                  +-------+
--R        +-------+            2    2              2     2          | 2    2
--R        | 2    2         ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R       \|q  + p  atan(--------------------------------------------------------)
--R                          2    3         2        2     3               2    3
--R                      (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                                       +-------+
--R        +-------+                      | 2    2
--R        | 2    2            p sin(a x)\|q  + p
--R       \|q  + p  atan(-------------------------------)
--R                         2     2              2     2
--R                      (2q  + 2p )cos(a x) + 2q  + 2p
--R  /
--R          2      3
--R     a p q  + a p
--R                                                     Type: Expression Integer
--E

--S 109 of 136
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (5)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (5)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 110 of 136
ee:=atanrule dd
 

   (6)
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                +-------+
                                | 2    2          2        2                 2
                   - p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
                 + 
                        2
                   2%i p
              /
                              +-------+
                              | 2    2          2        2                 2
                   p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
                 + 
                        2
                   2%i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                              +-------+
                         2    2              2     2          | 2    2
                   ((- 2q  - p )cos(a x) - 2q  - 2p )sin(a x)\|q  + p
                 + 
                          2       3         2           2        3
                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
                 + 
                         2       3
                   %i p q  + %i p
              /
                                                            +-------+
                       2    2              2     2          | 2    2
                   ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
                 + 
                          2       3         2           2        3
                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
                 + 
                         2       3
                   %i p q  + %i p
     + 
                                  +-------+
          +-------+               | 2    2
          | 2    2     - tan(a x)\|q  + p   + %i p
       %i\|q  + p  log(---------------------------)
                                 +-------+
                                 | 2    2
                        tan(a x)\|q  + p   + %i p
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (6)
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                +-------+
--R                                | 2    2          2        2                 2
--R                   - p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
--R                 + 
--R                        2
--R                   2%i p
--R              /
--R                              +-------+
--R                              | 2    2          2        2                 2
--R                   p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
--R                 + 
--R                        2
--R                   2%i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                              +-------+
--R                         2    2              2     2          | 2    2
--R                   ((- 2q  - p )cos(a x) - 2q  - 2p )sin(a x)\|q  + p
--R                 + 
--R                          2       3         2           2        3
--R                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
--R                 + 
--R                         2       3
--R                   %i p q  + %i p
--R              /
--R                                                            +-------+
--R                       2    2              2     2          | 2    2
--R                   ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R                 + 
--R                          2       3         2           2        3
--R                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
--R                 + 
--R                         2       3
--R                   %i p q  + %i p
--R     + 
--R                                  +-------+
--R          +-------+               | 2    2
--R          | 2    2     - tan(a x)\|q  + p   + %i p
--R       %i\|q  + p  log(---------------------------)
--R                                 +-------+
--R                                 | 2    2
--R                        tan(a x)\|q  + p   + %i p
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 111 of 136
ff:=expandLog ee
 

   (7)
            +-------+             +-------+
            | 2    2              | 2    2
       - %i\|q  + p  log(tan(a x)\|q  + p   + %i p)
     + 
          +-------+             +-------+
          | 2    2              | 2    2
       %i\|q  + p  log(tan(a x)\|q  + p   - %i p)
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
         log
                                                       +-------+
                  2    2              2     2          | 2    2
              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
            + 
                  3
              %i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                          +-------+
                     2    2              2     2          | 2    2
                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  - %i p
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
                      +-------+
                      | 2    2          2        2                 2        2
       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                            +-------+
                            | 2    2            2        2                 2
                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
               + 
                        2
                 - 2%i p
     + 
                     +-------+
                     | 2    2
       - %i log(- 1)\|q  + p
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (7)
--R            +-------+             +-------+
--R            | 2    2              | 2    2
--R       - %i\|q  + p  log(tan(a x)\|q  + p   + %i p)
--R     + 
--R          +-------+             +-------+
--R          | 2    2              | 2    2
--R       %i\|q  + p  log(tan(a x)\|q  + p   - %i p)
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R         log
--R                                                       +-------+
--R                  2    2              2     2          | 2    2
--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
--R            + 
--R                  3
--R              %i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                          +-------+
--R                     2    2              2     2          | 2    2
--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  - %i p
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R                      +-------+
--R                      | 2    2          2        2                 2        2
--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                            +-------+
--R                            | 2    2            2        2                 2
--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
--R               + 
--R                        2
--R                 - 2%i p
--R     + 
--R                     +-------+
--R                     | 2    2
--R       - %i log(- 1)\|q  + p
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 112 of 136
tanrule2:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (8)  tan(a) == ------
                  cos(a)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                  sin(a)
--R   (8)  tan(a) == ------
--R                  cos(a)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 113 of 136
gg:=tanrule2 ff
 

   (9)
            +-------+
            | 2    2
         %i\|q  + p
      *
         log
                                                       +-------+
                  2    2              2     2          | 2    2
              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
            + 
                  3
              %i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                          +-------+
                     2    2              2     2          | 2    2
                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  - %i p
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
                      +-------+
                      | 2    2          2        2                 2        2
       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                            +-------+
                            | 2    2            2        2                 2
                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
               + 
                        2
                 - 2%i p
     + 
                                  +-------+
            +-------+             | 2    2
            | 2    2     sin(a x)\|q  + p   + %i p cos(a x)
       - %i\|q  + p  log(----------------------------------)
                                      cos(a x)
     + 
                              +-------+
        +-------+             | 2    2                                 +-------+
        | 2    2     sin(a x)\|q  + p   - %i p cos(a x)                | 2    2
     %i\|q  + p  log(----------------------------------) - %i log(- 1)\|q  + p
                                  cos(a x)
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (9)
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R         log
--R                                                       +-------+
--R                  2    2              2     2          | 2    2
--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
--R            + 
--R                  3
--R              %i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                          +-------+
--R                     2    2              2     2          | 2    2
--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  - %i p
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R                      +-------+
--R                      | 2    2          2        2                 2        2
--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                            +-------+
--R                            | 2    2            2        2                 2
--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
--R               + 
--R                        2
--R                 - 2%i p
--R     + 
--R                                  +-------+
--R            +-------+             | 2    2
--R            | 2    2     sin(a x)\|q  + p   + %i p cos(a x)
--R       - %i\|q  + p  log(----------------------------------)
--R                                      cos(a x)
--R     + 
--R                              +-------+
--R        +-------+             | 2    2                                 +-------+
--R        | 2    2     sin(a x)\|q  + p   - %i p cos(a x)                | 2    2
--R     %i\|q  + p  log(----------------------------------) - %i log(- 1)\|q  + p
--R                                  cos(a x)
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 114 of 136
hh:=expandLog gg
 

   (10)
            +-------+
            | 2    2
         %i\|q  + p
      *
         log
                                                       +-------+
                  2    2              2     2          | 2    2
              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
            + 
                  3
              %i p
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                                                          +-------+
                     2    2              2     2          | 2    2
                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  - %i p
     + 
            +-------+
            | 2    2
         %i\|q  + p
      *
                      +-------+
                      | 2    2          2        2                 2        2
       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
     + 
       -
               +-------+
               | 2    2
            %i\|q  + p
         *
            log
                            +-------+
                            | 2    2            2        2                 2
                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
               + 
                        2
                 - 2%i p
     + 
            +-------+             +-------+
            | 2    2              | 2    2
       - %i\|q  + p  log(sin(a x)\|q  + p   + %i p cos(a x))
     + 
        +-------+             +-------+                                +-------+
        | 2    2              | 2    2                                 | 2    2
     %i\|q  + p  log(sin(a x)\|q  + p   - %i p cos(a x)) - %i log(- 1)\|q  + p
  /
           2       3
     2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R   (10)
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R         log
--R                                                       +-------+
--R                  2    2              2     2          | 2    2
--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
--R            + 
--R                  3
--R              %i p
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                                                          +-------+
--R                     2    2              2     2          | 2    2
--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  - %i p
--R     + 
--R            +-------+
--R            | 2    2
--R         %i\|q  + p
--R      *
--R                      +-------+
--R                      | 2    2          2        2                 2        2
--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
--R     + 
--R       -
--R               +-------+
--R               | 2    2
--R            %i\|q  + p
--R         *
--R            log
--R                            +-------+
--R                            | 2    2            2        2                 2
--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
--R               + 
--R                        2
--R                 - 2%i p
--R     + 
--R            +-------+             +-------+
--R            | 2    2              | 2    2
--R       - %i\|q  + p  log(sin(a x)\|q  + p   + %i p cos(a x))
--R     + 
--R        +-------+             +-------+                                +-------+
--R        | 2    2              | 2    2                                 | 2    2
--R     %i\|q  + p  log(sin(a x)\|q  + p   - %i p cos(a x)) - %i log(- 1)\|q  + p
--R  /
--R           2       3
--R     2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E

--S 115 of 136    14:362 Schaums and Axiom differ by a constant
ii:=complexNormalize hh
 

                                                   +-------+
                                                   | 2    2
         (%i log(%i) - %i log(- %i) - %i log(- 1))\|q  + p
   (11)  ---------------------------------------------------
                                 2       3
                           2a p q  + 2a p
                                             Type: Expression Complex Integer
--R
--R                                                   +-------+
--R                                                   | 2    2
--R         (%i log(%i) - %i log(- %i) - %i log(- 1))\|q  + p
--R   (11)  ---------------------------------------------------
--R                                 2       3
--R                           2a p q  + 2a p
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 116 of 136
aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x)
 

   (1)
   [
       log
                                                +-------+
                   2     2         2    2    2  | 2    2
              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
            + 
                   2     3
              (2p q  - 2p )cos(a x)sin(a x)
         /
             2        2    2    2
            q cos(a x)  - q  + p
    /
            +-------+
            | 2    2
       2a p\|q  - p
     ,

                                +---------+
                                |   2    2
                     p sin(a x)\|- q  + p
         - atan(-------------------------------)
                   2     2              2     2
                (2q  - 2p )cos(a x) + 2q  - 2p
       + 
                      2    2              2     2
                  ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
         - atan(-------------------------------------------)
                                                +---------+
                           2                    |   2    2
                (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
    /
           +---------+
           |   2    2
       a p\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                                +-------+
--R                   2     2         2    2    2  | 2    2
--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
--R            + 
--R                   2     3
--R              (2p q  - 2p )cos(a x)sin(a x)
--R         /
--R             2        2    2    2
--R            q cos(a x)  - q  + p
--R    /
--R            +-------+
--R            | 2    2
--R       2a p\|q  - p
--R     ,
--R
--R                                +---------+
--R                                |   2    2
--R                     p sin(a x)\|- q  + p
--R         - atan(-------------------------------)
--R                   2     2              2     2
--R                (2q  - 2p )cos(a x) + 2q  - 2p
--R       + 
--R                      2    2              2     2
--R                  ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R         - atan(-------------------------------------------)
--R                                                +---------+
--R                           2                    |   2    2
--R                (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R    /
--R           +---------+
--R           |   2    2
--R       a p\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 117 of 136
bb1:=1/(a*p*sqrt(p^2-q^2))*atan((sqrt(p^2-q^2)*tan(a*x))/p)
 

                      +---------+
                      |   2    2
             tan(a x)\|- q  + p
        atan(--------------------)
                       p
   (2)  --------------------------
                  +---------+
                  |   2    2
              a p\|- q  + p
                                                     Type: Expression Integer
--R
--R                      +---------+
--R                      |   2    2
--R             tan(a x)\|- q  + p
--R        atan(--------------------)
--R                       p
--R   (2)  --------------------------
--R                  +---------+
--R                  |   2    2
--R              a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 118 of 136
bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((sqrt(q^2-p^2)*tan(a*x)+p)/(sqrt(q^2-p^2)*tan(a*x)-p))
 

                     +-------+
                     | 2    2
            tan(a x)\|q  - p   + p
        log(----------------------)
                     +-------+
                     | 2    2
            tan(a x)\|q  - p   - p
   (3)  ---------------------------
                    +-------+
                    | 2    2
               2a p\|q  - p
                                                     Type: Expression Integer
--R
--R                     +-------+
--R                     | 2    2
--R            tan(a x)\|q  - p   + p
--R        log(----------------------)
--R                     +-------+
--R                     | 2    2
--R            tan(a x)\|q  - p   - p
--R   (3)  ---------------------------
--R                    +-------+
--R                    | 2    2
--R               2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 119 of 136
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |   2    2
         \|- q  + p
      *
         log
                                                  +-------+
                     2     2         2    2    2  | 2    2
                ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
              + 
                     2     3
                (2p q  - 2p )cos(a x)sin(a x)
           /
               2        2    2    2
              q cos(a x)  - q  + p
     + 
                                  +---------+
           +-------+              |   2    2
           | 2    2      tan(a x)\|- q  + p
       - 2\|q  - p  atan(--------------------)
                                   p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R         log
--R                                                  +-------+
--R                     2     2         2    2    2  | 2    2
--R                ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
--R              + 
--R                     2     3
--R                (2p q  - 2p )cos(a x)sin(a x)
--R           /
--R               2        2    2    2
--R              q cos(a x)  - q  + p
--R     + 
--R                                  +---------+
--R           +-------+              |   2    2
--R           | 2    2      tan(a x)\|- q  + p
--R       - 2\|q  - p  atan(--------------------)
--R                                   p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 120 of 136
cc2:=aa.2-bb1
 

   (5)
                       +---------+                         +---------+
                       |   2    2                          |   2    2
              tan(a x)\|- q  + p                p sin(a x)\|- q  + p
       - atan(--------------------) - atan(-------------------------------)
                        p                     2     2              2     2
                                           (2q  - 2p )cos(a x) + 2q  - 2p
     + 
                    2    2              2     2
                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
       - atan(-------------------------------------------)
                                              +---------+
                         2                    |   2    2
              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
         +---------+
         |   2    2
     a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R                       +---------+                         +---------+
--R                       |   2    2                          |   2    2
--R              tan(a x)\|- q  + p                p sin(a x)\|- q  + p
--R       - atan(--------------------) - atan(-------------------------------)
--R                        p                     2     2              2     2
--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
--R     + 
--R                    2    2              2     2
--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R       - atan(-------------------------------------------)
--R                                              +---------+
--R                         2                    |   2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 121 of 136
cc3:=aa.1-bb2
 

   (6)
                      +-------+
                      | 2    2
             tan(a x)\|q  - p   + p
       - log(----------------------)
                      +-------+
                      | 2    2
             tan(a x)\|q  - p   - p
     + 
       log
                                                +-------+
                   2     2         2    2    2  | 2    2
              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
            + 
                   2     3
              (2p q  - 2p )cos(a x)sin(a x)
         /
             2        2    2    2
            q cos(a x)  - q  + p
  /
          +-------+
          | 2    2
     2a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                      +-------+
--R                      | 2    2
--R             tan(a x)\|q  - p   + p
--R       - log(----------------------)
--R                      +-------+
--R                      | 2    2
--R             tan(a x)\|q  - p   - p
--R     + 
--R       log
--R                                                +-------+
--R                   2     2         2    2    2  | 2    2
--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
--R            + 
--R                   2     3
--R              (2p q  - 2p )cos(a x)sin(a x)
--R         /
--R             2        2    2    2
--R            q cos(a x)  - q  + p
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 122 of 136
cc4:=aa.2-bb2
 

   (7)
                                  +-------+
          +---------+             | 2    2
          |   2    2     tan(a x)\|q  - p   + p
       - \|- q  + p  log(----------------------)
                                  +-------+
                                  | 2    2
                         tan(a x)\|q  - p   - p
     + 
                                         +---------+
           +-------+                     |   2    2
           | 2    2           p sin(a x)\|- q  + p
       - 2\|q  - p  atan(-------------------------------)
                            2     2              2     2
                         (2q  - 2p )cos(a x) + 2q  - 2p
     + 
           +-------+           2    2              2     2
           | 2    2        ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
       - 2\|q  - p  atan(-------------------------------------------)
                                                         +---------+
                                    2                    |   2    2
                         (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                  +-------+
--R          +---------+             | 2    2
--R          |   2    2     tan(a x)\|q  - p   + p
--R       - \|- q  + p  log(----------------------)
--R                                  +-------+
--R                                  | 2    2
--R                         tan(a x)\|q  - p   - p
--R     + 
--R                                         +---------+
--R           +-------+                     |   2    2
--R           | 2    2           p sin(a x)\|- q  + p
--R       - 2\|q  - p  atan(-------------------------------)
--R                            2     2              2     2
--R                         (2q  - 2p )cos(a x) + 2q  - 2p
--R     + 
--R           +-------+           2    2              2     2
--R           | 2    2        ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R       - 2\|q  - p  atan(-------------------------------------------)
--R                                                         +---------+
--R                                    2                    |   2    2
--R                         (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 123 of 136
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (8)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (8)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 124 of 136
dd2:=tanrule cc2
 

   (9)
                       +---------+                         +---------+
                       |   2    2                          |   2    2
              sin(a x)\|- q  + p                p sin(a x)\|- q  + p
       - atan(--------------------) - atan(-------------------------------)
                   p cos(a x)                 2     2              2     2
                                           (2q  - 2p )cos(a x) + 2q  - 2p
     + 
                    2    2              2     2
                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
       - atan(-------------------------------------------)
                                              +---------+
                         2                    |   2    2
              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
         +---------+
         |   2    2
     a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (9)
--R                       +---------+                         +---------+
--R                       |   2    2                          |   2    2
--R              sin(a x)\|- q  + p                p sin(a x)\|- q  + p
--R       - atan(--------------------) - atan(-------------------------------)
--R                   p cos(a x)                 2     2              2     2
--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
--R     + 
--R                    2    2              2     2
--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
--R       - atan(-------------------------------------------)
--R                                              +---------+
--R                         2                    |   2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 125 of 136
ee2:=ratDenom dd2
 

   (10)
       -
             +---------+
             |   2    2
            \|- q  + p
         *
                                                            +---------+
                       2    2              2     2          |   2    2
                   ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
            atan(--------------------------------------------------------)
                     2    3         2        2     3               2    3
                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                 +---------+
        +---------+              |   2    2
        |   2    2      sin(a x)\|- q  + p
       \|- q  + p  atan(--------------------)
                             p cos(a x)
     + 
                                        +---------+
        +---------+                     |   2    2
        |   2    2           p sin(a x)\|- q  + p
       \|- q  + p  atan(-------------------------------)
                           2     2              2     2
                        (2q  - 2p )cos(a x) + 2q  - 2p
  /
          2      3
     a p q  - a p
                                                     Type: Expression Integer
--R
--R   (10)
--R       -
--R             +---------+
--R             |   2    2
--R            \|- q  + p
--R         *
--R                                                            +---------+
--R                       2    2              2     2          |   2    2
--R                   ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R            atan(--------------------------------------------------------)
--R                     2    3         2        2     3               2    3
--R                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                 +---------+
--R        +---------+              |   2    2
--R        |   2    2      sin(a x)\|- q  + p
--R       \|- q  + p  atan(--------------------)
--R                             p cos(a x)
--R     + 
--R                                        +---------+
--R        +---------+                     |   2    2
--R        |   2    2           p sin(a x)\|- q  + p
--R       \|- q  + p  atan(-------------------------------)
--R                           2     2              2     2
--R                        (2q  - 2p )cos(a x) + 2q  - 2p
--R  /
--R          2      3
--R     a p q  - a p
--R                                                     Type: Expression Integer
--E

--S 126 of 136
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                             - x + %i
                      %i log(--------)
                              x + %i
   (11)  atan(x) == - ----------------
                              2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             - x + %i
--R                      %i log(--------)
--R                              x + %i
--R   (11)  atan(x) == - ----------------
--R                              2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 127 of 136
ff2:=atanrule ee2
 

   (12)
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                +---------+
                                |   2    2          2        2                 2
                   - p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
                 + 
                          2
                   - 2%i p
              /
                              +---------+
                              |   2    2          2        2                 2
                   p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
                 + 
                          2
                   - 2%i p
     + 
                                      +---------+
            +---------+               |   2    2
            |   2    2     - sin(a x)\|- q  + p   + %i p cos(a x)
       - %i\|- q  + p  log(--------------------------------------)
                                     +---------+
                                     |   2    2
                            sin(a x)\|- q  + p   + %i p cos(a x)
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                                           +---------+
                      2    2              2     2          |   2    2
                ((- 2q  + p )cos(a x) - 2q  + 2p )sin(a x)\|- q  + p
              + 
                       2       3         2           2        3
                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
              + 
                      2       3
                %i p q  - %i p
           /
                                                         +---------+
                    2    2              2     2          |   2    2
                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
              + 
                       2       3         2           2        3
                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
              + 
                      2       3
                %i p q  - %i p
  /
           2       3
     2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R   (12)
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                +---------+
--R                                |   2    2          2        2                 2
--R                   - p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
--R                 + 
--R                          2
--R                   - 2%i p
--R              /
--R                              +---------+
--R                              |   2    2          2        2                 2
--R                   p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
--R                 + 
--R                          2
--R                   - 2%i p
--R     + 
--R                                      +---------+
--R            +---------+               |   2    2
--R            |   2    2     - sin(a x)\|- q  + p   + %i p cos(a x)
--R       - %i\|- q  + p  log(--------------------------------------)
--R                                     +---------+
--R                                     |   2    2
--R                            sin(a x)\|- q  + p   + %i p cos(a x)
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                                           +---------+
--R                      2    2              2     2          |   2    2
--R                ((- 2q  + p )cos(a x) - 2q  + 2p )sin(a x)\|- q  + p
--R              + 
--R                       2       3         2           2        3
--R                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R              + 
--R                      2       3
--R                %i p q  - %i p
--R           /
--R                                                         +---------+
--R                    2    2              2     2          |   2    2
--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R              + 
--R                       2       3         2           2        3
--R                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R              + 
--R                      2       3
--R                %i p q  - %i p
--R  /
--R           2       3
--R     2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E

--S 128 of 136
gg2:=expandLog ff2
 

   (13)
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                                                          +---------+
                     2    2              2     2          |   2    2
                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
               + 
                        2       3         2           2        3
                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
               + 
                       2       3
                 %i p q  - %i p
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
         log
                                                       +---------+
                  2    2              2     2          |   2    2
              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
            + 
                       2       3         2             2        3
              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
            + 
                      2       3
              - %i p q  + %i p
     + 
            +---------+
            |   2    2
         %i\|- q  + p
      *
                      +---------+
                      |   2    2          2        2                 2        2
       log(p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q  - 2%i p )
     + 
       -
               +---------+
               |   2    2
            %i\|- q  + p
         *
            log
                            +---------+
                            |   2    2            2        2                 2
                 p sin(a x)\|- q  + p   + (- 2%i q  + 2%i p )cos(a x) - 2%i q
               + 
                      2
                 2%i p
     + 
          +---------+             +---------+
          |   2    2              |   2    2
       %i\|- q  + p  log(sin(a x)\|- q  + p   + %i p cos(a x))
     + 
            +---------+             +---------+
            |   2    2              |   2    2
       - %i\|- q  + p  log(sin(a x)\|- q  + p   - %i p cos(a x))
     + 
                     +---------+
                     |   2    2
       - %i log(- 1)\|- q  + p
  /
           2       3
     2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R   (13)
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                                                          +---------+
--R                     2    2              2     2          |   2    2
--R                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R               + 
--R                        2       3         2           2        3
--R                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R               + 
--R                       2       3
--R                 %i p q  - %i p
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R         log
--R                                                       +---------+
--R                  2    2              2     2          |   2    2
--R              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
--R            + 
--R                       2       3         2             2        3
--R              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
--R            + 
--R                      2       3
--R              - %i p q  + %i p
--R     + 
--R            +---------+
--R            |   2    2
--R         %i\|- q  + p
--R      *
--R                      +---------+
--R                      |   2    2          2        2                 2        2
--R       log(p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q  - 2%i p )
--R     + 
--R       -
--R               +---------+
--R               |   2    2
--R            %i\|- q  + p
--R         *
--R            log
--R                            +---------+
--R                            |   2    2            2        2                 2
--R                 p sin(a x)\|- q  + p   + (- 2%i q  + 2%i p )cos(a x) - 2%i q
--R               + 
--R                      2
--R                 2%i p
--R     + 
--R          +---------+             +---------+
--R          |   2    2              |   2    2
--R       %i\|- q  + p  log(sin(a x)\|- q  + p   + %i p cos(a x))
--R     + 
--R            +---------+             +---------+
--R            |   2    2              |   2    2
--R       - %i\|- q  + p  log(sin(a x)\|- q  + p   - %i p cos(a x))
--R     + 
--R                     +---------+
--R                     |   2    2
--R       - %i log(- 1)\|- q  + p
--R  /
--R           2       3
--R     2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E

--S 129 of 136
rootrule4a:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(sqrt(p^2-q^2)==sqrt(p-q)*sqrt(q+p))
 

          +---------+
          |   2    2      +-------+ +-----+
   (14)  \|- q  + p   == \|- q + p \|q + p
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R          +---------+
--R          |   2    2      +-------+ +-----+
--R   (14)  \|- q  + p   == \|- q + p \|q + p
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 130 of 136
hh2:=rootrule4a gg2
 

   (15)
       -
               +-------+ +-----+
            %i\|- q + p \|q + p
         *
            log
                     2    2              2     2          +-------+ +-----+
                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
               + 
                        2       3         2           2        3
                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
               + 
                       2       3
                 %i p q  - %i p
     + 
            +-------+ +-----+
         %i\|- q + p \|q + p
      *
         log
                  2    2              2     2          +-------+ +-----+
              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
            + 
                       2       3         2             2        3
              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
            + 
                      2       3
              - %i p q  + %i p
     + 
            +-------+ +-----+
         %i\|- q + p \|q + p
      *
         log
                         +-------+ +-----+         2        2                 2
              p sin(a x)\|- q + p \|q + p  + (2%i q  - 2%i p )cos(a x) + 2%i q
            + 
                     2
              - 2%i p
     + 
       -
               +-------+ +-----+
            %i\|- q + p \|q + p
         *
            log
                            +-------+ +-----+           2        2
                 p sin(a x)\|- q + p \|q + p  + (- 2%i q  + 2%i p )cos(a x)
               + 
                        2        2
                 - 2%i q  + 2%i p
     + 
          +-------+ +-----+             +-------+ +-----+
       %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  + %i p cos(a x))
     + 
            +-------+ +-----+             +-------+ +-----+
       - %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  - %i p cos(a x))
     + 
                     +-------+ +-----+
       - %i log(- 1)\|- q + p \|q + p
  /
           2       3
     2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R   (15)
--R       -
--R               +-------+ +-----+
--R            %i\|- q + p \|q + p
--R         *
--R            log
--R                     2    2              2     2          +-------+ +-----+
--R                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
--R               + 
--R                        2       3         2           2        3
--R                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
--R               + 
--R                       2       3
--R                 %i p q  - %i p
--R     + 
--R            +-------+ +-----+
--R         %i\|- q + p \|q + p
--R      *
--R         log
--R                  2    2              2     2          +-------+ +-----+
--R              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
--R            + 
--R                       2       3         2             2        3
--R              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
--R            + 
--R                      2       3
--R              - %i p q  + %i p
--R     + 
--R            +-------+ +-----+
--R         %i\|- q + p \|q + p
--R      *
--R         log
--R                         +-------+ +-----+         2        2                 2
--R              p sin(a x)\|- q + p \|q + p  + (2%i q  - 2%i p )cos(a x) + 2%i q
--R            + 
--R                     2
--R              - 2%i p
--R     + 
--R       -
--R               +-------+ +-----+
--R            %i\|- q + p \|q + p
--R         *
--R            log
--R                            +-------+ +-----+           2        2
--R                 p sin(a x)\|- q + p \|q + p  + (- 2%i q  + 2%i p )cos(a x)
--R               + 
--R                        2        2
--R                 - 2%i q  + 2%i p
--R     + 
--R          +-------+ +-----+             +-------+ +-----+
--R       %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  + %i p cos(a x))
--R     + 
--R            +-------+ +-----+             +-------+ +-----+
--R       - %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  - %i p cos(a x))
--R     + 
--R                     +-------+ +-----+
--R       - %i log(- 1)\|- q + p \|q + p
--R  /
--R           2       3
--R     2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E

--S 131 of 136    14:363 Schaums and Axiom differ by a constant
ii2:=complexNormalize hh2
 

                                                   +-------+ +-----+
         (%i log(%i) - %i log(- %i) - %i log(- 1))\|- q + p \|q + p
   (16)  -----------------------------------------------------------
                                     2       3
                               2a p q  - 2a p
                                             Type: Expression Complex Integer
--R
--R                                                   +-------+ +-----+
--R         (%i log(%i) - %i log(- %i) - %i log(- 1))\|- q + p \|q + p
--R   (16)  -----------------------------------------------------------
--R                                     2       3
--R                               2a p q  - 2a p
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 132 of 136    14:364 Axiom cannot compute this integral
aa:=integrate(x^m*sin(a*x),x)
 

           x
         ++             m
   (1)   |   sin(%I a)%I d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             m
--I   (1)   |   sin(%I a)%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 133 of 136    14:365 Axiom cannot compute this integral
aa:=integrate(sin(a*x)/x^n,x)
 

           x
         ++  sin(%I a)
   (1)   |   --------- d%I
        ++        n
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  sin(%I a)
--I   (1)   |   --------- d%I
--R        ++        n
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 134 of 136    14:366 Axiom cannot compute this integral
aa:=integrate(sin(a*x)^n,x)
 

           x
         ++           n
   (1)   |   sin(%I a) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   sin(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 135 of 136    14:367 Axiom cannot compute this integral
aa:=integrate(1/(sin(a*x))^n,x)
 

           x
         ++       1
   (1)   |   ---------- d%I
        ++            n
             sin(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ---------- d%I
--R        ++            n
--I             sin(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 136 of 136    14:368 Axiom cannot compute this integral
aa:=integrate(x/sin(a*x)^n,x)
 

           x
         ++      %I
   (1)   |   ---------- d%I
        ++            n
             sin(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   ---------- d%I
--R        ++            n
--I             sin(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to asinhatanh.output (2010/3/27, 18:23:8).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.00,0.000000000,asinh(0.00),asinh(0.00)-0.000000000],_
[0.01,0.009999833,asinh(0.01),asinh(0.01)-0.009999833],_
[0.02,0.019998667,asinh(0.02),asinh(0.02)-0.019998667],_
[0.03,0.029995502,asinh(0.03),asinh(0.03)-0.029995502],_
[0.04,0.039989341,asinh(0.04),asinh(0.04)-0.039989341],_
[0.05,0.049979190,asinh(0.05),asinh(0.05)-0.049979190],_
[0.06,0.059964058,asinh(0.06),asinh(0.06)-0.059964058],_
[0.07,0.069942959,asinh(0.07),asinh(0.07)-0.069942959],_
[0.08,0.079914912,asinh(0.08),asinh(0.08)-0.079914912],_
[0.09,0.089878941,asinh(0.09),asinh(0.09)-0.089878941],_
[0.10,0.099834079,asinh(0.10),asinh(0.10)-0.099834079],_
[0.11,0.109779366,asinh(0.11),asinh(0.11)-0.109779366],_
[0.12,0.119713851,asinh(0.12),asinh(0.12)-0.119713851],_
[0.13,0.129636590,asinh(0.13),asinh(0.13)-0.129636590],_
[0.14,0.139546654,asinh(0.14),asinh(0.14)-0.139546654],_
[0.15,0.149443120,asinh(0.15),asinh(0.15)-0.149443120],_
[0.16,0.159325080,asinh(0.16),asinh(0.16)-0.159325080],_
[0.17,0.169191636,asinh(0.17),asinh(0.17)-0.169191636],_
[0.18,0.179041904,asinh(0.18),asinh(0.18)-0.179041904],_
[0.19,0.188875015,asinh(0.19),asinh(0.19)-0.188875015],_
[0.20,0.198690110,asinh(0.20),asinh(0.20)-0.198690110],_
[0.21,0.208486350,asinh(0.21),asinh(0.21)-0.208486350],_
[0.22,0.218262908,asinh(0.22),asinh(0.22)-0.218262908],_
[0.23,0.228018972,asinh(0.23),asinh(0.23)-0.228018972],_
[0.24,0.237753749,asinh(0.24),asinh(0.24)-0.237753749],_
[0.25,0.247466462,asinh(0.25),asinh(0.25)-0.247466462],_
[0.26,0.257156349,asinh(0.26),asinh(0.26)-0.257156349],_
[0.27,0.266822667,asinh(0.27),asinh(0.27)-0.266822667],_
[0.28,0.276464691,asinh(0.28),asinh(0.28)-0.276464691],_
[0.29,0.286081715,asinh(0.29),asinh(0.29)-0.286081715],_
[0.30,0.295673048,asinh(0.30),asinh(0.30)-0.295673048],_
[0.31,0.305238020,asinh(0.31),asinh(0.31)-0.305238020],_
[0.32,0.314775980,asinh(0.32),asinh(0.32)-0.314775980],_
[0.33,0.324286295,asinh(0.33),asinh(0.33)-0.324286295],_
[0.34,0.333768352,asinh(0.34),asinh(0.34)-0.333768352],_
[0.35,0.343221555,asinh(0.35),asinh(0.35)-0.343221555],_
[0.36,0.352645330,asinh(0.36),asinh(0.36)-0.352645330],_
[0.37,0.362039121,asinh(0.37),asinh(0.37)-0.362039121],_
[0.38,0.371402391,asinh(0.38),asinh(0.38)-0.371402391],_
[0.39,0.380734624,asinh(0.39),asinh(0.39)-0.380734624],_
[0.40,0.390035320,asinh(0.40),asinh(0.40)-0.390035320],_
[0.41,0.399304001,asinh(0.41),asinh(0.41)-0.399304001],_
[0.42,0.408540208,asinh(0.42),asinh(0.42)-0.408540208],_
[0.43,0.417743500,asinh(0.43),asinh(0.43)-0.417743500],_
[0.44,0.426913454,asinh(0.44),asinh(0.44)-0.426913454],_
[0.45,0.436049669,asinh(0.45),asinh(0.45)-0.436049669],_
[0.46,0.445151759,asinh(0.46),asinh(0.46)-0.445151759],_
[0.47,0.454219359,asinh(0.47),asinh(0.47)-0.454219359],_
[0.48,0.463252120,asinh(0.48),asinh(0.48)-0.463252120],_
[0.49,0.472249713,asinh(0.49),asinh(0.49)-0.472249713],_
[0.50,0.481211825,asinh(0.50),asinh(0.50)-0.481211825],_
[0.51,0.490138161,asinh(0.51),asinh(0.51)-0.490138161],_
[0.52,0.499028444,asinh(0.52),asinh(0.52)-0.499028444],_
[0.53,0.507882413,asinh(0.53),asinh(0.53)-0.507882413],_
[0.54,0.516699824,asinh(0.54),asinh(0.54)-0.516699824],_
[0.55,0.525480448,asinh(0.55),asinh(0.55)-0.525480448],_
[0.56,0.534224074,asinh(0.56),asinh(0.56)-0.534224074],_
[0.57,0.542930505,asinh(0.57),asinh(0.57)-0.542930505],_
[0.58,0.551599562,asinh(0.58),asinh(0.58)-0.551599562],_
[0.59,0.560231077,asinh(0.59),asinh(0.59)-0.560231077],_
[0.60,0.568824899,asinh(0.60),asinh(0.60)-0.568824899],_
[0.61,0.577380892,asinh(0.61),asinh(0.61)-0.577380892],_
[0.62,0.585898932,asinh(0.62),asinh(0.62)-0.585898932],_
[0.63,0.594378911,asinh(0.63),asinh(0.63)-0.594378911],_
[0.64,0.602820733,asinh(0.64),asinh(0.64)-0.602820733],_
[0.65,0.611224314,asinh(0.65),asinh(0.65)-0.611224314],_
[0.66,0.619589584,asinh(0.66),asinh(0.66)-0.619589584],_
[0.67,0.627916485,asinh(0.67),asinh(0.67)-0.627916485],_
[0.68,0.636204970,asinh(0.68),asinh(0.68)-0.636204970],_
[0.69,0.644455005,asinh(0.69),asinh(0.69)-0.644455005],_
[0.70,0.652666566,asinh(0.70),asinh(0.70)-0.652666566],_
[0.71,0.660839641,asinh(0.71),asinh(0.71)-0.660839641],_
[0.72,0.668974227,asinh(0.72),asinh(0.72)-0.668974227],_
[0.73,0.677070332,asinh(0.73),asinh(0.73)-0.677070332],_
[0.74,0.685127974,asinh(0.74),asinh(0.74)-0.685127974],_
[0.75,0.693147181,asinh(0.75),asinh(0.75)-0.693147181],_
[0.76,0.701127988,asinh(0.76),asinh(0.76)-0.701127988],_
[0.77,0.709070441,asinh(0.77),asinh(0.77)-0.709070441],_
[0.78,0.716974594,asinh(0.78),asinh(0.78)-0.716974594],_
[0.79,0.724840509,asinh(0.79),asinh(0.79)-0.724840509],_
[0.80,0.732668256,asinh(0.80),asinh(0.80)-0.732668256],_
[0.81,0.740457912,asinh(0.81),asinh(0.81)-0.740457912],_
[0.82,0.748209563,asinh(0.82),asinh(0.82)-0.748209563],_
[0.83,0.755923300,asinh(0.83),asinh(0.83)-0.755923300],_
[0.84,0.763599222,asinh(0.84),asinh(0.84)-0.763599222],_
[0.85,0.771237433,asinh(0.85),asinh(0.85)-0.771237433],_
[0.86,0.778838046,asinh(0.86),asinh(0.86)-0.778838046],_
[0.87,0.786401177,asinh(0.87),asinh(0.87)-0.786401177],_
[0.88,0.793926950,asinh(0.88),asinh(0.88)-0.793926950],_
[0.89,0.801415491,asinh(0.89),asinh(0.89)-0.801415491],_
[0.90,0.808866936,asinh(0.90),asinh(0.90)-0.808866936],_
[0.91,0.816281421,asinh(0.91),asinh(0.91)-0.816281421],_
[0.92,0.823659091,asinh(0.92),asinh(0.92)-0.823659091],_
[0.93,0.831000091,asinh(0.93),asinh(0.93)-0.831000091],_
[0.94,0.838304575,asinh(0.94),asinh(0.94)-0.838304575],_
[0.95,0.845572697,asinh(0.95),asinh(0.95)-0.845572697],_
[0.96,0.852804617,asinh(0.96),asinh(0.96)-0.852804617],_
[0.97,0.860000498,asinh(0.97),asinh(0.97)-0.860000498],_
[0.98,0.867160507,asinh(0.98),asinh(0.98)-0.867160507],_
[0.99,0.874284812,asinh(0.99),asinh(0.99)-0.874284812],_
[1.00,0.881373587,asinh(1.00),asinh(1.00)-0.881373587]]
 

   (1)
   [[0.0,0.0,0.0,0.0],
    [0.01,0.009999833,0.0099998333 4083288693 52,0.3408328869 35 E -9],
    [0.02,0.019998667,0.0199986669 0660953936,- 0.9339046064 E -10],
    [0.03,0.029995502,0.0299955018 2152425832 6,- 0.1784757416 74 E -9],
    [0.04,0.039989341,0.0399893410 0602700269 1,0.6027002691 E -11],
    [0.05,0.04997919,0.0499791900 6934866523 2,0.6934866523 2 E -10],
    [0.06,0.059964058,0.0599640581 9533394203 3,0.1953339420 3 E -9],
    [0.07,0.069942959,0.0699429590 1940182241 9,0.1940182242 E -10],
    [0.08,0.079914912,0.0799149114 9449676816 5,- 0.5055032318 35 E -9],
    [0.09,0.089878941,0.0898789407 4394680193 8,- 0.2560531980 6 E -9],
    [0.1,0.099834079,0.0998340788 9920756332 7,- 0.1007924366 7 E -9],
    [0.11,0.109779366,0.1097793659 2054342078,- 0.7945657921 7 E -10],
    [0.12,0.119713851,0.1197138503 9877738636,- 0.6012226136 36 E -9],
    [0.13,0.12963659,0.1296365903 3633024308,0.3363302430 8 E -9],
    [0.14,0.139546654,0.1395466539 0586528422,- 0.9413471578 E -10],
    [0.15,0.14944312,0.1494431201 8495765616,0.1849576561 6 E -9],
    [0.16,0.15932508,0.1593250798 6531572882,- 0.1346842711 8 E -9],
    [0.17,0.169191636,0.1691916359 3519539889,- 0.6480460111 E -10],
    [0.18,0.179041904,0.1790419043 3376594692,0.3337659469 2 E -9],
    [0.19,0.188875015,0.1888750145 7630719416,- 0.4236928058 4 E -9],
    [0.2,0.19869011,0.1986901103 4924140647,0.3492414064 7 E -9],
    [0.21,0.20848635,0.2084863500 7412884481,0.7412884481 E -10],
    [0.22,0.218262908,0.2182629074 3988224632,- 0.5601177536 8 E -9],
    [0.23,0.228018972,0.2280189719 0258204081,- 0.9741795919 E -10],
    [0.24,0.237753749,0.2377537491 5239999115,0.1523999911 5 E -9],
    [0.25,0.247466462,0.2474664615 4726345294,- 0.4527365470 6 E -9],
    [0.26,0.257156349,0.2571563485 1301487614,- 0.4869851238 6 E -9],
    [0.27,0.266822667,0.2668226669 0994085825,- 0.9005914175 E -10],
    [0.28,0.276464691,0.2764646913 6566139339,0.3656613933 9 E -9],
    [0.29,0.286081715,0.2860817145 7448237948,- 0.4255176205 2 E -9],
    [0.3,0.295673048,0.2956730475 634224391,- 0.4365775609 E -9],
    [0.31,0.30523802,0.3052380199 2522822388,- 0.7477177612 E -10],
    [0.32,0.31477598,0.3147759800 1879020946,0.187902095 E -10],
    [0.33,0.324286295,0.3242862951 3746321043,0.1374632104 E -9],
    [0.34,0.333768352,0.3337683516 4588216777,- 0.3541178322 3 E -9],
    [0.35,0.343221555,0.3432215550 8594396213,0.8594396213 E -10],
    [0.36,0.35264533,0.3526453302 5269991354,0.2526999135 4 E -9],
    [0.37,0.362039121,0.3620391212 4097112736,0.2409711273 6 E -9],
    [0.38,0.371402391,0.3714023914 6355987334,0.4635598733 4 E -9],
    [0.39,0.380734624,0.3807346236 4198472547,- 0.3580152745 3 E -9],
    [0.4,0.39003532,0.3900353197 7071527608,- 0.2292847239 E -9],
    [0.41,0.399304001,0.3993040010 5592394477,0.5592394477 E -10],
    [0.42,0.408540208,0.4085402078 298078441,- 0.1701921559 E -9],
    [0.43,0.4177435,0.4177434994 4156299241,- 0.5584370075 9 E -9],
    [0.44,0.426913454,0.4269134541 2611656164,0.1261165616 E -9],
    [0.45,0.436049669,0.4360496688 517405265,- 0.1482594735 E -9],
    [0.46,0.445151759,0.4451517591 4768227909,0.1476822791 E -9],
    [0.47,0.454219359,0.4542193589 1295474595,- 0.8704525405 E -10],
    [0.48,0.46325212,0.4632521202 0743057053,0.2074305705 E -9],
    [0.49,0.472249713,0.4722497130 2638229031,0.263822903 E -10],
    [0.5,0.481211825,0.4812118250 596034475,0.596034475 E -10],
    [0.51,0.490138161,0.4901381614 3623452983,0.4362345298 3 E -9],
    [0.52,0.499028444,0.4990284444 564028591,0.4564028591 E -9],
    [0.53,0.507882413,0.5078824133 1076734063,0.3107673406 E -9],
    [0.54,0.516699824,0.5166998237 890376715,- 0.2109623285 E -9],
    [0.55,0.525480448,0.5254804479 7851348895,- 0.214865111 E -10],
    [0.56,0.534224074,0.5342240739 5366232528,- 0.463376747 E -10],
    [0.57,0.542930505,0.5429305054 5772642154,0.4577264215 E -9],
    [0.58,0.551599562,0.5515995615 7731772498,- 0.422682275 E -9],
    [0.59,0.560231077,0.5602310764 1092803468,- 0.5890719653 2 E -9],
    [0.6,0.568824899,0.5688248987 322475301,- 0.2677524699 E -9],
    [0.61,0.577380892,0.5773808916 4915007492,- 0.3508499251 E -9],
    [0.62,0.585898932,0.5858989322 5916797142,0.2591679714 E -9],
    [0.63,0.594378911,0.5943789113 0224247799,0.302242478 E -9],
    [0.64,0.602820733,0.6028207328 1149960517,- 0.1885003948 E -9],
    [0.65,0.611224314,0.6112243137 62763672,- 0.237236328 E -9],
    [0.66,0.619589584,0.6195895837 234840191,- 0.2765159809 E -9],
    [0.67,0.627916485,0.6279164845 0171330467,- 0.4982866953 3 E -9],
    [0.68,0.63620497,0.6362049697 9573911039,- 0.2042608896 E -9],
    [0.69,0.644455005,0.6444550048 449342957,- 0.1550657043 E -9],
    [0.7,0.652666566,0.6526665660 8235578681,0.8235578681 E -10],
    [0.71,0.660839641,0.6608396407 8958638519,- 0.2104136148 E -9],
    [0.72,0.668974227,0.6689742267 542798277,- 0.2457201723 E -9],
    [0.73,0.677070332,0.6770703319 3083581572,- 0.6916418427 E -10],
    [0.74,0.685127974,0.6851279741 0459912826,0.1045991283 E -9],
    [0.75,0.693147181,0.6931471805 5994530942,- 0.4400546906 E -9],
    [0.76,0.701127988,0.7011279877 5258482712,- 0.2474151729 E -9],
    [0.77,0.709070441,0.7090704409 8638808148,- 0.136119185 E -10],
    [0.78,0.716974594,0.7169745940 9500523361,0.9500523361 E -10],
    [0.79,0.724840509,0.7248405091 2852755291,0.1285275529 E -9],
    [0.8,0.732668256,0.7326682560 4541086415,0.454108642 E -10],
    [0.81,0.740457912,0.7404579124 098567228,0.4098567228 E -9],
    [0.82,0.748209563,0.7482095630 9482316487,0.9482316487 E -10],
    [0.83,0.7559233,0.7559232999 9081426309,- 0.918573691 E -11],
    [0.84,0.763599222,0.7635992217 205762674,- 0.2794237326 E -9],
    [0.85,0.771237433,0.7712374333 5980780282,0.3598078028 E -9],
    [0.86,0.778838046,0.7788380461 6397242546,0.1639724255 E -9],
    [0.87,0.786401177,0.7864011773 0128377712,0.3012837771 E -9],
    [0.88,0.79392695,0.7939269495 9191660771,- 0.4080833923 E -9],
    [0.89,0.801415491,0.8014154912 5348102582,0.2534810258 E -9],
    [0.9,0.808866936,0.8088669356 5278246251,- 0.3472175375 E -9],
    [0.91,0.816281421,0.8162814210 6387596132,0.6387596132 E -10],
    [0.92,0.823659091,0.8236590904 3241050549,- 0.5675894945 2 E -9],
    [0.93,0.831000091,0.8310000911 4624712798,0.146247128 E -9],
    [0.94,0.838304575,0.8383045748 1232348677,- 0.1876765132 E -9],
    [0.95,0.845572697,0.8455726970 3972738992,0.397273899 E -10],
    [0.96,0.852804617,0.8528046172 2893238837,0.2289323884 E -9],
    [0.97,0.860000498,0.8600004983 6713998068,0.3671399807 E -9],
    [0.98,0.867160507,0.8671605068 2966515846,- 0.1703348415 E -9],
    [0.99,0.874284812,0.8742848121 8729492676,0.1872949268 E -9],
    [1.0,0.881373587,0.8813735870 1954302523,0.195430252 E -10]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.0,0.0,0.0,0.0],
--R    [0.01,0.009999833,0.0099998333 4083288693 52,0.3408328869 35 E -9],
--R    [0.02,0.019998667,0.0199986669 0660953936,- 0.9339046064 E -10],
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--R    [1.0,0.881373587,0.8813735870 1954302523,0.195430252 E -10]]
--R                                                        Type: List List Float
--E 1
--S 2 of 2
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[0.99,2.646652412,atanh(0.99),atanh(0.99)-2.646652412]]
 

   (2)
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    [0.16,0.161386696,0.1613866961 3152551534,0.1315255153 4 E -9],
    [0.17,0.171666663,0.1716666635 0057909768,0.5005790976 8 E -9],
    [0.18,0.181982689,0.1819826886 0070582337,- 0.3992941766 3 E -9],
    [0.19,0.192337169,0.1923371692 1954530989,0.2195453098 9 E -9],
    [0.2,0.202732554,0.2027325540 5408219099,0.5408219099 E -10],
    [0.21,0.213171346,0.2131713465 6485979698,0.5648597969 8 E -9],
    [0.22,0.223656109,0.2236561090 2183241065,0.2183241065 E -10],
    [0.23,0.234189466,0.2341894667 5936682305,0.7593668230 5 E -9],
    [0.24,0.244774112,0.2447741126 5935289296,0.6593528929 6 E -9],
    [0.25,0.255412812,0.2554128118 829953416,- 0.1170046584 E -9],
    [0.26,0.266108407,0.2661084068 7365412176,- 0.1263458782 E -9],
    [0.27,0.276863823,0.2768638226 5510007198,- 0.3448999280 2 E -9],
    [0.28,0.287682072,0.2876820724 5178092744,0.4517809274 4 E -9],
    [0.29,0.298566264,0.2985662636 6017834677,- 0.3398216532 3 E -9],
    [0.3,0.309519604,0.3095196042 0311171547,0.2031117155 E -9],
    [0.31,0.320545409,0.3205454093 0194608097,0.3019460809 7 E -9],
    [0.32,0.331647108,0.3316471087 051320776,0.7051320776 E -9],
    [0.33,0.342828254,0.3428282544 1539385272,0.4153938527 2 E -9],
    [0.34,0.354092528,0.3540925289 6224291211,0.9622429121 E -9],
    [0.35,0.365443754,0.3654437542 7139616907,0.2713961690 7 E -9],
    [0.36,0.376885901,0.3768859011 88190076,0.188190076 E -9],
    [0.37,0.3884231,0.3884230997 1829611371,- 0.2817038862 9 E -9],
    [0.38,0.40005965,0.4000596500 5605656814,0.5605656814 E -10],
    [0.39,0.411800034,0.4118000344 7869025422,0.4786902542 2 E -9],
    [0.4,0.42364893,0.4236489301 9360180685,0.1936018069 E -9],
    [0.41,0.435611223,0.4356112232 362244138,0.2362244138 E -9],
    [0.42,0.447692023,0.4476920235 2742069707,0.5274206970 7 E -9],
    [0.43,0.459896681,0.4598966812 1267856435,0.2126785644 E -9],
    [0.44,0.472230804,0.4722308044 2042569355,0.4204256935 5 E -9],
    [0.45,0.484700279,0.4847002785 9405174156,- 0.4059482584 4 E -9],
    [0.46,0.497311288,0.4973112875 7203102745,- 0.4279689725 5 E -9],
    [0.47,0.510070337,0.5100703366 1330723373,- 0.3866927663 E -9],
    [0.48,0.522984278,0.5229842775 9134385416,- 0.4086561458 E -9],
    [0.49,0.536060337,0.5360603366 1056668467,- 0.3894333153 E -9],
    [0.5,0.549306144,0.5493061443 340548457,0.3340548457 E -9],
    [0.51,0.562729769,0.5627297693 521488593,0.3521488593 E -9],
    [0.52,0.576339754,0.5763397549 691927296,0.9691927296 E -9],
    [0.53,0.59014516,0.5901451598 4118843811,- 0.1588115619 E -9],
    [0.54,0.604155603,0.6041556029 6226707918,- 0.377329208 E -10],
    [0.55,0.618381313,0.6183813135 7446343157,0.5744634315 7 E -9],
    [0.56,0.632833186,0.6328331866 6563794169,0.6656379416 9 E -9],
    [0.57,0.647522844,0.6475228448 2737281698,0.8273728169 8 E -9],
    [0.58,0.662462707,0.6624627073 7179924883,0.3717992488 E -9],
    [0.59,0.677666068,0.6776660677 5796186084,- 0.2420381392 E -9],
    [0.6,0.69314718,0.6931471805 5994530942,0.5599453094 2 E -9],
    [0.61,0.708921359,0.7089213594 2740828423,0.4274082842 E -9],
    [0.62,0.725005087,0.7250050877 5299915279,0.7529991527 9 E -9],
    [0.63,0.741416144,0.7414161440 8126894485,0.8126894484 E -10],
    [0.64,0.758173745,0.7581737446 8404421054,- 0.3159557895 E -9],
    [0.65,0.775298706,0.7752987062 0558346517,0.2055834652 E -9],
    [0.66,0.792813631,0.7928136318 7019092161,0.8701909216 1 E -9],
    [0.67,0.810743125,0.8107431254 7513743591,0.4751374359 1 E -9],
    [0.68,0.829114038,0.8291140383 0176618883,0.3017661888 E -9],
    [0.69,0.847955755,0.8479557552 1896361309,0.2189636131 E -9],
    [0.7,0.867300527,0.8673005276 9405319443,0.6940531944 3 E -9],
    [0.71,0.887183863,0.8871838632 5809290781,0.2580929078 E -9],
    [0.72,0.907644983,0.9076449833 1912455918,0.3191245592 E -9],
    [0.73,0.928727364,0.9287273642 4672493638,0.2467249364 E -9],
    [0.74,0.950479381,0.9504793805 9652349126,- 0.4034765087 E -9],
    [0.75,0.972955074,0.9729550745 2765665255,0.5276566525 5 E -9],
    [0.76,0.996215082,0.9962150823 4510308105,0.345103081 E -9],
    [0.77,1.020327758,1.0203277583 223397256,0.3223397256 E -9],
    [0.78,1.045370548,1.0453705484 668846471,0.4668846471 E -9],
    [0.79,1.071431684,1.0714316840 586659998,0.586659998 E -10],
    [0.8,1.098612289,1.0986122886 681096914,- 0.3318903086 E -9],
    [0.81,1.127029026,1.1270290260 496926434,0.496926434 E -10],
    [0.82,1.156817465,1.1568174645 903153292,- 0.4096846708 E -9],
    [0.83,1.188136404,1.1881364043 926024299,0.3926024299 E -9],
    [0.84,1.221173518,1.2211735176 846021907,- 0.3153978093 E -9],
    [0.85,1.256152811,1.2561528119 880573765,0.9880573764 9 E -9],
    [0.86,1.293344672,1.2933446720 489713161,0.489713161 E -10],
    [0.87,1.333079629,1.3330796296 965249441,0.6965249441 E -9],
    [0.88,1.375767657,1.3757676565 209744477,- 0.4790255523 E -9],
    [0.89,1.421925871,1.4219258711 306359176,0.1306359176 E -9],
    [0.9,1.47221949,1.4722194895 8322023,- 0.41677977 E -9],
    [0.91,1.527524425,1.5275244253 55205245,0.355205245 E -9],
    [0.92,1.589026915,1.5890269151 739728098,0.1739728098 E -9],
    [0.93,1.65839002,1.6583900199 247861234,- 0.752138766 E -10],
    [0.94,1.738049345,1.7380493449 176365654,- 0.823634346 E -10],
    [0.95,1.831780823,1.8317808230 648232137,0.648232137 E -10],
    [0.96,1.945910149,1.9459101490 553133051,0.553133051 E -10],
    [0.97,2.09229572,2.0922957200 349394077,0.349394077 E -10],
    [0.98,2.297559925,2.2975599250 672949634,0.672949634 E -10],
    [0.99,2.646652412,2.6466524123 622461976,0.3622461976 E -9]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.0,0.0,0.0,0.0],
--R    [0.01,0.010000333,0.0100003333 5333476201 6,0.3533347620 16 E -9],
--R    [0.02,0.020002667,0.0200026673 0684958071 7,0.3068495807 17 E -9],
--R    [0.03,0.030009004,0.0300090048 6312647432 6,0.8631264743 26 E -9],
--R    [0.04,0.040021353,0.0400213538 3676821291 2,0.8367682129 12 E -9],
--R    [0.05,0.050041729,0.0500417292 7849126824 6,0.2784912682 46 E -9],
--R    [0.06,0.060072156,0.0600721559 2103162366 2,- 0.7896837633 8 E -10],
--R    [0.07,0.070114671,0.0701146706 5432511799,- 0.3456748820 1 E -9],
--R    [0.08,0.080171325,0.0801713250 3758969169,0.3758969169 E -10],
--R    [0.09,0.090244188,0.0902441878 5614682960 9,- 0.1438531703 9 E -9],
--R    [0.1,0.100335347,0.1003353477 3107558064,0.7310755806 36 E -9],
--R    [0.11,0.110446915,0.1104469157 9009714872,0.7900971487 22 E -9],
--R    [0.12,0.120581028,0.1205810284 0844403523,0.4084440352 3 E -9],
--R    [0.13,0.13073985,0.1307398500 28878425,0.28878425 E -10],
--R    [0.14,0.140925576,0.1409255760 7049386396,0.7049386396 E -10],
--R    [0.15,0.151140436,0.1511404359 3646680528,- 0.6353319472 E -10],
--R    [0.16,0.161386696,0.1613866961 3152551534,0.1315255153 4 E -9],
--R    [0.17,0.171666663,0.1716666635 0057909768,0.5005790976 8 E -9],
--R    [0.18,0.181982689,0.1819826886 0070582337,- 0.3992941766 3 E -9],
--R    [0.19,0.192337169,0.1923371692 1954530989,0.2195453098 9 E -9],
--R    [0.2,0.202732554,0.2027325540 5408219099,0.5408219099 E -10],
--R    [0.21,0.213171346,0.2131713465 6485979698,0.5648597969 8 E -9],
--R    [0.22,0.223656109,0.2236561090 2183241065,0.2183241065 E -10],
--R    [0.23,0.234189466,0.2341894667 5936682305,0.7593668230 5 E -9],
--R    [0.24,0.244774112,0.2447741126 5935289296,0.6593528929 6 E -9],
--R    [0.25,0.255412812,0.2554128118 829953416,- 0.1170046584 E -9],
--R    [0.26,0.266108407,0.2661084068 7365412176,- 0.1263458782 E -9],
--R    [0.27,0.276863823,0.2768638226 5510007198,- 0.3448999280 2 E -9],
--R    [0.28,0.287682072,0.2876820724 5178092744,0.4517809274 4 E -9],
--R    [0.29,0.298566264,0.2985662636 6017834677,- 0.3398216532 3 E -9],
--R    [0.3,0.309519604,0.3095196042 0311171547,0.2031117155 E -9],
--R    [0.31,0.320545409,0.3205454093 0194608097,0.3019460809 7 E -9],
--R    [0.32,0.331647108,0.3316471087 051320776,0.7051320776 E -9],
--R    [0.33,0.342828254,0.3428282544 1539385272,0.4153938527 2 E -9],
--R    [0.34,0.354092528,0.3540925289 6224291211,0.9622429121 E -9],
--R    [0.35,0.365443754,0.3654437542 7139616907,0.2713961690 7 E -9],
--R    [0.36,0.376885901,0.3768859011 88190076,0.188190076 E -9],
--R    [0.37,0.3884231,0.3884230997 1829611371,- 0.2817038862 9 E -9],
--R    [0.38,0.40005965,0.4000596500 5605656814,0.5605656814 E -10],
--R    [0.39,0.411800034,0.4118000344 7869025422,0.4786902542 2 E -9],
--R    [0.4,0.42364893,0.4236489301 9360180685,0.1936018069 E -9],
--R    [0.41,0.435611223,0.4356112232 362244138,0.2362244138 E -9],
--R    [0.42,0.447692023,0.4476920235 2742069707,0.5274206970 7 E -9],
--R    [0.43,0.459896681,0.4598966812 1267856435,0.2126785644 E -9],
--R    [0.44,0.472230804,0.4722308044 2042569355,0.4204256935 5 E -9],
--R    [0.45,0.484700279,0.4847002785 9405174156,- 0.4059482584 4 E -9],
--R    [0.46,0.497311288,0.4973112875 7203102745,- 0.4279689725 5 E -9],
--R    [0.47,0.510070337,0.5100703366 1330723373,- 0.3866927663 E -9],
--R    [0.48,0.522984278,0.5229842775 9134385416,- 0.4086561458 E -9],
--R    [0.49,0.536060337,0.5360603366 1056668467,- 0.3894333153 E -9],
--R    [0.5,0.549306144,0.5493061443 340548457,0.3340548457 E -9],
--R    [0.51,0.562729769,0.5627297693 521488593,0.3521488593 E -9],
--R    [0.52,0.576339754,0.5763397549 691927296,0.9691927296 E -9],
--R    [0.53,0.59014516,0.5901451598 4118843811,- 0.1588115619 E -9],
--R    [0.54,0.604155603,0.6041556029 6226707918,- 0.377329208 E -10],
--R    [0.55,0.618381313,0.6183813135 7446343157,0.5744634315 7 E -9],
--R    [0.56,0.632833186,0.6328331866 6563794169,0.6656379416 9 E -9],
--R    [0.57,0.647522844,0.6475228448 2737281698,0.8273728169 8 E -9],
--R    [0.58,0.662462707,0.6624627073 7179924883,0.3717992488 E -9],
--R    [0.59,0.677666068,0.6776660677 5796186084,- 0.2420381392 E -9],
--R    [0.6,0.69314718,0.6931471805 5994530942,0.5599453094 2 E -9],
--R    [0.61,0.708921359,0.7089213594 2740828423,0.4274082842 E -9],
--R    [0.62,0.725005087,0.7250050877 5299915279,0.7529991527 9 E -9],
--R    [0.63,0.741416144,0.7414161440 8126894485,0.8126894484 E -10],
--R    [0.64,0.758173745,0.7581737446 8404421054,- 0.3159557895 E -9],
--R    [0.65,0.775298706,0.7752987062 0558346517,0.2055834652 E -9],
--R    [0.66,0.792813631,0.7928136318 7019092161,0.8701909216 1 E -9],
--R    [0.67,0.810743125,0.8107431254 7513743591,0.4751374359 1 E -9],
--R    [0.68,0.829114038,0.8291140383 0176618883,0.3017661888 E -9],
--R    [0.69,0.847955755,0.8479557552 1896361309,0.2189636131 E -9],
--R    [0.7,0.867300527,0.8673005276 9405319443,0.6940531944 3 E -9],
--R    [0.71,0.887183863,0.8871838632 5809290781,0.2580929078 E -9],
--R    [0.72,0.907644983,0.9076449833 1912455918,0.3191245592 E -9],
--R    [0.73,0.928727364,0.9287273642 4672493638,0.2467249364 E -9],
--R    [0.74,0.950479381,0.9504793805 9652349126,- 0.4034765087 E -9],
--R    [0.75,0.972955074,0.9729550745 2765665255,0.5276566525 5 E -9],
--R    [0.76,0.996215082,0.9962150823 4510308105,0.345103081 E -9],
--R    [0.77,1.020327758,1.0203277583 223397256,0.3223397256 E -9],
--R    [0.78,1.045370548,1.0453705484 668846471,0.4668846471 E -9],
--R    [0.79,1.071431684,1.0714316840 586659998,0.586659998 E -10],
--R    [0.8,1.098612289,1.0986122886 681096914,- 0.3318903086 E -9],
--R    [0.81,1.127029026,1.1270290260 496926434,0.496926434 E -10],
--R    [0.82,1.156817465,1.1568174645 903153292,- 0.4096846708 E -9],
--R    [0.83,1.188136404,1.1881364043 926024299,0.3926024299 E -9],
--R    [0.84,1.221173518,1.2211735176 846021907,- 0.3153978093 E -9],
--R    [0.85,1.256152811,1.2561528119 880573765,0.9880573764 9 E -9],
--R    [0.86,1.293344672,1.2933446720 489713161,0.489713161 E -10],
--R    [0.87,1.333079629,1.3330796296 965249441,0.6965249441 E -9],
--R    [0.88,1.375767657,1.3757676565 209744477,- 0.4790255523 E -9],
--R    [0.89,1.421925871,1.4219258711 306359176,0.1306359176 E -9],
--R    [0.9,1.47221949,1.4722194895 8322023,- 0.41677977 E -9],
--R    [0.91,1.527524425,1.5275244253 55205245,0.355205245 E -9],
--R    [0.92,1.589026915,1.5890269151 739728098,0.1739728098 E -9],
--R    [0.93,1.65839002,1.6583900199 247861234,- 0.752138766 E -10],
--R    [0.94,1.738049345,1.7380493449 176365654,- 0.823634346 E -10],
--R    [0.95,1.831780823,1.8317808230 648232137,0.648232137 E -10],
--R    [0.96,1.945910149,1.9459101490 553133051,0.553133051 E -10],
--R    [0.97,2.09229572,2.0922957200 349394077,0.349394077 E -10],
--R    [0.98,2.297559925,2.2975599250 672949634,0.672949634 E -10],
--R    [0.99,2.646652412,2.6466524123 622461976,0.3622461976 E -9]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to exint.output (2010/3/27, 18:25:38).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 10
integrate(1/(x**2 + a),x)
 

               2      +---+
             (x  - a)\|- a  + 2a x         +-+
         log(---------------------)      x\|a
                      2             atan(-----)
                     x  + a                a
   (1)  [--------------------------,-----------]
                     +---+               +-+
                   2\|- a               \|a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R               2      +---+
--R             (x  - a)\|- a  + 2a x         +-+
--R         log(---------------------)      x\|a
--R                      2             atan(-----)
--R                     x  + a                a
--R   (1)  [--------------------------,-----------]
--R                     +---+               +-+
--R                   2\|- a               \|a
--R                                     Type: Union(List Expression Integer,...)
--E 1

)clear all
 

--S 2 of 10
integrate((x**2+2*x+1)/((x+1)**6+1),x)
 

              3     2
        atan(x  + 3x  + 3x + 1)
   (1)  -----------------------
                   3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              3     2
--R        atan(x  + 3x  + 3x + 1)
--R   (1)  -----------------------
--R                   3
--R                                          Type: Union(Expression Integer,...)
--E 2

)clear all
 

--S 3 of 10
integrate(tan(atan(x)/3),x)
 

                  atan(x) 2             atan(x) 2           atan(x)
        8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
                     3                     3                   3
   (1)  ------------------------------------------------------------
                                     18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  atan(x) 2             atan(x) 2           atan(x)
--R        8log(3tan(-------)  - 1) - 3tan(-------)  + 18x tan(-------)
--R                     3                     3                   3
--R   (1)  ------------------------------------------------------------
--R                                     18
--R                                          Type: Union(Expression Integer,...)
--E 3

)clear all
 

--S 4 of 10
complexIntegrate(1/(x**2 + a),x)
 

         +---+      +---+         +---+        +---+
         |  1       |  1          |  1         |  1
         |- - log(a |- -  + x) -  |- - log(- a |- -  + x)
        \|  a      \|  a         \|  a        \|  a
   (1)  -------------------------------------------------
                                2
                                                     Type: Expression Integer
--R 
--R
--R         +---+      +---+         +---+        +---+
--R         |  1       |  1          |  1         |  1
--R         |- - log(a |- -  + x) -  |- - log(- a |- -  + x)
--R        \|  a      \|  a         \|  a        \|  a
--R   (1)  -------------------------------------------------
--R                                2
--R                                                     Type: Expression Integer
--E 4

)clear all
 

--S 5 of 10
integrate(log(1 + sqrt(a*x + b)) / x,x)
 

           x      +--------+
         ++  log(\|b + %P a  + 1)
   (1)   |   -------------------- d%P
        ++            %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x      +--------+
--R         ++  log(\|b + %P a  + 1)
--R   (1)   |   -------------------- d%P
--R        ++            %P
--R                                          Type: Union(Expression Integer,...)
--E 5

)clear all
 

--S 6 of 10
integrate(x**3 / (a+b*x)**(1/3),x)
 

             3 3         2 2       2          3 3+-------+2
        (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
   (1)  ---------------------------------------------------
                                   4
                               440b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             3 3         2 2       2          3 3+-------+2
--R        (120b x  - 135a b x  + 162a b x - 243a )\|b x + a
--R   (1)  ---------------------------------------------------
--R                                   4
--R                               440b
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 10
integrate(1 / (x**3 * (a+b*x)**(1/3)),x)
 

   (2)
           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
     + 
         2 2 +-+    3+-+2 3+-------+
       4b x \|3 log(\|a   \|b x + a - a)
     + 
                  +-+3+-+2 3+-------+    +-+
        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
                             3a
  /
        2 2 +-+3+-+
     18a x \|3 \|a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)
--R           2 2 +-+    3+-+3+-------+2   3+-+2 3+-------+
--R       - 2b x \|3 log(\|a \|b x + a   + \|a   \|b x + a + a)
--R     + 
--R         2 2 +-+    3+-+2 3+-------+
--R       4b x \|3 log(\|a   \|b x + a - a)
--R     + 
--R                  +-+3+-+2 3+-------+    +-+
--R        2 2     2\|3 \|a   \|b x + a + a\|3                  +-+3+-+3+-------+2
--R     12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a
--R                             3a
--R  /
--R        2 2 +-+3+-+
--R     18a x \|3 \|a
--R                                          Type: Union(Expression Integer,...)
--E 7

)clear all
 

--S 8 of 10
integrate((x + 1) / (x * (x + log x)**(3/2)),x)
 

            +----------+
          2\|log(x) + x
   (1)  - --------------
            log(x) + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            +----------+
--R          2\|log(x) + x
--R   (1)  - --------------
--R            log(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 8

)clear all
 

--S 9 of 10
integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)
 

                     +---+    erf(x) - 1      +---+
        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
                              erf(x) + 1
   (1)  -------------------------------------------
                        8erf(x) - 8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     +---+    erf(x) - 1      +---+
--R        (erf(x) - 1)\|%pi log(----------) - 2\|%pi
--R                              erf(x) + 1
--R   (1)  -------------------------------------------
--R                        8erf(x) - 8
--R                                          Type: Union(Expression Integer,...)
--E 9

)clear all
 

--S 10 of 10
integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)
 

                             +-----+
                    - 2cosh(\|x + b  + 1) - 2x            +-----+
   (1)  2log(---------------------------------------) - 2\|x + b
                   +-----+              +-----+
             sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                             +-----+
--R                    - 2cosh(\|x + b  + 1) - 2x            +-----+
--R   (1)  2log(---------------------------------------) - 2\|x + b
--R                   +-----+              +-----+
--R             sinh(\|x + b  + 1) - cosh(\|x + b  + 1)
--R                                          Type: Union(Expression Integer,...)
--E 10
)spool 
 
Starts dribbling to UnivariatePolynomial.output (2010/3/27, 18:46:41).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 35
(p,q) : UP(x,INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 35
p := (3*x-1)**2 * (2*x + 8)
 

           3      2
   (2)  18x  + 60x  - 46x + 8
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R           3      2
--R   (2)  18x  + 60x  - 46x + 8
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 2

--S 3 of 35
q := (1 - 6*x + 9*x**2)**2
 

           4       3      2
   (3)  81x  - 108x  + 54x  - 12x + 1
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R           4       3      2
--R   (3)  81x  - 108x  + 54x  - 12x + 1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 3

--S 4 of 35
p**2 + p*q 
 

             7        6        5         4        3        2
   (4)  1458x  + 3240x  - 7074x  + 10584x  - 9282x  + 4120x  - 878x + 72
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R             7        6        5         4        3        2
--R   (4)  1458x  + 3240x  - 7074x  + 10584x  - 9282x  + 4120x  - 878x + 72
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 4

--S 5 of 35
leadingCoefficient p
 

   (5)  18
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  18
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 35
degree p
 

   (6)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  3
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 35
reductum p
 

           2
   (7)  60x  - 46x + 8
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R           2
--R   (7)  60x  - 46x + 8
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 35
gcd(p,q)
 

          2
   (8)  9x  - 6x + 1
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R          2
--R   (8)  9x  - 6x + 1
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 8

--S 9 of 35
lcm(p,q)
 

            5       4       3       2
   (9)  162x  + 432x  - 756x  + 408x  - 94x + 8
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R            5       4       3       2
--R   (9)  162x  + 432x  - 756x  + 408x  - 94x + 8
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 9

--S 10 of 35
resultant(p,q)
 

   (10)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (10)  0
--R                                                     Type: NonNegativeInteger
--E 10

--S 11 of 35
D p
 

            2
   (11)  54x  + 120x - 46
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R            2
--R   (11)  54x  + 120x - 46
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 11

--S 12 of 35
p(2)
 

   (12)  300
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  300
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 35
p(q)
 

   (13)
             12            11            10            9            8
     9565938x   - 38263752x   + 70150212x   - 77944680x  + 58852170x
   + 
                7            6           5           4          3         2
     - 32227632x  + 13349448x  - 4280688x  + 1058184x  - 192672x  + 23328x
   + 
     - 1536x + 40
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)
--R             12            11            10            9            8
--R     9565938x   - 38263752x   + 70150212x   - 77944680x  + 58852170x
--R   + 
--R                7            6           5           4          3         2
--R     - 32227632x  + 13349448x  - 4280688x  + 1058184x  - 192672x  + 23328x
--R   + 
--R     - 1536x + 40
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 35
q(p)
 

   (14)
             12             11             10             9              8
     8503056x   + 113374080x   + 479950272x   + 404997408x  - 1369516896x
   + 
                 7              6              5              4             3
     - 626146848x  + 2939858712x  - 2780728704x  + 1364312160x  - 396838872x
   + 
              2
     69205896x  - 6716184x + 279841
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (14)
--R             12             11             10             9              8
--R     8503056x   + 113374080x   + 479950272x   + 404997408x  - 1369516896x
--R   + 
--R                 7              6              5              4             3
--R     - 626146848x  + 2939858712x  - 2780728704x  + 1364312160x  - 396838872x
--R   + 
--R              2
--R     69205896x  - 6716184x + 279841
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 14

--S 15 of 35
l := coefficients p
 

   (15)  [18,60,- 46,8]
                                                           Type: List Integer
--R 
--R
--R   (15)  [18,60,- 46,8]
--R                                                           Type: List Integer
--E 15

--S 16 of 35
reduce(gcd,l)
 

   (16)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 35
content p
 

   (17)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  2
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 35
ux := (x**4+2*x+3)::UP(x,INT)
 

          4
   (18)  x  + 2x + 3
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R          4
--R   (18)  x  + 2x + 3
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 18

--S 19 of 35
vectorise(ux,5)
 

   (19)  [3,2,0,0,1]
                                                         Type: Vector Integer
--R 
--R
--R   (19)  [3,2,0,0,1]
--R                                                         Type: Vector Integer
--E 19

--S 20 of 35
squareTerms(p) ==   reduce(+,[t**2 for t in monomials p])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 35
p
 

            3      2
   (21)  18x  + 60x  - 46x + 8
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R            3      2
--R   (21)  18x  + 60x  - 46x + 8
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 21

--S 22 of 35
squareTerms p
 
   Compiling function squareTerms with type UnivariatePolynomial(x,
      Integer) -> UnivariatePolynomial(x,Integer) 

             6        4        2
   (22)  324x  + 3600x  + 2116x  + 64
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R   Compiling function squareTerms with type UnivariatePolynomial(x,
--R      Integer) -> UnivariatePolynomial(x,Integer) 
--R
--R             6        4        2
--R   (22)  324x  + 3600x  + 2116x  + 64
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 22

--S 23 of 35
(r,s) : UP(a1,FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 35
r := a1**2 - 2/3
 

           2   2
   (24)  a1  - -
               3
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R           2   2
--R   (24)  a1  - -
--R               3
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 24

--S 25 of 35
s := a1 + 4
 

   (25)  a1 + 4
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R   (25)  a1 + 4
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 25

--S 26 of 35
r quo s
 

   (26)  a1 - 4
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R   (26)  a1 - 4
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 26

--S 27 of 35
r rem s
 

         46
   (27)  --
          3
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R         46
--R   (27)  --
--R          3
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 27

--S 28 of 35
d := divide(r, s)
 

                                      46
   (28)  [quotient= a1 - 4,remainder= --]
                                       3
Type: Record(quotient: UnivariatePolynomial(a1,Fraction Integer),remainder: UnivariatePolynomial(a1,Fraction Integer))
--R 
--R
--R                                      46
--R   (28)  [quotient= a1 - 4,remainder= --]
--R                                       3
--RType: Record(quotient: UnivariatePolynomial(a1,Fraction Integer),remainder: UnivariatePolynomial(a1,Fraction Integer))
--E 28

--S 29 of 35
r - (d.quotient * s + d.remainder) 
 

   (29)  0
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R   (29)  0
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 29

--S 30 of 35
integrate r
 

         1   3   2
   (30)  - a1  - - a1
         3       3
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R         1   3   2
--R   (30)  - a1  - - a1
--R         3       3
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 30

--S 31 of 35
integrate s
 

         1   2
   (31)  - a1  + 4a1
         2
                              Type: UnivariatePolynomial(a1,Fraction Integer)
--R 
--R
--R         1   2
--R   (31)  - a1  + 4a1
--R         2
--R                              Type: UnivariatePolynomial(a1,Fraction Integer)
--E 31

--S 32 of 35
t : UP(a1,FRAC POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 35
t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3)
 

                         2
           2    1      b1  - b1
   (33)  a1  - -- a1 + --------
               b2       b2 + 3
                   Type: UnivariatePolynomial(a1,Fraction Polynomial Integer)
--R 
--R
--R                         2
--R           2    1      b1  - b1
--R   (33)  a1  - -- a1 + --------
--R               b2       b2 + 3
--R                   Type: UnivariatePolynomial(a1,Fraction Polynomial Integer)
--E 33

--S 34 of 35
u : FRAC POLY INT := t
 

           2  2      2           2
         a1 b2  + (b1  - b1 + 3a1  - a1)b2 - 3a1
   (34)  ---------------------------------------
                          2
                        b2  + 3b2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2  2      2           2
--R         a1 b2  + (b1  - b1 + 3a1  - a1)b2 - 3a1
--R   (34)  ---------------------------------------
--R                          2
--R                        b2  + 3b2
--R                                            Type: Fraction Polynomial Integer
--E 34

--S 35 of 35
u :: UP(b1,?)
 

                                    2
            1     2      1        a1 b2 - a1
   (35)  ------ b1  - ------ b1 + ----------
         b2 + 3       b2 + 3          b2
                   Type: UnivariatePolynomial(b1,Fraction Polynomial Integer)
--R 
--R
--R                                    2
--R            1     2      1        a1 b2 - a1
--R   (35)  ------ b1  - ------ b1 + ----------
--R         b2 + 3       b2 + 3          b2
--R                   Type: UnivariatePolynomial(b1,Fraction Polynomial Integer)
--E 35
)spool
 
Starts dribbling to schaum12.output (2010/3/27, 18:37:33).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 84
aa:=integrate(1/(a*x^2+b*x+c),x)
 

   (1)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 2 of 84
bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2))
 

                2a x + b
        2atan(------------)
               +---------+
               |        2
              \|4a c - b
   (2)  -------------------
             +---------+
             |        2
            \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R                2a x + b
--R        2atan(------------)
--R               +---------+
--R               |        2
--R              \|4a c - b
--R   (2)  -------------------
--R             +---------+
--R             |        2
--R            \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 3 of 84
bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c)))
 

               +-----------+
               |          2
            - \|- 4a c + b   + 2a x + b
        log(---------------------------)
              +-----------+
              |          2
             \|- 4a c + b   + 2a x + b
   (3)  --------------------------------
                  +-----------+
                  |          2
                 \|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R               +-----------+
--R               |          2
--R            - \|- 4a c + b   + 2a x + b
--R        log(---------------------------)
--R              +-----------+
--R              |          2
--R             \|- 4a c + b   + 2a x + b
--R   (3)  --------------------------------
--R                  +-----------+
--R                  |          2
--R                 \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 4 of 84
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |        2
         \|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
           +-----------+
           |          2        2a x + b
       - 2\|- 4a c + b  atan(------------)
                              +---------+
                              |        2
                             \|4a c - b
  /
      +-----------+ +---------+
      |          2  |        2
     \|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |        2
--R         \|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R           +-----------+
--R           |          2        2a x + b
--R       - 2\|- 4a c + b  atan(------------)
--R                              +---------+
--R                              |        2
--R                             \|4a c - b
--R  /
--R      +-----------+ +---------+
--R      |          2  |        2
--R     \|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 5 of 84
cc2:=aa.1-bb2
 

   (5)
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
     + 
                +-----------+
                |          2
             - \|- 4a c + b   + 2a x + b
       - log(---------------------------)
               +-----------+
               |          2
              \|- 4a c + b   + 2a x + b
  /
      +-----------+
      |          2
     \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R     + 
--R                +-----------+
--R                |          2
--R             - \|- 4a c + b   + 2a x + b
--R       - log(---------------------------)
--R               +-----------+
--R               |          2
--R              \|- 4a c + b   + 2a x + b
--R  /
--R      +-----------+
--R      |          2
--R     \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 6 of 84
cc3:=aa.2-bb1
 

                         +---------+
                         |        2
              (2a x + b)\|4a c - b              2a x + b
        2atan(----------------------) - 2atan(------------)
                             2                 +---------+
                     4a c - b                  |        2
                                              \|4a c - b
   (6)  ---------------------------------------------------
                             +---------+
                             |        2
                            \|4a c - b
                                                     Type: Expression Integer
--R
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b              2a x + b
--R        2atan(----------------------) - 2atan(------------)
--R                             2                 +---------+
--R                     4a c - b                  |        2
--R                                              \|4a c - b
--R   (6)  ---------------------------------------------------
--R                             +---------+
--R                             |        2
--R                            \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 7 of 84
cc4:=aa.2-bb2
 

   (7)
                            +-----------+
          +---------+       |          2
          |        2     - \|- 4a c + b   + 2a x + b
       - \|4a c - b  log(---------------------------)
                           +-----------+
                           |          2
                          \|- 4a c + b   + 2a x + b
     + 
                                      +---------+
         +-----------+                |        2
         |          2      (2a x + b)\|4a c - b
       2\|- 4a c + b  atan(----------------------)
                                          2
                                  4a c - b
  /
      +-----------+ +---------+
      |          2  |        2
     \|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-----------+
--R          +---------+       |          2
--R          |        2     - \|- 4a c + b   + 2a x + b
--R       - \|4a c - b  log(---------------------------)
--R                           +-----------+
--R                           |          2
--R                          \|- 4a c + b   + 2a x + b
--R     + 
--R                                      +---------+
--R         +-----------+                |        2
--R         |          2      (2a x + b)\|4a c - b
--R       2\|- 4a c + b  atan(----------------------)
--R                                          2
--R                                  4a c - b
--R  /
--R      +-----------+ +---------+
--R      |          2  |        2
--R     \|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 8 of 84
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                            - x + %i
                     %i log(--------)
                             x + %i
   (8)  atan(x) == - ----------------
                             2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                            - x + %i
--R                     %i log(--------)
--R                             x + %i
--R   (8)  atan(x) == - ----------------
--R                             2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 9 of 84
dd3:=atanrule cc3
 

   (9)
               +---------+
               |        2
              \|4a c - b   + 2%i a x + %i b
       %i log(-----------------------------)
               +---------+
               |        2
              \|4a c - b   - 2%i a x - %i b
     + 
                             +---------+
                             |        2                  2
                (- 2a x - b)\|4a c - b   + 4%i a c - %i b
       - %i log(------------------------------------------)
                            +---------+
                            |        2                  2
                 (2a x + b)\|4a c - b   + 4%i a c - %i b
  /
      +---------+
      |        2
     \|4a c - b
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +---------+
--R               |        2
--R              \|4a c - b   + 2%i a x + %i b
--R       %i log(-----------------------------)
--R               +---------+
--R               |        2
--R              \|4a c - b   - 2%i a x - %i b
--R     + 
--R                             +---------+
--R                             |        2                  2
--R                (- 2a x - b)\|4a c - b   + 4%i a c - %i b
--R       - %i log(------------------------------------------)
--R                            +---------+
--R                            |        2                  2
--R                 (2a x + b)\|4a c - b   + 4%i a c - %i b
--R  /
--R      +---------+
--R      |        2
--R     \|4a c - b
--R                                             Type: Expression Complex Integer
--E

--S 10 of 84
ee3:=expandLog dd3
 

   (10)
                         +---------+
                         |        2                  2
       %i log((2a x + b)\|4a c - b   + 4%i a c - %i b )
     + 
                           +---------+
                           |        2                  2
       - %i log((2a x + b)\|4a c - b   - 4%i a c + %i b )
     + 
               +---------+
               |        2
       %i log(\|4a c - b   + 2%i a x + %i b)
     + 
                 +---------+
                 |        2
       - %i log(\|4a c - b   - 2%i a x - %i b) - %i log(- 1)
  /
      +---------+
      |        2
     \|4a c - b
                                             Type: Expression Complex Integer
--R
--R   (10)
--R                         +---------+
--R                         |        2                  2
--R       %i log((2a x + b)\|4a c - b   + 4%i a c - %i b )
--R     + 
--R                           +---------+
--R                           |        2                  2
--R       - %i log((2a x + b)\|4a c - b   - 4%i a c + %i b )
--R     + 
--R               +---------+
--R               |        2
--R       %i log(\|4a c - b   + 2%i a x + %i b)
--R     + 
--R                 +---------+
--R                 |        2
--R       - %i log(\|4a c - b   - 2%i a x - %i b) - %i log(- 1)
--R  /
--R      +---------+
--R      |        2
--R     \|4a c - b
--R                                             Type: Expression Complex Integer
--E

--S 11 of 84     14:265 Schaums and Axiom agree
ff3:=complexNormalize ee3
 

   (11)  0
                                             Type: Expression Complex Integer
--R
--R   (11)  0
--R                                             Type: Expression Complex Integer
--E
)clear all
 

--S 12 of 84
aa:=integrate(x/(a*x^2+b*x+c),x)
 

   (1)
   [
           b
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                             +-----------+
                2            |          2
         log(a x  + b x + c)\|- 4a c + b
    /
          +-----------+
          |          2
       2a\|- 4a c + b
     ,
                         +---------+
                         |        2                         +---------+
              (2a x + b)\|4a c - b             2            |        2
    - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
                             2
                     4a c - b
    -------------------------------------------------------------------]
                                  +---------+
                                  |        2
                               2a\|4a c - b
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R   [
--R           b
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                             +-----------+
--R                2            |          2
--R         log(a x  + b x + c)\|- 4a c + b
--R    /
--R          +-----------+
--R          |          2
--R       2a\|- 4a c + b
--R     ,
--R                         +---------+
--R                         |        2                         +---------+
--R              (2a x + b)\|4a c - b             2            |        2
--R    - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
--R                             2
--R                     4a c - b
--R    -------------------------------------------------------------------]
--R                                  +---------+
--R                                  |        2
--R                               2a\|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 13 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 14 of 84
bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1
 

   (3)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
                           +-----------+
              2            |          2
       log(a x  + b x + c)\|- 4a c + b
  /
        +-----------+
        |          2
     2a\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                           +-----------+
--R              2            |          2
--R       log(a x  + b x + c)\|- 4a c + b
--R  /
--R        +-----------+
--R        |          2
--R     2a\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 15 of 84
bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2
 

                             +---------+
                             |        2                         +---------+
                  (2a x + b)\|4a c - b             2            |        2
        - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
                                 2
                         4a c - b
   (4)  -------------------------------------------------------------------
                                      +---------+
                                      |        2
                                   2a\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R                             +---------+
--R                             |        2                         +---------+
--R                  (2a x + b)\|4a c - b             2            |        2
--R        - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
--R                                 2
--R                         4a c - b
--R   (4)  -------------------------------------------------------------------
--R                                      +---------+
--R                                      |        2
--R                                   2a\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 16 of 84
cc1:=aa.1-bb1
 

   (5)
         b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
         b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
        +-----------+
        |          2
     2a\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R         b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R         b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R        +-----------+
--R        |          2
--R     2a\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 17 of 84
cc2:=aa.2-bb1
 

   (6)
           +---------+
           |        2
         b\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                         +---------+
            +-----------+                |        2
            |          2      (2a x + b)\|4a c - b
       - 2b\|- 4a c + b  atan(----------------------)
                                             2
                                     4a c - b
  /
        +-----------+ +---------+
        |          2  |        2
     2a\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (6)
--R           +---------+
--R           |        2
--R         b\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                         +---------+
--R            +-----------+                |        2
--R            |          2      (2a x + b)\|4a c - b
--R       - 2b\|- 4a c + b  atan(----------------------)
--R                                             2
--R                                     4a c - b
--R  /
--R        +-----------+ +---------+
--R        |          2  |        2
--R     2a\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 18 of 84
cc3:=aa.2-bb1
 

   (7)
           +---------+
           |        2
         b\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                         +---------+
            +-----------+                |        2
            |          2      (2a x + b)\|4a c - b
       - 2b\|- 4a c + b  atan(----------------------)
                                             2
                                     4a c - b
  /
        +-----------+ +---------+
        |          2  |        2
     2a\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (7)
--R           +---------+
--R           |        2
--R         b\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                         +---------+
--R            +-----------+                |        2
--R            |          2      (2a x + b)\|4a c - b
--R       - 2b\|- 4a c + b  atan(----------------------)
--R                                             2
--R                                     4a c - b
--R  /
--R        +-----------+ +---------+
--R        |          2  |        2
--R     2a\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 19 of 84     14:266 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 20 of 84
aa:=integrate(x^2/(a*x^2+b*x+c),x)
 

   (1)
   [
                    2
           (2a c - b )
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                          +-----------+
                     2                    |          2
         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
    /
           +-----------+
         2 |          2
       2a \|- 4a c + b
     ,

                                       +---------+
                                       |        2
                     2      (2a x + b)\|4a c - b
         (- 4a c + 2b )atan(----------------------)
                                           2
                                   4a c - b
       + 
                                          +---------+
                     2                    |        2
         (- b log(a x  + b x + c) + 2a x)\|4a c - b
    /
           +---------+
         2 |        2
       2a \|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                    2
--R           (2a c - b )
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                          +-----------+
--R                     2                    |          2
--R         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
--R    /
--R           +-----------+
--R         2 |          2
--R       2a \|- 4a c + b
--R     ,
--R
--R                                       +---------+
--R                                       |        2
--R                     2      (2a x + b)\|4a c - b
--R         (- 4a c + 2b )atan(----------------------)
--R                                           2
--R                                   4a c - b
--R       + 
--R                                          +---------+
--R                     2                    |        2
--R         (- b log(a x  + b x + c) + 2a x)\|4a c - b
--R    /
--R           +---------+
--R         2 |        2
--R       2a \|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 21 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 22 of 84
bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1
 

   (3)
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                        +-----------+
                   2                    |          2
       (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
  /
         +-----------+
       2 |          2
     2a \|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                        +-----------+
--R                   2                    |          2
--R       (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
--R  /
--R         +-----------+
--R       2 |          2
--R     2a \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 23 of 84
bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2
 

   (4)
                                     +---------+
                                     |        2
                   2      (2a x + b)\|4a c - b
       (- 4a c + 2b )atan(----------------------)
                                         2
                                 4a c - b
     + 
                                        +---------+
                   2                    |        2
       (- b log(a x  + b x + c) + 2a x)\|4a c - b
  /
         +---------+
       2 |        2
     2a \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                     +---------+
--R                                     |        2
--R                   2      (2a x + b)\|4a c - b
--R       (- 4a c + 2b )atan(----------------------)
--R                                         2
--R                                 4a c - b
--R     + 
--R                                        +---------+
--R                   2                    |        2
--R       (- b log(a x  + b x + c) + 2a x)\|4a c - b
--R  /
--R         +---------+
--R       2 |        2
--R     2a \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 24 of 84
cc1:=bb1-aa.1
 

   (5)
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
         +-----------+
       2 |          2
     2a \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R         +-----------+
--R       2 |          2
--R     2a \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 25 of 84     14:267 Schaums and Axiom differ by a constant
dd1:=complexNormalize cc1
 

                   2          3      2 2
        (- 2a c + b )log(- 16a c + 4a b )
   (6)  ---------------------------------
                    +-----------+
                  2 |          2
                2a \|- 4a c + b
                                                     Type: Expression Integer
--R
--R                   2          3      2 2
--R        (- 2a c + b )log(- 16a c + 4a b )
--R   (6)  ---------------------------------
--R                    +-----------+
--R                  2 |          2
--R                2a \|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 26 of 84     14:268 Axiom cannot compute this integral
aa:=integrate(x^m/(a*x^2+b*x+c),x)
 

           x         m
         ++        %Q
   (1)   |   --------------- d%Q
        ++                2
             c + %Q b + %Q a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x         m
--I         ++        %N
--I   (1)   |   --------------- d%N
--R        ++                2
--I             c + %N b + %N a
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 27 of 84
aa:=integrate(1/(x*(a*x^2+b*x+c)),x)
 

   (1)
   [
           b
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                           +-----------+
                   2                       |          2
         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
    /
          +-----------+
          |          2
       2c\|- 4a c + b
     ,

                              +---------+
                              |        2
                   (2a x + b)\|4a c - b
         - 2b atan(----------------------)
                                  2
                          4a c - b
       + 
                                           +---------+
                   2                       |        2
         (- log(a x  + b x + c) + 2log(x))\|4a c - b
    /
          +---------+
          |        2
       2c\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R           b
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                           +-----------+
--R                   2                       |          2
--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
--R    /
--R          +-----------+
--R          |          2
--R       2c\|- 4a c + b
--R     ,
--R
--R                              +---------+
--R                              |        2
--R                   (2a x + b)\|4a c - b
--R         - 2b atan(----------------------)
--R                                  2
--R                          4a c - b
--R       + 
--R                                           +---------+
--R                   2                       |        2
--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
--R    /
--R          +---------+
--R          |        2
--R       2c\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 28 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 29 of 84
bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1
 

   (3)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
                  2        +-----------+
                 x         |          2
       log(--------------)\|- 4a c + b
              2
           a x  + b x + c
  /
        +-----------+
        |          2
     2c\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                  2        +-----------+
--R                 x         |          2
--R       log(--------------)\|- 4a c + b
--R              2
--R           a x  + b x + c
--R  /
--R        +-----------+
--R        |          2
--R     2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 30 of 84
bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2
 

                             +---------+
                             |        2                2        +---------+
                  (2a x + b)\|4a c - b                x         |        2
        - 2b atan(----------------------) + log(--------------)\|4a c - b
                                 2                 2
                         4a c - b               a x  + b x + c
   (4)  -------------------------------------------------------------------
                                      +---------+
                                      |        2
                                   2c\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R                             +---------+
--R                             |        2                2        +---------+
--R                  (2a x + b)\|4a c - b                x         |        2
--R        - 2b atan(----------------------) + log(--------------)\|4a c - b
--R                                 2                 2
--R                         4a c - b               a x  + b x + c
--R   (4)  -------------------------------------------------------------------
--R                                      +---------+
--R                                      |        2
--R                                   2c\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 31 of 84
cc1:=bb1-aa.1
 

   (5)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                 + 
                        2        2               3
                   (- 8a c + 2a b )x - 4a b c + b
              /
                    2
                 a x  + b x + c
     + 
                                                   2         +-----------+
               2                                  x          |          2
       (log(a x  + b x + c) - 2log(x) + log(--------------))\|- 4a c + b
                                               2
                                            a x  + b x + c
  /
        +-----------+
        |          2
     2c\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                 + 
--R                        2        2               3
--R                   (- 8a c + 2a b )x - 4a b c + b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                                                   2         +-----------+
--R               2                                  x          |          2
--R       (log(a x  + b x + c) - 2log(x) + log(--------------))\|- 4a c + b
--R                                               2
--R                                            a x  + b x + c
--R  /
--R        +-----------+
--R        |          2
--R     2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 32 of 84
dd1:=expandLog cc1
 

   (6)
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2       2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
               + 
                           3
                 4a b c - b
     + 
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2         2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
               + 
                             3
                 - 4a b c + b
     + 
                 2
       2b log(a x  + b x + c)
  /
        +-----------+
        |          2
     2c\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (6)
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2       2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R               + 
--R                           3
--R                 4a b c - b
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2         2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R               + 
--R                             3
--R                 - 4a b c + b
--R     + 
--R                 2
--R       2b log(a x  + b x + c)
--R  /
--R        +-----------+
--R        |          2
--R     2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 33 of 84     14:269 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                     3      2 2
          b log(- 16a c + 4a b )
   (7)  - ----------------------
                +-----------+
                |          2
             2c\|- 4a c + b
                                                     Type: Expression Integer
--R
--R                     3      2 2
--R          b log(- 16a c + 4a b )
--R   (7)  - ----------------------
--R                +-----------+
--R                |          2
--R             2c\|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 34 of 84
aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
 

   (1)
   [
                    2
           (2a c - b )x
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                                      +-----------+
                     2                                |          2
         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
    /
            +-----------+
         2  |          2
       2c x\|- 4a c + b
     ,

                                         +---------+
                                         |        2
                     2        (2a x + b)\|4a c - b
         (- 4a c + 2b )x atan(----------------------)
                                             2
                                     4a c - b
       + 
                                                      +---------+
                     2                                |        2
         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
    /
            +---------+
         2  |        2
       2c x\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                    2
--R           (2a c - b )x
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                                      +-----------+
--R                     2                                |          2
--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
--R    /
--R            +-----------+
--R         2  |          2
--R       2c x\|- 4a c + b
--R     ,
--R
--R                                         +---------+
--R                                         |        2
--R                     2        (2a x + b)\|4a c - b
--R         (- 4a c + 2b )x atan(----------------------)
--R                                             2
--R                                     4a c - b
--R       + 
--R                                                      +---------+
--R                     2                                |        2
--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
--R    /
--R            +---------+
--R         2  |        2
--R       2c x\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 35 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 36 of 84
bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1
 

   (3)
                    2
         (- 2a c + b )x
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                   2                  +-----------+
                a x  + b x + c        |          2
       (b x log(--------------) - 2c)\|- 4a c + b
                       2
                      x
  /
          +-----------+
       2  |          2
     2c x\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                    2
--R         (- 2a c + b )x
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                   2                  +-----------+
--R                a x  + b x + c        |          2
--R       (b x log(--------------) - 2c)\|- 4a c + b
--R                       2
--R                      x
--R  /
--R          +-----------+
--R       2  |          2
--R     2c x\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 37 of 84
bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2
 

   (4)
                                       +---------+
                                       |        2
                   2        (2a x + b)\|4a c - b
       (- 4a c + 2b )x atan(----------------------)
                                           2
                                   4a c - b
     + 
                   2                  +---------+
                a x  + b x + c        |        2
       (b x log(--------------) - 2c)\|4a c - b
                       2
                      x
  /
          +---------+
       2  |        2
     2c x\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                       +---------+
--R                                       |        2
--R                   2        (2a x + b)\|4a c - b
--R       (- 4a c + 2b )x atan(----------------------)
--R                                           2
--R                                   4a c - b
--R     + 
--R                   2                  +---------+
--R                a x  + b x + c        |        2
--R       (b x log(--------------) - 2c)\|4a c - b
--R                       2
--R                      x
--R  /
--R          +---------+
--R       2  |        2
--R     2c x\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 38 of 84
cc1:=bb1-aa.1
 

   (5)
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                    2
         (- 2a c + b )
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                                                     2             +-----------+
                 2                                a x  + b x + c   |          2
     (- b log(a x  + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b
                                                         2
                                                        x
  /
         +-----------+
       2 |          2
     2c \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                                     2             +-----------+
--R                 2                                a x  + b x + c   |          2
--R     (- b log(a x  + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b
--R                                                         2
--R                                                        x
--R  /
--R         +-----------+
--R       2 |          2
--R     2c \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 39 of 84
dd1:=expandLog cc1
 

   (6)
                    2
         (- 2a c + b )
      *
         log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
     + 
                    2
         (- 2a c + b )
      *
         log
                                           +-----------+
                 2 2                    2  |          2         2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
            + 
                          3
              - 4a b c + b
     + 
                 2        2
       (4a c - 2b )log(a x  + b x + c)
  /
         +-----------+
       2 |          2
     2c \|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (6)
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R     + 
--R                    2
--R         (- 2a c + b )
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2         2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R            + 
--R                          3
--R              - 4a b c + b
--R     + 
--R                 2        2
--R       (4a c - 2b )log(a x  + b x + c)
--R  /
--R         +-----------+
--R       2 |          2
--R     2c \|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 40 of 84     14:270 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                   2          3      2 2
        (- 2a c + b )log(- 16a c + 4a b )
   (7)  ---------------------------------
                    +-----------+
                  2 |          2
                2c \|- 4a c + b
                                                     Type: Expression Integer
--R
--R                   2          3      2 2
--R        (- 2a c + b )log(- 16a c + 4a b )
--R   (7)  ---------------------------------
--R                    +-----------+
--R                  2 |          2
--R                2c \|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 41 of 84     14:271 Axiom cannot compute this integral
aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
 

           x
         ++            1
   (1)   |   -------------------- d%Q
        ++                 2    n
             (c + %Q b + %Q a)%Q
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            1
--I   (1)   |   -------------------- d%N
--R        ++                 2    n
--I             (c + %N b + %N a)%N
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 42 of 84
aa:=integrate(1/(a*x^2+b*x+c)^2,x)
 

   (1)
   [
              2 2
           (2a x  + 2a b x + 2a c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                    +-----------+
                    |          2
         (2a x + b)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,
                                           +---------+
                                           |        2                +---------+
       2 2                      (2a x + b)\|4a c - b                 |        2
    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                               2
                                       4a c - b
    ----------------------------------------------------------------------------
                                                             +---------+
                2       2  2              3         2    2   |        2
            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R              2 2
--R           (2a x  + 2a b x + 2a c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                    +-----------+
--R                    |          2
--R         (2a x + b)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R                                           +---------+
--R                                           |        2                +---------+
--R       2 2                      (2a x + b)\|4a c - b                 |        2
--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                               2
--R                                       4a c - b
--R    ----------------------------------------------------------------------------
--R                                                             +---------+
--R                2       2  2              3         2    2   |        2
--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 43 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 44 of 84
bb1:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.1
 

   (3)
            2 2
         (2a x  + 2a b x + 2a c)
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                  +-----------+
                  |          2
       (2a x + b)\|- 4a c + b
  /
                                                      +-----------+
         2       2  2              3         2    2   |          2
     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (3)
--R            2 2
--R         (2a x  + 2a b x + 2a c)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                  +-----------+
--R                  |          2
--R       (2a x + b)\|- 4a c + b
--R  /
--R                                                      +-----------+
--R         2       2  2              3         2    2   |          2
--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 45 of 84
bb2:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.2
 

   (4)
                                          +---------+
                                          |        2                +---------+
      2 2                      (2a x + b)\|4a c - b                 |        2
   (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                              2
                                      4a c - b
   ----------------------------------------------------------------------------
                                                            +---------+
               2       2  2              3         2    2   |        2
           ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
                                                     Type: Expression Integer
--R
--R   (4)
--R                                          +---------+
--R                                          |        2                +---------+
--R      2 2                      (2a x + b)\|4a c - b                 |        2
--R   (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                              2
--R                                      4a c - b
--R   ----------------------------------------------------------------------------
--R                                                            +---------+
--R               2       2  2              3         2    2   |        2
--R           ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 46 of 84
cc1:=aa.1-bb1
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E

--S 47 of 84
cc2:=aa.2-bb1
 

   (6)
       -
               +---------+
               |        2
            2a\|4a c - b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
                                       +---------+
          +-----------+                |        2
          |          2      (2a x + b)\|4a c - b
       4a\|- 4a c + b  atan(----------------------)
                                           2
                                   4a c - b
  /
                 +-----------+ +---------+
              2  |          2  |        2
     (4a c - b )\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (6)
--R       -
--R               +---------+
--R               |        2
--R            2a\|4a c - b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R                                       +---------+
--R          +-----------+                |        2
--R          |          2      (2a x + b)\|4a c - b
--R       4a\|- 4a c + b  atan(----------------------)
--R                                           2
--R                                   4a c - b
--R  /
--R                 +-----------+ +---------+
--R              2  |          2  |        2
--R     (4a c - b )\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 48 of 84
cc3:=aa.1-bb2
 

   (7)
            +---------+
            |        2
         2a\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                                         +---------+
            +-----------+                |        2
            |          2      (2a x + b)\|4a c - b
       - 4a\|- 4a c + b  atan(----------------------)
                                             2
                                     4a c - b
  /
                 +-----------+ +---------+
              2  |          2  |        2
     (4a c - b )\|- 4a c + b  \|4a c - b
                                                     Type: Expression Integer
--R
--R   (7)
--R            +---------+
--R            |        2
--R         2a\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                         +---------+
--R            +-----------+                |        2
--R            |          2      (2a x + b)\|4a c - b
--R       - 4a\|- 4a c + b  atan(----------------------)
--R                                             2
--R                                     4a c - b
--R  /
--R                 +-----------+ +---------+
--R              2  |          2  |        2
--R     (4a c - b )\|- 4a c + b  \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 49 of 84     14:272 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 50 of 84
aa:=integrate(x/(a*x^2+b*x+c)^2,x)
 

   (1)
   [
                 2    2
           (a b x  + b x + b c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                      +-----------+
                      |          2
         (- b x - 2c)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,

                                                  +---------+
                                                  |        2
                  2     2              (2a x + b)\|4a c - b
         (- 2a b x  - 2b x - 2b c)atan(----------------------)
                                                      2
                                              4a c - b
       + 
                      +---------+
                      |        2
         (- b x - 2c)\|4a c - b
    /
                                                        +---------+
           2       2  2              3         2    2   |        2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                 2    2
--R           (a b x  + b x + b c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                      +-----------+
--R                      |          2
--R         (- b x - 2c)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R
--R                                                  +---------+
--R                                                  |        2
--R                  2     2              (2a x + b)\|4a c - b
--R         (- 2a b x  - 2b x - 2b c)atan(----------------------)
--R                                                      2
--R                                              4a c - b
--R       + 
--R                      +---------+
--R                      |        2
--R         (- b x - 2c)\|4a c - b
--R    /
--R                                                        +---------+
--R           2       2  2              3         2    2   |        2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 51 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 52 of 84
bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1
 

   (3)
                 2    2
         (- a b x  - b x - b c)
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                    +-----------+
                    |          2
       (- b x - 2c)\|- 4a c + b
  /
                                                      +-----------+
         2       2  2              3         2    2   |          2
     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (3)
--R                 2    2
--R         (- a b x  - b x - b c)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                    +-----------+
--R                    |          2
--R       (- b x - 2c)\|- 4a c + b
--R  /
--R                                                      +-----------+
--R         2       2  2              3         2    2   |          2
--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 53 of 84
bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2
 

   (4)
                                                +---------+
                                                |        2
                2     2              (2a x + b)\|4a c - b
       (- 2a b x  - 2b x - 2b c)atan(----------------------)
                                                    2
                                            4a c - b
     + 
                    +---------+
                    |        2
       (- b x - 2c)\|4a c - b
  /
                                                      +---------+
         2       2  2              3         2    2   |        2
     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                                +---------+
--R                                                |        2
--R                2     2              (2a x + b)\|4a c - b
--R       (- 2a b x  - 2b x - 2b c)atan(----------------------)
--R                                                    2
--R                                            4a c - b
--R     + 
--R                    +---------+
--R                    |        2
--R       (- b x - 2c)\|4a c - b
--R  /
--R                                                      +---------+
--R         2       2  2              3         2    2   |        2
--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 54 of 84
cc1:=bb1-aa.1
 

   (5)
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2       2        2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                 + 
                             3
                   4a b c - b
              /
                    2
                 a x  + b x + c
     + 
       -
            b
         *
            log
                                                +-----------+
                      2 2                    2  |          2
                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
                 + 
                        2        2               3
                   (- 8a c + 2a b )x - 4a b c + b
              /
                    2
                 a x  + b x + c
  /
                 +-----------+
              2  |          2
     (4a c - b )\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (5)
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2       2        2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                 + 
--R                             3
--R                   4a b c - b
--R              /
--R                    2
--R                 a x  + b x + c
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                                +-----------+
--R                      2 2                    2  |          2
--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
--R                 + 
--R                        2        2               3
--R                   (- 8a c + 2a b )x - 4a b c + b
--R              /
--R                    2
--R                 a x  + b x + c
--R  /
--R                 +-----------+
--R              2  |          2
--R     (4a c - b )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 55 of 84
dd1:=expandLog cc1
 

   (6)
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2       2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
               + 
                           3
                 4a b c - b
     + 
       -
            b
         *
            log
                                              +-----------+
                    2 2                    2  |          2         2        2
                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
               + 
                             3
                 - 4a b c + b
     + 
                 2
       2b log(a x  + b x + c)
  /
                 +-----------+
              2  |          2
     (4a c - b )\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (6)
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2       2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R               + 
--R                           3
--R                 4a b c - b
--R     + 
--R       -
--R            b
--R         *
--R            log
--R                                              +-----------+
--R                    2 2                    2  |          2         2        2
--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R               + 
--R                             3
--R                 - 4a b c + b
--R     + 
--R                 2
--R       2b log(a x  + b x + c)
--R  /
--R                 +-----------+
--R              2  |          2
--R     (4a c - b )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 56 of 84     14:273 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                       3      2 2
            b log(- 16a c + 4a b )
   (7)  - -------------------------
                      +-----------+
                   2  |          2
          (4a c - b )\|- 4a c + b
                                                     Type: Expression Integer
--R
--R                       3      2 2
--R            b log(- 16a c + 4a b )
--R   (7)  - -------------------------
--R                      +-----------+
--R                   2  |          2
--R          (4a c - b )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 57 of 84
aa:=integrate(x^2/(a*x^2+b*x+c)^2,x)
 

   (1)
   [
              2   2                  2
           (2a c x  + 2a b c x + 2a c )
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                                +-----------+
                     2          |          2
         ((- 2a c + b )x + b c)\|- 4a c + b
    /
                                                            +-----------+
           3     2 2  2      2         3       2 2      2   |          2
       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
     ,

                                                     +---------+
                                                     |        2
            2   2                  2      (2a x + b)\|4a c - b
         (4a c x  + 4a b c x + 4a c )atan(----------------------)
                                                         2
                                                 4a c - b
       + 
                                +---------+
                     2          |        2
         ((- 2a c + b )x + b c)\|4a c - b
    /
                                                            +---------+
           3     2 2  2      2         3       2 2      2   |        2
       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R              2   2                  2
--R           (2a c x  + 2a b c x + 2a c )
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                +-----------+
--R                     2          |          2
--R         ((- 2a c + b )x + b c)\|- 4a c + b
--R    /
--R                                                            +-----------+
--R           3     2 2  2      2         3       2 2      2   |          2
--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
--R     ,
--R
--R                                                     +---------+
--R                                                     |        2
--R            2   2                  2      (2a x + b)\|4a c - b
--R         (4a c x  + 4a b c x + 4a c )atan(----------------------)
--R                                                         2
--R                                                 4a c - b
--R       + 
--R                                +---------+
--R                     2          |        2
--R         ((- 2a c + b )x + b c)\|4a c - b
--R    /
--R                                                            +---------+
--R           3     2 2  2      2         3       2 2      2   |        2
--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 58 of 84
t1:=integrate(1/(a*x^2+b*x+c),x)
 

   (2)
   [
       log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
         /
               2
            a x  + b x + c
    /
        +-----------+
        |          2
       \|- 4a c + b
     ,
                     +---------+
                     |        2
          (2a x + b)\|4a c - b
    2atan(----------------------)
                         2
                 4a c - b
    -----------------------------]
              +---------+
              |        2
             \|4a c - b
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R       log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R         /
--R               2
--R            a x  + b x + c
--R    /
--R        +-----------+
--R        |          2
--R       \|- 4a c + b
--R     ,
--R                     +---------+
--R                     |        2
--R          (2a x + b)\|4a c - b
--R    2atan(----------------------)
--R                         2
--R                 4a c - b
--R    -----------------------------]
--R              +---------+
--R              |        2
--R             \|4a c - b
--R                                     Type: Union(List Expression Integer,...)
--E

--S 59 of 84
bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1
 

   (3)
            2   2                  2
         (2a c x  + 2a b c x + 2a c )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
                              +-----------+
                   2          |          2
       ((- 2a c + b )x + b c)\|- 4a c + b
  /
                                                          +-----------+
         3     2 2  2      2         3       2 2      2   |          2
     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (3)
--R            2   2                  2
--R         (2a c x  + 2a b c x + 2a c )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                              +-----------+
--R                   2          |          2
--R       ((- 2a c + b )x + b c)\|- 4a c + b
--R  /
--R                                                          +-----------+
--R         3     2 2  2      2         3       2 2      2   |          2
--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 60 of 84
bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2
 

   (4)
                                                   +---------+
                                                   |        2
          2   2                  2      (2a x + b)\|4a c - b
       (4a c x  + 4a b c x + 4a c )atan(----------------------)
                                                       2
                                               4a c - b
     + 
                              +---------+
                   2          |        2
       ((- 2a c + b )x + b c)\|4a c - b
  /
                                                          +---------+
         3     2 2  2      2         3       2 2      2   |        2
     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                   +---------+
--R                                                   |        2
--R          2   2                  2      (2a x + b)\|4a c - b
--R       (4a c x  + 4a b c x + 4a c )atan(----------------------)
--R                                                       2
--R                                               4a c - b
--R     + 
--R                              +---------+
--R                   2          |        2
--R       ((- 2a c + b )x + b c)\|4a c - b
--R  /
--R                                                          +---------+
--R         3     2 2  2      2         3       2 2      2   |        2
--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 61 of 84     14:274 Schaums and Axiom agree
cc1:=aa.1-bb1
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 62 of 84     14:275 Axiom cannot compute this integral
aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
 

           x           m
         ++          %Q
   (1)   |   ------------------ d%Q
        ++                 2  n
             (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x           m
--I         ++          %N
--I   (1)   |   ------------------ d%N
--R        ++                 2  n
--I             (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 63 of 84     14:276 Axiom cannot compute this integral
aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
 

           x        2n - 1
         ++       %Q
   (1)   |   ------------------ d%Q
        ++                 2  n
             (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x        2n - 1
--I         ++       %N
--I   (1)   |   ------------------ d%N
--R        ++                 2  n
--I             (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 64 of 84
aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
 

   (1)
   [
               2         3  2        2     4           2    3
           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +-----------+
            |          2
           \|- 4a c + b
    /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
     ,

                  2          3  2           2      4            2     3
           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
        *
                           +---------+
                           |        2
                (2a x + b)\|4a c - b
           atan(----------------------)
                               2
                       4a c - b
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +---------+
            |        2
           \|4a c - b
    /
                                                                  +---------+
           2 3       2 2  2          3     3 2         4     2 3  |        2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R               2         3  2        2     4           2    3
--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R    /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R     ,
--R
--R                  2          3  2           2      4            2     3
--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
--R        *
--R                           +---------+
--R                           |        2
--R                (2a x + b)\|4a c - b
--R           atan(----------------------)
--R                               2
--R                       4a c - b
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +---------+
--R            |        2
--R           \|4a c - b
--R    /
--R                                                                  +---------+
--R           2 3       2 2  2          3     3 2         4     2 3  |        2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 65 of 84
t1:=integrate(1/(a*x^2+b*x+c)^2,x)
 

   (2)
   [
              2 2
           (2a x  + 2a b x + 2a c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                    +-----------+
                    |          2
         (2a x + b)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,
                                           +---------+
                                           |        2                +---------+
       2 2                      (2a x + b)\|4a c - b                 |        2
    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                               2
                                       4a c - b
    ----------------------------------------------------------------------------
                                                             +---------+
                2       2  2              3         2    2   |        2
            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R              2 2
--R           (2a x  + 2a b x + 2a c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                    +-----------+
--R                    |          2
--R         (2a x + b)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R                                           +---------+
--R                                           |        2                +---------+
--R       2 2                      (2a x + b)\|4a c - b                 |        2
--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                               2
--R                                       4a c - b
--R    ----------------------------------------------------------------------------
--R                                                             +---------+
--R                2       2  2              3         2    2   |        2
--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 66 of 84
t2:=integrate(1/(x*(a*x^2+b*x+c)),x)
 

   (3)
   [
           b
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                                           +-----------+
                   2                       |          2
         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
    /
          +-----------+
          |          2
       2c\|- 4a c + b
     ,

                              +---------+
                              |        2
                   (2a x + b)\|4a c - b
         - 2b atan(----------------------)
                                  2
                          4a c - b
       + 
                                           +---------+
                   2                       |        2
         (- log(a x  + b x + c) + 2log(x))\|4a c - b
    /
          +---------+
          |        2
       2c\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (3)
--R   [
--R           b
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                                           +-----------+
--R                   2                       |          2
--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
--R    /
--R          +-----------+
--R          |          2
--R       2c\|- 4a c + b
--R     ,
--R
--R                              +---------+
--R                              |        2
--R                   (2a x + b)\|4a c - b
--R         - 2b atan(----------------------)
--R                                  2
--R                          4a c - b
--R       + 
--R                                           +---------+
--R                   2                       |        2
--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
--R    /
--R          +---------+
--R          |        2
--R       2c\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 67 of 84
bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1
 

   (4)
              2     2       2            2
         (- 2a b c x  - 2a b c x - 2a b c )
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
             2         3  2        2     4           2    3
         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +-----------+
          |          2
         \|- 4a c + b
  /
                                                                +-----------+
         2 3       2 2  2          3     3 2         4     2 3  |          2
     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R              2     2       2            2
--R         (- 2a b c x  - 2a b c x - 2a b c )
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R             2         3  2        2     4           2    3
--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +-----------+
--R          |          2
--R         \|- 4a c + b
--R  /
--R                                                                +-----------+
--R         2 3       2 2  2          3     3 2         4     2 3  |          2
--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 68 of 84
bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1
 

   (5)
                                                              +---------+
             2         3  2        2     4           2    3   |        2
         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                                            +-----------+
              2     2       2            2  |          2
         (- 4a b c x  - 4a b c x - 4a b c )\|- 4a c + b
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (5)
--R                                                              +---------+
--R             2         3  2        2     4           2    3   |        2
--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                            +-----------+
--R              2     2       2            2  |          2
--R         (- 4a b c x  - 4a b c x - 4a b c )\|- 4a c + b
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 69 of 84
bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2
 

   (6)
                                            +---------+
              2     2       2            2  |        2
         (- 2a b c x  - 2a b c x - 2a b c )\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
               2          3  2          2      4           2     3
         ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x - 8a b c  + 2b c)
      *
                                       +---------+
          +-----------+                |        2
          |          2      (2a x + b)\|4a c - b
         \|- 4a c + b  atan(----------------------)
                                           2
                                   4a c - b
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                                            +---------+
--R              2     2       2            2  |        2
--R         (- 2a b c x  - 2a b c x - 2a b c )\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R               2          3  2          2      4           2     3
--R         ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x - 8a b c  + 2b c)
--R      *
--R                                       +---------+
--R          +-----------+                |        2
--R          |          2      (2a x + b)\|4a c - b
--R         \|- 4a c + b  atan(----------------------)
--R                                           2
--R                                   4a c - b
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 70 of 84
bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2
 

   (7)
                2          3  2           2      4            2     3
         ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                   2       2  2                3         2    2
             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
          *
                    2
             log(a x  + b x + c)
         + 
               2        2  2               3         2     2
           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
         + 
               2     2
           4a c  - 2b c
      *
          +---------+
          |        2
         \|4a c - b
  /
                                                                +---------+
         2 3       2 2  2          3     3 2         4     2 3  |        2
     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                2          3  2           2      4            2     3
--R         ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                   2       2  2                3         2    2
--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R               2        2  2               3         2     2
--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
--R         + 
--R               2     2
--R           4a c  - 2b c
--R      *
--R          +---------+
--R          |        2
--R         \|4a c - b
--R  /
--R                                                                +---------+
--R         2 3       2 2  2          3     3 2         4     2 3  |        2
--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 71 of 84
cc1:=aa.1-bb1
 

   (8)
         a b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
         a b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (8)
--R         a b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R         a b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 72 of 84
dd1:=expandLog cc1
 

   (9)
         a b
      *
         log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
     + 
         a b
      *
         log
                                           +-----------+
                 2 2                    2  |          2         2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
            + 
                          3
              - 4a b c + b
     + 
                     2
       - 2a b log(a x  + b x + c)
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (9)
--R         a b
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R     + 
--R         a b
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2         2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R            + 
--R                          3
--R              - 4a b c + b
--R     + 
--R                     2
--R       - 2a b log(a x  + b x + c)
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 73 of 84     14:277 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

                        3      2 2
           a b log(- 16a c + 4a b )
   (10)  ---------------------------
                       +-----------+
              2    2   |          2
         (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R                        3      2 2
--R           a b log(- 16a c + 4a b )
--R   (10)  ---------------------------
--R                       +-----------+
--R              2    2   |          2
--R         (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 74 of 84
aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x)
 

   (1)
   [
                3 2     2 2       4  3      2   2       3     5  2
             (6a c  - 6a b c + a b )x  + (6a b c  - 6a b c + b )x
           + 
                2 3       2 2    4
             (6a c  - 6a b c  + b c)x
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                   2         3  3        2     4  2          2    3
               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
            *
                      2
               log(a x  + b x + c)
           + 
                     2          3  3          2      4  2            2     3
               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
            *
               log(x)
           + 
                  2 2       2   2            2     3          3    2 2
             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
        *
            +-----------+
            |          2
           \|- 4a c + b
    /
                                                                   +-----------+
           2 4      2 3  3          4    3 3  2        5    2 4    |          2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
     ,

                   3 2      2 2        4  3         2   2        3      5  2
             (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
           + 
                   2 3        2 2     4
             (- 12a c  + 12a b c  - 2b c)x
        *
                           +---------+
                           |        2
                (2a x + b)\|4a c - b
           atan(----------------------)
                               2
                       4a c - b
       + 
                   2         3  3        2     4  2          2    3
               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
            *
                      2
               log(a x  + b x + c)
           + 
                     2          3  3          2      4  2            2     3
               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
            *
               log(x)
           + 
                  2 2       2   2            2     3          3    2 2
             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
        *
            +---------+
            |        2
           \|4a c - b
    /
                                                                   +---------+
           2 4      2 3  3          4    3 3  2        5    2 4    |        2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                3 2     2 2       4  3      2   2       3     5  2
--R             (6a c  - 6a b c + a b )x  + (6a b c  - 6a b c + b )x
--R           + 
--R                2 3       2 2    4
--R             (6a c  - 6a b c  + b c)x
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                   2         3  3        2     4  2          2    3
--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                     2          3  3          2      4  2            2     3
--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R            *
--R               log(x)
--R           + 
--R                  2 2       2   2            2     3          3    2 2
--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R        *
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R    /
--R                                                                   +-----------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R     ,
--R
--R                   3 2      2 2        4  3         2   2        3      5  2
--R             (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
--R           + 
--R                   2 3        2 2     4
--R             (- 12a c  + 12a b c  - 2b c)x
--R        *
--R                           +---------+
--R                           |        2
--R                (2a x + b)\|4a c - b
--R           atan(----------------------)
--R                               2
--R                       4a c - b
--R       + 
--R                   2         3  3        2     4  2          2    3
--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                     2          3  3          2      4  2            2     3
--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R            *
--R               log(x)
--R           + 
--R                  2 2       2   2            2     3          3    2 2
--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R        *
--R            +---------+
--R            |        2
--R           \|4a c - b
--R    /
--R                                                                   +---------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |        2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 75 of 84
t1:=integrate(1/(a*x^2+b*x+c)^2,x)
 

   (2)
   [
              2 2
           (2a x  + 2a b x + 2a c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2       2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
                + 
                            3
                  4a b c - b
             /
                   2
                a x  + b x + c
       + 
                    +-----------+
                    |          2
         (2a x + b)\|- 4a c + b
    /
                                                        +-----------+
           2       2  2              3         2    2   |          2
       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
     ,
                                           +---------+
                                           |        2                +---------+
       2 2                      (2a x + b)\|4a c - b                 |        2
    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
                                               2
                                       4a c - b
    ----------------------------------------------------------------------------
                                                             +---------+
                2       2  2              3         2    2   |        2
            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (2)
--R   [
--R              2 2
--R           (2a x  + 2a b x + 2a c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2       2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R                + 
--R                            3
--R                  4a b c - b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                    +-----------+
--R                    |          2
--R         (2a x + b)\|- 4a c + b
--R    /
--R                                                        +-----------+
--R           2       2  2              3         2    2   |          2
--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
--R     ,
--R                                           +---------+
--R                                           |        2                +---------+
--R       2 2                      (2a x + b)\|4a c - b                 |        2
--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
--R                                               2
--R                                       4a c - b
--R    ----------------------------------------------------------------------------
--R                                                             +---------+
--R                2       2  2              3         2    2   |        2
--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 76 of 84
t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
 

   (3)
   [
               2         3  2        2     4           2    3
           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
        *
           log
                                               +-----------+
                     2 2                    2  |          2         2        2
                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
                + 
                              3
                  - 4a b c + b
             /
                   2
                a x  + b x + c
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +-----------+
            |          2
           \|- 4a c + b
    /
                                                                  +-----------+
           2 3       2 2  2          3     3 2         4     2 3  |          2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
     ,

                  2          3  2           2      4            2     3
           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
        *
                           +---------+
                           |        2
                (2a x + b)\|4a c - b
           atan(----------------------)
                               2
                       4a c - b
       + 
                     2       2  2                3         2    2
               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
            *
                      2
               log(a x  + b x + c)
           + 
                 2        2  2               3         2     2
             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
           + 
                              2     2
             - 2a b c x + 4a c  - 2b c
        *
            +---------+
            |        2
           \|4a c - b
    /
                                                                  +---------+
           2 3       2 2  2          3     3 2         4     2 3  |        2
       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (3)
--R   [
--R               2         3  2        2     4           2    3
--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
--R        *
--R           log
--R                                               +-----------+
--R                     2 2                    2  |          2         2        2
--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R                + 
--R                              3
--R                  - 4a b c + b
--R             /
--R                   2
--R                a x  + b x + c
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +-----------+
--R            |          2
--R           \|- 4a c + b
--R    /
--R                                                                  +-----------+
--R           2 3       2 2  2          3     3 2         4     2 3  |          2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
--R     ,
--R
--R                  2          3  2           2      4            2     3
--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
--R        *
--R                           +---------+
--R                           |        2
--R                (2a x + b)\|4a c - b
--R           atan(----------------------)
--R                               2
--R                       4a c - b
--R       + 
--R                     2       2  2                3         2    2
--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
--R            *
--R                      2
--R               log(a x  + b x + c)
--R           + 
--R                 2        2  2               3         2     2
--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
--R           + 
--R                              2     2
--R             - 2a b c x + 4a c  - 2b c
--R        *
--R            +---------+
--R            |        2
--R           \|4a c - b
--R    /
--R                                                                  +---------+
--R           2 3       2 2  2          3     3 2         4     2 3  |        2
--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E

--S 77 of 84
bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1
 

   (4)
              3 2 3     2   2 2     2 3
         (- 6a c x  - 6a b c x  - 6a c x)
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
               2 2       4  3          3     5  2          2 2    4
         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +-----------+
          |          2
         \|- 4a c + b
  /
                                                                 +-----------+
         2 4      2 3  3          4    3 3  2        5    2 4    |          2
     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R              3 2 3     2   2 2     2 3
--R         (- 6a c x  - 6a b c x  - 6a c x)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R               2 2       4  3          3     5  2          2 2    4
--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +-----------+
--R          |          2
--R         \|- 4a c + b
--R  /
--R                                                                 +-----------+
--R         2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 78 of 84
bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1
 

   (5)
               2 2       4  3          3     5  2          2 2    4
         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
      *
          +---------+
          |        2
         \|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
     + 
                                             +-----------+
               3 2 3      2   2 2      2 3   |          2
         (- 12a c x  - 12a b c x  - 12a c x)\|- 4a c + b
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                   +-----------+
           2 4      2 3  3          4    3 3  2        5    2 4    |          2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (5)
--R               2 2       4  3          3     5  2          2 2    4
--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
--R      *
--R          +---------+
--R          |        2
--R         \|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R                                             +-----------+
--R               3 2 3      2   2 2      2 3   |          2
--R         (- 12a c x  - 12a b c x  - 12a c x)\|- 4a c + b
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                   +-----------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 79 of 84
bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2
 

   (6)
                                          +---------+
              3 2 3     2   2 2     2 3   |        2
         (- 6a c x  - 6a b c x  - 6a c x)\|4a c - b
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
              2 2        4  3         3      5  2         2 2     4
         ((12a b c - 2a b )x  + (12a b c - 2b )x  + (12a b c  - 2b c)x)
      *
                                       +---------+
          +-----------+                |        2
          |          2      (2a x + b)\|4a c - b
         \|- 4a c + b  atan(----------------------)
                                           2
                                   4a c - b
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +-----------+ +---------+
          |          2  |        2
         \|- 4a c + b  \|4a c - b
  /
                                                                   +-----------+
           2 4      2 3  3          4    3 3  2        5    2 4    |          2
       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
    *
        +---------+
        |        2
       \|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (6)
--R                                          +---------+
--R              3 2 3     2   2 2     2 3   |        2
--R         (- 6a c x  - 6a b c x  - 6a c x)\|4a c - b
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R              2 2        4  3         3      5  2         2 2     4
--R         ((12a b c - 2a b )x  + (12a b c - 2b )x  + (12a b c  - 2b c)x)
--R      *
--R                                       +---------+
--R          +-----------+                |        2
--R          |          2      (2a x + b)\|4a c - b
--R         \|- 4a c + b  atan(----------------------)
--R                                           2
--R                                   4a c - b
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +-----------+ +---------+
--R          |          2  |        2
--R         \|- 4a c + b  \|4a c - b
--R  /
--R                                                                   +-----------+
--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
--R    *
--R        +---------+
--R        |        2
--R       \|4a c - b
--R                                                     Type: Expression Integer
--E

--S 80 of 84
bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2
 

   (7)
                 3 2      2 2        4  3         2   2        3      5  2
           (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
         + 
                 2 3        2 2     4
           (- 12a c  + 12a b c  - 2b c)x
      *
                         +---------+
                         |        2
              (2a x + b)\|4a c - b
         atan(----------------------)
                             2
                     4a c - b
     + 
                 2         3  3        2     4  2          2    3
             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
          *
                    2
             log(a x  + b x + c)
         + 
                   2          3  3          2      4  2            2     3
             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
          *
             log(x)
         + 
                2 2       2   2            2     3          3    2 2
           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
      *
          +---------+
          |        2
         \|4a c - b
  /
                                                                 +---------+
         2 4      2 3  3          4    3 3  2        5    2 4    |        2
     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
                                                     Type: Expression Integer
--R 
--R
--R   (7)
--R                 3 2      2 2        4  3         2   2        3      5  2
--R           (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
--R         + 
--R                 2 3        2 2     4
--R           (- 12a c  + 12a b c  - 2b c)x
--R      *
--R                         +---------+
--R                         |        2
--R              (2a x + b)\|4a c - b
--R         atan(----------------------)
--R                             2
--R                     4a c - b
--R     + 
--R                 2         3  3        2     4  2          2    3
--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
--R          *
--R                    2
--R             log(a x  + b x + c)
--R         + 
--R                   2          3  3          2      4  2            2     3
--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
--R          *
--R             log(x)
--R         + 
--R                2 2       2   2            2     3          3    2 2
--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
--R      *
--R          +---------+
--R          |        2
--R         \|4a c - b
--R  /
--R                                                                 +---------+
--R         2 4      2 3  3          4    3 3  2        5    2 4    |        2
--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
--R                                                     Type: Expression Integer
--E

--S 81 of 84
cc1:=aa.1-bb1
 

   (8)
           2
         6a
      *
         log
                                             +-----------+
                   2 2                    2  |          2       2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
              + 
                          3
                4a b c - b
           /
                 2
              a x  + b x + c
     + 
           2
         6a
      *
         log
                                             +-----------+
                   2 2                    2  |          2         2        2
                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
              + 
                            3
                - 4a b c + b
           /
                 2
              a x  + b x + c
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (8)
--R           2
--R         6a
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2       2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R              + 
--R                          3
--R                4a b c - b
--R           /
--R                 2
--R              a x  + b x + c
--R     + 
--R           2
--R         6a
--R      *
--R         log
--R                                             +-----------+
--R                   2 2                    2  |          2         2        2
--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R              + 
--R                            3
--R                - 4a b c + b
--R           /
--R                 2
--R              a x  + b x + c
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 82 of 84
dd1:=expandLog cc1
 

   (9)
           2
         6a
      *
         log
                                           +-----------+
                 2 2                    2  |          2       2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
            + 
                        3
              4a b c - b
     + 
           2
         6a
      *
         log
                                           +-----------+
                 2 2                    2  |          2         2        2
              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
            + 
                          3
              - 4a b c + b
     + 
            2       2
       - 12a log(a x  + b x + c)
  /
                   +-----------+
          2    2   |          2
     (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R   (9)
--R           2
--R         6a
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2       2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
--R            + 
--R                        3
--R              4a b c - b
--R     + 
--R           2
--R         6a
--R      *
--R         log
--R                                           +-----------+
--R                 2 2                    2  |          2         2        2
--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
--R            + 
--R                          3
--R              - 4a b c + b
--R     + 
--R            2       2
--R       - 12a log(a x  + b x + c)
--R  /
--R                   +-----------+
--R          2    2   |          2
--R     (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E

--S 83 of 84     14:278 Schaums and Axiom differ by a constant
ee1:=complexNormalize dd1
 

             2         3      2 2
           6a log(- 16a c + 4a b )
   (10)  ---------------------------
                       +-----------+
              2    2   |          2
         (4a c  - b c)\|- 4a c + b
                                                     Type: Expression Integer
--R
--R             2         3      2 2
--R           6a log(- 16a c + 4a b )
--R   (10)  ---------------------------
--R                       +-----------+
--R              2    2   |          2
--R         (4a c  - b c)\|- 4a c + b
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 84 of 84     14:279 Axiom cannot compute this integral
aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x)
 

           x
         ++            1
   (1)   |   --------------------- d%Q
        ++     m              2  n
             %Q (c + %Q b + %Q a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            1
--I   (1)   |   --------------------- d%N
--R        ++     m              2  n
--I             %N (c + %N b + %N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to explim.output (2010/3/27, 18:25:42).
)set message test on
 
)set message auto off
 
)clear all
 
)clear all
 

--S 1 of 12
limit(x/exp(x),x = %plusInfinity)              -- 0
 

   (1)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (1)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 1

--S 2 of 12
limit(x**10000/exp(x),x = %plusInfinity)       -- 0
 

   (2)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (2)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 2

--S 3 of 12
limit(x**(10**20)/exp(x),x = %plusInfinity)    -- 0
 

   (3)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (3)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 3

--S 4 of 12
limit(x**h/exp(x),x = %plusInfinity)           -- 0
 

   (4)  0
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)  0
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 12
limit(x/exp(x),x = %minusInfinity)             -- %minusInfinity
 

   (5)  - infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (5)  - infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 12
limit(x**10000/exp(x),x = %minusInfinity)      -- %plusInfinity
 

   (6)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (6)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 6

--S 7 of 12
limit(x**(10**20)/exp(x),x = %minusInfinity)   -- %plusInfinity
 

   (7)   + infinity
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (7)   + infinity
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 7

--S 8 of 12
limit(x**h/exp(x),x = %minusInfinity)          -- "failed"
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8

--S 9 of 12
limit(exp(-x) * sinh(x),x = %plusInfinity)     -- 1/2
 

        1
   (9)  -
        2
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R        1
--R   (9)  -
--R        2
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 9

--S 10 of 12
limit(exp(-x) * cosh(x),x = %plusInfinity)     -- 1/2
 

         1
   (10)  -
         2
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         1
--R   (10)  -
--R         2
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 10

--S 11 of 12
limit(exp(-x) * exp(x),x = %plusInfinity)      -- 1
 

   (11)  1
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (11)  1
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 11

--S 12 of 12
limit((x + 1)**(x + 1)/x**x - x**x/(x - 1)**(x - 1),x = %plusInfinity)  -- %e
 

   (12)  %e
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (12)  %e
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 12
)spool 
 
Starts dribbling to lodo.output (2010/3/27, 18:28:51).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 55
RN:=FRAC INT
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 55
Dx: LODO2(RN, UP(x,RN))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 55
Dx := D()                  
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 55
a  := Dx  + 1
 

   (4)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 55
b  := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (5)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (5)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 55
p: UP(x,RN) := 4*x**2 + 2/3      
 

          2   2
   (6)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (6)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 6
 
--S 7 of 55
a p                        
 

          2        2
   (7)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (7)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 55
(a*b) p = a b p            
 

          2         37    2         37
   (8)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (8)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 8


--S 9 of 55
c := (1/9)*b*(a + b)**2    
 

         1  6    5  5   13  4   19  3   79  2    7     1
   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
        72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R         1  6    5  5   13  4   19  3   79  2    7     1
--R   (9)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R        72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 55
(a**2 - 3/4*b + c) (p + 1) 
 

           2   44     541
   (10)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (10)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 10


)clear all
 
--S 11 of 55
RFZ := FRAC UP(x,INT)
 

   (1)  Fraction UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 11

--S 12 of 55
(Dx, a, b): LODO1 RFZ
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 55
Dx := D()
 

   (3)  D
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (3)  D
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 55
b := 3*x**2*Dx**2 + 2*Dx + 1/x
 

          2 2        1
   (4)  3x D  + 2D + -
                     x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 14

--S 15 of 55
a := b*(5*x*Dx + 7)
 

           3 3       2        2         7
   (5)  15x D  + (51x  + 10x)D  + 29D + -
                                        x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 15

--S 16 of 55
p: RFZ := x**2 + 1/x**2
 

         4
        x  + 1
   (6)  ------
           2
          x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 16

--S 17 of 55
(a*b - b*a) p 
 

             4
        - 75x  + 540x - 75
   (7)  ------------------
                 4
                x
                               Type: Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                               Type: Fraction UnivariatePolynomial(x,Integer)
--E 17

--S 18 of 55
leftDivide(a,b)      
 

   (8)  [quotient= 5x D + 7,remainder= 0]
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 55
a - (b * %.quotient + %.remainder)
 

   (9)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (9)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 19

--S 20 of 55
rightDivide(a,b)
 

                                              5
   (10)  [quotient= 5x D + 7,remainder= 10D + -]
                                              x
Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--R 
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))
--E 20

--S 21 of 55
a - (%.quotient * b + %.remainder)
 

   (11)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (11)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 21

--S 22 of 55
e := leftGcd(a,b)
 

           2 2        1
   (12)  3x D  + 2D + -
                      x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R           2 2        1
--R   (12)  3x D  + 2D + -
--R                      x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 22

--S 23 of 55
leftRemainder(a, e)    
 

   (13)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (13)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 23

--S 24 of 55
rightRemainder(a, e)    
 

               5
   (14)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (14)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 24

--S 25 of 55
f := rightLcm(a,b)
 

            3 3       2        2         7
   (15)  15x D  + (51x  + 10x)D  + 29D + -
                                         x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R            3 3       2        2         7
--R   (15)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 25

--S 26 of 55
leftRemainder(f, b)
 

   (16)  0
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R   (16)  0
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 26

--S 27 of 55
rightRemainder(f, b)  
 

               5
   (17)  10D + -
               x
Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--R 
--R
--R               5
--R   (17)  10D + -
--R               x
--RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)
--E 27

)clear all
 
--S 28 of 55
Dx: LODO(EXPR INT, f +-> D(f, x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 55
Dx := D()
 

   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1774 envArg,SPADCALL(G1774,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R   (2)  D
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1500 envArg,SPADCALL(G1500,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 29

--S 30 of 55
Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1
 

                       3
         3    G     - x  + H
   (3)  D  + -- D + --------
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1774 envArg,SPADCALL(G1774,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--R 
--R
--R                       3
--R         3    G     - x  + H
--R   (3)  D  + -- D + --------
--R              2         3
--R             x         x
--IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1500 envArg,SPADCALL(G1500,QUOTE x,ELT(*1;anonymousFunction;0;initial;internal;MV,0))))
--E 30

--S 31 of 55
n == 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 55
phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 55
phi1 ==  Dop(phi) / exp x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 55
phi2 == phi1 *x**(n+3)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 34

--S 35 of 55
phi3 == retract(phi2)@(POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 35

--S 36 of 55
pans == phi3 ::UP(x,POLY INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 55
pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 37

--S 38 of 55
leq == solve(pans1,[subscript(s,[i]) for i in 1..n])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 38

--S 39 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 
   Compiling function G1900 with type Integer -> Boolean 

   (12)
                           2                                3        2
         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
          0        0     0       0         0       0      0        0        0
   [[s = ---,s = ------------------,s = --------------------------------------]]
      1   3   2          18          3                    162
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--I   Compiling function G3445 with type Integer -> Boolean 
--R
--R   (12)
--R                           2                                3        2
--R         s G     3s H + s G  + 6s G     (9s G + 54s )H + s G  + 18s G  + 72s G
--R          0        0     0       0         0       0      0        0        0
--R   [[s = ---,s = ------------------,s = --------------------------------------]]
--R      1   3   2          18          3                    162
--R                         Type: List List Equation Fraction Polynomial Integer
--E 39

--S 40 of 55
n==4
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 40

--S 41 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (14)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 41

--S 42 of 55
n==7
 
   Compiled code for n has been cleared.
   Compiled code for leq has been cleared.
   Compiled code for pans1 has been cleared.
   Compiled code for phi2 has been cleared.
   Compiled code for phi has been cleared.
   Compiled code for phi3 has been cleared.
   Compiled code for phi1 has been cleared.
   Compiled code for pans has been cleared.
   1 old definition(s) deleted for function or rule n 
                                                                   Type: Void
--R 
--R   Compiled code for n has been cleared.
--R   Compiled code for leq has been cleared.
--R   Compiled code for pans1 has been cleared.
--R   Compiled code for phi2 has been cleared.
--R   Compiled code for phi has been cleared.
--R   Compiled code for phi3 has been cleared.
--R   Compiled code for phi1 has been cleared.
--R   Compiled code for pans has been cleared.
--R   1 old definition(s) deleted for function or rule n 
--R                                                                   Type: Void
--E 42

--S 43 of 55
leq
 
   Compiling body of rule n to compute value of type PositiveInteger 
   Compiling body of rule phi to compute value of type Expression 
      Integer 
   Compiling body of rule phi1 to compute value of type Expression 
      Integer 
   Compiling body of rule phi2 to compute value of type Expression 
      Integer 
   Compiling body of rule phi3 to compute value of type Polynomial 
      Integer 
   Compiling body of rule pans to compute value of type 
      UnivariatePolynomial(x,Polynomial Integer) 
   Compiling body of rule pans1 to compute value of type List 
      Polynomial Integer 
   Compiling body of rule leq to compute value of type List List 
      Equation Fraction Polynomial Integer 

   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ---, s = ------------------,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = --------------------------------------,
       3                    162

       s  =
        4
                  2         2                          4        3         2
             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
                0         0         0         0      0        0         0
           + 
             1296s G
                  0
        /
           1944
       ,

       s  =
        5
                               2         3          2
             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
                  0         0          0          0           0          0
           + 
                5        4          3          2
             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
              0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                   4          3           2                                6
             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
                 0          0           0            0            0      0
           + 
                  5          4           3           2
             90s G  + 2628s G  + 27864s G  + 90720s G
                0          0           0           0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                    3           2                            2
             (945s G  + 81648s G  + 2082996s G + 14171760s )H
                  0           0             0             0
           + 
                   5          4            3             2
             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
                 0          0            0             0              0
           + 
                7         6          5           4             3              2
             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
              0         0          0           0             0              0
           + 
             - 97977600s G
                        0
        /
           11022480
       ]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R   Compiling body of rule n to compute value of type PositiveInteger 
--R   Compiling body of rule phi to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi1 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi2 to compute value of type Expression 
--R      Integer 
--R   Compiling body of rule phi3 to compute value of type Polynomial 
--R      Integer 
--R   Compiling body of rule pans to compute value of type 
--R      UnivariatePolynomial(x,Polynomial Integer) 
--R   Compiling body of rule pans1 to compute value of type List 
--R      Polynomial Integer 
--R   Compiling body of rule leq to compute value of type List List 
--R      Equation Fraction Polynomial Integer 
--R
--R   (16)
--R   [
--R                             2
--R          s G      3s H + s G  + 6s G
--R           0         0     0       0
--R     [s = ---, s = ------------------,
--R       1   3    2          18
--R                              3        2
--R          (9s G + 54s )H + s G  + 18s G  + 72s G
--R             0       0      0        0        0
--R      s = --------------------------------------,
--R       3                    162
--R
--R       s  =
--R        4
--R                  2         2                          4        3         2
--R             27s H  + (18s G  + 378s G + 1296s )H + s G  + 36s G  + 396s G
--R                0         0         0         0      0        0         0
--R           + 
--R             1296s G
--R                  0
--R        /
--R           1944
--R       ,
--R
--R       s  =
--R        5
--R                               2         3          2
--R             (135s G + 2268s )H  + (30s G  + 1350s G  + 16416s G + 38880s )H
--R                  0         0          0          0           0          0
--R           + 
--R                5        4          3          2
--R             s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
--R              0        0          0          0           0
--R        /
--R           29160
--R       ,
--R
--R       s  =
--R        6
--R                   3          2                        2
--R             405s H  + (405s G  + 18468s G + 174960s )H
--R                 0          0           0           0
--R           + 
--R                   4          3           2                                6
--R             (45s G  + 3510s G  + 88776s G  + 777600s G + 1166400s )H + s G
--R                 0          0           0            0            0      0
--R           + 
--R                  5          4           3           2
--R             90s G  + 2628s G  + 27864s G  + 90720s G
--R                0          0           0           0
--R        /
--R           524880
--R       ,
--R
--R       s  =
--R        7
--R                                 3
--R             (2835s G + 91854s )H
--R                   0          0
--R           + 
--R                    3           2                            2
--R             (945s G  + 81648s G  + 2082996s G + 14171760s )H
--R                  0           0             0             0
--R           + 
--R                   5          4            3             2
--R             (63s G  + 7560s G  + 317520s G  + 5554008s G  + 34058880s G)H
--R                 0          0            0             0              0
--R           + 
--R                7         6          5           4             3              2
--R             s G  + 126s G  + 4788s G  + 25272s G  - 1744416s G  - 26827200s G
--R              0         0          0           0             0              0
--R           + 
--R             - 97977600s G
--R                        0
--R        /
--R           11022480
--R       ]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 43
 
)clear all
 

--S 44 of 55
PZ := UP(x,INT); Vect := DPMM(3, PZ, SQMATRIX(3,PZ), PZ);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 44

--S 45 of 55
Modo := LODO2(SQMATRIX(3,PZ), Vect);
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 45

--S 46 of 55
p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect
 

           2          3
   (3)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (3)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 46

--S 47 of 55
m := [[x**2, 1, 0], [1, x**4, 0], [0, 0, 4*x**2]]::(SQMATRIX(3,PZ))
 

        + 2         +
        |x   1    0 |
        |           |
   (4)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (4)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 47

--S 48 of 55
q: Vect := m * p
 

           4    2        5     2        5     3
   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (5)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 48
 
--S 49 of 55
Dx:  Modo := D()
 

   (6)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (6)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 49

--S 50 of 55
a:   Modo := 1*Dx  + m
 

            + 2         +
            |x   1    0 |
            |           |
   (7)  D + |     4     |
            |1   x    0 |
            |           |
            |          2|
            +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R            + 2         +
--R            |x   1    0 |
--R            |           |
--R   (7)  D + |     4     |
--R            |1   x    0 |
--R            |           |
--R            |          2|
--R            +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 50

--S 51 of 55
b:   Modo := m*Dx  + 1
 

        + 2         +
        |x   1    0 |    +1  0  0+
        |           |    |       |
   (8)  |     4     |D + |0  1  0|
        |1   x    0 |    |       |
        |           |    +0  0  1+
        |          2|
        +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R        + 2         +
--R        |x   1    0 |    +1  0  0+
--R        |           |    |       |
--R   (8)  |     4     |D + |0  1  0|
--R        |1   x    0 |    |       |
--R        |           |    +0  0  1+
--R        |          2|
--R        +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 51

--S 52 of 55
a*b
 

   (9)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 52

--S 53 of 55
a p
 

            4    2        5     2        5     3      2
   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (10)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 53

--S 54 of 55
b p
 

            3     2       4         4     3     2
   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (11)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 54

--S 55 of 55
(a+b) (p + q)
 

   (12)
      6      5      4      3      2
   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
      9      8     6      5      4      3     2
    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
        7       6      5       4      3      2
    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (12)
--R      6      5      4      3      2
--R   [3x  + 14x  + 17x  + 22x  + 10x  + 18x + 6,
--R      9      8     6      5      4      3     2
--R    2x  + 10x  + 3x  + 10x  + 16x  + 12x  + 7x  + 18x + 6,
--R        7       6      5       4      3      2
--R    112x  + 560x  + 88x  + 320x  + 23x  + 53x  + 2x + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 55
)spool 
 
Starts dribbling to elemfun.output (2010/3/27, 18:25:22).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 28
cos 0
 

   (1)  1
                                                     Type: Expression Integer
--R 
--R
--R   (1)  1
--R                                                     Type: Expression Integer
--E 1

--S 2 of 28
sin 0
 

   (2)  0
                                                     Type: Expression Integer
--R 
--R
--R   (2)  0
--R                                                     Type: Expression Integer
--E 2

--S 3 of 28
exp 0
 

   (3)  1
                                                     Type: Expression Integer
--R 
--R
--R   (3)  1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 28
log 1
 

   (4)  0
                                                     Type: Expression Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 4

--S 5 of 28
sin(%pi/2)
 

   (5)  1
                                                     Type: Expression Integer
--R 
--R
--R   (5)  1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 28
simplify %
 

   (6)  1
                                                     Type: Expression Integer
--R 
--R
--R   (6)  1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 28
sin(3)**2 + cos(3)**2
 

              2         2
   (7)  sin(3)  + cos(3)
                                                     Type: Expression Integer
--R 
--R
--R              2         2
--R   (7)  sin(3)  + cos(3)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 28
simplify %
 

   (8)  1
                                                     Type: Expression Integer
--R 
--R
--R   (8)  1
--R                                                     Type: Expression Integer
--E 8

--S 9  of 28
a := atan 1
 

        %pi
   (9)  ---
         4
                                                     Type: Expression Integer
--R 
--R
--R        %pi
--R   (9)  ---
--R         4
--R                                                     Type: Expression Integer
--E 9

--S 10 of 28
t := cos(a)*sin(a)*tan(a)*sec(a)*csc(a)*cot(a)
 

   (10)  1
                                                     Type: Expression Integer
--R 
--R
--R   (10)  1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 28
simplify t
 

   (11)  1
                                                     Type: Expression Integer
--R 
--R
--R   (11)  1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 28
cot2tan t
 

   (12)  1
                                                     Type: Expression Integer
--R 
--R
--R   (12)  1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 28
cot2trig t
 

   (13)  1
                                                     Type: Expression Integer
--R 
--R
--R   (13)  1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 28
tan2cot t
 

   (14)  1
                                                     Type: Expression Integer
--R 
--R
--R   (14)  1
--R                                                     Type: Expression Integer
--E 14

--S 15 of 28
tan2trig t
 

   (15)  1
                                                     Type: Expression Integer
--R 
--R
--R   (15)  1
--R                                                     Type: Expression Integer
--E 15

--S 16 of 28
cos2sec t
 

   (16)  1
                                                     Type: Expression Integer
--R 
--R
--R   (16)  1
--R                                                     Type: Expression Integer
--E 16
 
--S 17 of 28
t := sin(7)**2 - sec(7)/(1 - cot(7) + csc(7)**3)
 

                3                    2
         (csc(7)  - cot(7) + 1)sin(7)  - sec(7)
   (17)  --------------------------------------
                        3
                  csc(7)  - cot(7) + 1
                                                     Type: Expression Integer
--R 
--R
--R                3                    2
--R         (csc(7)  - cot(7) + 1)sin(7)  - sec(7)
--R   (17)  --------------------------------------
--R                        3
--R                  csc(7)  - cot(7) + 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 28
simplify t
 

   (18)
                5          3         2                             6          4
       (- cos(7)  + 2cos(7)  - cos(7)  - cos(7) + 1)sin(7) + cos(7)  - 2cos(7)
     + 
             3         2
       cos(7)  + cos(7)  - cos(7)
  /
            3                         4         2
     (cos(7)  - cos(7))sin(7) - cos(7)  + cos(7)  - cos(7)
                                                     Type: Expression Integer
--R 
--R
--R   (18)
--R                5          3         2                             6          4
--R       (- cos(7)  + 2cos(7)  - cos(7)  - cos(7) + 1)sin(7) + cos(7)  - 2cos(7)
--R     + 
--R             3         2
--R       cos(7)  + cos(7)  - cos(7)
--R  /
--R            3                         4         2
--R     (cos(7)  - cos(7))sin(7) - cos(7)  + cos(7)  - cos(7)
--R                                                     Type: Expression Integer
--E 18

--S 19 of 28
numeric %
 

   (19)  0.0390653254 8092347922 2
                                                                  Type: Float
--R 
--R
--R   (19)  0.0390653254 8092347922 2
--R                                                                  Type: Float
--E 19

--S 20 of 28
numeric t
 

   (20)  0.0390653254 8092347921 5
                                                                  Type: Float
--R 
--R
--R   (20)  0.0390653254 8092347921 5
--R                                                                  Type: Float
--E 20

--S 21 of 28
numeric(t, 100)
 

   (21)
  0.0390653254 8092347921 8900669391 6314051319 2684833219 8927261332 141491473
  3 4130898335 0601081135 3732125345 8
                                                                  Type: Float
--R 
--R
--R   (21)
--R  0.0390653254 8092347921 8900669391 6314051319 2684833219 8927261332 141491473
--R  3 4130898335 0601081135 3732125345 8
--R                                                                  Type: Float
--E 21
 
--S 22 of 28
u := exp(sin(x-1)**2 - cos(x-1)/sec(x-1))
 

                               2
           sec(x - 1)sin(x - 1)  - cos(x - 1)
           ----------------------------------
                       sec(x - 1)
   (22)  %e
                                                     Type: Expression Integer
--R 
--R
--R                               2
--R           sec(x - 1)sin(x - 1)  - cos(x - 1)
--R           ----------------------------------
--R                       sec(x - 1)
--R   (22)  %e
--R                                                     Type: Expression Integer
--E 22

--S 23 of 28
eval(u,x=1)
 

          1
   (23)  --
         %e
                                                     Type: Expression Integer
--R 
--R
--R          1
--R   (23)  --
--R         %e
--R                                                     Type: Expression Integer
--E 23
 
--S 24 of 28
v(x) == exp(sin(x-1)**2 - cos(x-1)/sec(x-1))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 28
v x
 
   Compiling function v with type Variable x -> Expression Integer 

                               2
           sec(x - 1)sin(x - 1)  - cos(x - 1)
           ----------------------------------
                       sec(x - 1)
   (25)  %e
                                                     Type: Expression Integer
--R 
--R   Compiling function v with type Variable x -> Expression Integer 
--R
--R                               2
--R           sec(x - 1)sin(x - 1)  - cos(x - 1)
--R           ----------------------------------
--R                       sec(x - 1)
--R   (25)  %e
--R                                                     Type: Expression Integer
--E 25

--S 26 of 28
v 1
 
   Compiling function v with type PositiveInteger -> Expression Integer
      

          1
   (26)  --
         %e
                                                     Type: Expression Integer
--R 
--R   Compiling function v with type PositiveInteger -> Expression Integer
--R      
--R
--R          1
--R   (26)  --
--R         %e
--R                                                     Type: Expression Integer
--E 26

--S 27 of 28
v(%pi/3)
 
   Compiling function v with type Pi -> Expression Integer 

               %pi - 3     %pi - 3 2       %pi - 3
           sec(-------)sin(-------)  - cos(-------)
                  3           3               3
           ----------------------------------------
                             %pi - 3
                         sec(-------)
                                3
   (27)  %e
                                                     Type: Expression Integer
--R 
--R   Compiling function v with type Pi -> Expression Integer 
--R
--R               %pi - 3     %pi - 3 2       %pi - 3
--R           sec(-------)sin(-------)  - cos(-------)
--R                  3           3               3
--R           ----------------------------------------
--R                             %pi - 3
--R                         sec(-------)
--R                                3
--R   (27)  %e
--R                                                     Type: Expression Integer
--E 27

--S 28 of 28
numeric %
 

   (28)  0.3695208585 287457761
                                                                  Type: Float
--R 
--R
--R   (28)  0.3695208585 287457761
--R                                                                  Type: Float
--E 28
)spool
 
Starts dribbling to eval.output (2010/3/27, 18:25:36).
)set message test on
 
)set message auto off
 
)clear all
 

--** This line will be optional interactively, since the a := f(x**2)
--** will prompt you if you don't declare f this way.
--S 1 of 23
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 1

--S 2 of 23
a := f(x**2)
 

           2
   (2)  f(x )
                                                     Type: Expression Integer
--R 
--R
--R           2
--R   (2)  f(x )
--R                                                     Type: Expression Integer
--E 2

--S 3 of 23
b := differentiate(a,x,2) + f 5
 

          2 ,,  2      ,  2
   (3)  4x f  (x ) + 2f (x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R          2 ,,  2      ,  2
--R   (3)  4x f  (x ) + 2f (x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 3

--S 4 of 23
eval(b, x = x + y)
 

           2            2  ,,  2           2      ,  2           2
   (4)  (4y  + 8x y + 4x )f  (y  + 2x y + x ) + 2f (y  + 2x y + x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R           2            2  ,,  2           2      ,  2           2
--R   (4)  (4y  + 8x y + 4x )f  (y  + 2x y + x ) + 2f (y  + 2x y + x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 23
eval(b, f 5 = 1)
 

          2 ,,  2      ,  2
   (5)  4x f  (x ) + 2f (x ) + 1

                                                     Type: Expression Integer
--R 
--R
--R          2 ,,  2      ,  2
--R   (5)  4x f  (x ) + 2f (x ) + 1
--R
--R                                                     Type: Expression Integer
--E 5

--** will eventually use the +-> notation in the eval statement
--S 6 of 23
foo(u:EXPR INT):EXPR INT == exp u
 
   Function declaration foo : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration foo : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 6

--S 7 of 23
c := eval(b, 'f, foo)
 
   Compiling function foo with type Expression Integer -> Expression 
      Integer 

                    2
           2       x      5
   (7)  (4x  + 2)%e   + %e
                                                     Type: Expression Integer
--R 
--R   Compiling function foo with type Expression Integer -> Expression 
--R      Integer 
--R
--R                    2
--R           2       x      5
--R   (7)  (4x  + 2)%e   + %e
--R                                                     Type: Expression Integer
--E 7


--S 8 of 23
oof(u:EXPR INT):EXPR INT == f u
 
   Function declaration oof : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration oof : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 8

--S 9 of 23
eval(c, 'exp, oof)
 
   Compiling function oof with type Expression Integer -> Expression 
      Integer 

           2        2
   (9)  (4x  + 2)f(x ) + f(5)
                                                     Type: Expression Integer
--R 
--R   Compiling function oof with type Expression Integer -> Expression 
--R      Integer 
--R
--R           2        2
--R   (9)  (4x  + 2)f(x ) + f(5)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 23
f'(u:EXPR INT):EXPR INT == f u
 
   Function declaration f' : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f' : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 10

--S 11 of 23
derivative(f,f')
 
   Compiling function f' with type Expression Integer -> Expression 
      Integer 

   (11)  f
                                                          Type: BasicOperator
--R 
--R   Compiling function f' with type Expression Integer -> Expression 
--R      Integer 
--R
--R   (11)  f
--R                                                          Type: BasicOperator
--E 11

--S 12 of 23
b
 

           2 ,,  2      ,  2
   (12)  4x f  (x ) + 2f (x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R           2 ,,  2      ,  2
--R   (12)  4x f  (x ) + 2f (x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 12

--** The coercion is needed to avoid an interpreter bug.
--** This will just be eval(b) eventually:
--S 13 of 23
eval(b, x = x::(EXPR INT))
 

           2 ,,  2      ,  2
   (13)  4x f  (x ) + 2f (x ) + f(5)

                                                     Type: Expression Integer
--R 
--R
--R           2 ,,  2      ,  2
--R   (13)  4x f  (x ) + 2f (x ) + f(5)
--R
--R                                                     Type: Expression Integer
--E 13

--S 14 of 23
differentiate(%, x)
 

           3 ,,,  2        ,,  2
   (14)  8x f   (x ) + 12xf  (x )

                                                     Type: Expression Integer
--R 
--R
--R           3 ,,,  2        ,,  2
--R   (14)  8x f   (x ) + 12xf  (x )
--R
--R                                                     Type: Expression Integer
--E 14

--S 15 of 23
a3 := a * a * a
 

            2 3
   (15)  f(x )
                                                     Type: Expression Integer
--R 
--R
--R            2 3
--R   (15)  f(x )
--R                                                     Type: Expression Integer
--E 15

--S 16 of 23
foo
 

   (16)  foo u == exp(u)
                                                     Type: FunctionCalled foo
--R 
--R
--R   (16)  foo u == exp(u)
--R                                                     Type: FunctionCalled foo
--E 16

--S 17 of 23
eval(a3,'f,2,foo)
 

                 2
            2   x
   (17)  f(x )%e
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R            2   x
--R   (17)  f(x )%e
--R                                                     Type: Expression Integer
--E 17

--S 18 of 23
g := operator 'g
 

   (18)  g
                                                          Type: BasicOperator
--R 
--R
--R   (18)  g
--R                                                          Type: BasicOperator
--E 18

--S 19 of 23
bar(u:EXPR INT):EXPR INT == sin(u) + cos(2*u)
 
   Function declaration bar : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration bar : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 19

--S 20 of 23
a + g a
 

              2        2
   (20)  g(f(x )) + f(x )
                                                     Type: Expression Integer
--R 
--R
--R              2        2
--R   (20)  g(f(x )) + f(x )
--R                                                     Type: Expression Integer
--E 20

--S 21 of 23
eval(%,['f,'g],[foo,bar])
 
   Compiling function bar with type Expression Integer -> Expression 
      Integer 

                2            2       2
               x            x       x
   (21)  sin(%e  ) + cos(2%e  ) + %e
                                                     Type: Expression Integer
--R 
--R   Compiling function bar with type Expression Integer -> Expression 
--R      Integer 
--R
--R                2            2       2
--R               x            x       x
--R   (21)  sin(%e  ) + cos(2%e  ) + %e
--R                                                     Type: Expression Integer
--E 21

--S 22 of 23
a3 + g a
 

              2        2 3
   (22)  g(f(x )) + f(x )
                                                     Type: Expression Integer
--R 
--R
--R              2        2 3
--R   (22)  g(f(x )) + f(x )
--R                                                     Type: Expression Integer
--E 22

--S 23 of 23
eval(%,['f,'g],[2,1],[foo,bar])
 

                                            2
                2             2        2   x
   (23)  sin(f(x )) + cos(2f(x )) + f(x )%e
                                                     Type: Expression Integer
--R 
--R
--R                                            2
--R                2             2        2   x
--R   (23)  sin(f(x )) + cos(2f(x )) + f(x )%e
--R                                                     Type: Expression Integer
--E 23
)spool
 
Starts dribbling to LyndonWord.output (2010/3/27, 18:46:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
a:Symbol :='a
 

   (1)  a
                                                                 Type: Symbol
--R 
--R
--R   (1)  a
--R                                                                 Type: Symbol
--E 1

--S 2 of 22
b:Symbol :='b
 

   (2)  b
                                                                 Type: Symbol
--R 
--R
--R   (2)  b
--R                                                                 Type: Symbol
--E 2

--S 3 of 22
c:Symbol :='c
 

   (3)  c
                                                                 Type: Symbol
--R 
--R
--R   (3)  c
--R                                                                 Type: Symbol
--E 3

--S 4 of 22
lword:= LyndonWord(Symbol)
 

   (4)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 22
magma := Magma(Symbol)
 

   (5)  Magma Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  Magma Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 22
word := OrderedFreeMonoid(Symbol)
 

   (6)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (6)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 6

--S 7 of 22
LyndonWordsList1([a,b,c],3)$lword
 

   (7)
   [[[a],[b],[c]], [[a b],[a c],[b c]],
       2     2       2                      2    2       2
    [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]]
                             Type: OneDimensionalArray List LyndonWord Symbol
--R 
--R
--R   (7)
--R   [[[a],[b],[c]], [[a b],[a c],[b c]],
--R       2     2       2                      2    2       2
--R    [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]]
--R                             Type: OneDimensionalArray List LyndonWord Symbol
--E 7

--S 8 of 22
LyndonWordsList([a,b,c],3)$lword
 

   (8)
                                          2      2        2
   [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b],
        2     2        2
    [a c ], [b c], [b c ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (8)
--R                                          2      2        2
--R   [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b],
--R        2     2        2
--R    [a c ], [b c], [b c ]]
--R                                                 Type: List LyndonWord Symbol
--E 8

--S 9 of 22
lw := LyndonWordsList([a,b],5)$lword
 

   (9)
                       2        2     3      2 2       3     4      3 2
   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
      2          2 3           2       4
    [a b a b], [a b ], [a b a b ], [a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (9)
--R                       2        2     3      2 2       3     4      3 2
--R   [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ],
--R      2          2 3           2       4
--R    [a b a b], [a b ], [a b a b ], [a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 9

--S 10 of 22
w1 : word := lw.4 :: word
 

          2
   (10)  a b
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R          2
--R   (10)  a b
--R                                               Type: OrderedFreeMonoid Symbol
--E 10

--S 11 of 22
w2 : word := lw.5 :: word
 

            2
   (11)  a b
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R            2
--R   (11)  a b
--R                                               Type: OrderedFreeMonoid Symbol
--E 11

--S 12 of 22
factor(a::word)$lword
 

   (12)  [[a]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R   (12)  [[a]]
--R                                                 Type: List LyndonWord Symbol
--E 12

--S 13 of 22
factor(w1*w2)$lword
 

            2     2
   (13)  [[a b a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R            2     2
--R   (13)  [[a b a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 13

--S 14 of 22
factor(w2*w2)$lword
 

              2      2
   (14)  [[a b ],[a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R              2      2
--R   (14)  [[a b ],[a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 14

--S 15 of 22
factor(w2*w1)$lword
 

              2    2
   (15)  [[a b ],[a b]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R              2    2
--R   (15)  [[a b ],[a b]]
--R                                                 Type: List LyndonWord Symbol
--E 15

--S 16 of 22
lyndon?(w1)$lword
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 22
lyndon?(w1*w2)$lword
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 22
lyndon?(w2*w1)$lword
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 22
lyndonIfCan(w1)$lword
 

           2
   (19)  [a b]
                                           Type: Union(LyndonWord Symbol,...)
--R 
--R
--R           2
--R   (19)  [a b]
--R                                           Type: Union(LyndonWord Symbol,...)
--E 19

--S 20 of 22
lyndonIfCan(w2*w1)$lword
 

   (20)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (20)  "failed"
--R                                                    Type: Union("failed",...)
--E 20

--S 21 of 22
lyndon(w1)$lword
 

           2
   (21)  [a b]
                                                      Type: LyndonWord Symbol
--R 
--R
--R           2
--R   (21)  [a b]
--R                                                      Type: LyndonWord Symbol
--E 21

--S 22 of 22
lyndon(w1*w2)$lword
 

           2     2
   (22)  [a b a b ]
                                                      Type: LyndonWord Symbol
--R 
--R
--R           2     2
--R   (22)  [a b a b ]
--R                                                      Type: LyndonWord Symbol
--E 22
)spool
 
Starts dribbling to streams.output (2010/3/27, 18:41:7).
)set message test on
 
)set message auto off
 
)clear all
 
 
)set streams calculate 5
 
 
)set streams showall on
 
 
--S 1 of 26
a := [i for i in 1..]
 

   (1)  [1,2,3,4,5,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (1)  [1,2,3,4,5,...]
--R                                                 Type: Stream PositiveInteger
--E 1

--S 2 of 26
b := [i+1 for i in a]
 

   (2)  [2,3,4,5,6,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (2)  [2,3,4,5,6,...]
--R                                                 Type: Stream PositiveInteger
--E 2

--S 3 of 26
b.20
 

   (3)  21
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  21
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 26
b
 

   (4)  [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (4)  [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,...]
--R                                                 Type: Stream PositiveInteger
--E 4

--S 5 of 26
a
 

   (5)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (5)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
--R                                                 Type: Stream PositiveInteger
--E 5

--S 6 of 26
first(a,10)
 

   (6)  [1,2,3,4,5,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (6)  [1,2,3,4,5,...]
--R                                                 Type: Stream PositiveInteger
--E 6

--S 7 of 26
rest(a,10)
 

   (7)  [11,12,13,14,15,16,17,18,19,20,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (7)  [11,12,13,14,15,16,17,18,19,20,...]
--R                                                 Type: Stream PositiveInteger
--E 7

--S 8 of 26
[i for i in a | odd? i]
 

   (8)  [1,3,5,7,9,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (8)  [1,3,5,7,9,...]
--R                                                 Type: Stream PositiveInteger
--E 8

--S 9 of 26
c := [[i,j] for i in a for j in b]
 

   (9)  [[1,2],[2,3],[3,4],[4,5],[5,6],...]
                                            Type: Stream List PositiveInteger
--R 
--R
--R   (9)  [[1,2],[2,3],[3,4],[4,5],[5,6],...]
--R                                            Type: Stream List PositiveInteger
--E 9

--S 10 of 26
[first i for i in c]
 

   (10)  [1,2,3,4,5,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (10)  [1,2,3,4,5,...]
--R                                                 Type: Stream PositiveInteger
--E 10

)set streams calculate 10
 

--S 11 of 26
concat([i for i in a while i<7],a)
 

   (11)  [1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (11)  [1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...]
--R                                                 Type: Stream PositiveInteger
--E 11

--S 12 of 26
concat(a,a)
 

   (12)  [1,2,3,4,5,6,7,8,9,10,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (12)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                 Type: Stream PositiveInteger
--E 12

--S 13 of 26
upto:NNI->STREAM INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 26
upto n == first(a,n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 26
d := [upto n for n in a]
 
   Compiling function upto with type NonNegativeInteger -> Stream 
      Integer 

   (15)
   [[1], [1,2], [1,2,3], [1,2,3,4], [1,2,3,4,5], [1,2,3,4,5,6],
    [1,2,3,4,5,6,7], [1,2,3,4,5,6,7,8], [1,2,3,4,5,6,7,8,9],
    [1,2,3,4,5,6,7,8,9,10,...], ...]
                                                  Type: Stream Stream Integer
--R 
--R   Compiling function upto with type NonNegativeInteger -> Stream 
--R      Integer 
--R
--R   (15)
--R   [[1], [1,2], [1,2,3], [1,2,3,4], [1,2,3,4,5], [1,2,3,4,5,6],
--R    [1,2,3,4,5,6,7], [1,2,3,4,5,6,7,8], [1,2,3,4,5,6,7,8,9],
--R    [1,2,3,4,5,6,7,8,9,10,...], ...]
--R                                                  Type: Stream Stream Integer
--E 15

--S 16 of 26
concat d
 

   (16)  [1,1,2,1,2,3,1,2,3,4,...]
                                                         Type: Stream Integer
--R 
--R
--R   (16)  [1,1,2,1,2,3,1,2,3,4,...]
--R                                                         Type: Stream Integer
--E 16

--S 17 of 26
reduce(0,_+$INT,first(a,10))
 

   (17)  55
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  55
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 26
scan(0,_+$INT,a)
 

   (18)  [1,3,6,10,15,21,28,36,45,55,...]
                                                         Type: Stream Integer
--R 
--R
--R   (18)  [1,3,6,10,15,21,28,36,45,55,...]
--R                                                         Type: Stream Integer
--E 18

--S 19 of 26
scan(0,_+$INT,[2*i-1 for i in a])
 

   (19)  [1,4,9,16,25,36,49,64,81,100,...]
                                                         Type: Stream Integer
--R 
--R
--R   (19)  [1,4,9,16,25,36,49,64,81,100,...]
--R                                                         Type: Stream Integer
--E 19

--S 20 of 26
ff:(LIST INT)->(LIST INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 26
ff(x)==[x.1+x.2,x.1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 26
fibs := generate(ff,[1,1])
 
   Compiling function ff with type List Integer -> List Integer 

   (22)
   [[1,1],[2,1],[3,2],[5,3],[8,5],[13,8],[21,13],[34,21],[55,34],[89,55],...]
                                             Type: InfiniteTuple List Integer
--R 
--R   Compiling function ff with type List Integer -> List Integer 
--R
--R   (22)
--R   [[1,1],[2,1],[3,2],[5,3],[8,5],[13,8],[21,13],[34,21],[55,34],[89,55],...]
--R                                             Type: InfiniteTuple List Integer
--E 22

--first([first i for i in fibs], 100)

--S 23 of 26
mt:SQMATRIX(2,INT) := matrix [[1,2],[3,4]]
 

         +1  2+
   (23)  |    |
         +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +1  2+
--R   (23)  |    |
--R         +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 23

--S 24 of 26
mplm:SQMATRIX(2,INT)->SQMATRIX(2,INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 26
mplm x == x*mt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 26
generate(mplm,mt)
 
   Compiling function mplm with type SquareMatrix(2,Integer) -> 
      SquareMatrix(2,Integer) 

   (26)
    +1  2+  +7   10+  +37  54 +  +199  290+  +1069  1558+  +5743   8370 +
   [|    |, |      |, |       |, |        |, |          |, |            |,
    +3  4+  +15  22+  +81  118+  +435  634+  +2337  3406+  +12555  18298+
    +30853  44966+  +165751  241570+  +890461   1297782+  +4783807   6972050 +
    |            |, |              |, |                |, |                  |,
    +67449  98302+  +362355  528106+  +1946673  2837134+  +10458075  15241882+
    ...]
                                  Type: InfiniteTuple SquareMatrix(2,Integer)
--R 
--R   Compiling function mplm with type SquareMatrix(2,Integer) -> 
--R      SquareMatrix(2,Integer) 
--R
--R   (26)
--R    +1  2+  +7   10+  +37  54 +  +199  290+  +1069  1558+  +5743   8370 +
--R   [|    |, |      |, |       |, |        |, |          |, |            |,
--R    +3  4+  +15  22+  +81  118+  +435  634+  +2337  3406+  +12555  18298+
--R    +30853  44966+  +165751  241570+  +890461   1297782+  +4783807   6972050 +
--R    |            |, |              |, |                |, |                  |,
--R    +67449  98302+  +362355  528106+  +1946673  2837134+  +10458075  15241882+
--R    ...]
--R                                  Type: InfiniteTuple SquareMatrix(2,Integer)
--E 26
)spool 
 
Starts dribbling to None.output (2010/3/27, 18:46:8).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
[ ]
 

   (1)  []
                                                              Type: List None
--R 
--R
--R   (1)  []
--R                                                              Type: List None
--E 1

--S 2 of 3
[ ] :: List Float
 

   (2)  []
                                                             Type: List Float
--R 
--R
--R   (2)  []
--R                                                             Type: List Float
--E 2

--S 3 of 3
[ ]$List(NonNegativeInteger)
 

   (3)  []
                                                Type: List NonNegativeInteger
--R 
--R
--R   (3)  []
--R                                                Type: List NonNegativeInteger
--E 3 
)spool
 
Starts dribbling to page.output (2010/3/27, 18:30:40).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 18
a1:="(a/x)+(a/y)"
 

   (1)  "(a/x)+(a/y)"
                                                                 Type: String
--R
--R   (1)  "(a/x)+(a/y)"
--R                                                                 Type: String
--E 1

--S 2 of 18
a2:="(a/x) + (a/y)"
 

   (2)  "(a/x) + (a/y)"
                                                                 Type: String
--R
--R   (2)  "(a/x) + (a/y)"
--R                                                                 Type: String
--E 2

--S 3 of 18
a3:="(a*x+a*y)/(x*y)"
 

   (3)  "(a*x+a*y)/(x*y)"
                                                                 Type: String
--R
--R   (3)  "(a*x+a*y)/(x*y)"
--R                                                                 Type: String
--E 3


--S 4 of 18
(a1=a2)::Boolean
 

   (4)  false
                                                                Type: Boolean
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 18
(a1=a3)::Boolean
 

   (5)  false
                                                                Type: Boolean
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 18
(a2=a3)::Boolean
 

   (6)  false
                                                                Type: Boolean
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 18
interpretString(a1."=".a2)::Boolean
 

   (7)  true
                                                                Type: Boolean
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 18
interpretString(a1."=".a3)::Boolean
 

   (8)  true
                                                                Type: Boolean
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 18
interpretString(a2."=".a3)::Boolean
 

   (9)  true
                                                                Type: Boolean
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 18
x:INFORM:=x
 

   (10)  x
                                                              Type: InputForm
--R
--R   (10)  x
--R                                                              Type: InputForm
--E 10

--S 11 of 18
y:INFORM:=y
 

   (11)  y
                                                              Type: InputForm
--R
--R   (11)  y
--R                                                              Type: InputForm
--E 11

--S 12 of 18
a:INFORM:=a
 

   (12)  a
                                                              Type: InputForm
--R
--R   (12)  a
--R                                                              Type: InputForm
--E 12

--S 13 of 18
interpretString(a1."=".a2)::Boolean
 

   (13)  true
                                                                Type: Boolean
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 18
interpretString(a1."=".a3)::Boolean
 

   (14)  false
                                                                Type: Boolean
--R
--R   (14)  false
--R                                                                Type: Boolean
--E 14

--S 15 of 18
interpretString(a2."=".a3)::Boolean
 

   (15)  false
                                                                Type: Boolean
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 18
map(expr,map(interpretString,a1=a2)::Equation(INFORM))
 

         a   a  a   a
   (16)  - + -= - + -
         x   y  x   y
                                                    Type: Equation OutputForm
--R
--R         a   a  a   a
--R   (16)  - + -= - + -
--R         x   y  x   y
--R                                                    Type: Equation OutputForm
--E 16

--S 17 of 18
map(expr,map(interpretString,a2=a3)::Equation(INFORM))
 

         a   a  a x + a y
   (17)  - + -= ---------
         x   y     x y
                                                    Type: Equation OutputForm
--R
--R         a   a  a x + a y
--R   (17)  - + -= ---------
--R         x   y     x y
--R                                                    Type: Equation OutputForm
--E 17

--S 18 of 18
map(expr,map(interpretString,a1=a3)::Equation(INFORM))
 

         a   a  a x + a y
   (18)  - + -= ---------
         x   y     x y
                                                    Type: Equation OutputForm
--R
--R         a   a  a x + a y
--R   (18)  - + -= ---------
--R         x   y     x y
--R                                                    Type: Equation OutputForm
--E 18
)spool 
 
Starts dribbling to radix.output (2010/3/27, 18:36:41).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 17
111::RadixExpansion(5)
 

   (1)  421
                                                       Type: RadixExpansion 5
--R 
--R
--R   (1)  421
--R                                                       Type: RadixExpansion 5
--E 1

--S 2 of 17
(5/24)::RadixExpansion(2)
 

             __
   (2)  0.00110
                                                       Type: RadixExpansion 2
--R 
--R
--R             __
--R   (2)  0.00110
--R                                                       Type: RadixExpansion 2
--E 2

--S 3 of 17
(5/24)::RadixExpansion(3)
 

           __
   (3)  0.012
                                                       Type: RadixExpansion 3
--R 
--R
--R           __
--R   (3)  0.012
--R                                                       Type: RadixExpansion 3
--E 3

--S 4 of 17
(5/24)::RadixExpansion(8)
 

           __
   (4)  0.152
                                                       Type: RadixExpansion 8
--R 
--R
--R           __
--R   (4)  0.152
--R                                                       Type: RadixExpansion 8
--E 4

--S 5 of 17
(5/24)::RadixExpansion(10)
 

             _
   (5)  0.2083
                                                      Type: RadixExpansion 10
--R 
--R
--R             _
--R   (5)  0.2083
--R                                                      Type: RadixExpansion 10
--E 5

--S 6 of 17
(5/24)::RadixExpansion(12)
 

   (6)  0.26
                                                      Type: RadixExpansion 12
--R 
--R
--R   (6)  0.26
--R                                                      Type: RadixExpansion 12
--E 6

--S 7 of 17
(5/24)::RadixExpansion(16)
 

           _
   (7)  0.35
                                                      Type: RadixExpansion 16
--R 
--R
--R           _
--R   (7)  0.35
--R                                                      Type: RadixExpansion 16
--E 7

--S 8 of 17
(5/24)::RadixExpansion(36)
 

   (8)  0.7I
                                                      Type: RadixExpansion 36
--R 
--R
--R   (8)  0.7I
--R                                                      Type: RadixExpansion 36
--E 8

--S 9 of 17
(5/24)::RadixExpansion(38)
 

                    _____
   (9)  0 . 7 34 31 25 12
                                                      Type: RadixExpansion 38
--R 
--R
--R                    _____
--R   (9)  0 . 7 34 31 25 12
--R                                                      Type: RadixExpansion 38
--E 9

--S 10 of 17
a := (76543/210)::RadixExpansion(8)
 

              ____
   (10)  554.37307
                                                       Type: RadixExpansion 8
--R 
--R
--R              ____
--R   (10)  554.37307
--R                                                       Type: RadixExpansion 8
--E 10

--S 11 of 17
w := wholeRagits a
 

   (11)  [5,5,4]
                                                           Type: List Integer
--R 
--R
--R   (11)  [5,5,4]
--R                                                           Type: List Integer
--E 11

--S 12 of 17
f0 := prefixRagits a
 

   (12)  [3]
                                                           Type: List Integer
--R 
--R
--R   (12)  [3]
--R                                                           Type: List Integer
--E 12

--S 13 of 17
f1 := cycleRagits a
 

   (13)  [7,3,0,7]
                                                           Type: List Integer
--R 
--R
--R   (13)  [7,3,0,7]
--R                                                           Type: List Integer
--E 13

--S 14 of 17
u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1)
 

              ____
   (14)  554.37307
                                                       Type: RadixExpansion 8
--R 
--R
--R              ____
--R   (14)  554.37307
--R                                                       Type: RadixExpansion 8
--E 14

--S 15 of 17
v: RadixExpansion(12) := fractRadix([1,2,3,11], [0])
 

               _
   (15)  0.123B0
                                                      Type: RadixExpansion 12
--R 
--R
--R               _
--R   (15)  0.123B0
--R                                                      Type: RadixExpansion 12
--E 15

--S 16 of 17
fractRagits(u)
 

              _______
   (16)  [3,7,3,0,7,7]
                                                         Type: Stream Integer
--R 
--R
--R              _______
--R   (16)  [3,7,3,0,7,7]
--R                                                         Type: Stream Integer
--E 16

--S 17 of 17
a :: Fraction(Integer)
 

         76543
   (17)  -----
          210
                                                       Type: Fraction Integer
--R 
--R
--R         76543
--R   (17)  -----
--R          210
--R                                                       Type: Fraction Integer
--E 17
)spool 
 
Starts dribbling to nonlinhomodiffeq.output (2010/3/27, 18:30:15).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 59
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 59
deq1 := D(y(x),x) = 9-y(x)^2
 

         ,           2
   (2)  y (x)= - y(x)  + 9

                                            Type: Equation Expression Integer
--R 
--R
--R         ,           2
--R   (2)  y (x)= - y(x)  + 9
--R
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 59
solve(deq1,y,x)
 

        - log(y(x) + 3) + log(y(x) - 3) + 6x
   (3)  ------------------------------------
                          6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(y(x) + 3) + log(y(x) - 3) + 6x
--R   (3)  ------------------------------------
--R                          6
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 59
deq2a := D(y(x),x) = c - p*y(x)^2
 

         ,             2
   (4)  y (x)= - p y(x)  + c

                                            Type: Equation Expression Integer
--R 
--R
--R         ,             2
--R   (4)  y (x)= - p y(x)  + c
--R
--R                                            Type: Equation Expression Integer
--E 4

--S 5 of 59
xpr2b := solve(deq2a,y,x)
 

                   2      +---+
            (p y(x)  + c)\|c p  - 2c p y(x)       +---+
        log(-------------------------------) + 2x\|c p
                            2
                      p y(x)  - c
   (5)  -----------------------------------------------
                              +---+
                            2\|c p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2      +---+
--R            (p y(x)  + c)\|c p  - 2c p y(x)       +---+
--R        log(-------------------------------) + 2x\|c p
--R                            2
--R                      p y(x)  - c
--R   (5)  -----------------------------------------------
--R                              +---+
--R                            2\|c p
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 59
simplify(x-xpr2b)
 

                     2      +---+
              (p y(x)  + c)\|c p  - 2c p y(x)
          log(-------------------------------)
                              2
                        p y(x)  - c
   (6)  - ------------------------------------
                           +---+
                         2\|c p
                                                     Type: Expression Integer
--R 
--R
--R                     2      +---+
--R              (p y(x)  + c)\|c p  - 2c p y(x)
--R          log(-------------------------------)
--R                              2
--R                        p y(x)  - c
--R   (6)  - ------------------------------------
--R                           +---+
--R                         2\|c p
--R                                                     Type: Expression Integer
--E 6

--S 7 of 59
f := operator f
 

   (7)  f
                                                          Type: BasicOperator
--R 
--R
--R   (7)  f
--R                                                          Type: BasicOperator
--E 7

--S 8 of 59
deq3 := D(y(x),x) = f(y(x))
 

         ,
   (8)  y (x)= f(y(x))

                                            Type: Equation Expression Integer
--R 
--R
--R         ,
--R   (8)  y (x)= f(y(x))
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 59
solve(deq3,y,x)
 

           y(x)
         ++       1
   (9)   |      ----- d%P  - x
        ++      f(%P)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           y(x)
--R         ++       1
--R   (9)   |      ----- d%P  - x
--R        ++      f(%P)
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 59
integrate(1/(1-x^2),x)
 

         log(x + 1) - log(x - 1)
   (10)  -----------------------
                    2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         log(x + 1) - log(x - 1)
--R   (10)  -----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 59
xpr5 := (log(x+1)-log(x-1))/2
 

         log(x + 1) - log(x - 1)
   (11)  -----------------------
                    2
                                                     Type: Expression Integer
--R 
--R
--R         log(x + 1) - log(x - 1)
--R   (11)  -----------------------
--R                    2
--R                                                     Type: Expression Integer
--E 11

--S 12 of 59
D(xpr5,x)
 

              1
   (12)  - ------
            2
           x  - 1
                                                     Type: Expression Integer
--R 
--R
--R              1
--R   (12)  - ------
--R            2
--R           x  - 1
--R                                                     Type: Expression Integer
--E 12

--S 13 of 59
xpr6 := log(1+2/(x-1))/2
 

             x + 1
         log(-----)
             x - 1
   (13)  ----------
              2
                                                     Type: Expression Integer
--R 
--R
--R             x + 1
--R         log(-----)
--R             x - 1
--R   (13)  ----------
--R              2
--R                                                     Type: Expression Integer
--E 13

--S 14 of 59
D(xpr6,x)
 

              1
   (14)  - ------
            2
           x  - 1
                                                     Type: Expression Integer
--R 
--R
--R              1
--R   (14)  - ------
--R            2
--R           x  - 1
--R                                                     Type: Expression Integer
--E 14

--S 15 of 59
eq7a := x = (log(z+1)-log(z-1))/2
 

            log(z + 1) - log(z - 1)
   (15)  x= -----------------------
                       2
                                            Type: Equation Expression Integer
--R 
--R
--R            log(z + 1) - log(z - 1)
--R   (15)  x= -----------------------
--R                       2
--R                                            Type: Equation Expression Integer
--E 15

--S 16 of 59
solve(eq7a,z)
 

                 - 2x
             - %e     - 1
   (16)  [z= ------------]
                - 2x
              %e     - 1
                                       Type: List Equation Expression Integer
--R 
--R
--R                 - 2x
--R             - %e     - 1
--R   (16)  [z= ------------]
--R                - 2x
--R              %e     - 1
--R                                       Type: List Equation Expression Integer
--E 16

--S 17 of 59
xpr7b := (1+exp(-2*z))/(1-exp(-2*z))
 

             - 2z
         - %e     - 1
   (17)  ------------
            - 2z
          %e     - 1
                                                     Type: Expression Integer
--R 
--R
--R             - 2z
--R         - %e     - 1
--R   (17)  ------------
--R            - 2z
--R          %e     - 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 59
simplify(xpr7b)
 

             - 2z
         - %e     - 1
   (18)  ------------
            - 2z
          %e     - 1
                                                     Type: Expression Integer
--R 
--R
--R             - 2z
--R         - %e     - 1
--R   (18)  ------------
--R            - 2z
--R          %e     - 1
--R                                                     Type: Expression Integer
--E 18

--S 19 of 59
xpr8 := (1+exp(-2*x))/(1-exp(-2*x)) - (1+2/(exp(2*x)-1))
 

                    - 2x  2x
               - 2%e    %e   + 2
   (19)  -----------------------------
            - 2x       2x     - 2x
         (%e     - 1)%e   - %e     + 1
                                                     Type: Expression Integer
--R 
--R
--R                    - 2x  2x
--R               - 2%e    %e   + 2
--R   (19)  -----------------------------
--R            - 2x       2x     - 2x
--R         (%e     - 1)%e   - %e     + 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 59
simplify(xpr8)
 

   (20)  0
                                                     Type: Expression Integer
--R 
--R
--R   (20)  0
--R                                                     Type: Expression Integer
--E 20

--S 21 of 59
xpr9a := (1+2/(exp(2*x)-1))
 

           2x
         %e   + 1
   (21)  --------
           2x
         %e   - 1
                                                     Type: Expression Integer
--R 
--R
--R           2x
--R         %e   + 1
--R   (21)  --------
--R           2x
--R         %e   - 1
--R                                                     Type: Expression Integer
--E 21

--S 22 of 59
xpr9b := D(xpr9a,x)
 

                     2x
                  4%e
   (22)  - -------------------
              2x 2      2x
           (%e  )  - 2%e   + 1
                                                     Type: Expression Integer
--R 
--R
--R                     2x
--R                  4%e
--R   (22)  - -------------------
--R              2x 2      2x
--R           (%e  )  - 2%e   + 1
--R                                                     Type: Expression Integer
--E 22

--S 23 of 59
xpr9c := 1-(xpr9a)^2
 

                     2x
                  4%e
   (23)  - -------------------
              2x 2      2x
           (%e  )  - 2%e   + 1
                                                     Type: Expression Integer
--R 
--R
--R                     2x
--R                  4%e
--R   (23)  - -------------------
--R              2x 2      2x
--R           (%e  )  - 2%e   + 1
--R                                                     Type: Expression Integer
--E 23

--S 24 of 59
wcp := sqrt(c*p)
 

          +---+
   (24)  \|c p
                                                     Type: Expression Integer
--R 
--R
--R          +---+
--R   (24)  \|c p
--R                                                     Type: Expression Integer
--E 24

--S 25 of 59
xpr10a := log(((p*z^2+c)*wcp-2*c*p*z)/(p*z^2-c))/(2*wcp)
 

                 2      +---+
             (p z  + c)\|c p  - 2c p z
         log(-------------------------)
                         2
                      p z  - c
   (25)  ------------------------------
                       +---+
                     2\|c p
                                                     Type: Expression Integer
--R 
--R
--R                 2      +---+
--R             (p z  + c)\|c p  - 2c p z
--R         log(-------------------------)
--R                         2
--R                      p z  - c
--R   (25)  ------------------------------
--R                       +---+
--R                     2\|c p
--R                                                     Type: Expression Integer
--E 25

--S 26 of 59
solve(x = xpr10a,z)
 

   (26)
   [
     z =
                      +---+ 2              +---+
                   2x\|c p       +---+  2x\|c p
             (- (%e        )  + \|c p %e        )
          *
             ROOT
                         +---+
                      2x\|c p      +---+
                  c %e         - c\|c p
               /
                            +---+ 3                 +---+ 2             +---+
                         2x\|c p         +---+   2x\|c p          2  2x\|c p
                    p (%e        )  - 3p\|c p (%e        )  + 3c p %e
                  + 
                         2 +---+
                    - c p \|c p
         + 
           - c
      /
              +---+
           2x\|c p     +---+
         %e         - \|c p
     ,

     z =
                    +---+ 2              +---+
                 2x\|c p       +---+  2x\|c p
             ((%e        )  - \|c p %e        )
          *
             ROOT
                         +---+
                      2x\|c p      +---+
                  c %e         - c\|c p
               /
                            +---+ 3                 +---+ 2             +---+
                         2x\|c p         +---+   2x\|c p          2  2x\|c p
                    p (%e        )  - 3p\|c p (%e        )  + 3c p %e
                  + 
                         2 +---+
                    - c p \|c p
         + 
           - c
      /
              +---+
           2x\|c p     +---+
         %e         - \|c p
     ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (26)
--R   [
--R     z =
--R                      +---+ 2              +---+
--R                   2x\|c p       +---+  2x\|c p
--R             (- (%e        )  + \|c p %e        )
--R          *
--R             ROOT
--R                         +---+
--R                      2x\|c p      +---+
--R                  c %e         - c\|c p
--R               /
--R                            +---+ 3                 +---+ 2             +---+
--R                         2x\|c p         +---+   2x\|c p          2  2x\|c p
--R                    p (%e        )  - 3p\|c p (%e        )  + 3c p %e
--R                  + 
--R                         2 +---+
--R                    - c p \|c p
--R         + 
--R           - c
--R      /
--R              +---+
--R           2x\|c p     +---+
--R         %e         - \|c p
--R     ,
--R
--R     z =
--R                    +---+ 2              +---+
--R                 2x\|c p       +---+  2x\|c p
--R             ((%e        )  - \|c p %e        )
--R          *
--R             ROOT
--R                         +---+
--R                      2x\|c p      +---+
--R                  c %e         - c\|c p
--R               /
--R                            +---+ 3                 +---+ 2             +---+
--R                         2x\|c p         +---+   2x\|c p          2  2x\|c p
--R                    p (%e        )  - 3p\|c p (%e        )  + 3c p %e
--R                  + 
--R                         2 +---+
--R                    - c p \|c p
--R         + 
--R           - c
--R      /
--R              +---+
--R           2x\|c p     +---+
--R         %e         - \|c p
--R     ]
--R                                       Type: List Equation Expression Integer
--E 26

--S 27 of 59
eq10c := (p*z^2+c)*wcp - 2*c*p*z
 

             2      +---+
   (27)  (p z  + c)\|c p  - 2c p z
                                                     Type: Expression Integer
--R 
--R
--R             2      +---+
--R   (27)  (p z  + c)\|c p  - 2c p z
--R                                                     Type: Expression Integer
--E 27

--S 28 of 59
solve(eq10c=0,z)
 

                c         c
   (28)  [z= ------,z= ------]
              +---+     +---+
             \|c p     \|c p
                                       Type: List Equation Expression Integer
--R 
--R
--R                c         c
--R   (28)  [z= ------,z= ------]
--R              +---+     +---+
--R             \|c p     \|c p
--R                                       Type: List Equation Expression Integer
--E 28

--S 29 of 59
xpr10d := p*wcp*(z-wcp/p)^2
 

             2      +---+
   (29)  (p z  + c)\|c p  - 2c p z
                                                     Type: Expression Integer
--R 
--R
--R             2      +---+
--R   (29)  (p z  + c)\|c p  - 2c p z
--R                                                     Type: Expression Integer
--E 29

--S 30 of 59
simplify(xpr10d/eq10c)
 

   (30)  1
                                                     Type: Expression Integer
--R 
--R
--R   (30)  1
--R                                                     Type: Expression Integer
--E 30

--S 31 of 59
xpr10e := (wcp/p)*(2/(1-exp(-2*wcp*x)/wcp)-1)
 

                        +---+
            +---+  - 2x\|c p
         - \|c p %e           - c p
   (31)  --------------------------
                   +---+
              - 2x\|c p      +---+
          p %e           - p\|c p
                                                     Type: Expression Integer
--R 
--R
--R                        +---+
--R            +---+  - 2x\|c p
--R         - \|c p %e           - c p
--R   (31)  --------------------------
--R                   +---+
--R              - 2x\|c p      +---+
--R          p %e           - p\|c p
--R                                                     Type: Expression Integer
--E 31

--S 32 of 59
xpr10f := D(xpr10e,x)
 

                                      +---+
                          +---+  - 2x\|c p
                       4c\|c p %e
   (32)  - -------------------------------------------
                   +---+ 2                 +---+
              - 2x\|c p        +---+  - 2x\|c p
           (%e          )  - 2\|c p %e           + c p
                                                     Type: Expression Integer
--R 
--R
--R                                      +---+
--R                          +---+  - 2x\|c p
--R                       4c\|c p %e
--R   (32)  - -------------------------------------------
--R                   +---+ 2                 +---+
--R              - 2x\|c p        +---+  - 2x\|c p
--R           (%e          )  - 2\|c p %e           + c p
--R                                                     Type: Expression Integer
--E 32

--S 33 of 59
xpr10g := c-p*(xpr10e)^2
 

                                      +---+
                          +---+  - 2x\|c p
                       4c\|c p %e
   (33)  - -------------------------------------------
                   +---+ 2                 +---+
              - 2x\|c p        +---+  - 2x\|c p
           (%e          )  - 2\|c p %e           + c p
                                                     Type: Expression Integer
--R 
--R
--R                                      +---+
--R                          +---+  - 2x\|c p
--R                       4c\|c p %e
--R   (33)  - -------------------------------------------
--R                   +---+ 2                 +---+
--R              - 2x\|c p        +---+  - 2x\|c p
--R           (%e          )  - 2\|c p %e           + c p
--R                                                     Type: Expression Integer
--E 33

--S 34 of 59
simplify(xpr10f/xpr10g)
 

   (34)  1
                                                     Type: Expression Integer
--R 
--R
--R   (34)  1
--R                                                     Type: Expression Integer
--E 34

--S 35 of 59
deq11a := D(y(x),x) = a*x+b-p*y(x)^2
 

          ,             2
   (35)  y (x)= - p y(x)  + a x + b

                                            Type: Equation Expression Integer
--R 
--R
--R          ,             2
--R   (35)  y (x)= - p y(x)  + a x + b
--R
--R                                            Type: Equation Expression Integer
--E 35

--S 36 of 59
solve(deq11a,y,x)
 

   (36)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

--S 37 of 59
c := operator c
 

   (37)  c
                                                          Type: BasicOperator
--R 
--R
--R   (37)  c
--R                                                          Type: BasicOperator
--E 37

--S 38 of 59
deq12a := D(y(x),x) = c(x) - p*y(x)^2
 

          ,             2
   (38)  y (x)= - p y(x)  + c(x)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,             2
--R   (38)  y (x)= - p y(x)  + c(x)
--R
--R                                            Type: Equation Expression Integer
--E 38

--S 39 of 59
solve(deq12a,y,x)
 

   (39)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (39)  "failed"
--R                                                    Type: Union("failed",...)
--E 39

--S 40 of 59
wpcx := sqrt(c(x))*sqrt(p)
 

          +-+ +----+
   (40)  \|p \|c(x)
                                                     Type: Expression Integer
--R 
--R
--R          +-+ +----+
--R   (40)  \|p \|c(x)
--R                                                     Type: Expression Integer
--E 40

--S 41 of 59
xpr13a := log((p*wpcx*(z-wpcx/p)^2)/(p*z^2-c(x)))/(2*wpcx)
 

                          2  +-+ +----+
             (- c(x) - p z )\|p \|c(x)  + 2p z c(x)
         log(--------------------------------------)
                                     2
                           c(x) - p z
   (41)  -------------------------------------------
                           +-+ +----+
                         2\|p \|c(x)
                                                     Type: Expression Integer
--R 
--R
--R                          2  +-+ +----+
--R             (- c(x) - p z )\|p \|c(x)  + 2p z c(x)
--R         log(--------------------------------------)
--R                                     2
--R                           c(x) - p z
--R   (41)  -------------------------------------------
--R                           +-+ +----+
--R                         2\|p \|c(x)
--R                                                     Type: Expression Integer
--E 41

--S 42 of 59
xpr13b := (wpcx/p)*(2/(1-exp(-2*wpcx*x)/wpcx)-1)
 

                             +-+ +----+
            +-+ +----+  - 2x\|p \|c(x)
         - \|p \|c(x) %e                - p c(x)
   (42)  ---------------------------------------
                     +-+ +----+
                - 2x\|p \|c(x)      +-+ +----+
            p %e                - p\|p \|c(x)
                                                     Type: Expression Integer
--R 
--R
--R                             +-+ +----+
--R            +-+ +----+  - 2x\|p \|c(x)
--R         - \|p \|c(x) %e                - p c(x)
--R   (42)  ---------------------------------------
--R                     +-+ +----+
--R                - 2x\|p \|c(x)      +-+ +----+
--R            p %e                - p\|p \|c(x)
--R                                                     Type: Expression Integer
--E 42

--S 43 of 59
xpr13c := D(xpr13b,x)
 

   (43)
                          +-+ +----+ 2
          +-+ ,      - 2x\|p \|c(x)
       - \|p c (x)(%e               )

     + 
                                                                 +-+ +----+
              +----+             +-+  ,             2 +-+   - 2x\|p \|c(x)
       ((- 2p\|c(x)  - 4p x c(x)\|p )c (x) - 8p c(x) \|p )%e

     + 
              +-+ ,
       p c(x)\|p c (x)

  /
                        +-+ +----+ 2                     +-+ +----+
          +----+   - 2x\|p \|c(x)              +-+  - 2x\|p \|c(x)
       2p\|c(x) (%e               )  - 4p c(x)\|p %e
     + 
         2     +----+
       2p c(x)\|c(x)
                                                     Type: Expression Integer
--R 
--R
--R   (43)
--R                          +-+ +----+ 2
--R          +-+ ,      - 2x\|p \|c(x)
--R       - \|p c (x)(%e               )
--R
--R     + 
--R                                                                 +-+ +----+
--R              +----+             +-+  ,             2 +-+   - 2x\|p \|c(x)
--R       ((- 2p\|c(x)  - 4p x c(x)\|p )c (x) - 8p c(x) \|p )%e
--R
--R     + 
--R              +-+ ,
--R       p c(x)\|p c (x)
--R
--R  /
--R                        +-+ +----+ 2                     +-+ +----+
--R          +----+   - 2x\|p \|c(x)              +-+  - 2x\|p \|c(x)
--R       2p\|c(x) (%e               )  - 4p c(x)\|p %e
--R     + 
--R         2     +----+
--R       2p c(x)\|c(x)
--R                                                     Type: Expression Integer
--E 43

--S 44 of 59
xpr13d := c(x) - p*(xpr13b)^2
 

                                                +-+ +----+
                               +-+ +----+  - 2x\|p \|c(x)
                         4c(x)\|p \|c(x) %e
   (44)  - -------------------------------------------------------------
                   +-+ +----+ 2                      +-+ +----+
              - 2x\|p \|c(x)        +-+ +----+  - 2x\|p \|c(x)
           (%e               )  - 2\|p \|c(x) %e                + p c(x)
                                                     Type: Expression Integer
--R 
--R
--R                                                +-+ +----+
--R                               +-+ +----+  - 2x\|p \|c(x)
--R                         4c(x)\|p \|c(x) %e
--R   (44)  - -------------------------------------------------------------
--R                   +-+ +----+ 2                      +-+ +----+
--R              - 2x\|p \|c(x)        +-+ +----+  - 2x\|p \|c(x)
--R           (%e               )  - 2\|p \|c(x) %e                + p c(x)
--R                                                     Type: Expression Integer
--E 44

--S 45 of 59
simplify(xpr13d/xpr13c)
 

   (45)
                          +-+ +----+                          +-+ +----+
         2    3 +-+  - 2x\|p \|c(x)       2    2 +----+  - 4x\|p \|c(x)
       8p c(x) \|p %e                - 16p c(x) \|c(x) %e
     + 
                          +-+ +----+
              2 +-+  - 6x\|p \|c(x)
       8p c(x) \|p %e
  /
                                                                     +-+ +----+
           2     +----+     2      2 +-+  ,        2    3 +-+   - 2x\|p \|c(x)
       ((4p c(x)\|c(x)  + 4p x c(x) \|p )c (x) + 8p c(x) \|p )%e

     + 
               2       +----+           +-+  ,         2    2 +----+
         ((- 8p x c(x)\|c(x)  - 4p c(x)\|p )c (x) - 16p c(x) \|c(x) )

      *
                +-+ +----+
           - 4x\|p \|c(x)
         %e
     + 
                                                 +-+ +----+
                  +-+ ,             2 +-+   - 6x\|p \|c(x)
       (4p x c(x)\|p c (x) + 8p c(x) \|p )%e

     + 
                       +-+ +----+
        +-+ ,     - 8x\|p \|c(x)     2    2 +-+ ,
       \|p c (x)%e                - p c(x) \|p c (x)

                                                     Type: Expression Integer
--R 
--R
--R   (45)
--R                          +-+ +----+                          +-+ +----+
--R         2    3 +-+  - 2x\|p \|c(x)       2    2 +----+  - 4x\|p \|c(x)
--R       8p c(x) \|p %e                - 16p c(x) \|c(x) %e
--R     + 
--R                          +-+ +----+
--R              2 +-+  - 6x\|p \|c(x)
--R       8p c(x) \|p %e
--R  /
--R                                                                     +-+ +----+
--R           2     +----+     2      2 +-+  ,        2    3 +-+   - 2x\|p \|c(x)
--R       ((4p c(x)\|c(x)  + 4p x c(x) \|p )c (x) + 8p c(x) \|p )%e
--R
--R     + 
--R               2       +----+           +-+  ,         2    2 +----+
--R         ((- 8p x c(x)\|c(x)  - 4p c(x)\|p )c (x) - 16p c(x) \|c(x) )
--R
--R      *
--R                +-+ +----+
--R           - 4x\|p \|c(x)
--R         %e
--R     + 
--R                                                 +-+ +----+
--R                  +-+ ,             2 +-+   - 6x\|p \|c(x)
--R       (4p x c(x)\|p c (x) + 8p c(x) \|p )%e
--R
--R     + 
--R                       +-+ +----+
--R        +-+ ,     - 8x\|p \|c(x)     2    2 +-+ ,
--R       \|p c (x)%e                - p c(x) \|p c (x)
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 59
xpr13e := simplify(D((2/(1-exp(-2*wpcx*x)/wpcx)-1),x))
 

                                                                +-+ +----+
                    +----+    +-+  ,              +----+   - 2x\|p \|c(x)
             ((2p x\|c(x)  + \|p )c (x) + 4p c(x)\|c(x) )%e

   (46)  ---------------------------------------------------------------------
                         +-+ +----+                 +-+ +----+
               +-+  - 2x\|p \|c(x)     +----+  - 4x\|p \|c(x)           +----+
         2c(x)\|p %e                - \|c(x) %e                - p c(x)\|c(x)
                                                     Type: Expression Integer
--R 
--R
--R                                                                +-+ +----+
--R                    +----+    +-+  ,              +----+   - 2x\|p \|c(x)
--R             ((2p x\|c(x)  + \|p )c (x) + 4p c(x)\|c(x) )%e
--R
--R   (46)  ---------------------------------------------------------------------
--R                         +-+ +----+                 +-+ +----+
--R               +-+  - 2x\|p \|c(x)     +----+  - 4x\|p \|c(x)           +----+
--R         2c(x)\|p %e                - \|c(x) %e                - p c(x)\|c(x)
--R                                                     Type: Expression Integer
--E 46

--S 47 of 59
xpr13f := (wpcx-exp(-2*wpcx*x))^2
 

                 +-+ +----+ 2                      +-+ +----+
            - 2x\|p \|c(x)        +-+ +----+  - 2x\|p \|c(x)
   (47)  (%e               )  - 2\|p \|c(x) %e                + p c(x)
                                                     Type: Expression Integer
--R 
--R
--R                 +-+ +----+ 2                      +-+ +----+
--R            - 2x\|p \|c(x)        +-+ +----+  - 2x\|p \|c(x)
--R   (47)  (%e               )  - 2\|p \|c(x) %e                + p c(x)
--R                                                     Type: Expression Integer
--E 47

--S 48 of 59
xpr13g := simplify(((2*p*c(x)*x+wpcx)*D(c(x),x)+4*p*c(x)^2)/wpcx)
 

           +-+ +----+              ,             2
         (\|p \|c(x)  + 2p x c(x))c (x) + 4p c(x)

   (48)  -----------------------------------------
                         +-+ +----+
                        \|p \|c(x)
                                                     Type: Expression Integer
--R 
--R
--R           +-+ +----+              ,             2
--R         (\|p \|c(x)  + 2p x c(x))c (x) + 4p c(x)
--R
--R   (48)  -----------------------------------------
--R                         +-+ +----+
--R                        \|p \|c(x)
--R                                                     Type: Expression Integer
--E 48

--S 49 of 59
xpr13h := simplify((1+2*wpcx*x)*D(c(x),x)+4*wpcx*c(x))
 

             +-+ +----+      ,            +-+ +----+
   (49)  (2x\|p \|c(x)  + 1)c (x) + 4c(x)\|p \|c(x)

                                                     Type: Expression Integer
--R 
--R
--R             +-+ +----+      ,            +-+ +----+
--R   (49)  (2x\|p \|c(x)  + 1)c (x) + 4c(x)\|p \|c(x)
--R
--R                                                     Type: Expression Integer
--E 49

--S 50 of 59
simplify(xpr13h/xpr13g)
 

   (50)  1
                                                     Type: Expression Integer
--R 
--R
--R   (50)  1
--R                                                     Type: Expression Integer
--E 50

--S 51 of 59
xpr13i:=simplify((1/(wpcx-z)-1/(2*wpcx))*D(c(x),x)+_
                 ((1+2*wpcx*x)*D(c(x),x)+4*wpcx*c(x))*z/(wpcx-z)^2)
 

   (51)
                                2  +-+ +----+          2               3  ,
       (((- 4p x z - p)c(x) + 3z )\|p \|c(x)  + (4p x z  - p z)c(x) - z )c (x)

     + 
                  2 +-+ +----+       2    2
       - 8p z c(x) \|p \|c(x)  + 8p z c(x)
  /
                    3  +-+ +----+     2    2       2
     (6p z c(x) + 2z )\|p \|c(x)  - 2p c(x)  - 6p z c(x)
                                                     Type: Expression Integer
--R 
--R
--R   (51)
--R                                2  +-+ +----+          2               3  ,
--R       (((- 4p x z - p)c(x) + 3z )\|p \|c(x)  + (4p x z  - p z)c(x) - z )c (x)
--R
--R     + 
--R                  2 +-+ +----+       2    2
--R       - 8p z c(x) \|p \|c(x)  + 8p z c(x)
--R  /
--R                    3  +-+ +----+     2    2       2
--R     (6p z c(x) + 2z )\|p \|c(x)  - 2p c(x)  - 6p z c(x)
--R                                                     Type: Expression Integer
--E 51

--S 52 of 59
w := operator w
 

   (52)  w
                                                          Type: BasicOperator
--R 
--R
--R   (52)  w
--R                                                          Type: BasicOperator
--E 52

--S 53 of 59
z := operator z
 

   (53)  z
                                                          Type: BasicOperator
--R 
--R
--R   (53)  z
--R                                                          Type: BasicOperator
--E 53

--S 54 of 59
simplify(D((2/(1-z(x)/w(x))-1)*c(x)/w(x),x))
 

   (54)
                2 ,               2                           2  ,
       2c(x)w(x) z (x) + (c(x)z(x)  - 2c(x)w(x)z(x) - c(x)w(x) )w (x)

     + 
                  2       3  ,
       (- w(x)z(x)  + w(x) )c (x)

  /
         2    2        3           4
     w(x) z(x)  - 2w(x) z(x) + w(x)
                                                     Type: Expression Integer
--R 
--R
--R   (54)
--R                2 ,               2                           2  ,
--R       2c(x)w(x) z (x) + (c(x)z(x)  - 2c(x)w(x)z(x) - c(x)w(x) )w (x)
--R
--R     + 
--R                  2       3  ,
--R       (- w(x)z(x)  + w(x) )c (x)
--R
--R  /
--R         2    2        3           4
--R     w(x) z(x)  - 2w(x) z(x) + w(x)
--R                                                     Type: Expression Integer
--E 54

--S 55 of 59
simplify((2*c(x)*w(x)^2*D(z(x),x)+(z(x)^2-2*w(x)*z(x)-w(x)^2)*c(x)*D(w(x),x)+_
         (w(x)^3-w(x)*z(x)^2)*D(c(x),x))/(w(x)^2*(z(x)-w(x))^2))
 

   (55)
                2 ,               2                           2  ,
       2c(x)w(x) z (x) + (c(x)z(x)  - 2c(x)w(x)z(x) - c(x)w(x) )w (x)

     + 
                  2       3  ,
       (- w(x)z(x)  + w(x) )c (x)

  /
         2    2        3           4
     w(x) z(x)  - 2w(x) z(x) + w(x)
                                                     Type: Expression Integer
--R 
--R
--R   (55)
--R                2 ,               2                           2  ,
--R       2c(x)w(x) z (x) + (c(x)z(x)  - 2c(x)w(x)z(x) - c(x)w(x) )w (x)
--R
--R     + 
--R                  2       3  ,
--R       (- w(x)z(x)  + w(x) )c (x)
--R
--R  /
--R         2    2        3           4
--R     w(x) z(x)  - 2w(x) z(x) + w(x)
--R                                                     Type: Expression Integer
--E 55

--S 56 of 59
xpr13j:=simplify((2*c(x)*w(x)^2*w(x)*z(x)*(x/c(x)-1/2)+(z(x)^2-2*w(x)*z(x)-_
                 w(x)^2)*c(x)*(-w(x)/(2*c(x)))+(w(x)^2-w(x)*z(x)^2)*D(c(x),x))_
               /(w(x)^2*(z(x)-w(x))^2))
 

   (56)
           2          ,          2                      2                    2
   (- 2z(x)  + 2w(x))c (x) - z(x)  + ((- 2c(x) + 4x)w(x)  + 2w(x))z(x) + w(x)

   ---------------------------------------------------------------------------
                                  2        2            3
                         2w(x)z(x)  - 4w(x) z(x) + 2w(x)
                                                     Type: Expression Integer
--R 
--R
--R   (56)
--R           2          ,          2                      2                    2
--R   (- 2z(x)  + 2w(x))c (x) - z(x)  + ((- 2c(x) + 4x)w(x)  + 2w(x))z(x) + w(x)
--R
--R   ---------------------------------------------------------------------------
--R                                  2        2            3
--R                         2w(x)z(x)  - 4w(x) z(x) + 2w(x)
--R                                                     Type: Expression Integer
--E 56

--S 57 of 59
xpr13k:=simplify((1/(w(x)-z(x))-1/(2*w(x)))*D(c(x),x)+_
                 ((1+2*w(x)*x)*D(c(x),x)+4*w(x)*c(x))*z(x)/(w(x)-z(x))^2)
 

                2           2                    2  ,               2
         (- z(x)  + (4x w(x)  + 2w(x))z(x) + w(x) )c (x) + 8c(x)w(x) z(x)

   (57)  ----------------------------------------------------------------
                                  2        2            3
                         2w(x)z(x)  - 4w(x) z(x) + 2w(x)
                                                     Type: Expression Integer
--R 
--R
--R                2           2                    2  ,               2
--R         (- z(x)  + (4x w(x)  + 2w(x))z(x) + w(x) )c (x) + 8c(x)w(x) z(x)
--R
--R   (57)  ----------------------------------------------------------------
--R                                  2        2            3
--R                         2w(x)z(x)  - 4w(x) z(x) + 2w(x)
--R                                                     Type: Expression Integer
--E 57

--S 58 of 59
simplify(xpr13k/xpr13j)
 

   (58)
            2             2                    2  ,               2
       (z(x)  + (- 4x w(x)  - 2w(x))z(x) - w(x) )c (x) - 8c(x)w(x) z(x)

   -----------------------------------------------------------------------
         2          ,          2                    2                    2
   (2z(x)  - 2w(x))c (x) + z(x)  + ((2c(x) - 4x)w(x)  - 2w(x))z(x) - w(x)

                                                     Type: Expression Integer
--R 
--R
--R   (58)
--R            2             2                    2  ,               2
--R       (z(x)  + (- 4x w(x)  - 2w(x))z(x) - w(x) )c (x) - 8c(x)w(x) z(x)
--R
--R   -----------------------------------------------------------------------
--R         2          ,          2                    2                    2
--R   (2z(x)  - 2w(x))c (x) + z(x)  + ((2c(x) - 4x)w(x)  - 2w(x))z(x) - w(x)
--R
--R                                                     Type: Expression Integer
--E 58

--S 59 of 59
simplify(xpr13k-xpr13j)
 

   (59)
            2           2                    2          ,          2
       (z(x)  + (4x w(x)  + 2w(x))z(x) + w(x)  - 2w(x))c (x) + z(x)

     + 
                         2                    2
       ((10c(x) - 4x)w(x)  - 2w(x))z(x) - w(x)
  /
              2        2            3
     2w(x)z(x)  - 4w(x) z(x) + 2w(x)
                                                     Type: Expression Integer
--R 
--R
--R   (59)
--R            2           2                    2          ,          2
--R       (z(x)  + (4x w(x)  + 2w(x))z(x) + w(x)  - 2w(x))c (x) + z(x)
--R
--R     + 
--R                         2                    2
--R       ((10c(x) - 4x)w(x)  - 2w(x))z(x) - w(x)
--R  /
--R              2        2            3
--R     2w(x)z(x)  - 4w(x) z(x) + 2w(x)
--R                                                     Type: Expression Integer
--E 59

)spool
 
Starts dribbling to directproduct.output (2010/3/27, 18:24:57).
)set message auto off
 
)set message test on
 
)clear all
 

--S 1 of 12
NNI has Monoid
 

   (1)  true
                                                                Type: Boolean
--R 
--R
--R   (1)  true
--R                                                                Type: Boolean
--E 1

--S 2 of 12
NNI2:=DirectProduct(2,NNI)
 

   (2)  DirectProduct(2,NonNegativeInteger)
                                                                 Type: Domain
--R 
--R
--R   (2)  DirectProduct(2,NonNegativeInteger)
--R                                                                 Type: Domain
--E 2

--S 3 of 12
NNI2 has Monoid
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 12
a:NNI2:=directProduct([3,5])
 

   (4)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (4)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 4

--S 5 of 12
3*a
 

   (5)  [9,15]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (5)  [9,15]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 5

--S 6 of 12
b:NNI2:=1
 

   (6)  [1,1]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (6)  [1,1]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 6

--S 7 of 12
1*a
 

   (7)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (7)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 7

--S 8 of 12
b*a
 

   (8)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (8)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 8

--S 9 of 12
c:NNI2:=directProduct([1,1])
 

   (9)  [1,1]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (9)  [1,1]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 9

--S 10 of 12
c*a
 

   (10)  [3,5]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (10)  [3,5]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 10

--S 11 of 12
d:NNI2:=directProduct([1,2])
 

   (11)  [1,2]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (11)  [1,2]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 11

--S 12 of 12
d*a
 

   (12)  [3,10]
                                    Type: DirectProduct(2,NonNegativeInteger)
--R 
--R
--R   (12)  [3,10]
--R                                    Type: DirectProduct(2,NonNegativeInteger)
--E 12

)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read tutchap2
 
--Copyright The Numerical Algorithms Group Limited 1996.
solve(3*x=x+2)
 

   (1)  [x= 1]
                              Type: List Equation Fraction Polynomial Integer
x
 

   (2)  x
                                                             Type: Variable x
solve(3*x - 1 = 0)
 

            1
   (3)  [x= -]
            3
                              Type: List Equation Fraction Polynomial Integer
solve(3*x - 1)
 

            1
   (4)  [x= -]
            3
                              Type: List Equation Fraction Polynomial Integer
solve(3*x^2 - 7*x + 2)
 

                 1
   (5)  [x= 2,x= -]
                 3
                              Type: List Equation Fraction Polynomial Integer
solve(x^2 - 2)
 

          2
   (6)  [x  - 2= 0]
                              Type: List Equation Fraction Polynomial Integer
solve(x^4 - 8*x^3 + 23*x^2 - 28*x + 12)
 

   (7)  [x= 3,x= 2,x= 1]
                              Type: List Equation Fraction Polynomial Integer
factor(x^4 - 8*x^3 + 23*x^2 - 28*x + 12)
 

                      2
   (8)  (x - 3)(x - 2) (x - 1)
                                            Type: Factored Polynomial Integer
radicalSolve(x^2 - 2)
 

             +-+       +-+
   (9)  [x= \|2 ,x= - \|2 ]
                                       Type: List Equation Expression Integer
radicalSolve(x^5+x^2+1)
 

   (10)  []
                                       Type: List Equation Expression Integer
solve(x^2 - 2, 0.00001)
 

   (11)  [x= - 1.4142112731 93359375,x= 1.4142112731 93359375]
                                         Type: List Equation Polynomial Float
outputGeneral 6
 
                                                                   Type: Void
%%(11)
 

   (13)  [x= - 1.41421,x= 1.41421]
                                         Type: List Equation Polynomial Float
solve(x^2 - 2, 1/100000)
 

               370727    370727
   (14)  [x= - ------,x= ------]
               262144    262144
                              Type: List Equation Polynomial Fraction Integer
solve(x^2-2*x+3,0.00001)
 

   (15)  []
                                         Type: List Equation Polynomial Float
complexSolve(x^2-2*x+3,0.00001)
 

   (16)  [x= 1.0 - 1.41421 %i,x= 1.0 + 1.41421 %i]
                                 Type: List Equation Polynomial Complex Float
solve((x^2 - 1.21) :: Polynomial Fraction Integer,0.00001)
 

   (17)  [x= - 1.1,x= 1.1]
                                         Type: List Equation Polynomial Float
radicalSolve(a*x^2 + b*x + c, x)
 

                +-----------+         +-----------+
                |          2          |          2
             - \|- 4a c + b   - b    \|- 4a c + b   - b
   (18)  [x= --------------------,x= ------------------]
                      2a                     2a
                                       Type: List Equation Expression Integer
qs := %; -- the semicolon (;) inhibits AXIOM's output display
 

                                       Type: List Equation Expression Integer
qs1 := qs.1
 

               +-----------+
               |          2
            - \|- 4a c + b   - b
   (20)  x= --------------------
                     2a
                                            Type: Equation Expression Integer
x1 := rhs %
 

            +-----------+
            |          2
         - \|- 4a c + b   - b
   (21)  --------------------
                  2a
                                                     Type: Expression Integer
numeric rhs %%(9).1
 

   (22)  1.41421
                                                                  Type: Float
xs := map(rhs, qs)
 

             +-----------+      +-----------+
             |          2       |          2
          - \|- 4a c + b   - b \|- 4a c + b   - b
   (23)  [--------------------,------------------]
                   2a                  2a
                                                Type: List Expression Integer
xs.1 + xs.2
 

           b
   (24)  - -
           a
                                                     Type: Expression Integer
xs.1 * xs.2
 

         c
   (25)  -
         a
                                                     Type: Expression Integer
solve [x + 2*y + z = 5, 2*x - y - z = 6, x + y + 2*z = 0]
 

                21    19    23
   (26)  [[z= - --,y= --,x= --]]
                 8     8     8
                         Type: List List Equation Fraction Polynomial Integer
solve [x^2 + y + 1, x + y^2 - 1]
 

                               2      3
   (27)  [[y= - 1,x= 0],[y= - x  - 1,x  + 2x + 1= 0]]
                         Type: List List Equation Fraction Polynomial Integer
solve([x^2 + y + 1, x + y^2 - 1], 0.00001)
 

   (28)  [[y= - 1.20557,x= - 0.453396],[y= - 1.0,x= 0.0]]
                                    Type: List List Equation Polynomial Float
complexSolve([x^2 + y + 1, x + y^2 - 1], 0.00001)
 

   (29)
   [[y= - 1.20557,x= - 0.453396],
    [y= 1.10278 + 0.665415 %i,x= 0.226685 - 1.46771 %i],
    [y= 1.10278 - 0.665415 %i,x= 0.226685 + 1.46771 %i], [y= - 1.0,x= 0.0]]
                            Type: List List Equation Polynomial Complex Float
solve([x^2-y^2, (x^2 -1)/(x+y)])
 

   (30)  [[y= 1,x= 1],[y= - 1,x= - 1]]
                         Type: List List Equation Fraction Polynomial Integer
a := (x + y)/2
 

         1     1
   (31)  - y + - x
         2     2
                                            Type: Polynomial Fraction Integer
a :: Fraction Polynomial Integer
 

         y + x
   (32)  -----
           2
                                            Type: Fraction Polynomial Integer
a
 

         1     1
   (33)  - y + - x
         2     2
                                            Type: Polynomial Fraction Integer
a := a :: Fraction Polynomial Integer
 

         y + x
   (34)  -----
           2
                                            Type: Fraction Polynomial Integer
a
 

         y + x
   (35)  -----
           2
                                            Type: Fraction Polynomial Integer
a := (x + y)/2;                       
 

                                            Type: Polynomial Fraction Integer
b : Fraction Polynomial Integer := a
 

         y + x
   (37)  -----
           2
                                            Type: Fraction Polynomial Integer
a : Fraction Polynomial Integer := a
 
 
Daly Bug
   You cannot declare a to be of type Fraction Polynomial Integer 
      because either the declared type of a or the type of the value of
      a is different from Fraction Polynomial Integer .
y := x^2 + 3*x + 2
 

          2
   (38)  x  + 3x + 2
                                                     Type: Polynomial Integer
y := y :: Factored Polynomial Integer
 

   (39)  (x + 1)(x + 2)
                                            Type: Factored Polynomial Integer
)clear p y -- since y has a value
 
P := (y + z)*x^2 + z*x + c           
 

           2          2
   (40)  (x  + x)z + x y + c
                                                     Type: Polynomial Integer
P :: UP(x, POLY INT)
 

                 2
   (41)  (z + y)x  + z x + c
                             Type: UnivariatePolynomial(x,Polynomial Integer)
P :: UP(x, UP(y, POLY INT))
 

                 2
   (42)  (y + z)x  + z x + c
     Type: UnivariatePolynomial(x,UnivariatePolynomial(y,Polynomial Integer))
P := P :: UP(x, UP(y, UP(z, UP(c, INT))))
 

                 2
   (43)  (y + z)x  + z x + c
Type: UnivariatePolynomial(x,UnivariatePolynomial(y,UnivariatePolynomial(z,UnivariatePolynomial(c,Integer))))
)clear p all
 
sum(1/((3*r-2)*(3*r+1)*(3*r+4)), r=1..n)
 

               2
             3n  + 5n
   (44)  ----------------
            2
         72n  + 120n + 32
                                 Type: Union(Fraction Polynomial Integer,...)
limit(%, n=%plusInfinity)
 

          1
   (45)  --
         24
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
SA := sum(a + (r-1)*b, r = 1..n)
 

            2
         b n  + (- b + 2a)n
   (46)  ------------------
                  2
                                            Type: Fraction Polynomial Integer
SA :: UP(a, Polynomial Fraction Integer)
 

               1    2   1
   (47)  n a + - b n  - - b n
               2        2
                    Type: UnivariatePolynomial(a,Polynomial Fraction Integer)
SA :: UP(a, UP(b, FRAC FR POLY INT))
 

               (n - 1)n
   (48)  n a + -------- b
                   2
Type: UnivariatePolynomial(a,UnivariatePolynomial(b,Fraction Factored Polynomial Integer))
SG := sum(a*b^(r-1), r=1..n)
 

              n - 1
         a b b      - a
   (49)  --------------
              b - 1
                                                     Type: Expression Integer
)set stream calculate 5                      
 
series((1 + x)^n, x=0)    
 

   (50)
                2           3     2            4     3      2
               n  - n  2   n  - 3n  + 2n  3   n  - 6n  + 11n  - 6n  4
     1 + n x + ------ x  + ------------- x  + -------------------- x
                  2              6                     24
   + 
      5      4      3      2
     n  - 10n  + 35n  - 50n  + 24n  5      6
     ----------------------------- x  + O(x )
                  120
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
taylor((1 + x)^n, x=0) 
 

   (51)
                2           3     2            4     3      2
               n  - n  2   n  - 3n  + 2n  3   n  - 6n  + 11n  - 6n  4
     1 + n x + ------ x  + ------------- x  + -------------------- x
                  2              6                     24
   + 
      5      4      3      2
     n  - 10n  + 35n  - 50n  + 24n  5      6
     ----------------------------- x  + O(x )
                  120
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
%.6
 

          6      5      4       3       2
         n  - 15n  + 85n  - 225n  + 274n  - 120n
   (52)  ---------------------------------------
                           720
                                                     Type: Expression Integer
xPositive? == (x :: Float > 0)
 
                                                                   Type: Void
x := 17-sqrt(300);
 

                                                        Type: AlgebraicNumber
xPositive?
 
   Compiling body of rule xPositive? to compute value of type Boolean 

   (55)  false
                                                                Type: Boolean
x := 18-sqrt(300);
 

                                                        Type: AlgebraicNumber
xPositive?
 

   (57)  true
                                                                Type: Boolean
)clear p x
 
   Compiled code for xPositive? has been cleared.
x
 

   (58)  x
                                                             Type: Variable x
xPositive?
 
   There are 4 exposed and 1 unexposed library operations named < 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op <
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named < 
      with argument type(s) 
                             NonNegativeInteger
                                    Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   Cannot convert from type Variable x to Float for value
   x

halfSum(x, y) == (x + y)/2
 
                                                                   Type: Void
halfSum(1, 3)
 
   Compiling function halfSum with type (PositiveInteger,
      PositiveInteger) -> Fraction Integer 

   (60)  2
                                                       Type: Fraction Integer
halfSum(1.5, 2.5)
 
   Compiling function halfSum with type (Float,Float) -> Float 

   (61)  2.0
                                                                  Type: Float
halfSum(2, 4)
 

   (62)  3
                                                       Type: Fraction Integer
f(n)==#((2^n)::String)   
 
                                                                   Type: Void
f(20)
 
   Compiling function f with type PositiveInteger -> NonNegativeInteger
      

   (64)  7
                                                        Type: PositiveInteger
f(n) == (local length; length := #((2^n)::String);     _
                 if length > 120 then "Too long!" else length)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
f 100
 
   Compiling function f with type PositiveInteger -> Any 

   (66)  31
                                                     Type: NonNegativeInteger
f 1000
 

   (67)  "Too long!"
                                                                 Type: String
f(n : PositiveInteger) : Any ==                   _
          (local length; length := #((2^n)::String);      _
           if length > 120 then "Too long!" else length)
 
   Function declaration f : PositiveInteger -> Any has been added to 
      workspace.
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
-- this takes too long to compute -- f 0
g1(x) == 2*x
 
                                                                   Type: Void
g2(x) == %
 
                                                                   Type: Void
G := 2*x
 

   (71)  2x
                                                     Type: Polynomial Integer
g3(x) == G
 
                                                                   Type: Void
g1(1)
 
   Compiling function g1 with type PositiveInteger -> PositiveInteger 

   (73)  2
                                                        Type: PositiveInteger
g2(2)
 
   Compiling function g2 with type PositiveInteger -> PositiveInteger 

   (74)  2
                                                        Type: PositiveInteger
g3(3)
 
   Compiling function g3 with type PositiveInteger -> Polynomial 
      Integer 

   (75)  2x
                                                     Type: Polynomial Integer
l1 := [1,2,3,4,5]
 

   (76)  [1,2,3,4,5]
                                                   Type: List PositiveInteger
l2 := map(x +-> x^2,l1)
 

   (77)  [1,4,9,16,25]
                                                   Type: List PositiveInteger
BE(n) == taylor((1+x)^n, x=0)
 
                                                                   Type: Void
BE(5)
 
   Compiling function BE with type PositiveInteger -> Any 

                     2      3     4    5
   (79)  1 + 5x + 10x  + 10x  + 5x  + x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
BE(6)
 

                     2      3      4     5      6
   (80)  1 + 6x + 15x  + 20x  + 15x  + 6x  + O(x )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
)lisp (bye)
 
Starts dribbling to ndftip.output (2010/3/27, 18:30:3).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 45
outputGeneral 6
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 45
seqA := [0.34907,0.54890,0.74776,0.94459,1.1385,1.3285,1.5137];
 

                                                             Type: List Float
--R 
--R
--R                                                             Type: List Float
--E 2

--S 3 of 45
seqB := [0.34907 - 0.37168*%i,  _
         0.54890 - 0.35669*%i,  _
         0.74776 - 0.31175*%i,  _
         0.94459 - 0.23702*%i,  _
         1.13850 - 0.13274*%i,  _
         1.32850 + 0.00074*%i,  _
         1.51370 + 0.16298*%i];
 

                                                     Type: List Complex Float
--R 
--R
--R                                                     Type: List Complex Float
--E 3

--S 4 of 45
hseqC : PackedHermitianSequence DoubleFloat
 
 
Daly Bug
   Category, domain or package constructor PackedHermitianSequence is 
      not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is 
--R      not available.
--E 4 of 45

--S 5 of 45
hseqC := packHS [0.34907,        _
                 0.54890 + %i*1.51370,  _
                 0.74776 + %i*1.32850,  _
                 0.94459 + %i*1.13850,  _
                 0.94459 - %i*1.13850,  _
                 0.74776 - %i*1.32850,  _
                 0.54890 - %i*1.51370];
 

                                                                 Type: Symbol
--R 
--R
--R                                                                 Type: Symbol
--E 5

--S 6 of 45
seqsD : List Vector DoubleFloat;
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 45
seqsD := [vector [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _
          vector [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
          vector [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
 

                                                Type: List Vector DoubleFloat
--R 
--R
--R                                                Type: List Vector DoubleFloat
--E 7

--S 8 of 45
seqsE : List PackedHermitianSequence DoubleFloat;
 
 
Daly Bug
   Category, domain or package constructor PackedHermitianSequence is 
      not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is 
--R      not available.
--E 8

--S 9 of 45
seqsE := [pHS [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _
          pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
          pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
 

                                                            Type: List Symbol
--R 
--R
--R                                                            Type: List Symbol
--E 9

--S 10 of 45
seqsF : List Vector Complex DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 45
seqsF := [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i,   _
                  0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i,   _
                  0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i],  _
          vector [0.9172 + 0.9089*%i, 0.0644 + 0.3118*%i,   _
                  0.6037 + 0.3465*%i, 0.6430 + 0.6198*%i,   _
                  0.0428 + 0.2668*%i, 0.4815 + 0.1614*%i],  _
          vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i,   _
                  0.2060 + 0.7060*%i, 0.8630 + 0.8652*%i,   _
                  0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]];
 

                                        Type: List Vector Complex DoubleFloat
--R 
--R
--R                                        Type: List Vector Complex DoubleFloat
--E 11

--S 12 of 45
dftA := nagDFT seqA;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                                 List Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                                 List Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 12

--S 13 of 45 used to work?
dftA :: Vector Complex Float :: Matrix Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftA to Vector Complex Float for 
      value
   dftA

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftA to Vector Complex Float for 
--R      value
--R   dftA
--R
--E 13
                             -- Matrix to force display as a column,
                             -- Float to allow outputGeneral to work.

--       +         2.48361         +
--       |                         |
--       |- 0.265985 + 0.530898 %i |
--       |                         |
--       |- 0.257682 + 0.202979 %i |
--       |                         |
--       |- 0.256363 + 0.0580623 %i|
--       |                         |
--       |- 0.256363 - 0.0580623 %i|
--       |                         |
--       |- 0.257682 - 0.202979 %i |
--       |                         |
--       +- 0.265985 - 0.530898 %i +

-- test  2

--S 14 of 45 used to work?
nagInverseDFT dftA :: Vector Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                                Variable dftA
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                                Variable dftA
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 14 
--       [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137]

-- test  3
--S 15 of 45
dftB := nagDFT seqB;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                             List Complex Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                             List Complex Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 15

--S 16 of 45 used to work?
dftB :: Vector Complex Float :: Matrix Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftB to Vector Complex Float for 
      value
   dftB

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftB to Vector Complex Float for 
--R      value
--R   dftB
--R
--E 16

--       +  2.48361 - 0.471004 %i  +
--       |                         |
--       | - 0.5518 + 0.496841 %i  |
--       |                         |
--       |- 0.367113 + 0.0975621 %i|
--       |                         |
--       |- 0.287669 - 0.0586476 %i|
--       |                         |
--       |- 0.225057 - 0.174772 %i |
--       |                         |
--       |- 0.148251 - 0.308396 %i |
--       |                         |
--       + 0.0198297 - 0.564956 %i +
 
-- test  4

--S 17 of 45 used to work?
(nagInverseDFT dftB) :: Vector Complex Float :: Matrix Complex Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                                Variable dftB
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                                Variable dftB
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 17
--       +0.34907 - 0.37168 %i+
--       |                    |
--       |0.5489 - 0.35669 %i |
--       |                    |
--       |0.74776 - 0.31175 %i|
--       |                    |
--       |0.94459 - 0.23702 %i|
--       |                    |
--       |1.1385 - 0.13274 %i |
--       |                    |
--       |1.3285 + 0.00074 %i |
--       |                    |
--       +1.5137 + 0.16298 %i +

-- test  5

--S 18 of 45
hdftA := nagHermitianDFT seqA;
 
   There are no library operations named nagHermitianDFT 
      Use HyperDoc Browse or issue
                          )what op nagHermitianDFT
      to learn if there is any operation containing " nagHermitianDFT "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianDFT with argument type(s) 
                                 List Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianDFT 
--R      Use HyperDoc Browse or issue
--R                          )what op nagHermitianDFT
--R      to learn if there is any operation containing " nagHermitianDFT "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianDFT with argument type(s) 
--R                                 List Float
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 18

--S 19 of 45 used to work?
(expand hdftA) :: Vector Complex Float :: Matrix Complex Float
 
 
Daly Bug
   Cannot convert from type Polynomial Integer to Vector Complex Float 
      for value
   hdftA

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Polynomial Integer to Vector Complex Float 
--R      for value
--R   hdftA
--R
--E 19
--       +         2.48361         +
--       |                         |
--       |- 0.265985 + 0.530898 %i |
--       |                         |
--       |- 0.257682 + 0.202979 %i |
--       |                         |
--       |- 0.256363 + 0.0580623 %i|
--       |                         |
--       |- 0.256363 - 0.0580623 %i|
--       |                         |
--       |- 0.257682 - 0.202979 %i |
--       |                         |
--       +- 0.265985 - 0.530898 %i +
 
-- test  6

--S 20 of 45 used to work? 
(nagInverseDFT hdftA) :: Vector Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable hdftA
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable hdftA
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
--       [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137]

-- test  7

--S 21 of 45
dftC := nagDFT hseqC;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                                   Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                                   Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 21

--S 22 of 45 used to work?
dftC :: Vector Float
 
 
Daly Bug
   Cannot convert from type Variable dftC to Vector Float for value
   dftC

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftC to Vector Float for value
--R   dftC
--R
--E 22
-- [1.82616,1.86862,- 0.017503,0.502001,- 0.598725,- 0.0314404,- 2.62557]

-- test  8

--S 23 of 45 used to work?
(nagInverseDFT dftC) :: Vector Complex Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                                Variable dftC
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                                Variable dftC
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 23 
-- [0.34907, 0.5489 + 1.5137 %i, 0.74776 + 1.3285 %i, 0.94459 + 1.1385 %i,
--  0.94459 - 1.1385 %i, 0.74776 - 1.3285 %i, 0.5489 - 1.5137 %i]

-- test  9

--S 24 of 45 used to work?
nagHermitianInverseDFT dftC
 
   There are no library operations named nagHermitianInverseDFT 
      Use HyperDoc Browse or issue
                       )what op nagHermitianInverseDFT
      to learn if there is any operation containing " 
      nagHermitianInverseDFT " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianInverseDFT with argument type(s) 
                                Variable dftC
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianInverseDFT 
--R      Use HyperDoc Browse or issue
--R                       )what op nagHermitianInverseDFT
--R      to learn if there is any operation containing " 
--R      nagHermitianInverseDFT " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianInverseDFT with argument type(s) 
--R                                Variable dftC
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 24 
-- [0.34907000000000005, 0.54889999999999983, 0.74775999999999987,
--  0.94459000000000004, 1.1385000000000003, 1.3284999999999998,
--  1.5136999999999998]

-- test 10:

--S 25 of 45
dftsD := nagDFT seqsD;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                           List Vector DoubleFloat
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                           List Vector DoubleFloat
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 25

--S 26 of 45 used to work?
dftsD :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftsD to List Vector Complex Float
      for value
   dftsD

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftsD to List Vector Complex Float
--R      for value
--R   dftsD
--R
--E 26
 
-- [
--   [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684,
--    0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i]
--   ,

--   [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072,
--    0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i]
--   ,

--   [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011,
--    0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i]
--   ]

-- test 11:

--S 27 of 45
invdftsD := nagInverseDFT dftsD ;
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable dftsD
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable dftsD
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 27

--S 28 of 45 used to work?
invdftsD :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable invdftsD to List Vector Complex 
      Float for value
   invdftsD

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable invdftsD to List Vector Complex 
--R      Float for value
--R   invdftsD
--R
--E 28 
-- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424],
--  [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723],
--  [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]]

-- test 12:
--S 29 of 45
dftsE := nagDFT seqsE;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                                 List Symbol
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                                 List Symbol
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 29

--S 30 of 45 used to work?
dftsE :: List Vector Float
 
 
Daly Bug
   Cannot convert from type Variable dftsE to List Vector Float for 
      value
   dftsE

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftsE to List Vector Float for 
--R      value
--R   dftsE
--R
--E 30
-- [[1.0788,0.662291,- 0.239146,- 0.578284,0.459192,- 0.438816],
--  [0.857321,1.22614,0.353348,- 0.222169,0.341327,- 1.22908],
--  [1.18245,0.262509,0.674406,0.552278,0.0539906,- 0.478963]]

-- test 13:
--S 31 of 45
invdftsE := nagInverseDFT dftsE;
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable dftsE
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable dftsE
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 31

--S 32 of 45 used to work?
invdftsE :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable invdftsE to List Vector Complex 
      Float for value
   invdftsE

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable invdftsE to List Vector Complex 
--R      Float for value
--R   invdftsE
--R
--E 32
-- [
--   [0.3854, 0.6772 + 0.1424 %i, 0.1138 + 0.6362 %i, 0.6751,
--    0.1138 - 0.6362 %i, 0.6772 - 0.1424 %i]
--   ,

--   [0.5417, 0.2983 + 0.8723 %i, 0.1181 + 0.8638 %i, 0.7255,
--    0.1181 - 0.8638 %i, 0.2983 - 0.8723 %i]
--   ,

--   [0.9172, 0.0644 + 0.4815 %i, 0.6037 + 0.0428 %i, 0.643,
--    0.6037 - 0.0428 %i, 0.0644 - 0.4815 %i]
--   ]

-- test 14:
--S 33 of 45
hdftsD := nagHermitianDFT seqsD;
 
   There are no library operations named nagHermitianDFT 
      Use HyperDoc Browse or issue
                          )what op nagHermitianDFT
      to learn if there is any operation containing " nagHermitianDFT "
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianDFT with argument type(s) 
                           List Vector DoubleFloat
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianDFT 
--R      Use HyperDoc Browse or issue
--R                          )what op nagHermitianDFT
--R      to learn if there is any operation containing " nagHermitianDFT "
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianDFT with argument type(s) 
--R                           List Vector DoubleFloat
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 33

--S 34 of 45 used to work?
map(expand,hdftsD) :: List Vector Complex Float
 
   There are 74 exposed and 8 unexposed library operations named map 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op map
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named map 
      with argument type(s) 
                               Variable expand
                               Variable hdftsD
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 74 exposed and 8 unexposed library operations named map 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op map
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named map 
--R      with argument type(s) 
--R                               Variable expand
--R                               Variable hdftsD
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 34 
-- [
--   [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684,
--    0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i]
--   ,

--   [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072,
--    0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i]
--   ,

--   [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011,
--    0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i]
--   ]

-- test 15:

--S 35 of 45 used to work?
(nagInverseDFT hdftsD) :: List Vector Float
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable hdftsD
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable hdftsD
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 35 
-- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424],
--  [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723],
--  [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]]

-- test 16:
--S 36 of 45
dftsF := nagDFT seqsF;
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                       List Vector Complex DoubleFloat
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                       List Vector Complex DoubleFloat
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 36

--S 37 of 45 used to work?
dftsF :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable dftsF to List Vector Complex Float
      for value
   dftsF

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable dftsF to List Vector Complex Float
--R      for value
--R   dftsF
--R
--E 37
-- [
--   [1.07373 + 1.39609 %i, - 0.570647 - 0.0409019 %i, 0.173259 - 0.295822 %i,
--    - 0.146684 - 0.152072 %i, 0.0518489 + 0.451732 %i,
--    0.362522 - 0.0321337 %i]
--   ,

--   [1.12374 + 1.06765 %i, 0.172759 + 0.0385858 %i, 0.418548 + 0.748083 %i,
--    0.153011 + 0.17522 %i, 0.368555 + 0.0565331 %i, 0.0100542 + 0.140268 %i]
--   ,

--   [0.909985 + 1.76167 %i, - 0.305418 + 0.0624335 %i,
--    0.407884 - 0.0694786 %i, - 0.078547 + 0.0725049 %i,
--    - 0.119334 + 0.128511 %i, - 0.531409 - 0.433531 %i]
--   ]

-- test 17:
--S 38 of 45
invdftsF := nagInverseDFT dftsF ;
 
   There are no library operations named nagInverseDFT 
      Use HyperDoc Browse or issue
                           )what op nagInverseDFT
      to learn if there is any operation containing " nagInverseDFT " 
      in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagInverseDFT with argument type(s) 
                               Variable dftsF
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagInverseDFT 
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT " 
--R      in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagInverseDFT with argument type(s) 
--R                               Variable dftsF
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 38

--S 39 of 45
invdftsF :: List Vector Complex Float
 
 
Daly Bug
   Cannot convert from type Variable invdftsF to List Vector Complex 
      Float for value
   invdftsF

--R 
--R 
--RDaly Bug
--R   Cannot convert from type Variable invdftsF to List Vector Complex 
--R      Float for value
--R   invdftsF
--R
--E 39 
-- [
--   [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
--    0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
--   ,

--   [0.9172 + 0.9089 %i, 0.0644 + 0.3118 %i, 0.6037 + 0.3465 %i,
--    0.643 + 0.6198 %i, 0.0428 + 0.2668 %i, 0.4815 + 0.1614 %i]
--   ,

--   [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.206 + 0.706 %i,
--    0.863 + 0.8652 %i, 0.6967 + 0.919 %i, 0.2792 + 0.3355 %i]
--   ]

-- test 18:
--S 40 of 45 used to work?
nagHermitianInverseDFT dftsE
 
   There are no library operations named nagHermitianInverseDFT 
      Use HyperDoc Browse or issue
                       )what op nagHermitianInverseDFT
      to learn if there is any operation containing " 
      nagHermitianInverseDFT " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagHermitianInverseDFT with argument type(s) 
                               Variable dftsE
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagHermitianInverseDFT 
--R      Use HyperDoc Browse or issue
--R                       )what op nagHermitianInverseDFT
--R      to learn if there is any operation containing " 
--R      nagHermitianInverseDFT " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagHermitianInverseDFT with argument type(s) 
--R                               Variable dftsE
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 40 
-- [
--   [0.38540000000000013, 0.67720000000000025, 0.11380000000000001,
--    0.67510000000000014, 0.63620000000000021, 0.14240000000000003]
--   ,

--   [0.54170000000000018, 0.29830000000000012, 0.1181, 0.72550000000000014,
--    0.86380000000000023, 0.87230000000000019]
--   ,

--   [0.91720000000000035, 0.064399999999999999, 0.60370000000000024,
--    0.64300000000000013, 0.042799999999999991, 0.48150000000000015]
--   ]

-- error tests:

-- test 19:
--S 41 of 45
nagDFT [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i,   _
                0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i,   _
                0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i],  _
        vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i,   _
                0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]]
 

   (10)
   SUB
      nagDFT
  ,
      [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
       0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
  ,
      [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.6967 + 0.919 %i,
       0.2792 + 0.3355 %i]
                                                                 Type: Symbol
--R 
--R
--R   (10)
--R   SUB
--R      nagDFT
--R  ,
--R      [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
--R       0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
--R  ,
--R      [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.6967 + 0.919 %i,
--R       0.2792 + 0.3355 %i]
--R                                                                 Type: Symbol
--E 41

-- test 20:
--S 42 of 45
nagHermitianDFT [vector [0.3854, 0.6751, 0.6362, 0.1424], _
                 vector [0.5417, 0.7255, 0.8638, 0.8723], _
                 vector [0.9172, 0.0428, 0.4815]]
 

   (11)
   SUB
      nagHermitianDFT
  ,
      [0.3854,0.6751,0.6362,0.1424]
  ,
      [0.5417,0.7255,0.8638,0.8723]
  ,
      [0.9172,0.0428,0.4815]
                                                                 Type: Symbol
--R 
--R
--R   (11)
--R   SUB
--R      nagHermitianDFT
--R  ,
--R      [0.3854,0.6751,0.6362,0.1424]
--R  ,
--R      [0.5417,0.7255,0.8638,0.8723]
--R  ,
--R      [0.9172,0.0428,0.4815]
--R                                                                 Type: Symbol
--E 42

-- test 21:
--S 43 of 45 used to work?
badSeqs : List PackedHermitianSequence DoubleFloat
 
 
Daly Bug
   Category, domain or package constructor PackedHermitianSequence is 
      not available.
--R 
--R 
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is 
--R      not available.
--E 43
--badSeqs := [pHS [0.3854, 0.1138, 0.6751, 0.6362, 0.1424],         _
--            pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
--            pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
-- 
--
--                                                            Type: List Symbol

--S 44 of 45
nagDFT badSeqs
 
   There are no library operations named nagDFT 
      Use HyperDoc Browse or issue
                               )what op nagDFT
      to learn if there is any operation containing " nagDFT " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      nagDFT with argument type(s) 
                              Variable badSeqs
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named nagDFT 
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      nagDFT with argument type(s) 
--R                              Variable badSeqs
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 44

--S 45 of 45
outputGeneral()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 45
)spool 
 
Starts dribbling to negfloats.output (2010/3/27, 18:30:4).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
truncate(-9.6571)
 

   (1)  - 9.0
                                                                  Type: Float
--R 
--R
--R   (1)  - 9.0
--R                                                                  Type: Float
--E 1

--S 2 of 3
fractionPart(-3.432)
 

   (2)  - 0.432
                                                                  Type: Float
--R 
--R
--R   (2)  - 0.432
--R                                                                  Type: Float
--E 2

--S 3 of 3
round(-9.6571)
 

   (3)  - 10.0
                                                                  Type: Float
--R 
--R
--R   (3)  - 10.0
--R                                                                  Type: Float
--E 3
)spool 
 
Starts dribbling to Factored.output (2010/3/27, 18:42:0).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 38
g := factor(4312)
 

         3 2
   (1)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R         3 2
--R   (1)  2 7 11
--R                                                       Type: Factored Integer
--E 1

--S 2 of 38
unit(g)
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 38
numberOfFactors(g)
 

   (3)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  3
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 38
[nthFactor(g,i) for i in 1..numberOfFactors(g)]
 

   (4)  [2,7,11]
                                                           Type: List Integer
--R 
--R
--R   (4)  [2,7,11]
--R                                                           Type: List Integer
--E 4

--S 5 of 38
[nthExponent(g,i) for i in 1..numberOfFactors(g)] 
 

   (5)  [3,2,1]
                                                           Type: List Integer
--R 
--R
--R   (5)  [3,2,1]
--R                                                           Type: List Integer
--E 5

--S 6 of 38
[nthFlag(g,i) for i in 1..numberOfFactors(g)] 
 

   (6)  ["prime","prime","prime"]
                               Type: List Union("nil","sqfr","irred","prime")
--R 
--R
--R   (6)  ["prime","prime","prime"]
--R                               Type: List Union("nil","sqfr","irred","prime")
--E 6

--S 7 of 38
factorList(g) 
 

   (7)
   [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2],
    [flg= "prime",fctr= 11,xpnt= 1]]
Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--R 
--R
--R   (7)
--R   [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2],
--R    [flg= "prime",fctr= 11,xpnt= 1]]
--RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)
--E 7

--S 8 of 38
factors(g) 
 

   (8)
   [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]]
                         Type: List Record(factor: Integer,exponent: Integer)
--R 
--R
--R   (8)
--R   [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]]
--R                         Type: List Record(factor: Integer,exponent: Integer)
--E 8

--S 9 of 38
first(%).factor 
 

   (9)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  2
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 38
g := factor(4312) 
 

          3 2
   (10)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R          3 2
--R   (10)  2 7 11
--R                                                       Type: Factored Integer
--E 10

--S 11 of 38
expand(g)
 

   (11)  4312
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  4312
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 38
reduce(*,[t.factor for t in factors(g)]) 
 

   (12)  154
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  154
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 38
g := factor(4312) 
 

          3 2
   (13)  2 7 11
                                                       Type: Factored Integer
--R 
--R
--R          3 2
--R   (13)  2 7 11
--R                                                       Type: Factored Integer
--E 13

--S 14 of 38
f := factor(246960) 
 

          4 2   3
   (14)  2 3 5 7
                                                       Type: Factored Integer
--R 
--R
--R          4 2   3
--R   (14)  2 3 5 7
--R                                                       Type: Factored Integer
--E 14

--S 15 of 38
f * g 
 

          7 2   5
   (15)  2 3 5 7 11
                                                       Type: Factored Integer
--R 
--R
--R          7 2   5
--R   (15)  2 3 5 7 11
--R                                                       Type: Factored Integer
--E 15

--S 16 of 38
f**500 
 

          2000 1000 500 1500
   (16)  2    3    5   7
                                                       Type: Factored Integer
--R 
--R
--R          2000 1000 500 1500
--R   (16)  2    3    5   7
--R                                                       Type: Factored Integer
--E 16

--S 17 of 38
gcd(f,g) 
 

          3 2
   (17)  2 7
                                                       Type: Factored Integer
--R 
--R
--R          3 2
--R   (17)  2 7
--R                                                       Type: Factored Integer
--E 17

--S 18 of 38
lcm(f,g) 
 

          4 2   3
   (18)  2 3 5 7 11
                                                       Type: Factored Integer
--R 
--R
--R          4 2   3
--R   (18)  2 3 5 7 11
--R                                                       Type: Factored Integer
--E 18

--S 19 of 38
f + g 
 

          3 2
   (19)  2 7 641
                                                       Type: Factored Integer
--R 
--R
--R          3 2
--R   (19)  2 7 641
--R                                                       Type: Factored Integer
--E 19

--S 20 of 38
f - g 
 

          3 2
   (20)  2 7 619
                                                       Type: Factored Integer
--R 
--R
--R          3 2
--R   (20)  2 7 619
--R                                                       Type: Factored Integer
--E 20

--S 21 of 38
zero?(factor(0))
 

   (21)  true
                                                                Type: Boolean
--R 
--R
--R   (21)  true
--R                                                                Type: Boolean
--E 21

--S 22 of 38
zero?(g) 
 

   (22)  false
                                                                Type: Boolean
--R 
--R
--R   (22)  false
--R                                                                Type: Boolean
--E 22

--S 23 of 38
one?(factor(1))
 

   (23)  true
                                                                Type: Boolean
--R 
--R
--R   (23)  true
--R                                                                Type: Boolean
--E 23

--S 24 of 38
one?(f) 
 

   (24)  false
                                                                Type: Boolean
--R 
--R
--R   (24)  false
--R                                                                Type: Boolean
--E 24

--S 25 of 38
0$Factored(Integer)
 

   (25)  0
                                                       Type: Factored Integer
--R 
--R
--R   (25)  0
--R                                                       Type: Factored Integer
--E 25

--S 26 of 38
1$Factored(Integer)
 

   (26)  1
                                                       Type: Factored Integer
--R 
--R
--R   (26)  1
--R                                                       Type: Factored Integer
--E 26

--S 27 of 38
nilFactor(24,2) 
 

           2
   (27)  24
                                                       Type: Factored Integer
--R 
--R
--R           2
--R   (27)  24
--R                                                       Type: Factored Integer
--E 27

--S 28 of 38
nthFlag(%,1) 
 

   (28)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (28)  "nil"
--R                                                       Type: Union("nil",...)
--E 28

--S 29 of 38
sqfrFactor(30,2)
 

           2
   (29)  30
                                                       Type: Factored Integer
--R 
--R
--R           2
--R   (29)  30
--R                                                       Type: Factored Integer
--E 29

--S 30 of 38
irreducibleFactor(13,10) 
 

           10
   (30)  13
                                                       Type: Factored Integer
--R 
--R
--R           10
--R   (30)  13
--R                                                       Type: Factored Integer
--E 30

--S 31 of 38
primeFactor(11,5) 
 

           5
   (31)  11
                                                       Type: Factored Integer
--R 
--R
--R           5
--R   (31)  11
--R                                                       Type: Factored Integer
--E 31

--S 32 of 38
h := factor(-720) 
 

            4 2
   (32)  - 2 3 5
                                                       Type: Factored Integer
--R 
--R
--R            4 2
--R   (32)  - 2 3 5
--R                                                       Type: Factored Integer
--E 32

--S 33 of 38
h - makeFR(unit(h),factorList(h))
 

   (33)  0
                                                       Type: Factored Integer
--R 
--R
--R   (33)  0
--R                                                       Type: Factored Integer
--E 33

--S 34 of 38
p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63 
 

            2            2      2                  2
   (34)  (4x  - 12x + 9)y  + (4x  - 12x + 9)y + 28x  - 84x + 63
                                                     Type: Polynomial Integer
--R 
--R
--R            2            2      2                  2
--R   (34)  (4x  - 12x + 9)y  + (4x  - 12x + 9)y + 28x  - 84x + 63
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 38
fp := factor(p) 
 

                 2  2
   (35)  (2x - 3) (y  + y + 7)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                 2  2
--R   (35)  (2x - 3) (y  + y + 7)
--R                                            Type: Factored Polynomial Integer
--E 35

--S 36 of 38
D(p,x) 
 

                   2
   (36)  (8x - 12)y  + (8x - 12)y + 56x - 84
                                                     Type: Polynomial Integer
--R 
--R
--R                   2
--R   (36)  (8x - 12)y  + (8x - 12)y + 56x - 84
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 38
D(fp,x) 
 

                    2
   (37)  4(2x - 3)(y  + y + 7)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                    2
--R   (37)  4(2x - 3)(y  + y + 7)
--R                                            Type: Factored Polynomial Integer
--E 37

--S 38 of 38
numberOfFactors(%) 
 

   (38)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (38)  3
--R                                                        Type: PositiveInteger
--E 38
)spool
 
Starts dribbling to fr2.output (2010/3/27, 18:26:21).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 6
double(x) == x + x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 6
f := factor(720)
 

         4 2
   (2)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         4 2
--R   (2)  2 3 5
--R                                                       Type: Factored Integer
--E 2

--S 3 of 6
map(double,f)
 
   Compiling function double with type Integer -> Integer 

           4 2
   (3)  2 4 6 10
                                                       Type: Factored Integer
--R 
--R   Compiling function double with type Integer -> Integer 
--R
--R           4 2
--R   (3)  2 4 6 10
--R                                                       Type: Factored Integer
--E 3

--S 4 of 6
makePoly(b) == x + b
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 6
g := map(makePoly,f)
 
   Compiling function makePoly with type Integer -> Polynomial Integer 

                      4       2
   (5)  (x + 1)(x + 2) (x + 3) (x + 5)
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function makePoly with type Integer -> Polynomial Integer 
--R
--R                      4       2
--R   (5)  (x + 1)(x + 2) (x + 3) (x + 5)
--R                                            Type: Factored Polynomial Integer
--E 5

--S 6 of 6
nthFlag(g,1)
 

   (6)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (6)  "nil"
--R                                                       Type: Union("nil",...)
--E 6
)spool 
 
Starts dribbling to fparfrc.output (2010/3/27, 18:26:19).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 16
Fx := FRAC UP(x, FRAC INT)
 

   (1)  Fraction UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 16
f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2)
 

                     36
   (2)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (2)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 2

--S 3 of 16
g := fullPartialFraction f
 

          4       4        --+      - 3%A - 6
   (3)  ----- - ----- +    >        ---------
        x - 2   x + 1      --+              2
                          2         (x - %A)
                        %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          4       4        --+      - 3%A - 6
--R   (3)  ----- - ----- +    >        ---------
--R        x - 2   x + 1      --+              2
--R                          2         (x - %A)
--R                        %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 3

--S 4 of 16
g :: Fx
 

                     36
   (4)  ----------------------------
         5     4     3     2
        x  - 2x  - 2x  + 4x  + x - 2
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                     36
--R   (4)  ----------------------------
--R         5     4     3     2
--R        x  - 2x  - 2x  + 4x  + x - 2
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 4

--S 5 of 16
g5 := D(g, 5)
 

             480        480        --+      2160%A + 4320
   (5)  - -------- + -------- +    >        -------------
                 6          6      --+                7
          (x - 2)    (x + 1)      2           (x - %A)
                                %A  - 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R             480        480        --+      2160%A + 4320
--R   (5)  - -------- + -------- +    >        -------------
--R                 6          6      --+                7
--R          (x - 2)    (x + 1)      2           (x - %A)
--R                                %A  - 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 16
f5 := D(f, 5)
 

   (6)
                10           9            8            7            6
       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
     + 
                5            4            3           2
       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
  /
        20      19      18      17       16       15       14        13
       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
     + 
            12        11        10        9        8        7        6        5
       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
     + 
           4        3       2
       276x  - 1184x  + 208x  + 192x - 64
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (6)
--R                10           9            8            7            6
--R       - 544320x   + 4354560x  - 14696640x  + 28615680x  - 40085280x
--R     + 
--R                5            4            3           2
--R       46656000x  - 39411360x  + 18247680x  - 5870880x  + 3317760x + 246240
--R  /
--R        20      19      18      17       16       15       14        13
--R       x   - 12x   + 53x   - 76x   - 159x   + 676x   - 391x   - 1596x
--R     + 
--R            12        11        10        9        8        7        6        5
--R       2527x   + 1148x   - 4977x   + 1372x  + 4907x  - 3444x  - 2381x  + 2924x
--R     + 
--R           4        3       2
--R       276x  - 1184x  + 208x  + 192x - 64
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 6

--S 7 of 16
g5::Fx - f5
 

   (7)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (7)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 16
f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)
 

                       6    5
                      x  - x
   (8)  -----------------------------------
         7     6     5     3     2
        x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                       6    5
--R                      x  - x
--R   (8)  -----------------------------------
--R         7     6     5     3     2
--R        x  - 4x  + 3x  + 9x  - 6x  - 4x - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 16
g := fullPartialFraction f
 

   (9)
      1952       464        32                          179       135
      ----       ---        --                       - ---- %A + ----
      2401       343        49            --+          2401      2401
     ------ + -------- + -------- +       >          ----------------
      x - 2          2          3         --+             x - %A
              (x - 2)    (x - 2)      2
                                    %A  + %A + 1= 0
   + 
                       37        20
                      ---- %A + ----
           --+        1029      1029
           >          --------------
           --+                   2
       2                 (x - %A)
     %A  + %A + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (9)
--R      1952       464        32                          179       135
--R      ----       ---        --                       - ---- %A + ----
--R      2401       343        49            --+          2401      2401
--R     ------ + -------- + -------- +       >          ----------------
--R      x - 2          2          3         --+             x - %A
--R              (x - 2)    (x - 2)      2
--R                                    %A  + %A + 1= 0
--R   + 
--R                       37        20
--R                      ---- %A + ----
--R           --+        1029      1029
--R           >          --------------
--R           --+                   2
--R       2                 (x - %A)
--R     %A  + %A + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 9

--S 10 of 16
g :: Fx - f
 

   (10)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (10)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 10

--S 11 of 16
f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8)
 

             7     5      3
           2x  - 7x  + 26x  + 8x
   (11)  ------------------------
          8     6     4     2
         x  - 5x  + 6x  + 4x  - 8
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             7     5      3
--R           2x  - 7x  + 26x  + 8x
--R   (11)  ------------------------
--R          8     6     4     2
--R         x  - 5x  + 6x  + 4x  - 8
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 11

--S 12 of 16
g := fullPartialFraction f
 

                        1                                            1
                        -                                            -
            --+         2        --+          1          --+         2
   (12)     >        ------ +    >        --------- +    >        ------
            --+      x - %A      --+              3      --+      x - %A
           2                    2         (x - %A)      2
         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R                        1                                            1
--R                        -                                            -
--R            --+         2        --+          1          --+         2
--R   (12)     >        ------ +    >        --------- +    >        ------
--R            --+      x - %A      --+              3      --+      x - %A
--R           2                    2         (x - %A)      2
--R         %A  - 2= 0           %A  - 2= 0              %A  + 1= 0
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 12

--S 13 of 16
g :: Fx - f
 

   (13)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (13)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 13

--S 14 of 16
f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x**15 + 30*x**14 + 36*x**13 + 40*x**12 + 47*x**11 + 46*x**10 + 49*x**9 + 43*x**8 + 38*x**7 + 32*x**6 + 23*x**5 + 19*x**4 + 10*x**3 + 7*x**2 + 2*x + 1)
 

   (14)
      3
     x
  /
        21     20     19     18      17      16      15      14      13      12
       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
     + 
          11      10      9      8      7      6      5      4      3     2
       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
     + 
       1
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (14)
--R      3
--R     x
--R  /
--R        21     20     19     18      17      16      15      14      13      12
--R       x   + 2x   + 4x   + 7x   + 10x   + 17x   + 22x   + 30x   + 36x   + 40x
--R     + 
--R          11      10      9      8      7      6      5      4      3     2
--R       47x   + 46x   + 49x  + 43x  + 38x  + 32x  + 23x  + 19x  + 10x  + 7x  + 2x
--R     + 
--R       1
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 14

--S 15 of 16
g := fullPartialFraction f
 

   (15)
                  1                        1      19
                  - %A                     - %A - --
        --+       2             --+        9      27
        >        ------ +       >          ---------
        --+      x - %A         --+          x - %A
       2                    2
     %A  + 1= 0           %A  + %A + 1= 0
   + 
                       1       1
                      -- %A - --
           --+        27      27
           >          ----------
           --+                 2
       2               (x - %A)
     %A  + %A + 1= 0
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
               96556567040   4   420961732891   3    59101056149   2
            - ------------ %A  + ------------ %A  - ------------ %A
              912390759099       912390759099       912390759099
          + 
              373545875923      529673492498
            - ------------ %A + ------------
              912390759099      912390759099
       /
          x - %A
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
           5580868   4    2024443   3    4321919   2    84614        5070620
        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
          94070601       94070601       94070601       1542141      94070601
        --------------------------------------------------------------------
                                              2
                                      (x - %A)
   + 
     SIGMA
          5     2
        %A  + %A  + 1= 0
    ,
         1610957   4    2763014   3    2016775   2    266953        4529359
        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
        94070601       94070601       94070601       94070601      94070601
        -------------------------------------------------------------------
                                             3
                                     (x - %A)
Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (15)
--R                  1                        1      19
--R                  - %A                     - %A - --
--R        --+       2             --+        9      27
--R        >        ------ +       >          ---------
--R        --+      x - %A         --+          x - %A
--R       2                    2
--R     %A  + 1= 0           %A  + %A + 1= 0
--R   + 
--R                       1       1
--R                      -- %A - --
--R           --+        27      27
--R           >          ----------
--R           --+                 2
--R       2               (x - %A)
--R     %A  + %A + 1= 0
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R               96556567040   4   420961732891   3    59101056149   2
--R            - ------------ %A  + ------------ %A  - ------------ %A
--R              912390759099       912390759099       912390759099
--R          + 
--R              373545875923      529673492498
--R            - ------------ %A + ------------
--R              912390759099      912390759099
--R       /
--R          x - %A
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R           5580868   4    2024443   3    4321919   2    84614        5070620
--R        - -------- %A  - -------- %A  + -------- %A  - ------- %A - --------
--R          94070601       94070601       94070601       1542141      94070601
--R        --------------------------------------------------------------------
--R                                              2
--R                                      (x - %A)
--R   + 
--R     SIGMA
--R          5     2
--R        %A  + %A  + 1= 0
--R    ,
--R         1610957   4    2763014   3    2016775   2    266953        4529359
--R        -------- %A  + -------- %A  - -------- %A  + -------- %A + --------
--R        94070601       94070601       94070601       94070601      94070601
--R        -------------------------------------------------------------------
--R                                             3
--R                                     (x - %A)
--RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 15

--S 16 of 16
g :: Fx - f
 

   (16)  0
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (16)  0
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 16
)spool 
 
Starts dribbling to intaf.output (2010/3/27, 18:26:57).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 20
x**2 / sqrt(a + b*x**3)
 

              2
             x
   (1)  -----------
         +--------+
         |   3
        \|b x  + a
                                                     Type: Expression Integer
--R 
--R
--R              2
--R             x
--R   (1)  -----------
--R         +--------+
--R         |   3
--R        \|b x  + a
--R                                                     Type: Expression Integer
--E 1

--S 2 of 20
integrate(%,x)
 

          +--------+
          |   3
        2\|b x  + a
   (2)  ------------
             3b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          +--------+
--R          |   3
--R        2\|b x  + a
--R   (2)  ------------
--R             3b
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 20
x**3 * sqrt(a + b*x**4)
 

           +--------+
         3 |   4
   (3)  x \|b x  + a
                                                     Type: Expression Integer
--R 
--R
--R           +--------+
--R         3 |   4
--R   (3)  x \|b x  + a
--R                                                     Type: Expression Integer
--E 3

--S 4 of 20
integrate(%,x)
 

                   +--------+
            4      |   4
        (b x  + a)\|b x  + a
   (4)  ---------------------
                  6b
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   +--------+
--R            4      |   4
--R        (b x  + a)\|b x  + a
--R   (4)  ---------------------
--R                  6b
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 20
1/sqrt(1+x**3)
 

            1
   (5)  ---------
         +------+
         | 3
        \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R            1
--R   (5)  ---------
--R         +------+
--R         | 3
--R        \|x  + 1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 20
integrate(%,x)
 

           x
         ++       1
   (6)   |   ---------- d%N
        ++    +-------+
              |  3
             \|%N  + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--R   (6)   |   ---------- d%N
--R        ++    +-------+
--R              |  3
--R             \|%N  + 1
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 20
sqrt(1+x**3)
 

         +------+
         | 3
   (7)  \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R         +------+
--R         | 3
--R   (7)  \|x  + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 20
integrate(%,x)
 

           x  +-------+
         ++   |  3
   (8)   |   \|%N  + 1 d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x  +-------+
--R         ++   |  3
--R   (8)   |   \|%N  + 1 d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 20
1/(x * sqrt(1 + x**3))
 

             1
   (9)  ----------
          +------+
          | 3
        x\|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R             1
--R   (9)  ----------
--R          +------+
--R          | 3
--R        x\|x  + 1
--R                                                     Type: Expression Integer
--E 9

--S 10 of 20
integrate(%,x)
 

                +------+             +------+
                | 3                  | 3
         - log(\|x  + 1  + 1) + log(\|x  + 1  - 1)
   (10)  -----------------------------------------
                             3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +------+             +------+
--R                | 3                  | 3
--R         - log(\|x  + 1  + 1) + log(\|x  + 1  - 1)
--R   (10)  -----------------------------------------
--R                             3
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 20
x**3/sqrt(1+x**8)
 

              3
             x
   (11)  ---------
          +------+
          | 8
         \|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R              3
--R             x
--R   (11)  ---------
--R          +------+
--R          | 8
--R         \|x  + 1
--R                                                     Type: Expression Integer
--E 11

--S 12 of 20
integrate(%,x)
 

                +------+
                | 8         4
           log(\|x  + 1  - x )
   (12)  - -------------------
                    4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +------+
--R                | 8         4
--R           log(\|x  + 1  - x )
--R   (12)  - -------------------
--R                    4
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 20
x/sqrt(1-x**4)
 

              x
   (13)  -----------
          +--------+
          |   4
         \|- x  + 1
                                                     Type: Expression Integer
--R 
--R
--R              x
--R   (13)  -----------
--R          +--------+
--R          |   4
--R         \|- x  + 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 20
integrate(%,x)
 

                 +--------+
                 |   4
                \|- x  + 1  - 1
   (14)  - atan(---------------)
                        2
                       x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +--------+
--R                 |   4
--R                \|- x  + 1  - 1
--R   (14)  - atan(---------------)
--R                        2
--R                       x
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 20
(x+1)/((x-2) * sqrt(1 + x**3))
 

               x + 1
   (15)  ----------------
                 +------+
                 | 3
         (x - 2)\|x  + 1
                                                     Type: Expression Integer
--R 
--R
--R               x + 1
--R   (15)  ----------------
--R                 +------+
--R                 | 3
--R         (x - 2)\|x  + 1
--R                                                     Type: Expression Integer
--E 15

--S 16 of 20
integrate(%,x)
 

                        +------+
                        | 3         3      2
               (6x + 6)\|x  + 1  + x  + 12x  - 6x + 10
           log(---------------------------------------)
                           3     2
                          x  - 6x  + 12x - 8
   (16)  - --------------------------------------------
                                 3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        +------+
--R                        | 3         3      2
--R               (6x + 6)\|x  + 1  + x  + 12x  - 6x + 10
--R           log(---------------------------------------)
--R                           3     2
--R                          x  - 6x  + 12x - 8
--R   (16)  - --------------------------------------------
--R                                 3
--R                                          Type: Union(Expression Integer,...)
--E 16

--S 17 of 20
x**6/sqrt((x**7+1)*(x**7+2))
 

                 6
                x
   (17)  ----------------
          +-------------+
          | 14     7
         \|x   + 3x  + 2
                                                     Type: Expression Integer
--R 
--R
--R                 6
--R                x
--R   (17)  ----------------
--R          +-------------+
--R          | 14     7
--R         \|x   + 3x  + 2
--R                                                     Type: Expression Integer
--E 17

--S 18 of 20
integrate(%,x)
 

                 +-------------+
                 | 14     7          7
           log(2\|x   + 3x  + 2  - 2x  - 3)
   (18)  - --------------------------------
                           7
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-------------+
--R                 | 14     7          7
--R           log(2\|x   + 3x  + 2  - 2x  - 3)
--R   (18)  - --------------------------------
--R                           7
--R                                          Type: Union(Expression Integer,...)
--E 18

--S 19 of 20
sqrt(1 + sqrt(1 + x))
 

          +------------+
          | +-----+
   (19)  \|\|x + 1  + 1
                                                     Type: Expression Integer
--R 
--R
--R          +------------+
--R          | +-----+
--R   (19)  \|\|x + 1  + 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 20
integrate(%,x)
 

                               +------------+
            +-----+            | +-----+
         (4\|x + 1  + 12x + 4)\|\|x + 1  + 1
   (20)  ------------------------------------
                          15
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +------------+
--R            +-----+            | +-----+
--R         (4\|x + 1  + 12x + 4)\|\|x + 1  + 1
--R   (20)  ------------------------------------
--R                          15
--R                                          Type: Union(Expression Integer,...)
--E 20
)spool 
 
Starts dribbling to sincosex.output (2010/3/27, 18:40:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 1
sinCosExpand := rule
  sin(-x)    == - sin(x)
  cos(-x)    == cos(x)
  sin(x + y) == sin(x) * cos(y) + sin(y) * cos(x)
  cos(x + y) == cos(x) * cos(y) - sin(x) * sin(y)
  sin((n | integer? n and n > 1) * x) ==_
       sin(x) * cos((n-1)*x) + sin((n-1)*x) * cos(x)
  cos((n | integer? n and n > 1) * x) ==_
       cos(x) * cos((n-1)*x) - sin(x) * sin((n-1)*x)
 

   (1)
   {- %B sin(x) == - %B sin(x), cos(x) == cos(x),
    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (1)
--R   {- %B sin(x) == - %B sin(x), cos(x) == cos(x),
--R    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
--R    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
--R    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 1
)spool 
 
Starts dribbling to segbind.output (2010/3/27, 18:38:53).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
x = a..b
 

   (1)  x= a..b
                                                  Type: SegmentBinding Symbol
--R 
--R
--R   (1)  x= a..b
--R                                                  Type: SegmentBinding Symbol
--E 1

--S 2 of 6
sum(i**2, i = 0..n)
 

          3     2
        2n  + 3n  + n
   (2)  -------------
              6
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          3     2
--R        2n  + 3n  + n
--R   (2)  -------------
--R              6
--R                                            Type: Fraction Polynomial Integer
--E 2

--S 3 of 6
draw(x**2, x = -2..2)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (3)  TwoDimensionalViewport: "x*x"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (3)  TwoDimensionalViewport: "x*x"
--R                                                 Type: TwoDimensionalViewport
--E 3

--S 4 of 6
sb := y = 1/2..3/2
 

            1    3
   (4)  y= (-)..(-)
            2    2
                                        Type: SegmentBinding Fraction Integer
--R 
--R
--R            1    3
--R   (4)  y= (-)..(-)
--R            2    2
--R                                        Type: SegmentBinding Fraction Integer
--E 4

--S 5 of 6
variable(sb)
 

   (5)  y
                                                                 Type: Symbol
--R 
--R
--R   (5)  y
--R                                                                 Type: Symbol
--E 5

--S 6 of 6
segment(sb)
 

         1    3
   (6)  (-)..(-)
         2    2
                                               Type: Segment Fraction Integer
--R 
--R
--R         1    3
--R   (6)  (-)..(-)
--R         2    2
--R                                               Type: Segment Fraction Integer
--E 6
)spool 
 
Starts dribbling to alist.output (2010/3/27, 18:23:2).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 10
Data := Record(monthsOld : Integer, gender : String)
 

   (1)  Record(monthsOld: Integer,gender: String)
                                                                 Type: Domain
--R 
--R
--R   (1)  Record(monthsOld: Integer,gender: String)
--R                                                                 Type: Domain
--E 1

--S 2 of 10
al : AssociationList(String,Data)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 10
al := table()
 

   (3)  table()
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (3)  table()
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 3

--S 4 of 10
al."bob" := [407,"male"]$Data
 

   (4)  [monthsOld= 407,gender= "male"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (4)  [monthsOld= 407,gender= "male"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 4

--S 5 of 10
al."judith" := [366,"female"]$Data
 

   (5)  [monthsOld= 366,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (5)  [monthsOld= 366,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 5

--S 6 of 10
al."katie" := [24,"female"]$Data
 

   (6)  [monthsOld= 24,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (6)  [monthsOld= 24,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 6

--S 7 of 10
al."smokie" := [200,"female"]$Data
 

   (7)  [monthsOld= 200,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (7)  [monthsOld= 200,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 7

--S 8 of 10
al
 

   (8)
   table
      "smokie"= [monthsOld= 200,gender= "female"]
  ,
      "katie"= [monthsOld= 24,gender= "female"]
  ,
      "judith"= [monthsOld= 366,gender= "female"]
  ,
      "bob"= [monthsOld= 407,gender= "male"]
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (8)
--R   table
--R      "smokie"= [monthsOld= 200,gender= "female"]
--R  ,
--R      "katie"= [monthsOld= 24,gender= "female"]
--R  ,
--R      "judith"= [monthsOld= 366,gender= "female"]
--R  ,
--R      "bob"= [monthsOld= 407,gender= "male"]
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 8

--S 9 of 10
al."katie" := [23,"female"]$Data
 

   (9)  [monthsOld= 23,gender= "female"]
                              Type: Record(monthsOld: Integer,gender: String)
--R 
--R
--R   (9)  [monthsOld= 23,gender= "female"]
--R                              Type: Record(monthsOld: Integer,gender: String)
--E 9

--S 10 of 10
delete!(al,1)
 

   (10)
   table
      "katie"= [monthsOld= 23,gender= "female"]
  ,
      "judith"= [monthsOld= 366,gender= "female"]
  ,
      "bob"= [monthsOld= 407,gender= "male"]
      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--R 
--R
--R   (10)
--R   table
--R      "katie"= [monthsOld= 23,gender= "female"]
--R  ,
--R      "judith"= [monthsOld= 366,gender= "female"]
--R  ,
--R      "bob"= [monthsOld= 407,gender= "male"]
--R      Type: AssociationList(String,Record(monthsOld: Integer,gender: String))
--E 10 
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read up
 

-- Input generated from UnivariatePolynomialXmpPage
)clear all
 

(p,q) : UP(x,INT)
 
                                                                   Type: Void
p := (3*x-1)**2 * (2*x + 8)
 

           3      2
   (2)  18x  + 60x  - 46x + 8
                                        Type: UnivariatePolynomial(x,Integer)
q := (1 - 6*x + 9*x**2)**2
 

           4       3      2
   (3)  81x  - 108x  + 54x  - 12x + 1
                                        Type: UnivariatePolynomial(x,Integer)
p**2 + p*q
 

             7        6        5         4        3        2
   (4)  1458x  + 3240x  - 7074x  + 10584x  - 9282x  + 4120x  - 878x + 72
                                        Type: UnivariatePolynomial(x,Integer)
leadingCoefficient p
 

   (5)  18
                                                        Type: PositiveInteger
degree p
 

   (6)  3
                                                        Type: PositiveInteger
reductum p
 

           2
   (7)  60x  - 46x + 8
                                        Type: UnivariatePolynomial(x,Integer)
gcd(p,q)
 

          2
   (8)  9x  - 6x + 1
                                        Type: UnivariatePolynomial(x,Integer)
lcm(p,q)
 

            5       4       3       2
   (9)  162x  + 432x  - 756x  + 408x  - 94x + 8
                                        Type: UnivariatePolynomial(x,Integer)
resultant(p,q)
 

   (10)  0
                                                     Type: NonNegativeInteger
D p
 

            2
   (11)  54x  + 120x - 46
                                        Type: UnivariatePolynomial(x,Integer)
p(2)
 

   (12)  300
                                                        Type: PositiveInteger
p(q)
 

   (13)
             12            11            10            9            8
     9565938x   - 38263752x   + 70150212x   - 77944680x  + 58852170x
   + 
                7            6           5           4          3         2
     - 32227632x  + 13349448x  - 4280688x  + 1058184x  - 192672x  + 23328x
   + 
     - 1536x + 40
                                        Type: UnivariatePolynomial(x,Integer)
q(p)
 

   (14)
             12             11             10             9              8
     8503056x   + 113374080x   + 479950272x   + 404997408x  - 1369516896x
   + 
                 7              6              5              4             3
     - 626146848x  + 2939858712x  - 2780728704x  + 1364312160x  - 396838872x
   + 
              2
     69205896x  - 6716184x + 279841
                                        Type: UnivariatePolynomial(x,Integer)
l := coefficients p
 

   (15)  [18,60,- 46,8]
                                                           Type: List Integer
reduce(gcd,l)
 

   (16)  2
                                                        Type: PositiveInteger
content p
 

   (17)  2
                                                        Type: PositiveInteger
ux := (x**4+2*x+3)::UP(x,INT)
 

          4
   (18)  x  + 2x + 3
                                        Type: UnivariatePolynomial(x,Integer)
vectorise(ux,5)
 

   (19)  [3,2,0,0,1]
                                                         Type: Vector Integer
squareTerms(p) ==
  reduce(+,[t**2 for t in monomials p])
 
                                                                   Type: Void
p
 

            3      2
   (21)  18x  + 60x  - 46x + 8
                                        Type: UnivariatePolynomial(x,Integer)
squareTerms p
 
   Compiling function squareTerms with type UnivariatePolynomial(x,
      Integer) -> UnivariatePolynomial(x,Integer) 

             6        4        2
   (22)  324x  + 3600x  + 2116x  + 64
                                        Type: UnivariatePolynomial(x,Integer)
(r,s) : UP(a1,FRAC INT)
 
                                                                   Type: Void
r := a1**2 - 2/3
 

           2   2
   (24)  a1  - -
               3
                              Type: UnivariatePolynomial(a1,Fraction Integer)
s := a1 + 4
 

   (25)  a1 + 4
                              Type: UnivariatePolynomial(a1,Fraction Integer)
r quo s
 

   (26)  a1 - 4
                              Type: UnivariatePolynomial(a1,Fraction Integer)
r rem s
 

         46
   (27)  --
          3
                              Type: UnivariatePolynomial(a1,Fraction Integer)
d := divide(r, s)
 

                                      46
   (28)  [quotient= a1 - 4,remainder= --]
                                       3
Type: Record(quotient: UnivariatePolynomial(a1,Fraction Integer),remainder: UnivariatePolynomial(a1,Fraction Integer))
r - (d.quotient * s + d.remainder)
 

   (29)  0
                              Type: UnivariatePolynomial(a1,Fraction Integer)
integrate r
 

         1   3   2
   (30)  - a1  - - a1
         3       3
                              Type: UnivariatePolynomial(a1,Fraction Integer)
integrate s
 

         1   2
   (31)  - a1  + 4a1
         2
                              Type: UnivariatePolynomial(a1,Fraction Integer)
t : UP(a1,FRAC POLY INT)
 
                                                                   Type: Void
t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3)
 

                         2
           2    1      b1  - b1
   (33)  a1  - -- a1 + --------
               b2       b2 + 3
                   Type: UnivariatePolynomial(a1,Fraction Polynomial Integer)
u : FRAC POLY INT := t
 

           2  2      2           2
         a1 b2  + (b1  - b1 + 3a1  - a1)b2 - 3a1
   (34)  ---------------------------------------
                          2
                        b2  + 3b2
                                            Type: Fraction Polynomial Integer
u :: UP(b1,?)
 

                                    2
            1     2      1        a1 b2 - a1
   (35)  ------ b1  - ------ b1 + ----------
         b2 + 3       b2 + 3          b2
                   Type: UnivariatePolynomial(b1,Fraction Polynomial Integer)
)lisp (bye)
 
Starts dribbling to asec.output (2010/3/27, 18:23:10).
)set message test off
 
)set message auto off
 
)set break resume
 
digits(22)
 

   (1)  20
                                                        Type: PositiveInteger
)clear all
 
 
--S 1 of 10
asec(-2.0)
 

   (1)  2.0943951023 9319549230 8
                                                                  Type: Float
--R
--R   (1)  2.0943951023 9319549230 8
--R                                                                  Type: Float
--E 1

--S 2 of 10
asec(-1.5)
 

   (2)  2.3005239830 2186298268 6
                                                                  Type: Float
--R
--R   (2)  2.3005239830 2186298268 6
--R                                                                  Type: Float
--E 2

--S 3 of 10
asec(-1.0)
 

   (3)  3.1415926535 8979323846 3
                                                                  Type: Float
--R
--R   (3)  3.1415926535 8979323846 3
--R                                                                  Type: Float
--E 3

--S 4 of 10
asec(-0.5)
 
 
   >> Error detected within library code:
   acos: argument > 1 in magnitude

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   acos: argument > 1 in magnitude
--R
--R   Continuing to read the file...
--R
--E 4

--S 5 of 10
asec(-0.0)
 
 
   >> Error detected within library code:
   asec: no reciprocal

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   asec: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 5

--S 6 of 10
asec(0.0)
 
 
   >> Error detected within library code:
   asec: no reciprocal

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   asec: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 6

--S 7 of 10
asec(0.5)
 
 
   >> Error detected within library code:
   acos: argument > 1 in magnitude

   Continuing to read the file...

--R 
--R   >> Error detected within library code:
--R   acos: argument > 1 in magnitude
--R
--R   Continuing to read the file...
--R
--E 7

--S 8 of 10
asec(1.0)
 

   (4)  0.0
                                                                  Type: Float
--R
--R   (4)  0.0
--R                                                                  Type: Float
--E 8

--S 9 of 10
asec(1.5)
 

   (5)  0.8410686705 6793025577 652
                                                                  Type: Float
--R
--R   (5)  0.8410686705 6793025577 652
--R                                                                  Type: Float
--E 9

--S 10 of 10
asec(2.0)
 

   (6)  1.0471975511 9659774615 42
                                                                  Type: Float
--R
--R   (6)  1.0471975511 9659774615 42
--R                                                                  Type: Float
--E 10
)spool 
 
Starts dribbling to Segment.output (2010/3/27, 18:46:32).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
s := 3..10
 

   (1)  3..10
                                                Type: Segment PositiveInteger
--R 
--R
--R   (1)  3..10
--R                                                Type: Segment PositiveInteger
--E 1

--S 2 of 10
lo s
 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 10
hi s
 

   (3)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  10
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 10
t := 10..3 by -2
 

   (4)  10..3 by - 2
                                                Type: Segment PositiveInteger
--R 
--R
--R   (4)  10..3 by - 2
--R                                                Type: Segment PositiveInteger
--E 4

--S 5 of 10
incr s
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
incr t
 

   (6)  - 2
                                                                Type: Integer
--R 
--R
--R   (6)  - 2
--R                                                                Type: Integer
--E 6

--S 7 of 10
l := [1..3, 5, 9, 15..11 by -1]
 

   (7)  [1..3,5..5,9..9,15..11 by - 1]
                                           Type: List Segment PositiveInteger
--R 
--R
--R   (7)  [1..3,5..5,9..9,15..11 by - 1]
--R                                           Type: List Segment PositiveInteger
--E 7

--S 8 of 10
expand s
 

   (8)  [3,4,5,6,7,8,9,10]
                                                           Type: List Integer
--R 
--R
--R   (8)  [3,4,5,6,7,8,9,10]
--R                                                           Type: List Integer
--E 8

--S 9 of 10
expand t
 

   (9)  [10,8,6,4]
                                                           Type: List Integer
--R 
--R
--R   (9)  [10,8,6,4]
--R                                                           Type: List Integer
--E 9

--S 10 of 10
expand l
 

   (10)  [1,2,3,5,9,15,14,13,12,11]
                                                           Type: List Integer
--R 
--R
--R   (10)  [1,2,3,5,9,15,14,13,12,11]
--R                                                           Type: List Integer
--E 10
)spool
 
Starts dribbling to newtonlisp.output (2010/3/27, 18:30:9).
)set message test on
 
)set message auto off
 
)clear all
 


)sys cp $AXIOM/../../src/input/newtonlisp.input.pamphlet .
 
)lisp (tangle "newtonlisp.input.pamphlet" "funcall.lisp" "funcall.lisp")
 
Value = NIL
)lisp (compile-file "funcall.lisp")
 
Value = #p"funcall.o"
)lisp (load "funcall.o")
 
Value = 280
)lisp (tangle "newtonlisp.input.pamphlet" "MKULF.spad" "MKULF.spad")
 
Value = NIL
)co MKULF
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/MKULF.spad using
      old system compiler.
   MKULF abbreviates package MakeUnaryLispFunction 
   processing macro definition SY ==> Symbol 
   processing macro definition DI ==> (elt Lisp devaluate) D -> I 
   processing macro definition Exports ==> -- the constructor category 
   processing macro definition Implementation ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing nrlib MKULF for MakeUnaryLispFunction 
   compiling into nrlib MKULF 
   importing MakeFunction S
   compiling exported compiledFunction : (S,Symbol) -> Symbol
Time: 0.03 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |MakeUnaryLispFunction| REDEFINED

;;;     ***       |MakeUnaryLispFunction| REDEFINED
Time: 0 SEC.


   Cumulative Statistics for Constructor MakeUnaryLispFunction
      Time: 0.03 seconds
 
   finalizing nrlib MKULF 
   Processing MakeUnaryLispFunction for Browser database:
--------(compiledFunction (SY S SY))---------
--------constructor---------
------------------------------------------------------------------------
   MakeUnaryLispFunction is now explicitly exposed in frame initial 
   MakeUnaryLispFunction will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/MKULF.nrlib/code

)lisp (tangle "newtonlisp.input.pamphlet" "newton.lisp" "newton.lisp")
 
Value = NIL
)lisp (compile-file "newton.lisp")
 
Value = #p"newton.o"
)lisp (load "newton.o")
 
Value = 752
)lisp (tangle "newtonlisp.input.pamphlet" "TESTP.spad" "TESTP.spad")
 
Value = NIL
)co TESTP
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/TESTP.spad using
      old system compiler.
   TESTP abbreviates package TestPackage 
   processing macro definition R ==> DoubleFloat 

------------------------------------------------------------------------
   initializing nrlib TESTP for TestPackage 
   compiling into nrlib TESTP 
   compiling exported f : DoubleFloat -> DoubleFloat
Time: 0 SEC.

   compiling exported dfdx : DoubleFloat -> DoubleFloat
Time: 0.02 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |TestPackage| REDEFINED

;;;     ***       |TestPackage| REDEFINED
Time: 0 SEC.


   Cumulative Statistics for Constructor TestPackage
      Time: 0.02 seconds
 
   finalizing nrlib TESTP 
   Processing TestPackage for Browser database:
--->-->TestPackage((f (R R))): Not documented!!!!
--->-->TestPackage((dfdx (R R))): Not documented!!!!
--->-->TestPackage(constructor): Not documented!!!!
--->-->TestPackage(): Missing Description
------------------------------------------------------------------------
   TestPackage is now explicitly exposed in frame initial 
   TestPackage will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/TESTP.nrlib/code

)lisp (tangle "newtonlisp.input.pamphlet" "lispspad.lisp" "lispspad.lisp")
 
Value = NIL
)lisp (compile-file "lispspad.lisp")
 
Value = #p"lispspad.o"
)lisp (load "lispspad.o")
 
Value = 480
)lisp (tangle "newtonlisp.input.pamphlet" "mklispfn.lisp" "mklispfn.lisp")
 
Value = NIL
)lisp (compile-file "mklispfn.lisp")
 
Value = #p"mklispfn.o"
)lisp (load "mklispfn.o")
 
Value = 340
)lisp (tangle "newtonlisp.input.pamphlet" "TESTP2.spad" "TESTP2.spad")
 
Value = NIL
)co TESTP2
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/TESTP2.spad 
      using old system compiler.
   TESTP2 abbreviates package TestPackage2 
   processing macro definition R ==> DoubleFloat 

   processing macro definition I ==> Integer 

------------------------------------------------------------------------
   initializing nrlib TESTP2 for TestPackage2 
   compiling into nrlib TESTP2 
   compiling exported newton : (DoubleFloat -> DoubleFloat,DoubleFloat -> DoubleFloat,DoubleFloat,DoubleFloat,Integer) -> DoubleFloat
Time: 0 SEC.

   compiling exported newton : (DoubleFloat -> DoubleFloat,DoubleFloat -> DoubleFloat,DoubleFloat) -> DoubleFloat
Time: 0.01 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |TestPackage2| REDEFINED

;;;     ***       |TestPackage2| REDEFINED
Time: 0 SEC.


   Cumulative Statistics for Constructor TestPackage2
      Time: 0.01 seconds
 
   finalizing nrlib TESTP2 
   Processing TestPackage2 for Browser database:
--->-->TestPackage2((newton (R (Mapping R R) (Mapping R R) R R I))): Not documented!!!!
--->-->TestPackage2((newton (R (Mapping R R) (Mapping R R) R))): Not documented!!!!
--->-->TestPackage2(constructor): Not documented!!!!
--->-->TestPackage2(): Missing Description
------------------------------------------------------------------------
   TestPackage2 is now explicitly exposed in frame initial 
   TestPackage2 will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/TESTP2.nrlib/code



--S 1 of 14
R ==> Float
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 14
I ==> Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 14
newton(f:Expression R,x:Symbol,x0:R):R ==
  dfdx:Expression R := D(f,x)
  xt:R := x0
  fxt:R := subst(f,x=xt)
  iterNum:I :=0
  maxIt:I := 100
  repeat
    xt := xt - fxt/subst(dfdx,x=xt)
    fxt := subst(f,x=xt)
    if abs(fxt)<1.0e-10 then return xt
    iterNum:=iterNum+1::I
    if iterNum >= maxIt then
      error "Maximum iterations exceeded."
 
   Function declaration newton : (Expression Float,Symbol,Float) -> 
      Float has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration newton : (Expression Float,Symbol,Float) -> 
--R      Float has been added to workspace.
--R                                                                   Type: Void
--E 3

--S 4 of 14
newton(x^2-2.0,x,2.0)
 
   Compiling function newton with type (Expression Float,Symbol,Float)
       -> Float 

   (4)  1.4142135623 746899106
                                                                  Type: Float
--R 
--R   Compiling function newton with type (Expression Float,Symbol,Float)
--R       -> Float 
--R
--R   (4)  1.4142135623 746899106
--R                                                                  Type: Float
--E 4

--S 5 of 14
newton(y^2-2.0,y,2.0)
 

   (5)  1.4142135623 746899106
                                                                  Type: Float
--R 
--R
--R   (5)  1.4142135623 746899106
--R                                                                  Type: Float
--E 5

--S 6 of 14
newton(x^2-2.0,x,2.0)-sqrt(2.0)
 

   (6)  0.15948618 E -11
                                                                  Type: Float
--R 
--R
--R   (6)  0.15948618 E -11
--R                                                                  Type: Float
--E 6


--S 7 of 14
compiledDF(expr: EXPR FLOAT, x:Symbol):Symbol ==
  compiledFunction(expr,x)$MakeUnaryLispFunction(EXPR FLOAT,DFLOAT,DFLOAT)
 
   Function declaration compiledDF : (Expression Float,Symbol) -> 
      Symbol has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration compiledDF : (Expression Float,Symbol) -> 
--R      Symbol has been added to workspace.
--R                                                                   Type: Void
--E 7

--S 8 of 14
newtonUsingLisp(f:Expression Float,x:Symbol,x0:DFLOAT):DFLOAT ==
  float(NEWTON(compiledDF(f,x),compiledDF(D(f,x),x),x0)$Lisp)
 
   Function declaration newtonUsingLisp : (Expression Float,Symbol,
      DoubleFloat) -> DoubleFloat has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration newtonUsingLisp : (Expression Float,Symbol,
--R      DoubleFloat) -> DoubleFloat has been added to workspace.
--R                                                                   Type: Void
--E 8

--S 9 of 14
newtonUsingLisp(x**2-2.0,x,2.0::SF)-sqrt(2.0::SF)
 
   Compiling function compiledDF with type (Expression Float,Symbol)
       -> Symbol 
   Compiling function newtonUsingLisp with type (Expression Float,
      Symbol,DoubleFloat) -> DoubleFloat 
   Compiling function %A with type DoubleFloat -> DoubleFloat 
   Compiling function %B with type DoubleFloat -> DoubleFloat 

   (9)  1.5947243525715749E-12
                                                            Type: DoubleFloat
--R 
--R   Compiling function compiledDF with type (Expression Float,Symbol)
--R       -> Symbol 
--R   Compiling function newtonUsingLisp with type (Expression Float,
--R      Symbol,DoubleFloat) -> DoubleFloat 
--I   Compiling function %A with type DoubleFloat -> DoubleFloat 
--I   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R
--R   (9)  1.5947243525715749E-12
--R                                                            Type: DoubleFloat
--E 9


--S 10 of 14
float(NEWTON(lispFromSpad(f,'TestPackage,['DoubleFloat])$Lisp,_
             lispFromSpad(dfdx,'TestPackage,['DoubleFloat])$Lisp,2::SF)$Lisp)_
       -sqrt(2.0::SF)
 

   (10)  1.5947243525715749E-12
                                                            Type: DoubleFloat
--R 
--R
--R   (10)  1.5947243525715749E-12
--R                                                            Type: DoubleFloat
--E 10


--S 11 of 14
R ==> DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 14
newton((x:R):R +-> x^2-2.0::R,_
       (x:R):R +-> 2.0::R*x, 3.0::SF, 1.0e-15, 100)$TestPackage2_
          -sqrt(2.0)
 

   (12)  0.
                                                            Type: DoubleFloat
--R 
--R
--R   (12)  0.
--R                                                            Type: DoubleFloat
--E 12

--S 13 of 14
newtonExpression(f,x,x0) ==
  dfdx := D(f,x)
  newton((xt:R):R +-> eval(f,x,xt), _
         (xt:R):R +-> eval(dfdx,x,xt),x0)$TestPackage2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 14
newtonExpression(x^2-2.0,x,2.0)-sqrt(2.0)
 
   Compiling function newtonExpression with type (Polynomial Float,
      Variable x,Float) -> DoubleFloat 

   (14)  1.5949463971764999E-12
                                                            Type: DoubleFloat
--R 
--R   Compiling function newtonExpression with type (Polynomial Float,
--R      Variable x,Float) -> DoubleFloat 
--R
--R   (14)  1.5949463971764999E-12
--R                                                            Type: DoubleFloat
--E 14

)spool 
 
Starts dribbling to torus.output (2010/3/27, 18:41:24).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
f(x:SF):SF == x
 
   Function declaration f : DoubleFloat -> DoubleFloat has been added 
      to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : DoubleFloat -> DoubleFloat has been added 
--R      to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 3
torus : TUBE := tubePlot(sin t,cos t,0,f,0..2*%pi,0.5::SF,12,"closed")
 
 
Daly Bug
   Although TubePlot is the name of a constructor, a full type must be 
      specified in the context you have used it. Issue )show TubePlot 
      for more information.
--R 
--R 
--RDaly Bug
--R   Although TubePlot is the name of a constructor, a full type must be 
--R      specified in the context you have used it. Issue )show TubePlot 
--R      for more information.
--E 2

--S 3 of 3
makeViewport3D(torus,"torus")$VIEW3D
 
   There are 2 exposed and 0 unexposed library operations named 
      makeViewport3D having 2 argument(s) but none was determined to be
      applicable. Use HyperDoc Browse, or issue
                         )display op makeViewport3D
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      makeViewport3D with argument type(s) 
                                   Symbol
                                   String
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 2 exposed and 0 unexposed library operations named 
--R      makeViewport3D having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                         )display op makeViewport3D
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      makeViewport3D with argument type(s) 
--R                                   Symbol
--R                                   String
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 3
)spool 
 
Starts dribbling to pascal.output (2010/3/27, 18:30:38).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 10
)set fun cache all
 
   In general, interpreter functions will cache all values.
--R 
--R   In general, interpreter functions will cache all values.
--E 1

--S 2 of 10
p(m,n | m=1)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 10
p(m,n | m=n)==1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 10
p(i,n | 1 < i and i < n) == p(i-1,n-1) + p(i,n-1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 10
p(2,3)
 
   Compiling function p with type (Integer,Integer) -> PositiveInteger 
   p will cache all previously computed values.

   (4)  2
                                                        Type: PositiveInteger
--R 
--R   Compiling function p with type (Integer,Integer) -> PositiveInteger 
--R   p will cache all previously computed values.
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
pn(n) == [p(i,n) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
pn(50)
 
   Compiling function pn with type PositiveInteger -> List 
      PositiveInteger 
   pn will cache all previously computed values.

   (6)
   [1, 49, 1176, 18424, 211876, 1906884, 13983816, 85900584, 450978066,
    2054455634, 8217822536, 29135916264, 92263734836, 262596783764,
    675248872536, 1575580702584, 3348108992991, 6499270398159, 11554258485616,
    18851684897584, 28277527346376, 39049918716424, 49699896548176,
    58343356817424, 63205303218876, 63205303218876, 58343356817424,
    49699896548176, 39049918716424, 28277527346376, 18851684897584,
    11554258485616, 6499270398159, 3348108992991, 1575580702584, 675248872536,
    262596783764, 92263734836, 29135916264, 8217822536, 2054455634, 450978066,
    85900584, 13983816, 1906884, 211876, 18424, 1176, 49, 1]
                                                   Type: List PositiveInteger
--R 
--R   Compiling function pn with type PositiveInteger -> List 
--R      PositiveInteger 
--R   pn will cache all previously computed values.
--R
--R   (6)
--R   [1, 49, 1176, 18424, 211876, 1906884, 13983816, 85900584, 450978066,
--R    2054455634, 8217822536, 29135916264, 92263734836, 262596783764,
--R    675248872536, 1575580702584, 3348108992991, 6499270398159, 11554258485616,
--R    18851684897584, 28277527346376, 39049918716424, 49699896548176,
--R    58343356817424, 63205303218876, 63205303218876, 58343356817424,
--R    49699896548176, 39049918716424, 28277527346376, 18851684897584,
--R    11554258485616, 6499270398159, 3348108992991, 1575580702584, 675248872536,
--R    262596783764, 92263734836, 29135916264, 8217822536, 2054455634, 450978066,
--R    85900584, 13983816, 1906884, 211876, 18424, 1176, 49, 1]
--R                                                   Type: List PositiveInteger
--E 7

--S 8 of 10
pk n == [pn(i) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 10
pk 10
 
   Compiling function pk with type PositiveInteger -> List List 
      PositiveInteger 
   pk will cache all previously computed values.

   (8)
   [[1], [1,1], [1,2,1], [1,3,3,1], [1,4,6,4,1], [1,5,10,10,5,1],
    [1,6,15,20,15,6,1], [1,7,21,35,35,21,7,1], [1,8,28,56,70,56,28,8,1],
    [1,9,36,84,126,126,84,36,9,1]]
                                              Type: List List PositiveInteger
--R 
--R   Compiling function pk with type PositiveInteger -> List List 
--R      PositiveInteger 
--R   pk will cache all previously computed values.
--R
--R   (8)
--R   [[1], [1,1], [1,2,1], [1,3,3,1], [1,4,6,4,1], [1,5,10,10,5,1],
--R    [1,6,15,20,15,6,1], [1,7,21,35,35,21,7,1], [1,8,28,56,70,56,28,8,1],
--R    [1,9,36,84,126,126,84,36,9,1]]
--R                                              Type: List List PositiveInteger
--E 9

--S 10 of 10
)set fun cache 10
 
   In general, interpreter functions will cache the last 10 values.
--R 
--R   In general, interpreter functions will cache the last 10 values.
--E 10
)spool 
 
Starts dribbling to bug9057.output (2010/3/27, 18:23:26).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 9
g:=operator 'g
 

   (1)  g
                                                          Type: BasicOperator
--R 
--R
--R   (1)  g
--R                                                          Type: BasicOperator
--E 1

--S 2 of 9
f==n+->sum(g(j),j=1..n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 9
f(1)
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

   (3)  g(1)
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R   (3)  g(1)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 9
f==n+->product(sum(1/i,i=1..j),j=1..n)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
--R 
--R   Compiled code for f has been cleared.
--R   1 old definition(s) deleted for function or rule f 
--R                                                                   Type: Void
--E 4

--S 5 of 9
f(1)
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

   (5)  1
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R   (5)  1
--R                                                     Type: Expression Integer
--E 5

--S 6 of 9
f==n+->product(product(1/i,i=1..j),j=1..n)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
--R 
--R   Compiled code for f has been cleared.
--R   1 old definition(s) deleted for function or rule f 
--R                                                                   Type: Void
--E 6

--S 7 of 9
f(1)
 
   Compiling function f with type PositiveInteger -> Expression Integer
      

   (7)  1
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type PositiveInteger -> Expression Integer
--R      
--R
--R   (7)  1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 9
f==n+->sum(sum(1/i,i=1..j),j=1..n)
 
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
--R 
--R   Compiled code for f has been cleared.
--R   1 old definition(s) deleted for function or rule f 
--R                                                                   Type: Void
--E 8

--S 9 of 9
f(1)
 
   There are 6 exposed and 2 unexposed library operations named sum 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op sum
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named sum 
      with argument type(s) 
            Union(Fraction Polynomial Integer,Expression Integer)
                       SegmentBinding PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.

   (9)  1
                                                     Type: Expression Integer
--R 
--R   There are 6 exposed and 2 unexposed library operations named sum 
--R      having 2 argument(s) but none was determined to be applicable. 
--R      Use HyperDoc Browse, or issue
--R                               )display op sum
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named sum 
--R      with argument type(s) 
--R            Union(Fraction Polynomial Integer,Expression Integer)
--R                       SegmentBinding PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R
--R   (9)  1
--R                                                     Type: Expression Integer
--E 9
)spool
 
Starts dribbling to QuaternionCategoryFunctions2.output (2010/3/27, 18:46:18).
)set message test on
 
)set message auto off
 
)clear all
 

(1) -> )read af
 
  Line   6: 
  Line   7: (1) -> )read af
           .......A
  Error  A: Improper syntax.
   1 error(s) parsing 
--S 1 of 4
q := quatern(2/11,-8,3/4,1)
 

         2        3
   (1)  -- - 8i + - j + k
        11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         2        3
--R   (1)  -- - 8i + - j + k
--R        11        4
--R                                            Type: Quaternion Fraction Integer
--E 1

--S 2 of 4
f(a:Fraction Integer):Complex Fraction Integer == a::Complex Fraction Integer
 
   Function declaration f : Fraction Integer -> Complex Fraction 
      Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration f : Fraction Integer -> Complex Fraction 
--R      Integer has been added to workspace.
--R                                                                   Type: Void
--E 3

--S 3 of 4
map(f,q)
 
   Compiling function f with type Fraction Integer -> Complex Fraction 
      Integer 

         2        3
   (3)  -- - 8i + - j + k
        11        4
                                    Type: Quaternion Complex Fraction Integer
--R 
--R   Compiling function f with type Fraction Integer -> Complex Fraction 
--R      Integer 
--R
--R         2        3
--R   (3)  -- - 8i + - j + k
--R        11        4
--R                                    Type: Quaternion Complex Fraction Integer
--E 3

--S 4 of 4
)show QuaternionCategoryFunctions2
 
 QuaternionCategoryFunctions2(QR: QuaternionCategory R,R: CommutativeRing,QS: QuaternionCategory S,S: CommutativeRing)  is a package constructor
 Abbreviation for QuaternionCategoryFunctions2 is QUATCT2 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for QUATCT2 

------------------------------- Operations --------------------------------
 map : ((R -> S),QR) -> QS            

--R 
--R QuaternionCategoryFunctions2(QR: QuaternionCategory R,R: CommutativeRing,QS: QuaternionCategory S,S: CommutativeRing)  is a package constructor
--R Abbreviation for QuaternionCategoryFunctions2 is QUATCT2 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.4.spad.pamphlet to see algebra source code for QUATCT2 
--R
--R------------------------------- Operations --------------------------------
--R map : ((R -> S),QR) -> QS            
--R
--E 4

)spool
 
Starts dribbling to pmint.output (2010/3/27, 18:30:48).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 29
f:=(x^7-24*x^4-4*x^2+8*x-8)/(x^8+6*x^6+12*x^4+8*x^2)
 

         7      4     2
        x  - 24x  - 4x  + 8x - 8
   (1)  ------------------------
           8     6      4     2
          x  + 6x  + 12x  + 8x
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         7      4     2
--R        x  - 24x  - 4x  + 8x - 8
--R   (1)  ------------------------
--R           8     6      4     2
--R          x  + 6x  + 12x  + 8x
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 29
g:=integrate(f,x)
 

          5     3                 3     2
        (x  + 4x  + 4x)log(x) + 3x  + 8x  + 6x + 4
   (2)  ------------------------------------------
                        5     3
                       x  + 4x  + 4x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          5     3                 3     2
--R        (x  + 4x  + 4x)log(x) + 3x  + 8x  + 6x + 4
--R   (2)  ------------------------------------------
--R                        5     3
--R                       x  + 4x  + 4x
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 29
differentiate(g,x)
 

         7      4     2
        x  - 24x  - 4x  + 8x - 8
   (3)  ------------------------
           8     6      4     2
          x  + 6x  + 12x  + 8x
                                                     Type: Expression Integer
--R 
--R
--R         7      4     2
--R        x  - 24x  - 4x  + 8x - 8
--R   (3)  ------------------------
--R           8     6      4     2
--R          x  + 6x  + 12x  + 8x
--R                                                     Type: Expression Integer
--E 3

)clear all
 

--S 4 of 29
f:=(x-tan(x))/tan(x)^2 + tan(x)
 

              3
        tan(x)  - tan(x) + x
   (1)  --------------------
                     2
               tan(x)
                                                     Type: Expression Integer
--R 
--R
--R              3
--R        tan(x)  - tan(x) + x
--R   (1)  --------------------
--R                     2
--R               tan(x)
--R                                                     Type: Expression Integer
--E 4

--S 5 of 29
g:=integrate(f,x)
 

                        2         2
        tan(x)log(tan(x)  + 1) - x tan(x) - 2x
   (2)  --------------------------------------
                        2tan(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2         2
--R        tan(x)log(tan(x)  + 1) - x tan(x) - 2x
--R   (2)  --------------------------------------
--R                        2tan(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 29
differentiate(g,x)
 

              3
        tan(x)  - tan(x) + x
   (3)  --------------------
                     2
               tan(x)
                                                     Type: Expression Integer
--R 
--R
--R              3
--R        tan(x)  - tan(x) + x
--R   (3)  --------------------
--R                     2
--R               tan(x)
--R                                                     Type: Expression Integer
--E 6

)clear all
 

--S 7 of 29
f:=(1+x+x*exp(x))*(x+log(x)+exp(x)-1)/(x+log(x)+exp(x))^2/x
 

              x                       x 2     2       x    2
         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
   (1)  ---------------------------------------------------------
                2         x     2               x 2     2  x    3
        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R              x                       x 2     2       x    2
--R         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
--R   (1)  ---------------------------------------------------------
--R                2         x     2               x 2     2  x    3
--R        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 7

--S 8 of 29
g:=integrate(f,x)
 

                    x                    x
        (log(x) + %e  + x)log(log(x) + %e  + x) + 1
   (2)  -------------------------------------------
                                 x
                      log(x) + %e  + x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    x                    x
--R        (log(x) + %e  + x)log(log(x) + %e  + x) + 1
--R   (2)  -------------------------------------------
--R                                 x
--R                      log(x) + %e  + x
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 29
differentiate(g,x)
 

              x                       x 2     2       x    2
         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
   (3)  ---------------------------------------------------------
                2         x     2               x 2     2  x    3
        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R              x                       x 2     2       x    2
--R         (x %e  + x + 1)log(x) + x (%e )  + (x  + 1)%e  + x  - 1
--R   (3)  ---------------------------------------------------------
--R                2         x     2               x 2     2  x    3
--R        x log(x)  + (2x %e  + 2x )log(x) + x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 9

)clear all
 

--S 10 of 29
f:=exp(-x^2)+erf(x)/(erf(x)^3-erf(x)^2-erf(x)+1)
 

                                             2
               3         2                - x
        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
   (1)  -----------------------------------------------
                       3         2
                 erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R                                             2
--R               3         2                - x
--R        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
--R   (1)  -----------------------------------------------
--R                       3         2
--R                 erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 29 
g:=integrate(f,x)
 

                                                      2
           x         3          2                 - %G
         ++  (erf(%G)  - erf(%G)  - erf(%G) + 1)%e      + erf(%G)
   (2)   |   ---------------------------------------------------- d%G
        ++                    3          2
                       erf(%G)  - erf(%G)  - erf(%G) + 1
                                          Type: Union(Expression Integer,...)
--R
--R                                                      2
--I           x         3          2                 - %G
--I         ++  (erf(%G)  - erf(%G)  - erf(%G) + 1)%e      + erf(%G)
--I   (2)   |   ---------------------------------------------------- d%G
--R        ++                    3          2
--I                       erf(%G)  - erf(%G)  - erf(%G) + 1
--R                                          Type: Union(Expression Integer,...)
--E 11

--S 12 of 29
differentiate(g,x)
 

                                             2
               3         2                - x
        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
   (3)  -----------------------------------------------
                       3         2
                 erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R
--R                                             2
--R               3         2                - x
--R        (erf(x)  - erf(x)  - erf(x) + 1)%e     + erf(x)
--R   (3)  -----------------------------------------------
--R                       3         2
--R                 erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 12

)clear all
 

--S 13 of 29
f:=(exp(-x^2)+erf(x))/(erf(x)^3-erf(x)^2-erf(x)+1)
 

                     2
                  - x
                %e     + erf(x)
   (1)  ------------------------------
              3         2
        erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R 
--R
--R                     2
--R                  - x
--R                %e     + erf(x)
--R   (1)  ------------------------------
--R              3         2
--R        erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 13

--S 14 of 29 used to work!
g:=integrate(f,x)
 

                           2
           x           - %G
         ++          %e      + erf(%G)
   (2)   |   --------------------------------- d%G
        ++          3          2
             erf(%G)  - erf(%G)  - erf(%G) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                           2
--I           x           - %G
--I         ++          %e      + erf(%G)
--I   (3)   |   --------------------------------- d%G
--R        ++          3          2
--I             erf(%G)  - erf(%G)  - erf(%G) + 1
--R                                          Type: Union(Expression Integer,...)
--E 14
-- should be:
--    1   sqrt(%pi)     1                           1
-- -  - ------------  - - sqrt(%pi) log(erf(x)+1) + - sqrt(%pi) log(erf(x)-1)
--    4  erf(x) - 1     8                           8

--S 15 of 29
differentiate(g,x)
 

                     2
                  - x
                %e     + erf(x)
   (3)  ------------------------------
              3         2
        erf(x)  - erf(x)  - erf(x) + 1
                                                     Type: Expression Integer
--R
--R                     2
--R                  - x
--R                %e     + erf(x)
--R   (3)  ------------------------------
--R              3         2
--R        erf(x)  - erf(x)  - erf(x) + 1
--R                                                     Type: Expression Integer
--E 15

)clear all
 
 
-- Axiom does not have a 2 argument form of the airyAi function
--  f:=(x-airyAi(x)*airyAi(1,x))/(x^2-airyAi(x)^2)
--it has the integral
--R
--R  1                    1
--R  - log(x+airyAi(x)) + - log(x-airyAi(x))
--R  2                    2


--S 16 of 29 will certainly fail
f:=(x-airyAi(x))/(x^2-airyAi(x)^2)
 

              1
   (1)  -------------
        airyAi(x) + x
                                                     Type: Expression Integer
--R
--R              1
--R   (1)  -------------
--R        airyAi(x) + x
--R                                                     Type: Expression Integer
--E 16

--S 17 of 29 will certainly fail
g:=integrate(f,x)
 

           x
         ++         1
   (2)   |   --------------- d%G
        ++   airyAi(%G) + %G
                                          Type: Union(Expression Integer,...)
--R
--R           x
--R         ++         1
--R   (2)   |   --------------- d%G
--R        ++   airyAi(%G) + %G
--R                                          Type: Union(Expression Integer,...)
--E 17

--S 18 of 29
differentiate(g,x)
 

              1
   (3)  -------------
        airyAi(x) + x
                                                     Type: Expression Integer
--R
--R              1
--R   (3)  -------------
--R        airyAi(x) + x
--R                                                     Type: Expression Integer
--E 18

)clear all
 

--S 19 of 29
f:=x^2*airyAi(x)
 

         2
   (1)  x airyAi(x)
                                                     Type: Expression Integer
--R 
--R
--R         2
--R   (1)  x airyAi(x)
--R                                                     Type: Expression Integer
--E 19

--S 20 of 29 used to work
g:=integrate(f,x)
 

           x
         ++    2
   (2)   |   %G airyAi(%G)d%G
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++    2
--I   (2)   |   %G airyAi(%G)d%G
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 20
-- should be:
--  -airyAi(x) + airyAi(1,x) x

--S 21 of 29
differentiate(g,x)
 

         2
   (3)  x airyAi(x)
                                                     Type: Expression Integer
--R
--R         2
--R   (3)  x airyAi(x)
--R                                                     Type: Expression Integer
--E 21

)clear all
 

--S 22 of 29
f:=besselJ(y+1,x)/besselJ(y,x)
 

        besselJ(y + 1,x)
   (1)  ----------------
          besselJ(y,x)
                                                     Type: Expression Integer
--R 
--R
--R        besselJ(y + 1,x)
--R   (1)  ----------------
--R          besselJ(y,x)
--R                                                     Type: Expression Integer
--E 22

--S 23 of 29 used to work
g:=integrate(f,x)
 

           x
         ++  besselJ(y + 1,%G)
   (2)   |   ----------------- d%G
        ++     besselJ(y,%G)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  besselJ(y + 1,%G)
--I   (2)   |   ----------------- d%G
--I        ++     besselJ(y,%G)
--R                                          Type: Union(Expression Integer,...)
--E 23
-- should be:
--  y log(x) - log(besselJ(y,x))

--S 24 of 29
differentiate(g,x)
 

        besselJ(y + 1,x)
   (3)  ----------------
          besselJ(y,x)
                                                     Type: Expression Integer
--R
--R        besselJ(y + 1,x)
--R   (3)  ----------------
--R          besselJ(y,x)
--R                                                     Type: Expression Integer
--E 24

)clear all
 


-- Axiom does not have Maple's normal function
--S 25 of 29 used to work
--f:=normal(y*besselJ(y,x)/x - besselJ(y+1,x))
f:=y*besselJ(y,x)/x - besselJ(y+1,x)
 

        - x besselJ(y + 1,x) + y besselJ(y,x)
   (1)  -------------------------------------
                          x
                                                     Type: Expression Integer
--R
--R        - x besselJ(y + 1,x) + y besselJ(y,x)
--R   (1)  -------------------------------------
--R                          x
--R                                                     Type: Expression Integer
--E 25

--S 26 of 29
g:=integrate(f,x)
 

           x
         ++  - %G besselJ(y + 1,%G) + y besselJ(y,%G)
   (2)   |   ---------------------------------------- d%G
        ++                      %G
                                          Type: Union(Expression Integer,...)
--R
--R           x
--I         ++  - %G besselJ(y + 1,%G) + y besselJ(y,%G)
--I   (2)   |   ---------------------------------------- d%G
--I        ++                      %G
--R                                          Type: Union(Expression Integer,...)
--E 26

--S 27 of 29
differentiate(g,x)
 

        - x besselJ(y + 1,x) + y besselJ(y,x)
   (3)  -------------------------------------
                          x
                                                     Type: Expression Integer
--R
--R        - x besselJ(y + 1,x) + y besselJ(y,x)
--R   (3)  -------------------------------------
--R                          x
--R                                                     Type: Expression Integer
--E 27
)clear all
 

--S 28 of 29 used to work
f:=WhittakerW(u+1,n,x)/(WhittakerW(u,n,x)*x)
 
   There are no library operations named WhittakerW 
      Use HyperDoc Browse or issue
                             )what op WhittakerW
      to learn if there is any operation containing " WhittakerW " in 
      its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      WhittakerW with argument type(s) 
                             Polynomial Integer
                                 Variable n
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named WhittakerW 
--R      Use HyperDoc Browse or issue
--R                             )what op WhittakerW
--R      to learn if there is any operation containing " WhittakerW " in 
--R      its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      WhittakerW with argument type(s) 
--R                             Polynomial Integer
--R                                 Variable n
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 28

-- Axiom does not implement WhittakerW
-- should be:
--  Whittaker(u+1,n,x)
--  ------------------
--  Whittaker(u,n,x) x

-- of 29 used to work
--integrate(f,x)
-- 22
-- should be:
--  x
--  -  - u log(x) - log(WhattakerW(u,n,x))
--  2

)clear all
 

-- Axiom does not implement LambertW
--S 29 of 29 used to work
f:=LambertW(x)
 
   There are no library operations named LambertW 
      Use HyperDoc Browse or issue
                              )what op LambertW
      to learn if there is any operation containing " LambertW " in its
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      LambertW with argument type(s) 
                                 Variable x
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named LambertW 
--R      Use HyperDoc Browse or issue
--R                              )what op LambertW
--R      to learn if there is any operation containing " LambertW " in its
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      LambertW with argument type(s) 
--R                                 Variable x
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 29

-- of 29 used to work
-- g:=integrate(f,x)
-- 24
-- should be:
--    2             2  2                2
--   x + LambertW(x)  x  - LambertW(x) x
--   ------------------------------------
--          x LambertW(x)

-- of 29 used to work
-- integrate(sin(LambertW(x)),x)
-- 25
--should be:
-- +-                                                  -+
-- |                                     2              |
-- |                    +-             -+               |
-- |  1                 | 1             |  2            |
-- |  - LambertW(x) tan | - LambertW(x) | x   +         |
-- |  2                 | 2             |               |
-- |                    +-             -+               |
-- |                                                    |
-- |                  +-             -+                 |
-- |                  | 1             |  2              |
-- |  LambertW(x) tan | - LambertW(x) | x  +            |
-- |                  | 2             |                 |
-- |                  +-             -+                 |
-- |                                                    |
-- |      +-             -+                             |
-- |      | 1             |  2      1              2    |
-- |  tan | - LambertW(x) | x  -    - LambertW(x) x     |
-- |      | 2             |         2                   |
-- |      +-             -+                             |
-- +-                                                  -+
-- ------------------------------------------------------
--                  +-                         2 -+
--                  |         +-             -+   |
--                  |         | 1             |   |
--    x LambertW(x) | 1 + tan | - LambertW(x) |   |
--                  |         | 2             |   |
--                  |         +-             -+   |
--                  +-                           -+

-- of 29 used to work
--f:=((x^2+2)*LambertW(x^2)^2+x^2*(2*LambertW(x^2)+1))/(x*(1+LambertW(x^2)^3))
-- 26
--should be:
--                       2
--    2                2      2              2
--  (x  + 2) LambertW(x )  + x  (2 LambertW(x ) + 1)
--  ------------------------------------------------
--                               3
--                            2  
--           x (1 + LambertW(x ))

-- of 29 used to work
--integrate(f,x)
-- 27
--should be:
--                 2                    4
--1  4           2     4          2    x              2   2    2           2
--- x  LambertW(x ) + x LambertW(x ) + -- + LambertW(x ) x  + x  LambertW(x )
--2                                    2
-----------------------------------------------------------------------------
--                                              2
--              2          2                 2
--             x LambertW(x ) (1 + LambertW(x ))
--
--  +
--                     2
--   log(1 + LambertW(x ))

-- of 29 used to work
--f:=(2*LambertW(x^2)*cos(LambertW(x^2))*(a*x+LambertW(x^2))+a*x*(1+LambertW(x^2)) + 2*LambertW(x^2))/((1+LambertW(x^2))*(a*x+LambertW(x^2))*x)
--
-- 28
--+-                                                       -+
--|                                                         |
--|             2                2                    2     |
--| 2 LambertW(x ) cos(LambertW(x )) (a x + LambertW(x )) + |
--|                                                         |
--|                   2                 2                   |
--| a x (1 + LambertW(x )) + 2 LambertW(x )                 |
--|                                                         |
--+-                                                       -+
-------------------------------------------------------------
--                2                 2
-- (1 + LambertW(x ))(a x+LambertW(x )) x
--

-- 29 of 29 used to work
integrate(f,x)
 

   (1)  f x
                                            Type: Polynomial Fraction Integer
--
-- 29
--   
--        +-              -+
--        | 1           2  |
--  2 tan | - LambertW(x ) |
--        | 2              |
--        +-              -+                          2
--  --------------------------- + log(a x + LambertW(x ))
--                            2
--          +-              -+
--          | 1           2  |
--  1 + tan | - LambertW(x ) |
--          | 2              |
--          +-              -+
--
--
)spool 
 
Starts dribbling to perm.output (2010/3/27, 18:30:42).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 51
x : List List PrimeField 29 :=
 [[23,19,7,9,12,11,15],[22,4,14,18,2,5,8],[21,20,10,16,13,6,17]]
 

   (1)  [[23,19,7,9,12,11,15],[22,4,14,18,2,5,8],[21,20,10,16,13,6,17]]
                                                Type: List List PrimeField 29
--R 
--R
--R   (1)  [[23,19,7,9,12,11,15],[22,4,14,18,2,5,8],[21,20,10,16,13,6,17]]
--R                                                Type: List List PrimeField 29
--E 1

--S 2 of 51
px : PERM PrimeField 29 := x
 

   (2)  (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (2)  (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
--R                                              Type: Permutation PrimeField 29
--E 2

--S 3 of 51
w : List PrimeField 29 :=
 [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
 

   (3)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
                                                     Type: List PrimeField 29
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
--R                                                     Type: List PrimeField 29
--E 3

--S 4 of 51
pw : PERM PrimeField 29 := cycle w
 

   (4)  (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (4)  (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
--R                                              Type: Permutation PrimeField 29
--E 4

--S 5 of 51
k : List List PrimeField 29 :=
 [[23,24],[22,16],[21,9],[20,19],[18,12],[17,14],[15,7],[10,6]]
 

   (5)  [[23,24],[22,16],[21,9],[20,19],[18,12],[17,14],[15,7],[10,6]]
                                                Type: List List PrimeField 29
--R 
--R
--R   (5)  [[23,24],[22,16],[21,9],[20,19],[18,12],[17,14],[15,7],[10,6]]
--R                                                Type: List List PrimeField 29
--E 5

--S 6 of 51
pk : PERM PrimeField 29 := cycles k
 

   (6)  (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (6)  (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
--R                                              Type: Permutation PrimeField 29
--E 6

--S 7 of 51
pw*pk
 

   (7)  (13 14 18)(8 9 22 17 15)(1 2 3 4 5 6 11 12 19 21 10 7 16 23 24)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (7)  (13 14 18)(8 9 22 17 15)(1 2 3 4 5 6 11 12 19 21 10 7 16 23 24)
--R                                              Type: Permutation PrimeField 29
--E 7

--S 8 of 51
px**3
 

   (8)  (2 22 18 8 14 5 4)(6 20 13 21 16 17 10)(7 11 19 12 23 9 15)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (8)  (2 22 18 8 14 5 4)(6 20 13 21 16 17 10)(7 11 19 12 23 9 15)
--R                                              Type: Permutation PrimeField 29
--E 8

--S 9 of 51
inv px
 

   (9)  (2 18 14 4 22 8 5)(6 13 16 10 20 21 17)(7 19 23 15 11 12 9)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (9)  (2 18 14 4 22 8 5)(6 13 16 10 20 21 17)(7 19 23 15 11 12 9)
--R                                              Type: Permutation PrimeField 29
--E 9

--S 10 of 51
eval(px,17::PrimeField(29))
 

   (10)  21
                                                          Type: PrimeField 29
--R 
--R
--R   (10)  21
--R                                                          Type: PrimeField 29
--E 10

--S 11 of 51
commutator(pk,pw)
 

   (11)  (5 21 7 15 9)(6 17 11 14 10)(8 19 12 18 20)(13 22 23 24 16)
                                              Type: Permutation PrimeField 29
--R 
--R
--R   (11)  (5 21 7 15 9)(6 17 11 14 10)(8 19 12 18 20)(13 22 23 24 16)
--R                                              Type: Permutation PrimeField 29
--E 11

--S 12 of 51
orbit(px,11::PrimeField(29))
 

   (12)  {11,15,23,19,7,9,12}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (12)  {11,15,23,19,7,9,12}
--R                                                      Type: Set PrimeField 29
--E 12

--S 13 of 51
movedPoints(pk)
 

   (13)  {16,22,19,20,14,17,6,10,15,7,18,12,21,9,23,24}
                                                      Type: Set PrimeField 29
--R 
--R
--R   (13)  {16,22,19,20,14,17,6,10,15,7,18,12,21,9,23,24}
--R                                                      Type: Set PrimeField 29
--E 13

--S 14 of 51
gp1 : PERMGRP PrimeField 29 := [ px , pk ]
 

   (14)
   <
       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
    ,
       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
     >
                                         Type: PermutationGroup PrimeField 29
--R 
--R
--R   (14)
--R   <
--R       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
--R    ,
--R       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
--R     >
--R                                         Type: PermutationGroup PrimeField 29
--E 14

--S 15 of 51
gp2 : PERMGRP PrimeField 29 := [ pw , px ]
 

   (15)
   <
       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
    ,
       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
     >
                                         Type: PermutationGroup PrimeField 29
--R 
--R
--R   (15)
--R   <
--R       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
--R    ,
--R       (2 5 8 22 4 14 18)(6 17 21 20 10 16 13)(7 9 12 11 15 23 19)
--R     >
--R                                         Type: PermutationGroup PrimeField 29
--E 15

--S 16 of 51
gp3 : PERMGRP PrimeField 29 := [ pw , pk ]
 

   (16)
   <
       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
    ,
       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
     >
                                         Type: PermutationGroup PrimeField 29
--R 
--R
--R   (16)
--R   <
--R       (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
--R    ,
--R       (6 10)(7 15)(9 21)(12 18)(14 17)(16 22)(19 20)(23 24)
--R     >
--R                                         Type: PermutationGroup PrimeField 29
--E 16

--S 17 of 51
order gp1
 

   (17)  443520
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  443520
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 51
order gp2
 

   (18)  10200960
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  10200960
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 51
order gp3
 

   (19)  244823040
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  244823040
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 51
(m1,m2,m3,m4): Matrix PrimeField 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 51
m1 := [[1,1,0],[0,1,0],[0,0,1]]
 

         +1  1  0+
         |       |
   (21)  |0  1  0|
         |       |
         +0  0  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  1  0+
--R         |       |
--R   (21)  |0  1  0|
--R         |       |
--R         +0  0  1+
--R                                                    Type: Matrix PrimeField 2
--E 21

--S 22 of 51
m2 := [[1,0,0],[0,1,1],[0,0,1]]
 

         +1  0  0+
         |       |
   (22)  |0  1  1|
         |       |
         +0  0  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  0  0+
--R         |       |
--R   (22)  |0  1  1|
--R         |       |
--R         +0  0  1+
--R                                                    Type: Matrix PrimeField 2
--E 22

--S 23 of 51
m3 := [[1,0,0],[1,1,0],[0,0,1]]
 

         +1  0  0+
         |       |
   (23)  |1  1  0|
         |       |
         +0  0  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  0  0+
--R         |       |
--R   (23)  |1  1  0|
--R         |       |
--R         +0  0  1+
--R                                                    Type: Matrix PrimeField 2
--E 23

--S 24 of 51
m4 := [[1,0,0],[0,1,0],[0,1,1]]
 

         +1  0  0+
         |       |
   (24)  |0  1  0|
         |       |
         +0  1  1+
                                                    Type: Matrix PrimeField 2
--R 
--R
--R         +1  0  0+
--R         |       |
--R   (24)  |0  1  0|
--R         |       |
--R         +0  1  1+
--R                                                    Type: Matrix PrimeField 2
--E 24

--S 25 of 51
vl : List Vector PrimeField 2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 51
vl := [[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
 

   (26)  [[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
                                               Type: List Vector PrimeField 2
--R 
--R
--R   (26)  [[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
--R                                               Type: List Vector PrimeField 2
--E 26

--S 28 of 51
ll1 : List List Vector PrimeField 2 :=
   [ [ vl.i , m1*(vl.i) ] for i in 1..7 ]
 

   (27)
   [[[0,0,1],[0,0,1]], [[0,1,0],[1,1,0]], [[0,1,1],[1,1,1]], [[1,0,0],[1,0,0]],
    [[1,0,1],[1,0,1]], [[1,1,0],[0,1,0]], [[1,1,1],[0,1,1]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (27)
--R   [[[0,0,1],[0,0,1]], [[0,1,0],[1,1,0]], [[0,1,1],[1,1,1]], [[1,0,0],[1,0,0]],
--R    [[1,0,1],[1,0,1]], [[1,1,0],[0,1,0]], [[1,1,1],[0,1,1]]]
--R                                          Type: List List Vector PrimeField 2
--E 28

--S 29 of 51
ll2 : List List Vector PrimeField 2 :=
   [ [ vl.i , m2*(vl.i) ] for i in 1..7 ]
 

   (28)
   [[[0,0,1],[0,1,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,0,1]], [[1,0,0],[1,0,0]],
    [[1,0,1],[1,1,1]], [[1,1,0],[1,1,0]], [[1,1,1],[1,0,1]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (28)
--R   [[[0,0,1],[0,1,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,0,1]], [[1,0,0],[1,0,0]],
--R    [[1,0,1],[1,1,1]], [[1,1,0],[1,1,0]], [[1,1,1],[1,0,1]]]
--R                                          Type: List List Vector PrimeField 2
--E 29

--S 30 of 51
ll3 : List List Vector PrimeField 2 :=
   [ [ vl.i , m3*(vl.i) ] for i in 1..7 ]
 

   (29)
   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,1,1]], [[1,0,0],[1,1,0]],
    [[1,0,1],[1,1,1]], [[1,1,0],[1,0,0]], [[1,1,1],[1,0,1]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (29)
--R   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,0]], [[0,1,1],[0,1,1]], [[1,0,0],[1,1,0]],
--R    [[1,0,1],[1,1,1]], [[1,1,0],[1,0,0]], [[1,1,1],[1,0,1]]]
--R                                          Type: List List Vector PrimeField 2
--E 30

--S 31 of 51
ll4 : List List Vector PrimeField 2 :=
   [ [ vl.i , m4*(vl.i) ] for i in 1..7 ]
 

   (30)
   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,1]], [[0,1,1],[0,1,0]], [[1,0,0],[1,0,0]],
    [[1,0,1],[1,0,1]], [[1,1,0],[1,1,1]], [[1,1,1],[1,1,0]]]
                                          Type: List List Vector PrimeField 2
--R 
--R
--R   (30)
--R   [[[0,0,1],[0,0,1]], [[0,1,0],[0,1,1]], [[0,1,1],[0,1,0]], [[1,0,0],[1,0,0]],
--R    [[1,0,1],[1,0,1]], [[1,1,0],[1,1,1]], [[1,1,1],[1,1,0]]]
--R                                          Type: List List Vector PrimeField 2
--E 31

--S 32 of 51
el1 : PERM Vector PrimeField 2 := coerceListOfPairs ll1
 

   (31)  ([1,1,0] [0,1,0])([1,1,1] [0,1,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (31)  ([1,1,0] [0,1,0])([1,1,1] [0,1,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 32

--S 33 of 51
el2 : PERM Vector PrimeField 2 := coerceListOfPairs ll2
 

   (32)  ([0,1,1] [0,0,1])([1,1,1] [1,0,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (32)  ([0,1,1] [0,0,1])([1,1,1] [1,0,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 33

--S 34 of 51
el3 : PERM Vector PrimeField 2 := coerceListOfPairs ll3
 

   (33)  ([1,1,0] [1,0,0])([1,1,1] [1,0,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (33)  ([1,1,0] [1,0,0])([1,1,1] [1,0,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 34

--S 35 of 51
el4 : PERM Vector PrimeField 2 := coerceListOfPairs ll4
 

   (34)  ([0,1,1] [0,1,0])([1,1,1] [1,1,0])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (34)  ([0,1,1] [0,1,0])([1,1,1] [1,1,0])
--R                                        Type: Permutation Vector PrimeField 2
--E 35

--S 36 of 51
eval ( el3 , vl.5 )
 

   (35)  [1,1,1]
                                                    Type: Vector PrimeField 2
--R 
--R
--R   (35)  [1,1,1]
--R                                                    Type: Vector PrimeField 2
--E 36

--S 37 of 51
el2 * el1
 

   (36)  ([0,1,0] [1,1,0])([0,1,1] [1,0,1] [1,1,1] [0,0,1])
                                        Type: Permutation Vector PrimeField 2
--R 
--R
--R   (36)  ([0,1,0] [1,1,0])([0,1,1] [1,0,1] [1,1,1] [0,0,1])
--R                                        Type: Permutation Vector PrimeField 2
--E 37

--S 38 of 51
movedPoints el4
 

   (37)  {[1,1,1],[1,1,0],[0,1,1],[0,1,0]}
                                                Type: Set Vector PrimeField 2
--R 
--R
--R   (37)  {[1,1,1],[1,1,0],[0,1,1],[0,1,0]}
--R                                                Type: Set Vector PrimeField 2
--E 38

--S 39 of 51
gl : PERMGRP Vector PrimeField 2 := [ el1 , el2 , el3 , el4 ]
 

   (38)
   <
       ([1,1,0] [0,1,0])([1,1,1] [0,1,1]),([0,1,1] [0,0,1])([1,1,1] [1,0,1])
    ,
       ([1,1,0] [1,0,0])([1,1,1] [1,0,1]),([0,1,1] [0,1,0])([1,1,1] [1,1,0])
     >
                                   Type: PermutationGroup Vector PrimeField 2
--R 
--R
--R   (38)
--R   <
--R       ([1,1,0] [0,1,0])([1,1,1] [0,1,1]),([0,1,1] [0,0,1])([1,1,1] [1,0,1])
--R    ,
--R       ([1,1,0] [1,0,0])([1,1,1] [1,0,1]),([0,1,1] [0,1,0])([1,1,1] [1,1,0])
--R     >
--R                                   Type: PermutationGroup Vector PrimeField 2
--E 39

--S 40 of 51
order gl
 

   (39)  168
                                                        Type: PositiveInteger
--R 
--R
--R   (39)  168
--R                                                        Type: PositiveInteger
--E 40

--S 41 of 51
setOfVectors : Set Vector PrimeField 2 := brace [ vl.2 , vl.4 , vl.6 ]
 

   (40)  {[0,1,0],[1,0,0],[1,1,0]}
                                                Type: Set Vector PrimeField 2
--R 
--R
--R   (40)  {[0,1,0],[1,0,0],[1,1,0]}
--R                                                Type: Set Vector PrimeField 2
--E 41

--S 42 of 51
orbit ( gl, setOfVectors )
 

   (41)
   {{[0,1,0],[1,0,0],[1,1,0]}, {[0,1,1],[1,0,0],[1,1,1]},
    {[0,0,1],[1,0,0],[1,0,1]}, {[0,1,1],[1,1,0],[1,0,1]},
    {[0,0,1],[1,1,0],[1,1,1]}, {[1,1,1],[0,1,0],[1,0,1]},
    {[0,0,1],[0,1,0],[0,1,1]}}
                                            Type: Set Set Vector PrimeField 2
--R 
--R
--R   (41)
--R   {{[0,1,0],[1,0,0],[1,1,0]}, {[0,1,1],[1,0,0],[1,1,1]},
--R    {[0,0,1],[1,0,0],[1,0,1]}, {[0,1,1],[1,1,0],[1,0,1]},
--R    {[0,0,1],[1,1,0],[1,1,1]}, {[1,1,1],[0,1,0],[1,0,1]},
--R    {[0,0,1],[0,1,0],[0,1,1]}}
--R                                            Type: Set Set Vector PrimeField 2
--E 42

--S 43 of 51
listOfVectors : List Vector PrimeField 2 := parts setOfVectors
 

   (42)  [[0,1,0],[1,0,0],[1,1,0]]
                                               Type: List Vector PrimeField 2
--R 
--R
--R   (42)  [[0,1,0],[1,0,0],[1,1,0]]
--R                                               Type: List Vector PrimeField 2
--E 43

--S 44 of 51
orbit ( gl, listOfVectors )
 

   (43)
   {[[0,1,0],[1,0,0],[1,1,0]], [[1,1,0],[1,0,0],[0,1,0]],
    [[0,1,0],[1,1,0],[1,0,0]], [[0,1,1],[1,0,0],[1,1,1]],
    [[1,0,0],[1,1,0],[0,1,0]], [[1,1,1],[1,0,0],[0,1,1]],
    [[1,1,0],[0,1,0],[1,0,0]], [[0,1,1],[1,1,1],[1,0,0]],
    [[0,0,1],[1,0,0],[1,0,1]], [[0,1,1],[1,1,0],[1,0,1]],
    [[1,0,0],[0,1,0],[1,1,0]], [[1,0,0],[1,1,1],[0,1,1]],
    [[1,0,1],[1,0,0],[0,0,1]], [[1,0,1],[1,1,0],[0,1,1]],
    [[1,1,1],[0,1,1],[1,0,0]], [[0,0,1],[1,0,1],[1,0,0]],
    [[0,1,1],[1,0,1],[1,1,0]], [[0,0,1],[1,1,0],[1,1,1]],
    [[1,1,1],[0,1,0],[1,0,1]], [[0,1,0],[1,1,1],[1,0,1]],
    [[1,0,0],[0,1,1],[1,1,1]], [[1,0,0],[1,0,1],[0,0,1]],
    [[1,1,0],[1,0,1],[0,1,1]], [[1,1,1],[1,1,0],[0,0,1]],
    [[1,0,1],[0,1,0],[1,1,1]], [[1,0,1],[1,1,1],[0,1,0]],
    [[1,0,1],[0,0,1],[1,0,0]], [[1,0,1],[0,1,1],[1,1,0]],
    [[0,0,1],[1,1,1],[1,1,0]], [[1,1,1],[1,0,1],[0,1,0]],
    [[0,1,0],[1,0,1],[1,1,1]], [[0,0,1],[0,1,0],[0,1,1]],
    [[1,1,0],[0,1,1],[1,0,1]], [[1,0,0],[0,0,1],[1,0,1]],
    [[1,1,0],[1,1,1],[0,0,1]], [[0,1,1],[0,1,0],[0,0,1]],
    [[1,1,1],[0,0,1],[1,1,0]], [[0,0,1],[0,1,1],[0,1,0]],
    [[1,1,0],[0,0,1],[1,1,1]], [[0,1,0],[0,1,1],[0,0,1]],
    [[0,1,1],[0,0,1],[0,1,0]], [[0,1,0],[0,0,1],[0,1,1]]}
                                           Type: Set List Vector PrimeField 2
--R 
--R
--R   (43)
--R   {[[0,1,0],[1,0,0],[1,1,0]], [[1,1,0],[1,0,0],[0,1,0]],
--R    [[0,1,0],[1,1,0],[1,0,0]], [[0,1,1],[1,0,0],[1,1,1]],
--R    [[1,0,0],[1,1,0],[0,1,0]], [[1,1,1],[1,0,0],[0,1,1]],
--R    [[1,1,0],[0,1,0],[1,0,0]], [[0,1,1],[1,1,1],[1,0,0]],
--R    [[0,0,1],[1,0,0],[1,0,1]], [[0,1,1],[1,1,0],[1,0,1]],
--R    [[1,0,0],[0,1,0],[1,1,0]], [[1,0,0],[1,1,1],[0,1,1]],
--R    [[1,0,1],[1,0,0],[0,0,1]], [[1,0,1],[1,1,0],[0,1,1]],
--R    [[1,1,1],[0,1,1],[1,0,0]], [[0,0,1],[1,0,1],[1,0,0]],
--R    [[0,1,1],[1,0,1],[1,1,0]], [[0,0,1],[1,1,0],[1,1,1]],
--R    [[1,1,1],[0,1,0],[1,0,1]], [[0,1,0],[1,1,1],[1,0,1]],
--R    [[1,0,0],[0,1,1],[1,1,1]], [[1,0,0],[1,0,1],[0,0,1]],
--R    [[1,1,0],[1,0,1],[0,1,1]], [[1,1,1],[1,1,0],[0,0,1]],
--R    [[1,0,1],[0,1,0],[1,1,1]], [[1,0,1],[1,1,1],[0,1,0]],
--R    [[1,0,1],[0,0,1],[1,0,0]], [[1,0,1],[0,1,1],[1,1,0]],
--R    [[0,0,1],[1,1,1],[1,1,0]], [[1,1,1],[1,0,1],[0,1,0]],
--R    [[0,1,0],[1,0,1],[1,1,1]], [[0,0,1],[0,1,0],[0,1,1]],
--R    [[1,1,0],[0,1,1],[1,0,1]], [[1,0,0],[0,0,1],[1,0,1]],
--R    [[1,1,0],[1,1,1],[0,0,1]], [[0,1,1],[0,1,0],[0,0,1]],
--R    [[1,1,1],[0,0,1],[1,1,0]], [[0,0,1],[0,1,1],[0,1,0]],
--R    [[1,1,0],[0,0,1],[1,1,1]], [[0,1,0],[0,1,1],[0,0,1]],
--R    [[0,1,1],[0,0,1],[0,1,0]], [[0,1,0],[0,0,1],[0,1,1]]}
--R                                           Type: Set List Vector PrimeField 2
--E 44

--S 45 of 51
f : PERM INT := cycles [[11,13,15,17],[12,14,16,18],[51,31,21,41],[53,33,23,43],_
             [52,32,22,42]]
 

   (44)  (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
                                                    Type: Permutation Integer
--R 
--R
--R   (44)  (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
--R                                                    Type: Permutation Integer
--E 45

--S 46 of 51
r : PERM INT := cycles [[21,23,25,27],[22,24,26,28],[13,37,67,43],[15,31,61,45],_
             [14,38,68,44]]
 

   (45)  (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
                                                    Type: Permutation Integer
--R 
--R
--R   (45)  (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
--R                                                    Type: Permutation Integer
--E 46

--S 47 of 51
(f**2*r**2)**3
 

   (46)  (12 16)(24 28)(32 42)(38 44)
                                                    Type: Permutation Integer
--R 
--R
--R   (46)  (12 16)(24 28)(32 42)(38 44)
--R                                                    Type: Permutation Integer
--E 47

--S 48 of 51
rc := rubiksGroup()
 

   (47)
   <
       (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
    ,
       (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
    ,
       (11 57 61 23)(12 58 62 24)(13 51 63 25)(31 33 35 37)(32 34 36 38)
    ,
       (15 27 65 53)(16 28 66 54)(17 21 67 55)(41 43 45 47)(42 44 46 48)
    ,
       (11 41 65 35)(17 47 63 33)(18 48 64 34)(51 53 55 57)(52 54 56 58)
    ,
       (25 35 55 45)(26 36 56 46)(27 37 57 47)(61 63 65 67)(62 64 66 68)
     >
                                               Type: PermutationGroup Integer
--R 
--R
--R   (47)
--R   <
--R       (11 13 15 17)(12 14 16 18)(21 41 51 31)(22 42 52 32)(23 43 53 33)
--R    ,
--R       (13 37 67 43)(14 38 68 44)(15 31 61 45)(21 23 25 27)(22 24 26 28)
--R    ,
--R       (11 57 61 23)(12 58 62 24)(13 51 63 25)(31 33 35 37)(32 34 36 38)
--R    ,
--R       (15 27 65 53)(16 28 66 54)(17 21 67 55)(41 43 45 47)(42 44 46 48)
--R    ,
--R       (11 41 65 35)(17 47 63 33)(18 48 64 34)(51 53 55 57)(52 54 56 58)
--R    ,
--R       (25 35 55 45)(26 36 56 46)(27 37 57 47)(61 63 65 67)(62 64 66 68)
--R     >
--R                                               Type: PermutationGroup Integer
--E 48

--S 49 of 51
order rc
 

   (48)  43252003274489856000
                                                        Type: PositiveInteger
--R 
--R
--R   (48)  43252003274489856000
--R                                                        Type: PositiveInteger
--E 49

--S 50 of 51
orbits rc
 

   (49)
   {{11,13,15,17,21,23,25,27,31,33,35,37,41,43,45,47,51,53,55,57,61,63,65,67},
    {12,14,16,18,22,24,26,28,32,34,36,38,42,44,46,48,52,54,56,58,62,64,66,68}}
                                                        Type: Set Set Integer
--R 
--R
--R   (49)
--R   {{11,13,15,17,21,23,25,27,31,33,35,37,41,43,45,47,51,53,55,57,61,63,65,67},
--R    {12,14,16,18,22,24,26,28,32,34,36,38,42,44,46,48,52,54,56,58,62,64,66,68}}
--R                                                        Type: Set Set Integer
--E 50

--S 51 of 51
member? (cycles([[12,14],[32,22]])$(PERM INT),rc)
 

   (50)  false
                                                                Type: Boolean
--R 
--R
--R   (50)  false
--R                                                                Type: Boolean
--E 51
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read zimmer
 
--Copyright The Numerical Algorithms Group Limited 1996.
)set break resume
 

-- First Order Equations

-- 1

u := operator 'u
 

   (1)  u
                                                          Type: BasicOperator
ode := (x^4-x^3)*D(u x,x) + 2*x^4*u(x) = x^3/3 + C
 

                                   3
          4    3  ,        4      x  + 3C
   (2)  (x  - x )u (x) + 2x u(x)= -------
                                     3
                                            Type: Equation Expression Integer
solve(ode,u,x)
 

                         3     2                     - 2x
                       2x  - 3x  + 6C              %e
   (3)  [particular= ------------------,basis= [-----------]]
                        4      3      2          2
                     12x  - 24x  + 12x          x  - 2x + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 2
)clear all
 

u := operator 'u
 

   (1)  u
                                                          Type: BasicOperator
ode := -D(u x,x)/2 + u(x) = sin(x)
 

           ,
        - u (x) + 2u(x)

   (2)  ---------------= sin(x)
               2
                                            Type: Equation Expression Integer
solve(ode,u,x)
 

                     4sin(x) + 2cos(x)           2x
   (3)  [particular= -----------------,basis= [%e  ]]
                             5
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 3
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x) = y(x)/(y(x)*log(y(x)) + x)
 

         ,            y(x)
   (2)  y (x)= -----------------
               y(x)log(y(x)) + x
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                     2
        y(x)log(y(x))  - 2x
   (3)  -------------------
               2y(x)
                                          Type: Union(Expression Integer,...)

-- 4
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := 2*y(x)*D(y x,x)^2 -2*x*D(y x,x)-y(x) = 0
 

              ,   2      ,
   (2)  2y(x)y (x)  - 2xy (x) - y(x)= 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 5
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x) + y(x) = y(x)^3*sin(x)
 

         ,                3
   (2)  y (x) + y(x)= y(x) sin(x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

               2              2
        - 4y(x) sin(x) - 2y(x) cos(x) + 5
   (3)  ---------------------------------
                         2  2x
                    5y(x) %e
                                          Type: Union(Expression Integer,...)

-- 6
)clear all 
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
P := operator 'P
 

   (2)  P
                                                          Type: BasicOperator
Q := operator 'Q
 

   (3)  Q
                                                          Type: BasicOperator
ode := D(y x,x) + P(x)*y(x) = Q(x)*y(x)^n
 

         ,                        n
   (4)  y (x) + P(x)y(x)= Q(x)y(x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (5)  "failed"
                                                    Type: Union("failed",...)
solve(eval(ode,n=1),y,x)
 

                                    x
                                  ++
                                  |   (Q(%M) - P(%M))d%M
                                 ++
   (6)  [particular= 0,basis= [%e                        ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
solve(eval(ode,n=2),y,x)
 
 
Daly Bug
   >> Error detected within library code:
   Function not supported by Risch d.e.

   Continuing to read the file...

solve(eval(ode,n=%pi),y,x)
 

   (7)  "failed"
                                                    Type: Union("failed",...)
solve(eval(ode,n=%e),y,x)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
solve(eval(ode,n=sqrt(2)),y,x)
 

   (9)  "failed"
                                                    Type: Union("failed",...)

-- 7
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := (x^2-1)*D(y x,x)^2 - 2*x*y(x)*D(y x,x)+(y x)^2 - 1 = 0
 

          2      ,   2           ,          2
   (2)  (x  - 1)y (x)  - 2x y(x)y (x) + y(x)  - 1= 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 8
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
f := operator 'f
 

   (2)  f
                                                          Type: BasicOperator
g := operator 'g
 

   (3)  g
                                                          Type: BasicOperator
ode := f(x*D(y x,x) - y(x)) = g(D(y x,x))
 

            ,                ,
   (4)  f(xy (x) - y(x))= g(y (x))

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...


-- 9
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x)  = (3*x^2-y(x)^2-7)/(exp(y(x))+2*x*y(x)+1)
 

                       2     2
         ,       - y(x)  + 3x  - 7
   (2)  y (x)= --------------------
                 y(x)
               %e     + 2x y(x) + 1
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

          y(x)         2           3
   (3)  %e     + x y(x)  + y(x) - x  + 7x
                                          Type: Union(Expression Integer,...)

-- 10
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x)  = (2*x^3*y(x) - (y x)^4)/(x^4 - 2*x*(y x)^3)
 

                   4     3
         ,     y(x)  - 2x y(x)
   (2)  y (x)= ---------------
                       3    4
                2x y(x)  - x
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)  "failed"
                                                    Type: Union("failed",...)

-- 11
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x)*(D(y x,x) + y(x)) = x*(x + y(x))
 

         ,   2        ,               2
   (2)  y (x)  + y(x)y (x)= x y(x) + x

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 12
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x) = x/(x^2*(y x)^2 + (y x)^5)
 

         ,            x
   (2)  y (x)= ---------------
                   5    2    2
               y(x)  + x y(x)
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                                     3
                                2y(x)
                              - ------
                3     2            3
        (- 2y(x)  - 2x  - 3)%e
   (3)  ------------------------------
                       4
                                          Type: Union(Expression Integer,...)

-- 13
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := y(x) = 2*x*D(y x,x) - a*D(y x,x)^3
 

                   ,   3      ,
   (2)  y(x)= - a y (x)  + 2xy (x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 14
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := y(x) = 2*x*D(y x,x) - D(y x,x)^3
 

                 ,   3      ,
   (2)  y(x)= - y (x)  + 2xy (x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 15
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x) = exp(x)*(y x)^2 - y(x) + exp(-x)
 

         ,         2  x     - x
   (2)  y (x)= y(x) %e  + %e    - y(x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)  "failed"
                                                    Type: Union("failed",...)

-- 16
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x) = (y x)^2 - x*y(x) + 1
 

         ,         2
   (2)  y (x)= y(x)  - x y(x) + 1

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                         2
                        x
                      - --   x
                         2 ++       1
        (- y(x) + x)%e     |   - ------- d%M  + 1
                          ++           2
                                     %M
                                   - ---
                                      2
                                 %e
   (3)  -----------------------------------------
                                    2
                                   x
                                 - --
                                    2
                     (y(x) - x)%e
                                          Type: Union(Expression Integer,...)

-- 17
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x) = (9*x^8 + 1)/((y x)^2 +1)
 

                  8
         ,      9x  + 1
   (2)  y (x)= ---------
                   2
               y(x)  + 1
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

            3             9
        y(x)  + 3y(x) - 3x  - 3x
   (3)  ------------------------
                    3
                                          Type: Union(Expression Integer,...)

-- 18
)clear all
 

y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := y(x)=2*x*D(y x,x) + y(x)*D(y x,x)^2
 

                   ,   2      ,
   (2)  y(x)= y(x)y (x)  + 2xy (x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 19
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := x = y(x)*D(y x,x) - x*D(y x,x)^2
 

                ,   2        ,
   (2)  x= - x y (x)  + y(x)y (x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- Second Order Equations

-- 20
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2)*(a*x+b)^2+4*D(y x,x)*(a*x+b)*a+2*y(x)*a^2=0
 

          2 2             2  ,,         2          ,        2
   (2)  (a x  + 2a b x + b )y  (x) + (4a x + 4a b)y (x) + 2a y(x)= 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                                        x              2a x + b
   (3)  [particular= 0,basis= [------------------,------------------]]
                                2 2             2  2 2             2
                               a x  + 2a b x + b  a x  + 2a b x + b
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 21
)clear all
 
u := operator 'u
 

   (1)  u
                                                          Type: BasicOperator
ode := (x^2 - x)*D(u x,x,2) + (2*x^2+4*x-3)*D(u x,x) + 8*x*u(x)=1
 

          2      ,,         2           ,
   (2)  (x  - x)u  (x) + (2x  + 4x - 3)u (x) + 8x u(x)= 1

                                            Type: Equation Expression Integer
solve(ode,u,x)
 

                         3     2                                   - 2x
                       2x  - 3x  + 53                 1          %e
   (3)  [particular= ------------------,basis= [-------------,-----------]]
                        4      3      2          4     3    2  2
                     12x  - 24x  + 12x          x  - 2x  + x  x  - 2x + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 22
)clear all
 
w := operator 'w
 

   (1)  w
                                                          Type: BasicOperator
ode := (x^2 - x)*D(w x,x,2) + (1-2*x^2)*D(w x,x) + (4*x - 2)*w(x) = 0
 

          2      ,,           2      ,
   (2)  (x  - x)w  (x) + (- 2x  + 1)w (x) + (4x - 2)w(x)= 0

                                            Type: Equation Expression Integer
solve(ode,w,x)
 

                                2   2x
   (3)  [particular= 0,basis= [x ,%e  ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 23
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2) - D(y x,x) = 2*y(x)*D(y x,x)
 

         ,,       ,           ,
   (2)  y  (x) - y (x)= 2y(x)y (x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getfreelincoeff: not a linear ordinary differential equation

   Continuing to read the file...


-- 24
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2)/y(x) - D(y x,x)^2/y(x)^2 -1 + y(x)^(-3) = 0
 

            2 ,,           ,   2       3
        y(x) y  (x) - y(x)y (x)  - y(x)  + 1

   (2)  ------------------------------------= 0
                            3
                        y(x)
                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...


-- 25
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode :=  D(y x,x,2) + 2*x*D(y x,x) = 2*x
 

         ,,         ,
   (2)  y  (x) + 2xy (x)= 2x

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)  [particular= x,basis= [1,erf(x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 26
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := 2*y(x)*D(y x,x,2) - D(y x,x)^2 = (D(y x,x) - x*D(y x,x,2))^2/3
 

                               2 ,,   2      ,    ,,       ,   2
                              x y  (x)  - 2xy (x)y  (x) + y (x)
              ,,       ,   2
   (2)  2y(x)y  (x) - y (x) = ----------------------------------
                                               3
                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 27
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := x*D(y x,x,2) = 2*y(x)*D(y x,x)
 

          ,,           ,
   (2)  xy  (x)= 2y(x)y (x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getfreelincoeff: not a linear ordinary differential equation

   Continuing to read the file...


-- 28
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := (1-x)*(y(x)*D(y x,x,2) - D(y x,x)^2) + x^2*y(x)^2 = 0
 

                      ,,              ,   2    2    2
   (2)  (- x + 1)y(x)y  (x) + (x - 1)y (x)  + x y(x) = 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...


-- 29
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := x*y(x)*D(y x,x,2) + x*D(y x,x)^2 + y(x)*D(y x,x) = 0
 

               ,,         ,   2        ,
   (2)  x y(x)y  (x) + x y (x)  + y(x)y (x)= 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...


-- 30
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2)^2 - 2*D(y x,x,2)*D(y x,x) + 2*y(x)*D(y x,x) -y(x)^2 = 0
 

         ,,   2     ,    ,,            ,          2
   (2)  y  (x)  - 2y (x)y  (x) + 2y(x)y (x) - y(x) = 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 31 
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := (x^3/2-x^2)*D(y x,x,2) + (2*x^2-3*x+1)*D(y x,x) + (x-1)*y(x) = 0
 

          3     2  ,,         2           ,
        (x  - 2x )y  (x) + (4x  - 6x + 2)y (x) + (2x - 2)y(x)

   (2)  -----------------------------------------------------= 0
                                  2
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)
   [particular= 0,
                1               1                  1
              - - +-------+   - - +-------+   x   -- +----------+
                x |   1         x |   1     ++    %M |     1
    basis= [%e    |------- ,%e    |-------  |   %e   |---------- d%M ]]
                  | 2             | 2      ++        |  4      3
                 \|x  - 2x       \|x  - 2x          \|%M  - 2%M
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 32
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2) - 2*x*D(y x,x) + 2*y(x) = 3
 

         ,,         ,
   (2)  y  (x) - 2xy (x) + 2y(x)= 3

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                                           2
                                     x   %M
                     3             ++  %e
   (3)  [particular= -,basis= [x,x |   ----- d%M ]]
                     2            ++      2
                                        %M
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 33
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := sqrt(x)*D(y x,x,2) + 2*x*D(y x,x) + 3*y(x) = 0
 

         +-+ ,,         ,
   (2)  \|x y  (x) + 2xy (x) + 3y(x)= 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)  [particular= 0,basis= []]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 34
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := x^2*D(y x,x,2) + 3*x*D(y x,x) = 1/(x^4*y(x)^3)
 

         2 ,,         ,        1
   (2)  x y  (x) + 3xy (x)= -------
                             4    3
                            x y(x)
                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 35
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2) - 2/x^2*y(x) = 7*x^4 +3*x^3
 

         2 ,,
        x y  (x) - 2y(x)
                            4     3
   (2)  ----------------= 7x  + 3x
                2
               x
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                       7     6     3               3      3
                     3x  + 2x  - 7x  + 14         x  - 1 x  + 2
   (3)  [particular= --------------------,basis= [------,------]]
                              12x                    x      x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 36
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2) +y(x) = csc(x)
 

         ,,
   (2)  y  (x) + y(x)= csc(x)

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)
                            sin(x)                     2
   [particular= sin(x)log(----------) - sin(x)log(----------) - x cos(x),
                          cos(x) + 1              cos(x) + 1
    basis= [cos(x),sin(x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- Higher Order Equations

-- 37
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,7) - 14*D(y x,x,6) +80*D(y x,x,5) -242*D(y x,x,4) + _
         419*D(y x,x,3) - 416*D(y x,x,2) +220*D(y x,x) -48*y(x) = 0
 

   (2)
      (vii)         (vi)         (v)          (iv)          ,,,          ,,
     y     (x) - 14y    (x) + 80y   (x) - 242y    (x) + 419y   (x) - 416y  (x)

   + 
         ,
     220y (x) - 48y(x)

     =
     0
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                                 4x   3x   2x     2x   x     x  2  x
   (3)  [particular= 0,basis= [%e  ,%e  ,%e  ,x %e  ,%e ,x %e ,x %e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 38
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,4) -4/x^2*D(y x,x,2) + 8/x^3*D(y x,x) -8/x^4*D(y x,x) = 0
 

         4 (iv)        2 ,,               ,
        x y    (x) - 4x y  (x) + (8x - 8)y (x)

   (2)  --------------------------------------= 0
                           4
                          x
                                            Type: Equation Expression Integer
solve(ode,y,x)
 

   (3)  [particular= 0,basis= [1]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 39
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := (1+x+x^2)*D(y x,x,3) + (3+6*x)*D(y x,x,2) +6*D(y x,x) = 6*x
 

          2          ,,,               ,,        ,
   (2)  (x  + x + 1)y   (x) + (6x + 3)y  (x) + 6y (x)= 6x

                                            Type: Equation Expression Integer
solve(ode,y,x)
 

                         4
                        x  - 4                 1        x + 1
   (3)  [particular= ------------,basis= [----------,----------,1]]
                       2                   2          2
                     4x  + 4x + 4         x  + x + 1 x  + x + 1
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

-- 40
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := (D(y x,x)^2 +1)*D(y x,x,3) - 3*D(y x,x)*D(y x,x,2) = 0
 

          ,   2      ,,,        ,    ,,
   (2)  (y (x)  + 1)y   (x) - 3y (x)y  (x)= 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...


-- 41
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := 3*D(y x,x,2)*D(y x,x,4) - 5*D(y x,x,3)^2 = 0
 

          ,,    (iv)        ,,,   2
   (2)  3y  (x)y    (x) - 5y   (x) = 0

                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseLODE: not a linear ordinary differential equation

   Continuing to read the file...


-- Special Equations

-- 42
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y t,t) + a*y(t-1) = 0
 

         ,
   (2)  y (t) + a y(t - 1)= 0

                                            Type: Equation Expression Integer
solve(ode,y,t)
 

           t
         ++
   (3)   |   a y(%M - 1)d%M  + y(t)
        ++
                                          Type: Union(Expression Integer,...)

-- 43
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y(x,a),x) = a*y(x,a)
 

   (2)  y  (x,a)= a y(x,a)
         ,1
                                            Type: Equation Expression Integer
solve(ode,y,x)
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...


-- 44
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,4) = sin(x)
 

         (iv)
   (2)  y    (x)= sin(x)

                                            Type: Equation Expression Integer
solve(ode,y,x=0,[0,0,0,0])
 

                   3
        6sin(x) + x  - 6x
   (3)  -----------------
                6
                                          Type: Union(Expression Integer,...)

-- 45
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := x*D(y x,x,2) + D(y x,x) +2*x*y(x) =0
 

          ,,       ,
   (2)  xy  (x) + y (x) + 2x y(x)= 0

                                            Type: Equation Expression Integer
solve(ode,y,x=0,[1,0])
 

   (3)  "failed"
                                                    Type: Union("failed",...)

-- 46
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := x*D(y x,x)^2 -(y x)^2 + 1 = 0
 

           ,   2       2
   (2)  x y (x)  - y(x)  + 1= 0

                                            Type: Equation Expression Integer
solve(ode,y,x=0,[1])
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 47
)clear all
 
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
ode := D(y x,x,2) + y(x)*D(y x,x)^3 = 0
 

         ,,           ,   3
   (2)  y  (x) + y(x)y (x) = 0

                                            Type: Equation Expression Integer
solve(ode,y,x=0,[0,2])
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- Systems Of equations

-- 48
)clear all
 
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
y := operator 'y
 

   (2)  y
                                                          Type: BasicOperator
z := operator 'z
 

   (3)  z
                                                          Type: BasicOperator
odes := [D(x t,t) = -3*y(t)*z(t), D(y t,t) = 3*x(t)*z(t), D(z t,t) = -x(t)*y(t)]
 

          ,                  ,                ,
   (4)  [x (t)= - 3y(t)z(t),y (t)= 3x(t)z(t),z (t)= - x(t)y(t)]

                                       Type: List Equation Expression Integer
solve(odes,[x,y,z],t)
 
 
Daly Bug
   >> Error detected within library code:
   getfreelincoeff: not a linear ordinary differential equation

   Continuing to read the file...


-- 49
)clear all
 
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
y := operator 'y
 

   (2)  y
                                                          Type: BasicOperator
a := operator 'a
 

   (3)  a
                                                          Type: BasicOperator
b := operator 'b
 

   (4)  b
                                                          Type: BasicOperator
odes := [D(x t,t) = a(t)*((y t)^2 - (x t)^2) + 2*b(t)*x(t)*y(t) + 2*c*x(t),
         D(y t,t) = b(t)*((y t)^2 - (x t)^2) - 2*a(t)*x(t)*y(t) + 2*c*y(t)]
 

   (5)
     ,             2                           2
   [x (t)= a(t)y(t)  + 2b(t)x(t)y(t) - a(t)x(t)  + 2c x(t),

     ,             2                                    2
    y (t)= b(t)y(t)  + (- 2a(t)x(t) + 2c)y(t) - b(t)x(t) ]

                                       Type: List Equation Expression Integer
solve(odes,[x,y],t)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...


-- 50
)clear all
 
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
y := operator 'y
 

   (2)  y
                                                          Type: BasicOperator
odes := [D(x t,t) = x(t)*(1+cos(t)/(2+sin(t))), D(y t,t) = x(t) - y(t)]
 

          ,     x(t)sin(t) + x(t)cos(t) + 2x(t)  ,
   (3)  [x (t)= -------------------------------,y (t)= - y(t) + x(t)]
                           sin(t) + 2
                                       Type: List Equation Expression Integer
solve(odes,[x,y],t)
 

   (4)  "failed"
                                                    Type: Union("failed",...)

-- 51
)clear all
 
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
y := operator 'y
 

   (2)  y
                                                          Type: BasicOperator
odes := [D(x t,t) = 9*x(t) + 2*y(t), D(y t,t) = x(t) + 8*y(t)]
 

          ,                    ,
   (3)  [x (t)= 2y(t) + 9x(t),y (t)= 8y(t) + x(t)]

                                       Type: List Equation Expression Integer
solve(odes,[x,y],t)
 

                                            10t
                                      10t %e        7t     7t
   (4)  [particular= [0,0],basis= [[%e   ,-----],[%e  ,- %e  ]]]
                                            2
Type: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...)

-- 52
)clear all
 
x := operator 'x
 

   (1)  x
                                                          Type: BasicOperator
y := operator 'y
 

   (2)  y
                                                          Type: BasicOperator
odes := [D(x t,t) - x(t) - 2*y(t) = 0, D(x t,t,2) - 2*D(y t,t) = 2*t - cos(2*t)]
 

          ,                       ,,        ,
   (3)  [x (t) - 2y(t) - x(t)= 0,x  (t) - 2y (t)= - cos(2t) + 2t]

                                       Type: List Equation Expression Integer
solve(odes,[x,y],t)
 
 
Daly Bug
   >> Error detected within library code:
   solve: not a first order linear system

   Continuing to read the file...


-- 53
)clear all
 
y1 := operator 'y1
 

   (1)  y1
                                                          Type: BasicOperator
y2 := operator 'y2
 

   (2)  y2
                                                          Type: BasicOperator
odes := [D(y1 x,x) = -1/(x*(x^2 + 1))*y1(x) + 1/(x^2*(x^2 + 1))*y2(x)+1/x,
         D(y2 x,x) = -x^2/(x^2 + 1)*y1(x) + (2*x^2+1)/x/(x^2+1)*y2(x)+1]
 

   (3)
                               3                2              3         3
      ,     y2(x) - x y1(x) + x  + x   ,     (2x  + 1)y2(x) - x y1(x) + x  + x
   [y1 (x)= ------------------------,y2 (x)= ---------------------------------]
                      4    2                                3
                     x  + x                                x  + x
                                       Type: List Equation Expression Integer
solve(odes,[y1,y2],x)
 

                                                        1    2
   (4)  [particular= [log(x) - 1,x log(x) - x],basis= [[-,- x ],[1,x]]]
                                                        x
Type: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...)
)lisp (bye)
 
Starts dribbling to tancot.output (2010/3/27, 18:41:11).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
[[0.01,0.010000333,tan(0.01),tan(0.01)-(0.010000333)],_
[0.02,0.020002667,tan(0.02),tan(0.02)-(0.020002667)],_
[0.03,0.030009003,tan(0.03),tan(0.03)-(0.030009003)],_
[0.04,0.040021347,tan(0.04),tan(0.04)-(0.040021347)],_
[0.05,0.050041708,tan(0.05),tan(0.05)-(0.050041708)],_
[0.06,0.060072104,tan(0.06),tan(0.06)-(0.060072104)],_
[0.07,0.070114558,tan(0.07),tan(0.07)-(0.070114558)],_
[0.08,0.080171105,tan(0.08),tan(0.08)-(0.080171105)],_
[0.09,0.090243790,tan(0.09),tan(0.09)-(0.090243790)],_
[0.10,0.10033467,tan(0.10),tan(0.10)-(0.10033467)],_
[0.11,0.11044582,tan(0.11),tan(0.11)-(0.11044582)],_
[0.12,0.12057934,tan(0.12),tan(0.12)-(0.12057934)],_
[0.13,0.13073732,tan(0.13),tan(0.13)-(0.13073732)],_
[0.14,0.14092189,tan(0.14),tan(0.14)-(0.14092189)],_
[0.15,0.15113522,tan(0.15),tan(0.15)-(0.15113522)],_
[0.16,0.16137946,tan(0.16),tan(0.16)-(0.16137946)],_
[0.17,0.17165682,tan(0.17),tan(0.17)-(0.17165682)],_
[0.18,0.18196953,tan(0.18),tan(0.18)-(0.18196953)],_
[0.19,0.19231984,tan(0.19),tan(0.19)-(0.19231984)],_
[0.20,0.20271004,tan(0.20),tan(0.20)-(0.20271004)],_
[0.21,0.21314244,tan(0.21),tan(0.21)-(0.21314244)],_
[0.22,0.22361942,tan(0.22),tan(0.22)-(0.22361942)],_
[0.23,0.23414336,tan(0.23),tan(0.23)-(0.23414336)],_
[0.24,0.24471670,tan(0.24),tan(0.24)-(0.24471670)],_
[0.25,0.25534192,tan(0.25),tan(0.25)-(0.25534192)],_
[0.26,0.26602154,tan(0.26),tan(0.26)-(0.26602154)],_
[0.27,0.27675814,tan(0.27),tan(0.27)-(0.27675814)],_
[0.28,0.28755433,tan(0.28),tan(0.28)-(0.28755433)],_
[0.29,0.29841279,tan(0.29),tan(0.29)-(0.29841279)],_
[0.30,0.30933625,tan(0.30),tan(0.30)-(0.30933625)],_
[0.31,0.32032751,tan(0.31),tan(0.31)-(0.32032751)],_
[0.32,0.33138941,tan(0.32),tan(0.32)-(0.33138941)],_
[0.33,0.34252487,tan(0.33),tan(0.33)-(0.34252487)],_
[0.34,0.35373688,tan(0.34),tan(0.34)-(0.35373688)],_
[0.35,0.36502849,tan(0.35),tan(0.35)-(0.36502849)],_
[0.36,0.37640285,tan(0.36),tan(0.36)-(0.37640285)],_
[0.37,0.38786316,tan(0.37),tan(0.37)-(0.38786316)],_
[0.38,0.39941272,tan(0.38),tan(0.38)-(0.39941272)],_
[0.39,0.41105492,tan(0.39),tan(0.39)-(0.41105492)],_
[0.40,0.42279322,tan(0.40),tan(0.40)-(0.42279322)],_
[0.41,0.43463120,tan(0.41),tan(0.41)-(0.43463120)],_
[0.42,0.44657255,tan(0.42),tan(0.42)-(0.44657255)],_
[0.43,0.45862102,tan(0.43),tan(0.43)-(0.45862102)],_
[0.44,0.47078053,tan(0.44),tan(0.44)-(0.47078053)],_
[0.45,0.48305507,tan(0.45),tan(0.45)-(0.48305507)],_
[0.46,0.49544877,tan(0.46),tan(0.46)-(0.49544877)],_
[0.47,0.50796590,tan(0.47),tan(0.47)-(0.50796590)],_
[0.48,0.52061084,tan(0.48),tan(0.48)-(0.52061084)],_
[0.49,0.53338815,tan(0.49),tan(0.49)-(0.53338815)],_
[0.50,0.54630249,tan(0.50),tan(0.50)-(0.54630249)],_
[0.51,0.55935872,tan(0.51),tan(0.51)-(0.55935872)],_
[0.52,0.57256183,tan(0.52),tan(0.52)-(0.57256183)],_
[0.53,0.58591701,tan(0.53),tan(0.53)-(0.58591701)],_
[0.54,0.59942962,tan(0.54),tan(0.54)-(0.59942962)],_
[0.55,0.61310521,tan(0.55),tan(0.55)-(0.61310521)],_
[0.56,0.62694954,tan(0.56),tan(0.56)-(0.62694954)],_
[0.57,0.64096855,tan(0.57),tan(0.57)-(0.64096855)],_
[0.58,0.65516845,tan(0.58),tan(0.58)-(0.65516845)],_
[0.59,0.66955565,tan(0.59),tan(0.59)-(0.66955565)],_
[0.60,0.68413681,tan(0.60),tan(0.60)-(0.68413681)],_
[0.61,0.69891886,tan(0.61),tan(0.61)-(0.69891886)],_
[0.62,0.71390901,tan(0.62),tan(0.62)-(0.71390901)],_
[0.63,0.72911473,tan(0.63),tan(0.63)-(0.72911473)],_
[0.64,0.74454382,tan(0.64),tan(0.64)-(0.74454382)],_
[0.65,0.76020440,tan(0.65),tan(0.65)-(0.76020440)],_
[0.66,0.77610491,tan(0.66),tan(0.66)-(0.77610491)],_
[0.67,0.79225417,tan(0.67),tan(0.67)-(0.79225417)],_
[0.68,0.80866138,tan(0.68),tan(0.68)-(0.80866138)],_
[0.69,0.82533611,tan(0.69),tan(0.69)-(0.82533611)],_
[0.70,0.84228838,tan(0.70),tan(0.70)-(0.84228838)],_
[0.71,0.85952867,tan(0.71),tan(0.71)-(0.85952867)],_
[0.72,0.87706790,tan(0.72),tan(0.72)-(0.87706790)],_
[0.73,0.89491753,tan(0.73),tan(0.73)-(0.89491753)],_
[0.74,0.91308953,tan(0.74),tan(0.74)-(0.91308953)],_
[0.75,0.93159646,tan(0.75),tan(0.75)-(0.93159646)],_
[0.76,0.95045146,tan(0.76),tan(0.76)-(0.95045146)],_
[0.77,0.96966833,tan(0.77),tan(0.77)-(0.96966833)],_
[0.78,0.98926154,tan(0.78),tan(0.78)-(0.98926154)],_
[0.79,1.00924629,tan(0.79),tan(0.79)-(1.00924629)],_
[0.80,1.02963857,tan(0.80),tan(0.80)-(1.02963857)],_
[0.81,1.05045514,tan(0.81),tan(0.81)-(1.05045514)],_
[0.82,1.07171372,tan(0.82),tan(0.82)-(1.07171372)],_
[0.83,1.09343292,tan(0.83),tan(0.83)-(1.09343292)],_
[0.84,1.11563235,tan(0.84),tan(0.84)-(1.11563235)],_
[0.85,1.13833271,tan(0.85),tan(0.85)-(1.13833271)],_
[0.86,1.16155586,tan(0.86),tan(0.86)-(1.16155586)],_
[0.87,1.18532486,tan(0.87),tan(0.87)-(1.18532486)],_
[0.88,1.20966412,tan(0.88),tan(0.88)-(1.20966412)],_
[0.89,1.23459946,tan(0.89),tan(0.89)-(1.23459946)],_
[0.90,1.26015822,tan(0.90),tan(0.90)-(1.26015822)],_
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[1.59,-52.0669696,tan(1.59),tan(1.59)-(-52.0669696)],_
[1.60,-34.2325327,tan(1.60),tan(1.60)-(-34.2325327)]]
 

   (1)
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    [1.6,- 34.2325327,- 34.2325327355 57417056,- 0.3555741705 7 E -7]]
                                                        Type: List List Float
--R 
--R
--R   (1)
--R   [[0.01,0.010000333,0.0100003333 4666720637 1,0.3466672063 71 E -9],
--R    [0.02,0.020002667,0.0200026670 9340242389 7,0.9340242389 7 E -10],
--R    [0.03,0.030009003,0.0300090032 4118071632 9,0.2411807163 29 E -9],
--R    [0.04,0.040021347,0.0400213469 9551456207 2,- 0.4485437928 E -11],
--R    [0.05,0.050041708,0.0500417083 7553878891 2,0.3755387889 12 E -9],
--R    [0.06,0.060072104,0.0600721038 3129728751 1,- 0.1687027124 9 E -9],
--R    [0.07,0.070114558,0.0701145578 7200271322 9,- 0.1279972867 7 E -9],
--R    [0.08,0.080171105,0.0801711047 0807255711 8,- 0.2919274428 8 E -9],
--R    [0.09,0.09024379,0.0902437899 0978545046 6,- 0.9021454953 4 E -10],
--R    [0.1,0.10033467,0.1003346720 8545054506,0.2085450545 06 E -8],
--R    [0.11,0.11044582,0.1104458245 820405045,0.4582040504 5 E -8],
--R    [0.12,0.12057934,0.1205793372 1130531183,- 0.2788694688 17 E -8],
--R    [0.13,0.13073732,0.1307373180 0446004867,- 0.1995539951 33 E -8],
--R    [0.14,0.14092189,0.1409218949 9862537921,0.4998625379 21 E -8],
--R    [0.15,0.15113522,0.1511352180 5829507125,- 0.1941704928 75 E -8],
--R    [0.16,0.16137946,0.1613794607 3521095024,0.7352109502 4 E -9],
--R    [0.17,0.17165682,0.1716568221 7014270414,0.2170142704 14 E -8],
--R    [0.18,0.18196953,0.1819695290 4019848684,- 0.9598015131 64 E -9],
--R    [0.19,0.19231984,0.1923198375 554329145,- 0.2444567085 5 E -8],
--R    [0.2,0.20271004,0.2027100355 0867248332,- 0.4491327516 68 E -8],
--R    [0.21,0.21314244,0.2131424443 8264539723,0.4382645397 23 E -8],
--R    [0.22,0.22361942,0.2236194215 1868409245,0.1518684092 45 E -8],
--R    [0.23,0.23414336,0.2341433623 5146527061,0.2351465270 61 E -8],
--R    [0.24,0.2447167,0.2447167027 1446497862,0.2714464978 62 E -8],
--R    [0.25,0.25534192,0.2553419212 2103626651,0.1221036266 5 E -8],
--R    [0.26,0.26602154,0.2660215417 2626537908,0.1726265379 1 E -8],
--R    [0.27,0.27675814,0.2767581358 7503056579,- 0.4124969434 21 E -8],
--R    [0.28,0.28755433,0.2875543257 41976815,- 0.4258023185 E -8],
--R    [0.29,0.29841279,0.2984127865 694316513,- 0.3430568348 7 E -8],
--R    [0.3,0.30933625,0.3093362496 0962323304,- 0.3903767669 6 E -9],
--R    [0.31,0.32032751,0.3203275050 7792416023,- 0.4922075839 77 E -8],
--R    [0.32,0.33138941,0.3313894052 2423462352,- 0.4775765376 48 E -8],
--R    [0.33,0.34252487,0.3425248675 3003894803,- 0.2469961051 97 E -8],
--R    [0.34,0.35373688,0.3537368780 3912256577,- 0.1960877434 23 E -8],
--R    [0.35,0.36502849,0.3650284948 3042455832,0.4830424558 32 E -8],
--R    [0.36,0.37640285,0.3764028516 4202695764,0.1642026957 6 E -8],
--R    [0.37,0.38786316,0.3878631616 5584905222,0.1655849052 2 E -8],
--R    [0.38,0.39941272,0.3994127214 5322637827,0.1453226378 3 E -8],
--R    [0.39,0.41105492,0.4110549151 5221356343,- 0.4847786436 57 E -8],
--R    [0.4,0.42279322,0.4227932187 3816176198,- 0.1261838238 E -8],
--R    [0.41,0.4346312,0.4346312045 9988949299,0.4599889492 99 E -8],
--R    [0.42,0.44657255,0.4465725462 8459510803,- 0.3715404891 96 E -8],
--R    [0.43,0.45862102,0.4586210234 8555518632,0.3485555186 32 E -8],
--R    [0.44,0.47078053,0.4707805272 7762171492,- 0.2722378285 08 E -8],
--R    [0.45,0.48305507,0.4830550656 1657837051,- 0.4383421629 49 E -8],
--R    [0.46,0.49544877,0.4954487691 1954962242,- 0.8804503775 8 E -9],
--R    [0.47,0.5079659,0.5079658971 4488348004,- 0.285511652 E -8],
--R    [0.48,0.52061084,0.5206108441 9125804964,0.4191258049 65 E -8],
--R    [0.49,0.53338815,0.5333881466 3720305695,- 0.3362796943 1 E -8],
--R    [0.5,0.54630249,0.5463024898 4379051326,- 0.1562094867 E -9],
--R    [0.51,0.55935872,0.5593587156 4494521344,- 0.4355054786 56 E -8],
--R    [0.52,0.57256183,0.5725618302 5166841478,0.2516684148 E -9],
--R    [0.53,0.58591701,0.5859170125 9847085812,0.2598470858 1 E -8],
--R    [0.54,0.59942962,0.5994296231 6248975451,0.3162489754 5 E -8],
--R    [0.55,0.61310521,0.6131052132 8813564222,0.3288135642 2 E -8],
--R    [0.56,0.62694954,0.6269495350 5269815933,- 0.4947301840 67 E -8],
--R    [0.57,0.64096855,0.6409685517 1115591313,0.1711155913 1 E -8],
--R    [0.58,0.65516845,0.6551684487 6150824025,- 0.1238491759 7 E -8],
--R    [0.59,0.66955565,0.6695556456 753018611,- 0.4324698138 9 E -8],
--R    [0.6,0.68413681,0.6841368083 4169231707,- 0.1658307682 9 E -8],
--R    [0.61,0.69891886,0.6989188622 7739105048,0.2277391050 5 E -8],
--R    [0.62,0.71390901,0.7139090066 5924020594,- 0.3340759794 1 E -8],
--R    [0.63,0.72911473,0.7291147292 4096908976,- 0.7590309102 4 E -9],
--R    [0.64,0.74454382,0.7445438222 2096388599,0.2220963886 E -8],
--R    [0.65,0.7602044,0.7602043991 3367625635,- 0.8663237436 5 E -9],
--R    [0.66,0.77610491,0.7761049128 4366351779,0.2843663517 8 E -8],
--R    [0.67,0.79225417,0.7922541747 2825678628,0.4728256786 28 E -8],
--R    [0.68,0.80866138,0.8086613751 4256524544,- 0.4857434754 56 E -8],
--R    [0.69,0.82533611,0.8253361052 6902491172,- 0.4730975088 28 E -8],
--R    [0.7,0.84228838,0.8422883804 6307944813,0.4630794481 E -9],
--R    [0.71,0.85952867,0.8595286652 1694081593,- 0.4783059184 07 E -8],
--R    [0.72,0.8770679,0.8770678998 7483414069,- 0.1251658593 E -9],
--R    [0.73,0.89491753,0.8949175292 4581448181,- 0.7541855181 9 E -9],
--R    [0.74,0.91308953,0.9130895332 7430087206,0.3274300872 1 E -8],
--R    [0.75,0.93159646,0.9315964599 4407246117,- 0.559275388 E -10],
--R    [0.76,0.95045146,0.9504514606 0880299797,0.6088029979 7 E -9],
--R    [0.77,0.96966833,0.9696683279 6148947799,- 0.2038510522 E -8],
--R    [0.78,0.98926154,0.9892615368 7660491155,- 0.3123395088 4 E -8],
--R    [0.79,1.00924629,1.0092462883 827548811,- 0.1617245118 9 E -8],
--R    [0.8,1.02963857,1.0296385570 503640128,- 0.1294963598 73 E -7],
--R    [0.81,1.05045514,1.0504551421 088292806,0.2108829280 6 E -8],
--R    [0.82,1.07171372,1.0717137226 410736441,0.2641073644 1 E -8],
--R    [0.83,1.09343292,1.0934329172 409999188,- 0.2759000081 2 E -8],
--R    [0.84,1.11563235,1.1156323485 615378951,- 0.1438462104 9 E -8],
--R    [0.85,1.13833271,1.1383327132 284394134,0.3228439413 4 E -8],
--R    [0.86,1.16155586,1.1615558576 484476046,- 0.2351552395 4 E -8],
--R    [0.87,1.18532486,1.1853248603 008053505,0.3008053505 E -9],
--R    [0.88,1.20966412,1.2096641211 692683367,0.1169268336 7 E -8],
--R    [0.89,1.23459946,1.2345994590 490045825,- 0.9509954175 3 E -9],
--R    [0.9,1.26015822,1.2601582175 503391371,- 0.2449660862 9 E -8],
--R    [0.91,1.28636938,1.2863693807 208075758,0.7208075758 E -9],
--R    [0.92,1.3132637,1.3132636993 202478365,- 0.6797521635 E -9],
--R    [0.93,1.34087383,1.3408738289 128343042,- 0.1087165695 8 E -8],
--R    [0.94,1.36923448,1.3692344810 875628038,0.1087562803 8 E -8],
--R    [0.95,1.39838259,1.3983825892 876991461,- 0.7123008539 E -9],
--R    [0.96,1.42835749,1.4283574909 236105601,0.9236105601 E -9],
--R    [0.97,1.45920113,1.4592011276 663536858,- 0.2333646314 2 E -8],
--R    [0.98,1.49095827,1.4909582660 763114779,- 0.3923688522 1 E -8],
--R    [0.99,1.52367674,1.5236767410 179022725,0.1017902272 5 E -8],
--R    [1.0,1.55740772,1.5574077246 549022305,0.4654902230 5 E -8],
--R    [1.01,1.592206,1.5922060242 195703744,0.2421957037 44 E -7],
--R    [1.02,1.6281304,1.6281304122 125526001,0.1221255260 01 E -7],
--R    [1.03,1.665244,1.6652439932 315124346,- 0.6768487565 4 E -8],
--R    [1.04,1.7036146,1.7036146122 591331094,0.1225913310 94 E -7],
--R    [1.05,1.7433153,1.7433153099 831702625,0.9983170262 47 E -8],
--R    [1.06,1.7844248,1.7844248315 940126524,0.3159401265 24 E -7],
--R    [1.07,1.8270282,1.8270281965 348367381,- 0.3465163261 9 E -8],
--R    [1.08,1.8712173,1.8712173378 97878195,0.3789787819 5 E -7],
--R    [1.09,1.9170918,1.9170918216 068594024,0.2160685940 24 E -7],
--R    [1.1,1.9647597,1.9647596572 486519509,- 0.4275134804 91 E -7],
--R    [1.11,2.0143382,2.0143382144 768273135,0.1447682731 3 E -7],
--R    [1.12,2.0659553,2.0659552613 80510241,- 0.3861948975 9 E -7],
--R    [1.13,2.1197501,2.1197501441 871810139,0.4418718101 39 E -7],
--R    [1.14,2.1758751,2.1758751312 648761686,0.3126487616 86 E -7],
--R    [1.15,2.2344969,2.2344969487 553259802,0.4875532598 02 E -7],
--R    [1.16,2.2957985,2.2957985404 922076011,0.4049220760 11 E -7],
--R    [1.17,2.3599811,2.3599810913 765482032,- 0.8623451796 7 E -8],
--R    [1.18,2.4272664,2.4272663614 002235775,- 0.3859977642 25 E -7],
--R    [1.19,2.4978994,2.4978993874 226530062,- 0.1257734699 4 E -7],
--R    [1.2,2.5721516,2.5721516221 263189354,0.2212631893 54 E -7],
--R    [1.21,2.6503246,2.6503245949 706014665,- 0.5029398533 5 E -8],
--R    [1.22,2.7327542,2.7327541993 067149987,- 0.6932850013 E -9],
--R    [1.23,2.8198157,2.8198157342 681519748,0.3426815197 48 E -7],
--R    [1.24,2.9119299,2.9119298611 552260267,- 0.3884477397 34 E -7],
--R    [1.25,3.0095697,3.0095696738 628312882,- 0.2613716871 18 E -7],
--R    [1.26,3.1132691,3.1132691342 651312093,0.3426513120 93 E -7],
--R    [1.27,3.2236332,3.2236331902 040711359,- 0.9795928864 E -8],
--R    [1.28,3.34135,3.3413499811 153736983,- 0.1888462630 17 E -7],
--R    [1.29,3.4672057,3.4672056517 213857853,- 0.4827861421 47 E -7],
--R    [1.3,3.6021024,3.6021024479 679781512,0.4796797815 12 E -7],
--R    [1.31,3.747081,3.7470809761 884290733,- 0.2381157092 67 E -7],
--R    [1.32,3.9033478,3.9033477874 966235656,- 0.1250337643 4 E -7],
--R    [1.33,4.0723098,4.0723098354 650698554,0.3546506985 54 E -7],
--R    [1.34,4.2556179,4.2556178917 394653427,- 0.8260534657 3 E -8],
--R    [1.35,4.4552218,4.4552217595 627031753,- 0.4043729682 47 E -7],
--R    [1.36,4.6734412,4.6734412029 885596449,0.2988559645 E -8],
--R    [1.37,4.9130581,4.9130580704 624720101,- 0.2953752799 E -7],
--R    [1.38,5.1774374,5.1774373886 304102949,- 0.1136958970 5 E -7],
--R    [1.39,5.4706886,5.4706886429 532054937,0.4295320549 37 E -7],
--R    [1.4,5.7978837,5.7978837154 828896437,0.1548288964 4 E -7],
--R    [1.41,6.1653561,6.1653561445 520255476,0.4455202554 75 E -7],
--R    [1.42,6.5811195,6.5811194561 942543239,- 0.4380574567 61 E -7],
--R    [1.43,7.0554638,7.0554637664 342109722,- 0.3356578902 78 E -7],
--R    [1.44,7.6018261,7.6018260620 257232407,- 0.3797427675 94 E -7],
--R    [1.45,8.2380928,8.2380927529 656070833,- 0.4703439291 7 E -7],
--R    [1.46,8.9886076,8.9886076017 241695008,0.1724169501 E -8],
--R    [1.47,9.8873749,9.8873748919 855531724,- 0.8014446827 5 E -8],
--R    [1.48,10.9833793,10.9833793143 26067301,0.1432606730 1 E -7],
--R    [1.49,12.3498564,12.3498564416 25802114,0.4162580211 4 E -7],
--R    [1.5,14.1014199,14.1014199471 71719388,0.4717171938 8 E -7],
--R    [1.51,16.4280917,16.4280917038 85335336,0.3885335336 E -8],
--R    [1.52,19.6695278,19.6695278205 58866232,0.2055886623 2 E -7],
--R    [1.53,24.4984104,24.4984104418 38034593,0.4183803459 3 E -7],
--R    [1.54,32.4611389,32.4611389128 56765176,0.1285676518 E -7],
--R    [1.55,48.0784825,48.0784824792 18968279,- 0.2078103172 E -7],
--R    [1.56,92.6204963,92.6204963167 04102469,0.1670410247 E -7],
--R    [1.57,1255.7655915,1255.7655915006 916051,0.6916051 E -9],
--R    [1.58,- 108.6492036,- 108.6492036048 4393447,- 0.484393447 E -8],
--R    [1.59,- 52.0669696,- 52.0669696509 12563554,- 0.5091256355 4 E -7],
--R    [1.6,- 34.2325327,- 34.2325327355 57417056,- 0.3555741705 7 E -7]]
--R                                                        Type: List List Float
--E 1

--S 2 of 2
[[0.01,99.9966666,cot(0.01),cot(0.01)-(99.9966666)],_
[0.02,49.9933332,cot(0.02),cot(0.02)-(49.9933332)],_
[0.03,33.3233327,cot(0.03),cot(0.03)-(33.3233327)],_
[0.04,24.9866652,cot(0.04),cot(0.04)-(24.9866652)],_
[0.05,19.9833306,cot(0.05),cot(0.05)-(19.9833306)],_
[0.06,16.6466619,cot(0.06),cot(0.06)-(16.6466619)],_
[0.07,14.2623733,cot(0.07),cot(0.07)-(14.2623733)],_
[0.08,12.4733219,cot(0.08),cot(0.08)-(12.4733219)],_
[0.09,11.0810949,cot(0.09),cot(0.09)-(11.0810949)],_
[0.10,9.9666444,cot(0.10),cot(0.10)-(9.9666444)],_
[0.11,9.0542128,cot(0.11),cot(0.11)-(9.0542128)],_
[0.12,8.2932949,cot(0.12),cot(0.12)-(8.2932949)],_
[0.13,7.6489255,cot(0.13),cot(0.13)-(7.6489255)],_
[0.14,7.0961294,cot(0.14),cot(0.14)-(7.0961294)],_
[0.15,6.6165915,cot(0.15),cot(0.15)-(6.6165915)],_
[0.16,6.1965754,cot(0.16),cot(0.16)-(6.1965754)],_
[0.17,5.8255768,cot(0.17),cot(0.17)-(5.8255768)],_
[0.18,5.4954256,cot(0.18),cot(0.18)-(5.4954256)],_
[0.19,5.1996716,cot(0.19),cot(0.19)-(5.1996716)],_
[0.20,4.9331549,cot(0.20),cot(0.20)-(4.9331549)],_
[0.21,4.6916981,cot(0.21),cot(0.21)-(4.6916981)],_
[0.22,4.4718835,cot(0.22),cot(0.22)-(4.4718835)],_
[0.23,4.2708877,cot(0.23),cot(0.23)-(4.2708877)],_
[0.24,4.0863578,cot(0.24),cot(0.24)-(4.0863578)],_
[0.25,3.9163174,cot(0.25),cot(0.25)-(3.9163174)],_
[0.26,3.7590941,cot(0.26),cot(0.26)-(3.7590941)],_
[0.27,3.6132632,cot(0.27),cot(0.27)-(3.6132632)],_
[0.28,3.4776037,cot(0.28),cot(0.28)-(3.4776037)],_
[0.29,3.3510628,cot(0.29),cot(0.29)-(3.3510628)],_
[0.30,3.2327281,cot(0.30),cot(0.30)-(3.2327281)],_
[0.31,3.1218050,cot(0.31),cot(0.31)-(3.1218050)],_
[0.32,3.0175980,cot(0.32),cot(0.32)-(3.0175980)],_
[0.33,2.9194961,cot(0.33),cot(0.33)-(2.9194961)],_
[0.34,2.8269600,cot(0.34),cot(0.34)-(2.8269600)],_
[0.35,2.7395122,cot(0.35),cot(0.35)-(2.7395122)],_
[0.36,2.6567280,cot(0.36),cot(0.36)-(2.6567280)],_
[0.37,2.5782289,cot(0.37),cot(0.37)-(2.5782289)],_
[0.38,2.5036759,cot(0.38),cot(0.38)-(2.5036759)],_
[0.39,2.4327650,cot(0.39),cot(0.39)-(2.4327650)],_
[0.40,2.3652224,cot(0.40),cot(0.40)-(2.3652224)],_
[0.41,2.3008012,cot(0.41),cot(0.41)-(2.3008012)],_
[0.42,2.2392778,cot(0.42),cot(0.42)-(2.2392778)],_
[0.43,2.1804495,cot(0.43),cot(0.43)-(2.1804495)],_
[0.44,2.1241320,cot(0.44),cot(0.44)-(2.1241320)],_
[0.45,2.0701574,cot(0.45),cot(0.45)-(2.0701574)],_
[0.46,2.0183722,cot(0.46),cot(0.46)-(2.0183722)],_
[0.47,1.9686361,cot(0.47),cot(0.47)-(1.9686361)],_
[0.48,1.9208205,cot(0.48),cot(0.48)-(1.9208205)],_
[0.49,1.8748073,cot(0.49),cot(0.49)-(1.8748073)],_
[0.50,1.83048772,cot(0.50),cot(0.50)-(1.83048772)],_
[0.51,1.78776154,cot(0.51),cot(0.51)-(1.78776154)],_
[0.52,1.74653626,cot(0.52),cot(0.52)-(1.74653626)],_
[0.53,1.70672634,cot(0.53),cot(0.53)-(1.70672634)],_
[0.54,1.66825255,cot(0.54),cot(0.54)-(1.66825255)],_
[0.55,1.63104142,cot(0.55),cot(0.55)-(1.63104142)],_
[0.56,1.59502471,cot(0.56),cot(0.56)-(1.59502471)],_
[0.57,1.56013894,cot(0.57),cot(0.57)-(1.56013894)],_
[0.58,1.52632503,cot(0.58),cot(0.58)-(1.52632503)],_
[0.59,1.49352784,cot(0.59),cot(0.59)-(1.49352784)],_
[0.60,1.46169595,cot(0.60),cot(0.60)-(1.46169595)],_
[0.61,1.43078125,cot(0.61),cot(0.61)-(1.43078125)],_
[0.62,1.40073873,cot(0.62),cot(0.62)-(1.40073873)],_
[0.63,1.37152626,cot(0.63),cot(0.63)-(1.37152626)],_
[0.64,1.34310429,cot(0.64),cot(0.64)-(1.34310429)],_
[0.65,1.31543569,cot(0.65),cot(0.65)-(1.31543569)],_
[0.66,1.28848559,cot(0.66),cot(0.66)-(1.28848559)],_
[0.67,1.26222118,cot(0.67),cot(0.67)-(1.26222118)],_
[0.68,1.23661155,cot(0.68),cot(0.68)-(1.23661155)],_
[0.69,1.21162759,cot(0.69),cot(0.69)-(1.21162759)],_
[0.70,1.18724183,cot(0.70),cot(0.70)-(1.18724183)],_
[0.71,1.16342833,cot(0.71),cot(0.71)-(1.16342833)],_
[0.72,1.14016258,cot(0.72),cot(0.72)-(1.14016258)],_
[0.73,1.11742140,cot(0.73),cot(0.73)-(1.11742140)],_
[0.74,1.09518285,cot(0.74),cot(0.74)-(1.09518285)],_
[0.75,1.07342615,cot(0.75),cot(0.75)-(1.07342615)],_
[0.76,1.05213158,cot(0.76),cot(0.76)-(1.05213158)],_
[0.77,1.03128046,cot(0.77),cot(0.77)-(1.03128046)],_
[0.78,1.01085503,cot(0.78),cot(0.78)-(1.01085503)],_
[0.79,0.99083842,cot(0.79),cot(0.79)-(0.99083842)],_
[0.80,0.97121460,cot(0.80),cot(0.80)-(0.97121460)],_
[0.81,0.95196830,cot(0.81),cot(0.81)-(0.95196830)],_
[0.82,0.93308500,cot(0.82),cot(0.82)-(0.93308500)],_
[0.83,0.91455085,cot(0.83),cot(0.83)-(0.91455085)],_
[0.84,0.89635264,cot(0.84),cot(0.84)-(0.89635264)],_
[0.85,0.87847778,cot(0.85),cot(0.85)-(0.87847778)],_
[0.86,0.86091426,cot(0.86),cot(0.86)-(0.86091426)],_
[0.87,0.84365058,cot(0.87),cot(0.87)-(0.84365058)],_
[0.88,0.82667575,cot(0.88),cot(0.88)-(0.82667575)],_
[0.89,0.80997930,cot(0.89),cot(0.89)-(0.80997930)],_
[0.90,0.79355115,cot(0.90),cot(0.90)-(0.79355115)],_
[0.91,0.77738169,cot(0.91),cot(0.91)-(0.77738169)],_
[0.92,0.76146169,cot(0.92),cot(0.92)-(0.76146169)],_
[0.93,0.74578232,cot(0.93),cot(0.93)-(0.74578232)],_
[0.94,0.73033510,cot(0.94),cot(0.94)-(0.73033510)],_
[0.95,0.71511188,cot(0.95),cot(0.95)-(0.71511188)],_
[0.96,0.70010485,cot(0.96),cot(0.96)-(0.70010485)],_
[0.97,0.68530649,cot(0.97),cot(0.97)-(0.68530649)],_
[0.98,0.67070959,cot(0.98),cot(0.98)-(0.67070959)],_
[0.99,0.65630719,cot(0.99),cot(0.99)-(0.65630719)],_
[1.00,0.64209262,cot(1.00),cot(1.00)-(0.64209262)],_
[1.01,0.62805942,cot(1.01),cot(1.01)-(0.62805942)],_
[1.02,0.61420141,cot(1.02),cot(1.02)-(0.61420141)],_
[1.03,0.60051260,cot(1.03),cot(1.03)-(0.60051260)],_
[1.04,0.58698722,cot(1.04),cot(1.04)-(0.58698722)],_
[1.05,0.57361970,cot(1.05),cot(1.05)-(0.57361970)],_
[1.06,0.56040467,cot(1.06),cot(1.06)-(0.56040467)],_
[1.07,0.54733693,cot(1.07),cot(1.07)-(0.54733693)],_
[1.08,0.53441147,cot(1.08),cot(1.08)-(0.53441147)],_
[1.09,0.52162342,cot(1.09),cot(1.09)-(0.52162342)],_
[1.10,0.50896811,cot(1.10),cot(1.10)-(0.50896811)],_
[1.11,0.49644096,cot(1.11),cot(1.11)-(0.49644096)],_
[1.12,0.48403759,cot(1.12),cot(1.12)-(0.48403759)],_
[1.13,0.47175371,cot(1.13),cot(1.13)-(0.47175371)],_
[1.14,0.45958520,cot(1.14),cot(1.14)-(0.45958520)],_
[1.15,0.44752802,cot(1.15),cot(1.15)-(0.44752802)],_
[1.16,0.43557829,cot(1.16),cot(1.16)-(0.43557829)],_
[1.17,0.42373221,cot(1.17),cot(1.17)-(0.42373221)],_
[1.18,0.41198610,cot(1.18),cot(1.18)-(0.41198610)],_
[1.19,0.40033638,cot(1.19),cot(1.19)-(0.40033638)],_
[1.20,0.38877957,cot(1.20),cot(1.20)-(0.38877957)],_
[1.21,0.37731227,cot(1.21),cot(1.21)-(0.37731227)],_
[1.22,0.36593119,cot(1.22),cot(1.22)-(0.36593119)],_
[1.23,0.35463310,cot(1.23),cot(1.23)-(0.35463310)],_
[1.24,0.34341486,cot(1.24),cot(1.24)-(0.34341486)],_
[1.25,0.33227342,cot(1.25),cot(1.25)-(0.33227342)],_
[1.26,0.32120577,cot(1.26),cot(1.26)-(0.32120577)],_
[1.27,0.31020899,cot(1.27),cot(1.27)-(0.31020899)],_
[1.28,0.29928023,cot(1.28),cot(1.28)-(0.29928023)],_
[1.29,0.28841670,cot(1.29),cot(1.29)-(0.28841670)],_
[1.30,0.27761565,cot(1.30),cot(1.30)-(0.27761565)],_
[1.31,0.26687440,cot(1.31),cot(1.31)-(0.26687440)],_
[1.32,0.25619034,cot(1.32),cot(1.32)-(0.25619034)],_
[1.33,0.24556088,cot(1.33),cot(1.33)-(0.24556088)],_
[1.34,0.23498350,cot(1.34),cot(1.34)-(0.23498350)],_
[1.35,0.22445572,cot(1.35),cot(1.35)-(0.22445572)],_
[1.36,0.21397509,cot(1.36),cot(1.36)-(0.21397509)],_
[1.37,0.20353922,cot(1.37),cot(1.37)-(0.20353922)],_
[1.38,0.19314574,cot(1.38),cot(1.38)-(0.19314574)],_
[1.39,0.18279234,cot(1.39),cot(1.39)-(0.18279234)],_
[1.40,0.17247673,cot(1.40),cot(1.40)-(0.17247673)],_
[1.41,0.16219663,cot(1.41),cot(1.41)-(0.16219663)],_
[1.42,0.15194983,cot(1.42),cot(1.42)-(0.15194983)],_
[1.43,0.14173413,cot(1.43),cot(1.43)-(0.14173413)],_
[1.44,0.13154734,cot(1.44),cot(1.44)-(0.13154734)],_
[1.45,0.12138732,cot(1.45),cot(1.45)-(0.12138732)],_
[1.46,0.11125194,cot(1.46),cot(1.46)-(0.11125194)],_
[1.47,0.10113908,cot(1.47),cot(1.47)-(0.10113908)],_
[1.48,0.091046660,cot(1.48),cot(1.48)-(0.091046660)],_
[1.49,0.080972601,cot(1.49),cot(1.49)-(0.080972601)],_
[1.50,0.070914844,cot(1.50),cot(1.50)-(0.070914844)],_
[1.51,0.060871343,cot(1.51),cot(1.51)-(0.060871343)],_
[1.52,0.050840061,cot(1.52),cot(1.52)-(0.050840061)],_
[1.53,0.040818975,cot(1.53),cot(1.53)-(0.040818975)],_
[1.54,0.030806066,cot(1.54),cot(1.54)-(0.030806066)],_
[1.55,0.020799325,cot(1.55),cot(1.55)-(0.020799325)],_
[1.56,0.010796746,cot(1.56),cot(1.56)-(0.010796746)],_
[1.57,0.000796327,cot(1.57),cot(1.57)-(0.000796327)],_
[1.58,-0.009203933,cot(1.58),cot(1.58)-(-0.009203933)],_
[1.59,-0.019206034,cot(1.59),cot(1.59)-(-0.019206034)],_
[1.60,-0.029211978,cot(1.60),cot(1.60)-(-0.029211978)]]
 

   (2)
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    [1.28,0.29928023,0.2992802327 358089858,0.2735808985 8 E -8],
    [1.29,0.2884167,0.2884166964 5511900872,- 0.3544880991 28 E -8],
    [1.3,0.27761565,0.2776156465 411251863,- 0.3458874813 7 E -8],
    [1.31,0.2668744,0.2668744033 9685712292,0.3396857122 92 E -8],
    [1.32,0.25619034,0.2561903408 1545187187,0.8154518718 7 E -9],
    [1.33,0.24556088,0.2455608832 341699844,0.3234169984 4 E -8],
    [1.34,0.2349835,0.2349835030 8684653553,0.3086846535 53 E -8],
    [1.35,0.22445572,0.2244557182 4872613589,- 0.1751273864 11 E -8],
    [1.36,0.21397509,0.2139750895 6794464051,- 0.4320553594 9 E -9],
    [1.37,0.20353922,0.2035392184 7821123118,- 0.1521788768 82 E -8],
    [1.38,0.19314574,0.1931457446 8751430396,0.4687514303 96 E -8],
    [1.39,0.18279234,0.1827923439 3792453991,0.3937924539 91 E -8],
    [1.4,0.17247673,0.1724767258 3179995277,- 0.4168200047 23 E -8],
    [1.41,0.16219663,0.1621966317 1991176955,0.1719911769 56 E -8],
    [1.42,0.15194983,0.1519498326 4720777741,0.2647207777 41 E -8],
    [1.43,0.14173413,0.1417341273 5211224764,- 0.2647887752 36 E -8],
    [1.44,0.13154734,0.1315473403 1542961869,0.3154296186 9 E -9],
    [1.45,0.12138732,0.1213873198 5507360359,- 0.1449263964 1 E -9],
    [1.46,0.11125194,0.1112519362 6298502613,- 0.3737014973 87 E -8],
    [1.47,0.10113908,0.1011390799 8073116239,- 0.1926883761 E -10],
    [1.48,0.09104666,0.0910466598 1039728128,- 0.1896027187 2 E -9],
    [1.49,0.080972601,0.0809726011 5748799537,0.1574879953 7 E -9],
    [1.5,0.070914844,0.0709148443 0265244878 9,0.3026524487 9 E -9],
    [1.51,0.060871343,0.0608713426 9913372964 9,- 0.3008662703 51 E -9],
    [1.52,0.050840061,0.0508400612 9291959823 6,0.2929195982 36 E -9],
    [1.53,0.040818975,0.0408189748 6263901912 7,- 0.1373609808 7 E -9],
    [1.54,0.030806066,0.0308060663 7630738330 6,0.3763073833 07 E -9],
    [1.55,0.020799325,0.0207993253 6207296975 6,0.3620729697 56 E -9],
    [1.56,0.010796746,0.0107967462 901583485,0.2901583485 E -9],
    [1.57,0.000796327,0.0007963269 6322325475 679,- 0.3677674524 32 E -10],
    [1.58,- 0.009203933,- 0.0092039330 8759988693 76,- 0.8759988693 75 E -10],
    [1.59,- 0.019206034,- 0.0192060342 0373002777 9,- 0.2037300277 79 E -9],
    [1.6,- 0.029211978,- 0.0292119781 9994480011 4,- 0.1999448001 14 E -9]]
                                                        Type: List List Float
--R 
--R
--R   (2)
--R   [[0.01,99.9966666,99.9966666444 44232802,0.444442328 E -7],
--R    [0.02,49.9933332,49.9933331555 48782798,- 0.4445121720 2 E -7],
--R    [0.03,33.3233327,33.3233327332 81900133,0.3328190013 3 E -7],
--R    [0.04,24.9866652,24.9866652442 27690187,0.4422769018 7 E -7],
--R    [0.05,19.9833306,19.9833305548 94014508,- 0.4510598549 1 E -7],
--R    [0.06,16.6466619,16.6466618650 20359708,- 0.3497964029 2 E -7],
--R    [0.07,14.2623733,14.2623733265 9994931,0.2659994931 E -7],
--R    [0.08,12.4733219,12.4733219486 16087812,0.4861608781 2 E -7],
--R    [0.09,11.0810949,11.0810948986 03837279,- 0.1396162721 E -8],
--R    [0.1,9.9666444,9.9666444232 592378598,0.2325923786 E -7],
--R    [0.11,9.0542128,9.0542128123 384855803,0.1233848558 E -7],
--R    [0.12,8.2932949,8.2932948805 945312103,- 0.1940546879 E -7],
--R    [0.13,7.6489255,7.6489254580 38579468,- 0.4196142053 2 E -7],
--R    [0.14,7.0961294,7.0961293843 639732986,- 0.1563602670 1 E -7],
--R    [0.15,6.6165915,6.6165915055 899500987,0.5589950098 7 E -8],
--R    [0.16,6.1965754,6.1965754219 540076277,0.2195400762 8 E -7],
--R    [0.17,5.8255768,5.8255767953 622059416,- 0.4637794058 4 E -8],
--R    [0.18,5.4954256,5.4954255543 470259144,- 0.4565297408 56 E -7],
--R    [0.19,5.1996716,5.1996716132 404544488,0.1324045444 9 E -7],
--R    [0.2,4.9331549,4.9331548755 868936573,- 0.2441310634 3 E -7],
--R    [0.21,4.6916981,4.6916980937 15878191,- 0.6284121809 E -8],
--R    [0.22,4.4718835,4.4718834938 782225379,- 0.6121777462 1 E -8],
--R    [0.23,4.2708877,4.2708876730 783907862,- 0.2692160921 4 E -7],
--R    [0.24,4.0863578,4.0863577716 916129493,- 0.2830838705 1 E -7],
--R    [0.25,3.9163174,3.9163173646 45940105,- 0.3535405989 5 E -7],
--R    [0.26,3.7590941,3.7590940700 170597097,- 0.2998294029 03 E -7],
--R    [0.27,3.6132632,3.6132632445 954451122,0.4459544511 22 E -7],
--R    [0.28,3.4776037,3.4776037446 826739597,0.4468267395 97 E -7],
--R    [0.29,3.3510628,3.3510628398 201367735,0.3982013677 35 E -7],
--R    [0.3,3.2327281,3.2327281437 658275137,0.4376582751 37 E -7],
--R    [0.31,3.121805,3.1218049781 792418003,- 0.2182075819 97 E -7],
--R    [0.32,3.017598,3.0175979806 093983387,- 0.1939060166 13 E -7],
--R    [0.33,2.9194961,2.9194960564 791734711,- 0.4352082652 89 E -7],
--R    [0.34,2.82696,2.8269599865 960316187,- 0.1340396838 1 E -7],
--R    [0.35,2.7395122,2.7395121590 837832657,- 0.4091621673 43 E -7],
--R    [0.36,2.656728,2.6567280126 534137138,0.1265341371 4 E -7],
--R    [0.37,2.5782289,2.5782288674 460399215,- 0.3255396007 85 E -7],
--R    [0.38,2.5036759,2.5036758878 425107672,- 0.1215748923 3 E -7],
--R    [0.39,2.432765,2.4327649740 660567805,- 0.2593394321 95 E -7],
--R    [0.4,2.3652224,2.3652224200 39110587,0.2003911058 7 E -7],
--R    [0.41,2.3008012,2.3008012066 70318891,0.6670318891 E -8],
--R    [0.42,2.2392778,2.2392778246 666163969,0.2466661639 69 E -7],
--R    [0.43,2.1804495,2.1804495406 685083798,0.4066850837 98 E -7],
--R    [0.44,2.124132,2.1241320361 797692227,0.3617976922 27 E -7],
--R    [0.45,2.0701574,2.0701573613 012126215,- 0.3869878737 85 E -7],
--R    [0.46,2.0183722,2.0183721553 634627578,- 0.4463653724 22 E -7],
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--R    [0.48,1.9208205,1.9208205344 885739853,0.3448857398 53 E -7],
--R    [0.49,1.8748073,1.8748073167 815901303,0.1678159013 03 E -7],
--R    [0.5,1.83048772,1.8304877217 124519193,0.1712451919 3 E -8],
--R    [0.51,1.78776154,1.7877615419 775693505,0.1977569350 5 E -8],
--R    [0.52,1.74653626,1.7465362641 453971653,0.4145397165 3 E -8],
--R    [0.53,1.70672634,1.7067263426 353184999,0.2635318499 9 E -8],
--R    [0.54,1.66825255,1.6682525543 602072732,0.4360207273 2 E -8],
--R    [0.55,1.63104142,1.6310414237 662644566,0.3766264456 6 E -8],
--R    [0.56,1.59502471,1.5950247094 703485723,- 0.5296514276 E -9],
--R    [0.57,1.56013894,1.5601389449 30073432,0.4930073431 9 E -8],
--R    [0.58,1.52632503,1.5263250266 253525611,- 0.3374647438 9 E -8],
--R    [0.59,1.49352784,1.4935278441 14312362,0.4114312362 E -8],
--R    [0.6,1.46169595,1.4616959470 781021403,- 0.2921897859 7 E -8],
--R    [0.61,1.43078125,1.4307812451 098423602,- 0.4890157639 8 E -8],
--R    [0.62,1.40073873,1.4007387365 5065882,0.655065882 E -8],
--R    [0.63,1.37152626,1.3715262631 452128637,0.3145212863 7 E -8],
--R    [0.64,1.34310429,1.3431042876 925818576,- 0.2307418142 4 E -8],
--R    [0.65,1.31543569,1.3154356922 15926629,0.2215926629 E -8],
--R    [0.66,1.28848559,1.2884855944 745672615,0.4474567261 5 E -8],
--R    [0.67,1.26222118,1.2622211809 019498574,0.9019498574 E -9],
--R    [0.68,1.23661155,1.2366115542 784545265,0.4278454526 5 E -8],
--R    [0.69,1.21162759,1.2116275946 440535197,0.4644053519 7 E -8],
--R    [0.7,1.18724183,1.1872418321 266793537,0.2126679353 7 E -8],
--R    [0.71,1.16342833,1.1634283305 113563708,0.5113563708 E -9],
--R    [0.72,1.14016258,1.1401625805 056933781,0.5056933781 E -9],
--R    [0.73,1.1174214,1.1174214017 717845341,0.1771784534 1 E -8],
--R    [0.74,1.09518285,1.0951828528 950954346,0.2895095434 6 E -8],
--R    [0.75,1.07342615,1.0734261485 493773587,- 0.1450622641 3 E -8],
--R    [0.76,1.05213158,1.0521315831 946421944,0.3194642194 4 E -8],
--R    [0.77,1.03128046,1.0312804607 141042446,0.7141042446 E -9],
--R    [0.78,1.01085503,1.0108550294 569216086,- 0.5430783914 E -9],
--R    [0.79,0.99083842,0.9908384222 0755510722,0.2207555107 2 E -8],
--R    [0.8,0.9712146,0.9712146006 5047441252,0.6504744125 2 E -9],
--R    [0.81,0.9519683,0.9519683039 4152897039,0.3941528970 39 E -8],
--R    [0.82,0.933085,0.9330850010 3521469901,0.1035214699 E -8],
--R    [0.83,0.91455085,0.9145508464 5086948692,- 0.3549130513 1 E -8],
--R    [0.84,0.89635264,0.8963526391 9101064443,- 0.8089893555 7 E -9],
--R    [0.85,0.87847778,0.8784777845 5201177212,0.4552011772 12 E -8],
--R    [0.86,0.86091426,0.8609142585 9147659674,- 0.1408523403 3 E -8],
--R    [0.87,0.84365058,0.8436505750 3832779908,- 0.4961672200 92 E -8],
--R    [0.88,0.82667575,0.8266757544 5107375391,0.4451073753 91 E -8],
--R    [0.89,0.8099793,0.8099792954 4719434615,- 0.4552805653 85 E -8],
--R    [0.9,0.79355115,0.7935511478 423171255,- 0.2157682874 5 E -8],
--R    [0.91,0.77738169,0.7773816875 5202909939,- 0.2447970900 6 E -8],
--R    [0.92,0.76146169,0.7614616931 2195656768,0.3121956567 7 E -8],
--R    [0.93,0.74578232,0.7457823237 6329468591,0.3763294685 91 E -8],
--R    [0.94,0.7303351,0.7303350987 8141157551,- 0.1218588424 5 E -8],
--R    [0.95,0.71511188,0.7151118782 9460519926,- 0.1705394800 7 E -8],
--R    [0.96,0.70010485,0.7001048451 4865796784,- 0.4851342032 16 E -8],
--R    [0.97,0.68530649,0.6853064879 4060552823,- 0.2059394471 8 E -8],
--R    [0.98,0.67070959,0.6707095850 721935367,- 0.4927806463 3 E -8],
--R    [0.99,0.65630719,0.6563071897 5991155454,- 0.2400884455 E -9],
--R    [1.0,0.64209262,0.6420926159 3433070301,- 0.4065669296 99 E -8],
--R    [1.01,0.62805942,0.6280594249 6678856739,0.4966788567 39 E -8],
--R    [1.02,0.61420141,0.6142014131 6631206854,0.3166312068 5 E -8],
--R    [1.03,0.6005126,0.6005125999 9409219665,- 0.590780335 E -11],
--R    [1.04,0.58698722,0.5869872169 4686437526,- 0.3053135624 7 E -8],
--R    [1.05,0.5736197,0.5736196970 6424127541,- 0.2935758724 6 E -8],
--R    [1.06,0.56040467,0.5604046650 184238209,- 0.4981576179 09 E -8],
--R    [1.07,0.54733693,0.5473369277 478102494,- 0.2252189750 6 E -8],
--R    [1.08,0.53441147,0.5344114655 9885875935,- 0.4401141240 65 E -8],
--R    [1.09,0.52162342,0.5216234239 4316016472,0.3943160164 72 E -8],
--R    [1.1,0.50896811,0.5089681052 3906440719,- 0.4760935592 81 E -8],
--R    [1.11,0.49644096,0.4964409615 0939793968,0.1509397939 7 E -8],
--R    [1.12,0.48403759,0.4840375872 0882520651,- 0.2791174793 49 E -8],
--R    [1.13,0.47175371,0.4717537124 562623272,0.2456262327 2 E -8],
--R    [1.14,0.4595852,0.4595851966 0945875941,- 0.3390541240 59 E -8],
--R    [1.15,0.44752802,0.4475280221 6043593272,0.2160435932 72 E -8],
--R    [1.16,0.43557829,0.4355782889 3192216044,- 0.1068077839 6 E -8],
--R    [1.17,0.42373221,0.4237322085 562610121,- 0.1443738987 9 E -8],
--R    [1.18,0.4119861,0.4119860992 1950525045,- 0.7804947495 5 E -9],
--R    [1.19,0.40033638,0.4003363806 5454900775,0.6545490077 5 E -9],
--R    [1.2,0.38877957,0.3887795693 6820491163,- 0.6317950883 7 E -9],
--R    [1.21,0.37731227,0.3773122740 8810747104,0.4088107471 05 E -8],
--R    [1.22,0.36593119,0.3659311914 1622565487,0.1416225654 9 E -8],
--R    [1.23,0.3546331,0.3546331016 7660211852,0.1676602118 5 E -8],
--R    [1.24,0.34341486,0.3434148649 4570930705,0.4945709307 05 E -8],
--R    [1.25,0.33227342,0.3322734172 5452856774,- 0.2745471432 26 E -8],
--R    [1.26,0.32120577,0.3212057669 5212188699,- 0.3047878113 01 E -8],
--R    [1.27,0.31020899,0.3102089912 2108098744,0.1221080987 4 E -8],
--R    [1.28,0.29928023,0.2992802327 358089858,0.2735808985 8 E -8],
--R    [1.29,0.2884167,0.2884166964 5511900872,- 0.3544880991 28 E -8],
--R    [1.3,0.27761565,0.2776156465 411251863,- 0.3458874813 7 E -8],
--R    [1.31,0.2668744,0.2668744033 9685712292,0.3396857122 92 E -8],
--R    [1.32,0.25619034,0.2561903408 1545187187,0.8154518718 7 E -9],
--R    [1.33,0.24556088,0.2455608832 341699844,0.3234169984 4 E -8],
--R    [1.34,0.2349835,0.2349835030 8684653553,0.3086846535 53 E -8],
--R    [1.35,0.22445572,0.2244557182 4872613589,- 0.1751273864 11 E -8],
--R    [1.36,0.21397509,0.2139750895 6794464051,- 0.4320553594 9 E -9],
--R    [1.37,0.20353922,0.2035392184 7821123118,- 0.1521788768 82 E -8],
--R    [1.38,0.19314574,0.1931457446 8751430396,0.4687514303 96 E -8],
--R    [1.39,0.18279234,0.1827923439 3792453991,0.3937924539 91 E -8],
--R    [1.4,0.17247673,0.1724767258 3179995277,- 0.4168200047 23 E -8],
--R    [1.41,0.16219663,0.1621966317 1991176955,0.1719911769 56 E -8],
--R    [1.42,0.15194983,0.1519498326 4720777741,0.2647207777 41 E -8],
--R    [1.43,0.14173413,0.1417341273 5211224764,- 0.2647887752 36 E -8],
--R    [1.44,0.13154734,0.1315473403 1542961869,0.3154296186 9 E -9],
--R    [1.45,0.12138732,0.1213873198 5507360359,- 0.1449263964 1 E -9],
--R    [1.46,0.11125194,0.1112519362 6298502613,- 0.3737014973 87 E -8],
--R    [1.47,0.10113908,0.1011390799 8073116239,- 0.1926883761 E -10],
--R    [1.48,0.09104666,0.0910466598 1039728128,- 0.1896027187 2 E -9],
--R    [1.49,0.080972601,0.0809726011 5748799537,0.1574879953 7 E -9],
--R    [1.5,0.070914844,0.0709148443 0265244878 9,0.3026524487 9 E -9],
--R    [1.51,0.060871343,0.0608713426 9913372964 9,- 0.3008662703 51 E -9],
--R    [1.52,0.050840061,0.0508400612 9291959823 6,0.2929195982 36 E -9],
--R    [1.53,0.040818975,0.0408189748 6263901912 7,- 0.1373609808 7 E -9],
--R    [1.54,0.030806066,0.0308060663 7630738330 6,0.3763073833 07 E -9],
--R    [1.55,0.020799325,0.0207993253 6207296975 6,0.3620729697 56 E -9],
--R    [1.56,0.010796746,0.0107967462 901583485,0.2901583485 E -9],
--R    [1.57,0.000796327,0.0007963269 6322325475 679,- 0.3677674524 32 E -10],
--R    [1.58,- 0.009203933,- 0.0092039330 8759988693 76,- 0.8759988693 75 E -10],
--R    [1.59,- 0.019206034,- 0.0192060342 0373002777 9,- 0.2037300277 79 E -9],
--R    [1.6,- 0.029211978,- 0.0292119781 9994480011 4,- 0.1999448001 14 E -9]]
--R                                                        Type: List List Float
--E 2

)spool 
 
Starts dribbling to LinearOrdinaryDifferentialOperator2.output (2010/3/27, 18:46:0).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 26
Q  := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 26
PQ := UnivariatePolynomial('x, Q)
 

   (2)  UnivariatePolynomial(x,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(x,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 26
x: PQ := 'x
 

   (3)  x
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (3)  x
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 3

--S 4 of 26
Dx: LODO2(Q, PQ) := D()
 

   (4)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (4)  D
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 4

--S 5 of 26
a := Dx  + 1
 

   (5)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R   (5)  D + 1
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 5

--S 6 of 26
b := a + 1/2*Dx**2 - 1/2
 

        1  2       1
   (6)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R        1  2       1
--R   (6)  - D  + D + -
--R        2          2
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 6

--S 7 of 26
p := 4*x**2 + 2/3
 

          2   2
   (7)  4x  + -
              3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2   2
--R   (7)  4x  + -
--R              3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 7

--S 8 of 26
a p 
 

          2        2
   (8)  4x  + 8x + -
                   3
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2        2
--R   (8)  4x  + 8x + -
--R                   3
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 8

--S 9 of 26
(a * b) p = a b p
 

          2         37    2         37
   (9)  2x  + 12x + --= 2x  + 12x + --
                     3               3
                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R          2         37    2         37
--R   (9)  2x  + 12x + --= 2x  + 12x + --
--R                     3               3
--R                      Type: Equation UnivariatePolynomial(x,Fraction Integer)
--E 9

--S 10 of 26
c := (1/9)*b*(a + b)^2
 

          1  6    5  5   13  4   19  3   79  2    7     1
   (10)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
         72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--R 
--R
--R          1  6    5  5   13  4   19  3   79  2    7     1
--R   (10)  -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
--R         72      36      24      18      72      12     8
--RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer))
--E 10

--S 11 of 26
(a**2 - 3/4*b + c) (p + 1)
 

           2   44     541
   (11)  3x  + -- x + ---
                3      36
                               Type: UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2   44     541
--R   (11)  3x  + -- x + ---
--R                3      36
--R                               Type: UnivariatePolynomial(x,Fraction Integer)
--E 11
)clear all
 
--S 12 of 26
PZ := UnivariatePolynomial(x,Integer)
 

   (1)  UnivariatePolynomial(x,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  UnivariatePolynomial(x,Integer)
--R                                                                 Type: Domain
--E 12

--S 13 of 26
x:PZ := 'x
 

   (2)  x
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (2)  x
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 13

--S 14 of 26
Mat  := SquareMatrix(3,PZ)
 

   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
                                                                 Type: Domain
--R 
--R
--R   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 14

--S 15 of 26
Vect := DPMM(3, PZ, Mat, PZ)
 

   (4)
  DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,Un
  ivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
                                                                 Type: Domain
--R 
--R
--R   (4)
--R  DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,Un
--R  ivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 15

--S 16 of 26
Modo := LODO2(Mat, Vect)
 

   (5)
  LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Int
  eger)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatr
  ix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
                                                                 Type: Domain
--R 
--R
--R   (5)
--R  LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Int
--R  eger)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatr
--R  ix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R                                                                 Type: Domain
--E 16

--S 17 of 26
m:Mat := matrix [ [x^2,1,0],[1,x^4,0],[0,0,4*x^2] ]
 

        + 2         +
        |x   1    0 |
        |           |
   (6)  |     4     |
        |1   x    0 |
        |           |
        |          2|
        +0   0   4x +
                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--R 
--R
--R        + 2         +
--R        |x   1    0 |
--R        |           |
--R   (6)  |     4     |
--R        |1   x    0 |
--R        |           |
--R        |          2|
--R        +0   0   4x +
--R                        Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
--E 17

--S 18 of 26
p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x]
 

           2          3
   (7)  [3x  + 1,2x,7x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           2          3
--R   (7)  [3x  + 1,2x,7x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 18

--S 19 of 26
q: Vect := m * p
 

           4    2        5     2        5     3
   (8)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R           4    2        5     2        5     3
--R   (8)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 19

--S 20 of 26
Dx : Modo := D()
 

   (9)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (9)  D
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 20

--S 21 of 26
a : Modo := Dx  + m
 

             + 2         +
             |x   1    0 |
             |           |
   (10)  D + |     4     |
             |1   x    0 |
             |           |
             |          2|
             +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R             + 2         +
--R             |x   1    0 |
--R             |           |
--R   (10)  D + |     4     |
--R             |1   x    0 |
--R             |           |
--R             |          2|
--R             +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 21

--S 22 of 26
b : Modo := m*Dx  + 1
 

         + 2         +
         |x   1    0 |    +1  0  0+
         |           |    |       |
   (11)  |     4     |D + |0  1  0|
         |1   x    0 |    |       |
         |           |    +0  0  1+
         |          2|
         +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R         + 2         +
--R         |x   1    0 |    +1  0  0+
--R         |           |    |       |
--R   (11)  |     4     |D + |0  1  0|
--R         |1   x    0 |    |       |
--R         |           |    +0  0  1+
--R         |          2|
--R         +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 22

--S 23 of 26
c := a*b
 

   (12)
   + 2         +     + 4              4    2                  +    + 2         +
   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
   |           | 2   |                                        |    |           |
   |     4     |D  + |   4    2     8     3                   |D + |     4     |
   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
   |           |     |                                        |    |           |
   |          2|     |                              4         |    |          2|
   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--R 
--R
--R   (12)
--R   + 2         +     + 4              4    2                  +    + 2         +
--R   |x   1    0 |     |x  + 2x + 2    x  + x            0      |    |x   1    0 |
--R   |           | 2   |                                        |    |           |
--R   |     4     |D  + |   4    2     8     3                   |D + |     4     |
--R   |1   x    0 |     |  x  + x     x  + 4x  + 2        0      |    |1   x    0 |
--R   |           |     |                                        |    |           |
--R   |          2|     |                              4         |    |          2|
--R   +0   0   4x +     +     0            0        16x  + 8x + 1+    +0   0   4x +
--RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
--E 23

--S 24 of 26
a p
 

            4    2        5     2        5     3      2
   (13)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            4    2        5     2        5     3      2
--R   (13)  [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 2]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 24

--S 25 of 26
b p
 

            3     2       4         4     3     2
   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R            3     2       4         4     3     2
--R   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 25

--S 26 of 26
(a + b + c) (p + q)
 

   (15)
       8      7      6      5      4      3      2
   [10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x  + 40x + 17,
       12      9      8      7     6      5      4      3      2
    10x   + 10x  + 12x  + 92x  + 6x  + 32x  + 72x  + 28x  + 49x  + 32x + 19,
         8       7        6        5       4       3      2
    2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x  + 98x  + 18x + 4]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--R 
--R
--R   (15)
--R       8      7      6      5      4      3      2
--R   [10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x  + 40x + 17,
--R       12      9      8      7     6      5      4      3      2
--R    10x   + 10x  + 12x  + 92x  + 6x  + 32x  + 72x  + 28x  + 49x  + 32x + 19,
--R         8       7        6        5       4       3      2
--R    2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x  + 98x  + 18x + 4]
--RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
--E 26
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read lib
 

-- Input generated from LibraryXmpPage
)clear all
 

stuff := library "/tmp/Neat.stuff"
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "/tmp/Neat.stuff"

(1) -> 
Starts dribbling to schaum33.output (2010/3/27, 18:38:47).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 49
aa:=integrate(csch(a*x),x)
 

        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
   (1)  -----------------------------------------------------------------
                                        a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
--R   (1)  -----------------------------------------------------------------
--R                                        a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 49
bb:=1/a*log(tanh((a*x)/2))
 

                 a x
        log(tanh(---))
                  2
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R                 a x
--R        log(tanh(---))
--R                  2
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 3 of 49
cc:=aa-bb
 

   (3)
                  a x
       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
                   2
     + 
       log(sinh(a x) + cosh(a x) - 1)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  a x
--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
--R                   2
--R     + 
--R       log(sinh(a x) + cosh(a x) - 1)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 4 of 49      14:636 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 5 of 49
aa:=integrate(csch(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 6 of 49
bb:=-coth(a*x)/a
 

          coth(a x)
   (2)  - ---------
              a
                                                     Type: Expression Integer
--R
--R          coth(a x)
--R   (2)  - ---------
--R              a
--R                                                     Type: Expression Integer
--E

--S 7 of 49      14:637 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                         2
       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
     + 
                 2
       (cosh(a x)  - 1)coth(a x) - 2
  /
                2                                      2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                         2
--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
--R     + 
--R                 2
--R       (cosh(a x)  - 1)coth(a x) - 2
--R  /
--R                2                                      2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 8 of 49
aa:=integrate(csch(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                   3                      2                2
       - 2sinh(a x)  - 6cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
     + 
                   3
       - 2cosh(a x)  - 2cosh(a x)
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
     + 
       2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                   3                      2                2
--R       - 2sinh(a x)  - 6cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
--R     + 
--R                   3
--R       - 2cosh(a x)  - 2cosh(a x)
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
--R     + 
--R       2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 49
bb:=-(csch(a*x)*coth(a*x))/(2*a)-1/(2*a)*log(tanh((a*x)/2))
 

                   a x
        - log(tanh(---)) - coth(a x)csch(a x)
                    2
   (2)  -------------------------------------
                          2a
                                                     Type: Expression Integer
--R
--R                   a x
--R        - log(tanh(---)) - coth(a x)csch(a x)
--R                    2
--R   (2)  -------------------------------------
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 10 of 49     14:638 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
                  a x
         log(tanh(---))
                   2
     + 
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                                  4
       coth(a x)csch(a x)sinh(a x)
     + 
                                                  3
       (4cosh(a x)coth(a x)csch(a x) - 2)sinh(a x)
     + 
                   2                                              2
       ((6cosh(a x)  - 2)coth(a x)csch(a x) - 6cosh(a x))sinh(a x)
     + 
                   3                                             2
       ((4cosh(a x)  - 4cosh(a x))coth(a x)csch(a x) - 6cosh(a x)  - 2)sinh(a x)
     + 
               4             2                                    3
     (cosh(a x)  - 2cosh(a x)  + 1)coth(a x)csch(a x) - 2cosh(a x)  - 2cosh(a x)
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
     + 
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R                  a x
--R         log(tanh(---))
--R                   2
--R     + 
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                  4
--R       coth(a x)csch(a x)sinh(a x)
--R     + 
--R                                                  3
--R       (4cosh(a x)coth(a x)csch(a x) - 2)sinh(a x)
--R     + 
--R                   2                                              2
--R       ((6cosh(a x)  - 2)coth(a x)csch(a x) - 6cosh(a x))sinh(a x)
--R     + 
--R                   3                                             2
--R       ((4cosh(a x)  - 4cosh(a x))coth(a x)csch(a x) - 6cosh(a x)  - 2)sinh(a x)
--R     + 
--R               4             2                                    3
--R     (cosh(a x)  - 2cosh(a x)  + 1)coth(a x)csch(a x) - 2cosh(a x)  - 2cosh(a x)
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
--R     + 
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 11 of 49
aa:=integrate(csch(a*x)^n*coth(a*x),x)
 

   (1)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
  /
     a n
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R  /
--R     a n
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12 of 49
bb:=-csch(a*x)^n/(n*a)
 

                   n
          csch(a x)
   (2)  - ----------
              a n
                                                     Type: Expression Integer
--R
--R                   n
--R          csch(a x)
--R   (2)  - ----------
--R              a n
--R                                                     Type: Expression Integer
--E

--S 13 of 49
cc:=aa-bb
 

   (3)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                n
       csch(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (3)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                n
--R       csch(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 14 of 49
cschrule:=rule(csch(x) == 1/sinh(x))
 

                      1
   (4)  csch(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                      1
--R   (4)  csch(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 15 of 49
dd:=cschrule cc
 

   (5)
                                 2sinh(a x) + 2cosh(a x)
       - sinh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
                                 2sinh(a x) + 2cosh(a x)
       - cosh(n log(-------------------------------------------------))
                             2                                  2
                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (5)
--R                                 2sinh(a x) + 2cosh(a x)
--R       - sinh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R                                 2sinh(a x) + 2cosh(a x)
--R       - cosh(n log(-------------------------------------------------))
--R                             2                                  2
--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 16 of 49
ee:=expandLog dd
 

   (6)
       sinh
                           2                                  2
            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
                              2                                  2
               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (6)
--R       sinh
--R                           2                                  2
--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R                              2                                  2
--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 17 of 49
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (7)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (7)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 18 of 49
ff:=sinhsqrrule ee
 

   (8)
       sinh
                                                               2
                  4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
            n log(--------------------------------------------------)
                                           2
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
                                                                  2
                     4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
               n log(--------------------------------------------------)
                                              2
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (8)
--R       sinh
--R                                                               2
--R                  4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
--R            n log(--------------------------------------------------)
--R                                           2
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R                                                                  2
--R                     4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
--R               n log(--------------------------------------------------)
--R                                              2
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 19 of 49
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (9)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (9)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 20 of 49
gg:=coshsqrrule ff
 

   (10)
       sinh
            n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
          + 
            - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
       -
          cosh
               n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
             + 
               - n log(sinh(a x) + cosh(a x)) - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (10)
--R       sinh
--R            n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
--R          + 
--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R       -
--R          cosh
--R               n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
--R             + 
--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 21 of 49
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %K sinh(y + x) - %K sinh(y - x)
   (11)  %K cosh(y)sinh(x) == -------------------------------
                                             2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %O sinh(y + x) - %O sinh(y - x)
--I   (11)  %O cosh(y)sinh(x) == -------------------------------
--R                                             2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 22 of 49
hh:=sinhcoshrule gg
 

   (12)
       sinh
            n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
          + 
            - n log(2)
     + 
       -
          cosh
               n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
             + 
               - n log(2)
     + 
            1     n
       (---------)
        sinh(a x)
  /
     a n
                                                     Type: Expression Integer
--R
--R   (12)
--R       sinh
--R            n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
--R          + 
--R            - n log(2)
--R     + 
--R       -
--R          cosh
--R               n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
--R             + 
--R               - n log(2)
--R     + 
--R            1     n
--R       (---------)
--R        sinh(a x)
--R  /
--R     a n
--R                                                     Type: Expression Integer
--E

--S 23 of 49     14:639 Schaums and Axiom agree
ii:=complexNormalize hh
 

   (13)  0
                                                     Type: Expression Integer
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 24 of 49
aa:=integrate(1/csch(a*x),x)
 

        cosh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cosh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 25 of 49
bb:=1/a*cosh(a*x)
 

        cosh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        cosh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 26 of 49     14:640 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 49     14:641 Axiom cannot compute this integral
aa:=integrate(x*csch(a*x),x)
 

           x
         ++
   (1)   |   %P csch(%P a)d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O csch(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 28 of 49
aa:=integrate(x*csch(a*x)^2,x)
 

   (1)
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                       2                                           2
       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                       2                                           2
--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                          Type: Union(Expression Integer,...)
--E

--S 29 of 49
bb:=-(x*coth(a*x))/a+1/a^2*log(sinh(a*x))
 

        log(sinh(a x)) - a x coth(a x)
   (2)  ------------------------------
                       2
                      a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x)) - a x coth(a x)
--R   (2)  ------------------------------
--R                       2
--R                      a
--R                                                     Type: Expression Integer
--E

--S 30 of 49
cc:=aa-bb
 

   (3)
                   2                                  2
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                                      2
       (a x coth(a x) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
     + 
                     2                                 2
       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                                      2
--R       (a x coth(a x) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
--R     + 
--R                     2                                 2
--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 31 of 49
dd:=expandLog cc
 

   (4)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                                                 2
       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
                     2                                             2
       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (4)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                                                 2
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R                     2                                             2
--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 32 of 49
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 33 of 49
ee:=sinhsqrrule dd
 

   (6)
                                                         2
         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
      *
         log(sinh(a x) - cosh(a x))
     + 
       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
     + 
                                       2
       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
     + 
                                                                2
       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
     + 
       2a x
  /
       2                      2               2         2     2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                         2
--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
--R     + 
--R                                       2
--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
--R     + 
--R                                                                2
--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
--R     + 
--R       2a x
--R  /
--R       2                      2               2         2     2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
--R                                                     Type: Expression Integer
--E

--S 34 of 49
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35 of 49
ff:=coshsqrrule ee
 

   (8)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 36 of 49
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %Q sinh(y + x) - %Q sinh(y - x)
   (9)  %Q cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %P sinh(y + x) - %P sinh(y - x)
--I   (9)  %P cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37 of 49
gg:=sinhcoshrule ff
 

   (10)
       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 38 of 49     14:642 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         - log(- 1) + log(- 2)
   (11)  ---------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R         - log(- 1) + log(- 2)
--R   (11)  ---------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 39 of 49     14:643 Axiom cannot compute this integral
aa:=integrate(csch(a*x)/x,x)
 

           x
         ++  csch(%P a)
   (1)   |   ---------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  csch(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 40 of 49
aa:=integrate(1/(q+p*csch(a*x)),x)
 

   (1)
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
           +-------+
           | 2    2
       a x\|q  + p
  /
         +-------+
         | 2    2
     a q\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R           +-------+
--R           | 2    2
--R       a x\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 41 of 49
t1:=integrate(1/(p+q*sinh(a*x)),x)
 

   (2)
     log
                 2         2      2                              2         2
                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
              + 
                                  2     2
                2p q cosh(a x) + q  + 2p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                 3     2                   3     2                  2     3
            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
       /
                       2                                             2
            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
          + 
            2p cosh(a x) - q
  /
       +-------+
       | 2    2
     a\|q  + p
                                          Type: Union(Expression Integer,...)
--R
--R   (2)
--R     log
--R                 2         2      2                              2         2
--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R              + 
--R                                  2     2
--R                2p q cosh(a x) + q  + 2p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                 3     2                   3     2                  2     3
--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R       /
--R                       2                                             2
--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R          + 
--R            2p cosh(a x) - q
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E

--S 42 of 49
bb:=x/q-p/q*t1
 

   (3)
       -
            p
         *
            log
                        2         2      2
                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                     + 
                        2         2                     2     2
                       q cosh(a x)  + 2p q cosh(a x) + q  + 2p
                  *
                      +-------+
                      | 2    2
                     \|q  + p
                 + 
                      3     2                   3     2                  2     3
                 (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
              /
                              2                                             2
                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                 + 
                   2p cosh(a x) - q
     + 
           +-------+
           | 2    2
       a x\|q  + p
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R       -
--R            p
--R         *
--R            log
--R                        2         2      2
--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                     + 
--R                        2         2                     2     2
--R                       q cosh(a x)  + 2p q cosh(a x) + q  + 2p
--R                  *
--R                      +-------+
--R                      | 2    2
--R                     \|q  + p
--R                 + 
--R                      3     2                   3     2                  2     3
--R                 (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R              /
--R                              2                                             2
--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                 + 
--R                   2p cosh(a x) - q
--R     + 
--R           +-------+
--R           | 2    2
--R       a x\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 43 of 49
cc:=aa-bb
 

   (4)
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
     + 
         p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) - q
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R     + 
--R         p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) - q
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 44 of 49
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 45 of 49
dd:=sinhsqrrule cc
 

   (6)
         p
      *
         log
                       2                              2
                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
                  + 
                      2         2                     2     2
                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (4q  + 4p q)sinh(a x) + (4q  + 4p q)cosh(a x) + 4p q  + 4p
           /
                                                                          2
                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
              + 
                4p cosh(a x) - 3q
     + 
         p
      *
         log
                       2                              2
                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
                  + 
                      2         2                     2     2
                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 4q  - 4p q)sinh(a x) + (- 4q  - 4p q)cosh(a x) - 4p q  - 4p
           /
                                                                          2
                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
              + 
                4p cosh(a x) - 3q
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (6)
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                      2         2                     2     2
--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (4q  + 4p q)sinh(a x) + (4q  + 4p q)cosh(a x) + 4p q  + 4p
--R           /
--R                                                                          2
--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
--R              + 
--R                4p cosh(a x) - 3q
--R     + 
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                      2         2                     2     2
--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 4q  - 4p q)sinh(a x) + (- 4q  - 4p q)cosh(a x) - 4p q  - 4p
--R           /
--R                                                                          2
--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
--R              + 
--R                4p cosh(a x) - 3q
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 46 of 49
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 47 of 49
ee:=coshsqrrule dd
 

   (8)
         p
      *
         log
                       2                              2
                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
           /
              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
     + 
         p
      *
         log
                       2                              2
                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
                  + 
                                      2     2
                    2p q cosh(a x) + q  + 2p
               *
                   +-------+
                   | 2    2
                  \|q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
           /
              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
  /
         +-------+
         | 2    2
     a q\|q  + p
                                                     Type: Expression Integer
--R
--R   (8)
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
--R           /
--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
--R     + 
--R         p
--R      *
--R         log
--R                       2                              2
--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) + q  + 2p
--R               *
--R                   +-------+
--R                   | 2    2
--R                  \|q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
--R           /
--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
--R  /
--R         +-------+
--R         | 2    2
--R     a q\|q  + p
--R                                                     Type: Expression Integer
--E

--S 48 of 49     14:644 Schaums and Axiom differ by a constant
ff:=complexNormalize ee
 

               4    2 2
        p log(q  + p q )
   (9)  ----------------
              +-------+
              | 2    2
          a q\|q  + p
                                                     Type: Expression Integer
--R
--R               4    2 2
--R        p log(q  + p q )
--R   (9)  ----------------
--R              +-------+
--R              | 2    2
--R          a q\|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 49 of 49     14:645 Axiom cannot compute this integral
aa:=integrate(csch(a*x)^n,x)
 

           x
         ++            n
   (1)   |   csch(%P a) d%P
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   csch(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to calcprob.output (2010/3/27, 18:24:19).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 12
solve(3*x-(x-7)=4*x-5,x)
 

   (1)  [x= 6]
                              Type: List Equation Fraction Polynomial Integer
--R
--R   (1)  [x= 6]
--R                              Type: List Equation Fraction Polynomial Integer
--E 1

--S 2 of 12
solve(4*x-3*y=9,y)::List Equation Polynomial Fraction Integer
 

            4
   (2)  [y= - x - 3]
            3
                              Type: List Equation Polynomial Fraction Integer
--R
--R            4
--R   (2)  [y= - x - 3]
--R            3
--R                              Type: List Equation Polynomial Fraction Integer
--E 2

--S 3 of 12
solve(A*x+B*y=C,y)
 

            - A x + C
   (3)  [y= ---------]
                B
                              Type: List Equation Fraction Polynomial Integer
--R
--R            - A x + C
--R   (3)  [y= ---------]
--R                B
--R                              Type: List Equation Fraction Polynomial Integer
--E 3

--S 4 of 12
m:=3*x-4*(x-(2/3)*y)=(4/5)*x-(7*y+3)
 

        8               4
   (4)  - y - x= - 7y + - x - 3
        3               5
                                   Type: Equation Polynomial Fraction Integer
--R
--R        8               4
--R   (4)  - y - x= - 7y + - x - 3
--R        3               5
--R                                   Type: Equation Polynomial Fraction Integer
--E 4

--S 5 of 12
n:=solve(m*15,y)
 

            27x - 45
   (5)  [y= --------]
               145
                              Type: List Equation Fraction Polynomial Integer
--R
--R            27x - 45
--R   (5)  [y= --------]
--R               145
--R                              Type: List Equation Fraction Polynomial Integer
--E 5

--S 6 of 12
p:=n.1*145-27*x
 

   (6)  145y - 27x= - 45
                                   Type: Equation Fraction Polynomial Integer
--R
--R   (6)  145y - 27x= - 45
--R                                   Type: Equation Fraction Polynomial Integer
--E 6

--S 7 of 12
(x1,y1):=(-3,-8)
 

   (7)  - 8
                                                                Type: Integer
--R
--R   (7)  - 8
--R                                                                Type: Integer
--E 7

--S 8 of 12
(x2,y2):=(-6,2)
 

   (8)  2
                                                        Type: PositiveInteger
--R
--R   (8)  2
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 12
m:=(y2-y1)/(x2-x1)
 

          10
   (9)  - --
           3
                                                       Type: Fraction Integer
--R
--R          10
--R   (9)  - --
--R           3
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 12
solve(y1=m*x1+b,b)
 

   (10)  [b= - 18]
                              Type: List Equation Fraction Polynomial Integer
--R
--R   (10)  [b= - 18]
--R                              Type: List Equation Fraction Polynomial Integer
--E 10

--S 11 of 12
b:=-18
 

   (11)  - 18
                                                                Type: Integer
--R
--R   (11)  - 18
--R                                                                Type: Integer
--E 11

--S 12 of 12
y=m*x+b
 

              10
   (12)  y= - -- x - 18
               3
                                   Type: Equation Polynomial Fraction Integer
--R
--R              10
--R   (12)  y= - -- x - 18
--R               3
--R                                   Type: Equation Polynomial Fraction Integer
--E 12
)spool 
 
Starts dribbling to kamke6.output (2010/3/27, 18:28:28).
)set break resume
 
)set mes auto off
 
)clear all
 

--S 1 of 120
y:=operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 120
--Rf:=operator 'f
--R 
--R
--R   (2)  f
--R                                                          Type: BasicOperator
--E 2

--S 3 of 120
--Rg:=operator 'g
--R 
--R
--R   (3)  g
--R                                                          Type: BasicOperator
--R
--E 3

--S 4 of 120
--Rode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x)
--R 
--R
--R                2    2  ,           3
--R   (4)  (6x y(x)  + x )y (x) - 3y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 4

--S 5 of 120
--Rsolve(ode301,y,x)
--R 
--R
--R   (5)  "failed"
--R                                                    Type: Union("failed",...)
--E 5

--S 6 of 120
--Rode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x)
--R 
--R
--R          2    2      ,
--R   (6)  (x y(x)  + x)y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 6

--S 7 of 120
--Rsolve(ode302,y,x)
--R 
--R
--R   (7)  "failed"
--R                                                    Type: Union("failed",...)
--E 7

--S 8 of 120
--Rode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x)
--R 
--R
--R          3    2     2          ,       2    3
--R   (8)  (x y(x)  - 2x y(x) + x)y (x) + x y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 8

--S 9 of 120
--Rsolve(ode303,y,x)
--R 
--R
--R   (9)  "failed"
--R                                                    Type: Union("failed",...)
--E 9

--S 10 of 120
--Rode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2
--R 
--R
--R             3    2    2           ,        2    3         2
--R   (10)  (10x y(x)  + x y(x) + 2x)y (x) + 5x y(x)  + x y(x)
--R
--R                                                     Type: Expression Integer
--E 10

--S 11 of 120
--Rsolve(ode304,y,x)
--R 
--R
--R   (11)  "failed"
--R                                                    Type: Union("failed",...)
--E 11

--S 12 of 120
--Rode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2
--R 
--R
--R              3       ,               2
--R   (12)  (y(x)  - 3x)y (x) - 3y(x) + x
--R
--R                                                     Type: Expression Integer
--E 12

--S 13 of 120
--Ryx:=solve(ode305,y,x)
--R 
--R
--R              4                3
--R         3y(x)  - 36x y(x) + 4x
--R   (13)  -----------------------
--R                    12
--R                                          Type: Union(Expression Integer,...)
--E 13

--S 14 of 120
--Rode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2
--R 
--R
--R   (14)
--R                 15             12       3    11         2    9        4    8
--R           27y(x)   - 1053x y(x)   + 108x y(x)   + 14580x y(x)  - 2916x y(x)
--R         + 
--R               6    7         3    6         5    5        7    4
--R           144x y(x)  - 81648x y(x)  + 23328x y(x)  - 2160x y(x)
--R         + 
--R               9          4             3         6    2        8           10
--R           (64x  + 139968x  - 5184x)y(x)  - 46656x y(x)  + 5184x y(x) - 192x
--R         + 
--R                 2
--R           15552x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R               13      2    12             10        3    9       5    8
--R       - 81y(x)   + 27x y(x)   + 2916x y(x)   - 1296x y(x)  + 108x y(x)
--R     + 
--R               2    7         4    6        6    5
--R       - 34992x y(x)  + 19440x y(x)  - 3024x y(x)
--R     + 
--R            8          3            4         5    3         7    2
--R       (144x  + 139968x  - 1296)y(x)  - 93312x y(x)  + 20736x y(x)
--R     + 
--R               9                    11        3        2
--R       (- 1920x  + 31104x)y(x) + 64x   - 6912x  + 1728x
--R  /
--R     1728
--R                                                     Type: Expression Integer
--E 14

--S 15 of 120
--Rode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x)
--R 
--R
--R              3    3  ,       2
--R   (15)  (y(x)  - x )y (x) - x y(x)
--R
--R                                                     Type: Expression Integer
--E 15

--S 16 of 120
--Ryx:=solve(ode306,y,x)
--R 
--R
--R             6     3    3
--R         y(x)  - 2x y(x)
--R   (16)  ----------------
--R                 6
--R                                          Type: Union(Expression Integer,...)
--E 16

--S 17 of 120
--Rode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx
--R 
--R
--R   (17)
--R               23     3    20      6    17      9    14     12    11
--R           y(x)   - 7x y(x)   + 18x y(x)   - 20x y(x)   + 8x  y(x)
--R         + 
--R                 3    5       6    2
--R           - 216x y(x)  + 216x y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R        2    21     5    18      8    15     11    12      2    6       5    3
--R     - x y(x)   + 6x y(x)   - 12x y(x)   + 8x  y(x)   - 36x y(x)  + 288x y(x)
--R  /
--R     216
--R                                                     Type: Expression Integer
--E 17

--S 18 of 120
--Rode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x
--R 
--R
--R              3     2           ,            2    3
--R   (18)  (y(x)  + (x  + a)y(x))y (x) + x y(x)  + x  - a x
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 120
--Ryx:=solve(ode307,y,x)
--R 
--R
--R             4      2          2    4       2
--R         y(x)  + (2x  + 2a)y(x)  + x  - 2a x
--R   (19)  ------------------------------------
--R                           4
--R                                          Type: Union(Expression Integer,...)
--E 19

--S 20 of 120
--Rode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x
--R 
--R
--R   (20)
--R               15      2          13       4        2      2     11
--R           y(x)   + (7x  + 7a)y(x)   + (21x  + 30a x  + 18a )y(x)
--R         + 
--R               6        4      2 2      3     9
--R           (35x  + 45a x  + 30a x  + 20a )y(x)
--R         + 
--R               8        6      2 4         3       2     4           7
--R           (35x  + 20a x  - 12a x  + (- 16a  + 16)x  + 8a  + 16a)y(x)
--R         + 
--R                    10        8      2 6         3       4         4        2
--R                 21x   - 15a x  - 36a x  + (- 24a  + 48)x  + (- 24a  + 96a)x
--R               + 
--R                    2
--R                 48a
--R          *
--R                 5
--R             y(x)
--R         + 
--R                 12        10     2 8       3       6       4        4      2 2
--R               7x   - 18a x   - 6a x  + (16a  + 48)x  + (24a  + 80a)x  + 64a x
--R             + 
--R                  3
--R               32a
--R          *
--R                 3
--R             y(x)
--R         + 
--R             14       12     2 10      3       8     4 6      2 4      3 2
--R           (x   - 5a x   + 6a x   + (4a  + 16)x  - 8a x  - 48a x  - 32a x )y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             14      3            12       5        3     2      10
--R       x y(x)   + (7x  + 5a x)y(x)   + (21x  + 18a x  + 6a x)y(x)
--R     + 
--R           7        5     2 3        3           8
--R       (35x  + 15a x  - 6a x  + (- 4a  + 4)x)y(x)
--R     + 
--R           9        7      2 5         3       3        4             6
--R       (35x  - 20a x  - 36a x  + (- 16a  + 32)x  + (- 8a  + 32a)x)y(x)
--R     + 
--R           11        9      2 7       3       5       4        3      2      4
--R       (21x   - 45a x  - 12a x  + (24a  + 72)x  + (24a  + 80a)x  + 32a x)y(x)
--R     + 
--R          13        11      2 9       3       7      4 5      2 3      3      2
--R       (7x   - 30a x   + 30a x  + (16a  + 64)x  - 24a x  - 96a x  - 32a x)y(x)
--R     + 
--R        15       13      2 11         3       9      4        7       3       3
--R       x   - 7a x   + 18a x   + (- 20a  + 20)x  + (8a  - 48a)x  + (32a  + 64)x
--R     + 
--R       - 64a x
--R  /
--R     64
--R                                                     Type: Expression Integer
--E 20

--S 21 of 120
--Rode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2
--R 
--R
--R              3 ,            2
--R   (21)  2y(x) y (x) + x y(x)
--R
--R                                                     Type: Expression Integer
--E 21

--S 22 of 120
--Ryx:=solve(ode308,y,x)
--R 
--R
--R              2    2
--R         2y(x)  + x
--R   (22)  -----------
--R              2
--R                                          Type: Union(Expression Integer,...)
--E 22

--S 23 of 120
--Rode308expr := 2*yx**3*D(yx,x)+x*yx**2
--R 
--R
--R   (23)
--R              7      2    5      4    3     6      ,             6
--R       (16y(x)  + 24x y(x)  + 12x y(x)  + 2x y(x))y (x) + 8x y(x)
--R
--R     + 
--R           3          4      5     3     2    7    5
--R       (12x  + 4x)y(x)  + (6x  + 4x )y(x)  + x  + x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 23

--S 24 of 120
--Rode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x
--R 
--R
--R               3         ,        3
--R   (24)  (2y(x)  + y(x))y (x) - 2x  - x
--R
--R                                                     Type: Expression Integer
--E 24

--S 25 of 120
--Ryx:=solve(ode309,y,x)
--R 
--R
--R             4       2    4    2
--R         y(x)  + y(x)  - x  - x
--R   (25)  -----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 25

--S 26 of 120
--Rode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x
--R 
--R
--R   (26)
--R                15        13        4     2         11
--R           2y(x)   + 7y(x)   + (- 6x  - 6x  + 9)y(x)
--R         + 
--R                 4      2         9      8      6     4      2         7
--R           (- 15x  - 15x  + 5)y(x)  + (6x  + 12x  - 6x  - 12x  + 5)y(x)
--R         + 
--R              8      6     4     2         5
--R           (9x  + 18x  + 6x  - 3x  + 6)y(x)
--R         + 
--R                12     10     8     6    4     2         3
--R           (- 2x   - 6x   - 3x  + 4x  - x  - 4x  + 2)y(x)
--R         + 
--R               12     10     8    6     4     2
--R           (- x   - 3x   - 3x  - x  - 2x  - 2x )y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R            3         12        3          10      7     5     3          8
--R       (- 2x  - x)y(x)   + (- 6x  - 3x)y(x)   + (6x  + 9x  - 3x  - 3x)y(x)
--R     + 
--R           7      5     3         6        11      9     7     5    3          4
--R       (12x  + 18x  + 4x  - x)y(x)  + (- 6x   - 15x  - 6x  + 6x  - x  - 2x)y(x)
--R     + 
--R            11      9      7     5     3          2     15     13     11     9
--R       (- 6x   - 15x  - 12x  - 3x  - 4x  - 2x)y(x)  + 2x   + 7x   + 9x   + 5x
--R     + 
--R         7     5     3
--R       5x  + 6x  - 6x  - 4x
--R  /
--R     4
--R                                                     Type: Expression Integer
--E 26

--S 27 of 120
--Rode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3
--R 
--R
--R               3     2      ,             2    3
--R   (27)  (2y(x)  + 5x y(x))y (x) + 5x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 27

--S 28 of 120
--Ryx:=solve(ode310,y,x)
--R 
--R
--R              4      2    2    4
--R         2y(x)  + 10x y(x)  + x
--R   (28)  -----------------------
--R                    4
--R                                          Type: Union(Expression Integer,...)
--E 28

--S 29 of 120
--Rode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3
--R 
--R
--R   (29)
--R                 15       2    13        4    11        6    9
--R           16y(x)   + 280x y(x)   + 1824x y(x)   + 5300x y(x)
--R         + 
--R                 8       2     7         10        4     5
--R           (6212x  + 160x )y(x)  + (1590x   + 1200x )y(x)
--R         + 
--R                12        6     3      14       8
--R           (152x   + 2080x )y(x)  + (5x   + 200x )y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R               14       3    12        5    10         7           8
--R       40x y(x)   + 608x y(x)   + 3180x y(x)   + (6212x  + 40x)y(x)
--R     + 
--R             9       3     6        11        5     4       13       7     2
--R       (2650x  + 800x )y(x)  + (456x   + 3120x )y(x)  + (35x   + 800x )y(x)
--R     + 
--R        15      9      3
--R       x   + 50x  + 32x
--R  /
--R     32
--R                                                     Type: Expression Integer
--E 29

--S 30 of 120
--Rode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_
--R             y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3
--R 
--R
--R   (30)
--R          3          2     2         3  ,          3          2     2         3
--R   (20y(x)  - 3x y(x)  + 6x y(x) + 3x )y (x) - y(x)  + 6x y(x)  + 9x y(x) + 4x
--R
--R                                                     Type: Expression Integer
--E 30

--S 31 of 120
--Ryx:=solve(ode311,y,x)
--R 
--R
--R              4         3     2    2     3        4
--R   (31)  5y(x)  - x y(x)  + 3x y(x)  + 3x y(x) + x
--R                                          Type: Union(Expression Integer,...)
--E 31

--S 32 of 120
--Rode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_
--R                yx**3+6*x*yx**2+9*x**2*yx+4*x**3
--R 
--R
--R   (32)
--R                  15              14          2    13         3    12
--R         50000y(x)   - 37500x y(x)   + 115500x y(x)   + 37700x y(x)
--R       + 
--R                4             11           5       2     10
--R         (67860x  - 1500x)y(x)   + (111540x  + 825x )y(x)
--R       + 
--R                6        3     9          7        4     8
--R         (90600x  - 2400x )y(x)  + (72720x  - 1206x )y(x)
--R       + 
--R                8        5       2     7          9        6       3     6
--R         (71880x  - 1032x  + 600x )y(x)  + (52080x  - 1554x  - 210x )y(x)
--R       + 
--R                10        7       4     5          11       8       5     4
--R         (29880x   - 1206x  + 558x )y(x)  + (17100x   - 630x  + 360x )y(x)
--R       + 
--R               12       9       6      3     3
--R         (8860x   - 420x  + 156x  + 60x )y(x)
--R       + 
--R               13       10       7     4     2
--R         (3180x   - 234x   + 144x  - 9x )y(x)
--R       + 
--R              14      11      8      5           15     12      9     6
--R         (660x   - 72x   + 90x  + 18x )y(x) + 60x   - 9x   + 18x  + 9x
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R               15              14        2    13          3           12
--R     - 2500y(x)   + 16500x y(x)   + 8700x y(x)   + (22620x  - 125)y(x)
--R   + 
--R            4            11          5       2     10          6       3     9
--R     (50700x  + 150x)y(x)   + (54360x  - 720x )y(x)   + (56560x  - 536x )y(x)
--R   + 
--R            7       4            8          8        5      2     7
--R     (71880x  - 645x  + 150x)y(x)  + (66960x  - 1332x  - 90x )y(x)
--R   + 
--R            9        6       3     6          10        7       4     5
--R     (49800x  - 1407x  + 372x )y(x)  + (37620x   - 1008x  + 360x )y(x)
--R   + 
--R            11       8       5      2     4
--R     (26580x   - 945x  + 234x  + 45x )y(x)
--R   + 
--R            12       9       6      3     3
--R     (13780x   - 780x  + 336x  - 12x )y(x)
--R   + 
--R           13       10       7      4     2
--R     (4620x   - 396x   + 360x  + 45x )y(x)
--R   + 
--R          14       11       8      5           15      12      9      6     3
--R     (900x   - 108x   + 162x  + 54x )y(x) + 80x   - 13x   + 30x  + 21x  + 4x
--R                                                     Type: Expression Integer
--E 32

--S 33 of 120
--Rode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_
--R             (y(x)*D(y(x),x)-x)
--R 
--R
--R   (33)
--R                2     3      2        2      2    2        ,
--R       ((a b + a )y(x)  + ((b  + a b)x  - a b  + a b)y(x))y (x)
--R
--R     + 
--R               2       2     2        3       2    2
--R       (a b + a )x y(x)  + (b  + a b)x  + (a b  - a b)x
--R  /
--R        2    2
--R     a b  + a b
--R                                                     Type: Expression Integer
--E 33

--S 34 of 120
--Rsolve(ode312,y,x)
--R 
--R
--R   (34)  "failed"
--R                                                    Type: Union("failed",...)
--E 34

--S 35 of 120
--Rode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_
--R             a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3
--R 
--R
--R   (35)
--R             3            2      3      2  ,            3         2       2
--R     (2a y(x)  + 3a x y(x)  - b x  + c x )y (x) - a y(x)  + c y(x)  + 3b x y(x)
--R
--R   + 
--R         3
--R     2b x
--R                                                     Type: Expression Integer
--E 35

--S 36 of 120
--Rsolve(ode313,y,x)
--R 
--R
--R   (36)  "failed"
--R                                                    Type: Union("failed",...)
--E 36

--S 37 of 120
--Rode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x)
--R 
--R
--R               3 ,                     4
--R   (37)  x y(x) y (x) - x sin(x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 37

--S 38 of 120
--Ryx:=solve(ode314,y,x)
--R 
--R
--R               3                   4      2                4    4
--R         (- 16x  + 96x)sin(x) + (4x  - 48x  + 96)cos(x) + x y(x)
--R   (38)  --------------------------------------------------------
--R                                     4
--R                                          Type: Union(Expression Integer,...)
--E 38

--S 39 of 120
--Rode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x)
--R 
--R
--R   (39)
--R                    14          12           10           8     3      3
--R           (- 16384x   + 294912x   - 1769472x   + 3538944x )y(x) sin(x)
--R         + 
--R                        15          13           11           9            7
--R                 (12288x   - 294912x   + 2506752x   - 8847360x  + 10616832x )
--R              *
--R                     3
--R                 y(x) cos(x)
--R             + 
--R                     15         13          11     7
--R               (3072x   - 36864x   + 110592x  )y(x)
--R          *
--R                   2
--R             sin(x)
--R         + 
--R                          16         14           12           10            8
--R                   - 3072x   + 92160x   - 1032192x   + 5308416x   - 12386304x
--R                 + 
--R                            6
--R                   10616832x
--R              *
--R                     3      2
--R                 y(x) cos(x)
--R             + 
--R                       16         14          12          10     7
--R               (- 1536x   + 27648x   - 147456x   + 221184x  )y(x) cos(x)
--R             + 
--R                      16        14     11
--R               (- 192x   + 1152x  )y(x)
--R          *
--R             sin(x)
--R         + 
--R                   17        15          13          11           9           7
--R               256x   - 9216x   + 129024x   - 884736x   + 3096576x  - 5308416x
--R             + 
--R                       5
--R               3538944x
--R          *
--R                 3      3
--R             y(x) cos(x)
--R         + 
--R                17        15         13          11          9     7      2
--R           (192x   - 4608x   + 36864x   - 110592x   + 110592x )y(x) cos(x)
--R         + 
--R               17       15        13     11           17    15
--R           (48x   - 576x   + 1152x  )y(x)  cos(x) + 4x  y(x)
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                   14          12          10            8            6
--R             16384x   - 229376x   + 196608x   + 10616832x  - 56623104x
--R           + 
--R                      4
--R             84934656x
--R      *
--R               4
--R         sin(x)
--R     + 
--R                       15          13          11            9             7
--R               - 12288x   + 229376x   - 540672x   - 13959168x  + 116785152x
--R             + 
--R                           5             3
--R               - 339738624x  + 339738624x
--R          *
--R             cos(x)
--R         + 
--R                   15        13          11           9           7     4
--R           (- 3072x   + 4096x   + 479232x   - 3538944x  + 7077888x )y(x)
--R      *
--R               3
--R         sin(x)
--R     + 
--R                    16         14          12           10            8
--R               3072x   - 67584x   + 147456x   + 7372800x   - 79626240x
--R             + 
--R                         6             4             2
--R               343277568x  - 679477248x  + 509607936x
--R          *
--R                   2
--R             cos(x)
--R         + 
--R                    16        14          12           10            8
--R               1536x   - 3072x   - 442368x   + 4792320x   - 17694720x
--R             + 
--R                        6
--R               21233664x
--R          *
--R                 4
--R             y(x) cos(x)
--R         + 
--R                16        14         12          10     8
--R           (192x   + 3456x   - 55296x   + 165888x  )y(x)
--R      *
--R               2
--R         sin(x)
--R     + 
--R                     17        15         13           11            9
--R               - 256x   + 5120x   + 43008x   - 2064384x   + 23445504x
--R             + 
--R                           7             5             3
--R               - 129171456x  + 378667008x  - 566231040x  + 339738624x
--R          *
--R                   3
--R             cos(x)
--R         + 
--R                     17        15          13           11            9
--R               - 192x   - 1536x   + 147456x   - 1953792x   + 10506240x
--R             + 
--R                          7            5
--R               - 24772608x  + 21233664x
--R          *
--R                 4      2
--R             y(x) cos(x)
--R         + 
--R                 17        15         13          11          9     8
--R           (- 48x   - 1728x   + 40320x   - 221184x   + 331776x )y(x) cos(x)
--R         + 
--R                17       15        13     12
--R           (- 4x   - 256x   + 1536x  )y(x)   - 256x
--R      *
--R         sin(x)
--R     + 
--R               16         14          12           10            8            6
--R           256x   - 12288x   + 245760x   - 2654208x   + 16809984x  - 63700992x
--R         + 
--R                     4             2
--R           141557760x  - 169869312x  + 84934656
--R      *
--R               4
--R         cos(x)
--R     + 
--R               16         14          12           10           8            6
--R           512x   - 18432x   + 258048x   - 1769472x   + 6193152x  - 10616832x
--R         + 
--R                   4
--R           7077888x
--R      *
--R             4      3
--R         y(x) cos(x)
--R     + 
--R            16        14         12          10          8     8      2
--R       (288x   - 6912x   + 55296x   - 165888x   + 165888x )y(x) cos(x)
--R     + 
--R           16       14        12     12           16    16
--R       (64x   - 768x   + 1536x  )y(x)  cos(x) + 5x  y(x)
--R  /
--R     256
--R                                                     Type: Expression Integer
--E 39

--S 40 of 120
--Rode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x)
--R 
--R
--R                 3    4  ,          4     3
--R   (40)  (2x y(x)  - x )y (x) - y(x)  + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 40

--S 41 of 120
--Rsolve(ode315,y,x)
--R 
--R
--R   (41)  "failed"
--R                                                    Type: Union("failed",...)
--E 41

--S 42 of 120
--Rode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2
--R 
--R
--R                 3         ,           2
--R   (42)  (2x y(x)  + y(x))y (x) + 2y(x)
--R
--R                                                     Type: Expression Integer
--E 42

--S 43 of 120
--Ryx:=solve(ode316,y,x)
--R 
--R
--R                  2
--R              y(x)
--R              -----          2
--R                2        y(x)
--R         4x %e      + Ei(-----)
--R                           2
--R   (43)  ----------------------
--R                    2
--R                                          Type: Union(Expression Integer,...)
--E 43

--S 44 of 120
--Rode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2
--R 
--R
--R   (44)
--R                                     2 4                                     2 3
--R                                 y(x)                                    y(x)
--R                                 -----                              2    -----
--R                5    2      4      2           4    2      3    y(x)       2
--R           (128x y(x)  + 64x )(%e     )  + (96x y(x)  + 48x )Ei(-----)(%e     )
--R                                                                  2
--R         + 
--R                                                                 2 2
--R                                                             y(x)
--R                                     2 2                     -----
--R                3    2      2    y(x)         2    2           2
--R           ((24x y(x)  + 12x )Ei(-----)  + 16x y(x)  + 8x)(%e     )
--R                                   2
--R         + 
--R                                                                     2
--R                                                                 y(x)
--R                                 2 3                        2    -----
--R               2    2        y(x)              2        y(x)       2
--R           ((2x y(x)  + x)Ei(-----)  + (4x y(x)  + 2)Ei(-----))%e
--R                               2                          2
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                       2 4                           2 3
--R                   y(x)                          y(x)
--R                   -----                    2    -----
--R           4         2          3       y(x)       2
--R       128x y(x)(%e     )  + 96x y(x)Ei(-----)(%e     )
--R                                          2
--R     + 
--R                                                     2 2
--R                                                 y(x)
--R                       2 2                       -----
--R           2       y(x)          2                 2
--R       (24x y(x)Ei(-----)  + (32x  + 16x)y(x))(%e     )
--R                     2
--R     + 
--R                                                         2
--R                                                     y(x)
--R                      2 3                       2    -----               2 2
--R                  y(x)                      y(x)       2             y(x)
--R       (2x y(x)Ei(-----)  + (16x + 4)y(x)Ei(-----))%e      + 2y(x)Ei(-----)
--R                    2                         2                        2
--R  /
--R     4y(x)
--R                                                     Type: Expression Integer
--E 44

--S 45 of 120
--Rode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x)
--R 
--R
--R                 3             2  ,          2
--R   (45)  (2x y(x)  + x y(x) + x )y (x) + y(x)  - x y(x)
--R
--R                                                     Type: Expression Integer
--E 45

--S 46 of 120
--Rsolve(ode317,y,x)
--R 
--R
--R   (46)  "failed"
--R                                                    Type: Union("failed",...)
--E 46

--S 47 of 120
--Rode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2)
--R 
--R
--R                 3                   ,          4        2
--R   (47)  (3x y(x)  + (- 4x + 1)y(x))y (x) + y(x)  - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 47

--S 48 of 120
--Ryx:=solve(ode318,y,x)
--R 
--R
--R   (48)
--R                                       +---------+
--R                4               2      |    2              5                 3
--R       (- x y(x)  + (2x - 1)y(x)  + 2)\|y(x)  - 2  + x y(x)  + (- 2x + 1)y(x)
--R     + 
--R       - 2y(x)
--R  /
--R          +---------+
--R          |    2            2
--R     y(x)\|y(x)  - 2  - y(x)  + 2
--R                                          Type: Union(Expression Integer,...)
--E 48

--S 49 of 120
--Rode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2)
--R 
--R
--R   (49)
--R           5    11         5      4     9       5      4      3     7
--R         9x y(x)   + (- 30x  + 30x )y(x)  + (24x  - 96x  + 36x )y(x)
--R       + 
--R             4       3      2     5       3      2          3
--R         (72x  - 120x  + 21x )y(x)  + (88x  - 68x  + 7x)y(x)
--R       + 
--R             2
--R         (40x  - 14x + 1)y(x)
--R    *
--R        ,
--R       y (x)
--R
--R   + 
--R       4    12         4      3     10       4      3      2     8
--R     4x y(x)   + (- 16x  + 13x )y(x)   + (16x  - 52x  + 15x )y(x)
--R   + 
--R         3      2          6       2               4                2
--R     (52x  - 66x  + 8x)y(x)  + (72x  - 38x + 2)y(x)  + (44x - 8)y(x)  + 8
--R                                                     Type: Expression Integer
--E 49

--S 50 of 120
--Rode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x)
--R 
--R
--R                 3              ,          4
--R   (50)  (7x y(x)  + y(x) - 5x)y (x) + y(x)  - 5y(x)
--R
--R                                                     Type: Expression Integer
--E 50

--S 51 of 120
--Ryx:=solve(ode319,y,x)
--R 
--R
--R                 7        5            4         2
--R         10x y(x)  + 2y(x)  - 100x y(x)  - 25y(x)  + 250x y(x)
--R   (51)  -----------------------------------------------------
--R                                   10
--R                                          Type: Union(Expression Integer,...)
--E 51

--S 52 of 120
--Rode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx
--R 
--R
--R   (52)
--R                  5    27          4    25            5    24          3    23
--R           490000x y(x)   + 364000x y(x)   - 17500000x y(x)   + 100800x y(x)
--R         + 
--R                      4    22              5         2     21           3    20
--R           - 13685000x y(x)   + (269500000x  + 12320x )y(x)   - 3969000x y(x)
--R         + 
--R                      4            19                 5          2     18
--R           (210000000x  + 560x)y(x)   + (- 2327500000x  - 505400x )y(x)
--R         + 
--R                    3    17                 4              16
--R           60952500x y(x)   + (- 1710625000x  - 23800x)y(x)
--R         + 
--R                        5           2     15             3    14
--R           (12250000000x  + 7784000x )y(x)   - 464625000x y(x)
--R         + 
--R                       4         2               13
--R           (7962500000x  + 70000x  + 367500x)y(x)
--R         + 
--R                          5            2     12               3              11
--R           (- 39812500000x  - 55168750x )y(x)   + (1842750000x  + 24000x)y(x)
--R         + 
--R                          4           2                10
--R           (- 20934375000x  - 1100000x  - 2406250x)y(x)
--R         + 
--R                        5             2            9
--R           (76562500000x  + 175000000x  + 2000)y(x)
--R         + 
--R                         3               8
--R           (- 3543750000x  - 405000x)y(x)
--R         + 
--R                        4           2                7
--R           (28000000000x  + 6000000x  + 5468750x)y(x)
--R         + 
--R                          5             2             6
--R           (- 76562500000x  - 191756250x  - 35000)y(x)
--R         + 
--R                       3                5
--R           (2460937500x  + 1800000x)y(x)
--R         + 
--R                          4            2              4
--R           (- 13671875000x  - 12500000x  - 50000x)y(x)
--R         + 
--R                        5           2              3                2
--R           (27343750000x  + 2000000x  + 125000)y(x)  - 1875000x y(x)
--R         + 
--R                    2                          2
--R           (6250000x  + 250000x)y(x) - 1250000x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             4    28         3    26           4    25         2    24
--R       80000x y(x)   + 50000x y(x)   - 3200000x y(x)   + 10800x y(x)
--R     + 
--R                 3    23             4            22          2    21
--R       - 2125000x y(x)   + (56000000x  + 880x)y(x)   - 486000x y(x)
--R     + 
--R                 3          20                4              19
--R       (37500000x  + 16)y(x)   + (- 560000000x  - 41800x)y(x)
--R     + 
--R               2    18                3           17
--R       8707500x y(x)   + (- 359375000x  - 800)y(x)
--R     + 
--R                   4               16            2    15
--R       (3500000000x  + 764500x)y(x)   - 79650000x y(x)
--R     + 
--R                   3                      14
--R       (2031250000x  + 10000x + 15000)y(x)
--R     + 
--R                      4                13              2            12
--R       (- 14000000000x  - 6668750x)y(x)   + (394875000x  + 2000)y(x)
--R     + 
--R                     3                        11
--R       (- 6796875000x  - 200000x - 125000)y(x)
--R     + 
--R                    4                 10                 2             9
--R       (35000000000x  + 27500000x)y(x)   + (- 1012500000x  - 45000)y(x)
--R     + 
--R                    3                         8
--R       (12500000000x  + 1500000x + 390625)y(x)
--R     + 
--R                      4                 7               2              6
--R       (- 50000000000x  - 43068750x)y(x)  + (1054687500x  + 300000)y(x)
--R     + 
--R                     3                        5
--R       (- 9765625000x  - 5000000x - 10000)y(x)
--R     + 
--R                    4                4             3                          2
--R       (31250000000x  + 1000000x)y(x)  - 625000y(x)  + (6250000x + 125000)y(x)
--R     + 
--R       - 2500000x y(x)
--R  /
--R     10000
--R                                                     Type: Expression Integer
--E 52

--S 53 of 120
--Rode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1
--R 
--R
--R           2    3           ,
--R   (53)  (x y(x)  + x y(x))y (x) - 1
--R
--R                                                     Type: Expression Integer
--E 53

--S 54 of 120
--Rsolve(ode320,y,x)
--R 
--R
--R   (54)  "failed"
--R                                                    Type: Union("failed",...)
--E 54

--S 55 of 120
--Rode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1
--R 
--R
--R            2    3    2    2       ,
--R   (55)  (2x y(x)  + x y(x)  - 2x)y (x) - 2y(x) - 1
--R
--R                                                     Type: Expression Integer
--E 55

--S 56 of 120
--Rsolve(ode321,y,x)
--R 
--R
--R   (56)  "failed"
--R                                                    Type: Union("failed",...)
--E 56

--S 57 of 120
--Rode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x
--R 
--R
--R             2    3        2      ,             4
--R   (57)  (10x y(x)  - 3y(x)  - 2)y (x) + 5x y(x)  + x
--R
--R                                                     Type: Expression Integer
--E 57

--S 58 of 120
--Ryx:=solve(ode322,y,x)
--R 
--R
--R           2    4        3            2
--R         5x y(x)  - 2y(x)  - 4y(x) + x
--R   (58)  ------------------------------
--R                        2
--R                                          Type: Union(Expression Integer,...)
--E 58

--S 59 of 120
--Rode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x
--R 
--R
--R   (59)
--R                 10    15         8    14         6    13
--R           25000x  y(x)   - 37500x y(x)   + 21000x y(x)
--R         + 
--R                    8        4     12          10         6       2     11
--R           (- 65000x  - 5200x )y(x)   + (15000x   + 69000x  + 480x )y(x)
--R         + 
--R                    8         4     10          6        2     9
--R           (- 16500x  - 23100x )y(x)   + (66000x  + 2000x )y(x)
--R         + 
--R                    8         4           8         10         6        2     7
--R           (- 27000x  - 38520x  + 144)y(x)  + (3000x   + 18000x  + 3840x )y(x)
--R         + 
--R                   8         4           6          6        2     5
--R           (- 2100x  - 24920x  + 672)y(x)  + (14760x  + 4656x )y(x)
--R         + 
--R                   8        4           4        10       6        2     3
--R           (- 3000x  - 3600x  + 960)y(x)  + (200x   + 840x  + 1856x )y(x)
--R         + 
--R               8        4           2        6       2           8      4
--R         (- 60x  - 1884x  + 480)y(x)  + (480x  - 192x )y(x) - 40x  + 24x  + 64
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R             9    16         7    15        5    14            7        3     13
--R       15625x y(x)   - 20000x y(x)   + 9000x y(x)   + (- 40000x  - 1600x )y(x)
--R     + 
--R              9         5           12            7        3     11
--R       (12500x  + 34500x  + 80x)y(x)   + (- 12000x  - 8400x )y(x)
--R     + 
--R              5            10            7         3     9
--R       (39600x  + 400x)y(x)   + (- 24000x  - 17120x )y(x)
--R     + 
--R             9         5            8           7         3     7
--R       (3750x  + 13500x  + 960x)y(x)  + (- 2400x  - 14240x )y(x)
--R     + 
--R              5             6           7        3     5
--R       (14760x  + 1552x)y(x)  + (- 4800x  - 2880x )y(x)
--R     + 
--R            9        5            4          7        3     3
--R       (500x  + 1260x  + 928x)y(x)  + (- 160x  - 2512x )y(x)
--R     + 
--R             5            2          7      3           9      5
--R       (1440x  - 192x)y(x)  + (- 320x  + 96x )y(x) + 25x  - 12x  - 16x
--R  /
--R     16
--R                                                     Type: Expression Integer
--E 59

--S 60 of 120
--Rode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x)
--R 
--R
--R             2    3        ,         3    2
--R   (60)  (a x y(x)  + c x)y (x) + b x y(x)  + c y(x)
--R
--R                                                     Type: Expression Integer
--E 60

--S 61 of 120
--Rsolve(ode323,y,x)
--R 
--R
--R   (61)  "failed"
--R                                                    Type: Union("failed",...)
--E 61

--S 62 of 120
--Rode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x)
--R 
--R
--R            3    3      ,        3    3
--R   (62)  (2x y(x)  - x)y (x) + 2x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 62

--S 63 of 120
--Rsolve(ode324,y,x)
--R 
--R
--R   (63)  "failed"
--R                                                    Type: Union("failed",...)
--E 63

--S 64 of 120
--Rode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x
--R 
--R
--R              4     3      ,             3    4
--R   (64)  (y(x)  - 2x y(x))y (x) + 2x y(x)  - x
--R
--R                                                     Type: Expression Integer
--E 64

--S 65 of 120
--Rsolve(ode325,y,x)
--R 
--R
--R   (65)  "failed"
--R                                                    Type: Union("failed",...)
--E 65

--S 66 of 120
--Rode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3)
--R 
--R
--R   (66)
--R       3    4     2        3       2 2    2     3      3      ,
--R     (a y(x)  + 3a b x y(x)  + 3a b x y(x)  + (b  + b)x y(x))y (x)
--R
--R   + 
--R       3           3     2   2    2       2 3        3 4
--R     (a  + a)x y(x)  + 3a b x y(x)  + 3a b x y(x) + b x
--R                                                     Type: Expression Integer
--E 66

--S 67 of 120
--Rsolve(ode326,y,x)
--R 
--R
--R   (67)  "failed"
--R                                                    Type: Union("failed",...)
--E 67

--S 68 of 120
--Rode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x)
--R 
--R
--R                4     2    3              ,          5
--R   (68)  (x y(x)  + 2x y(x)  + 2y(x) + x)y (x) + y(x)  + y(x)
--R
--R                                                     Type: Expression Integer
--E 68

--S 69 of 120
--Rsolve(ode327,y,x)
--R 
--R
--R   (69)  "failed"
--R                                                    Type: Union("failed",...)
--E 69

--S 70 of 120
--Rode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x)
--R 
--R
--R             2    n       ,
--R   (70)  (a x y(x)  - 2x)y (x) + y(x)
--R
--R                                                     Type: Expression Integer
--E 70

--S 71 of 120
--Rsolve(ode328,y,x)
--R 
--R
--R   (71)  "failed"
--R                                                    Type: Union("failed",...)
--E 71

--S 72 of 120
--Rode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x)
--R 
--R
--R               n    m            ,             n    m
--R   (72)  (a x x y(x)  + alpha x)y (x) + b y(x)x y(x)  + beta y(x)
--R
--R                                                     Type: Expression Integer
--E 72

--S 73 of 120
--Rsolve(ode329,y,x)
--R 
--R
--R   (73)  "failed"
--R                                                    Type: Union("failed",...)
--E 73

--S 74 of 120
--Rode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x))
--R 
--R
--R                           ,
--R   (74)  (f(y(x) + x) + 1)y (x) + f(y(x) + x)
--R
--R                                                     Type: Expression Integer
--E 74

--S 75 of 120
--Rsolve(ode330,y,x)
--R 
--R 
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 75

--R
--S 76 of 120
--Rode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_
--R            x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x)
--R 
--R
--R   (75)
--R      2     +-+ +----+    2          ,            2 +-+ +----+         2
--R   (2x y(x)\|x \|y(x)  + x y(x) - x)y (x) - x y(x) \|x \|y(x)  + x y(x)  - y(x)
--R
--R                                                     Type: Expression Integer
--E 76

--S 77 of 120
--Rsolve(ode333,y,x)
--R 
--R
--R   (76)  "failed"
--R                                                    Type: Union("failed",...)
--E 77

--S 78 of 120
--Rode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1
--R 
--R
--R           +--------+      ,
--R   (77)  (\|y(x) + x  + 1)y (x) + 1
--R
--R                                                     Type: Expression Integer
--E 78

--S 79 of 120
--Rsolve(ode334,y,x)
--R 
--R
--R   (78)  "failed"
--R                                                    Type: Union("failed",...)
--E 79

--S 80 of 120
--Rode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1)
--R 
--R
--R          +---------+         +------+
--R          |    2      ,       | 2
--R   (79)  \|y(x)  - 1 y (x) - \|x  - 1
--R
--R                                                     Type: Expression Integer
--E 80

--S 81 of 120
--Ryx:=solve(ode335,y,x)
--R 
--R
--R   (80)
--R                    +------+                    +---------+
--R                    | 2             2           |    2
--R           (4x y(x)\|x  - 1  + (- 4x  + 2)y(x))\|y(x)  - 1
--R         + 
--R                             +------+
--R                     2       | 2           2         2     2
--R           (- 4x y(x)  + 2x)\|x  - 1  + (4x  - 2)y(x)  - 2x  + 1
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  - 1  - y(x))
--R     + 
--R                      +------+                      +------+
--R                      | 2           2               | 2
--R           (- 4x y(x)\|x  - 1  + (4x  - 2)y(x))log(\|x  - 1  - x)
--R         + 
--R                                  +------+
--R                     3     3      | 2           2         3
--R           (- 4x y(x)  + 4x y(x))\|x  - 1  + (4x  - 2)y(x)
--R         + 
--R                4     2
--R           (- 4x  + 2x  + 1)y(x)
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                        +------+                                   +------+
--R                2       | 2             2         2     2          | 2
--R       ((4x y(x)  - 2x)\|x  - 1  + (- 4x  + 2)y(x)  + 2x  - 1)log(\|x  - 1  - x)
--R     + 
--R                                                +------+
--R               4        3          2     3      | 2             2         4
--R       (4x y(x)  + (- 4x  - 2x)y(x)  + 2x  - x)\|x  - 1  + (- 4x  + 2)y(x)
--R     + 
--R          4         2     4     2
--R       (4x  - 2)y(x)  - 2x  + 2x
--R  /
--R                +------+                    +---------+
--R                | 2             2           |    2
--R       (8x y(x)\|x  - 1  + (- 8x  + 4)y(x))\|y(x)  - 1
--R     + 
--R                         +------+
--R                 2       | 2           2         2     2
--R       (- 8x y(x)  + 4x)\|x  - 1  + (8x  - 4)y(x)  - 4x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 81

--S 82 of 120
--Rode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1)
--R 
--R
--R   (81)
--R                             4      2         5       4      2          3
--R                       (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R                     + 
--R                             4      2
--R                       (- 32x  + 32x  - 4)y(x)
--R                  *
--R                      +------+
--R                      | 2
--R                     \|x  - 1
--R                 + 
--R                       5      3           5         5       3           3
--R                   (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R                 + 
--R                       5      3
--R                   (32x  - 48x  + 16x)y(x)
--R              *
--R                  +---------+
--R                  |    2
--R                 \|y(x)  - 1
--R             + 
--R                       4      2         6          4       2          4
--R                   (64x  - 64x  + 8)y(x)  + (- 128x  + 128x  - 16)y(x)
--R                 + 
--R                       4      2         2     4     2
--R                   (72x  - 72x  + 9)y(x)  - 8x  + 8x  - 1
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     5      3           6        5       3           4
--R               (- 64x  + 96x  - 32x)y(x)  + (128x  - 192x  + 64x)y(x)
--R             + 
--R                     5       3           2     5      3
--R               (- 72x  + 108x  - 36x)y(x)  + 8x  - 12x  + 4x
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                       5      3           4         5      3           2     5
--R                   (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R                 + 
--R                        3
--R                   - 12x  + 4x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  - 1
--R             + 
--R                     6       4      2         4       6       4      2         2
--R               (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R             + 
--R                   6      4     2
--R               - 8x  + 16x  - 9x  + 1
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  - 1
--R         + 
--R                     5      3           5       5       3           3
--R               (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R             + 
--R                     5      3
--R               (- 32x  + 48x  - 16x)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R               6       4      2         5         6       4       2          3
--R           (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R         + 
--R               6      4      2
--R           (32x  - 64x  + 36x  - 4)y(x)
--R      *
--R         ROOT
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +---------+        2
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                      +------+
--R                                    3           3       3             | 2
--R                            ((- 128x  + 64x)y(x)  + (64x  - 32x)y(x))\|x  - 1
--R                          + 
--R                                 4       2          3         4      2
--R                            (128x  - 128x  + 16)y(x)  + (- 64x  + 64x  - 8)y(x)
--R                       *
--R                               +------+
--R                               | 2
--R                          log(\|x  - 1  - x)
--R                      + 
--R                                   3           5        5           3
--R                            (- 128x  + 64x)y(x)  + (128x  - 48x)y(x)
--R                          + 
--R                                  5      3
--R                            (- 64x  + 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                             4       2          5
--R                        (128x  - 128x  + 16)y(x)
--R                      + 
--R                               6      4      2          3
--R                        (- 128x  + 64x  + 64x  - 16)y(x)
--R                      + 
--R                            6      4      2
--R                        (64x  - 80x  + 16x  + 2)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  - 1
--R                  + 
--R                                   3           4          3           2      3
--R                              (128x  - 64x)y(x)  + (- 128x  + 64x)y(x)  + 16x
--R                            + 
--R                              - 8x
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          4        4       2          2
--R                        (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 16)y(x)
--R                      + 
--R                             4      2
--R                        - 16x  + 16x  - 2
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                             3           6          5      3           4
--R                        (128x  - 64x)y(x)  + (- 128x  - 64x  + 80x)y(x)
--R                      + 
--R                             5      3           2      5      3
--R                        (128x  - 64x  - 16x)y(x)  - 16x  + 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                           4       2          6        6       2          4
--R                    (- 128x  + 128x  - 16)y(x)  + (128x  - 128x  + 24)y(x)
--R                  + 
--R                           6       4         2      6      4     2
--R                    (- 128x  + 128x  - 8)y(x)  + 16x  - 24x  + 8x
--R               *
--R                       +---------+
--R                       |    2
--R                  log(\|y(x)  - 1  - y(x))
--R              + 
--R                                                                 +------+
--R                             3           3         3             | 2
--R                        ((64x  - 32x)y(x)  + (- 32x  + 16x)y(x))\|x  - 1
--R                      + 
--R                              4      2         3       4      2
--R                        (- 64x  + 64x  - 8)y(x)  + (32x  - 32x  + 4)y(x)
--R                   *
--R                           +------+     2
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                                 3           5          5           3
--R                            (128x  - 64x)y(x)  + (- 128x  + 48x)y(x)
--R                          + 
--R                                5      3
--R                            (64x  - 48x )y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  - 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  + 128x  - 16)y(x)
--R                      + 
--R                             6      4      2          3
--R                        (128x  - 64x  - 64x  + 16)y(x)
--R                      + 
--R                              6      4      2
--R                        (- 64x  + 80x  - 16x  - 2)y(x)
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  - 1  - x)
--R                  + 
--R                            3           7          5      3           5
--R                        (64x  - 32x)y(x)  + (- 128x  + 32x  + 32x)y(x)
--R                      + 
--R                            7      5       3            3
--R                        (64x  + 32x  - 320x  + 128x)y(x)
--R                      + 
--R                              7      5       3
--R                        (- 32x  + 32x  + 128x  - 66x)y(x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                          4      2         7        6      4      2          5
--R                    (- 64x  + 64x  - 8)y(x)  + (128x  - 96x  - 32x  + 12)y(x)
--R                  + 
--R                          8       4       2          3
--R                    (- 64x  + 344x  - 280x  + 28)y(x)
--R                  + 
--R                        8      6       4       2
--R                    (32x  - 48x  - 116x  + 132x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                             3           4       3           2     3
--R                      ((- 64x  + 32x)y(x)  + (64x  - 32x)y(x)  - 8x  + 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                        4      2         4         4      2         2     4
--R                    (64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x
--R                  + 
--R                        2
--R                    - 8x  + 1
--R               *
--R                       +------+     2
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                               3           6        5      3           4
--R                        (- 128x  + 64x)y(x)  + (128x  + 64x  - 80x)y(x)
--R                      + 
--R                               5      3           2      5      3
--R                        (- 128x  + 64x  + 16x)y(x)  + 16x  - 16x  + 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  - 1
--R                  + 
--R                         4       2          6          6       2          4
--R                    (128x  - 128x  + 16)y(x)  + (- 128x  + 128x  - 24)y(x)
--R                  + 
--R                         6       4         2      6      4     2
--R                    (128x  - 128x  + 8)y(x)  - 16x  + 24x  - 8x
--R               *
--R                       +------+
--R                       | 2
--R                  log(\|x  - 1  - x)
--R              + 
--R                          3           8        5           6
--R                    (- 64x  + 32x)y(x)  + (128x  - 48x)y(x)
--R                  + 
--R                          7      5       3            4
--R                    (- 64x  - 96x  + 344x  - 116x)y(x)
--R                  + 
--R                        7      5       3            2     7      5      3
--R                    (64x  - 32x  - 280x  + 132x)y(x)  - 8x  + 12x  + 28x  - 16x
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                    4      2         8          6      4      2          6
--R                (64x  - 64x  + 8)y(x)  + (- 128x  + 64x  + 64x  - 16)y(x)
--R              + 
--R                    8      6       4       2          4
--R                (64x  + 64x  - 400x  + 272x  - 23)y(x)
--R              + 
--R                      8      6       4       2          2     8      6      4
--R                (- 64x  + 64x  + 272x  - 272x  + 31)y(x)  + 8x  - 16x  - 23x
--R              + 
--R                   2
--R                31x  - 4
--R           /
--R                                                                +------+
--R                          3            3          3             | 2
--R                    ((256x  - 128x)y(x)  + (- 128x  + 64x)y(x))\|x  - 1
--R                  + 
--R                           4       2          3        4       2
--R                    (- 256x  + 256x  - 32)y(x)  + (128x  - 128x  + 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  - 1
--R              + 
--R                          3            4        3            2      3
--R                  ((- 256x  + 128x)y(x)  + (256x  - 128x)y(x)  - 32x  + 16x)
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  - 1
--R              + 
--R                     4       2          4          4       2          2      4
--R                (256x  - 256x  + 32)y(x)  + (- 256x  + 256x  - 32)y(x)  + 32x
--R              + 
--R                     2
--R                - 32x  + 4
--R     + 
--R                   5      3           4         5      3           2     5
--R               (64x  - 96x  + 32x)y(x)  + (- 64x  + 96x  - 32x)y(x)  + 8x
--R             + 
--R                    3
--R               - 12x  + 4x
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R                 6       4      2         4       6       4      2         2
--R           (- 64x  + 128x  - 72x  + 8)y(x)  + (64x  - 128x  + 72x  - 8)y(x)
--R         + 
--R               6      4     2
--R           - 8x  + 16x  - 9x  + 1
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                 5      3           5       5       3           3
--R           (- 64x  + 96x  - 32x)y(x)  + (96x  - 144x  + 48x)y(x)
--R         + 
--R                 5      3
--R           (- 32x  + 48x  - 16x)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  - 1
--R     + 
--R           6       4      2         5         6       4       2          3
--R       (64x  - 128x  + 72x  - 8)y(x)  + (- 96x  + 192x  - 108x  + 12)y(x)
--R     + 
--R           6      4      2
--R       (32x  - 64x  + 36x  - 4)y(x)
--R  /
--R                  4      2         4         4      2         2     4     2
--R             ((64x  - 64x  + 8)y(x)  + (- 64x  + 64x  - 8)y(x)  + 8x  - 8x  + 1)
--R          *
--R              +------+
--R              | 2
--R             \|x  - 1
--R         + 
--R               5      3           4       5      3           2     5      3
--R         (- 64x  + 96x  - 32x)y(x)  + (64x  - 96x  + 32x)y(x)  - 8x  + 12x  - 4x
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  - 1
--R     + 
--R                 4      2         5       4      2          3
--R           (- 64x  + 64x  - 8)y(x)  + (96x  - 96x  + 12)y(x)
--R         + 
--R                 4      2
--R           (- 32x  + 32x  - 4)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  - 1
--R     + 
--R           5      3           5         5       3           3
--R       (64x  - 96x  + 32x)y(x)  + (- 96x  + 144x  - 48x)y(x)
--R     + 
--R           5      3
--R       (32x  - 48x  + 16x)y(x)
--R                                                     Type: Expression Integer
--E 82

--S 83 of 120
--Rode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x)
--R 
--R
--R           +---------+                +------+
--R           |    2             ,       | 2
--R   (82)  (\|y(x)  + 1  + a x)y (x) + \|x  + 1  + a y(x)
--R
--R                                                     Type: Expression Integer
--E 83

--S 84 of 120
--Ryx:=solve(ode336,y,x)
--R 
--R
--R   (83)
--R                      +------+                  +---------+
--R                      | 2           2           |    2
--R           (- 4x y(x)\|x  + 1  + (4x  + 2)y(x))\|y(x)  + 1
--R         + 
--R                           +------+
--R                   2       | 2             2         2     2
--R           (4x y(x)  + 2x)\|x  + 1  + (- 4x  - 2)y(x)  - 2x  - 1
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  + 1  - y(x))
--R     + 
--R                      +------+                      +------+
--R                      | 2           2               | 2
--R           (- 4x y(x)\|x  + 1  + (4x  + 2)y(x))log(\|x  + 1  - x)
--R         + 
--R                                                        +------+
--R                     3       2    2        3            | 2
--R           (- 4x y(x)  + 8a x y(x)  + (- 4x  - 4x)y(x))\|x  + 1
--R         + 
--R              2         3          3            2      4     2
--R           (4x  + 2)y(x)  + (- 8a x  - 4a x)y(x)  + (4x  + 6x  + 1)y(x)
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  + 1
--R     + 
--R                        +------+                                   +------+
--R                2       | 2             2         2     2          | 2
--R       ((4x y(x)  + 2x)\|x  + 1  + (- 4x  - 2)y(x)  - 2x  - 1)log(\|x  + 1  - x)
--R     + 
--R                                                                       +------+
--R               4       2    3      3          2       2         3      | 2
--R       (4x y(x)  - 8a x y(x)  + (4x  + 6x)y(x)  - 4a x y(x) + 2x  + x)\|x  + 1
--R     + 
--R            2         4        3            3        4     2         2
--R       (- 4x  - 2)y(x)  + (8a x  + 4a x)y(x)  + (- 4x  - 8x  - 2)y(x)
--R     + 
--R            3                 4     2
--R       (4a x  + 2a x)y(x) - 2x  - 2x
--R  /
--R                +------+                    +---------+
--R                | 2             2           |    2
--R       (8x y(x)\|x  + 1  + (- 8x  - 4)y(x))\|y(x)  + 1
--R     + 
--R                         +------+
--R                 2       | 2           2         2     2
--R       (- 8x y(x)  - 4x)\|x  + 1  + (8x  + 4)y(x)  + 4x  + 2
--R                                          Type: Union(Expression Integer,...)
--E 84

--S 85 of 120
--Rode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx
--R 
--R
--R   (84)
--R                               6        4        2          7
--R                       (- 2048x  - 3072x  - 1152x  - 64)y(x)
--R                     + 
--R                               7          5          3             6
--R                       (2048a x  + 3072a x  + 1152a x  + 64a x)y(x)
--R                     + 
--R                               6        4        2           5
--R                       (- 4096x  - 6144x  - 2304x  - 128)y(x)
--R                     + 
--R                               7          5          3             4
--R                       (3072a x  + 4608a x  + 1728a x  + 96a x)y(x)
--R                     + 
--R                               6        4        2          3
--R                       (- 2432x  - 3648x  - 1368x  - 76)y(x)
--R                     + 
--R                               7          5         3             2
--R                       (1152a x  + 1728a x  + 648a x  + 36a x)y(x)
--R                     + 
--R                              6       4       2                  7        5
--R                       (- 384x  - 576x  - 216x  - 12)y(x) + 64a x  + 96a x
--R                     + 
--R                            3
--R                       36a x  + 2a x
--R                  *
--R                      +------+
--R                      | 2
--R                     \|x  + 1
--R                 + 
--R                         7        5        3            7
--R                   (2048x  + 4096x  + 2432x  + 384x)y(x)
--R                 + 
--R                             8          6          4         2     6
--R                   (- 2048a x  - 4096a x  - 2432a x  - 384a x )y(x)
--R                 + 
--R                         7        5        3            5
--R                   (4096x  + 8192x  + 4864x  + 768x)y(x)
--R                 + 
--R                             8          6          4         2     4
--R                   (- 3072a x  - 6144a x  - 3648a x  - 576a x )y(x)
--R                 + 
--R                         7        5        3            3
--R                   (2432x  + 4864x  + 2888x  + 456x)y(x)
--R                 + 
--R                             8          6          4         2     2
--R                   (- 1152a x  - 2304a x  - 1368a x  - 216a x )y(x)
--R                 + 
--R                        7       5       3                   8         6        4
--R                   (384x  + 768x  + 456x  + 72x)y(x) - 64a x  - 128a x  - 76a x
--R                 + 
--R                          2
--R                   - 12a x
--R              *
--R                  +---------+
--R                  |    2
--R                 \|y(x)  + 1
--R             + 
--R                         6        4        2          8
--R                   (2048x  + 3072x  + 1152x  + 64)y(x)
--R                 + 
--R                             7          5          3             7
--R                   (- 2048a x  - 3072a x  - 1152a x  - 64a x)y(x)
--R                 + 
--R                         6        4        2           6
--R                   (5120x  + 7680x  + 2880x  + 160)y(x)
--R                 + 
--R                             7          5          3              5
--R                   (- 4096a x  - 6144a x  - 2304a x  - 128a x)y(x)
--R                 + 
--R                         6        4        2           4
--R                   (4224x  + 6336x  + 2376x  + 132)y(x)
--R                 + 
--R                             7          5          3             3
--R                   (- 2432a x  - 3648a x  - 1368a x  - 76a x)y(x)
--R                 + 
--R                         6        4       2          2
--R                   (1216x  + 1824x  + 684x  + 38)y(x)
--R                 + 
--R                            7         5         3                   6      4
--R                   (- 384a x  - 576a x  - 216a x  - 12a x)y(x) + 64x  + 96x
--R                 + 
--R                      2
--R                   36x  + 2
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       7        5        3            8
--R               (- 2048x  - 4096x  - 2432x  - 384x)y(x)
--R             + 
--R                       8          6          4         2     7
--R               (2048a x  + 4096a x  + 2432a x  + 384a x )y(x)
--R             + 
--R                       7         5        3            6
--R               (- 5120x  - 10240x  - 6080x  - 960x)y(x)
--R             + 
--R                       8          6          4         2     5
--R               (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R             + 
--R                       7        5        3            4
--R               (- 4224x  - 8448x  - 5016x  - 792x)y(x)
--R             + 
--R                       8          6          4         2     3
--R               (2432a x  + 4864a x  + 2888a x  + 456a x )y(x)
--R             + 
--R                       7        5        3            2
--R               (- 1216x  - 2432x  - 1444x  - 228x)y(x)
--R             + 
--R                      8         6         4        2           7       5      3
--R               (384a x  + 768a x  + 456a x  + 72a x )y(x) - 64x  - 128x  - 76x
--R             + 
--R               - 12x
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R                           6          4          2           7
--R                   (2048a x  + 3072a x  + 1152a x  + 64a)y(x)
--R                 + 
--R                           7        5        3            6
--R                   (- 2048x  - 4096x  - 2432x  - 384x)y(x)
--R                 + 
--R                           6          4          2           5
--R                   (3072a x  + 4608a x  + 1728a x  + 96a)y(x)
--R                 + 
--R                           7        5        3            4
--R                   (- 3072x  - 6144x  - 3648x  - 576x)y(x)
--R                 + 
--R                           6          4         2           3
--R                   (1152a x  + 1728a x  + 648a x  + 36a)y(x)
--R                 + 
--R                           7        5        3            2
--R                   (- 1152x  - 2304x  - 1368x  - 216x)y(x)
--R                 + 
--R                       6        4        2                7       5      3
--R                 (64a x  + 96a x  + 36a x  + 2a)y(x) - 64x  - 128x  - 76x  - 12x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                         7          5          3              7
--R               (- 2048a x  - 4096a x  - 2432a x  - 384a x)y(x)
--R             + 
--R                     8        6        4        2          6
--R               (2048x  + 5120x  + 4224x  + 1216x  + 64)y(x)
--R             + 
--R                         7          5          3              5
--R               (- 3072a x  - 6144a x  - 3648a x  - 576a x)y(x)
--R             + 
--R                     8        6        4        2          4
--R               (3072x  + 7680x  + 6336x  + 1824x  + 96)y(x)
--R             + 
--R                         7          5          3              3
--R               (- 1152a x  - 2304a x  - 1368a x  - 216a x)y(x)
--R             + 
--R                     8        6        4       2          2
--R               (1152x  + 2880x  + 2376x  + 684x  + 36)y(x)
--R             + 
--R                       7         5        3                   8       6       4
--R               (- 64a x  - 128a x  - 76a x  - 12a x)y(x) + 64x  + 160x  + 132x
--R             + 
--R                  2
--R               38x  + 2
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  + 1
--R         + 
--R                         6          4          2           8
--R               (- 2048a x  - 3072a x  - 1152a x  - 64a)y(x)
--R             + 
--R                     7        5        3            7
--R               (2048x  + 4096x  + 2432x  + 384x)y(x)
--R             + 
--R                         6          4          2            6
--R               (- 4096a x  - 6144a x  - 2304a x  - 128a)y(x)
--R             + 
--R                     7        5        3            5
--R               (4096x  + 8192x  + 4864x  + 768x)y(x)
--R             + 
--R                         6          4          2           4
--R               (- 2432a x  - 3648a x  - 1368a x  - 76a)y(x)
--R             + 
--R                     7        5        3            3
--R               (2432x  + 4864x  + 2888x  + 456x)y(x)
--R             + 
--R                        6         4         2           2
--R               (- 384a x  - 576a x  - 216a x  - 12a)y(x)
--R             + 
--R                    7       5       3
--R               (384x  + 768x  + 456x  + 72x)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                   7          5          3              8
--R           (2048a x  + 4096a x  + 2432a x  + 384a x)y(x)
--R         + 
--R                   8        6        4        2          7
--R           (- 2048x  - 5120x  - 4224x  - 1216x  - 64)y(x)
--R         + 
--R                   7          5          3              6
--R           (4096a x  + 8192a x  + 4864a x  + 768a x)y(x)
--R         + 
--R                   8         6        4        2           5
--R           (- 4096x  - 10240x  - 8448x  - 2432x  - 128)y(x)
--R         + 
--R                   7          5          3              4
--R           (2432a x  + 4864a x  + 2888a x  + 456a x)y(x)
--R         + 
--R                   8        6        4        2          3
--R           (- 2432x  - 6080x  - 5016x  - 1444x  - 76)y(x)
--R         + 
--R                  7         5         3             2
--R           (384a x  + 768a x  + 456a x  + 72a x)y(x)
--R         + 
--R                  8       6       4       2
--R           (- 384x  - 960x  - 792x  - 228x  - 12)y(x)
--R      *
--R         ROOT
--R                                                               +------+
--R                             3           3       3             | 2
--R                        ((64x  + 32x)y(x)  + (32x  + 16x)y(x))\|x  + 1
--R                      + 
--R                              4      2         3         4      2
--R                        (- 64x  - 64x  - 8)y(x)  + (- 32x  - 32x  - 4)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  + 1
--R                  + 
--R                             3           4         3           2     3
--R                      ((- 64x  - 32x)y(x)  + (- 64x  - 32x)y(x)  - 8x  - 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                        4      2         4       4      2         2     4     2
--R                    (64x  + 64x  + 8)y(x)  + (64x  + 64x  + 8)y(x)  + 8x  + 8x
--R                  + 
--R                    1
--R               *
--R                       +---------+        2
--R                       |    2
--R                  log(\|y(x)  + 1  - y(x))
--R              + 
--R                                                                    +------+
--R                                  3           3       3             | 2
--R                            ((128x  + 64x)y(x)  + (64x  + 32x)y(x))\|x  + 1
--R                          + 
--R                                 4       2          3         4      2
--R                          (- 128x  - 128x  - 16)y(x)  + (- 64x  - 64x  - 8)y(x)
--R                       *
--R                               +------+
--R                               | 2
--R                          log(\|x  + 1  - x)
--R                      + 
--R                                 3           5            4         2     4
--R                            (128x  + 64x)y(x)  + (- 256a x  - 128a x )y(x)
--R                          + 
--R                                 5       3           3
--R                            (128x  + 256x  + 80x)y(x)
--R                          + 
--R                                     4        2     2       5      3
--R                            (- 128a x  - 64a x )y(x)  + (64x  + 80x  + 16x)y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  + 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  - 128x  - 16)y(x)
--R                      + 
--R                               5         3             4
--R                        (256a x  + 256a x  + 32a x)y(x)
--R                      + 
--R                               6       4       2          3
--R                        (- 128x  - 320x  - 192x  - 16)y(x)
--R                      + 
--R                               5         3             2
--R                        (128a x  + 128a x  + 16a x)y(x)
--R                      + 
--R                              6       4      2
--R                        (- 64x  - 112x  - 48x  - 2)y(x)
--R                   *
--R                       +---------+
--R                       |    2
--R                      \|y(x)  + 1
--R                  + 
--R                                   3           4          3           2      3
--R                            (- 128x  - 64x)y(x)  + (- 128x  - 64x)y(x)  - 16x
--R                          + 
--R                            - 8x
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  + 1
--R                      + 
--R                             4       2          4        4       2          2
--R                        (128x  + 128x  + 16)y(x)  + (128x  + 128x  + 16)y(x)
--R                      + 
--R                           4      2
--R                        16x  + 16x  + 2
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  + 1  - x)
--R                  + 
--R                               3           6          4         2     5
--R                        (- 128x  - 64x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3            4          4         2     3
--R                        (- 128x  - 320x  - 112x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3           2         4        2
--R                        (- 128x  - 192x  - 48x)y(x)  + (32a x  + 16a x )y(x)
--R                      + 
--R                             5      3
--R                        - 16x  - 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                         4       2          6
--R                    (128x  + 128x  + 16)y(x)
--R                  + 
--R                             5         3             5
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2          4
--R                    (128x  + 384x  + 256x  + 24)y(x)
--R                  + 
--R                             5         3             3
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2         2
--R                    (128x  + 256x  + 128x  + 8)y(x)
--R                  + 
--R                            5        3                  6      4     2
--R                    (- 32a x  - 32a x  - 4a x)y(x) + 16x  + 24x  + 8x
--R               *
--R                       +---------+
--R                       |    2
--R                  log(\|y(x)  + 1  - y(x))
--R              + 
--R                                                               +------+
--R                             3           3       3             | 2
--R                        ((64x  + 32x)y(x)  + (32x  + 16x)y(x))\|x  + 1
--R                      + 
--R                              4      2         3         4      2
--R                        (- 64x  - 64x  - 8)y(x)  + (- 32x  - 32x  - 4)y(x)
--R                   *
--R                           +------+     2
--R                           | 2
--R                      log(\|x  + 1  - x)
--R                  + 
--R                                 3           5            4         2     4
--R                            (128x  + 64x)y(x)  + (- 256a x  - 128a x )y(x)
--R                          + 
--R                                 5       3           3
--R                            (128x  + 256x  + 80x)y(x)
--R                          + 
--R                                     4        2     2       5      3
--R                            (- 128a x  - 64a x )y(x)  + (64x  + 80x  + 16x)y(x)
--R                       *
--R                           +------+
--R                           | 2
--R                          \|x  + 1
--R                      + 
--R                               4       2          5
--R                        (- 128x  - 128x  - 16)y(x)
--R                      + 
--R                               5         3             4
--R                        (256a x  + 256a x  + 32a x)y(x)
--R                      + 
--R                               6       4       2          3
--R                        (- 128x  - 320x  - 192x  - 16)y(x)
--R                      + 
--R                               5         3             2
--R                        (128a x  + 128a x  + 16a x)y(x)
--R                      + 
--R                              6       4      2
--R                        (- 64x  - 112x  - 48x  - 2)y(x)
--R                   *
--R                           +------+
--R                           | 2
--R                      log(\|x  + 1  - x)
--R                  + 
--R                            3           7            4         2     6
--R                        (64x  + 32x)y(x)  + (- 256a x  - 128a x )y(x)
--R                      + 
--R                              2        5        2        3           5
--R                        ((256a  + 128)x  + (128a  + 224)x  + 64x)y(x)
--R                      + 
--R                                 6         4         2     4
--R                        (- 256a x  - 512a x  - 160a x )y(x)
--R                      + 
--R                            7        2        5       2        3            3
--R                        (64x  + (128a  + 224)x  + (64a  + 448)x  + 160x)y(x)
--R                      + 
--R                                 6         4        2     2
--R                        (- 128a x  - 160a x  - 32a x )y(x)
--R                      + 
--R                            7      5       3
--R                        (32x  + 64x  + 160x  + 66x)y(x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                          4      2         7          5         3             6
--R                    (- 64x  - 64x  - 8)y(x)  + (256a x  + 256a x  + 32a x)y(x)
--R                  + 
--R                               2        6          2        4         2        2
--R                        (- 256a  - 128)x  + (- 256a  - 288)x  + (- 32a  - 160)x
--R                      + 
--R                        - 12
--R                   *
--R                          5
--R                      y(x)
--R                  + 
--R                           7         5         3             4
--R                    (256a x  + 640a x  + 384a x  + 32a x)y(x)
--R                  + 
--R                             8          2        6          2        4
--R                        - 64x  + (- 128a  - 256)x  + (- 128a  - 552)x
--R                      + 
--R                              2        2
--R                        (- 16a  - 360)x  - 36
--R                   *
--R                          3
--R                      y(x)
--R                  + 
--R                           7         5        3            2
--R                    (128a x  + 224a x  + 96a x  + 4a x)y(x)
--R                  + 
--R                          8      6       4       2
--R                    (- 32x  - 80x  - 188x  - 140x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  + 1
--R              + 
--R                             3           4         3           2     3
--R                      ((- 64x  - 32x)y(x)  + (- 64x  - 32x)y(x)  - 8x  - 4x)
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                        4      2         4       4      2         2     4     2
--R                    (64x  + 64x  + 8)y(x)  + (64x  + 64x  + 8)y(x)  + 8x  + 8x
--R                  + 
--R                    1
--R               *
--R                       +------+     2
--R                       | 2
--R                  log(\|x  + 1  - x)
--R              + 
--R                               3           6          4         2     5
--R                        (- 128x  - 64x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3            4          4         2     3
--R                        (- 128x  - 320x  - 112x)y(x)  + (256a x  + 128a x )y(x)
--R                      + 
--R                               5       3           2         4        2
--R                        (- 128x  - 192x  - 48x)y(x)  + (32a x  + 16a x )y(x)
--R                      + 
--R                             5      3
--R                        - 16x  - 16x  - 2x
--R                   *
--R                       +------+
--R                       | 2
--R                      \|x  + 1
--R                  + 
--R                         4       2          6
--R                    (128x  + 128x  + 16)y(x)
--R                  + 
--R                             5         3             5
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2          4
--R                    (128x  + 384x  + 256x  + 24)y(x)
--R                  + 
--R                             5         3             3
--R                    (- 256a x  - 256a x  - 32a x)y(x)
--R                  + 
--R                         6       4       2         2
--R                    (128x  + 256x  + 128x  + 8)y(x)
--R                  + 
--R                            5        3                  6      4     2
--R                    (- 32a x  - 32a x  - 4a x)y(x) + 16x  + 24x  + 8x
--R               *
--R                       +------+
--R                       | 2
--R                  log(\|x  + 1  - x)
--R              + 
--R                          3           8          4         2     7
--R                    (- 64x  - 32x)y(x)  + (256a x  + 128a x )y(x)
--R                  + 
--R                            2        5          2        3           6
--R                    ((- 256a  - 128)x  + (- 128a  - 256)x  - 80x)y(x)
--R                  + 
--R                           6         4         2     5
--R                    (256a x  + 640a x  + 224a x )y(x)
--R                  + 
--R                          7          2        5          2        3            4
--R                    (- 64x  + (- 256a  - 288)x  + (- 128a  - 552)x  - 188x)y(x)
--R                  + 
--R                           6         4        2     3
--R                    (256a x  + 384a x  + 96a x )y(x)
--R                  + 
--R                          7         2        5         2        3            2
--R                    (- 64x  + (- 32a  - 160)x  + (- 16a  - 360)x  - 140x)y(x)
--R                  + 
--R                          6        4       2          7      5      3
--R                    (32a x  + 32a x  + 4a x )y(x) - 8x  - 12x  - 36x  - 16x
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  + 1
--R              + 
--R                    4      2         8            5         3             7
--R                (64x  + 64x  + 8)y(x)  + (- 256a x  - 256a x  - 32a x)y(x)
--R              + 
--R                      2        6        2        4       2        2          6
--R                ((256a  + 128)x  + (256a  + 320)x  + (32a  + 192)x  + 16)y(x)
--R              + 
--R                         7         5         3             5
--R                (- 256a x  - 768a x  - 512a x  - 48a x)y(x)
--R              + 
--R                         8        2        6        2        4       2        2
--R                      64x  + (256a  + 320)x  + (256a  + 688)x  + (32a  + 432)x
--R                    + 
--R                      41
--R               *
--R                      4
--R                  y(x)
--R              + 
--R                         7         5         3             3
--R                (- 256a x  - 512a x  - 256a x  - 16a x)y(x)
--R              + 
--R                      8       2        6       2        4      2        2
--R                  (64x  + (32a  + 192)x  + (32a  + 432)x  + (4a  + 304)x  + 33)
--R               *
--R                      2
--R                  y(x)
--R              + 
--R                        7        5        3          8      6      4      2
--R                (- 32a x  - 48a x  - 16a x )y(x) + 8x  + 16x  + 41x  + 33x  + 4
--R           /
--R                                                              +------+
--R                          3            3        3             | 2
--R                    ((256x  + 128x)y(x)  + (128x  + 64x)y(x))\|x  + 1
--R                  + 
--R                           4       2          3          4       2
--R                    (- 256x  - 256x  - 32)y(x)  + (- 128x  - 128x  - 16)y(x)
--R               *
--R                   +---------+
--R                   |    2
--R                  \|y(x)  + 1
--R              + 
--R                          3            4          3            2      3
--R                  ((- 256x  - 128x)y(x)  + (- 256x  - 128x)y(x)  - 32x  - 16x)
--R               *
--R                   +------+
--R                   | 2
--R                  \|x  + 1
--R              + 
--R                     4       2          4        4       2          2      4
--R                (256x  + 256x  + 32)y(x)  + (256x  + 256x  + 32)y(x)  + 32x
--R              + 
--R                   2
--R                32x  + 4
--R     + 
--R                             6          4         2           6
--R                   (- 1024a x  - 1536a x  - 576a x  - 32a)y(x)
--R                 + 
--R                             6          4         2           4
--R                   (- 1536a x  - 2304a x  - 864a x  - 48a)y(x)
--R                 + 
--R                            6         4         2           2        6        4
--R                   (- 576a x  - 864a x  - 324a x  - 18a)y(x)  - 32a x  - 48a x
--R                 + 
--R                          2
--R                   - 18a x  - a
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       7          5          3              6
--R               (1024a x  + 2048a x  + 1216a x  + 192a x)y(x)
--R             + 
--R                       7          5          3              4
--R               (1536a x  + 3072a x  + 1824a x  + 288a x)y(x)
--R             + 
--R                      7          5         3              2        7        5
--R               (576a x  + 1152a x  + 684a x  + 108a x)y(x)  + 32a x  + 64a x
--R             + 
--R                    3
--R               38a x  + 6a x
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  + 1
--R         + 
--R                       6          4         2           7
--R               (1024a x  + 1536a x  + 576a x  + 32a)y(x)
--R             + 
--R                       6          4          2           5
--R               (2048a x  + 3072a x  + 1152a x  + 64a)y(x)
--R             + 
--R                       6          4         2           3
--R               (1216a x  + 1824a x  + 684a x  + 38a)y(x)
--R             + 
--R                      6         4         2
--R               (192a x  + 288a x  + 108a x  + 6a)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                     7          5          3              7
--R           (- 1024a x  - 2048a x  - 1216a x  - 192a x)y(x)
--R         + 
--R                     7          5          3              5
--R           (- 2048a x  - 4096a x  - 2432a x  - 384a x)y(x)
--R         + 
--R                     7          5          3              3
--R           (- 1216a x  - 2432a x  - 1444a x  - 228a x)y(x)
--R         + 
--R                    7         5         3
--R           (- 192a x  - 384a x  - 228a x  - 36a x)y(x)
--R      *
--R              +---------+
--R              |    2
--R         log(\|y(x)  + 1  - y(x))
--R     + 
--R                             7          5          3             7
--R                   (- 2048a x  - 3072a x  - 1152a x  - 64a x)y(x)
--R                 + 
--R                         2 8        2 6        2 4      2 2     6
--R                   (2048a x  + 3072a x  + 1152a x  + 64a x )y(x)
--R                 + 
--R                             7          5          3              5
--R                   (- 4096a x  - 6144a x  - 2304a x  - 128a x)y(x)
--R                 + 
--R                         2 8        2 6        2 4      2 2     4
--R                   (3072a x  + 4608a x  + 1728a x  + 96a x )y(x)
--R                 + 
--R                             7          5          3             3
--R                   (- 2432a x  - 3648a x  - 1368a x  - 76a x)y(x)
--R                 + 
--R                         2 8        2 6       2 4      2 2     2
--R                   (1152a x  + 1728a x  + 648a x  + 36a x )y(x)
--R                 + 
--R                            7         5         3                   2 8      2 6
--R                   (- 384a x  - 576a x  - 216a x  - 12a x)y(x) + 64a x  + 96a x
--R                 + 
--R                      2 4     2 2
--R                   36a x  + 2a x
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       8          6          4         2     7
--R               (2048a x  + 4096a x  + 2432a x  + 384a x )y(x)
--R             + 
--R                       2 9        2 7        2 5       2 3     6
--R               (- 2048a x  - 4096a x  - 2432a x  - 384a x )y(x)
--R             + 
--R                       8          6          4         2     5
--R               (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R             + 
--R                       2 9        2 7        2 5       2 3     4
--R               (- 3072a x  - 6144a x  - 3648a x  - 576a x )y(x)
--R             + 
--R                       8          6          4         2     3
--R               (2432a x  + 4864a x  + 2888a x  + 456a x )y(x)
--R             + 
--R                       2 9        2 7        2 5       2 3     2
--R               (- 1152a x  - 2304a x  - 1368a x  - 216a x )y(x)
--R             + 
--R                      8         6         4        2           2 9       2 7
--R               (384a x  + 768a x  + 456a x  + 72a x )y(x) - 64a x  - 128a x
--R             + 
--R                    2 5      2 3
--R               - 76a x  - 12a x
--R          *
--R              +---------+
--R              |    2
--R             \|y(x)  + 1
--R         + 
--R                       7          5          3             8
--R               (2048a x  + 3072a x  + 1152a x  + 64a x)y(x)
--R             + 
--R                       2 8        2 6        2 4      2 2     7
--R               (- 2048a x  - 3072a x  - 1152a x  - 64a x )y(x)
--R             + 
--R                       7          5          3              6
--R               (5120a x  + 7680a x  + 2880a x  + 160a x)y(x)
--R             + 
--R                       2 8        2 6        2 4       2 2     5
--R               (- 4096a x  - 6144a x  - 2304a x  - 128a x )y(x)
--R             + 
--R                       7          5          3              4
--R               (4224a x  + 6336a x  + 2376a x  + 132a x)y(x)
--R             + 
--R                       2 8        2 6        2 4      2 2     3
--R               (- 2432a x  - 3648a x  - 1368a x  - 76a x )y(x)
--R             + 
--R                       7          5         3             2
--R               (1216a x  + 1824a x  + 684a x  + 38a x)y(x)
--R             + 
--R                      2 8       2 6       2 4      2 2             7        5
--R               (- 384a x  - 576a x  - 216a x  - 12a x )y(x) + 64a x  + 96a x
--R             + 
--R                    3
--R               36a x  + 2a x
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                     8          6          4         2     8
--R           (- 2048a x  - 4096a x  - 2432a x  - 384a x )y(x)
--R         + 
--R                 2 9        2 7        2 5       2 3     7
--R           (2048a x  + 4096a x  + 2432a x  + 384a x )y(x)
--R         + 
--R                     8           6          4         2     6
--R           (- 5120a x  - 10240a x  - 6080a x  - 960a x )y(x)
--R         + 
--R                 2 9        2 7        2 5       2 3     5
--R           (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R         + 
--R                     8          6          4         2     4
--R           (- 4224a x  - 8448a x  - 5016a x  - 792a x )y(x)
--R         + 
--R                 2 9        2 7        2 5       2 3     3
--R           (2432a x  + 4864a x  + 2888a x  + 456a x )y(x)
--R         + 
--R                     8          6          4         2     2
--R           (- 1216a x  - 2432a x  - 1444a x  - 228a x )y(x)
--R         + 
--R                2 9       2 7       2 5      2 3             8         6
--R           (384a x  + 768a x  + 456a x  + 72a x )y(x) - 64a x  - 128a x
--R         + 
--R                  4        2
--R           - 76a x  - 12a x
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                             6          4         2           6
--R                   (- 1024a x  - 1536a x  - 576a x  - 32a)y(x)
--R                 + 
--R                             6          4         2           4
--R                   (- 1536a x  - 2304a x  - 864a x  - 48a)y(x)
--R                 + 
--R                            6         4         2           2        6        4
--R                   (- 576a x  - 864a x  - 324a x  - 18a)y(x)  - 32a x  - 48a x
--R                 + 
--R                          2
--R                   - 18a x  - a
--R              *
--R                  +------+
--R                  | 2
--R                 \|x  + 1
--R             + 
--R                       7          5          3              6
--R               (1024a x  + 2048a x  + 1216a x  + 192a x)y(x)
--R             + 
--R                       7          5          3              4
--R               (1536a x  + 3072a x  + 1824a x  + 288a x)y(x)
--R             + 
--R                      7          5         3              2        7        5
--R               (576a x  + 1152a x  + 684a x  + 108a x)y(x)  + 32a x  + 64a x
--R             + 
--R                    3
--R               38a x  + 6a x
--R          *
--R                  +------+
--R                  | 2
--R             log(\|x  + 1  - x)
--R         + 
--R                         6          4         2           8
--R               (- 1024a x  - 1536a x  - 576a x  - 32a)y(x)
--R             + 
--R                     2 7        2 5        2 3       2      7
--R               (4096a x  + 6144a x  + 2304a x  + 128a x)y(x)
--R             + 
--R                            8        7          6        5          4        3
--R                   - 3072a x  - 2048x  - 8192a x  - 4096x  - 6720a x  - 2432x
--R                 + 
--R                            2
--R                   - 1728a x  - 384x - 64a
--R              *
--R                     6
--R                 y(x)
--R             + 
--R                     2 7        2 5        2 3       2      5
--R               (6144a x  + 9216a x  + 3456a x  + 192a x)y(x)
--R             + 
--R                            8        7           6        5          4        3
--R                   - 4608a x  - 3072x  - 10432a x  - 6144x  - 7296a x  - 3648x
--R                 + 
--R                            2
--R                   - 1548a x  - 576x - 38a
--R              *
--R                     4
--R                 y(x)
--R             + 
--R                     2 7        2 5        2 3      2      3
--R               (2304a x  + 3456a x  + 1296a x  + 72a x)y(x)
--R             + 
--R                            8        7          6        5          4        3
--R                   - 1728a x  - 1152x  - 3648a x  - 2304x  - 2340a x  - 1368x
--R                 + 
--R                           2
--R                   - 432a x  - 216x - 6a
--R              *
--R                     2
--R                 y(x)
--R             + 
--R                    2 7       2 5      2 3     2              8      7         6
--R               (128a x  + 192a x  + 72a x  + 4a x)y(x) - 96a x  - 64x  - 192a x
--R             + 
--R                     5         4      3        2
--R               - 128x  - 114a x  - 76x  - 18a x  - 12x
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                   7          5          3              8
--R           (1024a x  + 2048a x  + 1216a x  + 192a x)y(x)
--R         + 
--R                   2 8        2 6        2 4       2 2     7
--R           (- 4096a x  - 8192a x  - 4864a x  - 768a x )y(x)
--R         + 
--R                      9        8          7        6           5        4
--R               3072a x  + 2048x  + 9728a x  + 5120x  + 10432a x  + 4224x
--R             + 
--R                      3        2
--R               4256a x  + 1216x  + 480a x + 64
--R          *
--R                 6
--R             y(x)
--R         + 
--R                   2 8         2 6        2 4        2 2     5
--R           (- 6144a x  - 12288a x  - 7296a x  - 1152a x )y(x)
--R         + 
--R                      9        8           7        6           5        4
--R               4608a x  + 3072x  + 12736a x  + 7680x  + 11936a x  + 6336x
--R             + 
--R                      3        2
--R               4180a x  + 1824x  + 372a x + 96
--R          *
--R                 4
--R             y(x)
--R         + 
--R                   2 8        2 6        2 4       2 2     3
--R           (- 2304a x  - 4608a x  - 2736a x  - 432a x )y(x)
--R         + 
--R                      9        8          7        6          5        4
--R               1728a x  + 1152x  + 4512a x  + 2880x  + 3948a x  + 2376x
--R             + 
--R                      3       2
--R               1254a x  + 684x  + 90a x + 36
--R          *
--R                 2
--R             y(x)
--R         + 
--R                  2 8       2 6       2 4      2 2             9      8
--R           (- 128a x  - 256a x  - 152a x  - 24a x )y(x) + 96a x  + 64x
--R         + 
--R                 7       6         5       4        3      2
--R           240a x  + 160x  + 198a x  + 132x  + 57a x  + 38x  + 3a x + 2
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  + 1
--R     + 
--R                       6          4         2           7
--R               (1024a x  + 1536a x  + 576a x  + 32a)y(x)
--R             + 
--R                       6          4          2           5
--R               (2048a x  + 3072a x  + 1152a x  + 64a)y(x)
--R             + 
--R                       6          4         2           3
--R               (1216a x  + 1824a x  + 684a x  + 38a)y(x)
--R             + 
--R                      6         4         2
--R               (192a x  + 288a x  + 108a x  + 6a)y(x)
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                     7          5          3              7
--R           (- 1024a x  - 2048a x  - 1216a x  - 192a x)y(x)
--R         + 
--R                     7          5          3              5
--R           (- 2048a x  - 4096a x  - 2432a x  - 384a x)y(x)
--R         + 
--R                     7          5          3              3
--R           (- 1216a x  - 2432a x  - 1444a x  - 228a x)y(x)
--R         + 
--R                    7         5         3
--R           (- 192a x  - 384a x  - 228a x  - 36a x)y(x)
--R      *
--R              +------+
--R              | 2
--R         log(\|x  + 1  - x)
--R     + 
--R                   6          4         2           9
--R           (1024a x  + 1536a x  + 576a x  + 32a)y(x)
--R         + 
--R                   2 7        2 5        2 3       2      8
--R           (- 4096a x  - 6144a x  - 2304a x  - 128a x)y(x)
--R         + 
--R                      8        7          6        5          4        3
--R               3072a x  + 2048x  + 8704a x  + 4096x  + 7488a x  + 2432x
--R             + 
--R                      2
--R               2016a x  + 384x + 80a
--R          *
--R                 7
--R             y(x)
--R         + 
--R                   2 7         2 5        2 3       2      6
--R           (- 8192a x  - 12288a x  - 4608a x  - 256a x)y(x)
--R         + 
--R                      8        7           6        5           4        3
--R               6144a x  + 4096x  + 14400a x  + 8192x  + 10464a x  + 4864x
--R             + 
--R                      2
--R               2340a x  + 768x + 66a
--R          *
--R                 5
--R             y(x)
--R         + 
--R                   2 7        2 5        2 3       2      4
--R           (- 4864a x  - 7296a x  - 2736a x  - 152a x)y(x)
--R         + 
--R                      8        7          6        5          4        3
--R               3648a x  + 2432x  + 7904a x  + 4864x  + 5244a x  + 2888x
--R             + 
--R                      2
--R               1026a x  + 456x + 19a
--R          *
--R                 3
--R             y(x)
--R         + 
--R                  2 7        2 5       2 3      2      2
--R           (- 768a x  - 1152a x  - 432a x  - 24a x)y(x)
--R         + 
--R                     8       7          6       5         4       3         2
--R               576a x  + 384x  + 1184a x  + 768x  + 732a x  + 456x  + 126a x
--R             + 
--R               72x + a
--R          *
--R             y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  + 1
--R     + 
--R                 7          5          3              9
--R       (- 1024a x  - 2048a x  - 1216a x  - 192a x)y(x)
--R     + 
--R             2 8        2 6        2 4       2 2     8
--R       (4096a x  + 8192a x  + 4864a x  + 768a x )y(x)
--R     + 
--R                    9        8           7        6           5        4
--R           - 3072a x  - 2048x  - 10240a x  - 5120x  - 11456a x  - 4224x
--R         + 
--R                    3        2
--R           - 4864a x  - 1216x  - 576a x - 64
--R      *
--R             7
--R         y(x)
--R     + 
--R             2 8         2 6        2 4        2 2     6
--R       (8192a x  + 16384a x  + 9728a x  + 1536a x )y(x)
--R     + 
--R                    9        8           7         6           5        4
--R           - 6144a x  - 4096x  - 17472a x  - 10240x  - 16896a x  - 8448x
--R         + 
--R                    3        2
--R           - 6156a x  - 2432x  - 588a x - 128
--R      *
--R             5
--R         y(x)
--R     + 
--R             2 8        2 6        2 4       2 2     4
--R       (4864a x  + 9728a x  + 5776a x  + 912a x )y(x)
--R     + 
--R                    9        8          7        6          5        4
--R           - 3648a x  - 2432x  - 9728a x  - 6080x  - 8740a x  - 5016x
--R         + 
--R                    3        2
--R           - 2888a x  - 1444x  - 228a x - 76
--R      *
--R             3
--R         y(x)
--R     + 
--R            2 8        2 6       2 4       2 2     2
--R       (768a x  + 1536a x  + 912a x  + 144a x )y(x)
--R     + 
--R                   9       8          7       6          5       4         3
--R           - 576a x  - 384x  - 1472a x  - 960x  - 1252a x  - 792x  - 380a x
--R         + 
--R                 2
--R           - 228x  - 24a x - 12
--R      *
--R         y(x)
--R  /
--R                     6        4        2          6
--R               (2048x  + 3072x  + 1152x  + 64)y(x)
--R             + 
--R                     6        4        2          4
--R               (3072x  + 4608x  + 1728x  + 96)y(x)
--R             + 
--R                     6        4       2          2      6      4      2
--R               (1152x  + 1728x  + 648x  + 36)y(x)  + 64x  + 96x  + 36x  + 2
--R          *
--R              +------+
--R              | 2
--R             \|x  + 1
--R         + 
--R                   7        5        3            6
--R           (- 2048x  - 4096x  - 2432x  - 384x)y(x)
--R         + 
--R                   7        5        3            4
--R           (- 3072x  - 6144x  - 3648x  - 576x)y(x)
--R         + 
--R                   7        5        3            2      7       5      3
--R           (- 1152x  - 2304x  - 1368x  - 216x)y(x)  - 64x  - 128x  - 76x  - 12x
--R      *
--R          +---------+
--R          |    2
--R         \|y(x)  + 1
--R     + 
--R                   6        4        2          7
--R           (- 2048x  - 3072x  - 1152x  - 64)y(x)
--R         + 
--R                   6        4        2           5
--R           (- 4096x  - 6144x  - 2304x  - 128)y(x)
--R         + 
--R                   6        4        2          3
--R           (- 2432x  - 3648x  - 1368x  - 76)y(x)
--R         + 
--R                  6       4       2
--R           (- 384x  - 576x  - 216x  - 12)y(x)
--R      *
--R          +------+
--R          | 2
--R         \|x  + 1
--R     + 
--R             7        5        3            7
--R       (2048x  + 4096x  + 2432x  + 384x)y(x)
--R     + 
--R             7        5        3            5
--R       (4096x  + 8192x  + 4864x  + 768x)y(x)
--R     + 
--R           7        5        3            3        7       5       3
--R     (2432x  + 4864x  + 2888x  + 456x)y(x)  + (384x  + 768x  + 456x  + 72x)y(x)
--R                                                     Type: Expression Integer
--E 85

--S 86 of 120
--Rode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x)
--R 
--R
--R           +----------+
--R           |    2    2       ,
--R   (85)  (\|y(x)  + x   + x)y (x) - y(x)
--R
--R                                                     Type: Expression Integer
--E 86

--S 87 of 120
--Rsolve(ode337,y,x)
--R 
--R
--R   (86)  "failed"
--R                                                    Type: Union("failed",...)
--E 87

--S 88 of 120
--Rode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_
--R            2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_
--R            2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha)
--R 
--R
--R   (87)
--R           +----------+
--R           |    2    2         2    2                                 ,
--R     (y(x)\|y(x)  + x   + (y(x)  - x )sin(alpha) - 2x y(x)cos(alpha))y (x)
--R
--R   + 
--R       +----------+
--R       |    2    2                             2    2
--R     x\|y(x)  + x   + 2x y(x)sin(alpha) + (y(x)  - x )cos(alpha)
--R                                                     Type: Expression Integer
--E 88

--S 89 of 120
--Rsolve(ode338,y,x)
--R 
--R
--R   (88)  "failed"
--R                                                    Type: Union("failed",...)
--E 89

--S 90 of 120
--Rode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_
--R            y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2)
--R 
--R
--R   (89)
--R        +--------------+                               +--------------+
--R        |    2    2            3    2      ,           |    2    2
--R     (x\|y(x)  + x  + 1  - y(x)  - x y(x))y (x) - y(x)\|y(x)  + x  + 1
--R
--R   + 
--R             2    3
--R     - x y(x)  - x
--R                                                     Type: Expression Integer
--E 90

--S 91 of 120
--Rsolve(ode339,y,x)
--R 
--R
--R   (90)  "failed"
--R                                                    Type: Union("failed",...)
--E 91

--S 92 of 120
--Rode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_
--R           ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_
--R           (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2))
--R 
--R
--R   (91)
--R                               2       3         2    2        3
--R             ((e2 x - a e2)y(x)  + e2 x  + a e2 x  - a e2 x - a e2)
--R          *
--R              +----------------------+
--R              |    2    2           2
--R             \|y(x)  + x  + 2a x + a
--R         + 
--R                               2       3         2    2        3
--R             ((e1 x + a e1)y(x)  + e1 x  - a e1 x  - a e1 x + a e1)
--R          *
--R              +----------------------+
--R              |    2    2           2
--R             \|y(x)  + x  - 2a x + a
--R      *
--R          ,
--R         y (x)
--R
--R     + 
--R                                                     +----------------------+
--R                 3          2              2         |    2    2           2
--R       (- e2 y(x)  + (- e2 x  - 2a e2 x - a e2)y(x))\|y(x)  + x  + 2a x + a
--R     + 
--R                                                     +----------------------+
--R                 3          2              2         |    2    2           2
--R       (- e1 y(x)  + (- e1 x  + 2a e1 x - a e1)y(x))\|y(x)  + x  - 2a x + a
--R  /
--R                                                    +----------------------+
--R            4      2     2     2    4     2 2    4  |    2    2           2
--R       (y(x)  + (2x  + 2a )y(x)  + x  - 2a x  + a )\|y(x)  + x  - 2a x + a
--R    *
--R        +----------------------+
--R        |    2    2           2
--R       \|y(x)  + x  + 2a x + a
--R                                                     Type: Expression Integer
--E 92

--S 93 of 120
--Rsolve(ode340,y,x)
--R 
--R
--R   (92)  "failed"
--R                                                    Type: Union("failed",...)
--E 93

--S 94 of 120
--Rode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x)
--R 
--R
--R              y(x)     x  ,        y(x)         x
--R   (93)  (x %e     + %e )y (x) + %e     + y(x)%e
--R
--R                                                     Type: Expression Integer
--E 94

--S 95 of 120
--Ryx:=solve(ode341,y,x)
--R 
--R
--R             y(x)         x
--R   (94)  x %e     + y(x)%e
--R                                          Type: Union(Expression Integer,...)
--E 95

--S 96 of 120
--Rode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x)
--R 
--R
--R   (95)
--R                                                               y(x)         x
--R        2  y(x)       x  ,          y(x)           x       x %e     + y(x)%e
--R     ((x %e     + x %e )y (x) + x %e     + x y(x)%e  + 1)%e
--R
--R   + 
--R          x  y(x)      x 2  ,               x  y(x)           x 2
--R     (x %e %e     + (%e ) )y (x) + (x + 1)%e %e     + 2y(x)(%e )
--R
--R                                                     Type: Expression Integer
--E 96

--S 97 of 120
--Rode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1
--R 
--R
--R   (96)
--R      2  x y(x)     2  - x y(x)  ,               x y(x)            - x y(x)
--R   (3x %e       + 2x %e        )y (x) + 3x y(x)%e       + 2x y(x)%e         + 1
--R
--R                                                     Type: Expression Integer
--E 97

--S 98 of 120
--Ryx:=solve(ode342,y,x)
--R 
--R
--R             x y(x) 2           x y(x)
--R         3(%e      )  + log(x)%e       - 2
--R   (97)  ---------------------------------
--R                        x y(x)
--R                      %e
--R                                          Type: Union(Expression Integer,...)
--E 98

--S 99 of 120
--Rode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1
--R 
--R
--R   (98)
--R              3   x y(x) 2     3  ,         2             x y(x) 2
--R           (9x (%e      )  + 6x )y (x) + (9x y(x) + 9x)(%e      )
--R
--R         + 
--R                             x y(x)     2
--R           (3x log(x) + 3x)%e       + 6x y(x) - 6x
--R      *
--R                 x y(x) 2             x y(x)
--R           3x (%e      )  + x log(x)%e       - 2x
--R           --------------------------------------
--R                            x y(x)
--R                          %e
--R         %e
--R     + 
--R              3   x y(x) 2     3  ,         2             x y(x) 2
--R           (6x (%e      )  + 4x )y (x) + (6x y(x) + 6x)(%e      )
--R
--R         + 
--R                             x y(x)     2
--R           (2x log(x) + 2x)%e       + 4x y(x) - 4x
--R      *
--R                   x y(x) 2             x y(x)
--R           - 3x (%e      )  - x log(x)%e       + 2x
--R           ----------------------------------------
--R                             x y(x)
--R                           %e
--R         %e
--R     + 
--R         x y(x)
--R       %e
--R  /
--R       x y(x)
--R     %e
--R                                                     Type: Expression Integer
--E 99

--S 100 of 120
--Rode343 := (log(y(x))+x)*D(y(x),x)-1
--R 
--R
--R                         ,
--R   (99)  (log(y(x)) + x)y (x) - 1
--R
--R                                                     Type: Expression Integer
--E 100

--S 101 of 120
--Ryx:=solve(ode343,y,x)
--R 
--R
--R              - y(x)                - y(x)
--R   (100)  - %e      log(y(x)) - x %e       + Ei(- y(x))
--R                                          Type: Union(Expression Integer,...)
--E 101

--S 102 of 120
--Rode343expr := (log(yx)+x)*D(yx,x)-1
--R 
--R
--R   (101)
--R           - y(x)                - y(x)  ,        - y(x)
--R       ((%e      log(y(x)) + x %e      )y (x) - %e      )
--R
--R    *
--R               - y(x)                - y(x)
--R       log(- %e      log(y(x)) - x %e       + Ei(- y(x)))
--R   + 
--R          - y(x)             2  - y(x)  ,          - y(x)
--R     (x %e      log(y(x)) + x %e      )y (x) - x %e       - 1
--R
--R                                                     Type: Expression Integer
--E 102

--S 103 of 120
--Rode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x)
--R 
--R
--R                               ,
--R   (102)  (log(y(x)) + 2x - 1)y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 103

--S 104 of 120
--Ryx:=solve(ode344,y,x)
--R 
--R
--R          - log(y(x)) - 2x
--R   (103)  ----------------
--R                y(x)
--R                                          Type: Union(Expression Integer,...)
--E 104

--S 105 of 120
--Rode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx
--R 
--R
--R   (104)
--R                             ,                - log(y(x)) - 2x
--R       ((log(y(x)) + 2x - 1)y (x) - 2y(x))log(----------------)
--R                                                    y(x)
--R     + 
--R                              2           ,
--R       ((2x - 1)log(y(x)) + 4x  - 4x + 1)y (x) + 2y(x)log(y(x)) + 2y(x)
--R
--R  /
--R         2
--R     y(x)
--R                                                     Type: Expression Integer
--E 105

--S 106 of 120
--Rode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x)
--R 
--R
--R             3                   ,
--R   (105)  (2x y(x)log(y(x)) + x)y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 106

--S 107 of 120
--Ryx:=solve(ode345,y,x)
--R 
--R
--R            2    2             2    2
--R          2x y(x) log(y(x)) - x y(x)  + 2y(x)
--R   (106)  -----------------------------------
--R                            2
--R                          2x
--R                                          Type: Union(Expression Integer,...)
--E 107

--S 108 of 120
--Rode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx
--R 
--R
--R   (107)
--R                 5    3         2        5    3     3    2              3    2
--R               4x y(x) log(y(x))  + (- 2x y(x)  + 6x y(x) )log(y(x)) - x y(x)
--R             + 
--R               2x y(x)
--R          *
--R              ,
--R             y (x)
--R
--R         + 
--R               2    3              2    3        2
--R           - 4x y(x) log(y(x)) + 2x y(x)  - 4y(x)
--R      *
--R               2    2             2    2
--R             2x y(x) log(y(x)) - x y(x)  + 2y(x)
--R         log(-----------------------------------)
--R                               2
--R                             2x
--R     + 
--R          3                   ,        2    2             2    2
--R       (2x y(x)log(y(x)) + x)y (x) - 2x y(x) log(y(x)) + x y(x)  - 4y(x)
--R
--R  /
--R      2
--R     x
--R                                                     Type: Expression Integer
--E 108

--S 109 of 120
--Rode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_
--R              y(x)*(a*x*log(x*y(x))-y(x)+a*x)
--R 
--R
--R   (108)
--R                                      2  ,                                2
--R     (x y(x)log(x y(x)) + x y(x) - a x )y (x) - a x y(x)log(x y(x)) + y(x)
--R
--R   + 
--R     - a x y(x)
--R                                                     Type: Expression Integer
--E 109

--S 110 of 120
--Rsolve(ode346,y,x)
--R 
--R
--R   (109)  "failed"
--R                                                    Type: Union("failed",...)
--E 110

--S 111 of 120
--Rode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1)
--R 
--R
--R                                ,
--R   (110)  (sin(x) + 1)sin(y(x))y (x) + cos(x)cos(y(x)) - cos(x)
--R
--R                                                     Type: Expression Integer
--E 111

--S 112 of 120
--Ryx:=solve(ode347,y,x)
--R 
--R
--R   (111)
--R                     2                     2             2
--R           (- 4cos(x)  - 8cos(x) - 4)sin(x)  + (- 8cos(x)  - 16cos(x) - 8)sin(x)
--R         + 
--R                    2
--R           - 4cos(x)  - 8cos(x) - 4
--R      *
--R         cos(y(x))
--R     + 
--R               5                        4             2                      3
--R       - sin(x)  + (- 4cos(x) - 4)sin(x)  + (- 6cos(x)  - 12cos(x) - 6)sin(x)
--R     + 
--R                 3           2                      2
--R       (- 4cos(x)  - 12cos(x)  - 12cos(x) - 4)sin(x)
--R     + 
--R                4          3          2
--R       (- cos(x)  - 4cos(x)  - 6cos(x)  - 4cos(x) - 1)sin(x)
--R  /
--R             5                      4           2                       3
--R       sin(x)  + (4cos(x) + 5)sin(x)  + (6cos(x)  + 16cos(x) + 10)sin(x)
--R     + 
--R               3           2                       2
--R       (4cos(x)  + 18cos(x)  + 24cos(x) + 10)sin(x)
--R     + 
--R              4          3           2                               4
--R       (cos(x)  + 8cos(x)  + 18cos(x)  + 16cos(x) + 5)sin(x) + cos(x)
--R     + 
--R              3          2
--R       4cos(x)  + 6cos(x)  + 4cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 112

--S 113 of 120
--Rode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1)
--R 
--R
--R   (112)
--R                         2                     4
--R               (- 4cos(x)  - 8cos(x) - 4)sin(x)
--R             + 
--R                         3           2                       3
--R               (- 4cos(x)  - 24cos(x)  - 36cos(x) - 16)sin(x)
--R             + 
--R                          3           2                       2
--R               (- 12cos(x)  - 48cos(x)  - 60cos(x) - 24)sin(x)
--R             + 
--R                          3           2                                 3
--R               (- 12cos(x)  - 40cos(x)  - 44cos(x) - 16)sin(x) - 4cos(x)
--R             + 
--R                         2
--R               - 12cos(x)  - 12cos(x) - 4
--R          *
--R                       ,
--R             sin(y(x))y (x)
--R
--R         + 
--R                                    5           2                      4
--R               (- 8cos(x) - 8)sin(x)  + (8cos(x)  - 8cos(x) - 16)sin(x)
--R             + 
--R                          3                  3
--R               (- 12cos(x)  + 12cos(x))sin(x)
--R             + 
--R                       4           3           2                      2
--R               (4cos(x)  - 28cos(x)  - 44cos(x)  + 4cos(x) + 16)sin(x)
--R             + 
--R                       4           3           2
--R               (8cos(x)  - 20cos(x)  - 56cos(x)  - 20cos(x) + 8)sin(x)
--R             + 
--R                      4          3           2
--R               4cos(x)  - 4cos(x)  - 20cos(x)  - 12cos(x)
--R          *
--R             cos(y(x))
--R         + 
--R                       5           2                 4
--R           cos(x)sin(x)  + (5cos(x)  + 5cos(x))sin(x)
--R         + 
--R                    3           2                  3
--R           (10cos(x)  + 20cos(x)  + 10cos(x))sin(x)
--R         + 
--R                    4           3           2                  2
--R           (10cos(x)  + 30cos(x)  + 30cos(x)  + 10cos(x))sin(x)
--R         + 
--R                   5           4           3           2
--R           (5cos(x)  + 20cos(x)  + 30cos(x)  + 20cos(x)  + 5cos(x))sin(x)
--R         + 
--R                 6          5           4           3          2
--R           cos(x)  + 5cos(x)  + 10cos(x)  + 10cos(x)  + 5cos(x)  + cos(x)
--R      *
--R         sin
--R                            2                     2
--R                    (4cos(x)  + 8cos(x) + 4)sin(x)
--R                  + 
--R                            2                                2
--R                    (8cos(x)  + 16cos(x) + 8)sin(x) + 4cos(x)  + 8cos(x) + 4
--R               *
--R                  cos(y(x))
--R              + 
--R                      5                      4
--R                sin(x)  + (4cos(x) + 4)sin(x)
--R              + 
--R                        2                      3
--R                (6cos(x)  + 12cos(x) + 6)sin(x)
--R              + 
--R                        3           2                      2
--R                (4cos(x)  + 12cos(x)  + 12cos(x) + 4)sin(x)
--R              + 
--R                       4          3          2
--R                (cos(x)  + 4cos(x)  + 6cos(x)  + 4cos(x) + 1)sin(x)
--R           /
--R                      5                      4
--R                sin(x)  + (4cos(x) + 5)sin(x)
--R              + 
--R                        2                       3
--R                (6cos(x)  + 16cos(x) + 10)sin(x)
--R              + 
--R                        3           2                       2
--R                (4cos(x)  + 18cos(x)  + 24cos(x) + 10)sin(x)
--R              + 
--R                       4          3           2                               4
--R                (cos(x)  + 8cos(x)  + 18cos(x)  + 16cos(x) + 5)sin(x) + cos(x)
--R              + 
--R                       3          2
--R                4cos(x)  + 6cos(x)  + 4cos(x) + 1
--R     + 
--R                       6           2                 5
--R           cos(x)sin(x)  + (5cos(x)  + 6cos(x))sin(x)
--R         + 
--R                    3           2                  4
--R           (10cos(x)  + 25cos(x)  + 15cos(x))sin(x)
--R         + 
--R                    4           3           2                  3
--R           (10cos(x)  + 40cos(x)  + 50cos(x)  + 20cos(x))sin(x)
--R         + 
--R                   5           4           3           2                  2
--R           (5cos(x)  + 30cos(x)  + 60cos(x)  + 50cos(x)  + 15cos(x))sin(x)
--R         + 
--R                    6           5           4           3           2
--R             (cos(x)  + 10cos(x)  + 30cos(x)  + 40cos(x)  + 25cos(x)  + 6cos(x))
--R          *
--R             sin(x)
--R         + 
--R                 6          5           4           3          2
--R           cos(x)  + 5cos(x)  + 10cos(x)  + 10cos(x)  + 5cos(x)  + cos(x)
--R      *
--R         cos
--R                            2                     2
--R                    (4cos(x)  + 8cos(x) + 4)sin(x)
--R                  + 
--R                            2                                2
--R                    (8cos(x)  + 16cos(x) + 8)sin(x) + 4cos(x)  + 8cos(x) + 4
--R               *
--R                  cos(y(x))
--R              + 
--R                      5                      4
--R                sin(x)  + (4cos(x) + 4)sin(x)
--R              + 
--R                        2                      3
--R                (6cos(x)  + 12cos(x) + 6)sin(x)
--R              + 
--R                        3           2                      2
--R                (4cos(x)  + 12cos(x)  + 12cos(x) + 4)sin(x)
--R              + 
--R                       4          3          2
--R                (cos(x)  + 4cos(x)  + 6cos(x)  + 4cos(x) + 1)sin(x)
--R           /
--R                      5                      4
--R                sin(x)  + (4cos(x) + 5)sin(x)
--R              + 
--R                        2                       3
--R                (6cos(x)  + 16cos(x) + 10)sin(x)
--R              + 
--R                        3           2                       2
--R                (4cos(x)  + 18cos(x)  + 24cos(x) + 10)sin(x)
--R              + 
--R                       4          3           2                               4
--R                (cos(x)  + 8cos(x)  + 18cos(x)  + 16cos(x) + 5)sin(x) + cos(x)
--R              + 
--R                       3          2
--R                4cos(x)  + 6cos(x)  + 4cos(x) + 1
--R     + 
--R                     6             2                 5
--R       - cos(x)sin(x)  + (- 5cos(x)  - 6cos(x))sin(x)
--R     + 
--R                  3           2                  4
--R       (- 10cos(x)  - 25cos(x)  - 15cos(x))sin(x)
--R     + 
--R                  4           3           2                  3
--R       (- 10cos(x)  - 40cos(x)  - 50cos(x)  - 20cos(x))sin(x)
--R     + 
--R                 5           4           3           2                  2
--R       (- 5cos(x)  - 30cos(x)  - 60cos(x)  - 50cos(x)  - 15cos(x))sin(x)
--R     + 
--R                  6           5           4           3           2
--R         (- cos(x)  - 10cos(x)  - 30cos(x)  - 40cos(x)  - 25cos(x)  - 6cos(x))
--R      *
--R         sin(x)
--R     + 
--R               6          5           4           3          2
--R       - cos(x)  - 5cos(x)  - 10cos(x)  - 10cos(x)  - 5cos(x)  - cos(x)
--R  /
--R             6                      5            2                       4
--R       sin(x)  + (5cos(x) + 6)sin(x)  + (10cos(x)  + 25cos(x) + 15)sin(x)
--R     + 
--R                3           2                       3
--R       (10cos(x)  + 40cos(x)  + 50cos(x) + 20)sin(x)
--R     + 
--R               4           3           2                       2
--R       (5cos(x)  + 30cos(x)  + 60cos(x)  + 50cos(x) + 15)sin(x)
--R     + 
--R              5           4           3           2
--R       (cos(x)  + 10cos(x)  + 30cos(x)  + 40cos(x)  + 25cos(x) + 6)sin(x)
--R     + 
--R             5          4           3           2
--R       cos(x)  + 5cos(x)  + 10cos(x)  + 10cos(x)  + 5cos(x) + 1
--R                                                     Type: Expression Integer
--E 113 

--S 114 of 120
--Rode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x))
--R 
--R
--R                                 ,
--R   (113)  (x cos(y(x)) + sin(x))y (x) + sin(y(x)) + y(x)cos(x)
--R
--R                                                     Type: Expression Integer
--E 114

--S 115 of 120
--Ryx:=solve(ode348,y,x)
--R 
--R
--R   (114)  x sin(y(x)) + y(x)sin(x)
--R                                          Type: Union(Expression Integer,...)
--E 115

--S 116 of 120
--Rode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx)
--R 
--R
--R   (115)
--R     sin(x sin(y(x)) + y(x)sin(x))
--R   + 
--R          2                      ,
--R       ((x cos(y(x)) + x sin(x))y (x) + x sin(y(x)) + x y(x)cos(x))
--R
--R    *
--R       cos(x sin(y(x)) + y(x)sin(x))
--R   + 
--R                                2  ,
--R     (x sin(x)cos(y(x)) + sin(x) )y (x) + (sin(x) + x cos(x))sin(y(x))
--R
--R   + 
--R     2y(x)cos(x)sin(x)
--R                                                     Type: Expression Integer
--E 116

--S 117 of 120
--Rode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x)
--R 
--R
--R                y(x)  ,             y(x)            y(x)
--R   (116)  x cot(----)y (x) + 2x sin(----) - y(x)cot(----)
--R                  x                   x               x
--R                                                     Type: Expression Integer
--E 117

--S 118 of 120
--Rsolve(ode349,y,x)
--R 
--R
--R   (117)  "failed"
--R                                                    Type: Union("failed",...)
--E 118

--S 119 of 120
--Rode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x))
--R 
--R
--R                    ,                     2
--R   (118)  cos(y(x))y (x) - cos(x)sin(y(x))  - sin(y(x))
--R
--R                                                     Type: Expression Integer
--E 119

--S 120 of 120
--Rsolve(ode350,y,x)
--R 
--R
--R   (119)  "failed"
--R                                                    Type: Union("failed",...)
--E 120
 

)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read tree
 
)set break resume
 
)spool tree.output
 
 
Daly Bug
   >> System error:
   file tree.output already exists

   Continuing to read the file...

)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 35
bt := BinaryTree INT
 

   (1)  BinaryTree Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  BinaryTree Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 35
ebtree:=empty()$(BTREE INT)
 

   (2)  []
                                                     Type: BinaryTree Integer
--R 
--R
--R   (2)  []
--R                                                     Type: BinaryTree Integer
--E 2

--S 3 of 35
insleaf:(INT,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 35
insleaf(x,t)==
     empty? t=> binaryTree(x)$(BTREE INT)
     x> value t => binaryTree(left t,value t,insleaf(x,right t))
     binaryTree(insleaf(x,left t),value t,right t)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 35
b:bt:=reduce(insleaf,[8,3,5,4,6,2,1,5,7],ebtree)
 
   Compiling function insleaf with type (Integer,BinaryTree Integer)
       -> BinaryTree Integer 

   (5)  [[[1,2,.],3,[[.,4,5],5,[.,6,7]]],8,.]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function insleaf with type (Integer,BinaryTree Integer)
--R       -> BinaryTree Integer 
--R
--R   (5)  [[[1,2,.],3,[[.,4,5],5,[.,6,7]]],8,.]
--R                                                     Type: BinaryTree Integer
--E 5

--S 6 of 35
bleaf x == reduce(insleaf,x,ebtree)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 35
fln:bt-> List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 35
fln t==
    empty? t => empty()$(List INT)
    concat(fln left t,concat(value t,fln right t))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 35
fln b
 
   Compiling function fln with type BinaryTree Integer -> List Integer 

   (9)  [1,2,3,4,5,5,6,7,8]
                                                           Type: List Integer
--R 
--R   Compiling function fln with type BinaryTree Integer -> List Integer 
--R
--R   (9)  [1,2,3,4,5,5,6,7,8]
--R                                                           Type: List Integer
--E 9

--S 10 of 35
split:(INT,bt)->List bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 35
split(x,t)==
     empty? t=> [ebtree,ebtree]
     x> value t =>
            a:=split(x,right t)
            [binaryTree(left t,value t,a.1),a.2]
     a:=split(x,left t)
     [a.1,binaryTree(a.2,value t,right t)]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 35
split(3,b)
 
   Compiling function split with type (Integer,BinaryTree Integer) -> 
      List BinaryTree Integer 

   (12)  [[1,2,.],[[.,3,[[.,4,5],5,[.,6,7]]],8,.]]
                                                Type: List BinaryTree Integer
--R 
--R   Compiling function split with type (Integer,BinaryTree Integer) -> 
--R      List BinaryTree Integer 
--R
--R   (12)  [[1,2,.],[[.,3,[[.,4,5],5,[.,6,7]]],8,.]]
--R                                                Type: List BinaryTree Integer
--E 12

--S 13 of 35
insroot:(INT,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13

--S 14 of 35
insroot(x,t)==
      a:=split(x,t)
      binaryTree(a.1,x,a.2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 35
broot x == reduce(insroot,x,ebtree)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 35
a:List INT:=[8,3,9,4,6,2,1,5,7]
 

   (16)  [8,3,9,4,6,2,1,5,7]
                                                           Type: List Integer
--R 
--R
--R   (16)  [8,3,9,4,6,2,1,5,7]
--R                                                           Type: List Integer
--E 16

--S 17 of 35
l1:=bleaf a
 
   Compiling function bleaf with type List Integer -> BinaryTree 
      Integer 

   (17)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function bleaf with type List Integer -> BinaryTree 
--R      Integer 
--R
--R   (17)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
--R                                                     Type: BinaryTree Integer
--E 17

--S 18 of 35
r1:=broot reverse a
 
   Compiling function broot with type List Integer -> BinaryTree 
      Integer 
   Compiling function insroot with type (Integer,BinaryTree Integer)
       -> BinaryTree Integer 

   (18)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function broot with type List Integer -> BinaryTree 
--R      Integer 
--R   Compiling function insroot with type (Integer,BinaryTree Integer)
--R       -> BinaryTree Integer 
--R
--R   (18)  [[[1,2,.],3,[.,4,[5,6,7]]],8,9]
--R                                                     Type: BinaryTree Integer
--E 18

--S 19 of 35
(l1=r1)::Boolean
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19

--S 20 of 35
broot a
 

   (20)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
                                                     Type: BinaryTree Integer
--R 
--R
--R   (20)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
--R                                                     Type: BinaryTree Integer
--E 20

--S 21 of 35
bleaf reverse a
 

   (21)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
                                                     Type: BinaryTree Integer
--R 
--R
--R   (21)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
--R                                                     Type: BinaryTree Integer
--E 21

--S 22 of 35
mg:(bt,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 35
mg(x,y)==
    empty? x => y
    empty? y => x
    value x > value y => binaryTree(mg(y,left x),value x,right x)
    binaryTree(left y,value y,mg(x,right y))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 35
mg1:(INT,bt)->bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 24

--S 25 of 35
mg1(x,t)==mg(binaryTree x,t)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 25

--S 26 of 35
btourn:List INT-> bt
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 26

--S 27 of 35
btourn x == reduce(mg1,x,ebtree)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28 of 35
btourn a
 
   Compiling function btourn with type List Integer -> BinaryTree 
      Integer 
   Compiling function mg with type (BinaryTree Integer,BinaryTree 
      Integer) -> BinaryTree Integer 
   Compiling function mg1 with type (Integer,BinaryTree Integer) -> 
      BinaryTree Integer 

   (28)  [[.,8,3],9,[[4,6,[[.,2,1],5,.]],7,.]]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function btourn with type List Integer -> BinaryTree 
--R      Integer 
--R   Compiling function mg with type (BinaryTree Integer,BinaryTree 
--R      Integer) -> BinaryTree Integer 
--R   Compiling function mg1 with type (Integer,BinaryTree Integer) -> 
--R      BinaryTree Integer 
--R
--R   (28)  [[.,8,3],9,[[4,6,[[.,2,1],5,.]],7,.]]
--R                                                     Type: BinaryTree Integer
--E 28

--S 29 of 35
cmp:(List INT,List INT)-> Boolean
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 35
cmp(x,y)== x.2<y.2
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 35
sort2 : List List INT -> List List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 31

--S 32 of 35
sort2 x== sort(cmp,x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 35
invert x==[i.1 for i in  sort2  [[k,l]
          for k in 1..#x for  l in x]]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 35
broot a
 

   (34)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
                                                     Type: BinaryTree Integer
--R 
--R
--R   (34)  [[[.,1,[.,2,[3,4,.]]],5,6],7,[8,9,.]]
--R                                                     Type: BinaryTree Integer
--E 34

--S 35 of 35
btourn invert a
 
   Compiling function sort2 with type List List Integer -> List List 
      Integer 
   Compiling function invert with type List Integer -> List Integer 
   Compiling function cmp with type (List Integer,List Integer) -> 
      Boolean 

   (35)  [[[.,7,[.,6,[2,4,.]]],8,5],9,[1,3,.]]
                                                     Type: BinaryTree Integer
--R 
--R   Compiling function sort2 with type List List Integer -> List List 
--R      Integer 
--R   Compiling function invert with type List Integer -> List Integer 
--R   Compiling function cmp with type (List Integer,List Integer) -> 
--R      Boolean 
--R
--R   (35)  [[[.,7,[.,6,[2,4,.]]],8,5],9,[1,3,.]]
--R                                                     Type: BinaryTree Integer
--E 35
)spool 
 
 
Daly Bug
   >> System error:
   Not in dribble.

   Continuing to read the file...

)lisp (bye)
 
Starts dribbling to reclos.output (2010/3/27, 18:36:42).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 70
Ran := RECLOS(FRAC INT)
 

   (1)  RealClosure Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  RealClosure Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 70
fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran == sqrt(a)+sqrt(b) - sqrt(c)-sqrt(d)
 
   Function declaration fourSquares : (RealClosure Fraction Integer,
      RealClosure Fraction Integer,RealClosure Fraction Integer,
      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration fourSquares : (RealClosure Fraction Integer,
--R      RealClosure Fraction Integer,RealClosure Fraction Integer,
--R      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 70
squareDiff1 := fourSquares(73,548,60,586)
 
   Compiling function fourSquares with type (RealClosure Fraction 
      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 

           +---+    +--+    +---+    +--+
   (3)  - \|586  - \|60  + \|548  + \|73
                                           Type: RealClosure Fraction Integer
--R 
--R   Compiling function fourSquares with type (RealClosure Fraction 
--R      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
--R      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 
--R
--R           +---+    +--+    +---+    +--+
--R   (3)  - \|586  - \|60  + \|548  + \|73
--R                                           Type: RealClosure Fraction Integer
--E 3

--S 4 of 70
recip(squareDiff1)
 

   (4)
             +---+          +--+  +--+         +--+ +---+            +---+
     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
   + 
             +--+ +---+             +--+            +---+            +--+
     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (4)
--R             +---+          +--+  +--+         +--+ +---+            +---+
--R     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
--R   + 
--R             +--+ +---+             +--+            +---+            +--+
--R     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 4

--S 5 of 70
sign(squareDiff1)
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 70
squareDiff2 := fourSquares(165,778,86,990)
 

           +---+    +--+    +---+    +---+
   (6)  - \|990  - \|86  + \|778  + \|165
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +--+    +---+    +---+
--R   (6)  - \|990  - \|86  + \|778  + \|165
--R                                           Type: RealClosure Fraction Integer
--E 6

--S 7 of 70
recip(squareDiff2)
 

   (7)
                +---+           +---+  +--+          +---+ +---+
       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
    *
        +---+
       \|990
   + 
              +---+ +---+              +--+             +---+             +---+
     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (7)
--R                +---+           +---+  +--+          +---+ +---+
--R       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
--R    *
--R        +---+
--R       \|990
--R   + 
--R              +---+ +---+              +--+             +---+             +---+
--R     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 7

--S 8 of 70
sign(squareDiff2)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 70
squareDiff3 := fourSquares(217,708,226,692)
 

           +---+    +---+    +---+    +---+
   (9)  - \|692  - \|226  + \|708  + \|217
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +---+    +---+    +---+
--R   (9)  - \|692  - \|226  + \|708  + \|217
--R                                           Type: RealClosure Fraction Integer
--E 9

--S 10 of 70
recip(squareDiff3)
 

   (10)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (10)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 10

--S 11 of 70
sign(squareDiff3)
 

   (11)  - 1
                                                                Type: Integer
--R 
--R
--R   (11)  - 1
--R                                                                Type: Integer
--E 11

--S 12 of 70
squareDiff4 := fourSquares(155,836,162,820)
 

            +---+    +---+    +---+    +---+
   (12)  - \|820  - \|162  + \|836  + \|155
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (12)  - \|820  - \|162  + \|836  + \|155
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 70
recip(squareDiff4)
 

   (13)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (13)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 13

--S 14 of 70
sign(squareDiff4)
 

   (14)  - 1
                                                                Type: Integer
--R 
--R
--R   (14)  - 1
--R                                                                Type: Integer
--E 14

--S 15 of 70
squareDiff5 := fourSquares(591,772,552,818)
 

            +---+    +---+    +---+    +---+
   (15)  - \|818  - \|552  + \|772  + \|591
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (15)  - \|818  - \|552  + \|772  + \|591
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 70
recip(squareDiff5)
 

   (16)
             +---+         +---+  +---+         +---+ +---+             +---+
     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
   + 
            +---+ +---+             +---+            +---+            +---+
     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (16)
--R             +---+         +---+  +---+         +---+ +---+             +---+
--R     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
--R   + 
--R            +---+ +---+             +---+            +---+            +---+
--R     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 16

--S 17 of 70
sign(squareDiff5)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 70
squareDiff6 := fourSquares(434,1053,412,1088)
 

            +----+    +---+    +----+    +---+
   (18)  - \|1088  - \|412  + \|1053  + \|434
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (18)  - \|1088  - \|412  + \|1053  + \|434
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 70
recip(squareDiff6)
 

   (19)
                +----+          +---+  +---+          +---+ +----+
       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
    *
        +----+
       \|1088
   + 
           +---+ +----+              +---+            +----+             +---+
   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (19)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
--R    *
--R        +----+
--R       \|1088
--R   + 
--R           +---+ +----+              +---+            +----+             +---+
--R   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 19

--S 20 of 70
sign(squareDiff6)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 70
squareDiff7 := fourSquares(514,1049,446,1152)
 

            +----+    +---+    +----+    +---+
   (21)  - \|1152  - \|446  + \|1049  + \|514
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (21)  - \|1152  - \|446  + \|1049  + \|514
--R                                           Type: RealClosure Fraction Integer
--E 21

--S 22 of 70
recip(squareDiff7)
 

   (22)
                +----+          +---+  +---+          +---+ +----+
       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
    *
        +----+
       \|1152
   + 
           +---+ +----+              +---+             +----+             +---+
   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (22)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
--R    *
--R        +----+
--R       \|1152
--R   + 
--R           +---+ +----+              +---+             +----+             +---+
--R   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 22

--S 23 of 70
sign(squareDiff7)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 70
squareDiff8 := fourSquares(190,1751,208,1698)
 

            +----+    +---+    +----+    +---+
   (24)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (24)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 24

--S 25 of 70
recip(squareDiff8)
 

   (25)
                     +----+          +---+  +---+          +---+ +----+
           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
         + 
           - 129571901
    *
        +----+
       \|1698
   + 
               +---+ +----+              +---+             +----+
     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
   + 
                 +---+
     - 387349387\|190
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (25)
--R                     +----+          +---+  +---+          +---+ +----+
--R           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
--R         + 
--R           - 129571901
--R    *
--R        +----+
--R       \|1698
--R   + 
--R               +---+ +----+              +---+             +----+
--R     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
--R   + 
--R                 +---+
--R     - 387349387\|190
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 25

--S 26 of 70
sign(squareDiff8)
 

   (26)  - 1
                                                                Type: Integer
--R 
--R
--R   (26)  - 1
--R                                                                Type: Integer
--E 26

--S 27 of 70
relativeApprox(squareDiff8,10**(-3))::Float
 

   (27)  - 0.2340527771 5937700123 E -10
                                                                  Type: Float
--R 
--R
--R   (27)  - 0.2340527771 5937700123 E -10
--R                                                                  Type: Float
--E 27

--S 28 of 70
allRootsOf((x-2)*(x-3)*(x-4))$RECLOS(FRAC INT)
 

   (28)  [2,3,4]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (28)  [2,3,4]
--R                                      Type: List RealClosure Fraction Integer
--E 28

--S 29 of 70
l := allRootsOf((x**2-2)**2-2)$Ran
 

   (29)  [%A33,%A34,%A35,%A36]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (29)  [%A33,%A34,%A35,%A36]
--R                                      Type: List RealClosure Fraction Integer
--E 29

--S 30 of 70
l.1+l.2+l.3+l.4
 

   (30)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (30)  0
--R                                           Type: RealClosure Fraction Integer
--E 30

--S 31 of 70
removeDuplicates map(mainDefiningPolynomial,l)
 

           4     2
   (31)  [?  - 4?  + 2]
Type: List Union(SparseUnivariatePolynomial RealClosure Fraction Integer,"failed")
--R 
--R
--R           4     2
--R   (31)  [?  - 4?  + 2]
--RType: List Union(SparseUnivariatePolynomial RealClosure Fraction Integer,"failed")
--E 31

--S 32 of 70
map(mainCharacterization,l)
 

   (32)  [[- 2,- 1[,[- 1,0[,[0,1[,[1,2[]
Type: List Union(RightOpenIntervalRootCharacterization(RealClosure Fraction Integer,SparseUnivariatePolynomial RealClosure Fraction Integer),"failed")
--R 
--R
--R   (32)  [[- 2,- 1[,[- 1,0[,[0,1[,[1,2[]
--RType: List Union(RightOpenIntervalRootCharacterization(RealClosure Fraction Integer,SparseUnivariatePolynomial RealClosure Fraction Integer),"failed")
--E 32

--S 33 of 70
[reduce(+,l),reduce(*,l)-2]
 

   (33)  [0,0]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (33)  [0,0]
--R                                      Type: List RealClosure Fraction Integer
--E 33

)cl prop s2 s5 10
 
 
--S 34 of 70
(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran)
 

          +--+
   (34)  \|10
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R   (34)  \|10
--R                                           Type: RealClosure Fraction Integer
--E 34

--S 35 of 70
eq1:=sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
 

            +---------+ +--------+    +---------+ +--------+   +-----------+
            | +--+      | +-+         | +--+      | +-+        |   +-+
   (35)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +---------+ +--------+    +---------+ +--------+   +-----------+
--R            | +--+      | +-+         | +--+      | +-+        |   +-+
--R   (35)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
--R                                  Type: Equation RealClosure Fraction Integer
--E 35

--S 36 of 70
eq1::Boolean
 

   (36)  true
                                                                Type: Boolean
--R 
--R
--R   (36)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 70
eq2:=sqrt(s5+2)*sqrt(s2+1) - sqrt(s5-2)*sqrt(s2-1) = sqrt(2*s10+2)
 

            +--------+ +--------+    +--------+ +--------+   +----------+
            | +-+      | +-+         | +-+      | +-+        |  +--+
   (37)  - \|\|5  - 2 \|\|2  - 1  + \|\|5  + 2 \|\|2  + 1 = \|2\|10  + 2
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +--------+ +--------+    +--------+ +--------+   +----------+
--R            | +-+      | +-+         | +-+      | +-+        |  +--+
--R   (37)  - \|\|5  - 2 \|\|2  - 1  + \|\|5  + 2 \|\|2  + 1 = \|2\|10  + 2
--R                                  Type: Equation RealClosure Fraction Integer
--E 37

--S 38 of 70
eq2::Boolean
 

   (38)  true
                                                                Type: Boolean
--R 
--R
--R   (38)  true
--R                                                                Type: Boolean
--E 38


)cl prop s4 s7 e1 e2
 

--S 39 of 70
s3 := sqrt(3)$Ran
 

          +-+
   (39)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (39)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 39

--S 40 of 70
s7:= sqrt(7)$Ran
 

          +-+
   (40)  \|7
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (40)  \|7
--R                                           Type: RealClosure Fraction Integer
--E 40

--S 41 of 70
e1 := sqrt(2*s7-3*s3,3)
 

          +-------------+
         3|  +-+     +-+
   (41)  \|2\|7  - 3\|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-------------+
--R         3|  +-+     +-+
--R   (41)  \|2\|7  - 3\|3
--R                                           Type: RealClosure Fraction Integer
--E 41

--S 42 of 70
e2 := sqrt(2*s7+3*s3,3)
 

          +-------------+
         3|  +-+     +-+
   (42)  \|2\|7  + 3\|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-------------+
--R         3|  +-+     +-+
--R   (42)  \|2\|7  + 3\|3
--R                                           Type: RealClosure Fraction Integer
--E 42

--S 43 of 70
ee1:=e2-e1=s3
 

          +-------------+    +-------------+
         3|  +-+     +-+    3|  +-+     +-+    +-+
   (43)  \|2\|7  + 3\|3   - \|2\|7  - 3\|3  = \|3
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +-------------+    +-------------+
--R         3|  +-+     +-+    3|  +-+     +-+    +-+
--R   (43)  \|2\|7  + 3\|3   - \|2\|7  - 3\|3  = \|3
--R                                  Type: Equation RealClosure Fraction Integer
--E 43

--S 44 of 70
ee1::Boolean
 

   (44)  true
                                                                Type: Boolean
--R 
--R
--R   (44)  true
--R                                                                Type: Boolean
--E 44

)cl prop pol r1 alpha beta
 

--S 45 of 70
pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3)
 

          4   7  2         100
   (45)  x  + - x  + 30x - ---
              3             3
                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--R 
--R
--R          4   7  2         100
--R   (45)  x  + - x  + 30x - ---
--R              3             3
--R                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--E 45

--S 46 of 70
r1 := sqrt(7633)$Ran
 

          +----+
   (46)  \|7633
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +----+
--R   (46)  \|7633
--R                                           Type: RealClosure Fraction Integer
--E 46

--S 47 of 70
alpha := sqrt(5*r1-436,3)/3
 

            +--------------+
         1 3|  +----+
   (47)  - \|5\|7633  - 436
         3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +--------------+
--R         1 3|  +----+
--R   (47)  - \|5\|7633  - 436
--R         3
--R                                           Type: RealClosure Fraction Integer
--E 47

--S 48 of 70
beta := -sqrt(5*r1+436,3)/3
 

              +--------------+
           1 3|  +----+
   (48)  - - \|5\|7633  + 436
           3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R              +--------------+
--R           1 3|  +----+
--R   (48)  - - \|5\|7633  + 436
--R           3
--R                                           Type: RealClosure Fraction Integer
--E 48


--S 49 of 70
pol.(alpha+beta-1/3)
 

   (49)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (49)  0
--R                                           Type: RealClosure Fraction Integer
--E 49

)cl prop qol r2 alpha beta
 

--S 50 of 70
r2 := sqrt(153)$Ran
 

          +---+
   (50)  \|153
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +---+
--R   (50)  \|153
--R                                           Type: RealClosure Fraction Integer
--E 50

--S 51 of 70
alpha2 := sqrt(r2-11,5)
 

          +-----------+
         5| +---+
   (51)  \|\|153  - 11
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-----------+
--R         5| +---+
--R   (51)  \|\|153  - 11
--R                                           Type: RealClosure Fraction Integer
--E 51

--S 52 of 70
beta2 := -sqrt(r2+11,5)
 

            +-----------+
           5| +---+
   (52)  - \|\|153  + 11
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +-----------+
--R           5| +---+
--R   (52)  - \|\|153  + 11
--R                                           Type: RealClosure Fraction Integer
--E 52

--S 53 of 70
qol : UP(x,Ran) := x**5+10*x**3+20*x+22
 

          5      3
   (53)  x  + 10x  + 20x + 22
                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--R 
--R
--R          5      3
--R   (53)  x  + 10x  + 20x + 22
--R                   Type: UnivariatePolynomial(x,RealClosure Fraction Integer)
--E 53

--S 54 of 70
qol(alpha2+beta2)
 

   (54)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (54)  0
--R                                           Type: RealClosure Fraction Integer
--E 54

--S 55 of 70
dst1:=sqrt(9+4*s2)=1+2*s2
 

          +---------+
          |  +-+         +-+
   (55)  \|4\|2  + 9 = 2\|2  + 1
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +---------+
--R          |  +-+         +-+
--R   (55)  \|4\|2  + 9 = 2\|2  + 1
--R                                  Type: Equation RealClosure Fraction Integer
--E 55

--S 56 of 70
dst1::Boolean
 

   (56)  true
                                                                Type: Boolean
--R 
--R
--R   (56)  true
--R                                                                Type: Boolean
--E 56

--S 57 of 70
s6:Ran:=sqrt 6
 

          +-+
   (57)  \|6
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +-+
--R   (57)  \|6
--R                                           Type: RealClosure Fraction Integer
--E 57

--S 58 of 70
dst2:=sqrt(5+2*s6)+sqrt(5-2*s6) = 2*s3
 

          +-----------+    +---------+
          |    +-+         |  +-+         +-+
   (58)  \|- 2\|6  + 5  + \|2\|6  + 5 = 2\|3
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +-----------+    +---------+
--R          |    +-+         |  +-+         +-+
--R   (58)  \|- 2\|6  + 5  + \|2\|6  + 5 = 2\|3
--R                                  Type: Equation RealClosure Fraction Integer
--E 58

--S 59 of 70
dst2::Boolean
 

   (59)  true
                                                                Type: Boolean
--R 
--R
--R   (59)  true
--R                                                                Type: Boolean
--E 59

--S 60 of 70
s29:Ran:=sqrt 29
 

          +--+
   (60)  \|29
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R   (60)  \|29
--R                                           Type: RealClosure Fraction Integer
--E 60

--S 61 of 70
dst4:=sqrt(16-2*s29+2*sqrt(55-10*s29)) = sqrt(22+2*s5)-sqrt(11+2*s29)+s5
 

   (61)
    +--------------------------------+
    |  +--------------+                    +-----------+    +----------+
    |  |     +--+           +--+           |  +--+          |  +-+          +-+
   \|2\|- 10\|29  + 55  - 2\|29  + 16 = - \|2\|29  + 11  + \|2\|5  + 22  + \|5
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R   (61)
--R    +--------------------------------+
--R    |  +--------------+                    +-----------+    +----------+
--R    |  |     +--+           +--+           |  +--+          |  +-+          +-+
--R   \|2\|- 10\|29  + 55  - 2\|29  + 16 = - \|2\|29  + 11  + \|2\|5  + 22  + \|5
--R                                  Type: Equation RealClosure Fraction Integer
--E 61

--S 62 of 70
dst4::Boolean
 

   (62)  true
                                                                Type: Boolean
--R 
--R
--R   (62)  true
--R                                                                Type: Boolean
--E 62

--S 63 of 70
dst6:=sqrt((112+70*s2)+(46+34*s2)*s5) = (5+4*s2)+(3+s2)*s5
 

          +--------------------------------+
          |    +-+       +-+      +-+           +-+      +-+     +-+
   (63)  \|(34\|2  + 46)\|5  + 70\|2  + 112 = (\|2  + 3)\|5  + 4\|2  + 5
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +--------------------------------+
--R          |    +-+       +-+      +-+           +-+      +-+     +-+
--R   (63)  \|(34\|2  + 46)\|5  + 70\|2  + 112 = (\|2  + 3)\|5  + 4\|2  + 5
--R                                  Type: Equation RealClosure Fraction Integer
--E 63

--S 64 of 70
dst6::Boolean
 

   (64)  true
                                                                Type: Boolean
--R 
--R
--R   (64)  true
--R                                                                Type: Boolean
--E 64

--S 65 of 70
f3:Ran:=sqrt(3,5)
 

         5+-+
   (65)  \|3
                                           Type: RealClosure Fraction Integer
--R 
--R
--R         5+-+
--R   (65)  \|3
--R                                           Type: RealClosure Fraction Integer
--E 65

--S 66 of 70
f25:Ran:=sqrt(1/25,5)
 

          +--+
          | 1
   (66)  5|--
         \|25
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          | 1
--R   (66)  5|--
--R         \|25
--R                                           Type: RealClosure Fraction Integer
--E 66

--S 67 of 70
f32:Ran:=sqrt(32/5,5)
 

          +--+
          |32
   (67)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |32
--R   (67)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 67

--S 68 of 70
f27:Ran:=sqrt(27/5,5)
 

          +--+
          |27
   (68)  5|--
         \| 5
                                           Type: RealClosure Fraction Integer
--R 
--R
--R          +--+
--R          |27
--R   (68)  5|--
--R         \| 5
--R                                           Type: RealClosure Fraction Integer
--E 68

--S 69 of 70
dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3**2)
 

          +---------------+
          |   +--+    +--+                         +--+
          |   |27     |32       5+-+2   5+-+       | 1
   (69)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
         \|  \| 5    \| 5                         \|25
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R          +---------------+
--R          |   +--+    +--+                         +--+
--R          |   |27     |32       5+-+2   5+-+       | 1
--R   (69)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
--R         \|  \| 5    \| 5                         \|25
--R                                  Type: Equation RealClosure Fraction Integer
--E 69

--S 70 of 70
dst5::Boolean
 

   (70)  true
                                                                Type: Boolean
--R 
--R
--R   (70)  true
--R                                                                Type: Boolean
--E 70
)spool 
 
Starts dribbling to contfrc.output (2010/3/27, 18:24:38).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from ContinuedFractionXmpPage

--S 1 of 22
c := continuedFraction(314159/100000)
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (1)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 1

--S 2 of 22
partialQuotients c
 

   (2)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (2)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 2

--S 3 of 22
convergents c
 

           22 333 355 9208 9563 76149 314159
   (3)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R           22 333 355 9208 9563 76149 314159
--R   (3)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 3

--S 4 of 22
approximants c
 

                                      ______
           22 333 355 9208 9563 76149 314159
   (4)  [3,--,---,---,----,----,-----,------]
            7 106 113 2931 3044 24239 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R                                      ______
--R           22 333 355 9208 9563 76149 314159
--R   (4)  [3,--,---,---,----,----,-----,------]
--R            7 106 113 2931 3044 24239 100000
--R                                                Type: Stream Fraction Integer
--E 4

--S 5 of 22
pq := partialQuotients(1/c)
 

   (5)  [0,3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 5

--S 6 of 22
continuedFraction(first pq,repeating [1],rest pq)
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (6)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 6

--S 7 of 22
z:=continuedFraction(3,repeating [1],repeating [3,6])
 

   (7)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
   + 
       1 |
     +---+ + ...
     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R     3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
--R         | 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 6
--R                                              Type: ContinuedFraction Integer
--E 7

--S 8 of 22
dens:Stream Integer := cons(1,generate((x+->x+4),6))
 

   (8)  [1,6,10,14,18,22,26,30,34,38,...]
                                                         Type: Stream Integer
--R 
--R
--R   (8)  [1,6,10,14,18,22,26,30,34,38,...]
--R                                                         Type: Stream Integer
--E 8

--S 9 of 22
cf := continuedFraction(0,repeating [1],dens)
 

   (9)
       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
   + 
       1  |     1  |
     +----+ + +----+ + ...
     | 34     | 38
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (9)
--R       1 |     1 |     1  |     1  |     1  |     1  |     1  |     1  |
--R     +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + +----+
--R     | 1     | 6     | 10     | 14     | 18     | 22     | 26     | 30
--R   + 
--R       1  |     1  |
--R     +----+ + +----+ + ...
--R     | 34     | 38
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 22
ccf := convergents cf
 

              6 61  860 15541 342762  8927353 268163352  9126481321
   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
              7 71 1001 18089 398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              6 61  860 15541 342762  8927353 268163352  9126481321
--R   (10)  [0,1,-,--,----,-----,------,--------,---------,-----------,...]
--R              7 71 1001 18089 398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 10

--S 11 of 22
eConvergents := [2*e + 1 for e in ccf]
 

              19 193 2721 49171 1084483 28245729 848456353 28875761731
   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
               7  71 1001 18089  398959 10391023 312129649 10622799089
                                                Type: Stream Fraction Integer
--R 
--R
--R              19 193 2721 49171 1084483 28245729 848456353 28875761731
--R   (11)  [1,3,--,---,----,-----,-------,--------,---------,-----------,...]
--R               7  71 1001 18089  398959 10391023 312129649 10622799089
--R                                                Type: Stream Fraction Integer
--E 11

--S 12 of 22
eConvergents :: Stream Float
 

   (12)
   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (12)
--R   [1.0, 3.0, 2.7142857142 857142857, 2.7183098591 549295775,
--R    2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113,
--R    2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354,
--R    ...]
--R                                                           Type: Stream Float
--E 12

--S 13 of 22
exp 1.0
 

   (13)  2.7182818284 590452354
                                                                  Type: Float
--R 
--R
--R   (13)  2.7182818284 590452354
--R                                                                  Type: Float
--E 13

--S 14 of 22
cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])
 

   (14)
           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
   + 
       289 |     361 |
     +-----+ + +-----+ + ...
     |  2      |  2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (14)
--R           1 |     9 |     25 |     49 |     81 |     121 |     169 |     225 |
--R     1 + +---+ + +---+ + +----+ + +----+ + +----+ + +-----+ + +-----+ + +-----+
--R         | 2     | 2     | 2      | 2      | 2      |  2      |  2      |  2
--R   + 
--R       289 |     361 |
--R     +-----+ + +-----+ + ...
--R     |  2      |  2
--R                                              Type: ContinuedFraction Integer
--E 14

--S 15 of 22
ccf := convergents cf
 

            3 15 105 315 3465 45045 45045 765765 14549535
   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
            2 13  76 263 2578 36979 33976 622637 11064338
                                                Type: Stream Fraction Integer
--R 
--R
--R            3 15 105 315 3465 45045 45045 765765 14549535
--R   (15)  [1,-,--,---,---,----,-----,-----,------,--------,...]
--R            2 13  76 263 2578 36979 33976 622637 11064338
--R                                                Type: Stream Fraction Integer
--E 15

--S 16 of 22
piConvergents := [4/p for p in ccf]
 

            8 52 304 1052 10312 147916 135904 2490548 44257352
   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
            3 15 105  315  3465  45045  45045  765765 14549535
                                                Type: Stream Fraction Integer
--R 
--R
--R            8 52 304 1052 10312 147916 135904 2490548 44257352
--R   (16)  [4,-,--,---,----,-----,------,------,-------,--------,...]
--R            3 15 105  315  3465  45045  45045  765765 14549535
--R                                                Type: Stream Fraction Integer
--E 16

--S 17 of 22
piConvergents :: Stream Float
 

   (17)
   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
    3.0418396189 294022111, ...]
                                                           Type: Stream Float
--R 
--R
--R   (17)
--R   [4.0, 2.6666666666 666666667, 3.4666666666 666666667,
--R    2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462,
--R    3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953,
--R    3.0418396189 294022111, ...]
--R                                                           Type: Stream Float
--E 17

--S 18 of 22
continuedFraction((- 122 + 597*%i)/(4 - 4*%i))
 

                            1    |         1     |
   (18)  - 90 + 59%i + +---------+ + +-----------+
                       | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1    |         1     |
--R   (18)  - 90 + 59%i + +---------+ + +-----------+
--R                       | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 18

--S 19 of 22
r : Fraction UnivariatePolynomial(x,Fraction Integer)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 19

--S 20 of 22
r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))
 

           2
          x  - 3x + 2
   (20)  ------------
          2
         x  - 7x + 12
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R           2
--R          x  - 3x + 2
--R   (20)  ------------
--R          2
--R         x  - 7x + 12
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 20

--S 21 of 22
continuedFraction r
 

                  1    |         1     |
   (21)  1 + +---------+ + +-----------+
             | 1     9     | 16     40
             | - x - -     | -- x - --
             | 4     8     |  3      3
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                  1    |         1     |
--R   (21)  1 + +---------+ + +-----------+
--R             | 1     9     | 16     40
--R             | - x - -     | -- x - --
--R             | 4     8     |  3      3
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 21

--S 22 of 22
[i*i for i in convergents(z) :: Stream Float]
 

   (22)
   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
    ...]
                                                           Type: Stream Float
--R 
--R
--R   (22)
--R   [9.0, 11.1111111111 11111111, 10.9944598337 9501385, 11.0002777777 77777778,
--R    10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446,
--R    11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066,
--R    ...]
--R                                                           Type: Stream Float
--E 22
)spool
 
Starts dribbling to dhtri.output (2010/3/27, 18:24:57).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 5
tri2tri(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  n1 := triangleNormal(t1)
  n2 := triangleNormal(t2)
  tet2tet(concat(t1, n1), concat(t2, n2))
 
   Function declaration tri2tri : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tri2tri : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 5
tet2tet(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  m1 := makeColumnMatrix t1
  m2 := makeColumnMatrix t2
  m2 * inverse(m1)
 
   Function declaration tet2tet : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tet2tet : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 5
makeColumnMatrix(t) ==
  m := new(4,4,0)$DHMATRIX(DoubleFloat)
  for x in t for i in 1..repeat
    for j in 1..3 repeat
      m(j,i) := x.j
    m(4,i) := 1
  m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
triangleNormal(t) ==
  a := triangleArea t
  p1 := t.2 - t.1
  p2 := t.3 - t.2
  c := cross(p1, p2)
  len := length(c)
  len = 0 => error "degenerate triangle!"
  c := (1/len)*c
  t.1 + sqrt(a) * c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
triangleArea t ==
  a := length(t.2 - t.1)
  b := length(t.3 - t.2)
  c := length(t.1 - t.3)
  s := (a+b+c)/2
  sqrt(s*(s-a)*(s-b)*(s-c))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
)spool
 
Starts dribbling to bug10069.output (2010/3/27, 18:23:22).
)set message test on
 
)set message auto off
 
)clear all
 

)set break resume
 

--S 1  of 8
cot(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   csc: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   csc: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 1

--S 2 of 8
csc(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   csc: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   csc: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 2

--S 3 of 8
asec(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   asec: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   asec: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 3

--S 4 of 8
acsc(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   acsc: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   acsc: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 4

--S 5 of 8
asech(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   asech: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   asech: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 5

--S 6 of 8
acsch(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   acsch: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   acsch: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 6

--S 7 of 8
coth(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   csch: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   csch: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 7

--S 8 of 8
acoth(0.0)
 
 
Daly Bug
   >> Error detected within library code:
   acoth: no reciprocal

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   acoth: no reciprocal
--R
--R   Continuing to read the file...
--R
--E 8
)spool
 
Starts dribbling to roman.output (2010/3/27, 18:36:56).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
f := operator 'f
 

   (1)  f
                                                          Type: BasicOperator
--R 
--R
--R   (1)  f
--R                                                          Type: BasicOperator
--E 1

--S 2 of 10
D(f x,x,7)
 

         (vii)
   (2)  f     (x)

                                                     Type: Expression Integer
--R 
--R
--R         (vii)
--R   (2)  f     (x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 10
a := roman(1978 - 1965)
 

   (3)  XIII
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XIII
--R                                                           Type: RomanNumeral
--E 3

--S 4 of 10
x : UTS(ROMAN,'x,0) := x
 

   (4)  x
                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--R 
--R
--R   (4)  x
--R                               Type: UnivariateTaylorSeries(RomanNumeral,x,0)
--E 4

--S 5 of 10
recip(1 - x - x**2)
 

   (5)
                 2        3      4         5         6        7          8
     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
   + 
         9           10      11
     LV x  + LXXXIX x   + O(x  )
                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--R 
--R
--R   (5)
--R                 2        3      4         5         6        7          8
--R     I + x + II x  + III x  + V x  + VIII x  + XIII x  + XXI x  + XXXIV x
--R   + 
--R         9           10      11
--R     LV x  + LXXXIX x   + O(x  )
--R                    Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)
--E 5

--S 6 of 10
m : MATRIX FRAC ROMAN
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
m := matrix [[1/(i + j) for i in 1..3] for j in 1..3]
 

        + I    I    I+
        |--   ---  --|
        |II   III  IV|
        |            |
        | I    I   I |
   (7)  |---  --   - |
        |III  IV   V |
        |            |
        | I    I    I|
        |--    -   --|
        +IV    V   VI+
                                           Type: Matrix Fraction RomanNumeral
--R 
--R
--R        + I    I    I+
--R        |--   ---  --|
--R        |II   III  IV|
--R        |            |
--R        | I    I   I |
--R   (7)  |---  --   - |
--R        |III  IV   V |
--R        |            |
--R        | I    I    I|
--R        |--    -   --|
--R        +IV    V   VI+
--R                                           Type: Matrix Fraction RomanNumeral
--E 7

--S 8 of 10
inverse m
 

        +LXXII   - CCXL    CLXXX +
        |                        |
   (8)  |- CCXL    CM     - DCCXX|
        |                        |
        +CLXXX   - DCCXX    DC   +
                                Type: Union(Matrix Fraction RomanNumeral,...)
--R 
--R
--R        +LXXII   - CCXL    CLXXX +
--R        |                        |
--R   (8)  |- CCXL    CM     - DCCXX|
--R        |                        |
--R        +CLXXX   - DCCXX    DC   +
--R                                Type: Union(Matrix Fraction RomanNumeral,...)
--E 8

--S 9 of 10
y := factorial 10
 

   (9)  3628800
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  3628800
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 10
roman y
 

   (10)
  ((((I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))(
  (I)) MMMMMMMMDCCC
                                                           Type: RomanNumeral
--R 
--R
--R   (10)
--R  ((((I))))((((I))))((((I)))) (((I)))(((I)))(((I)))(((I)))(((I)))(((I))) ((I))(
--R  (I)) MMMMMMMMDCCC
--R                                                           Type: RomanNumeral
--E 10
)spool 
 
Starts dribbling to unit-macro.output (2010/3/27, 18:41:39).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 9
)lisp (trace |clearParserMacro| |displayMacro| |getParserMacroNames|)
 
Value = (|clearParserMacro| |displayMacro| |getParserMacroNames|)
--R 
--RValue = (|clearParserMacro| |displayMacro| |getParserMacroNames|)
--E 1

--S 2 of 9
a ==> 3
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 9
a ==> 4
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 9
b ==> 7
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 9
)d macros
 
  1> (|getParserMacroNames|)
  <1 (|getParserMacroNames| (|b| |a|))

User-defined macros:
   b ==> 7
   a ==> 4

System-defined macros:
  1> (|displayMacro| |%e|)
   macro %e () == exp(1)
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%i|)
   macro %i () == complex(0,1)
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%infinity|)
   macro %infinity () == infinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%minusInfinity|)
   macro %minusInfinity () == minusInfinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%pi|)
   macro %pi () == pi()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%plusInfinity|)
   macro %plusInfinity () == plusInfinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| SF)
   macro SF () == DoubleFloat()
  <1 (|displayMacro| NIL)
--R 
--R  1> (|getParserMacroNames|)
--R  <1 (|getParserMacroNames| (|b| |a|))
--R
--RUser-defined macros:
--R   b ==> 7
--R   a ==> 4
--R
--RSystem-defined macros:
--R  1> (|displayMacro| |%e|)
--R   macro %e () == exp(1)
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%i|)
--R   macro %i () == complex(0,1)
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%infinity|)
--R   macro %infinity () == infinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%minusInfinity|)
--R   macro %minusInfinity () == minusInfinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%pi|)
--R   macro %pi () == pi()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%plusInfinity|)
--R   macro %plusInfinity () == plusInfinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| SF)
--R   macro SF () == DoubleFloat()
--R  <1 (|displayMacro| NIL)
--E 5

--S 6 of 9
)clear prop a
 
  1> (|getParserMacroNames|)
  <1 (|getParserMacroNames| (|b| |a|))
  1> (|clearParserMacro| |a|)
  <1 (|clearParserMacro| ((|b| |mbody| ((|integer| (|posn| (0 "b ==> 7" 27 27 "/home/camm/debian/axiom/axiom-20091101/int/input/unit-macro.input") . 6)) . "7")) (|a| |mbody| ((|integer| (|posn| (0 "a ==> 3" 15 15 "/home/camm/debian/axiom/axiom-20091101/int/input/unit-macro.input") . 6)) . "3"))))
--R 
--R  1> (|getParserMacroNames|)
--R  <1 (|getParserMacroNames| (|b| |a|))
--R  1> (|clearParserMacro| |a|)
--I  <1 (|clearParserMacro| ((|b| |mbody| ((|integer| (|posn| (0 "b ==> 7" 9 9 "/tmp/i.input") . 6)) . "7")) (|a| |mbody| ((|integer| (|posn| (0 "a ==> 3" 7 7 "/tmp/i.input") . 6)) . "3"))))
--E 6

--S 7 of 9
)d macros
 
  1> (|getParserMacroNames|)
  <1 (|getParserMacroNames| (|b| |a|))

User-defined macros:
   b ==> 7
   a ==> 3

System-defined macros:
  1> (|displayMacro| |%e|)
   macro %e () == exp(1)
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%i|)
   macro %i () == complex(0,1)
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%infinity|)
   macro %infinity () == infinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%minusInfinity|)
   macro %minusInfinity () == minusInfinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%pi|)
   macro %pi () == pi()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%plusInfinity|)
   macro %plusInfinity () == plusInfinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| SF)
   macro SF () == DoubleFloat()
  <1 (|displayMacro| NIL)
--R 
--R  1> (|getParserMacroNames|)
--R  <1 (|getParserMacroNames| (|b| |a|))
--R
--RUser-defined macros:
--R   b ==> 7
--R   a ==> 3
--R
--RSystem-defined macros:
--R  1> (|displayMacro| |%e|)
--R   macro %e () == exp(1)
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%i|)
--R   macro %i () == complex(0,1)
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%infinity|)
--R   macro %infinity () == infinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%minusInfinity|)
--R   macro %minusInfinity () == minusInfinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%pi|)
--R   macro %pi () == pi()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%plusInfinity|)
--R   macro %plusInfinity () == plusInfinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| SF)
--R   macro SF () == DoubleFloat()
--R  <1 (|displayMacro| NIL)
--E 7

--S 8 of 9
)clear prop a
 
  1> (|getParserMacroNames|)
  <1 (|getParserMacroNames| (|b| |a|))
  1> (|clearParserMacro| |a|)
  <1 (|clearParserMacro| ((|b| |mbody| ((|integer| (|posn| (0 "b ==> 7" 27 27 "/home/camm/debian/axiom/axiom-20091101/int/input/unit-macro.input") . 6)) . "7"))))
--R 
--R  1> (|getParserMacroNames|)
--R  <1 (|getParserMacroNames| (|b| |a|))
--R  1> (|clearParserMacro| |a|)
--I  <1 (|clearParserMacro| ((|b| |mbody| ((|integer| (|posn| (0 "b ==> 7" 9 9 "/tmp/i.input") . 6)) . "7"))))
--E 8

--S 9 of 9
)d macros
 
  1> (|getParserMacroNames|)
  <1 (|getParserMacroNames| (|b|))

User-defined macros:
   b ==> 7

System-defined macros:
  1> (|displayMacro| |%e|)
   macro %e () == exp(1)
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%i|)
   macro %i () == complex(0,1)
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%infinity|)
   macro %infinity () == infinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%minusInfinity|)
   macro %minusInfinity () == minusInfinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%pi|)
   macro %pi () == pi()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| |%plusInfinity|)
   macro %plusInfinity () == plusInfinity()
  <1 (|displayMacro| NIL)
  1> (|displayMacro| SF)
   macro SF () == DoubleFloat()
  <1 (|displayMacro| NIL)
--R 
--R  1> (|getParserMacroNames|)
--R  <1 (|getParserMacroNames| (|b|))
--R
--RUser-defined macros:
--R   b ==> 7
--R
--RSystem-defined macros:
--R  1> (|displayMacro| |%e|)
--R   macro %e () == exp(1)
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%i|)
--R   macro %i () == complex(0,1)
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%infinity|)
--R   macro %infinity () == infinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%minusInfinity|)
--R   macro %minusInfinity () == minusInfinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%pi|)
--R   macro %pi () == pi()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| |%plusInfinity|)
--R   macro %plusInfinity () == plusInfinity()
--R  <1 (|displayMacro| NIL)
--R  1> (|displayMacro| SF)
--R   macro SF () == DoubleFloat()
--R  <1 (|displayMacro| NIL)
--E 9

)spool
 
Starts dribbling to array2.output (2010/3/27, 18:23:7).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 20
arr : ARRAY2 INT := new(5,4,0)
 

        +0  0  0  0+
        |          |
        |0  0  0  0|
        |          |
   (1)  |0  0  0  0|
        |          |
        |0  0  0  0|
        |          |
        +0  0  0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R        +0  0  0  0+
--R        |          |
--R        |0  0  0  0|
--R        |          |
--R   (1)  |0  0  0  0|
--R        |          |
--R        |0  0  0  0|
--R        |          |
--R        +0  0  0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 1

--S 2 of 20
setelt(arr,1,1,17)
 

   (2)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  17
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 20
arr
 

        +17  0  0  0+
        |           |
        |0   0  0  0|
        |           |
   (3)  |0   0  0  0|
        |           |
        |0   0  0  0|
        |           |
        +0   0  0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R        +17  0  0  0+
--R        |           |
--R        |0   0  0  0|
--R        |           |
--R   (3)  |0   0  0  0|
--R        |           |
--R        |0   0  0  0|
--R        |           |
--R        +0   0  0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 3

--S 4 of 20
elt(arr,1,1)
 

   (4)  17
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  17
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 20
arr(3,2) := 15
 

   (5)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  15
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 20
arr(3,2)
 

   (6)  15
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  15
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 20
row(arr,1)
 

   (7)  [17,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (7)  [17,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 7

--S 8 of 20
column(arr,1)
 

   (8)  [17,0,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (8)  [17,0,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 8

--S 9 of 20
nrows(arr)
 

   (9)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  5
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 20
ncols(arr)
 

   (10)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  4
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 20
map(-,arr)
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (11)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (11)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 11

--S 12 of 20
map((x +-> x + x),arr)
 

         +34  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (12)  |0   30  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +34  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (12)  |0   30  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 12

--S 13 of 20
arrc := copy(arr)
 

         +17  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (13)  |0   15  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +17  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (13)  |0   15  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 13

--S 14 of 20
map!(-,arrc)
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (14)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (14)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 14

--S 15 of 20
arrc
 

         +- 17   0    0  0+
         |                |
         | 0     0    0  0|
         |                |
   (15)  | 0    - 15  0  0|
         |                |
         | 0     0    0  0|
         |                |
         + 0     0    0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +- 17   0    0  0+
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R   (15)  | 0    - 15  0  0|
--R         |                |
--R         | 0     0    0  0|
--R         |                |
--R         + 0     0    0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 15

--S 16 of 20
arr
 

         +17  0   0  0+
         |            |
         |0   0   0  0|
         |            |
   (16)  |0   15  0  0|
         |            |
         |0   0   0  0|
         |            |
         +0   0   0  0+
                                            Type: TwoDimensionalArray Integer
--R 
--R
--R         +17  0   0  0+
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R   (16)  |0   15  0  0|
--R         |            |
--R         |0   0   0  0|
--R         |            |
--R         +0   0   0  0+
--R                                            Type: TwoDimensionalArray Integer
--E 16

--S 17 of 20
member?(17,arr)
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 20
member?(10317,arr)
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 20
count(17,arr)
 

   (19)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  1
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 20
count(0,arr)
 

   (20)  18
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  18
--R                                                        Type: PositiveInteger
--E 20
)spool
 
Starts dribbling to eq.output (2010/3/27, 18:25:31).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 12
eq1 := 3*x + 4*y = 5
 

   (1)  4y + 3x= 5
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (1)  4y + 3x= 5
--R                                            Type: Equation Polynomial Integer
--E 1

--S 2 of 12
eq2 := 2*x + 2*y = 3
 

   (2)  2y + 2x= 3
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (2)  2y + 2x= 3
--R                                            Type: Equation Polynomial Integer
--E 2

--S 3 of 12
lhs eq1
 

   (3)  4y + 3x
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)  4y + 3x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 12
rhs eq1
 

   (4)  5
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  5
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 12
eq1 + eq2
 

   (5)  6y + 5x= 8
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (5)  6y + 5x= 8
--R                                            Type: Equation Polynomial Integer
--E 5

--S 6 of 12
eq1 * eq2
 

          2             2
   (6)  8y  + 14x y + 6x = 15
                                            Type: Equation Polynomial Integer
--R 
--R
--R          2             2
--R   (6)  8y  + 14x y + 6x = 15
--R                                            Type: Equation Polynomial Integer
--E 6

--S 7 of 12
2*eq2 - eq1
 

   (7)  x= 1
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (7)  x= 1
--R                                            Type: Equation Polynomial Integer
--E 7

--S 8 of 12
eq1**2
 

           2             2
   (8)  16y  + 24x y + 9x = 25
                                            Type: Equation Polynomial Integer
--R 
--R
--R           2             2
--R   (8)  16y  + 24x y + 9x = 25
--R                                            Type: Equation Polynomial Integer
--E 8

--S 9 of 12
if x+1 = y then "equal" else "unequal"
 

   (9)  "unequal"
                                                                 Type: String
--R 
--R
--R   (9)  "unequal"
--R                                                                 Type: String
--E 9

--S 10 of 12
eqpol := x+1 = y
 

   (10)  x + 1= y
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (10)  x + 1= y
--R                                            Type: Equation Polynomial Integer
--E 10

--S 11 of 12
if eqpol then "equal" else "unequal"
 

   (11)  "unequal"
                                                                 Type: String
--R 
--R
--R   (11)  "unequal"
--R                                                                 Type: String
--E 11

--S 12 of 12
eqpol::Boolean
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12
)spool
 
Starts dribbling to Operator.output (2010/3/27, 18:46:10).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 21
R := SQMATRIX(2, INT)
 

   (1)  SquareMatrix(2,Integer)
                                                                 Type: Domain
--R 
--R
--R   (1)  SquareMatrix(2,Integer)
--R                                                                 Type: Domain
--E 1

--S 2 of 21
t := operator("tilde") :: OP(R)
 

   (2)  tilde
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R   (2)  tilde
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 2

--S 3 of 21
)set expose add constructor Operator
 
   Operator is now explicitly exposed in frame initial 
--R 
--I   Operator is now explicitly exposed in frame frame0 
--E 3

--S 4 of 21
evaluate(t, m +-> transpose m)
 

   (3)  tilde
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R   (3)  tilde
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 4

--S 5 of 21
s : R := matrix [ [0, 1], [1, 0] ]
 

        +0  1+
   (4)  |    |
        +1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  1+
--R   (4)  |    |
--R        +1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 5

--S 6 of 21
rho := t * s
 

             +0  1+
   (5)  tilde|    |
             +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R             +0  1+
--R   (5)  tilde|    |
--R             +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 6

--S 7 of 21
z := rho**4 - 1
 

                   +0  1+     +0  1+     +0  1+     +0  1+
   (6)  - 1 + tilde|    |tilde|    |tilde|    |tilde|    |
                   +1  0+     +1  0+     +1  0+     +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R                   +0  1+     +0  1+     +0  1+     +0  1+
--R   (6)  - 1 + tilde|    |tilde|    |tilde|    |tilde|    |
--R                   +1  0+     +1  0+     +1  0+     +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 7

--S 8 of 21
m:R := matrix [ [1, 2], [3, 4] ]
 

        +1  2+
   (7)  |    |
        +3  4+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +1  2+
--R   (7)  |    |
--R        +3  4+
--R                                                Type: SquareMatrix(2,Integer)
--E 8

--S 9 of 21
z m
 

        +0  0+
   (8)  |    |
        +0  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +0  0+
--R   (8)  |    |
--R        +0  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 9

--S 10 of 21
rho m
 

        +3  1+
   (9)  |    |
        +4  2+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        +3  1+
--R   (9)  |    |
--R        +4  2+
--R                                                Type: SquareMatrix(2,Integer)
--E 10

--S 11 of 21
rho rho m
 

         +4  3+
   (10)  |    |
         +2  1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +4  3+
--R   (10)  |    |
--R         +2  1+
--R                                                Type: SquareMatrix(2,Integer)
--E 11

--S 12 of 21
(rho^3) m
 

         +2  4+
   (11)  |    |
         +1  3+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +2  4+
--R   (11)  |    |
--R         +1  3+
--R                                                Type: SquareMatrix(2,Integer)
--E 12

--S 13 of 21
b := t * s - s * t
 

           +0  1+             +0  1+
   (12)  - |    |tilde + tilde|    |
           +1  0+             +1  0+
                                       Type: Operator SquareMatrix(2,Integer)
--R 
--R
--R           +0  1+             +0  1+
--R   (12)  - |    |tilde + tilde|    |
--R           +1  0+             +1  0+
--R                                       Type: Operator SquareMatrix(2,Integer)
--E 13

--S 14 of 21
b m
 

         +1  - 3+
   (13)  |      |
         +3  - 1+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R         +1  - 3+
--R   (13)  |      |
--R         +3  - 1+
--R                                                Type: SquareMatrix(2,Integer)
--E 14

--S 15 of 21
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 21
dx := operator("D") :: OP(POLY FRAC INT)
 

   (15)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (15)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 16

--S 17 of 21
evaluate(dx, p +-> D(p, 'x))
 

   (16)  D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R
--R   (16)  D
--R                                   Type: Operator Polynomial Fraction Integer
--E 17

--S 18 of 21
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 21
L 15
 
   Compiling function L with type Integer -> Polynomial Fraction 
      Integer 
   Compiling function L as a recurrence relation.

   (18)
     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
       2048          2048           2048           2048          2048
   + 
       2909907  5   255255  3   6435
     - ------- x  + ------ x  - ---- x
         2048        2048       2048
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function L with type Integer -> Polynomial Fraction 
--R      Integer 
--R   Compiling function L as a recurrence relation.
--R
--R   (18)
--R     9694845  15   35102025  13   50702925  11   37182145  9   14549535  7
--R     ------- x   - -------- x   + -------- x   - -------- x  + -------- x
--R       2048          2048           2048           2048          2048
--R   + 
--R       2909907  5   255255  3   6435
--R     - ------- x  + ------ x  - ---- x
--R         2048        2048       2048
--R                                            Type: Polynomial Fraction Integer
--E 19

--S 20 of 21
E 15
 
   Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer 

                        2      2
   (19)  240 - 2x D - (x  - 1)D
                                   Type: Operator Polynomial Fraction Integer
--R 
--R   Compiling function E with type PositiveInteger -> Operator 
--R      Polynomial Fraction Integer 
--R
--R                        2      2
--R   (19)  240 - 2x D - (x  - 1)D
--R                                   Type: Operator Polynomial Fraction Integer
--E 20

--S 21 of 21
(E 15)(L 15)
 

   (20)  0
                                            Type: Polynomial Fraction Integer
--R 
--R
--R   (20)  0
--R                                            Type: Polynomial Fraction Integer
--E 21
)spool
 
Starts dribbling to antoine.output (2010/3/27, 18:23:5).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 11
)set expose add con DenavitHartenbergMatrix
 
   DenavitHartenbergMatrix is now explicitly exposed in frame initial 
--R 
--I   DenavitHartenbergMatrix is now explicitly exposed in frame frame0 
--E 1
--S 2 of 11
tri2tri(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  n1 := triangleNormal(t1)
  n2 := triangleNormal(t2)
  tet2tet(concat(t1, n1), concat(t2, n2))
 
   Function declaration tri2tri : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tri2tri : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 2
--S 3 of 11
tet2tet(t1: List Point DoubleFloat, t2: List Point DoubleFloat): DHMATRIX(DoubleFloat) ==
  m1 := makeColumnMatrix t1
  m2 := makeColumnMatrix t2
  m2 * inverse(m1)
 
   Function declaration tet2tet : (List Point DoubleFloat,List Point 
      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration tet2tet : (List Point DoubleFloat,List Point 
--R      DoubleFloat) -> DenavitHartenbergMatrix DoubleFloat has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 3
--S 4 of 11
makeColumnMatrix(t) ==
  m := new(4,4,0)$DHMATRIX(DoubleFloat)
  for x in t for i in 1..repeat
    for j in 1..3 repeat
      m(j,i) := x.j
    m(4,i) := 1
  m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
--S 5 of 11
triangleNormal(t) ==
  a := triangleArea t
  p1 := t.2 - t.1
  p2 := t.3 - t.2
  c := cross(p1, p2)
  len := length(c)
  len = 0 => error "degenerate triangle!"
  c := (1/len)*c
  t.1 + sqrt(a) * c
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5
--S 6 of 11
triangleArea t ==
  a := length(t.2 - t.1)
  b := length(t.3 - t.2)
  c := length(t.1 - t.3)
  s := (a+b+c)/2
  sqrt(s*(s-a)*(s-b)*(s-c))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6
--S 7 of 11
torusRot: DHMATRIX(DoubleFloat)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
--S 8 of 11
drawRings(n) ==
  s := create3Space()$ThreeSpace DoubleFloat
  -- create an identity transformation
  dh:DHMATRIX(DoubleFloat) := identity()
  drawRingsInner(s, n, dh)
  makeViewport3D(s, "Antoine's Necklace")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8
--S 9 of 11
drawRingsInner(s, n, dh) ==
  n = 0 =>
    drawRing(s, dh)
    void()
  t := 0.0@DoubleFloat             -- the current angle around the ring
  p := 0.0@DoubleFloat             -- the angle of the subring from the plane
  tr := 1.0@DoubleFloat            -- the amount to translate the subring
  inc := 0.1@DoubleFloat           -- translation increment
  -- subdivide the ring into 10 linked rings
  for i in 1..10 repeat
    tr := tr + inc
    inc := -inc
    dh' := dh * rotatez(t) * translate(tr, 0.0@DoubleFloat, 0.0@DoubleFloat) *
           rotatey(p) * scale(0.35@DoubleFloat, 0.48@DoubleFloat, 0.4@DoubleFloat)
    drawRingsInner(s, n-1, dh')
    t := t + 36.0@DoubleFloat
    p := p + 90.0@DoubleFloat
  void()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9
--S 10 of 11
drawRing(s, dh) ==
  free torusRot
  torusRot := dh
  makeObject(torus, 0..2*%pi, 0..2*%pi, var1Steps == 6, space == s,
             var2Steps == 15)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10
--S 11 of 11
torus(u ,v) ==
  cu := cos(u)/6
  torusRot * point [(1+cu)*cos(v), (1+cu)*sin(v), (sin u)/6]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11
)spool
 
Starts dribbling to binary.output (2010/3/27, 18:23:12).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 7
r := binary(22/7)
 

           ___
   (1)  11.001
                                                        Type: BinaryExpansion
--R 
--R
--R           ___
--R   (1)  11.001
--R                                                        Type: BinaryExpansion
--E 1

--S 2 of 7
r + binary(6/7)
 

   (2)  100
                                                        Type: BinaryExpansion
--R 
--R
--R   (2)  100
--R                                                        Type: BinaryExpansion
--E 2

--S 3 of 7
[binary(1/i) for i in 102..106] 
 

   (3)
       ________    ___________________________________________________
   [0.000000101, 0.000000100111110001000101100101111001110010010101001,
         ____________    ____________
    0.000000100111011, 0.000000100111,
       ____________________________________________________
    0.00000010011010100100001110011111011001010110111100011]
                                                   Type: List BinaryExpansion
--R 
--R
--R   (3)
--R       ________    ___________________________________________________
--R   [0.000000101, 0.000000100111110001000101100101111001110010010101001,
--R         ____________    ____________
--R    0.000000100111011, 0.000000100111,
--R       ____________________________________________________
--R    0.00000010011010100100001110011111011001010110111100011]
--R                                                   Type: List BinaryExpansion
--E 3

--S 4 of 7
binary(1/1007) 
 

   (4)
   0.
     OVERBAR
        00000000010000010001010010010111100000111111000010111111001011000111110
          100010011100100110011000110010010101011110110100110000000011000011001
          111011100011010001011110100100011110110000101011101110011101010111001
          100101001011100000001110001111001000000100100100110111001010100111010
          001101110110101110001001000001100101101100000010110010111110001010000
          010101010110101100000110110111010010101111111010111010100110010000101
          0011011000100110001000100001000011000111010011110001
                                                        Type: BinaryExpansion
--R 
--R
--R   (4)
--R   0.
--R     OVERBAR
--R        00000000010000010001010010010111100000111111000010111111001011000111110
--R          100010011100100110011000110010010101011110110100110000000011000011001
--R          111011100011010001011110100100011110110000101011101110011101010111001
--R          100101001011100000001110001111001000000100100100110111001010100111010
--R          001101110110101110001001000001100101101100000010110010111110001010000
--R          010101010110101100000110110111010010101111111010111010100110010000101
--R          0011011000100110001000100001000011000111010011110001
--R                                                        Type: BinaryExpansion
--E 4

--S 5 of 7
p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9)
 

             2     __      ______
   (5)  0.01x  + 0.10x + 0.011100
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R             2     __      ______
--R   (5)  0.01x  + 0.10x + 0.011100
--R                                             Type: Polynomial BinaryExpansion
--E 5

--S 6 of 7
q := D(p, x)
 

                 __
   (6)  0.1x + 0.10
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R                 __
--R   (6)  0.1x + 0.10
--R                                             Type: Polynomial BinaryExpansion
--E 6

--S 7 of 7
g := gcd(p, q)
 

              __
   (7)  x + 1.01
                                             Type: Polynomial BinaryExpansion
--R 
--R
--R              __
--R   (7)  x + 1.01
--R                                             Type: Polynomial BinaryExpansion
--E 7
)spool
 
Starts dribbling to curl.output (2010/3/27, 18:24:38).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 1
draw(curve(sin(t)*sin(2*t)*sin(3*t),sin(4*t)*sin(5*t)*sin(6*t)),t = 0..2*%pi)
 
   Compiling function %B with type DoubleFloat -> DoubleFloat 
   Compiling function %D with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (1)  TwoDimensionalViewport: "DSIN(t)*DSIN(2*t)*DSIN(3*t)"
                                                 Type: TwoDimensionalViewport
--R 
--R   Compiling function %B with type DoubleFloat -> DoubleFloat 
--R   Compiling function %D with type DoubleFloat -> DoubleFloat 
--R   Graph data being transmitted to the viewport manager...
--R   AXIOM2D data being transmitted to the viewport manager...
--R
--R   (1)  TwoDimensionalViewport: "DSIN(t)*DSIN(2*t)*DSIN(3*t)"
--R                                                 Type: TwoDimensionalViewport
--E 1
)spool
 
Starts dribbling to Vector.output (2010/3/27, 18:46:42).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 11
u : VECTOR INT := new(5,12)
 

   (1)  [12,12,12,12,12]
                                                         Type: Vector Integer
--R 
--R
--R   (1)  [12,12,12,12,12]
--R                                                         Type: Vector Integer
--E 1

--S 2 of 11
v : VECTOR INT := vector([1,2,3,4,5])
 

   (2)  [1,2,3,4,5]
                                                         Type: Vector Integer
--R 
--R
--R   (2)  [1,2,3,4,5]
--R                                                         Type: Vector Integer
--E 2

--S 3 of 11
#(v)
 

   (3)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  5
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 11
v.2
 

   (4)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  2
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 11
v.3 := 99
 

   (5)  99
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  99
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 11
v
 

   (6)  [1,2,99,4,5]
                                                         Type: Vector Integer
--R 
--R
--R   (6)  [1,2,99,4,5]
--R                                                         Type: Vector Integer
--E 6

--S 7 of 11
5 * v
 

   (7)  [5,10,495,20,25]
                                                         Type: Vector Integer
--R 
--R
--R   (7)  [5,10,495,20,25]
--R                                                         Type: Vector Integer
--E 7

--S 8 of 11
v * 7
 

   (8)  [7,14,693,28,35]
                                                         Type: Vector Integer
--R 
--R
--R   (8)  [7,14,693,28,35]
--R                                                         Type: Vector Integer
--E 8

--S 9 of 11
w : VECTOR INT := vector([2,3,4,5,6])
 

   (9)  [2,3,4,5,6]
                                                         Type: Vector Integer
--R 
--R
--R   (9)  [2,3,4,5,6]
--R                                                         Type: Vector Integer
--E 9

--S 10 of 11
v + w
 

   (10)  [3,5,103,9,11]
                                                         Type: Vector Integer
--R 
--R
--R   (10)  [3,5,103,9,11]
--R                                                         Type: Vector Integer
--E 10

--S 11 of 11
v - w
 

   (11)  [- 1,- 1,95,- 1,- 1]
                                                         Type: Vector Integer
--R 
--R
--R   (11)  [- 1,- 1,95,- 1,- 1]
--R                                                         Type: Vector Integer
--E 11
)spool
 
Starts dribbling to lpoly.output (2010/3/27, 18:28:55).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 28
RN    := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 28
Lpoly := LiePolynomial(Symbol,RN)
 

   (2)  LiePolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  LiePolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 28
Dpoly := XDPOLY(Symbol,RN)
 

   (3)  XDistributedPolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (3)  XDistributedPolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 3

--S 4 of 28
Lword := LyndonWord Symbol
 

   (4)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 28
a:Symbol := 'a
 

   (5)  a
                                                                 Type: Symbol
--R 
--R
--R   (5)  a
--R                                                                 Type: Symbol
--E 5

--S 6 of 28
b:Symbol := 'b
 

   (6)  b
                                                                 Type: Symbol
--R 
--R
--R   (6)  b
--R                                                                 Type: Symbol
--E 6

--S 7 of 28
c:Symbol := 'c
 

   (7)  c
                                                                 Type: Symbol
--R 
--R
--R   (7)  c
--R                                                                 Type: Symbol
--E 7

--S 8 of 28
aa: Lpoly := a
 

   (8)  [a]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (8)  [a]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 8

--S 9 of 28
bb: Lpoly := b
 

   (9)  [b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (9)  [b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 9

--S 10 of 28
cc: Lpoly := c
 

   (10)  [c]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (10)  [c]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 10

--S 11 of 28
p : Lpoly := [aa,bb]
 

   (11)  [a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (11)  [a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 11

--S 12 of 28
q : Lpoly := [p,bb]
 

             2
   (12)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R             2
--R   (12)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 12

--S 13 of 28
liste : List Lword := LyndonWordsList([a,b], 4)
 

                          2       2    3     2 2      3
   (13)  [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R                          2       2    3     2 2      3
--R   (13)  [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 13

--S 14 of 28
r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly
 

                    2         2
   (14)  [a b] + 3[a b] + [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                    2         2
--R   (14)  [a b] + 3[a b] + [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 14

--S 15 of 28
s:Lpoly := [p,r]
 

              2                 2
   (15)  - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R              2                 2
--R   (15)  - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 15

--S 16 of 28
t:Lpoly  := s  + 2*LiePoly(liste.3) - 5*LiePoly(liste.5)
 

                       2       2                 2
   (16)  2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                       2       2                 2
--R   (16)  2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 16

--S 17 of 28
degree t
 

   (17)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  5
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 28
mirror t
 

                         2       2                 2
   (18)  - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                         2       2                 2
--R   (18)  - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 18

--S 19 of 28
Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == [[p,q]$Lpoly, r] + [[q,r]$Lpoly, p] + [[r,p]$Lpoly, q]
 
   Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer
      ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol,
      Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer
--R      ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol,
--R      Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 19

--S 20 of 28
test: Lpoly := Jacobi(a,b,b)
 
   Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction 
      Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(
      Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction 
      Integer) 

   (20)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R   Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction 
--R      Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(
--R      Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction 
--R      Integer) 
--R
--R   (20)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 20

--S 21 of 28
test: Lpoly := Jacobi(p,q,r)
 

   (21)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (21)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 21

--S 22 of 28
test: Lpoly := Jacobi(r,s,t)
 

   (22)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (22)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 22

--S 23 of 28
eval(p, a, p)$Lpoly
 

             2
   (23)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R             2
--R   (23)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 23

--S 24 of 28
eval(p, [a,b], [2*bb, 3*aa])$Lpoly
 

   (24)  - 6[a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (24)  - 6[a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 24

--S 25 of 28
r: Lpoly := [p,c]
 

   (25)  [a b c] + [a c b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (25)  [a b c] + [a c b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 25

--S 26 of 28
r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly
 

   (26)  - [a b c]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (26)  - [a b c]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 26

--S 27 of 28
r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly
 

   (27)  - [a c b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (27)  - [a c b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 27

--S 28 of 28
r + r1 + r2
 

   (28)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (28)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 28
)spool 
 
Starts dribbling to BalancedBinaryTree.output (2010/3/27, 18:41:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 7
lm := [3,5,7,11]
 

   (1)  [3,5,7,11]
                                                   Type: List PositiveInteger
--E 1

--S 2 of 7
t := balancedBinaryTree(#lm, 0)
 

   (2)  [[0,0,0],0,[0,0,0]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--E 2

--S 3 of 7
setleaves!(t,lm)
 

   (3)  [[3,0,5],0,[7,0,11]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--E 3

--S 4 of 7
mapUp!(t,_*)
 

   (4)  1155
                                                        Type: PositiveInteger
--E 4

--S 5 of 7
t
 

   (5)  [[3,15,5],1155,[7,77,11]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--E 5

--S 6 of 7
mapDown!(t,12,_rem)
 

   (6)  [[0,12,2],12,[5,12,1]]
                                  Type: BalancedBinaryTree NonNegativeInteger
--E 6

--S 7 of 7
leaves %
 

   (7)  [0,2,5,1]
                                                Type: List NonNegativeInteger
--E 7

)spool
 
Starts dribbling to fns.output (2010/3/27, 18:26:17).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 20
odd(i) == 2*i - 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 20
[odd(i) for i in 1..10]
 
   Compiling function odd with type PositiveInteger -> Integer 

   (2)  [1,3,5,7,9,11,13,15,17,19]
                                                           Type: List Integer
--R 
--R   Compiling function odd with type PositiveInteger -> Integer 
--R
--R   (2)  [1,3,5,7,9,11,13,15,17,19]
--R                                                           Type: List Integer
--E 2

--S 3 of 20
odd == i +-> 2*i - 1
 
   Compiled code for odd has been cleared.
   1 old definition(s) deleted for function or rule odd 
                                                                   Type: Void
--R 
--R   Compiled code for odd has been cleared.
--R   1 old definition(s) deleted for function or rule odd 
--R                                                                   Type: Void
--E 3

--S 4 of 20
odd(1111)
 
   Compiling function odd with type PositiveInteger -> Integer 

   (4)  2221
                                                        Type: PositiveInteger
--R 
--R   Compiling function odd with type PositiveInteger -> Integer 
--R
--R   (4)  2221
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 20
[i for i in 2.. | prime? i]
 

   (5)  [2,3,5,7,11,13,17,19,23,29,...]
                                                 Type: Stream PositiveInteger
--R 
--R
--R   (5)  [2,3,5,7,11,13,17,19,23,29,...]
--R                                                 Type: Stream PositiveInteger
--E 5

--S 6 of 20
primes := /
 

   (6)  /
                                                             Type: Variable /
--R 
--R
--R   (6)  /
--R                                                             Type: Variable /
--E 6

--S 7 of 20
primes == [p := nextPrime(i = 0 => 2; p) for i in 1..]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7

--S 8 of 20
primes
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 8

--S 9 of 20
primes(20)
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 9

--S 10 of 20
firstPrimes(n) == [primes(i) for i in 1..n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 20
firstPrimes(25)
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 11

--S 12 of 20
primesLessThan(n) == [p for p in primes while p < n]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12

--S 13 of 20
primesLessThan 1000
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 13

--S 14 of 20
isPrime? n == reduce(_or,[n = p for p in primes while n <= p])
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 14

--S 15 of 20
isPrime?(1111)
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 15

--S 16 of 20
twins := [p,p+2 for p in primes | prime?(p+2)]
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
 
Daly Bug
   AXIOM can only iterate over lists now and you supplied an object of 
      type UniversalSegment PositiveInteger .
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R 
--RDaly Bug
--R   AXIOM can only iterate over lists now and you supplied an object of 
--R      type UniversalSegment PositiveInteger .
--E 16

--S 17 of 20
twins := [p, p+2 for i in 1.. | (p := primes(i)) + 2 = primes(i+1)]
 
   There are 1 exposed and 0 unexposed library operations named 
      nextPrime having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op nextPrime
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      nextPrime with argument type(s) 
                             Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   Interpret-Code mode is not supported for stream bodies.
--R 
--R   There are 1 exposed and 0 unexposed library operations named 
--R      nextPrime having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op nextPrime
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R   Cannot find a definition or applicable library operation named 
--R      nextPrime with argument type(s) 
--R                             Polynomial Integer
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   Interpret-Code mode is not supported for stream bodies.
--E 17

--S 18 of 20
firsts := [p for i in 1.. | (p := primes(i)) + 2 = primes(i+1)]
 
   Cannot compile map: primes 
   We will attempt to interpret the code.
 
Daly Bug
   Interpret-Code mode is not supported for stream bodies.
--R 
--R   Cannot compile map: primes 
--R   We will attempt to interpret the code.
--R 
--RDaly Bug
--R   Interpret-Code mode is not supported for stream bodies.
--E 18

--S 19 of 20
twins := [p, p + 2 for p in firsts]
 
 
Daly Bug
   AXIOM cannot iterate with p over your form now. Perhaps you should 
      try using a conversion to make sure your form is a list or 
      stream, for example.
--R 
--R 
--RDaly Bug
--R   AXIOM cannot iterate with p over your form now. Perhaps you should 
--R      try using a conversion to make sure your form is a list or 
--R      stream, for example.
--E 19

--S 20 of 20
twins(i) ==firsts(i),2 + firsts(i)
 
   There are no library operations named firsts 
      Use HyperDoc Browse or issue
                               )what op firsts
      to learn if there is any operation containing " firsts " in its 
      name.
 
Daly Bug
   Cannot find a definition or applicable library operation named 
      firsts with argument type(s) 
                                 Variable i
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named firsts 
--R      Use HyperDoc Browse or issue
--R                               )what op firsts
--R      to learn if there is any operation containing " firsts " in its 
--R      name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named 
--R      firsts with argument type(s) 
--R                                 Variable i
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 20
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read viewdef
 
--Copyright The Numerical Algorithms Group Limited 1994.
-- test for ViewDefaultsPackage package

--Operations to set 2D graph defaults:

axesColorDefault dark blue()
 

   (1)  [Hue: 22  Weight: 1.] from the Dark palette
                                                                Type: Palette

lineColorDefault pastel yellow()
 

   (2)  [Hue: 11  Weight: 1.] from the Pastel palette
                                                                Type: Palette

pointColorDefault bright red()
 

   (3)  [Hue: 1  Weight: 1.] from the Bright palette
                                                                Type: Palette

pointSizeDefault(5)
 

   (4)  5
                                                        Type: PositiveInteger

unitsColorDefault dim green()
 

   (5)  [Hue: 14  Weight: 1.] from the Dim palette
                                                                Type: Palette

viewDefaults()
 
                                                                   Type: Void


--Operations which return 2D graph default information:

axesColorDefault()
 

   (7)  [Hue: 1  Weight: 1.] from the Dim palette
                                                                Type: Palette

lineColorDefault()
 

   (8)  [Hue: 14  Weight: 1.] from the Pastel palette
                                                                Type: Palette

pointColorDefault()
 

   (9)  [Hue: 1  Weight: 1.] from the Bright palette
                                                                Type: Palette

pointColorDefault()
 

   (10)  [Hue: 1  Weight: 1.] from the Bright palette
                                                                Type: Palette

unitsColorDefault()
 

   (11)  [Hue: 11  Weight: 1.] from the Dim palette
                                                                Type: Palette


--Operations to set 3D graph defaults:

tubePointsDefault(6)
 

   (12)  6
                                                        Type: PositiveInteger

tubeRadiusDefault(.2)
 

   (13)  0.20000000000000001
                                                            Type: DoubleFloat

var1StepsDefault(35)
 

   (14)  35
                                                        Type: PositiveInteger

var2StepsDefault(35)
 

   (15)  35
                                                        Type: PositiveInteger

--Operations which return 3D graph default information:

tubePointsDefault()
 

   (16)  6
                                                        Type: PositiveInteger

tubeRadiusDefault()
 

   (17)  0.20000000000000001
                                                            Type: DoubleFloat

var1StepsDefault()
 

   (18)  35
                                                        Type: PositiveInteger

var2StepsDefault()
 

   (19)  35
                                                        Type: PositiveInteger

--Operations on viewport/output characteristics:

viewPosDefault([100,100])
 

   (20)  [100,100]
                                                Type: List NonNegativeInteger

viewPosDefault()
 

   (21)  [100,100]
                                                Type: List NonNegativeInteger

viewSizeDefault([200,200])
 

   (22)  [200,200]
                                                   Type: List PositiveInteger

viewSizeDefault()
 

   (23)  [200,200]
                                                   Type: List PositiveInteger

viewWriteAvailable()
 

   (24)  ["PIXMAP","BITMAP","POSTSCRIPT","IMAGE"]
                                                            Type: List String

viewWriteDefault(["PIXMAP","POSTSCRIPT"])
 

   (25)  ["PIXMAP","POSTSCRIPT"]
                                                            Type: List String

viewWriteDefault()
 

   (26)  ["PIXMAP","POSTSCRIPT"]
                                                            Type: List String
)lisp (bye)
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read huang
 
)lisp (bye)
 
Starts dribbling to iprntpk.output (2010/3/27, 18:27:16).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 3
)set expose add constructor IPRNTPK
 
   InternalPrintPackage is now explicitly exposed in frame initial 
--R   InternalPrintPackage is now explicitly exposed in frame initial 
--E 1

--S 2 of 3
iprint("Release the hounds!")
 
Release the hounds!                                                                   Type: Void
--RRelease the hounds!                                                                   Type: Void
--E 2

--S 3 of 3
for i in 1..10 repeat iprint(i::String)
 
12345678910                                                                   Type: Void
--R12345678910                                                                   Type: Void
--E 3

)spool 
 
Starts dribbling to LieExponentials.output (2010/3/27, 18:45:55).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 13
a: Symbol := 'a
 

   (1)  a
                                                                 Type: Symbol
--R 
--R
--R   (1)  a
--R                                                                 Type: Symbol
--E 1

--S 2 of 13
b: Symbol := 'b
 

   (2)  b
                                                                 Type: Symbol
--R 
--R
--R   (2)  b
--R                                                                 Type: Symbol
--E 2

--S 3 of 13
coef := Fraction(Integer) 
 

   (3)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (3)  Fraction Integer
--R                                                                 Type: Domain
--E 3

--S 4 of 13
group := LieExponentials(Symbol, coef, 3)
 

   (4)  LieExponentials(Symbol,Fraction Integer,3)
                                                                 Type: Domain
--R 
--R
--R   (4)  LieExponentials(Symbol,Fraction Integer,3)
--R                                                                 Type: Domain
--E 4

--S 5 of 13
lpoly := LiePolynomial(Symbol, coef)
 

   (5)  LiePolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (5)  LiePolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 5

--S 6 of 13
poly := XPBWPolynomial(Symbol, coef)
 

   (6)  XPBWPolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (6)  XPBWPolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 6

--S 7 of 13
ea := exp(a::lpoly)$group
 

         [a]
   (7)  e
                             Type: LieExponentials(Symbol,Fraction Integer,3)
--R 
--R
--R         [a]
--R   (7)  e
--R                             Type: LieExponentials(Symbol,Fraction Integer,3)
--E 7

--S 8 of 13
eb := exp(b::lpoly)$group
 

         [b]
   (8)  e
                             Type: LieExponentials(Symbol,Fraction Integer,3)
--R 
--R
--R         [b]
--R   (8)  e
--R                             Type: LieExponentials(Symbol,Fraction Integer,3)
--E 8

--S 9 of 13
g: group := ea*eb
 

             1     2        1   2
             - [a b ]       - [a b]
         [b] 2        [a b] 2       [a]
   (9)  e   e        e     e       e
                             Type: LieExponentials(Symbol,Fraction Integer,3)
--R 
--R
--R             1     2        1   2
--R             - [a b ]       - [a b]
--R         [b] 2        [a b] 2       [a]
--R   (9)  e   e        e     e       e
--R                             Type: LieExponentials(Symbol,Fraction Integer,3)
--E 9

--S 10 of 13
g :: poly
 

   (10)
                     1                           1          1
     1 + [a] + [b] + - [a][a] + [a b] + [b][a] + - [b][b] + - [a][a][a]
                     2                           2          6
   + 
     1   2                1     2    1                        1
     - [a b] + [a b][a] + - [a b ] + - [b][a][a] + [b][a b] + - [b][b][a]
     2                    2          2                        2
   + 
     1
     - [b][b][b]
     6
                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (10)
--R                     1                           1          1
--R     1 + [a] + [b] + - [a][a] + [a b] + [b][a] + - [b][b] + - [a][a][a]
--R                     2                           2          6
--R   + 
--R     1   2                1     2    1                        1
--R     - [a b] + [a b][a] + - [a b ] + - [b][a][a] + [b][a b] + - [b][b][a]
--R     2                    2          2                        2
--R   + 
--R     1
--R     - [b][b][b]
--R     6
--R                                Type: XPBWPolynomial(Symbol,Fraction Integer)
--E 10

--S 11 of 13
log(g)$group
 

                     1          1   2      1     2
   (11)  [a] + [b] + - [a b] + -- [a b] + -- [a b ]
                     2         12         12
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                     1          1   2      1     2
--R   (11)  [a] + [b] + - [a b] + -- [a b] + -- [a b ]
--R                     2         12         12
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 11

--S 12 of 13
g1: group := inv(g)
 

          - [b] - [a]
   (12)  e     e
                             Type: LieExponentials(Symbol,Fraction Integer,3)
--R 
--R
--R          - [b] - [a]
--R   (12)  e     e
--R                             Type: LieExponentials(Symbol,Fraction Integer,3)
--E 12

--S 13 of 13
g*g1
 

   (13)  1
                             Type: LieExponentials(Symbol,Fraction Integer,3)
--R 
--R
--R   (13)  1
--R                             Type: LieExponentials(Symbol,Fraction Integer,3)
--E 13
)spool
 
Starts dribbling to MappingPackage3.output (2010/3/27, 18:46:5).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 26
power(q: FRAC INT, n: INT): FRAC INT == q**n
 
   Function declaration power : (Fraction Integer,Integer) -> Fraction 
      Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration power : (Fraction Integer,Integer) -> Fraction 
--R      Integer has been added to workspace.
--R                                                                   Type: Void
--E 1

--S 2 of 26
power(2,3)
 
   Compiling function power with type (Fraction Integer,Integer) -> 
      Fraction Integer 

   (2)  8
                                                       Type: Fraction Integer
--R 
--R   Compiling function power with type (Fraction Integer,Integer) -> 
--R      Fraction Integer 
--R
--R   (2)  8
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 26
rewop := twist power
 

   (3)  theMap(MAPPKG3;twist;MM;5!0)
                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--I   (3)  theMap(MAPPKG3;twist;MM;5!0)
--R                       Type: ((Integer,Fraction Integer) -> Fraction Integer)
--E 3

--S 4 of 26
rewop(3, 2)
 

   (4)  8
                                                       Type: Fraction Integer
--R 
--R
--R   (4)  8
--R                                                       Type: Fraction Integer
--E 4

--S 5 of 26
square: FRAC INT -> FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 26
square:= curryRight(power, 2)
 

   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--I   (6)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 6

--S 7 of 26
square 4
 

   (7)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (7)  16
--R                                                       Type: Fraction Integer
--E 7

--S 8 of 26
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
 

   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--R 
--R
--I   (8)  theMap(MAPPKG3;constantRight;MM;3!0)
--R              Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)
--E 8

--S 9 of 26
squirrel(1/2, 1/3)
 

        1
   (9)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        1
--R   (9)  -
--R        4
--R                                                       Type: Fraction Integer
--E 9

--S 10 of 26
sixteen := curry(square, 4/1)
 

   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                               Type: (() -> Fraction Integer)
--R 
--R
--I   (10)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                               Type: (() -> Fraction Integer)
--E 10

--S 11 of 26
sixteen()
 

   (11)  16
                                                       Type: Fraction Integer
--R 
--R
--R   (11)  16
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 26
square2:=square*square
 

   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
                                 Type: (Fraction Integer -> Fraction Integer)
--R 
--R
--I   (12)  theMap(MAPPKG3;*;MMM;6!0,0)
--R                                 Type: (Fraction Integer -> Fraction Integer)
--E 12

--S 13 of 26
square2 3
 

   (13)  81
                                                       Type: Fraction Integer
--R 
--R
--R   (13)  81
--R                                                       Type: Fraction Integer
--E 13

--S 14 of 26
sc(x: FRAC INT): FRAC INT == x + 1
 
   Function declaration sc : Fraction Integer -> Fraction Integer has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration sc : Fraction Integer -> Fraction Integer has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 14

--S 15 of 26
incfns := [sc**i for i in 0..10]
 
   Compiling function sc with type Fraction Integer -> Fraction Integer
      

   (15)
   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
    theMap(MAPPKG1;**;MNniM;6!0,0)]
                            Type: List (Fraction Integer -> Fraction Integer)
--R 
--R   Compiling function sc with type Fraction Integer -> Fraction Integer
--R      
--R
--R   (15)
--I   [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
--I    theMap(MAPPKG1;**;MNniM;6!0,0)]
--R                            Type: List (Fraction Integer -> Fraction Integer)
--E 15

--S 16 of 26
[f 4 for f in incfns]
 

   (16)  [4,5,6,7,8,9,10,11,12,13,14]
                                                  Type: List Fraction Integer
--R 
--R
--R   (16)  [4,5,6,7,8,9,10,11,12,13,14]
--R                                                  Type: List Fraction Integer
--E 16

--S 17 of 26
times(n:NNI, i:INT):INT == n*i
 
   Function declaration times : (NonNegativeInteger,Integer) -> Integer
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration times : (NonNegativeInteger,Integer) -> Integer
--R      has been added to workspace.
--R                                                                   Type: Void
--E 17

--S 18 of 26
r := recur(times)
 
   Compiling function times with type (NonNegativeInteger,Integer) -> 
      Integer 

   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
                              Type: ((NonNegativeInteger,Integer) -> Integer)
--R 
--R   Compiling function times with type (NonNegativeInteger,Integer) -> 
--R      Integer 
--R
--I   (18)  theMap(MAPPKG1;recur;2M;7!0,0)
--R                              Type: ((NonNegativeInteger,Integer) -> Integer)
--E 18

--S 19 of 26
fact := curryRight(r, 1)
 

   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
                                        Type: (NonNegativeInteger -> Integer)
--R 
--R
--I   (19)  theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R                                        Type: (NonNegativeInteger -> Integer)
--E 19

--S 20 of 26
fact 4
 

   (20)  24
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  24
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 26
mto2ton(m, n) ==
  raiser := square^n
  raiser m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 26
mto2ton(3, 3)
 
   Compiling function mto2ton with type (PositiveInteger,
      PositiveInteger) -> Fraction Integer 

   (22)  6561
                                                       Type: Fraction Integer
--R 
--R   Compiling function mto2ton with type (PositiveInteger,
--R      PositiveInteger) -> Fraction Integer 
--R
--R   (22)  6561
--R                                                       Type: Fraction Integer
--E 22

--S 23 of 26
shiftfib(r: List INT) : INT ==
  t := r.1
  r.1 := r.2
  r.2 := r.2 + t
  t
 
   Function declaration shiftfib : List Integer -> Integer has been 
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration shiftfib : List Integer -> Integer has been 
--R      added to workspace.
--R                                                                   Type: Void
--E 23

--S 24 of 26
fibinit: List INT := [0, 1]
 

   (24)  [0,1]
                                                           Type: List Integer
--R 
--R
--R   (24)  [0,1]
--R                                                           Type: List Integer
--E 24

--S 25 of 26
fibs := curry(shiftfib, fibinit)
 
   Compiling function shiftfib with type List Integer -> Integer 

   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
                                                        Type: (() -> Integer)
--R 
--R   Compiling function shiftfib with type List Integer -> Integer 
--R
--I   (25)  theMap(MAPPKG2;curry;MAM;2!0,0)
--R                                                        Type: (() -> Integer)
--E 25

--S 26 of 26
[fibs() for i in 0..30]
 

   (26)
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
    317811, 514229, 832040]
                                                           Type: List Integer
--R 
--R
--R   (26)
--R   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
--R    2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
--R    317811, 514229, 832040]
--R                                                           Type: List Integer
--E 26
)spool
 
Starts dribbling to heat.output (2010/3/27, 18:26:48).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 11
u:= operator('u);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 1

--S 2 of 11
heat:= D(u(x, t), t) - D(u(x, t), x, 2) = 0
 

   (2)  - u    (x,t) + u  (x,t)= 0
           ,1,1         ,2
                                            Type: Equation Expression Integer
--R 
--R
--R   (2)  - u    (x,t) + u  (x,t)= 0
--R           ,1,1         ,2
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 11
f:= operator('f);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 3

--S 4 of 11
s:= rule(u(x, t) == f(x/sqrt(t))/sqrt(t))
 

                       x
                  'f(----)
                      +-+
                     \|t
   (4)  u(x,t) == --------
                     +-+
                    \|t
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                       x
--R                  'f(----)
--R                      +-+
--R                     \|t
--R   (4)  u(x,t) == --------
--R                     +-+
--R                    \|t
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 4

--S 5 of 11
s(lhs(heat)) = 0
 

             ,,   x       +-+ ,   x           x
        - 2tf  (----) - x\|t f (----) - t f(----)
                 +-+             +-+         +-+
                \|t             \|t         \|t
   (5)  -----------------------------------------= 0
                           2 +-+
                         2t \|t
                                            Type: Equation Expression Integer
--R 
--R
--R             ,,   x       +-+ ,   x           x
--R        - 2tf  (----) - x\|t f (----) - t f(----)
--R                 +-+             +-+         +-+
--R                \|t             \|t         \|t
--R   (5)  -----------------------------------------= 0
--R                           2 +-+
--R                         2t \|t
--R                                            Type: Equation Expression Integer
--E 5

--S 6 of 11
subst(lhs(%), x = z*sqrt(t)) = 0
 

            ,,        ,
        - 2f  (z) - zf (z) - f(z)

   (6)  -------------------------= 0
                     +-+
                  2t\|t
                                            Type: Equation Expression Integer
--R 
--R
--R            ,,        ,
--R        - 2f  (z) - zf (z) - f(z)
--R
--R   (6)  -------------------------= 0
--R                     +-+
--R                  2t\|t
--R                                            Type: Equation Expression Integer
--E 6

--S 7 of 11
% * denom(lhs(%))
 

            ,,        ,
   (7)  - 2f  (z) - zf (z) - f(z)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            ,,        ,
--R   (7)  - 2f  (z) - zf (z) - f(z)= 0
--R
--R                                            Type: Equation Expression Integer
--E 7

--S 8 of 11
eq:=%
 

            ,,        ,
   (8)  - 2f  (z) - zf (z) - f(z)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            ,,        ,
--R   (8)  - 2f  (z) - zf (z) - f(z)= 0
--R
--R                                            Type: Equation Expression Integer
--E 8

--S 9 of 11
solve(%, f, z=0,[k1,k2])
 

                2         2               2         2               2
               z        %P               z        %P               z
             - --   z   ---            - --   0   ---            - --
                4 ++     4                4 ++     4                4
   (9)  k2 %e     |   %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
                 ++                        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                2         2               2         2               2
--R               z        %P               z        %P               z
--R             - --   z   ---            - --   0   ---            - --
--R                4 ++     4                4 ++     4                4
--R   (9)  k2 %e     |   %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
--R                 ++                        ++
--R                                          Type: Union(Expression Integer,...)
--E 9

--S 10 of 11
subst(%, z = x/sqrt(t))/sqrt(t)
 

                       x
                 2   ----     2               2         2               2
                x     +-+   %P               x        %P               x
              - --   \|t    ---            - --   0   ---            - --
                4t ++        4               4t ++     4               4t
         k2 %e     |      %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
                  ++                           ++
   (10)  ----------------------------------------------------------------
                                        +-+
                                       \|t
                                                     Type: Expression Integer
--R 
--R
--R                       x
--R                 2   ----     2               2         2               2
--R                x     +-+   %P               x        %P               x
--R              - --   \|t    ---            - --   0   ---            - --
--R                4t ++        4               4t ++     4               4t
--R         k2 %e     |      %e   d%P  - k2 %e     |   %e   d%P  + k1 %e
--R                  ++                           ++
--R   (10)  ----------------------------------------------------------------
--R                                        +-+
--R                                       \|t
--R                                                     Type: Expression Integer
--E 10

--S 11 of 11
subst(%, [k2 = 0, k1 = 1/(2*sqrt(%pi))])
 

                 2
                x
              - --
                4t
            %e
   (11)  -----------
           +---+ +-+
         2\|%pi \|t
                                                     Type: Expression Integer
--R 
--R
--R                 2
--R                x
--R              - --
--R                4t
--R            %e
--R   (11)  -----------
--R           +---+ +-+
--R         2\|%pi \|t
--R                                                     Type: Expression Integer
--E 11
)spool 
 
Starts dribbling to List.output (2010/3/27, 18:46:1).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 34
[2, 4, 5, 6]
 

   (1)  [2,4,5,6]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [2,4,5,6]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 34
[1]
 

   (2)  [1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (2)  [1]
--R                                                   Type: List PositiveInteger
--E 2

--S 3 of 34
list(1)
 

   (3)  [1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (3)  [1]
--R                                                   Type: List PositiveInteger
--E 3

--S 4 of 34
append([1,2,3],[5,6,7])
 

   (4)  [1,2,3,5,6,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (4)  [1,2,3,5,6,7]
--R                                                   Type: List PositiveInteger
--E 4

--S 5 of 34
cons(10,[9,8,7])
 

   (5)  [10,9,8,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [10,9,8,7]
--R                                                   Type: List PositiveInteger
--E 5

--S 6 of 34
empty? [x+1]
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 34
([] = nil)@Boolean
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 34
k := [4,3,7,3,8,5,9,2]
 

   (8)  [4,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (8)  [4,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 8

--S 9 of 34
first k
 

   (9)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  4
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 34
k.first
 

   (10)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  4
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 34
k.1
 

   (11)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 34
k(1)
 

   (12)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 34
n := #k
 

   (13)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  8
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 34
last k
 

   (14)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (14)  2
--R                                                        Type: PositiveInteger
--E 14

--S 15 of 34
k.last
 

   (15)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (15)  2
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 34
k.(#k)
 

   (16)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  2
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 34
k := [4,3,7,3,8,5,9,2]
 

   (17)  [4,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (17)  [4,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 17

--S 18 of 34
k.1 := 999
 

   (18)  999
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  999
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 34
k
 

   (19)  [999,3,7,3,8,5,9,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (19)  [999,3,7,3,8,5,9,2]
--R                                                   Type: List PositiveInteger
--E 19

--S 20 of 34
k := [1,2]
 

   (20)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (20)  [1,2]
--R                                                   Type: List PositiveInteger
--E 20

--S 21 of 34
m := cons(0,k)
 

   (21)  [0,1,2]
                                                           Type: List Integer
--R 
--R
--R   (21)  [0,1,2]
--R                                                           Type: List Integer
--E 21

--S 22 of 34
m.2 := 99 
 

   (22)  99
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  99
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 34
m 
 

   (23)  [0,99,2]
                                                           Type: List Integer
--R 
--R
--R   (23)  [0,99,2]
--R                                                           Type: List Integer
--E 23

--S 24 of 34
k
 

   (24)  [99,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (24)  [99,2]
--R                                                   Type: List PositiveInteger
--E 24

--S 25 of 34
k := [1,2,3]
 

   (25)  [1,2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (25)  [1,2,3]
--R                                                   Type: List PositiveInteger
--E 25

--S 26 of 34
rest k
 

   (26)  [2,3]
                                                   Type: List PositiveInteger
--R 
--R
--R   (26)  [2,3]
--R                                                   Type: List PositiveInteger
--E 26

--S 27 of 34
removeDuplicates [4,3,4,3,5,3,4]
 

   (27)  [4,3,5]
                                                   Type: List PositiveInteger
--R 
--R
--R   (27)  [4,3,5]
--R                                                   Type: List PositiveInteger
--E 27

--S 28 of 34
reverse [1,2,3,4,5,6]
 

   (28)  [6,5,4,3,2,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (28)  [6,5,4,3,2,1]
--R                                                   Type: List PositiveInteger
--E 28

--S 29 of 34
member?(1/2,[3/4,5/6,1/2])
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 34
member?(1/12,[3/4,5/6,1/2])
 

   (30)  false
                                                                Type: Boolean
--R 
--R
--R   (30)  false
--R                                                                Type: Boolean
--E 30

--S 31 of 34
reverse(rest(reverse(k)))
 

   (31)  [1,2]
                                                   Type: List PositiveInteger
--R 
--R
--R   (31)  [1,2]
--R                                                   Type: List PositiveInteger
--E 31

--S 32 of 34
[1..3,10,20..23]
 

   (32)  [1..3,10..10,20..23]
                                           Type: List Segment PositiveInteger
--R 
--R
--R   (32)  [1..3,10..10,20..23]
--R                                           Type: List Segment PositiveInteger
--E 32

--S 33 of 34
expand [1..3,10,20..23]
 

   (33)  [1,2,3,10,20,21,22,23]
                                                           Type: List Integer
--R 
--R
--R   (33)  [1,2,3,10,20,21,22,23]
--R                                                           Type: List Integer
--E 33

--S 34 of 34
expand [1..]
 

   (34)  [1,2,3,4,5,6,7,8,9,10,...]
                                                         Type: Stream Integer
--R 
--R
--R   (34)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                                         Type: Stream Integer
--E 34
)spool
 
Starts dribbling to lupfact.output (2010/3/27, 18:28:56).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 18
field := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 18
permMat: (INT, INT, INT) -> Matrix field
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2
 
--S 3 of 18
permMat(dim, i, j) ==
  m : Matrix field :=
    diagonalMatrix [(if i = k or j = k then 0 else 1) for k in 1..dim]
  m(i,j) := 1
  m(j,i) := 1
  m
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 18
nonZeroCol: Matrix field -> INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 18
nonZeroCol(m) ==
  foundit := false
  col := 1
  for i in 1..ncols(m) while not foundit repeat
    for j in 1..nrows(m) while not foundit repeat
      if not(m(j,i) = 0) then
        col := i
        foundit := true
  col
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 18
embedMatrix: (Matrix field,NNI,NNI) -> Matrix field
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6
 
--S 7 of 18
embedMatrix(m, oldDim, newDim) ==
  n := diagonalMatrix([1 for i in 1..newDim])$(Matrix(field))
  setsubMatrix!(n,1,1,m)
  n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 7
 
--S 8 of 18
lupFactorEngine: (Matrix field, INT, INT)  -> List Matrix field
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 18
lupFactorEngine(a, m, p) ==
  m = 1 =>
    l : Matrix field := diagonalMatrix [1]
    pm : Matrix field := permMat(p,1,nonZeroCol a)
    [l,a*pm,pm]
  m2 : NNI := m quo 2
  b : Matrix field := subMatrix(a,1,m2,1,p)
  c : Matrix field := subMatrix(a,m2+1,m,1,p)
  lup := lupFactorEngine(b,m2,p)
  l1 := lup.1
  u1 := lup.2
  pm1 := lup.3
  d : Matrix field := c * (inverse(pm1) :: Matrix(field))
  e : Matrix field := subMatrix(u1,1,m2,1,m2)
  f : Matrix field := subMatrix(d,1,m2,1,m2)
  g : Matrix field := d - f * (inverse(e) :: Matrix(field)) * u1
  pmin2 : NNI := p - m2
  g' : Matrix field := subMatrix(g,1,nrows(g),p - pmin2 + 1,p)
  lup := lupFactorEngine(g',m2,pmin2)
  l2 := lup.1
  u2 := lup.2
  pm2 := lup.3
  pm3 := horizConcat(zero(pmin2,m2)$(Matrix field), pm2)
  pm3 := vertConcat(horizConcat(diagonalMatrix [1 for i in 1..m2],
    zero(m2,pmin2)$(Matrix field)),pm3)
  h : Matrix field := u1 * (inverse(pm3) :: Matrix(field))
  l : Matrix field := horizConcat(l1, zero(m2,m2)$(Matrix field))
  l := vertConcat(l,horizConcat(f * (inverse(e) :: Matrix(field)), l2))
  u : Matrix field := horizConcat(zero(m2,m2)$(Matrix field), u2)
  u := vertConcat(h,u)
  pm := pm3 * pm1
  [l,u,pm]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9
 
--S 10 of 18
intLog2: NNI -> NNI
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10
 
--S 11 of 18
intLog2 n == if n = 1 then 0 else 1 + intLog2(n quo 2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11
 
--S 12 of 18
lupFactor: Matrix field -> Union(List Matrix field,"failed")
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 12
 
--S 13 of 18
lupFactor m ==
  not((r := nrows m) = ncols m) =>
    messagePrint("Matrix must be square")$OUTFORM
    "failed"
  ilog := intLog2(2)
  not(r = 2 ** ilog) =>
    m := embedMatrix(m,r,(n := 2 ** (ilog + 1)))
    l := lupFactorEngine(m,n,n)
    [subMatrix(l.1,1,r,1,r),subMatrix(l.2,1,r,1,r),
      subMatrix(l.3,1,r,1,r)]
  lupFactorEngine(m,r,r)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 13
 
--S 14 of 18
m : Matrix field := zero(4,4)
 

         +0  0  0  0+
         |          |
         |0  0  0  0|
   (14)  |          |
         |0  0  0  0|
         |          |
         +0  0  0  0+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +0  0  0  0+
--R         |          |
--R         |0  0  0  0|
--R   (14)  |          |
--R         |0  0  0  0|
--R         |          |
--R         +0  0  0  0+
--R                                                Type: Matrix Fraction Integer
--E 14

--S 15 of 18
for i in 4..1 by -1 repeat m(5-i,i) := i
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 15

--S 16 of 18
m
 

         +0  0  0  4+
         |          |
         |0  0  3  0|
   (16)  |          |
         |0  2  0  0|
         |          |
         +1  0  0  0+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +0  0  0  4+
--R         |          |
--R         |0  0  3  0|
--R   (16)  |          |
--R         |0  2  0  0|
--R         |          |
--R         +1  0  0  0+
--R                                                Type: Matrix Fraction Integer
--E 16
 
--S 17 of 18
lupFactor m
 
   Compiling function intLog2 with type NonNegativeInteger -> 
      NonNegativeInteger 
   Compiling function embedMatrix with type (Matrix Fraction Integer,
      NonNegativeInteger,NonNegativeInteger) -> Matrix Fraction Integer
      
   Compiling function nonZeroCol with type Matrix Fraction Integer -> 
      Integer 
   Compiling function permMat with type (Integer,Integer,Integer) -> 
      Matrix Fraction Integer 
   Compiling function lupFactorEngine with type (Matrix Fraction 
      Integer,Integer,Integer) -> List Matrix Fraction Integer 
   Compiling function lupFactor with type Matrix Fraction Integer -> 
      Union(List Matrix Fraction Integer,"failed") 
   Compiling function G1875 with type Integer -> Boolean 

          +1  0  0  0+ +4  0  0  0+ +0  0  0  1+
          |          | |          | |          |
          |0  1  0  0| |0  3  0  0| |0  0  1  0|
   (17)  [|          |,|          |,|          |]
          |0  0  1  0| |0  0  2  0| |0  1  0  0|
          |          | |          | |          |
          +0  0  0  1+ +0  0  0  1+ +1  0  0  0+
                                Type: Union(List Matrix Fraction Integer,...)
--R 
--R   Compiling function intLog2 with type NonNegativeInteger -> 
--R      NonNegativeInteger 
--R   Compiling function embedMatrix with type (Matrix Fraction Integer,
--R      NonNegativeInteger,NonNegativeInteger) -> Matrix Fraction Integer
--R      
--R   Compiling function nonZeroCol with type Matrix Fraction Integer -> 
--R      Integer 
--R   Compiling function permMat with type (Integer,Integer,Integer) -> 
--R      Matrix Fraction Integer 
--R   Compiling function lupFactorEngine with type (Matrix Fraction 
--R      Integer,Integer,Integer) -> List Matrix Fraction Integer 
--R   Compiling function lupFactor with type Matrix Fraction Integer -> 
--R      Union(List Matrix Fraction Integer,"failed") 
--I   Compiling function G7005 with type Integer -> Boolean 
--R
--R          +1  0  0  0+ +4  0  0  0+ +0  0  0  1+
--R          |          | |          | |          |
--R          |0  1  0  0| |0  3  0  0| |0  0  1  0|
--R   (17)  [|          |,|          |,|          |]
--R          |0  0  1  0| |0  0  2  0| |0  1  0  0|
--R          |          | |          | |          |
--R          +0  0  0  1+ +0  0  0  1+ +1  0  0  0+
--R                                Type: Union(List Matrix Fraction Integer,...)
--E 17

--S 18 of 18
m := [[1,2,3],[2,3,1],[3,1,2]]
 

         +1  2  3+
         |       |
   (18)  |2  3  1|
         |       |
         +3  1  2+
                                                Type: Matrix Fraction Integer
--R 
--R
--R         +1  2  3+
--R         |       |
--R   (18)  |2  3  1|
--R         |       |
--R         +3  1  2+
--R                                                Type: Matrix Fraction Integer
--E 18
)spool 
 
Starts dribbling to slowint.output (2010/3/27, 18:40:45).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
k := 7/5
 

        7
   (1)  -
        5
                                                       Type: Fraction Integer
--R 
--R
--R        7
--R   (1)  -
--R        5
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 5
mu := sqrt ( ((k-1)*m**2 + 2)/(2*k*m**2 -(k-1)))
 

         +-------+
         |  2
         | m  + 5
   (2)   |-------
         |  2
        \|7m  - 1
                                                     Type: Expression Integer
--R 
--R
--R         +-------+
--R         |  2
--R         | m  + 5
--R   (2)   |-------
--R         |  2
--R        \|7m  - 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 5
km := 2/ ( (1+(2/(k+1)) * (1-mu**2)/mu)*(2*mu + 1 + 1/(m**2)))
 

                                +-------+
                                |  2
                       4     2  | m  + 5
                   (14m  - 2m ) |-------
                                |  2
                               \|7m  - 1
   (3)  -------------------------------------------
                         +-------+
                         |  2
            4     2      | m  + 5      4      2
        (17m  - 4m  - 1) |-------  + 7m  + 10m  - 5
                         |  2
                        \|7m  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                +-------+
--R                                |  2
--R                       4     2  | m  + 5
--R                   (14m  - 2m ) |-------
--R                                |  2
--R                               \|7m  - 1
--R   (3)  -------------------------------------------
--R                         +-------+
--R                         |  2
--R            4     2      | m  + 5      4      2
--R        (17m  - 4m  - 1) |-------  + 7m  + 10m  - 5
--R                         |  2
--R                        \|7m  - 1
--R                                                     Type: Expression Integer
--E 3

--S 4 of 5
f := - 2*m / ((m**2-1)*km)
 

                           +-------+
                           |  2
              4     2      | m  + 5      4      2
        (- 17m  + 4m  + 1) |-------  - 7m  - 10m  + 5
                           |  2
                          \|7m  - 1
   (4)  ---------------------------------------------
                                  +-------+
                                  |  2
                     5     3      | m  + 5
                  (7m  - 8m  + m) |-------
                                  |  2
                                 \|7m  - 1
                                                     Type: Expression Integer
--R 
--R
--R                           +-------+
--R                           |  2
--R              4     2      | m  + 5      4      2
--R        (- 17m  + 4m  + 1) |-------  - 7m  - 10m  + 5
--R                           |  2
--R                          \|7m  - 1
--R   (4)  ---------------------------------------------
--R                                  +-------+
--R                                  |  2
--R                     5     3      | m  + 5
--R                  (7m  - 8m  + m) |-------
--R                                  |  2
--R                                 \|7m  - 1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 5
integrate(f,m)
 

   (5)
                       +-------+
                       |  2
                2      | m  + 5      2
             (7m  - 1) |-------  + 4m  + 2
                       |  2
                      \|7m  - 1
       14log(-----------------------------)
                            2
                           m
     + 
                           +-------+
                           |  2
                    2      | m  + 5      2
               (- 7m  + 1) |-------  + 4m  + 2
                           |  2
                          \|7m  - 1
       - 14log(-------------------------------)
                               2
                              m
     + 
                                          +-------+
                                          |  2
         +-+          4       2       +-+ | m  + 5       4       2
       7\|7 log((- 49m  - 112m  + 17)\|7  |-------  + 49m  + 238m  + 127)
                                          |  2
                                         \|7m  - 1
     + 
                               2
            +-+             17m  - 5                   2               2
       - 14\|5 atan(-----------------------) - 20log(7m  - 1) - 28log(m  - 1)
                                  +-------+
                                  |  2
                       2      +-+ | m  + 5
                    (7m  - 1)\|5  |-------
                                  |  2
                                 \|7m  - 1
     + 
       28log(m)
  /
     28
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (5)
--R                       +-------+
--R                       |  2
--R                2      | m  + 5      2
--R             (7m  - 1) |-------  + 4m  + 2
--R                       |  2
--R                      \|7m  - 1
--R       14log(-----------------------------)
--R                            2
--R                           m
--R     + 
--R                           +-------+
--R                           |  2
--R                    2      | m  + 5      2
--R               (- 7m  + 1) |-------  + 4m  + 2
--R                           |  2
--R                          \|7m  - 1
--R       - 14log(-------------------------------)
--R                               2
--R                              m
--R     + 
--R                                          +-------+
--R                                          |  2
--R         +-+          4       2       +-+ | m  + 5       4       2
--R       7\|7 log((- 49m  - 112m  + 17)\|7  |-------  + 49m  + 238m  + 127)
--R                                          |  2
--R                                         \|7m  - 1
--R     + 
--R                               2
--R            +-+             17m  - 5                   2               2
--R       - 14\|5 atan(-----------------------) - 20log(7m  - 1) - 28log(m  - 1)
--R                                  +-------+
--R                                  |  2
--R                       2      +-+ | m  + 5
--R                    (7m  - 1)\|5  |-------
--R                                  |  2
--R                                 \|7m  - 1
--R     + 
--R       28log(m)
--R  /
--R     28
--R                                          Type: Union(Expression Integer,...)
--E 5
)spool 
 
Starts dribbling to WuWenTsunTriangularSet.output (2010/3/27, 18:46:43).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
R := Integer
 

   (1)  Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 16
ls : List Symbol := [x,y,z,t]
 

   (2)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (2)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 2

--S 3 of 16
V := OVAR(ls)
 

   (3)  OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (3)  OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 3

--S 4 of 16
E := IndexedExponents V
 

   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
                                                                 Type: Domain
--R 
--R
--R   (4)  IndexedExponents OrderedVariableList [x,y,z,t]
--R                                                                 Type: Domain
--E 4

--S 5 of 16
P := NSMP(R, V)
 

   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
                                                                 Type: Domain
--R 
--R
--R   (5)  NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R                                                                 Type: Domain
--E 5

--S 6 of 16
x: P := 'x
 

   (6)  x
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (6)  x
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 6

--S 7 of 16
y: P := 'y
 

   (7)  y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (7)  y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 7

--S 8 of 16
z: P := 'z
 

   (8)  z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (8)  z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 8

--S 9 of 16
t: P := 't
 

   (9)  t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R   (9)  t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 9

--S 10 of 16
T := WUTSET(R,E,V,P)
 

   (10)
  WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t]
  ,OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,Ordere
  dVariableList [x,y,z,t]))
                                                                 Type: Domain
--R 
--R
--R   (10)
--R  WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t]
--R  ,OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,Ordere
--R  dVariableList [x,y,z,t]))
--R                                                                 Type: Domain
--E 10

--S 11 of 16
p1 := x ** 31 - x ** 6 - x - y
 

          31    6
   (11)  x   - x  - x - y
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          31    6
--R   (11)  x   - x  - x - y
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 11

--S 12 of 16
p2 := x ** 8  - z
 

          8
   (12)  x  - z
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          8
--R   (12)  x  - z
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 12

--S 13 of 16
p3 := x ** 10 - t
 

          10
   (13)  x   - t
 Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R          10
--R   (13)  x   - t
--R Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 13

--S 14 of 16
lp := [p1, p2, p3]
 

           31    6          8      10
   (14)  [x   - x  - x - y,x  - z,x   - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--R 
--R
--R           31    6          8      10
--R   (14)  [x   - x  - x - y,x  - z,x   - t]
--RType: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
--E 14

--S 15 of 16
characteristicSet(lp)$T
 

   (15)
     5    4  4 2 2     3 4        7     4      6    6    3      3     3     3
   {z  - t ,t z y  + 2t z y + (- t  + 2t  - t)z  + t z,(t  - 1)z x - z y - t }
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])),...)
--R 
--R
--R   (15)
--R     5    4  4 2 2     3 4        7     4      6    6    3      3     3     3
--R   {z  - t ,t z y  + 2t z y + (- t  + 2t  - t)z  + t z,(t  - 1)z x - z y - t }
--RType: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])),...)
--E 15

--S 16 of 16
zeroSetSplit(lp)$T
 

   (16)
                 3      5    4  3     3    2
   [{t,z,y,x}, {t  - 1,z  - t ,z y + t ,z x  - t},
      5    4  4 2 2     3 4        7     4      6    6    3      3     3     3
    {z  - t ,t z y  + 2t z y + (- t  + 2t  - t)z  + t z,(t  - 1)z x - z y - t }]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--R 
--R
--R   (16)
--R                 3      5    4  3     3    2
--R   [{t,z,y,x}, {t  - 1,z  - t ,z y + t ,z x  - t},
--R      5    4  4 2 2     3 4        7     4      6    6    3      3     3     3
--R    {z  - t ,t z y  + 2t z y + (- t  + 2t  - t)z  + t z,(t  - 1)z x - z y - t }]
--RType: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
--E 16
)spool
 
Starts dribbling to cardinal.output (2010/3/27, 18:24:24).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 16
(c0, c1, c2, c3, A0, A1): CardinalNumber
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 16
c0 := 0::NNI
 

   (2)  0
                                                         Type: CardinalNumber
--R 
--R
--R   (2)  0
--R                                                         Type: CardinalNumber
--E 2

--S 3 of 16
c1 := 1::NNI
 

   (3)  1
                                                         Type: CardinalNumber
--R 
--R
--R   (3)  1
--R                                                         Type: CardinalNumber
--E 3

--S 4 of 16
c2 := 2::NNI
 

   (4)  2
                                                         Type: CardinalNumber
--R 
--R
--R   (4)  2
--R                                                         Type: CardinalNumber
--E 4

--S 5 of 16
c3 := 3::NNI
 

   (5)  3
                                                         Type: CardinalNumber
--R 
--R
--R   (5)  3
--R                                                         Type: CardinalNumber
--E 5

--S 6 of 16
A0 := Aleph 0
 

   (6)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (6)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 6

--S 7 of 16
A1 := Aleph 1
 

   (7)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (7)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 7

--S 8 of 16
[finite? c2,    finite? A0]
 

   (8)  [true,false]
                                                           Type: List Boolean
--R 
--R
--R   (8)  [true,false]
--R                                                           Type: List Boolean
--E 8

--S 9 of 16
[finite?  c2,    finite?  A0]
 

   (9)  [true,false]
                                                           Type: List Boolean
--R 
--R
--R   (9)  [true,false]
--R                                                           Type: List Boolean
--E 9

--S 10 of 16
[countable? c2, countable? A0, countable? A1]
 

   (10)  [true,true,false]
                                                           Type: List Boolean
--R 
--R
--R   (10)  [true,true,false]
--R                                                           Type: List Boolean
--E 10

--S 11 of 16
[c2 + c2, c2 + A1]
 

   (11)  [4,Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (11)  [4,Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 11

--S 12 of 16
[c2 - c1, c2 - c2, c2 - c3, A1 - c2, A1 - A0, A1 - A1]
 

   (12)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
                                    Type: List Union(CardinalNumber,"failed")
--R 
--R
--R   (12)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
--R                                    Type: List Union(CardinalNumber,"failed")
--E 12

--S 13 of 16
[c0 * c2, c1 * c2, c2 * c2, c0 * A1, c1 * A1, c2 * A1, A0 * A1]
 

   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 13

--S 14 of 16
[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]
 

   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 14

--S 15 of 16
generalizedContinuumHypothesisAssumed true
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 16
[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1]
 

   (16)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (16)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
--R                                                    Type: List CardinalNumber
--E 16
)spool
 
Starts dribbling to set.output (2010/3/27, 18:38:57).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 20
s := set [x**2-1, y**2-1, z**2-1]
 

          2      2      2
   (1)  {x  - 1,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      2      2
--R   (1)  {x  - 1,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 1

--S 2 of 20
t := set [x**i - i+1 for i in 2..10 | prime? i]
 

          2      3      5      7
   (2)  {x  - 1,x  - 2,x  - 4,x  - 6}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      3      5      7
--R   (2)  {x  - 1,x  - 2,x  - 4,x  - 6}
--R                                                 Type: Set Polynomial Integer
--E 2

--S 3 of 20
i := intersect(s,t)
 

          2
   (3)  {x  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2
--R   (3)  {x  - 1}
--R                                                 Type: Set Polynomial Integer
--E 3

--S 4 of 20
u := union(s,t)
 

          2      3      5      7      2      2
   (4)  {x  - 1,x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      3      5      7      2      2
--R   (4)  {x  - 1,x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 4

--S 5 of 20
difference(s,t)
 

          2      2
   (5)  {y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          2      2
--R   (5)  {y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 5

--S 6 of 20
symmetricDifference(s,t)
 

          3      5      7      2      2
   (6)  {x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
                                                 Type: Set Polynomial Integer
--R 
--R
--R          3      5      7      2      2
--R   (6)  {x  - 2,x  - 4,x  - 6,y  - 1,z  - 1}
--R                                                 Type: Set Polynomial Integer
--E 6

--S 7 of 20
member?(y, s)
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 7

--S 8 of 20
member?((y+1)*(y-1), s)
 

   (8)  true
                                                                Type: Boolean
--R 
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

--S 9 of 20
subset?(i, s)
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 20
subset?(u, s)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 20
gs := set [g for i in 1..11 | primitive?(g := i::PF 11)]
 

   (11)  {2,6,7,8}
                                                      Type: Set PrimeField 11
--R 
--R
--R   (11)  {2,6,7,8}
--R                                                      Type: Set PrimeField 11
--E 11

--S 12 of 20
complement gs
 

   (12)  {1,3,4,5,9,10,0}
                                                      Type: Set PrimeField 11
--R 
--R
--R   (12)  {1,3,4,5,9,10,0}
--R                                                      Type: Set PrimeField 11
--E 12

--S 13 of 20
a := set [i**2 for i in 1..5]
 

   (13)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (13)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 13

--S 14 of 20
insert!(32, a)
 

   (14)  {1,4,9,16,25,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (14)  {1,4,9,16,25,32}
--R                                                    Type: Set PositiveInteger
--E 14

--S 15 of 20
remove!(25, a)
 

   (15)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (15)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 15

--S 16 of 20
a
 

   (16)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (16)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 16

--S 17 of 20
b := b0 := set [i**2 for i in 1..5]
 

   (17)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (17)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 17

--S 18 of 20
b := union(b, {32})
 

   (18)  {1,4,9,16,25,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (18)  {1,4,9,16,25,32}
--R                                                    Type: Set PositiveInteger
--E 18

--S 19 of 20
b := difference(b, {25})
 

   (19)  {1,4,9,16,32}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (19)  {1,4,9,16,32}
--R                                                    Type: Set PositiveInteger
--E 19

--S 20 of 20
b0
 

   (20)  {1,4,9,16,25}
                                                    Type: Set PositiveInteger
--R 
--R
--R   (20)  {1,4,9,16,25}
--R                                                    Type: Set PositiveInteger
--E 20
)spool 
 
Starts dribbling to defintef.output (2010/3/27, 18:24:53).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 8
sin(x)**3/(sin(x)**3+cos(x)**3)
 

                   3
             sin(x)
   (1)  -----------------
              3         3
        sin(x)  + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                   3
--R             sin(x)
--R   (1)  -----------------
--R              3         3
--R        sin(x)  + cos(x)
--R                                                     Type: Expression Integer
--E 1

--S 2 of 8
integrate(%, x = 0..%pi/2, "noPole")
 

        2log(16) - 4log(4) + 3%pi
   (2)  -------------------------
                    12
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R        2log(16) - 4log(4) + 3%pi
--R   (2)  -------------------------
--R                    12
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 2

--S 3 of 8
x**2/(1+x**3)
 

           2
          x
   (3)  ------
         3
        x  + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R           2
--R          x
--R   (3)  ------
--R         3
--R        x  + 1
--R                                            Type: Fraction Polynomial Integer
--E 3

--S 4 of 8
integrate(%, x=0..%plusInfinity)
 

   (4)   + infinity
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R   (4)   + infinity
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 8
exp(-x**2)*log(x)**2
 

             2
          - x       2
   (5)  %e    log(x)
                                                     Type: Expression Integer
--R 
--R
--R             2
--R          - x       2
--R   (5)  %e    log(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 8
integrate(%, x=0..%plusInfinity)
 

         _ 1             1     _ 1         1 2
        | (-)polygamma(1,-) + | (-)digamma(-)
           2             2       2         2
   (6)  --------------------------------------
                           8
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R         _ 1             1     _ 1         1 2
--R        | (-)polygamma(1,-) + | (-)digamma(-)
--R           2             2       2         2
--R   (6)  --------------------------------------
--R                           8
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 6

--S 7 of 8
x * asin(x/(x+1))
 

                 x
   (7)  x asin(-----)
               x + 1
                                                     Type: Expression Integer
--R 
--R
--R                 x
--R   (7)  x asin(-----)
--R               x + 1
--R                                                     Type: Expression Integer
--E 7

--S 8 of 8
integrate(%, x=0..1)
 

          +-+
        3\|3  - 4
   (8)  ---------
            6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          +-+
--R        3\|3  - 4
--R   (8)  ---------
--R            6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 8
)spool
 
Starts dribbling to tpiezas001.output (2010/3/27, 18:41:25).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 91
t1a:=(a+b)^3 + (a+c)^3 + (a+d)^3 + (a-b)^3 + (a-c)^3 + (a-d)^3
 

            2       2       2     3
   (1)  6a d  + 6a c  + 6a b  + 6a
                                                     Type: Polynomial Integer
--R 
--R
--R            2       2       2     3
--R   (1)  6a d  + 6a c  + 6a b  + 6a
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 91
t1b:=6*a*(a^2+b^2+c^2+d^2)
 

            2       2       2     3
   (2)  6a d  + 6a c  + 6a b  + 6a
                                                     Type: Polynomial Integer
--R 
--R
--R            2       2       2     3
--R   (2)  6a d  + 6a c  + 6a b  + 6a
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 91
t1a-t1b
 

   (3)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (3)  0
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 91
t2a(k)==(a+b)^k + (a+c)^k + (a+d)^k + (b+c)^k + (b+d)^k + (c+d)^k +_
        (a-b)^k + (a-c)^k + (a-d)^k + (b-c)^k + (b-d)^k + (c-d)^k 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 91
t2b(k)==6*(a^2+b^2+c^2+d^2)^(k/2)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 91
t2a(k)
 
   Compiling function t2a with type Variable k -> Expression Integer 

   (6)
            k          k          k          k          k          k
     (d + c)  + (d + b)  + (d + a)  + (c + b)  + (c + a)  + (b + a)
   + 
            k            k            k            k            k            k
   (- b + a)  + (- c + b)  + (- c + a)  + (- d + c)  + (- d + b)  + (- d + a)
                                                     Type: Expression Integer
--R 
--R   Compiling function t2a with type Variable k -> Expression Integer 
--R
--R   (6)
--R            k          k          k          k          k          k
--R     (d + c)  + (d + b)  + (d + a)  + (c + b)  + (c + a)  + (b + a)
--R   + 
--R            k            k            k            k            k            k
--R   (- b + a)  + (- c + b)  + (- c + a)  + (- d + c)  + (- d + b)  + (- d + a)
--R                                                     Type: Expression Integer
--E 6

--S 7 of 91
t2b(k)
 
   Compiling function t2b with type Variable k -> Expression Integer 

                            k
                            -
           2    2    2    2 2
   (7)  6(d  + c  + b  + a )
                                                     Type: Expression Integer
--R 
--R   Compiling function t2b with type Variable k -> Expression Integer 
--R
--R                            k
--R                            -
--R           2    2    2    2 2
--R   (7)  6(d  + c  + b  + a )
--R                                                     Type: Expression Integer
--E 7

--S 8 of 91
t2a(2)
 
   Compiling function t2a with type PositiveInteger -> Polynomial 
      Integer 

          2     2     2     2
   (8)  6d  + 6c  + 6b  + 6a
                                                     Type: Polynomial Integer
--R 
--R   Compiling function t2a with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R          2     2     2     2
--R   (8)  6d  + 6c  + 6b  + 6a
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 91
t2b(2)
 
   Compiling function t2b with type PositiveInteger -> Expression 
      Integer 

          2     2     2     2
   (9)  6d  + 6c  + 6b  + 6a
                                                     Type: Expression Integer
--R 
--R   Compiling function t2b with type PositiveInteger -> Expression 
--R      Integer 
--R
--R          2     2     2     2
--R   (9)  6d  + 6c  + 6b  + 6a
--R                                                     Type: Expression Integer
--E 9

--S 10 of 91
t2a(2)-t2b(2)
 

   (10)  0
                                                     Type: Expression Integer
--R 
--R
--R   (10)  0
--R                                                     Type: Expression Integer
--E 10

--S 11 of 91
t2a(4)
 

   (11)
     4       2      2      2  2     4       2      2  2     4      2 2     4
   6d  + (12c  + 12b  + 12a )d  + 6c  + (12b  + 12a )c  + 6b  + 12a b  + 6a
                                                     Type: Polynomial Integer
--R 
--R
--R   (11)
--R     4       2      2      2  2     4       2      2  2     4      2 2     4
--R   6d  + (12c  + 12b  + 12a )d  + 6c  + (12b  + 12a )c  + 6b  + 12a b  + 6a
--R                                                     Type: Polynomial Integer
--E 11

--S 12 of 91
t2b(4)
 

   (12)
     4       2      2      2  2     4       2      2  2     4      2 2     4
   6d  + (12c  + 12b  + 12a )d  + 6c  + (12b  + 12a )c  + 6b  + 12a b  + 6a
                                                     Type: Expression Integer
--R 
--R
--R   (12)
--R     4       2      2      2  2     4       2      2  2     4      2 2     4
--R   6d  + (12c  + 12b  + 12a )d  + 6c  + (12b  + 12a )c  + 6b  + 12a b  + 6a
--R                                                     Type: Expression Integer
--E 12

--S 13 of 91
t2a(4)-t2b(4)
 

   (13)  0
                                                     Type: Expression Integer
--R 
--R
--R   (13)  0
--R                                                     Type: Expression Integer
--E 13

--S 14 of 91
t3a1 := (a+b)^2 - (a-b)^2
 

   (14)  4a b
                                                     Type: Polynomial Integer
--R 
--R
--R   (14)  4a b
--R                                                     Type: Polynomial Integer
--E 14

--S 15 of 91
t3b1 := 4*a*b
 

   (15)  4a b
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  4a b
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 91
t3a1-t3b1
 

   (16)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (16)  0
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 91
t3a2 := (a+b+c)^3 - (a-b+c)^3 - (a+b-c)^3 + (a-b-c)^3
 

   (17)  24a b c
                                                     Type: Polynomial Integer
--R 
--R
--R   (17)  24a b c
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 91
t3b2 := 24*a*b*c
 

   (18)  24a b c
                                                     Type: Polynomial Integer
--R 
--R
--R   (18)  24a b c
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 91
t3a2-t3b2
 

   (19)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (19)  0
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 91
t3a3 := (a+b+c+d)^4 - (a-b+c+d)^4 - (a+b-c+d)^4 - (a+b+c-d)^4 
      + (a-b-c+d)^4 + (a-b+c-d)^4 + (a+b-c-d)^4 - (a-b-c-d)^4
 

   (20)  192a b c d
                                                     Type: Polynomial Integer
--R 
--R
--R   (20)  192a b c d
--R                                                     Type: Polynomial Integer
--E 20

--S 21 of 91
t3b3 := 192*a*b*c*d
 

   (21)  192a b c d
                                                     Type: Polynomial Integer
--R 
--R
--R   (21)  192a b c d
--R                                                     Type: Polynomial Integer
--E 21

--S 22 of 91
t3a3-t3b3
 

   (22)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (22)  0
--R                                                     Type: Polynomial Integer
--E 22

--S 23 of 91
bitlist(size:Integer):List List INT ==
  result:List List INT:=[]
  size <= 1 => result
  bound:PI:=size-1
  bitlength:INT:=2^bound
  for i in (bitlength-1)::PI..0 by -1 repeat
    t1:=[1::INT for k in 1..bound]
    for j in 0..(#t1-1) repeat 
      if not bit?(i,j) then t1(bound-j):=0
    result:=cons(t1,result)
  result
 
   Function declaration bitlist : Integer -> List List Integer has been
      added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration bitlist : Integer -> List List Integer has been
--R      added to workspace.
--R                                                                   Type: Void
--E 23

--S 24 of 91
bitlist(1)
 
   Compiling function bitlist with type Integer -> List List Integer 

   (24)  []
                                                      Type: List List Integer
--R 
--R   Compiling function bitlist with type Integer -> List List Integer 
--R
--R   (24)  []
--R                                                      Type: List List Integer
--E 24

--S 25 of 91
bitlist(2)
 
   Compiling function G1955 with type Integer -> Boolean 
   Compiling function G1969 with type NonNegativeInteger -> Boolean 

   (25)  [[0],[1]]
                                                      Type: List List Integer
--R 
--I   Compiling function G7153 with type Integer -> Boolean 
--I   Compiling function G7332 with type NonNegativeInteger -> Boolean 
--R
--R   (25)  [[0],[1]]
--R                                                      Type: List List Integer
--E 25

--S 26 of 91
bitlist(3)
 

   (26)  [[0,0],[0,1],[1,0],[1,1]]
                                                      Type: List List Integer
--R 
--R
--R   (26)  [[0,0],[0,1],[1,0],[1,1]]
--R                                                      Type: List List Integer
--E 26

--S 27 of 91
bitlist(4)
 

   (27)  [[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
                                                      Type: List List Integer
--R 
--R
--R   (27)  [[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
--R                                                      Type: List List Integer
--E 27

--S 28 of 91
symgen(var:Symbol,size:PI):List Symbol == [var.[i] for i in size..1 by -1]
 
   Function declaration symgen : (Symbol,PositiveInteger) -> List 
      Symbol has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration symgen : (Symbol,PositiveInteger) -> List 
--R      Symbol has been added to workspace.
--R                                                                   Type: Void
--E 28

--S 29 of 91
symgen('a,4)
 
   Compiling function symgen with type (Symbol,PositiveInteger) -> List
      Symbol 

   (29)  [a ,a ,a ,a ]
           4  3  2  1
                                                            Type: List Symbol
--R 
--R   Compiling function symgen with type (Symbol,PositiveInteger) -> List
--R      Symbol 
--R
--R   (29)  [a ,a ,a ,a ]
--R           4  3  2  1
--R                                                            Type: List Symbol
--E 29

--S 30 of 91
term(size:PI,signs:List INT):Polynomial Integer ==
  syms:=symgen('x,size)
  t1:POLY(INT):=first syms
  sign:INT:=if odd? size then 1 else -1
  for i in 1..#signs repeat
    if (signs.i = 0)
      then t1:=t1-syms.(i+1)
       else ( t1:=t1+syms.(i+1) ; sign:=sign*-1 )
  sign*(t1^size)
 
   Function declaration term : (PositiveInteger,List Integer) -> 
      Polynomial Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration term : (PositiveInteger,List Integer) -> 
--R      Polynomial Integer has been added to workspace.
--R                                                                   Type: Void
--E 30

--S 31 of 91
factor term(4,[0,0,0])
 
   Compiling function term with type (PositiveInteger,List Integer) -> 
      Polynomial Integer 

                              4
   (31)  - (x  - x  - x  - x )
             4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R   Compiling function term with type (PositiveInteger,List Integer) -> 
--R      Polynomial Integer 
--R
--R                              4
--R   (31)  - (x  - x  - x  - x )
--R             4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 31

--S 32 of 91
factor term(4,[0,0,1])
 

                            4
   (32)  (x  - x  - x  + x )
           4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                            4
--R   (32)  (x  - x  - x  + x )
--R           4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 32

--S 33 of 91
factor term(4,[0,1,0])
 

                            4
   (33)  (x  - x  + x  - x )
           4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                            4
--R   (33)  (x  - x  + x  - x )
--R           4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 33

--S 34 of 91
factor term(4,[0,1,1])
 

                              4
   (34)  - (x  - x  + x  + x )
             4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                              4
--R   (34)  - (x  - x  + x  + x )
--R             4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 34

--S 35 of 91
factor term(4,[1,0,0])
 

                            4
   (35)  (x  + x  - x  - x )
           4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                            4
--R   (35)  (x  + x  - x  - x )
--R           4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 35

--S 36 of 91
factor term(4,[1,0,1])
 

                              4
   (36)  - (x  + x  - x  + x )
             4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                              4
--R   (36)  - (x  + x  - x  + x )
--R             4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 36

--S 37 of 91
factor term(4,[1,1,0])
 

                              4
   (37)  - (x  + x  + x  - x )
             4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                              4
--R   (37)  - (x  + x  + x  - x )
--R             4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 37

--S 38 of 91
factor term(4,[1,1,1])
 

                            4
   (38)  (x  + x  + x  + x )
           4    3    2    1
                                            Type: Factored Polynomial Integer
--R 
--R
--R                            4
--R   (38)  (x  + x  + x  + x )
--R           4    3    2    1
--R                                            Type: Factored Polynomial Integer
--E 38

--S 39 of 91
map(x+->factor(term(1,x)),bitlist(1))
 

   (39)  []
                                       Type: List Factored Polynomial Integer
--R 
--R
--R   (39)  []
--R                                       Type: List Factored Polynomial Integer
--E 39

--S 40 of 91
map(x+->factor(term(2,x)),bitlist(2))
 

                     2          2
   (40)  [- (x  - x ) ,(x  + x ) ]
              2    1     2    1
                                       Type: List Factored Polynomial Integer
--R 
--R
--R                     2          2
--R   (40)  [- (x  - x ) ,(x  + x ) ]
--R              2    1     2    1
--R                                       Type: List Factored Polynomial Integer
--E 40

--S 41 of 91
map(x+->factor(term(3,x)),bitlist(3))
 

                        3                 3                 3               3
   (41)  [(x  - x  - x ) ,- (x  - x  + x ) ,- (x  + x  - x ) ,(x  + x  + x ) ]
            3    2    1       3    2    1       3    2    1     3    2    1
                                       Type: List Factored Polynomial Integer
--R 
--R
--R                        3                 3                 3               3
--R   (41)  [(x  - x  - x ) ,- (x  - x  + x ) ,- (x  + x  - x ) ,(x  + x  + x ) ]
--R            3    2    1       3    2    1       3    2    1     3    2    1
--R                                       Type: List Factored Polynomial Integer
--E 41

--S 42 of 91
map(x+->factor(term(4,x)),bitlist(4))
 

   (42)
                         4                     4                     4
   [- (x  - x  - x  - x ) , (x  - x  - x  + x ) , (x  - x  + x  - x ) ,
        4    3    2    1      4    3    2    1      4    3    2    1
                         4                     4                       4
    - (x  - x  + x  + x ) , (x  + x  - x  - x ) , - (x  + x  - x  + x ) ,
        4    3    2    1      4    3    2    1        4    3    2    1
                         4                     4
    - (x  + x  + x  - x ) , (x  + x  + x  + x ) ]
        4    3    2    1      4    3    2    1
                                       Type: List Factored Polynomial Integer
--R 
--R
--R   (42)
--R                         4                     4                     4
--R   [- (x  - x  - x  - x ) , (x  - x  - x  + x ) , (x  - x  + x  - x ) ,
--R        4    3    2    1      4    3    2    1      4    3    2    1
--R                         4                     4                       4
--R    - (x  - x  + x  + x ) , (x  + x  - x  - x ) , - (x  + x  - x  + x ) ,
--R        4    3    2    1      4    3    2    1        4    3    2    1
--R                         4                     4
--R    - (x  + x  + x  - x ) , (x  + x  + x  + x ) ]
--R        4    3    2    1      4    3    2    1
--R                                       Type: List Factored Polynomial Integer
--E 42

--S 43 of 91
lhs(size:PI):POLY(INT) ==
  size = 1 => 0::POLY(INT)
  reduce(+,map(x+->term(size,x),bitlist(size)))
 
   Function declaration lhs : PositiveInteger -> Polynomial Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration lhs : PositiveInteger -> Polynomial Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 43

--S 44 of 91
rhs(size:PI):POLY(INT) == 
 size = 1 => 0
 bound:PI:=(size-1)
 factorial(size)*2^bound*reduce(*,symgen('x,size))@POLY(INT)
 
   Function declaration rhs : PositiveInteger -> Polynomial Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration rhs : PositiveInteger -> Polynomial Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 44

--S 45 of 91
map(x+->factor term(2,x),bitlist(2))
 

                     2          2
   (45)  [- (x  - x ) ,(x  + x ) ]
              2    1     2    1
                                       Type: List Factored Polynomial Integer
--R 
--R
--R                     2          2
--R   (45)  [- (x  - x ) ,(x  + x ) ]
--R              2    1     2    1
--R                                       Type: List Factored Polynomial Integer
--E 45

--S 46 of 91
lhs(2)
 
   Compiling function lhs with type PositiveInteger -> Polynomial 
      Integer 

   (46)  4x x
           1 2
                                                     Type: Polynomial Integer
--R 
--R   Compiling function lhs with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R   (46)  4x x
--R           1 2
--R                                                     Type: Polynomial Integer
--E 46

--S 47 of 91
rhs(2)
 
   Compiling function rhs with type PositiveInteger -> Polynomial 
      Integer 

   (47)  4x x
           1 2
                                                     Type: Polynomial Integer
--R 
--R   Compiling function rhs with type PositiveInteger -> Polynomial 
--R      Integer 
--R
--R   (47)  4x x
--R           1 2
--R                                                     Type: Polynomial Integer
--E 47

--S 48 of 91
lhs(2)-rhs(2)
 

   (48)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (48)  0
--R                                                     Type: Polynomial Integer
--E 48

--S 49 of 91
map(x+->factor term(3,x),bitlist(3))
 

                        3                 3                 3               3
   (49)  [(x  - x  - x ) ,- (x  - x  + x ) ,- (x  + x  - x ) ,(x  + x  + x ) ]
            3    2    1       3    2    1       3    2    1     3    2    1
                                       Type: List Factored Polynomial Integer
--R 
--R
--R                        3                 3                 3               3
--R   (49)  [(x  - x  - x ) ,- (x  - x  + x ) ,- (x  + x  - x ) ,(x  + x  + x ) ]
--R            3    2    1       3    2    1       3    2    1     3    2    1
--R                                       Type: List Factored Polynomial Integer
--E 49

--S 50 of 91
lhs(3)
 

   (50)  24x x x
            1 2 3
                                                     Type: Polynomial Integer
--R 
--R
--R   (50)  24x x x
--R            1 2 3
--R                                                     Type: Polynomial Integer
--E 50

--S 51 of 91
rhs(3)
 

   (51)  24x x x
            1 2 3
                                                     Type: Polynomial Integer
--R 
--R
--R   (51)  24x x x
--R            1 2 3
--R                                                     Type: Polynomial Integer
--E 51

--S 52 of 91
lhs(3)-rhs(3)
 

   (52)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (52)  0
--R                                                     Type: Polynomial Integer
--E 52

--S 53 of 91
map(x+->factor term(4,x),bitlist(4))
 

   (53)
                         4                     4                     4
   [- (x  - x  - x  - x ) , (x  - x  - x  + x ) , (x  - x  + x  - x ) ,
        4    3    2    1      4    3    2    1      4    3    2    1
                         4                     4                       4
    - (x  - x  + x  + x ) , (x  + x  - x  - x ) , - (x  + x  - x  + x ) ,
        4    3    2    1      4    3    2    1        4    3    2    1
                         4                     4
    - (x  + x  + x  - x ) , (x  + x  + x  + x ) ]
        4    3    2    1      4    3    2    1
                                       Type: List Factored Polynomial Integer
--R 
--R
--R   (53)
--R                         4                     4                     4
--R   [- (x  - x  - x  - x ) , (x  - x  - x  + x ) , (x  - x  + x  - x ) ,
--R        4    3    2    1      4    3    2    1      4    3    2    1
--R                         4                     4                       4
--R    - (x  - x  + x  + x ) , (x  + x  - x  - x ) , - (x  + x  - x  + x ) ,
--R        4    3    2    1      4    3    2    1        4    3    2    1
--R                         4                     4
--R    - (x  + x  + x  - x ) , (x  + x  + x  + x ) ]
--R        4    3    2    1      4    3    2    1
--R                                       Type: List Factored Polynomial Integer
--E 53

--S 54 of 91
lhs(4)
 

   (54)  192x x x x
             1 2 3 4
                                                     Type: Polynomial Integer
--R 
--R
--R   (54)  192x x x x
--R             1 2 3 4
--R                                                     Type: Polynomial Integer
--E 54

--S 55 of 91
rhs(4)
 

   (55)  192x x x x
             1 2 3 4
                                                     Type: Polynomial Integer
--R 
--R
--R   (55)  192x x x x
--R             1 2 3 4
--R                                                     Type: Polynomial Integer
--E 55

--S 56 of 91
lhs(4)-rhs(4)
 

   (56)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (56)  0
--R                                                     Type: Polynomial Integer
--E 56

--S 57 of 91
symgen2(var1:Symbol,var2:Symbol,size:PI):List POLY INT ==
  [(var1.[i]*var2.[i]) for i in size..1 by -1]
 
   Function declaration symgen2 : (Symbol,Symbol,PositiveInteger) -> 
      List Polynomial Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration symgen2 : (Symbol,Symbol,PositiveInteger) -> 
--R      List Polynomial Integer has been added to workspace.
--R                                                                   Type: Void
--E 57

--S 58 of 91
symgen2('a,'b,4)
 
   Compiling function symgen2 with type (Symbol,Symbol,PositiveInteger)
       -> List Polynomial Integer 

   (58)  [a b ,a b ,a b ,a b ]
           4 4  3 3  2 2  1 1
                                                Type: List Polynomial Integer
--R 
--R   Compiling function symgen2 with type (Symbol,Symbol,PositiveInteger)
--R       -> List Polynomial Integer 
--R
--R   (58)  [a b ,a b ,a b ,a b ]
--R           4 4  3 3  2 2  1 1
--R                                                Type: List Polynomial Integer
--E 58

--S 59 of 91
symgen3(var1:Symbol,var2:Symbol,size:PI):LIST POLY INT == 
  result:LIST(POLY(INT)):=[]
  for j in 1..size repeat
    for k in 1..j repeat
      p:POLY(INT):=var1.[k]*var2.[j]-var1.[j]*var2.[k]
      result:=cons(p,result)
  result
 
   Function declaration symgen3 : (Symbol,Symbol,PositiveInteger) -> 
      List Polynomial Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration symgen3 : (Symbol,Symbol,PositiveInteger) -> 
--R      List Polynomial Integer has been added to workspace.
--R                                                                   Type: Void
--E 59

--S 60 of 91
symgen3('a,'b,4)
 
   Compiling function symgen3 with type (Symbol,Symbol,PositiveInteger)
       -> List Polynomial Integer 

   (60)
   [0, a b  - a b , a b  - a b , a b  - a b , 0, a b  - a b , a b  - a b , 0,
        3 4    4 3   2 4    4 2   1 4    4 1      2 3    3 2   1 3    3 1
    a b  - a b , 0]
     1 2    2 1
                                                Type: List Polynomial Integer
--R 
--R   Compiling function symgen3 with type (Symbol,Symbol,PositiveInteger)
--R       -> List Polynomial Integer 
--R
--R   (60)
--R   [0, a b  - a b , a b  - a b , a b  - a b , 0, a b  - a b , a b  - a b , 0,
--R        3 4    4 3   2 4    4 2   1 4    4 1      2 3    3 2   1 3    3 1
--R    a b  - a b , 0]
--R     1 2    2 1
--R                                                Type: List Polynomial Integer
--E 60

--S 61 of 91
lagrange(size:PI):POLY(INT) ==
  t1:=factor reduce(+,map(x+->x^2,symgen('a,size)))
  print ["t1=",t1]
  t2:=factor reduce(+,map(x+->x^2,symgen('b,size)))
  print ["t2=",t2]
  t3:=factor reduce(+,symgen2('a,'b,size))^2
  print ["t3=",t3]
  t4:=factor reduce(+,map(x+->x^2,symgen3('a,'b,size)))
  print ["t4=",t4]
  lhs:=t1*t2
  print ["lhs=",lhs]
  rhs:=t3+t4
  print ["rhs=",rhs]
  lhs-rhs
 
   Function declaration lagrange : PositiveInteger -> Polynomial 
      Integer has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration lagrange : PositiveInteger -> Polynomial 
--R      Integer has been added to workspace.
--R                                                                   Type: Void
--E 61

--S 62 of 91
lagrange(2)
 
   Function definition for lhs is being overwritten.
   Function definition for rhs is being overwritten.
   Compiling function lagrange with type PositiveInteger -> Polynomial 
      Integer 
            2     2
   ["t1=",a   + a  ]
           2     1
            2     2
   ["t2=",b   + b  ]
           2     1
                       2
   ["t3=",(a b  + a b ) ]
            2 2    1 1
                       2
   ["t4=",(a b  - a b ) ]
            1 2    2 1
              2     2    2     2
   ["lhs=",(a   + a  )(b   + b  )]
             2     1    2     1
              2     2   2      2     2   2
   ["rhs=",(a   + a  )b   + (a   + a  )b  ]
             2     1   2      2     1   1

   (62)  0
                                                     Type: Polynomial Integer
--R 
--R   Function definition for lhs is being overwritten.
--R   Function definition for rhs is being overwritten.
--R   Compiling function lagrange with type PositiveInteger -> Polynomial 
--R      Integer 
--R            2     2
--R   ["t1=",a   + a  ]
--R           2     1
--R            2     2
--R   ["t2=",b   + b  ]
--R           2     1
--R                       2
--R   ["t3=",(a b  + a b ) ]
--R            2 2    1 1
--R                       2
--R   ["t4=",(a b  - a b ) ]
--R            1 2    2 1
--R              2     2    2     2
--R   ["lhs=",(a   + a  )(b   + b  )]
--R             2     1    2     1
--R              2     2   2      2     2   2
--R   ["rhs=",(a   + a  )b   + (a   + a  )b  ]
--R             2     1   2      2     1   1
--R
--R   (62)  0
--R                                                     Type: Polynomial Integer
--E 62

--S 63 of 91
lagrange(3)
 
            2     2     2
   ["t1=",a   + a   + a  ]
           3     2     1
            2     2     2
   ["t2=",b   + b   + b  ]
           3     2     1
                              2
   ["t3=",(a b  + a b  + a b ) ]
            3 3    2 2    1 1
   ["t4=",

          2     2   2                                2     2   2
       (a   + a  )b   + (- 2a a b  - 2a a b )b  + (a   + a  )b   - 2a a b b
         2     1   3         2 3 2     1 3 1  3     3     1   2      1 2 1 2
     + 
          2     2   2
       (a   + a  )b
         3     2   1
     ]
              2     2     2    2     2     2
   ["lhs=",(a   + a   + a  )(b   + b   + b  )]
             3     2     1    3     2     1
              2     2     2   2      2     2     2   2      2     2     2   2
   ["rhs=",(a   + a   + a  )b   + (a   + a   + a  )b   + (a   + a   + a  )b  ]
             3     2     1   3      3     2     1   2      3     2     1   1

   (63)  0
                                                     Type: Polynomial Integer
--R 
--R            2     2     2
--R   ["t1=",a   + a   + a  ]
--R           3     2     1
--R            2     2     2
--R   ["t2=",b   + b   + b  ]
--R           3     2     1
--R                              2
--R   ["t3=",(a b  + a b  + a b ) ]
--R            3 3    2 2    1 1
--R   ["t4=",
--R
--R          2     2   2                                2     2   2
--R       (a   + a  )b   + (- 2a a b  - 2a a b )b  + (a   + a  )b   - 2a a b b
--R         2     1   3         2 3 2     1 3 1  3     3     1   2      1 2 1 2
--R     + 
--R          2     2   2
--R       (a   + a  )b
--R         3     2   1
--R     ]
--R              2     2     2    2     2     2
--R   ["lhs=",(a   + a   + a  )(b   + b   + b  )]
--R             3     2     1    3     2     1
--R              2     2     2   2      2     2     2   2      2     2     2   2
--R   ["rhs=",(a   + a   + a  )b   + (a   + a   + a  )b   + (a   + a   + a  )b  ]
--R             3     2     1   3      3     2     1   2      3     2     1   1
--R
--R   (63)  0
--R                                                     Type: Polynomial Integer
--E 63

)clear all
 

--S 64 of 91
p:=m^2+3*n^3
 

          3    2
   (1)  3n  + m
                                                     Type: Polynomial Integer
--R 
--R
--R          3    2
--R   (1)  3n  + m
--R                                                     Type: Polynomial Integer
--E 64

--S 65 of 91
q:=m^2-3*n^3
 

            3    2
   (2)  - 3n  + m
                                                     Type: Polynomial Integer
--R 
--R
--R            3    2
--R   (2)  - 3n  + m
--R                                                     Type: Polynomial Integer
--E 65

--S 66 of 91
r:=36*m^2*n^3
 

           2 3
   (3)  36m n
                                                     Type: Polynomial Integer
--R 
--R
--R           2 3
--R   (3)  36m n
--R                                                     Type: Polynomial Integer
--E 66

--S 67 of 91
lhs:=(p^3+q*r)^3 + (-p^3+p*r)^3 + (-q*r)^3
 

   (4)
            4 21          6 18          8 15          10 12         12 9
     157464m n   + 314928m n   + 262440m n   + 116640m  n   + 29160m  n
   + 
          14 6       16 3
     3888m  n  + 216m  n
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)
--R            4 21          6 18          8 15          10 12         12 9
--R     157464m n   + 314928m n   + 262440m n   + 116640m  n   + 29160m  n
--R   + 
--R          14 6       16 3
--R     3888m  n  + 216m  n
--R                                                     Type: Polynomial Integer
--E 67

--S 68 of 91
rhs:=m*(6*m*n*p^2)^3
 

   (5)
            4 21          6 18          8 15          10 12         12 9
     157464m n   + 314928m n   + 262440m n   + 116640m  n   + 29160m  n
   + 
          14 6       16 3
     3888m  n  + 216m  n
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)
--R            4 21          6 18          8 15          10 12         12 9
--R     157464m n   + 314928m n   + 262440m n   + 116640m  n   + 29160m  n
--R   + 
--R          14 6       16 3
--R     3888m  n  + 216m  n
--R                                                     Type: Polynomial Integer
--E 68

--S 69 of 91
lhs-rhs
 

   (6)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  0
--R                                                     Type: Polynomial Integer
--E 69

)clear all
 

--S 70 of 91
b:=c^8-d^8
 

           8    8
   (1)  - d  + c
                                                     Type: Polynomial Integer
--R 
--R
--R           8    8
--R   (1)  - d  + c
--R                                                     Type: Polynomial Integer
--E 70

--S 71 of 91
lhs:=((2*a+b)*c^3*d)^4+(2*a*c^4-b*d^4)^4-(2*a*c^4+b*d^4)^4-((2*a-b)*c^3*d)^4
 

             4 36        12 28        20 20        28 12        36 4
   (2)  16a c d   - 64a c  d   + 96a c  d   - 64a c  d   + 16a c  d
                                                     Type: Polynomial Integer
--R 
--R
--R             4 36        12 28        20 20        28 12        36 4
--R   (2)  16a c d   - 64a c  d   + 96a c  d   - 64a c  d   + 16a c  d
--R                                                     Type: Polynomial Integer
--E 71

--S 72 of 91
rhs:=a*(2*b*c*d)^4
 

             4 36        12 28        20 20        28 12        36 4
   (3)  16a c d   - 64a c  d   + 96a c  d   - 64a c  d   + 16a c  d
                                                     Type: Polynomial Integer
--R 
--R
--R             4 36        12 28        20 20        28 12        36 4
--R   (3)  16a c d   - 64a c  d   + 96a c  d   - 64a c  d   + 16a c  d
--R                                                     Type: Polynomial Integer
--E 72

--S 73 of 91
lhs-rhs
 

   (4)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Polynomial Integer
--E 73

)clear all
 

--S 74 of 91
u:=a^2*c-b^3
 

         2     3
   (1)  a c - b
                                                     Type: Polynomial Integer
--R 
--R
--R         2     3
--R   (1)  a c - b
--R                                                     Type: Polynomial Integer
--E 74

--S 75 of 91
x:=a^2*b-a*c^2
 

             2    2
   (2)  - a c  + a b
                                                     Type: Polynomial Integer
--R 
--R
--R             2    2
--R   (2)  - a c  + a b
--R                                                     Type: Polynomial Integer
--E 75

--S 76 of 91
y:=a^3-b^2*c
 

           2     3
   (3)  - b c + a
                                                     Type: Polynomial Integer
--R 
--R
--R           2     3
--R   (3)  - b c + a
--R                                                     Type: Polynomial Integer
--E 76

--S 77 of 91
z:=b*c^2-a*b^2
 

           2      2
   (4)  b c  - a b
                                                     Type: Polynomial Integer
--R 
--R
--R           2      2
--R   (4)  b c  - a b
--R                                                     Type: Polynomial Integer
--E 77

--S 78 of 91
u^2*x+x^2*y+y^2*z+z^2*u
 

   (5)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)  0
--R                                                     Type: Polynomial Integer
--E 78

)clear all
 

--S 79 of 91
c:=a^2-2*a*b+2*b^2
 

          2           2
   (1)  2b  - 2a b + a
                                                     Type: Polynomial Integer
--R 
--R
--R          2           2
--R   (1)  2b  - 2a b + a
--R                                                     Type: Polynomial Integer
--E 79

--S 80 of 91
u:=a*b+b^2+c
 

          2          2
   (2)  3b  - a b + a
                                                     Type: Polynomial Integer
--R 
--R
--R          2          2
--R   (2)  3b  - a b + a
--R                                                     Type: Polynomial Integer
--E 80

--S 81 of 91
x:=3*(a*b-b^2+c)
 

          2            2
   (3)  3b  - 3a b + 3a
                                                     Type: Polynomial Integer
--R 
--R
--R          2            2
--R   (3)  3b  - 3a b + 3a
--R                                                     Type: Polynomial Integer
--E 81

--S 82 of 91
y:=a*b-3*b^2-c
 

            2           2
   (4)  - 5b  + 3a b - a
                                                     Type: Polynomial Integer
--R 
--R
--R            2           2
--R   (4)  - 5b  + 3a b - a
--R                                                     Type: Polynomial Integer
--E 82

--S 83 of 91
z:=3*(a*b-b^2-c)
 

            2            2
   (5)  - 9b  + 9a b - 3a
                                                     Type: Polynomial Integer
--R 
--R
--R            2            2
--R   (5)  - 9b  + 9a b - 3a
--R                                                     Type: Polynomial Integer
--E 83

--S 84 of 91
u^2*x+x^2*y+y^2*z+z^2*u
 

   (6)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  0
--R                                                     Type: Polynomial Integer
--E 84

)clear all
 

--S 85 of 91
c:=a^3*b-1
 

         3
   (1)  a b - 1
                                                     Type: Polynomial Integer
--R 
--R
--R         3
--R   (1)  a b - 1
--R                                                     Type: Polynomial Integer
--E 85

--S 86 of 91
d:=a*b^2+1
 

           2
   (2)  a b  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (2)  a b  + 1
--R                                                     Type: Polynomial Integer
--E 86

--S 87 of 91
u:=c
 

         3
   (3)  a b - 1
                                                     Type: Polynomial Integer
--R 
--R
--R         3
--R   (3)  a b - 1
--R                                                     Type: Polynomial Integer
--E 87

--S 88 of 91
x:=a^2*d
 

         3 2    2
   (4)  a b  + a
                                                     Type: Polynomial Integer
--R 
--R
--R         3 2    2
--R   (4)  a b  + a
--R                                                     Type: Polynomial Integer
--E 88

--S 89 of 91
y:=-a*b*c
 

           4 2
   (5)  - a b  + a b
                                                     Type: Polynomial Integer
--R 
--R
--R           4 2
--R   (5)  - a b  + a b
--R                                                     Type: Polynomial Integer
--E 89

--S 90 of 91
z:=a*d
 

         2 2
   (6)  a b  + a
                                                     Type: Polynomial Integer
--R 
--R
--R         2 2
--R   (6)  a b  + a
--R                                                     Type: Polynomial Integer
--E 90

--S 91 of 91
u^2*x+x^2*y+y^2*z+z^2*u
 

   (7)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  0
--R                                                     Type: Polynomial Integer
--E 91

)spool 
 
Starts dribbling to RadixExpansion.output (2010/3/27, 18:46:21).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 17
111::RadixExpansion(5)
 

   (1)  421
                                                       Type: RadixExpansion 5
--R 
--R
--R   (1)  421
--R                                                       Type: RadixExpansion 5
--E 1

--S 2 of 17
(5/24)::RadixExpansion(2)
 

             __
   (2)  0.00110
                                                       Type: RadixExpansion 2
--R 
--R
--R             __
--R   (2)  0.00110
--R                                                       Type: RadixExpansion 2
--E 2

--S 3 of 17
(5/24)::RadixExpansion(3)
 

           __
   (3)  0.012
                                                       Type: RadixExpansion 3
--R 
--R
--R           __
--R   (3)  0.012
--R                                                       Type: RadixExpansion 3
--E 3

--S 4 of 17
(5/24)::RadixExpansion(8)
 

           __
   (4)  0.152
                                                       Type: RadixExpansion 8
--R 
--R
--R           __
--R   (4)  0.152
--R                                                       Type: RadixExpansion 8
--E 4

--S 5 of 17
(5/24)::RadixExpansion(10)
 

             _
   (5)  0.2083
                                                      Type: RadixExpansion 10
--R 
--R
--R             _
--R   (5)  0.2083
--R                                                      Type: RadixExpansion 10
--E 5

--S 6 of 17
(5/24)::RadixExpansion(12)
 

   (6)  0.26
                                                      Type: RadixExpansion 12
--R 
--R
--R   (6)  0.26
--R                                                      Type: RadixExpansion 12
--E 6

--S 7 of 17
(5/24)::RadixExpansion(16)
 

           _
   (7)  0.35
                                                      Type: RadixExpansion 16
--R 
--R
--R           _
--R   (7)  0.35
--R                                                      Type: RadixExpansion 16
--E 7

--S 8 of 17
(5/24)::RadixExpansion(36)
 

   (8)  0.7I
                                                      Type: RadixExpansion 36
--R 
--R
--R   (8)  0.7I
--R                                                      Type: RadixExpansion 36
--E 8

--S 9 of 17
(5/24)::RadixExpansion(38)
 

                    _____
   (9)  0 . 7 34 31 25 12
                                                      Type: RadixExpansion 38
--R 
--R
--R                    _____
--R   (9)  0 . 7 34 31 25 12
--R                                                      Type: RadixExpansion 38
--E 9

--S 10 of 17
a := (76543/210)::RadixExpansion(8)
 

              ____
   (10)  554.37307
                                                       Type: RadixExpansion 8
--R 
--R
--R              ____
--R   (10)  554.37307
--R                                                       Type: RadixExpansion 8
--E 10

--S 11 of 17
w := wholeRagits a
 

   (11)  [5,5,4]
                                                           Type: List Integer
--R 
--R
--R   (11)  [5,5,4]
--R                                                           Type: List Integer
--E 11

--S 12 of 17
f0 := prefixRagits a
 

   (12)  [3]
                                                           Type: List Integer
--R 
--R
--R   (12)  [3]
--R                                                           Type: List Integer
--E 12

--S 13 of 17
f1 := cycleRagits a
 

   (13)  [7,3,0,7]
                                                           Type: List Integer
--R 
--R
--R   (13)  [7,3,0,7]
--R                                                           Type: List Integer
--E 13

--S 14 of 17
u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1)
 

              ____
   (14)  554.37307
                                                       Type: RadixExpansion 8
--R 
--R
--R              ____
--R   (14)  554.37307
--R                                                       Type: RadixExpansion 8
--E 14

--S 15 of 17
v: RadixExpansion(12) := fractRadix([1,2,3,11], [0])
 

               _
   (15)  0.123B0
                                                      Type: RadixExpansion 12
--R 
--R
--R               _
--R   (15)  0.123B0
--R                                                      Type: RadixExpansion 12
--E 15

--S 16 of 17
fractRagits(u)
 

              _______
   (16)  [3,7,3,0,7,7]
                                                         Type: Stream Integer
--R 
--R
--R              _______
--R   (16)  [3,7,3,0,7,7]
--R                                                         Type: Stream Integer
--E 16

--S 17 of 17
a :: Fraction(Integer)
 

         76543
   (17)  -----
          210
                                                       Type: Fraction Integer
--R 
--R
--R         76543
--R   (17)  -----
--R          210
--R                                                       Type: Fraction Integer
--E 17
)spool
 
Starts dribbling to Heap.output (2010/3/27, 18:42:9).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 42
a:Heap INT:= heap [1,2,3,4,5]
 

   (1)  [5,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (1)  [5,4,2,1,3]
--R                                                           Type: Heap Integer
--E 1

--S 2 of 42
bag([1,2,3,4,5])$Heap(INT)
 

   (2)  [5,4,3,1,2]
                                                           Type: Heap Integer
--R 
--R
--R   (2)  [5,4,3,1,2]
--R                                                           Type: Heap Integer
--E 2

--S 3 of 42
c:=copy a
 

   (3)  [5,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (3)  [5,4,2,1,3]
--R                                                           Type: Heap Integer
--E 3

--S 4 of 42
empty? a
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 42
b:=empty()$(Heap INT)
 

   (5)  []
                                                           Type: Heap Integer
--R 
--R
--R   (5)  []
--R                                                           Type: Heap Integer
--E 5

--S 6 of 42
empty? b
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 42
eq?(a,c)
 

   (7)  false
                                                                Type: Boolean
--R 
--R
--R   (7)  false
--R                                                                Type: Boolean
--E 7

--S 8 of 42
extract! a
 

   (8)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  5
--R                                                        Type: PositiveInteger
--E 8

--S 8 of 42
h:=heap [17,-4,9,-11,2,7,-7]
 

   (9)  [17,2,9,- 11,- 4,7,- 7]
                                                           Type: Heap Integer
--R 
--R
--R   (9)  [17,2,9,- 11,- 4,7,- 7]
--R                                                           Type: Heap Integer
--E 8

--S 9 of 42
[extract!(h) while not empty?(h)]
 

   (10)  [17,9,7,2,- 4,- 7,- 11]
                                                           Type: List Integer
--R 
--R
--R   (10)  [17,9,7,2,- 4,- 7,- 11]
--R                                                           Type: List Integer
--E 9

--S 10 of 42
heapsort(x) == (empty? x => []; cons(extract!(x),heapsort x))
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 42
h1 := heapsort heap [17,-4,9,-11,2,7,-7]
 
   Compiling function heapsort with type Heap Integer -> List Integer 

   (12)  [17,9,7,2,- 4,- 7,- 11]
                                                           Type: List Integer
--R 
--R   Compiling function heapsort with type Heap Integer -> List Integer 
--R
--R   (12)  [17,9,7,2,- 4,- 7,- 11]
--R                                                           Type: List Integer
--E 11

--S 12 of 42
(a=c)@Boolean
 

   (13)  false
                                                                Type: Boolean
--R 
--R
--R   (13)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 42
(a~=c)
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 42
a
 

   (15)  [4,3,2,1]
                                                           Type: Heap Integer
--R 
--R
--R   (15)  [4,3,2,1]
--R                                                           Type: Heap Integer
--E 14

--S 15 of 42
inspect a
 

   (16)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  4
--R                                                        Type: PositiveInteger
--E 15

--S 16 of 42
insert!(9,a)
 

   (17)  [9,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (17)  [9,4,2,1,3]
--R                                                           Type: Heap Integer
--E 16

--S 17 of 42
map(x+->x+10,a)
 

   (18)  [19,14,12,11,13]
                                                           Type: Heap Integer
--R 
--R
--R   (18)  [19,14,12,11,13]
--R                                                           Type: Heap Integer
--E 17

--S 18 of 42
a
 

   (19)  [9,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (19)  [9,4,2,1,3]
--R                                                           Type: Heap Integer
--E 18

--S 19 of 42
map!(x+->x+10,a)
 

   (20)  [19,14,12,11,13]
                                                           Type: Heap Integer
--R 
--R
--R   (20)  [19,14,12,11,13]
--R                                                           Type: Heap Integer
--E 19

--S 20 of 42
a
 

   (21)  [19,14,12,11,13]
                                                           Type: Heap Integer
--R 
--R
--R   (21)  [19,14,12,11,13]
--R                                                           Type: Heap Integer
--E 20

--S 21 of 42
max a
 

   (22)  19
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  19
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 42
merge(a,c)
 

   (23)  [19,14,12,11,13,5,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (23)  [19,14,12,11,13,5,4,2,1,3]
--R                                                           Type: Heap Integer
--E 22

--S 23 of 42
a
 

   (24)  [19,14,12,11,13]
                                                           Type: Heap Integer
--R 
--R
--R   (24)  [19,14,12,11,13]
--R                                                           Type: Heap Integer
--E 23

--S 24 of 42
merge!(a,c)
 

   (25)  [19,14,12,11,13,5,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (25)  [19,14,12,11,13,5,4,2,1,3]
--R                                                           Type: Heap Integer
--E 24

--S 25 of 42
a
 

   (26)  [19,14,12,11,13,5,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (26)  [19,14,12,11,13,5,4,2,1,3]
--R                                                           Type: Heap Integer
--E 25

--S 26 of 42
c
 

   (27)  [5,4,2,1,3]
                                                           Type: Heap Integer
--R 
--R
--R   (27)  [5,4,2,1,3]
--R                                                           Type: Heap Integer
--E 26

--S 27 of 42
sample()$Heap(INT)
 

   (28)  []
                                                           Type: Heap Integer
--R 
--R
--R   (28)  []
--R                                                           Type: Heap Integer
--E 27

--S 28 of 42
#a
 

   (29)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (29)  10
--R                                                        Type: PositiveInteger
--E 28

--S 29 of 42
any?(x+->(x=14),a)
 

   (30)  true
                                                                Type: Boolean
--R 
--R
--R   (30)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 42
every?(x+->(x=11),a)
 

   (31)  false
                                                                Type: Boolean
--R 
--R
--R   (31)  false
--R                                                                Type: Boolean
--E 30

--S 31 of 42
parts a
 

   (32)  [19,14,12,11,13,5,4,2,1,3]
                                                           Type: List Integer
--R 
--R
--R   (32)  [19,14,12,11,13,5,4,2,1,3]
--R                                                           Type: List Integer
--E 31

--S 32 of 42
size?(a,9)
 

   (33)  false
                                                                Type: Boolean
--R 
--R
--R   (33)  false
--R                                                                Type: Boolean
--E 32

--S 33 of 42
more?(a,9)
 

   (34)  true
                                                                Type: Boolean
--R 
--R
--R   (34)  true
--R                                                                Type: Boolean
--E 33

--S 34 of 42
less?(a,9)
 

   (35)  false
                                                                Type: Boolean
--R 
--R
--R   (35)  false
--R                                                                Type: Boolean
--E 34

--S 35 of 42
members a
 

   (36)  [19,14,12,11,13,5,4,2,1,3]
                                                           Type: List Integer
--R 
--R
--R   (36)  [19,14,12,11,13,5,4,2,1,3]
--R                                                           Type: List Integer
--E 35

--S 36 of 42
member?(14,a)
 

   (37)  true
                                                                Type: Boolean
--R 
--R
--R   (37)  true
--R                                                                Type: Boolean
--E 36

--S 37 of 42
latex a
 

   (38)  "\mbox{\bf Unimplemented}"
                                                                 Type: String
--R 
--R
--R   (38)  "\mbox{\bf Unimplemented}"
--R                                                                 Type: String
--E 37

--S 38 of 42
hash a
 

   (39)  37072924
                                                          Type: SingleInteger
--R 
--R
--I   (39)  36647017
--R                                                          Type: SingleInteger
--E 38

--S 39 of 42
count(14,a)
 

   (40)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (40)  1
--R                                                        Type: PositiveInteger
--E 39

--S 40 of 42
count(x+->(x>13),a)
 

   (41)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (41)  2
--R                                                        Type: PositiveInteger
--E 40

--S 41 of 42
coerce a
 

   (42)  [19,14,12,11,13,5,4,2,1,3]
                                                             Type: OutputForm
--R 
--R
--R   (42)  [19,14,12,11,13,5,4,2,1,3]
--R                                                             Type: OutputForm
--E 41

--S 42 of 42
)show Heap
 
 Heap S: OrderedSet  is a domain constructor
 Abbreviation for Heap is HEAP 
 This constructor is exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for HEAP 

------------------------------- Operations --------------------------------
 bag : List S -> %                     copy : % -> %
 empty : () -> %                       empty? : % -> Boolean
 eq? : (%,%) -> Boolean                extract! : % -> S
 heap : List S -> %                    insert! : (S,%) -> %
 inspect : % -> S                      map : ((S -> S),%) -> %
 max : % -> S                          merge : (%,%) -> %
 merge! : (%,%) -> %                   sample : () -> %
 #? : % -> NonNegativeInteger if $ has finiteAggregate
 ?=? : (%,%) -> Boolean if S has SETCAT
 any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 coerce : % -> OutputForm if S has SETCAT
 count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
 count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
 eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
 eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
 every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
 hash : % -> SingleInteger if S has SETCAT
 latex : % -> String if S has SETCAT
 less? : (%,NonNegativeInteger) -> Boolean
 map! : ((S -> S),%) -> % if $ has shallowlyMutable
 member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
 members : % -> List S if $ has finiteAggregate
 more? : (%,NonNegativeInteger) -> Boolean
 parts : % -> List S if $ has finiteAggregate
 size? : (%,NonNegativeInteger) -> Boolean
 ?~=? : (%,%) -> Boolean if S has SETCAT

--R 
--R Heap S: OrderedSet  is a domain constructor
--R Abbreviation for Heap is HEAP 
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for HEAP 
--R
--R------------------------------- Operations --------------------------------
--R bag : List S -> %                     copy : % -> %
--R empty : () -> %                       empty? : % -> Boolean
--R eq? : (%,%) -> Boolean                extract! : % -> S
--R heap : List S -> %                    insert! : (S,%) -> %
--R inspect : % -> S                      map : ((S -> S),%) -> %
--R max : % -> S                          merge : (%,%) -> %
--R merge! : (%,%) -> %                   sample : () -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
--R members : % -> List S if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R parts : % -> List S if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
--E 42

)spool
 
Starts dribbling to CliffordAlgebra.output (2010/3/27, 18:41:48).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 36
m := matrix [ [-1] ]
 

   (2)  [- 1]
                                                         Type: Matrix Integer
--R 
--R
--R   (2)  [- 1]
--R                                                         Type: Matrix Integer
--E 2

--S 3 of 36
C := CliffordAlgebra(1, K, quadraticForm m)
 

   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 3

--S 4 of 36
i: C := e(1)
 

   (4)  e
         1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 4

--S 5 of 36
x := a + b * i
 

   (5)  a + b e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  a + b e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 5

--S 6 of 36
y := c + d * i
 

   (6)  c + d e
               1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  c + d e
--R               1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 6

--S 7 of 36
x * y
 

   (7)  - b d + a c + (a d + b c)e
                                  1
                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  - b d + a c + (a d + b c)e
--R                                  1
--R                  Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX)
--E 7
)clear all
 
 
--S 8 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 8

--S 9 of 36
m := matrix [ [-1,0],[0,-1] ]
 

        +- 1   0 +
   (2)  |        |
        + 0   - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +- 1   0 +
--R   (2)  |        |
--R        + 0   - 1+
--R                                                         Type: Matrix Integer
--E 9

--S 10 of 36
H  := CliffordAlgebra(2, K, quadraticForm m)
 

   (3)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 10

--S 11 of 36
i: H  := e(1)
 

   (4)  e
         1
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         1
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 11

--S 12 of 36
j: H  := e(2)
 

   (5)  e
         2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  e
--R         2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 12

--S 13 of 36
k: H  := i * j
 

   (6)  e e
         1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  e e
--R         1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 13

--S 14 of 36
x := a + b * i + c * j + d * k
 

   (7)  a + b e  + c e  + d e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  a + b e  + c e  + d e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 14

--S 15 of 36
y := e + f * i + g * j + h * k 
 

   (8)  e + f e  + g e  + h e e
               1      2      1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (8)  e + f e  + g e  + h e e
--R               1      2      1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 15

--S 16 of 36
x + y
 

   (9)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
                        1           2           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (9)  e + a + (f + b)e  + (g + c)e  + (h + d)e e
--R                        1           2           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 16

--S 17 of 36
x * y
 

   (10)
     - d h - c g - b f + a e + (c h - d g + a f + b e)e
                                                       1
   + 
     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
                               2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (10)
--R     - d h - c g - b f + a e + (c h - d g + a f + b e)e
--R                                                       1
--R   + 
--R     (- b h + a g + d f + c e)e  + (a h + b g - c f + d e)e e
--R                               2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 17

--S 18 of 36
y * x
 

   (11)
     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
                                                         1
   + 
     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
                             2                           1 2
                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (11)
--R     - d h - c g - b f + a e + (- c h + d g + a f + b e)e
--R                                                         1
--R   + 
--R     (b h + a g - d f + c e)e  + (a h - b g + c f + d e)e e
--R                             2                           1 2
--R                  Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)
--E 18
)clear all
 
 
--S 19 of 36
K := Fraction Polynomial Integer
 

   (1)  Fraction Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Polynomial Integer
--R                                                                 Type: Domain
--E 19

--S 20 of 36
Ext := CliffordAlgebra(3, K, quadraticForm 0)
 

   (2)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (2)  CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R                                                                 Type: Domain
--E 20

--S 21 of 36
i: Ext := e(1)
 

   (3)  e
         1
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (3)  e
--R         1
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 21

--S 22 of 36
j: Ext := e(2)
 

   (4)  e
         2
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (4)  e
--R         2
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 22

--S 23 of 36
k: Ext := e(3)
 

   (5)  e
         3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (5)  e
--R         3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 23

--S 24 of 36
x := x1*i + x2*j + x3*k
 

   (6)  x1 e  + x2 e  + x3 e
            1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (6)  x1 e  + x2 e  + x3 e
--R            1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 24

--S 25 of 36
y := y1*i + y2*j + y3*k
 

   (7)  y1 e  + y2 e  + y3 e
            1       2       3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (7)  y1 e  + y2 e  + y3 e
--R            1       2       3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 25

--S 26 of 36
x + y
 

   (8)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
                  1             2             3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (8)  (y1 + x1)e  + (y2 + x2)e  + (y3 + x3)e
--R                  1             2             3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 26

--S 27 of 36
x * y + y * x
 

   (9)  0
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R
--R   (9)  0
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 27

--S 28 of 36
dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 36
dual2(x*y)
 
   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
      Polynomial Integer,MATRIX) 

   (11)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
                         1                     2                   3
                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--R 
--R   Compiling function dual2 with type CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction 
--R      Polynomial Integer,MATRIX) 
--R
--R   (11)  (x2 y3 - x3 y2)e  + (- x1 y3 + x3 y1)e  + (x1 y2 - x2 y1)e
--R                         1                     2                   3
--R                  Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)
--E 29
)clear all
 
 
--S 30 of 36
K := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 30

--S 31 of 36
g := matrix [ [1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1] ]
 

        +1   0    0    0 +
        |                |
        |0  - 1   0    0 |
   (2)  |                |
        |0   0   - 1   0 |
        |                |
        +0   0    0   - 1+
                                                         Type: Matrix Integer
--R 
--R
--R        +1   0    0    0 +
--R        |                |
--R        |0  - 1   0    0 |
--R   (2)  |                |
--R        |0   0   - 1   0 |
--R        |                |
--R        +0   0    0   - 1+
--R                                                         Type: Matrix Integer
--E 31

--S 32 of 36
D := CliffordAlgebra(4,K, quadraticForm g)
 

   (3)  CliffordAlgebra(4,Fraction Integer,MATRIX)
                                                                 Type: Domain
--R 
--R
--R   (3)  CliffordAlgebra(4,Fraction Integer,MATRIX)
--R                                                                 Type: Domain
--E 32

--S 33 of 36
gam := [e(i)$D for i in 1..4]
 

   (4)  [e ,e ,e ,e ]
          1  2  3  4
                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (4)  [e ,e ,e ,e ]
--R          1  2  3  4
--R                        Type: List CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 33

--S 34 of 36
m := 1; n:= 2; r := 3; s := 4;
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 36
lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4])
 

   (6)  - 4e e e e
            1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (6)  - 4e e e e
--R            1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 35

--S 36 of 36
rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s) 
 

   (7)  - 4e e e e
            1 2 3 4
                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--R 
--R
--R   (7)  - 4e e e e
--R            1 2 3 4
--R                             Type: CliffordAlgebra(4,Fraction Integer,MATRIX)
--E 36
)spool
 
Starts dribbling to Polynomial.output (2010/3/27, 18:46:17).
)set message test on
 
)set message auto off
 
--S 1 of 46
x + 1
 

   (1)  x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (1)  x + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 46
z - 2.3
 

   (2)  z - 2.3
                                                       Type: Polynomial Float
--R 
--R
--R   (2)  z - 2.3
--R                                                       Type: Polynomial Float
--E 2

--S 3 of 46
y**2 - z + 3/4
 

               2   3
   (3)  - z + y  + -
                   4
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2   3
--R   (3)  - z + y  + -
--R                   4
--R                                            Type: Polynomial Fraction Integer
--E 3

--S 4 of 46
y **2 + x*y + y
 

         2
   (4)  y  + (x + 1)y
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (4)  y  + (x + 1)y
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 46
% :: DMP([y,x],INT)
 

         2
   (5)  y  + y x + y
                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--R 
--R
--R         2
--R   (5)  y  + y x + y
--R                       Type: DistributedMultivariatePolynomial([y,x],Integer)
--E 5

--S 6 of 46
p := (y-1)**2 * x * z
 

            2
   (6)  (x y  - 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (6)  (x y  - 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 6

--S 7 of 46
q := (y-1) * x * (z+5)
 

   (7)  (x y - x)z + 5x y - 5x
                                                     Type: Polynomial Integer
--R 
--R
--R   (7)  (x y - x)z + 5x y - 5x
--R                                                     Type: Polynomial Integer
--E 7

--S 8 of 46
factor(q)
 

   (8)  x(y - 1)(z + 5)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (8)  x(y - 1)(z + 5)
--R                                            Type: Factored Polynomial Integer
--E 8

--S 9 of 46
p - q**2
 

   (9)
         2 2     2     2  2          2      2       2             2
     (- x y  + 2x y - x )z  + ((- 10x  + x)y  + (20x  - 2x)y - 10x  + x)z
   + 
          2 2      2       2
     - 25x y  + 50x y - 25x
                                                     Type: Polynomial Integer
--R 
--R
--R   (9)
--R         2 2     2     2  2          2      2       2             2
--R     (- x y  + 2x y - x )z  + ((- 10x  + x)y  + (20x  - 2x)y - 10x  + x)z
--R   + 
--R          2 2      2       2
--R     - 25x y  + 50x y - 25x
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 46
gcd(p,q)
 

   (10)  x y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)  x y - x
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 46
factor %
 

   (11)  x(y - 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (11)  x(y - 1)
--R                                            Type: Factored Polynomial Integer
--E 11

--S 12 of 46
lcm(p,q)
 

             2             2        2
   (12)  (x y  - 2x y + x)z  + (5x y  - 10x y + 5x)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2             2        2
--R   (12)  (x y  - 2x y + x)z  + (5x y  - 10x y + 5x)z
--R                                                     Type: Polynomial Integer
--E 12

--S 13 of 46
content p
 

   (13)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  1
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 46
resultant(p,q,z)
 

           2 3      2 2      2      2
   (14)  5x y  - 15x y  + 15x y - 5x
                                                     Type: Polynomial Integer
--R 
--R
--R           2 3      2 2      2      2
--R   (14)  5x y  - 15x y  + 15x y - 5x
--R                                                     Type: Polynomial Integer
--E 14

--S 15 of 46
resultant(p,q,x)
 

   (15)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  0
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 46
mainVariable p
 

   (16)  z
                                                      Type: Union(Symbol,...)
--R 
--R
--R   (16)  z
--R                                                      Type: Union(Symbol,...)
--E 16

--S 17 of 46
mainVariable(1 :: POLY INT)
 

   (17)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (17)  "failed"
--R                                                    Type: Union("failed",...)
--E 17

--S 18 of 46
ground? p
 

   (18)  false
                                                                Type: Boolean
--R 
--R
--R   (18)  false
--R                                                                Type: Boolean
--E 18

--S 19 of 46
ground?(1 :: POLY INT)
 

   (19)  true
                                                                Type: Boolean
--R 
--R
--R   (19)  true
--R                                                                Type: Boolean
--E 19

--S 20 of 46
variables p
 

   (20)  [z,y,x]
                                                            Type: List Symbol
--R 
--R
--R   (20)  [z,y,x]
--R                                                            Type: List Symbol
--E 20

--S 21 of 46
degree(p,x)
 

   (21)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (21)  1
--R                                                        Type: PositiveInteger
--E 21

--S 22 of 46
degree(p,y)
 

   (22)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  2
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 46
degree(p,z)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 46
degree(p,[x,y,z])
 

   (24)  [1,2,1]
                                                Type: List NonNegativeInteger
--R 
--R
--R   (24)  [1,2,1]
--R                                                Type: List NonNegativeInteger
--E 24

--S 25 of 46
minimumDegree(p,z)
 

   (25)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  1
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 46
totalDegree p
 

   (26)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  4
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 46
leadingMonomial p
 

            2
   (27)  x y z
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (27)  x y z
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 46
reductum p
 

   (28)  (- 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R   (28)  (- 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 28

--S 29 of 46
p - leadingMonomial p - reductum p
 

   (29)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (29)  0
--R                                                     Type: Polynomial Integer
--E 29

--S 30 of 46
leadingCoefficient p
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 46
p
 

             2
   (31)  (x y  - 2x y + x)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (31)  (x y  - 2x y + x)z
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 46
eval(p,x,w)
 

             2
   (32)  (w y  - 2w y + w)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (32)  (w y  - 2w y + w)z
--R                                                     Type: Polynomial Integer
--E 32

--S 33 of 46
eval(p,x,1)
 

           2
   (33)  (y  - 2y + 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (33)  (y  - 2y + 1)z
--R                                                     Type: Polynomial Integer
--E 33

--S 34 of 46
eval(p,x,y^2 - 1)
 

           4     3
   (34)  (y  - 2y  + 2y - 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           4     3
--R   (34)  (y  - 2y  + 2y - 1)z
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 46
D(p,x)
 

           2
   (35)  (y  - 2y + 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (35)  (y  - 2y + 1)z
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 46
D(p,y)
 

   (36)  (2x y - 2x)z
                                                     Type: Polynomial Integer
--R 
--R
--R   (36)  (2x y - 2x)z
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 46
D(p,z)
 

            2
   (37)  x y  - 2x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R            2
--R   (37)  x y  - 2x y + x
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 46
integrate(p,y)
 

          1    3      2
   (38)  (- x y  - x y  + x y)z
          3
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1    3      2
--R   (38)  (- x y  - x y  + x y)z
--R          3
--R                                            Type: Polynomial Fraction Integer
--E 38

--S 39 of 46
qr := monicDivide(p,x+1,x)
 

                      2                           2
   (39)  [quotient= (y  - 2y + 1)z,remainder= (- y  + 2y - 1)z]
     Type: Record(quotient: Polynomial Integer,remainder: Polynomial Integer)
--R 
--R
--R                      2                           2
--R   (39)  [quotient= (y  - 2y + 1)z,remainder= (- y  + 2y - 1)z]
--R     Type: Record(quotient: Polynomial Integer,remainder: Polynomial Integer)
--E 39

--S 40 of 46
qr.remainder
 

             2
   (40)  (- y  + 2y - 1)z
                                                     Type: Polynomial Integer
--R 
--R
--R             2
--R   (40)  (- y  + 2y - 1)z
--R                                                     Type: Polynomial Integer
--E 40

--S 41 of 46
p - ((x+1) * qr.quotient + qr.remainder)
 

   (41)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (41)  0
--R                                                     Type: Polynomial Integer
--E 41

--S 42 of 46
p/q
 

         (y - 1)z
   (42)  --------
           z + 5
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         (y - 1)z
--R   (42)  --------
--R           z + 5
--R                                            Type: Fraction Polynomial Integer
--E 42

--S 43 of 46
(2/3) * x**2 - y + 4/5 
 

               2  2   4
   (43)  - y + - x  + -
               3      5
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2  2   4
--R   (43)  - y + - x  + -
--R               3      5
--R                                            Type: Polynomial Fraction Integer
--E 43

--S 44 of 46
% :: FRAC POLY INT
 

                    2
         - 15y + 10x  + 12
   (44)  -----------------
                 15
                                            Type: Fraction Polynomial Integer
--R 
--R
--R                    2
--R         - 15y + 10x  + 12
--R   (44)  -----------------
--R                 15
--R                                            Type: Fraction Polynomial Integer
--E 44

--S 45 of 46
% :: POLY FRAC INT
 

               2  2   4
   (45)  - y + - x  + -
               3      5
                                            Type: Polynomial Fraction Integer
--R 
--R
--R               2  2   4
--R   (45)  - y + - x  + -
--R               3      5
--R                                            Type: Polynomial Fraction Integer
--E 45

--S 46 of 46
map(numeric,%)
 

                                            2
   (46)  - 1.0 y + 0.6666666666 6666666667 x  + 0.8
                                                       Type: Polynomial Float
--R 
--R
--R                                            2
--R   (46)  - 1.0 y + 0.6666666666 6666666667 x  + 0.8
--R                                                       Type: Polynomial Float
--E 46
)spool
 
Starts dribbling to elfuts.output (2010/3/27, 18:25:25).
)set message test on
 
)set message auto off
 
)clear all
 
)set streams calculate 10
 

 
)expose ELFUTS
 
   EllipticFunctionsUnivariateTaylorSeries is now explicitly exposed in
      frame initial 

--S 1 of 40
macro RN == FRAC INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 40
macro QF == FRAC
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 40
xx:UTS(RN,'x,0):=x
 

   (3)  x
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R   (3)  x
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 3

--S 4 of 40
sn(xx,1::RN)
 

            1  3    2  5    17  7    62   9      11
   (4)  x - - x  + -- x  - --- x  + ---- x  + O(x  )
            3      15      315      2835
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R            1  3    2  5    17  7    62   9      11
--R   (4)  x - - x  + -- x  - --- x  + ---- x  + O(x  )
--R            3      15      315      2835
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 4

--S 5 of 40
cn(xx,1::RN)
 

            1  2    5  4    61  6    277  8    50521   10      11
   (5)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
            2      24      720      8064      3628800
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R            1  2    5  4    61  6    277  8    50521   10      11
--R   (5)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
--R            2      24      720      8064      3628800
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 5

--S 6 of 40
dn(xx,1::RN)
 

            1  2    5  4    61  6    277  8    50521   10      11
   (6)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
            2      24      720      8064      3628800
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--R 
--R
--R            1  2    5  4    61  6    277  8    50521   10      11
--R   (6)  1 - - x  + -- x  - --- x  + ---- x  - ------- x   + O(x  )
--R            2      24      720      8064      3628800
--R                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
--E 6

--S 7 of 40
yy:UTS(FRAC UP(k,RN),'y,0):=y
 

   (7)  y
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (7)  y
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 7

--S 8 of 40
snn:=sn(yy,k::QF UP(k,RN))
 

   (8)
            1  2   1  3     1   4    7  2    1   5
     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
            6      6       120      60      120
   + 
          1   6    3   4    3   2     1   7
     (- ---- k  - --- k  - --- k  - ----)y
        5040      112      112      5040
   + 
         1    8    307   6    913   4    307   2      1    9      11
     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
      362880      90720      60480      90720      362880
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (8)
--R            1  2   1  3     1   4    7  2    1   5
--R     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
--R            6      6       120      60      120
--R   + 
--R          1   6    3   4    3   2     1   7
--R     (- ---- k  - --- k  - --- k  - ----)y
--R        5040      112      112      5040
--R   + 
--R         1    8    307   6    913   4    307   2      1    9      11
--R     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
--R      362880      90720      60480      90720      362880
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 8

--S 9 of 40
cnn:=cn(yy,k::QF UP(k,RN))
 

   (9)
         1  2    1  2    1  4       1  4    11  2    1   6
     1 - - y  + (- k  + --)y  + (- -- k  - --- k  - ---)y
         2       6      24         45      180      720
   + 
       1   6    19  4    17   2     1    8
     (--- k  + --- k  + ---- k  + -----)y
      630      840      1680      40320
   + 
          1    8    247   6    641   4     461   2      1     10      11
     (- ----- k  - ----- k  - ----- k  - ------ k  - -------)y   + O(y  )
        14175      56700      75600      453600      3628800
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (9)
--R         1  2    1  2    1  4       1  4    11  2    1   6
--R     1 - - y  + (- k  + --)y  + (- -- k  - --- k  - ---)y
--R         2       6      24         45      180      720
--R   + 
--R       1   6    19  4    17   2     1    8
--R     (--- k  + --- k  + ---- k  + -----)y
--R      630      840      1680      40320
--R   + 
--R          1    8    247   6    641   4     461   2      1     10      11
--R     (- ----- k  - ----- k  - ----- k  - ------ k  - -------)y   + O(y  )
--R        14175      56700      75600      453600      3628800
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 9

--S 10 of 40
dnn:=dn(yy,k::QF UP(k,RN))
 

   (10)
         1  2 2     1  4   1  2  4       1   6    11  4    1  2  6
     1 - - k y  + (-- k  + - k )y  + (- --- k  - --- k  - -- k )y
         2         24      6            720      180      45
   + 
        1    8    17   6    19  4    1   2  8
     (----- k  + ---- k  + --- k  + --- k )y
      40320      1680      840      630
   + 
           1     10     461   8    641   6    247   4     1    2  10      11
     (- ------- k   - ------ k  - ----- k  - ----- k  - ----- k )y   + O(y  )
        3628800       453600      75600      56700      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (10)
--R         1  2 2     1  4   1  2  4       1   6    11  4    1  2  6
--R     1 - - k y  + (-- k  + - k )y  + (- --- k  - --- k  - -- k )y
--R         2         24      6            720      180      45
--R   + 
--R        1    8    17   6    19  4    1   2  8
--R     (----- k  + ---- k  + --- k  + --- k )y
--R      40320      1680      840      630
--R   + 
--R           1     10     461   8    641   6    247   4     1    2  10      11
--R     (- ------- k   - ------ k  - ----- k  - ----- k  - ----- k )y   + O(y  )
--R        3628800       453600      75600      56700      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 10

--S 11 of 40
snn**2+cnn**2
 

                11
   (11)  1 + O(y  )
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R                11
--R   (11)  1 + O(y  )
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 11

--S 12 of 40
ksquared:=(k::UP(k,RN))**2
 

          2
   (12)  k
                               Type: UnivariatePolynomial(k,Fraction Integer)
--R 
--R
--R          2
--R   (12)  k
--R                               Type: UnivariatePolynomial(k,Fraction Integer)
--E 12

--S 13 of 40
dnn**2+ksquared*snn**2
 

                11
   (13)  1 + O(y  )
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R                11
--R   (13)  1 + O(y  )
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 13

--S 14 of 40
(differentiate snn)**2
 

   (14)
             2      2    1  4   5  2   1  4       2  6    4    2    2  6
     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
                         3      3      3         45                45
   + 
       1   8    94  6   104  4    94  2    1   8
     (--- k  + --- k  + --- k  + --- k  + ---)y
      315      315      105      315      315
   + 
        2    10    109  8    6977  6    6977  4    109  2     2    10      11
   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
      14175       2025      14175      14175      2025      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (14)
--R             2      2    1  4   5  2   1  4       2  6    4    2    2  6
--R     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
--R                         3      3      3         45                45
--R   + 
--R       1   8    94  6   104  4    94  2    1   8
--R     (--- k  + --- k  + --- k  + --- k  + ---)y
--R      315      315      105      315      315
--R   + 
--R        2    10    109  8    6977  6    6977  4    109  2     2    10      11
--R   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
--R      14175       2025      14175      14175      2025      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 14

--S 15 of 40
(1-snn**2)*(1-ksquared*snn**2)
 

   (15)
             2      2    1  4   5  2   1  4       2  6    4    2    2  6
     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
                         3      3      3         45                45
   + 
       1   8    94  6   104  4    94  2    1   8
     (--- k  + --- k  + --- k  + --- k  + ---)y
      315      315      105      315      315
   + 
        2    10    109  8    6977  6    6977  4    109  2     2    10      11
   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
      14175       2025      14175      14175      2025      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (15)
--R             2      2    1  4   5  2   1  4       2  6    4    2    2  6
--R     1 + (- k  - 1)y  + (- k  + - k  + -)y  + (- -- k  - k  - k  - --)y
--R                         3      3      3         45                45
--R   + 
--R       1   8    94  6   104  4    94  2    1   8
--R     (--- k  + --- k  + --- k  + --- k  + ---)y
--R      315      315      105      315      315
--R   + 
--R        2    10    109  8    6977  6    6977  4    109  2     2    10      11
--R   (- ----- k   - ---- k  - ----- k  - ----- k  - ---- k  - -----)y   + O(y  )
--R      14175       2025      14175      14175      2025      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 15

--S 16 of 40
(differentiate cnn)**2
 

   (16)
      2      4  2   1  4    32  4   43  2    2  6
     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
             3      3       45      45      45
   + 
         64  6    94  4    31  2    1   8
     (- --- k  - --- k  - --- k  - ---)y
        315      105      105      315
   + 
       512   8    6101  6   2242  4    761   2     2    10      11
     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
      14175      14175      4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (16)
--R      2      4  2   1  4    32  4   43  2    2  6
--R     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
--R             3      3       45      45      45
--R   + 
--R         64  6    94  4    31  2    1   8
--R     (- --- k  - --- k  - --- k  - ---)y
--R        315      105      105      315
--R   + 
--R       512   8    6101  6   2242  4    761   2     2    10      11
--R     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
--R      14175      14175      4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 16

--S 17 of 40
(1-cnn**2)*(1-ksquared+ksquared*cnn**2)
 

   (17)
      2      4  2   1  4    32  4   43  2    2  6
     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
             3      3       45      45      45
   + 
         64  6    94  4    31  2    1   8
     (- --- k  - --- k  - --- k  - ---)y
        315      105      105      315
   + 
       512   8    6101  6   2242  4    761   2     2    10      11
     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
      14175      14175      4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (17)
--R      2      4  2   1  4    32  4   43  2    2  6
--R     y  + (- - k  - -)y  + (-- k  + -- k  + --)y
--R             3      3       45      45      45
--R   + 
--R         64  6    94  4    31  2    1   8
--R     (- --- k  - --- k  - --- k  - ---)y
--R        315      105      105      315
--R   + 
--R       512   8    6101  6   2242  4    761   2     2    10      11
--R     (----- k  + ----- k  + ---- k  + ----- k  + -----)y   + O(y  )
--R      14175      14175      4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 17

--S 18 of 40
(differentiate dnn)**2
 

   (18)
      4 2      1  6   4  4  4     2  8   43  6   32  4  6
     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
               3      3          45      45      45
   + 
         1   10    31  8    94  6    64  4  8
     (- --- k   - --- k  - --- k  - --- k )y
        315       105      105      315
   + 
        2    12    761   10   2242  8    6101  6    512   4  10      11
     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
      14175       14175       4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (18)
--R      4 2      1  6   4  4  4     2  8   43  6   32  4  6
--R     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
--R               3      3          45      45      45
--R   + 
--R         1   10    31  8    94  6    64  4  8
--R     (- --- k   - --- k  - --- k  - --- k )y
--R        315       105      105      315
--R   + 
--R        2    12    761   10   2242  8    6101  6    512   4  10      11
--R     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
--R      14175       14175       4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 18

--S 19 of 40
(1-dnn**2)*(dnn**2-1+ksquared)
 

   (19)
      4 2      1  6   4  4  4     2  8   43  6   32  4  6
     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
               3      3          45      45      45
   + 
         1   10    31  8    94  6    64  4  8
     (- --- k   - --- k  - --- k  - --- k )y
        315       105      105      315
   + 
        2    12    761   10   2242  8    6101  6    512   4  10      11
     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
      14175       14175       4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (19)
--R      4 2      1  6   4  4  4     2  8   43  6   32  4  6
--R     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
--R               3      3          45      45      45
--R   + 
--R         1   10    31  8    94  6    64  4  8
--R     (- --- k   - --- k  - --- k  - --- k )y
--R        315       105      105      315
--R   + 
--R        2    12    761   10   2242  8    6101  6    512   4  10      11
--R     (----- k   + ----- k   + ---- k  + ----- k  + ----- k )y   + O(y  )
--R      14175       14175       4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 19

--S 20 of 40
kkk:=integrate(1/((1-yy**2)*(1-ksquared*yy**2))**(1/2))
 

   (20)
          1  2   1  3     3  4    1  2    3  5
     y + (- k  + -)y  + (-- k  + -- k  + --)y
          6      6       40      20      40
   + 
       5   6    3   4    3   2    5   7
     (--- k  + --- k  + --- k  + ---)y
      112      112      112      112
   + 
       35   8    5   6    1  4    5   2    35   9      11
     (---- k  + --- k  + -- k  + --- k  + ----)y  + O(y  )
      1152      288      64      288      1152
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (20)
--R          1  2   1  3     3  4    1  2    3  5
--R     y + (- k  + -)y  + (-- k  + -- k  + --)y
--R          6      6       40      20      40
--R   + 
--R       5   6    3   4    3   2    5   7
--R     (--- k  + --- k  + --- k  + ---)y
--R      112      112      112      112
--R   + 
--R       35   8    5   6    1  4    5   2    35   9      11
--R     (---- k  + --- k  + -- k  + --- k  + ----)y  + O(y  )
--R      1152      288      64      288      1152
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 20

--S 21 of 40
revert kkk
 

   (21)
            1  2   1  3     1   4    7  2    1   5
     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
            6      6       120      60      120
   + 
          1   6    3   4    3   2     1   7
     (- ---- k  - --- k  - --- k  - ----)y
        5040      112      112      5040
   + 
         1    8    307   6    913   4    307   2      1    9      11
     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
      362880      90720      60480      90720      362880
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (21)
--R            1  2   1  3     1   4    7  2    1   5
--R     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
--R            6      6       120      60      120
--R   + 
--R          1   6    3   4    3   2     1   7
--R     (- ---- k  - --- k  - --- k  - ----)y
--R        5040      112      112      5040
--R   + 
--R         1    8    307   6    913   4    307   2      1    9      11
--R     (------ k  + ----- k  + ----- k  + ----- k  + ------)y  + O(y  )
--R      362880      90720      60480      90720      362880
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 21

--S 22 of 40
snn
 

   (22)
            1  2   1  3     1   4    7  2    1   5
     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
            6      6       120      60      120
   + 
          1   6    3   4    3   2     1   7
     (- ---- k  - --- k  - --- k  - ----)y
        5040      112      112      5040
   + 
         1    8    307   6    913   4    307   2      1    9
     (------ k  + ----- k  + ----- k  + ----- k  + ------)y
      362880      90720      60480      90720      362880
   + 
               1     10     11069   8     82913   6     82913   4     11069   2
         - -------- k   - -------- k  - -------- k  - -------- k  - -------- k
           39916800       39916800      19958400      19958400      39916800
       + 
               1
         - --------
           39916800
    *
        11
       y
   + 
        12
     O(y  )
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (22)
--R            1  2   1  3     1   4    7  2    1   5
--R     y + (- - k  - -)y  + (--- k  + -- k  + ---)y
--R            6      6       120      60      120
--R   + 
--R          1   6    3   4    3   2     1   7
--R     (- ---- k  - --- k  - --- k  - ----)y
--R        5040      112      112      5040
--R   + 
--R         1    8    307   6    913   4    307   2      1    9
--R     (------ k  + ----- k  + ----- k  + ----- k  + ------)y
--R      362880      90720      60480      90720      362880
--R   + 
--R               1     10     11069   8     82913   6     82913   4     11069   2
--R         - -------- k   - -------- k  - -------- k  - -------- k  - -------- k
--R           39916800       39916800      19958400      19958400      39916800
--R       + 
--R               1
--R         - --------
--R           39916800
--R    *
--R        11
--R       y
--R   + 
--R        12
--R     O(y  )
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 22
 
q0=*/[1-q**2*n for n in 1..]
 
   There are 14 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                          Stream Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
q1=*/[1+q**2*n for n in 1..]
 
   There are 14 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                          Stream Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
q2=*/[1+q**(2*n-1) for n in 1..]
 
   There are 14 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                     Stream Fraction Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
q3=*/[1-q**(2*n-1) for n in 1..]
 
   There are 14 exposed and 12 unexposed library operations named / 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op /
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named / 
      with argument type(s) 
                                 Variable *
                     Stream Fraction Polynomial Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--S 23 of 40
eprod x==exp evenlambert log x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 23

--S 24 of 40
qq:UTS(RN,'q,0):=q
 

   (24)  q
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R   (24)  q
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 24

--S 25 of 40
q0:=eprod(1-qq)
 
   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 

              2    4    10      11
   (25)  1 - q  - q  + q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
--R      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 
--R
--R              2    4    10      11
--R   (25)  1 - q  - q  + q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 25

--S 26 of 40
q1:=eprod(1+qq)
 

              2    4     6     8     10      11
   (26)  1 + q  + q  + 2q  + 2q  + 3q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R              2    4     6     8     10      11
--R   (26)  1 + q  + q  + 2q  + 2q  + 3q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 26

--S 27 of 40
oprod x == exp oddlambert log x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 27

--S 28 of 40
q2:=oprod(1+qq)
 
   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 

                  3    4    5    6    7     8     9     10      11
   (28)  1 + q + q  + q  + q  + q  + q  + 2q  + 2q  + 2q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
--R      Integer,q,0) -> UnivariateTaylorSeries(Fraction Integer,q,0) 
--R
--R                  3    4    5    6    7     8     9     10      11
--R   (28)  1 + q + q  + q  + q  + q  + q  + 2q  + 2q  + 2q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 28

--S 29 of 40
q3:=oprod(1-qq)
 

                  3    4    5    6    7     8     9     10      11
   (29)  1 - q - q  + q  - q  + q  - q  + 2q  - 2q  + 2q   + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                  3    4    5    6    7     8     9     10      11
--R   (29)  1 - q - q  + q  - q  + q  - q  + 2q  - 2q  + 2q   + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 29

--S 30 of 40
q1*q2*q3
 

                11
   (30)  1 + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                11
--R   (30)  1 + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 30

--S 31 of 40
q2**8-q3**8
 

                   3       5        7        9      11
   (31)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                   3       5        7        9      11
--R   (31)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 31

--S 32 of 40
16*qq*q1**8
 

                   3       5        7        9      11
   (32)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                   3       5        7        9      11
--R   (32)  16q + 128q  + 576q  + 2048q  + 6304q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 32

--(q1**2/q2**2)**2
--(q3**2/q2**2)**2

--S 33 of 40
q0**3
 

               2     6      11
   (33)  1 - 3q  + 5q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R               2     6      11
--R   (33)  1 - 3q  + 5q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 33

--S 34 of 40
q1**2*q0
 

              2    6      11
   (34)  1 + q  + q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R              2    6      11
--R   (34)  1 + q  + q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 34

--S 35 of 40
q2**2*q0
 

                    4     9      11
   (35)  1 + 2q + 2q  + 2q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                    4     9      11
--R   (35)  1 + 2q + 2q  + 2q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 35

--S 36 of 40
q3**2*q0
 

                    4     9      11
   (36)  1 - 2q + 2q  - 2q  + O(q  )
                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--R 
--R
--R                    4     9      11
--R   (36)  1 - 2q + 2q  - 2q  + O(q  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,q,0)
--E 36

--S 37 of 40
qqq:UTS(FRAC UP(a,RN),'q,0):=q
 

   (37)  q
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--R 
--R
--R   (37)  q
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--E 37

--S 38 of 40
a:=a::FRAC UP(a,RN)
 

   (38)  a
                      Type: Fraction UnivariatePolynomial(a,Fraction Integer)
--R 
--R
--R   (38)  a
--R                      Type: Fraction UnivariatePolynomial(a,Fraction Integer)
--E 38

--S 39 of 40
eprod(1-qqq)*oprod(1-a*qqq)*oprod(1-qqq/a)
 
   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
      Integer),q,0) 
   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
      Integer),q,0) 

                2          4             6
             - a  - 1     a  + 1  4   - a  - 1  9      11
   (39)  1 + -------- q + ------ q  + -------- q  + O(q  )
                 a           2            3
                            a            a
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--R 
--R   Compiling function eprod with type UnivariateTaylorSeries(Fraction 
--R      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
--R      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
--R      Integer),q,0) 
--R   Compiling function oprod with type UnivariateTaylorSeries(Fraction 
--R      UnivariatePolynomial(a,Fraction Integer),q,0) -> 
--R      UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction 
--R      Integer),q,0) 
--R
--R                2          4             6
--R             - a  - 1     a  + 1  4   - a  - 1  9      11
--R   (39)  1 + -------- q + ------ q  + -------- q  + O(q  )
--R                 a           2            3
--R                            a            a
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(a,Fraction Integer),q,0)
--E 39

--S 40 of 40
sq:=ksquared*snn**2
 

   (40)
      2 2      1  4   1  2  4     2  6   13  4    2  2  6
     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
               3      3          45      45      45
   + 
         1   8    2  6    2  4    1   2  8
     (- --- k  - -- k  - -- k  - --- k )y
        315      21      21      315
   + 
        2    10    251   8    292  6    251   4     2    2  10      11
     (----- k   + ----- k  + ---- k  + ----- k  + ----- k )y   + O(y  )
      14175       14175      4725      14175      14175
Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--R 
--R
--R   (40)
--R      2 2      1  4   1  2  4     2  6   13  4    2  2  6
--R     k y  + (- - k  - - k )y  + (-- k  + -- k  + -- k )y
--R               3      3          45      45      45
--R   + 
--R         1   8    2  6    2  4    1   2  8
--R     (- --- k  - -- k  - -- k  - --- k )y
--R        315      21      21      315
--R   + 
--R        2    10    251   8    292  6    251   4     2    2  10      11
--R     (----- k   + ----- k  + ---- k  + ----- k  + ----- k )y   + O(y  )
--R      14175       14175      4725      14175      14175
--RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0)
--E 40
)spool 
 
Starts dribbling to poly.output (2010/3/27, 18:30:50).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 54
a := rootOf(a**4+1,a)
 

   (1)  a
                                                     Type: Expression Integer
--R 
--R
--R   (1)  a
--R                                                     Type: Expression Integer
--E 1

--S 2 of 54
definingPolynomial a
 

         4
   (2)  a  + 1
                                                     Type: Expression Integer
--R 
--R
--R         4
--R   (2)  a  + 1
--R                                                     Type: Expression Integer
--E 2

--S 3 of 54
b := rootOf(b**2-a-1,b)
 

   (3)  b
                                                     Type: Expression Integer
--R 
--R
--R   (3)  b
--R                                                     Type: Expression Integer
--E 3

--S 4 of 54
a + b
 

   (4)  b + a
                                                     Type: Expression Integer
--R 
--R
--R   (4)  b + a
--R                                                     Type: Expression Integer
--E 4

--S 5 of 54
% ** 5
 

            3      2                 3      2
   (5)  (10a  + 11a  + 2a - 4)b + 15a  + 10a  + 4a - 10
                                                     Type: Expression Integer
--R 
--R
--R            3      2                 3      2
--R   (5)  (10a  + 11a  + 2a - 4)b + 15a  + 10a  + 4a - 10
--R                                                     Type: Expression Integer
--E 5

--S 6 of 54
rootOf(c**2+c+1,c)
 

   (6)  c
                                                     Type: Expression Integer
--R 
--R
--R   (6)  c
--R                                                     Type: Expression Integer
--E 6

--S 7 of 54
zeroOf(d**2+d+1,d)
 

         +---+
        \|- 3  - 1
   (7)  ----------
             2
                                                     Type: Expression Integer
--R 
--R
--R         +---+
--R        \|- 3  - 1
--R   (7)  ----------
--R             2
--R                                                     Type: Expression Integer
--E 7

--S 8 of 54
rootOf(e**5-2,e)
 

   (8)  e
                                                     Type: Expression Integer
--R 
--R
--R   (8)  e
--R                                                     Type: Expression Integer
--E 8

--S 9 of 54
zeroOf(f**5-2,f)
 

        5+-+
   (9)  \|2
                                                     Type: Expression Integer
--R 
--R
--R        5+-+
--R   (9)  \|2
--R                                                     Type: Expression Integer
--E 9

)clear all
 

--S 10 of 54
p := 3*x**8 + 2*x**7 + 6*x**2 + 7*x + 2
 

          8     7     2
   (1)  3x  + 2x  + 6x  + 7x + 2
                                                     Type: Polynomial Integer
--R 
--R
--R          8     7     2
--R   (1)  3x  + 2x  + 6x  + 7x + 2
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 54
q := 2*x**13 + 9*x**7 + 2*x**6 + 10*x + 5
 

          13     7     6
   (2)  2x   + 9x  + 2x  + 10x + 5
                                                     Type: Polynomial Integer
--R 
--R
--R          13     7     6
--R   (2)  2x   + 9x  + 2x  + 10x + 5
--R                                                     Type: Polynomial Integer
--E 11

--S 12 of 54
gcd(p,q)
 

         7
   (3)  x  + 2x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         7
--R   (3)  x  + 2x + 1
--R                                                     Type: Polynomial Integer
--E 12

--S 13 of 54
resultant(p,q,x)
 

   (4)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (4)  0
--R                                                     Type: Polynomial Integer
--E 13

)clear all
 

--S 14 of 54
p := x**2 + y**2
 

         2    2
   (1)  y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2    2
--R   (1)  y  + x
--R                                                     Type: Polynomial Integer
--E 14

--S 15 of 54
eval(p,x=5)
 

         2
   (2)  y  + 25
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (2)  y  + 25
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 54
eval(p,[x = a + b,y = c + d])
 

         2           2    2           2
   (3)  d  + 2c d + c  + b  + 2a b + a
                                                     Type: Polynomial Integer
--R 
--R
--R         2           2    2           2
--R   (3)  d  + 2c d + c  + b  + 2a b + a
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 54
q := x**3 + 5*x - y**4
 

           4    3
   (4)  - y  + x  + 5x
                                                     Type: Polynomial Integer
--R 
--R
--R           4    3
--R   (4)  - y  + x  + 5x
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 54
eval(q,[x=y,y=x])
 

         3         4
   (5)  y  + 5y - x
                                                     Type: Polynomial Integer
--R 
--R
--R         3         4
--R   (5)  y  + 5y - x
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 54
px := eval(p, y = sin(2.0))
 

         2
   (6)  x  + 0.8268218104 3180595732
                                                       Type: Polynomial Float
--R 
--R
--R         2
--R   (6)  x  + 0.8268218104 3180595732
--R                                                       Type: Polynomial Float
--E 19

--S 20 of 54
eval(px, x = cos(2.0))
 

   (7)  1.0
                                                       Type: Polynomial Float
--R 
--R
--R   (7)  1.0
--R                                                       Type: Polynomial Float
--E 20

)clear all
 

--S 21 of 54
factor(x**3 - 3*x + 2)
 

               2
   (1)  (x - 1) (x + 2)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2
--R   (1)  (x - 1) (x + 2)
--R                                            Type: Factored Polynomial Integer
--E 21

--S 22 of 54
factor(x**2/4 + x*y + y**2)
 

             1   2
   (2)  (y + - x)
             2
                                   Type: Factored Polynomial Fraction Integer
--R 
--R
--R             1   2
--R   (2)  (y + - x)
--R             2
--R                                   Type: Factored Polynomial Fraction Integer
--E 22

--S 23 of 54
p := x**3 + x*y + 2*x**2*y**2 + 2*y**3 + 3*x**2*z + 6*x*y**2*z
 

             2     2       3     2 2          3
   (3)  (6x y  + 3x )z + 2y  + 2x y  + x y + x
                                                     Type: Polynomial Integer
--R 
--R
--R             2     2       3     2 2          3
--R   (3)  (6x y  + 3x )z + 2y  + 2x y  + x y + x
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 54
factors := factor p
 

           2                  2
   (4)  (2y  + x)(3x z + y + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R           2                  2
--R   (4)  (2y  + x)(3x z + y + x )
--R                                            Type: Factored Polynomial Integer
--E 24

--S 25 of 54
nthFactor(factors,1)
 

          2
   (5)  2y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (5)  2y  + x
--R                                                     Type: Polynomial Integer
--E 25

--S 26 of 54
nthFactor(factors,2)
 

                    2
   (6)  3x z + y + x
                                                     Type: Polynomial Integer
--R 
--R
--R                    2
--R   (6)  3x z + y + x
--R                                                     Type: Polynomial Integer
--E 26

)clear all
 

--S 27 of 54
p := a*x**2 + b*x*y + c*y**2
 

           2              2
   (1)  c y  + b x y + a x
                                                     Type: Polynomial Integer
--R 
--R
--R           2              2
--R   (1)  c y  + b x y + a x
--R                                                     Type: Polynomial Integer
--E 27

--S 28 of 54
q := 13*x**2 + 3*z
 

                2
   (2)  3z + 13x
                                                     Type: Polynomial Integer
--R 
--R
--R                2
--R   (2)  3z + 13x
--R                                                     Type: Polynomial Integer
--E 28

--S 29 of 54
p + q
 

                2                    2
   (3)  3z + c y  + b x y + (a + 13)x
                                                     Type: Polynomial Integer
--R 
--R
--R                2                    2
--R   (3)  3z + c y  + b x y + (a + 13)x
--R                                                     Type: Polynomial Integer
--E 29

--S 30 of 54
p - 3*q
 

                  2                    2
   (4)  - 9z + c y  + b x y + (a - 39)x
                                                     Type: Polynomial Integer
--R 
--R
--R                  2                    2
--R   (4)  - 9z + c y  + b x y + (a - 39)x
--R                                                     Type: Polynomial Integer
--E 30

--S 31 of 54
p**2 + p*q
 

   (5)
          2                2      2 4           3                  2  2 2
     (3c y  + 3b x y + 3a x )z + c y  + 2b c x y  + ((2a + 13)c + b )x y
   + 
                 3      2        4
     (2a + 13)b x y + (a  + 13a)x
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)
--R          2                2      2 4           3                  2  2 2
--R     (3c y  + 3b x y + 3a x )z + c y  + 2b c x y  + ((2a + 13)c + b )x y
--R   + 
--R                 3      2        4
--R     (2a + 13)b x y + (a  + 13a)x
--R                                                     Type: Polynomial Integer
--E 31

--S 32 of 54
r := (p + q)**2
 

   (6)
       2        2                      2      2 4           3
     9z  + (6c y  + 6b x y + (6a + 78)x )z + c y  + 2b c x y
   + 
                    2  2 2               3      2              4
     ((2a + 26)c + b )x y  + (2a + 26)b x y + (a  + 26a + 169)x
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)
--R       2        2                      2      2 4           3
--R     9z  + (6c y  + 6b x y + (6a + 78)x )z + c y  + 2b c x y
--R   + 
--R                    2  2 2               3      2              4
--R     ((2a + 26)c + b )x y  + (2a + 26)b x y + (a  + 26a + 169)x
--R                                                     Type: Polynomial Integer
--E 32

--S 33 of 54
setVariableOrder [a,b,c,x,y,z]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 54
p
 

         2             2
   (8)  x a + y x b + y c
                                                     Type: Polynomial Integer
--R 
--R
--R         2             2
--R   (8)  x a + y x b + y c
--R                                                     Type: Polynomial Integer
--E 34

--S 35 of 54
q
 

           2
   (9)  13x  + 3z
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (9)  13x  + 3z
--R                                                     Type: Polynomial Integer
--E 35

--S 36 of 54
r
 

   (10)
      4 2        3      2 2       4       2      2 2 2
     x a  + (2y x b + 2y x c + 26x  + 6z x )a + y x b
   + 
      3           3               4 2       2 2       2         4        2     2
   (2y x c + 26y x  + 6z y x)b + y c  + (26y x  + 6z y )c + 169x  + 78z x  + 9z
                                                     Type: Polynomial Integer
--R 
--R
--R   (10)
--R      4 2        3      2 2       4       2      2 2 2
--R     x a  + (2y x b + 2y x c + 26x  + 6z x )a + y x b
--R   + 
--R      3           3               4 2       2 2       2         4        2     2
--R   (2y x c + 26y x  + 6z y x)b + y c  + (26y x  + 6z y )c + 169x  + 78z x  + 9z
--R                                                     Type: Polynomial Integer
--E 36

--S 37 of 54
resetVariableOrder()
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 37

--S 38 of 54
p
 

            2              2
   (12)  c y  + b x y + a x
                                                     Type: Polynomial Integer
--R 
--R
--R            2              2
--R   (12)  c y  + b x y + a x
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 54
coefficient(q,x,2)
 

   (13)  13
                                                     Type: Polynomial Integer
--R 
--R
--R   (13)  13
--R                                                     Type: Polynomial Integer
--E 39

--S 40 of 54
coefficient(r,x,3)
 

   (14)  (2a + 26)b y
                                                     Type: Polynomial Integer
--R 
--R
--R   (14)  (2a + 26)b y
--R                                                     Type: Polynomial Integer
--E 40

--S 41 of 54
c := coefficient(r,z,1)
 

             2                      2
   (15)  6c y  + 6b x y + (6a + 78)x
                                                     Type: Polynomial Integer
--R 
--R
--R             2                      2
--R   (15)  6c y  + 6b x y + (6a + 78)x
--R                                                     Type: Polynomial Integer
--E 41

--S 42 of 54
coefficient(c,x,2)
 

   (16)  6a + 78
                                                     Type: Polynomial Integer
--R 
--R
--R   (16)  6a + 78
--R                                                     Type: Polynomial Integer
--E 42

--S 43 of 54
coefficient(q**2, [x,z], [2,1])
 

   (17)  78
                                                     Type: Polynomial Integer
--R 
--R
--R   (17)  78
--R                                                     Type: Polynomial Integer
--E 43

--S 44 of 54
coefficient(r, [x,y], [2,2])
 

                       2
   (18)  (2a + 26)c + b
                                                     Type: Polynomial Integer
--R 
--R
--R                       2
--R   (18)  (2a + 26)c + b
--R                                                     Type: Polynomial Integer
--E 44


)clear all
 

--S 45 of 54
l := rootsOf(x**4+1,x)
 

   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
                                                Type: List Expression Integer
--R 
--R
--R   (1)  [%x0,%x0 %x1,- %x0,- %x0 %x1]
--R                                                Type: List Expression Integer
--E 45

--S 46 of 54
x0**5
 

          5
   (2)  x0
                                                     Type: Polynomial Integer
--R 
--R
--R          5
--R   (2)  x0
--R                                                     Type: Polynomial Integer
--E 46

--S 47 of 54
definingPolynomial x0
 

   (3)  - x0 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (3)  - x0 + %%var
--R                                                     Type: Expression Integer
--E 47

--S 48 of 54
definingPolynomial x1
 

   (4)  - x1 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (4)  - x1 + %%var
--R                                                     Type: Expression Integer
--E 48

--S 49 of 54
definingPolynomial x2
 

   (5)  - x2 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (5)  - x2 + %%var
--R                                                     Type: Expression Integer
--E 49

--S 50 of 54
x3 := last l
 

   (6)  - %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R   (6)  - %x0 %x1
--R                                                     Type: Expression Integer
--E 50

--S 51 of 54
x0 + x1 + x2 + x3
 

   (7)  - %x0 %x1 + x2 + x1 + x0
                                                     Type: Expression Integer
--R 
--R
--R   (7)  - %x0 %x1 + x2 + x1 + x0
--R                                                     Type: Expression Integer
--E 51

--S 52 of 54
x0 * x1 * x2 * x3
 

   (8)  - x0 x1 x2 %x0 %x1
                                                     Type: Expression Integer
--R 
--R
--R   (8)  - x0 x1 x2 %x0 %x1
--R                                                     Type: Expression Integer
--E 52

--S 53 of 54
zerosOf(y**4+1,y)
 

          +---+      +---+        +---+        +---+
         \|- 1  + 1 \|- 1  - 1 - \|- 1  - 1 - \|- 1  + 1
   (9)  [----------,----------,------------,------------]
             +-+        +-+         +-+          +-+
            \|2        \|2         \|2          \|2
                                                Type: List Expression Integer
--R 
--R
--R          +---+      +---+        +---+        +---+
--R         \|- 1  + 1 \|- 1  - 1 - \|- 1  - 1 - \|- 1  + 1
--R   (9)  [----------,----------,------------,------------]
--R             +-+        +-+         +-+          +-+
--R            \|2        \|2         \|2          \|2
--R                                                Type: List Expression Integer
--E 53

--S 54 of 54
definingPolynomial y1
 

   (10)  - y1 + %%var
                                                     Type: Expression Integer
--R 
--R
--R   (10)  - y1 + %%var
--R                                                     Type: Expression Integer
--E 54
)spool 
 
Starts dribbling to stream.output (2010/3/27, 18:41:7).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
ints := [i for i in 0..]
 

   (1)  [0,1,2,3,4,5,6,7,8,9,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (1)  [0,1,2,3,4,5,6,7,8,9,...]
--R                                              Type: Stream NonNegativeInteger
--E 1

--S 2 of 12
f : List INT -> List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 12
f x == [x.1 + x.2, x.1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 12
fibs := [i.2 for i in [generate(f,[1,1])]]
 
   Compiling function f with type List Integer -> List Integer 

   (4)  [1,1,2,3,5,8,13,21,34,55,...]
                                                         Type: Stream Integer
--R 
--R   Compiling function f with type List Integer -> List Integer 
--R
--R   (4)  [1,1,2,3,5,8,13,21,34,55,...]
--R                                                         Type: Stream Integer
--E 4

--S 5 of 12
[i for i in ints | odd? i]
 

   (5)  [1,3,5,7,9,11,13,15,17,19,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (5)  [1,3,5,7,9,11,13,15,17,19,...]
--R                                              Type: Stream NonNegativeInteger
--E 5

--S 6 of 12
odds := [2*i+1 for i in ints]
 

   (6)  [1,3,5,7,9,11,13,15,17,19,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (6)  [1,3,5,7,9,11,13,15,17,19,...]
--R                                              Type: Stream NonNegativeInteger
--E 6

--S 7 of 12
scan(0,+,odds)
 

   (7)  [1,4,9,16,25,36,49,64,81,100,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (7)  [1,4,9,16,25,36,49,64,81,100,...]
--R                                              Type: Stream NonNegativeInteger
--E 7

--S 8 of 12
[i*j for i in ints for j in odds]
 

   (8)  [0,3,10,21,36,55,78,105,136,171,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (8)  [0,3,10,21,36,55,78,105,136,171,...]
--R                                              Type: Stream NonNegativeInteger
--E 8

--S 9 of 12
map(*,ints,odds)
 

   (9)  [0,3,10,21,36,55,78,105,136,171,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (9)  [0,3,10,21,36,55,78,105,136,171,...]
--R                                              Type: Stream NonNegativeInteger
--E 9

--S 10 of 12
first ints
 

   (10)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (10)  0
--R                                                     Type: NonNegativeInteger
--E 10

--S 11 of 12
rest ints
 

   (11)  [1,2,3,4,5,6,7,8,9,10,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (11)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                              Type: Stream NonNegativeInteger
--E 11

--S 12 of 12
fibs 20
 

   (12)  6765
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  6765
--R                                                        Type: PositiveInteger
--E 12
)spool 
 
Starts dribbling to dmp.output (2010/3/27, 18:25:2).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input generated from DistributedMultivariatePolynomialXmpPage

--S 1 of 8
(d1,d2,d3) : DMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 8
d1 := -4*z + 4*y**2*x + 16*x**2 + 1
 

                 2       2
   (2)  - 4z + 4y x + 16x  + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R                 2       2
--R   (2)  - 4z + 4y x + 16x  + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 2

--S 3 of 8
d2 := 2*z*y**2 + 4*x + 1
 

            2
   (3)  2z y  + 4x + 1
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2
--R   (3)  2z y  + 4x + 1
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 3

--S 4 of 8
d3 := 2*z*x**2 - 2*y**2 - x
 

            2     2
   (4)  2z x  - 2y  - x
            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (4)  2z x  - 2y  - x
--R            Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 4

--S 5 of 8
groebner [d1,d2,d3]
 

   (5)
        1568  6   1264  5    6   4   182  3   2047  2    103      2857
   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
        2745       305      305      549       610      2745     10980
     2    112  6    84  5   1264  4    13  3    84  2   1772       2
    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
         2745      305       305      549      305      2745     2745
     7   29  6   17  4   11  3    1  2   15     1
    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
          4      16       8      32      16     4
       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (5)
--R        1568  6   1264  5    6   4   182  3   2047  2    103      2857
--R   [z - ---- x  - ---- x  + --- x  + --- x  - ---- x  - ---- x - -----,
--R        2745       305      305      549       610      2745     10980
--R     2    112  6    84  5   1264  4    13  3    84  2   1772       2
--R    y  + ---- x  - --- x  - ---- x  - --- x  + --- x  + ---- x + ----,
--R         2745      305       305      549      305      2745     2745
--R     7   29  6   17  4   11  3    1  2   15     1
--R    x  + -- x  - -- x  - -- x  + -- x  + -- x + -]
--R          4      16       8      32      16     4
--R       Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 5

--S 6 of 8
(n1,n2,n3) : HDMP([z,y,x],FRAC INT)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 8
(n1,n2,n3) := (d1,d2,d3)
 

            2     2
   (7)  2z x  - 2y  - x
 Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R            2     2
--R   (7)  2z x  - 2y  - x
--R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 7

--S 8 of 8
groebner [n1,n2,n3]
 

   (8)
     4     3   3  2   1     1   4   29  3   1  2   7        9     1
   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
               2      2     8        4      8      4       16     4
       2        1   2      2       1     2    2   1
    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
                2                  4              2
     2     2     2   1     3
    z  - 4y  + 2x  - - z - - x]
                     4     2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--R 
--R
--R   (8)
--R     4     3   3  2   1     1   4   29  3   1  2   7        9     1
--R   [y  + 2x  - - x  + - z - -, x  + -- x  - - y  - - z x - -- x - -,
--R               2      2     8        4      8      4       16     4
--R       2        1   2      2       1     2    2   1
--R    z y  + 2x + -, y x + 4x  - z + -, z x  - y  - - x,
--R                2                  4              2
--R     2     2     2   1     3
--R    z  - 4y  + 2x  - - z - - x]
--R                     4     2
--RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
--E 8
)spool
 
Starts dribbling to r21bugs.output (2010/3/27, 18:36:36).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 95
)set expose add constructor PolynomialNumberTheoryFunctions
 
   PolynomialNumberTheoryFunctions is now explicitly exposed in frame 
      initial 
--R 
--R   PolynomialNumberTheoryFunctions is now explicitly exposed in frame 
--R      initial 
--E 1

--S 2 of 95
X : UP('x, Integer) := x
 

   (1)  x
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R   (1)  x
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 2

--S 3 of 95
[chebyshevU(n) - X*chebyshevU(n-1) - chebyshevT(n) for n in 1 .. ]
 

   (2)  [0,0,0,0,0,0,0,0,0,0,...]
                              Type: Stream SparseUnivariatePolynomial Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0,0,0,0,0,...]
--R                              Type: Stream SparseUnivariatePolynomial Integer
--E 3

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 4 of 95
Fp:=PF 2
 

   (1)  PrimeField 2
                                                                 Type: Domain
--R 
--R
--R   (1)  PrimeField 2
--R                                                                 Type: Domain
--E 4

--S 5 of 95
poly:=createIrreduciblePoly(4)$FFPOLY(Fp)
 

         4
   (2)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
--R 
--R
--R         4
--R   (2)  ?  + ? + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 2
--E 5

--S 6 of 95
Fq:=FFP(Fp, poly)    -- Field with 16 elements
 

   (3)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
                                                                 Type: Domain
--R 
--R
--R   (3)  FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1)
--R                                                                 Type: Domain
--E 6

--S 7 of 95
R:=DMP([X,Y,Z],Fq)
 

   (4)
  DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(Pr
  imeField 2,?**4+?+1))
                                                                 Type: Domain
--R 
--R
--R   (4)
--R  DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(Pr
--R  imeField 2,?**4+?+1))
--R                                                                 Type: Domain
--E 7

--S 8 of 95
Q:=FRAC R
 

   (5)
  Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPoly
  nomial(PrimeField 2,?**4+?+1))
                                                                 Type: Domain
--R 
--R
--R   (5)
--R  Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPoly
--R  nomial(PrimeField 2,?**4+?+1))
--R                                                                 Type: Domain
--E 8

--S 9 of 95
F:=X**4+X*Z**3
 

           3    4
   (6)  X Z  + X
                                                     Type: Polynomial Integer
--R 
--R
--R           3    4
--R   (6)  X Z  + X
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 95
G:=X**4+X**2*Y**2+Z**4
 

         4    2 2    4
   (7)  Z  + X Y  + X
                                                     Type: Polynomial Integer
--R 
--R
--R         4    2 2    4
--R   (7)  Z  + X Y  + X
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 95
h:Q:=F/G
 

            4      3
           X  + X Z
   (8)  --------------
         4    2 2    4
        X  + X Y  + Z
Type: Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--R 
--R
--R            4      3
--R           X  + X Z
--R   (8)  --------------
--R         4    2 2    4
--R        X  + X Y  + Z
--RType: Fraction DistributedMultivariatePolynomial([X,Y,Z],FiniteFieldExtensionByPolynomial(PrimeField 2,?**4+?+1))
--E 11

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 12 of 95
squareFree ((c^15*e^8+c^23*d^4)::POLY PF 2) 
 

         15  2    2  4
   (1)  c  (e  + c d)
                                       Type: Factored Polynomial PrimeField 2
--R 
--R
--R         15  2    2  4
--R   (1)  c  (e  + c d)
--R                                       Type: Factored Polynomial PrimeField 2
--E 12

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

--S 13 of 95
FiniteFieldExtensionByPolynomial(FF(3,3),1+2*x**2+x**3)
 

   (1)  FiniteFieldExtensionByPolynomial(FiniteField(3,3),?**3+2*?*?+1)
                                                                 Type: Domain
--R 
--R
--R   (1)  FiniteFieldExtensionByPolynomial(FiniteField(3,3),?**3+2*?*?+1)
--R                                                                 Type: Domain
--E 13

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 14 of 95
Field has Ring
 

   (1)  true
                                                                Type: Boolean
--R 
--R
--R   (1)  true
--R                                                                Type: Boolean
--E 14

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

-- from bmt
--S 15 of 95
y:=operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 15

--S 16 of 95
u:=operator u
 

   (2)  u
                                                          Type: BasicOperator
--R 
--R
--R   (2)  u
--R                                                          Type: BasicOperator
--E 16

--S 17 of 95
eval(y x, y, c[1]*x,x)
 
   Compiling function %B with type Expression Integer -> Expression 
      Integer 

   (3)  c x
         1
                                                     Type: Expression Integer
--R 
--R   Compiling function %B with type Expression Integer -> Expression 
--R      Integer 
--R
--R   (3)  c x
--R         1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 95
eval(y x, y, D(u t,t),t)
 
   Compiling function %C with type Expression Integer -> Expression 
      Integer 

         ,
   (4)  u (x)

                                                     Type: Expression Integer
--R 
--R   Compiling function %C with type Expression Integer -> Expression 
--R      Integer 
--R
--R         ,
--R   (4)  u (x)
--R
--R                                                     Type: Expression Integer
--E 18

--S 19 of 95
eval(y x ,y, integral(u t,t),t)
 
   Compiling function %E with type Expression Integer -> Expression 
      Integer 

           x
         ++
   (5)   |   u(%D)d%D
        ++
                                                     Type: Expression Integer
--R 
--R   Compiling function %E with type Expression Integer -> Expression 
--R      Integer 
--R
--R           x
--R         ++
--R   (5)   |   u(%D)d%D
--R        ++
--R                                                     Type: Expression Integer
--E 19

--S 20 of 95
eval(y x ,y, integral(u z,z=z0..t),t)
 
   Compiling function %F with type Expression Integer -> Expression 
      Integer 

           x
         ++
   (6)   |   u(z)dz
        ++
        z0
                                                     Type: Expression Integer
--R 
--R   Compiling function %F with type Expression Integer -> Expression 
--R      Integer 
--R
--R           x
--R         ++
--R   (6)   |   u(z)dz
--R        ++
--R        z0
--R                                                     Type: Expression Integer
--E 20

--S 21 of 95
eval(y x+D(y x,x), y, u t+ D(u t,t),t)
 
   Compiling function %G with type Expression Integer -> Expression 
      Integer 

         ,,        ,
   (7)  u  (x) + 2u (x) + u(x)

                                                     Type: Expression Integer
--R 
--R   Compiling function %G with type Expression Integer -> Expression 
--R      Integer 
--R
--R         ,,        ,
--R   (7)  u  (x) + 2u (x) + u(x)
--R
--R                                                     Type: Expression Integer
--E 21

--S 22 of 95
eval(D(y x,x)+y(x),y,D(u x,x)+u(x),x)
 
   Compiling function %H with type Expression Integer -> Expression 
      Integer 

         ,,        ,
   (8)  u  (x) + 2u (x) + u(x)

                                                     Type: Expression Integer
--R 
--R   Compiling function %H with type Expression Integer -> Expression 
--R      Integer 
--R
--R         ,,        ,
--R   (8)  u  (x) + 2u (x) + u(x)
--R
--R                                                     Type: Expression Integer
--E 22

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 23 of 95
ps:=x::TS FRAC INT
 

   (1)  x
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (1)  x
--R                                          Type: TaylorSeries Fraction Integer
--E 23

--S 24 of 95
D(ps,x) -- fails to find function
 

   (2)  1
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (2)  1
--R                                          Type: TaylorSeries Fraction Integer
--E 24

--S 25 of 95
D(ps,[x]) -- works
 

   (3)  1
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (3)  1
--R                                          Type: TaylorSeries Fraction Integer
--E 25

--S 26 of 95
D(ps,[y]) -- causes ccl to disappear (at least under windows)
 

   (4)  0
                                          Type: TaylorSeries Fraction Integer
--R 
--R
--R   (4)  0
--R                                          Type: TaylorSeries Fraction Integer
--E 26

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 27 of 95
T1:=3
 

   (1)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  3
--R                                                        Type: PositiveInteger
--E 27

--S 28 of 95
a | a^2+1
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
   a : SAEa := a

   (2)  a
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--R   a : SAEa := a
--R
--R   (2)  a
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(a,Fraction Integer),a*a+1)
--E 28


)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 29 of 95
u1 := operator 'u1
 

   (1)  u1
                                                          Type: BasicOperator
--R 
--R
--R   (1)  u1
--R                                                          Type: BasicOperator
--E 29

--S 30 of 95
u2 := operator 'u2
 

   (2)  u2
                                                          Type: BasicOperator
--R 
--R
--R   (2)  u2
--R                                                          Type: BasicOperator
--E 30

--S 31 of 95
eq1 := D(u1(t),t,2) + 5*u1(t) = 2*u2(t)
 

          ,,
   (3)  u1  (t) + 5u1(t)= 2u2(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (3)  u1  (t) + 5u1(t)= 2u2(t)
--R
--R                                            Type: Equation Expression Integer
--E 31

--S 32 of 95
eq2 := D(u2(t),t,2) + 2*u2(t) = 2*u1(t)
 

          ,,
   (4)  u2  (t) + 2u2(t)= 2u1(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (4)  u2  (t) + 2u2(t)= 2u1(t)
--R
--R                                            Type: Equation Expression Integer
--E 32

--S 33 of 95
eq1/2
 

          ,,
        u1  (t) + 5u1(t)

   (5)  ----------------= u2(t)
                2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R        u1  (t) + 5u1(t)
--R
--R   (5)  ----------------= u2(t)
--R                2
--R                                            Type: Equation Expression Integer
--E 33

--S 34 of 95
_rule(rhs %, lhs %)
 

                   ,,
                 u1  (t) + 5u1(t)

   (6)  u2(t) == ----------------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                   ,,
--R                 u1  (t) + 5u1(t)
--R
--R   (6)  u2(t) == ----------------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 34

--S 35 of 95
%(lhs eq2)
 

          (iv)         ,,
        u1    (t) + 7u1  (t) + 10u1(t)

   (7)  ------------------------------
                       2
                                                     Type: Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (t) + 7u1  (t) + 10u1(t)
--R
--R   (7)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E 35

--S 36 of 95
eval(%,t=0)
 

          (iv)         ,,
        u1    (0) + 7u1  (0) + 10u1(0)

   (8)  ------------------------------
                       2
                                                     Type: Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (0) + 7u1  (0) + 10u1(0)
--R
--R   (8)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E 36

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 37 of 95
bug := [exp(sqrt(-5))]
 

            +---+
           \|- 5
   (1)  [%e      ]
                                                Type: List Expression Integer
--R 
--R
--R            +---+
--R           \|- 5
--R   (1)  [%e      ]
--R                                                Type: List Expression Integer
--E 37

--S 38 of 95
complexForm(bug.1) -- works
 

             +-+         +-+
   (2)  cos(\|5 ) + sin(\|5 )%i
                                             Type: Complex Expression Integer
--R 
--R
--R             +-+         +-+
--R   (2)  cos(\|5 ) + sin(\|5 )%i
--R                                             Type: Complex Expression Integer
--E 38

--S 39 of 95
map(complexForm,bug::List EXPR COMPLEX INT) -- works
 

              +-+         +-+
   (3)  [cos(\|5 ) + sin(\|5 )%i]
                                        Type: List Complex Expression Integer
--R 
--R
--R              +-+         +-+
--R   (3)  [cos(\|5 ) + sin(\|5 )%i]
--R                                        Type: List Complex Expression Integer
--E 39

--S 40 of 95
map(complexForm,bug) -- fails
 

              +-+         +-+
   (4)  [cos(\|5 ) + sin(\|5 )%i]
                                        Type: List Complex Expression Integer
--R 
--R
--R              +-+         +-+
--R   (4)  [cos(\|5 ) + sin(\|5 )%i]
--R                                        Type: List Complex Expression Integer
--E 40

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.


-- from bmt
--S 41 of 95
f x == c[1]*exp(x)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 41

--S 42 of 95
f x -- works
 
   Compiling function f with type Variable x -> Expression Integer 

            x
   (2)  c %e
         1
                                                     Type: Expression Integer
--R 
--R   Compiling function f with type Variable x -> Expression Integer 
--R
--R            x
--R   (2)  c %e
--R         1
--R                                                     Type: Expression Integer
--E 42

--S 43 of 95
g(x:EXPR(INT)):EXPR(INT) == c[1]*exp(x) 
 
   Function declaration g : Expression Integer -> Expression Integer 
      has been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration g : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R                                                                   Type: Void
--E 43

--S 44 of 95
g x -- fails
 
   There are no library operations named c 
      Use HyperDoc Browse or issue
                                 )what op c
      to learn if there is any operation containing " c " in its name.
   Cannot find a definition or applicable library operation named c 
      with argument type(s) 
                            List PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function g with type Expression Integer -> Expression 
      Integer 
   There are no library operations named c 
      Use HyperDoc Browse or issue
                                 )what op c
      to learn if there is any operation containing " c " in its name.
 
Daly Bug
   Cannot find a definition or applicable library operation named c 
      with argument type(s) 
                            List PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are no library operations named c 
--R      Use HyperDoc Browse or issue
--R                                 )what op c
--R      to learn if there is any operation containing " c " in its name.
--R   Cannot find a definition or applicable library operation named c 
--R      with argument type(s) 
--R                            List PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--R   AXIOM will attempt to step through and interpret the code.
--R   Compiling function g with type Expression Integer -> Expression 
--R      Integer 
--R   There are no library operations named c 
--R      Use HyperDoc Browse or issue
--R                                 )what op c
--R      to learn if there is any operation containing " c " in its name.
--R 
--RDaly Bug
--R   Cannot find a definition or applicable library operation named c 
--R      with argument type(s) 
--R                            List PositiveInteger
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 44

--S 45 of 95
g(x:EXPR(INT)):EXPR(INT) == (c[1]::EXPR INT)*exp(x) 
 
   Function declaration g : Expression Integer -> Expression Integer 
      has been added to workspace.
   Compiled code for g has been cleared.
   1 old definition(s) deleted for function or rule g 
                                                                   Type: Void
--R 
--R   Function declaration g : Expression Integer -> Expression Integer 
--R      has been added to workspace.
--R   Compiled code for g has been cleared.
--R   1 old definition(s) deleted for function or rule g 
--R                                                                   Type: Void
--E 45

--S 46 of 95
g x -- fails
 
   Compiling function g with type Expression Integer -> Expression 
      Integer 

            x
   (5)  c %e
         1
                                                     Type: Expression Integer
--R 
--R   Compiling function g with type Expression Integer -> Expression 
--R      Integer 
--R
--R            x
--R   (5)  c %e
--R         1
--R                                                     Type: Expression Integer
--E 46

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 47 of 95
a | a**8+a**4+a**3+a**2+(1::PF 2)
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEa := SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
   a : SAEa := a

   (1)  a
Type: SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEa := SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R   a : SAEa := a
--R
--R   (1)  a
--RType: SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 47

--S 48 of 95
tt:Matrix SAEa:=[_
[0,0,0,1,1,1,0,1],_
[1,0,0,0,0,0,0,0],_
[0,1,0,0,0,0,0,0],_
[0,0,1,0,0,0,0,0],_
[0,0,0,1,0,0,0,0],_
[0,0,0,0,1,0,0,0],_
[0,0,0,0,0,1,0,0],_
[0,0,0,0,0,0,1,0]];
 

Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 48

--S 49 of 95
T:=transpose tt
 

        +0  1  0  0  0  0  0  0+
        |                      |
        |0  0  1  0  0  0  0  0|
        |                      |
        |0  0  0  1  0  0  0  0|
        |                      |
        |1  0  0  0  1  0  0  0|
   (3)  |                      |
        |1  0  0  0  0  1  0  0|
        |                      |
        |1  0  0  0  0  0  1  0|
        |                      |
        |0  0  0  0  0  0  0  1|
        |                      |
        +1  0  0  0  0  0  0  0+
Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--R        +0  1  0  0  0  0  0  0+
--R        |                      |
--R        |0  0  1  0  0  0  0  0|
--R        |                      |
--R        |0  0  0  1  0  0  0  0|
--R        |                      |
--R        |1  0  0  0  1  0  0  0|
--R   (3)  |                      |
--R        |1  0  0  0  0  1  0  0|
--R        |                      |
--R        |1  0  0  0  0  0  1  0|
--R        |                      |
--R        |0  0  0  0  0  0  0  1|
--R        |                      |
--R        +1  0  0  0  0  0  0  0+
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 49

--S 50 of 95
T0:=T**91
 

        +0  1  1  1  0  1  0  1+
        |                      |
        |1  0  1  1  1  0  1  0|
        |                      |
        |0  1  0  1  1  1  0  1|
        |                      |
        |0  0  1  0  1  1  1  0|
   (4)  |                      |
        |0  1  1  0  0  0  1  0|
        |                      |
        |0  1  0  0  0  1  0  0|
        |                      |
        |1  1  0  1  0  1  1  1|
        |                      |
        +1  1  1  0  1  0  1  1+
Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--R        +0  1  1  1  0  1  0  1+
--R        |                      |
--R        |1  0  1  1  1  0  1  0|
--R        |                      |
--R        |0  1  0  1  1  1  0  1|
--R        |                      |
--R        |0  0  1  0  1  1  1  0|
--R   (4)  |                      |
--R        |0  1  1  0  0  0  1  0|
--R        |                      |
--R        |0  1  0  0  0  1  0  0|
--R        |                      |
--R        |1  1  0  1  0  1  1  1|
--R        |                      |
--R        +1  1  1  0  1  0  1  1+
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 50

--S 51 of 95
T1:=T**95
 

        +0  0  0  1  0  1  1  1+
        |                      |
        |1  0  0  0  1  0  1  1|
        |                      |
        |0  1  0  0  0  1  0  1|
        |                      |
        |0  0  1  0  0  0  1  0|
   (5)  |                      |
        |0  0  0  0  0  1  1  0|
        |                      |
        |1  0  0  1  0  1  0  0|
        |                      |
        |0  1  0  1  1  1  0  1|
        |                      |
        +0  0  1  0  1  1  1  0+
Type: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--R 
--R
--R        +0  0  0  1  0  1  1  1+
--R        |                      |
--R        |1  0  0  0  1  0  1  1|
--R        |                      |
--R        |0  1  0  0  0  1  0  1|
--R        |                      |
--R        |0  0  1  0  0  0  1  0|
--R   (5)  |                      |
--R        |0  0  0  0  0  1  1  0|
--R        |                      |
--R        |1  0  0  1  0  1  0  0|
--R        |                      |
--R        |0  1  0  1  1  1  0  1|
--R        |                      |
--R        +0  0  1  0  1  1  1  0+
--RType: Matrix SimpleAlgebraicExtension(PrimeField 2,UnivariatePolynomial(a,PrimeField 2),a**8+a**4+a**3+a*a+1)
--E 51

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 52 of 95
u1:=operator 'u1
 

   (1)  u1
                                                          Type: BasicOperator
--R 
--R
--R   (1)  u1
--R                                                          Type: BasicOperator
--E 52

--S 53 of 95
u2:=operator 'u2
 

   (2)  u2
                                                          Type: BasicOperator
--R 
--R
--R   (2)  u2
--R                                                          Type: BasicOperator
--E 53

--S 54 of 95
eq1 := D(u1(t),t,2) + 5*u1(t) = 2*u2(t)
 

          ,,
   (3)  u1  (t) + 5u1(t)= 2u2(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (3)  u1  (t) + 5u1(t)= 2u2(t)
--R
--R                                            Type: Equation Expression Integer
--E 54

--S 55 of 95
eq2 := D(u2(t),t,2) + 2*u2(t) = 2*u1(t)
 

          ,,
   (4)  u2  (t) + 2u2(t)= 2u1(t)

                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R   (4)  u2  (t) + 2u2(t)= 2u1(t)
--R
--R                                            Type: Equation Expression Integer
--E 55

--S 56 of 95
eq1/2
 

          ,,
        u1  (t) + 5u1(t)

   (5)  ----------------= u2(t)
                2
                                            Type: Equation Expression Integer
--R 
--R
--R          ,,
--R        u1  (t) + 5u1(t)
--R
--R   (5)  ----------------= u2(t)
--R                2
--R                                            Type: Equation Expression Integer
--E 56

--S 57 of 95
_rule(rhs %, lhs %)
 

                   ,,
                 u1  (t) + 5u1(t)

   (6)  u2(t) == ----------------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                   ,,
--R                 u1  (t) + 5u1(t)
--R
--R   (6)  u2(t) == ----------------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 57

--S 58 of 95
%(lhs eq2)=%(rhs eq2)
 

          (iv)         ,,
        u1    (t) + 7u1  (t) + 10u1(t)

   (7)  ------------------------------= 2u1(t)
                       2
                                            Type: Equation Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (t) + 7u1  (t) + 10u1(t)
--R
--R   (7)  ------------------------------= 2u1(t)
--R                       2
--R                                            Type: Equation Expression Integer
--E 58

--S 59 of 95
rightZero %
 

          (iv)         ,,
        u1    (t) + 7u1  (t) + 6u1(t)

   (8)  -----------------------------= 0
                      2
                                            Type: Equation Expression Integer
--R 
--R
--R          (iv)         ,,
--R        u1    (t) + 7u1  (t) + 6u1(t)
--R
--R   (8)  -----------------------------= 0
--R                      2
--R                                            Type: Equation Expression Integer
--E 59

--S 60 of 95
-2*%
 

            (iv)         ,,
   (9)  - u1    (t) - 7u1  (t) - 6u1(t)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R            (iv)         ,,
--R   (9)  - u1    (t) - 7u1  (t) - 6u1(t)= 0
--R
--R                                            Type: Equation Expression Integer
--E 60

--S 61 of 95
eval(lhs %,u1,exp(r*t),t)
 
   Compiling function %B with type Expression Integer -> Expression 
      Integer 

             4     2       r t
   (10)  (- r  - 7r  - 6)%e
                                                     Type: Expression Integer
--R 
--R   Compiling function %B with type Expression Integer -> Expression 
--R      Integer 
--R
--R             4     2       r t
--R   (10)  (- r  - 7r  - 6)%e
--R                                                     Type: Expression Integer
--E 61

--S 62 of 95
%/exp(r*t)
 

            4     2
   (11)  - r  - 7r  - 6
                                                     Type: Expression Integer
--R 
--R
--R            4     2
--R   (11)  - r  - 7r  - 6
--R                                                     Type: Expression Integer
--E 62

--S 63 of 95
solve(%,r)
 

              +---+       +---+     +---+       +---+
   (12)  [r= \|- 1 ,r= - \|- 1 ,r= \|- 6 ,r= - \|- 6 ]
                                       Type: List Equation Expression Integer
--R 
--R
--R              +---+       +---+     +---+       +---+
--R   (12)  [r= \|- 1 ,r= - \|- 1 ,r= \|- 6 ,r= - \|- 6 ]
--R                                       Type: List Equation Expression Integer
--E 63

--S 64 of 95
[eval(exp(r*t),eq) for eq in %]
 

              +---+       +---+     +---+       +---+
            t\|- 1    - t\|- 1    t\|- 6    - t\|- 6
   (13)  [%e       ,%e         ,%e       ,%e         ]
                                                Type: List Expression Integer
--R 
--R
--R              +---+       +---+     +---+       +---+
--R            t\|- 1    - t\|- 1    t\|- 6    - t\|- 6
--R   (13)  [%e       ,%e         ,%e       ,%e         ]
--R                                                Type: List Expression Integer
--E 64

--S 65 of 95
map(complexForm, %::List EXPR COMPLEX INT)
 

   (14)
                                                +-+          +-+
   [cos(t) + sin(t)%i, cos(t) - sin(t)%i, cos(t\|6 ) + sin(t\|6 )%i,
          +-+          +-+
    cos(t\|6 ) - sin(t\|6 )%i]
                                        Type: List Complex Expression Integer
--R 
--R
--R   (14)
--R                                                +-+          +-+
--R   [cos(t) + sin(t)%i, cos(t) - sin(t)%i, cos(t\|6 ) + sin(t\|6 )%i,
--R          +-+          +-+
--R    cos(t\|6 ) - sin(t\|6 )%i]
--R                                        Type: List Complex Expression Integer
--E 65

--S 66 of 95
[real %(1), imag %(1), real %(3), imag %(3)]
 

                              +-+        +-+
   (15)  [cos(t),sin(t),cos(t\|6 ),sin(t\|6 )]
                                                Type: List Expression Integer
--R 
--R
--R                              +-+        +-+
--R   (15)  [cos(t),sin(t),cos(t\|6 ),sin(t\|6 )]
--R                                                Type: List Expression Integer
--E 66

--S 67 of 95
gform:= u1(t)=reduce(+, [c[i]*%.i for i in 1..#%])
 

                        +-+                       +-+
   (16)  u1(t)= c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
                 4              2          3              1
                                            Type: Equation Expression Integer
--R 
--R
--R                        +-+                       +-+
--R   (16)  u1(t)= c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
--R                 4              2          3              1
--R                                            Type: Equation Expression Integer
--E 67

--S 68 of 95
_rule(lhs %, rhs %)
 

                          +-+                       +-+
   (17)  u1(t) == c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
                   4              2          3              1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--R                          +-+                       +-+
--R   (17)  u1(t) == c sin(t\|6 ) + c sin(t) + c cos(t\|6 ) + c cos(t)
--R                   4              2          3              1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 68

--S 69 of 95
%(lhs eq1)=rhs eq1
 

                   +-+                        +-+
   (18)  - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)= 2u2(t)
            4               2          3               1
                                            Type: Equation Expression Integer
--R 
--R
--R                   +-+                        +-+
--R   (18)  - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)= 2u2(t)
--R            4               2          3               1
--R                                            Type: Equation Expression Integer
--E 69

--S 70 of 95
%/2
 

                   +-+                        +-+
         - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)
            4               2          3               1
   (19)  -----------------------------------------------------= u2(t)
                                   2
                                            Type: Equation Expression Integer
--R 
--R
--R                   +-+                        +-+
--R         - c sin(t\|6 ) + 4c sin(t) - c cos(t\|6 ) + 4c cos(t)
--R            4               2          3               1
--R   (19)  -----------------------------------------------------= u2(t)
--R                                   2
--R                                            Type: Equation Expression Integer
--E 70

--part c
--S 71 of 95
inits := [u1(0)=1, eval(D(u1 t,t),t=0)=0, u2(0)=2, eval(D(u2 t,t),t=0)=0]
 

                     ,                  ,
   (20)  [u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]

                                       Type: List Equation Expression Integer
--R 
--R
--R                     ,                  ,
--R   (20)  [u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]
--R
--R                                       Type: List Equation Expression Integer
--E 71

--S 72 of 95
eqq := eq1-5*u1(t)
 

           ,,
   (21)  u1  (t)= 2u2(t) - 5u1(t)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (21)  u1  (t)= 2u2(t) - 5u1(t)
--R
--R                                            Type: Equation Expression Integer
--E 72

--S 73 of 95
eval(eqq,t=0)
 

           ,,
   (22)  u1  (0)= 2u2(0) - 5u1(0)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (22)  u1  (0)= 2u2(0) - 5u1(0)
--R
--R                                            Type: Equation Expression Integer
--E 73

--S 74 of 95
eval(%,inits)
 

           ,,
   (23)  u1  (0)= - 1

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (23)  u1  (0)= - 1
--R
--R                                            Type: Equation Expression Integer
--E 74

--S 75 of 95
inits:=cons(%,inits)
 

            ,,                    ,                  ,
   (24)  [u1  (0)= - 1,u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]

                                       Type: List Equation Expression Integer
--R 
--R
--R            ,,                    ,                  ,
--R   (24)  [u1  (0)= - 1,u1(0)= 1,u1 (0)= 0,u2(0)= 2,u2 (0)= 0]
--R
--R                                       Type: List Equation Expression Integer
--E 75

--S 76 of 95
D(eqq,t)
 

           ,,,        ,         ,
   (25)  u1   (t)= 2u2 (t) - 5u1 (t)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,,        ,         ,
--R   (25)  u1   (t)= 2u2 (t) - 5u1 (t)
--R
--R                                            Type: Equation Expression Integer
--E 76

--S 77 of 95
eval(%,t=0)
 

           ,,,        ,         ,
   (26)  u1   (0)= 2u2 (0) - 5u1 (0)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,,        ,         ,
--R   (26)  u1   (0)= 2u2 (0) - 5u1 (0)
--R
--R                                            Type: Equation Expression Integer
--E 77

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
-- from bmt
--S 78 of 95
u:=operator 'u
 

   (1)  u
                                                          Type: BasicOperator
--R 
--R
--R   (1)  u
--R                                                          Type: BasicOperator
--E 78

--S 79 of 95
exp:=D(u t,t)
 

         ,
   (2)  u (t)

                                                     Type: Expression Integer
--R 
--R
--R         ,
--R   (2)  u (t)
--R
--R                                                     Type: Expression Integer
--E 79

--S 80 of 95
k:=kernels(exp).1
 

         ,
   (3)  u (t)

                                              Type: Kernel Expression Integer
--R 
--R
--R         ,
--R   (3)  u (t)
--R
--R                                              Type: Kernel Expression Integer
--E 80

--S 81 of 95
l:=argument %
 

   (4)  [u(%%01),%%01,t]
                                                Type: List Expression Integer
--R 
--R
--R   (4)  [u(%%01),%%01,t]
--R                                                Type: List Expression Integer
--E 81

--S 82 of 95
difop:=operator k
 

   (5)  %diff
                                                          Type: BasicOperator
--R 
--R
--R   (5)  %diff
--R                                                          Type: BasicOperator
--E 82

--S 83 of 95
l2:=[l.1+l.2,l.2,l.3]
 

   (6)  [u(%%01) + %%01,%%01,t]
                                                Type: List Expression Integer
--R 
--R
--R   (6)  [u(%%01) + %%01,%%01,t]
--R                                                Type: List Expression Integer
--E 83

--S 84 of 95
bug:=evaluate(difop,l2)
 

         ,
   (7)  u (t) + 1

                                          Type: Union(Expression Integer,...)
--R 
--R
--R         ,
--R   (7)  u (t) + 1
--R
--R                                          Type: Union(Expression Integer,...)
--E 84

--S 85 of 95
kernels(bug).1
 

         ,
   (8)  u (t)

                                              Type: Kernel Expression Integer
--R 
--R
--R         ,
--R   (8)  u (t)
--R
--R                                              Type: Kernel Expression Integer
--E 85

--S 86 of 95
argument %
 

   (9)  [u(%%01),%%01,t]
                                                Type: List Expression Integer
--R 
--R
--R   (9)  [u(%%01),%%01,t]
--R                                                Type: List Expression Integer
--E 86

--S 87 of 95
eval(bug,t=0)
 

          ,
   (10)  u (0) + 1

                                                     Type: Expression Integer
--R 
--R
--R          ,
--R   (10)  u (0) + 1
--R
--R                                                     Type: Expression Integer
--E 87

)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
 
--S 88 of 95
R := Polynomial(PrimeField(3)) ; 
 

                                                                 Type: Domain
--R 
--R
--R                                                                 Type: Domain
--E 88

--S 89 of 95
A := UP('X, R) 
 

   (2)  UnivariatePolynomial(X,Polynomial PrimeField 3)
                                                                 Type: Domain
--R 
--R
--R   (2)  UnivariatePolynomial(X,Polynomial PrimeField 3)
--R                                                                 Type: Domain
--E 89

--S 90 of 95
X : A := monomial(1, 1) ;
 

                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--R 
--R
--R                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--E 90

--S 91 of 95
f : A := a*X^3 + b*X^2 + c*X + d
 

           3      2
   (4)  a X  + b X  + c X + d
                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--R 
--R
--R           3      2
--R   (4)  a X  + b X  + c X + d
--R                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--E 91

--S 92 of 95
discriminant(f)
 

          3        3    2 2
   (5)  2b d + 2a c  + b c
                                                Type: Polynomial PrimeField 3
--R 
--R
--R          3        3    2 2
--R   (5)  2b d + 2a c  + b c
--R                                                Type: Polynomial PrimeField 3
--E 92

--S 93 of 95
s := differentiate f
 

   (6)  2b X + c
                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--R 
--R
--R   (6)  2b X + c
--R                        Type: UnivariatePolynomial(X,Polynomial PrimeField 3)
--E 93

--S 94 of 95
resultant(f,s)
 

         3       3     2 2
   (7)  b d + a c  + 2b c
                                                Type: Polynomial PrimeField 3
--R 
--R
--R         3       3     2 2
--R   (7)  b d + a c  + 2b c
--R                                                Type: Polynomial PrimeField 3
--E 94

--S 95 of 95
exquo(%,leadingCoefficient(f))
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 95
)spool 
 
Starts dribbling to OrderedVariableList.output (2010/3/27, 18:46:12).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 5
ls:List Symbol:=['x,'a,'z]
 

   (1)  [x,a,z]
                                                            Type: List Symbol
--R 
--R
--R   (1)  [x,a,z]
--R                                                            Type: List Symbol
--E 1

--S 2 of 5
Z:=OVAR ls
 

   (2)  OrderedVariableList [x,a,z]
                                                                 Type: Domain
--R 
--R
--R   (2)  OrderedVariableList [x,a,z]
--R                                                                 Type: Domain
--E 2

--S 3 of 5
size()$Z
 

   (3)  3
                                                     Type: NonNegativeInteger
--R 
--R
--R   (3)  3
--R                                                     Type: NonNegativeInteger
--E 3

--S 4 of 5
lv:=[index(i::PI)$Z for i in 1..size()$Z]
 
   Compiling function G1683 with type Integer -> Boolean 
   Compiling function G1697 with type NonNegativeInteger -> Boolean 

   (4)  [x,a,z]
                                       Type: List OrderedVariableList [x,a,z]
--R 
--I   Compiling function G1408 with type Integer -> Boolean 
--I   Compiling function G1572 with type NonNegativeInteger -> Boolean 
--R
--R   (4)  [x,a,z]
--R                                       Type: List OrderedVariableList [x,a,z]
--E 4

--S 5 of 5
sorted?(>,lv)
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5
)spool
 
Starts dribbling to kovacic.output (2010/3/27, 18:28:33).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 3
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 3
eq := 2*x**3 * differentiate(y x,x,2) + 3*x**2 * differentiate(y x,x) - 2 * y x
 

          3 ,,        2 ,
   (2)  2x y  (x) + 3x y (x) - 2y(x)

                                                     Type: Expression Integer
--R 
--R
--R          3 ,,        2 ,
--R   (2)  2x y  (x) + 3x y (x) - 2y(x)
--R
--R                                                     Type: Expression Integer
--E 2

--S 3 of 3
solve(eq,y,x).basis
 

               2      2
           - ----   ----
              +-+    +-+
             \|x    \|x
   (3)  [%e      ,%e    ]
                                                Type: List Expression Integer
--R 
--R
--R               2      2
--R           - ----   ----
--R              +-+    +-+
--R             \|x    \|x
--R   (3)  [%e      ,%e    ]
--R                                                Type: List Expression Integer
--E 3
)spool 
 
Starts dribbling to function.output (2010/3/27, 18:26:27).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 33
f := (x - y) / (x + y)
 

        - y + x
   (1)  -------
         y + x
                                            Type: Fraction Polynomial Integer
--R
--R        - y + x
--R   (1)  -------
--R         y + x
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 33
numer f
 

   (2)  - y + x
                                                     Type: Polynomial Integer
--R
--R   (2)  - y + x
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 33
denom f
 

   (3)  y + x
                                                     Type: Polynomial Integer
--R
--R   (3)  y + x
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 33
eval(f, x = 1/x)
 

        - x y + 1
   (4)  ---------
         x y + 1
                                            Type: Fraction Polynomial Integer
--R
--R        - x y + 1
--R   (4)  ---------
--R         x y + 1
--R                                            Type: Fraction Polynomial Integer
--E 4

--S 5 of 33
eval(f, [x = y, y = x])
 

        y - x
   (5)  -----
        y + x
                                            Type: Fraction Polynomial Integer
--R
--R        y - x
--R   (5)  -----
--R        y + x
--R                                            Type: Fraction Polynomial Integer
--E 5

)clear all
 

--S 6 of 33
f := sqrt(1 + x ** (1/3))
 

         +--------+
         |3+-+
   (1)  \|\|x  + 1
                                                     Type: Expression Integer
--R
--R         +--------+
--R         |3+-+
--R   (1)  \|\|x  + 1
--R                                                     Type: Expression Integer
--E 6

--S 7 of 33
y := rootOf(y**3 + y**2 - x*y + x**3 - 1, y)
 

   (2)  y
                                                     Type: Expression Integer
--R
--R   (2)  y
--R                                                     Type: Expression Integer
--E 7

--S 8 of 33
differentiate(y, x)
 

                 2
           y - 3x
   (3)  ------------
          2
        3y  + 2y - x
                                                     Type: Expression Integer
--R
--R                 2
--R           y - 3x
--R   (3)  ------------
--R          2
--R        3y  + 2y - x
--R                                                     Type: Expression Integer
--E 8

--S 9 of 33
(y + 1) ** 3
 

          2               3
   (4)  2y  + (x + 3)y - x  + 2
                                                     Type: Expression Integer
--R
--R          2               3
--R   (4)  2y  + (x + 3)y - x  + 2
--R                                                     Type: Expression Integer
--E 9

--S 10 of 33
g := inv f
 

             1
   (5)  -----------
         +--------+
         |3+-+
        \|\|x  + 1
                                                     Type: Expression Integer
--R
--R             1
--R   (5)  -----------
--R         +--------+
--R         |3+-+
--R        \|\|x  + 1
--R                                                     Type: Expression Integer
--E 10

--S 11 of 33
ratPoly g
 

                6     4     2
   (6)  (x + 1)?  - 3?  + 3?  - 1
                          Type: SparseUnivariatePolynomial Expression Integer
--R
--R                6     4     2
--R   (6)  (x + 1)?  - 3?  + 3?  - 1
--R                          Type: SparseUnivariatePolynomial Expression Integer
--E 11

)clear all
 

--S 12 of 33
f := x * log y * sin(1/(x+y))
 

                      1
   (1)  x log(y)sin(-----)
                    y + x
                                                     Type: Expression Integer
--R
--R                      1
--R   (1)  x log(y)sin(-----)
--R                    y + x
--R                                                     Type: Expression Integer
--E 12

--S 13 of 33
eval(f, [x = y, y = x])
 

                      1
   (2)  y log(x)sin(-----)
                    y + x
                                                     Type: Expression Integer
--R
--R                      1
--R   (2)  y log(x)sin(-----)
--R                    y + x
--R                                                     Type: Expression Integer
--E 13

--S 14 of 33
eval(f, log y = acosh(x + sqrt y))
 

                1          +-+
   (3)  x sin(-----)acosh(\|y  + x)
              y + x
                                                     Type: Expression Integer
--R
--R                1          +-+
--R   (3)  x sin(-----)acosh(\|y  + x)
--R              y + x
--R                                                     Type: Expression Integer
--E 14

)clear all
 

--S 15 of 33
f := cos(x)/sec(x) * log(sin(x)**2/(cos(x)**2+sin(x)**2))
 

                             2
                       sin(x)
        cos(x)log(-----------------)
                        2         2
                  sin(x)  + cos(x)
   (1)  ----------------------------
                   sec(x)
                                                     Type: Expression Integer
--R
--R                             2
--R                       sin(x)
--R        cos(x)log(-----------------)
--R                        2         2
--R                  sin(x)  + cos(x)
--R   (1)  ----------------------------
--R                   sec(x)
--R                                                     Type: Expression Integer
--E 15

--S 16 of 33
g := simplify f
 

              2            2
   (2)  cos(x) log(- cos(x)  + 1)
                                                     Type: Expression Integer
--R
--R              2            2
--R   (2)  cos(x) log(- cos(x)  + 1)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 33
h := sin2csc cos2sec g
 

                  2
            sec(x)  - 1
        log(-----------)
                    2
              sec(x)
   (3)  ----------------
                   2
             sec(x)
                                                     Type: Expression Integer
--R
--R                  2
--R            sec(x)  - 1
--R        log(-----------)
--R                    2
--R              sec(x)
--R   (3)  ----------------
--R                   2
--R             sec(x)
--R                                                     Type: Expression Integer
--E 17

--S 18 of 33
expandLog h
 

                  2
        log(sec(x)  - 1) - 2log(sec(x))
   (4)  -------------------------------
                          2
                    sec(x)
                                                     Type: Expression Integer
--R
--R                  2
--R        log(sec(x)  - 1) - 2log(sec(x))
--R   (4)  -------------------------------
--R                          2
--R                    sec(x)
--R                                                     Type: Expression Integer
--E 18

--S 19 of 33
f1 := sqrt((x+1)**3)
 

         +-----------------+
         | 3     2
   (5)  \|x  + 3x  + 3x + 1
                                                     Type: Expression Integer
--R
--R         +-----------------+
--R         | 3     2
--R   (5)  \|x  + 3x  + 3x + 1
--R                                                     Type: Expression Integer
--E 19

--S 20 of 33
rootSimp f1
 

                +-----+
   (6)  (x + 1)\|x + 1
                                                     Type: Expression Integer
--R
--R                +-----+
--R   (6)  (x + 1)\|x + 1
--R                                                     Type: Expression Integer
--E 20

--S 21 of 33
g1 := sin(x + cos x)
 

   (7)  sin(cos(x) + x)
                                                     Type: Expression Integer
--R
--R   (7)  sin(cos(x) + x)
--R                                                     Type: Expression Integer
--E 21

--S 22 of 33
g2 := complexElementary g1
 

                              +---+ 2               +---+          2
                    +---+   x\|- 1         +---+  x\|- 1     +---+
                   \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
                   -----------------------------------------------
                                           +---+
                                         x\|- 1
           +---+                      2%e                               +---+
        - \|- 1 (%e                                               )  + \|- 1
   (8)  ---------------------------------------------------------------------
                                +---+ 2               +---+
                      +---+   x\|- 1         +---+  x\|- 1     +---+
                     \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
                     -----------------------------------------------
                                             +---+
                                           x\|- 1
                                        2%e
                  2%e
                                                     Type: Expression Integer
--R
--R                              +---+ 2               +---+          2
--R                    +---+   x\|- 1         +---+  x\|- 1     +---+
--R                   \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
--R                   -----------------------------------------------
--R                                           +---+
--R                                         x\|- 1
--R           +---+                      2%e                               +---+
--R        - \|- 1 (%e                                               )  + \|- 1
--R   (8)  ---------------------------------------------------------------------
--R                                +---+ 2               +---+
--R                      +---+   x\|- 1         +---+  x\|- 1     +---+
--R                     \|- 1 (%e       )  + 2x\|- 1 %e        + \|- 1
--R                     -----------------------------------------------
--R                                             +---+
--R                                           x\|- 1
--R                                        2%e
--R                  2%e
--R                                                     Type: Expression Integer
--E 22

--S 23 of 33
trigs g2
 

   (9)  sin(cos(x) + x)
                                                     Type: Expression Integer
--R
--R   (9)  sin(cos(x) + x)
--R                                                     Type: Expression Integer
--E 23

--S 24 of 33
h1 := sinh(x + cosh x)
 

   (10)  sinh(cosh(x) + x)
                                                     Type: Expression Integer
--R
--R   (10)  sinh(cosh(x) + x)
--R                                                     Type: Expression Integer
--E 24

--S 25 of 33
h2 := realElementary h1
 

               x 2        x     2
            (%e )  + 2x %e  + 1
            -------------------
                       x
                    2%e
         (%e                   )  - 1
   (11)  ----------------------------
                  x 2        x
               (%e )  + 2x %e  + 1
               -------------------
                          x
                       2%e
            2%e
                                                     Type: Expression Integer
--R
--R               x 2        x     2
--R            (%e )  + 2x %e  + 1
--R            -------------------
--R                       x
--R                    2%e
--R         (%e                   )  - 1
--R   (11)  ----------------------------
--R                  x 2        x
--R               (%e )  + 2x %e  + 1
--R               -------------------
--R                          x
--R                       2%e
--R            2%e
--R                                                     Type: Expression Integer
--E 25

--S 26 of 33
htrigs h2
 

   (12)  sinh(cosh(x) + x)
                                                     Type: Expression Integer
--R
--R   (12)  sinh(cosh(x) + x)
--R                                                     Type: Expression Integer
--E 26

)clear all
 

--S 27 of 33
groupSqrt := _rule(sqrt(a) * sqrt(b), sqrt(a*b))
 

           +-+ +-+       +---+
   (1)  %P\|a \|b  == %P\|a b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R           +-+ +-+       +---+
--I   (1)  %B\|a \|b  == %B\|a b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 27

--S 28 of 33
a := sqrt(2) * sqrt(3)
 

         +-+ +-+
   (2)  \|2 \|3
                                                        Type: AlgebraicNumber
--R
--R         +-+ +-+
--R   (2)  \|2 \|3
--R                                                        Type: AlgebraicNumber
--E 28

--S 29 of 33
groupSqrt a
 

         +-+
   (3)  \|6
                                                     Type: Expression Integer
--R
--R         +-+
--R   (3)  \|6
--R                                                     Type: Expression Integer
--E 29

--S 30 of 33
a := (sqrt(x) + sqrt(y))**4
 

                  +-+ +-+    2           2
   (4)  (4y + 4x)\|x \|y  + y  + 6x y + x
                                                     Type: Expression Integer
--R
--R                  +-+ +-+    2           2
--R   (4)  (4y + 4x)\|x \|y  + y  + 6x y + x
--R                                                     Type: Expression Integer
--E 30

--S 31 of 33
groupSqrt a
 

                  +---+    2           2
   (5)  (4y + 4x)\|x y  + y  + 6x y + x
                                                     Type: Expression Integer
--R
--R                  +---+    2           2
--R   (5)  (4y + 4x)\|x y  + y  + 6x y + x
--R                                                     Type: Expression Integer
--E 31

--S 32 of 33
sinCosExpand := rule
  sin(-x)    == - sin(x)
  cos(-x)    == cos(x)
  sin(x + y) == sin(x) * cos(y) + sin(y) * cos(x)
  cos(x + y) == cos(x) * cos(y) - sin(x) * sin(y)
  sin((n | integer? n and n > 1) * x) ==_
       sin(x) * cos((n-1)*x) + sin((n-1)*x) * cos(x)
  cos((n | integer? n and n > 1) * x) ==_
       cos(x) * cos((n-1)*x) - sin(x) * sin((n-1)*x)
 

   (6)
   {- %Q sin(x) == - %Q sin(x), cos(x) == cos(x),
    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (6)
--I   {- %BC sin(x) == - %BC sin(x), cos(x) == cos(x),
--R    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
--R    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
--R    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 32

--S 33 of 33
sinCosExpand(sin(x+y-2*z) * cos y)
 

   (7)  - cos(y)sin(2z - y - x)
                                                     Type: Expression Integer
--R
--R   (7)  - cos(y)sin(2z - y - x)
--R                                                     Type: Expression Integer
--E 33

)spool
 
Starts dribbling to Stream.output (2010/3/27, 18:46:36).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 12
ints := [i for i in 0..]
 

   (1)  [0,1,2,3,4,5,6,7,8,9,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (1)  [0,1,2,3,4,5,6,7,8,9,...]
--R                                              Type: Stream NonNegativeInteger
--E 1

--S 2 of 12
f : List INT -> List INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 12
f x == [x.1 + x.2, x.1]
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 12
fibs := [i.2 for i in [generate(f,[1,1])]]
 
   Compiling function f with type List Integer -> List Integer 

   (4)  [1,1,2,3,5,8,13,21,34,55,...]
                                                         Type: Stream Integer
--R 
--R   Compiling function f with type List Integer -> List Integer 
--R
--R   (4)  [1,1,2,3,5,8,13,21,34,55,...]
--R                                                         Type: Stream Integer
--E 4

--S 5 of 12
[i for i in ints | odd? i]
 

   (5)  [1,3,5,7,9,11,13,15,17,19,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (5)  [1,3,5,7,9,11,13,15,17,19,...]
--R                                              Type: Stream NonNegativeInteger
--E 5

--S 6 of 12
odds := [2*i+1 for i in ints]
 

   (6)  [1,3,5,7,9,11,13,15,17,19,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (6)  [1,3,5,7,9,11,13,15,17,19,...]
--R                                              Type: Stream NonNegativeInteger
--E 6

--S 7 of 12
scan(0,+,odds)
 

   (7)  [1,4,9,16,25,36,49,64,81,100,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (7)  [1,4,9,16,25,36,49,64,81,100,...]
--R                                              Type: Stream NonNegativeInteger
--E 7

--S 8 of 12
[i*j for i in ints for j in odds]
 

   (8)  [0,3,10,21,36,55,78,105,136,171,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (8)  [0,3,10,21,36,55,78,105,136,171,...]
--R                                              Type: Stream NonNegativeInteger
--E 8

--S 9 of 12
map(*,ints,odds)
 

   (9)  [0,3,10,21,36,55,78,105,136,171,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (9)  [0,3,10,21,36,55,78,105,136,171,...]
--R                                              Type: Stream NonNegativeInteger
--E 9

--S 10 of 12
first ints
 

   (10)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (10)  0
--R                                                     Type: NonNegativeInteger
--E 10

--S 11 of 12
rest ints
 

   (11)  [1,2,3,4,5,6,7,8,9,10,...]
                                              Type: Stream NonNegativeInteger
--R 
--R
--R   (11)  [1,2,3,4,5,6,7,8,9,10,...]
--R                                              Type: Stream NonNegativeInteger
--E 11

--S 12 of 12
fibs 20
 

   (12)  6765
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  6765
--R                                                        Type: PositiveInteger
--E 12
)spool
 
Starts dribbling to LiePolynomial.output (2010/3/27, 18:45:55).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 28
RN := Fraction Integer
 

   (1)  Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 28
Lpoly := LiePolynomial(Symbol,RN)
 

   (2)  LiePolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (2)  LiePolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 2

--S 3 of 28
Dpoly := XDPOLY(Symbol,RN)
 

   (3)  XDistributedPolynomial(Symbol,Fraction Integer)
                                                                 Type: Domain
--R 
--R
--R   (3)  XDistributedPolynomial(Symbol,Fraction Integer)
--R                                                                 Type: Domain
--E 3

--S 4 of 28
Lword := LyndonWord Symbol
 

   (4)  LyndonWord Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  LyndonWord Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 28
a:Symbol := 'a
 

   (5)  a
                                                                 Type: Symbol
--R 
--R
--R   (5)  a
--R                                                                 Type: Symbol
--E 5

--S 6 of 28
b:Symbol := 'b 
 

   (6)  b
                                                                 Type: Symbol
--R 
--R
--R   (6)  b
--R                                                                 Type: Symbol
--E 6

--S 7 of 28
c:Symbol := 'c
 

   (7)  c
                                                                 Type: Symbol
--R 
--R
--R   (7)  c
--R                                                                 Type: Symbol
--E 7

--S 8 of 28
aa: Lpoly := a 
 

   (8)  [a]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (8)  [a]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 8

--S 9 of 28
bb: Lpoly := b
 

   (9)  [b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (9)  [b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 9

--S 10 of 28
cc: Lpoly := c
 

   (10)  [c]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (10)  [c]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 10

--S 11 of 28
p : Lpoly := [aa,bb]
 

   (11)  [a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (11)  [a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 11

--S 12 of 28
q : Lpoly := [p,bb]
 

             2
   (12)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R             2
--R   (12)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 12

--S 13 of 28
liste : List Lword := LyndonWordsList([a,b], 4)
 

                          2       2    3     2 2      3
   (13)  [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]]
                                                 Type: List LyndonWord Symbol
--R 
--R
--R                          2       2    3     2 2      3
--R   (13)  [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]]
--R                                                 Type: List LyndonWord Symbol
--E 13

--S 14 of 28
r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly
 

                    2         2
   (14)  [a b] + 3[a b] + [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                    2         2
--R   (14)  [a b] + 3[a b] + [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 14

--S 15 of 28
s:Lpoly := [p,r]
 

              2                 2
   (15)  - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R              2                 2
--R   (15)  - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 15

--S 16 of 28
t:Lpoly  := s  + 2*LiePoly(liste.3) - 5*LiePoly(liste.5)
 

                       2       2                 2
   (16)  2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                       2       2                 2
--R   (16)  2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 16

--S 17 of 28
degree t
 

   (17)  5
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  5
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 28
mirror t
 

                         2       2                 2
   (18)  - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R                         2       2                 2
--R   (18)  - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 18

--S 19 of 28
Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == _
   [ [p,q]$Lpoly, r] + [ [q,r]$Lpoly, p] + [ [r,p]$Lpoly, q]  
 
   Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer
      ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol,
      Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has 
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer
--R      ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol,
--R      Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has 
--R      been added to workspace.
--R                                                                   Type: Void
--E 19

--S 20 of 28
test: Lpoly := Jacobi(a,b,b)
 
   Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction 
      Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(
      Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction 
      Integer) 

   (20)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R   Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction 
--R      Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(
--R      Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction 
--R      Integer) 
--R
--R   (20)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 20

--S 21 of 28
test: Lpoly := Jacobi(p,q,r)
 

   (21)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (21)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 21

--S 22 of 28
test: Lpoly := Jacobi(r,s,t)
 

   (22)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (22)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 22

--S 23 of 28
eval(p, a, p)$Lpoly
 

             2
   (23)  [a b ]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R             2
--R   (23)  [a b ]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 23

--S 24 of 28
eval(p, [a,b], [2*bb, 3*aa])$Lpoly
 

   (24)  - 6[a b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (24)  - 6[a b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 24

--S 25 of 28
r: Lpoly := [p,c]
 

   (25)  [a b c] + [a c b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (25)  [a b c] + [a c b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 25

--S 26 of 28
r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly 
 

   (26)  - [a b c]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (26)  - [a b c]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 26

--S 27 of 28
r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly 
 

   (27)  - [a c b]
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (27)  - [a c b]
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 27

--S 28 of 28
r + r1 + r2
 

   (28)  0
                                 Type: LiePolynomial(Symbol,Fraction Integer)
--R 
--R
--R   (28)  0
--R                                 Type: LiePolynomial(Symbol,Fraction Integer)
--E 28
)spool
 
Starts dribbling to float.output (2010/3/27, 18:26:16).
)set message test on
 
)set message auto off
 
)clear all
 

-- look at 28 digits of accuracy (default is 20)
--S 1 of 13
digits 28
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 13
p := numeric %pi
 

   (2)  3.1415926535 8979323846 2643383
                                                                  Type: Float
--R 
--R
--R   (2)  3.1415926535 8979323846 2643383
--R                                                                  Type: Float
--E 2

--S 3 of 13
a := 163.0
 

   (3)  163.0
                                                                  Type: Float
--R 
--R
--R   (3)  163.0
--R                                                                  Type: Float
--E 3

--S 4 of 13
b := sqrt a
 

   (4)  12.7671453348 0370466171 095201
                                                                  Type: Float
--R 
--R
--R   (4)  12.7671453348 0370466171 095201
--R                                                                  Type: Float
--E 4

-- following appears to be an integer
--S 5 of 13
exp(p * b)
 

   (5)  26253741 2640768744.0000000003
                                                                  Type: Float
--R 
--R
--R   (5)  26253741 2640768744.0000000003
--R                                                                  Type: Float
--E 5

-- increase the precision to 60 and recalculate
--S 6 of 13
digits 60
 

   (6)  28
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  28
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 13
p := numeric %pi
 

   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
                                                                  Type: Float
--R 
--R
--R   (7)  3.1415926535 8979323846 2643383279 5028841971 6939937510 582097494
--R                                                                  Type: Float
--E 7

--S 8 of 13
a := 163.0
 

   (8)  163.0
                                                                  Type: Float
--R 
--R
--R   (8)  163.0
--R                                                                  Type: Float
--E 6

--S 9 of 13
b := sqrt a
 

   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
                                                                  Type: Float
--R 
--R
--R   (9)  12.7671453348 0370466171 0952009780 8923473823 6378030125 88512126
--R                                                                  Type: Float
--E 9

--S 10 of 13
exp(p * b)
 

   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
                                                                  Type: Float
--R 
--R
--R   (10)  26253741 2640768743.9999999999 9925007259 7198185688 8793538563 39
--R                                                                  Type: Float
--E 10

--S 11 of 13
c := cos(p/12)
 

   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
                                                                  Type: Float
--R 
--R
--R   (11)  0.9659258262 8906828674 9743199728 8973676339 0483900840 4550402343
--R                                                                  Type: Float
--E 11

-- we have enough precision to get 0 in following
--S 12 of 13
16*c**4 - 16*c**2 + 1
 

   (12)  0.0
                                                                  Type: Float
--R 
--R
--R   (12)  0.0
--R                                                                  Type: Float
--E 12

-- look at PI to 200 places
--S 13 of 13
numeric(%pi, 200)
 

   (13)
  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
  2 5359408128 4811174502 8410270193 8521105559 6446229489 54930382
                                                                  Type: Float
--R 
--R
--R   (13)
--R  3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 592307816
--R  4 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 505822317
--R  2 5359408128 4811174502 8410270193 8521105559 6446229489 54930382
--R                                                                  Type: Float
--E 13
)spool 
 
Starts dribbling to RealSolvePackage.output (2010/3/27, 18:46:28).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 13
p := 4*x^3 - 3*x^2 + 2*x - 4
 

          3     2
   (1)  4x  - 3x  + 2x - 4
                                                     Type: Polynomial Integer
--R 
--R
--R          3     2
--R   (1)  4x  - 3x  + 2x - 4
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 13
ans1 := solve(p,0.01)$REALSOLV
 

   (2)  [1.11328125]
                                                             Type: List Float
--R 
--R
--R   (2)  [1.11328125]
--R                                                             Type: List Float
--E 2

--S 3 of 13
ans2 := solve(p::POLY(FRAC(INT)),0.01)$REALSOLV
 

   (3)  [1.11328125]
                                                             Type: List Float
--R 
--R
--R   (3)  [1.11328125]
--R                                                             Type: List Float
--E 3

--S 4 of 13
R := Integer
 

   (4)  Integer
                                                                 Type: Domain
--R 
--R
--R   (4)  Integer
--R                                                                 Type: Domain
--E 4

--S 5 of 13
ls : List Symbol := [x,y,z,t]
 

   (5)  [x,y,z,t]
                                                            Type: List Symbol
--R 
--R
--R   (5)  [x,y,z,t]
--R                                                            Type: List Symbol
--E 5

--S 6 of 13
ls2 : List Symbol := [x,y,z,t,new()$Symbol]
 

   (6)  [x,y,z,t,%A]
                                                            Type: List Symbol
--R 
--R
--R   (6)  [x,y,z,t,%A]
--R                                                            Type: List Symbol
--E 6

--S 7 of 13
pack := ZDSOLVE(R,ls,ls2)
 

   (7)  ZeroDimensionalSolvePackage(Integer,[x,y,z,t],[x,y,z,t,%A])
                                                                 Type: Domain
--R 
--R
--R   (7)  ZeroDimensionalSolvePackage(Integer,[x,y,z,t],[x,y,z,t,%A])
--R                                                                 Type: Domain
--E 7

--S 8 of 13
p1 := x**2*y*z + y*z
 

          2
   (8)  (x  + 1)y z
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (8)  (x  + 1)y z
--R                                                     Type: Polynomial Integer
--E 8

--S 9 of 13
p2 := x**2*y**2*z + x + z
 

          2 2
   (9)  (x y  + 1)z + x
                                                     Type: Polynomial Integer
--R 
--R
--R          2 2
--R   (9)  (x y  + 1)z + x
--R                                                     Type: Polynomial Integer
--E 9

--S 10 of 13
p3 := x**2*y**2*z**2 +  z + 1
 

          2 2 2
   (10)  x y z  + z + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          2 2 2
--R   (10)  x y z  + z + 1
--R                                                     Type: Polynomial Integer
--E 10

--S 11 of 13
lp := [p1, p2, p3]
 

            2           2 2            2 2 2
   (11)  [(x  + 1)y z,(x y  + 1)z + x,x y z  + z + 1]
                                                Type: List Polynomial Integer
--R 
--R
--R            2           2 2            2 2 2
--R   (11)  [(x  + 1)y z,(x y  + 1)z + x,x y z  + z + 1]
--R                                                Type: List Polynomial Integer
--E 11

--S 12 of 13
lsv:List(Symbol):=[x,y,z]
 

   (12)  [x,y,z]
                                                            Type: List Symbol
--R 
--R
--R   (12)  [x,y,z]
--R                                                            Type: List Symbol
--E 12

--S 13 of 13
ans3 := realSolve(lp,lsv,0.01)$REALSOLV
 

   (13)  [[1.0,0.0,- 1.0]]
                                                        Type: List List Float
--R 
--R
--R   (13)  [[1.0,0.0,- 1.0]]
--R                                                        Type: List List Float
--E 13
)spool
 
Starts dribbling to isprime.output (2010/3/27, 18:27:19).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 15
n := 6763*10627*29947 
 

   (1)  2152302898747
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  2152302898747
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 15
prime?(n)  
 

   (2)  false
                                                                Type: Boolean
--R 
--R
--R   (2)  false
--R                                                                Type: Boolean
--E 2

--S 3 of 15
factor(n)
 

   (3)  6763 10627 29947
                                                       Type: Factored Integer
--R 
--R
--R   (3)  6763 10627 29947
--R                                                       Type: Factored Integer
--E 3

--S 4 of 15
n := 1303*16927*157543  
 

   (4)  3474749660383
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  3474749660383
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 15
prime?(n)
 

   (5)  false
                                                                Type: Boolean
--R 
--R
--R   (5)  false
--R                                                                Type: Boolean
--E 5

--S 6 of 15
factor(n)
 

   (6)  1303 16927 157543
                                                       Type: Factored Integer
--R 
--R
--R   (6)  1303 16927 157543
--R                                                       Type: Factored Integer
--E 6

--S 7 of 15
n := 3739*18691*153259  
 

   (7)  10710604680091
                                                        Type: PositiveInteger
--R 
--R
--R   (7)  10710604680091
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 15
prime?(n)
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 15
factor(n)
 

   (9)  3739 18691 153259
                                                       Type: Factored Integer
--R 
--R
--R   (9)  3739 18691 153259
--R                                                       Type: Factored Integer
--E 9

--S 10 of 15
n := 46411*232051*417691  
 

   (10)  4498414682539051
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  4498414682539051
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 15
prime?(n)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 15
factor(n)
 

   (12)  46411 232051 417691
                                                       Type: Factored Integer
--R 
--R
--R   (12)  46411 232051 417691
--R                                                       Type: Factored Integer
--E 12

--S 13 of 15
n := 21319*106591*3005839  
 

   (13)  6830509209595831
                                                        Type: PositiveInteger
--R 
--R
--R   (13)  6830509209595831
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 15
prime?(n)
 

   (14)  false
                                                                Type: Boolean
--R 
--R
--R   (14)  false
--R                                                                Type: Boolean
--E 14

--S 15 of 15
factor(n)
 

   (15)  21319 106591 3005839
                                                       Type: Factored Integer
--R 
--R
--R   (15)  21319 106591 3005839
--R                                                       Type: Factored Integer
--E 15
)spool 
 
Starts dribbling to help.output (2010/3/27, 18:26:49).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 2
a:= x**2 + 1
 

         2
   (1)  x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (1)  x  + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 2
(a - 2)**2
 

         4     2
   (2)  x  - 2x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         4     2
--R   (2)  x  - 2x  + 1
--R                                                     Type: Polynomial Integer
--E 2
)spool 
 
Starts dribbling to limit.output (2010/3/27, 18:28:38).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 15
limit((x^2-4)/(x-2),x=2)
 

   (1)  4
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (1)  4
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 1
--S 2 of 15
limit(sqrt(9-x^2),x=-4)
 

   (2)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (2)  "failed"
--R                                                    Type: Union("failed",...)
--E 2

--S 3 of 15
limit(sqrt(9-x^2),x=-3)
 

   (3)  [leftHandLimit= "failed",rightHandLimit= 0]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (3)  [leftHandLimit= "failed",rightHandLimit= 0]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 3

--S 4 of 15
limit(sqrt(9-x^2),x=-2)
 

         +-+
   (4)  \|5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         +-+
--R   (4)  \|5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 4

--S 5 of 15
limit(sqrt(9-x^2),x=0)
 

   (5)  3
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (5)  3
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 5

--S 6 of 15
limit(sqrt(9-x^2),x=2)
 

         +-+
   (6)  \|5
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R         +-+
--R   (6)  \|5
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 6

--S 7 of 15
limit(sqrt(9-x^2),x=3)
 

   (7)  [leftHandLimit= 0,rightHandLimit= "failed"]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--R 
--R
--R   (7)  [leftHandLimit= 0,rightHandLimit= "failed"]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...)
--E 7

--S 8 of 15
limit(sqrt(9-x^2),x=4)
 

   (8)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8

--S 9 of 15
limit(1/x^2,x=0)
 

   (9)   + infinity
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (9)   + infinity
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 9

--S 10 of 15
limit(-1/(x-1)^2,x=1)
 

   (10)  - infinity
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (10)  - infinity
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 10

--S 11 of 15
limit(1/x,x=0)
 

   (11)  [leftHandLimit= - infinity,rightHandLimit=  + infinity]
Type: Union(Record(leftHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed"),rightHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed")),...)
--R 
--R
--R   (11)  [leftHandLimit= - infinity,rightHandLimit=  + infinity]
--RType: Union(Record(leftHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed"),rightHandLimit: Union(OrderedCompletion Fraction Polynomial Integer,"failed")),...)
--E 11

--S 12 of 15
limit(1/x,x=%plusInfinity)
 

   (12)  0
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (12)  0
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 12

--S 13 of 15
limit(2+(1/x^2),x=%plusInfinity)
 

   (13)  2
               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--R 
--R
--R   (13)  2
--R               Type: Union(OrderedCompletion Fraction Polynomial Integer,...)
--E 13

)clear all
 

--S 14 of 15
f := exp(n) * (sin(1/n + exp(-n)) - sin(1/n))
 

                   - n
          n    n %e    + 1      n    1
   (1)  %e sin(-----------) - %e sin(-)
                    n                n
                                                     Type: Expression Integer
--R 
--R
--R                   - n
--R          n    n %e    + 1      n    1
--R   (1)  %e sin(-----------) - %e sin(-)
--R                    n                n
--R                                                     Type: Expression Integer
--E 14

--S 15 of 15
limit(f,n=%plusInfinity)
 

   (2)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (2)  "failed"
--R                                                    Type: Union("failed",...)
--E 15
)spool 
 
Starts dribbling to schaum1.output (2010/3/27, 18:37:7).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 108
aa:=integrate(1/(a*x+b),x)
 

        log(a x + b)
   (1)  ------------
              a
                                          Type: Union(Expression Integer,...)
--R
--R        log(a x + b)
--R   (1)  ------------
--R              a
--R                                          Type: Union(Expression Integer,...)
--E 1

--S 2 of 108
bb:=1/a*log(a*x+b)
 

        log(a x + b)
   (2)  ------------
              a
                                                     Type: Expression Integer
--R
--R        log(a x + b)
--R   (2)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 3 of 108      14:59 Schaums and Axiom agree
cc:=bb-aa
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 108
aa:=integrate(x/(a*x+b),x)
 

        - b log(a x + b) + a x
   (1)  ----------------------
                   2
                  a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - b log(a x + b) + a x
--R   (1)  ----------------------
--R                   2
--R                  a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 108
bb:=x/a-b/a^2*log(a*x+b)
 

        - b log(a x + b) + a x
   (2)  ----------------------
                   2
                  a
                                                     Type: Expression Integer
--R
--R        - b log(a x + b) + a x
--R   (2)  ----------------------
--R                   2
--R                  a
--R                                                     Type: Expression Integer
--E

--S 6 of 108      14:60 Schaums and Axiom agree
cc:=bb-aa
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 108
aa:=integrate(x^2/(a*x+b),x)
 

          2                2 2
        2b log(a x + b) + a x  - 2a b x
   (1)  -------------------------------
                        3
                      2a
                                          Type: Union(Expression Integer,...)
--R
--R          2                2 2
--R        2b log(a x + b) + a x  - 2a b x
--R   (1)  -------------------------------
--R                        3
--R                      2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 108
bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b)
 

          2                2 2              2
        2b log(a x + b) + a x  - 2a b x - 3b
   (2)  -------------------------------------
                           3
                         2a
                                                     Type: Expression Integer
--R
--R          2                2 2              2
--R        2b log(a x + b) + a x  - 2a b x - 3b
--R   (2)  -------------------------------------
--R                           3
--R                         2a
--R                                                     Type: Expression Integer
--E

--S 9 of 108
cc:=bb-aa
 

            2
          3b
   (3)  - ---
            3
          2a
                                                     Type: Expression Integer
--R
--R            2
--R          3b
--R   (3)  - ---
--R            3
--R          2a
--R                                                     Type: Expression Integer
--E
--S 10 of 108     14:61 Schaums and Axiom differ by a constant
differentiate(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 11 of 108
aa:=integrate(x^3/(a*x+b),x)
 

            3                 3 3     2   2       2
        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x
   (1)  --------------------------------------------
                               4
                             6a
                                          Type: Union(Expression Integer,...)
--R
--R            3                 3 3     2   2       2
--R        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x
--R   (1)  --------------------------------------------
--R                               4
--R                             6a
--R                                          Type: Union(Expression Integer,...)
--E
--S 12 of 108
bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(a*x+b)
 

            3                 3 3     2   2       2       3
        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x + 11b
   (2)  ---------------------------------------------------
                                  4
                                6a
                                                     Type: Expression Integer
--R
--R            3                 3 3     2   2       2       3
--R        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x + 11b
--R   (2)  ---------------------------------------------------
--R                                  4
--R                                6a
--R                                                     Type: Expression Integer
--E 
--S 13 of 108
cc:=aa-bb
 

             3
          11b
   (3)  - ----
             4
           6a
                                                     Type: Expression Integer
--R
--R             3
--R          11b
--R   (3)  - ----
--R             4
--R           6a
--R                                                     Type: Expression Integer
--E 
--S 14 of 108     14:62 Schaums and Axiom differ by a constant
dd:=D(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 

--S 15 of 108
aa:=integrate(1/(x*(a*x+b)),x)
 

        - log(a x + b) + log(x)
   (1)  -----------------------
                   b
                                          Type: Union(Expression Integer,...)
--R
--R        - log(a x + b) + log(x)
--R   (1)  -----------------------
--R                   b
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16 of 108
bb:=1/b*log(x/(a*x+b))
 

               x
        log(-------)
            a x + b
   (2)  ------------
              b
                                                     Type: Expression Integer
--R
--R               x
--R        log(-------)
--R            a x + b
--R   (2)  ------------
--R              b
--R                                                     Type: Expression Integer
--E

--S 17 of 108
cc:=aa-bb
 

                                         x
        - log(a x + b) + log(x) - log(-------)
                                      a x + b
   (3)  --------------------------------------
                           b
                                                     Type: Expression Integer
--R
--R                                         x
--R        - log(a x + b) + log(x) - log(-------)
--R                                      a x + b
--R   (3)  --------------------------------------
--R                           b
--R                                                     Type: Expression Integer
--E
--S 18 of 108
logdiv:=rule(log(a)-log(b) == log(a/b))
 

                                      a
   (4)  - log(b) + log(a) + %G == log(-) + %G
                                      b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                                      a
--I   (4)  - log(b) + log(a) + %I == log(-) + %I
--R                                      b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 
--S 19 of 108     14:63 Schaums and Axiom agree
dd:=logdiv cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 20 of 108
aa:=integrate(1/(x^2*(a*x+b)),x)
 

        a x log(a x + b) - a x log(x) - b
   (1)  ---------------------------------
                        2
                       b x
                                          Type: Union(Expression Integer,...)
--R
--R        a x log(a x + b) - a x log(x) - b
--R   (1)  ---------------------------------
--R                        2
--R                       b x
--R                                          Type: Union(Expression Integer,...)
--E 
--S 21 of 108
bb:=-1/(b*x)+a/b^2*log((a*x+b)/x)
 

                a x + b
        a x log(-------) - b
                   x
   (2)  --------------------
                  2
                 b x
                                                     Type: Expression Integer
--R
--R                a x + b
--R        a x log(-------) - b
--R                   x
--R   (2)  --------------------
--R                  2
--R                 b x
--R                                                     Type: Expression Integer
--E 

--S 22 of 108
cc:=aa-bb
 

                                          a x + b
        a log(a x + b) - a log(x) - a log(-------)
                                             x
   (3)  ------------------------------------------
                             2
                            b
                                                     Type: Expression Integer
--R
--R                                          a x + b
--R        a log(a x + b) - a log(x) - a log(-------)
--R                                             x
--R   (3)  ------------------------------------------
--R                             2
--R                            b
--R                                                     Type: Expression Integer
--E
--S 23 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E 
--S 24 of 108     14:64 Schaums and Axiom agree
divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
--S 25 of 108
aa:=integrate(1/(x^3*(a*x+b)),x)
 

            2 2                 2 2                   2
        - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
   (1)  -----------------------------------------------
                               3 2
                             2b x
                                          Type: Union(Expression Integer,...)
--R
--R            2 2                 2 2                   2
--R        - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
--R   (1)  -----------------------------------------------
--R                               3 2
--R                             2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 26 of 108
bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b))
 

          2 2       x                 2
        2a x log(-------) + 2a b x - b
                 a x + b
   (2)  -------------------------------
                       3 2
                     2b x
                                                     Type: Expression Integer
--R
--R          2 2       x                 2
--R        2a x log(-------) + 2a b x - b
--R                 a x + b
--R   (2)  -------------------------------
--R                       3 2
--R                     2b x
--R                                                     Type: Expression Integer
--E

--S 27 of 108
cc:=aa-bb
 

           2                2          2       x
        - a log(a x + b) + a log(x) - a log(-------)
                                            a x + b
   (3)  --------------------------------------------
                              3
                             b
                                                     Type: Expression Integer
--R
--R           2                2          2       x
--R        - a log(a x + b) + a log(x) - a log(-------)
--R                                            a x + b
--R   (3)  --------------------------------------------
--R                              3
--R                             b
--R                                                     Type: Expression Integer
--E

--S 28 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 29 of 108     14:65 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 

--S 30 of 108
aa:=integrate(1/(a*x+b)^2,x)
 

              1
   (1)  - ---------
           2
          a x + a b
                                          Type: Union(Expression Integer,...)
--R
--R              1
--R   (1)  - ---------
--R           2
--R          a x + a b
--R                                          Type: Union(Expression Integer,...)
--E 

--S 31 of 108
bb:=-1/(a*(a*x+b))
 

              1
   (2)  - ---------
           2
          a x + a b
                                            Type: Fraction Polynomial Integer
--R
--R              1
--R   (2)  - ---------
--R           2
--R          a x + a b
--R                                            Type: Fraction Polynomial Integer
--E

--S 32 of 108     14:66 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 33 of 108
aa:=integrate(x/(a*x+b)^2,x)
 

        (a x + b)log(a x + b) + b
   (1)  -------------------------
                 3     2
                a x + a b
                                          Type: Union(Expression Integer,...)
--R
--R        (a x + b)log(a x + b) + b
--R   (1)  -------------------------
--R                 3     2
--R                a x + a b
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34 of 108
bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b)
 

        (a x + b)log(a x + b) + b
   (2)  -------------------------
                 3     2
                a x + a b
                                                     Type: Expression Integer
--R
--R        (a x + b)log(a x + b) + b
--R   (2)  -------------------------
--R                 3     2
--R                a x + a b
--R                                                     Type: Expression Integer
--E

--S 35 of 108     14:67 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 36 of 108
aa:=integrate(x^2/(a*x+b)^2,x)
 

                      2                 2 2            2
        (- 2a b x - 2b )log(a x + b) + a x  + a b x - b
   (1)  ------------------------------------------------
                             4     3
                            a x + a b
                                          Type: Union(Expression Integer,...)
--R
--R                      2                 2 2            2
--R        (- 2a b x - 2b )log(a x + b) + a x  + a b x - b
--R   (1)  ------------------------------------------------
--R                             4     3
--R                            a x + a b
--R                                          Type: Union(Expression Integer,...)
--E 
--S 37 of 108
bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b)
 

                      2                 2 2
        (- 2a b x - 2b )log(a x + b) + a x  + 2a b x
   (2)  --------------------------------------------
                           4     3
                          a x + a b
                                                     Type: Expression Integer
--R
--R                      2                 2 2
--R        (- 2a b x - 2b )log(a x + b) + a x  + 2a b x
--R   (2)  --------------------------------------------
--R                           4     3
--R                          a x + a b
--R                                                     Type: Expression Integer
--E 
--S 38 of 108
cc:=aa-bb
 

           b
   (3)  - --
           3
          a
                                                     Type: Expression Integer
--R
--R           b
--R   (3)  - --
--R           3
--R          a
--R                                                     Type: Expression Integer
--E 
--S 39 of 108     14:68 Schaums and Axiom differ by a constant
D(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E 
)clear all
 

--S 40 of 108
aa:=integrate(x^3/(a*x+b)^2,x)
 

             2      3                 3 3     2   2       2      3
        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 4a b x + 2b
   (1)  ----------------------------------------------------------
                                  5      4
                                2a x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R             2      3                 3 3     2   2       2      3
--R        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 4a b x + 2b
--R   (1)  ----------------------------------------------------------
--R                                  5      4
--R                                2a x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 41 of 108
bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b)
 

             2      3                 3 3     2   2       2      3
        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 9a b x - 3b
   (2)  ----------------------------------------------------------
                                  5      4
                                2a x + 2a b
                                                     Type: Expression Integer
--R
--R             2      3                 3 3     2   2       2      3
--R        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 9a b x - 3b
--R   (2)  ----------------------------------------------------------
--R                                  5      4
--R                                2a x + 2a b
--R                                                     Type: Expression Integer
--E

--S 42 of 108
cc:=aa-bb
 

          2
        5b
   (3)  ---
          4
        2a
                                                     Type: Expression Integer
--R
--R          2
--R        5b
--R   (3)  ---
--R          4
--R        2a
--R                                                     Type: Expression Integer
--E

--S 43 of 108     14:69 Schaums and Axiom differ by a constant
dd:=D(cc,x)
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 44 of 108
aa:=integrate(1/(x*(a*x+b)^2),x)
 

        (- a x - b)log(a x + b) + (a x + b)log(x) + b
   (1)  ---------------------------------------------
                             2     3
                          a b x + b
                                          Type: Union(Expression Integer,...)
--R
--R        (- a x - b)log(a x + b) + (a x + b)log(x) + b
--R   (1)  ---------------------------------------------
--R                             2     3
--R                          a b x + b
--R                                          Type: Union(Expression Integer,...)
--E
--S 45 of 108
bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b)))
 

                        x
        (a x + b)log(-------) + b
                     a x + b
   (2)  -------------------------
                   2     3
                a b x + b
                                                     Type: Expression Integer
--R
--R                        x
--R        (a x + b)log(-------) + b
--R                     a x + b
--R   (2)  -------------------------
--R                   2     3
--R                a b x + b
--R                                                     Type: Expression Integer
--E

--S 46 of 108
cc:=aa-bb
 

                                         x
        - log(a x + b) + log(x) - log(-------)
                                      a x + b
   (3)  --------------------------------------
                           2
                          b
                                                     Type: Expression Integer
--R
--R                                         x
--R        - log(a x + b) + log(x) - log(-------)
--R                                      a x + b
--R   (3)  --------------------------------------
--R                           2
--R                          b
--R                                                     Type: Expression Integer
--E
--S 47 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E
--S 48 of 108     14:70 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 49 of 108
aa:=integrate(1/(x^2*(a*x+b)^2),x)
 

           2 2                              2 2                             2
        (2a x  + 2a b x)log(a x + b) + (- 2a x  - 2a b x)log(x) - 2a b x - b
   (1)  ---------------------------------------------------------------------
                                        3 2    4
                                     a b x  + b x
                                          Type: Union(Expression Integer,...)
--R
--R           2 2                              2 2                             2
--R        (2a x  + 2a b x)log(a x + b) + (- 2a x  - 2a b x)log(x) - 2a b x - b
--R   (1)  ---------------------------------------------------------------------
--R                                        3 2    4
--R                                     a b x  + b x
--R                                          Type: Union(Expression Integer,...)
--E
--S 50 of 108
bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x)
 

           2 2              a x + b              2
        (2a x  + 2a b x)log(-------) - 2a b x - b
                               x
   (2)  ------------------------------------------
                          3 2    4
                       a b x  + b x
                                                     Type: Expression Integer
--R
--R           2 2              a x + b              2
--R        (2a x  + 2a b x)log(-------) - 2a b x - b
--R                               x
--R   (2)  ------------------------------------------
--R                          3 2    4
--R                       a b x  + b x
--R                                                     Type: Expression Integer
--E

--S 51 of 108
cc:=aa-bb
 

                                             a x + b
        2a log(a x + b) - 2a log(x) - 2a log(-------)
                                                x
   (3)  ---------------------------------------------
                               3
                              b
                                                     Type: Expression Integer
--R
--R                                             a x + b
--R        2a log(a x + b) - 2a log(x) - 2a log(-------)
--R                                                x
--R   (3)  ---------------------------------------------
--R                               3
--R                              b
--R                                                     Type: Expression Integer
--E
--S 52 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E
--S 53 of 108     14:71 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 54 of 108
aa:=integrate(1/(x^3*(a*x+b)^2),x)
 

   (1)
            3 3     2   2                   3 3     2   2            2   2
       (- 6a x  - 6a b x )log(a x + b) + (6a x  + 6a b x )log(x) + 6a b x
     + 
           2     3
       3a b x - b
  /
         4 3     5 2
     2a b x  + 2b x
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R            3 3     2   2                   3 3     2   2            2   2
--R       (- 6a x  - 6a b x )log(a x + b) + (6a x  + 6a b x )log(x) + 6a b x
--R     + 
--R           2     3
--R       3a b x - b
--R  /
--R         4 3     5 2
--R     2a b x  + 2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 55 of 108
bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/b^4)*log((a*x+b)/x)
 

             3 3     2   2     a x + b      3 3     2   2       2     3
        (- 6a x  - 6a b x )log(-------) + 3a x  + 9a b x  + 3a b x - b
                                  x
   (2)  ---------------------------------------------------------------
                                    4 3     5 2
                                2a b x  + 2b x
                                                     Type: Expression Integer
--R
--R             3 3     2   2     a x + b      3 3     2   2       2     3
--R        (- 6a x  - 6a b x )log(-------) + 3a x  + 9a b x  + 3a b x - b
--R                                  x
--R   (2)  ---------------------------------------------------------------
--R                                    4 3     5 2
--R                                2a b x  + 2b x
--R                                                     Type: Expression Integer
--E

--S 56 of 108
cc:=aa-bb
 

            2                 2           2    a x + b      2
        - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a
                                                  x
   (3)  -----------------------------------------------------
                                   4
                                 2b
                                                     Type: Expression Integer
--R
--R            2                 2           2    a x + b      2
--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a
--R                                                  x
--R   (3)  -----------------------------------------------------
--R                                   4
--R                                 2b
--R                                                     Type: Expression Integer
--E

--S 57 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 58 of 108
dd:=divlog cc
 

            2
          3a
   (5)  - ---
            4
          2b
                                                     Type: Expression Integer
--R
--R            2
--R          3a
--R   (5)  - ---
--R            4
--R          2b
--R                                                     Type: Expression Integer
--E

--S 59 of 108     14:72 Schaums and Axiom differ by a constant
ee:=D(dd,x)
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 60 of 108
aa:=integrate(1/(a*x+b)^3,x)
 

                     1
   (1)  - ----------------------
            3 2     2          2
          2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R                     1
--R   (1)  - ----------------------
--R            3 2     2          2
--R          2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 61 of 108
bb:=-1/(2*(a*x+b)^2)
 

                    1
   (2)  - --------------------
            2 2              2
          2a x  + 4a b x + 2b
                                            Type: Fraction Polynomial Integer
--R
--R                    1
--R   (2)  - --------------------
--R            2 2              2
--R          2a x  + 4a b x + 2b
--R                                            Type: Fraction Polynomial Integer
--E

--S 62 of 108
cc:=aa-bb
 

                 a - 1
   (3)  ----------------------
          3 2     2          2
        2a x  + 4a b x + 2a b
                                                     Type: Expression Integer
--R
--R                 a - 1
--R   (3)  ----------------------
--R          3 2     2          2
--R        2a x  + 4a b x + 2a b
--R                                                     Type: Expression Integer
--E

--S 63 of 108
dd:=aa/bb
 

        1
   (4)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (4)  -
--R        a
--R                                                     Type: Expression Integer
--E

--S 64 of 108     14:73 Schaums and Axiom differ by a constant
ee:=D(dd,x)
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 65 of 108
aa:=integrate(x/(a*x+b)^3,x)
 

              - 2a x - b
   (1)  ----------------------
          4 2     3        2 2
        2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R              - 2a x - b
--R   (1)  ----------------------
--R          4 2     3        2 2
--R        2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 66 of 108
bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2)
 

              - 2a x - b
   (2)  ----------------------
          4 2     3        2 2
        2a x  + 4a b x + 2a b
                                            Type: Fraction Polynomial Integer
--R
--R              - 2a x - b
--R   (2)  ----------------------
--R          4 2     3        2 2
--R        2a x  + 4a b x + 2a b
--R                                            Type: Fraction Polynomial Integer
--E

--S 67 of 108     14:74 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 68 of 108
aa:=integrate(x^2/(a*x+b)^3,x)
 

           2 2              2                           2
        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
   (1)  -------------------------------------------------
                        5 2     4        3 2
                      2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R           2 2              2                           2
--R        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
--R   (1)  -------------------------------------------------
--R                        5 2     4        3 2
--R                      2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 69 of 108
bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b)
 

           2 2              2                           2
        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
   (2)  -------------------------------------------------
                        5 2     4        3 2
                      2a x  + 4a b x + 2a b
                                                     Type: Expression Integer
--R
--R           2 2              2                           2
--R        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
--R   (2)  -------------------------------------------------
--R                        5 2     4        3 2
--R                      2a x  + 4a b x + 2a b
--R                                                     Type: Expression Integer
--E

--S 70 of 108     14:75 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
--S 71 of 108
aa:=integrate(x^3/(a*x+b)^3,x)
 

   (1)
        2   2        2      3                  3 3     2   2       2      3
   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
   ------------------------------------------------------------------------
                              6 2     5        4 2
                            2a x  + 4a b x + 2a b
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R        2   2        2      3                  3 3     2   2       2      3
--R   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
--R   ------------------------------------------------------------------------
--R                              6 2     5        4 2
--R                            2a x  + 4a b x + 2a b
--R                                          Type: Union(Expression Integer,...)
--E

--S 72 of 108
bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b)
 

   (2)
        2   2        2      3                  3 3     2   2       2      3
   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
   ------------------------------------------------------------------------
                              6 2     5        4 2
                            2a x  + 4a b x + 2a b
                                                     Type: Expression Integer
--R
--R   (2)
--R        2   2        2      3                  3 3     2   2       2      3
--R   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
--R   ------------------------------------------------------------------------
--R                              6 2     5        4 2
--R                            2a x  + 4a b x + 2a b
--R                                                     Type: Expression Integer
--E

--S 73 of 108     14:76 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 74 of 108
aa:=integrate(1/(x*(a*x+b)^3),x)
 

   (1)
            2 2              2                   2 2              2
       (- 2a x  - 4a b x - 2b )log(a x + b) + (2a x  + 4a b x + 2b )log(x)
     + 
                  2
       2a b x + 3b
  /
       2 3 2       4      5
     2a b x  + 4a b x + 2b
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R            2 2              2                   2 2              2
--R       (- 2a x  - 4a b x - 2b )log(a x + b) + (2a x  + 4a b x + 2b )log(x)
--R     + 
--R                  2
--R       2a b x + 3b
--R  /
--R       2 3 2       4      5
--R     2a b x  + 4a b x + 2b
--R                                          Type: Union(Expression Integer,...)
--E

--S 75 of 108
bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x)
 

             2 2              2     a x + b      2 2
        (- 2a x  - 4a b x - 2b )log(-------) - 3a x  - 4a b x
                                       x
   (2)  -----------------------------------------------------
                          2 3 2       4      5
                        2a b x  + 4a b x + 2b
                                                     Type: Expression Integer
--R
--R             2 2              2     a x + b      2 2
--R        (- 2a x  - 4a b x - 2b )log(-------) - 3a x  - 4a b x
--R                                       x
--R   (2)  -----------------------------------------------------
--R                          2 3 2       4      5
--R                        2a b x  + 4a b x + 2b
--R                                                     Type: Expression Integer
--E

--S 76 of 108
cc:=aa-bb
 

                                         a x + b
        - 2log(a x + b) + 2log(x) + 2log(-------) + 3
                                            x
   (3)  ---------------------------------------------
                               3
                             2b
                                                     Type: Expression Integer
--R
--R                                         a x + b
--R        - 2log(a x + b) + 2log(x) + 2log(-------) + 3
--R                                            x
--R   (3)  ---------------------------------------------
--R                               3
--R                             2b
--R                                                     Type: Expression Integer
--E

--S 77 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 78 of 108
dd:=divlog cc
 

         3
   (5)  ---
          3
        2b
                                                     Type: Expression Integer
--R
--R         3
--R   (5)  ---
--R          3
--R        2b
--R                                                     Type: Expression Integer
--E

--S 79 of 108     14:77 Schaums and Axiom differ by a constant
ee:=D(dd,x)
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 80 of 108
aa:=integrate(1/(x^2*(a*x+b)^3),x)
 

   (1)
          3 3      2   2       2
       (6a x  + 12a b x  + 6a b x)log(a x + b)
     + 
            3 3      2   2       2             2   2       2      3
       (- 6a x  - 12a b x  - 6a b x)log(x) - 6a b x  - 9a b x - 2b
  /
       2 4 3       5 2     6
     2a b x  + 4a b x  + 2b x
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R          3 3      2   2       2
--R       (6a x  + 12a b x  + 6a b x)log(a x + b)
--R     + 
--R            3 3      2   2       2             2   2       2      3
--R       (- 6a x  - 12a b x  - 6a b x)log(x) - 6a b x  - 9a b x - 2b
--R  /
--R       2 4 3       5 2     6
--R     2a b x  + 4a b x  + 2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 81 of 108
bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x)
 

           3 3      2   2       2      a x + b      2   2       2      3
        (6a x  + 12a b x  + 6a b x)log(-------) - 6a b x  - 9a b x - 2b
                                          x
   (2)  ----------------------------------------------------------------
                              2 4 3       5 2     6
                            2a b x  + 4a b x  + 2b x
                                                     Type: Expression Integer
--R
--R           3 3      2   2       2      a x + b      2   2       2      3
--R        (6a x  + 12a b x  + 6a b x)log(-------) - 6a b x  - 9a b x - 2b
--R                                          x
--R   (2)  ----------------------------------------------------------------
--R                              2 4 3       5 2     6
--R                            2a b x  + 4a b x  + 2b x
--R                                                     Type: Expression Integer
--E

--S 82 of 108
cc:=aa-bb
 

                                             a x + b
        3a log(a x + b) - 3a log(x) - 3a log(-------)
                                                x
   (3)  ---------------------------------------------
                               4
                              b
                                                     Type: Expression Integer
--R
--R                                             a x + b
--R        3a log(a x + b) - 3a log(x) - 3a log(-------)
--R                                                x
--R   (3)  ---------------------------------------------
--R                               4
--R                              b
--R                                                     Type: Expression Integer
--E

--S 83 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 84 of 108     14:78 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 85 of 108
aa:=integrate(1/(x^3*(a*x+b)^3),x)
 

   (1)
             4 4      3   3      2 2 2
       (- 12a x  - 24a b x  - 12a b x )log(a x + b)
     + 
           4 4      3   3      2 2 2             3   3      2 2 2       3     4
       (12a x  + 24a b x  + 12a b x )log(x) + 12a b x  + 18a b x  + 4a b x - b
  /
       2 5 4       6 3     7 2
     2a b x  + 4a b x  + 2b x
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R             4 4      3   3      2 2 2
--R       (- 12a x  - 24a b x  - 12a b x )log(a x + b)
--R     + 
--R           4 4      3   3      2 2 2             3   3      2 2 2       3     4
--R       (12a x  + 24a b x  + 12a b x )log(x) + 12a b x  + 18a b x  + 4a b x - b
--R  /
--R       2 5 4       6 3     7 2
--R     2a b x  + 4a b x  + 2b x
--R                                          Type: Union(Expression Integer,...)
--E

--S 86 of 108
bb:=-1/(2*b*x^2*(a*x+b)^2)_
    +(2*a)/(b^2*x*(a*x+b)^2)_
    +(9*a^2)/(b^3*(a*x+b)^2)_
    +(6*a^3*x)/(b^4*(a*x+b)^2)_
    +(-6*a^2)/b^5*log((a*x+b)/x)
 

   (2)
             4 4      3   3      2 2 2     a x + b       3   3      2 2 2
       (- 12a x  - 24a b x  - 12a b x )log(-------) + 12a b x  + 18a b x
                                              x
     + 
           3     4
       4a b x - b
  /
       2 5 4       6 3     7 2
     2a b x  + 4a b x  + 2b x
                                                     Type: Expression Integer
--R
--R   (2)
--R             4 4      3   3      2 2 2     a x + b       3   3      2 2 2
--R       (- 12a x  - 24a b x  - 12a b x )log(-------) + 12a b x  + 18a b x
--R                                              x
--R     + 
--R           3     4
--R       4a b x - b
--R  /
--R       2 5 4       6 3     7 2
--R     2a b x  + 4a b x  + 2b x
--R                                                     Type: Expression Integer
--E

--S 87 of 108
cc:=aa-bb
 

            2                 2           2    a x + b
        - 6a log(a x + b) + 6a log(x) + 6a log(-------)
                                                  x
   (3)  -----------------------------------------------
                                5
                               b
                                                     Type: Expression Integer
--R
--R            2                 2           2    a x + b
--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------)
--R                                                  x
--R   (3)  -----------------------------------------------
--R                                5
--R                               b
--R                                                     Type: Expression Integer
--E

--S 88 of 108
divlog:=rule(log(a/b) == log(a) - log(b))
 

            a
   (4)  log(-) == - log(b) + log(a)
            b
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R            a
--R   (4)  log(-) == - log(b) + log(a)
--R            b
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 89 of 108     14:79 Schaums and Axiom agree
dd:=divlog cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
--S 90 of 108
aa:=integrate((a*x+b)^n,x)
 

                   n log(a x + b)
        (a x + b)%e
   (1)  -------------------------
                 a n + a
                                          Type: Union(Expression Integer,...)
--R
--R                   n log(a x + b)
--R        (a x + b)%e
--R   (1)  -------------------------
--R                 a n + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 91 of 108
bb:=(a*x+b)^(n+1)/((n+1)*a)
 

                 n + 1
        (a x + b)
   (2)  --------------
            a n + a
                                                     Type: Expression Integer
--R
--R                 n + 1
--R        (a x + b)
--R   (2)  --------------
--R            a n + a
--R                                                     Type: Expression Integer
--E

--S 92 of 108
cc:=aa-bb
 

                   n log(a x + b)            n + 1
        (a x + b)%e               - (a x + b)
   (3)  ------------------------------------------
                          a n + a
                                                     Type: Expression Integer
--R
--R                   n log(a x + b)            n + 1
--R        (a x + b)%e               - (a x + b)
--R   (3)  ------------------------------------------
--R                          a n + a
--R                                                     Type: Expression Integer
--E
--S 93 of 108
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 94 of 108
dd:=explog cc
 

                   n + 1                     n
        - (a x + b)      + (a x + b)(a x + b)
   (5)  --------------------------------------
                        a n + a
                                                     Type: Expression Integer
--R
--R                   n + 1                     n
--R        - (a x + b)      + (a x + b)(a x + b)
--R   (5)  --------------------------------------
--R                        a n + a
--R                                                     Type: Expression Integer
--E

--S 95 of 108     14:80 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
--S 96 of 108
aa:=integrate(x*(a*x+b)^n,x)
 

           2     2  2              2   n log(a x + b)
        ((a n + a )x  + a b n x - b )%e
   (1)  ---------------------------------------------
                       2 2     2      2
                      a n  + 3a n + 2a
                                          Type: Union(Expression Integer,...)
--R
--R           2     2  2              2   n log(a x + b)
--R        ((a n + a )x  + a b n x - b )%e
--R   (1)  ---------------------------------------------
--R                       2 2     2      2
--R                      a n  + 3a n + 2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 97 of 108
bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2)
 

                        n + 2                        n + 1
        (n + 1)(a x + b)      + (- b n - 2b)(a x + b)
   (2)  --------------------------------------------------
                          2 2     2      2
                         a n  + 3a n + 2a
                                                     Type: Expression Integer
--R
--R                        n + 2                        n + 1
--R        (n + 1)(a x + b)      + (- b n - 2b)(a x + b)
--R   (2)  --------------------------------------------------
--R                          2 2     2      2
--R                         a n  + 3a n + 2a
--R                                                     Type: Expression Integer
--E

--S 98 of 108
cc:=aa-bb
 

   (3)
          2     2  2              2   n log(a x + b)                     n + 2
       ((a n + a )x  + a b n x - b )%e               + (- n - 1)(a x + b)
     + 
                          n + 1
       (b n + 2b)(a x + b)
  /
      2 2     2      2
     a n  + 3a n + 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R          2     2  2              2   n log(a x + b)                     n + 2
--R       ((a n + a )x  + a b n x - b )%e               + (- n - 1)(a x + b)
--R     + 
--R                          n + 1
--R       (b n + 2b)(a x + b)
--R  /
--R      2 2     2      2
--R     a n  + 3a n + 2a
--R                                                     Type: Expression Integer
--E

--S 99 of 108
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 100 of 108
dd:=explog cc
 

   (5)
                         n + 2                      n + 1
       (- n - 1)(a x + b)      + (b n + 2b)(a x + b)
     + 
          2     2  2              2          n
       ((a n + a )x  + a b n x - b )(a x + b)
  /
      2 2     2      2
     a n  + 3a n + 2a
                                                     Type: Expression Integer
--R
--R   (5)
--R                         n + 2                      n + 1
--R       (- n - 1)(a x + b)      + (b n + 2b)(a x + b)
--R     + 
--R          2     2  2              2          n
--R       ((a n + a )x  + a b n x - b )(a x + b)
--R  /
--R      2 2     2      2
--R     a n  + 3a n + 2a
--R                                                     Type: Expression Integer
--E

--S 101 of 108
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 
--S 102 of 108
aa:=integrate(x^2*(a*x+b)^n,x)
 

   (1)
      3 2     3      3  3     2   2    2     2       2        3   n log(a x + b)
   ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )%e
   -----------------------------------------------------------------------------
                              3 3     3 2      3      3
                             a n  + 6a n  + 11a n + 6a
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R      3 2     3      3  3     2   2    2     2       2        3   n log(a x + b)
--R   ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )%e
--R   -----------------------------------------------------------------------------
--R                              3 3     3 2      3      3
--R                             a n  + 6a n  + 11a n + 6a
--R                                          Type: Union(Expression Integer,...)
--E

--S 103 of 108
bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3)
 

   (2)
         2                   n + 3          2                      n + 2
       (n  + 3n + 2)(a x + b)      + (- 2b n  - 8b n - 6b)(a x + b)
     + 
         2 2     2      2          n + 1
       (b n  + 5b n + 6b )(a x + b)
  /
      3 3     3 2      3      3
     a n  + 6a n  + 11a n + 6a
                                                     Type: Expression Integer
--R
--R   (2)
--R         2                   n + 3          2                      n + 2
--R       (n  + 3n + 2)(a x + b)      + (- 2b n  - 8b n - 6b)(a x + b)
--R     + 
--R         2 2     2      2          n + 1
--R       (b n  + 5b n + 6b )(a x + b)
--R  /
--R      3 3     3 2      3      3
--R     a n  + 6a n  + 11a n + 6a
--R                                                     Type: Expression Integer
--E

--S 104 of 108
cc:=aa-bb
 

   (3)
            3 2     3      3  3     2   2    2     2       2        3
         ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )
      *
           n log(a x + b)
         %e
     + 
           2                   n + 3        2                      n + 2
       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
     + 
           2 2     2      2          n + 1
       (- b n  - 5b n - 6b )(a x + b)
  /
      3 3     3 2      3      3
     a n  + 6a n  + 11a n + 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R            3 2     3      3  3     2   2    2     2       2        3
--R         ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )
--R      *
--R           n log(a x + b)
--R         %e
--R     + 
--R           2                   n + 3        2                      n + 2
--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
--R     + 
--R           2 2     2      2          n + 1
--R       (- b n  - 5b n - 6b )(a x + b)
--R  /
--R      3 3     3 2      3      3
--R     a n  + 6a n  + 11a n + 6a
--R                                                     Type: Expression Integer
--E

--S 105 of 108
explog:=rule(%e^(n*log(x)) == x^n)
 

          n log(x)     n
   (4)  %e         == x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R          n log(x)     n
--R   (4)  %e         == x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 106 of 108
dd:=explog cc
 

   (5)
           2                   n + 3        2                      n + 2
       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
     + 
           2 2     2      2          n + 1
       (- b n  - 5b n - 6b )(a x + b)
     + 
          3 2     3      3  3     2   2    2     2       2        3          n
       ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )(a x + b)
  /
      3 3     3 2      3      3
     a n  + 6a n  + 11a n + 6a
                                                     Type: Expression Integer
--R
--R   (5)
--R           2                   n + 3        2                      n + 2
--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
--R     + 
--R           2 2     2      2          n + 1
--R       (- b n  - 5b n - 6b )(a x + b)
--R     + 
--R          3 2     3      3  3     2   2    2     2       2        3          n
--R       ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )(a x + b)
--R  /
--R      3 3     3 2      3      3
--R     a n  + 6a n  + 11a n + 6a
--R                                                     Type: Expression Integer
--E

--S 107 of 108    14:82 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
--S 108 of 108    14:83 Axiom cannot do this integration
aa:=integrate(x^m*(a*x+b)^n,x)
 

           x
         ++    m          n
   (7)   |   %M (b + %M a) d%M
        ++
                                          Type: Union(Expression Integer,...)
--R
--R           x
--R         ++    m          n
--I   (1)   |   %U (b + %U a) d%U
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E

)spool
 
Starts dribbling to OneDimensionalArray.output (2010/3/27, 18:46:9).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 9
oneDimensionalArray [i**2 for i in 1..10]
 

   (1)  [1,4,9,16,25,36,49,64,81,100]
                                    Type: OneDimensionalArray PositiveInteger
--R 
--R
--R   (1)  [1,4,9,16,25,36,49,64,81,100]
--R                                    Type: OneDimensionalArray PositiveInteger
--E 1

--S 2 of 9
a : ARRAY1 INT := new(10,0)
 

   (2)  [0,0,0,0,0,0,0,0,0,0]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (2)  [0,0,0,0,0,0,0,0,0,0]
--R                                            Type: OneDimensionalArray Integer
--E 2

--S 3 of 9
for i in 1..10 repeat a.i := i; a
 

   (3)  [1,2,3,4,5,6,7,8,9,10]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (3)  [1,2,3,4,5,6,7,8,9,10]
--R                                            Type: OneDimensionalArray Integer
--E 3

--S 4 of 9
map!(i +-> i ** 2,a); a
 

   (4)  [1,4,9,16,25,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (4)  [1,4,9,16,25,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 4

--S 5 of 9
reverse! a
 

   (5)  [100,81,64,49,36,25,16,9,4,1]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (5)  [100,81,64,49,36,25,16,9,4,1]
--R                                            Type: OneDimensionalArray Integer
--E 5

--S 6 of 9
swap!(a,4,5); a
 

   (6)  [100,81,64,36,49,25,16,9,4,1]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (6)  [100,81,64,36,49,25,16,9,4,1]
--R                                            Type: OneDimensionalArray Integer
--E 6

--S 7 of 9
sort! a 
 

   (7)  [1,4,9,16,25,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (7)  [1,4,9,16,25,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 7

--S 8 of 9
b := a(6..10)
 

   (8)  [36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (8)  [36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 8

--S 9 of 9
copyInto!(a,b,1)
 

   (9)  [36,49,64,81,100,36,49,64,81,100]
                                            Type: OneDimensionalArray Integer
--R 
--R
--R   (9)  [36,49,64,81,100,36,49,64,81,100]
--R                                            Type: OneDimensionalArray Integer
--E 9
)spool
 
Starts dribbling to contfrac.output (2010/3/27, 18:24:37).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 40
r1 := 3/4
 

        3
   (1)  -
        4
                                                       Type: Fraction Integer
--R 
--R
--R        3
--R   (1)  -
--R        4
--R                                                       Type: Fraction Integer
--E 1

--S 2 of 40
r2 := 314159/100000
 

        314159
   (2)  ------
        100000
                                                       Type: Fraction Integer
--R 
--R
--R        314159
--R   (2)  ------
--R        100000
--R                                                       Type: Fraction Integer
--E 2

--S 3 of 40
c1 := r1 :: ContinuedFraction Integer
 

          1 |     1 |
   (3)  +---+ + +---+
        | 1     | 3
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |
--R   (3)  +---+ + +---+
--R        | 1     | 3
--R                                              Type: ContinuedFraction Integer
--E 3

--S 4 of 40
c2 := r2 :: ContinuedFraction Integer
 

              1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (4)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
            | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (4)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R            | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 4

-- We can view these in the list notation
--S 5 of 40
partialQuotients c1
 

   (5)  [0,1,3]
                                                         Type: Stream Integer
--R 
--R
--R   (5)  [0,1,3]
--R                                                         Type: Stream Integer
--E 5

--S 6 of 40
partialQuotients c2
 

   (6)  [3,7,15,1,25,1,7,4]
                                                         Type: Stream Integer
--R 
--R
--R   (6)  [3,7,15,1,25,1,7,4]
--R                                                         Type: Stream Integer
--E 6
 
-- These are algebraic objects, so we can manipulate them accordingly
--S 7 of 40
c1 + c2
 

   (7)
         1 |     1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |
   3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+
       | 1     | 8     | 4     | 2     | 5     | 1     | 2     | 32     | 2
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (7)
--R         1 |     1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |
--R   3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+
--R       | 1     | 8     | 4     | 2     | 5     | 1     | 2     | 32     | 2
--R                                              Type: ContinuedFraction Integer
--E 7

--S 8 of 40
c1 * c2
 

   (8)
           1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |     1 |
     2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+ + +---+
         | 2     | 1     | 4     | 5     | 6     | 2     | 13     | 1     | 1
   + 
       1 |
     +---+ + ...
     | 1
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (8)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1  |     1 |     1 |
--R     2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +----+ + +---+ + +---+
--R         | 2     | 1     | 4     | 5     | 6     | 2     | 13     | 1     | 1
--R   + 
--R       1 |
--R     +---+ + ...
--R     | 1
--R                                              Type: ContinuedFraction Integer
--E 8

--S 9 of 40
1 / c2
 

          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
   (9)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1 |     1  |     1 |     1 |     1 |
--R   (9)  +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
--R        | 3     | 7     | 15     | 1     | 25     | 1     | 7     | 4
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 40
c1 - c2
 

   (10)
           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
   - 3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
         | 1     | 1     | 1     | 1     | 4     | 6     | 2     | 2     | 131
                                              Type: ContinuedFraction Integer
--R 
--R
--R   (10)
--R           1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
--R   - 3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
--R         | 1     | 1     | 1     | 1     | 4     | 6     | 2     | 2     | 131
--R                                              Type: ContinuedFraction Integer
--E 10

--S 11 of 40
c2 - c1
 

               1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
   (11)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
             | 2     | 1     | 1     | 4     | 6     | 2     | 2     | 131
                                              Type: ContinuedFraction Integer
--R 
--R
--R               1 |     1 |     1 |     1 |     1 |     1 |     1 |      1  |
--R   (11)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-----+
--R             | 2     | 1     | 1     | 4     | 6     | 2     | 2     | 131
--R                                              Type: ContinuedFraction Integer
--E 11
 
-- and can convert them back to rational numbers.

--S 12 of 40
convergents %
 

            5 7 12 55 342 739 1820 239159
   (12)  [2,-,-,--,--,---,---,----,------]
            2 3  5 23 143 309  761 100000
                                                Type: Stream Fraction Integer
--R 
--R
--R            5 7 12 55 342 739 1820 239159
--R   (12)  [2,-,-,--,--,---,---,----,------]
--R            2 3  5 23 143 309  761 100000
--R                                                Type: Stream Fraction Integer
--E 12 
 
)clear all
 

-- Continued fractions over other Euclidean domains
--S 13 of 40
a0 := ((-122 + 597* %i)/(4 - 4*%i))
 

          719   475
   (1)  - --- + --- %i
           8     8
                                               Type: Complex Fraction Integer
--R 
--R
--R          719   475
--R   (1)  - --- + --- %i
--R           8     8
--R                                               Type: Complex Fraction Integer
--E 13

--S 14 of 40
b0 := ((-595 - %i)/(3 - 4*%i))
 

          1781   2383
   (2)  - ---- - ---- %i
           25     25
                                               Type: Complex Fraction Integer
--R 
--R
--R          1781   2383
--R   (2)  - ---- - ---- %i
--R           25     25
--R                                               Type: Complex Fraction Integer
--E 14

--S 15 of 40
a  := continuedFraction(a0)
 

                           1    |         1     |
   (3)  - 90 + 59%i + +---------+ + +-----------+
                      | 1 - 2%i     | - 1 + 2%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                           1    |         1     |
--R   (3)  - 90 + 59%i + +---------+ + +-----------+
--R                      | 1 - 2%i     | - 1 + 2%i
--R                                      Type: ContinuedFraction Complex Integer
--E 15

--S 16 of 40
b  := continuedFraction(b0)
 

                            1     |      1  |
   (4)  - 71 - 95%i + +-----------+ + +-----+
                      | - 1 + 2%i     | - 2
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                            1     |      1  |
--R   (4)  - 71 - 95%i + +-----------+ + +-----+
--R                      | - 1 + 2%i     | - 2
--R                                      Type: ContinuedFraction Complex Integer
--E 16

--S 17 of 40
a + b
 

                             1     |      1  |        1     |
   (5)  - 161 - 36%i + +-----------+ + +-----+ + +----------+
                       | - 7 - 3%i     | 2%i     | - 1 - %i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R                             1     |      1  |        1     |
--R   (5)  - 161 - 36%i + +-----------+ + +-----+ + +----------+
--R                       | - 7 - 3%i     | 2%i     | - 1 - %i
--R                                      Type: ContinuedFraction Complex Integer
--E 17

--S 18 of 40
convergents % 
 

                      - 1020 - 735%i - 2004 - 1631%i 362 - 4655%i
   (6)  [- 161 - 36%i,--------------,---------------,------------]
                          7 + 3%i        14 + 7%i      4 + 28%i
                                        Type: Stream Fraction Complex Integer
--R 
--R
--R                      - 1020 - 735%i - 2004 - 1631%i 362 - 4655%i
--R   (6)  [- 161 - 36%i,--------------,---------------,------------]
--R                          7 + 3%i        14 + 7%i      4 + 28%i
--R                                        Type: Stream Fraction Complex Integer
--E 18

--S 19 of 40
last % - (a0 + b0)
 

   (7)  0
                                               Type: Complex Fraction Integer
--R 
--R
--R   (7)  0
--R                                               Type: Complex Fraction Integer
--E 19

--S 20 of 40
a / b
 

   (8)
                 1    |     1 |        1     |        1     |      1  |
     - %i + +---------+ + +---+ + +----------+ + +----------+ + +-----+
            | 4 - 8%i     | 3     | - 4 - %i     | - 2 - %i     | 3%i
   + 
          1    |
     +---------+
     | 2 + 4%i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (8)
--R                 1    |     1 |        1     |        1     |      1  |
--R     - %i + +---------+ + +---+ + +----------+ + +----------+ + +-----+
--R            | 4 - 8%i     | 3     | - 4 - %i     | - 2 - %i     | 3%i
--R   + 
--R          1    |
--R     +---------+
--R     | 2 + 4%i
--R                                      Type: ContinuedFraction Complex Integer
--E 20

--S 21 of 40
convergents %
 

   (9)
         4 - 7%i 13 - 21%i 69 - 64%i  215 - 80%i 709 - 171%i 2279 - 2022%i
   [- %i,-------,---------,---------,-----------,-----------,-------------]
         8 + 4%i 24 + 13%i 75 + 72%i 102 + 232%i 234 + 771%i 2376 + 2384%i
                                        Type: Stream Fraction Complex Integer
--R 
--R
--R   (9)
--R         4 - 7%i 13 - 21%i 69 - 64%i  215 - 80%i 709 - 171%i 2279 - 2022%i
--R   [- %i,-------,---------,---------,-----------,-----------,-------------]
--R         8 + 4%i 24 + 13%i 75 + 72%i 102 + 232%i 234 + 771%i 2376 + 2384%i
--R                                        Type: Stream Fraction Complex Integer
--E 21

--S 22 of 40
last % - (a0/b0)
 

   (10)  0
                                               Type: Complex Fraction Integer
--R 
--R
--R   (10)  0
--R                                               Type: Complex Fraction Integer
--E 22

--S 23 of 40
(a = b)::Boolean
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 32

--S 24 of 40
c := continuedFraction(3 + 4*%i, repeating [1 + %i], repeating [5 - %i])
 

   (12)
                 1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
     3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
               | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
   + 
       1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
     +--------+ + +--------+ + +--------+ + +--------+ + +--------+ + ...
     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (12)
--R                 1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
--R     3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
--R               | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
--R   + 
--R       1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
--R     +--------+ + +--------+ + +--------+ + +--------+ + +--------+ + ...
--R     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i     | 5 - %i
--R                                      Type: ContinuedFraction Complex Integer
--E 24

--S 25 of 40
a/c
 

   (13)
                        1     |          1      |        1     |         1     |
     - 1 + 20%i + +-----------+ + +-------------+ + +----------+ + +-----------+
                  | - 1 - 2%i     | - 11 - 16%i     | - 1 + %i     | - 9 - 2%i
   + 
          1    |      1  |        1    |      1  |         1     |        1    |
     +---------+ + +-----+ + +---------+ + +-----+ + +-----------+ + +---------+
     | 1 + 2%i     | 2%i     | 8 - 2%i     | - 2     | - 1 + 8%i     | 3 - 3%i
   + 
     ...
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (13)
--R                        1     |          1      |        1     |         1     |
--R     - 1 + 20%i + +-----------+ + +-------------+ + +----------+ + +-----------+
--R                  | - 1 - 2%i     | - 11 - 16%i     | - 1 + %i     | - 9 - 2%i
--R   + 
--R          1    |      1  |        1    |      1  |         1     |        1    |
--R     +---------+ + +-----+ + +---------+ + +-----+ + +-----------+ + +---------+
--R     | 1 + 2%i     | 2%i     | 8 - 2%i     | - 2     | - 1 + 8%i     | 3 - 3%i
--R   + 
--R     ...
--R                                      Type: ContinuedFraction Complex Integer
--E 25

-- (a = c)::Boolean -- should give error

--S 26 of 40
d := complete continuedFraction(3+4*%i, repeating [1+%i],[i-%i for i in 1..5])
 

   (14)
               1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
   3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
             | 1 - %i     | 2 - %i     | 3 - %i     | 4 - %i     | 5 - %i
                                      Type: ContinuedFraction Complex Integer
--R 
--R
--R   (14)
--R               1 + %i |     1 + %i |     1 + %i |     1 + %i |     1 + %i |
--R   3 + 4%i + +--------+ + +--------+ + +--------+ + +--------+ + +--------+
--R             | 1 - %i     | 2 - %i     | 3 - %i     | 4 - %i     | 5 - %i
--R                                      Type: ContinuedFraction Complex Integer
--E 26

--S 27 of 40
(a = d)::Boolean
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 27

--S 28 of 40
q : Fraction UnivariatePolynomial('x, Fraction Integer) 
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 28

--S 29 of 40
q := (2*x**2 - x + 1) / (3*x**3 - x + 8)
 

         2  2   1     1
         - x  - - x + -
         3      3     3
   (17)  --------------
           3   1     8
          x  - - x + -
               3     3
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R         2  2   1     1
--R         - x  - - x + -
--R         3      3     3
--R   (17)  --------------
--R           3   1     8
--R          x  - - x + -
--R               3     3
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 29

--S 30  of 40
c := continuedFraction q
 

              1    |          1      |            1        |
   (18)  +---------+ + +-------------+ + +-----------------+
         | 3     3     |   8     204     |    343     1421
         | - x + -     | - - x - ---     | - ---- x + ----
         | 2     4     |   7      49     |   6112     6112
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R              1    |          1      |            1        |
--R   (18)  +---------+ + +-------------+ + +-----------------+
--R         | 3     3     |   8     204     |    343     1421
--R         | - x + -     | - - x - ---     | - ---- x + ----
--R         | 2     4     |   7      49     |   6112     6112
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 30

--S 31 of 40
d := continuedFraction differentiate q
 

   (19)
              1         |          1       |               1            |
     +------------------+ + +--------------+ + +------------------------+
     |   3  2   3     9     |    1      47     |   69696     6381055032
     | - - x  - - x + -     | - -- x + ---     | - ----- x - ----------
     |   2      2     4     |   11     264     |   32963     1086559369
   + 
                            1                      |
     +---------------------------------------------+
     |    35816256480347      79911907817759707445
     | - --------------- x + ---------------------
     |   218199728406528     307361810626373910528
   + 
                                   1                              |
     +------------------------------------------------------------+
     |   39359803441398779644674048     9259889268740766802477056
     | - -------------------------- x + -------------------------
     |    1979914602262093317951025     1979914602262093317951025
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (19)
--R              1         |          1       |               1            |
--R     +------------------+ + +--------------+ + +------------------------+
--R     |   3  2   3     9     |    1      47     |   69696     6381055032
--R     | - - x  - - x + -     | - -- x + ---     | - ----- x - ----------
--R     |   2      2     4     |   11     264     |   32963     1086559369
--R   + 
--R                            1                      |
--R     +---------------------------------------------+
--R     |    35816256480347      79911907817759707445
--R     | - --------------- x + ---------------------
--R     |   218199728406528     307361810626373910528
--R   + 
--R                                   1                              |
--R     +------------------------------------------------------------+
--R     |   39359803441398779644674048     9259889268740766802477056
--R     | - -------------------------- x + -------------------------
--R     |    1979914602262093317951025     1979914602262093317951025
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 31

--S 32 of 40
c/d
 

   (20)
           1         1     |              1          |
     - x - - + +-----------+ + +---------------------+
           2   | 6     219     |  686       83926465
               | - x + ---     | ----- x - ---------
               | 7      49     | 20131     405257161
   + 
                        1                  |
     +-------------------------------------+
     |   8158231908091     299222030081511
     | - ------------- x - ---------------
     |    268162004432     350018456284868
   + 
                              1                        |
     +-------------------------------------------------+
     |    7309785441053183312      1206863637270224864
     | - -------------------- x + --------------------
     |   30383172810229285385     30383172810229285385
             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (20)
--R           1         1     |              1          |
--R     - x - - + +-----------+ + +---------------------+
--R           2   | 6     219     |  686       83926465
--R               | - x + ---     | ----- x - ---------
--R               | 7      49     | 20131     405257161
--R   + 
--R                        1                  |
--R     +-------------------------------------+
--R     |   8158231908091     299222030081511
--R     | - ------------- x - ---------------
--R     |    268162004432     350018456284868
--R   + 
--R                              1                        |
--R     +-------------------------------------------------+
--R     |    7309785441053183312      1206863637270224864
--R     | - -------------------- x + --------------------
--R     |   30383172810229285385     30383172810229285385
--R             Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
--E 32

--S 33 of 40
convergents %
 

   (21)
                2   40     121     3   14615  2   114691     168376
             - x  - -- x - ---  - x  + ----- x  - ------ x - ------
          1          7      84         40262      120786      20131
   [- x - -, -----------------, -----------------------------------,
          2            73               2   17373     307727
                   x + --              x  - ----- x + ------
                       14                   20131     120786
       4    3497  3    791   2   15030     18082
    - x  + ----- x  + ----- x  - ----- x + -----
           10442      31326       5221     15663
    --------------------------------------------,
            3   4359  2   48833     25886
           x  - ---- x  + ----- x - -----
                5221      31326      5221
       5   1  4   1  3   17  2   3     4
    - x  + - x  - - x  - -- x  + - x - -
           2      6       6      2     3
    ------------------------------------]
          4    3   11  2   16     7
         x  - x  + -- x  - -- x + -
                    6       3     6
               Type: Stream Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (21)
--R                2   40     121     3   14615  2   114691     168376
--R             - x  - -- x - ---  - x  + ----- x  - ------ x - ------
--R          1          7      84         40262      120786      20131
--R   [- x - -, -----------------, -----------------------------------,
--R          2            73               2   17373     307727
--R                   x + --              x  - ----- x + ------
--R                       14                   20131     120786
--R       4    3497  3    791   2   15030     18082
--R    - x  + ----- x  + ----- x  - ----- x + -----
--R           10442      31326       5221     15663
--R    --------------------------------------------,
--R            3   4359  2   48833     25886
--R           x  - ---- x  + ----- x - -----
--R                5221      31326      5221
--R       5   1  4   1  3   17  2   3     4
--R    - x  + - x  - - x  - -- x  + - x - -
--R           2      6       6      2     3
--R    ------------------------------------]
--R          4    3   11  2   16     7
--R         x  - x  + -- x  - -- x + -
--R                    6       3     6
--R               Type: Stream Fraction UnivariatePolynomial(x,Fraction Integer)
--E 33

--S 34 of 40
q/differentiate q
 

            5   1  4   1  3   17  2   3     4
         - x  + - x  - - x  - -- x  + - x - -
                2      6       6      2     3
   (22)  ------------------------------------
               4    3   11  2   16     7
              x  - x  + -- x  - -- x + -
                         6       3     6
                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R            5   1  4   1  3   17  2   3     4
--R         - x  + - x  - - x  - -- x  + - x - -
--R                2      6       6      2     3
--R   (22)  ------------------------------------
--R               4    3   11  2   16     7
--R              x  - x  + -- x  - -- x + -
--R                         6       3     6
--R                      Type: Fraction UnivariatePolynomial(x,Fraction Integer)
--E 34

)clear all
 

)set streams calculate 7
 

--S 35 of 40
s := continuedFraction(0, expand [1..], expand [1..])
 

          1 |     2 |     3 |     4 |     5 |     6 |     7 |
   (1)  +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
        | 1     | 2     | 3     | 4     | 5     | 6     | 7
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     2 |     3 |     4 |     5 |     6 |     7 |
--R   (1)  +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
--R        | 1     | 2     | 3     | 4     | 5     | 6     | 7
--R                                              Type: ContinuedFraction Integer
--E 35

--S 36 of 40
t := reducedContinuedFraction(0, [4*i-2 for i in 1..])
 

          1 |     1 |     1  |     1  |     1  |     1  |     1  |
   (2)  +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + ...
        | 2     | 6     | 10     | 14     | 18     | 22     | 26
                                              Type: ContinuedFraction Integer
--R 
--R
--R          1 |     1 |     1  |     1  |     1  |     1  |     1  |
--R   (2)  +---+ + +---+ + +----+ + +----+ + +----+ + +----+ + +----+ + ...
--R        | 2     | 6     | 10     | 14     | 18     | 22     | 26
--R                                              Type: ContinuedFraction Integer
--E 36

--S 37 of 40
e := 1/(s*t) - 1
 

              1 |     1 |     1 |     1 |     1 |     1 |     1 |
   (3)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
            | 1     | 2     | 1     | 1     | 4     | 1     | 1
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1 |     1 |     1 |     1 |     1 |     1 |
--R   (3)  2 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + ...
--R            | 1     | 2     | 1     | 1     | 4     | 1     | 1
--R                                              Type: ContinuedFraction Integer
--E 37

--S 38 of 40
c := convergents e
 

             8 11 19 87 106
   (4)  [2,3,-,--,--,--,---,...]
             3  4  7 32  39
                                                Type: Stream Fraction Integer
--R 
--R
--R             8 11 19 87 106
--R   (4)  [2,3,-,--,--,--,---,...]
--R             3  4  7 32  39
--R                                                Type: Stream Fraction Integer
--E 38

--S 39 of 40
for i in 1..15 repeat
  output numeric c.i
 
   2.0
   3.0
   2.6666666666 666666667
   2.75
   2.7142857142 857142857
   2.71875
   2.7179487179 487179487
   2.7183098591 549295775
   2.7182795698 924731183
   2.7182835820 895522388
   2.7182817182 817182817
   2.7182818352 059925094
   2.7182818229 439497119
   2.7182818287 356957267
   2.7182818284 45401318
                                                                   Type: Void
--R 
--R   2.0
--R   3.0
--R   2.6666666666 666666667
--R   2.75
--R   2.7142857142 857142857
--R   2.71875
--R   2.7179487179 487179487
--R   2.7183098591 549295775
--R   2.7182795698 924731183
--R   2.7182835820 895522388
--R   2.7182817182 817182817
--R   2.7182818352 059925094
--R   2.7182818229 439497119
--R   2.7182818287 356957267
--R   2.7182818284 45401318
--R                                                                   Type: Void
--E 39

--S 40 of 40
(s = t)::Boolean
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 40
)spool
 
Starts dribbling to infprod.output (2010/3/27, 18:26:56).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 11
f : UTS(INT,x,0) := 1 - x
 

   (1)  1 - x
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (1)  1 - x
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 1

--S 2 of 11
g : UTS(INT,x,0) := recip f
 

                 2    3    4    5    6    7    8    9    10      11
   (2)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R                 2    3    4    5    6    7    8    9    10      11
--R   (2)  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 2

--S 3 of 11
infiniteProduct g
 

   (3)
             2     3     4     5      6      7      8      9      10      11
   1 + x + 2x  + 3x  + 5x  + 7x  + 11x  + 15x  + 22x  + 30x  + 42x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (3)
--R             2     3     4     5      6      7      8      9      10      11
--R   1 + x + 2x  + 3x  + 5x  + 7x  + 11x  + 15x  + 22x  + 30x  + 42x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 3

--S 4 of 11
h := infiniteProduct(f ** 24)
 

   (4)
                   2        3        4        5         6         7          8
     1 - 24x + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
   + 
              9          10      11
     - 115920x  + 534612x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (4)
--R                   2        3        4        5         6         7          8
--R     1 - 24x + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
--R   + 
--R              9          10      11
--R     - 115920x  + 534612x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 4

--S 5 of 11
delta := x * h
 

   (5)
            2       3        4        5        6         7         8          9
     x - 24x  + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
   + 
              10      11
     - 115920x   + O(x  )
                                    Type: UnivariateTaylorSeries(Integer,x,0)
--R 
--R
--R   (5)
--R            2       3        4        5        6         7         8          9
--R     x - 24x  + 252x  - 1472x  + 4830x  - 6048x  - 16744x  + 84480x  - 113643x
--R   + 
--R              10      11
--R     - 115920x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Integer,x,0)
--E 5

--S 6 of 11
coefficient(delta,21)
 

   (6)  - 4219488
                                                                Type: Integer
--R 
--R
--R   (6)  - 4219488
--R                                                                Type: Integer
--E 6

--S 7 of 11
coefficient(delta,3) * coefficient(delta,7)
 

   (7)  - 4219488
                                                                Type: Integer
--R 
--R
--R   (7)  - 4219488
--R                                                                Type: Integer
--E 7

--S 8 of 11
coefficient(delta,20)
 

   (8)  - 7109760
                                                                Type: Integer
--R 
--R
--R   (8)  - 7109760
--R                                                                Type: Integer
--E 8

--S 9 of 11
coefficient(delta,4) * coefficient(delta,5)
 

   (9)  - 7109760
                                                                Type: Integer
--R 
--R
--R   (9)  - 7109760
--R                                                                Type: Integer
--E 9

--S 10 of 11
coefficient(delta,65)
 

   (10)  - 2790474540
                                                                Type: Integer
--R 
--R
--R   (10)  - 2790474540
--R                                                                Type: Integer
--E 10

--S 11 of 11
coefficient(delta,13) * coefficient(delta,5)
 

   (11)  - 2790474540
                                                                Type: Integer
--R 
--R
--R   (11)  - 2790474540
--R                                                                Type: Integer
--E 11
)spool 
 
Starts dribbling to card.output (2010/3/27, 18:24:24).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 20
c0 := 0 :: CardinalNumber
 

   (1)  0
                                                         Type: CardinalNumber
--R 
--R
--R   (1)  0
--R                                                         Type: CardinalNumber
--E 1

--S 2 of 20
c1 := 1 :: CardinalNumber
 

   (2)  1
                                                         Type: CardinalNumber
--R 
--R
--R   (2)  1
--R                                                         Type: CardinalNumber
--E 2

--S 3 of 20
c2 := 2 :: CardinalNumber
 

   (3)  2
                                                         Type: CardinalNumber
--R 
--R
--R   (3)  2
--R                                                         Type: CardinalNumber
--E 3

--S 4 of 20
c3 := 3 :: CardinalNumber
 

   (4)  3
                                                         Type: CardinalNumber
--R 
--R
--R   (4)  3
--R                                                         Type: CardinalNumber
--E 4

--S 5 of 20
A0 := Aleph 0
 

   (5)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (5)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 5

--S 6 of 20
A1 := Aleph 1
 

   (6)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (6)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 6

--S 7 of 20
finite? c2
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 20
finite? A0
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 20
countable? c2
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 20
countable? A0
 

   (10)  true
                                                                Type: Boolean
--R 
--R
--R   (10)  true
--R                                                                Type: Boolean
--E 10

--S 11 of 20
countable? A1
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 20
[c2 + c2, c2 + A1]
 

   (12)  [4,Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (12)  [4,Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 12

--S 13 of 20
[c0*c2, c1*c2, c2*c2, c0*A1, c1*A1, c2*A1, A0*A1]
 

   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (13)  [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 13

--S 14 of 20
[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]
 

   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (14)  [1,2,4,1,Aleph(1),Aleph(1)]
--R                                                    Type: List CardinalNumber
--E 14

--S 15 of 20
[c2-c1, c2-c2, c2-c3, A1-c2, A1-A0, A1-A1]
 

   (15)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
                                    Type: List Union(CardinalNumber,"failed")
--R 
--R
--R   (15)  [1,0,"failed",Aleph(1),Aleph(1),"failed"]
--R                                    Type: List Union(CardinalNumber,"failed")
--E 15

--S 16 of 20
generalizedContinuumHypothesisAssumed true
 

   (16)  true
                                                                Type: Boolean
--R 
--R
--R   (16)  true
--R                                                                Type: Boolean
--E 16

--S 17 of 20
[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1]
 

   (17)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
                                                    Type: List CardinalNumber
--R 
--R
--R   (17)  [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)]
--R                                                    Type: List CardinalNumber
--E 17

--S 18 of 20
a := Aleph 0
 

   (18)  Aleph(0)
                                                         Type: CardinalNumber
--R 
--R
--R   (18)  Aleph(0)
--R                                                         Type: CardinalNumber
--E 18

--S 19 of 20
c := 2**a
 

   (19)  Aleph(1)
                                                         Type: CardinalNumber
--R 
--R
--R   (19)  Aleph(1)
--R                                                         Type: CardinalNumber
--E 19

--S 20 of 20
f := 2**c
 

   (20)  Aleph(2)
                                                         Type: CardinalNumber
--R 
--R
--R   (20)  Aleph(2)
--R                                                         Type: CardinalNumber
--E 20
)spool
 
Starts dribbling to ffx72.output (2010/3/27, 18:25:56).
)set message test on
 
)set message auto off
 
)clear all
 
 

--S 1 of 13
gf72 := FF(7, 2)
 

   (1)  FiniteField(7,2)
                                                                 Type: Domain
--R 
--R
--R   (1)  FiniteField(7,2)
--R                                                                 Type: Domain
--E 1

--S 2 of 13
u: UP(x,PF 7) := x**2 + 1
 

         2
   (2)  x  + 1
                                   Type: UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R         2
--R   (2)  x  + 1
--R                                   Type: UnivariatePolynomial(x,PrimeField 7)
--E 2

--S 3 of 13
factor u
 

         2
   (3)  x  + 1
                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--R 
--R
--R         2
--R   (3)  x  + 1
--R                          Type: Factored UnivariatePolynomial(x,PrimeField 7)
--E 3 

--S 4 of 13
u2 : UP(x,gf72) := u
 

         2
   (4)  x  + 1
                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R         2
--R   (4)  x  + 1
--R                               Type: UnivariatePolynomial(x,FiniteField(7,2))
--E 4

--S 5 of 13
factor u2
 

   (5)  (x + %A)(x + 6%A)
                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--R 
--R
--R   (5)  (x + %A)(x + 6%A)
--R                      Type: Factored UnivariatePolynomial(x,FiniteField(7,2))
--E 5

--S 6 of 13
definingPolynomial()$gf72
 

         2
   (6)  ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 7
--R 
--R
--R         2
--R   (6)  ?  + 1
--R                                Type: SparseUnivariatePolynomial PrimeField 7
--E 6

--S 7 of 13
e := index(size()$gf72 quo 3)$gf72
 

   (7)  2%A + 2
                                                       Type: FiniteField(7,2)
--R 
--R
--R   (7)  2%A + 2
--R                                                       Type: FiniteField(7,2)
--E 7

--S 8 of 13
norm e
 

   (8)  1
                                                           Type: PrimeField 7
--R 
--R
--R   (8)  1
--R                                                           Type: PrimeField 7
--E 8

--S 9 of 13
trace e
 

   (9)  4
                                                           Type: PrimeField 7
--R 
--R
--R   (9)  4
--R                                                           Type: PrimeField 7
--E 9

--S 10 of 13
order e
 

   (10)  8
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  8
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 13
allElts := [index(i :: PI)$gf72 for i in 1..48]
 

   (11)
   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
    6%A + 5, 6%A + 6]
                                                  Type: List FiniteField(7,2)
--R 
--R
--R   (11)
--R   [1, 2, 3, 4, 5, 6, %A, %A + 1, %A + 2, %A + 3, %A + 4, %A + 5, %A + 6, 2%A,
--R    2%A + 1, 2%A + 2, 2%A + 3, 2%A + 4, 2%A + 5, 2%A + 6, 3%A, 3%A + 1,
--R    3%A + 2, 3%A + 3, 3%A + 4, 3%A + 5, 3%A + 6, 4%A, 4%A + 1, 4%A + 2,
--R    4%A + 3, 4%A + 4, 4%A + 5, 4%A + 6, 5%A, 5%A + 1, 5%A + 2, 5%A + 3,
--R    5%A + 4, 5%A + 5, 5%A + 6, 6%A, 6%A + 1, 6%A + 2, 6%A + 3, 6%A + 4,
--R    6%A + 5, 6%A + 6]
--R                                                  Type: List FiniteField(7,2)
--E 11

--S 12 of 13
reduce(+,allElts)
 

   (12)  0
                                                       Type: FiniteField(7,2)
--R 
--R
--R   (12)  0
--R                                                       Type: FiniteField(7,2)
--E 12 
--S 13 of 13
[order e for e in allElts]
 

   (13)
   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
    48, 4, 24, 48, 48, 48, 48, 24]
                                                   Type: List PositiveInteger
--R 
--R
--R   (13)
--R   [1, 3, 6, 3, 6, 2, 4, 24, 48, 48, 48, 48, 24, 12, 48, 8, 16, 16, 8, 48, 12,
--R    48, 16, 24, 24, 16, 48, 12, 48, 16, 24, 24, 16, 48, 12, 48, 8, 16, 16, 8,
--R    48, 4, 24, 48, 48, 48, 48, 24]
--R                                                   Type: List PositiveInteger
--E 13
)spool 
 
Starts dribbling to ico.output (2010/3/27, 18:26:53).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 65
)se exp add con InnerTrigonometricManipulations
 
   InnerTrigonometricManipulations is now explicitly exposed in frame 
      initial 
--R 
--R   InnerTrigonometricManipulations is now explicitly exposed in frame 
--R      initial 
--E 1

--S 2 of 65
exp(%i*2*%pi/5)
 

          2%i %pi
          -------
             5
   (1)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R          2%i %pi
--R          -------
--R             5
--R   (1)  %e
--R                                             Type: Expression Complex Integer
--E 2

--S 3 of 65
FG2F %
 

               +---+
          2%pi\|- 1
          ----------
               5
   (2)  %e
                                                     Type: Expression Integer
--R 
--R
--R               +---+
--R          2%pi\|- 1
--R          ----------
--R               5
--R   (2)  %e
--R                                                     Type: Expression Integer
--E 3

--S 4 of 65
% -1
 

               +---+
          2%pi\|- 1
          ----------
               5
   (3)  %e           - 1
                                                     Type: Expression Integer
--R 
--R
--R               +---+
--R          2%pi\|- 1
--R          ----------
--R               5
--R   (3)  %e           - 1
--R                                                     Type: Expression Integer
--E 4

--S 5 of 65
complexForm %
 

            2%pi            2%pi
   (4)  cos(----) - 1 + sin(----)%i
              5               5
                                             Type: Complex Expression Integer
--R 
--R
--R            2%pi            2%pi
--R   (4)  cos(----) - 1 + sin(----)%i
--R              5               5
--R                                             Type: Complex Expression Integer
--E 5

--S 6 of 65
norm %
 

            2%pi 2       2%pi 2        2%pi
   (5)  sin(----)  + cos(----)  - 2cos(----) + 1
              5            5             5
                                                     Type: Expression Integer
--R 
--R
--R            2%pi 2       2%pi 2        2%pi
--R   (5)  sin(----)  + cos(----)  - 2cos(----) + 1
--R              5            5             5
--R                                                     Type: Expression Integer
--E 6

--S 7 of 65
simplify %
 

               2%pi
   (6)  - 2cos(----) + 2
                 5
                                                     Type: Expression Integer
--R 
--R
--R               2%pi
--R   (6)  - 2cos(----) + 2
--R                 5
--R                                                     Type: Expression Integer
--E 7

--S 8 of 65
s:=sqrt %
 

         +----------------+
         |       2%pi
   (7)   |- 2cos(----) + 2
        \|         5
                                                     Type: Expression Integer
--R 
--R
--R         +----------------+
--R         |       2%pi
--R   (7)   |- 2cos(----) + 2
--R        \|         5
--R                                                     Type: Expression Integer
--E 8

--S 9 of 65
ph:=exp(%i*2*%pi/5)
 

          2%i %pi
          -------
             5
   (8)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R          2%i %pi
--R          -------
--R             5
--R   (8)  %e
--R                                             Type: Expression Complex Integer
--E 9

--S 10 of 65
A1:=complex(1,0)
 

   (9)  1
                                                        Type: Complex Integer
--R 
--R
--R   (9)  1
--R                                                        Type: Complex Integer
--E 10

--S 11 of 65
A2:=A1*ph
 

           2%i %pi
           -------
              5
   (10)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R           2%i %pi
--R           -------
--R              5
--R   (10)  %e
--R                                             Type: Expression Complex Integer
--E 11

--S 12 of 65
A3:=A2*ph
 

            2%i %pi 2
            -------
               5
   (11)  (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R            2%i %pi 2
--R            -------
--R               5
--R   (11)  (%e       )
--R                                             Type: Expression Complex Integer
--E 12

--S 13 of 65
A4:=A3*ph
 

            2%i %pi 3
            -------
               5
   (12)  (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R            2%i %pi 3
--R            -------
--R               5
--R   (12)  (%e       )
--R                                             Type: Expression Complex Integer
--E 13

--S 14 of 65
A5:=A4*ph
 

            2%i %pi 4
            -------
               5
   (13)  (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R            2%i %pi 4
--R            -------
--R               5
--R   (13)  (%e       )
--R                                             Type: Expression Complex Integer
--E 14

--S 15 of 65
ca1:=map(numeric , complexForm FG2F simplify A1)
 

   (14)  1.0
                                                          Type: Complex Float
--R 
--R
--R   (14)  1.0
--R                                                          Type: Complex Float
--E 15

--S 16 of 65
ca2:=map(numeric , complexForm FG2F simplify A2)
 

   (15)  0.3090169943 749474241 + 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (15)  0.3090169943 749474241 + 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 16

--S 17 of 65
ca3:=map(numeric ,complexForm FG2F simplify A3)
 

   (16)  - 0.8090169943 749474241 + 0.5877852522 9247312917 %i
                                                          Type: Complex Float
--R 
--R
--R   (16)  - 0.8090169943 749474241 + 0.5877852522 9247312917 %i
--R                                                          Type: Complex Float
--E 17

--S 18 of 65
ca4:=map(numeric ,complexForm FG2F simplify A4)
 

   (17)  - 0.8090169943 7494742411 - 0.5877852522 9247312917 %i
                                                          Type: Complex Float
--R 
--R
--R   (17)  - 0.8090169943 7494742411 - 0.5877852522 9247312917 %i
--R                                                          Type: Complex Float
--E 18

--S 19 of 65
ca5:=map(numeric ,complexForm FG2F simplify A5)
 

   (18)  0.3090169943 749474241 - 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (18)  0.3090169943 749474241 - 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 19

--S 20 of 65
B1:=A1*exp(2*%i*%pi/10)
 

           %i %pi
           ------
              5
   (19)  %e
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi
--R           ------
--R              5
--R   (19)  %e
--R                                             Type: Expression Complex Integer
--E 20

--S 21 of 65
B2:=B1*ph
 

           %i %pi  2%i %pi
           ------  -------
              5       5
   (20)  %e      %e
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi  2%i %pi
--R           ------  -------
--R              5       5
--R   (20)  %e      %e
--R                                             Type: Expression Complex Integer
--E 21

--S 22 of 65
B3:=B2*ph
 

           %i %pi   2%i %pi 2
           ------   -------
              5        5
   (21)  %e      (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi   2%i %pi 2
--R           ------   -------
--R              5        5
--R   (21)  %e      (%e       )
--R                                             Type: Expression Complex Integer
--E 22

--S 23 of 65
B4:=B3*ph
 

           %i %pi   2%i %pi 3
           ------   -------
              5        5
   (22)  %e      (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi   2%i %pi 3
--R           ------   -------
--R              5        5
--R   (22)  %e      (%e       )
--R                                             Type: Expression Complex Integer
--E 23

--S 24 of 65
B5:=B4*ph
 

           %i %pi   2%i %pi 4
           ------   -------
              5        5
   (23)  %e      (%e       )
                                             Type: Expression Complex Integer
--R 
--R
--R           %i %pi   2%i %pi 4
--R           ------   -------
--R              5        5
--R   (23)  %e      (%e       )
--R                                             Type: Expression Complex Integer
--E 24

--S 25 of 65
cb1:=map (numeric ,complexForm FG2F simplify B1)
 

   (24)  0.8090169943 749474241 + 0.5877852522 9247312917 %i
                                                          Type: Complex Float
--R 
--R
--R   (24)  0.8090169943 749474241 + 0.5877852522 9247312917 %i
--R                                                          Type: Complex Float
--E 25

--S 26 of 65
cb2:=map (numeric ,complexForm FG2F simplify B2)
 

   (25)  - 0.3090169943 749474241 + 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (25)  - 0.3090169943 749474241 + 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 26

--S 27 of 65
cb3:=map (numeric ,complexForm FG2F simplify B3)
 

   (26)  - 1.0
                                                          Type: Complex Float
--R 
--R
--R   (26)  - 1.0
--R                                                          Type: Complex Float
--E 27

--S 28 of 65
cb4:=map (numeric ,complexForm FG2F simplify B4)
 

   (27)  - 0.3090169943 7494742409 - 0.9510565162 9515357212 %i
                                                          Type: Complex Float
--R 
--R
--R   (27)  - 0.3090169943 7494742409 - 0.9510565162 9515357212 %i
--R                                                          Type: Complex Float
--E 28

--S 29 of 65
cb5:=map (numeric ,complexForm FG2F simplify B5)
 

   (28)  0.8090169943 7494742411 - 0.5877852522 9247312916 %i
                                                          Type: Complex Float
--R 
--R
--R   (28)  0.8090169943 7494742411 - 0.5877852522 9247312916 %i
--R                                                          Type: Complex Float
--E 29

--S 30 of 65
u:=numeric sqrt(s*s-1)
 

   (29)  0.6180339887 4989484821
                                                                  Type: Float
--R 
--R
--R   (29)  0.6180339887 4989484821
--R                                                                  Type: Float
--E 30

--S 31 of 65
p0:=point([0,0,u+1/2])@Point(SF)
 

   (30)  [0.,0.,1.1180339887498949]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (30)  [0.,0.,1.1180339887498949]
--R                                                      Type: Point DoubleFloat
--E 31

--S 32 of 65
p1:=point([real ca1,imag ca1,0.5])@Point(SF)
 

   (31)  [1.,0.,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (31)  [1.,0.,0.5]
--R                                                      Type: Point DoubleFloat
--E 32

--S 33 of 65
p2:=point([real ca2,imag ca2,0.5])@Point(SF)
 

   (32)  [0.30901699437494745,0.95105651629515353,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (32)  [0.30901699437494745,0.95105651629515353,0.5]
--R                                                      Type: Point DoubleFloat
--E 33

--S 34 of 65
p2:=point([real ca2,imag ca2,0.5])@Point(SF)
 

   (33)  [0.30901699437494745,0.95105651629515353,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (33)  [0.30901699437494745,0.95105651629515353,0.5]
--R                                                      Type: Point DoubleFloat
--E 34

--S 35 of 65
p3:=point([real ca3,imag ca3,0.5])@Point(SF)
 

   (34)  [- 0.80901699437494734,0.58778525229247314,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (34)  [- 0.80901699437494745,0.58778525229247314,0.5]
--R                                                      Type: Point DoubleFloat
--E 35

--S 36 of 65
p4:=point([real ca4,imag ca4,0.5])@Point(SF)
 

   (35)  [- 0.80901699437494734,- 0.58778525229247303,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (35)  [- 0.80901699437494745,- 0.58778525229247314,0.5]
--R                                                      Type: Point DoubleFloat
--E 36

--S 37 of 65
p5:=point([real ca5,imag ca5,0.5])@Point(SF)
 

   (36)  [0.30901699437494745,- 0.95105651629515364,0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (36)  [0.30901699437494745,- 0.95105651629515353,0.5]
--R                                                      Type: Point DoubleFloat
--E 37

--S 38 of 65
p6:=point([real cb1,imag cb1,-0.5])@Point(SF)
 

   (37)  [0.80901699437494745,0.58778525229247314,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (37)  [0.80901699437494745,0.58778525229247314,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 38

--S 39 of 65
p7:=point([real cb2,imag cb2,-0.5])@Point(SF)
 

   (38)  [- 0.3090169943749474,0.95105651629515353,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (38)  [- 0.30901699437494745,0.95105651629515353,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 39

--S 40 of 65
p8:=point([real cb3,imag cb3,-0.5])@Point(SF)
 

   (39)  [- 1.,0.,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (39)  [- 1.,0.,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 40

--S 41 of 65
p9:=point([real cb4,imag cb4,-0.5])@Point(SF)
 

   (40)  [- 0.3090169943749474,- 0.95105651629515364,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (40)  [- 0.30901699437494745,- 0.95105651629515353,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 41

--S 42 of 65
p10:=point([real cb5,imag cb5,-0.5])@Point(SF)
 

   (41)  [0.80901699437494745,- 0.58778525229247303,- 0.5]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (41)  [0.80901699437494745,- 0.58778525229247314,- 0.5]
--R                                                      Type: Point DoubleFloat
--E 42

--S 43 of 65
p11:=point([0,0,-u-1/2])@Point(SF)
 

   (42)  [0.,0.,- 1.1180339887498947]
                                                      Type: Point DoubleFloat
--R 
--R
--R   (42)  [0.,0.,- 1.1180339887498949]
--R                                                      Type: Point DoubleFloat
--E 43

--S 44 of 65
space:=create3Space()$ThreeSpace DFLOAT
 

   (43)  3-Space with 0 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (43)  3-Space with 0 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 44

--S 45 of 65
polygon(space,[p0,p1,p2])
 

   (44)  3-Space with 1 component
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (44)  3-Space with 1 component
--R                                                 Type: ThreeSpace DoubleFloat
--E 45

--S 46 of 65
polygon(space,[p0,p2,p3])
 

   (45)  3-Space with 2 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (45)  3-Space with 2 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 46

--S 47 of 65
polygon(space,[p0,p3,p4])
 

   (46)  3-Space with 3 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (46)  3-Space with 3 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 47

--S 48 of 65
polygon(space,[p0,p4,p5])
 

   (47)  3-Space with 4 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (47)  3-Space with 4 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 48

--S 49 of 65
polygon(space,[p0,p5,p1])
 

   (48)  3-Space with 5 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (48)  3-Space with 5 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 49

--S 50 of 65
polygon(space,[p1,p6,p2])
 

   (49)  3-Space with 6 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (49)  3-Space with 6 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 50

--S 51 of 65
polygon(space,[p2,p7,p3])
 

   (50)  3-Space with 7 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (50)  3-Space with 7 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 51

--S 52 of 65
polygon(space,[p3,p8,p4])
 

   (51)  3-Space with 8 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (51)  3-Space with 8 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 52

--S 53 of 65
polygon(space,[p4,p9,p5])
 

   (52)  3-Space with 9 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (52)  3-Space with 9 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 53

--S 54 of 65
polygon(space,[p5,p10,p1])
 

   (53)  3-Space with 10 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (53)  3-Space with 10 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 54

--S 55 of 65
polygon(space,[p2,p6,p7])
 

   (54)  3-Space with 11 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (54)  3-Space with 11 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 55

--S 56 of 65
polygon(space,[p3,p7,p8])
 

   (55)  3-Space with 12 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (55)  3-Space with 12 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 56

--S 57 of 65
polygon(space,[p4,p8,p9])
 

   (56)  3-Space with 13 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (56)  3-Space with 13 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 57

--S 58 of 65
polygon(space,[p5,p9,p10])
 

   (57)  3-Space with 14 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (57)  3-Space with 14 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 58

--S 59 of 65
polygon(space,[p1,p10,p6])
 

   (58)  3-Space with 15 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (58)  3-Space with 15 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 59

--S 60 of 65
polygon(space,[p6,p11,p7])
 

   (59)  3-Space with 16 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (59)  3-Space with 16 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 60

--S 61 of 65
polygon(space,[p7,p11,p8])
 

   (60)  3-Space with 17 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (60)  3-Space with 17 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 61

--S 62 of 65
polygon(space,[p8,p11,p9])
 

   (61)  3-Space with 18 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (61)  3-Space with 18 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 62

--S 63 of 65
polygon(space,[p9,p11,p10])
 

   (62)  3-Space with 19 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (62)  3-Space with 19 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 63

--S 64 of 65
polygon(space,[p10,p11,p6])
 

   (63)  3-Space with 20 components
                                                 Type: ThreeSpace DoubleFloat
--R 
--R
--R   (63)  3-Space with 20 components
--R                                                 Type: ThreeSpace DoubleFloat
--E 64

--S 65 of 65
makeViewport3D(space,title=="Icosahedron")
 
   Transmitting data...

   (64)  ThreeDimensionalViewport: "Icosahedron"
                                               Type: ThreeDimensionalViewport
--R 
--R   Transmitting data...
--R
--R   (64)  ThreeDimensionalViewport: "Icosahedron"
--R                                               Type: ThreeDimensionalViewport
--E 65

)spool 
 
Starts dribbling to Quaternion.output (2010/3/27, 18:46:17).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 13
q := quatern(2/11,-8,3/4,1)
 

         2        3
   (1)  -- - 8i + - j + k
        11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         2        3
--R   (1)  -- - 8i + - j + k
--R        11        4
--R                                            Type: Quaternion Fraction Integer
--E 1

--S 2 of 13
[real q, imagI q, imagJ q, imagK q]
 

          2     3
   (2)  [--,- 8,-,1]
         11     4
                                                  Type: List Fraction Integer
--R 
--R
--R          2     3
--R   (2)  [--,- 8,-,1]
--R         11     4
--R                                                  Type: List Fraction Integer
--E 2

--S 3 of 13
inv q
 

          352     15488      484       1936
   (3)  ------ + ------ i - ----- j - ------ k
        126993   126993     42331     126993
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          352     15488      484       1936
--R   (3)  ------ + ------ i - ----- j - ------ k
--R        126993   126993     42331     126993
--R                                            Type: Quaternion Fraction Integer
--E 3

--S 4 of 13
q^6
 

          2029490709319345   48251690851     144755072553     48251690851
   (4)  - ---------------- - ----------- i + ------------ j + ----------- k
             7256313856        1288408         41229056         10307264
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2029490709319345   48251690851     144755072553     48251690851
--R   (4)  - ---------------- - ----------- i + ------------ j + ----------- k
--R             7256313856        1288408         41229056         10307264
--R                                            Type: Quaternion Fraction Integer
--E 4

--S 5 of 13
r := quatern(-2,3,23/9,-89); q + r
 

          20        119
   (5)  - -- - 5i + --- j - 88k
          11         36
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          20        119
--R   (5)  - -- - 5i + --- j - 88k
--R          11         36
--R                                            Type: Quaternion Fraction Integer
--E 5

--S 6 of 13
q * r - r * q
 

          2495             817
   (6)  - ---- i - 1418j - --- k
           18               18
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2495             817
--R   (6)  - ---- i - 1418j - --- k
--R           18               18
--R                                            Type: Quaternion Fraction Integer
--E 6

--S 7 of 13
i:=quatern(0,1,0,0) 
 

   (7)  i
                                                     Type: Quaternion Integer
--R 
--R
--R   (7)  i
--R                                                     Type: Quaternion Integer
--E 7

--S 8 of 13
j:=quatern(0,0,1,0) 
 

   (8)  j
                                                     Type: Quaternion Integer
--R 
--R
--R   (8)  j
--R                                                     Type: Quaternion Integer
--E 8

--S 9 of 13
k:=quatern(0,0,0,1)
 

   (9)  k
                                                     Type: Quaternion Integer
--R 
--R
--R   (9)  k
--R                                                     Type: Quaternion Integer
--E 9

--S 10 of 13
[i*i, j*j, k*k, i*j, j*k, k*i, q*i]
 

                                 2         3
   (10)  [- 1,- 1,- 1,k,i,j,8 + -- i + j - - k]
                                11         4
                                       Type: List Quaternion Fraction Integer
--R 
--R
--R                                 2         3
--R   (10)  [- 1,- 1,- 1,k,i,j,8 + -- i + j - - k]
--R                                11         4
--R                                       Type: List Quaternion Fraction Integer
--E 10

--S 11 of 13
norm q
 

         126993
   (11)  ------
          1936
                                                       Type: Fraction Integer
--R 
--R
--R         126993
--R   (11)  ------
--R          1936
--R                                                       Type: Fraction Integer
--E 11

--S 12 of 13
conjugate q 
 

          2        3
   (12)  -- + 8i - - j - k
         11        4
                                            Type: Quaternion Fraction Integer
--R 
--R
--R          2        3
--R   (12)  -- + 8i - - j - k
--R         11        4
--R                                            Type: Quaternion Fraction Integer
--E 12

--S 13 of 13
q * %
 

         126993
   (13)  ------
          1936
                                            Type: Quaternion Fraction Integer
--R 
--R
--R         126993
--R   (13)  ------
--R          1936
--R                                            Type: Quaternion Fraction Integer
--E 13
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read zlindep
 

-- Input generated from IntegerLinearDependenceXmpPage
)clear all
 

M := SQMATRIX(2,INT)
 

   (1)  SquareMatrix(2,Integer)
                                                                 Type: Domain
m1: M := squareMatrix matrix [[1, 2], [0, -1]]
 

        +1   2 +
   (2)  |      |
        +0  - 1+
                                                Type: SquareMatrix(2,Integer)
m2: M := squareMatrix matrix [[2, 3], [1, -2]]
 

        +2   3 +
   (3)  |      |
        +1  - 2+
                                                Type: SquareMatrix(2,Integer)
m3: M := squareMatrix matrix [[3, 4], [2, -3]]
 

        +3   4 +
   (4)  |      |
        +2  - 3+
                                                Type: SquareMatrix(2,Integer)
linearlyDependentOverZ? vector [m1, m2, m3]
 

   (5)  true
                                                                Type: Boolean
c := linearDependenceOverZ vector [m1, m2, m3]
 

   (6)  [1,- 2,1]
                                              Type: Union(Vector Integer,...)
c.1 * m1 + c.2 * m2 + c.3 * m3
 

        +0  0+
   (7)  |    |
        +0  0+
                                                Type: SquareMatrix(2,Integer)
solveLinearlyOverQ(vector [m1, m3], m2)
 

         1 1
   (8)  [-,-]
         2 2
                                     Type: Union(Vector Fraction Integer,...)
)lisp (bye)
 
Starts dribbling to bop.output (2010/3/27, 18:23:18).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 17
y := operator 'y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 17
deq := D(y x, x, 2) + D(y x, x) + y x = 0
 

         ,,       ,
   (2)  y  (x) + y (x) + y(x)= 0

                                            Type: Equation Expression Integer
--R 
--R
--R         ,,       ,
--R   (2)  y  (x) + y (x) + y(x)= 0
--R
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 17
nary? y
 

   (3)  true
                                                                Type: Boolean
--R 
--R
--R   (3)  true
--R                                                                Type: Boolean
--E 3

--S 4 of 17
unary? y
 

   (4)  false
                                                                Type: Boolean
--R 
--R
--R   (4)  false
--R                                                                Type: Boolean
--E 4

--S 5 of 17
opOne := operator('opOne, 1)
 

   (5)  opOne
                                                          Type: BasicOperator
--R 
--R
--R   (5)  opOne
--R                                                          Type: BasicOperator
--E 5

--S 6 of 17
nary? opOne
 

   (6)  false
                                                                Type: Boolean
--R 
--R
--R   (6)  false
--R                                                                Type: Boolean
--E 6

--S 7 of 17
unary? opOne
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 17
arity opOne
 

   (8)  1
                                          Type: Union(NonNegativeInteger,...)
--R 
--R
--R   (8)  1
--R                                          Type: Union(NonNegativeInteger,...)
--E 8

--S 9 of 17
name opOne
 

   (9)  opOne
                                                                 Type: Symbol
--R 
--R
--R   (9)  opOne
--R                                                                 Type: Symbol
--E 9

--S 10 of 17
is?(opOne, 'z2)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 17
is?(opOne, "opOne")
 

   (11)  true
                                                                Type: Boolean
--R 
--R
--R   (11)  true
--R                                                                Type: Boolean
--E 11

--S 12 of 17
properties y
 

   (12)  table()
                                           Type: AssociationList(String,None)
--R 
--R
--R   (12)  table()
--R                                           Type: AssociationList(String,None)
--E 12

--S 13 of 17
setProperty(y, "use", "unknown function" :: None )
 

   (13)  y
                                                          Type: BasicOperator
--R 
--R
--R   (13)  y
--R                                                          Type: BasicOperator
--E 13

--S 14 of 17
properties y
 

   (14)  table("use"= NONE)
                                           Type: AssociationList(String,None)
--R 
--R
--R   (14)  table("use"= NONE)
--R                                           Type: AssociationList(String,None)
--E 14

--S 15 of 17
property(y, "use") :: None pretend String
 

   (15)  "unknown function"
                                                                 Type: String
--R 
--R
--R   (15)  "unknown function"
--R                                                                 Type: String
--E 15

--S 16 of 17
deleteProperty!(y, "use")
 

   (16)  y
                                                          Type: BasicOperator
--R 
--R
--R   (16)  y
--R                                                          Type: BasicOperator
--E 16

--S 17 of 17
properties y
 

   (17)  table()
                                           Type: AssociationList(String,None)
--R 
--R
--R   (17)  table()
--R                                           Type: AssociationList(String,None)
--E 17
)spool
 
Starts dribbling to octonion.output (2010/3/27, 18:30:29).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 39
e0:Octonion(Fraction(Integer)):=octon(1,0,0,0,0,0,0,0)
 

   (1)  1
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (1)  1
--R                                              Type: Octonion Fraction Integer
--E 1

--S 2 of 39
e1:Octonion(Fraction(Integer)):=octon(0,1,0,0,0,0,0,0)
 

   (2)  i
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (2)  i
--R                                              Type: Octonion Fraction Integer
--E 2

--S 3 of 39
e2:Octonion(Fraction(Integer)):=octon(0,0,1,0,0,0,0,0)
 

   (3)  j
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (3)  j
--R                                              Type: Octonion Fraction Integer
--E 3

--S 4 of 39
e3:Octonion(Fraction(Integer)):=octon(0,0,0,1,0,0,0,0)
 

   (4)  k
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (4)  k
--R                                              Type: Octonion Fraction Integer
--E 4

--S 5 of 39
e4:Octonion(Fraction(Integer)):=octon(0,0,0,0,1,0,0,0)
 

   (5)  E
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (5)  E
--R                                              Type: Octonion Fraction Integer
--E 5

--S 6 of 39
e5:Octonion(Fraction(Integer)):=octon(0,0,0,0,0,1,0,0)
 

   (6)  I
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (6)  I
--R                                              Type: Octonion Fraction Integer
--E 6

--S 7 of 39
e6:Octonion(Fraction(Integer)):=octon(0,0,0,0,0,0,1,0)
 

   (7)  J
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (7)  J
--R                                              Type: Octonion Fraction Integer
--E 7

--S 8 of 39
e7:Octonion(Fraction(Integer)):=octon(0,0,0,0,0,0,0,1)
 

   (8)  K
                                              Type: Octonion Fraction Integer
--R 
--R
--R   (8)  K
--R                                              Type: Octonion Fraction Integer
--E 8

--S 9 of 39
[e0,e1,e2,e3,e4,e5,e6,e7]
 

   (9)  [1,i,j,k,E,I,J,K]
                                         Type: List Octonion Fraction Integer
--R 
--R
--R   (9)  [1,i,j,k,E,I,J,K]
--R                                         Type: List Octonion Fraction Integer
--E 9
--S 10 of 39
for i in [e0,e1,e2,e3,e4,e5,e6,e7] repeat _
  print [ (i*e0),(i*e1),(i*e2),(i*e3),(i*e4),(i*e5),(i*e6),(i*e7) ]
 
   [1,i,j,k,E,I,J,K]
   [i,- 1,k,- j,I,- E,- K,J]
   [j,- k,- 1,i,J,K,- E,- I]
   [k,j,- i,- 1,K,- J,I,- E]
   [E,- I,- J,- K,- 1,i,j,k]
   [I,E,- K,J,- i,- 1,- k,j]
   [J,K,E,- I,- j,k,- 1,- i]
   [K,- J,I,E,- k,- j,i,- 1]
                                                                   Type: Void
--R 
--R   [1,i,j,k,E,I,J,K]
--R   [i,- 1,k,- j,I,- E,- K,J]
--R   [j,- k,- 1,i,J,K,- E,- I]
--R   [k,j,- i,- 1,K,- J,I,- E]
--R   [E,- I,- J,- K,- 1,i,j,k]
--R   [I,E,- K,J,- i,- 1,- k,j]
--R   [J,K,E,- I,- j,k,- 1,- i]
--R   [K,- J,I,E,- k,- j,i,- 1]
--R                                                                   Type: Void
--E 10
--S 11 of 39
oci1 := octon(1,2,3,4,5,6,7,8)
 

   (11)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
                                                       Type: Octonion Integer
--R 
--R
--R   (11)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
--R                                                       Type: Octonion Integer
--E 11

--S 12 of 39
oci2 := octon(7,2,3,-4,5,6,-7,0)
 

   (12)  7 + 2i + 3j - 4k + 5E + 6I - 7J
                                                       Type: Octonion Integer
--R 
--R
--R   (12)  7 + 2i + 3j - 4k + 5E + 6I - 7J
--R                                                       Type: Octonion Integer
--E 12

--S 13 of 39
oci3 := octon(-7,-12,3,-10,5,6,9,0)
 

   (13)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
                                                       Type: Octonion Integer
--R 
--R
--R   (13)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
--R                                                       Type: Octonion Integer
--E 13

--S 14 of 39
oci := oci1 * oci2 * oci3
 

   (14)  - 324 + 2104i - 1100j - 2984k - 1444E + 528I - 44J + 128K
                                                       Type: Octonion Integer
--R 
--R
--R   (14)  - 324 + 2104i - 1100j - 2984k - 1444E + 528I - 44J + 128K
--R                                                       Type: Octonion Integer
--E 14

--S 15 of 39
(oci1 * oci2) * oci3 - oci1 * (oci2 * oci3)
 

   (15)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
                                                       Type: Octonion Integer
--R 
--R
--R   (15)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
--R                                                       Type: Octonion Integer
--E 15

--S 16 of 39
octon(1,0,0,0,0,0,0,0)
 

   (16)  1
                                                       Type: Octonion Integer
--R 
--R
--R   (16)  1
--R                                                       Type: Octonion Integer
--E 16

--S 17 of 39
i := octon(0,1,0,0,0,0,0,0)
 

   (17)  i
                                                       Type: Octonion Integer
--R 
--R
--R   (17)  i
--R                                                       Type: Octonion Integer
--E 17

--S 18 of 39
j := octon(0,0,1,0,0,0,0,0)
 

   (18)  j
                                                       Type: Octonion Integer
--R 
--R
--R   (18)  j
--R                                                       Type: Octonion Integer
--E 18

--S 19 of 39
octon(0,0,0,1,0,0,0,0)
 

   (19)  k
                                                       Type: Octonion Integer
--R 
--R
--R   (19)  k
--R                                                       Type: Octonion Integer
--E 19

--S 20 of 39
octon(0,0,0,0,1,0,0,0)
 

   (20)  E
                                                       Type: Octonion Integer
--R 
--R
--R   (20)  E
--R                                                       Type: Octonion Integer
--E 20

--S 21 of 39
octon(0,0,0,0,0,1,0,0)
 

   (21)  I
                                                       Type: Octonion Integer
--R 
--R
--R   (21)  I
--R                                                       Type: Octonion Integer
--E 21

--S 22 of 39
J := octon(0,0,0,0,0,0,1,0)
 

   (22)  J
                                                       Type: Octonion Integer
--R 
--R
--R   (22)  J
--R                                                       Type: Octonion Integer
--E 22

--S 23 of 39
octon(0,0,0,0,0,0,0,1)
 

   (23)  K
                                                       Type: Octonion Integer
--R 
--R
--R   (23)  K
--R                                                       Type: Octonion Integer
--E 23

--S 24 of 39
i*(j*J)
 

   (24)  - I
                                                       Type: Octonion Integer
--R 
--R
--R   (24)  - I
--R                                                       Type: Octonion Integer
--E 24

--S 25 of 39
(i*j)*J
 

   (25)  I
                                                       Type: Octonion Integer
--R 
--R
--R   (25)  I
--R                                                       Type: Octonion Integer
--E 25

--S 26 of 39
imagi oci
 

   (26)  2104
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  2104
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 39
imagE oci
 

   (27)  - 1444
                                                                Type: Integer
--R 
--R
--R   (27)  - 1444
--R                                                                Type: Integer
--E 27

--S 28 of 39
qs := Quaternion Polynomial Integer
 

   (28)  Quaternion Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (28)  Quaternion Polynomial Integer
--R                                                                 Type: Domain
--E 28

--S 29 of 39
os := Octonion Polynomial Integer
 

   (29)  Octonion Polynomial Integer
                                                                 Type: Domain
--R 
--R
--R   (29)  Octonion Polynomial Integer
--R                                                                 Type: Domain
--E 29

--S 30 of 39
q : qs := quatern(q1,qi,qj,qk)
 

   (30)  q1 + qi i + qj j + qk k
                                          Type: Quaternion Polynomial Integer
--R 
--R
--R   (30)  q1 + qi i + qj j + qk k
--R                                          Type: Quaternion Polynomial Integer
--E 30

--S 31 of 39
E := octon(0,0,0,0,1,0,0,0)$os
 

   (31)  E
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (31)  E
--R                                            Type: Octonion Polynomial Integer
--E 31

--S 32 of 39
q * E
 

   (32)  q1 E + qi I + qj J + qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (32)  q1 E + qi I + qj J + qk K
--R                                            Type: Octonion Polynomial Integer
--E 32

--S 33 of 39
E * q
 

   (33)  q1 E - qi I - qj J - qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (33)  q1 E - qi I - qj J - qk K
--R                                            Type: Octonion Polynomial Integer
--E 33

--S 34 of 39
q * 1$os
 

   (34)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (34)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 34

--S 35 of 39
1$os * q
 

   (35)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (35)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 35

--S 36 of 39
o : os := octon(o1,oi,oj,ok,oE,oI,oJ,oK)
 

   (36)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (36)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
--R                                            Type: Octonion Polynomial Integer
--E 36

--S 37 of 39
p : os := octon(p1,pi,pj,pk,pE,pI,pJ,pK)
 

   (37)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (37)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
--R                                            Type: Octonion Polynomial Integer
--E 37


--S 38 of 39
norm o
 

           2     2     2     2     2     2     2     2
   (38)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
                                                     Type: Polynomial Integer
--R 
--R
--R           2     2     2     2     2     2     2     2
--R   (38)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
--R                                                     Type: Polynomial Integer
--E 38

--S 39 of 39
norm(o*p)-norm(p*o)
 

   (39)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (39)  0
--R                                                     Type: Polynomial Integer
--E 39
)spool 
 
Starts dribbling to matrix22.output (2010/3/27, 18:29:54).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 8
m:SQMATRIX(2,INT) := squareMatrix matrix [[0,1],[-1,0]]
 

        + 0   1+
   (1)  |      |
        +- 1  0+
                                                Type: SquareMatrix(2,Integer)
--R 
--R
--R        + 0   1+
--R   (1)  |      |
--R        +- 1  0+
--R                                                Type: SquareMatrix(2,Integer)
--E 1

--S 2 of 8
determinant m
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 8
n:SQMATRIX(2,SQMATRIX(2,INT)) :=
  squareMatrix matrix [[m,m**2],[m**3,m**4]]
 

        ++ 0   1+  +- 1   0 ++
        ||      |  |        ||
        |+- 1  0+  + 0   - 1+|
   (3)  |                    |
        |+0  - 1+    +1  0+  |
        ||      |    |    |  |
        ++1   0 +    +0  1+  +
                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--R 
--R
--R        ++ 0   1+  +- 1   0 ++
--R        ||      |  |        ||
--R        |+- 1  0+  + 0   - 1+|
--R   (3)  |                    |
--R        |+0  - 1+    +1  0+  |
--R        ||      |    |    |  |
--R        ++1   0 +    +0  1+  +
--R                                Type: SquareMatrix(2,SquareMatrix(2,Integer))
--E 3

)set mes test off
 
--S 4 of 8
determinant n
 
   There are 3 exposed and 1 unexposed library operations named 
      determinant having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op determinant
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
   Cannot find a definition or applicable library operation named 
      determinant with argument type(s) 
                   SquareMatrix(2,SquareMatrix(2,Integer))
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
--R 
--R   There are 3 exposed and 1 unexposed library operations named 
--R      determinant having 1 argument(s) but none was determined to be 
--R      applicable. Use HyperDoc Browse, or issue
--R                           )display op determinant
--R      to learn more about the available operations. Perhaps 
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R 
--R   Cannot find a definition or applicable library operation named 
--R      determinant with argument type(s) 
--R                   SquareMatrix(2,SquareMatrix(2,Integer))
--R      
--R      Perhaps you should use "@" to indicate the required return type, 
--R      or "$" to specify which version of the function you need.
--E 4
)set mes test on
 

--S 5 of 8
o:SQMATRIX(2,SQMATRIX(2,SQMATRIX(2,INT))) :=
   squareMatrix matrix [[n,n**2],[n**3,n**4]]
 

        +++ 0   1+  +- 1   0 ++  ++- 1   1 +  +- 1  - 1+++
        |||      |  |        ||  ||        |  |        |||
        ||+- 1  0+  + 0   - 1+|  |+- 1  - 1+  + 1   - 1+||
        ||                    |  |                      ||
        ||+0  - 1+    +1  0+  |  | +1  - 1+    + 1   1+ ||
        |||      |    |    |  |  | |      |    |      | ||
        |++1   0 +    +0  1+  +  + +1   1 +    +- 1  1+ +|
   (4)  |                                                |
        |++- 2   0 +  +0  - 2++  ++- 2  - 2+   +2  - 2+ +|
        |||        |  |      ||  ||        |   |      | ||
        ||+ 0   - 2+  +2   0 +|  |+ 2   - 2+   +2   2 + ||
        ||                    |  |                      ||
        ||  +2  0+    + 0   2+|  | + 2   2+   +- 2   2 +||
        ||  |    |    |      ||  | |      |   |        |||
        ++  +0  2+    +- 2  0++  + +- 2  2+   +- 2  - 2+++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        +++ 0   1+  +- 1   0 ++  ++- 1   1 +  +- 1  - 1+++
--R        |||      |  |        ||  ||        |  |        |||
--R        ||+- 1  0+  + 0   - 1+|  |+- 1  - 1+  + 1   - 1+||
--R        ||                    |  |                      ||
--R        ||+0  - 1+    +1  0+  |  | +1  - 1+    + 1   1+ ||
--R        |||      |    |    |  |  | |      |    |      | ||
--R        |++1   0 +    +0  1+  +  + +1   1 +    +- 1  1+ +|
--R   (4)  |                                                |
--R        |++- 2   0 +  +0  - 2++  ++- 2  - 2+   +2  - 2+ +|
--R        |||        |  |      ||  ||        |   |      | ||
--R        ||+ 0   - 2+  +2   0 +|  |+ 2   - 2+   +2   2 + ||
--R        ||                    |  |                      ||
--R        ||  +2  0+    + 0   2+|  | + 2   2+   +- 2   2 +||
--R        ||  |    |    |      ||  | |      |   |        |||
--R        ++  +0  2+    +- 2  0++  + +- 2  2+   +- 2  - 2+++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 5

--S 6 of 8
o ** 2
 

        +++- 1  - 3+   +3  - 1+ +  + +2  - 4+    + 4   2+ ++
        |||        |   |      | |  | |      |    |      | ||
        ||+ 3   - 1+   +1   3 + |  | +4   2 +    +- 2  4+ ||
        ||                      |  |                      ||
        || + 1   3+   +- 3   1 +|  |+- 2   4 +  +- 4  - 2+||
        || |      |   |        ||  ||        |  |        |||
        |+ +- 3  1+   +- 1  - 3++  ++- 4  - 2+  + 2   - 4++|
   (5)  |                                                  |
        |+ +6  - 2+    + 2   6+ +  + + 8   4+   +- 4   8 ++|
        || |      |    |      | |  | |      |   |        |||
        || +2   6 +    +- 6  2+ |  | +- 4  8+   +- 8  - 4+||
        ||                      |  |                      ||
        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +4  - 8+ ||
        |||        |  |        ||  ||        |   |      | ||
        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   4 + ++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        +++- 1  - 3+   +3  - 1+ +  + +2  - 4+    + 4   2+ ++
--R        |||        |   |      | |  | |      |    |      | ||
--R        ||+ 3   - 1+   +1   3 + |  | +4   2 +    +- 2  4+ ||
--R        ||                      |  |                      ||
--R        || + 1   3+   +- 3   1 +|  |+- 2   4 +  +- 4  - 2+||
--R        || |      |   |        ||  ||        |  |        |||
--R        |+ +- 3  1+   +- 1  - 3++  ++- 4  - 2+  + 2   - 4++|
--R   (5)  |                                                  |
--R        |+ +6  - 2+    + 2   6+ +  + + 8   4+   +- 4   8 ++|
--R        || |      |    |      | |  | |      |   |        |||
--R        || +2   6 +    +- 6  2+ |  | +- 4  8+   +- 8  - 4+||
--R        ||                      |  |                      ||
--R        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +4  - 8+ ||
--R        |||        |  |        ||  ||        |   |      | ||
--R        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   4 + ++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 6

--S 7 of 8
% + 2
 

        + ++1  - 3+   +3  - 1+ +   + +2  - 4+    + 4   2+ ++
        | ||      |   |      | |   | |      |    |      | ||
        | |+3   1 +   +1   3 + |   | +4   2 +    +- 2  4+ ||
        | |                    |   |                      ||
        | |+ 1   3+  +- 1   1 +|   |+- 2   4 +  +- 4  - 2+||
        | ||      |  |        ||   ||        |  |        |||
        | ++- 3  1+  +- 1  - 1++   ++- 4  - 2+  + 2   - 4++|
   (6)  |                                                  |
        |+ +6  - 2+    + 2   6+ +  ++10   4 +   +- 4   8 ++|
        || |      |    |      | |  ||       |   |        |||
        || +2   6 +    +- 6  2+ |  |+- 4  10+   +- 8  - 4+||
        ||                      |  |                      ||
        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +6  - 8+ ||
        |||        |  |        ||  ||        |   |      | ||
        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   6 + ++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        + ++1  - 3+   +3  - 1+ +   + +2  - 4+    + 4   2+ ++
--R        | ||      |   |      | |   | |      |    |      | ||
--R        | |+3   1 +   +1   3 + |   | +4   2 +    +- 2  4+ ||
--R        | |                    |   |                      ||
--R        | |+ 1   3+  +- 1   1 +|   |+- 2   4 +  +- 4  - 2+||
--R        | ||      |  |        ||   ||        |  |        |||
--R        | ++- 3  1+  +- 1  - 1++   ++- 4  - 2+  + 2   - 4++|
--R   (6)  |                                                  |
--R        |+ +6  - 2+    + 2   6+ +  ++10   4 +   +- 4   8 ++|
--R        || |      |    |      | |  ||       |   |        |||
--R        || +2   6 +    +- 6  2+ |  |+- 4  10+   +- 8  - 4+||
--R        ||                      |  |                      ||
--R        ||+- 6   2 +  +- 2  - 6+|  |+- 8  - 4+   +6  - 8+ ||
--R        |||        |  |        ||  ||        |   |      | ||
--R        +++- 2  - 6+  + 6   - 2++  ++ 4   - 8+   +8   6 + ++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 7

--S 8 of 8
o := 2
 

        +++2  0+  +0  0++  ++0  0+  +0  0+++
        |||    |  |    ||  ||    |  |    |||
        ||+0  2+  +0  0+|  |+0  0+  +0  0+||
        ||              |  |              ||
        ||+0  0+  +2  0+|  |+0  0+  +0  0+||
        |||    |  |    ||  ||    |  |    |||
        |++0  0+  +0  2++  ++0  0+  +0  0++|
   (7)  |                                  |
        |++0  0+  +0  0++  ++2  0+  +0  0++|
        |||    |  |    ||  ||    |  |    |||
        ||+0  0+  +0  0+|  |+0  2+  +0  0+||
        ||              |  |              ||
        ||+0  0+  +0  0+|  |+0  0+  +2  0+||
        |||    |  |    ||  ||    |  |    |||
        +++0  0+  +0  0++  ++0  0+  +0  2+++
                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--R 
--R
--R        +++2  0+  +0  0++  ++0  0+  +0  0+++
--R        |||    |  |    ||  ||    |  |    |||
--R        ||+0  2+  +0  0+|  |+0  0+  +0  0+||
--R        ||              |  |              ||
--R        ||+0  0+  +2  0+|  |+0  0+  +0  0+||
--R        |||    |  |    ||  ||    |  |    |||
--R        |++0  0+  +0  2++  ++0  0+  +0  0++|
--R   (7)  |                                  |
--R        |++0  0+  +0  0++  ++2  0+  +0  0++|
--R        |||    |  |    ||  ||    |  |    |||
--R        ||+0  0+  +0  0+|  |+0  2+  +0  0+||
--R        ||              |  |              ||
--R        ||+0  0+  +0  0+|  |+0  0+  +2  0+||
--R        |||    |  |    ||  ||    |  |    |||
--R        +++0  0+  +0  0++  ++0  0+  +0  2+++
--R                Type: SquareMatrix(2,SquareMatrix(2,SquareMatrix(2,Integer)))
--E 8
)spool 
 
Starts dribbling to sint.output (2010/3/27, 18:40:44).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 11
min()$SingleInteger
 

   (1)  - 2147483648
                                                          Type: SingleInteger
--R 
--R
--R   (1)  - 2147483648
--R                                                          Type: SingleInteger
--E 1

--S 2 of 11
max()$SingleInteger
 

   (2)  2147483647
                                                          Type: SingleInteger
--R 
--R
--R   (2)  2147483647
--R                                                          Type: SingleInteger
--E 2

--S 3 of 11
a := 1234 :: SingleInteger
 

   (3)  1234
                                                          Type: SingleInteger
--R 
--R
--R   (3)  1234
--R                                                          Type: SingleInteger
--E 3

--S 4 of 11
b := 124$SingleInteger
 

   (4)  124
                                                          Type: SingleInteger
--R 
--R
--R   (4)  124
--R                                                          Type: SingleInteger
--E 4

--S 5 of 11
gcd(a,b)
 

   (5)  2
                                                          Type: SingleInteger
--R 
--R
--R   (5)  2
--R                                                          Type: SingleInteger
--E 5

--S 6 of 11
lcm(a,b)
 

   (6)  76508
                                                          Type: SingleInteger
--R 
--R
--R   (6)  76508
--R                                                          Type: SingleInteger
--E 6

--S 7 of 11
mulmod(5,6,13)$SingleInteger
 

   (7)  4
                                                          Type: SingleInteger
--R 
--R
--R   (7)  4
--R                                                          Type: SingleInteger
--E 7

--S 8 of 11
positiveRemainder(37,13)$SingleInteger
 

   (8)  11
                                                          Type: SingleInteger
--R 
--R
--R   (8)  11
--R                                                          Type: SingleInteger
--E 8

--S 9 of 11
And(3,4)$SingleInteger
 

   (9)  0
                                                          Type: SingleInteger
--R 
--R
--R   (9)  0
--R                                                          Type: SingleInteger
--E 9

--S 10 of 11
shift(1,4)$SingleInteger
 

   (10)  16
                                                          Type: SingleInteger
--R 
--R
--R   (10)  16
--R                                                          Type: SingleInteger
--E 10

--S 11 of 11
shift(31,-1)$SingleInteger
 

   (11)  15
                                                          Type: SingleInteger
--R 
--R
--R   (11)  15
--R                                                          Type: SingleInteger
--E 11
)spool 
 
Starts dribbling to elt.output (2010/3/27, 18:25:26).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 4
u : Bits := new(10,true)
 

   (1)  "1111111111"
                                                                   Type: Bits
--R 
--R
--R   (1)  "1111111111"
--R                                                                   Type: Bits
--E 1

--S 2 of 4
u(3..5) := false; u
 

   (2)  "1100011111"
                                                                   Type: Bits
--R 
--R
--R   (2)  "1100011111"
--R                                                                   Type: Bits
--E 2

)clear all
 

--S 3 of 4
u:Any := [1, 7.2, 3/2, x**2, "wally"]
 

               3  2
   (1)  [1,7.2,-,x ,"wally"]
               2
                                                               Type: List Any
--R 
--R
--R               3  2
--R   (1)  [1,7.2,-,x ,"wally"]
--R               2
--R                                                               Type: List Any
--E 3

--S 4 of 4
u.1
 

   (2)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1
--R                                                        Type: PositiveInteger
--E 4
)spool
 
Starts dribbling to cwmmt.output (2010/3/27, 18:24:39).
)sys cp $AXIOM/../../src/input/cwmmt.input.pamphlet .
 
)lisp (tangle "cwmmt.input.pamphlet" "cwmmt.spad" "cwmmt.spad" )
 
Value = NIL
)co cwmmt.spad
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/cwmmt.spad using
      old system compiler.
   CWMMT abbreviates domain CompWithMappingModeTest 
------------------------------------------------------------------------
   initializing nrlib CWMMT for CompWithMappingModeTest 
   compiling into nrlib CWMMT 
   processing macro definition REC ==> Record(field1: Integer,field2: String) 
   processing macro definition UN ==> Union(rec: Record(field1: Integer,field2: String),str: String) 
   compiling local mapper : (Integer -> Boolean,Integer) -> Boolean
      CWMMT;mapper is replaced by SPADCALLnfn 
Time: 0 SEC.

   compiling local pred : (Integer,Integer) -> Boolean
Time: 0 SEC.

   compiling local test1 : Integer -> Boolean
Time: 0 SEC.

   compiling local test2 : Integer -> Boolean
Time: 0.01 SEC.

   compiling local test3 : Integer -> Boolean
Time: 0.01 SEC.

   compiling local test4 : Integer -> Boolean
Time: 0.02 SEC.

   compiling local test5 : Integer -> Boolean
Time: 0 SEC.

   compiling local test6 : Integer -> Boolean
Time: 0.01 SEC.

   compiling local test7 : Integer -> Boolean
Time: 0 SEC.

   compiling local test8 : Integer -> Boolean
Time: 0.01 SEC.

   compiling local test9 : Integer -> Boolean
Time: 0 SEC.

   compiling local test10 : Integer -> Boolean
Time: 0 SEC.

   compiling exported runTests : () -> Boolean
Time: 0.01 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |CompWithMappingModeTest| REDEFINED

;;;     ***       |CompWithMappingModeTest| REDEFINED
Time: 0 SEC.

 
   Warnings: 
      [1] test6:  rec has no value
      [2] test7:  rec has no value
      [3] test8:  rec has no value
      [4] test9:  rec has no value
      [5] test10:  rec has no value
 

   Cumulative Statistics for Constructor CompWithMappingModeTest
      Time: 0.07 seconds
 
   finalizing nrlib CWMMT 
   Processing CompWithMappingModeTest for Browser database:
--->-->CompWithMappingModeTest((runTests ((Boolean)))): Not documented!!!!
--->-->CompWithMappingModeTest(constructor): Not documented!!!!
--->-->CompWithMappingModeTest(): Missing Description
------------------------------------------------------------------------
   CompWithMappingModeTest is now explicitly exposed in frame initial 
   CompWithMappingModeTest will be automatically loaded when needed 
      from 
      /home/camm/debian/axiom/axiom-20091101/int/input/CWMMT.nrlib/code

)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 1
runTests()
 

   (1)  true
                                                                Type: Boolean
--R
--R   (1)  true
--R                                                                Type: Boolean
--E 1
)spool 
 
Starts dribbling to patmatch.output (2010/3/27, 18:30:40).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
p := 3 * n ** 2 + 1
 

          2
   (1)  3n  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (1)  3n  + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 22
q := 3 * n% ** 2 + 1
 

           2
   (2)  3n%  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R           2
--R   (2)  3n%  + 1
--R                                                     Type: Polynomial Integer
--E 2

--S 3 of 22
a := roman 49
 

   (3)  XLIX
                                                           Type: RomanNumeral
--R 
--R
--R   (3)  XLIX
--R                                                           Type: RomanNumeral
--E 3

--S 4 of 22
b := roman IV
 

   (4)  IV
                                                           Type: RomanNumeral
--R 
--R
--R   (4)  IV
--R                                                           Type: RomanNumeral
--E 4

--S 5 of 22
c := a - 1
 

   (5)  XLVIII
                                                           Type: RomanNumeral
--R 
--R
--R   (5)  XLVIII
--R                                                           Type: RomanNumeral
--E 5

--S 6 of 22
Is(a, p)
 

   (6)  [n= IV]
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (6)  [n= IV]
--R                                  Type: List Equation Polynomial RomanNumeral
--E 6

--S 7 of 22
Is(a, q)
 

   (7)  [n%= IV]
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (7)  [n%= IV]
--R                                  Type: List Equation Polynomial RomanNumeral
--E 7

--S 8 of 22
Is(b, p)
 

   (8)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (8)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 8

--S 9 of 22
Is(b, q)
 

   (9)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (9)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 9

--S 10 of 22
Is(c, p)
 

   (10)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (10)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 10

--S 11 of 22
Is(c, q)
 

   (11)  []
                                  Type: List Equation Polynomial RomanNumeral
--R 
--R
--R   (11)  []
--R                                  Type: List Equation Polynomial RomanNumeral
--E 11

--S 12 of 22
ab := a / b
 

         XLIX
   (12)  ----
          IV
                                                  Type: Fraction RomanNumeral
--R 
--R
--R         XLIX
--R   (12)  ----
--R          IV
--R                                                  Type: Fraction RomanNumeral
--E 12

--S 13 of 22
pq := p / q
 

            2
          3n  + 1
   (13)  --------
            2
         3n%  + 1
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            2
--R          3n  + 1
--R   (13)  --------
--R            2
--R         3n%  + 1
--R                                            Type: Fraction Polynomial Integer
--E 13

--S 14 of 22
Is(ab, pq)
 

   (14)  []
                         Type: List Equation Polynomial Fraction RomanNumeral
--R 
--R
--R   (14)  []
--R                         Type: List Equation Polynomial Fraction RomanNumeral
--E 14

--S 15 of 22
ab := rational ab
 

         49
   (15)  --
          4
                                                       Type: Fraction Integer
--R 
--R
--R         49
--R   (15)  --
--R          4
--R                                                       Type: Fraction Integer
--E 15

--S 16 of 22
a  := rational a
 

   (16)  49
                                                       Type: Fraction Integer
--R 
--R
--R   (16)  49
--R                                                       Type: Fraction Integer
--E 16

--Is([ab, a], [pq, _:l, p])
--Is([ab, a], [pq, _:l%, p])
--Is([ab, 1, 2, a], [pq, _:l, p])
-- foo?(x:LIST FRAC INT):BOOLEAN == odd? _# x
-- qq := suchThat(_:l%, foo?)
-- Is([ab, 1, 2, a], [pq, qq, p])
-- Is([ab, 1, 2, 3, a], [pq, qq, p])
-- creating streams using pattern matching
-- want the streams of all primes of the form m**2+1

--S 17 of 22
bar?(n:INT):BOOLEAN == prime? n and is?(n, m**2 + 1)
 
   Function declaration bar? : Integer -> Boolean has been added to 
      workspace.
                                                                   Type: Void
--R 
--R   Function declaration bar? : Integer -> Boolean has been added to 
--R      workspace.
--R                                                                   Type: Void
--E 17

--S 18 of 22
myprimes := [i for i in 1.. | bar? i]
 
   Compiling function bar? with type Integer -> Boolean 

   (18)  [5,17,37,101,197,257,401,577,677,1297,...]
                                                 Type: Stream PositiveInteger
--R 
--R   Compiling function bar? with type Integer -> Boolean 
--R
--R   (18)  [5,17,37,101,197,257,401,577,677,1297,...]
--R                                                 Type: Stream PositiveInteger
--E 18

--S 19 of 22
p := x**2 + 3*x + 1
 

          2
   (19)  x  + 3x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          2
--R   (19)  x  + 3x + 1
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 22
Is(p, n * y**2 + (2*n+1)*y + 1)
 

   (20)  []
                                       Type: List Equation Polynomial Integer
--R 
--R
--R   (20)  []
--R                                       Type: List Equation Polynomial Integer
--E 20

--S 21 of 22
Is(p, n% * y**2 + (2*n%+1)*y + 1)
 

   (21)  []
                                       Type: List Equation Polynomial Integer
--R 
--R
--R   (21)  []
--R                                       Type: List Equation Polynomial Integer
--E 21

--S 22 of 22
Is(3*x**2 + 9*x + 1, n * y**2 + n**2 * y + 1)
 

   (22)  [n= x,y= 3]
                                       Type: List Equation Polynomial Integer
--R 
--R
--R   (22)  [n= x,y= 3]
--R                                       Type: List Equation Polynomial Integer
--E 22
)spool 
 
Starts dribbling to solveperf.output (2010/3/27, 18:40:46).
)set message test on
 
)set message auto off
 
)clear all
 
 
)set mes time on
 

--S 1 of 9
list:=[p,Vr,Vt,e]
 

   (1)  [p,Vr,Vt,e]
                                   Type: List OrderedVariableList [p,Vr,Vt,e]
                                       Time: 0.04 (OT) + 0.01 (GC) = 0.05 sec
--R 
--R
--R   (1)  [p,Vr,Vt,e]
--R                                   Type: List OrderedVariableList [p,Vr,Vt,e]
--I                                                   Time: 0.04 (OT) = 0.04 sec
--E 1

--S 2 of 9
eq1a:=((-Vr^3+Vr^2)*Vt+Vr^3-Vr^2)
 

             3     2        3     2
   (2)  (- Vr  + Vr )Vt + Vr  - Vr
                                                     Type: Polynomial Integer
                                                   Time: 0.03 (OT) = 0.03 sec
--R 
--R
--R             3     2        3     2
--R   (2)  (- Vr  + Vr )Vt + Vr  - Vr
--R                                                     Type: Polynomial Integer
--I                           Time: 0.02 (EV) + 0.04 (OT) + 0.02 (GC) = 0.08 sec
--E 2

--S 3 of 9
eq1:=((-Vr^3+Vr^2)*Vt+Vr^3-Vr^2)*R*p
 

                3       2          3       2
   (3)  ((- R Vr  + R Vr )Vt + R Vr  - R Vr )p
                                                     Type: Polynomial Integer
                                                                  Time: 0 sec
--R 
--R
--R                3       2          3       2
--R   (3)  ((- R Vr  + R Vr )Vt + R Vr  - R Vr )p
--R                                                     Type: Polynomial Integer
--I                                                                  Time: 0 sec
--E 3

--S 4 of 9
eq2:=Vr*Vt^3+Vr*Vt^2-Vr*Vt+Vr*p
 

                    3        2
   (4)  Vr p + Vr Vt  + Vr Vt  - Vr Vt
                                                     Type: Polynomial Integer
                                       Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec
--R 
--R
--R                    3        2
--R   (4)  Vr p + Vr Vt  + Vr Vt  - Vr Vt
--R                                                     Type: Polynomial Integer
--I                                                   Time: 0.02 (IN) = 0.02 sec
--E 4

--S 5 of 9
eq3:=(R*Vr*Vt+R*Vr)*e+((R-1)*Vr+1)*Vt-R*Vr
 

   (5)  (R Vr Vt + R Vr)e + ((R - 1)Vr + 1)Vt - R Vr
                                                     Type: Polynomial Integer
                                       Time: 0.02 (IN) + 0.02 (GC) = 0.04 sec
--R 
--R
--R   (5)  (R Vr Vt + R Vr)e + ((R - 1)Vr + 1)Vt - R Vr
--R                                                     Type: Polynomial Integer
--I                                                   Time: 0.01 (OT) = 0.01 sec
--E 5

--S 6 of 9
eq4:=-r^2+(Vt^2)+(Vr^2)
 

           2     2     2
   (6)  - r  + Vt  + Vr
                                                     Type: Polynomial Integer
                                                                  Time: 0 sec
--R 
--R
--R           2     2     2
--R   (6)  - r  + Vt  + Vr
--R                                                     Type: Polynomial Integer
--I                                                                  Time: 0 sec
--E 6

--S 7 of 9
Eqlista:=[eq1a,eq2,eq3,eq4]
 

   (7)
         3     2        3     2              3        2
   [(- Vr  + Vr )Vt + Vr  - Vr , Vr p + Vr Vt  + Vr Vt  - Vr Vt,
                                                     2     2     2
    (R Vr Vt + R Vr)e + ((R - 1)Vr + 1)Vt - R Vr, - r  + Vt  + Vr ]
                                                Type: List Polynomial Integer
                                                                  Time: 0 sec
--R 
--R
--R   (7)
--R         3     2        3     2              3        2
--R   [(- Vr  + Vr )Vt + Vr  - Vr , Vr p + Vr Vt  + Vr Vt  - Vr Vt,
--R                                                     2     2     2
--R    (R Vr Vt + R Vr)e + ((R - 1)Vr + 1)Vt - R Vr, - r  + Vt  + Vr ]
--R                                                Type: List Polynomial Integer
--I                                                                  Time: 0 sec
--E 7

--S 8 of 9
Eqlist:=[eq1,eq2,eq3,eq4]
 

   (8)
            3       2          3       2                3        2
   [((- R Vr  + R Vr )Vt + R Vr  - R Vr )p, Vr p + Vr Vt  + Vr Vt  - Vr Vt,
                                                     2     2     2
    (R Vr Vt + R Vr)e + ((R - 1)Vr + 1)Vt - R Vr, - r  + Vt  + Vr ]
                                                Type: List Polynomial Integer
                                                                  Time: 0 sec
--R 
--R
--R   (8)
--R            3       2          3       2                3        2
--R   [((- R Vr  + R Vr )Vt + R Vr  - R Vr )p, Vr p + Vr Vt  + Vr Vt  - Vr Vt,
--R                                                     2     2     2
--R    (R Vr Vt + R Vr)e + ((R - 1)Vr + 1)Vt - R Vr, - r  + Vt  + Vr ]
--R                                                Type: List Polynomial Integer
--I                                                                  Time: 0 sec
--E 8

--S 9 of 9
solve(Eqlista,list)
 

   (9)
   [
                   4       2                              2
         (- e - 1)r  + 4e r  - 4e + 2             (e + 1)r  - 2e
     [p= ----------------------------, Vr= 1, Vt= --------------,
                       2                                 2
        2           2     2
      (e  + 2e + 1)r  - 2e  - 2= 0]
     ,

                               2
     [p= - 1, Vr= (- 2R e + 1)r  + 2R e - 1, Vt= 1,
         2 2             2     2 2
      (4R e  - 4R e + 1)r  - 4R e  + 4R e - 2= 0]
     ]
                         Type: List List Equation Fraction Polynomial Integer
               Time: 0.03 (IN) + 1.34 (EV) + 0.14 (OT) + 0.18 (GC) = 1.69 sec
--R 
--R
--R   (9)
--R   [
--R                   4       2                              2
--R         (- e - 1)r  + 4e r  - 4e + 2             (e + 1)r  - 2e
--R     [p= ----------------------------, Vr= 1, Vt= --------------,
--R                       2                                 2
--R        2           2     2
--R      (e  + 2e + 1)r  - 2e  - 2= 0]
--R     ,
--R
--R                               2
--R     [p= - 1, Vr= (- 2R e + 1)r  + 2R e - 1, Vt= 1,
--R         2 2             2     2 2
--R      (4R e  - 4R e + 1)r  - 4R e  + 4R e - 2= 0]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--I               Time: 0.02 (IN) + 0.87 (EV) + 0.07 (OT) + 0.11 (GC) = 1.07 sec
--E 9

-- This takes a long time. Figure out why.
--
--solve(Eqlist,list)
--

 
)spool 
 
Starts dribbling to schaum28.output (2010/3/27, 18:38:37).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 139
aa:=integrate(cosh(a*x),x)
 

        sinh(a x)
   (1)  ---------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sinh(a x)
--R   (1)  ---------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 139
bb:=sinh(a*x)/a
 

        sinh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        sinh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 3 of 139      14:562 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 139
aa:=integrate(x*cosh(a*x),x)
 

        a x sinh(a x) - cosh(a x)
   (1)  -------------------------
                     2
                    a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a x sinh(a x) - cosh(a x)
--R   (1)  -------------------------
--R                     2
--R                    a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 139
bb:=(x*sinh(a*x))/a-cosh(a*x)/a^2
 

        a x sinh(a x) - cosh(a x)
   (2)  -------------------------
                     2
                    a
                                                     Type: Expression Integer
--R
--R        a x sinh(a x) - cosh(a x)
--R   (2)  -------------------------
--R                     2
--R                    a
--R                                                     Type: Expression Integer
--E

--S 6 of 139      14:563 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 139
aa:=integrate(x^2*cosh(a*x),x)
 

          2 2
        (a x  + 2)sinh(a x) - 2a x cosh(a x)
   (1)  ------------------------------------
                          3
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2 2
--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
--R   (1)  ------------------------------------
--R                          3
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 139
bb:=-(2*x*cosh(a*x))/a^2+(x^2/a+2/a^3)*sinh(a*x)
 

          2 2
        (a x  + 2)sinh(a x) - 2a x cosh(a x)
   (2)  ------------------------------------
                          3
                         a
                                                     Type: Expression Integer
--R
--R          2 2
--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
--R   (2)  ------------------------------------
--R                          3
--R                         a
--R                                                     Type: Expression Integer
--E

--S 9 of 139      14:564 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 139     14:565 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)/x,x)
 

           x
         ++  cosh(%N a)
   (1)   |   ---------- d%N
        ++       %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cosh(%N a)
--I   (1)   |   ---------- d%N
--I        ++       %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 11 of 139     14:566 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)/x^2,x)
 

           x
         ++  cosh(%N a)
   (1)   |   ---------- d%N
        ++         2
                 %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cosh(%N a)
--I   (1)   |   ---------- d%N
--R        ++         2
--I                 %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 12 of 139
aa:=integrate(1/cosh(a*x),x)
 

        2atan(sinh(a x) + cosh(a x))
   (1)  ----------------------------
                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        2atan(sinh(a x) + cosh(a x))
--R   (1)  ----------------------------
--R                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 13 of 139
bb:=2/a*atan(%e^(a*x))
 

                a x
        2atan(%e   )
   (2)  ------------
              a
                                                     Type: Expression Integer
--R
--R                a x
--R        2atan(%e   )
--R   (2)  ------------
--R              a
--R                                                     Type: Expression Integer
--E

--S 14 of 139
cc:=aa-bb
 

                                               a x
        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
   (3)  -------------------------------------------
                             a
                                                     Type: Expression Integer
--R
--R                                               a x
--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
--R   (3)  -------------------------------------------
--R                             a
--R                                                     Type: Expression Integer
--E

--S 15 of 139     14:567 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 16 of 139     14:568 Axiom cannot compute this integral
aa:=integrate(x/cosh(a*x),x)
 

           x
         ++      %N
   (1)   |   ---------- d%N
        ++   cosh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %N
--I   (1)   |   ---------- d%N
--I        ++   cosh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 17 of 139
aa:=integrate(cosh(a*x)^2,x)
 

        cosh(a x)sinh(a x) + a x
   (1)  ------------------------
                   2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cosh(a x)sinh(a x) + a x
--R   (1)  ------------------------
--R                   2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 18 of 139
bb:=x/2+(sinh(a*x)*cosh(a*x))/(2*a)
 

        cosh(a x)sinh(a x) + a x
   (2)  ------------------------
                   2a
                                                     Type: Expression Integer
--R
--R        cosh(a x)sinh(a x) + a x
--R   (2)  ------------------------
--R                   2a
--R                                                     Type: Expression Integer
--E

--S 19 of 139     14:569 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 20 of 139
aa:=integrate(x*cosh(a*x)^2,x)
 

                   2                                      2     2 2
        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  + 2a x
   (1)  -----------------------------------------------------------
                                      2
                                    8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                   2                                      2     2 2
--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  + 2a x
--R   (1)  -----------------------------------------------------------
--R                                      2
--R                                    8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 21 of 139
bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)
 

                                         2 2
        2a x sinh(2a x) - cosh(2a x) + 2a x
   (2)  ------------------------------------
                           2
                         8a
                                                     Type: Expression Integer
--R
--R                                         2 2
--R        2a x sinh(2a x) - cosh(2a x) + 2a x
--R   (2)  ------------------------------------
--R                           2
--R                         8a
--R                                                     Type: Expression Integer
--E

--S 22 of 139
cc:=aa-bb
 

   (3)
                                    2
       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
     + 
                  2
       - cosh(a x)
  /
       2
     8a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                    2
--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
--R     + 
--R                  2
--R       - cosh(a x)
--R  /
--R       2
--R     8a
--R                                                     Type: Expression Integer
--E

--S 23 of 139
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 24 of 139
dd:=sinhsqrrule cc
 

   (5)
                                                                        2
   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
   --------------------------------------------------------------------------
                                         2
                                      16a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                                        2
--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
--R   --------------------------------------------------------------------------
--R                                         2
--R                                      16a
--R                                                     Type: Expression Integer
--E

--S 25 of 139
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26 of 139
ee:=coshsqrrule dd
 

        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
   (7)  --------------------------------------
                          4a
                                                     Type: Expression Integer
--R
--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
--R   (7)  --------------------------------------
--R                          4a
--R                                                     Type: Expression Integer
--E

--S 27 of 139
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (8)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %S sinh(y + x) - %S sinh(y - x)
--I   (8)  %S cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 28 of 139     14:570 Schaums and Axiom agree
ff:=sinhcoshrule ee
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 29 of 139
aa:=integrate(1/cosh(a*x)^2,x)
 

                                     2
   (1)  - -------------------------------------------------------
                     2                                      2
          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                     2
--R   (1)  - -------------------------------------------------------
--R                     2                                      2
--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 30 of 139
bb:=tanh(a*x)/a
 

        tanh(a x)
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R        tanh(a x)
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 31 of 139
cc:=aa-bb
 

                    2                                  2
        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
   (3)  ------------------------------------------------------------------
                         2                                      2
              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R                    2                                  2
--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
--R   (3)  ------------------------------------------------------------------
--R                         2                                      2
--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 32 of 139     14:571 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

          1
   (4)  - -
          a
                                                     Type: Expression Integer
--R
--R          1
--R   (4)  - -
--R          a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 33  of 139
aa:=integrate(cosh(a*x)*cosh(p*x),x)
 

        - p cosh(a x)sinh(p x) + a cosh(p x)sinh(a x)
   (1)  ---------------------------------------------
           2    2          2       2    2          2
         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - p cosh(a x)sinh(p x) + a cosh(p x)sinh(a x)
--R   (1)  ---------------------------------------------
--R           2    2          2       2    2          2
--R         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 34 of 139
bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p))
 

        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
   (2)  -------------------------------------------
                           2     2
                         2p  - 2a
                                                     Type: Expression Integer
--R
--R        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
--R   (2)  -------------------------------------------
--R                           2     2
--R                         2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 35 of 139
cc:=aa-bb
 

   (3)
       - 2p cosh(a x)sinh(p x)
     + 
                                                                 2
       ((- p + a)x sinh(p + a) + (- p - a)x sinh(p - a))sinh(a x)
     + 
                                                 2
       2a cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
     + 
                         2
       (p + a)x cosh(a x) sinh(p - a)
  /
        2     2          2        2     2          2
     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R       - 2p cosh(a x)sinh(p x)
--R     + 
--R                                                                 2
--R       ((- p + a)x sinh(p + a) + (- p - a)x sinh(p - a))sinh(a x)
--R     + 
--R                                                 2
--R       2a cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
--R     + 
--R                         2
--R       (p + a)x cosh(a x) sinh(p - a)
--R  /
--R        2     2          2        2     2          2
--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 36 of 139
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37 of 139
dd:=sinhsqrrule cc
 

   (5)
       - 4p cosh(a x)sinh(p x) + 4a cosh(p x)sinh(a x)
     + 
                                                    2
       ((- p + a)x cosh(2a x) + (2p - 2a)x cosh(a x)  + (p - a)x)sinh(p + a)
     + 
                                                    2
       ((- p - a)x cosh(2a x) + (2p + 2a)x cosh(a x)  + (p + a)x)sinh(p - a)
  /
        2     2                   2     2          2     2     2
     (2p  - 2a )cosh(2a x) + (- 4p  + 4a )cosh(a x)  - 2p  + 2a
                                                     Type: Expression Integer
--R
--R   (5)
--R       - 4p cosh(a x)sinh(p x) + 4a cosh(p x)sinh(a x)
--R     + 
--R                                                    2
--R       ((- p + a)x cosh(2a x) + (2p - 2a)x cosh(a x)  + (p - a)x)sinh(p + a)
--R     + 
--R                                                    2
--R       ((- p - a)x cosh(2a x) + (2p + 2a)x cosh(a x)  + (p + a)x)sinh(p - a)
--R  /
--R        2     2                   2     2          2     2     2
--R     (2p  - 2a )cosh(2a x) + (- 4p  + 4a )cosh(a x)  - 2p  + 2a
--R                                                     Type: Expression Integer
--E

--S 38 of 139
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 39 of 139
ee:=coshsqrrule dd
 

   (7)
       2p cosh(a x)sinh(p x) - 2a cosh(p x)sinh(a x) + (- p + a)x sinh(p + a)
     + 
       (- p - a)x sinh(p - a)
  /
       2     2
     2p  - 2a
                                                     Type: Expression Integer
--R
--R   (7)
--R       2p cosh(a x)sinh(p x) - 2a cosh(p x)sinh(a x) + (- p + a)x sinh(p + a)
--R     + 
--R       (- p - a)x sinh(p - a)
--R  /
--R       2     2
--R     2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 40 of 139
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %Q sinh(y + x) - %Q sinh(y - x)
   (8)  %Q cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %V sinh(y + x) - %V sinh(y - x)
--I   (8)  %V cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 41 of 139     14:572 Axiom cannot simplify this expression
ff:=sinhcoshrule ee
 

   (9)
       (p - a)sinh((p + a)x) + (p + a)sinh((p - a)x) + (- p + a)x sinh(p + a)
     + 
       (- p - a)x sinh(p - a)
  /
       2     2
     2p  - 2a
                                                     Type: Expression Integer
--R
--R   (9)
--R       (p - a)sinh((p + a)x) + (p + a)sinh((p - a)x) + (- p + a)x sinh(p + a)
--R     + 
--R       (- p - a)x sinh(p - a)
--R  /
--R       2     2
--R     2p  - 2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 42 of 139
aa:=integrate(cosh(a*x)*sin(p*x),x)
 

   (1)
                                         2
       (a sin(p x) - p cos(p x))sinh(a x)
     + 
       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (a cosh(a x)  - a)sin(p x) - p cos(p x)cosh(a x)  - p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (a sin(p x) - p cos(p x))sinh(a x)
--R     + 
--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (a cosh(a x)  - a)sin(p x) - p cos(p x)cosh(a x)  - p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 43 of 139
bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2)
 

        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
   (2)  -----------------------------------------
                          2    2
                         p  + a
                                                     Type: Expression Integer
--R
--R        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
--R   (2)  -----------------------------------------
--R                          2    2
--R                         p  + a
--R                                                     Type: Expression Integer
--E

--S 44 of 139
cc:=aa-bb
 

   (3)
                                           2               2
       (- a sin(p x) - p cos(p x))sinh(a x)  + (a cosh(a x)  - a)sin(p x)
     + 
                          2
       p cos(p x)cosh(a x)  - p cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                           2               2
--R       (- a sin(p x) - p cos(p x))sinh(a x)  + (a cosh(a x)  - a)sin(p x)
--R     + 
--R                          2
--R       p cos(p x)cosh(a x)  - p cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 45 of 139
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (4)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (4)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 46 of 139
dd:=coshsqrrule cc
 

   (5)
                                             2
       (- 2a sin(p x) - 2p cos(p x))sinh(a x)  + (a cosh(2a x) - a)sin(p x)
     + 
       p cos(p x)cosh(2a x) - p cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                             2
--R       (- 2a sin(p x) - 2p cos(p x))sinh(a x)  + (a cosh(2a x) - a)sin(p x)
--R     + 
--R       p cos(p x)cosh(2a x) - p cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 47 of 139
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 48 of 139     14:573 Schaums and Axiom agree
ee:=sinhsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 49 of 139
aa:=integrate(cosh(a*x)*cos(p*x),x)
 

   (1)
                                         2
       (p sin(p x) + a cos(p x))sinh(a x)
     + 
       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
     + 
                   2                                   2
       (p cosh(a x)  + p)sin(p x) + a cos(p x)cosh(a x)  - a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                         2
--R       (p sin(p x) + a cos(p x))sinh(a x)
--R     + 
--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
--R     + 
--R                   2                                   2
--R       (p cosh(a x)  + p)sin(p x) + a cos(p x)cosh(a x)  - a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50 of 139
bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2)
 

        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
   (2)  -----------------------------------------
                          2    2
                         p  + a
                                                     Type: Expression Integer
--R
--R        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
--R   (2)  -----------------------------------------
--R                          2    2
--R                         p  + a
--R                                                     Type: Expression Integer
--E

--S 51 of 139
cc:=aa-bb
 

   (3)
                                         2                 2
       (p sin(p x) - a cos(p x))sinh(a x)  + (- p cosh(a x)  + p)sin(p x)
     + 
                          2
       a cos(p x)cosh(a x)  - a cos(p x)
  /
        2     2                2     2
     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                                         2                 2
--R       (p sin(p x) - a cos(p x))sinh(a x)  + (- p cosh(a x)  + p)sin(p x)
--R     + 
--R                          2
--R       a cos(p x)cosh(a x)  - a cos(p x)
--R  /
--R        2     2                2     2
--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 52 of 139
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (4)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (4)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 53 of 139
dd:=coshsqrrule cc
 

   (5)
                                           2
       (2p sin(p x) - 2a cos(p x))sinh(a x)  + (- p cosh(2a x) + p)sin(p x)
     + 
       a cos(p x)cosh(2a x) - a cos(p x)
  /
        2     2                2     2
     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
                                                     Type: Expression Integer
--R
--R   (5)
--R                                           2
--R       (2p sin(p x) - 2a cos(p x))sinh(a x)  + (- p cosh(2a x) + p)sin(p x)
--R     + 
--R       a cos(p x)cosh(2a x) - a cos(p x)
--R  /
--R        2     2                2     2
--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 54 of 139
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (6)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (6)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 55 of 139     14:574 Schaums and Axiom agree
ee:=sinhsqrrule dd
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 56 of 139
aa:=integrate(1/(cosh(a*x)+1),x)
 

                        2
   (1)  - -----------------------------
          a sinh(a x) + a cosh(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2
--R   (1)  - -----------------------------
--R          a sinh(a x) + a cosh(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 57 of 139
bb:=1/a*tanh((a*x)/2)
 

             a x
        tanh(---)
              2
   (2)  ---------
            a
                                                     Type: Expression Integer
--R
--R             a x
--R        tanh(---)
--R              2
--R   (2)  ---------
--R            a
--R                                                     Type: Expression Integer
--E

--S 58 of 139
cc:=aa-bb
 

                                          a x
        (- sinh(a x) - cosh(a x) - 1)tanh(---) - 2
                                           2
   (3)  ------------------------------------------
               a sinh(a x) + a cosh(a x) + a
                                                     Type: Expression Integer
--R
--R                                          a x
--R        (- sinh(a x) - cosh(a x) - 1)tanh(---) - 2
--R                                           2
--R   (3)  ------------------------------------------
--R               a sinh(a x) + a cosh(a x) + a
--R                                                     Type: Expression Integer
--E

--S 59 of 139
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 60 of 139
dd:=tanhrule cc
 

               a x                                   a x          a x
        - sinh(---)sinh(a x) + (- cosh(a x) - 1)sinh(---) - 2cosh(---)
                2                                     2            2
   (5)  --------------------------------------------------------------
                  a x                    a x                    a x
           a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
                   2                      2                      2
                                                     Type: Expression Integer
--R
--R               a x                                   a x          a x
--R        - sinh(---)sinh(a x) + (- cosh(a x) - 1)sinh(---) - 2cosh(---)
--R                2                                     2            2
--R   (5)  --------------------------------------------------------------
--R                  a x                    a x                    a x
--R           a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
--R                   2                      2                      2
--R                                                     Type: Expression Integer
--E

--S 61 of 139
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BB sinh(y + x) - %BB sinh(y - x)
   (6)  %BB cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BC sinh(y + x) - %BC sinh(y - x)
--I   (6)  %BC cosh(y)sinh(x) == -------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 62 of 139
ee:=sinhcoshrule dd
 

                  3a x          a x                  a x          a x
           - sinh(----) - 2sinh(---)sinh(a x) - sinh(---) - 4cosh(---)
                    2            2                    2            2
   (7)  -----------------------------------------------------------------
               3a x           a x            a x                     a x
        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
                 2             2              2                       2
                                                     Type: Expression Integer
--R
--R                  3a x          a x                  a x          a x
--R           - sinh(----) - 2sinh(---)sinh(a x) - sinh(---) - 4cosh(---)
--R                    2            2                    2            2
--R   (7)  -----------------------------------------------------------------
--R               3a x           a x            a x                     a x
--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
--R                 2             2              2                       2
--R                                                     Type: Expression Integer
--E

--S 63 of 139
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %BC cosh(y + x) - %BC cosh(y - x)
   (8)  %BC sinh(x)sinh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BD sinh(y + x) - %BD sinh(y - x)
--I   (8)  %BD cosh(y)sinh(x) == -------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 64 of 139
ff:=sinhsinhrule ee
 

                       3a x         a x         3a x          a x
                - sinh(----) - sinh(---) - cosh(----) - 3cosh(---)
                         2           2            2            2
   (9)  -----------------------------------------------------------------
               3a x           a x            a x                     a x
        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
                 2             2              2                       2
                                                     Type: Expression Integer
--R
--R                       3a x         a x         3a x          a x
--R                - sinh(----) - sinh(---) - cosh(----) - 3cosh(---)
--R                         2           2            2            2
--R   (9)  -----------------------------------------------------------------
--R               3a x           a x            a x                     a x
--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
--R                 2             2              2                       2
--R                                                     Type: Expression Integer
--E

--S 65 of 139
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                               %BD cosh(y + x) + %BD cosh(y - x)
   (10)  %BD cosh(x)cosh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BC cosh(y + x) + %BC cosh(y - x)
--I   (10)  %BC cosh(x)cosh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 66 of 139     14:575 Schaums and Axiom differ by a constant
gg:=coshcoshrule ff
 

           1
   (11)  - -
           a
                                                     Type: Expression Integer
--R
--R           1
--R   (11)  - -
--R           a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 67 of 139
aa:=integrate(1/(cosh(a*x)-1),x)
 

                        2
   (1)  - -----------------------------
          a sinh(a x) + a cosh(a x) - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2
--R   (1)  - -----------------------------
--R          a sinh(a x) + a cosh(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 68 of 139
bb:=-1/a*coth((a*x)/2)
 

               a x
          coth(---)
                2
   (2)  - ---------
              a
                                                     Type: Expression Integer
--R
--R               a x
--R          coth(---)
--R                2
--R   (2)  - ---------
--R              a
--R                                                     Type: Expression Integer
--E

--S 69 of 139
cc:=aa-bb
 

             a x                                 a x
        coth(---)sinh(a x) + (cosh(a x) - 1)coth(---) - 2
              2                                   2
   (3)  -------------------------------------------------
                  a sinh(a x) + a cosh(a x) - a
                                                     Type: Expression Integer
--R
--R             a x                                 a x
--R        coth(---)sinh(a x) + (cosh(a x) - 1)coth(---) - 2
--R              2                                   2
--R   (3)  -------------------------------------------------
--R                  a sinh(a x) + a cosh(a x) - a
--R                                                     Type: Expression Integer
--E

--S 70 of 139
cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 

                   cosh(x)
   (4)  coth(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   cosh(x)
--R   (4)  coth(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 71 of 139
dd:=cothrule cc
 

             a x                   a x         a x                  a x
        cosh(---)sinh(a x) - 2sinh(---) + cosh(---)cosh(a x) - cosh(---)
              2                     2           2                    2
   (5)  ----------------------------------------------------------------
                       a x                                   a x
                a sinh(---)sinh(a x) + (a cosh(a x) - a)sinh(---)
                        2                                     2
                                                     Type: Expression Integer
--R
--R             a x                   a x         a x                  a x
--R        cosh(---)sinh(a x) - 2sinh(---) + cosh(---)cosh(a x) - cosh(---)
--R              2                     2           2                    2
--R   (5)  ----------------------------------------------------------------
--R                       a x                                   a x
--R                a sinh(---)sinh(a x) + (a cosh(a x) - a)sinh(---)
--R                        2                                     2
--R                                                     Type: Expression Integer
--E

--S 72 of 139
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BE sinh(y + x) - %BE sinh(y - x)
   (6)  %BE cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BD sinh(y + x) - %BD sinh(y - x)
--I   (6)  %BD cosh(y)sinh(x) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 73 of 139
ee:=sinhcoshrule dd
 

             3a x          a x          a x                   a x
        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
               2            2            2                     2
   (7)  ----------------------------------------------------------
                   3a x            a x                     a x
            a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
                     2              2                       2
                                                     Type: Expression Integer
--R
--R             3a x          a x          a x                   a x
--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
--R               2            2            2                     2
--R   (7)  ----------------------------------------------------------
--R                   3a x            a x                     a x
--R            a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
--R                     2              2                       2
--R                                                     Type: Expression Integer
--E

--S 74 of 139
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %BF cosh(y + x) - %BF cosh(y - x)
   (8)  %BF sinh(x)sinh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BE cosh(y + x) - %BE cosh(y - x)
--I   (8)  %BE sinh(x)sinh(y) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 75 of 139
ff:=sinhsinhrule ee
 

             3a x          a x          a x                   a x
        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
               2            2            2                     2
   (9)  ----------------------------------------------------------
                3a x            a x           3a x           a x
         a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
                  2              2              2             2
                                                     Type: Expression Integer
--R
--R             3a x          a x          a x                   a x
--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
--R               2            2            2                     2
--R   (9)  ----------------------------------------------------------
--R                3a x            a x           3a x           a x
--R         a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
--R                  2              2              2             2
--R                                                     Type: Expression Integer
--E

--S 76 of 139
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                               %BG cosh(y + x) + %BG cosh(y - x)
   (10)  %BG cosh(x)cosh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BF cosh(y + x) + %BF cosh(y - x)
--I   (10)  %BF cosh(x)cosh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 77 of 139     14:576 Schaums and Axiom differ by a constant
gg:=coshcoshrule ff
 

         1
   (11)  -
         a
                                                     Type: Expression Integer
--R
--R         1
--R   (11)  -
--R         a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 78 of 139
aa:=integrate(x/(cosh(a*x)+1),x)
 

   (1)
       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
     + 
       2a x sinh(a x) + 2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R       2a x sinh(a x) + 2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 79 of 139
bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2))
 

                    a x              a x
        - 2log(cosh(---)) + a x tanh(---)
                     2                2
   (2)  ---------------------------------
                         2
                        a
                                                     Type: Expression Integer
--R
--R                    a x              a x
--R        - 2log(cosh(---)) + a x tanh(---)
--R                     2                2
--R   (2)  ---------------------------------
--R                         2
--R                        a
--R                                                     Type: Expression Integer
--E

--S 80 of 139
cc:=aa-bb
 

   (3)
       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
     + 
                                             a x
       (2sinh(a x) + 2cosh(a x) + 2)log(cosh(---))
                                              2
     + 
                                                   a x
       (- a x sinh(a x) - a x cosh(a x) - a x)tanh(---) + 2a x sinh(a x)
                                                    2
     + 
       2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) + a
                                                     Type: Expression Integer
--R
--R   (3)
--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R                                             a x
--R       (2sinh(a x) + 2cosh(a x) + 2)log(cosh(---))
--R                                              2
--R     + 
--R                                                   a x
--R       (- a x sinh(a x) - a x cosh(a x) - a x)tanh(---) + 2a x sinh(a x)
--R                                                    2
--R     + 
--R       2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) + a
--R                                                     Type: Expression Integer
--E

--S 81 of 139
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 82 of 139
dd:=tanhrule cc
 

   (5)
                  a x                   a x                   a x
         (- 2cosh(---)sinh(a x) - 2cosh(---)cosh(a x) - 2cosh(---))
                   2                     2                     2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
              a x                   a x                   a x           a x
       (2cosh(---)sinh(a x) + 2cosh(---)cosh(a x) + 2cosh(---))log(cosh(---))
               2                     2                     2             2
     + 
                   a x              a x
       (- a x sinh(---) + 2a x cosh(---))sinh(a x)
                    2                2
     + 
                                   a x              a x
       (- a x cosh(a x) - a x)sinh(---) + 2a x cosh(---)cosh(a x)
                                    2                2
  /
      2     a x              2     a x              2     a x
     a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
             2                      2                      2
                                                     Type: Expression Integer
--R
--R   (5)
--R                  a x                   a x                   a x
--R         (- 2cosh(---)sinh(a x) - 2cosh(---)cosh(a x) - 2cosh(---))
--R                   2                     2                     2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R              a x                   a x                   a x           a x
--R       (2cosh(---)sinh(a x) + 2cosh(---)cosh(a x) + 2cosh(---))log(cosh(---))
--R               2                     2                     2             2
--R     + 
--R                   a x              a x
--R       (- a x sinh(---) + 2a x cosh(---))sinh(a x)
--R                    2                2
--R     + 
--R                                   a x              a x
--R       (- a x cosh(a x) - a x)sinh(---) + 2a x cosh(---)cosh(a x)
--R                                    2                2
--R  /
--R      2     a x              2     a x              2     a x
--R     a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
--R             2                      2                      2
--R                                                     Type: Expression Integer
--E

--S 83 of 139
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                              %BH cosh(y + x) + %BH cosh(y - x)
   (6)  %BH cosh(x)cosh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BG cosh(y + x) + %BG cosh(y - x)
--I   (6)  %BG cosh(x)cosh(y) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 84 of 139
ee:=coshcoshrule dd
 

   (7)
                  a x                   3a x          a x
         (- 4cosh(---)sinh(a x) - 2cosh(----) - 6cosh(---))
                   2                      2            2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
              a x                   3a x          a x           a x
       (4cosh(---)sinh(a x) + 2cosh(----) + 6cosh(---))log(cosh(---))
               2                      2            2             2
     + 
                    a x              a x
       (- 2a x sinh(---) + 4a x cosh(---))sinh(a x)
                     2                2
     + 
                                     a x              3a x              a x
       (- 2a x cosh(a x) - 2a x)sinh(---) + 2a x cosh(----) + 2a x cosh(---)
                                      2                 2                2
  /
       2     a x              2     3a x      2     a x
     2a cosh(---)sinh(a x) + a cosh(----) + 3a cosh(---)
              2                       2              2
                                                     Type: Expression Integer
--R
--R   (7)
--R                  a x                   3a x          a x
--R         (- 4cosh(---)sinh(a x) - 2cosh(----) - 6cosh(---))
--R                   2                      2            2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R              a x                   3a x          a x           a x
--R       (4cosh(---)sinh(a x) + 2cosh(----) + 6cosh(---))log(cosh(---))
--R               2                      2            2             2
--R     + 
--R                    a x              a x
--R       (- 2a x sinh(---) + 4a x cosh(---))sinh(a x)
--R                     2                2
--R     + 
--R                                     a x              3a x              a x
--R       (- 2a x cosh(a x) - 2a x)sinh(---) + 2a x cosh(----) + 2a x cosh(---)
--R                                      2                 2                2
--R  /
--R       2     a x              2     3a x      2     a x
--R     2a cosh(---)sinh(a x) + a cosh(----) + 3a cosh(---)
--R              2                       2              2
--R                                                     Type: Expression Integer
--E

--S 85 of 139
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BI sinh(y + x) - %BI sinh(y - x)
   (8)  %BI cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BH sinh(y + x) - %BH sinh(y - x)
--I   (8)  %BH cosh(y)sinh(x) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 86 of 139
ff:=sinhcoshrule ee
 

   (9)
                  3a x          a x          3a x          a x
         (- 2sinh(----) - 2sinh(---) - 2cosh(----) - 6cosh(---))
                    2            2             2            2
      *
         log(sinh(a x) + cosh(a x) + 1)
     + 
              3a x          a x          3a x          a x           a x
       (2sinh(----) + 2sinh(---) + 2cosh(----) + 6cosh(---))log(cosh(---))
                2            2             2            2             2
     + 
                3a x              a x                      a x
       a x sinh(----) - 2a x sinh(---)sinh(a x) + a x sinh(---)
                  2                2                        2
     + 
                 3a x              a x
       2a x cosh(----) + 2a x cosh(---)
                   2                2
  /
      2     3a x     2     a x     2     3a x      2     a x
     a sinh(----) + a sinh(---) + a cosh(----) + 3a cosh(---)
              2             2              2              2
                                                     Type: Expression Integer
--R
--R   (9)
--R                  3a x          a x          3a x          a x
--R         (- 2sinh(----) - 2sinh(---) - 2cosh(----) - 6cosh(---))
--R                    2            2             2            2
--R      *
--R         log(sinh(a x) + cosh(a x) + 1)
--R     + 
--R              3a x          a x          3a x          a x           a x
--R       (2sinh(----) + 2sinh(---) + 2cosh(----) + 6cosh(---))log(cosh(---))
--R                2            2             2            2             2
--R     + 
--R                3a x              a x                      a x
--R       a x sinh(----) - 2a x sinh(---)sinh(a x) + a x sinh(---)
--R                  2                2                        2
--R     + 
--R                 3a x              a x
--R       2a x cosh(----) + 2a x cosh(---)
--R                   2                2
--R  /
--R      2     3a x     2     a x     2     3a x      2     a x
--R     a sinh(----) + a sinh(---) + a cosh(----) + 3a cosh(---)
--R              2             2              2              2
--R                                                     Type: Expression Integer
--E

--S 87 of 139
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                               %BJ cosh(y + x) - %BJ cosh(y - x)
   (10)  %BJ sinh(x)sinh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BI cosh(y + x) - %BI cosh(y - x)
--I   (10)  %BI sinh(x)sinh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 88 of 139
gg:=sinhsinhrule ff
 

                                                       a x
         - 2log(sinh(a x) + cosh(a x) + 1) + 2log(cosh(---)) + a x
                                                        2
   (11)  ---------------------------------------------------------
                                      2
                                     a
                                                     Type: Expression Integer
--R
--R                                                       a x
--R         - 2log(sinh(a x) + cosh(a x) + 1) + 2log(cosh(---)) + a x
--R                                                        2
--R   (11)  ---------------------------------------------------------
--R                                      2
--R                                     a
--R                                                     Type: Expression Integer
--E

--S 89 of 139     14:577 Schaums and Axiom differ by a constant
complexNormalize gg
 

           2log(2)
   (12)  - -------
               2
              a
                                                     Type: Expression Integer
--R
--R           2log(2)
--R   (12)  - -------
--R               2
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 90 of 139
aa:=integrate(x/(cosh(a*x)-1),x)
 

   (1)
       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
     + 
       - 2a x sinh(a x) - 2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) - a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R       - 2a x sinh(a x) - 2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) - a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 91 of 139
bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2))
 

                  a x              a x
        2log(sinh(---)) - a x coth(---)
                   2                2
   (2)  -------------------------------
                        2
                       a
                                                     Type: Expression Integer
--R
--R                  a x              a x
--R        2log(sinh(---)) - a x coth(---)
--R                   2                2
--R   (2)  -------------------------------
--R                        2
--R                       a
--R                                                     Type: Expression Integer
--E

--S 92 of 139
cc:=aa-bb
 

   (3)
       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
     + 
                                               a x
       (- 2sinh(a x) - 2cosh(a x) + 2)log(sinh(---))
                                                2
     + 
                 a x                                               a x
       (a x coth(---) - 2a x)sinh(a x) + (a x cosh(a x) - a x)coth(---)
                  2                                                 2
     + 
       - 2a x cosh(a x)
  /
      2             2             2
     a sinh(a x) + a cosh(a x) - a
                                                     Type: Expression Integer
--R
--R   (3)
--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                                               a x
--R       (- 2sinh(a x) - 2cosh(a x) + 2)log(sinh(---))
--R                                                2
--R     + 
--R                 a x                                               a x
--R       (a x coth(---) - 2a x)sinh(a x) + (a x cosh(a x) - a x)coth(---)
--R                  2                                                 2
--R     + 
--R       - 2a x cosh(a x)
--R  /
--R      2             2             2
--R     a sinh(a x) + a cosh(a x) - a
--R                                                     Type: Expression Integer
--E

--S 93 of 139
cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 

                   cosh(x)
   (4)  coth(x) == -------
                   sinh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   cosh(x)
--R   (4)  coth(x) == -------
--R                   sinh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 94 of 139
dd:=cothrule cc
 

   (5)
                a x                                  a x
         (2sinh(---)sinh(a x) + (2cosh(a x) - 2)sinh(---))
                 2                                    2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                a x                                    a x           a x
       (- 2sinh(---)sinh(a x) + (- 2cosh(a x) + 2)sinh(---))log(sinh(---))
                 2                                      2             2
     + 
                    a x             a x                                 a x
       (- 2a x sinh(---) + a x cosh(---))sinh(a x) - 2a x cosh(a x)sinh(---)
                     2               2                                   2
     + 
                a x                      a x
       a x cosh(---)cosh(a x) - a x cosh(---)
                 2                        2
  /
      2     a x               2             2      a x
     a sinh(---)sinh(a x) + (a cosh(a x) - a )sinh(---)
             2                                      2
                                                     Type: Expression Integer
--R
--R   (5)
--R                a x                                  a x
--R         (2sinh(---)sinh(a x) + (2cosh(a x) - 2)sinh(---))
--R                 2                                    2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                a x                                    a x           a x
--R       (- 2sinh(---)sinh(a x) + (- 2cosh(a x) + 2)sinh(---))log(sinh(---))
--R                 2                                      2             2
--R     + 
--R                    a x             a x                                 a x
--R       (- 2a x sinh(---) + a x cosh(---))sinh(a x) - 2a x cosh(a x)sinh(---)
--R                     2               2                                   2
--R     + 
--R                a x                      a x
--R       a x cosh(---)cosh(a x) - a x cosh(---)
--R                 2                        2
--R  /
--R      2     a x               2             2      a x
--R     a sinh(---)sinh(a x) + (a cosh(a x) - a )sinh(---)
--R             2                                      2
--R                                                     Type: Expression Integer
--E

--S 95 of 139
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                              %BK sinh(y + x) - %BK sinh(y - x)
   (6)  %BK cosh(y)sinh(x) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BJ sinh(y + x) - %BJ sinh(y - x)
--I   (6)  %BJ cosh(y)sinh(x) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 96 of 139
ee:=sinhcoshrule dd
 

   (7)
                3a x          a x                   a x
         (2sinh(----) + 4sinh(---)sinh(a x) - 6sinh(---))
                  2            2                     2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                3a x          a x                   a x           a x
       (- 2sinh(----) - 4sinh(---)sinh(a x) + 6sinh(---))log(sinh(---))
                  2            2                     2             2
     + 
                  3a x              a x                       a x
       - a x sinh(----) - 4a x sinh(---)sinh(a x) + 3a x sinh(---)
                    2                2                         2
     + 
                 a x                       a x
       2a x cosh(---)cosh(a x) - 2a x cosh(---)
                  2                         2
  /
      2     3a x      2     a x               2     a x
     a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
              2              2                       2
                                                     Type: Expression Integer
--R
--R   (7)
--R                3a x          a x                   a x
--R         (2sinh(----) + 4sinh(---)sinh(a x) - 6sinh(---))
--R                  2            2                     2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                3a x          a x                   a x           a x
--R       (- 2sinh(----) - 4sinh(---)sinh(a x) + 6sinh(---))log(sinh(---))
--R                  2            2                     2             2
--R     + 
--R                  3a x              a x                       a x
--R       - a x sinh(----) - 4a x sinh(---)sinh(a x) + 3a x sinh(---)
--R                    2                2                         2
--R     + 
--R                 a x                       a x
--R       2a x cosh(---)cosh(a x) - 2a x cosh(---)
--R                  2                         2
--R  /
--R      2     3a x      2     a x               2     a x
--R     a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
--R              2              2                       2
--R                                                     Type: Expression Integer
--E

--S 97 of 139
sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 

                              %BL cosh(y + x) - %BL cosh(y - x)
   (8)  %BL sinh(x)sinh(y) == ---------------------------------
                                              2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                              %BK cosh(y + x) - %BK cosh(y - x)
--I   (8)  %BK sinh(x)sinh(y) == ---------------------------------
--R                                              2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 98 of 139
ff:=sinhsinhrule ee
 

   (9)
                3a x          a x          3a x          a x
         (2sinh(----) - 6sinh(---) + 2cosh(----) - 2cosh(---))
                  2            2             2            2
      *
         log(sinh(a x) + cosh(a x) - 1)
     + 
                3a x          a x          3a x          a x           a x
       (- 2sinh(----) + 6sinh(---) - 2cosh(----) + 2cosh(---))log(sinh(---))
                  2            2             2            2             2
     + 
                  3a x              a x              3a x
       - a x sinh(----) + 3a x sinh(---) - 2a x cosh(----)
                    2                2                 2
     + 
                 a x
       2a x cosh(---)cosh(a x)
                  2
  /
      2     3a x      2     a x     2     3a x     2     a x
     a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
              2              2              2             2
                                                     Type: Expression Integer
--R
--R   (9)
--R                3a x          a x          3a x          a x
--R         (2sinh(----) - 6sinh(---) + 2cosh(----) - 2cosh(---))
--R                  2            2             2            2
--R      *
--R         log(sinh(a x) + cosh(a x) - 1)
--R     + 
--R                3a x          a x          3a x          a x           a x
--R       (- 2sinh(----) + 6sinh(---) - 2cosh(----) + 2cosh(---))log(sinh(---))
--R                  2            2             2            2             2
--R     + 
--R                  3a x              a x              3a x
--R       - a x sinh(----) + 3a x sinh(---) - 2a x cosh(----)
--R                    2                2                 2
--R     + 
--R                 a x
--R       2a x cosh(---)cosh(a x)
--R                  2
--R  /
--R      2     3a x      2     a x     2     3a x     2     a x
--R     a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
--R              2              2              2             2
--R                                                     Type: Expression Integer
--E

--S 99 of 139
coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 

                               %BM cosh(y + x) + %BM cosh(y - x)
   (10)  %BM cosh(x)cosh(y) == ---------------------------------
                                               2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                               %BL cosh(y + x) + %BL cosh(y - x)
--I   (10)  %BL cosh(x)cosh(y) == ---------------------------------
--R                                               2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 100 of 139
gg:=coshcoshrule ff
 

                                                     a x
         2log(sinh(a x) + cosh(a x) - 1) - 2log(sinh(---)) - a x
                                                      2
   (11)  -------------------------------------------------------
                                     2
                                    a
                                                     Type: Expression Integer
--R
--R                                                     a x
--R         2log(sinh(a x) + cosh(a x) - 1) - 2log(sinh(---)) - a x
--R                                                      2
--R   (11)  -------------------------------------------------------
--R                                     2
--R                                    a
--R                                                     Type: Expression Integer
--E

--S 101 of 139    14:578 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         2log(2)
   (12)  -------
             2
            a
                                                     Type: Expression Integer
--R
--R         2log(2)
--R   (12)  -------
--R             2
--R            a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 102 of 139
aa:=integrate(1/(cosh(a*x)+1)^2,x)
 

   (1)
     - 6sinh(a x) - 6cosh(a x) - 2
  /
                   3                               2
       3a sinh(a x)  + (9a cosh(a x) + 9a)sinh(a x)
     + 
                    2                                              3
       (9a cosh(a x)  + 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
     + 
                   2
       9a cosh(a x)  + 9a cosh(a x) + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     - 6sinh(a x) - 6cosh(a x) - 2
--R  /
--R                   3                               2
--R       3a sinh(a x)  + (9a cosh(a x) + 9a)sinh(a x)
--R     + 
--R                    2                                              3
--R       (9a cosh(a x)  + 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
--R     + 
--R                   2
--R       9a cosh(a x)  + 9a cosh(a x) + 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 103 of 139
bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3
 

               a x 3         a x
        - tanh(---)  + 3tanh(---)
                2             2
   (2)  -------------------------
                    6a
                                                     Type: Expression Integer
--R
--R               a x 3         a x
--R        - tanh(---)  + 3tanh(---)
--R                2             2
--R   (2)  -------------------------
--R                    6a
--R                                                     Type: Expression Integer
--E

--S 104 of 139    14:579 Axiom cannot compute this integral
cc:=aa-bb
 

   (3)
                    3                            2
           sinh(a x)  + (3cosh(a x) + 3)sinh(a x)
         + 
                      2                                       3             2
           (3cosh(a x)  + 6cosh(a x) + 3)sinh(a x) + cosh(a x)  + 3cosh(a x)
         + 
           3cosh(a x) + 1
      *
              a x 3
         tanh(---)
               2
     + 
                       3                              2
           - 3sinh(a x)  + (- 9cosh(a x) - 9)sinh(a x)
         + 
                        2                                         3
           (- 9cosh(a x)  - 18cosh(a x) - 9)sinh(a x) - 3cosh(a x)
         + 
                       2
           - 9cosh(a x)  - 9cosh(a x) - 3
      *
              a x
         tanh(---)
               2
     + 
       - 12sinh(a x) - 12cosh(a x) - 4
  /
                   3                                 2
       6a sinh(a x)  + (18a cosh(a x) + 18a)sinh(a x)
     + 
                     2                                               3
       (18a cosh(a x)  + 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
     + 
                    2
       18a cosh(a x)  + 18a cosh(a x) + 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R                    3                            2
--R           sinh(a x)  + (3cosh(a x) + 3)sinh(a x)
--R         + 
--R                      2                                       3             2
--R           (3cosh(a x)  + 6cosh(a x) + 3)sinh(a x) + cosh(a x)  + 3cosh(a x)
--R         + 
--R           3cosh(a x) + 1
--R      *
--R              a x 3
--R         tanh(---)
--R               2
--R     + 
--R                       3                              2
--R           - 3sinh(a x)  + (- 9cosh(a x) - 9)sinh(a x)
--R         + 
--R                        2                                         3
--R           (- 9cosh(a x)  - 18cosh(a x) - 9)sinh(a x) - 3cosh(a x)
--R         + 
--R                       2
--R           - 9cosh(a x)  - 9cosh(a x) - 3
--R      *
--R              a x
--R         tanh(---)
--R               2
--R     + 
--R       - 12sinh(a x) - 12cosh(a x) - 4
--R  /
--R                   3                                 2
--R       6a sinh(a x)  + (18a cosh(a x) + 18a)sinh(a x)
--R     + 
--R                     2                                               3
--R       (18a cosh(a x)  + 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
--R     + 
--R                    2
--R       18a cosh(a x)  + 18a cosh(a x) + 6a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 105 of 139
aa:=integrate(1/(cosh(a*x)-1)^2,x)
 

   (1)
     - 6sinh(a x) - 6cosh(a x) + 2
  /
                   3                               2
       3a sinh(a x)  + (9a cosh(a x) - 9a)sinh(a x)
     + 
                    2                                              3
       (9a cosh(a x)  - 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
     + 
                     2
       - 9a cosh(a x)  + 9a cosh(a x) - 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     - 6sinh(a x) - 6cosh(a x) + 2
--R  /
--R                   3                               2
--R       3a sinh(a x)  + (9a cosh(a x) - 9a)sinh(a x)
--R     + 
--R                    2                                              3
--R       (9a cosh(a x)  - 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
--R     + 
--R                     2
--R       - 9a cosh(a x)  + 9a cosh(a x) - 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 106 of 139
bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
 

               a x 3         a x
        - coth(---)  + 3coth(---)
                2             2
   (2)  -------------------------
                    6a
                                                     Type: Expression Integer
--R
--R               a x 3         a x
--R        - coth(---)  + 3coth(---)
--R                2             2
--R   (2)  -------------------------
--R                    6a
--R                                                     Type: Expression Integer
--E

--S 107 of 139    14:580 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
             a x 3         a x           3
       (coth(---)  - 3coth(---))sinh(a x)
              2             2
     + 
                             a x 3                          a x           2
       ((3cosh(a x) - 3)coth(---)  + (- 9cosh(a x) + 9)coth(---))sinh(a x)
                              2                              2
     + 
                      2                       a x 3
           (3cosh(a x)  - 6cosh(a x) + 3)coth(---)
                                               2
         + 
                        2                        a x
           (- 9cosh(a x)  + 18cosh(a x) - 9)coth(---) - 12
                                                  2
      *
         sinh(a x)
     + 
                 3             2                       a x 3
       (cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1)coth(---)
                                                        2
     + 
                  3             2                       a x
     (- 3cosh(a x)  + 9cosh(a x)  - 9cosh(a x) + 3)coth(---) - 12cosh(a x) + 4
                                                         2
  /
                   3                                 2
       6a sinh(a x)  + (18a cosh(a x) - 18a)sinh(a x)
     + 
                     2                                               3
       (18a cosh(a x)  - 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
     + 
                      2
       - 18a cosh(a x)  + 18a cosh(a x) - 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R             a x 3         a x           3
--R       (coth(---)  - 3coth(---))sinh(a x)
--R              2             2
--R     + 
--R                             a x 3                          a x           2
--R       ((3cosh(a x) - 3)coth(---)  + (- 9cosh(a x) + 9)coth(---))sinh(a x)
--R                              2                              2
--R     + 
--R                      2                       a x 3
--R           (3cosh(a x)  - 6cosh(a x) + 3)coth(---)
--R                                               2
--R         + 
--R                        2                        a x
--R           (- 9cosh(a x)  + 18cosh(a x) - 9)coth(---) - 12
--R                                                  2
--R      *
--R         sinh(a x)
--R     + 
--R                 3             2                       a x 3
--R       (cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1)coth(---)
--R                                                        2
--R     + 
--R                  3             2                       a x
--R     (- 3cosh(a x)  + 9cosh(a x)  - 9cosh(a x) + 3)coth(---) - 12cosh(a x) + 4
--R                                                         2
--R  /
--R                   3                                 2
--R       6a sinh(a x)  + (18a cosh(a x) - 18a)sinh(a x)
--R     + 
--R                     2                                               3
--R       (18a cosh(a x)  - 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
--R     + 
--R                      2
--R       - 18a cosh(a x)  + 18a cosh(a x) - 6a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 108 of 139
aa:=integrate(1/(p+q*cosh(a*x)),x)
 

   (1)
   [
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
    /
         +---------+
         |   2    2
       a\|- q  + p
     ,
                                          +-------+
                                          | 2    2
          (q sinh(a x) + q cosh(a x) + p)\|q  - p
    2atan(-----------------------------------------)
                            2    2
                           q  - p
    ------------------------------------------------]
                         +-------+
                         | 2    2
                       a\|q  - p
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R    /
--R         +---------+
--R         |   2    2
--R       a\|- q  + p
--R     ,
--R                                          +-------+
--R                                          | 2    2
--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R    2atan(-----------------------------------------)
--R                            2    2
--R                           q  - p
--R    ------------------------------------------------]
--R                         +-------+
--R                         | 2    2
--R                       a\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 109 of 139
bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2))
 

                  a x
              q %e    + p
        2atan(-----------)
                +-------+
                | 2    2
               \|q  - p
   (2)  ------------------
              +-------+
              | 2    2
            a\|q  - p
                                                     Type: Expression Integer
--R
--R                  a x
--R              q %e    + p
--R        2atan(-----------)
--R                +-------+
--R                | 2    2
--R               \|q  - p
--R   (2)  ------------------
--R              +-------+
--R              | 2    2
--R            a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 110 of 139
bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2-q^2)))
 

               +---------+
               |   2    2        a x
            - \|- q  + p   + q %e    + p
        log(----------------------------)
              +---------+
              |   2    2        a x
             \|- q  + p   + q %e    + p
   (3)  ---------------------------------
                    +---------+
                    |   2    2
                  a\|- q  + p
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2        a x
--R            - \|- q  + p   + q %e    + p
--R        log(----------------------------)
--R              +---------+
--R              |   2    2        a x
--R             \|- q  + p   + q %e    + p
--R   (3)  ---------------------------------
--R                    +---------+
--R                    |   2    2
--R                  a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 111 of 139
cc1:=aa.1-bb1
 

   (4)
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
           +---------+         a x
           |   2    2      q %e    + p
       - 2\|- q  + p  atan(-----------)
                             +-------+
                             | 2    2
                            \|q  - p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R           +---------+         a x
--R           |   2    2      q %e    + p
--R       - 2\|- q  + p  atan(-----------)
--R                             +-------+
--R                             | 2    2
--R                            \|q  - p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 112 of 139
cc2:=aa.2-bb1
 

                                              +-------+
                                              | 2    2               a x
              (q sinh(a x) + q cosh(a x) + p)\|q  - p            q %e    + p
        2atan(-----------------------------------------) - 2atan(-----------)
                                2    2                             +-------+
                               q  - p                              | 2    2
                                                                  \|q  - p
   (5)  ---------------------------------------------------------------------
                                       +-------+
                                       | 2    2
                                     a\|q  - p
                                                     Type: Expression Integer
--R
--R                                              +-------+
--R                                              | 2    2               a x
--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p            q %e    + p
--R        2atan(-----------------------------------------) - 2atan(-----------)
--R                                2    2                             +-------+
--R                               q  - p                              | 2    2
--R                                                                  \|q  - p
--R   (5)  ---------------------------------------------------------------------
--R                                       +-------+
--R                                       | 2    2
--R                                     a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 113 of 139
cc3:=aa.1-bb2
 

   (6)
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
     + 
                +---------+
                |   2    2        a x
             - \|- q  + p   + q %e    + p
       - log(----------------------------)
               +---------+
               |   2    2        a x
              \|- q  + p   + q %e    + p
  /
       +---------+
       |   2    2
     a\|- q  + p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R     + 
--R                +---------+
--R                |   2    2        a x
--R             - \|- q  + p   + q %e    + p
--R       - log(----------------------------)
--R               +---------+
--R               |   2    2        a x
--R              \|- q  + p   + q %e    + p
--R  /
--R       +---------+
--R       |   2    2
--R     a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 114 of 139    14:581 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (7)
                          +---------+
          +-------+       |   2    2        a x
          | 2    2     - \|- q  + p   + q %e    + p
       - \|q  - p  log(----------------------------)
                         +---------+
                         |   2    2        a x
                        \|- q  + p   + q %e    + p
     + 
                                                         +-------+
         +---------+                                     | 2    2
         |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       2\|- q  + p  atan(-----------------------------------------)
                                           2    2
                                          q  - p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                          +---------+
--R          +-------+       |   2    2        a x
--R          | 2    2     - \|- q  + p   + q %e    + p
--R       - \|q  - p  log(----------------------------)
--R                         +---------+
--R                         |   2    2        a x
--R                        \|- q  + p   + q %e    + p
--R     + 
--R                                                         +-------+
--R         +---------+                                     | 2    2
--R         |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       2\|- q  + p  atan(-----------------------------------------)
--R                                           2    2
--R                                          q  - p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 115 of 139
aa:=integrate(1/(p+q*cosh(a*x))^2,x)
 

   (1)
   [
                          2                       2                          2
             p q sinh(a x)  + (2p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
           + 
               2
             2p cosh(a x) + p q
        *
           log
                       2         2      2
                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
                    + 
                       2         2                     2     2
                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
                 *
                     +---------+
                     |   2    2
                    \|- q  + p
                + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
             /
                             2                                             2
                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
                + 
                  2p cosh(a x) + q
       + 
                                              +---------+
                                              |   2    2
         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|- q  + p
    /
               3      2           2
           (a q  - a p q)sinh(a x)
         + 
                 3       2                    2       3
           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
         + 
               3      2           2          2       3                3      2
           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
      *
          +---------+
          |   2    2
         \|- q  + p
     ,

                             2                         2
             - 2p q sinh(a x)  + (- 4p q cosh(a x) - 4p )sinh(a x)
           + 
                             2     2
             - 2p q cosh(a x)  - 4p cosh(a x) - 2p q
        *
                                                +-------+
                                                | 2    2
                (q sinh(a x) + q cosh(a x) + p)\|q  - p
           atan(-----------------------------------------)
                                  2    2
                                 q  - p
       + 
                                              +-------+
                                              | 2    2
         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|q  - p
    /
               3      2           2
           (a q  - a p q)sinh(a x)
         + 
                 3       2                    2       3
           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
         + 
               3      2           2          2       3                3      2
           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
      *
          +-------+
          | 2    2
         \|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                          2                       2                          2
--R             p q sinh(a x)  + (2p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R           + 
--R               2
--R             2p cosh(a x) + p q
--R        *
--R           log
--R                       2         2      2
--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
--R                    + 
--R                       2         2                     2     2
--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
--R                 *
--R                     +---------+
--R                     |   2    2
--R                    \|- q  + p
--R                + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R             /
--R                             2                                             2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R                + 
--R                  2p cosh(a x) + q
--R       + 
--R                                              +---------+
--R                                              |   2    2
--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|- q  + p
--R    /
--R               3      2           2
--R           (a q  - a p q)sinh(a x)
--R         + 
--R                 3       2                    2       3
--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
--R         + 
--R               3      2           2          2       3                3      2
--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
--R      *
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R     ,
--R
--R                             2                         2
--R             - 2p q sinh(a x)  + (- 4p q cosh(a x) - 4p )sinh(a x)
--R           + 
--R                             2     2
--R             - 2p q cosh(a x)  - 4p cosh(a x) - 2p q
--R        *
--R                                                +-------+
--R                                                | 2    2
--R                (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R           atan(-----------------------------------------)
--R                                  2    2
--R                                 q  - p
--R       + 
--R                                              +-------+
--R                                              | 2    2
--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|q  - p
--R    /
--R               3      2           2
--R           (a q  - a p q)sinh(a x)
--R         + 
--R                 3       2                    2       3
--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
--R         + 
--R               3      2           2          2       3                3      2
--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 116 of 139
t1:=integrate(1/(p+q*cosh(a*x)),x)
 

   (2)
   [
       log
                   2         2      2                              2         2
                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                + 
                                    2     2
                  2p q cosh(a x) - q  + 2p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                 3     2                 3     2                  2     3
              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
         /
                         2                                             2
              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
            + 
              2p cosh(a x) + q
    /
         +---------+
         |   2    2
       a\|- q  + p
     ,
                                          +-------+
                                          | 2    2
          (q sinh(a x) + q cosh(a x) + p)\|q  - p
    2atan(-----------------------------------------)
                            2    2
                           q  - p
    ------------------------------------------------]
                         +-------+
                         | 2    2
                       a\|q  - p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R   [
--R       log
--R                   2         2      2                              2         2
--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                + 
--R                                    2     2
--R                  2p q cosh(a x) - q  + 2p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                 3     2                 3     2                  2     3
--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R         /
--R                         2                                             2
--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R            + 
--R              2p cosh(a x) + q
--R    /
--R         +---------+
--R         |   2    2
--R       a\|- q  + p
--R     ,
--R                                          +-------+
--R                                          | 2    2
--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R    2atan(-----------------------------------------)
--R                            2    2
--R                           q  - p
--R    ------------------------------------------------]
--R                         +-------+
--R                         | 2    2
--R                       a\|q  - p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 117 of 139
bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1
 

   (3)
                             2
         (- p q cosh(a x) - p )
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                   +---------+
                   |   2    2
       q sinh(a x)\|- q  + p
  /
                                               +---------+
          3      2                   2      3  |   2    2
     ((a q  - a p q)cosh(a x) + a p q  - a p )\|- q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                             2
--R         (- p q cosh(a x) - p )
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                   +---------+
--R                   |   2    2
--R       q sinh(a x)\|- q  + p
--R  /
--R                                               +---------+
--R          3      2                   2      3  |   2    2
--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 118 of 139
bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2
 

   (4)
                                                                    +-------+
                                                                    | 2    2
                             2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
       (- 2p q cosh(a x) - 2p )atan(-----------------------------------------)
                                                      2    2
                                                     q  - p
     + 
                   +-------+
                   | 2    2
       q sinh(a x)\|q  - p
  /
                                               +-------+
          3      2                   2      3  | 2    2
     ((a q  - a p q)cosh(a x) + a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                    +-------+
--R                                                                    | 2    2
--R                             2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R       (- 2p q cosh(a x) - 2p )atan(-----------------------------------------)
--R                                                      2    2
--R                                                     q  - p
--R     + 
--R                   +-------+
--R                   | 2    2
--R       q sinh(a x)\|q  - p
--R  /
--R                                               +-------+
--R          3      2                   2      3  | 2    2
--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 119 of 139
cc1:=aa.1-bb1
 

   (5)
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
              2         3        2                          2
           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
         + 
               2         2                     2     2
           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
         + 
                           2        2     2
           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
      *
          +---------+
          |   2    2
         \|- q  + p
  /
              4      2 2                  3      3           2
         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
       + 
                  4       2 2          2          3       3                  2 2
             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
           + 
                   4
             - 2a p
        *
           sinh(a x)
       + 
             4      2 2          3          3       3           2
         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
       + 
             4      2 2       4                  3      3
         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
    *
        +---------+
        |   2    2
       \|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R              2         3        2                          2
--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R               2         2                     2     2
--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
--R         + 
--R                           2        2     2
--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
--R      *
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R  /
--R              4      2 2                  3      3           2
--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R       + 
--R                  4       2 2          2          3       3                  2 2
--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R           + 
--R                   4
--R             - 2a p
--R        *
--R           sinh(a x)
--R       + 
--R             4      2 2          3          3       3           2
--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R       + 
--R             4      2 2       4                  3      3
--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R    *
--R        +---------+
--R        |   2    2
--R       \|- q  + p
--R                                                     Type: Expression Integer
--E

--S 120 of 139
cc2:=aa.2-bb1
 

   (6)
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                   3     2                 3     2                  2     3
                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                  2              2           2
           (- 2p q cosh(a x) - 2p q)sinh(a x)
         + 
                  2         2     2                3                 2         3
           (- 4p q cosh(a x)  - 8p q cosh(a x) - 4p )sinh(a x) - 2p q cosh(a x)
         + 
               2           2          2     3               2
           - 6p q cosh(a x)  + (- 2p q  - 4p )cosh(a x) - 2p q
      *
                                                          +-------+
          +---------+                                     | 2    2
          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
         \|- q  + p  atan(-----------------------------------------)
                                            2    2
                                           q  - p
     + 
              2         3        2                          2
           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
         + 
               2         2                     2     2
           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
         + 
                           2        2     2
           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
      *
          +---------+ +-------+
          |   2    2  | 2    2
         \|- q  + p  \|q  - p
  /
              4      2 2                  3      3           2
         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
       + 
                  4       2 2          2          3       3                  2 2
             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
           + 
                   4
             - 2a p
        *
           sinh(a x)
       + 
             4      2 2          3          3       3           2
         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
       + 
             4      2 2       4                  3      3
         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
    *
        +---------+ +-------+
        |   2    2  | 2    2
       \|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                   3     2                 3     2                  2     3
--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                  2              2           2
--R           (- 2p q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R                  2         2     2                3                 2         3
--R           (- 4p q cosh(a x)  - 8p q cosh(a x) - 4p )sinh(a x) - 2p q cosh(a x)
--R         + 
--R               2           2          2     3               2
--R           - 6p q cosh(a x)  + (- 2p q  - 4p )cosh(a x) - 2p q
--R      *
--R                                                          +-------+
--R          +---------+                                     | 2    2
--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R         \|- q  + p  atan(-----------------------------------------)
--R                                            2    2
--R                                           q  - p
--R     + 
--R              2         3        2                          2
--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R               2         2                     2     2
--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
--R         + 
--R                           2        2     2
--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
--R      *
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R         \|- q  + p  \|q  - p
--R  /
--R              4      2 2                  3      3           2
--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R       + 
--R                  4       2 2          2          3       3                  2 2
--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R           + 
--R                   4
--R             - 2a p
--R        *
--R           sinh(a x)
--R       + 
--R             4      2 2          3          3       3           2
--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R       + 
--R             4      2 2       4                  3      3
--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R    *
--R        +---------+ +-------+
--R        |   2    2  | 2    2
--R       \|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 121 of 139
cc3:=aa.1-bb2
 

   (7)
               2             2           2
           (p q cosh(a x) + p q)sinh(a x)
         + 
                2         2     2                3                2         3
           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
         + 
             2           2       2     3              2
           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
      *
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     2         2      2                              2         2
                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
                  + 
                                      2     2
                    2p q cosh(a x) - q  + 2p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                     3     2                   3     2                  2     3
                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
           /
                           2                                             2
                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
              + 
                2p cosh(a x) + q
     + 
                2              2           2
           (2p q cosh(a x) + 2p q)sinh(a x)
         + 
                2         2     2                3                 2         3
           (4p q cosh(a x)  + 8p q cosh(a x) + 4p )sinh(a x) + 2p q cosh(a x)
         + 
             2           2        2     3               2
           6p q cosh(a x)  + (2p q  + 4p )cosh(a x) + 2p q
      *
                                                          +-------+
          +---------+                                     | 2    2
          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
         \|- q  + p  atan(-----------------------------------------)
                                            2    2
                                           q  - p
     + 
              2         3        2                          2
           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
         + 
               2         2                     2     2
           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
         + 
                           2        2     2
           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
      *
          +---------+ +-------+
          |   2    2  | 2    2
         \|- q  + p  \|q  - p
  /
              4      2 2                  3      3           2
         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
       + 
                  4       2 2          2          3       3                  2 2
             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
           + 
                   4
             - 2a p
        *
           sinh(a x)
       + 
             4      2 2          3          3       3           2
         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
       + 
             4      2 2       4                  3      3
         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
    *
        +---------+ +-------+
        |   2    2  | 2    2
       \|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R               2             2           2
--R           (p q cosh(a x) + p q)sinh(a x)
--R         + 
--R                2         2     2                3                2         3
--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
--R         + 
--R             2           2       2     3              2
--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
--R      *
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     2         2      2                              2         2
--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
--R                  + 
--R                                      2     2
--R                    2p q cosh(a x) - q  + 2p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                     3     2                   3     2                  2     3
--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
--R           /
--R                           2                                             2
--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
--R              + 
--R                2p cosh(a x) + q
--R     + 
--R                2              2           2
--R           (2p q cosh(a x) + 2p q)sinh(a x)
--R         + 
--R                2         2     2                3                 2         3
--R           (4p q cosh(a x)  + 8p q cosh(a x) + 4p )sinh(a x) + 2p q cosh(a x)
--R         + 
--R             2           2        2     3               2
--R           6p q cosh(a x)  + (2p q  + 4p )cosh(a x) + 2p q
--R      *
--R                                                          +-------+
--R          +---------+                                     | 2    2
--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
--R         \|- q  + p  atan(-----------------------------------------)
--R                                            2    2
--R                                           q  - p
--R     + 
--R              2         3        2                          2
--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R         + 
--R               2         2                     2     2
--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
--R         + 
--R                           2        2     2
--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
--R      *
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R         \|- q  + p  \|q  - p
--R  /
--R              4      2 2                  3      3           2
--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R       + 
--R                  4       2 2          2          3       3                  2 2
--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R           + 
--R                   4
--R             - 2a p
--R        *
--R           sinh(a x)
--R       + 
--R             4      2 2          3          3       3           2
--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R       + 
--R             4      2 2       4                  3      3
--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R    *
--R        +---------+ +-------+
--R        |   2    2  | 2    2
--R       \|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 122 of 139    14:582 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (8)
          2         3        2                          2
       - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
     + 
           2         2                     2     2                           2
       (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x) - 2p q cosh(a x)
     + 
            2     2
       (- 2q  - 2p )cosh(a x) - 2p q
  /
            4      2 2                  3      3           2
       ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
     + 
                4       2 2          2          3       3                  2 2
           (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
         + 
                 4
           - 2a p
      *
         sinh(a x)
     + 
           4      2 2          3          3       3           2
       (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
     + 
           4      2 2       4                  3      3
       (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
                                                     Type: Expression Integer
--R
--R   (8)
--R          2         3        2                          2
--R       - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
--R     + 
--R           2         2                     2     2                           2
--R       (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x) - 2p q cosh(a x)
--R     + 
--R            2     2
--R       (- 2q  - 2p )cosh(a x) - 2p q
--R  /
--R            4      2 2                  3      3           2
--R       ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
--R     + 
--R                4       2 2          2          3       3                  2 2
--R           (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
--R         + 
--R                 4
--R           - 2a p
--R      *
--R         sinh(a x)
--R     + 
--R           4      2 2          3          3       3           2
--R       (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
--R     + 
--R           4      2 2       4                  3      3
--R       (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 123 of 139
aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
 

   (1)
   [
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  - 4p )cosh(a x)  + q
    /
            +---------+
            |   2    2
       2a p\|- q  + p
     ,

     -
          atan
                      2         2     2                      2         2    2
                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
                   + 
                         2
                     - 2p
              *
                  +-------+
                  | 2    2
                 \|q  - p
            /
                   2     3
               2p q  - 2p
       /
              +-------+
              | 2    2
          a p\|q  - p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  - 4p )cosh(a x)  + q
--R    /
--R            +---------+
--R            |   2    2
--R       2a p\|- q  + p
--R     ,
--R
--R     -
--R          atan
--R                      2         2     2                      2         2    2
--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
--R                   + 
--R                         2
--R                     - 2p
--R              *
--R                  +-------+
--R                  | 2    2
--R                 \|q  - p
--R            /
--R                   2     3
--R               2p q  - 2p
--R       /
--R              +-------+
--R              | 2    2
--R          a p\|q  - p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 124 of 139
bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p^2-q^2)))
 

               +---------+
               |   2    2
            - \|- q  + p   - p tanh(a x)
        log(----------------------------)
              +---------+
              |   2    2
             \|- q  + p   - p tanh(a x)
   (2)  ---------------------------------
                      +---------+
                      |   2    2
                 2a p\|- q  + p
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R            - \|- q  + p   - p tanh(a x)
--R        log(----------------------------)
--R              +---------+
--R              |   2    2
--R             \|- q  + p   - p tanh(a x)
--R   (2)  ---------------------------------
--R                      +---------+
--R                      |   2    2
--R                 2a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 125 of 139
bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2))
 

               p tanh(a x)
          atan(-----------)
                 +-------+
                 | 2    2
                \|q  - p
   (3)  - -----------------
                +-------+
                | 2    2
            a p\|q  - p
                                                     Type: Expression Integer
--R
--R               p tanh(a x)
--R          atan(-----------)
--R                 +-------+
--R                 | 2    2
--R                \|q  - p
--R   (3)  - -----------------
--R                +-------+
--R                | 2    2
--R            a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 126 of 139
cc1:=aa.1-bb1
 

   (4)
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
             *
                 +---------+
                 |   2    2
                \|- q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  - 4p )cosh(a x)  + q
     + 
                +---------+
                |   2    2
             - \|- q  + p   - p tanh(a x)
       - log(----------------------------)
               +---------+
               |   2    2
              \|- q  + p   - p tanh(a x)
  /
          +---------+
          |   2    2
     2a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
--R             *
--R                 +---------+
--R                 |   2    2
--R                \|- q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  - 4p )cosh(a x)  + q
--R     + 
--R                +---------+
--R                |   2    2
--R             - \|- q  + p   - p tanh(a x)
--R       - log(----------------------------)
--R               +---------+
--R               |   2    2
--R              \|- q  + p   - p tanh(a x)
--R  /
--R          +---------+
--R          |   2    2
--R     2a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 127 of 139
cc2:=aa.2-bb1
 

   (5)
                          +---------+
          +-------+       |   2    2
          | 2    2     - \|- q  + p   - p tanh(a x)
       - \|q  - p  log(----------------------------)
                         +---------+
                         |   2    2
                        \|- q  + p   - p tanh(a x)
     + 
       -
              +---------+
              |   2    2
            2\|- q  + p
         *
            atan
                      2         2     2                      2         2    2
                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
                   + 
                         2
                     - 2p
                *
                    +-------+
                    | 2    2
                   \|q  - p
              /
                     2     3
                 2p q  - 2p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                          +---------+
--R          +-------+       |   2    2
--R          | 2    2     - \|- q  + p   - p tanh(a x)
--R       - \|q  - p  log(----------------------------)
--R                         +---------+
--R                         |   2    2
--R                        \|- q  + p   - p tanh(a x)
--R     + 
--R       -
--R              +---------+
--R              |   2    2
--R            2\|- q  + p
--R         *
--R            atan
--R                      2         2     2                      2         2    2
--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
--R                   + 
--R                         2
--R                     - 2p
--R                *
--R                    +-------+
--R                    | 2    2
--R                   \|q  - p
--R              /
--R                     2     3
--R                 2p q  - 2p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 128 of 139
cc3:=aa.1-bb2
 

   (6)
          +-------+
          | 2    2
         \|q  - p
      *
         log
                     4         4     4                  3
                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
                  + 
                       4         2     4     2 2          2
                    (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
                  + 
                       4         3      4     2 2
                    (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
                  + 
                     4         4      4     2 2          2    4     2 2     4
                    q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
               *
                   +---------+
                   |   2    2
                  \|- q  + p
              + 
                       4     3 2          2
                (- 4p q  + 4p q )sinh(a x)
              + 
                       4     3 2
                (- 8p q  + 8p q )cosh(a x)sinh(a x)
              + 
                       4     3 2          2       4      3 2     5
                (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
           /
                 2         4     2                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   2         2     2     2          2
                (6q cosh(a x)  + 2q  - 4p )sinh(a x)
              + 
                   2         3      2     2                        2         4
                (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                   2     2          2    2
                (2q  - 4p )cosh(a x)  + q
     + 
         +---------+
         |   2    2      p tanh(a x)
       2\|- q  + p  atan(-----------)
                           +-------+
                           | 2    2
                          \|q  - p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R          +-------+
--R          | 2    2
--R         \|q  - p
--R      *
--R         log
--R                     4         4     4                  3
--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                  + 
--R                       4         2     4     2 2          2
--R                    (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
--R                  + 
--R                       4         3      4     2 2
--R                    (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
--R                  + 
--R                     4         4      4     2 2          2    4     2 2     4
--R                    q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
--R               *
--R                   +---------+
--R                   |   2    2
--R                  \|- q  + p
--R              + 
--R                       4     3 2          2
--R                (- 4p q  + 4p q )sinh(a x)
--R              + 
--R                       4     3 2
--R                (- 8p q  + 8p q )cosh(a x)sinh(a x)
--R              + 
--R                       4     3 2          2       4      3 2     5
--R                (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
--R           /
--R                 2         4     2                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   2         2     2     2          2
--R                (6q cosh(a x)  + 2q  - 4p )sinh(a x)
--R              + 
--R                   2         3      2     2                        2         4
--R                (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                   2     2          2    2
--R                (2q  - 4p )cosh(a x)  + q
--R     + 
--R         +---------+
--R         |   2    2      p tanh(a x)
--R       2\|- q  + p  atan(-----------)
--R                           +-------+
--R                           | 2    2
--R                          \|q  - p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 129 of 139    14:583 Axiom cannot simplify this expression
cc4:=aa.2-bb2
 

   (7)
       -
          atan
                      2         2     2                      2         2    2
                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
                   + 
                         2
                     - 2p
              *
                  +-------+
                  | 2    2
                 \|q  - p
            /
                   2     3
               2p q  - 2p
     + 
            p tanh(a x)
       atan(-----------)
              +-------+
              | 2    2
             \|q  - p
  /
         +-------+
         | 2    2
     a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R       -
--R          atan
--R                      2         2     2                      2         2    2
--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
--R                   + 
--R                         2
--R                     - 2p
--R              *
--R                  +-------+
--R                  | 2    2
--R                 \|q  - p
--R            /
--R                   2     3
--R               2p q  - 2p
--R     + 
--R            p tanh(a x)
--R       atan(-----------)
--R              +-------+
--R              | 2    2
--R             \|q  - p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  - p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 130 of 139
aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
 

   (1)
     log
                 4         4     4                  3
                q sinh(a x)  + 4q cosh(a x)sinh(a x)
              + 
                   4         2     4     2 2          2
                (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
              + 
                   4         3      4     2 2                        4         4
                (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x) + q cosh(a x)
              + 
                   4     2 2          2    4     2 2     4
                (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
           *
               +-------+
               | 2    2
              \|q  + p
          + 
                   4     3 2          2          4     3 2
            (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
          + 
                   4     3 2          2       4      3 2     5
            (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
       /
             2         4     2                  3
            q sinh(a x)  + 4q cosh(a x)sinh(a x)
          + 
               2         2     2     2          2
            (6q cosh(a x)  + 2q  + 4p )sinh(a x)
          + 
               2         3      2     2                        2         4
            (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
          + 
               2     2          2    2
            (2q  + 4p )cosh(a x)  + q
  /
          +-------+
          | 2    2
     2a p\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R     log
--R                 4         4     4                  3
--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R              + 
--R                   4         2     4     2 2          2
--R                (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
--R              + 
--R                   4         3      4     2 2                        4         4
--R                (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x) + q cosh(a x)
--R              + 
--R                   4     2 2          2    4     2 2     4
--R                (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
--R           *
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R          + 
--R                   4     3 2          2          4     3 2
--R            (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
--R          + 
--R                   4     3 2          2       4      3 2     5
--R            (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
--R       /
--R             2         4     2                  3
--R            q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R          + 
--R               2         2     2     2          2
--R            (6q cosh(a x)  + 2q  + 4p )sinh(a x)
--R          + 
--R               2         3      2     2                        2         4
--R            (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R          + 
--R               2     2          2    2
--R            (2q  + 4p )cosh(a x)  + q
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 131 of 139
bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p^2+q^2)))
 

               +-------+
               | 2    2
            - \|q  + p   - p tanh(a x)
        log(--------------------------)
              +-------+
              | 2    2
             \|q  + p   - p tanh(a x)
   (2)  -------------------------------
                      +-------+
                      | 2    2
                 2a p\|q  + p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R            - \|q  + p   - p tanh(a x)
--R        log(--------------------------)
--R              +-------+
--R              | 2    2
--R             \|q  + p   - p tanh(a x)
--R   (2)  -------------------------------
--R                      +-------+
--R                      | 2    2
--R                 2a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 132 of 139
bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2))
 

             p tanh(a x)
        atan(-----------)
               +-------+
               | 2    2
              \|q  + p
   (3)  -----------------
              +-------+
              | 2    2
          a p\|q  + p
                                                     Type: Expression Integer
--R
--R             p tanh(a x)
--R        atan(-----------)
--R               +-------+
--R               | 2    2
--R              \|q  + p
--R   (3)  -----------------
--R              +-------+
--R              | 2    2
--R          a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 133 of 139
cc1:=aa-bb1
 

   (4)
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
             *
                 +-------+
                 | 2    2
                \|q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  + 4p )cosh(a x)  + q
     + 
                +-------+
                | 2    2
             - \|q  + p   - p tanh(a x)
       - log(--------------------------)
               +-------+
               | 2    2
              \|q  + p   - p tanh(a x)
  /
          +-------+
          | 2    2
     2a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  + 4p )cosh(a x)  + q
--R     + 
--R                +-------+
--R                | 2    2
--R             - \|q  + p   - p tanh(a x)
--R       - log(--------------------------)
--R               +-------+
--R               | 2    2
--R              \|q  + p   - p tanh(a x)
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 134 of 139    14:584 Axiom cannot simplify this expression
cc2:=aa-bb2
 

   (5)
       log
                   4         4     4                  3
                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
                + 
                     4         2     4     2 2          2
                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
                + 
                     4         3      4     2 2
                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
                + 
                   4         4      4     2 2          2    4     2 2     4
                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
             *
                 +-------+
                 | 2    2
                \|q  + p
            + 
                     4     3 2          2          4     3 2
              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
            + 
                     4     3 2          2       4      3 2     5
              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
         /
               2         4     2                  3
              q sinh(a x)  + 4q cosh(a x)sinh(a x)
            + 
                 2         2     2     2          2
              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
            + 
                 2         3      2     2                        2         4
              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
            + 
                 2     2          2    2
              (2q  + 4p )cosh(a x)  + q
     + 
               p tanh(a x)
       - 2atan(-----------)
                 +-------+
                 | 2    2
                \|q  + p
  /
          +-------+
          | 2    2
     2a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R       log
--R                   4         4     4                  3
--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R                + 
--R                     4         2     4     2 2          2
--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
--R                + 
--R                     4         3      4     2 2
--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
--R                + 
--R                   4         4      4     2 2          2    4     2 2     4
--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
--R             *
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R            + 
--R                     4     3 2          2          4     3 2
--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
--R            + 
--R                     4     3 2          2       4      3 2     5
--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
--R         /
--R               2         4     2                  3
--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
--R            + 
--R                 2         2     2     2          2
--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
--R            + 
--R                 2         3      2     2                        2         4
--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
--R            + 
--R                 2     2          2    2
--R              (2q  + 4p )cosh(a x)  + q
--R     + 
--R               p tanh(a x)
--R       - 2atan(-----------)
--R                 +-------+
--R                 | 2    2
--R                \|q  + p
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  + p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 135 of 139    14:585 Axiom cannot compute this integral
aa:=integrate(x^m*cosh(a*x),x)
 

           x
         ++              m
   (1)   |   cosh(%N a)%N d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++              m
--I   (1)   |   cosh(%N a)%N d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 136 of 139    14:586 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)^n,x)
 

           x
         ++            n
   (1)   |   cosh(%N a) d%N
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   cosh(%N a) d%N
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 137 of 139    14:587 Axiom cannot compute this integral
aa:=integrate(cosh(a*x)/x^n,x)
 

           x
         ++  cosh(%N a)
   (1)   |   ---------- d%N
        ++         n
                 %N
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cosh(%N a)
--I   (1)   |   ---------- d%N
--R        ++         n
--I                 %N
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 138 of 139    14:588 Axiom cannot compute this integral
aa:=integrate(1/cosh(a*x)^n,x)
 

           x
         ++       1
   (1)   |   ----------- d%N
        ++             n
             cosh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%N
--R        ++             n
--I             cosh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 139 of 139    14:589 Axiom cannot compute this integral
aa:=integrate(1/cosh(a*x)^n,x)
 

           x
         ++       1
   (1)   |   ----------- d%N
        ++             n
             cosh(%N a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ----------- d%N
--R        ++             n
--I             cosh(%N a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to schaum18.output (2010/3/27, 18:38:8).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 127
aa:=integrate(cos(a*x),x)
 

        sin(a x)
   (1)  --------
            a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        sin(a x)
--R   (1)  --------
--R            a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 127
bb:=sin(a*x)/a
 

        sin(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        sin(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E

--S 3 of 127      14:369 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 4 of 127
aa:=integrate(x*cos(a*x),x)
 

        a x sin(a x) + cos(a x)
   (1)  -----------------------
                    2
                   a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        a x sin(a x) + cos(a x)
--R   (1)  -----------------------
--R                    2
--R                   a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 5 of 127
bb:=cos(a*x)/a^2+(x*sin(a*x))/a
 

        a x sin(a x) + cos(a x)
   (2)  -----------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R        a x sin(a x) + cos(a x)
--R   (2)  -----------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E

--S 6 of 127      14:370 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 7 of 127
aa:=integrate(x^2*cos(a*x),x)
 

          2 2
        (a x  - 2)sin(a x) + 2a x cos(a x)
   (1)  ----------------------------------
                         3
                        a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2 2
--R        (a x  - 2)sin(a x) + 2a x cos(a x)
--R   (1)  ----------------------------------
--R                         3
--R                        a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 8 of 127
bb:=(2*x)/a^2*cos(a*x)+(x^2/a-2/a^3)*sin(a*x)
 

          2 2
        (a x  - 2)sin(a x) + 2a x cos(a x)
   (2)  ----------------------------------
                         3
                        a
                                                     Type: Expression Integer
--R
--R          2 2
--R        (a x  - 2)sin(a x) + 2a x cos(a x)
--R   (2)  ----------------------------------
--R                         3
--R                        a
--R                                                     Type: Expression Integer
--E

--S 9 of 127      14:371 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 127
aa:=integrate(x^3*cos(a*x),x)
 

          3 3                      2 2
        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
   (1)  -------------------------------------------
                              4
                             a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          3 3                      2 2
--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
--R   (1)  -------------------------------------------
--R                              4
--R                             a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 127
bb:=((3*x^2)/a^2-6/a^4)*cos(a*x)+(x^3/a-(6*x)/a^3)*sin(a*x)
 

          3 3                      2 2
        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
   (2)  -------------------------------------------
                              4
                             a
                                                     Type: Expression Integer
--R
--R          3 3                      2 2
--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
--R   (2)  -------------------------------------------
--R                              4
--R                             a
--R                                                     Type: Expression Integer
--E

--S 12 of 127     14:372 Schaums and Axiom agree
cc:=aa-bb
 

   (3)  0
                                                     Type: Expression Integer
--R
--R   (3)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 127     14:373 Schaums and Axiom agree by definition
aa:=integrate(cos(x)/x,x)
 

   (1)  Ci(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)  Ci(x)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 14 of 127     14:374 Axiom cannot compute this integral
aa:=integrate(cos(a*x)/x^2,x)
 

           x
         ++  cos(%I a)
   (1)   |   --------- d%I
        ++        2
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cos(%I a)
--I   (1)   |   --------- d%I
--R        ++        2
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 15 of 127
aa:=integrate(1/cos(a*x),x)
 

            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
        log(-----------------------) - log(-----------------------)
                  cos(a x) + 1                   cos(a x) + 1
   (1)  -----------------------------------------------------------
                                     a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
--R        log(-----------------------) - log(-----------------------)
--R                  cos(a x) + 1                   cos(a x) + 1
--R   (1)  -----------------------------------------------------------
--R                                     a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16 of 127
bb1:=1/a*log(sec(a*x)+tan(a*x))
 

        log(tan(a x) + sec(a x))
   (2)  ------------------------
                    a
                                                     Type: Expression Integer
--R
--R        log(tan(a x) + sec(a x))
--R   (2)  ------------------------
--R                    a
--R                                                     Type: Expression Integer
--E

--S 17 of 127
bb2:=1/a*log(tan(%pi/4+(a*x)/2))
 

                2a x + %pi
        log(tan(----------))
                     4
   (3)  --------------------
                  a
                                                     Type: Expression Integer
--R
--R                2a x + %pi
--R        log(tan(----------))
--R                     4
--R   (3)  --------------------
--R                  a
--R                                                     Type: Expression Integer
--E

--S 18 of 127
cc1:=aa-bb1
 

   (4)
                                        sin(a x) + cos(a x) + 1
       - log(tan(a x) + sec(a x)) + log(-----------------------)
                                              cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                        sin(a x) + cos(a x) + 1
--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
--R                                              cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 19 of 127
cc2:=aa-bb2
 

   (5)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 20 of 127     14:375 Schaums and Axiom differ by a constant
complexNormalize cc1
 

        log(- 1)
   (6)  --------
            a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (6)  --------
--R            a
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 21 of 127     14:376 Axiom cannot compute this integral
aa:=integrate(x/cos(a*x),x)
 

           x
         ++      %I
   (1)   |   --------- d%I
        ++   cos(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   --------- d%I
--I        ++   cos(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 22 of 127
aa:=integrate(cos(a*x)^2,x)
 

        cos(a x)sin(a x) + a x
   (1)  ----------------------
                  2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        cos(a x)sin(a x) + a x
--R   (1)  ----------------------
--R                  2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 23 of 127
bb:=x/2+sin(2*a*x)/(4*a)
 

        sin(2a x) + 2a x
   (2)  ----------------
               4a
                                                     Type: Expression Integer
--R
--R        sin(2a x) + 2a x
--R   (2)  ----------------
--R               4a
--R                                                     Type: Expression Integer
--E

--S 24 of 127
cc:=aa-bb
 

        - sin(2a x) + 2cos(a x)sin(a x)
   (3)  -------------------------------
                       4a
                                                     Type: Expression Integer
--R
--R        - sin(2a x) + 2cos(a x)sin(a x)
--R   (3)  -------------------------------
--R                       4a
--R                                                     Type: Expression Integer
--E

--S 25 of 127
cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
 

                           %S sin(b + a) - %S sin(b - a)
   (4)  %S cos(b)sin(a) == -----------------------------
                                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                           %M sin(b + a) - %M sin(b - a)
--I   (4)  %M cos(b)sin(a) == -----------------------------
--R                                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 26 of 127     14:377 Schaums and Axiom agree
dd:=cossinrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 27 of 127
aa:=integrate(x*cos(a*x)^2,x)
 

                                        2    2 2
        2a x cos(a x)sin(a x) + cos(a x)  + a x
   (1)  ----------------------------------------
                             2
                           4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                        2    2 2
--R        2a x cos(a x)sin(a x) + cos(a x)  + a x
--R   (1)  ----------------------------------------
--R                             2
--R                           4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 28 of 127
bb:=x^2/4+(x*sin(2*a*x))/(4*a)+cos(2*a*x)/(8*a^2)
 

                                       2 2
        2a x sin(2a x) + cos(2a x) + 2a x
   (2)  ----------------------------------
                          2
                        8a
                                                     Type: Expression Integer
--R
--R                                       2 2
--R        2a x sin(2a x) + cos(2a x) + 2a x
--R   (2)  ----------------------------------
--R                          2
--R                        8a
--R                                                     Type: Expression Integer
--E

--S 29 of 127
cc:=aa-bb
 

                                                                        2
        - 2a x sin(2a x) + 4a x cos(a x)sin(a x) - cos(2a x) + 2cos(a x)
   (3)  -----------------------------------------------------------------
                                         2
                                       8a
                                                     Type: Expression Integer
--R
--R                                                                        2
--R        - 2a x sin(2a x) + 4a x cos(a x)sin(a x) - cos(2a x) + 2cos(a x)
--R   (3)  -----------------------------------------------------------------
--R                                         2
--R                                       8a
--R                                                     Type: Expression Integer
--E

--S 30 of 127
cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
 

                           %T sin(b + a) - %T sin(b - a)
   (4)  %T cos(b)sin(a) == -----------------------------
                                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                           %N sin(b + a) - %N sin(b - a)
--I   (4)  %N cos(b)sin(a) == -----------------------------
--R                                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 31 of 127
dd:=cossinrule cc
 

                               2
        - cos(2a x) + 2cos(a x)
   (5)  ------------------------
                     2
                   8a
                                                     Type: Expression Integer
--R
--R                               2
--R        - cos(2a x) + 2cos(a x)
--R   (5)  ------------------------
--R                     2
--R                   8a
--R                                                     Type: Expression Integer
--E

--S 32 of 127
coscosrule:=rule(cos(a)*cos(b) == 1/2*(cos(a-b)+cos(a+b)))
 

                           %U cos(b + a) + %U cos(b - a)
   (6)  %U cos(a)cos(b) == -----------------------------
                                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R 
--R
--I                           %O cos(b + a) + %O cos(b - a)
--I   (6)  %O cos(a)cos(b) == -----------------------------
--I                                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 33 of 127
ee:=coscosrule dd
 

                               2
        - cos(2a x) + 2cos(a x)
   (7)  ------------------------
                     2
                   8a
                                                     Type: Expression Integer
--R
--R                               2
--R        - cos(2a x) + 2cos(a x)
--R   (7)  ------------------------
--R                     2
--R                   8a
--R                                                     Type: Expression Integer
--E

--S 34 of 127
cossqrrule1:=rule(cos(a)^2 == 1/2+1/2*cos(2*a))
 

              2    cos(2a) + 1
   (8)  cos(a)  == -----------
                        2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2    cos(2a) + 1
--R   (8)  cos(a)  == -----------
--R                        2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35 of 127     14:378 Schaums and Axiom differ by a constant
ff:=cossqrrule1 ee
 

         1
   (9)  ---
          2
        8a
                                                     Type: Expression Integer
--R
--R         1
--R   (9)  ---
--R          2
--R        8a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 36 of 127
aa:=integrate(cos(a*x)^3,x)
 

                 2
        (cos(a x)  + 2)sin(a x)
   (1)  -----------------------
                   3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2
--R        (cos(a x)  + 2)sin(a x)
--R   (1)  -----------------------
--R                   3a
--R                                          Type: Union(Expression Integer,...)
--E

--S 37 of 127
bb:=sin(a*x)/a-sin(a*x)^3/(3*a)
 

                  3
        - sin(a x)  + 3sin(a x)
   (2)  -----------------------
                   3a
                                                     Type: Expression Integer
--R
--R                  3
--R        - sin(a x)  + 3sin(a x)
--R   (2)  -----------------------
--R                   3a
--R                                                     Type: Expression Integer
--E 

--S 38 of 127
cc:=aa-bb
 

                3            2
        sin(a x)  + (cos(a x)  - 1)sin(a x)
   (3)  -----------------------------------
                         3a
                                                     Type: Expression Integer
--R
--R                3            2
--R        sin(a x)  + (cos(a x)  - 1)sin(a x)
--R   (3)  -----------------------------------
--R                         3a
--R                                                     Type: Expression Integer
--E

--S 39 of 127
cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
 

              2            2
   (4)  cos(a)  == - sin(a)  + 1
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R              2            2
--R   (4)  cos(a)  == - sin(a)  + 1
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 40 of 127     14:379 Schaums and Axiom agree
dd:=cossqrrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 41 of 127
aa:=integrate(cos(a*x)^4,x)
 

                  3
        (2cos(a x)  + 3cos(a x))sin(a x) + 3a x
   (1)  ---------------------------------------
                           8a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  3
--R        (2cos(a x)  + 3cos(a x))sin(a x) + 3a x
--R   (1)  ---------------------------------------
--R                           8a
--R                                          Type: Union(Expression Integer,...)
--E

--S 42 of 127
bb:=(3*x)/8+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
 

        sin(4a x) + 8sin(2a x) + 12a x
   (2)  ------------------------------
                      32a
                                                     Type: Expression Integer
--R
--R        sin(4a x) + 8sin(2a x) + 12a x
--R   (2)  ------------------------------
--R                      32a
--R                                                     Type: Expression Integer
--E 

--S 43 of 127
cc:=aa-bb
 

                                             3
        - sin(4a x) - 8sin(2a x) + (8cos(a x)  + 12cos(a x))sin(a x)
   (3)  ------------------------------------------------------------
                                     32a
                                                     Type: Expression Integer
--R
--R                                             3
--R        - sin(4a x) - 8sin(2a x) + (8cos(a x)  + 12cos(a x))sin(a x)
--R   (3)  ------------------------------------------------------------
--R                                     32a
--R                                                     Type: Expression Integer
--E

--S 44 of 127     14:380 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 45 of 127
aa:=integrate(1/cos(a*x)^2,x)
 

         sin(a x)
   (1)  ----------
        a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         sin(a x)
--R   (1)  ----------
--R        a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 46 of 127
bb:=tan(a*x)/a
 

        tan(a x)
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R        tan(a x)
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E 

--S 47 of 127
cc:=aa-bb
 

        - cos(a x)tan(a x) + sin(a x)
   (3)  -----------------------------
                  a cos(a x)
                                                     Type: Expression Integer
--R
--R        - cos(a x)tan(a x) + sin(a x)
--R   (3)  -----------------------------
--R                  a cos(a x)
--R                                                     Type: Expression Integer
--E

--S 48 of 127
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (4)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (4)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 49 of 127     14:381 Schaums and Axiom agree
dd:=tanrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 50 of 127
aa:=integrate(1/cos(a*x)^3,x)
 

   (1)
               2    sin(a x) + cos(a x) + 1
       cos(a x) log(-----------------------)
                          cos(a x) + 1
     + 
                 2    sin(a x) - cos(a x) - 1
       - cos(a x) log(-----------------------) + sin(a x)
                            cos(a x) + 1
  /
                2
     2a cos(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R               2    sin(a x) + cos(a x) + 1
--R       cos(a x) log(-----------------------)
--R                          cos(a x) + 1
--R     + 
--R                 2    sin(a x) - cos(a x) - 1
--R       - cos(a x) log(-----------------------) + sin(a x)
--R                            cos(a x) + 1
--R  /
--R                2
--R     2a cos(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 51 of 127
bb:=sin(a*x)/(2*a*cos(a*x)^2)+1/(2*a)*log(tan(%pi/4+(a*x)/2))
 

                2        2a x + %pi
        cos(a x) log(tan(----------)) + sin(a x)
                              4
   (2)  ----------------------------------------
                                 2
                      2a cos(a x)
                                                     Type: Expression Integer
--R
--R                2        2a x + %pi
--R        cos(a x) log(tan(----------)) + sin(a x)
--R                              4
--R   (2)  ----------------------------------------
--R                                 2
--R                      2a cos(a x)
--R                                                     Type: Expression Integer
--E 

--S 52 of 127
cc:=aa-bb
 

   (3)
                 2a x + %pi         sin(a x) + cos(a x) + 1
       - log(tan(----------)) + log(-----------------------)
                      4                   cos(a x) + 1
     + 
             sin(a x) - cos(a x) - 1
       - log(-----------------------)
                   cos(a x) + 1
  /
     2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                 2a x + %pi         sin(a x) + cos(a x) + 1
--R       - log(tan(----------)) + log(-----------------------)
--R                      4                   cos(a x) + 1
--R     + 
--R             sin(a x) - cos(a x) - 1
--R       - log(-----------------------)
--R                   cos(a x) + 1
--R  /
--R     2a
--R                                                     Type: Expression Integer
--E

--S 53 of 127     14:382 Schaums and Axiom differ by a constant
complexNormalize cc
 

        log(- 1)
   (4)  --------
           2a
                                                     Type: Expression Integer
--R
--R        log(- 1)
--R   (4)  --------
--R           2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 54 of 127
aa:=integrate(cos(a*x)*cos(p*x),x)
 

        p cos(a x)sin(p x) - a cos(p x)sin(a x)
   (1)  ---------------------------------------
                         2    2
                        p  - a
                                          Type: Union(Expression Integer,...)
--R
--R        p cos(a x)sin(p x) - a cos(p x)sin(a x)
--R   (1)  ---------------------------------------
--R                         2    2
--R                        p  - a
--R                                          Type: Union(Expression Integer,...)
--E

--S 55 of 127
bb:=(sin((a-p)*x))/(2*(a-p))+(sin((a+p)*x))/(2*(a+p))
 

        (p - a)sin((p + a)x) + (p + a)sin((p - a)x)
   (2)  -------------------------------------------
                           2     2
                         2p  - 2a
                                                     Type: Expression Integer
--R
--R        (p - a)sin((p + a)x) + (p + a)sin((p - a)x)
--R   (2)  -------------------------------------------
--R                           2     2
--R                         2p  - 2a
--R                                                     Type: Expression Integer
--E 

--S 56 of 127
cc:=aa-bb
 

   (3)
       (- p + a)sin((p + a)x) + 2p cos(a x)sin(p x) + (- p - a)sin((p - a)x)
     + 
       - 2a cos(p x)sin(a x)
  /
       2     2
     2p  - 2a
                                                     Type: Expression Integer
--R
--R   (3)
--R       (- p + a)sin((p + a)x) + 2p cos(a x)sin(p x) + (- p - a)sin((p - a)x)
--R     + 
--R       - 2a cos(p x)sin(a x)
--R  /
--R       2     2
--R     2p  - 2a
--R                                                     Type: Expression Integer
--E

--S 57 of 127     14:383 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 58 of 127
aa:=integrate(1/(1-cos(a*x)),x)
 

        - cos(a x) - 1
   (1)  --------------
          a sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - cos(a x) - 1
--R   (1)  --------------
--R          a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 59 of 127
bb:=-1/a*cot((a*x)/2)
 

              a x
          cot(---)
               2
   (2)  - --------
              a
                                                     Type: Expression Integer
--R
--R              a x
--R          cot(---)
--R               2
--R   (2)  - --------
--R              a
--R                                                     Type: Expression Integer
--E

--S 60 of 127
cc:=aa-bb
 

            a x
        cot(---)sin(a x) - cos(a x) - 1
             2
   (3)  -------------------------------
                   a sin(a x)
                                                     Type: Expression Integer
--R
--R            a x
--R        cot(---)sin(a x) - cos(a x) - 1
--R             2
--R   (3)  -------------------------------
--R                   a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 61 of 127     14:384 Schaums and Axiom agree
dd:=complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 62 of 127
aa:=integrate(x/(1-cos(a*x)),x)
 

   (1)
                  sin(a x)                        2
   2sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x) - a x
                cos(a x) + 1                cos(a x) + 1
   ---------------------------------------------------------------------------
                                     2
                                    a sin(a x)
                                          Type: Union(Expression Integer,...)
--R
--R   (1)
--R                  sin(a x)                        2
--R   2sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x) - a x
--R                cos(a x) + 1                cos(a x) + 1
--R   ---------------------------------------------------------------------------
--R                                     2
--R                                    a sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 63 of 127
bb:=-x/a*cot((a*x)/2)+2/a^2*log(sin((a*x)/2))
 

                 a x             a x
        2log(sin(---)) - a x cot(---)
                  2               2
   (2)  -----------------------------
                       2
                      a
                                                     Type: Expression Integer
--R
--R                 a x             a x
--R        2log(sin(---)) - a x cot(---)
--R                  2               2
--R   (2)  -----------------------------
--R                       2
--R                      a
--R                                                     Type: Expression Integer
--E

--S 64 of 127
cc:=aa-bb
 

   (3)
                      sin(a x)                       a x
       2sin(a x)log(------------) - 2sin(a x)log(sin(---))
                    cos(a x) + 1                      2
     + 
                           2                 a x
       - sin(a x)log(------------) + a x cot(---)sin(a x) - a x cos(a x) - a x
                     cos(a x) + 1             2
  /
      2
     a sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                      sin(a x)                       a x
--R       2sin(a x)log(------------) - 2sin(a x)log(sin(---))
--R                    cos(a x) + 1                      2
--R     + 
--R                           2                 a x
--R       - sin(a x)log(------------) + a x cot(---)sin(a x) - a x cos(a x) - a x
--R                     cos(a x) + 1             2
--R  /
--R      2
--R     a sin(a x)
--R                                                     Type: Expression Integer
--E

--S 65 of 127
cotrule:=rule(cot(a) == cos(a)/sin(a))
 

                  cos(a)
   (4)  cot(a) == ------
                  sin(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  cos(a)
--R   (4)  cot(a) == ------
--R                  sin(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 66 of 127
dd:=cotrule cc
 

   (5)
            a x               sin(a x)           a x                 a x
       2sin(---)sin(a x)log(------------) - 2sin(---)sin(a x)log(sin(---))
             2              cos(a x) + 1          2                   2
     + 
             a x                   2                 a x
       - sin(---)sin(a x)log(------------) + a x cos(---)sin(a x)
              2              cos(a x) + 1             2
     + 
                                 a x
       (- a x cos(a x) - a x)sin(---)
                                  2
  /
      2    a x
     a sin(---)sin(a x)
            2
                                                     Type: Expression Integer
--R
--R   (5)
--R            a x               sin(a x)           a x                 a x
--R       2sin(---)sin(a x)log(------------) - 2sin(---)sin(a x)log(sin(---))
--R             2              cos(a x) + 1          2                   2
--R     + 
--R             a x                   2                 a x
--R       - sin(---)sin(a x)log(------------) + a x cos(---)sin(a x)
--R              2              cos(a x) + 1             2
--R     + 
--R                                 a x
--R       (- a x cos(a x) - a x)sin(---)
--R                                  2
--R  /
--R      2    a x
--R     a sin(---)sin(a x)
--R            2
--R                                                     Type: Expression Integer
--E

--S 67 of 127
ee:=expandLog dd
 

   (6)
            a x                              a x                 a x
       2sin(---)sin(a x)log(sin(a x)) - 2sin(---)sin(a x)log(sin(---))
             2                                2                   2
     + 
             a x
       - sin(---)sin(a x)log(cos(a x) + 1)
              2
     + 
                  a x            a x                                       a x
     (- log(2)sin(---) + a x cos(---))sin(a x) + (- a x cos(a x) - a x)sin(---)
                   2              2                                         2
  /
      2    a x
     a sin(---)sin(a x)
            2
                                                     Type: Expression Integer
--R
--R   (6)
--R            a x                              a x                 a x
--R       2sin(---)sin(a x)log(sin(a x)) - 2sin(---)sin(a x)log(sin(---))
--R             2                                2                   2
--R     + 
--R             a x
--R       - sin(---)sin(a x)log(cos(a x) + 1)
--R              2
--R     + 
--R                  a x            a x                                       a x
--R     (- log(2)sin(---) + a x cos(---))sin(a x) + (- a x cos(a x) - a x)sin(---)
--R                   2              2                                         2
--R  /
--R      2    a x
--R     a sin(---)sin(a x)
--R            2
--R                                                     Type: Expression Integer
--E

--S 68 of 127     14:385 Schaums and Axiom agree
complexNormalize ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 69 of 127
aa:=integrate(1/(1+cos(a*x)),x)
 

           sin(a x)
   (1)  --------------
        a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R
--R           sin(a x)
--R   (1)  --------------
--R        a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E

--S 70 of 127
bb:=1/a*tan((a*x)/2)
 

            a x
        tan(---)
             2
   (2)  --------
            a
                                                     Type: Expression Integer
--R
--R            a x
--R        tan(---)
--R             2
--R   (2)  --------
--R            a
--R                                                     Type: Expression Integer
--E

--S 71 of 127
cc:=aa-bb
 

                            a x
        (- cos(a x) - 1)tan(---) + sin(a x)
                             2
   (3)  -----------------------------------
                   a cos(a x) + a
                                                     Type: Expression Integer
--R
--R                            a x
--R        (- cos(a x) - 1)tan(---) + sin(a x)
--R                             2
--R   (3)  -----------------------------------
--R                   a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 72 of 127     14:386 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 73 of 127
aa:=integrate(x/(1+cos(a*x)),x)
 

                                  2
        (- cos(a x) - 1)log(------------) + a x sin(a x)
                            cos(a x) + 1
   (1)  ------------------------------------------------
                          2            2
                         a cos(a x) + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                  2
--R        (- cos(a x) - 1)log(------------) + a x sin(a x)
--R                            cos(a x) + 1
--R   (1)  ------------------------------------------------
--R                          2            2
--R                         a cos(a x) + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 74 of 127
bb:=x/a*tan((a*x)/2)+2/a^2*log(cos((a*x)/2))
 

                 a x             a x
        2log(cos(---)) + a x tan(---)
                  2               2
   (2)  -----------------------------
                       2
                      a
                                                     Type: Expression Integer
--R
--R                 a x             a x
--R        2log(cos(---)) + a x tan(---)
--R                  2               2
--R   (2)  -----------------------------
--R                       2
--R                      a
--R                                                     Type: Expression Integer
--E

--S 75 of 127
cc:=aa-bb
 

   (3)
                                a x                               2
       (- 2cos(a x) - 2)log(cos(---)) + (- cos(a x) - 1)log(------------)
                                 2                          cos(a x) + 1
     + 
                                 a x
       (- a x cos(a x) - a x)tan(---) + a x sin(a x)
                                  2
  /
      2            2
     a cos(a x) + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                a x                               2
--R       (- 2cos(a x) - 2)log(cos(---)) + (- cos(a x) - 1)log(------------)
--R                                 2                          cos(a x) + 1
--R     + 
--R                                 a x
--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x)
--R                                  2
--R  /
--R      2            2
--R     a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 76 of 127
dd:=expandLog cc
 

   (4)
                                                                  a x
       (cos(a x) + 1)log(cos(a x) + 1) + (- 2cos(a x) - 2)log(cos(---))
                                                                   2
     + 
                                 a x
       (- a x cos(a x) - a x)tan(---) + a x sin(a x) - log(2)cos(a x) - log(2)
                                  2
  /
      2            2
     a cos(a x) + a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                                                  a x
--R       (cos(a x) + 1)log(cos(a x) + 1) + (- 2cos(a x) - 2)log(cos(---))
--R                                                                   2
--R     + 
--R                                 a x
--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x) - log(2)cos(a x) - log(2)
--R                                  2
--R  /
--R      2            2
--R     a cos(a x) + a
--R                                                     Type: Expression Integer
--E

--S 77 of 127     14:387 Schaums and Axiom agree
complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 78 of 127
aa:=integrate(1/(1-cos(a*x))^2,x)
 

                  2
        - cos(a x)  + cos(a x) + 2
   (1)  --------------------------
        (3a cos(a x) - 3a)sin(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2
--R        - cos(a x)  + cos(a x) + 2
--R   (1)  --------------------------
--R        (3a cos(a x) - 3a)sin(a x)
--R                                          Type: Union(Expression Integer,...)
--E

--S 79 of 127
bb:=-1/(2*a)*cot((a*x)/2)-1/(6*a)*cot((a*x)/2)^3
 

              a x 3        a x
        - cot(---)  - 3cot(---)
               2            2
   (2)  -----------------------
                   6a
                                                     Type: Expression Integer
--R
--R              a x 3        a x
--R        - cot(---)  - 3cot(---)
--R               2            2
--R   (2)  -----------------------
--R                   6a
--R                                                     Type: Expression Integer
--E 

--S 80 of 127
cc:=aa-bb
 

   (3)
                          a x 3                      a x                      2
       ((cos(a x) - 1)cot(---)  + (3cos(a x) - 3)cot(---))sin(a x) - 2cos(a x)
                           2                          2
     + 
       2cos(a x) + 4
  /
     (6a cos(a x) - 6a)sin(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                          a x 3                      a x                      2
--R       ((cos(a x) - 1)cot(---)  + (3cos(a x) - 3)cot(---))sin(a x) - 2cos(a x)
--R                           2                          2
--R     + 
--R       2cos(a x) + 4
--R  /
--R     (6a cos(a x) - 6a)sin(a x)
--R                                                     Type: Expression Integer
--E

--S 81 of 127     14:388 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 82 of 127
aa:=integrate(1/(1+cos(a*x))^2,x)
 

             (cos(a x) + 2)sin(a x)
   (1)  -------------------------------
                   2
        3a cos(a x)  + 6a cos(a x) + 3a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             (cos(a x) + 2)sin(a x)
--R   (1)  -------------------------------
--R                   2
--R        3a cos(a x)  + 6a cos(a x) + 3a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 83 of 127
bb:=1/(2*a)*tan((a*x)/2)+1/(6*a)*tan((a*x)/2)^3
 

            a x 3        a x
        tan(---)  + 3tan(---)
             2            2
   (2)  ---------------------
                  6a
                                                     Type: Expression Integer
--R
--R            a x 3        a x
--R        tan(---)  + 3tan(---)
--R             2            2
--R   (2)  ---------------------
--R                  6a
--R                                                     Type: Expression Integer
--E

--S 84 of 127
cc:=aa-bb
 

   (3)
                  2                     a x 3
       (- cos(a x)  - 2cos(a x) - 1)tan(---)
                                         2
     + 
                   2                     a x
       (- 3cos(a x)  - 6cos(a x) - 3)tan(---) + (2cos(a x) + 4)sin(a x)
                                          2
  /
                2
     6a cos(a x)  + 12a cos(a x) + 6a
                                                     Type: Expression Integer
--R
--R   (3)
--R                  2                     a x 3
--R       (- cos(a x)  - 2cos(a x) - 1)tan(---)
--R                                         2
--R     + 
--R                   2                     a x
--R       (- 3cos(a x)  - 6cos(a x) - 3)tan(---) + (2cos(a x) + 4)sin(a x)
--R                                          2
--R  /
--R                2
--R     6a cos(a x)  + 12a cos(a x) + 6a
--R                                                     Type: Expression Integer
--E

--S 85 of 127     14:389 Schaums and Axiom agree
complexNormalize cc
 

   (4)  0
                                                     Type: Expression Integer
--R
--R   (4)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 86 of 127
aa:=integrate(1/(p+q*cos(a*x)),x)
 

   (1)
                           +-------+
                           | 2    2        2    2
        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
    log(--------------------------------------------------)
                          q cos(a x) + p
   [-------------------------------------------------------,
                            +-------+
                            | 2    2
                          a\|q  - p
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p
    2atan(-----------------------)
          (q + p)cos(a x) + q + p
    ------------------------------]
               +---------+
               |   2    2
             a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (1)
--R                           +-------+
--R                           | 2    2        2    2
--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R    log(--------------------------------------------------)
--R                          q cos(a x) + p
--R   [-------------------------------------------------------,
--R                            +-------+
--R                            | 2    2
--R                          a\|q  - p
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p
--R    2atan(-----------------------)
--R          (q + p)cos(a x) + q + p
--R    ------------------------------]
--R               +---------+
--R               |   2    2
--R             a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 87 of 127
bb1:=2/(a*sqrt(p^2-q^2))*atan(sqrt((p-q)/(p+q))*tan(1/2*a*x))
 

                       +-------+
                  a x  |- q + p
        2atan(tan(---) |------- )
                   2  \| q + p
   (2)  -------------------------
                +---------+
                |   2    2
              a\|- q  + p
                                                     Type: Expression Integer
--R 
--R
--R                       +-------+
--R                  a x  |- q + p
--R        2atan(tan(---) |------- )
--R                   2  \| q + p
--R   (2)  -------------------------
--R                +---------+
--R                |   2    2
--R              a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 88 of 127
bb2:=1/(a*sqrt(q^2-p^2))*log((tan(1/2*a*x)+sqrt((q+p)/(q-p)))/(tan(1/2*a*x)-sqrt((q+p)/(q-p))))
 

               +-----+
               |q + p        a x
            -  |-----  - tan(---)
              \|q - p         2
        log(---------------------)
              +-----+
              |q + p        a x
              |-----  - tan(---)
             \|q - p         2
   (3)  --------------------------
                  +-------+
                  | 2    2
                a\|q  - p
                                                     Type: Expression Integer
--R
--R               +-----+
--R               |q + p        a x
--R            -  |-----  - tan(---)
--R              \|q - p         2
--R        log(---------------------)
--R              +-----+
--R              |q + p        a x
--R              |-----  - tan(---)
--R             \|q - p         2
--R   (3)  --------------------------
--R                  +-------+
--R                  | 2    2
--R                a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 89 of 127
cc1:=aa.1-bb1
 

   (4)
                                          +-------+
        +---------+                       | 2    2        2    2
        |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       \|- q  + p  log(--------------------------------------------------)
                                         q cos(a x) + p
     + 
           +-------+              +-------+
           | 2    2          a x  |- q + p
       - 2\|q  - p  atan(tan(---) |------- )
                              2  \| q + p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R 
--R
--R   (4)
--R                                          +-------+
--R        +---------+                       | 2    2        2    2
--R        |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       \|- q  + p  log(--------------------------------------------------)
--R                                         q cos(a x) + p
--R     + 
--R           +-------+              +-------+
--R           | 2    2          a x  |- q + p
--R       - 2\|q  - p  atan(tan(---) |------- )
--R                              2  \| q + p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 90 of 127
cc2:=aa.2-bb1
 

                                                       +---------+
                         +-------+                     |   2    2
                    a x  |- q + p             sin(a x)\|- q  + p
        - 2atan(tan(---) |------- ) + 2atan(-----------------------)
                     2  \| q + p            (q + p)cos(a x) + q + p
   (5)  ------------------------------------------------------------
                                  +---------+
                                  |   2    2
                                a\|- q  + p
                                                     Type: Expression Integer
--R 
--R
--R                                                       +---------+
--R                         +-------+                     |   2    2
--R                    a x  |- q + p             sin(a x)\|- q  + p
--R        - 2atan(tan(---) |------- ) + 2atan(-----------------------)
--R                     2  \| q + p            (q + p)cos(a x) + q + p
--R   (5)  ------------------------------------------------------------
--R                                  +---------+
--R                                  |   2    2
--R                                a\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 91 of 127
cc3:=aa.1-bb2
 

   (6)
                +-----+
                |q + p        a x
             -  |-----  - tan(---)
               \|q - p         2
       - log(---------------------)
               +-----+
               |q + p        a x
               |-----  - tan(---)
              \|q - p         2
     + 
                              +-------+
                              | 2    2        2    2
           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       log(--------------------------------------------------)
                             q cos(a x) + p
  /
       +-------+
       | 2    2
     a\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                +-----+
--R                |q + p        a x
--R             -  |-----  - tan(---)
--R               \|q - p         2
--R       - log(---------------------)
--R               +-----+
--R               |q + p        a x
--R               |-----  - tan(---)
--R              \|q - p         2
--R     + 
--R                              +-------+
--R                              | 2    2        2    2
--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       log(--------------------------------------------------)
--R                             q cos(a x) + p
--R  /
--R       +-------+
--R       | 2    2
--R     a\|q  - p
--R                                                     Type: Expression Integer
--E

--S 92 of 127     14:390 Axiom cannot simplify these expressions
cc4:=aa.2-bb2
 

   (7)
                            +-----+
                            |q + p        a x
          +---------+    -  |-----  - tan(---)
          |   2    2       \|q - p         2
       - \|- q  + p  log(---------------------)
                           +-----+
                           |q + p        a x
                           |-----  - tan(---)
                          \|q - p         2
     + 
                                  +---------+
         +-------+                |   2    2
         | 2    2        sin(a x)\|- q  + p
       2\|q  - p  atan(-----------------------)
                       (q + p)cos(a x) + q + p
  /
       +---------+ +-------+
       |   2    2  | 2    2
     a\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-----+
--R                            |q + p        a x
--R          +---------+    -  |-----  - tan(---)
--R          |   2    2       \|q - p         2
--R       - \|- q  + p  log(---------------------)
--R                           +-----+
--R                           |q + p        a x
--R                           |-----  - tan(---)
--R                          \|q - p         2
--R     + 
--R                                  +---------+
--R         +-------+                |   2    2
--R         | 2    2        sin(a x)\|- q  + p
--R       2\|q  - p  atan(-----------------------)
--R                       (q + p)cos(a x) + q + p
--R  /
--R       +---------+ +-------+
--R       |   2    2  | 2    2
--R     a\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 93 of 127
aa:=integrate(1/(p+q*cos(a*x))^2,x)
 

   (1)
   [
                            2
           (p q cos(a x) + p )
        *
                                  +-------+
                                  | 2    2      2    2
               (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
           log(------------------------------------------------)
                                q cos(a x) + p
       + 
                    +-------+
                    | 2    2
         q sin(a x)\|q  - p
    /
                                                +-------+
            3      2                  2      3  | 2    2
       ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
     ,

                                                +---------+
                                                |   2    2
                              2        sin(a x)\|- q  + p
         (- 2p q cos(a x) - 2p )atan(-----------------------)
                                     (q + p)cos(a x) + q + p
       + 
                    +---------+
                    |   2    2
         q sin(a x)\|- q  + p
    /
                                                +---------+
            3      2                  2      3  |   2    2
       ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R   [
--R                            2
--R           (p q cos(a x) + p )
--R        *
--R                                  +-------+
--R                                  | 2    2      2    2
--R               (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R           log(------------------------------------------------)
--R                                q cos(a x) + p
--R       + 
--R                    +-------+
--R                    | 2    2
--R         q sin(a x)\|q  - p
--R    /
--R                                                +-------+
--R            3      2                  2      3  | 2    2
--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
--R     ,
--R
--R                                                +---------+
--R                                                |   2    2
--R                              2        sin(a x)\|- q  + p
--R         (- 2p q cos(a x) - 2p )atan(-----------------------)
--R                                     (q + p)cos(a x) + q + p
--R       + 
--R                    +---------+
--R                    |   2    2
--R         q sin(a x)\|- q  + p
--R    /
--R                                                +---------+
--R            3      2                  2      3  |   2    2
--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 94 of 127
t1:=integrate(1/(p+q*cos(a*x)),x)
 

   (2)
                           +-------+
                           | 2    2        2    2
        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
    log(--------------------------------------------------)
                          q cos(a x) + p
   [-------------------------------------------------------,
                            +-------+
                            | 2    2
                          a\|q  - p
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p
    2atan(-----------------------)
          (q + p)cos(a x) + q + p
    ------------------------------]
               +---------+
               |   2    2
             a\|- q  + p
                                     Type: Union(List Expression Integer,...)
--R
--R   (2)
--R                           +-------+
--R                           | 2    2        2    2
--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R    log(--------------------------------------------------)
--R                          q cos(a x) + p
--R   [-------------------------------------------------------,
--R                            +-------+
--R                            | 2    2
--R                          a\|q  - p
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p
--R    2atan(-----------------------)
--R          (q + p)cos(a x) + q + p
--R    ------------------------------]
--R               +---------+
--R               |   2    2
--R             a\|- q  + p
--R                                     Type: Union(List Expression Integer,...)
--E

--S 95 of 127
bb1:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.1
 

   (3)
                            2
         (- p q cos(a x) - p )
      *
                                +-------+
                                | 2    2        2    2
             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
         log(--------------------------------------------------)
                               q cos(a x) + p
     + 
                  +-------+
                  | 2    2
       q sin(a x)\|q  - p
  /
                                              +-------+
          3      2                  2      3  | 2    2
     ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (3)
--R                            2
--R         (- p q cos(a x) - p )
--R      *
--R                                +-------+
--R                                | 2    2        2    2
--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R         log(--------------------------------------------------)
--R                               q cos(a x) + p
--R     + 
--R                  +-------+
--R                  | 2    2
--R       q sin(a x)\|q  - p
--R  /
--R                                              +-------+
--R          3      2                  2      3  | 2    2
--R     ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 96 of 127
bb2:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.2
 

   (4)
                                          +---------+
                                          |   2    2                 +---------+
                        2        sin(a x)\|- q  + p                  |   2    2
   (- 2p q cos(a x) - 2p )atan(-----------------------) + q sin(a x)\|- q  + p
                               (q + p)cos(a x) + q + p
   -----------------------------------------------------------------------------
                                                         +---------+
                     3      2                  2      3  |   2    2
                ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                          +---------+
--R                                          |   2    2                 +---------+
--R                        2        sin(a x)\|- q  + p                  |   2    2
--R   (- 2p q cos(a x) - 2p )atan(-----------------------) + q sin(a x)\|- q  + p
--R                               (q + p)cos(a x) + q + p
--R   -----------------------------------------------------------------------------
--R                                                         +---------+
--R                     3      2                  2      3  |   2    2
--R                ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 97 of 127
cc1:=aa.1-bb1
 

   (5)
                                +-------+
                                | 2    2      2    2
             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p log(------------------------------------------------)
                              q cos(a x) + p
     + 
                                +-------+
                                | 2    2        2    2
             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p log(--------------------------------------------------)
                               q cos(a x) + p
  /
                   +-------+
         2      2  | 2    2
     (a q  - a p )\|q  - p
                                                     Type: Expression Integer
--R
--R   (5)
--R                                +-------+
--R                                | 2    2      2    2
--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p log(------------------------------------------------)
--R                              q cos(a x) + p
--R     + 
--R                                +-------+
--R                                | 2    2        2    2
--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p log(--------------------------------------------------)
--R                               q cos(a x) + p
--R  /
--R                   +-------+
--R         2      2  | 2    2
--R     (a q  - a p )\|q  - p
--R                                                     Type: Expression Integer
--E

--S 98 of 127
cc2:=aa.2-bb1
 

   (6)
                                           +-------+
         +---------+                       | 2    2        2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
       p\|- q  + p  log(--------------------------------------------------)
                                          q cos(a x) + p
     + 
                                     +---------+
            +-------+                |   2    2
            | 2    2        sin(a x)\|- q  + p
       - 2p\|q  - p  atan(-----------------------)
                          (q + p)cos(a x) + q + p
  /
                   +---------+ +-------+
         2      2  |   2    2  | 2    2
     (a q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R                                           +-------+
--R         +---------+                       | 2    2        2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
--R       p\|- q  + p  log(--------------------------------------------------)
--R                                          q cos(a x) + p
--R     + 
--R                                     +---------+
--R            +-------+                |   2    2
--R            | 2    2        sin(a x)\|- q  + p
--R       - 2p\|q  - p  atan(-----------------------)
--R                          (q + p)cos(a x) + q + p
--R  /
--R                   +---------+ +-------+
--R         2      2  |   2    2  | 2    2
--R     (a q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 99 of 127
cc3:=aa.1-bb2
 

   (7)
                                           +-------+
         +---------+                       | 2    2      2    2
         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
       p\|- q  + p  log(------------------------------------------------)
                                         q cos(a x) + p
     + 
                                   +---------+
          +-------+                |   2    2
          | 2    2        sin(a x)\|- q  + p
       2p\|q  - p  atan(-----------------------)
                        (q + p)cos(a x) + q + p
  /
                   +---------+ +-------+
         2      2  |   2    2  | 2    2
     (a q  - a p )\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                                           +-------+
--R         +---------+                       | 2    2      2    2
--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
--R       p\|- q  + p  log(------------------------------------------------)
--R                                         q cos(a x) + p
--R     + 
--R                                   +---------+
--R          +-------+                |   2    2
--R          | 2    2        sin(a x)\|- q  + p
--R       2p\|q  - p  atan(-----------------------)
--R                        (q + p)cos(a x) + q + p
--R  /
--R                   +---------+ +-------+
--R         2      2  |   2    2  | 2    2
--R     (a q  - a p )\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 100 of 127    14:391 Schaums and Axiom agree
cc4:=aa.2-bb2
 

   (8)  0
                                                     Type: Expression Integer
--R
--R   (8)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 101 of 127
aa:=integrate(1/(p^2+q^2*cos(a*x)^2),x)
 

   (1)
                 +-------+
                 | 2    2                 2    2              2
        sin(a x)\|q  + p               ((q  - p )cos(a x) - 2p )sin(a x)
   atan(------------------) - atan(-----------------------------------------)
         2p cos(a x) + 2p                                          +-------+
                                              2                    | 2    2
                                   (p cos(a x)  + 2p cos(a x) + p)\|q  + p
   --------------------------------------------------------------------------
                                      +-------+
                                      | 2    2
                                  a p\|q  + p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                 +-------+
--R                 | 2    2                 2    2              2
--R        sin(a x)\|q  + p               ((q  - p )cos(a x) - 2p )sin(a x)
--R   atan(------------------) - atan(-----------------------------------------)
--R         2p cos(a x) + 2p                                          +-------+
--R                                              2                    | 2    2
--R                                   (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R   --------------------------------------------------------------------------
--R                                      +-------+
--R                                      | 2    2
--R                                  a p\|q  + p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 102 of 127
bb:=1/(a*p*sqrt(p^2+q^2))*atan((p*tan(a*x))/sqrt(p^2+q^2))
 

             p tan(a x)
        atan(----------)
              +-------+
              | 2    2
             \|q  + p
   (2)  ----------------
              +-------+
              | 2    2
          a p\|q  + p
                                                     Type: Expression Integer
--R
--R             p tan(a x)
--R        atan(----------)
--R              +-------+
--R              | 2    2
--R             \|q  + p
--R   (2)  ----------------
--R              +-------+
--R              | 2    2
--R          a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 103 of 127
cc:=aa-bb
 

   (3)
                     +-------+
                     | 2    2
            sin(a x)\|q  + p           p tan(a x)
       atan(------------------) - atan(----------)
             2p cos(a x) + 2p           +-------+
                                        | 2    2
                                       \|q  + p
     + 
                     2    2              2
                  ((q  - p )cos(a x) - 2p )sin(a x)
       - atan(-----------------------------------------)
                                              +-------+
                         2                    | 2    2
              (p cos(a x)  + 2p cos(a x) + p)\|q  + p
  /
         +-------+
         | 2    2
     a p\|q  + p
                                                     Type: Expression Integer
--R
--R   (3)
--R                     +-------+
--R                     | 2    2
--R            sin(a x)\|q  + p           p tan(a x)
--R       atan(------------------) - atan(----------)
--R             2p cos(a x) + 2p           +-------+
--R                                        | 2    2
--R                                       \|q  + p
--R     + 
--R                     2    2              2
--R                  ((q  - p )cos(a x) - 2p )sin(a x)
--R       - atan(-----------------------------------------)
--R                                              +-------+
--R                         2                    | 2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|q  + p
--R  /
--R         +-------+
--R         | 2    2
--R     a p\|q  + p
--R                                                     Type: Expression Integer
--E

--S 104 of 127
dd:=ratDenom cc
 

   (4)
                                   +-------+
          +-------+                | 2    2
          | 2    2      p tan(a x)\|q  + p
       - \|q  + p  atan(--------------------)
                                2    2
                               q  + p
     + 
       -
             +-------+
             | 2    2
            \|q  + p
         *
                                                          +-------+
                           2    2              2          | 2    2
                        ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
            atan(--------------------------------------------------------)
                     2    3         2        2     3               2    3
                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                               +-------+
        +-------+              | 2    2
        | 2    2      sin(a x)\|q  + p
       \|q  + p  atan(------------------)
                       2p cos(a x) + 2p
  /
          2      3
     a p q  + a p
                                                     Type: Expression Integer
--R
--R   (4)
--R                                   +-------+
--R          +-------+                | 2    2
--R          | 2    2      p tan(a x)\|q  + p
--R       - \|q  + p  atan(--------------------)
--R                                2    2
--R                               q  + p
--R     + 
--R       -
--R             +-------+
--R             | 2    2
--R            \|q  + p
--R         *
--R                                                          +-------+
--R                           2    2              2          | 2    2
--R                        ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
--R            atan(--------------------------------------------------------)
--R                     2    3         2        2     3               2    3
--R                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                               +-------+
--R        +-------+              | 2    2
--R        | 2    2      sin(a x)\|q  + p
--R       \|q  + p  atan(------------------)
--R                       2p cos(a x) + 2p
--R  /
--R          2      3
--R     a p q  + a p
--R                                                     Type: Expression Integer
--E

--S 105 of 127
atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
 

                     1                    1
   (5)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
                     2                    2
Type: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--R
--R                     1                    1
--R   (5)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
--R                     2                    2
--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--E

--S 106 of 127
ee:=atanrule2 dd
 

   (6)
                                       +-------+
            +-------+                  | 2    2     2    2
       1    | 2    2     %i p tan(a x)\|q  + p   + q  + p
       - %i\|q  + p  log(---------------------------------)
       2                               2    2
                                      q  + p
     + 
              +-------+
         1    | 2    2
         - %i\|q  + p
         2
      *
         log
                                                           +-------+
                      2       2                 2          | 2    2
                ((%i q  - %i p )cos(a x) - 2%i p )sin(a x)\|q  + p
              + 
                    2    3         2        2     3               2    3
                (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
           /
                  2    3         2        2     3               2    3
              (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                                         +-------+
                           1             | 2    2
              +-------+    - %i sin(a x)\|q  + p   + p cos(a x) + p
         1    | 2    2     2
       - - %i\|q  + p  log(----------------------------------------)
         2                              p cos(a x) + p
     + 
                                         +-------+
                           1             | 2    2
            +-------+    - - %i sin(a x)\|q  + p   + p cos(a x) + p
       1    | 2    2       2
       - %i\|q  + p  log(------------------------------------------)
       2                               p cos(a x) + p
     + 
       -
                 +-------+
            1    | 2    2
            - %i\|q  + p
            2
         *
            log
                                                                +-------+
                           2       2                 2          | 2    2
                   ((- %i q  + %i p )cos(a x) + 2%i p )sin(a x)\|q  + p
                 + 
                       2    3         2        2     3               2    3
                   (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
              /
                     2    3         2        2     3               2    3
                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
     + 
                                           +-------+
              +-------+                    | 2    2     2    2
         1    | 2    2     - %i p tan(a x)\|q  + p   + q  + p
       - - %i\|q  + p  log(-----------------------------------)
         2                                2    2
                                         q  + p
  /
          2      3
     a p q  + a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (6)
--R                                       +-------+
--R            +-------+                  | 2    2     2    2
--R       1    | 2    2     %i p tan(a x)\|q  + p   + q  + p
--R       - %i\|q  + p  log(---------------------------------)
--R       2                               2    2
--R                                      q  + p
--R     + 
--R              +-------+
--R         1    | 2    2
--R         - %i\|q  + p
--R         2
--R      *
--R         log
--R                                                           +-------+
--R                      2       2                 2          | 2    2
--R                ((%i q  - %i p )cos(a x) - 2%i p )sin(a x)\|q  + p
--R              + 
--R                    2    3         2        2     3               2    3
--R                (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R           /
--R                  2    3         2        2     3               2    3
--R              (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                                         +-------+
--R                           1             | 2    2
--R              +-------+    - %i sin(a x)\|q  + p   + p cos(a x) + p
--R         1    | 2    2     2
--R       - - %i\|q  + p  log(----------------------------------------)
--R         2                              p cos(a x) + p
--R     + 
--R                                         +-------+
--R                           1             | 2    2
--R            +-------+    - - %i sin(a x)\|q  + p   + p cos(a x) + p
--R       1    | 2    2       2
--R       - %i\|q  + p  log(------------------------------------------)
--R       2                               p cos(a x) + p
--R     + 
--R       -
--R                 +-------+
--R            1    | 2    2
--R            - %i\|q  + p
--R            2
--R         *
--R            log
--R                                                                +-------+
--R                           2       2                 2          | 2    2
--R                   ((- %i q  + %i p )cos(a x) + 2%i p )sin(a x)\|q  + p
--R                 + 
--R                       2    3         2        2     3               2    3
--R                   (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R              /
--R                     2    3         2        2     3               2    3
--R                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
--R     + 
--R                                           +-------+
--R              +-------+                    | 2    2     2    2
--R         1    | 2    2     - %i p tan(a x)\|q  + p   + q  + p
--R       - - %i\|q  + p  log(-----------------------------------)
--R         2                                2    2
--R                                         q  + p
--R  /
--R          2      3
--R     a p q  + a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 107 of 127
ff:=expandLog ee
 

   (7)
              +-------+               +-------+
         1    | 2    2                | 2    2        2       2
       - - %i\|q  + p  log(p tan(a x)\|q  + p   + %i q  + %i p )
         2
     + 
            +-------+               +-------+
       1    | 2    2                | 2    2        2       2
       - %i\|q  + p  log(p tan(a x)\|q  + p   - %i q  - %i p )
       2
     + 
       -
                 +-------+
            1    | 2    2
            - %i\|q  + p
            2
         *
            log
                                                   +-------+
                    2    2              2          | 2    2
                 ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
               + 
                        2       3         2           2        3
                 (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
               + 
                       2       3
                 %i p q  + %i p
     + 
              +-------+
         1    | 2    2
         - %i\|q  + p
         2
      *
         log
                                                +-------+
                 2    2              2          | 2    2
              ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
            + 
                       2       3         2             2        3
              (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
            + 
                      2       3
              - %i p q  - %i p
     + 
            +-------+             +-------+
       1    | 2    2              | 2    2
       - %i\|q  + p  log(sin(a x)\|q  + p   + 2%i p cos(a x) + 2%i p)
       2
     + 
              +-------+             +-------+
         1    | 2    2              | 2    2
       - - %i\|q  + p  log(sin(a x)\|q  + p   - 2%i p cos(a x) - 2%i p)
         2
     + 
                                                                     +-------+
                   1        1       1          1                     | 2    2
     (%i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i))\|q  + p
                   2        2       2          2
  /
          2      3
     a p q  + a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (7)
--R              +-------+               +-------+
--R         1    | 2    2                | 2    2        2       2
--R       - - %i\|q  + p  log(p tan(a x)\|q  + p   + %i q  + %i p )
--R         2
--R     + 
--R            +-------+               +-------+
--R       1    | 2    2                | 2    2        2       2
--R       - %i\|q  + p  log(p tan(a x)\|q  + p   - %i q  - %i p )
--R       2
--R     + 
--R       -
--R                 +-------+
--R            1    | 2    2
--R            - %i\|q  + p
--R            2
--R         *
--R            log
--R                                                   +-------+
--R                    2    2              2          | 2    2
--R                 ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
--R               + 
--R                        2       3         2           2        3
--R                 (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
--R               + 
--R                       2       3
--R                 %i p q  + %i p
--R     + 
--R              +-------+
--R         1    | 2    2
--R         - %i\|q  + p
--R         2
--R      *
--R         log
--R                                                +-------+
--R                 2    2              2          | 2    2
--R              ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
--R            + 
--R                       2       3         2             2        3
--R              (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
--R            + 
--R                      2       3
--R              - %i p q  - %i p
--R     + 
--R            +-------+             +-------+
--R       1    | 2    2              | 2    2
--R       - %i\|q  + p  log(sin(a x)\|q  + p   + 2%i p cos(a x) + 2%i p)
--R       2
--R     + 
--R              +-------+             +-------+
--R         1    | 2    2              | 2    2
--R       - - %i\|q  + p  log(sin(a x)\|q  + p   - 2%i p cos(a x) - 2%i p)
--R         2
--R     + 
--R                                                                     +-------+
--R                   1        1       1          1                     | 2    2
--R     (%i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i))\|q  + p
--R                   2        2       2          2
--R  /
--R          2      3
--R     a p q  + a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 108 of 127    14:392 Schaums and Axiom differ by a constant
complexNormalize ff
 

   (8)
                      1        1       1          1
         %i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i)
                      2        2       2          2
       + 
           1
         - - %i log(- 1)
           2
    *
        +-------+
        | 2    2
       \|q  + p
  /
          2      3
     a p q  + a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (8)
--R                      1        1       1          1
--R         %i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i)
--R                      2        2       2          2
--R       + 
--R           1
--R         - - %i log(- 1)
--R           2
--R    *
--R        +-------+
--R        | 2    2
--R       \|q  + p
--R  /
--R          2      3
--R     a p q  + a p
--R                                    Type: Expression Complex Fraction Integer
--E

)clear all
 

--S 109 of 127
aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x)
 

   (1)
                                   +-------+
           2     2         2    2  | 2    2           2     3
        ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
    log(----------------------------------------------------------------------)
                                    2        2    2
                                   q cos(a x)  - p
   [---------------------------------------------------------------------------,
                                        +-------+
                                        | 2    2
                                   2a p\|q  - p

                       +---------+
                       |   2    2
              sin(a x)\|- q  + p
         atan(--------------------)
                2p cos(a x) + 2p
       + 
                      2    2              2
                   ((q  + p )cos(a x) + 2p )sin(a x)
         atan(-------------------------------------------)
                                              +---------+
                         2                    |   2    2
              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
    /
           +---------+
           |   2    2
       a p\|- q  + p
     ]
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (1)
--R                                   +-------+
--R           2     2         2    2  | 2    2           2     3
--R        ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
--R    log(----------------------------------------------------------------------)
--R                                    2        2    2
--R                                   q cos(a x)  - p
--R   [---------------------------------------------------------------------------,
--R                                        +-------+
--R                                        | 2    2
--R                                   2a p\|q  - p
--R
--R                       +---------+
--R                       |   2    2
--R              sin(a x)\|- q  + p
--R         atan(--------------------)
--R                2p cos(a x) + 2p
--R       + 
--R                      2    2              2
--R                   ((q  + p )cos(a x) + 2p )sin(a x)
--R         atan(-------------------------------------------)
--R                                              +---------+
--R                         2                    |   2    2
--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R    /
--R           +---------+
--R           |   2    2
--R       a p\|- q  + p
--R     ]
--R                                     Type: Union(List Expression Integer,...)
--E 

--S 110 of 127
bb1:=1/(a*p*sqrt(p^2-q^2))*atan((p*tan(a*x))/sqrt(p^2-q^2))
 

              p tan(a x)
        atan(------------)
              +---------+
              |   2    2
             \|- q  + p
   (2)  ------------------
              +---------+
              |   2    2
          a p\|- q  + p
                                                     Type: Expression Integer
--R
--R              p tan(a x)
--R        atan(------------)
--R              +---------+
--R              |   2    2
--R             \|- q  + p
--R   (2)  ------------------
--R              +---------+
--R              |   2    2
--R          a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 111 of 127
bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((p*tan(a*x)-sqrt(q^2-p^2))/(p*tan(a*x)+sqrt(q^2-p^2)))
 

               +-------+
               | 2    2
            - \|q  - p   + p tan(a x)
        log(-------------------------)
              +-------+
              | 2    2
             \|q  - p   + p tan(a x)
   (3)  ------------------------------
                     +-------+
                     | 2    2
                2a p\|q  - p
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R            - \|q  - p   + p tan(a x)
--R        log(-------------------------)
--R              +-------+
--R              | 2    2
--R             \|q  - p   + p tan(a x)
--R   (3)  ------------------------------
--R                     +-------+
--R                     | 2    2
--R                2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 112 of 127
cc1:=aa.1-bb1
 

   (4)
          +---------+
          |   2    2
         \|- q  + p
      *
         log
                                           +-------+
                   2     2         2    2  | 2    2
                ((q  - 2p )cos(a x)  + p )\|q  - p
              + 
                       2     3
                (- 2p q  + 2p )cos(a x)sin(a x)
           /
               2        2    2
              q cos(a x)  - p
     + 
           +-------+
           | 2    2       p tan(a x)
       - 2\|q  - p  atan(------------)
                          +---------+
                          |   2    2
                         \|- q  + p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R         log
--R                                           +-------+
--R                   2     2         2    2  | 2    2
--R                ((q  - 2p )cos(a x)  + p )\|q  - p
--R              + 
--R                       2     3
--R                (- 2p q  + 2p )cos(a x)sin(a x)
--R           /
--R               2        2    2
--R              q cos(a x)  - p
--R     + 
--R           +-------+
--R           | 2    2       p tan(a x)
--R       - 2\|q  - p  atan(------------)
--R                          +---------+
--R                          |   2    2
--R                         \|- q  + p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 113 of 127
cc2:=aa.2-bb1
 

   (5)
                     +---------+
                     |   2    2
            sin(a x)\|- q  + p            p tan(a x)
       atan(--------------------) - atan(------------)
              2p cos(a x) + 2p            +---------+
                                          |   2    2
                                         \|- q  + p
     + 
                    2    2              2
                 ((q  + p )cos(a x) + 2p )sin(a x)
       atan(-------------------------------------------)
                                            +---------+
                       2                    |   2    2
            (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
         +---------+
         |   2    2
     a p\|- q  + p
                                                     Type: Expression Integer
--R
--R   (5)
--R                     +---------+
--R                     |   2    2
--R            sin(a x)\|- q  + p            p tan(a x)
--R       atan(--------------------) - atan(------------)
--R              2p cos(a x) + 2p            +---------+
--R                                          |   2    2
--R                                         \|- q  + p
--R     + 
--R                    2    2              2
--R                 ((q  + p )cos(a x) + 2p )sin(a x)
--R       atan(-------------------------------------------)
--R                                            +---------+
--R                       2                    |   2    2
--R            (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R         +---------+
--R         |   2    2
--R     a p\|- q  + p
--R                                                     Type: Expression Integer
--E

--S 114 of 127
cc3:=aa.1-bb2
 

   (6)
       log
                                     +-------+
             2     2         2    2  | 2    2           2     3
          ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
          ----------------------------------------------------------------------
                                      2        2    2
                                     q cos(a x)  - p
     + 
                +-------+
                | 2    2
             - \|q  - p   + p tan(a x)
       - log(-------------------------)
               +-------+
               | 2    2
              \|q  - p   + p tan(a x)
  /
          +-------+
          | 2    2
     2a p\|q  - p
                                                     Type: Expression Integer
--R
--R   (6)
--R       log
--R                                     +-------+
--R             2     2         2    2  | 2    2           2     3
--R          ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
--R          ----------------------------------------------------------------------
--R                                      2        2    2
--R                                     q cos(a x)  - p
--R     + 
--R                +-------+
--R                | 2    2
--R             - \|q  - p   + p tan(a x)
--R       - log(-------------------------)
--R               +-------+
--R               | 2    2
--R              \|q  - p   + p tan(a x)
--R  /
--R          +-------+
--R          | 2    2
--R     2a p\|q  - p
--R                                                     Type: Expression Integer
--E

--S 115 of 127
cc4:=aa.2-bb2
 

   (7)
                            +-------+
          +---------+       | 2    2
          |   2    2     - \|q  - p   + p tan(a x)
       - \|- q  + p  log(-------------------------)
                           +-------+
                           | 2    2
                          \|q  - p   + p tan(a x)
     + 
                                +---------+
         +-------+              |   2    2
         | 2    2      sin(a x)\|- q  + p
       2\|q  - p  atan(--------------------)
                         2p cos(a x) + 2p
     + 
         +-------+             2    2              2
         | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
       2\|q  - p  atan(-------------------------------------------)
                                                       +---------+
                                  2                    |   2    2
                       (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
  /
          +---------+ +-------+
          |   2    2  | 2    2
     2a p\|- q  + p  \|q  - p
                                                     Type: Expression Integer
--R
--R   (7)
--R                            +-------+
--R          +---------+       | 2    2
--R          |   2    2     - \|q  - p   + p tan(a x)
--R       - \|- q  + p  log(-------------------------)
--R                           +-------+
--R                           | 2    2
--R                          \|q  - p   + p tan(a x)
--R     + 
--R                                +---------+
--R         +-------+              |   2    2
--R         | 2    2      sin(a x)\|- q  + p
--R       2\|q  - p  atan(--------------------)
--R                         2p cos(a x) + 2p
--R     + 
--R         +-------+             2    2              2
--R         | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
--R       2\|q  - p  atan(-------------------------------------------)
--R                                                       +---------+
--R                                  2                    |   2    2
--R                       (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
--R  /
--R          +---------+ +-------+
--R          |   2    2  | 2    2
--R     2a p\|- q  + p  \|q  - p
--R                                                     Type: Expression Integer
--E

--S 116 of 127
dd2:=ratDenom cc2
 

   (8)
                                     +---------+
          +---------+                |   2    2
          |   2    2      p tan(a x)\|- q  + p
       - \|- q  + p  atan(----------------------)
                                   2    2
                                  q  - p
     + 
          +---------+
          |   2    2
         \|- q  + p
      *
                                                      +---------+
                       2    2              2          |   2    2
                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
         atan(--------------------------------------------------------)
                  2    3         2        2     3               2    3
              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                   +---------+
          +---------+              |   2    2
          |   2    2      sin(a x)\|- q  + p
       - \|- q  + p  atan(--------------------)
                            2p cos(a x) + 2p
  /
          2      3
     a p q  - a p
                                                     Type: Expression Integer
--R
--R   (8)
--R                                     +---------+
--R          +---------+                |   2    2
--R          |   2    2      p tan(a x)\|- q  + p
--R       - \|- q  + p  atan(----------------------)
--R                                   2    2
--R                                  q  - p
--R     + 
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R                                                      +---------+
--R                       2    2              2          |   2    2
--R                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R         atan(--------------------------------------------------------)
--R                  2    3         2        2     3               2    3
--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                   +---------+
--R          +---------+              |   2    2
--R          |   2    2      sin(a x)\|- q  + p
--R       - \|- q  + p  atan(--------------------)
--R                            2p cos(a x) + 2p
--R  /
--R          2      3
--R     a p q  - a p
--R                                                     Type: Expression Integer
--E

--S 117 of 127
tanrule:=rule(tan(a) == sin(a)/cos(a))
 

                  sin(a)
   (9)  tan(a) == ------
                  cos(a)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                  sin(a)
--R   (9)  tan(a) == ------
--R                  cos(a)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 118 of 127
ee2:=tanrule dd2
 

   (10)
          +---------+
          |   2    2
         \|- q  + p
      *
                                                      +---------+
                       2    2              2          |   2    2
                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
         atan(--------------------------------------------------------)
                  2    3         2        2     3               2    3
              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                   +---------+
          +---------+              |   2    2
          |   2    2      sin(a x)\|- q  + p
       - \|- q  + p  atan(--------------------)
                            2p cos(a x) + 2p
     + 
                                     +---------+
          +---------+                |   2    2
          |   2    2      p sin(a x)\|- q  + p
       - \|- q  + p  atan(----------------------)
                               2    2
                             (q  - p )cos(a x)
  /
          2      3
     a p q  - a p
                                                     Type: Expression Integer
--R
--R   (10)
--R          +---------+
--R          |   2    2
--R         \|- q  + p
--R      *
--R                                                      +---------+
--R                       2    2              2          |   2    2
--R                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R         atan(--------------------------------------------------------)
--R                  2    3         2        2     3               2    3
--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                   +---------+
--R          +---------+              |   2    2
--R          |   2    2      sin(a x)\|- q  + p
--R       - \|- q  + p  atan(--------------------)
--R                            2p cos(a x) + 2p
--R     + 
--R                                     +---------+
--R          +---------+                |   2    2
--R          |   2    2      p sin(a x)\|- q  + p
--R       - \|- q  + p  atan(----------------------)
--R                               2    2
--R                             (q  - p )cos(a x)
--R  /
--R          2      3
--R     a p q  - a p
--R                                                     Type: Expression Integer
--E

--S 119 of 127
atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
 

                      1                    1
   (11)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
                      2                    2
Type: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--R
--R                      1                    1
--R   (11)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
--R                      2                    2
--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
--E

--S 120 of 127
ff2:=atanrule2 ee2
 

   (12)
       -
                 +---------+
            1    |   2    2
            - %i\|- q  + p
            2
         *
            log
                                                              +---------+
                         2       2                 2          |   2    2
                   ((%i q  + %i p )cos(a x) + 2%i p )sin(a x)\|- q  + p
                 + 
                       2    3         2        2     3               2    3
                   (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
              /
                     2    3         2        2     3               2    3
                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
     + 
                                         +---------+
                           1             |   2    2
            +---------+    - %i sin(a x)\|- q  + p   + p cos(a x) + p
       1    |   2    2     2
       - %i\|- q  + p  log(------------------------------------------)
       2                                 p cos(a x) + p
     + 
                                         +---------+
            +---------+                  |   2    2      2    2
       1    |   2    2     %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
       - %i\|- q  + p  log(---------------------------------------------)
       2                                   2    2
                                         (q  - p )cos(a x)
     + 
                                             +---------+
              +---------+                    |   2    2      2    2
         1    |   2    2     - %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
       - - %i\|- q  + p  log(-----------------------------------------------)
         2                                    2    2
                                            (q  - p )cos(a x)
     + 
                                             +---------+
                               1             |   2    2
              +---------+    - - %i sin(a x)\|- q  + p   + p cos(a x) + p
         1    |   2    2       2
       - - %i\|- q  + p  log(--------------------------------------------)
         2                                  p cos(a x) + p
     + 
              +---------+
         1    |   2    2
         - %i\|- q  + p
         2
      *
         log
                                                             +---------+
                        2       2                 2          |   2    2
                ((- %i q  - %i p )cos(a x) - 2%i p )sin(a x)\|- q  + p
              + 
                    2    3         2        2     3               2    3
                (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
           /
                  2    3         2        2     3               2    3
              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
  /
          2      3
     a p q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (12)
--R       -
--R                 +---------+
--R            1    |   2    2
--R            - %i\|- q  + p
--R            2
--R         *
--R            log
--R                                                              +---------+
--R                         2       2                 2          |   2    2
--R                   ((%i q  + %i p )cos(a x) + 2%i p )sin(a x)\|- q  + p
--R                 + 
--R                       2    3         2        2     3               2    3
--R                   (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R              /
--R                     2    3         2        2     3               2    3
--R                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R     + 
--R                                         +---------+
--R                           1             |   2    2
--R            +---------+    - %i sin(a x)\|- q  + p   + p cos(a x) + p
--R       1    |   2    2     2
--R       - %i\|- q  + p  log(------------------------------------------)
--R       2                                 p cos(a x) + p
--R     + 
--R                                         +---------+
--R            +---------+                  |   2    2      2    2
--R       1    |   2    2     %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
--R       - %i\|- q  + p  log(---------------------------------------------)
--R       2                                   2    2
--R                                         (q  - p )cos(a x)
--R     + 
--R                                             +---------+
--R              +---------+                    |   2    2      2    2
--R         1    |   2    2     - %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
--R       - - %i\|- q  + p  log(-----------------------------------------------)
--R         2                                    2    2
--R                                            (q  - p )cos(a x)
--R     + 
--R                                             +---------+
--R                               1             |   2    2
--R              +---------+    - - %i sin(a x)\|- q  + p   + p cos(a x) + p
--R         1    |   2    2       2
--R       - - %i\|- q  + p  log(--------------------------------------------)
--R         2                                  p cos(a x) + p
--R     + 
--R              +---------+
--R         1    |   2    2
--R         - %i\|- q  + p
--R         2
--R      *
--R         log
--R                                                             +---------+
--R                        2       2                 2          |   2    2
--R                ((- %i q  - %i p )cos(a x) - 2%i p )sin(a x)\|- q  + p
--R              + 
--R                    2    3         2        2     3               2    3
--R                (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R           /
--R                  2    3         2        2     3               2    3
--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
--R  /
--R          2      3
--R     a p q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 121 of 127
gg2:=expandLog ff2
 

   (13)
              +---------+
         1    |   2    2
         - %i\|- q  + p
         2
      *
         log
                                                +---------+
                 2    2              2          |   2    2
              ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
            + 
                     2       3         2           2        3                  2
              (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x) + %i p q
            + 
                    3
              - %i p
     + 
       -
                 +---------+
            1    |   2    2
            - %i\|- q  + p
            2
         *
            log
                                                   +---------+
                    2    2              2          |   2    2
                 ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
               + 
                          2       3         2             2        3
                 (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
               + 
                         2       3
                 - %i p q  + %i p
     + 
              +---------+               +---------+
         1    |   2    2                |   2    2         2       2
       - - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (%i q  - %i p )cos(a x))
         2
     + 
            +---------+               +---------+
       1    |   2    2                |   2    2           2       2
       - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (- %i q  + %i p )cos(a x))
       2
     + 
              +---------+             +---------+
         1    |   2    2              |   2    2
       - - %i\|- q  + p  log(sin(a x)\|- q  + p   + 2%i p cos(a x) + 2%i p)
         2
     + 
            +---------+             +---------+
       1    |   2    2              |   2    2
       - %i\|- q  + p  log(sin(a x)\|- q  + p   - 2%i p cos(a x) - 2%i p)
       2
     + 
                                           +---------+
        1        1       1          1      |   2    2
       (- %i log(- %i) - - %i log(- - %i))\|- q  + p
        2        2       2          2
  /
          2      3
     a p q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (13)
--R              +---------+
--R         1    |   2    2
--R         - %i\|- q  + p
--R         2
--R      *
--R         log
--R                                                +---------+
--R                 2    2              2          |   2    2
--R              ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R            + 
--R                     2       3         2           2        3                  2
--R              (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x) + %i p q
--R            + 
--R                    3
--R              - %i p
--R     + 
--R       -
--R                 +---------+
--R            1    |   2    2
--R            - %i\|- q  + p
--R            2
--R         *
--R            log
--R                                                   +---------+
--R                    2    2              2          |   2    2
--R                 ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
--R               + 
--R                          2       3         2             2        3
--R                 (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
--R               + 
--R                         2       3
--R                 - %i p q  + %i p
--R     + 
--R              +---------+               +---------+
--R         1    |   2    2                |   2    2         2       2
--R       - - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (%i q  - %i p )cos(a x))
--R         2
--R     + 
--R            +---------+               +---------+
--R       1    |   2    2                |   2    2           2       2
--R       - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (- %i q  + %i p )cos(a x))
--R       2
--R     + 
--R              +---------+             +---------+
--R         1    |   2    2              |   2    2
--R       - - %i\|- q  + p  log(sin(a x)\|- q  + p   + 2%i p cos(a x) + 2%i p)
--R         2
--R     + 
--R            +---------+             +---------+
--R       1    |   2    2              |   2    2
--R       - %i\|- q  + p  log(sin(a x)\|- q  + p   - 2%i p cos(a x) - 2%i p)
--R       2
--R     + 
--R                                           +---------+
--R        1        1       1          1      |   2    2
--R       (- %i log(- %i) - - %i log(- - %i))\|- q  + p
--R        2        2       2          2
--R  /
--R          2      3
--R     a p q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E

--S 122 of 127    14:393 Schaums and Axiom differ by a constant
hh2:=complexNormalize gg2
 

   (14)
          1              1        1       1          1       1
       (- - %i log(%i) + - %i log(- %i) - - %i log(- - %i) + - %i log(- %i))
          2              2        2       2          2       2
    *
        +---------+
        |   2    2
       \|- q  + p
  /
          2      3
     a p q  - a p
                                    Type: Expression Complex Fraction Integer
--R
--R   (14)
--R          1              1        1       1          1       1
--R       (- - %i log(%i) + - %i log(- %i) - - %i log(- - %i) + - %i log(- %i))
--R          2              2        2       2          2       2
--R    *
--R        +---------+
--R        |   2    2
--R       \|- q  + p
--R  /
--R          2      3
--R     a p q  - a p
--R                                    Type: Expression Complex Fraction Integer
--E
)clear all
 

--S 123 of 127    14:394 Axiom cannot compute this integral
aa:=integrate(x^m*cos(a*x),x)
 

           x
         ++             m
   (1)   |   cos(%I a)%I d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++             m
--I   (1)   |   cos(%I a)%I d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 124 of 127    14:395 Axiom cannot compute this integral
aa:=integrate(cos(a*x)/x^n,x)
 

           x
         ++  cos(%I a)
   (1)   |   --------- d%I
        ++        n
                %I
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  cos(%I a)
--I   (1)   |   --------- d%I
--R        ++        n
--I                %I
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 125 of 127    14:396 Axiom cannot compute this integral
aa:=integrate(cos(a*x)^n,x)
 

           x
         ++           n
   (1)   |   cos(%I a) d%I
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++           n
--I   (1)   |   cos(%I a) d%I
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 126 of 127    14:397 Axiom cannot compute this integral
aa:=integrate(1/(cos(a*x))^n,x)
 

           x
         ++       1
   (1)   |   ---------- d%I
        ++            n
             cos(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++       1
--I   (1)   |   ---------- d%I
--R        ++            n
--I             cos(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 127 of 127    14:398 Axiom cannot compute this integral
aa:=integrate(x/cos(a*x)^n,x)
 

           x
         ++      %I
   (1)   |   ---------- d%I
        ++            n
             cos(%I a)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++      %I
--I   (1)   |   ---------- d%I
--R        ++            n
--I             cos(%I a)
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to UnivariateSkewPolynomial.output (2010/3/27, 18:46:40).
)set message test on
 
)set message auto off
 
)set message type off
 
)clear all
 

--S 1 of 33
F:=EXPR(FRAC(INT))
 

   (1)  Expression Fraction Integer
--R 
--R
--R   (1)  Expression Fraction Integer
--E 1

--S 2 of 33
Dx:F->F:=f+->D(f,['x])
 

   (2)  theMap(Closure)
--R 
--R
--R   (2)  theMap(Closure)
--E 2

--S 3 of 33
D0:=OREUP('d,F,1,Dx)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R 
--R
--R   (3)
--I  UnivariateSkewPolynomial(d,Expression Fraction Integer,R -> R,theMap LAMBDA-C
--I  LOSURE(NIL,NIL,NIL,G9057 envArg,SPADCALL(G9057,coerceOrCroak(CONS(QUOTE List 
--I  Variable x,wrap LIST QUOTE x),QUOTE List Symbol,QUOTE *1;anonymousFunction;2;
--I  frame0;internal),ELT(*1;anonymousFunction;2;frame0;internal;MV,0))))
--E 3

--S 4 of 33
u:D0:=(operator 'u)(x)
 

   (3)  u(x)
--R 
--R
--R   (4)  u(x)
--E 4

--S 5 of 33
d:D0:='d
 

   (4)  d
--R 
--R
--R   (5)  d
--E 5

--S 6 of 33
a:D0:=u^3*d^3+u^2*d^2+u*d+1
 

            3 3       2 2
   (5)  u(x) d  + u(x) d  + u(x)d + 1
--R 
--R
--R            3 3       2 2
--R   (6)  u(x) d  + u(x) d  + u(x)d + 1
--E 6

--S 7 of 33
b:D0:=(u+1)*d^2+2*d
 

                   2
   (6)  (u(x) + 1)d  + 2d
--R 
--R
--R                   2
--R   (7)  (u(x) + 1)d  + 2d
--E 7

--S 8 of 33
r:=rightDivide(a,b)
 

   (7)
                                 3 ,          3       2
                    3      - u(x) u (x) - u(x)  + u(x)
                u(x)
   [quotient= -------- d + ----------------------------,
              u(x) + 1               2
                                 u(x)  + 2u(x) + 1
                    3 ,           3
               2u(x) u (x) + 3u(x)  + u(x)

    remainder= --------------------------- d + 1]
                        2
                    u(x)  + 2u(x) + 1
--R 
--R
--R   (8)
--R                                 3 ,          3       2
--R                    3      - u(x) u (x) - u(x)  + u(x)
--R                u(x)
--R   [quotient= -------- d + ----------------------------,
--R              u(x) + 1               2
--R                                 u(x)  + 2u(x) + 1
--R                    3 ,           3
--R               2u(x) u (x) + 3u(x)  + u(x)
--R
--R    remainder= --------------------------- d + 1]
--R                        2
--R                    u(x)  + 2u(x) + 1
--E 8

--S 9 of 33
r.quotient
 

                           3 ,          3       2
              3      - u(x) u (x) - u(x)  + u(x)
          u(x)
   (8)  -------- d + ----------------------------
        u(x) + 1               2
                           u(x)  + 2u(x) + 1
--R 
--R
--R                           3 ,          3       2
--R              3      - u(x) u (x) - u(x)  + u(x)
--R          u(x)
--R   (9)  -------- d + ----------------------------
--R        u(x) + 1               2
--R                           u(x)  + 2u(x) + 1
--E 9

--S 10 of 33
r.remainder
 

             3 ,           3
        2u(x) u (x) + 3u(x)  + u(x)

   (9)  --------------------------- d + 1
                 2
             u(x)  + 2u(x) + 1
--R 
--R
--R              3 ,           3
--R         2u(x) u (x) + 3u(x)  + u(x)
--R
--R   (10)  --------------------------- d + 1
--R                  2
--R              u(x)  + 2u(x) + 1
--E 10

)clear all
 
 
--S 11 of 33
R:=UP('t,INT)
 

   (1)  UnivariatePolynomial(t,Integer)
--R 
--R
--R   (1)  UnivariatePolynomial(t,Integer)
--E 11

--S 12 of 33
W:=OREUP('x,R,1,D)
 

   (2)
  UnivariateSkewPolynomial(x,UnivariatePolynomial(t,Integer),R -> R,theMap(DIFR
  ING-;D;2S;1,0))
--R 
--R
--R   (2)
--R  UnivariateSkewPolynomial(x,UnivariatePolynomial(t,Integer),R -> R,theMap(DIFR
--I  ING-;D;2S;1,411))
--E 12

--S 13 of 33
t:W:='t
 

   (3)  t
--R 
--R
--R   (3)  t
--E 13

--S 14 of 33
x:W:='x
 

   (4)  x
--R 
--R
--R   (4)  x
--E 14

--S 15 of 33
a:W:=(t-1)*x^4+(t^3+3*t+1)*x^2+2*t*x+t^3
 

                4     3           2           3
   (5)  (t - 1)x  + (t  + 3t + 1)x  + 2t x + t
--R 
--R
--R                4     3           2           3
--R   (5)  (t - 1)x  + (t  + 3t + 1)x  + 2t x + t
--E 15

--S 16 of 33
b:W:=(6*t^4+2*t^2)*x^3+3*t^2*x^2
 

           4     2  3     2 2
   (6)  (6t  + 2t )x  + 3t x
--R 
--R
--R           4     2  3     2 2
--R   (6)  (6t  + 2t )x  + 3t x
--E 16

--S 17 of 33
a*b
 

   (7)
        5     4     3     2  7       4      3      2        6
     (6t  - 6t  + 2t  - 2t )x  + (96t  - 93t  + 13t  - 16t)x
   + 
        7      5     4       3       2       5
     (6t  + 20t  + 6t  + 438t  - 406t  - 24)x
   + 
         6      5       4      3       2              4
     (48t  + 15t  + 152t  + 61t  + 603t  - 532t - 36)x
   + 
        7      5      4       3       2               3
     (6t  + 74t  + 60t  + 226t  + 116t  + 168t - 140)x
   + 
        5     3      2            2
     (3t  + 6t  + 12t  + 18t + 6)x
--R 
--R
--R   (7)
--R        5     4     3     2  7       4      3      2        6
--R     (6t  - 6t  + 2t  - 2t )x  + (96t  - 93t  + 13t  - 16t)x
--R   + 
--R        7      5     4       3       2       5
--R     (6t  + 20t  + 6t  + 438t  - 406t  - 24)x
--R   + 
--R         6      5       4      3       2              4
--R     (48t  + 15t  + 152t  + 61t  + 603t  - 532t - 36)x
--R   + 
--R        7      5      4       3       2               3
--R     (6t  + 74t  + 60t  + 226t  + 116t  + 168t - 140)x
--R   + 
--R        5     3      2            2
--R     (3t  + 6t  + 12t  + 18t + 6)x
--E 17

--S 18 of 33
a^3
 

   (8)
       3     2           12      5     4      3      2           10
     (t  - 3t  + 3t - 1)x   + (3t  - 6t  + 12t  - 15t  + 3t + 3)x
   + 
        3      2       9      7     6      5      4      3     2            8
     (6t  - 12t  + 6t)x  + (3t  - 3t  + 21t  - 18t  + 24t  - 9t  - 15t - 3)x
   + 
         5      4      3      2        7
     (12t  - 12t  + 36t  - 24t  - 12t)x
   + 
       9      7     6      5     4      3      2           6
     (t  + 15t  - 3t  + 45t  + 6t  + 36t  + 15t  + 9t + 1)x
   + 
        7      5      3      2       5
     (6t  + 48t  + 54t  + 36t  + 6t)x
   + 
        9      7     6      5      4      3      2  4
     (3t  + 21t  + 3t  + 39t  + 18t  + 39t  + 12t )x
   + 
         7      5      4     3  3      9     7     6      5  2     7     9
     (12t  + 36t  + 12t  + 8t )x  + (3t  + 9t  + 3t  + 12t )x  + 6t x + t
--R 
--R
--R   (8)
--R       3     2           12      5     4      3      2           10
--R     (t  - 3t  + 3t - 1)x   + (3t  - 6t  + 12t  - 15t  + 3t + 3)x
--R   + 
--R        3      2       9      7     6      5      4      3     2            8
--R     (6t  - 12t  + 6t)x  + (3t  - 3t  + 21t  - 18t  + 24t  - 9t  - 15t - 3)x
--R   + 
--R         5      4      3      2        7
--R     (12t  - 12t  + 36t  - 24t  - 12t)x
--R   + 
--R       9      7     6      5     4      3      2           6
--R     (t  + 15t  - 3t  + 45t  + 6t  + 36t  + 15t  + 9t + 1)x
--R   + 
--R        7      5      3      2       5
--R     (6t  + 48t  + 54t  + 36t  + 6t)x
--R   + 
--R        9      7     6      5      4      3      2  4
--R     (3t  + 21t  + 3t  + 39t  + 18t  + 39t  + 12t )x
--R   + 
--R         7      5      4     3  3      9     7     6      5  2     7     9
--R     (12t  + 36t  + 12t  + 8t )x  + (3t  + 9t  + 3t  + 12t )x  + 6t x + t
--E 18

)clear all
 
 
--S 19 of 33
S:EXPR(INT)->EXPR(INT):=e+->eval(e,[n],[n+1])
 

   (1)  theMap(Closure)
--R 
--R
--R   (1)  theMap(Closure)
--E 19

--S 20 of 33
DF:EXPR(INT)->EXPR(INT):=e+->eval(e,[n],[n+1])-e
 

   (2)  theMap(Closure)
--R 
--R
--R   (2)  theMap(Closure)
--E 20

--S 21 of 33
D0:=OREUP('D,EXPR(INT),morphism S,DF)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R 
--R
--R   (3)
--I  UnivariateSkewPolynomial(D,Expression Integer,R -> R,theMap LAMBDA-CLOSURE(NI
--I  L,NIL,NIL,G9384 envArg,SPADCALL(SPADCALL(G9384,coerceOrCroak(CONS(QUOTE List 
--I  Variable n,wrap LIST QUOTE n),QUOTE List Expression Integer,QUOTE *1;anonymou
--I  sFunction;9;frame0;internal),coerceOrCroak(CONS(QUOTE List Polynomial Integer
--I  ,wrap LIST SPADCALL(QUOTE 1(n,1 0),QUOTE 0,ELT(*1;anonymousFunction;9;frame0;
--I  internal;MV,0))),QUOTE List Expression Integer,QUOTE *1;anonymousFunction;9;f
--I  rame0;internal),ELT(*1;anonymousFunction;9;frame0;internal;MV,1)),G9384,ELT(*
--I  1;anonymousFunction;9;frame0;internal;MV,2))))
--E 21

--S 22 of 33
u:=(operator 'u)[n]
 

   (3)  u(n)
--R 
--R
--R   (4)  u(n)
--E 22

--S 23 of 33
L:D0:='D+u
 

   (4)  D + u(n)
--R 
--R
--R   (5)  D + u(n)
--E 23

--S 24 of 33
L^2
 

         2                2
   (5)  D  + 2u(n)D + u(n)
--R 
--R
--R         2                2
--R   (6)  D  + 2u(n)D + u(n)
--E 24

)clear all
 
 
--S 25 of 33
)set expose add constructor SquareMatrix
 
   SquareMatrix is now explicitly exposed in frame initial 
--R 
--I   SquareMatrix is now explicitly exposed in frame frame0 
--E 25

--S 26 of 33
R:=SQMATRIX(2,INT)
 

   (1)  SquareMatrix(2,Integer)
--R 
--R
--R   (1)  SquareMatrix(2,Integer)
--E 26

--S 27 of 33
y:R:=matrix [[1,1],[0,1]]
 

        +1  1+
   (2)  |    |
        +0  1+
--R 
--R
--R        +1  1+
--R   (2)  |    |
--R        +0  1+
--E 27

--S 28 of 33
delta:R->R:=r+->y*r-r*y
 

   (3)  theMap(Closure)
--R 
--R
--R   (3)  theMap(Closure)
--E 28

--S 29 of 33
S:=OREUP('x,R,1,delta)
 

 
Daly Bug
   >> System error:
    Lisps arglist maximum surpassed

   Continuing to read the file...

--R 
--R
--R   (4)
--I  UnivariateSkewPolynomial(x,SquareMatrix(2,Integer),R -> R,theMap LAMBDA-CLOSU
--I  RE(NIL,NIL,NIL,G9459 envArg,SPADCALL(SPADCALL(getValueFromEnvironment(QUOTE y
--I  ,QUOTE SquareMatrix(2,Integer)),G9459,ELT(*1;anonymousFunction;13;frame0;inte
--I  rnal;MV,0)),SPADCALL(G9459,getValueFromEnvironment(QUOTE y,QUOTE SquareMatrix
--I  (2,Integer)),ELT(*1;anonymousFunction;13;frame0;internal;MV,0)),ELT(*1;anonym
--I  ousFunction;13;frame0;internal;MV,1))))
--E 29

--S 30 of 33
x:S:='x
 

   (4)  x
--R 
--R
--R   (5)  x
--E 30

--S 31 of 33
a:S:=matrix [[2,3],[1,1]]
 

        +2  3+
   (5)  |    |
        +1  1+
--R 
--R
--R        +2  3+
--R   (6)  |    |
--R        +1  1+
--E 31

--S 32 of 33
x^2*a
 

        +2  3+ 2   +2  - 2+    +0  - 2+
   (6)  |    |x  + |      |x + |      |
        +1  1+     +0  - 2+    +0   0 +
--R 
--R
--R        +2  3+ 2   +2  - 2+    +0  - 2+
--R   (7)  |    |x  + |      |x + |      |
--R        +1  1+     +0  - 2+    +0   0 +
--E 32

--S 33 of 33
)show UnivariateSkewPolynomial
 
 UnivariateSkewPolynomial(x: Symbol,R: Ring,sigma: Automorphism R,delta: (R -> R))  is a domain constructor
 Abbreviation for UnivariateSkewPolynomial is OREUP 
 This constructor is not exposed in this frame.
 Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for OREUP 

------------------------------- Operations --------------------------------
 ?*? : (R,%) -> %                      ?*? : (%,R) -> %
 ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
 ?+? : (%,%) -> %                      ?-? : (%,%) -> %
 -? : % -> %                           ?=? : (%,%) -> Boolean
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        apply : (%,R,R) -> R
 coefficients : % -> List R            coerce : Variable x -> %
 coerce : R -> %                       coerce : Integer -> %
 coerce : % -> OutputForm              degree : % -> NonNegativeInteger
 hash : % -> SingleInteger             latex : % -> String
 leadingCoefficient : % -> R           one? : % -> Boolean
 recip : % -> Union(%,"failed")        reductum : % -> %
 retract : % -> R                      sample : () -> %
 zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %
 characteristic : () -> NonNegativeInteger
 coefficient : (%,NonNegativeInteger) -> R
 coerce : Fraction Integer -> % if R has RETRACT FRAC INT
 content : % -> R if R has GCDDOM
 exquo : (%,R) -> Union(%,"failed") if R has INTDOM
 leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
 leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD
 leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
 leftGcd : (%,%) -> % if R has FIELD
 leftLcm : (%,%) -> % if R has FIELD
 leftQuotient : (%,%) -> % if R has FIELD
 leftRemainder : (%,%) -> % if R has FIELD
 minimumDegree : % -> NonNegativeInteger
 monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM
 monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM
 monomial : (R,NonNegativeInteger) -> %
 primitivePart : % -> % if R has GCDDOM
 retract : % -> Fraction Integer if R has RETRACT FRAC INT
 retract : % -> Integer if R has RETRACT INT
 retractIfCan : % -> Union(R,"failed")
 retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
 retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
 rightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
 rightExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD
 rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
 rightGcd : (%,%) -> % if R has FIELD
 rightLcm : (%,%) -> % if R has FIELD
 rightQuotient : (%,%) -> % if R has FIELD
 rightRemainder : (%,%) -> % if R has FIELD
 subtractIfCan : (%,%) -> Union(%,"failed")

--R 
--R UnivariateSkewPolynomial(x: Symbol,R: Ring,sigma: Automorphism R,delta: (R -> R))  is a domain constructor
--R Abbreviation for UnivariateSkewPolynomial is OREUP 
--R This constructor is not exposed in this frame.
--R Issue )edit bookvol10.3.spad.pamphlet to see algebra source code for OREUP 
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (R,%) -> %                      ?*? : (%,R) -> %
--R ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> %        ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> %                      ?-? : (%,%) -> %
--R -? : % -> %                           ?=? : (%,%) -> Boolean
--R 1 : () -> %                           0 : () -> %
--R ?^? : (%,PositiveInteger) -> %        apply : (%,R,R) -> R
--R coefficients : % -> List R            coerce : Variable x -> %
--R coerce : R -> %                       coerce : Integer -> %
--R coerce : % -> OutputForm              degree : % -> NonNegativeInteger
--R hash : % -> SingleInteger             latex : % -> String
--R leadingCoefficient : % -> R           one? : % -> Boolean
--R recip : % -> Union(%,"failed")        reductum : % -> %
--R retract : % -> R                      sample : () -> %
--R zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R coefficient : (%,NonNegativeInteger) -> R
--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
--R content : % -> R if R has GCDDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
--R leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD
--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
--R leftGcd : (%,%) -> % if R has FIELD
--R leftLcm : (%,%) -> % if R has FIELD
--R leftQuotient : (%,%) -> % if R has FIELD
--R leftRemainder : (%,%) -> % if R has FIELD
--R minimumDegree : % -> NonNegativeInteger
--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM
--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM
--R monomial : (R,NonNegativeInteger) -> %
--R primitivePart : % -> % if R has GCDDOM
--R retract : % -> Fraction Integer if R has RETRACT FRAC INT
--R retract : % -> Integer if R has RETRACT INT
--R retractIfCan : % -> Union(R,"failed")
--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
--R rightExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD
--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
--R rightGcd : (%,%) -> % if R has FIELD
--R rightLcm : (%,%) -> % if R has FIELD
--R rightQuotient : (%,%) -> % if R has FIELD
--R rightRemainder : (%,%) -> % if R has FIELD
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 33
)set expose drop constructor SquareMatrix
 
   SquareMatrix is now explicitly hidden in frame initial 

)spool
 
Starts dribbling to heugcd.output (2010/3/27, 18:26:50).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 5
gcd([0,0,x^2-1,x^2+2*x+1])
 

   (1)  x + 1
                                                     Type: Polynomial Integer
--R
--R   (1)  x + 1
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 5
gcd([0,0,x^2-1,x^2+2*x+1])$HeuGcd(SparseUnivariatePolynomial Integer)
 

   (2)  ? + 1
                                     Type: SparseUnivariatePolynomial Integer
--R
--R   (2)  ? + 1
--R                                     Type: SparseUnivariatePolynomial Integer
--E 2

--S 3 of 5
gcd(6*x^2-1,36*x^2+12*x+1)
 

   (3)  1
                                                     Type: Polynomial Integer
--R
--R   (3)  1
--R                                                     Type: Polynomial Integer
--E 3

--S 4 of 5
gcd([36*x^2-1,36*x^2+12*x+1])
 

   (4)  6x + 1
                                                     Type: Polynomial Integer
--R
--R   (4)  6x + 1
--R                                                     Type: Polynomial Integer
--E 4

--S 5 of 5
gcd([36*x^2-1,36*x^2+12*x+1])$HeuGcd(SparseUnivariatePolynomial Integer)
 

   (5)  6? + 1
                                     Type: SparseUnivariatePolynomial Integer
--R
--R   (5)  6? + 1
--R                                     Type: SparseUnivariatePolynomial Integer
--E 5
)spool 
 
Starts dribbling to en.output (2010/3/27, 18:25:27).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 7
f(x)==En(2,x)-x*log(x)
 
                                                                   Type: Void
--E 1

--S 2 of 7
[[0.01,0.9957222,f(0.01),f(0.01)-0.9957222],_
[0.02,0.9913450,f(0.02),f(0.02)-0.9913450],_
[0.03,0.9868687,f(0.03),f(0.03)-0.9868687],_
[0.04,0.9822939,f(0.04),f(0.04)-0.9822939],_
[0.05,0.9776211,f(0.05),f(0.05)-0.9776211],_
[0.06,0.9728508,f(0.06),f(0.06)-0.9728508],_
[0.07,0.9679834,f(0.07),f(0.07)-0.9679834],_
[0.08,0.9630194,f(0.08),f(0.08)-0.9630194],_
[0.09,0.9579593,f(0.09),f(0.09)-0.9579593],_
[0.10,0.9528035,f(0.10),f(0.10)-0.9528035],_
[0.11,0.9475526,f(0.11),f(0.11)-0.9475526],_
[0.12,0.9422071,f(0.12),f(0.12)-0.9422071],_
[0.13,0.9367672,f(0.13),f(0.13)-0.9367672],_
[0.14,0.9312336,f(0.14),f(0.14)-0.9312336],_
[0.15,0.9256067,f(0.15),f(0.15)-0.9256067],_
[0.16,0.9198870,f(0.16),f(0.16)-0.9198870],_
[0.17,0.9140748,f(0.17),f(0.17)-0.9140748],_
[0.18,0.9081706,f(0.18),f(0.18)-0.9081706],_
[0.19,0.9021750,f(0.19),f(0.19)-0.9021750],_
[0.20,0.8960882,f(0.20),f(0.20)-0.8960882],_
[0.21,0.8899109,f(0.21),f(0.21)-0.8899109],_
[0.22,0.8836433,f(0.22),f(0.22)-0.8836433],_
[0.23,0.8772860,f(0.23),f(0.23)-0.8772860],_
[0.24,0.8708393,f(0.24),f(0.24)-0.8708393],_
[0.25,0.8643037,f(0.25),f(0.25)-0.8643037],_
[0.26,0.8576797,f(0.26),f(0.26)-0.8576797],_
[0.27,0.8509676,f(0.27),f(0.27)-0.8509676],_
[0.28,0.8441678,f(0.28),f(0.28)-0.8441678],_
[0.29,0.8372808,f(0.29),f(0.29)-0.8372808],_
[0.30,0.8303071,f(0.30),f(0.30)-0.8303071],_
[0.31,0.8232469,f(0.31),f(0.31)-0.8232469],_
[0.32,0.8161007,f(0.32),f(0.32)-0.8161007],_
[0.33,0.8088690,f(0.33),f(0.33)-0.8088690],_
[0.34,0.8015521,f(0.34),f(0.34)-0.8015521],_
[0.35,0.7941504,f(0.35),f(0.35)-0.7941504],_
[0.36,0.7866644,f(0.36),f(0.36)-0.7866644],_
[0.37,0.7790943,f(0.37),f(0.37)-0.7790943],_
[0.38,0.7714407,f(0.38),f(0.38)-0.7714407],_
[0.39,0.7637039,f(0.39),f(0.39)-0.7637039],_
[0.40,0.7558843,f(0.40),f(0.40)-0.7558843],_
[0.41,0.7479823,f(0.41),f(0.41)-0.7479823],_
[0.42,0.7399982,f(0.42),f(0.42)-0.7399982],_
[0.43,0.7319324,f(0.43),f(0.43)-0.7319324],_
[0.44,0.7237854,f(0.44),f(0.44)-0.7237854],_
[0.45,0.7155575,f(0.45),f(0.45)-0.7155575],_
[0.46,0.7072491,f(0.46),f(0.46)-0.7072491],_
[0.47,0.6988605,f(0.47),f(0.47)-0.6988605],_
[0.48,0.6903921,f(0.48),f(0.48)-0.6903921],_
[0.49,0.6818443,f(0.49),f(0.49)-0.6818443],_
[0.50,0.6732175,f(0.50),f(0.50)-0.6732175]]
 
   Compiling function f with type Float -> OnePointCompletion 
      DoubleFloat 

   (2)
   [
     [9.9999999999999985E-3, 0.99572219999999989, 0.99572223984366792,
      3.9843668031558366E-8]
     ,

     [1.9999999999999997E-2, 0.99134499999999992, 0.991344977749124,
      - 2.2250875919560542E-8]
     ,

     [2.9999999999999999E-2, 0.98686870000000004, 0.98686870874746913,
      8.7474690824151935E-9]
     ,

     [3.9999999999999994E-2, 0.98229389999999994, 0.98229392458604003,
      2.4586040092700046E-8]
     ,

     [5.0000000000000003E-2, 0.97762109999999991, 0.97762111375291494,
      1.3752915029030532E-8]
     ,

     [5.9999999999999998E-2, 0.97285080000000002, 0.97285076150122396,
      - 3.8498776055995165E-8]
     ,

     [7.0000000000000007E-2, 0.96798340000000005, 0.96798334987326684,
      - 5.0126733208699648E-8]
     ,

     [7.9999999999999988E-2, 0.96301939999999997, 0.96301935772443681,
      - 4.2275563161275898E-8]
     ,

     [8.9999999999999997E-2, 0.95795929999999996, 0.95795926074695692,
      - 3.9253043038200985E-8]
     ,

     [0.10000000000000001, 0.95280349999999991, 0.95280353149342489,
      3.1493424978989992E-8]
     ,

     [0.10999999999999999, 0.94755259999999997, 0.94755263940017342,
      3.9400173457160292E-8]
     ,
    [0.12,0.94220709999999996,0.94220705081044243,- 4.9189557538298345E-8],
    [0.13,0.93676720000000002,0.93676722899736986,2.8997369838634768E-8],

     [0.14000000000000001, 0.93123359999999999, 0.93123363418679772,
      3.4186797726043494E-8]
     ,

     [0.14999999999999999, 0.92560669999999989, 0.92560672357989859,
      2.3579898700276658E-8]
     ,

     [0.15999999999999998, 0.9198869999999999, 0.91988695137562193,
      - 4.8624377968486954E-8]
     ,

     [0.16999999999999998, 0.91407479999999997, 0.91407476879296246,
      - 3.1207037509695112E-8]
     ,

     [0.17999999999999999, 0.90817060000000005, 0.90817062409305227,
      2.4093052219953393E-8]
     ,
    [0.19,0.90217499999999995,0.9021749626010781,- 3.7398921848286193E-8],

     [0.20000000000000001, 0.89608819999999989, 0.89608822672802313,
      2.6728023239108722E-8]
     ,

     [0.20999999999999999, 0.88991089999999995, 0.88991085599223996,
      - 4.4007759991693263E-8]
     ,

     [0.21999999999999997, 0.88364329999999991, 0.88364328704084927,
      - 1.2959150641478345E-8]
     ,

     [0.22999999999999998, 0.87728600000000001, 0.87728595367097117,
      - 4.6329028835501163E-8]
     ,

     [0.23999999999999999, 0.87083929999999998, 0.8708392868507886,
      - 1.3149211386398463E-8]
     ,
    [0.25,0.86430370000000001,0.86430371474044299,1.4740442977334567E-8],

     [0.26000000000000001, 0.85767970000000004, 0.85767966271276586,
      - 3.7287234189165019E-8]
     ,

     [0.27000000000000002, 0.85096759999999994, 0.85096755337384566,
      - 4.6626154270867914E-8]
     ,

     [0.28000000000000003, 0.84416779999999991, 0.84416780658343327,
      6.5834333540237822E-9]
     ,

     [0.28999999999999998, 0.83728080000000005, 0.83728083947518439,
      3.9475184343551462E-8]
     ,

     [0.29999999999999999, 0.83030709999999996, 0.83030706647674457,
      - 3.352325539385248E-8]
     ,
    [0.31,0.8232469,0.82324689932967399,- 6.7032601691607852E-10],

     [0.31999999999999995, 0.81610070000000001, 0.81610074710921554,
      4.7109215528529091E-8]
     ,

     [0.32999999999999996, 0.80886899999999995, 0.80886901624390695,
      1.6243906997281954E-8]
     ,

     [0.33999999999999997, 0.80155209999999999, 0.80155211053503883,
      1.0535038841297251E-8]
     ,

     [0.34999999999999998, 0.79415039999999992, 0.79415043117595796,
      3.1175958037366058E-8]
     ,

     [0.35999999999999999, 0.78666440000000004, 0.78666437677122092,
      - 2.3228779122419496E-8]
     ,
    [0.37,0.77909429999999991,0.77909434335559369,4.3355593781768675E-8],
    [0.38,0.77144069999999998,0.77144072441290445,2.4412904475745734E-8],

     [0.39000000000000001, 0.76370389999999999, 0.76370391089474698,
      1.089474699345061E-8]
     ,

     [0.40000000000000002, 0.75588429999999995, 0.75588429123903633,
      - 8.7609636212349074E-9]
     ,

     [0.40999999999999998, 0.74798229999999999, 0.74798225138841912,
      - 4.8611580871771309E-8]
     ,

     [0.41999999999999998, 0.73999820000000005, 0.7399981748085398,
      - 2.5191460251150488E-8]
     ,

     [0.42999999999999999, 0.73193240000000004, 0.73193244250616207,
      4.2506162034605666E-8]
     ,

     [0.43999999999999995, 0.72378539999999991, 0.7237854330471486,
      3.3047148684239858E-8]
     ,

     [0.44999999999999996, 0.71555749999999996, 0.71555752257429928,
      2.2574299318733893E-8]
     ,

     [0.45999999999999996, 0.70724909999999996, 0.70724908482505056,
      - 1.517494940816988E-8]
     ,
    [0.46999999999999997,0.6988605,0.6988604911490337,- 8.8509662932167998E-9],

     [0.47999999999999998, 0.69039209999999995, 0.69039211052549776,
      1.0525497806668227E-8]
     ,

     [0.48999999999999999, 0.68184429999999996, 0.68184430958059394,
      9.5805939848148114E-9]
     ,
    [0.5,0.67321750000000002,0.6732174526045257,- 4.7395474322975417E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R   Compiling function f with type Float -> OnePointCompletion 
--R      DoubleFloat 
--R
--R   (2)
--R   [[1.0E-2,0.9957222,0.99572223984366792,3.9843667920536063E-8],
--R    [2.0E-2,0.99134500000000003,0.991344977749124,- 2.2250876030582845E-8],
--R
--R     [2.9999999999999999E-2, 0.98686870000000004, 0.98686870874746913,
--R      8.7474690824151935E-9]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.98229390000000005, 0.98229392458604003,
--R      2.4586039981677743E-8]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.97762110000000002, 0.97762111375291483,
--R      1.3752914806985927E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.97285080000000002, 0.97285076150122396,
--R      - 3.8498776055995165E-8]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.96798340000000005, 0.96798334987326684,
--R      - 5.0126733208699648E-8]
--R     ,
--R
--R     [8.0000000000000002E-2, 0.96301939999999997, 0.96301935772443681,
--R      - 4.2275563161275898E-8]
--R     ,
--R
--R     [8.9999999999999997E-2, 0.95795929999999996, 0.95795926074695703,
--R      - 3.9253042927178683E-8]
--R     ,
--R
--R     [0.10000000000000001, 0.95280350000000003, 0.95280353149342489,
--R      3.149342486796769E-8]
--R     ,
--R    [0.11,0.94755259999999997,0.94755263940017342,3.9400173457160292E-8],
--R    [0.12,0.94220709999999996,0.94220705081044254,- 4.9189557427276043E-8],
--R    [0.13,0.93676720000000002,0.93676722899736986,2.8997369838634768E-8],
--R
--R     [0.14000000000000001, 0.93123359999999999, 0.93123363418679772,
--R      3.4186797726043494E-8]
--R     ,
--R    [0.14999999999999999,0.9256067,0.92560672357989859,2.3579898589254356E-8],
--R    [0.16,0.91988700000000001,0.91988695137562182,- 4.8624378190531559E-8],
--R
--R     [0.17000000000000001, 0.91407479999999997, 0.91407476879296246,
--R      - 3.1207037509695112E-8]
--R     ,
--R
--R     [0.17999999999999999, 0.90817060000000005, 0.90817062409305238,
--R      2.4093052330975695E-8]
--R     ,
--R    [0.19,0.90217499999999995,0.90217496260107799,- 3.7398921959308495E-8],
--R    [0.20000000000000001,0.8960882,0.89608822672802324,2.6728023239108722E-8],
--R
--R     [0.20999999999999999, 0.88991089999999995, 0.88991085599224007,
--R      - 4.400775988067096E-8]
--R     ,
--R    [0.22,0.88364330000000002,0.88364328704084927,- 1.2959150752500648E-8],
--R
--R     [0.23000000000000001, 0.87728600000000001, 0.87728595367097117,
--R      - 4.6329028835501163E-8]
--R     ,
--R
--R     [0.23999999999999999, 0.87083929999999998, 0.8708392868507886,
--R      - 1.3149211386398463E-8]
--R     ,
--R    [0.25,0.86430370000000001,0.86430371474044287,1.4740442866312264E-8],
--R
--R     [0.26000000000000001, 0.85767970000000004, 0.85767966271276586,
--R      - 3.7287234189165019E-8]
--R     ,
--R
--R     [0.27000000000000002, 0.85096760000000005, 0.85096755337384578,
--R      - 4.6626154270867914E-8]
--R     ,
--R
--R     [0.28000000000000003, 0.84416780000000002, 0.84416780658343327,
--R      6.5834332430014797E-9]
--R     ,
--R
--R     [0.28999999999999998, 0.83728080000000005, 0.8372808394751845,
--R      3.9475184454573764E-8]
--R     ,
--R
--R     [0.29999999999999999, 0.83030709999999996, 0.83030706647674468,
--R      - 3.3523255282830178E-8]
--R     ,
--R    [0.31,0.8232469,0.82324689932967399,- 6.7032601691607852E-10],
--R
--R     [0.32000000000000001, 0.81610070000000001, 0.81610074710921554,
--R      4.7109215528529091E-8]
--R     ,
--R
--R     [0.33000000000000002, 0.80886899999999995, 0.80886901624390695,
--R      1.6243906997281954E-8]
--R     ,
--R
--R     [0.34000000000000002, 0.80155209999999999, 0.80155211053503872,
--R      1.0535038730274948E-8]
--R     ,
--R
--R     [0.34999999999999998, 0.79415040000000003, 0.79415043117595796,
--R      3.1175957926343756E-8]
--R     ,
--R
--R     [0.35999999999999999, 0.78666440000000004, 0.78666437677122092,
--R      - 2.3228779122419496E-8]
--R     ,
--R    [0.37,0.77909430000000002,0.77909434335559369,4.3355593670746373E-8],
--R    [0.38,0.77144069999999998,0.77144072441290445,2.4412904475745734E-8],
--R
--R     [0.39000000000000001, 0.76370389999999999, 0.76370391089474698,
--R      1.089474699345061E-8]
--R     ,
--R
--R     [0.40000000000000002, 0.75588429999999995, 0.75588429123903633,
--R      - 8.7609636212349074E-9]
--R     ,
--R
--R     [0.40999999999999998, 0.74798229999999999, 0.74798225138841923,
--R      - 4.8611580760749007E-8]
--R     ,
--R
--R     [0.41999999999999998, 0.73999820000000005, 0.73999817480853991,
--R      - 2.5191460140128186E-8]
--R     ,
--R
--R     [0.42999999999999999, 0.73193240000000004, 0.73193244250616207,
--R      4.2506162034605666E-8]
--R     ,
--R    [0.44,0.72378540000000002,0.7237854330471486,3.3047148573217555E-8],
--R
--R     [0.45000000000000001, 0.71555749999999996, 0.71555752257429939,
--R      2.2574299429756195E-8]
--R     ,
--R
--R     [0.46000000000000002, 0.70724909999999996, 0.70724908482505056,
--R      - 1.517494940816988E-8]
--R     ,
--R    [0.46999999999999997,0.6988605,0.6988604911490337,- 8.8509662932167998E-9],
--R
--R     [0.47999999999999998, 0.69039209999999995, 0.69039211052549776,
--R      1.0525497806668227E-8]
--R     ,
--R
--R     [0.48999999999999999, 0.68184429999999996, 0.68184430958059394,
--R      9.5805939848148114E-9]
--R     ,
--R    [0.5,0.67321750000000002,0.67321745260452559,- 4.739547443399772E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 2

--S 3 of 7
[[0.50,0.3266439,En(2,0.50),En(2,0.50)-0.3266439],_
[0.51,0.3211062,En(2,0.51),En(2,0.51)-0.3211062],_
[0.52,0.3156863,En(2,0.52),En(2,0.52)-0.3156863],_
[0.53,0.3103807,En(2,0.53),En(2,0.53)-0.3103807],_
[0.54,0.3051862,En(2,0.54),En(2,0.54)-0.3051862],_
[0.55,0.3000996,En(2,0.55),En(2,0.55)-0.3000996],_
[0.56,0.2951179,En(2,0.56),En(2,0.56)-0.2951179],_
[0.57,0.2902382,En(2,0.57),En(2,0.57)-0.2902382],_
[0.58,0.2854578,En(2,0.58),En(2,0.58)-0.2854578],_
[0.59,0.2807739,En(2,0.59),En(2,0.59)-0.2807739],_
[0.60,0.2761839,En(2,0.60),En(2,0.60)-0.2761839],_
[0.61,0.2716855,En(2,0.61),En(2,0.61)-0.2716855],_
[0.62,0.2672761,En(2,0.62),En(2,0.62)-0.2672761],_
[0.63,0.2629535,En(2,0.63),En(2,0.63)-0.2629535],_
[0.64,0.2587154,En(2,0.64),En(2,0.64)-0.2587154],_
[0.65,0.2545597,En(2,0.65),En(2,0.65)-0.2545597],_
[0.66,0.2504844,En(2,0.66),En(2,0.66)-0.2504844],_
[0.67,0.2464874,En(2,0.67),En(2,0.67)-0.2464874],_
[0.68,0.2425667,En(2,0.68),En(2,0.68)-0.2425667],_
[0.69,0.2387206,En(2,0.69),En(2,0.69)-0.2387206],_
[0.70,0.2349471,En(2,0.70),En(2,0.70)-0.2349471],_
[0.71,0.2312446,En(2,0.71),En(2,0.71)-0.2312446],_
[0.72,0.2276114,En(2,0.72),En(2,0.72)-0.2276114],_
[0.73,0.2240457,En(2,0.73),En(2,0.73)-0.2240457],_
[0.74,0.2205461,En(2,0.74),En(2,0.74)-0.2205461],_
[0.75,0.2171109,En(2,0.75),En(2,0.75)-0.2171109],_
[0.76,0.2137388,En(2,0.76),En(2,0.76)-0.2137388],_
[0.77,0.2104282,En(2,0.77),En(2,0.77)-0.2104282],_
[0.78,0.2071777,En(2,0.78),En(2,0.78)-0.2071777],_
[0.79,0.2039860,En(2,0.79),En(2,0.79)-0.2039860],_
[0.80,0.2008517,En(2,0.80),En(2,0.80)-0.2008517],_
[0.81,0.1977736,En(2,0.81),En(2,0.81)-0.1977736],_
[0.82,0.1947504,En(2,0.82),En(2,0.82)-0.1947504],_
[0.83,0.1917810,En(2,0.83),En(2,0.83)-0.1917810],_
[0.84,0.1888641,En(2,0.84),En(2,0.84)-0.1888641],_
[0.85,0.1859986,En(2,0.85),En(2,0.85)-0.1859986],_
[0.86,0.1831833,En(2,0.86),En(2,0.86)-0.1831833],_
[0.87,0.1804173,En(2,0.87),En(2,0.87)-0.1804173],_
[0.88,0.1776994,En(2,0.88),En(2,0.88)-0.1776994],_
[0.89,0.1750287,En(2,0.89),En(2,0.89)-0.1750287],_
[0.90,0.1724041,En(2,0.90),En(2,0.90)-0.1724041],_
[0.91,0.1698247,En(2,0.91),En(2,0.91)-0.1698247],_
[0.92,0.1672895,En(2,0.92),En(2,0.92)-0.1672895],_
[0.93,0.1647977,En(2,0.93),En(2,0.93)-0.1647977],_
[0.94,0.1623482,En(2,0.94),En(2,0.94)-0.1623482],_
[0.95,0.1599404,En(2,0.95),En(2,0.95)-0.1599404],_
[0.96,0.1575732,En(2,0.96),En(2,0.96)-0.1575732],_
[0.97,0.1552459,En(2,0.97),En(2,0.97)-0.1552459],_
[0.98,0.1529578,En(2,0.98),En(2,0.98)-0.1529578],_
[0.99,0.1507079,En(2,0.99),En(2,0.99)-0.1507079],_
[1.00,0.1484955,En(2,1.00),En(2,1.00)-0.1484955],_
[1.01,0.1463199,En(2,1.01),En(2,1.01)-0.1463199],_
[1.02,0.1441804,En(2,1.02),En(2,1.02)-0.1441804],_
[1.03,0.1420763,En(2,1.03),En(2,1.03)-0.1420763],_
[1.04,0.1400068,En(2,1.04),En(2,1.04)-0.1400068],_
[1.05,0.1379713,En(2,1.05),En(2,1.05)-0.1379713],_
[1.06,0.1359691,En(2,1.06),En(2,1.06)-0.1359691],_
[1.07,0.1339996,En(2,1.07),En(2,1.07)-0.1339996],_
[1.08,0.1320622,En(2,1.08),En(2,1.08)-0.1320622],_
[1.09,0.1301562,En(2,1.09),En(2,1.09)-0.1301562],_
[1.10,0.1282811,En(2,1.10),En(2,1.10)-0.1282811],_
[1.11,0.1264362,En(2,1.11),En(2,1.11)-0.1264362],_
[1.12,0.1246210,En(2,1.12),En(2,1.12)-0.1246210],_
[1.13,0.1228350,En(2,1.13),En(2,1.13)-0.1228350],_
[1.14,0.1210775,En(2,1.14),En(2,1.14)-0.1210775],_
[1.15,0.1193481,En(2,1.15),En(2,1.15)-0.1193481],_
[1.16,0.1176462,En(2,1.16),En(2,1.16)-0.1176462],_
[1.17,0.1159714,En(2,1.17),En(2,1.17)-0.1159714],_
[1.18,0.1143231,En(2,1.18),En(2,1.18)-0.1143231],_
[1.19,0.1127008,En(2,1.19),En(2,1.19)-0.1127008],_
[1.20,0.1111041,En(2,1.20),En(2,1.20)-0.1111041],_
[1.21,0.1095325,En(2,1.21),En(2,1.21)-0.1095325],_
[1.22,0.1079855,En(2,1.22),En(2,1.22)-0.1079855],_
[1.23,0.1064627,En(2,1.23),En(2,1.23)-0.1064627],_
[1.24,0.1049637,En(2,1.24),En(2,1.24)-0.1049637],_
[1.25,0.1034881,En(2,1.25),En(2,1.25)-0.1034881],_
[1.26,0.1020353,En(2,1.26),En(2,1.26)-0.1020353],_
[1.27,0.1006051,En(2,1.27),En(2,1.27)-0.1006051],_
[1.28,0.0991970,En(2,1.28),En(2,1.28)-0.0991970],_
[1.29,0.0978106,En(2,1.29),En(2,1.29)-0.0978106],_
[1.30,0.0964455,En(2,1.30),En(2,1.30)-0.0964455],_
[1.31,0.0951015,En(2,1.31),En(2,1.31)-0.0951015],_
[1.32,0.0937780,En(2,1.32),En(2,1.32)-0.0937780],_
[1.33,0.0924747,En(2,1.33),En(2,1.33)-0.0924747],_
[1.34,0.0911913,En(2,1.34),En(2,1.34)-0.0911913],_
[1.35,0.0899275,En(2,1.35),En(2,1.35)-0.0899275],_
[1.36,0.0886829,En(2,1.36),En(2,1.36)-0.0886829],_
[1.37,0.0874571,En(2,1.37),En(2,1.37)-0.0874571],_
[1.38,0.0862499,En(2,1.38),En(2,1.38)-0.0862499],_
[1.39,0.0850610,En(2,1.39),En(2,1.39)-0.0850610],_
[1.40,0.0838899,En(2,1.40),En(2,1.40)-0.0838899],_
[1.41,0.0827365,En(2,1.41),En(2,1.41)-0.0827365],_
[1.42,0.0816004,En(2,1.42),En(2,1.42)-0.0816004],_
[1.43,0.0804813,En(2,1.43),En(2,1.43)-0.0804813],_
[1.44,0.0793789,En(2,1.44),En(2,1.44)-0.0793789],_
[1.45,0.0782930,En(2,1.45),En(2,1.45)-0.0782930],_
[1.46,0.0772233,En(2,1.46),En(2,1.46)-0.0772233],_
[1.47,0.0761694,En(2,1.47),En(2,1.47)-0.0761694],_
[1.48,0.0751313,En(2,1.48),En(2,1.48)-0.0751313],_
[1.49,0.0741085,En(2,1.49),En(2,1.49)-0.0741085],_
[1.50,0.0731008,En(2,1.50),En(2,1.50)-0.0731008],_
[1.51,0.0721080,En(2,1.51),En(2,1.51)-0.0721080],_
[1.52,0.0711298,En(2,1.52),En(2,1.52)-0.0711298],_
[1.53,0.0701660,En(2,1.53),En(2,1.53)-0.0701660],_
[1.54,0.0692164,En(2,1.54),En(2,1.54)-0.0692164],_
[1.55,0.0682807,En(2,1.55),En(2,1.55)-0.0682807],_
[1.56,0.0673587,En(2,1.56),En(2,1.56)-0.0673587],_
[1.57,0.0664502,En(2,1.57),En(2,1.57)-0.0664502],_
[1.58,0.0655549,En(2,1.58),En(2,1.58)-0.0655549],_
[1.59,0.0646726,En(2,1.59),En(2,1.59)-0.0646726],_
[1.60,0.0638032,En(2,1.60),En(2,1.60)-0.0638032],_
[1.61,0.0629464,En(2,1.61),En(2,1.61)-0.0629464],_
[1.62,0.0621020,En(2,1.62),En(2,1.62)-0.0621020],_
[1.63,0.0612698,En(2,1.63),En(2,1.63)-0.0612698],_
[1.64,0.0604497,En(2,1.64),En(2,1.64)-0.0604497],_
[1.65,0.0596413,En(2,1.65),En(2,1.65)-0.0596413],_
[1.66,0.0588446,En(2,1.66),En(2,1.66)-0.0588446],_
[1.67,0.0580594,En(2,1.67),En(2,1.67)-0.0580594],_
[1.68,0.0572854,En(2,1.68),En(2,1.68)-0.0572854],_
[1.69,0.0565226,En(2,1.69),En(2,1.69)-0.0565226],_
[1.70,0.0557706,En(2,1.70),En(2,1.70)-0.0557706],_
[1.71,0.0550294,En(2,1.71),En(2,1.71)-0.0550294],_
[1.72,0.0542988,En(2,1.72),En(2,1.72)-0.0542988],_
[1.73,0.0535786,En(2,1.73),En(2,1.73)-0.0535786],_
[1.74,0.0528686,En(2,1.74),En(2,1.74)-0.0528686],_
[1.75,0.0521687,En(2,1.75),En(2,1.75)-0.0521687],_
[1.76,0.0514788,En(2,1.76),En(2,1.76)-0.0514788],_
[1.77,0.0507986,En(2,1.77),En(2,1.77)-0.0507986],_
[1.78,0.0501281,En(2,1.78),En(2,1.78)-0.0501281],_
[1.79,0.0494670,En(2,1.79),En(2,1.79)-0.0494670],_
[1.80,0.0488153,En(2,1.80),En(2,1.80)-0.0488153],_
[1.81,0.0481727,En(2,1.81),En(2,1.81)-0.0481727],_
[1.82,0.0475392,En(2,1.82),En(2,1.82)-0.0475392],_
[1.83,0.0469146,En(2,1.83),En(2,1.83)-0.0469146],_
[1.84,0.0462987,En(2,1.84),En(2,1.84)-0.0462987],_
[1.85,0.0456915,En(2,1.85),En(2,1.85)-0.0456915],_
[1.86,0.0450928,En(2,1.86),En(2,1.86)-0.0450928],_
[1.87,0.0445024,En(2,1.87),En(2,1.87)-0.0445024],_
[1.88,0.0439203,En(2,1.88),En(2,1.88)-0.0439203],_
[1.89,0.0433463,En(2,1.89),En(2,1.89)-0.0433463],_
[1.90,0.0427803,En(2,1.90),En(2,1.90)-0.0427803],_
[1.91,0.0422222,En(2,1.91),En(2,1.91)-0.0422222],_
[1.92,0.0416718,En(2,1.92),En(2,1.92)-0.0416718],_
[1.93,0.0411291,En(2,1.93),En(2,1.93)-0.0411291],_
[1.94,0.0405938,En(2,1.94),En(2,1.94)-0.0405938],_
[1.95,0.0400660,En(2,1.95),En(2,1.95)-0.0400660],_
[1.96,0.0395455,En(2,1.96),En(2,1.96)-0.0395455],_
[1.97,0.0390322,En(2,1.97),En(2,1.97)-0.0390322],_
[1.98,0.0385259,En(2,1.98),En(2,1.98)-0.0385259],_
[1.99,0.0380267,En(2,1.99),En(2,1.99)-0.0380267],_
[2.00,0.0375343,En(2,2.00),En(2,2.00)-0.0375343]]
 

   (3)
   [[0.5,0.32664389999999999,0.326643862324553,- 3.7675446984408723E-8],

     [0.51000000000000001, 0.32110620000000001, 0.32110617940404323,
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     ,

     [0.52000000000000002, 0.31568629999999998, 0.31568625309046355,
      - 4.6909536421946285E-8]
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     [0.53000000000000003, 0.31038069999999995, 0.31038066931747649,
      - 3.0682523466385447E-8]
     ,

     [0.54000000000000004, 0.30518619999999996, 0.30518615409477512,
      - 4.5905224843600934E-8]
     ,

     [0.55000000000000004, 0.30009960000000002, 0.30009956561466999,
      - 3.4385330027753014E-8]
     ,

     [0.56000000000000005, 0.29511789999999999, 0.29511788693397883,
      - 1.3066021153917973E-8]
     ,
    [0.56999999999999995,0.2902382,0.29023821917982273,1.9179822730031049E-8],

     [0.57999999999999996, 0.28545779999999998, 0.28545777523334881,
      - 2.4766651174346066E-8]
     ,

     [0.58999999999999997, 0.28077390000000002, 0.28077387385015457,
      - 2.6149845455680776E-8]
     ,

     [0.59999999999999998, 0.27618389999999998, 0.27618393418038506,
      3.4180385077853259E-8]
     ,

     [0.60999999999999999, 0.27168550000000002, 0.27168547065517928,
      - 2.9344820740018207E-8]
     ,
    [0.62,0.26727610000000002,0.26727608820941567,- 1.1790584342197263E-8],

     [0.62999999999999989, 0.26295349999999995, 0.2629534778136256,
      - 2.2186374348809323E-8]
     ,

     [0.6399999999999999, 0.25871539999999998, 0.25871541229051531,
      1.2290515327695317E-8]
     ,
    [0.64999999999999991,0.2545597,0.25455974239385426,4.2393854260414088E-8],
    [0.65999999999999992,0.2504844,0.2504843931295298,- 6.8704701927657652E-9],
    [0.66999999999999993,0.2464874,0.24648736030041074,- 3.969958925487127E-8],
    [0.67999999999999994,0.2425667,0.24256670725830815,7.2583081489607792E-9],

     [0.68999999999999995, 0.23872060000000001, 0.23872056184779239,
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     ,

     [0.69999999999999996, 0.23494709999999999, 0.23494711352795306,
      1.3527953063308118E-8]
     ,

     [0.70999999999999996, 0.23124459999999999, 0.23124461065938429,
      1.0659384291900054E-8]
     ,

     [0.71999999999999997, 0.22761139999999999, 0.22761135794474674,
      - 4.2055253252071267E-8]
     ,

     [0.72999999999999998, 0.22404569999999999, 0.22404571401223494,
      1.4012234955673719E-8]
     ,

     [0.73999999999999999, 0.22054609999999999, 0.22054608913215246,
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     ,
    [0.75,0.2171109,0.21711094305759215,4.3057592158390889E-8],

     [0.76000000000000001, 0.21373880000000001, 0.21373878298094046,
      - 1.7019059550538174E-8]
     ,

     [0.77000000000000002, 0.21042820000000001, 0.21042816159857808,
      - 3.8401421931233415E-8]
     ,

     [0.78000000000000003, 0.20717769999999999, 0.2071776752767438,
      - 2.4723256192293874E-8]
     ,
    [0.79000000000000004,0.203986,0.20398596231206947,- 3.7687930526386637E-8],

     [0.80000000000000004, 0.20085169999999999, 0.20085170128078714,
      1.2807871430098317E-9]
     ,

     [0.81000000000000005, 0.19777359999999999, 0.19777360947106051,
      9.4710605191838937E-9]
     ,

     [0.81999999999999995, 0.19475039999999999, 0.1947504413933023,
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     ,

     [0.82999999999999996, 0.19178099999999998, 0.19178098736371621,
      - 1.2636283769351664E-8]
     ,

     [0.83999999999999997, 0.18886409999999998, 0.18886407215664666,
      - 2.784335331740273E-8]
     ,

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      - 4.6278365556373657E-8]
     ,

     [0.85999999999999999, 0.18318329999999999, 0.1831833219613668,
      2.1961366808431748E-8]
     ,
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     [0.87999999999999989, 0.17769940000000001, 0.17769943090737961,
      3.0907379600098039E-8]
     ,

     [0.8899999999999999, 0.17502869999999998, 0.17502870096960521,
      9.6960522943945193E-10]
     ,
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    [0.90999999999999992,0.1698247,0.16982470427407523,4.2740752326242415E-9],

     [0.91999999999999993, 0.16728949999999998, 0.16728952970127758,
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     ,
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     [0.94999999999999996, 0.15994039999999998, 0.15994037598345329,
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     [0.96999999999999997, 0.15524589999999999, 0.15524594476761389,
      4.4767613893714753E-8]
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     [0.97999999999999998, 0.15295779999999998, 0.15295775478567628,
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    [1.02,0.14418039999999999,0.14418043507218442,3.5072184434437048E-8],

     [1.0299999999999998, 0.14207629999999999, 0.1420762844890415,
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     ,
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     [1.0499999999999998, 0.13797129999999999, 0.13797129522994897,
      - 4.7700510208414926E-9]
     ,

     [1.0600000000000001, 0.13596910000000001, 0.13596912300504763,
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     ,
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     [1.0800000000000001, 0.13206219999999999, 0.13206220822231926,
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     ,
    [1.0899999999999999,0.1301562,0.13015622510971897,2.5109718970739436E-8],

     [1.1000000000000001, 0.12828109999999998, 0.12828108870843541,
      - 1.1291564572246671E-8]
     ,
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    [1.1200000000000001,0.124621,0.12462103126751783,3.1267517838773351E-8],
    [1.1299999999999999,0.122835,0.12283498128064527,- 1.8719354732965598E-8],
    [1.1399999999999999,0.1210775,0.12107751934064426,1.9340644252796579E-8],
    [1.1499999999999999,0.1193481,0.11934811270455489,1.270455489421618E-8],

     [1.1599999999999999, 0.11764620000000001, 0.11764624067609286,
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    [1.1799999999999999,0.1143231,0.11432307586814175,- 2.4131858247788962E-8],

     [1.1899999999999999, 0.11270079999999999, 0.11270079893724061,
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    [1.21,0.1095325,0.10953247680961009,- 2.3190389913940734E-8],
    [1.22,0.1079855,0.107985511157423,1.1157422999397149E-8],
    [1.23,0.10646269999999999,0.10646274550249626,4.5502496270888315E-8],
    [1.24,0.10496369999999999,0.10496374425361371,4.4253613717959439E-8],
    [1.25,0.1034881,0.10348808120280223,- 1.8797197770537011E-8],
    [1.2599999999999998,0.1020353,0.10203533927685368,3.9276853686098789E-8],
    [1.27,0.1006051,0.10060511029696775,1.0296967750678121E-8],

     [1.2799999999999998, 9.9196999999999994E-2, 9.9196994746190897E-2,
      - 5.2538090961062878E-9]
     ,
    [1.29,9.7810599999999998E-2,9.7810601544343179E-2,1.5443431811146269E-9],

     [1.2999999999999998, 9.644549999999999E-2, 9.644554783014464E-2,
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     ,

     [1.3100000000000001, 9.5101500000000005E-2, 9.5101458750257717E-2,
      - 4.1249742288584912E-8]
     ,
    [1.3199999999999998,9.3778E-2,9.3777967254982525E-2,- 3.2745017475299676E-8]
     ,

     [1.3300000000000001, 9.2474699999999993E-2, 9.2474713900349198E-2,
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     ,

     [1.3399999999999999, 9.1191300000000003E-2, 9.1191346656366634E-2,
      4.6656366631259161E-8]
     ,

     [1.3500000000000001, 8.9927499999999994E-2, 8.9927520721194559E-2,
      2.072119456575372E-8]
     ,

     [1.3599999999999999, 8.8682899999999995E-2, 8.8682898341016059E-2,
      - 1.6589839363367886E-9]
     ,

     [1.3700000000000001, 8.7457099999999996E-2, 8.7457148635403298E-2,
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     ,

     [1.3799999999999999, 8.624989999999999E-2, 8.6249947427970763E-2,
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     ,

     [1.3899999999999999, 8.5060999999999998E-2, 8.5060977082121292E-2,
      - 2.291787870589701E-8]
     ,

     [1.3999999999999999, 8.3889899999999989E-2, 8.3889926341705251E-2,
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     ,

     [1.4099999999999999, 8.2736499999999991E-2, 8.2736490176409022E-2,
      - 9.8235909684607492E-9]
     ,

     [1.4199999999999999, 8.160039999999999E-2, 8.1600369631709052E-2,
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     ,

     [1.4299999999999999, 8.0481300000000006E-2, 8.0481271683224637E-2,
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     ,

     [1.4399999999999999, 7.9378900000000002E-2, 7.9378909095316558E-2,
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     ,
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    [1.46,7.7223299999999995E-2,7.722326918249886E-2,- 3.0817501134317027E-8],
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     [1.5099999999999998, 7.2108000000000005E-2, 7.210798726481607E-2,
      - 1.2735183935186356E-8]
     ,
    [1.52,7.1129799999999993E-2,7.1129818181354831E-2,1.8181354838331387E-8],

     [1.5299999999999998, 7.0166000000000006E-2, 7.0166038419312127E-2,
      3.8419312120563376E-8]
     ,
    [1.54,6.9216399999999997E-2,6.9216411688142465E-2,1.1688142467769502E-8],
    [1.5499999999999998,6.82807E-2,6.8280706172218653E-2,6.1722186528445633E-9],

     [1.5600000000000001, 6.7358699999999994E-2, 6.7358694430315169E-2,
      - 5.5696848244579655E-9]
     ,

     [1.5699999999999998, 6.6450199999999987E-2, 6.6450153297810566E-2,
      - 4.6702189421266027E-8]
     ,

     [1.5800000000000001, 6.5554899999999999E-2, 6.5554863791512041E-2,
      - 3.6208487957933855E-8]
     ,

     [1.5899999999999999, 6.4672599999999997E-2, 6.4672611017026621E-2,
      1.1017026624315918E-8]
     ,

     [1.6000000000000001, 6.3803200000000004E-2, 6.380318407859184E-2,
      - 1.5921408164087936E-8]
     ,

     [1.6099999999999999, 6.29464E-2, 6.2946375991286774E-2,
      - 2.4008713225831535E-8]
     ,

     [1.6200000000000001, 6.2101999999999997E-2, 6.210198359555763E-2,
      - 1.6404442367001781E-8]
     ,

     [1.6299999999999999, 6.1269799999999999E-2, 6.1269807473971261E-2,
      7.4739712613292042E-9]
     ,

     [1.6399999999999999, 6.0449699999999995E-2, 6.0449651870139065E-2,
      - 4.8129860930057333E-8]
     ,

     [1.6499999999999999, 5.9641299999999994E-2, 5.9641324609737895E-2,
      2.4609737900305184E-8]
     ,

     [1.6599999999999999, 5.8844599999999997E-2, 5.884463702356188E-2,
      3.702356188295397E-8]
     ,

     [1.6699999999999999, 5.8059399999999997E-2, 5.8059403872549598E-2,
      3.8725496004365922E-9]
     ,
    [1.6799999999999999,5.72854E-2,5.7285443274719294E-2,4.3274719294106312E-8],

     [1.6899999999999999, 5.6522599999999999E-2, 5.6522576633957461E-2,
      - 2.3366042538330856E-8]
     ,
    [1.7,5.5770599999999997E-2,5.577062857060433E-2,2.8570604333755245E-8],
    [1.71,5.5029399999999999E-2,5.5029426853783564E-2,2.6853783564873002E-8],
    [1.72,5.4298799999999994E-2,5.4298802335420795E-2,2.3354208011916455E-9],
    [1.73,5.3578599999999997E-2,5.3578588885902612E-2,- 1.1114097385467314E-8],
    [1.74,5.2868600000000002E-2,5.2868623331333131E-2,2.3331333129372744E-8],
    [1.75,5.2168699999999998E-2,5.2168745392326937E-2,4.5392326938897831E-8],

     [1.7599999999999998, 5.1478799999999998E-2, 5.1478797624312095E-2,
      - 2.3756879033443035E-9]
     ,
    [1.77,5.0798599999999999E-2,5.0798625359279356E-2,2.5359279356984565E-8],

     [1.7799999999999998, 5.0128099999999995E-2, 5.0128076648957673E-2,
      - 2.3351042321984039E-8]
     ,
    [1.79,4.9466999999999997E-2,4.9467002209351393E-2,2.2093513962762046E-9],

     [1.7999999999999998, 4.8815299999999999E-2, 4.8815255366623025E-2,
      - 4.4633376973524097E-8]
     ,

     [1.8100000000000001, 4.8172699999999999E-2, 4.8172692004261553E-2,
      - 7.995738446342493E-9]
     ,

     [1.8199999999999998, 4.7539199999999997E-2, 4.7539170511522399E-2,
      - 2.9488477597261475E-8]
     ,

     [1.8300000000000001, 4.6914600000000001E-2, 4.6914551733080068E-2,
      - 4.8266919933093178E-8]
     ,

     [1.8399999999999999, 4.6298699999999998E-2, 4.6298698919879006E-2,
      - 1.0801209926469824E-9]
     ,

     [1.8500000000000001, 4.5691499999999996E-2, 4.5691477681136752E-2,
      - 2.2318863243664389E-8]
     ,

     [1.8599999999999999, 4.5092800000000002E-2, 4.5092755937471404E-2,
      - 4.4062528598010076E-8]
     ,

     [1.8700000000000001, 4.4502399999999998E-2, 4.4502403875127772E-2,
      3.8751277742221646E-9]
     ,

     [1.8799999999999999, 4.3920299999999995E-2, 4.3920293901256249E-2,
      - 6.0987437461301752E-9]
     ,

     [1.8899999999999999, 4.3346299999999997E-2, 4.3346300600240958E-2,
      6.0024096110167235E-10]
     ,

     [1.8999999999999999, 4.2780299999999993E-2, 4.2780300691018888E-2,
      6.9101889488276669E-10]
     ,

     [1.9099999999999999, 4.2222200000000001E-2, 4.2222172985386774E-2,
      - 2.7014613226961082E-8]
     ,

     [1.9199999999999999, 4.1671799999999995E-2, 4.1671798347258343E-2,
      - 1.6527416518696825E-9]
     ,

     [1.9299999999999999, 4.1129100000000002E-2, 4.1129059652846342E-2,
      - 4.0347153659747725E-8]
     ,

     [1.9399999999999999, 4.0593799999999999E-2, 4.0593841751749682E-2,
      4.1751749682572559E-8]
     ,
    [1.95,4.0065999999999997E-2,4.0066031428915988E-2,3.142891599056119E-8],
    [1.96,3.9545499999999997E-2,3.9545517367460342E-2,1.7367460344863694E-8],
    [1.97,3.9032200000000003E-2,3.9032190112314194E-2,- 9.8876858090068964E-9],
    [1.98,3.8525900000000002E-2,3.8525942034687163E-2,4.2034687161573991E-8],
    [1.99,3.8026699999999997E-2,3.8026667297318517E-2,- 3.2702681479479523E-8],
    [2.,3.75343E-2,3.7534261820490689E-2,- 3.817950931100933E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (3)
--R   [[0.5,0.32664389999999999,0.326643862324553,- 3.7675446984408723E-8],
--R
--R     [0.51000000000000001, 0.32110620000000001, 0.32110617940404323,
--R      - 2.0595956773394875E-8]
--R     ,
--R
--R     [0.52000000000000002, 0.31568629999999998, 0.31568625309046355,
--R      - 4.6909536421946285E-8]
--R     ,
--R
--R     [0.53000000000000003, 0.31038070000000001, 0.31038066931747649,
--R      - 3.0682523521896599E-8]
--R     ,
--R
--R     [0.54000000000000004, 0.30518620000000002, 0.30518615409477512,
--R      - 4.5905224899112085E-8]
--R     ,
--R
--R     [0.55000000000000004, 0.30009960000000002, 0.30009956561466999,
--R      - 3.4385330027753014E-8]
--R     ,
--R
--R     [0.56000000000000005, 0.29511789999999999, 0.29511788693397883,
--R      - 1.3066021153917973E-8]
--R     ,
--R    [0.56999999999999995,0.2902382,0.29023821917982273,1.9179822730031049E-8],
--R
--R     [0.57999999999999996, 0.28545779999999998, 0.28545777523334881,
--R      - 2.4766651174346066E-8]
--R     ,
--R
--R     [0.58999999999999997, 0.28077390000000002, 0.28077387385015457,
--R      - 2.6149845455680776E-8]
--R     ,
--R
--R     [0.59999999999999998, 0.27618389999999998, 0.27618393418038506,
--R      3.4180385077853259E-8]
--R     ,
--R
--R     [0.60999999999999999, 0.27168550000000002, 0.27168547065517928,
--R      - 2.9344820740018207E-8]
--R     ,
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--R    [0.63,0.26295350000000001,0.26295347781362555,- 2.2186374459831626E-8],
--R
--R     [0.64000000000000001, 0.25871539999999998, 0.25871541229051526,
--R      1.2290515272184166E-8]
--R     ,
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--R    [0.67000000000000004,0.2464874,0.24648736030041074,- 3.969958925487127E-8],
--R    [0.68000000000000005,0.2425667,0.24256670725830815,7.2583081489607792E-9],
--R
--R     [0.68999999999999995, 0.23872060000000001, 0.23872056184779239,
--R      - 3.8152207615382849E-8]
--R     ,
--R
--R     [0.69999999999999996, 0.23494709999999999, 0.23494711352795306,
--R      1.3527953063308118E-8]
--R     ,
--R
--R     [0.70999999999999996, 0.23124459999999999, 0.23124461065938429,
--R      1.0659384291900054E-8]
--R     ,
--R
--R     [0.71999999999999997, 0.22761139999999999, 0.22761135794474674,
--R      - 4.2055253252071267E-8]
--R     ,
--R
--R     [0.72999999999999998, 0.22404569999999999, 0.22404571401223494,
--R      1.4012234955673719E-8]
--R     ,
--R
--R     [0.73999999999999999, 0.22054609999999999, 0.22054608913215246,
--R      - 1.0867847538564845E-8]
--R     ,
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--R
--R     [0.76000000000000001, 0.21373880000000001, 0.21373878298094046,
--R      - 1.7019059550538174E-8]
--R     ,
--R
--R     [0.77000000000000002, 0.21042820000000001, 0.21042816159857808,
--R      - 3.8401421931233415E-8]
--R     ,
--R
--R     [0.78000000000000003, 0.20717769999999999, 0.2071776752767438,
--R      - 2.4723256192293874E-8]
--R     ,
--R    [0.79000000000000004,0.203986,0.20398596231206947,- 3.7687930526386637E-8],
--R
--R     [0.80000000000000004, 0.20085169999999999, 0.20085170128078714,
--R      1.2807871430098317E-9]
--R     ,
--R
--R     [0.81000000000000005, 0.19777359999999999, 0.19777360947106051,
--R      9.4710605191838937E-9]
--R     ,
--R
--R     [0.81999999999999995, 0.19475039999999999, 0.19475044139330239,
--R      4.1393302396830478E-8]
--R     ,
--R
--R     [0.82999999999999996, 0.19178100000000001, 0.19178098736371621,
--R      - 1.2636283797107239E-8]
--R     ,
--R
--R     [0.83999999999999997, 0.18886410000000001, 0.18886407215664666,
--R      - 2.7843353345158306E-8]
--R     ,
--R
--R     [0.84999999999999998, 0.18599859999999999, 0.18599855372163451,
--R      - 4.627836547310693E-8]
--R     ,
--R
--R     [0.85999999999999999, 0.18318329999999999, 0.1831833219613668,
--R      2.1961366808431748E-8]
--R     ,
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--R    [0.88,0.17769940000000001,0.17769943090737958,3.0907379572342464E-8],
--R
--R     [0.89000000000000001, 0.17502870000000001, 0.17502870096960518,
--R      9.696051739283007E-10]
--R     ,
--R    [0.90000000000000002,0.1724041,0.17240411434719952,1.4347199511766107E-8],
--R    [0.91000000000000003,0.1698247,0.16982470427407523,4.2740752326242415E-9],
--R
--R     [0.92000000000000004, 0.16728950000000001, 0.1672895297012775,
--R      2.9701277493021649E-8]
--R     ,
--R
--R     [0.93000000000000005, 0.16479769999999999, 0.16479767441433715,
--R      - 2.5585662838389922E-8]
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--R
--R     [0.94999999999999996, 0.15994040000000001, 0.15994037598345329,
--R      - 2.4016546723570897E-8]
--R     ,
--R    [0.95999999999999996,0.1575732,0.15757321716462735,1.7164627358345896E-8],
--R
--R     [0.96999999999999997, 0.15524589999999999, 0.15524594476761389,
--R      4.4767613893714753E-8]
--R     ,
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--R
--R     [0.98999999999999999, 0.15070790000000001, 0.15070786348977031,
--R      - 3.6510229700636998E-8]
--R     ,
--R    [1.,0.1484955,0.14849550677592205,6.7759220456764524E-9],
--R    [1.01,0.1463199,0.14631993953908851,3.9539088503293129E-8],
--R    [1.02,0.14418039999999999,0.14418043507218453,3.5072184545459351E-8],
--R    [1.03,0.14207629999999999,0.1420762844890415,- 1.551095848983941E-8],
--R    [1.04,0.14000679999999999,0.14000679617012995,- 3.8298700322236812E-9],
--R    [1.05,0.13797129999999999,0.13797129522994891,- 4.7700510763526438E-9],
--R
--R     [1.0600000000000001, 0.13596910000000001, 0.13596912300504763,
--R      2.3005047616875274E-8]
--R     ,
--R    [1.0700000000000001,0.1339996,0.13399963656170108,3.6561701083348552E-8],
--R
--R     [1.0800000000000001, 0.13206219999999999, 0.13206220822231926,
--R      8.2223192698904768E-9]
--R     ,
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--R
--R     [1.1000000000000001, 0.12828110000000001, 0.12828108870843541,
--R      - 1.1291564600002246E-8]
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--R     [1.1599999999999999, 0.11764620000000001, 0.11764624067609286,
--R      4.0676092855074231E-8]
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--R    [1.2,0.1111041,0.11110408769044711,- 1.2309552890887865E-8],
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--R    [1.22,0.1079855,0.10798551115742314,1.1157423138175027E-8],
--R    [1.23,0.10646269999999999,0.10646274550249626,4.5502496270888315E-8],
--R    [1.24,0.10496369999999999,0.10496374425361385,4.4253613856737317E-8],
--R    [1.25,0.1034881,0.10348808120280234,- 1.8797197659514708E-8],
--R    [1.26,0.1020353,0.10203533927685385,3.9276853852632243E-8],
--R    [1.27,0.1006051,0.10060511029696789,1.0296967889455999E-8],
--R    [1.28,9.9196999999999994E-2,9.9196994746190731E-2,- 5.2538092626397415E-9],
--R    [1.29,9.7810599999999998E-2,9.7810601544343179E-2,1.5443431811146269E-9],
--R    [1.3,9.6445500000000003E-2,9.6445547830144779E-2,4.7830144775384831E-8],
--R
--R     [1.3100000000000001, 9.5101500000000005E-2, 9.5101458750257717E-2,
--R      - 4.1249742288584912E-8]
--R     ,
--R    [1.3200000000000001,9.3778E-2,9.3777967254982664E-2,- 3.2745017336521798E-8]
--R     ,
--R
--R     [1.3300000000000001, 9.2474700000000007E-2, 9.2474713900349198E-2,
--R      1.3900349191131589E-8]
--R     ,
--R
--R     [1.3400000000000001, 9.1191300000000003E-2, 9.1191346656366773E-2,
--R      4.6656366770037039E-8]
--R     ,
--R
--R     [1.3500000000000001, 8.9927499999999994E-2, 8.9927520721194559E-2,
--R      2.072119456575372E-8]
--R     ,
--R
--R     [1.3600000000000001, 8.8682899999999995E-2, 8.8682898341016198E-2,
--R      - 1.6589837975589106E-9]
--R     ,
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--R     [1.3700000000000001, 8.7457099999999996E-2, 8.7457148635403298E-2,
--R      4.8635403301910962E-8]
--R     ,
--R
--R     [1.3799999999999999, 8.6249900000000004E-2, 8.6249947427970763E-2,
--R      4.7427970759073013E-8]
--R     ,
--R
--R     [1.3899999999999999, 8.5060999999999998E-2, 8.5060977082121597E-2,
--R      - 2.2917878400585678E-8]
--R     ,
--R
--R     [1.3999999999999999, 8.3889900000000003E-2, 8.3889926341705251E-2,
--R      2.6341705247623359E-8]
--R     ,
--R
--R     [1.4099999999999999, 8.2736500000000004E-2, 8.2736490176409327E-2,
--R      - 9.8235906770272052E-9]
--R     ,
--R
--R     [1.4199999999999999, 8.1600400000000003E-2, 8.1600369631709052E-2,
--R      - 3.0368290951376942E-8]
--R     ,
--R
--R     [1.4299999999999999, 8.0481300000000006E-2, 8.0481271683224637E-2,
--R      - 2.8316775368963931E-8]
--R     ,
--R
--R     [1.4399999999999999, 7.9378900000000002E-2, 7.9378909095316863E-2,
--R      9.0953168607743606E-9]
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--R    [1.47,7.6169399999999998E-2,7.6169445113894313E-2,4.5113894314718905E-8],
--R    [1.48,7.5131299999999998E-2,7.5131262663086618E-2,- 3.7336913380481285E-8],
--R    [1.49,7.4108499999999994E-2,7.4108461555594529E-2,- 3.844440546463268E-8],
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--R    [1.51,7.2108000000000005E-2,7.2107987264816237E-2,- 1.2735183768652902E-8],
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--R    [1.53,7.0166000000000006E-2,7.0166038419312571E-2,3.8419312564652586E-8],
--R    [1.54,6.9216399999999997E-2,6.9216411688142798E-2,1.168814280083641E-8],
--R    [1.55,6.82807E-2,6.8280706172218819E-2,6.172218819378017E-9],
--R
--R     [1.5600000000000001, 6.7358699999999994E-2, 6.735869443031553E-2,
--R      - 5.5696844636354825E-9]
--R     ,
--R
--R     [1.5700000000000001, 6.6450200000000001E-2, 6.6450153297810788E-2,
--R      - 4.670218921309921E-8]
--R     ,
--R
--R     [1.5800000000000001, 6.5554899999999999E-2, 6.5554863791512402E-2,
--R      - 3.6208487597111372E-8]
--R     ,
--R
--R     [1.5900000000000001, 6.4672599999999997E-2, 6.4672611017026815E-2,
--R      1.1017026818604947E-8]
--R     ,
--R
--R     [1.6000000000000001, 6.3803200000000004E-2, 6.380318407859184E-2,
--R      - 1.5921408164087936E-8]
--R     ,
--R    [1.6100000000000001,6.29464E-2,6.2946375991286996E-2,- 2.400871300378693E-8]
--R     ,
--R
--R     [1.6200000000000001, 6.2101999999999997E-2, 6.210198359555763E-2,
--R      - 1.6404442367001781E-8]
--R     ,
--R
--R     [1.6299999999999999, 6.1269799999999999E-2, 6.1269807473971261E-2,
--R      7.4739712613292042E-9]
--R     ,
--R
--R     [1.6399999999999999, 6.0449700000000002E-2, 6.0449651870139426E-2,
--R      - 4.8129860576173744E-8]
--R     ,
--R
--R     [1.6499999999999999, 5.9641300000000001E-2, 5.9641324609737895E-2,
--R      2.460973789336629E-8]
--R     ,
--R
--R     [1.6599999999999999, 5.8844599999999997E-2, 5.884463702356188E-2,
--R      3.702356188295397E-8]
--R     ,
--R
--R     [1.6699999999999999, 5.8059399999999997E-2, 5.8059403872549598E-2,
--R      3.8725496004365922E-9]
--R     ,
--R    [1.6799999999999999,5.72854E-2,5.7285443274719294E-2,4.3274719294106312E-8],
--R
--R     [1.6899999999999999, 5.6522599999999999E-2, 5.6522576633957849E-2,
--R      - 2.3366042149752797E-8]
--R     ,
--R    [1.7,5.5770599999999997E-2,5.5770628570604719E-2,2.8570604722333304E-8],
--R    [1.71,5.5029399999999999E-2,5.5029426853783953E-2,2.685378395345106E-8],
--R    [1.72,5.4298800000000001E-2,5.4298802335420795E-2,2.3354207942527516E-9],
--R    [1.73,5.3578599999999997E-2,5.3578588885902612E-2,- 1.1114097385467314E-8],
--R    [1.74,5.2868600000000002E-2,5.2868623331333131E-2,2.3331333129372744E-8],
--R    [1.75,5.2168699999999998E-2,5.2168745392327326E-2,4.539232732747589E-8],
--R    [1.76,5.1478799999999998E-2,5.1478797624312636E-2,- 2.375687362110579E-9],
--R    [1.77,5.0798599999999999E-2,5.0798625359279745E-2,2.5359279745562624E-8],
--R    [1.78,5.0128100000000002E-2,5.0128076648957798E-2,- 2.3351042204022843E-8],
--R    [1.79,4.9466999999999997E-2,4.9467002209351796E-2,2.209351798732051E-9],
--R    [1.8,4.8815299999999999E-2,4.8815255366622776E-2,- 4.4633377223324278E-8],
--R
--R     [1.8100000000000001, 4.8172699999999999E-2, 4.8172692004261553E-2,
--R      - 7.995738446342493E-9]
--R     ,
--R
--R     [1.8200000000000001, 4.7539199999999997E-2, 4.7539170511522538E-2,
--R      - 2.9488477458483597E-8]
--R     ,
--R
--R     [1.8300000000000001, 4.6914600000000001E-2, 4.691455173308047E-2,
--R      - 4.8266919530637331E-8]
--R     ,
--R
--R     [1.8400000000000001, 4.6298699999999998E-2, 4.6298698919879575E-2,
--R      - 1.0801204236576822E-9]
--R     ,
--R
--R     [1.8500000000000001, 4.5691500000000003E-2, 4.5691477681136752E-2,
--R      - 2.2318863250603282E-8]
--R     ,
--R
--R     [1.8600000000000001, 4.5092800000000002E-2, 4.5092755937471779E-2,
--R      - 4.4062528223309805E-8]
--R     ,
--R
--R     [1.8700000000000001, 4.4502399999999998E-2, 4.4502403875127772E-2,
--R      3.8751277742221646E-9]
--R     ,
--R
--R     [1.8799999999999999, 4.3920300000000002E-2, 4.3920293901256249E-2,
--R      - 6.0987437530690691E-9]
--R     ,
--R
--R     [1.8899999999999999, 4.3346299999999997E-2, 4.3346300600241791E-2,
--R      6.0024179376894082E-10]
--R     ,
--R    [1.8999999999999999,4.27803E-2,4.2780300691019318E-2,6.9101931815529483E-10]
--R     ,
--R
--R     [1.9099999999999999, 4.2222200000000001E-2, 4.2222172985387205E-2,
--R      - 2.701461279674966E-8]
--R     ,
--R
--R     [1.9199999999999999, 4.1671800000000002E-2, 4.1671798347258343E-2,
--R      - 1.6527416588085764E-9]
--R     ,
--R
--R     [1.9299999999999999, 4.1129100000000002E-2, 4.1129059652846772E-2,
--R      - 4.0347153229536303E-8]
--R     ,
--R
--R     [1.9399999999999999, 4.0593799999999999E-2, 4.0593841751750112E-2,
--R      4.1751750112783981E-8]
--R     ,
--R    [1.95,4.0065999999999997E-2,4.0066031428916418E-2,3.1428916420772612E-8],
--R    [1.96,3.9545499999999997E-2,3.9545517367460342E-2,1.7367460344863694E-8],
--R    [1.97,3.9032200000000003E-2,3.9032190112315068E-2,- 9.8876849347062645E-9],
--R    [1.98,3.8525900000000002E-2,3.8525942034688052E-2,4.2034688049752411E-8],
--R    [1.99,3.8026699999999997E-2,3.8026667297318961E-2,- 3.2702681035390313E-8],
--R    [2.,3.75343E-2,3.7534261820490689E-2,- 3.817950931100933E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 3

--S 4 of 7
[[0.01,0.4902766,En(3,0.01),En(3,0.01)-0.4902766],_
[0.02,0.4809683,En(3,0.02),En(3,0.02)-0.4809683],_
[0.03,0.4719977,En(3,0.03),En(3,0.03)-0.4719977],_
[0.04,0.4633239,En(3,0.04),En(3,0.04)-0.4633239],_
[0.05,0.4549188,En(3,0.05),En(3,0.05)-0.4549188],_
[0.06,0.4467609,En(3,0.06),En(3,0.06)-0.4467609],_
[0.07,0.4388327,En(3,0.07),En(3,0.07)-0.4388327],_
[0.08,0.4311197,En(3,0.08),En(3,0.08)-0.4311197],_
[0.09,0.4236096,En(3,0.09),En(3,0.09)-0.4236096],_
[0.10,0.4162915,En(3,0.10),En(3,0.10)-0.4162915],_
[0.11,0.4091557,En(3,0.11),En(3,0.11)-0.4091557],_
[0.12,0.4021937,En(3,0.12),En(3,0.12)-0.4021937],_
[0.13,0.3953977,En(3,0.13),En(3,0.13)-0.3953977],_
[0.14,0.3887607,En(3,0.14),En(3,0.14)-0.3887607],_
[0.15,0.3822761,En(3,0.15),En(3,0.15)-0.3822761],_
[0.16,0.3759380,En(3,0.16),En(3,0.16)-0.3759380],_
[0.17,0.3697408,En(3,0.17),En(3,0.17)-0.3697408],_
[0.18,0.3636795,En(3,0.18),En(3,0.18)-0.3636795],_
[0.19,0.3577491,En(3,0.19),En(3,0.19)-0.3577491],_
[0.20,0.3519453,En(3,0.20),En(3,0.20)-0.3519453],_
[0.21,0.3462638,En(3,0.21),En(3,0.21)-0.3462638],_
[0.22,0.3407005,En(3,0.22),En(3,0.22)-0.3407005],_
[0.23,0.3352518,En(3,0.23),En(3,0.23)-0.3352518],_
[0.24,0.3299142,En(3,0.24),En(3,0.24)-0.3299142],_
[0.25,0.3246841,En(3,0.25),En(3,0.25)-0.3246841],_
[0.26,0.3195585,En(3,0.26),En(3,0.26)-0.3195585],_
[0.27,0.3145343,En(3,0.27),En(3,0.27)-0.3145343],_
[0.28,0.3096086,En(3,0.28),En(3,0.28)-0.3096086],_
[0.29,0.3047787,En(3,0.29),En(3,0.29)-0.3047787],_
[0.30,0.3000418,En(3,0.30),En(3,0.30)-0.3000418],_
[0.31,0.2953956,En(3,0.31),En(3,0.31)-0.2953956],_
[0.32,0.2908374,En(3,0.32),En(3,0.32)-0.2908374],_
[0.33,0.2863652,En(3,0.33),En(3,0.33)-0.2863652],_
[0.34,0.2819765,En(3,0.34),En(3,0.34)-0.2819765],_
[0.35,0.2776693,En(3,0.35),En(3,0.35)-0.2776693],_
[0.36,0.2734416,En(3,0.36),En(3,0.36)-0.2734416],_
[0.37,0.2692913,En(3,0.37),En(3,0.37)-0.2692913],_
[0.38,0.2652165,En(3,0.38),En(3,0.38)-0.2652165],_
[0.39,0.2612155,En(3,0.39),En(3,0.39)-0.2612155],_
[0.40,0.2572864,En(3,0.40),En(3,0.40)-0.2572864],_
[0.41,0.2534276,En(3,0.41),En(3,0.41)-0.2534276],_
[0.42,0.2496373,En(3,0.42),En(3,0.42)-0.2496373],_
[0.43,0.2459141,En(3,0.43),En(3,0.43)-0.2459141],_
[0.44,0.2422563,En(3,0.44),En(3,0.44)-0.2422563],_
[0.45,0.2386625,En(3,0.45),En(3,0.45)-0.2386625],_
[0.46,0.2351313,En(3,0.46),En(3,0.46)-0.2351313],_
[0.47,0.2316612,En(3,0.47),En(3,0.47)-0.2316612],_
[0.48,0.2282508,En(3,0.48),En(3,0.48)-0.2282508],_
[0.49,0.2248990,En(3,0.49),En(3,0.49)-0.2248990],_
[0.50,0.2216044,En(3,0.50),En(3,0.50)-0.2216044],_
[0.51,0.2183657,En(3,0.51),En(3,0.51)-0.2183657],_
[0.52,0.2151818,En(3,0.52),En(3,0.52)-0.2151818],_
[0.53,0.2120516,En(3,0.53),En(3,0.53)-0.2120516],_
[0.54,0.2089739,En(3,0.54),En(3,0.54)-0.2089739],_
[0.55,0.2059475,En(3,0.55),En(3,0.55)-0.2059475],_
[0.56,0.2029715,En(3,0.56),En(3,0.56)-0.2029715],_
[0.57,0.2000448,En(3,0.57),En(3,0.57)-0.2000448],_
[0.58,0.1971664,En(3,0.58),En(3,0.58)-0.1971664],_
[0.59,0.1943353,En(3,0.59),En(3,0.59)-0.1943353],_
[0.60,0.1915506,En(3,0.60),En(3,0.60)-0.1915506],_
[0.61,0.1888114,En(3,0.61),En(3,0.61)-0.1888114],_
[0.62,0.1861166,En(3,0.62),En(3,0.62)-0.1861166],_
[0.63,0.1834656,En(3,0.63),En(3,0.63)-0.1834656],_
[0.64,0.1808573,En(3,0.64),En(3,0.64)-0.1808573],_
[0.65,0.1782910,En(3,0.65),En(3,0.65)-0.1782910],_
[0.66,0.1757658,En(3,0.66),En(3,0.66)-0.1757658],_
[0.67,0.1732810,En(3,0.67),En(3,0.67)-0.1732810],_
[0.68,0.1708358,En(3,0.68),En(3,0.68)-0.1708358],_
[0.69,0.1684294,En(3,0.69),En(3,0.69)-0.1684294],_
[0.70,0.1660612,En(3,0.70),En(3,0.70)-0.1660612],_
[0.71,0.1637303,En(3,0.71),En(3,0.71)-0.1637303],_
[0.72,0.1614360,En(3,0.72),En(3,0.72)-0.1614360],_
[0.73,0.1591778,En(3,0.73),En(3,0.73)-0.1591778],_
[0.74,0.1569549,En(3,0.74),En(3,0.74)-0.1569549],_
[0.75,0.1547667,En(3,0.75),En(3,0.75)-0.1547667],_
[0.76,0.1526125,En(3,0.76),En(3,0.76)-0.1526125],_
[0.77,0.1504917,En(3,0.77),En(3,0.77)-0.1504917],_
[0.78,0.1484037,En(3,0.78),En(3,0.78)-0.1484037],_
[0.79,0.1463479,En(3,0.79),En(3,0.79)-0.1463479],_
[0.80,0.1443238,En(3,0.80),En(3,0.80)-0.1443238],_
[0.81,0.1423307,En(3,0.81),En(3,0.81)-0.1423307],_
[0.82,0.1403681,En(3,0.82),En(3,0.82)-0.1403681],_
[0.83,0.1384355,En(3,0.83),En(3,0.83)-0.1384355],_
[0.84,0.1365324,En(3,0.84),En(3,0.84)-0.1365324],_
[0.85,0.1346581,En(3,0.85),En(3,0.85)-0.1346581],_
[0.86,0.1328122,En(3,0.86),En(3,0.86)-0.1328122],_
[0.87,0.1309943,En(3,0.87),En(3,0.87)-0.1309943],_
[0.88,0.1292037,En(3,0.88),En(3,0.88)-0.1292037],_
[0.89,0.1274401,En(3,0.89),En(3,0.89)-0.1274401],_
[0.90,0.1257030,En(3,0.90),En(3,0.90)-0.1257030],_
[0.91,0.1239919,En(3,0.91),En(3,0.91)-0.1239919],_
[0.92,0.1223063,En(3,0.92),En(3,0.92)-0.1223063],_
[0.93,0.1206459,En(3,0.93),En(3,0.93)-0.1206459],_
[0.94,0.1190102,En(3,0.94),En(3,0.94)-0.1190102],_
[0.95,0.1173988,En(3,0.95),En(3,0.95)-0.1173988],_
[0.96,0.1158113,En(3,0.96),En(3,0.96)-0.1158113],_
[0.97,0.1142472,En(3,0.97),En(3,0.97)-0.1142472],_
[0.98,0.1127063,En(3,0.98),En(3,0.98)-0.1127063],_
[0.99,0.1111880,En(3,0.99),En(3,0.99)-0.1111880],_
[1.00,0.1096920,En(3,1.00),En(3,1.00)-0.1096920],_
[1.01,0.1082179,En(3,1.01),En(3,1.01)-0.1082179],_
[1.02,0.1067654,En(3,1.02),En(3,1.02)-0.1067654],_
[1.03,0.1053342,En(3,1.03),En(3,1.03)-0.1053342],_
[1.04,0.1039238,En(3,1.04),En(3,1.04)-0.1039238],_
[1.05,0.1025339,En(3,1.05),En(3,1.05)-0.1025339],_
[1.06,0.1011643,En(3,1.06),En(3,1.06)-0.1011643],_
[1.07,0.0998145,En(3,1.07),En(3,1.07)-0.0998145],_
[1.08,0.0984842,En(3,1.08),En(3,1.08)-0.0984842],_
[1.09,0.0971731,En(3,1.09),En(3,1.09)-0.0971731],_
[1.10,0.0958809,En(3,1.10),En(3,1.10)-0.0958809],_
[1.11,0.0946074,En(3,1.11),En(3,1.11)-0.0946074],_
[1.12,0.0933521,En(3,1.12),En(3,1.12)-0.0933521],_
[1.13,0.0921149,En(3,1.13),En(3,1.13)-0.0921149],_
[1.14,0.0908953,En(3,1.14),En(3,1.14)-0.0908953],_
[1.15,0.0896932,En(3,1.15),En(3,1.15)-0.0896932],_
[1.16,0.0885083,En(3,1.16),En(3,1.16)-0.0885083],_
[1.17,0.0873402,En(3,1.17),En(3,1.17)-0.0873402],_
[1.18,0.0861888,En(3,1.18),En(3,1.18)-0.0861888],_
[1.19,0.0850537,En(3,1.19),En(3,1.19)-0.0850537],_
[1.20,0.0839347,En(3,1.20),En(3,1.20)-0.0839347],_
[1.21,0.0828315,En(3,1.21),En(3,1.21)-0.0828315],_
[1.22,0.0817439,En(3,1.22),En(3,1.22)-0.0817439],_
[1.23,0.0806717,En(3,1.23),En(3,1.23)-0.0806717],_
[1.24,0.0796146,En(3,1.24),En(3,1.24)-0.0796146],_
[1.25,0.0785723,En(3,1.25),En(3,1.25)-0.0785723],_
[1.26,0.0775447,En(3,1.26),En(3,1.26)-0.0775447],_
[1.27,0.0765316,En(3,1.27),En(3,1.27)-0.0765316],_
[1.28,0.0755326,En(3,1.28),En(3,1.28)-0.0755326],_
[1.29,0.0745476,En(3,1.29),En(3,1.29)-0.0745476],_
[1.30,0.0735763,En(3,1.30),En(3,1.30)-0.0735763],_
[1.31,0.0726186,En(3,1.31),En(3,1.31)-0.0726186],_
[1.32,0.0716742,En(3,1.32),En(3,1.32)-0.0716742],_
[1.33,0.0707429,En(3,1.33),En(3,1.33)-0.0707429],_
[1.34,0.0698246,En(3,1.34),En(3,1.34)-0.0698246],_
[1.35,0.0689191,En(3,1.35),En(3,1.35)-0.0689191],_
[1.36,0.0680260,En(3,1.36),En(3,1.36)-0.0680260],_
[1.37,0.0671453,En(3,1.37),En(3,1.37)-0.0671453],_
[1.38,0.0662768,En(3,1.38),En(3,1.38)-0.0662768],_
[1.39,0.0654203,En(3,1.39),En(3,1.39)-0.0654203],_
[1.40,0.0645755,En(3,1.40),En(3,1.40)-0.0645755],_
[1.41,0.0637424,En(3,1.41),En(3,1.41)-0.0637424],_
[1.42,0.0629207,En(3,1.42),En(3,1.42)-0.0629207],_
[1.43,0.0621104,En(3,1.43),En(3,1.43)-0.0621104],_
[1.44,0.0613111,En(3,1.44),En(3,1.44)-0.0613111],_
[1.45,0.0605227,En(3,1.45),En(3,1.45)-0.0605227],_
[1.46,0.0597452,En(3,1.46),En(3,1.46)-0.0597452],_
[1.47,0.0589782,En(3,1.47),En(3,1.47)-0.0589782],_
[1.48,0.0582217,En(3,1.48),En(3,1.48)-0.0582217],_
[1.49,0.0574755,En(3,1.49),En(3,1.49)-0.0574755],_
[1.50,0.0567395,En(3,1.50),En(3,1.50)-0.0567395],_
[1.51,0.0560135,En(3,1.51),En(3,1.51)-0.0560135],_
[1.52,0.0552973,En(3,1.52),En(3,1.52)-0.0552973],_
[1.53,0.0545908,En(3,1.53),En(3,1.53)-0.0545908],_
[1.54,0.0538939,En(3,1.54),En(3,1.54)-0.0538939],_
[1.55,0.0532064,En(3,1.55),En(3,1.55)-0.0532064],_
[1.56,0.0525283,En(3,1.56),En(3,1.56)-0.0525283],_
[1.57,0.0518592,En(3,1.57),En(3,1.57)-0.0518592],_
[1.58,0.0511992,En(3,1.58),En(3,1.58)-0.0511992],_
[1.59,0.0505481,En(3,1.59),En(3,1.59)-0.0505481],_
[1.60,0.0499057,En(3,1.60),En(3,1.60)-0.0499057],_
[1.61,0.0492720,En(3,1.61),En(3,1.61)-0.0492720],_
[1.62,0.0486467,En(3,1.62),En(3,1.62)-0.0486467],_
[1.63,0.0480299,En(3,1.63),En(3,1.63)-0.0480299],_
[1.64,0.0474213,En(3,1.64),En(3,1.64)-0.0474213],_
[1.65,0.0468209,En(3,1.65),En(3,1.65)-0.0468209],_
[1.66,0.0462284,En(3,1.66),En(3,1.66)-0.0462284],_
[1.67,0.0456439,En(3,1.67),En(3,1.67)-0.0456439],_
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[1.69,0.0444982,En(3,1.69),En(3,1.69)-0.0444982],_
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[1.72,0.0428361,En(3,1.72),En(3,1.72)-0.0428361],_
[1.73,0.0422967,En(3,1.73),En(3,1.73)-0.0422967],_
[1.74,0.0417645,En(3,1.74),En(3,1.74)-0.0417645],_
[1.75,0.0412393,En(3,1.75),En(3,1.75)-0.0412393],_
[1.76,0.0407211,En(3,1.76),En(3,1.76)-0.0407211],_
[1.77,0.0402097,En(3,1.77),En(3,1.77)-0.0402097],_
[1.78,0.0397051,En(3,1.78),En(3,1.78)-0.0397051],_
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[1.80,0.0387157,En(3,1.80),En(3,1.80)-0.0387157],_
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[1.83,0.0372800,En(3,1.83),En(3,1.83)-0.0372800],_
[1.84,0.0368139,En(3,1.84),En(3,1.84)-0.0368139],_
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[1.87,0.0354521,En(3,1.87),En(3,1.87)-0.0354521],_
[1.88,0.0350100,En(3,1.88),En(3,1.88)-0.0350100],_
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[1.95,0.0320727,En(3,1.95),En(3,1.95)-0.0320727],_
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[1.99,0.0305112,En(3,1.99),En(3,1.99)-0.0305112],_
[2.00,0.0301334,En(3,2.00),En(3,2.00)-0.0301334]]
 

   (4)
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      - 4.8131628335723597E-8]
     ,

     [1.4399999999999999, 6.1311099999999993E-2, 6.1311064792432965E-2,
      - 3.5207567028461284E-8]
     ,
    [1.45,6.0522699999999999E-2,6.0522718841157223E-2,1.8841157224669391E-8],
    [1.46,5.9745199999999998E-2,5.9745150861655251E-2,- 4.9138344747345908E-8],
    [1.47,5.8978199999999995E-2,5.8978200434649845E-2,4.346498508334129E-10],
    [1.48,5.8221700000000001E-2,5.8221709821222517E-2,9.8212225158045285E-9],
    [1.49,5.7475499999999999E-2,5.7475523910801435E-2,2.3910801436044515E-8],
    [1.5,5.6739499999999998E-2,5.6739490170354422E-2,- 9.8296455766644364E-9],

     [1.5099999999999998, 5.6013499999999994E-2, 5.6013458594752999E-2,
      - 4.1405246994918876E-8]
     ,
    [1.52,5.5297299999999994E-2,5.52972816582777E-2,- 1.8341722293757634E-8],

     [1.5299999999999998, 5.4590799999999995E-2, 5.4590814267229781E-2,
      1.4267229786479874E-8]
     ,
    [1.54,5.3893899999999995E-2,5.3893913713619269E-2,1.3713619274879907E-8],

     [1.5499999999999998, 5.3206400000000001E-2, 5.3206439629902097E-2,
      3.9629902096049996E-8]
     ,

     [1.5600000000000001, 5.25283E-2, 5.2528253944736522E-2,
      - 4.6055263477895458E-8]
     ,

     [1.5699999999999998, 5.1859199999999994E-2, 5.1859220839728958E-2,
      2.0839728963328863E-8]
     ,
    [1.5800000000000001,5.11992E-2,5.1199206707147206E-2,6.7071472056867698E-9],

     [1.5899999999999999, 5.0548099999999999E-2, 5.0548080108570578E-2,
      - 1.9891429420271223E-8]
     ,

     [1.6000000000000001, 4.9905699999999997E-2, 4.9905711734454218E-2,
      1.1734454220813095E-8]
     ,

     [1.6099999999999999, 4.9271999999999996E-2, 4.9271974364586413E-2,
      - 2.5635413583580124E-8]
     ,

     [1.6200000000000001, 4.8646700000000001E-2, 4.8646742829405641E-2,
      4.2829405640099072E-8]
     ,

     [1.6299999999999999, 4.80299E-2, 4.8029893972168107E-2,
      - 6.0278318933515429E-9]
     ,
    [1.6399999999999999,4.74213E-2,4.7421306611931925E-2,6.6119319255819597E-9],

     [1.6499999999999999, 4.6820899999999999E-2, 4.6820861507343305E-2,
      - 3.8492656694033567E-8]
     ,

     [1.6599999999999999, 4.6228400000000003E-2, 4.622844132120392E-2,
      4.1321203916866445E-8]
     ,

     [1.6699999999999999, 4.5643900000000001E-2, 4.5643930585794489E-2,
      3.0585794487392182E-8]
     ,

     [1.6799999999999999, 4.5067200000000002E-2, 4.5067215668940779E-2,
      1.5668940776814022E-8]
     ,

     [1.6899999999999999, 4.4498200000000002E-2, 4.4498184740800577E-2,
      - 1.5259199424855208E-8]
     ,
    [1.7,4.3936699999999995E-2,4.3936727741353654E-2,2.7741353658683465E-8],
    [1.71,4.3382699999999996E-2,4.3382736348576104E-2,3.6348576107347874E-8],
    [1.72,4.2836100000000002E-2,4.283610394728473E-2,3.9472847282451262E-9],
    [1.73,4.22967E-2,4.229672559863315E-2,2.559863315071409E-8],
    [1.74,4.1764499999999996E-2,4.1764498010238606E-2,- 1.9897613903752109E-9],
    [1.75,4.12393E-2,4.1239319506936503E-2,1.9506936503599359E-8],

     [1.7599999999999998, 4.0721099999999996E-2, 4.0721090002130644E-2,
      - 9.9978693518520956E-9]
     ,
    [1.77,4.0209700000000001E-2,4.0209710969742483E-2,1.0969742482436207E-8],

     [1.7799999999999998, 3.9705099999999993E-2, 3.9705085416725454E-2,
      - 1.4583274539348157E-8]
     ,
    [1.79,3.9207099999999995E-2,3.9207117856150851E-2,1.7856150856532249E-8],

     [1.7999999999999998, 3.8715699999999999E-2, 3.8715714280832564E-2,
      1.4280832565105595E-8]
     ,

     [1.8100000000000001, 3.8230799999999995E-2, 3.8230782137495319E-2,
      - 1.7862504676779967E-8]
     ,
    [1.8199999999999998,3.77522E-2,3.7752230301455018E-2,3.0301455018755252E-8],

     [1.8300000000000001, 3.7279999999999994E-2, 3.7279969051818108E-2,
      - 3.0948181885259718E-8]
     ,

     [1.8399999999999999, 3.6813899999999997E-2, 3.6813910047171675E-2,
      1.0047171677962652E-8]
     ,

     [1.8500000000000001, 3.6353999999999997E-2, 3.6353966301762304E-2,
      - 3.3698237693335908E-8]
     ,

     [1.8599999999999999, 3.5900099999999997E-2, 3.590005216215026E-2,
      - 4.7837849737053517E-8]
     ,

     [1.8700000000000001, 3.54521E-2, 3.5452083284321229E-2,
      - 1.6715678771705988E-8]
     ,

     [1.8799999999999999, 3.5009999999999999E-2, 3.5009976611261075E-2,
      - 2.3388738924767782E-8]
     ,

     [1.8899999999999999, 3.4573699999999999E-2, 3.4573650350957726E-2,
      - 4.964904227328093E-8]
     ,
    [1.8999999999999999,3.4143E-2,3.414302395484959E-2,2.395484959005767E-8],

     [1.9099999999999999, 3.3717999999999998E-2, 3.3718018096686862E-2,
      1.8096686864310652E-8]
     ,

     [1.9199999999999999, 3.3298599999999998E-2, 3.3298554651807068E-2,
      - 4.5348192929950404E-8]
     ,

     [1.9299999999999999, 3.28846E-2, 3.2884556676815148E-2,
      - 4.3323184852062102E-8]
     ,

     [1.9399999999999999, 3.2475900000000002E-2, 3.2475948389654272E-2,
      4.8389654269676008E-8]
     ,
    [1.95,3.2072699999999996E-2,3.207265515006371E-2,- 4.4849936285673575E-8],
    [1.96,3.1674599999999997E-2,3.167460344041137E-2,3.4404113724573193E-9],
    [1.97,3.1281699999999996E-2,3.128172084689599E-2,2.0846895994186543E-8],
    [1.98,3.0893899999999998E-2,3.0893936041106122E-2,3.6041106123846367E-8],
    [1.99,3.0511199999999999E-2,3.0511178761929998E-2,- 2.1238070000567655E-8],
    [2.,3.0133399999999998E-2,3.0133379797815663E-2,- 2.0202184335127438E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (4)
--R   [[1.0E-2,0.49027660000000001,0.49027656418466514,- 3.5815334864519599E-8],
--R    [2.0E-2,0.48096830000000002,0.48096829147697201,- 8.5230280055803576E-9],
--R
--R     [2.9999999999999999E-2, 0.47199770000000002, 0.47199768719683605,
--R      - 1.2803163973451603E-8]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.46332390000000001, 0.46332394174433533,
--R      4.1744335321780568E-8]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.45491880000000001, 0.45491884974847663,
--R      4.9748476615985027E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.44676090000000002, 0.44676088323725571,
--R      - 1.6762744303733257E-8]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.43883270000000002, 0.43883267979789509,
--R      - 2.0202104933364495E-8]
--R     ,
--R
--R     [8.0000000000000002E-2, 0.43111969999999999, 0.43111973054612684,
--R      3.054612685016167E-8]
--R     ,
--R
--R     [8.9999999999999997E-2, 0.42360959999999998, 0.42360960561704109,
--R      5.6170411100175954E-9]
--R     ,
--R
--R     [0.10000000000000001, 0.41629149999999998, 0.41629145790827876,
--R      - 4.2091721219605915E-8]
--R     ,
--R    [0.11,0.40915570000000001,0.40915568570605237,- 1.4293947636634385E-8],
--R    [0.12,0.40219369999999999,0.40219369277059286,- 7.2294071284950689E-9],
--R    [0.13,0.39539770000000002,0.395397711576501,1.1576500980048365E-8],
--R
--R     [0.14000000000000001, 0.38876070000000001, 0.38876066929878084,
--R      - 3.0701219178030925E-8]
--R     ,
--R
--R     [0.14999999999999999, 0.38227610000000001, 0.38227608377400268,
--R      - 1.6225997323537911E-8]
--R     ,
--R    [0.16,0.37593799999999999,0.37593798110903431,- 1.8890965680640193E-8],
--R
--R     [0.17000000000000001, 0.36974079999999998, 0.36974082931670565,
--R      2.9316705674187205E-8]
--R     ,
--R
--R     [0.17999999999999999, 0.36367949999999999, 0.36367948407235051,
--R      - 1.5927649477109895E-8]
--R     ,
--R    [0.19,0.35774909999999999,0.3577491438077095,4.3807709515508719E-8],
--R
--R     [0.20000000000000001, 0.35194530000000002, 0.35194531211487057,
--R      1.2114870551194201E-8]
--R     ,
--R
--R     [0.20999999999999999, 0.34626380000000001, 0.3462637659551443,
--R      - 3.4044855712345168E-8]
--R     ,
--R    [0.22,0.34070050000000002,0.34070052853638638,2.8536386365018984E-8],
--R
--R     [0.23000000000000001, 0.33525179999999999, 0.33525184598756436,
--R      4.5987564367688805E-8]
--R     ,
--R
--R     [0.23999999999999999, 0.32991419999999999, 0.32991416715361832,
--R      - 3.2846381670115221E-8]
--R     ,
--R    [0.25,0.32468409999999998,0.32468412597814367,2.5978143691762767E-8],
--R
--R     [0.26000000000000001, 0.31955850000000002, 0.31955852605039498,
--R      2.6050394952292777E-8]
--R     ,
--R
--R     [0.27000000000000002, 0.31453429999999999, 0.31453432697636552,
--R      2.6976365530284596E-8]
--R     ,
--R
--R     [0.28000000000000003, 0.30960860000000001, 0.30960863229804725,
--R      3.2298047236700711E-8]
--R     ,
--R
--R     [0.28999999999999998, 0.30477870000000001, 0.30477867873524889,
--R      - 2.126475112662618E-8]
--R     ,
--R
--R     [0.29999999999999999, 0.30004180000000003, 0.30004182656401435,
--R      2.6564014321550644E-8]
--R     ,
--R    [0.31,0.29539559999999998,0.29539555097726167,- 4.9022738313198033E-8],
--R
--R     [0.32000000000000001, 0.29083740000000002, 0.29083743429861525,
--R      3.4298615225747398E-8]
--R     ,
--R
--R     [0.33000000000000002, 0.28636519999999999, 0.28636515894092018,
--R      - 4.1059079802785448E-8]
--R     ,
--R
--R     [0.34000000000000002, 0.28197650000000002, 0.28197650101764582,
--R      1.0176458009603095E-9]
--R     ,
--R
--R     [0.34999999999999998, 0.27766930000000001, 0.27766932452910809,
--R      2.4529108078041872E-8]
--R     ,
--R
--R     [0.35999999999999999, 0.27344160000000001, 0.27344157605676817,
--R      - 2.3943231841627721E-8]
--R     ,
--R    [0.37,0.26929130000000001,0.26929127990828022,- 2.0091719787895812E-8],
--R    [0.38,0.26521650000000002,0.2652165336638212,3.3663821175089481E-8],
--R
--R     [0.39000000000000001, 0.26121549999999999, 0.26121550408084138,
--R      4.0808413870330185E-9]
--R     ,
--R
--R     [0.40000000000000002, 0.25728640000000003, 0.25728642331994478,
--R      2.3319944753019684E-8]
--R     ,
--R
--R     [0.40999999999999998, 0.25342759999999998, 0.25342758545933575,
--R      - 1.45406642282353E-8]
--R     ,
--R
--R     [0.41999999999999998, 0.24963730000000001, 0.24963734326929157,
--R      4.3269291566394585E-8]
--R     ,
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--R    [0.44,0.24225630000000001,0.24225633271155758,3.2711557573783523E-8],
--R    [0.45000000000000001,0.2386625,0.23866253747371868,3.7473718683678214E-8],
--R
--R     [0.46000000000000002, 0.23513129999999999, 0.23513127917269516,
--R      - 2.082730482522166E-8]
--R     ,
--R
--R     [0.46999999999999997, 0.23166120000000001, 0.2316611631548362,
--R      - 3.6845163808862935E-8]
--R     ,
--R    [0.47999999999999998,0.2282508,0.22825083834619003,3.8346190028848426E-8],
--R
--R     [0.48999999999999999, 0.22489899999999999, 0.22489899528465218,
--R      - 4.7153478066608301E-9]
--R     ,
--R    [0.5,0.22160440000000001,0.22160436427517846,- 3.572482154545753E-8],
--R    [0.51000000000000001,0.2183657,0.21836571365810192,1.3658101927216393E-8],
--R
--R     [0.52000000000000002, 0.21518180000000001, 0.21518184818157665,
--R      4.8181576645101032E-8]
--R     ,
--R
--R     [0.53000000000000003, 0.21205160000000001, 0.21205160747004631,
--R      7.4700463037480347E-9]
--R     ,
--R
--R     [0.54000000000000004, 0.20897389999999999, 0.20897386458140554,
--R      - 3.541859444622375E-8]
--R     ,
--R
--R     [0.55000000000000004, 0.20594750000000001, 0.20594752464620908,
--R      2.4646209073608816E-8]
--R     ,
--R    [0.56000000000000005,0.2029715,0.20297152358289336,2.3582893360352131E-8],
--R
--R     [0.56999999999999995, 0.20004479999999999, 0.20004482688351907,
--R      2.6883519077536278E-8]
--R     ,
--R
--R     [0.57999999999999996, 0.19716639999999999, 0.19716642846502985,
--R      2.8465029860980096E-8]
--R     ,
--R
--R     [0.58999999999999997, 0.19433529999999999, 0.19433534958145796,
--R      4.9581457967073916E-8]
--R     ,
--R
--R     [0.59999999999999998, 0.19155059999999999, 0.19155063779289766,
--R      3.7792897672472847E-8]
--R     ,
--R
--R     [0.60999999999999999, 0.18881139999999999, 0.18881136598742021,
--R      - 3.4012579780418051E-8]
--R     ,
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--R    [0.63,0.18346560000000001,0.18346555499215655,- 4.5007843452182783E-8],
--R    [0.64000000000000001,0.1808573,0.18085728008855939,- 1.9911440607423003E-8],
--R
--R     [0.65000000000000002, 0.17829100000000001, 0.17829097210250539,
--R      - 2.7897494619955054E-8]
--R     ,
--R    [0.66000000000000003,0.1757658,0.17576581751310477,1.7513104771937904E-8],
--R
--R     [0.67000000000000004, 0.17328099999999999, 0.17328102319263361,
--R      2.3192633619162351E-8]
--R     ,
--R
--R     [0.68000000000000005, 0.17083580000000001, 0.17083581571497,
--R      1.5714969991975636E-8]
--R     ,
--R
--R     [0.68999999999999995, 0.16842940000000001, 0.16842944069553942,
--R      4.0695539410551262E-8]
--R     ,
--R
--R     [0.69999999999999996, 0.16606119999999999, 0.16606116216092121,
--R      - 3.7839078786960911E-8]
--R     ,
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--R    [0.71999999999999997,0.161436,0.16143603911987703,3.9119877032200989E-8],
--R
--R     [0.72999999999999998, 0.15917780000000001, 0.15917780943063548,
--R      9.4306354669893011E-9]
--R     ,
--R
--R     [0.73999999999999999, 0.15695490000000001, 0.15695490478162077,
--R      4.7816207660034138E-9]
--R     ,
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--R     [0.76000000000000001, 0.15261250000000001, 0.15261247597219724,
--R      - 2.4027802775217211E-8]
--R     ,
--R
--R     [0.77000000000000002, 0.15049170000000001, 0.15049169194016149,
--R      - 8.0598385188146437E-9]
--R     ,
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--R
--R     [0.82999999999999996, 0.13843549999999999, 0.13843553340482559,
--R      3.3404825600102939E-8]
--R     ,
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--R
--R     [0.85999999999999999, 0.13281219999999999, 0.13281221271548668,
--R      1.2715486691350364E-8]
--R     ,
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--R    [0.89000000000000001,0.1274401,0.12744010444469844,4.4446984426294023E-9],
--R
--R     [0.90000000000000002, 0.12570300000000001, 0.12570297841405975,
--R      - 2.1585940257473624E-8]
--R     ,
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--R
--R     [0.92000000000000004, 0.12230630000000001, 0.12230633687966941,
--R      3.6879669401690407E-8]
--R     ,
--R    [0.93000000000000005,0.1206459,0.12064593658313376,3.6583133758427699E-8],
--R    [0.93999999999999995,0.1190102,0.1190102419704193,4.1970419306647244E-8],
--R    [0.94999999999999996,0.1173988,0.11739883313511031,3.3135110308335491E-8],
--R
--R     [0.95999999999999996, 0.11581130000000001, 0.11581129874853491,
--R      - 1.2514650982176079E-9]
--R     ,
--R
--R     [0.96999999999999997, 0.11424719999999999, 0.11424723583940669,
--R      3.5839406692383946E-8]
--R     ,
--R    [0.97999999999999998,0.1127063,0.11270624958071841,- 5.0419281583113928E-8],
--R    [0.98999999999999999,0.111188,0.11118795308358656,- 4.6916413434794357E-8],
--R    [1.,0.109692,0.10969196719776014,- 3.2802239854912152E-8],
--R    [1.01,0.10821790000000001,0.10821792031852197,2.031852196215933E-8],
--R    [1.02,0.1067654,0.10676544819972504,4.8199725044550945E-8],
--R    [1.03,0.1053342,0.10533419377271731,- 6.2272826895082289E-9],
--R    [1.04,0.1039238,0.1039238069709225,6.9709225059000346E-9],
--R    [1.05,0.1025339,0.10253394455985448,4.455985448681421E-8],
--R    [1.0600000000000001,0.1011643,0.10116426997235345,- 3.0027646549801723E-8],
--R
--R     [1.0700000000000001, 9.98145E-2, 9.9814453148843241E-2,
--R      - 4.6851156759730728E-8]
--R     ,
--R
--R     [1.0800000000000001, 9.8484199999999994E-2, 9.8484170382417149E-2,
--R      - 2.9617582844587709E-8]
--R     ,
--R
--R     [1.0900000000000001, 9.7173099999999998E-2, 9.7173104168569752E-2,
--R      4.1685697532711785E-9]
--R     ,
--R
--R     [1.1000000000000001, 9.5880900000000005E-2, 9.58809430594003E-2,
--R      4.305940029536437E-8]
--R     ,
--R
--R     [1.1100000000000001, 9.4607399999999994E-2, 9.4607381522120698E-2,
--R      - 1.8477879296097122E-8]
--R     ,
--R
--R     [1.1200000000000001, 9.3352099999999993E-2, 9.3352119801709738E-2,
--R      1.9801709744138307E-8]
--R     ,
--R
--R     [1.1299999999999999, 9.21149E-2, 9.2114863787561826E-2,
--R      - 3.6212438173088835E-8]
--R     ,
--R
--R     [1.1399999999999999, 9.0895299999999998E-2, 9.0895324883984607E-2,
--R      2.4883984608981002E-8]
--R     ,
--R
--R     [1.1499999999999999, 8.9693200000000001E-2, 8.969321988440758E-2,
--R      1.9884407578829588E-8]
--R     ,
--R
--R     [1.1599999999999999, 8.8508299999999998E-2, 8.8508270849168805E-2,
--R      - 2.9150831193369697E-8]
--R     ,
--R
--R     [1.1699999999999999, 8.7340200000000007E-2, 8.7340204986753447E-2,
--R      4.9867534407388447E-9]
--R     ,
--R
--R     [1.1799999999999999, 8.6188799999999996E-2, 8.6188754538362E-2,
--R      - 4.5461637995791726E-8]
--R     ,
--R
--R     [1.1899999999999999, 8.5053699999999996E-2, 8.505365666569388E-2,
--R      - 4.3334306115694332E-8]
--R     ,
--R    [1.2,8.3934700000000001E-2,8.393465334183281E-2,- 4.6658167190960498E-8],
--R    [1.21,8.2831500000000002E-2,8.283149124512959E-2,- 8.7548704119644327E-9],
--R    [1.22,8.1743899999999994E-2,8.1743921655978991E-2,2.1655978996171221E-8],
--R    [1.23,8.0671699999999999E-2,8.067170035639451E-2,3.5639451112512432E-10],
--R    [1.24,7.9614599999999994E-2,7.9614587532284717E-2,- 1.2467715276853752E-8],
--R    [1.25,7.8572299999999998E-2,7.857234767834359E-2,4.7678343592649775E-8],
--R    [1.26,7.7544699999999994E-2,7.7544749505467275E-2,4.950546728110794E-8],
--R    [1.27,7.6531600000000005E-2,7.6531565850615282E-2,- 3.4149384722792497E-8],
--R    [1.28,7.5532600000000005E-2,7.5532573589034993E-2,- 2.6410965012213516E-8],
--R    [1.29,7.4547600000000006E-2,7.454755354877482E-2,- 4.6451225185761835E-8],
--R    [1.3,7.3576299999999997E-2,7.3576290427412191E-2,- 9.5725878057617564E-9],
--R
--R     [1.3100000000000001, 7.2618600000000005E-2, 7.2618572710924589E-2,
--R      - 2.7289075416048192E-8]
--R     ,
--R
--R     [1.3200000000000001, 7.1674199999999993E-2, 7.1674192594636615E-2,
--R      - 7.4053633780657435E-9]
--R     ,
--R
--R     [1.3300000000000001, 7.0742899999999997E-2, 7.0742945906179772E-2,
--R      4.5906179774179989E-8]
--R     ,
--R
--R     [1.3400000000000001, 6.9824600000000001E-2, 6.9824632030397252E-2,
--R      3.203039725119261E-8]
--R     ,
--R
--R     [1.3500000000000001, 6.8919099999999997E-2, 6.8919053836139416E-2,
--R      - 4.6163860581427407E-8]
--R     ,
--R
--R     [1.3600000000000001, 6.8026000000000003E-2, 6.8026017604886913E-2,
--R      1.7604886909383666E-8]
--R     ,
--R
--R     [1.3700000000000001, 6.7145300000000005E-2, 6.7145332961148871E-2,
--R      3.29611488658621E-8]
--R     ,
--R
--R     [1.3799999999999999, 6.6276799999999997E-2, 6.6276812804578436E-2,
--R      1.2804578439218339E-8]
--R     ,
--R
--R     [1.3899999999999999, 6.5420300000000001E-2, 6.5420273243759597E-2,
--R      - 2.6756240403824627E-8]
--R     ,
--R
--R     [1.3999999999999999, 6.4575499999999994E-2, 6.457553353160958E-2,
--R      3.3531609586190392E-8]
--R     ,
--R
--R     [1.4099999999999999, 6.3742400000000005E-2, 6.3742416002349978E-2,
--R      1.6002349972898955E-8]
--R     ,
--R
--R     [1.4199999999999999, 6.2920699999999996E-2, 6.2920746010004802E-2,
--R      4.6010004806085192E-8]
--R     ,
--R
--R     [1.4299999999999999, 6.2110400000000003E-2, 6.211035186837166E-2,
--R      - 4.8131628342662491E-8]
--R     ,
--R
--R     [1.4399999999999999, 6.13111E-2, 6.1311064792432743E-2,
--R      - 3.5207567257444783E-8]
--R     ,
--R    [1.45,6.0522699999999999E-2,6.0522718841157001E-2,1.8841157002624787E-8],
--R    [1.46,5.9745199999999998E-2,5.9745150861655022E-2,- 4.9138344976329407E-8],
--R    [1.47,5.8978200000000001E-2,5.8978200434649602E-2,4.3464960103323236E-10],
--R    [1.48,5.8221700000000001E-2,5.8221709821222274E-2,9.8212222729432419E-9],
--R    [1.49,5.7475499999999999E-2,5.7475523910801435E-2,2.3910801436044515E-8],
--R    [1.5,5.6739499999999998E-2,5.6739490170354172E-2,- 9.8296458264646169E-9],
--R    [1.51,5.6013500000000001E-2,5.6013458594752839E-2,- 4.140524716145233E-8],
--R    [1.52,5.5297300000000001E-2,5.52972816582777E-2,- 1.8341722300696528E-8],
--R    [1.53,5.4590800000000002E-2,5.4590814267229414E-2,1.4267229411779603E-8],
--R    [1.54,5.3893900000000002E-2,5.3893913713619013E-2,1.3713619011201938E-8],
--R    [1.55,5.3206400000000001E-2,5.3206439629901937E-2,3.9629901936455436E-8],
--R
--R     [1.5600000000000001, 5.25283E-2, 5.2528253944736245E-2,
--R      - 4.6055263755451215E-8]
--R     ,
--R
--R     [1.5700000000000001, 5.1859200000000001E-2, 5.1859220839728763E-2,
--R      2.083972876210094E-8]
--R     ,
--R    [1.5800000000000001,5.11992E-2,5.1199206707146921E-2,6.7071469211921197E-9],
--R
--R     [1.5900000000000001, 5.0548099999999999E-2, 5.0548080108570391E-2,
--R      - 1.9891429607621358E-8]
--R     ,
--R
--R     [1.6000000000000001, 4.9905699999999997E-2, 4.9905711734454218E-2,
--R      1.1734454220813095E-8]
--R     ,
--R
--R     [1.6100000000000001, 4.9272000000000003E-2, 4.9271974364586212E-2,
--R      - 2.5635413791746942E-8]
--R     ,
--R
--R     [1.6200000000000001, 4.8646700000000001E-2, 4.8646742829405641E-2,
--R      4.2829405640099072E-8]
--R     ,
--R
--R     [1.6299999999999999, 4.80299E-2, 4.8029893972168107E-2,
--R      - 6.0278318933515429E-9]
--R     ,
--R    [1.6399999999999999,4.74213E-2,4.7421306611931634E-2,6.6119316341484158E-9],
--R
--R     [1.6499999999999999, 4.6820899999999999E-2, 4.6820861507343305E-2,
--R      - 3.8492656694033567E-8]
--R     ,
--R
--R     [1.6599999999999999, 4.6228400000000003E-2, 4.622844132120392E-2,
--R      4.1321203916866445E-8]
--R     ,
--R
--R     [1.6699999999999999, 4.5643900000000001E-2, 4.5643930585794489E-2,
--R      3.0585794487392182E-8]
--R     ,
--R
--R     [1.6799999999999999, 4.5067200000000002E-2, 4.5067215668940779E-2,
--R      1.5668940776814022E-8]
--R     ,
--R
--R     [1.6899999999999999, 4.4498200000000002E-2, 4.4498184740800251E-2,
--R      - 1.5259199750983221E-8]
--R     ,
--R    [1.7,4.3936700000000002E-2,4.3936727741353321E-2,2.7741353318677664E-8],
--R    [1.71,4.3382700000000003E-2,4.3382736348575771E-2,3.6348575767342073E-8],
--R    [1.72,4.2836100000000002E-2,4.283610394728473E-2,3.9472847282451262E-9],
--R    [1.73,4.22967E-2,4.229672559863315E-2,2.559863315071409E-8],
--R    [1.74,4.1764500000000003E-2,4.1764498010238606E-2,- 1.9897613973141048E-9],
--R    [1.75,4.12393E-2,4.1239319506936156E-2,1.9506936156654664E-8],
--R    [1.76,4.0721100000000003E-2,4.0721090002130152E-2,- 9.9978698514524567E-9],
--R    [1.77,4.0209700000000001E-2,4.0209710969742136E-2,1.0969742135491511E-8],
--R    [1.78,3.97051E-2,3.9705085416725308E-2,- 1.4583274692003823E-8],
--R    [1.79,3.9207100000000002E-2,3.920711785615049E-2,1.7856150488770872E-8],
--R    [1.8,3.8715699999999999E-2,3.8715714280832765E-2,1.4280832766333518E-8],
--R
--R     [1.8100000000000001, 3.8230800000000002E-2, 3.8230782137495319E-2,
--R      - 1.7862504683718861E-8]
--R     ,
--R    [1.8200000000000001,3.77522E-2,3.7752230301454859E-2,3.0301454859160692E-8],
--R
--R     [1.8300000000000001, 3.7280000000000001E-2, 3.7279969051817741E-2,
--R      - 3.0948182259959989E-8]
--R     ,
--R
--R     [1.8400000000000001, 3.6813899999999997E-2, 3.6813910047171126E-2,
--R      1.0047171129790033E-8]
--R     ,
--R
--R     [1.8500000000000001, 3.6353999999999997E-2, 3.6353966301762304E-2,
--R      - 3.3698237693335908E-8]
--R     ,
--R
--R     [1.8600000000000001, 3.5900099999999997E-2, 3.5900052162149899E-2,
--R      - 4.7837850097876E-8]
--R     ,
--R
--R     [1.8700000000000001, 3.54521E-2, 3.5452083284321229E-2,
--R      - 1.6715678771705988E-8]
--R     ,
--R
--R     [1.8799999999999999, 3.5009999999999999E-2, 3.5009976611261075E-2,
--R      - 2.3388738924767782E-8]
--R     ,
--R
--R     [1.8899999999999999, 3.4573699999999999E-2, 3.4573650350956942E-2,
--R      - 4.9649043057375941E-8]
--R     ,
--R    [1.8999999999999999,3.4143E-2,3.414302395484918E-2,2.3954849180662929E-8],
--R
--R     [1.9099999999999999, 3.3717999999999998E-2, 3.3718018096686453E-2,
--R      1.8096686454915911E-8]
--R     ,
--R
--R     [1.9199999999999999, 3.3298599999999998E-2, 3.3298554651807068E-2,
--R      - 4.5348192929950404E-8]
--R     ,
--R
--R     [1.9299999999999999, 3.28846E-2, 3.2884556676814732E-2,
--R      - 4.3323185268395736E-8]
--R     ,
--R
--R     [1.9399999999999999, 3.2475900000000002E-2, 3.2475948389653855E-2,
--R      4.8389653853342374E-8]
--R     ,
--R    [1.95,3.2072700000000003E-2,3.2072655150063287E-2,- 4.4849936715884997E-8],
--R    [1.96,3.1674599999999997E-2,3.167460344041137E-2,3.4404113724573193E-9],
--R    [1.97,3.1281700000000003E-2,3.1281720846895129E-2,2.0846895126824805E-8],
--R    [1.98,3.0893899999999998E-2,3.0893936041105241E-2,3.6041105242606841E-8],
--R    [1.99,3.0511199999999999E-2,3.0511178761929561E-2,- 2.1238070437717971E-8],
--R    [2.,3.0133400000000001E-2,3.0133379797815663E-2,- 2.0202184338596885E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 4

--S 5 of 7
[[0.01,0.3283824,En(4,0.01),En(4,0.01)-0.3283824],_
[0.02,0.3235264,En(4,0.02),En(4,0.02)-0.3235264],_
[0.03,0.3187619,En(4,0.03),En(4,0.03)-0.3187619],_
[0.04,0.3140855,En(4,0.04),En(4,0.04)-0.3140855],_
[0.05,0.3094945,En(4,0.05),En(4,0.05)-0.3094945],_
[0.06,0.3049863,En(4,0.06),En(4,0.06)-0.3049863],_
[0.07,0.3005585,En(4,0.07),En(4,0.07)-0.3005585],_
[0.08,0.2962089,En(4,0.08),En(4,0.08)-0.2962089],_
[0.09,0.2919354,En(4,0.09),En(4,0.09)-0.2919354],_
[0.10,0.2877361,En(4,0.10),En(4,0.10)-0.2877361],_
[0.11,0.2836090,En(4,0.11),En(4,0.11)-0.2836090],_
[0.12,0.2795524,En(4,0.12),En(4,0.12)-0.2795524],_
[0.13,0.2755646,En(4,0.13),En(4,0.13)-0.2755646],_
[0.14,0.2716439,En(4,0.14),En(4,0.14)-0.2716439],_
[0.15,0.2677889,En(4,0.15),En(4,0.15)-0.2677889],_
[0.16,0.2639979,En(4,0.16),En(4,0.16)-0.2639979],_
[0.17,0.2602696,En(4,0.17),En(4,0.17)-0.2602696],_
[0.18,0.2566026,En(4,0.18),En(4,0.18)-0.2566026],_
[0.19,0.2529956,En(4,0.19),En(4,0.19)-0.2529956],_
[0.20,0.2494472,En(4,0.20),En(4,0.20)-0.2494472],_
[0.21,0.2459563,En(4,0.21),En(4,0.21)-0.2459563],_
[0.22,0.2425216,En(4,0.22),En(4,0.22)-0.2425216],_
[0.23,0.2391419,En(4,0.23),En(4,0.23)-0.2391419],_
[0.24,0.2358162,En(4,0.24),En(4,0.24)-0.2358162],_
[0.25,0.2325432,En(4,0.25),En(4,0.25)-0.2325432],_
[0.26,0.2293221,En(4,0.26),En(4,0.26)-0.2293221],_
[0.27,0.2261517,En(4,0.27),En(4,0.27)-0.2261517],_
[0.28,0.2230311,En(4,0.28),En(4,0.28)-0.2230311],_
[0.29,0.2199593,En(4,0.29),En(4,0.29)-0.2199593],_
[0.30,0.2169352,En(4,0.30),En(4,0.30)-0.2169352],_
[0.31,0.2139581,En(4,0.31),En(4,0.31)-0.2139581],_
[0.32,0.2110270,En(4,0.32),En(4,0.32)-0.2110270],_
[0.33,0.2081411,En(4,0.33),En(4,0.33)-0.2081411],_
[0.34,0.2052994,En(4,0.34),En(4,0.34)-0.2052994],_
[0.35,0.2025013,En(4,0.35),En(4,0.35)-0.2025013],_
[0.36,0.1997458,En(4,0.36),En(4,0.36)-0.1997458],_
[0.37,0.1970322,En(4,0.37),En(4,0.37)-0.1970322],_
[0.38,0.1943597,En(4,0.38),En(4,0.38)-0.1943597],_
[0.39,0.1917276,En(4,0.39),En(4,0.39)-0.1917276],_
[0.40,0.1891352,En(4,0.40),En(4,0.40)-0.1891352],_
[0.41,0.1865816,En(4,0.41),En(4,0.41)-0.1865816],_
[0.42,0.1840664,En(4,0.42),En(4,0.42)-0.1840664],_
[0.43,0.1815887,En(4,0.43),En(4,0.43)-0.1815887],_
[0.44,0.1791479,En(4,0.44),En(4,0.44)-0.1791479],_
[0.45,0.1767433,En(4,0.45),En(4,0.45)-0.1767433],_
[0.46,0.1743744,En(4,0.46),En(4,0.46)-0.1743744],_
[0.47,0.1720405,En(4,0.47),En(4,0.47)-0.1720405],_
[0.48,0.1697410,En(4,0.48),En(4,0.48)-0.1697410],_
[0.49,0.1674753,En(4,0.49),En(4,0.49)-0.1674753],_
[0.50,0.1652428,En(4,0.50),En(4,0.50)-0.1652428],_
[0.51,0.1630430,En(4,0.51),En(4,0.51)-0.1630430],_
[0.52,0.1608753,En(4,0.52),En(4,0.52)-0.1608753],_
[0.53,0.1587392,En(4,0.53),En(4,0.53)-0.1587392],_
[0.54,0.1566341,En(4,0.54),En(4,0.54)-0.1566341],_
[0.55,0.1545596,En(4,0.55),En(4,0.55)-0.1545596],_
[0.56,0.1525150,En(4,0.56),En(4,0.56)-0.1525150],_
[0.57,0.1505000,En(4,0.57),En(4,0.57)-0.1505000],_
[0.58,0.1485139,En(4,0.58),En(4,0.58)-0.1485139],_
[0.59,0.1465565,En(4,0.59),En(4,0.59)-0.1465565],_
[0.60,0.1446271,En(4,0.60),En(4,0.60)-0.1446271],_
[0.61,0.1427253,En(4,0.61),En(4,0.61)-0.1427253],_
[0.62,0.1408507,En(4,0.62),En(4,0.62)-0.1408507],_
[0.63,0.1390028,En(4,0.63),En(4,0.63)-0.1390028],_
[0.64,0.1371813,En(4,0.64),En(4,0.64)-0.1371813],_
[0.65,0.1353855,En(4,0.65),En(4,0.65)-0.1353855],_
[0.66,0.1336153,En(4,0.66),En(4,0.66)-0.1336153],_
[0.67,0.1318701,En(4,0.67),En(4,0.67)-0.1318701],_
[0.68,0.1301495,En(4,0.68),En(4,0.68)-0.1301495],_
[0.69,0.1284533,En(4,0.69),En(4,0.69)-0.1284533],_
[0.70,0.1267808,En(4,0.70),En(4,0.70)-0.1267808],_
[0.71,0.1251319,En(4,0.71),En(4,0.71)-0.1251319],_
[0.72,0.1235061,En(4,0.72),En(4,0.72)-0.1235061],_
[0.73,0.1219031,En(4,0.73),En(4,0.73)-0.1219031],_
[0.74,0.1203224,En(4,0.74),En(4,0.74)-0.1203224],_
[0.75,0.1187638,En(4,0.75),En(4,0.75)-0.1187638],_
[0.76,0.1172270,En(4,0.76),En(4,0.76)-0.1172270],_
[0.77,0.1157115,En(4,0.77),En(4,0.77)-0.1157115],_
[0.78,0.1142170,En(4,0.78),En(4,0.78)-0.1142170],_
[0.79,0.1127433,En(4,0.79),En(4,0.79)-0.1127433],_
[0.80,0.1112900,En(4,0.80),En(4,0.80)-0.1112900],_
[0.81,0.1098567,En(4,0.81),En(4,0.81)-0.1098567],_
[0.82,0.1084433,En(4,0.82),En(4,0.82)-0.1084433],_
[0.83,0.1070493,En(4,0.83),En(4,0.83)-0.1070493],_
[0.84,0.1056744,En(4,0.84),En(4,0.84)-0.1056744],_
[0.85,0.1043185,En(4,0.85),En(4,0.85)-0.1043185],_
[0.86,0.1029812,En(4,0.86),En(4,0.86)-0.1029812],_
[0.87,0.1016622,En(4,0.87),En(4,0.87)-0.1016622],_
[0.88,0.1003612,En(4,0.88),En(4,0.88)-0.1003612],_
[0.89,0.0990780,En(4,0.89),En(4,0.89)-0.0990780],_
[0.90,0.0978123,En(4,0.90),En(4,0.90)-0.0978123],_
[0.91,0.0965639,En(4,0.91),En(4,0.91)-0.0965639],_
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[0.93,0.0941177,En(4,0.93),En(4,0.93)-0.0941177],_
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[0.99,0.0871669,En(4,0.99),En(4,0.99)-0.0871669],_
[1.00,0.0860625,En(4,1.00),En(4,1.00)-0.0860625],_
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[1.06,0.0797406,En(4,1.06),En(4,1.06)-0.0797406],_
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[1.42,0.0507889,En(4,1.42),En(4,1.42)-0.0507889],_
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[1.44,0.0495466,En(4,1.44),En(4,1.44)-0.0495466],_
[1.45,0.0489374,En(4,1.45),En(4,1.45)-0.0489374],_
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[1.48,0.0471565,En(4,1.48),En(4,1.48)-0.0471565],_
[1.49,0.0465780,En(4,1.49),En(4,1.49)-0.0465780],_
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[2.00,0.0250228,En(4,2.00),En(4,2.00)-0.0250228]]
 

   (5)
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     [0.91999999999999993, 9.5332399999999998E-2, 9.5332403718406122E-2,
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     [1.1299999999999999, 7.2981199999999996E-2, 7.2981153447435998E-2,
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     ,

     [1.1399999999999999, 7.2066099999999994E-2, 7.2066117149520437E-2,
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     ,

     [1.1499999999999999, 7.1163199999999996E-2, 7.1163188837328195E-2,
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     ,

     [1.1599999999999999, 7.0272200000000007E-2, 7.027219556585651E-2,
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     ,

     [1.1699999999999999, 6.9392999999999996E-2, 6.9392967143661166E-2,
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     ,

     [1.1799999999999999, 6.8525299999999997E-2, 6.8525336081954685E-2,
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     ,

     [1.1899999999999999, 6.7669099999999996E-2, 6.7669137544842786E-2,
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    [1.24,6.3553999999999999E-2,6.3554043133005805E-2,4.3133005805939817E-8],
    [1.25,6.2763099999999988E-2,6.276312075408684E-2,2.0754086851870746E-8],

     [1.2599999999999998, 6.1982499999999996E-2, 6.1982547374293831E-2,
      4.7374293835056314E-8]
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    [1.27,6.1212199999999994E-2,6.1212177716032747E-2,- 2.2283967247849201E-8],

     [1.2799999999999998, 6.0451900000000003E-2, 6.0451868753076489E-2,
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     [1.2999999999999998, 5.8960899999999997E-2, 5.8960871826125541E-2,
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     ,

     [1.3100000000000001, 5.8229900000000001E-2, 5.822990871112519E-2,
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     [1.3199999999999998, 5.7508499999999997E-2, 5.75084559136433E-2,
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     ,

     [1.3300000000000001, 5.6796399999999997E-2, 5.6796381081534952E-2,
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     ,

     [1.3399999999999999, 5.6093599999999993E-2, 5.6093553886531186E-2,
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     ,

     [1.3500000000000001, 5.5399799999999999E-2, 5.5399845989034427E-2,
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     ,

     [1.3599999999999999, 5.4715100000000003E-2, 5.4715131003636515E-2,
      3.1003636512261235E-8]
     ,

     [1.3700000000000001, 5.4039299999999998E-2, 5.4039284465342098E-2,
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     ,

     [1.3799999999999999, 5.3372199999999995E-2, 5.3372183796479428E-2,
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     ,

     [1.3899999999999999, 5.2713700000000002E-2, 5.2713708274280693E-2,
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     ,

     [1.3999999999999999, 5.2063699999999997E-2, 5.206373899911769E-2,
      3.8999117692173346E-8]
     ,

     [1.4099999999999999, 5.1422200000000001E-2, 5.1422158863374437E-2,
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     ,

     [1.4199999999999999, 5.0788899999999998E-2, 5.0788852520943208E-2,
      - 4.7479056790311613E-8]
     ,

     [1.4299999999999999, 5.0163699999999999E-2, 5.0163706357327698E-2,
      6.357327698991444E-9]
     ,

     [1.4399999999999999, 4.9546599999999996E-2, 4.9546608460339432E-2,
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     ,
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    [1.46,4.83361E-2,4.8336118157247379E-2,1.8157247379246844E-8],
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    [1.48,4.7156499999999997E-2,4.7156519282801138E-2,1.9282801140552142E-8],
    [1.49,4.6577999999999994E-2,4.6578041637448199E-2,4.1637448204567828E-8],
    [1.5,4.6006999999999999E-2,4.6006974964299396E-2,- 2.50357006029156E-8],

     [1.5099999999999998, 4.5443200000000003E-2, 4.5443218493767069E-2,
      1.8493767066363187E-8]
     ,
    [1.52,4.4886700000000002E-2,4.4886672943877548E-2,- 2.7056122453572584E-8],

     [1.5299999999999998, 4.4337199999999993E-2, 4.4337240495715177E-2,
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     ,
    [1.54,4.3794799999999995E-2,4.3794824769334752E-2,2.4769334756868933E-8],

     [1.5499999999999998, 4.3259300000000001E-2, 4.3259330800131612E-2,
      3.0800131611830039E-8]
     ,

     [1.5600000000000001, 4.2730699999999996E-2, 4.2730665015658587E-2,
      - 3.498434140991602E-8]
     ,

     [1.5699999999999998, 4.2208700000000002E-2, 4.2208735212882001E-2,
      3.5212881999147072E-8]
     ,

     [1.5800000000000001, 4.1693499999999994E-2, 4.169345053586361E-2,
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     ,

     [1.5899999999999999, 4.1184699999999998E-2, 4.1184721453862087E-2,
      2.1453862089626519E-8]
     ,

     [1.6000000000000001, 4.0682499999999996E-2, 4.0682459739842872E-2,
      - 4.0260157124771823E-8]
     ,

     [1.6099999999999999, 4.0186600000000003E-2, 4.0186578449386799E-2,
      - 2.1550613203691338E-8]
     ,

     [1.6200000000000001, 3.9696999999999996E-2, 3.9696991899992498E-2,
      - 8.1000074980686065E-9]
     ,

     [1.6299999999999999, 3.9213600000000001E-2, 3.9213615650758454E-2,
      1.5650758453111813E-8]
     ,

     [1.6399999999999999, 3.8736399999999997E-2, 3.8736366482441185E-2,
      - 3.3517558811757553E-8]
     ,

     [1.6499999999999999, 3.8265199999999999E-2, 3.8265162377879226E-2,
      - 3.7622120772906609E-8]
     ,

     [1.6599999999999999, 3.7799899999999997E-2, 3.7799922502774017E-2,
      2.2502774019161897E-8]
     ,

     [1.6699999999999999, 3.7340600000000002E-2, 3.7340567186823333E-2,
      - 3.2813176668866628E-8]
     ,

     [1.6799999999999999, 3.6887000000000003E-2, 3.6887017905196488E-2,
      1.7905196485201724E-8]
     ,

     [1.6899999999999999, 3.6439199999999998E-2, 3.6439197260345432E-2,
      - 2.7396545657087934E-9]
     ,
    [1.7,3.5997000000000001E-2,3.5997028964144487E-2,2.8964144485610355E-8],
    [1.71,3.5560399999999999E-2,3.5560437820352321E-2,3.7820352322137651E-8],
    [1.72,3.5129300000000002E-2,3.5129349707387826E-2,4.9707387823894056E-8],
    [1.73,3.4703699999999997E-2,3.4703691561414153E-2,- 8.4385858439839367E-9],
    [1.74,3.4283399999999999E-2,3.4283391359727231E-2,- 8.6402727680900959E-9],
    [1.75,3.38684E-2,3.3868378104435416E-2,- 2.1895564583651606E-8],

     [1.7599999999999998, 3.3458599999999998E-2, 3.3458581806433546E-2,
      - 1.8193566451996102E-8]
     ,
    [1.77,3.3053899999999997E-2,3.3053933469655072E-2,3.346965507522448E-8],
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     ,
    [1.79,3.2259799999999998E-2,3.2259809568176888E-2,9.5681768896849206E-9],

     [1.7999999999999998, 3.1870200000000001E-2, 3.1870200838695982E-2,
      8.3869598072050522E-10]
     ,
    [1.8100000000000001,3.14855E-2,3.1485473711279174E-2,- 2.628872082521827E-8]
     ,

     [1.8199999999999998, 3.1105599999999997E-2, 3.1105563928410893E-2,
      - 3.6071589104569313E-8]
     ,

     [1.8300000000000001, 3.0730399999999998E-2, 3.0730408136781864E-2,
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     ,

     [1.8399999999999999, 3.0359899999999999E-2, 3.0359943873374942E-2,
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     ,

     [1.8500000000000001, 2.9994099999999999E-2, 2.9994109551789112E-2,
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     ,

     [1.8599999999999999, 2.9632800000000001E-2, 2.9632844448799284E-2,
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     ,

     [1.8700000000000001, 2.9276099999999999E-2, 2.9276088691150233E-2,
      - 1.1308849766356044E-8]
     ,

     [1.8799999999999999, 2.89238E-2, 2.8923783242571027E-2,
      - 1.6757428972224986E-8]
     ,

     [1.8899999999999999, 2.8575900000000001E-2, 2.8575869891020254E-2,
      - 3.0108979746923392E-8]
     ,

     [1.8999999999999999, 2.8232299999999998E-2, 2.8232291236140281E-2,
      - 8.763859717791922E-9]
     ,

     [1.9099999999999999, 2.7893000000000001E-2, 2.7892990676930185E-2,
      - 9.3230698161583803E-9]
     ,
    [1.9199999999999999,2.75579E-2,2.7557912399626863E-2,1.2399626863474067E-8],

     [1.9299999999999999, 2.7227000000000001E-2, 2.7227001365790166E-2,
      1.3657901649921644E-9]
     ,

     [1.9399999999999999, 2.6900199999999999E-2, 2.6900203300591216E-2,
      3.3005912170036567E-9]
     ,
    [1.95,2.6577499999999997E-2,2.6577464681296452E-2,- 3.5318703545117458E-8],
    [1.96,2.6258699999999999E-2,2.6258732725946241E-2,3.2725946241124459E-8],
    [1.97,2.5943999999999998E-2,2.5943955382221946E-2,- 4.4617778052064017E-8],
    [1.98,2.5633099999999999E-2,2.56330813165009E-2,- 1.8683499098531842E-8],
    [1.99,2.5326099999999997E-2,2.5326059903094382E-2,- 4.0096905615238931E-8],
    [2.,2.5022799999999998E-2,2.5022841213660458E-2,4.1213660460087675E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (5)
--R   [[1.0E-2,0.32838240000000002,0.32838235603577381,- 4.3964226204007417E-8],
--R    [2.0E-2,0.32352639999999999,0.32352643582573859,3.5825738597949908E-8],
--R
--R     [2.9999999999999999E-2, 0.31876189999999999, 0.318761867644201,
--R      - 3.2355798984529116E-8]
--R     ,
--R
--R     [4.0000000000000001E-2, 0.31408550000000002, 0.3140854938275166,
--R      - 6.1724834132803608E-9]
--R     ,
--R
--R     [5.0000000000000003E-2, 0.30949450000000001, 0.30949449400443008,
--R      - 5.9955699294178544E-9]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.30498629999999999, 0.30498629353000445,
--R      - 6.4699955393265896E-9]
--R     ,
--R
--R     [7.0000000000000007E-2, 0.30055850000000001, 0.30055851077336515,
--R      1.0773365144434166E-8]
--R     ,
--R    [8.0000000000000002E-2,0.2962089,0.29620892264764853,2.2647648534324105E-8],
--R
--R     [8.9999999999999997E-2, 0.29193540000000001, 0.29193544025523149,
--R      4.0255231481545195E-8]
--R     ,
--R
--R     [0.10000000000000001, 0.28773609999999999, 0.28773609074837719,
--R      - 9.2516228011874091E-9]
--R     ,
--R    [0.11,0.283609,0.2836090032896208,3.2896207979860037E-9],
--R    [0.12,0.27955239999999998,0.27955239786156211,- 2.1384378712241414E-9],
--R    [0.13,0.27556459999999999,0.27556457613853869,- 2.3861461306839971E-8],
--R
--R     [0.14000000000000001, 0.27164389999999999, 0.27164391389899217,
--R      1.3898992179406378E-8]
--R     ,
--R    [0.14999999999999999,0.2677889,0.26778885461965246,- 4.5380347535317611E-8],
--R    [0.16,0.26399790000000001,0.26399790399625528,3.9962552711436672E-9],
--R
--R     [0.17000000000000001, 0.26026959999999999, 0.26026962520418123,
--R      2.5204181242077794E-8]
--R     ,
--R
--R     [0.17999999999999999, 0.25660260000000001, 0.25660263475941625,
--R      3.4759416234209084E-8]
--R     ,
--R    [0.19,0.25299559999999999,0.25299559887329914,- 1.1267008437343407E-9],
--R
--R     [0.20000000000000001, 0.24944720000000001, 0.24944723021833587,
--R      3.021833586136502E-8]
--R     ,
--R
--R     [0.20999999999999999, 0.24595629999999999, 0.24595628503986891,
--R      - 1.496013107837868E-8]
--R     ,
--R    [0.22,0.2425216,0.24252156056149116,- 3.9438508847577936E-8],
--R
--R     [0.23000000000000001, 0.23914189999999999, 0.23914189264206476,
--R      - 7.3579352333208448E-9]
--R     ,
--R    [0.23999999999999999,0.2358162,0.235816153649895,- 4.6350105004089315E-8],
--R    [0.25,0.23254320000000001,0.232543250525623,5.0525622991015595E-8],
--R    [0.26000000000000001,0.2293221,0.22932212301015453,2.3010154531766247E-8],
--R
--R     [0.27000000000000002, 0.22615170000000001, 0.22615174201774482,
--R      4.2017744811273516E-8]
--R     ,
--R
--R     [0.28000000000000003, 0.22303110000000001, 0.22303110813742405,
--R      8.1374240401554943E-9]
--R     ,
--R    [0.28999999999999998,0.2199593,0.21995925024844767,- 4.9751552322341297E-8],
--R
--R     [0.29999999999999999, 0.21693519999999999, 0.2169352242375045,
--R      2.4237504503421547E-8]
--R     ,
--R    [0.31,0.21395810000000001,0.21395811180711269,1.1807112676454068E-8],
--R
--R     [0.32000000000000001, 0.21102699999999999, 0.21102701936604468,
--R      1.9366044684554495E-8]
--R     ,
--R    [0.33000000000000002,0.2081411,0.20814107699380749,- 2.3006192506613843E-8],
--R
--R     [0.34000000000000002, 0.20529939999999999, 0.20529943747220336,
--R      3.7472203368027479E-8]
--R     ,
--R    [0.34999999999999998,0.2025013,0.20250127537784185,- 2.4622158145692907E-8],
--R    [0.35999999999999999,0.1997458,0.19974578623019815,- 1.3769801854301988E-8],
--R    [0.37,0.19703219999999999,0.19703218569043029,- 1.4309569695836188E-8],
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--R     [1.8799999999999999, 2.89238E-2, 2.8923783242571027E-2,
--R      - 1.6757428972224986E-8]
--R     ,
--R
--R     [1.8899999999999999, 2.8575900000000001E-2, 2.8575869891020747E-2,
--R      - 3.0108979254261925E-8]
--R     ,
--R
--R     [1.8999999999999999, 2.8232299999999998E-2, 2.8232291236140537E-2,
--R      - 8.7638594610528475E-9]
--R     ,
--R
--R     [1.9099999999999999, 2.7893000000000001E-2, 2.7892990676930449E-2,
--R      - 9.3230695524804119E-9]
--R     ,
--R    [1.9199999999999999,2.75579E-2,2.7557912399626863E-2,1.2399626863474067E-8],
--R
--R     [1.9299999999999999, 2.7227000000000001E-2, 2.7227001365790433E-2,
--R      1.3657904321395797E-9]
--R     ,
--R
--R     [1.9399999999999999, 2.6900199999999999E-2, 2.6900203300591483E-2,
--R      3.300591484151072E-9]
--R     ,
--R    [1.95,2.65775E-2,2.6577464681296726E-2,- 3.5318703274500596E-8],
--R    [1.96,2.6258699999999999E-2,2.6258732725946241E-2,3.2725946241124459E-8],
--R    [1.97,2.5943999999999998E-2,2.5943955382222512E-2,- 4.4617777486544163E-8],
--R    [1.98,2.5633099999999999E-2,2.5633081316501483E-2,- 1.8683498515664754E-8],
--R    [1.99,2.5326100000000001E-2,2.5326059903094673E-2,- 4.0096905327274834E-8],
--R    [2.,2.5022800000000001E-2,2.5022841213660458E-2,4.1213660456618229E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 5

--S 6 of 7
[[0.01,0.1098682,En(10,0.01),En(10,0.01)-0.1098682],_
[0.02,0.1086395,En(10,0.02),En(10,0.02)-0.1086395],_
[0.03,0.1074246,En(10,0.03),En(10,0.03)-0.1074246],_
[0.04,0.1062236,En(10,0.04),En(10,0.04)-0.1062236],_
[0.05,0.1050363,En(10,0.05),En(10,0.05)-0.1050363],_
[0.06,0.1038624,En(10,0.06),En(10,0.06)-0.1038624],_
[0.07,0.1027018,En(10,0.07),En(10,0.07)-0.1027018],_
[0.08,0.1015544,En(10,0.08),En(10,0.08)-0.1015544],_
[0.09,0.1004200,En(10,0.09),En(10,0.09)-0.1004200],_
[0.10,0.0992984,En(10,0.10),En(10,0.10)-0.0992984],_
[0.11,0.0981896,En(10,0.11),En(10,0.11)-0.0981896],_
[0.12,0.0970934,En(10,0.12),En(10,0.12)-0.0970934],_
[0.13,0.0960095,En(10,0.13),En(10,0.13)-0.0960095],_
[0.14,0.0949380,En(10,0.14),En(10,0.14)-0.0949380],_
[0.15,0.0938786,En(10,0.15),En(10,0.15)-0.0938786],_
[0.16,0.0928312,En(10,0.16),En(10,0.16)-0.0928312],_
[0.17,0.0917956,En(10,0.17),En(10,0.17)-0.0917956],_
[0.18,0.0907718,En(10,0.18),En(10,0.18)-0.0907718],_
[0.19,0.0897595,En(10,0.19),En(10,0.19)-0.0897595],_
[0.20,0.0887587,En(10,0.20),En(10,0.20)-0.0887587],_
[0.21,0.0877693,En(10,0.21),En(10,0.21)-0.0877693],_
[0.22,0.0867910,En(10,0.22),En(10,0.22)-0.0867910],_
[0.23,0.0858238,En(10,0.23),En(10,0.23)-0.0858238],_
[0.24,0.0848675,En(10,0.24),En(10,0.24)-0.0848675],_
[0.25,0.0839220,En(10,0.25),En(10,0.25)-0.0839220],_
[0.26,0.0829872,En(10,0.26),En(10,0.26)-0.0829872],_
[0.27,0.0820630,En(10,0.27),En(10,0.27)-0.0820630],_
[0.28,0.0811492,En(10,0.28),En(10,0.28)-0.0811492],_
[0.29,0.0802457,En(10,0.29),En(10,0.29)-0.0802457],_
[0.30,0.0793524,En(10,0.30),En(10,0.30)-0.0793524],_
[0.31,0.0784693,En(10,0.31),En(10,0.31)-0.0784693],_
[0.32,0.0775960,En(10,0.32),En(10,0.32)-0.0775960],_
[0.33,0.0767327,En(10,0.33),En(10,0.33)-0.0767327],_
[0.34,0.0758790,En(10,0.34),En(10,0.34)-0.0758790],_
[0.35,0.0750350,En(10,0.35),En(10,0.35)-0.0750350],_
[0.36,0.0742006,En(10,0.36),En(10,0.36)-0.0742006],_
[0.37,0.0733755,En(10,0.37),En(10,0.37)-0.0733755],_
[0.38,0.0725597,En(10,0.38),En(10,0.38)-0.0725597],_
[0.39,0.0717531,En(10,0.39),En(10,0.39)-0.0717531],_
[0.40,0.0709557,En(10,0.40),En(10,0.40)-0.0709557],_
[0.41,0.0701671,En(10,0.41),En(10,0.41)-0.0701671],_
[0.42,0.0693875,En(10,0.42),En(10,0.42)-0.0693875],_
[0.43,0.0686167,En(10,0.43),En(10,0.43)-0.0686167],_
[0.44,0.0678545,En(10,0.44),En(10,0.44)-0.0678545],_
[0.45,0.0671009,En(10,0.45),En(10,0.45)-0.0671009],_
[0.46,0.0663558,En(10,0.46),En(10,0.46)-0.0663558],_
[0.47,0.0656191,En(10,0.47),En(10,0.47)-0.0656191],_
[0.48,0.0648907,En(10,0.48),En(10,0.48)-0.0648907],_
[0.49,0.0641704,En(10,0.49),En(10,0.49)-0.0641704],_
[0.50,0.0634583,En(10,0.50),En(10,0.50)-0.0634583],_
[0.51,0.0627542,En(10,0.51),En(10,0.51)-0.0627542],_
[0.52,0.0620580,En(10,0.52),En(10,0.52)-0.0620580],_
[0.53,0.0613696,En(10,0.53),En(10,0.53)-0.0613696],_
[0.54,0.0606889,En(10,0.54),En(10,0.54)-0.0606889],_
[0.55,0.0600159,En(10,0.55),En(10,0.55)-0.0600159],_
[0.56,0.0593505,En(10,0.56),En(10,0.56)-0.0593505],_
[0.57,0.0586925,En(10,0.57),En(10,0.57)-0.0586925],_
[0.58,0.0580419,En(10,0.58),En(10,0.58)-0.0580419],_
[0.59,0.0573986,En(10,0.59),En(10,0.59)-0.0573986],_
[0.60,0.0567626,En(10,0.60),En(10,0.60)-0.0567626],_
[0.61,0.0561336,En(10,0.61),En(10,0.61)-0.0561336],_
[0.62,0.0555118,En(10,0.62),En(10,0.62)-0.0555118],_
[0.63,0.0548969,En(10,0.63),En(10,0.63)-0.0548969],_
[0.64,0.0542889,En(10,0.64),En(10,0.64)-0.0542889],_
[0.65,0.0536877,En(10,0.65),En(10,0.65)-0.0536877],_
[0.66,0.0530933,En(10,0.66),En(10,0.66)-0.0530933],_
[0.67,0.0525055,En(10,0.67),En(10,0.67)-0.0525055],_
[0.68,0.0519243,En(10,0.68),En(10,0.68)-0.0519243],_
[0.69,0.0513497,En(10,0.69),En(10,0.69)-0.0513497],_
[0.70,0.0507815,En(10,0.70),En(10,0.70)-0.0507815],_
[0.71,0.0502196,En(10,0.71),En(10,0.71)-0.0502196],_
[0.72,0.0496640,En(10,0.72),En(10,0.72)-0.0496640],_
[0.73,0.0491147,En(10,0.73),En(10,0.73)-0.0491147],_
[0.74,0.0485715,En(10,0.74),En(10,0.74)-0.0485715],_
[0.75,0.0480344,En(10,0.75),En(10,0.75)-0.0480344],_
[0.76,0.0475033,En(10,0.76),En(10,0.76)-0.0475033],_
[0.77,0.0469781,En(10,0.77),En(10,0.77)-0.0469781],_
[0.78,0.0464588,En(10,0.78),En(10,0.78)-0.0464588],_
[0.79,0.0459453,En(10,0.79),En(10,0.79)-0.0459453],_
[0.80,0.0454376,En(10,0.80),En(10,0.80)-0.0454376],_
[0.81,0.0449356,En(10,0.81),En(10,0.81)-0.0449356],_
[0.82,0.0444391,En(10,0.82),En(10,0.82)-0.0444391],_
[0.83,0.0439482,En(10,0.83),En(10,0.83)-0.0439482],_
[0.84,0.0434628,En(10,0.84),En(10,0.84)-0.0434628],_
[0.85,0.0429829,En(10,0.85),En(10,0.85)-0.0429829],_
[0.86,0.0425082,En(10,0.86),En(10,0.86)-0.0425082],_
[0.87,0.0420389,En(10,0.87),En(10,0.87)-0.0420389],_
[0.88,0.0415749,En(10,0.88),En(10,0.88)-0.0415749],_
[0.89,0.0411160,En(10,0.89),En(10,0.89)-0.0411160],_
[0.90,0.0406622,En(10,0.90),En(10,0.90)-0.0406622],_
[0.91,0.0402135,En(10,0.91),En(10,0.91)-0.0402135],_
[0.92,0.0397698,En(10,0.92),En(10,0.92)-0.0397698],_
[0.93,0.0393311,En(10,0.93),En(10,0.93)-0.0393311],_
[0.94,0.0388973,En(10,0.94),En(10,0.94)-0.0388973],_
[0.95,0.0384683,En(10,0.95),En(10,0.95)-0.0384683],_
[0.96,0.0380441,En(10,0.96),En(10,0.96)-0.0380441],_
[0.97,0.0376246,En(10,0.97),En(10,0.97)-0.0376246],_
[0.98,0.0372098,En(10,0.98),En(10,0.98)-0.0372098],_
[0.99,0.0367996,En(10,0.99),En(10,0.99)-0.0367996],_
[1.00,0.0363940,En(10,1.00),En(10,1.00)-0.0363940],_
[1.01,0.0359929,En(10,1.01),En(10,1.01)-0.0359929],_
[1.02,0.0355963,En(10,1.02),En(10,1.02)-0.0355963],_
[1.03,0.0352041,En(10,1.03),En(10,1.03)-0.0352041],_
[1.04,0.0348163,En(10,1.04),En(10,1.04)-0.0348163],_
[1.05,0.0344328,En(10,1.05),En(10,1.05)-0.0344328],_
[1.06,0.0340535,En(10,1.06),En(10,1.06)-0.0340535],_
[1.07,0.0336785,En(10,1.07),En(10,1.07)-0.0336785],_
[1.08,0.0333077,En(10,1.08),En(10,1.08)-0.0333077],_
[1.09,0.0329410,En(10,1.09),En(10,1.09)-0.0329410],_
[1.10,0.0325784,En(10,1.10),En(10,1.10)-0.0325784],_
[1.11,0.0322198,En(10,1.11),En(10,1.11)-0.0322198],_
[1.12,0.0318652,En(10,1.12),En(10,1.12)-0.0318652],_
[1.13,0.0315145,En(10,1.13),En(10,1.13)-0.0315145],_
[1.14,0.0311678,En(10,1.14),En(10,1.14)-0.0311678],_
[1.15,0.0308249,En(10,1.15),En(10,1.15)-0.0308249],_
[1.16,0.0304858,En(10,1.16),En(10,1.16)-0.0304858],_
[1.17,0.0301505,En(10,1.17),En(10,1.17)-0.0301505],_
[1.18,0.0298189,En(10,1.18),En(10,1.18)-0.0298189],_
[1.19,0.0294910,En(10,1.19),En(10,1.19)-0.0294910],_
[1.20,0.0291668,En(10,1.20),En(10,1.20)-0.0291668],_
[1.21,0.0288461,En(10,1.21),En(10,1.21)-0.0288461],_
[1.22,0.0285290,En(10,1.22),En(10,1.22)-0.0285290],_
[1.23,0.0282155,En(10,1.23),En(10,1.23)-0.0282155],_
[1.24,0.0279054,En(10,1.24),En(10,1.24)-0.0279054],_
[1.25,0.0275988,En(10,1.25),En(10,1.25)-0.0275988],_
[1.26,0.0272955,En(10,1.26),En(10,1.26)-0.0272955],_
[1.27,0.0269957,En(10,1.27),En(10,1.27)-0.0269957],_
[1.28,0.0266991,En(10,1.28),En(10,1.28)-0.0266991],_
[1.29,0.0264059,En(10,1.29),En(10,1.29)-0.0264059],_
[1.30,0.0261159,En(10,1.30),En(10,1.30)-0.0261159],_
[1.31,0.0258291,En(10,1.31),En(10,1.31)-0.0258291],_
[1.32,0.0255455,En(10,1.32),En(10,1.32)-0.0255455],_
[1.33,0.0252651,En(10,1.33),En(10,1.33)-0.0252651],_
[1.34,0.0249878,En(10,1.34),En(10,1.34)-0.0249878],_
[1.35,0.0247135,En(10,1.35),En(10,1.35)-0.0247135],_
[1.36,0.0244423,En(10,1.36),En(10,1.36)-0.0244423],_
[1.37,0.0241741,En(10,1.37),En(10,1.37)-0.0241741],_
[1.38,0.0239088,En(10,1.38),En(10,1.38)-0.0239088],_
[1.39,0.0236465,En(10,1.39),En(10,1.39)-0.0236465],_
[1.40,0.0233872,En(10,1.40),En(10,1.40)-0.0233872],_
[1.41,0.0231306,En(10,1.41),En(10,1.41)-0.0231306],_
[1.42,0.0228770,En(10,1.42),En(10,1.42)-0.0228770],_
[1.43,0.0226261,En(10,1.43),En(10,1.43)-0.0226261],_
[1.44,0.0223780,En(10,1.44),En(10,1.44)-0.0223780],_
[1.45,0.0221327,En(10,1.45),En(10,1.45)-0.0221327],_
[1.46,0.0218901,En(10,1.46),En(10,1.46)-0.0218901],_
[1.47,0.0216501,En(10,1.47),En(10,1.47)-0.0216501],_
[1.48,0.0214128,En(10,1.48),En(10,1.48)-0.0214128],_
[1.49,0.0211782,En(10,1.49),En(10,1.49)-0.0211782],_
[1.50,0.0209461,En(10,1.50),En(10,1.50)-0.0209461],_
[1.51,0.0207167,En(10,1.51),En(10,1.51)-0.0207167],_
[1.52,0.0204897,En(10,1.52),En(10,1.52)-0.0204897],_
[1.53,0.0202653,En(10,1.53),En(10,1.53)-0.0202653],_
[1.54,0.0200433,En(10,1.54),En(10,1.54)-0.0200433],_
[1.55,0.0198238,En(10,1.55),En(10,1.55)-0.0198238],_
[1.56,0.0196067,En(10,1.56),En(10,1.56)-0.0196067],_
[1.57,0.0193921,En(10,1.57),En(10,1.57)-0.0193921],_
[1.58,0.0191798,En(10,1.58),En(10,1.58)-0.0191798],_
[1.59,0.0189698,En(10,1.59),En(10,1.59)-0.0189698],_
[1.60,0.0187622,En(10,1.60),En(10,1.60)-0.0187622],_
[1.61,0.0185568,En(10,1.61),En(10,1.61)-0.0185568],_
[1.62,0.0183538,En(10,1.62),En(10,1.62)-0.0183538],_
[1.63,0.0181530,En(10,1.63),En(10,1.63)-0.0181530],_
[1.64,0.0179543,En(10,1.64),En(10,1.64)-0.0179543],_
[1.65,0.0177579,En(10,1.65),En(10,1.65)-0.0177579],_
[1.66,0.0175637,En(10,1.66),En(10,1.66)-0.0175637],_
[1.67,0.0173716,En(10,1.67),En(10,1.67)-0.0173716],_
[1.68,0.0171816,En(10,1.68),En(10,1.68)-0.0171816],_
[1.69,0.0169937,En(10,1.69),En(10,1.69)-0.0169937],_
[1.70,0.0168079,En(10,1.70),En(10,1.70)-0.0168079],_
[1.71,0.0166242,En(10,1.71),En(10,1.71)-0.0166242],_
[1.72,0.0164424,En(10,1.72),En(10,1.72)-0.0164424],_
[1.73,0.0162627,En(10,1.73),En(10,1.73)-0.0162627],_
[1.74,0.0160850,En(10,1.74),En(10,1.74)-0.0160850],_
[1.75,0.0159092,En(10,1.75),En(10,1.75)-0.0159092],_
[1.76,0.0157354,En(10,1.76),En(10,1.76)-0.0157354],_
[1.77,0.0155634,En(10,1.77),En(10,1.77)-0.0155634],_
[1.78,0.0153934,En(10,1.78),En(10,1.78)-0.0153934],_
[1.79,0.0152253,En(10,1.79),En(10,1.79)-0.0152253],_
[1.80,0.0150590,En(10,1.80),En(10,1.80)-0.0150590],_
[1.81,0.0148945,En(10,1.81),En(10,1.81)-0.0148945],_
[1.82,0.0147318,En(10,1.82),En(10,1.82)-0.0147318],_
[1.83,0.0145710,En(10,1.83),En(10,1.83)-0.0145710],_
[1.84,0.0144119,En(10,1.84),En(10,1.84)-0.0144119],_
[1.85,0.0142546,En(10,1.85),En(10,1.85)-0.0142546],_
[1.86,0.0140990,En(10,1.86),En(10,1.86)-0.0140990],_
[1.87,0.0139451,En(10,1.87),En(10,1.87)-0.0139451],_
[1.88,0.0137929,En(10,1.88),En(10,1.88)-0.0137929],_
[1.89,0.0136424,En(10,1.89),En(10,1.89)-0.0136424],_
[1.90,0.0134935,En(10,1.90),En(10,1.90)-0.0134935],_
[1.91,0.0133463,En(10,1.91),En(10,1.91)-0.0133463],_
[1.92,0.0132007,En(10,1.92),En(10,1.92)-0.0132007],_
[1.93,0.0130567,En(10,1.93),En(10,1.93)-0.0130567],_
[1.94,0.0129143,En(10,1.94),En(10,1.94)-0.0129143],_
[1.95,0.0127734,En(10,1.95),En(10,1.95)-0.0127734],_
[1.96,0.0126341,En(10,1.96),En(10,1.96)-0.0126341],_
[1.97,0.0124964,En(10,1.97),En(10,1.97)-0.0124964],_
[1.98,0.0123601,En(10,1.98),En(10,1.98)-0.0123601],_
[1.99,0.0122254,En(10,1.99),En(10,1.99)-0.0122254],_
[2.00,0.0120921,En(10,2.00),En(10,2.00)-0.0120921]]
 

   (6)
   [[9.9999999999999985E-3,0.1098682,0.10986822627360165,2.6273601655413259E-8],

     [1.9999999999999997E-2, 0.1086395, 0.10863946164415648,
      - 3.8355843515192056E-8]
     ,
    [2.9999999999999999E-2,0.1074246,0.10742465352510716,5.3525107165941499E-8],
    [3.9999999999999994E-2,0.1062236,0.10622364016949924,4.016949924079416E-8],

     [5.0000000000000003E-2, 0.1050363, 0.10503626175690921,
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    [1.6499999999999999,1.77579E-2,1.77579365115926E-2,3.6511592600013687E-8],

     [1.6599999999999999, 1.7563700000000002E-2, 1.7563692904101796E-2,
      - 7.0958982058277886E-9]
     ,

     [1.6699999999999999, 1.7371600000000001E-2, 1.7371594215528752E-2,
      - 5.7844712492149952E-9]
     ,

     [1.6799999999999999, 1.7181599999999998E-2, 1.718161648822112E-2,
      1.6488221121768731E-8]
     ,
    [1.6899999999999999,1.69937E-2,1.6993736035910194E-2,3.6035910193354947E-8],
    [1.7,1.6807900000000001E-2,1.6807929440582167E-2,2.9440582166584406E-8],
    [1.71,1.6624199999999999E-2,1.6624173549386351E-2,- 2.6450613647283072E-8],
    [1.72,1.6442399999999999E-2,1.6442445471579824E-2,4.5471579824402086E-8],
    [1.73,1.6262699999999998E-2,1.6262722575508065E-2,2.2575508067113059E-8],
    [1.74,1.6084999999999999E-2,1.6084982485621131E-2,- 1.7514378867350411E-8],
    [1.75,1.5909199999999998E-2,1.590920307952504E-2,3.0795250412218866E-9],

     [1.7599999999999998, 1.5735399999999997E-2, 1.5735362485067746E-2,
      - 3.7514932250959365E-8]
     ,
    [1.77,1.55634E-2,1.5563439077459485E-2,3.9077459485295507E-8],
    [1.7799999999999998,1.53934E-2,1.539341147642701E-2,1.1476427010104207E-8],
    [1.79,1.5225300000000001E-2,1.5225258543401142E-2,- 4.1456598858652383E-8],

     [1.7999999999999998, 1.5058999999999999E-2, 1.5058959378737588E-2,
      - 4.062126241106967E-8]
     ,

     [1.8100000000000001, 1.48945E-2, 1.4894493318970201E-2,
      - 6.6810297988384448E-9]
     ,
    [1.8199999999999998,1.47318E-2,1.4731839934096687E-2,3.993409668744119E-8],

     [1.8300000000000001, 1.4571000000000001E-2, 1.4570979024896022E-2,
      - 2.0975103978346232E-8]
     ,

     [1.8399999999999999, 1.4411899999999998E-2, 1.4411890620277507E-2,
      - 9.3797224917646638E-9]
     ,

     [1.8500000000000001, 1.4254599999999999E-2, 1.4254554974660784E-2,
      - 4.5025339215701288E-8]
     ,
    [1.8599999999999999,1.4099E-2,1.4098952565386716E-2,- 4.7434613284144667E-8]
     ,

     [1.8700000000000001, 1.3945099999999998E-2, 1.3945064090158516E-2,
      - 3.5909841482328897E-8]
     ,

     [1.8799999999999999, 1.37929E-2, 1.3792870464512974E-2,
      - 2.9535487026596807E-8]
     ,

     [1.8899999999999999, 1.3642399999999999E-2, 1.3642352819321198E-2,
      - 4.7180678801328479E-8]
     ,

     [1.8999999999999999, 1.3493499999999999E-2, 1.3493492498318767E-2,
      - 7.5016812310646497E-9]
     ,

     [1.9099999999999999, 1.3346299999999998E-2, 1.3346271055664704E-2,
      - 2.8944335294864287E-8]
     ,

     [1.9199999999999999, 1.3200699999999999E-2, 1.3200670253529076E-2,
      - 2.9746470923616708E-8]
     ,

     [1.9299999999999999, 1.3056699999999999E-2, 1.3056672059708807E-2,
      - 2.7940291191796973E-8]
     ,

     [1.9399999999999999, 1.29143E-2, 1.2914258645271409E-2,
      - 4.1354728591222467E-8]
     ,
    [1.95,1.2773400000000001E-2,1.2773412382226235E-2,1.2382226233925708E-8],
    [1.96,1.2634099999999999E-2,1.2634115841222995E-2,1.5841222996554327E-8],
    [1.97,1.24964E-2,1.2496351789277165E-2,- 4.8210722834035602E-8],
    [1.98,1.2360099999999999E-2,1.236010318752195E-2,3.1875219512478292E-9],
    [1.99,1.2225400000000001E-2,1.222535318898654E-2,- 4.6811013461323103E-8],
    [2.,1.20921E-2,1.2092085136400298E-2,- 1.4863599701736563E-8]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (6)
--R   [[1.0E-2,0.1098682,0.10986822627360165,2.6273601655413259E-8],
--R    [2.0E-2,0.1086395,0.10863946164415648,- 3.8355843515192056E-8],
--R    [2.9999999999999999E-2,0.1074246,0.10742465352510716,5.3525107165941499E-8],
--R    [4.0000000000000001E-2,0.1062236,0.10622364016949924,4.016949924079416E-8],
--R
--R     [5.0000000000000003E-2, 0.1050363, 0.10503626175690921,
--R      - 3.8243090791367784E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 0.10386239999999999, 0.10386236036958028,
--R      - 3.9630419709779652E-8]
--R     ,
--R    [7.0000000000000007E-2,0.1027018,0.1027017799688722,- 2.0031127798136872E-8]
--R     ,
--R    [8.0000000000000002E-2,0.1015544,0.1015543663720207,- 3.3627979303951783E-8]
--R     ,
--R    [8.9999999999999997E-2,0.10042,0.1004199672292018,- 3.2770798200076889E-8],
--R
--R     [0.10000000000000001, 9.9298399999999995E-2, 9.9298432000896802E-2,
--R      3.2000896807438117E-8]
--R     ,
--R    [0.11,9.8189600000000002E-2,9.8189611935553478E-2,1.1935553476116745E-8],
--R    [0.12,9.7093399999999996E-2,9.7093360047539198E-2,- 3.9952460798020617E-8],
--R    [0.13,9.6009499999999998E-2,9.6009531095381809E-2,3.109538181111926E-8],
--R
--R     [0.14000000000000001, 9.4937999999999995E-2, 9.4937981560294218E-2,
--R      - 1.8439705776196469E-8]
--R     ,
--R
--R     [0.14999999999999999, 9.3878600000000006E-2, 9.3878569624978384E-2,
--R      - 3.037502162295258E-8]
--R     ,
--R    [0.16,9.2831200000000003E-2,9.2831155152705111E-2,- 4.4847294891625644E-8],
--R
--R     [0.17000000000000001, 9.1795600000000005E-2, 9.1795599666665256E-2,
--R      - 3.3333474869223778E-10]
--R     ,
--R
--R     [0.17999999999999999, 9.07718E-2, 9.0771766329588957E-2,
--R      - 3.3670411042630022E-8]
--R     ,
--R    [0.19,8.9759500000000006E-2,8.9759519923628739E-2,1.9923628732931853E-8],
--R
--R     [0.20000000000000001, 8.8758699999999996E-2, 8.8758726830502982E-2,
--R      2.6830502986019411E-8]
--R     ,
--R
--R     [0.20999999999999999, 8.7769299999999995E-2, 8.7769255011895919E-2,
--R      - 4.4988104075383006E-8]
--R     ,
--R    [0.22,8.6790999999999993E-2,8.6790973990110751E-2,- 2.6009889242395445E-8],
--R
--R     [0.23000000000000001, 8.5823800000000006E-2, 8.5823754828972157E-2,
--R      - 4.5171027848733836E-8]
--R     ,
--R
--R     [0.23999999999999999, 8.4867499999999998E-2, 8.4867470114974794E-2,
--R      - 2.9885025204512417E-8]
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--R    [0.25,8.3921999999999997E-2,8.3921993938674291E-2,- 6.0613257052422043E-9],
--R
--R     [0.26000000000000001, 8.2987199999999997E-2, 8.2987201876317501E-2,
--R      1.8763175041458524E-9]
--R     ,
--R
--R     [0.27000000000000002, 8.2062999999999997E-2, 8.2062970971708463E-2,
--R      - 2.9028291534394235E-8]
--R     ,
--R
--R     [0.28000000000000003, 8.1149200000000005E-2, 8.1149179718306999E-2,
--R      - 2.0281693005608226E-8]
--R     ,
--R
--R     [0.28999999999999998, 8.0245700000000003E-2, 8.0245708041556577E-2,
--R      8.041556573412656E-9]
--R     ,
--R
--R     [0.29999999999999999, 7.9352400000000003E-2, 7.9352437281438454E-2,
--R      3.7281438450276205E-8]
--R     ,
--R    [0.31,7.8469300000000006E-2,7.8469250175248736E-2,- 4.9824751269245127E-8],
--R
--R     [0.32000000000000001, 7.7595999999999998E-2, 7.7596030840595492E-2,
--R      3.0840595494074918E-8]
--R     ,
--R
--R     [0.33000000000000002, 7.6732700000000001E-2, 7.6732664758612748E-2,
--R      - 3.5241387252860079E-8]
--R     ,
--R
--R     [0.34000000000000002, 7.5879000000000002E-2, 7.5879038757388551E-2,
--R      3.8757388548527061E-8]
--R     ,
--R
--R     [0.34999999999999998, 7.5035000000000004E-2, 7.5035040995603944E-2,
--R      4.0995603939331104E-8]
--R     ,
--R
--R     [0.35999999999999999, 7.4200600000000005E-2, 7.4200560946380167E-2,
--R      - 3.9053619838025355E-8]
--R     ,
--R    [0.37,7.3375499999999996E-2,7.3375489381331219E-2,- 1.0618668777606644E-8],
--R    [0.38,7.2559700000000005E-2,7.2559718354818795E-2,1.8354818789867444E-8],
--R    [0.39000000000000001,7.17531E-2,7.1753141188407144E-2,4.1188407143288863E-8]
--R     ,
--R
--R     [0.40000000000000002, 7.0955699999999997E-2, 7.0955652455514773E-2,
--R      - 4.7544485223816046E-8]
--R     ,
--R
--R     [0.40999999999999998, 7.0167099999999996E-2, 7.0167147966260709E-2,
--R      4.7966260713350195E-8]
--R     ,
--R
--R     [0.41999999999999998, 6.9387500000000005E-2, 6.93875247525024E-2,
--R      2.4752502394975728E-8]
--R     ,
--R
--R     [0.42999999999999999, 6.8616700000000003E-2, 6.8616681053062775E-2,
--R      - 1.8946937227481975E-8]
--R     ,
--R    [0.44,6.7854499999999998E-2,6.7854516299143935E-2,1.6299143937303917E-8],
--R
--R     [0.45000000000000001, 6.7100900000000005E-2, 6.7100931099924779E-2,
--R      3.1099924774347087E-8]
--R     ,
--R
--R     [0.46000000000000002, 6.6355800000000006E-2, 6.6355827228340464E-2,
--R      2.7228340457319256E-8]
--R     ,
--R    [0.46999999999999997,6.56191E-2,6.5619107607040858E-2,7.6070408583372995E-9]
--R     ,
--R
--R     [0.47999999999999998, 6.4890699999999996E-2, 6.4890676294525704E-2,
--R      - 2.3705474291868533E-8]
--R     ,
--R
--R     [0.48999999999999999, 6.4170400000000002E-2, 6.4170438471454316E-2,
--R      3.8471454313904196E-8]
--R     ,
--R    [0.5,6.3458299999999995E-2,6.3458300427127218E-2,4.2712722247983947E-10],
--R
--R     [0.51000000000000001, 6.2754199999999996E-2, 6.2754169546137606E-2,
--R      - 3.0453862390200648E-8]
--R     ,
--R
--R     [0.52000000000000002, 6.2058000000000002E-2, 6.2057954295190239E-2,
--R      - 4.5704809763236209E-8]
--R     ,
--R
--R     [0.53000000000000003, 6.1369600000000003E-2, 6.136956421008552E-2,
--R      - 3.5789914483441709E-8]
--R     ,
--R
--R     [0.54000000000000004, 6.0688899999999997E-2, 6.06889098828668E-2,
--R      9.8828668027017841E-9]
--R     ,
--R
--R     [0.55000000000000004, 6.0015899999999997E-2, 6.0015902949128445E-2,
--R      2.9491284483929014E-9]
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--R     [0.56000000000000005, 5.93505E-2, 5.9350456075482616E-2,
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--R     [0.56999999999999995, 5.8692500000000002E-2, 5.8692482947182836E-2,
--R      - 1.7052817165297274E-8]
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--R     [0.57999999999999996, 5.80419E-2, 5.8041898255901947E-2,
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--R     [0.58999999999999997, 5.7398600000000001E-2, 5.7398617687662766E-2,
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--R     [0.59999999999999998, 5.6762600000000003E-2, 5.6762557910919068E-2,
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--R     [0.60999999999999999, 5.6133599999999999E-2, 5.6133636564785275E-2,
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--R     [0.64000000000000001, 5.4288900000000001E-2, 5.4288893818006168E-2,
--R      - 6.1819938335094804E-9]
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--R     [0.65000000000000002, 5.3687699999999998E-2, 5.3687721594857608E-2,
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--R     [0.66000000000000003, 5.3093300000000003E-2, 5.3093290155987988E-2,
--R      - 9.8440120152587518E-9]
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--R     [0.67000000000000004, 5.2505499999999997E-2, 5.2505522725370901E-2,
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--R     [0.68999999999999995, 5.1349699999999998E-2, 5.1349677235465116E-2,
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--R     [0.69999999999999996, 5.07815E-2, 5.0781450042980847E-2,
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--R     [0.70999999999999996, 5.0219600000000003E-2, 5.0219588571451021E-2,
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--R     [0.72999999999999998, 4.9114699999999997E-2, 4.9114673951996674E-2,
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--R     [0.73999999999999999, 4.8571499999999997E-2, 4.85714784752228E-2,
--R      - 2.1524777196746392E-8]
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--R     [0.76000000000000001, 4.7503299999999998E-2, 4.7503261533576278E-2,
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--R     [0.77000000000000002, 4.6978100000000002E-2, 4.6978102633344329E-2,
--R      2.6333443273185431E-9]
--R     ,
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--R     [0.78000000000000003, 4.6458800000000001E-2, 4.6458819815439867E-2,
--R      1.9815439865344953E-8]
--R     ,
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--R     [0.79000000000000004, 4.5945300000000001E-2, 4.5945346336274485E-2,
--R      4.6336274484026774E-8]
--R     ,
--R
--R     [0.80000000000000004, 4.5437600000000002E-2, 4.5437616225057327E-2,
--R      1.6225057325458536E-8]
--R     ,
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--R     [0.81000000000000005, 4.4935599999999999E-2, 4.4935564274618756E-2,
--R      - 3.5725381243578713E-8]
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--R     [0.81999999999999995, 4.4439100000000002E-2, 4.4439126032346843E-2,
--R      2.6032346840676457E-8]
--R     ,
--R    [0.82999999999999996,4.39482E-2,4.3948237791235037E-2,3.7791235037165638E-8]
--R     ,
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--R     [0.83999999999999997, 4.3462800000000003E-2, 4.3462836581039874E-2,
--R      3.6581039870864362E-8]
--R     ,
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--R     [0.84999999999999998, 4.2982899999999997E-2, 4.2982860159546922E-2,
--R      - 3.9840453075479232E-8]
--R     ,
--R
--R     [0.85999999999999999, 4.2508200000000003E-2, 4.2508247003943962E-2,
--R      4.7003943959289529E-8]
--R     ,
--R    [0.87,4.2038899999999997E-2,4.2038936302299747E-2,3.6302299749602085E-8],
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--R    [0.89000000000000001,4.1116E-2,4.111598251716897E-2,- 1.7482831030091184E-8]
--R     ,
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--R     [0.90000000000000002, 4.0662200000000003E-2, 4.0662221288986326E-2,
--R      2.1288986323808601E-8]
--R     ,
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--R     [0.91000000000000003, 4.0213499999999999E-2, 4.0213526209046141E-2,
--R      2.6209046141700831E-8]
--R     ,
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--R     [0.92000000000000004, 3.9769800000000001E-2, 3.9769839895608665E-2,
--R      3.9895608663909066E-8]
--R     ,
--R
--R     [0.93000000000000005, 3.9331100000000001E-2, 3.9331105628832443E-2,
--R      5.628832441817444E-9]
--R     ,
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--R     [0.93999999999999995, 3.8897300000000003E-2, 3.8897267342955913E-2,
--R      - 3.2657044089778875E-8]
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--R     [0.94999999999999996, 3.8468299999999997E-2, 3.8468269618574302E-2,
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--R     ,
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--R     [0.95999999999999996, 3.8044099999999997E-2, 3.8044057675010727E-2,
--R      - 4.2324989270314806E-8]
--R     ,
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--R     [0.96999999999999997, 3.7624600000000001E-2, 3.7624577362780139E-2,
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--R     ,
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--R     [0.97999999999999998, 3.7209800000000001E-2, 3.7209775156145049E-2,
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--R     [0.98999999999999999, 3.6799600000000002E-2, 3.6799598145761836E-2,
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--R
--R     [1.0800000000000001, 3.3307700000000003E-2, 3.3307704757373741E-2,
--R      4.757373738006887E-9]
--R     ,
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--R     [1.0900000000000001, 3.2940999999999998E-2, 3.2941000220027501E-2,
--R      2.20027503161635E-10]
--R     ,
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--R     [1.1000000000000001, 3.25784E-2, 3.2578377542274328E-2,
--R      - 2.2457725672164752E-8]
--R     ,
--R
--R     [1.1100000000000001, 3.22198E-2, 3.2219790669352259E-2,
--R      - 9.3306477405574739E-9]
--R     ,
--R
--R     [1.1200000000000001, 3.1865200000000003E-2, 3.186519407503445E-2,
--R      - 5.924965552905892E-9]
--R     ,
--R
--R     [1.1299999999999999, 3.1514500000000001E-2, 3.1514542755429475E-2,
--R      4.275542947462796E-8]
--R     ,
--R
--R     [1.1399999999999999, 3.1167799999999999E-2, 3.1167792222856549E-2,
--R      - 7.777143450071744E-9]
--R     ,
--R
--R     [1.1499999999999999, 3.0824899999999999E-2, 3.0824898499794556E-2,
--R      - 1.5002054425117262E-9]
--R     ,
--R    [1.1599999999999999,3.04858E-2,3.0485818112904201E-2,1.811290420081213E-8],
--R    [1.1699999999999999,3.01505E-2,3.0150508087122076E-2,8.0871220761724594E-9],
--R
--R     [1.1799999999999999, 2.9818899999999999E-2, 2.9818925939826001E-2,
--R      2.5939826002463473E-8]
--R     ,
--R    [1.1899999999999999,2.9491E-2,2.9491029675070599E-2,2.9675070598728093E-8],
--R    [1.2,2.91668E-2,2.9166777777892276E-2,- 2.222210772340194E-8],
--R    [1.21,2.88461E-2,2.8846129208682729E-2,2.9208682729431334E-8],
--R    [1.22,2.8528999999999999E-2,2.8529043397630106E-2,4.33976301075778E-8],
--R    [1.23,2.8215500000000001E-2,2.8215480239227052E-2,- 1.9760772948518301E-8],
--R    [1.24,2.79054E-2,2.7905400086844646E-2,8.6844646057793184E-11],
--R    [1.25,2.75988E-2,2.7598763747371625E-2,- 3.6252628374949802E-8],
--R    [1.26,2.72955E-2,2.7295532475917882E-2,3.2475917881996663E-8],
--R    [1.27,2.6995700000000001E-2,2.699566797058155E-2,- 3.2029418450818525E-8],
--R    [1.28,2.66991E-2,2.6699132367278861E-2,3.2367278860606641E-8],
--R    [1.29,2.64059E-2,2.6405888234635966E-2,- 1.1765364033716752E-8],
--R    [1.3,2.6115900000000001E-2,2.6115898568942E-2,- 1.4310580012666385E-9],
--R
--R     [1.3100000000000001, 2.5829100000000001E-2, 2.5829126789162573E-2,
--R      2.678916257228825E-8]
--R     ,
--R
--R     [1.3200000000000001, 2.5545499999999999E-2, 2.5545536732012972E-2,
--R      3.673201297293982E-8]
--R     ,
--R
--R     [1.3300000000000001, 2.5265099999999999E-2, 2.5265092647090353E-2,
--R      - 7.3529096457358722E-9]
--R     ,
--R
--R     [1.3400000000000001, 2.4987800000000001E-2, 2.4987759192064113E-2,
--R      - 4.0807935888093061E-8]
--R     ,
--R
--R     [1.3500000000000001, 2.4713499999999999E-2, 2.471350142792382E-2,
--R      1.42792382085144E-9]
--R     ,
--R
--R     [1.3600000000000001, 2.44423E-2, 2.4442284814283937E-2,
--R      - 1.5185716063098598E-8]
--R     ,
--R
--R     [1.3700000000000001, 2.41741E-2, 2.4174075204744596E-2,
--R      - 2.4795255404441718E-8]
--R     ,
--R
--R     [1.3799999999999999, 2.3908800000000001E-2, 2.3908838842307847E-2,
--R      3.8842307845815549E-8]
--R     ,
--R
--R     [1.3899999999999999, 2.3646500000000001E-2, 2.3646542354848549E-2,
--R      4.2354848548559199E-8]
--R     ,
--R
--R     [1.3999999999999999, 2.33872E-2, 2.3387152750639354E-2,
--R      - 4.7249360646262062E-8]
--R     ,
--R
--R     [1.4099999999999999, 2.3130600000000001E-2, 2.3130637413929071E-2,
--R      3.7413929069446406E-8]
--R     ,
--R
--R     [1.4199999999999999, 2.2877000000000002E-2, 2.2876964100573671E-2,
--R      - 3.5899426330948669E-8]
--R     ,
--R    [1.4299999999999999,2.26261E-2,2.2626100933719476E-2,9.3371947673670519E-10]
--R     ,
--R
--R     [1.4399999999999999, 2.2377999999999999E-2, 2.237801639953766E-2,
--R      1.6399537661887509E-8]
--R     ,
--R    [1.45,2.2132700000000002E-2,2.2132679343009602E-2,- 2.065699039946467E-8],
--R    [1.46,2.1890099999999999E-2,2.18900589637624E-2,- 4.1036237598962577E-8],
--R    [1.47,2.1650099999999999E-2,2.1650124811953917E-2,2.4811953918540963E-8],
--R    [1.48,2.1412799999999999E-2,2.1412846784206772E-2,4.678420677250994E-8],
--R    [1.49,2.1178200000000001E-2,2.1178195119590685E-2,- 4.8804093162602147E-9],
--R    [1.5,2.0946099999999999E-2,2.094614039565253E-2,4.0395652531333148E-8],
--R    [1.51,2.0716700000000001E-2,2.0716653524493592E-2,- 4.647550640862752E-8],
--R    [1.52,2.04897E-2,2.0489705748893364E-2,5.748893364826424E-9],
--R    [1.53,2.02653E-2,2.0265268638479383E-2,- 3.1361520616557392E-8],
--R    [1.54,2.00433E-2,2.0043314085942482E-2,1.4085942481867342E-8],
--R    [1.55,1.9823799999999999E-2,1.9823814303296966E-2,1.4303296966972079E-8],
--R
--R     [1.5600000000000001, 1.9606700000000001E-2, 1.9606741818185093E-2,
--R      4.1818185091829774E-8]
--R     ,
--R
--R     [1.5700000000000001, 1.9392099999999999E-2, 1.9392069470225374E-2,
--R      - 3.0529774625032147E-8]
--R     ,
--R
--R     [1.5800000000000001, 1.91798E-2, 1.9179770407404116E-2,
--R      - 2.9592595884170292E-8]
--R     ,
--R
--R     [1.5900000000000001, 1.8969799999999998E-2, 1.8969818082509717E-2,
--R      1.8082509718742035E-8]
--R     ,
--R
--R     [1.6000000000000001, 1.87622E-2, 1.8762186249609149E-2,
--R      - 1.3750390850247873E-8]
--R     ,
--R
--R     [1.6100000000000001, 1.8556799999999998E-2, 1.8556848960566173E-2,
--R      4.8960566174233167E-8]
--R     ,
--R    [1.6200000000000001,1.83538E-2,1.835378056160069E-2,- 1.9438399310317545E-8]
--R     ,
--R
--R     [1.6299999999999999, 1.8152999999999999E-2, 1.8152955689888815E-2,
--R      - 4.431011118438688E-8]
--R     ,
--R
--R     [1.6399999999999999, 1.7954299999999999E-2, 1.7954349270203122E-2,
--R      4.927020312225916E-8]
--R     ,
--R    [1.6499999999999999,1.77579E-2,1.77579365115926E-2,3.6511592600013687E-8],
--R
--R     [1.6599999999999999, 1.7563700000000002E-2, 1.7563692904101796E-2,
--R      - 7.0958982058277886E-9]
--R     ,
--R
--R     [1.6699999999999999, 1.7371600000000001E-2, 1.7371594215528752E-2,
--R      - 5.7844712492149952E-9]
--R     ,
--R
--R     [1.6799999999999999, 1.7181600000000002E-2, 1.718161648822112E-2,
--R      1.6488221118299284E-8]
--R     ,
--R    [1.6899999999999999,1.69937E-2,1.6993736035910194E-2,3.6035910193354947E-8],
--R    [1.7,1.6807900000000001E-2,1.6807929440582167E-2,2.9440582166584406E-8],
--R    [1.71,1.6624199999999999E-2,1.6624173549386351E-2,- 2.6450613647283072E-8],
--R    [1.72,1.6442399999999999E-2,1.6442445471579824E-2,4.5471579824402086E-8],
--R    [1.73,1.6262700000000001E-2,1.6262722575508065E-2,2.2575508063643612E-8],
--R    [1.74,1.6084999999999999E-2,1.6084982485621131E-2,- 1.7514378867350411E-8],
--R    [1.75,1.5909199999999998E-2,1.590920307952504E-2,3.0795250412218866E-9],
--R    [1.76,1.57354E-2,1.5735362485067742E-2,- 3.7514932257898259E-8],
--R    [1.77,1.55634E-2,1.5563439077459485E-2,3.9077459485295507E-8],
--R    [1.78,1.53934E-2,1.5393411476427005E-2,1.1476427004900036E-8],
--R    [1.79,1.5225300000000001E-2,1.5225258543401145E-2,- 4.1456598855182936E-8],
--R    [1.8,1.5058999999999999E-2,1.5058959378737585E-2,- 4.0621262414539117E-8],
--R
--R     [1.8100000000000001, 1.48945E-2, 1.4894493318970201E-2,
--R      - 6.6810297988384448E-9]
--R     ,
--R    [1.8200000000000001,1.47318E-2,1.4731839934096682E-2,3.9934096682237019E-8],
--R
--R     [1.8300000000000001, 1.4571000000000001E-2, 1.4570979024896022E-2,
--R      - 2.0975103978346232E-8]
--R     ,
--R
--R     [1.8400000000000001, 1.44119E-2, 1.4411890620277503E-2,
--R      - 9.3797224969688342E-9]
--R     ,
--R
--R     [1.8500000000000001, 1.4254599999999999E-2, 1.4254554974660784E-2,
--R      - 4.5025339215701288E-8]
--R     ,
--R    [1.8600000000000001,1.4099E-2,1.4098952565386716E-2,- 4.7434613284144667E-8]
--R     ,
--R    [1.8700000000000001,1.39451E-2,1.3945064090158516E-2,- 3.590984148406362E-8]
--R     ,
--R
--R     [1.8799999999999999, 1.37929E-2, 1.3792870464512974E-2,
--R      - 2.9535487026596807E-8]
--R     ,
--R
--R     [1.8899999999999999, 1.3642400000000001E-2, 1.3642352819321199E-2,
--R      - 4.7180678801328479E-8]
--R     ,
--R
--R     [1.8999999999999999, 1.34935E-2, 1.3493492498318767E-2,
--R      - 7.5016812327993732E-9]
--R     ,
--R
--R     [1.9099999999999999, 1.33463E-2, 1.3346271055664704E-2,
--R      - 2.8944335296599011E-8]
--R     ,
--R
--R     [1.9199999999999999, 1.3200699999999999E-2, 1.3200670253529076E-2,
--R      - 2.9746470923616708E-8]
--R     ,
--R
--R     [1.9299999999999999, 1.3056699999999999E-2, 1.3056672059708809E-2,
--R      - 2.794029119006225E-8]
--R     ,
--R
--R     [1.9399999999999999, 1.29143E-2, 1.2914258645271409E-2,
--R      - 4.1354728591222467E-8]
--R     ,
--R    [1.95,1.2773400000000001E-2,1.2773412382226235E-2,1.2382226233925708E-8],
--R    [1.96,1.2634100000000001E-2,1.2634115841222995E-2,1.5841222994819604E-8],
--R    [1.97,1.24964E-2,1.2496351789277165E-2,- 4.8210722834035602E-8],
--R    [1.98,1.2360100000000001E-2,1.236010318752195E-2,3.1875219495131057E-9],
--R    [1.99,1.2225400000000001E-2,1.222535318898654E-2,- 4.6811013461323103E-8],
--R    [2.,1.20921E-2,1.2092085136400298E-2,- 1.4863599701736563E-8]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 6

--S 7 of 7
[[0.01,0.0520790,En(20,0.01),En(20,0.01)-0.0520790],_
[0.02,0.0515321,En(20,0.02),En(20,0.02)-0.0515321],_
[0.03,0.0509911,En(20,0.03),En(20,0.03)-0.0509911],_
[0.04,0.0504558,En(20,0.04),En(20,0.04)-0.0504558],_
[0.05,0.0499260,En(20,0.05),En(20,0.05)-0.0499260],_
[0.06,0.0494019,En(20,0.06),En(20,0.06)-0.0494019],_
[0.07,0.0488833,En(20,0.07),En(20,0.07)-0.0488833],_
[0.08,0.0483702,En(20,0.08),En(20,0.08)-0.0483702],_
[0.09,0.0478624,En(20,0.09),En(20,0.09)-0.0478624],_
[0.10,0.0473600,En(20,0.10),En(20,0.10)-0.0473600],_
[0.11,0.0468629,En(20,0.11),En(20,0.11)-0.0468629],_
[0.12,0.0463710,En(20,0.12),En(20,0.12)-0.0463710],_
[0.13,0.0458843,En(20,0.13),En(20,0.13)-0.0458843],_
[0.14,0.0454027,En(20,0.14),En(20,0.14)-0.0454027],_
[0.15,0.0449262,En(20,0.15),En(20,0.15)-0.0449262],_
[0.16,0.0444547,En(20,0.16),En(20,0.16)-0.0444547],_
[0.17,0.0439882,En(20,0.17),En(20,0.17)-0.0439882],_
[0.18,0.0435266,En(20,0.18),En(20,0.18)-0.0435266],_
[0.19,0.0430698,En(20,0.19),En(20,0.19)-0.0430698],_
[0.20,0.0426179,En(20,0.20),En(20,0.20)-0.0426179],_
[0.21,0.0421707,En(20,0.21),En(20,0.21)-0.0421707],_
[0.22,0.0417282,En(20,0.22),En(20,0.22)-0.0417282],_
[0.23,0.0412903,En(20,0.23),En(20,0.23)-0.0412903],_
[0.24,0.0408571,En(20,0.24),En(20,0.24)-0.0408571],_
[0.25,0.0404285,En(20,0.25),En(20,0.25)-0.0404285],_
[0.26,0.0400043,En(20,0.26),En(20,0.26)-0.0400043],_
[0.27,0.0395846,En(20,0.27),En(20,0.27)-0.0395846],_
[0.28,0.0391693,En(20,0.28),En(20,0.28)-0.0391693],_
[0.29,0.0387584,En(20,0.29),En(20,0.29)-0.0387584],_
[0.30,0.0383518,En(20,0.30),En(20,0.30)-0.0383518],_
[0.31,0.0379495,En(20,0.31),En(20,0.31)-0.0379495],_
[0.32,0.0375515,En(20,0.32),En(20,0.32)-0.0375515],_
[0.33,0.0371576,En(20,0.33),En(20,0.33)-0.0371576],_
[0.34,0.0367678,En(20,0.34),En(20,0.34)-0.0367678],_
[0.35,0.0363822,En(20,0.35),En(20,0.35)-0.0363822],_
[0.36,0.0360006,En(20,0.36),En(20,0.36)-0.0360006],_
[0.37,0.0356231,En(20,0.37),En(20,0.37)-0.0356231],_
[0.38,0.0352495,En(20,0.38),En(20,0.38)-0.0352495],_
[0.39,0.0348798,En(20,0.39),En(20,0.39)-0.0348798],_
[0.40,0.0345140,En(20,0.40),En(20,0.40)-0.0345140],_
[0.41,0.0341521,En(20,0.41),En(20,0.41)-0.0341521],_
[0.42,0.0337939,En(20,0.42),En(20,0.42)-0.0337939],_
[0.43,0.0334396,En(20,0.43),En(20,0.43)-0.0334396],_
[0.44,0.0330889,En(20,0.44),En(20,0.44)-0.0330889],_
[0.45,0.0327420,En(20,0.45),En(20,0.45)-0.0327420],_
[0.46,0.0323987,En(20,0.46),En(20,0.46)-0.0323987],_
[0.47,0.0320590,En(20,0.47),En(20,0.47)-0.0320590],_
[0.48,0.0317229,En(20,0.48),En(20,0.48)-0.0317229],_
[0.49,0.0313903,En(20,0.49),En(20,0.49)-0.0313903],_
[0.50,0.0310612,En(20,0.50),En(20,0.50)-0.0310612],_
[0.51,0.0307356,En(20,0.51),En(20,0.51)-0.0307356],_
[0.52,0.0304134,En(20,0.52),En(20,0.52)-0.0304134],_
[0.53,0.0300946,En(20,0.53),En(20,0.53)-0.0300946],_
[0.54,0.0297791,En(20,0.54),En(20,0.54)-0.0297791],_
[0.55,0.0294670,En(20,0.55),En(20,0.55)-0.0294670],_
[0.56,0.0291581,En(20,0.56),En(20,0.56)-0.0291581],_
[0.57,0.0288525,En(20,0.57),En(20,0.57)-0.0288525],_
[0.58,0.0285501,En(20,0.58),En(20,0.58)-0.0285501],_
[0.59,0.0282508,En(20,0.59),En(20,0.59)-0.0282508],_
[0.60,0.0279548,En(20,0.60),En(20,0.60)-0.0279548],_
[0.61,0.0276618,En(20,0.61),En(20,0.61)-0.0276618],_
[0.62,0.0273719,En(20,0.62),En(20,0.62)-0.0273719],_
[0.63,0.0270850,En(20,0.63),En(20,0.63)-0.0270850],_
[0.64,0.0268012,En(20,0.64),En(20,0.64)-0.0268012],_
[0.65,0.0265204,En(20,0.65),En(20,0.65)-0.0265204],_
[0.66,0.0262425,En(20,0.66),En(20,0.66)-0.0262425],_
[0.67,0.0259675,En(20,0.67),En(20,0.67)-0.0259675],_
[0.68,0.0256954,En(20,0.68),En(20,0.68)-0.0256954],_
[0.69,0.0254262,En(20,0.69),En(20,0.69)-0.0254262],_
[0.70,0.0251598,En(20,0.70),En(20,0.70)-0.0251598],_
[0.71,0.0248962,En(20,0.71),En(20,0.71)-0.0248962],_
[0.72,0.0246353,En(20,0.72),En(20,0.72)-0.0246353],_
[0.73,0.0243772,En(20,0.73),En(20,0.73)-0.0243772],_
[0.74,0.0241219,En(20,0.74),En(20,0.74)-0.0241219],_
[0.75,0.0238692,En(20,0.75),En(20,0.75)-0.0238692],_
[0.76,0.0236191,En(20,0.76),En(20,0.76)-0.0236191],_
[0.77,0.0233717,En(20,0.77),En(20,0.77)-0.0233717],_
[0.78,0.0231269,En(20,0.78),En(20,0.78)-0.0231269],_
[0.79,0.0228846,En(20,0.79),En(20,0.79)-0.0228846],_
[0.80,0.0226449,En(20,0.80),En(20,0.80)-0.0226449],_
[0.81,0.0224078,En(20,0.81),En(20,0.81)-0.0224078],_
[0.82,0.0221731,En(20,0.82),En(20,0.82)-0.0221731],_
[0.83,0.0219408,En(20,0.83),En(20,0.83)-0.0219408],_
[0.84,0.0217111,En(20,0.84),En(20,0.84)-0.0217111],_
[0.85,0.0214837,En(20,0.85),En(20,0.85)-0.0214837],_
[0.86,0.0212587,En(20,0.86),En(20,0.86)-0.0212587],_
[0.87,0.0210361,En(20,0.87),En(20,0.87)-0.0210361],_
[0.88,0.0208158,En(20,0.88),En(20,0.88)-0.0208158],_
[0.89,0.0205978,En(20,0.89),En(20,0.89)-0.0205978],_
[0.90,0.0203821,En(20,0.90),En(20,0.90)-0.0203821],_
[0.91,0.0201687,En(20,0.91),En(20,0.91)-0.0201687],_
[0.92,0.0199575,En(20,0.92),En(20,0.92)-0.0199575],_
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[0.97,0.0189344,En(20,0.97),En(20,0.97)-0.0189344],_
[0.98,0.0187362,En(20,0.98),En(20,0.98)-0.0187362],_
[0.99,0.0185401,En(20,0.99),En(20,0.99)-0.0185401],_
[1.00,0.0183460,En(20,1.00),En(20,1.00)-0.0183460],_
[1.01,0.0181539,En(20,1.01),En(20,1.01)-0.0181539],_
[1.02,0.0179639,En(20,1.02),En(20,1.02)-0.0179639],_
[1.03,0.0177759,En(20,1.03),En(20,1.03)-0.0177759],_
[1.04,0.0175898,En(20,1.04),En(20,1.04)-0.0175898],_
[1.05,0.0174057,En(20,1.05),En(20,1.05)-0.0174057],_
[1.06,0.0172235,En(20,1.06),En(20,1.06)-0.0172235],_
[1.07,0.0170433,En(20,1.07),En(20,1.07)-0.0170433],_
[1.08,0.0168649,En(20,1.08),En(20,1.08)-0.0168649],_
[1.09,0.0166884,En(20,1.09),En(20,1.09)-0.0166884],_
[1.10,0.0165137,En(20,1.10),En(20,1.10)-0.0165137],_
[1.11,0.0163409,En(20,1.11),En(20,1.11)-0.0163409],_
[1.12,0.0161699,En(20,1.12),En(20,1.12)-0.0161699],_
[1.13,0.0160007,En(20,1.13),En(20,1.13)-0.0160007],_
[1.14,0.0158333,En(20,1.14),En(20,1.14)-0.0158333],_
[1.15,0.0156676,En(20,1.15),En(20,1.15)-0.0156676],_
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[1.43,0.0116719,En(20,1.43),En(20,1.43)-0.0116719],_
[1.44,0.0115499,En(20,1.44),En(20,1.44)-0.0115499],_
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[1.51,0.0107307,En(20,1.51),En(20,1.51)-0.0107307],_
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[2.00,0.0064143,En(20,2.00),En(20,2.00)-0.0064143]]
 

   (7)
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     ,

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     [0.8899999999999999, 2.0597799999999999E-2, 2.0597804466129153E-2,
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     ,

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     [0.92999999999999994, 1.9748599999999998E-2, 1.9748556776953662E-2,
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     [0.93999999999999995, 1.9541799999999998E-2, 1.9541788209521748E-2,
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     ,

     [0.94999999999999996, 1.9337199999999999E-2, 1.9337190406710072E-2,
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     [0.95999999999999996, 1.9134699999999998E-2, 1.9134740509808349E-2,
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     ,

     [0.96999999999999997, 1.8934399999999997E-2, 1.8934415901628112E-2,
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     [0.97999999999999998, 1.8736200000000001E-2, 1.8736194203941098E-2,
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     ,

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     [1.0499999999999998, 1.74057E-2, 1.7405693065938001E-2,
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     ,

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     ,

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     ,

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     ,

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     ,

     [1.1000000000000001, 1.6513699999999999E-2, 1.6513730498807128E-2,
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     ,

     [1.1099999999999999, 1.6340899999999998E-2, 1.6340914448843672E-2,
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     ,

     [1.1200000000000001, 1.6169900000000001E-2, 1.6169911733677846E-2,
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     ,
    [1.1299999999999999,1.60007E-2,1.6000703269971401E-2,3.269971401292926E-9],

     [1.1399999999999999, 1.5833300000000002E-2, 1.5833270175880269E-2,
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     ,

     [1.1499999999999999, 1.5667599999999997E-2, 1.566759376891921E-2,
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     ,

     [1.1599999999999999, 1.5503699999999999E-2, 1.5503655563849129E-2,
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     ,
    [1.1699999999999999,1.53414E-2,1.5341437270586872E-2,3.7270586871959721E-8],

     [1.1799999999999999, 1.5180900000000001E-2, 1.5180920792137275E-2,
      2.079213727405882E-8]
     ,

     [1.1899999999999999, 1.50221E-2, 1.5022088222547223E-2,
      - 1.1777452776917663E-8]
     ,
    [1.2,1.48649E-2,1.4864921844881475E-2,2.1844881474900046E-8],
    [1.21,1.4709399999999999E-2,1.4709404129220015E-2,4.129220016260704E-9],
    [1.22,1.4555499999999999E-2,1.4555517730676726E-2,1.773067672718176E-8],
    [1.23,1.44032E-2,1.4403245487439129E-2,4.5487439129590634E-8],
    [1.24,1.4252600000000001E-2,1.4252570418828979E-2,- 2.9581171021378361E-8],
    [1.25,1.41035E-2,1.4103475723383493E-2,- 2.427661650698798E-8],
    [1.2599999999999998,1.39559E-2,1.3955944776956993E-2,4.4776956992925721E-8],
    [1.27,1.3809999999999999E-2,1.3809961130842716E-2,- 3.8869157283419331E-8],

     [1.2799999999999998, 1.3665500000000001E-2, 1.3665508509914655E-2,
      8.5099146548972548E-9]
     ,
    [1.29,1.3522599999999999E-2,1.3522570810789076E-2,- 2.9189210923319386E-8],
    [1.2999999999999998,1.33811E-2,1.3381132100005693E-2,3.2100005693466716E-8],

     [1.3100000000000001, 1.32412E-2, 1.3241176612228069E-2,
      - 2.3387771930921675E-8]
     ,

     [1.3199999999999998, 1.3102699999999998E-2, 1.310268874846327E-2,
      - 1.125153672835999E-8]
     ,

     [1.3300000000000001, 1.29657E-2, 1.2965653074300341E-2,
      - 4.6925699659361442E-8]
     ,

     [1.3399999999999999, 1.2830100000000001E-2, 1.2830054318167609E-2,
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     ,
    [1.3500000000000001,1.26959E-2,1.2695877369608423E-2,- 2.263039157630875E-8]
     ,

     [1.3599999999999999, 1.2563100000000001E-2, 1.2563107277575323E-2,
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     ,
    [1.3700000000000001,1.24317E-2,1.2431729248742227E-2,2.9248742226817281E-8],

     [1.3799999999999999, 1.2301699999999999E-2, 1.2301728645834703E-2,
      2.8645834704299489E-8]
     ,

     [1.3899999999999999, 1.2173099999999999E-2, 1.2173090985977835E-2,
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     ,

     [1.3999999999999999, 1.2045799999999999E-2, 1.2045801939061785E-2,
      1.9390617861381187E-9]
     ,

     [1.4099999999999999, 1.1919799999999999E-2, 1.1919847326124635E-2,
      4.7326124635524436E-8]
     ,

     [1.4199999999999999, 1.1795199999999999E-2, 1.1795213117752473E-2,
      1.3117752474534061E-8]
     ,

     [1.4299999999999999, 1.1671899999999999E-2, 1.1671885432496448E-2,
      - 1.4567503550666494E-8]
     ,

     [1.4399999999999999, 1.1549899999999998E-2, 1.1549850535306669E-2,
      - 4.9464693329184795E-8]
     ,
    [1.45,1.1429099999999999E-2,1.1429094835982728E-2,- 5.1640172710892829E-9],
    [1.46,1.13096E-2,1.1309604887640717E-2,4.8876407175019176E-9],
    [1.47,1.1191400000000001E-2,1.1191367385196493E-2,- 3.2614803507219348E-8],
    [1.48,1.10744E-2,1.1074369163865097E-2,- 3.0836134902456624E-8],
    [1.49,1.0958599999999999E-2,1.0958597197676098E-2,- 2.8023239007080036E-9],
    [1.5,1.0843999999999999E-2,1.0844038598004712E-2,3.8598004712536715E-8],

     [1.5099999999999998, 1.0730699999999999E-2, 1.0730680612118527E-2,
      - 1.9387881472140989E-8]
     ,
    [1.52,1.0618499999999999E-2,1.0618510621739656E-2,1.062173965622748E-8],

     [1.5299999999999998, 1.0507499999999999E-2, 1.0507516141622202E-2,
      1.6141622202064942E-8]
     ,
    [1.54,1.0397699999999999E-2,1.0397684818144773E-2,- 1.5181855226101271E-8],
    [1.5499999999999998,1.0289E-2,1.0289004427918009E-2,4.4279180096834514E-9],

     [1.5600000000000001, 1.01815E-2, 1.0181462876406836E-2,
      - 3.7123593163088109E-8]
     ,

     [1.5699999999999998, 1.0075000000000001E-2, 1.0075048196567429E-2,
      4.8196567428021586E-8]
     ,

     [1.5800000000000001, 9.9696999999999997E-3, 9.9697485474985574E-3,
      4.8547498557663382E-8]
     ,

     [1.5899999999999999, 9.8655999999999987E-3, 9.8655522131073491E-3,
      - 4.7786892649545609E-8]
     ,

     [1.6000000000000001, 9.7623999999999992E-3, 9.7624476007891394E-3,
      4.7600789140206379E-8]
     ,

     [1.6099999999999999, 9.6603999999999995E-3, 9.6604232401214067E-3,
      2.32401214071698E-8]
     ,

     [1.6200000000000001, 9.5594999999999986E-3, 9.5594677815715092E-3,
      - 3.2218428489341755E-8]
     ,

     [1.6299999999999999, 9.4595999999999986E-3, 9.4595699952182213E-3,
      - 3.000478177722643E-8]
     ,

     [1.6399999999999999, 9.3606999999999996E-3, 9.3607187694867526E-3,
      1.8769486753028586E-8]
     ,

     [1.6499999999999999, 9.2628999999999993E-3, 9.2629031098972782E-3,
      3.1098972789328494E-9]
     ,

     [1.6599999999999999, 9.1660999999999999E-3, 9.1661121378267089E-3,
      1.2137826709002209E-8]
     ,

     [1.6699999999999999, 9.0702999999999999E-3, 9.0703350892836175E-3,
      3.5089283617617539E-8]
     ,

     [1.6799999999999999, 8.9756000000000002E-3, 8.9755613136961645E-3,
      - 3.8686303835758218E-8]
     ,

     [1.6899999999999999, 8.8817999999999987E-3, 8.8817802727129049E-3,
      - 1.9727287093804224E-8]
     ,
    [1.7,8.7889999999999999E-3,8.7889815390163051E-3,- 1.8460983694859601E-8],
    [1.71,8.6971999999999987E-3,8.6971547951488551E-3,- 4.5204851143593183E-8],
    [1.72,8.6063000000000008E-3,8.6062898323516594E-3,- 1.0167648341330437E-8],
    [1.73,8.5164000000000004E-3,8.5163765494153266E-3,- 2.345058467377592E-8],
    [1.74,8.4273999999999998E-3,8.4274049515430643E-3,4.9515430644575531E-9],
    [1.75,8.3394000000000003E-3,8.3393651492258501E-3,- 3.4850774150232966E-8],

     [1.7599999999999998, 8.2521999999999995E-3, 8.2522473571295125E-3,
      4.73571295130093E-8]
     ,
    [1.77,8.1659999999999996E-3,8.1660418929936432E-3,4.1892993643544152E-8],

     [1.7799999999999998, 8.0806999999999997E-3, 8.080739176542194E-3,
      3.9176542194346853E-8]
     ,
    [1.79,7.9962999999999996E-3,7.9963297284055979E-3,2.9728405598339336E-8],

     [1.7999999999999998, 7.9127999999999993E-3, 7.9128041690543788E-3,
      4.1690543794992152E-9]
     ,

     [1.8100000000000001, 7.830199999999999E-3, 7.8301532177440097E-3,
      - 4.678225598922503E-8]
     ,

     [1.8199999999999998, 7.7483999999999999E-3, 7.7483676914710453E-3,
      - 3.2308528954624882E-8]
     ,

     [1.8300000000000001, 7.6673999999999996E-3, 7.6674385039402267E-3,
      3.8503940227169187E-8]
     ,

     [1.8399999999999999, 7.5873999999999994E-3, 7.5873566645426544E-3,
      - 4.3335457344979844E-8]
     ,

     [1.8500000000000001, 7.5081000000000002E-3, 7.50811327734469E-3,
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     ,

     [1.8599999999999999, 7.4296999999999992E-3, 7.4296995400876748E-3,
      - 4.5991232437009311E-10]
     ,

     [1.8700000000000001, 7.3521000000000003E-3, 7.3521067431981824E-3,
      6.743198182126986E-9]
     ,

     [1.8799999999999999, 7.2753000000000002E-3, 7.2753262688088375E-3,
      2.6268808837361102E-8]
     ,

     [1.8899999999999999, 7.1992999999999996E-3, 7.1993495897894446E-3,
      4.9589789444942634E-8]
     ,

     [1.8999999999999999, 7.1241999999999998E-3, 7.1241682687884587E-3,
      - 3.1731211541131954E-8]
     ,

     [1.9099999999999999, 7.0498000000000002E-3, 7.049773957284575E-3,
      - 2.6042715425139695E-8]
     ,

     [1.9199999999999999, 6.9762000000000001E-3, 6.9761583946483935E-3,
      - 4.1605351606618934E-8]
     ,

     [1.9299999999999999, 6.9032999999999994E-3, 6.9033134072140311E-3,
      1.3407214031688208E-8]
     ,

     [1.9399999999999999, 6.8311999999999999E-3, 6.8312309073605745E-3,
      3.0907360574518317E-8]
     ,
    [1.95,6.7598999999999992E-3,6.759902892603269E-3,2.8926032697579318E-9],
    [1.96,6.6892999999999996E-3,6.6893214446943419E-3,2.1444694342336035E-8],
    [1.97,6.6195000000000004E-3,6.6194787287333721E-3,- 2.1271266628306029E-8],
    [1.98,6.5503999999999996E-3,6.5503669922870687E-3,- 3.3007712930965827E-8],
    [1.99,6.4819999999999999E-3,6.4819785645183897E-3,- 2.1435481610196372E-8],
    [2.,6.4142999999999995E-3,6.4143058553248998E-3,5.8553249002862851E-9]]
                               Type: List List OnePointCompletion DoubleFloat
--R 
--R
--R   (7)
--R   [[1.0E-2,5.2079E-2,5.2078954179335148E-2,- 4.5820664852647131E-8],
--R    [2.0E-2,5.1532099999999997E-2,5.1532149651352818E-2,4.9651352820867523E-8],
--R
--R     [2.9999999999999999E-2, 5.0991099999999998E-2, 5.0991103854550281E-2,
--R      3.8545502831222045E-9]
--R     ,
--R
--R     [4.0000000000000001E-2, 5.0455800000000002E-2, 5.0455755932602576E-2,
--R      - 4.4067397425573418E-8]
--R     ,
--R
--R     [5.0000000000000003E-2, 4.9925999999999998E-2, 4.9926045674777729E-2,
--R      4.5674777730819738E-8]
--R     ,
--R
--R     [5.9999999999999998E-2, 4.9401899999999999E-2, 4.9401913509057829E-2,
--R      1.3509057830707327E-8]
--R     ,
--R
--R     [7.0000000000000007E-2, 4.8883299999999998E-2, 4.8883300495333924E-2,
--R      4.9533392665335185E-10]
--R     ,
--R
--R     [8.0000000000000002E-2, 4.8370200000000002E-2, 4.83701483186737E-2,
--R      - 5.1681326301844521E-8]
--R     ,
--R
--R     [8.9999999999999997E-2, 4.7862399999999999E-2, 4.786239928266129E-2,
--R      - 7.1733870926626864E-10]
--R     ,
--R
--R     [0.10000000000000001, 4.7359999999999999E-2, 4.7359996302808287E-2,
--R      - 3.6971917125039333E-9]
--R     ,
--R    [0.11,4.6862899999999999E-2,4.6862882900035485E-2,- 1.7099964513822563E-8],
--R    [0.12,4.6371000000000002E-2,4.6371003194224242E-2,3.1942242392779541E-9],
--R    [0.13,4.5884300000000003E-2,4.5884301897836918E-2,1.8978369153987984E-9],
--R
--R     [0.14000000000000001, 4.5402699999999997E-2, 4.5402724309605645E-2,
--R      2.430960564792084E-8]
--R     ,
--R
--R     [0.14999999999999999, 4.4926199999999999E-2, 4.4926216308288566E-2,
--R      1.6308288566801998E-8]
--R     ,
--R    [0.16,4.44547E-2,4.4454724346493016E-2,2.4346493016080828E-8],
--R
--R     [0.17000000000000001, 4.3988199999999998E-2, 4.398819544456465E-2,
--R      - 4.5554353483856502E-9]
--R     ,
--R
--R     [0.17999999999999999, 4.3526599999999999E-2, 4.3526577184542115E-2,
--R      - 2.2815457884073354E-8]
--R     ,
--R    [0.19,4.3069799999999998E-2,4.3069817704176359E-2,1.7704176361044155E-8],
--R
--R     [0.20000000000000001, 4.26179E-2, 4.2617865691013848E-2,
--R      - 3.4308986152087328E-8]
--R     ,
--R
--R     [0.20999999999999999, 4.2170699999999998E-2, 4.2170670376543248E-2,
--R      - 2.962345675011635E-8]
--R     ,
--R    [0.22,4.17282E-2,4.1728181530404598E-2,- 1.8469595401693351E-8],
--R
--R     [0.23000000000000001, 4.1290300000000002E-2, 4.1290349454660515E-2,
--R      4.9454660512593396E-8]
--R     ,
--R    [0.23999999999999999,4.08571E-2,4.0857124978128601E-2,2.4978128600194882E-8]
--R     ,
--R    [0.25,4.0428499999999999E-2,4.0428459450774591E-2,- 4.0549225407970901E-8],
--R    [0.26000000000000001,4.00043E-2,4.0004304738165339E-2,4.7381653392464251E-9]
--R     ,
--R
--R     [0.27000000000000002, 3.9584599999999998E-2, 3.9584613215981258E-2,
--R      1.3215981260750187E-8]
--R     ,
--R
--R     [0.28000000000000003, 3.9169299999999997E-2, 3.916933776458735E-2,
--R      3.7764587353106283E-8]
--R     ,
--R
--R     [0.28999999999999998, 3.8758399999999998E-2, 3.8758431763662324E-2,
--R      3.1763662325379194E-8]
--R     ,
--R
--R     [0.29999999999999999, 3.8351799999999998E-2, 3.8351849086885194E-2,
--R      4.908688519544846E-8]
--R     ,
--R    [0.31,3.7949499999999997E-2,3.7949544096678632E-2,4.4096678634975017E-8],
--R
--R     [0.32000000000000001, 3.7551500000000002E-2, 3.7551471639008578E-2,
--R      - 2.8360991423392878E-8]
--R     ,
--R
--R     [0.33000000000000002, 3.7157599999999999E-2, 3.7157587038239355E-2,
--R      - 1.2961760643970255E-8]
--R     ,
--R
--R     [0.34000000000000002, 3.6767800000000003E-2, 3.6767846092043928E-2,
--R      4.6092043924639281E-8]
--R     ,
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--R    [1.77,8.1659999999999996E-3,8.1660418929936432E-3,4.1892993643544152E-8],
--R    [1.78,8.0806999999999997E-3,8.0807391765421923E-3,3.9176542192612129E-8],
--R    [1.79,7.9962999999999996E-3,7.9963297284055979E-3,2.9728405598339336E-8],
--R    [1.8,7.9127999999999993E-3,7.9128041690543771E-3,4.1690543777644917E-9],
--R
--R     [1.8100000000000001, 7.8302000000000007E-3, 7.8301532177440097E-3,
--R      - 4.6782255990959754E-8]
--R     ,
--R
--R     [1.8200000000000001, 7.7483999999999999E-3, 7.7483676914710427E-3,
--R      - 3.2308528957226967E-8]
--R     ,
--R
--R     [1.8300000000000001, 7.6674000000000004E-3, 7.6674385039402267E-3,
--R      3.8503940226301825E-8]
--R     ,
--R
--R     [1.8400000000000001, 7.5874000000000002E-3, 7.5873566645426526E-3,
--R      - 4.3335457347581929E-8]
--R     ,
--R
--R     [1.8500000000000001, 7.5081000000000002E-3, 7.50811327734469E-3,
--R      1.327734468984515E-8]
--R     ,
--R    [1.8600000000000001,7.4297E-3,7.429699540087673E-3,- 4.5991232697217832E-10]
--R     ,
--R
--R     [1.8700000000000001, 7.3521000000000003E-3, 7.3521067431981824E-3,
--R      6.743198182126986E-9]
--R     ,
--R
--R     [1.8799999999999999, 7.2753000000000002E-3, 7.2753262688088375E-3,
--R      2.6268808837361102E-8]
--R     ,
--R
--R     [1.8899999999999999, 7.1992999999999996E-3, 7.1993495897894446E-3,
--R      4.9589789444942634E-8]
--R     ,
--R
--R     [1.8999999999999999, 7.1241999999999998E-3, 7.1241682687884587E-3,
--R      - 3.1731211541131954E-8]
--R     ,
--R
--R     [1.9099999999999999, 7.0498000000000002E-3, 7.049773957284575E-3,
--R      - 2.6042715425139695E-8]
--R     ,
--R
--R     [1.9199999999999999, 6.9762000000000001E-3, 6.9761583946483935E-3,
--R      - 4.1605351606618934E-8]
--R     ,
--R
--R     [1.9299999999999999, 6.9033000000000002E-3, 6.9033134072140311E-3,
--R      1.3407214030820847E-8]
--R     ,
--R
--R     [1.9399999999999999, 6.8311999999999999E-3, 6.8312309073605745E-3,
--R      3.0907360574518317E-8]
--R     ,
--R    [1.95,6.7599000000000001E-3,6.759902892603269E-3,2.8926032688905701E-9],
--R    [1.96,6.6892999999999996E-3,6.6893214446943419E-3,2.1444694342336035E-8],
--R    [1.97,6.6195000000000004E-3,6.6194787287333721E-3,- 2.1271266628306029E-8],
--R    [1.98,6.5503999999999996E-3,6.5503669922870687E-3,- 3.3007712930965827E-8],
--R    [1.99,6.4819999999999999E-3,6.4819785645183897E-3,- 2.1435481610196372E-8],
--R    [2.,6.4143000000000004E-3,6.4143058553248998E-3,5.8553248994189233E-9]]
--R                               Type: List List OnePointCompletion DoubleFloat
--E 7
)spool 
 
Starts dribbling to sqmatrix.output (2010/3/27, 18:40:59).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 6
)set expose add constructor SquareMatrix
 
   SquareMatrix is now explicitly exposed in frame initial 
--R 
--R   SquareMatrix is now explicitly exposed in frame initial 
--E 1

--S 2 of 6
m := squareMatrix [[1,-%i],[%i,4]]
 

        +1   - %i+
   (1)  |        |
        +%i   4  +
                                        Type: SquareMatrix(2,Complex Integer)
--R 
--R
--R        +1   - %i+
--R   (1)  |        |
--R        +%i   4  +
--R                                        Type: SquareMatrix(2,Complex Integer)
--E 2

--S 3 of 6
m*m - m
 

        + 1   - 4%i+
   (2)  |          |
        +4%i   13  +
                                        Type: SquareMatrix(2,Complex Integer)
--R 
--R
--R        + 1   - 4%i+
--R   (2)  |          |
--R        +4%i   13  +
--R                                        Type: SquareMatrix(2,Complex Integer)
--E 3

--S 4 of 6
mm := squareMatrix [[m, 1], [1-m, m**2]]
 

        ++1   - %i+      +1  0+   +
        ||        |      |    |   |
        |+%i   4  +      +0  1+   |
   (3)  |                         |
        |+ 0    %i +  + 2   - 5%i+|
        ||         |  |          ||
        ++- %i  - 3+  +5%i   17  ++
                        Type: SquareMatrix(2,SquareMatrix(2,Complex Integer))
--R 
--R
--R        ++1   - %i+      +1  0+   +
--R        ||        |      |    |   |
--R        |+%i   4  +      +0  1+   |
--R   (3)  |                         |
--R        |+ 0    %i +  + 2   - 5%i+|
--R        ||         |  |          ||
--R        ++- %i  - 3+  +5%i   17  ++
--R                        Type: SquareMatrix(2,SquareMatrix(2,Complex Integer))
--E 4

--S 5 of 6
p := (x + m)**2
 

         2   + 2   - 2%i+    + 2   - 5%i+
   (4)  x  + |          |x + |          |
             +2%i    8  +    +5%i   17  +
                             Type: Polynomial SquareMatrix(2,Complex Integer)
--R 
--R
--R         2   + 2   - 2%i+    + 2   - 5%i+
--R   (4)  x  + |          |x + |          |
--R             +2%i    8  +    +5%i   17  +
--R                             Type: Polynomial SquareMatrix(2,Complex Integer)
--E 5

--S 6 of 6
p::SquareMatrix(2, ?)
 

        + 2                        +
        |x  + 2x + 2  - 2%i x - 5%i|
   (5)  |                          |
        |              2           |
        +2%i x + 5%i  x  + 8x + 17 +
                             Type: SquareMatrix(2,Polynomial Complex Integer)
--R 
--R
--R        + 2                        +
--R        |x  + 2x + 2  - 2%i x - 5%i|
--R   (5)  |                          |
--R        |              2           |
--R        +2%i x + 5%i  x  + 8x + 17 +
--R                             Type: SquareMatrix(2,Polynomial Complex Integer)
--E 6
)spool 
 
Starts dribbling to defintrf.output (2010/3/27, 18:24:54).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 3
f := (x**4 - 3*x**2 + 6)/(x**6-5*x**4+5*x**2+4)
 

            4     2
           x  - 3x  + 6
   (1)  ------------------
         6     4     2
        x  - 5x  + 5x  + 4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R            4     2
--R           x  - 3x  + 6
--R   (1)  ------------------
--R         6     4     2
--R        x  - 5x  + 5x  + 4
--R                                            Type: Fraction Polynomial Integer
--E 1

--S 2 of 3
integrate(f, x = 1..2)
 

                                               1
        2atan(8) + 2atan(5) + 2atan(2) + 2atan(-) - %pi
                                               2
   (2)  -----------------------------------------------
                               2
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R                                               1
--R        2atan(8) + 2atan(5) + 2atan(2) + 2atan(-) - %pi
--R                                               2
--R   (2)  -----------------------------------------------
--R                               2
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 2

--S 3 of 3
numeric %
 

   (3)  2.8198420991 931510451
                                                                  Type: Float
--R 
--R
--R   (3)  2.8198420991 931510451
--R                                                                  Type: Float
--E 3
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read xpoly
 
)cl all
 

poly := XPolynomial(Integer)
 

   (1)  XPolynomial Integer
                                                                 Type: Domain
pr: poly := 2*x + 3*y-5
 

   (2)  - 5 + x 2 + y 3
                                                    Type: XPolynomial Integer
pr2: poly := pr*pr
 

   (3)  25 + x(- 20 + x 4 + y 6) + y(- 30 + x 6 + y 9)
                                                    Type: XPolynomial Integer
pd  := expand pr
 

   (4)  - 5 + 2x + 3y
                                 Type: XDistributedPolynomial(Symbol,Integer)
pd2 := pd*pd
 

                           2                   2
   (5)  25 - 20x - 30y + 4x  + 6x y + 6y x + 9y
                                 Type: XDistributedPolynomial(Symbol,Integer)
expand(pr2) - pd2
 

   (6)  0
                                 Type: XDistributedPolynomial(Symbol,Integer)
qr :=  pr**3
 

   (7)
     - 125 + x(150 + x(- 60 + x 8 + y 12) + y(- 90 + x 12 + y 18))
   + 
     y(225 + x(- 90 + x 12 + y 18) + y(- 135 + x 18 + y 27))
                                                    Type: XPolynomial Integer
qd :=  pd**3
 trunc(qd,2)
 
   There are 2 exposed and 0 unexposed library operations named trunc 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op trunc
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
 
Daly Bug
   Cannot find a definition or applicable library operation named trunc
      with argument type(s) 
                                 Variable qd
                               PositiveInteger
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
trunc(qr,2)
 

   (8)  - 125 + x(150 + x(- 60) + y(- 90)) + y(225 + x(- 90) + y(- 135))
                                                    Type: XPolynomial Integer
Word := OrderedFreeMonoid Symbol
 

   (9)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
w: Word := x*y**2
 

            2
   (10)  x y
                                               Type: OrderedFreeMonoid Symbol
rquo(qr,w)
 

   (11)  18
                                                    Type: XPolynomial Integer
sh(pr,w::poly)
 

   (12)  x(x y y 4 + y(x y 2 + y(- 5 + x 2 + y 9))) + y x y y 3
                                                    Type: XPolynomial Integer
)lisp (bye)
 
Starts dribbling to pfr.output (2010/3/27, 18:30:47).
)set message test on
 
)set message auto off
 
)clear all
 
 
)set out len 57
 
)time off
 
--S 1 of 16
partialFraction(1,factor factorial 10)
 

        159   23   12   1
   (1)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                            Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (1)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                            Type: PartialFraction Integer
--E 1

--S 2 of 16
f := padicFraction %
 

   (2)
   1    1    1    1    1    1    2    1    2   2    2   1
   - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
   2    4    5    6    7    8    2    3    4   5    2   7
       2    2    2    2    2    3    3    3        5
                            Type: PartialFraction Integer
--R 
--R
--R   (2)
--R   1    1    1    1    1    1    2    1    2   2    2   1
--R   - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
--R   2    4    5    6    7    8    2    3    4   5    2   7
--R       2    2    2    2    2    3    3    3        5
--R                            Type: PartialFraction Integer
--E 2

--S 3 of 16
compactFraction %
 

        159   23   12   1
   (3)  --- - -- - -- + -
          8    4    2   7
         2    3    5
                            Type: PartialFraction Integer
--R 
--R
--R        159   23   12   1
--R   (3)  --- - -- - -- + -
--R          8    4    2   7
--R         2    3    5
--R                            Type: PartialFraction Integer
--E 3

--S 4 of 16
numberOfFractionalTerms f
 

   (4)  12
                                    Type: PositiveInteger
--R 
--R
--R   (4)  12
--R                                    Type: PositiveInteger
--E 4

--S 5 of 16
wholePart f
 

   (5)  0
                                 Type: NonNegativeInteger
--R 
--R
--R   (5)  0
--R                                 Type: NonNegativeInteger
--E 5

--S 6 of 16
t3 := nthFractionalTerm(f,3)
 

         1
   (6)  --
         5
        2
                            Type: PartialFraction Integer
--R 
--R
--R         1
--R   (6)  --
--R         5
--R        2
--R                            Type: PartialFraction Integer
--E 6

--S 7 of 16
firstNumer t3
 

   (7)  1
                                    Type: PositiveInteger
--R 
--R
--R   (7)  1
--R                                    Type: PositiveInteger
--E 7

--S 8 of 16
firstDenom t3
 

         5
   (8)  2
                                   Type: Factored Integer
--R 
--R
--R         5
--R   (8)  2
--R                                   Type: Factored Integer
--E 8

--S 9 of 16
g := - 13 + 14 * %i
 

   (9)  - 13 + 14%i
                                    Type: Complex Integer
--R 
--R
--R   (9)  - 13 + 14%i
--R                                    Type: Complex Integer
--E 9

--S 10 of 16
1/g
 

               %i
   (10)  - ---------
           14 + 13%i
                           Type: Fraction Complex Integer
--R 
--R
--R               %i
--R   (10)  - ---------
--R           14 + 13%i
--R                           Type: Fraction Complex Integer
--E 10

--S 11 of 16
partialFraction(1,factor g)
 

              1         4
   (11)  - ------- + -------
           1 + 2%i   3 + 8%i
                    Type: PartialFraction Complex Integer
--R 
--R
--R              1         4
--R   (11)  - ------- + -------
--R           1 + 2%i   3 + 8%i
--R                    Type: PartialFraction Complex Integer
--E 11

--S 12 of 16
% :: FRAC COMPLEX INT
 

               %i
   (12)  - ---------
           14 + 13%i
                           Type: Fraction Complex Integer
--R 
--R
--R               %i
--R   (12)  - ---------
--R           14 + 13%i
--R                           Type: Fraction Complex Integer
--E 12

--S 13 of 16
% :: COMPLEX FRAC INT
 

            13    14
   (13)  - --- - --- %i
           365   365
                           Type: Complex Fraction Integer
--R 
--R
--R            13    14
--R   (13)  - --- - --- %i
--R           365   365
--R                           Type: Complex Fraction Integer
--E 13

)clear all
 

--S 14 of 16
u : FR UP(x,FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 0..4])
 

                      2       3       4
   (1)  (x + 1)(x + 2) (x + 3) (x + 4)
  Type: Factored UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R                      2       3       4
--R   (1)  (x + 1)(x + 2) (x + 3) (x + 4)
--R  Type: Factored UnivariatePolynomial(x,Fraction Integer)
--E 14

--S 15 of 16
partialFraction(1,u)
 

   (2)
       1     1      7     17  2         139
      ---    - x + --   - -- x  - 12x - ---
      648    4     16      8             8
     ----- + -------- + -------------------
     x + 1          2                3
             (x + 2)          (x + 3)
   + 
     607  3   10115  2   391     44179
     --- x  + ----- x  + --- x + -----
     324       432        4       324
     ---------------------------------
                         4
                  (x + 4)
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (2)
--R       1     1      7     17  2         139
--R      ---    - x + --   - -- x  - 12x - ---
--R      648    4     16      8             8
--R     ----- + -------- + -------------------
--R     x + 1          2                3
--R             (x + 2)          (x + 3)
--R   + 
--R     607  3   10115  2   391     44179
--R     --- x  + ----- x  + --- x + -----
--R     324       432        4       324
--R     ---------------------------------
--R                         4
--R                  (x + 4)
--RType: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 15

--S 16 of 16
padicFraction %
 

   (3)
       1       1         1        17        3          1
      ---      -        --        --        -          -
      648      4        16         8        4          2
     ----- + ----- - -------- - ----- + -------- - --------
     x + 1   x + 2          2   x + 3          2          3
                     (x + 2)            (x + 3)    (x + 3)
   + 
      607       403        13          1
      ---       ---        --         --
      324       432        36         12
     ----- + -------- + -------- + --------
     x + 4          2          3          4
             (x + 4)    (x + 4)    (x + 4)
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R   (3)
--R       1       1         1        17        3          1
--R      ---      -        --        --        -          -
--R      648      4        16         8        4          2
--R     ----- + ----- - -------- - ----- + -------- - --------
--R     x + 1   x + 2          2   x + 3          2          3
--R                     (x + 2)            (x + 3)    (x + 3)
--R   + 
--R      607       403        13          1
--R      ---       ---        --         --
--R      324       432        36         12
--R     ----- + -------- + -------- + --------
--R     x + 4          2          3          4
--R             (x + 4)    (x + 4)    (x + 4)
--RType: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 16
)spool 
 
Starts dribbling to schaum31.output (2010/3/27, 18:38:44).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 46
aa:=integrate(coth(a*x),x)
 

                    2sinh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2sinh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 46
bb:=1/a*log(sinh(a*x))
 

        log(sinh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 3 of 46
cc:=aa-bb
 

                                       2sinh(a x)
        - log(sinh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2sinh(a x)
--R        - log(sinh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 4 of 46
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 5 of 46      14:615 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 6 of 46
aa:=integrate(coth(a*x)^2,x)
 

        (a x + 1)sinh(a x) - cosh(a x)
   (1)  ------------------------------
                  a sinh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        (a x + 1)sinh(a x) - cosh(a x)
--R   (1)  ------------------------------
--R                  a sinh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7 of 46
bb:=x-coth(a*x)/a
 

        - coth(a x) + a x
   (2)  -----------------
                a
                                                     Type: Expression Integer
--R
--R        - coth(a x) + a x
--R   (2)  -----------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 8 of 46
cc:=aa-bb
 

        (coth(a x) + 1)sinh(a x) - cosh(a x)
   (3)  ------------------------------------
                     a sinh(a x)
                                                     Type: Expression Integer
--R
--R        (coth(a x) + 1)sinh(a x) - cosh(a x)
--R   (3)  ------------------------------------
--R                     a sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 9 of 46      14:616 Schaums and Axiom differ by a constant
dd:=complexNormalize cc
 

        1
   (4)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (4)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 10 of 46
aa:=integrate(coth(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                      4                          3
       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
     + 
                        2                     2
       (- 6a x cosh(a x)  + 2a x - 2)sinh(a x)
     + 
                        3                                                4
       (- 4a x cosh(a x)  + (4a x - 4)cosh(a x))sinh(a x) - a x cosh(a x)
     + 
                          2
       (2a x - 2)cosh(a x)  - a x
  /
                  4                        3                2               2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  - 2a)sinh(a x)
     + 
                  3                                       4               2
     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                      4                          3
--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
--R     + 
--R                        2                     2
--R       (- 6a x cosh(a x)  + 2a x - 2)sinh(a x)
--R     + 
--R                        3                                                4
--R       (- 4a x cosh(a x)  + (4a x - 4)cosh(a x))sinh(a x) - a x cosh(a x)
--R     + 
--R                          2
--R       (2a x - 2)cosh(a x)  - a x
--R  /
--R                  4                        3                2               2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  - 2a)sinh(a x)
--R     + 
--R                  3                                       4               2
--R     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 11 of 46
bb:=1/a*log(sinh(a*x)-coth(a*x)^2)/(2*a)
 

                                 2
        log(sinh(a x) - coth(a x) )
   (2)  ---------------------------
                      2
                    2a
                                                     Type: Expression Integer
--R
--R                                 2
--R        log(sinh(a x) - coth(a x) )
--R   (2)  ---------------------------
--R                      2
--R                    2a
--R                                                     Type: Expression Integer
--E

--S 12 of 46     14:617 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                      4                      3                2              2
           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
         + 
                        3                                   4             2
           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
      *
                                  2
         log(sinh(a x) - coth(a x) )
     + 
                       4                        3
           2a sinh(a x)  + 8a cosh(a x)sinh(a x)
         + 
                         2               2
           (12a cosh(a x)  - 4a)sinh(a x)
         + 
                        3                                        4
           (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)
         + 
                         2
           - 4a cosh(a x)  + 2a
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
           2           4     2                    3
       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
     + 
             2           2     2                2
       (- 12a x cosh(a x)  + 4a x - 4a)sinh(a x)
     + 
            2           3      2                               2           4
       (- 8a x cosh(a x)  + (8a x - 8a)cosh(a x))sinh(a x) - 2a x cosh(a x)
     + 
          2                2     2
       (4a x - 4a)cosh(a x)  - 2a x
  /
         2         4     2                  3       2         2     2          2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a )sinh(a x)
     + 
          2         3     2                        2         4     2         2
       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
     + 
         2
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                      4                      3                2              2
--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                        3                                   4             2
--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
--R      *
--R                                  2
--R         log(sinh(a x) - coth(a x) )
--R     + 
--R                       4                        3
--R           2a sinh(a x)  + 8a cosh(a x)sinh(a x)
--R         + 
--R                         2               2
--R           (12a cosh(a x)  - 4a)sinh(a x)
--R         + 
--R                        3                                        4
--R           (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)
--R         + 
--R                         2
--R           - 4a cosh(a x)  + 2a
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R           2           4     2                    3
--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
--R     + 
--R             2           2     2                2
--R       (- 12a x cosh(a x)  + 4a x - 4a)sinh(a x)
--R     + 
--R            2           3      2                               2           4
--R       (- 8a x cosh(a x)  + (8a x - 8a)cosh(a x))sinh(a x) - 2a x cosh(a x)
--R     + 
--R          2                2     2
--R       (4a x - 4a)cosh(a x)  - 2a x
--R  /
--R         2         4     2                  3       2         2     2          2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a )sinh(a x)
--R     + 
--R          2         3     2                        2         4     2         2
--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
--R     + 
--R         2
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 13 of 46
aa:=integrate(coth(a*x)^n*csch(a*x)^2,x)
 

                              cosh(a x)                         cosh(a x)
        - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
                              sinh(a x)                         sinh(a x)
   (1)  -------------------------------------------------------------------
                                 (a n + a)sinh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                              cosh(a x)                         cosh(a x)
--R        - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
--R                              sinh(a x)                         sinh(a x)
--R   (1)  -------------------------------------------------------------------
--R                                 (a n + a)sinh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 14 of 46
bb:=-coth(a*x)^(n+1)/((n+1)*a)
 

                   n + 1
          coth(a x)
   (2)  - --------------
              a n + a
                                                     Type: Expression Integer
--R
--R                   n + 1
--R          coth(a x)
--R   (2)  - --------------
--R              a n + a
--R                                                     Type: Expression Integer
--E

--S 15 of 46
cc:=aa-bb
 

   (3)
                             cosh(a x)                         cosh(a x)
       - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
                             sinh(a x)                         sinh(a x)
     + 
                         n + 1
       sinh(a x)coth(a x)
  /
     (a n + a)sinh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                             cosh(a x)                         cosh(a x)
--R       - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
--R                             sinh(a x)                         sinh(a x)
--R     + 
--R                         n + 1
--R       sinh(a x)coth(a x)
--R  /
--R     (a n + a)sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 16 of 46
dd:=expandLog cc
 

   (4)
       cosh(a x)sinh(n log(sinh(a x)) - n log(cosh(a x)))
     + 
       - cosh(a x)cosh(n log(sinh(a x)) - n log(cosh(a x)))
     + 
                         n + 1
       sinh(a x)coth(a x)
  /
     (a n + a)sinh(a x)
                                                     Type: Expression Integer
--R
--R   (4)
--R       cosh(a x)sinh(n log(sinh(a x)) - n log(cosh(a x)))
--R     + 
--R       - cosh(a x)cosh(n log(sinh(a x)) - n log(cosh(a x)))
--R     + 
--R                         n + 1
--R       sinh(a x)coth(a x)
--R  /
--R     (a n + a)sinh(a x)
--R                                                     Type: Expression Integer
--E

--S 17 of 46     14:618 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 18 of 46
aa:=integrate(csch(a*x)^2/coth(a*x),x)
 

                      2cosh(a x)                     2sinh(a x)
        - log(- ---------------------) + log(- ---------------------)
                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   (1)  -------------------------------------------------------------
                                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2cosh(a x)                     2sinh(a x)
--R        - log(- ---------------------) + log(- ---------------------)
--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   (1)  -------------------------------------------------------------
--R                                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 19 of 46
bb:=-1/a*log(coth(a*x))
 

          log(coth(a x))
   (2)  - --------------
                 a
                                                     Type: Expression Integer
--R
--R          log(coth(a x))
--R   (2)  - --------------
--R                 a
--R                                                     Type: Expression Integer
--E

--S 20 of 46
cc:=aa-bb
 

   (3)
                                2cosh(a x)                     2sinh(a x)
   log(coth(a x)) - log(- ---------------------) + log(- ---------------------)
                          sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   ----------------------------------------------------------------------------
                                         a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                2cosh(a x)                     2sinh(a x)
--R   log(coth(a x)) - log(- ---------------------) + log(- ---------------------)
--R                          sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   ----------------------------------------------------------------------------
--R                                         a
--R                                                     Type: Expression Integer
--E

--S 21 of 46
dd:=expandLog cc
 

        log(sinh(a x)) + log(coth(a x)) - log(cosh(a x))
   (4)  ------------------------------------------------
                                a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x)) + log(coth(a x)) - log(cosh(a x))
--R   (4)  ------------------------------------------------
--R                                a
--R                                                     Type: Expression Integer
--E

--S 22 of 46     14:619 Schaums and Axiom agree
ee:=complexNormalize dd
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 23 of 46
aa:=integrate(1/coth(a*x),x)
 

                    2cosh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2cosh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 46
bb:=1/a*log(cosh(a*x))
 

        log(cosh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(cosh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 25 of 46
cc:=aa-bb
 

                                       2cosh(a x)
        - log(cosh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2cosh(a x)
--R        - log(cosh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 26 of 46
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 27 of 46     14:620 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 46     14:621 Axiom cannot compute this integral
aa:=integrate(x*coth(a*x),x)
 

           x
         ++
   (1)   |   %O coth(%O a)d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O coth(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 29 of 46
aa:=integrate(x*coth(a*x)^2,x)
 

   (1)
                    2                                   2
         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  - 2)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
         2 2                 2      2 2
       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
     + 
         2 2                 2    2 2
       (a x  - 4a x)cosh(a x)  - a x
  /
       2         2     2                       2         2     2
     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    2                                   2
--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  - 2)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R         2 2                 2      2 2
--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
--R     + 
--R         2 2                 2    2 2
--R       (a x  - 4a x)cosh(a x)  - a x
--R  /
--R       2         2     2                       2         2     2
--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 30 of 46
bb:=x^2/2-(x*coth(a*x)/a)+1/a^2*log(sinh(a*x))
 

                                            2 2
        2log(sinh(a x)) - 2a x coth(a x) + a x
   (2)  ---------------------------------------
                            2
                          2a
                                                     Type: Expression Integer
--R
--R                                            2 2
--R        2log(sinh(a x)) - 2a x coth(a x) + a x
--R   (2)  ---------------------------------------
--R                            2
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 31 of 46
cc:=aa-bb
 

   (3)
                   2                                  2
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
      *
                     2sinh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                                      2
       (a x coth(a x) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
     + 
                     2                                 2
       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
--R      *
--R                     2sinh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                                      2
--R       (a x coth(a x) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
--R     + 
--R                     2                                 2
--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 32 of 46
dd:=expandLog cc
 

   (4)
                     2                                  2
         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
      *
         log(sinh(a x) - cosh(a x))
     + 
                                                 2
       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
                     2                                             2
       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
                                                     Type: Expression Integer
--R
--R   (4)
--R                     2                                  2
--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R                                                 2
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R                     2                                             2
--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
--R                                                     Type: Expression Integer
--E

--S 33 of 46
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (5)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (5)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 34 of 46
ee:=sinhsqrrule dd
 

   (6)
                                                         2
         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
      *
         log(sinh(a x) - cosh(a x))
     + 
       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
     + 
                                       2
       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
     + 
                                                                2
       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
     + 
       2a x
  /
       2                      2               2         2     2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
                                                     Type: Expression Integer
--R
--R   (6)
--R                                                         2
--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
--R      *
--R         log(sinh(a x) - cosh(a x))
--R     + 
--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
--R     + 
--R                                       2
--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
--R     + 
--R                                                                2
--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
--R     + 
--R       2a x
--R  /
--R       2                      2               2         2     2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
--R                                                     Type: Expression Integer
--E

--S 35 of 46
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (7)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (7)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 36 of 46
ff:=coshsqrrule ee
 

   (8)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 37 of 46
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (9)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %L sinh(y + x) - %L sinh(y - x)
--I   (9)  %L cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38 of 46
gg:=sinhcoshrule ff
 

   (10)
       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
     + 
       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
     + 
       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) - a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
--R     + 
--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) - a
--R                                                     Type: Expression Integer
--E

--S 39 of 46     14:622 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         - log(- 1) + log(- 2)
   (11)  ---------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R         - log(- 1) + log(- 2)
--R   (11)  ---------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 40 of 46     14:623 Axiom cannot compute this integral
aa:=integrate(coth(a*x)/x,x)
 

           x
         ++  coth(%O a)
   (1)   |   ---------- d%O
        ++       %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  coth(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 41 of 46
aa:=integrate(1/(p+q*coth(a*x)),x)
 

              - 2p sinh(a x) - 2q cosh(a x)
        q log(-----------------------------) + (- a q - a p)x
                  sinh(a x) - cosh(a x)
   (1)  -----------------------------------------------------
                                2      2
                             a q  - a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - 2p sinh(a x) - 2q cosh(a x)
--R        q log(-----------------------------) + (- a q - a p)x
--R                  sinh(a x) - cosh(a x)
--R   (1)  -----------------------------------------------------
--R                                2      2
--R                             a q  - a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42 of 46
bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(p*sinh(a*x)+q*cosh(a*x))
 

        q log(p sinh(a x) + q cosh(a x)) - a p x
   (2)  ----------------------------------------
                          2      2
                       a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(p sinh(a x) + q cosh(a x)) - a p x
--R   (2)  ----------------------------------------
--R                          2      2
--R                       a q  - a p
--R                                                     Type: Expression Integer
--E

--S 43 of 46
cc:=aa-bb
 

   (3)
                                                  - 2p sinh(a x) - 2q cosh(a x)
       - q log(p sinh(a x) + q cosh(a x)) + q log(-----------------------------)
                                                      sinh(a x) - cosh(a x)
     + 
       - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                  - 2p sinh(a x) - 2q cosh(a x)
--R       - q log(p sinh(a x) + q cosh(a x)) + q log(-----------------------------)
--R                                                      sinh(a x) - cosh(a x)
--R     + 
--R       - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 44 of 46
dd:=expandLog cc
 

   (4)
       - q log(p sinh(a x) + q cosh(a x)) - q log(sinh(a x) - cosh(a x))
     + 
       q log(- p sinh(a x) - q cosh(a x)) + q log(2) - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R       - q log(p sinh(a x) + q cosh(a x)) - q log(sinh(a x) - cosh(a x))
--R     + 
--R       q log(- p sinh(a x) - q cosh(a x)) + q log(2) - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 45 of 46     14:624 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        q log(2) - 2q log(- 1)
   (5)  ----------------------
                 2      2
              a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(2) - 2q log(- 1)
--R   (5)  ----------------------
--R                 2      2
--R              a q  - a p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 46 of 46     14:625 Axiom cannot compute this integral
aa:=integrate(coth(a*x)^n,x)
 

           x
         ++            n
   (1)   |   coth(%O a) d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   coth(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to magma.output (2010/3/27, 18:28:58).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 22
x:Symbol :='x
 

   (1)  x
                                                                 Type: Symbol
--R 
--R
--R   (1)  x
--R                                                                 Type: Symbol
--E 1

--S 2 of 22
y:Symbol :='y
 

   (2)  y
                                                                 Type: Symbol
--R 
--R
--R   (2)  y
--R                                                                 Type: Symbol
--E 2

--S 3 of 22
z:Symbol :='z
 

   (3)  z
                                                                 Type: Symbol
--R 
--R
--R   (3)  z
--R                                                                 Type: Symbol
--E 3

--S 4 of 22
word := OrderedFreeMonoid(Symbol)
 

   (4)  OrderedFreeMonoid Symbol
                                                                 Type: Domain
--R 
--R
--R   (4)  OrderedFreeMonoid Symbol
--R                                                                 Type: Domain
--E 4

--S 5 of 22
tree := Magma(Symbol)
 

   (5)  Magma Symbol
                                                                 Type: Domain
--R 
--R
--R   (5)  Magma Symbol
--R                                                                 Type: Domain
--E 5

--S 6 of 22
a:tree := x*x
 

   (6)  [x,x]
                                                           Type: Magma Symbol
--R 
--R
--R   (6)  [x,x]
--R                                                           Type: Magma Symbol
--E 6

--S 7 of 22
b:tree := y*y
 

   (7)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (7)  [y,y]
--R                                                           Type: Magma Symbol
--E 7

--S 8 of 22
c:tree := a*b
 

   (8)  [[x,x],[y,y]]
                                                           Type: Magma Symbol
--R 
--R
--R   (8)  [[x,x],[y,y]]
--R                                                           Type: Magma Symbol
--E 8

--S 9 of 22
left c
 

   (9)  [x,x]
                                                           Type: Magma Symbol
--R 
--R
--R   (9)  [x,x]
--R                                                           Type: Magma Symbol
--E 9

--S 10 of 22
right c
 

   (10)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (10)  [y,y]
--R                                                           Type: Magma Symbol
--E 10

--S 11 of 22
length c
 

   (11)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 22
c::word
 

          2 2
   (12)  x y
                                               Type: OrderedFreeMonoid Symbol
--R 
--R
--R          2 2
--R   (12)  x y
--R                                               Type: OrderedFreeMonoid Symbol
--E 12

--S 13 of 22
a < b
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 22
a < c
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 22
b < c
 

   (15)  true
                                                                Type: Boolean
--R 
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 22
first c
 

   (16)  x
                                                                 Type: Symbol
--R 
--R
--R   (16)  x
--R                                                                 Type: Symbol
--E 16

--S 17 of 22
rest c
 

   (17)  [x,[y,y]]
                                                           Type: Magma Symbol
--R 
--R
--R   (17)  [x,[y,y]]
--R                                                           Type: Magma Symbol
--E 17

--S 18 of 22
rest rest c
 

   (18)  [y,y]
                                                           Type: Magma Symbol
--R 
--R
--R   (18)  [y,y]
--R                                                           Type: Magma Symbol
--E 18

--S 19 of 22
ax:tree := a*x
 

   (19)  [[x,x],x]
                                                           Type: Magma Symbol
--R 
--R
--R   (19)  [[x,x],x]
--R                                                           Type: Magma Symbol
--E 19

--S 20 of 22
xa:tree := x*a
 

   (20)  [x,[x,x]]
                                                           Type: Magma Symbol
--R 
--R
--R   (20)  [x,[x,x]]
--R                                                           Type: Magma Symbol
--E 20

--S 21 of 22
xa < ax
 

   (21)  true
                                                                Type: Boolean
--R 
--R
--R   (21)  true
--R                                                                Type: Boolean
--E 21

--S 22 of 22
lexico(xa,ax)
 

   (22)  false
                                                                Type: Boolean
--R 
--R
--R   (22)  false
--R                                                                Type: Boolean
--E 22
)spool 
 
Starts dribbling to repa6.output (2010/3/27, 18:36:53).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 33
genA6 : List PERM INT := [cycle [1,2,3], cycle [2,3,4,5,6]]
 

   (1)  [(1 2 3),(2 3 4 5 6)]
                                               Type: List Permutation Integer
--R 
--R
--R   (1)  [(1 2 3),(2 3 4 5 6)]
--R                                               Type: List Permutation Integer
--E 1

--S 2 of 33
pRA6 := permutationRepresentation (genA6, 6)
 

         +0  0  1  0  0  0+ +1  0  0  0  0  0+
         |                | |                |
         |1  0  0  0  0  0| |0  0  0  0  0  1|
         |                | |                |
         |0  1  0  0  0  0| |0  1  0  0  0  0|
   (2)  [|                |,|                |]
         |0  0  0  1  0  0| |0  0  1  0  0  0|
         |                | |                |
         |0  0  0  0  1  0| |0  0  0  1  0  0|
         |                | |                |
         +0  0  0  0  0  1+ +0  0  0  0  1  0+
                                                    Type: List Matrix Integer
--R 
--R
--R         +0  0  1  0  0  0+ +1  0  0  0  0  0+
--R         |                | |                |
--R         |1  0  0  0  0  0| |0  0  0  0  0  1|
--R         |                | |                |
--R         |0  1  0  0  0  0| |0  1  0  0  0  0|
--R   (2)  [|                |,|                |]
--R         |0  0  0  1  0  0| |0  0  1  0  0  0|
--R         |                | |                |
--R         |0  0  0  0  1  0| |0  0  0  1  0  0|
--R         |                | |                |
--R         +0  0  0  0  0  1+ +0  0  0  0  1  0+
--R                                                    Type: List Matrix Integer
--E 2

--S 3 of 33
pRA6m2 : List Matrix PrimeField 2 := pRA6
 

         +0  0  1  0  0  0+ +1  0  0  0  0  0+
         |                | |                |
         |1  0  0  0  0  0| |0  0  0  0  0  1|
         |                | |                |
         |0  1  0  0  0  0| |0  1  0  0  0  0|
   (3)  [|                |,|                |]
         |0  0  0  1  0  0| |0  0  1  0  0  0|
         |                | |                |
         |0  0  0  0  1  0| |0  0  0  1  0  0|
         |                | |                |
         +0  0  0  0  0  1+ +0  0  0  0  1  0+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R         +0  0  1  0  0  0+ +1  0  0  0  0  0+
--R         |                | |                |
--R         |1  0  0  0  0  0| |0  0  0  0  0  1|
--R         |                | |                |
--R         |0  1  0  0  0  0| |0  1  0  0  0  0|
--R   (3)  [|                |,|                |]
--R         |0  0  0  1  0  0| |0  0  1  0  0  0|
--R         |                | |                |
--R         |0  0  0  0  1  0| |0  0  0  1  0  0|
--R         |                | |                |
--R         +0  0  0  0  0  1+ +0  0  0  0  1  0+
--R                                               Type: List Matrix PrimeField 2
--E 3
 
--S 4 of 33
sp0 := meatAxe pRA6m2
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

          +0  0  1  0  0+ +1  0  0  0  0+
          |             | |             |
          |1  0  0  0  0| |1  1  1  1  1|
          |             | |             |
   (4)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
          |             | |             |
          |0  0  0  1  0| |0  0  1  0  0|
          |             | |             |
          +0  0  0  0  1+ +0  0  0  1  0+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R          +0  0  1  0  0+ +1  0  0  0  0+
--R          |             | |             |
--R          |1  0  0  0  0| |1  1  1  1  1|
--R          |             | |             |
--R   (4)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
--R          |             | |             |
--R          |0  0  0  1  0| |0  0  1  0  0|
--R          |             | |             |
--R          +0  0  0  0  1+ +0  0  0  1  0+
--R                                          Type: List List Matrix PrimeField 2
--E 4
 
--S 5 of 33
dA6d1 := sp0.2
 

   (5)  [[1],[1]]
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (5)  [[1],[1]]
--R                                               Type: List Matrix PrimeField 2
--E 5

--S 6 of 33
sp1 := meatAxe sp0.1
 
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices
     Representation is not irreducible and it will be split:

                    +0  1  0  0+ +0  1  1  1+
                    |          | |          |
                    |0  0  1  0| |1  1  0  1|
   (6)  [[[1],[1]],[|          |,|          |]]
                    |1  0  0  0| |1  1  1  0|
                    |          | |          |
                    +0  0  0  1+ +1  1  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R     Representation is not irreducible and it will be split:
--R
--R                    +0  1  0  0+ +0  1  1  1+
--R                    |          | |          |
--R                    |0  0  1  0| |1  1  0  1|
--R   (6)  [[[1],[1]],[|          |,|          |]]
--R                    |1  0  0  0| |1  1  1  0|
--R                    |          | |          |
--R                    +0  0  0  1+ +1  1  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 6
 
--S 7 of 33
dA6d4a := sp1.2
 

         +0  1  0  0+ +0  1  1  1+
         |          | |          |
         |0  0  1  0| |1  1  0  1|
   (7)  [|          |,|          |]
         |1  0  0  0| |1  1  1  0|
         |          | |          |
         +0  0  0  1+ +1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R         +0  1  0  0+ +0  1  1  1+
--R         |          | |          |
--R         |0  0  1  0| |1  1  0  1|
--R   (7)  [|          |,|          |]
--R         |1  0  0  0| |1  1  1  0|
--R         |          | |          |
--R         +0  0  0  1+ +1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 7
 
--S 8 of 33 random input, FAILURE OK
isAbsolutelyIrreducible? dA6d4a
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (8)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (8)  true
--R                                                                Type: Boolean
--E 8

-- lambda : PRTITION := partition [2,2,1,1]
--S 9 of 33
lambda := [2,2,1,1]
 

   (9)  [2,2,1,1]
                                                   Type: List PositiveInteger
--R 
--R
--R   (9)  [2,2,1,1]
--R                                                   Type: List PositiveInteger
--E 9

--S 10 of 33
dimensionOfIrreducibleRepresentation lambda
 

   (10)  9
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  9
--R                                                        Type: PositiveInteger
--E 10


--S 11 of 33
d2211  := irreducibleRepresentation(lambda, genA6)
 

   (11)
    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
    |                                     | |                                 |
    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
    |                                     | |                                 |
    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
    |                                     | |                                 |
   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
    |                                     | |                                 |
    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
    |                                     | |                                 |
    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
    |                                     | |                                 |
    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
    |                                     | |                                 |
    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
                                                    Type: List Matrix Integer
--R 
--R
--R   (11)
--R    +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
--R    |                                     | |                                 |
--R    |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
--R    |                                     | |                                 |
--R   [|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
--R    |                                     | |                                 |
--R    |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
--R    |                                     | |                                 |
--R    |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
--R    |                                     | |                                 |
--R    +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
--R                                                    Type: List Matrix Integer
--E 11

--S 12 of 33
d2211m2 : List Matrix PrimeField 2 := d2211
 

          +1  0  0  1  1  0  0  0  0+ +0  0  1  0  0  0  1  0  0+
          |                         | |                         |
          |0  1  0  1  0  1  0  0  0| |0  0  0  0  1  0  1  0  0|
          |                         | |                         |
          |0  0  1  0  1  1  0  0  0| |0  0  0  0  0  1  1  0  0|
          |                         | |                         |
          |0  0  0  1  0  0  1  0  0| |0  0  0  0  0  0  1  1  0|
          |                         | |                         |
   (12)  [|0  0  0  0  1  0  0  1  0|,|0  0  0  0  0  0  1  0  1|]
          |                         | |                         |
          |0  0  0  0  0  1  0  0  1| |0  0  0  0  0  0  1  0  0|
          |                         | |                         |
          |0  0  0  1  0  0  0  0  0| |1  0  0  0  0  0  1  0  0|
          |                         | |                         |
          |0  0  0  0  1  0  0  0  0| |0  1  0  0  0  0  1  0  0|
          |                         | |                         |
          +0  0  0  0  0  1  0  0  0+ +0  0  0  1  0  0  1  0  0+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  0  1  1  0  0  0  0+ +0  0  1  0  0  0  1  0  0+
--R          |                         | |                         |
--R          |0  1  0  1  0  1  0  0  0| |0  0  0  0  1  0  1  0  0|
--R          |                         | |                         |
--R          |0  0  1  0  1  1  0  0  0| |0  0  0  0  0  1  1  0  0|
--R          |                         | |                         |
--R          |0  0  0  1  0  0  1  0  0| |0  0  0  0  0  0  1  1  0|
--R          |                         | |                         |
--R   (12)  [|0  0  0  0  1  0  0  1  0|,|0  0  0  0  0  0  1  0  1|]
--R          |                         | |                         |
--R          |0  0  0  0  0  1  0  0  1| |0  0  0  0  0  0  1  0  0|
--R          |                         | |                         |
--R          |0  0  0  1  0  0  0  0  0| |1  0  0  0  0  0  1  0  0|
--R          |                         | |                         |
--R          |0  0  0  0  1  0  0  0  0| |0  1  0  0  0  0  1  0  0|
--R          |                         | |                         |
--R          +0  0  0  0  0  1  0  0  0+ +0  0  0  1  0  0  1  0  0+
--R                                               Type: List Matrix PrimeField 2
--E 12

--S 13 of 33
sp2 := meatAxe d2211m2
 
   Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

                                       +1  0  0  0  0+ +1  1  1  0  0+
           +1  0  1  1+ +0  0  1  0+   |             | |             |
           |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
           |0  1  0  1| |1  1  1  1|   |             | |             |
   (13)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
           |1  1  0  0| |1  0  1  1|   |             | |             |
           |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
           +0  1  0  0+ +0  1  0  1+   |             | |             |
                                       +0  1  1  1  0+ +1  0  0  1  1+
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is singular
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R                                       +1  0  0  0  0+ +1  1  1  0  0+
--R           +1  0  1  1+ +0  0  1  0+   |             | |             |
--R           |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
--R           |0  1  0  1| |1  1  1  1|   |             | |             |
--R   (13)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
--R           |1  1  0  0| |1  0  1  1|   |             | |             |
--R           |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
--R           +0  1  0  0+ +0  1  0  1+   |             | |             |
--R                                       +0  1  1  1  0+ +1  0  0  1  1+
--R                                          Type: List List Matrix PrimeField 2
--E 13

--S 14 of 33
dA6d4b := sp2.1
 

          +1  0  1  1+ +0  0  1  0+
          |          | |          |
          |0  1  0  1| |1  1  1  1|
   (14)  [|          |,|          |]
          |1  1  0  0| |1  0  1  1|
          |          | |          |
          +0  1  0  0+ +0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  1  1+ +0  0  1  0+
--R          |          | |          |
--R          |0  1  0  1| |1  1  1  1|
--R   (14)  [|          |,|          |]
--R          |1  1  0  0| |1  0  1  1|
--R          |          | |          |
--R          +0  1  0  0+ +0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 14

--S 15 of 33 random generation, FAILURE OK.
isAbsolutelyIrreducible? dA6d4b
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (15)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (15)  true
--R                                                                Type: Boolean
--E 15

--S 16 of 33 random generation, FAILURE OK.
areEquivalent? ( dA6d4a , dA6d4b )
 
   Dimensions of kernels differ

   Representations are not equivalent.

   (16)  [0]
                                                    Type: Matrix PrimeField 2
--R 
--R   Dimensions of kernels differ
--R
--R   Representations are not equivalent.
--R
--R   (16)  [0]
--R                                                    Type: Matrix PrimeField 2
--E 16

--S 17 of 33
dA6d16 := tensorProduct ( dA6d4a , dA6d4b )
 

   (17)
    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
    |                                              |
    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
   [|                                              |,
    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
    |                                              |
    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
    |                                              |
    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
    |                                              |
    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
    |                                              |]
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
    |                                              |
    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (17)
--R    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R   [|                                              |,
--R    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
--R    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
--R    |                                              |
--R    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R    |                                              |]
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 17

--S 18 of 33
sp3 := meatAxe dA6d16
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is irreducible, but we don't know
       whether it is absolutely irreducible

   (18)
   [
      +0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0+
      |                                              |
      |0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
      |                                              |
      |1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
     [|                                              |,
      |0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
      |                                              |
      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0|
      |                                              |
      |0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1|
      |                                              |
      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0|
      |                                              |
      +0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0+
      +0  0  0  0  0  1  1  0  0  1  1  0  0  1  1  0+
      |                                              |
      |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
      |                                              |
      |0  0  0  0  1  1  1  0  1  1  1  0  1  1  1  0|
      |                                              |
      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
      |                                              |
      |0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0|
      |                                              |
      |0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1|
      |                                              |
      |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
      |                                              |
      |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
      |                                              |]
      |0  1  1  0  0  0  0  0  0  1  1  0  0  1  1  0|
      |                                              |
      |0  1  0  1  0  0  0  0  0  1  0  1  0  1  0  1|
      |                                              |
      |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
      |                                              |
      |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
      |                                              |
      |0  1  1  0  0  1  1  0  0  0  0  0  0  1  1  0|
      |                                              |
      |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
      |                                              |
      |1  1  1  0  1  1  1  0  0  0  0  0  1  1  1  0|
      |                                              |
      +0  1  1  1  0  1  1  1  0  0  0  0  0  1  1  1+
     ]
                                          Type: List List Matrix PrimeField 2
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is irreducible, but we don't know
--R       whether it is absolutely irreducible
--R
--R   (18)
--R   [
--R      +0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0+
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R     [|                                              |,
--R      |0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1|
--R      |                                              |
--R      |0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0|
--R      |                                              |
--R      +0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0+
--R      +0  0  0  0  0  1  1  0  0  1  1  0  0  1  1  0+
--R      |                                              |
--R      |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R      |                                              |
--R      |0  0  0  0  1  1  1  0  1  1  1  0  1  1  1  0|
--R      |                                              |
--R      |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1|
--R      |                                              |
--R      |0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0|
--R      |                                              |
--R      |0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1|
--R      |                                              |
--R      |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
--R      |                                              |
--R      |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
--R      |                                              |]
--R      |0  1  1  0  0  0  0  0  0  1  1  0  0  1  1  0|
--R      |                                              |
--R      |0  1  0  1  0  0  0  0  0  1  0  1  0  1  0  1|
--R      |                                              |
--R      |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
--R      |                                              |
--R      |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
--R      |                                              |
--R      |0  1  1  0  0  1  1  0  0  0  0  0  0  1  1  0|
--R      |                                              |
--R      |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R      |                                              |
--R      |1  1  1  0  1  1  1  0  0  0  0  0  1  1  1  0|
--R      |                                              |
--R      +0  1  1  1  0  1  1  1  0  0  0  0  0  1  1  1+
--R     ]
--R                                          Type: List List Matrix PrimeField 2
--E 18

--S 19 of 33
isAbsolutelyIrreducible? dA6d16
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   We have not found a one-dimensional kernel so far,
     as we do a random search you could try again

   (19)  false
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   We have not found a one-dimensional kernel so far,
--R     as we do a random search you could try again
--R
--R   (19)  false
--R                                                                Type: Boolean
--E 19

--S 20 of 33
gf4 := FiniteField(2,2)
 

   (20)  FiniteField(2,2)
                                                                 Type: Domain
--R 
--R
--R   (20)  FiniteField(2,2)
--R                                                                 Type: Domain
--E 20

--S 21 of 33
dA6d16gf4 : List Matrix gf4 := dA6d16
 

   (21)
    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
    |                                              |
    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
   [|                                              |,
    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
    |                                              |
    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
    |                                              |
    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
    |                                              |
    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
    |                                              |]
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
    |                                              |
    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (21)
--R    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R   [|                                              |,
--R    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
--R    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
--R    |                                              |
--R    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R    |                                              |]
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
--R                                           Type: List Matrix FiniteField(2,2)
--E 21

--S 22 of 33
sp4 := meatAxe dA6d16gf4
 
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is non-singular
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
   Fingerprint element in generated algebra is singular
     The generated cyclic submodule was not proper
     The generated cyclic submodule was not proper
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices

   (22)
   [
      +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
      |                                                          |
      |  0       0       %A    %A + 1    %A      %A      0     0 |
      |                                                          |
      |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
      |                                                          |
      |  %A    %A + 1    %A      1       %A      0       0     0 |
     [|                                                          |,
      |%A + 1    1       1       1       0       0     %A + 1  %A|
      |                                                          |
      |  0       0     %A + 1    1       0       0       %A    0 |
      |                                                          |
      |  1       0       1       1       0       0       0     0 |
      |                                                          |
      +  1       1       0       0       0       0       0     0 +
      +  1       0       %A      0       1       1       %A    %A + 1+
      |                                                              |
      |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
      |                                                              |
      |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
      |                                                              |
      |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
      |                                                              |]
      |  1       0     %A + 1    0       1       1       %A      %A  |
      |                                                              |
      |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
      |                                                              |
      |  0       0       1       0       0       1       0       1   |
      |                                                              |
      +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
     ,

      +0     1       1     %A + 1  0  0  0  0+
      |                                      |
      |1     1     %A + 1    0     0  0  0  0|
      |                                      |
      |%A    0       0       0     0  0  0  0|
      |                                      |
      |1     %A      0       0     0  0  0  0|
     [|                                      |,
      |%A  %A + 1    1       1     1  0  1  1|
      |                                      |
      |0     0       %A      1     0  1  0  1|
      |                                      |
      |%A    1       0       1     1  1  0  0|
      |                                      |
      +1     %A    %A + 1    %A    0  1  0  0+
      +%A + 1    1       %A      0       0     %A + 1    0       1   +
      |                                                              |
      |  0       %A      1       1       1       0     %A + 1    %A  |
      |                                                              |
      |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
      |                                                              |
      |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
      |                                                              |]
      |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
      |                                                              |
      |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
      |                                                              |
      |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
      |                                                              |
      +  %A      %A      %A      1       %A      %A      1     %A + 1+
     ]
                                      Type: List List Matrix FiniteField(2,2)
--R 
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is non-singular
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R   Fingerprint element in generated algebra is singular
--R     The generated cyclic submodule was not proper
--R     The generated cyclic submodule was not proper
--R     A proper cyclic submodule is found.
--R     Transition matrix computed
--R     The inverse of the transition matrix computed
--R     Now transform the matrices
--R
--R   (22)
--R   [
--R      +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
--R      |                                                          |
--R      |  0       0       %A    %A + 1    %A      %A      0     0 |
--R      |                                                          |
--R      |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
--R      |                                                          |
--R      |  %A    %A + 1    %A      1       %A      0       0     0 |
--R     [|                                                          |,
--R      |%A + 1    1       1       1       0       0     %A + 1  %A|
--R      |                                                          |
--R      |  0       0     %A + 1    1       0       0       %A    0 |
--R      |                                                          |
--R      |  1       0       1       1       0       0       0     0 |
--R      |                                                          |
--R      +  1       1       0       0       0       0       0     0 +
--R      +  1       0       %A      0       1       1       %A    %A + 1+
--R      |                                                              |
--R      |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
--R      |                                                              |
--R      |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
--R      |                                                              |
--R      |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
--R      |                                                              |]
--R      |  1       0     %A + 1    0       1       1       %A      %A  |
--R      |                                                              |
--R      |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
--R      |                                                              |
--R      |  0       0       1       0       0       1       0       1   |
--R      |                                                              |
--R      +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
--R     ,
--R
--R      +0     1       1     %A + 1  0  0  0  0+
--R      |                                      |
--R      |1     1     %A + 1    0     0  0  0  0|
--R      |                                      |
--R      |%A    0       0       0     0  0  0  0|
--R      |                                      |
--R      |1     %A      0       0     0  0  0  0|
--R     [|                                      |,
--R      |%A  %A + 1    1       1     1  0  1  1|
--R      |                                      |
--R      |0     0       %A      1     0  1  0  1|
--R      |                                      |
--R      |%A    1       0       1     1  1  0  0|
--R      |                                      |
--R      +1     %A    %A + 1    %A    0  1  0  0+
--R      +%A + 1    1       %A      0       0     %A + 1    0       1   +
--R      |                                                              |
--R      |  0       %A      1       1       1       0     %A + 1    %A  |
--R      |                                                              |
--R      |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
--R      |                                                              |
--R      |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
--R      |                                                              |]
--R      |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
--R      |                                                              |
--R      |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
--R      |                                                              |
--R      |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
--R      |                                                              |
--R      +  %A      %A      %A      1       %A      %A      1     %A + 1+
--R     ]
--R                                      Type: List List Matrix FiniteField(2,2)
--E 22

--S 23 of 33
dA6d8a : List Matrix gf4  := sp4.1
 

   (23)
    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
    |                                                          |
    |  0       0       %A    %A + 1    %A      %A      0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1       %A      0       0     0 |
   [|                                                          |,
    |%A + 1    1       1       1       0       0     %A + 1  %A|
    |                                                          |
    |  0       0     %A + 1    1       0       0       %A    0 |
    |                                                          |
    |  1       0       1       1       0       0       0     0 |
    |                                                          |
    +  1       1       0       0       0       0       0     0 +
    +  1       0       %A      0       1       1       %A    %A + 1+
    |                                                              |
    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
    |                                                              |
    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
    |                                                              |
    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
    |                                                              |]
    |  1       0     %A + 1    0       1       1       %A      %A  |
    |                                                              |
    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
    |                                                              |
    |  0       0       1       0       0       1       0       1   |
    |                                                              |
    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (23)
--R    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
--R    |                                                          |
--R    |  0       0       %A    %A + 1    %A      %A      0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1       %A      0       0     0 |
--R   [|                                                          |,
--R    |%A + 1    1       1       1       0       0     %A + 1  %A|
--R    |                                                          |
--R    |  0       0     %A + 1    1       0       0       %A    0 |
--R    |                                                          |
--R    |  1       0       1       1       0       0       0     0 |
--R    |                                                          |
--R    +  1       1       0       0       0       0       0     0 +
--R    +  1       0       %A      0       1       1       %A    %A + 1+
--R    |                                                              |
--R    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
--R    |                                                              |
--R    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
--R    |                                                              |
--R    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
--R    |                                                              |]
--R    |  1       0     %A + 1    0       1       1       %A      %A  |
--R    |                                                              |
--R    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
--R    |                                                              |
--R    |  0       0       1       0       0       1       0       1   |
--R    |                                                              |
--R    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
--R                                           Type: List Matrix FiniteField(2,2)
--E 23

--S 24 of 33
dA6d8b : List Matrix gf4  := sp4.2
 

   (24)
    +0     1       1     %A + 1  0  0  0  0+
    |                                      |
    |1     1     %A + 1    0     0  0  0  0|
    |                                      |
    |%A    0       0       0     0  0  0  0|
    |                                      |
    |1     %A      0       0     0  0  0  0|
   [|                                      |,
    |%A  %A + 1    1       1     1  0  1  1|
    |                                      |
    |0     0       %A      1     0  1  0  1|
    |                                      |
    |%A    1       0       1     1  1  0  0|
    |                                      |
    +1     %A    %A + 1    %A    0  1  0  0+
    +%A + 1    1       %A      0       0     %A + 1    0       1   +
    |                                                              |
    |  0       %A      1       1       1       0     %A + 1    %A  |
    |                                                              |
    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
    |                                                              |
    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
    |                                                              |]
    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
    |                                                              |
    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
    |                                                              |
    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
    |                                                              |
    +  %A      %A      %A      1       %A      %A      1     %A + 1+
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (24)
--R    +0     1       1     %A + 1  0  0  0  0+
--R    |                                      |
--R    |1     1     %A + 1    0     0  0  0  0|
--R    |                                      |
--R    |%A    0       0       0     0  0  0  0|
--R    |                                      |
--R    |1     %A      0       0     0  0  0  0|
--R   [|                                      |,
--R    |%A  %A + 1    1       1     1  0  1  1|
--R    |                                      |
--R    |0     0       %A      1     0  1  0  1|
--R    |                                      |
--R    |%A    1       0       1     1  1  0  0|
--R    |                                      |
--R    +1     %A    %A + 1    %A    0  1  0  0+
--R    +%A + 1    1       %A      0       0     %A + 1    0       1   +
--R    |                                                              |
--R    |  0       %A      1       1       1       0     %A + 1    %A  |
--R    |                                                              |
--R    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
--R    |                                                              |
--R    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
--R    |                                                              |]
--R    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
--R    |                                                              |
--R    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
--R    |                                                              |
--R    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
--R    |                                                              |
--R    +  %A      %A      %A      1       %A      %A      1     %A + 1+
--R                                           Type: List Matrix FiniteField(2,2)
--E 24

--S 25 of 33 random generation, FAILURE OK.
isAbsolutelyIrreducible? dA6d8a
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (25)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (25)  true
--R                                                                Type: Boolean
--E 25

--S 26 of 33 random generation, FAILURE OK.
isAbsolutelyIrreducible? dA6d8b
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     We know that all the cyclic submodules generated by all
       non-trivial element of the singular matrix under view are
       not proper, hence Norton's irreducibility test can be done:
     The generated cyclic submodule was not proper
     Representation is absolutely irreducible

   (26)  true
                                                                Type: Boolean
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     We know that all the cyclic submodules generated by all
--R       non-trivial element of the singular matrix under view are
--R       not proper, hence Norton's irreducibility test can be done:
--R     The generated cyclic submodule was not proper
--R     Representation is absolutely irreducible
--R
--R   (26)  true
--R                                                                Type: Boolean
--E 26

--S 27 of 33 random generation, FAILURE OK.
areEquivalent? ( dA6d8a, dA6d8b )
 
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra does
     not have a one-dimensional kernel
   Random element in generated algebra has
     one-dimensional kernel
     There is no isomorphism, as the only possible one
       fails to do the necessary base change

   Representations are not equivalent.

   (27)  [0]
                                                Type: Matrix FiniteField(2,2)
--R 
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra does
--R     not have a one-dimensional kernel
--R   Random element in generated algebra has
--R     one-dimensional kernel
--R     There is no isomorphism, as the only possible one
--R       fails to do the necessary base change
--R
--R   Representations are not equivalent.
--R
--R   (27)  [0]
--R                                                Type: Matrix FiniteField(2,2)
--E 27

--S 28 of 33
dA6d1
 

   (28)  [[1],[1]]
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (28)  [[1],[1]]
--R                                               Type: List Matrix PrimeField 2
--E 28

--S 29 of 33
dA6d4a
 

          +0  1  0  0+ +0  1  1  1+
          |          | |          |
          |0  0  1  0| |1  1  0  1|
   (29)  [|          |,|          |]
          |1  0  0  0| |1  1  1  0|
          |          | |          |
          +0  0  0  1+ +1  1  1  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +0  1  0  0+ +0  1  1  1+
--R          |          | |          |
--R          |0  0  1  0| |1  1  0  1|
--R   (29)  [|          |,|          |]
--R          |1  0  0  0| |1  1  1  0|
--R          |          | |          |
--R          +0  0  0  1+ +1  1  1  1+
--R                                               Type: List Matrix PrimeField 2
--E 29

--S 30 of 33
dA6d4b
 

          +1  0  1  1+ +0  0  1  0+
          |          | |          |
          |0  1  0  1| |1  1  1  1|
   (30)  [|          |,|          |]
          |1  1  0  0| |1  0  1  1|
          |          | |          |
          +0  1  0  0+ +0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R          +1  0  1  1+ +0  0  1  0+
--R          |          | |          |
--R          |0  1  0  1| |1  1  1  1|
--R   (30)  [|          |,|          |]
--R          |1  1  0  0| |1  0  1  1|
--R          |          | |          |
--R          +0  1  0  0+ +0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 30

--S 31 of 33
dA6d8a
 

   (31)
    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
    |                                                          |
    |  0       0       %A    %A + 1    %A      %A      0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
    |                                                          |
    |  %A    %A + 1    %A      1       %A      0       0     0 |
   [|                                                          |,
    |%A + 1    1       1       1       0       0     %A + 1  %A|
    |                                                          |
    |  0       0     %A + 1    1       0       0       %A    0 |
    |                                                          |
    |  1       0       1       1       0       0       0     0 |
    |                                                          |
    +  1       1       0       0       0       0       0     0 +
    +  1       0       %A      0       1       1       %A    %A + 1+
    |                                                              |
    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
    |                                                              |
    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
    |                                                              |
    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
    |                                                              |]
    |  1       0     %A + 1    0       1       1       %A      %A  |
    |                                                              |
    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
    |                                                              |
    |  0       0       1       0       0       1       0       1   |
    |                                                              |
    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (31)
--R    +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
--R    |                                                          |
--R    |  0       0       %A    %A + 1    %A      %A      0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
--R    |                                                          |
--R    |  %A    %A + 1    %A      1       %A      0       0     0 |
--R   [|                                                          |,
--R    |%A + 1    1       1       1       0       0     %A + 1  %A|
--R    |                                                          |
--R    |  0       0     %A + 1    1       0       0       %A    0 |
--R    |                                                          |
--R    |  1       0       1       1       0       0       0     0 |
--R    |                                                          |
--R    +  1       1       0       0       0       0       0     0 +
--R    +  1       0       %A      0       1       1       %A    %A + 1+
--R    |                                                              |
--R    |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
--R    |                                                              |
--R    |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
--R    |                                                              |
--R    |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
--R    |                                                              |]
--R    |  1       0     %A + 1    0       1       1       %A      %A  |
--R    |                                                              |
--R    |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  |
--R    |                                                              |
--R    |  0       0       1       0       0       1       0       1   |
--R    |                                                              |
--R    +  0       %A      0       %A      1     %A + 1  %A + 1    %A  +
--R                                           Type: List Matrix FiniteField(2,2)
--E 31

--S 32 of 33
dA6d8b
 

   (32)
    +0     1       1     %A + 1  0  0  0  0+
    |                                      |
    |1     1     %A + 1    0     0  0  0  0|
    |                                      |
    |%A    0       0       0     0  0  0  0|
    |                                      |
    |1     %A      0       0     0  0  0  0|
   [|                                      |,
    |%A  %A + 1    1       1     1  0  1  1|
    |                                      |
    |0     0       %A      1     0  1  0  1|
    |                                      |
    |%A    1       0       1     1  1  0  0|
    |                                      |
    +1     %A    %A + 1    %A    0  1  0  0+
    +%A + 1    1       %A      0       0     %A + 1    0       1   +
    |                                                              |
    |  0       %A      1       1       1       0     %A + 1    %A  |
    |                                                              |
    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
    |                                                              |
    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
    |                                                              |]
    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
    |                                                              |
    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
    |                                                              |
    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
    |                                                              |
    +  %A      %A      %A      1       %A      %A      1     %A + 1+
                                           Type: List Matrix FiniteField(2,2)
--R 
--R
--R   (32)
--R    +0     1       1     %A + 1  0  0  0  0+
--R    |                                      |
--R    |1     1     %A + 1    0     0  0  0  0|
--R    |                                      |
--R    |%A    0       0       0     0  0  0  0|
--R    |                                      |
--R    |1     %A      0       0     0  0  0  0|
--R   [|                                      |,
--R    |%A  %A + 1    1       1     1  0  1  1|
--R    |                                      |
--R    |0     0       %A      1     0  1  0  1|
--R    |                                      |
--R    |%A    1       0       1     1  1  0  0|
--R    |                                      |
--R    +1     %A    %A + 1    %A    0  1  0  0+
--R    +%A + 1    1       %A      0       0     %A + 1    0       1   +
--R    |                                                              |
--R    |  0       %A      1       1       1       0     %A + 1    %A  |
--R    |                                                              |
--R    |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
--R    |                                                              |
--R    |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
--R    |                                                              |]
--R    |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
--R    |                                                              |
--R    |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
--R    |                                                              |
--R    |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
--R    |                                                              |
--R    +  %A      %A      %A      1       %A      %A      1     %A + 1+
--R                                           Type: List Matrix FiniteField(2,2)
--E 32

--S 33 of 33
dA6d16
 

   (33)
    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
    |                                              |
    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
   [|                                              |,
    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
    |                                              |
    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
    |                                              |
    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
    |                                              |
    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
    |                                              |
    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
    |                                              |]
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
    |                                              |
    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
    |                                              |
    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
    |                                              |
    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
    |                                              |
    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
    |                                              |
    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
                                               Type: List Matrix PrimeField 2
--R 
--R
--R   (33)
--R    +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
--R   [|                                              |,
--R    |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1|
--R    |                                              |
--R    |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
--R    |                                              |
--R    +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+
--R    +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+
--R    |                                              |
--R    |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
--R    |                                              |]
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
--R    |                                              |
--R    |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
--R    |                                              |
--R    |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
--R    |                                              |
--R    |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
--R    |                                              |
--R    |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
--R    |                                              |
--R    +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
--R                                               Type: List Matrix PrimeField 2
--E 33
)spool 
 
Starts dribbling to series.output (2010/3/27, 18:38:56).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 17
xT := taylor(x)
 

   (1)  x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (1)  x
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 1

--S 2 of 17
sin(tan(xT))
 

            1  3    1  5    55   7    143  9      11
   (2)  x + - x  - -- x  - ---- x  - ---- x  + O(x  )
            6      40      1008      3456
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R            1  3    1  5    55   7    143  9      11
--R   (2)  x + - x  - -- x  - ---- x  - ---- x  + O(x  )
--R            6      40      1008      3456
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 2

--S 3 of 17
taylor(asec(2+x))
 

   (3)
                 1          7    2     13    3      205    4      1069    5
     asec(2) + ----- x - ------ x  + ------ x  - -------- x  + --------- x
                 +-+        +-+         +-+           +-+            +-+
               2\|3      24\|3       72\|3       1728\|3       12960\|3
   + 
          1877    6      10043    7      54593     8      33437     9
     - --------- x  + ---------- x  - ----------- x  + ----------- x
             +-+             +-+              +-+              +-+
       31104\|3       217728\|3       1492992\|3       1119744\|3
   + 
          5034373     10      11
     - ------------- x   + O(x  )
                 +-+
       201553920\|3
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R   (3)
--R                 1          7    2     13    3      205    4      1069    5
--R     asec(2) + ----- x - ------ x  + ------ x  - -------- x  + --------- x
--R                 +-+        +-+         +-+           +-+            +-+
--R               2\|3      24\|3       72\|3       1728\|3       12960\|3
--R   + 
--R          1877    6      10043    7      54593     8      33437     9
--R     - --------- x  + ---------- x  - ----------- x  + ----------- x
--R             +-+             +-+              +-+              +-+
--R       31104\|3       217728\|3       1492992\|3       1119744\|3
--R   + 
--R          5034373     10      11
--R     - ------------- x   + O(x  )
--R                 +-+
--R       201553920\|3
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 17
sec %
 

                   11
   (4)  2 + x + O(x  )
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--R 
--R
--R                   11
--R   (4)  2 + x + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 17
taylor(sin(x),x = %pi/4)
 

   (5)
      +-+    +-+              +-+               +-+               +-+
     \|2    \|2       %pi    \|2       %pi 2   \|2       %pi 3   \|2       %pi 4
     ---- + ---- (x - ---) - ---- (x - ---)  - ---- (x - ---)  + ---- (x - ---)
       2      2        4       4        4       12        4       48        4
   + 
      +-+               +-+                +-+                +-+
     \|2       %pi 5   \|2       %pi 6    \|2       %pi 7    \|2       %pi 8
     ---- (x - ---)  - ---- (x - ---)  - ----- (x - ---)  + ----- (x - ---)
      240       4      1440       4      10080       4      80640       4
   + 
       +-+                  +-+
      \|2        %pi 9     \|2        %pi 10          %pi 11
     ------ (x - ---)  - ------- (x - ---)   + O((x - ---)  )
     725760       4      7257600       4               4
                      Type: UnivariateTaylorSeries(Expression Integer,x,pi/4)
--R 
--R
--R   (5)
--R      +-+    +-+              +-+               +-+               +-+
--R     \|2    \|2       %pi    \|2       %pi 2   \|2       %pi 3   \|2       %pi 4
--R     ---- + ---- (x - ---) - ---- (x - ---)  - ---- (x - ---)  + ---- (x - ---)
--R       2      2        4       4        4       12        4       48        4
--R   + 
--R      +-+               +-+                +-+                +-+
--R     \|2       %pi 5   \|2       %pi 6    \|2       %pi 7    \|2       %pi 8
--R     ---- (x - ---)  - ---- (x - ---)  - ----- (x - ---)  + ----- (x - ---)
--R      240       4      1440       4      10080       4      80640       4
--R   + 
--R       +-+                  +-+
--R      \|2        %pi 9     \|2        %pi 10          %pi 11
--R     ------ (x - ---)  - ------- (x - ---)   + O((x - ---)  )
--R     725760       4      7257600       4               4
--R                      Type: UnivariateTaylorSeries(Expression Integer,x,pi/4)
--E 5

--S 6 of 17
xL := laurent(x)
 

   (6)  x
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R   (6)  x
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 6

--S 7 of 17
1/xL - cot(xL)
 

        1      1  3    2   5     1   7     2    9      1382    11      12
   (7)  - x + -- x  + --- x  + ---- x  + ----- x  + --------- x   + O(x  )
        3     45      945      4725      93555      638512875
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R        1      1  3    2   5     1   7     2    9      1382    11      12
--R   (7)  - x + -- x  + --- x  + ---- x  + ----- x  + --------- x   + O(x  )
--R        3     45      945      4725      93555      638512875
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 7

--S 8 of 17
laurent(csc(x))
 

         - 1   1      7   3     31   5     127   7      73    9      10
   (8)  x    + - x + --- x  + ----- x  + ------ x  + ------- x  + O(x  )
               6     360      15120      604800      3421440
                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--R 
--R
--R         - 1   1      7   3     31   5     127   7      73    9      10
--R   (8)  x    + - x + --- x  + ----- x  + ------ x  + ------- x  + O(x  )
--R               6     360      15120      604800      3421440
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,0)
--E 8

--S 9 of 17
laurent(1/log(x),x = 1)
 

   (9)
            - 1   1    1            1        2    19        3    3         4
     (x - 1)    + - - -- (x - 1) + -- (x - 1)  - --- (x - 1)  + --- (x - 1)
                  2   12           24            720            160
   + 
        863         5    275         6    33953         7     8183         8
     - ----- (x - 1)  + ----- (x - 1)  - ------- (x - 1)  + ------- (x - 1)
       60480            24192            3628800            1036800
   + 
        3250433         9            10
     - --------- (x - 1)  + O((x - 1)  )
       479001600
                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--R 
--R
--R   (9)
--R            - 1   1    1            1        2    19        3    3         4
--R     (x - 1)    + - - -- (x - 1) + -- (x - 1)  - --- (x - 1)  + --- (x - 1)
--R                  2   12           24            720            160
--R   + 
--R        863         5    275         6    33953         7     8183         8
--R     - ----- (x - 1)  + ----- (x - 1)  - ------- (x - 1)  + ------- (x - 1)
--R       60480            24192            3628800            1036800
--R   + 
--R        3250433         9            10
--R     - --------- (x - 1)  + O((x - 1)  )
--R       479001600
--R                        Type: UnivariateLaurentSeries(Expression Integer,x,1)
--E 9

--S 10 of 17
xP := puiseux(x)
 

   (10)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (10)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 10

--S 11 of 17
sqrt(xP) - sqrt(sin(xP))
 

             5         9          13
             -         -          --
          1  2     1   2     1     2      8
   (11)  -- x  - ---- x  + ----- x   + O(x )
         12      1440      24192
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R             5         9          13
--R             -         -          --
--R          1  2     1   2     1     2      8
--R   (11)  -- x  - ---- x  + ----- x   + O(x )
--R         12      1440      24192
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 11

--S 12 of 17
puiseux(sqrt(1 - cos(x))/x)
 

   (12)
       1       1    2       1     4        1      6         1       8
     ---- - ------ x  + -------- x  - ---------- x  + ------------ x
      +-+      +-+           +-+             +-+               +-+
     \|2    24\|2       1920\|2       322560\|2       92897280\|2
   + 
              1         10      11
     - --------------- x   + O(x  )
                   +-+
       40874803200\|2
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (12)
--R       1       1    2       1     4        1      6         1       8
--R     ---- - ------ x  + -------- x  - ---------- x  + ------------ x
--R      +-+      +-+           +-+             +-+               +-+
--R     \|2    24\|2       1920\|2       322560\|2       92897280\|2
--R   + 
--R              1         10      11
--R     - --------------- x   + O(x  )
--R                   +-+
--R       40874803200\|2
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 12

--S 13 of 17
puiseux(sqrt(1 - tan(x)),x = %pi/2)
 

   (13)
                1              1               3               5
              - -              -               -               -
          %pi   2   1      %pi 2    7      %pi 2    7      %pi 2
     (x - ---)    + - (x - ---)  - -- (x - ---)  + -- (x - ---)
           2        2       2      24       2      48       2
   + 
                    7                  9
                    -                  -
        81      %pi 2    1219      %pi 2          %pi 5
     - --- (x - ---)  + ----- (x - ---)  + O((x - ---) )
       640       2      11520       2              2
                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--R 
--R
--R   (13)
--R                1              1               3               5
--R              - -              -               -               -
--R          %pi   2   1      %pi 2    7      %pi 2    7      %pi 2
--R     (x - ---)    + - (x - ---)  - -- (x - ---)  + -- (x - ---)
--R           2        2       2      24       2      48       2
--R   + 
--R                    7                  9
--R                    -                  -
--R        81      %pi 2    1219      %pi 2          %pi 5
--R     - --- (x - ---)  + ----- (x - ---)  + O((x - ---) )
--R       640       2      11520       2              2
--R                     Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2)
--E 13

--S 14 of 17
xS := series(x)
 

   (14)  x
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (14)  x
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 14

--S 15 of 17
sin(xS)**(1/3) - sin(xS**(1/3))
 

   (15)
              5        7                         11               13      14
              -        -                         --               --      --
   1      1   3    31  3      1    3       1      3     1921921    3       3
   - x - --- x  - --- x  - ------ x  + -------- x   - ---------- x   + O(x  )
   6     120      560      362880      39916800       6227020800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R   (15)
--R              5        7                         11               13      14
--R              -        -                         --               --      --
--R   1      1   3    31  3      1    3       1      3     1921921    3       3
--R   - x - --- x  - --- x  - ------ x  + -------- x   - ---------- x   + O(x  )
--R   6     120      560      362880      39916800       6227020800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 15

--S 16 of 17
series(log(tan(x)))
 

                  1  2    7  4    62   6    127   8    146   10      11
   (16)  log(x) + - x  + -- x  + ---- x  + ----- x  + ----- x   + O(x  )
                  3      90      2835      18900      66825
                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--R 
--R
--R                  1  2    7  4    62   6    127   8    146   10      11
--R   (16)  log(x) + - x  + -- x  + ---- x  + ----- x  + ----- x   + O(x  )
--R                  3      90      2835      18900      66825
--R                   Type: GeneralUnivariatePowerSeries(Expression Integer,x,0)
--E 16

--S 17 of 17
series(log(cot(x)),x = %pi/2)
 

   (17)
         - 2x + %pi    1      %pi 2    7      %pi 4    62       %pi 6
     log(----------) + - (x - ---)  + -- (x - ---)  + ---- (x - ---)
              2        3       2      90       2      2835       2
   + 
      127       %pi 8    146       %pi 10          %pi 11
     ----- (x - ---)  + ----- (x - ---)   + O((x - ---)  )
     18900       2      66825       2               2
                Type: GeneralUnivariatePowerSeries(Expression Integer,x,pi/2)
--R 
--R
--R   (17)
--R         - 2x + %pi    1      %pi 2    7      %pi 4    62       %pi 6
--R     log(----------) + - (x - ---)  + -- (x - ---)  + ---- (x - ---)
--R              2        3       2      90       2      2835       2
--R   + 
--R      127       %pi 8    146       %pi 10          %pi 11
--R     ----- (x - ---)  + ----- (x - ---)   + O((x - ---)  )
--R     18900       2      66825       2               2
--R                Type: GeneralUnivariatePowerSeries(Expression Integer,x,pi/2)
--E 17
)spool 
 
Starts dribbling to intef2.output (2010/3/27, 18:27:0).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
(a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x)
 

                        a x + b
   (1)  --------------------------------------
         2        2         2          2 3
        b x log(x)  + 2a b x log(x) + a x  + x
                                                     Type: Expression Integer
--R 
--R
--R                        a x + b
--R   (1)  --------------------------------------
--R         2        2         2          2 3
--R        b x log(x)  + 2a b x log(x) + a x  + x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 10
integrate(%,x)
 

   (2)  atan(b log(x) + a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (2)  atan(b log(x) + a x)
--R                                          Type: Union(Expression Integer,...)
--E 2

--S 3 of 10
((exp(x)-x**2+2*x)/(x**2*(exp(x)+x)**2))*exp((x**2-1)/x+1/(exp(x)+x))
 

                           2       x    3
                         (x  - 1)%e  + x
                         ----------------
                                x    2
           x    2           x %e  + x
        (%e  - x  + 2x)%e
   (3)  ---------------------------------
               2   x 2     3  x    4
              x (%e )  + 2x %e  + x
                                                     Type: Expression Integer
--R 
--R
--R                           2       x    3
--R                         (x  - 1)%e  + x
--R                         ----------------
--R                                x    2
--R           x    2           x %e  + x
--R        (%e  - x  + 2x)%e
--R   (3)  ---------------------------------
--R               2   x 2     3  x    4
--R              x (%e )  + 2x %e  + x
--R                                                     Type: Expression Integer
--E 3

--S 4 of 10
integrate(%,x)
 

            2       x    3
          (x  - 1)%e  + x
          ----------------
                 x    2
             x %e  + x
        %e
   (4)  ------------------
                  x
                %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            2       x    3
--R          (x  - 1)%e  + x
--R          ----------------
--R                 x    2
--R             x %e  + x
--R        %e
--R   (4)  ------------------
--R                  x
--R                %e
--R                                          Type: Union(Expression Integer,...)
--E 4

--S 5 of 10
x * cot x
 

   (5)  x cot(x)
                                                     Type: Expression Integer
--R 
--R
--R   (5)  x cot(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 10
integrate(%,x)
 

           x
         ++
   (6)   |   %J cot(%J)d%J
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--R   (6)   |   %J cot(%J)d%J
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 10
tan x + cos x
 

   (7)  tan(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (7)  tan(x) + cos(x)
--R                                                     Type: Expression Integer
--E 7

--S 8 of 10
integrate(%,x)
 

                 2                2cos(x)
   (8)  log(----------) - log(- ----------) + sin(x)
            cos(x) + 1          cos(x) + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2                2cos(x)
--R   (8)  log(----------) - log(- ----------) + sin(x)
--R            cos(x) + 1          cos(x) + 1
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 10
cosh(a*x)*sinh(a*x)
 

   (9)  cosh(a x)sinh(a x)
                                                     Type: Expression Integer
--R 
--R
--R   (9)  cosh(a x)sinh(a x)
--R                                                     Type: Expression Integer
--E 9

--S 10 of 10
integrate(%,x)
 

                  2            2
         sinh(a x)  + cosh(a x)
   (10)  -----------------------
                    4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  2            2
--R         sinh(a x)  + cosh(a x)
--R   (10)  -----------------------
--R                    4a
--R                                          Type: Union(Expression Integer,...)
--E 10
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read marcbench
 

)set break resume
 
)clear completely
 
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.
)set message type off
 
)set message time off
 

output(" Ex. 1: 4-body ")$OutputPackage
 
    Ex. 1: 4-body

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [p,s,phi];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

p: P := 'p;
 

s: P := 's;
 

phi: P := 'phi;
 

p1:=-2*p^3+2*p^3*phi^3-4*phi^3*s*p^2+5*phi^3*s^3*p-phi^3*s^5;
 

p2:=-2*s*p^3-2*phi^3*s^2+phi^3*s^4-3*phi^3*s^2*p+2*phi^3*p;
 

p3:=-2*s^2+s^4-4*s^2*p+phi^2+1+4*p;
 

lp:=[p1,p2,p3];
 



T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 1.84 (EV) + 0.34 (GC) = 2.18 sec
)set message time off
 

output(" Ex. 2:  Wang-16 ")$OutputPackage
 
    Ex. 2:  Wang-16

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [x,y,z,t,u];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
 

y: P := 'y;
 

z: P := 'z;
 

t: P := 't;
 

u: P := 'u;
 

f0 := u-2;
 

f1:= 2*(u-1)^2+2*(x-z*x+z^2)+y^2*(x-1)^2-2*u*x+2*y*t*(1-x)*(x-z)+2*u*z*t*(t-y)+u^2*t^2*(1-2*z)+2*u*t^2*(z-x)+2*u*t*y*(z-1)+2*u*z*x*(y+1)+(u^2-2*u)*z^2*t^2+2*u^2*z^2+4*u*(1-u)*z+t^2*(z-x)^2;
 

f2:= t*(2*z+1)*(x-z)+y*(z+2)*(1-x)+u*(u-2)*t+u*(1-2*u)*z*t+u*y*(x+u-z*x-1)+u*(u+1)*z^2*t;
 

f3:= -u^2*(z-1)^2+2*z*(z-x)-2*(x-1);
 

f4:= u^2+4*(z-x^2)+3*y^2*(x-1)^2-3*t^2*(z-x)^2 +3*u^2*t^2*(z-1)^2+u^2*z*(z-2)+6*u*t*y*(z+x+z*x-1);
 

lp :=[f0,f1,f2,f3,f4];
 



T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 1.69 (EV) + 0.19 (GC) = 1.88 sec
)set message time off
 

output(" Ex. 3: Rose ")$OutputPackage
 
    Ex. 3: Rose

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [z,y,x];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
 

y: P := 'y;
 

z: P := 'z;
 

f1 := 7*y**4 - 20*x**2 ;
 

f2:=  (2160*x**2 + 1512*x +315)*z**4-4000*x**2-2800*x-490 ;
 

f3 :=  (67200000*x**5 + 94080000*x**4 + 40924800*x**3 + 2634240*x**2-2300844*x-432180)*y**3 + ((40320000*x**6 + 28800000*x**5 + 21168000*x**3 + 4939200*x**2 + 347508*x)*z)*y**2 + ((-23520000*x**4-41395200*x**3-26726560*x**2-7727104*x-852355)*z**2)*y + (-10080000*x**4-28224000*x**3-15288000*x**2-1978032*x-180075)*z**3 ;
 

lp := [f1,f2,f3];
 



T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 0.57 (EV) + 0.05 (GC) = 0.62 sec
)set message time off
 

output(" Ex. 4: L-3 ")$OutputPackage
 
    Ex. 4: L-3

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls: List Symbol := [x,y,z,t];
 

V := OVAR ls;
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := `x;
 

y: P := `y;
 

z: P := `z
 

   (9)  z
t: P := `t;
 

p1 := x^3 + y + z + t- 1;
 

p2 := x + y^3 + z + t -1;
 

p3 := x + y + z^3 + t-1;
 

p4 := x + y + z + t^3 -1;
 

lp := [p1,p2,p3,p4];
 


T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 0.41 (EV) + 0.09 (GC) = 0.50 sec
)set message time off
 

output(" Ex. 5:Butcher ")$OutputPackage
 
    Ex. 5:Butcher

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [b1,x,y,z,t,v,u,w];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

b1: P := 'b1;
 

x: P := 'x;
 

y: P := 'y;
 

z: P := 'z;
 

t: P := 't;
 

u: P := 'u;
 

v: P := 'v;
 

w: P := 'w;
 

f0 := b1 + y + z - t - w;
 

f1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 ;
 

f2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w  ;
 

f3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w  ;
 

f4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1  ;
 

f5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1  ;
 

f6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1;
 

f7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 ;
 


lp := [f0,f1,f2,f3,f4,f5,f6,f7];
 

T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                                   Time: 0.10 (EV) = 0.10 sec
)set message time off
 

output(" Ex. 6 : Hairer-2 ")$OutputPackage
 
    Ex. 6 : Hairer-2

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [A43,A42,A41,A32,A31,A21,B1,B2,B3,B4,C4,C3,C2];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

A43: P := 'A43;
 

A42: P := 'A42;
 

A41: P := 'A41;
 

A32: P := 'A32;
 

A31: P := 'A31;
 

A21: P := 'A21;
 

B1: P := 'B1;
 

B2: P := 'B2;
 

B3: P := `B3;
 

B4: P := `B4;
 

C4: P := `C4;
 

C3: P := `C3;
 

C2: P := `C2;
 

f1 := B1+B2+B3+B4-1 ;
 

f2 := 2*B2*C2 + 2*B3*C3 + 2*B4*C4 - 1 ;
 

f3 := 3*B2*C2**2 +3*B3*C3**2 +3*B4*C4**2 -1 ;
 

f4 := 6*B3*A32*C2 +6*B4*A42*C2 +6*B4*A43*C3 -1 ;
 

f5 := 4*B2*C2**3 +4*B3*C3**3 +4*B4*C4**3 -1 ;
 

f6 := 8*B3*C3*A32*C2 +8*B4*C4*A42*C2 +8*B4*C4*A43*C3 -1 ;
 

f7 := 12*B3*A32*C2**2 +12*B4*A42*C2**2 +12*B4*A43*C3**2 -1 ;
 

f8 := 24*B4*A43*A32*C2 -1 ;
 

f9 := -A21+C2 ;
 

f10 := -A31-A32+C3 ;
 

f11 := -A41-A42-A43+C4 ;
 


lp := [f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11];
 


T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 0.62 (EV) + 0.12 (GC) = 0.74 sec
)set message time off
 

output(" Ex. 7 : Lichtblau ")$OutputPackage
 
    Ex. 7 : Lichtblau

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [t,y,x];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
 

y: P := 'y;
 

t: P := 't;
 

p1 := x-110*t^2+495*t^3-1320*t^4+2772*t^5-5082*t^6+7590*t^7-8085*t^8+5555*t^9-2189*t^10+374*t^11;
 

p2 :=  y-22*t+110*t^2-330*t^3+1848*t^5-3696*t^6+3300*t^7-1650*t^8+550*t^9-88*t^10-22*t^11;
 

lp := [p1, p2];
 


T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 2.19 (EV) + 0.50 (GC) = 2.69 sec
)set message time off
 

output(" Ex. 8: Liu original ")$OutputPackage
 
    Ex. 8: Liu original

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [x,y,z,t,a];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
 

y: P := 'y;
 

z: P := 'z;
 

t: P := 't;
 

a: P := 'a;
 

p1 := y*(z-t)-x+a ;
 

p2 := z*(t-x)-y+a ;
 

p3 := t*(x-y)-z+a ;
 

p4 := x*(y-z)-t+a ;
 

lp := [p1,p2,p3,p4] ;
 



T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 0.39 (EV) + 0.08 (GC) = 0.47 sec
)set message time off
 

output(" Ex. 9: Liu homog. ")$OutputPackage
 
    Ex. 9: Liu homog.

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [x,y,z,t,a,h];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
 

y: P := 'y;
 

z: P := 'z;
 

t: P := 't;
 

a: P := 'a;
 

h: P := 'h;
 

p1 := y*z-y*t-x*h+a*h;
 

p2 := z*t-z*x-y*h+a*h;
 

p3 := t*x-y*t-z*h+a*h;
 

p4 := x*y-z*x-t*h+a*h;
 

lp := [p1,p2,p3,p4] ;
 



T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 2.00 (EV) + 0.45 (GC) = 2.45 sec
)set message time off
 

output(" Ex. 10: Vermeer ")$OutputPackage
 
    Ex. 10: Vermeer

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [w,v,u,y,x];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
 

y: P := 'y;
 

u: P := 'u;
 

v: P := 'v;
 

w: P := 'w;
 

p1 := (x - u) ** 2 + (y - v) ** 2 - 1 ;
 

p2 := v ** 2 - u ** 3 ;
 

p3 := 2 * v * (x - u) + 3 * u ** 2 * (y - v) ;
 

f1 := (3 * w * u ** 2 - 1) ;
 

f2 := (2 * w * v - 1) ;
 

p4 := f1 * f2 ;
 

lp := [p1,p2,p3,p4] ;
 



T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 0.33 (EV) + 0.06 (GC) = 0.39 sec
)set message time off
 

output(" Ex. 11: Wu-Wang-2" )
 
    Ex. 11: Wu-Wang-2

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := reverse [x10,x11,x12,x13,x21,x22,x23,x30,x101,x102,x103,x104,x105];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x10: P := 'x10;
 

x11:P := 'x11;
 

x12:P := 'x12;
 

x13:P := 'x13;
 

x21:P := 'x21;
 

x22:P := 'x22;
 

x23:P := 'x23;
 

x30:P := 'x30;
 

x101:P := 'x101;
 

x102:P := 'x102;
 

x103:P := 'x103;
 

x104:P := 'x104;
 

x105:P := 'x105;f1:=x21-x12-x13;
 

f2:=x22-x11-x13;
 

f3:=x23-x11-x12;
 

f4:=x30-x11^3-x12^3-x13^3;
 

f5:=x21*x22*x23-x10*x30;
 

f6:=x10+x101*f1+x102*f2+x103*f3+x104*f4+x105*f5;
 

f7 := differentiate(f6,'x11);
 

f8 := differentiate(f6,'x12);
 

f9 := differentiate(f6,'x13);
 

f10 := differentiate(f6,'x21);
 

f11 := differentiate(f6,'x21);
 

f12 := differentiate(f6,'x22);
 

f13 := differentiate(f6,'x23);
 

f14 := differentiate(f6,'x23);
 

f15 := differentiate(f6,'x30);
 

f16 := differentiate(f6,'x10);
 

lp:=[f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16];
 




T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                     Time: 14.23 (EV) + 0.55 (GC) = 14.78 sec
)set message time off
 

output(" Ex. 12: f-633 ")$OutputPackage
 
    Ex. 12: f-633

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
 
ls : List Symbol := [U6,U5,U4,U3,U2,u6,u5,u4,u3,u2];
 

V := OVAR(ls);
 

R := Integer;
 

E := IndexedExponents V;
 

P := NSMP(R, V);
 

LP := List(P);
 


-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

U6: P := 'U6;
 

U5: P := 'U5;
 

U4: P := 'U4;
 

U3: P := 'U3;
 

U2: P := 'U2;
 

u6: P := 'u6;
 

u5: P := 'u5;
 

u4: P := 'u4;
 

u3: P := 'u3;
 

u2: P := 'u2;
 

p1 := 2*u6 + 2*u5 + 2*u4 + 2*u3 + 2*u2 + 1;
 

p2 := 8*U5*u6 + 8*U5*u5 + 8*U4*u6 +8*U4*u5 + 8*U4*u4 + 8*U3*u6 + 8*U3*u5 + 8*U3*u4 + 8*U3*u3 + 8*U2*u6 +8*U2*u5 + 8*U2*u4 + 8*U2*u3 + 8*U2*u2 -13;
 

p3 := 2*U6 + 2*U5 + 2*U4 + 2*U3 +2*U2 + 1;
 

p4 := 8*U6*u5 + 8*U6*u4 + 8*U6*u3 + 8*U6*u2 + 8*U5*u5 + 8*U5*u4 +8*U5*u3 + 8*U5*u2 + 8*U4*u4 + 8*U4*u3 + 8*U4*u2 + 8*U3*u3 + 8*U3*u2 +8*U2*u2 -13;
 

p6 := U2*u2 -1;
 

p7 := U3*u3 -1;
 

p8 := U4*u4 -1;
 

p9 := U5*u5 -1;
 

p10 := U6*u6 -1;
 

lp := [p1,p2,p3,p4,p6,p7,p8,p9,p10];
 




T := REGSET(R,E,V,P);
 

)set message time off
 
zeroSetSplit(lp)$T;
 

)set message time on
 
zeroSetSplit(lp)$T;
 

                                       Time: 0.33 (EV) + 0.04 (GC) = 0.37 sec
)set message time off
 
)lisp (bye)
 
Starts dribbling to nlode.output (2010/3/27, 18:30:14).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 16
y := operator y
 

   (1)  y
                                                          Type: BasicOperator
--R 
--R
--R   (1)  y
--R                                                          Type: BasicOperator
--E 1

--S 2 of 16
deq := (sin y x - x / y(x)) * differentiate(y x, x) = 1
 

                            ,
        (y(x)sin(y(x)) - x)y (x)

   (2)  ------------------------= 1
                  y(x)
                                            Type: Equation Expression Integer
--R 
--R
--R                            ,
--R        (y(x)sin(y(x)) - x)y (x)
--R
--R   (2)  ------------------------= 1
--R                  y(x)
--R                                            Type: Equation Expression Integer
--E 2

--S 3 of 16
solve(deq, y, x)
 

   (3)  sin(y(x)) - y(x)cos(y(x)) - x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (3)  sin(y(x)) - y(x)cos(y(x)) - x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 3

--S 4 of 16
deq := differentiate(y x, x) = y(x) / (x + y(x) * log y x)
 

         ,            y(x)
   (4)  y (x)= -----------------
               y(x)log(y(x)) + x
                                            Type: Equation Expression Integer
--R 
--R
--R         ,            y(x)
--R   (4)  y (x)= -----------------
--R               y(x)log(y(x)) + x
--R                                            Type: Equation Expression Integer
--E 4

--S 5 of 16
solve(deq, y, x)
 

                     2
        y(x)log(y(x))  - 2x
   (5)  -------------------
               2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R        y(x)log(y(x))  - 2x
--R   (5)  -------------------
--R               2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 5

--S 6 of 16
solve(deq, y, x = 1, [1])
 

                     2
        y(x)log(y(x))  + 2y(x) - 2x
   (6)  ---------------------------
                   2y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                     2
--R        y(x)log(y(x))  + 2y(x) - 2x
--R   (6)  ---------------------------
--R                   2y(x)
--R                                          Type: Union(Expression Integer,...)
--E 6

--S 7 of 16
deq := (exp(- 2 * y x) - 2 * x * y x) * differentiate(y x, x) = y x
 

           - 2y(x)            ,
   (7)  (%e        - 2x y(x))y (x)= y(x)

                                            Type: Equation Expression Integer
--R 
--R
--R           - 2y(x)            ,
--R   (7)  (%e        - 2x y(x))y (x)= y(x)
--R
--R                                            Type: Equation Expression Integer
--E 7

--S 8 of 16
solve(deq, y, x)
 

                        2y(x)
   (8)  log(y(x)) - x %e
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                        2y(x)
--R   (8)  log(y(x)) - x %e
--R                                          Type: Union(Expression Integer,...)
--E 8

--S 9 of 16
deq := differentiate(y x, x) = w + y(x) / (1 - y x)
 

         ,     (w - 1)y(x) - w
   (9)  y (x)= ---------------
                   y(x) - 1
                                            Type: Equation Expression Integer
--R 
--R
--R         ,     (w - 1)y(x) - w
--R   (9)  y (x)= ---------------
--R                   y(x) - 1
--R                                            Type: Equation Expression Integer
--E 9

--S 10 of 16
solve(deq, y, x = 0, [0])
 

                                                             2
         log((w - 1)y(x) - w) - log(- w) + (w - 1)y(x) + (- w  + 2w - 1)x
   (10)  ----------------------------------------------------------------
                                     2
                                    w  - 2w + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                                             2
--R         log((w - 1)y(x) - w) - log(- w) + (w - 1)y(x) + (- w  + 2w - 1)x
--R   (10)  ----------------------------------------------------------------
--R                                     2
--R                                    w  - 2w + 1
--R                                          Type: Union(Expression Integer,...)
--E 10

--S 11 of 16
deq := x**2 * differentiate(y x, x) + 2 * x * y x - y(x)**3
 

          2 ,          3
   (11)  x y (x) - y(x)  + 2x y(x)

                                                     Type: Expression Integer
--R 
--R
--R          2 ,          3
--R   (11)  x y (x) - y(x)  + 2x y(x)
--R
--R                                                     Type: Expression Integer
--E 11

--S 12 of 16
solve(deq, y, x)
 

              5         2
         (- 3x  - 2)y(x)  + 5x
   (12)  ---------------------
                  5    2
                5x y(x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              5         2
--R         (- 3x  - 2)y(x)  + 5x
--R   (12)  ---------------------
--R                  5    2
--R                5x y(x)
--R                                          Type: Union(Expression Integer,...)
--E 12

--S 13 of 16
deq := differentiate(y x,x) = 1 + x**2 - 2 * x * y x + y(x)**2
 

          ,         2              2
   (13)  y (x)= y(x)  - 2x y(x) + x  + 1

                                            Type: Equation Expression Integer
--R 
--R
--R          ,         2              2
--R   (13)  y (x)= y(x)  - 2x y(x) + x  + 1
--R
--R                                            Type: Equation Expression Integer
--E 13

--S 14 of 16
solve(deq, y, x)
 

            - y(x) + x
   (14)  ---------------
                   2
         x y(x) - x  + 1
                                          Type: Union(Expression Integer,...)
--R 
--R
--R            - y(x) + x
--R   (14)  ---------------
--R                   2
--R         x y(x) - x  + 1
--R                                          Type: Union(Expression Integer,...)
--E 14

--S 15 of 16
deq := x**2 * differentiate(y x,x) = -1 - x * y x + x**2 * y(x)**2
 

          2 ,      2    2
   (15)  x y (x)= x y(x)  - x y(x) - 1

                                            Type: Equation Expression Integer
--R 
--R
--R          2 ,      2    2
--R   (15)  x y (x)= x y(x)  - x y(x) - 1
--R
--R                                            Type: Equation Expression Integer
--E 15

--S 16 of 16
solve(deq, y, x)
 

               3              2
           (- x  - 8x)y(x) - x  + 8
   (16)  ----------------------------
             3                 2
         (18x  - 18x)y(x) + 18x  + 18
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               3              2
--R           (- x  - 8x)y(x) - x  + 8
--R   (16)  ----------------------------
--R             3                 2
--R         (18x  - 18x)y(x) + 18x  + 18
--R                                          Type: Union(Expression Integer,...)
--E 16
)spool 
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read tutchap4
 
--Copyright The Numerical Algorithms Group Limited 1996.
s := operator 's
 

   (1)  s
                                                          Type: BasicOperator
solve(D(s(t),t,2) = -k^2*s(t), s, t)
 

   (2)  [particular= 0,basis= [cos(k t),sin(k t)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
solve(D(s(t),t,2) = -k^2*s(t), s, t=0, [A, 0])
 

   (3)  A cos(k t)
                                          Type: Union(Expression Integer,...)
DE := D(s(t),t,2) = -k^2*s(t) - c*D(s(t),t)
 

         ,,         ,       2
   (4)  s  (t)= - cs (t) - k s(t)

                                            Type: Equation Expression Integer
S := solve(DE, s, t=0, [A, 0])
 

   (5)
                                 +----------+
                                 |    2    2
                               t\|- 4k  + c   - c t
          +----------+         --------------------
          |    2    2                    2
       (A\|- 4k  + c   + A c)%e
     + 
                                   +----------+
                                   |    2    2
                               - t\|- 4k  + c   - c t
          +----------+         ----------------------
          |    2    2                     2
       (A\|- 4k  + c   - A c)%e
  /
       +----------+
       |    2    2
     2\|- 4k  + c
                                          Type: Union(Expression Integer,...)
S1 == eval(S,[A=1,k=1,c=3])
 
                                                                   Type: Void
draw(S1, t=0..100)
 
   Compiling body of rule S1 to compute value of type Expression 
      Integer 
   Compiling function %E with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (7)  TwoDimensionalViewport: "AXIOM2D"
                                                 Type: TwoDimensionalViewport
S
 

   (8)
                                 +----------+
                                 |    2    2
                               t\|- 4k  + c   - c t
          +----------+         --------------------
          |    2    2                    2
       (A\|- 4k  + c   + A c)%e
     + 
                                   +----------+
                                   |    2    2
                               - t\|- 4k  + c   - c t
          +----------+         ----------------------
          |    2    2                     2
       (A\|- 4k  + c   - A c)%e
  /
       +----------+
       |    2    2
     2\|- 4k  + c
                                          Type: Union(Expression Integer,...)
kernels S
 

             +----------+             +----------+
             |    2    2              |    2    2
           t\|- 4k  + c   - c t   - t\|- 4k  + c   - c t
           --------------------   ----------------------  +----------+
                     2                       2            |    2    2
   (9)  [%e                    ,%e                      ,\|- 4k  + c  ,c,A]
                                         Type: List Kernel Expression Integer
k3 := %.3
 

          +----------+
          |    2    2
   (10)  \|- 4k  + c
                                              Type: Kernel Expression Integer
eval(S,k3,%i*sqrt(4*k^2 - c^2))
 

   (11)
                                     +--------+
                                     |  2    2
                                %i t\|4k  - c   - c t
          +--------+            ---------------------
          |  2    2                       2
       (A\|4k  - c   - %i A c)%e
     + 
                                       +--------+
                                       |  2    2
                                - %i t\|4k  - c   - c t
          +--------+            -----------------------
          |  2    2                        2
       (A\|4k  - c   + %i A c)%e
  /
       +--------+
       |  2    2
     2\|4k  - c
                                             Type: Expression Complex Integer
ST := trigs %
 

                 c t      +--------+          c t                 +--------+
               - ---      |  2    2         - --- +--------+      |  2    2
                  2     t\|4k  - c             2  |  2    2     t\|4k  - c
         A c %e     sin(------------) + A %e     \|4k  - c  cos(------------)
                              2                                       2
   (12)  --------------------------------------------------------------------
                                       +--------+
                                       |  2    2
                                      \|4k  - c
                                             Type: Expression Complex Integer
S2 == eval(ST,[A=1,k=1,c=0.1])
 
                                                                   Type: Void
draw(S2::EXPR FLOAT,t=0..100)
 
   Compiling body of rule S2 to compute value of type Expression 
      Complex Float 
   Compiling function %W with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (14)  TwoDimensionalViewport: "AXIOM2D"
                                                 Type: TwoDimensionalViewport
S3==eval(S,[A=1,k=1,c=0.1])
 
                                                                   Type: Void
draw(S3,t=0..100)
 
   There are 10 exposed and 4 unexposed library operations named eval 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op eval
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named eval 
      with argument type(s) 
                     Union(Expression Integer,"failed")
                       List Equation Polynomial Float
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   AXIOM will attempt to step through and interpret the code.
   Compiling function %Y with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   AXIOM2D data being transmitted to the viewport manager...

   (16)  TwoDimensionalViewport: "AXIOM2D"
                                                 Type: TwoDimensionalViewport
function(S1,'s1,'t)
 

   (17)  s1
                                                                 Type: Symbol
s1(1)
 
   Compiling function s1 with type PositiveInteger -> Expression 
      Integer 

                      +-+       +-+
                     \|5  - 3  \|5  + 3
                     --------  --------
           +-+           2         2       +-+
         (\|5  + 3)%e        %e         + \|5  - 3
   (18)  -----------------------------------------
                              +-+
                             \|5  + 3
                             --------
                        +-+      2
                      2\|5 %e
                                                     Type: Expression Integer
function(S2,'s2,'t)
 

   (19)  s2
                                                                 Type: Symbol
s2(0.1)
 
   Compiling function s2 with type Float -> Complex Float 

   (20)  0.9950207737 4207759557 - 0.1263157039 3106975913 E -21 %i
                                                          Type: Complex Float
)lisp (bye)
 
Starts dribbling to KeyedAccessFile.output (2010/3/27, 18:42:22).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 20
ey: KeyedAccessFile(Integer) := open("editor.year", "output")
 

   (1)  "editor.year"
                                                Type: KeyedAccessFile Integer
--R 
--R
--R   (1)  "editor.year"
--R                                                Type: KeyedAccessFile Integer
--E 1

--S 2 of 20
ey."Char":= 1986
 

   (2)  1986
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  1986
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 20
ey."Caviness" := 1985
 

   (3)  1985
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  1985
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 20
ey."Fitch"    := 1984
 

   (4)  1984
                                                        Type: PositiveInteger
--R 
--R
--R   (4)  1984
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 20
ey."Char"
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "editor.year"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   File is not readable
--R   "editor.year"
--R
--R   Continuing to read the file...
--R
--E 5

--S 6 of 20
ey("Char")
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "editor.year"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   File is not readable
--R   "editor.year"
--R
--R   Continuing to read the file...
--R
--E 6

--S 7 of 20
ey "Char"
 
 
Daly Bug
   >> Error detected within library code:
   File is not readable
   "editor.year"

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   File is not readable
--R   "editor.year"
--R
--R   Continuing to read the file...
--R
--E 7

--S 8 of 20
search("Char", ey)
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 8

--S 9 of 20
search("Smith", ey)
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 9

--S 10 of 20
remove!("Char", ey)
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 10

--S 11 of 20
keys ey
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 11

--S 12 of 20
#ey
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 12

--S 13 of 20
KE := Record(key: String, entry: Integer)
 

   (5)  Record(key: String,entry: Integer)
                                                                 Type: Domain
--R 
--R
--R   (5)  Record(key: String,entry: Integer)
--R                                                                 Type: Domain
--E 13

--S 14 of 20
reopen!(ey, "output")
 

   (6)  "editor.year"
                                                Type: KeyedAccessFile Integer
--R 
--R
--R   (6)  "editor.year"
--R                                                Type: KeyedAccessFile Integer
--E 14

--S 15 of 20
write!(ey, ["van Hulzen", 1983]$KE)
 

   (7)  [key= "van Hulzen",entry= 1983]
                                     Type: Record(key: String,entry: Integer)
--R 
--R
--R   (7)  [key= "van Hulzen",entry= 1983]
--R                                     Type: Record(key: String,entry: Integer)
--E 15

--S 16 of 20
write!(ey, ["Calmet", 1982]$KE)
 

   (8)  [key= "Calmet",entry= 1982]
                                     Type: Record(key: String,entry: Integer)
--R 
--R
--R   (8)  [key= "Calmet",entry= 1982]
--R                                     Type: Record(key: String,entry: Integer)
--E 16

--S 17 of 20
write!(ey, ["Wang", 1981]$KE)
 

   (9)  [key= "Wang",entry= 1981]
                                     Type: Record(key: String,entry: Integer)
--R 
--R
--R   (9)  [key= "Wang",entry= 1981]
--R                                     Type: Record(key: String,entry: Integer)
--E 17

--S 18 of 20
close! ey
 

   (10)  "editor.year"
                                                Type: KeyedAccessFile Integer
--R 
--R
--R   (10)  "editor.year"
--R                                                Type: KeyedAccessFile Integer
--E 18

--S 19 of 20
keys ey
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 19

--S 20 of 20
members ey
 
 
Daly Bug
   >> System error:
   Cannot create the file NIL/index.kaf.

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> System error:
--R   Cannot create the file NIL/index.kaf.
--R
--R   Continuing to read the file...
--R
--E 20

)system rm -r editor.year
 
)spool
 
Starts dribbling to ch.output (2010/3/27, 18:24:26).
)set message test on
 
)set message auto off
 
)clear all
 

--Cyclohexan

--S 1 of 7
mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) :=_
  [[0,1,1,1,1,1],[1,0,1,8/3,x,8/3],[1,1,0,1,8/3,y],_
   [1,8/3,1,0,1,8/3],[1,x,8/3,1,0,1],[1,8/3,y,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  x  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  y|
        |            3   |
        |                |
   (1)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  x  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  y  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  x  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  y|
--R        |            3   |
--R        |                |
--R   (1)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  x  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  y  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 1

--S 2 of 7
fzn := determinant mfzn
 

   (2)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (2)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x y  + -- x y - -- x  + -- x y  - --- x y - --- x - -- y  - --- y + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 2

--S 3 of 7
mfxn : SQMATRIX(6,DMP([x,y,z],Fraction Integer)) :=_
  [[0,1,1,1,1,1],[1,0,1,8/3,y,8/3],[1,1,0,1,8/3,z],_
   [1,8/3,1,0,1,8/3],[1,y,8/3,1,0,1],[1,8/3,z,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  y  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  z|
        |            3   |
        |                |
   (3)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  y  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  z  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  y  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  z|
--R        |            3   |
--R        |                |
--R   (3)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  y  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  z  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 3

--S 4 of 7
fxn := determinant mfxn
 

   (4)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - y z  + -- y z - -- y  + -- y z  - --- y z - --- y - -- z  - --- z + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (4)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - y z  + -- y z - -- y  + -- y z  - --- y z - --- y - -- z  - --- z + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 4

--S 5 of 7
mfyn : SQMATRIX(6,DMP([x,y,z],Fraction Integer)) :=_
  [[0,1,1,1,1,1],[1,0,1,8/3,z,8/3],[1,1,0,1,8/3,x],_
   [1,8/3,1,0,1,8/3],[1,z,8/3,1,0,1],[1,8/3,x,8/3,1,0]]
 

        +0  1  1  1  1  1+
        |                |
        |         8     8|
        |1  0  1  -  z  -|
        |         3     3|
        |                |
        |            8   |
        |1  1  0  1  -  x|
        |            3   |
        |                |
   (5)  |   8           8|
        |1  -  1  0  1  -|
        |   3           3|
        |                |
        |      8         |
        |1  z  -  1  0  1|
        |      3         |
        |                |
        |   8     8      |
        |1  -  x  -  1  0|
        +   3     3      +
Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--R 
--R
--R        +0  1  1  1  1  1+
--R        |                |
--R        |         8     8|
--R        |1  0  1  -  z  -|
--R        |         3     3|
--R        |                |
--R        |            8   |
--R        |1  1  0  1  -  x|
--R        |            3   |
--R        |                |
--R   (5)  |   8           8|
--R        |1  -  1  0  1  -|
--R        |   3           3|
--R        |                |
--R        |      8         |
--R        |1  z  -  1  0  1|
--R        |      3         |
--R        |                |
--R        |   8     8      |
--R        |1  -  x  -  1  0|
--R        +   3     3      +
--RType: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))
--E 5

--S 6 of 7
fyn := determinant mfyn
 

   (6)
      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
   - x z  + -- x z - -- x  + -- x z  - --- x z - --- x - -- z  - --- z + -----
             3        9       3         9         27      9       27       81
            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (6)
--R      2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R   - x z  + -- x z - -- x  + -- x z  - --- x z - --- x - -- z  - --- z + -----
--R             3        9       3         9         27      9       27       81
--R            Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 6

--S 7 of 7
gb := groebnerFactorize [fxn,fyn,fzn] 
 

   (7)
   [
                  22           22     22     121
     [x y + x z - -- x + y z - -- y - -- z + ---,
                   3            3      3      3
         2   22       25        2   22       25     22  2   388     250
      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
              3        9             3        9      3       9       27
       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
              3        9       3         9         27      9       27       81
     ,
             21994  2   21994     4427     463
    [x + y - -----,y  - ----- y + ----,z - ---],
              5625       5625      675      87
      2   1       11     5     265        2   38     265
    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
          2        2     6      18             3      9
         25     11     11        11     11     11        5     5     5
    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
          9      3      3         3      3      3        3     3     3
         19     5     5
    [x - --,y + -,z + -]]
          3     3     3
  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R   (7)
--R   [
--R                  22           22     22     121
--R     [x y + x z - -- x + y z - -- y - -- z + ---,
--R                   3            3      3      3
--R         2   22       25        2   22       25     22  2   388     250
--R      x z  - -- x z + -- x + y z  - -- y z + -- y - -- z  + --- z + ---,
--R              3        9             3        9      3       9       27
--R       2 2   22  2    25  2   22    2   388       250     25  2   250     14575
--R      y z  - -- y z + -- y  - -- y z  + --- y z + --- y + -- z  + --- z - -----]
--R              3        9       3         9         27      9       27       81
--R     ,
--R             21994  2   21994     4427     463
--R    [x + y - -----,y  - ----- y + ----,z - ---],
--R              5625       5625      675      87
--R      2   1       11     5     265        2   38     265
--R    [x  - - x z - -- x - - z + ---,y - z,z  - -- z + ---],
--R          2        2     6      18             3      9
--R         25     11     11        11     11     11        5     5     5
--R    [x - --,y - --,z - --], [x - --,y - --,z - --], [x + -,y + -,z + -],
--R          9      3      3         3      3      3        3     3     3
--R         19     5     5
--R    [x - --,y + -,z + -]]
--R          3     3     3
--R  Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)
--E 7
)spool
 
Starts dribbling to easter.output (2010/3/27, 18:25:10).
)set message test on
 
)set message auto off
 
)clear all
 

)set break resume
 
)set messages time off
 
)set quit unprotected
 
)set streams calculate 7
 
 
--S 1 of 200
factorial(50)
 

   (1)  30414093201713378043612608166064768844377641568960512000000000000
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  30414093201713378043612608166064768844377641568960512000000000000
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 200
factor(%)
 

         47 22 12 8  4  3  2  2  2
   (2)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
                                                       Type: Factored Integer
--R 
--R
--R         47 22 12 8  4  3  2  2  2
--R   (2)  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47
--R                                                       Type: Factored Integer
--E 2

--S 3 of 200
1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10
 

        4861
   (3)  ----
        2520
                                                       Type: Fraction Integer
--R 
--R
--R        4861
--R   (3)  ----
--R        2520
--R                                                       Type: Fraction Integer
--E 3

--S 4 of 200
digits(50);
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 4

--S 5 of 200
exp(sqrt(163.)*%pi)
 

   (5)  26253741 2640768743.9999999999 9925007259 7198185688 9
                                                                  Type: Float
--R 
--R
--R   (5)  26253741 2640768743.9999999999 9925007259 7198185688 9
--R                                                                  Type: Float
--E 5

--S 6 of 200
digits(20);
 

                                                        Type: PositiveInteger
--R 
--R
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 200
besselJ(2, 1 + %i)
 

   (7)  4.1579886943962155E-2 + 0.24739764151330637 %i
                                                    Type: Complex DoubleFloat
--R 
--R
--R   (7)  4.1579886943962155E-2 + 0.24739764151330637 %i
--R                                                    Type: Complex DoubleFloat
--E 7

--S 8 of 200
decimal(1/7)
 

          ______
   (8)  0.142857
                                                       Type: DecimalExpansion
--R 
--R
--R          ______
--R   (8)  0.142857
--R                                                       Type: DecimalExpansion
--E 8

--S 9 of 200
continuedFraction(3.1415926535)
 

              1 |     1  |     1 |      1  |     1 |     1 |     1 |
   (9)  3 + +---+ + +----+ + +---+ + +-----+ + +---+ + +---+ + +---+ + ...
            | 7     | 15     | 1     | 292     | 1     | 1     | 6
                                              Type: ContinuedFraction Integer
--R 
--R
--R              1 |     1  |     1 |      1  |     1 |     1 |     1 |
--R   (9)  3 + +---+ + +----+ + +---+ + +-----+ + +---+ + +---+ + +---+ + ...
--R            | 7     | 15     | 1     | 292     | 1     | 1     | 6
--R                                              Type: ContinuedFraction Integer
--E 9

--S 10 of 200
sqrt(2*sqrt(3) + 4)
 

          +---------+
          |  +-+
   (10)  \|2\|3  + 4
                                                        Type: AlgebraicNumber
--R 
--R
--R          +---------+
--R          |  +-+
--R   (10)  \|2\|3  + 4
--R                                                        Type: AlgebraicNumber
--E 10

--S 11 of 200
simplify(%)
 

          +---------+
          |  +-+
   (11)  \|2\|3  + 4
                                                     Type: Expression Integer
--R 
--R
--R          +---------+
--R          |  +-+
--R   (11)  \|2\|3  + 4
--R                                                     Type: Expression Integer
--E 11

--S 12 of 200
sqrt(14 + 3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2)))))
 

          +---------------------------------------+
          |  +------------------------------+
          |  |  +----------------------+
          |  |  |     +-----------+
          |  |  |     |    +-+
   (12)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
                                                        Type: AlgebraicNumber
--R 
--R
--R          +---------------------------------------+
--R          |  +------------------------------+
--R          |  |  +----------------------+
--R          |  |  |     +-----------+
--R          |  |  |     |    +-+
--R   (12)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
--R                                                        Type: AlgebraicNumber
--E 12

--S 13 of 200
simplify(%)
 

          +---------------------------------------+
          |  +------------------------------+
          |  |  +----------------------+
          |  |  |     +-----------+
          |  |  |     |    +-+
   (13)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
                                                     Type: Expression Integer
--R 
--R
--R          +---------------------------------------+
--R          |  +------------------------------+
--R          |  |  +----------------------+
--R          |  |  |     +-----------+
--R          |  |  |     |    +-+
--R   (13)  \|3\|2\|- 12\|- 2\|2  + 3  + 5  + 3  + 14
--R                                                     Type: Expression Integer
--E 13

--S 14 of 200
2*Aleph(0) - 3
 

   (14)  Aleph(0)
                                              Type: Union(CardinalNumber,...)
--R 
--R
--R   (14)  Aleph(0)
--R                                              Type: Union(CardinalNumber,...)
--E 14

--S 15 of 200
(x**2 - 4)/(x**2 + 4*x + 4)
 

         x - 2
   (15)  -----
         x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R         x - 2
--R   (15)  -----
--R         x + 2
--R                                            Type: Fraction Polynomial Integer
--E 15

--S 16 of 200
(%e**x - 1)/(%e**(x/2) + 1)
 

           x
         %e  - 1
   (16)  -------
           x
           -
           2
         %e  + 1
                                                     Type: Expression Integer
--R 
--R
--R           x
--R         %e  - 1
--R   (16)  -------
--R           x
--R           -
--R           2
--R         %e  + 1
--R                                                     Type: Expression Integer
--E 16

--S 17 of 200
normalize(%)
 

           x
           -
           2
   (17)  %e  - 1
                                                     Type: Expression Integer
--R 
--R
--R           x
--R           -
--R           2
--R   (17)  %e  - 1
--R                                                     Type: Expression Integer
--E 17

--S 18 of 200
(x + 1)**20
 

   (18)
      20      19       18        17        16         15         14         13
     x   + 20x   + 190x   + 1140x   + 4845x   + 15504x   + 38760x   + 77520x
   + 
            12          11          10          9          8         7         6
     125970x   + 167960x   + 184756x   + 167960x  + 125970x  + 77520x  + 38760x
   + 
           5        4        3       2
     15504x  + 4845x  + 1140x  + 190x  + 20x + 1
                                                     Type: Polynomial Integer
--R 
--R
--R   (18)
--R      20      19       18        17        16         15         14         13
--R     x   + 20x   + 190x   + 1140x   + 4845x   + 15504x   + 38760x   + 77520x
--R   + 
--R            12          11          10          9          8         7         6
--R     125970x   + 167960x   + 184756x   + 167960x  + 125970x  + 77520x  + 38760x
--R   + 
--R           5        4        3       2
--R     15504x  + 4845x  + 1140x  + 190x  + 20x + 1
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 200
D(%, x)
 

   (19)
        19       18        17         16         15          14          13
     20x   + 380x   + 3420x   + 19380x   + 77520x   + 232560x   + 542640x
   + 
             12           11           10           9           8           7
     1007760x   + 1511640x   + 1847560x   + 1847560x  + 1511640x  + 1007760x
   + 
            6          5         4         3        2
     542640x  + 232560x  + 77520x  + 19380x  + 3420x  + 380x + 20
                                                     Type: Polynomial Integer
--R 
--R
--R   (19)
--R        19       18        17         16         15          14          13
--R     20x   + 380x   + 3420x   + 19380x   + 77520x   + 232560x   + 542640x
--R   + 
--R             12           11           10           9           8           7
--R     1007760x   + 1511640x   + 1847560x   + 1847560x  + 1511640x  + 1007760x
--R   + 
--R            6          5         4         3        2
--R     542640x  + 232560x  + 77520x  + 19380x  + 3420x  + 380x + 20
--R                                                     Type: Polynomial Integer
--E 19

--S 20 of 200
factor(%)
 

                  19
   (20)  20(x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  19
--R   (20)  20(x + 1)
--R                                            Type: Factored Polynomial Integer
--E 20

--S 21 of 200
x**100 - 1
 

          100
   (21)  x    - 1
                                                     Type: Polynomial Integer
--R 
--R
--R          100
--R   (21)  x    - 1
--R                                                     Type: Polynomial Integer
--E 21

--S 22 of 200
factor(%)
 

   (22)
                     2       4    3    2           4    3    2
     (x - 1)(x + 1)(x  + 1)(x  - x  + x  - x + 1)(x  + x  + x  + x + 1)
  *
       8    6    4    2       20    15    10    5       20    15    10    5
     (x  - x  + x  - x  + 1)(x   - x   + x   - x  + 1)(x   + x   + x   + x  + 1)
  *
       40    30    20    10
     (x   - x   + x   - x   + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (22)
--R                     2       4    3    2           4    3    2
--R     (x - 1)(x + 1)(x  + 1)(x  - x  + x  - x + 1)(x  + x  + x  + x + 1)
--R  *
--R       8    6    4    2       20    15    10    5       20    15    10    5
--R     (x  - x  + x  - x  + 1)(x   - x   + x   - x  + 1)(x   + x   + x   + x  + 1)
--R  *
--R       40    30    20    10
--R     (x   - x   + x   - x   + 1)
--R                                            Type: Factored Polynomial Integer
--E 22

--S 23 of 200
p:= x**4 - 3*x**2 + 1
 

          4     2
   (23)  x  - 3x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R          4     2
--R   (23)  x  - 3x  + 1
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 200
factor(p)
 

           2           2
   (24)  (x  - x - 1)(x  + x - 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R           2           2
--R   (24)  (x  - x - 1)(x  + x - 1)
--R                                            Type: Factored Polynomial Integer
--E 24

--S 25 of 200
phi:= rootOf(phi**2 - phi - 1);
 

                                                        Type: AlgebraicNumber
--R 
--R
--R                                                        Type: AlgebraicNumber
--E 25

--S 26 of 200
factor(p, [phi])
 

   (26)  (x - phi)(x - phi + 1)(x + phi - 1)(x + phi)
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R   (26)  (x - phi)(x - phi + 1)(x + phi - 1)(x + phi)
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 26

--S 27 of 200
factor(p :: Polynomial(PrimeField(5)))
 

                2       2
   (27)  (x + 2) (x + 3)
                                       Type: Factored Polynomial PrimeField 5
--R 
--R
--R                2       2
--R   (27)  (x + 2) (x + 3)
--R                                       Type: Factored Polynomial PrimeField 5
--E 27

--S 28 of 200
expand(%)
 

          4     2
   (28)  x  + 2x  + 1
                                                Type: Polynomial PrimeField 5
--R 
--R
--R          4     2
--R   (28)  x  + 2x  + 1
--R                                                Type: Polynomial PrimeField 5
--E 28

--S 29 of 200
(x**2 + 2*x + 3)/(x**3 + 4*x**2 + 5*x + 2)
 

             2
            x  + 2x + 3
   (29)  -----------------
          3     2
         x  + 4x  + 5x + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             2
--R            x  + 2x + 3
--R   (29)  -----------------
--R          3     2
--R         x  + 4x  + 5x + 2
--R                                            Type: Fraction Polynomial Integer
--E 29

--S 30 of 200
padicFraction(
   partialFraction(numerator(%) :: UnivariatePolynomial(x, Fraction Integer),
                   factor(denominator(%) :: Polynomial Integer) ::
                      Factored UnivariatePolynomial(x, Fraction Integer)))
 

             2         2        3
   (30)  - ----- + -------- + -----
           x + 1          2   x + 2
                   (x + 1)
               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--R 
--R
--R             2         2        3
--R   (30)  - ----- + -------- + -----
--R           x + 1          2   x + 2
--R                   (x + 1)
--R               Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
--E 30

--S 31 of 200
r:= cos(3*x)/cos(x)
 

         cos(3x)
   (31)  -------
          cos(x)
                                                     Type: Expression Integer
--R 
--R
--R         cos(3x)
--R   (31)  -------
--R          cos(x)
--R                                                     Type: Expression Integer
--E 31

--S 32 of 200
real(complexNormalize(%))
 

                  2          2
   (32)  - 2sin(x)  + 2cos(x)  - 1
                                                     Type: Expression Integer
--R 
--R
--R                  2          2
--R   (32)  - 2sin(x)  + 2cos(x)  - 1
--R                                                     Type: Expression Integer
--E 32

--S 33 of 200
real(normalize(simplify(complexNormalize(r))))
 

   (33)  2cos(2x) - 1
                                                     Type: Expression Integer
--R 
--R
--R   (33)  2cos(2x) - 1
--R                                                     Type: Expression Integer
--E 33

--S 34 of 200
sincosAngles:= rule _
  (cos((n | integer?(n)) * x) == _
      cos((n - 1)*x) * cos(x) - sin((n - 1)*x) * sin(x); _
   sin((n | integer?(n)) * x) == _
      sin((n - 1)*x) * cos(x) + cos((n - 1)*x) * sin(x) )
 

   (34)
   {cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x),
    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x)}
                            Type: Ruleset(Integer,Integer,Expression Integer)
--R 
--R
--R   (34)
--R   {cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x)}
--R                            Type: Ruleset(Integer,Integer,Expression Integer)
--E 34

--S 35 of 200
sincosAngles r
 

                  2         2
   (35)  - 3sin(x)  + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R                  2         2
--R   (35)  - 3sin(x)  + cos(x)
--R                                                     Type: Expression Integer
--E 35

--S 36 of 200
r:= 'r;
 

                                                             Type: Variable r
--R 
--R
--R                                                             Type: Variable r
--E 36

--S 37 of 200
sqrt(997) - (997**3)**(1/6)
 

   (37)  0
                                                        Type: AlgebraicNumber
--R 
--R
--R   (37)  0
--R                                                        Type: AlgebraicNumber
--E 37

--S 38 of 200
sqrt(999983) - (999983**3)**(1/6)
 

   (38)  0
                                                        Type: AlgebraicNumber
--R 
--R
--R   (38)  0
--R                                                        Type: AlgebraicNumber
--E 38

--S 39 of 200
(2**(1/3) + 4**(1/3))**3 - 6*(2**(1/3) + 4**(1/3)) - 6
 

          3+-+3+-+2     3+-+2     3+-+    3+-+
   (39)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
                                                        Type: AlgebraicNumber
--R 
--R
--R          3+-+3+-+2     3+-+2     3+-+    3+-+
--R   (39)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
--R                                                        Type: AlgebraicNumber
--E 39

--S 40 of 200
simplify(%)
 

          3+-+3+-+2     3+-+2     3+-+    3+-+
   (40)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
                                                     Type: Expression Integer
--R 
--R
--R          3+-+3+-+2     3+-+2     3+-+    3+-+
--R   (40)  3\|2 \|4   + (3\|2   - 6)\|4  - 6\|2
--R                                                     Type: Expression Integer
--E 40

--S 41 of 200
x**(1/n)*y**(1/n) - (x*y)**(1/n)
 

                1    1 1
                -    - -
                n    n n
   (41)  - (x y)  + x y
                                                     Type: Expression Integer
--R 
--R
--R                1    1 1
--R                -    - -
--R                n    n n
--R   (41)  - (x y)  + x y
--R                                                     Type: Expression Integer
--E 41

--S 42 of 200
normalize(%)
 

   (42)  0
                                                     Type: Expression Integer
--R 
--R
--R   (42)  0
--R                                                     Type: Expression Integer
--E 42

--S 43 of 200
expr:= log(tan(1/2*x + %pi/4)) - asinh(tan(x))
 

                 2x + %pi
   (43)  log(tan(--------)) - asinh(tan(x))
                     4
                                                     Type: Expression Integer
--R 
--R
--R                 2x + %pi
--R   (43)  log(tan(--------)) - asinh(tan(x))
--R                     4
--R                                                     Type: Expression Integer
--E 43

--S 44 of 200
complexNormalize(%)
 

   (44)
     -
        log
                                +---+ 4
                     (2x + %pi)\|- 1
                     ----------------
                             4
                 ((%e                )  - 1)
              *
                  +----------------------------------------------------+
                  |                               +---+ 4
                  |                    (2x + %pi)\|- 1
                  |                    ----------------
                  |                            4
                  |                4(%e                )
                  |- --------------------------------------------------
                  |                +---+ 8                  +---+ 4
                  |     (2x + %pi)\|- 1          (2x + %pi)\|- 1
                  |     ----------------         ----------------
                  |             4                        4
                 \|  (%e                )  - 2(%e                )  + 1
             + 
                                     +---+ 4
                          (2x + %pi)\|- 1
                          ----------------
                  +---+           4             +---+
               - \|- 1 (%e                )  - \|- 1
          /
                           +---+ 4
                (2x + %pi)\|- 1
                ----------------
                        4
             (%e                )  - 1
   + 
                               +---+ 2
                    (2x + %pi)\|- 1
                    ----------------
            +---+           4             +---+
         - \|- 1 (%e                )  + \|- 1
     log(--------------------------------------)
                              +---+ 2
                   (2x + %pi)\|- 1
                   ----------------
                           4
                (%e                )  + 1
                                                     Type: Expression Integer
--R 
--R
--R   (44)
--R     -
--R        log
--R                                +---+ 4
--R                     (2x + %pi)\|- 1
--R                     ----------------
--R                             4
--R                 ((%e                )  - 1)
--R              *
--R                  +----------------------------------------------------+
--R                  |                               +---+ 4
--R                  |                    (2x + %pi)\|- 1
--R                  |                    ----------------
--R                  |                            4
--R                  |                4(%e                )
--R                  |- --------------------------------------------------
--R                  |                +---+ 8                  +---+ 4
--R                  |     (2x + %pi)\|- 1          (2x + %pi)\|- 1
--R                  |     ----------------         ----------------
--R                  |             4                        4
--R                 \|  (%e                )  - 2(%e                )  + 1
--R             + 
--R                                     +---+ 4
--R                          (2x + %pi)\|- 1
--R                          ----------------
--R                  +---+           4             +---+
--R               - \|- 1 (%e                )  - \|- 1
--R          /
--R                           +---+ 4
--R                (2x + %pi)\|- 1
--R                ----------------
--R                        4
--R             (%e                )  - 1
--R   + 
--R                               +---+ 2
--R                    (2x + %pi)\|- 1
--R                    ----------------
--R            +---+           4             +---+
--R         - \|- 1 (%e                )  + \|- 1
--R     log(--------------------------------------)
--R                              +---+ 2
--R                   (2x + %pi)\|- 1
--R                   ----------------
--R                           4
--R                (%e                )  + 1
--R                                                     Type: Expression Integer
--E 44

--S 45 of 200
D(expr, x)
 

   (45)
                        +-----------+
        2x + %pi 2      |      2             2x + %pi       2        2x + %pi
   (tan(--------)  + 1)\|tan(x)  + 1  - 2tan(--------)tan(x)  - 2tan(--------)
            4                                    4                       4
   ---------------------------------------------------------------------------
                                          +-----------+
                                2x + %pi  |      2
                           2tan(--------)\|tan(x)  + 1
                                    4
                                                     Type: Expression Integer
--R 
--R
--R   (45)
--R                        +-----------+
--R        2x + %pi 2      |      2             2x + %pi       2        2x + %pi
--R   (tan(--------)  + 1)\|tan(x)  + 1  - 2tan(--------)tan(x)  - 2tan(--------)
--R            4                                    4                       4
--R   ---------------------------------------------------------------------------
--R                                          +-----------+
--R                                2x + %pi  |      2
--R                           2tan(--------)\|tan(x)  + 1
--R                                    4
--R                                                     Type: Expression Integer
--E 45

--S 46 of 200
simplify(real(complexNormalize(expand(simplify(%)))))
 

   (46)
                       +------------------------------------------------+
             x 2       |                        1
       (2cos(-)  - 1)  |------------------------------------------------ - 1
             2         |      x 8         x 6         x 4        x 2
                      4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
                      \|      2           2           2          2
   ----------------------------------------------------------------------------
                              +------------------------------------------------+
         x 4        x 2       |                        1
   (4cos(-)  - 4cos(-)  + 1)  |------------------------------------------------
         2          2         |      x 8         x 6         x 4        x 2
                             4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
                             \|      2           2           2          2
                                                     Type: Expression Integer
--R 
--R
--R   (46)
--R                       +------------------------------------------------+
--R             x 2       |                        1
--R       (2cos(-)  - 1)  |------------------------------------------------ - 1
--R             2         |      x 8         x 6         x 4        x 2
--R                      4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
--R                      \|      2           2           2          2
--R   ----------------------------------------------------------------------------
--R                              +------------------------------------------------+
--R         x 4        x 2       |                        1
--R   (4cos(-)  - 4cos(-)  + 1)  |------------------------------------------------
--R         2          2         |      x 8         x 6         x 4        x 2
--R                             4|16cos(-)  - 32cos(-)  + 24cos(-)  - 8cos(-)  + 1
--R                             \|      2           2           2          2
--R                                                     Type: Expression Integer
--E 46

--S 47 of 200
normalize(eval(expr, x = 0))
 

   (47)  0
                                                     Type: Expression Integer
--R 
--R
--R   (47)  0
--R                                                     Type: Expression Integer
--E 47

--S 48 of 200
log((2*sqrt(r) + 1)/sqrt(4*r + 4*sqrt(r) + 1))
 

                   +-+
                 2\|r  + 1
   (48)  log(-----------------)
              +--------------+
              |  +-+
             \|4\|r  + 4r + 1
                                                     Type: Expression Integer
--R 
--R
--R                   +-+
--R                 2\|r  + 1
--R   (48)  log(-----------------)
--R              +--------------+
--R              |  +-+
--R             \|4\|r  + 4r + 1
--R                                                     Type: Expression Integer
--E 48

--S 49 of 200
simplify(%)
 

                   +-+
                 2\|r  + 1
   (49)  log(-----------------)
              +--------------+
              |  +-+
             \|4\|r  + 4r + 1
                                                     Type: Expression Integer
--R 
--R
--R                   +-+
--R                 2\|r  + 1
--R   (49)  log(-----------------)
--R              +--------------+
--R              |  +-+
--R             \|4\|r  + 4r + 1
--R                                                     Type: Expression Integer
--E 49

--S 50 of 200
(4*r + 4*sqrt(r) + 1)**(sqrt(r)/(2*sqrt(r) + 1)) _
   * (2*sqrt(r) + 1)**(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1
 

                                                 +-+
                        1                       \|r
                    ---------                ---------
                      +-+                      +-+
            +-+     2\|r  + 1   +-+          2\|r  + 1     +-+
   (50)  (2\|r  + 1)         (4\|r  + 4r + 1)          - 2\|r  - 1
                                                     Type: Expression Integer
--R 
--R
--R                                                 +-+
--R                        1                       \|r
--R                    ---------                ---------
--R                      +-+                      +-+
--R            +-+     2\|r  + 1   +-+          2\|r  + 1     +-+
--R   (50)  (2\|r  + 1)         (4\|r  + 4r + 1)          - 2\|r  - 1
--R                                                     Type: Expression Integer
--E 50

--S 51 of 200
normalize(%)
 

   (51)  0
                                                     Type: Expression Integer
--R 
--R
--R   (51)  0
--R                                                     Type: Expression Integer
--E 51

--S 52 of 200
rectform(z) == real(z) + %i*imag(z)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 52

--S 53 of 200
rectform(log(3 + 4*%i))
 
   Compiling function rectform with type Expression Complex Integer -> 
      Expression Complex Integer 

                            4
         log(25) + 2%i atan(-)
                            3
   (53)  ---------------------
                   2
                                             Type: Expression Complex Integer
--R 
--R   Compiling function rectform with type Expression Complex Integer -> 
--R      Expression Complex Integer 
--R
--R                            4
--R         log(25) + 2%i atan(-)
--R                            3
--R   (53)  ---------------------
--R                   2
--R                                             Type: Expression Complex Integer
--E 53

--S 54 of 200
simplify(rectform(tan(x + %i*y)))
 

                       - 2y                   2       - 2y
         - 2%i cos(x)%e    sin(x) + (- 2cos(x)  + 1)%e     + 1
   (54)  -----------------------------------------------------
                  - 2y                      2        - 2y
         2cos(x)%e    sin(x) + (- 2%i cos(x)  + %i)%e     - %i
                                             Type: Expression Complex Integer
--R 
--R
--R                       - 2y                   2       - 2y
--R         - 2%i cos(x)%e    sin(x) + (- 2cos(x)  + 1)%e     + 1
--R   (54)  -----------------------------------------------------
--R                  - 2y                      2        - 2y
--R         2cos(x)%e    sin(x) + (- 2%i cos(x)  + %i)%e     - %i
--R                                             Type: Expression Complex Integer
--E 54

--S 55 of 200
sqrt(x*y*abs(z)**2) / (sqrt(x)*abs(z))
 

          +-----------+
          |          2
         \|x y abs(z)
   (55)  --------------
                  +-+
           abs(z)\|x
                                                     Type: Expression Integer
--R 
--R
--R          +-----------+
--R          |          2
--R         \|x y abs(z)
--R   (55)  --------------
--R                  +-+
--R           abs(z)\|x
--R                                                     Type: Expression Integer
--E 55

--S 56 of 200
sqrt(1/z) - 1/sqrt(z)
 

          +-+
          |1  +-+
          |- \|z  - 1
         \|z
   (56)  ------------
              +-+
             \|z
                                                     Type: Expression Integer
--R 
--R
--R          +-+
--R          |1  +-+
--R          |- \|z  - 1
--R         \|z
--R   (56)  ------------
--R              +-+
--R             \|z
--R                                                     Type: Expression Integer
--E 56

--S 57 of 200
log(%e**z)
 

   (57)  z
                                                     Type: Expression Integer
--R 
--R
--R   (57)  z
--R                                                     Type: Expression Integer
--E 57

--S 58 of 200
normalize(%)
 

   (58)  z
                                                     Type: Expression Integer
--R 
--R
--R   (58)  z
--R                                                     Type: Expression Integer
--E 58

--S 59 of 200
log(%e**(10*%i))
 

               10%i
   (59)  log(%e    )
                                             Type: Expression Complex Integer
--R 
--R
--R               10%i
--R   (59)  log(%e    )
--R                                             Type: Expression Complex Integer
--E 59

--S 60 of 200
normalize(%)
 

               10%i
   (60)  log(%e    )
                                             Type: Expression Complex Integer
--R 
--R
--R               10%i
--R   (60)  log(%e    )
--R                                             Type: Expression Complex Integer
--E 60

--S 61 of 200
atan(tan(z))
 

   (61)  z
                                                     Type: Expression Integer
--R 
--R
--R   (61)  z
--R                                                     Type: Expression Integer
--E 61

--S 62 of 200
sqrt(%e**z) - %e**(z/2)
 

                    z
          +---+     -
          |  z      2
   (62)  \|%e   - %e
                                                     Type: Expression Integer
--R 
--R
--R                    z
--R          +---+     -
--R          |  z      2
--R   (62)  \|%e   - %e
--R                                                     Type: Expression Integer
--E 62

--S 63 of 200
(x = 0)/2 + 1
 

         x + 2
   (63)  -----= 1
           2
                                   Type: Equation Fraction Polynomial Integer
--R 
--R
--R         x + 2
--R   (63)  -----= 1
--R           2
--R                                   Type: Equation Fraction Polynomial Integer
--E 63

--S 64 of 200
radicalSolve(3*x**3 - 18*x**2 + 33*x - 19 = 0, x)
 

   (64)
                        +-------------+2                 +-------------+
                        | +-+    +---+                   | +-+    +---+
            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
       (- 3\|- 3  + 3)  |-------------  + (6\|- 3  + 6)  |------------- - 2
                       3|      +-+                      3|      +-+
                       \|    6\|3                       \|    6\|3
   [x= --------------------------------------------------------------------,
                                          +-------------+
                                          | +-+    +---+
                              +---+       |\|3  + \|- 1
                           (3\|- 3  + 3)  |-------------
                                         3|      +-+
                                         \|    6\|3
                        +-------------+2                 +-------------+
                        | +-+    +---+                   | +-+    +---+
            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
       (- 3\|- 3  - 3)  |-------------  + (6\|- 3  - 6)  |------------- + 2
                       3|      +-+                      3|      +-+
                       \|    6\|3                       \|    6\|3
    x= --------------------------------------------------------------------,
                                          +-------------+
                                          | +-+    +---+
                              +---+       |\|3  + \|- 1
                           (3\|- 3  - 3)  |-------------
                                         3|      +-+
                                         \|    6\|3
          +-------------+2     +-------------+
          | +-+    +---+       | +-+    +---+
          |\|3  + \|- 1        |\|3  + \|- 1
       3  |-------------  + 6  |------------- + 1
         3|      +-+          3|      +-+
         \|    6\|3           \|    6\|3
    x= ------------------------------------------]
                       +-------------+
                       | +-+    +---+
                       |\|3  + \|- 1
                    3  |-------------
                      3|      +-+
                      \|    6\|3
                                       Type: List Equation Expression Integer
--R 
--R
--R   (64)
--R                        +-------------+2                 +-------------+
--R                        | +-+    +---+                   | +-+    +---+
--R            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
--R       (- 3\|- 3  + 3)  |-------------  + (6\|- 3  + 6)  |------------- - 2
--R                       3|      +-+                      3|      +-+
--R                       \|    6\|3                       \|    6\|3
--R   [x= --------------------------------------------------------------------,
--R                                          +-------------+
--R                                          | +-+    +---+
--R                              +---+       |\|3  + \|- 1
--R                           (3\|- 3  + 3)  |-------------
--R                                         3|      +-+
--R                                         \|    6\|3
--R                        +-------------+2                 +-------------+
--R                        | +-+    +---+                   | +-+    +---+
--R            +---+       |\|3  + \|- 1        +---+       |\|3  + \|- 1
--R       (- 3\|- 3  - 3)  |-------------  + (6\|- 3  - 6)  |------------- + 2
--R                       3|      +-+                      3|      +-+
--R                       \|    6\|3                       \|    6\|3
--R    x= --------------------------------------------------------------------,
--R                                          +-------------+
--R                                          | +-+    +---+
--R                              +---+       |\|3  + \|- 1
--R                           (3\|- 3  - 3)  |-------------
--R                                         3|      +-+
--R                                         \|    6\|3
--R          +-------------+2     +-------------+
--R          | +-+    +---+       | +-+    +---+
--R          |\|3  + \|- 1        |\|3  + \|- 1
--R       3  |-------------  + 6  |------------- + 1
--R         3|      +-+          3|      +-+
--R         \|    6\|3           \|    6\|3
--R    x= ------------------------------------------]
--R                       +-------------+
--R                       | +-+    +---+
--R                       |\|3  + \|- 1
--R                    3  |-------------
--R                      3|      +-+
--R                      \|    6\|3
--R                                       Type: List Equation Expression Integer
--E 64

--S 65 of 200
map(e +-> lhs(e) = rectform(rhs(e)), %)
 
   Compiling function rectform with type Expression Integer -> 
      Expression Complex Integer 

   (65)
   [
     x =
             +-+          %pi 2           +-+         %pi      +-+     %pi
           (\|3  - %i)sin(---)  + ((- 2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
                           18                          18               18
         + 
               +-+          %pi 2       +-+    %pi     +-+
           (- \|3  + %i)cos(---)  - 4%i\|3 cos(---) + \|3  + %i
                             18                 18
      /
           +-+    %pi        +-+    %pi
         2\|3 sin(---) - 2%i\|3 cos(---)
                   18                18
     ,

     x =
               +-+          %pi 2         +-+         %pi      +-+     %pi
           (- \|3  - %i)sin(---)  + ((2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
                             18                        18               18
         + 
             +-+          %pi 2       +-+    %pi     +-+
           (\|3  + %i)cos(---)  - 4%i\|3 cos(---) - \|3  + %i
                           18                 18
      /
           +-+    %pi        +-+    %pi
         2\|3 sin(---) - 2%i\|3 cos(---)
                   18                18
     ,

     x =
                  %pi 2         %pi      +-+     %pi           %pi 2
           %i sin(---)  + (2cos(---) + 2\|3 )sin(---) - %i cos(---)
                   18            18               18            18
         + 
                 +-+    %pi
           - 2%i\|3 cos(---) - %i
                         18
      /
          +-+    %pi       +-+    %pi
         \|3 sin(---) - %i\|3 cos(---)
                  18               18
     ]
                               Type: List Equation Expression Complex Integer
--R 
--R   Compiling function rectform with type Expression Integer -> 
--R      Expression Complex Integer 
--R
--R   (65)
--R   [
--R     x =
--R             +-+          %pi 2           +-+         %pi      +-+     %pi
--R           (\|3  - %i)sin(---)  + ((- 2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
--R                           18                          18               18
--R         + 
--R               +-+          %pi 2       +-+    %pi     +-+
--R           (- \|3  + %i)cos(---)  - 4%i\|3 cos(---) + \|3  + %i
--R                             18                 18
--R      /
--R           +-+    %pi        +-+    %pi
--R         2\|3 sin(---) - 2%i\|3 cos(---)
--R                   18                18
--R     ,
--R
--R     x =
--R               +-+          %pi 2         +-+         %pi      +-+     %pi
--R           (- \|3  - %i)sin(---)  + ((2%i\|3  - 2)cos(---) + 4\|3 )sin(---)
--R                             18                        18               18
--R         + 
--R             +-+          %pi 2       +-+    %pi     +-+
--R           (\|3  + %i)cos(---)  - 4%i\|3 cos(---) - \|3  + %i
--R                           18                 18
--R      /
--R           +-+    %pi        +-+    %pi
--R         2\|3 sin(---) - 2%i\|3 cos(---)
--R                   18                18
--R     ,
--R
--R     x =
--R                  %pi 2         %pi      +-+     %pi           %pi 2
--R           %i sin(---)  + (2cos(---) + 2\|3 )sin(---) - %i cos(---)
--R                   18            18               18            18
--R         + 
--R                 +-+    %pi
--R           - 2%i\|3 cos(---) - %i
--R                         18
--R      /
--R          +-+    %pi       +-+    %pi
--R         \|3 sin(---) - %i\|3 cos(---)
--R                  18               18
--R     ]
--R                               Type: List Equation Expression Complex Integer
--E 65

--S 66 of 200
eqn:= x**4 + x**3 + x**2 + x + 1 = 0
 

          4    3    2
   (66)  x  + x  + x  + x + 1= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R          4    3    2
--R   (66)  x  + x  + x  + x + 1= 0
--R                                            Type: Equation Polynomial Integer
--E 66

--S 67 of 200
radicalSolve(eqn, x)
 

   (67)
   [
     x =
           -
                2
             *
                ROOT
                                 +-------------------+2
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 36  |-------------------
                                3|          +-+
                                \|       54\|3
                         + 
                                 +-------------------+
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 30  |------------------- - 40
                                3|          +-+
                                \|       54\|3
                      *
                         ROOT
                                    +-------------------+2
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                                36  |-------------------
                                   3|          +-+
                                   \|       54\|3
                              + 
                                      +-------------------+
                                      |     +-+      +---+
                                      |- 25\|3  + 45\|- 5
                                - 15  |------------------- + 40
                                     3|          +-+
                                     \|       54\|3
                           /
                                  +-------------------+
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                     + 
                             +-------------------+
                             |     +-+      +---+
                             |- 25\|3  + 45\|- 5
                       - 45  |-------------------
                            3|          +-+
                            \|       54\|3
                  /
                           +-------------------+
                           |     +-+      +---+
                           |- 25\|3  + 45\|- 5
                       36  |-------------------
                          3|          +-+
                          \|       54\|3
                    *
                       ROOT
                                  +-------------------+2
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                            + 
                                    +-------------------+
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                              - 15  |------------------- + 40
                                   3|          +-+
                                   \|       54\|3
                         /
                                +-------------------+
                                |     +-+      +---+
                                |- 25\|3  + 45\|- 5
                            36  |-------------------
                               3|          +-+
                               \|       54\|3
         + 
             +---------------------------------------------------------+
             |    +-------------------+2      +-------------------+
             |    |     +-+      +---+        |     +-+      +---+
             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
             |36  |-------------------  - 15  |------------------- + 40
             |   3|          +-+             3|          +-+
             |   \|       54\|3              \|       54\|3
           2 |---------------------------------------------------------  - 1
             |                     +-------------------+
             |                     |     +-+      +---+
             |                     |- 25\|3  + 45\|- 5
             |                 36  |-------------------
             |                    3|          +-+
            \|                    \|       54\|3
      /
         4
     ,

     x =
             2
          *
             ROOT
                              +-------------------+2      +-------------------+
                              |     +-+      +---+        |     +-+      +---+
                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                        - 36  |-------------------  - 30  |-------------------
                             3|          +-+             3|          +-+
                             \|       54\|3              \|       54\|3
                      + 
                        - 40
                   *
                     +---------------------------------------------------------+
                     |    +-------------------+2      +-------------------+
                     |    |     +-+      +---+        |     +-+      +---+
                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                     |36  |-------------------  - 15  |------------------- + 40
                     |   3|          +-+             3|          +-+
                     |   \|       54\|3              \|       54\|3
                     |---------------------------------------------------------
                     |                     +-------------------+
                     |                     |     +-+      +---+
                     |                     |- 25\|3  + 45\|- 5
                     |                 36  |-------------------
                     |                    3|          +-+
                    \|                    \|       54\|3
                  + 
                          +-------------------+
                          |     +-+      +---+
                          |- 25\|3  + 45\|- 5
                    - 45  |-------------------
                         3|          +-+
                         \|       54\|3
               /
                        +-------------------+
                        |     +-+      +---+
                        |- 25\|3  + 45\|- 5
                    36  |-------------------
                       3|          +-+
                       \|       54\|3
                 *
                   +---------------------------------------------------------+
                   |    +-------------------+2      +-------------------+
                   |    |     +-+      +---+        |     +-+      +---+
                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                   |36  |-------------------  - 15  |------------------- + 40
                   |   3|          +-+             3|          +-+
                   |   \|       54\|3              \|       54\|3
                   |---------------------------------------------------------
                   |                     +-------------------+
                   |                     |     +-+      +---+
                   |                     |- 25\|3  + 45\|- 5
                   |                 36  |-------------------
                   |                    3|          +-+
                  \|                    \|       54\|3
         + 
             +---------------------------------------------------------+
             |    +-------------------+2      +-------------------+
             |    |     +-+      +---+        |     +-+      +---+
             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
             |36  |-------------------  - 15  |------------------- + 40
             |   3|          +-+             3|          +-+
             |   \|       54\|3              \|       54\|3
           2 |---------------------------------------------------------  - 1
             |                     +-------------------+
             |                     |     +-+      +---+
             |                     |- 25\|3  + 45\|- 5
             |                 36  |-------------------
             |                    3|          +-+
            \|                    \|       54\|3
      /
         4
     ,

     x =
           -
                2
             *
                ROOT
                                 +-------------------+2
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 36  |-------------------
                                3|          +-+
                                \|       54\|3
                         + 
                                 +-------------------+
                                 |     +-+      +---+
                                 |- 25\|3  + 45\|- 5
                           - 30  |------------------- - 40
                                3|          +-+
                                \|       54\|3
                      *
                         ROOT
                                    +-------------------+2
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                                36  |-------------------
                                   3|          +-+
                                   \|       54\|3
                              + 
                                      +-------------------+
                                      |     +-+      +---+
                                      |- 25\|3  + 45\|- 5
                                - 15  |------------------- + 40
                                     3|          +-+
                                     \|       54\|3
                           /
                                  +-------------------+
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                     + 
                           +-------------------+
                           |     +-+      +---+
                           |- 25\|3  + 45\|- 5
                       45  |-------------------
                          3|          +-+
                          \|       54\|3
                  /
                           +-------------------+
                           |     +-+      +---+
                           |- 25\|3  + 45\|- 5
                       36  |-------------------
                          3|          +-+
                          \|       54\|3
                    *
                       ROOT
                                  +-------------------+2
                                  |     +-+      +---+
                                  |- 25\|3  + 45\|- 5
                              36  |-------------------
                                 3|          +-+
                                 \|       54\|3
                            + 
                                    +-------------------+
                                    |     +-+      +---+
                                    |- 25\|3  + 45\|- 5
                              - 15  |------------------- + 40
                                   3|          +-+
                                   \|       54\|3
                         /
                                +-------------------+
                                |     +-+      +---+
                                |- 25\|3  + 45\|- 5
                            36  |-------------------
                               3|          +-+
                               \|       54\|3
         + 
               +---------------------------------------------------------+
               |    +-------------------+2      +-------------------+
               |    |     +-+      +---+        |     +-+      +---+
               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
               |36  |-------------------  - 15  |------------------- + 40
               |   3|          +-+             3|          +-+
               |   \|       54\|3              \|       54\|3
           - 2 |---------------------------------------------------------  - 1
               |                     +-------------------+
               |                     |     +-+      +---+
               |                     |- 25\|3  + 45\|- 5
               |                 36  |-------------------
               |                    3|          +-+
              \|                    \|       54\|3
      /
         4
     ,

     x =
             2
          *
             ROOT
                              +-------------------+2      +-------------------+
                              |     +-+      +---+        |     +-+      +---+
                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                        - 36  |-------------------  - 30  |-------------------
                             3|          +-+             3|          +-+
                             \|       54\|3              \|       54\|3
                      + 
                        - 40
                   *
                     +---------------------------------------------------------+
                     |    +-------------------+2      +-------------------+
                     |    |     +-+      +---+        |     +-+      +---+
                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                     |36  |-------------------  - 15  |------------------- + 40
                     |   3|          +-+             3|          +-+
                     |   \|       54\|3              \|       54\|3
                     |---------------------------------------------------------
                     |                     +-------------------+
                     |                     |     +-+      +---+
                     |                     |- 25\|3  + 45\|- 5
                     |                 36  |-------------------
                     |                    3|          +-+
                    \|                    \|       54\|3
                  + 
                        +-------------------+
                        |     +-+      +---+
                        |- 25\|3  + 45\|- 5
                    45  |-------------------
                       3|          +-+
                       \|       54\|3
               /
                        +-------------------+
                        |     +-+      +---+
                        |- 25\|3  + 45\|- 5
                    36  |-------------------
                       3|          +-+
                       \|       54\|3
                 *
                   +---------------------------------------------------------+
                   |    +-------------------+2      +-------------------+
                   |    |     +-+      +---+        |     +-+      +---+
                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                   |36  |-------------------  - 15  |------------------- + 40
                   |   3|          +-+             3|          +-+
                   |   \|       54\|3              \|       54\|3
                   |---------------------------------------------------------
                   |                     +-------------------+
                   |                     |     +-+      +---+
                   |                     |- 25\|3  + 45\|- 5
                   |                 36  |-------------------
                   |                    3|          +-+
                  \|                    \|       54\|3
         + 
               +---------------------------------------------------------+
               |    +-------------------+2      +-------------------+
               |    |     +-+      +---+        |     +-+      +---+
               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
               |36  |-------------------  - 15  |------------------- + 40
               |   3|          +-+             3|          +-+
               |   \|       54\|3              \|       54\|3
           - 2 |---------------------------------------------------------  - 1
               |                     +-------------------+
               |                     |     +-+      +---+
               |                     |- 25\|3  + 45\|- 5
               |                 36  |-------------------
               |                    3|          +-+
              \|                    \|       54\|3
      /
         4
     ]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (67)
--R   [
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                                 +-------------------+2
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 36  |-------------------
--R                                3|          +-+
--R                                \|       54\|3
--R                         + 
--R                                 +-------------------+
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 30  |------------------- - 40
--R                                3|          +-+
--R                                \|       54\|3
--R                      *
--R                         ROOT
--R                                    +-------------------+2
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                                36  |-------------------
--R                                   3|          +-+
--R                                   \|       54\|3
--R                              + 
--R                                      +-------------------+
--R                                      |     +-+      +---+
--R                                      |- 25\|3  + 45\|- 5
--R                                - 15  |------------------- + 40
--R                                     3|          +-+
--R                                     \|       54\|3
--R                           /
--R                                  +-------------------+
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                     + 
--R                             +-------------------+
--R                             |     +-+      +---+
--R                             |- 25\|3  + 45\|- 5
--R                       - 45  |-------------------
--R                            3|          +-+
--R                            \|       54\|3
--R                  /
--R                           +-------------------+
--R                           |     +-+      +---+
--R                           |- 25\|3  + 45\|- 5
--R                       36  |-------------------
--R                          3|          +-+
--R                          \|       54\|3
--R                    *
--R                       ROOT
--R                                  +-------------------+2
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                            + 
--R                                    +-------------------+
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                              - 15  |------------------- + 40
--R                                   3|          +-+
--R                                   \|       54\|3
--R                         /
--R                                +-------------------+
--R                                |     +-+      +---+
--R                                |- 25\|3  + 45\|- 5
--R                            36  |-------------------
--R                               3|          +-+
--R                               \|       54\|3
--R         + 
--R             +---------------------------------------------------------+
--R             |    +-------------------+2      +-------------------+
--R             |    |     +-+      +---+        |     +-+      +---+
--R             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R             |36  |-------------------  - 15  |------------------- + 40
--R             |   3|          +-+             3|          +-+
--R             |   \|       54\|3              \|       54\|3
--R           2 |---------------------------------------------------------  - 1
--R             |                     +-------------------+
--R             |                     |     +-+      +---+
--R             |                     |- 25\|3  + 45\|- 5
--R             |                 36  |-------------------
--R             |                    3|          +-+
--R            \|                    \|       54\|3
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                              +-------------------+2      +-------------------+
--R                              |     +-+      +---+        |     +-+      +---+
--R                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                        - 36  |-------------------  - 30  |-------------------
--R                             3|          +-+             3|          +-+
--R                             \|       54\|3              \|       54\|3
--R                      + 
--R                        - 40
--R                   *
--R                     +---------------------------------------------------------+
--R                     |    +-------------------+2      +-------------------+
--R                     |    |     +-+      +---+        |     +-+      +---+
--R                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                     |36  |-------------------  - 15  |------------------- + 40
--R                     |   3|          +-+             3|          +-+
--R                     |   \|       54\|3              \|       54\|3
--R                     |---------------------------------------------------------
--R                     |                     +-------------------+
--R                     |                     |     +-+      +---+
--R                     |                     |- 25\|3  + 45\|- 5
--R                     |                 36  |-------------------
--R                     |                    3|          +-+
--R                    \|                    \|       54\|3
--R                  + 
--R                          +-------------------+
--R                          |     +-+      +---+
--R                          |- 25\|3  + 45\|- 5
--R                    - 45  |-------------------
--R                         3|          +-+
--R                         \|       54\|3
--R               /
--R                        +-------------------+
--R                        |     +-+      +---+
--R                        |- 25\|3  + 45\|- 5
--R                    36  |-------------------
--R                       3|          +-+
--R                       \|       54\|3
--R                 *
--R                   +---------------------------------------------------------+
--R                   |    +-------------------+2      +-------------------+
--R                   |    |     +-+      +---+        |     +-+      +---+
--R                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                   |36  |-------------------  - 15  |------------------- + 40
--R                   |   3|          +-+             3|          +-+
--R                   |   \|       54\|3              \|       54\|3
--R                   |---------------------------------------------------------
--R                   |                     +-------------------+
--R                   |                     |     +-+      +---+
--R                   |                     |- 25\|3  + 45\|- 5
--R                   |                 36  |-------------------
--R                   |                    3|          +-+
--R                  \|                    \|       54\|3
--R         + 
--R             +---------------------------------------------------------+
--R             |    +-------------------+2      +-------------------+
--R             |    |     +-+      +---+        |     +-+      +---+
--R             |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R             |36  |-------------------  - 15  |------------------- + 40
--R             |   3|          +-+             3|          +-+
--R             |   \|       54\|3              \|       54\|3
--R           2 |---------------------------------------------------------  - 1
--R             |                     +-------------------+
--R             |                     |     +-+      +---+
--R             |                     |- 25\|3  + 45\|- 5
--R             |                 36  |-------------------
--R             |                    3|          +-+
--R            \|                    \|       54\|3
--R      /
--R         4
--R     ,
--R
--R     x =
--R           -
--R                2
--R             *
--R                ROOT
--R                                 +-------------------+2
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 36  |-------------------
--R                                3|          +-+
--R                                \|       54\|3
--R                         + 
--R                                 +-------------------+
--R                                 |     +-+      +---+
--R                                 |- 25\|3  + 45\|- 5
--R                           - 30  |------------------- - 40
--R                                3|          +-+
--R                                \|       54\|3
--R                      *
--R                         ROOT
--R                                    +-------------------+2
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                                36  |-------------------
--R                                   3|          +-+
--R                                   \|       54\|3
--R                              + 
--R                                      +-------------------+
--R                                      |     +-+      +---+
--R                                      |- 25\|3  + 45\|- 5
--R                                - 15  |------------------- + 40
--R                                     3|          +-+
--R                                     \|       54\|3
--R                           /
--R                                  +-------------------+
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                     + 
--R                           +-------------------+
--R                           |     +-+      +---+
--R                           |- 25\|3  + 45\|- 5
--R                       45  |-------------------
--R                          3|          +-+
--R                          \|       54\|3
--R                  /
--R                           +-------------------+
--R                           |     +-+      +---+
--R                           |- 25\|3  + 45\|- 5
--R                       36  |-------------------
--R                          3|          +-+
--R                          \|       54\|3
--R                    *
--R                       ROOT
--R                                  +-------------------+2
--R                                  |     +-+      +---+
--R                                  |- 25\|3  + 45\|- 5
--R                              36  |-------------------
--R                                 3|          +-+
--R                                 \|       54\|3
--R                            + 
--R                                    +-------------------+
--R                                    |     +-+      +---+
--R                                    |- 25\|3  + 45\|- 5
--R                              - 15  |------------------- + 40
--R                                   3|          +-+
--R                                   \|       54\|3
--R                         /
--R                                +-------------------+
--R                                |     +-+      +---+
--R                                |- 25\|3  + 45\|- 5
--R                            36  |-------------------
--R                               3|          +-+
--R                               \|       54\|3
--R         + 
--R               +---------------------------------------------------------+
--R               |    +-------------------+2      +-------------------+
--R               |    |     +-+      +---+        |     +-+      +---+
--R               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R               |36  |-------------------  - 15  |------------------- + 40
--R               |   3|          +-+             3|          +-+
--R               |   \|       54\|3              \|       54\|3
--R           - 2 |---------------------------------------------------------  - 1
--R               |                     +-------------------+
--R               |                     |     +-+      +---+
--R               |                     |- 25\|3  + 45\|- 5
--R               |                 36  |-------------------
--R               |                    3|          +-+
--R              \|                    \|       54\|3
--R      /
--R         4
--R     ,
--R
--R     x =
--R             2
--R          *
--R             ROOT
--R                              +-------------------+2      +-------------------+
--R                              |     +-+      +---+        |     +-+      +---+
--R                              |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                        - 36  |-------------------  - 30  |-------------------
--R                             3|          +-+             3|          +-+
--R                             \|       54\|3              \|       54\|3
--R                      + 
--R                        - 40
--R                   *
--R                     +---------------------------------------------------------+
--R                     |    +-------------------+2      +-------------------+
--R                     |    |     +-+      +---+        |     +-+      +---+
--R                     |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                     |36  |-------------------  - 15  |------------------- + 40
--R                     |   3|          +-+             3|          +-+
--R                     |   \|       54\|3              \|       54\|3
--R                     |---------------------------------------------------------
--R                     |                     +-------------------+
--R                     |                     |     +-+      +---+
--R                     |                     |- 25\|3  + 45\|- 5
--R                     |                 36  |-------------------
--R                     |                    3|          +-+
--R                    \|                    \|       54\|3
--R                  + 
--R                        +-------------------+
--R                        |     +-+      +---+
--R                        |- 25\|3  + 45\|- 5
--R                    45  |-------------------
--R                       3|          +-+
--R                       \|       54\|3
--R               /
--R                        +-------------------+
--R                        |     +-+      +---+
--R                        |- 25\|3  + 45\|- 5
--R                    36  |-------------------
--R                       3|          +-+
--R                       \|       54\|3
--R                 *
--R                   +---------------------------------------------------------+
--R                   |    +-------------------+2      +-------------------+
--R                   |    |     +-+      +---+        |     +-+      +---+
--R                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                   |36  |-------------------  - 15  |------------------- + 40
--R                   |   3|          +-+             3|          +-+
--R                   |   \|       54\|3              \|       54\|3
--R                   |---------------------------------------------------------
--R                   |                     +-------------------+
--R                   |                     |     +-+      +---+
--R                   |                     |- 25\|3  + 45\|- 5
--R                   |                 36  |-------------------
--R                   |                    3|          +-+
--R                  \|                    \|       54\|3
--R         + 
--R               +---------------------------------------------------------+
--R               |    +-------------------+2      +-------------------+
--R               |    |     +-+      +---+        |     +-+      +---+
--R               |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R               |36  |-------------------  - 15  |------------------- + 40
--R               |   3|          +-+             3|          +-+
--R               |   \|       54\|3              \|       54\|3
--R           - 2 |---------------------------------------------------------  - 1
--R               |                     +-------------------+
--R               |                     |     +-+      +---+
--R               |                     |- 25\|3  + 45\|- 5
--R               |                 36  |-------------------
--R               |                    3|          +-+
--R              \|                    \|       54\|3
--R      /
--R         4
--R     ]
--R                                       Type: List Equation Expression Integer
--E 67

--S 68 of 200
eval(eqn, %.1)
 

   (68)
                                      +-------------------+
                                      |     +-+      +---+
             +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
         (90\|- 5 \|3   - 270\|- 5 )  |-------------------
                                     3|          +-+
                                     \|       54\|3
      *
         ROOT
                         +-------------------+2      +-------------------+
                         |     +-+      +---+        |     +-+      +---+
                         |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                  (- 36  |-------------------  - 30  |------------------- - 40)
                        3|          +-+             3|          +-+
                        \|       54\|3              \|       54\|3
               *
                   +---------------------------------------------------------+
                   |    +-------------------+2      +-------------------+
                   |    |     +-+      +---+        |     +-+      +---+
                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                   |36  |-------------------  - 15  |------------------- + 40
                   |   3|          +-+             3|          +-+
                   |   \|       54\|3              \|       54\|3
                   |---------------------------------------------------------
                   |                     +-------------------+
                   |                     |     +-+      +---+
                   |                     |- 25\|3  + 45\|- 5
                   |                 36  |-------------------
                   |                    3|          +-+
                  \|                    \|       54\|3
              + 
                      +-------------------+
                      |     +-+      +---+
                      |- 25\|3  + 45\|- 5
                - 45  |-------------------
                     3|          +-+
                     \|       54\|3
           /
                    +-------------------+
                    |     +-+      +---+
                    |- 25\|3  + 45\|- 5
                36  |-------------------
                   3|          +-+
                   \|       54\|3
             *
                 +---------------------------------------------------------+
                 |    +-------------------+2      +-------------------+
                 |    |     +-+      +---+        |     +-+      +---+
                 |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
                 |36  |-------------------  - 15  |------------------- + 40
                 |   3|          +-+             3|          +-+
                 |   \|       54\|3              \|       54\|3
                 |---------------------------------------------------------
                 |                     +-------------------+
                 |                     |     +-+      +---+
                 |                     |- 25\|3  + 45\|- 5
                 |                 36  |-------------------
                 |                    3|          +-+
                \|                    \|       54\|3
     + 
                                       +-------------------+
                                       |     +-+      +---+
              +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
       (- 135\|- 5 \|3   + 405\|- 5 )  |-------------------
                                      3|          +-+
                                      \|       54\|3
  /
                                    +-------------------+2
                                    |     +-+      +---+
            +---+ +-+2        +-+   |- 25\|3  + 45\|- 5
       (432\|- 5 \|3   + 1584\|3 )  |-------------------
                                   3|          +-+
                                   \|       54\|3
     + 
                                   +-------------------+
                                   |     +-+      +---+
            +---+ +-+2       +-+   |- 25\|3  + 45\|- 5         +-+        +---+
     (- 180\|- 5 \|3   - 660\|3 )  |------------------- + 1760\|3  + 1440\|- 5
                                  3|          +-+
                                  \|       54\|3
     =
     0
                                            Type: Equation Expression Integer
--R 
--R
--R   (68)
--R                                      +-------------------+
--R                                      |     +-+      +---+
--R             +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
--R         (90\|- 5 \|3   - 270\|- 5 )  |-------------------
--R                                     3|          +-+
--R                                     \|       54\|3
--R      *
--R         ROOT
--R                         +-------------------+2      +-------------------+
--R                         |     +-+      +---+        |     +-+      +---+
--R                         |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                  (- 36  |-------------------  - 30  |------------------- - 40)
--R                        3|          +-+             3|          +-+
--R                        \|       54\|3              \|       54\|3
--R               *
--R                   +---------------------------------------------------------+
--R                   |    +-------------------+2      +-------------------+
--R                   |    |     +-+      +---+        |     +-+      +---+
--R                   |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                   |36  |-------------------  - 15  |------------------- + 40
--R                   |   3|          +-+             3|          +-+
--R                   |   \|       54\|3              \|       54\|3
--R                   |---------------------------------------------------------
--R                   |                     +-------------------+
--R                   |                     |     +-+      +---+
--R                   |                     |- 25\|3  + 45\|- 5
--R                   |                 36  |-------------------
--R                   |                    3|          +-+
--R                  \|                    \|       54\|3
--R              + 
--R                      +-------------------+
--R                      |     +-+      +---+
--R                      |- 25\|3  + 45\|- 5
--R                - 45  |-------------------
--R                     3|          +-+
--R                     \|       54\|3
--R           /
--R                    +-------------------+
--R                    |     +-+      +---+
--R                    |- 25\|3  + 45\|- 5
--R                36  |-------------------
--R                   3|          +-+
--R                   \|       54\|3
--R             *
--R                 +---------------------------------------------------------+
--R                 |    +-------------------+2      +-------------------+
--R                 |    |     +-+      +---+        |     +-+      +---+
--R                 |    |- 25\|3  + 45\|- 5         |- 25\|3  + 45\|- 5
--R                 |36  |-------------------  - 15  |------------------- + 40
--R                 |   3|          +-+             3|          +-+
--R                 |   \|       54\|3              \|       54\|3
--R                 |---------------------------------------------------------
--R                 |                     +-------------------+
--R                 |                     |     +-+      +---+
--R                 |                     |- 25\|3  + 45\|- 5
--R                 |                 36  |-------------------
--R                 |                    3|          +-+
--R                \|                    \|       54\|3
--R     + 
--R                                       +-------------------+
--R                                       |     +-+      +---+
--R              +---+ +-+2       +---+   |- 25\|3  + 45\|- 5
--R       (- 135\|- 5 \|3   + 405\|- 5 )  |-------------------
--R                                      3|          +-+
--R                                      \|       54\|3
--R  /
--R                                    +-------------------+2
--R                                    |     +-+      +---+
--R            +---+ +-+2        +-+   |- 25\|3  + 45\|- 5
--R       (432\|- 5 \|3   + 1584\|3 )  |-------------------
--R                                   3|          +-+
--R                                   \|       54\|3
--R     + 
--R                                   +-------------------+
--R                                   |     +-+      +---+
--R            +---+ +-+2       +-+   |- 25\|3  + 45\|- 5         +-+        +---+
--R     (- 180\|- 5 \|3   - 660\|3 )  |------------------- + 1760\|3  + 1440\|- 5
--R                                  3|          +-+
--R                                  \|       54\|3
--R     =
--R     0
--R                                            Type: Equation Expression Integer
--E 68

--S 69 of 200
%e**(2*x) + 2*%e**x + 1 = z
 

           2x      x
   (69)  %e   + 2%e  + 1= z
                                            Type: Equation Expression Integer
--R 
--R
--R           2x      x
--R   (69)  %e   + 2%e  + 1= z
--R                                            Type: Equation Expression Integer
--E 69

--S 70 of 200
solve(%, x)
 

                  +-+                +-+
   (70)  [x= log(\|z  - 1),x= log(- \|z  - 1)]
                                       Type: List Equation Expression Integer
--R 
--R
--R                  +-+                +-+
--R   (70)  [x= log(\|z  - 1),x= log(- \|z  - 1)]
--R                                       Type: List Equation Expression Integer
--E 70

--S 71 of 200
(x + 1) * (sin(x)**2 + 1)**2 * cos(3*x)**3 = 0
 

                       3      4                  3      2                 3
   (71)  (x + 1)cos(3x) sin(x)  + (2x + 2)cos(3x) sin(x)  + (x + 1)cos(3x) = 0
                                            Type: Equation Expression Integer
--R 
--R
--R                       3      4                  3      2                 3
--R   (71)  (x + 1)cos(3x) sin(x)  + (2x + 2)cos(3x) sin(x)  + (x + 1)cos(3x) = 0
--R                                            Type: Equation Expression Integer
--E 71

--S 72 of 200
solve(%, x)
 

                   +---+             +---+     %pi
   (72)  [x= asin(\|- 1 ),x= - asin(\|- 1 ),x= ---,x= - 1]
                                                6
                                       Type: List Equation Expression Integer
--R 
--R
--R                   +---+             +---+     %pi
--R   (72)  [x= asin(\|- 1 ),x= - asin(\|- 1 ),x= ---,x= - 1]
--R                                                6
--R                                       Type: List Equation Expression Integer
--E 72

--S 73 of 200
solve(%e**z = 1, z)
 

   (73)  [z= 0]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (73)  [z= 0]
--R                                       Type: List Equation Expression Integer
--E 73

--S 74 of 200
solve(sin(x) = cos(x), x)
 

             %pi
   (74)  [x= ---]
              4
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi
--R   (74)  [x= ---]
--R              4
--R                                       Type: List Equation Expression Integer
--E 74

--S 75 of 200
solve(tan(x) = 1, x)
 

             %pi
   (75)  [x= ---]
              4
                                       Type: List Equation Expression Integer
--R 
--R
--R             %pi
--R   (75)  [x= ---]
--R              4
--R                                       Type: List Equation Expression Integer
--E 75

--S 76 of 200
solve(sin(x) = tan(x), x)
 

   (76)  [x= 0]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (76)  [x= 0]
--R                                       Type: List Equation Expression Integer
--E 76

--S 77 of 200
solve(sqrt(x**2 + 1) = x - 2, x)
 

   (77)  []
                                       Type: List Equation Expression Integer
--R 
--R
--R   (77)  []
--R                                       Type: List Equation Expression Integer
--E 77

--S 78 of 200
eq1:=   x +   y +   z =  6
 

   (78)  z + y + x= 6
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (78)  z + y + x= 6
--R                                            Type: Equation Polynomial Integer
--E 78

--S 79 of 200
eq2:= 2*x +   y + 2*z = 10
 

   (79)  2z + y + 2x= 10
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (79)  2z + y + 2x= 10
--R                                            Type: Equation Polynomial Integer
--E 79

--S 80 of 200
eq3:=   x + 3*y +   z = 10
 

   (80)  z + 3y + x= 10
                                            Type: Equation Polynomial Integer
--R 
--R
--R   (80)  z + 3y + x= 10
--R                                            Type: Equation Polynomial Integer
--E 80

--S 81 of 200
solve([eq1, eq2, eq3], [x, y, z])
 

   (81)  [[x= - %CA + 4,y= 2,z= %CA]]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--I   (81)  [[x= - %BU + 4,y= 2,z= %BU]]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 81
--S 82 of 200
eq1:= x**2*y + 3*y*z - 4 = 0
 

                 2
   (82)  3y z + x y - 4= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R                 2
--R   (82)  3y z + x y - 4= 0
--R                                            Type: Equation Polynomial Integer
--E 82

--S 83 of 200
eq2:= -3*x**2*z + 2*y**2 + 1 = 0
 

             2      2
   (83)  - 3x z + 2y  + 1= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R             2      2
--R   (83)  - 3x z + 2y  + 1= 0
--R                                            Type: Equation Polynomial Integer
--E 83

--S 84 of 200
eq3:= 2*y*z**2 - z**2 - 1 = 0
 

                  2
   (84)  (2y - 1)z  - 1= 0
                                            Type: Equation Polynomial Integer
--R 
--R
--R                  2
--R   (84)  (2y - 1)z  - 1= 0
--R                                            Type: Equation Polynomial Integer
--E 84

--S 85 of 200
solve([eq1, eq2, eq3], [x, y, z])
 

   (85)
   [[x= 1,y= 1,z= 1], [x= - 1,y= 1,z= 1],
             2                      2
    [- 3z + x  + 2= 0,y= - 3z + 1,3z  - 2z + 1= 0],

                                                4      3      2
         4      3      2          2        - 18z  + 24z  + 21z  + 12z + 3
     [12z  - 12z  - 30z  + 7z + 3x = 0, y= ------------------------------,
                                                          2
        5     4     3     2
      6z  - 6z  - 9z  - 7z  - 3z - 1= 0]
     ]
                         Type: List List Equation Fraction Polynomial Integer
--R 
--R
--R   (85)
--R   [[x= 1,y= 1,z= 1], [x= - 1,y= 1,z= 1],
--R             2                      2
--R    [- 3z + x  + 2= 0,y= - 3z + 1,3z  - 2z + 1= 0],
--R
--R                                                4      3      2
--R         4      3      2          2        - 18z  + 24z  + 21z  + 12z + 3
--R     [12z  - 12z  - 30z  + 7z + 3x = 0, y= ------------------------------,
--R                                                          2
--R        5     4     3     2
--R      6z  - 6z  - 9z  - 7z  - 3z - 1= 0]
--R     ]
--R                         Type: List List Equation Fraction Polynomial Integer
--E 85

--S 86 of 200
m:= matrix([[a, b], [1, a*b]])
 

         +a   b +
   (86)  |      |
         +1  a b+
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +a   b +
--R   (86)  |      |
--R         +1  a b+
--R                                              Type: Matrix Polynomial Integer
--E 86

--S 87 of 200
minv:= inverse(m)
 

         +     a            1   +
         |  ------     - ------ |
         |   2            2     |
         |  a  - 1       a  - 1 |
   (87)  |                      |
         |      1          a    |
         |- ---------  ---------|
         |    2          2      |
         +  (a  - 1)b  (a  - 1)b+
                          Type: Union(Matrix Fraction Polynomial Integer,...)
--R 
--R
--R         +     a            1   +
--R         |  ------     - ------ |
--R         |   2            2     |
--R         |  a  - 1       a  - 1 |
--R   (87)  |                      |
--R         |      1          a    |
--R         |- ---------  ---------|
--R         |    2          2      |
--R         +  (a  - 1)b  (a  - 1)b+
--R                          Type: Union(Matrix Fraction Polynomial Integer,...)
--E 87

--S 88 of 200
m * minv
 

         +1  0+
   (88)  |    |
         +0  1+
                                     Type: Matrix Fraction Polynomial Integer
--R 
--R
--R         +1  0+
--R   (88)  |    |
--R         +0  1+
--R                                     Type: Matrix Fraction Polynomial Integer
--E 88

--S 89 of 200
matrix([[1,    1,    1,    1   ], _
        [w,    x,    y,    z   ], _
        [w**2, x**2, y**2, z**2], _
        [w**3, x**3, y**3, z**3]])
 

         +1   1   1   1 +
         |              |
         |w   x   y   z |
         |              |
   (89)  | 2   2   2   2|
         |w   x   y   z |
         |              |
         | 3   3   3   3|
         +w   x   y   z +
                                              Type: Matrix Polynomial Integer
--R 
--R
--R         +1   1   1   1 +
--R         |              |
--R         |w   x   y   z |
--R         |              |
--R   (89)  | 2   2   2   2|
--R         |w   x   y   z |
--R         |              |
--R         | 3   3   3   3|
--R         +w   x   y   z +
--R                                              Type: Matrix Polynomial Integer
--E 89

--S 90 of 200
determinant(%)
 

   (90)
              2       2    2        2    2   3
     ((x - w)y  + (- x  + w )y + w x  - w x)z
   + 
                3     3    3        3    3   2
     ((- x + w)y  + (x  - w )y - w x  + w x)z
   + 
        2    2  3       3    3  2    2 3    3 2           2    2   3
     ((x  - w )y  + (- x  + w )y  + w x  - w x )z + (- w x  + w x)y
   + 
         3    3   2       2 3    3 2
     (w x  - w x)y  + (- w x  + w x )y
                                                     Type: Polynomial Integer
--R 
--R
--R   (90)
--R              2       2    2        2    2   3
--R     ((x - w)y  + (- x  + w )y + w x  - w x)z
--R   + 
--R                3     3    3        3    3   2
--R     ((- x + w)y  + (x  - w )y - w x  + w x)z
--R   + 
--R        2    2  3       3    3  2    2 3    3 2           2    2   3
--R     ((x  - w )y  + (- x  + w )y  + w x  - w x )z + (- w x  + w x)y
--R   + 
--R         3    3   2       2 3    3 2
--R     (w x  - w x)y  + (- w x  + w x )y
--R                                                     Type: Polynomial Integer
--E 90

--S 91 of 200
factor(%)
 

   (91)  (x - w)(y - x)(y - w)(z - y)(z - x)(z - w)
                                            Type: Factored Polynomial Integer
--R 
--R
--R   (91)  (x - w)(y - x)(y - w)(z - y)(z - x)(z - w)
--R                                            Type: Factored Polynomial Integer
--E 91

--S 92 of 200
m:= matrix([[ 5, -3, -7], _
            [-2,  1,  2], _
            [ 2, -3, -4]])
 

         + 5   - 3  - 7+
         |             |
   (92)  |- 2   1    2 |
         |             |
         + 2   - 3  - 4+
                                                         Type: Matrix Integer
--R 
--R
--R         + 5   - 3  - 7+
--R         |             |
--R   (92)  |- 2   1    2 |
--R         |             |
--R         + 2   - 3  - 4+
--R                                                         Type: Matrix Integer
--E 92

--S 93 of 200
characteristicPolynomial(m, lambda)
 

                 3          2
   (93)  - lambda  + 2lambda  + 5lambda - 6
                                                     Type: Polynomial Integer
--R 
--R
--R                 3          2
--R   (93)  - lambda  + 2lambda  + 5lambda - 6
--R                                                     Type: Polynomial Integer
--E 93

--S 94 of 200
solve(% = 0, lambda)
 

   (94)  [lambda= 3,lambda= 1,lambda= - 2]
                              Type: List Equation Fraction Polynomial Integer
--R 
--R
--R   (94)  [lambda= 3,lambda= 1,lambda= - 2]
--R                              Type: List Equation Fraction Polynomial Integer
--E 94

--S 95 of 200
m:= 'm;
 

                                                             Type: Variable m
--R 
--R
--R                                                             Type: Variable m
--E 95

--S 96 of 200
summation(k**3, k = 1..n)
 

          n
         --+    3
   (96)  >     k
         --+
         k= 1
                                                     Type: Expression Integer
--R 
--R
--R          n
--R         --+    3
--R   (96)  >     k
--R         --+
--R         k= 1
--R                                                     Type: Expression Integer
--E 96

--S 97 of 200
sum(k**3, k = 1..n)
 

          4     3    2
         n  + 2n  + n
   (97)  -------------
               4
                                            Type: Fraction Polynomial Integer
--R 
--R
--R          4     3    2
--R         n  + 2n  + n
--R   (97)  -------------
--R               4
--R                                            Type: Fraction Polynomial Integer
--E 97

--S 98 of 200
limit(sum(1/k**2 + 1/k**3, k = 1..n), n = %plusInfinity)
 

   (98)  "failed"
                                                    Type: Union("failed",...)
--R 
--R
--R   (98)  "failed"
--R                                                    Type: Union("failed",...)
--E 98
--S 99 of 200
product(k, k = 1..n)
 

           n
         ++-++
   (99)   | |   k
          | |
         k= 1
                                                     Type: Expression Integer
--R 
--R
--R           n
--R         ++-++
--R   (99)   | |   k
--R          | |
--R         k= 1
--R                                                     Type: Expression Integer
--E 99

--S 100 of 200
limit((1 + 1/n)**n, n = %plusInfinity)
 

   (100)  %e
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R   (100)  %e
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 100

--S 101 of 200
limit((1 - cos(x))/x**2, x = 0)
 

          1
   (101)  -
          2
                        Type: Union(OrderedCompletion Expression Integer,...)
--R 
--R
--R          1
--R   (101)  -
--R          2
--R                        Type: Union(OrderedCompletion Expression Integer,...)
--E 101

--S 102 of 200
y:= operator('y);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 102

--S 103 of 200
x:= operator('x);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 103

--S 104 of 200
D(y(x(t)), t, 2)
 

           ,   2 ,,          ,       ,,
   (104)  x (t) y  (x(t)) + y (x(t))x  (t)

                                                     Type: Expression Integer
--R 
--R
--R           ,   2 ,,          ,       ,,
--R   (104)  x (t) y  (x(t)) + y (x(t))x  (t)
--R
--R                                                     Type: Expression Integer
--E 104

)clear properties x y
 

--S 105 of 200
1/(x**3 + 2)
 

             1
   (105)  ------
           3
          x  + 2
                                            Type: Fraction Polynomial Integer
--R 
--R
--R             1
--R   (105)  ------
--R           3
--R          x  + 2
--R                                            Type: Fraction Polynomial Integer
--E 105

--S 106 of 200
integrate(%, x)
 

   (106)
          +-+     2 3+-+2    3+-+          +-+     3+-+
       - \|3 log(x  \|4  - 2x\|4  + 4) + 2\|3 log(x\|4  + 2)
     + 
               +-+3+-+    +-+
             x\|3 \|4  - \|3
       6atan(----------------)
                     3
  /
       +-+3+-+
     6\|3 \|4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (106)
--R          +-+     2 3+-+2    3+-+          +-+     3+-+
--R       - \|3 log(x  \|4  - 2x\|4  + 4) + 2\|3 log(x\|4  + 2)
--R     + 
--R               +-+3+-+    +-+
--R             x\|3 \|4  - \|3
--R       6atan(----------------)
--R                     3
--R  /
--R       +-+3+-+
--R     6\|3 \|4
--R                                          Type: Union(Expression Integer,...)
--E 106

--S 107 of 200
D(%, x)
 

             1
   (107)  ------
           3
          x  + 2
                                                     Type: Expression Integer
--R 
--R
--R             1
--R   (107)  ------
--R           3
--R          x  + 2
--R                                                     Type: Expression Integer
--E 107

--S 108 of 200
integrate(1/(a + b*cos(x)), x)
 

   (108)
                         +-------+
                         | 2    2        2    2
        (- a cos(x) - b)\|b  - a   + (- b  + a )sin(x)
    log(----------------------------------------------)
                         b cos(x) + a
   [---------------------------------------------------,
                          +-------+
                          | 2    2
                         \|b  - a
                   +---------+
                   |   2    2
            sin(x)\|- b  + a
    2atan(---------------------)
          (b + a)cos(x) + b + a
    ----------------------------]
             +---------+
             |   2    2
            \|- b  + a
                                     Type: Union(List Expression Integer,...)
--R 
--R
--R   (108)
--R                         +-------+
--R                         | 2    2        2    2
--R        (- a cos(x) - b)\|b  - a   + (- b  + a )sin(x)
--R    log(----------------------------------------------)
--R                         b cos(x) + a
--R   [---------------------------------------------------,
--R                          +-------+
--R                          | 2    2
--R                         \|b  - a
--R                   +---------+
--R                   |   2    2
--R            sin(x)\|- b  + a
--R    2atan(---------------------)
--R          (b + a)cos(x) + b + a
--R    ----------------------------]
--R             +---------+
--R             |   2    2
--R            \|- b  + a
--R                                     Type: Union(List Expression Integer,...)
--E 108

--S 109 of 200
map(simplify, map(f +-> D(f, x), %))
 

                 1            1
   (109)  [------------,------------]
           b cos(x) + a b cos(x) + a
                                                Type: List Expression Integer
--R 
--R
--R                 1            1
--R   (109)  [------------,------------]
--R           b cos(x) + a b cos(x) + a
--R                                                Type: List Expression Integer
--E 109

--S 110 of 200
D(abs(x), x)
 

          abs(x)
   (110)  ------
             x
                                                     Type: Expression Integer
--R 
--R
--R          abs(x)
--R   (110)  ------
--R             x
--R                                                     Type: Expression Integer
--E 110

--S 111 of 200
integrate(abs(x), x)
 

             x
           ++
   (111)   |   abs(%M)d%M
          ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R             x
--R           ++
--I   (111)   |   abs(%J)d%J
--R          ++
--R                                          Type: Union(Expression Integer,...)
--E 111

--S 112 of 200
a(x) == if x < 0 then -x else x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 112

--S 113 of 200
D(a(x), x)
 
   Compiling function a with type Variable x -> Polynomial Integer 

   (113)  1
                                                     Type: Polynomial Integer
--R 
--R   Compiling function a with type Variable x -> Polynomial Integer 
--R
--R   (113)  1
--R                                                     Type: Polynomial Integer
--E 113

--S 114 of 200
integrate(a(x), x)
 

          1  2
   (114)  - x
          2
                                            Type: Polynomial Fraction Integer
--R 
--R
--R          1  2
--R   (114)  - x
--R          2
--R                                            Type: Polynomial Fraction Integer
--E 114

)clear properties a
 
   Compiled code for a has been cleared.
 
--S 115 of 200
integrate(x/(sqrt(1 + x) + sqrt(1 - x)), x)
 

                  +-----+             +-------+
          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
   (115)  -------------------------------------
                            3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +-----+             +-------+
--R          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (115)  -------------------------------------
--R                            3
--R                                          Type: Union(Expression Integer,...)
--E 115

--S 116 of 200
integrate((sqrt(1 + x) - sqrt(1 - x))/2, x)
 

                  +-----+             +-------+
          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
   (116)  -------------------------------------
                            3
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                  +-----+             +-------+
--R          (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (116)  -------------------------------------
--R                            3
--R                                          Type: Union(Expression Integer,...)
--E 116

--S 117 of 200
integrate(1/x, x = -1..1)
 
 
Daly Bug
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 117

--S 118 of 200
integrate(1/x**2, x = -1..1)
 
 
Daly Bug
   >> Error detected within library code:
   integrate: pole in path of integration

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 118

--S 119 of 200
integrate(sqrt(x + 1/x - 2), x = 0..1)
 

   (117)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (117)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 119

--S 120 of 200
integrate(sqrt(x + 1/x - 2), x = 0..1, "noPole")
 

            4
   (118)  - -
            3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R            4
--R   (118)  - -
--R            3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 120

--S 121 of 200
integrate(sqrt(x + 1/x - 2), x = 1..2)
 

   (119)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (119)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 121

--S 122 of 200
integrate(sqrt(x + 1/x - 2), x = 1..2, "noPole")
 

              +-+
          - 2\|2  + 4
   (120)  -----------
               3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R              +-+
--R          - 2\|2  + 4
--R   (120)  -----------
--R               3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 122

--S 123 of 200
integrate(sqrt(x + 1/x - 2), x = 0..2)
 

   (121)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (121)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 123

--S 124 of 200
integrate(sqrt(x + 1/x - 2), x = 0..2, "noPole")
 

              +-+
            2\|2
   (122)  - -----
              3
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R              +-+
--R            2\|2
--R   (122)  - -----
--R              3
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 124

--S 125 of 200
integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity)
 

   (123)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (123)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 125

--S 126 of 200
integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity, "noPole")
 

   (124)  "failed"
                                                Type: Union(fail: failed,...)
--R 
--R
--R   (124)  "failed"
--R                                                Type: Union(fail: failed,...)
--E 126

--S 127 of 200
integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity)
 

   (125)  potentialPole
                                         Type: Union(pole: potentialPole,...)
--R 
--R
--R   (125)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 127

--S 128 of 200
integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity, "noPole")
 

   (126)  "failed"
                                                Type: Union(fail: failed,...)
--R 
--R
--R   (126)  "failed"
--R                                                Type: Union(fail: failed,...)
--E 128

--S 129 of 200
integrate(integrate(integrate(1, z = 0..c*(1 - x/a - y/b)), _
                    y = 0..b*(1 - x/a)), _
          x = 0..a)
 

          a b c
   (127)  -----
            6
                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--R 
--R
--R          a b c
--R   (127)  -----
--R            6
--R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
--E 129

--S 130 of 200
1/sqrt(1 - (v/c)**2)
 

                1
   (128)  ------------
           +---------+
           |   2    2
           |- v  + c
           |---------
           |     2
          \|    c
                                                     Type: Expression Integer
--R 
--R
--R                1
--R   (128)  ------------
--R           +---------+
--R           |   2    2
--R           |- v  + c
--R           |---------
--R           |     2
--R          \|    c
--R                                                     Type: Expression Integer
--E 130

--S 131 of 200
series(%, v = 0)
 

               1   2    3   4     5   6      8
   (129)  1 + --- v  + --- v  + ---- v  + O(v )
                2        4         6
              2c       8c       16c
                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--R 
--R
--R               1   2    3   4     5   6      8
--R   (129)  1 + --- v  + --- v  + ---- v  + O(v )
--R                2        4         6
--R              2c       8c       16c
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--E 131

--S 132 of 200
1/%**2
 

               1  2      8
   (130)  1 - -- v  + O(v )
               2
              c
                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--R 
--R
--R               1  2      8
--R   (130)  1 - -- v  + O(v )
--R               2
--R              c
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,v,0)
--E 132

--S 133 of 200
tsin:= series(sin(x), x = 0)
 

              1  3    1   5     1   7      9
   (131)  x - - x  + --- x  - ---- x  + O(x )
              6      120      5040
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  3    1   5     1   7      9
--R   (131)  x - - x  + --- x  - ---- x  + O(x )
--R              6      120      5040
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 133 

--S 134 of 200
tcos:= series(cos(x), x = 0)
 

              1  2    1  4    1   6      8
   (132)  1 - - x  + -- x  - --- x  + O(x )
              2      24      720
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  2    1  4    1   6      8
--R   (132)  1 - - x  + -- x  - --- x  + O(x )
--R              2      24      720
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 134

--S 135 of 200
tsin/tcos
 

              1  3    2  5    17  7      9
   (133)  x + - x  + -- x  + --- x  + O(x )
              3      15      315
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  3    2  5    17  7      9
--R   (133)  x + - x  + -- x  + --- x  + O(x )
--R              3      15      315
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 135

--S 136 of 200
series(tan(x), x = 0)
 

              1  3    2  5    17  7      9
   (134)  x + - x  + -- x  + --- x  + O(x )
              3      15      315
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R              1  3    2  5    17  7      9
--R   (134)  x + - x  + -- x  + --- x  + O(x )
--R              3      15      315
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 136


)set streams calculate 1
 

--S 137 of 200
log(x)**a*exp(-b*x)
 

            - b x      a
   (135)  %e     log(x)
                                                     Type: Expression Integer
--R 
--R
--R            - b x      a
--R   (135)  %e     log(x)
--R                                                     Type: Expression Integer
--E 137

--S 138 of 200
series(%, x = 1)
 
 
Daly Bug
   >> Error detected within library code:
   No series expansion

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   No series expansion
--R
--R   Continuing to read the file...
--R
--E 138

)set streams calculate 7
 

--S 139 of 200
taylor(log(sinh(z)) + log(cosh(z + w)), z = 0)
 
 
Daly Bug
   >> Error detected within library code:
   No Taylor expansion: logarithmic singularity

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   No Taylor expansion: logarithmic singularity
--R
--R   Continuing to read the file...
--R
--E 139

--S 140 of 200
% - taylor(log(sinh(z) * cosh(z + w)), z = 0)
 
 
Daly Bug
   >> Error detected within library code:
   No Taylor expansion: logarithmic singularity

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   No Taylor expansion: logarithmic singularity
--R
--R   Continuing to read the file...
--R
--E 140

--S 141 of 200
log(sin(x)/x)
 

              sin(x)
   (136)  log(------)
                 x
                                                     Type: Expression Integer
--R 
--R
--R              sin(x)
--R   (136)  log(------)
--R                 x
--R                                                     Type: Expression Integer
--E 141

--S 142 of 200
series(%, x = 0)
 

            1  2    1   4     1   6     1    8      10
   (137)  - - x  - --- x  - ---- x  - ----- x  + O(x  )
            6      180      2835      37800
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R            1  2    1   4     1   6     1    8      10
--R   (137)  - - x  - --- x  - ---- x  - ----- x  + O(x  )
--R            6      180      2835      37800
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 142

--S 143 of 200
exp(-x)*sin(x)
 

            - x
   (138)  %e   sin(x)
                                                     Type: Expression Integer
--R 
--R
--R            - x
--R   (138)  %e   sin(x)
--R                                                     Type: Expression Integer
--E 143

--S 144 of 200
series(%, x = 0)
 

               2   1  3    1  5    1  6    1   7      9
   (139)  x - x  + - x  - -- x  + -- x  - --- x  + O(x )
                   3      30      90      630
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--R 
--R
--R               2   1  3    1  5    1  6    1   7      9
--R   (139)  x - x  + - x  - -- x  + -- x  - --- x  + O(x )
--R                   3      30      90      630
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
--E 144

--S 145 of 200
y:= operator('y);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 145

--S 146 of 200
x = sin(y(x)) + cos(y(x))
 

   (141)  x= sin(y(x)) + cos(y(x))
                                            Type: Equation Expression Integer
--R 
--R
--R   (141)  x= sin(y(x)) + cos(y(x))
--R                                            Type: Equation Expression Integer
--E 146

--S 147 of 200
seriesSolve(%, y, x = 1, 0)
 
 
Daly Bug
   >> Error detected within library code:
   Improper initial value

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   Improper initial value
--R
--R   Continuing to read the file...
--R
--E 147

)clear properties y
 

--S 148 of 200
pade(1, 1, taylor(exp(-x), x = 0))
 

          - x + 2
   (142)  -------
           x + 2
         Type: Union(Fraction UnivariatePolynomial(x,Expression Integer),...)
--R 
--R
--R          - x + 2
--R   (142)  -------
--R           x + 2
--R         Type: Union(Fraction UnivariatePolynomial(x,Expression Integer),...)
--E 148

--S 149 of 200
laplace(cos((w - 1)*t), t, s)
 

                  s
   (143)  ----------------
           2         2
          w  - 2w + s  + 1
                                                     Type: Expression Integer
--R 
--R
--R                  s
--R   (143)  ----------------
--R           2         2
--R          w  - 2w + s  + 1
--R                                                     Type: Expression Integer
--E 149

--S 150 of 200
inverseLaplace(%, s, t)
 

                +-----------+
                | 2
   (144)  cos(t\|w  - 2w + 1 )
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                +-----------+
--R                | 2
--R   (144)  cos(t\|w  - 2w + 1 )
--R                                          Type: Union(Expression Integer,...)
--E 150

--S 151 of 200
r:= operator('r);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 151

--S 152 of 200
r(n + 2) - 2 * r(n + 1) + r(n) = 2
 

   (146)  r(n + 2) - 2r(n + 1) + r(n)= 2
                                            Type: Equation Expression Integer
--R 
--R
--R   (146)  r(n + 2) - 2r(n + 1) + r(n)= 2
--R                                            Type: Equation Expression Integer
--E 152

--S 153 of 200
[%, r(0) = 1, r(1) = m]
 

   (147)  [r(n + 2) - 2r(n + 1) + r(n)= 2,r(0)= 1,r(1)= m]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (147)  [r(n + 2) - 2r(n + 1) + r(n)= 2,r(0)= 1,r(1)= m]
--R                                       Type: List Equation Expression Integer
--E 153

)clear properties r
 
 
--S 154 of 200
f:= operator('f);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 154

--S 155 of 200
ode:= D(f(t), t, 2) + 4*f(t) = sin(2*t)
 

           ,,
   (149)  f  (t) + 4f(t)= sin(2t)

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,
--R   (149)  f  (t) + 4f(t)= sin(2t)
--R
--R                                            Type: Equation Expression Integer
--E 155

--S 156 of 200
map(e +-> laplace(e, t, s), %)
 

            2                          ,                2
   (150)  (s  + 4)laplace(f(t),t,s) - f (0) - f(0)s= ------
                                                      2
                                                     s  + 4
                                            Type: Equation Expression Integer
--R 
--R
--R            2                          ,                2
--R   (150)  (s  + 4)laplace(f(t),t,s) - f (0) - f(0)s= ------
--R                                                      2
--R                                                     s  + 4
--R                                            Type: Equation Expression Integer
--E 156

--S 157 of 200
solve(ode, f, t = 0, [0, 0])
 

          sin(2t) - 2t cos(2t)
   (151)  --------------------
                    8
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          sin(2t) - 2t cos(2t)
--R   (151)  --------------------
--R                    8
--R                                          Type: Union(Expression Integer,...)
--E 157

--S 158 of 200
y:= operator('y);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 158

--S 159 of 200
x**2 * D(y(x), x) + 3*x*y(x) = sin(x)/x
 

           2 ,               sin(x)
   (153)  x y (x) + 3x y(x)= ------
                                x
                                            Type: Equation Expression Integer
--R 
--R
--R           2 ,               sin(x)
--R   (153)  x y (x) + 3x y(x)= ------
--R                                x
--R                                            Type: Equation Expression Integer
--E 159

--S 160 of 200
solve(%, y, x)
 

                         cos(x)          1
   (154)  [particular= - ------,basis= [--]]
                            3            3
                           x            x
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                         cos(x)          1
--R   (154)  [particular= - ------,basis= [--]]
--R                            3            3
--R                           x            x
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 160

--S 161 of 200
D(y(x), x, 2) + y(x)*D(y(x), x)**3 = 0
 

           ,,           ,   3
   (155)  y  (x) + y(x)y (x) = 0

                                            Type: Equation Expression Integer
--R 
--R
--R           ,,           ,   3
--R   (155)  y  (x) + y(x)y (x) = 0
--R
--R                                            Type: Equation Expression Integer
--E 161

--S 162 of 200
solve(%, y, x)
 
 
Daly Bug
   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   getlincoeff: not an appropriate ordinary differential equation
--R
--R   Continuing to read the file...
--R
--E 162

--S 163 of 200
D(y(x, a), x) = a*y(x, a)
 

   (156)  y  (x,a)= a y(x,a)
           ,1
                                            Type: Equation Expression Integer
--R 
--R
--R   (156)  y  (x,a)= a y(x,a)
--R           ,1
--R                                            Type: Equation Expression Integer
--E 163

--S 164 of 200
solve(%, y, x);
 
 
Daly Bug
   >> Error detected within library code:
   parseODE: equation has order 0

   Continuing to read the file...

--R 
--R 
--RDaly Bug
--R   >> Error detected within library code:
--R   parseODE: equation has order 0
--R
--R   Continuing to read the file...
--R
--E 164

--S 165 of 200
solve(D(y(x), x, 2) + k**2*y(x) = 0, y, x)
 

   (157)  [particular= 0,basis= [cos(k x),sin(k x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (157)  [particular= 0,basis= [cos(k x),sin(k x)]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 165

-- bc(%, x = 0, y = 0, x = 1, D(y(x), x) = 0)

--S 166 of 200
x:= operator('x);
 

                                                          Type: BasicOperator
--R 
--R
--R                                                          Type: BasicOperator
--E 166

--S 167 of 200
system:= [D(x(t), t) = x(t) - y(t), D(y(t), t) = x(t) + y(t)]
 

            ,                    ,
   (159)  [x (t)= - y(t) + x(t),y (t)= y(t) + x(t)]

                                       Type: List Equation Expression Integer
--R 
--R
--R            ,                    ,
--R   (159)  [x (t)= - y(t) + x(t),y (t)= y(t) + x(t)]
--R
--R                                       Type: List Equation Expression Integer
--E 167

--S 168 of 200
system:= [D(x(t), t) = x(t) * (1 + cos(t)/(2 + sin(t))), _
          D(y(t), t) = x(t) - y(t)]
 

            ,     x(t)sin(t) + x(t)cos(t) + 2x(t)  ,
   (160)  [x (t)= -------------------------------,y (t)= - y(t) + x(t)]
                             sin(t) + 2
                                       Type: List Equation Expression Integer
--R 
--R
--R            ,     x(t)sin(t) + x(t)cos(t) + 2x(t)  ,
--R   (160)  [x (t)= -------------------------------,y (t)= - y(t) + x(t)]
--R                             sin(t) + 2
--R                                       Type: List Equation Expression Integer
--E 168

--S 169 of 200
s:=solve(system.1, x, t)
 

                                   t            t
   (161)  [particular= 0,basis= [%e sin(t) + 2%e ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R                                   t            t
--R   (161)  [particular= 0,basis= [%e sin(t) + 2%e ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 169

--S 170 of 200
eq1 := x(t) = C1 * s.basis.1
 

                     t               t
   (162)  x(t)= C1 %e sin(t) + 2C1 %e
                                            Type: Equation Expression Integer
--R 
--R
--R                     t               t
--R   (162)  x(t)= C1 %e sin(t) + 2C1 %e
--R                                            Type: Equation Expression Integer
--E 170

--S 171 of 200
s1:=solve(map(e +-> subst(e, eq1), system.2), y, t)
 

   (163)
                      - t   t 2                              - t   t 2
                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
   [particular= ------------------------------------------------------,
                                           5
              - t
    basis= [%e   ]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--R 
--R
--R   (163)
--R                      - t   t 2                              - t   t 2
--R                2C1 %e   (%e ) sin(t) + (- C1 cos(t) + 5C1)%e   (%e )
--R   [particular= ------------------------------------------------------,
--R                                           5
--R              - t
--R    basis= [%e   ]]
--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)
--E 171

--S 172 of 200
eq2 := y(t) = simplify(s1.particular) + C2 * s1.basis.1
 

                      t                              t         - t
                2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
   (164)  y(t)= --------------------------------------------------
                                         5
                                            Type: Equation Expression Integer
--R 
--R
--R                      t                              t         - t
--R                2C1 %e sin(t) + (- C1 cos(t) + 5C1)%e  + 5C2 %e
--R   (164)  y(t)= --------------------------------------------------
--R                                         5
--R                                            Type: Equation Expression Integer
--E 172

--S 173 of 200
map(e +-> rightZero eval(e, [eq1, D(eq1,t), eq2 , D(eq2,t)]), system)
 

   (165)  [0= 0,0= 0]
                                       Type: List Equation Expression Integer
--R 
--R
--R   (165)  [0= 0,0= 0]
--R                                       Type: List Equation Expression Integer
--E 173
)clear properties x y
 
 
--S 174 of 200
DD:= operator("D") :: Operator(Expression Integer)
 

   (166)  D
                                            Type: Operator Expression Integer
--R 
--R
--R   (166)  D
--R                                            Type: Operator Expression Integer
--E 174

--S 175 of 200
evaluate(DD, e +-> D(e, x))$Operator(Expression Integer)
 

   (167)  D
                                            Type: Operator Expression Integer
--R 
--R
--R   (167)  D
--R                                            Type: Operator Expression Integer
--E 175

--S 176 of 200
L:= (DD - 1) * (DD + 2)
 

                 2
   (168)  D 2 + D  - D - 2
                                            Type: Operator Expression Integer
--R 
--R
--R                 2
--R   (168)  D 2 + D  - D - 2
--R                                            Type: Operator Expression Integer
--E 176

--S 177 of 200
g:= operator('g)
 

   (169)  g
                                                          Type: BasicOperator
--R 
--R
--R   (169)  g
--R                                                          Type: BasicOperator
--E 177

--S 178 of 200
L(f(x))
 

           ,,       ,
   (170)  f  (x) + f (x) - 2f(x)

                                                     Type: Expression Integer
--R 
--R
--R           ,,       ,
--R   (170)  f  (x) + f (x) - 2f(x)
--R
--R                                                     Type: Expression Integer
--E 178

--S 179 of 200
subst(L(subst(g(y), y = x)), x = y)
 

           ,,       ,
   (171)  g  (y) + g (y) - 2g(y)

                                                     Type: Expression Integer
--R 
--R
--R           ,,       ,
--R   (171)  g  (y) + g (y) - 2g(y)
--R
--R                                                     Type: Expression Integer
--E 179

--S 180 of 200
subst(L(subst(A * sin(z**2), z = x)), x = z)
 

                 2           2                    2
   (172)  (- 4A z  - 2A)sin(z ) + (2A z + 2A)cos(z )
                                                     Type: Expression Integer
--R 
--R
--R                 2           2                    2
--R   (172)  (- 4A z  - 2A)sin(z ) + (2A z + 2A)cos(z )
--R                                                     Type: Expression Integer
--E 180

--S 181 of 200
T:= (f, xx, a) +-> subst((DD**0)(f(x)), x = a)/factorial(0) * (xx - a)**0 + _
                   subst((DD**1)(f(x)), x = a)/factorial(1) * (xx - a)**1 + _
                   subst((DD**2)(f(x)), x = a)/factorial(2) * (xx - a)**2
 

   (173)
     (f,xx,a)
   +-> 
               0                                 1
       subst(DD (f(x)),x= a)         0   subst(DD (f(x)),x= a)         1
       --------------------- (xx - a)  + --------------------- (xx - a)
            factorial(0)                      factorial(1)
     + 
               2
       subst(DD (f(x)),x= a)         2
       --------------------- (xx - a)
            factorial(2)
                                                      Type: AnonymousFunction
--R 
--R
--R   (173)
--R     (f,xx,a)
--R   +-> 
--R               0                                 1
--R       subst(DD (f(x)),x= a)         0   subst(DD (f(x)),x= a)         1
--R       --------------------- (xx - a)  + --------------------- (xx - a)
--R            factorial(0)                      factorial(1)
--R     + 
--R               2
--R       subst(DD (f(x)),x= a)         2
--R       --------------------- (xx - a)
--R            factorial(2)
--R                                                      Type: AnonymousFunction
--E 181

--S 182 of 200
T(f, x, a)
 

            2           2  ,,                ,
          (x  - 2a x + a )f  (a) + (2x - 2a)f (a) + 2f(a)

   (174)  -----------------------------------------------
                                 2
                                                     Type: Expression Integer
--R 
--R
--R            2           2  ,,                ,
--R          (x  - 2a x + a )f  (a) + (2x - 2a)f (a) + 2f(a)
--R
--R   (174)  -----------------------------------------------
--R                                 2
--R                                                     Type: Expression Integer
--E 182

--S 183 of 200
T(g, y, b)
 

            2           2  ,,                ,
          (y  - 2b y + b )g  (b) + (2y - 2b)g (b) + 2g(b)

   (175)  -----------------------------------------------
                                 2
                                                     Type: Expression Integer
--R 
--R
--R            2           2  ,,                ,
--R          (y  - 2b y + b )g  (b) + (2y - 2b)g (b) + 2g(b)
--R
--R   (175)  -----------------------------------------------
--R                                 2
--R                                                     Type: Expression Integer
--E 183

--S 184 of 200
Sin:= operator("sin") :: Operator(Expression Integer)
 

   (176)  sin
                                            Type: Operator Expression Integer
--R 
--R
--R   (176)  sin
--R                                            Type: Operator Expression Integer
--E 184

--S 185 of 200
evaluate(Sin, x +-> sin(x))$Operator(Expression Integer)
 

   (177)  sin
                                            Type: Operator Expression Integer
--R 
--R
--R   (177)  sin
--R                                            Type: Operator Expression Integer
--E 185

--S 186 of 200
T(Sin, z, c)
 

              2           2
          (- z  + 2c z - c  + 2)sin(c) + (2z - 2c)cos(c)
   (178)  ----------------------------------------------
                                 2
                                                     Type: Expression Integer
--R 
--R
--R              2           2
--R          (- z  + 2c z - c  + 2)sin(c) + (2z - 2c)cos(c)
--R   (178)  ----------------------------------------------
--R                                 2
--R                                                     Type: Expression Integer
--E 186

--S 187 of 200
p(n, x) == 1/(2**n*factorial(n)) * D((x**2 - 1)**n, x, n)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 187

--S 188 of 200
for i in 0..4 repeat {  output("");    output(concat(["p(", string(i), ", x) = "]));    output(p(i, x))}
 
   Compiling function p with type (NonNegativeInteger,Variable x) -> 
      Polynomial Fraction Integer 

   p(0, x) =
   1

   p(1, x) =
   x

   p(2, x) =
   3  2   1
   - x  - -
   2      2

   p(3, x) =
   5  3   3
   - x  - - x
   2      2

   p(4, x) =
   35  4   15  2   3
   -- x  - -- x  + -
    8       4      8
                                                                   Type: Void
--R 
--R   Compiling function p with type (NonNegativeInteger,Variable x) -> 
--R      Polynomial Fraction Integer 
--R
--R   p(0, x) =
--R   1
--R
--R   p(1, x) =
--R   x
--R
--R   p(2, x) =
--R   3  2   1
--R   - x  - -
--R   2      2
--R
--R   p(3, x) =
--R   5  3   3
--R   - x  - - x
--R   2      2
--R
--R   p(4, x) =
--R   35  4   15  2   3
--R   -- x  - -- x  + -
--R    8       4      8
--R                                                                   Type: Void
--E 188

--S 189 of 200
eval(p(4, x), x = 1)
 
   Compiling function p with type (PositiveInteger,Variable x) -> 
      Polynomial Fraction Integer 

   (181)  1
                                            Type: Polynomial Fraction Integer
--R 
--R   Compiling function p with type (PositiveInteger,Variable x) -> 
--R      Polynomial Fraction Integer 
--R
--R   (181)  1
--R                                            Type: Polynomial Fraction Integer
--E 189

--S 190 of 200
pp(0, x) == 1
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 190

--S 191 of 200
pp(1, x) == x
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 191

--S 192 of 200
pp(n, x) == ((2*n - 1)*x*pp(n - 1, x) - (n - 1)*pp(n - 2, x))/n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 192

--S 193 of 200
for i in 0..4 repeat {   output("");   output(concat(["pp(", string(i), ", x) = "]));   output(pp(i, x))}
 
   Compiling function pp with type (Integer,Variable x) -> Polynomial 
      Fraction Integer 

   pp(0, x) =
   1

   pp(1, x) =
   x

   pp(2, x) =
   3  2   1
   - x  - -
   2      2

   pp(3, x) =
   5  3   3
   - x  - - x
   2      2

   pp(4, x) =
   35  4   15  2   3
   -- x  - -- x  + -
    8       4      8
                                                                   Type: Void
--R 
--R   Compiling function pp with type (Integer,Variable x) -> Polynomial 
--R      Fraction Integer 
--R
--R   pp(0, x) =
--R   1
--R
--R   pp(1, x) =
--R   x
--R
--R   pp(2, x) =
--R   3  2   1
--R   - x  - -
--R   2      2
--R
--R   pp(3, x) =
--R   5  3   3
--R   - x  - - x
--R   2      2
--R
--R   pp(4, x) =
--R   35  4   15  2   3
--R   -- x  - -- x  + -
--R    8       4      8
--R                                                                   Type: Void
--E 193

)clear properties p pp
 
   Compiled code for p has been cleared.
   Compiled code for pp has been cleared.

--S 194 of 200
a:= operator('a)
 

   (186)  a
                                                          Type: BasicOperator
--R 
--R
--R   (186)  a
--R                                                          Type: BasicOperator
--E 194

--S 195 of 200
sum(a(i)*x**i, i = 1..5)
 

               5        4        3        2
   (187)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
                                                     Type: Expression Integer
--R 
--R
--R               5        4        3        2
--R   (187)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
--R                                                     Type: Expression Integer
--E 195

--S 196 of 200
p:= factor(%)
 

               5        4        3        2
   (188)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
                                            Type: Factored Expression Integer
--R 
--R
--R               5        4        3        2
--R   (188)  a(5)x  + a(4)x  + a(3)x  + a(2)x  + a(1)x
--R                                            Type: Factored Expression Integer
--E 196


)set fortran ints2floats off
 

--S 197 of 200
outputAsFortran('p = p)
 
      p=a(5)*x**5+a(4)*x**4+a(3)*x**3+a(2)*x*x+a(1)*x
                                                                   Type: Void
--R 
--R      p=a(5)*x**5+a(4)*x**4+a(3)*x**3+a(2)*x*x+a(1)*x
--R                                                                   Type: Void
--E 197

--S 198 of 200
true and false
 

   (190)  false
                                                                Type: Boolean
--R 
--R
--R   (190)  false
--R                                                                Type: Boolean
--E 198

--S 199 of 200
x or (not x)
 
 
Daly Bug
   Argument number 1 to "or" must be a Boolean.
--R 
--R 
--RDaly Bug
--R   Argument number 1 to "or" must be a Boolean.
--E 199

--S 200 of 200
x or y or (x and y)
 
 
Daly Bug
   Argument number 1 to "or" must be a Boolean.
--R 
--R 
--RDaly Bug
--R   Argument number 1 to "or" must be a Boolean.
--E 200
)spool
 
Starts dribbling to bug10312.output (2010/3/27, 18:23:25).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 2
p:=(1/2+n)::UTS(FRAC INT, 'n, 0)
 

        1
   (1)  - + n
        2
                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--R 
--R
--R        1
--R   (1)  - + n
--R        2
--R                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--E 1

--S 2 of 2
(p**(-1))$UTS(FRAC INT, 'n, 0)
 
   Compiling function G1747 with type Integer -> Boolean 

   (2)
                2      3      4      5       6       7       8        9
     2 - 4n + 8n  - 16n  + 32n  - 64n  + 128n  - 256n  + 512n  - 1024n
   + 
          10      11
     2048n   + O(n  )
                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--R 
--I   Compiling function G1473 with type Integer -> Boolean 
--R
--R   (2)
--R                2      3      4      5       6       7       8        9
--R     2 - 4n + 8n  - 16n  + 32n  - 64n  + 128n  - 256n  + 512n  - 1024n
--R   + 
--R          10      11
--R     2048n   + O(n  )
--R                           Type: UnivariateTaylorSeries(Fraction Integer,n,0)
--E 2
)spool
 
Starts dribbling to Octonion.output (2010/3/27, 18:46:9).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 15
oci1 := octon(1,2,3,4,5,6,7,8)
 

   (1)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
                                                       Type: Octonion Integer
--R 
--R
--R   (1)  1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K
--R                                                       Type: Octonion Integer
--E 1

--S 2 of 15
oci2 := octon(7,2,3,-4,5,6,-7,0)
 

   (2)  7 + 2i + 3j - 4k + 5E + 6I - 7J
                                                       Type: Octonion Integer
--R 
--R
--R   (2)  7 + 2i + 3j - 4k + 5E + 6I - 7J
--R                                                       Type: Octonion Integer
--E 2

--S 3 of 15
oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0))
 

   (3)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
                                                       Type: Octonion Integer
--R 
--R
--R   (3)  - 7 - 12i + 3j - 10k + 5E + 6I + 9J
--R                                                       Type: Octonion Integer
--E 3

--S 4 of 15
(oci1 * oci2) * oci3 - oci1 * (oci2 * oci3)
 

   (4)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
                                                       Type: Octonion Integer
--R 
--R
--R   (4)  2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K
--R                                                       Type: Octonion Integer
--E 4

--S 5 of 15
[real oci1, imagi oci1, imagj oci1, imagk oci1, _
 imagE oci1, imagI oci1, imagJ oci1, imagK oci1]
 

   (5)  [1,2,3,4,5,6,7,8]
                                                   Type: List PositiveInteger
--R 
--R
--R   (5)  [1,2,3,4,5,6,7,8]
--R                                                   Type: List PositiveInteger
--E 5

--S 6 of 15
q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk)
 

   (6)  q1 + qi i + qj j + qk k
                                          Type: Quaternion Polynomial Integer
--R 
--R
--R   (6)  q1 + qi i + qj j + qk k
--R                                          Type: Quaternion Polynomial Integer
--E 6

--S 7 of 15
E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0)
 

   (7)  E
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (7)  E
--R                                            Type: Octonion Polynomial Integer
--E 7

--S 8 of 15
q * E
 

   (8)  q1 E + qi I + qj J + qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (8)  q1 E + qi I + qj J + qk K
--R                                            Type: Octonion Polynomial Integer
--E 8

--S 9 of 15
E * q
 

   (9)  q1 E - qi I - qj J - qk K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (9)  q1 E - qi I - qj J - qk K
--R                                            Type: Octonion Polynomial Integer
--E 9

--S 10 of 15
q * 1$(Octonion Polynomial Integer)
 

   (10)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (10)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 10

--S 11 of 15
1$(Octonion Polynomial Integer) * q
 

   (11)  q1 + qi i + qj j + qk k
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (11)  q1 + qi i + qj j + qk k
--R                                            Type: Octonion Polynomial Integer
--E 11

--S 12 of 15
o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK)
 

   (12)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (12)  o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K
--R                                            Type: Octonion Polynomial Integer
--E 12

--S 13 of 15
norm o
 

           2     2     2     2     2     2     2     2
   (13)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
                                                     Type: Polynomial Integer
--R 
--R
--R           2     2     2     2     2     2     2     2
--R   (13)  ok  + oj  + oi  + oK  + oJ  + oI  + oE  + o1
--R                                                     Type: Polynomial Integer
--E 13

--S 14 of 15
p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK)
 

   (14)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
                                            Type: Octonion Polynomial Integer
--R 
--R
--R   (14)  p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K
--R                                            Type: Octonion Polynomial Integer
--E 14

--S 15 of 15
norm(o*p)-norm(p)*norm(o)
 

   (15)  0
                                                     Type: Polynomial Integer
--R 
--R
--R   (15)  0
--R                                                     Type: Polynomial Integer
--E 15
)spool
 
GCL (GNU Common Lisp)  2.6.7 CLtL1    Jan 28 2010 00:41:24
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License:  GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files set to /home/camm/debian/axiom/axiom-20091101/obj/tmp/
                        AXIOM Computer Algebra System 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/compress.daase..   Re-reading compress.daase   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/interp.daase..   Re-reading interp.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/operation.daase..   Re-reading operation.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/category.daase..   Re-reading category.daase
   Using local database /home/camm/debian/axiom/axiom-20091101/mnt/linux/algebra/browse.daase..   Re-reading browse.daase
(1) -> )set message test on
 
)set message auto off
 
)read synonym
 
)lisp (bye)
 
Starts dribbling to evalex.output (2010/3/27, 18:25:35).
)set message test on
 
)set message auto off
 
)clear all
 

-- Input for page PrefixEval
--S 1 of 3
cos(2)
 

   (1)  cos(2)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  cos(2)
--R                                                     Type: Expression Integer
--E 1

-- Input for page PrefixEval
)clear all
 

--S 2 of 3
cos(2)
 

   (1)  cos(2)
                                                     Type: Expression Integer
--R 
--R
--R   (1)  cos(2)
--R                                                     Type: Expression Integer
--E 2

-- Input for page InfixEval
)clear all
 

--S 3 of 3
2 + 3.4
 

   (1)  5.4
                                                                  Type: Float
--R 
--R
--R   (1)  5.4
--R                                                                  Type: Float
--E 3
)spool
 
Starts dribbling to seg.output (2010/3/27, 18:38:54).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
s := 3..10
 

   (1)  3..10
                                                Type: Segment PositiveInteger
--R 
--R
--R   (1)  3..10
--R                                                Type: Segment PositiveInteger
--E 1

--S 2 of 10
lo s
 

   (2)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  3
--R                                                        Type: PositiveInteger
--E 2

--S 3 of 10
hi s
 

   (3)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  10
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 10
t := 10..3 by -2
 

   (4)  10..3 by - 2
                                                Type: Segment PositiveInteger
--R 
--R
--R   (4)  10..3 by - 2
--R                                                Type: Segment PositiveInteger
--E 4

--S 5 of 10
incr s
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 10
incr t
 

   (6)  - 2
                                                                Type: Integer
--R 
--R
--R   (6)  - 2
--R                                                                Type: Integer
--E 6

--S 7 of 10
l := [1..3, 5, 9, 15..11 by -1]
 

   (7)  [1..3,5..5,9..9,15..11 by - 1]
                                           Type: List Segment PositiveInteger
--R 
--R
--R   (7)  [1..3,5..5,9..9,15..11 by - 1]
--R                                           Type: List Segment PositiveInteger
--E 7

--S 8 of 10
expand s
 

   (8)  [3,4,5,6,7,8,9,10]
                                                           Type: List Integer
--R 
--R
--R   (8)  [3,4,5,6,7,8,9,10]
--R                                                           Type: List Integer
--E 8

--S 9 of 10
expand t
 

   (9)  [10,8,6,4]
                                                           Type: List Integer
--R 
--R
--R   (9)  [10,8,6,4]
--R                                                           Type: List Integer
--E 9

--S 10 of 10
expand l
 

   (10)  [1,2,3,5,9,15,14,13,12,11]
                                                           Type: List Integer
--R 
--R
--R   (10)  [1,2,3,5,9,15,14,13,12,11]
--R                                                           Type: List Integer
--E 10
)spool 
 
Starts dribbling to constant.output (2010/3/27, 18:24:35).
)set message test on
 
)set message auto off
 
)clear all
 

-- knuth volume 2 p596 tables of numerical quantities
--S 1 of 37
digits(42)
 

   (1)  20
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  20
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 37
outputSpacing(5)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 37
numeric(sqrt(2))
 

   (3)  1.41421 35623 73095 04880 16887 24209 69807 85696 7
                                                                  Type: Float
--R 
--R
--R   (3)  1.41421 35623 73095 04880 16887 24209 69807 85696 7
--R                                                                  Type: Float
--E 3

--S 4 of 37
numeric(sqrt(3))
 

   (4)  1.73205 08075 68877 29352 74463 41505 87236 69428 1
                                                                  Type: Float
--R 
--R
--R   (4)  1.73205 08075 68877 29352 74463 41505 87236 69428 1
--R                                                                  Type: Float
--E 4

--S 5 of 37
numeric(sqrt(5))
 

   (5)  2.23606 79774 99789 69640 91736 68731 27623 54406 2
                                                                  Type: Float
--R 
--R
--R   (5)  2.23606 79774 99789 69640 91736 68731 27623 54406 2
--R                                                                  Type: Float
--E 5

--S 6 of 37
numeric(sqrt(10))
 

   (6)  3.16227 76601 68379 33199 88935 44432 71853 37195 6
                                                                  Type: Float
--R 
--R
--R   (6)  3.16227 76601 68379 33199 88935 44432 71853 37195 6
--R                                                                  Type: Float
--E 6

--S 7 of 37
numeric(2**(1/3))
 

   (7)  1.25992 10498 94873 16476 72106 07278 22835 05702 5
                                                                  Type: Float
--R 
--R
--R   (7)  1.25992 10498 94873 16476 72106 07278 22835 05702 5
--R                                                                  Type: Float
--E 7

--S 8 of 37
numeric(3**(1/3))
 

   (8)  1.44224 95703 07408 38232 16383 10780 10958 83918 7
                                                                  Type: Float
--R 
--R
--R   (8)  1.44224 95703 07408 38232 16383 10780 10958 83918 7
--R                                                                  Type: Float
--E 8

--S 9 of 37
numeric(2**(1/4))
 

   (9)  1.18920 71150 02721 06671 74999 70560 47591 52929 7
                                                                  Type: Float
--R 
--R
--R   (9)  1.18920 71150 02721 06671 74999 70560 47591 52929 7
--R                                                                  Type: Float
--E 9

--S 10 of 37
numeric(log(2))
 

   (10)  0.69314 71805 59945 30941 72321 21458 17656 80755
                                                                  Type: Float
--R 
--R
--R   (10)  0.69314 71805 59945 30941 72321 21458 17656 80755
--R                                                                  Type: Float
--E 10

--S 11 of 37
numeric(log(3))
 

   (11)  1.09861 22886 68109 69139 52452 36922 52570 46474 9
                                                                  Type: Float
--R 
--R
--R   (11)  1.09861 22886 68109 69139 52452 36922 52570 46474 9
--R                                                                  Type: Float
--E 11

--S 12 of 37
numeric(log(10))
 

   (12)  2.30258 50929 94045 68401 79914 54684 36420 76011
                                                                  Type: Float
--R 
--R
--R   (12)  2.30258 50929 94045 68401 79914 54684 36420 76011
--R                                                                  Type: Float
--E 12

--S 13 of 37
numeric(1/log(2))
 

   (13)  1.44269 50408 88963 40735 99246 81001 89213 74266 5
                                                                  Type: Float
--R 
--R
--R   (13)  1.44269 50408 88963 40735 99246 81001 89213 74266 5
--R                                                                  Type: Float
--E 13

--S 14 of 37
numeric(1/log(10))
 

   (14)  0.43429 44819 03251 82765 11289 18916 60508 22943 97
                                                                  Type: Float
--R 
--R
--R   (14)  0.43429 44819 03251 82765 11289 18916 60508 22943 97
--R                                                                  Type: Float
--E 14

--S 15 of 37
numeric(%pi)
 

   (15)  3.14159 26535 89793 23846 26433 83279 50288 41971 7
                                                                  Type: Float
--R 
--R
--R   (15)  3.14159 26535 89793 23846 26433 83279 50288 41971 7
--R                                                                  Type: Float
--E 15

--S 16 of 37
numeric(%pi/180)
 

   (16)  0.01745 32925 19943 29576 92369 07684 88612 71344 287
                                                                  Type: Float
--R 
--R
--R   (16)  0.01745 32925 19943 29576 92369 07684 88612 71344 287
--R                                                                  Type: Float
--E 16

--S 17 of 37
numeric(1/%pi)
 

   (17)  0.31830 98861 83790 67153 77675 26745 02872 40689 19
                                                                  Type: Float
--R 
--R
--R   (17)  0.31830 98861 83790 67153 77675 26745 02872 40689 19
--R                                                                  Type: Float
--E 17

--S 18 of 37
numeric(%pi**2)
 

   (18)  9.86960 44010 89358 61883 44909 99876 15113 53136 9
                                                                  Type: Float
--R 
--R
--R   (18)  9.86960 44010 89358 61883 44909 99876 15113 53136 9
--R                                                                  Type: Float
--E 18

--S 19 of 37
numeric(sqrt(%pi))
 

   (19)  1.77245 38509 05516 02729 81674 83341 14518 27975 5
                                                                  Type: Float
--R 
--R
--R   (19)  1.77245 38509 05516 02729 81674 83341 14518 27975 5
--R                                                                  Type: Float
--E 19

--S 20 of 37
numeric(Gamma(1/2))
 

   (20)  1.77245 38509 05516 32600 86374 06630 44154 64401 2
                                                                  Type: Float
--R 
--R
--R   (20)  1.77245 38509 05516 32600 86374 06630 44154 64401 2
--R                                                                  Type: Float
--E 20

--S 21 of 37
numeric(Gamma(1/3))
 

   (21)  2.67893 85347 07747 45417 77064 58722 24122 28584 3
                                                                  Type: Float
--R 
--R
--R   (21)  2.67893 85347 07747 45417 77064 58722 24122 28584 3
--R                                                                  Type: Float
--E 21

--S 22 of 37
numeric(Gamma(2/3))
 

   (22)  1.35411 79394 26400 46317 64919 39520 92900 87223 1
                                                                  Type: Float
--R 
--R
--R   (22)  1.35411 79394 26400 46317 64919 39520 92900 87223 1
--R                                                                  Type: Float
--E 22

--S 23 of 37
numeric(%e)
 

   (23)  2.71828 18284 59045 23536 02874 71352 66249 77572 5
                                                                  Type: Float
--R 
--R
--R   (23)  2.71828 18284 59045 23536 02874 71352 66249 77572 5
--R                                                                  Type: Float
--E 23

--S 24 of 37
numeric(1/%e)
 

   (24)  0.36787 94411 71442 32159 55237 70161 46086 74458 11
                                                                  Type: Float
--R 
--R
--R   (24)  0.36787 94411 71442 32159 55237 70161 46086 74458 11
--R                                                                  Type: Float
--E 24

--S 25 of 37
numeric(%e**2)
 

   (25)  7.38905 60989 30650 22723 04274 60575 00781 31803 1
                                                                  Type: Float
--R 
--R
--R   (25)  7.38905 60989 30650 22723 04274 60575 00781 31803 1
--R                                                                  Type: Float
--E 25

--S 26 of 37
gamma:=numeric(sum(1/x,x=1..10000)-log(10000))
 

   (26)  0.57726 56640 68199 52810 65120 86114 14850 44548 58
                                                                  Type: Float
--R 
--R
--R   (26)  0.57726 56640 68199 52810 65120 86114 14850 44548 58
--R                                                                  Type: Float
--E 26

--S 27 of 37
numeric(log(%pi))
 

   (27)  1.14472 98858 49400 17414 34273 51353 05871 16472 9
                                                                  Type: Float
--R 
--R
--R   (27)  1.14472 98858 49400 17414 34273 51353 05871 16472 9
--R                                                                  Type: Float
--E 27

--S 28 of 37
phi:=(1+sqrt(5))/2
 

          +-+
         \|5  + 1
   (28)  --------
             2
                                                        Type: AlgebraicNumber
--R 
--R
--R          +-+
--R         \|5  + 1
--R   (28)  --------
--R             2
--R                                                        Type: AlgebraicNumber
--E 28

--S 29 of 37
numeric(phi)
 

   (29)  1.61803 39887 49894 84820 45868 34365 63811 77203 1
                                                                  Type: Float
--R 
--R
--R   (29)  1.61803 39887 49894 84820 45868 34365 63811 77203 1
--R                                                                  Type: Float
--E 29

--S 30 of 37
gamma:=0.5772156649015328606065120900824024310422
 

   (30)  0.57721 56649 01532 86060 65120 90082 40243 10422
                                                                  Type: Float
--R 
--R
--R   (30)  0.57721 56649 01532 86060 65120 90082 40243 10422
--R                                                                  Type: Float
--E 30

--S 31 of 37
numeric(%e**gamma)
 

   (31)  1.78107 24179 90197 98523 65041 03107 17954 91697 2
                                                                  Type: Float
--R 
--R
--R   (31)  1.78107 24179 90197 98523 65041 03107 17954 91697 2
--R                                                                  Type: Float
--E 31

--S 32 of 37
numeric(%e**(%pi/4))
 

   (32)  2.19328 00507 38015 45655 97696 59278 73822 34616 4
                                                                  Type: Float
--R 
--R
--R   (32)  2.19328 00507 38015 45655 97696 59278 73822 34616 4
--R                                                                  Type: Float
--E 32

--S 33 of 37
numeric(sin(1))
 

   (33)  0.84147 09848 07896 50665 25023 21630 29899 96225 63
                                                                  Type: Float
--R 
--R
--R   (33)  0.84147 09848 07896 50665 25023 21630 29899 96225 63
--R                                                                  Type: Float
--E 33

--S 34 of 37
numeric(cos(1))
 

   (34)  0.54030 23058 68139 71740 09366 07442 97660 37323 1
                                                                  Type: Float
--R 
--R
--R   (34)  0.54030 23058 68139 71740 09366 07442 97660 37323 1
--R                                                                  Type: Float
--E 34

--S 35 of 37
numeric(log(phi))
 

   (35)  0.48121 18250 59603 44749 77589 13424 36842 31351 85
                                                                  Type: Float
--R 
--R
--R   (35)  0.48121 18250 59603 44749 77589 13424 36842 31351 85
--R                                                                  Type: Float
--E 35

--S 36 of 37
numeric(1/log(phi))
 

   (36)  2.07808 69212 35027 53760 13226 06117 79576 77421 9
                                                                  Type: Float
--R 
--R
--R   (36)  2.07808 69212 35027 53760 13226 06117 79576 77421 9
--R                                                                  Type: Float
--E 36

--S 37 of 37
numeric(-log(log(2)))
 

   (37)  0.36651 29205 81664 32701 24391 58232 66946 94542 64
                                                                  Type: Float
--R 
--R
--R   (37)  0.36651 29205 81664 32701 24391 58232 66946 94542 64
--R                                                                  Type: Float
--E 37
)spool
 
Starts dribbling to CharacterClass.output (2010/3/27, 18:41:48).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 16
cl1:=charClass[char "a",char "e",char "i",char "o",char "u",char "y"]
 

   (1)  "aeiouy"
                                                         Type: CharacterClass
--R 
--R
--R   (1)  "aeiouy"
--R                                                         Type: CharacterClass
--E 1

--S 2 of 16
cl2 := charClass "bcdfghjklmnpqrstvwxyz"
 

   (2)  "bcdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (2)  "bcdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 2

--S 3 of 16
digit()
 

   (3)  "0123456789"
                                                         Type: CharacterClass
--R 
--R
--R   (3)  "0123456789"
--R                                                         Type: CharacterClass
--E 3

--S 4 of 16
hexDigit()
 

   (4)  "0123456789ABCDEFabcdef"
                                                         Type: CharacterClass
--R 
--R
--R   (4)  "0123456789ABCDEFabcdef"
--R                                                         Type: CharacterClass
--E 4

--S 5 of 16
upperCase()
 

   (5)  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
                                                         Type: CharacterClass
--R 
--R
--R   (5)  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
--R                                                         Type: CharacterClass
--E 5

--S 6 of 16
lowerCase()
 

   (6)  "abcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (6)  "abcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 6

--S 7 of 16
alphabetic()
 

   (7)  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (7)  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 7

--S 8 of 16
alphanumeric()
 

   (8)  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (8)  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 8

--S 9 of 16
member?(char "a", cl1)
 

   (9)  true
                                                                Type: Boolean
--R 
--R
--R   (9)  true
--R                                                                Type: Boolean
--E 9

--S 10 of 16
member?(char "a", cl2)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 16
intersect(cl1, cl2)
 

   (11)  "y"
                                                         Type: CharacterClass
--R 
--R
--R   (11)  "y"
--R                                                         Type: CharacterClass
--E 11

--S 12 of 16
union(cl1,cl2)
 

   (12)  "abcdefghijklmnopqrstuvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (12)  "abcdefghijklmnopqrstuvwxyz"
--R                                                         Type: CharacterClass
--E 12

--S 13 of 16
difference(cl1,cl2)
 

   (13)  "aeiou"
                                                         Type: CharacterClass
--R 
--R
--R   (13)  "aeiou"
--R                                                         Type: CharacterClass
--E 13

--S 14 of 16
intersect(complement(cl1),cl2)
 

   (14)  "bcdfghjklmnpqrstvwxz"
                                                         Type: CharacterClass
--R 
--R
--R   (14)  "bcdfghjklmnpqrstvwxz"
--R                                                         Type: CharacterClass
--E 14

--S 15 of 16
insert!(char "a", cl2)
 

   (15)  "abcdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (15)  "abcdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 15

--S 16 of 16
remove!(char "b", cl2)
 

   (16)  "acdfghjklmnpqrstvwxyz"
                                                         Type: CharacterClass
--R 
--R
--R   (16)  "acdfghjklmnpqrstvwxyz"
--R                                                         Type: CharacterClass
--E 16
)spool
 
Starts dribbling to bstree.output (2010/3/27, 18:23:19).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 12
lv := [8,3,5,4,6,2,1,5,7]
 

   (1)  [8,3,5,4,6,2,1,5,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (1)  [8,3,5,4,6,2,1,5,7]
--R                                                   Type: List PositiveInteger
--E 1

--S 2 of 12
t := binarySearchTree lv
 

   (2)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
                                       Type: BinarySearchTree PositiveInteger
--R 
--R
--R   (2)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
--R                                       Type: BinarySearchTree PositiveInteger
--E 2

--S 3 of 12
emptybst := empty()$BSTREE(INT)
 

   (3)  []
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (3)  []
--R                                               Type: BinarySearchTree Integer
--E 3

--S 4 of 12
t1 := insert!(8,emptybst)
 

   (4)  8
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (4)  8
--R                                               Type: BinarySearchTree Integer
--E 4

--S 5 of 12
insert!(3,t1)
 

   (5)  [3,8,.]
                                               Type: BinarySearchTree Integer
--R 
--R
--R   (5)  [3,8,.]
--R                                               Type: BinarySearchTree Integer
--E 5

--S 6 of 12
leaves t
 

   (6)  [1,4,5,7]
                                                   Type: List PositiveInteger
--R 
--R
--R   (6)  [1,4,5,7]
--R                                                   Type: List PositiveInteger
--E 6

--S 7 of 12
split(3,t)
 

   (7)  [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]]
Type: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger)
--R 
--R
--R   (7)  [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]]
--RType: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger)
--E 7

--S 8 of 12
insertRoot: (INT,BSTREE INT) -> BSTREE INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 8

--S 9 of 12
insertRoot(x, t) ==
    a := split(x, t)
    node(a.less, x, a.greater)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 12
buildFromRoot ls == reduce(insertRoot,ls,emptybst)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 12
rt := buildFromRoot reverse lv
 
   Compiling function buildFromRoot with type List PositiveInteger -> 
      BinarySearchTree Integer 
   Compiling function insertRoot with type (Integer,BinarySearchTree 
      Integer) -> BinarySearchTree Integer 

   (11)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
                                               Type: BinarySearchTree Integer
--R 
--R   Compiling function buildFromRoot with type List PositiveInteger -> 
--R      BinarySearchTree Integer 
--R   Compiling function insertRoot with type (Integer,BinarySearchTree 
--R      Integer) -> BinarySearchTree Integer 
--R
--R   (11)  [[[1,2,.],3,[4,5,[5,6,7]]],8,.]
--R                                               Type: BinarySearchTree Integer
--E 11

--S 12 of 12
(t = rt)@Boolean
 

   (12)  true
                                                                Type: Boolean
--R 
--R
--R   (12)  true
--R                                                                Type: Boolean
--E 12 
)spool
 
Starts dribbling to tuplebug.output (2010/3/27, 18:41:24).
)set message test on
 
)set message auto off
 
)clear all
 
)sys cp $AXIOM/../../src/input/tuplebug.input.pamphlet .
 
)lisp (tangle "tuplebug.input.pamphlet" "tuplebug.spad" "tuplebug.spad")
 
Value = NIL

--S 1 of 1
)co tuplebug
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/tuplebug.spad 
      using old system compiler.
   BUG abbreviates package Bug 
------------------------------------------------------------------------
   initializing nrlib BUG for Bug 
   compiling into nrlib BUG 
   compiling exported bug : R -> Tuple R -> Tuple R
Time: 0.01 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |Bug| REDEFINED

;;;     ***       |Bug| REDEFINED
Time: 0 SEC.

 
   Warnings: 
      [1] bug:  p has no value
 

   Cumulative Statistics for Constructor Bug
      Time: 0.01 seconds
 
   finalizing nrlib BUG 
   Processing Bug for Browser database:
--->-->Bug((bug ((Mapping (Tuple R) (Tuple R)) R))): Not documented!!!!
--->-->Bug(constructor): Not documented!!!!
--->-->Bug(): Missing Description
------------------------------------------------------------------------
   Bug is now explicitly exposed in frame initial 
   Bug will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/BUG.nrlib/code

--R 
--R   Compiling AXIOM source code from file 
--I      /research/test/int/input/tuplebug.spad using old system compiler.
--R   BUG abbreviates package Bug 
--R------------------------------------------------------------------------
--R   initializing nrlib BUG for Bug 
--R   compiling into nrlib BUG 
--R   compiling exported bug : R -> Tuple R -> Tuple R
--ITime: 0.01 SEC.
--R
--I(time taken in buildFunctor:  0 . NIL)
--R
--R;;;     ***       |Bug| REDEFINED
--R
--R;;;     ***       |Bug| REDEFINED
--ITime: 0 SEC.
--R
--R 
--R   Warnings: 
--R      [1] bug:  p has no value
--R 
--R
--R   Cumulative Statistics for Constructor Bug
--I      Time: 0.01 seconds
--R 
--R   finalizing nrlib BUG 
--R   Processing Bug for Browser database:
--R--->-->Bug((bug ((Mapping (Tuple R) (Tuple R)) R))): Not documented!!!!
--R--->-->Bug(constructor): Not documented!!!!
--R--->-->Bug(): Missing Description
--R------------------------------------------------------------------------
--I   Bug is now explicitly exposed in frame frame0 
--R   Bug will be automatically loaded when needed from 
--I      /research/test/int/input/BUG.nrlib/code
--R
--E 1
)spool 
 
Starts dribbling to algfacob.output (2010/3/27, 18:23:0).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 37
(w,x,y,z): FR INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 37
x := 2**8 * 78**7 * 111**3 * 74534
 

         16 10  7  3
   (2)  2  3  13 37 83 449
                                                       Type: Factored Integer
--R 
--R
--R         16 10  7  3
--R   (2)  2  3  13 37 83 449
--R                                                       Type: Factored Integer
--E 2

--S 3 of 37
y := nilFactor(2,10) * nilFactor(3,20) * nilFactor(5,30)
 

         10 20 30
   (3)  2  3  5
                                                       Type: Factored Integer
--R 
--R
--R         10 20 30
--R   (3)  2  3  5
--R                                                       Type: Factored Integer
--E 3

--S 4 of 37
x*y
 

         26 30 30  7  3
   (4)  2  3  5  13 37 83 449
                                                       Type: Factored Integer
--R 
--R
--R         26 30 30  7  3
--R   (4)  2  3  5  13 37 83 449
--R                                                       Type: Factored Integer
--E 4

--S 5 of 37
w := x+y
 

         10 10
   (5)  2  3  13535311 4062978256593778783
                                                       Type: Factored Integer
--R 
--R
--R         10 10
--R   (5)  2  3  13535311 4062978256593778783
--R                                                       Type: Factored Integer
--E 5

--S 6 of 37
expand w
 

   (6)  3325257188459534016841161201804288
                                                        Type: PositiveInteger
--R 
--R
--R   (6)  3325257188459534016841161201804288
--R                                                        Type: PositiveInteger
--E 6

--S 7 of 37
f := x/y
 

         6  7  3
        2 13 37 83 449
   (7)  --------------
             10 30
            3  5
                                              Type: Fraction Factored Integer
--R 
--R
--R         6  7  3
--R        2 13 37 83 449
--R   (7)  --------------
--R             10 30
--R            3  5
--R                                              Type: Fraction Factored Integer
--E 7

--S 8 of 37
g := (x**9)/y
 

         134 70  63  27  9   9
        2   3  13  37  83 449
   (8)  ----------------------
                   30
                  5
                                              Type: Fraction Factored Integer
--R 
--R
--R         134 70  63  27  9   9
--R        2   3  13  37  83 449
--R   (8)  ----------------------
--R                   30
--R                  5
--R                                              Type: Fraction Factored Integer
--E 8

--S 9 of 37
f*g
 

         140 60  70  30  10   10
        2   3  13  37  83  449
   (9)  ------------------------
                    60
                   5
                                              Type: Fraction Factored Integer
--R 
--R
--R         140 60  70  30  10   10
--R        2   3  13  37  83  449
--R   (9)  ------------------------
--R                    60
--R                   5
--R                                              Type: Fraction Factored Integer
--E 9

--S 10 of 37
h := (f*g)/(g*nilFactor(2,200))
 

           7  3
         13 37 83 449
   (10)  ------------
           194 10 30
          2   3  5
                                              Type: Fraction Factored Integer
--R 
--R
--R           7  3
--R         13 37 83 449
--R   (10)  ------------
--R           194 10 30
--R          2   3  5
--R                                              Type: Fraction Factored Integer
--E 10

)clear all
 

--S 11 of 37
(u,v,w) : FR POLY INT
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 11

--S 12 of 37
u := factor (x**4 - y**4)
 

                          2    2
   (2)  - (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                          2    2
--R   (2)  - (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 12

--S 13 of 37
v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1)
 

               2       2  2    2
   (3)  (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2       2  2    2
--R   (3)  (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 13

--S 14 of 37
w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * nilFactor(x-y,2)
 

               2           2
   (4)  (y - x) (y + x + 1)
                                            Type: Factored Polynomial Integer
--R 
--R
--R               2           2
--R   (4)  (y - x) (y + x + 1)
--R                                            Type: Factored Polynomial Integer
--E 14

--S 15 of 37
nthFactor(u,1)
 

   (5)  y - x
                                                     Type: Polynomial Integer
--R 
--R
--R   (5)  y - x
--R                                                     Type: Polynomial Integer
--E 15

--S 16 of 37
nthFactor(u,2)
 

   (6)  y + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (6)  y + x
--R                                                     Type: Polynomial Integer
--E 16

--S 17 of 37
nthFactor(u,3)
 

         2    2
   (7)  y  + x
                                                     Type: Polynomial Integer
--R 
--R
--R         2    2
--R   (7)  y  + x
--R                                                     Type: Polynomial Integer
--E 17

--S 18 of 37
nthFactor(u,4)
 

   (8)  1
                                                     Type: Polynomial Integer
--R 
--R
--R   (8)  1
--R                                                     Type: Polynomial Integer
--E 18

--S 19 of 37
gcd(u,v)
 

                        2    2
   (9)  (y - x)(y + x)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                        2    2
--R   (9)  (y - x)(y + x)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 19

--S 20 of 37
u + v
 

                         2    2       2    2
   (10)  (y - x)(y + x)(y  - x  - 1)(y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                         2    2       2    2
--R   (10)  (y - x)(y + x)(y  - x  - 1)(y  + x )
--R                                            Type: Factored Polynomial Integer
--E 20

--S 21 of 37
lcm(u,v)
 

                  2       2  2    2
   (11)  - (y - x) (y + x) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  2       2  2    2
--R   (11)  - (y - x) (y + x) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 21

--S 22 of 37
u * v * w
 

                  5       3           2  2    2 2
   (12)  - (y - x) (y + x) (y + x + 1) (y  + x )
                                            Type: Factored Polynomial Integer
--R 
--R
--R                  5       3           2  2    2 2
--R   (12)  - (y - x) (y + x) (y + x + 1) (y  + x )
--R                                            Type: Factored Polynomial Integer
--E 22

--S 23 of 37
expand %
 

   (13)
        14     13      2           12      2       11       4     3  10
     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
   + 
        4     3  9        6     5     4  8        6     5  7      8     7  6
     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
   + 
        8     7  5     10     9     8  4      10     9  3        12     11  2
     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
   + 
          12     11      14     13    12
     (- 2x   - 2x  )y + x   + 2x   + x
                                                     Type: Polynomial Integer
--R 
--R
--R   (13)
--R        14     13      2           12      2       11       4     3  10
--R     - y   - 2y   + (3x  + 2x - 1)y   + (4x  + 2x)y   + (- x  - 4x )y
--R   + 
--R        4     3  9        6     5     4  8        6     5  7      8     7  6
--R     (2x  - 2x )y  + (- 5x  - 2x  + 3x )y  + (- 8x  - 4x )y  + (5x  + 8x )y
--R   + 
--R        8     7  5     10     9     8  4      10     9  3        12     11  2
--R     (2x  + 4x )y  + (x   - 2x  - 3x )y  + (4x   + 2x )y  + (- 3x   - 4x  )y
--R   + 
--R          12     11      14     13    12
--R     (- 2x   - 2x  )y + x   + 2x   + x
--R                                                     Type: Polynomial Integer
--E 23

--S 24 of 37
u/w
 

                      2    2
             (y + x)(y  + x )
   (14)  - -------------------
                             2
           (y - x)(y + x + 1)
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                      2    2
--R             (y + x)(y  + x )
--R   (14)  - -------------------
--R                             2
--R           (y - x)(y + x + 1)
--R                                   Type: Fraction Factored Polynomial Integer
--E 24

--S 25 of 37
w/(u*v)
 

                             2
                  (y + x + 1)
   (15)  - -------------------------
                         3  2    2 2
           (y - x)(y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                             2
--R                  (y + x + 1)
--R   (15)  - -------------------------
--R                         3  2    2 2
--R           (y - x)(y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 25

--S 26 of 37
%%(-1) * %%(-2)
 

                     1
   (16)  -------------------------
                2       2  2    2
         (y - x) (y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                     1
--R   (16)  -------------------------
--R                2       2  2    2
--R         (y - x) (y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 26

--S 27 of 37
%%(-1) + %%(-2)
 

             2        2           3     2
           2y  + (- 2x  + 1)y - 2x  - 2x  - x
   (17)  - ----------------------------------
                      2       3  2    2 2
               (y - x) (y + x) (y  + x )
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R             2        2           3     2
--R           2y  + (- 2x  + 1)y - 2x  - 2x  - x
--R   (17)  - ----------------------------------
--R                      2       3  2    2 2
--R               (y - x) (y + x) (y  + x )
--R                                   Type: Fraction Factored Polynomial Integer
--E 27

)clear all
 
 
--S 28 of 37
f : FR INT := 144000
 

         7 2 3
   (1)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         7 2 3
--R   (1)  2 3 5
--R                                                       Type: Factored Integer
--E 28

--S 29 of 37
nthFactor(f,1)
 

   (2)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (2)  2
--R                                                        Type: PositiveInteger
--E 29

--S 30 of 37
nthExponent(f,1)
 

   (3)  7
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  7
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 37
nthFlag(f,1)
 

   (4)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (4)  "prime"
--R                                                     Type: Union("prime",...)
--E 31

--S 32 of 37
nthFlag(nilFactor(20,4),1)
 

   (5)  "nil"
                                                       Type: Union("nil",...)
--R 
--R
--R   (5)  "nil"
--R                                                       Type: Union("nil",...)
--E 32

--S 33 of 37
nthFlag(primeFactor(7,9),1)
 

   (6)  "prime"
                                                     Type: Union("prime",...)
--R 
--R
--R   (6)  "prime"
--R                                                     Type: Union("prime",...)
--E 33

--S 34 of 37
factors f
 

   (7)
   [[factor= 2,exponent= 7],[factor= 3,exponent= 2],[factor= 5,exponent= 3]]
                         Type: List Record(factor: Integer,exponent: Integer)
--R 
--R
--R   (7)
--R   [[factor= 2,exponent= 7],[factor= 3,exponent= 2],[factor= 5,exponent= 3]]
--R                         Type: List Record(factor: Integer,exponent: Integer)
--E 34

--S 35 of 37
numberOfFactors f
 

   (8)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  3
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 37
f
 

         7 2 3
   (9)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R         7 2 3
--R   (9)  2 3 5
--R                                                       Type: Factored Integer
--E 36

--S 37 of 37
reduce(*,[nthFactor(f,i) :: (FR INT) for i in 1..numberOfFactors(f)])
 

   (10)  2 3 5
                                                       Type: Factored Integer
--R 
--R
--R   (10)  2 3 5
--R                                                       Type: Factored Integer
--E 37
)spool
 
Starts dribbling to schaum30.output (2010/3/27, 18:38:42).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 46
aa:=integrate(tanh(a*x),x)
 

                    2cosh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2cosh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 46
bb:=1/a*log(cosh(a*x))
 

        log(cosh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(cosh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 3 of 46
cc:=aa-bb
 

                                       2cosh(a x)
        - log(cosh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2cosh(a x)
--R        - log(cosh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 4 of 46
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 5 of 46      14:604 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 6 of 46
aa:=integrate(tanh(a*x)^2,x)
 

        - sinh(a x) + (a x + 1)cosh(a x)
   (1)  --------------------------------
                   a cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R        - sinh(a x) + (a x + 1)cosh(a x)
--R   (1)  --------------------------------
--R                   a cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 7 of 46
bb:=x-tanh(a*x)/a
 

        - tanh(a x) + a x
   (2)  -----------------
                a
                                                     Type: Expression Integer
--R
--R        - tanh(a x) + a x
--R   (2)  -----------------
--R                a
--R                                                     Type: Expression Integer
--E

--S 8 of 46
cc:=aa-bb
 

        cosh(a x)tanh(a x) - sinh(a x) + cosh(a x)
   (3)  ------------------------------------------
                        a cosh(a x)
                                                     Type: Expression Integer
--R
--R        cosh(a x)tanh(a x) - sinh(a x) + cosh(a x)
--R   (3)  ------------------------------------------
--R                        a cosh(a x)
--R                                                     Type: Expression Integer
--E

--S 9 of 46
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 10 of 46     14:605 Schaums and Axiom differ by a constant
dd:=tanhrule cc
 

        1
   (5)  -
        a
                                                     Type: Expression Integer
--R
--R        1
--R   (5)  -
--R        a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 11 of 46
aa:=integrate(tanh(a*x)^3,x)
 

   (1)
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                      4                          3
       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
     + 
                        2                     2
       (- 6a x cosh(a x)  - 2a x + 2)sinh(a x)
     + 
                        3                                                  4
       (- 4a x cosh(a x)  + (- 4a x + 4)cosh(a x))sinh(a x) - a x cosh(a x)
     + 
                            2
       (- 2a x + 2)cosh(a x)  - a x
  /
                  4                        3                2               2
       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
     + 
                  3                                       4               2
     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                      4                          3
--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
--R     + 
--R                        2                     2
--R       (- 6a x cosh(a x)  - 2a x + 2)sinh(a x)
--R     + 
--R                        3                                                  4
--R       (- 4a x cosh(a x)  + (- 4a x + 4)cosh(a x))sinh(a x) - a x cosh(a x)
--R     + 
--R                            2
--R       (- 2a x + 2)cosh(a x)  - a x
--R  /
--R                  4                        3                2               2
--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
--R     + 
--R                  3                                       4               2
--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 12 of 46
bb:=1/a*log(cosh(a*x))-tanh(a*x)^2/(2*a)
 

                                   2
        2log(cosh(a x)) - tanh(a x)
   (2)  ----------------------------
                     2a
                                                     Type: Expression Integer
--R
--R                                   2
--R        2log(cosh(a x)) - tanh(a x)
--R   (2)  ----------------------------
--R                     2a
--R                                                     Type: Expression Integer
--E

--S 13 of 46     14:606 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                       4                      3                 2              2
           - 2sinh(a x)  - 8cosh(a x)sinh(a x)  + (- 12cosh(a x)  - 4)sinh(a x)
         + 
                      3                                    4             2
         (- 8cosh(a x)  - 8cosh(a x))sinh(a x) - 2cosh(a x)  - 4cosh(a x)  - 2
      *
         log(cosh(a x))
     + 
                     4                      3               2              2
           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
         + 
                      3                                    4             2
           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                    4                      3              2              2
           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
         + 
                      3                                   4             2
           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
      *
                  2
         tanh(a x)
     + 
                       4                          3
       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
     + 
                         2                     2
       (- 12a x cosh(a x)  - 4a x + 4)sinh(a x)
     + 
                        3                                                   4
       (- 8a x cosh(a x)  + (- 8a x + 8)cosh(a x))sinh(a x) - 2a x cosh(a x)
     + 
                            2
       (- 4a x + 4)cosh(a x)  - 2a x
  /
                   4                        3                 2               2
       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
     + 
                    3                                        4               2
       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
     + 
       2a
                                                     Type: Expression Integer
--R
--R   (3)
--R                       4                      3                 2              2
--R           - 2sinh(a x)  - 8cosh(a x)sinh(a x)  + (- 12cosh(a x)  - 4)sinh(a x)
--R         + 
--R                      3                                    4             2
--R         (- 8cosh(a x)  - 8cosh(a x))sinh(a x) - 2cosh(a x)  - 4cosh(a x)  - 2
--R      *
--R         log(cosh(a x))
--R     + 
--R                     4                      3               2              2
--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
--R         + 
--R                      3                                    4             2
--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                    4                      3              2              2
--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
--R         + 
--R                      3                                   4             2
--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
--R      *
--R                  2
--R         tanh(a x)
--R     + 
--R                       4                          3
--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
--R     + 
--R                         2                     2
--R       (- 12a x cosh(a x)  - 4a x + 4)sinh(a x)
--R     + 
--R                        3                                                   4
--R       (- 8a x cosh(a x)  + (- 8a x + 8)cosh(a x))sinh(a x) - 2a x cosh(a x)
--R     + 
--R                            2
--R       (- 4a x + 4)cosh(a x)  - 2a x
--R  /
--R                   4                        3                 2               2
--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
--R     + 
--R                    3                                        4               2
--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
--R     + 
--R       2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 14 of 46
aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x)
 

                            sinh(a x)                         sinh(a x)
        sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
                            cosh(a x)                         cosh(a x)
   (1)  -----------------------------------------------------------------
                                (a n + a)cosh(a x)
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                            sinh(a x)                         sinh(a x)
--R        sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
--R                            cosh(a x)                         cosh(a x)
--R   (1)  -----------------------------------------------------------------
--R                                (a n + a)cosh(a x)
--R                                          Type: Union(Expression Integer,...)
--E 

--S 15 of 46
bb:=tanh(a*x)^(n+1)/((n+1)*a)
 

                 n + 1
        tanh(a x)
   (2)  --------------
            a n + a
                                                     Type: Expression Integer
--R
--R                 n + 1
--R        tanh(a x)
--R   (2)  --------------
--R            a n + a
--R                                                     Type: Expression Integer
--E

--S 16 of 46     14:607 Axiom cannot simplify this expression
cc:=aa-bb
 

   (3)
                           sinh(a x)                         sinh(a x)
       sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
                           cosh(a x)                         cosh(a x)
     + 
                           n + 1
       - cosh(a x)tanh(a x)
  /
     (a n + a)cosh(a x)
                                                     Type: Expression Integer
--R
--R   (3)
--R                           sinh(a x)                         sinh(a x)
--R       sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
--R                           cosh(a x)                         cosh(a x)
--R     + 
--R                           n + 1
--R       - cosh(a x)tanh(a x)
--R  /
--R     (a n + a)cosh(a x)
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 17 of 46
aa:=integrate(sech(a*x)^2/tanh(a*x),x)
 

                      2cosh(a x)                     2sinh(a x)
        - log(- ---------------------) + log(- ---------------------)
                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
   (1)  -------------------------------------------------------------
                                      a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                      2cosh(a x)                     2sinh(a x)
--R        - log(- ---------------------) + log(- ---------------------)
--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
--R   (1)  -------------------------------------------------------------
--R                                      a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 18 of 46
bb:=1/a*log(tanh(a*x))
 

        log(tanh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(tanh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 19 of 46
cc:=aa-bb
 

   (3)
                                      2cosh(a x)
       - log(tanh(a x)) - log(- ---------------------)
                                sinh(a x) - cosh(a x)
     + 
                   2sinh(a x)
       log(- ---------------------)
             sinh(a x) - cosh(a x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (3)
--R                                      2cosh(a x)
--R       - log(tanh(a x)) - log(- ---------------------)
--R                                sinh(a x) - cosh(a x)
--R     + 
--R                   2sinh(a x)
--R       log(- ---------------------)
--R             sinh(a x) - cosh(a x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 20 of 46
tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 

                   sinh(x)
   (4)  tanh(x) == -------
                   cosh(x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                   sinh(x)
--R   (4)  tanh(x) == -------
--R                   cosh(x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 21 of 46
dd:=tanhrule cc
 

   (5)
             sinh(a x)                2cosh(a x)
       - log(---------) - log(- ---------------------)
             cosh(a x)          sinh(a x) - cosh(a x)
     + 
                   2sinh(a x)
       log(- ---------------------)
             sinh(a x) - cosh(a x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (5)
--R             sinh(a x)                2cosh(a x)
--R       - log(---------) - log(- ---------------------)
--R             cosh(a x)          sinh(a x) - cosh(a x)
--R     + 
--R                   2sinh(a x)
--R       log(- ---------------------)
--R             sinh(a x) - cosh(a x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 22 of 46     14:608 Schaums and Axiom agree
ee:=expandLog dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 23 of 46
aa:=integrate(1/tanh(a*x),x)
 

                    2sinh(a x)
        log(- ---------------------) - a x
              sinh(a x) - cosh(a x)
   (1)  ----------------------------------
                         a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                    2sinh(a x)
--R        log(- ---------------------) - a x
--R              sinh(a x) - cosh(a x)
--R   (1)  ----------------------------------
--R                         a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 46
bb:=1/a*log(sinh(a*x))
 

        log(sinh(a x))
   (2)  --------------
               a
                                                     Type: Expression Integer
--R
--R        log(sinh(a x))
--R   (2)  --------------
--R               a
--R                                                     Type: Expression Integer
--E

--S 25 of 46
cc:=aa-bb
 

                                       2sinh(a x)
        - log(sinh(a x)) + log(- ---------------------) - a x
                                 sinh(a x) - cosh(a x)
   (3)  -----------------------------------------------------
                                  a
                                                     Type: Expression Integer
--R
--R                                       2sinh(a x)
--R        - log(sinh(a x)) + log(- ---------------------) - a x
--R                                 sinh(a x) - cosh(a x)
--R   (3)  -----------------------------------------------------
--R                                  a
--R                                                     Type: Expression Integer
--E

--S 26 of 46
dd:=expandLog cc
 

        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
   (4)  ---------------------------------------------
                              a
                                                     Type: Expression Integer
--R
--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
--R   (4)  ---------------------------------------------
--R                              a
--R                                                     Type: Expression Integer
--E

--S 27 of 46     14:609 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        - log(- 1) + log(- 2)
   (5)  ---------------------
                  a
                                                     Type: Expression Integer
--R
--R        - log(- 1) + log(- 2)
--R   (5)  ---------------------
--R                  a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 28 of 46     14:610 Axiom cannot compute this integral
aa:=integrate(x*tanh(a*x),x)
 

           x
         ++
   (1)   |   %O tanh(%O a)d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++
--I   (1)   |   %O tanh(%O a)d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 29 of 46
aa:=integrate(x*tanh(a*x)^2,x)
 

   (1)
                    2                                   2
         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  + 2)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
         2 2                 2      2 2
       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
     + 
         2 2                 2    2 2
       (a x  - 4a x)cosh(a x)  + a x
  /
       2         2     2                       2         2     2
     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                    2                                   2
--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  + 2)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R         2 2                 2      2 2
--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
--R     + 
--R         2 2                 2    2 2
--R       (a x  - 4a x)cosh(a x)  + a x
--R  /
--R       2         2     2                       2         2     2
--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
--R                                          Type: Union(Expression Integer,...)
--E

--S 30 of 46
bb:=x^2/2-(x*tanh(a*x))/a+1/a^2*log(cosh(a*x))
 

                                            2 2
        2log(cosh(a x)) - 2a x tanh(a x) + a x
   (2)  ---------------------------------------
                            2
                          2a
                                                     Type: Expression Integer
--R
--R                                            2 2
--R        2log(cosh(a x)) - 2a x tanh(a x) + a x
--R   (2)  ---------------------------------------
--R                            2
--R                          2a
--R                                                     Type: Expression Integer
--E

--S 31 of 46
cc:=aa-bb
 

   (3)
                   2                                  2
       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(cosh(a x))
     + 
                   2                                  2
         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                       2                                          2
         (a x sinh(a x)  + 2a x cosh(a x)sinh(a x) + a x cosh(a x)  + a x)
      *
         tanh(a x)
     + 
                       2                                           2
       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
  /
      2         2     2                      2         2    2
     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (3)
--R                   2                                  2
--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(cosh(a x))
--R     + 
--R                   2                                  2
--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                       2                                          2
--R         (a x sinh(a x)  + 2a x cosh(a x)sinh(a x) + a x cosh(a x)  + a x)
--R      *
--R         tanh(a x)
--R     + 
--R                       2                                           2
--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
--R  /
--R      2         2     2                      2         2    2
--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 32 of 46
sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 

               2    cosh(2x) - 1
   (4)  sinh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) - 1
--R   (4)  sinh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 33 of 46
dd:=sinhsqrrule cc
 

   (5)
                                                       2
       (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)log(cosh(a x))
     + 
                                                       2
         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
      *
                     2cosh(a x)
         log(- ---------------------)
               sinh(a x) - cosh(a x)
     + 
                                                                   2
         (4a x cosh(a x)sinh(a x) + a x cosh(2a x) + 2a x cosh(a x)  + a x)
      *
         tanh(a x)
     + 
                                                                   2
       - 8a x cosh(a x)sinh(a x) - 2a x cosh(2a x) - 4a x cosh(a x)  + 2a x
  /
       2                      2               2         2    2
     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                       2
--R       (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)log(cosh(a x))
--R     + 
--R                                                       2
--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
--R      *
--R                     2cosh(a x)
--R         log(- ---------------------)
--R               sinh(a x) - cosh(a x)
--R     + 
--R                                                                   2
--R         (4a x cosh(a x)sinh(a x) + a x cosh(2a x) + 2a x cosh(a x)  + a x)
--R      *
--R         tanh(a x)
--R     + 
--R                                                                   2
--R       - 8a x cosh(a x)sinh(a x) - 2a x cosh(2a x) - 4a x cosh(a x)  + 2a x
--R  /
--R       2                      2               2         2    2
--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
--R                                                     Type: Expression Integer
--E

--S 34 of 46
coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 

               2    cosh(2x) + 1
   (6)  cosh(x)  == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R               2    cosh(2x) + 1
--R   (6)  cosh(x)  == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 35 of 46
ee:=coshsqrrule dd
 

   (7)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(cosh(a x))
     + 
                                                         2cosh(a x)
       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(- ---------------------)
                                                   sinh(a x) - cosh(a x)
     + 
       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
     + 
       - 4a x cosh(a x)sinh(a x) - 2a x cosh(2a x)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (7)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(cosh(a x))
--R     + 
--R                                                         2cosh(a x)
--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(- ---------------------)
--R                                                   sinh(a x) - cosh(a x)
--R     + 
--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
--R     + 
--R       - 4a x cosh(a x)sinh(a x) - 2a x cosh(2a x)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 36 of 46
ff:=expandLog ee
 

   (8)
       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
     + 
       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
     + 
       (2log(- 2) - 4a x)cosh(a x)sinh(a x) + (log(- 2) - 2a x)cosh(2a x)
     + 
       log(- 2)
  /
       2                      2              2
     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (8)
--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
--R     + 
--R       (2log(- 2) - 4a x)cosh(a x)sinh(a x) + (log(- 2) - 2a x)cosh(2a x)
--R     + 
--R       log(- 2)
--R  /
--R       2                      2              2
--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 37 of 46
sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 

                             %P sinh(y + x) - %P sinh(y - x)
   (9)  %P cosh(y)sinh(x) == -------------------------------
                                            2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--I                             %N sinh(y + x) - %N sinh(y - x)
--I   (9)  %N cosh(y)sinh(x) == -------------------------------
--R                                            2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 38 of 46
gg:=sinhcoshrule ff
 

   (10)
       (- sinh(2a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
     + 
       (a x sinh(2a x) + a x cosh(2a x) + a x)tanh(a x)
     + 
       (log(- 2) - 2a x)sinh(2a x) + (log(- 2) - 2a x)cosh(2a x) + log(- 2)
  /
      2              2              2
     a sinh(2a x) + a cosh(2a x) + a
                                                     Type: Expression Integer
--R
--R   (10)
--R       (- sinh(2a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
--R     + 
--R       (a x sinh(2a x) + a x cosh(2a x) + a x)tanh(a x)
--R     + 
--R       (log(- 2) - 2a x)sinh(2a x) + (log(- 2) - 2a x)cosh(2a x) + log(- 2)
--R  /
--R      2              2              2
--R     a sinh(2a x) + a cosh(2a x) + a
--R                                                     Type: Expression Integer
--E

--S 39 of 46     14:611 Schaums and Axiom differ by a constant
hh:=complexNormalize gg
 

         - log(- 1) + log(- 2)
   (11)  ---------------------
                    2
                   a
                                                     Type: Expression Integer
--R
--R         - log(- 1) + log(- 2)
--R   (11)  ---------------------
--R                    2
--R                   a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 40 of 46     14:612 Axiom cannot compute this integral
aa:=integrate(tanh(a*x)/x,x)
 

           x
         ++  tanh(%O a)
   (1)   |   ---------- d%O
        ++       %O
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++  tanh(%O a)
--I   (1)   |   ---------- d%O
--I        ++       %O
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 41 of 46
aa:=integrate(1/(p+q*tanh(a*x)),x)
 

              - 2q sinh(a x) - 2p cosh(a x)
        q log(-----------------------------) + (- a q - a p)x
                  sinh(a x) - cosh(a x)
   (1)  -----------------------------------------------------
                                2      2
                             a q  - a p
                                          Type: Union(Expression Integer,...)
--R 
--R
--R              - 2q sinh(a x) - 2p cosh(a x)
--R        q log(-----------------------------) + (- a q - a p)x
--R                  sinh(a x) - cosh(a x)
--R   (1)  -----------------------------------------------------
--R                                2      2
--R                             a q  - a p
--R                                          Type: Union(Expression Integer,...)
--E 

--S 42 of 46
bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(q*sinh(a*x)+p*cosh(a*x))
 

        q log(q sinh(a x) + p cosh(a x)) - a p x
   (2)  ----------------------------------------
                          2      2
                       a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(q sinh(a x) + p cosh(a x)) - a p x
--R   (2)  ----------------------------------------
--R                          2      2
--R                       a q  - a p
--R                                                     Type: Expression Integer
--E

--S 43 of 46
cc:=aa-bb
 

   (3)
                                                  - 2q sinh(a x) - 2p cosh(a x)
       - q log(q sinh(a x) + p cosh(a x)) + q log(-----------------------------)
                                                      sinh(a x) - cosh(a x)
     + 
       - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                  - 2q sinh(a x) - 2p cosh(a x)
--R       - q log(q sinh(a x) + p cosh(a x)) + q log(-----------------------------)
--R                                                      sinh(a x) - cosh(a x)
--R     + 
--R       - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 44 of 46
dd:=expandLog cc
 

   (4)
       - q log(q sinh(a x) + p cosh(a x)) - q log(sinh(a x) - cosh(a x))
     + 
       q log(- q sinh(a x) - p cosh(a x)) + q log(2) - a q x
  /
        2      2
     a q  - a p
                                                     Type: Expression Integer
--R
--R   (4)
--R       - q log(q sinh(a x) + p cosh(a x)) - q log(sinh(a x) - cosh(a x))
--R     + 
--R       q log(- q sinh(a x) - p cosh(a x)) + q log(2) - a q x
--R  /
--R        2      2
--R     a q  - a p
--R                                                     Type: Expression Integer
--E

--S 45 of 46     14:613 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        q log(2) - 2q log(- 1)
   (5)  ----------------------
                 2      2
              a q  - a p
                                                     Type: Expression Integer
--R
--R        q log(2) - 2q log(- 1)
--R   (5)  ----------------------
--R                 2      2
--R              a q  - a p
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 46 of 46     14:614 Axiom cannot compute this integral
aa:=integrate(tanh(a*x)^n,x)
 

           x
         ++            n
   (1)   |   tanh(%O a) d%O
        ++
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--R         ++            n
--I   (1)   |   tanh(%O a) d%O
--R        ++
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to Integer.output (2010/3/27, 18:42:10).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 42
2**(5678 - 4856 + 2 * 17)
 

   (1)
  4804810770435008147181540925125924391239526139871682263473855610088084200076_
   308293086342527091412083743074572278211496076276922026433435687527334980249_
   539302425425230458177649495442143929053063884787051467457680738771416988598_
   15495632935288783334250628775936
                                                        Type: PositiveInteger
--R 
--R
--R   (1)
--R  4804810770435008147181540925125924391239526139871682263473855610088084200076_
--R   308293086342527091412083743074572278211496076276922026433435687527334980249_
--R   539302425425230458177649495442143929053063884787051467457680738771416988598_
--R   15495632935288783334250628775936
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 42
x := -101
 

   (2)  - 101
                                                                Type: Integer
--R 
--R
--R   (2)  - 101
--R                                                                Type: Integer
--E 2

--S 3 of 42
abs(x)
 

   (3)  101
                                                        Type: PositiveInteger
--R 
--R
--R   (3)  101
--R                                                        Type: PositiveInteger
--E 3

--S 4 of 42
sign(x)
 

   (4)  - 1
                                                                Type: Integer
--R 
--R
--R   (4)  - 1
--R                                                                Type: Integer
--E 4

--S 5 of 42
x < 0
 

   (5)  true
                                                                Type: Boolean
--R 
--R
--R   (5)  true
--R                                                                Type: Boolean
--E 5

--S 6 of 42
x <= -1
 

   (6)  true
                                                                Type: Boolean
--R 
--R
--R   (6)  true
--R                                                                Type: Boolean
--E 6

--S 7 of 42
negative?(x)
 

   (7)  true
                                                                Type: Boolean
--R 
--R
--R   (7)  true
--R                                                                Type: Boolean
--E 7

--S 8 of 42
x > 0
 

   (8)  false
                                                                Type: Boolean
--R 
--R
--R   (8)  false
--R                                                                Type: Boolean
--E 8

--S 9 of 42
x >= 1
 

   (9)  false
                                                                Type: Boolean
--R 
--R
--R   (9)  false
--R                                                                Type: Boolean
--E 9

--S 10 of 42
positive?(x)
 

   (10)  false
                                                                Type: Boolean
--R 
--R
--R   (10)  false
--R                                                                Type: Boolean
--E 10

--S 11 of 42
zero?(x)
 

   (11)  false
                                                                Type: Boolean
--R 
--R
--R   (11)  false
--R                                                                Type: Boolean
--E 11

--S 12 of 42
one?(x)
 

   (12)  false
                                                                Type: Boolean
--R 
--R
--R   (12)  false
--R                                                                Type: Boolean
--E 12

--S 13 of 42
(x = -101)@Boolean
 

   (13)  true
                                                                Type: Boolean
--R 
--R
--R   (13)  true
--R                                                                Type: Boolean
--E 13

--S 14 of 42
odd?(x)
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 42
even?(x)
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 42
gcd(56788,43688)
 

   (16)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (16)  4
--R                                                        Type: PositiveInteger
--E 16

--S 17 of 42
lcm(56788,43688)
 

   (17)  620238536
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  620238536
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 42
max(678,567)
 

   (18)  678
                                                        Type: PositiveInteger
--R 
--R
--R   (18)  678
--R                                                        Type: PositiveInteger
--E 18

--S 19 of 42
min(678,567)
 

   (19)  567
                                                        Type: PositiveInteger
--R 
--R
--R   (19)  567
--R                                                        Type: PositiveInteger
--E 19

--S 20 of 42
reduce(max,[2,45,-89,78,100,-45])
 

   (20)  100
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  100
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 42
reduce(min,[2,45,-89,78,100,-45])
 

   (21)  - 89
                                                                Type: Integer
--R 
--R
--R   (21)  - 89
--R                                                                Type: Integer
--E 21

--S 22 of 42
reduce(gcd,[2,45,-89,78,100,-45])
 

   (22)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (22)  1
--R                                                        Type: PositiveInteger
--E 22

--S 23 of 42
reduce(lcm,[2,45,-89,78,100,-45])
 

   (23)  1041300
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1041300
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 42
13 / 4
 

         13
   (24)  --
          4
                                                       Type: Fraction Integer
--R 
--R
--R         13
--R   (24)  --
--R          4
--R                                                       Type: Fraction Integer
--E 24

--S 25 of 42
13 quo 4
 

   (25)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (25)  3
--R                                                        Type: PositiveInteger
--E 25

--S 26 of 42
13 rem 4
 

   (26)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (26)  1
--R                                                        Type: PositiveInteger
--E 26

--S 27 of 42
zero?(167604736446952 rem 2003644)
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 42
d := divide(13,4)
 

   (28)  [quotient= 3,remainder= 1]
                           Type: Record(quotient: Integer,remainder: Integer)
--R 
--R
--R   (28)  [quotient= 3,remainder= 1]
--R                           Type: Record(quotient: Integer,remainder: Integer)
--E 28

--S 29 of 42
d.quotient
 

   (29)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (29)  3
--R                                                        Type: PositiveInteger
--E 29

--S 30 of 42
d.remainder
 

   (30)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (30)  1
--R                                                        Type: PositiveInteger
--E 30

--S 31 of 42
factor 102400
 

          12 2
   (31)  2  5
                                                       Type: Factored Integer
--R 
--R
--R          12 2
--R   (31)  2  5
--R                                                       Type: Factored Integer
--E 31

--S 32 of 42
prime? 7
 

   (32)  true
                                                                Type: Boolean
--R 
--R
--R   (32)  true
--R                                                                Type: Boolean
--E 32

--S 33 of 42
prime? 8
 

   (33)  false
                                                                Type: Boolean
--R 
--R
--R   (33)  false
--R                                                                Type: Boolean
--E 33

--S 34 of 42
nextPrime 100
 

   (34)  101
                                                        Type: PositiveInteger
--R 
--R
--R   (34)  101
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 42
prevPrime 100
 

   (35)  97
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  97
--R                                                        Type: PositiveInteger
--E 35

--S 36 of 42
primes(100,175)
 

   (36)  [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101]
                                                           Type: List Integer
--R 
--R
--R   (36)  [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101]
--R                                                           Type: List Integer
--E 36

--S 37 of 42
factor(2 :: Complex Integer)
 

                      2
   (37)  - %i (1 + %i)
                                               Type: Factored Complex Integer
--R 
--R
--R                      2
--R   (37)  - %i (1 + %i)
--R                                               Type: Factored Complex Integer
--E 37

--S 38 of 42
[fibonacci(k) for k in 0..]
 

   (38)  [0,1,1,2,3,5,8,13,21,34,...]
                                                         Type: Stream Integer
--R 
--R
--R   (38)  [0,1,1,2,3,5,8,13,21,34,...]
--R                                                         Type: Stream Integer
--E 38

--S 39 of 42
[legendre(i,11) for i in 0..10]
 

   (39)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
                                                           Type: List Integer
--R 
--R
--R   (39)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
--R                                                           Type: List Integer
--E 39

--S 40 of 42
[jacobi(i,15) for i in 0..9]
 

   (40)  [0,1,1,0,1,0,0,- 1,1,0]
                                                           Type: List Integer
--R 
--R
--R   (40)  [0,1,1,0,1,0,0,- 1,1,0]
--R                                                           Type: List Integer
--E 40

--S 41 of 42
[eulerPhi i for i in 1..]
 

   (41)  [1,1,2,2,4,2,6,4,6,4,...]
                                                         Type: Stream Integer
--R 
--R
--R   (41)  [1,1,2,2,4,2,6,4,6,4,...]
--R                                                         Type: Stream Integer
--E 41

--S 42 of 42
[moebiusMu i for i in 1..]
 

   (42)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
                                                         Type: Stream Integer
--R 
--R
--R   (42)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
--R                                                         Type: Stream Integer
--E 42
)spool
 
Starts dribbling to macros.output (2010/3/27, 18:28:58).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 4
macro I == Integer
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 4
macro M(R) == Matrix(R)
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 2

--S 3 of 4
macro p(n) == x < n
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 4
macro q(i,j) == if x < i then i else j
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 4
)spool 
 
Starts dribbling to finitegraph.output (2010/3/27, 18:25:57).
)set message test on
 
)set message auto off
 
)clear all
 
)sys cp $AXIOM/../../src/input/finitegraph.input.pamphlet .
 
)lisp (tangle "finitegraph.input.pamphlet" "fgraf.spad" "fgraf.spad")
 
Value = NIL
)co fgraf
 
   Compiling AXIOM source code from file 
      /home/camm/debian/axiom/axiom-20091101/int/input/fgraf.spad using
      old system compiler.
   GRAPHS abbreviates category GraphCategory 
------------------------------------------------------------------------
   initializing nrlib GRAPHS for GraphCategory 
   compiling into nrlib GRAPHS 

;;;     ***       |GraphCategory| REDEFINED
Time: 0 SEC.

   finalizing nrlib GRAPHS 
   Processing GraphCategory for Browser database:
--->-->GraphCategory((source (nodes edges))): Not documented!!!!
--->-->GraphCategory((target (nodes edges))): Not documented!!!!
--->-->GraphCategory(constructor): Not documented!!!!
--->-->GraphCategory(): Missing Description
; (DEFUN |GraphCategory| ...) is being compiled.
;; The variable |GraphCategory;AL| is undefined.
;; The compiler will assume this variable is a global.
; (DEFUN |GraphCategory;| ...) is being compiled.
;; The variable |GraphCategory;CAT| is undefined.
;; The compiler will assume this variable is a global.
------------------------------------------------------------------------
   GraphCategory is now explicitly exposed in frame initial 
   GraphCategory will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/GRAPHS.nrlib/code

   FGRAPHS abbreviates domain FiniteGraph 
   processing macro definition edges ==> Record(source: nodes,target: nodes) 
------------------------------------------------------------------------
   initializing nrlib FGRAPHS for FiniteGraph 
   compiling into nrlib FGRAPHS 
   compiling exported new : () -> $
Time: 0.01 SEC.

   compiling exported addNode : ($,List nodes) -> List nodes
Time: 0.05 SEC.

   compiling exported addNode : ($,nodes) -> List nodes
Time: 0 SEC.

   compiling exported addEdge : ($,nodes,nodes) -> Record(source: nodes,target: nodes)
Time: 0.01 SEC.

   compiling exported edgeList : $ -> List Record(source: nodes,target: nodes)
Time: 0.01 SEC.

   compiling exported nodeList : $ -> List nodes
Time: 0 SEC.

   compiling exported source : Record(source: nodes,target: nodes) -> nodes
      FGRAPHS;source;Rnodes;7 is replaced by QCAR 
Time: 0 SEC.

   compiling exported target : Record(source: nodes,target: nodes) -> nodes
      FGRAPHS;target;Rnodes;8 is replaced by QCDR 
Time: 0 SEC.

(time taken in buildFunctor:  0 . NIL)

;;;     ***       |FiniteGraph| REDEFINED

;;;     ***       |FiniteGraph| REDEFINED
Time: 0 SEC.


   Cumulative Statistics for Constructor FiniteGraph
      Time: 0.08 seconds
 
   finalizing nrlib FGRAPHS 
   Processing FiniteGraph for Browser database:
--->-->FiniteGraph((new (%))): Not documented!!!!
--->-->FiniteGraph((addNode ((List nodes) % (List nodes)))): Not documented!!!!
--->-->FiniteGraph((addNode ((List nodes) % nodes))): Not documented!!!!
--->-->FiniteGraph((addEdge (edges % nodes nodes))): Not documented!!!!
--->-->FiniteGraph((edgeList ((List edges) %))): Not documented!!!!
--->-->FiniteGraph((nodeList ((List nodes) %))): Not documented!!!!
--->-->FiniteGraph(constructor): Not documented!!!!
--->-->FiniteGraph(): Missing Description
------------------------------------------------------------------------
   FiniteGraph is now explicitly exposed in frame initial 
   FiniteGraph will be automatically loaded when needed from 
      /home/camm/debian/axiom/axiom-20091101/int/input/FGRAPHS.nrlib/code


--S 1 of 8
g:FiniteGraph(INT):=new();
 

                                                    Type: FiniteGraph Integer
--R 
--R
--R                                                    Type: FiniteGraph Integer
--E 1

--S 2 of 8
addNode(g,1)
 

   (2)  [1]
                                                           Type: List Integer
--R 
--R
--R   (2)  [1]
--R                                                           Type: List Integer
--E 2

--S 3 of 8
addNode(g,2)
 

   (3)  [2]
                                                           Type: List Integer
--R 
--R
--R   (3)  [2]
--R                                                           Type: List Integer
--E 3

--S 4 of 8
e:=addEdge(g,1,2)
 

   (4)  [source= 1,target= 2]
                                Type: Record(source: Integer,target: Integer)
--R 
--R
--R   (4)  [source= 1,target= 2]
--R                                Type: Record(source: Integer,target: Integer)
--E 4

--S 5 of 8
source(e)$FiniteGraph(INT)
 

   (5)  1
                                                                Type: Integer
--R 
--R
--R   (5)  1
--R                                                                Type: Integer
--E 5

--S 6 of 8
target(e)$FiniteGraph(INT)
 

   (6)  2
                                                                Type: Integer
--R 
--R
--R   (6)  2
--R                                                                Type: Integer
--E 6

--S 7 of 8
edgeList(g)
 

   (7)  [[source= 1,target= 2]]
                           Type: List Record(source: Integer,target: Integer)
--R 
--R
--R   (7)  [[source= 1,target= 2]]
--R                           Type: List Record(source: Integer,target: Integer)
--E 7

--S 8 of 8
nodeList(g)
 

   (8)  [1,2]
                                                           Type: List Integer
--R 
--R
--R   (8)  [1,2]
--R                                                           Type: List Integer
--E 8

)spool 
 
Starts dribbling to DoubleFloat.output (2010/3/27, 18:41:56).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 10
2.71828
 

   (1)  2.71828
                                                                  Type: Float
--R 
--R
--R   (1)  2.71828
--R                                                                  Type: Float
--E 1

--S 2 of 10
2.71828@DoubleFloat
 

   (2)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (2)  2.71828
--R                                                            Type: DoubleFloat
--E 2

--S 3 of 10
2.71828 :: DoubleFloat
 

   (3)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (3)  2.71828
--R                                                            Type: DoubleFloat
--E 3

--S 4 of 10
eApprox : DoubleFloat := 2.71828
 

   (4)  2.71828
                                                            Type: DoubleFloat
--R 
--R
--R   (4)  2.71828
--R                                                            Type: DoubleFloat
--E 4

--S 5 of 10
avg : List DoubleFloat -> DoubleFloat
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 5

--S 6 of 10
avg l ==
  empty? l => 0 :: DoubleFloat
  reduce(_+,l) / #l
 
                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 6

--S 7 of 10
avg []
 
   Compiling function avg with type List DoubleFloat -> DoubleFloat 

   (7)  0.
                                                            Type: DoubleFloat
--R 
--R   Compiling function avg with type List DoubleFloat -> DoubleFloat 
--R
--R   (7)  0.
--R                                                            Type: DoubleFloat
--E 7

--S 8 of 10
avg [3.4,9.7,-6.8]
 

   (8)  2.0999999999999996
                                                            Type: DoubleFloat
--R 
--R
--R   (8)  2.1000000000000001
--R                                                            Type: DoubleFloat
--E 8

--S 9 of 10
cos(3.1415926)$DoubleFloat
 

   (9)  - 0.99999999999999856
                                                            Type: DoubleFloat
--R 
--R
--R   (9)  - 0.99999999999999856
--R                                                            Type: DoubleFloat
--E 9

--S 10 of 10
cos(3.1415926 :: DoubleFloat)
 

   (10)  - 0.99999999999999856
                                                            Type: DoubleFloat
--R 
--R
--R   (10)  - 0.99999999999999856
--R                                                            Type: DoubleFloat
--E 10
)spool
 
Starts dribbling to schaum34.output (2010/3/27, 18:38:49).
)set message test on
 
)set message auto off
 
)clear all
 

--S 1 of 156
aa:=integrate(asinh(x/a),x)
 

                               +-------+
           +-------+           | 2    2           +-------+
           | 2    2     2     \|x  + a   + x      | 2    2     2    2
        (x\|x  + a   - x )log(--------------) + x\|x  + a   - x  - a
                                     a
   (1)  -------------------------------------------------------------
                                 +-------+
                                 | 2    2
                                \|x  + a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R           +-------+           | 2    2           +-------+
--R           | 2    2     2     \|x  + a   + x      | 2    2     2    2
--R        (x\|x  + a   - x )log(--------------) + x\|x  + a   - x  - a
--R                                     a
--R   (1)  -------------------------------------------------------------
--R                                 +-------+
--R                                 | 2    2
--R                                \|x  + a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 2 of 156
bb:=x*asinh(x/a)-sqrt(x^2+a^2)
 

           +-------+
           | 2    2            x
   (2)  - \|x  + a   + x asinh(-)
                               a
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2            x
--R   (2)  - \|x  + a   + x asinh(-)
--R                               a
--R                                                     Type: Expression Integer
--E

--S 3 of 156
cc:=aa-bb
 

               +-------+
               | 2    2
              \|x  + a   + x            x
   (3)  x log(--------------) - x asinh(-)
                     a                  a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  + a   + x            x
--R   (3)  x log(--------------) - x asinh(-)
--R                     a                  a
--R                                                     Type: Expression Integer
--E

--S 4 of 156
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 5 of 156
dd:=asinhlogrule cc
 

                                        +-------+
                                        | 2    2
                                        |x  + a
               +-------+              a |-------  + x
               | 2    2                 |    2
              \|x  + a   + x           \|   a
   (5)  x log(--------------) - x log(---------------)
                     a                       a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  + a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R              \|x  + a   + x           \|   a
--R   (5)  x log(--------------) - x log(---------------)
--R                     a                       a
--R                                                     Type: Expression Integer
--E

--S 6 of 156
ee:=expandLog dd
 

                                        +-------+
               +-------+                | 2    2
               | 2    2                 |x  + a
   (6)  x log(\|x  + a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R               | 2    2                 |x  + a
--R   (6)  x log(\|x  + a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R                                                     Type: Expression Integer
--E

--S 7 of 156      14:646 Schaums and Axiom agree
ff:=rootSimp ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 8 of 156
aa:=integrate(x*asinh(x/a),x)
 

   (1)
                                                       +-------+
                     +-------+                         | 2    2
           3     2   | 2    2      4     2 2    4     \|x  + a   + x
       ((4x  + 2a x)\|x  + a   - 4x  - 4a x  - a )log(--------------)
                                                             a
     + 
                   +-------+
          3    2   | 2    2      4     2 2
       (2x  + a x)\|x  + a   - 2x  - 2a x
  /
        +-------+
        | 2    2      2     2
     8x\|x  + a   - 8x  - 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                       +-------+
--R                     +-------+                         | 2    2
--R           3     2   | 2    2      4     2 2    4     \|x  + a   + x
--R       ((4x  + 2a x)\|x  + a   - 4x  - 4a x  - a )log(--------------)
--R                                                             a
--R     + 
--R                   +-------+
--R          3    2   | 2    2      4     2 2
--R       (2x  + a x)\|x  + a   - 2x  - 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     8x\|x  + a   - 8x  - 4a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 9 of 156
bb:=(x^2/2+a^2/4)*asinh(x/a)-(x*sqrt(x^2+a^2))/4
 

            +-------+
            | 2    2       2    2       x
        - x\|x  + a   + (2x  + a )asinh(-)
                                        a
   (2)  ----------------------------------
                         4
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2       2    2       x
--R        - x\|x  + a   + (2x  + a )asinh(-)
--R                                        a
--R   (2)  ----------------------------------
--R                         4
--R                                                     Type: Expression Integer
--E

--S 10 of 156
cc:=aa-bb
 

                       +-------+
                       | 2    2
           2    2     \|x  + a   + x         2    2       x
        (2x  + a )log(--------------) + (- 2x  - a )asinh(-)
                             a                            a
   (3)  ----------------------------------------------------
                                  4
                                                     Type: Expression Integer
--R
--R                       +-------+
--R                       | 2    2
--R           2    2     \|x  + a   + x         2    2       x
--R        (2x  + a )log(--------------) + (- 2x  - a )asinh(-)
--R                             a                            a
--R   (3)  ----------------------------------------------------
--R                                  4
--R                                                     Type: Expression Integer
--E

--S 11 of 156
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 12 of 156
dd:=asinhlogrule cc
 

                                                          +-------+
                                                          | 2    2
                                                          |x  + a
                       +-------+                        a |-------  + x
                       | 2    2                           |    2
           2    2     \|x  + a   + x         2    2      \|   a
        (2x  + a )log(--------------) + (- 2x  - a )log(---------------)
                             a                                 a
   (5)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                                                          | 2    2
--R                                                          |x  + a
--R                       +-------+                        a |-------  + x
--R                       | 2    2                           |    2
--R           2    2     \|x  + a   + x         2    2      \|   a
--R        (2x  + a )log(--------------) + (- 2x  - a )log(---------------)
--R                             a                                 a
--R   (5)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 13 of 156
ee:=expandLog dd
 

                                                          +-------+
                       +-------+                          | 2    2
           2    2      | 2    2              2    2       |x  + a
        (2x  + a )log(\|x  + a   + x) + (- 2x  - a )log(a |-------  + x)
                                                          |    2
                                                         \|   a
   (6)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                       +-------+                          | 2    2
--R           2    2      | 2    2              2    2       |x  + a
--R        (2x  + a )log(\|x  + a   + x) + (- 2x  - a )log(a |-------  + x)
--R                                                          |    2
--R                                                         \|   a
--R   (6)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 14 of 156     14:647 Schaums and Axiom agree
ff:=rootSimp ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 15 of 156
aa:=integrate(x^2*asinh(x/a),x)
 

   (1)
                                                     +-------+
                       +-------+                     | 2    2
            5     2 3  | 2    2       6     2 4     \|x  + a   + x
       ((12x  + 3a x )\|x  + a   - 12x  - 9a x )log(--------------)
                                                           a
     + 
                            +-------+
          5     2 3     4   | 2    2      6     2 4     4 2     6
       (4x  - 5a x  - 6a x)\|x  + a   - 4x  + 3a x  + 9a x  + 2a
  /
                  +-------+
         2     2  | 2    2       3      2
     (36x  + 9a )\|x  + a   - 36x  - 27a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                     +-------+
--R                       +-------+                     | 2    2
--R            5     2 3  | 2    2       6     2 4     \|x  + a   + x
--R       ((12x  + 3a x )\|x  + a   - 12x  - 9a x )log(--------------)
--R                                                           a
--R     + 
--R                            +-------+
--R          5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (4x  - 5a x  - 6a x)\|x  + a   - 4x  + 3a x  + 9a x  + 2a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3      2
--R     (36x  + 9a )\|x  + a   - 36x  - 27a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 16 of 156
bb:=x^3/3*asinh(x/a)+((2*a^2-x^2)*sqrt(x^2+a^2))/9
 

                     +-------+
            2     2  | 2    2      3      x
        (- x  + 2a )\|x  + a   + 3x asinh(-)
                                          a
   (2)  ------------------------------------
                          9
                                                     Type: Expression Integer
--R
--R                     +-------+
--R            2     2  | 2    2      3      x
--R        (- x  + 2a )\|x  + a   + 3x asinh(-)
--R                                          a
--R   (2)  ------------------------------------
--R                          9
--R                                                     Type: Expression Integer
--E

--S 17 of 156
cc:=aa-bb
 

               +-------+
               | 2    2
         3    \|x  + a   + x     3      x
        x log(--------------) - x asinh(-)
                     a                  a
   (3)  ----------------------------------
                         3
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R         3    \|x  + a   + x     3      x
--R        x log(--------------) - x asinh(-)
--R                     a                  a
--R   (3)  ----------------------------------
--R                         3
--R                                                     Type: Expression Integer
--E

--S 18 of 156
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 19 of 156
dd:=asinhlogrule cc
 

                                        +-------+
                                        | 2    2
                                        |x  + a
               +-------+              a |-------  + x
               | 2    2                 |    2
         3    \|x  + a   + x     3     \|   a
        x log(--------------) - x log(---------------)
                     a                       a
   (5)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  + a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R         3    \|x  + a   + x     3     \|   a
--R        x log(--------------) - x log(---------------)
--R                     a                       a
--R   (5)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 20 of 156
ee:=expandLog dd
 

                                        +-------+
               +-------+                | 2    2
         3     | 2    2          3      |x  + a
        x log(\|x  + a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
   (6)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R         3     | 2    2          3      |x  + a
--R        x log(\|x  + a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R   (6)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 21 of 156     14:648 Schaums and Axiom agree
ff:=rootSimp ee
 

   (7)  0
                                                     Type: Expression Integer
--R
--R   (7)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 22 of 156     14:649 Axiom cannot compute this integral
aa:=integrate(asinh(x/a)/x,x)
 

                   %P
           x asinh(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x asinh(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 23 of 156
aa:=integrate(asinh(x/a)/x^2,x)
 

   (1)
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
                +-------+
                | 2    2
               \|x  + a   + x
       - a log(--------------)
                      a
  /
     a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R                +-------+
--R                | 2    2
--R               \|x  + a   + x
--R       - a log(--------------)
--R                      a
--R  /
--R     a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 24 of 156
bb:=-asinh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2
                \|x  + a   + a            x
        - x log(--------------) - a asinh(-)
                       x                  a
   (2)  ------------------------------------
                         a x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  + a   + a            x
--R        - x log(--------------) - a asinh(-)
--R                       x                  a
--R   (2)  ------------------------------------
--R                         a x
--R                                                     Type: Expression Integer
--E

--S 25 of 156
cc:=aa-bb
 

   (3)
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
                +-------+               +-------+
                | 2    2                | 2    2
               \|x  + a   + x          \|x  + a   + a            x
       - a log(--------------) + x log(--------------) + a asinh(-)
                      a                       x                  a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R                +-------+               +-------+
--R                | 2    2                | 2    2
--R               \|x  + a   + x          \|x  + a   + a            x
--R       - a log(--------------) + x log(--------------) + a asinh(-)
--R                      a                       x                  a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 26 of 156
asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
 

                         +------+
                         | 2
   (4)  asinh(x) == log(\|x  + 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (4)  asinh(x) == log(\|x  + 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 27 of 156
dd:=asinhlogrule cc
 

   (5)
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
                                                                 +-------+
                                                                 | 2    2
                                                                 |x  + a
                +-------+               +-------+              a |-------  + x
                | 2    2                | 2    2                 |    2
               \|x  + a   + x          \|x  + a   + a           \|   a
       - a log(--------------) + x log(--------------) + a log(---------------)
                      a                       x                       a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (5)
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R                                                                 +-------+
--R                                                                 | 2    2
--R                                                                 |x  + a
--R                +-------+               +-------+              a |-------  + x
--R                | 2    2                | 2    2                 |    2
--R               \|x  + a   + x          \|x  + a   + a           \|   a
--R       - a log(--------------) + x log(--------------) + a log(---------------)
--R                      a                       x                       a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 28 of 156
ee:=expandLog dd
 

   (6)
                +-------+               +-------+
                | 2    2                | 2    2
       - a log(\|x  + a   + x) + x log(\|x  + a   + a)
     + 
                +-------+                   +-------+
                | 2    2                    | 2    2
       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
     + 
               +-------+
               | 2    2
               |x  + a
       a log(a |-------  + x) - x log(x)
               |    2
              \|   a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (6)
--R                +-------+               +-------+
--R                | 2    2                | 2    2
--R       - a log(\|x  + a   + x) + x log(\|x  + a   + a)
--R     + 
--R                +-------+                   +-------+
--R                | 2    2                    | 2    2
--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
--R     + 
--R               +-------+
--R               | 2    2
--R               |x  + a
--R       a log(a |-------  + x) - x log(x)
--R               |    2
--R              \|   a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 29 of 156
ff:=rootSimp ee
 

   (7)
            +-------+             +-------+                 +-------+
            | 2    2              | 2    2                  | 2    2
       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
     + 
       - log(x)
  /
     a
                                                     Type: Expression Integer
--R
--R   (7)
--R            +-------+             +-------+                 +-------+
--R            | 2    2              | 2    2                  | 2    2
--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
--R     + 
--R       - log(x)
--R  /
--R     a
--R                                                     Type: Expression Integer
--E

--S 30 of 156     14:650 Schaums and Axiom differ by a constant
gg:=complexNormalize ff
 

          log(- 1)
   (8)  - --------
              a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (8)  - --------
--R              a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 31 of 156
aa:=integrate(acosh(x/a),x)
 

                               +-------+
           +-------+           | 2    2           +-------+
           | 2    2     2     \|x  - a   + x      | 2    2     2    2
        (x\|x  - a   - x )log(--------------) + x\|x  - a   - x  + a
                                     a
   (1)  -------------------------------------------------------------
                                 +-------+
                                 | 2    2
                                \|x  - a   - x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                               +-------+
--R           +-------+           | 2    2           +-------+
--R           | 2    2     2     \|x  - a   + x      | 2    2     2    2
--R        (x\|x  - a   - x )log(--------------) + x\|x  - a   - x  + a
--R                                     a
--R   (1)  -------------------------------------------------------------
--R                                 +-------+
--R                                 | 2    2
--R                                \|x  - a   - x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 32 of 156
bb1:=x*acosh(x/a)-sqrt(x^2-a^2)
 

           +-------+
           | 2    2            x
   (2)  - \|x  - a   + x acosh(-)
                               a
                                                     Type: Expression Integer
--R
--R           +-------+
--R           | 2    2            x
--R   (2)  - \|x  - a   + x acosh(-)
--R                               a
--R                                                     Type: Expression Integer
--E

--S 33 of 156
bb2:=x*acosh(x/a)+sqrt(x^2-a^2)
 

         +-------+
         | 2    2            x
   (3)  \|x  - a   + x acosh(-)
                             a
                                                     Type: Expression Integer
--R
--R         +-------+
--R         | 2    2            x
--R   (3)  \|x  - a   + x acosh(-)
--R                             a
--R                                                     Type: Expression Integer
--E

--S 34 of 156
cc1:=aa-bb1
 

               +-------+
               | 2    2
              \|x  - a   + x            x
   (4)  x log(--------------) - x acosh(-)
                     a                  a
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  - a   + x            x
--R   (4)  x log(--------------) - x acosh(-)
--R                     a                  a
--R                                                     Type: Expression Integer
--E

--S 35 of 156
cc2:=aa-bb2
 

   (5)
                              +-------+
          +-------+           | 2    2                             +-------+
          | 2    2     2     \|x  - a   + x               x        | 2    2
       (x\|x  - a   - x )log(--------------) + (- x acosh(-) + 2x)\|x  - a
                                    a                     a
     + 
        2      x      2     2
       x acosh(-) - 2x  + 2a
               a
  /
      +-------+
      | 2    2
     \|x  - a   - x
                                                     Type: Expression Integer
--R
--R   (5)
--R                              +-------+
--R          +-------+           | 2    2                             +-------+
--R          | 2    2     2     \|x  - a   + x               x        | 2    2
--R       (x\|x  - a   - x )log(--------------) + (- x acosh(-) + 2x)\|x  - a
--R                                    a                     a
--R     + 
--R        2      x      2     2
--R       x acosh(-) - 2x  + 2a
--R               a
--R  /
--R      +-------+
--R      | 2    2
--R     \|x  - a   - x
--R                                                     Type: Expression Integer
--E

--S 36 of 156
acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (6)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (6)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 37 of 156
dd1:=acoshlogrule cc1
 

                                        +-------+
                                        | 2    2
                                        |x  - a
               +-------+              a |-------  + x
               | 2    2                 |    2
              \|x  - a   + x           \|   a
   (7)  x log(--------------) - x log(---------------)
                     a                       a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  - a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R              \|x  - a   + x           \|   a
--R   (7)  x log(--------------) - x log(---------------)
--R                     a                       a
--R                                                     Type: Expression Integer
--E

--S 38 of 156
ee1:=expandLog dd1
 

                                        +-------+
               +-------+                | 2    2
               | 2    2                 |x  - a
   (8)  x log(\|x  - a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R               | 2    2                 |x  - a
--R   (8)  x log(\|x  - a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R                                                     Type: Expression Integer
--E

--S 39 of 156     14:651 Schaums and Axiom agree
ff1:=rootSimp ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E

)clear all
 

--S 40 of 156
aa:=integrate(x*acosh(x/a),x)
 

   (1)
                                                       +-------+
                     +-------+                         | 2    2
           3     2   | 2    2      4     2 2    4     \|x  - a   + x
       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
                                                             a
     + 
                   +-------+
          3    2   | 2    2      4     2 2
       (2x  - a x)\|x  - a   - 2x  + 2a x
  /
        +-------+
        | 2    2      2     2
     8x\|x  - a   - 8x  + 4a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                       +-------+
--R                     +-------+                         | 2    2
--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
--R                                                             a
--R     + 
--R                   +-------+
--R          3    2   | 2    2      4     2 2
--R       (2x  - a x)\|x  - a   - 2x  + 2a x
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     8x\|x  - a   - 8x  + 4a
--R                                          Type: Union(Expression Integer,...)
--E

--S 41 of 156
bb1:=1/4*(2*x^2-a^2)*acosh(x/a)-1/4*x*sqrt(x^2-a^2)
 

            +-------+
            | 2    2       2    2       x
        - x\|x  - a   + (2x  - a )acosh(-)
                                        a
   (2)  ----------------------------------
                         4
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2       2    2       x
--R        - x\|x  - a   + (2x  - a )acosh(-)
--R                                        a
--R   (2)  ----------------------------------
--R                         4
--R                                                     Type: Expression Integer
--E

--S 42 of 156
bb2:=1/4*(2*x^2-a^2)*acosh(x/a)+1/4*x*sqrt(x^2-a^2)
 

          +-------+
          | 2    2       2    2       x
        x\|x  - a   + (2x  - a )acosh(-)
                                      a
   (3)  --------------------------------
                        4
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2       2    2       x
--R        x\|x  - a   + (2x  - a )acosh(-)
--R                                      a
--R   (3)  --------------------------------
--R                        4
--R                                                     Type: Expression Integer
--E

--S 43 of 156
cc1:=aa-bb1
 

                       +-------+
                       | 2    2
           2    2     \|x  - a   + x         2    2       x
        (2x  - a )log(--------------) + (- 2x  + a )acosh(-)
                             a                            a
   (4)  ----------------------------------------------------
                                  4
                                                     Type: Expression Integer
--R
--R                       +-------+
--R                       | 2    2
--R           2    2     \|x  - a   + x         2    2       x
--R        (2x  - a )log(--------------) + (- 2x  + a )acosh(-)
--R                             a                            a
--R   (4)  ----------------------------------------------------
--R                                  4
--R                                                     Type: Expression Integer
--E

--S 44 of 156
cc2:=aa-bb2
 

   (5)
                                                       +-------+
                     +-------+                         | 2    2
           3     2   | 2    2      4     2 2    4     \|x  - a   + x
       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
                                                             a
     + 
                                             +-------+
             3     2        x      3     2   | 2    2
       ((- 4x  + 2a x)acosh(-) + 4x  - 2a x)\|x  - a
                            a
     + 
          4     2 2    4       x      4     2 2
       (4x  - 4a x  + a )acosh(-) - 4x  + 4a x
                               a
  /
        +-------+
        | 2    2      2     2
     8x\|x  - a   - 8x  + 4a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                       +-------+
--R                     +-------+                         | 2    2
--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
--R                                                             a
--R     + 
--R                                             +-------+
--R             3     2        x      3     2   | 2    2
--R       ((- 4x  + 2a x)acosh(-) + 4x  - 2a x)\|x  - a
--R                            a
--R     + 
--R          4     2 2    4       x      4     2 2
--R       (4x  - 4a x  + a )acosh(-) - 4x  + 4a x
--R                               a
--R  /
--R        +-------+
--R        | 2    2      2     2
--R     8x\|x  - a   - 8x  + 4a
--R                                                     Type: Expression Integer
--E

--S 45 of 156
acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (6)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (6)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 46 of 156
dd1:=acoshlogrule cc1
 

                                                          +-------+
                                                          | 2    2
                                                          |x  - a
                       +-------+                        a |-------  + x
                       | 2    2                           |    2
           2    2     \|x  - a   + x         2    2      \|   a
        (2x  - a )log(--------------) + (- 2x  + a )log(---------------)
                             a                                 a
   (7)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                                                          | 2    2
--R                                                          |x  - a
--R                       +-------+                        a |-------  + x
--R                       | 2    2                           |    2
--R           2    2     \|x  - a   + x         2    2      \|   a
--R        (2x  - a )log(--------------) + (- 2x  + a )log(---------------)
--R                             a                                 a
--R   (7)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 47 of 156
ee1:=expandLog dd1
 

                                                          +-------+
                       +-------+                          | 2    2
           2    2      | 2    2              2    2       |x  - a
        (2x  - a )log(\|x  - a   + x) + (- 2x  + a )log(a |-------  + x)
                                                          |    2
                                                         \|   a
   (8)  ----------------------------------------------------------------
                                        4
                                                     Type: Expression Integer
--R
--R                                                          +-------+
--R                       +-------+                          | 2    2
--R           2    2      | 2    2              2    2       |x  - a
--R        (2x  - a )log(\|x  - a   + x) + (- 2x  + a )log(a |-------  + x)
--R                                                          |    2
--R                                                         \|   a
--R   (8)  ----------------------------------------------------------------
--R                                        4
--R                                                     Type: Expression Integer
--E

--S 48 of 156     14:652 Schaums and Axiom agree
ff1:=rootSimp ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 49 of 156
aa:=integrate(x^2*acosh(x/a),x)
 

   (1)
                                                     +-------+
                       +-------+                     | 2    2
            5     2 3  | 2    2       6     2 4     \|x  - a   + x
       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
                                                           a
     + 
                            +-------+
          5     2 3     4   | 2    2      6     2 4     4 2     6
       (4x  + 5a x  - 6a x)\|x  - a   - 4x  - 3a x  + 9a x  - 2a
  /
                  +-------+
         2     2  | 2    2       3      2
     (36x  - 9a )\|x  - a   - 36x  + 27a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R   (1)
--R                                                     +-------+
--R                       +-------+                     | 2    2
--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
--R                                                           a
--R     + 
--R                            +-------+
--R          5     2 3     4   | 2    2      6     2 4     4 2     6
--R       (4x  + 5a x  - 6a x)\|x  - a   - 4x  - 3a x  + 9a x  - 2a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3      2
--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 50 of 156
bb1:=1/3*x^3*acosh(x/a)-1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
 

                     +-------+
            2     2  | 2    2      3      x
        (- x  - 2a )\|x  - a   + 3x acosh(-)
                                          a
   (2)  ------------------------------------
                          9
                                                     Type: Expression Integer
--R
--R                     +-------+
--R            2     2  | 2    2      3      x
--R        (- x  - 2a )\|x  - a   + 3x acosh(-)
--R                                          a
--R   (2)  ------------------------------------
--R                          9
--R                                                     Type: Expression Integer
--E

--S 51 of 156
bb2:=1/3*x^3*acosh(x/a)+1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
 

                   +-------+
          2     2  | 2    2      3      x
        (x  + 2a )\|x  - a   + 3x acosh(-)
                                        a
   (3)  ----------------------------------
                         9
                                                     Type: Expression Integer
--R
--R                   +-------+
--R          2     2  | 2    2      3      x
--R        (x  + 2a )\|x  - a   + 3x acosh(-)
--R                                        a
--R   (3)  ----------------------------------
--R                         9
--R                                                     Type: Expression Integer
--E

--S 52 of 156
cc1:=aa-bb1
 

               +-------+
               | 2    2
         3    \|x  - a   + x     3      x
        x log(--------------) - x acosh(-)
                     a                  a
   (4)  ----------------------------------
                         3
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R         3    \|x  - a   + x     3      x
--R        x log(--------------) - x acosh(-)
--R                     a                  a
--R   (4)  ----------------------------------
--R                         3
--R                                                     Type: Expression Integer
--E

--S 53 of 156
cc2:=aa-bb2
 

   (5)
                                                     +-------+
                       +-------+                     | 2    2
            5     2 3  | 2    2       6     2 4     \|x  - a   + x
       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
                                                           a
     + 
                                                         +-------+
              5     2 3       x      5      2 3      4   | 2    2
       ((- 12x  + 3a x )acosh(-) + 8x  + 10a x  - 12a x)\|x  - a
                              a
     + 
           6     2 4       x      6     2 4      4 2     6
       (12x  - 9a x )acosh(-) - 8x  - 6a x  + 18a x  - 4a
                           a
  /
                  +-------+
         2     2  | 2    2       3      2
     (36x  - 9a )\|x  - a   - 36x  + 27a x
                                                     Type: Expression Integer
--R
--R   (5)
--R                                                     +-------+
--R                       +-------+                     | 2    2
--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
--R                                                           a
--R     + 
--R                                                         +-------+
--R              5     2 3       x      5      2 3      4   | 2    2
--R       ((- 12x  + 3a x )acosh(-) + 8x  + 10a x  - 12a x)\|x  - a
--R                              a
--R     + 
--R           6     2 4       x      6     2 4      4 2     6
--R       (12x  - 9a x )acosh(-) - 8x  - 6a x  + 18a x  - 4a
--R                           a
--R  /
--R                  +-------+
--R         2     2  | 2    2       3      2
--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
--R                                                     Type: Expression Integer
--E

--S 54 of 156
acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
 

                         +------+
                         | 2
   (6)  acosh(x) == log(\|x  - 1  + x)
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                         +------+
--R                         | 2
--R   (6)  acosh(x) == log(\|x  - 1  + x)
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 55 of 156
dd1:=acoshlogrule cc1
 

                                        +-------+
                                        | 2    2
                                        |x  - a
               +-------+              a |-------  + x
               | 2    2                 |    2
         3    \|x  - a   + x     3     \|   a
        x log(--------------) - x log(---------------)
                     a                       a
   (7)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R                                        | 2    2
--R                                        |x  - a
--R               +-------+              a |-------  + x
--R               | 2    2                 |    2
--R         3    \|x  - a   + x     3     \|   a
--R        x log(--------------) - x log(---------------)
--R                     a                       a
--R   (7)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 56 of 156
ee1:=expandLog dd1
 

                                        +-------+
               +-------+                | 2    2
         3     | 2    2          3      |x  - a
        x log(\|x  - a   + x) - x log(a |-------  + x)
                                        |    2
                                       \|   a
   (8)  ----------------------------------------------
                               3
                                                     Type: Expression Integer
--R
--R                                        +-------+
--R               +-------+                | 2    2
--R         3     | 2    2          3      |x  - a
--R        x log(\|x  - a   + x) - x log(a |-------  + x)
--R                                        |    2
--R                                       \|   a
--R   (8)  ----------------------------------------------
--R                               3
--R                                                     Type: Expression Integer
--E

--S 57 of 156     14:653 Schaums and Axiom agree
ff1:=rootSimp ee1
 

   (9)  0
                                                     Type: Expression Integer
--R
--R   (9)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 58 of 156     14:654 Axiom cannot compute this integral
aa:=integrate(acosh(x/a)/x,x)
 

                   %P
           x acosh(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x acosh(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 59 of 156
aa:=integrate(acosh(x/a)/x^2,x)
 

                 +-------+                 +-------+
                 | 2    2                  | 2    2
                \|x  - a   + x            \|x  - a   - x
        - a log(--------------) + 2x atan(--------------)
                       a                         a
   (1)  -------------------------------------------------
                               a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 +-------+                 +-------+
--R                 | 2    2                  | 2    2
--R                \|x  - a   + x            \|x  - a   - x
--R        - a log(--------------) + 2x atan(--------------)
--R                       a                         a
--R   (1)  -------------------------------------------------
--R                               a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 60 of 156
bb1:=-acosh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
 

                 +-------+
                 | 2    2
                \|x  + a   + a            x
        - x log(--------------) - a acosh(-)
                       x                  a
   (2)  ------------------------------------
                         a x
                                                     Type: Expression Integer
--R
--R                 +-------+
--R                 | 2    2
--R                \|x  + a   + a            x
--R        - x log(--------------) - a acosh(-)
--R                       x                  a
--R   (2)  ------------------------------------
--R                         a x
--R                                                     Type: Expression Integer
--E

--S 61 of 156
bb2:=-acosh(x/a)/x+1/a*log((a+sqrt(x^2+a^2))/x)
 

               +-------+
               | 2    2
              \|x  + a   + a            x
        x log(--------------) - a acosh(-)
                     x                  a
   (3)  ----------------------------------
                        a x
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R              \|x  + a   + a            x
--R        x log(--------------) - a acosh(-)
--R                     x                  a
--R   (3)  ----------------------------------
--R                        a x
--R                                                     Type: Expression Integer
--E

--S 62 of 156
cc1:=aa-bb1
 

   (4)
              +-------+               +-------+                 +-------+
              | 2    2                | 2    2                  | 2    2
             \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
       x log(--------------) - a log(--------------) + 2x atan(--------------)
                    x                       a                         a
     + 
               x
       a acosh(-)
               a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (4)
--R              +-------+               +-------+                 +-------+
--R              | 2    2                | 2    2                  | 2    2
--R             \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
--R       x log(--------------) - a log(--------------) + 2x atan(--------------)
--R                    x                       a                         a
--R     + 
--R               x
--R       a acosh(-)
--R               a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E

--S 63 of 156     14:655 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                +-------+               +-------+                 +-------+
                | 2    2                | 2    2                  | 2    2
               \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
       - x log(--------------) - a log(--------------) + 2x atan(--------------)
                      x                       a                         a
     + 
               x
       a acosh(-)
               a
  /
     a x
                                                     Type: Expression Integer
--R
--R   (5)
--R                +-------+               +-------+                 +-------+
--R                | 2    2                | 2    2                  | 2    2
--R               \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
--R       - x log(--------------) - a log(--------------) + 2x atan(--------------)
--R                      x                       a                         a
--R     + 
--R               x
--R       a acosh(-)
--R               a
--R  /
--R     a x
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 64 of 156
aa:=integrate(atanh(x/a),x)
 

               2    2          - x - a
        a log(x  - a ) + x log(-------)
                                x - a
   (1)  -------------------------------
                       2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2          - x - a
--R        a log(x  - a ) + x log(-------)
--R                                x - a
--R   (1)  -------------------------------
--R                       2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 65 of 156
bb:=x*atanh(x/a)+a/2*log(a^2-x^2)
 

                 2    2             x
        a log(- x  + a ) + 2x atanh(-)
                                    a
   (2)  ------------------------------
                       2
                                                     Type: Expression Integer
--R
--R                 2    2             x
--R        a log(- x  + a ) + 2x atanh(-)
--R                                    a
--R   (2)  ------------------------------
--R                       2
--R                                                     Type: Expression Integer
--E

--S 66 of 156
cc:=aa-bb
 

               2    2          - x - a             2    2             x
        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
                                x - a                                 a
   (3)  ----------------------------------------------------------------
                                        2
                                                     Type: Expression Integer
--R
--R               2    2          - x - a             2    2             x
--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
--R                                x - a                                 a
--R   (3)  ----------------------------------------------------------------
--R                                        2
--R                                                     Type: Expression Integer
--E

--S 67 of 156
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 68 of 156
dd:=atanhrule cc
 

               2    2             2    2
        a log(x  - a ) - a log(- x  + a )
   (5)  ---------------------------------
                        2
                                                     Type: Expression Integer
--R
--R               2    2             2    2
--R        a log(x  - a ) - a log(- x  + a )
--R   (5)  ---------------------------------
--R                        2
--R                                                     Type: Expression Integer
--E

--S 69 of 156     14:656 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

        a log(- 1)
   (6)  ----------
             2
                                                     Type: Expression Integer
--R
--R        a log(- 1)
--R   (6)  ----------
--R             2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 70 of 156
aa:=integrate(x*atanh(x/a),x)
 

          2    2     - x - a
        (x  - a )log(-------) + 2a x
                      x - a
   (1)  ----------------------------
                      4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2     - x - a
--R        (x  - a )log(-------) + 2a x
--R                      x - a
--R   (1)  ----------------------------
--R                      4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 71 of 156
bb:=(a*x)/2+1/2*(x^2-a^2)*atanh(x/a)
 

          2    2       x
        (x  - a )atanh(-) + a x
                       a
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          2    2       x
--R        (x  - a )atanh(-) + a x
--R                       a
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 72 of 156
cc:=aa-bb
 

          2    2     - x - a         2     2       x
        (x  - a )log(-------) + (- 2x  + 2a )atanh(-)
                      x - a                        a
   (3)  ---------------------------------------------
                              4
                                                     Type: Expression Integer
--R
--R          2    2     - x - a         2     2       x
--R        (x  - a )log(-------) + (- 2x  + 2a )atanh(-)
--R                      x - a                        a
--R   (3)  ---------------------------------------------
--R                              4
--R                                                     Type: Expression Integer
--E

--S 73 of 156
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 74 of 156     14:657 Schaums and Axiom agree
dd:=atanhrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 75 of 156
aa:=integrate(x^2*atanh(x/a),x)
 

         3     2    2     3    - x - a       2
        a log(x  - a ) + x log(-------) + a x
                                x - a
   (1)  --------------------------------------
                           6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         3     2    2     3    - x - a       2
--R        a log(x  - a ) + x log(-------) + a x
--R                                x - a
--R   (1)  --------------------------------------
--R                           6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 76 of 156
bb:=(a*x^2)/6+x^3/3*atanh(x/a)+a^3/6*log(a^2-x^2)
 

         3       2    2      3      x       2
        a log(- x  + a ) + 2x atanh(-) + a x
                                    a
   (2)  -------------------------------------
                          6
                                                     Type: Expression Integer
--R
--R         3       2    2      3      x       2
--R        a log(- x  + a ) + 2x atanh(-) + a x
--R                                    a
--R   (2)  -------------------------------------
--R                          6
--R                                                     Type: Expression Integer
--E

--S 77 of 156
cc:=aa-bb
 

         3     2    2     3    - x - a     3       2    2      3      x
        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
                                x - a                                 a
   (3)  ----------------------------------------------------------------
                                        6
                                                     Type: Expression Integer
--R
--R         3     2    2     3    - x - a     3       2    2      3      x
--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
--R                                x - a                                 a
--R   (3)  ----------------------------------------------------------------
--R                                        6
--R                                                     Type: Expression Integer
--E

--S 78 of 156
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 79 of 156
dd:=atanhrule cc
 

         3     2    2     3       2    2
        a log(x  - a ) - a log(- x  + a )
   (5)  ---------------------------------
                        6
                                                     Type: Expression Integer
--R
--R         3     2    2     3       2    2
--R        a log(x  - a ) - a log(- x  + a )
--R   (5)  ---------------------------------
--R                        6
--R                                                     Type: Expression Integer
--E

--S 80 of 156     14:658 Schaums and Axiom differ by a constant
ee:=complexNormalize dd
 

         3
        a log(- 1)
   (6)  ----------
             6
                                                     Type: Expression Integer
--R
--R         3
--R        a log(- 1)
--R   (6)  ----------
--R             6
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 81 of 156     14:659 Axiom cannot compute this integral
aa:=integrate(atanh(x/a)/x,x)
 

                   %P
           x atanh(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x atanh(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 82 of 156
aa:=integrate(atanh(x/a)/x^2,x)
 

                 2    2                      - x - a
        - x log(x  - a ) + 2x log(x) - a log(-------)
                                              x - a
   (1)  ---------------------------------------------
                             2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2                      - x - a
--R        - x log(x  - a ) + 2x log(x) - a log(-------)
--R                                              x - a
--R   (1)  ---------------------------------------------
--R                             2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 83 of 156
bb:=-atanh(x/a)/x+1/(2*a)*log(x^2/(a^2-x^2))
 

                    2
                   x                x
        x log(- -------) - 2a atanh(-)
                 2    2             a
                x  - a
   (2)  ------------------------------
                     2a x
                                                     Type: Expression Integer
--R
--R                    2
--R                   x                x
--R        x log(- -------) - 2a atanh(-)
--R                 2    2             a
--R                x  - a
--R   (2)  ------------------------------
--R                     2a x
--R                                                     Type: Expression Integer
--E

--S 84 of 156
cc:=aa-bb
 

   (3)
                                                  2
                2    2                           x             - x - a
       - x log(x  - a ) + 2x log(x) - x log(- -------) - a log(-------)
                                               2    2           x - a
                                              x  - a
     + 
                x
       2a atanh(-)
                a
  /
     2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                  2
--R                2    2                           x             - x - a
--R       - x log(x  - a ) + 2x log(x) - x log(- -------) - a log(-------)
--R                                               2    2           x - a
--R                                              x  - a
--R     + 
--R                x
--R       2a atanh(-)
--R                a
--R  /
--R     2a x
--R                                                     Type: Expression Integer
--E

--S 85 of 156
atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
 

                        - x - 1
                    log(-------)
                         x - 1
   (4)  atanh(x) == ------------
                          2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        - x - 1
--R                    log(-------)
--R                         x - 1
--R   (4)  atanh(x) == ------------
--R                          2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 86 of 156
dd:=atanhrule cc
 

                                             2
               2    2                       x
        - log(x  - a ) + 2log(x) - log(- -------)
                                          2    2
                                         x  - a
   (5)  -----------------------------------------
                            2a
                                                     Type: Expression Integer
--R
--R                                             2
--R               2    2                       x
--R        - log(x  - a ) + 2log(x) - log(- -------)
--R                                          2    2
--R                                         x  - a
--R   (5)  -----------------------------------------
--R                            2a
--R                                                     Type: Expression Integer
--E

--S 87 of 156     14:660 Schaums and Axiom agree
ee:=expandLog dd
 

          log(- 1)
   (6)  - --------
             2a
                                                     Type: Expression Integer
--R
--R          log(- 1)
--R   (6)  - --------
--R             2a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 88 of 156
aa:=integrate(acoth(x/a),x)
 

               2    2          x + a
        a log(x  - a ) + x log(-----)
                               x - a
   (1)  -----------------------------
                      2
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               2    2          x + a
--R        a log(x  - a ) + x log(-----)
--R                               x - a
--R   (1)  -----------------------------
--R                      2
--R                                          Type: Union(Expression Integer,...)
--E 

--S 89 of 156
bb:=x*acoth(x/a)+a/2*log(x^2-a^2)
 

               2    2             x
        a log(x  - a ) + 2x acoth(-)
                                  a
   (2)  ----------------------------
                      2
                                                     Type: Expression Integer
--R
--R               2    2             x
--R        a log(x  - a ) + 2x acoth(-)
--R                                  a
--R   (2)  ----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 90 of 156
cc:=aa-bb
 

              x + a             x
        x log(-----) - 2x acoth(-)
              x - a             a
   (3)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R              x + a             x
--R        x log(-----) - 2x acoth(-)
--R              x - a             a
--R   (3)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 91 of 156
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 92 of 156     14:661 Schaums and Axiom agree
dd:=acothrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 93 of 156
aa:=integrate(x*acoth(x/a),x)
 

          2    2     x + a
        (x  - a )log(-----) + 2a x
                     x - a
   (1)  --------------------------
                     4
                                          Type: Union(Expression Integer,...)
--R 
--R
--R          2    2     x + a
--R        (x  - a )log(-----) + 2a x
--R                     x - a
--R   (1)  --------------------------
--R                     4
--R                                          Type: Union(Expression Integer,...)
--E 

--S 94 of 156
bb:=(a*x)/2+1/2*(x^2-a^2)*acoth(x/a)
 

          2    2       x
        (x  - a )acoth(-) + a x
                       a
   (2)  -----------------------
                   2
                                                     Type: Expression Integer
--R
--R          2    2       x
--R        (x  - a )acoth(-) + a x
--R                       a
--R   (2)  -----------------------
--R                   2
--R                                                     Type: Expression Integer
--E

--S 95 of 156
cc:=aa-bb
 

          2    2     x + a         2     2       x
        (x  - a )log(-----) + (- 2x  + 2a )acoth(-)
                     x - a                       a
   (3)  -------------------------------------------
                             4
                                                     Type: Expression Integer
--R
--R          2    2     x + a         2     2       x
--R        (x  - a )log(-----) + (- 2x  + 2a )acoth(-)
--R                     x - a                       a
--R   (3)  -------------------------------------------
--R                             4
--R                                                     Type: Expression Integer
--E

--S 96 of 156
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 97 of 156     14:662 Schaums and Axiom agree
dd:=acothrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 98 of 156
aa:=integrate(x^2*acoth(x/a),x)
 

         3     2    2     3    x + a       2
        a log(x  - a ) + x log(-----) + a x
                               x - a
   (1)  ------------------------------------
                          6
                                          Type: Union(Expression Integer,...)
--R 
--R
--R         3     2    2     3    x + a       2
--R        a log(x  - a ) + x log(-----) + a x
--R                               x - a
--R   (1)  ------------------------------------
--R                          6
--R                                          Type: Union(Expression Integer,...)
--E 

--S 99 of 156
bb:=(a*x^2)/6+x^3/3*acoth(x/a)+a^3/6*log(x^2-a^2)
 

         3     2    2      3      x       2
        a log(x  - a ) + 2x acoth(-) + a x
                                  a
   (2)  -----------------------------------
                         6
                                                     Type: Expression Integer
--R
--R         3     2    2      3      x       2
--R        a log(x  - a ) + 2x acoth(-) + a x
--R                                  a
--R   (2)  -----------------------------------
--R                         6
--R                                                     Type: Expression Integer
--E

--S 100 of 156
cc:=aa-bb
 

         3    x + a      3      x
        x log(-----) - 2x acoth(-)
              x - a             a
   (3)  --------------------------
                     6
                                                     Type: Expression Integer
--R
--R         3    x + a      3      x
--R        x log(-----) - 2x acoth(-)
--R              x - a             a
--R   (3)  --------------------------
--R                     6
--R                                                     Type: Expression Integer
--E

--S 101 of 156
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 102 of 156    14:663 Schaums and Axiom agree
dd:=acothrule cc
 

   (5)  0
                                                     Type: Expression Integer
--R
--R   (5)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 103 of 156    14:664 Axiom cannot compute this integral
aa:=integrate(acoth(x/a)/x,x)
 

                   %P
           x acoth(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x acoth(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 104 of 156
aa:=integrate(acoth(x/a)/x^2,x)
 

                 2    2                      x + a
        - x log(x  - a ) + 2x log(x) - a log(-----)
                                             x - a
   (1)  -------------------------------------------
                            2a x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                 2    2                      x + a
--R        - x log(x  - a ) + 2x log(x) - a log(-----)
--R                                             x - a
--R   (1)  -------------------------------------------
--R                            2a x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 105 of 156
bb:=-acoth(x/a)/x+1/(2*a)*log(x^2/(x^2-a^2))
 

                  2
                 x                x
        x log(-------) - 2a acoth(-)
               2    2             a
              x  - a
   (2)  ----------------------------
                    2a x
                                                     Type: Expression Integer
--R
--R                  2
--R                 x                x
--R        x log(-------) - 2a acoth(-)
--R               2    2             a
--R              x  - a
--R   (2)  ----------------------------
--R                    2a x
--R                                                     Type: Expression Integer
--E

--S 106 of 156
cc:=aa-bb
 

   (3)
                                                           2
            2    2                      x + a             x                x
   - x log(x  - a ) + 2x log(x) - a log(-----) - x log(-------) + 2a acoth(-)
                                        x - a           2    2             a
                                                       x  - a
   --------------------------------------------------------------------------
                                      2a x
                                                     Type: Expression Integer
--R
--R   (3)
--R                                                           2
--R            2    2                      x + a             x                x
--R   - x log(x  - a ) + 2x log(x) - a log(-----) - x log(-------) + 2a acoth(-)
--R                                        x - a           2    2             a
--R                                                       x  - a
--R   --------------------------------------------------------------------------
--R                                      2a x
--R                                                     Type: Expression Integer
--E

--S 107 of 156
acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
 

                        x + 1
                    log(-----)
                        x - 1
   (4)  acoth(x) == ----------
                         2
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                        x + 1
--R                    log(-----)
--R                        x - 1
--R   (4)  acoth(x) == ----------
--R                         2
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 108 of 156
dd:=acothrule cc
 

                                           2
               2    2                     x
        - log(x  - a ) + 2log(x) - log(-------)
                                        2    2
                                       x  - a
   (5)  ---------------------------------------
                           2a
                                                     Type: Expression Integer
--R
--R                                           2
--R               2    2                     x
--R        - log(x  - a ) + 2log(x) - log(-------)
--R                                        2    2
--R                                       x  - a
--R   (5)  ---------------------------------------
--R                           2a
--R                                                     Type: Expression Integer
--E

--S 109 of 156    14:665 Schaums and Axiom agree
ee:=expandLog dd
 

   (6)  0
                                                     Type: Expression Integer
--R
--R   (6)  0
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 110 of 156
aa:=integrate(asech(x/a),x)
 

               +---------+                 +---------+
               |   2    2                  |   2    2
              \|- x  + a   + a            \|- x  + a   - a
   (1)  x log(----------------) - 2a atan(----------------)
                      x                           x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R               +---------+                 +---------+
--R               |   2    2                  |   2    2
--R              \|- x  + a   + a            \|- x  + a   - a
--R   (1)  x log(----------------) - 2a atan(----------------)
--R                      x                           x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 111 of 156
bb1:=x*asech(x/a)+a*asin(x/a)
 

               x            x
   (2)  a asin(-) + x asech(-)
               a            a
                                                     Type: Expression Integer
--R
--R               x            x
--R   (2)  a asin(-) + x asech(-)
--R               a            a
--R                                                     Type: Expression Integer
--E

--S 112 of 156
bb2:=x*asech(x/a)-a*asin(x/a)
 

                 x            x
   (3)  - a asin(-) + x asech(-)
                 a            a
                                                     Type: Expression Integer
--R
--R                 x            x
--R   (3)  - a asin(-) + x asech(-)
--R                 a            a
--R                                                     Type: Expression Integer
--E

--S 113 of 156
cc1:=aa-bb1
 

   (4)
          +---------+                 +---------+
          |   2    2                  |   2    2
         \|- x  + a   + a            \|- x  + a   - a           x            x
   x log(----------------) - 2a atan(----------------) - a asin(-) - x asech(-)
                 x                           x                  a            a
                                                     Type: Expression Integer
--R
--R   (4)
--R          +---------+                 +---------+
--R          |   2    2                  |   2    2
--R         \|- x  + a   + a            \|- x  + a   - a           x            x
--R   x log(----------------) - 2a atan(----------------) - a asin(-) - x asech(-)
--R                 x                           x                  a            a
--R                                                     Type: Expression Integer
--E

--S 114 of 156
cc2:=aa-bb2
 

   (5)
          +---------+                 +---------+
          |   2    2                  |   2    2
         \|- x  + a   + a            \|- x  + a   - a           x            x
   x log(----------------) - 2a atan(----------------) + a asin(-) - x asech(-)
                 x                           x                  a            a
                                                     Type: Expression Integer
--R
--R   (5)
--R          +---------+                 +---------+
--R          |   2    2                  |   2    2
--R         \|- x  + a   + a            \|- x  + a   - a           x            x
--R   x log(----------------) - 2a atan(----------------) + a asin(-) - x asech(-)
--R                 x                           x                  a            a
--R                                                     Type: Expression Integer
--E

--S 115 of 156
asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
 

                          +--------+
                          |   2
                          |- x  + 1
                        x |--------  + 1
                          |    2
                         \|   x
   (6)  asech(x) == log(----------------)
                                x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          +--------+
--R                          |   2
--R                          |- x  + 1
--R                        x |--------  + 1
--R                          |    2
--R                         \|   x
--R   (6)  asech(x) == log(----------------)
--R                                x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 116 of 156
dd1:=asechrule cc1
 

   (7)
               +---------+
               |   2    2
               |- x  + a
             x |---------  + a           +---------+
               |     2                   |   2    2
              \|    x                   \|- x  + a   + a
     - x log(-----------------) + x log(----------------)
                     x                          x
   + 
                +---------+
                |   2    2
               \|- x  + a   - a           x
     - 2a atan(----------------) - a asin(-)
                       x                  a
                                                     Type: Expression Integer
--R
--R   (7)
--R               +---------+
--R               |   2    2
--R               |- x  + a
--R             x |---------  + a           +---------+
--R               |     2                   |   2    2
--R              \|    x                   \|- x  + a   + a
--R     - x log(-----------------) + x log(----------------)
--R                     x                          x
--R   + 
--R                +---------+
--R                |   2    2
--R               \|- x  + a   - a           x
--R     - 2a atan(----------------) - a asin(-)
--R                       x                  a
--R                                                     Type: Expression Integer
--E

--S 117 of 156
asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
 

                           +--------+
                           |   2
   (8)  asin(x) == %i log(\|- x  + 1  - %i x)
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                           +--------+
--R                           |   2
--R   (8)  asin(x) == %i log(\|- x  + 1  - %i x)
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 118 of 156
ee1:=asinrule dd1
 

   (9)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) - %i a log(--------------------)
                     x                               a
   + 
            +---------+                 +---------+
            |   2    2                  |   2    2
           \|- x  + a   + a            \|- x  + a   - a
     x log(----------------) - 2a atan(----------------)
                   x                           x
                                             Type: Expression Complex Integer
--R
--R   (9)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) - %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                 +---------+
--R            |   2    2                  |   2    2
--R           \|- x  + a   + a            \|- x  + a   - a
--R     x log(----------------) - 2a atan(----------------)
--R                   x                           x
--R                                             Type: Expression Complex Integer
--E

--S 119 of 156
atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 

                             - x + %i
                      %i log(--------)
                              x + %i
   (10)  atan(x) == - ----------------
                              2
        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--R
--R                             - x + %i
--R                      %i log(--------)
--R                              x + %i
--R   (10)  atan(x) == - ----------------
--R                              2
--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
--E

--S 120 of 156
ff1:=atanrule ee1
 

   (11)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) - %i a log(--------------------)
                     x                               a
   + 
            +---------+                    +---------+
            |   2    2                     |   2    2
           \|- x  + a   + a             - \|- x  + a   + %i x + a
     x log(----------------) + %i a log(-------------------------)
                   x                      +---------+
                                          |   2    2
                                         \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R   (11)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) - %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                    +---------+
--R            |   2    2                     |   2    2
--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
--R     x log(----------------) + %i a log(-------------------------)
--R                   x                      +---------+
--R                                          |   2    2
--R                                         \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 121 of 156
gg1:=expandLog ff1
 

   (12)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
     - x log(x |---------  + a) - %i a log(a |---------  - %i x)
               |     2                       |     2
              \|    x                       \|    a
   + 
                 +---------+                      +---------+
                 |   2    2                       |   2    2
     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
   + 
               +---------+
               |   2    2
     %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (12)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R     - x log(x |---------  + a) - %i a log(a |---------  - %i x)
--R               |     2                       |     2
--R              \|    x                       \|    a
--R   + 
--R                 +---------+                      +---------+
--R                 |   2    2                       |   2    2
--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
--R   + 
--R               +---------+
--R               |   2    2
--R     %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 122 of 156
hh1:=rootSimp gg1
 

   (13)
                   +-------+                           +-------+
                   | 2    2                            | 2    2
     - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (13)
--R                   +-------+                           +-------+
--R                   | 2    2                            | 2    2
--R     - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 123 of 156    14:666 Schaums and Axiom agree
ii1:=complexNormalize hh1
 

   (14)  0
                                             Type: Expression Complex Integer
--R
--R   (14)  0
--R                                             Type: Expression Complex Integer
--E

--S 124 of 156
dd2:=asechrule cc2
 

   (15)
               +---------+
               |   2    2
               |- x  + a
             x |---------  + a           +---------+
               |     2                   |   2    2
              \|    x                   \|- x  + a   + a
     - x log(-----------------) + x log(----------------)
                     x                          x
   + 
                +---------+
                |   2    2
               \|- x  + a   - a           x
     - 2a atan(----------------) + a asin(-)
                       x                  a
                                                     Type: Expression Integer
--R
--R   (15)
--R               +---------+
--R               |   2    2
--R               |- x  + a
--R             x |---------  + a           +---------+
--R               |     2                   |   2    2
--R              \|    x                   \|- x  + a   + a
--R     - x log(-----------------) + x log(----------------)
--R                     x                          x
--R   + 
--R                +---------+
--R                |   2    2
--R               \|- x  + a   - a           x
--R     - 2a atan(----------------) + a asin(-)
--R                       x                  a
--R                                                     Type: Expression Integer
--E

--S 125 of 156
ee2:=asinrule dd2
 

   (16)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) + %i a log(--------------------)
                     x                               a
   + 
            +---------+                 +---------+
            |   2    2                  |   2    2
           \|- x  + a   + a            \|- x  + a   - a
     x log(----------------) - 2a atan(----------------)
                   x                           x
                                             Type: Expression Complex Integer
--R
--R   (16)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) + %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                 +---------+
--R            |   2    2                  |   2    2
--R           \|- x  + a   + a            \|- x  + a   - a
--R     x log(----------------) - 2a atan(----------------)
--R                   x                           x
--R                                             Type: Expression Complex Integer
--E

--S 126 of 156
ff2:=atanrule ee2
 

   (17)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
             x |---------  + a             a |---------  - %i x
               |     2                       |     2
              \|    x                       \|    a
     - x log(-----------------) + %i a log(--------------------)
                     x                               a
   + 
            +---------+                    +---------+
            |   2    2                     |   2    2
           \|- x  + a   + a             - \|- x  + a   + %i x + a
     x log(----------------) + %i a log(-------------------------)
                   x                      +---------+
                                          |   2    2
                                         \|- x  + a   + %i x - a
                                             Type: Expression Complex Integer
--R
--R   (17)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R             x |---------  + a             a |---------  - %i x
--R               |     2                       |     2
--R              \|    x                       \|    a
--R     - x log(-----------------) + %i a log(--------------------)
--R                     x                               a
--R   + 
--R            +---------+                    +---------+
--R            |   2    2                     |   2    2
--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
--R     x log(----------------) + %i a log(-------------------------)
--R                   x                      +---------+
--R                                          |   2    2
--R                                         \|- x  + a   + %i x - a
--R                                             Type: Expression Complex Integer
--E

--S 127 of 156
gg2:=expandLog ff2
 

   (18)
               +---------+                   +---------+
               |   2    2                    |   2    2
               |- x  + a                     |- x  + a
     - x log(x |---------  + a) + %i a log(a |---------  - %i x)
               |     2                       |     2
              \|    x                       \|    a
   + 
                 +---------+                      +---------+
                 |   2    2                       |   2    2
     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
   + 
               +---------+
               |   2    2
     %i a log(\|- x  + a   - %i x - a) - %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (18)
--R               +---------+                   +---------+
--R               |   2    2                    |   2    2
--R               |- x  + a                     |- x  + a
--R     - x log(x |---------  + a) + %i a log(a |---------  - %i x)
--R               |     2                       |     2
--R              \|    x                       \|    a
--R   + 
--R                 +---------+                      +---------+
--R                 |   2    2                       |   2    2
--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
--R   + 
--R               +---------+
--R               |   2    2
--R     %i a log(\|- x  + a   - %i x - a) - %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 128 of 156
hh2:=rootSimp gg2
 

   (19)
                   +-------+                           +-------+
                   | 2    2                            | 2    2
     - %i a log(%i\|x  - a   + %i x - a) + %i a log(%i\|x  - a   - %i x)
   + 
                 +-------+
                 | 2    2
     %i a log(%i\|x  - a   - %i x - a) - %i a log(a) + %i a log(- 1)
                                             Type: Expression Complex Integer
--R
--R   (19)
--R                   +-------+                           +-------+
--R                   | 2    2                            | 2    2
--R     - %i a log(%i\|x  - a   + %i x - a) + %i a log(%i\|x  - a   - %i x)
--R   + 
--R                 +-------+
--R                 | 2    2
--R     %i a log(%i\|x  - a   - %i x - a) - %i a log(a) + %i a log(- 1)
--R                                             Type: Expression Complex Integer
--E

--S 129 of 156
ii2:=complexNormalize hh2
 

                      +-------+
                      | 2    2
   (20)  2%i a log(%i\|x  - a   - %i x) - 2%i a log(a)
                                             Type: Expression Complex Integer
--R
--R                      +-------+
--R                      | 2    2
--R   (20)  2%i a log(%i\|x  - a   - %i x) - 2%i a log(a)
--R                                             Type: Expression Complex Integer
--E

)clear all
 

--S 130 of 156
aa:=integrate(x*asech(x/a),x)
 

                                    +---------+
            +---------+             |   2    2
          2 |   2    2       2     \|- x  + a   + a       2
        (x \|- x  + a   - a x )log(----------------) + a x
                                           x
   (1)  ---------------------------------------------------
                           +---------+
                           |   2    2
                         2\|- x  + a   - 2a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                    +---------+
--R            +---------+             |   2    2
--R          2 |   2    2       2     \|- x  + a   + a       2
--R        (x \|- x  + a   - a x )log(----------------) + a x
--R                                           x
--R   (1)  ---------------------------------------------------
--R                           +---------+
--R                           |   2    2
--R                         2\|- x  + a   - 2a
--R                                          Type: Union(Expression Integer,...)
--E 

--S 131 of 156
bb1:=1/2*x^2*asech(x/a)-1/2*a*sqrt(a^2-x^2)
 

            +---------+
            |   2    2     2      x
        - a\|- x  + a   + x asech(-)
                                  a
   (2)  ----------------------------
                      2
                                                     Type: Expression Integer
--R
--R            +---------+
--R            |   2    2     2      x
--R        - a\|- x  + a   + x asech(-)
--R                                  a
--R   (2)  ----------------------------
--R                      2
--R                                                     Type: Expression Integer
--E

--S 132 of 156
bb2:=1/2*x^2*asech(x/a)+1/2*a*sqrt(a^2-x^2)
 

          +---------+
          |   2    2     2      x
        a\|- x  + a   + x asech(-)
                                a
   (3)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R          +---------+
--R          |   2    2     2      x
--R        a\|- x  + a   + x asech(-)
--R                                a
--R   (3)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 133 of 156
cc1:=aa-bb1
 

               +---------+
               |   2    2
         2    \|- x  + a   + a     2      x     2
        x log(----------------) - x asech(-) - a
                      x                   a
   (4)  -----------------------------------------
                            2
                                                     Type: Expression Integer
--R
--R               +---------+
--R               |   2    2
--R         2    \|- x  + a   + a     2      x     2
--R        x log(----------------) - x asech(-) - a
--R                      x                   a
--R   (4)  -----------------------------------------
--R                            2
--R                                                     Type: Expression Integer
--E

--S 134 of 156
cc2:=aa-bb2
 

   (5)
                                   +---------+
           +---------+             |   2    2
         2 |   2    2       2     \|- x  + a   + a
       (x \|- x  + a   - a x )log(----------------)
                                          x
     + 
                           +---------+
           2      x     2  |   2    2       2      x        2    3
       (- x asech(-) + a )\|- x  + a   + a x asech(-) + 2a x  - a
                  a                                a
  /
       +---------+
       |   2    2
     2\|- x  + a   - 2a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                   +---------+
--R           +---------+             |   2    2
--R         2 |   2    2       2     \|- x  + a   + a
--R       (x \|- x  + a   - a x )log(----------------)
--R                                          x
--R     + 
--R                           +---------+
--R           2      x     2  |   2    2       2      x        2    3
--R       (- x asech(-) + a )\|- x  + a   + a x asech(-) + 2a x  - a
--R                  a                                a
--R  /
--R       +---------+
--R       |   2    2
--R     2\|- x  + a   - 2a
--R                                                     Type: Expression Integer
--E

--S 135 of 156
asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
 

                          +--------+
                          |   2
                          |- x  + 1
                        x |--------  + 1
                          |    2
                         \|   x
   (6)  asech(x) == log(----------------)
                                x
                        Type: RewriteRule(Integer,Integer,Expression Integer)
--R
--R                          +--------+
--R                          |   2
--R                          |- x  + 1
--R                        x |--------  + 1
--R                          |    2
--R                         \|   x
--R   (6)  asech(x) == log(----------------)
--R                                x
--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
--E

--S 136 of 156
dd1:=asechrule cc1
 

                  +---------+
                  |   2    2
                  |- x  + a
                x |---------  + a           +---------+
                  |     2                   |   2    2
           2     \|    x              2    \|- x  + a   + a     2
        - x log(-----------------) + x log(----------------) - a
                        x                          x
   (7)  ---------------------------------------------------------
                                    2
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2
--R                  |- x  + a
--R                x |---------  + a           +---------+
--R                  |     2                   |   2    2
--R           2     \|    x              2    \|- x  + a   + a     2
--R        - x log(-----------------) + x log(----------------) - a
--R                        x                          x
--R   (7)  ---------------------------------------------------------
--R                                    2
--R                                                     Type: Expression Integer
--E

--S 137 of 156
ee1:=expandLog dd1
 

                  +---------+
                  |   2    2                +---------+
           2      |- x  + a           2     |   2    2          2
        - x log(x |---------  + a) + x log(\|- x  + a   + a) - a
                  |     2
                 \|    x
   (8)  ---------------------------------------------------------
                                    2
                                                     Type: Expression Integer
--R
--R                  +---------+
--R                  |   2    2                +---------+
--R           2      |- x  + a           2     |   2    2          2
--R        - x log(x |---------  + a) + x log(\|- x  + a   + a) - a
--R                  |     2
--R                 \|    x
--R   (8)  ---------------------------------------------------------
--R                                    2
--R                                                     Type: Expression Integer
--E

--S 138 of 156    14:667 Schaums and Axiom differ by a constant
ff1:=rootSimp ee1
 

           2
          a
   (9)  - --
           2
                                                     Type: Expression Integer
--R
--R           2
--R          a
--R   (9)  - --
--R           2
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 139 of 156    14:668 Axiom cannot compute this integral
aa:=integrate(asech(x/a)/x,x)
 

                   %P
           x asech(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x asech(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 140 of 156
aa:=integrate(acsch(x/a),x)
 

                                         +-------+
                 +-------+               | 2    2
                 | 2    2               \|x  + a   + a
   (1)  - a log(\|x  + a   - x) + x log(--------------)
                                               x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                         +-------+
--R                 +-------+               | 2    2
--R                 | 2    2               \|x  + a   + a
--R   (1)  - a log(\|x  + a   - x) + x log(--------------)
--R                                               x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 141 of 156
bb1:=x*acsch(x/a)+a*asinh(x/a)
 

                x            x
   (2)  a asinh(-) + x acsch(-)
                a            a
                                                     Type: Expression Integer
--R
--R                x            x
--R   (2)  a asinh(-) + x acsch(-)
--R                a            a
--R                                                     Type: Expression Integer
--E

--S 142 of 156
bb2:=x*acsch(x/a)-a*asinh(x/a)
 

                  x            x
   (3)  - a asinh(-) + x acsch(-)
                  a            a
                                                     Type: Expression Integer
--R
--R                  x            x
--R   (3)  - a asinh(-) + x acsch(-)
--R                  a            a
--R                                                     Type: Expression Integer
--E

--S 143 of 156
cc1:=aa-bb1
 

   (4)
                                    +-------+
            +-------+               | 2    2
            | 2    2               \|x  + a   + a            x            x
   - a log(\|x  + a   - x) + x log(--------------) - a asinh(-) - x acsch(-)
                                          x                  a            a
                                                     Type: Expression Integer
--R
--R   (4)
--R                                    +-------+
--R            +-------+               | 2    2
--R            | 2    2               \|x  + a   + a            x            x
--R   - a log(\|x  + a   - x) + x log(--------------) - a asinh(-) - x acsch(-)
--R                                          x                  a            a
--R                                                     Type: Expression Integer
--E

--S 144 of 156    14:669 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                                    +-------+
            +-------+               | 2    2
            | 2    2               \|x  + a   + a            x            x
   - a log(\|x  + a   - x) + x log(--------------) + a asinh(-) - x acsch(-)
                                          x                  a            a
                                                     Type: Expression Integer
--R
--R   (5)
--R                                    +-------+
--R            +-------+               | 2    2
--R            | 2    2               \|x  + a   + a            x            x
--R   - a log(\|x  + a   - x) + x log(--------------) + a asinh(-) - x acsch(-)
--R                                          x                  a            a
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 145 of 156
aa:=integrate(x*acsch(x/a),x)
 

                                +-------+
            +-------+           | 2    2             +-------+
          2 | 2    2     3     \|x  + a   + a        | 2    2       2    3
        (x \|x  + a   - x )log(--------------) - a x\|x  + a   + a x  + a
                                      x
   (1)  ------------------------------------------------------------------
                                   +-------+
                                   | 2    2
                                 2\|x  + a   - 2x
                                          Type: Union(Expression Integer,...)
--R 
--R
--R                                +-------+
--R            +-------+           | 2    2             +-------+
--R          2 | 2    2     3     \|x  + a   + a        | 2    2       2    3
--R        (x \|x  + a   - x )log(--------------) - a x\|x  + a   + a x  + a
--R                                      x
--R   (1)  ------------------------------------------------------------------
--R                                   +-------+
--R                                   | 2    2
--R                                 2\|x  + a   - 2x
--R                                          Type: Union(Expression Integer,...)
--E 

--S 146 of 156
bb1:=x^2/2*acsch(x/a)+(a*sqrt(x^2+a^2))/2
 

          +-------+
          | 2    2     2      x
        a\|x  + a   + x acsch(-)
                              a
   (2)  ------------------------
                    2
                                                     Type: Expression Integer
--R
--R          +-------+
--R          | 2    2     2      x
--R        a\|x  + a   + x acsch(-)
--R                              a
--R   (2)  ------------------------
--R                    2
--R                                                     Type: Expression Integer
--E

--S 147 of 156
bb2:=x^2/2*acsch(x/a)-(a*sqrt(x^2+a^2))/2
 

            +-------+
            | 2    2     2      x
        - a\|x  + a   + x acsch(-)
                                a
   (3)  --------------------------
                     2
                                                     Type: Expression Integer
--R
--R            +-------+
--R            | 2    2     2      x
--R        - a\|x  + a   + x acsch(-)
--R                                a
--R   (3)  --------------------------
--R                     2
--R                                                     Type: Expression Integer
--E

--S 148 of 156
cc1:=aa-bb1
 

               +-------+
               | 2    2
         2    \|x  + a   + a     2      x
        x log(--------------) - x acsch(-)
                     x                  a
   (4)  ----------------------------------
                         2
                                                     Type: Expression Integer
--R
--R               +-------+
--R               | 2    2
--R         2    \|x  + a   + a     2      x
--R        x log(--------------) - x acsch(-)
--R                     x                  a
--R   (4)  ----------------------------------
--R                         2
--R                                                     Type: Expression Integer
--E

--S 149 of 156    14:670 Axiom cannot simplify these expressions
cc2:=aa-bb2
 

   (5)
                               +-------+
           +-------+           | 2    2                               +-------+
         2 | 2    2     3     \|x  + a   + a        2      x          | 2    2
       (x \|x  + a   - x )log(--------------) + (- x acsch(-) - 2a x)\|x  + a
                                     x                     a
     + 
        3      x        2     3
       x acsch(-) + 2a x  + 2a
               a
  /
       +-------+
       | 2    2
     2\|x  + a   - 2x
                                                     Type: Expression Integer
--R
--R   (5)
--R                               +-------+
--R           +-------+           | 2    2                               +-------+
--R         2 | 2    2     3     \|x  + a   + a        2      x          | 2    2
--R       (x \|x  + a   - x )log(--------------) + (- x acsch(-) - 2a x)\|x  + a
--R                                     x                     a
--R     + 
--R        3      x        2     3
--R       x acsch(-) + 2a x  + 2a
--R               a
--R  /
--R       +-------+
--R       | 2    2
--R     2\|x  + a   - 2x
--R                                                     Type: Expression Integer
--E
)clear all
 

--S 150 of 156    14:671 Axiom cannot compute this integral
aa:=integrate(acsch(x/a)/x,x)
 

                   %P
           x acsch(--)
         ++         a
   (1)   |   --------- d%P
        ++       %P
                                          Type: Union(Expression Integer,...)
--R 
--R
--I                   %P
--R           x acsch(--)
--R         ++         a
--I   (1)   |   --------- d%P
--I        ++       %P
--R                                          Type: Union(Expression Integer,...)
--E 

)clear all
 

--S 151 of 156    14:672 Axiom cannot compute this integral
aa:=integrate(x^m*asinh(x/a),x)
 

           x
         ++        %P   m
   (1)   |   asinh(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   asinh(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 152 of 156    14:673 Axiom cannot compute this integral
aa:=integrate(x^m*acosh(x/a),x)
 

           x
         ++        %P   m
   (1)   |   acosh(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   acosh(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 153 of 156    14:674 Axiom cannot compute this integral
aa:=integrate(x^m*atanh(x/a),x)
 

           x
         ++        %P   m
   (1)   |   atanh(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   atanh(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 154 of 156    14:675 Axiom cannot compute this integral
aa:=integrate(x^m*acoth(x/a),x)
 

           x
         ++        %P   m
   (1)   |   acoth(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   acoth(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 155 of 156    14:676 Axiom cannot compute this integral
aa:=integrate(x^m*asech(x/a),x)
 

           x
         ++        %P   m
   (1)   |   asech(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   asech(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 
)clear all
 

--S 156 of 156    14:677 Axiom cannot compute this integral
aa:=integrate(x^m*acsch(x/a),x)
 

           x
         ++        %P   m
   (1)   |   acsch(--)%P d%P
        ++          a
                                          Type: Union(Expression Integer,...)
--R 
--R
--R           x
--I         ++        %P   m
--I   (1)   |   acsch(--)%P d%P
--R        ++          a
--R                                          Type: Union(Expression Integer,...)
--E 

)spool
 
Starts dribbling to Symbol.output (2010/3/27, 18:46:37).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 24
X: Symbol := 'x
 

   (1)  x
                                                                 Type: Symbol
--R 
--R
--R   (1)  x
--R                                                                 Type: Symbol
--E 1

--S 2 of 24
XX: Symbol := x
 

   (2)  x
                                                                 Type: Symbol
--R 
--R
--R   (2)  x
--R                                                                 Type: Symbol
--E 2

--S 3 of 24
A := 'a
 

   (3)  a
                                                             Type: Variable a
--R 
--R
--R   (3)  a
--R                                                             Type: Variable a
--E 3

--S 4 of 24
B := b
 

   (4)  b
                                                             Type: Variable b
--R 
--R
--R   (4)  b
--R                                                             Type: Variable b
--E 4

--S 5 of 24
x**2 + 1
 

         2
   (5)  x  + 1
                                                     Type: Polynomial Integer
--R 
--R
--R         2
--R   (5)  x  + 1
--R                                                     Type: Polynomial Integer
--E 5

--S 6 of 24
"Hello"::Symbol
 

   (6)  Hello
                                                                 Type: Symbol
--R 
--R
--R   (6)  Hello
--R                                                                 Type: Symbol
--E 6

--S 7 of 24
new()$Symbol
 

   (7)  %A
                                                                 Type: Symbol
--R 
--R
--R   (7)  %A
--R                                                                 Type: Symbol
--E 7

--S 8 of 24
new()$Symbol
 

   (8)  %B
                                                                 Type: Symbol
--R 
--R
--R   (8)  %B
--R                                                                 Type: Symbol
--E 8

--S 9 of 24
new("xyz")$Symbol
 

   (9)  %xyz0
                                                                 Type: Symbol
--R 
--R
--R   (9)  %xyz0
--R                                                                 Type: Symbol
--E 9

--S 10 of 24
X[i,j]
 

   (10)  x
          i,j
                                                                 Type: Symbol
--R 
--R
--R   (10)  x
--R          i,j
--R                                                                 Type: Symbol
--E 10

--S 11 of 24
U := subscript(u, [1,2,1,2])
 

   (11)  u
          1,2,1,2
                                                                 Type: Symbol
--R 
--R
--R   (11)  u
--R          1,2,1,2
--R                                                                 Type: Symbol
--E 11

--S 12 of 24
V := superscript(v, [n])
 

          n
   (12)  v
                                                                 Type: Symbol
--R 
--R
--R          n
--R   (12)  v
--R                                                                 Type: Symbol
--E 12

--S 13 of 24
P := argscript(p, [t])
 

   (13)  p(t)
                                                                 Type: Symbol
--R 
--R
--R   (13)  p(t)
--R                                                                 Type: Symbol
--E 13

--S 14 of 24
scripted? U
 

   (14)  true
                                                                Type: Boolean
--R 
--R
--R   (14)  true
--R                                                                Type: Boolean
--E 14

--S 15 of 24
scripted? X
 

   (15)  false
                                                                Type: Boolean
--R 
--R
--R   (15)  false
--R                                                                Type: Boolean
--E 15

--S 16 of 24
string X
 

   (16)  "x"
                                                                 Type: String
--R 
--R
--R   (16)  "x"
--R                                                                 Type: String
--E 16

--S 17 of 24
name U
 

   (17)  u
                                                                 Type: Symbol
--R 
--R
--R   (17)  u
--R                                                                 Type: Symbol
--E 17

--S 18 of 24
scripts U
 

   (18)  [sub= [1,2,1,2],sup= [],presup= [],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (18)  [sub= [1,2,1,2],sup= [],presup= [],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 18

--S 19 of 24
name X
 

   (19)  x
                                                                 Type: Symbol
--R 
--R
--R   (19)  x
--R                                                                 Type: Symbol
--E 19

--S 20 of 24
scripts X
 

   (20)  [sub= [],sup= [],presup= [],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (20)  [sub= [],sup= [],presup= [],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 20

--S 21 of 24
M := script(Mammoth, [ [i,j],[k,l],[0,1],[2],[u,v,w] ])
 

         0,1       k,l
   (21)     Mammoth   (u,v,w)
           2       i,j
                                                                 Type: Symbol
--R 
--R
--R         0,1       k,l
--R   (21)     Mammoth   (u,v,w)
--R           2       i,j
--R                                                                 Type: Symbol
--E 21

--S 22 of 24
scripts M
 

   (22)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [2],args= [u,v,w]]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (22)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [2],args= [u,v,w]]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 22

--S 23 of 24
N := script(Nut, [ [i,j],[k,l],[0,1] ])
 

         0,1   k,l
   (23)     Nut
               i,j
                                                                 Type: Symbol
--R 
--R
--R         0,1   k,l
--R   (23)     Nut
--R               i,j
--R                                                                 Type: Symbol
--E 23

--S 24 of 24
scripts N
 

   (24)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []]
Type: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--R 
--R
--R   (24)  [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []]
--RType: Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)
--E 24
)spool
 
Starts dribbling to allfact.output (2010/3/27, 18:23:2).
)set message test on
 
)set message auto off
 
)clear all
 
-- factorization of integer numbers
--S 1 of 21
n:=45234258258293
 

   (1)  45234258258293
                                                        Type: PositiveInteger
--R 
--R
--R   (1)  45234258258293
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 21
factor n
 

   (2)  13 19 269 8387 81173
                                                       Type: Factored Integer
--R 
--R
--R   (2)  13 19 269 8387 81173
--R                                                       Type: Factored Integer
--E 2

-- factorization of gaussian integers
--S 3 of 21
m:(Complex Integer) := 1324567+%i*53523582
 

   (3)  1324567 + 53523582%i
                                                        Type: Complex Integer
--R 
--R
--R   (3)  1324567 + 53523582%i
--R                                                        Type: Complex Integer
--E 3

--S 4 of 21
factor m
 

   (4)  (2 + 7%i)(7119136 + 1844815%i)
                                               Type: Factored Complex Integer
--R 
--R
--R   (4)  (2 + 7%i)(7119136 + 1844815%i)
--R                                               Type: Factored Complex Integer
--E 4

-- factorization of polynomials over finite fields
--S 5 of 21
u:UP(x,PF(19)) :=3*x**4+2*x**2+15*x+18
 

          4     2
   (5)  3x  + 2x  + 15x + 18
                                  Type: UnivariatePolynomial(x,PrimeField 19)
--R 
--R
--R          4     2
--R   (5)  3x  + 2x  + 15x + 18
--R                                  Type: UnivariatePolynomial(x,PrimeField 19)
--E 5

--S 6 of 21
factor u
 

                   3    2
   (6)  3(x + 18)(x  + x  + 8x + 13)
                         Type: Factored UnivariatePolynomial(x,PrimeField 19)
--R 
--R
--R                   3    2
--R   (6)  3(x + 18)(x  + x  + 8x + 13)
--R                         Type: Factored UnivariatePolynomial(x,PrimeField 19)
--E 6

-- factorization of polynomials over the integers
--S 7 of 21
v:UP(x,INT):= (4*x**3+2*x**2+1)*(12*x**5-x**3+12)
 

           8      7     6      5      3      2
   (7)  48x  + 24x  - 4x  + 10x  + 47x  + 24x  + 12
                                        Type: UnivariatePolynomial(x,Integer)
--R 
--R
--R           8      7     6      5      3      2
--R   (7)  48x  + 24x  - 4x  + 10x  + 47x  + 24x  + 12
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 21
factor v
 

           3     2         5    3
   (8)  (4x  + 2x  + 1)(12x  - x  + 12)
                               Type: Factored UnivariatePolynomial(x,Integer)
--R 
--R
--R           3     2         5    3
--R   (8)  (4x  + 2x  + 1)(12x  - x  + 12)
--R                               Type: Factored UnivariatePolynomial(x,Integer)
--E 8

-- factorization of multivariate polynomial over the integers
--S 9 of 21
w:MPOLY([x,y,z],INT) :=(x**2-y**2-z**2)*(x**2+y**2+z**2)*(z*y+3*z)
 

                   4      5       4     3 3     3 2    5      5
   (9)  (z y + 3z)x  - z y  - 3z y  - 2z y  - 6z y  - z y - 3z
                                Type: MultivariatePolynomial([x,y,z],Integer)
--R 
--R
--R                   4      5       4     3 3     3 2    5      5
--R   (9)  (z y + 3z)x  - z y  - 3z y  - 2z y  - 6z y  - z y - 3z
--R                                Type: MultivariatePolynomial([x,y,z],Integer)
--E 9

--S 10 of 21
factor w
 

                   2    2    2   2    2    2
   (10)  z(y + 3)(x  - y  - z )(x  + y  + z )
                       Type: Factored MultivariatePolynomial([x,y,z],Integer)
--R 
--R
--R                   2    2    2   2    2    2
--R   (10)  z(y + 3)(x  - y  - z )(x  + y  + z )
--R                       Type: Factored MultivariatePolynomial([x,y,z],Integer)
--E 10

-- factorization of univariate and multivariate over the rational numbers
--S 11 of 21
f:MPOLY([x,y,z],FRAC INT) :=(4/9*x**2-1/16)*(x**3/27+125)
 

          4   5    1   3   500  2   125
   (11)  --- x  - --- x  + --- x  - ---
         243      432       9        16
                       Type: MultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R          4   5    1   3   500  2   125
--R   (11)  --- x  - --- x  + --- x  - ---
--R         243      432       9        16
--R                       Type: MultivariatePolynomial([x,y,z],Fraction Integer)
--E 11

--S 12 of 21
factor f
 

          4       3      3           2
   (12)  --- (x - -)(x + -)(x + 15)(x  - 15x + 225)
         243      8      8
              Type: Factored MultivariatePolynomial([x,y,z],Fraction Integer)
--R 
--R
--R          4       3      3           2
--R   (12)  --- (x - -)(x + -)(x + 15)(x  - 15x + 225)
--R         243      8      8
--R              Type: Factored MultivariatePolynomial([x,y,z],Fraction Integer)
--E 12

-- factorization over rational functions
--S 13 of 21
g:DMP([x,y],FRAC POLY INT):=a**2*x**2/b**2 -c**2*y**2/d**2
 

          2       2
         a   2   c   2
   (13)  -- x  - -- y
          2       2
         b       d
   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R          2       2
--R         a   2   c   2
--R   (13)  -- x  - -- y
--R          2       2
--R         b       d
--R   Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 13

--S 14 of 21
factor g
 

          2
         a       b c        b c
   (14)  -- (x - --- y)(x + --- y)
          2      a d        a d
         b
Type: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--R 
--R
--R          2
--R         a       b c        b c
--R   (14)  -- (x - --- y)(x + --- y)
--R          2      a d        a d
--R         b
--RType: Factored DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer)
--E 14

-- decomposition of a rational function
--S 15 of 21
r:FRAC POLY INT:= (a**3/b**3-c**3/(b+1)**3)*(a*d+a/c)
 

   (15)
         3 4     4 3     4 2     4     4          3 3    4 3     4 2     4     4
   (- a b c  + (a b  + 3a b  + 3a b + a )c)d - a b c  + a b  + 3a b  + 3a b + a
   -----------------------------------------------------------------------------
                                 6     5     4    3
                               (b  + 3b  + 3b  + b )c
                                            Type: Fraction Polynomial Integer
--R 
--R
--R   (15)
--R         3 4     4 3     4 2     4     4          3 3    4 3     4 2     4     4
--R   (- a b c  + (a b  + 3a b  + 3a b + a )c)d - a b c  + a b  + 3a b  + 3a b + a
--R   -----------------------------------------------------------------------------
--R                                 6     5     4    3
--R                               (b  + 3b  + 3b  + b )c
--R                                            Type: Fraction Polynomial Integer
--E 15

--S 16 of 21
factorFraction r
 

                             2 2       2            2 2     2     2
           a(b c - a b - a)(b c  + (a b  + a b)c + a b  + 2a b + a )(c d + 1)
   (16)  - ------------------------------------------------------------------
                                        3       3
                                       b (b + 1) c
                                   Type: Fraction Factored Polynomial Integer
--R 
--R
--R                             2 2       2            2 2     2     2
--R           a(b c - a b - a)(b c  + (a b  + a b)c + a b  + 2a b + a )(c d + 1)
--R   (16)  - ------------------------------------------------------------------
--R                                        3       3
--R                                       b (b + 1) c
--R                                   Type: Fraction Factored Polynomial Integer
--E 16

-- factorization over simple algebraic extensions
--S 17 of 21
aa|aa**2+aa+1
 
   Your statement has resulted in the following assignments and 
      declaration:

   SAEaa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
   aa : SAEaa := aa

   (17)  aa
Type: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--R   SAEaa := SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
--R   aa : SAEaa := aa
--R
--R   (17)  aa
--RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1)
--E 17

--S 18 of 21
p:UP(x,SAEaa) :=(x**3+aa**2*x+1)*(aa*x**2+aa*x+aa)**2
 

   (18)
                7               6               5              4     3
     (- aa - 1)x  + (- 2aa - 2)x  + (- 2aa - 3)x  + (- aa - 3)x  - 3x
   + 
                2
     (- aa - 3)x  + (- aa - 2)x - aa - 1
Type: UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--R 
--R
--R   (18)
--R                7               6               5              4     3
--R     (- aa - 1)x  + (- 2aa - 2)x  + (- 2aa - 3)x  + (- aa - 3)x  - 3x
--R   + 
--R                2
--R     (- aa - 3)x  + (- aa - 2)x - aa - 1
--RType: UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--E 18

--S 19 of 21
factor(p)$SAEFACT(UP('aa,FRAC INT),SAEaa,UP(x,SAEaa))
 

                           2            2  3
   (19)  (- aa - 1)(x - aa) (x + aa + 1) (x  + (- aa - 1)x + 1)
Type: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--R 
--R
--R                           2            2  3
--R   (19)  (- aa - 1)(x - aa) (x + aa + 1) (x  + (- aa - 1)x + 1)
--RType: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(aa,Fraction Integer),aa*aa+aa+1))
--E 19

-- factorization over algebraic numbers
--S 20 of 21
a:=rootOf(a**2+3)$AN
 

   (20)  a
                                                        Type: AlgebraicNumber
--R 
--R
--R   (20)  a
--R                                                        Type: AlgebraicNumber
--E 20

--S 21 of 21
factor(x**2+x+1,[a])
 

              - a + 1      a + 1
   (21)  (x + -------)(x + -----)
                 2           2
                                    Type: Factored Polynomial AlgebraicNumber
--R 
--R
--R              - a + 1      a + 1
--R   (21)  (x + -------)(x + -----)
--R                 2           2
--R                                    Type: Factored Polynomial AlgebraicNumber
--E 21
)spool
 
Starts dribbling to realclos.output (2010/3/27, 18:36:41).
)set message test on
 
)set message auto off
 
)clear all
 
 
--S 1 of 31
Ran := RECLOS(FRAC INT)
 

   (1)  RealClosure Fraction Integer
                                                                 Type: Domain
--R 
--R
--R   (1)  RealClosure Fraction Integer
--R                                                                 Type: Domain
--E 1

--S 2 of 31
fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran ==
           sqrt(a)+sqrt(b) - sqrt(c)-sqrt(d)
 
   Function declaration fourSquares : (RealClosure Fraction Integer,
      RealClosure Fraction Integer,RealClosure Fraction Integer,
      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
      been added to workspace.
                                                                   Type: Void
--R 
--R   Function declaration fourSquares : (RealClosure Fraction Integer,
--R      RealClosure Fraction Integer,RealClosure Fraction Integer,
--R      RealClosure Fraction Integer) -> RealClosure Fraction Integer has
--R      been added to workspace.
--R                                                                   Type: Void
--E 2

--S 3 of 31
squareDiff := fourSquares(73,548,60,586)
 
   Compiling function fourSquares with type (RealClosure Fraction 
      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 

           +---+    +--+    +---+    +--+
   (3)  - \|586  - \|60  + \|548  + \|73
                                           Type: RealClosure Fraction Integer
--R 
--R   Compiling function fourSquares with type (RealClosure Fraction 
--R      Integer,RealClosure Fraction Integer,RealClosure Fraction Integer
--R      ,RealClosure Fraction Integer) -> RealClosure Fraction Integer 
--R
--R           +---+    +--+    +---+    +--+
--R   (3)  - \|586  - \|60  + \|548  + \|73
--R                                           Type: RealClosure Fraction Integer
--E 3

--S 4 of 31
recip(squareDiff)
 

   (4)
             +---+          +--+  +--+         +--+ +---+            +---+
     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
   + 
             +--+ +---+             +--+            +---+            +--+
     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (4)
--R             +---+          +--+  +--+         +--+ +---+            +---+
--R     ((54602\|548  + 149602\|73 )\|60  + 49502\|73 \|548  + 9900895)\|586
--R   + 
--R             +--+ +---+             +--+            +---+            +--+
--R     (154702\|73 \|548  + 30941947)\|60  + 10238421\|548  + 28051871\|73
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 4

--S 5 of 31
sign(squareDiff)
 

   (5)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  1
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 31
squareDiff := fourSquares(165,778,86,990)
 

           +---+    +--+    +---+    +---+
   (6)  - \|990  - \|86  + \|778  + \|165
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +--+    +---+    +---+
--R   (6)  - \|990  - \|86  + \|778  + \|165
--R                                           Type: RealClosure Fraction Integer
--E 6

--S 7 of 31
recip(squareDiff)
 

   (7)
                +---+           +---+  +--+          +---+ +---+
       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
    *
        +---+
       \|990
   + 
              +---+ +---+              +--+             +---+             +---+
     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (7)
--R                +---+           +---+  +--+          +---+ +---+
--R       ((556778\|778  + 1209010\|165 )\|86  + 401966\|165 \|778  + 144019431)
--R    *
--R        +---+
--R       \|990
--R   + 
--R              +---+ +---+              +--+             +---+             +---+
--R     (1363822\|165 \|778  + 488640503)\|86  + 162460913\|778  + 352774119\|165
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 7

--S 8 of 31
sign(squareDiff)
 

   (8)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (8)  1
--R                                                        Type: PositiveInteger
--E 8

--S 9 of 31
squareDiff := fourSquares(217,708,226,692)
 

           +---+    +---+    +---+    +---+
   (9)  - \|692  - \|226  + \|708  + \|217
                                           Type: RealClosure Fraction Integer
--R 
--R
--R           +---+    +---+    +---+    +---+
--R   (9)  - \|692  - \|226  + \|708  + \|217
--R                                           Type: RealClosure Fraction Integer
--E 9

--S 10 of 31
recip(squareDiff)
 

   (10)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (10)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 34102\|708  - 61598\|217 )\|226  - 34802\|217 \|708  - 13641141)\|692
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 60898\|217 \|708  - 23869841)\|226  - 13486123\|708  - 24359809\|217
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 10

--S 11 of 31
sign(squareDiff)
 

   (11)  - 1
                                                                Type: Integer
--R 
--R
--R   (11)  - 1
--R                                                                Type: Integer
--E 11

--S 12 of 31
squareDiff := fourSquares(155,836,162,820) 
 

            +---+    +---+    +---+    +---+
   (12)  - \|820  - \|162  + \|836  + \|155
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (12)  - \|820  - \|162  + \|836  + \|155
--R                                           Type: RealClosure Fraction Integer
--E 12

--S 13 of 31
recip(squareDiff)
 

   (13)
               +---+         +---+  +---+         +---+ +---+             +---+
     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
   + 
              +---+ +---+             +---+            +---+            +---+
     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (13)
--R               +---+         +---+  +---+         +---+ +---+             +---+
--R     ((- 37078\|836  - 86110\|155 )\|162  - 37906\|155 \|836  - 13645107)\|820
--R   + 
--R              +---+ +---+             +---+            +---+            +---+
--R     (- 85282\|155 \|836  - 30699151)\|162  - 13513901\|836  - 31384703\|155
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 13

--S 14 of 31
sign(squareDiff)
 

   (14)  - 1
                                                                Type: Integer
--R 
--R
--R   (14)  - 1
--R                                                                Type: Integer
--E 14

--S 15 of 31
squareDiff := fourSquares(591,772,552,818)
 

            +---+    +---+    +---+    +---+
   (15)  - \|818  - \|552  + \|772  + \|591
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +---+    +---+    +---+    +---+
--R   (15)  - \|818  - \|552  + \|772  + \|591
--R                                           Type: RealClosure Fraction Integer
--E 15

--S 16 of 31
recip(squareDiff)
 

   (16)
             +---+         +---+  +---+         +---+ +---+             +---+
     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
   + 
            +---+ +---+             +---+            +---+            +---+
     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (16)
--R             +---+         +---+  +---+         +---+ +---+             +---+
--R     ((70922\|772  + 81058\|591 )\|552  + 68542\|591 \|772  + 46297673)\|818
--R   + 
--R            +---+ +---+             +---+            +---+            +---+
--R     (83438\|591 \|772  + 56359389)\|552  + 47657051\|772  + 54468081\|591
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 16

--S 17 of 31
sign(squareDiff)
 

   (17)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (17)  1
--R                                                        Type: PositiveInteger
--E 17

--S 18 of 31
squareDiff := fourSquares(434,1053,412,1088)
 

            +----+    +---+    +----+    +---+
   (18)  - \|1088  - \|412  + \|1053  + \|434
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (18)  - \|1088  - \|412  + \|1053  + \|434
--R                                           Type: RealClosure Fraction Integer
--E 18

--S 19 of 31
recip(squareDiff)
 

   (19)
                +----+          +---+  +---+          +---+ +----+
       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
    *
        +----+
       \|1088
   + 
           +---+ +----+              +---+            +----+             +---+
   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (19)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((115442\|1053  + 179818\|434 )\|412  + 112478\|434 \|1053  + 76037291)
--R    *
--R        +----+
--R       \|1088
--R   + 
--R           +---+ +----+              +---+            +----+             +---+
--R   (182782\|434 \|1053  + 123564147)\|412  + 77290639\|1053  + 120391609\|434
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 19

--S 20 of 31
sign(squareDiff)
 

   (20)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (20)  1
--R                                                        Type: PositiveInteger
--E 20

--S 21 of 31
squareDiff := fourSquares(514,1049,446,1152)
 

            +----+    +---+    +----+    +---+
   (21)  - \|1152  - \|446  + \|1049  + \|514
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (21)  - \|1152  - \|446  + \|1049  + \|514
--R                                           Type: RealClosure Fraction Integer
--E 21

--S 22 of 31
recip(squareDiff)
 

   (22)
                +----+          +---+  +---+          +---+ +----+
       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
    *
        +----+
       \|1152
   + 
           +---+ +----+              +---+             +----+             +---+
   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (22)
--R                +----+          +---+  +---+          +---+ +----+
--R       ((349522\|1049  + 499322\|514 )\|446  + 325582\|514 \|1049  + 239072537)
--R    *
--R        +----+
--R       \|1152
--R   + 
--R           +---+ +----+              +---+             +----+             +---+
--R   (523262\|514 \|1049  + 384227549)\|446  + 250534873\|1049  + 357910443\|514
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 22

--S 23 of 31
sign(squareDiff)
 

   (23)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (23)  1
--R                                                        Type: PositiveInteger
--E 23

--S 24 of 31
squareDiff := fourSquares(190,1751,208,1698)
 

            +----+    +---+    +----+    +---+
   (24)  - \|1698  - \|208  + \|1751  + \|190
                                           Type: RealClosure Fraction Integer
--R 
--R
--R            +----+    +---+    +----+    +---+
--R   (24)  - \|1698  - \|208  + \|1751  + \|190
--R                                           Type: RealClosure Fraction Integer
--E 24

--S 25 of 31
recip(squareDiff)
 

   (25)
                     +----+          +---+  +---+          +---+ +----+
           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
         + 
           - 129571901
    *
        +----+
       \|1698
   + 
               +---+ +----+              +---+             +----+
     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
   + 
                 +---+
     - 387349387\|190
                                Type: Union(RealClosure Fraction Integer,...)
--R 
--R
--R   (25)
--R                     +----+          +---+  +---+          +---+ +----+
--R           (- 214702\|1751  - 651782\|190 )\|208  - 224642\|190 \|1751
--R         + 
--R           - 129571901
--R    *
--R        +----+
--R       \|1698
--R   + 
--R               +---+ +----+              +---+             +----+
--R     (- 641842\|190 \|1751  - 370209881)\|208  - 127595865\|1751
--R   + 
--R                 +---+
--R     - 387349387\|190
--R                                Type: Union(RealClosure Fraction Integer,...)
--E 25

--S 26 of 31
sign(squareDiff)
 

   (26)  - 1
                                                                Type: Integer
--R 
--R
--R   (26)  - 1
--R                                                                Type: Integer
--E 26

)cl prop s2 s5 s10 l
 

--S 27 of 31
(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran);
 

                                           Type: RealClosure Fraction Integer
--R 
--R
--R                                           Type: RealClosure Fraction Integer
--E 27

--S 28 of 31
sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
 

            +---------+ +--------+    +---------+ +--------+   +-----------+
            | +--+      | +-+         | +--+      | +-+        |   +-+
   (28)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
                                  Type: Equation RealClosure Fraction Integer
--R 
--R
--R            +---------+ +--------+    +---------+ +--------+   +-----------+
--R            | +--+      | +-+         | +--+      | +-+        |   +-+
--R   (28)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
--R                                  Type: Equation RealClosure Fraction Integer
--E 28

--S 29 of 31
%::Boolean
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 31
l := allRootsOf((x^2-2)^2-2)$Ran
 

   (30)  [%A41,%A42,%A43,%A44]
                                      Type: List RealClosure Fraction Integer
--R 
--R
--R   (30)  [%A41,%A42,%A43,%A44]
--R                                      Type: List RealClosure Fraction Integer
--E 30

--S 31 of 31
l.1+l.2+l.3+l.4
 

   (31)  0
                                           Type: RealClosure Fraction Integer
--R 
--R
--R   (31)  0
--R                                           Type: RealClosure Fraction Integer
--E 31
)spool 
 
Starts dribbling to String.output (2010/3/27, 18:46:36).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 35
hello := "Hello, I'm AXIOM!"
 

   (1)  "Hello, I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (1)  "Hello, I'm AXIOM!"
--R                                                                 Type: String
--E 1

--S 2 of 35
said := "Jane said, \_"Look!\_""
 

   (2)  "Jane said, \"Look!\""
                                                                 Type: String
--R 
--R
--R   (2)  "Jane said, \"Look!\""
--R                                                                 Type: String
--E 2

--S 3 of 35
saw := "She saw exactly one underscore: \_\_." 
 

   (3)  "She saw exactly one underscore: \\."
                                                                 Type: String
--R 
--R
--R   (3)  "She saw exactly one underscore: \\."
--R                                                                 Type: String
--E 3

--S 4 of 35
gasp: String := new(32, char "x")
 

   (4)  "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
                                                                 Type: String
--R 
--R
--R   (4)  "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
--R                                                                 Type: String
--E 4

--S 5 of 35
#gasp
 

   (5)  32
                                                        Type: PositiveInteger
--R 
--R
--R   (5)  32
--R                                                        Type: PositiveInteger
--E 5

--S 6 of 35
hello.2
 

   (6)  e
                                                              Type: Character
--R 
--R
--R   (6)  e
--R                                                              Type: Character
--E 6

--S 7 of 35
hello 2
 

   (7)  e
                                                              Type: Character
--R 
--R
--R   (7)  e
--R                                                              Type: Character
--E 7

--S 8 of 35
hello(2)
 

   (8)  e
                                                              Type: Character
--R 
--R
--R   (8)  e
--R                                                              Type: Character
--E 8

--S 9 of 35
hullo := copy hello
 

   (9)  "Hello, I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (9)  "Hello, I'm AXIOM!"
--R                                                                 Type: String
--E 9

--S 10 of 35
hullo.2 := char "u"; [hello, hullo]
 

   (10)  ["Hello, I'm AXIOM!","Hullo, I'm AXIOM!"]
                                                            Type: List String
--R 
--R
--R   (10)  ["Hello, I'm AXIOM!","Hullo, I'm AXIOM!"]
--R                                                            Type: List String
--E 10

--S 11 of 35
saidsaw := concat ["alpha","---","omega"]
 

   (11)  "alpha---omega"
                                                                 Type: String
--R 
--R
--R   (11)  "alpha---omega"
--R                                                                 Type: String
--E 11

--S 12 of 35
concat("hello ","goodbye")
 

   (12)  "hello goodbye"
                                                                 Type: String
--R 
--R
--R   (12)  "hello goodbye"
--R                                                                 Type: String
--E 12

--S 13 of 35
"This " "is " "several " "strings " "concatenated."
 

   (13)  "This is several strings concatenated."
                                                                 Type: String
--R 
--R
--R   (13)  "This is several strings concatenated."
--R                                                                 Type: String
--E 13

--S 14 of 35
hello(1..5)
 

   (14)  "Hello"
                                                                 Type: String
--R 
--R
--R   (14)  "Hello"
--R                                                                 Type: String
--E 14

--S 15 of 35
hello(8..)
 

   (15)  "I'm AXIOM!"
                                                                 Type: String
--R 
--R
--R   (15)  "I'm AXIOM!"
--R                                                                 Type: String
--E 15

--S 16 of 35
split(hello, char " ")
 

   (16)  ["Hello,","I'm","AXIOM!"]
                                                            Type: List String
--R 
--R
--R   (16)  ["Hello,","I'm","AXIOM!"]
--R                                                            Type: List String
--E 16

--S 17 of 35
other := complement alphanumeric();
 

                                                         Type: CharacterClass
--R
--R                                                         Type: CharacterClass
--E 17

--S 18 of 35
split(saidsaw, other)
 

   (18)  ["alpha","omega"]
                                                            Type: List String
--R 
--R
--R   (18)  ["alpha","omega"]
--R                                                            Type: List String
--E 18

--S 19 of 35
trim("## ++ relax ++ ##", char "#")
 

   (19)  " ++ relax ++ "
                                                                 Type: String
--R 
--R
--R   (19)  " ++ relax ++ "
--R                                                                 Type: String
--E 19

--S 20 of 35
trim("## ++ relax ++ ##", other)
 

   (20)  "relax"
                                                                 Type: String
--R 
--R
--R   (20)  "relax"
--R                                                                 Type: String
--E 20

--S 21 of 35
leftTrim("## ++ relax ++ ##", other)
 

   (21)  "relax ++ ##"
                                                                 Type: String
--R 
--R
--R   (21)  "relax ++ ##"
--R                                                                 Type: String
--E 21

--S 22 of 35
rightTrim("## ++ relax ++ ##", other)
 

   (22)  "## ++ relax"
                                                                 Type: String
--R 
--R
--R   (22)  "## ++ relax"
--R                                                                 Type: String
--E 22

--S 23 of 35
upperCase hello
 

   (23)  "HELLO, I'M AXIOM!"
                                                                 Type: String
--R 
--R
--R   (23)  "HELLO, I'M AXIOM!"
--R                                                                 Type: String
--E 23

--S 24 of 35
lowerCase hello
 

   (24)  "hello, i'm axiom!"
                                                                 Type: String
--R 
--R
--R   (24)  "hello, i'm axiom!"
--R                                                                 Type: String
--E 24

--S 25 of 35
prefix?("He", "Hello")
 

   (25)  true
                                                                Type: Boolean
--R 
--R
--R   (25)  true
--R                                                                Type: Boolean
--E 25

--S 26 of 35
prefix?("Her", "Hello")
 

   (26)  false
                                                                Type: Boolean
--R 
--R
--R   (26)  false
--R                                                                Type: Boolean
--E 26

--S 27 of 35
suffix?("", "Hello")
 

   (27)  true
                                                                Type: Boolean
--R 
--R
--R   (27)  true
--R                                                                Type: Boolean
--E 27

--S 28 of 35
suffix?("LO", "Hello")
 

   (28)  false
                                                                Type: Boolean
--R 
--R
--R   (28)  false
--R                                                                Type: Boolean
--E 28

--S 29 of 35
substring?("ll", "Hello", 3)
 

   (29)  true
                                                                Type: Boolean
--R 
--R
--R   (29)  true
--R                                                                Type: Boolean
--E 29

--S 30 of 35
substring?("ll", "Hello", 4)
 

   (30)  false
                                                                Type: Boolean
--R 
--R
--R   (30)  false
--R                                                                Type: Boolean
--E 30

--S 31 of 35
n := position("nd", "underground", 1)
 

   (31)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (31)  2
--R                                                        Type: PositiveInteger
--E 31

--S 32 of 35
n := position("nd", "underground", n+1)
 

   (32)  10
                                                        Type: PositiveInteger
--R 
--R
--R   (32)  10
--R                                                        Type: PositiveInteger
--E 32

--S 33 of 35
n := position("nd", "underground", n+1)
 

   (33)  0
                                                     Type: NonNegativeInteger
--R 
--R
--R   (33)  0
--R                                                     Type: NonNegativeInteger
--E 33

--S 34 of 35
position(char "d", "underground", 1)
 

   (34)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (34)  3
--R                                                        Type: PositiveInteger
--E 34

--S 35 of 35
position(hexDigit(), "underground", 1)
 

   (35)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (35)  3
--R                                                        Type: PositiveInteger
--E 35
)spool
 
Starts dribbling to Kernel.output (2010/3/27, 18:42:22).
)set message test on
 
)set message auto off
 
)clear all
 
--S 1 of 19
x :: Expression Integer
 

   (1)  x
                                                     Type: Expression Integer
--R 
--R
--R   (1)  x
--R                                                     Type: Expression Integer
--E 1

--S 2 of 19
kernel x
 

   (2)  x
                                              Type: Kernel Expression Integer
--R 
--R
--R   (2)  x
--R                                              Type: Kernel Expression Integer
--E 2

--S 3 of 19
sin(x) + cos(x)
 

   (3)  sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R   (3)  sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 3

--S 4 of 19
kernels %
 

   (4)  [sin(x),cos(x)]
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (4)  [sin(x),cos(x)]
--R                                         Type: List Kernel Expression Integer
--E 4

--S 5 of 19
sin(x)**2 + sin(x) + cos(x)
 

              2
   (5)  sin(x)  + sin(x) + cos(x)
                                                     Type: Expression Integer
--R 
--R
--R              2
--R   (5)  sin(x)  + sin(x) + cos(x)
--R                                                     Type: Expression Integer
--E 5

--S 6 of 19
kernels %
 

   (6)  [sin(x),cos(x)]
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (6)  [sin(x),cos(x)]
--R                                         Type: List Kernel Expression Integer
--E 6

--S 7 of 19
kernels(1 :: Expression Integer)
 

   (7)  []
                                         Type: List Kernel Expression Integer
--R 
--R
--R   (7)  []
--R                                         Type: List Kernel Expression Integer
--E 7

--S 8 of 19
mainKernel(cos(x) + tan(x))
 

   (8)  tan(x)
                                   Type: Union(Kernel Expression Integer,...)
--R 
--R
--R   (8)  tan(x)
--R                                   Type: Union(Kernel Expression Integer,...)
--E 8

--S 9 of 19
height kernel x
 

   (9)  1
                                                        Type: PositiveInteger
--R 
--R
--R   (9)  1
--R                                                        Type: PositiveInteger
--E 9

--S 10 of 19
height mainKernel(sin x)
 

   (10)  2
                                                        Type: PositiveInteger
--R 
--R
--R   (10)  2
--R                                                        Type: PositiveInteger
--E 10

--S 11 of 19
height mainKernel(sin cos x)
 

   (11)  3
                                                        Type: PositiveInteger
--R 
--R
--R   (11)  3
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 19
height mainKernel(sin cos (tan x + sin x))
 

   (12)  4
                                                        Type: PositiveInteger
--R 
--R
--R   (12)  4
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 19
operator mainKernel(sin cos (tan x + sin x))
 

   (13)  sin
                                                          Type: BasicOperator
--R 
--R
--R   (13)  sin
--R                                                          Type: BasicOperator
--E 13

--S 14 of 19
name mainKernel(sin cos (tan x + sin x))
 

   (14)  sin
                                                                 Type: Symbol
--R 
--R
--R   (14)  sin
--R                                                                 Type: Symbol
--E 14

--S 15 of 19
f := operator 'f 
 

   (15)  f
                                                          Type: BasicOperator
--R 
--R
--R   (15)  f
--R                                                          Type: BasicOperator
--E 15

--S 16 of 19
e := f(x, y, 10) 
 

   (16)  f(x,y,10)
                                                     Type: Expression Integer
--R 
--R
--R   (16)  f(x,y,10)
--R                                                     Type: Expression Integer
--E 16

--S 17 of 19
is?(e, f) 
 

   (17)  true
                                                                Type: Boolean
--R 
--R
--R   (17)  true
--R                                                                Type: Boolean
--E 17

--S 18 of 19
is?(e, 'f)
 

   (18)  true
                                                                Type: Boolean
--R 
--R
--R   (18)  true
--R                                                                Type: Boolean
--E 18

--S 19 of 19
argument mainKernel e
 

   (19)  [x,y,10]
                                                Type: List Expression Integer
--R 
--R
--R   (19)  [x,y,10]
--R                                                Type: List Expression Integer
--E 19
)spool
 
